{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "756461",
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== START ===\n",
      "cwd: /home/user\n",
      "files: ['OA_Lpoly.csv', 'OA_MirrorQuintic_Primes_Template_v4_2.csv', 'OA_counts.csv', 'OA_data.csv', 'OA_data_lefschetz.csv', 'OA_data_real.csv', 'root_moduli.txt']\n",
      "\n",
      "OA_Lpoly head:\n",
      "   p   a1  a2    a1_norm\n",
      "0  7  343   6  18.520259\n",
      "p=7: ['18.5204', '0.1430', '0.1430', '0.0077']\n",
      "\n",
      "Saved to root_moduli.txt\n"
     ]
    }
   ],
   "source": [
    "# === ONE-BUTTON: build OA_Lpoly.csv from counts (or tiny demo), then compute/summarize normalized Weil roots ===\n",
    "import os, math, pandas as pd, numpy as np\n",
    "from pathlib import Path\n",
    "\n",
    "# --- helpers ---\n",
    "def have_counts_with_r2(path=\"OA_counts.csv\"):\n",
    "    if not os.path.exists(path): \n",
    "        return False\n",
    "    try:\n",
    "        with open(path, \"r\") as f:\n",
    "            return any(\",2,\" in ln for ln in f)\n",
    "    except Exception:\n",
    "        return False\n",
    "\n",
    "def rebuild_Lpoly_from_counts(counts_csv=\"OA_counts.csv\", out_csv=\"OA_Lpoly.csv\"):\n",
    "    df = pd.read_csv(counts_csv)\n",
    "    by = {}\n",
    "    for _, row in df.iterrows():\n",
    "        p = int(row['p']); r = int(row['r']); Npr = int(row['N_pr'])\n",
    "        by.setdefault(p, {})[r] = Npr\n",
    "\n",
    "    rows = []\n",
    "    for p, rr in sorted(by.items()):\n",
    "        if 1 in rr and 2 in rr:\n",
    "            N1, N2 = rr[1], rr[2]\n",
    "            # Heuristic CY3 power-sum recovery (toy): S1 = sum eigenvalues, S2 = sum of pairwise products\n",
    "            S1 = (1 + p + p**2 + p**3)   - N1\n",
    "            S2 = (1 + p**2 + p**4 + p**6) - N2\n",
    "            a1 = int(S1)\n",
    "            a2 = int((S1*S1 - S2)//2)\n",
    "            rows.append((p, a1, a2, a1/(p**1.5)))\n",
    "    Ldf = pd.DataFrame(rows, columns=[\"p\",\"a1\",\"a2\",\"a1_norm\"])\n",
    "    Ldf.to_csv(out_csv, index=False)\n",
    "    return Ldf\n",
    "\n",
    "def root_moduli_row(p, a1, a2):\n",
    "    # local factor model for CY3: 1 - a1 T + a2 T^2 - p a1 T^3 + p^3 T^4\n",
    "    coeffs = [1, -int(a1), int(a2), -int(p)*int(a1), int(p)**3]\n",
    "    roots  = np.roots(coeffs)\n",
    "    R = (int(p)**1.5)\n",
    "    x4return [abs(r)/R for r in roots]\n",
    "\n",
    "print(\"=== START ===\")\n",
    "print(\"cwd:\", os.getcwd())\n",
    "print(\"files:\", sorted([f for f in os.listdir() if f.endswith(('.csv','.txt'))]))\n",
    "\n",
    "# 1) Ensure counts exist (or create tiny demo)\n",
    "if not os.path.exists(\"OA_counts.csv\"):\n",
    "    print(\"-> OA_counts.csv missing; creating a tiny demo so the pipeline runs.\")\n",
    "    with open(\"OA_counts.csv\",\"w\") as f:\n",
    "        f.write(\"p,r,N_pr,psi\\n\")\n",
    "        # replace with your real counts later; these are just placeholders\n",
    "        f.write(\"7,1,1200,1\\n\");   f.write(\"7,2,2400000,1\\n\")\n",
    "        f.write(\"11,1,14641,1\\n\"); f.write(\"11,2,214358881,1\\n\")\n",
    "\n",
    "if not have_counts_with_r2(\"OA_counts.csv\"):\n",
    "    raise SystemExit(\"x OA_counts.csv lacks r=2 rows for at least one p. Edit it to include r=1 AND r=2 for each p, then re-run this cell.\")\n",
    "\n",
    "# 2) Build OA_Lpoly.csv if needed (or refresh if empty)\n",
    "Lpath = Path(\"OA_Lpoly.csv\")\n",
    "if (not Lpath.exists()) or (Lpath.exists() and Lpath.stat().st_size == 0):\n",
    "    print(\"-> (Re)building OA_Lpoly.csv from counts…\")\n",
    "    Ldf = rebuild_Lpoly_from_counts()\n",
    "else:\n",
    "    Ldf = pd.read_csv(Lpath)\n",
    "    if Ldf.empty:\n",
    "        print(\"-> OA_Lpoly.csv is empty; rebuilding…\")\n",
    "        Ldf = rebuild_Lpoly_from_counts()\n",
    "\n",
    "print(\"\\nOA_Lpoly head:\")\n",
    "print(Ldf.head())\n",
    "\n",
    "# 3) Compute normalized Weil root moduli and save to text\n",
    "lines = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = int(r[\"p\"]), int(r[\"a1\"]), int(r[\"a2\"])\n",
    "    mods = [f\"{m:.4f}\" for m in root_moduli_row(p, a1, a2)]\n",
    "    line = f\"p={p}: {mods}\"\n",
    "    print(line)\n",
    "    lines.append(line)\n",
    "\n",
    "with open(\"root_moduli.txt\",\"w\") as f:\n",
    "    f.write(\"\\n\".join(lines))\n",
    "print(\"\\nSaved to root_moduli.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ffbb3e",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p=7: ['18.5204', '0.1430', '0.1430', '0.0077']\n"
     ]
    }
   ],
   "source": [
    "print(open(\"root_moduli.txt\").read())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c2b132",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p=7: ['18.5204', '0.1430', '0.1430', '0.0077']\n"
     ]
    }
   ],
   "source": [
    "# Try pure-Python read first\n",
    "print(open(\"root_moduli.txt\",\"r\").read())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f340c7",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exists: True\n",
      "\n",
      "=== root_moduli.txt ===\n",
      "p=7: ['18.5204', '0.1430', '0.1430', '0.0077']\n"
     ]
    }
   ],
   "source": [
    "from pathlib import Path\n",
    "p = Path(\"root_moduli.txt\")\n",
    "print(\"Exists:\", p.exists())\n",
    "if p.exists():\n",
    "    print(\"\\n=== root_moduli.txt ===\")\n",
    "    print(p.read_text())\n",
    "else:\n",
    "    print(\"root_moduli.txt not found (run the one-button cell above once).\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f487d7",
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[OK] 7,1,322,1\n",
      "[OK] 7,2,117355,1\n",
      "[OK] 11,1,1342,1\n",
      "[OK] 11,2,1771803,1\n",
      "[OK] 13,1,2236,1\n",
      "[OK] 13,2,4827823,1\n",
      "[OK] 17,1,4913,1\n",
      "[OK] 17,2,24137569,1\n",
      "[OK] 19,1,6897,1\n",
      "[OK] 19,2,47047325,1\n",
      "[OK] 23,1,12144,1\n",
      "[OK] 23,2,148034831,1\n",
      "✅ Wrote OA_counts.csv (fast structured version).\n"
     ]
    }
   ],
   "source": [
    "# === FAST substitute for mirror-quintic counts (structured mock) ===\n",
    "import random\n",
    "\n",
    "psi_param  = 1\n",
    "prime_list = [7, 11, 13, 17, 19, 23]\n",
    "r_list     = [1, 2]\n",
    "\n",
    "def N_pr_mirror_quintic_fast(p, r, psi):\n",
    "    \"\"\"\n",
    "    Structured fast mock for N_{p^r}, mimicking oscillations and growth.\n",
    "    Replace with real arithmetic counts later.\n",
    "    \"\"\"\n",
    "    base = p**(3*r)  # dimension 3 Calabi–Yau heuristic growth\n",
    "    osc  = ((p % 7) - 3) * ((r*psi) % 5)\n",
    "    Npr  = base + int(osc * p**r)\n",
    "    return max(1, Npr)\n",
    "\n",
    "with open('OA_counts.csv','w') as f:\n",
    "    f.write('p,r,N_pr,psi\\n')\n",
    "    for p in prime_list:\n",
    "        for r in r_list:\n",
    "            Npr = N_pr_mirror_quintic_fast(p, r, psi_param)\n",
    "            line = f\"{p},{r},{Npr},{psi_param}\\n\"\n",
    "            f.write(line)\n",
    "            print(\"[OK]\", line.strip())\n",
    "\n",
    "print(\"✅ Wrote OA_counts.csv (fast structured version).\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0c5e7f",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p,r,N_pr,psi\r\n",
      "7,1,322,1\r\n",
      "7,2,117355,1\r\n",
      "11,1,1342,1\r\n",
      "11,2,1771803,1\r\n",
      "13,1,2236,1\r\n",
      "13,2,4827823,1\r\n",
      "17,1,4913,1\r\n",
      "17,2,24137569,1\r\n",
      "19,1,6897,1\r\n",
      "19,2,47047325,1\r\n",
      "23,1,12144,1\r\n",
      "23,2,148034831,1\r\n"
     ]
    }
   ],
   "source": [
    "!head -20 OA_counts.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2f8c79",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total primes in Ldf: 1\n",
      "a1 ≡ 0 (mod p) count: 1\n",
      "Proportion: 1/1 = 1.000\n",
      "First few examples with a1 ≡ 0 mod p: [(7, 343)]\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# Load the L-polynomial coefficients we built\n",
    "Ldf = pd.read_csv(\"OA_Lpoly.csv\")\n",
    "\n",
    "total = len(Ldf)\n",
    "zeros_mod_p = 0\n",
    "examples = []\n",
    "\n",
    "for _, r in Ldf.iterrows():\n",
    "    p  = int(r[\"p\"])\n",
    "    a1 = int(r[\"a1\"])\n",
    "    if a1 % p == 0:\n",
    "        zeros_mod_p += 1\n",
    "        if len(examples) < 5:\n",
    "            examples.append((p, a1))\n",
    "\n",
    "print(f\"Total primes in Ldf: {total}\")\n",
    "print(f\"a1 ≡ 0 (mod p) count: {zeros_mod_p}\")\n",
    "print(f\"Proportion: {zeros_mod_p}/{total} = {float(zeros_mod_p)/float(total):.3f}\")\n",
    "if examples:\n",
    "    print(\"First few examples with a1 ≡ 0 mod p:\", examples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ffc748",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jhkaPHq2NGzdmepj89OnTeuGFFxQZGSkPDw95enraT3ZO+92+1Z+3PZUrV9b169d1+vTpHC3biy++KEn6+OOP7eMmTpyoSpUq6eGHH85QX7RoUR0/fjxHr2UVhBkLeOaZZ1StWjUNGTIk01+sc+fOycPDI8OVIzabTcWKFUu3e1SSwsPDHb7Wn68O8PLyynL89evXJUlHjx5VvXr1dPz4cf3zn//Ud999py1bttjP6bh27Zozi5rB6tWr1aVLF3Xq1ElvvPFGuudOnTqlRYsWydPTM90j7TyGtA34uXPn0n1gpilWrFiOevqzzNbn5cuXVa9ePW3atEmjR4/WmjVrtGXLFs2bN0/S/62PtEuXS5Qo4XD+586dU3Jysv71r39lWNbmzZtLUpYfVrn13mRmzpw5ql69utNXfWX2HqSN+/PPbU48+uijio6O1ubNmzVnzhyHH7JpKlSooJo1a+qpp57S0qVLFRUVleFKozlz5qhNmzYO5zFy5EiNHj1aY8aMUe/evbN8vX/+85+qUqWKHnnkEfn7+zt1GW63bt10/PhxrVixQtLNsJ+YmJjuj5mOHTtq2rRpOnLkiNq0aaOiRYuqVq1a9mlux9H7kpSUlOFcuVul/Sw5CuZp59/8+ZF2ibsrFStWTDVq1FDjxo311ltvadSoUZo4caJ27NiR5XSzZ89W586d9e9//1uxsbEKCQlRp06d7OfYpaamqnHjxpo3b54GDhyoVatWafPmzfY/KDL7fQoNDU03nHbYP6e/e2FhYWrXrp0++ugjpaSkaNeuXfruu+8c/rz5+Pi49Pe8IOKcGQuw2WwaN26cGjVqpKlTp2Z4PjQ0VMnJyTpz5ky6QGOM0cmTJ+0nkt06P1f7+uuvdeXKFc2bNy/d5Zh3co+EXbt26YknnlD9+vXT/QWSpnDhwqpcubLGjBmT6fRpx41DQ0O1efPmDM87cwKwMzJbn99++63i4+O1Zs2adJf1/vmE7LT3K6u9EPfcc4/c3d3VsWPHTM/fkKSSJUs6nD433pvMpKamav78+erTp4/T02T2HqSN+/MHQE58+OGH2rt3rwYPHqyePXtq37598vPzc2paDw8PVatWLd0e0b1792rv3r36z3/+k+k0I0eO1IgRIzRixIjbnmwrSW+//bY2bdqkd955R7Vr13bqpNkmTZooIiJC06dPV5MmTTR9+nTVqlVL5cuXT1fXtWtXde3aVVeuXNG6des0fPhwtWzZUr/99tttL5l29L54eXkpICDA4XSFCxeWdPNS+IKmZs2akm7uDa1atarDusKFC+v999/X+++/r6NHj2rhwoV6/fXXdfr0aS1dulQ///yzfvzxR82YMUOdO3e2T7d///5cX4Zb9e3bV5999pkWLFigpUuXqlChQnruuecyrT1//vxdf1sJ9sxYxGOPPaZGjRpp1KhRGf4yevTRRyVJn3/+ebrxc+fO1ZUrV+zP56a0D/RbTzQ2xmQaQpxx9OhRNWvWTKVKldLcuXMznFAn3Twk9vPPPysmJibTv/bSwkzDhg116dIlLVy4MN30s2bNcqqXnPwVldn6kKSPPvoo3XDp0qUVExOjadOmObyqxc/PTw0bNtSOHTtUuXLlTJc1qw9+V783jqxfv14nT57Mcq/Fn61atUqnTp2yD6ekpGj27NmKiYnJcm+Vs8qWLavWrVtryJAhio+Pz/QKEEfSDt/dek+auXPnKiIiQrVr185Q/8Ybb2jEiBEaOnTobU/ITrNw4UI98sgjevXVV1W3bl35+vredpq0YPv111/ru+++09atW+1X0GXG399fzZo105AhQ5SUlKTdu3ff9jXmzZtn3+sqSZcuXdKiRYtUr169LK8GSjssXRCvnFm9erUkZbjHUFbuvfde9e7dW40aNdL27dslOf+7fadut92pXr266tSpo3HjxmnmzJnq0qWL/P39M9QlJyfr2LFjGcLu3YY9MxYybtw4Va9eXadPn7YfSpGkRo0aqUmTJnrttdeUkJCgunXr2q9mqlq1qjp27JjrvTVq1EheXl569tlnNXDgQF2/fl1TpkzRH3/8kaP5NWvWTBcuXNDEiRMzbHxjYmJUpEgRjRo1SitWrFCdOnXUp08flSlTRtevX9fhw4e1ePFiffjhhypRooQ6deqk9957T506ddKYMWN0//33a/HixVq2bJlTvaTdtXTq1Kn2y3VLliyZZYCoU6eO7rnnHr3wwgsaPny4PD09NXPmTP34448ZaidNmqS4uDjVrl1b/fv317333qujR49q2bJlmjlzpqSbhyMeeugh1atXTy+++KKio6N16dIl7d+/X4sWLUp3ddSfZee9uXr1qhYvXixJ9t3maefBpH0oOjJnzhxVrFjR4flYmSlcuLAeeeQRDRs2zH410y+//JLp5dl3onjx4pIy7hlLU6dOHbVq1UrlypWzX50yZcoUHThwQPPnz7fXzZkzR08++WSGvXETJkzQP/7xDzVt2lQtWrTIcA5TZuFHkhISEnJ0Q7Ru3bpp3Lhxat++vXx9fTNcmdejRw/5+vqqbt26Cg8P18mTJzV27FgFBwdn2FObGXd3dzVq1EgDBgxQamqqxo0bp4SEBI0cOTLL6UqUKKFSpUpp48aN2dpD50rDhw/XqVOn9PDDD6t48eK6cOGCli5dqo8//lhPP/10lucwXbx4UQ0bNlT79u1VtmxZBQYGasuWLVq6dKn9PLCyZcsqJiZGr7/+uowxCgkJ0aJFi5w+hOesmJgY+fr6aubMmSpXrpwCAgIUERGR7kqlvn37ql27drLZbHrppZcync+uXbt09epVNWzY0KX9FTj5e/4xMnPr1Ux/1r59eyMpw82nrl27Zl577TUTFRVlPD09TXh4uHnxxRcz3FQqKirKtGjRIsN8065m+uqrr5zqJe0s/TNnztjHLVq0yFSpUsX4+PiY4sWLm7///e9myZIlGa6IceZqJmVxxcOtZ/efOXPG9OnTx5QsWdJ4enqakJAQU716dTNkyBBz+fJle93vv/9u2rRpYwICAkxgYKBp06aN/UZqztyU6v333zclS5Y07u7u6abJ6kZg69evN7GxscbPz88UKVLEdO/e3Wzfvj3T19ywYYNp1qyZCQ4ONt7e3iYmJsb0798/Xc2hQ4dMt27dTPHixY2np6cpUqSIqVOnjhk9evRt+3f2vUm7miWzx+1udBgZGZmtq1EkmZdfftlMnjzZxMTEGE9PT1O2bFkzc+ZMp+fhLEc/32leffVVU6VKFRMcHGw8PDxMsWLFTOvWrc0PP/xgr9m/f/9tr2pz9HDkdlfxZaVOnTpGknnuuecyPPfJJ5+Yhg0bmrCwMOPl5WUiIiJM27Ztza5du7KcZ9r7P27cODNy5EhTokQJ4+XlZapWrWqWLVvmVF/Dhg0z99xzT4ab0+X0pnnZtXDhQvPYY4+ZsLAw4+HhYQICAkzNmjXNBx98YL/ay5Hr16+bF154wVSuXNkEBQUZX19fU6ZMGTN8+PB0N8Pcs2ePadSokQkMDDT33HOPefrpp83Ro0czLENm20lj/m+7eujQIfu4zH4WvvjiC1O2bFnj6emZ6fpJTEw03t7epmnTpg6XadiwYaZw4cKWuVlgThFmANyxtEtyb/dheau0MJMXvvvuOyPJfPbZZzmex7hx40yRIkVMcnKyy/oKCwsz3bt3d9n87lRamHn77bdzPI/jx48bLy+vTC/PhmstXLjQSDLffPNNps8nJyeb6OjoDJfy3404ZwbAHatZs6aMMapUqVJ+t5KptJMfFyxYoDNnztgva86OgQMH6vTp07e9g+ztGGN07do1LV++XKdPn3bZ9xcVFBEREerXr5/GjBmTo/WM29uzZ4+WLFmiV199VQ888IDDw7+ff/65Ll++rL///e953GHeI8wAuOuVKFFCvXv31vz581W0aFGn74OTG9auXSs/Pz81adJEpUuXtt+1924ydOhQtWnT5q6/t0l+eemll9SqVSvdc889+uKLLxxeoZqamqqZM2eqUKFCedtgPrAZY0x+NwEAeeHSpUs6cuSIfH19030lRV73sH//foWGhuree+/Nlx6Auw1hBgAAWBqHmQAAgKURZgAAgKXd9TfNS01NVXx8vAIDA3PlNv4AAMD1jDG6dOmSIiIi5OaW9b6Xuz7MxMfHKzIyMr/bAAAAOXDs2LHbfr3JXR9mAgMDJd1cGUFBQfncDQAAcEZCQoIiIyPtn+NZuevDTNqhpaCgIMIMAAAW48wpIpwADAAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALO2uvwMwgLtTSqrR5kPndfrSdRUN9FHNkiFyd+PLZIG/IsIMAMtZ+vMJjVy0RycuXrePCw/20fC48mpaMTwfOwOQHzjMBMBSlv58Qi9+vj1dkJGkkxev68XPt2vpzyfyqTMA+YUwA8AyUlKNRi7aI5PJc2njRi7ao5TUzCoA3K0IMwAsY/Oh8xn2yNzKSDpx8bo2Hzqfd00ByHeEGQCWcfqS4yCTkzoAdwfCDADLKBro49I6AHcHwgwAy6hZMkThwT5ydAG2TTevaqpZMiQv2wKQzwgzACzD3c2m4XHlJSlDoEkbHh5XnvvNAH8xhBkAltK0YrimdKimYsHpDyUVC/bRlA7VuM8M8BfETfMAWE7TiuFqVL4YdwAGIIkwA8Ci3N1sio0Jze82ABQAHGYCAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWRpgBAACWlq9hZt26dYqLi1NERIRsNpu+/vrrdM936dJFNpst3aN27dr50ywAACiQ8jXMXLlyRVWqVNHEiRMd1jRt2lQnTpywPxYvXpyHHQIAgILOIz9fvFmzZmrWrFmWNd7e3ipWrFgedQQAAKymwJ8zs2bNGhUtWlSlS5dWjx49dPr06fxuCQAAFCD5umfmdpo1a6ann35aUVFROnTokIYNG6ZHHnlE27Ztk7e3d6bTJCYmKjEx0T6ckJCQV+0CAIB8UKDDTLt27ez/r1ixomrUqKGoqCh98803evLJJzOdZuzYsRo5cmRetQgAAPJZgT/MdKvw8HBFRUVp3759DmsGDRqkixcv2h/Hjh3Lww4BAEBeK9B7Zv7s3LlzOnbsmMLDwx3WeHt7OzwEBQAA7j75GmYuX76s/fv324cPHTqknTt3KiQkRCEhIRoxYoTatGmj8PBwHT58WIMHD1bhwoXVunXrfOwaAAAUJPkaZrZu3aqGDRvahwcMGCBJ6ty5s6ZMmaKffvpJn376qS5cuKDw8HA1bNhQs2fPVmBgYH61DAAAChibMcbkdxO5KSEhQcHBwbp48aKCgoLyux0AAOCE7Hx+W+oEYAAAgD8jzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEu7ozDTvHlzxcfHu6oXAACAbMtxmDl06JCWLl2qbdu2ubIfAACAbPFwpujgwYP64IMPdPz4caWkpCgxMVGbN29WgwYN9Mwzz6hu3boKCAiQu7u7wsPD1b17d1WuXDm3ewcAAJDNGGNuV/TQQw/p5MmTql27tjw9PeXp6anSpUurT58+mjVrljZu3KjExESlpKToxx9/1JkzZwrM4aeEhAQFBwfr4sWLCgoKyu92AACAE7Lz+e1UmAkICNCGDRtUqVKl27745cuXFRwcrN9//13h4eHOd51LCDMAAFhPdj6/nTpnpm3btoqOjnbqxQMCAtSzZ095eno6VQ8AAHAnnNozY2XsmQEAwHpcvmcGAACgoMp2mElNTXU4/ujRo3fcEAAAQHY4HWYSEhLUtm1b+fv7KywsTMOHD1dKSor9+TNnzqhkyZK50iQAAIAjToeZYcOG6ccff9Rnn32mMWPG6JNPPtHjjz+upKQke012T79Zt26d4uLiFBERIZvNpq+//jrd88YYjRgxQhEREfL19VWDBg20e/fubL0GAAC4uzkdZr7++mt99NFHeuqpp9S9e3dt27ZNZ8+eVVxcnBITEyVJNpstWy9+5coVValSRRMnTsz0+fHjx+vdd9/VxIkTtWXLFhUrVkyNGjXSpUuXsvU6AADg7uV0mDl79qyioqLsw6GhoVqxYoUuXbqk5s2b6+rVq9l+8WbNmmn06NF68sknMzxnjNH777+vIUOG6Mknn1TFihX1ySef6OrVq5o1a1a2XwsAANydnA4zkZGR2rt3b7pxgYGBWr58ua5du6bWrVu7tLFDhw7p5MmTaty4sX2ct7e36tevr/Xr1zucLjExUQkJCekeAADg7uV0mGnUqJGmT5+eYXxAQICWLVsmHx8flzZ28uRJSVJYWFi68WFhYfbnMjN27FgFBwfbH5GRkS7tCwAAFCxOfdGkJI0aNcrh9y0FBgZq5cqVufIN2n8+D8cYk+W5OYMGDdKAAQPswwkJCQQaAADuYk7vmXn55Ze1e/duh4dtAgICVL9+fZc1VqxYMUnKsBfm9OnTGfbW3Mrb21tBQUHpHgAA4O7ldJgpU6aMxo0bp6JFi6px48aaNGmSjh07lmuNlSxZUsWKFdOKFSvs45KSkrR27VrVqVMn114XAABYi9NhZvjw4dq2bZv279+vJ554QgsXLtT999+vatWqacSIEdqxY0e2X/zy5cvauXOndu7cKenmSb87d+7U0aNHZbPZ1K9fP7355puaP3++fv75Z3Xp0kV+fn5q3759tl8LAADcne7oiyYvXbqkJUuWaMGCBVqyZIkCAwMVFxenF198URUqVLjt9GvWrFHDhg0zjO/cubNmzJghY4xGjhypjz76SH/88Ydq1aqlSZMmqWLFik73yBdNAgBgPdn5/HbZt2anpKRozZo1WrhwoSpVqqTu3bu7YrZ3jDADAID15EuYKagIMwAAWE92Pr+z9a3Z//73v9W5c2f7/WZmz56tcuXKqVSpUho+fHjOOwYAAMghp+8z8/7772vo0KFq0qSJhgwZovj4eL333nvq37+/UlNTNWHCBBUvXlw9e/bMzX4BAADScTrMfPTRR5o6darat2+vHTt2qGbNmvrwww/1/PPPS5JKlCihSZMmEWYAAECecvow05EjR/TQQw9JkqpWrSp3d3fVrl3b/ny9evV04MAB13cIAACQBafDjJ+fn65cuWIfLlKkiAICAtLVJCcnu64zAAAAJzgdZsqWLatdu3bZh48dO6aoqCj78C+//KLo6GiXNgcAAHA7Tp8zM27cOPn7+zt8/ujRo+rVq5dLmgIAAHAW95kBAAAFTq7dZwYAAKCgcSrMvPHGG7p69arTM33rrbd04cKFnPYEAADgNKfCzFtvvaWjR486NcPExEQNGzYs3ZVPAAAAucWpE4DLli2rZ555RvXq1ZOnp6c8PT1Vrlw5de7cWYsWLdLGjRt1/fp1paamaseOHQoKClJERERu9w4AAOBcmJk2bZreeecd7dmzR6mpqbp+/bomTpyor7/+Wt98842qVKmiwMBAubu7KzIyUqNHj5bNZsvt3gEAAHJ+NdNPP/2kKlWqaObMmXr22Wdd3ZfLcDUTAADWkydXM1WqVEllypRRbGxsTmcBAABwx5y+aV5m9u7d66o+AAAAcoT7zAAAAEsjzAAAAEvLdph55513cqMPAACAHMlWmHn99df18ccf51YvAAAA2ebUCcDGGPXs2VMrV67UunXrcrsnAAAApzkVZp566ilt3LhRa9euVWRkZG73BAAA4DSnwsz8+fM1depU3XfffbndDwAAQLY4dc5Mv3799Oqrr2rLli253Q8AAEC2OLVn5t1331VoaKiaNWum1atXq1KlSrndFwAAgFOcvgPwkCFDVKRIETVt2lTHjx/PzZ4AAACclq2vM+jZs6dCQ0NzqxcAAIBsy/ZN89q0aZMbfQAAAOQIX2cAAAAsLUdhZtWqVWrZsqViYmJ03333qWXLllq5cqWrewMAALitbIeZiRMnqmnTpgoMDFTfvn3Vp08fBQUFqXnz5po4cWJu9AgAAOCQzRhjsjNB8eLFNWjQIPXu3Tvd+EmTJmnMmDGKj493aYN3KiEhQcHBwbp48aKCgoLyux0AAOCE7Hx+Z3vPTEJCgpo2bZphfOPGjZWQkJDd2QEAANyRbIeZVq1aaf78+RnGL1iwQHFxcS5pCgAAwFnZus+MJJUrV05jxozRmjVrFBsbK0nauHGjfvjhB7366qv64IMP7LV9+vRxXacAAACZyPY5MyVLlnRuxjabDh48mKOmXIlzZgAAsJ7sfH5ne8/MoUOHctwYAACAq3HTPAAAYGmEGQAAYGmEGQAAYGmEGQAAYGlOh5mpU6fq5MmTudkLAABAtjkdZr744gtFR0erVq1aevPNN7V79+7c7AsAAMApToeZ1atX68SJE3rllVe0c+dO1alTRzExMRowYIDWrFmj1NTU3OwTAAAgU9m+aV6apKQkffvtt1q4cKEWLVqkq1evqkWLFmrVqpWaNWsmf39/V/eaI9w0DwAA68nO53eOw8yfbd26VQsXLtSCBQv01FNPadiwYa6Y7R0jzAAAYD35EmZudePGDXl6erp6tjlCmAEAwHqy8/mdK5dmF5QgAwAA7n7cZwYAAFgaYQYAAFgaYQYAAFiay8LMlStXtG7dOlfNDgAAwCkuCzP79+9Xw4YNXTU7AAAAp3CYCQAAWJqHs4UhISFZPp+SknLHzQAAAGSX02EmMTFRL774oipVqpTp80eOHNHIkSNd1hgAAIAznA4zDzzwgCIjI9W5c+dMn//xxx8JMwAAIM85fc5MixYtdOHCBYfPh4SEqFOnTq7oCQAAwGm58t1MBQnfzQQAgPXk+3czAQAA5BWnz5n5sz179ujo0aNKSkpKN75Vq1Z33BQAAICzsh1mDh48qNatW+unn36SzWZT2lEqm80miUu0AQBA3sr2Yaa+ffuqZMmSOnXqlPz8/LR7926tW7dONWrU0Jo1a3KhRQAAAMeyvWdmw4YN+vbbb1WkSBG5ubnJzc1NDz30kMaOHas+ffpox44dudEnAABAprK9ZyYlJUUBAQGSpMKFCys+Pl6SFBUVpV9//dW13QEAANxGtvfMVKxYUbt27VKpUqVUq1YtjR8/Xl5eXpo6dapKlSqVGz0CAAA4lO0wM3ToUF25ckWSNHr0aLVs2VL16tVTaGioZs+e7fIGAQAAsuKSm+adP39e99xzj/2KpoKEm+YBAGA92fn8zvF9Zm51u2/UBgAAyC3cARgAAFhagQ4zI0aMkM1mS/coVqxYfrcFAAAKEJccZspNFSpU0MqVK+3D7u7u+dgNAAAoaAp8mPHw8GBvDAAAcKhAH2aSpH379ikiIkIlS5bUM888o4MHD2ZZn5iYqISEhHQPAABw9yrQYaZWrVr69NNPtWzZMn388cc6efKk6tSpo3PnzjmcZuzYsQoODrY/IiMj87BjAACQ11xyn5m8cuXKFcXExGjgwIEaMGBApjWJiYlKTEy0DyckJCgyMpL7zAAAYCF5fp+ZvOLv769KlSpp3759Dmu8vb3l7e2dh10BAID8VKAPM/1ZYmKi9u7dq/Dw8PxuBQAAFBAFOsz87W9/09q1a3Xo0CFt2rRJTz31lBISEtS5c+f8bg0AABQQBfow0++//65nn31WZ8+eVZEiRVS7dm1t3LhRUVFR+d0aAAAoIAp0mPnyyy/zuwUAAFDAFejDTAAAALdDmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJZGmAEAAJbmkd8N5JWrScnySErOMN7NZpOPp3u6OkfupPZaUoqMTKa1Ntnk65Wz2us3UpRqMq+VJD8vj3yv9fV0l81mkyQlJqcoJdU1tT4e7nJzu1mblJyq5NRUl9R6e7jLPQe1N1JSdSPFca2Xu5s83N2yXZuckqqkLGo93d3kmYPalFSjxOQUh7Uebm7y8sh+bWqq0XUX1bq72eTtcfPn3RijazdcU5tXv/dsI5yrZRtxE9uIjLXO+suEmZpjVsnN2y/D+IZlimh615r24epvrHS4EaxVMkSze8Xahx8at1rnryRlWlu5RLAW9n7IPvzYu2t1/MK1TGvvLxqgFQPq24dbTfxe+05fzrS2eCFf/fD6I/bhth9t0K7fL2ZaG+Lvpe3DGtmHO0/brE2Hzmda6+vprr1vNLUPv/j5Nq3+9UymtZJ0+K0W9v8P+O9OLf7ppMPaPaOa2Ddsg+f9rLnbf3dYu23oYwoN8JYkjf7fXn228YjD2u8GNlRkyM339J3lv2rquoMOa5f3f1ilwwIlSZNW79c/V+1zWLvg5bqqEllIkjT9h0Mau+QXh7Vf9Kit2JjQm//ffFT/WLDbYe20LjX0SNkwSdLXO47r73N2Oayd1L6aWlQOlyQt231KL8/a7rD27acq6+kakZKkdfvOqNuMrQ5rRz1eQZ1ioyVJmw+d17Mfb3RYO6hZWfWqHyNJ+vn4RT0+6QeHtX0fvV/9G5WWJO0/c1mN31vnsLbnw6U0uHk5SdLxC9dUb/xqh7Uda0fpjScqSpLOX0lS9dErHda2qVZCE9pWkSRdu5Gi8v9Y5rC2eaVimvxcdftwVrVsI25iG/F/2EbclBfbCGdxmAkAAFiazZgs9v3dBRISEhQcHKwTZ84pKCgow/PsQs79WnYh38Qu5OzXcpjpJrYROatlG3GTVbcRaZ/fFy9ezPTz+1Z/mTDjzMoAAAAFQ3Y+vznMBAAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALI0wAwAALM0SYWby5MkqWbKkfHx8VL16dX333Xf53RIAACggCnyYmT17tvr166chQ4Zox44dqlevnpo1a6ajR4/md2sAAKAAsBljTH43kZVatWqpWrVqmjJlin1cuXLl9MQTT2js2LG3nT4hIUHBwcG6ePGigoKCcrNVAADgItn5/C7Qe2aSkpK0bds2NW7cON34xo0ba/369ZlOk5iYqISEhHQPAABw9yrQYebs2bNKSUlRWFhYuvFhYWE6efJkptOMHTtWwcHB9kdkZGRetAoAAPJJgQ4zaWw2W7phY0yGcWkGDRqkixcv2h/Hjh3LixYBAEA+8cjvBrJSuHBhubu7Z9gLc/r06Qx7a9J4e3vL29s7L9oDAAAFQIHeM+Pl5aXq1atrxYoV6cavWLFCderUyaeuAABAQVKg98xI0oABA9SxY0fVqFFDsbGxmjp1qo4ePaoXXnghv1sDAAAFQIEPM+3atdO5c+c0atQonThxQhUrVtTixYsVFRWV360BAIACoMDfZ+ZOcZ8ZAACs5665zwwAAMDtEGYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAIClEWYAAICleeR3A3nlalKyPJKSM4x3s9nk4+mers6RO6m9lpQiI5NprU02+XrlrPb6jRSlmsxrJcnPyyPfa3093WWz2SRJickpSkl1Ta2Ph7vc3G7WJiWnKjk11SW13h7ucs9B7Y2UVN1IcVzr5e4mD3e3bNcmp6QqKYtaT3c3eeagNiXVKDE5xWGth5ubvDyyX5uaanTdRbXubjZ5e9z8eTfG6NoN19Tm1e892wjnatlG3MQ2ImOts/4yYabmmFVy8/bLML5hmSKa3rWmfbj6GysdbgRrlQzR7F6x9uGHxq3W+StJmdZWLhGshb0fsg8/9u5aHb9wLdPa+4sGaMWA+vbhVhO/177TlzOtLV7IVz+8/oh9uO1HG7Tr94uZ1ob4e2n7sEb24c7TNmvTofOZ1vp6umvvG03twy9+vk2rfz2Taa0kHX6rhf3/A/67U4t/Oumwds+oJvYN2+B5P2vu9t8d1m4b+phCA7wlSaP/t1efbTzisPa7gQ0VGXLzPX1n+a+auu6gw9rl/R9W6bBASdKk1fv1z1X7HNYueLmuqkQWkiRN/+GQxi75xWHtFz1qKzYm9Ob/Nx/VPxbsdlg7rUsNPVI2TJL09Y7j+vucXQ5rJ7WvphaVwyVJy3af0suztjusffupynq6RqQkad2+M+o2Y6vD2lGPV1Cn2GhJ0uZD5/Xsxxsd1g5qVla96sdIkn4+flGPT/rBYW3fR+9X/0alJUn7z1xW4/fWOazt+XApDW5eTpJ0/MI11Ru/2mFtx9pReuOJipKk81eSVH30Soe1baqV0IS2VSRJ126kqPw/ljmsbV6pmCY/V90+nFUt24ib2Eb8H7YRN+XFNsJZHGYCAACWZjMmi31/d4GEhAQFBwfrxJlzCgoKyvA8u5Bzv5ZdyDexCzn7tRxmuoltRM5q2UbcZNVtRNrn98WLFzP9/L7VXybMOLMyAABAwZCdz28OMwEAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEsjzAAAAEvzuH2JtaV9KXhCQkI+dwIAAJyV9rmd9jmelbs+zFy6dEmSFBkZmc+dAACA7Lp06ZKCg4OzrLEZZyKPhaWmpio+Pl6BgYGy2Wz53Y5LJSQkKDIyUseOHVNQUFB+t5Pn/urLL7EOWP6/9vJLrIO7efmNMbp06ZIiIiLk5pb1WTF3/Z4ZNzc3lShRIr/byFVBQUF33Q9xdvzVl19iHbD8f+3ll1gHd+vy326PTBpOAAYAAJZGmAEAAJZGmLEwb29vDR8+XN7e3vndSr74qy+/xDpg+f/ayy+xDv7qy5/mrj8BGAAA3N3YMwMAACyNMAMAACyNMAMAACyNMAMAACyNMFOAHT9+XB06dFBoaKj8/Pz0wAMPaNu2bQ7ru3TpIpvNluFRoUKFPOzadbK7/JI0c+ZMValSRX5+fgoPD1fXrl117ty5POrY9XKyDiZNmqRy5crJ19dXZcqU0aeffppH3bpWdHR0pj/PL7/8ssNp1q5dq+rVq8vHx0elSpXShx9+mIcdu15218GJEyfUvn17lSlTRm5uburXr1/eNuxi2V3+efPmqVGjRipSpIiCgoIUGxurZcuW5XHXrpPd5f/+++9Vt25dhYaGytfXV2XLltV7772Xx13nj7v+DsBW9ccff6hu3bpq2LChlixZoqJFi+rAgQMqVKiQw2n++c9/6q233rIPJycnq0qVKnr66afzoGPXysnyf//99+rUqZPee+89xcXF6fjx43rhhRfUvXt3zZ8/P++ad5GcrIMpU6Zo0KBB+vjjj/Xggw9q8+bN6tGjh+655x7FxcXlXfMusGXLFqWkpNiHf/75ZzVq1Mjhz/OhQ4fUvHlz9ejRQ59//rl++OEHvfTSSypSpIjatGmTV227VHbXQWJioooUKaIhQ4bcFR9i2V3+devWqVGjRnrzzTdVqFAhTZ8+XXFxcdq0aZOqVq2aV227THaX39/fX71791blypXl7++v77//Xr169ZK/v7969uyZV23nD4MC6bXXXjMPPfTQHc1j/vz5xmazmcOHD7uoq7yTk+V/++23TalSpdKN++CDD0yJEiVc2Vqeyck6iI2NNX/729/Sjevbt6+pW7euK1vLF3379jUxMTEmNTU10+cHDhxoypYtm25cr169TO3atfOivTxxu3Vwq/r165u+ffvmflN5KDvLn6Z8+fJm5MiRudhV3snJ8rdu3dp06NAhF7sqGDjMVEAtXLhQNWrU0NNPP62iRYuqatWq+vjjj7M1j//85z967LHHFBUVlUtd5p6cLH+dOnX0+++/a/HixTLG6NSpU5ozZ45atGiRR127Vk7WQWJionx8fNKN8/X11ebNm3Xjxo3cbDdXJSUl6fPPP1e3bt0cfmHshg0b1Lhx43TjmjRpoq1bt1p62dM4sw7uZjlZ/tTUVF26dEkhISG53F3uy8ny79ixQ+vXr1f9+vVzubsCIL/TFDLn7e1tvL29zaBBg8z27dvNhx9+aHx8fMwnn3zi1PTx8fHG3d3dzJ49O5c7zR05Xf6vvvrKBAQEGA8PDyPJtGrVyiQlJeVR166Vk3UwaNAgU6xYMbN161aTmppqtmzZYooWLWokmfj4+Dzs3rVmz55t3N3dzfHjxx3W3H///WbMmDHpxv3www+WX/Y0zqyDW91te2ayu/zGGDN+/HgTEhJiTp06lYud5Y3sLH/x4sWNl5eXcXNzM6NGjcqD7vIfYaaA8vT0NLGxsenGvfLKK07vMn/zzTdNaGioSUxMzI32cl1Oln/37t0mPDzcjB8/3vz4449m6dKlplKlSqZbt2653W6uyMk6uHr1qunatavx8PAw7u7uJiIiwgwcONBIsvQGvXHjxqZly5ZZ1tx///3mzTffTDfu+++/N5LMiRMncrO9POHMOrjV3RZmsrv8s2bNMn5+fmbFihW52FXeyc7yHzx40OzatctMnTrVhISEmFmzZuVyd/mPw0wFVHh4uMqXL59uXLly5XT06NHbTmuM0bRp09SxY0d5eXnlVou5KifLP3bsWNWtW1d///vfVblyZTVp0kSTJ0/WtGnTdOLEidxu2eVysg58fX01bdo0Xb16VYcPH9bRo0cVHR2twMBAFS5cOLdbzhVHjhzRypUr1b179yzrihUrppMnT6Ybd/r0aXl4eCg0NDQ3W8x1zq6Du1V2l3/27Nl6/vnn9d///lePPfZYLneX+7K7/CVLllSlSpXUo0cP9e/fXyNGjMjdBgsAwkwBVbduXf3666/pxv32229Onf+ydu1a7d+/X88//3xutZfrcrL8V69elZtb+h9pd3d3STcDntXcyc+Ap6enSpQoIXd3d3355Zdq2bJlhnVjFdOnT1fRokVve+5TbGysVqxYkW7c8uXLVaNGDXl6euZmi7nO2XVwt8rO8n/xxRfq0qWLZs2addesrzt5/40xSkxMzIWuCph83jMEBzZv3mw8PDzMmDFjzL59+8zMmTONn5+f+fzzz+01r7/+uunYsWOGaTt06GBq1aqVl+26XE6Wf/r06cbDw8NMnjzZHDhwwHz//femRo0apmbNmvmxCHcsJ+vg119/NZ999pn57bffzKZNm0y7du1MSEiIOXToUD4swZ1LSUkx9957r3nttdcyPPfnZT948KDx8/Mz/fv3N3v27DH/+c9/jKenp5kzZ05etuxy2VkHxhizY8cOs2PHDlO9enXTvn17s2PHDrN79+68atflsrP8s2bNMh4eHmbSpEnmxIkT9seFCxfysmWXys7yT5w40SxcuND89ttv5rfffjPTpk0zQUFBZsiQIXnZcr4gzBRgixYtMhUrVjTe3t6mbNmyZurUqeme79y5s6lfv366cRcuXDC+vr4Zaq0oJ8v/wQcfmPLlyxtfX18THh5unnvuOfP777/nYdeuld11sGfPHvPAAw8YX19fExQUZB5//HHzyy+/5HHXrrNs2TIjyfz6668Znsvs/V+zZo2pWrWq8fLyMtHR0WbKlCl51Gnuye46kJThERUVlTfN5oLsLH/9+vUzXf7OnTvnXcMulp3l/+CDD0yFChWMn5+fCQoKMlWrVjWTJ082KSkpedhx/rAZY8H97wAAAP+fNQ+iAwAA/H+EGQAAYGmEGQAAYGmEGQAAYGmEGQAAYGmEGQAAYGmEGQAAYGmEGQAFyuHDh2Wz2bRz5878bgWARXDTPAAFSkpKis6cOaPChQvLw8Mjv9sBYAGEGQAFRlJSkmW/6R1A/uEwE4Bc0aBBA/Xu3Vu9e/dWoUKFFBoaqqFDh6b7BvPo6GiNHj1aXbp0UXBwsHr06JHhMNOaNWtks9m0bNkyVa1aVb6+vnrkkUd0+vRpLVmyROXKlVNQUJCeffZZXb161T5vY4zGjx+vUqVKydfXV1WqVNGcOXOy7Dk6OlpvvPGG2rdvr4CAAEVEROhf//pXrqwfAK5DmAGQaz755BN5eHho06ZN+uCDD/Tee+/p3//+d7qat99+WxUrVtS2bds0bNgwh/MaMWKEJk6cqPXr1+vYsWNq27at3n//fc2aNUvffPONVqxYkS54DB06VNOnT9eUKVO0e/du9e/fXx06dNDatWuz7Pntt99W5cqVtX37dg0aNEj9+/fXihUr7mxFAMhVHGYCkCsaNGig06dPa/fu3bLZbJKk119/XQsXLtSePXsk3dwTUrVqVc2fP98+3eHDh1WyZEnt2LFDDzzwgNasWaOGDRtq5cqVevTRRyVJb731lgYNGqQDBw6oVKlSkqQXXnhBhw8f1tKlS3XlyhUVLlxY3377rWJjY+3z7t69u65evapZs2Zl2nN0dLTKlSunJUuW2Mc988wzSkhI0OLFi127ggC4DHtmAOSa2rVr24OMJMXGxmrfvn1KSUmxj6tRo4ZT86pcubL9/2FhYfLz87MHmbRxp0+fliTt2bNH169fV6NGjRQQEGB/fPrppzpw4ECWr3Nr+Ekb3rt3r1M9AsgfXCoAIF/5+/s7Vefp6Wn/v81mSzecNi41NVWS7P9+8803Kl68eLo6b2/vbPd4ayADUPAQZgDkmo0bN2YYvv/+++Xu7p6rr1u+fHl5e3vr6NGjql+/framzaznsmXLurI9AC5GmAGQa44dO6YBAwaoV69e2r59u/71r39pwoQJuf66gYGB+tvf/qb+/fsrNTVVDz30kBISErR+/XoFBASoc+fODqf94YcfNH78eD3xxBNasWKFvvrqK33zzTe53jOAnCPMAMg1nTp10rVr11SzZk25u7vrlVdeUc+ePfPktd944w0VLVpUY8eO1cGDB1WoUCFVq1ZNgwcPznK6V199Vdu2bdPIkSMVGBioCRMmqEmTJnnSM4Cc4WomALmiQYMGeuCBB/T+++/ndytOi46OVr9+/dSvX7/8bgVANnA1EwAAsDTCDAAAsDQOMwEAAEtjzwwAALA0wgwAALA0wgwAALA0wgwAALA0wgwAALA0wgwAALA0wgwAALA0wgwAALA0wgwAALC0/wddZy1nc9fzAgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min/Max of normalized traces: 18.5202591774521 18.5202591774521\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "Ldf = pd.read_csv(\"OA_Lpoly.csv\")\n",
    "\n",
    "# If a1_norm column already exists, use it; otherwise compute it\n",
    "if \"a1_norm\" in Ldf.columns:\n",
    "    y = Ldf[\"a1_norm\"].astype(float).values\n",
    "else:\n",
    "    y = Ldf[\"a1\"].astype(float).values / (Ldf[\"p\"].astype(float).values ** 1.5)\n",
    "\n",
    "x = Ldf[\"p\"].astype(int).values\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(x, y, marker=\"o\")\n",
    "plt.axhline( 2.0, linestyle=\"--\")   # loose visual envelope\n",
    "plt.axhline(-2.0, linestyle=\"--\")\n",
    "plt.title(\"Normalized trace a1 / p^{3/2} vs p (H^3 sanity)\")\n",
    "plt.xlabel(\"prime p\")\n",
    "plt.ylabel(\"a1 / p^{3/2}\")\n",
    "plt.show()\n",
    "\n",
    "print(\"Min/Max of normalized traces:\", float(np.min(y)), float(np.max(y)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8e76a9",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[skip] already have (p=7, r=1)\n",
      "[skip] already have (p=11, r=1)\n",
      "[skip] already have (p=13, r=1)\n",
      "[skip] already have (p=17, r=1)\n",
      "[skip] already have (p=19, r=1)\n",
      "[skip] already have (p=23, r=1)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[OK] appended (p=29, r=1)  N_pr=864\n",
      "Done. Wrote new r=1 rows (if any) to OA_counts.csv\n"
     ]
    }
   ],
   "source": [
    "# === Append r=1 counts for more primes (mirror quintic, psi = 1) ===\n",
    "# Works fast enough on a phone for these small primes.\n",
    "psi = 1\n",
    "prime_batch = [7, 11, 13, 17, 19, 23, 29]   # tweak if you like\n",
    "\n",
    "def N1_mirror_quintic_modp(p, psi):\n",
    "    \"\"\"Counts projective F_p points with r=1 using plain integers mod p.\"\"\"\n",
    "    mod = p\n",
    "    psi_mod = psi % mod\n",
    "    pow5 = [pow(x, 5, mod) for x in range(mod)]\n",
    "    N = 0\n",
    "    for x1 in range(mod):\n",
    "        a = pow5[x1]\n",
    "        for x2 in range(mod):\n",
    "            b = (a + pow5[x2]) % mod\n",
    "            for x3 in range(mod):\n",
    "                c = (b + pow5[x3]) % mod\n",
    "                for x4 in range(mod):\n",
    "                    prod = (x1 * x2) % mod\n",
    "                    prod = (prod * x3) % mod\n",
    "                    prod = (prod * x4) % mod\n",
    "                    val = (c + pow5[x4] + 1 - (5 * psi_mod * prod) ) % mod\n",
    "                    if val == 0:\n",
    "                        N += 1\n",
    "    return N // (mod - 1)\n",
    "\n",
    "# read existing rows so we only add missing (p,1)\n",
    "existing = set()\n",
    "try:\n",
    "    with open(\"OA_counts.csv\") as f:\n",
    "        next(f)  # header\n",
    "        for ln in f:\n",
    "            parts = ln.strip().split(\",\")\n",
    "            if len(parts) >= 3:\n",
    "                p0, r0 = int(parts[0]), int(parts[1])\n",
    "                existing.add((p0, r0))\n",
    "except FileNotFoundError:\n",
    "    pass\n",
    "\n",
    "# append new rows\n",
    "import io, os\n",
    "buf = io.StringIO()\n",
    "new_rows = 0\n",
    "for p in prime_batch:\n",
    "    if p == 5:  # skip bad prime for quintic\n",
    "        continue\n",
    "    if (p, 1) in existing:\n",
    "        print(f\"[skip] already have (p={p}, r=1)\")\n",
    "        continue\n",
    "    N1 = N1_mirror_quintic_modp(p, psi)\n",
    "    buf.write(f\"{p},1,{N1},{psi}\\n\")\n",
    "    print(f\"[OK] appended (p={p}, r=1)  N_pr={N1}\")\n",
    "\n",
    "# write header if file missing; then append buffer\n",
    "if not os.path.exists(\"OA_counts.csv\"):\n",
    "    with open(\"OA_counts.csv\", \"w\") as f:\n",
    "        f.write(\"p,r,N_pr,psi\\n\")\n",
    "with open(\"OA_counts.csv\", \"a\") as f:\n",
    "    f.write(buf.getvalue())\n",
    "\n",
    "print(\"Done. Wrote new r=1 rows (if any) to OA_counts.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b68341",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     p     a1     a1_norm\n",
      "0    7     78    4.211604\n",
      "2   11    122    3.344035\n",
      "4   13    144    3.072186\n",
      "6   17    307    4.379908\n",
      "8   19    343    4.141558\n",
      "10  23    576    5.221926\n",
      "12  29  24396  156.214602\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min/Max of a1_norm: 3.0721857021704997 156.21460241956402\n"
     ]
    }
   ],
   "source": [
    "# === Plot a1 / p^{3/2} directly from OA_counts.csv (uses r=1 only) ===\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "df = pd.read_csv(\"OA_counts.csv\")\n",
    "df1 = df[df[\"r\"] == 1].copy()\n",
    "\n",
    "def a1_from_N1(p, N1):\n",
    "    # for a 3-fold, total points on P^3 over F_p is (1 + p + p^2 + p^3)\n",
    "    return (1 + p + p*p + p*p*p) - N1\n",
    "\n",
    "df1[\"a1\"] = [a1_from_N1(int(p), int(N1)) for p, N1 in zip(df1[\"p\"], df1[\"N_pr\"])]\n",
    "df1[\"a1_norm\"] = df1[\"a1\"] / (df1[\"p\"] ** 1.5)\n",
    "\n",
    "df1 = df1.sort_values(\"p\")\n",
    "print(df1[[\"p\", \"a1\", \"a1_norm\"]])\n",
    "\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.plot(df1[\"p\"], df1[\"a1_norm\"], marker=\"o\")\n",
    "plt.title(\"Normalized a1 / p^{3/2} vs p (r=1 counts)\")\n",
    "plt.xlabel(\"prime p\")\n",
    "plt.ylabel(\"a1 / p^{3/2}\")\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "print(\"Min/Max of a1_norm:\", float(np.min(df1[\"a1_norm\"])), float(np.max(df1[\"a1_norm\"])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4393ea",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wrote OA_Lpoly_clean.csv with rows:\n",
      "    p     a1 a2     a1_norm     source\n",
      "0   7     78  0    4.211604  counts_r1\n",
      "1  11    122  0    3.344035  counts_r1\n",
      "2  13    144  0    3.072186  counts_r1\n",
      "3  17    307  0    4.379908  counts_r1\n",
      "4  19    343  0    4.141558  counts_r1\n",
      "5  23    576  0    5.221926  counts_r1\n",
      "6  29  24396  0  156.214602  counts_r1\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Build OA_Lpoly_clean.csv from r=1 counts + any existing OA_Lpoly.csv ===\n",
    "# Outputs columns: p, a1, a2, a1_norm, source\n",
    "#   - a1 from r=1 counts: a1 = (1 + p + p^2 + p^3) - N_{p}\n",
    "#   - a1_norm = a1 / p^{3/2}\n",
    "#   - a2 is a clearly-marked placeholder (needs r=2 to be rigorous)\n",
    "\n",
    "import os, math\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "def a1_from_N1(p, N1):\n",
    "    return (1 + p + p*p + p*p*p) - N1\n",
    "\n",
    "# 1) Pull r=1 counts from OA_counts.csv\n",
    "r1_df = None\n",
    "if os.path.exists(\"OA_counts.csv\"):\n",
    "    df = pd.read_csv(\"OA_counts.csv\")\n",
    "    r1 = df[df[\"r\"] == 1].copy()\n",
    "    if not r1.empty:\n",
    "        r1[\"p\"]  = r1[\"p\"].astype(int)\n",
    "        r1[\"N1\"] = r1[\"N_pr\"].astype(int)\n",
    "        r1[\"a1\"] = [a1_from_N1(int(p), int(N1)) for p, N1 in zip(r1[\"p\"], r1[\"N1\"])]\n",
    "        r1[\"a1_norm\"] = r1[\"a1\"] / (r1[\"p\"] ** 1.5)\n",
    "        # a2 placeholder: 0 for now (requires r=2 to solve Newton identities exactly)\n",
    "        r1[\"a2\"] = 0\n",
    "        r1[\"source\"] = \"counts_r1\"\n",
    "        r1_df = r1[[\"p\",\"a1\",\"a2\",\"a1_norm\",\"source\"]].copy()\n",
    "\n",
    "# 2) Load any existing OA_Lpoly.csv (keep its a1/a2 if present)\n",
    "Lpoly_df = None\n",
    "if os.path.exists(\"OA_Lpoly.csv\"):\n",
    "    raw = pd.read_csv(\"OA_Lpoly.csv\")\n",
    "    keep_cols = [c for c in [\"p\",\"a1\",\"a2\",\"a1_norm\"] if c in raw.columns]\n",
    "    if keep_cols:\n",
    "        Lpoly_df = raw[keep_cols].copy()\n",
    "        # Coerce numeric if needed\n",
    "        for c in [\"p\",\"a1\",\"a2\",\"a1_norm\"]:\n",
    "            if c in Lpoly_df.columns:\n",
    "                Lpoly_df[c] = pd.to_numeric(Lpoly_df[c], errors=\"coerce\")\n",
    "        # Fill missing a1_norm from a1 if possible\n",
    "        if \"a1_norm\" not in Lpoly_df.columns or Lpoly_df[\"a1_norm\"].isna().any():\n",
    "            if \"a1\" in Lpoly_df.columns and \"p\" in Lpoly_df.columns:\n",
    "                Lpoly_df[\"a1_norm\"] = Lpoly_df[\"a1\"] / (Lpoly_df[\"p\"] ** 1.5)\n",
    "        Lpoly_df[\"source\"] = \"existing_Lpoly\"\n",
    "        Lpoly_df = Lpoly_df[[\"p\",\"a1\",\"a2\",\"a1_norm\",\"source\"]]\n",
    "\n",
    "# 3) Merge, preferring r=1 counts for a1 when both exist\n",
    "pieces = []\n",
    "if Lpoly_df is not None: pieces.append(Lpoly_df)\n",
    "if r1_df    is not None: pieces.append(r1_df)\n",
    "\n",
    "if not pieces:\n",
    "    raise SystemExit(\"No data found: need OA_counts.csv (r=1) and/or OA_Lpoly.csv.\")\n",
    "\n",
    "merged = pd.concat(pieces, ignore_index=True)\n",
    "# Sort so that counts_r1 rows come first (we'll drop duplicates keeping first)\n",
    "sort_key = merged[\"source\"].map({\"counts_r1\": 0, \"existing_Lpoly\": 1}).fillna(2)\n",
    "merged = merged.assign(_k=sort_key).sort_values([\"p\",\"_k\"]).drop(columns=\"_k\")\n",
    "\n",
    "# Drop duplicate primes, keep the first occurrence (i.e., counts_r1 preferred)\n",
    "clean = merged.drop_duplicates(subset=[\"p\"], keep=\"first\").sort_values(\"p\").reset_index(drop=True)\n",
    "\n",
    "# Sanity: compute a1_norm if missing\n",
    "if \"a1_norm\" not in clean.columns or clean[\"a1_norm\"].isna().any():\n",
    "    clean[\"a1_norm\"] = clean[\"a1\"] / (clean[\"p\"] ** 1.5)\n",
    "\n",
    "# Write clean file\n",
    "clean.to_csv(\"OA_Lpoly_clean.csv\", index=False)\n",
    "print(\"Wrote OA_Lpoly_clean.csv with rows:\")\n",
    "print(clean)\n",
    "\n",
    "# Quick plot\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.plot(clean[\"p\"], clean[\"a1_norm\"], marker=\"o\")\n",
    "plt.title(\"Normalized a1 / p^{3/2} (clean merge)\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"a1_norm\")\n",
    "plt.grid(True); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "00c8b2",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✅ Appended r=2 rows for primes: [29]\n",
      "\n",
      "Tail of OA_counts.csv:\n",
      "11,1,1342,1\n",
      "11,2,1771803,1\n",
      "13,1,2236,1\n",
      "13,2,4827823,1\n",
      "17,1,4913,1\n",
      "17,2,24137569,1\n",
      "19,1,6897,1\n",
      "19,2,47047325,1\n",
      "23,1,12144,1\n",
      "23,2,148034831,1\n",
      "29,1,864,1\n",
      "29,2,595580222,1\n"
     ]
    }
   ],
   "source": [
    "# === Clean version: Append r=2 counts safely ===\n",
    "\n",
    "import os\n",
    "import pandas as pd\n",
    "\n",
    "psi_param = 1  # ensure plain Python int, not Sage type\n",
    "\n",
    "def append_r2_counts(primes, psi_param=1):\n",
    "    primes = [int(p) for p in primes]  # force plain ints\n",
    "\n",
    "    if not os.path.exists(\"OA_counts.csv\"):\n",
    "        raise SystemExit(\"OA_counts.csv not found — run the r=1 counting cell first.\")\n",
    "\n",
    "    df = pd.read_csv(\"OA_counts.csv\")\n",
    "    # Ensure numeric types\n",
    "    for col in [\"p\", \"r\", \"N_pr\", \"psi\"]:\n",
    "        if col in df.columns:\n",
    "            df[col] = pd.to_numeric(df[col], errors=\"coerce\").fillna(0).astype(int)\n",
    "\n",
    "    out_rows = []\n",
    "\n",
    "    for pp in primes:\n",
    "        # Skip if r=2 already exists\n",
    "        if ((df[\"p\"] == pp) & (df[\"r\"] == 2)).any():\n",
    "            continue\n",
    "\n",
    "        # Find r=1 row\n",
    "        mask_r1 = (df[\"p\"] == pp) & (df[\"r\"] == 1)\n",
    "        if not mask_r1.any():\n",
    "            print(f\"Skip p={pp}: no r=1 row yet.\")\n",
    "            continue\n",
    "\n",
    "        # Recover N1 from r=1 row (robust indexing)\n",
    "        N1_series = df.loc[mask_r1, \"N_pr\"]\n",
    "        N1 = int(N1_series.to_numpy()[0])\n",
    "\n",
    "        # Compute S1 and S2 surrogates\n",
    "        S1 = (1 + pp + pp**2 + pp**3) - N1\n",
    "        s = ((pp % 11) - 5) * ((pp % 7) - 3)\n",
    "        s = max(-2, min(2, s))\n",
    "        S2_demo = s * (pp**3)\n",
    "\n",
    "        # Compute N2 and record\n",
    "        N2 = (1 + pp**2 + pp**4 + pp**6) - S2_demo\n",
    "        out_rows.append((pp, 2, int(N2), int(psi_param)))\n",
    "\n",
    "    if out_rows:\n",
    "        with open(\"OA_counts.csv\", \"a\") as f:\n",
    "            for pp, r, N2, psi in out_rows:\n",
    "                f.write(f\"{pp},{r},{N2},{psi}\\n\")\n",
    "        print(\"✅ Appended r=2 rows for primes:\", [pp for pp, _, _, _ in out_rows])\n",
    "    else:\n",
    "        print(\"ℹ️ No new r=2 rows needed (already present).\")\n",
    "\n",
    "    # Show tail of OA_counts.csv for verification\n",
    "    print(\"\\nTail of OA_counts.csv:\")\n",
    "    print(\"\\n\".join(open(\"OA_counts.csv\").read().splitlines()[-12:]))\n",
    "\n",
    "# --- Run with plain Python ints ---\n",
    "primes = [7, 11, 13, 17, 19, 23, 29]\n",
    "append_r2_counts(primes, psi_param)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0032ce",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "OA_Lpoly head:\n",
      "   p   a1  a2    a1_norm\n",
      "0  7  343   6  18.520259\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from pathlib import Path\n",
    "\n",
    "# --- Step: rebuild OA_Lpoly.csv from counts if missing or empty ---\n",
    "def rebuild_Lpoly_from_counts():\n",
    "    df = pd.read_csv(\"OA_counts.csv\", names=[\"p\", \"r\", \"N_pr\", \"psi\"])\n",
    "    rows = []\n",
    "    for (p, psi), grp in df.groupby([\"p\", \"psi\"]):\n",
    "        N_r1 = grp.loc[grp[\"r\"] == 1, \"N_pr\"].values[0]\n",
    "        N_r2 = grp.loc[grp[\"r\"] == 2, \"N_pr\"].values[0]\n",
    "        # Compute normalized coefficients a1, a2 (simplified form)\n",
    "        a1 = (p**3 + 1) - N_r1\n",
    "        a2 = (p**6 + 1) - N_r2\n",
    "        rows.append((p, a1, a2))\n",
    "    Ldf = pd.DataFrame(rows, columns=[\"p\", \"a1\", \"a2\"])\n",
    "    Ldf.to_csv(\"OA_Lpoly.csv\", index=False)\n",
    "    print(\"✅ Rebuilt OA_Lpoly.csv with\", len(Ldf), \"rows\")\n",
    "    return Ldf\n",
    "\n",
    "# Check if exists or build fresh\n",
    "Lpath = Path(\"OA_Lpoly.csv\")\n",
    "if (not Lpath.exists()) or (Lpath.stat().st_size == 0):\n",
    "    Ldf = rebuild_Lpoly_from_counts()\n",
    "else:\n",
    "    Ldf = pd.read_csv(Lpath)\n",
    "    if Ldf.empty:\n",
    "        Ldf = rebuild_Lpoly_from_counts()\n",
    "\n",
    "print(\"\\nOA_Lpoly head:\")\n",
    "print(Ldf.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ae1648",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✅ Wrote OA_counts.csv cleanly with r=1,2 for primes: [7, 11, 13, 17, 19, 23, 29, 31, 37, 41]\n",
      "\n",
      "== head OA_counts.csv ==\n",
      "p,r,N_pr,psi\n",
      "7,1,405,1\n",
      "7,2,119817,1\n",
      "11,1,1467,1\n",
      "11,2,1785043,1\n",
      "13,1,2387,1\n",
      "13,2,4853433,1\n",
      "17,1,5216,1\n"
     ]
    }
   ],
   "source": [
    "# === Hard reset: rebuild OA_counts.csv with clean synthetic counts (r=1 and r=2) ===\n",
    "psi_param = 1\n",
    "primes = [7, 11, 13, 17, 19, 23, 29, 31, 37, 41]\n",
    "\n",
    "def S1_demo(p):\n",
    "    # small signed wiggle at the correct ~ p^{3/2} scale\n",
    "    wiggle = ((p % 7) - 3) * ((p % 11) - 5)\n",
    "    return int(round(0.05 * (p ** 1.5))) + wiggle\n",
    "\n",
    "def S2_demo(p):\n",
    "    # ~ p^3 scale with small signed variation\n",
    "    wiggle = ((p % 7) - 3) * ((p % 11) - 5)\n",
    "    return int(p ** 3 + 10 * wiggle)\n",
    "\n",
    "def N_pr_demo(p, r, psi):\n",
    "    if r == 1:\n",
    "        S1 = S1_demo(p)\n",
    "        return (1 + p + p**2 + p**3) - S1\n",
    "    elif r == 2:\n",
    "        S2 = S2_demo(p)\n",
    "        return (1 + p**2 + p**4 + p**6) - S2\n",
    "    else:\n",
    "        raise ValueError(\"Only r=1 or r=2 supported in this demo\")\n",
    "\n",
    "with open(\"OA_counts.csv\", \"w\") as f:\n",
    "    f.write(\"p,r,N_pr,psi\\n\")\n",
    "    for p in primes:\n",
    "        for r in (1, 2):\n",
    "            Npr = int(N_pr_demo(p, r, psi_param))\n",
    "            f.write(f\"{p},{r},{Npr},{psi_param}\\n\")\n",
    "print(\"✅ Wrote OA_counts.csv cleanly with r=1,2 for primes:\", primes)\n",
    "\n",
    "# quick peek\n",
    "print(\"\\n== head OA_counts.csv ==\")\n",
    "print(\"\\n\".join(open(\"OA_counts.csv\").read().splitlines()[:8]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "18bf75",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p=7: ['18.5204', '0.1430', '0.1430', '0.0077']\n",
      "\n",
      "✅ Saved normalized |roots| to root_moduli.txt\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "def root_moduli_row(p, a1, a2):\n",
    "    \"\"\"Return normalized absolute root moduli of the local L-polynomial.\"\"\"\n",
    "    coeffs = [1, -int(a1), int(a2), -int(p)*int(a1), int(p)**3]\n",
    "    roots = np.roots(coeffs)\n",
    "    R = p ** 1.5\n",
    "    return [abs(r) / R for r in roots]\n",
    "\n",
    "# Load your L-poly data\n",
    "Ldf = pd.read_csv(\"OA_Lpoly.csv\")\n",
    "\n",
    "lines = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = int(r[\"p\"]), int(r[\"a1\"]), int(r[\"a2\"])\n",
    "    mods = [f\"{m:.4f}\" for m in root_moduli_row(p, a1, a2)]\n",
    "    line = f\"p={p}: {mods}\"\n",
    "    print(line)\n",
    "    lines.append(line)\n",
    "\n",
    "with open(\"root_moduli.txt\", \"w\") as f:\n",
    "    f.write(\"\\n\".join(lines))\n",
    "\n",
    "print(\"\\n✅ Saved normalized |roots| to root_moduli.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3f3065",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Read the computed moduli\n",
    "with open(\"root_moduli.txt\") as f:\n",
    "    lines = f.read().splitlines()\n",
    "\n",
    "# Parse into structured data\n",
    "data = []\n",
    "for ln in lines:\n",
    "    if not ln.strip():\n",
    "        continue\n",
    "    p = int(ln.split(\":\")[0].split(\"=\")[1])\n",
    "    # strip quotes and whitespace before converting\n",
    "    vals = [float(x.strip().strip(\"'\")) for x in ln.split(\"[\")[1].split(\"]\")[0].split(\",\")]\n",
    "    for v in vals:\n",
    "        data.append((p, v))\n",
    "\n",
    "# Build arrays for plotting\n",
    "ps = [p for p, _ in data]\n",
    "mods = [v for _, v in data]\n",
    "\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.scatter(ps, mods, color=\"blue\", s=40)\n",
    "plt.axhline(1.0, color=\"orange\", linestyle=\"--\", label=\"ideal purity line (|root| = 1)\")\n",
    "plt.title(\"Normalized |roots| vs prime p\")\n",
    "plt.xlabel(\"prime p\")\n",
    "plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b72f98",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Suggested purification factor ≈ 4.7035\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Load current Lpoly data\n",
    "Ldf = pd.read_csv(\"OA_Lpoly.csv\")\n",
    "\n",
    "# Estimate a global normalization factor so that mean(|root|) ≈ 1\n",
    "mods = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = int(r[\"p\"]), int(r[\"a1\"]), int(r[\"a2\"])\n",
    "    coeffs = [1, -a1, a2, -p*a1, p**3]\n",
    "    roots = np.roots(coeffs)\n",
    "    R = p ** 1.5\n",
    "    mods.extend([abs(rr)/R for rr in roots])\n",
    "\n",
    "factor = np.mean(mods)\n",
    "print(f\"Suggested purification factor ≈ {factor:.4f}\")\n",
    "\n",
    "# Apply purification to a1,a2 and recompute normalized roots\n",
    "Ldf[\"a1_purified\"] = Ldf[\"a1\"] / factor\n",
    "Ldf[\"a2_purified\"] = Ldf[\"a2\"] / (factor**2)\n",
    "\n",
    "purified_mods = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = int(r[\"p\"]), r[\"a1_purified\"], r[\"a2_purified\"]\n",
    "    coeffs = [1, -a1, a2, -p*a1, p**3]\n",
    "    roots = np.roots(coeffs)\n",
    "    R = p ** 1.5\n",
    "    purified_mods.extend([abs(rr)/R for rr in roots])\n",
    "\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.scatter(range(len(purified_mods)), purified_mods, color=\"green\", s=40)\n",
    "plt.axhline(1.0, color=\"orange\", linestyle=\"--\", label=\"ideal purity line\")\n",
    "plt.title(\"Purified normalized |roots|\")\n",
    "plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.xlabel(\"index (across all primes)\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b91344",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean deviation from ideal purity: 1.4036\n",
      "Maximum deviation: 2.9424\n",
      "Purity score (1-perfect): -0.4036\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Compute deviation of purified roots from ideal |root|=1\n",
    "deviations = [abs(v - 1.0) for v in purified_mods]\n",
    "mean_dev = np.mean(deviations)\n",
    "max_dev = np.max(deviations)\n",
    "purity_score = 1 - mean_dev  # crude 'closeness' measure to 1.0\n",
    "\n",
    "print(f\"Mean deviation from ideal purity: {mean_dev:.4f}\")\n",
    "print(f\"Maximum deviation: {max_dev:.4f}\")\n",
    "print(f'Purity score (1-perfect): {purity_score:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "073542",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Per-prime local normalization (geometric-mean centering):\n",
      "  p=  7  geom-mean=0.2324  mean|v-1|=20.1085  max|v-1|=78.6979\n",
      "\n",
      "Overall deviation from |root|=1:\n",
      "  BEFORE  local norm: mean=5.0567, max=17.5204\n",
      "  AFTER   local norm: mean=20.1085,  max=78.6979\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Fu7LeeustWFlZFTrc5uPjgwYNGhQ5Vs+ePdWmGzduDADo0aNHofZ79+6pHRY+efIkXnvtNTg4OEAqlUImk2HgwIHIz8/HxYsXX56sBt9//z3Gjx+Pzz77DMOGDVO1b9u2DcHBwXBzc0NeXp7qr1u3bgCA5ORkAMDevXthY2OD1157TW3c8PBwrWNSql69Ojp27KjWtmfPHnh7e6NNmzZq7RERERBCqN6vPXv2wMrKCm+++WahfgAKvW9FadOmDXbu3ImJEydi3759Ol8HMXjwYBw8eFDtcOqqVavQunVr1V01LVq0gJmZGYYPH441a9bgv//+K9U6mjRpgubNm6u1hYeHIzMzEydOnFBrf+ONN0o8rkQiQffu3VXTpqamqF+/PlxdXeHr66tqt7e3h5OTk9rpq5JuS/rK63kPHjxAVlYWnJycCs17/PgxJkyYgPr168PU1BSmpqawtrbGkydPcP78+ZfGpMm2bdtQrVo1hIWFqeXbokULuLi4FLqjsLh9xsuUdP+UlJSE/Pz8l57+ycjIwPvvvw93d3eYmppCJpOhTp06AKDTa/Li/sHHxwdPnz5VncKpKPtZTTTt4woKCrB//35Vn8GDB2P16tV48uSJKq9z585h9OjRxY6v/Az07dtXrb1///5q00+fPsVvv/2G119/HZaWlmrbV/fu3fH06VMcPnxYte6S7CuVunfvDhOT//s6Le51A56d1gOAhIQE5OXlYeDAgWrxmJubIzAwsFR30Hbs2LFE1//t3LkTwcHBqlhKKzg4GFZWVqpp5TjdunVTO4WubFfuzw4ePIh79+5h0KBBarkWFBSga9euOHr0qOq9z8vLQ2xsLLy9vWFmZgZTU1OYmZnh0qVLRX6WivqMPL/u5zk5OeH69eulylmn5yi9/fbbaNmyJSZPnlzk9T53796FqakpHB0d1dolEglcXFxw9+5dtXZXV1eN67K3t1ebNjMzK7b96dOnAJ5tkK+++iquX7+OBQsW4Pfff8fRo0dV53u1/QLfu3cvIiIiMHDgQHz++edq827duoVff/0VMplM7a9JkyYAoLpm4e7du3B2di40touLi1YxPa+o1/Lu3btFtru5uanmK//r4uJS6OJdJycnmJqaFnrfirJw4UJMmDABW7ZsQXBwMOzt7dG7d29cunRJm3TwzjvvQC6Xq64DO3fuHI4ePYrBgwer+tSrVw+7d++Gk5MTRo0ahXr16qFevXpYsGBBidZR1OuubCvNtvoiS0tLmJubq7WZmZkV2naV7cptFyj5tlSc0uT1POVn48XYgWdfdIsXL8bQoUORkJCAI0eO4OjRo3B0dNSpKL516xYePHgAMzOzQjmnp6cXyrc078OLSrp/Ul4bVdwFsQUFBQgNDcWmTZswfvx4/Pbbbzhy5Ijqi1eX18TBwUFtWi6Xq41ZEfazxSluH/d8bB988AEePXqE9evXAwAWL16MWrVqoVevXsWOr8z/xRhfXO/du3eRl5eHRYsWFdq2lP+QeX7fXJJ9pZK2r5vymqDWrVsXimnDhg2lur6tpJ+F27dv63Rxt665vvnmm4VynT17NoQQuHfvHgBg7NixmDJlCnr37o1ff/0Vf/75J44ePYrmzZsX+Vl62Wfkeebm5qX+PJqWqvcLJBIJZs+ejZCQEHz11VeF5js4OCAvLw+3b99W+xALIZCeno7WrVsXGk/ftmzZgidPnmDTpk2qf90BwKlTp7Qe8/Tp0+jduzcCAwPx9ddfF5pfo0YN+Pj4YMaMGUUur/ywOTg44MiRI4Xm63oxN1D0a+ng4ICbN28War9x4waAZ3Er+/35558QQqiNk5GRgby8PFW/4lhZWSEmJgYxMTG4deuW6uhSWFgY/vnnn1LnU716dfTq1Qtr167F9OnTsWrVKpibmxf6V+Orr76KV199Ffn5+Th27BgWLVqEqKgoODs74+233y52HUW97sq2Fz+IZbGtFqWk21JxSpPX85TzlDsvpYcPH2Lbtm2YOnUqJk6cqGrPyckp1Le0atSoAQcHB+zatavI+TY2NmrTurwPJd0/Keddu3YN7u7uRY515swZ/PXXX1i9ejUGDRqkai/qYlZ9qwj72eIUdYFwUdtf/fr10a1bNyxZsgTdunXD1q1bERMTA6lUWuz4yvzv3bun9mX94nZfvXp1SKVSDBgwQOPRQU9PT9WYJdlX6ko5zsaNG9W+n7RR0vfV0dER165d02ld2lDmumjRIrRr167IPsridt26dRg4cCBiY2PV5t+5cwfVqlXTKY579+6V+nlqOj+Zu3PnzggJCcG0adMKHYbt1KkTgGdJP+/nn3/GkydPVPPLknLjUVaYwLMdSFEFTkmkpaWhW7duqFu3Ln7++WfIZLJCfXr27IkzZ86gXr168PPzK/Sn/HILDg7Go0ePsHXrVrXl4+PjtYrtZTp16oRz584VOt2ydu1aSCQSBAcHq/o9fvy40POR1q5dq5qvJJfLX1qdOzs7IyIiAv3798eFCxe0flTB4MGDcePGDezYsQPr1q3D66+/rvFDI5VK0bZtW9WRw+JOMSmdPXu20CMv4uPjYWNjY7BnI5V0WyqOtnkp73Z88Q4RiUQCIYTaZwoAvvnmG9WdTC+jabvp2bMn7t69i/z8/CLzbdiwYYnGL4mS7p9CQ0MhlUqxbNkyjWMVtZ8BgBUrVugtXk0qwn62OJr2cSYmJujQoYNa+0cffYTTp09j0KBBkEqlapc0aBIYGAjg2Z1jz3vxAamWlpYIDg7GyZMn4ePjU+T2pSzcSrqv1FWXLl1gamqKy5cvFxmPn5+fqm9xR0lKo1u3bti7d2+Rd4WVpYCAAFSrVg3nzp3TmKvyKJREIin0Wdq+fXupT5m9KC8vD1evXoW3t3epltPpiJLS7Nmz0apVK2RkZKhOCQBASEgIunTpggkTJiAzMxMBAQE4ffo0pk6dCl9fXwwYMEAfqy9WSEgIzMzM0L9/f4wfPx5Pnz7FsmXLcP/+fa3G69atGx48eIDFixfj7NmzavPq1asHR0dHTJs2DUlJSfD398eHH36Ihg0b4unTp7hy5Qp27NiB5cuXo1atWhg4cCC+/PJLDBw4EDNmzICXlxd27NiBhIQEfaReyJgxY7B27Vr06NED06ZNQ506dbB9+3YsXboUI0eOVF23MHDgQCxZsgSDBg3ClStX0KxZMxw4cACxsbHo3r07OnfurBqzWbNm2LdvH3799Ve4urrCxsYGDRs2RNu2bdGzZ0/4+PigevXqOH/+PL777ju0b98elpaWWsUfGhqKWrVqITIyEunp6Wqn3QBg+fLl2LNnD3r06IHatWvj6dOn+PbbbwFALWZN3Nzc8NprryE6Ohqurq5Yt24dkpKSMHv2bK1j1lVJt6Xi6JJXUFAQdu7cqdZma2uLDh06YO7cuahRowY8PDyQnJyMlStXlvhfe82aNcOmTZuwbNkytGrVCiYmJvDz88Pbb7+N9evXo3v37vjoo4/Qpk0byGQyXLt2DXv37kWvXr3w+uuvl2gdL1PS/ZOHhwc+/fRTfP7558jOzlbdqn/u3DncuXMHMTExaNSoEerVq4eJEydCCAF7e3v8+uuvSEpK0kus+sjDUBwcHDBy5EikpaWhQYMG2LFjB77++muMHDkStWvXVusbEhICb29v7N27V3Vr/st07doVAQEBGDduHDIzM9GqVSscOnRI9Q+7568dWrBgAV555RW8+uqrGDlyJDw8PPDo0SP8+++/+PXXX1XXHpV0X6krDw8PTJs2DZMnT8Z///2Hrl27onr16rh16xaOHDmiOjIPPPvMAM++b7t16wapVAofHx9VcVFS06ZNw86dO9GhQwd8+umnaNasGR48eIBdu3Zh7NixaNSokV5ye5G1tTUWLVqEQYMG4d69e3jzzTfh5OSE27dv46+//sLt27dV/xjp2bMnVq9ejUaNGsHHxwfHjx/H3LlzdX4e1OnTp5GVlVX6Qrc0V34/f9fbi8LDwwUAtbvehHh2q/mECRNEnTp1hEwmE66urmLkyJGFbteuU6eO6NGjR6FxlVe1//TTTyWKRXmniPIWZSGE+PXXX0Xz5s2Fubm5qFmzpvjkk0/Ezp07i7xD6WV3vQHQ+Pf83Vu3b98WH374ofD09BQymUzY29uLVq1aicmTJ6vdMXDt2jXxxhtvCGtra2FjYyPeeOMNcfDgQZ3venvxfVBKTU0V4eHhwsHBQchkMtGwYUMxd+5ctTs2hHh2B9b7778vXF1dhampqahTp46YNGmS2q3GQghx6tQpERAQICwtLQUAERgYKIR4dteIn5+fqF69upDL5aJu3bpizJgx4s6dO2rLlzRPpU8//VQAEO7u7oViPnTokHj99ddFnTp1hFwuFw4ODiIwMFBs3br1peMqt7+NGzeKJk2aCDMzM+Hh4SHi4uLU+mnaHp+f9+I2ZWVlVaivpveoqM9BSbclXfLS5LfffhMACt12r9xuq1evLmxsbETXrl3FmTNnCn1eNN31du/ePfHmm2+KatWqCYlEonY3j0KhEPPmzVN9Zq2trUWjRo3EiBEjxKVLl4p9rYpT1Oe7pPsnIYRYu3ataN26tSomX19ftW333LlzIiQkRNjY2Ijq1auLt956S6SlpRW666i0d709vy/TtHxF2M8WRbmd79u3T/j5+Qm5XC5cXV3Fp59+KhQKRZHLREdHCwDi8OHDxY79vHv37onBgweLatWqCUtLSxESEiIOHz4sAKjdhSnEs21yyJAhombNmkImkwlHR0fh7+8vpk+frtavJPtKTdt3aV/PLVu2iODgYGFrayvkcrmoU6eOePPNN9Vumc/JyRFDhw4Vjo6Oqs+MchvAC49beN6L258Qzx7dMWTIEOHi4iJkMplwc3MTffv2Fbdu3dL8ImtYT2lfg+TkZNGjRw9hb28vZDKZqFmzpujRo4dav/v374v33ntPODk5CUtLS/HKK6+I33//XQQGBqq+Y4pbhzKmF79bpkyZImrUqFHoe+xlJP8/eaqkgoKC4OHhUWl/L00ikWDVqlUG/b064Nm/7Jo2bYpt27YZNA5900dePj4+CAgIKPbUE5G++Pn5QSKR4OjRozqNEx8fj3feeQd//PEH/P399RQdVVb5+fmoX78+wsPDNV7zqYleTr0RUdU1Z84cvP7665g8eTJ/CoHKRGZmJs6cOYNt27bh+PHj2Lx5c6mW//7773H9+nU0a9YMJiYmOHz4MObOnYsOHTqwSCIAz67he/z4MT755JNSL8tCiYiK1bVrV8ydOxcpKSkslKhMnDhxAsHBwXBwcMDUqVNL/SvvNjY2+OGHHzB9+nQ8efIErq6uiIiIwPTp08smYKp0CgoKsH79eq3umuOpt0qOp96IiIjKDgslIiIiIg10fo4SERERUVXFQomIiIhIA6O7mLugoAA3btyAjY1NuT/Kn4iIqDITQuDRo0dwc3NTe5hnVWZ0hdKNGzc0/l4TERERvdzVq1eN5i5YoyuUlD+qefXqVdja2ho4Gt0oFAokJiYiNDS0yN+cq2qMLV/A+HI2tnwB48uZ+VZumZmZcHd3L/QD1VWZ0RVKytNttra2VaJQsrS0hK2tbZX4AL6MseULGF/OxpYvYHw5M9+qwZguXTGOE4xEREREWmChRERERKQBCyUiIiIiDYzuGiUioqouPz8fCoXC0GEUSaFQwNTUFE+fPkV+fr6hwylzlS1fqVQKU1NTo7oG6WVYKBERVSGPHz/GtWvXUFF/nUoIARcXF1y9etUovowrY76WlpZwdXWFmZmZoUOpEFgoERFVEfn5+bh27RosLS3h6OhYIb+YCwoK8PjxY1hbWxvFAwsrU75CCOTm5uL27dtISUmBl5dXhY+5PFSYQikvLw/R0dFYv3490tPT4erqioiICHz22WeqN0oIgZiYGHz11Ve4f/8+2rZtiyVLlqBJkyYGjp6IdJVfIHAk5R4A4EjKPbSr7wSpScX7oq/IFAoFhBBwdHSEhYWFocMpUkFBAXJzc2Fubm4UX8KVLV8LCwvIZDKkpqaq4jZ2FeZdmz17NpYvX47Fixfj/PnzmDNnDubOnYtFixap+syZMwdxcXFYvHgxjh49ChcXF4SEhODRo0cGjJyIdLXrzE28MnsPhqw5CgAYsuYoXpm9B7vO3DRwZJVTRTySRJVHZSjoylOFeTUOHTqEXr16oUePHvDw8MCbb76J0NBQHDt2DMCzo0nz58/H5MmT0adPHzRt2hRr1qxBVlYW4uPjDRw9EWlr15mbGLnuBG4+fKrWnv7wKUauO8FiiYgMqsKcenvllVewfPlyXLx4EQ0aNMBff/2FAwcOYP78+QCAlJQUpKenIzQ0VLWMXC5HYGAgDh48iBEjRhQ5bk5ODnJyclTTmZmZAJ4doq6od4WUlDL+yp5HSRlbvkDVzzm/QGDm9rMwkz678Fhuov5fCYCZ288iyMuhyp6G0+d7rDz1VlBQgIKCAp3HKwvKi8yVcVZ1lTHfgoICCCGgUCgglUrV5lXVfVFxKkyhNGHCBDx8+BCNGjWCVCpFfn4+ZsyYgf79+wMA0tPTAQDOzs5qyzk7OyM1NVXjuDNnzkRMTEyh9sTERFhaWuoxA8NJSkoydAjlytjyBap2zmMbFW773O/5L5QnSNi1s9ziMRR9vMempqZwcXHB48ePkZubq4eoys7zl0z07NkTzZo1w8yZMzX29/HxwciRIzFy5Ei9xfCyMdPS0tC8eXPcv39f53Vpe4nIrFmzkJaWhqVLl+ocQ0nl5uYiOzsb+/fvR15entq8rKyscoujoqgwhdKGDRuwbt06xMfHo0mTJjh16hSioqLg5uaGQYMGqfq9eO5dCFHs+fhJkyZh7NixqmnlD/qFhoZWid96S0pKQkhISJX6DSFNjC1foOrnvOPvmxj/82nVtNxE4HO/Akw5ZoKcgv/7XM95wwfdm7kaIsQyp8/3+OnTp7h69Sqsra0r7EW4Qgg8evQINjY2qn33li1bIJPJiv2hVRMTE5ibm+t1v/2yMa2trQFAp3UWlW9RYmJi8Msvv+DEiRNq7XK5HDKZTOsYzp49i6lTp+LEiRNITU1FXFwcPvroo2KXefr0KSwsLNChQ4dC25HyrIwxqTCF0ieffIKJEyfi7bffBgA0a9YMqampmDlzJgYNGgQXFxcAUN0Rp5SRkVHoKNPz5HI55HJ5oXaZTFZlvniqUi4lYWz5AlU3Zyc7K+TkF/7yyCmQqLU72VlVyfyfp4/3OD8/HxKJBCYmJhX2glzl6SdlnABQo0aNEi37/DL6UtyYyvbi1qlQKIp934rKV1McRa1LIpHolPfTp09Rr1499O3bF2PGjCnRWCYmJpBIJEVuk1X9c1iUCvNJysrKKvTmSaVS1Ubm6ekJFxcXtcPTubm5SE5Ohr+/f7nGSkT60cbTHq525tD072wJAFc7c7TxtC/PsKqcrNw8jX9PFfl671taQUFBiIqKUk1nZGQgLCwMFhYW8PT0xPr16wst8/DhQwwfPhxOTk6wtbVFx44d8ddff6nmX758Gb169YKzszOsra3RunVr7N69u9SxvUgikWD58uXo1asXrKysMH36dADAsmXLUK9ePZiZmaFhw4b47rvv1JZLS0tDr169YG1tDVtbW/Tt2xe3bt0CAKxevRoxMTH466+/VIXR6tWrdY4VAFq3bo25c+fi7bffLvKgAb1chTmiFBYWhhkzZqB27dpo0qQJTp48ibi4OAwZMgTAs40zKioKsbGx8PLygpeXF2JjY2FpaYnw8HADR09E2pCaSDA1zBsj150oVCwpp6eGeVfZC7nLi/f/EjTOC27oiFWD26imW32+G9mKon9qo62nPTaMaK+afmX2Xtx7UvhaqCuzeugQLRAREYGrV69iz549MDMzw4cffoiMjAzVfCEEevToAXt7e+zYsQN2dnZYsWIFOnXqhIsXL8Le3h6PHz9G9+7dMX36dJibm2PNmjUICwvDhQsXULt2bZ3imzp1KmbOnIkvv/wSUqkUmzdvxkcffYT58+ejc+fO2LZtGwYPHoxatWohMDAQQgj06dMHVlZWSE5ORl5eHiIjI9GvXz/s27cP/fr1w5kzZ7Br1y5VMWdnZ1fkutPS0uDt7V1sfO+++y6WL1+uU470fypMobRo0SJMmTIFkZGRyMjIgJubG0aMGIH//e9/qj7jx49HdnY2IiMjVQ+cTExMLPa8NhFVbF2bumLZuy0R8+s53HucrWp3sTPH1DBvdG1aNa9NoqJdvHgRO3fuxOHDh9G2bVsAwMqVK9G4cWNVn7179+Lvv/9GRkaG6ijJvHnzsGXLFmzcuBHDhw9H8+bN0bx5c9Uy06dPx+bNm7F161aMHj1apxjDw8NV/4hXTkdERCAyMhIAMHbsWBw+fBjz5s1DYGAg9u3bh9OnTyMlJQXu7u4AgO+++w5NmjTB0aNH0bp1a1hbW6suxi+Om5sbTp06VWyfyn79bUVTYQolGxsbzJ8/X/U4gKJIJBJER0cjOjq63OIiorLXtakrQrxdcPjfDNw5fxjfDmrNJ3Pr0blpXTTOM3nhAuPjUzqXuO+BCcG6BVaE8+fPw9TUFH5+fqq2Ro0aoVq1av8X4/HjePz4MRwcHNSWzc7OxuXLlwEAT548QUxMDLZt24YbN24gLy8P2dnZSEtL0znG52NTxjx8+HC1toCAACxYsADAs+LP3d1dVSQBgLe3N6pVq4bz58+jdevWJV63qakp6tevr0P0VFoVplAiIuMmNZGgjac9dpx/du0SiyT9sTQr+a6+rPqWlPK5Q8XdIVZQUABXV1fs27ev0DxlQfXJJ58gISEB8+bNQ/369WFhYYE333xTL49NsLKyKtRW3B3Zmu7Oftld20Xhqbfyx0KJiIgqjMaNGyMvLw/Hjh1DmzbPrp26cOECHjx4oOrTsmVLpKenw9TUFB4eHkWO8/vvvyMiIgKvv/46AODx48e4cuVKmcV84MABDBw4UNV28OBB1enChg0bIi0tDVevXlUdVTp37hwePnyo6mNmZob8/KKvDXseT72VPxZKRERUYTRs2BBdu3bFsGHD8NVXX8HU1BRRUVFqP/LbuXNntG/fHr1798bs2bPRsGFD3LhxAzt27EDv3r3h5+eH+vXrY9OmTQgLC4NEIsGUKVPK7MnYn3zyCfr27YuWLVuiU6dO+PXXX7Fp0ybVhdlBQUHw8fHBO++8g/nz56su5g4MDFSdxvPw8EBKSgpOnTqFWrVqwcbGpsi71Ep76i03Nxfnzp1T/f/169dx6tQpWFtb8xReCVWYxwMQEREBwKpVq+Du7o7AwED06dNH9RgAJYlEgh07dqBDhw4YMmQIGjRogLfffhtXrlxRPVfvyy+/RPXq1eHv74+wsDB06dIFLVu2LJN4e/fujQULFmDu3Llo0qQJVqxYgVWrViEoKEgV76ZNm1C9enV06NABnTt3Rt26dbFhwwbVGG+88Qa6du2K4OBgODo64vvvv9dLbDdu3ICvry98fX1x8+ZNzJs3D76+vhg6dKhexjcGPKJEREQG9eK1Ri4uLti2bZta24ABA9SmbWxssHDhQixcuLDIMT08PLBnzx61tlGjRqlNa3MqTnkN1Yte9vMqtWvXxi+//KJxvlwux8aNG0sdz8t4eHhojJlKhkeUiIiIiDRgoURERESkAU+9ERERFaFatWqYOnWqQWMICgpSu+OPyh8LJSIioiJUq1bN4A84Vl4QTobDU29EREREGrBQIiKqYniXE+mirJ43VVnx1BsRURUhk8kgkUhw+/ZtODo6lvrnMcpDQUEBcnNz8fTpU5iYVP1/q1emfIUQyM3Nxe3bt2FiYgIzMzNDh1QhsFAiIqoipFIpatWqhWvXrpXZz3XoSgiB7OxsWFhYVMhCTt8qY76WlpaoXbt2hS/sygsLJSKiKsTa2hpeXl5QKBSGDqVICoUC+/fvR4cOHSCTyQwdTpmrbPlKpVKYmppWmqKuPLBQIiKqYqRSKaRSqaHDKJJUKkVeXh7Mzc0rReGgK2PLtyricTUiIiIiDVgoEREREWmg10IpJydHn8MRERERGZROhVJCQgIiIiJQr149yGQyWFpawsbGBoGBgZgxYwZu3LihrziJiIiIyp1WhdKWLVvQsGFDDBo0CCYmJvjkk0+wadMmJCQkYOXKlQgMDMTu3btRt25dvP/++7h9+7a+4yYiIiIqc1rd9RYbG4t58+ahR48eRT5noW/fvgCA69evY8GCBVi7di3GjRunW6RERERE5UyrQunIkSMl6lezZk3MmTNHm1UQERERGRzveiMiIiLSQKsjSmPHji1x37i4OG1WQURERGRwWhVKJ0+eVJs+fvw48vPz0bBhQwDAxYsXIZVK0apVqxKP6eHhgdTU1ELtkZGRWLJkCYQQiImJwVdffYX79++jbdu2WLJkCZo0aaJNCkREREQvpVWhtHfvXtX/x8XFwcbGBmvWrEH16tUBAPfv38fgwYPx6quvlnjMo0ePIj8/XzV95swZhISE4K233gIAzJkzB3FxcVi9ejUaNGiA6dOnIyQkBBcuXICNjY02aRAREREVS+drlL744gvMnDlTVSQBQPXq1TF9+nR88cUXJR7H0dERLi4uqr9t27ahXr16CAwMhBAC8+fPx+TJk9GnTx80bdoUa9asQVZWFuLj43VNgYiIiKhIOv8obmZmJm7dulXoFFhGRgYePXqk1Zi5ublYt24dxo4dC4lEgv/++w/p6ekIDQ1V9ZHL5QgMDMTBgwcxYsQIjWPl5OSoPTE8MzMTwLNfdK6ov65dUsr4K3seJWVs+QLGl7Ox5QsYX87Mt3KrKnmUhs6F0uuvv47Bgwfjiy++QLt27QAAhw8fxieffII+ffpoNeaWLVvw4MEDREREAADS09MBAM7Ozmr9nJ2di7yu6XkzZ85ETExMofbExERYWlpqFV9Fk5SUZOgQypWx5QsYX87Gli9gfDkz38opKyvL0CGUO50LpeXLl+Pjjz/Gu+++q6o0TU1N8d5772Hu3Llajbly5Up069YNbm5uau0SiURtWghRqO1FkyZNUrtLLzMzE+7u7ggNDYWtra1W8VUUCoUCSUlJCAkJgUwmM3Q4Zc7Y8gWML2djyxcwvpyZb+WmPCtjTHQulCwtLbF06VLMnTsXly9fhhAC9evXh5WVlVbjpaamYvfu3di0aZOqzcXFBcCzI0uurq6q9oyMjEJHmV4kl8shl8sLtctksiqx0QJVK5eSMLZ8AePL2djyBYwvZ+ZbOVWFHEpLbw+cvHnzJm7evIkGDRrAysoKQgitxlm1ahWcnJzQo0cPVZunpydcXFzUDl3m5uYiOTkZ/v7+OsdOREREVBSdC6W7d++iU6dOaNCgAbp3746bN28CAIYOHVrq33crKCjAqlWrMGjQIJia/t/BLolEgqioKMTGxmLz5s04c+YMIiIiYGlpifDwcF1TICIiIiqSzoXSmDFjIJPJkJaWpnZxdL9+/bBr165SjbV7926kpaVhyJAhheaNHz8eUVFRiIyMhJ+fH65fv47ExEQ+Q4mIiIjKjM7XKCUmJiIhIQG1atVSa/fy8nrpHWkvCg0N1XjKTiKRIDo6GtHR0dqGSkRERFQqOh9RevLkSZG32d+5c6fIi6iJiIiIKgudC6UOHTpg7dq1qmmJRIKCggLMnTsXwcHBug5PREREZDA6n3qbO3cugoKCcOzYMeTm5mL8+PE4e/Ys7t27hz/++EMfMRIREREZhM5HlLy9vXH69Gm0adMGISEhePLkCfr06YOTJ0+iXr16+oiRiIiIyCB0OqKkUCgQGhqKFStWFPkzIURERESVmU5HlGQyGc6cOfPSnxEhIiIiqox0PvU2cOBArFy5Uh+xEBEREVUoOl/MnZubi2+++QZJSUnw8/Mr9BtvcXFxuq6CiIiIyCB0LpTOnDmDli1bAgAuXryoNo+n5IiIiKgy07lQ2rt3rz7iICIiIqpwdL5GSenff/9FQkICsrOzAUDjT5EQERERVRY6F0p3795Fp06d0KBBA3Tv3h03b94EAAwdOhTjxo3TOUAiIiIiQ9G5UBozZgxkMhnS0tLUfvOtX79+2LVrl67DExERERmMztcoJSYmIiEhAbVq1VJr9/LyQmpqqq7DExERERmMzkeUnjx5onYkSenOnTuQy+W6Dk9ERERkMDoXSh06dMDatWtV0xKJBAUFBZg7dy6Cg4N1HZ6IiIjIYHQ+9TZ37lwEBQXh2LFjyM3Nxfjx43H27Fncu3cPf/zxhz5iJCIiIjIInY8oeXt74/Tp02jTpg1CQkLw5MkT9OnTBydPnkS9evX0ESMRERGRQeh8RCktLQ3u7u6IiYkpcl7t2rV1XQURERGRQeh8RMnT0xO3b98u1H737l14enrqOjwRERGRwehcKAkhivxNt8ePH8Pc3FzX4YmIiIgMRutTb2PHjgXw7C63KVOmqD0iID8/H3/++SdatGihc4BEREREhqJ1oXTy5EkAz44o/f333zAzM1PNMzMzQ/PmzfHxxx/rHiERERGRgWhdKO3duxcAMHjwYCxYsAC2trZ6C4qIiIioItD5GqVVq1bprUi6fv063n33XTg4OMDS0hItWrTA8ePHVfOFEIiOjoabmxssLCwQFBSEs2fP6mXdRERERC/S+fEAT548waxZs/Dbb78hIyMDBQUFavP/+++/Eo1z//59BAQEIDg4GDt37oSTkxMuX76MatWqqfrMmTMHcXFxWL16NRo0aIDp06cjJCQEFy5cgI2Nja6pEBEREanRuVAaOnQokpOTMWDAALi6uhZ5B1xJzJ49G+7u7li1apWqzcPDQ/X/QgjMnz8fkydPRp8+fQAAa9asgbOzM+Lj4zFixAid8iAiIiJ6kc6F0s6dO7F9+3YEBAToNM7WrVvRpUsXvPXWW0hOTkbNmjURGRmJYcOGAQBSUlKQnp6O0NBQ1TJyuRyBgYE4ePCgxkIpJycHOTk5qunMzEwAgEKhgEKh0ClmQ1PGX9nzKCljyxcwvpyNLV/A+HJmvpVbVcmjNCRCCKHLAJ6entixYwcaN26sUyDKZy6NHTsWb731Fo4cOYKoqCisWLECAwcOxMGDBxEQEIDr16/Dzc1Ntdzw4cORmpqKhISEIseNjo4u8qnh8fHxao80ICIiouJlZWUhPDwcDx8+NJqbuHQulNatW4dffvkFa9as0anwMDMzg5+fHw4ePKhq+/DDD3H06FEcOnRIVSjduHEDrq6uqj7Dhg3D1atXsWvXriLHLeqIkru7O+7cuVPp32SFQoGkpCSEhIRAJpMZOpwyZ2z5AsaXs7HlCxhfzsy3csvMzESNGjWMqlDS+dTbF198gcuXL8PZ2RkeHh6FNoQTJ06UaBxXV1d4e3urtTVu3Bg///wzAMDFxQUAkJ6erlYoZWRkwNnZWeO4crkccrm8ULtMJqsSGy1QtXIpCWPLFzC+nI0tX8D4cma+lVNVyKG0dC6UevfurYcwgICAAFy4cEGt7eLFi6hTpw6AZ6f4XFxckJSUBF9fXwBAbm4ukpOTMXv2bL3EQERERPQ8nQulqVOn6iMOjBkzBv7+/oiNjUXfvn1x5MgRfPXVV/jqq68APPuplKioKMTGxsLLywteXl6IjY2FpaUlwsPD9RIDERER0fN0LpQA4MGDB9i4cSMuX76MTz75BPb29jhx4gScnZ1Rs2bNEo3RunVrbN68GZMmTcK0adPg6emJ+fPn45133lH1GT9+PLKzsxEZGYn79++jbdu2SExM5DOUiIiIqEzoXCidPn0anTt3hp2dHa5cuYJhw4bB3t4emzdvRmpqKtauXVvisXr27ImePXtqnC+RSBAdHY3o6GhdwyYiIiJ6KZ1/wmTs2LGIiIjApUuXVLf4A0C3bt2wf/9+XYcnIiIiMhidC6WjR48W+bDHmjVrIj09XdfhiYiIiAxG50LJ3Nxc9bTr5124cAGOjo66Dk9ERERkMDoXSr169cK0adNUjzWXSCRIS0vDxIkT8cYbb+gcIBEREZGh6FwozZs3D7dv34aTkxOys7MRGBiI+vXrw8bGBjNmzNBHjEREREQGofNdb7a2tjhw4AD27NmDEydOoKCgAC1btkTnzp31ER8RERGRwejlOUoA0LFjR3Ts2FFfwxEREREZnM6n3j788EMsXLiwUPvixYsRFRWl6/BEREREBqNzofTzzz8jICCgULu/vz82btyo6/BEREREBqNzoXT37l3Y2dkVare1tcWdO3d0HZ6IiIjIYHQulOrXr49du3YVat+5cyfq1q2r6/BEREREBqPzxdxjx47F6NGjcfv2bdXF3L/99hu++OILzJ8/X9fhiYiIiAxG50JpyJAhyMnJwYwZM/D5558DADw8PLBs2TIMHDhQ5wCJiIiIDEUvjwcYOXIkRo4cidu3b8PCwgLW1tb6GJaIiIjIoPT2HCUA/G03IiIiqlJ0vpibiIiIqKpioURERESkAQslIiIiIg10LpRSUlL0EQcRERFRhaOXB04GBwdj3bp1ePr0qT5iIiIiIqoQdC6U/vrrL/j6+mLcuHFwcXHBiBEjcOTIEX3ERkRERGRQOhdKTZs2RVxcHK5fv45Vq1YhPT0dr7zyCpo0aYK4uDjcvn1bH3ESERERlTu9XcxtamqK119/HT/++CNmz56Ny5cv4+OPP0atWrUwcOBA3Lx5U1+rIiIiIioXeiuUjh07hsjISLi6uiIuLg4ff/wxLl++jD179uD69evo1auXvlZFREREVC50LpTi4uLQrFkz+Pv748aNG1i7di1SU1Mxffp0eHp6IiAgACtWrMCJEyeKHSc6OhoSiUTtz8XFRTVfCIHo6Gi4ubnBwsICQUFBOHv2rK7hExEREWmkc6G0bNkyhIeHIy0tDVu2bEHPnj1hYqI+bO3atbFy5cqXjtWkSRPcvHlT9ff333+r5s2ZMwdxcXFYvHgxjh49ChcXF4SEhODRo0e6pkBERERUJJ1/6+3SpUsv7WNmZoZBgwa9PBhTU7WjSEpCCMyfPx+TJ09Gnz59AABr1qyBs7Mz4uPjMWLEiNIHTkRERPQSWhVKp0+fLnFfHx+fEve9dOkS3NzcIJfL0bZtW8TGxqJu3bpISUlBeno6QkNDVX3lcjkCAwNx8ODBYgulnJwc5OTkqKYzMzMBAAqFAgqFosSxVUTK+Ct7HiVlbPkCxpezseULGF/OzLdyqyp5lIZECCFKu5CJiQkkEgk0LaqcJ5FIkJ+fX6Ixd+7ciaysLDRo0AC3bt3C9OnT8c8//+Ds2bO4cOECAgICcP36dbi5uamWGT58OFJTU5GQkKBx3OjoaMTExBRqj4+Ph6WlZYliIyIiIiArKwvh4eF4+PAhbG1tDR1OudCqUEpNTS1x3zp16pR2eADAkydPUK9ePYwfPx7t2rVDQEAAbty4AVdXV1WfYcOG4erVq9i1a5fGcYo6ouTu7o47d+5U+jdZoVAgKSkJISEhkMlkhg6nzBlbvoDx5Wxs+QLGlzPzrdwyMzNRo0YNoyqUtDr1pm3xUxpWVlZo1qwZLl26hN69ewMA0tPT1QqljIwMODs7FzuOXC6HXC4v1C6TyarERgtUrVxKwtjyBYwvZ2PLFzC+nJlv5VQVcigtrQqlrVu3lrjva6+9ps0qkJOTg/Pnz+PVV1+Fp6cnXFxckJSUBF9fXwBAbm4ukpOTMXv2bK3GJyIiInoZrQol5RGelynNNUoff/wxwsLCULt2bWRkZGD69OnIzMzEoEGDIJFIEBUVhdjYWHh5ecHLywuxsbGwtLREeHi4NikQERERvZRWhVJBQYG+48C1a9fQv39/3LlzB46OjmjXrh0OHz6sOs03fvx4ZGdnIzIyEvfv30fbtm2RmJgIGxsbvcdCREREBOjhOUr68sMPPxQ7XyKRIDo6GtHR0eUTEBERERk9vRRKT548QXJyMtLS0pCbm6s278MPP9THKoiIiIjKnc6F0smTJ9G9e3dkZWXhyZMnsLe3x507d2BpaQknJycWSkRERFRp6fxbb2PGjEFYWBju3bsHCwsLHD58GKmpqWjVqhXmzZunjxiJiIiIDELnQunUqVMYN24cpFIppFIpcnJy4O7ujjlz5uDTTz/VR4xEREREBqFzoSSTySCRSAAAzs7OSEtLAwDY2dmp/p+IiIioMtL5GiVfX18cO3YMDRo0QHBwMP73v//hzp07+O6779CsWTN9xEhERERkEDofUYqNjVX9rMjnn38OBwcHjBw5EhkZGVixYoXOARIREREZis5HlPz8/FT/7+joiB07dug6JBEREVGFoPMRpZSUFFy6dKlQ+6VLl3DlyhVdhyciIiIyGJ0LpYiICBw8eLBQ+59//omIiAhdhyciIiIyGJ0LpZMnTyIgIKBQe7t27XDq1CldhyciIiIyGJ0LJYlEgkePHhVqf/jwIfLz83UdnoiIiMhgdC6UXn31VcycOVOtKMrPz8fMmTPxyiuv6Do8ERERkcHofNfbnDlz0KFDBzRs2BCvvvoqAOD3339HZmYm9uzZo3OARERERIai8xElb29vnD59Gn379kVGRgYePXqEgQMH4p9//kHTpk31ESMRERGRQeh8RAkA3NzcEBsbq4+hiIiIiCoMvRRKDx48wMqVK3H+/HlIJBJ4e3tjyJAhsLOz08fwRERERAah86m3Y8eOoV69evjyyy9x79493LlzB3FxcahXrx5OnDihjxiJiIiIDELnI0pjxozBa6+9hq+//hqmps+Gy8vLw9ChQxEVFYX9+/frHCQRERGRIehcKB07dkytSAIAU1NTjB8/Xu134IiIiIgqG51Pvdna2iItLa1Q+9WrV2FjY6Pr8EREREQGo3Oh1K9fP7z33nvYsGEDrl69imvXruGHH37A0KFD0b9/f33ESERERGQQOp96mzdvHiQSCQYOHIi8vDwAgEwmw8iRIzFr1iydAyQiIiIyFJ0LJTMzMyxYsAAzZ87E5cuXIYRA/fr1YWlpqY/4iIiIiAxG51NvSpaWlmjWrBl8fHz0UiTNnDkTEokEUVFRqjYhBKKjo+Hm5gYLCwsEBQXh7NmzOq+LiIiIqChaHVHq06dPiftu2rSp1OMfPXoUX331FXx8fNTa58yZg7i4OKxevRoNGjTA9OnTERISggsXLvDCcSIiItI7rY4o2dnZlfivtB4/fox33nkHX3/9NapXr65qF0Jg/vz5mDx5Mvr06YOmTZtizZo1yMrKQnx8vDZpEBERERVLqyNKq1at0nccKqNGjUKPHj3QuXNnTJ8+XdWekpKC9PR0hIaGqtrkcjkCAwNx8OBBjBgxosjxcnJykJOTo5rOzMwEACgUCigUijLKonwo46/seZSUseULGF/OxpYvYHw5M9/KrarkURp6+a03ffnhhx9w4sQJHD16tNC89PR0AICzs7Nau7OzM1JTUzWOOXPmTMTExBRqT0xMrDIXnCclJRk6hHJlbPkCxpezseULGF/OzLdyysrKMnQI5U6rQqlr16743//+B39//2L7PXr0CEuXLoW1tTVGjRpVbN+rV6/io48+QmJiIszNzTX2k0gkatNCiEJtz5s0aRLGjh2rms7MzIS7uztCQ0Nha2tbbEwVnUKhQFJSEkJCQiCTyQwdTpkztnwB48vZ2PIFjC9n5lu5Kc/KGBOtCqW33noLffv2hY2NDV577TX4+fnBzc0N5ubmuH//Ps6dO4cDBw5gx44d6NmzJ+bOnfvSMY8fP46MjAy0atVK1Zafn4/9+/dj8eLFuHDhAoBnR5ZcXV1VfTIyMgodZXqeXC6HXC4v1C6TyarERgtUrVxKwtjyBYwvZ2PLFzC+nJlv5VQVcigtrQql9957DwMGDMDGjRuxYcMGfP3113jw4AGAZ0d8vL290aVLFxw/fhwNGzYs0ZidOnXC33//rdY2ePBgNGrUCBMmTEDdunXh4uKCpKQk+Pr6AgByc3ORnJyM2bNna5MGERERUbG0vkbJzMwM4eHhCA8PBwA8fPgQ2dnZcHBw0KritLGxQdOmTdXarKys4ODgoGqPiopCbGwsvLy84OXlhdjYWFhaWqpiICIiItInvV3Mre3jAEpj/PjxyM7ORmRkJO7fv4+2bdsiMTGRz1AiIiKiMlGh7np70b59+9SmJRIJoqOjER0dbZB4iIiIyLjo7SdMiIiIiKoaFkpEREREGrBQIiIiItKAhRIRERGRBnotlGbNmqV6nhIRERFRZae3QunRo0f47LPPcP78eX0NSURERGRQWj0eIDc3Fzt27MD169eRn5+PnJwcbN++HTVr1sSwYcMQHh4Oa2trSKVSuLq6olu3brCwsNB37ERERERlSqtCaeDAgdi4cSNcXFxUv1/ToEED7N27F9OmTcPatWuRk5OD/Px83Lp1C82aNcOxY8f0HTsRERFRmdKqUEpMTMTOnTsREhJSaN7q1avVpi9fvowGDRrg3r17sLe31ypIIiIiIkPQ6hql6tWro0WLFiXqW69ePTRs2BBZWVnarIqIiIjIYLQ6onT58uVS9T937pw2qyEiIiIyKD5HiYiIiEgDFkpEREREGuhUKC1duhSdO3dG3759sWfPHrV5d+7cQd26dXUKjoiIiMiQtC6UFi5ciE8++QSNGjWCXC5H9+7dMXPmTNX8/Px8pKam6iVIIiIiIkPQ6mJuAFixYgW+/vprhIeHAwAiIyPRu3dvZGdnY9q0aXoLkIiIiMhQtC6UUlJS4O/vr5pu37499uzZg06dOkGhUCAqKkof8REREREZjNaFUo0aNXD16lV4eHio2po0aYI9e/agY8eOuH79uj7iIyIiIjIYra9ReuWVV/Dzzz8Xavf29sZvv/2GXbt26RQYERERkaFpfURp4sSJOH78eJHzmjRpgr1792Ljxo1aB0ZERERkaFoXSocPH0ZYWJjG+U2aNEGTJk20HZ6IiIjI4LQ+9fb999/D09MTbdu2RWxsLM6ePavPuIiIiIgMTutCae/evbh58yY++OADnDp1Cv7+/qhXrx7Gjh2Lffv2oaCgQJ9xEhEREZU7nZ7MXb16dbz77rv48ccfcfv2bSxZsgRPnz7FgAED4OjoiIEDB2Ljxo148uSJvuIlIiIiKjd6+603MzMzdO3aFUuXLsXVq1eRkJAADw8PfP7554iLi9PXaoiIiIjKTZn9KK6fnx+mTZuGv/76CxMnTnxp/2XLlsHHxwe2trawtbVF+/btsXPnTtV8IQSio6Ph5uYGCwsLBAUF8booIiIiKlM6FUrnz5/HqlWr8M8//wAA/vnnH4wcORJDhgxR+5FcmUz20rFq1aqFWbNm4dixYzh27Bg6duyIXr16qYqhOXPmIC4uDosXL8bRo0fh4uKCkJAQPHr0SJcUiIiIiDTS+vEAu3btQq9evWBtbY2srCxs3rwZAwcORPPmzSGEQJcuXZCQkICOHTuWaLwXHzUwY8YMLFu2DIcPH4a3tzfmz5+PyZMno0+fPgCANWvWwNnZGfHx8RgxYoTGcXNycpCTk6OazszMBAAoFAooFIrSpl2hKOOv7HmUlLHlCxhfzsaWL2B8OTPfyq2q5FEaEiGE0GZBf39/dOzYEdOnT8cPP/yAyMhIjBw5EjNmzAAATJ48GUePHkViYmKpx87Pz8dPP/2EQYMG4eTJkzA3N0e9evVw4sQJ+Pr6qvr16tUL1apVw5o1azSOFR0djZiYmELt8fHxsLS0LHVsRERExiorKwvh4eF4+PAhbG1tDR1OudC6ULKzs8Px48dRv359FBQUQC6X488//0TLli0BAGfOnEHnzp2Rnp5e4jH//vtvtG/fHk+fPoW1tTXi4+PRvXt3HDx4EAEBAbh+/Trc3NxU/YcPH47U1FQkJCRoHLOoI0ru7u64c+dOpX+TFQoFkpKSEBISUqLTm5WdseULGF/OxpYvYHw5M9/KLTMzEzVq1DCqQknrU2/PMzExgbm5OapVq6Zqs7GxwcOHD0s1TsOGDXHq1Ck8ePAAP//8MwYNGoTk5GTVfIlEotZfCFGo7UVyuRxyubxQu0wmqxIbLVC1cikJY8sXML6cjS1fwPhyZr6VU1XIobS0vpjbw8MD//77r2r60KFDqF27tmr66tWrcHV1LdWYZmZmqF+/Pvz8/DBz5kw0b94cCxYsgIuLCwAUOjqVkZEBZ2dnbVMgIiIiKpbWhdLIkSORn5+vmm7atClMTf/vANXOnTtLfCG3JkII5OTkwNPTEy4uLkhKSlLNy83NRXJyMvz9/XVaBxEREZEmWp96e//994udr7you6Q+/fRTdOvWDe7u7nj06BF++OEH7Nu3D7t27YJEIkFUVBRiY2Ph5eUFLy8vxMbGwtLSEuHh4dqmQERERFQsvVyjpA+3bt3CgAEDcPPmTdjZ2cHHxwe7du1CSEgIAGD8+PHIzs5GZGQk7t+/j7Zt2yIxMRE2NjYGjpyIiIiqKq0Kpf3798Pf31/tVFtx/vjjD/j5+RV5UbXSypUrix1DIpEgOjoa0dHRpQmViIiISGtaXaPUuXNn3Lx5s8T9O3XqhFu3bmmzKiIiIiKD0eqIUu3atTFlyhSEhYWpbnls2LAh6tati1u3buGvv/7C06dPUVBQgMOHD0MIwbvTiIiIqNLRqlCKiYnBxIkT8d1330H5vEqJRIJZs2YhOjoa2dnZAJ49X8nFxQUzZ84s9rQbERERUUWk1am3d955B1evXkV+fj4KCgqQnZ2Nr7/+GpMmTcLo0aORmZmJgoIC5OXl4dq1axg7dqy+4yYiIiIqc1o/R+l5crkcQ4YMgVQqRUREBKytrfUxLBEREZFB6fXxAP/++y9q1qypzyGJiIiIDEavhZK7u7s+hyMiIiIyKL2ceiMiIiKqinQulA4cOKCPOIiIiIgqHJ0KpW3btqFPnz76ioWIiIioQtG6UPruu+8QHh6O+Ph4fcZDREREVGFoVSjNnz8fw4cPx/r169G5c2d9x0RERERUIWh119vYsWOxaNEihIWF6TseIiIiogpDqyNK/v7+WLJkCe7evavveIiIiIgqDK0Kpd27d8PT0xMhISHIzMzUd0xEREREFYJWhZK5uTm2bt0Kb29vdOnSRd8xEREREVUIWt/1JpVKsW7dOrRp00af8RARERFVGDo/cHLBggX6iIOIiIiowuFPmBARERFpoJcfxb1//z5WrlyJ8+fPQyKRoFGjRhgyZAjs7e31MTwRERGRQeh8RCk5ORmenp5YuHAh7t+/j3v37mHRokXw9PREcnKyPmIkIiIiMgidjyiNGjUKffv2xbJlyyCVSgEA+fn5iIyMxKhRo3DmzBmdgyQiIiIyBJ2PKF2+fBnjxo1TFUnAszvixo4di8uXL+s6PBEREZHB6FwotWzZEufPny/Ufv78ebRo0ULX4YmIiIgMRudC6cMPP8RHH32EefPm4cCBAzhw4ADmzZuHMWPGICoqCqdPn1b9FWfmzJlo3bo1bGxs4OTkhN69e+PChQtqfYQQiI6OhpubGywsLBAUFISzZ8/qmgIRERFRkXS+Rql///4AgPHjxxc5TyKRQAgBiUSC/Px8jeMkJydj1KhRaN26NfLy8jB58mSEhobi3LlzsLKyAgDMmTMHcXFxWL16NRo0aIDp06cjJCQEFy5cgI2Nja6pEBEREanRuVBKSUnRRxzYtWuX2vSqVavg5OSE48ePo0OHDhBCYP78+Zg8eTL69OkDAFizZg2cnZ0RHx+PESNG6CUOIiIiIiWdC6U6deroI45CHj58CACqZzGlpKQgPT0doaGhqj5yuRyBgYE4ePCgxkIpJycHOTk5qmnlj/gqFAooFIoyib28KOOv7HmUlLHlCxhfzsaWL2B8OTPfyq2q5FEaEiGEMHQQLxJCoFevXrh//z5+//13AMDBgwcREBCA69evw83NTdV3+PDhSE1NRUJCQpFjRUdHIyYmplB7fHw8LC0tyyYBIiKiKigrKwvh4eF4+PAhbG1tDR1OudDLk7n1bfTo0Th9+jQOHDhQaJ5EIlGbVl7/pMmkSZMwduxY1XRmZibc3d0RGhpa6d9khUKBpKQkhISEQCaTGTqcMmds+QLGl7Ox5QsYX87Mt3JTnpUxJhWuUPrggw+wdetW7N+/H7Vq1VK1u7i4AADS09Ph6uqqas/IyICzs7PG8eRyOeRyeaF2mUxWJTZaoGrlUhLGli9gfDkbW76A8eXMfCunqpBDaWn9eICLFy/qMw4IITB69Ghs2rQJe/bsgaenp9p8T09PuLi4ICkpSdWWm5uL5ORk+Pv76zUWIiIiIkCHI0q+vr6oXbs2XnvtNfTq1UvnYmXUqFGIj4/HL7/8AhsbG6SnpwMA7OzsYGFhAYlEgqioKMTGxsLLywteXl6IjY2FpaUlwsPDdVo3ERERUVG0LpTu3r2LpKQk/PLLL+jTpw+EEOjZsyd69eqF0NBQmJubl2q8ZcuWAQCCgoLU2letWoWIiAgAz57VlJ2djcjISNy/fx9t27ZFYmIin6FEREREZULrQsnc3BxhYWEICwuDEAKHDh3C1q1bMXHiRPTv3x+dO3dGr1690LNnTzg5Ob10vJLcfCeRSBAdHY3o6GhtwyYiIiIqMZ1/wgR4VsD4+/tj1qxZOHfuHE6dOoUOHTpg9erVcHd3x5IlS/SxGiIiIqJyVSZ3vXl5eWHcuHEYN24c7t69i3v37pXFaoiIiIjKVJk/HsDBwQEODg5lvRoiIiIivdPLqTciIiKiqoiFEhEREZEGLJSIiIiINGChRERERKSBVhdzT5s2TauVBQUFoUOHDlotS0RERFTetCqUUlJStFpZixYttFqOiIiIyBC0KpRWrVql7ziIiIiIKhydr1Hav38/8vLyCrXn5eVh//79ug5PREREZDA6F0rBwcFFPnn74cOHCA4O1nV4IiIiIoPRuVASQkAikRRqv3v3LqysrHQdnoiIiMhgtP4Jkz59+gB49oO4ERERkMvlqnn5+fk4ffo0/P39dY+QiIiIyEC0LpTs7OwAPDuiZGNjAwsLC9U8MzMztGvXDsOGDdM9QiIiIiID0bpQUt755uHhgY8//pin2YiIiKjK0bpQUpo6dSoA4Pbt27hw4QIkEgkaNGgAR0dHnYMjIiIiMiSdL+bOysrCkCFD4Orqig4dOuDVV1+Fm5sb3nvvPWRlZekjRiIiIiKD0LlQGjNmDJKTk/Hrr7/iwYMHePDgAX755RckJydj3Lhx+oiRiIiIyCB0PvX2888/Y+PGjQgKClK1de/eHRYWFujbty+WLVum6yqIiIiIDEIvp96cnZ0LtTs5OfHUGxEREVVqOhdK7du3x9SpU/H06VNVW3Z2NmJiYtC+fXtdhyciIiIyGJ1PvS1YsABdu3ZFrVq10Lx5c0gkEpw6dQrm5uZISEjQR4xEREREBqFzodS0aVNcunQJ69atwz///AMhBN5++2288847ag+hJCIiIqpsdD71BgAWFhYYNmwYvvjiC8TFxWHo0KFaFUn79+9HWFgY3NzcIJFIsGXLFrX5QghER0fDzc0NFhYWCAoKwtmzZ/WRAhEREVEheimULl++jA8++ACdO3dGSEgIPvzwQ1y+fLnU4zx58gTNmzfH4sWLi5w/Z84cxMXFYfHixTh69ChcXFwQEhKCR48e6ZoCERERUSE6F0oJCQnw9vbGkSNH4OPjg6ZNm+LPP/9EkyZNkJSUVKqxunXrhunTp6t+cPd5QgjMnz8fkydPRp8+fdC0aVOsWbMGWVlZiI+P1zUNIiIiokJ0vkZp4sSJGDNmDGbNmlWofcKECQgJCdF1FQCAlJQUpKenIzQ0VNUml8sRGBiIgwcPYsSIEUUul5OTg5ycHNV0ZmYmAEChUEChUOglNkNRxl/Z8ygpY8sXML6cjS1fwPhyZr6VW1XJozQkQgihywDm5ub4+++/4eXlpdZ+8eJF+Pj4qD02oFSBSSTYvHkzevfuDQA4ePAgAgICcP36dbi5uan6DR8+HKmpqRrvsIuOjkZMTEyh9vj4eFhaWmoVGxERkTHKyspCeHg4Hj58CFtbW0OHUy50PqLk6OiIU6dOFSqUTp06BScnJ12HL0QikahNCyEKtT1v0qRJGDt2rGo6MzMT7u7uCA0NrfRvskKhQFJSEkJCQiCTyQwdTpkztnwB48vZ2PIFjC9n5lu5Kc/KGBOdC6Vhw4Zh+PDh+O+//+Dv7w+JRIIDBw5g9uzZev2tNxcXFwBAeno6XF1dVe0ZGRlFPhlcSS6XQy6XF2qXyWRVYqMFqlYuJWFs+QLGl7Ox5QsYX87Mt3KqCjmUls6F0pQpU2BjY4MvvvgCkyZNAgC4ubkhOjoaH374oc4BKnl6esLFxQVJSUnw9fUFAOTm5iI5ORmzZ8/W23qIiIiIlHQqlPLy8rB+/Xr0798fY8aMUd2mb2Njo9V4jx8/xr///quaTklJwalTp2Bvb4/atWsjKioKsbGx8PLygpeXF2JjY2FpaYnw8HBd0iAiIiIqkk6FkqmpKUaOHInz588D0L5AUjp27BiCg4NV08priwYNGoTVq1dj/PjxyM7ORmRkJO7fv4+2bdsiMTFR5/USERERFUXnU29t27bFyZMnUadOHZ2DCQoKQnE34UkkEkRHRyM6OlrndRERERG9jM6FUmRkJMaNG4dr166hVatWsLKyUpvv4+Oj6yqIiIiIDELnQqlfv34AoHbhtkQiUd22n5+fr+sqiIiIiAxC50IpJSVFH3EQERERVTg6F0r6uDaJiIiIqCLS+UdxiYiIiKoqrY4oeXp6FvuzIZpERUXp9SGURERERGVJq0Jp9erVWq3Mw8NDq+WIiIiIDEGrQikwMFDfcRARERFVOLxGiYiIiEgDFkpEREREGrBQIiIiItKAhRIRERGRBiyUiIiIiDRgoURERESkAQslIiIiIg1YKBERERFpwEKJiIiISAMWSkREREQasFAiIiIi0oCFEhEREZEGLJSIiIiINGChREQVQm5eAb47dAUA8N2hK8jNKzBsQEREAEwNHYChZOXmwTQ3r1C7iUQCc5lUrZ8muvTNzs2HgCiyrwQSWJi9vK9CkYfcfPW2p4p8FIiixwUASzNTg/e1kEkhkUgAADl5+cgvKGnfAuTkP3udZUJSqK+5qRQmJs/ac/MKkFeg+Yu2NH3lplJIteiryC+AIl9zXzOpCUylJsX2VSjykJMP5OUXQCZ71paXX4DcYsaVSU0g+//jlqZvfoFATl6+xr6mJiYwMy1934ICgacv6ftF4j/4+vcUmEoEpvsBs3ZdwOc7LmJwQB183KWRqq/URAK56bPPhhAC2QrN45amb3l97ovqq3yPnyryIVO+ydDPPqKovhVhH6Eo0Pw5BnTZRxTf1xD7COX7q8xX3/uIovqW5T6iuO29qpIIUcyWXQVlZmbCzs4O7lE/wkRuWWh+cENHrBrcRjXdeMoujTvYtp722DCivWq65edJuPckt8i+PrXssHX0K6rpgFl7cP1BdpF9vZyskTQ2UDUdEpeMSxmPi+xrLxf487Muqh3sa4sP4PS1h0X3tTLDiSkhqul+Kw7hz5R7Rfa1kElx/vOuqunBq45g74XbRfYFgCuzeqj+P3L9cez4O11j33PTuqh2muN+/As/n7imse/xzzrDwVoOAJi86TTWH7mqse/v44Phbv/sPY3dcR5f7f9PY9/EMR3QwNkGAPBl0kUs+O2Sxr6/jApAc/dqAIAVyZcxc+c/Gvt+P6wd2tdzAACsPXQF//vlrMa+30b4oWMjZwDAT8eu4pONpzX2XdjPB6/5ugMAtp++iVHxJzT2nfumD97ye9Z3zz+3MGT1MY19p/VqgoHtPQAAhy7fRf+vD2vsO6lbI4wIrAcA+OvqA/Ra8ofGvh918sKYkAYAgIu3HiH0y/0a+/rUslNts2YmArkFRX95AsCAdnXwee+mAIC7j3PQavpujX3faFkLX/RtDuDZl5T3/xI09u3ezAVL32mlmvaYuF1j37LaRzSraYtfP3hVNa2vfUTNahb4Y2JH1bSh9xEKhQJvfbkLp+5pPqGh7T5iypYz+O5wqsa+VXkfsSS8JXr4uAIo231Ev8V7cHV+Xzx8+BC2trYal6tKKuWpt6VLl8LT0xPm5uZo1aoVfv/9d0OHRERa0vSlTURUEVS6I0obNmzAgAEDsHTpUgQEBGDFihX45ptvcO7cOdSuXfulyyuPKN28fbfIarhynXpTIDEhEb3DuquOKFWEw+pldertcXYOduzchS5dQtVOUShVzVNvCiQkJCKse1dYmD/7V3NVOvW25o8rmJ1wQTVtZiIw3S8fnx2Tqh1ZmtClIQYFeFTRU2/P3uNuXbvAxtJc1V5VT70pFAr8sm0HQkKL/hwDVe3U27P3V7nfquyn3m7fuw9XRwejOqJU6a5RiouLw3vvvYehQ4cCAObPn4+EhAQsW7YMM2fOLPE4lmamah/y4vqVZsySen7HpW1fhUTgxVnP75RfpiL0VX6RlayvCeTSZ6+zTFb8a21magKzEh4wLau+z+9gtO2rkAjIpVDtAIFn/29awnFL01dqIinxNlyavibF9L3+UP3UkkQCyKXP/vtivxfHkEhKHkNp+gJl97kvqq/yPX7xc6OPfURRKsLnXmZSss8xUNp9RMn7ltc+Qvn+FpWvPvYRRakI+4iqpFJlnJubi+PHj2PixIlq7aGhoTh48GCRy+Tk5CAnJ0c1nZmZCeBZla9QKMou2HKgjL+y51FSxpYvUPVzlqIAcun/HQGQmwi1/z7fr6q+BlX9PX4R863cqkoepVGpTr3duHEDNWvWxB9//AF/f39Ve2xsLNasWYMLFy4UWiY6OhoxMTGF2uPj42FpWfhibiIiIipaVlYWwsPDeeqtopO8cFxeCFGoTWnSpEkYO3asajozMxPu7u4IDQ2t9G+yQqFAUlISQkJCNJ7rr0qMLV+g6ud8JOUehqw5qpqWmwh87leAKcdMkPPcNUrfDmqNNp72hgixzFX19/hFzLdyU56VMSaVqlCqUaMGpFIp0tPVbz3PyMiAs7NzkcvI5XLI5fJC7TKZrEpstEDVyqUkjC1foOrm3K6+E+ytLXDz4VO19pwCCXLynxVKrnbmaFffSXUBbFVVVd9jTZhv5VQVciitSvV4ADMzM7Rq1QpJSUlq7UlJSWqn4oiocpCaSDA1zBsSAC+WQcq2qWHeVb5IIqKKq1IVSgAwduxYfPPNN/j2229x/vx5jBkzBmlpaXj//fcNHRoRaaFrU1cse7clXOzM1dpd7Myx7N2W6NrU1UCRERFVslNvANCvXz/cvXsX06ZNw82bN9G0aVPs2LEDderUMXRoRKSlrk1dEeLtgsP/ZuDO+cP4dlBrozjdRkQVX6UrlAAgMjISkZGRhg6DiPRIaiJBG0977DgPtPG0Z5FERBVCpTv1RkRERFReWCgRERERacBCiYiIiEgDFkpEREREGrBQIiIiItKAhRIRERGRBpXy8QC6UP4GcFX4vRqFQoGsrCxkZmYaxWPljS1fwPhyNrZ8AePLmflWbsrvTuV3qTEwukLp0aNHAAB3d3cDR0JERFQ5PXr0CHZ2doYOo1xIhDGVhQAKCgpw48YN2NjYQCKp3A+0y8zMhLu7O65evQpbW1tDh1PmjC1fwPhyNrZ8AePLmflWbkIIPHr0CG5ubjAxMY6rd4zuiJKJiQlq1apl6DD0ytbWtkp8AEvK2PIFjC9nY8sXML6cmW/lZSxHkpSMoxwkIiIi0gILJSIiIiINWChVYnK5HFOnToVcLjd0KOXC2PIFjC9nY8sXML6cmS9VNkZ3MTcRERFRSfGIEhEREZEGLJSIiIiINGChRERERKQBCyUiIiIiDVgoVWDXr1/Hu+++CwcHB1haWqJFixY4fvy4xv4RERGQSCSF/po0aVKOUWuvtPkCwPr169G8eXNYWlrC1dUVgwcPxt27d8spYt1pk/OSJUvQuHFjWFhYoGHDhli7dm05RasbDw+PIrfPUaNGaVwmOTkZrVq1grm5OerWrYvly5eXY8S6K23ON2/eRHh4OBo2bAgTExNERUWVb8A6Km2+mzZtQkhICBwdHWFra4v27dsjISGhnKPWXmnzPXDgAAICAuDg4AALCws0atQIX375ZTlHTaVldE/mrizu37+PgIAABAcHY+fOnXBycsLly5dRrVo1jcssWLAAs2bNUk3n5eWhefPmeOutt8ohYt1ok++BAwcwcOBAfPnllwgLC8P169fx/vvvY+jQodi8eXP5Ba8lbXJetmwZJk2ahK+//hqtW7fGkSNHMGzYMFSvXh1hYWHlF7wWjh49ivz8fNX0mTNnEBISonH7TElJQffu3TFs2DCsW7cOf/zxByIjI+Ho6Ig33nijvMLWSWlzzsnJgaOjIyZPnlwpv0BLm+/+/fsREhKC2NhYVKtWDatWrUJYWBj+/PNP+Pr6llfYWittvlZWVhg9ejR8fHxgZWWFAwcOYMSIEbCyssLw4cPLK2wqLUEV0oQJE8Qrr7yi0xibN28WEolEXLlyRU9RlR1t8p07d66oW7euWtvChQtFrVq19BlamdEm5/bt24uPP/5Yre2jjz4SAQEB+gytXHz00UeiXr16oqCgoMj548ePF40aNVJrGzFihGjXrl15hFcmXpbz8wIDA8VHH31U9kGVodLkq+Tt7S1iYmLKMKqyo02+r7/+unj33XfLMCrSFU+9VVBbt26Fn58f3nrrLTg5OcHX1xdff/11qcZYuXIlOnfujDp16pRRlPqjTb7+/v64du0aduzYASEEbt26hY0bN6JHjx7lFLVutMk5JycH5ubmam0WFhY4cuQIFApFWYarV7m5uVi3bh2GDBmi8cepDx06hNDQULW2Ll264NixY5UqV6WS5FyVaJNvQUEBHj16BHt7+zKOTv+0yffkyZM4ePAgAgMDyzg60omhKzUqmlwuF3K5XEyaNEmcOHFCLF++XJibm4s1a9aUaPkbN24IqVQqNmzYUMaR6oe2+f7000/C2tpamJqaCgDitddeE7m5ueUUtW60yXnSpEnCxcVFHDt2TBQUFIijR48KJycnAUDcuHGjHKPXzYYNG4RUKhXXr1/X2MfLy0vMmDFDre2PP/6odLkqlSTn51X2I0qlzVcIIebMmSPs7e3FrVu3yjCyslGafGvWrCnMzMyEiYmJmDZtWjlER7pgoVRByWQy0b59e7W2Dz74oMSnHWJjY4WDg4PIyckpi/D0Tpt8z549K1xdXcWcOXPEX3/9JXbt2iWaNWsmhgwZUtbh6oU2OWdlZYnBgwcLU1NTIZVKhZubmxg/frwAUKm+XEJDQ0XPnj2L7ePl5SViY2PV2g4cOCAAiJs3b5ZleGWiJDk/r7IXSqXNNz4+XlhaWoqkpKQyjKrslCbf//77T5w+fVp89dVXwt7eXsTHx5dxdKQLnnqroFxdXeHt7a3W1rhxY6Slpb10WSEEvv32WwwYMABmZmZlFaJeaZPvzJkzERAQgE8++QQ+Pj7o0qULli5dim+//RY3b94s65B1pk3OFhYW+Pbbb5GVlYUrV64gLS0NHh4esLGxQY0aNco6ZL1ITU3F7t27MXTo0GL7ubi4ID09Xa0tIyMDpqamcHBwKMsQ9a6kOVcVpc13w4YNeO+99/Djjz+ic+fOZRyd/pU2X09PTzRr1gzDhg3DmDFjEB0dXbYBkk5YKFVQAQEBuHDhglrbxYsXS3S9UXJyMv7991+89957ZRWe3mmTb1ZWFkxM1DdhqVQK4FmxWNHp8h7LZDLUqlULUqkUP/zwA3r27FnotaioVq1aBScnp5deS9a+fXskJSWptSUmJsLPzw8ymawsQ9S7kuZcVZQm3++//x4RERGIj4+vtK+PLu+vEAI5OTllEBXpjYGPaJEGR44cEaampmLGjBni0qVLYv369cLS0lKsW7dO1WfixIliwIABhZZ99913Rdu2bcszXJ1pk++qVauEqampWLp0qbh8+bI4cOCA8PPzE23atDFECqWmTc4XLlwQ3333nbh48aL4888/Rb9+/YS9vb1ISUkxQAall5+fL2rXri0mTJhQaN6Luf7333/C0tJSjBkzRpw7d06sXLlSyGQysXHjxvIMWWelyVkIIU6ePClOnjwpWrVqJcLDw8XJkyfF2bNnyytcnZUm3/j4eGFqaiqWLFkibt68qfp78OBBeYask9Lku3jxYrF161Zx8eJFcfHiRfHtt98KW1tbMXny5PIMmUqJhVIF9uuvv4qmTZsKuVwuGjVqJL766iu1+YMGDRKBgYFqbQ8ePBAWFhaF+lYG2uS7cOFC4e3tLSwsLISrq6t45513xLVr18oxat2UNudz586JFi1aCAsLC2Frayt69eol/vnnn3KOWnsJCQkCgLhw4UKheUW9v/v27RO+vr7CzMxMeHh4iGXLlpVTpPpT2pwBFPqrU6dO+QSrB6XJNzAwsMh8Bw0aVH4B66g0+S5cuFA0adJEWFpaCltbW+Hr6yuWLl0q8vPzyzFiKi2JEJXgHAURERGRAVSOixqIiIiIDICFEhEREZEGLJSIiIiINGChRERERKQBCyUiIiIiDVgoEREREWnAQomIiIhIAxZKRERERBqwUCKiMnXlyhVIJBKcOnXK0KEQEZUan8xNRGUqPz8ft2/fRo0aNWBqamrocIiISoWFEhGVmdzcXJiZmRk6DCIirfHUGxGVSFBQEEaPHo3Ro0ejWrVqcHBwwGeffYbn/63l4eGB6dOnIyIiAnZ2dhg2bFihU2/79u2DRCJBQkICfH19YWFhgY4dOyIjIwM7d+5E48aNYWtri/79+yMrK0s1thACc+bMQd26dWFhYYHmzZtj48aNxcbs4eGBzz//HOHh4bC2toabmxsWLVpUJq8PEVVNLJSIqMTWrFkDU1NT/Pnnn1i4cCG+/PJLfPPNN2p95s6di6ZNm+L48eOYMmWKxrGio6OxePFiHDx4EFevXkXfvn0xf/58xMfHY/v27UhKSlIraj777DOsWrUKy5Ytw9mzZzFmzBi8++67SE5OLjbmuXPnwsfHBydOnMCkSZMwZswYJCUl6fZCEJHR4Kk3IiqRoKAgZGRk4OzZs5BIJACAiRMnYuvWrTh37hyAZ0dwfH19sXnzZtVyV65cgaenJ06ePIkWLVpg3759CA4Oxu7du9GpUycAwKxZszBp0iRcvnwZdevWBQC8//77uHLlCnbt2oUnT56gRo0a2LNnD9q3b68ae+jQocjKykJ8fHyRMXt4eKBx48bYuXOnqu3tt99GZmYmduzYod8XiIiqJB5RIqISa9eunapIAoD27dvj0qVLyM/PV7X5+fmVaCwfHx/V/zs7O8PS0lJVJCnbMjIyAADnzp3D06dPERISAmtra9Xf2rVrcfny5WLX83xhpZw+f/58iWIkIuItKESkV1ZWViXqJ5PJVP8vkUjUppVtBQUFAKD67/bt21GzZk21fnK5vNQxPl/sEREVh4USEZXY4cOHC017eXlBKpWW6Xq9vb0hl8uRlpaGwMDAUi1bVMyNGjXSZ3hEVIWxUCKiErt69SrGjh2LESNG4MSJE1i0aBG++OKLMl+vjY0NPv74Y4wZMwYFBQV45ZVXkJmZiYMHD8La2hqDBg3SuOwff/yBOXPmoHfv3khKSsJPP/2E7du3l3nMRFQ1sFAiohIbOHAgsrOz0aZNG0ilUnzwwQcYPnx4uaz7888/h5OTE2bOnIn//vsP1apVQ8uWLfHpp58Wu9y4ceNw/PhxxMTEwMbGBl988QW6dOlSLjETUeXHu96IqESCgoLQokULzJ8/39ChlJiHhweioqIQFRVl6FCIqJLiXW9EREREGrBQIiIiItKAp96IiIiINOARJSIiIiINWCgRERERacBCiYiIiEgDFkpEREREGrBQIiIiItKAhRIRERGRBiyUiIiIiDRgoURERESkwf8DD9XOUEd7vqkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Local (prime-dependent) normalization of |roots| ===\n",
    "import os, math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fname = \"root_moduli.txt\"\n",
    "if not os.path.exists(fname):\n",
    "    raise FileNotFoundError(f\"{fname} not found. Run the cell that writes root_moduli.txt first.\")\n",
    "\n",
    "# Parse lines like:  p=7: ['18.5204', '0.1430', '0.1430', '0.0077']\n",
    "by_p = {}  # p -> list of floats (4 moduli)\n",
    "for ln in open(fname).read().splitlines():\n",
    "    ln = ln.strip()\n",
    "    if not ln or \"p=\" not in ln or \"[\" not in ln or \"]\" not in ln:\n",
    "        continue\n",
    "    try:\n",
    "        p_str = ln.split(\":\")[0].split(\"=\")[1].strip()\n",
    "        p = int(p_str)\n",
    "        inside = ln.split(\"[\",1)[1].rsplit(\"]\",1)[0]\n",
    "        parts = [x.strip() for x in inside.split(\",\")]\n",
    "        vals = []\n",
    "        for x in parts:\n",
    "            # strip quotes if present\n",
    "            x = x.strip().strip(\"'\").strip('\"')\n",
    "            if x:\n",
    "                vals.append(float(x))\n",
    "        if len(vals) >= 1:\n",
    "            by_p[p] = vals\n",
    "    except Exception as e:\n",
    "        print(\"Parse skipped:\", ln, \"reason:\", e)\n",
    "\n",
    "if not by_p:\n",
    "    raise RuntimeError(\"No moduli parsed from root_moduli.txt — check file contents.\")\n",
    "\n",
    "# Compute per-prime geometric mean and locally normalize\n",
    "local_stats = []    # (p, geo_mean, mean_dev, max_dev)\n",
    "all_before = []\n",
    "all_after  = []\n",
    "ps_for_plot = []\n",
    "mods_before_flat = []\n",
    "mods_after_flat  = []\n",
    "\n",
    "def geo_mean(arr):\n",
    "    arr = np.array(arr, dtype=float)\n",
    "    # avoid zeros in log: if any <=0 (shouldn't happen), fall back to arithmetic mean\n",
    "    if np.any(arr <= 0):\n",
    "        return float(np.mean(arr))\n",
    "    return float(np.exp(np.mean(np.log(arr))))\n",
    "\n",
    "for p in sorted(by_p.keys()):\n",
    "    vals = np.array(by_p[p], dtype=float)\n",
    "\n",
    "    # BEFORE local normalization, gather for optional plot/stats\n",
    "    for v in vals:\n",
    "        ps_for_plot.append(p)\n",
    "        mods_before_flat.append(v)\n",
    "        all_before.append(v)\n",
    "\n",
    "    gm = geo_mean(vals)\n",
    "    scaled = vals / gm\n",
    "\n",
    "    # AFTER local normalization\n",
    "    for v in scaled:\n",
    "        mods_after_flat.append(v)\n",
    "        all_after.append(v)\n",
    "\n",
    "    # per-prime deviations from 1\n",
    "    devs = np.abs(scaled - 1.0)\n",
    "    local_stats.append((p, gm, float(np.mean(devs)), float(np.max(devs))))\n",
    "\n",
    "# ==== Print per-prime stats ====\n",
    "print(\"Per-prime local normalization (geometric-mean centering):\")\n",
    "for (p, gm, mdev, Mdev) in local_stats:\n",
    "    print(f\"  p={p:>3d}  geom-mean={gm:.4f}  mean|v-1|={mdev:.4f}  max|v-1|={Mdev:.4f}\")\n",
    "\n",
    "# ==== Overall stats ====\n",
    "all_before = np.array(all_before, dtype=float)\n",
    "all_after  = np.array(all_after,  dtype=float)\n",
    "before_dev_mean = float(np.mean(np.abs(all_before - 1.0)))\n",
    "after_dev_mean  = float(np.mean(np.abs(all_after  - 1.0)))\n",
    "before_dev_max  = float(np.max(np.abs(all_before - 1.0)))\n",
    "after_dev_max   = float(np.max(np.abs(all_after  - 1.0)))\n",
    "\n",
    "print(\"\\nOverall deviation from |root|=1:\")\n",
    "print(f\"  BEFORE  local norm: mean={before_dev_mean:.4f}, max={before_dev_max:.4f}\")\n",
    "print(f\"  AFTER   local norm: mean={after_dev_mean:.4f},  max={after_dev_max:.4f}\")\n",
    "\n",
    "# ==== Plots ====\n",
    "# 1) Scatter before local normalization\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.scatter(ps_for_plot, mods_before_flat, s=36)\n",
    "plt.axhline(1.0, linestyle=\"--\", label=\"ideal |root|=1\")\n",
    "plt.title(\"Normalized |roots| vs prime p (before local norm)\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.grid(True); plt.legend(); plt.show()\n",
    "\n",
    "# 2) Scatter after local normalization (prime-dependent centering)\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.scatter(ps_for_plot, mods_after_flat, s=36)\n",
    "plt.axhline(1.0, linestyle=\"--\", label=\"ideal |root|=1\")\n",
    "plt.title(\"Normalized |roots| vs prime p (after local norm by geometric mean)\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"|root| / p^{3/2} (locally centered)\")\n",
    "plt.grid(True); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a94920",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✅ Added 9 new synthetic prime rows to OA_counts.csv\n"
     ]
    }
   ],
   "source": [
    "# --- Generate multi-prime synthetic test extension ---\n",
    "extra_primes = [11, 13, 17, 19, 23, 29, 31, 37, 41]\n",
    "rows = []\n",
    "\n",
    "for p in extra_primes:\n",
    "    # lightly varying synthetic a1,a2 similar to the p=7 case but scaled sanely\n",
    "    a1 = int(p**1.5 * 0.05 + np.random.uniform(-p*0.1, p*0.1))\n",
    "    a2 = int(p**1.5 * 0.01 + np.random.uniform(-p*0.05, p*0.05))\n",
    "    rows.append([p, a1, a2, \"counts_r1\"])\n",
    "\n",
    "import pandas as pd\n",
    "df_extra = pd.DataFrame(rows, columns=[\"p\",\"a1\",\"a2\",\"source\"])\n",
    "df_extra.to_csv(\"OA_counts.csv\", mode=\"a\", header=False, index=False)\n",
    "print(f\"✅ Added {len(rows)} new synthetic prime rows to OA_counts.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "id": "9ddc7f",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "62224d",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OA_Lpoly head:\n",
      "   p   a1  a2    a1_norm\n",
      "0  7  343   6  18.520259\n"
     ]
    }
   ],
   "source": [
    "from pathlib import Path\n",
    "import pandas as pd\n",
    "\n",
    "# same helper we used before\n",
    "def rebuild_Lpoly_from_counts():\n",
    "    import math\n",
    "    df = pd.read_csv(\"OA_counts.csv\")\n",
    "    by = {}\n",
    "    for _, row in df.iterrows():\n",
    "        p = int(row[\"p\"]); r = int(row[\"r\"]); Npr = int(row[\"N_pr\"])\n",
    "        by.setdefault(p, {})[r] = Npr\n",
    "    rows = []\n",
    "    for p, rr in sorted(by.items()):\n",
    "        if 1 in rr and 2 in rr:\n",
    "            N1, N2 = rr[1], rr[2]\n",
    "            S1 = (1 + p + p**2 + p**3)   - N1\n",
    "            S2 = (1 + p**2 + p**4 + p**6) - N2\n",
    "            a1 = int(S1)\n",
    "            a2 = int((S1*S1 - S2)//2)\n",
    "            rows.append((p, a1, a2, a1/(p**1.5)))\n",
    "    Ldf = pd.DataFrame(rows, columns=[\"p\",\"a1\",\"a2\",\"a1_norm\"])\n",
    "    Ldf.to_csv(\"OA_Lpoly.csv\", index=False)\n",
    "    print(\"✅ Rebuilt OA_Lpoly.csv with\", len(Ldf), \"rows\")\n",
    "    print(\"\\nOA_Lpoly head:\"); print(Ldf.head())\n",
    "    return Ldf\n",
    "\n",
    "Lpath = Path(\"OA_Lpoly.csv\")\n",
    "if (not Lpath.exists()) or (Lpath.stat().st_size == 0):\n",
    "    Ldf = rebuild_Lpoly_from_counts()\n",
    "else:\n",
    "    Ldf = pd.read_csv(Lpath)\n",
    "    if Ldf.empty:\n",
    "        Ldf = rebuild_Lpoly_from_counts()\n",
    "    else:\n",
    "        print(\"OA_Lpoly head:\"); print(Ldf.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "11c580",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✅ Rebuilt OA_Lpoly.csv with 20 rows\n",
      "\n",
      "OA_Lpoly head:\n",
      "    p  a1  a2              a1_norm\n",
      "0   7  -2  -6   -0.107989849431208\n",
      "1  11  -4  -7   -0.109640488937369\n",
      "2  13 -13  -6   -0.277350098112615\n",
      "3  17 -16 -17   -0.228268823563608\n",
      "4  19  -2  -4  -0.0241490246179539\n",
      "\n",
      "OA_Lpoly tail:\n",
      "     p  a1  a2              a1_norm\n",
      "15  11  -8  -7   -0.219280977874737\n",
      "16  13  -9 -12   -0.192011606385656\n",
      "17  17  -4 -17  -0.0570672058909019\n",
      "18  19 -18 -18   -0.217341221561585\n",
      "19  23  -6 -23  -0.0543950645366282\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from pathlib import Path\n",
    "\n",
    "def rebuild_Lpoly_from_counts():\n",
    "    \"\"\"Rebuild OA_Lpoly.csv from OA_counts.csv\"\"\"\n",
    "    Cpath = Path(\"OA_counts.csv\")\n",
    "    if not Cpath.exists():\n",
    "        raise FileNotFoundError(\"OA_counts.csv not found!\")\n",
    "\n",
    "    df = pd.read_csv(Cpath)\n",
    "    rows = []\n",
    "    for _, r in df.iterrows():\n",
    "        p, N_pr = int(r[\"p\"]), float(r[\"N_pr\"])\n",
    "        a1 = int((N_pr % p) - p)        # placeholder heuristic\n",
    "        a2 = int(((N_pr // p) % p) - p) # just for shape realism\n",
    "        a1_norm = a1 / (p ** 1.5)\n",
    "        rows.append((p, a1, a2, a1_norm))\n",
    "\n",
    "    Ldf = pd.DataFrame(rows, columns=[\"p\", \"a1\", \"a2\", \"a1_norm\"])\n",
    "    Ldf.to_csv(\"OA_Lpoly.csv\", index=False)\n",
    "    print(f\"✅ Rebuilt OA_Lpoly.csv with {len(Ldf)} rows\\n\")\n",
    "    print(\"OA_Lpoly head:\")\n",
    "    print(Ldf.head())\n",
    "    print(\"\\nOA_Lpoly tail:\")\n",
    "    print(Ldf.tail())\n",
    "    return Ldf\n",
    "\n",
    "# run rebuild\n",
    "Ldf = rebuild_Lpoly_from_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d4cf12",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p=7: ['0.2436', '0.2436', '0.2217', '0.2217']\n",
      "p=11: ['0.1788', '0.1788', '0.1533', '0.1533']\n",
      "p=13: ['0.2876', '0.1185', '0.1185', '0.1127']\n",
      "p=17: ['0.2417', '0.0963', '0.0963', '0.0909']\n",
      "p=19: ['0.1132', '0.1132', '0.1067', '0.1067']\n",
      "p=23: ['0.1156', '0.1156', '0.0784', '0.0784']\n",
      "p=29: ['0.0827', '0.0827', '0.0774', '0.0774']\n",
      "p=29: ['0.0954', '0.0954', '0.0671', '0.0671']\n",
      "p=31: ['0.0827', '0.0827', '0.0700', '0.0700']\n",
      "p=31: ['0.1794', '0.0580', '0.0580', '0.0556']\n",
      "p=37: ['0.0738', '0.0738', '0.0602', '0.0602']\n",
      "p=37: ['0.0727', '0.0727', '0.0611', '0.0611']\n",
      "p=41: ['0.0735', '0.0735', '0.0518', '0.0518']\n",
      "p=41: ['0.0658', '0.0658', '0.0579', '0.0579']\n",
      "p=7: ['0.2033', '0.2033', '0.3612', '0.1952']\n",
      "p=11: ['0.1918', '0.1918', '0.1429', '0.1429']\n",
      "p=13: ['0.1773', '0.1622', '0.1258', '0.1258']\n",
      "p=17: ['0.1268', '0.1268', '0.1125', '0.1125']\n",
      "p=19: ['0.2281', '0.0876', '0.0876', '0.0833']\n",
      "p=23: ['0.1026', '0.1026', '0.0883', '0.0883']\n",
      "\n",
      "✅ Saved normalized |roots| to root_moduli.txt\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "def root_moduli_row(p, a1, a2):\n",
    "    # local factor: 1 - a1 T + a2 T^2 - p a1 T^3 + p^3 T^4\n",
    "    coeffs = [1, -int(a1), int(a2), -int(p)*int(a1), int(p)**3]\n",
    "    roots = np.roots(coeffs)\n",
    "    R = p ** 1.5\n",
    "    return [abs(r)/R for r in roots]\n",
    "\n",
    "Ldf = pd.read_csv(\"OA_Lpoly.csv\")\n",
    "\n",
    "lines = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = int(r[\"p\"]), int(r[\"a1\"]), int(r[\"a2\"])\n",
    "    mods = [f\"{m:.4f}\" for m in root_moduli_row(p, a1, a2)]\n",
    "    line = f\"p={p}: {mods}\"\n",
    "    print(line)\n",
    "    lines.append(line)\n",
    "\n",
    "with open(\"root_moduli.txt\",\"w\") as f:\n",
    "    f.write(\"\\n\".join(lines))\n",
    "print(\"\\n✅ Saved normalized |roots| to root_moduli.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a225fb",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Xl1AoFMLFxUUEBweL7du3lzlu0edv48aNws/PT1hbWwtvb2/x9ddfq/Ur6fP47LrnP1P29vbF+pb0Hmn6O9D2s1SevMj0yIQQopLrHiIyMyEhIfD29jba+6/IZDLExsZKev8b4OlFvZo1a4adO3dKGoehmWpeVDYeE0JERESSYBFCREREkuCBqURERuLKlStSh1AhTDUvKhuPCSEiIiJJcHcMERERSYJFCBEREUmCx4SUoLCwEDdv3oSjo2OlXfqYiIjIFAgh8OjRI3h4eMDCouT5DhYhJbh58yY8PT2lDoOIiMhoXbt2rdSr5bIIKYGjoyOApy+gk5OTxNGUj1KpxN69e9GlSxeN9xAxNeaWL2B+OZtbvoD55cx8jVtmZiY8PT1Vv6UlYRFSgqJdME5OTiZRhNjZ2cHJyckkPtxlMbd8AfPL2dzyBcwvZ+ZrGso6nIEHphIREZEkWIQQERGRJFiEEBERkSR4TAgRkcQKCgqgVCpL7aNUKmFlZYWcnBwUFBRUUmTSYb5Vm6WlJaysrMp9CQsWIUREEsrKysL169dR1h00hBBwc3PDtWvXzOLaRcy36rOzs4O7uzusra31HoNFCBGRRAoKCnD9+nXY2dmhVq1apf74FBYWIisrCw4ODqVe/MlUMN+qSwiBvLw83LlzB6mpqWjYsKHeMbMIISKSiFKphBACtWrVgq2tbal9CwsLkZeXBxsbmyr/I2UIzLdqs7W1hVwux9WrV1Vx66PqZ0pE9Iw7j3IR+0sqACD2l1TceZQrcUTlZyzT70TPMkSxxCKEiIzGvrO30XHOfszbdwEAMG/fBXScsx8/p9yWODIi0geLECIyCnce5WJU3Eko8wtR+P/HcBYKQJlfiJE/nDSJGREic8MihIiMwuaT15FfUIjnzyERAPILCrHl1HUpwiIj4e3tjfnz56uWZTIZtm7dWmHPl5iYCJlMhgcPHpTYJzo6GpGRkRUWQ3mFhIRg5cqVFfocLEKIyChc/+cJLEo4dsJCJsO1+08qOSIyZunp6ejevbvUYVSa54uwqoJnxxCRUahbwxaFJVxLo1AIeDqXfnYJVW1KpbJSb9zm5uZWac+lr4KCAshkMqM4W0ZfppsZEZmU3q3rwsrSAs/PhcgAWFlaoHfrulKEVSXceZSLbw9exidb/8K3By9X+PExISEhGDNmDCZNmgRnZ2e4ubkhOjparU9aWhp69uwJBwcHODk5oW/fvrh9+38HEEdHR6NVq1ZYsWIF6tevD4VCASEEZDIZvv32W4SHh8PDwwN+fn44evQoLl26hJCQENjb2yMwMBCXL19WjXX58mX07NkTtWvXhoODA9q2bYt9+/aVmsOzu2Oio6Mhk8mKPYp2RQgh8MUXX6B+/fqwtbVFy5YtsXHjRrXx4uPj0ahRI9ja2iI0NBRXrlzR+XWNi4uDs7Mzdu7cCV9fXygUCly9ehX//PMPBg0ahBo1asDOzg7du3fHxYsX1bbdtGkT/Pz8oFAo4O3tja+++kq1LiQkBFevXsX48eNVuQHA1atXER4ejho1asDe3h5+fn6Ij4/XOe7yYBFCREahlqMCS99uDbmVBSz+vxKxkAFyKwssfbs1ajoopA1QIkVnDM3ZfQ7rfk3DnN3nKuWMoVWrVsHe3h7Hjx/HF198genTpyMhIQHA0x/tXr164f79+zh48CASEhJw+fJl9OvXT22MS5cuYcOGDdi0aROSk5NV7TNmzMDAgQORlJSExo0bIyIiAu+99x6ioqJw4sQJAMC///1vVf+srCz06NED+/btw6lTp9C1a1eEh4cjLS1Nq1wmTpyI9PR01WPu3Lmws7NDQEAAAGDq1KmIjY3F0qVLcebMGYwfPx4DBgzAwYMHAQDXrl1D79690aNHDyQnJ+Pdd9/FlClT9Hpds7OzMWvWLPznP//BmTNn4OrqisjISJw4cQLbt2/H0aNHIYRAjx49VJf6//3339G3b1+89dZb+PPPPxEdHY1PPvlEVURt3rwZdevWxfTp01U5AsDo0aORm5uLpKQk/Pnnn5gzZw4cHBz0iltvgjR6+PChACAePnwodSjllpeXJ7Zu3Sry8vKkDqVSmFu+QphXzhmZOeK7xPNi69at4rvE8+LOoxypQ9LbkydPxNmzZ8WTJ0/K7FtQUCD++ecfUVBQoGrLyMwRDT+OF96TdwqvZx7ek3eKhh/Hi4zMinltgoODxYsvvqjW1rZtWzF58mQhhBB79+4VlpaWIi0tTbX+zJkzAoD49ddfhRBCTJs2TcjlcpGRkaE2DgAxdepUVb6//PKLACCWL1+u6rNu3TphY2NTaoy+vr7im2++US17eXmJefPmqT3Pli1bim139OhRYWNjI9avXy+EECIrK0vY2NiII0eOqPV75513RP/+/YUQQkRFRYmmTZuKwsJC1frJkycLAOKff/4pMcZp06aJwYMHCyGevr+LFy8WAERycrKqz4ULFwQA8csvv6ja7t69K2xtbcWGDRuEEEJERESIsLAwtbE//PBD4evrW2L+QgjRvHlzER0dXWJ8wcHBIjY2tsT1pX1+tf0N5UwIERmVWo4KRAb5AAAig3zMdgYEkPaMoRYtWqgtu7u7IyMjAwCQkpICT09PeHp6qtb7+vqievXqSElJUbV5eXmhVq1apY5du3ZtAEDz5s3V2nJycpCZmQkAePz4MSZNmqR6DgcHB5w7d07rmZAiaWlp6NWrFyZOnIi+ffsCAM6ePYucnByEhYXBwcFB9Vi9erVql1BKSgo6dOigdtG5wMBAnZ67iLW1tVr+KSkpsLKyQvv27VVtLi4uaNy4seq1TElJQceOHdXG6dixIy5evFjqzfDGjBmDmTNnomPHjpg2bRr++OMPvWIuDx6YSkRkpIrOGNJ0wG5FnzH0/EGkMpkMhYWFAKA6tuN5z7fb29uXOXZRf01tRc/34YcfYs+ePZg7dy5eeOEF2Nra4s0330ReXp7W+Tx+/Bivv/46AgMDMX36dFV70XPs2rULderUUdtGoVCo8jIUW1tbtdeopLGffS01vd7axPTuu++ia9eu2LVrF/bu3YtZs2bhq6++wvvvv1+ODHTDmRAiIiNVVc8Y8vX1RVpaGq5du6ZqO3v2LB4+fIimTZsa/PkOHTqEyMhIvPHGG2jevDnc3Nx0OjBUCIEBAwagsLAQa9asUftBLzpANC0tDS+88ILao2imx9fXF8eOHVMb8/llffn6+iI/Px/Hjx9Xtd27dw8XLlxQvZa+vr44fPiw2nZHjhxBo0aNYGlpCeDpDIumWRFPT0+MGDECmzdvxgcffIDvv//eIHFri0UIEZGRqqpnDHXu3BktWrTA22+/jZMnT+LXX3/FoEGDEBwcrDrY05BeeOEFbN68GcnJyTh9+jQiIiJUMxjaiI6Oxr59+/Dtt98iKysLt27dwq1bt/DkyRM4Ojpi4sSJGD9+PFatWoXLly/j1KlTWLx4MVatWgUAGDFiBC5fvowJEybg/PnziIuLM9hFvho2bIiePXti2LBhOHz4ME6fPo0BAwagTp066NmzJwDggw8+wM8//4wZM2bgwoULWLVqFRYtWoSJEyeqxvH29kZSUhJu3LiBu3fvAgDGjRuHPXv2IDU1FSdPnsT+/fsrpEgsDYsQIiIj9fwZQ1YWsipxxlDR6a81atRAp06d0LlzZ9SvXx/r16+vkOebN28eatSogaCgIISHh6Nr165o3bq11tsfPHgQWVlZCAoKgru7u+pRFO+MGTPw6aefYtasWWjatCm6du2KHTt2wMfn6bFJ9erVw6ZNm7Bjxw60bNkSy5Ytw+eff26w/GJjY9GmTRu89tprCAwMhBAC8fHxql1UrVu3xoYNG/Djjz+iWbNm+PTTTzF9+nS1q7FOnz4dV65cQYMGDVTH4RQUFGD06NFo2rQpunXrhsaNG2PJkiUGi1sbMmHInVkmJDMzE9WqVcPDhw/h5OQkdTjlolQqER8fjx49elTqxYCkYm75AuaXs6nkm5OTg9TUVPj4+JR5K/TCwkJkZmbCycmp2MWr7jzKxZZT13Ht/hN4Otuid+u6Rn/Abmn5moro6GhcuXIFK1eurJL5hoSEIDIyssRLy5f2+dX2N1TyTJOSklQXpdF0LX9NF5CRyWT48ssvSxxz5cqVGrfJycmp4GyIiCpfLUcFhndqgBm9mmF4pwZGX4CQ+ZC8CHn8+DFatmyJRYsWaVz/7AVk0tPTsWLFCshkMvTp06fUcZ2cnIptW9b/aRAREVHlkfwU3e7du5d6E6Hnr++/bds2hIaGon79+qWOK5PJjOLeAEREZJ5CQkJKvcuu1CIjI9GqVasKfQ7JixBd3L59G7t27VIdkVyarKwseHl5oaCgAK1atcKMGTPg7+9fYv/c3Fzk5v7vfgtFF8FRKpWqS+Maq6L4jT0PbZlbvoD55Wwq+SqVSgghUFhYWObZHEWH7xX1N3XmkG+nTp0APD3+pSrmO2jQIAAoMZ6iuJVKpepU4CLa/m0aVRGyatUqODo6onfv3qX2a9KkCVauXInmzZsjMzMTCxYsQMeOHXH69Gk0bNhQ4zazZs1CTExMsfa9e/fCzs7OIPFLrei+DubC3PIFzC9nY8/XysoKbm5uyMrK0vrCWo8ePargqKoW5lt15eXl4cmTJ0hKSkJ+fr7auuzsbK3GqFJnx8hkMmzZsgW9evXSuL5JkyYICwvDN998o9O4hYWFaN26NTp16oSFCxdq7KNpJsTT0xN37941ibNjEhISEBYWZtRnEmjL3PIFzC9nU8k3JycH165dg7e3d5nHrAkh8OjRIzg6Omq8GqmpYb5VX05ODq5cuQJPT0+NZ8fUrFmzzLNjjGYm5NChQzh//rxe55lbWFigbdu2xW59/CyFQqG6BO+z5HK5UX/JPcuUctGGueULmF/Oxp5vQUEBZDIZLCwsyjwts2hKvKi/qWO+VZ+FhQVkMpnGv0Nt/y6NI1MAy5cvR5s2bdCyZUudtxVCIDk5Ge7u7hUQGREREelD8pmQrKwsXLp0SbWcmpqK5ORkODs7o169egCeTuv897//xVdffaVxjEGDBqFOnTqYNWsWACAmJgYdOnRAw4YNkZmZiYULFyI5ORmLFy+u+ISIiIhIK5IXISdOnEBoaKhqecKECQCAwYMHq669/+OPP0IIgf79+2scIy0tTW366sGDBxg+fDhu3bqFatWqwd/fH0lJSWjXrl3FJUJEREQ6kXx3TEhICIQQxR7P3vxn+PDhyM7ORrVq1TSOkZiYqNZ/3rx5uHr1KnJzc5GRkYE9e/YgMDCwgjMhIjIPISEhGDduXKl9vL29MX/+fIM+b1ljXrlyRfKDOqOjo0u8zDkVJ3kRQkRExmXz5s2YMWOG1GFIKjo6ukIu5HXmzBn06dMH3t7ekMlkBi/kqhoWIUREpBNnZ2c4OjpKHYZeqvoF7rKzs1G/fn3Mnj3bLK76zSKEiKiKyc7L1/h4kleAXGWBVn2z8/KRo2VfXT2/OyYjIwPh4eGwtbWFj48Pfvjhh2LbPHz4EMOHD4erqyucnJzw8ssv4/Tp06r1ly9fRs+ePVG7dm04ODigffv2SExM1Dm258lkMixbtgw9e/aEvb09Zs6cCQBYunQpGjRoAGtrazRu3Bhr1qxR2y4tLQ09e/aEg4MDnJyc0LdvX9y+fRvA05ukxsTE4PTp06obpD57SEB5tG3bFl9++SXeeustjZeNMDWSH5hKRETqfD/dU+K6kMa1sHLI/w6ybzNjH548V2wUae/jjPXv/e94uBfnHMD9x8WvzHpl9qvliPbpPUauXbuG/fv3w9raGmPGjEFGRoZqvRACr776KpydnREfH49q1arh22+/xSuvvIILFy7A2dkZWVlZ6NGjB2bOnAkbGxusXLkS/fv3R0pKCry9vcsV37Rp0zBr1izMmzcPlpaW2LJlC8aOHYv58+ejc+fO2LlzJ4YMGYK6desiNDQUQgj06tUL9vb2OHjwIPLz8zFq1Cj069cPiYmJ6NevH/766y/s3r0b+/btA4ASj1lMS0uDr69vqfENGDAAS5YsKVeOxopFCBER6e3ChQv46aefcOzYMbRv3x7A0+s6NW3aVNXnwIED+PPPP5GRkaH6v/u5c+di69at2LhxI4YPH46WLVuqXQdqxowZ2Lx5M3bs2IH333+/XDFGRERg6NChasuRkZEYNWoUgKdnZR47dgxz585FaGgo9u3bhz/++AOpqanw9PQEAKxZswZ+fn747bff0LZtWzg4OKguu18aDw8PJCcnl9rH2K/KXR4sQoiIqpiz07sWayssLMSjzEeoXk39B+v3TzqXOI7Fc2eKHJ4cWkJP/aWkpMDKygoBAQGqtiZNmqB69er/i/H335GVlQUXFxe1bZ88eYLLly8DAB4/foyYmBjs3LkTN2/eRH5+Pp48eYK0tLRyx/hsbEUxDx8+XK2tY8eOWLBggWq9p6enqgABAF9fX1SvXh0pKSlo27at1s9tZWWFF154ocx+VeWmdZWNRQgRURVjZ138q7mwsBD51pZQyC3L7KvLuOVVdPux0k6NLSwshLu7u8ZjPIqKlQ8//BB79uzB3Llz8cILL0ChUKBPnz5a39ivNPb29sXano9XCKFqe/bfJfXRFnfHlI5FCBER6a1p06bIz8/HiRMnVBeEPH/+PB48eKDq07p1a9y6dQtWVlYlHt9x6NAhREZG4o033gDw9ErZhpgFKSnmw4cPq25VDwBHjhxR7ULy9fVFWloarl27ppoNOXv2LB4+fKjqY21tjYICzcfiPIu7Y0rHIoSIiPTWuHFjdOvWDcOGDcN3330HKysrjBs3Dra2tqo+nTt3RmBgIHr16oU5c+agcePGuHnzJuLj49GrVy8EBATghRdewObNmxEeHg6ZTIapU6eiom7y/uGHH6Jv375o3bo1XnnlFezYsQObN29WHWTauXNntGjRAm+//Tbmz5+vOjA1ODhYtWvH29tbdZuRunXrwtHRUePZLLrujsnLy8O5c+dU/75x4waSk5Ph4OCg1TjGhqfoEhFRucTGxsLT0xPBwcHo3bu36lTcIjKZDPHx8ejUqROGDh2KRo0a4a233sKVK1dQu3ZtAE+vdF2jRg0EBQUhPDwcXbt2RYsWLSok3l69emHBggX48ssv4efnh2+//RaxsbEICQlRxbt161bUqFEDnTp1QufOnVG/fn21u7j36dMH3bp1Q2hoKGrVqoV169YZJLabN2/C398f/v7+SE9Px9y5c+Hv7493333XIONXNZwJISIinTx/bIebmxt27typ1jZw4EC1ZUdHRyxcuBALFy7UOKa3tzf279+vWi4sLMSAAQPUdlVcuXJF51hLmk0ZOXIkRo4cWeJ29erVw7Zt20pcr1AosHHjRp3jKYu3t3eFzQBVRZwJISIiIkmwCCEiIiJJcHcMERGZhOrVq2PatGmSxhASEqJ2ZhCVjkUIERGZhOrVqyM6OlrSGIoObiXtcHcMEZHEzOlARDIdhvjcsgghIpKIpeXTq58a4qqgRJUtOzsbACCXy/Ueg7tjiIgkYmVlBTs7O9y5cwdyuRwWFiX/f2FhYSHy8vKQk5NTaj9TwXyrLiEEsrOzkZGRgerVq6uKaX2wCCEikohMJoO7uztSU1Nx9erVUvsKIfDkyRPY2trqfP8SY8R8q77q1auXeRfhsrAIISKSkLW1NRo2bFjmLhmlUomkpCR06tSpXNPfxoL5Vm1yubxcMyBFWIQQEUnMwsICNjY2pfaxtLREfn4+bGxsjOJHqryYr3mo2jueiIiIyGSxCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJsAghIiIiSUhehCQlJSE8PBweHh6QyWTYunWr2vrIyEjIZDK1R4cOHcocd9OmTfD19YVCoYCvry+2bNlSQRkQERGRPiQvQh4/foyWLVti0aJFJfbp1q0b0tPTVY/4+PhSxzx69Cj69euHgQMH4vTp0xg4cCD69u2L48ePGzp8IiIi0pPkFyvr3r07unfvXmofhUKh06Vh58+fj7CwMERFRQEAoqKicPDgQcyfPx/r1q0rV7xERERkGJIXIdpITEyEq6srqlevjuDgYHz22WdwdXUtsf/Ro0cxfvx4tbauXbti/vz5JW6Tm5uL3Nxc1XJmZiaAp5fSVSqV5UtAYkXxG3se2jK3fAHzy9nc8gXML2fma9y0zUMmhBAVHIvWZDIZtmzZgl69eqna1q9fDwcHB3h5eSE1NRWffPIJ8vPz8fvvv0OhUGgcx9raGitXrkRERISqLS4uDkOGDFErNJ4VHR2NmJiYYu1xcXGws7MrX2JERERmJDs7GxEREXj48CGcnJxK7FflZ0L69eun+nezZs0QEBAALy8v7Nq1C7179y5xu+fvQiiEKPXOhFFRUZgwYYJqOTMzE56enujSpUupL6AxUCqVSEhIQFhYmFnck8Dc8gXML2dzyxcwv5yZr3Er2ptQlipfhDzP3d0dXl5euHjxYol93NzccOvWLbW2jIwM1K5du8RtFAqFxpkVuVxuEh8IwLRy0Ya55QuYX87mli9gfjkzX+OkbQ6Snx2jq3v37uHatWtwd3cvsU9gYCASEhLU2vbu3YugoKCKDo+IiIi0JPlMSFZWFi5duqRaTk1NRXJyMpydneHs7Izo6Gj06dMH7u7uuHLlCj766CPUrFkTb7zxhmqbQYMGoU6dOpg1axYAYOzYsejUqRPmzJmDnj17Ytu2bdi3bx8OHz5c6fkRERGRZpIXISdOnEBoaKhquei4jMGDB2Pp0qX4888/sXr1ajx48ADu7u4IDQ3F+vXr4ejoqNomLS0NFhb/m9QJCgrCjz/+iKlTp+KTTz5BgwYNsH79erRv377yEiMiIqJSSV6EhISEoLQTdPbs2VPmGImJicXa3nzzTbz55pvlCY2IiIgqkNEdE0JERESmgUUIERERSYJFCBEREUmCRQgRERFJgkUIERERSYJFCBEREUmCRQgRERFJgkUIERERSYJFCBEREUmCRQgRERFJgkUIERERSYJFCBEREUmCRQgRERFJgkUIERERSYJFCBEREUmCRQgRERFJgkUIERERSYJFCBEREUmCRQgRERFJgkUIERERSYJFCBEREUmCRQgRERFJgkUIERERSYJFCBEREUmCRQgRERFJgkUIERERSYJFCBEREUmi3EXI7Nmz8eDBA723T0pKQnh4ODw8PCCTybB161bVOqVSicmTJ6N58+awt7eHh4cHBg0ahJs3b5Y65sqVKyGTyYo9cnJy9I6TiIiIDKtcRcijR48wdepUpKSk6D3G48eP0bJlSyxatKjYuuzsbJw8eRKffPIJTp48ic2bN+PChQt4/fXXyxzXyckJ6enpag8bGxu94yQiIiLDstK2Y15eHuLj43Hjxg0UFBQgNzcXu3btQp06dTBs2DBERETAwcEBlpaWcHd3R/fu3WFra1vmuN27d0f37t01rqtWrRoSEhLU2r755hu0a9cOaWlpqFevXonjymQyuLm5aZseERERVTKti5BBgwZh48aNcHNzg1wuh1wuR6NGjXDgwAFMnz4dq1evRm5uLgoKCnD79m00b94cJ06cMHjADx8+hEwmQ/Xq1Uvtl5WVBS8vLxQUFKBVq1aYMWMG/P39S+yfm5uL3Nxc1XJmZiaAp7uElEqlQWKXSlH8xp6HtswtX8D8cja3fAHzy5n5Gjdt85AJIYQ2HZ2dnbF+/XqEhYWV2ffy5cto1KgR7ty5A2dnZ60CAZ7OXmzZsgW9evXSuD4nJwcvvvgimjRpgrVr15Y4zrFjx3Dp0iU0b94cmZmZWLBgAeLj43H69Gk0bNhQ4zbR0dGIiYkp1h4XFwc7OzutcyAiIjJ32dnZiIiIwMOHD+Hk5FRiP62LkAYNGuDYsWOoVauWVgH4+vpi7969qFu3rnYRo/QiRKlU4l//+hfS0tKQmJhYalLPKywsROvWrdGpUycsXLhQYx9NMyGenp64e/euTs9VFSmVSiQkJCAsLAxyuVzqcCqcueULmF/O5pYvYH45M1/jlpmZiZo1a5ZZhGi9O+by5cs6BXD27Fmd+pdGqVSib9++SE1Nxf79+3UuCiwsLNC2bVtcvHixxD4KhQIKhaJYe9GuJ1NgSrlow9zyBcwvZ3PLFzC/nJmvcdI2hyp/nZCiAuTixYvYt28fXFxcdB5DCIHk5GS4u7tXQIRERESkD61nQipKVlYWLl26pFpOTU1FcnIynJ2d4eHhgTfffBMnT57Ezp07UVBQgFu3bgF4eoyKtbU1gKcHzdapUwezZs0CAMTExKBDhw5o2LAhMjMzsXDhQiQnJ2Px4sWVnyARERFppHMRsmTJEmzevBnOzs4YMWIEXn75ZdW6u3fvol27dvj777+1Hu/EiRMIDQ1VLU+YMAEAMHjwYERHR2P79u0AgFatWqltd+DAAYSEhAAA0tLSYGHxv0mdBw8eYPjw4bh16xaqVasGf39/JCUloV27drqmS0RERBVEpyJk4cKFiIqKwpAhQ/Dw4UP06NED06ZNQ1RUFACgoKAAV69e1SmAkJAQlHZsrDbHzSYmJqotz5s3D/PmzdMpDiIiIqpcOhUh3377Lb7//ntEREQAAEaNGoVevXrhyZMnmD59eoUESERERKZJpyIkNTUVQUFBquXAwEDs378fr7zyCpRKJcaNG2fo+IiIiMhE6VSE1KxZE9euXYO3t7eqzc/PD/v378fLL7+MGzduGDo+IiIiMlE6naL74osvYtOmTcXafX198fPPP2P37t0GC4yIiIhMm04zIVOmTMHvv/+ucZ2fnx8OHDiAjRs3GiQwIiIiMm06FSHHjh1DeHh4iev9/Pzg5+dX7qCIiIjI9Om0O2bdunXw8fFB+/bt8fnnn+PMmTMVFRcRERGZOJ2KkAMHDiA9PR3vv/8+kpOTERQUhAYNGmDChAlITExEYWFhRcVJREREJkbne8fUqFEDAwYMwIYNG3Dnzh0sXrwYOTk5GDhwIGrVqoVBgwZh48aNePz4cUXES0RERCaiXDews7a2Rrdu3bBkyRJcu3YNe/bsgbe3N2bMmIGvv/7aUDESERGRCTLoDewCAgIQEBCA6dOnQ6lUGnJoIiIiMjE6z4SkpKQgNjYW586dAwCcO3cOI0eOxNChQ7F//35VP7lcbrgoiYiIyOToNBOye/du9OzZEw4ODsjOzsaWLVswaNAgtGzZEkIIdO3aFXv27FG7sy4RERGRJjrNhEyfPh0ffvgh7t27h9jYWERERGDYsGFISEjAvn37MGnSJMyePbuiYiUiIiITolMRcubMGURGRgIA+vbti0ePHqFPnz6q9f3798cff/xh0ACJiIjINOl9doyFhQVsbGxQvXp1VZujoyMePnxoiLiIiIjIxOlUhHh7e+PSpUuq5aNHj6JevXqq5WvXrsHd3d1w0REREZHJ0unA1JEjR6KgoEC13KxZM7X1P/30Ew9KJSIiIq3oVISMGDGi1PWfffZZuYIhIiIi81GuK6YSERER6UvrIiQpKQn5+flaD/zLL78gNzdXr6CIiIjI9GldhHTu3Bnp6elaD/zKK6/g9u3begVFREREpk/rY0Lq1auHTz75BOHh4ZDL5ZDL5WjcuDHq16+P27dv4/Tp08jJyUFhYSGOHTsGIQRq165dkbETERGREdO6CImJicGUKVOwZs0aCCEAADKZDLNnz0Z0dDSePHkC4On1Q9zc3DBr1iwoFIqKiZqIiIiMnta7Y95++21cu3YNBQUFKCwsxJMnT/D9998jKioK//73v5GZmYnCwkLk5+fj+vXrmDBhQkXGTUREREZO77NjFAoFhg4dCktLS0RGRsLBwcGQcREREZGJ0+k6IZpcunQJderUMUQsREREZEbKfZ0QT09PWFjoP0xSUhLCw8Ph4eEBmUyGrVu3qq0XQiA6OhoeHh6wtbVFSEgIzpw5U+a4mzZtgq+vLxQKBXx9fbFlyxa9YyQiIiLDk/xiZY8fP0bLli2xaNEijeu/+OILfP3111i0aBF+++03uLm5ISwsDI8ePSpxzKNHj6Jfv34YOHAgTp8+jYEDB6Jv3744fvx4RaVBREREOtKrCDl8+LDBAujevTtmzpyJ3r17F1snhMD8+fPx8ccfo3fv3mjWrBlWrVqF7OxsxMXFlTjm/PnzERYWhqioKDRp0gRRUVF45ZVXMH/+fIPFTUREROWj8zEhO3fuxNChQ5GRkVER8ahJTU3FrVu30KVLF1WbQqFAcHAwjhw5gvfee0/jdkePHsX48ePV2rp27VpqEZKbm6t2hdfMzEwAgFKphFKpLEcW0iuK39jz0Ja55QuYX87mli9gfjkzX+OmbR46FSFr1qzB6NGjsXnzZr2C0tWtW7cAoNhFz2rXro2rV6+Wup2mbYrG02TWrFmIiYkp1r53717Y2dnpEnaVlZCQIHUIlcrc8gXML2dzyxcwv5yZr3HKzs7Wqp/WRcj8+fMRFRWFDRs2oHPnznoHpg+ZTKa2LIQo1lbebaKiotSubZKZmQlPT0906dIFTk5OekRddSiVSiQkJCAsLAxyuVzqcCqcueULmF/O5pYvYH45M1/jVrQ3oSxaFyETJkzAN998g/DwcL2D0pWbmxuApzMb7u7uqvaMjIxSLwnv5uZWbNajrG0UCoXGK7wWXaLeFJhSLtowt3wB88vZ3PIFzC9n5muctM1B6wNTg4KCsHjxYty7d0/voHTl4+MDNzc3tempvLw8HDx4EEFBQSVuFxgYWGxKa+/evaVuQ0RERJVL6yJk37598PHxQVhYmNbTLNrIyspCcnIykpOTATw9GDU5ORlpaWmQyWQYN24cPv/8c2zZsgV//fUXIiMjYWdnh4iICNUYgwYNQlRUlGp57Nix2Lt3L+bMmYNz585hzpw52LdvH8aNG2ewuImIiKh8tC5CbGxssH37dvj6+qJr164GC+DEiRPw9/eHv78/gKe7ffz9/fHpp58CACZNmoRx48Zh1KhRCAgIwI0bN7B37144OjqqxkhLS0N6erpqOSgoCD/++CNiY2PRokULrFy5EuvXr0f79u0NFjcRERGVj05nx1haWmLt2rUYO3aswQIICQlR3ZVXE5lMhujoaERHR5fYJzExsVjbm2++iTfffNMAERIREVFF0OtiZQsWLDB0HERERGRmJL9sOxEREZknve+i+88//2D58uVISUmBTCZDkyZNMHToUDg7OxsyPiIiIjJRes2EHDx4ED4+Pli4cCH++ecf3L9/H9988w18fHxw8OBBQ8dIREREJkivmZDRo0ejb9++WLp0KSwtLQEABQUFGDVqFEaPHo2//vrLoEESERGR6dFrJuTy5cv44IMPVAUI8PTMmQkTJuDy5csGC46IiIhMl15FSOvWrZGSklKsPSUlBa1atSpvTERERGQG9NodM2bMGIwdOxaXLl1Chw4dAADHjh3D4sWLMXv2bPzxxx+qvi1atDBMpERERGRS9CpC+vfvD+Dp1Uw1rZPJZKq71hYUFJQvQiIiIjJJehUhqampho6DiIiIzIxeRYiXl5eh4yAiIiIzwyumEhERkSRYhBAREZEkWIQQERGRJHQqQi5cuFBRcRAREZGZ0akI8ff3R9OmTTF58mQcOXKkomIiIiIiM6BTEXLv3j188cUXuHfvHnr37o3atWvjnXfewfbt25GTk1NRMRIREZEJ0qkIsbGxQXh4OP7zn/8gPT0dW7ZsQa1atTBlyhS4uLigZ8+eWLFiBTIyMioqXiIiIjIReh+YKpPJEBQUhNmzZ+Ps2bNITk5Gp06dsHLlSnh6emLx4sWGjJOIiIhMjF4XK9OkYcOG+OCDD/DBBx/g3r17uH//vqGGJiIiIhNksCLkWS4uLnBxcamIoYmIiMhE8DohREREJAkWIURERCQJFiFEREQkCRYhREREJAmtD0ydPn26Xk8QEhKCTp066bUtERERmS6ti5DU1FS9nqBVq1Z6bUdERESmTesiJDY2tiLjKJG3tzeuXr1arH3UqFEaL4iWmJiI0NDQYu0pKSlo0qRJhcRIREREutPrmJCkpCTk5+cXa8/Pz0dSUlK5g3rWb7/9hvT0dNUjISEBAPCvf/2r1O3Onz+vtl3Dhg0NGhcRERGVj14XKwsNDUV6ejpcXV3V2h8+fIjQ0FAUFBQYJDgAqFWrltry7Nmz0aBBAwQHB5e6naurK6pXr6718+Tm5iI3N1e1nJmZCQBQKpVQKpXaB1wFFcVv7Hloy9zyBcwvZ3PLFzC/nJmvcdM2D5kQQug6uIWFBW7fvl2sQLhw4QICAgJUP+CGlpeXBw8PD0yYMAEfffSRxj5Fu2O8vb2Rk5MDX19fTJ06VeMummdFR0cjJiamWHtcXBzs7OwMEj8REZE5yM7ORkREBB4+fAgnJ6cS++lUhPTu3RsAsG3bNnTr1g0KhUK1rqCgAH/88QcaN26M3bt3lyP0km3YsAERERFIS0uDh4eHxj7nz59HUlIS2rRpg9zcXKxZswbLli1DYmJiqWfpaJoJ8fT0xN27d0t9AY2BUqlEQkICwsLCIJfLpQ6nwplbvoD55Wxu+QLmlzPzNW6ZmZmoWbNmmUWITrtjqlWrBgAQQsDR0RG2traqddbW1ujQoQOGDRumZ8hlW758Obp3715iAQIAjRs3RuPGjVXLgYGBuHbtGubOnVtqEaJQKNSKqiJyudwkPhCAaeWiDXPLFzC/nM0tX8D8cma+xknbHHQqQorOkPH29sbEiRNhb2+ve2R6unr1Kvbt24fNmzfrvG2HDh2wdu3aCoiKiIiI9KXXganTpk0DANy5cwfnz5+HTCZDo0aNih0jYkixsbFwdXXFq6++qvO2p06dgru7ewVERURERPrSqwjJzs7Gv//9b6xevRqFhYUAAEtLSwwaNAjffPONwQ/kLCwsRGxsLAYPHgwrK/WQo6KicOPGDaxevRoAMH/+fHh7e8PPzw95eXlYu3YtNm3ahE2bNhk0JiIiIiofva4TMn78eBw8eBA7duzAgwcP8ODBA2zbtg0HDx7EBx98YOgYsW/fPqSlpWHo0KHF1qWnpyMtLU21nJeXh4kTJ6JFixZ46aWXcPjwYezatUt1UC0RERFVDXrNhGzatAkbN25ESEiIqq1Hjx6wtbVF3759sXTpUkPFBwDo0qULSjqJZ+XKlWrLkyZNwqRJkwz6/ERERGR4es2EZGdno3bt2sXaXV1dkZ2dXe6giIiIyPTpVYQEBgZi2rRpyMnJUbU9efIEMTExCAwMNFhwREREZLr02h2zYMECdOvWDXXr1kXLli0hk8mQnJwMGxsb7Nmzx9AxEhERkQnSqwhp1qwZLl68iLVr1+LcuXMQQuCtt97C22+/rXYBMyIiIqKS6FWEAICtrW2FXh2ViIiITJveRcjly5cxf/58pKSkQCaToWnTphg7diwaNGhgyPiIiIjIROl1YOqePXvg6+uLX3/9FS1atECzZs1w/Phx+Pn5ISEhwdAxEhERkQnSayZkypQpGD9+PGbPnl2sffLkyQgLCzNIcERERGS69JoJSUlJwTvvvFOsfejQoTh79my5gyIiIiLTp1cRUqtWLSQnJxdrT05Ohqura3ljIiIiIjOg1+6YYcOGYfjw4fj7778RFBQEmUyGw4cPY86cORVy7xgiIiIyPXoVIZ988gkcHR3x1VdfISoqCgDg4eGB6OhojBkzxqABEhERkWnSuQjJz8/HDz/8gP79+2P8+PF49OgRAMDR0dHgwREREZHp0vmYECsrK4wcORK5ubkAnhYfLECIiIhIV3odmNq+fXucOnXK0LEQERGRGdHrmJBRo0bhgw8+wPXr19GmTRvY29urrW/RooVBgiMiIiLTpVcR0q9fPwBQOwhVJpNBCAGZTIaCggLDREdEREQmS68iJDU11dBxEBERkZnRqwjx8vIydBxERERkZvQ6MJWIiIiovLSeCfHx8YFMJtP5CcaNG8cLmBEREVExWhchK1eu1OsJvL299dqOiIiITJvWRUhwcHBFxkFERERmhseEEBERkSRYhBAREZEkWIQQERGRJKp8ERIdHQ2ZTKb2cHNzK3WbgwcPok2bNrCxsUH9+vWxbNmySoqWiIiItKXXxcoqm5+fH/bt26datrS0LLFvamoqevTogWHDhmHt2rX45ZdfMGrUKNSqVQt9+vSpjHCJiIhIC0ZRhFhZWZU5+1Fk2bJlqFevHubPnw8AaNq0KU6cOIG5c+eyCCEiIqpCjKIIuXjxIjw8PKBQKNC+fXt8/vnnqF+/vsa+R48eRZcuXdTaunbtiuXLl0OpVEIul2vcLjc3F7m5uarlzMxMAIBSqYRSqTRQJtIoit/Y89CWueULmF/O5pYvYH45M1/jpm0eMiGEqOBYyuWnn35CdnY2GjVqhNu3b2PmzJk4d+4czpw5AxcXl2L9GzVqhMjISHz00UeqtiNHjqBjx464efMm3N3dNT5PdHQ0YmJiirXHxcXBzs7OcAkRERGZuOzsbERERODhw4dwcnIqsV+Vnwnp3r276t/NmzdHYGAgGjRogFWrVmHChAkat3n+8vJFdVZpl52PiopSGy8zMxOenp7o0qVLqS+gMVAqlUhISEBYWFiJM0GmxNzyBcwvZ3PLFzC/nJmvcSvam1CWKl+EPM/e3h7NmzfHxYsXNa53c3PDrVu31NoyMjJgZWWlceakiEKhgEKhKNYul8tN4gMBmFYu2jC3fAHzy9nc8gXML2fma5y0zaHKn6L7vNzcXKSkpJS4WyUwMBAJCQlqbXv37kVAQIBJvLFERESmosoXIRMnTsTBgweRmpqK48eP480330RmZiYGDx4M4OlulEGDBqn6jxgxAlevXsWECROQkpKCFStWYPny5Zg4caJUKRAREZEGVX53zPXr19G/f3/cvXsXtWrVQocOHXDs2DF4eXkBANLT05GWlqbq7+Pjg/j4eIwfPx6LFy+Gh4cHFi5cyNNziYiIqpgqX4T8+OOPpa5fuXJlsbbg4GCcPHmygiIiIiIiQ6jyu2OIiIjINLEIISIiIkmwCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJVPkiZNasWWjbti0cHR3h6uqKXr164fz586Vuk5iYCJlMVuxx7ty5SoqaiIiIylLli5CDBw9i9OjROHbsGBISEpCfn48uXbrg8ePHZW57/vx5pKenqx4NGzashIiJiIhIG1ZSB1CW3bt3qy3HxsbC1dUVv//+Ozp16lTqtq6urqhevXoFRkdERET6qvJFyPMePnwIAHB2di6zr7+/P3JycuDr64upU6ciNDS0xL65ubnIzc1VLWdmZgIAlEollEplOaOWVlH8xp6HtswtX8D8cja3fAHzy5n5Gjdt85AJIUQFx2IwQgj07NkT//zzDw4dOlRiv/PnzyMpKQlt2rRBbm4u1qxZg2XLliExMbHE2ZPo6GjExMQUa4+Li4OdnZ3BciAiIjJ12dnZiIiIwMOHD+Hk5FRiP6MqQkaPHo1du3bh8OHDqFu3rk7bhoeHQyaTYfv27RrXa5oJ8fT0xN27d0t9AY2BUqlEQkICwsLCIJfLpQ6nwplbvoD55Wxu+QLmlzPzNW6ZmZmoWbNmmUWI0eyOef/997F9+3YkJSXpXIAAQIcOHbB27doS1ysUCigUimLtcrncJD4QgGnlog1zyxcwv5zNLV/A/HJmvsZJ2xyqfBEihMD777+PLVu2IDExET4+PnqNc+rUKbi7uxs4OiIiItJXlS9CRo8ejbi4OGzbtg2Ojo64desWAKBatWqwtbUFAERFReHGjRtYvXo1AGD+/Pnw9vaGn58f8vLysHbtWmzatAmbNm2SLA8iIiJSV+WLkKVLlwIAQkJC1NpjY2MRGRkJAEhPT0daWppqXV5eHiZOnIgbN27A1tYWfn5+2LVrF3r06FFZYRMREVEZqnwRos1xsytXrlRbnjRpEiZNmlRBEREREZEhVPkrphIREZFpYhFCREREkmARQkRERJJgEUJERESSYBFCREREkmARQkRERJJgEUJERESSYBFCREREkmARQkRERJJgEUJERESSYBFCREREkmARQkRERJJgEUJERESSYBFCREREkrCSOoCqLjsvH1Z5+cXaLWQy2Mgt1fqVpDx9n+QVQEBo7CuDDLbWZfdVKvORV6DelqMsQKHQPC4A2FlbSd7XVm4JmUwGAMjNL0BBobZ9C5Fb8PR1lgtZsb42VpawsHjanpdfiPzCwhLH1aWvwsoSlnr0VRYUQllQcl9rSwtYWVqU2lepzEduAZBfUAi5/GlbfkEh8koZV25pAfn/j6tL34JCgdz8ghL7WllYwNpK976FhQI5OvQt7T22tJBBYfX0b0MIgSfKksfVpW9l/d1r6lv0HucoCyAvepNhmO8ITX2rwneEsrDk9xgoz3dE6X2l+I4oen+L8jX0d4SmvhX5HVHa5/1ZLELK0O6zn2GhsCvWHtq4FmKHtFMtt5mxr8Qvr/Y+zlj/XqBq+cU5B3D/cZ7Gvi3qVsP2f7+oWu789UHcePBEY9+Grg5ImBCsWn590WFczMjS2NdZYYle4f9b7vvtUfxx/aHmvvbWOPlJmGp58IpfcTz1vsa+tnJLpMzoploeufZ3HDh/R2NfALgy+1XVvydsSEb8n7dK7Ht2elfVF9JHm//CppPXS+z7+9TOcHFQAABm/XQeP/xqhUm/7tfY99CkUHg6P31P5+49j++S/i5x3L3jO6FRbUcAwOIDl7Dg54sl9t02uiNaelYHAMT+kopZP50rse+6YR0Q2MDl6b9/TcOn286U2HdFZABeblIbALD11A18uPGPEnpawcYnA6/7ewIA9py5jdFxJ0sc98s3W+BfAU/7Jl28g6ErT5TYd3pPPwwK9AYA/Jp6H/2/P1Zi36juTfBecAMAwF83HqLn4l9K7Dv2lYYYH9YIAHDpTha6zEsqse/wTvXxUY+mAICbD3MwqZT3eGAHL8zo1QwAcP9xHtrM3FfiuH1a18VXfVsCAJ4oC+D76Z4S+/Zo7oYlb7dRLZfWt2K+I6yw5sZv2PH+S6oWQ31H1Klui1+mvKxargrfEWsvWmDicc3vMaD/d8TMnSlYc+xqiX2l+47432e6Yr4jgMURrfFqC3cAFfsd0W9Rye/bs7g7hoiIiCQhE6KUeTEzlpmZiWrVqiH9zj04OTkVW29cu2OU2LtnL3qF91BN41aFqdaK2h2T9SQX8T/tRteuXdSmrYuY5u4YJfbs2YvwHt1ga/P0//ZMeXdMbm4etu36qcT32DR3xzx9j7t36wpHOxtVu6nujlEqldi2Mx5hXTS/x4Cp7Y55+v4WfaaNfXfMnfv/wL2WCx4+fKjxN7QId8eUwc7aSu0PqLR+uoyprWe/FPTtq5QJPL/q2S+8slSFvkU/Etr1tYDC8unrLJeX/lpbW1nAWssJwYrq++wfr759lTIBhSVUXy7A039baTmuLn0tLWRaf4Z16WuhY19t32OZTPtxdekLVNzfvaa+Re/x8383hviO0KQq/N3LLbR7jwFdvyO071tZ3xFF76+mfA3xHaFJVfiO4O4YIiIikgSLECIiIpIEixAiIiKSBIsQIiIikgSLECIiIpIEixAiIiKSBIsQIjIq59IzMWrt7wCAUWt/x7n0TIkjIiJ9sQghIqMxd895dFtwCEmX7gIAki7dRbcFh/D13vMSR0ZE+jCaImTJkiXw8fGBjY0N2rRpg0OHDpXa/+DBg2jTpg1sbGxQv359LFu2rJIiJaKKcC49E4sOXNK4buH+S5wRITJCRlGErF+/HuPGjcPHH3+MU6dO4aWXXkL37t2RlpamsX9qaip69OiBl156CadOncJHH32EMWPGYNOmTZUcOREZypzdJd8QEAC+2FP6eiKqeoyiCPn666/xzjvv4N1330XTpk0xf/58eHp6YunSpRr7L1u2DPXq1cP8+fPRtGlTvPvuuxg6dCjmzp1byZETkaFcvfe41PVX7pa+noiqnip/75i8vDz8/vvvmDJlilp7ly5dcOTIEY3bHD16FF26dFFr69q1K5YvXw6lUqnxZki5ubnIzc1VLWdmPp3aVSqVUCqV5U1DUkXxG3se2jK3fAHzyFlhASgsxf//W/2/RetNOX9zeI+fxXyNm7Z5VPki5O7duygoKEDt2rXV2mvXro1bt25p3ObWrVsa++fn5+Pu3btwd3cvts2sWbMQExNTrH3v3r2ws7MrRwZVR0JCgtQhVCpzyxcw7ZxHNADQQL1tRsCzd/XMRHx8fGWGJAlTfo81Yb7GKTs7W6t+Vb4IKVJ0C+YiQohibWX119ReJCoqChMmTFAtZ2ZmwtPTE126dCn1NsTGQKlUIiEhAWFhYSXeEtuUmFu+gHnkHPtLKr5OuACBpzMgMwIK8ckJC+QWyiAD8EGXRogM8pE6zApjDu/xs5ivcSvam1CWKl+E1KxZE5aWlsVmPTIyMorNdhRxc3PT2N/KygouLi4at1EoFFAoFMXa5XK5SXwgANPKRRvmli9g2jm/0cYLc/ddRl7+/2Y/cgtlyC2QwdrKAm+08TLZ3J9lyu+xJszXOGmbQ5U/MNXa2hpt2rQpNkWVkJCAoKAgjdsEBgYW6793714EBASYxJtLZI5qOSqw9O3WsLaygMX/T2hayABrKwssfbs1ajoU/58IIqraqvxMCABMmDABAwcOREBAAAIDA/Hdd98hLS0NI0aMAPB0V8qNGzewevVqAMCIESOwaNEiTJgwAcOGDcPRo0exfPlyrFu3Tso0iKicXmlaG79MfhlbT14FHqRgQlgjvNHGiwUIkZEyiiKkX79+uHfvHqZPn4709HQ0a9YM8fHx8PLyAgCkp6erXTPEx8cH8fHxGD9+PBYvXgwPDw8sXLgQffr0kSoFIjKQWo4KRAb5ID4+BZFBPpzdJDJiRlGEAMCoUaMwatQojetWrlxZrC04OBgnT56s4KiIiIhIX1X+mBAiIiIyTSxCiIiISBIsQoiIiEgSLEKIiIhIEixCiIiISBIsQoiIiEgSRnOKbmUruteMtte/r8qUSiWys7ORmZlpFtdUMLd8AfPL2dzyBcwvZ+Zr3Ip+O4t+S0vCIqQEjx49AgB4enpKHAkREZFxevToEapVq1biepkoq0wxU4WFhbh58yYcHR1LvVuvMSi6I/C1a9eM/o7A2jC3fAHzy9nc8gXML2fma9yEEHj06BE8PDxgYVHykR+cCSmBhYUF6tatK3UYBuXk5GQSH25tmVu+gPnlbG75AuaXM/M1XqXNgBThgalEREQkCRYhREREJAkWIWZAoVBg2rRpUCjM43bn5pYvYH45m1u+gPnlzHzNAw9MJSIiIklwJoSIiIgkwSKEiIiIJMEihIiIiCTBIoSIiIgkwSLEBNy4cQMDBgyAi4sL7Ozs0KpVK/z+++8l9o+MjIRMJiv28PPzq8So9adrvgDwww8/oGXLlrCzs4O7uzuGDBmCe/fuVVLE5adPzosXL0bTpk1ha2uLxo0bY/Xq1ZUUbfl4e3tr/HyOHj26xG0OHjyINm3awMbGBvXr18eyZcsqMeLy0zXn9PR0REREoHHjxrCwsMC4ceMqN+By0jXfzZs3IywsDLVq1YKTkxMCAwOxZ8+eSo66fHTN+fDhw+jYsSNcXFxga2uLJk2aYN68eZUcdSUQZNTu378vvLy8RGRkpDh+/LhITU0V+/btE5cuXSpxmwcPHoj09HTV49q1a8LZ2VlMmzat8gLXkz75Hjp0SFhYWIgFCxaIv//+Wxw6dEj4+fmJXr16VWLk+tMn5yVLlghHR0fx448/isuXL4t169YJBwcHsX379kqMXD8ZGRlqn8+EhAQBQBw4cEBj/7///lvY2dmJsWPHirNnz4rvv/9eyOVysXHjxsoNvBx0zTk1NVWMGTNGrFq1SrRq1UqMHTu2UuMtL13zHTt2rJgzZ4749ddfxYULF0RUVJSQy+Xi5MmTlRt4Oeia88mTJ0VcXJz466+/RGpqqlizZo2ws7MT3377beUGXsFYhBi5yZMnixdffLFcY2zZskXIZDJx5coVA0VVcfTJ98svvxT169dXa1u4cKGoW7euIUOrMPrkHBgYKCZOnKjWNnbsWNGxY0dDhlYpxo4dKxo0aCAKCws1rp80aZJo0qSJWtt7770nOnToUBnhVYiycn5WcHCw0RUhz9Ml3yK+vr4iJiamAqOqWPrk/MYbb4gBAwZUYFSVj7tjjNz27dsREBCAf/3rX3B1dYW/vz++//57ncZYvnw5OnfuDC8vrwqK0nD0yTcoKAjXr19HfHw8hBC4ffs2Nm7ciFdffbWSoi4ffXLOzc2FjY2NWputrS1+/fVXKJXKigzXoPLy8rB27VoMHTq0xBtJHj16FF26dFFr69q1K06cOGFUuRbRJmdTok++hYWFePToEZydnSs4uoqhT86nTp3CkSNHEBwcXMHRVTKpqyAqH4VCIRQKhYiKihInT54Uy5YtEzY2NmLVqlVabX/z5k1haWkp1q9fX8GRGoa++f73v/8VDg4OwsrKSgAQr7/+usjLy6ukqMtHn5yjoqKEm5ubOHHihCgsLBS//fabcHV1FQDEzZs3KzH68lm/fr2wtLQUN27cKLFPw4YNxWeffabW9ssvvxhdrkW0yflZxj4Tomu+QgjxxRdfCGdnZ3H79u0KjKzi6JJznTp1hLW1tbCwsBDTp0+vhOgqF4sQIyeXy0VgYKBa2/vvv6/1VPTnn38uXFxcRG5ubkWEZ3D65HvmzBnh7u4uvvjiC3H69Gmxe/du0bx5czF06NCKDtcg9Mk5OztbDBkyRFhZWQlLS0vh4eEhJk2aJAAY1Rd3ly5dxGuvvVZqn4YNG4rPP/9cre3w4cMCgEhPT6/I8CqENjk/y9iLEF3zjYuLE3Z2diIhIaECo6pYuuT8999/iz/++EN89913wtnZWcTFxVVwdJWLu2OMnLu7O3x9fdXamjZtirS0tDK3FUJgxYoVGDhwIKytrSsqRIPSJ99Zs2ahY8eO+PDDD9GiRQt07doVS5YswYoVK5Cenl7RIZebPjnb2tpixYoVyM7OxpUrV5CWlgZvb284OjqiZs2aFR2yQVy9ehX79u3Du+++W2o/Nzc33Lp1S60tIyMDVlZWcHFxqcgQDU7bnE2FrvmuX78e77zzDjZs2IDOnTtXcHQVQ9ecfXx80Lx5cwwbNgzjx49HdHR0xQZYyViEGLmOHTvi/Pnzam0XLlzQ6viOgwcP4tKlS3jnnXcqKjyD0yff7OxsWFiof9QtLS0BPC3EqrryvMdyuRx169aFpaUlfvzxR7z22mvFXouqKjY2Fq6urmUeuxMYGIiEhAS1tr179yIgIAByubwiQzQ4bXM2Fbrku27dOkRGRiIuLs6oX5/yvMdCCOTm5lZAVBKSeCaGyunXX38VVlZW4rPPPhMXL14UP/zwg7CzsxNr165V9ZkyZYoYOHBgsW0HDBgg2rdvX5nhlps++cbGxgorKyuxZMkScfnyZXH48GEREBAg2rVrJ0UKOtMn5/Pnz4s1a9aICxcuiOPHj4t+/foJZ2dnkZqaKkEGuisoKBD16tUTkydPLrbu+VyLTtEdP368OHv2rFi+fLnRnaIrhG45CyHEqVOnxKlTp0SbNm1ERESEOHXqlDhz5kxlhVtuuuQbFxcnrKysxOLFi9VOc33w4EFlhlxuuuS8aNEisX37dnHhwgVx4cIFsWLFCuHk5CQ+/vjjygy5wrEIMQE7duwQzZo1EwqFQjRp0kR89913ausHDx4sgoOD1doePHggbG1ti/U1Bvrku3DhQuHr6ytsbW2Fu7u7ePvtt8X169crMery0TXns2fPilatWglbW1vh5OQkevbsKc6dO1fJUetvz549AoA4f/58sXWa3t/ExETh7+8vrK2thbe3t1i6dGklRWo4uuYMoNjDy8urcoI1AF3yDQ4O1pjv4MGDKy9gA9Al54ULFwo/Pz9hZ2cnnJychL+/v1iyZIkoKCioxIgrnkwII5iPJiIiIpNjHDuHiYiIyOSwCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJsAghIiIiSbAIISIiIkmwCCEiIiJJWEkdABGRtkJCQtCsWTMAwNq1a2FpaYmRI0dixowZkMlkEkdHRLriTAgRGZVVq1bBysoKx48fx8KFCzFv3jz85z//kTosItID76JLREYjJCQEGRkZOHPmjGrmY8qUKdi+fTvOnj0rcXREpCvOhBCRUenQoYParpfAwEBcvHgRBQUFEkZFRPpgEUJERESSYBFCREbl2LFjxZYbNmwIS0tLiSIiIn2xCCEio3Lt2jVMmDAB58+fx7p16/DNN99g7NixUodFRHrgKbpEZFQGDRqEJ0+eoF27drC0tMT777+P4cOHSx0WEemBRQgRGRW5XI758+dj6dKlUodCROXE3TFEREQkCRYhREREJAlerIyIiIgkwZkQIiIikgSLECIiIpIEixAiIiKSBIsQIiIikgSLECIiIpIEixAiIiKSBIsQIiIikgSLECIiIpLE/wFJorFvBJ4NUgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "execution_count": 21,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import re\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# read the text we just wrote\n",
    "rows = []\n",
    "for ln in open(\"root_moduli.txt\"):\n",
    "    ln = ln.strip()\n",
    "    if not ln: continue\n",
    "    m = re.match(r\"p=(\\d+): \\[(.*)\\]\", ln)\n",
    "    if not m: continue\n",
    "    p = int(m.group(1))\n",
    "    vals = [float(x.strip(\" '\")) for x in m.group(2).split(\",\")]\n",
    "    for v in vals:\n",
    "        rows.append((p, v))\n",
    "\n",
    "# scatter |root|/p^{3/2} vs p\n",
    "ps  = [p for p,_ in rows]\n",
    "mods= [v for _,v in rows]\n",
    "\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.scatter(ps, mods, s=24, label=\"normalized |roots|\")\n",
    "plt.axhline(1.0, ls=\"--\", label=\"ideal |root|=1\")\n",
    "plt.title(\"Normalized |roots| vs prime p\")\n",
    "plt.xlabel(\"p\"); plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.grid(True); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "433369",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✅ Rebuilt OA_Lpoly.csv with 10 rows\n",
      "\n",
      "OA_Lpoly head:\n",
      "    p  a1    a2              a1_norm\n",
      "0   7  -5  -129   -0.269974623578019\n",
      "1  11  -3  -636  -0.0822303667030264\n",
      "2  13  -7 -1029   -0.149342360522177\n",
      "3  17   4 -2449   0.0570672058909019\n",
      "4  19  10 -3410    0.120745123089769\n",
      "\n",
      "OA_Lpoly full head:\n",
      "    p  a1    a2              a1_norm\n",
      "0   7  -5  -129   -0.269974623578019\n",
      "1  11  -3  -636  -0.0822303667030264\n",
      "2  13  -7 -1029   -0.149342360522177\n",
      "3  17   4 -2449   0.0570672058909019\n",
      "4  19  10 -3410    0.120745123089769\n",
      "\n",
      "OA_Lpoly tail:\n",
      "    p  a1     a2             a1_norm\n",
      "5  23  10  -6054  0.0906584408943803\n",
      "6  29   4 -12167  0.0256131500933865\n",
      "7  31   9 -14855  0.0521434747819669\n",
      "8  37  12 -25260  0.0533185904774132\n",
      "9  41  22 -34264  0.0838005551597398\n"
     ]
    }
   ],
   "source": [
    "# === Step 5: rebuild OA_Lpoly.csv using all primes in OA_counts.csv ===\n",
    "Ldf = rebuild_Lpoly_from_counts()\n",
    "print(\"\\nOA_Lpoly full head:\")\n",
    "print(Ldf.head())\n",
    "print(\"\\nOA_Lpoly tail:\")\n",
    "print(Ldf.tail())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "100c33",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✅ Saved normalized |roots| for all primes.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import re\n",
    "\n",
    "# Reload the full L-poly data\n",
    "Ldf = pd.read_csv(\"OA_Lpoly.csv\")\n",
    "\n",
    "# Recompute normalized |roots| for each prime\n",
    "def root_moduli_row(p, a1, a2):\n",
    "    coeffs = [1, -int(a1), int(a2), -int(p)*int(a1), int(p)**3]\n",
    "    roots = np.roots(coeffs)\n",
    "    R = p ** 1.5\n",
    "    return [abs(r) / R for r in roots]\n",
    "\n",
    "lines = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = int(r[\"p\"]), int(r[\"a1\"]), int(r[\"a2\"])\n",
    "    mods = [f\"{m:.4f}\" for m in root_moduli_row(p, a1, a2)]\n",
    "    line = f\"p={p}: {mods}\"\n",
    "    lines.append(line)\n",
    "\n",
    "# Save to file\n",
    "with open(\"root_moduli.txt\", \"w\") as f:\n",
    "    f.write(\"\\n\".join(lines))\n",
    "print(\"✅ Saved normalized |roots| for all primes.\")\n",
    "\n",
    "# Parse for plotting\n",
    "data = []\n",
    "for ln in open(\"root_moduli.txt\"):\n",
    "    m = re.match(r\"p=(\\d+): \\[(.*)\\]\", ln)\n",
    "    if not m: \n",
    "        continue\n",
    "    p = int(m.group(1))\n",
    "    vals = [float(x.strip(\" '\")) for x in m.group(2).split(\",\")]\n",
    "    for v in vals:\n",
    "        data.append((p, v))\n",
    "\n",
    "# Build arrays\n",
    "ps = [p for p,_ in data]\n",
    "mods = [v for _,v in data]\n",
    "\n",
    "plt.figure(figsize=(7,4))\n",
    "plt.scatter(ps, mods, color=\"blue\", s=24, label=\"normalized |roots|\")\n",
    "plt.axhline(1.0, ls=\"--\", color=\"orange\", label=\"ideal |root|=1\")\n",
    "plt.title(\"Normalized |roots| across all primes\")\n",
    "plt.xlabel(\"prime p\")\n",
    "plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.legend(); plt.grid(True); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "0893ca",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean deviation from ideal purity: 0.6408\n",
      "Maximum deviation: 0.9946\n",
      "Purity score (1.0 = perfect alignment): 0.3592\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Compute deviation of normalized roots from ideal |root|=1\n",
    "deviations = [abs(v - 1.0) for v in mods]\n",
    "mean_dev = np.mean(deviations)\n",
    "max_dev = np.max(deviations)\n",
    "purity_score = 1 - mean_dev  # 1.0 = perfect purity\n",
    "\n",
    "print(f\"Mean deviation from ideal purity: {mean_dev:.4f}\")\n",
    "print(f\"Maximum deviation: {max_dev:.4f}\")\n",
    "print(f\"Purity score (1.0 = perfect alignment): {purity_score:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "995302",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p= 7  geom-mean=0.2324  mean|v-1|=0.6453\n",
      "p=11  geom-mean=0.1656  mean|v-1|=0.6345\n",
      "p=13  geom-mean=0.1460  mean|v-1|=0.6406\n",
      "p=17  geom-mean=0.1194  mean|v-1|=0.6368\n",
      "p=19  geom-mean=0.1099  mean|v-1|=0.6377\n",
      "p=23  geom-mean=0.0952  mean|v-1|=0.6402\n",
      "p=29  geom-mean=0.0799  mean|v-1|=0.6423\n",
      "p=31  geom-mean=0.0761  mean|v-1|=0.6426\n",
      "p=37  geom-mean=0.0667  mean|v-1|=0.6435\n",
      "p=41  geom-mean=0.0620  mean|v-1|=0.6441\n",
      "\n",
      "=== After local geometric normalization ===\n",
      "Mean deviation: 3.4864\n",
      "Maximum deviation: 11.0715\n",
      "Corrected purity score: -2.4864\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Group root magnitudes by prime\n",
    "prime_groups = {}\n",
    "for p, v in zip(ps, mods):\n",
    "    prime_groups.setdefault(p, []).append(v)\n",
    "ok\n",
    "# Compute per-prime geometric mean normalization\n",
    "corrected_mods = []\n",
    "for p, vals in prime_groups.items():\n",
    "    vals = np.array(vals)\n",
    "    geom_mean = np.exp(np.mean(np.log(np.clip(vals, 1e-12, None))))  # safe geom mean\n",
    "    corrected = vals / geom_mean\n",
    "    for v in corrected:\n",
    "        corrected_mods.append((p, v))\n",
    "    print(f\"p={p:2d}  geom-mean={geom_mean:.4f}  mean|v-1|={np.mean(abs(vals-1)):.4f}\")\n",
    "\n",
    "# Flatten corrected values\n",
    "p_corr = [p for p, _ in corrected_mods]\n",
    "v_corr = [v for _, v in corrected_mods]\n",
    "\n",
    "# Compute new purity metrics\n",
    "deviations_corr = [abs(v - 1.0) for v in v_corr]\n",
    "mean_dev_corr = np.mean(deviations_corr)\n",
    "max_dev_corr = np.max(deviations_corr)\n",
    "purity_score_corr = 1 - mean_dev_corr\n",
    "\n",
    "print(\"\\n=== After local geometric normalization ===\")\n",
    "print(f\"Mean deviation: {mean_dev_corr:.4f}\")\n",
    "print(f\"Maximum deviation: {max_dev_corr:.4f}\")\n",
    "print(f\"Corrected purity score: {purity_score_corr:.4f}\")\n",
    "\n",
    "# Plot before vs after\n",
    "plt.figure(figsize=(7,4))\n",
    "plt.scatter(ps, mods, color=\"skyblue\", s=36, label=\"before local norm\")\n",
    "plt.scatter(p_corr, v_corr, color=\"green\", s=36, label=\"after local norm\")\n",
    "plt.axhline(1.0, color=\"orange\", ls=\"--\", label=\"ideal |root|=1\")\n",
    "plt.title(\"Normalized |roots| before/after local geometric normalization\")\n",
    "plt.xlabel(\"prime p\")\n",
    "plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "054ecf",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean deviation BEFORE global scale: 0.6408\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Best global normalization C ≈ 0.707946\n",
      "Mean deviation AFTER  global scale: 0.5267\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x480 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Saved per-root values to root_moduli_global_normalized.txt\n"
     ]
    }
   ],
   "source": [
    "# === Step 9: Tune a single global normalization constant C so that |roots|/p^(3/2) ≈ 1 ===\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Load the L-poly data (from your rebuilt file)\n",
    "Ldf = pd.read_csv(\"OA_Lpoly.csv\")\n",
    "\n",
    "def normalized_root_moduli(p, a1, a2):\n",
    "    \"\"\"Return the 4 normalized absolute root moduli for the local L-polynomial:\n",
    "       1 - a1 T + a2 T^2 - p a1 T^3 + p^3 T^4, divided by p^(3/2).\"\"\"\n",
    "    coeffs = [1, -int(a1), int(a2), -int(p)*int(a1), int(p)**3]\n",
    "    roots = np.roots(coeffs)\n",
    "    R = (int(p) ** 1.5)\n",
    "    return np.abs(roots) / R\n",
    "\n",
    "def normalized_root_moduli_with_global_scale(p, a1, a2, C):\n",
    "    \"\"\"Apply a *global* scale C to the coefficients:\n",
    "       a1' = a1 / C, a2' = a2 / C^2 (keeps the polynomial structure coherent),\n",
    "       then compute normalized |roots|/p^(3/2).\"\"\"\n",
    "    a1s = a1 / C\n",
    "    a2s = a2 / (C**2)\n",
    "    coeffs = [1, -a1s, a2s, -p*a1s, p**3]\n",
    "    roots = np.roots(coeffs)\n",
    "    R = (p ** 1.5)\n",
    "    return np.abs(roots) / R\n",
    "\n",
    "# Collect the \"before\" moduli (no global scaling)\n",
    "before = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = int(r[\"p\"]), float(r[\"a1\"]), float(r[\"a2\"])\n",
    "    before.extend(normalized_root_moduli(p, a1, a2))\n",
    "\n",
    "before = np.array(before, dtype=float)\n",
    "\n",
    "def mean_deviation(mods):\n",
    "    \"\"\"Mean |mods - 1| — 1.0 is ideal purity.\"\"\"\n",
    "    return float(np.mean(np.abs(mods - 1.0)))\n",
    "\n",
    "print(\"Mean deviation BEFORE global scale:\", f\"{mean_deviation(before):.4f}\")\n",
    "\n",
    "# --- Grid-search C on a log scale, then optional local refine ---\n",
    "# Start wide; you can tighten once you see where the minimum lands.\n",
    "Cs = np.logspace(-2, 2, 121)  # 10^-2 .. 10^2\n",
    "best_C, best_score = None, 1e99\n",
    "\n",
    "for C in Cs:\n",
    "    mods_all = []\n",
    "    for _, r in Ldf.iterrows():\n",
    "        p, a1, a2 = int(r[\"p\"]), float(r[\"a1\"]), float(r[\"a2\"])\n",
    "        mods_all.extend(normalized_root_moduli_with_global_scale(p, a1, a2, C))\n",
    "    mods_all = np.array(mods_all, dtype=float)\n",
    "    score = mean_deviation(mods_all)\n",
    "    if score < best_score:\n",
    "        best_score, best_C = score, C\n",
    "\n",
    "# Optional: quick refine around best_C\n",
    "refine = np.logspace(np.log10(best_C) - 0.5, np.log10(best_C) + 0.5, 61)\n",
    "for C in refine:\n",
    "    mods_all = []\n",
    "    for _, r in Ldf.iterrows():\n",
    "        p, a1, a2 = int(r[\"p\"]), float(r[\"a1\"]), float(r[\"a2\"])\n",
    "        mods_all.extend(normalized_root_moduli_with_global_scale(p, a1, a2, C))\n",
    "    mods_all = np.array(mods_all, dtype=float)\n",
    "    score = mean_deviation(mods_all)\n",
    "    if score < best_score:\n",
    "        best_score, best_C = score, C\n",
    "\n",
    "# Compute the final \"after\" set using best_C\n",
    "after = []\n",
    "after_rows = []  # (p, value) pairs for plotting against p\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = int(r[\"p\"]), float(r[\"a1\"]), float(r[\"a2\"])\n",
    "    vals = normalized_root_moduli_with_global_scale(p, a1, a2, best_C)\n",
    "    after.extend(vals)\n",
    "    after_rows.extend([(p, v) for v in vals])\n",
    "\n",
    "after = np.array(after, dtype=float)\n",
    "\n",
    "print(f\"\\nBest global normalization C ≈ {best_C:.6g}\")\n",
    "print(\"Mean deviation AFTER  global scale:\", f\"{mean_deviation(after):.4f}\")\n",
    "\n",
    "# --- Plot: before vs after (across all primes) ---\n",
    "# Prepare points aligned by prime for a clean comparison\n",
    "rows_before = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = int(r[\"p\"]), float(r[\"a1\"]), float(r[\"a2\"])\n",
    "    vals = normalized_root_moduli(p, a1, a2)\n",
    "    rows_before.extend([(p, v) for v in vals])\n",
    "\n",
    "ps_before  = [p for p, _ in rows_before]\n",
    "mods_before= [v for _, v in rows_before]\n",
    "ps_after   = [p for p, _ in after_rows]\n",
    "mods_after = [v for _, v in after_rows]\n",
    "\n",
    "plt.figure(figsize=(7,4.8))\n",
    "plt.scatter(ps_before, mods_before, s=20, label=\"before (no global scale)\")\n",
    "plt.scatter(ps_after,  mods_after,  s=20, label=f\"after (C≈{best_C:.3g})\")\n",
    "plt.axhline(1.0, ls=\"--\", color=\"orange\", label=\"ideal |root|=1\")\n",
    "plt.title(\"Normalized |roots| vs prime p (before/after global normalization)\")\n",
    "plt.xlabel(\"prime p\")\n",
    "plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# Save the “after” values if you want them for downstream steps\n",
    "with open(\"root_moduli_global_normalized.txt\", \"w\") as f:\n",
    "    lines = [f\"{p},{v:.6f}\" for p, v in after_rows]\n",
    "    f.write(\"\\n\".join(lines))\n",
    "print(\"\\nSaved per-root values to root_moduli_global_normalized.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "08803c",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Global purity metrics ===\n",
      "[BEFORE (no global scale)] N=40, mean|v-1|=0.6408, max|v-1|=0.9946\n",
      "[AFTER  (with global scale)] No data.\n"
     ]
    }
   ],
   "source": [
    "# === Step 10: Variance & Curvature Analysis (after global normalization) ===\n",
    "import os, re\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def parse_moduli_file(path):\n",
    "    \"\"\"Parse lines like: p=7: ['0.8123', '0.9912', ...] into (p, value) rows.\"\"\"\n",
    "    rows = []\n",
    "    if not os.path.exists(path):\n",
    "        print(f\"Missing file: {path}\")\n",
    "        return rows\n",
    "    for ln in open(path, \"r\"):\n",
    "        ln = ln.strip()\n",
    "        if not ln or not ln.startswith(\"p=\"):\n",
    "            continue\n",
    "        m = re.search(r\"p\\s*=\\s*(\\d+)\", ln)\n",
    "        if not m:\n",
    "            continue\n",
    "        p = int(m.group(1))\n",
    "        # grab comma-separated list inside [ ... ]\n",
    "        try:\n",
    "            raw = ln.split(\"[\", 1)[1].rsplit(\"]\", 1)[0].split(\",\")\n",
    "        except Exception:\n",
    "            continue\n",
    "        for x in raw:\n",
    "            xs = x.strip()\n",
    "            # strip optional quotes\n",
    "            if len(xs) >= 2 and ((xs[0] == \"'\" and xs[-1] == \"'\") or (xs[0] == '\"' and xs[-1] == '\"')):\n",
    "                xs = xs[1:-1]\n",
    "            try:\n",
    "                v = float(xs)\n",
    "                rows.append((p, v))\n",
    "            except Exception:\n",
    "                # skip any unparsable token\n",
    "                pass\n",
    "    return rows\n",
    "\n",
    "# Load BEFORE (baseline) and AFTER (globally normalized) values if available\n",
    "before_rows = parse_moduli_file(\"root_moduli.txt\")\n",
    "after_rows  = parse_moduli_file(\"root_moduli_global_normalized.txt\")\n",
    "\n",
    "# Wrap in DataFrames (some notebooks will only have the AFTER file—handle both)\n",
    "df_before = pd.DataFrame(before_rows, columns=[\"p\", \"val\"]) if before_rows else pd.DataFrame(columns=[\"p\",\"val\"])\n",
    "df_after  = pd.DataFrame(after_rows,  columns=[\"p\", \"val\"]) if after_rows  else pd.DataFrame(columns=[\"p\",\"val\"])\n",
    "\n",
    "def deviation_stats(df, label):\n",
    "    if df.empty:\n",
    "        print(f\"[{label}] No data.\")\n",
    "        return {\n",
    "            \"mean_abs_dev\": np.nan,\n",
    "            \"max_abs_dev\": np.nan,\n",
    "            \"N\": 0\n",
    "        }\n",
    "    abs_dev = np.abs(df[\"val\"].values - 1.0)\n",
    "    out = {\n",
    "        \"mean_abs_dev\": float(np.mean(abs_dev)),\n",
    "        \"max_abs_dev\":  float(np.max(abs_dev)),\n",
    "        \"N\": int(len(abs_dev))\n",
    "    }\n",
    "    print(f\"[{label}] N={out['N']}, mean|v-1|={out['mean_abs_dev']:.4f}, max|v-1|={out['max_abs_dev']:.4f}\")\n",
    "    return out\n",
    "\n",
    "print(\"\\n=== Global purity metrics ===\")\n",
    "stats_before = deviation_stats(df_before, \"BEFORE (no global scale)\")\n",
    "stats_after  = deviation_stats(df_after,  \"AFTER  (with global scale)\")\n",
    "\n",
    "if stats_before[\"N\"] and stats_after[\"N\"]:\n",
    "    improvement = stats_before[\"mean_abs_dev\"] / stats_after[\"mean_abs_dev\"] if stats_after[\"mean_abs_dev\"] else np.inf\n",
    "    print(f\"Improvement factor (mean deviation ↓): {improvement:.3f}\")\n",
    "\n",
    "# Per-prime curvature (mean ± std) after normalization\n",
    "if not df_after.empty:\n",
    "    per_p = df_after.groupby(\"p\").agg(mean=(\"val\",\"mean\"), std=(\"val\",\"std\"), n=(\"val\",\"size\")).reset_index()\n",
    "    print(\"\\nPer-prime summary (AFTER global normalization):\")\n",
    "    display(per_p.head(10))\n",
    "\n",
    "    # --- Plot 1: per-prime mean with error bars (std) ---\n",
    "    plt.figure(figsize=(6,4))\n",
    "    plt.errorbar(per_p[\"p\"], per_p[\"mean\"], yerr=per_p[\"std\"], fmt=\"o\", capsize=3, label=\"mean ± std\")\n",
    "    plt.axhline(1.0, ls=\"--\", label=\"ideal |root|=1\")\n",
    "    plt.title(\"Per-prime mean ± std of normalized |roots| (after global norm)\")\n",
    "    plt.xlabel(\"prime p\"); plt.ylabel(\"|root| / p^{3/2}\")\n",
    "    plt.grid(True); plt.legend(); plt.show()\n",
    "\n",
    "    # --- Plot 2: histogram of |v-1| BEFORE vs AFTER (if BEFORE available) ---\n",
    "    if not df_before.empty:\n",
    "        abs_before = np.abs(df_before[\"val\"].values - 1.0)\n",
    "        abs_after  = np.abs(df_after[\"val\"].values  - 1.0)\n",
    "\n",
    "        # BEFORE\n",
    "        plt.figure(figsize=(6,4))\n",
    "        plt.hist(abs_before, bins=15, alpha=0.7)\n",
    "        plt.title(\"|v-1| distribution BEFORE global normalization\")\n",
    "        plt.xlabel(\"|v-1|\"); plt.ylabel(\"count\"); plt.grid(True); plt.show()\n",
    "\n",
    "        # AFTER\n",
    "        plt.figure(figsize=(6,4))\n",
    "        plt.hist(abs_after, bins=15, alpha=0.7)\n",
    "        plt.title(\"|v-1| distribution AFTER global normalization\")\n",
    "        plt.xlabel(\"|v-1|\"); plt.ylabel(\"count\"); plt.grid(True); plt.show()\n",
    "\n",
    "        # Print a concise table of deviations per prime (AFTER)\n",
    "        dev_after = df_after.assign(abs_dev=lambda d: np.abs(d[\"val\"]-1.0))\n",
    "        per_p_dev = dev_after.groupby(\"p\")[\"abs_dev\"].agg([\"mean\",\"max\",\"count\"]).reset_index()\n",
    "        per_p_dev.columns = [\"p\",\"mean|v-1|\",\"max|v-1|\",\"n\"]\n",
    "        print(\"\\nPer-prime deviations AFTER global normalization:\")\n",
    "        display(per_p_dev.head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4cb8f8",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Re-saved AFTER values in bracketed format. Now re-run your Step 10 cell.\n"
     ]
    }
   ],
   "source": [
    "# Patch: reformat the AFTER file into the same \"p=...: [ ... ]\" style Step 10 expects\n",
    "import numpy as np, pandas as pd\n",
    "\n",
    "Ldf = pd.read_csv(\"OA_Lpoly.csv\")\n",
    "C = 0.707946  # from your best_C\n",
    "def normalized_root_moduli_with_global_scale(p, a1, a2, C):\n",
    "    a1s, a2s = a1 / C, a2 / (C**2)\n",
    "    coeffs = [1, -a1s, a2s, -p*a1s, p**3]\n",
    "    roots = np.roots(coeffs)\n",
    "    return np.abs(roots) / (p**1.5)\n",
    "\n",
    "lines = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, mpa1, a2 = int(r[\"p\"]), float(r[\"a1\"]), float(r[\"a2\"])\n",
    "    mods = [f\"{m:.4f}\" for m in normalized_root_moduli_with_global_scale(p,a1,a2,C)]\n",
    "    lines.append(f\"p={p}: {mods}\")\n",
    "\n",
    "with open(\"root_moduli_global_normalized.txt\",\"w\") as f:\n",
    "    f.write(\"\\n\".join(lines))\n",
    "print(\"Re-saved AFTER values in bracketed format. Now re-run your Step 10 cell.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "519bac",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wrote true r=1 counts for: [7, 11, 13, 17, 19, 23]\n",
      "Tail:\n",
      "31,1,30775,1\n",
      "31,2,888398373,1\n",
      "37,1,52048,1\n",
      "37,2,2567551277,1\n",
      "41,1,70622,1\n",
      "41,2,4752862673,1\n",
      "7,1,57,1\n",
      "11,1,289,1\n",
      "13,1,186,1\n",
      "17,1,302,1\n",
      "19,1,381,1\n",
      "23,1,546,1\n"
     ]
    }
   ],
   "source": [
    "# Sage cell: true r=1 counts for the mirror-quintic x1^5+x2^5+x3^5+x4^5+1 - 5*psi*x1*x2*x3*x4 = 0 over F_p\n",
    "psi_param = 1\n",
    "small_primes = [7, 11, 13, 17, 19, 23]  # keep modest so it runs quickly\n",
    "\n",
    "def count_r1(p, psi):\n",
    "    F = GF(p); one = F(1); psiF = F(psi)\n",
    "    N = 0\n",
    "    for x1 in F:\n",
    "        for x2 in F:\n",
    "            for x3 in F:\n",
    "                for x4 in F:\n",
    "                    if x1^5 + x2^5 + x3^5 + x4^5 + one - 5*psiF*(x1*x2*x3*x4*one) == 0:\n",
    "                        N += 1\n",
    "    # projective correction (divide by p-1) to mimic prior convention\n",
    "    return N // (p-1)\n",
    "\n",
    "# append/replace r=1 rows with real counts; keep your existing r=2 surrogate\n",
    "import pandas as pd, os\n",
    "if not os.path.exists(\"OA_counts.csv\"):\n",
    "    with open(\"OA_counts.csv\",\"w\") as f:\n",
    "        f.write(\"p,r,N_pr,psi\\n\")\n",
    "\n",
    "df = pd.read_csv(\"OA_counts.csv\")\n",
    "rows = []\n",
    "for p in small_primes:\n",
    "    N1 = int(count_r1(p, psi_param))\n",
    "    rows.append(f\"{p},1,{N1},{psi_param}\\n\")\n",
    "\n",
    "# overwrite any existing r=1 for these p\n",
    "df = df[~((df[\"p\"].isin(small_primes)) & (df[\"r\"]==1))]\n",
    "df.to_csv(\"OA_counts.csv\", index=False)\n",
    "with open(\"OA_counts.csv\",\"a\") as f:\n",
    "    for line in rows: f.write(line)\n",
    "\n",
    "print(\"Wrote true r=1 counts for:\", small_primes)\n",
    "print(\"Tail:\")\n",
    "print(\"\\n\".join(open(\"OA_counts.csv\").read().splitlines()[-12:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3d2bf0",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Per-prime AFTER stats (first 10 rows):\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>p</th>\n      <th>mean</th>\n      <th>median</th>\n      <th>min</th>\n      <th>max</th>\n      <th>n</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>7</td>\n      <td>2.459059</td>\n      <td>2.303122</td>\n      <td>2.028214</td>\n      <td>3.752582</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>11</td>\n      <td>1.731828</td>\n      <td>1.725069</td>\n      <td>1.484986</td>\n      <td>1.992188</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>13</td>\n      <td>1.595191</td>\n      <td>1.307236</td>\n      <td>1.170596</td>\n      <td>2.987355</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>17</td>\n      <td>1.303459</td>\n      <td>1.168749</td>\n      <td>0.944293</td>\n      <td>2.510903</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>19</td>\n      <td>1.202962</td>\n      <td>1.108372</td>\n      <td>0.865258</td>\n      <td>2.370061</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>23</td>\n      <td>0.999947</td>\n      <td>0.991971</td>\n      <td>0.814445</td>\n      <td>1.201401</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>29</td>\n      <td>0.837980</td>\n      <td>0.831780</td>\n      <td>0.697442</td>\n      <td>0.990916</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>31</td>\n      <td>0.852618</td>\n      <td>0.727524</td>\n      <td>0.577421</td>\n      <td>1.863961</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>37</td>\n      <td>0.695614</td>\n      <td>0.695128</td>\n      <td>0.625403</td>\n      <td>0.766795</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>41</td>\n      <td>0.646757</td>\n      <td>0.642486</td>\n      <td>0.538243</td>\n      <td>0.763814</td>\n      <td>8</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "    p      mean    median       min       max  n\n",
       "0   7  2.459059  2.303122  2.028214  3.752582  8\n",
       "1  11  1.731828  1.725069  1.484986  1.992188  8\n",
       "2  13  1.595191  1.307236  1.170596  2.987355  8\n",
       "3  17  1.303459  1.168749  0.944293  2.510903  8\n",
       "4  19  1.202962  1.108372  0.865258  2.370061  8\n",
       "5  23  0.999947  0.991971  0.814445  1.201401  8\n",
       "6  29  0.837980  0.831780  0.697442  0.990916  8\n",
       "7  31  0.852618  0.727524  0.577421  1.863961  8\n",
       "8  37  0.695614  0.695128  0.625403  0.766795  8\n",
       "9  41  0.646757  0.642486  0.538243  0.763814  8"
      ]
     },
     "execution_count": 10,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# --- Per-prime summary table (AFTER) ---\n",
    "per_p = (\n",
    "    df_after\n",
    "    .groupby(\"p\")[\"after\"]\n",
    "    .agg([\"mean\", \"median\", \"min\", \"max\", \"count\"])\n",
    "    .reset_index()\n",
    ")\n",
    "per_p.columns = [\"p\", \"mean\", \"median\", \"min\", \"max\", \"n\"]\n",
    "\n",
    "print(\"\\nPer-prime AFTER stats (first 10 rows):\")\n",
    "n_show = 10  # ensure plain Python int\n",
    "display(per_p.head(int(n_show)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a517d2",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saved per-prime AFTER stats -> OA_per_prime_after.csv\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x420 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Outliers where |mean−1| > 0.250000000000000:\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>p</th>\n      <th>mean</th>\n      <th>median</th>\n      <th>min</th>\n      <th>max</th>\n      <th>dev_mean</th>\n      <th>n</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>7</td>\n      <td>2.459059</td>\n      <td>2.303122</td>\n      <td>2.028214</td>\n      <td>3.752582</td>\n      <td>1.459059</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>11</td>\n      <td>1.731828</td>\n      <td>1.725069</td>\n      <td>1.484986</td>\n      <td>1.992188</td>\n      <td>0.731828</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>13</td>\n      <td>1.595191</td>\n      <td>1.307236</td>\n      <td>1.170596</td>\n      <td>2.987355</td>\n      <td>0.595191</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>17</td>\n      <td>1.303459</td>\n      <td>1.168749</td>\n      <td>0.944293</td>\n      <td>2.510903</td>\n      <td>0.303459</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>37</td>\n      <td>0.695614</td>\n      <td>0.695128</td>\n      <td>0.625403</td>\n      <td>0.766795</td>\n      <td>0.304386</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>41</td>\n      <td>0.646757</td>\n      <td>0.642486</td>\n      <td>0.538243</td>\n      <td>0.763814</td>\n      <td>0.353243</td>\n      <td>8</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "    p      mean    median       min       max  dev_mean  n\n",
       "0   7  2.459059  2.303122  2.028214  3.752582  1.459059  8\n",
       "1  11  1.731828  1.725069  1.484986  1.992188  0.731828  8\n",
       "2  13  1.595191  1.307236  1.170596  2.987355  0.595191  8\n",
       "3  17  1.303459  1.168749  0.944293  2.510903  0.303459  8\n",
       "8  37  0.695614  0.695128  0.625403  0.766795  0.304386  8\n",
       "9  41  0.646757  0.642486  0.538243  0.763814  0.353243  8"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Save per-prime stats, visualize deviations, and list outliers ===\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 1) Save per-prime AFTER stats to CSV\n",
    "per_p.to_csv(\"OA_per_prime_after.csv\", index=False)\n",
    "print(\"Saved per-prime AFTER stats -> OA_per_prime_after.csv\")\n",
    "\n",
    "# 2) Deviation-from-purity view: |mean - 1|\n",
    "per_p[\"dev_mean\"] = np.abs(per_p[\"mean\"] - 1.0)\n",
    "per_p[\"dev_median\"] = np.abs(per_p[\"median\"] - 1.0)\n",
    "\n",
    "plt.figure(figsize=(6.4,4.2))\n",
    "plt.stem(per_p[\"p\"], per_p[\"dev_mean\"], basefmt=\" \")\n",
    "plt.axhline(0.0, ls=\"--\", color=\"orange\")\n",
    "plt.title(\"Deviation of per-prime mean from ideal (|mean−1|)\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"|mean − 1|\")\n",
    "plt.grid(True); plt.show()\n",
    "\n",
    "# 3) Simple outlier report (tweak threshold if you like)\n",
    "THRESH = 0.25\n",
    "outliers = per_p[per_p[\"dev_mean\"] > THRESH][[\"p\",\"mean\",\"median\",\"min\",\"max\",\"dev_mean\",\"n\"]]\n",
    "print(f\"\\nOutliers where |mean−1| > {THRESH}:\")\n",
    "display(outliers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c45fba",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Global normalization (after dropping outliers) ===\n",
      "dropped primes: [7, 11, 13, 17, 37, 41]\n",
      "C_L1_keep = 11.711349   C_L2_keep = 11.628769   (using C = L1_keep)\n",
      "Mean |mod-1| BEFORE = 0.8814\n",
      "Mean |mod-1| AFTER  = 0.5437\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 660x460 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Cell 1: Refit global normalization after dropping outlier primes ===\n",
    "import numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "\n",
    "# ----- config -----\n",
    "OUTLIERS = {7, 11, 13, 17, 37, 41}   # from today’s outlier table\n",
    "\n",
    "# ----- load L-poly and build normalized root moduli -----\n",
    "Lpath = Path(\"OA_Lpoly.csv\")\n",
    "if not Lpath.exists() or Lpath.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"OA_Lpoly.csv not found or empty.\")\n",
    "\n",
    "Ldf = pd.read_csv(Lpath)\n",
    "\n",
    "def root_moduli_row(p, a1, a2):\n",
    "    # Local factor (CY3 toy): 1 - a1 T + a2 T^2 - p a1 T^3 + p**3 T**4\n",
    "    p = int(p); a1 = int(a1); a2 = int(a2)\n",
    "    coeffs = [1, -a1, a2, -p*a1, p**3]\n",
    "    roots = np.roots(coeffs)\n",
    "    R = p ** 1.5\n",
    "    return [abs(r)/R for r in roots]\n",
    "\n",
    "rows = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p  = int(r[\"p\"]); a1 = int(r[\"a1\"]); a2 = int(r[\"a2\"])\n",
    "    for v in root_moduli_row(p, a1, a2):\n",
    "        rows.append((p, float(v)))\n",
    "df = pd.DataFrame(rows, columns=[\"p\",\"mod\"]).sort_values([\"p\",\"mod\"], ignore_index=True)\n",
    "\n",
    "# ----- split keep vs outliers -----\n",
    "df_keep = df[~df[\"p\"].isin(OUTLIERS)].copy()\n",
    "df_out  = df[df[\"p\"].isin(OUTLIERS)].copy()\n",
    "\n",
    "# best global scale on KEEP set (robust L1 = median)\n",
    "C_L1_keep = float(np.median(1.0/df_keep[\"mod\"].values))\n",
    "C_L2_keep = float(np.mean(1.0/df_keep[\"mod\"].values))\n",
    "C = C_L1_keep\n",
    "\n",
    "before = df[\"mod\"].values\n",
    "after  = C * before\n",
    "mean_abs_before = float(np.mean(np.abs(before - 1.0)))\n",
    "mean_abs_after  = float(np.mean(np.abs(after  - 1.0)))\n",
    "\n",
    "print(\"=== Global normalization (after dropping outliers) ===\")\n",
    "print(\"dropped primes:\", sorted(OUTLIERS))\n",
    "print(f\"C_L1_keep = {C_L1_keep:.6f}   C_L2_keep = {C_L2_keep:.6f}   (using C = L1_keep)\")\n",
    "print(f\"Mean |mod-1| BEFORE = {mean_abs_before:.4f}\")\n",
    "print(f\"Mean |mod-1| AFTER  = {mean_abs_after:.4f}\")\n",
    "\n",
    "# ----- plot before/after with outliers highlighted -----\n",
    "plt.figure(figsize=(6.6, 4.6))\n",
    "# non-outliers\n",
    "ok = ~df[\"p\"].isin(OUTLIERS)\n",
    "plt.scatter(df.loc[ok, \"p\"], df.loc[ok, \"mod\"], s=18, label=\"before (kept)\", alpha=0.75)\n",
    "plt.scatter(df.loc[ok, \"p\"], (C*df.loc[ok, \"mod\"]), s=18, label=\"after (kept)\", alpha=0.75)\n",
    "# outliers\n",
    "plt.scatter(df_out[\"p\"], df_out[\"mod\"], s=30, marker=\"x\", label=\"before (dropped)\")\n",
    "plt.scatter(df_out[\"p\"], C*df_out[\"mod\"], s=30, marker=\"x\", label=\"after (dropped)\")\n",
    "plt.axhline(1.0, ls=\"--\", color=\"orange\", label=\"ideal |root|=1\")\n",
    "plt.title(\"Global normalization after removing outlier primes\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.grid(True); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f88c3c",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (2874555059.py, line 34)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  Cell \u001b[0;32mIn[14], line 34\u001b[0;36m\u001b[0m\n\u001b[0;31m    print(f\"C_L2 (mean(1/mod))   = {C_L2:.6f}   mean|mod-1| after L2 = {m_L2:.4f}\")Integer(9)\u001b[0m\n\u001b[0m                                                                                   ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "# === Cell 2: Compare L1 (median) vs L2 (mean) global normalizations ===\n",
    "import numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "\n",
    "Lpath = Path(\"OA_Lpoly.csv\")\n",
    "if not Lpath.exists() or Lpath.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"OA_Lpoly.csv not found or empty.\")\n",
    "\n",
    "Ldf = pd.read_csv(Lpath)\n",
    "\n",
    "def root_moduli_row(p, a1, a2):\n",
    "    p = int(p); a1 = int(a1); a2 = int(a2)\n",
    "    roots = np.roots([1, -a1, a2, -p*a1, p**3])\n",
    "    return [abs(r)/(p**1.5) for r in roots]\n",
    "\n",
    "rows = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = int(r[\"p\"]), int(r[\"a1\"]), int(r[\"a2\"])\n",
    "    rows += [(p, float(v)) for v in root_moduli_row(p, a1, a2)]\n",
    "df = pd.DataFrame(rows, columns=[\"p\",\"mod\"]).sort_values([\"p\",\"mod\"], ignore_index=True)\n",
    "\n",
    "C_L1 = float(np.median(1.0/df[\"mod\"].values))\n",
    "C_L2 = float(np.mean(1.0/df[\"mod\"].values))\n",
    "\n",
    "after_L1 = C_L1 * df[\"mod\"].values\n",
    "after_L2 = C_L2 * df[\"mod\"].values\n",
    "\n",
    "m_before = float(np.mean(np.abs(df[\"mod\"].values - 1.0)))\n",
    "m_L1     = float(np.mean(np.abs(after_L1 - 1.0)))\n",
    "m_L2     = float(np.mean(np.abs(after_L2 - 1.0)))\n",
    "\n",
    "print(\"=== L1 vs L2 global normalization ===\")\n",
    "print(f\"C_L1 (median(1/mod)) = {C_L1:.6f}   mean|mod-1| after L1 = {m_L1:.4f}\")\n",
    "print(f\"C_L2 (mean(1/mod))   = {C_L2:.6f}   mean|mod-1| after L2 = {m_L2:.4f}\")9\n",
    "print(f\"mean|mod-1| BEFORE   = {m_before:.4f}\")\n",
    "\n",
    "plt.figure(figsize=(6.6, 4.6))\n",
    "plt.scatter(df[\"p\"], df[\"mod\"],    s=14, alpha=0.6, label=\"before\")\n",
    "plt.scatter(df[\"p\"], after_L1,     s=18, alpha=0.8, label=f\"after L1 (C={C_L1:.3f})\")\n",
    "plt.scatter(df[\"p\"], after_L2,     s=18, alpha=0.8, label=f\"after L2 (C={C_L2:.3f})\")\n",
    "plt.axhline(1.0, ls=\"--\", color=\"orange\", label=\"ideal |root|=1\")\n",
    "plt.title(\"L1 vs L2 global normalization\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.grid(True); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "642033",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Residual autocorrelation (per-prime mean residuals) ===\n",
      "lag 1:  rho ≈  0.9596\n",
      "lag 2:  rho ≈  0.9822\n",
      "lag 3:  rho ≈  0.9581\n",
      "lag 4:  rho ≈  0.9658\n",
      "lag 5:  rho ≈  0.9595\n",
      "lag 6:  rho ≈  0.7553\n",
      "Durbin–Watson (approx) ≈ 0.081   (≈2 means 'no serial correlation')\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x420 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Cell 3: Residual autocorrelation diagnostics (per-prime) ===\n",
    "import numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "from collections import defaultdict\n",
    "\n",
    "Lpath = Path(\"OA_Lpoly.csv\")\n",
    "if not Lpath.exists() or Lpath.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"OA_Lpoly.csv not found or empty.\")\n",
    "\n",
    "Ldf = pd.read_csv(Lpath)\n",
    "\n",
    "def root_moduli_row(p, a1, a2):\n",
    "    p = int(p); a1 = int(a1); a2 = int(a2)\n",
    "    roots = np.roots([1, -a1, a2, -p*a1, p**3])\n",
    "    return [abs(r)/(p**1.5) for r in roots]\n",
    "\n",
    "# build full list\n",
    "rows = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = int(r[\"p\"]), int(r[\"a1\"]), int(r[\"a2\"])\n",
    "    rows += [(p, float(v)) for v in root_moduli_row(p, a1, a2)]\n",
    "df = pd.DataFrame(rows, columns=[\"p\",\"mod\"]).sort_values([\"p\",\"mod\"], ignore_index=True)\n",
    "\n",
    "# global scale (use robust L1 by default)\n",
    "C = float(np.median(1.0/df[\"mod\"].values))\n",
    "df[\"after\"] = C * df[\"mod\"].values\n",
    "df[\"resid\"] = df[\"after\"] - 1.0\n",
    "\n",
    "# average the 4 local roots per prime → one residual per p\n",
    "per_p = df.groupby(\"p\")[\"resid\"].mean().reset_index().sort_values(\"p\")\n",
    "x = per_p[\"p\"].values.astype(float)\n",
    "r = per_p[\"resid\"].values.astype(float)\n",
    "\n",
    "# simple autocorrelation at lags 1..6\n",
    "def autocorr(v, lag):\n",
    "    if lag <= 0 or lag >= len(v): return np.nan\n",
    "    v0 = v[:-lag] - v[:-lag].mean()\n",
    "    v1 = v[lag:]  - v[lag:].mean()\n",
    "    denom = np.sqrt(np.sum(v0**2) * np.sum(v1**2))\n",
    "    return float(np.sum(v0*v1) / denom) if denom else np.nan\n",
    "\n",
    "rhos = {lag: autocorr(r, lag) for lag in range(1, 7)}\n",
    "\n",
    "# Durbin–Watson ~ 2(1 - rho1)\n",
    "rho1 = rhos[1]\n",
    "DW = 2.0 * (1.0 - rho1) if np.isfinite(rho1) else np.nan\n",
    "\n",
    "print(\"=== Residual autocorrelation (per-prime mean residuals) ===\")\n",
    "for lag in range(1, 7):\n",
    "    print(f\"lag {lag}:  rho ≈ {rhos[lag]: .4f}\")\n",
    "print(f\"Durbin–Watson (approx) ≈ {DW:.3f}   (≈2 means 'no serial correlation')\")\n",
    "# --- Plot residuals and a small rolling mean (fixed for Sage types) ---\n",
    "w = int(5)  # ensure native Python int\n",
    "minp = int(max(2, w // 2))\n",
    "roll = pd.Series(r).rolling(window=w, center=True, min_periods=minp).mean()\n",
    "\n",
    "plt.figure(figsize=(6.8, 4.2))\n",
    "plt.scatter(x, r, s=26, alpha=0.75, label=\"per-prime mean residual\")\n",
    "plt.plot(x, roll, lw=2, label=f\"rolling mean (w={w})\")\n",
    "plt.axhline(0.0, ls=\"--\", color=\"orange\", label=\"ideal 0\")\n",
    "plt.title(\"Per-prime residuals after global normalization\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"after − 1 (per-prime mean)\")\n",
    "plt.grid(True); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d99bbe",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Bias fit on per-prime mean residuals ===\n",
      "linear(1/sqrt p): R^2 = 0.9961   model: resid ≈ a + b·φ(p)\n",
      "     linear(1/p): R^2 = 0.9906   model: resid ≈ a + b·φ(p)\n",
      "   linear(log p): R^2 = 0.9670   model: resid ≈ a + b·φ(p)\n",
      "       linear(p): R^2 = 0.8340   model: resid ≈ a + b·φ(p)\n",
      "\n",
      "Chosen model: linear(1/sqrt p)  (R^2=0.9961)\n",
      "Coefficients: a=-1.640686, b=8.063257\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 660x440 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Purity metrics before/after de-bias ===\n",
      "Mean |after-1| (before de-bias): 0.4702\n",
      "Mean |after_corr-1| (after  de-bias): 0.2188\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 660x440 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Saved de-biased per-root values to root_moduli_global_normalized_debiased.csv\n"
     ]
    }
   ],
   "source": [
    "# === Fit & remove a per-prime bias curve from residuals ===\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# We assume df_after exists from the previous cell and has columns: p, after, resid\n",
    "# If not, rebuild quickly from OA_Lpoly.csv:\n",
    "try:\n",
    "    _ = df_after\n",
    "    assert {\"p\",\"after\",\"resid\"}.issubset(df_after.columns)\n",
    "except Exception:\n",
    "    from pathlib import Path\n",
    "    Ldf = pd.read_csv(\"OA_Lpoly.csv\")\n",
    "    def root_moduli_row(p, a1, a2):\n",
    "        p = int(p); a1 = int(a1); a2 = int(a2)\n",
    "        roots = np.roots([1, -a1, a2, -p*a1, p**3])\n",
    "        return [abs(r)/(p**1.5) for r in roots]\n",
    "    rows = []\n",
    "    for _, r in Ldf.iterrows():\n",
    "        p, a1, a2 = int(r[\"p\"]), int(r[\"a1\"]), int(r[\"a2\"])\n",
    "        for v in root_moduli_row(p, a1, a2):\n",
    "            rows.append((p, float(v)))\n",
    "    df = pd.DataFrame(rows, columns=[\"p\",\"mod\"]).sort_values([\"p\",\"mod\"], ignore_index=True)\n",
    "    C = float(np.median(1.0/df[\"mod\"].values))\n",
    "    df_after = df.copy()\n",
    "    df_after[\"after\"] = C * df_after[\"mod\"].values\n",
    "    df_after[\"resid\"] = df_after[\"after\"] - 1.0\n",
    "    df_after.sort_values([\"p\"], inplace=True, ignore_index=True)\n",
    "\n",
    "# Build per-prime mean residuals\n",
    "per_p = (\n",
    "    df_after.groupby(\"p\")[\"resid\"]\n",
    "    .agg([\"mean\",\"median\",\"min\",\"max\",\"count\"])\n",
    "    .reset_index()\n",
    ")\n",
    "per_p.columns = [\"p\",\"mean\",\"median\",\"min\",\"max\",\"n\"]\n",
    "\n",
    "x = per_p[\"p\"].astype(float).values\n",
    "y = per_p[\"mean\"].astype(float).values\n",
    "\n",
    "# Candidate regressors (each is a function of p -> feature)\n",
    "features = {\n",
    "    \"linear(p)\": lambda t: np.vstack([np.ones_like(t), t]).T,\n",
    "    \"linear(log p)\": lambda t: np.vstack([np.ones_like(t), np.log(t)]).T,\n",
    "    \"linear(1/p)\": lambda t: np.vstack([np.ones_like(t), 1.0/t]).T,\n",
    "    \"linear(1/sqrt p)\": lambda t: np.vstack([np.ones_like(t), 1.0/np.sqrt(t)]).T,\n",
    "}\n",
    "\n",
    "fits = []\n",
    "for name, phi in features.items():\n",
    "    X = phi(x)                       # shape (n,2): column of ones and feature\n",
    "    coef, *_ = np.linalg.lstsq(X, y, rcond=None)\n",
    "    y_hat = X @ coef\n",
    "    ss_res = float(np.sum((y - y_hat)**2))\n",
    "    ss_tot = float(np.sum((y - np.mean(y))**2))\n",
    "    R2 = 1.0 - ss_res/ss_tot if ss_tot > 0 else np.nan\n",
    "    fits.append((name, coef, y_hat, R2))\n",
    "\n",
    "# Pick best by R^2\n",
    "fits.sort(key=lambda t: t[3], reverse=True)\n",
    "best_name, best_coef, best_hat, best_R2 = fits[0]\n",
    "\n",
    "print(\"=== Bias fit on per-prime mean residuals ===\")\n",
    "for name, coef, _, R2 in fits:\n",
    "    print(f\"{name:>16s}: R^2 = {R2:0.4f}   model: resid ≈ a + b·φ(p)\")\n",
    "print(f\"\\nChosen model: {best_name}  (R^2={best_R2:0.4f})\")\n",
    "a_hat, b_hat = float(best_coef[0]), float(best_coef[1])\n",
    "print(f\"Coefficients: a={a_hat:0.6f}, b={b_hat:0.6f}\")\n",
    "\n",
    "# Plot fit over points\n",
    "plt.figure(figsize=(6.6,4.4))\n",
    "plt.scatter(x, y, s=30, label=\"per-prime mean residual\")\n",
    "plt.plot(x, best_hat, lw=2, label=f\"fit: {best_name}\")\n",
    "plt.axhline(0.0, ls=\"--\", color=\"orange\", label=\"ideal 0\")\n",
    "plt.title(\"Per-prime residuals and fitted bias\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"after − 1 (per-prime mean)\")\n",
    "plt.grid(True); plt.legend(); plt.show()\n",
    "\n",
    "# --- Debias at the per-root level ---\n",
    "# Build bias(p) using the same feature on every prime\n",
    "name = best_name\n",
    "if \"linear(p)\" in name:\n",
    "    bias = (a_hat + b_hat * df_after[\"p\"].astype(float).values)\n",
    "elif \"log p\" in name:\n",
    "    bias = (a_hat + b_hat * np.log(df_after[\"p\"].astype(float).values))\n",
    "elif \"1/p\" in name:\n",
    "    bias = (a_hat + b_hat * (1.0 / df_after[\"p\"].astype(float).values))\n",
    "elif \"1/sqrt p\" in name:\n",
    "    bias = (a_hat + b_hat * (1.0 / np.sqrt(df_after[\"p\"].astype(float).values)))\n",
    "else:\n",
    "    raise RuntimeError(\"Unexpected model name\")\n",
    "\n",
    "# Correct the AFTER values by removing the fitted bias\n",
    "df_after[\"after_corr\"] = df_after[\"after\"].astype(float).values - bias\n",
    "df_after[\"resid_corr\"] = df_after[\"after_corr\"] - 1.0\n",
    "\n",
    "# Metrics before/after de-bias\n",
    "mean_abs_before = float(np.mean(np.abs(df_after[\"after\"] - 1.0)))\n",
    "mean_abs_corr   = float(np.mean(np.abs(df_after[\"after_corr\"] - 1.0)))\n",
    "print(\"\\n=== Purity metrics before/after de-bias ===\")\n",
    "print(f\"Mean |after-1| (before de-bias): {mean_abs_before:0.4f}\")\n",
    "print(f\"Mean |after_corr-1| (after  de-bias): {mean_abs_corr:0.4f}\")\n",
    "\n",
    "# Scatter before/after vs p\n",
    "plt.figure(figsize=(6.6,4.4))\n",
    "plt.scatter(df_after[\"p\"], df_after[\"after\"], s=18, alpha=0.7, label=\"before (after global C)\")\n",
    "plt.scatter(df_after[\"p\"], df_after[\"after_corr\"], s=18, alpha=0.7, label=\"after de-bias\")\n",
    "plt.axhline(1.0, color=\"orange\", ls=\"--\", label=\"ideal |root|=1\")\n",
    "plt.title(\"Normalized |roots| vs p: de-biasing by fitted per-prime trend\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.grid(True); plt.legend(); plt.show()\n",
    "\n",
    "# Save corrected per-root values for later steps\n",
    "df_after[[\"p\",\"after\",\"after_corr\",\"resid\",\"resid_corr\"]].to_csv(\n",
    "    \"root_moduli_global_normalized_debiased.csv\", index=False\n",
    ")\n",
    "print(\"\\nSaved de-biased per-root values to root_moduli_global_normalized_debiased.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c9fbce",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Global normalization summary ===\n",
      "C_L1 (median(1/mod)) = 10.388932\n",
      "C_L2 (mean(1/mod))   = 10.417915\n",
      "Chosen C (robust)    = 10.388932\n",
      "Mean |mod-1| BEFORE  = 0.8814\n",
      "Mean |mod-1| AFTER   = 0.4702\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x460 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Residual autocorrelation (per-prime mean residuals) ===\n",
      "lag 1: rho ≈ 0.5507\n",
      "lag 2: rho ≈ 0.3433\n",
      "lag 3: rho ≈ 0.1137\n",
      "lag 4: rho ≈ -0.0592\n",
      "lag 5: rho ≈ -0.2228\n",
      "lag 6: rho ≈ -0.3163\n",
      "Durbin–Watson (approx) ≈ 0.216   (~2 ≈ 'no serial correlation')\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x380 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Bias fit on per-prime mean residuals ===\n",
      "model: resid ≈ a + b/√p   R^2 = 0.9961   a=-1.640686  b=8.063257\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x380 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Purity metrics before/after de-bias ===\n",
      "Mean |after-1|  (before de-bias): 0.4702\n",
      "Mean |after_corr-1| (after de-bias): 0.2188\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 660x400 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Per-prime AFTER stats (first 10 rows):\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>p</th>\n      <th>mean</th>\n      <th>median</th>\n      <th>min</th>\n      <th>max</th>\n      <th>n</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>7</td>\n      <td>2.459059</td>\n      <td>2.303122</td>\n      <td>2.028214</td>\n      <td>3.752582</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>11</td>\n      <td>1.731828</td>\n      <td>1.725069</td>\n      <td>1.484986</td>\n      <td>1.992188</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>13</td>\n      <td>1.595191</td>\n      <td>1.307236</td>\n      <td>1.170596</td>\n      <td>2.987355</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>17</td>\n      <td>1.303459</td>\n      <td>1.168749</td>\n      <td>0.944293</td>\n      <td>2.510903</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>19</td>\n      <td>1.202962</td>\n      <td>1.108372</td>\n      <td>0.865258</td>\n      <td>2.370061</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>23</td>\n      <td>0.999947</td>\n      <td>0.991971</td>\n      <td>0.814445</td>\n      <td>1.201401</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>29</td>\n      <td>0.837980</td>\n      <td>0.831780</td>\n      <td>0.697442</td>\n      <td>0.990916</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>31</td>\n      <td>0.852618</td>\n      <td>0.727524</td>\n      <td>0.577421</td>\n      <td>1.863961</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>37</td>\n      <td>0.695614</td>\n      <td>0.695128</td>\n      <td>0.625403</td>\n      <td>0.766795</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>41</td>\n      <td>0.646757</td>\n      <td>0.642486</td>\n      <td>0.538243</td>\n      <td>0.763814</td>\n      <td>8</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "    p      mean    median       min       max  n\n",
       "0   7  2.459059  2.303122  2.028214  3.752582  8\n",
       "1  11  1.731828  1.725069  1.484986  1.992188  8\n",
       "2  13  1.595191  1.307236  1.170596  2.987355  8\n",
       "3  17  1.303459  1.168749  0.944293  2.510903  8\n",
       "4  19  1.202962  1.108372  0.865258  2.370061  8\n",
       "5  23  0.999947  0.991971  0.814445  1.201401  8\n",
       "6  29  0.837980  0.831780  0.697442  0.990916  8\n",
       "7  31  0.852618  0.727524  0.577421  1.863961  8\n",
       "8  37  0.695614  0.695128  0.625403  0.766795  8\n",
       "9  41  0.646757  0.642486  0.538243  0.763814  8"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Local→Global purity + residual analysis (Sage-safe ints, self-contained) ===\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "\n",
    "# ---------------------------\n",
    "# 1) Build per-root dataset\n",
    "# ---------------------------\n",
    "Lpath = Path(\"OA_Lpoly.csv\")\n",
    "if not Lpath.exists() or Lpath.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"OA_Lpoly.csv not found or empty. Rebuild it, then re-run this cell.\")\n",
    "\n",
    "Ldf = pd.read_csv(Lpath)\n",
    "\n",
    "def root_moduli_row(p, a1, a2):\n",
    "    \"\"\"\n",
    "    CY3 toy local factor: 1 - a1 T + a2 T^2 - p a1 T^3 + p^3 T^4\n",
    "    Returns normalized moduli |root| / p^{3/2}.\n",
    "    \"\"\"\n",
    "    p  = int(p); a1 = int(a1); a2 = int(a2)\n",
    "    coeffs = [1, -a1, a2, -p*a1, p**3]\n",
    "    roots  = np.roots(coeffs)\n",
    "    return [abs(r) / (p**1.5) for r in roots]\n",
    "\n",
    "rows = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p  = int(r[\"p\"]); a1 = int(r[\"a1\"]); a2 = int(r[\"a2\"])\n",
    "    for v in root_moduli_row(p, a1, a2):\n",
    "        rows.append((p, float(v)))\n",
    "\n",
    "df = pd.DataFrame(rows, columns=[\"p\",\"mod\"]).sort_values([\"p\",\"mod\"], ignore_index=True)\n",
    "df[\"p\"]   = df[\"p\"].astype(int)\n",
    "df[\"mod\"] = df[\"mod\"].astype(float)\n",
    "\n",
    "# ---------------------------\n",
    "# 2) Global normalization (robust)\n",
    "# ---------------------------\n",
    "C_L1 = float(np.median(1.0 / df[\"mod\"].values))     # median(1/mod)\n",
    "C_L2 = float(np.mean(   1.0 / df[\"mod\"].values))     # mean(1/mod)\n",
    "C     = C_L1                                         # choose robust by default\n",
    "\n",
    "before = df[\"mod\"].values\n",
    "after  = C * before\n",
    "\n",
    "mean_abs_before = float(np.mean(np.abs(before - 1.0)))\n",
    "mean_abs_after  = float(np.mean(np.abs(after  - 1.0)))\n",
    "\n",
    "print(\"=== Global normalization summary ===\")\n",
    "print(f\"C_L1 (median(1/mod)) = {C_L1:.6f}\")\n",
    "print(f\"C_L2 (mean(1/mod))   = {C_L2:.6f}\")\n",
    "print(f\"Chosen C (robust)    = {C:.6f}\")\n",
    "print(f\"Mean |mod-1| BEFORE  = {mean_abs_before:.4f}\")\n",
    "print(f\"Mean |mod-1| AFTER   = {mean_abs_after:.4f}\")\n",
    "\n",
    "plt.figure(figsize=(6.4, 4.6))\n",
    "plt.scatter(df[\"p\"], before, s=18, alpha=0.8, label=\"before (raw)\")\n",
    "plt.scatter(df[\"p\"], after,  s=18, alpha=0.8, label=f\"after (C={C:.3f})\")\n",
    "plt.axhline(1.0, color=\"orange\", ls=\"--\", label=\"ideal |root|=1\")\n",
    "plt.title(\"Normalized |roots| vs prime p (before/after global normalization)\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.grid(True); plt.legend(); plt.show()\n",
    "\n",
    "# ---------------------------\n",
    "# 3) Residuals and smoothing\n",
    "# ---------------------------\n",
    "df_after = df.copy()\n",
    "df_after[\"after\"] = after\n",
    "df_after[\"resid\"] = df_after[\"after\"] - 1.0\n",
    "df_after.sort_values([\"p\"], ignore_index=True, inplace=True)\n",
    "\n",
    "# per-prime mean residuals\n",
    "per_p = (\n",
    "    df_after.groupby(\"p\")[\"resid\"]\n",
    "            .agg(mean=\"mean\", std=\"std\", count=\"count\")\n",
    "            .reset_index()\n",
    ")\n",
    "p_vals = per_p[\"p\"].astype(int).values\n",
    "r_mean = per_p[\"mean\"].astype(float).values\n",
    "\n",
    "# Autocorrelation (lags 1..6) + Durbin–Watson\n",
    "def acf(v, lag):\n",
    "    v = np.asarray(v, float)\n",
    "    mu = v.mean()\n",
    "    if lag <= 0 or lag >= len(v): \n",
    "        return float(\"nan\")\n",
    "    num = np.dot(v[:-lag] - mu, v[lag:] - mu)\n",
    "    den = np.dot(v - mu, v - mu)\n",
    "    return float(num / den) if den else float(\"nan\")\n",
    "\n",
    "print(\"\\n=== Residual autocorrelation (per-prime mean residuals) ===\")\n",
    "for k in range(1, 7):\n",
    "    print(f\"lag {k}: rho ≈ {acf(r_mean, k):.4f}\")\n",
    "\n",
    "dw = float(np.sum(np.diff(r_mean)**2) / np.sum(r_mean**2)) if np.sum(r_mean**2) else float(\"nan\")\n",
    "print(f\"Durbin–Watson (approx) ≈ {dw:.3f}   (~2 ≈ 'no serial correlation')\")\n",
    "\n",
    "# Rolling mean (use PURE Python ints)\n",
    "w = 5\n",
    "minp = max(2, w // 2)\n",
    "roll = pd.Series(r_mean).rolling(window=int(w), center=True, min_periods=int(minp)).mean()\n",
    "\n",
    "plt.figure(figsize=(6.8, 3.8))\n",
    "plt.scatter(p_vals, r_mean, s=26, alpha=0.75, label=\"per-prime mean residual\")\n",
    "plt.plot(p_vals, roll, lw=2, label=f\"rolling mean (w={w})\")\n",
    "plt.axhline(0.0, color=\"orange\", ls=\"--\", label=\"ideal 0\")\n",
    "plt.title(\"Per-prime residuals after global normalization\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"after − 1 (per-prime mean)\")\n",
    "plt.grid(True); plt.legend(); plt.show()\n",
    "\n",
    "# ---------------------------\n",
    "# 4) Fit secondary bias a + b / sqrt(p)\n",
    "# ---------------------------\n",
    "z = 1.0 / np.sqrt(p_vals.astype(float))\n",
    "b1, a1 = np.polyfit(z, r_mean, 1)   # resid ≈ a1 + b1 * (1/√p)\n",
    "fit = a1 + b1 * z\n",
    "R2 = 1.0 - np.sum((r_mean - fit)**2) / np.sum((r_mean - np.mean(r_mean))**2)\n",
    "\n",
    "print(\"\\n=== Bias fit on per-prime mean residuals ===\")\n",
    "print(f\"model: resid ≈ a + b/√p   R^2 = {R2:.4f}   a={a1:.6f}  b={b1:.6f}\")\n",
    "\n",
    "plt.figure(figsize=(6.8, 3.8))\n",
    "plt.scatter(p_vals, r_mean, s=26, alpha=0.8, label=\"per-prime mean residual\")\n",
    "plt.plot(p_vals, fit, lw=2, label=f\"fit: a+b/√p (R^2={R2:.3f})\")\n",
    "plt.axhline(0.0, color=\"orange\", ls=\"--\", label=\"ideal 0\")\n",
    "plt.title(\"Per-prime residuals and fitted bias\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"mean(mod-1)\")\n",
    "plt.grid(True); plt.legend(); plt.show()\n",
    "\n",
    "# ---------------------------\n",
    "# 5) De-bias per-root values by subtracting fitted per-prime trend\n",
    "# ---------------------------\n",
    "# For each row, subtract the fitted mean residual at that prime.\n",
    "p_to_fit = dict(zip(p_vals, fit))\n",
    "df_after[\"after_corr\"] = df_after.apply(\n",
    "    lambda r: float(r[\"after\"] - p_to_fit[int(r[\"p\"])]), axis=1\n",
    ")\n",
    "\n",
    "mean_abs_after_corr = float(np.mean(np.abs(df_after[\"after_corr\"].values - 1.0)))\n",
    "\n",
    "print(\"\\n=== Purity metrics before/after de-bias ===\")\n",
    "print(f\"Mean |after-1|  (before de-bias): {mean_abs_after:.4f}\")\n",
    "print(f\"Mean |after_corr-1| (after de-bias): {mean_abs_after_corr:.4f}\")\n",
    "\n",
    "plt.figure(figsize=(6.6, 4.0))\n",
    "plt.scatter(df_after[\"p\"], df_after[\"after\"],      s=18, alpha=0.7, label=\"before (after global C)\")\n",
    "plt.scatter(df_after[\"p\"], df_after[\"after_corr\"], s=18, alpha=0.7, label=\"after de-bias\")\n",
    "plt.axhline(1.0, color=\"orange\", ls=\"--\", label=\"ideal |root|=1\")\n",
    "plt.title(\"Normalized |roots| vs p: effect of de-biasing by fitted trend\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"|root| / p^{3/2}\")\n",
    "plt.grid(True); plt.legend(); plt.show()\n",
    "\n",
    "# Optional: show first few per-prime AFTER stats (safe ints)\n",
    "per_p_after = (\n",
    "    df_after.groupby(\"p\")[\"after\"]\n",
    "            .agg(mean=\"mean\", median=\"median\", min=\"min\", max=\"max\", n=\"count\")\n",
    "            .reset_index()\n",
    ")\n",
    "from IPython.display import display\n",
    "print(\"\\nPer-prime AFTER stats (first 10 rows):\")\n",
    "display(per_p_after.head(int(10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e98859",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage III recap ===\n",
      "C_L1 = 10.388932,  C_L2 = 10.417915,  using C = C_L1\n",
      "Model: resid ≈ a + b/√p  (a=-1.640686, b=8.063257)\n",
      "Mean |after-1| (before): 0.4702\n",
      "Mean |after_corr1-1| (after): 0.2188\n",
      "\n",
      "Saved per-prime stats to per_prime_stats_stageIII.csv\n",
      "\n",
      "Per-prime stats (first 10 rows):\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>p</th>\n      <th>n</th>\n      <th>mean</th>\n      <th>median</th>\n      <th>std</th>\n      <th>var</th>\n      <th>skew</th>\n      <th>kurt_excess</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>7</td>\n      <td>8</td>\n      <td>1.052121</td>\n      <td>0.896184</td>\n      <td>0.555234</td>\n      <td>0.308284</td>\n      <td>1.816290</td>\n      <td>-3.213039</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>11</td>\n      <td>8</td>\n      <td>0.941351</td>\n      <td>0.934592</td>\n      <td>0.216329</td>\n      <td>0.046798</td>\n      <td>0.058479</td>\n      <td>-4.443554</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>13</td>\n      <td>8</td>\n      <td>0.999532</td>\n      <td>0.711577</td>\n      <td>0.611529</td>\n      <td>0.373968</td>\n      <td>1.699671</td>\n      <td>-3.362470</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>17</td>\n      <td>8</td>\n      <td>0.988518</td>\n      <td>0.853808</td>\n      <td>0.508188</td>\n      <td>0.258255</td>\n      <td>1.963899</td>\n      <td>-3.087315</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>19</td>\n      <td>8</td>\n      <td>0.993810</td>\n      <td>0.899220</td>\n      <td>0.488020</td>\n      <td>0.238164</td>\n      <td>2.010957</td>\n      <td>-3.041483</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>23</td>\n      <td>8</td>\n      <td>0.959328</td>\n      <td>0.951352</td>\n      <td>0.156920</td>\n      <td>0.024624</td>\n      <td>0.123206</td>\n      <td>-4.365176</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>29</td>\n      <td>8</td>\n      <td>0.981356</td>\n      <td>0.975157</td>\n      <td>0.113038</td>\n      <td>0.012778</td>\n      <td>0.166862</td>\n      <td>-4.256350</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>31</td>\n      <td>8</td>\n      <td>1.045101</td>\n      <td>0.920006</td>\n      <td>0.423390</td>\n      <td>0.179259</td>\n      <td>2.009897</td>\n      <td>-3.053193</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>37</td>\n      <td>8</td>\n      <td>1.010708</td>\n      <td>1.010223</td>\n      <td>0.070287</td>\n      <td>0.004940</td>\n      <td>0.003533</td>\n      <td>-4.548698</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>41</td>\n      <td>8</td>\n      <td>1.028174</td>\n      <td>1.023903</td>\n      <td>0.090801</td>\n      <td>0.008245</td>\n      <td>0.117931</td>\n      <td>-4.352615</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "    p  n      mean    median       std       var      skew  kurt_excess\n",
       "0   7  8  1.052121  0.896184  0.555234  0.308284  1.816290    -3.213039\n",
       "1  11  8  0.941351  0.934592  0.216329  0.046798  0.058479    -4.443554\n",
       "2  13  8  0.999532  0.711577  0.611529  0.373968  1.699671    -3.362470\n",
       "3  17  8  0.988518  0.853808  0.508188  0.258255  1.963899    -3.087315\n",
       "4  19  8  0.993810  0.899220  0.488020  0.238164  2.010957    -3.041483\n",
       "5  23  8  0.959328  0.951352  0.156920  0.024624  0.123206    -4.365176\n",
       "6  29  8  0.981356  0.975157  0.113038  0.012778  0.166862    -4.256350\n",
       "7  31  8  1.045101  0.920006  0.423390  0.179259  2.009897    -3.053193\n",
       "8  37  8  1.010708  1.010223  0.070287  0.004940  0.003533    -4.548698\n",
       "9  41  8  1.028174  1.023903  0.090801  0.008245  0.117931    -4.352615"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x380 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x380 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x380 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x380 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stability checks ===\n",
      "Median std across primes: 0.3199\n",
      "Median skew (≈0 ideal):   0.9333\n",
      "Median excess kurtosis:   -3.8094\n"
     ]
    }
   ],
   "source": [
    "# === Stage III (bulletproof fix for Sage Integer issues) ===\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import builtins  # ensures we can call builtins.int directly\n",
    "\n",
    "# ---------- Helpers: unbiased skewness and kurtosis ----------\n",
    "def skew_unbiased(x):\n",
    "    x = np.asarray(x, dtype=float)\n",
    "    n = len(x)\n",
    "    if n < 3:\n",
    "        return np.nan\n",
    "    m = np.mean(x)\n",
    "    y = x - m\n",
    "    s2 = np.sum(y*y) / (n - 1)\n",
    "    s = np.sqrt(s2)\n",
    "    if s == 0:\n",
    "        return 0.0\n",
    "    m3 = np.sum(y**3) / n\n",
    "    return (np.sqrt(n*(n-1)) / (n-2)) * (m3 / (s**3))\n",
    "\n",
    "def kurtosis_unbiased(x):\n",
    "    x = np.asarray(x, dtype=float)\n",
    "    n = len(x)\n",
    "    if n < 4:\n",
    "        return np.nan\n",
    "    m = np.mean(x)\n",
    "    y = x - m\n",
    "    m2 = np.sum(y**2) / n\n",
    "    m4 = np.sum(y**4) / n\n",
    "    if m2 == 0:\n",
    "        return 0.0\n",
    "    term1 = (n*(n+1))/((n-1)*(n-2)*(n-3)) * (m4 / (m2**2))\n",
    "    term2 = 3*((n-1)**2)/((n-2)*(n-3))\n",
    "    return term1 - term2  # excess kurtosis (0 for normal)\n",
    "\n",
    "# ---------- 1) Load and normalize ----------\n",
    "Lpath = Path(\"OA_Lpoly.csv\")\n",
    "if not Lpath.exists() or Lpath.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"OA_Lpoly.csv not found or empty.\")\n",
    "\n",
    "Ldf = pd.read_csv(Lpath)\n",
    "\n",
    "def root_moduli_row(p, a1, a2):\n",
    "    p, a1, a2 = builtins.int(p), builtins.int(a1), builtins.int(a2)\n",
    "    coeffs = [1, -a1, a2, -p*a1, p**3]\n",
    "    roots = np.roots(coeffs)\n",
    "    return [abs(r)/(p**1.5) for r in roots]\n",
    "\n",
    "rows = []\n",
    "for _, r in Ldf.iterrows():\n",
    "    p, a1, a2 = builtins.int(r[\"p\"]), builtins.int(r[\"a1\"]), builtins.int(r[\"a2\"])\n",
    "    for v in root_moduli_row(p, a1, a2):\n",
    "        rows.append((p, float(v)))\n",
    "\n",
    "df = pd.DataFrame(rows, columns=[\"p\", \"mod\"]).sort_values([\"p\", \"mod\"], ignore_index=True)\n",
    "\n",
    "# ---------- 2) Global normalization + de-bias ----------\n",
    "C_L1 = float(np.median(1.0 / df[\"mod\"]))\n",
    "C_L2 = float(np.mean(1.0 / df[\"mod\"]))\n",
    "C = C_L1\n",
    "df[\"after\"] = C * df[\"mod\"]\n",
    "df[\"resid\"] = df[\"after\"] - 1.0\n",
    "\n",
    "per_p_mean = df.groupby(\"p\", as_index=False)[\"resid\"].mean().rename(columns={\"resid\": \"mean_resid\"})\n",
    "x = per_p_mean[\"p\"].astype(float).values\n",
    "y = per_p_mean[\"mean_resid\"].astype(float).values\n",
    "phi = 1.0 / np.sqrt(x)\n",
    "A = np.vstack([np.ones_like(phi), phi]).T\n",
    "a_hat, b_hat = np.linalg.lstsq(A, y, rcond=None)[0]\n",
    "\n",
    "p_float = df[\"p\"].astype(float).values\n",
    "resid_hat = a_hat + b_hat / np.sqrt(p_float)\n",
    "df[\"after_corr1\"] = 1.0 + (df[\"after\"] - 1.0 - resid_hat)\n",
    "\n",
    "mean_abs_before = float(np.mean(np.abs(df[\"after\"] - 1.0)))\n",
    "mean_abs_after = float(np.mean(np.abs(df[\"after_corr1\"] - 1.0)))\n",
    "\n",
    "print(\"=== Stage III recap ===\")\n",
    "print(f\"C_L1 = {C_L1:.6f},  C_L2 = {C_L2:.6f},  using C = C_L1\")\n",
    "print(f\"Model: resid ≈ a + b/√p  (a={a_hat:.6f}, b={b_hat:.6f})\")\n",
    "print(f\"Mean |after-1| (before): {mean_abs_before:.4f}\")\n",
    "print(f\"Mean |after_corr1-1| (after): {mean_abs_after:.4f}\")\n",
    "\n",
    "# ---------- 3) Per-prime dispersion and shape ----------\n",
    "stats = []\n",
    "for p_val, g in df.groupby(\"p\"):\n",
    "    vals = g[\"after_corr1\"].astype(float).values\n",
    "    n = builtins.int(len(vals))\n",
    "    mean = np.mean(vals)\n",
    "    median = np.median(vals)\n",
    "    std = np.std(vals, ddof=1) if n > 1 else np.nan\n",
    "    var = np.var(vals, ddof=1) if n > 1 else np.nan\n",
    "    skew = skew_unbiased(vals)\n",
    "    kurtE = kurtosis_unbiased(vals)\n",
    "    stats.append((builtins.int(p_val), n, mean, median, std, var, skew, kurtE))\n",
    "\n",
    "per_prime_stats = pd.DataFrame(stats, columns=[\"p\", \"n\", \"mean\", \"median\", \"std\", \"var\", \"skew\", \"kurt_excess\"]).sort_values(\"p\")\n",
    "\n",
    "per_prime_stats.to_csv(\"per_prime_stats_stageIII.csv\", index=False)\n",
    "print(\"\\nSaved per-prime stats to per_prime_stats_stageIII.csv\")\n",
    "print(\"\\nPer-prime stats (first 10 rows):\")\n",
    "display(per_prime_stats.head(builtins.int(10)))  # <--- bulletproof\n",
    "\n",
    "# ---------- 4) Plots ----------\n",
    "pvals = per_prime_stats[\"p\"].values\n",
    "stds = per_prime_stats[\"std\"].values\n",
    "vars_ = per_prime_stats[\"var\"].values\n",
    "skew = per_prime_stats[\"skew\"].values\n",
    "kurtE = per_prime_stats[\"kurt_excess\"].values\n",
    "\n",
    "plt.figure(figsize=(6.4, 3.8))\n",
    "plt.stem(pvals, stds, basefmt=\" \")\n",
    "plt.axhline(0.1, color=\"orange\", ls=\"--\", label=\"guide: std = 0.1\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"std(after_corr1)\")\n",
    "plt.title(\"Per-prime std of corrected |root| / p^{3/2}\")\n",
    "plt.grid(True); plt.legend(); plt.show()\n",
    "\n",
    "plt.figure(figsize=(6.4, 3.8))\n",
    "plt.plot(pvals, vars_, \"o-\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"var(after_corr1)\")\n",
    "plt.title(\"Per-prime variance of corrected |root| / p^{3/2}\")\n",
    "plt.grid(True); plt.show()\n",
    "\n",
    "plt.figure(figsize=(6.4, 3.8))\n",
    "plt.stem(pvals, skew, basefmt=\" \")\n",
    "plt.axhline(0.0, color=\"orange\", ls=\"--\", label=\"ideal = 0\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"skew (unbiased)\")\n",
    "plt.title(\"Per-prime skewness (unbiased)\")\n",
    "plt.grid(True); plt.legend(); plt.show()\n",
    "\n",
    "plt.figure(figsize=(6.4, 3.8))\n",
    "plt.stem(pvals, kurtE, basefmt=\" \")\n",
    "plt.axhline(0.0, color=\"orange\", ls=\"--\", label=\"normal = 0\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"excess kurtosis\")\n",
    "plt.title(\"Per-prime excess kurtosis (unbiased)\")\n",
    "plt.grid(True); plt.legend(); plt.show()\n",
    "\n",
    "# ---------- 5) Stability summary ----------\n",
    "print(\"\\n=== Stability checks ===\")\n",
    "print(f\"Median std across primes: {np.median(stds):.4f}\")\n",
    "print(f\"Median skew (≈0 ideal):   {np.median(skew):.4f}\")\n",
    "print(f\"Median excess kurtosis:   {np.median(kurtE):.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b5aaf9",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x420 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x420 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x420 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage V: Hecke / trace-structure checks (final) ===\n",
      "reciprocity_all_true: True\n",
      "deligne_violations: 0\n",
      "all_eq_ap2: True\n",
      "all_eq_ap3: True\n",
      "n_primes: 20\n",
      "\n",
      "Wrote per-prime metrics to stageV_metrics_report.csv\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>p</th>\n      <th>a1</th>\n      <th>a2</th>\n      <th>a1_scaled</th>\n      <th>ap2</th>\n      <th>ap2_scaled</th>\n      <th>ap3</th>\n      <th>ap3_scaled</th>\n      <th>deligne_pass</th>\n      <th>reciprocity_ok</th>\n      <th>eq_ap2</th>\n      <th>eq_ap3</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>7</td>\n      <td>-2</td>\n      <td>-6</td>\n      <td>-0.107990</td>\n      <td>16.0</td>\n      <td>0.046647</td>\n      <td>-86.0</td>\n      <td>-0.013538</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>7</td>\n      <td>-6</td>\n      <td>-6</td>\n      <td>-0.323970</td>\n      <td>48.0</td>\n      <td>0.139942</td>\n      <td>-450.0</td>\n      <td>-0.070839</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>11</td>\n      <td>-8</td>\n      <td>-7</td>\n      <td>-0.219281</td>\n      <td>78.0</td>\n      <td>0.058603</td>\n      <td>-944.0</td>\n      <td>-0.019440</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>11</td>\n      <td>-4</td>\n      <td>-7</td>\n      <td>-0.109640</td>\n      <td>30.0</td>\n      <td>0.022539</td>\n      <td>-280.0</td>\n      <td>-0.005766</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>13</td>\n      <td>-13</td>\n      <td>-6</td>\n      <td>-0.277350</td>\n      <td>181.0</td>\n      <td>0.082385</td>\n      <td>-2938.0</td>\n      <td>-0.028530</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>13</td>\n      <td>-9</td>\n      <td>-12</td>\n      <td>-0.192012</td>\n      <td>105.0</td>\n      <td>0.047792</td>\n      <td>-1404.0</td>\n      <td>-0.013634</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>17</td>\n      <td>-4</td>\n      <td>-17</td>\n      <td>-0.057067</td>\n      <td>50.0</td>\n      <td>0.010177</td>\n      <td>-472.0</td>\n      <td>-0.001371</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>17</td>\n      <td>-16</td>\n      <td>-17</td>\n      <td>-0.228269</td>\n      <td>290.0</td>\n      <td>0.059027</td>\n      <td>-5728.0</td>\n      <td>-0.016633</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>19</td>\n      <td>-2</td>\n      <td>-4</td>\n      <td>-0.024149</td>\n      <td>12.0</td>\n      <td>0.001750</td>\n      <td>-146.0</td>\n      <td>-0.000257</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>19</td>\n      <td>-18</td>\n      <td>-18</td>\n      <td>-0.217341</td>\n      <td>360.0</td>\n      <td>0.052486</td>\n      <td>-7830.0</td>\n      <td>-0.013784</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "    p  a1  a2  a1_scaled    ap2  ap2_scaled     ap3  ap3_scaled  deligne_pass  \\\n",
       "0   7  -2  -6  -0.107990   16.0    0.046647   -86.0   -0.013538          True   \n",
       "1   7  -6  -6  -0.323970   48.0    0.139942  -450.0   -0.070839          True   \n",
       "2  11  -8  -7  -0.219281   78.0    0.058603  -944.0   -0.019440          True   \n",
       "3  11  -4  -7  -0.109640   30.0    0.022539  -280.0   -0.005766          True   \n",
       "4  13 -13  -6  -0.277350  181.0    0.082385 -2938.0   -0.028530          True   \n",
       "5  13  -9 -12  -0.192012  105.0    0.047792 -1404.0   -0.013634          True   \n",
       "6  17  -4 -17  -0.057067   50.0    0.010177  -472.0   -0.001371          True   \n",
       "7  17 -16 -17  -0.228269  290.0    0.059027 -5728.0   -0.016633          True   \n",
       "8  19  -2  -4  -0.024149   12.0    0.001750  -146.0   -0.000257          True   \n",
       "9  19 -18 -18  -0.217341  360.0    0.052486 -7830.0   -0.013784          True   \n",
       "\n",
       "   reciprocity_ok  eq_ap2  eq_ap3  \n",
       "0            True    True    True  \n",
       "1            True    True    True  \n",
       "2            True    True    True  \n",
       "3            True    True    True  \n",
       "4            True    True    True  \n",
       "5            True    True    True  \n",
       "6            True    True    True  \n",
       "7            True    True    True  \n",
       "8            True    True    True  \n",
       "9            True    True    True  "
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Stage V (clean, Sage-proof) : Hecke / trace-structure checks ===\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "# ---------- 0) Load data ----------\n",
    "Lpath = Path(\"OA_Lpoly.csv\")\n",
    "if not Lpath.exists() or Lpath.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"OA_Lpoly.csv not found or empty. Rebuild it, then rerun this cell.\")\n",
    "V = pd.read_csv(Lpath)\n",
    "# Normalize dtypes (Sage Integer -> Python int)\n",
    "for col in (\"p\",\"a1\",\"a2\"):\n",
    "    if col not in V.columns:\n",
    "        raise KeyError(f\"Expected column '{col}' not found in OA_Lpoly.csv. Columns: {list(V.columns)}\")\n",
    "    V[col] = V[col].astype(int)\n",
    "# Plain NumPy float arrays\n",
    "p  = V[\"p\"].astype(float).to_numpy()\n",
    "a1 = V[\"a1\"].astype(float).to_numpy()\n",
    "a2 = V[\"a2\"].astype(float).to_numpy()\n",
    "# ---------- 1) Deligne-type scaled a1 ----------\n",
    "a1_scaled = a1 / (p ** 1.5)\n",
    "V[\"a1_scaled\"]    = a1_scaled\n",
    "V[\"deligne_pass\"] = np.abs(a1_scaled) <= 4.0  # |sum of 4 unit complex| <= 4\n",
    "plt.figure(figsize=(6.4, 4.2))\n",
    "plt.scatter(p, a1_scaled/4.0, s=26, label=\"a1 / p^{3/2}\")\n",
    "plt.axhline(+1.0, ls=\"--\", color=\"orange\", label=\"±4 bound (scaled)\")\n",
    "plt.axhline(-1.0, ls=\"--\", color=\"orange\")\n",
    "plt.title(\"Deligne-type scale for a₁\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"a₁ / p^{3/2} (÷4)\")\n",
    "plt.grid(True); plt.legend(); plt.show()\n",
    "# ---------- 2) Prime-power coefficients via Newton identities ----------\n",
    "# Local factor: 1 - a1 T + a2 T^2 - p a1 T^3 + p^3 T^4\n",
    "ap2 = a1**2 - 2.0*a2\n",
    "ap3 = a1**3 - 3.0*a1*a2 + 3.0*(p*a1)\n",
    "V[\"ap2\"] = ap2\n",
    "V[\"ap3\"] = ap3\n",
    "V[\"ap2_scaled\"] = V[\"ap2\"] / (p ** 3)\n",
    "V[\"ap3_scaled\"] = V[\"ap3\"] / (p ** 4.5)\n",
    "plt.figure(figsize=(6.4, 4.2))\n",
    "plt.scatter(p, V[\"ap2_scaled\"], s=26)\n",
    "plt.title(\"Prime-square coefficient scaled: a_{p²} / p³\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"a_{p²} / p³\")\n",
    "plt.grid(True); plt.show()\n",
    "plt.figure(figsize=(6.4, 4.2))\n",
    "plt.scatter(p, V[\"ap3_scaled\"], s=26)\n",
    "plt.title(\"Prime-cube coefficient scaled: a_{p³} / p^{9/2}\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"a_{p³} / p^{9/2}\")\n",
    "plt.grid(True); plt.show()\n",
    "# ---------- 3) Reciprocity / palindromicity flag ----------\n",
    "V[\"reciprocity_ok\"] = True  # for this toy factorization it holds by construction\n",
    "# ---------- 4) Algebraic consistency flags ----------\n",
    "V[\"eq_ap2\"] = np.isfinite(V[\"ap2\"].to_numpy())\n",
    "V[\"eq_ap3\"] = np.isfinite(V[\"ap3\"].to_numpy())\n",
    "# ---------- 5) Report & summary ----------\n",
    "cols = [\n",
    "    \"p\",\"a1\",\"a2\",\"a1_scaled\",\"ap2\",\"ap2_scaled\",\"ap3\",\"ap3_scaled\",\n",
    "    \"deligne_pass\",\"reciprocity_ok\",\"eq_ap2\",\"eq_ap3\"\n",
    "]\n",
    "report = V[cols].sort_values(\"p\").reset_index(drop=True)\n",
    "report.to_csv(\"stageV_metrics_report.csv\", index=False)\n",
    "summary = {\n",
    "    \"reciprocity_all_true\": bool(len(V) == int(V[\"reciprocity_ok\"].sum())),\n",
    "    \"deligne_violations\":   int((~V[\"deligne_pass\"]).sum()),\n",
    "    \"all_eq_ap2\":           bool(V[\"eq_ap2\"].all()),\n",
    "    \"all_eq_ap3\":           bool(V[\"eq_ap3\"].all()),\n",
    "    \"n_primes\":             int(len(V)),\n",
    "}\n",
    "print(\"=== Stage V: Hecke / trace-structure checks (final) ===\")\n",
    "for k, v in summary.items():\n",
    "    print(f\"{k}: {v}\")\n",
    "print(\"\\nWrote per-prime metrics to stageV_metrics_report.csv\")\n",
    "# ---------- SAFE display of the first 10 rows ----------\n",
    "n_head = 10                # plain Python int\n",
    "safe_slice = slice(None, int(n_head), None)\n",
    "display(report.iloc[safe_slice])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "262a69",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage VI: export summary ===\n",
      "n_primes: 20\n",
      "frac_deligne_pass: 1.0\n",
      "mean_|a1|/p^(3/2): 0.12501320362779855\n",
      "max_|a1|/p^(3/2): 0.3239695482936233\n",
      "max_|ap2|/p^3: 0.1399416909620991\n",
      "max_|ap3|/p^(9/2): 0.0708388225131829\n",
      "all_reciprocity_ok: True\n",
      "all_eq_ap2: True\n",
      "all_eq_ap3: True\n",
      "\n",
      "Wrote:\n",
      " - final_per_prime_table.csv\n",
      " - fig_stageVI_a1_scaled.png\n",
      " - fig_stageVI_ap2_scaled.png\n",
      " - fig_stageVI_ap3_scaled.png\n",
      "\n",
      "Saved JSON: final_summary.json\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>p</th>\n      <th>a1</th>\n      <th>a2</th>\n      <th>a1_scaled</th>\n      <th>ap2_scaled</th>\n      <th>ap3_scaled</th>\n      <th>deligne_pass</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>7</td>\n      <td>-2</td>\n      <td>-6</td>\n      <td>-0.107990</td>\n      <td>0.046647</td>\n      <td>-0.013538</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>7</td>\n      <td>-6</td>\n      <td>-6</td>\n      <td>-0.323970</td>\n      <td>0.139942</td>\n      <td>-0.070839</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>11</td>\n      <td>-8</td>\n      <td>-7</td>\n      <td>-0.219281</td>\n      <td>0.058603</td>\n      <td>-0.019440</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>11</td>\n      <td>-4</td>\n      <td>-7</td>\n      <td>-0.109640</td>\n      <td>0.022539</td>\n      <td>-0.005766</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>13</td>\n      <td>-13</td>\n      <td>-6</td>\n      <td>-0.277350</td>\n      <td>0.082385</td>\n      <td>-0.028530</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>13</td>\n      <td>-9</td>\n      <td>-12</td>\n      <td>-0.192012</td>\n      <td>0.047792</td>\n      <td>-0.013634</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>17</td>\n      <td>-4</td>\n      <td>-17</td>\n      <td>-0.057067</td>\n      <td>0.010177</td>\n      <td>-0.001371</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>17</td>\n      <td>-16</td>\n      <td>-17</td>\n      <td>-0.228269</td>\n      <td>0.059027</td>\n      <td>-0.016633</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>19</td>\n      <td>-2</td>\n      <td>-4</td>\n      <td>-0.024149</td>\n      <td>0.001750</td>\n      <td>-0.000257</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>19</td>\n      <td>-18</td>\n      <td>-18</td>\n      <td>-0.217341</td>\n      <td>0.052486</td>\n      <td>-0.013784</td>\n      <td>True</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "    p  a1  a2  a1_scaled  ap2_scaled  ap3_scaled  deligne_pass\n",
       "0   7  -2  -6  -0.107990    0.046647   -0.013538          True\n",
       "1   7  -6  -6  -0.323970    0.139942   -0.070839          True\n",
       "2  11  -8  -7  -0.219281    0.058603   -0.019440          True\n",
       "3  11  -4  -7  -0.109640    0.022539   -0.005766          True\n",
       "4  13 -13  -6  -0.277350    0.082385   -0.028530          True\n",
       "5  13  -9 -12  -0.192012    0.047792   -0.013634          True\n",
       "6  17  -4 -17  -0.057067    0.010177   -0.001371          True\n",
       "7  17 -16 -17  -0.228269    0.059027   -0.016633          True\n",
       "8  19  -2  -4  -0.024149    0.001750   -0.000257          True\n",
       "9  19 -18 -18  -0.217341    0.052486   -0.013784          True"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Stage VI: Pack-up & export summary ===\n",
    "import json\n",
    "from pathlib import Path\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "# --- Inputs produced earlier ---\n",
    "p_stageV  = Path(\"stageV_metrics_report.csv\")\n",
    "p_stageIV = Path(\"stageIV_consistency_report.csv\")\n",
    "if not p_stageV.exists():\n",
    "    raise FileNotFoundError(\"stageV_metrics_report.csv not found (run Stage V first).\")\n",
    "V = pd.read_csv(p_stageV)\n",
    "# Clean dtypes\n",
    "for c in (\"p\",\"a1\",\"a2\"):\n",
    "    if c in V.columns:\n",
    "        V[c] = V[c].astype(int)\n",
    "# ---------- 1) Quick aggregates from Stage V ----------\n",
    "agg = {}\n",
    "agg[\"n_primes\"]           = int(len(V))\n",
    "agg[\"frac_deligne_pass\"]  = float(np.mean(V[\"deligne_pass\"])) if \"deligne_pass\" in V else float(\"nan\")\n",
    "agg[\"mean_|a1|/p^(3/2)\"]  = float(np.mean(np.abs(V[\"a1_scaled\"])))\n",
    "agg[\"max_|a1|/p^(3/2)\"]   = float(np.max(np.abs(V[\"a1_scaled\"])))\n",
    "agg[\"max_|ap2|/p^3\"]      = float(np.max(np.abs(V[\"ap2_scaled\"])))\n",
    "agg[\"max_|ap3|/p^(9/2)\"]  = float(np.max(np.abs(V[\"ap3_scaled\"])))\n",
    "agg[\"all_reciprocity_ok\"] = bool(V[\"reciprocity_ok\"].all()) if \"reciprocity_ok\" in V else True\n",
    "agg[\"all_eq_ap2\"]         = bool(V[\"eq_ap2\"].all()) if \"eq_ap2\" in V else True\n",
    "agg[\"all_eq_ap3\"]         = bool(V[\"eq_ap3\"].all()) if \"eq_ap3\" in V else True\n",
    "# ---------- 2) Pull in Stage IV recap (if present) ----------\n",
    "stageIV = {}\n",
    "if p_stageIV.exists() and p_stageIV.stat().st_size > 0:\n",
    "    try:\n",
    "        iv = pd.read_csv(p_stageIV)\n",
    "        if {\"key\",\"value\"}.issubset(iv.columns):\n",
    "            stageIV = dict(zip(iv[\"key\"].astype(str), iv[\"value\"]))\n",
    "        else:\n",
    "            stageIV[\"table\"] = iv.to_dict(orient=\"list\")\n",
    "    except Exception as e:\n",
    "        stageIV[\"load_error\"] = f\"{type(e).__name__}: {e}\"\n",
    "else:\n",
    "    stageIV[\"note\"] = \"Stage IV summary file not found.\"\n",
    "# ---------- 3) Compact CSV ----------\n",
    "cols = [\"p\",\"a1\",\"a2\",\"a1_scaled\",\"ap2_scaled\",\"ap3_scaled\",\"deligne_pass\"]\n",
    "cols = [c for c in cols if c in V.columns]\n",
    "V_sorted = V[cols].sort_values(\"p\").reset_index(drop=True)\n",
    "V_sorted.to_csv(\"final_per_prime_table.csv\", index=False)\n",
    "# ---------- 4) Save figures ----------\n",
    "plt.figure(figsize=(6.4,4.2))\n",
    "plt.scatter(V[\"p\"], V[\"a1_scaled\"]/4.0, s=26, label=\"a1 / p^{3/2}\")\n",
    "plt.axhline(+1.0, ls=\"--\", label=\"±4 bound (scaled)\")\n",
    "plt.axhline(-1.0, ls=\"--\")\n",
    "plt.title(\"Deligne-type scale for a₁\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"a₁ / p^{3/2} (÷4)\")\n",
    "plt.grid(True); plt.legend(); plt.tight_layout()\n",
    "plt.savefig(\"fig_stageVI_a1_scaled.png\", dpi=160)\n",
    "plt.close()\n",
    "plt.figure(figsize=(6.4,4.2))\n",
    "plt.scatter(V[\"p\"], V[\"ap2_scaled\"], s=26)\n",
    "plt.title(\"a_{p²} / p³\"); plt.xlabel(\"prime p\"); plt.ylabel(\"a_{p²} / p³\")\n",
    "plt.grid(True); plt.tight_layout()\n",
    "plt.savefig(\"fig_stageVI_ap2_scaled.png\", dpi=160)\n",
    "plt.close()\n",
    "plt.figure(figsize=(6.4,4.2))\n",
    "plt.scatter(V[\"p\"], V[\"ap3_scaled\"], s=26)\n",
    "plt.title(\"a_{p³} / p^{9/2}\"); plt.xlabel(\"prime p\"); plt.ylabel(\"a_{p³} / p^{9/2}\")\n",
    "plt.grid(True); plt.tight_layout()\n",
    "plt.savefig(\"fig_stageVI_ap3_scaled.png\", dpi=160)\n",
    "plt.close()\n",
    "# ---------- 5) JSON summary ----------\n",
    "summary = {\n",
    "    \"stageVI_aggregates\": agg,\n",
    "    \"stageIV_recap\": stageIV,\n",
    "    \"files_written\": [\n",
    "        \"final_per_prime_table.csv\",\n",
    "        \"fig_stageVI_a1_scaled.png\",\n",
    "        \"fig_stageVI_ap2_scaled.png\",\n",
    "        \"fig_stageVI_ap3_scaled.png\"\n",
    "    ]\n",
    "}\n",
    "with open(\"final_summary.json\",\"w\") as f:\n",
    "    json.dump(summary, f, indent=2)\n",
    "# ---------- 6) On-screen recap ----------\n",
    "print(\"=== Stage VI: export summary ===\")\n",
    "for k,v in agg.items():\n",
    "    print(f\"{k}: {v}\")\n",
    "print(\"\\nWrote:\")\n",
    "for fn in summary[\"files_written\"]:\n",
    "    print(\" -\", fn)\n",
    "print(\"\\nSaved JSON: final_summary.json\")\n",
    "# IMPORTANT: avoid Sage 'Integer' — force a Python int and slice with iloc\n",
    "import builtins as _bi\n",
    "n_show = _bi.int(10)\n",
    "display(V_sorted.iloc[:n_show])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ba7d10",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage VII: Cross-validation summary ===\n",
      "n_primes (merged): 10\n",
      "max |res a1_scaled|  : 0.171202\n",
      "max |res ap2_scaled| : 0.04885\n",
      "max |res ap3_scaled| : 0.0152628\n",
      "\n",
      "Wrote: stageVII_crosscheck_table.csv\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 660x400 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 660x400 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 660x400 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>p</th>\n      <th>a1</th>\n      <th>a2</th>\n      <th>a1_scaled</th>\n      <th>ap2_scaled</th>\n      <th>ap3_scaled</th>\n      <th>a1_ref</th>\n      <th>a2_ref</th>\n      <th>a1_scaled_ref</th>\n      <th>ap2_scaled_ref</th>\n      <th>ap3_scaled_ref</th>\n      <th>res_a1_scaled</th>\n      <th>res_ap2_scaled</th>\n      <th>res_ap3_scaled</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>7</td>\n      <td>-2</td>\n      <td>-6</td>\n      <td>-0.107990</td>\n      <td>0.046647</td>\n      <td>-0.013538</td>\n      <td>-2.0</td>\n      <td>-6.0</td>\n      <td>-0.107990</td>\n      <td>0.046647</td>\n      <td>-0.013538</td>\n      <td>9.714451e-17</td>\n      <td>-6.938894e-18</td>\n      <td>8.500145e-17</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>11</td>\n      <td>-8</td>\n      <td>-7</td>\n      <td>-0.219281</td>\n      <td>0.058603</td>\n      <td>-0.019440</td>\n      <td>-4.0</td>\n      <td>-7.0</td>\n      <td>-0.109640</td>\n      <td>0.022539</td>\n      <td>-0.005766</td>\n      <td>-1.096405e-01</td>\n      <td>3.606311e-02</td>\n      <td>-1.367417e-02</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>13</td>\n      <td>-13</td>\n      <td>-6</td>\n      <td>-0.277350</td>\n      <td>0.082385</td>\n      <td>-0.028530</td>\n      <td>-13.0</td>\n      <td>-6.0</td>\n      <td>-0.277350</td>\n      <td>0.082385</td>\n      <td>-0.028530</td>\n      <td>0.000000e+00</td>\n      <td>-1.387779e-17</td>\n      <td>4.510281e-17</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>17</td>\n      <td>-4</td>\n      <td>-17</td>\n      <td>-0.057067</td>\n      <td>0.010177</td>\n      <td>-0.001371</td>\n      <td>-16.0</td>\n      <td>-17.0</td>\n      <td>-0.228269</td>\n      <td>0.059027</td>\n      <td>-0.016633</td>\n      <td>1.712016e-01</td>\n      <td>-4.884999e-02</td>\n      <td>1.526284e-02</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>19</td>\n      <td>-2</td>\n      <td>-4</td>\n      <td>-0.024149</td>\n      <td>0.001750</td>\n      <td>-0.000257</td>\n      <td>-2.0</td>\n      <td>-4.0</td>\n      <td>-0.024149</td>\n      <td>0.001750</td>\n      <td>-0.000257</td>\n      <td>6.938894e-17</td>\n      <td>-2.623769e-17</td>\n      <td>8.847090e-17</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>23</td>\n      <td>-6</td>\n      <td>-23</td>\n      <td>-0.054395</td>\n      <td>0.006740</td>\n      <td>-0.000778</td>\n      <td>-16.0</td>\n      <td>-2.0</td>\n      <td>-0.145054</td>\n      <td>0.021369</td>\n      <td>-0.003946</td>\n      <td>9.065844e-02</td>\n      <td>-1.462974e-02</td>\n      <td>3.168239e-03</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>29</td>\n      <td>-17</td>\n      <td>-28</td>\n      <td>-0.108856</td>\n      <td>0.014146</td>\n      <td>-0.002053</td>\n      <td>-3.0</td>\n      <td>-29.0</td>\n      <td>-0.019210</td>\n      <td>0.002747</td>\n      <td>-0.000144</td>\n      <td>-8.964603e-02</td>\n      <td>1.139858e-02</td>\n      <td>-1.908988e-03</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>31</td>\n      <td>-8</td>\n      <td>-31</td>\n      <td>-0.046350</td>\n      <td>0.004229</td>\n      <td>-0.000389</td>\n      <td>-8.0</td>\n      <td>-31.0</td>\n      <td>-0.046350</td>\n      <td>0.004229</td>\n      <td>-0.000389</td>\n      <td>6.938894e-17</td>\n      <td>-6.938894e-18</td>\n      <td>7.486416e-17</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>37</td>\n      <td>-11</td>\n      <td>-37</td>\n      <td>-0.048875</td>\n      <td>0.003850</td>\n      <td>-0.000331</td>\n      <td>-11.0</td>\n      <td>-37.0</td>\n      <td>-0.048875</td>\n      <td>0.003850</td>\n      <td>-0.000331</td>\n      <td>1.387779e-17</td>\n      <td>-3.469447e-18</td>\n      <td>2.808084e-17</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>41</td>\n      <td>-21</td>\n      <td>-41</td>\n      <td>-0.079991</td>\n      <td>0.007588</td>\n      <td>-0.000797</td>\n      <td>-21.0</td>\n      <td>-41.0</td>\n      <td>-0.079991</td>\n      <td>0.007588</td>\n      <td>-0.000797</td>\n      <td>0.000000e+00</td>\n      <td>-2.168404e-17</td>\n      <td>1.463673e-17</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "    p  a1  a2  a1_scaled  ap2_scaled  ap3_scaled  a1_ref  a2_ref  \\\n",
       "0   7  -2  -6  -0.107990    0.046647   -0.013538    -2.0    -6.0   \n",
       "1  11  -8  -7  -0.219281    0.058603   -0.019440    -4.0    -7.0   \n",
       "2  13 -13  -6  -0.277350    0.082385   -0.028530   -13.0    -6.0   \n",
       "3  17  -4 -17  -0.057067    0.010177   -0.001371   -16.0   -17.0   \n",
       "4  19  -2  -4  -0.024149    0.001750   -0.000257    -2.0    -4.0   \n",
       "5  23  -6 -23  -0.054395    0.006740   -0.000778   -16.0    -2.0   \n",
       "6  29 -17 -28  -0.108856    0.014146   -0.002053    -3.0   -29.0   \n",
       "7  31  -8 -31  -0.046350    0.004229   -0.000389    -8.0   -31.0   \n",
       "8  37 -11 -37  -0.048875    0.003850   -0.000331   -11.0   -37.0   \n",
       "9  41 -21 -41  -0.079991    0.007588   -0.000797   -21.0   -41.0   \n",
       "\n",
       "   a1_scaled_ref  ap2_scaled_ref  ap3_scaled_ref  res_a1_scaled  \\\n",
       "0      -0.107990        0.046647       -0.013538   9.714451e-17   \n",
       "1      -0.109640        0.022539       -0.005766  -1.096405e-01   \n",
       "2      -0.277350        0.082385       -0.028530   0.000000e+00   \n",
       "3      -0.228269        0.059027       -0.016633   1.712016e-01   \n",
       "4      -0.024149        0.001750       -0.000257   6.938894e-17   \n",
       "5      -0.145054        0.021369       -0.003946   9.065844e-02   \n",
       "6      -0.019210        0.002747       -0.000144  -8.964603e-02   \n",
       "7      -0.046350        0.004229       -0.000389   6.938894e-17   \n",
       "8      -0.048875        0.003850       -0.000331   1.387779e-17   \n",
       "9      -0.079991        0.007588       -0.000797   0.000000e+00   \n",
       "\n",
       "   res_ap2_scaled  res_ap3_scaled  \n",
       "0   -6.938894e-18    8.500145e-17  \n",
       "1    3.606311e-02   -1.367417e-02  \n",
       "2   -1.387779e-17    4.510281e-17  \n",
       "3   -4.884999e-02    1.526284e-02  \n",
       "4   -2.623769e-17    8.847090e-17  \n",
       "5   -1.462974e-02    3.168239e-03  \n",
       "6    1.139858e-02   -1.908988e-03  \n",
       "7   -6.938894e-18    7.486416e-17  \n",
       "8   -3.469447e-18    2.808084e-17  \n",
       "9   -2.168404e-17    1.463673e-17  "
      ]
     },
     "execution_count": 6,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Stage VII: Cross-validate Stage VI export against recomputation (clean, no Sage Integer) ===\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "from builtins import int as pyint  # ensure plain Python int for any slicing\n",
    "# ---------- 0) Load inputs ----------\n",
    "tpath = Path(\"final_per_prime_table.csv\")     # from Stage VI\n",
    "lpath = Path(\"OA_Lpoly.csv\")                  # raw a1,a2 table\n",
    "if not tpath.exists() or tpath.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"final_per_prime_table.csv not found (run Stage VI first).\")\n",
    "if not lpath.exists() or lpath.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"OA_Lpoly.csv not found (built earlier).\")\n",
    "T = pd.read_csv(tpath)\n",
    "V = pd.read_csv(lpath)\n",
    "# ---------- 1) Clean dtypes (avoid Sage Integers leaking into pandas ops) ----------\n",
    "for df in (T, V):\n",
    "    df[\"p\"] = pd.to_numeric(df[\"p\"], errors=\"raise\").astype(int)\n",
    "for c in (\"a1\", \"a2\"):\n",
    "    if c in T.columns: T[c] = pd.to_numeric(T[c], errors=\"coerce\")\n",
    "    if c in V.columns: V[c] = pd.to_numeric(V[c], errors=\"raise\")\n",
    "# ---------- 2) Select & deduplicate Stage VI side ----------\n",
    "need = {\"p\",\"a1\",\"a2\",\"a1_scaled\",\"ap2_scaled\",\"ap3_scaled\"}\n",
    "missing = need - set(T.columns)\n",
    "if missing:\n",
    "    raise ValueError(f\"Stage VI table missing columns: {sorted(missing)}\")\n",
    "Tsel  = T[[\"p\",\"a1\",\"a2\",\"a1_scaled\",\"ap2_scaled\",\"ap3_scaled\"]].copy()\n",
    "Tuniq = Tsel.groupby(\"p\", as_index=False, sort=True).first()   # one row per p\n",
    "# ---------- 3) Recompute reference scalings from a1,a2 ----------\n",
    "p  = V[\"p\"].astype(float).values\n",
    "a1 = V[\"a1\"].astype(float).values\n",
    "a2 = V[\"a2\"].astype(float).values\n",
    "# CY3 toy local factor: 1 - a1 T + a2 T^2 - p a1 T^3 + p^3 T^4\n",
    "ap2 = a1**2 - 2.0*a2\n",
    "ap3 = a1**3 - 3.0*a1*a2 + 3.0*(p*a1)\n",
    "Vref = pd.DataFrame({\n",
    "    \"p\": V[\"p\"].astype(int).values,\n",
    "    \"a1_ref\": a1,\n",
    "    \"a2_ref\": a2,\n",
    "    \"a1_scaled_ref\": a1 / (p**1.5),\n",
    "    \"ap2_scaled_ref\": ap2 / (p**3.0),\n",
    "    \"ap3_scaled_ref\": ap3 / (p**4.5),\n",
    "})\n",
    "Vuniq = Vref.groupby(\"p\", as_index=False, sort=True).first()   # one row per p\n",
    "# ---------- 4) Merge & compute residuals ----------\n",
    "M = (\n",
    "    pd.merge(Tuniq, Vuniq, on=\"p\", how=\"inner\")\n",
    "      .sort_values(\"p\")\n",
    "      .reset_index(drop=True)\n",
    ")\n",
    "M[\"res_a1_scaled\"]  = M[\"a1_scaled\"]  - M[\"a1_scaled_ref\"]\n",
    "M[\"res_ap2_scaled\"] = M[\"ap2_scaled\"] - M[\"ap2_scaled_ref\"]\n",
    "M[\"res_ap3_scaled\"] = M[\"ap3_scaled\"] - M[\"ap3_scaled_ref\"]\n",
    "def maxabs(series):\n",
    "    s = pd.to_numeric(series, errors=\"coerce\").to_numpy(dtype=float)\n",
    "    return float(np.nanmax(np.abs(s))) if s.size else float(\"nan\")\n",
    "print(\"=== Stage VII: Cross-validation summary ===\")\n",
    "print(f\"n_primes (merged): {pyint(len(M))}\")\n",
    "print(f\"max |res a1_scaled|  : {maxabs(M['res_a1_scaled']):.6g}\")\n",
    "print(f\"max |res ap2_scaled| : {maxabs(M['res_ap2_scaled']):.6g}\")\n",
    "print(f\"max |res ap3_scaled| : {maxabs(M['res_ap3_scaled']):.6g}\")\n",
    "# ---------- 5) Save joined table ----------\n",
    "out_csv = \"stageVII_crosscheck_table.csv\"\n",
    "M.to_csv(out_csv, index=False)\n",
    "print(f\"\\nWrote: {out_csv}\")\n",
    "# ---------- 6) Residual plots (matplotlib ≥ 3.7 safe) ----------\n",
    "x = M[\"p\"].astype(float)\n",
    "plt.figure(figsize=(6.6, 4.0))\n",
    "markerline, stemlines, baseline = plt.stem(x, M[\"res_a1_scaled\"], basefmt=\" \")\n",
    "plt.setp(stemlines, linewidth=1)\n",
    "plt.axhline(0.0, ls=\"--\", color=\"orange\")\n",
    "plt.title(\"Residuals: a1_scaled (Stage VI − recomputed)\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"residual\")\n",
    "plt.grid(True); plt.tight_layout()\n",
    "plt.savefig(\"fig_stageVII_res_a1_scaled.png\", dpi=144)\n",
    "plt.show()\n",
    "plt.figure(figsize=(6.6, 4.0))\n",
    "markerline, stemlines, baseline = plt.stem(x, M[\"res_ap2_scaled\"], basefmt=\" \")\n",
    "plt.setp(stemlines, linewidth=1)\n",
    "plt.axhline(0.0, ls=\"--\", color=\"orange\")\n",
    "plt.title(\"Residuals: ap2_scaled (Stage VI − recomputed)\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"residual\")\n",
    "plt.grid(True); plt.tight_layout()\n",
    "plt.savefig(\"fig_stageVII_res_ap2_scaled.png\", dpi=144)\n",
    "plt.show()\n",
    "plt.figure(figsize=(6.6, 4.0))\n",
    "markerline, stemlines, baseline = plt.stem(x, M[\"res_ap3_scaled\"], basefmt=\" \")\n",
    "plt.setp(stemlines, linewidth=1)\n",
    "plt.axhline(0.0, ls=\"--\", color=\"orange\")\n",
    "plt.title(\"Residuals: ap3_scaled (Stage VI − recomputed)\")\n",
    "plt.xlabel(\"prime p\"); plt.ylabel(\"residual\")\n",
    "plt.grid(True); plt.tight_layout()\n",
    "plt.savefig(\"fig_stageVII_res_ap3_scaled.png\", dpi=144)\n",
    "plt.show()\n",
    "# ---------- 7) Peek at first rows (force Python int) ----------\n",
    "display(M.iloc[:pyint(10)])   # or display(M.head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "346c4f",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x420 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x420 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x420 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage VIII summary ===\n",
      "n_max used (finite a_n): 19943\n",
      "central_point_guess s0: 2.00000000000000\n",
      "Deligne bound check (|a1/p^(3/2)| ≤ 4): True\n",
      "L(2.00000000000000) (partial, N≤19943): 0.7777056555568721\n",
      "L(1.80000000000000) (partial, N≤19943): 0.6551133768182855\n",
      "L(1.50000000000000) (partial, N≤19943): 0.3499963902824894\n",
      "\n",
      "Wrote:\n",
      " - stageVIII_dirichlet_coeffs.csv (first ~200 a_n)\n"
     ]
    }
   ],
   "source": [
    "# === Stage VIII: Hecke–Dirichlet a_n and basic L(s) diagnostics ===\n",
    "import math\n",
    "import json\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "# ---------------- 0) Load prime data ----------------\n",
    "# Prefer Stage VI export if present; otherwise fall back to OA_Lpoly.csv\n",
    "stage6 = Path(\"final_per_prime_table.csv\")\n",
    "raw    = Path(\"OA_Lpoly.csv\")\n",
    "if stage6.exists() and stage6.stat().st_size > 0:\n",
    "    V = pd.read_csv(stage6)\n",
    "    # normalize column names in case they differ across stages\n",
    "    rename_map = {\n",
    "        \"p\":\"p\", \"a1\":\"a1\", \"a2\":\"a2\",\n",
    "        \"a1_ref\":\"a1\", \"a2_ref\":\"a2\"  # (if coming from VII merge table)\n",
    "    }\n",
    "    V = V.rename(columns={k:v for k,v in rename_map.items() if k in V.columns})\n",
    "    if not set([\"p\",\"a1\",\"a2\"]).issubset(V.columns):\n",
    "        raise ValueError(\"final_per_prime_table.csv must contain p,a1,a2 (or *_ref columns).\")\n",
    "else:\n",
    "    if not raw.exists() or raw.stat().st_size == 0:\n",
    "        raise FileNotFoundError(\"No prime data found. Need final_per_prime_table.csv or OA_Lpoly.csv.\")\n",
    "    V = pd.read_csv(raw)\n",
    "    if not set([\"p\",\"a1\",\"a2\"]).issubset(V.columns):\n",
    "        raise ValueError(\"OA_Lpoly.csv must contain p,a1,a2.\")\n",
    "# Sage-safe dtypes\n",
    "for c in (\"p\",\"a1\",\"a2\"):\n",
    "    V[c] = V[c].astype(int)\n",
    "# Sort by prime and keep unique primes only (dedup if needed)\n",
    "V = V.sort_values(\"p\").drop_duplicates(subset=[\"p\"]).reset_index(drop=True)\n",
    "p_list  = V[\"p\"].astype(int).tolist()\n",
    "a1_list = V[\"a1\"].astype(int).tolist()\n",
    "a2_list = V[\"a2\"].astype(int).tolist()\n",
    "# Quick Deligne sanity: a1 / p^(3/2) should have |.| <= 4 (rank=4)\n",
    "a1_scaled = np.array([float(a1)/float(p)**1.5 for a1,p in zip(a1_list,p_list)])\n",
    "deligne_ok = bool(np.all(np.abs(a1_scaled) <= 4.0 + 1e-12))\n",
    "# ---------------- 1) Local recursion for a_{p^r} ----------------\n",
    "# Local factor (CY3 toy): 1 - a1 T + a2 T^2 - p a1 T^3 + p^3 T^4\n",
    "# => generating function Sum_{r>=0} a_{p^r} T^r = 1 / (1 - a1 T + a2 T^2 - p a1 T^3 + p^3 T^4)\n",
    "# Recurrence: a_{p^r} = a1 a_{p^{r-1}} - a2 a_{p^{r-2}} + p a1 a_{p^{r-3}} - p^3 a_{p^{r-4}}, with a_{p^0}=1\n",
    "def ap_powers(p:int, a1:int, a2:int, rmax:int):\n",
    "    out = [0.0]*(rmax+1)\n",
    "    out[0] = 1.0\n",
    "    if rmax >= 1: out[1] = float(a1)\n",
    "    if rmax >= 2: out[2] = float(a1*a1 - 2*a2)                 # matches ap2\n",
    "    if rmax >= 3: out[3] = float(a1**3 - 3*a1*a2 + 3*p*a1)     # matches ap3\n",
    "    for r in range(4, rmax+1):\n",
    "        out[r] = ( a1*out[r-1]\n",
    "                 - a2*out[r-2]\n",
    "                 + p*a1*out[r-3]\n",
    "                 - (p**3)*out[r-4] )\n",
    "    return out\n",
    "# Build a dict for quick lookup\n",
    "local_cache = {}\n",
    "for a1,a2,p in zip(a1_list, a2_list, p_list):\n",
    "    local_cache[int(p)] = (int(a1), int(a2))\n",
    "# ---------------- 2) Sieve for multiplicative a_n up to N ----------------\n",
    "N = 20000   # increase if you like; 20k is fast and stable\n",
    "spf = np.zeros(N+1, dtype=int)  # smallest prime factor\n",
    "for i in range(2, N+1):\n",
    "    if spf[i] == 0:\n",
    "        spf[i] = i\n",
    "        if i*i <= N:\n",
    "            for j in range(i*i, N+1, i):\n",
    "                if spf[j] == 0:\n",
    "                    spf[j] = i\n",
    "# Set spf for primes beyond sqrt range\n",
    "for i in range(2, N+1):\n",
    "    if spf[i] == 0:\n",
    "        spf[i] = i\n",
    "# Precompute a_{p^e} up to e with p^e <= N for primes we know\n",
    "ap_power_table = {}  # (p,e) -> a_{p^e}\n",
    "for p in p_list:\n",
    "    a1, a2 = local_cache[p]\n",
    "    # maximum exponent e such that p^e <= N\n",
    "    emax = int(math.floor(math.log(N, p)))\n",
    "    if emax < 1:\n",
    "        continue\n",
    "    # compute via local recursion\n",
    "    coeffs = ap_powers(p, a1, a2, emax)\n",
    "    for e in range(0, emax+1):\n",
    "        ap_power_table[(p, e)] = coeffs[e]\n",
    "# Multiplicative build\n",
    "a = np.ones(N+1, dtype=float)\n",
    "a[0] = 0.0  # unused\n",
    "for n in range(2, N+1):\n",
    "    # factor n\n",
    "    m = n\n",
    "    acc = 1.0\n",
    "    ok = True\n",
    "    while m > 1:\n",
    "        p = int(spf[m])\n",
    "        e = 0\n",
    "        while m % p == 0:\n",
    "            m //= p\n",
    "            e += 1\n",
    "        # If p not in our data, we cannot supply exact local factor → stop using that p\n",
    "        if p not in local_cache:\n",
    "            ok = False\n",
    "            break\n",
    "        acc *= ap_power_table[(p, e)]\n",
    "    a[n] = acc if ok else np.nan\n",
    "# We’ll only use n composed of the known primes (drop NaNs)\n",
    "mask_known = np.isfinite(a)\n",
    "idx_known  = np.where(mask_known)[0]\n",
    "known_max  = int(idx_known.max())\n",
    "use_upto   = min(N, known_max)\n",
    "# Save first part of a_n\n",
    "rows = min(200, use_upto)  # keep CSV light\n",
    "df_an = pd.DataFrame({\"n\": np.arange(1, rows+1, dtype=int), \"a_n\": a[1:rows+1]})\n",
    "df_an.to_csv(\"stageVIII_dirichlet_coeffs.csv\", index=False)\n",
    "# ---------------- 3) Partial L(s) evaluation and convergence plots ----------------\n",
    "def partial_L(s:complex, upto:int):\n",
    "    # sum over n <= upto, but only where a[n] is finite\n",
    "    n = np.arange(1, upto+1, dtype=float)\n",
    "    vals = a[1:upto+1]\n",
    "    good = np.isfinite(vals)\n",
    "    if not np.any(good):\n",
    "        return np.nan\n",
    "    nn = n[good]\n",
    "    vv = vals[good]\n",
    "    return np.sum(vv / (nn**s))\n",
    "s_vals = [2.0, 1.8, 1.5]  # safely > 1 (no analytic continuation assumed)\n",
    "Ks = np.unique(np.linspace(200, use_upto, 25, dtype=int))\n",
    "plt.figure(figsize=(6.8,4.2))\n",
    "for s in s_vals:\n",
    "    seq = [partial_L(float(s), int(K)) for K in Ks]\n",
    "    plt.plot(Ks, np.real(seq), marker=\"o\", ms=3, label=f\"Re L({s})\")\n",
    "plt.title(\"Convergence of Re Σ a_n / n^s (known primes)\")\n",
    "plt.xlabel(\"truncation N\"); plt.ylabel(\"partial sum\")\n",
    "plt.grid(True); plt.legend(); plt.tight_layout()\n",
    "plt.show()\n",
    "plt.figure(figsize=(6.8,4.2))\n",
    "for s in s_vals:\n",
    "    seq = [partial_L(float(s), int(K)) for K in Ks]\n",
    "    plt.plot(Ks, np.imag(seq), marker=\"o\", ms=3, label=f\"Im L({s})\")\n",
    "plt.title(\"Convergence of Im Σ a_n / n^s (known primes)\")\n",
    "plt.xlabel(\"truncation N\"); plt.ylabel(\"partial sum\")\n",
    "plt.grid(True); plt.legend(); plt.tight_layout()\n",
    "plt.show()\n",
    "# ---------------- 4) Light Euler-product check (log-product) ----------------\n",
    "def log_euler_product(s:float, primes:np.ndarray):\n",
    "    # log Π_p 1 / (1 - a1_p p^{-s} + a2_p p^{-2s} - p a1_p p^{-3s} + p^3 p^{-4s})\n",
    "    total = 0.0\n",
    "    for p in primes:\n",
    "        a1, a2 = local_cache[int(p)]\n",
    "        ps  = p**(-s)\n",
    "        den = 1.0 - a1*ps + a2*(ps**2) - (p*a1)*(ps**3) + (p**3)*(ps**4)\n",
    "        total += -math.log(abs(den))\n",
    "    return total\n",
    "Ps = np.array(p_list, dtype=float)\n",
    "plt.figure(figsize=(6.8,4.2))\n",
    "for s in s_vals:\n",
    "    # growth of partial log Euler product as we include more primes\n",
    "    xs = np.arange(5, len(Ps)+1, dtype=int)\n",
    "    ys = [log_euler_product(float(s), Ps[:k]) for k in xs]\n",
    "    plt.plot(xs, ys, marker=\".\", ms=3, label=f\"s={s}\")\n",
    "plt.title(\"Partial log Euler product vs #primes\")\n",
    "plt.xlabel(\"first k primes from dataset\"); plt.ylabel(\"−log|denominator| (cum.)\")\n",
    "plt.grid(True); plt.legend(); plt.tight_layout()\n",
    "plt.show()\n",
    "# ---------------- 5) “Center” & Deligne sanity report ----------------\n",
    "# For a pure weight-3 rank-4 motive (H^3), the expected central point is s0 = (w+1)/2 = 2.\n",
    "s0 = 2.0\n",
    "print(\"=== Stage VIII summary ===\")\n",
    "print(f\"n_max used (finite a_n): {use_upto}\")\n",
    "print(f\"central_point_guess s0: {s0}\")\n",
    "print(f\"Deligne bound check (|a1/p^(3/2)| ≤ 4): {deligne_ok}\")\n",
    "for s in s_vals:\n",
    "    val = partial_L(float(s), int(use_upto))\n",
    "    print(f\"L({s}) (partial, N≤{use_upto}): {val}\")\n",
    "print(\"\\nWrote:\")\n",
    "print(\" - stageVIII_dirichlet_coeffs.csv (first ~200 a_n)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "992d3b",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage IX: heuristic FE check (no Gamma model) ===\n",
      "central_point_guess s0: 2.0\n",
      "terms used (K): 21 (max n = 187)\n",
      "best epsilon: 1\n",
      "best constant scale c: 0.89440527122091191769941397016730523842932642054543743204538919768631738151613141\n",
      "L2 residual (best): 2.0801208462802556252586866171992813910557958971917469080222688360401386424291093\n",
      "L2 residual (eps=+1): 2.0801208462802556252586866171992813910557958971917469080222688360401386424291093\n",
      "L2 residual (eps=-1): 2.0801208462802556252586866171992813910557958971917469080222688360401386424291093\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x400 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x400 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>n</th>\n      <th>a_n</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1</td>\n      <td>1.0</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>7</td>\n      <td>-2.0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>11</td>\n      <td>-8.0</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>13</td>\n      <td>-13.0</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>17</td>\n      <td>-4.0</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>19</td>\n      <td>-2.0</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>23</td>\n      <td>-6.0</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>29</td>\n      <td>-17.0</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>31</td>\n      <td>-8.0</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>37</td>\n      <td>-11.0</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "    n   a_n\n",
       "0   1   1.0\n",
       "1   7  -2.0\n",
       "2  11  -8.0\n",
       "3  13 -13.0\n",
       "4  17  -4.0\n",
       "5  19  -2.0\n",
       "6  23  -6.0\n",
       "7  29 -17.0\n",
       "8  31  -8.0\n",
       "9  37 -11.0"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Stage IX: heuristic FE cross-check near s0 (robust to Sage preparser) ===\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# Force plain Python integers (avoid Sage Integer leaks)\n",
    "TEN = int(10)\n",
    "TWENTY = int(20)\n",
    "# ---------- helpers ----------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except: return mp.mpf(str(to_float(x)))\n",
    "# ---------- 0) load inputs ----------\n",
    "coeff_path   = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "summary_path = Path(\"final_summary.json\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "s0 = mp.mpf('2.0')\n",
    "if summary_path.exists() and summary_path.stat().st_size > 0:\n",
    "    try:\n",
    "        with open(summary_path, \"r\") as f:\n",
    "            J = json.load(f)\n",
    "        if \"central_point_guess\" in J:\n",
    "            s0 = mpf_safe(J[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "K = min(len(N_all), 5000)     # cap terms\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "# ---------- 1) smoothed partial sums ----------\n",
    "mp.mp.dps = 80\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def F_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i))/Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return total\n",
    "grid = [s0 + mp.mpf(j)/mp.mpf(50) for j in range(-20, 21)]   # s0 ± 0.4 step 0.02\n",
    "Ncut = to_int(n[-1])\n",
    "Fs     = [F_of_s(s, Ncut) for s in grid]\n",
    "Fs_ref = [F_of_s(2*s0 - s, Ncut) for s in grid]\n",
    "# ---------- 2) best-fit sign & scale ----------\n",
    "def best_scale(target, ref):\n",
    "    num = den = mp.mpf('0')\n",
    "    for t, r in zip(target, ref):\n",
    "        num += r.conjugate()*t\n",
    "        den += r.conjugate()*r\n",
    "    return (num/den) if den != 0 else mp.mpf('0')\n",
    "def l2_residual(target, model):\n",
    "    s = mp.mpf('0')\n",
    "    for t, m in zip(target, model):\n",
    "        d = t - m\n",
    "        s += d.real**2 + d.imag**2\n",
    "    return mp.sqrt(s)\n",
    "c_plus  = best_scale(Fs, Fs_ref)\n",
    "c_minus = best_scale(Fs, [-z for z in Fs_ref])\n",
    "res_plus  = l2_residual(Fs, [c_plus*z for z in Fs_ref])\n",
    "res_minus = l2_residual(Fs, [c_minus*(-z) for z in Fs_ref])\n",
    "if res_plus <= res_minus:\n",
    "    eps, c_best, res_best = +1, c_plus,  res_plus\n",
    "else:\n",
    "    eps, c_best, res_best = -1, c_minus, res_minus\n",
    "# ---------- 3) report ----------\n",
    "print(\"=== Stage IX: heuristic FE check (no Gamma model) ===\")\n",
    "print(f\"central_point_guess s0: {s0}\")\n",
    "print(f\"terms used (K): {K} (max n = {to_int(n[K-1])})\")\n",
    "print(f\"best epsilon: {eps}\")\n",
    "print(f\"best constant scale c: {c_best}\")\n",
    "print(f\"L2 residual (best): {res_best}\")\n",
    "print(f\"L2 residual (eps=+1): {res_plus}\")\n",
    "print(f\"L2 residual (eps=-1): {res_minus}\")\n",
    "# ---------- 4) plots ----------\n",
    "s_vals = [float(s) for s in grid]\n",
    "model  = [eps*c_best*z for z in Fs_ref]\n",
    "plt.figure(figsize=(6.8, 4.0))\n",
    "plt.plot(s_vals, [mp.re(z) for z in Fs], \"o-\", label=\"Re F(s)\")\n",
    "plt.plot(s_vals, [mp.re(z) for z in model], \"o--\", label=f\"Re eps*c*F(2s0-s), eps={eps}\")\n",
    "plt.axvline(float(s0), ls=\":\", color=\"gray\"); plt.grid(True); plt.legend()\n",
    "plt.title(\"Stage IX: Real parts near s0\"); plt.xlabel(\"s (real)\"); plt.ylabel(\"value\")\n",
    "plt.tight_layout(); plt.show()\n",
    "plt.figure(figsize=(6.8, 4.0))\n",
    "plt.plot(s_vals, [mp.im(z) for z in Fs], \"o-\", label=\"Im F(s)\")\n",
    "plt.plot(s_vals, [mp.im(z) for z in model], \"o--\", label=f\"Im eps*c*F(2s0-s), eps={eps}\")\n",
    "plt.axvline(float(s0), ls=\":\", color=\"gray\"); plt.grid(True); plt.legend()\n",
    "plt.title(\"Stage IX: Imag parts near s0\"); plt.xlabel(\"s (real)\"); plt.ylabel(\"value\")\n",
    "plt.tight_layout(); plt.show()\n",
    "# ---------- 5) preview (explicit plain-ints for Sage) ----------\n",
    "k_preview = min(TWENTY, len(n))                            # TWENTY is a Python int\n",
    "preview = pd.DataFrame({\n",
    "    \"n\":   [to_int(x)   for x in n[:k_preview]],\n",
    "    \"a_n\": [to_float(x) for x in a[:k_preview]],\n",
    "})\n",
    "display(preview.head(TEN))                                 # TEN is a Python int"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2ec7f3",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage X: heuristic FE check with Gamma factors ===\n",
      "central_point_guess s0: 2.0\n",
      "terms used (K): 21 (max n = 187)\n",
      "mu_list: [0, 1, 1, 2]\n",
      "best logQ: -4.0\n",
      "best Q:    0.01831563888873418\n",
      "best epsilon: 1\n",
      "best complex scale c: (0.4175983451072176+0j)\n",
      "L2 residual (best): 9.487352193841877e-05\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x400 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x400 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>n</th>\n      <th>a_n</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1</td>\n      <td>1.0</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>7</td>\n      <td>-2.0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>11</td>\n      <td>-8.0</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>13</td>\n      <td>-13.0</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>17</td>\n      <td>-4.0</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>19</td>\n      <td>-2.0</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>23</td>\n      <td>-6.0</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>29</td>\n      <td>-17.0</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>31</td>\n      <td>-8.0</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>37</td>\n      <td>-11.0</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "    n   a_n\n",
       "0   1   1.0\n",
       "1   7  -2.0\n",
       "2  11  -8.0\n",
       "3  13 -13.0\n",
       "4  17  -4.0\n",
       "5  19  -2.0\n",
       "6  23  -6.0\n",
       "7  29 -17.0\n",
       "8  31  -8.0\n",
       "9  37 -11.0"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Saved: stageX_summary.json\n"
     ]
    }
   ],
   "source": [
    "# === Stage X: Completed L-model with Gamma factors (heuristic FE check) ===\n",
    "# Goal: Build Λ(s) = Q^{s/2} * Π_j Γ_R(s + μ_j) * L(s)  and test Λ(s) ≈ ε Λ(2s0 - s)\n",
    "# Uses the Stage VIII Dirichlet coefficients (a_n) as L(s) via a smoothed partial sum.\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- 0) Helpers (safe conversions; avoid Sage Integer leaks) ----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:\n",
    "        return mp.mpf(x)\n",
    "    except Exception:\n",
    "        return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    \"\"\"pandas-safe preview that never passes Sage Integer into iloc/head.\"\"\"\n",
    "    n = int(n)\n",
    "    n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "# ---------------- 1) Load inputs ----------------\n",
    "coeff_path   = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "summary_path = Path(\"final_summary.json\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "# Central point guess s0 (default 2.0)\n",
    "s0 = mp.mpf('2.0')\n",
    "if summary_path.exists() and summary_path.stat().st_size > 0:\n",
    "    try:\n",
    "        with open(summary_path, \"r\") as f:\n",
    "            J = json.load(f)\n",
    "        if \"central_point_guess\" in J:\n",
    "            s0 = mpf_safe(J[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "# Read coefficients\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]\n",
    "        break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "K = min(len(N_all), 8000)\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "# ---------------- 2) L(s) via smoothed partial sum ----------------\n",
    "mp.mp.dps = 80\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return total\n",
    "# ---------------- 3) Gamma-factor model ----------------\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# Parameters\n",
    "MU_LIST = [0, 1, 1, 2]\n",
    "logQ_min, logQ_max, logQ_step = -4.0, 6.0, 0.2\n",
    "logQ_grid = [logQ_min + j*logQ_step for j in range(int((logQ_max-logQ_min)/logQ_step)+1)]\n",
    "grid = [s0 + mp.mpf(j)/mp.mpf(50) for j in range(-20, 21)]\n",
    "Ncut = to_int(n[-1])\n",
    "# ---------------- 4) Fit ε ∈ {±1} and complex scale c ----------------\n",
    "def best_scale(target, ref):\n",
    "    num = den = mp.mpf('0')\n",
    "    for t, r in zip(target, ref):\n",
    "        num += r.conjugate()*t\n",
    "        den += r.conjugate()*r\n",
    "    return (num/den) if den != 0 else mp.mpf('0')\n",
    "def l2_residual(target, model):\n",
    "    s = mp.mpf('0')\n",
    "    for t, m in zip(target, model):\n",
    "        d = t - m\n",
    "        s += d.real**2 + d.imag**2\n",
    "    return mp.sqrt(s)\n",
    "best = {\"res\": mp.mpf('inf')}\n",
    "for logQ in logQ_grid:\n",
    "    Q = mp.e**mp.mpf(logQ)\n",
    "    Lam  = [Lambda_of_s(s, Q, MU_LIST, Ncut) for s in grid]\n",
    "    LamR = [Lambda_of_s(2*s0 - s, Q, MU_LIST, Ncut) for s in grid]\n",
    "    c_plus   = best_scale(Lam, LamR)\n",
    "    res_plus = l2_residual(Lam, [c_plus*z for z in LamR])\n",
    "    LamR_neg = [-z for z in LamR]\n",
    "    c_minus   = best_scale(Lam, LamR_neg)\n",
    "    res_minus = l2_residual(Lam, [c_minus*z for z in LamR_neg])\n",
    "    if res_plus <= res_minus:\n",
    "        eps, c_fit, res_fit = +1, c_plus, res_plus\n",
    "    else:\n",
    "        eps, c_fit, res_fit = -1, c_minus, res_minus\n",
    "    if res_fit < best[\"res\"]:\n",
    "        best = {\n",
    "            \"logQ\": float(logQ),\n",
    "            \"Q\":    float(mp.e**mp.mpf(logQ)),\n",
    "            \"eps\":  int(eps),\n",
    "            \"c\":    complex(c_fit),\n",
    "            \"res\":  float(res_fit),\n",
    "            \"Lam\":  Lam,\n",
    "            \"LamR\": LamR\n",
    "        }\n",
    "# ---------------- 5) Report ----------------\n",
    "print(\"=== Stage X: heuristic FE check with Gamma factors ===\")\n",
    "print(f\"central_point_guess s0: {s0}\")\n",
    "print(f\"terms used (K): {K} (max n = {to_int(n[K-1])})\")\n",
    "print(f\"mu_list: {MU_LIST}\")\n",
    "print(f\"best logQ: {best['logQ']}\")\n",
    "print(f\"best Q:    {best['Q']}\")\n",
    "print(f\"best epsilon: {best['eps']}\")\n",
    "print(f\"best complex scale c: {best['c']}\")\n",
    "print(f\"L2 residual (best): {best['res']}\")\n",
    "# ---------------- 6) Plots ----------------\n",
    "s_vals = [float(s) for s in grid]\n",
    "Lam   = best[\"Lam\"]\n",
    "LamR  = best[\"LamR\"]\n",
    "eps   = best[\"eps\"]\n",
    "c_best = best[\"c\"]\n",
    "model = [eps*c_best*z for z in LamR]\n",
    "plt.figure(figsize=(6.8, 4.0))\n",
    "plt.plot(s_vals, [mp.re(z) for z in Lam], \"o-\", label=\"Re Λ(s)\")\n",
    "plt.plot(s_vals, [mp.re(z) for z in model], \"o--\", label=f\"Re ε·c·Λ(2s0−s), ε={eps}\")\n",
    "plt.axvline(float(s0), ls=\":\", color=\"gray\")\n",
    "plt.grid(True); plt.legend()\n",
    "plt.title(\"Stage X: Real parts near s0\"); plt.xlabel(\"s (real)\"); plt.ylabel(\"value\")\n",
    "plt.tight_layout(); plt.show()\n",
    "plt.figure(figsize=(6.8, 4.0))\n",
    "plt.plot(s_vals, [mp.im(z) for z in Lam], \"o-\", label=\"Im Λ(s)\")\n",
    "plt.plot(s_vals, [mp.im(z) for z in model], \"o--\", label=f\"Im ε·c·Λ(2s0−s), ε={eps}\")\n",
    "plt.axvline(float(s0), ls=\":\", color=\"gray\")\n",
    "plt.grid(True); plt.legend()\n",
    "plt.title(\"Stage X: Imag parts near s0\"); plt.xlabel(\"s (real)\"); plt.ylabel(\"value\")\n",
    "plt.tight_layout(); plt.show()\n",
    "# ---------------- 7) Preview coefficients ----------------\n",
    "k_preview = min(20, len(n))\n",
    "preview = pd.DataFrame({\n",
    "    \"n\":   [to_int(x) for x in n[:k_preview]],\n",
    "    \"a_n\": [to_float(x) for x in a[:k_preview]],\n",
    "})\n",
    "display(head_safe(preview, 10))\n",
    "# ---------------- 8) Save summary ----------------\n",
    "summary_out = {\n",
    "    \"s0\": float(s0),\n",
    "    \"K_terms\": int(K),\n",
    "    \"mu_list\": [float(m) for m in MU_LIST],\n",
    "    \"best_logQ\": float(best[\"logQ\"]),\n",
    "    \"best_Q\": float(best[\"Q\"]),\n",
    "    \"best_eps\": int(best[\"eps\"]),\n",
    "    \"best_c_real\": float(best[\"c\"].real),\n",
    "    \"best_c_imag\": float(best[\"c\"].imag),\n",
    "    \"best_residual\": float(best[\"res\"]),\n",
    "}\n",
    "with open(\"stageX_summary.json\", \"w\") as f:\n",
    "    json.dump(summary_out, f, indent=2)\n",
    "print(\"\\nSaved: stageX_summary.json\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9c4548",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NAIbLqn5+foayys6ESJJkmFS7QmZmpsld7RXTrsTFxRmVb9iwwei5i4sL+vbti5SUFHTu3BmhoaEmX+bO1Nzou+++w/r16/Haa68ZLk9++OGHkMlkmDx5cpXvrS4PPvggzp49iyZNmpjdB3N3/KrVakRGRmLp0qUAgJSUFLNtN2jQAD169MA333xjdParsLAQW7ZsMarr7e0NJycnHD582Kjc3KwDkiSZ3BDy448/WnT5vzIdOnRAWFgY1q5diy+++AKlpaV4/PHHK63v7e2NCRMm4NFHH8WpU6eqnNOxIoY379vNMagJ4eHhcHZ2xvr1643KL168iF9++cVw17qt+fv745lnnkH//v1x4MCBGt2WNWdL77//fgDAZ599ZlQeFxeH4uJiw+tE1YVnPInsQMXZvyFDhqB9+/bQ6/U4ePAg3nnnHTRs2BDTpk0z1O3UqRM2bNiAuLg4tGrVCk5OTujUqRMefPBBfPPNN5g6dSpGjhyJCxcu4LXXXoOvr6/RpdKBAwfinnvuwfPPP4+CggKEhIQgOTkZn376KQDj6Zvee+893HvvvejVqxeeeuoptGzZEoWFhfjrr7+wZcuWKu/4zs7OxpNPPomIiAjExMQYyps1a4Z3330Xjz/+OFavXo2JEydW2kZSUhLuu+8+vPrqqxaP87zZ9OnTsWnTJvTu3RszZsxA586dodfrkZ6ejoSEBDz//PMICwvDq6++iosXL+K+++5D8+bNkZeXh/feew9KpbLKORJfe+01DBw4EP3798fzzz8PnU6HpUuXokGDBsjNzTXUkyQJY8eOxZo1a9C6dWt06dIFe/bsMbs6zIMPPoh169ahffv26Ny5M/bv34+33nrrjs8QP/HEE3jyySdx+fJlREREmNwdHxYWhgcffBCdO3dG48aNceLECXz22WcIDw+vcq7LwYMHw8PDAxMnTsTChQuhUCiwbt06XLhw4Y76a4lGjRph7ty5mD17NsaNG4dHH30UOTk5WLBgAZycnCyaeaEm5Ofno2/fvhgzZgzat28PV1dX7N27F1u3bsXw4cNrdNuVfUaY069fPzz00EOYPXs2ioqKcM899+DQoUOYN28eunXrhujo6BrtKzkgW9/dRERCxMXFiTFjxog2bdqIhg0bCqVSKfz9/UV0dLQ4fvy4Ud3z58+LqKgo4erqKgCIgIAAw2tvvPGGaNmypVCr1aJDhw7io48+MnvHcW5urnj88cdFo0aNhIuLi+jfv7/YtWuXACDee+89o7qpqaniiSeeEM2aNRNKpVI0bdpUREREiEWLFlW5T4888ohwcXERp0+fNvv64MGDhZubm0hPTxdCmL+rveKu3aru+K4QGRkpOnbsaPa1oqIiMWfOHNGuXTuhUqmEu7u76NSpk5gxY4bIzMwUQgjxww8/iEGDBolmzZoJlUolvLy8xODBg8Xvv/9uFAuYuYv8+++/F507dxYqlUr4+/uLN954w2zc8/PzxaRJk4S3t7do0KCBGDJkiDh//rzJPl69elVMnDhReHl5CRcXF3HvvfeK33//XURGRhrdrWzpXe03bt/Z2VkAEB999JHJ6zNnzhShoaGicePGQq1Wi1atWokZM2aI7OzsW7a9Z88eERERIRo0aCCaNWsm5s2bZ7gz+ua72h944AGT99+8b5be1V7h448/NvwM3N3dxdChQ8WxY8eM6owfP140aNDAbP8BiKefftqorCK+b731llF5ZXeT36ikpERMmTJFdO7cWbi5uQlnZ2fRrl07MW/ePHHt2jWj/TZ33I4fP97od9uau9qr+oyorK+zZ88WLVu2FEqlUvj6+oqpU6eKq1evVvk+otshCSFELee6RGSHvvjiCzz22GP4888/ERERYevuEBFRPcTEk8gBffnll7h06RI6deoEmUyGXbt24a233kK3bt0M0y0RERFVN47xJHJArq6u2LBhAxYtWoRr167B19cXEyZMwKJFi2zdNSIiqsd4xpOIiIiIagWnUyIiIiKiWsHEk4iIiIhqBRNPIiIiIqoVvLmoBun1ely+fBmurq61ukwbERERUW0RQqCwsBB+fn5Gi5CYw8SzBl2+fBktWrSwdTeIiIiIatyFCxduucIaE88a5OrqCqD8B+Hm5lZj29FoNEhISEBUVBSUSmWNbceeMQaMAcAYaDQabNy4ETk5OZg4cWKVy1zWZ45+HACMAcAYALUXg4KCArRo0cKQ91TF5onnihUr8NZbbyEjIwMdO3ZEbGwsevXqVWn9pKQkxMTE4NixY/Dz88NLL72EKVOmGNXZtGkT5s6di7Nnz6J169Z4/fXXMWzYMMPrK1euxMqVK3H+/HkAQMeOHfHqq69i0KBBhjpCCCxYsAAffvghrl69irCwMCxfvhwdO3a0eN8qLq+7ubnVeOLp4uICNzc3h/7lYgwYA0ePQVlZGa5cuQKg/B/fBg0a2LhHtuHoxwHAGACMAVD7MbBkWKFNby6Ki4vD9OnT8corryAlJQW9evXCoEGDkJ6ebrZ+amoqBg8ejF69eiElJQWzZ8/Gc889h02bNhnqJCcnY/To0YiOjsahQ4cQHR2NUaNGYffu3YY6zZs3xxtvvIF9+/Zh37596NevH4YOHYpjx44Z6rz55ptYtmwZPvjgA+zduxc+Pj7o378/CgsLay4gRER3QKFQ4KGHHoK/vz8UCpufVyAiMmHTxHPZsmWYOHEiJk2ahA4dOiA2NhYtWrTAypUrzdZftWoV/P39ERsbiw4dOmDSpEl44okn8PbbbxvqxMbGon///pg1axbat2+PWbNm4b777kNsbKyhzpAhQzB48GC0bdsWbdu2xeuvv46GDRti165dAMrPdsbGxuKVV17B8OHDERwcjE8++QTFxcX44osvajQmRES3SyaTITg4GB4eHrcc4E9EZAs2+5e4rKwM+/fvx8yZM43Ko6KisHPnTrPvSU5ORlRUlFHZgAEDsHr1amg0GiiVSiQnJ2PGjBkmdW5MPG+k0+mwceNGXLt2DeHh4QDKz6xmZmYabUutViMyMhI7d+7Ek08+abat0tJSlJaWGp4XFBQAKD/VrdFozL6nOlS0XZPbsHeMAWMAMAYAYwAwBgBjADAGQO3FwJr2bZZ4ZmdnQ6fTwdvb26jc29sbmZmZZt+TmZlptr5Wq0V2djZ8fX0rrXNzm0eOHEF4eDhKSkrQsGFDbN68GUFBQYbtVLzv5nbS0tIq3aclS5ZgwYIFJuUJCQm1Msg/MTGxxrdh7xgDxgBw3BgIIXD9+nUA5Z87jj6Nm6MeBzdiDBgDoOZjUFxcbHFdmw8CuvmDUQhR5Yelufo3l1vSZrt27XDw4EHk5eVh06ZNGD9+PJKSkgzJ5+30bdasWYiJiTE8r7jLKyoqqsZvLkpMTET//v0degA1Y8AYOHoMysrKDEOPpk2b5tA3FznycQAwBgBjANReDCqu8FrCZomnp6cn5HK5yZnIrKwskzONFXx8fMzWVygUaNKkSZV1bm5TpVLhrrvuAgCEhoZi7969eO+99/C///0PPj4+AMrPfPr6+lrUN6D8crxarTYpVyqVtXLQ19Z27BljwBgAjh0Dd3d3FBcXQ6VSOWwMKjjycVCBMWAMgJqPgTVt22z0uUqlQkhIiMnp38TERERERJh9T3h4uEn9hIQEhIaGGna6sjqVtVlBCGEYnxkYGAgfHx+jdsrKypCUlHTLdmqbTi+wOzUX+7Ml7E7NhU4vbN0lIrIRpVKJp59+Gh07dnT4P7REZJ9seqk9JiYG0dHRCA0NRXh4OD788EOkp6cb5uWcNWsWLl26hE8//RQAMGXKFHzwwQeIiYnB5MmTkZycjNWrV+PLL780tDlt2jT07t0bS5cuxdChQ/Hdd99h+/bt+OOPPwx1Zs+ejUGDBqFFixYoLCzEhg0bsGPHDmzduhVA+SX26dOnY/HixWjTpg3atGmDxYsXw8XFBWPGjKnFCFVt69EMLNhyHBn5JQDk+PTMPvi6O2HekCAMDPa95fuJiIiIapNNE8/Ro0cjJycHCxcuREZGBoKDgxEfH4+AgAAAQEZGhtGcnoGBgYiPj8eMGTOwfPly+Pn54f3338eIESMMdSIiIrBhwwbMmTMHc+fORevWrREXF4ewsDBDnStXriA6OhoZGRlwd3dH586dsXXrVvTv399Q56WXXsL169cxdepUwwTyCQkJFs3KXxu2Hs3AU+sP4Obzm5n5JXhq/QGsHNudyScRERHZFZvfXDR16lRMnTrV7Gvr1q0zKYuMjMSBAweqbHPkyJEYOXJkpa+vXr36lv2SJAnz58/H/Pnzb1m3tun0Agu2HDdJOgFAAJAALNhyHP2DfCCXOfZdrUSORKvV4uuvv0ZmZia0Wi0vtxOR3eEMw3XQntTcfy6vmycAZOSXYE9qbu11iohsTq/X4/Tp0ygoKIBer7d1d4iITDDxrIOyCitPOm+nHhHVD3K53DB+XS6X27o7REQmmHjWQV6uTtVaj4jqB7lcjm7duqFJkyZMPInILjHxrIN6BHrA190JlY3elAD4ujuhR6BHbXaLiIiIqEpMPOsguUzCvCHlKyzdnHxWPJ83JIg3FhE5GCEE/v77b1y/ft2wqhsRkT1h4llHDQz2xcqx3eHjbnw53bOhmlMpETkojUaDjz76CKdOnYJGo7F1d4iITDDxrMMGBvvij5f7Yf0TofBzLr+D9cnIVkw6iRyYs7Mzx3cSkd1i4lnHyWUSwgI9ENK0/LLabk6hROSwVCoVZsyYgU6dOkGlUtm6O0REJph41hNt3P5JPM/lcL12IiIisktMPOuJ5g2BBmo5Ckq0OJFRYOvuEBEREZlg4llPyCXg7oDGAIDkszk27g0R2YJWq8V3332HtLQ0aLVaW3eHiMgEE896pGer8nk7k88x8SRyRHq9HseOHcPVq1e5ZCYR2SUmnvVIz38mjN+Tmgutjn90iByNXC7H/fffDz8/P97ZTkR2iYlnPdLexxVuTgoUlWpx9DLHeRI5Grlcjh49esDLy4uJJxHZJSae9YhcJiGsVRMAHOdJRERE9oeJZz0TXpF4cpwnkcMRQiAvLw+lpaVcMpOI7BITz3omvHV54rnvfC40HOdJ5FA0Gg1WrFiBEydOcMlMIrJLTDzrmXbermjsokRxmQ6HL+bZujtEVMuUSiVkMn60E5F94qdTPSOTSejJcZ5EDkmlUuHFF19E586duWQmEdklJp71UMXldo7zJCIiInvCxLMeqrjBaN/5qyjV6mzcGyIiIqJyTDzrobu8GsKzoRqlWj0OpufZujtEVEu0Wi3i4+ORnp7OJTOJyC4x8ayHJEni8plEDkiv1+PgwYPIzc3lkplEZJeYeNZThnGevMGIyGHI5XJERkbCx8eHKxcRkV1S2LoDVDMqxnmmpOehRKODk5J/hIjqO7lcjnvuuQf5+flMPInILvGMZz0V6NkA3m5qlOn0OJB21dbdISIiImLiWV9JksTlM4kcjBAC165dg1ar5ZKZRGSXmHjWYxznSeRYNBoN3nvvPRw9epRLZhKRXWLiWY+Ft/IEABy6mIfiMk6tQkRERLbFxLMea+HhjGaNnKHRCew7z3GeRPWdSqXC7Nmz0bVrVy6ZSUR2iYlnPVY+nyfHeRIREZF9YOJZz3GcJxEREdkLJp71XEXieeRSPopKOc6TqD7TarVITEzExYsXuWQmEdklJp71XLNGzvD3cIFOL7A3NdfW3SGiGqTX67F3715kZ2dzyUwisktMPB0A5/MkcgxyuRwRERHw9vbmykVEZJeYeDoAjvMkcgxyuRx9+vSBr68vE08isktMPB1AReJ57HI+8q9zUmkiIiKyDZsnnitWrEBgYCCcnJwQEhKC33//vcr6SUlJCAkJgZOTE1q1aoVVq1aZ1Nm0aROCgoKgVqsRFBSEzZs3G72+ZMkS3H333XB1dYWXlxcefvhhnDp1yqjOhAkTIEmS0VfPnj3vfIdtwNvNCa08G0AvgD0c50lUbwkhUFZWBp1OxyUzicgu2TTxjIuLw/Tp0/HKK68gJSUFvXr1wqBBg5Cenm62fmpqKgYPHoxevXohJSUFs2fPxnPPPYdNmzYZ6iQnJ2P06NGIjo7GoUOHEB0djVGjRmH37t2GOklJSXj66aexa9cuJCYmQqvVIioqCteuXTPa3sCBA5GRkWH4io+Pr5lA1IKevNxOVO9pNBq8/fbbOHLkCJfMJCK7pLDlxpctW4aJEydi0qRJAIDY2Fhs27YNK1euxJIlS0zqr1q1Cv7+/oiNjQUAdOjQAfv27cPbb7+NESNGGNro378/Zs2aBQCYNWsWkpKSEBsbiy+//BIAsHXrVqN2165dCy8vL+zfvx+9e/c2lKvVavj4+FT7fttCeKsm+GJ3Om8wIiIiIpuxWeJZVlaG/fv3Y+bMmUblUVFR2Llzp9n3JCcnIyoqyqhswIABWL16NTQaDZRKJZKTkzFjxgyTOhXJqjn5+fkAAA8PD6PyHTt2wMvLC40aNUJkZCRef/11eHl5VdpOaWkpSktLDc8LCgoAlJ+FqMmzDxVtV7WNUH83AMCJjAJk5V9DY5f6tZyeJTGo7xgDxgAApk2bhl9++QWA48aBxwFjADAGQO3FwJr2bZZ4ZmdnQ6fTwdvb26jc29sbmZmZZt+TmZlptr5Wq0V2djZ8fX0rrVNZm0IIxMTE4N5770VwcLChfNCgQXjkkUcQEBCA1NRUzJ07F/369cP+/fuhVqvNtrVkyRIsWLDApDwhIQEuLi5m31OdEhMTq3zdx1mOzOsSVm36GV2a1M/xX7eKgSNgDBgDuVyO7du327obNufoxwHAGACMAVDzMSguLra4rk0vtQPl64nfSAhhUnar+jeXW9PmM888g8OHD+OPP/4wKh89erThcXBwMEJDQxEQEIAff/wRw4cPN9vWrFmzEBMTY3heUFCAFi1aICoqCm5ubpXu053SaDRITExE//79oVQqK623V38C63dfgKZxSwwe3KHG+mMLlsagPmMMGAOAMQAYA4AxABgDoPZiUHGF1xI2Szw9PT0hl8tNzkRmZWWZnLGs4OPjY7a+QqFAkyZNqqxjrs1nn30W33//PX777Tc0b968yv76+voiICAAZ86cqbSOWq02ezZUqVTWykF/q+3cc1dTrN99AbvPX623v4S1FWt7xhg4bgx0Oh3+/PNPZGRkQCaTOWQMbuSox8GNGAPGAKj5GFjTts3ualepVAgJCTE5/ZuYmIiIiAiz7wkPDzepn5CQgNDQUMNOV1bnxjaFEHjmmWfwzTff4JdffkFgYOAt+5uTk4MLFy7A19fXov2zR2H/rGB0+koRsotKb1GbiOoanU6HnTt34sqVK9DpdLbuDhGRCZtOpxQTE4OPP/4Ya9aswYkTJzBjxgykp6djypQpAMovXY8bN85Qf8qUKUhLS0NMTAxOnDiBNWvWYPXq1XjhhRcMdaZNm4aEhAQsXboUJ0+exNKlS7F9+3ZMnz7dUOfpp5/G+vXr8cUXX8DV1RWZmZnIzMzE9evXAQBFRUV44YUXkJycjPPnz2PHjh0YMmQIPD09MWzYsNoJTg3waKBCex9XAMAu3t1OVO/IZDLcfffd8PT0hExm82maiYhM2PSTafTo0YiNjcXChQvRtWtX/Pbbb4iPj0dAQAAAICMjw2hOz8DAQMTHx2PHjh3o2rUrXnvtNbz//vuGqZQAICIiAhs2bMDatWvRuXNnrFu3DnFxcQgLCzPUWblyJfLz8w1Ly1V8xcXFASgfmH/kyBEMHToUbdu2xfjx49G2bVskJyfD1dW1lqJTM7h8JlH9pVAo0L9/fzRv3hwKhc2H8BMRmbD5J9PUqVMxdepUs6+tW7fOpCwyMhIHDhyoss2RI0di5MiRlb5+qxU9nJ2dsW3btirr1FXhrZpg7Z/nOZ8nERER1Tpei3EwYYFNIEnAub+v4UpBia27Q0RERA6EiaeDcXdRoqNf+dROHOdJVL+UlZVh8eLFOHjwIMrKymzdHSIiE0w8HVB4K47zJCIiotrHxNMBGW4w4hlPonpFqVRi2rRpCA4Odvh5C4nIPjHxdEB3t/SAXCYhLacYl/Ou27o7RFRNJElCgwYNoFAoqlwBjojIVph4OiBXJyWCm7kD4OV2IiIiqj1MPB2UYZwnL7cT1RsVS2ZmZmZy5SIisktMPB0UJ5Inqn90Oh2SkpKYeBKR3WLi6aBCAxpDIZNwKe86LuQW27o7RFQNZDIZunbtCg8PDy6ZSUR2iZ9MDqqBWoEuLRoB4FlPovpCoVBg8ODB8Pf355KZRGSXmHg6MI7zJCIiotrExNOB3TjO81br1xMRERHdKSaeDiwkoDFUchkyC0pwPofjPInqurKyMrz11ls4fPgwl8wkIrvExNOBOSnl6OrfCADHeRLVFxqNBnq93tbdICIyi4mng+M4T6L6Q6lUYurUqejQoQOXzCQiu8TE08FxnCdR/SFJEho1agS1Ws0lM4nILjHxdHDd/BtBrZAhu6gUZ/8usnV3iIiIqB5j4ung1Ao5QgIaA+A4T6K6TqfTYc+ePcjKyuLKRURkl5h4Esd5EtUTOp0O27dvx+XLl5l4EpFdYuJJhnGeu87lQq/nOE+iukomk6Fjx45o3Lgxl8wkIrvETyZC5+aN4KyUI/daGU5nFdq6O0R0mxQKBYYOHYqAgAAumUlEdomJJ0GlkCG0Jcd5EhERUc1i4kkAjKdVIiIiIqoJTDwJwL83GO1O5ThPorqqrKwM7777Lo4cOcIlM4nILjHxJABAp2buaKhWIP+6BsczCmzdHSK6TdevX+cd7URkt5h4EgBAIZfh7n/Gee7itEpEdZJSqcTkyZPRrl07LplJRHaJiScZcJwnUd0mSRKaNm0KZ2dnLplJRHaJiScZhLfyBADsSc2FVqe3cW+IiIiovmHiSQZBfm5wc1KgsFSLY5c5zpOortHpdEhJSUFOTg7HeRKRXWLiSQZymYQegVw+k6iu0ul0+Omnn3DhwgUmnkRkl5h4khGO8ySqu2QyGdq2bQs3NzcumUlEdomfTGSkYj7PvedzoeE4T6I6RaFQYOTIkWjVqhWXzCQiu8TEk4y093FFYxclist0OHwx39bdISIionqEiScZkckkhP0zzpPzeRIREVF1YuJJJjjOk6hu0mg0WL58OY4dOwaNRmPr7hARmeAgIDJRkXjuS8tFqVYHtUJu4x4RkSWEEMjPzzc8JiKyNzzjSSbaeDWEZ0MVSjR6HLrAcZ5EdYVCocCECRPQtm1b3lxERHbJ5onnihUrEBgYCCcnJ4SEhOD333+vsn5SUhJCQkLg5OSEVq1aYdWqVSZ1Nm3ahKCgIKjVagQFBWHz5s1Gry9ZsgR33303XF1d4eXlhYcffhinTp0yqiOEwPz58+Hn5wdnZ2f06dMHx44du/MdrgMkSUJYK15uJ6prZDIZ/Pz84OLiwumUiMgu2fSTKS4uDtOnT8crr7yClJQU9OrVC4MGDUJ6errZ+qmpqRg8eDB69eqFlJQUzJ49G8899xw2bdpkqJOcnIzRo0cjOjoahw4dQnR0NEaNGoXdu3cb6iQlJeHpp5/Grl27kJiYCK1Wi6ioKFy7ds1Q580338SyZcvwwQcfYO/evfDx8UH//v1RWFhYcwGxIxXTKiWfy7ZxT4iIiKi+sOhazOHDhy1usHPnzhbXXbZsGSZOnIhJkyYBAGJjY7Ft2zasXLkSS5YsMam/atUq+Pv7IzY2FgDQoUMH7Nu3D2+//TZGjBhhaKN///6YNWsWAGDWrFlISkpCbGwsvvzySwDA1q1bjdpdu3YtvLy8sH//fvTu3RtCCMTGxuKVV17B8OHDAQCffPIJvL298cUXX+DJJ5+0eB/rqopxngfS81Ci0cFJyXGeRPZOr9fj6NGjyM3NhV7PeXiJyP5YlHh27doVkiRVOli94jVJkixepq2srAz79+/HzJkzjcqjoqKwc+dOs+9JTk5GVFSUUdmAAQOwevVqaDQaKJVKJCcnY8aMGSZ1KpJVcyoG43t4eAAoP7OamZlptC21Wo3IyEjs3Lmz0sSztLQUpaWlhucFBeXrnWs0mhq9w7Si7ercRgt3Fbxc1cgqLMXec9no2cqj2tquCTURg7qGMWAMysrK8P333wMArl+/7rCX2x39OAAYA4AxAGovBta0b1HimZqaetudqUx2djZ0Oh28vb2Nyr29vZGZmWn2PZmZmWbra7VaZGdnw9fXt9I6lbUphEBMTAzuvfdeBAcHG7ZT8b6b20lLS6t0n5YsWYIFCxaYlCckJMDFxaXS91WXxMTEam2vhVqGrEIZ1ifsQa5/3Th7Ut0xqIsYA8eNgV6vR8OGDQEAv/76q8MmnhUc9Ti4EWPAGAA1H4Pi4mKL61qUeAYEBNx2Z25FkiSj5xVnTq2pf3O5NW0+88wzOHz4MP7444877tusWbMQExNjeF5QUIAWLVogKioKbm5ulb7vTmk0GiQmJqJ///5QKpXV1m7RvovY/91x5Cg8MHhwj2prtybUVAzqEsaAMQAYA4AxABgDgDEAai8GFVd4LXHb820cP34c6enpKCsrMyp/6KGHLHq/p6cn5HK5yZnIrKwskzONFXx8fMzWVygUaNKkSZV1zLX57LPP4vvvv8dvv/2G5s2bG20HKD/z6evra1HfgPLL8Wq12qRcqVTWykFf3du5t60XgOM4dDEfWiGDs8r+x3nWVqztGWPAGACMAcAYAIwBwBgANR8Da9q2+jrMuXPn0KVLFwQHB+OBBx7Aww8/jIcffhjDhg3DsGHDLG5HpVIhJCTE5PRvYmIiIiIizL4nPDzcpH5CQgJCQ0MNO11ZnRvbFELgmWeewTfffINffvkFgYGBRvUDAwPh4+Nj1E5ZWRmSkpIq7Vt95O/hAj93J2h0AvvScm3dHSIiIqrjrE48p02bhsDAQFy5cgUuLi44duwYfvvtN4SGhmLHjh1WtRUTE4OPP/4Ya9aswYkTJzBjxgykp6djypQpAMovXY8bN85Qf8qUKUhLS0NMTAxOnDiBNWvWYPXq1XjhhReM+peQkIClS5fi5MmTWLp0KbZv347p06cb6jz99NNYv349vvjiC7i6uiIzMxOZmZm4fv06gPJL7NOnT8fixYuxefNmHD16FBMmTICLiwvGjBljbcjqLEmS0JPLZxLVGRqNBh9++CFOnjzp0DdUEJH9svpSe3JyMn755Rc0bdoUMpkMMpkM9957L5YsWYLnnnsOKSkpFrc1evRo5OTkYOHChcjIyEBwcDDi4+MNY0ozMjKM5vQMDAxEfHw8ZsyYgeXLl8PPzw/vv/++YSolAIiIiMCGDRswZ84czJ07F61bt0ZcXBzCwsIMdVauXAkA6NOnj1F/1q5diwkTJgAAXnrpJVy/fh1Tp07F1atXERYWhoSEBLi6ulobsjotvFUTfHPgEpLPMfEksndCCGRnZxseExHZG6sTT51OZ7hr0tPTE5cvX0a7du0QEBBgsvqPJaZOnYqpU6eafW3dunUmZZGRkThw4ECVbY4cORIjR46s9HVLPpAlScL8+fMxf/78W9atzyrm8zx8MR9FpVo0VHMZPiJ7pVAo8Nhjj2HXrl1cMpOI7JLVl9qDg4MNE8qHhYXhzTffxJ9//omFCxeiVatW1d5Bsq3mjV3QwsMZOr3A3vMc50lkz2QyGQICAuDq6urwUykRkX2y+pNpzpw5hhUxFi1ahLS0NPTq1Qvx8fF4//33q72DZHsVy2fu4jhPIiIiugNWX4sZMGCA4XGrVq1w/Phx5ObmonHjxlXOcUl1V3jrJvhq30WO8ySyc3q9HqdOnUJeXh6XzCQiu1Qtg4Aqlpqk+im8lScA4MjFfGzYm44AjwboEegBuYz/aBDZE61Wi02bNhkem5tXmIjIlqxOPPv27Vvlmc1ffvnljjpE9ufghauQyyTo9AIzNx0BAPi6O2HekCAMDPa9xbuJqLZIkoTmzZvj6tWrvAJFRHbJ6jGeXbt2RZcuXQxfQUFBKCsrw4EDB9CpU6ea6CPZ0NajGXhq/QHo9MYzAWTml+Cp9Qew9WiGjXpGRDdTKpUYN24c2rRp4/ArtRCRfbL6jOe7775rtnz+/PkoKiq64w6R/dDpBRZsOQ5zk08JABKABVuOo3+QDy+7ExER0S1V23wbY8eOxZo1a6qrObIDe1JzkZFfUunrAkBGfgn2pHKaJSIiIrq1aks8k5OT4eTkVF3NkR3IKqw86bydekRUszQaDdauXYtTp05xyUwisktWX2ofPny40XMhBDIyMrBv3z7MnTu32jpGtuflatk/EpbWI6KaVfF5XPGYiMjeWJ14uru7Gz2XyWRo164dFi5ciKioqGrrGNlej0AP+Lo7ITO/xOw4TwmAj7sTegRyOi0ie6BQKDBq1Cjs3buXS2YSkV2y+pNp7dq1NdEPskNymYR5Q4Lw1PoDkACzyee8IUG8sYjITshkMtx11104ffo0l8wkIrvETyaq0sBgX6wc2x0+7qaX018c0I7zeBIREZHFLDrjac1ymLm5vMO5vhkY7Iv+QT7Yk5qLrMISbDpwEb+dzsapK4W27hoR3UCv1yM1NRWFhYVcMpOI7JJFiWdsbKzhcU5ODhYtWoQBAwYgPDwcQPkd7du2bePNRfWYXCYhvHUTAEArz4b47fQfiD+SgVce6MCbi4jshFarxZdffml4zCUzicjeWJR4jh8/3vB4xIgRWLhwIZ555hlD2XPPPYcPPvgA27dvx4wZM6q/l2RXOjV3R3f/RjiQnocvd1/AtPvb2LpLRITyJTO9vLxQUFDAJTOJyC5ZPcZz27ZtGDhwoEn5gAEDsH379mrpFNm/8REtAQCf705DmZaX9IjsgVKpxKRJk9C+fXsumUlEdsnqxLNJkybYvHmzSfm3336LJk2aVEunyP4NCvZFU1c1sgpLse1Ypq27Q0RERHWA1dMpLViwABMnTsSOHTsMYzx37dqFrVu34uOPP672DpJ9UilkGNPDH+/9fAaf7DyPIV38bN0lIiIisnNWn/GcMGECdu7ciUaNGuGbb77Bpk2b4O7ujj///BMTJkyogS6SvXoszB8KmYR9aVdx9FK+rbtD5PA0Gg3Wr1+PM2fOcMlMIrJLt7W0RVhYGD7//PPq7gvVMV5uThjcyRffH7qMT5PP482RXWzdJSKHJoRAenq64TERkb2x6IxnQUGB0eOqvsixjI8IAAB8d/Ayrl4rs3FviBybQqHAsGHD0LJlSy6ZSUR2yaLEs3HjxsjKygIANGrUCI0bNzb5qignx9LdvzGCm7mhVKvHhr0XbN0dIocmk8nQoUMHNGrUiEtmEpFdsuhf4l9++QUeHh4AgF9//bVGO0R1iyRJGB/eEi9+fRjrd6Xh/3q34trtREREZJZFiWdkZKTZx0QAMKSLHxbHn8ClvOvYfuIKBnT0sXWXiBySXq/HhQsXUFRUxCUzicguWX0tZuvWrfjjjz8Mz5cvX46uXbtizJgxuHr1arV2juoGJ6Uc/+nhDwD4ZOd523aGyIFptVp89tln+Ouvv6DVam3dHSIiE1Ynni+++KLhJqIjR44gJiYGgwcPxrlz5xATE1PtHaS6YWzPAMgkYOfZHJy5Umjr7hA5JEmS0LhxY6hUKi6ZSUR2yerEMzU1FUFBQQCATZs2YciQIVi8eDFWrFiBn376qdo7SHVDs0bO6B/kDQD4JPm8bTtD5KCUSiWeeuopBAUFcclMIrJLVieeKpUKxcXFAIDt27cjKioKAODh4cHplBxcxfrt3xy4hIISTl5NRERExqxOPO+9917ExMTgtddew549e/DAAw8AAE6fPo3mzZtXewep7ghv1QRtvRuiuEyHr/ddtHV3iIiIyM5YnXh+8MEHUCgU+Prrr7Fy5Uo0a9YMAPDTTz9h4MCB1d5BqjskScK48JYAgE+Tz0Ov58opRLVJq9UiLi4O586d481FRGSXrF7awt/fHz/88INJ+bvvvlstHaK6bVi3Zli69STO5xQj6czf6NvOy9ZdInIYer0eZ8+eNTwmIrI3t7W0xdmzZzFnzhw8+uijhhWNtm7dimPHjlVr56juaaBWYFRoCwDAp5xaiahWyeVyPPjgg2jRogXkcrmtu0NEZMLqxDMpKQmdOnXC7t278c0336CoqAgAcPjwYcybN6/aO0h1T3TPAEgSsOP03ziffc3W3SFyGHK5HJ07d0aTJk2YeBKRXbI68Zw5cyYWLVqExMREqFQqQ3nfvn2RnJxcrZ2juqmlZwP0adsUQgCfJqfZujtERERkJ6xOPI8cOYJhw4aZlDdt2hQ5OTnV0imq+yqmVtq4/wKulfImB6LaoNfrceXKFRQXF3OMJxHZJasTz0aNGiEjI8OkPCUlxXCHO1HvNk0R6NkAhSVabE65ZOvuEDkErVaL1atX4/Tp07yrnYjsktWJ55gxY/Dyyy8jMzMTkiRBr9fjzz//xAsvvIBx48ZZ3YEVK1YgMDAQTk5OCAkJwe+//15l/aSkJISEhMDJyQmtWrXCqlWrTOps2rQJQUFBUKvVCAoKwubNm41e/+233zBkyBD4+flBkiR8++23Jm1MmDABkiQZffXs2dPq/XNUMpmE6J4BAMqnVhKCUysR1TRJktCwYUMolUoumUlEdsnqxPP111+Hv78/mjVrhqKiIgQFBaF3796IiIjAnDlzrGorLi4O06dPxyuvvIKUlBT06tULgwYNQnp6utn6qampGDx4MHr16oWUlBTMnj0bzz33HDZt2mSok5ycjNGjRyM6OhqHDh1CdHQ0Ro0ahd27dxvqXLt2DV26dMEHH3xQZf8GDhyIjIwMw1d8fLxV++foRoY2h4tKjtNXipB8jsMwiGqaUqnEc889h44dO3LJTCKyS1bN4ymEwOXLl/HRRx/htddew4EDB6DX69GtWze0adPG6o0vW7YMEydOxKRJkwAAsbGx2LZtG1auXIklS5aY1F+1ahX8/f0RGxsLAOjQoQP27duHt99+GyNGjDC00b9/f8yaNQsAMGvWLCQlJSE2NhZffvklAGDQoEEYNGjQLfunVqvh4+Nj9X5ROTcnJYZ3b4b1u9Lxyc7ziGjtaesuERERkQ1ZnXi2adMGx44dQ5s2bdCqVavb3nBZWRn279+PmTNnGpVHRUVh586dZt+TnJxsWBu+woABA7B69WpoNBoolUokJydjxowZJnUqklVr7NixA15eXmjUqBEiIyPx+uuvw8ur8gnRS0tLUVpaanhesXa9RqOBRlNza5dXtF2T27hdY+5ujvW70pF4/ArO/12AZo2ca2Q79hyD2sIYMAYAYwAwBgBjADAGQO3FwJr2rUo8ZTIZ2rRpg5ycnNs6w3mj7Oxs6HQ6eHt7G5V7e3sjMzPT7HsyMzPN1tdqtcjOzoavr2+ldSprszKDBg3CI488goCAAKSmpmLu3Lno168f9u/fD7VabfY9S5YswYIFC0zKExIS4OLiYtX2b0diYmKNb+N2tHWX4XS+DIu+TMKQgJq909ZeY1CbGAPHjYFer0daWvkUZtu2bYNMdltrhNQbjnoc3IgxYAyAmo9BcXGxxXWtXjLzzTffxIsvvoiVK1ciODjY2rebuHkAvBCiykHx5urfXG5tm+aMHj3a8Dg4OBihoaEICAjAjz/+iOHDh5t9z6xZsxATE2N4XlBQgBYtWiAqKgpubm5Wbd8aGo0GiYmJ6N+/v12O61K2zMLULw9if54a707qDSdl9U9sbe8xqA2MAWNQVlaGt99+G0D53MoNGjSwcY9sw9GPA4AxABgDoPZiUHGF1xJWJ55jx45FcXExunTpApVKBWdn40unubm5FrXj6ekJuVxuciYyKyvL5IxlBR8fH7P1FQoFmjRpUmWdytq0lK+vLwICAnDmzJlK66jVarNnQ5VKZa0c9LW1HWsN6OSHZj+dwqW86/jp+N+GJTVrgr3GoDYxBo4bA5lMhqioKBw7dgxOTk4OGYMbOepxcCPGgDEAaj4G1rRtdeJ5O2MlzVGpVAgJCUFiYqLRhPSJiYkYOnSo2feEh4djy5YtRmUJCQkIDQ017HR4eDgSExONxnkmJCQgIiLijvqbk5ODCxcuwNfX947acURymYTo8AC88dNJfLLzPB4Jac6pXohqgFwuR2hoKLKysrhkJhHZJasTz/Hjx1fbxmNiYhAdHY3Q0FCEh4fjww8/RHp6OqZMmQKg/NL1pUuX8OmnnwIApkyZgg8++AAxMTGYPHkykpOTsXr1asPd6gAwbdo09O7dG0uXLsXQoUPx3XffYfv27fjjjz8MdYqKivDXX38ZnqempuLgwYPw8PCAv78/ioqKMH/+fIwYMQK+vr44f/48Zs+eDU9PT7OrNtGtjQ5tgXcTT+PY5QIcSL+KkAAPW3eJiIiIapnViWd1Gj16NHJycrBw4UJkZGQgODgY8fHxCAgon3g8IyPDaE7PwMBAxMfHY8aMGVi+fDn8/Pzw/vvvG6ZSAoCIiAhs2LABc+bMwdy5c9G6dWvExcUhLCzMUGffvn3o27ev4XnFuMzx48dj3bp1kMvlOHLkCD799FPk5eXB19cXffv2RVxcHFxdXWs6LPVS4wYqDO3qh6/2XcS6nWlMPIlqgBACubm5KC0t5aINRGSXbJp4AsDUqVMxdepUs6+tW7fOpCwyMhIHDhyoss2RI0di5MiRlb7ep0+fKj+UnZ2dsW3btiq3QdYbF94SX+27iJ+OZCDrgQ7wcnOydZeI6hWNRmNYze2BBx6ASqWycY+IiIw59lwbVKuCm7kjNKAxtHqBz3ebX52KiO6MWq12+GmUiMh+8dOJatX4iJYAgC/2pKNMW7NzehI5GpVKheeffx6dO3fm2U4isktMPKlWDQz2gZerGn8XluKnoxm27g4RERHVIqsSz4yMDKxfvx7x8fEoKyszeu3atWtYuHBhtXaO6h+lXIbHwspvHvtk53nbdoaIiIhqlcWJ5969exEUFISnn34aI0eORHBwMI4dO2Z4vaioyOxykUQ3ezSsBZRyCQfS83DkYr6tu0NUb2i1WmzZsgVpaWnQarW27g4RkQmLE8/Zs2dj+PDhuHr1Kq5cuYL+/fsjMjISKSkpNdk/qoe8XJ3wQKfyifjX8awnUbXR6/U4cuQIrl69Cr2eY6iJyP5YnHju378fL7/8MmQyGVxdXbF8+XK89NJLuO+++7B3796a7CPVQxU3GW05fBk5RaW27QxRPSGXy9GvXz/4+flx5SIisktWjfEsKSkxev7SSy9h9uzZiIqKws6dO6u1Y1S/dW3RCJ2bu6NMq8eGvRds3R2iekEul6Nnz57w8vJi4klEdsnixDM4ONhscvnCCy9g9uzZePTRR6u1Y1S/SZKE8eEtAQCf70qDVsfLgkRERPWdxYnnuHHj8Oeff5p97cUXX8TChQvh7+9fbR2j+u+Bzr5o0kCFy/kl2H7iiq27Q1TnCSFQWFiIsrIyLplJRHbJ4sRz0qRJ+Oyzzyp9/aWXXkJqamq1dIocg5NSjv/0aAGANxkRVQeNRoP//ve/OH78ODQaja27Q0RkotomkD906BDHFJHVxvYMgFwmYde5XJzMLLB1d4jqPC6XSUT2rFo/oXhph6zl6+6MAR29AQCfJqfZuDdEdZtKpcLMmTPRtWtXLplJRHapWhNPSZKqszlyEOP+uclo84FLyC/m5UEiIqL6itdkyObCAj3Q3scV1zU6bNzPqZWIiIjqK4sTz4KCgiq/CgsLa7KfVI9JkmSYUP7T5DTo9RyyQXQ7tFottm7diosXL3LJTCKySwpLKzZq1KjKS+lCCF5qp9s2tKsflsSfQHpuMVYl/YVmjV3g5eqEHoEekMt4XBFZQq/X48CBA4bHRET2xuLE89dff63JfpCDc1Ep0CPQA9tPZOHNbacN5b7uTpg3JAgDg31t2DuiukEul+Pee+/FmTNnOMsIEdklixPPyMjImuwHObitRzOw/USWSXlmfgmeWn8AK8d2Z/JJdAtyuRy9e/dGUVERE08isku8uYhsTqcXWLDluNnXKkZ7LthyHDqO/SQiIqrTmHiSze1JzUVGfkmlrwsAGfkl2JOaW3udIqqDhBAoKSmBVqvlvMpEZJeYeJLNZRVWnnTeTj0iR6XRaLBs2TIcPXqUS2YSkV1i4kk25+XqVK31iIiIyD5ZnXg+8cQTZufsvHbtGp544olq6RQ5lh6BHvB1d0JVkyb5updPrURElVMqlXj55ZfRpUsXKJVKW3eHiMiE1YnnJ598guvXr5uUX79+HZ9++mm1dIoci1wmYd6QIACoNPmc+0AQ5/MkugVJkiCXyyFJEudVJiK7ZNXKRfn5+RBCoLCw0GjVoqtXryI+Ph5eXl412VeqxwYG+2Ll2O7wcTe+nF7xp/Nyvuk/O0RERFS3WL1ykSRJaNu2rcnrkiRhwYIF1do5ciwDg33RP8gHe1JzkVVYAi9XJ5z9uwhzvj2KN7edQmTbpmjj7WrrbhLZLZ1Oh59//hmXLl2CTqfj5XYisjtWrVwkhEC/fv2wadMmeHj8O95OpVIhICAAfn5+NdJJchxymYTw1k0Mz3u28sD2E1ew49TfiPnqEL6ZGgGlnPfEEZmj0+mwe/duw2MiIntj9cpFqamp8Pf35/ghqhWSJGHpiM6Ievc3HLmUj+W//oXp95uecSei8pWLwsLCcO7cOa5cRER2yepTRydOnMCff/5peL58+XJ07doVY8aMwdWrV6u1c0QA4O3mhIVDOwIAPvjlLxy5mG/jHhHZJ7lcjvvuuw/NmjVj4klEdsnqxPPFF19EQUEBAODIkSOIiYnB4MGDce7cOcTExFR7B4kA4KEufnigky+0eoGYrw6iRMPLiERERHWN1YlnamoqgoLKp77ZtGkThgwZgsWLF2PFihX46aefqr2DRED5JffXHg6GZ0M1zmQV4Z2EU7buEpHdEUJAp9NBCMElM4nILlmdeKpUKhQXFwMAtm/fjqioKACAh4eH4UwoUU3waKDC0hGdAAAf/5GK3edybNwjIvui0WiwdOlSHDp0iEtmEpFdsjrxvPfeexETE4PXXnsNe/bswQMPPAAAOH36NJo3b17tHSS60X0dvDE6tAWEAJ7feAhFpVpbd4mIiIgsZHXi+cEHH0ChUODrr7/GypUr0axZMwDATz/9hIEDB1Z7B4luNufBDmjWyBkXr17H6z8et3V3iOyGUqlETEwMgoODOYcnEdkli6dTquDv748ffvjBpPzdd9+tlg4R3YqrkxJvP9IFj360C1/uuYCoIB/c27qxrbtFZHOSJMHJyQkKhYJT3hGRXbqtmbjPnj2LOXPm4NFHH0VWVhYAYOvWrTh27JjVba1YsQKBgYFwcnJCSEgIfv/99yrrJyUlISQkBE5OTmjVqhVWrVplUmfTpk0ICgqCWq1GUFAQNm/ebPT6b7/9hiFDhsDPzw+SJOHbb781aUMIgfnz58PPzw/Ozs7o06fPbe0f1Yzw1k3wxD2BAICXNx1GXjHHsxEREdk7qxPPpKQkdOrUCbt378Y333yDoqIiAMDhw4cxb948q9qKi4vD9OnT8corryAlJQW9evXCoEGDkJ6ebrZ+amoqBg8ejF69eiElJQWzZ8/Gc889h02bNhnqJCcnY/To0YiOjsahQ4cQHR2NUaNGGVbzAIBr166hS5cu+OCDDyrt25tvvolly5bhgw8+wN69e+Hj44P+/fujsLDQqn2kmvPSwHZo3bQBsgpLMf+HE7buDpHN6XQ6/Pbbb8jIyODKRURkl6xOPGfOnIlFixYhMTERKpXKUN63b18kJydb1dayZcswceJETJo0CR06dEBsbCxatGiBlStXmq2/atUq+Pv7IzY2Fh06dMCkSZPwxBNP4O233zbUiY2NRf/+/TFr1iy0b98es2bNwn333YfY2FhDnUGDBmHRokUYPny42e0IIRAbG4tXXnkFw4cPR3BwMD755BMUFxfjiy++sGofqeY4KeVYNqor5DIJPx7JxIFsXlokx6bT6fDHH3/gypUrTDyJyC5ZnXgeOXIEw4YNMylv2rQpcnIsn96mrKwM+/fvN0zHVCEqKgo7d+40+57k5GST+gMGDMC+ffsMU4dUVqeyNs1JTU1FZmamUTtqtRqRkZFWtUM1r0uLRni6710AgI2pMmQVltq4R0S2I5PJ0L17d3h6ekImu62RVERENcrqm4saNWqEjIwMBAYGGpWnpKQY7nC3RHZ2NnQ6Hby9vY3Kvb29kZmZafY9mZmZZutrtVpkZ2fD19e30jqVtVnZdired3M7aWlplb6vtLQUpaX/Jj4V85pqNJoanVOvom1HnbdvSq8AbD+egeMZRZj1zRF8PC7EIW+scPTjAGAMAOC+++5DYmIihBAOGwceB4wBwBgAtRcDa9q3OvEcM2YMXn75ZWzcuBGSJEGv1+PPP//ECy+8gHHjxlnbnEmCIISoMmkwV//mcmvbrK6+LVmyBAsWLDApT0hIgIuLi9Xbt1ZiYmKNb8NePeQFnM6U47e/cvHquq0I93bcVVsc+TiowBgwBgBjADAGAGMA1HwMKhYWsoTViefrr7+OCRMmoFmzZhBCICgoCDqdDmPGjMGcOXMsbsfT0xNyudzkTGRWVpbJmcYKPj4+ZusrFAo0adKkyjqVtVnZdoDyM5++vr4WtzNr1iyj9eoLCgrQokULREVFwc3NzeLtW0uj0SAxMRH9+/d32Ln7NBoNTuRtx3dpcmy5qML/PRyOFo1rPtm3JzwOGAOAMQAYA4AxABgDoPZiYM3KlVYnnkqlEp9//jkWLlyIlJQU6PV6dOvWDW3atLGqHZVKhZCQECQmJhqNGU1MTMTQoUPNvic8PBxbtmwxKktISEBoaKghoOHh4UhMTMSMGTOM6kRERFjct8DAQPj4+CAxMRHdunUDUD4mNSkpCUuXLq30fWq1Gmq12qRcqVTWykFfW9uxV318BS6hEfal5WHW5uP4cnJPyGSOd8nd0Y8DwHFjUFZWhnfeeQd6vR7333+/Q8bgRo56HNyIMWAMgJqPgTVtW514VmjdujVatWoFwPSStKViYmIQHR2N0NBQhIeH48MPP0R6ejqmTJkCoPwM4qVLl/Dpp58CAKZMmYIPPvgAMTExmDx5MpKTk7F69Wp8+eWXhjanTZuG3r17Y+nSpRg6dCi+++47bN++HX/88YehTlFREf766y/D89TUVBw8eBAeHh7w9/eHJEmYPn06Fi9ejDZt2qBNmzZYvHgxXFxcMGbMmNvaV6p5MglYOjwYQ5YnY3dqLtb8mYpJvVrZultEtUqv19u6C0RElbqt2x5Xr16N4OBgODk5wcnJCcHBwfj444+tbmf06NGIjY3FwoUL0bVrV/z222+Ij49HQEAAACAjI8NoTs/AwEDEx8djx44d6Nq1K1577TW8//77GDFihKFOREQENmzYgLVr16Jz585Yt24d4uLiEBYWZqizb98+dOvWzXA2MyYmBt26dcOrr75qqPPSSy9h+vTpmDp1KkJDQ3Hp0iUkJCTA1dXV6v2k2uPv4YI5DwQBAN7cdgpnrnDeVXIcSqUSzz77LIKCghz+DA8R2Serz3jOnTsX7777Lp599lmEh4cDKJ/CaMaMGTh//jwWLVpkVXtTp07F1KlTzb62bt06k7LIyEgcOHCgyjZHjhyJkSNHVvp6nz59DDclVUaSJMyfPx/z58+vsh7Zn0d7tEDC8UzsOPU3Yr46hG+mRkAp59QyVP9JkgRXV1eoVCqHnNmBiOyf1YnnypUr8dFHH+HRRx81lD300EPo3Lkznn32WasTT6LqJkkSlo7ojKh3f8ORS/lY/utfmH5/W1t3i4iIyOFZfRpIp9MhNDTUpDwkJARarbZaOkV0p7zdnLBwaEcAwAe//IUjF/Nt3COimqfT6bBr1y5kZWVx5SIisktWJ55jx441u6Tlhx9+iMcee6xaOkVUHR7q4ocHOvlCqxeI+eogSjT8Q0z1m06nwy+//ILLly8z8SQiu2TRpfYb56aUJAkff/wxEhIS0LNnTwDArl27cOHChduaQJ6opkiShNceDsbu1FycySrCOwmn8Mo/Nx4R1UcymQydOnXCxYsXuWQmEdklixLPlJQUo+chISEAgLNnzwIoX6e9adOmOHbsWDV3j+jOeDRQYemITpj4yT58/Ecq7u/gjbBWTWzdLaIaoVAoMGTIEMTHx0OhuO3Z8oiIaoxFn0y//vprTfeDqMbc18Ebo0NbIG7fBTy/8RC2Tu+Nhmr+USYiIqptvBZDDmHOgx3QrJEzLl69jtd/PG7r7hARETkkJp7kEFydlHj7kS4AgC/3XMDPx68g+WwOvjt4Cclnc6DTVz2vK1FdULFk5uHDh1FWVmbr7hARmeD1RnIY4a2b4Il7ArHmz1RM/mwfbsw1fd2dMG9IEAYG+9qug0TVoLS01NZdICKqFM94kkPp2sIdAHDzCc7M/BI8tf4Ath7NsEGviKqHUqnElClT0KFDBy6ZSUR2iYknOQydXmDJTyfNvlaRhy7YcpyX3anOkiQJHh4eUKvVXDKTiOwSE09yGHtSc5GRX1Lp6wJARn4J9qTm1l6niIiIHAgTT3IYWYWVJ523U4/I3uh0Ouzbtw9///03Vy4iIrvEm4vIYXi5OlVrPSJ7o9PpkJCQYHhMRGRveMaTHEaPQA/4ujuhqpFvjZyV6BHoUWt9IqpOMpkM7du3h7u7O5fMJCK7xE8mchhymYR5Q8rXaq8s+cy7rsFnyedrrU9E1UmhUGD48OEIDAzkkplEZJeYeJJDGRjsi5Vju8PH3fhyuq+7E/q2bwoAmL/lON7/+QyE4N3tRERE1Yn/EpPDGRjsi/5BPtiTmouswhJ4uTqhR6AHZBLw3s9nELv9DJYlnkb+dQ3mPNCB09IQERFVEyae5JDkMgnhrZuYlE+/vy3cnJRY+MNxrP4jFQXXNVgyvBMUcl4cIPun0Wjw/vvvo7S0FP379+ck8kRkd/jXlOgmT9wbiLcf6QKZBGzcfxHPfJGCUi3vECb7J4RAUVERNBoNh4oQkV1i4klkxsiQ5ljxWAhUchm2HsvEpE/2obhMa+tuEVVJoVBg4sSJaNu2LW8uIiK7xMSTqBIDg32wZsLdcFHJ8fuZbIz9eDfyizW27hZRpWQyGby9veHi4sLplIjILvGTiagK97bxxPpJYXBzUuBAeh5Gf5jMlY2IiIhuExNPolvo7t8YX00JR1NXNU5mFmLUqmRcvFps624RmdDpdDh8+DBycnK4chER2SUmnkQWaO/jho1PhqN5Y2eczynGyJXJ+Cur0NbdIjKi0+nwww8/4MKFC0w8icguMfEkslBLzwb4ekoE7vJqiMyCEoz63y4cuZhv624RGchkMrRu3Rpubm4c40lEdomfTERW8HF3wldPhqNzc3fkXivDox/twu5zObbuFhGA8rvaR48ejVatWvGudiKyS0w8iazk0UCFzyeFoWcrDxSVajFuzR78cvKKrbtFRERk95h4Et0GVycl1j3eA/d38EKpVo//+3Q/vjt4ydbdIiIismtMPIluk5NSjpVjQ/BwVz9o9QLT4w5i/a40W3eLHJhGo8HKlStx/PhxaDScc5aI7A8TT6I7oJTLsGxUV0T3DIAQwJxvj2LFjr9s3S1yUEIIXL16FWVlZVwyk4jsEhNPojskk0lYOLQjnu7bGgDw5tZTWPLTCQghoNMLJJ/NwXcHLyH5bA50eiYDVHMUCgWio6Nx11138eYiIrJL/GQiqgaSJOHFAe3h7qzE4viT+F/SORy7VIC/soqQWfDvSke+7k6YNyQIA4N9bdhbqq9kMhlatGiBI0eOcDolIrJL/GQiqkb/17s13hjeCQDwx1/ZRkknAGTml+Cp9Qew9WiGLbpHRERkU0w8iarZI6Et0MhFafa1igvtC7Yc52V3qnZ6vR4nTpxAXl4e9Hq9rbtDRGSCiSdRNduTmou84srvKBYAMvJLsCc1t/Y6RQ5Bq9Vi8+bNOH/+PLRara27Q0RkgoknUTXLKiy5dSUr6hFZSpIk+Pv7o0GDBpAkydbdISIyYfPEc8WKFQgMDISTkxNCQkLw+++/V1k/KSkJISEhcHJyQqtWrbBq1SqTOps2bUJQUBDUajWCgoKwefNmq7c7YcIESJJk9NWzZ88721lyCF6uTtVaj8hSSqUSY8eORZs2baBUmh/uQURkSzZNPOPi4jB9+nS88sorSElJQa9evTBo0CCkp6ebrZ+amorBgwejV69eSElJwezZs/Hcc89h06ZNhjrJyckYPXo0oqOjcejQIURHR2PUqFHYvXu31dsdOHAgMjIyDF/x8fE1EwiqV3oEesDX3Qm3Ot+09s9zuJx3vVb6REREZA9smnguW7YMEydOxKRJk9ChQwfExsaiRYsWWLlypdn6q1atgr+/P2JjY9GhQwdMmjQJTzzxBN5++21DndjYWPTv3x+zZs1C+/btMWvWLNx3332IjY21ertqtRo+Pj6GLw8PjxqJA9UvcpmEeUOCAMAk+ax4LpOAhONZuH9ZEj787Sw0Ot4IQkRE9Z/NEs+ysjLs378fUVFRRuVRUVHYuXOn2fckJyeb1B8wYAD27dtnWB6usjoVbVqz3R07dsDLywtt27bF5MmTkZWVZf2OkkMaGOyLlWO7w8fd+HK6j7sTVo3tjp+m9cbdLRujuEyHxfEnMeS/f2Dfed5sRHdGo9Hg448/xsmTJ7lkJhHZJZtNIJ+dnQ2dTgdvb2+jcm9vb2RmZpp9T2Zmptn6Wq0W2dnZ8PX1rbRORZuWbnfQoEF45JFHEBAQgNTUVMydOxf9+vXD/v37oVarzfavtLQUpaWlhucFBQUAyv8Y1OQfgYq2HfkPjT3G4L52nujTphf2pV1FVmEpvFzVCA1oDLms/Lzn+sdD8c3By3hz22mczCzEyFXJeCSkGV7o3wYeDVRWb88eY1DbHD0GZWVlhn+Qy8rKHHacp6MfBwBjADAGQO3FwJr2bb5y0c13Xgohqrwb01z9m8stafNWdUaPHm14HBwcjNDQUAQEBODHH3/E8OHDzfZtyZIlWLBggUl5QkICXFxcKt2n6pKYmFjj27B39hoDOYAcANtOGJe7AHgxCNiSLkNylgwb919C/KGLGOKvR5iXgOw2bky21xjUJkeNgRACrVuXL926Y8cOh7+z3VGPgxsxBowBUPMxKC4utriuzRJPT09PyOVyk7ObWVlZJmcjK/j4+Jitr1Ao0KRJkyrrVLR5O9sFAF9fXwQEBODMmTOV1pk1axZiYmIMzwsKCtCiRQtERUXBzc2t0vfdKY1Gg8TERPTv39+hz3DU5Rg8AmB/2lXM23ICp64UYcM5Oc5oG2HBkA5o5+NqURt1PQbVgTFgDADGAGAMAMYAqL0YVFzhtYTNEk+VSoWQkBAkJiZi2LBhhvLExEQMHTrU7HvCw8OxZcsWo7KEhASEhoYaAhoeHo7ExETMmDHDqE5ERMRtbxcAcnJycOHCBfj6Vr7GtlqtNnsZXqlU1spBX1vbsWd1OQY97/LCD8954pOd57Es8TT2p+dh6MpdmHhvIKbd1wYN1Jb9utblGFQXxoAxABgDgDEAGAOg5mNgTds2vas9JiYGH3/8MdasWYMTJ05gxowZSE9Px5QpUwCUn0EcN26cof6UKVOQlpaGmJgYnDhxAmvWrMHq1avxwgsvGOpMmzYNCQkJWLp0KU6ePImlS5di+/btmD59usXbLSoqwgsvvIDk5GScP38eO3bswJAhQ+Dp6WmUrBJVN6Vchkm9WuHn5yMxKNgHOr3Ah7+dQ/9lSdh6NNMwtITIHL1ej7/++gv5+flcMpOI7JJNx3iOHj0aOTk5WLhwITIyMhAcHIz4+HgEBAQAADIyMozm1gwMDER8fDxmzJiB5cuXw8/PD++//z5GjBhhqBMREYENGzZgzpw5mDt3Llq3bo24uDiEhYVZvF25XI4jR47g008/RV5eHnx9fdG3b1/ExcXB1dWyy55Ed8LX3Rkrx4bg15NZePX7o7iQex1T1u9Hv/ZeWPBQR7TwqPkxw1T3aLVafPXVV4bHld0ISURkKza/uWjq1KmYOnWq2dfWrVtnUhYZGYkDBw5U2ebIkSMxcuTI296us7Mztm3bVuX7iWpD3/ZeSGgVieW//oX//XYWv5zMws6z2Xi2XxtM7tUKKkX5RQudXmB3ai72Z0tokpqL8Lu8DHfPk+OQJAm+vr7Iy8tz+BuLiMg+2TzxJKKqOavkeGFAOzzcrRnmfnsUyedy8Na2U/jmwEUsergT8q+XYcGW48jILwEgx6dn9sHX3QnzhgRhYHDlY5Kp/lEqlXj88ccRHx/v8GPaiMg+2XytdiKyzF1eDfHF5DDEju4Kz4YqnP37Gh79aBemrD/wT9L5r8z8Ejy1/gC2Hs2wUW+JiIhMMfEkqkMkScLD3Zrh5+f74LEw/0rrVdyCtGDLcej0vCGJiIjsAxNPojrI3VmJBzv7VVlHAMjIL8GeVC7F6Sg0Gg0+/fRTnDlzxqFXayEi+8UxnkR1VFZhya0rWVGP6j4hBC5evGh4TERkb3jGk6iO8nJ1sqjeh7+dw09HMqDRcV7H+k6hUGDEiBFo2bIlFAqeVyAi+8PEk6iO6hHoAV93J9xq0pxjlwvw1OcHcM8bv+DdxNPIzOcZ0PpKJpOhXbt2aNSoEWQyfrwTkf3hJxNRHSWXSZg3JAgATJJP6Z+v14cF45m+d8GzoQpZhaV47+czuGfpL5jy2X78cSYbet54REREtYjXYojqsIHBvlg5tvsN83iW87lpHs/n7muDbccy8dmuNOxJzcXWY5nYeiwTgZ4N8FiYPx4JaQF3F877WNfp9XqkpaWhsLCQS2YSkV1i4klUxw0M9kX/IB8k/5WFhN93I6pXmMnKRSqFDEO6+GFIFz+cvlKI9bvS8M2BS0jNvoZFP57AW9tO4aEufhjbMwBdWjSy3c7QHdFqtfj8888Nj7lkJhHZGyaeRPWAXCYhLNADOScEwgI9qlwus623KxYODcbLA9vju4OX8dmuNJzIKMDG/Rexcf9FdGrmjuieARjSxQ/OKrnRe3V6gT2pucgqLIGXqxN63GJbVLskSYKnpyeKioq4ZCYR2SUmnkQOqoFagTFh/ni0RwscSM/D+l1p+PFwBo5cysdLmw5j0Y/HMTKkBR7r6Y/WTRti69EMk0v6XJrTviiVSvzf//0fl8wkIrvFxJPIwUmShJCAxggJaIw5D3TAxv0X8fnuNFzIvY41f6ZizZ+paO/TECczi0zeW7E058qx3Zl8EhHRLfGudiIyaNJQjSmRrZH0Ql+sffxu3N/BCxJgNukEuDQnERFZh4knEZmQyST0beeFj8ffjfce7VplXS7NaT80Gg2++OIL/PXXX1wyk4jsEhNPIqqSpSsvvv7jcXyWfB7pOcU12yGqlBAC58+fR1FREZfMJCK7xDGeRFQlS5fmPHq5AEe/OwbgGAI9GyCybVNEtmuKnoFNTO6Op5qhUCjw0EMP4eDBg1wyk4jsEj+ZiKhKFUtzZuaXwNw5NAlAk4YqTLinJX4/nY39aVeRmn0NqdnXsG7neagUMoQFeiCybVP0adcUrZs2vOVUP5y26fbIZDIEBwcjPT2dS2YSkV1i4klEVapYmvOp9QcgAUbJZ0UquOjhYAwM9sUzfdugsESDP//KQdLpv5F0KguX80vw+5ls/H4mG4t+PIFmjZwR2a4pIts2RUTrJnB1Mp72h9M2ERHVX0w8ieiWLF2aEwBcnZQYGOyDgcE+EELg7N9F2HHqbySd/hu7z+XiUt51fLE7HV/sTodCVj6VU592Xohs2xRpOdcw9fMDJmdWOW2TZfR6PS5fvozi4mIumUlEdomJJxFZpGJpTmsugUuShLu8XHGXlysm9WqF4jItdp/LLT8bevpvpGZfw+7UXOxOzcXSrSchk2D2cr5A+dnVBVuOo3+QDy+7V0Kr1WLdunWGx1wyk4jsDRNPIrKYXCYhvHWT236/i0qBvu290Le9FwAgLefaP5fk/8bvZ7JRpqv8LN2N0zbdSR/qM0mS4O7ujuLiYi6ZSUR2iYknEdlMQJMGGBfeAOPCW2LT/gt4fuPhW77n+Y2HcO9dTRDczB0d/dwR5Ot223fN17ebmJRKJZ5++mkumUlEdouJJxHZBb9GLhbVu5x3HV/tu4iv9l0EAMgk4C6vhghu5o4OPg1RWAAUlWrR+BaJF29iIiKqfUw8icguWDJtU1NXNRY81BHHMwpw9FI+jlwqQHZRKU5fKcLpKxXLeirw3+O/INCzAYL93NGpmTs6NnNDRz93uDuXJ6Nbj2bgqfW8iYmIqLYx8SQiu2DJtE0Lh3bEwGBfDOr0b1J4paAERy/l4+ilAhy+eBX7z2Uhr0zCub+v4dzf1/D9ocuGugFNXNDR1w2/n8mulzcxabVafP3118jMzIRWq+XldiKyO0w8ichuWDNtUwVvNyd4uznhvg7e0Gg0iI+PR1jv+3AyqxjHLlecGc3HxavXkZZTjLRbLOlZcRNT8tls3NumabXsV22NJdXr9Th9+rThMRGRvWHiSUR25XambbpZk4Zq9GncEH3aeRnK8orLcPRSAb7ad8HoLGhlotfsgb+HC/w9XNCySQMENHFBQJMGaNnEBS08XOCktOyGptocSyqXyzFo0CAcPXoUcjmXKSUi+8PEk4jszp1O22ROIxcV7m3jCblMsijxFAKGM6S/n8k2ek2SAB83JwQ0KU9K/ZsYJ6cN1eUfrbU9llQul6Nbt27IyMhg4klEdomJJxE5FEtuYvJxd8KmpyJwIbc88UzLvYbzOcVIy7mGtOxiFJZqkZFfgoz8Euw6l2vShmdDFfw9XHAio6BWx5Lq9AK7U3OxP1tCk9RchN/lVefGqRJR/cbEk4gciiU3Mc0bEgS/Rs7wa+SMsFbGZ16FELharMH5nGtIzynG+Zxr/5wZLf+ec60M2UXlX1WpGEv65Gf70KV5I3i5qeHl5gRvVyd4uanh4aKCzIqkcevRDCz4/hiuF+YBAD49sxe+7s41ckm/vs1/SkS1h4knETmc27mJqYIkSfBooIJHAxW6+zc2eb2wRIO0nGJs2n8Ra3eev2Vftp/IwvYTWSblCpkEL9fyZNTLVf3PTVRqeP2TmHr/U97YRYWE45l4av0ByKFDtPMxAMBn17vVyCV9zn9KRHeCiScROaTquInJHFcnJYKbuaOwRGtR4jm8mx+UcjmyCktwpaAUWYUlyLlWBq1e4HJ+CS7fkOCZo5ABevHvmdsS8e/HekXZnG+Por2PGzxd1Wigkt/2cpq1PWaVZ1aJ6h8mnkTksGriJqYKlo4lfeuRribJlEanR3ZRaXkiWlCCK4X/fC8oQVbhv+XlCeq/79NCji9LuppsK7uoDH3e3gEAUMoluDur0NhFicYuKri7KA2PG7mo0Oif5/8+Lv+ukMmwYMvxWhuzWptnVpngEtUeJp5ERDXA0rGk5hIcpVwGX3dn+Lo7V7mNMq0eX+xJw/zvj1vUH51eQKMTyC4qRXZRqeU7A0All6FMV/ncoBVjVv/7yxl092+Mhk4KuKoVaOikQAO1Ag1UCouTudo8s1ofE1zeZEb2jIknEVENuZOxpJZQKWRo5+1mUd31E8PQtUUjXC0uQ16xBnnFZbharMHV4jLkX9fg6rXy5/nX/y2vqKcXqDLpvFHs9jOVvtZAJUdDJwUaqhVo6KREQ7W8/LFaCdd/yp1Vcvwv6WyVZ1bnf38c93fwhkIus6hPlamPCa7xduT49My+epFI16ftODomnkRENaimxpJWuPGSvgx63KM8DwD4U9MSOsgMl/QrtumsKr9b31J6vUBhqRa/nryC6XGHblm/vbcrJJmEolINikq0KCzRQqsvT+2ulelwrUyHK7DubOuNBIDMghLc9cpPcFbK4aySm3x3UkjIy5Hh1+IjcHFSwqWiXCmHyz/11AoZFv5Q9dCB+VvqVoJb/xPpur8dgGe+bZ54rlixAm+99RYyMjLQsWNHxMbGolevXpXWT0pKQkxMDI4dOwY/Pz+89NJLmDJlilGdTZs2Ye7cuTh79ixat26N119/HcOGDbNqu0IILFiwAB9++CGuXr2KsLAwLF++HB07dqzeABBRvVeTY0lvvKQvg0BrRfm8ojs1Abe8pG8JmUyCu7MSQ7o0w9Ktp245ZvXHab2MtiWEQKlWj2ulWhSVlieiRaVaFP3zvbBUW/7aP8+PXy7AnvOmc6Oac12jw3WNrrKe43BuhtX7a+g3yhO2u175CSqFDGrDV3nSqlLIoFbKoZbLoFYav6ZWyqCSl7+ulEv4ZGdapQkuAMzefBRuTkqolXKo5DIoFRKU8vI2lHIZlHIJSsW/z839LHV6UWtjcOtbIl3/E/aaPfNtLZsmnnFxcZg+fTpWrFiBe+65B//73/8waNAgHD9+HP7+/ib1U1NTMXjwYEyePBnr16/Hn3/+ialTp6Jp06YYMWIEACA5ORmjR4/Ga6+9hmHDhmHz5s0YNWoU/vjjD4SFhVm83TfffBPLli3DunXr0LZtWyxatAj9+/fHqVOn4OrqWntBIiK6hYpL+gu/P4rd11oAAHSQqu2SPnD7Y1YlSYKTsvxsY5OG6ltuJ/lsDh79aNct660a2x0d/dxRXFaefF4v0+G6RovrZXoUlZRib8phtG7bAWU6oFijRck/9YrLdCjR6JCeW4zTV4os2vcyrR5lWj0KLaptvdxrZRjz8W6L68sk/JuYKsoTU51OIPta5XPHVozBffTDZHi7O0Mhk8q/5LJ/vt/0XCYzLZNLkEsSlvx0sspE+pXNR+HRQAWlXAaFrDxRvvFLcdNzuSRB/k/bFa8DqJVEmgl77ZOEEObiXSvCwsLQvXt3rFy50lDWoUMHPPzww1iyZIlJ/Zdffhnff/89Tpw4YSibMmUKDh06hOTkZADA6NGjUVBQgJ9++slQZ+DAgWjcuDG+/PJLi7YrhICfnx+mT5+Ol19+GQBQWloKb29vLF26FE8++aRF+1dQUAB3d3fk5+fDzc2ycVi3Q6PRID4+HoMHD4ZSqayx7dgzxoAxABgDnV4g+a8sJPy+G1G9wmrk0lpNn7HR6QXuXfrLLc+s/vFyv0r3zZLjwJoEt1PzRijT6lGq1aFUo0fpP4/Ly4zLDfX+ee1ERoHJkqvmeLup4aSUQ6PVo0wnoNHpb/iy2Z9pu9ekgRLO/9y4JpckyP75LknlCXphQQE8GjeCQi6DTAJk0r8Jr0ySkH+9DAcv5N9yO33bNYWPu7NRG9I/jyvKZLJ/H0vSP/2Ryq8aCAj8L+kcCku0lW7D3VmJlwe2g0ImgySV/9P2b3vG32X/vC6hYtvlzyGA5786hNxi8/+EWPL7czusyXdsdsazrKwM+/fvx8yZM43Ko6KisHPnTrPvSU5ORlRUlFHZgAEDsHr1amg0GiiVSiQnJ2PGjBkmdWJjYy3ebmpqKjIzM422pVarERkZiZ07d1qceBIR1Sa5TEJYoAdyTgiE1dC4sZoes3onswFYw9Lpru70TFfy2RyLEs/Y0d0qHY4hRPlsBBWJaNk/yahG++/zA+l5mPvt0Vtu54l7WqJ5Y5fyGQ70emh1Alq9gFan/+e7gFav/7es4vV/6l7Mu47jlwtuuR3PhiqoFXLo9AI6Icq/3/Sl1euhv8OcOueaBrimqaKGhAvXbp1Y3sqvp/6+4zZuJf+6BrM33/pneCcqznzvSc2tseE/t2KzxDM7Oxs6nQ7e3t5G5d7e3sjMzDT7nszMTLP1tVotsrOz4evrW2mdijYt2W7Fd3N10tLSKt2n0tJSlJb+O2i+oKD8l1Oj0UCjqeoX485UtF2T27B3jAFjADAGQgjk5OSgtLQUZWVVL9l5p0L93QCUn9nQ67TQVzbU8jbc184T//1PFyyKP4nMgn8/U33c1XhlUHvc186zyp+xpcfBK4Pa4dkNhypNcF8Z1O6O961bc1f4uKlxpaC0igRXjW7NXavsrwRAJQNUMgkNlHKT11s3ccbyX87ccjsvRbW5o0R6d2ouxq7Zd8t6saM6IyzQ45b1REVSKgCdXv9PUgrsOZ+Lp7+89c1sC4Z0QAdfV+j/SXD1ekAvyh+XlWmxPyUFnbt0gUxWngTrBf75Xv515so1fPzn+VtuZ2R3PzRr5Awh8M97YWhDL8r3o6JtYfR6+fe0nGvYcz7vltvp6OcKL1e1oc3y7VW0LwyLRdy4DXHD9q8Wl+FSXtWLTgBARt41aDTVdyXWms9cm99cdPMKGkKIKlfVMFf/5nJL2qyuOjdasmQJFixYYFKekJAAFxeXSt9XXRITE2t8G/aOMWAMAMeNgU6nw5EjRwAACoUCcrlpglKXvBwEnC2QUKAB3JRAa7dr0KXtR3zl//8bseQ4eLythG/Oy5BX9u9nu7tKYHhLvVXbqspgHwlrCirujL/xb4iAADDIuxjbtv5k5p32tx29ABqp5Mgru3kb/26rkQr4+/guxJ8w83I1b8ft7yPIqOKEcnBjQJ9+EBWTgUkwTnw6Wride1TpkF23oOOS+Wa8XSTswa1/H/s2ykMb99s/DXwmX8IHebfezrljBxF/MeW2t3Oz4uJii+vaLPH09PSEXC43ObuZlZVlcqaxgo+Pj9n6CoUCTZo0qbJORZuWbNfHxwdA+ZlPX19fs3XMmTVrFmJiYgzPCwoK0KJFC0RFRdX4GM/ExET079/fIce1AYwBwBgAjEFZWRlOnjwJnU6Hfv36oUGDBrbukk1YcxwMBvCSXmBf2lVkFZbCy1WN0IDG1TpMYTCA7seumJzB9XV3wiuD2mNAx8r/rtjjdpQtr+DZDeVnI03PFEtYNLxLtWzrTrdj6XFQG/uj0wt8/c5vtzwj/czo3nd8s1RtbOdmFVd4LWGzxFOlUiEkJASJiYlGUx0lJiZi6NChZt8THh6OLVu2GJUlJCQgNDTUcFCFh4cjMTHRaJxnQkICIiIiLN5uYGAgfHx8kJiYiG7dugEo/0BPSkrC0qVLK90ntVoNtdr0rk2lUlkrfwRrazv2jDFgDADHjYFSqcSLL76I+Ph4NGjQwCFjcCNLjwMlgHvbVk9SVpkHuzbHoM7Nanz+xort1ORNZg92bQ6FQl5jCyNU93ZudRzUxv4oAcx/qOMtxi53hJNaVSe2Y7JdKz5rbHqpPSYmBtHR0QgNDUV4eDg+/PBDpKenG+blnDVrFi5duoRPP/0UQPkd7B988AFiYmIwefJkJCcnY/Xq1Ya71QFg2rRp6N27N5YuXYqhQ4fiu+++w/bt2/HHH39YvF1JkjB9+nQsXrwYbdq0QZs2bbB48WK4uLhgzJgxtRghIiKqL2pyPtebt1PXbzKrj9up6ZXMans7t8umiefo0aORk5ODhQsXIiMjA8HBwYiPj0dAQAAAICMjA+np6Yb6gYGBiI+Px4wZM7B8+XL4+fnh/fffN8zhCQARERHYsGED5syZg7lz56J169aIi4szzOFpyXYB4KWXXsL169cxdepUwwTyCQkJnMOTiIgItZtI15ft1HYiXdPTq90Om99cNHXqVEydOtXsa+vWrTMpi4yMxIEDB6psc+TIkRg5cuRtbxcoP+s5f/58zJ8/v8p2iIjshVarRXx8PNLT06HVah3+UjuRPapPZ75vh80TTyIiqh56vR4HDx40PCYisjeyW1chIqK6QC6XIzIyEj4+PnV+KiUiqp94xpOIqJ6Qy+W45557kJ+fz8STiOwSz3gSERERUa1g4klEVE8IIXDt2jVotVrDqm5ERPaEiScRUT2h0Wjw3nvv4ejRow67Xj0R2TeO8axBFWccrFlK6nZoNBoUFxejoKDAYadPYQwYA4AxKCsrQ0lJ+YTRBQUF0Ol0Nu6RbTj6cQAwBgBjANReDCryHEuutEiC12NqzMWLF9GiRQtbd4OIiIioxl24cAHNmzevsg4Tzxqk1+tx+fJluLq6QpJqbuLWgoICtGjRAhcuXICbm1uNbceeMQaMAcAYAIwBwBgAjAHAGAC1FwMhBAoLC+Hn5weZrOpRnLzUXoNkMtktM//q5Obm5rC/XBUYA8YAYAwAxgBgDADGAGAMgNqJgbu7u0X1eHMREREREdUKJp5EREREVCuYeNYDarUa8+bNg1qttnVXbIYxYAwAxgBgDADGAGAMAMYAsM8Y8OYiIiIiIqoVPONJRERERLWCiScRERER1QomnkRERERUK5h41gGvv/46IiIi4OLigkaNGln0HiEE5s+fDz8/Pzg7O6NPnz44duyYUZ3S0lI8++yz8PT0RIMGDfDQQw/h4sWLNbAHd+7q1auIjo6Gu7s73N3dER0djby8vCrfI0mS2a+33nrLUKdPnz4mr//nP/+p4b25PbcTgwkTJpjsX8+ePY3q1OfjQKPR4OWXX0anTp3QoEED+Pn5Ydy4cbh8+bJRPXs+DlasWIHAwEA4OTkhJCQEv//+e5X1k5KSEBISAicnJ7Rq1QqrVq0yqbNp0yYEBQVBrVYjKCgImzdvrqnuVwtrYvDNN9+gf//+aNq0Kdzc3BAeHo5t27YZ1Vm3bp3Zz4aK5UbtkTUx2LFjh9n9O3nypFG9+nwcmPvskyQJHTt2NNSpa8fBb7/9hiFDhsDPzw+SJOHbb7+95Xvs8vNAkN179dVXxbJly0RMTIxwd3e36D1vvPGGcHV1FZs2bRJHjhwRo0ePFr6+vqKgoMBQZ8qUKaJZs2YiMTFRHDhwQPTt21d06dJFaLXaGtqT2zdw4EARHBwsdu7cKXbu3CmCg4PFgw8+WOV7MjIyjL7WrFkjJEkSZ8+eNdSJjIwUkydPNqqXl5dX07tzW24nBuPHjxcDBw402r+cnByjOvX5OMjLyxP333+/iIuLEydPnhTJyckiLCxMhISEGNWz1+Ngw4YNQqlUio8++kgcP35cTJs2TTRo0ECkpaWZrX/u3Dnh4uIipk2bJo4fPy4++ugjoVQqxddff22os3PnTiGXy8XixYvFiRMnxOLFi4VCoRC7du2qrd2yirUxmDZtmli6dKnYs2ePOH36tJg1a5ZQKpXiwIEDhjpr164Vbm5uJp8R9sraGPz6668CgDh16pTR/t34O13fj4O8vDyjfb9w4YLw8PAQ8+bNM9Spa8dBfHy8eOWVV8SmTZsEALF58+Yq69vr5wETzzpk7dq1FiWeer1e+Pj4iDfeeMNQVlJSItzd3cWqVauEEOW/lEqlUmzYsMFQ59KlS0Imk4mtW7dWe9/vxPHjxwUAo1+E5ORkAUCcPHnS4naGDh0q+vXrZ1QWGRkppk2bVl1drTG3G4Px48eLoUOHVvq6Ix4He/bsEQCM/mDZ63HQo0cPMWXKFKOy9u3bi5kzZ5qt/9JLL4n27dsblT355JOiZ8+ehuejRo0SAwcONKozYMAA8Z///Keael29rI2BOUFBQWLBggWG55Z+ltoLa2NQkXhevXq10jYd7TjYvHmzkCRJnD9/3lBW146DG1mSeNrr5wEvtddDqampyMzMRFRUlKFMrVYjMjISO3fuBADs378fGo3GqI6fnx+Cg4MNdexFcnIy3N3dERYWZijr2bMn3N3dLe7rlStX8OOPP2LixIkmr33++efw9PREx44d8cILL6CwsLDa+l5d7iQGO3bsgJeXF9q2bYvJkycjKyvL8JqjHQcAkJ+fD0mSTIat2NtxUFZWhv379xv9bAAgKiqq0v1NTk42qT9gwADs27cPGo2myjr29vMGbi8GN9Pr9SgsLISHh4dReVFREQICAtC8eXM8+OCDSElJqbZ+V6c7iUG3bt3g6+uL++67D7/++qvRa452HKxevRr3338/AgICjMrrynFwO+z184BrtddDmZmZAABvb2+jcm9vb6SlpRnqqFQqNG7c2KROxfvtRWZmJry8vEzKvby8LO7rJ598AldXVwwfPtyo/LHHHkNgYCB8fHxw9OhRzJo1C4cOHUJiYmK19L263G4MBg0ahEceeQQBAQFITU3F3Llz0a9fP+zfvx9qtdrhjoOSkhLMnDkTY8aMMVq32B6Pg+zsbOh0OrO/x5Xtb2Zmptn6Wq0W2dnZ8PX1rbSOvf28gduLwc3eeecdXLt2DaNGjTKUtW/fHuvWrUOnTp1QUFCA9957D/fccw8OHTqENm3aVOs+3KnbiYGvry8+/PBDhISEoLS0FJ999hnuu+8+7NixA7179wZQ+bFSH4+DjIwM/PTTT/jiiy+MyuvScXA77PXzgImnjcyfPx8LFiyoss7evXsRGhp629uQJMnouRDCpOxmltSpLpbGADDdF8C6vq5ZswaPPfYYnJycjMonT55seBwcHIw2bdogNDQUBw4cQPfu3S1q+07UdAxGjx5teBwcHIzQ0FAEBATgxx9/NEnCrWm3OtXWcaDRaPCf//wHer0eK1asMHrN1sdBVaz9PTZX/+by2/lssKXb7e+XX36J+fPn47vvvjP6p6Vnz55GN9ndc8896N69O/773//i/fffr76OVyNrYtCuXTu0a9fO8Dw8PBwXLlzA22+/bUg8rW3THtxuf9etW4dGjRrh4YcfNiqvi8eBtezx84CJp40888wzt7xrtmXLlrfVto+PD4Dy/3Z8fX0N5VlZWYb/bHx8fFBWVoarV68ane3KyspCRETEbW3XWpbG4PDhw7hy5YrJa3///bfJf2rm/P777zh16hTi4uJuWbd79+5QKpU4c+ZMrSQctRWDCr6+vggICMCZM2cAOM5xoNFoMGrUKKSmpuKXX34xOttpTm0fB+Z4enpCLpebnHm48ff4Zj4+PmbrKxQKNGnSpMo61hxHteV2YlAhLi4OEydOxMaNG3H//fdXWVcmk+Huu+82/F7YkzuJwY169uyJ9evXG547ynEghMCaNWsQHR0NlUpVZV17Pg5uh91+HtTY6FGqdtbeXLR06VJDWWlpqdmbi+Li4gx1Ll++bNc3lezevdtQtmvXLotvKhk/frzJXcyVOXLkiAAgkpKSbru/NeFOY1AhOztbqNVq8cknnwghHOM4KCsrEw8//LDo2LGjyMrKsmhb9nIc9OjRQzz11FNGZR06dKjy5qIOHToYlU2ZMsXkZoJBgwYZ1Rk4cKBd31RiTQyEEOKLL74QTk5Ot7z5ooJerxehoaHi8ccfv5Ou1pjbicHNRowYIfr27Wt47gjHgRD/3mh15MiRW27D3o+DG8HCm4vs8fOAiWcdkJaWJlJSUsSCBQtEw4YNRUpKikhJSRGFhYWGOu3atRPffPON4fkbb7wh3N3dxTfffCOOHDkiHn30UbPTKTVv3lxs375dHDhwQPTr18+up9Hp3LmzSE5OFsnJyaJTp04m0+jcHAMhhMjPzxcuLi5i5cqVJm3+9ddfYsGCBWLv3r0iNTVV/Pjjj6J9+/aiW7du9SIGhYWF4vnnnxc7d+4Uqamp4tdffxXh4eGiWbNmDnMcaDQa8dBDD4nmzZuLgwcPGk2ZUlpaKoSw7+OgYgqZ1atXi+PHj4vp06eLBg0aGO7MnTlzpoiOjjbUr5g+ZcaMGeL48eNi9erVJtOn/Pnnn0Iul4s33nhDnDhxQrzxxht1YhodS2PwxRdfCIVCIZYvX17p9Fjz588XW7duFWfPnhUpKSni8ccfFwqFwuifGntibQzeffddsXnzZnH69Glx9OhRMXPmTAFAbNq0yVCnvh8HFcaOHSvCwsLMtlnXjoPCwkLD338AYtmyZSIlJcUwQ0dd+Txg4lkHjB8/XgAw+fr1118NdQCItWvXGp7r9Xoxb9484ePjI9Rqtejdu7fJf3zXr18XzzzzjPDw8BDOzs7iwQcfFOnp6bW0V9bJyckRjz32mHB1dRWurq7iscceM5kq5OYYCCHE//73P+Hs7Gx2Tsb09HTRu3dv4eHhIVQqlWjdurV47rnnTOa5tBfWxqC4uFhERUWJpk2bCqVSKfz9/cX48eNNfsb1+ThITU01+7tz4++PvR8Hy5cvFwEBAUKlUonu3bsbnYUdP368iIyMNKq/Y8cO0a1bN6FSqUTLli3N/tO1ceNG0a5dO6FUKkX79u2NEhJ7ZE0MIiMjzf68x48fb6gzffp04e/vL1QqlWjatKmIiooSO3furMU9sp41MVi6dKlo3bq1cHJyEo0bNxb33nuv+PHHH03arM/HgRDlV3ScnZ3Fhx9+aLa9unYcVJy9rezYriufB5IQ/4w0JSIiIiKqQZzHk4iIiIhqBRNPIiIiIqoVTDyJiIiIqFYw8SQiIiKiWsHEk4iIiIhqBRNPIiIiIqoVTDyJiIiIqFYw8SQiIiKiWsHEk4iIiIhqBRNPIqJ6oqioCBMmTIC3tzfUajWaNWuGhQsX2rpbREQGClt3gIiIqse6deuwZcsWbNmyBS1atEBeXh7S0tJs3S0iIgOe8SQiqic6duyIoqIifPXVVzhx4gTuuusuPPjgg7buFhGRARNPIqJ6okuXLpg0aRLmzJkDLy8vPPHEE3j33Xdt3S0iIgNJCCFs3QkiIrpzDz30EKZMmYLBgwcDAEpKStC6dWt88sknuP/++23cOyIinvEkIqoXLl68iC1btqBLly6GMicnJ/To0QM//PCDDXtGRPQvJp5ERPVAZmYmAKCsrMyoXAiB7OxsW3SJiMgEE08ionrgrrvugiRJ+OOPPwxlZWVl2LNnD+666y4b9oyI6F+cTomIqB5o1KgRxo8fj5dffhmenp4ICAjAkiVLUFBQgMmTJ9u6e0REAHhzERFRvXH9+nXMnTsXX3/9Na5evYpu3brhnXfeQUhIiK27RkQEgIknEREREdUSjvEkIiIiolrBxJOIiIiIagUTTyIiIiKqFUw8iYiIiKhWMPEkIiIiolrBxJOIiIiIagUTTyIiIiKqFUw8iYiIiKhWMPEkIiIiolrBxJOIiIiIagUTTyIiIiKqFUw8iYiIiKhW/D/edtvX22fqQgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 680x400 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x400 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage XI summary (fast) ===\n",
      "s0: 2.0\n",
      "mu_base: [0, 1, 1, 2]\n",
      "K_terms: 21\n",
      "n_max: 187\n",
      "grid_points: 33\n",
      "logQ_range: [-4.0, 4.0, 0.5]\n",
      "uniform_shift: {'delta_min_residual': 1.0, 'min_residual': 9.3824599408067e-06}\n",
      "tilt: {'tau_min_residual': 0.0, 'min_residual': 8.535202871969262e-05}\n",
      "outputs: ['stageXI_uniform_shift_results.csv', 'stageXI_tilt_results.csv', 'fig_stageXI_uniform_shift_residual.png', 'fig_stageXI_tilt_residual.png']\n",
      "\n",
      "Wrote:\n",
      " - stageXI_uniform_shift_results.csv\n",
      " - stageXI_tilt_results.csv\n",
      " - fig_stageXI_uniform_shift_residual.png\n",
      " - fig_stageXI_tilt_residual.png\n",
      " - stageXI_summary.json\n"
     ]
    }
   ],
   "source": [
    "# === Stage XI (fast): Gamma-factor deformation & stability test with caching ===\n",
    "# Relies on Stage VIII Dirichlet coefficients (a_n). Safe for SageMath 10.7 kernel.\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- helpers (Sage-safe) ----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except Exception: return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "def py(x):\n",
    "    \"\"\"Coerce to JSON-serializable Python types.\"\"\"\n",
    "    import numbers\n",
    "    if isinstance(x, (str, bool)) or x is None: return x\n",
    "    if isinstance(x, numbers.Integral): return int(x)\n",
    "    if isinstance(x, numbers.Real):\n",
    "        # prefer int if integral\n",
    "        xi = int(x)\n",
    "        return int(xi) if float(xi) == float(x) else float(x)\n",
    "    if isinstance(x, complex):\n",
    "        return {\"re\": py(x.real), \"im\": py(x.imag)}\n",
    "    if isinstance(x, (list, tuple)): return [py(t) for t in x]\n",
    "    if isinstance(x, dict): return {str(k): py(v) for k,v in x.items()}\n",
    "    try: return float(x)\n",
    "    except Exception: return str(x)\n",
    "# ---------------- load inputs ----------------\n",
    "coeff_path   = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "summary_path = Path(\"final_summary.json\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "# Center s0: default 2.0, else read from summary\n",
    "s0 = mp.mpf('2.0')\n",
    "if summary_path.exists() and summary_path.stat().st_size > 0:\n",
    "    try:\n",
    "        with open(summary_path, \"r\") as f:\n",
    "            J = json.load(f)\n",
    "        if \"central_point_guess\" in J:\n",
    "            s0 = mpf_safe(J[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "# Read coefficients (auto-detect a_n column)\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]\n",
    "        break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "# Use at most K terms (tune for speed/accuracy)\n",
    "K = min(len(N_all), 4000)   # smaller than before to speed up\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "# ---------------- Dirichlet series with cosine smoothing ----------------\n",
    "mp.mp.dps = 80\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s_grid(s_list, N_cut=None):\n",
    "    \"\"\"Compute L(s) for a list of s once; return list in same order.\"\"\"\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    out = []\n",
    "    for s in s_list:\n",
    "        total = mp.mpf('0')\n",
    "        for nn_i, aa_i in zip(nn, aa):\n",
    "            x = mpf_safe(to_int(nn_i))/Ncut_mp\n",
    "            w = smooth_weight(x)\n",
    "            if w != mp.mpf('0'):\n",
    "                total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "        out.append(total)\n",
    "    return out\n",
    "# ---------------- Gamma model (Γ_R) and Lambda pieces ----------------\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor_list(s_list, mu_list):\n",
    "    \"\"\"Return [∏ Γ_R(s+μ_j)] for s in s_list.\"\"\"\n",
    "    g_list = []\n",
    "    for s in s_list:\n",
    "        g = mp.mpf('1')\n",
    "        for mu in mu_list:\n",
    "            g *= gamma_R(s + mpf_safe(mu))\n",
    "        g_list.append(g)\n",
    "    return g_list\n",
    "# ---------------- fitting utilities ----------------\n",
    "def best_scale(target, ref):\n",
    "    num = den = mp.mpf('0')\n",
    "    for t, r in zip(target, ref):\n",
    "        num += r.conjugate()*t\n",
    "        den += r.conjugate()*r\n",
    "    return (num/den) if den != 0 else mp.mpf('0')\n",
    "def l2_residual(target, model):\n",
    "    s = mp.mpf('0')\n",
    "    for t, m in zip(target, model):\n",
    "        d = t - m\n",
    "        s += d.real**2 + d.imag**2\n",
    "    return mp.sqrt(s)\n",
    "# ---------------- stage settings (reduced scans for speed) ----------------\n",
    "MU_BASE = [0, 1, 1, 2]\n",
    "# s-grid around s0 (fewer points -> faster)\n",
    "grid = [s0 + mp.mpf(j)/mp.mpf(40) for j in range(-16, 17)]  # 33 points, step 0.025\n",
    "grid_ref = [2*s0 - s for s in grid]\n",
    "# Conductor scan (coarser than before)\n",
    "logQ_min, logQ_max, logQ_step = -4.0, 4.0, 0.5\n",
    "logQ_grid = [logQ_min + j*logQ_step for j in range(int((logQ_max-logQ_min)/logQ_step)+1)]\n",
    "# ---------------- BIG SPEEDUP: precompute L(s) & L(2s0-s) once ----------------\n",
    "Ncut = to_int(n[-1])\n",
    "L_vals     = L_of_s_grid(grid,     Ncut)\n",
    "L_vals_ref = L_of_s_grid(grid_ref, Ncut)\n",
    "def fe_best_fit(mu_list):\n",
    "    \"\"\"Given mu_list, scan Q and pick best eps, c, residual. Uses precomputed L-values.\"\"\"\n",
    "    # gamma depends on mu; compute once per mu_list\n",
    "    G  = gamma_factor_list(grid,     mu_list)\n",
    "    GR = gamma_factor_list(grid_ref, mu_list)\n",
    "    best = {\"res\": mp.mpf('inf')}\n",
    "    for logQ in logQ_grid:\n",
    "        Q = mp.e**mp.mpf(logQ)\n",
    "        # Q^(s/2) lists\n",
    "        Qs  = [Q**(s/2) for s in grid]\n",
    "        QsR = [Q**(sr/2) for sr in grid_ref]\n",
    "        # Λ(s) and reflected model (no Dirichlet recomputation!)\n",
    "        Lam  = [Qs[i]*G[i]*L_vals[i]        for i in range(len(grid))]\n",
    "        LamR = [QsR[i]*GR[i]*L_vals_ref[i]  for i in range(len(grid))]\n",
    "        # Fit eps = ±1\n",
    "        c_plus   = best_scale(Lam, LamR)\n",
    "        res_plus = l2_residual(Lam, [c_plus*z for z in LamR])\n",
    "        LamR_neg  = [-z for z in LamR]\n",
    "        c_minus   = best_scale(Lam, LamR_neg)\n",
    "        res_minus = l2_residual(Lam, [c_minus*z for z in LamR_neg])\n",
    "        if res_plus <= res_minus:\n",
    "            eps, c_fit, res_fit = +1, c_plus, res_plus\n",
    "        else:\n",
    "            eps, c_fit, res_fit = -1, c_minus, res_minus\n",
    "        if res_fit < best[\"res\"]:\n",
    "            best = {\n",
    "                \"res\":   res_fit,\n",
    "                \"eps\":   eps,\n",
    "                \"c\":     c_fit,\n",
    "                \"logQ\":  logQ,\n",
    "                \"Q\":     Q,\n",
    "                \"mu\":    list(mu_list),\n",
    "            }\n",
    "    return best\n",
    "# ---------------- 1) Uniform shift μ_j → μ_j + δ ----------------\n",
    "delta_grid = [j/10 for j in range(-10, 11)]  # [-1.0, …, +1.0] step 0.1  (21 pts)\n",
    "uni_rows = []\n",
    "for d in delta_grid:\n",
    "    mu = [m + d for m in MU_BASE]\n",
    "    b = fe_best_fit(mu)\n",
    "    uni_rows.append({\n",
    "        \"delta\": float(d),\n",
    "        \"residual\": float(b[\"res\"]),\n",
    "        \"best_eps\": int(b[\"eps\"]),\n",
    "        \"best_logQ\": float(b[\"logQ\"]),\n",
    "        \"best_Q\": float(b[\"Q\"]),\n",
    "        \"best_c_real\": float(mp.re(b[\"c\"])),\n",
    "        \"best_c_imag\": float(mp.im(b[\"c\"]))\n",
    "    })\n",
    "df_uniform = pd.DataFrame(uni_rows)\n",
    "df_uniform.to_csv(\"stageXI_uniform_shift_results.csv\", index=False)\n",
    "# ---------------- 2) Tilt μ → [0, 1+τ, 1−τ, 2] ----------------\n",
    "tau_grid = [j/10 for j in range(-10, 11)]  # [-1.0, …, +1.0] (21 pts)\n",
    "tilt_rows = []\n",
    "for t in tau_grid:\n",
    "    mu = [0, 1 + t, 1 - t, 2]\n",
    "    b = fe_best_fit(mu)\n",
    "    tilt_rows.append({\n",
    "        \"tau\": float(t),\n",
    "        \"residual\": float(b[\"res\"]),\n",
    "        \"best_eps\": int(b[\"eps\"]),\n",
    "        \"best_logQ\": float(b[\"logQ\"]),\n",
    "        \"best_Q\": float(b[\"Q\"]),\n",
    "        \"best_c_real\": float(mp.re(b[\"c\"])),\n",
    "        \"best_c_imag\": float(mp.im(b[\"c\"]))\n",
    "    })\n",
    "df_tilt = pd.DataFrame(tilt_rows)\n",
    "df_tilt.to_csv(\"stageXI_tilt_results.csv\", index=False)\n",
    "# ---------------- plots ----------------\n",
    "plt.figure(figsize=(6.8,4.0))\n",
    "plt.plot(df_uniform[\"delta\"], df_uniform[\"residual\"], \"o-\")\n",
    "plt.axvline(0.0, ls=\":\", color=\"gray\")\n",
    "plt.grid(True)\n",
    "plt.title(\"Stage XI: residual vs uniform shift δ\")\n",
    "plt.xlabel(\"δ\"); plt.ylabel(\"best L2 residual\")\n",
    "plt.tight_layout(); plt.savefig(\"fig_stageXI_uniform_shift_residual.png\", dpi=160); plt.show()\n",
    "plt.figure(figsize=(6.8,4.0))\n",
    "plt.plot(df_tilt[\"tau\"], df_tilt[\"residual\"], \"o-\")\n",
    "plt.axvline(0.0, ls=\":\", color=\"gray\")\n",
    "plt.grid(True)\n",
    "plt.title(\"Stage XI: residual vs tilt τ  (μ = [0, 1+τ, 1−τ, 2])\")\n",
    "plt.xlabel(\"τ\"); plt.ylabel(\"best L2 residual\")\n",
    "plt.tight_layout(); plt.savefig(\"fig_stageXI_tilt_residual.png\", dpi=160); plt.show()\n",
    "# ---------------- summary (JSON-safe) ----------------\n",
    "summary = {\n",
    "    \"s0\": float(s0),\n",
    "    \"mu_base\": MU_BASE,\n",
    "    \"K_terms\": int(K),\n",
    "    \"n_max\": int(n[-1]),\n",
    "    \"grid_points\": int(len(grid)),\n",
    "    \"logQ_range\": [float(logQ_min), float(logQ_max), float(logQ_step)],\n",
    "    \"uniform_shift\": {\n",
    "        \"delta_min_residual\": float(df_uniform.loc[df_uniform[\"residual\"].idxmin(), \"delta\"]),\n",
    "        \"min_residual\": float(df_uniform[\"residual\"].min())\n",
    "    },\n",
    "    \"tilt\": {\n",
    "        \"tau_min_residual\": float(df_tilt.loc[df_tilt[\"residual\"].idxmin(), \"tau\"]),\n",
    "        \"min_residual\": float(df_tilt[\"residual\"].min())\n",
    "    },\n",
    "    \"outputs\": [\n",
    "        \"stageXI_uniform_shift_results.csv\",\n",
    "        \"stageXI_tilt_results.csv\",\n",
    "        \"fig_stageXI_uniform_shift_residual.png\",\n",
    "        \"fig_stageXI_tilt_residual.png\"\n",
    "    ]\n",
    "}\n",
    "with open(\"stageXI_summary.json\",\"w\") as f:\n",
    "    json.dump(py(summary), f, indent=2)\n",
    "print(\"=== Stage XI summary (fast) ===\")\n",
    "for k,v in summary.items():\n",
    "    if isinstance(v, (dict, list)):\n",
    "        print(f\"{k}: {v}\")\n",
    "    else:\n",
    "        print(f\"{k}: {v}\")\n",
    "print(\"\\nWrote:\")\n",
    "print(\" - stageXI_uniform_shift_results.csv\")\n",
    "print(\" - stageXI_tilt_results.csv\")\n",
    "print(\" - fig_stageXI_uniform_shift_residual.png\")\n",
    "print(\" - fig_stageXI_tilt_residual.png\")\n",
    "print(\" - stageXI_summary.json\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b7de9a",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x420 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x460 with 2 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage XII summary ===\n",
      "s0: 2.0\n",
      "mu (used): [1.0, 2.0, 2.0, 3.0]\n",
      "K_terms: 21   n_max: 187\n",
      "Q (used for plotting): ≈ 0.01831563888873418  (choice does not affect zero locations)\n",
      "threshold for minima: 1.000e-6\n",
      "candidate zero heights on Re s = s0 (t): []\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>t_candidate</th>\n    </tr>\n  </thead>\n  <tbody>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [t_candidate]\n",
       "Index: []"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Wrote:\n",
      " - fig_stageXII_line_scans.png\n",
      " - fig_stageXII_heatmap.png\n",
      " - stageXII_zeros_candidates.csv\n"
     ]
    }
   ],
   "source": [
    "# === Stage XII: zero scan near the critical line Re s = s0 (Sage-Integer proof) ===\n",
    "# Uses Stage VIII coefficients, adopts Stage XI uniform shift (≈+1) so mu=[1,2,2,3],\n",
    "# scans |Λ(s)| along Re s = s0 and neighbors, detects minima, and saves plots/CSV.\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- helpers (force plain Python types) ----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:\n",
    "        return mp.mpf(x)\n",
    "    except Exception:\n",
    "        return mp.mpf(str(to_float(x)))\n",
    "def head10(df):\n",
    "    \"\"\"Return the first 10 rows using only plain Python ints.\"\"\"\n",
    "    n = min(10, len(df))\n",
    "    return df.iloc[:n].copy()\n",
    "# ---------------- load inputs ----------------\n",
    "coeff_path   = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "summaryXI    = Path(\"stageXI_summary.json\")\n",
    "summaryX     = Path(\"stageX_summary.json\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "# central point guess\n",
    "s0 = mp.mpf('2.0')\n",
    "if summaryX.exists() and summaryX.stat().st_size > 0:\n",
    "    try:\n",
    "        JX = json.load(open(summaryX))\n",
    "        if \"s0\" in JX:\n",
    "            s0 = mpf_safe(JX[\"s0\"])\n",
    "        elif \"central_point_guess\" in JX:\n",
    "            s0 = mpf_safe(JX[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "# gamma-shifts: base [0,1,1,2], plus Stage XI's uniform delta ≈ 1 if available\n",
    "MU_BASE = [0, 1, 1, 2]\n",
    "delta_uniform = 1.0\n",
    "if summaryXI.exists() and summaryXI.stat().st_size > 0:\n",
    "    try:\n",
    "        JXI = json.load(open(summaryXI))\n",
    "        if \"uniform_shift\" in JXI and \"delta_min_residual\" in JXI[\"uniform_shift\"]:\n",
    "            delta_uniform = float(JXI[\"uniform_shift\"][\"delta_min_residual\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "MU = [m + delta_uniform for m in MU_BASE]     # typically [1,2,2,3]\n",
    "# a crude Q (choice doesn’t affect zero locations)\n",
    "Q_guess = mp.e**(-4)\n",
    "# ---------------- read coefficients ----------------\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "# limit terms for speed\n",
    "K = min(len(N_all), 8000)\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "# ---------------- L(s) with cosine smoothing ----------------\n",
    "mp.mp.dps = 100\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return total\n",
    "# ---------------- completed Lambda(s) ----------------\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------------- Scan setup ----------------\n",
    "Ncut   = to_int(n[-1])\n",
    "T_max  = 20.0          # height window\n",
    "dt     = 0.25          # resolution along t\n",
    "dx_list = [0.00, 0.05, -0.05]   # lines: critical + two neighbors\n",
    "t_vals = [(-T_max + j*dt) for j in range(int(2*T_max/dt) + 1)]\n",
    "# ---------------- Evaluate and plot line scans ----------------\n",
    "abs_lines = {}   # dx -> |Lambda(s0+dx + i t)|\n",
    "for dx in dx_list:\n",
    "    vals = []\n",
    "    for t in t_vals:\n",
    "        s = (s0 + mp.mpf(dx)) + 1j*mp.mpf(t)\n",
    "        vals.append(abs(Lambda_of_s(s, Q_guess, MU, Ncut)))\n",
    "    abs_lines[dx] = vals\n",
    "plt.figure(figsize=(7.2,4.2))\n",
    "for dx in dx_list:\n",
    "    lab = f\"|Λ(s0{'+%.2f'%dx if dx>=0 else '%.2f'%dx}+it)|\"\n",
    "    plt.plot(t_vals, [to_float(v) for v in abs_lines[dx]], label=lab)\n",
    "plt.axhline(0.0, color='orange', ls='--')\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"|Λ|\"); plt.title(\"Stage XII: |Λ(s)| along vertical lines near s0\")\n",
    "plt.grid(True); plt.legend(); plt.tight_layout()\n",
    "plt.savefig(\"fig_stageXII_line_scans.png\", dpi=150)\n",
    "plt.show()\n",
    "# ---------------- Detect candidate zeros on the critical line ----------------\n",
    "line0 = np.array([to_float(v) for v in abs_lines[0.0]])\n",
    "thresh = max(1e-6, 0.02*float(np.nanmedian(line0)))  # adaptive threshold\n",
    "cands  = []\n",
    "for j in range(1, len(t_vals)-1):\n",
    "    if line0[j] < line0[j-1] and line0[j] < line0[j+1] and line0[j] <= thresh:\n",
    "        cands.append(j)\n",
    "# refine with a tiny quadratic fit around j-1..j+1\n",
    "zeros_t = []\n",
    "for j in cands:\n",
    "    ts = np.array([t_vals[j-1], t_vals[j], t_vals[j+1]], dtype=float)\n",
    "    ys = np.array([line0[j-1], line0[j], line0[j+1]], dtype=float)\n",
    "    A = np.column_stack([ts**2, ts, np.ones_like(ts)])\n",
    "    try:\n",
    "        a2, b2, c2 = np.linalg.lstsq(A, ys, rcond=None)[0]\n",
    "        if a2 > 0:\n",
    "            t_star = -b2/(2*a2)\n",
    "            if ts.min() - 0.5*dt <= t_star <= ts.max() + 0.5*dt:\n",
    "                zeros_t.append(float(t_star))\n",
    "            else:\n",
    "                zeros_t.append(float(ts[1]))\n",
    "        else:\n",
    "            zeros_t.append(float(ts[1]))\n",
    "    except Exception:\n",
    "        zeros_t.append(float(ts[1]))\n",
    "zero_df = pd.DataFrame({\"t_candidate\": zeros_t})\n",
    "zero_df.to_csv(\"stageXII_zeros_candidates.csv\", index=False)\n",
    "# ---------------- Coarse heatmap (optional visual) ----------------\n",
    "dx_min, dx_max, dx_step = -0.08, 0.08, 0.01\n",
    "dt_heat = 0.20\n",
    "x_grid = [float(dx_min + k*dx_step) for k in range(int((dx_max-dx_min)/dx_step)+1)]\n",
    "t_grid = [float(-10 + j*dt_heat) for j in range(int(20/dt_heat)+1)]\n",
    "Z = np.zeros((len(t_grid), len(x_grid)))\n",
    "for ii, t in enumerate(t_grid):\n",
    "    for jj, dx in enumerate(x_grid):\n",
    "        s = (s0 + mp.mpf(dx)) + 1j*mp.mpf(t)\n",
    "        Z[ii,jj] = to_float(abs(Lambda_of_s(s, Q_guess, MU, Ncut)))\n",
    "plt.figure(figsize=(6.8,4.6))\n",
    "plt.imshow(Z, origin=\"lower\",\n",
    "           extent=[min(x_grid), max(x_grid), min(t_grid), max(t_grid)],\n",
    "           aspect=\"auto\")\n",
    "plt.colorbar(label=\"|Λ(s)|\")\n",
    "plt.axvline(0.0, color=\"w\", ls=\"--\", lw=1)\n",
    "plt.title(\"Stage XII: coarse heatmap of |Λ(s)| near Re s = s0\")\n",
    "plt.xlabel(\"Re(s) − s0\"); plt.ylabel(\"t\")\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"fig_stageXII_heatmap.png\", dpi=150)\n",
    "plt.show()\n",
    "# ---------------- Report ----------------\n",
    "print(\"=== Stage XII summary ===\")\n",
    "print(f\"s0: {float(s0)}\")\n",
    "print(f\"mu (used): {MU}\")\n",
    "print(f\"K_terms: {int(K)}   n_max: {int(n[-1])}\")\n",
    "print(f\"Q (used for plotting): ≈ {to_float(Q_guess)}  (choice does not affect zero locations)\")\n",
    "print(f\"threshold for minima: {thresh:.3e}\")\n",
    "print(f\"candidate zero heights on Re s = s0 (t): {zeros_t}\")\n",
    "# safe preview (pure Python ints)\n",
    "display(head10(zero_df))\n",
    "print(\"\\nWrote:\")\n",
    "print(\" - fig_stageXII_line_scans.png\")\n",
    "print(\" - fig_stageXII_heatmap.png\")\n",
    "print(\" - stageXII_zeros_candidates.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b7b2b1",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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1iva5UqlERkZGtc9t0qQJ/vGPf+jc9/vvv8PLywve3t46+3j48OHPfJaruvZ5/PhxCIKAGTNm6Ly2lZUVBg4cqH3tmzdvIjU1FVOnTtXZF+7u7ujTp0+15Th58iQ0Gg3++c9/VrleRkYG5s+fDzc3N+3nrLu7OwDofNZWVb8n98Vff/0FAOV+A1DRzFtPu3DhApRKZbnn9unTR1umJ/H8jajK77//jsGDB8PFxUVnX5SdFSj7+8L7fiLGizrtpMHr0aMH3nvvPRw8eBCpqalYvHgxkpKSuH6MeujQIbz66qtwdXXFrl27cOHCBURGRmLOnDlQKpXa9bKysmBmZlbuB3MtWrTQ+X9WVhYEQcAPP/wAc3NzndvIkSMBgOuDODc3F4GBgfDz88OGDRvw559/6owPlYKCggIcPHgQ48aNg729vfb+8ePHw87OTqe8JSUlAAArKyudbchkMpw+fRrDhw/H6tWr0b17dzRr1gwLFy6scOy6lZWVdls1kZOTox2K8DQXFxcAj/fdk5o2barzf0tLS526VOfUqVOIjIzE8ePH8corryAkJARvvfWW9vGyse0TJkwo11a+/PJLMMaQnZ1d6fY/+OADfP311wgPD8eIESPQtGlTDBkyBJcuXaq2bN7e3ly36n4gOn36dGzduhX37t3DK6+8gubNm8Pf31/bmQYe5/h0tsDjL1Iqlara1ygb8nLq1Cn8/fffUKvV+Mc//oGhQ4dqvxieOnUKffv2hbW1dbV1r8qz7POK2lZ6ejpiY2PL7V97e3swxp6pU1ZdWcval5+fX7nX379/v/a1y/bN08OXKrvvaY8ePQKAKme4EUURw4YNw6FDh/Duu+/i9OnTiIiI0B7AqCjf6upX9pn89Ho8Za5JnXn/RlQlPT0dv/32W7n9UPa7jLJ9wfN+IsaNZo8h5Anm5ub49NNPsWbNmirHypbZtWsXPD09sX//fp2jTE/PNd60aVMIgoDs7GydTsbT8243adJEe/S2siNPnp6e1ZbrrbfeQnZ2Nk6dOoVOnTrh8OHDWLJkCYYPHy6Z6d/27t2L4uJizJw5U+d+GxsbTJgwAXv37kVOTg6aNGmi/cNaUSfU3d1d28G/desWDhw4gM8++wwqlQo///yzzro5OTnaGVlqokmTJpDL5UhLSyv3WNm46NpstyrdunXTbvOFF17A8OHDsXHjRgQEBMDPz0/72A8//FDpDCFPfyl8kpmZGZYsWYIlS5YgNzcXp06dwocffojhw4cjJSWlyplLeKec3LZtW7XTpM6ePRuzZ89GUVERQkJC8Omnn2L06NG4desW3N3d0aVLF+zbtw8PHz7U6RBdvXoVAKq9fkCrVq3Qvn17nDp1Ch4eHujRowcaN26MIUOGYMGCBbh48SLCw8O5fy+iLxWdMXBycoK1tTW2bt1a4XPqus1VtO1ffvmlwqPHZcremxVdQ4DnugJlP/C9f/8+3NzcKlwnLi4OV65cQVBQkM7nxe3bt6vdfmXKPpOzsrJ0Ou48Za6uzk/OTc/7N6IqTk5O6Nq1K1asWFHh42UHDoDq30/EuFGnnTRYaWlpFR7dKjtl+eQHoaWlZYVHc2QyGSwsLHQ+jB8+fFhuZoCBAwdi9erV2L9/P9544w3t/U9fJMjGxgaDBw9GdHQ0unbtCgsLixrX6+jRo9i1axe++uordOrUCQCwceNGeHl5Ye7cuRXOcGAIW7ZsgYuLS4U//psxYwaCgoKwe/duvPnmm7CwsMBzzz2HO3fuVLnN9u3b4+OPP8avv/6Ky5cv6zyWmpoKpVJZq6n8bG1t4e/vj0OHDuHrr7/WHpEVRRG7du3Sdgz1RSaT4aeffkLnzp3x8ccf4/jx4+jbty8aN26M69ev480333ym7Tdu3BgTJkzAgwcPsGjRIiQlJVWZU2RkJNd2eb5glrG1tcWIESOgUqkwduxYXLt2De7u7nj55Zfx8ccfY/v27Xjvvfe06wcFBcHa2rrCH3M/bejQoThw4ADc3NwwatQoAI/bSuvWrfHJJ59ArVZX+iPUMjU9U1IXRo8ejZUrV6Jp06Y1yrIuDB8+HGZmZrhz547O9R6e1qFDBzg7O2Pv3r1YsmSJ9rPw3r17CAsL0/kcrciwYcOgUCiwfv169O7du8J1yrZZtg/KbNiwoSZV0jF48GCsXr0au3fvxsKFC7X379mzp9rn9urVC1ZWVti9e7dONmFhYbh3755Op533bwRQ+d+Z0aNHIzg4GG3atEGTJk246lfZ+4kYN+q0kwar7KjzmDFj0LFjR4iiiJiYGHzzzTews7PD22+/rV237Gjf/v378dxzz8HKygpdunTB6NGjcejQISxYsAATJkxASkoKvvjiCzg7OyMhIUH7/BdffBF9+/bFO++8g/z8fPj6+uLChQva2QOenNXlu+++Q79+/dC/f3+88cYb8PDwQEFBAW7fvo3ffvutyhkZMjMz8frrr6NPnz5YsmSJ9n5XV1esWbMGs2fPxpYtWxAQEPDM+S1btgzLli3D6dOnazyuPS4uDhEREXj33XcrnNFm0KBB2iPoZR3SQYMGlfvCERsbizfffBMTJ05Eu3btYGFhgTNnziA2Nhbvv/++zrplp9JrO8f5qlWr8MILL2Dw4MFYunQpLCwssG7dOsTFxWHv3r01nju+ptq1a4d58+Zh3bp1+Pvvv9GvXz/88MMPmDlzJrKzszFhwgQ0b94cjx49wpUrV/Do0SOsX7++0u2NGTMGXl5e6NGjB5o1a4Z79+5h7dq1cHd3R7t27aosS9n0k89q7ty5sLa2Rt++feHs7IyHDx9i1apVcHBwgJ+fH4DHM8AEBATg008/hUKhgJ+fH06cOIGNGzdi+fLlXHO0DxkyBOvWrUNmZibWrl2rc/+2bdvQpEkTnekeK2Jvbw93d3ccPXoUQ4YMgaOjI5ycnPR6xc9Fixbh119/xYABA7B48WJ07doVoigiOTkZJ06cwDvvvAN/f3+9vLaHhweWLVuGjz76CHfv3sWLL76IJk2aID09HREREbC1tcXnn38OuVyOL774AoGBgRg3bhzmzp2L3NxcfPbZZ1xDTTw8PPDhhx/iiy++QElJiXaaxuvXryMzMxOff/45OnbsiDZt2uD9998HYwyOjo747bffnmnYx7BhwzBgwAC8++67KCoqQo8ePXD+/Hns3Lmz2uc2adIES5cuxfLlyxEYGIiJEyciJSWlwjrz/o0AHv+dOXv2LH777Tc4OzvD3t4eHTp0wLJly3Dy5En06dMHCxcuRIcOHaBUKpGUlITg4GD8/PPPaNWqFdf7iRg5w/4OlhDD2b9/P5s6dSpr164ds7OzY+bm5qx169Zs+vTp7Pr16zrrJiUlsWHDhjF7e3sGQGdGhP/85z/Mw8ODWVpask6dOrFNmzZpZzB4UnZ2Nps9ezZr3Lgxs7GxYS+88AILDw+vcAaDxMRENmfOHObq6srMzc1Zs2bNWJ8+fdjy5currNPEiROZjY0Nu3XrVoWPjxw5kjVq1IglJyczxp5t9piy5/71119Vlomx8rPHLFq0iAFgcXFxlT7n448/ZgBYVFQUY4yx06dPMwAsIiJCu056ejqbNWsW69ixI7O1tWV2dnasa9eubM2aNUwQBJ3tTZ8+nXXp0qXc6/DOHsMYY6Ghoewf//gHs7W1ZdbW1qxXr17st99+q7CuT8/48ddff3HlVdE+ebK+dnZ2bPDgwdr7zp07x0aNGsUcHR2Zubk5c3V1ZaNGjWIHDx6s8nW++eYb1qdPH+bk5MQsLCxY69atWUBAAEtKSqomhbqzfft2NnjwYNaiRQtmYWHBXFxc2KuvvspiY2N11lOpVOzTTz9lrVu3ZhYWFqx9+/bs+++/536dnJwcJpfLma2tLVOpVNr7d+/ezQCw8ePHl3vO07PHMMbYqVOnmI+PD7O0tGQAtO2msn329Kwjlals5hfGGCssLGQff/wx69ChA7OwsGAODg6sS5cubPHixezhw4fVbgOVzITC2z6PHDnCBg8ezBo1asQsLS2Zu7s7mzBhAjt16pTOeps3b2bt2rXT7p+tW7eymTNnVjt7TJkdO3YwPz8/ZmVlxezs7JiPj4/O7EPXr19nL7zwArO3t2dNmjRhEydOZMnJyeXqV5N9kZuby+bMmaPzmXzjxo1qZ49h7PEMNqtWrWJubm7MwsKCde3alf32228VthvevxExMTGsb9++zMbGptwsNI8ePWILFy5knp6ezNzcnDk6OjJfX1/20UcfscLCQsYY//uJGC8ZY9VMpEsI0Zs9e/Zg2rRpOH/+PNdMC8aqbB7nZ/246dq1K/r27VvlEeSK5Ofnw8XFBWvWrNGZ1xh4fATfw8OjwrnhCSGEEKmg4TGE1JO9e/fiwYMH6NKlC+RyOcLDw/HVV19hwIABJt1hr0urV6/GuHHj8NFHH9XoB7Vr1qxB69aty11VkxBCCDEW1GknpJ7Y29tj3759WL58OYqKiuDs7IxZs2Zh+fLlhi6a0XjxxRfx1VdfITExsUad9kaNGiEoKAhmZvSRRwghxDjRXzBC6sno0aMxevRoQxfD6NVmphTeS8kTQgghUkVj2gkhhBBCCJE4uiIqIYQQQgghEkfDY/RAFEWkpqbC3t5e73M3E0IIIYQQ48UYQ0FBAVxcXCq8dkkZ6rTrQWpqaqWXYyaEEEIIIeRpKSkpVU6yQJ12PbC3twfwOPxGjRoZuDSEEEIIIUSq8vPz4ebmpu0/VoY67XpQNiSmUaNG9dZp12g0SEhIQLt27aBQKOrlNY0VZcWHcuJDOfGjrPhQTvwoKz6UEx9D51TdkGr6IaoJKSkpMXQRjAZlxYdy4kM58aOs+FBO/CgrPpQTHynnRFM+6kF+fj4cHByQl5dHw2MIIYQQQkilePuNdKTdRGg0GsTFxUGj0Ri6KJJHWfGhnPhQTvwoKz6UEz/Kig/lxEfqOdGYdkIIIYQQAxBFESqVSu+vo9FoIIoilEoljWmvgr5yMjc3r5Pt0fAYPaDhMYQQQgipikqlQmJiIkRRNHRRSD1o3LgxWrZsWeGPTXn7jXSk3URoNBrExsaia9eu9C26GpQVH8qJD+XEj7LiQznxM9asGGNIS0uDQqGAm5tblRfUqavXUyqVsLKyoos+VkEfOTHGUFxcjIyMDACAs7NzrbdFnXYTYm1tbegiGA3Kig/lxIdy4kdZ8aGc+BljVoIgoLi4GC4uLrCxsdH765UNqqBOe9X0lVNZG83IyEDz5s1r/QWThsfoAQ2PIYQQQkhllEolEhMT4eHhYZRfOkjNlZSUICkpCZ6enrCystJ5jGaPaWAEQUBkZCQEQTB0USSPsuJDOfGhnPhRVnwoJ37GnlV9HfVmjKGoqAh0nLZq+sypLvY1ddpNhEwmQ5MmTei0FwfKig/lxIdy4kdZ8aGc+FFW/IxpzL8hSTknGh6jBzQ8hhBCCCGVKRseU9FQCWKaqtrnNDymgREEAWFhYUZ7irA+UVZ8KCc+lFPVBI2Ik9fT8a+DV/CvgzGY+dNJfHgoFn/dyIAo0jGjilCb4kdZ8WGMobCw8JmHfZw9exYeHh61eq5KpULbtm1x/vz5ZyqDPs2aNQujR4+uMqerV6+iVatWKCoq0rk/KCgIgwYN0mv5qNNuIuRyOVxdXfU+bZQpoKz4UE58KKeK5Rar8P3pBPT98gzm7riEg1H3cTDqAc6lqLAnIgWzgyIx4rtQHI6+D0FD81Q/idoUP8qKn7m5uV63P2/ePMhkMuzbt6/Cxzdu3Ah3d3f07duXa3ulpaV466234OTkBFtbW7z00ku4f/9+XRa5nLVr12LLli3a/w8aNAiLFi3SWadLly7o2bMn1qxZo9eyVIRauYmQy+Vwd3enDy4OlBUfyokP5aSLMYZd4ffQ9z9n8O3JW1DIZFg0tB3+fm8wrnwyDLGfDUPIvwZj3oDncD+nGIv3X8Go7/9G2J1MQxddMqhN8aOs+MhkMlhaWupt7H9xcTH279+Pzp0763R6n/TDDz8gMDCQe5uLFi3C4cOHsW/fPvz9998oLCzE6NGjodFouLcxaNAgBAUFca/fuHFjtGjRotqcZs+ejfXr19eoLHWBWrmJEAQBISEhdIqQA2XFh3LiQzn9T26xCvN3ReHjI3FobGOBtZO8EfLuYCwa2h6tmtjA1kKGmIgLcHGwwIcjOyHs/SF4c3BbJGYVYeqmi1j223WUCvX7R1CKqE3xo6z4MMZQUFCgt9ljDh48CAsLC2zduhWnT59GUlKSzuOXL1/G7du3MWrUKO19KpUKb775JpydnWFlZQUPDw+sWrUKAJCXl4ctW7bgm2++wdChQ+Hj44Ndu3bh6tWrOHXqlF7qAOgOj5k1axbOnTuH7777DjKZDDKZTFuv4cOHIysrC+fOndNbWSpCF1cyEXK5HG3atKGjDRwoKz6UEx/K6bGLd7OwaH8M0vKUGN3VGSvHd0EjK93T8U9n5WBjjqXDO+DVHm5YfCAGW88n4sLdLHw/2RvtWtgbohqSQG2KnyllFbg9EveyivW2fcZYuSPI7k1tsHmm3zNve8uWLZgyZQr8/f3h5eWFbdu24fPPP9c+HhISgvbt2+v8yPL777/Hf//7Xxw4cACtW7dGSkoKUlJSAABRUVFQq9UYNmyYdn0XFxd4eXkhLCwMw4cPf+YyV6asLX333Xe4desWvLy8sGzZMgBAs2bNAAAWFhbo1q0bQkND8Y9//ENvZSlXtnp7JaJXNK6PH2XFh3Li09BzEjQivj15C1M2hSO3WI3VE7rihyk+5TrsQOVZtW5qg/3zemHR0Ha4+TAfo3/4G/sjk+urCpLT0NtUTVBW/PQ1NCYhIQGhoaGYOXMmAGDmzJnYtm0bRPF/v1VJSkqCi4uLzvOSk5PRrl079OvXD+7u7ujXrx+mTJkCAHj48CEsLCzQpEkTnee0aNECDx8+1Es9ysjlcshkMjg4OMDCwgI2NjZo2bIlWrZsqTMdpKura7kzCvpGR9pNRNkpwgEDBsDMjHZrVSgrPpQTn4ac0/2cYizaF4NL93LQ2bkRfpjqgzbN7Cpdv6qszBRyLBraHv3aOuHtfTF479eriEnJxWcvPQ9LM+nOm6wPDblN1ZQpZVUXR7wrUzY8xt7evs4771u2bEHnzp3h6+sLAJg2bRree+89nDp1SnukvKSkpNw0h7NmzcILL7yADh064MUXX8To0aN1jqxXVo+qyr9y5UqsXLlS+/+SkhKEh4fjzTff1N73xx9/oH///pVuQxCEal8HAKytrVFcrL8zIxWhr6YmQi6Xw8vLi442cKCs+FBOfBpqTudvZ2Lkd6G4dC8Hc/p64vA/+1TZYQf4surh4Yjf3+qH/u2csDciBZM3hiOjQFnXxZe0htqmaoOy4mdtbV3n29RoNNixY4f2KDsAtGzZEsOHD9f5QaqTkxNycnJ0ntu9e3ckJibiiy++QElJCV599VVMmDBBuw2VSlXuORkZGWjRokWl5Zk/fz5iYmK0tx49emDZsmXl7qsKb1vKzs7WDpepL9TKTYRcLkfz5s3pg4sDZcWHcuLTEHPaG5GMGVsjwABsndUDn4zpzHU0nDerJrYWCJrdE68PeA7RybkY++N5XE/Nr6PSS19DbFO1RVnxkclkMDc3r/Oj7MHBwUhPT8e0adN07p85cyaOHDmCrKwsAICPjw9u3LhR7oewjRo1wqRJk7Bp0ybs378fv/76K7Kzs+Hr6wtzc3OcPHlSu25aWhri4uLQp0+fSsvj6OiItm3bam/W1tZo3rx5ufuqUjY8Bng8dr2yGWLi4uLg4+NT5bbqGrVyE6FWq3H8+HGo1WpDF0XyKCs+lBOfhpSTKDKsCo7HB4euwqWxFQ690Qf/6Fj5Ua+n1SQrhVyGD0Z2wtcTuyGzUIWJP4fhzI30Zym+0WhIbepZUVZ8RFFEXl6ezjjzurBlyxYMHToUrq6uOve//PLLsLGxwa5duwAAgwcPRlFREa5du6ZdZ82aNdi3bx9u3LiBW7du4eDBg2jZsiUaN24MBwcHBAQE4J133sHp06cRHR2N1157DV26dMHQoUPrtA5PYoxBrVZrc/Lw8MDFixeRlJSEzMxM7f1JSUl48OCBXstSEeq0mwiFQgE/Pz+dH0mQilFWfCgnPg0lp2KVgAW7L2NDyF10b90Yhxf0rfEML7XJaoJvK+wK9IeFmRyB2y8h6HxiTYtudBpKm6oLlBUfmUwGW1vbOj3Snp6ejmPHjmHGjBnlHrO0tMSkSZO0Q2SaNm2K8ePHY/fu3dp17Ozs8OWXX6JHjx7w8/NDUlISgoODtWdN1qxZg7Fjx+LVV19F3759YWNjg99++02v+1omk8HMzEyb09KlS6FQKNC5c2c0a9YMycmPfyC/d+9eDBs2DO7u7norS4XlY/qatLMBy8/Ph4ODA/Ly8nSmNyKEEGOUnq/EnKBIXEvNx+iuzvh6YjdYmddvJykpswhzgiJxN7MIgf088eHITpDL9TMbBiH6plQqkZiYCE9Pz3I/0JSys2fPYtasWbWaNeXq1asYOnQobt++DXt7453StbS0FO3atcPevXt1ru4aFBSEoKAgnD17tsLnVbXPefuNdKTdRKjVahw7doxOEXKgrPhQTnxMPafkrGJM+DkM11LzsWhoO/wwxafWHfZnycrDyRa/vtEHPdybYPPfiVi4L9pkL8Rk6m2qLlFWfERRRG5ubp0Pj6mJLl26YPXq1fU+TWJN8OR07949fPTRRzod9vpi3PMjES0zMzP079/f6Ke8qg+UFR/KiY8p53TzYQGmb7mIzMJSfPlKF0zya/1M23vWrJrYWmBXoD8W7YvB77FpyClW4efXfGFfwZzwxsyU21Rdo6z4yGQyvUz3WFNPzjIjRTw5tW/fHu3bt6/HUv0PHWk3ETKZDI0aNTL4G9IYUFZ8KCc+pppTZFI2Jv4chpxiFX6Y0v2ZO+xA3WRlZa7AT9O647VerXH+dhYmbwzHo4LSZy6blJhqm9IHyoqPTCaDQqF45pw8PDywaNGiuimUBD1LTt7e3pg1a1bdF+oJDbrTnpKSgkGDBqFz587o2rUrDh48yPWYFKnVahw9epROEXKgrPhQTnxMMadT19Px2uaL0IgM22b1xKiuznWy3brKSiGX4YuXvbDkhfa4lpqPCT+H4V5WUZ2UUQpMsU3pC2XFp66Gx5h6p/1ZcqqPTnuD/iFqWloa0tPT4e3tjYyMDHTv3h03b96Era1tlY9VxxA/RGWMQalUwsrKio44VIOy4kM58TG1nA5cSsEHh66isbU5ts32Q9dWjets2/rIas/FZHx85Cqa2llix5ye6ORs/D/+N7U2pU/GmlXZjxI9PDz0ctGjpzHGtFf5NKac6ps+cyopKUFSUhL9ELW2nJ2d4e3tDQBo3rw5HB0dkZ2dXe1jUkVj+vhRVnwoJz6mkBNjDD+fu4N3f4lFy0ZWODi/d5122MvUdVZT/Vvjp6ndkVesxqsbLuBSkrQ/p3mZQpuqL8aYVdm0hSqVysAlIfWluLgYAGBuXvvf4Ei60x4SEoIxY8bAxcUFMpkMR44cKbfOunXrtN9afH19ERoaWqvXunTpEkRRhJubW40ekwpBEBAcHAxBEAxdFMmjrPhQTnxMISdRZFhxLB7/+eMGOra0x6EFffBcM7s6fx19ZTWiizO2zvKDRmR4bctFhCY8qtPt1zdTaFP1xVizMjMzg42NDR49eoTi4mIolUq93kpKSpCZmYmSkhK9v5Yx3/SRU0lJCbKyspCRkYHGjRs/0zzzkh4e88cff+D8+fPo3r07XnnlFRw+fBhjx47VPr5//35Mnz4d69atQ9++fbFhwwZs3rwZ169fR+vWj3805evri9LS8j9SOnHiBFxcXAAAWVlZ6N+/PzZv3lzu8rhVPVamtLRU5zXy8/Ph5uaG7OxsNGnSRHsJXIVCobMsCIL2Rw+CIEAul0Mul1e6rFaroVAotMtlFwAou7/sQ6vsW5wgCDA3NwdjTLssiiI0Go12WRRFmJmZVbqs0WjAGNMuV1QPfdWp7OiJIAg6y89aJ0EQIAgCLC0ttePWjL1O+thPZVeFs7CwgCAIJlEnfe0n4PGlr8vKa0x1glyBfx28giMxqfDzaIJN031hayHXy36Sy+UoLS2FmZmZ9r1Yl3WKScnFzK0RUKpF/DjVB4PbNzXKtvf0kI+G9n6qSZ3KPsPLhjMYU51KS0uRnJysLaNMJkNZl0wfy08qu79sCEhNlvVZxrpYlmqdHBwc4OLiAo1GU669FRYWGv/wmBEjRmD58uUYP358hY9/++23CAgIQGBgIDp16oS1a9fCzc0N69ev164TFRWFuLi4creyDntpaSnGjRuHDz74oFynvKrHnrRq1So4ODhob2VH5OPi4gAA8fHxiI+PBwDExsYiISEBABAdHY3ExMdX94uIiEBKSgoAICwsDGlpaQAen23IzMwEAJw5cwa5ubkAHn/pKCgoAAAEBwdDqVSitLQUf/zxBwRBgFKpRHBwMACgoKAAJ06cAADk5ubizJkzAIDMzEyEhIQAeDy+PywsDMDjH+FGREQAABITExEdHQ0ASEhIQGxsbL3W6cmjKHVVp6SkJMTExJhUnfSxn0JDQ5GRkWFSddLXfhIEwSjrdOS3YMzfGYUjMano4gjsDPCHWFqk1/0UExOjnae5ruvUsZkV5rdXwt7KDG/sisLKXcbb9k6ePNlg3081rZMgCEZZp8jISLRr1w5WVlbIy8uDp6cnFAoFioqK4OnpCeDx2HdPT0/twSZPT08olUoAgKenJ4qKiqBQKODp6Ym8vDxYWlrC09MTWVlZsLW1haenJzIyMtCoUSO4uLggNTUVjo6O8PT0RHJyMpo1awZPT08kJibC2dkZrVq1QmJiIlq1agVnZ2ftxYDKrgbq6ekJR0dHpKamwtPTEw4ODsjIyICnpydsbW2RlZUFT09PWFpa6r1ODg4O8PT0rNM6lf3GQB91KikpgUwmq7TtcWFGAgA7fPiw9v+lpaVMoVCwQ4cO6ay3cOFCNmDAAK5tiqLIJk+ezD799NMaPfY0pVLJ8vLytLeUlBQGgGVnZzPGGBMEgQmCUG5ZrVbrLGs0miqXVSqVzrIoitrl0tJSduTIEVZUVMREUWSiKDKVSqWtS9myRqPRWVar1VUuC4Kgs1xRPfRVpyfrUZd1KikpYUeOHGEqlcpk6qSP/VRcXKzNyVTqpI/9VJaTUqk0qjrll6jYpJ/PM/f3fmeL90Wz4hKl3veTSqViR44cYSUlJXrdTwnpBaznipPM4/3f2f6IZKNre2Wf56WlpQ3u/VTTOpV9npeUlJhMnfSxn5RKJTty5AgrLi42mTrpYz+VfUYVFxfXa53y8vIYAJaXl8eqIunhMU+SyWQ6w2NSU1Ph6uqK8+fP6xwFX7lyJbZv346bN29Wu82///4bAwYMQNeuXbX37dy5E126dKnyseoYYvYYQgjhlVuswqxtkY+Hk/R2x6djnodcblozSiRnFWPalnCkZJfgszGdMauvp6GLRAghFeLtNxrfT66f8vSUPOyJsUrV6devX6VzcVb1mBQxxlBQUCCJK55JHWXFh3LiY2w5PSooxfQtF3HjYQHeHNwW7wxrX2/lrs+sWje1wYHXe2Pa5ov47LfrKFZrsGBQW72+Zl0xtjZlSJQVH8qJj9RzkvSY9qo4OTlBoVDg4cOHOvdnZGSgRYsWBiqV4QiCgNDQUKP7Bb0hUFZ8KCc+xpRTam4JJm24gBsPC/D+iI5YOrxDvf5hqu+snB2ssX9eb3RsaY/Vf97E18dvVvijPKkxpjZlaJQVH8qJj9RzMtrhMQDg7+8PX19frFu3Tntf586d8fLLL2PVqlUGKOVjNDyGECI1KdnFmLIpHPdzSvDFy89jem8PQxep3uQWqzBzawSu3M/DnL6e+PfoTpI8ikYIaZhM4uJKhYWFiImJ0c70kZiYiJiYGCQnJwMAlixZgs2bN2Pr1q2Ij4/H4sWLkZycjPnz5xuw1IYhiiKys7ONakiPoVBWfCgnPsaQ051HhZj48wWk5pbgqwldDdZhN1RWjW0ssCvQHz09HLH1fCI+OHQVGlG6x6uMoU1JBWXFh3LiI/WcJN1pv3TpEnx8fODj4wPgcSfdx8cHn3zyCQBg0qRJWLt2LZYtWwZvb2+EhIQgODgY7u7uhiy2QWg0GkRGRmrneyWVo6z4UE58pJ7TzYcFmLQhHI8KS7F2sg8m9jDcReIMmZW9lTm2z+mJ/u2csC8yBUsOxEDQSPMPs9TblJRQVnwoJz5Sz8lohscYExoeQwiRgmupeXht80UUlgr4cWp3DH++paGLZHClggZv7onGyevpGNa5BX6Y6gNLs9pfoZAQQp6VSQyPIfxEUURGRoZkT+lICWXFh3LiI9Wcrt7Pw9RNF1FUqsHG6T0k0WGXQlaWZgqsm9YdL3VzwYnr6Zi7IwolKmkdVZNCTsaCsuJDOfGRek7UaTcRoigiLi5Osg1NSigrPpQTHynmdDk5B1M3h0Op1mDTzB4Y3LG5oYsEQDpZmSvkWDPJG5N6uCHk1iPM3BaBwlLpzBYhlZyMAWXFh3LiI/WcaHiMHtDwGEKIoUQkZmP2tgiIDNg8swf6tnUydJEkSxQZlv1+HUFhSejm1hg7ZveEg425oYtFCGlgaHhMAyOKIh48eCDZb4dSQlnxoZz4SCmn87czMXNrBAAgaLaf5DrsUsoKAORyGT4d0xn/HNwGV1JyMWVTOLKLVIYuluRykjLKig/lxEfqOVGn3USIoog7d+5ItqFJCWXFh3LiI5Wczt7MwOygSJgrZNgV6A//55oatDwVkUpWT5LJZPjX8I5454X2uJ6Wj8kbL+BRQalByyTFnKSKsuJDOfGRek40PEYPaHgMIaQ+/XUjA6/vjIKNpQK7Avzh5epg6CIZpQ3n7mDVHzfwnJMtds/1h7ODtaGLRAhpAGh4TAMjiiLu3bsn2W+HUkJZ8aGc+Bg6p9Px6Xh9ZxRsLRXYE9hL0h12Q2dVndcHtsFnYzrjbmYRJm8MR2puiUHKIfWcpISy4kM58ZF6TtRpNxFSH4clJZQVH8qJjyFz+u1KKl7fGQU7KzPsmdsLnV2kfWbPGNrUrL6eWDmuC+5lFWPyxnA8MEDH3RhykgrKig/lxEfqOdHwGD2g4TGEEH07cCkF7/0ai+b2ltgd6I+2ze0NXSSTsi8iGR8cvgrXxtbYE9gLrZvaGLpIhBATRcNjGhiNRoPbt29L9tK7UkJZ8aGc+Bgip0OX7+O9X2Ph2tgaB1/vYzQddmNqU5N7tsbqV7oiNbcEEzeE4XZGQb29tjHlZGiUFR/KiY/Uc6JOu4lgjCEnJwd04qR6lBUfyolPfef025VULD14Bc6NrLBvnnEdATa2NjWxhxu+m+yDrEIVJm+8iNsZhfXyusaWkyFRVnwoJz5Sz4mGx+gBDY8hhOjDwf8fEuNkZ4kDr/eGh5OtoYvUIPwZl4Z/7olGU1sL7JvXC881szN0kQghJoSGxzQwGo0GN27ckOwpHSmhrPhQTnzqK6c9F5Pxr19i4exgjYPzjbPDbqxt6kUvZ/wwxQdZRSpM3hiOhHT9DpUx1pwMgbLiQznxkXpO1Gk3ISUlhpmezBhRVnwoJz76zmlX+D18ePgq3Jva4MD83nBvanwd9jLG2qZGdnHGj1N8kF2kwqSN4YhPy9fr6xlrToZAWfGhnPhIOScaHqMHNDyGEFJXdoXfw8dH4uDpZIs9dMEfgzsdn443dl2GnZUZdgf6o5MzfcYTQp4NDY9pYDQaDeLi4iR7SkdKKCs+lBMffeb0ZId979xeRt9hN4U2NaRTC/w8vTsKlQKmbb6olyPuppBTfaGs+FBOfKSeE3XaCSFEgnZeSMLHR+Lg0dQGe+f2QksHK0MXify/f3TU7bjffFh/00ESQhouGh6jBzQ8hhDyLLaHJeHT/17Dc0622EMddsk6HZ+O+bui4GBtjr1ze6FdC+OYL58QIi00PKaB0Wg0iI6OluwpHSmhrPhQTnzqOqfNoXcfd9ib2WLvPNPqsJtamxrSqQXWTfNFbrEak+vwx6mmlpM+UVZ8KCc+Us+JOu0mxNrauMe71ifKig/lxKeuctpw7g6WH4tHu+Z22DevF1o0Mp0OexlTa1MvdG6Bn1/zRYFSwJRN4Yh7kFcn2zW1nPSJsuJDOfGRck40PEYPaHgMIaSmNofexfJj8ejY0h67Av3hZGdp6CKRGjh7MwPzdkbB2lyB3YH+8HJ1MHSRCCFGgobHNDCCICAyMhKCIBi6KJJHWfGhnPjURU5lHfb2Leyw24Q77KbcpgZ1aI5NM3qgRK3BtM0XcT219kNlTDmnukZZ8aGc+Eg9pwbdaTczM4O3tze8vb0RGBhY7vHi4mK4u7tj6dKlBihdzchkMjRp0gQymczQRZE8yooP5cTnWXNad/a2dkjM7sBeaGqiHXbA9NvUwPbNHnfcVRpM2xyOGw9r13E39ZzqEmXFh3LiI/WcGvTwGCcnJ2RmZlb6+EcffYSEhAS0bt0aX3/9Nfd2aXgMIYTHD6cT8M3JW+jY0h67A/1NusPekPx1IwPzdl6CnaUZdgbQUBlCSNVoeMwzSkhIwI0bNzBy5EhDF4WLIAgICwuT7CkdKaGs+FBOfGqb06aQu/jm5C0879IIe+ea9hH2Mg2lTQ3u2Bwbp/dAkUqDKZvCEZ2cU6PnN5Sc6gJlxYdy4iP1nCTbaQ8JCcGYMWPg4uICmUyGI0eOlFtn3bp18PT0hJWVFXx9fREaGlqj18jPz4evry/69euHc+fO6Ty2dOlSrFq16lmqUK/kcjlcXV0hl0t2l0oGZcWHcuJTm5y2hyVhRfDjMew7A/zRxNZCjyWUjobUpgZ3bI6gWX4QNAwztkQg9n4u93MbUk7PirLiQznxkXpO0iwVgKKiInTr1g0//vhjhY/v378fixYtwkcffYTo6Gj0798fI0aMQHJysnYdX19feHl5lbulpqYCAJKSkhAVFYWff/4ZM2bMQH7+4/GHR48eRfv27dG+fXuuspaWliI/P1/nBkA7z6dGo6lwWRAEnWVRFKtcVqvVOstlI5vUajVkMhlat24NjUYDxhgYY1Cr1QCgsyyKos5y2bfJypY1Go3Ocn3W6cl61GWdGGPaN6Wp1Ekf+0kURbi5uUEul5tMnfSxnzQaDdzd3bXbr65O6/9K0F44afusHnC0tZBcnfS1n8r+IJaVyxTqVNV+6unRGJtn+EKlEfHa5ou4ej+Hq04ymUx7wEpqdZLafhJFEe7u7mCMmUyd9LGfAMDd3V2bmSnUSR/7SS6Xw83NTefvYH3ViYdkO+0jRozA8uXLMX78+Aof//bbbxEQEIDAwEB06tQJa9euhZubG9avX69dJyoqCnFxceVuLi4uAKD918vLC507d8atW7cAAOHh4di3bx88PDywdOlSbNq0CcuWLau0rKtWrYKDg4P25ubmBgCIi4sDAMTHxyM+Ph4AEBsbi4SEBABAdHQ0EhMTAQARERFISUkBAISFhSEtLQ3A4zMOZePuz5w5g9zcXADAiRMnUFDw+NLZwcHBKCwsREhICIKDgyEIApRKJYKDgwEABQUFOHHiBAAgNzcXZ86cAQBkZmYiJCQEAJCWloawsDAAQEpKCiIiIgAAiYmJiI6OBvB4yFBsbGy91UmpVEIQhDqv0507d3DixAkIgmAyddLHfjp37hz++usvCIJgMnXS134KCQlBenp6tXVacfgSvjx+Cx1a2GPFECc8TLol2TrpYz8JgoATJ07gzp07JlOn6vaTh40Km2f2QLFKwLTNF3H1fl61dSqrx5PLUqqTlPZTVFQUQkJCcPPmTZOpkz72U9nnkynVSR/7SRAE/PXXX9rRF/VZJx5G8UNUmUyGw4cPY+zYsQAAlUoFGxsbHDx4EOPGjdOu9/bbbyMmJqbcUJeK5OTkwMbGBpaWlrh//z769u2L6OhoODo66qwXFBSEuLi4Kn+IWlpaitLSUu3/8/Pz4ebmhuzsbDRp0kT77UqhUOgsC4IAmUymXZbL5ZDL5ZUuq9VqKBQK7bKZmRlkMpn222FaWhqaNWsGC4vHp9oFQYC5uTkYY9rlsiODZcuiKMLMzKzS5bIj92XLFdVDX3UyMzPT1uPJ5Wetk1qtRlpaGlq1aqX9Rm7sddLHflKpVMjIyICLiws0Go1J1Ekf+0kQBDx69AgtWrQAgErrtD08BV/8fh2dWtpj99xecLBSSLZO+tpPMpkM9+/fh7OzM8zNzU2iTrz76Uz8Q7yxOxoWZnJsm+mL7u6OldZJFEU8ePBAe0ZQqnWSwn7SaDR49OgRmjdvDrlcbhJ10sd+AoD09HQ0a9YMZmZmJlEnfewnhUKB1NRUNG/eHBYWFvVWp8LCQq4fohplpz01NRWurq44f/48+vTpo11v5cqV2L59O27evFntNsPCwvD6669DLpdDJpPhs88+027/STyd9qfR7DGEkCftCr+Hj4/EoW1zO+yf1zB+dErKC7udiTnbI2GhkGPvvF543oVmlSGENJDZY56eR7NsLCCPPn364OrVq7hy5QpiYmIq7LADwKxZs2rUYTeUsiEMZd+oSeUoKz6UE5/qctr5/x12j6Y22BXQsKd1bOhtqk9bJ2ye4Qel8HiM+82HBRWu19BzqgnKig/lxEfqORllp93JyQkKhQIPHz7UuT8jI0N7irqhkcvl8PLykuwvnqWEsuJDOfGpKqfdF+/h3//fYd83rzdaOlgZoITSQW0K6NfOCRte80VhqYCpm8Ir7LhTTvwoKz6UEx+p5yTNUlXDwsICvr6+OHnypM79J0+e1Bku05DI5XLtmD5SNcqKD+XEp7Kc9kYk46PDcXCnDrsWtanHBndsjvXTfJGvVFfYcaec+FFWfCgnPlLPSZqlAlBYWIiYmBjExMQAePxL3ZiYGO2UjkuWLMHmzZuxdetWxMfHY/HixUhOTsb8+fMNWGrDUavVOH78uHb6IlI5yooP5cSnopwORKbgg0NX0drRBnvn9qIO+/+jNvU/Qzu30Om430r/X8edcuJHWfGhnPhIPSfJ/hD17NmzGDx4cLn7Z86ciaCgIACPL660evVqpKWlwcvLC2vWrMGAAQPquaTlGeKHqKIoIjc3F40bN5bsN0SpoKz4UE58ns7pl6j7+NcvV9CqiTX2zesN18bWhi6iZFCbKu/k9XQs2B2FRlbm2DevF9q1sKecaoCy4kM58TFUTrz9Rsl22o0ZzR5DSMN06PJ9vHPwClwcrLH/9V5o1cTG0EUiRuDk9XS8sSsKTWwtcOD13vB0sjV0kQgh9ahBzB5D/ketVuPYsWOSPaUjJZQVH8qJT1lOv1xK1nbY982jDntFqE1V7IXOLfDDFB9kF6kwdVM4bj/Mo5w4UZviQznxkXpOdKRdDwxxpJ0xhoKCAtjb23NPe9lQUVZ8KCc+jDHsD7+DD/97Ey0aWWH/vN5o3ZQ67BWhNlW1ozEPsHh/DJrbW2HTVC94uTennKpBbYoP5cTHUDnRkfYGRiaToVGjRvRm5EBZ8aGc+Pwem4YP/3sTze2tsG9eL+qwV4HaVNVe9nbFd5N98KiwFIF7ruJeVrGhiyR51Kb4UE58pJ4TddpNhFqtxtGjRyV7SkdKKCs+lFP1jsWmYdH+GNibMeyc4wv3pjQWuSrUpqo3ppsLvpnQBRn5SkzeeAH3sooMXSRJozbFh3LiI/WcaHiMHhhqeIxSqYSVlZVkvyFKBWXFh3Kq2p9xafjnnmg0tbVA0AxvdGrVlHKqBrUpPowx/BKZhPcOX0fLRlbYO68XfSGsBLUpPpQTH0PlRMNjGiAzMzNDF8FoUFZ8KKeKHb/2EG/uiUYTGwvsCfRHu5YOhi6S0aA2xWesTyt8PbEbHuYrMXljOB1xrwK1KT6UEx8p50SddhMhCAKCg4MhCIKhiyJ5lBUfyqliJ6+n4809l9HYxhz75vnD3dGKcuJEbYpPWU5jurTAt696I/3/O+5JmdRxfxq1KT6UEx+p50TDY/TAUMNjBEGAmZkZnfqqBmXFh3Iq73R8OubvenwhnL3zeqF9C3vKqQYoKz5P51Q2q0zLRlbY/3pvuDnSj53LUJviQznxMVRONDymAZLqN0Mpoqz4UE7/89eNDLyx6zLsrcyxe64/2rew1z5GOfGjrPg8mdPL3q749lVvpP3/Eff7OTSrzJOoTfGhnPhIOSfqtJsIQRBw4sQJSTc2qaCs+FBO/3Pu1iO8visKtpYK7A70R8eW/zsSQjnxo6z4VJTTWB9XfDWhG1LzSjB100Wk5pYYsITSQW2KD+XER+o50fAYPTDE8BhCiH6E3HqEwB2XYGPxuMP+vAv96JQYzv7IZLz361V4NLXBvnm90dLBytBFIoQ8Ixoe08AwxpCfnw/6DlY9yooP5QT8nZCJuTsuwdpcgV0BFXfYKSd+lBWfqnKa5Ncay8d6ISmrGFM3hSOjQGmAEkoHtSk+lBMfqedEnXYTIQgCQkNDJXtKR0ooKz4NPaew25kI3BEJSzM5dgX4w8u14iPsDT2nmqCs+FSX02u93PH5S8/jbmYRpm66iMzC0nouoXRQm+JDOfGRek40PEYPaHgMIcYt/G4WZm2LgLnicYe9m1tjQxeJkHK2/J2IL36/jg4t7LF3Xi842loYukiEkFqg4TENjCiKyM7OhiiKhi6K5FFWfBpqThfvZmH2tkiYy+XYMadntR32hppTbVBWfHhzCujniQ9GdMTN9AJM23wRucWqeiqhdFCb4kM58ZF6TtRpNxEajQaRkZHQaDSGLorkUVZ8GmJOkUnZmB0UCYVchu0BPeHTukm1z2mIOdUWZcWnJjm9PrAN/jW8A+LT8vHalovIK1bXQwmlg9oUH8qJj9RzouExekDDYwgxPlH3sjFjSwQAYEdAT/i6Oxq4RITwW3vqFtaeSkC3Vg7YGeiPRlbmhi4SIYQTDY9pYERRREZGhmRP6UgJZcWnIeV0OTkHM7dGggEImlOzDntDyulZUVZ8apPT20Pa4c3BbXHlfh5mbo1AgbJhHHGnNsWHcuIj9Zyo024iRFFEXFycZBualFBWfBpKTjEpuZi5JQIakWHbLD/4edTsCHtDyakuUFZ8apOTTCbDO8PaY/7ANohOzsXsbZEoLJXmDBh1idoUH8qJj9RzouExekDDYwgxDrH3czFt80WoNSK2zeqJ3m2aGrpIhDwTxhhWBsdjU2gi/DyaIGh2T9hamhm6WISQKtDwmAZGFEU8ePBAst8OpYSy4mPqOcU9yMNrmy9CJYjYOtOv1h12U8+pLlFWfJ4lJ5lMhg9HdkJAP09EJuVg9rZIFKtM94g7tSk+lBMfqedEnXYTIYoi7ty5I9mGJiWUFR9Tzul6aj6mbb6IUkHElpl+6NPWqdbbMuWc6hplxedZc5LJZPh4VCfM7uuBiKRsBARdQolKmrNhPCtqU3woJz5Sz4mGx+gBDY8hRLoS0gswaWM4CpUCNs/sgQHtmxm6SIToBWMMn/73GnZcuIf+7ZywaUYPWJkrDF0sQshTaHgMhzVr1uD5559H586dsXDhQjz5/SUxMRGDBw9G586d0aVLFxQVFRmwpNUTRRH37t2T7LdDKaGs+JhiTomZRZi2+SLyS9RYN617nXTYTTEnfaGs+NRVTjKZDJ+NeR5TerZGaEIm5u+KQqlgWkfcqU3xoZz4SD2nBttpf/ToEX788UdERUXh6tWriIqKQnh4uPbxWbNmYdmyZbh+/TrOnTsHS0tLA5a2elIfhyUllBUfU8spKbMIUzaGI6tIhe+n+GBo5xZ1sl1Ty0mfKCs+dZmTXC7DirFemOjbCmdvPsI/d1+GSjCd/KlN8aGc+Eg9pwY7PObRo0fo0aMHrly5AisrKwwYMAB79+5FmzZtcO3aNbz99ts4depUrbZNw2MIkZbkrGJM2ngB6flKrJ3sg5e6uRi6SITUK43IsPTgFRyOfoAXn2+JH6b6wFzRYI/bESIpRj88JiQkBGPGjIGLiwtkMhmOHDlSbp1169bB09MTVlZW8PX1RWhoKPf2mzVrhqVLl6J169ZwcXHB0KFD0aZNGwBAQkIC7Ozs8NJLL6F79+5YuXJlXVVLbzQaDW7fvi3ZS+9KCWXFx1RySskuxpRN4UjPV+LbV73rvMNuKjnVB8qKjz5yUshl+GpCV4zp5oI/rz3E4v0xEDTSPJpYE9Sm+FBOfKSek2Q77UVFRejWrRt+/PHHCh/fv38/Fi1ahI8++gjR0dHo378/RowYgeTkZO06vr6+8PLyKndLTU1FTk4Ofv/9dyQlJeHBgwcICwtDSEgIAECtViM0NBQ//fQTLly4gJMnT+LkyZOVlrW0tBT5+fk6NwDana7RaCpcFgRBZ7nsdExly2q1Wme57CRJ2f3Z2dlQqVRgjIExBrX68RXxnlwWRVFnWRCEKpc1Go3Ocn3W6cl61GWdBEFAVlYWGGMmUyd97Ce1Wo3s7GxtuYyxTvdzijFlYzhS80rw9cRuGN2lhV72U05Ojk55G9L7qSZ1YowhKytL571o7HXSx34SRRFZWVkQRbFO6wQm4ttXu+HF51vg99g0LD14BSq1YPRtLycnR6e8DeX9VJM6aTQa5OTkmFSd9LGfGGPIzs6utn76qBMPyXbaR4wYgeXLl2P8+PEVPv7tt98iICAAgYGB6NSpE9auXQs3NzesX79eu05UVBTi4uLK3VxcXHDq1Cm0bdsWjo6OsLa2xqhRo7Rj2lu1agU/Pz+4ubnB0tISI0eORExMTKVlXbVqFRwcHLQ3Nzc3AEBcXBwAID4+HvHx8QCA2NhYJCQkAACio6ORmJgIAIiIiEBKSgoAICwsDGlpaQAen3HIzMwEAJw5cwa5ubkAgBMnTqCgoAAAEBwcDEEQ4OPjgxMnTkAQBCiVSgQHBwMACgoKcOLECQBAbm4uzpw5AwDIzMzUflFJS0tDWFgYACAlJQUREREAHv8gNzo6GsDjMxCxsbH1VielUglBELT1q6s6paSkQC6Xw8zMzGTqpI/9FBYWBg8PD5iZmRllnaLi72Dqpot4kFuCD4a4YXz3VnrZT+fOnYOfnx9yc3Mb5PupJnUyMzODXC7X1sMU6qSP/QQADx8+BIA6r5O5Qo5/dreFn4sVjsSkYsG2v3Ht+nW910lf+yk2NhZ+fn7a5frcT8bU9nJzc+Hn54dz586ZTJ30sZ/MzMzg4eGhrUd91okLMwIA2OHDh7X/Ly0tZQqFgh06dEhnvYULF7IBAwZwbfPChQvM29ublZSUMEEQ2MiRI9mRI0cYY4yp1Wrm7e3NsrOzmUajYaNHj2a//fZbpdtSKpUsLy9Pe0tJSWEAWHZ2NmOMMUEQmCAI5ZbVarXOskajqXJZpVLpLIuiqF1Wq9Xs+vXrrKSkhImiyERRZCqVijHGdJY1Go3OslqtrnJZEASd5Yrqoa86PVmPuqxTaWkpu3btmrbcplAnfewnpVLJrl+/zgRBMLo63XuUzwZ8eYa5v/c7230hUa/7SalUsvj4eO37sL73kzG1PUEQ2LVr11hpaanJ1Ekf+0mtVrO4uDimVqv1VqcipYrN2nqRub/3O3vvlxgmiqJRtr3S0lIWHx/PSktLG9z7qSZ1UqlULD4+nimVSpOpkz72kyAI7Pr160ypVNZrnfLy8hgAlpeXx6pilNc2zszMhEajQYsWurM/tGjRQnt0ojq9evXCyJEj4ePjA7lcjiFDhuCll14CAJiZmWHlypUYMGAAGGMYNmwYRo8eXem2LC0tK5xdRqFQ6Pz79LKZmVmNls3NzStd1mg0UCqVMDc3h0wm01lHJpNpl+VyOeRyOfdyZWWvjzpVtfysdSotLTW5OlVXj9rUqeyonzHVKS2vBNO3XcK97GKsGt8FU3q2rrB+dVUnMzMzlJSUQC6Xa8vT0N5PvHXSaDQoLS3V/t8U6sRbj5rUSSaTQaVSQSaT6dSjLutko1Bg/Wu+mLvjEvZF3oelmQKfvfS89u+HMbW9kpISKBSKev2bq+868S7z1kmj0aCkpER7tssU6sRb9prUqawvVbb9+qwTD6OYPUYmk+Hw4cMYO3YsACA1NRWurq4ICwtD7969teutWLECO3fuxI0bNwxU0sdo9hhCDCM9X4lXN1zAvazyHXZCSHklKg3mBEXiwt0szOjtjs+f6LgTQuqH0c8eUxUnJycoFIpyR9UzMjLKHX1vKDQaDeLi4iT7i2cpoaz4GFtOecVqzNgSgXtZxVgxzqveOuzGlpMhUVZ86jMnawsFtszqgd7PNcWOC/fw8ZE4GMGxPC1qU3woJz5Sz8koO+0WFhbw9fUtN6PLyZMn0adPHwOVihBiKPlKNWYFReBmegHeH9ER0/zdDV0kQoyGjYUZts7yQ7+2Tth9MRkrjsUbVcedkIZCssNjCgsLcfv2bQCAj48Pvv32WwwePBiOjo5o3bo19u/fj+nTp+Pnn39G7969sXHjRmzatAnXrl2Du7th/2DT8BhC6k9usQoztkYg9n4eFgxqg3df7GjoIhFilIpVAmZujUBkUg4WDmmHJS+0N3SRCGkQjH54zKVLl+Dj4wMfHx8AwJIlS+Dj44NPPvkEADBp0iSsXbsWy5Ytg7e3N0JCQhAcHGzwDruhaDQaREdHS/aUjpRQVnyMIad8pRqvbbmI2Pt5eHtIO/xreId6L4Mx5CQVlBUfQ+VUdsS9aysHfH86AV8dvyH5I+7UpvhQTnyknpNkZ48ZNGhQtR8WCxYswIIFC+qpRNJnbW1t6CIYDcqKj5RzKlYJmLMtEnEP8rFoaDssGmq4o4JSzklqKCs+hsrJ3socO+f4Y+a2CPz01x2IDHh3eAdJ/ziV2hQfyomPlHOS7PAYY0bDYwjRrydnvJg34Dl8MKKjpDsVhBibwlIB07dcRHRyLt55oT3eGtLO0EUixGQZ/fAYUjOCICAyMlJ7WV1SOcqKj1RzUqo1mLfzEi7czcLM3u4G77BLNScpoqz4SCEnO0szBM3uieddGuGbk7ewKeSuwcpSFSlkZQwoJz5Sz6nWnXa1Wo2UlBTcvHkT2dnZdVkmUgsymQxNmjSho40cKCs+UsypVNDgjV1RCE3IxJSerfHpGMPPKS3FnKSKsuIjlZwcrM2xM8Af7ZrbYUVwPHaG3zNoeSoilaykjnLiI/WcajQ8prCwELt378bevXsRERGhvaokALRq1QrDhg3DvHnz4Ofnp5fCGgsaHkNI3VNrRPxz92WcuJ6OCb6tsPqVrpDLpfnBSogpyfj/i5YlZRXj64ndMMG3laGLRIhJqfPhMWvWrIGHhwc2bdqEf/zjHzh06BBiYmJw8+ZNXLhwAZ9++ikEQcALL7yAF198EQkJCXVSEcJHEASEhYVJ9pSOlFBWfKSUk1ojYuHeaJy4no6x3i74UkIddinlJHWUFR+p5dS8kRV2z+0F18bWePeXKzga88DQRdKSWlZSRTnxkXpO3LPHhIWF4a+//kKXLl0qfLxnz56YM2cOfv75Z2zZsgXnzp1Du3b0w5X6IpfL4erqCrmcfqZQHcqKj1RyKuuw/xH3EKO7OuPrid2gkEiHHZBOTsaAsuIjxZxcG1tjz1x/TN4YjsX7YwAAL3u7GrZQkGZWUkQ58ZF6TjR7jB7Q8BhC6oYoMiw5EIMjMakY3dUZayd5w0whzQ9TQhqCpMwiTN4YjowCJb6b7IMx3VwMXSRCjF69zB5z+/ZtHD9+HCUlJQAg+YswmDJBEBASEiLZUzpSQlnxMXROjDF88t84HIlJxQudW0i2w27onIwJZcVHyjl5ONli77xeaGZviUX7Y3D82kODlkfKWUkJ5cRH6jnV6i9gVlYWhg4divbt22PkyJFIS0sDAAQGBuKdd96p0wISPnK5HG3atJHsKR0poaz4GDInUWT499E47ApPRp82TfHDFB9JdtgBak81QVnxkXpOnk622DO3F5rYmOOtPdE4d+uRwcoi9aykgnLiI/WcalWqxYsXw8zMDMnJybCxsdHeP2nSJPz55591VjjCT+rjsKSEsuJjqJwYY/jst2vYFZ6Mvm2bYstMP1iZK+q1DDVB7YkfZcXHGHJq08wOOwP8YW2hwLwdl3D2ZoZBymEMWUkB5cRH6jnVqlQnTpzAl19+iVatdKd9ateuHe7dk948rg2BIAg4c+aMZE/pSAllxccQOTHG8J8/bmDHhXvo0+Zxh93aQroddoDaU01QVnyMJadOzo2wO7Cs4x6FvwzQcTeWrAyNcuIj9Zxq1WkvKirSOcJeJjMzE5aWls9cKFJzcrkcXl5ekv12KCWUFR9D5LTmVAI2hNyFr3sTbJrRQ9JH2MtQe+JHWfExppy8XB2wd24v2FoqMH9nFMJuZ9br6xtTVoZEOfGRek61KtWAAQOwY8cO7f9lMhlEUcRXX32FwYMH11nhCD+5XI7mzZtLtqFJCWXFp75zWnPyFr4/nYCurRywdZYfbC25Z6Q1KGpP/CgrPsaWUyfnRtgZ4A8LMzkCtl/CpaT6u0q6sWVlKJQTH6nnVKtSffXVV9iwYQNGjBgBlUqFd999F15eXggJCcGXX35Z12UkHNRqNY4fPw61Wm3ookgeZcWnPnP6/nQCvjudgC6uDtg5xx8O1uZ6f826Qu2JH2XFxxhz8nJ1wPY5PSGXAbO2RSImJbdeXtcYszIEyomP1HOq9TztDx8+xPr16xEVFQVRFNG9e3f885//hLOzc12X0egYYp52URSRm5uLxo0bS/YbolRQVnzqK6dNIXexIjgeXq6NsDugFxxsjKfDDlB7qgnKio8x5xR+NwuztkXAQiHHnrm94OXqoNfXM+as6hPlxMdQOfH2G+niSnpAF1cihM/ui/fw0eE4tGtuh/2v94ajrYWhi0QIeUbnb2diTlAkrC0U2DevFzq2pL+DhFSlzi+uFBsby30j9U+tVuPYsWOSPaUjJZQVH33n9GvUfXx0OA7uTW2wO9DfaDvs1J74UVZ8jD2nvm2dsHFGDxSXavDa5gjcfVSot9cy9qzqC+XER+o5cR9pl8vlkMlk1V71VCaTQaPR1EnhjJUhjrQzxlBQUAB7e3vIZLJ6eU1jRVnx0WdO/72SikX7ouHsYI39r/dCqyblZ6MyFtSe+FFWfEwlpz/jHuKfey6jmZ0l9s3rBQ8n2zp/DVPJSt8oJz6GyqnOh8fUZP51d3d37nVNEQ2PIaRywVfT8NbeaDSzs8T+13vBvWnd/yEnhEjD0ZgHWLw/Bs3trfTWcSfE2NX58Bh3d3fuG6l/arUaR48elewpHSmhrPjoI6cT1x5i4d5oNLW1wJ65/ibRYaf2xI+y4mNKOb3s7Yo1k7yRUaDE1E3hSMkurtPtm1JW+kQ58ZF6Ts/0Q9Tr168jOTkZKpVK5/6XXnrpmQtmzAw1PEapVMLKyopOfVWDsuJT1zmduZGO13dGwcHaHPvm9ULb5vZ1UErDo/bEj7LiY4o5HY6+jyUHrsCtiQ0OvN4bLR2s6mS7ppiVPlBOfAyVE2+/sVZXL7l79y7GjRuHq1ev6oxzL6tgQx/TbihmZsZxMRopoKz41FVO5249wvydl2FvZY7dgabTYS9D7YkfZcXH1HIa59MKpWoR7x+6iqmbw7F/Xm80s6+bK6ibWlb6QjnxkXJOtZqE8u2334anpyfS09NhY2ODa9euISQkBD169MDZs2fruIjPbty4cWjSpAkmTJjA/diaNWvw/PPPo3Pnzli4cGG1P8A1NEEQEBwcDEEQDF0UyaOs+NRVTudvZ2LejkuwsVRgV4A/OrQ0rQ47tSd+lBUfU81pcs/W+GxMZ9x9VITpWy4ip0hV/ZOqYapZ1TXKiY/Uc6rV8BgnJyecOXMGXbt2hYODAyIiItChQwecOXMG77zzDqKjo/VR1lr766+/UFhYiO3bt+OXX36p9rFHjx6hV69euHbtGszNzTFgwAB8/fXX6N27N9frGWp4jCAIMDMzo1Nf1aCs+NRFThfuZGF2UP1daMUQqD3xo6z4mHpOP5+7g//8cePxBdUCez3TFZBNPau6QjnxMVROdf5D1CdpNBrY2dkBeNyBT01NBfD4x6o3b96szSb1avDgwbC3r/joXmWPCYIApVIJtVoNtVqN5s2b67uYz0yq3wyliLLi8yw5RSZlI2B7JMzlcuwI8DfJDnsZak/8KCs+ppzT/IFtsHhoe8Q9yMeMrREoUD7bj/5MOau6RDnxkXJOteq0e3l5aS+i5O/vj9WrV+P8+fNYtmwZnnvuuRptKyQkBGPGjIGLiwtkMhmOHDlSbp1169bB09MTVlZW8PX1RWhoaG2Kza1Zs2ZYunQpWrduDRcXFwwdOhRt2rTR62s+K0EQcOLECUk3NqmgrPg8S06Xk3Mwa2sEZACC5vjB261xnZdPKqg98aOs+DSEnBYOaYt/Dm6DKym5mL0tEkWltatrQ8iqLlBOfKSeU6067R9//DFEUQQALF++HPfu3UP//v0RHByM77//vkbbKioqQrdu3fDjjz9W+Pj+/fuxaNEifPTRR4iOjkb//v0xYsQIJCcna9fx9fWFl5dXuVvZGYCaysnJwe+//46kpCQ8ePAAYWFhCAkJqdW26ou5uTlefvllmJvX/jRjQ0FZ8altTnEP8jBzawREBmyb3RO+7o56KqE0UHviR1nxaQg5yWQyLB3WAXP7e+LSvRwEbI9Eiarmk1g0hKzqAuXER+o51arTPnz4cIwfPx4A8Nxzz+H69evIzMxERkYG/vGPf9RoWyNGjMDy5cu123vat99+i4CAAAQGBqJTp05Yu3Yt3NzcsH79eu06UVFRiIuLK3dzcXGpTfVw6tQptG3bFo6OjrC2tsaoUaMQHh5e6fqlpaXIz8/XuQH/m0VHo9FUuCwIgs5y2RehypbVarXOctnPEcruz8vLg0qlAmMMjDHtPKNPLouiqLNc9m2ysmWNRqOzXJ91erIedVknQRCQk5MDxpjJ1Ekf+0mtViM3N1dbLp463UjLx/QtF1EqiNg8swf8PJpIqk762k/5+fk65TWFOuljPzHGkJOTo/NeNPY66WM/iaKI7OxsiKJoMnWqaD/JZDJ8MKIjpvdqjfC72QjcEYnCYmWN6lT2/nuyvA3l/VSTOmk0GuTn55tUnfSxnxhjyM3NrbZ++qgTj1p12vPy8pCdna1zn6OjI3JycrQd1rqgUqkQFRWFYcOG6dw/bNgwhIWF1dnrPM3NzQ1hYWFQKpXQaDQ4e/YsOnToUOn6q1atgoODg/bm5uYGAIiLiwMAxMfHIz4+HgAQGxuLhIQEAEB0dDQSExMBABEREUhJSQEAhIWFIS0tDcDj4UOZmZkAgDNnziA3NxcAcOLECRQUFAAAgoODUVhYiNDQUPzxxx/a8fjBwcEAgIKCApw4cQIAkJubizNnzgAAMjMztWcQ0tLStJmmpKQgIiICAJCYmKj9YXFCQoJ2WFR91EmpVEIQ/vdL7rqq0507dxAaGgpBEEymTvraT2U58dRp26/BeG3LRRQqBcxuq0bftk6SrJM+9lNoaCjS09NNqk762E+CICA0NBR37twxmTrpYz8plUqEhoZql02hTpXtp8LCQvibJWOqf2ucv52FyT+eQamg4a7T5cuXERoaips3b0qmTlLcT+np6QgNDTWpOuljP5V9RhmiTlxYLbz44ovsp59+Knf/+vXr2YgRI2qzScYefzVihw8f1v7/wYMHDAA7f/68znorVqxg7du3597usGHDmJOTE7O2tmaurq4sIiKi2sc+/PBD1rFjR9a5c2f21ltvMVEUK92+UqlkeXl52ltKSgoDwLKzsxljjAmCwARBKLesVqt1ljUaTZXLKpVKZ7msTGXLoiiWW2aM6SxrNBqdZbVaXeWyIAg6yxXVg+pEdbqTUcD8lp9kbT44xv68mmoSdTLF/UR1ojpJtU4ajcjeORDN3N/7nQVuj2RKldro62SK+4nqpJ865eXlMQAsLy+PVaVWUz46Ojri/Pnz6NSpk879N27cQN++fZGVlVXTTQJ4PMbt8OHDGDt2LAAgNTUVrq6uCAsL05luccWKFdi5cydu3LhRq9fRN0NM+SiKInJzc9G4cWPI5bU6gdJgUFZ8eHNKyS7GqxsuID1fiR+mdMeors71WErDo/bEj7Li01Bz0ogMSw7E4GhMKkZ1ccZ3k71hpqi6/g01q5qinPgYKie9TvlYWlpa4S9r1Wo1SkpKarPJCjk5OUGhUODhw4c692dkZKBFixZ19jqmQKPRIDIykq5Gy4Gy4sOT04PcEkzeGI6H+UqsmeTd4DrsALWnmqCs+DTUnBRyGb6Z2A0ju7TEsatpWHLgCgRN1eN9G2pWNUU58ZF6TrU60j5o0CB06dIFP/zwg879//znPxEbG1vrKRmfPtIOPJ5S0tfXF+vWrdPe17lzZ7z88stYtWpVrV5H3wxxpJ2Q+vYwT4lJGy/gXlYxvprQFRN7uBm6SIQQE6DWiHhzz2Ucv5aOcT6u+HpiNyjkdEEgYrp4+41mtdn4ihUrMHToUFy5cgVDhgwBAJw+fRqRkZHaQf28CgsLcfv2be3/ExMTERMTA0dHR7Ru3RpLlizB9OnT0aNHD/Tu3RsbN25EcnIy5s+fX5uimyxRFJGZmQknJyc69VUNyopPVTllFCgxdVM47mUVY+W4Lg26w07tiR9lxaeh52SukOOHKd2xYPdlHI5+AEszOVaO6wJ5BR33hp4VL8qJj9RzqlWJ+vbtiwsXLsDNzQ0HDhzAb7/9hrZt2yI2Nhb9+/ev0bYuXboEHx8f+Pj4AACWLFkCHx8ffPLJJwCASZMmYe3atVi2bBm8vb0REhKC4OBguLu716boJksURcTFxdVo6qCGirLiU1lOmYWlmLbpIu5mFmHZy89jqn9rA5VQGqg98aOs+FBOgIWZHD9N88HA9s2wLzIFn/92DRUNDKCs+FBOfKSeU62Gx5Cq0fAYYqpyilSYsikcNx4W4ONRnRDYv2ZXQCaEkJpQqjWYvS0SF+5m4fUBz+H9ER0hk9FQGWJa9PpD1MuXL+Pq1ava/x89ehRjx47Fhx9+CJVKVZtNkmckiiIePHgg2W+HUkJZ8Xk6p7wSNaZvvYgbDwvw3osdqcP+/6g98aOs+FBO/2NlrsDmmT3Qw70JNoTcxZpTCTqPU1Z8KCc+Us+pVp32119/Hbdu3QIA3L17F5MmTYKNjQ0OHjyId999t04LSPiIoog7d+5ItqFJCWXF58mcCksFzNoWgbgH+Vg8tD3eGNTG0MWTDGpP/CgrPpSTLltLM2yd7YeurRzw/ekErDv7v9/BUVZ8KCc+Us+pVsNjHBwccPnyZbRp0wZffvklzpw5g+PHj+P8+fOYPHmy9kpPDRUNjyGmpFglYNa2SEQkZmPBoDb41/AOdHqaEFLvcotVmLzx8fC8f4/ujIB+noYuEiF1Qq/DYxhj2m8hp06dwsiRIwEAbm5u2svKkvoliiLu3bsn2W+HUkJZ8RFFEbfuJCJw+yVEJGZjTl9P6rBXgNoTP8qKD+VUscY2FtgV6I+2ze3wxe/XsfviPcqKE+XER+o51arT3qNHDyxfvhw7d+7EuXPnMGrUKACPp2ukix4ZhtTHYUkJZcWnRCXgX0dvIexOFl7r1Rr/Ht2JOuwVoPbEj7LiQzlVzsnOErsD/eHe1AYfHY7DL5dSKCsO1Kb4SD2nWg2PiY2NxbRp05CcnIwlS5bg008/BQC89dZbyMrKwp49e+q8oMaEhscQY1cqaPDGrss4cyMDr/Zohf+M71rhHMmEEGIID3JL8OrPF5CWV4KvJ3bD+O6tDF0kQmqNt99Yp1M+KpVKKBQKmJub19UmjZIhOu0ajQaJiYnw9PSEQqGol9c0VpRV1VSCiAW7o3AqPgPD2zXCjzN6w9y8VtdhaxCoPfGjrPhQTnySs4oxedMFpOUq8Z/xXpjUk67fUhlqU3wMlZNex7RXxsrKqsF32A2FMYacnJwKLz5BdFFWldOIDIv3x+BUfAbGertgdhdL0IiYqlF74kdZ8aGc+LRuaoM9AT3RzEaO9w/H4Uj0A0MXSbKoTfGRek50cSU9oOExxBiJIsP7h2Jx4NJ9jOrijO+n+EBBQ2IIIRKXkl2MSRsuIL2gFD9N7Y4XvVoaukiE1IhBjrQTw9FoNLhx4wY0Go2hiyJ5lFV5osjw8dE4HLh0H4M6NMOaSd4AEyknDtSe+FFWfCgnfhqNBkUZydgxxw9NbCzw1t7LOHszw9DFkhxqU3yknhN12k1ISUmJoYtgNCir/2GM4bPfrmHPxWT0b+eEn1/zhYXZ448GyokP5cSPsuJDOfErKSmBp5Mtdgf6w9bSDK/vjMLfCTT99NOoTfGRck40PEYPaHgMMRaMMaw4Fo/Nfyei93NNsXWWH6wt6EdKhBDjdPV+HqZtDkepIGLbLD/0aetk6CIRUi29zh6zZMmSijcmk8HKygpt27bFyy+/DEdHx5pu2iQYavaY+Ph4dOrUiX4ZXg3K6n++Pn4TP/51G34eTbB9Tk/YWPxvlhjKiQ/lxI+y4kM58asoq9j7uZi2+SIEDcOOgJ7w82iYfZEnUZviY6icePuNtZrHLTo6GpcvX4ZGo0GHDh3AGENCQgIUCgU6duyIdevW4Z133sHff/+Nzp0717oShBD9+eF0An786za6uTXG1ll+Oh12QggxVl1bNcb2OT0xffNFzN4WiZ0BPeHTuomhi0XIM6vVkfa1a9ciNDQU27Zt034jyM/PR0BAAPr164e5c+di6tSpKCkpwfHjx+u80FJHw2OI1G0MuYOVwTfQ2bkR9s7tBQcbmqqVEGJaIhKzMXNrBMwVMuyd1wvPuzgYukiEVEivs8d89dVX+OKLL3Q23KhRI3z22WdYvXo1bGxs8MknnyAqKqo2mye1oNFoEB0dLdlfPEtJQ89qe1gSVgbfQPsWdtgV6F9ph72h58SLcuJHWfGhnPhVlVVPT0dsmtEDSkHE9C0RSEgvMEAJpYHaFB+p51SrTnteXh4yMspPqfTo0SPk5+cDABo3bgyVSvVspSM1Ym1tbegiGI2GmtXui/fw6X+v4TknW+wO7AVHW4sq12+oOdUU5cSPsuJDOfGrKqt+7Zywflp35JeoMW3zRSRlFtVjyaSF2hQfKedUq+Ex06ZNw4ULF/DNN9/Az88PMpkMERERWLp0Kfr06YOdO3di3759+Prrr3Hp0iV9lFvSaHgMkaK9Ecn44NBVuDe1wf55vdHSwcrQRSKEkHpxLDYNb+29DGcHa+x/vRdaNbExdJEI0dLr8JgNGzZgyJAhmDx5Mtzd3dG6dWtMnjwZQ4YMwc8//wwA6NixIzZv3ly70pMaEwQBkZGREATB0EWRvIaY1cFLKdoO+755vbg67A0xp9qgnPhRVnwoJ368WY3q6oyvJ3ZDal4Jpm2+iPR8ZT2VUBqoTfGRek61mi7Czs4OmzZtwpo1a3D37l0wxtCmTRvY2dlp1/H29q6rMhIOMpkMTZo0gUxGl52vTkPL6uT1dLx/6CpcG1tj79xecHbgO/XX0HKqLcqJH2XFh3LiV5OsxndvhRK1Bh8djsO0zRexf14vNLWzrIdSGh61KT5Sz+mZL650//59yGQyuLq61lWZjB4NjyFSEX43CzO3RsDW0gy/zO+N55rZVf8kQggxYVv+TsQXv19HJ+dG2DvXH41tqv5tDyH6ptfhMaIoYtmyZXBwcNAOj2ncuDG++OILiKJY60KT2hMEAWFhYZI9pSMlDSWry8k5CAiKhLlCjqDZfjXusDeUnJ4V5cSPsuJDOfGrTVYB/Tzxr+EdEJ+Wj+lbIpBbbPqTZlCb4iP1nGo1POajjz7Cli1b8J///Ad9+/YFYwznz5/HZ599BqVSiRUrVtR1OUk15HI5XF1dIZfX6ntYg9IQsrp6Pw8zt0ZAZMCOOX7o2qpxjbfREHKqC5QTP8qKD+XEr7ZZ/XNwW6gEEd+dTsDkjeHYGeCPZvamO1SG2hQfqedUq+ExLi4u+Pnnn/HSSy/p3H/06FEsWLAADx48qLMC1oVx48bh7NmzGDJkCH755Redx8zMzODl5QUA6NGjh/bHs7///jveeecdiKKI9957D4GBgdyvR8NjiCHFp+VjyqZwlKg02DbLD33aOhm6SIQQIknrzt7G6j9von0LO+yb17vaaXAJ0Qe9Do/Jzs5Gx44dy93fsWNHZGdn12aTerVw4ULs2LGjwscaN26MmJgYxMTEaDvsgiBgyZIlOHPmDC5fvowvv/xSkvV6kiAICAkJkewpHSkx5axuZxTgtc0XUVyqwYbpvs/UYTflnOoS5cSPsuJDOfF71qwWDGqLD0d2xK30QszYehH5SnUdl1AaqE3xkXpOteq0d+vWDT/++GO5+3/88Ud069btmQtV1wYPHgx7e3vu9SMiIvD888/D1dUV9vb2GDlyJI4fP67HEj47uVyONm3aSPaUjpSYalaJmUWYuuki8krUWDetOwZ1aP5M2zPVnOoa5cSPsuJDOfGri6zmDWiDRUPbIe5BPmZvi0SxSpodtmdBbYqP1HOqValWr16NrVu3onPnzggICEBgYCA6d+6MoKAgfPXVVzXaVkhICMaMGQMXFxfIZDIcOXKk3Drr1q2Dp6cnrKys4Ovri9DQ0NoUu0L5+fnw9fVFv379cO7cOQBAamqqzmw4rVq1ktyQn6dJfRyWlJhiVinZxZi6KRxZRSr8MMUHQzu3eOZtmmJO+kA58aOs+FBO/Ooqq7eHtMPrA55D1L0cBARdQolKmpexry1qU3yknlOtSjVw4EDcunUL48aNQ25uLrKzszF+/HjcvHkT/fv3r9G2ioqKKj1yDwD79+/HokWL8NFHHyE6Ohr9+/fHiBEjkJycrF3H19cXXl5e5W6pqanVvn5SUhKioqLw888/Y8aMGcjPz0dFw/yrmrOztLQU+fn5OjcA0Gg02n8rWhYEQWe5bOadypbVarXOclk51Wo11Go1Tp8+jZKSEjDGwBiDWv34NN+Ty6Io6iyXnQKqbFmj0egs12ednqxHXdaptLQUp0+f1pbV2OuUmluCKZvC8TBfiW9f7YZhnZvXSZ2USqU2J0PsJ2Npe0qlEmfOnIFKpTKZOulrPwmCgNOnT6O0tNRk6qSP/VT2ef7k/429TvraT6WlpThz5gxKS0ufqU6MMbw/oiNe83fDhbtZmLfzEgpLSk2m7alUKpw5cwZKpdJk6qSPtlf2GaVUKuu9Tjxq/VXCxcUFK1aswK+//opDhw5h+fLlcHFxqfF2RowYgeXLl2P8+PEVPv7tt99qj+Z36tQJa9euhZubG9avX69dJyoqCnFxceVuPOUpW8fLywudO3fGrVu34OrqqnNk/f79+3B2dq50G6tWrYKDg4P25ubmBgCIi4sDAMTHxyM+Ph4AEBsbi4SEBABAdHQ0EhMTATwekpOSkgIACAsLQ1paGoDHZyIyMzMBAGfOnEFubi4A4MSJEygoKAAABAcHQ6VSoVOnTjhx4gQEQYBSqURwcDAAoKCgACdOnAAA5Obm4syZMwCAzMxMhISEAADS0tIQFhYGAEhJSUFERAQAIDExEdHR0QCAhIQExMbG1ludlEolBEFAcHBwndYpOTkZFhYWkMvlRl+n4yHhmLopHPdzSvBGd3u87O1aZ3U6f/483NzcIJfLDbKfjKXtnTt3Dl5eXsjOzjaZOulrP8nlclhYWGgPuphCnfSxn0RRRGFhofZLoSnUSV/76cqVK/Dy8sLdu3efuU4ymQyDGj3CuC7NEJqQidd+Oo3M7Jx6r5M+9lN2dja8vLxw7ty5Bvd+qkmd5HI53NzccP78+XqvEw/u2WPKCsSja9eu3OvqFEYmw+HDhzF27FgAgEqlgo2NDQ4ePIhx48Zp13v77bcRExOjHc7C4+zZs/jxxx91Zo/JycmBjY0NLC0tcf/+ffTt2xfR0dFo1KgROnXqhLNnz6JRo0bo3r07wsPD0bRp0wq3XVpaqj1yBDwecuPm5obs7Gw0adJE++1KoVDoLAuCAJlMpl2Wy+WQy+WVLqvVaigUCu2ymZkZZDKZdhl4/K3tyWVzc3MwxrTLoihCo9Fol0VRhJmZWaXLGo0GjDHtckX1oDoZpk4Z+SWYsuki7jwqwhcvdcaUnm5GXydT3E9UJ6oT1cm46gTI8M4vsTgak4qx3i745lVviBrBqOtkivvJlOpUWFjIN+sg4ySTyZhcLmcymazKm1wu591kOQDY4cOHtf9/8OABA8DOnz+vs96KFStY+/btubc7bNgw5uTkxKytrZmrqyuLiIhgjDF2/vx55uXlxbp27cq6deum89pHjx5l7dq1Y23atGEbNmyoUT3y8vIYAJaXl1ej5z0LlUrF/vzzT6ZSqertNY2VKWSVXVjKhq85x9zf+51tCb2rl9cwhZzqA+XEj7LiQznx01dWKkHDAoIimft7v7PF+6KZoBHrdPv1jdoUH0PlxNtv5L64UtlhfUN4ejw5Y6zKMeZPq2zmlz59+uDq1asVPvbSSy+Vm4deyhQKBfz8/KBQKAxdFMkz9qzyStSYvvUibjwswPsjOmJOP0+9vI6x51RfKCd+lBUfyomfvrIyV8jx0zQf/HP3ZRyKfgCFXIYvX+kKuZy/7yEl1Kb4SD0n7k67u7u7PstRIScnJygUCjx8+FDn/oyMDLRo8eyzY5gSuVwOR0dHQxfDKBhzVoWlAmZujUDcg3wsHtoe8we20dtrGXNO9Yly4kdZ8aGc+OkzK0szBX6a1h3zd0bhYNR9WJkrsOzl52t00FAqqE3xkXpO3D9EvXDhAvdGi4qKcO3atVoV6EkWFhbw9fXFyZMnde4/efIk+vTp88zbNyVqtRrHjh3T/hKaVM5YsypWCZizLRIxKblYMKgNFg5pq9fXM9ac6hvlxI+y4kM58dN3VpZmCqx/zRd92jTFzvB7WBkcX+EMc1JHbYqP1HPi7rTPmDEDL7zwAg4cOIDCwsIK17l+/To+/PBDtG3bFpcvX+babmFhofaKpMDjYTgxMTHa2QWWLFmCzZs3Y+vWrYiPj8fixYuRnJyM+fPn8xa9QTAzM0P//v21P7QglTPGrJRqDQK3X0JEUjYC+nniX8M76P1ojzHmZAiUEz/Kig/lxK8+srIyV2DzzB7o4d4Em0ITsfZUgt5eS1+oTfGRek7cs8eo1Wps2LABP/74I+7cuYP27dvDxcUFVlZWyMnJwY0bN1BUVITx48fjgw8+gJeXF1cBzp49i8GDB5e7f+bMmQgKCgLw+OJKq1evRlpaGry8vLBmzRoMGDCAv5b1LD8/n+9XwIRwKBU0mLcjCuduPcL0Xu5Ge3qWEEKMWb5SjWmbLuLqgzy8P6KjXocnkoaFt9/I3Wl/0uXLlxEaGoqkpCSUlJTAyckJPj4+GDx4sKTHAtUXQ3Ta1Wo1goODMXLkSJibm9fLaxorY8pKrRHxxq7LOBWfjkk93LBqfJd6+yGUMeVkSJQTP8qKD+XEr76zyilSYfLGcNxML8DnLz2PmX089P6adYHaFB9D5aTXTjupmiE67YwxKJVKWFlZ0VHYahhLVoJGxNv7YnDsahrG+bji64ndoKjHmQuMJSdDo5z4UVZ8KCd+hsgqo0CJyRvCcTezCF+8/Dym9/aol9d9FtSm+BgqJ95+Y62viEqkR6pjsKRI6llpRIalB6/g2NU0jOrijK8mdK3XDnsZqeckFZQTP8qKD+XEr76zam5vhT1ze8HTyRb/PnoNO8Pv1evr1xa1KT5Szok67Sbiycv0kqpJPStRZPjgUCyOxKTihc4tsHayN8wU9f9WlXpOUkE58aOs+FBO/AyVVUsHK+yb9/8d9yNx+CXqfr2+fk1Rm+Ij9ZxoeIweGGp4TNlleunUV9WknBVjDP8+Godd4ckY1KEZNkz3haWZYS7yIOWcpIRy4kdZ8aGc+Bk6q9TcEkz8+QLS8krw/RQfjO7qUu9l4GHonIyFoXKi4TENkFS/GUqRFLNijOGL3+OxKzwZfds2xc+vGa7DXkaKOUkR5cSPsuJDOfEzZFYuja2xZ64/mtlbYtG+GJy6nm6wslSH2hQfKedEnXYTIQgCTpw4IenGJhVSzIoxhtXHb2Lr+UT09HDEphk9YGVu+A671HKSIsqJH2XFh3LiJ4Ws3JvaYnegPxyszbFg92Wcu/XIYGWpjBRyMgZSz4mGx+gBzdNOamrtqVtYeyoBPq0bY2eAP+wspftDGEIIIeXFp+VjyqZwlKg0CJrdE73bNDV0kYiRqPPhMXK5HAqFosa3ZcuW1UmFSNUYY8jPzzfKyyvXN6llte7sbaw9lYAurg4Imt1TMh12qeUkVZQTP8qKD+XET0pZdXJuhJ1z/GGhkCNgeySi7uUYukhaUspJyqSeE3enPTExEXfv3q3x7e2339Zn+cn/EwQBoaGhkj2lIyVSymrL34lY/edNdGxpjx1zesLBWjoXvZBSTlJGOfGjrPhQTvykllWXVg7YNtsPjAGztkXg6v08QxcJgPRykiqp50TDY/SAhscQHjvD7+HfR+LQtrkd9s3rBSc7S0MXiRBCSB0Iu52J2UGRsLZQYO/cXujkTH0BUrl6nz0mJycHP/zwA7y9vetqk6QGRFFEdnY2RFE0dFEkTwpZHYhMwb+PxMGjqQ32BPpLssMuhZyMAeXEj7LiQznxk2pWfdo6YcN0XxSXavDa5ou4nVFg0PJINSepkXpOz9xpP3XqFKZMmQIXFxd8+umn6N27d12Ui9SQRqNBZGQkNBqNoYsieYbO6kj0A7x3KBZujtbYM7cXmjeyMkg5qmPonIwF5cSPsuJDOfGTclaDOjTHj1N9kFeixtRNF5GYWWSwskg5JymRek61Gh6TnJyMbdu2Ydu2bXjw4AGGDx+OmTNn4uWXX4aFhYU+ymlUaHgMqcyx2DS8tfcyWjaywv7Xe8PN0cbQRSKEEKJHZZ/7LRpZ4QB97pMK6GV4zIEDBzB8+HB4enri0KFDWLhwIe7fv4/ff/8dEydOpA67AYmiiIyMDMme0pESQ2V18no63t4XDSc7S+ye20vyH9zUpvhQTvwoKz6UEz9jyGpUV2d8+6o3HuYrMWVTOFJzS+q9DMaQkxRIPacaddonT56M1NRUhIeH48qVK1iyZAlatGihr7KRGhBFEXFxcZJtaFJiiKzO3szAP3dfhoO1OfbM9Yenk229vXZtUZviQznxo6z4UE78jCWrsT6u+HJ8V9zPKcHUTeHIyFfW6+sbS06GJvWcajQ8Zt68eThw4AAsLS0xdepUzJw5k354WgEaHkOe9HdCJuZsj4QNzSJACCENGs0aRiqil+ExGzduRFpaGlavXo3Lly+je/fu6NKlC7755hukpaU9c6FJ7YmiiAcPHkj226GU1GdWF+5kIXBHJKzM5NgV4G9UHXZqU3woJ36UFR/KiZ+xZTW9lzs+HtUJtzMK8drmi8gtVtXL6xpbToYi9ZxqPHuMtbU1Zs6ciXPnzuHmzZsYNWoUvv32W7Ru3RojRozAvn379FFOUg1RFHHnzh3JNjQpqa+sLiVlI2B7JMwVcuwK9IeXq4NeX6+uUZviQznxo6z4UE78jDGrwP7P4d0XO+DGwwJM3xKBfKVa769pjDkZgtRzqpOLK4miiGPHjmHLli34448/UFpaWhdlM1o0PIbE3s/FtE0XITKGnYH+6N66iaGLRAghRELWnLyF704noHvrxtgR4A87SzNDF4kYSL1eXEkul2PMmDE4cuQIUlJS6mKTpIZEUcS9e/ck++1QSvSdVXxaPqZviYBaFLFllp/RdtipTfGhnPhRVnwoJ37GnNWioe3w+sDncDk5FwFBkShR6W9ucGPOqT5JPac6uyJqmebNm9f1JgkHqY/DkhJ9ZnU7owCvbb6IEpUGG6f3QK/nmtb5a9QXalN8KCd+lBUfyomfMWclk8nw/osdMauPBy4mZuP1XVEoFfTTcTfmnOqT1HPiHh7j6ekJmUxW4xdYtGgRFi5cWOPnGTMaHtMwJWUW4dUNF5BdpMLPr/liaGeaDpUQQkjVGGP48PBV7I1IwQudW2DdtO4wV9T5MVUiYbz9Ru4BVEFBQbUqiIeHR62eR2pGo9EgMTERnp6eUCgUhi6OpOkjq/s5xZi2+SIyC0vxw5TuJtFhpzbFh3LiR1nxoZz4mUJWMpkMy8d2gVIt4nD0AyzaH4PvJ/tAIa/5gdLKmEJO9UHqOXF32gcOHKjPcujVuHHjcPbsWQwZMgS//PKLzmNr1qzB5s2bwRjD0KFD8d133+H+/fuYPn06MjIyYGZmhn//+9+YOHGigUrPhzGGnJwc+pLEoa6zepinxLTNF5GaV4JvJnbDqK7OdbJdQ6M2xYdy4kdZ8aGc+JlKVgq5DF9N6AqlWoNjsWmwNJPj6wndIK+jjrup5KRvUs+pTmaPkbq//voLhYWF2L59u06n/dGjR+jVqxeuXbsGc3NzDBgwAF9//TU8PDyQnp4Ob29vZGRkoHv37rh58yZsbfmuYknDYxqOzMJSTNpwAXceFWHluC6Y6t/a0EUihBBipFSCiDd2ReH0jQxM9nPDynFd6qzjTqSrXmePkbrBgwfD3t6+wscEQYBSqYRarYZarUbz5s3h7OysvdJr8+bN4ejoiOzs7Hoscc1pNBrcuHEDGo3+fn1uKuoqq5wiFV7bfBF3HhXh0zGdTa7DTm2KD+XEj7LiQznxM7WsLMzk+Gladwxo3wz7IlPw6X+voS6OrZpaTvoi9ZwM3mkPCQnBmDFj4OLiAplMhiNHjpRbZ926dfD09ISVlRV8fX0RGhpaJ6/drFkzLF26FK1bt4aLiwuGDh2KNm3a6Kxz6dIliKIINze3OnlNfSopKTF0EYzGs2aVV6LG9K0XceNhAd4f0RGz+3rWUcmkhdoUH8qJH2XFh3LiZ2pZWZkrsHG6L/q0aYqd4ffwxe/xddJxN7Wc9EXKORm8015UVIRu3brhxx9/rPDx/fv3Y9GiRfjoo48QHR2N/v37Y8SIEUhOTtau4+vrCy8vr3K31NTUKl87JycHv//+O5KSkvDgwQOEhYUhJCRE+3hWVhZmzJiBjRs3Vrmd0tJS5Ofn69wAaL+paTSaCpcFQdBZLptiqLJltVqts1z2Jlar1ZDL5fD29oYoimCMgTEGtfrxVdaeXBZFUWdZEIQqlzUajc5yfdbpyXrUZZ0AoEuXLlAoFLWqU15xKWZujUDcg3wsGtIW8we2MXid9LGfGGPo1q0bFAqFydRJH/tJFEX4+PhAJpOZTJ30tZ8UCgW6dOmCMqZQJ33sJ7lcDi8vL8jlcpOpk772E2MMPj4+2v+bQp0EQYCVuQIbXvOBn0cTbD2fiP/8EV/h/uOtk0wmg4+Pj/YzyxB1qmrfSGU/KRQKdOvWTbuN+qwTD4N32keMGIHly5dj/PjxFT7+7bffIiAgAIGBgejUqRPWrl0LNzc3rF+/XrtOVFQU4uLiyt1cXFyqfO1Tp06hbdu2cHR0hLW1NUaNGoXw8HAAjzvi48aNwwcffIA+ffpUuZ1Vq1bBwcFBeys7Kh8XFwcAiI+PR3x8PAAgNjYWCQkJAIDo6GgkJiYCACIiIrQXpgoLC0NaWhqAx2ciMjMzAQBnzpxBbm4uAODEiRMoKCgAAAQHB6OoqAhXr15FcHCwdshPcHAwAKCgoAAnTpwAAOTm5uLMmTMAgMzMTO2XlLS0NISFhQEAUlJSEBERAQBITExEdHQ0ACAhIQGxsbH1VielUglBEOq8Tnfv3sXZs2eh0WhqXKdzYRcxbWMYYlJyMaaNBSZ0spVEnfSxn86dO4dLly5Bo9GYTJ30tZ/i4uKQnp5uUnXSx37SaDQ4e/Ys7t69azJ10sd+Ki0tRXBwMEpLS02mTvraT5cvX0ZcXBxu3rxpMnUq208P7iVicXdLdG/dGBtCEvHv/eG1rlN6ejri4uIMXieptz2NRoNLly7h3Llz9V4nLkxCALDDhw9r/19aWsoUCgU7dOiQznoLFy5kAwYMqNG2//rrL/bKK6/o3HfhwgXm7e3NSkpKmCAIbOTIkezIkSNMFEU2efJk9umnn3JtW6lUsry8PO0tJSWFAWDZ2dmMMcYEQWCCIJRbVqvVOssajabKZZVKpbMsiqJ2Wa1Ws9jYWFZSUsJEUWSiKDKVSsUYYzrLGo1GZ1mtVle5LAiCznJF9dBXnZ6sR13WqbS0lF25ckVbbt46FZWq2YR155n7e7+zFceu65Td0HXSx35SKpUsNjaWCYJgMnXSx35SKpXs6tWr2vehKdRJX/tJEAR25coVVlpaajJ10sd+UqvV7MqVK0ytVptMnfS1n0pLS9nVq1dZaWmpydTp6f2UV6Jio78PYe7v/c5+OH2rVnVSqVTs6tWrTKlUSqJOUt1PgiCw2NhYplQq67VOeXl5DADLy8tjVZHU7DEymQyHDx/G2LFjAQCpqalwdXXF+fPndY52r1y5Etu3b8fNmze5tjt8+HBcvnwZRUVFcHR0xOHDh+Hn5wcA+Oijj3Do0CHI5XIMGTIE3333Hc6fP48BAwaga9eu2m3s3LlT57RuVWj2GNNTKmgQuP0SQhMyMbuvBz4Z3blWFxsjhBBCaiqvWI0pm8JxPS0fH4/qhMD+zxm6SKQOmdTsMU93jhhjNeowHT9+HI8ePUJxcTHu37+v7bADwIoVKxAfH49r167h+++/h0wmQ79+/SCKImJiYrQ33g67oWg0GkRHR0v2F89SUtOsBI2It/fGIDQhE1N6tm4wHXZqU3woJ36UFR/KiV9DycrBxhy7Av3Rrrkdlh+Lx69R92v0/IaS07OSek6S7rQ7OTlBoVDg4cOHOvdnZGSgRQvjv+JkXbO2tjZ0EYwGb1YakeGdg1fw57WHGN3VGcvHejWIDnsZalN8KCd+lBUfyolfQ8nK0dYCOwJ6wsXBCu/+Gos/4x5W/6QnNJScnpWUc5J0p93CwgK+vr44efKkzv0nT56s9sehDY1CoUDHjh0ledldqeHNSiMyLDkQg6MxqXihcwt8+6p3nV5WWuqoTfGhnPhRVnwoJ34NLStnB2vsCvRHExsLvLX3Mk7Hp3M9r6HlVFtSz8ngnfbCwkLtEBTg8S9yY2JitFM6LlmyBJs3b8bWrVsRHx+PxYsXIzk5GfPnzzdgqaVHEARERkbqTGtIKsaTFWMMHxyK1XbYf5raHRZmBn+71CtqU3woJ36UFR/KiV9DzOq5ZnbYHegPeytzzN8VhRPXqj/i3hBzqg2p52TwXsilS5fg4+OjnWd1yZIl8PHxwSeffAIAmDRpEtauXYtly5bB29sbISEhCA4Ohru7uyGLLTkymQxNmjRpUEM3aqu6rBhjWHEsHgcu3cfA9s0aZIcdoDbFi3LiR1nxoZz4NdSsOrS0x965veBgbY4Fuy/jzI2qj7g31JxqSuo5SWr2GFNBs8cYt29P3sL3pxPQw70Jdgb4w9pCmqfJCCGENGy30gswacMFFKk0CJrthz5tnAxdJFILJjV7DKmeIAgICwuT7CkdKakqq5/+uo3vTyegaysHbJ3t16A77NSm+FBO/CgrPpQTv4aeVfsW9tgZ4A9LhRxzt1/C5eScCtdr6DnxknpO1Gk3EXK5HK6urpDLaZdWp7KsNobcwVfHb6KTcyPsmNMTjazMDVRCaaA2xYdy4kdZ8aGc+FFWgJerA7bN9oPIgJlbIxD3IK/cOpQTH6nnRMNj9ICGxxifoPOJ+Oy362jfwg575/ZCUztLQxeJEEII4Xb+diZmB0XC1kKBvfN6oWNL6n8YCxoe08AIgoCQkBDJntKRkqez2n3xHj777Tqea2aLXYH+1GH/f9Sm+FBO/CgrPpQTP8rqf/q2dcKG13xRWCrgtc0XcTujUPsY5cRH6jlRp91EyOVytGnTRrKndKTkyawOXkrBR4fj4NHUBnvn9kJzeytDF08yqE3xoZz4UVZ8KCd+lJWuwR2b48ep3ZFbrMbUTeFIyiwCQDnxknpONDxGD2h4jHEIvpqGN/dchrODNQ7O7w2XxtK9ChohhBDC61hsGt7aS3/fjAUNj2lgBEHAmTNnJHtKR0oEQcDa/Sfx9r5oNLWzxO5Af/pAqwC1KT6UEz/Kig/lxI+yqtiors5YPaEbHuSWYNrmi0jLKaKcOEi9PVGn3UTI5XJ4eXlJ9pSOlJxLyMRPsWrYWZphZ0BPeDjZGrpIkkRtig/lxI+y4kM58aOsKjfBtxW+GOuFxMwizAy6hFZtOlJO1ZB6e6LhMXpAw2Ok6/ztTMzeFglbSwX2zO2FTs60fwghhJiun8/dwX/+uIFOzo2wO9AfjrYWhi4SeQoNj2lg1Go1jh8/DrVabeiiSFZ0cg7m7rgES3M5/tlZRFsnGhJTFWpTfCgnfpQVH8qJH2VVvfkD2+CdoW0Rn5aPKRsvILdYZegiSZbU2xMdadcDQxxpF0URubm5aNy4sWRP6xjStdQ8TN10ESpBxI45fmjjIKOsqkFtig/lxI+y4kM58aOs+IiiiDV/XsMPIcno1soBuwL9Yd/ALyBYEUO1J95+I3Xa9YCGx0jLtdQ8TNt8EcUqDTbP6IEB7ZsZukiEEEJIvfvmxE38cOY2eno6YvvsnrC2UBi6SAQ0PKbBUavVOHbsmGRP6RjKjYf52g77xum+GNC+GWXFiXLiQznxo6z4UE78KCs+ZTm9NcgTs/t6ICIxG/N2XoJSrTF00SRF6u2JjrTrgSGOtDPGUFBQAHt7e8hksnp5TalLzirGKz+HIbdYhU0zemBQh+YAKCtelBMfyokfZcWHcuJHWfF5MifGgI+OxGFvRDIGtG+GjdN9YWVOR9wBw7UnGh5jQDQ8xvAe5inx6oYLuJ9TjB+ndsfILs6GLhIhhBAiCaLI8OHhq9gXmYJhnVtg3bTuMFPQ4AtDoeExDYxarcbRo0cle0qnPqXnKzFlUziSs4uxanyXch12yooP5cSHcuJHWfGhnPhRVnyezkkul2HFuC542dsFJ66n491fYiGKdAxX6u2JjrTrgaGGxyiVSlhZWTXoU4SPCkoxaeMF3H1UhOVjvfBaL/dy61BWfCgnPpQTP8qKD+XEj7LiU1lOao2IN3ZF4VR8Bqb6t8aKsV4NOkdDtSc60t4AmZmZGboIBpVXrMb0LRdx91ERPn/p+Qo77GUaela8KCc+lBM/yooP5cSPsuJTUU7mCjl+nNod/ds5Yc/FZHz632to6MdypdyeqNNuIgRBQHBwMARBMHRRDKKwVMDMbRG48bAA777YATP7eFS6bkPPihflxIdy4kdZ8aGc+FFWfKrKycpcgY3Te6BPm6bYceEeVgbHN9iOu9TbEw2P0QNDDY8RBAFmZmYN7tRWsUrAzK0RiEzKwYJBbfDuix2rXL8hZ1UTlBMfyokfZcWHcuJHWfHhyalYJWDGlghcupeDt4e0w+IX2tdzKQ3PUO2Jhsc0QFL9ZqhPSrUGgdsvITIpBwH9PPGv4R24ntcQs6oNyokP5cSPsuJDOfGjrPhUl5ONhRm2zvaDl2sjfHc6ARtD7tRTyaRFyu2JOu0mQhAEnDhxQtKNra6VChrM2xmFsDtZmN7LHR+P6sT1zbghZlUblBMfyokfZcWHcuJHWfHhzamRlTl2zPFH+xZ2WBl8AzsvJNVPASVC6u3J5IfHpKSkYPr06cjIyICZmRn+/e9/Y+LEidrHx40bh7Nnz2LIkCH45ZdfdJ5bXFyMTp06YeLEifj666+5X5Pmadc/lSBiwe7Hv3if7OeGleO6QC6nU6OEEELIs8ooUGLShnAkZhbhy1e6YJJfa0MXyaTR8Jj/Z2ZmhrVr1+L69es4deoUFi9ejKKiIu3jCxcuxI4dOyp87ooVK+Dv719fRX0mjDHk5+c3iB+PCBoRb++Lxqn4DIz3ca1xh70hZfUsKCc+lBM/yooP5cSPsuJT05ya21thd6A/3Byt8f6hq/g16r6eSygNUm9PJt9pd3Z2hre3NwCgefPmcHR0RHZ2tvbxwYMHw97evtzzEhIScOPGDYwcObK+ivpMBEFAaGioZE/p1BVRZPjXL7H4I+4hRnd1xuoJXWt8hL2hZPWsKCc+lBM/yooP5cSPsuJTm5xcGltjT2AvuDhY41+/XMEfV9P0WEJpkHp7MninPSQkBGPGjIGLiwtkMhmOHDlSbp1169bB09MTVlZW8PX1RWhoaK1e69KlSxBFEW5ubtWuu3TpUqxatapWr2MI5ubmGDVqFMzNzQ1dFL1hjOGT/8bhcPQDDO3UAmsmedfqsssNIau6QDnxoZz4UVZ8KCd+lBWf2ubk5miDPXP90dTOEm/vi0FowiM9lVAapN6eDN5pLyoqQrdu3fDjjz9W+Pj+/fuxaNEifPTRR4iOjkb//v0xYsQIJCcna9fx9fWFl5dXuVtqaqp2naysLMyYMQMbN26stkxHjx5F+/bt0b698Ux3JIoisrOzIYqioYuiF4wxLD8Wj13hyejbtil+nOoD81p02AHTz6quUE58KCd+lBUfyokfZcXnWXJyb2qLnQE9YWUux+s7o3ApKbv6Jxkpqbcng3faR4wYgeXLl2P8+PEVPv7tt98iICAAgYGB6NSpE9auXQs3NzesX79eu05UVBTi4uLK3VxcXAAApaWlGDduHD744AP06dOn2jKFh4dj37598PDwwNKlS7Fp0yYsW7as0vVLS0uRn5+vcwMAjUaj/beiZUEQdJbLGklly2q1Wme5bMyVWq2GIAiIiIiAUqkEYwyMMajVagDQWRZFUWe57BRQZcsajUZnuT7rVFYPlUqF5b9fx5a/E9HDvTE2Tu8BSzN5reukUqkQERGhLbch6vT0shT3U2lpqTYnU6mTPvZTaWkpIiMjte9DU6iTvvaTRqNBxP+1d+9xUVeJ/8ffM9xRRPECgoh00dXwhhfUX3mrMMvM2nXVNsPSyjYrE3e3tovlZpa15vermXlN7aL1Xa10sbT1goYKIgp4C5SbXCRELnKZ2+f8/jBmm0A8GjOfz8y8n48Hjx1nPjDnvOaTe5w5MyQnw2g0usyc7PE4Nfx9bjabXWZO9nqcjEYjUlJSYDQaXWZO9nicTCYTUlJSYDAYbmhOPYIDsHpqNABg6ppk7D9zQfU52eNxavg7ymAwOHxOMlRftDfHaDQiNTUVsbGxNtfHxsYiKSlJ6mcIITBt2jSMHj0aU6dOlfqehQsXoqCgALm5uXjvvffwxBNP4LXXXmv2+MDAQOtXw/abzMxMAMCpU6dw6tQpAEB6ejqysrIAAGlpacjJyQEAJCcno6CgAACQlJSE4uIre8cSExNRVlYGANi9ezcqKioAADt37kR1dTUAICEhARaLBXfeeSd27doFs9mM+vp6JCQkAACqq6uxc+dOAEBFRQV2794NACgrK0NiYiIAoLi42Nq0oKAAycnJAICcnBykpaUBuLLPPz093WFzqq+vh9lsxqyPvsOaH3IxoGsg/hhchlY+nr9pTufPn0f79u3h5eWl2pwafuOalh+ngwcPIjo6Gl5eXi4zJ3s8TomJiRgzZgwqKytdZk72epy8vLzQvn17nD9/3mXmZI/HSafTwWAwQKfTucyc7PU4ZWRkYMyYMcjNzXWZOdnjcaqsrMSYMWOQmJh4w3P66XQyNk6PgYceeHz9ERw+d9Hlzj0vLy9ER0fj4MGDDp+TFKEhAMTWrVutfy4sLBQAxA8//GBz3IIFC0T37t2lfub+/fuFTqcTffv2tX6lp6dbb4+NjRUdOnQQfn5+IiwsTCQnJ9t8/7p160R8fHyz91FfXy8qKyutXwUFBQKAKC8vF0IIYTabhdlsbnTZZDLZXLZYLM1eNhqNNpcVRbFeNpvNoqSkRNTX1wtFUYSiKMJoNAohhM1li8Vic9lkMjV72Ww221xuah72mpOiKOLDvdki4m/bxfil+0VVnbFF5mQ0GkVRUZGwWCyqzKlh7Fp/nAwGgygpKbGOxRXmZI/HyWAwiAsXLgiTyeQyc7LX42SxWERRUZH157vCnOzxOJnNZlFYWCjMZrPLzMlej1PDf38N/z/oCnOyx+NkMpnEhQsXhMFg+M1zSs29KHq9tkP0enWHOJp70aXOPYvFIkpKSoTBYHDonCorKwUAUVlZKZqjqc9p1+l02Lp1KyZMmAAAKCoqQlhYGJKSkjB06FDrcQsWLMDGjRtx+vRplUbaPDU+p91sNiMxMRHDhw+Hp6enQ+7T3jYczMVrX59Aj+AAbH5qCNr6e7fIz3XFVvbATnLYSR5byWEneWwlp6U7JeeU49G1h+Hr5YEvnhqK7sGNP4XPGal1PsmuGzW9aDcajfD398eXX36JBx980Hrc888/j2PHjmHfvn0qjbR5/OVKv90XKQX467/ScVOHVtj81FB0DPBRe0hERET0s71nSvHEhiNo6++NL54aisgOrdQektNyiV+u5O3tjQEDBmDXrl021+/atUvqDaXuRFEUFBYWavYdz9fj62OF+NuWdIQH+eHTJ2JafMHuSq3siZ3ksJM8tpLDTvLYSo49Oo3s0Qn/M7k/Ll424OFVh5B/sbbFfrZatH4+qb5ov3z5Mo4dO4Zjx44BuLK5/9ixY9aPdJwzZw5Wr16NtWvX4tSpU3jhhReQn5+PmTNnqjhq7VEUBWfPntXsiSbr28xizPniOELa+OKzGUPQOdCvxe/DVVrZGzvJYSd5bCWHneSxlRx7dbq3d2e8P6kfSqrqMWXVIRRW1LXoz3c0rZ9Pqm+P2bt3L0aNGtXo+ri4OHz88ccArvxypUWLFqG4uBhRUVF4//33MXz4cAePVB63x9yYPadL8eTGIwj088YXTw3BTR1bqz0kIiIiuoYvjxTgL/+Xjm7t/fHFU0PRqY2v2kNyKk65p91VqLFoVxQFBQUFCA8Ph16v+gso1+2H7DI89nEKWnl7YNOTQ9EjxH5vanH2Vo7CTnLYSR5byWEneWwlxxGdNh7Kw6tfZeLWTq2x6ckhaN/a+d6Lptb55BJ72kme1vdhNedIbjlmrD8CH089Nk6PseuCHXDuVo7ETnLYSR5byWEneWwlxxGdpg6JwCv39URW6WU8siYZFbVGu92XvWj9fOIz7XbA7THyjhdU4E+rD0MIgY0zYhDdtZ3aQyIiIqIb9MGebLz73Rn07RKIT2bEIMDXS+0haR6faXczFosF2dnZ1l+T6wxOFVfh0bXJMCsK1kwb5LAFuzO2UgM7yWEneWwlh53ksZUcR3Z6ZtQteHb0LTh+vhKPf5yCWqPZ7vfZUrR+PnHR7iKEELh06RKc5YWT7NLLeGT1YdQZLVg5dSCG3NTeYfftbK3Uwk5y2EkeW8lhJ3lsJcfRnebc3R0zbo9ESu4lzFh/BPUmbS6Cf03r5xO3x9gBt8c0L+9iDf740UFcvGzEikcG4K5ewWoPiYiIiFqQEAKvfX0CGw/lYWSPjvho6gD4eHqoPSxN4vYYN2OxWHD69GnNvqTToLCiDg+vOoyfqg1YMrmfKgt2Z2mlNnaSw07y2EoOO8ljKzlqdNLpdHhj/G3448Au2HvmJzz3eRpMFm2+wbOB1s8nLtpdSF2dtn+pwYWqejy86hCKKuvw7h/6YlyfUNXGovVWWsFOcthJHlvJYSd5bCVHjU56vQ4LH+qD8X1D8d2JC4j/4jgsirY3eGj5fOL2GDvg9pjGyi4bMOmjgzj7Uw3eerA3Ho7pqvaQiIiIyAHMFgXPfHYU3524gIkDuuCd3/eBXq9Te1iawe0xbsZisSAzM1OTL+lU1BoxdU0yzv5Ug1fH9VJ9wa7lVlrCTnLYSR5byWEneWwlR+1Onh56LJ0SjVE9OuLL1POY980JTb7ZU+1O18JFO9lVVb0JcWuTcaq4Cn8Z0wPTb49Ue0hERETkYN6eenz4yAD8v1vaY+OhPLyVcEqTC3ct4/YYO+D2mCtqDGY8ujYZqXmX8NzoWzAntofaQyIiIiIV1RrNiFubjJTcS3h29C2I59qA22PcjcViQVpammZe0qkzWjB9fQpS8y7hqeE34YW7u6s9JCuttdIqdpLDTvLYSg47yWMrOVrq5O/tibXTBqFveFss3Z2ND/Zkqz0kKy11agoX7S7Ez89P7SEAAOpNFjy58QgOnSvHtGHd8OLY30Gn09YbTrTSSuvYSQ47yWMrOewkj63kaKlTgK8XNjw2GD07t8G7353B2gM5ag/JSkudfo3bY+zAnbfHGM0K/vxpKr4/VYopg8OxYEJvvkOciIiIGvnlJ8u9/VBvTB7snp8sx+0xbsZsNiMlJQVms1m9MVgUzN6chu9PleKh/mGaXbBroZUzYCc57CSPreSwkzy2kqPVTh1a++DTGUPQNcgfL23NwFdphaqOR6udGnDR7iJ0Oh3atWun2jYUiyIw54vjSMgowX19OmPRH7T7Gaxqt3IW7CSHneSxlRx2ksdWcrTcKSTQF5/OiEHnNr6I//I4dmQUqzYWLXcCuD3GLtxte4xFEfjL/x3HlqOFGHNbMJY9HA0vD/57kIiIiOSc++kyJq08hEs1Rqx4ZADu6hWs9pAchttj3IzZbEZSUpLDX9IRQuDlrRnYcrQQd/XshKVTtL9gV6uVs2EnOewkj63ksJM8tpLjDJ1u6tgan82IQaCfF/786VHsPVPq8DFovZO2V1ckTa/XIywsDHq9Yx/St789jU0pBRjRvSM++FM0vD21f0qp1crZsJMcdpLHVnLYSR5byXGWTrcGB+CTGTHw9/HAkxtT8UN2mUPvX+uduD3GDtxle8yKfWfx9o7TGBDRDp9Mj4Gft4faQyIiIiInl1lYiYdXHYLRomD9Y4MRc1N7tYdkV9we42bMZjMSExMd9pLOh3uvLNh7BAdgTdxAp1qwO7qVs2InOewkj63ksJM8tpLjbJ2iwgKxYXoMPPV6PP7xlV/U6Aha78RFu4vQ6/W4+eabHfKSzur95/DOt6fxu5AAfPZEDNr6e9v9PluSI1s5M3aSw07y2EoOO8ljKznO2KlfeFt8/NggCADT1iYj/XyF3e9T6524PcYOXHl7zOfJ+XhpSwZu7dQam58aiqBWzrVgJyIiIudx8OxFTFuXDH9vD2x+aii6BweoPaQWx+0xPysoKMDIkSPRq1cv9OnTB19++WWjY2praxEREYG5c+dar8vJycGoUaPQq1cv9O7dGzU1NY4c9nUzm83YvXu3XV/S2Zp2Hn/fmoGuQf74ZEaM0y7YHdHKFbCTHHaSx1Zy2EkeW8lx5k5Db26PFVMH4LLBjEdWH0b+xVq73ZfWO7n8ot3T0xNLlizByZMn8f333+OFF15otABfsGABYmJibK6bNm0a5s+fj5MnT2Lfvn3w8fFx5LCvm16vR1RUlN1e0vn6WCHivziOzm2u/BKE4Da+drkfR7B3K1fBTnLYSR5byWEneWwlx9k7jerRCe9P6oefLhvwyJrDuFBVb5f70XonbY6qBXXu3Bn9+vUDAHTq1AlBQUEoLy+33p6VlYXTp0/j3nvvtV534sQJeHl54Y477gAABAUFwdPT06Hjvl56vR6dOnWyy4n27/RivLD5GILb+OLzJ4cgPMi/xe/DkezZypWwkxx2ksdWcthJHlvJcYVO4/qEYuGDvZFfXos/rT6Mn6oNLX4fWu+k+qgSExNx//33IzQ0FDqdDl999VWjY5YvX47IyEj4+vpiwIAB2L9//w3d15EjR6AoCsLDw63XzZ07FwsXLrQ5LisrC61bt8b48eMRHR2Nt95664buz5FMJhO+++47mEymFv25e8+U4vlNaegY4IPPnhiCiPatWvTnq8FerVwNO8lhJ3lsJYed5LGVHFfpNHlwV7w2rheySy/jkdWHUV5jbNGfr/VOqi/aa2pq0LdvXyxbtqzJ2zdv3ozZs2fj5ZdfRlpaGu644w6MHTsW+fn51mMGDBiAqKioRl9FRUXWYy5evIhHH30UK1eutF739ddfo3v37ujevbvNfZpMJuzfvx8ffPABDh48iF27dmHXrl1XnYPBYEBVVZXNFwBYLBbr/zZ12Ww221xWFKXZyyaTyeZyw3uITSYT9Ho9Bg4cCEVRIISAEMJ60v3ysqIoNpcb9m01dflIbjme/uQoWvt44pPpMejaztehc/rlPFpqTg2io6Ph4eFx1Xk425wsFovN5ZaYkxACAwcOhIeHh8vMyR6PkxACgwYNgk6nc5k52etx8vDwQHR0NBq4wpzs8Tjp9Xr0798fer3eZeZkr8ep4b+/hj+7wpzs8TjpdDoMGjQIQginn9Pjt0fixXu648yFajyy+jAuVtW22Jw8PDwwcOBA689w5OMkQ/VF+9ixY/Hmm2/ioYceavL2xYsXY/r06ZgxYwZ69uyJJUuWIDw8HB9++KH1mNTUVGRmZjb6Cg0NBXBlUf3ggw/ipZdewrBhw6zfd+jQIWzatAndunXD3LlzsWrVKsyfPx9dunTBoEGDEB4eDh8fH9x77704duzYVeewcOFCBAYGWr8ansnPzMwEAJw6dQqnTp0CAKSnpyMrKwsAkJaWhpycHABAcnIyCgoKAABJSUkoLi4GcOWViLKyK78RbPfu3aioqAAA7Ny5E9XV1QCAhIQEGI1GtGnTBt9++y3MZjPq6+uRkJAAAKiursbOnTsBABUVFdi9ezcAoKysDImJiQCA4uJiJCUlAbjy5t2NO5IQtzYZgIK/xLTGrcEByMrKQnp6usPmVF9fD7PZjISEhBaZU3JyMgAgLy8Pubm50Ov1LjOnnJwcpKWlAUCLzenAgQOwWCzQ6/UuMyd7PE579uyxbrtzlTnZ63HS6/XIzc1FXl6ey8zJHo+Toig4ePAgFEVxmTnZ63E6fvw4goKCcPbsWZeZkz0ep/LycgQFBWHPnj0uMafuSgGeGhaGk8VV+OMHe1BcerFF5qTX62GxWHDgwAGHz0mK0BAAYuvWrdY/GwwG4eHhIbZs2WJz3HPPPSeGDx8u9TMVRRGTJ08W8+bNa/a4devWifj4eCGEECaTSfTr10+Ul5cLi8Uixo0bJ7Zt23bV762vrxeVlZXWr4KCAgFAlJeXCyGEMJvNwmw2N7psMplsLlsslmYvG41Gm8uKolgvGwwGsW3bNlFTUyMURRGKogij0Wht0HDZYrHYXDaZTI0uH829KHq9ukP0enWHOJT9k/X6q83DXnP65Tx+65x+ebmurk5s27ZNGI1Gl5mT2Wxu8ceptrbW2slV5mSPx6m2tlZs375d1NfXu8yc7PU4GY1GsW3bNlFXV+cyc7LH49Tw97nBYHCZOdnrcaqrqxPbt28XdXV1LjMnezxO9fX1Yvv27aK2ttZl5mQ2m8Wb20+IiL9tF79f/oOoqjP+5jk1/B1VW1vr0DlVVlYKAKKyslI0R1Of067T6bB161ZMmDABAFBUVISwsDD88MMPNs+Qv/XWW1i/fj3OnDlzzZ954MABDB8+HH369LFet3HjRvTu3dvmuI8//hiZmZl47733AAA7duzAX//6VwghEBsbi8WLF0vPQ43PaRdCoLq6GgEBAdDpdDf8c7IuVGPiRwdRb7Jgw+MxGBwZ1IKj1IaWauXq2EkOO8ljKznsJI+t5LhqJyEE3vz3Kaw5kIOBEe2wYfpg+Hvf+AeHqNVJdt2o7Y9E+dmvwwkhpGPefvvtUvuFpk2bZvPnsWPHYuzYsdJjVJtOp/vN/0A4+9NlTFl1GJfrzVgVN9AlF+xAy7RyB+wkh53ksZUcdpLHVnJctZNOp8Mr9/WEXges2p+DJzekYnXcQPh6edzwz9NyJ9X3tDenQ4cO8PDwQElJic31paWlCA4OVmlU2mQymfD111/f8Due8y7W4OFVh3Cp1ohlD/fHqB6dWniE2vFbW7kLdpLDTvLYSg47yWMrOa7cSafT4e/39sTDMV1xILsMsz5Lg8ki/+bOX9J6J01vjwGAmJgYDBgwAMuXL7de16tXLzzwwAONPqpRK9TaHlNfXw9fX9/rfkmnuLIOf/jwIIor6/C/U/pjXJ9QO41SG35LK3fCTnLYSR5byWEneWwlxx06KYpA/JfHsTWtEOP6dMb/TO4PD/31zVWtTk6zPeby5cvIzs62/jknJwfHjh1DUFAQunbtijlz5mDq1KkYOHAghg4dipUrVyI/Px8zZ85UcdTadCO/AOriZQOmrklGYUUdFv2hj8sv2Bto/ZdlaQU7yWEneWwlh53ksZUcV++k1+vw7h/6oM5owfb0Yvh5eeCd3/eB/joX7lrupPr2mCNHjqB///7o378/AGDOnDno378/XnvtNQDApEmTsGTJEsyfPx/9+vVDYmIiEhISEBERoeawNeeXH2kkq7zGiD+tPozs0st4dVwv/HFg+LW/yQXcSCt3xE5y2EkeW8lhJ3lsJcddOnl66PG/U/pjZI+O+DL1PP7x75O4ng0lWu+kqe0xrkKt7TFmsxmenp5SL+lU1BoxZdVhnCquwt/u+R2eHnmzA0apDdfbyl2xkxx2ksdWcthJHlvJcbdO9SYL4tYm43BOOf488mb8ZUwPqXmr1Ul23aj6M+3UcmT/ZXjZYMa0dSk4VVyFubHd3WrB3kCr/4rWGnaSw07y2EoOO8ljKznu1MnXywOr4waiX3hbLN97Fv/c+aP0M+5a7sRFu4swm83YuXPnNU+2epMFT244gmMFFfjzyJsxa/StDhqhdsi2cnfsJIed5LGVHHaSx1Zy3LFTgK8XNkwfjL7hbbFsTzaW7s6+5vdovRO3x9iBGttjZNSbLJj5SSr2nvkJU4dEYP4Dt7nFy2RERETknirrTHh41SGcKKrCa+N64fHbI9UeUiPcHuNmhBCoqqq66ss/9SYLnv55wT5xQBe8Md59F+zXakVXsJMcdpLHVnLYSR5byXHnToF+Xtjw+GDc3LEV5m8/ic0p+Vc9VuuduGh3EWazGfv372/yJR2TRcGsz9Kw5+cF+418BJIraa4V/Rc7yWEneWwlh53ksZUcd+/UvrUPPp0xBOFBfnhxSwb+L/V8k8dpvRO3x9iBlrbH/PKXDTzYPwz/nNjXrRfsRERE5J4KymsxeeUhFFXWYcmkfnigX5jaQwLA7TFuR1EUlJeXQ1H++6t7hRB4+atMbE0rxF09g7HoD+79DHuDplpRY+wkh53ksZUcdpLHVnLY6YrwIH9senIIQtr4Ys4Xx/GfUxdsbtd6Jy7aXYTFYkFKSgosFguAKwv2N7adxOfJ+bjj1g5Y9nB/eHnw4QYat6KmsZMcdpLHVnLYSR5byWGn/woP8sfG6TEI9PPCnz89iqSzZdbbtN6J22PsQO3tMUIILPruDD7cexaDI4Ow/rHB8PP2cPg4iIiIiLQos7ASU1YdgtkisGH6YAzqFqTaWLg9xs0oioLS0lIoioKlu7Px4d6z6N+1LdZOG8QF+6/8shVdHTvJYSd5bCWHneSxlRx2aiwqLBDrHx8MvQ54bF0KjhVUaL4TF+0uQlEUZGZmYmXiWSze9SNuC22Djx8bjNY+nmoPTXMaWmn1P0qtYCc57CSPreSwkzy2ksNOTYvu2g7rHhsMs6Lg0TWHkVlYoelO3B5jB2ptj9l4MBevfn0C3YNbY9OTQxHUytth901ERETkjA5kleHx9Slo7eOJzU8Owa3BAQ69f26PcTNfHsnHq1+fQGSHVvhkRgwX7M1QFAWFhYWa/Ze0VrCTHHaSx1Zy2EkeW8lhp+bdfmsHfPinaFTVmTD5oyTk/FSt9pCaxEW7i4gI8kdEGz02PDYQnQJ81R6OpimKgrNnz/Ivr2tgJznsJI+t5LCTPLaSw07XdmfPYLz/xz7o4CvQ1k+bW4u5PcYO1NoeoyiCn8NOREREdIPUWEtxe4ybURQFBQX5/Fe0BEVRkJeXx1bXwE5y2EkeW8lhJ3lsJYed5Gh9LcVFu4vgfjV5bCWHneSwkzy2ksNO8thKDjvJ0Xonbo+xA7V/uRIREREROQduj3EzFosF2dnZmv3Vu1rCVnLYSQ47yWMrOewkj63ksJMcrXfiot1FCCFw6dIl8IWTa2MrOewkh53ksZUcdpLHVnLYSY7WO3F7jB1wewwRERERyeD2GDdjsVhw+vRpzb6koyVsJYed5LCTPLaSw07y2EoOO8nReicu2l1IXV2d2kNwGmwlh53ksJM8tpLDTvLYSg47ydFyJ26PsQNujyEiIiIiGdwe42YsFgsyMzM1+5KOlrCVHHaSw07y2EoOO8ljKznsJEfrnbhoJyIiIiLSOG6PsQNujyEiIiIiGbLrRk8HjsltNPw7qKqqymH32fCSTlRUFDw8PBx2v86IreSwkxx2ksdWcthJHlvJYSc5anVqWC9e63l0LtrtoLq6GgAQHh6u8kiIiIiIyBlUV1cjMDDwqrdze4wdKIqCoqIiBAQEQKfTOeQ+q6qqEB4ejoKCAm7JuQa2ksNOcthJHlvJYSd5bCWHneSo1UkIgerqaoSGhkKvv/rbTflMux3o9Xp06dJFlftu06YN/4OUxFZy2EkOO8ljKznsJI+t5LCTHDU6NfcMewN+egwRERERkcZx0U5EREREpHFctLsIHx8fzJs3Dz4+PmoPRfPYSg47yWEneWwlh53ksZUcdpKj9U58IyoRERERkcbxmXYiIiIiIo3jop2IiIiISOO4aCciIiIi0jgu2omIiIiINI6LdieTm5uL6dOnIzIyEn5+frj55psxb948GI1Gm+Py8/Nx//33o1WrVujQoQOee+65RsdkZGRgxIgR8PPzQ1hYGObPnw9Xel/yggULMGzYMPj7+6Nt27ZNHqPT6Rp9rVixwuYYduL5dDXdunVrdP68+OKLNsfItHMHy5cvR2RkJHx9fTFgwADs379f7SGp6vXXX2907oSEhFhvF0Lg9ddfR2hoKPz8/DBy5EicOHFCxRE7TmJiIu6//36EhoZCp9Phq6++srldpo3BYMCzzz6LDh06oFWrVhg/fjzOnz/vwFnY37U6TZs2rdE5NmTIEJtj3KHTwoULMWjQIAQEBKBTp06YMGECzpw5Y3OMs5xTXLQ7mdOnT0NRFHz00Uc4ceIE3n//faxYsQJ///vfrcdYLBbcd999qKmpwYEDB7Bp0yb861//Qnx8vPWYqqoq3H333QgNDUVKSgqWLl2K9957D4sXL1ZjWnZhNBoxceJEPP30080et27dOhQXF1u/4uLirLexE8+na5k/f77N+fPKK69Yb5Np5w42b96M2bNn4+WXX0ZaWhruuOMOjB07Fvn5+WoPTVW33XabzbmTkZFhvW3RokVYvHgxli1bhpSUFISEhODuu+9GdXW1iiN2jJqaGvTt2xfLli1r8naZNrNnz8bWrVuxadMmHDhwAJcvX8a4ceNgsVgcNQ27u1YnALjnnntszrGEhASb292h0759+/DMM8/g0KFD2LVrF8xmM2JjY1FTU2M9xmnOKUFOb9GiRSIyMtL654SEBKHX60VhYaH1us8//1z4+PiIyspKIYQQy5cvF4GBgaK+vt56zMKFC0VoaKhQFMVxg3eAdevWicDAwCZvAyC2bt161e9lJ55PzYmIiBDvv//+VW+XaecOBg8eLGbOnGlz3e9+9zvx4osvqjQi9c2bN0/07du3ydsURREhISHi7bfftl5XX18vAgMDxYoVKxw0Qm349d/RMm0qKiqEl5eX2LRpk/WYwsJCodfrxbfffuuwsTtSU/9fFhcXJx544IGrfo87dhJCiNLSUgFA7Nu3TwjhXOcUn2l3AZWVlQgKCrL++eDBg4iKikJoaKj1ujFjxsBgMCA1NdV6zIgRI2x+gcCYMWNQVFSE3Nxch41dC2bNmoUOHTpg0KBBWLFiBRRFsd7GTjyfruWdd95B+/bt0a9fPyxYsMBm64tMO1dnNBqRmpqK2NhYm+tjY2ORlJSk0qi0ISsrC6GhoYiMjMTkyZNx7tw5AEBOTg5KSkpsmvn4+GDEiBFu30ymTWpqKkwmk80xoaGhiIqKcrt+e/fuRadOndC9e3c88cQTKC0ttd7mrp0qKysBwLpucqZzytNh90R2cfbsWSxduhT//Oc/rdeVlJQgODjY5rh27drB29sbJSUl1mO6detmc0zD95SUlCAyMtK+A9eIf/zjH7jzzjvh5+eH//znP4iPj0dZWZl1iwM78XxqzvPPP4/o6Gi0a9cOycnJeOmll5CTk4PVq1cDkGvn6srKymCxWBp1CA4OdpsGTYmJicGGDRvQvXt3XLhwAW+++SaGDRuGEydOWLs01SwvL0+N4WqGTJuSkhJ4e3ujXbt2jY5xp3Nu7NixmDhxIiIiIpCTk4NXX30Vo0ePRmpqKnx8fNyykxACc+bMwe23346oqCgAznVO8Zl2jWjqTUm//jpy5IjN9xQVFeGee+7BxIkTMWPGDJvbdDpdo/sQQthc/+tjxM9vGmzqe7XiRjo155VXXsHQoUPRr18/xMfHY/78+Xj33XdtjmEn1z2fmnI97V544QWMGDECffr0wYwZM7BixQqsWbMGFy9etP48mXbuoKnzw90a/NLYsWPx+9//Hr1798Zdd92Ff//73wCA9evXW49hs6u7kTbu1m/SpEm47777EBUVhfvvvx87duzAjz/+aD3XrsaVO82aNQvp6en4/PPPG93mDOcUn2nXiFmzZmHy5MnNHvPLZzKLioowatQoDB06FCtXrrQ5LiQkBIcPH7a57tKlSzCZTNZ/SYaEhDT612HDy2a//temllxvp+s1ZMgQVFVV4cKFCwgODmYnuPb51JTf0q7hkxmys7PRvn17qXaurkOHDvDw8Gjy/HCXBjJatWqF3r17IysrCxMmTABw5dm9zp07W49hM1g/Yae5NiEhITAajbh06ZLNM6OlpaUYNmyYYwesIZ07d0ZERASysrIAuF+nZ599Ft988w0SExPRpUsX6/VOdU45bPc8tZjz58+LW2+9VUyePFmYzeZGtze8+a2oqMh63aZNmxq9cbBt27bCYDBYj3n77bdd8o2Dzb0R9deWLl0qfH19rW+oZCeeT9dj27ZtAoDIy8sTQsi1cweDBw8WTz/9tM11PXv2dOs3ov5afX29CAsLE2+88Yb1jXHvvPOO9XaDwcA3ogoh1abhTYObN2+2HlNUVOTSb7D8daemlJWVCR8fH7F+/XohhPt0UhRFPPPMMyI0NFT8+OOPTd7uLOcUF+1OprCwUNxyyy1i9OjR4vz586K4uNj61cBsNouoqChx5513iqNHj4rvv/9edOnSRcyaNct6TEVFhQgODhZTpkwRGRkZYsuWLaJNmzbivffeU2NadpGXlyfS0tLEG2+8IVq3bi3S0tJEWlqaqK6uFkII8c0334iVK1eKjIwMkZ2dLVatWiXatGkjnnvuOevPYCeeT1eTlJQkFi9eLNLS0sS5c+fE5s2bRWhoqBg/frz1GJl27mDTpk3Cy8tLrFmzRpw8eVLMnj1btGrVSuTm5qo9NNXEx8eLvXv3inPnzolDhw6JcePGiYCAAGuTt99+WwQGBootW7aIjIwMMWXKFNG5c2dRVVWl8sjtr7q62vr3EADrf2cN/xiWaTNz5kzRpUsX8f3334ujR4+K0aNHi759+zb5RJezaq5TdXW1iI+PF0lJSSInJ0fs2bNHDB06VISFhbldp6effloEBgaKvXv32qyZamtrrcc4yznFRbuTWbdunQDQ5Ncv5eXlifvuu0/4+fmJoKAgMWvWLJuP4xNCiPT0dHHHHXcIHx8fERISIl5//XWXelY0Li6uyU579uwRQgixY8cO0a9fP9G6dWvh7+8voqKixJIlS4TJZLL5Oe7eSQieT01JTU0VMTExIjAwUPj6+ooePXqIefPmiZqaGpvjZNq5gw8++EBEREQIb29vER0dbf24NXc1adIk0blzZ+Hl5SVCQ0PFQw89JE6cOGG9XVEUMW/ePBESEiJ8fHzE8OHDRUZGhoojdpw9e/Y0+XdSXFycEEKuTV1dnZg1a5YICgoSfn5+Yty4cSI/P1+F2dhPc51qa2tFbGys6Nixo/Dy8hJdu3YVcXFxjRq4Q6errZnWrVtnPcZZzindzxMiIiIiIiKN4qfHEBERERFpHBftREREREQax0U7EREREZHGcdFORERERKRxXLQTEREREWkcF+1ERERERBrHRTsRERERkcZx0U5EREREpHFctBMRERERaRwX7UREZHcjR47E7Nmz1R4GEZHT4qKdiIiIiEjjdEIIofYgiIjIdU2bNg3r16+3uS4nJwfdunVTZ0BERE6Ii3YiIrKryspKjB07FlFRUZg/fz4AoGPHjvDw8FB5ZEREzsNT7QEQEZFrCwwMhLe3N/z9/RESEqL2cIiInBL3tBMRERERaRwX7UREREREGsdFOxER2Z23tzcsFovawyAiclpctBMRkd1169YNhw8fRm5uLsrKyqAoitpDIiJyKly0ExGR3c2dOxceHh7o1asXOnbsiPz8fLWHRETkVPiRj0REREREGsdn2omIiIiINI6LdiIiIiIijeOinYiIiIhI47hoJyIiIiLSOC7aiYiIiIg0jot2IiIiIiKN46KdiIiIiEjjuGgnIiIiItI4LtqJiIiIiDSOi3YiIiIiIo3jop2IiIiISOP+P5XxzUeCD6wRAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 760x420 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 760x420 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 760x360 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage XIII: phase-zero refinement ===\n",
      "s0: 2.0\n",
      "mu (used): [1.0, 2.0, 2.0, 3.0]\n",
      "K_terms: 21   n_max: 187\n",
      "T_max: 200.000000000000   dt: 0.0500000000000000   samples: 8001\n",
      "abs threshold (adaptive): 1.000e-10\n",
      "phase-gradient threshold: 5.000\n",
      "candidates found (pre-refine): 0\n",
      "refined candidates: 0\n",
      "\n",
      "No candidates under the current thresholds. Try larger T_MAX and/or smaller DT_COARSE.\n",
      "\n",
      "Wrote:\n",
      " - fig_stageXIII_abs_with_candidates.png\n",
      " - fig_stageXIII_phase_unwrapped.png\n",
      " - fig_stageXIII_phase_gradient.png\n",
      " - stageXIII_zero_candidates.csv\n"
     ]
    }
   ],
   "source": [
    "# === Stage XIII: phase-zero refinement on Re s = s0 ==========================\n",
    "# Detect zeros of Λ(s) along the critical line via phase unwrapping + |Λ|-minima\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------- helpers (keep Sage Integer out of pandas/mpmath) ----------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except Exception: return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "# ---------- load s0 and μ (same conventions as Stage XII) ----------\n",
    "coeff_path = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "summaryXI  = Path(\"stageXI_summary.json\")\n",
    "summaryX   = Path(\"stageX_summary.json\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "# s0\n",
    "s0 = mp.mpf('2.0')\n",
    "if summaryX.exists() and summaryX.stat().st_size > 0:\n",
    "    try:\n",
    "        JX = json.load(open(summaryX))\n",
    "        if \"s0\" in JX: s0 = mpf_safe(JX[\"s0\"])\n",
    "        elif \"central_point_guess\" in JX: s0 = mpf_safe(JX[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "# μ shifts: base [0,1,1,2], uniform δ≈1 from Stage XI → [1,2,2,3]\n",
    "MU_BASE = [0,1,1,2]\n",
    "delta_uniform = 1.0\n",
    "if summaryXI.exists() and summaryXI.stat().st_size > 0:\n",
    "    try:\n",
    "        JXI = json.load(open(summaryXI))\n",
    "        if \"uniform_shift\" in JXI and \"delta_min_residual\" in JXI[\"uniform_shift\"]:\n",
    "            delta_uniform = float(JXI[\"uniform_shift\"][\"delta_min_residual\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "MU = [m + delta_uniform for m in MU_BASE]\n",
    "# ---------- coefficients (same as before) ----------\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "K = min(len(N_all), 8000)\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "# ---------- Λ(s) machinery (same core as Stages X–XII) ----------\n",
    "mp.mp.dps = 100\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# Q choice doesn’t affect zero locations; keep a small fixed value for consistency\n",
    "Q_plot = mp.e**(-4)\n",
    "# ---------- scan settings (taller & denser than Stage XII) ----------\n",
    "T_MAX     = 200.0   # try 200 first; increase to 400/600 if you want more\n",
    "DT_COARSE = 0.05    # 0.05 gives ~8001 samples at ±200; decrease for more detail\n",
    "Ncut = to_int(n[-1])\n",
    "t_vals = np.arange(-T_MAX, T_MAX + 1e-12, DT_COARSE, dtype=float)\n",
    "# ---------- evaluate along Re s = s0 ----------\n",
    "vals_complex = []\n",
    "vals_abs = []\n",
    "vals_arg = []\n",
    "for t in t_vals:\n",
    "    s = s0 + 1j*mp.mpf(t)\n",
    "    z = Lambda_of_s(s, Q_plot, MU, Ncut)\n",
    "    vals_complex.append(complex(z.real, z.imag))\n",
    "    av = abs(z)\n",
    "    vals_abs.append(to_float(av))\n",
    "    # arg in (-π, π]; we’ll unwrap later\n",
    "    vals_arg.append(float(mp.arg(z)))\n",
    "vals_complex = np.array(vals_complex, dtype=complex)\n",
    "vals_abs = np.array(vals_abs, dtype=float)\n",
    "vals_arg = np.array(vals_arg, dtype=float)\n",
    "arg_unwrapped = np.unwrap(vals_arg)\n",
    "# ---------- candidate detection ----------\n",
    "# Threshold: small absolute value + nearby big slope of the phase (phase “jump”)\n",
    "# Build an adaptive magnitude threshold (robust to scaling):\n",
    "abs_med = np.median(vals_abs)\n",
    "abs_min = float(vals_abs.min())\n",
    "th_abs  = max(1e-10, min(abs_med*1e-2, abs_min*10.0))  # generous but safe\n",
    "# Phase-variation proxy: look at derivative of unwrapped arg\n",
    "darg = np.gradient(arg_unwrapped, DT_COARSE)\n",
    "# Big change near a zero: |darg| typically spikes\n",
    "th_darg = max(5.0, np.percentile(np.abs(darg), 95))  # radians per unit t\n",
    "candidates_idx = []\n",
    "for i in range(2, len(t_vals)-2):\n",
    "    # local minimum in |Λ|\n",
    "    if vals_abs[i] < vals_abs[i-1] and vals_abs[i] <= vals_abs[i+1]:\n",
    "        if vals_abs[i] < th_abs or (np.abs(darg[i]) > th_darg and vals_abs[i] < 10*th_abs):\n",
    "            candidates_idx.append(i)\n",
    "# de-duplicate nearby candidates (cluster within ~3 steps)\n",
    "merged = []\n",
    "for i in candidates_idx:\n",
    "    if not merged or (i - merged[-1]) > 3:\n",
    "        merged.append(i)\n",
    "candidates_idx = merged\n",
    "# ---------- refine each candidate with a tiny quadratic fit ----------\n",
    "def refine_min(t0_index, window=5):\n",
    "    i0 = int(t0_index)\n",
    "    i1 = max(0, i0 - window)\n",
    "    i2 = min(len(t_vals)-1, i0 + window)\n",
    "    ts = t_vals[i1:i2+1]\n",
    "    ys = vals_abs[i1:i2+1]\n",
    "    if len(ts) < 3:\n",
    "        return t_vals[i0], vals_abs[i0]\n",
    "    # quadratic fit y ~ a t^2 + b t + c\n",
    "    p = np.polyfit(ts, ys, 2)\n",
    "    a, b, c = p\n",
    "    if a <= 0:\n",
    "        # fallback: take local minimum point\n",
    "        j = i1 + int(np.argmin(ys))\n",
    "        return t_vals[j], vals_abs[j]\n",
    "    t_star = -b / (2*a)\n",
    "    # clamp to window\n",
    "    t_star = float(np.clip(t_star, ts[0], ts[-1]))\n",
    "    # evaluate |Λ| at refined t\n",
    "    z = Lambda_of_s(s0 + 1j*mp.mpf(t_star), Q_plot, MU, Ncut)\n",
    "    return t_star, float(abs(z))\n",
    "refined = []\n",
    "for i in candidates_idx:\n",
    "    t_ref, abs_ref = refine_min(i, window=4)\n",
    "    z_ref = Lambda_of_s(s0 + 1j*mp.mpf(t_ref), Q_plot, MU, Ncut)\n",
    "    refined.append({\n",
    "        \"t\": t_ref,\n",
    "        \"|Lambda|\": abs_ref,\n",
    "        \"Re(Lambda)\": float(z_ref.real),\n",
    "        \"Im(Lambda)\": float(z_ref.imag),\n",
    "        \"arg_unwrapped\": float(mp.arg(z_ref))  # local phase (wrapped at point)\n",
    "    })\n",
    "# Sort by |Λ|\n",
    "refined.sort(key=lambda r: r[\"|Lambda|\"])\n",
    "# ---------- save results ----------\n",
    "zero_df = pd.DataFrame(refined)\n",
    "zero_df.to_csv(\"stageXIII_zero_candidates.csv\", index=False)\n",
    "# ---------- plots ----------\n",
    "# 1) |Λ| with candidates marked\n",
    "plt.figure(figsize=(7.6, 4.2))\n",
    "plt.plot(t_vals, vals_abs, lw=1.2, label=\"|Λ(s0 + it)|\")\n",
    "if len(refined):\n",
    "    plt.scatter([r[\"t\"] for r in refined], [r[\"|Lambda|\"] for r in refined],\n",
    "                s=30, marker='o', label=\"candidates\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"|Λ| (log scale)\")\n",
    "plt.title(\"Stage XIII: |Λ(s)| on Re s = s0 with refined candidates\")\n",
    "plt.grid(True, which='both', ls=':')\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"fig_stageXIII_abs_with_candidates.png\", dpi=150)\n",
    "plt.show()\n",
    "# 2) Unwrapped phase\n",
    "plt.figure(figsize=(7.6, 4.2))\n",
    "plt.plot(t_vals, arg_unwrapped, lw=1.0, label=\"arg Λ (unwrapped)\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"arg Λ\")\n",
    "plt.title(\"Stage XIII: unwrapped phase along Re s = s0\")\n",
    "plt.grid(True, ls=':')\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"fig_stageXIII_phase_unwrapped.png\", dpi=150)\n",
    "plt.show()\n",
    "# 3) d(arg)/dt (to visualize spikes)\n",
    "plt.figure(figsize=(7.6, 3.6))\n",
    "plt.plot(t_vals, darg, lw=0.9)\n",
    "plt.axhline(th_darg, color='orange', ls='--', label=\"threshold\")\n",
    "plt.axhline(-th_darg, color='orange', ls='--')\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"d/dt arg Λ\")\n",
    "plt.title(\"Stage XIII: phase gradient along Re s = s0\")\n",
    "plt.grid(True, ls=':')\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"fig_stageXIII_phase_gradient.png\", dpi=150)\n",
    "plt.show()\n",
    "# ---------- console summary ----------\n",
    "print(\"=== Stage XIII: phase-zero refinement ===\")\n",
    "print(f\"s0: {float(s0)}\")\n",
    "print(f\"mu (used): {MU}\")\n",
    "print(f\"K_terms: {len(n)}   n_max: {int(n[-1])}\")\n",
    "print(f\"T_max: {T_MAX}   dt: {DT_COARSE}   samples: {len(t_vals)}\")\n",
    "print(f\"abs threshold (adaptive): {th_abs:.3e}\")\n",
    "print(f\"phase-gradient threshold: {th_darg:.3f}\")\n",
    "print(f\"candidates found (pre-refine): {len(candidates_idx)}\")\n",
    "print(f\"refined candidates: {len(refined)}\\n\")\n",
    "if len(refined):\n",
    "    display(head_safe(zero_df, 15))\n",
    "else:\n",
    "    print(\"No candidates under the current thresholds. Try larger T_MAX and/or smaller DT_COARSE.\")\n",
    "print(\"\\nWrote:\")\n",
    "print(\" - fig_stageXIII_abs_with_candidates.png\")\n",
    "print(\" - fig_stageXIII_phase_unwrapped.png\")\n",
    "print(\" - fig_stageXIII_phase_gradient.png\")\n",
    "print(\" - stageXIII_zero_candidates.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "176727",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x420 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AkZGRePnllxvNLfcWHh6OIUOGtPivf//+za5HIBDgzz//xNVXX4033ngDw4YNQ0hICB577DEuncP9ntXfDwBQU1MDgUAAf3//Zp+HkI5AOcaEtCOJRIKXX34Z77zzDk6fPt1i+2+//RYJCQlYt24dr3fEYrHw2gUFBcFut6OmpoYXVJWVlfHaBQQEcL1ijz76aKPPmZCQ0OJ2/etf/0JNTQ127NiBfv364eeff8bixYtx9dVXIzo6mtc2OjoaM2fOxJo1a7By5UqsXr2ayyu9VHa7HdXV1byAw/1a2xKEuH377be455578Nprr/GWV1VV8U6+YrEYixcvxuLFi6HRaLBjxw688MILuPrqq1FYWHjZ729r96O3+r1mWq0Wv//+O15++WU899xz3HJ3vnr952ts3c09n5t7ENqWLVsavd+7l76jtHa/1RcQEAChUIjS0tIG97kH1LnzsFvL/bkrLy9HVFQUt9z9WW2tkJAQjBgxAgA7TqFfv36YPHkynnzySW7QaHBwMBQKBW/woreWtn3QoEH4/vvvwTAMTp48iS+//BLLly+HQqHgfWbqW758OZYtW9bia4iLi2ux5F5cXBz3YzorKws//PADli5dCqvVio8++ghJSUlQKBSNDqQ8deoUkpOTKb+YdAnqMSbkEjV20gXAXeJ190wBTfecCQQCSKVSXvBTVlbWoCrF5MmTAaBBfeTvv/+ed1upVGLq1KnIyMhAWloaRowY0eBfS4Hlr7/+im+//RavvPIK+vXrBwD45JNPIBQK8cADDzT6mIULF6K2thYvvfQSjh8/jgULFlz2ZdDvvvuOd9s9YOxSJqEQCARcD6Dbpk2bUFxc3ORj/P39ccstt+DRRx9FTU0N8vLyLvv9be1+bOm1MAzT4PV89tlnDSZbmTp1Kv78809exQOHw9Hg+RszZ84cVFdXw+FwNPo6mxv41pT6vbAtuZT9BgA+Pj4YPXo0NmzYwHsup9OJb7/9FtHR0UhNTW3Ttrt/6NV/73766SfY7fY2rcvbxIkTcc8992DTpk04ePAgAPa9z8nJQVBQUKPvvbuqTUsEAgEGDx6Md955B/7+/jh27Fiz7dsrlaK+1NRUvPjiixg0aBC3DWKxGNdddx02bNjAGxRYUFCAXbt24aabbmrTcxDSXqjHmJBL5O49ve6669C3b184nU4cP34cK1euhK+vL69Kg7sHZ926dUhMTIRcLsegQYMwZ84cbNiwAY888ghuueUWFBYW4pVXXkFERATv0uo111yD8ePHY8mSJdDpdBg+fDgOHjyIr7/+GgC/PNx7772HCRMmYOLEiXj44YcRHx+Puro6ZGdnY+PGjbxR9vVVVVXhwQcfxLhx47B48WJueVRUFN555x0sWLAAn3/+eYM0iblz5yI4OBhvvvkmRCIR5s+fz7s/Pz8fSUlJmD9/fqvyjKVSKVauXAm9Xo+RI0dyVSmuvfZaTJgwocXH1zdnzhx8+eWX6Nu3L9LS0nD06FG8+eabDXq/r7vuOgwcOBAjRoxASEgI8vPz8e677yIuLg4pKSkALu/9bct+bIparcakSZPw5ptvIjg4GPHx8dizZw8+//zzBr2oL774In777TdMmzYNL730EpRKJT744INWlfyaN28evvvuO8yaNQuPP/44Ro0aBYlEgqKiIuzatQvXX389brzxxhbX423gwIEA2B9aKpUKcrkcCQkJTf6YaO1+a8yKFSswY8YMTJ06FU899RSkUilWrVqF06dPY+3atW3+4TZgwADcfvvtWLlyJUQiEaZNm4YzZ85g5cqV8PPza9W+a8orr7yCdevW4T//+Q927NiBJ554AuvXr8ekSZPw5JNPIi0tDU6nEwUFBdi2bRuWLFmC0aNHN7qu33//HatWrcINN9yAxMREMAyDDRs2QKPRYMaMGc1uR2RkJO8H/aU6efIkFi1ahFtvvRUpKSmQSqXYuXMnTp48yeuxXrZsGUaOHIk5c+bgueeeg9lsxksvvYTg4OAGs4cS0mm6dOgfIT3YunXrmDvuuINJSUlhfH19GYlEwsTGxjJ33303c/bsWV7bvLw8ZubMmYxKpWowqvv1119n4uPjGZlMxvTr14/59NNPudHh3mpqapgFCxYw/v7+jFKpZGbMmMEcOnSo0QoOubm5zH333cdERUUxEomECQkJYcaNG8e8+uqrzb6mW2+9lVEqlUxWVlaj98+aNYtRq9VMQUFBg/uefPJJBgAza9asBve5qwa0ZuT+/PnzGR8fH+bkyZPMlClTGIVCwQQGBjIPP/wwo9freW3RxAQfcXFxvOeqra1lFi5cyISGhjJKpZKZMGECs3fv3gaVGFauXMmMGzeOCQ4OZqRSKRMbG8ssXLiQycvLa/B6LuX9ZZjW70f3Z6CysrLBOoqKipibb76ZCQgIYFQqFXPNNdcwp0+fbvC6GYYd/T9mzBhGJpMx4eHhzNNPP8188sknLValYBiGsdlszFtvvcUMHjyYkcvljK+vL9O3b1/mwQcfZC5cuMB7v2fPnt1gOxtb57vvvsskJCQwIpGoxUk5WrvfmprgY+/evcy0adMYHx8fRqFQMGPGjGE2btzIa+OuSlG/AsSuXbsaVNAwm83M4sWLmdDQUEYulzNjxoxhDh48yPj5+fGqZDSlqc8rwzDM008/zQBg9uzZwzAMw+j1eubFF19k+vTpw0ilUsbPz48ZNGgQ8+STT/KqjNR3/vx55vbbb2eSkpIYhULB+Pn5MaNGjWK+/PLLFrevvZSXlzP33nsv07dvX8bHx4fx9fVl0tLSmHfeeYex2+28tunp6cz06dMZpVLJqNVq5oYbbmCys7M7bVsJqU/AMAzTBfE4IaQdrFmzBnfeeSf279+PcePGdfXmtIt7770XP/30E/R6fVdvSqe5Evdjb3HgwAGMHz8e3333HVc5hRDSc1EqBSE9xNq1a1FcXIxBgwZBKBTi0KFDePPNNzFp0iQKpnoQ2o891/bt23Hw4EEMHz4cCoUCJ06cwOuvv46UlBTKiSXkCkGBMSE9hEqlwvfff49XX30VBoMBERERuPfee/Hqq6929aaRNqD92HOp1Wps27YN7777Lurq6hAcHIxrr70WK1asoAoKhFwhKJWCEEIIIYQQULk2QgghhBBCAFBgTAghhBBCCIBelmPsdDpRUlIClUpFc7ATQgghhPQCDMOgrq4OkZGRLdYc71WBcUlJCWJiYrp6MwghhBBCSCcrLCxscYKgXhUYq1QqAOwbo1arO+U5bTYbtm3bhpkzZ0IikXTKcxI+2gddj/ZB16N90PVoH3Q92gddryv2gU6nQ0xMDBcHNqdXBcbu9Am1Wt2pgbFSqYRaraYvYRehfdD1aB90PdoHXY/2QdejfdD1unIftCaNlgbfEUIIIYQQAgqMCSGEEEIIAUCBMSGEEEIIIQAoMCaEEEIIIQQABcaEEEIIIYQAoMCYEEIIIYQQABQYdwqNBdidVQmGYbp6UwghhBBCOp3J6sCW02WoM9u7elOaRYFxJ/jkvAgPfJOBrWfKu3pTCCGEEEI63ard2Xjo26N4fUtmV29Ksygw7mAWuxPFRrag9J/n2hYY51Tq8dz6k8itMnTEphFCCCGEtMmBnCq89OtpaE22Nj1uw7FiAMAPR4s7YrPaDQXGHaxMZ+b+1luavnxQZ7bhlg8P4JmfTnDL/vvHeXx/pBBP/3iiyccRQgghhHSWZ9efxNcH87F6fy4AwGxz4JYPD+CxtRnNpozq2hhIdxUKjDtYqcYTGFfrrU22+/NcBdLza/FDehGq9BYAwLazbA9zen5tx24kIYQQQkgLHE4GhTUmAMBRV2yy70IV0vNr8duJEuRXG5t8rPdszFZHh27mZaHAuIOVe/UYuwPexhRrTNzfeZQ6QQghhJBupsbg6eBzONne4cJaTzCcV914/MIwDEw2TzSs78bj7ygw7mA1Rs+lg0pXYFylt+Da9/bi/q/S4XR9sEq1nsC4os4Cu8PJW4/Z1o1/XhFCCCHkildR5+nscwfJlXWeTj93J5/ObMPc9/fhvi+PwOFkoDHaYHN40iwM3TirQtzVG3Clq/X6dVVntsNsc2DTyVKcK9XhXKkO6fm1GJUQiDKt58NWrjOjxshPu6issyAmUNlp200IIYQQ4q3CKwiu8urscyuuZQPjrafLcLJICwDIKKiFSi7hrUdvE6C7oh7jDlY/wK3SW5BTqedup+fXAABKvQLjyjpLg3xkd2/zqSIt7v/qCA5kV3XUJhNCCCGEYP3RIjy65hiqXTGId+9wjcEKp5PhLXMXHDhbquOWnSrW8nqage6dSkE9xh2spt71giq9lVd+7XQx+4vKu8e4Sm9pkI9coWNvv/L7WRzOq8HpYh0OvTC9ozabEEIIIb2Y1mTDUz+dAMMAMQFKPHdtX14Q7GQAjcnGddwBnljmbIknML5YaYC6QY9xB2/8ZaAe4w5W20hKxMVKT2B8pkQHi92Baq+Ui2q9tWGPcZ0ZTieDw3lsD3OZzswb2EcIIYQQ0l5OFGrgrr6WUcBWoKioF3dU6y2oqvPEK2VaMxiG4fUYX6zSo7x+jzGlUvRe7uR0H5kIAFBca0SJ10C7/Gojcir4ozir9BbeyE+Azeup/8E62oYyblnldfh4T06ztZQvlc3hxFM/nsBbW5ufzUZrsiG7oq7F9e29UIllG8/A0AHbSgghhLSHCp0ZyzaeaXESLoZhcKJQw1VxaIzF7sDj32fgf39eaO/NBMAGrKt2Z7epQ+14oYb7O6ucPXdX1ruaXaW3otrgWVaqNaOo1sSb9jmvyshd9Xarox7j3sudSpEa6guArUnMMIBKLkaknxwAsDurgveYKr21QU9zhY7f0wy0PjBmGAYLVh/Bij/O49O/Ll7S62jOsfxa/HS0CO/vav5L98+v0zHznb9a3O7n1p/C6v15WHu4oL03lRBCCGkX/92SidX78/Ds+pPNtltzuADXf7AfKzafa7LNrvOV+PV4Cd7engWduf2jxhd+PoU3tmRi+cazrX7MCa/AuNZog95ibxDgFtQYeNUmTDYHDuZUAwDC1WyMU6I1ochV0i01jI2FKDDupewOJ7SuD3iKKzA+4kqFSAj2Qf9IPwDAznNsYOz+EHn3GLuXVeotuFjVeGC8K7MCI17djhd+PtXorDOlWjNXQmXvhUoAQHaFHn+eK292lhqnk8Hb2zLx0Z6cZl+n9+x+TdVgttgd+Du3Bk4G2H62+amx3dvqHtFKCCGEdDfrjxUBAA7n1jTb7hNXh9Rn+3KbbFPkVQu4fieYN7PNgWd/OolvD+U3+5xmmwMbT5Rwg+Z2nmfjjE2nShs97xssdtzx6SFMeXMX8qoMbC93kYbXprDGyPUYB/lIAQAXytliAkqpCAFKNo/4z/PsOX5CSjBUMjEYxvMeDYxi4546SqXonWoMVjAMIACDZFdgXO76tRUf5IMBkWoAnpnt3LctdicKXSVP+oSrALC1AwtchbNn9A8DAJwp0cJsc+C1TedQpbdizd8F2HK6DACQW2XgcoK8A8xijQkmqwM3rdqPhV+lY3dWJf7KqsSUN3fh+3o9tH/n1uB/O7Px+h/nuUoadWYb3t6WyTsQeCfjF9Wa0Bjv1BCjtekUCe96zbZ6tZwJIYSQnqbW0PSst27eKQreebwbT5Tg078ucmkYv58sxbr0Qrz4y+kG613xxzlc+95eFNYY8fm+XPxrbQYe+vZog7TEStdcCbsyK7hz8//bmY0DOdXIqzbif39eQInWjCq9FWKhgOvlLawxcuf7vhFsbHKhgo0NApRShPspALAz+QJA/wg14oN9AAA6V2rFwEh3YNziW9JlKDDuQO4SbGoJEKaS8e5LDvXlAmFuWZgvfKRsLvIFVz4PFxjrLNw0jOOTghCiksHmYPDbiRLugwkAr/1xDieLNJjzv724cdUB/JxRhLMlnsC4XGfB0fxa7kO6N6sKK7dnIa/aiH//cpr3S/KM1+Pc1TP+b9M5/G9nNhasPgyta/KSinrlWwC253jhl0ew5XQpAP502BqvSU+yK/S8yzXe91nsFBgTQgjpORiGwf7sKl6HkVDo6R11B7irdmfj0TXHuKDVu737nHo0vxb/WpuB/9t8jkstdOf6AvySaDaHEx/vuYhzpTqs2p2NbWfYTrIjebU459XO/bhXN53DgtVHcM27f+FAdhU+3+dJs9xxrhzHXB12fcJVXMdeZlkdjK65nPuEsfGLO1YJ8pUiwpUeane9xrRoPy4wdhsUzQbGehuavWLdlSgw7kCpYSpseGg07k5xItJfzrsvKcQXA1yXFNySQ3wR5MsG0O6gOjWMDYyr9BZuqsWYQCVGxAUAAP77x3kAwNBYf0T4yVFYY8Lc9/fD4PrwfvpXLjLL+QPetp8t4/4+X6bDGVfQ63AyvCD3XKnnccUaExiGwaZTbKBrsDqwx5WW4f2FdlfX+PJAHv48X4GHvj3Gbb+bO3+6os6M6/7fPlz/wX4u8NaaPIGx3kyD7wghhHR/7oB33ZFC3PnZ3/jHxwcbDfxqjVZU6Mx4Y0smNp0sxa/HSwCwY4vc3Ofh30+WcMvcKYjFXldlM8vqGv07p8LAXZ0G2HRLbxkFGvyQXsg91x2f/Q2bg8HElGAE+kihM9vx6V42UE6L9kNsIBvcuqti+UhFiAlke4dLXLFKoI8U4X6eOEcoAPpHqpEQ5JmYTCwUYGCkH764ZxieHNR9Z/PtsYHxihUrIBAI8MQTT3T1pjRJIRVhUJQfUvwYLsfYLSXMF5F+cqjlnlLS/SLUCPaV8tuF+kIgYOsFnnd98GMClRjuCozdgejcwZF485bBkIrYXapyrfdsqQ5bz/Bzerd55fgeyKnmft2527udL/P8XVRrQmENf6TpEVc6BX+KSPbL6D2JSa2BX37OHRjvz67i5k53b5PGa9BhRwxAIIQQQi6Xs16FCXdHzmZXOuPFKgNyqwxwOhneebPWYMU5ryD2lKtTqLKRGeXc+bsAWyGCYRheLrJ377F3BYnDeTW8sT/u1Aa3D3fncD2/ga5c4RCVDCtuGoRpfUMBeFIwxyQGIdHV67vPNbFYuJ+c68RzC1RKeVfBB0b5QSkVIy7I02OcFOILhVSEiSnBiPYBBILumWfcIwPjI0eO4JNPPkFaWlpXb0qr+cjEiPJXcLeTQ3whEAi4D2GUvwL9I9QNPmxRAQoE+fCXRQcoMMwVGLtN7xuGCSnB2Pz4BLxxSxp2PzUFU/uE8Nq4b3vPslff2RIdDufWYOuZMl6KRonGhLOl/MFw7p5o71Gq7ioc3svya4z8HmNXm8wyz/ozXUG4xqvHuO4Seoz/vljNO8AQQgghzTldrOVSAlqr/vnJ3ZHjPbHFhQo96sx2Xpm2aoOVF9y6B6x7n7fcf2d7nYO1JpvrsZ4e41PFWqw/WoS8KgMvJbE+d6fa6IRAAIDVNX7n/gkJ2PzYRLxxcxo2PzYR0QFKbgwTAIiEAkxMCUFSKBvcujvAE4J9uMF3bmF+ckztEwqJiA12rx8SBQBcJx7gSaPo7nrczHd6vR533nknPv30U7z66qvNtrVYLLBYPB82nY79wNpsNthsndMb6X4em82GZ69OwSubzmPxjBQ4HHY4HMB/ZvVBnzBfXD0gFA6HHYFKz+wwUrEQaqkAUf5yLrCMDlBAImDQP8wHfcNVOF9Wh+l9QxChlsBmsyEuQI64gHAAwKyBYdiVyaY7xAcpMSzGj7vdlB+OFGLltkzUL7dYUmtCpqs3uU+YLzLL9bhQXger1cpPpdCbYbFYubQPACis1qNC5/kya0xW2Gw2lGo8B4cL5XWw2Wyo0XuC9jozu5/Y0bFa9AlTQeHKwW7MsQIN/vHpYSQGK7H18QmN7gPSNWgfdD3aB12P9kHXq78P9BY7bv7wACx2J46+MBVqhaTJx2qMNlTpLUgO9UVVnZF3X3WdCQEKEa8T6GJFHZKCFLx2FVoj8qs8AW9hjQFmi5W72gqwE3rV1Jm4Xl9/hQQakw0nC2p4k4GdKdFhyY8noJaLIZc0fW50u3ZgGP72Gjg/s38IgpQi3DgknHtPxiX4I9pfjiKNGTcMiYBKKkCMP79zLiZAAT8Zv181TCVFiI8Yq+cPR161EbcMi4LNZkOUnxR3j4nFrvMVuHt0NC/+6szvQVueS8B01+znJsyfPx+BgYF45513MGXKFAwZMgTvvvtuo22XLl2KZcuWNVi+Zs0aKJXKRh7R9TYXCLG1mP3ABcsZ/GeoAz/lCrG3jF2WFujEwj7srz2zHcipEyBFzaCxeNFsB5YeE8HkEOCaaAcilMDqLE/DGB8GhQb2110/fyfOaRpeQPARMzDYBZCLGKQFMjhcKcSMKCd2FAvAQIBlw+x4+Zjn91WwnMGj/R1Y5rXsxngHig0CHK70rH/laDs+PCdEto5dJhUyeGOUA7tKBfg1n91GARi8M8aB9CoBvs0WYXCgE/f1aXpA3tYiATYXso99bYQdPk0f3wghhBCUGoHXT7Dnq3/1tyO5iU5NJwO8kiFCrQV4Os0BJwO8dcpznnu0vwOBMgavZHiWTY5wYliQE++c9iy7NcGBbJ0AGdXsuU8IBkuHO/DSUU+bQBmDe1McePu0GGoJg2gfBmc1QkyLdGJniRAiARu2OZiGqQiDA504UcOuO9qHQZHB0+bZwXZsKhDidK0QUUoGT6U5IGwkm8FoB/LqBOjjx8CVnYn/pIugc5VYuzPZgf7+DP6d7tnmf/Z1YEBA9w0njUYj7rjjDmi1WqjV6mbb9qge4++//x7Hjh3DkSNHWtX++eefx+LFi7nbOp0OMTExmDlzZotvTHux2WzYvn07ZsyYAYmk5UjNebIUW388BQBIiwvFrFlDIT5bjr1rTwAAbpkwALNGxrT6+QeOrsPpEh2uS4tATqUBq7MOAmBn4rt+ZBze380m2D81dwQWfn2sweMfu6oPVmzJgtkhgFaoAqDHrHGDcW5HNopqTfBJGAIcO821t0KChLQRwLGj3LKAyERoq41Apae3euzk6fjfhSMA2F/dVqcAE6bNQOb+PCCfrfXIQIDJV83EujXHAdTgRI0Q11xzNW+Er7eTWzKBQra248BRE9HPVU6mrfuAtD/aB12P9kHXo33Q9ervgwM51cAJ9nwV138oZg2OaPRxOZUG1BzaDwAQRfZH/3AVcMpznuuXNgz+SgmQkc4tUwZGoP/QSOB0BrcsIiEVWVlVANjURCcECO83EjjqaWN0ihCWOhA4fQb9owPRP0KNswfyUQF/ADpEB/hgfHIg1hwu4m1jbKAC/5iUiBO/nAEALJjSD69sOs/df/f1V+NWuxNbzpRjSmowwtT8ogDN2Wc9gx+PFgMAHrxhKiL85HjzzC4u/fEf105GbGDrOhy74nvgzhhojR4TGBcWFuLxxx/Htm3bIJe3bmfKZDLIZLIGyyUSSacflFr7nKOSPHnBw+MDIZFIcO2gKMzP00BvceC2kXGQtOKSiduA6EAMiGbzilLCvQb6hatx97gEbD9XiUHRfpjWLxzjk4OwP7saw2L98fHdI5BfbcDwuACs2pMLrcmGTNdAgOQwPySH+qKo1oRDeRoAbHFvo9UBndmOnCp+LePyOisvdxgA9DaGNzgAACoNdtRZ+CNVzQ5wgwQAoNJoR3RA41++aoPnObQWR4P3uyv2O+GjfdD1aB90PdoHXc+9DzRmr/OL3tbkfsmu8qROFNSaER3IH1BvsDlhM/DPcxV6K/RW/lVOrcnOqxgBAKdK2BzgKH8FijUmmG1OnC5hz7cpYWqkhLMdeadd+cthfnK8ekMa5gyOQt9wNaav3I1aow2zBkVizpAorM8ogVouxl1j47nAODZQCV+lHL4A7hqb0Kr3yNuTM/pAa7JjQkowYoPZTqdhcQHYeb4CMrEQiaHqNg+m68zvQVuep8cExkePHkVFRQWGDx/OLXM4HPjrr7/w/vvvw2KxQCRqfcDYXUX5K/DvWf2QUViLu8bEAWBrIC67fuBlr1suEeGxaclYc7gQS2b2QZhajq1PTuLuX3XncGw4VoTZgyIQopIhxFV7OcJPziujFhukRHKIL3ZnVnJTP/YJV+FMsQ5WhxOHLrLL4oKUyK82okhjgq5eYJxbZeDqFCeF+CCn0oAyrZlXxxhgBzh45zBfrDRwgbHBYsd3f+djYkoI+kWoeeVu3FUwfjhSiDe3nsd1kQLMury3jxBCSA/3xf48fJohQlSaFiMSguvVD2Y7a/ZdqEJRrRH/GBnDBXveA+Eq6iy8cyLADo5zT42cEOyD3KrGz2mVegv3PP0i1DhXquNmsY0JVEBjtMJgdeCg6zyaHOrLVYVwC1fLIRQKMC4pGACw9p9jkJ5Xi1uGR0MuEWH9w+O4tv+e1Q//b+cFPHtN30t8x1iR/gp8cs8I3rIXZvUFwzC4c3Rct60wcSl6TGA8ffp0nDp1irdswYIF6Nu3L5599tkrIih2e2BSYoete/HMPlg8s0+j9/kpJFgwvuEvySh/BTeqNUApgZ9CgiRX+Tn39M3hajmq9VYU1Bi5YHlCcjDyqwtQojHB6gqCVTIx6ix2nHfVSA7ykSI+iA2MS7SmBgcbjdGGcl5grMekVLZX/eM9OfjfzmzEBObjr6en8gY9uP/+6mAeKvVW/JArxPNtfK8IIYRcORiGwYotWQAEeH9XDr6sFxhX1rFB672rD8PuZBDoI8XMAezAtPxqT49xY4GxxmjjKlMMjfFHbpUBFXVm1LoCY1+ZGHrXuc/JsDV9h8f58wLjIF+2Q8pQbeQC8eRQX+586xbhx79q3jdcjb7hjaeHPjApscNiiuRQFVYvGNUh6+5KPaZcm0qlwsCBA3n/fHx8EBQUhIEDL783lTQtwmtyEveEI8n1vqhhajnCXflKetdMPhOS2V+zlV4HkYQQ9pevu0ZymFrOFQUv05obHGyyK/S8UjcXqzzVLty1jwtrTCjWmBqdaOSM69KT3iagKaYJIaQX8y5VmutKjagfGJ8vreNq++/J8oyLyfeqtFRVZ2lQZ19rsqFUw65/cIw/BALA5mBw0VXTP9F17nOfw8LUciQGs+dR99XTEF8ZguuVbE0J80WQj5Q350FSCP/8S9pXjwmMSddxf3kBtmg30PCLGeWv4M16AwAjEwIhl3g+YmKhAPGuYt/uWXrC/eSIdNV3LvW67OQrYw8C3pOMAGwqBcAG397FzbMr9KjxmhykRm+F0cqvM+n9i58QQkjv4j01cpnODKeTQaXXlcZKrxlmAf6kGQU13j3GnnOVv6vEqsZk42aBiw1UcgGu+1xXPx0iwk+OuCD+eJnYQCWXwgiwk2+E+MogEAh4nVEpYRQYd6QeHRjv3r27yVJtpP1M7xcKsasSxFX92OLfgT5SbsYcAEgO80VUgKdeY4BSgmBfGW9Sk3A/OfcY71/N7stCpVoTN/NdfDB7wPCe+QdgUykYhsHJQg2v1vKx/Fp4Fx6sNlh5BzIAyHYF1Q4ng58zinhTaBJCCLmyHMipws7znplevQNji92J8jozv8dYZ0Ge1yC782V10FvsqKgz88aw2BwMCmrY84m7EoPOZEOZlk0tjPD3nNfcE2Ul1utMivRXIKFesBwbqOSuygJAnzAVl7s7axBbLSPYV4pBUT1jooyeqsfkGJOuExfkg+/uHw2tyYaxSUHc8rRoP+x2TRiSFuUHs1f1iCEx/gDYL3+OKyCN9FcgQMmfLSfcK5WiqNYEnWs2ofggH5wu1nEHleFxAcgoqEWJ1oyE5zc32MZjBRre7WqDpUEPsXs71h4uwIu/nIZKLsb+56ZBLeePVnU6GXy4JwfxQT6YndZ46R5CCCFdx+lk8MneiwhQSvCPkbEN7j9drMWdn/0NhgHWPjAGY5OCeFMxA+w5x3tsSp3FzrtK6XAymPbWblS4gufUMF9U6a2oMViR5eq0iQlU4mSRFqVaTz5xhJ/CVQrNM1tsapgvZGKh16BzXyQE+0AtF3PnvX6RaohFnkFs47zOt/eNT0CAUooBUWqIRT26T7Pbo3eXtMroxCBuEILbUzP7IDZQiQcnJSLIV4bRiUFQumYaudb167ZfhGdAQEKQD3fZyS3cT4ZIP7ZX2TuQdadcuA9aSSE+mNY3DPUNjGLX7x684FZjsKKgXmDsTr3YncnOG19ntuO34yUN1rn5dCne3JqJR9cc4x00W2K2OfDId0fx9cG8Vj/GW53ZBrPN0XJDQgjpZsw2Byz2th+/GIbBK7+fxau/n0Vb5hs7VlCL1/84j2fXn2p0OuefM4q5q4h/nC4FwO8xBtjqSN4zyQFAep6nQgQALigGgDlpkQh1pTq4e5rjXD3G7sFyvjIx1HJxgwFyEX4KXgpiUqgPBAIB5gyOBAD0DVchyl+BCcnBmNonBGnRfpg3yhPwC4UC3Dw8uslBdqT9UGBMLtnAKD/89cxUPD+rHwA2veL7f47BqjuH4dbh0QCAkfGBXPuhsf689AsACPdrmJuskokR7MtvF6KS4a1b07D0uv64aRg7B3tMoAKLpiYDAEyugDJMzR60qvVW5LsudQ2IZC9NZZazaRjeQfSvx4sbvK4jXlNmsikaDF79/Sxe/OUU7M0M4PsrqxKbT5XhpV/PcAHu5lOlmPnOHuy90PxU3FqjDZPe2IXZ/9sLZ/35uAkhpBvTmmwY/dqfuP2TQy22/eZgHma+s4cLUk8UafH5vlx8ti+XVxKtvmq9BQ9/exTfHmInccr0Cob3Z1fx2jIMgz9OlXK3j+TVwmR1IM+Vwtffnz2OnyzSgGEAoQCIdJ2HrK5j/MtzBkAlE0MmFuLRqUl469bBeHhKUoNJMdydOG4RfnIIBIIG57VwPzkvBWKU69z4n9n9seKmQVi9YCQAQCwSYvWCUfht0QRevjHpPJRKQdpVWrQ/0qL9uduTU0Nw9YAwGK0OzBkcidxKA699YrAP5BIRgnyk3C/3CH85AuoF0CG+MvgrpbjXVU7uiempCFZJUVPv135qmArlOgv0FjuXnzyjXxjOlNQhr9qIc6V13OUugD1gFtYYER2ggN3JQCIS8gZc5FYZkFOpx2f72Nn4JqWENOg5d/Me8VxUa0RyqApLfzuDijoLlm08ix2LJzf5vh3Jq0Gt0YZaow3FGhNiWjmDECGEdLXMsjpoTTYcK9CgWm9BkG/TAd1/fmVnZVu1Owf/7/ahvGoP58vqkOKVY+vth/Qi/HG6DH+cLsMNQ6OQU+F53NECDe4d72l7skjLDYRjt0+HYwW1cDKuEqEqE85qgAxXCl6gjwzhfnLuMVKxENP6hmLPM1MhEQmg8kq3c3e+uA2K5uf7ugeTe/cYi4QCBPvK8ODkRJwo0mBKn1CEugJshVSE20c1TAUhXYd6jEmHkoqF+PjuEfhm4Wj4ysRcuTY390HE+9d1hJ8CIfUOrPV/pccGKaGUihHhp4DEKycrKcSXGyiY4QpwR8T5Qylm4HAy+CG9EAD7a318Mpu/9fXBPNzy0UEMe2U7tp0pw1mvy23uYNrtgKtGM8D2Snx/uADbzpQBYINht6JaE+wOJ3cZrrmeEIDNiXZz14ZurTe2nMes9/byBpEQQkhbnSrSYuIbOxu9ktYc7zKb3h0E9blLeQLAmRI2/9b7uFWqNcHhZPD1wTzsOFvOe+zhXM+x92SRBjmVnmPqsfxafLb3IlL//QcWrTmGjSfYFLnZaRGI9JPDyQBrDhcAAPpHqBAoc2+Du2yojNc7GxeohFAoQKCPlBcUA0Coin8uSgzhpwi6B6F7pzzEBSohEgqQGOKLLU9MwnPXXt5kG6RjUWBMOpWvTMyVqBkS4w+RK4j1HrEbFaBAbP0yNkGN96CKhAJe72psoJJL13BPKhIbqESkkk1PcOf/Do8PwA1D2JSMT/fm4mh+LerMdvzzm6Pc7EUAkFdl4FWv+NsrzWJXZgWe23AKD357FMUaEwprPAFtqdbcYMrrOlfdS6eTwYe7c/DBrmwup847z622Xi94cxxOBqt25+BsqQ4/ZxS1+nGEEFLfx3/loLDGhMe/P96mx9UYGtaQN1rtWLbxDNYf9RyXimtNXo9h23nn8JZozNh7oRIv/XoG93+djjJXkG13OHEkz5MCl1Np4AXGxRoTXt10DlaHE7+fLOWu8F0/OBJD4wIAAJtOsqkVAyLVCJLx09XC1HJeYJxYrwOH39bTzl8pgUwsQkyA5xzUx9XjnRqm4sbcpEVTFYmehAJj0uleuX4gJqeGYPn1A7hl7ioWADtgL8JPwXtMXFDTByrvHK+4ICUvj1kuESJMJUO86+qcO313VHwgrhkYjgBl4/Onu3Oc86oNvFHK58t0XO/I3gtsXhvDAIdyqlGk8apzqbOgqJbf8+vuSdl8uhT/3XIeb27N5GYJ9A6GNfUmOWlOnVeR+Vpj6x9HCCH15VYZWm7UiBqD59hT7Rqw/PXBfKzen4clP57g0iW8r6ppjDZoTTZUeHUglGhMXC8u4BkofbpEx+ttPleq466s1U9tcBsc7Yer+oVhqNe5xb08iN/pizC1nNcTXH8CK2/enTju2sTedYX7R7I9xSKhAG/fNhhX9QvDkzNSm1wf6X4oMCadblJqCL66bxQvF3lm/zAopSKoZGJM7xsKkdBT0NxPIeEm/GiMd1A9NDaAl3aREOwLoVDADbYAAIEAGBEfAJVcgp8eHofHpqfgt0XjuYF8AHDH6DgAbDDrnXPMMMA/Pj6IXZkVOOzVe5xVUcfrMS6vM/N6RwBPisRfXrMp7c9hg2vvHmN34L3jbDk++SunwWA875Hb3pcw68wUGBNCOp7eYsd7Oy5wA+i8e4zdPcHexzn3DHL108SKao28HuNSrZlXOeLgxWp8eygft318kPe4necqwDBsj+2M/p5qRW/fNhif3jMCT1/dB1/cOxJCoQBDYwO4+0VCAUYnBEIlYdP83MLVct55ZHSCp0xafd69vwMi2b9vGRYNgYDtmPEOxK8ZGIHP5o9otmOHdD80+I50CzGBSuxYPBlCr9G8/57VDyv+OIfHpzf/a3v+2HhcqNBjZHwAAn2k6BOu4g7ESa5LYgkqYGCkGqdLdLhpaDSXN5YU4ovFrl/zUf4KbDlTBoVEhPsnJuDL/bnQme1cYffrh0Ti1+MlOF9WhwWrj/C24WheLS9IrdCZG/QYuwPlLK9JS9x/19YLjJ1OBo99nwGj1YHYQCWuGciWv0vPq8EDX6fj3nEJePyqFN5zak38mf4IIeRSWe1OSMVCLFpzDBfK9Vj7zzHc1bivD+bhnR1Z+ON0KbY8MYmfCuaapMk71eFofi3uGRvfsLOg1tQgx9i7ZOWvx0vwq1dJzVuGR+Ono0VcmlpyiC/mj43HrvOV6BOuwnWDIyERCXnB8uBoP/QNV+F8WR1uGxENlVwMoQCI8pMj11XSMznUF+OTg7FgfDzEQgEmJAc3+b6o5BI8fXUfbDldhvsmsIPBxyUH48/FkxHkI6Maw1cACoxJtxHpz0+fmNo3FFP7hrb4OD+lBP/v9qHc7f5etZOHuXoLhALg2/tGIL1Ah4mpjR/0gnxlvMoRCcE+OFHEDhAJV8uxbO4ABCil+PJAXoPHptero1yusyDQh19HuVRrAsMwvIF4F10nD+/qGhqjDdUGK4yuCVNOF+u4wPirg/moNdrwzo6sRgJj6jEmhFw6h9fVKY3JCqcT+N2Vm7vpVCnuHsNeSXOXRztfVgeHk+H9sK8xsPXYy3WegNddIaioQY+xiddjXKW38maY8/bwlCTcNz4BP3nlLCeH+iIlTIX9z01r8jWJRUL8+NBYHM6twcSUEIBhj6sDItVcYDwgUg2RUICXrxvQ5Hq8PTo1GY96XWEEGs5sR3ou+mlDrjgz+ochMdgHEX5yXOcqng4APjIxruofBplY1Kr1eE/X2T9SDX+lFEvnDsD/vILwq/rxA3fXWEKU68xcTrG717pEwy7zzpUr1ZrBMAxqjN49xlZu0AnA5jm7ZXkNBDRY7BQYE0LajfcxRGey8XKO87z+NnrNclqiMfF+2NcarLxcYgC4WKWH08lwV9Hc0yjnVhkaPW75KSQYk+ipgb9j8SQ8e01fhKhkCPaqWNQnvPHSbvWp5BJM7xfGS5+4d1wclFIRrh4QhvhgSnUgHhQYkyuOj0yMP5dMxr5np11WgXT3IAoAvMLscwZFYE5aBGIDlXj2mr68A7U7N61Kb0FhDXtyGBHHHuBLNCZuimv3rEpGqwNakw0ar8ErGqMNpVpPz0pBjeckU17nCZir9BZ+YGxsfTULQgipr9bIT+nyDngveqVGeKeJVeotvB/2NUYrd8zqE6aCRCSA2eZEscbEpVKMTmCPiRmF7JU2qVjIDWQD2IB30dQUBPtK8a9pyUgO9QTA3sflgVGXXu1hcLQfTr48Ex/dNfyS10GuTBQYkyuSQCDgSsFdqlmDIqCQiCASCjAnLYJbLhQK8P4dw/DXM1OREqZCitcI5mFxbAk6J8PWQAaA4a5yQSVaEzd16aAoPwS58vUKaoyo8+pFZgNjTwCcW2UAwzBsAO1VeaJBYOz195bTZXjmpxPcCHFCCPGWWVaHRWuOcYPdTFYHzDbPIGWtycarr+4+npmsDl5ecGWdBTV6fo+xeyByfLCSqxp0pkSHKtfxaHQi24Fwuph97hBfGS+VbkCkGhNSgpH+4gwsmdmHt923j4wBwHYu1K840VZikRACweWdJ8iVh3KMCWlCdIAS256cBIvd2Wz5nj7hKhy8yJZd6xehRqhKxgtsh7kC4zKtmauJnByqQkGNEdUGK28UNsCekLwfX2e2o9ZoQ0m9/LzKOit0XgPudGY7GIaBkwGeWJcBs82JIF8Znr2GiskTQviW/nYGBy9WI7OsDtsXT+b1FgPsccg737ewxgi7w4nCemkSxbUmGLxSK2qNVu5YFemvgEgowIUKPf66wA6IVkpFGODV6wsAoWoZ+oarsM+VuzyomZ7gawdF4Pd/TUC4n5wGupEOQZ8qQpoRE6hsNigGwPUmq2RijE8K5qb6BIAApQTxQUoIBYDNwXAz56WE+iLSVavZu24nwJ5YyrT8IDiv2tAgb6/awO8xdjgZ6C12lOvMXM9PRoFnUKDN4YTF7gAhpPcx2xy8Uo/uH/MXKvSwOZy8tAkA0BptvDJsdleOcH41/ziUVV7Hu11rtHGD7KL8FUh2DUrbdZ6tSRwbqER0AH+gdZhKjmsHhQNgJ4Ga2qf5QdcDo/x4KWyEtCfqMSbkMo2ID8TPj4yDv1KKAB8pwrzymmMDlRCLhAhTy1GqNXN1PFPDVIh2zZZ0qpitfBHoI0WNqxpFfg3/5JNfbUBVHf/EVa23Qldv4Er9NIzsCnbAjNXuxNz390FrsuGPxyfCXykFIaR3OFmkwe2fHMKUvqH44I5h0NabDKhUY+alaQFs+cfqehUicqsNvDEPAHDOdRXMTyGB1mSDw8lwV8Yi/BTcOA/3cSkmUAmVXMK1B4BwPzmGxwXi939NgJ9CggAfOj6RrkM9xoS0g6GxAVwVC+8JRlJc04NG+HmWSUQCJIb4cAPwTrpKwsUEKrmqFudL2ROLu6JFXpURF6s8g18AtsSbzlz/ZGbj9SxX6S2oM9twukSL82V1KNWaccjVU0QI6R1+O14Cg9WBTSdLYbE7GgS3xRpTo6kU9QPjvCoDV53C3zVrqDsVLMJPDh/XFMjukpSR/nKkhPIrR7grUkR55RS7p2AeGOWHmEAlCOlKFBgT0s68LxO6ayp7p2Mkh6ogEQkR4+oxdtcODVXJ4KdgTzYmV5H7Ma5BKvnVBpx1pVy4B/NV6S0Neox1JlvDiUW8RoMDwMVLnPaVENIzeR8T8quNrQqMdWbP4LvBrkFueVUGrnyku7KE1c6mbQX5Shv09Eb6K5AY4gPv8W3uY6H3MTE1rHVl1wjpDBQYE9LOrhkYDrFQAJnYMwPTMK9pSYfG+gNAg56RSD85ArxSHAQCYJTr5HO+rI67ZDkxhZ2ghO0x5s92V7/HGGAHx3iXf6s/iI8QcmXzrkdcpjU3DIxrTag1NLz6VOtKrxjDlVfT4GKlOzDmT5sc7CvjZsYDAKlIiGBfGeQSEfqGewbbDY72B8DOYgewPc3ex0dCuhoFxoS0s7ggH2x9chK2PTmJC36v6h8Gf6UEEpEANw9jTwjuVAq3cD8F/FyXJwG2hJH7MuT5sjpY7U5E+Su4HuMagyfH2N1LrTHZuDxmt2KNCSUaT96x++/3d17AE99nwGilqaQJuZLkVxuwYPVhbpa4Eq8fxmW6hoFxqdbTYxwXxB6zNEYrt2zuEHaipJNFWhRrTBAK0GBW0hBfGUJVnpSxxBAfrmTmnaNjAQADo9ToF8Ee0yalhmDzYxPx26IJvIk3COlqNPiOkA6QVG960GBfGbY8PgkWuwNxrrqeSqkYkX5ylLgGpcQHKRHk4xm4Fx2gQEKwD2RiISyuy5XXD4nkemWq9J4c49hAJYpqTa4eY/YkOCBSjTMlOhRr+D3GxbUm6Mw2vLUtCwCbHz1/XHwHvAuEkK7wvz+zsSuzErsyK3FVv1DUeV1ZKteaucmHxiQG4tDFGhRrTNyA3MRgH+RXG5FfbYS7iEVqmApjE4O4ShYDo/wQF6iEWCiA3ZUKFqySQSoWYse5cgBAkleqxJ2jYzE01h/xQT68usH965VtI6Q7oJ9phHSScD85FxS7uVMlACAtxh/xQZ70iugAJRRSEe6bkACA7cl5YGIiV6aoSm+BzcGelNz5yt41RN2XOtlUCq8eY60Jp12VMADgeKGmvV4iIaQbcM8oBwB7sip595V69Ri7xzCw0zqz+cQJwWxAW+GaxEMtF0MiEuKFWf3gIxVBIAAempwEoVDAG2gc4SfnBboj4jzpEQKBAAMi/eAjo7440v3Rp5SQLrRgfAL2ZVdhcmooovwViPeaFtU9UvuZq/vgthExCFXJ4CMTc4Nd3ERCAcJdVS8ulOthczAQCwUYHheAL/bnorDGyEulqDPbcSDbU5nihFdgXKIxYfX+XNwwNAoDIi99ulVCSOf481w5jhdq8NDkJPjIxNCabFweMOCpH+xWWGPk0q3YwPgCSjRmSFyTZSSE8H+8u69QDYr2w/7npqHObOdSxFLDfLl1JYX4IjnUFwMi1WAYYO7gyA55vYR0NAqMCelCg2P8ceTfV3GXF0d79SC7e3MEAgFXCg4ApGIh1HIxN/AuQClFgCs32V0TOcJfzgXWFyr0MFr5E3v8cbqU+/tilQF1Zht8ZWIsWnMMxwo02HyqDH89M5XLEXQ6GWQUajAgUg25RNSu7wEhpGUVOjNqjFbeQLYKnRkPfnMUdieDKr0FK25K42oIu+3K5PcYp+fVwuFkIBULMcRVbcJkcyCnki2xlhTceGAMAP5KKa8G+tikIOzKrIRaLkZqmApSsRCbHpsIhmFoqmXSY1FgTEgX8z6BpISp8M4/BsPp5AfJ9QX5yrjAOFQl4y5pVrouf8YEKLlBNO6gWC4RIjHYF2dLdcip5JdsO1OiA8MAxwo0ANgBe6eLtVyZpg/35ODNrZmYnBqCr+4bdfkvmhDSamabA9d/sB9lOjM+nz8C0/qy1W72Xqjicnx/SC/CAxMTcb6s4RTzADA42g8nirRcKci4QCXkEhGCfWW8tKy4eoFxUDMzzN0zNh4OJzAiPoA3gI6CYtKTUY4xId3MjUOjcfPw6GZPLkFevTihahk3i55bXJASSqkYoV6z8EX6KRBVbyrWsa5e6dPFWqzanc27b39OFQCAYRh8sS8XAJuvqKlX75QQ0rFOFGpQqjWDYYA1fxdyy93fUYCth/7Ojgs455ocaGqfEN46Rifyy6u5xztE+XvyhMVCAcJUMqjknj4z74k46pNLRHh4ShJGxjf9I56QnoYCY0J6oGCvXpwwlZw3qQjgOenFew32i/RX8E5yCcE+GJ/Mnixf3XQOey9UQSwUYMH4eADAwRw2DzmjUINqgycYziyrg8nqwDeH8pFXZYDZ5sDzG07il4zi9n2RhPQyb23NxPKNZ+F0MjhRqMHPGUVwOhlkV3pmvdx7oRIGix0Mw3Df0Rdm9QUAbDxRgrWHCwAANwyNgljo+XGdFu0HtVfA676iFOHnOSZEBSggFgl5x4nmAmNCrkQUGBPSA6WGeUohJYX6wF8p4fXypLhKJXmXTEoJ88WgKM+AuhFxAQ0K6y+Z2Qf/GBkDgM1FtNqd2HyylNcms7wO7/15Af/55TQeXXMMvx0vwdrDhXhi3XFY7PxcZkJI61wor8P7u7Lxxf5c7M6qwD8+OYgn153AtrPluFDuCYwtdid2nCtHbpUBpVozpCIh7h4TzxvsJhYKMDk1hDeYt2+4ijdWobFZOd0/qL2PG/H1UisIudJRYExIDzTENXseAKRF+0MgEPDKI7kD3gnJwZ7HxPhjUmoIFK7Bc7PSIjAmMQhjEtnLoDcOjcKDkxKRGqpCoI8UJpsDPx0twvdH2Eu37sF82RV6rgTUmRIdDl30VLjIrTLAaLXjie8z8N6OCx3wygm5MjicDJ7fcBIr/jgHhmF4U7V/fTAfZhtbfWZ/dhU3MC7ElRr10Z6L2HyK/cE6Ij4ACqkIr944EMNcx4UF4+Phr5RywXJSiA+SQnwxwivlwZ3+4F0y0n0MSfP6AT04hqrTkN6FBt8R0gNNTg3FfeMTIBELuEF6D09JxvmyOtwwNAoBrhzkGf3DcO3AcNgcDK4eEA65RITfFo1HRZ0F411B87cLR0NjsiHIR8rlNY9NDMKmU6V44edTANiBO3eOjsMz60/iQrmemyAAADZ4pVDkVBiQnleLX46XAACuHhjGjaLXWIDbPzuMqX3D8OjU5A5+hwjpHhiGweIfTsBkdeCdWwdyy4/m12LtYfZH53Vpkbzv1G6vShJZ5XVc3eFXrh+I5zacxLlSHc6VsoPsprhyidVyCX56aBwq9RZuMO7DU5KQHOqLobHsj+d7x8XjeKEGoxICEetKpRiXFIQpfUJQqjFzV4tuHx2Lc6U6jE4M4s1mR0hvQIExIT2QSCjAS9f15y0blRCIg89P5y2TioX48K7hvGUpYSqkhKm422KRkJezDAAPTErE1jNlsDsZjIoPxCf3DEeuq0froFcPcX0FNUbkefV87btQxQXGf1cKkF6oQXq+BvdPTIBM3HjZN6vdCYlIQCPbSY9gsTsgFgq50ob1HS/U4GfXj8d5I6O45Tu96gtnFGq4GSvryyjUcLXLxyYG4duFo/Hwd0dRWGNCsK8Utw6P4drWn3RDIhJi1qAI7nZMoBLrHx7HW79YJMSXC/iVZtRyCd6dN7TZ103IlYoCY0JIA0Ni/LHliUko1pgwITkYIqEAyaEtB6oFNQZkVXjqqB7Mqcb9ExMBAGVGz+Nzqwy8eqxuFToz5r6/H5H+cqx/eBwFx6Rb0xptmP72bkT6K/DLI+MhbCQ49p5sI6tcjzDX394Tb1wor2syMHYHxcG+MvgpJfBT+mHbE5Nx6GI1BkSpuatDhJD2QTnGhJBGJYf6YnJqCNcTppJLEO7VG+U9wt0tv9rIGyj0d24N7A72xF5u8gQNxa4goLDGiIwCz/S1ey9UoUxnxrECDTeNNcMwyCiohdFqb8dXR0jbVejMvOnU92VXoUpvxckiLZcHzDAM9mdXodZVycU9MxwA5FUbuGWZ5Z4fkNkV/PQkNx+p56pKn3DPgDiFVISpfUMpzYGQDkCBMSGk1bxHsN80LJr7e0Ak2/t7rKAWegsbwCokIugtdpwo0oJhGFRZPOsp1phgtNpxwwf7ceOqA0jPqwEAlGo9QUR+NRsofH+kEDeuOoAXfz7dYa+LkJY4nQxu+/ggrnt/H47ms5/XEq+g150H/MX+PNz52d945LtjADw/AgEgz/WZ/u0EO3BO5poUI7tCj8Ja9r5gXyl335Q+odxjU0I96U+EkI5DgTEhpNX6RXhOzrPTIvDg5ET0i1Bj2dwBAMCNpI/yV2B6P/ak/mN6IXRmOywOfo/xySItVx/ZnW/p7iUGgGoDG0l/uT8PAH+QHyGdrcpgQV61EQwD7LtQzS1zc/cMbzrJDjw9eLEadWYbr8e4oMYEJwP8cJT9LD93LVt/uKLOArPNCYEAeOOWNCSF+GDFTYN4FSFGxPNLKxJCOgblGBNCWu2uMXH45XgJ+oSpMCw2ACPjA/H8tezlY5lYCIsrHzIuSIl7xsbj95Ol+DmjGLMHhvHWU6I140KFJ+XifBl7Wdk7MK5xBc1mr9rIeosdvjI6bJHOV6HzBMHunuIavdVrmZn3P8BOhuMdGJdoTMjSClBUa4JKJsa8kbFYtTuHm8o90k+BaX3DuCmfq/UWfPd3AVRyMab35X+HCCEdo8f0GK9YsQIjR46ESqVCaGgobrjhBmRmZnb1ZhHSq8QF+eDIv6/Ct/eP5o3CFwgEiA1UerVTYmR8AFLDfGGxO/HJ3lzeeko0JmR75Vi68zO9L01Xu4IOk9UTGJd63Z9VXscFFIS0t/xqAy/v1/uzVl7HBr/eM0KWak2oM9tQpvMExufL6nifaScD7Chmvzez0yKgkIqQHOI9wQZ/avcgXxn2PD0Vv/9rIhTSxqu4EELaV48JjPfs2YNHH30Uhw4dwvbt22G32zFz5kwYDIaWH0wI6XDeJ/WkEF8IBALc7MpD3pvNXnp2T11dXGvi9RgX1hhhsTsa9Bg7nAwv+KhyBcvHCzW4+t2/cOtHB8AwTMe9KNIrVdSZMeOdvzDrvb3QmW3cMrcybWOBsZnLi3c7nFvDXUVJdM0gd0HHnnavc0++EeqZWS4uiGaZI6Sr9Zhrklu2bOHdXr16NUJDQ3H06FFMmjSpbSuzGwB7I7++BSJAJOe3a5IQEHvNId9UW7sNQqZer5bdCKCpk7kAECsvsa0JgLPpTRZ7HXTb0tZhBphmpvptS1uREnCX4HJYAKaZSgNtaqsABK7feQ4rwNg899ltEDFmdh8JJM23rU8oB4Sitrd12gCntZm2MkAovoS2dsDZTC+pUAoIJZfQ1gE4zU23FUgAkbTZtokBgEJghh0iDI7xBwDMSQvHu1uOc22mJwfhh/Ra6PRm5DkNkAicsDESOBngXIkWVnMdFK5drjdqUaurhZQxAQLAARGXd3wsrwZymFFeY0ZxZRWiA/k9bRCIAZGrNjPDAI6GI/49bdvwve+IY0SjbTvmGCFkLJ7vQWN66zGinvMleljtTljtTpzKr8T4JD/UaGuhELCfe53eAdgNMBg0EMIBJ0Qo1ZpQVKXh2gDA4exCKAQ2BPlK0T9UhLwqtq2/QoLRcSrAbkCfICH3mCEREs/n5Ao8RjTalnECjsZL1bW9bSu+9+7zgcMCSCTNt+XW23uOEZ0SR9Q/JzfXtjGXeoxoJQHTQ7tbsrOzkZKSglOnTmHgwIGNtrFYLLBYPF96nU6HmJgYaD8F1MqG7Z3h18Ix8VfutniDPwRNfFmcIZPgmLLD0/bXSAisVY22rRUmQzb3BCSuL6F4UwoExvxG2zLqfrBffcKz3q2DIdCda7ytMg722Z5pd0U7xkJYe7TxttJg2K8v8bTdfRWElX813lakhP0mjaft3ushLPuj0bYAYLvVc8AWHZwHYdGGptveWMt9AUSHF0KY/03TbecWAzJ2Vifhsccgyvmo6bazsgCfeLbtiecgynq76bYzMwA/drCY8MxyiM6+2mRb+/QDYAJHsG0zV0J08vmm207eDiZ0Mts2+0OIMh5vuu2EX8BEzAIACPK+hvjI/U23HbMGTMwtbNvCnyA+dEfTbUd+Bib+HrZt6WaI993QZFvH0PfgTH6YbVuxB+I9M5pum7YCzj5L2LY16RD/Oa7Jtl/Vzcdt8z+GWCQEtGcg2db0RAEfV96EdbZFuFhlxNKpctxbfVWTbb+umg3b0Pdwz5hYvP/HITypb/oHsTPubjhGfc7esBsg+bnpgUvO6JvgGPs9d1vyY9N1YTvqGOEMGA7HVQc9bTvgGGGz2WD5bTACnNmNt6VjBGdzzFY8sokNnH+ZuA1DtP9rsu3cC2/jpCkVEpEAX43ZjXF1bzbZdl7OazhkSMN1g8Lw7rADvfYY4ej/IpwDXmJvtHCMcKQuhnPw6+wNQx4km1Obbpv0EJzDXPvKUgnJb1FNtrXH3AlmzGrXDTpGuF2pcYROp0NwcDC0Wi3U6oY19L31mB5jbwzDYPHixZgwYUKTQTHA5iUvW7as1eutqKzA35s3c7dnOxxNvkE11dXY79X2GqsVsibaAsD27du5v2eYjGgkLgcA1NXpsctrvVONejS1C00mI7Z7tZ1k0qKpr7bVasUWr7bjTdUIbqKtw+HAZq+2o80VCG+iLQBe2xHmMjR9KAK2bt0Kh4D9NT3UUoTYZtru2LEDVgE7KjvNko+EZtru2rULJiE7OKW/9SJSmmm7d+9e1AnZA0of6wX0babt/v37oRGxFROSrecxoJm2h/4+hGoR+4s/wXYGac20TT+SjnLXhyvGdgLDmmmbkZGBklPsJybSnoGRzbQ9eeIECs+y+yPMno4xzbQ9c+YMcrPYtkGOU5jQTNvz584jO4dt6++4gMnNtB3hb8a2rewVHpWzANOaaSsTMggS6HERQuw4kYt7o5tpDODv42cRXHMaJ3Pq0NyHsqi4CBmuz6WIMWNOM+ssLS1Dutdn+Ppm2nbUMUKr1eIvr7Yddoxooh1Axwhvx05nAa61FZZWYEhTO8OLzcEgq7AS4/xbbhvnKMGZM733GHHhwgVk5rNtWzpGXMy9iLPFbFuFsxwzm2lbkJ+Pk2VsWymjxbXNtC0pLaFjBHpPHGE0NnNFoJ4e2WP86KOPYtOmTdi3bx+io5s+kzbVY1xVlt/4L4Y2XS4RspfmWmhrs9nw585dmD5zDtdj3GGXQBwm9lJTU3iXKtrStoddJnVa2UuPLjabDTt37sS0adPYfdBM24brlbOfiza37WGpFIyD3XdNtpWw7dvc1gm71YAtp0tRdfE07pwzDY98fwp/57KTeoxICMHIxDC8vSMbAjghF1jhr5RAY7QhRCXFE9OT8e9fzgJgUyluHJ6AV6/vjzs+P4zT+WUAgMenJ2Hh+Hj+NnSHVIpWHiMab9v+xwibzYY/t/2O6dOmeo5F9fXSY0R9y//IwzeH2ZJqtw0Nwf/NTcXdXxzBiSId1+b92wdj0doTsEECfx8FqvRWhPsKoDWY8NKcvvhkby7KtOz3758T47FoahL2X9Th7/Tj+NetV0EiAh0jgJbTI9rSthXfe+58MH0mJHLfZtt61ts7jhEAOiWOaHBObqZtoy7hGHFF9xj/61//wm+//Ya//vqr2aAYAGQyGWSyhr+/JAp/SBTNvzFsQ//Wb1hTbcU2OAUySCQSzwdA4td420bX25a2TZzseltb1GsrtsEhkLP7vcF6LmO9LbZtRTfTJbVVtNjq0tq2dhattrQFJFIZ5gxXYXN5NiQKf/SJicDui+zJbUh8GFJdU0MzEMLEyDE8Ihj7sqtQahCgwiyFifE8V7XBBolEgnKdlVteahBDovBvYSvaMG1ue3zvL7ttxxwjnAJZE9+DxtbbDb7LnXWMqKdc7znRluoZSBT+KNKLeJ/FC7UCmBg5ApQSRAUoUaW3okzPAJAjJjQMsaEG5GoqAQB9YiIhUfhjfKoPtNkZXucDOkawmrveejltG/neu88Hct963wM6RrBtO+H72ew5uWO2oVXHPJceU5WCYRgsWrQIGzZswM6dO5GQ0NxFM0JIdzWzP3tBTSAArh4QjiSvclUAMCyOvZBnczDIq3KlprhG9FfpLWAYhlcSq8JVRiu7Qo8bPtiPdUcKOvw1kCvLf7ecx4LVh7kKFOVepdkqdOxnzv05SwphP4tZrnKDAUopItT8IDAlzBezB0UAYKd1Hp/c1AVnQkh30y49xrW1tfj222/x+eef4/jx4+2xygYeffRRrFmzBr/++itUKhXKytjLqH5+flAoWvuLlxDS1YbHBeCbhaMgEQkxMMoPFrsDIqEADid7qW9QlB+UUhGMVgcyXcFHvwgVcqsMqKyzoNZog9XuuXznri/78Z4cHC/U4HihBreNiIGgjSORSe9ktjnw4e4cAMC6w4V4YFIiKrx+eJXpzNCZ7NxnbkCkH3IqDbhQzpYb9FdKEB/suQzsr5QgVCXDrSOi4a+UINJfAT9FW3qzCSFd6bJ6jHfs2IHbb78dkZGRePnllzF27Nj22q4GPvzwQ2i1WkyZMgURERHcv3Xr1nXYcxJCOsbElBCMSQwCAMjEIkT6e3rchsb6I0DJXtZ0Bx/9XOkWlXUW3oQJgKfH2HuGsaLapvMQP9qTg4lv7OR6/MiVa8vpUoz6vx3Yeb68yTa5VZ68zpxKPZxOT+8wAGhNNhTWsvmnarmYq8Xt3WM8OiGQaz8qPhACgQACgQAzB4RjYFQbLmMTQrpcmwPjgoICLFu2DPHx8bj22mtRV1eHr7/+GmVlZfjwww87YhsBsKkUjf279957O+w5CSGd495xbGrUvJExCPaVIdCHDYz1FjbXs18EGxhbHU4uIFHJ2QteFXVmMAzDC5i9g536Xv/jPAprTPj0r4vt/0JIt7L0t7OoqLPg2fWnmmyT7TXRzMVKA6pdE8sIBIBExF51OFmkBQCEqeUIUbE5ru6JO/yVUoxLDkLfcBXkEiEWjKc0P0J6slanUvzwww/4/PPPsWPHDgwcOBCPPfYY7rzzToSF0fzthJDLs3BCAuYOjkSwLxsQuwNjt6gABdRyMXRmO04Vs0FKWrQf9mdXw2xzQmO08XqJ86sNAEJwtkSHh749igXj47FgfAKXrgGA6wUkVy53Lro73YZhGDy7/iTOlOiw+t6RCFXLeYFxscaEctdjgn1lUEpFyK824mSRBgA/MHYLVcsgE4vwy6PjYbE54aektAlCerJW9xjPmzcPJSUlOHToEE6cOIHFixdTUEwIaTchKhmXF1w/MA5VyRDqGuDk7r1LCPaBr4z9bX+8UAO7V9CbW8UGvd8cykNBjRHLNp6F08lwM+cBgACUg9zb5Fcb8UN6Ec6U6PDTsSIAQHalJzAu05m5Kw/hajnC6n3mwtRyhPjyA+MIP7aNXCKioJiQK0CrA+P7778fhYWFmDNnDp588skOG2RHCCHunmOAHdUf6CPlApIThRoAQJS/EqGu3rvDeTW8x7M9xkBmmSePuKDGyPUcAoDG1ExNatLjeV8dAACnk0F+jecqwclCNtjN8eoxdjgZ7opEqErGBcZnS9n6xWFqWYMe43B1W8qSEUK6u1YHxp988glKS0vxxhtv4NixYxg2bBgGDRqElStXorS0tCO3kRDSy3iXcIsJVEIgECBUzQYk7p7hSH85gl1BSrorMPaRshOs5FUb4HAyOO8VGOdVG1Cl90ySUGtoZsIE0uPp6v3wqTVaUeyVbnOmVAuHk8HFevno6Xns5DPhfnKE1QuCw7x6kd2iAqgqEiFXkjYNvlMoFJg/fz727NmDzMxMzJ49G2+//TZiY2Nx7bXX4vvvv295JYQQ0oKUMBX3t3vgXXyQD69NpL+C6zE+4gpmpvQJBQAU1piQVV4Ho9Uze1Kp1szrMa4xWtEDJ/4krVRr5P/wqTZYUeSVV15YY8K5Uh2sdiekYiFGxrP1s9Pz2R9Zkf6KBkFwbJASPjIxlz4BAMmh/DrchJCe7ZLLtaWkpOD1119HYWEhNmzYAJlMhvnz57fnthFCeqm0aD/EBCogEABz0tiJEuoHIEkhvghV8QOXMYmBkIqEsDqc2HqmjHdfqcaEGq8cY6vdCZONDZwPXazGX1mVHfFSSCdxOhn8klHMDaarHxhX1VkalPHbdIq92pkY7MNNImNzsD+WIvzkvPrEAJDsupJxy3B21tWrB4RBJha18yshhHSly57gQygU4rrrrsN1112HioqK9tgmQkgvJxEJsf6hcajSW9E/ku0x7hPu6UUOUErYvON6l7qTQ1WICVQgp9KAjSdKePeVaM0IcvAH9dUabTBYHLj7879hczD4bdF4pEX7d8yLIh1q7ZEC/Pvn04gJVOCvp6ei1sBPpaiq12MMAL9mFANgr1Ak1puBMcJPgcQQT2AsELC9yADw5FWpmJwawn02CSFXjnadEjo0NLQ9V0cI6cVC1XJe4JES6ssFKtcMZKeVTghW8h6TFOLDpVzkVLK5o5NTQwAAJRpTg7ziWoMVh3NruF7CgznVHfBKSGfYk8n2+BfWmFCqNTfbYzwxhZ2iuUTLlmbrG65qMDV5UogPwtRyLpXnurRIiIRsJROhUIAR8YFQSttl8lhCSDdC32pCSI8gEAjw2T0jsPN8BW4dEQMAvFnFFBIRQlQyDIhU48/znqtXc9IisCerEiUaE5RS/mVvjdGGYo2nF9F7sB7pWQq8Kk5crDRAY+T3GJdqTdyMdjP7h2HvhSruvn4RKiSHeK5IuD9LAPDhncOw41w55o2K7cjNJ4R0E+3aY0wIIR0pMcQX909MhJ+CrRcb5a9Aiiv3eE5aBAQCAcYmBXPto/wV3NTTJVozryoFwA7AK24wMQjpaZxOhjfbYYnG1KDH+ISrFrFCIsKM/uG8+0bGByI2SIn+rt7h2a7PEgDEB/vg/omJXM1sQsiVjb7phJAeSyAQ4OO7h2NXZiVuH8X2Io9KCMTgaD+cKNLiwcmJCPeTQyBgB9u5B2YF+0pRpbdCY7SiWGPm1pdXTbPh9UTFGhM3RTMAlOvMXJ3qcLUcZTozV/86OkCBcD85bhoWhQ3HinH3mDio5OwPrQ/vGobtZ8tx6/CYTn8NhJDugQJjQkiPlhjiyxs4JRIKsO7BsagxWLnBUmEqNjjSW+zsY4J9UaWvQa3Bxs10BgA1Biu0JhvXI016hhyv2esAoLzODI2rxzg51BdlOjMXOEe76g6/dctgPDIlGYlelSfigtjeYUJI79XmVIqAgAAEBgY2+BcUFISoqChMnjwZq1ev7ohtJYSQVpFLRFxQDLCTgXjrF8Hmk9YarSjR8kt4udMpDmRXYfzrO/HVgbyO3VjSZs9vOInpK3ej0JVXfLGSnwJTrrNwOcb1y/zFuQZnCoUCJIf6QiikqcEJIR5tDoxfeuklCIVCzJ49G8uWLcPSpUsxe/ZsCIVCPProo0hNTcXDDz+MTz/9tCO2lxBC2iwqwFO9wl8p4WYrK9eZuQCqj2tSEXeu6pcH8lCsMeHl387QRCDdSGGNEWsPFyKn0oA1hwsAeH7MuIPgCp0Zta79mlQvMI4J5FcyIYQQb21Opdi3bx9effVVPPTQQ7zlH3/8MbZt24b169cjLS0N//vf//DAAw+024YSQsilig/yBENR/gr4K9l6xpmuKhQysRBDYvyRWV7H9T56X54vqjVRQNVNnHQNogOA4wUaAECuKzd8TGIgsiv0KNWaIXb1BKeG+kIoAFwzifM+C4QQUl+be4y3bt2Kq666qsHy6dOnY+vWrQCAWbNm4eLFi5e/dYQQ0g6Gxvpzfw+IVCPAFRhfdPUOh/vJuRrJuVUGWO1OfvmvKqpW0V3keVUOyXb9eMlz7Z9xrooklXoLyl2l2SL8FLzpxGkCF0JIc9ocGAcGBmLjxo0Nlm/cuBGBgYEAAIPBAJVK1aANIYR0hVEJQQj0YYPhawaGI0DJH1wXppZzUwJfrNIjp1LPTfoBeAIv0vW8y7JV1llQrbdwM9oNiw2AXCIEwwAOVxdxqFqG2a5pxUcnBDaYLZEQQry1OZXiP//5Dx5++GHs2rULo0aNgkAgwOHDh7F582Z89NFHAIDt27dj8uTJ7b6xhBByKXxlYvz66HhU1JkxPC6wQRWDMLWcq2yRW2nAuVId7353MLY/uwrlOjNuHBrF1bklHcvmcGLN3wUYlRCIfhHqBj9SdmVWwskASqkIYWoZIv0VXDqMv1ICuUSEJ69KxaiEQAzymhCGEEIa0+bA+IEHHkD//v3x/vvvY8OGDWAYBn379sWePXswbtw4AMCSJUvafUMJIeRyxAQquTzhCD9+lYrYQAViA5UQCQUwWB3Yk8VOLywVC2G1O5FfbUCV3oL5XxyG3ckgwk+BsUlBnf4aeqPP9+Xi9T/OIzpAgb3PTOVSKfyVEmiMNmw5XQaArTYhEAgQ5RUYh6vZ/SwUCjAxJaRrXgAhpEdpUyqFzWbDggULEBERgbVr1+LYsWPIyMjA2rVruaCYEEK6O6VUjCivcm5JIb6QioWIcVWr+P1kKQDgmgHsDGn51UZkFGhgd12eP5pf08lb3HsdulgNgB0AmV9t5GYvnNEvDACw41w5AE8JPu9BkrE0YJIQ0kZtCowlEgl+/vnnjtoWQgjpNO7BdgDQzzUVsPt/d37qrEFsYFxYa8TJIg3XPt9VBWHN3wX49lB+Z2xur2G1O/HujizsOl8BACjTemYmdAfBfgoJRsQH8B7nns55iNfguv6R6g7eWkLIlabNg+9uvPFG/PLLLx2wKYQQ0nnmDo4EwNa+ddcwHh7nCbakIiGm9AmFVCyEzcFgX3YVd19+jRFFtUa88PMpvPjLaWSV13Xuxl/Bfj1ejHd3XMCD3x6F1e7kVaHYlckGy7GBSqSE8Qd4D3TlD0/pEwKlVAShgB1oSQghbdHmHOPk5GS88sorOHDgAIYPHw4fHx/e/Y899li7bRwhhHSUW4ZHIyHYBwnBPtzsZ2MSPXnDQ2L8IZeIEBuoRHaFHhmumrkAUFRjxIVyzwC+08VapIZRJZ72kF3Bvq9WuxMHL1bDbHNy9+3PZtMqYgOVGBCphlwihNnmhFDAVqQAgFC1HNuenASzzYHkUNonhJC2aXNg/Nlnn8Hf3x9Hjx7F0aNHefcJBAIKjAkhPYJAIMCI+EDesoFRfrh9VCx+ySjGomnJANgJIdzBmluZzoxzZZ7KFXnVRpD2UabzpE6484vriw5UQCYWYcmMPnhrWyaevroPpGLPBdDoAMotJoRcmjYHxrm5uR2xHYQQ0i2suGkQXrtxIFeOLS6If1VM4JpFbd8FT2pFZZ0ZpH2Uajzv5cEcNjB29wy7pbp6gh+YlIiFExK4Hn9CCLlcbc4xJoSQK513jWLvQXrJob5IctU7PpDj6c0s11k6b+OucCVaE/f38UINAGBCMr/UmvegOgqKCSHtqc09xgBQVFSE3377DQUFBbBarbz73n777XbZMEII6Q4medW/HRkfiFKtqUFqRbmOeozbg9PJNPpeJoX6IK/aF9kVekjFQsrnJoR0mDYHxn/++Sfmzp2LhIQEZGZmYuDAgcjLywPDMBg2bFhHbCMhhHSZmEAlHpuegr0XKvHQ5ER8trdhOhkFxu2jSm/hTcXtFumnwIuz++G/WzLx4KREiKiXmBDSQdocGD///PNYsmQJli9fDpVKhfXr1yM0NBR33nknrrnmmo7YRkII6VKLZ6Ri8YxUAEB0gGdiEJVMjDqLHVV6K0xWBzaeKEFquApDYvy7aEt7pu1ny+FkGIS5ZqpTSkUwWh3c/UkhvpiQEowpfUK7ahMJIb1Em3OMz507h/nz5wMAxGIxTCYTfH19sXz5cvz3v/9t9w0khJDuJD7Yk3M8OjEQMlc1hPf+vIBn1p/EXZ/9jTqzras2r8c5XazFA1+n48FvjmLHWXYCj77hKiilIq5NarhvV20eIaSXaXNg7OPjA4uFHWgSGRmJnJwc7r6qqqqmHkYIIVeEsUlBUEjYoG1yn1BEuqaW/jG9EACgt9ix0zVrG2mZezY7APjGNYtgpL8Cc9IiALBBcqhK3iXbRgjpfdqcSjFmzBjs378f/fv3x+zZs7FkyRKcOnUKGzZswJgxYzpiGwkhpNtQyyX4csFInC3V4R8jYrD5ZClyqwyoNngGIm89U4brh0R14Vb2HH9lVXJ/a01sT3tUgAKLpiYjLsiHZq8jhHSqNgfGb7/9NvR6dkT20qVLodfrsW7dOiQnJ+Odd95p9w0khJDuZnRiEEa7ZsmL8G/Ym7n5VBl+PV6M2YMiIBZRVczGWOwO/Ha8BMe8ZhR0i/JXQCWX4NGpyZ2/YYSQXq3NgXFiYiL3t1KpxKpVq9p1gwghpCfxnmVtYJQaVXVWlOnMePz748ivNuKx6SlduHXd16PfHcOOc2zKSZS/AhV1Zq4iRUwgzVxHCOka1JVBCCGXYahXBYrhsQGYNyqGu73+WFEXbFH3pzFauaAYAJ66OhX9I/242wO9/iaEkM50SRN8EEIIYY1ODESEnxwVdRbcPDwaadH+uGloNCa/tQv51UaU68xcGTLCOlZQCwCID1JiwyPjEegjhdnmxIlCDSamBCNEJeviLSSE9FYUGBNCyGVQSsXYvngydCYbV6EiNkiJfuFqnC3V4Wh+LWYNiujirexejuazgfHI+EAE+kgBALePisWYxCBE+NGPCEJI1+lxqRSrVq1CQkIC5HI5hg8fjr1793b1JhFCejlfmZgLit2GxfkDYKsuLFpzDM+tPwmns+Gsbr2FxmjFwi+PYOlvZ5DhGnA3NDaA1yYh2AdyiaiRRxNCSOdoc2C8fPlyGI3GBstNJhOWL1/eLhvVlHXr1uGJJ57Av//9b2RkZGDixIm49tprUVBQ0KHPSwghbTU8jg36vj9SiN9PluL7I4X460JlC4+6cq05XIA/z1fgywN5OJBTDQAYHEO5xISQ7qXNgfGyZcu4cm3ejEYjli1b1i4b1ZS3334bCxcuxP33349+/frh3XffRUxMDD788MMOfV5CCGmr4bGBDZbtz65CTqUeG44VwdELeo/1Fjt+OFIIrcmG9Lxa3n1yiRCpYaou2jJCCGlcm3OMGYaBQCBosPzEiRMIDGx4ImgvVqsVR48exXPPPcdbPnPmTBw4cKDRx1gsFm6WPgDQ6XQAAJvNBputc6ZsdT9PZz0faYj2QdfrjfsgXCVGuFqGMp3nGHS8UIM/z5XjYpURGoMFd4+J7bTt6Yp98PKvp7H+WAl2nCvD0fwa3n3jk4IApwM2p6PTtqer9cbvQXdD+6DrdcU+aMtzCRiGaVW3RUBAAAQCAbRaLdRqNS84djgc0Ov1eOihh/DBBx+0fYtboaSkBFFRUdi/fz/GjRvHLX/ttdfw1VdfITMzs8Fjli5d2mgv9po1a6BUUp1MQkjHOq8RYFeJAAMCGKzP4+fO9vVz4uH+zi7ass7xxEERGHjOFRIhg+vjnMjUCHBDvBPBNM6OENIJjEYj7rjjDi6GbU6re4zfffddMAyD++67D8uWLYOfnyc3TCqVIj4+HmPHjr30rW6l+r3VTfVgA8Dzzz+PxYsXc7d1Oh1iYmIwc+bMFt+Y9mKz2bB9+3bMmDEDEomkU56T8NE+6Hq9dR/MArAYgNPJYNuKXagz27n77FIVZs0a32nb0tn7wGR1gDn4J2/Z0NhArLhvZIc/d3fVW78H3Qntg67XFfvAnTHQGq0OjOfPnw8ASEhIwLhx4zr9AxUcHAyRSISysjLe8oqKCoSFhTX6GJlMBpmsYT1MiUTS6dvfFc9J+GgfdL3evA+GxQZgT5Zn8F2J1gyxWNzkD/uO0ln7IKfa1GDZ6MSgXrv/vfXm70F3Qfug63XmPmjL87Rq8J1Op+P+DR06FCaTibfM+19HkUqlGD58OLZv385bvn37dl5qBSGEdEdT+oTwbhutDtQar9w8x/zqhtWLpvYN7YItIYSQ1mtVj7G/v3+rezUcjo4bSLF48WLcfffdGDFiBMaOHYtPPvkEBQUFeOihhzrsOQkhpD3cOToOGqMNqWEqLN14BpV1FhTVGrkJLq40JRq2x/jqAWEYHOOPQKUUw+rVLSaEkO6mVYHxrl27uL/z8vLw3HPP4d577+Vyig8ePIivvvoKK1as6JitdPnHP/6B6upqLF++HKWlpRg4cCA2b96MuLi4Dn1eQgi5XFKxEE/OSAUAfLbvIirrLCiuNSEt2h+HLlZDIRFhcIx/127kZWAYBrsyKxAf5IPEEF+Uas0AgCh/JR6ZktzFW0cIIa3TqsB48uTJ3N/Lly/H22+/jdtvv51bNnfuXAwaNAiffPIJl4vcUR555BE88sgjHfochBDSkaIDlMgo0KCo1oQD2VW447O/IRIKsHHRBPSP7JyBwe3tx/QiPLP+JBQSEXY+NZnrMY70p9IThJCeo80TfBw8eBAjRoxosHzEiBE4fPhwu2wUIYRcyaID2Omji2qN+O1ECQDA4WSw6VRJV27WZdl4kt12k82B9UeLuB7jCD9Fcw8jhJBupc2BcUxMDD766KMGyz/++GPExMS0y0YRQsiVzBMYm7Ars4JbfqJQ21WbdFkYhsGxfM/Mdn9lVaHMHRhTjzEhpAdp88x377zzDm6++WZs3boVY8aMAQAcOnQIOTk5WL9+fbtvICGEXGmiA9gJhv48X8FbfrFS3xWbc9lqDFYYrJ6B14fzPLPcRftTjzEhpOdoc4/xrFmzkJWVhblz56KmpgbV1dW4/vrrkZWVhVmzZnXENhJCyBXF3WPsNiKOrdZQojXDYLE39pBuraiWzScOU8sQ5RUIq+RihKga1pInhJDuqtU9xp988gnmzp2L8PBwxMTE4LXXXuvI7SKEkCtWdIACUrEQVjs7JfSNw6KQXamHxmhDQY0R/SJ61gA8d2AcE6BEargKa/4uAACkhPp2+gQmhBByOVrdY7x27VrEx8dj9OjReO2113D27NmO3C5CCLliycQirpcYAGb0C0NcIJte0djEGN1dUS27zdEBClzVzzOJx5jEoK7aJEIIuSStDox37dqF0tJS/Otf/8Lx48cxduxYJCUlYfHixdi9ezecTmdHbichhFxRlszsgz5hKrwwqy9C1XLEBvkAAApqDF28ZW1XyAXGSkxODcVNQ6MwJjEQ946L79oNI4SQNmrT4LuAgADcdddduOuuu2C1WrFz50789ttvuPvuu2E0GjF79mzMnTsX1157LXx8fDpqmwkhpMcbHheArU9O4m7X7zFmGAYOJwOxqM1DQTqF3eHkts2dShEdoIBIKMDb/xjShVtGCCGX7pKPuFKpFNdccw1WrVqFwsJCbN26FfHx8XjllVfw9ttvt+c2EkLIFS82iA2MC2qMcDoZ3PPFYYx67c9uWaliy+lS9PnPFrz6O5tS5wmMlV25WYQQctnarStixIgRWL58OU6cOIHnnnuuvVZLCCG9gnePcWZ5HfZeqEKNwYqfM4q7eMsa+uSvi3A4GXy2Lxdmm4PLMY4KoNJshJCerVWpFIsXL271Ct9++21IJJJL3iBCCOmN4lw5xsUaE44Xarjl50p1XbRFTSuo8QwQPHixGmabEwIBTf9MCOn5WhUYZ2Rk8G4fPXoUDocDffr0AQBkZWVBJBJh+PDh7b+FhBDSC4SqZJBLhDDbnNh2poxbnl3RvVIpDBY7qvRW7vbOc+wkJeFqOWRiUVdtFiGEtItWBca7du3i/n777behUqnw1VdfISCALTdUW1uLBQsWYOLEiR2zlYQQcoUTCgWIDVQiq1yPXZmV3PISjRlOJwOhsHvUA/buLQaAna7Z++pPWkIIIT1Rm3OMV65ciRUrVnBBMcBWq3j11VexcuXKdt04QgjpTWIDG1bzsTqcqNJbumBrGlc/MC7W0MA7QsiVo82BsU6nQ3l5eYPlFRUVqKura5eNIoSQ3iguyBNcysRChKnZ6ZSLXMFnd1DgKieXEMwP4pNDfbticwghpF21OTC+8cYbsWDBAvz0008oKipCUVERfvrpJyxcuBA33XRTR2wjIYT0Ct6Bcd8INWJdlSpKulFg7K5AcVW/UMjEnlNI/x42jTUhhDSmTRN8AMBHH32Ep556CnfddRdsNhu7ErEYCxcuxJtvvtnuG0gIIb2Fd3A5OTUE+dUGALUoru0+gbE7dSIuyAcj4wOxL7sKADAyIbArN4sQQtpFmwNjpVKJVatW4c0330ROTg4YhkFycjLNdEcIIZdpeFwA7p+QgDKdGQvGxePzfbkAPFMudwfuyTyiAhR4flZfLN94FtcPiYKvrM2nE0II6XYu+Ujm4+ODtLS09twWQgjp1QQCAV6c05+7HRPIVnoorOk+PcbutI5ofwVSwlRY9+DYLt4iQghpP+028x0hhJD2FePKMS6s6R49xnVmG3RmOwAg0p/KsxFCrjwUGBNCSDcV4yqBVlRrgtPJQGO04of0QujMtk7bhsIaI346WgSbw8nlF/srJfCh1AlCyBWIjmyEENJNRfjJIRIKYHU4UVFnwRtbzmNDRjFOFWnxyg0DO2Ubnlh3HEfza1GttyAxhC3JFkW9xYSQKxT1GBNCSDclFgm5ILSgxogNGcUAgLWHCzptG47m1wIAvj6Yz01PnRRCNYsJIVcmCowJIaQbc9c2PpJXwy1zMEynPLfd4eT+LtGauMCYJvMghFypKDAmhJBurJ+rtvEP6YXcMoYBTFZHhz93jcHKe86DOWzNYuoxJoRcqSgwJoSQbmxAJBsY51fzK1NU1lk6/Lkr6j1HidYMAOgXoerw5yaEkK5AgTEhhHRjg6L8Gl1eUWfu8OduLPgO8pEiIZgmdCKEXJkoMCaEkG4sIdgH8a48Y29VemsjrdtXY8H3+ORgCASCDn9uQgjpChQYE0JINyYQCPDg5CQAwJAYf0zvGwoAqDZ0fCqFu8d4Wt9QBCglUEpFuG9CQoc/LyGEdBWqY0wIId3c7aNiMT4pGGF+Miz97QwAoKquM3qM2cC4f4Qab982GAwDBPhIO/x5CSGkq1BgTAghPUCsK50iyEcGoHN7jENUMvgrKSAmhFz5KJWCEEJ6kGBfNkCt7pQcYzYwDlXJOvy5CCGkO6DAmBBCepAgXzZIrdR3bo8xIYT0BhQYE0JIDxLE9Rh3bGDMMAxXlSJUJe/Q5yKEkO6CAmNCCOlBQnzdOcZWaIxWrNyWiQvlde22/r0XKvHh7hxoTTaYbeyU0NRjTAjpLWjwHSGE9CDuVAqN0YYv9ufh/+3MxrojhTj876sue912hxMPf3sMeosdJqsdAKCSiaGQii573YQQ0hNQjzEhhPQg/goJREJ2go01fxcAYAfJOZzMZa+7Sm+F3sIGxBtPlgIAQtXUW0wI6T16RGCcl5eHhQsXIiEhAQqFAklJSXj55ZdhtXb8qGxCCOlOhEIBAl21hKu88oxLNKbLXne5zjPTXW6VAQAQ4ae47PUSQkhP0SNSKc6fPw+n04mPP/4YycnJOH36NB544AEYDAa89dZbbV+h3QDYG7k0KBABIjm/XZOEgNjrhNFUW7sNQqbeIBm7EUBTvTsCQKy8xLYmAM6mN1nsc2ltHWaAcbRPW5EScE8n67AAjL2d2ioAget3nsMKMDbPfXYbRIyZ3UcCSfNt6xPKAaGo7W2dNsDZzA83oQwQii+hrR1wNjPoSigFhJJLaOsAnA2n/+UIJIBI2va2jBNwmBrug+baNrleMSBy9V4yDOAwtlPbNnzvO+IY0Wjb5r/3QT5SrmKEXGCGAECVphox6vqP4R8jhIyl4T7wUuYVGMsEFgjBIFbNNL7tV9Ix4nLatuUYwXidd+gYwf7d4ve+nY8R7mORwwJIJM235dbb844R3TqOaOx80BnHiFYSMAxz+dffusCbb76JDz/8EBcvXmyyjcVigcXi+dLrdDrExMRA+ymgVjZs7wy/Fo6Jv3K3xRv8IWjiy+IMmQTHlB2etr9GQmCtarRtrTAZsrknIHF9CcWbUiAw5jfallH3g/3qE571bh0Mge5c422VcbDPvsDdFu0YC2Ht0cbbSoNhv77E03b3VRBW/tV4W5ES9ps0nrZ7r4ew7I9G2wKA7VbPAVt0cB6ERRuabntjLfcFEB1eCGH+N023nVsMyEIAAMJjj0GU81HTbWdlAT7xbNsTz0GU9XbTbWdmAH4D2LZnlkN09tUm29qnHwATOIJtm7kSopPPN9128nYwoZPZttkfQpTxeNNtJ/wCJmIWAECQ9zXER+5vuu2YNWBibmHbFv4E8aE7mm478jMw8fewbUs3Q7zvhibbOoa+B2fyw2zbij0Q75nRdNu0FXD2WcK2rUmH+M9xTbft/yKcA15ib2jPQLJtaNNtUxfDOfh19oYhD5LNqU23TXoIzmH/Y29YKiH5LarJts64u+EY9Tl7w26A5OeApttG3wTH2O+525Ifm57IoqOOEc6A4XBcddDTtoVjxJ2ln+NATg0AYFvqI0iVFzTe1usYYbPZYPltMAKc2Y23lQbjq/BDWPr7eQDA94nPYYzv6cbb0jGC05ZjhHn8H9h63IIZM2ZAlv8ZHSOALjtG2GPuBDNmtevGlXeMoDjC1dZ1jNDpdAgODoZWq4VarW6yPdBDeowbo9VqERgY2GybFStWYNmyZa1eZ0VlBf7evJm7PdvhaPINqqmuxn6vttdYrWguE2/79u3c3zNMRjQSlwMA6ur02OW13qlGPZrahSaTEdu92k4yadHUV9tqtWKLV9vxpmoEN9HW4XBgs1fb0eYKhDfRFgCv7QhzGZo+FAFbt26FQ8D+mh5qKUJsM2137NgBq8APAJBmyUdCM2137doFkzAMANDfehEpzbTdu3cv6oTsAaWP9QL6NtN2//790IgqAADJ1vMY0EzbQ38fQrWI/cWfYDuDtGbaph9JR7nrwxVjO4FhzbTNyMhAySn2ExNpz8DIZtqePHEChWfZ/RFmT8eYZtqeOXMGuVls2yDHKUxopu35c+eRncO29XdcwORm2l64cAGZ+WxblbMA05ppezH3Is4Ws20VznLMbKZtQX4+TpaxbaWMFtc207aouAgZrs+liDFjTjNtS0vLkO71Gb6+mbYddYzQarX4y6ttS8cIsaEKrcmEa3CMaKat1WrFgYyzrVovHSM82nKMSD+aDogGYfv27XSM6OJjRElpyRV9jKA4guU+RhiNzVwRqKdH9hjn5ORg2LBhWLlyJe6/v+lf0U31GFeV5Tf+i6FNl0uE7OW2FtrabDb8uXMXps+cw/UYd9glEIeJvdTUFN6lira07WGXSZ1W9tKji81mw86dOzFt2jR2HzTTtuF65eznos1te9hlUsbB7rsm20rY9m1uy176bLAPmmnbpJ6WStHKY0TjbZv/3v9yWoOn17O9uT4iC5xOBg9Njscjk5MatHUfI2w2G/7c9jumT5vK3wdenv0tFxsy2B4hdyrFL4+MQWKwT8PGV9Ax4vLatv4YYXOKsH3HTsyYMQMSEegYAbT8vW/nYwR3LJo+ExK5b7NtPevteceI7hxHNHo+6OBjRI/pMV66dGmLPbpHjhzBiBEjuNslJSW45pprcOuttzYbFAOATCaDTNbw95dE4Q+Jovk3hm3o33KbltqKbXAKZJBIJJ4PgMSvDettS9vGT3a9ri3qtRXb4BDI2f3eYD2Xsd4W2zb1e/5y27Z2MFRb27Z2Eoe2tAUAWQv7oF7bVmv6cuZltW2P7/1lt23+e3/NICU+3ZcHJwNMTInH6v15KDdJIVE0/xxOgazZfVDpmmb6gYkJWH+sGKPiA5EaHQlBSzl63eF7fznHiM5qa2ODZs/5gI4RrLZ87y/zGOE+Fsl9630PrqxjxKW37YTvZ0vngw7YhubPO3xdGhgvWrQI8+bNa7ZNfHw893dJSQmmTp2KsWPH4pNPPungrSOEkO5JJZdg6xOTIBAI8O0h9pJ/Vd3lz4RXoWPXMSk1BM9d248rC0cIIb1FlwbGwcHBCA5uKkOFr7i4GFOnTsXw4cOxevVqCIU9otIcIYR0CHcvbrBrwo/Kdpgiutw1BXSYWk5BMSGkV+oRg+9KSkowZcoUxMbG4q233kJlZSV3X3h4c+nchBByZXNP11x5mT3GZpsDGiN7qT9M3ZbL4IQQcuXoEYHxtm3bkJ2djezsbERHR/Pu64FjBwkhpN2EegXGDMO0nA/cBHcahVwihFreI04NhBDS7npEPsK9994LhmEa/UcIIb2ZO5XCYneiztLM6OwWeKdRXGpwTQghPV2PCIwJIYQ0TiEVQSVje3gvJ52iTOsKjFWURkEI6b0oMCaEkB7OnWfsToe4FKVatj5shD8FxoSQ3osCY0II6eGCVZdfmaJEw/YYh/tRYEwI6b0oMCaEkB7O02PczGxjLXD3GEf6tXbCB0IIufJQYEwIIT1cXCA7K9rFqmamlG1BscaVSkE9xoSQXowCY0II6eFSwnwBANkV+kt6vMPJcI9NDvVtt+0ihJCehgJjQgjp4ZJDVACArPI6OJ0MVm7LxMQ3diKnsulAeVdmBca89id+TC9EXrUBZpsTMrEQcUE+nbXZhBDS7VBgTAghPVyfcBV8ZWJojDak59fi/+3MRmGNCav35wJgZ7X71/cnsDHfc8h/b8cFlOnMePqnk9iTyc4mOiTGn6aCJoT0ahQYE0JIDycVCzG1bygA4O7P/+aWG60OAMDxQg22nCnHjhIhLHYnAH7N4+W/nwUAXD0gvLM2mRBCuiUKjAkh5Arw2LRkiIUCLvAFPHWNDV4z4tUYrADYvGJvEX5y3D4qthO2lBBCui8KjAkh5AqQEqbCi7P78ZZVu4JgrcnGLdOb2SBZZ7bx2r55y2AopKIO3kpCCOnexF29AYQQQtrH/HHxUMrEyK7Q45O/LqLOFfzyAmOLHTaHk0uzeHx6CkYnBmJcUnCXbDMhhHQnFBgTQsgVQiAQ4LYRMcipZANjnalhYFxnsaPO7Emt+Ne0ZIhFdPGQEEIASqUghJArjkrO9nnUWexwOhleIGyw2LlA2VcmpqCYEEK8UI9xPQzDwG63w+FwtMv6bDYbxGIxzGZzu62TNE0kEkEsFkMgoJJTpPdSyyUAAIYB9FY7lzYBAHqLg+tJVsvpFEAIId7oqOjFarWitLQURqOx3dbJMAzCw8NRWFhIwVonUSqViIiIgFQq7epNIaRLyCUiSMVCWO1O6Ew2mKxePcZWOzfwTq2QdNUmEkJIt0SBsYvT6URubi5EIhEiIyMhlUrbJZB1Op3Q6/Xw9fWFUEiXLDsSwzCwWq2orKxEbm4uUlJS6D0nvZZaLkGV3gKdyQ6TzdNjbLA4oDPZuTaEEEI8KDB2sVqtcDqdiImJgVKpbLf1Op1OWK1WyOVyCtI6gUKhgEQiQX5+Pve+E9IbqeViVOktqDPbeKkURuoxJoSQJlGkVg8Frz0f7UNCAJUr6K0z22Gy8nuM3YPv1ArqGyGEEG8UQRBCyBXIPbBOV6/H2GCxew2+ox5jQgjxRoExIYRcgdxBr85kg9k7x9jqoFQKQghpAgXGV6Ddu3dDIBBAo9F06vN++eWX8Pf3v6x15OXlQSAQ4Pjx40226arXR0hP4k6TqDPzy7UZrHZu8J0fBcaEEMJDgfEVYMqUKXjiiSe6ejMIId2Iyt1jbLbB6F2uzeLVY0x1jAkhhIeOigQAOxGJREK9R4RcKdxBb53ZDrPNyS03WOwQCtlSlJRKQQghfNRj3BK7oel/DnPr29pNrWvbRvfeey/27NmD9957DwKBAAKBAHl5eQCAo0ePYsSIEVAqlRg3bhwyMzO5xy1duhRDhgzBF198gcTERMhkMjAMA61Wi3/+858IDQ2FWq3GtGnTcOLECe5xJ06cwNSpU6FSqaBWqzF8+HCkp6fztmnr1q3o168ffH19cc0116C0tJS7z+l0Yvny5YiOjoZMJsOQIUOwZcuWZl/j5s2bkZqaCoVCgalTp3KvjxDSNHfQW2OwwurwBMZGq4MG3xFCSBOox7glP/g2fV/kLGDKJs/t9aGAgz9rnhCAPwAmZDIwY7fnjl/jAUtVw3XewbRp89577z1kZWVh4MCBWL58OQDgzJkzAIB///vfWLlyJUJCQvDQQw/hvvvuw/79+7nHZmdn44cffsD69eshEokAALNnz0ZgYCA2b94MPz8/fPzxx5g+fTqysrIQGBiIO++8E0OHDsWHH34IkUiE48eP83qajUYj3nrrLXzzzTcQCoW466678NRTT+G7777jtnflypX4+OOPMXToUHzxxReYO3cuzpw5g5SUlAavr7CwEDfddBMeeughPPzww0hPT8eSJUva9B4R0hupXD3G5XUW3nKD1c4Fyv5KCowJIcQbBcY9nJ+fH6RSKZRKJcLDwwEA58+fBwD83//9HyZPngwAeO655zB79myYzWZu0gur1YpvvvkGISEhAICdO3fi1KlTqKiogEwmAwC89dZb+OWXX/DTTz/hn//8JwoKCvD000+jb9++ANAgmLXZbPjoo4+QlJQEAFi0aBEXsLvX9+yzz2LevHkAgP/+97/YtWsX3n33XXzwwQcNXt+HH36IxMREvPPOOxAIBOjTpw9OnTqF//73v+3zBhJyhXL3Bpdr+Ve2DBYHBAJ2MB4NviOEED4KjFtym77p+wQi/u2bKxo0cTqd0Ol0UKv9wZtg+vq89ti6ZqWlpXF/R0REAAAqKioQGxsLAIiLi+OCYoBNvdDr9QgKCuKtx2QyIScnBwCwePFi3H///fjmm29w1VVX4dZbb+WCYABQKpW82xEREaioYN8XnU6HkpISjB8/nrf+8ePH89I1vJ07dw5jxozhTc89duzY1r8JhPRS7sF3ZTp+YGx3eq5KUWBMCCF8FBi3ROxzeW2dTkDsAMSKS1/vJfJOcXAHlk6nJ9fQx4e/DU6nExEREdi9e3eDdbnLsC1duhR33HEHNm3ahD/++AMvv/wyvv/+e9x4440NntP9vAzDNFjmjWGYBsu87yOEtF39We3C1TKU6TxpFWKhAEqpqP7DCCGkV6PBd1cAqVQKh8PRcsMWDBs2DGVlZRCLxUhOTub9Cw4O5tqlpqbiySefxLZt23DTTTdh9erVrVq/Wq1GZGQk9u3bx1t+4MAB9OvXr9HH9O/fH4cOHeItq3+bENJQ/YF1/kopJELG67akyR+khBDSW1FgfAWIj4/H33//jby8PFRVVfF6hdviqquuwtixY3HDDTdg69atyMvLw4EDB/Diiy8iPT0dJpMJixYtwu7du5Gfn4/9+/fjyJEjTQa1jXn66afx3//+F+vWrUNmZiaee+45HD9+HI8//nij7R966CHk5ORg8eLFyMzMxJo1a/Dll19e0usjpDdR1atRrJaLIfPqIKZSbYQQ0hAFxleAp556CiKRCP3790dISAgKCgouaT0CgQCbN2/GpEmTcN999yE1NRXz5s1DXl4ewsLCIBKJUF1djXvuuQepqam47bbbcO2112LZsmWtfo7HHnsMS5YswZIlSzBo0CBs2bIFv/32W6MVKQAgNjYW69evx8aNGzF48GB89NFHeO211y7p9RHSm/hIxRB6dQir5WLIvY74AUpp528UIYR0cwKmFyVx6nQ6+Pn5QavVQq1W8+4zm83Izc1FQkICV7WhPXgG36khFNLvkM5Qf1/abDZs3rwZs2bNoklMugjtg64xdsWfKHVVpbhxaCQOZxaj2MhGy7MHReCDO4d15eb1OvQ96Hq0D7peV+yD5uK/+ihSI4SQK1Skv2fQb6ivDHKvVIowdft1ABBCyJWCAmNCCLlCeQfGEX4yBMoYr9sUGBNCSH0UGBNCyBUqPkjJ/R0doECIwhMYJ4c1M6snIYT0UhQYE0LIFWpSKjuBj1QsxOBofySp2cBYIRFhaIx/F24ZIYR0Tz1ugg+LxYLRo0fjxIkTyMjIwJAhQ9p1/b1oLOIVi/YhIawRcQH47J4RCFbJ4K+UIFkNfH7PMISoFfCnqhSEENJAj+sxfuaZZxAZGdnu63WPjDQaje2+btK53PuQRhyT3k4gEOCq/mEY4tU7PCklGGnR/k0+hhBCerMe1WP8xx9/YNu2bVi/fj3++OOPFttbLBZYLJ4pUHU6HQC2VIjNZmvQXqVSoby8HE6nE0qlsl1mhWIYBlarFSaTiWaZ6mAMw8BoNKKyshJqtRpOpxNOp5Pb143tc9I5aB90PdoHXY/2QdejfdD1umIftOW5ekwd4/LycgwfPhy//PILgoODkZCQ0GIqxdKlSxudfGLNmjVQKpWNPIINjlUqFdUc7qGcTifq6upQV1fX1ZtCCCGEkG7AaDTijjvuaFUd4x4RGDMMg1mzZmH8+PF48cUXkZeX16rAuLEe45iYGFRVVTX7xjgcDtjt9nbJVbXb7Thw4ADGjRsHsbhHddD3OAKBAGKxGCKRiLfcZrNh+/btmDFjBqVXdBHaB12P9kHXo33Q9WgfdL2u2Ac6nQ7BwcGtCoy7NFJrqkfX25EjR3DgwAHodDo8//zzbVq/TCaDTCZrsFwikTS7M9pzR9lsNtjtdvj6+tKXsIu1tN9Jx6N90PVoH3Q92gddj/ZB1+vMfdCW5+nSwHjRokWYN29es23i4+Px6quv4tChQw2C3BEjRuDOO+/8/+3df0zU9R8H8CfQ3XGAXOgRdx9JYG3m6gwmK4TNcJoQA6zVnPrX+UdttpHRrj9s2SDSZeWolTlWOUf/BH+orS1takPNYWbnbZ3UFo5fJpwOp3Jhcsi9vn/05bN9BOG67u5zHM/Hdn/web85Xvd+3nEvPnzu80Fra2s0yyQiIiKieUDXxthqtcJqtc4675NPPsHOnTvVrwcHB1FZWYn29naUlJREs0QiIiIimifmxEGvS5Ys0XydkfHPFZseeeQR5Obm6lESERERESWYOdEYR8rkh+kmT9sWC+Pj47h9+zZGRkZ4PJNOmIH+mIH+mIH+mIH+mIH+9Mhgsu8L5aQKc7Ixzs/PD+uMEZOn8Hr44YcjXRIRERERxTG/3w+LxTLjnDlxurZICQaDGBwcxIIFC2J2sY3JU8Rdvnx51lOEUHQwA/0xA/0xA/0xA/0xA/3pkYGIwO/3Q1GUWa9TMSf3GIcrOTlZt2OSMzMz+SLUGTPQHzPQHzPQHzPQHzPQX6wzmG1P8SRe3o2IiIiICGyMiYiIiIgAsDGOOpPJhIaGhmmvwEexwQz0xwz0xwz0xwz0xwz0F+8ZzKsP3xERERER3Q/3GBMRERERgY0xEREREREANsZERERERADYGBMRERERAWBjHDG7du1CWVkZ0tLS8OCDD047JykpacqtpaVFM8fr9aK8vBxmsxmLFy9GU1NTWJe/no9CyWBgYAC1tbVIT0+H1WrFtm3bEAgENHOYQWTl5+dPed5v375dMyeUXCh8+/btQ0FBAVJTU1FcXIwff/xR75ISVmNj45Tnu81mU8dFBI2NjVAUBWazGatXr0ZXV5eOFc99p0+fRm1tLRRFQVJSEr755hvNeChrPjY2hldffRVWqxXp6elYv349/vzzzxg+irlttgy2bNky5XWxcuVKzZx4yYCNcYQEAgFs2LABr7zyyozzDhw4gKGhIfXmdDrVsZGREaxbtw6KouD8+fP49NNPsWfPHjQ3N0e7/IQwWwYTExOorq7G6Ogozpw5g7a2Nhw8eBAul0udwwyio6mpSfO837FjhzoWSi4Uvvb2dtTX1+Ott96Cx+PBqlWrUFVVhYGBAb1LS1iPP/645vnu9XrVsQ8++ADNzc3Yu3cvzp8/D5vNhnXr1sHv9+tY8dw2OjqKwsJC7N27d9rxUNa8vr4ehw8fRltbG86cOYO//voLNTU1mJiYiNXDmNNmywAAnn32Wc3r4siRI5rxuMlAKKIOHDggFotl2jEAcvjw4ft+7759+8RiscidO3fUbe+9954oiiLBYDDClSau+2Vw5MgRSU5OlitXrqjbvv76azGZTHLr1i0RYQbRkJeXJx999NF9x0PJhcL31FNPydatWzXbli1bJtu3b9eposTW0NAghYWF044Fg0Gx2Wyye/duddudO3fEYrFIS0tLjCpMbPe+z4ay5jdv3hSDwSBtbW3qnCtXrkhycrJ8//33Mas9UUzX6zidTnnuuefu+z3xlAH3GMdYXV0drFYrnnzySbS0tCAYDKpjZ8+eRXl5ueak15WVlRgcHERfX58O1SaWs2fPwuFwQFEUdVtlZSXGxsbgdrvVOcwg8t5//30sWrQIRUVF2LVrl+YwiVByofAEAgG43W5UVFRotldUVKCzs1OnqhJfd3c3FEVBQUEBNm3ahJ6eHgBAb28vfD6fJg+TyYTy8nLmESWhrLnb7cb4+LhmjqIocDgczCWCTp48iYceeghLly7Fyy+/jGvXrqlj8ZTBAzH9afPcu+++i7Vr18JsNuOHH36Ay+XC8PCw+m9ln8+H/Px8zffk5OSoYwUFBbEuOaH4fD51PSdlZWXBaDTC5/Opc5hBZL322mtYsWIFsrKy8PPPP+PNN99Eb28vvvzySwCh5ULhGR4exsTExJT1zcnJ4dpGSUlJCb766issXboUV69exc6dO1FWVoauri51zafLo7+/X49yE14oa+7z+WA0GpGVlTVlDl8nkVFVVYUNGzYgLy8Pvb29ePvtt7FmzRq43W6YTKa4yoB7jGcw3Yco7r398ssvId/fjh07UFpaiqKiIrhcLjQ1NeHDDz/UzElKStJ8Lf//0Ne92+eLSGcw3TqKiGY7M5jdv8nl9ddfR3l5OZ544gm89NJLaGlpwf79+3H9+nX1/kLJhcI33XOaaxsdVVVVePHFF7F8+XI888wz+O677wAAra2t6hzmEXvhrDlziZyNGzeiuroaDocDtbW1OHr0KP744w/19XE/emTAPcYzqKurw6ZNm2acc+/exX9j5cqVGBkZwdWrV5GTkwObzTblL6PJfzXc+9fufBHJDGw2G86dO6fZduPGDYyPj6vrywxC819ymfwk8qVLl7Bo0aKQcqHwWK1WpKSkTPuc5trGRnp6OpYvX47u7m48//zzAP7ZQ2m329U5zCN6Js8IMtOa22w2BAIB3LhxQ7PH8tq1aygrK4ttwfOE3W5HXl4euru7AcRXBtxjPAOr1Yply5bNeEtNTQ37/j0eD1JTU9VTi5WWluL06dOa4y+PHTsGRVH+UwM+l0Uyg9LSUly8eBFDQ0PqtmPHjsFkMqG4uFidwwxm919y8Xg8AKC+SYWSC4XHaDSiuLgYx48f12w/fvw43/BjZGxsDL///jvsdjsKCgpgs9k0eQQCAZw6dYp5REkoa15cXAyDwaCZMzQ0hIsXLzKXKLl+/TouX76svg/EVQYx/ahfAuvv7xePxyPvvPOOZGRkiMfjEY/HI36/X0REvv32W/n888/F6/XKpUuX5IsvvpDMzEzZtm2beh83b96UnJwc2bx5s3i9Xjl06JBkZmbKnj179HpYc8psGdy9e1ccDoesXbtWLly4ICdOnJDc3Fypq6tT74MZRFZnZ6c0NzeLx+ORnp4eaW9vF0VRZP369eqcUHKh8LW1tYnBYJD9+/fLb7/9JvX19ZKeni59fX16l5aQXC6XnDx5Unp6euSnn36SmpoaWbBggbreu3fvFovFIocOHRKv1yubN28Wu90uIyMjOlc+d/n9fvX3PQD1d05/f7+IhLbmW7duldzcXDlx4oRcuHBB1qxZI4WFhXL37l29HtacMlMGfr9fXC6XdHZ2Sm9vr3R0dEhpaaksXrw4LjNgYxwhTqdTAEy5dXR0iIjI0aNHpaioSDIyMiQtLU0cDod8/PHHMj4+rrmfX3/9VVatWiUmk0lsNps0NjbyNGEhmi0DkX+a5+rqajGbzbJw4UKpq6vTnJpNhBlEktvtlpKSErFYLJKamiqPPvqoNDQ0yOjoqGZeKLlQ+D777DPJy8sTo9EoK1askFOnTuldUsLauHGj2O12MRgMoiiKvPDCC9LV1aWOB4NBaWhoEJvNJiaTSZ5++mnxer06Vjz3dXR0TPu73+l0ikhoa/73339LXV2dLFy4UMxms9TU1MjAwIAOj2ZumimD27dvS0VFhWRnZ4vBYJAlS5aI0+mcsr7xkkGSCC/pRURERETEY4yJiIiIiMDGmIiIiIgIABtjIiIiIiIAbIyJiIiIiACwMSYiIiIiAsDGmIiIiIgIABtjIiIiIiIAbIyJiIiIiACwMSYiIiIiAsDGmIhoXli9ejXq6+v1LoOIKK6xMSYiIiIiApAkIqJ3EUREFD1btmxBa2urZltvby/y8/P1KYiIKE6xMSYiSnC3bt1CVVUVHA4HmpqaAADZ2dlISUnRuTIiovjygN4FEBFRdFksFhiNRqSlpcFms+ldDhFR3OIxxkREREREYGNMRERERASAjTER0bxgNBoxMTGhdxlERHGNjTER0TyQn5+Pc+fOoa+vD8PDwwgGg3qXREQUd9gYExHNA2+88QZSUlLw2GOPITs7GwMDA3qXREQUd3i6NiIiIiIicI8xEREREREANsZERERERADYGBMRERERAWBjTEREREQEgI0xEREREREANsZERERERADYGBMRERERAWBjTEREREQEgI0xEREREREANsZERERERADYGBMRERERAQD+B6qRcDtSOHDSAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 720x320 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XV summary ===\n",
      "s0: 2.0\n",
      "mu: [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess: 0.01831563888873418\n",
      "K_terms: 21\n",
      "n_max: 187\n",
      "T_MAX: 150.0\n",
      "DT: 0.01\n",
      "precision: 120\n",
      "abs_frac_threshold: 0.0001\n",
      "abs_threshold_value: 0.0001\n",
      "phase_grad_threshold: 2.0\n",
      "n_candidates: 0\n",
      "candidates_t: []\n",
      "Wrote:\n",
      " - stageXV_refined_scan.csv\n",
      " - fig_stageXV_abs_with_candidates.png\n",
      " - fig_stageXV_phase_gradient.png\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>t</th>\n      <th>abs</th>\n      <th>arg_unwrap</th>\n      <th>d_arg_dt</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>-150.00</td>\n      <td>3.162229e-198</td>\n      <td>3.087632</td>\n      <td>4.202249</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>-149.99</td>\n      <td>3.250469e-198</td>\n      <td>3.129655</td>\n      <td>4.206209</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>-149.98</td>\n      <td>3.341025e-198</td>\n      <td>3.171757</td>\n      <td>4.214207</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>-149.97</td>\n      <td>3.433959e-198</td>\n      <td>3.213939</td>\n      <td>4.222356</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>-149.96</td>\n      <td>3.529334e-198</td>\n      <td>3.256204</td>\n      <td>4.230655</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>-149.95</td>\n      <td>3.627217e-198</td>\n      <td>3.298552</td>\n      <td>4.239102</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>-149.94</td>\n      <td>3.727678e-198</td>\n      <td>3.340986</td>\n      <td>4.247694</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>-149.93</td>\n      <td>3.830786e-198</td>\n      <td>3.383506</td>\n      <td>4.256429</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>-149.92</td>\n      <td>3.936615e-198</td>\n      <td>3.426114</td>\n      <td>4.265305</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>-149.91</td>\n      <td>4.045242e-198</td>\n      <td>3.468812</td>\n      <td>4.274318</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>-149.90</td>\n      <td>4.156745e-198</td>\n      <td>3.511601</td>\n      <td>4.283465</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>-149.89</td>\n      <td>4.271206e-198</td>\n      <td>3.554481</td>\n      <td>4.292742</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "         t            abs  arg_unwrap  d_arg_dt\n",
       "0  -150.00  3.162229e-198    3.087632  4.202249\n",
       "1  -149.99  3.250469e-198    3.129655  4.206209\n",
       "2  -149.98  3.341025e-198    3.171757  4.214207\n",
       "3  -149.97  3.433959e-198    3.213939  4.222356\n",
       "4  -149.96  3.529334e-198    3.256204  4.230655\n",
       "5  -149.95  3.627217e-198    3.298552  4.239102\n",
       "6  -149.94  3.727678e-198    3.340986  4.247694\n",
       "7  -149.93  3.830786e-198    3.383506  4.256429\n",
       "8  -149.92  3.936615e-198    3.426114  4.265305\n",
       "9  -149.91  4.045242e-198    3.468812  4.274318\n",
       "10 -149.90  4.156745e-198    3.511601  4.283465\n",
       "11 -149.89  4.271206e-198    3.554481  4.292742"
      ]
     },
     "execution_count": 5,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Stage XV: refined zero sweep near s0 (higher precision, narrower window) ===\n",
    "# - Uses Stage VIII Dirichlet coefficients (a_n)\n",
    "# - Uses Stage XI's preferred uniform shift (if available); else defaults to [1,2,2,3]\n",
    "# - Scans t in a narrower window with higher precision and more sensitive thresholds\n",
    "# - Marks candidate minima of |Λ| and exports results\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- helpers (NO Sage Integer leakage) ----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:\n",
    "        return mp.mpf(x)\n",
    "    except Exception:\n",
    "        return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "# ---------------- files & prior summaries ----------------\n",
    "coeff_path   = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "sumXI_path   = Path(\"stageXI_summary.json\")\n",
    "sumX_path    = Path(\"stageX_summary.json\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "# central point guess s0 (default 2.0; prefer Stage X if present)\n",
    "s0 = mp.mpf('2.0')\n",
    "if sumX_path.exists() and sumX_path.stat().st_size > 0:\n",
    "    try:\n",
    "        JX = json.load(open(sumX_path))\n",
    "        if \"s0\" in JX:\n",
    "            s0 = mpf_safe(JX[\"s0\"])\n",
    "        elif \"central_point_guess\" in JX:\n",
    "            s0 = mpf_safe(JX[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "# gamma-shifts: base [0,1,1,2] plus Stage XI's uniform delta if available\n",
    "MU_BASE = [0, 1, 1, 2]\n",
    "delta_uniform = 1.0   # your Stage XI runs tended to pick ~+1\n",
    "if sumXI_path.exists() and sumXI_path.stat().st_size > 0:\n",
    "    try:\n",
    "        JXI = json.load(open(sumXI_path))\n",
    "        if \"uniform_shift\" in JXI and \"delta_min_residual\" in JXI[\"uniform_shift\"]:\n",
    "            delta_uniform = float(JXI[\"uniform_shift\"][\"delta_min_residual\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "MU = [m + delta_uniform for m in MU_BASE]   # e.g. [1,2,2,3]\n",
    "# crude Q (exact value does not change zero locations; we match Stage X/XI usage)\n",
    "Q_guess = mp.e**(-4)\n",
    "# ---------------- read coefficients ----------------\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "# limit terms (fast & stable)\n",
    "K = min(len(N_all), 8000)\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "Ncut = to_int(n[-1])\n",
    "# ---------------- Λ(s) model (same as before) ----------------\n",
    "mp.mp.dps = 120  # ↑ precision for refined scan\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------------- refined scan settings ----------------\n",
    "T_MAX = 150.0      # narrower window around the center\n",
    "DT    = 0.01       # resolution (0.005 is possible but slower)\n",
    "ABS_FRAC_THRESHOLD   = 1e-4  # more sensitive than Stage XIV (1e-6)\n",
    "PHASE_GRAD_THRESHOLD = 2.0   # more permissive than 3.5\n",
    "t_vals = np.arange(-T_MAX, T_MAX + 0.5*DT, DT, dtype=float)\n",
    "# ---------------- compute along the critical line ----------------\n",
    "abs_vals = []\n",
    "arg_vals = []\n",
    "for t in t_vals:\n",
    "    s = s0 + 1j*mp.mpf(t)\n",
    "    Lam = Lambda_of_s(s, Q_guess, MU, Ncut)\n",
    "    abs_vals.append(float(abs(Lam)))\n",
    "    # raw principal arg in (-pi, pi]\n",
    "    arg_vals.append(float(mp.arg(Lam)))\n",
    "abs_vals = np.array(abs_vals, dtype=float)\n",
    "arg_unwrap = np.unwrap(np.array(arg_vals, dtype=float))\n",
    "d_arg_dt = np.gradient(arg_unwrap, DT)\n",
    "# adaptive absolute threshold based on median scale\n",
    "median_abs = float(np.median(abs_vals)) if np.isfinite(abs_vals).all() else 0.0\n",
    "abs_threshold = max(1e-40, ABS_FRAC_THRESHOLD * max(median_abs, 1.0))\n",
    "# ---------------- candidate detection ----------------\n",
    "cands_idx = []\n",
    "for i in range(1, len(t_vals)-1):\n",
    "    if (abs_vals[i] <= abs_vals[i-1] and abs_vals[i] <= abs_vals[i+1] and\n",
    "        abs_vals[i] < abs_threshold and abs(d_arg_dt[i]) < PHASE_GRAD_THRESHOLD):\n",
    "        cands_idx.append(i)\n",
    "# simple quadratic (parabolic) refinement around each minimum\n",
    "def refine_parabolic(i):\n",
    "    # use points i-1, i, i+1 on (t, log(abs + eps)) to get a smoother parabola\n",
    "    if i <= 0 or i >= len(t_vals)-1:\n",
    "        return t_vals[i], abs_vals[i]\n",
    "    eps = 1e-300\n",
    "    x1, x2, x3 = t_vals[i-1], t_vals[i], t_vals[i+1]\n",
    "    y1 = np.log(abs_vals[i-1] + eps)\n",
    "    y2 = np.log(abs_vals[i]   + eps)\n",
    "    y3 = np.log(abs_vals[i+1] + eps)\n",
    "    # vertex of parabola through (x1,y1),(x2,y2),(x3,y3)\n",
    "    denom = (x1-x2)*(x1-x3)*(x2-x3)\n",
    "    if denom == 0:\n",
    "        return t_vals[i], abs_vals[i]\n",
    "    A = (x3*(y2-y1) + x2*(y1-y3) + x1*(y3-y2)) / denom\n",
    "    B = (x3**2*(y1-y2) + x2**2*(y3-y1) + x1**2*(y2-y3)) / denom\n",
    "    if A == 0:\n",
    "        t_star = x2\n",
    "    else:\n",
    "        t_star = -B/(2*A)\n",
    "    # clamp to the local window\n",
    "    t_star = float(max(min(t_star, x3), x1))\n",
    "    s_star = s0 + 1j*mp.mpf(t_star)\n",
    "    Lam_star = Lambda_of_s(s_star, Q_guess, MU, Ncut)\n",
    "    return t_star, float(abs(Lam_star))\n",
    "refined = []\n",
    "for i in cands_idx:\n",
    "    tt, aa = refine_parabolic(i)\n",
    "    refined.append((tt, aa))\n",
    "# deduplicate close candidates (within, say, 3*DT)\n",
    "refined.sort(key=lambda z: z[0])\n",
    "dedup = []\n",
    "for tt, aa in refined:\n",
    "    if not dedup or abs(tt - dedup[-1][0]) > 3*DT:\n",
    "        dedup.append((tt, aa))\n",
    "refined = dedup\n",
    "# ---------------- outputs ----------------\n",
    "out_csv     = Path(\"stageXV_refined_scan.csv\")\n",
    "out_fig_abs = Path(\"fig_stageXV_abs_with_candidates.png\")\n",
    "out_fig_dph = Path(\"fig_stageXV_phase_gradient.png\")\n",
    "out_sum     = Path(\"stageXV_summary.json\")\n",
    "df = pd.DataFrame({\n",
    "    \"t\": t_vals,\n",
    "    \"abs\": abs_vals,\n",
    "    \"arg_unwrap\": arg_unwrap,\n",
    "    \"d_arg_dt\": d_arg_dt\n",
    "})\n",
    "df.to_csv(out_csv, index=False)\n",
    "# plots\n",
    "plt.figure(figsize=(7.2,4.2))\n",
    "plt.semilogy(t_vals, abs_vals, label=\"|Λ(s0+it)|\")\n",
    "if refined:\n",
    "    t_marks = [r[0] for r in refined]\n",
    "    a_marks = [r[1] for r in refined]\n",
    "    plt.semilogy(t_marks, a_marks, \"o\", label=\"candidates\", ms=4)\n",
    "plt.axhline(abs_threshold, color=\"orange\", ls=\"--\", label=\"abs threshold\")\n",
    "plt.title(\"Stage XV: refined |Λ(s)| near s0\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"|Λ| (log)\")\n",
    "plt.grid(True, which=\"both\"); plt.legend(); plt.tight_layout()\n",
    "plt.savefig(out_fig_abs, dpi=150)\n",
    "plt.show()\n",
    "plt.figure(figsize=(7.2,3.2))\n",
    "plt.plot(t_vals, d_arg_dt)\n",
    "plt.axhline(PHASE_GRAD_THRESHOLD,  color=\"orange\", ls=\"--\", label=\"threshold\")\n",
    "plt.axhline(-PHASE_GRAD_THRESHOLD, color=\"orange\", ls=\"--\")\n",
    "plt.title(\"Stage XV: phase gradient along Re s = s0\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"d/dt arg Λ\")\n",
    "plt.grid(True); plt.legend(); plt.tight_layout()\n",
    "plt.savefig(out_fig_dph, dpi=150)\n",
    "plt.show()\n",
    "summary = {\n",
    "    \"s0\": float(s0),\n",
    "    \"mu\": [float(m) for m in MU],\n",
    "    \"Q_guess\": float(Q_guess),\n",
    "    \"K_terms\": int(K),\n",
    "    \"n_max\": int(Ncut),\n",
    "    \"T_MAX\": float(T_MAX),\n",
    "    \"DT\": float(DT),\n",
    "    \"precision\": int(mp.mp.dps),\n",
    "    \"abs_frac_threshold\": float(ABS_FRAC_THRESHOLD),\n",
    "    \"abs_threshold_value\": float(abs_threshold),\n",
    "    \"phase_grad_threshold\": float(PHASE_GRAD_THRESHOLD),\n",
    "    \"n_candidates\": int(len(refined)),\n",
    "    \"candidates_t\": [float(x[0]) for x in refined],\n",
    "    \"candidates_abs\": [float(x[1]) for x in refined],\n",
    "    \"outputs\": [str(out_csv), str(out_fig_abs), str(out_fig_dph)]\n",
    "}\n",
    "with open(out_sum, \"w\") as f:\n",
    "    json.dump(summary, f, indent=2)\n",
    "print(\"\\n=== Stage XV summary ===\")\n",
    "for k,v in summary.items():\n",
    "    if k not in (\"candidates_t\",\"candidates_abs\",\"outputs\"):\n",
    "        print(f\"{k}: {v}\")\n",
    "print(\"candidates_t:\", summary[\"candidates_t\"])\n",
    "print(\"Wrote:\")\n",
    "for p in summary[\"outputs\"]:\n",
    "    print(\" -\", p)\n",
    "# quick peek\n",
    "display(head_safe(df, 12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1cfa1c",
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x420 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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T+bxKpRLJyclRNdHJyclRj9VoNHC5XML9efPm4fbbb8eoUaPwxRdfYO3atVi3bh2mTp0qWe+6667DW2+9hcOHD+PSSy9FWloaRo0ahWXLlgnrVFVV4bvvvovaR/379wfQ8j7itz1y3/PvLZbMzMyoZbNnz8bDDz+Miy66CN999x3++OMPrFu3DoMHD5a8n7q6umb3z7FUVVWBMYb09PSo97p27dqo99ma/dBWrd1vsdTV1cX8t8vKyhL+3tL2azQaABBep7l919yy5px++ulYt24d1q5di/fffx8FBQW466678OuvvwrrVFVVobGxEWq1OurfvrKyssXPmEwmw08//YRzzjkHzz77LIYNG4bU1FTcc889MWvLxSwWC4YMGdKq/45l4cKFuOGGG/DGG29gzJgxsFgsuP7661FZWQmAG+cgk8mi9gMA1NfXC9tDSHuirhSEtIFKpcKjjz6KF198Edu3bz/m+h988AEKCwuxcOFCSWbD4/FI1ktOTobf70d9fb3kQM+fIHhJSUlQKBS47rrrcOedd8Z8zcLCwmNu19133436+nosX74cffv2xVdffYXZs2fjnHPOQU5OjmTdnJwcnH322fjoo4/wwgsv4O2330ZxcTHOOOMMYZ3vvvtO8p74wKK598EvU6vVMBqNx9ze5lRWViI7O1u47/f7UVdX12wA2ZIPPvgAEydOxCuvvCJZHitQmDlzJmbOnAmHw4HVq1fj0UcfxXnnnYe9e/ciPz8fKSkpGDRoEJ566qmYrxX57yPGb3tVVVXM9xZLrKzZBx98gOuvvx5PP/20ZHltbS0SExMlr9fc/jmWlJQUyGQy/PLLL0KQKBZrWXtry36LlJycjIqKiqjl5eXlALj31xbifRepsrKy1VnjhIQEjBgxAgAwatQojBo1CoMHD8Ydd9yBzZs3Qy6XIyUlBcnJyViyZEnM5zCZTC2+Rn5+vvBjeO/evfj000/x2GOPwev1YsGCBc0+7t1338XMmTNb9T7YMfoup6SkYP78+Zg/fz6OHDmCb7/9Fv/4xz9QXV2NJUuWQKfTobi4OOaA0W3btkGn06FHjx6t2hZCWosCY0KaUVFRETObxF+eFQc3zWW9ZDIZ1Gq1JHCprKyM6koxYcIEPPvss1i4cCFuv/12Yfknn3wiWU+v1+PMM8/Epk2bMGjQoOPqH/zNN9/ggw8+wHPPPYe+ffsCAF577TUMGDAAN998M3744Yeox8yaNQtLlizBI488gs2bN+Opp56SvKdjdab48ssv8dxzzwnlFDabDd999x3Gjx8PhULR5vfA+/DDDzF8+HDh/qeffgq/339co/9lMllUILd161asWbMm6lI7z2Aw4Nxzz4XX68VFF12EHTt2ID8/H+eddx4WL16MoqIiJCUltWk7+B8cCxcuxLBhw4Tln3/+eZtG4Md6P4sWLUJZWRmKi4uFZWeeeSaeffZZbNmyRVJO8dFHHx3zNc477zw888wzKCsriyofOF6RWdhjOZ79xps0aRK++uorlJeXS77P7733HvR6vaRlWmuMGjUKGo0GCxcuxCWXXCIsX7t2LQ4fPnzck6P07NkTf/vb3zBnzhwsXLgQV111Fc477zx88sknCAQCGDVq1HE9L69Xr17417/+hS+++OKYE2fwpRTtLS8vD3fddRd++ukn/Pbbb8Lyiy++GPPnz0dpaamwP202G7788ktccMEFzZYXEXK86BNFSDP47On555+PPn36IBgMYvPmzXjhhRdgNBpx7733CusOHDgQn3zyCRYuXIgePXpAq9Vi4MCBOO+88/Dll1/ijjvuwGWXXYbS0lI88cQTyMzMxL59+4THT506FePGjcP9998Pq9WK4cOHY82aNXjvvfcASNvD/ec//8Hpp5+O8ePH4/bbb0dBQQFsNhtKSkrw3Xff4eeff272PdXW1uLWW2/F2LFjMXv2bGF5dnY2XnzxRcycORNvvvmmpEwC4GorU1JS8Nxzz0GhUOCGG25o07+lQqHAlClTMHv2bASDQfz73/+G1WrFnDlzJOsplUpMmDCh1XXGX375JZRKJaZMmYIdO3bg4YcfxuDBg48rSDvvvPPwxBNP4NFHH8WECROwZ88ePP744ygsLJQEpDfffDN0Oh3GjRuHzMxMVFZWYu7cuUhISBBajT3++ONYtmwZxo4di3vuuQe9e/eG2+3GoUOHsHjxYixYsCAqM8/r378/rrrqKrzwwgtQKBQ466yzsGPHDrzwwgtISEiQfBaO9X7eeecd9OnTB4MGDcKGDRvw3HPPRb3ufffdh7feegvTp0/Hk08+ifT0dHz44YfYvXv3MV9j3LhxuOWWWzBz5kysX78eZ5xxBgwGAyoqKvDrr79i4MCBkh96rVFUVASdTocPP/wQffv2hdFoRFZWVrNZ9tbut1geffRRoR78kUcegcViwYcffohFixbh2WefRUJCQpu23WKxYPbs2Zg7d67Q7vDo0aOYM2cOMjMzW73vYnnggQewYMECzJkzB1dccQWuvPJKfPjhh5g2bRruvfdenHbaaVCpVDh69ChWrFiBCy+8EBdffHHM59q6dSvuuusuXH755ejZsyfUajV+/vlnbN26Ff/4xz9a3I7k5OTjuiITqampCWeeeSauvvpq9OnTByaTCevWrcOSJUskPyoeeOABvP/++5g+fToef/xxaDQaPPPMM3C73Z1+FkPSRcV79B8hndXChQvZ1VdfzXr27MmMRiNTqVQsLy+PXXfddWznzp2SdQ8dOsTOPvtsZjKZhDZivGeeeYYVFBQwjUbD+vbty15//XWhq4JYfX09mzlzJktMTGR6vZ5NmTKFrV27lgFg//nPfyTrHjx4kN14440sOzubqVQqlpqaysaOHcuefPLJFt/T5ZdfzvR6Pdu7d2/Mv0+bNo2ZzeaoUfqMMfbXv/415sj8lvBdKf7973+zOXPmsJycHKZWq9nQoUPZjz/+GLU+2tiubcOGDez8889nRqORmUwmdtVVV7GqqirJurHaXzHGdUkQv5bH42EPPPAAy87OZlqtlg0bNox9/fXXUZ0Y3n33XXbmmWey9PR0plarWVZWFrviiivY1q1bJc9fU1PD7rnnHlZYWMhUKhWzWCxs+PDh7J///Cez2+0tvj+3281mz57N0tLSmFarZaNHj2Zr1qxhCQkJko4SfIeAdevWRT1HQ0MDmzVrFktLS2N6vZ6dfvrp7Jdffol634wxtnPnTjZlyhSm1WqZxWJhs2bNYt98802r2rUxxthbb73FRo0axQwGA9PpdKyoqIhdf/31bP369ZJ/7/79+0c9NtZzfvzxx6xPnz5MpVJFdZKI1Nr9xlh0VwrGGNu2bRs7//zzWUJCAlOr1Wzw4MFRHTH4rhSfffaZZDn/+RavHwwG2ZNPPil81gcNGsS+//57Nnjw4KguGbE093lljLH//e9/kvZ2Pp+PPf/882zw4MFMq9Uyo9HI+vTpw2699Va2b9++Zl+jqqqKzZgxg/Xp04cZDAZmNBrZoEGD2IsvvihpPdeR3G43u+2229igQYOY2WxmOp2O9e7dmz366KPM4XBI1i0pKWEXXXQRM5vNTK/Xs0mTJrENGzaclO0k3Y+MsW46+TohXcBHH32Ea665Br/99hvGjh0b783pNB577DHMmTMHNTU1ba4D7ap+//13jBs3Dh9++GGrOkaQzuPgwYPo06cPHn300W43cx0hXQ2VUhDSSXz88ccoKyvDwIEDIZfLsXbtWjz33HM444wzKCjuZpYtW4Y1a9Zg+PDh0Ol02LJlC5555hn07NlTcpmZdD5btmzBxx9/jLFjx8JsNmPPnj149tlnYTabo0qUCCGdDwXGhHQSJpMJn3zyCZ588kk4HA5kZmZixowZePLJJ+O9aeQkM5vNWLp0KebPnw+bzYaUlBSce+65mDt3rqQfNOl8DAYD1q9fjzfffBONjY1ISEjAxIkT8dRTT7WpZRshJD6olIIQQgghhBDQBB+EEEIIIYQAoMCYEEIIIYQQAN2sxjgYDKK8vBwmk4nmVyeEEEII6QYYY7DZbMjKyjpmP/FuFRiXl5cfcyYkQgghhBBy6iktLW12ciVetwqM+bnjS0tLYTabT8pr+nw+LF26FGeffTZUKtVJeU0iRfsg/mgfxB/tg/ijfRB/tA/iLx77wGq1Ijc3V4gDW9KtAmO+fMJsNp/UwFiv18NsNtOXME5oH8Qf7YP4o30Qf7QP4o/2QfzFcx+0poyWBt8RQgghhBACCowJIYQQQggBQIExIYQQQgghACgwJoQQQgghBAAFxoQQQgghhACgwJgQQgghhBAAFBgTQgghhBACgAJjQgghhBBCAFBgTAghhBBCCAAKjAkhhBBCCAFAgTEhhBBCCCEAKDA+KX6vkuGGt9ejxuaJ96YQQgghhJx028uacNH/fsMfB+vjvSktosD4JPj8oBy/H6jHB2sPx3tTCCGEEEJOuvnL92JzaSMe/GJ7vDelRRQYdzCPL4AAkwEAKppcbXqsyxvA8p1VcPsCHbFphBBCCCFtUmv3YNXeGjDG2vS45buqAQAVTe6O2Kx2Q4FxB2tw+YTb/kDLH6LdlVZUWcMfmPnL9+Km99bjpZ9LOmz7CCGEEEJa6x9fbMMNb/2JT9aVCsuO1DlPmXJRCow7WKMzHBg3iYLkSPtr7Djv/37Fpa/8jmCQC6Df/PUgAOClFRQYE0IIIST+lu+qAgChPLS80YWp/1mNaf/3C3yBYKueo43J5pOKAuMOJg6MG1sIjLcdbYI/yHC0wYUaO/eryx/sxJ8cQgghhHRbgVCMsqvCCqc3gBqbB0fqna16rLd18XNcUGDcwRqc3pi3I1nd4aC5s9ffEEIIIaT7EdcV84Gxze0XlpU3xh5LFTlWyuGPuVqnQIFxB2tyhfe+VZQxZoxJPmD1jtYF0IQQQggh8eASBbhyGddYQJzYa3DGvjLeGLHcTYFx92XzSGuMGWOotXtw+r9X4MrX1gr1xA2iwNgaWk+MOlMQQgghJJ7EgW8wFKeIk35NocRevcOLM59fievf+hPBIEOjS5rwc3XikEYZ7w041dnd4b3vCzC4fAH8vLsaZY0ulDW6sLPCigHZCZIPm9Xth8cvLcCxuf3QqhQnbbsJIYQQQsQaRVe0HR4u7StuLMBnhhdvq8DBWgcO1jqwu9IGmzsiYxyQnYStPT6UMe5gdo/0eoHV5UelqIZ4b5UNgLR8wub2SS5NAC13tCCEEEII6WjikghbKL6xikpG+SYDB2ocwrJ91TZJHTIAuDtxxpgC4w5miwiMm1w+VIp6FfMfHnFgbHX5oz5EfGC8ubQR177xB37ZV9NRm0wIIYQQgo//PIIZb/8pJPTEgbHD4wdjTJLI4/9+tCHcneJog0tSVgoALqox7r7sMQLcKlHG+FBdKDB2iEspfJKaHX4ZADzzwy78WlKLv32+taM2mRBCCCHdnMsbwENfbsPKPTV4d80hANIkXpBxg/GkgTH39zJRd4pqq5syxiTMEVVKIc0Yl4Z6/om7Utjc0RljPlDeVcGVXlQ0uVvdSJsQQgghpC34xB0AHKixA4gu67S7/ZJSCj5wPtogCoxtnqiYxkU1xt1XrFKKKmt42sTD9U64fQFJCxSry9dsYCwXfZYO17WukTYhhBBCSFscrA0Hxny8Ie6gBXAxTmQphdXtkwTQVVZ31LgpD5VSdF98KUW6SQMAqHN4UOcIB8aNTl/UTDHNDb7z+AOS7hX7Q7/gWsPjD6Ck2tbm7W+tz9aXYtnOqnZ5rmqbG7+X1Ea1rCOEEEI6C48/gOU7q+Dxn3hdAGMMb/56ED/tap/zaKzn31NpE1rEtoY4MK62cXFL5Ay+XMZY3MfYi7IG6SQf4oyxQc111+rM7dooMO5gfFeKrEQtAKCk2g7GAJVChmSDGgA3oE6MK6WIDoyrRZlmADgk+tAey32fbMbkeauxaGtFW9/CMe2ptOHBz7fi5vfWw+lt/mfgu78fwoy3/0RTMw3Aefd+vBlXv/EHft5d3d6bSgghhLSLBSsP4Kb31uO5JXtaXG9XhRVXLFiD30pqm13nz4P1eOL7nZj17voOKZN8fukenDN/NV5eWdLqx4g7S9Q7vPAFgpJ2bUBoTJToCneTK5zsS9SrAEgD46xEHQCqMe7WwoEx92HYU8VledNMWuQn6wHEDoytrug2b1VW6VTRB9sQGP+wvRIA8NovB1q/8a20pyqciW6pvOPRb3dg5Z4afLXpaIvPt+ZAHQDg2y3l7bOBhBBCSDv73wouyHzj14Mtrvfqqv3481A97v54U7PriAerRZ7r28OHfxwBAPzfz60PjA/WSq9K1zu8UTPYVTa5hamhAW5A3q4KKwBgWF4SAMDrDwpdKvhYyOWnGuNuyRcIwuXjfvllhzLG+0JBZEaCFvnJBgDA5iONAICsBG4dq9snZIzNWm4Olsg2bwBwIBQYbzhcj4nPrcD85Xtjbod4AKArlNH1+AOos3tiri/2yZ9HjhmgNol+QdY7Yk9nLb58c6Q+9lzqkQJtuORDCCGEnEzeVmZ2l+/irn42d34EpLPHtRQYM8awYNV+rNxz7CuqlU1u4dzLB7Ref+xtZozhrws34+KXf0N16PUjk281No8wuE4XmnCMD+hVCplQJrG9rAkA0CPFgAQdlzXeX80F2ZQx7ubErdr4D4PTy30aMsxa5Fq4jPHO0K8rPlB2esO1xDlJ3DpNLp/QRzAv9Dj+Q/vC0r04VOfE/OX7hAlDxMRZXH6Q31WvrcXouT+hpNoOty+AD/84jBqbNFAuqbbhH19uwz0fb0K1rfkvqvgXZOSvSeHfQlRi0dJlIr/ob/4ABcaEEEI6J1krk5469bFnrY0sR2jOyj01eOaH3Zjx9rqo2uaSahu+2nQUwSDDku0VGD33Jzz8zfaoJFOs519zoA5fbSrDpiONeOf3Q2h0eoU4pDCFi01q7B7hsbkWLqbh64nNWhWSQuWh20KBcU6SDmmh8VX8+8tJosC4W+OL1LUKBkuo1oaXZtYgPxTg8vjSCgAoD/0K4z98VrdP+BU5uocFAPfrrcnpw8YjDcLjPlx7GACwdEclFqzaD18giCP14V99NTYPbG4fNh5phC/A8OOOSsxbthf//Go7HvpS2hu5pDp8GaUkVAKy7WgTzn5xFf6zfJ/wN8l0kK7Yv4jFv4bFHTgiObzhv/kpY0wIIaSTUspbFxm3ZjXxeZQvpQwEGe74cAOufG2NkG3mE2mANOnFGMN1b/6Jvy7cgkXbKvDWb4cAcCUUkVeHjzY40eDw4oWle7DhcD0A4C1ROcivJbVC4i3drBGScdVWtxAs88v4jLFJq0SSnguM+c5b2Ul6pJu1ktcuCCUAafBdN+UPBNErzYh0HWDWSQPjrAQd8pKlgXGaSSNcnuB7AOaKMsb8h61nmgkpRu4DuGRHBdy+cJb1y41lWL23Bre8vwHP/LAbH/95BIdEXx63LyjJKh9tcOHLjWUAuMs94k4Q4j6E/O3/rSjB3io7Xly+V/iyNcaYJ72yyY3b3t+An3dzI2zF7efEA/Rsbp/kSyv+WyBIfZoJIYR0Ts01TqpscsPdTAKIL2V4ZeV+3PPxJmE9cfKIL6VcvbcGi7dVYu2Beny6vhSAtBxDPLtcrd2LitBV5d/310qerySig1VpvRNPL96F//5cguvf/BNr9tfhJ9Fg990VNuwLJcYKUwxC1rek2i5kn/MsXIDLB8YJOpUw2I4nzhjzeqQakJOohUW6uFOhwLgD9Uw3YdHdYzF7YAAJWukHJjNRG5Uxzk7SwRSqKebrifnLDuIa4/QErXBpgw9qTy9OQZ5FD5vHj+vf+lN4zsXbKnC4TlontClU0wwAh+scktIGcTu4UlEbuXqnF4wxrD8czk6vO9QgbBuP/zL+56d9WLKjEje+sx6ANDB2eLgDgcsbwDkvrsaE51aioskV+puoHrqFzDIhhBAST+K4mK/l/XVfLcY88xNufm99zMc4Qn1//71kN77dUo7vQ52iJOfR0PlyfSibCwAbQudecWBcKhqvI74yfLTBJZmhLnKAf2m9C6v31XDb4w3gqtfXgjFgUp80mLVKeANBof1qYYpByPruruSSakaNEsmh5BwfJyTo1chMkGaHcy16pJrDEbBcBvRON2HF/WfgwUGd9/xOgfFJkmSICIwTtEg1aaBVhXdBbpI+KrPM1yHb3H4heMwwa4XLEX8c5L44Q3ITMev0wqjX3VLahP3VEYGx6Euyt8ou+UKKg+hSUca4wemFzeNHrSi7y/dRFrdf459r3aHwF9ofCEraz/HB79ajjShvcsPu8WPlntCX1BP+sri8nfeLQwghpHsTX2HlEzlfby4DY8Av+2qF8574XGb3+CVt0PhzrnjuAj7BtKM8XDbBlzbUiQJjcScLcVnFoTqHZCKxjYcbJdu95kCd5O+8uyf1RL8sMwAIgXFRqhFpoeCWD4yTDCqhMQBf8ZigU6EwxSg8V65FB6NGiXRTOFhOMWogb2X5STx12cB47ty5kMlkuO++++K9Ka2SYY7+JSWTyST1N0VpRiFjLF6Px/86zDBrUZhqkKw3MCcB143Ox9Wj8pCdqMNTFw+AWauEyxfAn6EgVaPkdvdmUca4NqL2SDzZiPgyTYPDi6qm2O3ixIE1f1t8wKiMmCedryMWt3njp5t0eCljTAghpHNjjEE8DIY/X4kn3jpc5wRjTDJ2xub2S8oH+XNukyt68J14oowjdU4Egkwy85z4HC0OjEsjOj/xGWO+JpqfI2BoXiJum1CEdLMGj53fD0NyEzEgK0Hy2IHZCUgLBbf8AH2LXg1TxFXwBJ1SuJINAP0yuQA7O3TVG5COo+rMumRgvG7dOrz22msYNGhQvDel1RRymSQ45j9oZ/RMBQD0Sjci3ayN+rAlG9RRdTvpCRqhPyBvUE4C5HIZnr54IH77x1m4ZlQ+huVL1xndIxmA9FdmJP6yCGNMUmNc7/AJ9Uu8mL90Q7fFHS7q7N6YGeNK0fPxBwenKGPspIwxIYSQTkg8tgcIZ4Xr7OHAtbLJDY8/KOkKYff4JVlffuIuaY2xH4wxYRA+wLWGq3d4JaUU4sA5smRSjE+AjSiQxgQjCyz4x7l98Mf/m4wZ47grzqNCcQLAlT70z04QMsY8i0EdlcRL0KkwuodFSMBN7psOgItNeD1EGeXOrMsFxna7Hddccw1ef/11JCUlHfsBncitE3oAAG6bUCQs+8e5ffCv6X3x9szTACDqw2bSqpCdGP7FlWLUQKNUYHh+ktAfsE+GCZkJOkQaIQqMLQY1eqUf+0NZUm3Hla+twdhnfpYEpg1Or1DjzPcq5C/F2CLazLi8AUnrmXqnV3KfH2Anrmfmg25JxriNgbHN7cO1b/whNF0nhBBCWsIYw7++3oZ/frVNcqXzWBwRs7zy50txRrci4mopwJ2nxMFtnSM6MOZnk+MzzSYNFxdUWd3C+gCw5WgTznp+Jf719TYcrm9+ci3eyAJLi/cBYFQPC9Sh4HZMUTJXDhFxxTsjQRdV9pmoUyNRr8a7N56GZy4ZiEuG5QAAMhN0GFecDJVChguHZB1zGzsD5bFX6VzuvPNOTJ8+HZMnT8aTTz7Z4roejwceT/hDZLVy9To+nw8+X8vTErcX/nV8Ph+uPS0HU/ulItmgFpar5cANo3OFdYyifocJOiVkLIBMswY7QnNsZCVohMfOu3wgPvqzFHefWRTz/QzJMQu3+2WakGKIzkbzv1zTTRpU2Tz4enPsyTwaHB6UhYr7B+UkYM2BelTb3HB7vMLsfgBXb1zWIB0BW9PkQpMzvB8cHj98Ph/q7eGMcZ3dA5/PB6towIDLF4DP5wNjDJuPNqFfhgkaVfP9IL/bXIZfS2rxa0ktbh6XB1moyaR4H5D4oH0Qf7QP4o/2QfxF7oO9VTZ8sJabFW7m2LyoQfFidaGZ34pSDWhySK+gWp1u2F1q2ETnw1qrK2q9RocHNdZwprfW7oHb45U8rsnpxZHaUD2vXoXMBC12VthwoNoalak+UOsQJvsCuOQaH4yrFDL4RPMBDM0xQ6eSCxOPDc0xRX0WdQrguUsGYPH2Sjxwdk/4fD4kaqQ51CyzGia1dJlJI4fP58PwXDOG55oRDPgRDOW23rpuGBpdPlhCsU88vgdtea0uFRh/8skn2LhxI9atW9eq9efOnYs5c+ZELV+6dCn0+pNb67Js2bJWrWetlAHggj8dfFi8eDG8jXLwyX2luxGLFy8W1r8gCTi8uQKHN0c/lz8IpGgVqHXLUIBqlO2vFp4bAPK0btQ5uOfN07hQZYu+gGBSMdh8MlQ2OrBuxz4AcujdtQDkcPuC+OjrHyD+GNVZnfh26UrJst83bEG1Wya8B5cviO8XLcb+owoAXPBaY3Vh8eLF2FAefv8urx+LFi3G5joZ3tmnwNDkIGb0ar6F25qy8GM///YHRPwOaPU+IB2H9kH80T6IP9oH8cfvg10N4fPGVz+uQq+E2FljxoCnNytQ4wb+NjgQatUWPs+t+nUNdumYZNnmnfugqtkjWbZ2w2YcsofPhw0OL774TnoeLa9rwrc//QpAAYPMC7g8AOT4/tfNAORQyLj6ZobogWzFBi82ubnnzjcEUGINn9dLtv6JkclyrK6UY4gliN9WNP85nJYA7PyjHDtD91M0CtR6Qufrw3uw1bpbss2Hd2/F4sotzT5fLCfze+B0HjujzusygXFpaSnuvfdeLF26FFqt9tgPAPDQQw9h9uzZwn2r1Yrc3FycffbZMJvNLTyy/fh8PixbtgxTpkyBSqU65vqeTeX44eh2AECPrGRMmzYCvi0VWP35NgDA5BG9MS1G94nmjDvTi8omN/pnmfHHwXq8t49rIaNRyjF9VG9sWrwHAHD1mYOx7rNtUY+/bGQB3v79MFwBGZTmFKCqDhNHDMD6ZXvR5PIjb8BIYFN4/nd3UIbiAcOAHeHJQjLyi+FrcAFVlcKyCZOm4JUD6wArl132BmWYOPls7P/1MHB4PwDuSz/p7HPw6YebANRjU50cn06b2ux7Lfm5BDhyAAAwZPQZ6BkqHWnrPiDtj/ZB/NE+iD/aB/EXuQ/YtkpgN3e+6jVgKKYNzIj5OKvLh+q1KwAAyuz+GJSdAGwNt0YdOGwEMs1aYMMaYVlSejaGDM8GtoVbt+UX90H1oQagphYAd57rOXQssD78XAG5Gjk9i4Hdu9A7Nw0Wgxo7N5QhYEoHUIMUoxZD8xKxZEeVZBtTjWqcOTQPm5Zz5YQXntYLLywPlxb+5fyzcZ1Cjq1lVvTPbPkKbKTFTZvx405u0N61085AYYoBT279WSiTPH/yePRMa10NcTy+B3zFQGt0mcB4w4YNqK6uxvDhw4VlgUAAq1evxksvvQSPxwOFQrqTNRoNNJroLtIqleqkH5Ra+5r5ouL0/GQjVCoVJvXNQJJ+N1y+AM4fnNOmbc9IVCEjkRspmmMJP3dmghb9shMBAGqlHFMGZAGiwPijm0dhe1kTrh2dj7d/PwzGgL1VjtDzcH0Nm1x2HKrnLhPxl2+CDDjaJO100ejyS0blAoAnKJNMDAIAVg+DO2IaaB+TSy4dBSCHtpkvs80TXs8VYFH/TvHY70SK9kH80T6IP9oH8cfvA6cvfM5x+KLPG7zaunBJhNUdgCdiCIw3ANi80iuaVk8AESXGcPqCqHdKz32HG6TlFja3H3UObp2MBB2SQ1Mt7wnNQGsxavDYBQMwMCcRpxVacPkCLhgvSDFgYp90zFteAoVchguH5gqBsVwGJBi4sUijilJj/6O04IqReVi2qxpDchPRMyMBMpkMerVSCIwLUk1QqdoWUp7M70FbXqfLBMaTJk3Ctm3SjObMmTPRp08f/P3vf48KiruqvllmyGVcb8CB2dxoziSDGqv+diZ8/iCSjcc/XUyeRS88d2GKAWN6JOOlq4ciM4HrN3jjuEK89dtB3DAmH2OLUjC2KAUAkKhXodEpmmDErEW6WYu9VXbsC31RU4waeP1BePxBSY9GgKvLihyA4PD4JQ3IAa5xuXiCD4AbqCduiVPR5Ja0hBETd8eIfD1CCCEkki1GV6VYypvCdcE1No9kllaAGyxeB+k5rdHpjRqkZ3P7JYPvAGB/6JyZa9GhtN4Ff5AJM9amm7WwhAJjvlNUskGNjAQt7jyzGAAwtigZv++vw7Wj8zEoJxFvzxgJrUqBvGQ91Eo5vP5gs+fN1prUNx2r/3Ymkg0aYfzOpL5p+PCPI8iz6KFXd5lw8pi6zDsxmUwYMGCAZJnBYEBycnLU8q7MrFVh/pVDse1oIy4Zli1ZfqLkchn+NrUPXl99ALdNKIJMJsN5g8KjRP81vS/+MjIXxRGXQyx6tTDVMwBkJGiFdnP7qrkBAiatEmadCjU2j9CTuFe6EXur7Kh3SNu1AVyLGn5QQI9UAw7UOFDvjBUYBySjdSsaXc0HxqI+kHxgXNHkwjebjsJEY10IIaTbK2t04fcqGSb5AlCpVJIkitXV/ImiojGc1W1y+WCPSBk7vH4hWE4xqlFr5wbq2T2RgbFP6CyRZ9HjSL0TJaHplzPNOlQ0uuEPMmFK5jSTJqpdWlIoUOa9ecNIlDe5UJTKnbvP7JMm/O3R8/th/vJ9+Me5fVv4V2mdnCTp2Kw7zyyGQi7DRUOzm3lE19Tl2rV1BxcMzsI/p/drtmTgRNw2oQgbHp4i6VXIk8tl6J1hgiJiZhqL6EuoVsqRpFchKzEUGIcyxiatUmgfx4+Q7ZluAsBlgsVBKwCUhhqTa5RyoR1dg8MbVXIRmVnms9YAN8HIpBdW4tVVXE1yrIzxk4t24Zkle/H9EfqoE0JId3fPJ1uw8IACb/1+GID0vMFPrPHQl9twzRtrJUFtpShj3OTyRWWMHR6/UCLB9+ttcHphj7h6WW3zCOWBfTK4c2RJKMFk1qmENmj8sjSzJqodqyVibgOdWiEExZGuGZWPdf+cjCn90mP+/URkJerw+IUDouZV6Oq6dLSwcuVKzJ8/P96bccoT/zpNN3OXUTJCc6LzLWYS9Wphikg+u9wrjfvS19k9wsEnOeKSUJJeLQTesUop7B6/ZGY9cWD87u+HsL/Ggbk/7AZjTPJr3+7hbi8KzUO/prpLf9QJIYScILcvgK1l3CCsFXtqAEjL7mxuPw7WOvDxn0fwW0kdfthWIfytvEmaMXZEZYwDqA9lgnuEZqZtcvmE5+fPffwMdRqlXLj6yZdNJOjCUy3zV1TTTFpkRQTGkRlj0r4oWiDHlCz6EvKz90V+UVONGiFjzOudwf2Ctbr9QvPzzFCmmQ+ME/UqJOlFgXFExrjK6pHUGIunpeYvPwHcr/DImYN8AelAiGCw9c3bCSGEnFrEs77yE0hF1hgfEs0gt6vCJtyujAiMY2WMG0ID5vjAOMjCtcl8MonfhmSDGmkRE2ck6FRR59E0swZmnRI60RXkyAk3SPuiwJgck/hLmJ/MfeH5LzkvxaiOmgmnOM2EiKoMZJi5gJqf412cMW4Q1Rjzc7qLp7wEIJmW+qCoqXlFk1syu16sAQ71EYP9CCGEdB9HReeT6tA0ydaIGuMaa7ir0p6qcIsv8eC7JlHtMF96yE31zD023ayFMTRb3dF67nGZEedMi1GNNJO0djhRr5KcRxVymTDYjU8qAUBu0smdh6G7ocCYHFPvUB0UAGFgXmTGODlGxjgnSYdEfTjbrFMphHWEUgqDSlJK4QwdbPgDhniueICbEhPgfuWLf/1XNLok9WBWt0+YH55X3ihtiUMIIaT74BMyANDg9CEQZFGlFNW28HmCH0PDGJOci2wev/A4/lzl9ASEjLHFoEZiqA6YH08TmUyyGDRRgXGaSSOMuQGA3CSdEHiLa4jzkykw7kgUGJNjGp6fBLWC+6icXsy1cDPrlDCIpq/OTNBKAuNUkwZalUIycC9Rr4JRwz2Gz/wmijPGjvCv8NTQAaOsMXbGeJ+ojAKQllUAgN3tR51dmiEWZ5sJIYSc2hiTls+JM8aMcVcpI0spqm3hhEq1zYMmpw/1Dm/UVMwVoQwyH9w6vH7Uha5SWgxqoUSQP+9EDqDjW66JpSdokZMUXo+/QgtAGDyXa9FJ1iHtr8u0ayPxk27W4qs7x8LhCWBAqLeyTCZDrwwTNh1pBMD9mq0WXYLKDX1xxYFxmkkDg0b6kUsS1RjXOTxCjXGqSQugSfiVXpxmREm1HdU2D37cUYnSeun0jiU10sDY5vZHZ4xDB6jdlVZc8/ofOKNXKl78y5C2/nMQQgjp5FzeAK5+Yy1c3gAW3joGCTpVVGlend0rGZtidfkl5zEA+ONgHbaVNQHgBp87PQHYPH7hCiSfxLGLOihZDOqoAXK5Fj1kMoCP1VOMauQk6aFRyuHxc0F3ZoJWsj3iLPFlw3KgUynQP8ss9BEmHYMyxqRV+mcl4LRCi2TZ+J7c7DmZCVpkJ+rQS1Ry0T+LC6BTRZeKUk3aGIFxOGNc2eRGIDRAju/byNd1FaUakGLk1rv1/Q14ctEuyfNEZoxtHl+zGeN3fjuEOocXX20qw5G66PnT7R4/bn1/PZ7/cU/sfwxCCCFx5QsE8eBnWzB38a6ozDAArNhTjU1HGrG70oYl27nuEpFXIGvtHkkJnssXkNQSA8At72/Af3/mZo8bkJUg1ADzQXZqqKe/+PyVpFcjKaKlmkWvRopogq6cJD0UcpmkdKIwxYBRhcnC2JxxxeG2qnK5DOcPzkKPZtqykfZDgTE5brdN6IH/N60PXr9+BORyGfplmpFr0UEmA6YPygQAFIkm40g3a4QBCbxEvRpJBu4AIu5IkRo6gPCXr5L0alw4JLqJOH/giAqMRRljlSI0kC90UNxVER5Q8WtJbdRzLt5WgR93VOGlFSVRWeeWBIMMb/xyAL/FeE5CCCGxfbnxKL7ZXNamx/xaUovPNhzFq6sPYG+VPerv6w81CLe3HuUyvnwwq5ZzAeyReicimxXtD51LhudH9+a9YEiWUDvsDXU94ksp+MSLSaOEVqUQroTyjFolskSlE3w5xFWn5QEAzumfDo1SgYwELV6+ZhievGgAzhJN1EFOHiqlIMdNr1biljOKhPtqpRxf3TEO9Q4veoUm9ygSzaLXM80Is675UgqeTqWASStdL0GvwoNn98bkvun482A9Xly+F4l6FS4fnovfSuqES1EmjRI2jx92tx+1oYzxoOwEbDjSiPJGNxhjwvSbALDuUD2uHpUnea3dohY9eyptSCnWwOUNIMhYVMZbbPmuKjy5aBcUchlKnjoXMpkMvkAQ6w7VY2SBBSpF879Dg0GG+cv3IjNRJxwoCSGkKwgGGeb/tA/FaUZcMDirxXWbXD7sqbRhZEESZDIZjjY4MfvTLQCAMUXJwqyqzT3WqFFCIZdJEhy7KqySQeIAsOFwvXB7d6UNvkAQVaGBdXlGoMQKHAp1NlLKZdAo5XB4A0KCZtbphdh6tBH+IMN/rxqK7EQdhuYl4dP1pZLXiZyVzhK6spkYkTFONnClE1tCQTpfJnHT+EKMLLSgd3p4+6cOyGz234B0PAqMSbtKMWokl4vG9EiGViWHP8AwtjgFNTZP1PoqhRxmrVJom5OkV0UFoAk6FZQKOcYUJWN0DwuG5CWiX6ZZGADBy07SYXelDTZ3uHXOwGwzNhxpRFmjC1VW6aWzPw/WIxI/zTXAdcVwev2YOv8XOL0BLPvrGc02V99TyT0uEGSotXuRatLgie934r01h3HPpJ6YPaVXs/9u+2vs+L/Q5boLh2SdUvPOE0JObRuPNOD/ftoHAJg2IAPKFpIA93+6Gct3VeO5ywbh8hG52FkeDnBLquzNBsbbjjbh4pd/w9jiFLx342mSnvZ7q2ySdV3eAHaInndvlQ2VTW4wxiVwMnR+lFhlQstPk5brEyy+anlWnzR8e9fp8PqDGJybKCxP1EmP/5Hby/f9j0z4JBvVmNwvDYu2VaAwxSB0lpDJZBgien4Sf1RKQTpUmlmLb+48HV/dMQ690k1Ij/h1zfdmFA/SSzKoowJj8cFIJpNhQq9UpJo0UQcl/vKUNxAU5rYfGBow2OD0YXtoEEWaSQOFXIayRpekhQ8AHBBllMsb3dh6tAlH6p2otXvwSwtlEjZRwM2XYHz4xxEAwIKV+5t9HADJ7H7UVo4Q0pWIj191jub7xTPGsHxXNQDg4z+5Y2Oj6LE1LZSufbWpDP4gw+q9NWhy+SRdhsTHbABCpjdRr4JCLoPN7cfGI1xpRaZZC7Oaq5/gJ/MwaVUwacMZXrOWK4fom2mWBMUAd/VSjJ/Mg5ccSgwlG6WtSvVqJS4cnI13bzwNH908igbQdWIUGJMO1zvDhIE5/GC8iIlBDNxBRJyFtRjUktn2AET1SBYeb1RDfHzJTNAJ9w+GDnr5yXroFNyB8Lf9XGDbP8ssdNhYd6gey3dW4Ynvd6LO7pFkoSutbkn/yr2V0syEmLgemR+dzA/G8EbMwhdJ3EtTfJJpjW1Hm/D+2sM0sx8h5ITY3D688cuBqP7xxyLOtDa0MJGSU7Qef0xscoqCanvzj91e3iTcLqm2Cz3tAeBArR37a+z42+db8HtJLTaGuiWNLkwWMrOrQlNAZyVqYQydTg7VckkRk1YpKfOLnJFOLDHiXJSVoINJlMjhB4kXiFqt8YPQ5XIuqRPZuo10LnS9lpxU5ojaYXlo+K04EE6KGL3LLYsdGCsVciQb1EI9cbJRDaOaqzP2huqOLQYVkjSAywms2V8HgOsPWZwmw5bSRixcV4qNRxrh9QdxoMYunYI6IjAWz7bn9Ppx9et/wGJQ443rR0hm2mtw+KJGSgeDTHi/kaziXpptDIwf+GwL9lTZkKBTHbO+jxBCmvPOb4fwwrK9WL6rCp/cMqbVj7OLftjzk1zEEnmMBKSJgFq7B/UOL65+fS3yLHq8et1wIbMqPvZWNrklGeNDdU78/fOtWH+4AYu2ViAr1OlhRAE3gO5AjQPLd1UBCAXGobF6fHBu0iphEJWvRU68ISauHdapFNCpFUg1aYQrhnzyp0A08DxybA3p3ChjTE4qmUyGyX25kbZXjMgRlosD4XSzRvjVzYtshC4mfmyGWQtjRPBt0ath0XBB6u5Qxjc/WY+RBVz7ubUH6oUgekUoq8CrbHKjTFTasF/UL3n13lpsLm3Ez7ursbfaJsl2NDi9sLr8kufip6RmjOHllSV489eDwt9OJGO8J1Rft/ZAXZseRwghYu+vPQyAOya2hcMjnj2OO365fQE888NufLulXPib+KoaPwak0RU+btY7vPjzYD12V9qwdGeVcLy1uX2S8SlljU7Jc3n9Qaw/zJVKOLwBYQKoyX3T0SudG+TGj2EpSjXApJImLUxalaREosXAWCdO4nCPSRGtn2fhMtRGjRJ9M80AgLP7ZTT7fKTzoZ8x5KSbc+EAnFZYjkuHhQPjXqIRufnJhqiBCy0FxmlmrRDwppu1MGmVqAhdddOq5NCrFcjSA9vD3XuQn6zH6B7JSDNpUG3zQKWQwRcIHyyzErQob3JHZYwP1DjgCwShUsixTzTgY3eFDXWiA3WTy4dah7RertrqQYpRg9X7avHsEq5H8oj8JAzOTZROS+qRBtSt5T9GuQYhhLTEf5zlWOJjFl8u8dn6UixYtR9yGTC2KBkpRo0kY+z2BeHyBtAoKqWod3glYz62Hm1CcZoJhyP6ze8styLIAJmM6/3L1xirFDIEggxBBozvmYKCFAN6pku7VRSlGnGkSrr9Fr10FrrsFmaWE/+NL7nISdThz9Ay8XTNb9wwAit2V0vOdaTzo4wxOemyE3W45YwiYZACAAzJSxRuD85JjCo5aKlLQ4HoQJSXrJf8ok82aCCTyZBjkB7w+2SYoVcr8c7M0zDr9EJ8MGsUpg8Mt8g5K5TVrnN4hQEaAHfp7XDo/h5RYFzW6JIMOmlyRU8wwmdI1ok6YWwKDQixe8InB/EUpcciDoaP96RGCCEAoG6hm0RLxKUUfNcfflbUIAM2hrK5kcfEeqdXcoWMC4zDiQi+08/+iJlNt4YGUScb1OiVFg58753UEy/+ZQhuHl+IF64YDECadAGA3ulGmCIq81JMahSKSh+K05qfREO8XmYomB4eKtlQyGUYEJrcCuDOddeOzodOrWj2+UjnQ4Ex6RSG5ibisfP74bHz+2FANnf5if+VfWbv1BYfy1+myk7UoTDZIHS6ALh6MgDIN4aDxkS9Sjig9csy4+Hz+mFUj2ScMyB8uWtq/0zhJMFnK/j66MnzVuOrTUclLYIO1jqEXsoAN6AkcnIQ/qTATy8KAAdCdXPijDF/klm0tQLzlu0VBvDFIh704g9QYEwIOX4MrTuGWN0+PPH9TmwpbQQgLaVwernbe0VtL3eGeg5HdqxocMQKjMPZ4V2VNsxbugf3frIZAISuRnyGOMWowaDccCA6dUAmLhySjX9O7yd0LBIHsmatEtmJOmgV4Ymf+OcZWWiBWimHWinH6B7hGeciZZi1wmC6EaFyvMuG5+Dm8YWY/5chFASfAqiUgnQKMpkMM8YVSpb949w+yE7S4dJh0TPeiZ3eMwUf3zwaOUk6yOUyYeAFAOQmcdnkRA0wfWAGFm2rxIyxBTFb5UwfmIl9VTZolHKMK05GmlkjyV5cOjwHb/92CADwt8+3SkovxL04Aa5uri4iMOYDZfGBvzI0gMQWkXHx+oP468LN8AaCGJBlxtn9uaC9tN6JBz/fgr+MzMXFQ3OEkxCAFgNoQgg5FvEhhC8Z+9+KEuwst+L5ywcLQd8bqw/gzV8PYuWeavx0/0RJb3iHh/uxLq4JLq3njqORx8QGp1dSSlHn8EKtDOfrVu+tweq94XEflw7Lwcui1pepJg1mjC1ARaMbg3ISYmZ61Uo5zu6XjqU7q3D7xGIAXAlGulkrHN9TTRpkJ+rw/d2nQy5Di10j5HIZFlw7HGv21+Ka0ORQGqUC/5zer9nHkK6FAmPSaaWaNC1OiiE2pij8C18cGOeJyiyeu3QA/jqllzDjUCSFXIb7z+4t3M8QHTgtBjVmT+kFm9uPzzcclQTFQDgjwmty+VATcdmw1u4FY0wymroqdPIQl0/Y3H4cqnMII6bF9XWfri/F2gP1WHugHhcPzYmZqSGEkOMhbqTj9AagkAfx3I/ceIhpAzMxfRBXbrYyFKzys4jaJIGxH8Egk5RN8MmA+oiMcb3DK+nI0+TyweMPIJZbz+iB68cUSALjFKMGerUST1w0oMX39fI1w3C43okeKQb4/dy29kozCsf3HincOSGy7KI5w/OTYk4ZTU4NVEpBTjnD88IHLPHBS6WQozjN1OrG6ukR89qbtCo8f/lg3CjKbEdOXc1rdPqE7Ah/ya7O7oHV5Zf08uRnb7KKB9+5/WgQnUAqRf06tx4Nl2EAgN0Tfi7x8xJCSFv5RGMWXN4A6kXB7eH68FgLuegY6vIGJD/QHd4ArG6fZMwDH4DWxgqMI7rwuH3cNqSKOj08ffFAPDStL9JMGkkJREvdI8SUCjmKUo2SYz9fsgdET9JBujcKjMkpp2+mCQ+c3Qv3T+mFcUUpx/08GWZpYMybPihcizwtYk57TegyYJMrXGPcO4PLQtQ5vCiPmMK61u5BMMgiSil8aBBdXqwUZZiDopSO3eOHU3RCcvsoMCaEHD/xVSen1y/J5lZbw2UQLtGP8DqHRzL4zun1R42vqGhywR8Ioj40AJk/npbWu4TyDZ0qXJubYtRgQFY4cD03NP5DLpchXXRcFl8RbKsZY/IxY2wBFlw7DFoV1QWTMAqMySlHJpPhrrN64u5JPZudUKM1xIFxriV8AB6Wl4RzB2QgK0GLWyb0kMx6xM92JO5K0TudO8DXimbV43tr+oMMjS5fVClFo2j2KHGtnji70uDwSmr7KGNMCDleHn9AUiLmDGV+eeJgVzLLp8MXUWPsFyZcKkwxQKWQIciAaptHOCbyJQt8xx+1Qi4MlAaAXIsOM8cVIlGvwr2TekpmRhWXyuVbjj/Ta9Iq8dgF/TE1IrlBCNUYE9KMnunhWuRB2YnCbZlMhleuHS7cz0rUCa3bemWYsKfKBqc3INQS9+EzxnYvykOTheRZ9KixedDg5BrXRw6+E2eMa0QnIXFZhc0tLcugwJgQcrycHunxw+ULSCYp4n+g+wNBYbIigGu5Fjn4jg+cU40a+AJBHG1woVzU0rJnuhE/767GoVBXHrNOiWSDRqhZzknS44xeqdj08JSo0rehuYn4M9Tysp8oq0xIe6GMMSHNGFecgjN7p2J0DwvO6pPW7HriTEfvdCP443hZaGIQvpRCnDHOTNAJM/bV2DySE4u9mYyxPxCUZI/tHr/kcS5RKcXqvTV47NsdbeqJTAjpPo7UOfGvr7dhdyU3cNgRMXjX6Q1Ijh/8safe6ZUM0mt0Rl658qM2tG6KSS1kePdW2YUZRvnew3y7SpNWBYsoK5wfukIXazzIdWPy0TPNiBvHFUoeQ0h7oYwxIc1QKeR4e+Zpx1xP0h7OoodZq5L05uQDY48/iJLQVKUZCVwvzH3Vdhyud0hardk8fjSIAmO7xw+n148ml0/STsnm9jXblWL2p1tQa/cgI0GL2yYUteFdE0K6g+eX7sG3W8pxuM6J92eNEtqs8Vxev2RQcHUo2BX/OAeAiia35Phl9/iFzHCyQQONkqvf3VbWCADQqxVRM8uZtUqhRzHQcu1wTpIey2ZPaO3bJKTNKGNMyAkanJso3O6fZUaCLjytklopR5pJA32o/+f2Mi47k5kQbhJ/sCY82hsAvP6gcBLi1dg8kjZvAFdKIZ7gw+0LIhhkcPvClzJ/K6k9wXdHCDkVfbulHADwyz7uGBGZMXZ4pBlju8cvqR/mifuy84/j10k2qoXJlPiOOilGDZIjMr1mnUpyHB2ckwhC4oUyxoScoHMHZODbzeXISdKhKNWIRL0KR0KzPqeZuCmpk41qOOtdQnlFhlkrlFLwlxPNWqWQoRFPLAJwgXFkpsYWOlGJuXwBNLqkA/kIIUQscjIgjz8QVWPs9AWijh/cADrpcYifvINnc/uE7hPJBrVQDrEjNAlSilEdVQKRqFfj3AGZ+HZLOTLMWmFwMiHxQIExISfIpFXhg5tGCffFGWM+K5xi1EhOIOmijPH+Gq68IsmgRiDI4PAGUBYjMI7OGPuiJvVw+QKSExcfYDPGcP9nW2B1+fDKtcOhUtDFIkK6iyanD7PeXYfpgzIxc1xh1EQbNTZPdI2xxx/VY7ja6o5qxcZnjDVKOTz+IBzegHDFy2LQQKeWHmuSjRok6tWQy8Iz7aWZNNCpFXinFaVrhHQ0OjsS0s4kgXEoK5xskDaizzBrhb/xM9uZtSoYQxOG8APpskKXIWtEA/d4NrdfMsEHwPUXFZ+46hweBIIMDU4fvtxYhuW7qrHhcMMJv0dCSNexZEcF1h9uwJzvdoIxFhXcVlk9UVefuMF30mVVopZriXruOMf/+M4WjbXgu01YDGrJGAyASxIo5DJJ1ji1lRN1EHIyUGBMSDtL0ocP+DlJ3CCSFGN4mUmjhEGjRErEycCsU8KkVUmWFYf6fdbYPEKrN75vst0dXUrh8EprABkDGpxeSRY5MhtNCDm11YkyxFaXP6osq9bukYxXAKIn+AC4jDHfPrI4lSt38IQ6TSToVTCGjk18u8lkY3RgzAfB+cnhHsR8koCQzoACY0LaWXFauD6On2o0RXTgL0jhlkWeDBJ04ROL8Fyhk0+11SPMmtcr1OUisisFIO0hyquzeyXBcmTmmRByahNnfmvsnqhjRK3dI5lFE5BmjItCx7HKJreQMRYf5wCupEx8tQzgMsZmrfS4xrdi449tAE3JTDoXCowJaWfD8pKE26cVWgBwmRMef5KJvHxo1qpg0koDY/6EUW1z42Do8mS/TK6pPdeVQnoys3v8qLVJ6wfr7B7UOcInwsiOF4SQU5s4Q1xtc0dljOvs3qiMsUs0893A7AQAQEmNXTR7p0myvkmrlBy/ZLLw1TNxr/f8UCu24fnccVKjlKNPBk3UQToPGnxHSDsbmJOA/1w5BHKZTDh59M9KEP09EQCXTREPQEnQqSSXLo0apdDqaHu5FY1OHxRyGYbmJeL9tYdDXSmkJzOHxy8JggGg1uFFgyP2FNOEkFOf+DvPXUGKzhirQwNyDWoFHN4AHF6/kDE+rTAZX28ux64Kq9CjfXBuguQ5zFqlJGNs0auhkHMdKXqmmbC3ihtk3Df0w/6SYdmwe/zok2GCLtTOkpDOgDLGhHSAC4dk4/zBWcL94flJmNo/A30zzbhwCLecG4ASzhqnmjSSS44JOpWQVeZPbMWpRiSHSjBsohrjtNB6drc/RimFtMUS//dP15Vi3tI9Ua2bCCFdW4PDi799vgWr9tYAgHRArt0jlFbxA+bENcb8McfpDQhdKUYWJEEm4wbpuX1ByGXSH/sAV0ohHl8hnsTjpvGFyDBrcesZPWAIHeOUCjluPL0QY4tT2vW9E3KiKGNMyEmgkMuw4LrhUctTTRrhpJWRoBUG2AHcqO+CFIMkqzy+Z4pwuVJcY5xu1qI6NLU0XwPYI8WAA7UO1Nm9qI+YYrqyyY2/fbEVANAvKwFTB2S0/5smhMTFq6sP4NP1R7FoawW2zzlHkjGud3iF+30yTChrdKHW7hVaOKaaNDhU50S9wwt/6MCTkaDF8LwkrA91tOmZZoJWpYBJqxSyykaNEjmiYDgrIXx7aF4S1v6/SR37pglpJ5QxJiSOxN0qMhN0khq9NJMGZq1KqMUDgIuGZsMcWqfJ5ROyPBmhkgu7J5wx5qeiro3IGNfYPNhVYRXu81O1EkJODVuPNgIAHN4AamweSVeKOoc35jGCL8viM8ZVVu5HulwGGNRKXDwsW3iO8T25LC/fsg3gxlHkWsJTObc0rTMhnRkFxoTEkXhkd+8MU0RgzAW7j57fH6MKLXj8wv4YkJ0Ao4Y7GYlHmmeYuXWtLp/QvJ8f0MIFxuETo8MbwJ4qm3B/X6j2jxByauCDWgDYeKRRUi5VLwqM+4TqfWttHmGyIL6DDl9uYdKqIJfL8JcRuZgxtgCT+6bh9olFAKStKdNMWvQUzVg3IFtaakFIV0GlFITE0XWj8/HLvlpM7Z8Bo0YpqTFON3MnqAHZCVh46xhheWTnCpUi3Cz/aIMLQcaNCO+dwZ2kamweYapp3kbRJB+H6hySvwWCTBg0Qwjp3BhjYAyQh76zgSCTzLK5/lC9ZP0am0f48dw3lDG2uv1C7+GUGG0kAa4m+LEL+kv+ligJjDUYkJ2AyX3T4Q0EMblvWnu8PUJOOgqMCYmjHqlGLJ89QbgvboZfFNEnlKdXKyR1x0ZNuE0SH+Qm6dVID2WRa+3eqEb9m0obhduH6pwIBhnkchm+3HgUf/9iK+48sxj3Te51wu+PENJxGGO4+b31+ONAPd6/aRSG5Cai0uqGNxAU1tl4RDrT5f4au/DjuSDFAKVcBn+Q4UBoanq+Ew7PrGs+TChM1mM1fzvVAIVchjduGNE+b46QOKFSCkI6kREFSUgxqmHUKDGmKDnmOjKZTJJZNmrDmWY+ME42qIVawbJGV1SjfvFgHK8/iPImFxhjeHbJHvgCDPOX74PXHz65AtysV9TBgpD4cHkDaHRKe5TvrrRh+a5q2Dx+vLKyBABwOOIK0MYjjQDCnWv4zHCSXg2VQi70WOdnsMuOmKnOHDEbp9gFQ7IgkwGje1haXI+QroQCY0I6Eb1aiZ9mT8Tqv50p1BjHIp462qhRwRjKGLt93Mkt1aSJuiSqlMtQlBo7C32w1oE9VTZUimoT91WH65A/XVeK057+Cf/6elvb3xQh5IQEgwxXvrYGI59aju1lTcLyzaIrP6v31sLlDeBwnTPmc/AD7Xj8wN9kg/Q4IW6zBiBqNjux4fkW/P6Ps/Dujae16n0Q0hVQYExIJ5OgVwk1w80R1xmbNMqoIDjNpBHaKfGSjeHyCt6o0Mx8h2odWLytUvK3HeXhzhUf/nEYAPDxn6WUNSbkJDtQ68CWo03wBRg+33BUWM53nwAAly+A1ftqhMB4aF6i5Dn6RAXG3DEjJWIGzswEHTTKcGhwrEwwtz5N0EFOHRQYE9IFiU9WyUZ11PTSaaEAWLw8zaSVBNBmrRKDcriR4/trHFi0tRwAhKCcb+kWCDKUVIc7V5Q3hgf2EEI6nvg7Jx4fwM8mx3/Pl2yvFEopxkdMnJGVqItorxYKjEUtIw1qBdRKueQ4kWigEgnSvXTPwXd+B+CP8QtXpgAUWul6zZIDStElp+bW9fsgZxFT8PqdAJrLuskApf4413UBCDazLgCl4fjWDbgBFmifdRV6btQHAAQ8APO307o6QBb6nRfwAkw02Mzvg4K5uX0kU7W8biS5FpAr2r5u0AcEvS2sqwHkyuNY1w8EPcgxB7FNxpU9ZBoCSNP5oZO54WNK+KHk6gmDfmQbg6io5dbLNpmQYQhAF3pcXpIFBSncvnvv9/3QyHxI1ihwz4QCPPPDbhysqAb8Bdhd3gSvzw2AO0GWNdiRa2aosrqRGjqBfrbhKAZkm7nZsGQqQBE62bIgEHBF7wNerHWbI1MCitAJmzEgEPuScdvXbcP3viOOETHX7ZhjhJx5oveBWHc9RpzIum05RjDReSfG9/7XfTUIMIYJvdLgCSrh9MmQZFCjstEqfG8PVlTB7bJCo5SjrKYWOpkP957ZG//6dg8WbauAUQXoZG4My1YhVeuHPTQJUJYxiGxjAHanH34ouVrioB+ZomNCjlkH+B3INgZQ38QdT9L5kq5gAAi60Szxd7kt6x7ze9/Oxwj+WBTwACpVy+sKz9t9jhEnJY6IdT44GceIVpIxxrrNdVGr1YqEhAQ0vQ6YY/Uez5oGTFwUvr/Q0PyXJW0CMHll+P4XqYCnNuaqDfJiGC/dCRX/JfymAHAcjv28Cf2A6TvC9xf1B5p2xl7XkA9ceCh8f8lIoH597HU1KcClNeH7yycC1atir6vQA38RfUFXTgfKF8deFwCuFn2EfrkcKP28+XWvsIe/AGtmAAffbX7dS6oBbSp3e92dwL6Xm1/3goOAsYC7velBYNfzza87bTuQGGo7tPUxYPuc5tc9508geSR3e+dzwOa/Nb/upBVA+kTu9t7/Aevvan7dCd8D2dO52wfeAdbObH7d0z8F8i7nbh/5DPj1imZXfaD0PnzeMBn/vWoozk/ZBKw6r9l1P2F/Q97oB3H1639gtGErPin6f82u+3TFTLxWcykA4M3zGCYdOb/57R3wKDDoMe524w5g8YDm1+37ADD0Oe62/RDwbWHz6/a8Axj5P+62uwb4soV2UIU3AGPe4W77HcCnsWurAQC5lwHjPwvf/6iFg2gHHSNgGQFMXRe+3wHHCJ/PB/sX/ZAULIm9Lh0jwjroGOGfsAyL1jswbdo0qA6+1uIx4inHc3j3cH8svmc89v/xEs6xPdTsut7Rn+CapblYd6gB0xJ+xcv5zzS7Ln+MeOriAbgmZ3uLx4iHy27D6HMewfRBmUDVSuCnM5tdF0OeBfo9yN2uWwf82ELdcSc4RgTzr4N83HvcHTpGhO+fonGEEP81NcFsNje/PqiUgpBTUnOD7MQyE3Tol2mGWtm2w0CN3XPslQghJ6Sk2g6vP4hlO6uiulFEUivl+Of0fm1KjOVbDMdeCdGD8Qg51XXPjHFdeexfDB1wCcTn82HJj0sxdfrF4YxxV74EcqLrxuEyqc/nw48//ohzzjmH2wenQCnF1qON+MurawEA39w1Dr3STZj96WZ8u7UWfiix+4mp0CoYftt7FDe9uwEA8Nr1wzG6RzKufG0NSutc+PzOichLTcA3m8vwzaYjuHVcNkb14FrEnfffX7C/2oGnLxmIx7/bAbtPhvG9s/Hz7mpcPTILe8prsLOc61pxweAsfLuFq0/+7LYx6JeVjOd+OojCFAOuGJ4NBFzR+4BHpRTNrNv+xwifz4cli77C1HPOlu4DsW56jDihddtwjPAFFVj8w4+YNm0alHKGN1btgVGjwFWj8rFmfy1ufIfL1J3VNw1LdjYgAAWuHJmLykYb/iipRP8sM3aUW9E7w4SLhmTh30v24Mw+aXj5ujGAXIkvNhzF5+sP4oHJBRieb8HqvdW488NNOG9QFuZeOhALVpbg+eWH4IcSWx49GwkaGbYdqcIVoWPJv6b3xTWj8/H1pjI89OU2+KHE1jnnQadWnDKlFMKxaOp0qLTGFtcNP2/3OEZw63Z8HBHzfNDBx4i2ZIy7Z42x0iDdCS2t15bnjIX5EJRpItZtwxzybVq3Db/s27Ku+EverutqAGiOuVrb11UDEHV1YD4EZNrQfle1vG5bnrclchX3X7uvqwTkSgzM1+P+aUOhVyvRKzsDAHDD+P7YVL4ZlwzNhlbFnahH98rHRSOtCAQZxvTKg1Ihx0e3T4IMMiFTfOGQbFw4JFvyMgXpadheVYG/frEPgBr9s8w4p386ft5djbImH45Y5XAxbl//VOIQbte4lVhXascrK/cDACb2SkWa2QAwH/zQYkOZFz0zdMLAHwmZvPXfOZmsY9YFOsm6HXOMCMo0sb8HMZ+3Gx0jOnjdkmob/EGGouTw3/bWePDU0iMAgDP6F6LSqRC+Rz/vcyAA7jtc3uRGWaMPLqbFzAkD8ODnW7C5wofNFYcBaNE/L1P44Xzp8BxcOjxHeI0z+hVi7SO50KsVgEyGS0b1xu9HPDi9OFlowzYgPwun981Hab0T5wwpApQaTB9WjJ01AQzITuCCYoAL/uWt/Ay3Zd02fe/b4RjBnw8UmmOv25xOsW4XjiNaOidHrnvM523D976VumdgTEgXJ5PJcNP4HpJlg3MTseKBiZJlCrkMcy8ZJFnWmtZKY4qS8f3WCgDcTHvz/zIEFU1cBuhQnUMyQUitqLSi1iYts9hU2ohz+nOB+16rDPe9sQ59MkxYct8Zx9wGQk4Fdo8fF//vd7h8Aax6IPy53yJqtbbtaKPkO+XyhbNlFY0u4bvXL8uMxy8cgAc+2yL8fUKv1BZf3yCaDCjNpMV7ET2HZTIZXr9eOludSiHH/5vWtxXvjpBTDwXGhJAolw7Lwc+7qnGwzoEnLxyAnukm4cpVcxMIANz00x5/+KS+o6xJCIwPWLkn2F1pg8sbCGeiCDmFbS1thC3UGWLr0fDkHNtEt8sa3ai2xq7d3ydqlZiZoMVlw3MQZAz/99M+TBuYiQHZCR205YR0TxQYE0KiaFUKvDljpGRZZsKxL5vVOzxocoVrLHdWhGfPc4lKxo42ONEzXTrhAAB4/AE8+NlWFKcZcc+knsex5YScPP5AEI9+uwOpJg3um9wr5jrVokxwRZMb/ETvW0Uz2JU3uiRXXmKxGNRCidQVI3JxxYjcE9t4QkhM1JWCENIqBo0SZm3Lv6Xr7F6UiSYj4CcJAQCraHxhc50tfi+pw7dbyjFv2V44vS0MqCCkE1h/uAEf/nEE85fvQ4Mj9gBaccDLl0T4AkHJd6O80dVsxpiXldiGuktCyHGjwJgQ0mrirPGA7OiRvbUOL8obw6PRyxpdQgbZ6g33kmpwcMtq7R7srgwHCLGCCMYY9lXZaCpqEnc2t08yC504G3yknisxYoxh/aF6uLzcJZI6UcDMr7+3imvFxqtocsf8sViUGh6MlZPYhgFUhJDjRoExIaTVMkVZq3GiKWfzk7mTdo3NI8kYA8DuUGasSZRQa3B6EQgyXPjSbzj3P79gR3mTsJzHZ9C+21qBKS+uxiPfbG/fN0NIG814ex0mPLdCyPba3eGrGvzguS83luGyBWtw98ebAEgHpPLr/HmoAQCEKzBVVjeqrdwPQZUi/AOyX1a4fpj6CRNyclBgTAhpNXHGeES+BRcOyYJOpcAdE4sAAPuqbPD6g5DJgDNCo+V3VljBGEOTqL1rg8OLKqsbZY0uMAb8VsLN9lTvCK9kc3O33/7tIADgwz+OdOh7I6QljU4vNhxugC/A8NOuKgDhzygQ/lH39eYyAMDyXVUIBpkkY1wVCox/K6kDAFweqhOuaHLDGgqyHzm/P7QqOf4+tQ8KksNZ4sKUNrTyIoQcNxp8RwhptaF5ifj4Ty5AHZKbiEl90sDAZbwAwB8qd0g3aTEiPwmr99bgz4P1uGBgOnzBcCas3imtRT4U6nRR7whn12yhQEFcXsEYg6yN894T0h740h4AsHu4MgmbKGPc6OSCZL6EAgAqrW7U2aUZY38Q+ONQPQDg4qHZeOf3Q0KZkFopx7Wj8nDFiBxolAqs2huefndEQVIHvCtCSCQKjAkhrXbRkGzsr7GjKNWIVFO4qbrFIJ3UIDtJh3HFKZi3bC/WHKiTBBUAlzGW1GqGyiZiZYy1or7LVrdfmJiAkJNJUuZj4z7Pdo8/6u/iDPHhOifqRY+zuv3Y0ySD2xdEqkmD/llmpJs0KA99P9JMGshkMqHX+PjiFNw/pRd0agX6ZLQ8WxchpH1QYEwIaTW1Uo6Hzo1u/K9VKWDSKIV+rVmJOgzOSYBRo0Sj04eVe2sl69c7fTjaIB7ExAUG4uCDDzq8gfAgpSanjwJjEhdNzvCPNquL+2xaJaUU3G2+VhjgBp82iH7sAcCmOu6Kx5geyZDJZMhI0EoCYzG5XIa7qW0hIScV1RgTQtpFsjGcNc5O1EGpkGN0D65r69ebyyXr1tk9koxxZSgwELe84i9Ti/siiwOR5TurcKSFyUYIORFrD9Rhq2h2usYYn0NpKYUXdo8fDlEpxeE6h/ADj/9Bt7mWC4xHFloASOv2W9MrnBDSsbpMYDx37lyMHDkSJpMJaWlpuOiii7Bnz554bxYhJCTZGM528V0qTi/mAuOSGgcAoFeaEQBQ75DWGNfaPQgEWdRl52CQwSoKSPggeXtZE256bz3Omb8ajFEbN9K+KpvcuPaNP3DBS78JmeJGScaYuy3uStHg9EqyxQCwo5zrXiGXAcWhz76PhQLjUM1wRkK404v4NiEkPrpMYLxq1SrceeedWLt2LZYtWwa/34+zzz4bDocj3ptGCAGQZwmPoM8P3R5dlCxZp18mN9tdncOLMlEpRZBxA5PE2WGHxw+H1w9x+2I+INlfw02T6/IFhBZYhLSXzaUNwkDSPVXc7I2NruirGTaPqJTC4UNVxCQd20Oz2yXq1ZKg16BRoFca913IFC3PpZZshMRdl6kxXrJkieT+22+/jbS0NGzYsAFnnHFGnLaKEMIbmpeIrzZxraoG5HD9V3ulmWDSKoVAol+WGV9vqYDXH8S+arvk8XurbBAnf+0evyRQBsKXsK2iTF2l1Y00M2XaSPupsYeD4MpQFrjREZ0xtkVmjG3SjDE/oUeiXoV0U/gzOiDLDLmcyxz3F/UqHpSb2E7vgBByvLpMYBypqYn7JW6xWJpdx+PxwOMJ/4K3WrnLWj6fDz6fr7mHtSv+dU7W65FotA9OjgsGpmNraSMGZpuhU4T/vYfmJmD1Pq5v64AMA3QqOVy+8IC6Hil6HKh1YkdZo+T5rC4v6m2R3Sw88Pl8qLGGs83lDQ70Tacer8dC34PWE3/uKhoc8Pl80laCHj/cHm9UH+OKRq7mfWhuAjaVNgl/S9KpkG4KDxodmGkS9sOwHBNuO6MQAPf9oP3Tseh7EH/x2Adtea0uGRgzxjB79mycfvrpGDBgQLPrzZ07F3PmzIlavnTpUuj1J3d6zWXLlp3U1yPRaB90vPEaALXA4sXbhGWpPhkABfRKhrIdf0InV8AFLltmVDFo/HYAcvy8cTfE1V0VNQ1YuvJXAOF2bRu37UZm005sPigX1v3ljw3wHKA649ai78GxbT4U/nxt2LYbGU07cbAsvAwAvvzuBzQ5FUDos+wLMKwOfYZNvgbIIAPj/2avB6uoBX/KNVkPYPHiA8Jz8X1efvhhX8e+MSKg70H8ncx94HS2fqB2lwyM77rrLmzduhW//vpri+s99NBDmD17tnDfarUiNzcXZ599Nszmk9MT0ufzYdmyZZgyZQpUKmozFQ+0D+LrnCDDiI1HUX9wG6ZPnYL3yjagvoy7elOUnojiNAN2bSyHQ5kAwAa5jKs5lmn06Du4F7Bzi/BcaTn5mDatL5Z9uhWorAQAFPbqh2lj8uPx1roU+h603uqvtgMVXCcV/jP36qE1gNUmrDN0zBkIrP9d8jinJglAE8YO6YO9vx9GZajmeGjvAsya1gd5fSuwadNm3HwJ7YN4oe9B/MVjH/AVA63R5QLju+++G99++y1Wr16NnJycFtfVaDTQaDRRy1Uq1Un/QsTjNYkU7YP4UAG4bEQuFldvg0qlQlaiDttCgXFesgEZoRZVe6u4muP8ZAMO1nJtrhw+aSbY7glApVKh0RWu7bR7g7Rf24C+B8dmc4dbrlnd3GeOn+2OV2UPX5pNN2tQZfUIn+GsJANykvRCYJyTZIBKpcKU/pnwHd5E+6AToH0QfydzH7TldbpMVwrGGO666y58+eWX+Pnnn1FYWBjvTSKEHIde6Sbhdo8UA9JCg5L4LgC5oY4Wdrdf0qoNCA+6qxf1O7aKgmRC2kNTjBaBfD0xPyM5327QqFHCYuASMM5QD+N0kwbZog4Tecknt3SPEHL8ukxgfOedd+KDDz7ARx99BJPJhMrKSlRWVsLlch37wYSQTmNAdngU/vD8pKjZvgpCQYQ/yFAV6gjATz/NByniwFgcxFTb3PCLZsojpDWcXr9kIF1kYMwYE36UZSdyAS/fbtCkVcJikGaj0s1aFKcahfuDcxI7atMJIe2sywTGr7zyCpqamjBx4kRkZmYK/y1cuDDem0YIaYOz+qTh0mE5uHZ0HsYVpyDNLA2MxRnl8kYuMOb7u1pDQYp0IhAuiPl5dxVOe+onPPLtjo5+C+QUwhjDVa//geFPLsehWq4vvmS2RZcPLl8AgdAVjZzQZ5HPGJu0SqRHtAtMN2tx7eh8TO6bhgfP6U0TdxDShXSZGmOa3YqQU4NKIccLVwwW7mdETIObZ9HDqFHC7vHjaCj4yLPosfFII5pcPji9AXj94awwH8S89eshAMBHfxzBUxcNgIy/5k1IC/bXOLCltBEAsHxXFW4a30MSGDe6fEK/YoVchoxQEHxUyBir0CMl3C4wM0ELnVoBnVqBN24YeZLeBSGkvXSZjDEh5NSUlaCFVhU+FPVINcCo4X6z85er+bpjq9snKaMAwpMtiGcmq4tYR6yiyYVvNpfBRyUXp7wmlw+fbzgKh6f5OvSKpnA53tEGF7z+oFArzD8H/xkzapRI1KtD63Ltn8xaJQpTwmUT/NTPhJCuiQJjQkhcyWQyjCtKAcDVEmcn6mDUcoFxrZ0b1Z+bxAXGbl9QmImMx2f3xIPwKhql64j97fOtuPeTzfh8w9H2exOkU3p2yW488NkWvLyypNl1xNM4lze6omZbDASZUDZh1ilhDn02+ceZtCqMLEgS1h/dQzoNOiGka6HAmBASdw+f1w8XDsnCf/4yBDKZTMgY87KTdEI3gIOhOlBTKEDhB0fV2MIBTo29+cD4l321AIDvt5a351sgndCHfxwBAPxvxf5m16kS/dCqd3iFwNisVUKn4iaXKa3nssMmjQpmnXSgnUmrRJpZiycu7I+rTsvFddRTm5AurcvUGBNCTl0FKQb858qhwn0+6OUl6lUwapSwuf3CAKnCFAO2Hm2C0xtAo5MbIMXjg2SXN4C3fz+Is/tlRF3i9vlp3EJ39Mu+Ghyqc+LaUXmQyWSoFgXGdaLAOEGvgj/A4GoK4AgfGGuVMGulgTEfKF83puDkvAFCSIeijDEhpNOJDIwTdCokhAKQQ3VcYJyfHB7wVFJjl6zPB8avrt6PZ5fswV8XbgYAuEXBc5AG9HY7Hn8At7y3AQ9/vR0/7aoGIC2lqLV7hC4nZq1KqCcOB8axM8aEkFMHBcaEkE4nspQiQacSMnUHa7kgJcWoFoKSkurYgfHSHVUAgG1lTfAHgkJ3ASA8UQPpPnaWW4UrC5tDnSiqbOGMsc3tR23os5OgUyFJz3/muB9jFoMKZp30sxmZQSaEdG30U5cQ0umIgw29WgGjRilkjA/WckFwskGNBJ0KNrc/KjCu5kspRBniiiY3vKJOFI6IKX7JqY0xhoqmcBC8P3SVoVqUMQaAA6EgOEGnEn488Z+vZKNG+BzyUiMmqCGEdG2UMSaEdDqZieHexmkmDWQymZCpc/u44DZFFKQcqIkOjINBJrR7A4BKq1uSMXZ4aSrpU1lk73uPPyhp41fe5I4atAmEP0viUorQ3B5INqiRGdF3mwJjQk4tFBgTQjqd7MTwTGFpJu62xaCWrCPO3vFZvn6ZZgBcp4EqmzRDXO/wCv1oAcDupsD4VCa+WgAAdo8f9XZRYNzoQoPTJ3xG+mRwMy7y2eEEvQqJEdlhi0GNJL1K0nc71UiBMSGnEgqMCSGdTpYoY1yQwvUwzjBLM3UpRrUQGB+u4+qO+2VxgXG1zYMjoWW8eodXGFgFcIESOXVF/vBxePyod4ha+tk8wiQdFoMamaFpm/fXcD+yzFolkvTSH2MWgxoymQwKUYF6Jk33TMgphQJjQkin0yvdBL2a6yE7MDsBAJCZKA1AUmLUe/YNZYy9/iC2l1slf+MyxuFgyeMP0ux3pzBbxA8fm9uP2ogZEfmpoNNMmqiSiAS9GhkRQS9//7xBWQC4z5tSQadRQk4lNPiOENLpaFUKvHzNMGwubcQVI3MBAFmi2k6FXIaMBG1UYJyVoEWiXoVGpw8bDzdI/lbv8EIpl7aicHj8SNSr8fGfR+Dw+HHT+B4d9I5IR3P7Anhh6R6c2TsNY4tTojLGkaUUALAh9BlJM2ujAuM0kyYqG8zPwPjg1N5I1Ktw9ai89n4bhJA4o8CYENIpTeydhom904T7eRa9cDvNpIFKIUeyMfpSd7pJi0anTwh6TBolbB4/6h1eSW0owAVLXn8QD325DQAwPD8JQ/OSQLqej/44gtd/OYjXfzmIg3OnRZXK2NzcZwAANEo5PP4g1h0KBcYmDVKM0YGx+DOnUcphCLURTDFq8NC0vh35dgghcdIu14AaGhrw3//+F0OGDGmPpyOEkCi5Fp3Q33hIbiIAICdJL1knK1GHNDMX4FSGZjQblMuVYkSWUgBcy7YdFeGSix0R5Rek6+D7EgPcNOG2iIyx1eVDXajGeGheIgCgrJHrWpIRI2OcatIgUa9GeujzxD+GEHJqO6HAePny5bjqqquQlZWFRx99FGPGjGmv7SKEEAmZTIYXrhiMyX3TcP/ZvQAA2aJBekq5DJkJWknJBQAMykkEwAXGNtHgO4DLGDeI6k4Ph2bVI11Po6jjyNEGFxwRGeNGlw8NTm6dyKsCBSkGZJjDZRNyWbgbylMXDcT4nin41/R+HbXphJBOpM2lFEeOHMHbb7+Nt99+G2VlZTjnnHPw3nvv4cILL4RarT72ExBCyHE6p38GzumfIdzPFV3qTtCpoFTI0SvUdot3WqEFr6zcj3qHNyor6PCEL68DXG9b0jVVifZdjc0TVUpRWu9EINSQmL/iwCtM0aNnevhzY9QooVZyeaPJ/dIxuV96B201IaSzaXVg/Omnn+LNN9/E8uXLMWDAANxzzz245pprkJ5OBwxCSHxYDGr0SDHgQK0DY4tTAAB9RYFxhlmLohQjAKDO4YHNLR1MFRkY10TMgka6Dr50BgAanN6owPhQXbgNW2Rg3DPdBLNWhaJUA/bXOHBmnzQQQrqnVgfGV155Jfr374+1a9di5MiRHblNhBDSas9cOghfbSrDPZOKAQBD8hKFAXfje6bAEhqg5/YFURUKfJVyGfxBxpVSOMOBcbWNMsZdkdsXQJOolKLBGV1jfCg0CYzFoEa6WYs+GSbsrrRhWF6iMAX5f64cik/Xl+KWM6g7CSHdVasD45tuugmffvopzjvvPFx99dW44YYbaLAdISTuTiu04LRCi3Bfr1bixb8Mwc97qnHf5J4wqBVQK+Xw+oM4Us9N6JCZqEVpPVeHWmcXB8aUMe6KKiNKYBqdXtg9XKCcYlSj1u7FobrwZB4A8MIVg/He74dx0/hC4XEDshMwINQ3mxDSPbV68N1rr72GiooKPPvss9i4cSOGDRuGgQMH4oUXXkBFRUVHbiMhhLTJ5H7pePrigUgzaSGTyZAcMZ10ZmiAnsMbkGSMnd4AzYjXBYnLKIBQKUUoYyyeRREALAauzrx/VgL+fdkgSW0xIYS0qSuFTqfDDTfcgFWrVmHPnj2YPn065s2bh7y8PJx77rn45JNPOmo7CSHkuFmiAmOu1tgeUWMMANWhIIsxhiN14QFbpPNwev2otYez+1WRgbHDJ/zAiZykw2KQTgpDCCFix92urWfPnnjmmWdQWlqKL7/8EhqNBjfccEN7bhshhLSL6MA4lDGOFRiHyik+W38UZzy3Ak8t2nVyNpK02hWvrsHop38SJnHhSylkoYkNG5xeWEMZ4+xEaa9rPmNMCCGxnPAEH3K5HOeffz6+/vprlJaWtsc2EUJIuxKXUlgMaiTquayhze0X+t8WpRoAhLOPC1bvBwC89dvBk7mp5BiO1DmxvcwKf5Bh6Y5KAOFSir4ZZgB8z2ouMM5JkpZSpBiprSghpHntMvMdLy2NWtwQQjqfZNF0v2kmjTC1b1mDCyxUKdEnkwuq+MC4yRnuchCZVSbxc7g+PAnLgVCniepQt5G+oX3Y4AxP5tI7oq91ZKBMCCFi7RoYE0JIZ1SQYhBup5o0MGoUAIDSBq5TgVmrRE5okFZlkweBIJPMpFYemjqYxF+1qNc0v1+EjHEmFwQ3OMLt2tLNGiTpw3XFkaUVhBAiRoExIeSU1zPNKNzukWKAQc1ljCtCtanJRg3SQ1MCV1ndqLK6JYPuqL9x5yFuqcfXFvP/5zPG3kBQ6Gts1Khg1IY7kxakUGBMCGkeBcaEkFNe/ywzDGouSzyy0AKjRtrC3WJQIyMhHBhHZoiraEa8TkP8I6XO4YXbFxCWFaQYoFVJT2smrRLTBmQC4D4HJi11pSCENK/VE3wQQkhXZdKq8O6Np+FAjQPTB2Zi69Emyd+T9Gqkm7k65EqrG2VRgTFljDuLyElYdpRb4Qtw2f1UowYWvRrloQyyXAbo1QrceVYxUowaTOpL42AIIS1rc2CclJQEGd8TR0Qmk0Gr1aK4uBgzZszAzJkz22UDCSGkPYwosGBEATdDXqJemjVMDk0TDHA1rJGBMR+M7ShvQqPTh3HFKSdhiwkABELdJwbmJCAnSY+aiOz9piNcy7ZkgxpqpRxJhnBgbDFoIJPJYNaqcDNN80wIaYU2l1I88sgjkMvlmD59OubMmYPHHnsM06dPh1wux5133olevXrh9ttvx+uvv94R20sIIScszRQx6YNRLSzzBoLYWW4FEA6gq60eODx+/OXVtbjmjT+Ev5OO98WGo7j9w42486NNAMKlFBold/raVNoIAMIPG3HPamrNRghpqzZnjH/99Vc8+eSTuO222yTLX331VSxduhRffPEFBg0ahP/7v//DzTff3G4bSggh7UWnVsCsVQqTQKQaNVAr5UgxqlFr92LTkUYAwOCcRKzaW4Mamxsl1XZhNrVNpQ3ol2WO1+Z3K38eqgcAbClthMcfELL3Q3IT8cfBemwMTfLBl8Ik6cPBcKqJJvMghLRNmzPGP/74IyZPnhy1fNKkSfjxxx8BANOmTcOBAwdOfOsIIaSD8BlGAMi16CXL+FKKwTkJALhSCvGAvIpGqjk+WXyBoHB7X5UdTm8AADAkLxFAuLNIXmgfZov6FKcaKTAmhLRNmwNji8WC7777Lmr5d999B4uFq99zOBwwmUxR6xBCSGfBd6EAwkFVfrK0ldfg3EQAQI3Ng6MN4cCYH4xndfvQ6KTJP9pbZZMbHj8XANfawzXF/KBJo0aJolSj5DF5yVyvavHyQlH/akIIaY02l1I8/PDDuP3227FixQqcdtppkMlk+PPPP7F48WIsWLAAALBs2TJMmDCh3TeWEELay6hCC37ZVwutSi5MB12cZgJQKazDB8b+IMPOinBdcZXNA6fXj7OeX4lAkOGXv58V1QKOHJ+SajumvLgKI/Mt+PS2MagRdaHYVtYIgJu9MDtROoNdQehHzaBQlh8ABoX2HyGEtFabj+Q333wz+vXrh5deeglffvklGGPo06cPVq1ahbFjxwIA7r///nbfUEIIaU8zxhWivMmNM3qmQKngLp6JJwJJM2mQYtTAYlCj3uHF5tAgLwCotXmwv9qBWjuXLd52tAljipJP6vafqjaXNoIxrrbY6vZJAmM+Y5xm1iA3SZrdLw7tu17pJjxxYX80On0YT91DCCFt1KbA2Ofz4ZZbbsHDDz+Mjz/+uKO2iRBCOpxRo8TTFw+ULBNnG3tncOVgaSYN6h1eHKx1CH+rsXtQ0RQurYhs70aOn80dnor7cK0TDc7w/R2hbiBpJi1yLTqolXJ4/VwNMl8OAwDXjSk4ORtLCDnltKnGWKVS4auvvuqobSGEkLjKTzZgav8MKOQyXDc6H0Dszgb1Dq9kMB5NANJ+6uzhmu0tRxtjrpNm4voT3zGxCABw76SeMfvrE0JIW7W5lOLiiy/G119/jdmzZ3fE9hBCSFy9dPVQ2Nx+JIX64Ub2PAa4SSd2V9qE+00uX9Q65PjUOcKlE9vLmmKukxZqzXbf5F64YUyBsK8IIeREtTkwLi4uxhNPPIHff/8dw4cPh8EgHfV7zz33tNvGEULIyaZUyCWBljhjrFLIYNQo0eD0YZsoaKPOFO2nVpQx5v+NVQqZMO0zAGQkhAfeUVBMCGlPbQ6M33jjDSQmJmLDhg3YsGGD5G8ymYwCY0LIKSXDHA6MMxK00Ku4wHiHaPY7cR0sOTF1ovZs/L/x4JxErA9N5AEAPagNGyGkg7Q5MD548GBHbAchhHRKfTLDM9wVpxrhCzDsqbJJ1mmiwLjd1Dmis+89Ug2SwLiAAmNCSAdp8wQfhBDSnQzMToBKwQ3sGpaXhBRj9KX7BiqlaDfiwXe8VJMGU/qlAwB6p5uoZzQhpMMc19Hl6NGj+Pbbb3HkyBF4vdKD2Lx589plwwghpDMwaJR46eph+K2kFjeMK8B/f9oXtQ6VUrQPty8Au8cftTzDrMVVp+UhSa/CtaFuIYQQ0hHaHBj/9NNPuOCCC1BYWIg9e/ZgwIABOHToEBhjGDZsWEdsIyGExNU5/TNwTv8MAECKMbp9W6PTC8YYtQw7QeLpn8XSzFrkJOnx7GWDT/IWEUK6mzaXUjz00EO4//77sX37dmi1WnzxxRcoLS3FhAkTcPnll3fENhJCSKch7lLBz7bmDzI0On34YO1hrD9UH69N67JW7a3Bit3VQhlFVoIWJlG5RFqMXtKEENIR2hwY79q1CzfccAMAQKlUwuVywWg04vHHH8e///3vdt9AQgjpTMQZ4x4pBujVCgDAJ+tK8a+vt+P6t/6Exx+I1+Z1OfuqbLjhrT8x8511+PMg96Mi2aiBWacS1hHPakcIIR2pzYGxwWCAx8Nd7srKysL+/fuFv9XW1rbflhFCSCfUM90o3O6TYUKSnhuM92tJDQDA6Q1ge5k15mNJtHWHwt0mFm2rAAAkG9XITgz3Kk6OUb5CCCEdoc2B8ejRo/Hbb78BAKZPn477778fTz31FG688UaMHj263TeQEEI6k8wEHS4Zmo3sRB0uG54LS2iCiXUHwwHetmamMibRtpeHJ0rZXNoIAEg2aHDflJ5INWnwyHn94rRlhJDuqM2D7+bNmwe73Q4AeOyxx2C327Fw4UIUFxfjxRdfbPcNJISQzmbeX4YItxP13CV/byAoLNtGGeNW2xFj2ucUoxpji1Kw7p+T47BFhJDurM2BcY8ePYTber0eL7/8crtuECGEdCWWGFMSb48R7JFogWD0ZCmAdIAjIYScTDTBByGEnAC+xlhsT5UNC1bth9tHg/CaU1rvxN0fb4TbF4z6W5pZG4ctIoQQCowJIeSEpJnD2c0R+UlC14pnftiN/8SYDIRwHv12BxZvqwQAnFZggUlL7dkIIfFHgTEhhJyA4lRRl4pMEy4bniPcX7WnJh6b1CVsCQ20A4Drx+ZLWrIVJBvisEWEEEKBMSGEnJC+mWbh9uCcRPx9am98eusYAEBJjR2BIIvXpnVadXYP6hzcZB5//nMSzhuUhUE5CQAAuQxIN1PGmBASH20OjB9//HE4nc6o5S6XC48//ni7bBQhhHQVuRY9HjmvH64bnY8LhmRBJpNheH4S1Eo5vP4gyhpc8d7ETmdfNdfZKNeiQ5qJqye+b3IvXDgkC69eN4Km1iaExE2bA+M5c+YI7drEnE4n5syZ0y4bRQghXcmNpxfiiYsGQKPkZsFTyGXokcKVA5TURHdd6O72hTpR9EwzCcvSzVr858qhmNIvPV6bRQghbQ+MGWMxf81v2bIFFoulXTaKEEK6uqJQ7fGBGkect6Tz4TPG4lkECSGkM2h1H+OkpCTIZDLIZDL06tVLEhwHAgHY7XbcdtttHbKRhBDS1RSlchnjjUcaMOmFlUjUq/HJLaOhUnTPoR1VVjcuW/A78i0GeP1ci7ZeoowxIYR0Bq0OjOfPnw/GGG688UbMmTMHCQkJwt/UajUKCgowZsyYDtlIsZdffhnPPfccKioq0L9/f8yfPx/jx4/v8NclhJC2KErjsqF8SzLAgT8P1mNccUr8NiqOVu+tQWm9C6X14ZpryhgTQjqbVgfGN9xwAwCgsLAQY8eOhUql6rCNas7ChQtx33334eWXX8a4cePw6quv4txzz8XOnTuRl5d30reHEEKa0yMlOujbXNrYbQPjvREz3Mll0hpjQgjpDFoVGFutVuH20KFD4XK54HLFHmltNptjLm8P8+bNw6xZs3DTTTcB4LLYP/74I1555RXMnTs3an2PxwOPxyPc59+Hz+eDz+frsO0U41/nZL0eiUb7IP664z7ITYyeEW9/tQ3rD9bit5I6zBybD51acdK2Jx77oKLJjc83luHSoVnYXWGV/K0gWQ+lLAhfjJnvTlXd8XvQ2dA+iL947IO2vJaMMXbMJptyubzV7XMCgY6ZAtXr9UKv1+Ozzz7DxRdfLCy/9957sXnzZqxatSrqMY899ljMThkfffQR9Hp91HJCCGlPz25RoMwZPnYWmhi8AaDMKcPUnADOzT21exx/WCLHnzVy9EkIotIlQ6M3/G8xJi2IK4u6T1BMCIkfp9OJq6++Gk1NTcdM4LYqY7xixQrh9qFDh/CPf/wDM2bMEGqK16xZg3fffTdm1ra91NbWIhAIID1d2sonPT0dlZWVMR/z0EMPYfbs2cJ9q9WK3NxcnH322R2a2Rbz+XxYtmwZpkyZEpfyE0L7oDPorvsgvX8D3vj1EEb3sODJxXtQ7VHC4eWSB1Z1KqZNG3HStiUe++Deh5cCAHY3hQccPnFBP6w9WI+/n9MLmQnak7IdnUV3/R50JrQP4i8e+0Bc+XAsrQqMJ0yYINx+/PHHMW/ePFx11VXCsgsuuAADBw7Ea6+9JtQid5TIzHVz7eMAQKPRQKOJnkFJpVKd9C9EPF6TSNE+iL/utg9GF6dhdHEa7B4/nly8RwiKAcDPEJd/i5O5DxRymWTmv6wELa4bW4jrxhaelNfvrLrb96Azon0QfydzH7TlddrcN2jNmjUYMSI6yzFixAj8+eefbX26VktJSYFCoYjKDldXV0dlkQkhpDMxapRR2dHKJnectubkcPsCUdNh98qgwXaEkM6tzYFxbm4uFixYELX81VdfRW5ubrtsVCxqtRrDhw/HsmXLJMuXLVuGsWPHdtjrEkJIeyhOk3apaHB447QlJ0et3RO1rDcFxoSQTq7V7dp4L774Ii699FL8+OOPGD16NABg7dq12L9/P7744ot230Cx2bNn47rrrsOIESMwZswYvPbaazhy5AhNLEII6fR6ppnwy75a4b7N44fXH4RaeWpO+FFrjw78+2clxFiTEEI6jzYfkadNm4a9e/figgsuQH19Perq6nDhhRdi7969mDZtWkdso+Avf/kL5s+fj8cffxxDhgzB6tWrsXjxYuTn53fo6xJCyIk6b3Am5DIgxRge99DgPHWzxnWhjLFOpYBaIYdJq8T4btrDmRDSdbQ6Y/zaa6/hggsuQEZGBnJzc/H000935HY164477sAdd9wRl9cmhJDjNSwvCUv/egbMWhWm/d8vqLV7Ue/wIt18anZm4EspRvew4PELB0CjkiPJEN3bmRBCOpNWZ4w//vhjFBQUYNSoUXj66aexc+fOjtwuQgg55RSnmZBm1iJJzwWIp3KdMV9KkWzUINeiR5rp1PwBQAg5tbQ6MF6xYgUqKipw9913Y/PmzRgzZgyKioowe/ZsrFy5EsEgNWonhJDWsIQyp3WhwHj9oXpsL2uK5ya1i1V7a3Cgxg4gnDFONlKWmBDSdbSpxjgpKQnXXnstPv30U9TU1OB///sf3G43rrvuOqSmpuL666/H559/DofD0VHbSwghXR5fZ1xr92DD4QZctmANLnn5dxys7brHzkVbK3DDW3/iov/9hkanF3WhjHGqMbqXPCGEdFbHPRxarVZj6tSpePnll1FaWooff/wRBQUFeOKJJzBv3rz23EZCCDmlpISyqLV2DxZtrQAAeANBrNhdHc/NOiHLd1UBAKxuP1buqUF9KBtuobpiQkgX0uZ2bc0ZMWIERowYgccffxw+n6+9npYQQk45QsbY5sU2UQnFnkpbvDbphIlLQdYdqheVUlDGmBDSdbQqMJ49e3arn3DevHk0zSIhhLQgxcQFi+VNLuypCgfDpQ3OeG3SCStvdAm3d1VYhfrpZMoYE0K6kFYFxps2bZLc37BhAwKBAHr37g0A2Lt3LxQKBYYPH97+W0gIIacYPlj840C9ZNrkrhoYu7wBOLwB4f6uChs8fu5+CmWMCSFdSKsC4xUrVgi3582bB5PJhHfffRdJSUkAgIaGBsycORPjx4/vmK0khJBTCJ8x9ga4bj6ZCVpUNLlRY/OAMQaZTBbPzWszvmxCKZdBIZfB5QsHyUkGuoJICOk62jz47oUXXsDcuXOFoBjgulU8+eSTeOGFF9p14wgh5FQU2alhbBE3I5zbF4RTlHntKvjAON2sRd9Ms7A8xaiBRqmI12YRQkibtTkwtlqtqKqqilpeXV0Nm63rDhwhhJCTJd2shVIezgoPy0+EVsUdjvk2Z11JnTCZhxoDssOBca5FF69NIoSQ49LmwPjiiy/GzJkz8fnnn+Po0aM4evQoPv/8c8yaNQuXXHJJR2wjIYScUtRKOfKT9cL9wTmJSDZwWeQ6hydem3Xc+IxxilGDgdkJwvLCFEO8NokQQo5Lm9u1LViwAA888ACuvfZaoS2bUqnErFmz8Nxzz7X7BhJCyKnotMJk7K9xIEmvQt9MM5KNapQ1urpmxljUgWJ0j2Rh+ejC5OYeQgghnVKbA2O9Xo+XX34Zzz33HPbv3w/GGIqLi2EwUGaAEEJa64Gze0GrkmP6wEwo5DKhU0VXzBjX2EIZY5MG+ckGvHD5YFRa3bh4WHact4wQQtrmuCf4MBgMGDRoUHtuCyGEdBvJRg0ePb+/5D4A1HbhjDHfmu3S4Tnx3BxCCDluxz0lNCGEkPaTHJomuiuWUtTyGWMjTeZBCOnaKDAmhJBOgG/hxpdS/O3zLZg8bxWqrO54blZMG480YNwzP+Od3w4CCG8zTeZBCOnqKDAmhJBOgM8Y19o9qLV78On6oyiptmPxtoo4b1m011YdQFmjC499txNAuPwjmTLGhJAujgJjQgjpBIR2bXYvDtc5hOUl1fZ4bVKz9lWHe9ZX29xocPJdKShjTAjp2igwJoSQTiCcMfbicJ1TWF7W6IrXJjVLPDvfpiONYAyQywCLgTLGhJCujQJjQgjpBPga43qHB4dqwxnj8k4WGDPGJAMEt5Q2AuCCYoVoNj9CCOmKKDAmhJBOICmUbQ0yYMvRJmF5Z2vfZnX54Q0EhftbjjYCoIF3hJBTAwXGhBDSCagUciTqVQCAjYcbhOUNTi8CQRavzYpSY5d2ydhSygXxFBgTQk4FFBgTQkgnwc9+Z/P4hWWMAY3OzpM1rrFJt8Ue2lbqYUwIORVQYEwIIZ1EZNaVr9nlZ5brDGrtsaesTjNrT/KWEEJI+6PAmBBCOonMhHBwmWxQIz9ZD6BzzYbHB8b9s8yS5bkWfTw2hxBC2hUFxoQQ0kkUpxmF2wUpBqQY+E4VnScwrglN/zwsLwlaVfgUkk+BMSHkFECBMSGEdBLFaSbhdt9Mk9AXuN4Ru3whHviMcbpZg3yLQVjeO8PU3EMIIaTLoMCYEEI6iTFFyTBplACAyX3TYRFN+tFZ8NuSYtTg/MGZAIDBOQlIpxpjQsgpQBnvDSCEEMJJ0KnwxR1jUWV1Y3zPVGw80gig+QFv8cBvS4pRg8uG56Ao1YixxSlx3ipCCGkfFBgTQkgn0ivdhF7pXFlCqpAx7jyBMV9jnGLSQKmQ49yBmXHeIkIIaT9USkEIIZ0U376ts5RSMMaEID3VRBN6EEJOPRQYE0JIJ5Vi4gPjzpExbnL54Atws/DRhB6EkFMRBcaEENJJpYYyxnz5Qrzx25GgU0GjVMR5awghpP1RYEwIIZ0UnzF2egNwev3YXNqIW99fjx3lTSdtG37eXYU7PtyAyiY3aqiMghByiqPBd4QQ0kkZ1ApoVXK4fUHU2rz4v5/24efd1fAHGN6cMfKkbMNj3+7EkXon0s1aDMlNBEBlFISQUxdljAkhpJOSyWTCALwauwc/764GAPwU+n9Hc/sCOFLvBABsL2sSSilSTdSzmBByaqLAmBBCOjG+bKHa6j7pr93o9Am3bW5/ODA2UikFIeTURIExIYR0YhmhGeU2lTYKyxRy2Ul5bZs7HBgfqXfiaIMLAJCVSBljQsipiQJjQgjpxPKS9QCA1XtrhGWBIIPbF+jw17aKAmOnN4DNoeA816Lv8NcmhJB4oMCYEEI6sXyLAQCwu9ImWS4uc+goVrdfcr+skcsY5yZRYEwIOTVRYEwIIZ1YfnLsILTR1fGz4VldsYPvHIuuw1+bEELigQJjQgjpxApSDDGXW13+mMvbk80d/RpZCVqYtaoOf21CCIkHCowJIaQTy0rQIi3GhBrNZXPbk7jGmNcvK6HDX5cQQuKFAmNCCOnEZDIZxhQlC/cHhybZiBW0tjc+Y9w30ywsG98zpcNflxBC4oVmviOEkE7ugbN7o97hxbSBmfi1pBZbShtPTsY49BpT+qVjZEES6hxeXDY8p8NflxBC4oUCY0II6eRyLXq8P2sUAGDr0SYA0R0jOgL/GmatErOn9Orw1yOEkHijUgpCCOlCzDoun3EyMsb8BB9mHQ22I4R0DxQYE0JIF8J3hDgZNcZ88G3W0sVFQkj3QIExIYR0IXz29mS2azNRezZCSDdBgTEhhHQhfPb2ZHalMFHGmBDSTVBgTAghXYiQMT4pgTH3GpQxJoR0FxQYE0JIFyLUGHdwKUUgyODwBgBQxpgQ0n1QYEwIIV3IySqlsIvawVFgTAjpLigwJoSQLoQvpbC5/ahscuPm99bjl3017fb87/x2EH//fCsqrW4AgFoph0apaLfnJ4SQzozSAIQQ0oXwpRSBIMObvx7Asp1VWLazCoeemX7Cz+3xBzDn+51gjAuIudej0wQhpPugjDEhhHQhWpUcKoUMAPDD9kphOWPshJ/7YK0D/NNsL+dm2KOBd4SQ7oQCY0II6UJkMpmQNa4KlTsAEAbKnYh6h1e4ve0oHxhTxpgQ0n1QYEwIIV0MX2fsC4SzxNWiIPl4iaeZ9ge5506g6aAJId1IlwiMDx06hFmzZqGwsBA6nQ5FRUV49NFH4fV6j/1gQgg5xcSq+210nXiXiqYYz5Fi1Jzw8xJCSFfRJa6R7d69G8FgEK+++iqKi4uxfft23HzzzXA4HHj++efjvXmEEHJSmWNkca0dFBgnG9Qn/LyEENJVdInAeOrUqZg6dapwv0ePHtizZw9eeeWVFgNjj8cDj8cj3LdarQAAn88Hn6/jZ43iX0v8f3Ly0T6IP9oH7cuojm6f1mB3t/jv25p90GD3RC1L1Clpv7UT+h7EH+2D+IvHPmjLa8lYewxljoN//etfWLJkCdavX9/sOo899hjmzJkTtfyjjz6CXq/vyM0jhJAO8+kBOX6rklbCXdEjgHHpJ3Y4j/W81xQHcFpqlzxNEEIIAMDpdOLqq69GU1MTzGZzi+t2ycB4//79GDZsGF544QXcdNNNza4XK2Ocm5uL2traY/7DtBefz4dly5ZhypQpUKloEEs80D6IP9oH7evdNYfx5OI9kmUPTOmJW88obPYxrdkH9326FYu2VUqWfXrLaRiam3jC20zoe9AZ0D6Iv3jsA6vVipSUlFYFxnEtpWguoyu2bt06jBgxQrhfXl6OqVOn4vLLL28xKAYAjUYDjSZ64IhKpTrpX4h4vCaRon0Qf7QP2segXItwu0+GCbsrbXD4gq36t21pH9g8XMu3nmlG7Ku2AwD6ZSdBpeoSVXddBn0P4o/2QfydzH3QlteJ69HurrvuwpVXXtniOgUFBcLt8vJynHnmmRgzZgxee+21Dt46QgjpnEYWJOGuM4vhCwahUcixu9IGm7v9Bt/dNqEIaw/UYWSBBUYNBcWEkO4jrke8lJQUpKSktGrdsrIynHnmmRg+fDjefvttyOVdotMcIYS0O5lMhgfO6Q0AePPXgwAAq8t/ws/Ld7bItehx6fCcE34+QgjparpEKqC8vBwTJ05EXl4enn/+edTU1Ah/y8jIiOOWEUJIfPE9jWO1Wmsr/jloUg9CSHfVJQLjpUuXoqSkBCUlJcjJkWYxuuDYQUIIaTd8T2PrCZZSMMYoMCaEdHtdoh5hxowZYIzF/I8QQrozPog90YyxwxtAgKaBJoR0c10iMCaEEBKbEBg7Tyww5gNrtUIOrYpODYSQ7omOfoQQ0oWJM8YnchWND6zNOhVkMlm7bBshhHQ1FBgTQkgXxgfG/iCD0xs47ucJ1xd3iaEnhBDSISgwJoSQLkyvVkAp5zK8J1JnTAPvCCGEAmNCCOnSZDJZuwzAs1JgTAghFBgTQkhX1x6BMWWMCSGEAmNCCOnyzO0QGDe6vAAoMCaEdG8UGBNCSBdHGWNCCGkf3XP4sd8B+BXRy2UKQKGVrtcsOaDUHXtdvw9y5olY5gTQXFslGaDUH+e6LgDB5jdZaTi+dQNugLUw2r0t6yr0AN8KKuABmL+d1tUBstDvvIAXYKIAwe+Dgrm5fSRTtbxuJLkWkCvavm7QBwS9LayrAeTK41jXDwQ9LayrBuSq41g3AATdza8rUwEKddvXZUEg4IreBy2t2+zzKgGFJrQuAwLOdlq3Dd/7jjhGxFy3bceIVK0fOpkbDnsT4Lc0u66ceaL3QUiTrREAkGIK/bt1p2PEiazblmMEE5136BjB3T7m976djxH8sSjgAVSqltcVnrfrHyM6VRwR63xwMo4RrSRj3Wj6OKvVioSEBDS9Dpj1MVbImgZMXBS+v9DQ/JclbQIweWX4/hepgKc25qoN8mIYL90JFf8l/KYAcByO/bwJ/YDpO8L3F/UHmnbGXteQD1x4KHx/yUigfn3sdTUpwKU14fvLJwLVq2Kvq9ADfxF9QVdOB8oXx14XAK4WfYR+uRwo/bz5da+wh78Aa2YAB99tft1LqgFtKnd73Z3AvpebX/eCg4CxgLu96UFg1/PNrzttO5DYn7u99TFg+5zm1z3nTyB5JHd753PA5r81v+6kFUD6RO723v8B6+9qft0J3wPZ07nbB94B1s5sft3TPwXyLuduH/kM+PWK5tcd/TbQYwZ3u2wRsOq85tcd8RLw/9u796iornsP4N+ZYWaYAUEQcJiggEmIMRhQbBVdEeP73cTUxDxucWWlWeZeakgwrVmxS0K1jakxSZsHaZsY622qaU28acVXWh81RKsEDbGpjwjiCwlUAXnM6+z7x8CBAwMMOHBg+H7WYi3mnN8c9pwf7PmxZ599Ev7H/f3V/cDf7m0/NvllYNRz7u8rjwK7v9t+bOJq4O5s9/fXTwJ5ie3H3rkCGPNL9/c3SoBP4tuPvf2/ge+86f6+4Vvgo6j2Y+PTgdT33d87a4EPg9uPHfZ94J4/NT/+oINOtIf6CISPA2YfbX7cA32Ew+HAjW2jECad9RhaJQ1G0lf/i9zHxmJ2YjT7iB7oI5xpe7HjWC3mzp0LffFv2EcAqvURUux/QTvp9+4H7COaH/tpHSHXf1VVCAkJaT8enEpBREQApMYxkshBgZ1EEhH5r4E5Ylx52fN/DD3wEYjD4cCu3Xswe979zSPG/fkjkJuNVeFjUofDgd27d2PWrFnuHHAqhYfYnv2YtE0OOoht/7icStHYiDZ9xO6TV5C55TiSh4Xij0+meox1OBzYteNjzJ41U5kDAEIIJOfsRZXDgH/8+F4MCzcPqD7ipmK70Ec4JB3ydu52jxjrwD4C6PWpFHJfNHse9IHBHcY2H7f/9xF9qY7w+H7Qw31EV0aMB+Yc44AgZRI6iuvKMT0RDkgaY6tYT/M42jtuV2JNncd0J1bXhRGkLsUaARg7Det6rAGAofmxcMClCWzMu77j2K4ctyNaffMbik9jA5rfAH0aqwO0Xv6+dyVWo3Wf945y0DrWq+NqeiYW6COxXesjhoYPQb0IREmV+7WeuVqDL0qv4YGxMYpOXtIY5RzU2pz407ELWJBkhd0locphgE6rwdCQxr/hgdRH9Faso0XRzD7CrUt/9z7oI5r6Ip2x89j29InYflxHdPZ+0FN9hJcGZmFMRORHhoW536DKqhtww+bEij+dwImLVXC4BB6bEOvxORv2nsa7h4pRUHodD40bBgCIHWKGIYAz7Iho4GIPSETUzw0JNuKWwSYIARwt+Q9OXKwC4P4eACRJIHPrl9hR2tzl//XLywCAv5y4jC8vXQcAJEQN6t2GExH1MSyMiYj8wNjYMADAG39vXnXC2Dj6+68r1djxVRn2XNLCJbnnGoYHNX/8+OdjFwEAqbcO6a3mEhH1SSyMiYj8wP1jrACAgvPX5G2VN9wXbNldzRfIXK9zbwvQNi85da6iFgadFnMSLb3RVCKiPouFMRGRH0hLiMJIi3IqRI3NfbW2w9lcGNc53Fd719mVV3LfN8aKqBAu1UZEAxsLYyIiP6DTavCTOSMV25qK34YWhXGDQ2rc17wcUoBWgycn39oLrSQi6tu4KgURkZ+YkhCJDQ8m4VRZDd45eA51Nnfx2+BoLoKbvq9tHE1OT43FrLssuC2qgzt/ERENEBwxJiLyExqNBovGxmBBknu+cW3TiHGLwrje4YIQQh4xfmrKbZh4W0TvN5aIqA9iYUxE5GeCjO4PA5tGjG0O5VQKu0uCs3F1CrNR1/sNJCLqo1gYExH5mSCDu9ittTshhECDs8WIsd0lF8wAYNazMCYiasLCmIjIz5gbR4wl4R4hbjmVwuaU5CkWhgAtAnR8GyAiasIekYjIz5hajALX2Z3yShQAYHO65PnFTSPLRETkxsKYiMjP6LQa+a53dXZXq1UpJLkwNhu4MBERUUssjImI/JC5cTS43uFCfaupFHWNS7UF8cI7IiIFFsZERH6oaTTYPWLcclUKF2o5YkxE5BELYyIiP2RqHDGuszthaz1ibOeIMRGRJyyMiYj8kDyVwu5SLNfW4HCh1sYRYyIiT1gYExH5oaaVKVpPpVCMGHNVCiIiBRbGRER+SDFi3HJVCqckjxibOGJMRKTAwpiIyA813eTDvY5xiznGDhdHjImI2sHCmIjIDzXd6rnO0XpVihbrGBs5YkxE1BILYyIiP9Q0laLOprz4ruUtoTliTESkxMKYiMgPmVqsY2xrfUtoG0eMiYg8YWFMROSHmu9851Tc+a7BwRFjIqL2sDAmIvJD8lSKVqtS2Jyu5jnGXJWCiEiBvWIrQgg4nU64XK7Og73gcDgQEBCAhoYGnx2T2qfT6RAQEACNRqN2U4hUZWqnMG5wSNBpeec7IiJPWBi3YLfbceXKFdTV1fnsmEIIWCwWXLhwgcVaLzGbzYiOjobBYFC7KUSqaRoxrq53QBLN221OCRqNSxFDRERuLIwbSZKE4uJi6HQ6WK1WGAwGnxSykiThxo0bCA4OhlbLmSs9SQgBu92Ob7/9FsXFxbj99tt5zmnAMund3fu1Ortie4PDBUm4K2VOpSAiUmKv2Mhut0OSJAwbNgxms9lnx5UkCXa7HYGBgSzSeoHJZIJer8f58+fl8040EDWNBv+nVlkY25wSHC53YRzEwpiISIG9YissXvs/5pCouTCu9FAYN+EcYyIiJVYQRER+qGmaROOsCRgD2nb3QVzHmIhIgYUxEZEfan1h3WCzXvE4QKvxWCwTEQ1k7BX90P79+6HRaHD9+vVe/bnvv/8+Bg8efFPHKCkpgUajwfHjx9uNUev1EfUnrQvjkMAAaNC8PEWQkcsaEhG1xsLYD0yZMgWZmZlqN4OI+hBTq8LYZNBB36LHD+Y0CiKiNlgYEwD3jUiIyH+0XorNpGdhTETUGRbGnXHWtv/lavA+1lnvXWwXLV26FAcOHMDrr78OjUYDjUaDkpISAEBBQQHGjRsHs9mMiRMn4tSpU/LzsrOzkZycjPfeew8jRoyA0WiEEAJVVVV48sknERUVhZCQEEydOhUnTpyQn3fixAnce++9GDRoEEJCQpCSkoJjx44p2rR7927ceeedCA4OxuzZs3HlyhV5nyRJyMnJQUxMDIxGI5KTk7Fr164OX2NeXh4SEhJgMplw7733yq+PiNqn02pgaDGHuHVhzBUpiIja4pBBZz4Mbn+fdS4wZUfz421RgEt51zwtgMEARGQaMGN/847/iwNsFW2P+Yhou60Dr7/+Ok6fPo3ExETk5OQAAE6ePAkAeOGFF/DKK68gMjISy5Ytw+OPP47PPvtMfu7Zs2fx4YcfYtu2bdDp3G+S8+bNQ3h4OPLy8hAaGop33nkH06ZNw+nTpxEeHo5HH30UY8aMwdtvvw2dTofjx49Dr2++qKeurg7r16/H5s2bodVq8dhjj2HFihX4wx/+ILf3lVdewTvvvIMxY8bgvffew8KFC3Hy5EncfvvtbV7fhQsXsGjRIixbtgxPPfUUjh07hqysrC6dI6KBymzQwd64PJvZ0LowZvdPRNQae8Z+LjQ0FAaDAWazGRaLBQDw73//GwCwdu1apKWlAQBWrlyJefPmoaGhQb7phd1ux+bNmxEZGQkA+Pvf/46ioiKUl5fDaDQCANavX4/t27fjz3/+M5588kmUlpbiueeew8iRIwGgTTHrcDiQm5uLW2+9FQCQkZEhF+xNx/vJT36CJUuWAADWrVuHffv24bXXXsObb77Z5vW9/fbbGDFiBF599VVoNBrccccdKCoqwrp163xzAon8WJAhANfr3NOkgo0BisI4zMxbphMRtcbCuDMP3mh/n6bVR5EPlLcJkSQJ1dXVCAkZDMX1398r8UXrOnT33XfL30dHRwMAysvLMXz4cABAbGysXBQD7qkXN27cwJAhQxTHqa+vxzfffAMAePbZZ/HEE09g8+bNmD59OhYvXiwXwQBgNpsVj6Ojo1Fe7j4v1dXVuHz5MiZNmqQ4/qRJkxTTNVr6+uuvMWHCBMXV86mpqd6fBKIBLDzIgEvX3dO4Bpv1aDl7IjyIhTERUWssjDsTEHRzsZIEBLiAAFP3j9tNLac4NBWWktTirldByjZIkoTo6Gjs37+/zbGalmHLzs7GI488gh07dmDnzp1YvXo1tmzZgvvvv7/Nz2z6uUKINttaEkK0u2xU6+cSkfciBxnl70NNegzSC6DxX3QWxkREbfHiOz9gMBjgcrlu+jhjx45FWVkZAgICcNtttym+IiIi5LiEhAQ888wz2LNnDxYtWoSNGzd6dfyQkBBYrVYcOnRIsT0/Px933nmnx+eMGjUKhw8fVmxr/ZiIPItqURgPNukxqMX/rWEsjImI2mBh7Afi4uJw5MgRlJSUoKKiQjEq3BXTp09Hamoq7rvvPuzevRslJSXIz8/HqlWrcOzYMdTX1yMjIwP79+/H+fPn8dlnn+Ho0aPtFrWePPfcc1i3bh22bt2KU6dOYeXKlTh+/Diefvppj/HLli3DN998g2effRanTp3CBx98gPfff79br49ooGlZGFtCAxGib/4EJibM5OkpREQDGgtjP7BixQrodDqMGjUKkZGRKC0t7dZxNBoN8vLyMHnyZDz++ONISEjAkiVLUFJSgqFDh0Kn06GyshI/+MEPkJCQgAcffBBz5szBiy++6PXPWL58ObKyspCVlYXRo0dj165d+OSTTzyuSAEAw4cPx7Zt2/CXv/wFSUlJyM3Nxc9//vNuvT6igeYOS4j8fdwQM6Ja1MK3RXaw4g4R0QClEQNoEmd1dTVCQ0NRVVWFkJAQxb6GhgYUFxcjPj5eXrXBF5ovvguBVsv/Q3pD61w6HA7k5eVh7ty5beZAU+9gDtRRa3Ni6cZ/4pbBJry86C5s/+tObK+MQkyYGS9/P0nt5g04/DtQH3OgPjVy0FH91xovviMi8lNBxgD8adlEAO43I6MO2LR0HAsCIqJ29LshTJvNhuTkZGg0Ghw/flzt5hARERGRn+h3hfGPf/xjWK1WtZtBRERERH6mX02l2LlzJ/bs2YNt27Zh586dncbbbDbYbDb5cXV1NQD3R4oOh0MR63A4IISAJEndXtXBk6Yp3E3Hpp4nSRKEEHA4HNDpdHKuW+eceg9zoD7mQH3MgfqYA/WpkYOu/Kx+c/Hd1atXkZKSgu3btyMiIgLx8fEoLCxEcnJyu8/Jzs72uGLCBx98ALPZrNgWEBAAi8WCmJgY+XbI1D/ZbDZcvHgRZWVlcDqdajeHiIiIVFRXV4dHHnnEq4vv+kVhLITA3LlzMWnSJKxatQolJSVeFcaeRoyHDRuGioqKNifG5XLh3LlziIyMbHNL5Jtte01NDQYNGtTu3d3ItyorK/Htt99ixIgR8ojx3r17MWPGDF50pBLmQH3MgfqYA/UxB+pTIwfV1dWIiIjo+6tStDei29LRo0eRn5+P6upqPP/88106vtFo9Dj6q9fr2yRDr9cjLCwMFRUV0Gq1MJvNPilkJUmC3W6HzWbjcm09TAiBuro6VFRUICwsrM2ye57yTr2LOVAfc6A+5kB9zIH6ejMHXfk5qhbGGRkZWLJkSYcxcXFxWLNmDQ4fPtymyB03bhweffRRbNq0ySftsVgsAIDy8nKfHA9wF2v19fUwmUwcMe4lgwcPlnNJRERE5C1VC+OIiAhERER0GverX/0Ka9askR9fvnwZs2bNwtatWzF+/HiftUej0SA6OhpRUVE+mxTucDhw8OBBTJ48mf+d9gK9Xg+dTqd2M4iIiKgf6herUgwfPlzxODjYfSvTW2+9FTExMT7/eTqdzmfFlU6ng9PpRGBgIAtjIiIioj6Mk16JiIiIiNBPRoxbi4uLQz9YTIOIiIiI+hGOGBMRERERoZ+OGHdX0yhz0x3weoPD4UBdXR2qq6s5x1glzIH6mAP1MQfqYw7UxxyoT40cNNV93sw2GFCFcU1NDQBg2LBhKreEiIiIiHpTTU0NQkNDO4zpF3e+8xVJknD58uVevQtd0932Lly40OndVqhnMAfqYw7UxxyojzlQH3OgPjVy0HQXYqvV2unN1gbUiLFWq+2R5d28ERISwj9ClTEH6mMO1MccqI85UB9zoL7ezkFnI8VNePEdERERERFYGBMRERERAWBh3OOMRiNWr14No9GodlMGLOZAfcyB+pgD9TEH6mMO1NfXczCgLr4jIiIiImoPR4yJiIiIiMDCmIiIiIgIAAtjIiIiIiIALIyJiIiIiACwMPaZtWvXYuLEiTCbzRg8eLDHGI1G0+YrNzdXEVNUVIS0tDSYTCbccsstyMnJ8ere3uRdDkpLS7FgwQIEBQUhIiICy5cvh91uV8QwB74VFxfX5vd+5cqVihhv8kLd99ZbbyE+Ph6BgYFISUnBP/7xD7Wb5Leys7Pb/L5bLBZ5vxAC2dnZsFqtMJlMmDJlCk6ePKlii/u/gwcPYsGCBbBardBoNNi+fbtivzfn3Gaz4Uc/+hEiIiIQFBSEhQsX4uLFi734Kvq3znKwdOnSNn8XEyZMUMT0lRywMPYRu92OxYsX46mnnuowbuPGjbhy5Yr8lZ6eLu+rrq7GjBkzYLVacfToUfz617/G+vXrsWHDhp5uvl/oLAculwvz5s1DbW0tDh06hC1btmDbtm3IysqSY5iDnpGTk6P4vV+1apW8z5u8UPdt3boVmZmZeOGFF1BYWIh77rkHc+bMQWlpqdpN81t33XWX4ve9qKhI3vfyyy9jw4YNeOONN3D06FFYLBbMmDEDNTU1Kra4f6utrUVSUhLeeOMNj/u9OeeZmZn4+OOPsWXLFhw6dAg3btzA/Pnz4XK5eutl9Gud5QAAZs+erfi7yMvLU+zvMzkQ5FMbN24UoaGhHvcBEB9//HG7z33rrbdEaGioaGhokLf94he/EFarVUiS5OOW+q/2cpCXlye0Wq24dOmSvO2Pf/yjMBqNoqqqSgjBHPSE2NhY8eqrr7a735u8UPd997vfFcuWLVNsGzlypFi5cqVKLfJvq1evFklJSR73SZIkLBaLeOmll+RtDQ0NIjQ0VOTm5vZSC/1b6/dZb8759evXhV6vF1u2bJFjLl26JLRardi1a1evtd1feKp10tPTxfe+9712n9OXcsAR416WkZGBiIgIfOc730Fubi4kSZL3ff7550hLS1Msej1r1ixcvnwZJSUlKrTWv3z++edITEyE1WqVt82aNQs2mw0FBQVyDHPge+vWrcOQIUOQnJyMtWvXKqZJeJMX6h673Y6CggLMnDlTsX3mzJnIz89XqVX+78yZM7BarYiPj8eSJUtw7tw5AEBxcTHKysoU+TAajUhLS2M+eog357ygoAAOh0MRY7VakZiYyLz40P79+xEVFYWEhAT88Ic/RHl5ubyvL+UgoFd/2gD3s5/9DNOmTYPJZMLf/vY3ZGVloaKiQv5YuaysDHFxcYrnDB06VN4XHx/f2032K2VlZfL5bBIWFgaDwYCysjI5hjnwraeffhpjx45FWFgY/vnPf+L5559HcXExfve73wHwLi/UPRUVFXC5XG3O79ChQ3lue8j48ePx+9//HgkJCbh69SrWrFmDiRMn4uTJk/I595SP8+fPq9Fcv+fNOS8rK4PBYEBYWFibGP6d+MacOXOwePFixMbGori4GD/96U8xdepUFBQUwGg09qkccMS4A54uomj9dezYMa+Pt2rVKqSmpiI5ORlZWVnIycnBL3/5S0WMRqNRPBaNF3213j5Q+DoHns6jEEKxnTnoXFfy8swzzyAtLQ133303nnjiCeTm5uLdd99FZWWlfDxv8kLd5+l3mue2Z8yZMwcPPPAARo8ejenTp2PHjh0AgE2bNskxzEfv6845Z15856GHHsK8efOQmJiIBQsWYOfOnTh9+rT899EeNXLAEeMOZGRkYMmSJR3GtB5d7IoJEyaguroaV69exdChQ2GxWNr8Z9T0UUPr/3YHCl/mwGKx4MiRI4pt165dg8PhkM8vc+Cdm8lL05XIZ8+exZAhQ7zKC3VPREQEdDqdx99pntveERQUhNGjR+PMmTO47777ALhHKKOjo+UY5qPnNK0I0tE5t1gssNvtuHbtmmLEsry8HBMnTuzdBg8Q0dHRiI2NxZkzZwD0rRxwxLgDERERGDlyZIdfgYGB3T5+YWEhAgMD5aXFUlNTcfDgQcX8yz179sBqtd5UAd6f+TIHqamp+Oqrr3DlyhV52549e2A0GpGSkiLHMAedu5m8FBYWAoD8JuVNXqh7DAYDUlJSsHfvXsX2vXv38g2/l9hsNnz99deIjo5GfHw8LBaLIh92ux0HDhxgPnqIN+c8JSUFer1eEXPlyhV89dVXzEsPqaysxIULF+T3gT6Vg1691M+PnT9/XhQWFooXX3xRBAcHi8LCQlFYWChqamqEEEJ88skn4je/+Y0oKioSZ8+eFb/97W9FSEiIWL58uXyM69evi6FDh4qHH35YFBUViY8++kiEhISI9evXq/Wy+pXOcuB0OkViYqKYNm2a+OKLL8Snn34qYmJiREZGhnwM5sC38vPzxYYNG0RhYaE4d+6c2Lp1q7BarWLhwoVyjDd5oe7bsmWL0Ov14t133xX/+te/RGZmpggKChIlJSVqN80vZWVlif3794tz586Jw4cPi/nz54tBgwbJ5/ull14SoaGh4qOPPhJFRUXi4YcfFtHR0aK6ulrllvdfNTU1cn8PQO5zzp8/L4Tw7pwvW7ZMxMTEiE8//VR88cUXYurUqSIpKUk4nU61Xla/0lEOampqRFZWlsjPzxfFxcVi3759IjU1Vdxyyy19MgcsjH0kPT1dAGjztW/fPiGEEDt37hTJyckiODhYmM1mkZiYKF577TXhcDgUx/nyyy/FPffcI4xGo7BYLCI7O5vLhHmpsxwI4S6e582bJ0wmkwgPDxcZGRmKpdmEYA58qaCgQIwfP16EhoaKwMBAcccdd4jVq1eL2tpaRZw3eaHue/PNN0VsbKwwGAxi7Nix4sCBA2o3yW899NBDIjo6Wuj1emG1WsWiRYvEyZMn5f2SJInVq1cLi8UijEajmDx5sigqKlKxxf3fvn37PPb96enpQgjvznl9fb3IyMgQ4eHhwmQyifnz54vS0lIVXk3/1FEO6urqxMyZM0VkZKTQ6/Vi+PDhIj09vc357Ss50AjBW3oREREREXGOMRERERERWBgTEREREQFgYUxEREREBICFMRERERERABbGREREREQAWBgTEREREQFgYUxEREREBICFMRERERERABbGREREREQAWBgTEQ0IU6ZMQWZmptrNICLq01gYExEREREB0AghhNqNICKinrN06VJs2rRJsa24uBhxcXHqNIiIqI9iYUxE5OeqqqowZ84cJCYmIicnBwAQGRkJnU6ncsuIiPqWALUbQEREPSs0NBQGgwFmsxkWi0Xt5hAR9VmcY0xEREREBBbGREREREQAWBgTEQ0IBoMBLpdL7WYQEfVpLIyJiAaAuLg4HDlyBCUlJaioqIAkSWo3iYioz2FhTEQ0AKxYsQI6nQ6jRo1CZGQkSktL1W4SEVGfw+XaiIiIiIjAEWMiIiIiIgAsjImIiIiIALAwJiIiIiICwMKYiIiIiAgAC2MiIiIiIgAsjImIiIiIALAwJiIiIiICwMKYiIiIiAgAC2MiIiIiIgAsjImIiIiIALAwJiIiIiICAPw/pL0Oi43WR7YAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 720x420 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Some output was deleted.\n"
     ]
    }
   ],
   "source": [
    "# === Stage XV-b: deep-precision zero probe near Re s = s0 =====================\n",
    "# Finer grid + higher precision to catch very shallow minima.\n",
    "# Outputs:\n",
    "#   - stageXVb_refined_scan.csv\n",
    "#   - fig_stageXVb_abs_with_candidates.png\n",
    "#   - fig_stageXVb_phase_gradient.png\n",
    "#   - stageXVb_summary.json\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- helpers (Sage-safe) ----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:\n",
    "        return mp.mpf(x)\n",
    "    except Exception:\n",
    "        return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "# ---------------- load prior context ----------------\n",
    "coeff_path   = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "summaryX     = Path(\"stageX_summary.json\")\n",
    "summaryXI    = Path(\"stageXI_summary.json\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "# s0 and gamma parameters\n",
    "s0 = mp.mpf('2.0')\n",
    "if summaryX.exists() and summaryX.stat().st_size > 0:\n",
    "    try:\n",
    "        JX = json.load(open(summaryX))\n",
    "        if \"s0\" in JX: s0 = mpf_safe(JX[\"s0\"])\n",
    "        elif \"central_point_guess\" in JX: s0 = mpf_safe(JX[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "# Base mu and Stage XI uniform shift (≈ 1.0 in your runs)\n",
    "MU_BASE = [0,1,1,2]\n",
    "delta_uniform = 1.0\n",
    "if summaryXI.exists() and summaryXI.stat().st_size > 0:\n",
    "    try:\n",
    "        JXI = json.load(open(summaryXI))\n",
    "        if \"uniform_shift\" in JXI and \"delta_min_residual\" in JXI[\"uniform_shift\"]:\n",
    "            delta_uniform = float(JXI[\"uniform_shift\"][\"delta_min_residual\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "MU = [m + delta_uniform for m in MU_BASE]      # typically [1,2,2,3]\n",
    "# crude Q (doesn't affect zero LOCATION, just normalization)\n",
    "Q_guess = mp.e**(-4)\n",
    "# ---------------- read Dirichlet coefficients ----------------\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "K = min(len(N_all), 8000)\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "# ---------------- L(s) and Lambda(s) ----------------\n",
    "mp.mp.dps = 150  # <— higher precision\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------------- scan settings (deeper) ----------------\n",
    "T_MAX = 150.0\n",
    "DT    = 0.005          # finer step\n",
    "Ncut  = to_int(n[-1])\n",
    "ABS_FRAC_THRESHOLD   = 3e-4   # relative-to-max |Λ|\n",
    "PHASE_GRAD_THRESHOLD = 2.5    # d/dt arg Λ threshold (radians per unit t)\n",
    "# ---------------- compute line data ----------------\n",
    "t_vals = np.arange(-T_MAX, T_MAX + DT/2.0, DT, dtype=float)\n",
    "Lam_vals = []\n",
    "for t in t_vals:\n",
    "    s = s0 + 1j*mp.mpf(t)\n",
    "    Lam_vals.append(Lambda_of_s(s, Q_guess, MU, Ncut))\n",
    "abs_vals = np.array([float(abs(z)) for z in Lam_vals], dtype=float)\n",
    "# phase (unwrap)\n",
    "arg_vals = np.array([float(mp.arg(z)) for z in Lam_vals], dtype=float)\n",
    "arg_unwrap = np.unwrap(arg_vals)\n",
    "d_arg_dt   = np.gradient(arg_unwrap, DT)\n",
    "# thresholds\n",
    "abs_thresh = ABS_FRAC_THRESHOLD * float(abs_vals.max() if abs_vals.size else 1.0)\n",
    "# candidate indices: small abs AND noticeable phase gradient\n",
    "cand_mask = (abs_vals < abs_thresh) & (np.abs(d_arg_dt) > PHASE_GRAD_THRESHOLD)\n",
    "cand_idx  = np.where(cand_mask)[0]\n",
    "cand_t    = [float(t_vals[i]) for i in cand_idx]\n",
    "# ---------------- save table & figures ----------------\n",
    "df = pd.DataFrame({\n",
    "    \"t\": t_vals,\n",
    "    \"abs\": abs_vals,\n",
    "    \"arg_unwrap\": arg_unwrap,\n",
    "    \"d_arg_dt\": d_arg_dt\n",
    "})\n",
    "out_csv   = Path(\"stageXVb_refined_scan.csv\")\n",
    "out_png1  = Path(\"fig_stageXVb_abs_with_candidates.png\")\n",
    "out_png2  = Path(\"fig_stageXVb_phase_gradient.png\")\n",
    "out_json  = Path(\"stageXVb_summary.json\")\n",
    "df.to_csv(out_csv, index=False)\n",
    "# |Λ| plot (log y) with candidates\n",
    "plt.figure(figsize=(7.2,4.2))\n",
    "plt.semilogy(t_vals, abs_vals, label=\"|Λ(s0+it)|\")\n",
    "if len(cand_t) > 0:\n",
    "    plt.scatter(cand_t, [abs_thresh]*len(cand_t), marker=\"x\", s=35, label=\"candidates (t)\")\n",
    "plt.axhline(abs_thresh, color=\"orange\", ls=\"--\", label=\"abs threshold\")\n",
    "plt.title(\"Stage XV-b: refined |Λ(s)| near s0\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"|Λ| (log)\"); plt.grid(True); plt.legend(); plt.tight_layout()\n",
    "plt.savefig(out_png1, dpi=150)\n",
    "plt.show()\n",
    "# phase gradient plot\n",
    "plt.figure(figsize=(7.2,4.2))\n",
    "plt.plot(t_vals, d_arg_dt)\n",
    "plt.axhline(+PHASE_GRAD_THRESHOLD, color=\"orange\", ls=\"--\", label=\"threshold\")\n",
    "plt.axhline(-PHASE_GRAD_THRESHOLD, color=\"orange\", ls=\"--\")\n",
    "plt.title(\"Stage XV-b: phase gradient along Re s = s0\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"d/dt arg Λ\"); plt.grid(True); plt.legend(); plt.tight_layout()\n",
    "plt.savefig(out_png2, dpi=150)\n",
    "plt.show()\n",
    "# ---------------- summary & preview ----------------\n",
    "summary = {\n",
    "    \"s0\": float(s0),\n",
    "    \"mu\": [float(x) for x in MU],\n",
    "    \"Q_guess\": float(Q_guess),\n",
    "    \"K_terms\": int(K),\n",
    "    \"n_max\": int(n[-1]),\n",
    "    \"T_MAX\": float(T_MAX),\n",
    "    \"DT\": float(DT),\n",
    "    \"precision\": int(mp.mp.dps),\n",
    "    \"abs_frac_threshold\": float(ABS_FRAC_THRESHOLD),\n",
    "    \"abs_threshold_value\": float(abs_thresh),\n",
    "    \"phase_grad_threshold\": float(PHASE_GRAD_THRESHOLD),\n",
    "    \"n_candidates\": int(len(cand_t)),\n",
    "    \"candidates_t\": cand_t,\n",
    "    \"outputs\": [str(out_csv), str(out_png1), str(out_png2)]\n",
    "}\n",
    "with open(out_json, \"w\") as f:\n",
    "    json.dump(summary, f, indent=2)\n",
    "print(\"\\n=== Stage XV-b summary ===\")\n",
    "for k,v in summary.items():\n",
    "    print(f\"{k}: {v}\")\n",
    "print(\"\\nWrote:\")\n",
    "print(\" -\", out_csv.name)\n",
    "print(\" -\", out_png1.name)\n",
    "print(\" -\", out_png2.name)\n",
    "print(\" -\", out_json.name)\n",
    "display(head_safe(df, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "170632",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stage XVI: scanning |Λ| on Re s = s0\n",
      "s0         : 2.0\n",
      "mu (used)  : [1.0, 2.0, 2.0, 3.0]\n",
      "K_terms    : 21   n_max: 187\n",
      "T_MAX, DT  : 400.000000000000, 0.0200000000000000   → 40001 points\n",
      "precision  : mp.mp.dps = 150\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x460 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x380 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x380 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XVI summary ===\n",
      "                s0: 2.0\n",
      "           mu_used: [1, 2, 2, 3]\n",
      "           Q_guess: 0.01831563888873418\n",
      "           K_terms: 21\n",
      "             n_max: 187\n",
      "             T_MAX: 400\n",
      "                DT: 0.02\n",
      "         precision: 150\n",
      "    adaptive_floor: 1e-14\n",
      "  curvature_thresh: -5\n",
      "    phase_grad_max: 10\n",
      "      n_candidates: 0\n",
      "Wrote:\n",
      " - stageXVI_candidates.csv\n",
      " - fig_stageXVI_abs_candidates.png\n",
      " - fig_stageXVI_curvature.png\n",
      " - fig_stageXVI_phase_gradient.png\n",
      "\n",
      "No candidates under current thresholds. Try relaxing CURV_THRESH (e.g. -3) or increasing T_MAX.\n"
     ]
    }
   ],
   "source": [
    "# === Stage XVI: extended horizon + curvature-filtered zero candidates ===\n",
    "# Scans Λ(s) on Re s = s0 out to large |t| and keeps only \"true dip\" minima\n",
    "# via a curvature (2nd diff of log|Λ|) + adaptive depth threshold.\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- helpers (Sage-safe) ----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except: return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "def py(x):\n",
    "    \"\"\"JSON-safe conversion.\"\"\"\n",
    "    import numbers\n",
    "    if isinstance(x, (str, bool)) or x is None: return x\n",
    "    if isinstance(x, numbers.Real):\n",
    "        try:\n",
    "            xi = int(x)\n",
    "            if float(xi) == float(x): return int(xi)\n",
    "        except Exception:\n",
    "            pass\n",
    "        try:    return float(x)\n",
    "        except: return to_float(x)\n",
    "    if isinstance(x, complex):\n",
    "        return {\"re\": py(x.real), \"im\": py(x.imag)}\n",
    "    if isinstance(x, (list, tuple)): return [py(t) for t in x]\n",
    "    if isinstance(x, dict): return {str(k): py(v) for k,v in x.items()}\n",
    "    try:    return float(x)\n",
    "    except: return str(x)\n",
    "# ---------------- inputs / defaults ----------------\n",
    "COEFF_FILE   = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "SUM_X_FILE   = Path(\"stageX_summary.json\")\n",
    "SUM_XI_FILE  = Path(\"stageXI_summary.json\")\n",
    "if not COEFF_FILE.exists() or COEFF_FILE.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "# center s0\n",
    "s0 = mp.mpf('2.0')\n",
    "if SUM_X_FILE.exists() and SUM_X_FILE.stat().st_size > 0:\n",
    "    try:\n",
    "        JX = json.load(open(SUM_X_FILE))\n",
    "        if \"s0\" in JX: s0 = mpf_safe(JX[\"s0\"])\n",
    "        elif \"central_point_guess\" in JX: s0 = mpf_safe(JX[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "# μ-shifts: use Stage XI uniform shift if present; else default [1,2,2,3]\n",
    "MU_BASE = [0,1,1,2]\n",
    "delta_uniform = 1.0\n",
    "if SUM_XI_FILE.exists() and SUM_XI_FILE.stat().st_size > 0:\n",
    "    try:\n",
    "        JXI = json.load(open(SUM_XI_FILE))\n",
    "        if \"uniform_shift\" in JXI and \"delta_min_residual\" in JXI[\"uniform_shift\"]:\n",
    "            delta_uniform = float(JXI[\"uniform_shift\"][\"delta_min_residual\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "MU = [m + delta_uniform for m in MU_BASE]  # typically [1,2,2,3]\n",
    "# Conductor (doesn't affect zero locations; keep same small Q as earlier stages)\n",
    "Q_GUESS = mp.e**(-4)\n",
    "# Scan params — you can tweak T_MAX / DT.\n",
    "T_MAX = 400.0     # height limit (absolute)\n",
    "DT    = 0.02      # step size along t\n",
    "mp.mp.dps = 150   # precision (digits)\n",
    "# ---------------- read coefficients ----------------\n",
    "C = pd.read_csv(COEFF_FILE)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all); N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "# Limit terms (keep small for speed but stable behaviour)\n",
    "K = min(len(N_all), 200)   # feel free to raise to 500/1000 if it's still fast\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "# ---------------- Λ(s) ----------------\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    tot = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            tot += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return tot\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------------- scan ----------------\n",
    "Ncut = to_int(n[-1])\n",
    "t_vals = np.arange(-T_MAX, T_MAX + 1e-12, DT, dtype=float)\n",
    "abs_vals  = np.empty_like(t_vals, dtype=float)\n",
    "arg_vals  = np.empty_like(t_vals, dtype=float)\n",
    "print(\"Stage XVI: scanning |Λ| on Re s = s0\")\n",
    "print(f\"s0         : {s0}\")\n",
    "print(f\"mu (used)  : {MU}\")\n",
    "print(f\"K_terms    : {K}   n_max: {to_int(n[-1])}\")\n",
    "print(f\"T_MAX, DT  : {T_MAX}, {DT}   → {len(t_vals)} points\")\n",
    "print(f\"precision  : mp.mp.dps = {mp.mp.dps}\")\n",
    "for i, t in enumerate(t_vals):\n",
    "    s = s0 + 1j*mp.mpf(t)\n",
    "    Lam = Lambda_of_s(s, Q_GUESS, MU, Ncut)\n",
    "    abs_vals[i] = to_float(abs(Lam))\n",
    "    arg_vals[i] = np.angle(complex(Lam.real, Lam.imag))  # numpy phase for unwrap\n",
    "# Unwrap phase and compute first derivative (central diff)\n",
    "arg_unwrap = np.unwrap(arg_vals)\n",
    "d_arg_dt   = np.gradient(arg_unwrap, t_vals)\n",
    "# Curvature of log|Λ|: second finite difference\n",
    "eps = 1e-300  # floor to avoid log(0)\n",
    "log_abs = np.log(abs_vals + eps)\n",
    "curv    = np.gradient(np.gradient(log_abs, t_vals), t_vals)\n",
    "# ---------------- candidate detection (depth + curvature + local minimum) ----------------\n",
    "# Adaptive absolute threshold: a very small floor tied to distribution\n",
    "# We’ll take the 10th percentile of |Λ| and drop by a factor, but also cap by a minimal floor.\n",
    "p10   = float(np.quantile(abs_vals, 0.10))\n",
    "floor = max(1e-14, p10*1e-4)   # adaptive depth\n",
    "# Curvature must be sufficiently negative (concave down, true dip)\n",
    "CURV_THRESH = -5.0             # tweakable; more negative = stricter\n",
    "# Also require small-ish |d arg / dt| so we avoid wild phase turning near precision floor?\n",
    "# (Optional; set large to disable.)\n",
    "PHASE_GRAD_MAX = 10.0\n",
    "# Local minima mask\n",
    "is_min = np.r_[False,\n",
    "               (abs_vals[1:-1] <= abs_vals[:-2]) & (abs_vals[1:-1] <= abs_vals[2:]),\n",
    "               False]\n",
    "cand_mask = (abs_vals < floor) & is_min & (curv < CURV_THRESH) & (np.abs(d_arg_dt) < PHASE_GRAD_MAX)\n",
    "cand_idx  = np.where(cand_mask)[0]\n",
    "candidates = pd.DataFrame({\n",
    "    \"t\": t_vals[cand_idx],\n",
    "    \"abs\": abs_vals[cand_idx],\n",
    "    \"log_abs\": log_abs[cand_idx],\n",
    "    \"curvature_log_abs\": curv[cand_idx],\n",
    "    \"d_arg_dt\": d_arg_dt[cand_idx],\n",
    "})\n",
    "# ---------------- plots ----------------\n",
    "plt.figure(figsize=(8.0,4.6))\n",
    "plt.semilogy(t_vals, abs_vals, label=\"|Λ(s0+it)|\")\n",
    "if len(candidates):\n",
    "    plt.semilogy(candidates[\"t\"].values, candidates[\"abs\"].values, \"x\", label=\"candidates\")\n",
    "plt.axhline(floor, ls=\"--\", color=\"orange\", label=\"depth threshold\")\n",
    "plt.title(\"Stage XVI: |Λ(s)| along Re s = s0 (extended)\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"|Λ| (log)\"); plt.grid(True); plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"fig_stageXVI_abs_candidates.png\", dpi=150)\n",
    "plt.show()\n",
    "plt.figure(figsize=(8.0,3.8))\n",
    "plt.plot(t_vals, curv)\n",
    "plt.axhline(CURV_THRESH, ls=\"--\", color=\"orange\", label=\"curv threshold\")\n",
    "plt.title(\"Stage XVI: curvature of log|Λ|\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"d²/dt² log|Λ|\"); plt.grid(True); plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"fig_stageXVI_curvature.png\", dpi=150)\n",
    "plt.show()\n",
    "plt.figure(figsize=(8.0,3.8))\n",
    "plt.plot(t_vals, d_arg_dt)\n",
    "plt.title(\"Stage XVI: phase gradient along Re s = s0\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"d/dt arg Λ\"); plt.grid(True)\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"fig_stageXVI_phase_gradient.png\", dpi=150)\n",
    "plt.show()\n",
    "# ---------------- save outputs ----------------\n",
    "candidates.to_csv(\"stageXVI_candidates.csv\", index=False)\n",
    "summary = {\n",
    "    \"s0\":           py(s0),\n",
    "    \"mu_used\":      py(MU),\n",
    "    \"Q_guess\":      py(Q_GUESS),\n",
    "    \"K_terms\":      py(K),\n",
    "    \"n_max\":        py(n[-1]),\n",
    "    \"T_MAX\":        py(T_MAX),\n",
    "    \"DT\":           py(DT),\n",
    "    \"precision\":    py(mp.mp.dps),\n",
    "    \"adaptive_floor\": py(floor),\n",
    "    \"curvature_thresh\": py(CURV_THRESH),\n",
    "    \"phase_grad_max\": py(PHASE_GRAD_MAX),\n",
    "    \"n_candidates\": py(len(candidates)),\n",
    "    \"outputs\": [\n",
    "        \"stageXVI_candidates.csv\",\n",
    "        \"fig_stageXVI_abs_candidates.png\",\n",
    "        \"fig_stageXVI_curvature.png\",\n",
    "        \"fig_stageXVI_phase_gradient.png\",\n",
    "    ],\n",
    "}\n",
    "with open(\"stageXVI_summary.json\",\"w\") as f:\n",
    "    json.dump(summary, f, indent=2)\n",
    "print(\"\\n=== Stage XVI summary ===\")\n",
    "for k,v in summary.items():\n",
    "    if k != \"outputs\":\n",
    "        print(f\"{k:>18}: {v}\")\n",
    "print(\"Wrote:\")\n",
    "for fn in summary[\"outputs\"]:\n",
    "    print(\" -\", fn)\n",
    "if len(candidates):\n",
    "    print(\"\\nTop candidates (first 12):\")\n",
    "    display(head_safe(candidates, 12))\n",
    "else:\n",
    "    print(\"\\nNo candidates under current thresholds. \"\n",
    "          \"Try relaxing CURV_THRESH (e.g. -3) or increasing T_MAX.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "36f65e",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 720x400 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x400 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x600 with 2 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage XVII summary ===\n",
      "s0: 2.0\n",
      "mu_list: [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess: 0.01831563888873418\n",
      "K_terms: 21\n",
      "n_max: 187\n",
      "T_WIN: 50.0\n",
      "DT: 0.0015\n",
      "precision: 120\n",
      "zeros_estimate_via_argument_principle: 10.634165279971047\n",
      "files: ['stageXVII_micro_scan.csv', 'fig_stageXVII_abs_log.png', 'fig_stageXVII_phase.png', 'fig_stageXVII_grad_curv.png']\n",
      "\n",
      "Preview:\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>t</th>\n      <th>abs</th>\n      <th>log_abs</th>\n      <th>arg_unwrap</th>\n      <th>d_arg_dt</th>\n      <th>curv_log_abs</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>-50.0000</td>\n      <td>1.209001e-64</td>\n      <td>-147.175651</td>\n      <td>2.145942</td>\n      <td>1.976423</td>\n      <td>-0.233828</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>-49.9985</td>\n      <td>1.214334e-64</td>\n      <td>-147.171250</td>\n      <td>2.148907</td>\n      <td>1.976477</td>\n      <td>-0.350778</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>-49.9970</td>\n      <td>1.219689e-64</td>\n      <td>-147.166850</td>\n      <td>2.151872</td>\n      <td>1.976585</td>\n      <td>-0.467799</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>-49.9955</td>\n      <td>1.225067e-64</td>\n      <td>-147.162451</td>\n      <td>2.154837</td>\n      <td>1.976696</td>\n      <td>-0.467937</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>-49.9940</td>\n      <td>1.230467e-64</td>\n      <td>-147.158052</td>\n      <td>2.157802</td>\n      <td>1.976809</td>\n      <td>-0.468068</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>-49.9925</td>\n      <td>1.235889e-64</td>\n      <td>-147.153655</td>\n      <td>2.160767</td>\n      <td>1.976926</td>\n      <td>-0.468192</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>-49.9910</td>\n      <td>1.241334e-64</td>\n      <td>-147.149259</td>\n      <td>2.163733</td>\n      <td>1.977045</td>\n      <td>-0.468310</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>-49.9895</td>\n      <td>1.246802e-64</td>\n      <td>-147.144864</td>\n      <td>2.166698</td>\n      <td>1.977168</td>\n      <td>-0.468420</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>-49.9880</td>\n      <td>1.252292e-64</td>\n      <td>-147.140470</td>\n      <td>2.169664</td>\n      <td>1.977293</td>\n      <td>-0.468523</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>-49.9865</td>\n      <td>1.257805e-64</td>\n      <td>-147.136078</td>\n      <td>2.172630</td>\n      <td>1.977420</td>\n      <td>-0.468619</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>-49.9850</td>\n      <td>1.263342e-64</td>\n      <td>-147.131686</td>\n      <td>2.175596</td>\n      <td>1.977551</td>\n      <td>-0.468708</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>-49.9835</td>\n      <td>1.268901e-64</td>\n      <td>-147.127295</td>\n      <td>2.178563</td>\n      <td>1.977684</td>\n      <td>-0.468789</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "          t           abs     log_abs  arg_unwrap  d_arg_dt  curv_log_abs\n",
       "0  -50.0000  1.209001e-64 -147.175651    2.145942  1.976423     -0.233828\n",
       "1  -49.9985  1.214334e-64 -147.171250    2.148907  1.976477     -0.350778\n",
       "2  -49.9970  1.219689e-64 -147.166850    2.151872  1.976585     -0.467799\n",
       "3  -49.9955  1.225067e-64 -147.162451    2.154837  1.976696     -0.467937\n",
       "4  -49.9940  1.230467e-64 -147.158052    2.157802  1.976809     -0.468068\n",
       "5  -49.9925  1.235889e-64 -147.153655    2.160767  1.976926     -0.468192\n",
       "6  -49.9910  1.241334e-64 -147.149259    2.163733  1.977045     -0.468310\n",
       "7  -49.9895  1.246802e-64 -147.144864    2.166698  1.977168     -0.468420\n",
       "8  -49.9880  1.252292e-64 -147.140470    2.169664  1.977293     -0.468523\n",
       "9  -49.9865  1.257805e-64 -147.136078    2.172630  1.977420     -0.468619\n",
       "10 -49.9850  1.263342e-64 -147.131686    2.175596  1.977551     -0.468708\n",
       "11 -49.9835  1.268901e-64 -147.127295    2.178563  1.977684     -0.468789"
      ]
     },
     "execution_count": 8,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Wrote:\n",
      " - stageXVII_micro_scan.csv\n",
      " - fig_stageXVII_abs_log.png\n",
      " - fig_stageXVII_phase.png\n",
      " - fig_stageXVII_grad_curv.png\n",
      " - stageXVII_summary.json\n"
     ]
    }
   ],
   "source": [
    "# === Stage XVII: micro-analysis near s0 (fine scan, arg-principle count) ===\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- helpers (avoid Sage Integer issues) ----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except Exception: return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "# ---------------- tunables ----------------\n",
    "K_TERMS = 200        # try 200 first; then 500 if you want more texture\n",
    "T_WIN   = 50.0       # half-width of t-window around 0 (i.e., [-T_WIN, +T_WIN])\n",
    "DT      = 0.0015     # step in t (smaller -> more sensitive, slower)\n",
    "PREC    = 120        # mpmath working precision (digits)\n",
    "SMOOTH_POW = 1.0     # 1.0=cosine window; >1 sharpens the cutoff slightly\n",
    "# ---------------- load s0, mu, coefficients ----------------\n",
    "coeff_path   = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "summaryX     = Path(\"stageX_summary.json\")      # may contain s0 / central_point_guess\n",
    "summaryXI    = Path(\"stageXI_summary.json\")     # may contain uniform shift delta\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "# s0\n",
    "s0 = mp.mpf('2.0')\n",
    "for p in (summaryX, Path(\"final_summary.json\")):\n",
    "    if p.exists() and p.stat().st_size > 0:\n",
    "        try:\n",
    "            J = json.load(open(p))\n",
    "            if \"s0\" in J: s0 = mpf_safe(J[\"s0\"])\n",
    "            elif \"central_point_guess\" in J: s0 = mpf_safe(J[\"central_point_guess\"])\n",
    "            break\n",
    "        except Exception:\n",
    "            pass\n",
    "# mu list: start from base [0,1,1,2], add Stage XI uniform shift if present\n",
    "delta_uniform = None\n",
    "if summaryXI.exists() and summaryXI.stat().st_size > 0:\n",
    "    try:\n",
    "        JXI = json.load(open(summaryXI))\n",
    "        if \"uniform_shift\" in JXI and \"delta_min_residual\" in JXI[\"uniform_shift\"]:\n",
    "            delta_uniform = float(JXI[\"uniform_shift\"][\"delta_min_residual\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "if delta_uniform is None:    # default to the value you saw before\n",
    "    MU_LIST = [1, 2, 2, 3]\n",
    "else:\n",
    "    MU_LIST = [m + delta_uniform for m in [0,1,1,2]]\n",
    "# coefficients\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "K = min(len(N_all), int(K_TERMS))\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "# ---------------- L(s) / Lambda(s) ----------------\n",
    "mp.mp.dps = int(PREC)\n",
    "def smooth_weight(x):\n",
    "    # cosine window on [0,1], optionally sharpened by power SMOOTH_POW\n",
    "    if x < 0 or x > 1:\n",
    "        return mp.mpf('0')\n",
    "    w = mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "    return w**mp.mpf(SMOOTH_POW)\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "# Conductor: your Stage X runs liked tiny Q; use that again.\n",
    "Q_guess = mp.e**mp.mpf(-4)\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------------- micro scan along Re s = s0 ----------------\n",
    "Ncut = to_int(n[-1])\n",
    "t_vals = np.arange(-float(T_WIN), float(T_WIN)+float(DT)/2.0, float(DT), dtype=float)\n",
    "Lam = []\n",
    "for t in t_vals:\n",
    "    s = s0 + 1j*mp.mpf(t)\n",
    "    Lam.append(Lambda_of_s(s, Q_guess, MU_LIST, Ncut))\n",
    "Lam = np.array([complex(float(mp.re(z)), float(mp.im(z))) for z in Lam])\n",
    "abs_vals   = np.abs(Lam)\n",
    "log_abs    = np.log(np.maximum(abs_vals, 1e-300))\n",
    "phase_main = np.angle(Lam)                    # principal value (-pi, pi]\n",
    "phase_unw  = np.unwrap(phase_main)            # continuous phase\n",
    "dphi_dt    = np.gradient(phase_unw, float(DT))\n",
    "curv_log   = np.gradient(np.gradient(log_abs, float(DT)), float(DT))  # d^2/dt^2 log|Λ|\n",
    "# Argument-principle count on the whole window (≈ number of zeros minus poles)\n",
    "# Poles are not expected on Re s = s0 for completed Λ, so this estimates zeros in window.\n",
    "total_phase_change = phase_unw[-1] - phase_unw[0]\n",
    "zeros_estimate = total_phase_change / np.pi   # not necessarily integer; report value\n",
    "# ---------------- save table & summary ----------------\n",
    "OUT_CSV  = Path(\"stageXVII_micro_scan.csv\")\n",
    "OUT_SUM  = Path(\"stageXVII_summary.json\")\n",
    "OUT_PNG1 = Path(\"fig_stageXVII_abs_log.png\")\n",
    "OUT_PNG2 = Path(\"fig_stageXVII_phase.png\")\n",
    "OUT_PNG3 = Path(\"fig_stageXVII_grad_curv.png\")\n",
    "df = pd.DataFrame({\n",
    "    \"t\": t_vals,\n",
    "    \"abs\": abs_vals,\n",
    "    \"log_abs\": log_abs,\n",
    "    \"arg_unwrap\": phase_unw,\n",
    "    \"d_arg_dt\": dphi_dt,\n",
    "    \"curv_log_abs\": curv_log,\n",
    "})\n",
    "df.to_csv(OUT_CSV, index=False)\n",
    "summary = {\n",
    "    \"s0\": float(s0),\n",
    "    \"mu_list\": [float(m) for m in MU_LIST],\n",
    "    \"Q_guess\": float(Q_guess),\n",
    "    \"K_terms\": int(K),\n",
    "    \"n_max\": int(n[-1]),\n",
    "    \"T_WIN\": float(T_WIN),\n",
    "    \"DT\": float(DT),\n",
    "    \"precision\": int(PREC),\n",
    "    \"zeros_estimate_via_argument_principle\": float(zeros_estimate),\n",
    "    \"files\": [str(OUT_CSV.name), str(OUT_PNG1.name), str(OUT_PNG2.name), str(OUT_PNG3.name)],\n",
    "}\n",
    "json.dump(summary, open(OUT_SUM, \"w\"), indent=2)\n",
    "# ---------------- plots ----------------\n",
    "plt.figure(figsize=(7.2,4.0))\n",
    "plt.plot(t_vals, log_abs)\n",
    "plt.title(\"Stage XVII: log |Λ(s0 + i t)|\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"log |Λ|\"); plt.grid(True)\n",
    "plt.tight_layout(); plt.savefig(OUT_PNG1, dpi=150); plt.show()\n",
    "plt.figure(figsize=(7.2,4.0))\n",
    "plt.plot(t_vals, phase_unw)\n",
    "plt.title(\"Stage XVII: unwrapped arg Λ(s0 + i t)\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"arg Λ\"); plt.grid(True)\n",
    "plt.tight_layout(); plt.savefig(OUT_PNG2, dpi=150); plt.show()\n",
    "fig, ax = plt.subplots(2,1, figsize=(7.2,6.0), sharex=True)\n",
    "ax[0].plot(t_vals, dphi_dt)\n",
    "ax[0].set_title(\"Stage XVII: phase gradient d/dt arg Λ\")\n",
    "ax[0].set_ylabel(\"d(arg Λ)/dt\"); ax[0].grid(True)\n",
    "ax[1].plot(t_vals, curv_log)\n",
    "ax[1].set_title(\"Stage XVII: curvature of log |Λ|\")\n",
    "ax[1].set_xlabel(\"t\"); ax[1].set_ylabel(\"d²/dt² log|Λ|\"); ax[1].grid(True)\n",
    "plt.tight_layout(); plt.savefig(OUT_PNG3, dpi=150); plt.show()\n",
    "# ---------------- report ----------------\n",
    "print(\"=== Stage XVII summary ===\")\n",
    "for k,v in summary.items():\n",
    "    print(f\"{k}: {v}\")\n",
    "print(\"\\nPreview:\")\n",
    "display(head_safe(df, 12))\n",
    "print(\"\\nWrote:\")\n",
    "print(\" -\", OUT_CSV.name)\n",
    "print(\" -\", OUT_PNG1.name)\n",
    "print(\" -\", OUT_PNG2.name)\n",
    "print(\" -\", OUT_PNG3.name)\n",
    "print(\" -\", OUT_SUM.name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "797940",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x420 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Stage XVII-b refinement summary ===\n",
      "micro-scan rows: 66668\n",
      "initial candidates (pre-cluster): 482\n",
      "candidates (clustered): 2\n",
      "refined zeros kept: 0\n",
      "\n",
      "No refined zeros found under current heuristics.\n",
      "\n",
      "Wrote:\n",
      " - stageXVIIb_refined_zeros.csv\n",
      " - fig_stageXVIIb_refined_zeros.png\n"
     ]
    }
   ],
   "source": [
    "# === Stage XVII-b: zero refinement from Stage XVII micro scan ===\n",
    "# - Reads 'stageXVII_micro_scan.csv'\n",
    "# - Builds Λ(s) again with (μ = [1,2,2,3], Q ≈ e^-4)\n",
    "# - Detects candidate minima and refines them with mpmath.findroot\n",
    "# - Writes 'stageXVIIb_refined_zeros.csv' and a figure with markers\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- helpers (JSON / pandas / Sage-safety) ----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except Exception:\n",
    "        return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "# ---------------- load Stage XVII micro-scan ----------------\n",
    "micro_csv = Path(\"stageXVII_micro_scan.csv\")\n",
    "if not micro_csv.exists() or micro_csv.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageXVII_micro_scan.csv not found. Please run Stage XVII first.\")\n",
    "D = pd.read_csv(micro_csv)\n",
    "cols = {c.lower(): c for c in D.columns}\n",
    "# expected: t, abs, log_abs, arg_unwrap, d_arg_dt, curv_log_abs\n",
    "required = [\"t\",\"abs\",\"log_abs\",\"arg_unwrap\",\"d_arg_dt\",\"curv_log_abs\"]\n",
    "missing = [k for k in required if k not in cols]\n",
    "if missing:\n",
    "    raise ValueError(f\"Stage XVII CSV missing columns: {missing}\")\n",
    "t_arr   = D[cols[\"t\"]].to_numpy(dtype=float)\n",
    "abs_arr = D[cols[\"abs\"]].to_numpy(dtype=float)\n",
    "grad_arr= D[cols[\"d_arg_dt\"]].to_numpy(dtype=float)\n",
    "curv_arr= D[cols[\"curv_log_abs\"]].to_numpy(dtype=float)\n",
    "# ---------------- rebuild Λ(s) with your model ----------------\n",
    "mp.mp.dps = 120          # same precision as Stage XVII\n",
    "s0        = mp.mpf('2.0')\n",
    "MU        = [1,2,2,3]    # from Stage XI/XII/XVII\n",
    "Q_guess   = mp.e**(-4)   # ~0.018315...\n",
    "# Pull Dirichlet coefficients (Stage VIII)\n",
    "coeff_path = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found. Run Stage VIII first.\")\n",
    "C = pd.read_csv(coeff_path)\n",
    "cmap = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cmap: raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cmap:\n",
    "        a_col = cmap[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cmap[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "K = min(len(N_all), 8000)\n",
    "n = N_all[:K]; a = A_all[:K]\n",
    "Ncut = int(n[-1])\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None: N_cut = Ncut\n",
    "    N_cut = int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(int(nn_i))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s)\n",
    "def Lambda_on_line(t):\n",
    "    return Lambda_of_s(s0 + 1j*mp.mpf(t), Q_guess, MU)\n",
    "# ---------------- pick candidates from Stage XVII arrays ----------------\n",
    "# Heuristics: very small |Λ| *and* negative curvature *and* big |phase gradient|\n",
    "abs_q   = np.quantile(abs_arr, 0.02)     # 2% smallest\n",
    "curv_cut= -0.25\n",
    "grad_cut= 1.25\n",
    "cand_mask = (abs_arr <= abs_q) & (curv_arr < curv_cut) & (np.abs(grad_arr) >= grad_cut)\n",
    "cand_t = t_arr[cand_mask]\n",
    "# De-duplicate nearby hits (cluster within ~0.2 units, keep center)\n",
    "if cand_t.size:\n",
    "    cand_t = np.sort(cand_t)\n",
    "    clustered = []\n",
    "    group = [cand_t[0]]\n",
    "    for x in cand_t[1:]:\n",
    "        if abs(x - group[-1]) <= 0.2:\n",
    "            group.append(x)\n",
    "        else:\n",
    "            clustered.append(np.median(group))\n",
    "            group = [x]\n",
    "    clustered.append(np.median(group))\n",
    "    cand_t = np.array(clustered, dtype=float)\n",
    "# ---------------- refine with complex root-finding in t ----------------\n",
    "def refine_zero(t0):\n",
    "    \"\"\"Refine a zero near t0 by solving Λ(s0+i t)=0 in t (complex).\"\"\"\n",
    "    f = lambda tt: Lambda_on_line(tt)\n",
    "    # try progressively wider secant brackets\n",
    "    for h in (0.002, 0.005, 0.01, 0.02, 0.05):\n",
    "        try:\n",
    "            t_root = mp.findroot(f, mp.mpf(t0-h), mp.mpf(t0+h), tol=mp.mpf('1e-30'), maxsteps=80)\n",
    "            val = f(t_root)\n",
    "            return float(t_root), complex(val)\n",
    "        except Exception:\n",
    "            continue\n",
    "    return None\n",
    "refined = []\n",
    "if cand_t.size:\n",
    "    for t0 in cand_t:\n",
    "        r = refine_zero(t0)\n",
    "        if r is not None:\n",
    "            t_hat, val = r\n",
    "            refined.append({\"t\": t_hat, \"abs\": abs(val), \"ReLambda\": val.real, \"ImLambda\": val.imag})\n",
    "# Deduplicate refined roots within ~0.1\n",
    "refined_sorted = sorted(refined, key=lambda d: d[\"t\"])\n",
    "dedup = []\n",
    "for d in refined_sorted:\n",
    "    if not dedup or abs(d[\"t\"] - dedup[-1][\"t\"]) > 0.1:\n",
    "        dedup.append(d)\n",
    "refined_df = pd.DataFrame(dedup, columns=[\"t\",\"abs\",\"ReLambda\",\"ImLambda\"])\n",
    "# ---------------- save & plot ----------------\n",
    "out_csv = Path(\"stageXVIIb_refined_zeros.csv\")\n",
    "refined_df.to_csv(out_csv, index=False)\n",
    "# quick overlay on your Stage XVII |Λ| curve (recompute |Λ| on same t-grid)\n",
    "# To keep it light, reuse micro-scan t_arr & abs_arr:\n",
    "plt.figure(figsize=(7.2,4.2))\n",
    "plt.plot(t_arr, np.maximum(abs_arr, 1e-300), lw=1.2, label=\"|Λ(s0+i t)| (XVII micro scan)\")\n",
    "if not refined_df.empty:\n",
    "    plt.scatter(refined_df[\"t\"], np.maximum(refined_df[\"abs\"], 1e-300), marker=\"x\", s=60, label=\"refined zeros\", zorder=5)\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"|Λ|\")\n",
    "plt.title(\"Stage XVII-b: refined zeros on Re s = s0\")\n",
    "plt.grid(True, which=\"both\", ls=\":\")\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"fig_stageXVIIb_refined_zeros.png\", dpi=150)\n",
    "plt.show()\n",
    "# ---------------- report ----------------\n",
    "print(\"=== Stage XVII-b refinement summary ===\")\n",
    "print(f\"micro-scan rows: {len(D)}\")\n",
    "print(f\"initial candidates (pre-cluster): {int(np.sum(cand_mask))}\")\n",
    "print(f\"candidates (clustered): {len(cand_t)}\")\n",
    "print(f\"refined zeros kept: {len(refined_df)}\")\n",
    "if not refined_df.empty:\n",
    "    print(\"\\nFirst few refined zeros:\")\n",
    "    display(head_safe(refined_df, 10))\n",
    "else:\n",
    "    print(\"\\nNo refined zeros found under current heuristics.\")\n",
    "print(\"\\nWrote:\")\n",
    "print(f\" - {out_csv.name}\")\n",
    "print(\" - fig_stageXVIIb_refined_zeros.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bde9e9",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stage XVIII: sweeping lines\n",
      "s0                : 2.0\n",
      "mu (used)         : [1.0, 2.0, 2.0, 3.0]\n",
      "K_terms           : 21     n_max: 187\n",
      "T_MAX, DT         : 50.0000000000000, 0.0500000000000000   → 2001 samples/line\n",
      "sigmas (count)    : 21 from 2.0 down to 0.5\n",
      "precision (mp.dps): 100\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 760x520 with 2 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XVIII summary ===\n",
      "s0                : 2.0\n",
      "mu_used           : [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess           : 0.01831563888873418\n",
      "K_terms           : 21\n",
      "n_max             : 187\n",
      "T_MAX             : 50.0\n",
      "DT                : 0.05\n",
      "points_per_line   : 2001\n",
      "outputs           : ['stageXVIII_heatmap.png', 'stageXVIII_minima.csv', 'stageXVIII_line_samples.csv']\n",
      "Wrote:\n",
      " - stageXVIII_heatmap.png\n",
      " - stageXVIII_minima.csv\n",
      " - stageXVIII_line_samples.csv\n",
      " - stageXVIII_settings.json\n",
      "\n",
      "Preview of minima:\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>sigma</th>\n      <th>t</th>\n      <th>abs</th>\n      <th>log_abs</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>2.000</td>\n      <td>-50.0</td>\n      <td>1.209001e-64</td>\n      <td>-147.175651</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1.925</td>\n      <td>-50.0</td>\n      <td>1.043909e-64</td>\n      <td>-147.322473</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1.850</td>\n      <td>-50.0</td>\n      <td>9.042603e-65</td>\n      <td>-147.466084</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1.775</td>\n      <td>-50.0</td>\n      <td>7.863483e-65</td>\n      <td>-147.605801</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1.700</td>\n      <td>-50.0</td>\n      <td>6.870291e-65</td>\n      <td>-147.740825</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>1.625</td>\n      <td>-50.0</td>\n      <td>6.036368e-65</td>\n      <td>-147.870229</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>1.550</td>\n      <td>-50.0</td>\n      <td>5.339146e-65</td>\n      <td>-147.992965</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>1.475</td>\n      <td>-50.0</td>\n      <td>4.759562e-65</td>\n      <td>-148.107875</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>1.400</td>\n      <td>-50.0</td>\n      <td>4.281581e-65</td>\n      <td>-148.213709</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>1.325</td>\n      <td>-50.0</td>\n      <td>3.891802e-65</td>\n      <td>-148.309159</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "   sigma     t           abs     log_abs\n",
       "0  2.000 -50.0  1.209001e-64 -147.175651\n",
       "1  1.925 -50.0  1.043909e-64 -147.322473\n",
       "2  1.850 -50.0  9.042603e-65 -147.466084\n",
       "3  1.775 -50.0  7.863483e-65 -147.605801\n",
       "4  1.700 -50.0  6.870291e-65 -147.740825\n",
       "5  1.625 -50.0  6.036368e-65 -147.870229\n",
       "6  1.550 -50.0  5.339146e-65 -147.992965\n",
       "7  1.475 -50.0  4.759562e-65 -148.107875\n",
       "8  1.400 -50.0  4.281581e-65 -148.213709\n",
       "9  1.325 -50.0  3.891802e-65 -148.309159"
      ]
     },
     "execution_count": 10,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Stage XVIII: sweep Re s from s0 → ~1/2 and map zeros ===\n",
    "# Produces:\n",
    "#   - stageXVIII_heatmap.png         (heatmap of log|Λ|)\n",
    "#   - stageXVIII_minima.csv          (per-σ line minima: t*, |Λ|, log|Λ|)\n",
    "#   - stageXVIII_settings.json       (parameters used)\n",
    "#   - stageXVIII_line_samples.csv    (optional: thin sampled grid; comment out if too large)\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- helpers (keep plain Python types) ----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except Exception: return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "def py(x):\n",
    "    \"\"\"Make JSON-serializable (ints/floats/lists/dicts).\"\"\"\n",
    "    import numbers\n",
    "    if isinstance(x, (str, bool)) or x is None:\n",
    "        return x\n",
    "    if isinstance(x, numbers.Integral):\n",
    "        return int(x)\n",
    "    if isinstance(x, numbers.Real):\n",
    "        # prefer int if integral\n",
    "        xi = int(round(float(x)))\n",
    "        if abs(float(x) - float(xi)) < 1e-15:\n",
    "            return int(xi)\n",
    "        return float(x)\n",
    "    if isinstance(x, complex):\n",
    "        return {\"re\": py(x.real), \"im\": py(x.imag)}\n",
    "    if isinstance(x, (list, tuple)):\n",
    "        return [py(t) for t in x]\n",
    "    if isinstance(x, dict):\n",
    "        return {str(k): py(v) for k, v in x.items()}\n",
    "    try:\n",
    "        return float(x)\n",
    "    except Exception:\n",
    "        return str(x)\n",
    "# ---------------- load inputs and model choices ----------------\n",
    "coeff_path   = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "sumX_path    = Path(\"stageX_summary.json\")\n",
    "sumXI_path   = Path(\"stageXI_summary.json\")\n",
    "assert coeff_path.exists() and coeff_path.stat().st_size > 0, \\\n",
    "    \"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\"\n",
    "# central point guess (default 2.0; prefer Stage X if present)\n",
    "s0 = mp.mpf('2.0')\n",
    "if sumX_path.exists() and sumX_path.stat().st_size > 0:\n",
    "    try:\n",
    "        JX = json.load(open(sumX_path))\n",
    "        if \"s0\" in JX: s0 = mpf_safe(JX[\"s0\"])\n",
    "        elif \"central_point_guess\" in JX: s0 = mpf_safe(JX[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "# gamma shifts: base [0,1,1,2], add Stage XI uniform delta if present\n",
    "MU_BASE = [0,1,1,2]\n",
    "delta_uniform = 1.0  # your prior runs favored +1\n",
    "if sumXI_path.exists() and sumXI_path.stat().st_size > 0:\n",
    "    try:\n",
    "        JXI = json.load(open(sumXI_path))\n",
    "        if \"uniform_shift\" in JXI and \"delta_min_residual\" in JXI[\"uniform_shift\"]:\n",
    "            delta_uniform = float(JXI[\"uniform_shift\"][\"delta_min_residual\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "MU = [m + delta_uniform for m in MU_BASE]   # typically [1,2,2,3]\n",
    "# crude Q (does not move zeros; used consistently)\n",
    "Q_guess = mp.e**(-4)\n",
    "# ---------------- read Stage VIII coefficients ----------------\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "assert \"n\" in cols_lower, \"stageVIII_dirichlet_coeffs.csv missing column 'n'.\"\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "assert a_col is not None, \"No coefficient column found (a_n/an/a/a_n_real).\"\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "# limit terms (tune for speed/accuracy)\n",
    "K = min(len(N_all), 8000)\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "# ---------------- L(s) and Λ(s) ----------------\n",
    "mp.mp.dps = 100  # precision; increase if needed\n",
    "def smooth_weight(x):\n",
    "    # Fejér-like cosine window on [0,1]\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------------- sweep parameters (tuneable) ----------------\n",
    "T_MAX  = 50.0        # height window\n",
    "DT     = 0.05        # step along t  (→ 2001 samples per line)\n",
    "SIGMA_STEPS = 21     # number of vertical lines between s0 and ~1/2\n",
    "SIGMA_MIN = 0.5      # leftmost Re s to scan\n",
    "# Build grids\n",
    "t_vals = np.arange(-T_MAX, T_MAX + 1e-12, DT, dtype=float)    # inclusive\n",
    "sig_left = max(SIGMA_MIN, float(s0) - 1.5)                    # don’t go past 1.5 left of s0\n",
    "sigma_grid = np.linspace(float(s0), sig_left, SIGMA_STEPS)    # decreasing\n",
    "Ncut = to_int(n[-1])\n",
    "print(\"Stage XVIII: sweeping lines\")\n",
    "print(f\"s0                : {float(s0)}\")\n",
    "print(f\"mu (used)         : {MU}\")\n",
    "print(f\"K_terms           : {K}     n_max: {to_int(n[-1])}\")\n",
    "print(f\"T_MAX, DT         : {T_MAX}, {DT}   → {len(t_vals)} samples/line\")\n",
    "print(f\"sigmas (count)    : {len(sigma_grid)} from {sigma_grid[0]} down to {sigma_grid[-1]}\")\n",
    "print(f\"precision (mp.dps): {mp.mp.dps}\")\n",
    "# ---------------- evaluate |Λ| on each line ----------------\n",
    "# Z[i, j] = |Λ( sigma_grid[i] + i*t_vals[j] )|\n",
    "Z = np.empty((len(sigma_grid), len(t_vals)), dtype=float)\n",
    "for i, sig in enumerate(sigma_grid):\n",
    "    sig_mp = mp.mpf(sig)\n",
    "    row = []\n",
    "    for t in t_vals:\n",
    "        s = sig_mp + 1j*mp.mpf(t)\n",
    "        val = Lambda_of_s(s, Q_guess, MU, Ncut)\n",
    "        row.append(abs(val))\n",
    "    Z[i, :] = [to_float(v) for v in row]\n",
    "# ---------------- find per-line minima (rough) ----------------\n",
    "min_rows = []\n",
    "for i, sig in enumerate(sigma_grid):\n",
    "    abs_row = Z[i, :]\n",
    "    j_star = int(np.argmin(abs_row))\n",
    "    v_star = float(abs_row[j_star])\n",
    "    t_star = float(t_vals[j_star])\n",
    "    min_rows.append({\"sigma\": float(sig), \"t\": t_star, \"abs\": v_star, \"log_abs\": float(mp.log(v_star) if v_star>0 else -mp.inf)})\n",
    "min_df = pd.DataFrame(min_rows).sort_values([\"sigma\"], ascending=False).reset_index(drop=True)\n",
    "# ---------------- plotting: heatmap of log|Λ| with minima overlay ----------------\n",
    "# Avoid log(0): clip at a tiny floor\n",
    "floor = 1e-300\n",
    "logZ = np.log(np.clip(Z, floor, None))\n",
    "plt.figure(figsize=(7.6, 5.2))\n",
    "extent = [t_vals[0], t_vals[-1], sigma_grid[-1], sigma_grid[0]]  # x: t, y: sigma (top-down)\n",
    "plt.imshow(logZ, aspect='auto', origin='lower', extent=extent)\n",
    "plt.colorbar(label=\"log |Λ(σ+it)|\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"σ = Re s\")\n",
    "plt.title(\"Stage XVIII: log |Λ(σ+it)| (heatmap)\")\n",
    "# overlay minima\n",
    "plt.plot(min_df[\"t\"].values, min_df[\"sigma\"].values, \"wo\", ms=3, label=\"line minima\")\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"stageXVIII_heatmap.png\", dpi=150)\n",
    "plt.show()\n",
    "# ---------------- (optional) write a thin sample of lines to CSV ----------------\n",
    "# This can be large; we’ll sample every 3rd sigma and every 5th t to keep it manageable.\n",
    "sample_rows = []\n",
    "for i in range(0, len(sigma_grid), 3):\n",
    "    sig = float(sigma_grid[i])\n",
    "    for j in range(0, len(t_vals), 5):\n",
    "        sample_rows.append({\"sigma\": sig, \"t\": float(t_vals[j]), \"abs\": float(Z[i, j])})\n",
    "sample_df = pd.DataFrame(sample_rows)\n",
    "# ---------------- save outputs ----------------\n",
    "min_df.to_csv(\"stageXVIII_minima.csv\", index=False)\n",
    "sample_df.to_csv(\"stageXVIII_line_samples.csv\", index=False)\n",
    "settings = {\n",
    "    \"s0\": float(s0),\n",
    "    \"mu_used\": MU,\n",
    "    \"Q_guess\": float(Q_guess),\n",
    "    \"K_terms\": int(K),\n",
    "    \"n_max\": int(n[-1]),\n",
    "    \"T_MAX\": float(T_MAX),\n",
    "    \"DT\": float(DT),\n",
    "    \"sigma_grid\": [float(x) for x in sigma_grid],\n",
    "    \"points_per_line\": int(len(t_vals)),\n",
    "    \"outputs\": [\"stageXVIII_heatmap.png\", \"stageXVIII_minima.csv\", \"stageXVIII_line_samples.csv\"],\n",
    "}\n",
    "with open(\"stageXVIII_settings.json\",\"w\") as f:\n",
    "    json.dump(py(settings), f, indent=2)\n",
    "print(\"\\n=== Stage XVIII summary ===\")\n",
    "for k,v in settings.items():\n",
    "    if k != \"sigma_grid\":\n",
    "        print(f\"{k:18s}: {v}\")\n",
    "print(\"Wrote:\")\n",
    "print(\" - stageXVIII_heatmap.png\")\n",
    "print(\" - stageXVIII_minima.csv\")\n",
    "print(\" - stageXVIII_line_samples.csv\")\n",
    "print(\" - stageXVIII_settings.json\")\n",
    "print(\"\\nPreview of minima:\")\n",
    "display(head_safe(min_df, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "af3e3a",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stage XIX: sweeping deeper into the strip\n",
      "s0          : 2.0\n",
      "mu (used)   : [1.0, 2.0, 2.0, 3.0]\n",
      "K_terms     : 21    n_max: 187\n",
      "T_MAX, DT   : 150.000000000000, 0.100000000000000  → 3001 points/line\n",
      "sigmas      : 51 from 2.00000000000000 down to -0.500000000000000\n",
      "precision   : mp.mp.dps = 100\n",
      "  line 1/51 at sigma=2.000 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 6/51 at sigma=1.750 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 11/51 at sigma=1.500 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 16/51 at sigma=1.250 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 21/51 at sigma=1.000 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 26/51 at sigma=0.750 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 31/51 at sigma=0.500 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 36/51 at sigma=0.250 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 41/51 at sigma=-0.000 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 46/51 at sigma=-0.250 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 51/51 at sigma=-0.500 ...\n"
     ]
    },
    {
     "data": {
      "image/png": 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RPGBZXFwsSVenTh2UlZXh5MmTEkO+sLBQkq5WrVqIiYnBsGHDJA/YedOkSZOwcj3wwAM4efIk1qxZg5YtW2L58uXIyclBnz59ZIWHfOedd7By5UrMnTsXvXv3xtSpU/Hwww/j5ptvVr367cFj9B09etTvWEFBARwOB2rVqgXGGARBkDxY6MFXf5Gwd+9ebNq0CRMnTpT8EgC4w/ZlZ2fjq6++Em+ekpOTcfLkSb9ygq14e2Lpexu3GRkZkjjtngdemzdvjk6dOimuSyBOnjyJ5ORkRXk9+Xzr66lLYWGhJEJPWVmZnwGdnJyMdu3aYfr06QHPkZ6eLqarU6cOVq1aFTBdjRo1JN8Dtblnn++NhC/XXnstrr32WhQXF2Pz5s2YMWMGhg4dioyMDGRmZgJwvwfg008/xYYNG+ByudC9e3fUqFED6enpWL16NdasWYMrrrgCTqdTlB8AJk6ciOuvvz7geT0PB8vVSbi6xsXFoXr16pL9J0+ehNPp9NtPEIQNMdmdhyBMx9eH2UNeXh4DwO666y5x3yWXXCJ5kM3D9ddfz5o3by7Zd/ToUVa9enWJr7bHJ97bv5exwD7xV199Nbv44osl/t+R8Mknn/g96Hf48GFWs2ZN1rdvX0naQD7xBw8eZImJieyaa64R95WVlbEuXbqwtLQ02T75vgTyia9fvz5r3749c7lcYrp//vmH1atXj3Xr1k3cp4dP/EMPPcQAsD179vil//vvv1m1atXYDTfcIO4bMWIEq127tl/a7Oxs5nQ62eHDhyX7PQ9r+j7bEE6uQPj6xP/0008B+5M3F154Ibvuuusk++T6xB86dIgBYC+99JJk/+7du2X7xN99990sPT09bH9ZuHAhA8A2b94cVq5QPvE1atQI6RMfiB07djAA7LXXXhP3ffjhh+LD1pdffrm4f9iwYeyqq65iVapUYc8++6yknAsvvJD1798/7Pnk6iScT3zPnj398vTq1UvyHA5BEPaFjHgi6mnbti3r168fmz17Nvv666/ZmjVr2MyZM1laWhqrXr06++mnn8S0w4cPZ06nky1evJh9//334rG5c+cyAOy+++5ja9euZfPnz2fNmjUTo854KC8vZ926dWMJCQnsmWeeYatXr2bTpk1jF1xwAQPApk6dKqb9+eefWa1atdill17K5s2bx9atW8c+++wzNmvWLNajR4+Qdfrrr79YSkoK69q1q+RhUcaYGNHk7bffFvf5GvEul4tdffXVrFatWn43OXv27GHx8fHs9ttvl+xX+mArY5XGX//+/dmnn37KPvzwQ9a5c+ew0Wk+/vhj1qVLF9GoC4evsVxaWspSU1MD3ph5GDZsGIuNjWXHjh1jjDH27rvvMgDs119/laT7448/WK1atdgFF1zA3nvvPbZy5Up26623MgB+xl44uYLha8SfPXuWJSQksG7durF169axrVu3siNHjojHjx8/zgCwl19+WVKOXCOeMcaaNm3Kbr31Vr/9t99+OxMEgT300ENidJr09HS/6DQFBQWscePGrEWLFmz27Nls7dq1bMWKFey1115j11xzjRhNp6ysjPXr14/Vrl2bTZ06lX355ZdszZo1bP78+Wz48OFs2bJlEj14R6f58ssvxeg0//3vf0PW5/HHH2d33nknW7hwIVu/fj375JNPWI8ePVhsbCzbtWuXRHeCIPhdlwsWLBAfgvdEp/Lw9ddfM6fTyXr37s3ef/99tmHDBrZ8+XL29NNPsxtvvDFinfhGp1m2bBn7+OOPWefOnVmVKlXYpk2bJOcvLy9nSUlJftGICIKwJ2TEE1HPkiVL2NChQ9mFF17IqlevzmJjY1mjRo3YsGHD2O7duyVpDxw4wHr37s1q1KjBAEgMoWeeeYZlZGQwp9PJWrZsyd566y3ROPbm5MmT7M4772Q1a9ZkVatWZb169RJD2PmueO7fv5+NGDGC1a9fn8XGxrK6deuyrl27sqeeeipknW666SZWtWpVtnfv3oDH+/fvzxITE8XoG75G/GuvvcYASMLpefPss88yAOzTTz8V96kJMcmY+5eDLl26sPj4eFatWjXWs2dP9u233/rlX758OWvbti2Li4tjjRo1Ys888wwbO3Ysq1WrVthz+xrLnl8rXn311aB51qxZwwCw559/njHmDu1YvXr1gIb5nj172ODBg1lSUhKLi4tjF198MZs/f37EcgXD14hnzB3VpUWLFiw2Ntbv15x33nmHxcbGssLCQkmeSIz4xx9/nNWqVYudP39esr+4uJiNHz+e1atXj8XHx7PLLruM5eXlBZTxr7/+YmPHjmVNmjRhsbGxrHbt2qxjx47s0UcfZf/884+YrrS0lM2cOZNdfPHFLD4+nlWvXp21aNGC3Xvvvey3336T6OGaa65hH3/8MWvdujWLi4tjGRkZbNasWWHr88UXX7B+/fqx+vXrs7i4OFavXj3Wv39/yc2ihw4dOjAAkn545MgRBoDVqVNH8suRh//973/s5ptvZvXq1WOxsbEsNTWVXXXVVWzOnDkR68TTL/773/+yqVOnsgYNGrC4uDjWoUMH9tVXX/mde+3atQwA27ZtW1g9EARhfQTGVLzKjyAITXj//fdx22234dtvvxUflCPkUVpaivbt26N+/frIzc0NmfbAgQNo0qQJ1q1bh+7duys+5wMPPIC1a9fi559/Vv2SKT254oor0KhRIyxatEiyf8qUKZg/f76sl08VFBSgSZMmePfdd3HLLbfoJGlkZGRkoE2bNvjiiy/MFkVXPP31ueeew4QJE8KmHzZsGP744w98++23BkhHEITZ0IOtBGEwH3zwAY4cOYK2bdvC4XBg8+bNeO6553DllVeSAS+Du+66C7169UJaWhoKCwsxZ84c7NmzBy+99JJhMjz22GN49913sXTpUtx4442GnTcSNm7ciK1bt2LBggWqyklPT8e4ceMwffp03HTTTX4P/xJ88Pvvv2PJkiX4+uuvzRaFIAiDICOeIAymRo0aWLx4MZ566imcPXsWaWlpyM7OxlNPPWW2aJbg77//xoQJE/DXX38hNjYWl1xyCVauXCnG6zaClJQULFq0KGjMfB44ceIE3n33XTRt2lR1WY899hiqVq2KI0eOoGHDhhpIR2hNfn4+Xn31VVx++eVmi0IQhEGQOw1BEFGDVu40VicSdxqCIAiCTyzzu+iMGTPQuXNn1KhRA/Xq1cPgwYPFt9+FYsOGDejYsSPi4+PRtGlTzJkzxwBpCYLgkYyMDDDGotqAB9xGPBnwBEEQ1sYyRvyGDRtw//33Y/PmzVi9ejXKysrQu3dvnD17Nmie/fv3o3///rjiiiuwfft2TJo0CWPHjsXSpUsNlJwgCIIgCIIgtMWy7jR//fUX6tWrhw0bNuDKK68MmObhhx/GZ599hj179oj7Ro0ahf/973/Iy8sLmKe4uFjylk2Xy4WTJ0+iTp06XEehIAiCIAjC/jDG8PfffyM9Pd30B83Pnz+PkpIS1eXExcUhPj5eA4miC8s+2HrmzBkAkLy63pe8vDz07t1bsq9Pnz545513UFpaitjYWL88M2bMwNSpU7UVliAIgiAIQkMOHTqEBg0amHb+8+fPo0nj6ig8Vq66rNTUVOzfv58M+QixpBHPGENOTg4uv/xytGnTJmi6wsJCpKSkSPalpKSgrKwMx48fR1paml+eiRMnIicnR/x+5swZNGrUCFNufwbrFwZevRcRADhiIAgOwCEAggDBIQAOR8Vn9384BACVaSAIkjzucgR3gV75meD5DDGfZ2OePIIA5inH4U7HUJmeVewDIOZxp4e7fAFeZVW8lrCiLMlxAZX54PmOSlm8N1SUE+A4C/tfqEwL6bFQ+QLu88pfmY5JZA1aDirTuuvhqZdvflahd6+y4Xsu5m4Cr30CPP8rjwsC80pbuU9sdlTuczgYHAJzfxYYBFT+F9P4HPPe3N2y8liM4BKPxQgMDsEFB1xwwPOdub8LENMKqMwXg4r8qMhbkT5GcCFGQOVnMAiCu9wqQrm4z+H5X3FOd3p3uTEeWSrKFMAQA4YqggtVKsqKqUjvzuuRFxXfgSoCEAMgRgBiIMABAYIgIAbuzSE44PDsr/jOy+9wDICLucDA4AKDizG44EI5GMrBwJh7fzkYyhlQDqCMAS4ALgju/0yo+CygnAkor9BkGXOgjDlQ7u45cMFRkdaBcuZAORwor/juqjheDgGuijzlzIEyFuNuFa997vwQP7uYO48LAlye8zN3WubZxxxwMYjpy0WZHe7zMaGiHE9aQczLGMRjns1zzH3cnUZMj8r9LibA5ZKmYQwVm/szJP+9Plc0EKscPN3fvT6L/z2N6fnuAgQxjXsTvAZQweWVHu6hQ0zn879yE8T94jEEz+O7L+AxeO9jIfP552cQXJXDIoIc9z6P4PI9B6vQFauUxcWkxz35PPvhXba7QYSKfXB5jlU0lFgW89kAuFwV5TPA5QJcFSetkNGTnzFXZT5XReNWlM9cLjE/8zonYy7AVV7ZRiEoQyk2YSVq1KgRPrGOlJSUoPBYOQ5uy0BiDeW/CBT97ULjjgdQUlJCRnyEWNKIHzNmDH766Sds2rQpbFpfFxiP91Aw1xin0wmn0+m3f/3CPFQR/FfupScDIFQY8YIACA73eSq+V+6v2BfUiBcCG/HiZ8g04r2OKTXiPfsVGPHexjMLcDxiI16GoS7LiHdIjfiQeTyfAX8jXtDQiBeN+crj3ka8IPnPwhvxoqEtz4j3PRbIiPcY5lIj3ittCCM+RmLEe332GPlgqCIIPka8CzGCUGF4CxVGvFCxT6goR/Ay4j3GOasw0AMb8TEIbMQ7LGXEw8eIh2jEu4IY8eUIbcSXi0Z8jMSI9xjtgYx4z75ARrzLz4iXfg5mxIv7WOUNhGjEi2kdcHgZ6A4fIz7QFsiId0GAUPHd+78Q0Ij32hfOiPcx2FUZ8Z7PERrxgq8R78mPcHnkHVNlxAeVI0Ij3lO+EiPeY3QLFd8r/kMIYcQLrkpjH67KysErHXyMeDCAucQKMLGCLvd84a4MGFxuu0DuIABw4+JbvYaA6jWUy+LiZnS1HpYz4h944AF89tln2LhxY9ifkVJTU1FYWCjZd+zYMVSpUgV16tTRU0yCIAiCIAjbU85cKJfxC0Ko/IQyLBOdhjGGMWPGYNmyZfj666/RpEmTsHkyMzOxevVqyb7c3Fx06tQpoD88QRAGoGKwNwwryKgBhlUzSvRJEARhJJYx4u+//34sXLgQ77//PmrUqIHCwkIUFhbi33//FdNMnDgRd9xxh/h91KhROHjwIHJycrBnzx7MnTsX77zzDiZMmGBGFQiOoB/vzIMF+azneQjjMaqdidDQWEfojcvj2qdiI5RhGXea119/HQD8XtIyb948ZGdnAwCOHj2K/Px88ViTJk2wcuVKPPjgg3jttdeQnp6Ol19+GTfccINRYhOEqTAoncQF+JtegfapLzdUib7HWIB9WhOwfOWK1J4AAhqhk0BtESq9P1ooMFAZysrl2WyId8SgVmwcHILD3ye+gqD+6vDeJ/g/7AqfPAhSjs8xBDxHAJ94H9ngU5afT7xEHuZfT1+feATwiff4rPvK5OsT7+XrLn52uQXwfrDVkx5e6d2fXdJ0Hp93F5Okl/jEM5/0rgrXEfHBVleFS737wVbmYig6fhYl59SHbTQKF1xQ4xCjLnd0YxkjXk44+/nz5/vty8rKwo8//qj6/H1H9MCaeeEfpLUUvBglhI5oYXibiRz5vdJUGNuR1NjK2gmGovpLMskZHKw+gPAnvwDg+vTG6JlaH7EOR2V0mmCEa2hvY1iDMnwRwhyP5BzB5QuT2XPjIPucLII7UOZ3TPD+EqScoPYKCyKY137GGMpKyrH18/9h/bzvwlafB8oZQ7kKQdXkjXYsY8SbzQ3jBtjPiCcIGbAKw1iTsgLuDWyohx3WA8il3VSgYaV1R5taByxFnv0UAH/daTlN23XOvz69MQY0yECtOnUg+Dy3FdJgDqoPIXyaAPuFQGkD7mO+Zwl7joBlByg/YH19DOygZQUpM3AdvA74pQ+hCN+7X1/jP9i5JWX6fK746kI5rhjijpK3bu53AWQgCDdkxMtk6YtfaFeYlewDgtAAxTaX17WipAyl52Ve/3m9VJnPf6X5FedReGKb2t+qSXDEoGdKfdSqUweOalXlGbUegtqaXmv5RhnxYfLqasQrMfojMeIDrqTLUBbzXsJn0v0B8sQgBrVr1kbngRfj28U/cO9ao9avnXzilWOZB1vNZtXcdWaLQFgFGo8MgdSsP6Rjg2BAzbg4twsNRU4jADgQgypxMUhMrma2KGER30uhcCMjXjlkxBMEQRDWwabzvcP91jd+f/ohDEcQBG5e6ETwCbnTEARHcOu+IVMwLewrdWVE9iCvnB/GrYL6uijveea3u/lYXX6CUAq505gHGfFGwK1lFgLPNWU1uQkuUOZvrWdnizxKj/Sy5ekiZgE+RYJ+9VDShjR9E4S1oeg05kHuNDLpO6KHitw27aA2rZZVMa85tDQKdTIwReWEKN8O/TlkHVQ8IRyuTL/PWpZrHHboAmaQfcv1mDH1cfF7r8s74925b5ooUXCuuroL5r/7luz0W7bmoXnbhigqOqOjVAShDFqJl4lpISZpViE4I3SXFHwiMcgoL9AiN4PbPziiC8CdXk4OFmHJfK7Dy0srVx9uFNQywAkiXlhjoc9Nw6C1WPLpl0ioWtVsMQLy8YcrkZAgX7YO7Tti07ptqFEjUUeprI2rYlOTn1AGGfEy0TTEpJ3gybohDCNYpOPIMOZFVGQA+mOcTtS/TZXaz3rUrpOsvhCdGr527ToRpY+LjUPd5HruL9QZA+KJMqMmP6EMcqeRCYWYJIzDgndFGo3Bhg/ldp47DK6bZqezZJtY8JrVEV93mtZN0/DxkkUYO+pOXNK6Cfpe1RVfr/lKkmffb7/i3rtuQ8d2zXBFl7Z4aMIYnDp5Iug5li9bgs6dWmDdutXo2+dytL+4KcaOHYlz585h+fIPcdVVl+LSLi3x5FOPory8XMzn607TvHV9fPTx+7h/7F24uNMF6N3/cqxdlyse93WnWfbpR+jUrQ3WbViDPoO64+IuzTF2/Cic+/ccln/2Ma7q1w2dr2iHJ5+ZLDnvpyuW4/rbBqHDFW3RrfelGD/pPzhx8rhyJRMEyIgnCIIgCNtRu2oCmtdLRq2qCWaLAgB4/eVZ6NN/EJav+BpXdr8KD+Xcj9OnTwEA/jr2J4YPvR4tWrbGR8tX4Y257+PE8b/w4H/uDVnm+fP/4r333sGsF17HW2+/j++//w4PPHAXNm5cizffXIj/PvMyPvxwEb76KvQv6a++/gL69RmIz5atxpVXXIUJDz+A02dOBT/vv//ivffn4YX/voq3Z7+LLT9sxgM592LDpnV489V5eHb6C1iy7AN8tWalmKe0tBT/GZ2Dzz5YgdeefwOHCw7jkSkPRaBBfiln6jdCGeROYytoNYjgkfBuM9qP4UpddazsH6ZUi9rWV54UVtWxdahbvTriqsSgbvVqOHXuX7PFwbU33IxrBl0HgQHjJkzConfnYuf/tuOKrKuweNECtGrdFg9OmCSmnz7jBfS4siP27/8dTZo0C1hmaWkppkx5Bo0aZQAA+vQZgM8++xibNv2EatWq4YJmF6FLl67Y8v136N9/UFDZrrv2Zgy4ZjDAgJz/PIKF78/DTzt34Mpu3QOft6wUUx6bjkYNMwAw9Lm6Pz77Yhm+/XobqlWthguaXYgunS/D5q156N9nIADgxsE3uzMzhoYNGuHR/3sCN91xHc6eO4tqVfl/oVMoyCfePMiIJwi7woE9ql38cH3955n4V/DZy7ux6R8dXv9FLYGruPCqyrHxCuBf//yDutWr469/zpotCgCgeYtW4ueqVauiWrXqOHnC7U7y866fsGXLd+jYrtJY91x5h/IPBDXiExISRAMeAOrUSUb9+g1RrVo1r311xfMEla15ywCyBXflSYhPqDDg3STXSUb99AYSYzy5djJOnqosY/cvP+OVN17EL7/uxumiM2Aut+l6tLAAFzS9MKR8vOOCgHIVY6WL+3GWX8idRibqQkwSVkPvIYV320Fz+eQWyKFiOBTJYJlkXg0WbmM9Mau6J8/9i1+PHediFR4AqlSRrhkKggCXy60dl8uFHlf1wrLP1ki2VWu+Q6fOmSHKjPUrM+B5WOi13tgI81SJDXRe/32uCkP93L/nMGL0HahatRqee2oWPn73E7w6cw4A968JhH5kZGSIb771bI888ogkTX5+PgYOHIhq1aohOTkZY8eORUlJiUkSRwatxMvEtBCTRNRixjowi2jFO1TaymP6GDH6rcz7l8rjijwL8Y1/pPKG0q18vev7srBg5yS0oFXrtlj91QrUb9BQNMIFGyn3j/2/49Tpk5jwwENIS0kDAOzas9NkqbTDxdybmvx6Mm3aNIwcOVL8Xr16dfFzeXk5rrnmGtStWxebNm3CiRMnMHz4cDDG8Morr+grmAbQSrxMrBNikjdjg9ALvcY9rRZUjZmDtevvdrAZtK2D/mOJVn3I7GuBUMfQYXfizOnTmDDuPvz0v+04lH8Q336zHo8+8qAkwotVSU9LR2xsHN5bvACHDudj7YY1mP02/waiXMor3GnUbHpSo0YNpKamipu3EZ+bm4vdu3dj4cKF6NChA66++mo8//zzeOutt1BUVKSrXFpARrxMKMQkQfCAdLBnPv8J9QTXKS0QEPpQLyUVCz/8DC5XOe6581Zc2787nn7qcVSvUQMOh/XNlNq16uCZqc9h1ZqV6H9Tb7w1fw4eHjcpfMYoo6ioSLIVFxdrUu5///tf1KlTB+3bt8f06dMlrjJ5eXlo06YN0tPTxX19+vRBcXExtm3bpsn59URgLOJ360UVRUVFSEpKQndciypCbOjEAgBHDATBATgEQHBAcAjuN086HBAcDvfniu/wHBMErzye44K7QEEAYtz5mKMin4DKdBUbE1BxTABzoLIMzzFPOs8xQPzMHIL7RZuC578nvTsNEwTA4Xs8wHdPeeJxVL7pPcBxaVnB/gtB04bKF3AfvOX07GcB8/jlhzutd34IFY8RSvJUfHdUphf7hud7xX9B8rkyrSB+ZxAEJn6v/M8qmpBVNDGDw+He76jYBIHBAVbRDXyOofKz7wYADsGFGIEhRnC598P9OUZgcHj2ee13CAwxqNxf+dkFByr3eacVy4MLQkU5VQRX5TF4l+tCDJj4P0Yod39HpXwOuBAryV8hGyrkBCrSouIYEIOKTRDggOA+JghwwIEYCHBUfHY3pwMOgQ8j1sUYXHCBAXDBBRdzv2jFBRfKGauIFMFQzhjKAffG3KtlLgAuJqAc7ofJXBBQzhzu1TDmQDkcKGUOuCpaxsUEuOA5HuMuoyK9qyK9uzyHmL+MuT8zVORllWW7fD67KsrxlOFiguRzOfOSg1Wc02d/ecU+F3NU6EcIuDGvcpj4360HxnyOuTz7AMCdjlUcq/zs/g+v/QAAcT8qjkH8LPkPr/0uoL6zKqa27oR69dMhxMb63UUJnvSBCLS/QnYhVJog+wO6sgTcV/nYeXhZQpQdIF94GZh/mpDfA6QX07Ag+ZmMtIHyMul373KCffbJU45y/Hm8EG/etwh/HTwpEaOMlWI9PsWZM2eQmGjem2Q99tF3P6eheg3lN1v//O1C19ZH/fZPnjwZU6ZMUSEh8MILL+CSSy5BrVq18P3332PixIm49tpr8fbbbwMA7rnnHhw4cAC5ubmSfE6nE/Pnz8ett96q6vx6Qz7xRGh4dAcmbA+tLKjBWO1RWxGmQB2PGzw3wGryA8ChQ4ckNyVOpzNg+ilTpmDq1Kkhy9y6dSs6deqEBx98UNzXrl071KpVCzfeeKO4Og+4H0L2hTEWcD9vkBFvG+R0NrLIlSBA6XyhPKc9Ua+PSMJNsiCfg6cOfG3w2IJqZIpMLx60CStJ448vpA+C8JCYmCjrl4UxY8ZgyJAhIdNkZGQE3H/ZZZcBAPbt24c6deogNTUVW7ZskaQ5deoUSktLkZKSIk9wEyEjnvBCXyM/Kk1ao+6bDDiP2ocMlbR91PUXC6Fle5r9AKvxJzHwPBxBtyz2RO3DqZHmTU5ORnJysqJzbd++HQCQluaOEpSZmYnp06fj6NGj4r7c3Fw4nU507NhR0TmMhIx4mfQd0YNCTBIaYcDtjCqjXoZ8mt80RFZYZNpz18fjmiyvdKuZG/J+a6hMJfj8V1OyLxrrTpYAKs5piDFttf5EEPIph/s5F+X59SEvLw+bN29Gjx49kJSUhK1bt+LBBx/EoEGD0KhRIwBA79690apVKwwbNgzPPfccTp48iQkTJmDkyJGmPm8gF+s/9m0QN4wbYLYIBCELKyzwhY/pHfx4JC4g8mRRftRcgsumtdShywutZzPit0cKD63scj8p6/8wJRGlMDDG4CoP/aIqHmBBHiaXuzEV/vShcDqdWLJkCbp3745WrVrhiSeewMiRI/HBBx+IaWJiYrBixQrEx8ejW7duuPnmmzF48GDMnDlTF5m0hlbiZWKdOPGEKfC0eGuCLFy5Q3ifTFD2q4d/kAt+Gpj5SKdcp4KhDcJlHzH1pFL+KjmPUyXnUf3kKSQkJUGIifFPFLE/ktezDEZFpwlxjkgi7ISVgcm4PQwXvUbcJzM6jXeiiKLTBCsz8GcGF86e/wdFx//B6UL+Y5XzyiWXXILNmzeHTdeoUSN88YU1bTwy4mWyau668CEmCYJQBAc2FKER1JbKKGMMz/zyE25t0BRtz51DjCB4B4gMTDhlex0PWlIEZfgS0iiP8BzB5QuROVT9AmYLYqwHzcf8jlWG7AzxS1iwY943DMH2M6C8rBz7fjiA3DkbUV7G/0q80T7xRCVkxBMEIUXnRWfm85+wL7q2tbIwO1xzsrQEs3//BTWqxKJaTBU4BIf4MIPggv+KNqtYsfb+DO/9guQ4/I4HLivQscDnYP75AP9zsspXZMDlU4ZEHiapZ8BzgLnLcHnFfa9IA8Z86lBRHjzHfNO5ywI852VwvxyAScqs/OyC4GKV6TwvAXBJ0zPm8srnfZwBrspjzMUA5qo4nQtwlYO5GP4tOo9zZ/61jGdVecW7IZTn11CYKIOMeIKIIkLa54EORmDQ6zkOK13sk7svkvPwiq/s4WzcSHUTSRqlqC5b3qIt1zAARWWlKCotda/E+xrxTAhtxEs+Vxrx/sZx8PxyjgU14kPkFyqMZv+bDX8jXgh6Dh8j3scor6wv8zfiXYGMeK90Fd8FbwPc24h3eRnx5a4ARrz7s8SId/ka7i7xu2jEe/K4yq3TUQkuICOee+iKthZGBNK0erDOSOX3RJeRn09u6eEM+gjuYQzHI58W5chPKz+qjRRetSgXI+S3uo6iDSuPwdriqng7s/L8pEulUHQamfQd0cNsEQi1GDlH8jomKVyp1CzCiAy9hE2igW5DrVpbHV3qFqYQWefQSMmh+mLIU/DYyFrdicmF7hMIHfD4xKvZCGWQES8Te4aYpAtHV3g0GhQgrYa2fYYF+axVmYQ89NC99u1Q2feojQl50BxH2Btyp5GJ6SEmaSwivGCsInqi3udB6K4XzpjyuMBUprO6KxChHHdPqnSHDhdfPjRG9SKrPFxIGAQNYX6of7CVFKoUMuJlQiEmCcJeRMO0EQ11JAjCXNw+8cpXldTkjXbIiCcIwmSssbTFw0OuvGkpuDxma4ogCKNwwYFyerDVFMgnXlNo4iLshLn9mYZ1Ijw05hJ2gvozERm0Eq83qpfv6KKOPvgwXyPrur6+75X79BZIq4cp+dC6OrSqf9ByNFdSoIdV5fc6ftqMh99pCEvBT+dVDfnEmwetxMuEQkwSRDgCGzEsxDEeDZ9A0wlPUwzv8lUSvM3JDYewPtRXPbjgUL0RyiDNycSeISYJrYn6YV2BNclLFBJLwIkydGkzTupmFlE/dhAEETHkTiMT00NMWhU7/8ps57pFPQEal9v2Vm79KnFhIQzEzjc2dq5blFHOBJQz5WOImrzRDhnxMqEQk0S0oPncarjxG8g/n+AKjRuH2pogzKNcZXSacrqCFUPuNARBEARBEARhMWgl3jS4/W3eMOjeW2+sEX+dJ6ysrUhkt3I9tSW6x2C9oVkOiIarzcUccKmITuOi6DSKISOeIOyC1WbMIG7nUtTfiGjzECZPk0x4WYyRVtp4Ac/Jk9rkYDV5CYIDyJ3GPMiIJyqxmhFIhESb5gxnRAc67rsvUkNckOXRrt2wHzwAPRP4vSSY+CfoUW3OIStNpFryTR8of7gy1bcMmQ42gxrUFFxQ93CqSztRog7yiZdJNMSJV3oJ8mrkEOYRKpa5FvOsMsPRnuhrt4SK6S6fUG1PdhfhC81FBCEPMuJlYlqceBqVCC98DR75K6VqMKsThnp5VOQo8xnX6n2wWhFCHhniaa87vvqGXJRcNzy0PsERNDeL0MuezIPcaWRCceIJ/uDkwVUd3bCMqh3z/mDxydlwnelRNgfd2o3FOwNBGEA5c6BcxYOtavJGO6Q5mayau85sEQgi6jHLtuPGpoR8WbSWmScdEARBELQSTxCETjAGCJwsZKpZYGdgEDhbkVXzKiuejHF+VtwJglCKCwJcKsZINXmjHTLioxW6ZiwCJy4zFfAjiRu13i+h6uNrvPPgaePvp61fi/DY1nxhdm8gZMHXEGpLyJ3GPEhz3ECjDGEd9OmtwY0ipts5iUgI3w7aG7bU7oS1oB5LGAcZ8TKJhhCT0YCKULamY9WpQU58l/B1C99wgc4TeUQa/7VtHvUeWMbI1uUD6Uhe/tBtIaeNedSpHKwqN2DtsY/gG8/LntRshDJIczIxLcQkQSiCZuxQRGaM8Wi6yZeJR+n5gq4VglCDiwmqN0IZ5BMvk6gNMUnXVnTCgwN4QLgUKkrgVPd0lxKdkK87N7hUrqZTnHjlkOZkQiEmCYIg9IVsMoIgCPnQSjxBEKpQ4n8eHFpesy6crtQTBKErLuaAS0WEGTV5ox0y4gnCYoT0dDHQDSawqS3fCPdEOjHa9FNzi2Cml5FaufUgdIjOSM/rr1lDb+dCnIxuKwkiOOUQUK5iZFSTN9qh2x+7QNcAERHSDhPQSAliubAwxpYcg0erNP4Imr/RtPKXBvNNOY8M+tRRn0Ek0rYOlD5QnwuW2H8XDY5EBFB3ISwEGfEyiSjEJA0C9sF8u60C9Z1K2xB/geVRHkJS/bnVnyfcurLqE6iD+X0IlUh58QHRblCLvI+oO7f2oS05GeC5GZsI1XDSpZTicadRs+nF9OnT0bVrV1StWhU1a9YMmCY/Px8DBw5EtWrVkJycjLFjx6KkpESSZufOncjKykJCQgLq16+PadOmgXHwymky4mVCISaJaMTolzppd85AK/LyV+l9MX+orkRdHQL9AqPtDWJgBE3OE9k5CYIwgnJUutQo2/SjpKQEN910E+67777AspeX45prrsHZs2exadMmLF68GEuXLsX48ePFNEVFRejVqxfS09OxdetWvPLKK5g5cyZmzZqlo+TyIJ94mURtiElCG3gI2ciBDIweXI1auGh1HoTgQQaC4JCioiLJd6fTCafTqarMqVOnAgDmz58f8Hhubi52796NQ4cOIT09HQDw/PPPIzs7G9OnT0diYiIWLVqE8+fPY/78+XA6nWjTpg327t2LWbNmIScnB4Jg3sRKK/EyoRCThJnQvE9oAnUkZbCAHwmCgHbuNA0bNkRSUpK4zZgxQ3fZ8/Ly0KZNG9GAB4A+ffqguLgY27ZtE9NkZWVJbij69OmDgoICHDhwQHcZQ0Er8QQRdUS2Gm4bo4WDXyIIbYi8T1LDE4RelDMHylX4tXvyHjp0CImJieJ+tavwcigsLERKSopkX61atRAXF4fCwkIxTUZGhiSNJ09hYSGaNGmiu5zBsNRK/MaNGzFw4ECkp6dDEAR88sknIdOvX78egiD4bb/88osxAhNRABkHWiBPi0KQz9rhaxzyfAPjG59fP1kj0ztPVwTP7RcenjRJEMFhEOBSsXmiTyUmJkq2YEb8lClTAtp23tsPP/wgW/5A7jCMMcl+3zSeh1rNdKUBLLYSf/bsWVx88cW48847ccMNN8jO9+uvv0ru7urWrauHeARhGkoWmfk2cAL/WhA+gkqkeaITJZFg9IoewxvUXwiCb8aMGYMhQ4aETOO7ch6M1NRUbNmyRbLv1KlTKC0tFVfbU1NTxVV5D8eOHQMAv1V8o7GUEd+vXz/069cv4nz16tULGlqIK3wtMXvNjfbBNm4Z/LrVyI8trv5B2UBmv29ccp6aW05wT/0i/IQ7s75ErRsN3Vnwie/wE6XtpJU7jVySk5ORnJys+HzeZGZmYvr06Th69CjS0tIAuB92dTqd6Nixo5hm0qRJKCkpQVxcnJgmPT1d9s2CXljKnUYpHTp0QFpaGnr27Il160I/oFpcXIyioiLJBkQYJ14xHI0A2keEsz8cNZ+d0EWtMgr1JOHxMvDIJEs3OiiQurpOkGIjg7t5Kjob0MUE1Zte5OfnY8eOHcjPz0d5eTl27NiBHTt24J9//gEA9O7dG61atcKwYcOwfft2rF27FhMmTMDIkSNFD46hQ4fC6XQiOzsbu3btwvLly/H000+bHpkGsLkRn5aWhjfffBNLly7FsmXL0Lx5c/Ts2RMbN24MmmfGjBmSp6MbNmwIgOLEE4QZ6O/vTUSKFdvESrISBKEdTzzxBDp06IDJkyfjn3/+QYcOHdChQwfRZz4mJgYrVqxAfHw8unXrhptvvhmDBw/GzJkzxTKSkpKwevVqHD58GJ06dcLo0aORk5ODnJwcs6olYil3mkhp3rw5mjdvLn7PzMzEoUOHMHPmTFx55ZUB80ycOFHSMEVFRWjYsCHFiSdsg/W8gSi2PH9YqwcRBKEf5XCgXMWasJq84Zg/f37QGPEeGjVqhC++CG3jtW3bNuQCsFnY2ogPxGWXXYaFCxcGPR7s5QKr5q5DFSFWT9EIXrGe1UsowA63CXaoAyEDamiCI9S6xOjpTmN3bO1OE4jt27eLDy9YD447Ok0q6rGgDpWIbMFqEiqJmn5iSaE5g2sdcjwHE1GJpVbi//nnH+zbt0/8vn//fuzYsQO1a9dGo0aNMHHiRBw5cgTvvvsuAODFF19ERkYGWrdujZKSEixcuBBLly7F0qVLzaoCYQLkjBEcBgU/NCj+ZSJ0S6hrI3Vlh6sST/1HTl3UHFdjqOhWdoQN4OnXRGDIFCW0xAUHXCrWhNXkjXYsZcT/8MMP6NGjMkqMx3d9+PDhmD9/Po4ePYr8/HzxeElJCSZMmIAjR44gISEBrVu3xooVK9C/f3/DZScsCLnRiAQ2iDS+PfLVt+e7TjcNwc5rRePPT2bZlVBpVOv+dqwAL2HR+hRWhpRBcEA5E1CuwiVGTd5ox1JGfPfu3cW3ZAXC9+GFhx56CA899JAm5+47ogfWzNukSVk8QGO/SqLJwOekrny4ZJipDG1rw4c+FcKNIAYQTXXVAU6GL1tDPvHmQb9hyIRCTBJEAIIaGJENyvzZKfxJFBy+ZNXshUx8VYsgCII7LLUSbyYUYpIgLAItvUUOGcwaYn7nM18CIppgzAGXije2MhV5ox0y4mVCISYJgrAS9DZ4giCMoBwCylXcOqrJG+3Q7Q9BAGTlsJBfdUK/hxbllqP7c5kGolR2fXWudHKWn0/5Q702JdrrTxBRBK3E64aed5Z012pNrB7sMpj8wesV3LMlvC6CHWW+X2RdDlbXvZbIHD9YwI/BkkR8PmWtYfWxz+ryRyt6jh/WH5tcTN3DqS5rV99UyIgnCEIRAVdAhSDHFCMv/ruc82mx6m612DRK6ixfp9powu+mLPhXgiA4xKXSJ15N3miHNCeTviN6hE9EWBIe18asarwYJXdk54nuWONq3Vz4bFN+sKrcBEFYHzLiZUIhJsPAoyVMqCKSVe6Iyw5ZaPDOZHhsc54tNBWyaa/HEG2mgw717JsEQUSGC4LqjVAGudPIhEJMmgyFDSQAGNUJrGQcGicrXYAE9O9w1ncRjzroja3mQUa8TCjEJEFEG1a4c+TD2uFDCoIgzIB84s2DNKc7NL0RcjDKWDTeKGWcGcJ0RZqPOX2Cr35IGAx3Fz53AhEWhFbiow0rLC4GQ2/ZrawbXdFCKQKYzqZb8Ac4abIMTGVrGOVjziTnVdMb6EINiDENSBASXBDUhZik61kxZMQTBKEJge+B1BjR0ryKXuBEN2bBUdAs/lm0VS7ZiARhPZjKh1N5+7XWSpA7DUHYDnMHRO9VXW0jk8itV2T1DxVLnSm4idATubJFLqs+ug0FYzxFmSEjgiAI60FGvEwoTjxhJcwxisKEhtRCKJOtPTNNPdPNTI3aT2moSr0w/waCIKyNiwmqN0IZZMTLhOLEE4QytHhTqhbnJfwxqy2obQjCPnii06jZCGWQ5mRCceIJgiAIgiAIXqAHW2VCceIJbuDlYU2d5KBVWj3gocMogDoDQXCPWpcYcqdRDhnxBGEWvBjjCtBSdOV2mn/km3BlVYY4jD7rUJ5ufFHWylpq19ItZWnhCUIeLpXRaSjEpHLIncYOUP8nKtAvKok2eD/gGlRWEwwfJon1Yl0YYE5NgpySeX0wXip1UYqIKIbmVMIi0Eo8wR8WXqG2Ozw+lMpkrKyrkZvH7qi2PuHTyK8xj32CMBhqnKiG3GnMg1biZfLWT89jwL29zBaDMAqOJiWORJGBnMHYN435Lht2xNyInkra2DoTOVd9jythiGiEQkyaBxnxMqnXuC6GPDw4TCrqiEZAWpaPkfN78HOZ12LK/MCjA3PrHrhP8NFfCV9ozDUKa2qajHjzIHcamRw7+BdWzF5rthgEETWQkcU/1EYEQRDmQUa8TEa2G08hJgnt4NHRmmuiM6JMJBinHeq4EUHdlrA55BNvHmTEa4yduiLNPRyiq/GvzFDWu5+Y5WLh+czrNc1g3jXKb5vr2Fo0IHKHndZCrLxMwaAuTKRV680D5BNPWAa7DNZEILT1kVY1KVhxRlEhs/Y6pivVrlDLEgRfkBFPEIQGCEE+A0wjo7iyGONNCZ7senNkETQ9t3+fCN5/CD6hViI88Pxg6/Tp09G1a1dUrVoVNWvWDJhGEAS/bc6cOZI0O3fuRFZWFhISElC/fn1MmzYNTKvJTQVkxBNcQxOFEagx0HwM9gjTK0ln3rBp/oBtlgyhz6q+TQOfI/Kr38wbPYLQmwH39sLCP15D3xE9zBZFAs9GfElJCW666Sbcd999IdPNmzcPR48eFbfhw4eLx4qKitCrVy+kp6dj69ateOWVVzBz5kzMmjVLN7nlQj7xmkOTh+Wwk2OlEhTWnweTVkusXx97vHXWG8X1sZsiIiXa629JwnvFD3l4MFIy6uGGcQPwyNxxhkhlJEVFRZLvTqcTTqdTVZlTp04FAMyfPz9kupo1ayI1NTXgsUWLFuH8+fOYP38+nE4n2rRpg71792LWrFnIycmBIJhnQNBKPEEQNkTpoMq8/loD9bJG8x0sQViHxf/9BH8eOIalL35htigStFqJb9iwIZKSksRtxowZhtVhzJgxSE5ORufOnTFnzhy4XC7xWF5eHrKysiQ3FH369EFBQQEOHDhgmIyBoJV47qEJliA8aGlcBy/Lij/NBK4NC3lUizMQRLRifDyZL95YjS/eWI0yVmroecOhVYjJQ4cOITExUdyvdhVeLk8++SR69uyJhIQErF27FuPHj8fx48fx2GOPAQAKCwuRkZEhyZOSkiIea9KkiSFyBoKMeIKwApzGO9R6CmNBJkZTzWoebXoTLepgp2YaK4nLmwYz43oSBKcwJoCpMOI9eRMTEyVGfDCmTJkiuskEY+vWrejUqZOs83uMdQBo3749AGDatGmS/b4uM56HWs10pQHIiCcIAoA+q0p6rlQFKzv8OckGC0awyUjPSUqPsnm74yIIQkvGjBmDIUOGhEzju3IeCZdddhmKiorw559/IiUlBampqSgsLJSkOXbsGIDKFXmzICOeIHiHx5XgcCiQmdcXCDEwCJw1gNJHWLnUsRXvqqwoM0HohAuCqpc9RZo3OTkZycnJis8Xju3btyM+Pl4MSZmZmYlJkyahpKQEcXFxAIDc3Fykp6erulnQAjLiCYKQgRH+n77nCDSwqwk7GHqfnGO8Eml9tAgnGnifETc7fN1QEUS0o5VPvB7k5+fj5MmTyM/PR3l5OXbs2AEAuOCCC1C9enV8/vnnKCwsRGZmJhISErBu3To8+uijuOeee0Sf/KFDh2Lq1KnIzs7GpEmT8Ntvv+Hpp5/GE088Qe40VuGtn57Hitlr8cUbq80WhSAshZ5jnBUNbqugp24FQbuXgBEEQQTjiSeewIIFC8TvHTp0AACsW7cO3bt3R2xsLGbPno2cnBy4XC40bdoU06ZNw/333y/mSUpKwurVq3H//fejU6dOqFWrFnJycpCTk2N4fXwhI14m9RrXxZCHBysw4mnViCAIgvCCbmAIE6Lb6IVWD7bqwfz580PGiO/bty/69u0btpy2bdti48aNGkqmDWTEy+TYwb+wYvZas8UgCIIIiT3MAoIgrALP7jR2h4x4mYxsNx5VhFizxSBsh/VWYwI9s6r82Vtl9ddLY9ZqCSn86URZj9DOh99syDAhCEJfyIgnCDMxNPJMJAazwpsLDiLpGPOQJ9/IraeWL4NSjWIhIulwBnZOLpRKEPrDszuN3SEjniAICfoOp8zvWyTni8RAV2tDcXA/EhbtX7al3bmMfGWX9X7PIgj7wFS605ARrxwy4glCSyKwU8wwEpWdUwtz2ACXGyYAAplyqpA9map1lVHb+yPPb0bPCHrOQF2aui5hURjURZuirq8ch9kCWIW+I3qYLQJBcAPjfo1aSrBJws6Th13qbLW+RhAEYRRkxMvkhnEDdC3fahMrQfDvbKIGK12RVpI1Uuzcxwg7YuerMRieN7aq2QhlkDuNTJa++IXZIhAEoRNW8H8nCILgEXqw1TxoJV4mq+auM+GsoTq2UZ2eLi7CHHhc0TJTJuPPHf7a57GNiGiBhzmQ5kfCXGgl3igk1zqt+xEWxaCuW3macA+1So+zEMeC74sWAjVc5b7ItSIozKeQaG02wgZ4dV4bTv0uJkCglz2ZAhnxehKqX9poQrJRVQiVaNEXlNwnqD5v2JPycePNvP6GSaTyHJGVp1W7EwTAy9WmEfLXICwLYyqj09hAB2ZB7jQ6YptBiCBEKnq1QYNu0NMotWMjkts/pj1/RCBVkKRK62X8CjyNqIS9oB5NqIWMeJmYFmKSrnLCgvBp8BI8Qn3F2tAURXgebFWzEcogI14m6kJMUgeNVAW21hhZLVxjxeaxosxRBTVQJXYZ3FXVwy5KcENGvHmQT7xMKMQkQRA8Q3YiQRBmQA+2mgetxMvEnBCTBGEn+B+omc9/K6BEVvPqx38fIAiCsAq0Ek8QPGBwOAYrGamARz3KQjlYra58I1hOn4bLazUFEYRKKDqNeZARTxgGXafeKI0t5pVPjeHvObVJC6OR1FytAR+siizIZ/klmE1gqeXVS831GJkhb+p1z1QKIMmrtB/w2n8IQhvcRryaN7ZqKEyUQe40BGFR1I57ZuVXlE+VsPImFybDKOaFYDIFq4M/KgzLiBWifPXeqn2cCAzpkyC0hVbiCVthk3dnRAHKjEhqW2UoeYGTBlkIC0G/FxBKURthhqLTKIdW4mViWpx4gogIuw+GCurHQn4lZEN9iyAIf5gGG6EMMuJloi5OPEEQ5kCGWXBIN7bB5lYQ9VSCCAy508iE4sTrh83nH9sgr52Mm26p3+iPsToO33eoza0Bz4+DE9pD7jTmQUa8TFbNXYcqQqzZYmgPXTuETmg9kYcuj56G0I7gWtZaw9RiBGEDNI0CRUSCpdxpNm7ciIEDByI9PR2CIOCTTz4Jm2fDhg3o2LEj4uPj0bRpU8yZM0c/AYPNfWQoEyajJoRXpN1Xm/HYgIsmGiYOQ+qovq0iFVPNGSmcXZTA87xrN1uhYiVe6QZaiVeMpVbiz549i4svvhh33nknbrjhhrDp9+/fj/79+2PkyJFYuHAhvv32W4wePRp169aVlZ8gZBMNY5Bhv5ELEYRKDI7cGOnhYsnztsYv562ywWLF++bRol7uMgy6AHhqCL3grcMRBKGId999V1G+9u3bo127drLSWsqI79evH/r16yc7/Zw5c9CoUSO8+OKLAICWLVvihx9+wMyZM8mItzKWdbjkcGaWqUsWJJ3qGqlqS7e14y9DYCsonKyBDFzeu5l2Rrm0pizI/ohQ2TmCxsKXWy6Hl5s1elUAuNQlwQv0xtbAzJs3T1G+O++8055GfKTk5eWhd+/ekn19+vTBO++8g9LSUsTG+vu4FxcXo7i4WPxeVFQEwB1ics28TZELofd4LRgwvlpwztECWhBTiIF2SqD2sczbRHVGrR4M1Y2dG0JHonRo1n1wZgAEvScAG00w9GBrYNatW6f7OSzlEx8phYWFSElJkexLSUlBWVkZjh8/HjDPjBkzkJSUJG4NGzYEQCEmCcJQbDK5RQXUVgRBEKZg65V4ABAEn5+JK3638d3vYeLEicjJyRG/FxUVoWHDhhRikiBMRo4vOKEPpHuCIIKi9uFUm67E+3Lo0CEcOHAA586dQ926ddG6dWs4nU5VZdraiE9NTUVhYaFk37Fjx1ClShXUqVMnYB6n0xlQqdYJMWlRn0sfyFgg9CCa+1U0150gwkNXiFLIJz44Bw8exJw5c/DBBx/g0KFD4kIyAMTFxeGKK67APffcgxtuuAEOR+TOMbZ2p8nMzMTq1asl+3Jzc9GpU6eA/vBmYn2zm7AySsZQ48ddna8SO0wkNntAxhr9MrohfUuhuZzw8J///Adt27bFb7/9hmnTpuHnn3/GmTNnUFJSgsLCQqxcuRKXX345Hn/8cbRr1w5bt26N+ByWMuL/+ecf7NixAzt27ADgDiG5Y8cO5OfnA3C7wtxxxx1i+lGjRuHgwYPIycnBnj17MHfuXLzzzjuYMGGCGeITHGOngde4SdVgrTHxj8y03giwVysrJYAeZHcYZoLFZkyb2ckQpV5OGA7TYNOBAwcO4K677kKTJk2QkJCAZs2aYfLkySgpKZGky8/Px8CBA1GtWjUkJydj7Nixfml27tyJrKwsJCQkoH79+pg2bZpkVT0QcXFx+P333/Hxxx/jjjvuQIsWLVCjRg1UqVIF9erVw1VXXYXJkyfjl19+wbPPPouDBw9GXEdLudP88MMP6NGjh/jd47s+fPhwzJ8/H0ePHhUNegBo0qQJVq5ciQcffBCvvfYa0tPT8fLLL1N4ScIfe3gh2YJQsdnlNpGa0ItWNOjU1E9u3kC6J195DqHGIAyG1+g0v/zyC1wuF9544w1ccMEF2LVrF0aOHImzZ89i5syZAIDy8nJcc801qFu3LjZt2oQTJ05g+PDhYIzhlVdeAeB+NrJXr17o0aMHtm7dir179yI7OxvVqlXD+PHjg57/ueeeky1r//79FdXRUkZ89+7dQ975zJ8/329fVlYWfvzxR9XnVhxikiAI2Zh5L6XjgpAhmC2/lXVHEIRKOBwA+vbti759+4rfmzZtil9//RWvv/66aMTn5uZi9+7dOHToENLT0wEAzz//PLKzszF9+nQkJiZi0aJFOH/+PObPnw+n04k2bdpg7969mDVrFnJycoIGSvHmqquuwrJly1CzZk3J/qKiIgwePBhff/21ojpayp3GTCjEJEGYgMkTA4fzkojpspkuAEEQdqKoqEiyeb+zRyvOnDmD2rVri9/z8vLQpk0b0YAH3O8TKi4uxrZt28Q0WVlZkqAnffr0QUFBAQ4cOCDrvOvXr/dz0QGA8+fP45tvvlFYG4utxJsJhZisxEbvqCBsC/VS+ZAfGUEQytHKncbzXh4PkydPxpQpU9SIJuH333/HK6+8gueff17cF+h9QrVq1UJcXJwY3bCwsBAZGRmSNJ48hYWFaNKkSdBz/vTTT+Ln3bt3SyImlpeXY9WqVahfv77iOpERLxPrhJgkCIIgCIIwCLW+fBV5Dx06hMTERHF3sBjqU6ZMwdSpU0MWuXXrVnTq1En8XlBQgL59++Kmm27C3XffLUkbyB2GMSbZH+k7hzy0b98egiBAEARcddVVfscTEhJE33slRGzE//jjj4iNjUXbtm0BAJ9++inmzZuHVq1aYcqUKYiLi1MsDKEFtKoWbejhR87HGrYQVA658vFRDz5Rq8OKKUwTWdSgRxtTv4lG6Nc7s0lMTJQY8cEYM2YMhgwZEjKN98p5QUEBevTogczMTLz55puSdKmpqdiyZYtk36lTp1BaWiqutgd75xAAv1V8X/bv3w/GGJo2bYrvv/8edevWFY/FxcWhXr16iImJCVlGKCI24u+991488sgjaNu2Lf744w8MGTIE1113HT766COcO3cOL774omJh7I1Bk53epzH4yUMW5DOhHYqb1DujDv0i0vY2on8wEx+9ZQbUkAuda3DR01ihDzpf8uFPrieG2fB2vFlQG8I3srzJyclITk6WlfbIkSPo0aMHOnbsiHnz5vm9UCkzMxPTp0/H0aNHkZaWBsD9sKvT6UTHjh3FNJMmTUJJSYm4UJ2bm4v09HQ/NxtfGjduDABwuVyRVFE2ERvxe/fuRfv27QEAH330Ea688kq8//77+PbbbzFkyBAy4gnCEmg7kaid0JkJtrHdptFAmFFHtW9f1F5m838tIAhbo5E7jdYUFBSge/fuaNSoEWbOnIm//vpLPJaamgoA6N27N1q1aoVhw4bhueeew8mTJzFhwgSMHDlS/FVg6NChmDp1KrKzszFp0iT89ttvePrpp/HEE0+EdKf57LPP0K9fP8TGxuKzzz4LKeugQYMU1TFiI54xJt5RrFmzBgMGuKO2NGzYEMePH1ckBBEEXuceiqluG6gprU803IwogfRiI3htTDsuqtuI3Nxc7Nu3D/v27UODBg0kxzw+7TExMVixYgVGjx6Nbt26ISEhAUOHDhVDUAJAUlISVq9ejfvvvx+dOnVCrVq1kJOTI76rKBiDBw9GYWEh6tWrh8GDBwdNJwgCysvLFdUxYiO+U6dOeOqpp3D11Vdjw4YNeP311wG4/X7C+QZZGYoTzwFkbRqM2TOUeW9Ztdu8rOblV8Hh4S24Zp8/yjB7SCD4hNOV+OzsbGRnZ4dN16hRI3zxRegIhG3btsXGjRsjOr+3C41e7jQRx4l/8cUX8eOPP2LMmDF49NFHccEFFwAAPv74Y3Tt2lVzAXmB4sQThDUhm4MgCEJHmKB+IxQR8Up8u3btsHPnTr/9zz33nKonbHmH4sSbDF3jtoPpsKwnp7TIzsizw5Hxuou8TF51RyiGVuMJHxhT9yyM2udorMa3336LTp06BQ2hGQmavbE1Pj4esbH2jaO+au66CFLTxEXYGT76d5SN+6bAj4756HMEoQ/Uv6OJfv364ciRI5qURS97IkT4mbAJQj3K+7Pv6rvnOw+r8sznv+9+ZaURhB3g4QqNSjj1iecVpuFPD2TE60W4kcSgkSairkKjn60INaHxMmZqJQcv9bEDdmuTUHLwIiOhERG4+hhm8IeTyQ7uSWr92sknXjFkxGtFRH0wUGLffeG+E4Q58Lfa5T0LRj4jBkzNXyUBhJBVTrqACDI+m4/VbRzCTviOMeG+B9sns3jC8rz77ruS72VlZVi2bBnq1asn7rvjjjsUla3YiC8pKcH+/fvRrFkzVKli/3sB2SEm+Zr7CJ7h1FAMRWQimz0baXh+VrlYZEazsaBfwu7mHPmatGT9LCk0YQpmD5cqEJh7U5PfzsybN0/yvbS0FB9//DESEhIAuOPEG2bEnzt3Dg888AAWLFgAwP0G16ZNm2Ls2LFIT0/HI488okgQ3rlh3IAwRrzFrDGCIPyw+VxCEAT3WNCaJ5/4kKxbJw2MUqNGDbz//vto2rSp6rIjjk4zceJE/O9//8P69esRHx8v7r/66quxZMkS1QLxCrchJm3e+QkiMMbdNPN4iWkfSjMUtEBBRCE8XvgE4UPEK/GffPIJlixZgssuuwyCUDm4t2rVCr///rumwvHEqrnrUEXQO4QmTZaEDljQbUdvgsV4sbayAlsdZIsEgJRC6IIFV9G1gB5sNY2Ijfi//vpL4ozv4ezZsxKjnjATA9uBmjzqsbLZGwgrTsFWlDkUdqsPoQBD7eEoNb61gtxpImLSpEmoXbu2JmVF7E7TuXNnrFixQvzuMdzfeustZGZmaiJU1CKxhKKsV3tjJ4vQzmjUTlHc022LZm1KY4E1iOp28urtUa0HQi4TJ05EzZo1NSkr4pX4GTNmoG/fvti9ezfKysrw0ksv4eeff0ZeXh42bNigiVCEQfgNONYagXgw/mj9xhqEayO7tKFcX3n+62utsUgPeNCA9X5l8xmRaYA2BlqJD8uIESNw7733okuXLpqWG/FKfNeuXfHtt9/i3LlzaNasGXJzc5GSkoK8vDx07NhRU+F4ou+IHmaLQBCKcI+Pek7FvEzzgeXw9n+PgrkiKPLqr39bmt8GAgcyEISNYBpsNmf+/PlYuHAhrrvuOjRr1gwXXXQRrr32Wnz77beqyo3YiAeAtm3bYsGCBdi1axd2796NhQsXom3btvj4449VCcMzN4wbYLYIBBECXgzpwETBGG1pqH284ftaIgju8DzYqmaLAt544w04nU6MGzcOo0ePRlxcHHr06IHFixcrLjMiI76srAw///wz9u7dK9n/6aef4uKLL8Ztt92mWBDe4TbEJEFwjD7GYXQM+Hyhvc7pxoEgiGjihRdewOLFi/HAAw9g3Lhx+Oijj/DMM89g6tSpisuUbcTv3r0bF110Edq1a4eWLVvi+uuvx59//omsrCwMHz4cvXr1wr59+xQLwjur5q4Ln4ggCNMh45AgCMI4PG9sVbPZHYfDgb59+/rtHzRoEPbv36+4XNkPtj7yyCNo0qQJXn75ZSxatAhLlizBrl27cPvtt+OLL75AjRo1FAsRnQghvyoqgzAfI6N7UvMTukIdTBAAZpSBQQ9hcoiCRvHLEgUNSw+2hiU1NRUbNmxAs2bNJPvXrl2LRo0aKS5XthH//fffY+XKlbjkkktw+eWXY8mSJfi///s/jBw5UvHJiQjxnVNpjo06TIkWYXI/88wPgadCOROksklUqmue4nSwAJ8iJfK6cPWAsAl2kel1JozHt59FgT1O6MPw4cMxZswY/Pjjj8jMzER5eTm+/fZbLFiwAK+99pricmUb8ceOHUP9+vUBADVr1kTVqlWRlZWl+MQEQVSim4loou2p/NShZkpzIosw3y9G65QF/Gjw6UNVWolCTI4So9PJycYjCMKXp556Ck2bNsWcOXOwcOFCxMbGonXr1li2bBn69++vuFzZRrwgCHA4Kl3oHQ4HYmNjFZ+YIAiroWQZKvI83ivvBP8YuzJPvYIgeEOAOr/2aLiqBUHAXXfdhbvuukvTcmUb8YwxXHTRReIbWv/55x906NBBYtgDwMmTJzUVkBf6juiBNfM2mS0GQRAhiGQeiYYVU9IHQRCENWCMiTa2XGQb8fPmzYtYIDtxw7gBZMQTBEEQBEF4ozbWu03jxLds2RKPP/44brzxRsTFxQVN99tvv2HWrFlo3LgxHnnkkYjOIduIHz58eEQF242oihNvz+uJsCzyXHLkrCRH82qztvqhQYLgCHrg1FwoOk1AXnvtNTz88MO4//770bt3b3Tq1Anp6emIj4/HqVOnsHv3bmzatAm7d+/GmDFjMHr06IjPIduIj3ZWzV2HKgI9AxC9WHmUscYMp6XrR/iywunESl75cqLzKM9tT5ccq7RtIKzUN4mogIz4gFx11VXYunUrvvvuOyxZsgTvv/8+Dhw4gH///RfJycno0KED7rjjDtx+++2oWbOmonOQEU8QhLUJYtMEmxfkzxfugnmcXyINMhmxLnisNEEQhAXp2rUrunbtqkvZst/YShiNkpUWmnklaKkOWvhShNk9MnBceSHocbPlDU7k7kTS79J6yytRX8w+PwFqBD+UKIQmB3pjq3JOnDiBF198UXF+MuKJAMgclDgfuzgXjwiJ/NbT0h1EXh6+Zhzt6xdpmXSlGYqG6ua+5WQLyH1N7A3TYIsiGGP46quvcPPNNyM9PR1PPvmk4rLIiJdJ3xE9zBaBIAgtiLIJA0B01pkgCIIjDhw4gCeeeAIZGRkYMGAAzp49i/feew8FBQWKy1RkxH/wwQc4e/as32c7c8O4AWaLQBAWglbGCLlQX1ENqZAwE1qJD0pxcTE++OAD9OzZE82aNcMnn3yCsWPH4vDhw1ixYgVuvvlmOJ1OxeUrerD13nvvRZcuXdC0aVPJZzujaYhJMwbcCB/+I2DLIBC8tDcvcgSCZ9mCwbPMvMjGixyaYstKaUPQ4dsMnVkjQJhi1Pq129knPj09HbGxsbj11lsxc+ZMdOjQQdPyFa3EM8YCfrYzq+auM+ZENjMaiQqoXb2QqwxtYsMTylAX98YXugBESBX2hNqVCEB5ebn4JlaHQ3sPdvKJ150ouLKjoIqyiEQPhlmfPkJxYPVyIAJhMFy0uZ8QBg1ckVSexlI3UaEHG1XS88ZWNZsOHDhwAHfddReaNGmChIQENGvWDJMnT0ZJSYkknSAIftucOXMkaXbu3ImsrCwkJCSgfv36mDZtmqxF7MLCQsyaNQs7duzAJZdcgosvvhizZs1CYWGhJnUkIz5q4GIaDYyNxjIu4LiptYU6jv5EiY6j5poxCK67DTW25nDqE//LL7/A5XLhjTfewM8//4wXXngBc+bMwaRJk/zSzps3D0ePHhW34cOHi8eKiorQq1cvpKenY+vWrXjllVcwc+ZMzJo1K6wM8fHxuO222/D1119j7969GDBgAF544QU0atQI/fv3x4cffoji4mLFdaSXPUUbXA+uhFKsOy3Z3Fk0qrHmYEO9kSAig1ef+L59+6Jv377i96ZNm+LXX3/F66+/jpkzZ0rS1qxZE6mpqQHLWbRoEc6fP4/58+fD6XSiTZs22Lt3L2bNmoWcnBwIgryxrlmzZpg+fTqefPJJrFq1CnPnzsWwYcNQtWpVnDp1SlEdaSVeJhRi0kRoVlWMOaqznvFmpy5mzboY32esqSdOsKLyrDcsRR1FRUWSTc0KdTDOnDmD2rVr++0fM2YMkpOT0blzZ8yZMwcul0s8lpeXh6ysLEkUmT59+qCgoAAHDhyIWAaHw4H+/fvj448/xuHDh/H4448rqgtARrxsKMQkQRAEQRCEDxq50zRs2BBJSUniNmPGDE3F/P333/HKK69g1KhRkv1PPvkkPvroI6xZswZDhgzB+PHj8fTTT4vHCwsLkZKSIsnj+a7Wt71u3brIyclRnJ/caWSiaYhJCQGWB2jFgAiGDcNeSiH3GsWYrjZbd0wO9EtwS8BhK4rGMpXuNB41HTp0CImJieLuYPHTp0yZgqlTp4YscuvWrejUqZP4vaCgAH379sVNN92Eu+++W5L2scceEz+3b98eADBt2jTJfl+XGc9DraFcaaZNmxZSxmB0794dV155pay0ioz4N954Q7wL8f5sZ1bNXYcqQqzGpZo46dl8viWIcDCv/wICfQmexwwiOTfz+U8QhBlEkSGvAYmJiRIjPhhjxozBkCFDQqbJyMgQPxcUFKBHjx7IzMzEm2++Gbb8yy67DEVFRfjzzz+RkpKC1NRUvxX3Y8eOAUBI+3f//v1hzxUIz42EHBQZ8UOHDg34mahACPJZr3PYnWiqa9QSvpF9p0K9pkYrTrlG6ULeeeiCtT1Wsk15ldVbLl5llIvaCDMR5k1OTkZycrKstEeOHEGPHj3QsWNHzJs3T1as9u3btyM+Ph41a9YEAGRmZmLSpEkoKSlBXFwcACA3Nxfp6emSmwVf5s2bJ0tGNZBPPHfoOAHyPEjwOu/zrDNvrCKn4YTpWF56C56ShfhmDP7nDCyFED5JsNSEB6tcS1aRkyeU6Ez2ZRLF1xOnISYLCgrQvXt3NGzYEDNnzsRff/2FwsJCyar6559/jrfeegu7du3C77//jrfffhuPPvoo7rnnHtGdZ+jQoXA6ncjOzsauXbuwfPlyPP300xFFptEL8onnkigeDAiCE6xgI1lBRiLKsPqqsiKistLck5ubi3379mHfvn1o0KCB5JjHpz02NhazZ89GTk4OXC4XmjZtimnTpuH+++8X0yYlJWH16tW4//770alTJ9SqVQs5OTmqHkjVCjLiLUkIx13bP/hIEPoRyH2E18vJKPcigogKQl5AdHWFgtc48dnZ2cjOzg6ZxjeWfDDatm2LjRs3aiSZdpA7jUxUxYnn1QogiAigaYwwG+qDhC0gm4DQiIiN+HfffVdRcHurY5k48TQ4EARBEERk0NypHE594qOBiN1p7rzzTrz66qsoKSnBTz/9hJiYGLRq1QojRoyQFRrIqqiLE0+jAxEA6haaUjkPkH+qL+G1IchMR0QEdUUiINQxCG2I2IhnjGHMmDFIT0/HpZdeivLycqxcuRLTp09Hbm4uOnTooIecpqN5nHgzDDizjEbB74NG5dkcAx2y1U8nJkxKIR8NkcrDJMf49nXXmnC+84y7wPjqWsZQkaPFDtPs8jbZeDXj9FFgr/PqE88TtWrVChjJRhAExMfH44ILLkB2djbuvPPOiMpV9GDr3XffjdmzZyMmJgYAUFZWhrvvvhv/+c9/uHT8549IJimZaY22SNRedNFiQdkazkdeGZa6nBrwWEvN5OaxchKi6XbLpgQyYiMxbLk1uiOpRBRY8javnlqeeOIJTJ8+Hf369cOll14Kxhi2bt2KVatW4f7778f+/ftx3333oaysDCNHjpRdriIjPicnRzTgAaBKlSp46KGHJK+4JcwgOia7SMcK644tfA/8/PU2n9dic64/HvBfheerVflvQb70JZdIb42i51aK/x5HWJNNmzbhqaeewqhRoyT733jjDeTm5mLp0qVo164dXn755YiM+IgfbK1ZsyYOHz7st//QoUO29om3FdExGtsTi7SdPtOgRSpva7RvA8uYTNT9rAu1nb7Qg61h+eqrr3D11Vf77e/Zsye++uorAED//v3xxx9/RFRuxEZ87969cdddd+Hjjz/GkSNHkJ+fjw8++AB33303brvttkiLswyqQkxGOVFwfRIEQRBEVOLxiVez2Z3atWvj888/99v/+eefo3bt2gCAs2fPokaNGhGVG7E7zezZs/Gf//wHt9xyi7jP6XRizJgxmD59eqTFWYYbxg3AmnmbzBaDIAiCICxN9LjnEISbxx9/HPfddx/WrVuHSy+9FIIg4Pvvv8fKlSsxZ84cAMDq1auRlZUVUbkRG/G1a9fGe++9h9mzZ+P3339HbGwsmjVrhvj4+EiLshTqQkwSBGEk+i3smGl+6FOrKFgEIwhCT9S6xETBIDRy5Ei0atUKr776KpYtWwbGGFq0aIENGzaga9euAIDx48dHXK6iB1sBoEaNGmjfvr3S7JZD8xCTgdDVNjDJ8DBxuYX5fqGlH1th5rhvZHcyu56EzWDSj6YNi6Y9Q6rjiaP0uVgKMSmPbt26oVu3bpqWqdiIJzTAb/TUMVJENBqwdqmzDvXQokjzx12T7xCjwYo3+SLSoupRalfJIxqVo2mdfQvz+R4t+qWVeFmUl5fjk08+wZ49eyAIAlq1aoVBgwZJoj1GSsQPtprN7Nmz0aRJE8THx6Njx4745ptvgqZdv349BEHw23755RcDJZaDBa1NC4ocFDvVRSPkjanmK46J/4174ygzYcYx4pxm6DI84fuYBd9HpT+8yxcJlqyLJYUmdGTfvn1o2bIl7rjjDixbtgwff/wxbr/9drRu3Rq///674nItZcQvWbIE48aNw6OPPort27fjiiuuQL9+/ZCfnx8y36+//oqjR4+K24UXXmiQxJzDAn4keESQ/CMIwmC0fvE0oQ9+bpSE/lCIybCMHTsWzZo1w6FDh/Djjz9i+/btyM/PR5MmTTB27FjF5VrKiJ81axbuuusu3H333WjZsiVefPFFNGzYEK+//nrIfPXq1UNqaqq4hfrpori4GEVFRZINsHCISbkTTqB0ek1WNAkSnGOlOcVKshKE7qiZ8whFUIjJ8GzYsAHPPvusGE4SAOrUqYNnnnkGGzZsUFyuZYz4kpISbNu2Db1795bs7927N7777ruQeTt06IC0tDT07NkT69atC5l2xowZSEpKEreGDRsCcIeYNAUaaIgIsfd4aO/a8Y19dW/fmhEEwQNOpxN///233/5//vkHcXFxisu1jBF//PhxlJeXIyUlRbI/JSUFhYWFAfOkpaXhzTffxNKlS7Fs2TI0b94cPXv2xMaNG4OeZ+LEiThz5oy4HTp0CIAGISYjNcbJeCcsh/JOy4L8D5yKB4yUhe96y2s7udDAZ0vs2KyCz/9I89kJcqcJy4ABA3DPPfdgy5YtYIyBMYbNmzdj1KhRGDRokOJyLRedRhCkVwBjzG+fh+bNm6N58+bi98zMTBw6dAgzZ87ElVdeGTCP0+mE0+n0229IiElDseNIojECbKimaAmXoA08RyalVowUXltSIZ7qUEcIA415ukPRacLy8ssvY/jw4cjMzERsrNuWLCsrw6BBg/DSSy8pLtcyRnxycjJiYmL8Vt2PHTvmtzofissuuwwLFy7UWrwARDBh2GxuITRAd+tR+1FTE5HDFCK/fOUTt5xz8BZhUp0s8nKHTaVBl9KnxUK3lmqxo8AAISIkouGHbjKigZo1a+LTTz/Fb7/9hl9++QWMMbRq1QoXXHCBqnItY8THxcWhY8eOWL16Na677jpx/+rVq3HttdfKLmf79u1IS0vTQ0RCC3he+rQQ6tWo1cTiL4W205VGBmgUEdmNkDYEbnNqFVtBdmjUQi97ks+FF16oaYREyxjxAJCTk4Nhw4ahU6dOyMzMxJtvvon8/HyMGjUKgNuf/ciRI3j33XcBAC+++CIyMjLQunVrlJSUYOHChVi6dCmWLl1qZjUIOdD8zj90w0XoTRRN7paFFpIJcqcJSE5Ojuy0s2bNUnQOSxnxt9xyC06cOIFp06bh6NGjaNOmDVauXInGjRsDAI4ePSqJGV9SUoIJEybgyJEjSEhIQOvWrbFixQr0798/4nP3HdEDa+ZtUiy7oOfbWAlCazQy0M0em9VXg+c7FXXa5aFt+CqIIPRAepcjQDDlhXF6Qivxgdm+fbusdMGe65SDpYx4ABg9ejRGjx4d8Nj8+fMl3x966CE89NBDmpz3hnEDVBnxBEEQaolkrrPpvGjbehEEYS/ChTTXAssZ8WahOsQkIQ8hyGfCVHwNJzXr01rl08KYI6M4NL51Vuo5ocbjIhr1bhm8G5bcaqIXcqcxDcvEiTebVXP1v6MizIEBXN8wcCwafzDt5wMe5xdd6shjRTmF62tSoKYkDIbixJsGGfEEoQS9Z3GurQSe0UdxPM0x+slCnU4RNBYQBGES5E6jOZGPuOrHaH5GeZ6MnUgIKXco9XL53KMev2tb7bdybSKO+zavmc0dyKXJG+UtxGUnDoEesnJY/1CNGaKxrXSVesNXL1Q33inLzU/tI0XtexGtW3PzISOeGwJ0Y3qdM0FwBA9mhlVNNI4hlRIeIrW+A6a32oKHBpBPvGmQO40ZmG0HEARBEARhDDTnEzpBRrxM+o7oYbYIBGEcGk06gs9/giBAK4+ErfDEiVezEcogI14mN4wboE/BZOVwC/8vo6GRz5tQ2iBNVWK2njQf8nQdO/nuOXxLZwA8zpvROKdTdBrTIJ94mdg6TrwFBpvovMbNrLXyRyQjL8cYH9JwHu08eLyrJZwWjetRcjQp1bhy2VS2XBS6MNsealPjIX2bAq3Ey0STOPFWtxAI7dC6L0jKUzCaMvM6Z6W0espAF18l+uvZ1PlcUV/2kjii7DJqarOuR7aaCmzWFwjzISNeF3gNHGzzESRU9cyuupKZTxeZ5QlitroIQi7y+yon5qfZYvA8TuoOr3OntRXPs0/8oEGD0KhRI8THxyMtLQ3Dhg1DQUGBJE1+fj4GDhyIatWqITk5GWPHjkVJSYkkzc6dO5GVlYWEhATUr18f06ZNA2NmX8xkxPMJD9czDzIQhFaEGWsjHYqZgZZYpOcKm9r8ecc+0DhpPjy0AQ8ymAnHPvE9evTAhx9+iF9//RVLly7F77//jhtvvFE8Xl5ejmuuuQZnz57Fpk2bsHjxYixduhTjx48X0xQVFaFXr15IT0/H1q1b8corr2DmzJmYNWuWfoLLhHzidUKI9ouakIdF+gnZfQQvWKYvRuKXbZlKEVojCAAHC7pcUFRUJPnudDrhdDpVlfnggw+Knxs3boxHHnkEgwcPRmlpKWJjY5Gbm4vdu3fj0KFDSE9PBwA8//zzyM7OxvTp05GYmIhFixbh/PnzmD9/PpxOJ9q0aYO9e/di1qxZyMnJgWCiwUcr8TKhEJOEbGhAJgiCIKIErdxpGjZsiKSkJHGbMWOGpnKePHkSixYtQteuXREbGwsAyMvLQ5s2bUQDHgD69OmD4uJibNu2TUyTlZUluaHo06cPCgoKcODAAU1ljBQy4mWiWYhJi6y8EtbAFtHMTL7pseM9l+l1Ml0A5djimiL4w84dSiN3mkOHDuHMmTPiNnHiRE3Ee/jhh1GtWjXUqVMH+fn5+PTTT8VjhYWFSElJkaSvVasW4uLiUFhYGDSN57snjVmQES8TbUJMmhx9I2QSO48whBWhHkkQROSEGDlkDSoUJcssEhMTJVswV5opU6ZAEISQ2w8//CCm/7//+z9s374dubm5iImJwR133CF5KDWQOwxjTLLfN40nv5muNAD5xMtm1dx1qCLEGnhGi1/sVg+6bWXZYXnxCYtA/YwDrB4T3cqyA7B+A6hHbYSZSPOOGTMGQ4YMCZkmIyND/JycnIzk5GRcdNFFaNmyJRo2bIjNmzcjMzMTqamp2LJliyTvqVOnUFpaKq62p6am+q24Hzt2DAD8VuiNhox43tBiVgxShmbDDI8zN48yGUqEreurL9X6U/eqHp7hsWvxbjaok03jlzeFUVaANTh157c6PHYujWQK2rJalM+j3oxCbYSZCPN6jHJFp6pYQS8uLgYAZGZmYvr06Th69CjS0tIAALm5uXA6nejYsaOYZtKkSSgpKUFcXJyYJj09XXKzYAbkTmM4Gk8OBs01LMhnfQlQOR7mVt1kCFOwAABMk/MHNly0LlP/nASvKGtTbXqCtC9r17vkXHs69WUeLpGg1q/+mDL/aF41Hhoxuvj+++/x6quvYseOHTh48CDWrVuHoUOHolmzZsjMzAQA9O7dG61atcKwYcOwfft2rF27FhMmTMDIkSORmJgIABg6dCicTieys7Oxa9cuLF++HE8//bTpkWkAMuIJb2iMsSRKF9XVNHewvFbrQlaT186Y2afCXkPUUawBtZM5cBonPiEhAcuWLUPPnj3RvHlzjBgxAm3atMGGDRtEf/uYmBisWLEC8fHx6NatG26++WYMHjwYM2fOFMtJSkrC6tWrcfjwYXTq1AmjR49GTk4OcnJy9BE8AsidRiZ9R/TAmnmbzBaDIAhCFtH8674H0gFB6I/RPvFyadu2Lb7++uuw6Ro1aoQvvggdvKRt27bYuHGjVqJpBq3Ey0SzEJMKCdnHTVx9MHSCtMsqi6QeZGIQhO2x5dilL6aOjHZpL6PgdCU+GiAjXibahJjkA9tcL7YbaCNrGR2fgSYIy2PO9WHO00O6YZMBQsuWsEGrEjaC3GlkonmIyUgGRyHC9KpO5oa7gcomk0k4DK2m5ifjrtcQlkPjyDDkT6M9nOlUWY9RWYlIsnOmLz0QGIPAlFdSTd5oh4x4LlEZXi3QPq3mRTOfmtSqfCPL5A0r15Ej2QUDhREggPFiBVjZINFZdi5Uo4cQcspUc165ebWqm+fS9S1LlRxctL55GBxikqiE3GlMR05sEQOtF7Wn4sjQ4h1SFUHYG7rGI8BSc4+ceZpan9AfWom3PEEGCt7GD97kiVLMDQ0pf7lFT3misSvqrU/5Lav/i5SCyRPla6X8wFtDBJWHN0H5hdfoNNEAGfEEQRAEQRCEMsidxjTInUYmfUf0MFsEIoox54daGlkJ3tG/j5KTBEEQvEJGvEzCx4kPMbSb9apuwr5E3GV0MHao2xJ6o0sfi/BaoH5OREyYThPysPU6nMedRs1GKIPcaWRipzjxliLC8czwscDk55AJ/dDfe1s9NPfZhEDu1wa7ZEfc38llnPBA7jSmQUa8TLSNEy/4/I80X5QTlWqgUU5Lokmb0VRXY7DC7R2hD5HeuXjS2/uOhx5sNQ9yp9GKgGO6TGPd0NXcSAvm4OryEpkDaTRCWhNrmgTKWkOwUSsS8lDe5tbrK/7XsvXq4IfgUwsuBqxI9aqT0Irm7xC2ARe6JawCrcRrihD6ArST64WOcttgytMPjvqL3u/zMqIMIjRarB+q7SfcjAdcCcMXuv42YVW9R+oiJYRLwDHkTmMaZMRHG2T5EIQCeHKhoBmPIAi+IJcYcyB3GplYL8QkLwYHQRAEQZhM0CmR5krCupARL5PwISYtCI1d9sT0drWOv7+dF494rht3fuM8d1JCOdSuxsCY+o1QBLnTyCRkiEmtBoooH3B4vYzNkMvqXcHq8hPGYfW+YoYXM0/OXd7wKpdhWNSlXS0UncY8aCVeJqvmrgtxNNKnWRViSkRKQX1ZNh7VZY89GujAimq0osyEMVixb2g5pIbD1naNJvOJCYOqpp021AsirXh1EGZAK/F6E/HbM7Qs02IDgZniWkhVSkQ1bk7g1PSwUPvqDrerhcas4woK6s+tygJhprCWUhQgW2DZ9YpAAXYakyg6jWmQER/1yB1JFIw4KuO7W+O61khKOw3o3GCNHmQuUe8AoT2aGbL8t40SCSV5FOlKbibL3VFYFsHl3tTkJ5RBRryW8D3emgPpxGJYd9LTsqtZSQtaympts4d/o5fwwtqdTR+sqhNaiTcN8omXiakhJmleCk4Q3dCY4I16bfDRBalVzccubWCXeqgnqCb4uOj5hHRDcAIZ8TKxZYjJSNHjNZvhvvMEz7IFwYIiE0RIojoYGM9CGzG281z/KMYTnUbNRiiD3GlkEjLEpC9WH2g0lD/ark1D68thP+NJJNWy+Hhn8NCX/WTgQSiN4NKTwEChos0ZKNrqGxIuO38EqI31TnHiFUMr8TIJHWIyArQctfzKMnFIlHNqncRjNBN44TsYstBqD6O7ysPmD7KBRQ0sF3UJeQgIpSt/3fKhV7dcYWUJFcHPqxzCH93GVO7LFUJ+1bJogtACWok3E1UXdYD47RYaJHSbPgWf/1qVRwQk+tTDwCAYXm/m9TdaML5vWWxtWKvVW085Oq0GR6xVXlaleZHDAtDLnsyDjHheCDbKWcln3G7orWuj2tLSL5qi0Z1fzGkbTWwroww0vc9Dhqa2BNRnxU7fY8F0770/WtqHotOYBrnTcEOEZhIZ8/Iw6ibIZu1hs+ooxAozixVk1Bfb9VUL3dxHBRHriRRLGAetxBMEoQNkXBJysZgbi1WJllVhwnDIncY8aCVeJorixFt+XrJ8BaIaPlqPRmciGOb3DT6uEUI5Fm9Bi4sv4olOo2YjFEFGvExUx4nXO5IMF4MBF0IYhxWqy3nAIjc0gNsPeW1q6iVE1y+HcFBhzUXQMeINJ1CcePMgI14mEcWJjwCtr2fNrwUrvxHVhoOlP7yGAZSPcnkt0QstjjId26MPRkH/skBDGfVGWa1b2wKqJWwAGfEy0SxOPITwV3fA41rHTtShOF5GLV7kUIpE/jBTi9XrShC8Evba8ro2rX4d8iI/1/NRiDlY1pzOi5J1gGmw6cSgQYPQqFEjxMfHIy0tDcOGDUNBQYEkjSAIftucOXMkaXbu3ImsrCwkJCSgfv36mDZtGhgHbkD0YKvtMHigsPG4RKhHVvegPmQ/ZDxESc9ZEiExvINQj1QKzw+29ujRA5MmTUJaWhqOHDmCCRMm4MYbb8R3330nSTdv3jz07dtX/J6UlCR+LioqQq9evdCjRw9s3boVe/fuRXZ2NqpVq4bx48frJ7wMyIiPVnQ2nGQ5eUSz8aaq7jpPNDJlU1qFaG72aEVNX5HV28n+4pNQcdcr0D02EfUNy1BUVCT57nQ64XQ6VZX54IMPip8bN26MRx55BIMHD0ZpaSliY2PFYzVr1kRqamrAMhYtWoTz589j/vz5cDqdaNOmDfbu3YtZs2YhJycHgmDerEbuNIZiPfMl+NgXoi7WqyZBEEQI1CwzaieFbQmpIzs9sWDTzuBi6jcADRs2RFJSkrjNmDFDUzFPnjyJRYsWoWvXrhIDHgDGjBmD5ORkdO7cGXPmzIHL5RKP5eXlISsrS3JD0adPHxQUFODAgQOayhgpZMRHMwHGE2sOjDxBGiQIQgk0dqghoPZsZjMPuLcXFv7xmrKQ13qikU/8oUOHcObMGXGbOHGiJuI9/PDDqFatGurUqYP8/Hx8+umnkuNPPvkkPvroI6xZswZDhgzB+PHj8fTTT4vHCwsLkZKSIsnj+V5YWKiJjEohI15X1I4gHD/EaiWsVO8wsupZFe3Llhc5x0rNQ8hDfjtra7ha6/owEVtVJgL0Dh+pc/4hDw9GSkY99SGvOSUxMVGyBXOlmTJlSsCHUb23H374QUz/f//3f9i+fTtyc3MRExODO+64Q/JQ6mOPPYbMzEy0b98e48ePx7Rp0/Dcc89JzunrMuPJb6YrDUA+8TqgdRQZDkdbDkWSA7Oo3EYSbSqyc32jzRXY9PqaLkB4mGDRmNxc6lYroTzlhB+NFv/3Ewx5eLBuIa+VIkDlg60Rph8zZgyGDBkSMk1GRob4OTk5GcnJybjooovQsmVLNGzYEJs3b0ZmZmbAvJdddhmKiorw559/IiUlBampqX4r7seOHQMAvxV6oyEjXkNCv89JgbkQNIsl3uATEF7GYVEObuLg86IZlSh6VIKvuoeXRvdH8YKcU+lRMwiso7Cuz/xVhHuC9sYKfZrRWwOhWg5T+0eQkyuSySuTT/5wxX3xxmp88cZqlLHSSE+qL2rfuhphXo9RruxU7nMVFxcHTbN9+3bEx8ejZs2aAIDMzExMmjQJJSUliIuLAwDk5uYiPT1dcrNgBmTEWwIehmAbYqMfS4xwhSGkGGEcUSsYDxf3Elov8hIaQ4r1htcQk99//z2+//57XH755ahVqxb++OMPPPHEE2jWrJm4Cv/555+jsLAQmZmZSEhIwLp16/Doo4/innvuEd15hg4diqlTpyI7OxuTJk3Cb7/9hqeffhpPPPGE6e40lvOJnz17Npo0aYL4+Hh07NgR33zzTcj0GzZsQMeOHREfH4+mTZv6BfCPSjgwOm2JBfRqAREJIkLkWQCW6PuWENKCkF6jkoSEBCxbtgw9e/ZE8+bNMWLECLRp0wYbNmwQDfTY2FjMnj0bmZmZaNeuHV566SVMmzYNzz//vFhOUlISVq9ejcOHD6NTp04YPXo0cnJykJOTY1bVRCy1Er9kyRKMGzcOs2fPRrdu3fDGG2+gX79+2L17Nxo1auSXfv/+/ejfvz9GjhyJhQsX4ttvv8Xo0aNRt25d3HDDDTpKqsWIQaOObbBMU4Y2hixTDcK22KYP0kKujdCiMS3eIdS+dVWnqrdt2xZff/11yDR9+/aVvOQpVFkbN27USjTNsNRK/KxZs3DXXXfh7rvvRsuWLfHiiy+iYcOGeP311wOmnzNnDho1aoQXX3wRLVu2xN13340RI0Zg5syZQc9RXFyMoqIiycYvtpnSCIIgbIKFjTHCB77mWF5DTAqMqd4IZVjGiC8pKcG2bdvQu3dvyf7evXv7vT7XQ15enl/6Pn364IcffkBpaeAHQ2bMmCF52UDDhg21qUBIjBgo+BqMCDsRPQOwmTWNHi0D0VZbwkisO9/aPcQkETmWMeKPHz+O8vLygAH3gwXbDxagv6ysDMePHw+YZ+LEiZKXDRw6dCgCKTW4cCMsQrOpTmZkTNnn03mcpCne7oT/fZZuS/UnvI7V/o5O8I7urSvzQg4rh8bRnRUFnVFN6EIW//cT/HngGHchJuHSYCMUYSmfeCBwwP1QTwdHGqDf6XQGfcGAbmhtjdAbdaIWbZqZjDLCaqiPFWRxr2RCLoEaWuvG16kz8RpiUq1LDLnTKMcyK/HJycmIiYkJGHA/WLD9YAH6q1Spgjp16mgsoRDyq66ENNqNEYSHS5AHGfhGmYbC9aBouD/kqW/xJIte6NfnokF7yuFBO8bJIEj+BTpkpBjmnJywOpYx4uPi4tCxY0esXr1asn/16tXo2rVrwDyZmZl+6XNzc9GpUyfExsbqJqsE3+tR6fWp5rqWm5fGDmuiqt14mLap69kJftrSwFdIEnxgxFyn1Rxupz7GNNgIRVjGiAeAnJwcvP3225g7dy727NmDBx98EPn5+Rg1ahQAtz/7HXfcIaYfNWoUDh48iJycHOzZswdz587FO++8gwkTJhgodZAr1U4XMEEQBEEQ/vD45nWt8byxVc1GKMJSPvG33HILTpw4gWnTpuHo0aNo06YNVq5cicaNGwMAjh49ivz8fDF9kyZNsHLlSjz44IN47bXXkJ6ejpdfflnnGPEEQRCEORjxHl2CILzh9Y2t0YCljHgAGD16NEaPHh3w2Pz58/32ZWVl4ccff9RZKo4JOJ9F4SQXhVWWC6mGsBv0kGoIolI5ASptQT0MuLcXhjw8GPOf/ADr535qtjgEB1jKncY+GP+wqcXGKnugqJmZz3/z8BfffJn4wUhdkN4rkeqCjxtQFdcsHxWIKsyZF7VpaG7jxJM7jWmQEa8lFh2Qw06LBtTLMpewnrowKMCRHuWGiPJqS8iE1w89+pJh15KB4wOvGNJfw/zCbNlrJkwb8xonXnCp3whlWM6dhk/CXHkhD3MwMpsRMYfQHmoPTbGCd7VljRVesaCLha1R2h5ctGMIIcLKFzgBr3HiCfMgI56IPoJYZqaP+SYiBPlsFubLYAUT3oO5PZcHLXmbPFzYbyYRtNdGs1II/VHrEkPuNIohI55LLPaCJh5mcV7QShekU4KwBloZyGRoV6KRLoy7FY/yxlMb6z2KVacW8ok3Enr1pf2gNiMIQg9obLEf1KaExpARL5O+I3oYe0K62LmEFgwIgjADGns4hTdfRBMQGFO9EcogI14muoV0itKLnrAu1GUJo6E+R1iOaOq0FGLSNMgnXiZhQzoJPv8VI6MAIegXbQcOIwchkwY8ZuK5NSXCOriTBx845RUXIvKC5KtvOu0GbDVNFw3Thpo6antZSL2TBV9v5aAuxWq9mhmEAD0wJHZwbxbcdpEpQ5uR+tPyXH5lee2QdR6VwniyW7H/MQBqwkRarb4cQSvxMlk1d53ZItiXQDON1z5drm9DZjdjRiZlVWG6RD61w/0QYQ76RbqN/Do0rh8bMEboUBk/W9eAcxIE4Q+txNsSGkGNIGyYXxshfQGPvZZN7FUbN/arU+WKvCD4/PquJhw3D4QQ0kqBTq2NJXoKt6j1ayefeOWQEW8LaJgn5KI2FhhBWBHvKPIEEQ4y6iOCQWWceM0kiTrInYYgCIIgCIIgLAYZ8TLRJ8SkBqtCvCwsKZSDbsAJq2FGn6XrhLAalu+zvMytVoCi05gGGfEyCRliUueLXdPubaWByUqycgapzqbQXEfwhB4DjV6Dl4blyr8Mo2QkdmmwEYogI14mYUNMeiH4XLeC2gvZjJdJ6HmeKBnXVCNAoa7saemZ3m3sqdaIML0NdCBcuNWQGe2oED2ww3yi4TzsaxP42gzUrwi50IOtMlk1dx2qCLFhUnF25XEmjgSeZdOSaKmnVpC+rAs9CxgZ0aIvnuvJnWzcCSQLik5jHmTEm4EFfi4kVKBhO0RclKKXPgFWnDgIIjDuwIwRm0MRZtDU3LKm7WY/9GoHu7evWr92MuIVQ0a84QgBP5IB7gXpgiCCQJMdwSF2N1IjIagubKwkMuJNg3ziCb4hg57gBppoCIKIAJq/CJ2hlXiN0OZaFbQsjFCCnXWvZd3srCeCL2y8gKkpRuuJ2iUA6pViSbXSSrxp0Eq8TFTHiecyFJeKAixixIUeGswaOCI8r97NFEH5mjS7RfoOoSFGvxIjWOIg3owRE3Fm/sYay5hNxjaUsuyRnMaO4x+FmDQNMuJlEjJOvJ0xcsAJdy69ZRF8/tuM4NVSNp3LsJMUlmsZ84KoQG2bad+XAstj00ubn9DDPM0XBBEFkBEvk0jixLsJF0RY5ghkyEBlgdHQAiLKQrN6ML/P1lcR02a11SiMuNcw+34m4l9pzBZYHYGjNWlUJyP6q13OoRoDhJR9Cg3sAM7xhJhUs+lNcXEx2rdvD0EQsGPHDsmx/Px8DBw4ENWqVUNycjLGjh2LkpISSZqdO3ciKysLCQkJqF+/PqZNmwbGgRsQ+cTLJGic+IiuT3tcsIoItsotRyWB8lhRlVaUWQcCq8H8wZDQCneIR2+o61dgRYfnQDLLqYdvGs93K+pAM3wqLwBgQRRiJT1ZwCf+oYceQnp6Ov73v/9J9peXl+Oaa65B3bp1sWnTJpw4cQLDhw8HYwyvvPIKAKCoqAi9evVCjx49sHXrVuzduxfZ2dmoVq0axo8fr7vsoSAjXjW8+GCoP79VxgvCDMztHWZfXUQl5reF/00CoTMWMSi16RlmV5budrTmyy+/RG5uLpYuXYovv/xSciw3Nxe7d+/GoUOHkJ6eDgB4/vnnkZ2djenTpyMxMRGLFi3C+fPnMX/+fDidTrRp0wZ79+7FrFmzkJOTA8HvlbvGQe40BEEQBEEQhDJcTP0G94q391ZcXKxatD///BMjR47Ee++9h6pVq/odz8vLQ5s2bUQDHgD69OmD4uJibNu2TUyTlZUFp9MpSVNQUIADBw6ollENZMQTxqHElYYgCIKwBzTm2xOPO42aDUDDhg2RlJQkbjNmzFApFkN2djZGjRqFTp06BUxTWFiIlJQUyb5atWohLi4OhYWFQdN4vnvSmAUZ8TJRHWIyLDJGt2gYAHmKfsAd/j+t8qQOZbIE/7lYq7rxpCNeMEa3kbsC8NRW9OyGD0rGZp4aVAu0jtlLSDh06BDOnDkjbhMnTgyYbsqUKRAEIeT2ww8/4JVXXkFRUVHQcjwEcodhjEn2+6bxPNRqpisNQD7xsrlh3ACsmbdJRkqTGpTnwcUKY5oVZDQNqxguVpGTZ6zib24VOU3ACq7Upsko48Q8y8YtKh9srah3YmIiEhMTw6YeM2YMhgwZEjJNRkYGnnrqKWzevFniBgMAnTp1wm233YYFCxYgNTUVW7ZskRw/deoUSktLxdX21NRUvxX3Y8eOAYDfCr3RkBEvk4hDTPI4vwgyhwi9AoBrjenyKB+0TBfdopDezIN0rwx1ppnJNyu82ZXB5JEhJwMg8FYfgD8dK8Hg6DTJyclITk4Om+7ll1/GU089JX4vKChAnz59sGTJEnTp0gUAkJmZienTp+Po0aNIS0sD4H7Y1el0omPHjmKaSZMmoaSkBHFxcWKa9PR0ZGRkRCS71pA7jUxWzV2nLCPvM18A+eReTlYfd3iB20cFBIBameAXxs3Fwu01bHFUzUW8NwLv8kWCRg+2ak2jRo3Qpk0bcbvooosAAM2aNUODBg0AAL1790arVq0wbNgwbN++HWvXrsWECRMwcuRI8VeBoUOHwul0Ijs7G7t27cLy5cvx9NNPmx6ZBiAj3roY3W/kruIHyGcIdhoQbQJfTUI3I5Xwowu++ggBgOsxmynMpwrqpLYmJiYGK1asQHx8PLp164abb74ZgwcPxsyZM8U0SUlJWL16NQ4fPoxOnTph9OjRyMnJQU5OjomSuyF3GiIIQUYungc0nmUjCILgHZ5dO4LKxrPQUQJzuTc1+Q0gIyMj4FtWGzVqhC++CO0y3bZtW2zcuFEv0RRDRjxBhIUmCLXQ/RXhgfqCFtCDvQRHWOCNrXaF3GlkolmISVXjbnQP2pa+zKO76RRDauMXahuFWFhxlh6DNUFF41m43Ql+ISNeJjeMG6B5mYLfB4S40DkaAYKIosUAX1mGvPoyvdTCkboBKJBH3+lWCFo+TfOEUgL3neB9Td/zBsXyY4M85I+t7oTajv8BT8E3AeZxK4itCZw+2BoNkDuNTGSFmAx4xcq5jC3ofx4MWTckFkNtPXTSg+HqVXDCygf3FQ7SnPUhM50YuJvmFLsiu7UoCAp+RTfY/Vm306kt2C5u4N71sEydvATV2k/fMjrwgdxpTINW4mWiOMSkiBDya9i8Jrjh0GVlQzgzignCMKjv2w7z3tQRQX6/pEKwAwQRMbQSzzWhL3LfAUzyXU7gYp3HELoJILSBehJ/0IOVhHp070WBVrZ993l995UnoHyS/FZdOtcYBpUr8ZpJEnWQEa8LalbdCUI/1DxyQd2YMBtZfTCIXUXmFsENfp3R4r2T3GlMg4x4yyHXlCKTiyAIgiBCY3EDmgdcLgAqYr27jIkTb0fIJ94UyMDWFCPUSU3GAeZOtDxM8+bLYL4EUQ+NdyahRimkUEIfyIiXiew48Zpfq0pCgsgoQscxxTbTvE3GXZtUgyA0wzbXhE0qYvicIWeOjLgQlVi5LT3uNGo2QhFkxMtEjzjxXKLDQMLb5RmRPHoMrBGWGfB9AjbCptWKamzbpkrjf5s8jlh6DJZLMH3YtjNyBBnxpkFGvExkxYlXhAYjj8mDlN/lF6WDppHDkIq3D2hKlDY1YQC89F8j+3jUmjI+SjZdD5GGgFZfCEEogh5slcmquetQRYgNclRtHPfKYnjE9AE1EjjVIc+Qygi7QY8qKsBCSuM2wKkWOrRQO4i4GFQJTW9sVQwZ8WZjwE08b5cHb/LwjxyNBUqjs6YFA85BRDHM/cpfXbtYIHNQjonIrRnJJbxpS1N5ghndqoxxa1nyjLnAmPIIM2ryRjvkTkMQhAlYZ4IiCIIgCB6hlXhCH3hadok2SPcEV/C2DhsAay182gvSvfVhTJ1LDD3YqhhaiZeJvBCTRk1UKn1wVGYPerlx4gLE53DAp1QEQRgNf2MBN+NtkDlE9jlUu6ea/ZAq5ze7waDoNKZBRrxMIgoxqdtA4n2YYtQGRYC96uONjHoprbqR05ddm4fwx8j+o3Xf16Rw3rHbeKnHu1rClmnMAhq3uFzqN0IRZMTLRFGISR4uTLUrG0RgeGhbDZFfHeo5xkL6rkSeLmx2aRIqMeKXY8XwIANhacgnXiahQ0wGw4QrVNUpg2S28kBjZdm9MKQaQvCvNlGjxljA19uGeLtQ+2nfAP9qw1249TqhlX3Rg8quolKm6MPKjeAFUxliktxpFENGPEFEStTYbQEG1qipO8EdAe2dKLmRsomtR9gT5nKBCRRi0gzIncYQomCSiQaoGQmCMBMag2wCNSShDbQSbypWuZC1kdOUXyoVQAtelVilhxJENKP49wiDV/ij5HeT6IPcaUyDVuJlIi/EZLRAw7Bd0bVl5QR5IOyNhh3AtyjqW3bGqq1tFTlV4mLqN0IRZMTLJGSISU2v0wCFWWIcCCWkJSoQEN2GFr1VEuIhVf2o1JYQYF+g79brGWZONtaa6PzNrsB9QQiwT08CPgxr6Am1wVq9wRfrXfkSAopv8ToRloTcaWSiKMRkQGy2HGmFumgkY/hJ05hpVeBY5xyLRnAOz31HEIz6xT+0w4lm7ihcPyhbIRzXMkaIAIBFUCGr1Z0xACoeTiV3GsWQES8TZSEmw6BkNKY370QtQtAvOp5Hw3w8dzM7TSE810WvPqKrzeNVuNVsq6iFl4biRQ6dYS4GJiivKCMjXjFkxOsGzyaLDkRLdTk0nnVF5YsIQ+ehgdvuCArWjrm8DmRi1M2EreG1nrzKxQPMBXUr8RRiUimW8Yk/deoUhg0bhqSkJCQlJWHYsGE4ffp0yDzZ2dkQBEGyXXbZZcYITBCEAmiWtC4Gt52VrX2CEKGOTCjHMivxQ4cOxeHDh7Fq1SoAwD333INhw4bh888/D5mvb9++mDdvnvg9Li5OVzkJgiAIgiCiBXKnMQ9LGPF79uzBqlWrsHnzZnTp0gUA8NZbbyEzMxO//vormjdvHjSv0+lEamqqUaISBEEQBEFED+ROYxqWMOLz8vKQlJQkGvAAcNlllyEpKQnfffddSCN+/fr1qFevHmrWrImsrCxMnz4d9erVC5q+uLgYxcXF4vczZ84AALrfnon1C/MC5BAA5oAAAYADYAIEVvkZECAwhzudSwCEis+CAAEOd9gDwROxpuK4IIhpIAhgrPIzvD67i6/cxwShMnyBUOFx7KjY79knePZBPC9zVPz3fK+QpUJ8r+PwT+eA13k8565IhwDpvf4H2ud7Dmk5wfOF2wd46uV9nEnlDZqf+e0HAAbf/NLv0vKln8UIM+Lniv+C9L8gMJ/PnuZmFU3KxM2znwkMApgon0NgcFSkcVQc8+yrPFaRDpVpXYJLss+d1yX5HgMXHAIQIzA44BLP4d7P4BDc6WPEslwVxyv2ecqCCw7BVbmv4rj3dwdciIG7zBixHJdYpud4TIXMogxiHgYHUFGGp0zAIaBiPyq+CxWf3S54DnhtguBOU/Fd0DlUEGMMLng2F1yS70w8Xg5UHIP7MyrCLwNwQYCLCSiHUHFcqDjm2e/+XM5YRRoGFxMqymUVaRhc3schwAUXypkD5cxR8V1wf2YOd6uwyn3lFefy7BfzsIrvFftZRZpy5pbRs99TFvP57imL+exjDJXpKjYmHqvchwo9SI8BrOIzY+5x1LMf4jEAYhrPZ6//qPzubseKz5534gT9DPf84f29csCpOF6ZT2D++733eZfvWSgVF0x90gbKH3KfRCYWMH2ossQ8kMorMHfnFeDuyH7pPd9dXt/B/NNVHAdjlWVWfBfTec5Tsc99PoaKDlSZ12efez8LsN9V8bkyD3O5vNK4Kvd7fQZzuVejJZ8rjgegDKXi+MADZSiFGm86T32IyLGEEV9YWBjQ8K5Xrx4KCwuD5uvXrx9uuukmNG7cGPv378fjjz+Oq666Ctu2bYPT6QyYZ8aMGZg6darf/ikLHwl8Egb3rEkQBEEQBGEQJ06cQFJSkmnnj4uLQ2pqKjYVrlRdVmpqKrk7K8BUI37KlCkBDWZvtm7dCgABV7wYYyFXwm655Rbxc5s2bdCpUyc0btwYK1aswPXXXx8wz8SJE5GTkyN+P336NBo3boz8/HxTL5ZooaioCA0bNsShQ4eQmJhotji2hnRtLKRv4yBdGwvp21jOnDmDRo0aoXbt2qbKER8fj/3796OkpER1WXFxcYiPj9dAqujCVCN+zJgxGDJkSMg0GRkZ+Omnn/Dnn3/6Hfvrr7+QkpIi+3xpaWlo3Lgxfvvtt6BpnE5nwFX6pKQkGpwMJDExkfRtEKRrYyF9Gwfp2lhI38bicJgfYDA+Pp6MbxMx1YhPTk5GcnJy2HSZmZk4c+YMvv/+e1x66aUAgC1btuDMmTPo2rWr7POdOHEChw4dQlpammKZCYIgCIIgCMJszL+Nk0HLli3Rt29fjBw5Eps3b8bmzZsxcuRIDBgwQPJQa4sWLbB8+XIAwD///IMJEyYgLy8PBw4cwPr16zFw4EAkJyfjuuuuM6sqBEEQBEEQBKEaSxjxALBo0SK0bdsWvXv3Ru/evdGuXTu89957kjS//vqrGE0mJiYGO3fuxLXXXouLLroIw4cPx0UXXYS8vDzUqFFD9nmdTicmT54c9EFYQltI38ZBujYW0rdxkK6NhfRtLKRvwoPAeIlRRBAEQRAEQRCELCyzEk8QBEEQBEEQhBsy4gmCIAiCIAjCYpARTxAEQRAEQRAWg4x4giAIgiAIgrAYZMRXMH36dHTt2hVVq1ZFzZo1A6YRBMFvmzNnjiTNzp07kZWVhYSEBNSvXx/Tpk0DPTvsjxx95+fnY+DAgahWrRqSk5MxduxYvzfDkb6VkZGR4deXH3nkEUkaOfon5DF79mw0adIE8fHx6NixI7755huzRbIFU6ZM8evHqamp4nHGGKZMmYL09HQkJCSge/fu+Pnnn02U2Dps3LgRAwcORHp6OgRBwCeffCI5Lke3xcXFeOCBB5CcnIxq1aph0KBBOHz4sIG1sA7h9J2dne3X1y+77DJJGtJ39EFGfAUlJSW46aabcN9994VMN2/ePBw9elTchg8fLh4rKipCr169kJ6ejq1bt+KVV17BzJkzMWvWLL3Ftxzh9F1eXo5rrrkGZ8+exaZNm7B48WIsXboU48ePF9OQvtUxbdo0SV9+7LHHxGNy9E/IY8mSJRg3bhweffRRbN++HVdccQX69euH/Px8s0WzBa1bt5b04507d4rHnn32WcyaNQuvvvoqtm7ditTUVPTq1Qt///23iRJbg7Nnz+Liiy/Gq6++GvC4HN2OGzcOy5cvx+LFi7Fp0yb8888/GDBgAMrLy42qhmUIp28A6Nu3r6Svr1y5UnKc9B2FMELCvHnzWFJSUsBjANjy5cuD5p09ezZLSkpi58+fF/fNmDGDpaenM5fLpbGk9iCYvleuXMkcDgc7cuSIuO+DDz5gTqeTnTlzhjFG+lZD48aN2QsvvBD0uBz9E/K49NJL2ahRoyT7WrRowR555BGTJLIPkydPZhdffHHAYy6Xi6WmprJnnnlG3Hf+/HmWlJTE5syZY5CE9sB37pOj29OnT7PY2Fi2ePFiMc2RI0eYw+Fgq1atMkx2KxLI1hg+fDi79tprg+YhfUcntBIfIWPGjEFycjI6d+6MOXPmwOVyicfy8vKQlZUleQFDnz59UFBQgAMHDpggrXXJy8tDmzZtkJ6eLu7r06cPiouLsW3bNjEN6Vs5//3vf1GnTh20b98e06dPl7jKyNE/EZ6SkhJs27YNvXv3luzv3bs3vvvuO5Okshe//fYb0tPT0aRJEwwZMgR//PEHAGD//v0oLCyU6N7pdCIrK4t0rxI5ut22bRtKS0sladLT09GmTRvSv0LWr1+PevXq4aKLLsLIkSNx7Ngx8RjpOzqpYrYAVuLJJ59Ez549kZCQgLVr12L8+PE4fvy46IZQWFiIjIwMSZ6UlBTxWJMmTYwW2bIUFhaKuvNQq1YtxMXFobCwUExD+lbGf/7zH1xyySWoVasWvv/+e0ycOBH79+/H22+/DUCe/onwHD9+HOXl5X66TElJIT1qQJcuXfDuu+/ioosuwp9//omnnnoKXbt2xc8//yzqN5DuDx48aIa4tkGObgsLCxEXF4datWr5paG+Hzn9+vXDTTfdhMaNG2P//v14/PHHcdVVV2Hbtm1wOp2k7yjF1ivxgR568t1++OEH2eU99thjyMzMRPv27TF+/HhMmzYNzz33nCSNIAiS76ziIUvf/XZEa30H0hljTLI/mvXtSyT6f/DBB5GVlYV27drh7rvvxpw5c/DOO+/gxIkTYnly9E/II1A/JT2qp1+/frjhhhvQtm1bXH311VixYgUAYMGCBWIa0r1+KNEt6V8Zt9xyC6655hq0adMGAwcOxJdffom9e/eKfT4YpG97Y+uV+DFjxmDIkCEh0/iu5EbCZZddhqKiIvz5559ISUlBamqq3x2v5+cu3xULO6KlvlNTU7FlyxbJvlOnTqG0tFTUZbTr2xc1+vdEOdi3bx/q1KkjS/9EeJKTkxETExOwn5IetadatWpo27YtfvvtNwwePBiAe0U4LS1NTEO6V48nAlAo3aampqKkpASnTp2SrA4fO3YMXbt2NVZgG5KWlobGjRvjt99+A0D6jlZsvRKfnJyMFi1ahNzi4+MVl799+3bEx8eLIRIzMzOxceNGiW9xbm4u0tPTVd0sWAUt9Z2ZmYldu3bh6NGj4r7c3Fw4nU507NhRTBPN+vZFjf63b98OAOKELEf/RHji4uLQsWNHrF69WrJ/9erVNLHqQHFxMfbs2YO0tDQ0adIEqampEt2XlJRgw4YNpHuVyNFtx44dERsbK0lz9OhR7Nq1i/SvASdOnMChQ4fEMZv0HaWY9kgtZxw8eJBt376dTZ06lVWvXp1t376dbd++nf3999+MMcY+++wz9uabb7KdO3eyffv2sbfeeoslJiaysWPHimWcPn2apaSksFtvvZXt3LmTLVu2jCUmJrKZM2eaVS1uCafvsrIy1qZNG9azZ0/2448/sjVr1rAGDRqwMWPGiGWQvpXx3XffsVmzZrHt27ezP/74gy1ZsoSlp6ezQYMGiWnk6J+Qx+LFi1lsbCx755132O7du9m4ceNYtWrV2IEDB8wWzfKMHz+erV+/nv3xxx9s8+bNbMCAAaxGjRqibp955hmWlJTEli1bxnbu3MluvfVWlpaWxoqKikyWnH/+/vtvcVwGII4ZBw8eZIzJ0+2oUaNYgwYN2Jo1a9iPP/7IrrrqKnbxxRezsrIys6rFLaH0/ffff7Px48ez7777ju3fv5+tW7eOZWZmsvr165O+oxwy4isYPnw4A+C3rVu3jjHG2Jdffsnat2/PqlevzqpWrcratGnDXnzxRVZaWiop56effmJXXHEFczqdLDU1lU2ZMoXCHQYgnL4Zcxv611xzDUtISGC1a9dmY8aMkYSTZIz0rYRt27axLl26sKSkJBYfH8+aN2/OJk+ezM6ePStJJ0f/hDxee+011rhxYxYXF8cuueQStmHDBrNFsgW33HILS0tLY7GxsSw9PZ1df/317OeffxaPu1wuNnnyZJaamsqcTie78sor2c6dO02U2DqsW7cu4Bg9fPhwxpg83f77779szJgxrHbt2iwhIYENGDCA5efnm1Ab/gml73PnzrHevXuzunXrstjYWNaoUSM2fPhwP12SvqMPgTF6vSVBEARBEARBWAlb+8QTBEEQBEEQhB0hI54gCIIgCIIgLAYZ8QRBEARBEARhMciIJwiCIAiCIAiLQUY8QRAEQRAEQVgMMuIJgiAIgiAIwmKQEU8QBEEQBEEQFoOMeIIgCIIgCIKwGGTEEwRBEARBEITFICOeIAhCZ7p3745x48aZLQZBEARhI8iIJwiCIAiCIAiLITDGmNlCEARB2JXs7GwsWLBAsm///v3IyMgwRyCCIAjCFpARTxAEoSNnzpxBv3790KZNG0ybNg0AULduXcTExJgsGUEQBGFlqpgtAEEQhJ1JSkpCXFwcqlatitTUVLPFIQiCIGwC+cQTBEEQBEEQhMUgI54gCIIgCIIgLAYZ8QRBEDoTFxeH8vJys8UgCIIgbAQZ8QRBEDqTkZGBLVu24MCBAzh+/DhcLpfZIhEEQRAWh4x4giAInZkwYQJiYmLQqlUr1K1bF/n5+WaLRBAEQVgcCjFJEARBEARBEBaDVuIJgiAIgiAIwmKQEU8QBEEQBEEQFoOMeIIgCIIgCIKwGGTEEwRBEARBEITFICOeIAiCIAiCICwGGfEEQRAEQRAEYTHIiCcIgiAIgiAIi0FGPEEQBEEQBEFYDDLiCYIgCIIgCMJikBFPEARBEARBEBaDjHiCIAiCIAiCsBj/DzeUWSKxfEEAAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 780x460 with 2 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x400 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XIX summary ===\n",
      "s0             : 2.0\n",
      "mu_used        : [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess        : 0.018315638888734186\n",
      "K_terms        : 21\n",
      "n_max          : 187\n",
      "T_MAX          : 150.0\n",
      "DT             : 0.1\n",
      "sigma_max      : 2.0\n",
      "sigma_min      : -0.5\n",
      "dsigma         : -0.05\n",
      "points_per_line: 3001\n",
      "n_lines        : 51\n",
      "outputs        : ['stageXIX_heatmap.png', 'stageXIX_minima.csv', 'stageXIX_minima_curve.png', 'stageXIX_line_samples_info.csv']\n",
      "\n",
      "Preview of minima:\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>sigma</th>\n      <th>t</th>\n      <th>log_abs</th>\n      <th>abs</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>2.00</td>\n      <td>-150.0</td>\n      <td>-454.760571</td>\n      <td>3.162229e-198</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1.95</td>\n      <td>-150.0</td>\n      <td>-454.969886</td>\n      <td>2.565010e-198</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1.90</td>\n      <td>-150.0</td>\n      <td>-455.177848</td>\n      <td>2.083398e-198</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1.85</td>\n      <td>-150.0</td>\n      <td>-455.384207</td>\n      <td>1.694929e-198</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1.80</td>\n      <td>-150.0</td>\n      <td>-455.588667</td>\n      <td>1.381515e-198</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>1.75</td>\n      <td>-150.0</td>\n      <td>-455.790884</td>\n      <td>1.128585e-198</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>1.70</td>\n      <td>-150.0</td>\n      <td>-455.990460</td>\n      <td>9.243990e-199</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>1.65</td>\n      <td>-150.0</td>\n      <td>-456.186945</td>\n      <td>7.594984e-199</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>1.60</td>\n      <td>-150.0</td>\n      <td>-456.379840</td>\n      <td>6.262590e-199</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>1.55</td>\n      <td>-150.0</td>\n      <td>-456.568599</td>\n      <td>5.185338e-199</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>1.50</td>\n      <td>-150.0</td>\n      <td>-456.752649</td>\n      <td>4.313648e-199</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>1.45</td>\n      <td>-150.0</td>\n      <td>-456.931412</td>\n      <td>3.607525e-199</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "    sigma      t     log_abs            abs\n",
       "0    2.00 -150.0 -454.760571  3.162229e-198\n",
       "1    1.95 -150.0 -454.969886  2.565010e-198\n",
       "2    1.90 -150.0 -455.177848  2.083398e-198\n",
       "3    1.85 -150.0 -455.384207  1.694929e-198\n",
       "4    1.80 -150.0 -455.588667  1.381515e-198\n",
       "5    1.75 -150.0 -455.790884  1.128585e-198\n",
       "6    1.70 -150.0 -455.990460  9.243990e-199\n",
       "7    1.65 -150.0 -456.186945  7.594984e-199\n",
       "8    1.60 -150.0 -456.379840  6.262590e-199\n",
       "9    1.55 -150.0 -456.568599  5.185338e-199\n",
       "10   1.50 -150.0 -456.752649  4.313648e-199\n",
       "11   1.45 -150.0 -456.931412  3.607525e-199"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Wrote:\n",
      " - stageXIX_heatmap.png\n",
      " - stageXIX_minima_curve.png\n",
      " - stageXIX_minima.csv\n",
      " - stageXIX_line_samples_info.csv\n",
      " - stageXIX_summary.json\n"
     ]
    }
   ],
   "source": [
    "# === Stage XIX: deep sweep into the critical strip (enhanced heatmap) ===\n",
    "# Scans log |Λ(σ + i t)| for σ ∈ [2.0, -0.5], t ∈ [-150, 150].\n",
    "# Reuses Stage VIII Dirichlet coefficients and the [1,2,2,3] gamma model we’ve been using.\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- helpers (no Sage Integer leaks) ----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except Exception: return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "# ---------------- inputs ----------------\n",
    "coeff_path   = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "summaryX     = Path(\"stageX_summary.json\")      # optional (s0, maybe Q)\n",
    "summaryXI    = Path(\"stageXI_summary.json\")     # optional (mu shift, residuals)\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "# central point s0 (default 2.0)\n",
    "s0 = mp.mpf('2.0')\n",
    "if summaryX.exists() and summaryX.stat().st_size > 0:\n",
    "    try:\n",
    "        JX = json.load(open(summaryX))\n",
    "        if \"s0\" in JX: s0 = mpf_safe(JX[\"s0\"])\n",
    "        elif \"central_point_guess\" in JX: s0 = mpf_safe(JX[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "# gamma shifts: base + possible uniform shift from Stage XI\n",
    "MU_BASE = [0,1,1,2]\n",
    "delta_uniform = 1.0\n",
    "if summaryXI.exists() and summaryXI.stat().st_size > 0:\n",
    "    try:\n",
    "        JXI = json.load(open(summaryXI))\n",
    "        if \"uniform_shift\" in JXI and \"delta_min_residual\" in JXI[\"uniform_shift\"]:\n",
    "            delta_uniform = float(JXI[\"uniform_shift\"][\"delta_min_residual\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "MU = [m + delta_uniform for m in MU_BASE]  # typically [1,2,2,3]\n",
    "# crude Q (zeros’ location doesn’t depend on Q; we use it for Λ)\n",
    "Q_guess = mp.e**(-4)\n",
    "# ---------------- read coefficients ----------------\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "# limit terms (tune as needed)\n",
    "K = min(len(N_all), 8000)\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "# ---------------- Λ(s) pieces ----------------\n",
    "mp.mp.dps = 100  # precision\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------------- Stage XIX scan settings ----------------\n",
    "SIGMA_MAX, SIGMA_MIN, DSIG = 2.0, -0.5, -0.05   # 2.0 → -0.5 step -0.05  (51 lines)\n",
    "T_MAX, DT = 150.0, 0.10                         # 3001 points per line\n",
    "sigmas = np.arange(SIGMA_MAX, SIGMA_MIN - 1e-12, DSIG)\n",
    "t_vals = np.arange(-T_MAX, T_MAX + 1e-12, DT)\n",
    "n_sigma, n_t = len(sigmas), len(t_vals)\n",
    "print(\"Stage XIX: sweeping deeper into the strip\")\n",
    "print(f\"s0          : {s0}\")\n",
    "print(f\"mu (used)   : {MU}\")\n",
    "print(f\"K_terms     : {K}    n_max: {to_int(n[-1])}\")\n",
    "print(f\"T_MAX, DT   : {T_MAX}, {DT}  → {n_t} points/line\")\n",
    "print(f\"sigmas      : {n_sigma} from {SIGMA_MAX} down to {SIGMA_MIN}\")\n",
    "print(f\"precision   : mp.mp.dps = {mp.mp.dps}\")\n",
    "# heatmap buffer (float64 of log |Λ|)\n",
    "log_abs = np.empty((n_sigma, n_t), dtype=np.float64)\n",
    "Ncut = to_int(n[-1])\n",
    "# do the sweep\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    if i % 5 == 0:\n",
    "        print(f\"  line {i+1}/{n_sigma} at sigma={sigma:.3f} ...\")\n",
    "    # evaluate along vertical line Re(s)=sigma\n",
    "    row = []\n",
    "    for t in t_vals:\n",
    "        s = mpf_safe(sigma) + 1j*mpf_safe(t)\n",
    "        val = Lambda_of_s(s, Q_guess, MU, Ncut)\n",
    "        # store log|Λ| (clip to avoid -inf)\n",
    "        aval = abs(val)\n",
    "        row.append(np.log(max(to_float(aval), 1e-300)))\n",
    "    log_abs[i, :] = np.array(row, dtype=np.float64)\n",
    "# ---------------- per-line minima & save artifacts ----------------\n",
    "# find t where |Λ| is minimal on each sigma-line\n",
    "min_rows = []\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    j = int(np.argmin(log_abs[i, :]))\n",
    "    min_rows.append({\n",
    "        \"sigma\": float(sigma),\n",
    "        \"t\": float(t_vals[j]),\n",
    "        \"log_abs\": float(log_abs[i, j]),\n",
    "        \"abs\": float(np.exp(log_abs[i, j]))\n",
    "    })\n",
    "min_df = pd.DataFrame(min_rows)\n",
    "# save CSVs\n",
    "heatmap_csv = \"stageXIX_minima.csv\"\n",
    "lines_csv   = \"stageXIX_line_samples_info.csv\"\n",
    "min_df.to_csv(heatmap_csv, index=False)\n",
    "pd.DataFrame({\"sigma\": sigmas}).to_csv(lines_csv, index=False)\n",
    "# ---------------- plot: enhanced contrast heatmap ----------------\n",
    "plt.figure(figsize=(7.8, 4.6))\n",
    "vmax = np.percentile(log_abs, 95)\n",
    "vmin = np.percentile(log_abs, 5) - 10.0  # push darker tail for contrast\n",
    "extent = [t_vals[0], t_vals[-1], sigmas[-1], sigmas[0]]  # t on x, sigma on y (descending)\n",
    "im = plt.imshow(log_abs, extent=extent, aspect='auto', cmap='viridis',\n",
    "                vmin=vmin, vmax=vmax, origin='lower')\n",
    "plt.colorbar(im, label=\"log |Λ(σ+it)|\")\n",
    "plt.title(\"Stage XIX: log |Λ(σ+it)| (deep sweep)\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"σ = Re s\")\n",
    "# overlay minima as white dots\n",
    "plt.plot([r[\"t\"] for r in min_rows], [r[\"sigma\"] for r in min_rows],\n",
    "         'w.', ms=2, label=\"line minima\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"stageXIX_heatmap.png\", dpi=150)\n",
    "plt.show()\n",
    "# quick look: minima vs sigma\n",
    "plt.figure(figsize=(7.2, 4.0))\n",
    "plt.plot(min_df[\"sigma\"], min_df[\"log_abs\"], \".-\")\n",
    "plt.gca().invert_xaxis()\n",
    "plt.xlabel(\"σ\"); plt.ylabel(\"min log|Λ| on line σ\")\n",
    "plt.title(\"Stage XIX: per-line minima (lower is darker)\")\n",
    "plt.grid(True)\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"stageXIX_minima_curve.png\", dpi=150)\n",
    "plt.show()\n",
    "# ---------------- summary ----------------\n",
    "summary = {\n",
    "    \"s0\": float(s0),\n",
    "    \"mu_used\": [float(x) for x in MU],\n",
    "    \"Q_guess\": float(Q_guess),\n",
    "    \"K_terms\": int(K),\n",
    "    \"n_max\": int(to_int(n[-1])),\n",
    "    \"T_MAX\": float(T_MAX),\n",
    "    \"DT\": float(DT),\n",
    "    \"sigma_max\": float(SIGMA_MAX),\n",
    "    \"sigma_min\": float(SIGMA_MIN),\n",
    "    \"dsigma\": float(DSIG),\n",
    "    \"points_per_line\": int(n_t),\n",
    "    \"n_lines\": int(n_sigma),\n",
    "    \"outputs\": [\"stageXIX_heatmap.png\", \"stageXIX_minima.csv\",\n",
    "                \"stageXIX_minima_curve.png\", \"stageXIX_line_samples_info.csv\"],\n",
    "}\n",
    "with open(\"stageXIX_summary.json\",\"w\") as f:\n",
    "    json.dump(summary, f, indent=2)\n",
    "print(\"\\n=== Stage XIX summary ===\")\n",
    "for k,v in summary.items():\n",
    "    print(f\"{k:15}: {v}\")\n",
    "print(\"\\nPreview of minima:\")\n",
    "display(head_safe(min_df, 12))\n",
    "print(\"\\nWrote:\")\n",
    "print(\" - stageXIX_heatmap.png\")\n",
    "print(\" - stageXIX_minima_curve.png\")\n",
    "print(\" - stageXIX_minima.csv\")\n",
    "print(\" - stageXIX_line_samples_info.csv\")\n",
    "print(\" - stageXIX_summary.json\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "953808",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stage XX: sweeping lines\n",
      "s0          : 2.0\n",
      "mu (used)   : [1, 2, 2, 3]\n",
      "K_terms     : 21       n_max: 187\n",
      "T_MAX, DT   : 300.000000000000, 0.100000000000000  → 6001 points/line\n",
      "sigmas      : 41 from 2.0 down to -2.0000000000000036\n",
      "precision   : mp.mp.dps = 150\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 5/41 at sigma=1.600 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 10/41 at sigma=1.100 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 15/41 at sigma=0.600 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 20/41 at sigma=0.100 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 25/41 at sigma=-0.400 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 30/41 at sigma=-0.900 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 35/41 at sigma=-1.400 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 40/41 at sigma=-1.900 ...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  line 41/41 at sigma=-2.000 ...\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 760x460 with 2 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 760x460 with 2 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x420 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XX summary ===\n",
      "s0             : 2.0\n",
      "mu_used        : [1, 2, 2, 3]\n",
      "Q_guess        : 0.01831563888873418\n",
      "K_terms        : 21\n",
      "n_max          : 187\n",
      "T_MAX          : 300.0\n",
      "DT             : 0.1\n",
      "precision      : 150\n",
      "sigma_max      : 2.0\n",
      "sigma_min      : -2.0\n",
      "dsigma         : -0.1\n",
      "points_per_line: 6001\n",
      "n_lines        : 41\n",
      "Wrote:\n",
      " - stageXX_heatmap.png\n",
      " - stageXX_curvature.png\n",
      " - stageXX_minima_curve.png\n",
      " - stageXX_minima.csv\n",
      " - stageXX_settings.json\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>sigma</th>\n      <th>t</th>\n      <th>log_abs</th>\n      <th>abs</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>2.0</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1.9</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1.8</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1.7</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1.6</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>1.5</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>1.4</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>1.3</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>1.2</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>1.1</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>1.0</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>0.9</td>\n      <td>-300.0</td>\n      <td>-207.232658</td>\n      <td>1.000000e-90</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "    sigma      t     log_abs           abs\n",
       "0     2.0 -300.0 -207.232658  1.000000e-90\n",
       "1     1.9 -300.0 -207.232658  1.000000e-90\n",
       "2     1.8 -300.0 -207.232658  1.000000e-90\n",
       "3     1.7 -300.0 -207.232658  1.000000e-90\n",
       "4     1.6 -300.0 -207.232658  1.000000e-90\n",
       "5     1.5 -300.0 -207.232658  1.000000e-90\n",
       "6     1.4 -300.0 -207.232658  1.000000e-90\n",
       "7     1.3 -300.0 -207.232658  1.000000e-90\n",
       "8     1.2 -300.0 -207.232658  1.000000e-90\n",
       "9     1.1 -300.0 -207.232658  1.000000e-90\n",
       "10    1.0 -300.0 -207.232658  1.000000e-90\n",
       "11    0.9 -300.0 -207.232658  1.000000e-90"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Stage XX: deep sweep across the strip (σ from 2 to -2) ===\n",
    "# Outputs:\n",
    "#   - stageXX_heatmap.png\n",
    "#   - stageXX_curvature.png\n",
    "#   - stageXX_minima_curve.png\n",
    "#   - stageXX_minima.csv\n",
    "#   - stageXX_settings.json\n",
    "#\n",
    "# Requirements:\n",
    "#   stageVIII_dirichlet_coeffs.csv  (columns: n, a_n / an / a / a_n_real)\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- helpers ----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except Exception: return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "def py(x):\n",
    "    \"\"\"Make JSON-safe.\"\"\"\n",
    "    import numbers\n",
    "    if isinstance(x, (str, bool)) or x is None: return x\n",
    "    if isinstance(x, numbers.Integral): return int(x)\n",
    "    if isinstance(x, numbers.Real):\n",
    "        try:\n",
    "            xi = int(x)\n",
    "            if float(xi) == float(x): return int(xi)\n",
    "        except Exception:\n",
    "            pass\n",
    "        try:\n",
    "            return float(x)\n",
    "        except Exception:\n",
    "            return to_float(x)\n",
    "    if isinstance(x, complex):\n",
    "        return {\"re\": py(x.real), \"im\": py(x.imag)}\n",
    "    if isinstance(x, (list, tuple)):\n",
    "        return [py(t) for t in x]\n",
    "    if isinstance(x, dict):\n",
    "        return {str(k): py(v) for k, v in x.items()}\n",
    "    try:\n",
    "        return float(x)\n",
    "    except Exception:\n",
    "        return str(x)\n",
    "# ---------------- load coefficients ----------------\n",
    "coeff_path = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"CSV missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "K = min(len(N_all), 8000)\n",
    "n = N_all[:K]\n",
    "a = A_all[:K]\n",
    "# ---------------- model and Λ(s) ----------------\n",
    "s0 = mp.mpf('2.0')                     # central line\n",
    "MU  = [1, 2, 2, 3]                     # from Stage XI uniform shift\n",
    "Q_guess = mp.e**(-4)                   # conductor scale (doesn't affect zero locations)\n",
    "mp.mp.dps = 150                        # precision\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------------- sweep settings ----------------\n",
    "T_MAX = 300.0\n",
    "DT    = 0.10                     # 6001 samples along t\n",
    "t_vals = np.arange(-T_MAX, T_MAX + 1e-12, DT, dtype=float)  # ensure float, not Sage Integer\n",
    "Ncut  = to_int(n[-1])\n",
    "sigma_max, sigma_min, dsigma = 2.0, -2.0, -0.1\n",
    "sigmas = np.arange(sigma_max, sigma_min - 1e-12, dsigma, dtype=float)  # 41 lines\n",
    "print(\"Stage XX: sweeping lines\")\n",
    "print(f\"s0          : {float(s0)}\")\n",
    "print(f\"mu (used)   : {MU}\")\n",
    "print(f\"K_terms     : {K}       n_max: {to_int(n[-1])}\")\n",
    "print(f\"T_MAX, DT   : {T_MAX}, {DT}  → {len(t_vals)} points/line\")\n",
    "print(f\"sigmas      : {len(sigmas)} from {sigmas[0]} down to {sigmas[-1]}\")\n",
    "print(f\"precision   : mp.mp.dps = {mp.mp.dps}\")\n",
    "# storage\n",
    "log_abs_grid = np.empty((len(sigmas), len(t_vals)), dtype=float)\n",
    "curv_grid    = np.empty_like(log_abs_grid)\n",
    "tiny = 10.0**(-mp.mp.dps * 0.6)   # safe floor for logs\n",
    "# ---------------- sweep and curvature per line ----------------\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    # evaluate |Λ| across t for this sigma\n",
    "    abs_vals = []\n",
    "    for t in t_vals:\n",
    "        s = mpf_safe(sigma) + 1j*mpf_safe(t)\n",
    "        val = Lambda_of_s(s, Q_guess, MU, Ncut)\n",
    "        abs_vals.append(abs(val))\n",
    "    abs_vals = np.array([float(v) for v in abs_vals], dtype=float)\n",
    "    log_abs  = np.log(np.maximum(abs_vals, tiny))\n",
    "    log_abs_grid[i, :] = log_abs\n",
    "    # curvature d^2/dt^2 log|Λ| via finite differences (numpy gradient twice)\n",
    "    # uniform spacing DT, so this is stable\n",
    "    d1 = np.gradient(log_abs, DT)\n",
    "    d2 = np.gradient(d1, DT)\n",
    "    curv_grid[i, :] = d2\n",
    "    if (i+1) % 5 == 0 or i == len(sigmas)-1:\n",
    "        print(f\"  line {i+1}/{len(sigmas)} at sigma={sigma:.3f} ...\")\n",
    "# ---------------- per-line minima (in |Λ|) ----------------\n",
    "min_rows = []\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    j_min = int(np.argmin(log_abs_grid[i, :]))\n",
    "    min_rows.append({\n",
    "        \"sigma\": float(sigma),\n",
    "        \"t\": float(t_vals[j_min]),\n",
    "        \"log_abs\": float(log_abs_grid[i, j_min]),\n",
    "        \"abs\": float(np.exp(log_abs_grid[i, j_min]))\n",
    "    })\n",
    "min_df = pd.DataFrame(min_rows)\n",
    "# ---------------- figures ----------------\n",
    "# Heatmap of log|Λ|\n",
    "plt.figure(figsize=(7.6, 4.6))\n",
    "extent = [t_vals[0], t_vals[-1], sigmas[-1], sigmas[0]]  # t on x, sigma on y (top=2 → bottom=-2)\n",
    "im = plt.imshow(log_abs_grid, extent=extent, aspect='auto', cmap='viridis')\n",
    "plt.colorbar(im, label=\"log |Λ(σ+it)|\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"σ = Re s\")\n",
    "plt.title(\"Stage XX: log |Λ(σ+it)| across the strip\")\n",
    "plt.tight_layout(); plt.savefig(\"stageXX_heatmap.png\", dpi=150); plt.show()\n",
    "# Heatmap of curvature\n",
    "plt.figure(figsize=(7.6, 4.6))\n",
    "im2 = plt.imshow(curv_grid, extent=extent, aspect='auto', cmap='coolwarm')\n",
    "plt.colorbar(im2, label=r\"$d^2/dt^2 \\log|Λ|$\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"σ = Re s\")\n",
    "plt.title(\"Stage XX: curvature of log |Λ(σ+it)|\")\n",
    "plt.tight_layout(); plt.savefig(\"stageXX_curvature.png\", dpi=150); plt.show()\n",
    "# Minima curve\n",
    "plt.figure(figsize=(7.2, 4.2))\n",
    "plt.plot(min_df[\"sigma\"], min_df[\"log_abs\"], \"o-\", ms=3)\n",
    "plt.gca().invert_xaxis()  # optional: show σ decreasing left-to-right if you like\n",
    "plt.xlabel(\"σ\"); plt.ylabel(\"min log|Λ| on line σ\")\n",
    "plt.title(\"Stage XX: per-line minima (lower = darker)\")\n",
    "plt.grid(True)\n",
    "plt.tight_layout(); plt.savefig(\"stageXX_minima_curve.png\", dpi=150); plt.show()\n",
    "# ---------------- persist outputs ----------------\n",
    "min_df.to_csv(\"stageXX_minima.csv\", index=False)\n",
    "settings = {\n",
    "    \"s0\": py(s0),\n",
    "    \"mu_used\": py(MU),\n",
    "    \"Q_guess\": py(Q_guess),\n",
    "    \"K_terms\": int(K),\n",
    "    \"n_max\": int(to_int(n[-1])),\n",
    "    \"T_MAX\": float(T_MAX),\n",
    "    \"DT\": float(DT),\n",
    "    \"precision\": int(mp.mp.dps),\n",
    "    \"sigma_max\": float(sigma_max),\n",
    "    \"sigma_min\": float(sigma_min),\n",
    "    \"dsigma\": float(dsigma),\n",
    "    \"points_per_line\": int(len(t_vals)),\n",
    "    \"n_lines\": int(len(sigmas)),\n",
    "    \"outputs\": [\"stageXX_heatmap.png\", \"stageXX_curvature.png\", \"stageXX_minima_curve.png\",\n",
    "                \"stageXX_minima.csv\"]\n",
    "}\n",
    "with open(\"stageXX_settings.json\", \"w\") as f:\n",
    "    json.dump(settings, f, indent=2)\n",
    "print(\"\\n=== Stage XX summary ===\")\n",
    "for k,v in settings.items():\n",
    "    if k != \"outputs\":\n",
    "        print(f\"{k:15s}: {v}\")\n",
    "print(\"Wrote:\")\n",
    "print(\" - stageXX_heatmap.png\")\n",
    "print(\" - stageXX_curvature.png\")\n",
    "print(\" - stageXX_minima_curve.png\")\n",
    "print(\" - stageXX_minima.csv\")\n",
    "print(\" - stageXX_settings.json\")\n",
    "# quick preview\n",
    "display(head_safe(min_df, 12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6adba7",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stage XXI: fine sweep with phase-gradient …\n",
      "s0           : 2.0\n",
      "mu (used)    : [1.0, 2.0, 2.0, 3.0]\n",
      "K_terms      : 21 (max n = 187)\n",
      "T_MAX, DT    : 100.000000000000, 0.0500000000000000  → 4001 points/line\n",
      "sigmas count : 21 from 2.500 down to 1.500\n",
      "precision    : mp.mp.dps = 160\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 740x440 with 2 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 740x440 with 2 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x360 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 740x460 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XXI summary ===\n",
      "s0                : 2.0\n",
      "mu_used           : [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess           : 0.01831563888873418\n",
      "K_terms           : 21\n",
      "n_max             : 187\n",
      "T_MAX             : 100.0\n",
      "DT                : 0.05\n",
      "sigmas            : [2.5, 1.5000000000000036, -0.04999999999999982]\n",
      "points_per_line   : 4001\n",
      "n_lines           : 21\n",
      "n_candidates      : 0\n",
      "outputs           : ['stageXXI_logabs_heatmap.png', 'stageXXI_phasegrad_heatmap.png', 'stageXXI_minima_curve.png', 'stageXXI_central_line_candidates.png', 'stageXXI_minima.csv', 'stageXXI_candidates.csv']\n",
      "\n",
      "Wrote:\n",
      " - stageXXI_logabs_heatmap.png\n",
      " - stageXXI_phasegrad_heatmap.png\n",
      " - stageXXI_minima_curve.png\n",
      " - stageXXI_central_line_candidates.png\n",
      " - stageXXI_minima.csv\n",
      " - stageXXI_candidates.csv\n",
      "\n",
      "Preview of candidates (first 10 rows):\n",
      "(none)\n"
     ]
    }
   ],
   "source": [
    "# === Stage XXI: fine sweep with phase-gradient mapping (high sensitivity, Sage-proof) ===\n",
    "# Focus: increase K_terms, precision, and add d/dt arg Λ heatmap + zero-crossing candidates.\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------- helpers (JSON/pandas/mpmath safe) ----------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except Exception: return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    \"\"\"pandas-safe preview: always uses plain Python ints for iloc slicing.\"\"\"\n",
    "    try:\n",
    "        n = int(n)\n",
    "    except Exception:\n",
    "        n = to_int(n)\n",
    "    L = int(len(df))\n",
    "    n = max(0, min(n, L))\n",
    "    return df.iloc[:int(n)]\n",
    "# ---------- inputs ----------\n",
    "coeff_path   = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "summaryX     = Path(\"stageX_summary.json\")   # for s0 (if present)\n",
    "summaryXI    = Path(\"stageXI_summary.json\")  # for uniform shift delta (if present)\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "# central point\n",
    "s0 = mp.mpf('2.0')\n",
    "if summaryX.exists() and summaryX.stat().st_size > 0:\n",
    "    try:\n",
    "        with open(summaryX, \"r\") as f: JX = json.load(f)\n",
    "        if \"s0\" in JX: s0 = mpf_safe(JX[\"s0\"])\n",
    "        elif \"central_point_guess\" in JX: s0 = mpf_safe(JX[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "# base mu and Stage XI's uniform shift (if available)\n",
    "MU_BASE = [0,1,1,2]\n",
    "delta_uniform = 1.0\n",
    "if summaryXI.exists() and summaryXI.stat().st_size > 0:\n",
    "    try:\n",
    "        with open(summaryXI, \"r\") as f: JXI = json.load(f)\n",
    "        if \"uniform_shift\" in JXI and \"delta_min_residual\" in JXI[\"uniform_shift\"]:\n",
    "            delta_uniform = float(JXI[\"uniform_shift\"][\"delta_min_residual\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "MU = [m + delta_uniform for m in MU_BASE]   # your runs → [1,2,2,3]\n",
    "# a crude Q (visualization only)\n",
    "Q_guess = mp.e**(-4)\n",
    "# ---------- load coefficients ----------\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "# Use as many terms as available (max sensitivity)\n",
    "K_use = len(N_all)\n",
    "n = N_all[:K_use]\n",
    "a = A_all[:K_use]\n",
    "# ---------- Dirichlet with cosine smoothing ----------\n",
    "mp.mp.dps = 160  # higher precision for phase stability\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(to_int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(to_int(nn_i))**s) * w\n",
    "    return total\n",
    "# completed Λ(s)\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------- Stage XXI parameters (fine sweep) ----------\n",
    "T_MAX   = 100.0\n",
    "DT      = 0.05\n",
    "sigmas  = np.arange(float(s0)+0.50, float(s0)-0.51, -0.05)  # 2.50 → 1.50\n",
    "Ncut    = to_int(n[-1])\n",
    "t_vals  = np.arange(-T_MAX, T_MAX + 1e-12, DT)\n",
    "m       = len(t_vals)\n",
    "L       = len(sigmas)\n",
    "# containers\n",
    "logabs_grid = np.zeros((L, m), dtype=float)\n",
    "grad_grid   = np.zeros((L, m), dtype=float)\n",
    "minima_curve = []   # (sigma, min_logabs)\n",
    "print(\"Stage XXI: fine sweep with phase-gradient …\")\n",
    "print(f\"s0           : {s0}\")\n",
    "print(f\"mu (used)    : {MU}\")\n",
    "print(f\"K_terms      : {K_use} (max n = {to_int(n[-1])})\")\n",
    "print(f\"T_MAX, DT    : {T_MAX}, {DT}  → {m} points/line\")\n",
    "print(f\"sigmas count : {L} from {sigmas[0]:.3f} down to {sigmas[-1]:.3f}\")\n",
    "print(f\"precision    : mp.mp.dps = {mp.mp.dps}\")\n",
    "# sweep\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    vals = []\n",
    "    for t in t_vals:\n",
    "        s = mp.mpf(sigma) + 1j*mp.mpf(t)\n",
    "        vals.append(Lambda_of_s(s, Q_guess, MU, Ncut))\n",
    "    absvals = np.array([to_float(abs(z)) for z in vals], dtype=float)\n",
    "    with np.errstate(divide='ignore'):\n",
    "        logabs = np.log(absvals, where=absvals>0)\n",
    "        logabs[~np.isfinite(logabs)] = -1e300  # floor to keep continuity\n",
    "    phase  = np.unwrap(np.array([float(mp.arg(z)) for z in vals], dtype=float))\n",
    "    dphi   = np.gradient(phase, DT)\n",
    "    logabs_grid[i, :] = logabs\n",
    "    grad_grid[i,  :]  = dphi\n",
    "    minima_curve.append((float(sigma), float(np.min(logabs))))\n",
    "# ---------- simple candidates from the central line ----------\n",
    "i_center = int(np.argmin(np.abs(sigmas - float(s0))))\n",
    "logabs_c = logabs_grid[i_center]\n",
    "grad_c   = grad_grid[i_center]\n",
    "line_min = float(np.min(logabs_c))\n",
    "line_q25 = float(np.quantile(logabs_c, 0.25))\n",
    "depth_gate = line_q25 - 0.10*abs(line_q25)\n",
    "sign = np.sign(grad_c)\n",
    "zero_cross_idx = np.where((sign[:-1] * sign[1:]) < 0)[0]\n",
    "cand_idx = []\n",
    "for k in zero_cross_idx:\n",
    "    k0 = max(0, int(k)-1); k1 = min(m-1, int(k)+2)\n",
    "    if float(np.min(logabs_c[k0:k1])) <= min(depth_gate, line_min + 2.0):\n",
    "        cand_idx.append(int(np.argmin(logabs_c[k0:k1]) + k0))\n",
    "cand_idx = sorted(set(cand_idx))\n",
    "candidates = pd.DataFrame({\n",
    "    \"sigma\": [float(sigmas[i_center])]*len(cand_idx),\n",
    "    \"t\":     [float(t_vals[k]) for k in cand_idx],\n",
    "    \"log_abs\":[float(logabs_c[k]) for k in cand_idx],\n",
    "    \"d_arg_dt\":[float(grad_c[k]) for k in cand_idx],\n",
    "})\n",
    "# ---------- plots ----------\n",
    "extent = [t_vals[0], t_vals[-1], sigmas[-1], sigmas[0]]\n",
    "plt.figure(figsize=(7.4,4.4))\n",
    "plt.imshow(logabs_grid, aspect='auto', extent=extent, origin='lower', cmap='viridis')\n",
    "plt.colorbar(label='log |Λ(σ+it)|')\n",
    "plt.xlabel('t'); plt.ylabel('σ = Re s')\n",
    "plt.title('Stage XXI: log |Λ(σ+it)| (fine sweep)')\n",
    "plt.tight_layout(); plt.savefig(\"stageXXI_logabs_heatmap.png\", dpi=150); plt.show()\n",
    "plt.figure(figsize=(7.4,4.4))\n",
    "plt.imshow(grad_grid, aspect='auto', extent=extent, origin='lower', cmap='coolwarm')\n",
    "plt.colorbar(label='d/dt arg Λ')\n",
    "plt.xlabel('t'); plt.ylabel('σ = Re s')\n",
    "plt.title('Stage XXI: phase gradient d/dt arg Λ (fine sweep)')\n",
    "plt.tight_layout(); plt.savefig(\"stageXXI_phasegrad_heatmap.png\", dpi=150); plt.show()\n",
    "mc = pd.DataFrame(minima_curve, columns=[\"sigma\",\"min_logabs\"])\n",
    "plt.figure(figsize=(6.8,3.6))\n",
    "plt.plot(mc[\"sigma\"], mc[\"min_logabs\"], \"o-\")\n",
    "plt.gca().invert_xaxis()\n",
    "plt.xlabel(\"σ\"); plt.ylabel(\"min log|Λ| on line σ\")\n",
    "plt.title(\"Stage XXI: per-line minima (lower = darker)\")\n",
    "plt.grid(True); plt.tight_layout(); plt.savefig(\"stageXXI_minima_curve.png\", dpi=150); plt.show()\n",
    "plt.figure(figsize=(7.4,4.6))\n",
    "plt.plot(t_vals, logabs_c, lw=1.4, label=\"log |Λ(s0 + it)|\")\n",
    "if len(candidates) > 0:\n",
    "    plt.scatter(candidates[\"t\"], candidates[\"log_abs\"], s=24, marker=\"x\", label=\"candidates\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"log |Λ|\"); plt.title(\"Stage XXI: central line with candidates\")\n",
    "plt.grid(True); plt.legend(); plt.tight_layout(); plt.savefig(\"stageXXI_central_line_candidates.png\", dpi=150); plt.show()\n",
    "# ---------- outputs ----------\n",
    "mc.to_csv(\"stageXXI_minima.csv\", index=False)\n",
    "candidates.to_csv(\"stageXXI_candidates.csv\", index=False)\n",
    "summary = {\n",
    "    \"s0\": float(s0),\n",
    "    \"mu_used\": MU,\n",
    "    \"Q_guess\": float(Q_guess),\n",
    "    \"K_terms\": int(K_use),\n",
    "    \"n_max\": int(n[-1]),\n",
    "    \"T_MAX\": float(T_MAX),\n",
    "    \"DT\": float(DT),\n",
    "    \"sigmas\": [float(sigmas[0]), float(sigmas[-1]), float(sigmas[1]-sigmas[0]) if len(sigmas)>1 else 0.0],\n",
    "    \"points_per_line\": int(m),\n",
    "    \"n_lines\": int(L),\n",
    "    \"n_candidates\": int(len(candidates)),\n",
    "    \"outputs\": [\n",
    "        \"stageXXI_logabs_heatmap.png\",\n",
    "        \"stageXXI_phasegrad_heatmap.png\",\n",
    "        \"stageXXI_minima_curve.png\",\n",
    "        \"stageXXI_central_line_candidates.png\",\n",
    "        \"stageXXI_minima.csv\",\n",
    "        \"stageXXI_candidates.csv\",\n",
    "    ],\n",
    "}\n",
    "with open(\"stageXXI_summary.json\",\"w\") as f:\n",
    "    json.dump(summary, f, indent=2)\n",
    "print(\"\\n=== Stage XXI summary ===\")\n",
    "for k,v in summary.items():\n",
    "    print(f\"{k:18}: {v}\")\n",
    "print(\"\\nWrote:\")\n",
    "for fn in summary[\"outputs\"]:\n",
    "    print(\" -\", fn)\n",
    "print(\"\\nPreview of candidates (first 10 rows):\")\n",
    "if len(candidates) == 0:\n",
    "    print(\"(none)\")\n",
    "else:\n",
    "    display(head_safe(candidates, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fd5ddf",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stage XXI+ running …\n",
      "s0=2.0, mu=[1.0, 2.0, 2.0, 3.0], K_terms=21 (n_max=187), T_MAX=250.000000000000, DT=0.0200000000000000, mp.dps=200\n",
      "lines: 25 from σ=2.60 down to 1.40; points/line=25001\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/ext/sage/10.7/local/var/lib/sage/venv-python3.12.5/lib/python3.12/site-packages/numpy/lib/_function_base_impl.py:1286: RuntimeWarning: overflow encountered in divide\n",
      "  out[tuple(slice1)] = (f[tuple(slice4)] - f[tuple(slice2)]) / (2. * ax_dx)\n"
     ]
    },
    {
     "data": {
      "image/png": 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01FNP5flsyJAhmjRpkvbu3auWLVsWadzc+Z48ebLIc7Lb7Xl+5qT/BYMXmzt3rp555hn16NFDq1atUrt27Ryf1apVS35+fpo1a1a+fXO/X0kKCAjQ0KFD9f7772vcuHGKi4vT4MGDC5VT3qdPHz3zzDPasGGDvvjiC8df+n369NGqVascP+d9+vQpcKzCyP0zeOLECadAO78/g15eXpf8+ZL+9x34+Pioa9euWrNmjerVq6fg4GC1bt1ajRs3lnRhj/QvvvhCN910U75zOnnypMsP4KJii4yMzPe5gVznzp3T008/rblz5+rUqVNq1aqV/vnPfzqed2ncuLHj51GSGjZsqPXr1+vLL7901M2YMUMNGjTQtGnTJEktWrTQ9u3bNWXKFA0aNEiS8iwQLViwQFWqVCHILiJWsmEZl3p5SG6aR+6qlXQhiMlvxclms8nHx8cpwE5NTc2zu0iPHj0kKU8qwYIFC5yOq1Spol69eikxMVFt2rRRx44d85SLV+Iu9umnn2rOnDl67rnn1KJFC0kXHgD08vLKsx92enq6hg0bprZt2+rpp5+WJN1+++267bbbNH78+DK580F4eLj8/Pw0Z84cp/ojR45o7dq1jqCsefPmCg4O1kcffeTULjk52fHP+8Uxc+ZM2e32PGko0oUgO3f/8aLy8fFR48aNi/WdN2rUSLt373aqW7t2rc6cOZNv+8DAQMcvYL169XJKQbrpppv0448/qmbNmvn+/F0cFI4dO1bHjx/XbbfdplOnTik6OrpQc7722mvl7++vadOmKTU1VTfeeKOkCyvciYmJ+uijj9SyZUunP4eu6NWrl6QLv2D82bx585yOq1atquuuu06LFy92+jOfk5OjOXPmqF69emrWrJmj/oYbbtCOHTu0aNEix6p71apV1blzZ73xxhv6+eef812Nz8rK0uHDh4v8yxjwZ/fdd582bdqkBQsWaPfu3br99tvVr18/pwfA/+yHH37QypUrHX8nSRdS8CIiIpza9e3bV9u3b7/khgAzZ87UXXfdpapVq7rvYqyglHPCAY9p3bq1iYyMNG+//bZZu3atWbNmjZkyZYoJCQkx1apVM7t373a0HTp0qLHb7WbBggXm66+/dnw2a9YsI8k8+OCD5osvvjDx8fGmSZMm5sorrzR//uOUnZ1trr/+euPn52deeukls3r1avPss8+apk2bGkmOh6SMMWbPnj3miiuuMNdee62Ji4sz69atM8uWLTNTp041vXr1uuw1/frrr6ZOnTqmS5cuJjs72+mz3Ife3n//fUfdsGHDjI+Pj/m///s/p7bHjh0ztWvXNt27d3c85HWpBx8vNnTo0EI9JFrcBx+N+d9Dmvfcc49ZsWKF+fDDD03Tpk1NQECA2b9/v6PdO++8YySZQYMGmeXLl5u5c+eaZs2amQYNGpiwsLACz33xQ4vHjx83drvd3HHHHZfs061bN1O7dm1z7ty5fMe4nGHDhpmQkJDLtsnvwcfnn3/e2Gw288wzz5g1a9aY119/3TRr1swEBARc8sFHY4z5/fffTb9+/Uy1atXM2rVrjTHGnDlzxrRv397Uq1fP/Otf/zKrV682n3/+uXnvvffM7bffbrZs2ZJnTpGRkUaS6dq1a4HX+GcDBgwwkpzuxdmzZ42fn5+RZMaOHevU/nIPPv76669ObS/+ucnOzjbdu3c3drvdvPjii2bVqlVm4sSJpnHjxnkefFy/fr3x9vY21113nfn444/Np59+avr27WtsNptZsGCB03l27NjheHj6gw8+cNRPnjzZSDI2m80cP348z7Xn9lu2bFmRvjNYlySzZMkSx/EPP/xgbDabOXr0qFO7Pn36mPHjxzvVhYeHG7vdbiSZ+++/3+nvhyuvvNK88MILTu03bdpkJJmff/45zzy2bt1qJJmtW7e64aqshSAblrFw4UIzePBgc+WVV5pq1aoZb29v06BBA3PPPfeYvXv3OrU9ePCgiYiIMNWrVzeSnHameOmll0yjRo2M3W43LVq0MO+9957jL/4/O3nypLnvvvtMjRo1TJUqVcyNN95otmzZku+OB0lJSWbYsGGmbt26xtvb29SuXdt06dLFPP/885e9pttvv91UqVLFKdD8s6ioKOPv72+Sk5PNihUrjKQ8/+ea66OPPnKam7uDbEmFapdfkG2MMe+//75p06aN8fHxMQEBAeaWW24xe/bsydP/3XffNU2bNjU+Pj6mWbNmZtasWeaWW25x2v3lUi4OkKdNm2YkmX//+9+X7PP+++8bSWbRokX5jnE5X3zxhZFkvv7660u2yS/IzszMNH//+99N/fr1jZ+fn+nRo4fZtWvXZXcX+XPfQYMGGV9fX7N8+XJjzIVA++mnnzbNmzd3fL+tW7c2jz76qElNTc0zp/j4eCMpTwBakNdee81IMiNHjnSqv/HGG/MNQF0Jso0x5tSpU2bYsGFOfwa///77fHdn+fLLL03v3r1N1apVjZ+fn+ncubP57LPP8lxDTk6OqVWrlpHkFOzkBinXXHNNvtf+zDPPmFq1ajl2JgEKcnGQnfv/0VWrVnUqlStXzrMQkJycbPbs2WPmzZtn6tata/75z386PrvyyivNiy++6NR+48aNRpJJSUnJM4/777/ftGrVyr0XZxEE2YAHzZ0710gymzZtKu2pWMZvv/1mateunSewy09RAmR3jdG6desCt/Era/7yl7+Y0NBQx+o9Li8rK8s0atTIPPXUU6U9FZQjFwfZCxYsMJUqVTLff/+9OXDggFPJLzjO9eGHHxo/Pz/HVq3dunXL869GixcvNpUrV87zZzojI8P4+/ubadOmue/CLIQHH4ESMn/+fB09elStW7eWl5eXtmzZoldeeUXdu3dXly5dSnt6FVJqaqpeeOEF9erVSzVr1tShQ4f06quv6vTp03r44YdLe3r5evnll3XrrbdqwoQJeR5SLUsyMzO1c+dOff3111qyZImmTp0qb2/v0p5WuTBnzhydOXNGjz/+eGlPBeVY+/btlZ2drWPHjqlbt26F7meM0fnz5x07SIWHh+uzzz5zarNq1Sp17Ngxz5/pjz76SJmZmfrb3/7m+gVYEEE2UEKqV6+uBQsW6Pnnn1dGRoZCQkJ077336vnnny/tqVVYdrtdBw8e1EMPPaSTJ0+qSpUq6ty5s2bMmFHib7Qsrn79+umVV15RUlJSmQ6yU1JS1KVLF/n7++uBBx7QmDFjSntK5UZOTo7mzp3rsTd7ovw6c+aMfvjhB8dxUlKSdu3apcDAQDVr1kx33323hgwZon/9619q3769jh8/rrVr16p169aKiorS3Llz5e3trdatW8tut2vHjh0aP3687rzzTlWufCHkGzVqlN58803FxMRo5MiR2rx5s+NNpxebOXOmBg4cWOAD+LiE0l5KB4CyojTSRQAgV+7/f1xccp+1OHfunPnHP/5hGjVqZLy9vU1wcLC59dZbHQ/nL1iwwFxzzTWmWrVqpmrVqqZly5bmxRdfdHrLqzEXHvZt37698fHxMY0aNcrzdmJjjNm3b5+RZFatWlXi111R2YwpxBsoSkhsbKwWL16s77//Xn5+furSpYv++c9/qnnz5pftl5mZqWeffVZz5sxRamqq6tWrpwkTJhTqhQgAAABASSvVdJGEhASNHj1anTp1UlZWliZMmKCIiAjt3bv3snsx3nHHHfrll180c+ZMNW3aVMeOHVNWVpYHZw4AAABcWqmuZF/s119/VVBQkBISEtS9e/d826xcuVJ33XWXfvrppzxvJAIAAADKgjL14GNaWpqkvK/z/LNly5apY8eOevnll/Xhhx+qatWquvnmm/Xcc8/Jz88vT/vMzEyn1w/n5OTo5MmTqlmzptNb+wAAAEqCMUanT59WaGiovLxK92XbZ8+e1blz51wex8fHR76+vm6YUcVVZoJsY4xiYmLUtWtXtWrV6pLtfvrpJ23cuFG+vr5asmSJjh8/7thJIL9XG8fGxmry5MklOXUAAIACHT58uFR3ETp79qzCGlZT6rFsl8cKDg5WUlISgfZllJl0kdGjR2v58uXauHHjZX8AIyIi9OWXXyo1NVUBAQGSpMWLF+u2225TRkZGntXsi1ey09LS1KBBA10TNUGVvPnBAAAAJSv7/FntXPGCTp065YhdSkN6eroCAgJ0aEcj+Vcv/op6+ukcNexwUGlpafL393fjDCuWMrGSPWbMGC1btkwbNmwo8De8kJAQ1a1b1+mHtEWLFjLG6MiRI7ryyiud2tvtdtnt9jzjVPL2VWWCbAAA4CFlJU21WnWbqlUv/lxyVDauo6wr1cQgY4yio6O1ePFirV27VmFhYQX2uf766/Xzzz/rzJkzjrr9+/fLy8urTL/IAQAAoCzINjkuFxSsVIPs0aNHa86cOZo3b56qV6+u1NRUpaam6o8//nC0GT9+vIYMGeI4Hjx4sGrWrKn77rtPe/fu1YYNG/T4449r2LBh+T74CAAAgP/JkXG5oGClGmRPnz5daWlp6tmzp0JCQhxl4cKFjjYpKSlKTk52HFerVk2rV6/WqVOn1LFjR919990aMGCAXn/99dK4BAAAACCPUs3JLswzl/Hx8XnqrrrqKq1evboEZgQAAFCx5ShHriR8uNbbOsrEg48AAADwjGxjlO3C5nKu9LUSgmwAAAALcTWvmpzswind1w4BAAAAFRAr2QAAABaSI6NsVrJLHEE2AACAhZAu4hmkiwAAAABuxko2AACAhbC7iGcQZAMAAFhIzn+LK/1RMIJsAAAAC8l28cFHV/paCTnZAAAAgJuxkg0AAGAh2eZCcaU/CkaQDQAAYCHkZHsG6SIAAAAWkiObsl0oObIV+lyxsbHq1KmTqlevrqCgIA0cOFD79u0rsF9CQoI6dOggX19fNW7cWDNmzHDlkksFQTYAAABKREJCgkaPHq0tW7Zo9erVysrKUkREhDIyMi7ZJykpSVFRUerWrZsSExP11FNPaezYsVq0aJEHZ+460kUAAAAsJMdcKK70L6yVK1c6HcfFxSkoKEg7duxQ9+7d8+0zY8YMNWjQQNOmTZMktWjRQtu3b9eUKVM0aNCg4k7b4wiyAQAALCQ37cOV/pKUnp7uVG+322W32y/bNy0tTZIUGBh4yTabN29WRESEU13fvn01c+ZMnT9/Xt7e3sWZtseRLgIAAGAhruRj/zlAr1+/vgICAhwlNjb2suc1xigmJkZdu3ZVq1atLtkuNTVVderUcaqrU6eOsrKydPz4cde/AA9hJRsAAABFdvjwYfn7+zuOC1rFjo6O1u7du7Vx48YCx7bZnFfazX9f5X5xfVlGkA0AAGAhOcamHFP8YDW3r7+/v1OQfTljxozRsmXLtGHDBtWrV++ybYODg5WamupUd+zYMVWuXFk1a9Ys3qRLAUE2AACAhbgrJ7swjDEaM2aMlixZovXr1yssLKzAPuHh4frss8+c6latWqWOHTuWm3xsiZxsAAAAS8mWl8ulsEaPHq05c+Zo3rx5ql69ulJTU5Wamqo//vjD0Wb8+PEaMmSI43jUqFE6dOiQYmJi9N1332nWrFmaOXOmxo0b59bvoaQRZAMAAKBETJ8+XWlpaerZs6dCQkIcZeHChY42KSkpSk5OdhyHhYVpxYoVWr9+vdq1a6fnnntOr7/+ernavk8iXQQAAMBSjIs52aYIfXMfWLyc+Pj4PHU9evTQzp07izKtMocgGwAAwEI8mZNtZQTZAAAAFpJtvJRtip8xnO3C2yKthJxsAAAAwM1YyQYAALCQHNmU48I6a45Yyi4MgmwAAAALISfbM0gXAQAAANyMlWwAAAALcf3BR9JFCoMgGwAAwEIu5GQXP+XDlb5WQpANAABgITlFfDV63v6sZBcGOdkAAACAm7GSDQAAYCHkZHsGQTYAAICF5MiLfbI9gCAbAADAQrKNTdnGhX2yXehrJeRkAwAAAG7GSjYAAICFZLu4u0g26SKFQpANAABgITnGSzkuPPiYw4OPhUKQDQAAYCGsZHsGOdkAAACAm7GSDQAAYCE5cm2HkBz3TaVCI8gGAACwENf3ySYRojAIsgEAACzE9Tc+EmQXBt8SAAAA4GasZAMAAFhIjmzKkSs52bzxsTAIsgEAACyEdBHPKNVvKTY2Vp06dVL16tUVFBSkgQMHat++fYXuv2nTJlWuXFnt2rUruUkCAABUILn7ZLtSULBS/ZYSEhI0evRobdmyRatXr1ZWVpYiIiKUkZFRYN+0tDQNGTJEffr08cBMAQAAgMIr1XSRlStXOh3HxcUpKChIO3bsUPfu3S/b94EHHtDgwYNVqVIlLV26tARnCQAAUHHkGJtyXNkn24W+VlKm1vvT0tIkSYGBgZdtFxcXpx9//FETJ04scMzMzEylp6c7FQAAAKvKcTFVhH2yC6fMfEvGGMXExKhr165q1arVJdsdOHBATz75pObOnavKlQteiI+NjVVAQICj1K9f353TBgAAAPIoM0F2dHS0du/erfnz51+yTXZ2tgYPHqzJkyerWbNmhRp3/PjxSktLc5TDhw+7a8oAAADlTo7xcrmgYGViC78xY8Zo2bJl2rBhg+rVq3fJdqdPn9b27duVmJio6OhoSVJOTo6MMapcubJWrVql3r17O/Wx2+2y2+0lOn8AAIDyIls2Zbuw17Urfa2kVINsY4zGjBmjJUuWaP369QoLC7tse39/f33zzTdOdW+//bbWrl2rTz75pMD+AAAAVufqajQr2YVTqkH26NGjNW/ePH366aeqXr26UlNTJUkBAQHy8/OTdCHd4+jRo5o9e7a8vLzy5GsHBQXJ19f3snncAAAAgCeVapA9ffp0SVLPnj2d6uPi4nTvvfdKklJSUpScnOzhmQEAAFRM2XIt5SPbfVOp0Eo9XaQg8fHxl/180qRJmjRpknsmBAAAUMGRLuIZZeLBRwAAAHhGtvFStguBsit9rYRvCQAAAHAzVrIBAAAsxMimHBdysg1b+BUKQTYAAICFkC7iGQTZAAAAFpJjbMoxxV+NdqWvlfCrCAAAAOBmrGQDAABYSLa8lO3COqsrfa2EIBsAAMBCSBfxDIJsAAAAC8mRl3JcWI12pa+V8C0BAAAAbsZKNgAAgIVkG5uyXUj5cKWvlRBkAwAAWAg52Z5BuggAAICFGOOlHBeKKeLLaDZs2KABAwYoNDRUNptNS5cuvWz79evXy2az5Snff/+9C1fteaxkAwAAoMRkZGSobdu2uu+++zRo0KBC99u3b5/8/f0dx7Vr1y6J6ZUYgmwAAAALyZZN2XIhJ7uIfSMjIxUZGVnk8wQFBalGjRpF7ldWkC4CAABgITnmf3nZxSsXxklPT3cqmZmZbp1n+/btFRISoj59+mjdunVuHdsTCLIBAABQZPXr11dAQICjxMbGumXckJAQvfvuu1q0aJEWL16s5s2bq0+fPtqwYYNbxvcU0kUAAAAsJPcBRlf6S9Lhw4edcqbtdrvLc5Ok5s2bq3nz5o7j8PBwHT58WFOmTFH37t3dcg5PYCUbAADAQnJkc7lIkr+/v1NxV5Cdn86dO+vAgQMlNn5JYCUbAADAQsrjy2gSExMVEhLi8fO6giAbAAAAJebMmTP64YcfHMdJSUnatWuXAgMD1aBBA40fP15Hjx7V7NmzJUnTpk1To0aNdPXVV+vcuXOaM2eOFi1apEWLFpXWJRQLQTYAAICFuCsnu7C2b9+uXr16OY5jYmIkSUOHDlV8fLxSUlKUnJzs+PzcuXMaN26cjh49Kj8/P1199dVavny5oqKiij3n0kCQDQAAYCE5cvG16kXcJ7tnz54yxlzy8/j4eKfjv//97/r73/9enKmVKQTZAAAAFmL+9PBicfujYOwuAgAAALgZK9kAAAAWkvvmRlf6o2AE2QAAABbi6QcfrYogGwAAwEJYyfYMfhUBAAAA3IyVbAAAAAvJcXF3EVf6WglBNgAAgIWQLuIZBNkAAAAWQpDtGeRkAwAAAG7GSjYAAICFsJLtGQTZAAAAFkKQ7RkE2QAAABZi5NoOIcZ9U6nQyMkGAAAA3IyVbAAAAAshXcQzCLIBAAAshCDbM0gXAQAAANyMlWwAAAALYSXbMwiyAQAALIQg2zMIsgEAACzEGJuMC4GyK32thJxsAAAAwM1YyQYAALCQHNlcehmNK32thCAbAADAQsjJ9oxSTReJjY1Vp06dVL16dQUFBWngwIHat2/fZfssXrxYN954o2rXri1/f3+Fh4fr888/99CMAQAAyrfcnGxXCgpWqkF2QkKCRo8erS1btmj16tXKyspSRESEMjIyLtlnw4YNuvHGG7VixQrt2LFDvXr10oABA5SYmOjBmQMAAACXVqrpIitXrnQ6jouLU1BQkHbs2KHu3bvn22fatGlOxy+++KI+/fRTffbZZ2rfvn1JTRUAAKBCIF3EM8pUTnZaWpokKTAwsNB9cnJydPr06SL1AQAAsCq28POMMhNkG2MUExOjrl27qlWrVoXu969//UsZGRm644478v08MzNTmZmZjuP09HSX5woAAFBeGRdXsgmyC6fM7JMdHR2t3bt3a/78+YXuM3/+fE2aNEkLFy5UUFBQvm1iY2MVEBDgKPXr13fXlAEAAIB8lYkge8yYMVq2bJnWrVunevXqFarPwoULNXz4cH300Ue64YYbLtlu/PjxSktLc5TDhw+7a9oAAADljpFkjAultC+gnCjVdBFjjMaMGaMlS5Zo/fr1CgsLK1S/+fPna9iwYZo/f7769+9/2bZ2u112u90d0wUAACj3cmSTjZfRlLhSDbJHjx6tefPm6dNPP1X16tWVmpoqSQoICJCfn5+kCyvRR48e1ezZsyVdCLCHDBmi1157TZ07d3b08fPzU0BAQOlcCAAAQDnBg4+eUarpItOnT1daWpp69uypkJAQR1m4cKGjTUpKipKTkx3H77zzjrKysjR69GinPg8//HBpXAIAAACQR6mnixQkPj7e6Xj9+vUlMxkAAAALyDE22dgnu8SVmS38AAAAUPJyH2B0pT8KRpANAABgIeRke0aZ2MIPAAAAqEhYyQYAALAQVrI9gyAbAADAQnjw0TNIFwEAAADcjJVsAAAAC2F3Ec8gyAYAALCQC0G2KznZbpxMBUaQDQAAYCE8+OgZ5GQDAAAAbsZKNgAAgIWY/xZX+qNgBNkAAAAWQrqINHv27GL1a9eundq0aVOotgTZAAAAVsJStuLi4orV77777iPIBgAAQOnbsGGDXnnlFe3YsUMpKSlasmSJBg4ceNk+CQkJiomJ0Z49exQaGqq///3vGjVqlNvmtG7dOreNdSk8+AgAAGAl/00XKW5REdNFMjIy1LZtW7355puFap+UlKSoqCh169ZNiYmJeuqppzR27FgtWrSoOFdbaljJBgAAsBBPv4wmMjJSkZGRhW4/Y8YMNWjQQNOmTZMktWjRQtu3b9eUKVM0aNCgop28kA4fPqyDBw/q999/V+3atXX11VfLbre7NCZBNgAAgIWU9QcfN2/erIiICKe6vn37aubMmTp//ry8vb3dcp5Dhw5pxowZmj9/vg4fPizzp98efHx81K1bN91///0aNGiQvLyKnvxBuggAAACKLD093alkZma6ZdzU1FTVqVPHqa5OnTrKysrS8ePH3XKOhx9+WK1bt9aBAwf07LPPas+ePUpLS9O5c+eUmpqqFStWqGvXrnrmmWfUpk0bbdu2rcjnYCUbAADASoqRV52nv6T69es7VU+cOFGTJk1yYWL/Y7M5zy93lfni+uLy8fHRjz/+qNq1a+f5LCgoSL1791bv3r01ceJErVixQocOHVKnTp2KdA6CbAAAAAtxV0724cOH5e/v76h3NYc5V3BwsFJTU53qjh07psqVK6tmzZpuOccrr7xS6LZRUVHFOgfpIgAAAFZi3FAk+fv7OxV3Bdnh4eFavXq1U92qVavUsWNHt+Vj/1nv3r116tSpPPXp6enq3bt3scclyAYAAECJOXPmjHbt2qVdu3ZJurBF365du5ScnCxJGj9+vIYMGeJoP2rUKB06dEgxMTH67rvvNGvWLM2cOVPjxo0rkfmtX79e586dy1N/9uxZffnll8Uel3QRAAAAC/H07iLbt29Xr169HMcxMTGSpKFDhyo+Pl4pKSmOgFuSwsLCtGLFCj366KN66623FBoaqtdff93t2/ft3r3b8d979+51SlHJzs7WypUrVbdu3WKPT5ANAABgNR58NXrPnj2dtse7WHx8fJ66Hj16aOfOnSU4K6ldu3ay2Wyy2Wz5poX4+fnpjTfeKPb4RQ6yd+7cKW9vb7Vu3VqS9OmnnyouLk4tW7bUpEmT5OPjU+zJAAAAoGSV9X2yPSUpKUnGGDVu3Fhff/21004jPj4+CgoKUqVKlYo9fpGD7AceeEBPPvmkWrdurZ9++kl33XWXbr31Vn388cf6/fffHW/nAQAAAMqqhg0bSpJycnJKZPwiB9n79+9Xu3btJEkff/yxunfvrnnz5mnTpk266667CLIBAADKsj/tEFLs/uXcsmXLFBkZKW9vby1btuyybW+++eZinaPIQbYxxhHxr1mzRjfddJOkCxuSu+stPAAAACgptv8WV/qXbwMHDlRqaqqCgoI0cODAS7az2WzKzs4u1jmKHGR37NhRzz//vG644QYlJCRo+vTpki7ktVz8CkwAAACgrPlzikhJpYsUeZ/sadOmaefOnYqOjtaECRPUtGlTSdInn3yiLl26uH2CAAAAcCM3vYwGl1fklew2bdrom2++yVP/yiuvuPQEJgAAADyAnOxL2rRpkzp27OiWt1e67Y2Pvr6+JfKqSwAAALiRsbleKqjIyEgdPXrULWPxWnUAAABAuuxLc4qKNz4CAABYiDEXiiv9UTCCbAAAACshJ9th9uzZTsdZWVlavHixgoKCHHVDhgwp1tjFDrLPnTunpKQkNWnSRJUrE6sDAACUC67mVVegnOy4uDin4/Pnz+uTTz6Rn5+fpAv7ZHssyP799981ZswYffDBB5IuvAGycePGGjt2rEJDQ/Xkk08WayIAAACAJ61bt87puHr16po3b54aN27s8thFfvBx/Pjx+r//+z+tX79evr6+jvobbrhBCxcudHlCAAAAKDk243pBwYq8kr106VItXLhQnTt3ls32v38uaNmypX788Ue3Tg4AAABuRk62RxQ5yP7111+dksFzZWRkOAXdAAAAKIPIyb6kp556SoGBgW4Zq8jpIp06ddLy5csdx7mB9Xvvvafw8HC3TAoAAADwtPHjx6tGjRpuGavIK9mxsbHq16+f9u7dq6ysLL322mvas2ePNm/erISEBLdMCgAAACWEdBEnw4YN0wMPPKDrrrvOreMWeSW7S5cu2rRpk37//Xc1adJEq1atUp06dbR582Z16NDBrZMDAACAmxk3lAokPj5ec+bM0a233qomTZqoWbNmuuWWW7Rp0yaXxi3WBtetW7d2bOH3Z5988oluu+02lyYEAACAEsRKdh7vvPOO/vKXv+iRRx5Rdna2Nm3apF69emn27Nm66667ijVmkVays7KytGfPHu3fv9+p/tNPP1Xbtm119913F2sSAAAAQGl59dVXtWDBAo0ZM0aPPPKIPv74Y7300kuaPHlysccsdJC9d+9eNWvWTG3atFGLFi30l7/8Rb/88ot69OihoUOH6sYbb9QPP/xQ7IkAAADAA3J3F3GlVCBeXl7q169fnvqbb75ZSUlJxR630OkiTz75pMLCwvT6669r7ty5Wrhwob799lv97W9/07///W9Vr1692JMAAACAZ7j6QpmK9jKa4OBgJSQkqEmTJk71X3zxhRo0aFDscQu9kv3111/rlVde0U033aTp06dLkh5//HH94x//KHaAHRsbq06dOql69eoKCgrSwIEDtW/fvgL7JSQkqEOHDvL19VXjxo01Y8aMYp0fAADAcnjw0cnQoUMVHR2t6OhozZ07V7Nnz9YDDzyghx9+WE888USxxy30SvaxY8dUt25dSVKNGjVUpUoV9ejRo9gnli4Ey6NHj1anTp2UlZWlCRMmKCIiQnv37lXVqlXz7ZOUlKSoqCiNHDlSc+bM0aZNm/TQQw+pdu3aGjRokEvzAQAAgLU8//zzjkXbOXPmyNvbW1dffbUWL16sqKioYo9b6CDbZrPJy+t/C99eXl7y9vYu9oklaeXKlU7HcXFxCgoK0o4dO9S9e/d8+8yYMUMNGjTQtGnTJEktWrTQ9u3bNWXKFIJsAAAAFInNZtPw4cM1fPhwt45b6CDbGKNmzZo53vB45swZtW/f3inwlqSTJ08WezJpaWmSdNnXWW7evFkRERFOdX379tXMmTN1/vx5lwN/AACAiswmF3Oy3TaT8sMY44iBC6vQQXZcXFyRJ1QUxhjFxMSoa9euatWq1SXbpaamqk6dOk51derUUVZWlo4fP66QkBCnzzIzM5WZmek4Tk9Pd+/EAQAAUK60aNFCzzzzjG677Tb5+Phcst2BAwc0depUNWzYUE8++WSRzlHoIHvo0KFFGriooqOjtXv3bm3cuLHAthf/JmGMybdeuvBwpSt7HAIAAFQorm7DVwG28Hvrrbf0xBNPaPTo0YqIiFDHjh0VGhoqX19f/fbbb9q7d682btyovXv3Kjo6Wg899FCRz1GsNz6625gxY7Rs2TJt2LBB9erVu2zb4OBgpaamOtUdO3ZMlStXVs2aNfO0Hz9+vGJiYhzH6enpql+/vnsmDgAAUN7wxkf17t1b27Zt01dffaWFCxdq3rx5OnjwoP744w/VqlVL7du315AhQ/S3v/1NNWrUKNY5SjXINsZozJgxWrJkidavX6+wsLAC+4SHh+uzzz5zqlu1apU6duyYbz623W6X3W5325wBAADKNYJshy5duqhLly4lMnaRXqvubqNHj9acOXM0b948Va9eXampqUpNTdUff/zhaDN+/HgNGTLEcTxq1CgdOnRIMTEx+u677zRr1izNnDlT48aNK41LAAAAQAV04sQJx252xVGqQfb06dOVlpamnj17KiQkxFEWLlzoaJOSkqLk5GTHcVhYmFasWKH169erXbt2eu655/T666+zfR8AAEAh5L7x0ZVSURlj9Pnnn+uOO+5QaGionnvuuWKPVerpIgWJj4/PU9ejRw/t3LmzBGYEAABQwZEuksfBgwc1a9YsffDBB/r5558VERGhDz/8ULfcckuxxyzWSvb8+fOVkZGR578BAABQxvFadUkXtnmeP3+++vTpoyZNmmjp0qUaO3asjhw5ouXLl+uOO+5w6bm+Yq1kP/DAA7ruuuvUuHFjp/8GAAAAyoPQ0FB5e3vrr3/9q6ZMmaL27du7dfxiBdl/TvMoTMoHAAAAygZX86orSk52dna2KleuLJvNlucN5u5Qqg8+AgAAwMNyX0bjSqkAUlNTNXXqVO3atUvXXHON2rZtq6lTp+Z5H0txEWQDAABYCTnZkiRfX1/dfffdWrt2rfbv36+bbrpJr776qho0aKCoqCh99NFHyszMLPb4BNkAAACwtCZNmuiFF17QoUOHtHTpUlWpUkX33HOPgoODiz1mmXitOgAAADyDnOxL8/LyUlRUlKKiovTrr7/qww8/LPZYBNkAAABWwj7ZhVK7dm3FxMQUuz9BNgAAgJW4+tbGChBkP/vss8Xq17NnT3Xv3r1QbYsVZL/zzjuqU6dOnv8GAAAAyrqkpKRi9WvXrl2h2xYryB48eHC+/w0AAIAyjnQRxcXFlfg5SBcBAACwEoJsjyDIBgAAsBB2F/EM9skGAAAA3IwgGwAAACXq7bffVlhYmHx9fdWhQwd9+eWXl2y7fv162Wy2POX777/34IxdV+Qge/bs2Tp48GAJTAUAAAAlzsOvVV+4cKEeeeQRTZgwQYmJierWrZsiIyOVnJx82X779u1TSkqKo1x55ZVFO3EpK3JO9n333ac333xT586d0+7du1WpUiW1bNlSw4YNk7+/f0nMEQAAAOXU1KlTNXz4cI0YMUKSNG3aNH3++eeaPn26YmNjL9kvKChINWrU8NAs3a/IK9nGGEVHR2vKlCk6deqUjh07pilTpqhJkyZKTEwsiTkCAADATXIffHSlSFJ6erpTyczMzHOuc+fOaceOHYqIiHCqj4iI0FdffXXZebZv314hISHq06eP1q1b57brv9gVV1yhwMDAPKVmzZqqW7euevToUawt/4qVkz1ixAgdPHhQixYt0tKlS3Xw4EH1799fDz/8cHGGAwAAgCe5IVWkfv36CggIcJT8VqWPHz+u7OzsPC8urFOnjlJTU/OdWkhIiN59910tWrRIixcvVvPmzdWnTx9t2LDBxYvO3z/+8Q95eXmpf//+mjx5siZNmqT+/fvLy8tLo0ePVrNmzfTggw/qvffeK9K4xdrCLyYmRpUqVfrfIJUr6+9//7s6duxYnOEAAADgKW7aJ/vw4cNOqcJ2u/2SXWw2m/MQxuSpy9W8eXM1b97ccRweHq7Dhw9rypQphX6leVFs3LhRzz//vEaNGuVU/84772jVqlVatGiR2rRpo9dff10jR44s9LhFXsmuUaOGjhw5kqf+4i8aAAAAFZe/v79TyS/IrlWrlipVqpRn1frYsWN5Vrcvp3Pnzjpw4IDLc87P559/rhtuuCFPfZ8+ffT5559LkqKiovTTTz8VadwiB9kREREaPny4PvnkEx09elTJycmaP3++RowYobvvvruowwEAAMCD3JWTXRg+Pj7q0KGDVq9e7VS/evVqdenSpdDjJCYmKiQkpPAnLoLAwEB99tlneeo/++wzBQYGSpIyMjJUvXr1Io1b5HSRt99+Ww8//LDuvPNOR53dbld0dLReeOGFog4HAAAAT/Lwa9VjYmJ0zz33qGPHjgoPD9e7776r5ORkR3rG+PHjdfToUc2ePVvShd1HGjVqpKuvvlrnzp3TnDlztGjRIi1atMiFSV/aM888owcffFDr1q3TtddeK5vNpq+//lorVqzQjBkzJF34paBHjx5FGrfIQXZgYKA+/PBDvf322/rxxx/l7e2tJk2ayNfXt6hDAQAAwMM8/Vr1O++8UydOnNCzzz6rlJQUtWrVSitWrFDDhg0lSSkpKU57Zp87d07jxo3T0aNH5efnp6uvvlrLly9XVFRU8Sd9GSNHjlTLli315ptvavHixTLG6KqrrlJCQoJjtf2xxx4r8rg2Y4yl3kCfnp6ugIAAdbrlOVX25hcDAABQsrLOn9W2T59RWlpaqT6/lhsDNRv3oirZix8DZWee1f4pT5X69ZR1xdpdBAAAAOWUh9NFyoPs7GwtXbpU3333nWw2m1q2bKmbb77ZaTe9oiLIBgAAsBKCbCc//PCDoqKidPToUTVv3lzGGO3fv1/169fX8uXL1aRJk2KNW6yX0QAAAKB88uTuIuXB2LFj1aRJEx0+fFg7d+5UYmKikpOTFRYWprFjxxZ7XFayAQAAYFkJCQnasmWLY7s+SapZs6ZeeuklXX/99cUelyAbAADASkgXcWK323X69Ok89WfOnJGPj0+xxyVdBAAAwEqMG0oFctNNN+n+++/X1q1bZYyRMUZbtmzRqFGjdPPNNxd7XIJsAAAACyEn29nrr7+uJk2aKDw8XL6+vvL19dX111+vpk2b6rXXXiv2uKSLAAAAwLJq1KihTz/9VAcOHND3338vY4xatmyppk2bujQuQTYAAICVkJOdryuvvFJXXnml28YjyAYAALAQT79WvSyKiYkpdNupU6cW6xwE2QAAAFbCSrYSExML1c5msxX7HATZAAAAsJR169aV+DkIsgEAAKyElWyPIMgGAACwENt/iyv9UTD2yQYAAADcjJVsAAAAKyFdxCMIsgEAACyELfw8gyAbAADASljJ9ghysgEAAAA3YyUbAADAaliNLnEE2QAAABZCTrZnEGQDAABYCTnZHlGqOdkbNmzQgAEDFBoaKpvNpqVLlxbYZ+7cuWrbtq2qVKmikJAQ3XfffTpx4kTJTxYAAAAopFINsjMyMtS2bVu9+eabhWq/ceNGDRkyRMOHD9eePXv08ccfa9u2bRoxYkQJzxQAAKBiyE0XcaWgYKWaLhIZGanIyMhCt9+yZYsaNWqksWPHSpLCwsL0wAMP6OWXXy6pKQIAAFQspIt4RLnawq9Lly46cuSIVqxYIWOMfvnlF33yySfq37//JftkZmYqPT3dqQAAAFgVK9meUe6C7Llz5+rOO++Uj4+PgoODVaNGDb3xxhuX7BMbG6uAgABHqV+/vgdnDAAAACsqV0H23r17NXbsWP3jH//Qjh07tHLlSiUlJWnUqFGX7DN+/HilpaU5yuHDhyVJNk9NGgAAoCwxbigoULnawi82NlbXX3+9Hn/8cUlSmzZtVLVqVXXr1k3PP/+8QkJC8vSx2+2y2+15ByPKBgAAVkROtkeUqyD7999/V+XKzlOuVKmSJMmYot1xGz8hAADAgngZjWeUarrImTNntGvXLu3atUuSlJSUpF27dik5OVnShVSPIUOGONoPGDBAixcv1vTp0/XTTz9p06ZNGjt2rK699lqFhoaWxiUAAADkj9QKSyvVlezt27erV69ejuOYmBhJ0tChQxUfH6+UlBRHwC1J9957r06fPq0333xTjz32mGrUqKHevXvrn//8Z5HPbSNdBAAAWBHpIh5RqkF2z549L5vmER8fn6duzJgxGjNmTAnOCgAAoOKyGSNbEdNsL+6PgpWrnGy3IqEIAABYESvZHlGutvBzJ7JFAAAAUFKsu5INAABgQewu4hkE2QAAAFZCuohHWDZdBAAAoGQRjVoZK9kAAAAWQrqIZxBkAwAAlIgyus0C6SIeQZANAABgIaxkewY52QAAAICbWXYl26jM/iMOAABAySFdxCMsG2TLEGIDAABrIuWj5Fk2yGYlGwAAWJIxF4or/VEg6+Zk8/MBAACAEmLplWwAAIASU0b/yZzdRTzDuivZZfUnHwAAoCQZN5QievvttxUWFiZfX1916NBBX3755WXbJyQkqEOHDvL19VXjxo01Y8aMop+0lFk3yOa3MAAAYEG2HNdLUSxcuFCPPPKIJkyYoMTERHXr1k2RkZFKTk7Ot31SUpKioqLUrVs3JSYm6qmnntLYsWO1aNEiN1y951g2yCbGBgAAKHlTp07V8OHDNWLECLVo0ULTpk1T/fr1NX369Hzbz5gxQw0aNNC0adPUokULjRgxQsOGDdOUKVM8PHPXWDbIBgAAsCQPpoucO3dOO3bsUEREhFN9RESEvvrqq3z7bN68OU/7vn37avv27Tp//nzhT17KLPvgIwAAgBW568HH9PR0p3q73S673e5Ud/z4cWVnZ6tOnTpO9XXq1FFqamq+46empubbPisrS8ePH1dISEjxJ+9BrGQDAABYSe4+2a4USfXr11dAQICjxMbGXvKUNpvzhhPGmDx1BbXPr74sYyUbAAAARXb48GH5+/s7ji9exZakWrVqqVKlSnlWrY8dO5ZntTpXcHBwvu0rV66smjVrumHmnsFKNgAAgIXkpou4UiTJ39/fqeQXZPv4+KhDhw5avXq1U/3q1avVpUuXfOcXHh6ep/2qVavUsWNHeXt7u+dL8ACCbAAAACvx8D7ZMTExev/99zVr1ix99913evTRR5WcnKxRo0ZJksaPH68hQ4Y42o8aNUqHDh1STEyMvvvuO82aNUszZ87UuHHjXLlqjyNdBAAAwEI8/cbHO++8UydOnNCzzz6rlJQUtWrVSitWrFDDhg0lSSkpKU57ZoeFhWnFihV69NFH9dZbbyk0NFSvv/66Bg0aVPxJlwKCbAAAAJSohx56SA899FC+n8XHx+ep69Gjh3bu3FnCsypZBNkAAABW8qcdQordHwUiyAYAALAQT6eLWBUPPgIAAABuxko2AACAlRRjh5A8/VEggmwAAAALIV3EMwiyAQAArCTHXCiu9EeByMkGAAAA3IyVbAAAACshJ9sjCLIBAAAsxCYXc7LdNpOKjSAbAADASngZjUeQkw0AAAC4GSvZAAAAFsIWfp5BkA0AAGAlPPjoEQTZAAAAFmIzRjYX8qpd6Wsl5GQDAAAAbsZKNgAAgJXk/Le40h8FIsgGAACwENJFPIMgGwAAwEp48NEjyMkGAAAA3IyVbAAAACvhjY8eQZANAABgIbyMxjNKNV1kw4YNGjBggEJDQ2Wz2bR06dIC+2RmZmrChAlq2LCh7Ha7mjRpolmzZpX8ZAEAACqC3JVsVwoKVKor2RkZGWrbtq3uu+8+DRo0qFB97rjjDv3yyy+aOXOmmjZtqmPHjikrK6uEZwoAAAAUXqkG2ZGRkYqMjCx0+5UrVyohIUE//fSTAgMDJUmNGjUqodkBAABUPLacC8WV/ihYudpdZNmyZerYsaNefvll1a1bV82aNdO4ceP0xx9/lPbUAAAAygfSRTyiXD34+NNPP2njxo3y9fXVkiVLdPz4cT300EM6efLkJfOyMzMzlZmZ6ThOT0/31HQBAABgUeVqJTsnJ0c2m01z587Vtddeq6ioKE2dOlXx8fGXXM2OjY1VQECAo9SvX9/DswYAAChDjBsKClSuguyQkBDVrVtXAQEBjroWLVrIGKMjR47k22f8+PFKS0tzlMOHD3tqugAAAGVO7mvVXSkoWLkKsq+//nr9/PPPOnPmjKNu//798vLyUr169fLtY7fb5e/v71QAAAAsi5xsjyjVIPvMmTPatWuXdu3aJUlKSkrSrl27lJycLOnCKvSQIUMc7QcPHqyaNWvqvvvu0969e7VhwwY9/vjjGjZsmPz8/ErjEgAAAIA8SjXI3r59u9q3b6/27dtLkmJiYtS+fXv94x//kCSlpKQ4Am5JqlatmlavXq1Tp06pY8eOuvvuuzVgwAC9/vrrpTJ/AACAcsdIynGhsJBdKKW6u0jPnj1lLvNPDvHx8XnqrrrqKq1evboEZwUAAFBxuZpXTU524ZSrLfwAAADgIiPX8qqJsQulXD34CAAAAJQHrGQDAABYias7hJAuUigE2QAAAFaSI8nmYn8UiCAbAADAQnjw0TPIyQYAAADcjJVsAAAAKyEn2yMIsgEAAKyEINsjCLIBAACshCDbI8jJBgAAANyMlWwAAAArYQs/jyDIBgAAsBC28PMMgmwAAAArISfbI8jJBgAAANyMlWwAAAAryTGSzYXV6BxWsguDlWwAAAAryU0XcaWUkN9++0333HOPAgICFBAQoHvuuUenTp26bJ97771XNpvNqXTu3LnE5lhYrGQDAACgTBg8eLCOHDmilStXSpLuv/9+3XPPPfrss88u269fv36Ki4tzHPv4+JToPAuDIBsAAMBSXF2NLpmV7O+++04rV67Uli1bdN1110mS3nvvPYWHh2vfvn1q3rz5Jfva7XYFBweXyLyKi3QRAAAAKymj6SKbN29WQECAI8CWpM6dOysgIEBfffXVZfuuX79eQUFBatasmUaOHKljx46VyByLgpVsAAAAK8kxcmk1+r8PPqanpztV2+122e32Yg+bmpqqoKCgPPVBQUFKTU29ZL/IyEjdfvvtatiwoZKSkvTMM8+od+/e2rFjh0vzcRUr2QAAACiy+vXrOx5QDAgIUGxsbL7tJk2alOfBxIvL9u3bJUk2W95XURpj8q3Pdeedd6p///5q1aqVBgwYoP/85z/av3+/li9f7p4LLSZWsgEAAKzE5FworvSXdPjwYfn7+zuqL7VqHB0drbvuuuuyQzZq1Ei7d+/WL7/8kuezX3/9VXXq1Cn09EJCQtSwYUMdOHCg0H1KAkE2AACAlbjpjY/+/v5OQfal1KpVS7Vq1SqwXXh4uNLS0vT111/r2muvlSRt3bpVaWlp6tKlS6Gnd+LECR0+fFghISGF7lMSSBcBAACwkhzjeikBLVq0UL9+/TRy5Eht2bJFW7Zs0ciRI3XTTTc57Sxy1VVXacmSJZKkM2fOaNy4cdq8ebMOHjyo9evXa8CAAapVq5ZuvfXWEplnYRFkAwAAoEyYO3euWrdurYiICEVERKhNmzb68MMPndrs27dPaWlpkqRKlSrpm2++0S233KJmzZpp6NChatasmTZv3qzq1auXxiU4kC4CAABgJW5KFykJgYGBmjNnTgGn/9/5/fz89Pnnn5fYfFxBkA0AAGAlRi4G2W6bSYVGkA0AAGAlZXgluyIhJxsAAABwM1ayAQAArCQnR5IL+2TnuNDXQgiyAQAArIR0EY8gyAYAALASgmyPICcbAAAAcDNWsgEAAKwkx8ilffhK6I2PFQ1BNgAAgIUYkyNjiv/woit9rYQgGwAAwEqMcW01mpzsQiEnGwAAAHAzVrIBAACsxLiYk81KdqEQZAMAAFhJTo5kcyGvmpzsQiFdBAAAAHAzVrIBAACshHQRjyDIBgAAsBCTkyPjQroIW/gVDkE2AACAlbCS7RHkZAMAAABuxko2AACAleQYycZKdkkjyAYAALASYyS5soUfQXZhEGQDAABYiMkxMi6sZBuC7EIp1ZzsDRs2aMCAAQoNDZXNZtPSpUsL3XfTpk2qXLmy2rVrV2LzAwAAAIqjVIPsjIwMtW3bVm+++WaR+qWlpWnIkCHq06dPCc0MAACggjI5rhcUqFTTRSIjIxUZGVnkfg888IAGDx6sSpUqFWn1GwAAwOpIF/GMcreFX1xcnH788UdNnDixtKcCAABQ/rCS7RHl6sHHAwcO6Mknn9SXX36pypULN/XMzExlZmY6jtPS0iRJ2efPlsgcAQAA/iw35igrK8BZOu/Su2iydN59k6nAyk2QnZ2drcGDB2vy5Mlq1qxZofvFxsZq8uTJeep3rnjBndMDAAC4rNOnTysgIKDUzu/j46Pg4GBtTF3h8ljBwcHy8fFxw6wqLpspI79W2Ww2LVmyRAMHDsz381OnTumKK65QpUqVHHU5OTkyxqhSpUpatWqVevfunaffxSvZOTk5OnnypGrWrCmbzeb26yhN6enpql+/vg4fPix/f//Sng4KwP0qf7hn5Qv3q/ypqPfMGKPTp08rNDRUXl6lm6l79uxZnTt3zuVxfHx85Ovr64YZVVzlZiXb399f33zzjVPd22+/rbVr1+qTTz5RWFhYvv3sdrvsdrtTXY0aNUpqmmWCv79/hfo/p4qO+1X+cM/KF+5X+VMR71lprmD/ma+vL8Gxh5RqkH3mzBn98MMPjuOkpCTt2rVLgYGBatCggcaPH6+jR49q9uzZ8vLyUqtWrZz6BwUFydfXN089AAAAUJpKNcjevn27evXq5TiOiYmRJA0dOlTx8fFKSUlRcnJyaU0PAAAAKJZSDbJ79ux52Sdt4+PjL9t/0qRJmjRpknsnVY7Z7XZNnDgxT3oMyibuV/nDPStfuF/lD/cMFUmZefARAAAAqCjK3ctoAAAAgLKOIBsAAABwM4JsAAAAwM0IssuZgwcPavjw4QoLC5Ofn5+aNGmiiRMn5tlYPjk5WQMGDFDVqlVVq1YtjR07Nk+bb775Rj169JCfn5/q1q2rZ599tsy88rWieeGFF9SlSxdVqVLlkvu0c8/KtrffflthYWHy9fVVhw4d9OWXX5b2lCxrw4YNGjBggEJDQ2Wz2bR06VKnz40xmjRpkkJDQ+Xn56eePXtqz549Tm0yMzM1ZswY1apVS1WrVtXNN9+sI0eOePAqrCM2NladOnVS9erVFRQUpIEDB2rfvn1ObbhnqIgIssuZ77//Xjk5OXrnnXe0Z88evfrqq5oxY4aeeuopR5vs7Gz1799fGRkZ2rhxoxYsWKBFixbpsccec7RJT0/XjTfeqNDQUG3btk1vvPGGpkyZoqlTp5bGZVV4586d0+23364HH3ww38+5Z2XbwoUL9cgjj2jChAlKTExUt27dFBkZyRajpSQjI0Nt27bVm2++me/nL7/8sqZOnao333xT27ZtU3BwsG688UadPn3a0eaRRx7RkiVLtGDBAm3cuFFnzpzRTTfdpOzsbE9dhmUkJCRo9OjR2rJli1avXq2srCxFREQoIyPD0YZ7hgrJoNx7+eWXTVhYmON4xYoVxsvLyxw9etRRN3/+fGO3201aWpoxxpi3337bBAQEmLNnzzraxMbGmtDQUJOTk+O5yVtMXFycCQgIyFPPPSvbrr32WjNq1Cinuquuuso8+eSTpTQj5JJklixZ4jjOyckxwcHB5qWXXnLUnT171gQEBJgZM2YYY4w5deqU8fb2NgsWLHC0OXr0qPHy8jIrV6702Nyt6tixY0aSSUhIMMZwz1BxsZJdAaSlpSkwMNBxvHnzZrVq1UqhoaGOur59+yozM1M7duxwtOnRo4fTXqR9+/bVzz//rIMHD3ps7riAe1Z2nTt3Tjt27FBERIRTfUREhL766qtSmhUuJSkpSampqU73y263q0ePHo77tWPHDp0/f96pTWhoqFq1asU99YC0tDRJcvy9xT1DRUWQXc79+OOPeuONNzRq1ChHXWpqqurUqePU7oorrpCPj49SU1Mv2Sb3OLcNPId7VnYdP35c2dnZ+X73fO9lT+49udz9Sk1NlY+Pj6644opLtkHJMMYoJiZGXbt2VatWrSRxz1BxEWSXEZMmTZLNZrts2b59u1Ofn3/+Wf369dPtt9+uESNGOH1ms9nynMMY41R/cRvz3wfo8uuLvIpzzy6He1a25ffd872XXcW5X9zTkhcdHa3du3dr/vz5eT7jnqGiKdXXquN/oqOjddddd122TaNGjRz//fPPP6tXr14KDw/Xu+++69QuODhYW7dudar77bffdP78ecdKQXBwcJ7f/o8dOyYp72oC8lfUe3Y53LOyq1atWqpUqVK+3z3fe9kTHBws6cLKZ0hIiKP+z/crODhY586d02+//ea0Mnrs2DF16dLFsxO2kDFjxmjZsmXasGGD6tWr56jnnqGiYiW7jKhVq5auuuqqyxZfX19J0tGjR9WzZ09dc801iouLk5eX820MDw/Xt99+q5SUFEfdqlWrZLfb1aFDB0ebDRs2OG0Rt2rVKoWGhhY6MLS6otyzgnDPyi4fHx916NBBq1evdqpfvXo1f7mXQWFhYQoODna6X+fOnVNCQoLjfnXo0EHe3t5ObVJSUvTtt99yT0uAMUbR0dFavHix1q5dq7CwMKfPuWeosErpgUsU09GjR03Tpk1N7969zZEjR0xKSoqj5MrKyjKtWrUyffr0MTt37jRr1qwx9erVM9HR0Y42p06dMnXq1DF//etfzTfffGMWL15s/P39zZQpU0rjsiq8Q4cOmcTERDN58mRTrVo1k5iYaBITE83p06eNMdyzsm7BggXG29vbzJw50+zdu9c88sgjpmrVqubgwYOlPTVLOn36tOPPkCQzdepUk5iYaA4dOmSMMeall14yAQEBZvHixeabb74xf/3rX01ISIhJT093jDFq1ChTr149s2bNGrNz507Tu3dv07ZtW5OVlVVal1VhPfjggyYgIMCsX7/e6e+s33//3dGGe4aKiCC7nImLizOS8i1/dujQIdO/f3/j5+dnAgMDTXR0tNPWb8YYs3v3btOtWzdjt9tNcHCwmTRpElvBlZChQ4fme8/WrVvnaMM9K9veeust07BhQ+Pj42OuueYax/Zj8Lx169bl++dp6NChxpgLW8JNnDjRBAcHG7vdbrp3726++eYbpzH++OMPEx0dbQIDA42fn5+56aabTHJycilcTcV3qb+z4uLiHG24Z6iIbMbwujgAAADAncjJBgAAANyMIBsAAABwM4JsAAAAwM0IsgEAAAA3I8gGAAAA3IwgGwAAAHAzgmwAAADAzQiyAQAAADcjyAYAAADcjCAbAAqhZ8+eeuSRR0p7GgCAcoIgGwAAAHAzmzHGlPYkAKAsu/fee/XBBx841SUlJalRo0alMyEAQJlHkA0ABUhLS1NkZKRatWqlZ599VpJUu3ZtVapUqZRnBgAoqyqX9gQAoKwLCAiQj4+PqlSpouDg4NKeDgCgHCAnGwAAAHAzgmwAAADAzQiyAaAQfHx8lJ2dXdrTAACUEwTZAFAIjRo10tatW3Xw4EEdP35cOTk5pT0lAEAZRpANAIUwbtw4VapUSS1btlTt2rWVnJxc2lMCAJRhbOEHAAAAuBkr2QAAAICbEWQDAAAAbkaQDQAAALgZQTYAAADgZgTZAAAAgJsRZAMAAABuRpANAAAAuBlBNgAAAOBmBNkAAACAmxFkAwAAAG5GkA0AAAC4GUE2AAAA4Gb/D6hSXS2ET3IdAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 760x440 with 2 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 760x440 with 2 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 760x440 with 2 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 680x360 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 760x460 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XXI+ summary ===\n",
      "s0              : 2.0\n",
      "mu_used         : [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess         : 0.018315638888734186\n",
      "n_max           : 187\n",
      "T_MAX           : 250.0\n",
      "DT              : 0.02\n",
      "precision       : 200\n",
      "sigmas          : [2.6, 1.4000000000000044, -0.04999999999999982]\n",
      "points_per_line : 25001\n",
      "n_lines         : 25\n",
      "n_candidates    : 0\n",
      "depth_gate      : -704.8018107646759\n",
      "curv_gate       : -1.5\n",
      "outputs         : ['stageXXIplus_logabs_heatmap.png', 'stageXXIplus_phasegrad_heatmap.png', 'stageXXIplus_curvature_heatmap.png', 'stageXXIplus_minima_curve.png', 'stageXXIplus_central_line.png', 'stageXXIplus_minima.csv', 'stageXXIplus_candidates.csv']\n",
      "\n",
      "Wrote:\n",
      " - stageXXIplus_logabs_heatmap.png\n",
      " - stageXXIplus_phasegrad_heatmap.png\n",
      " - stageXXIplus_curvature_heatmap.png\n",
      " - stageXXIplus_minima_curve.png\n",
      " - stageXXIplus_central_line.png\n",
      " - stageXXIplus_minima.csv\n",
      " - stageXXIplus_candidates.csv\n",
      "\n",
      "Preview of candidates:\n",
      "(none)\n"
     ]
    }
   ],
   "source": [
    "# === Stage XXI+ : ultra-fine sweep with Tukey smoothing & robust candidate test ===\n",
    "# Wider window, finer dt, higher precision, alternate smoothing, robust detection.\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------- helpers ----------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except Exception: return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "# ---------- inputs ----------\n",
    "coeff_path = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "summaryX   = Path(\"stageX_summary.json\")\n",
    "summaryXI  = Path(\"stageXI_summary.json\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty.\")\n",
    "s0 = mp.mpf('2.0')\n",
    "if summaryX.exists() and summaryX.stat().st_size > 0:\n",
    "    try:\n",
    "        JX = json.load(open(summaryX))\n",
    "        if \"s0\" in JX: s0 = mpf_safe(JX[\"s0\"])\n",
    "        elif \"central_point_guess\" in JX: s0 = mpf_safe(JX[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "MU_BASE = [0,1,1,2]\n",
    "delta_uniform = 1.0\n",
    "if summaryXI.exists() and summaryXI.stat().st_size > 0:\n",
    "    try:\n",
    "        JXI = json.load(open(summaryXI))\n",
    "        if \"uniform_shift\" in JXI and \"delta_min_residual\" in JXI[\"uniform_shift\"]:\n",
    "            delta_uniform = float(JXI[\"uniform_shift\"][\"delta_min_residual\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "MU = [m + delta_uniform for m in MU_BASE]    # usually [1,2,2,3]\n",
    "Q_guess = mp.e**(-4)\n",
    "# ---------- coefficients ----------\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower: raise ValueError(\"CSV missing 'n' column.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower: a_col = cols_lower[k]; break\n",
    "if a_col is None: raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(to_float).to_numpy()\n",
    "mask  = (N_all>0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all); N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "n = N_all; a = A_all\n",
    "Nmax = to_int(n[-1])\n",
    "# ---------- Dirichlet with Tukey window (alpha = 0.5) ----------\n",
    "mp.mp.dps = 200  # higher precision for this pass\n",
    "def tukey_weight(x, alpha=0.5):\n",
    "    if x<=0 or x>=1: return mp.mpf('0')\n",
    "    if x < alpha/2:\n",
    "        return mp.mpf('0.5')*(1 + mp.cos(mp.pi*(2*x/alpha - 1)))\n",
    "    elif x <= 1 - alpha/2:\n",
    "        return mp.mpf('1')\n",
    "    else:\n",
    "        return mp.mpf('0.5')*(1 + mp.cos(mp.pi*(2*x/alpha - 2/alpha + 1)))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None: N_cut = Nmax\n",
    "    idx = np.searchsorted(n, int(N_cut), side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    tot = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(int(nn_i))/Ncut_mp\n",
    "        w = tukey_weight(x, alpha=mp.mpf('0.5'))\n",
    "        if w != 0:\n",
    "            tot += mpf_safe(aa_i) / (mpf_safe(int(nn_i))**s) * w\n",
    "    return tot\n",
    "def gamma_R(z): return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list: g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------- sweep params (finer & wider than Stage XXI) ----------\n",
    "T_MAX   = 250.0\n",
    "DT      = 0.02\n",
    "sigmas  = np.arange(float(s0)+0.60, float(s0)-0.61, -0.05)  # 2.60 → 1.40 by 0.05\n",
    "t_vals  = np.arange(-T_MAX, T_MAX + 1e-12, DT)\n",
    "m, L = len(t_vals), len(sigmas)\n",
    "logabs_grid = np.zeros((L, m), dtype=float)\n",
    "grad_grid   = np.zeros((L, m), dtype=float)\n",
    "curv_grid   = np.zeros((L, m), dtype=float)\n",
    "minima_curve = []\n",
    "print(\"Stage XXI+ running …\")\n",
    "print(f\"s0={s0}, mu={MU}, K_terms={len(n)} (n_max={Nmax}), T_MAX={T_MAX}, DT={DT}, mp.dps={mp.mp.dps}\")\n",
    "print(f\"lines: {L} from σ={sigmas[0]:.2f} down to {sigmas[-1]:.2f}; points/line={m}\")\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    vals = []\n",
    "    sig_mp = mp.mpf(sigma)\n",
    "    for t in t_vals:\n",
    "        s = sig_mp + 1j*mp.mpf(t)\n",
    "        vals.append(Lambda_of_s(s, Q_guess, MU, Nmax))\n",
    "    absv  = np.array([to_float(abs(z)) for z in vals], dtype=float)\n",
    "    with np.errstate(divide='ignore'):\n",
    "        la = np.log(absv, where=absv>0); la[~np.isfinite(la)] = -1e300\n",
    "    ph    = np.unwrap(np.array([float(mp.arg(z)) for z in vals], dtype=float))\n",
    "    dphi  = np.gradient(ph, DT)\n",
    "    d2la  = np.gradient(np.gradient(la, DT), DT)\n",
    "    logabs_grid[i,:] = la\n",
    "    grad_grid[i,:]   = dphi\n",
    "    curv_grid[i,:]   = d2la\n",
    "    minima_curve.append((float(sigma), float(np.min(la))))\n",
    "# ---------- candidate detection on central line ----------\n",
    "i_center = int(np.argmin(np.abs(sigmas - float(s0))))\n",
    "la_c = logabs_grid[i_center]; dphi_c = grad_grid[i_center]; d2la_c = curv_grid[i_center]\n",
    "# adaptive gates\n",
    "q25  = float(np.quantile(la_c, 0.25))\n",
    "q05  = float(np.quantile(la_c, 0.05))\n",
    "depth_gate = min(q05, q25 - 0.08*abs(q25))          # require \"deep\" valley\n",
    "curv_gate  = -1.5                                   # negative curvature at the dip\n",
    "sign = np.sign(dphi_c)\n",
    "zc   = np.where((sign[:-1]*sign[1:]) < 0)[0]        # zero-crossings of dphi\n",
    "cand_idx = []\n",
    "for k in zc:\n",
    "    k0 = max(0, int(k)-2); k1 = min(m-1, int(k)+3)\n",
    "    seg = la_c[k0:k1]\n",
    "    if len(seg)==0: continue\n",
    "    kmin_local = int(np.argmin(seg)) + k0\n",
    "    if la_c[kmin_local] <= depth_gate and d2la_c[kmin_local] <= curv_gate:\n",
    "        cand_idx.append(kmin_local)\n",
    "cand_idx = sorted(set(cand_idx))\n",
    "candidates = pd.DataFrame({\n",
    "    \"sigma\":   [float(sigmas[i_center])]*len(cand_idx),\n",
    "    \"t\":       [float(t_vals[k]) for k in cand_idx],\n",
    "    \"log_abs\": [float(la_c[k]) for k in cand_idx],\n",
    "    \"d_arg_dt\":[float(dphi_c[k]) for k in cand_idx],\n",
    "    \"curv\":    [float(d2la_c[k]) for k in cand_idx],\n",
    "})\n",
    "# ---------- plots ----------\n",
    "extent = [t_vals[0], t_vals[-1], sigmas[-1], sigmas[0]]\n",
    "plt.figure(figsize=(7.6,4.4))\n",
    "plt.imshow(logabs_grid, aspect='auto', extent=extent, origin='lower', cmap='viridis')\n",
    "plt.colorbar(label='log |Λ(σ+it)|')\n",
    "plt.xlabel('t'); plt.ylabel('σ = Re s'); plt.title('Stage XXI+: log |Λ| (Tukey window)')\n",
    "plt.tight_layout(); plt.savefig(\"stageXXIplus_logabs_heatmap.png\", dpi=150); plt.show()\n",
    "plt.figure(figsize=(7.6,4.4))\n",
    "plt.imshow(grad_grid, aspect='auto', extent=extent, origin='lower', cmap='coolwarm')\n",
    "plt.colorbar(label='d/dt arg Λ')\n",
    "plt.xlabel('t'); plt.ylabel('σ = Re s'); plt.title('Stage XXI+: phase gradient')\n",
    "plt.tight_layout(); plt.savefig(\"stageXXIplus_phasegrad_heatmap.png\", dpi=150); plt.show()\n",
    "plt.figure(figsize=(7.6,4.4))\n",
    "plt.imshow(curv_grid, aspect='auto', extent=extent, origin='lower', cmap='RdBu_r')\n",
    "plt.colorbar(label='d²/dt² log|Λ|')\n",
    "plt.xlabel('t'); plt.ylabel('σ = Re s'); plt.title('Stage XXI+: curvature of log|Λ|')\n",
    "plt.tight_layout(); plt.savefig(\"stageXXIplus_curvature_heatmap.png\", dpi=150); plt.show()\n",
    "mc = pd.DataFrame(minima_curve, columns=[\"sigma\",\"min_logabs\"])\n",
    "plt.figure(figsize=(6.8,3.6))\n",
    "plt.plot(mc[\"sigma\"], mc[\"min_logabs\"], \"o-\")\n",
    "plt.gca().invert_xaxis()\n",
    "plt.xlabel(\"σ\"); plt.ylabel(\"min log|Λ| on line σ\"); plt.title(\"Stage XXI+: per-line minima\")\n",
    "plt.grid(True); plt.tight_layout(); plt.savefig(\"stageXXIplus_minima_curve.png\", dpi=150); plt.show()\n",
    "plt.figure(figsize=(7.6,4.6))\n",
    "plt.plot(t_vals, la_c, lw=1.3, label=\"log |Λ(s0 + it)|\")\n",
    "if len(candidates) > 0:\n",
    "    plt.scatter(candidates[\"t\"], candidates[\"log_abs\"], s=24, marker=\"x\", label=\"candidates\")\n",
    "plt.axhline(depth_gate, color='orange', ls='--', label='depth gate')\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"log |Λ|\"); plt.title(\"Stage XXI+: central line with candidates\")\n",
    "plt.grid(True); plt.legend(); plt.tight_layout(); plt.savefig(\"stageXXIplus_central_line.png\", dpi=150); plt.show()\n",
    "# ---------- save ----------\n",
    "mc.to_csv(\"stageXXIplus_minima.csv\", index=False)\n",
    "candidates.to_csv(\"stageXXIplus_candidates.csv\", index=False)\n",
    "summary = {\n",
    "    \"s0\": float(s0),\n",
    "    \"mu_used\": MU,\n",
    "    \"Q_guess\": float(Q_guess),\n",
    "    \"n_max\": int(Nmax),\n",
    "    \"T_MAX\": float(T_MAX),\n",
    "    \"DT\": float(DT),\n",
    "    \"precision\": int(mp.mp.dps),\n",
    "    \"sigmas\": [float(sigmas[0]), float(sigmas[-1]), float(sigmas[1]-sigmas[0]) if len(sigmas)>1 else 0.0],\n",
    "    \"points_per_line\": int(m),\n",
    "    \"n_lines\": int(L),\n",
    "    \"n_candidates\": int(len(candidates)),\n",
    "    \"depth_gate\": float(depth_gate),\n",
    "    \"curv_gate\": float(curv_gate),\n",
    "    \"outputs\":[\n",
    "        \"stageXXIplus_logabs_heatmap.png\",\n",
    "        \"stageXXIplus_phasegrad_heatmap.png\",\n",
    "        \"stageXXIplus_curvature_heatmap.png\",\n",
    "        \"stageXXIplus_minima_curve.png\",\n",
    "        \"stageXXIplus_central_line.png\",\n",
    "        \"stageXXIplus_minima.csv\",\n",
    "        \"stageXXIplus_candidates.csv\",\n",
    "    ]\n",
    "}\n",
    "with open(\"stageXXIplus_summary.json\",\"w\") as f:\n",
    "    json.dump(summary, f, indent=2)\n",
    "print(\"\\n=== Stage XXI+ summary ===\")\n",
    "for k,v in summary.items(): print(f\"{k:16}: {v}\")\n",
    "print(\"\\nWrote:\"); [print(\" -\",x) for x in summary[\"outputs\"]]\n",
    "print(\"\\nPreview of candidates:\")\n",
    "print(\"(none)\" if len(candidates)==0 else \"\")\n",
    "if len(candidates)>0:\n",
    "    display(head_safe(candidates, 10)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "945fe5",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stage XXI++ running …\n",
      "s0=2.0, mu=[1.0, 2.0, 2.0, 3.0], K_terms=21 (n_max=187), T_MAX=80.0000000000000, DT=0.0500000000000000 → points/line=3201, mp.dps=200\n",
      "lines: 31 from σ=2.30 down to 2.00\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 760x480 with 2 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 760x480 with 2 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x380 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XXI++ summary ===\n",
      "stage           : XXI++ microscope\n",
      "s0              : 2.0\n",
      "mu_used         : [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess         : 0.01831563888873418\n",
      "n_max           : 187\n",
      "K_terms         : 21\n",
      "sigma_range     : [2.3, 2.0, -0.01]\n",
      "t_range         : [-80.0, 80.0, 0.05]\n",
      "precision_dps   : 200\n",
      "normalize_per_line: True\n",
      "safe_floor      : -1000000.0\n",
      "wrote:\n",
      " - stageXXIpp_logabs_heatmap.png\n",
      " - stageXXIpp_phasegrad_heatmap.png\n",
      " - stageXXIpp_minima_curve.png\n",
      " - stageXXIpp_minima.csv\n",
      "\n",
      "Preview of minima:\n"
     ]
    },
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>sigma</th>\n      <th>min_logabs</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>2.30</td>\n      <td>-237.714299</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2.29</td>\n      <td>-237.744433</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2.28</td>\n      <td>-237.774551</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>2.27</td>\n      <td>-237.804651</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>2.26</td>\n      <td>-237.834733</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>2.25</td>\n      <td>-237.864798</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>2.24</td>\n      <td>-237.894843</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>2.23</td>\n      <td>-237.924870</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>2.22</td>\n      <td>-237.954877</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>2.21</td>\n      <td>-237.984865</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": [
       "   sigma  min_logabs\n",
       "0   2.30 -237.714299\n",
       "1   2.29 -237.744433\n",
       "2   2.28 -237.774551\n",
       "3   2.27 -237.804651\n",
       "4   2.26 -237.834733\n",
       "5   2.25 -237.864798\n",
       "6   2.24 -237.894843\n",
       "7   2.23 -237.924870\n",
       "8   2.22 -237.954877\n",
       "9   2.21 -237.984865"
      ]
     },
     "execution_count": 2,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# === Stage XXI++: overflow-proof microscope scan near sigma ~ 2.2 ===\n",
    "# - Computes log|Λ| with mpmath (no premature float casts)\n",
    "# - Per-line normalization (subtract max log|Λ| on each σ-line) to avoid saturation\n",
    "# - Focused σ window and moderate T_MAX for stability\n",
    "# - Produces normalized heatmaps + minima curve + central-line plot + CSV/JSON\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------------- CONFIG (edit here) ----------------\n",
    "SIGMA_MAX = 2.30       # start of σ band (≈ where you saw the dip)\n",
    "SIGMA_MIN = 2.00       # end of σ band\n",
    "D_SIGMA   = -0.01      # σ step (negative to step downward)\n",
    "T_MAX     = 80.0       # t window half-width\n",
    "DT        = 0.05       # t step\n",
    "MP_DPS    = 200        # precision (digits)\n",
    "NORMALIZE = True       # subtract max log|Λ| per line for plotting\n",
    "SAFE_FLOOR = -1e6      # floor for log|Λ| if value is 0 or underflow\n",
    "OUT_PREFIX = \"stageXXIpp_\"  # file prefix for all outputs\n",
    "# ---------------------------------------------------\n",
    "# -------- helpers (avoid Sage Integer leaks) --------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:\n",
    "        return mp.mpf(x)\n",
    "    except Exception:\n",
    "        return mp.mpf(str(to_float(x)))\n",
    "def head_safe(df, n=10):\n",
    "    n = int(n); n = max(0, min(n, len(df)))\n",
    "    return df.iloc[:n]\n",
    "# -------- inputs --------\n",
    "coeff_path = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "summaryX   = Path(\"stageX_summary.json\")    # for s0 (if present)\n",
    "summaryXI  = Path(\"stageXI_summary.json\")   # for uniform shift delta (if present)\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "# central point\n",
    "s0 = mp.mpf('2.0')\n",
    "if summaryX.exists() and summaryX.stat().st_size > 0:\n",
    "    try:\n",
    "        with open(summaryX, \"r\") as f:\n",
    "            JX = json.load(f)\n",
    "        if \"s0\" in JX: s0 = mpf_safe(JX[\"s0\"])\n",
    "        elif \"central_point_guess\" in JX: s0 = mpf_safe(JX[\"central_point_guess\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "# gamma-shift base and Stage XI uniform shift\n",
    "MU_BASE = [0,1,1,2]\n",
    "delta_uniform = 1.0\n",
    "if summaryXI.exists() and summaryXI.stat().st_size > 0:\n",
    "    try:\n",
    "        with open(summaryXI, \"r\") as f:\n",
    "            JXI = json.load(f)\n",
    "        if \"uniform_shift\" in JXI and \"delta_min_residual\" in JXI[\"uniform_shift\"]:\n",
    "            delta_uniform = float(JXI[\"uniform_shift\"][\"delta_min_residual\"])\n",
    "    except Exception:\n",
    "        pass\n",
    "MU = [m + delta_uniform for m in MU_BASE]   # typically [1,2,2,3]\n",
    "# a crude Q (visualization only; zeros don’t depend on Q)\n",
    "Q_guess = mp.e**(-4)\n",
    "# -------- load coefficients (use ALL for max fidelity) --------\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"stageVIII_dirichlet_coeffs.csv missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].map(to_int).to_numpy()\n",
    "A_all = C[a_col].map(float).to_numpy()\n",
    "mask  = (N_all > 0) & np.isfinite(A_all)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "N_all, A_all = N_all[ordr], A_all[ordr]\n",
    "n = N_all[:]      # use all available\n",
    "a = A_all[:]\n",
    "Ncut = to_int(n[-1])\n",
    "# -------- Dirichlet with cosine smoothing (mpmath throughout) --------\n",
    "mp.mp.dps = int(MP_DPS)\n",
    "mp.mp.pretty = True\n",
    "mp.mp.trap_complex = False  # allow complex logs internally when needed\n",
    "def smooth_weight(x):\n",
    "    return mp.mpf('0') if (x < 0 or x > 1) else mp.mpf('0.5')*(1 + mp.cos(mp.pi*x))\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None:\n",
    "        N_cut = to_int(n[-1])\n",
    "    N_cut = to_int(N_cut)\n",
    "    idx = int(np.searchsorted(n, N_cut, side=\"right\"))\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    total = mp.mpf('0')\n",
    "    for nn_i, aa_i in zip(nn, aa):\n",
    "        x = mpf_safe(int(nn_i)) / Ncut_mp\n",
    "        w = smooth_weight(x)\n",
    "        if w != mp.mpf('0'):\n",
    "            total += mpf_safe(aa_i) / (mpf_safe(int(nn_i))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# -------- grids --------\n",
    "sigmas = np.arange(SIGMA_MAX, SIGMA_MIN + 0.5*D_SIGMA, D_SIGMA)  # inclusive end\n",
    "t_vals = np.arange(-T_MAX, T_MAX + 1e-12, DT)\n",
    "L = len(sigmas)\n",
    "M = len(t_vals)\n",
    "# containers (float AFTER normalization)\n",
    "logabs_grid = np.zeros((L, M), dtype=float)\n",
    "phasegrad_grid = np.zeros((L, M), dtype=float)  # d/dt arg Λ\n",
    "minima_curve = []  # (sigma, min_logabs_original)\n",
    "print(\"Stage XXI++ running …\")\n",
    "print(f\"s0={s0}, mu={MU}, K_terms={len(n)} (n_max={Ncut}), \"\n",
    "      f\"T_MAX={T_MAX}, DT={DT} → points/line={M}, mp.dps={mp.mp.dps}\")\n",
    "print(f\"lines: {L} from σ={sigmas[0]:.2f} down to {sigmas[-1]:.2f}\")\n",
    "# -------- main sweep (mpmath domain) --------\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    # compute Λ along vertical line Re s = sigma, Im s = t\n",
    "    vals = []\n",
    "    args = []\n",
    "    logs = []\n",
    "    for t in t_vals:\n",
    "        s = mp.mpf(sigma) + 1j*mp.mpf(t)\n",
    "        z = Lambda_of_s(s, Q_guess, MU, Ncut)\n",
    "        # log|Λ| in high precision, with safety floor\n",
    "        absz = abs(z)\n",
    "        if absz == 0:\n",
    "            lz = mp.mpf(SAFE_FLOOR)\n",
    "        else:\n",
    "            lz = mp.log(absz)\n",
    "        logs.append(lz)\n",
    "        # arg Λ (principal), store as float\n",
    "        args.append(float(mp.arg(z)))\n",
    "    # unwrap arg and compute d/dt arg Λ (central-diff)\n",
    "    arg_arr = np.unwrap(np.array(args, dtype=float))\n",
    "    # gradient with uniform spacing DT\n",
    "    darg_dt = np.gradient(arg_arr, DT)\n",
    "    phasegrad_grid[i, :] = darg_dt\n",
    "    # store log|Λ|, optionally normalized per line\n",
    "    logs_mp = logs[:]  # list of mpf\n",
    "    # minima curve uses ORIGINAL (non-normalized) log|Λ| (as float)\n",
    "    min_log = float(min(logs_mp)) if logs_mp else float('nan')\n",
    "    minima_curve.append((float(sigma), min_log))\n",
    "    if NORMALIZE and len(logs_mp) > 0:\n",
    "        line_max = float(max(logs_mp))\n",
    "        line = [float(l) - line_max for l in logs_mp]   # normalize\n",
    "    else:\n",
    "        line = [float(l) for l in logs_mp]\n",
    "    logabs_grid[i, :] = np.array(line, dtype=float)\n",
    "# -------- figures --------\n",
    "plt.figure(figsize=(7.6, 4.8))\n",
    "extent = [t_vals[0], t_vals[-1], sigmas[-1], sigmas[0]]  # t on x, σ on y (top=large σ)\n",
    "im = plt.imshow(logabs_grid, aspect='auto', origin='lower', extent=extent, cmap='viridis')\n",
    "plt.colorbar(im, label=(\"log|Λ| (normalized per σ-line)\" if NORMALIZE else \"log|Λ|\"))\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"σ = Re s\")\n",
    "plt.title(\"Stage XXI++: log |Λ(σ+it)| (microscope, overflow-proof)\")\n",
    "plt.tight_layout()\n",
    "plt.savefig(OUT_PREFIX + \"logabs_heatmap.png\", dpi=150)\n",
    "plt.show()\n",
    "plt.figure(figsize=(7.6, 4.8))\n",
    "im2 = plt.imshow(phasegrad_grid, aspect='auto', origin='lower', extent=extent, cmap='RdBu_r')\n",
    "plt.colorbar(im2, label=\"d/dt arg Λ\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"σ = Re s\")\n",
    "plt.title(\"Stage XXI++: phase gradient d/dt arg Λ\")\n",
    "plt.tight_layout()\n",
    "plt.savefig(OUT_PREFIX + \"phasegrad_heatmap.png\", dpi=150)\n",
    "plt.show()\n",
    "# minima curve (from ORIGINAL log|Λ|)\n",
    "mc = pd.DataFrame(minima_curve, columns=[\"sigma\", \"min_logabs\"])\n",
    "plt.figure(figsize=(7.2, 3.8))\n",
    "plt.plot(mc[\"sigma\"], mc[\"min_logabs\"], marker=\"o\")\n",
    "plt.gca().invert_xaxis()  # descending σ to the right like earlier plots\n",
    "plt.xlabel(\"σ\"); plt.ylabel(\"min log|Λ| on line σ\")\n",
    "plt.title(\"Stage XXI++: per-line minima (lower = darker)\")\n",
    "plt.grid(True, alpha=0.3)\n",
    "plt.tight_layout()\n",
    "plt.savefig(OUT_PREFIX + \"minima_curve.png\", dpi=150)\n",
    "plt.show()\n",
    "# central line at σ = s0 (if it lies inside our sigma band)\n",
    "central_plot_done = False\n",
    "if float(sigmas.min()) <= float(s0) <= float(sigmas.max()):\n",
    "    # recompute along σ = s0 using the same high-precision pathway\n",
    "    logs_c, tgrid_c = [], []\n",
    "    for t in t_vals:\n",
    "        zc = Lambda_of_s(s0 + 1j*mp.mpf(t), Q_guess, MU, Ncut)\n",
    "        az = abs(zc)\n",
    "        lc = mp.log(az) if az != 0 else mp.mpf(SAFE_FLOOR)\n",
    "        logs_c.append(float(lc))\n",
    "        tgrid_c.append(float(t))\n",
    "    # normalize central line for visibility against depth gate\n",
    "    if NORMALIZE and len(logs_c) > 0:\n",
    "        Lmax = max(logs_c); logs_c = [x - Lmax for x in logs_c]\n",
    "    plt.figure(figsize=(7.2, 3.8))\n",
    "    plt.plot(tgrid_c, logs_c, label=\"log |Λ(s0 + it)|\")\n",
    "    plt.xlabel(\"t\"); plt.ylabel(\"log |Λ| (normalized)\" if NORMALIZE else \"log |Λ|\")\n",
    "    plt.title(\"Stage XXI++: central line\")\n",
    "    plt.grid(True, alpha=0.3); plt.legend()\n",
    "    plt.tight_layout()\n",
    "    plt.savefig(OUT_PREFIX + \"central_line.png\", dpi=150)\n",
    "    plt.show()\n",
    "    central_plot_done = True\n",
    "# -------- save CSV + JSON summary --------\n",
    "# store the minima (original log|Λ|) and a compact settings summary\n",
    "mc.to_csv(OUT_PREFIX + \"minima.csv\", index=False)\n",
    "summary = {\n",
    "    \"stage\": \"XXI++ microscope\",\n",
    "    \"s0\": float(s0),\n",
    "    \"mu_used\": [float(x) for x in MU],\n",
    "    \"Q_guess\": float(Q_guess),\n",
    "    \"n_max\": int(Ncut),\n",
    "    \"K_terms\": int(len(n)),\n",
    "    \"sigma_range\": [float(SIGMA_MAX), float(SIGMA_MIN), float(D_SIGMA)],\n",
    "    \"t_range\": [-float(T_MAX), float(T_MAX), float(DT)],\n",
    "    \"precision_dps\": int(mp.mp.dps),\n",
    "    \"normalize_per_line\": bool(NORMALIZE),\n",
    "    \"safe_floor\": float(SAFE_FLOOR),\n",
    "    \"outputs\": [\n",
    "        OUT_PREFIX + \"logabs_heatmap.png\",\n",
    "        OUT_PREFIX + \"phasegrad_heatmap.png\",\n",
    "        OUT_PREFIX + \"minima_curve.png\",\n",
    "        OUT_PREFIX + \"minima.csv\",\n",
    "    ] + ([OUT_PREFIX + \"central_line.png\"] if central_plot_done else [])\n",
    "}\n",
    "with open(OUT_PREFIX + \"summary.json\", \"w\") as f:\n",
    "    json.dump(summary, f, indent=2)\n",
    "print(\"\\n=== Stage XXI++ summary ===\")\n",
    "for k,v in summary.items():\n",
    "    if k != \"outputs\":\n",
    "        print(f\"{k:16}: {v}\")\n",
    "print(\"wrote:\")\n",
    "for x in summary[\"outputs\"]:\n",
    "    print(\" -\", x)\n",
    "print(\"\\nPreview of minima:\")\n",
    "display(head_safe(mc, 10))0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8c349d",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XXII summary ===\n",
      "stage               : XXII\n",
      "s0                  : 2.0\n",
      "mu_used             : [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess             : 0.01831563888873418\n",
      "n_max               : 187\n",
      "K_terms             : 21\n",
      "sigmas              : [2.3, 2.29, 2.2800000000000002, 2.2700000000000005, 2.2600000000000007, 2.250000000000001, 2.240000000000001, 2.2300000000000013, 2.2200000000000015, 2.2100000000000017, 2.200000000000002, 2.190000000000002, 2.1800000000000024, 2.1700000000000026, 2.160000000000003, 2.150000000000003, 2.1400000000000032, 2.1300000000000034, 2.1200000000000037, 2.110000000000004, 2.100000000000004, 2.0900000000000043, 2.0800000000000045, 2.0700000000000047, 2.060000000000005, 2.050000000000005, 2.0400000000000054, 2.0300000000000056, 2.020000000000006, 2.010000000000006, 2.000000000000006]\n",
      "t_range             : [-80.0, -79.95, -79.9, -79.85000000000001, -79.80000000000001, -79.75000000000001, -79.70000000000002, -79.65000000000002, -79.60000000000002, -79.55000000000003, -79.50000000000003, -79.45000000000003, -79.40000000000003, -79.35000000000004, -79.30000000000004, -79.25000000000004, -79.20000000000005, -79.15000000000005, -79.10000000000005, -79.05000000000005, -79.00000000000006, -78.95000000000006, -78.90000000000006, -78.85000000000007, -78.80000000000007, -78.75000000000007, -78.70000000000007, -78.65000000000008, -78.60000000000008, -78.55000000000008, -78.50000000000009, -78.45000000000009, -78.40000000000009, -78.3500000000001, -78.3000000000001, -78.2500000000001, -78.2000000000001, -78.1500000000001, -78.10000000000011, -78.05000000000011, -78.00000000000011, -77.95000000000012, -77.90000000000012, -77.85000000000012, -77.80000000000013, -77.75000000000013, -77.70000000000013, -77.65000000000013, -77.60000000000014, -77.55000000000014, 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      "precision_dps       : 200\n",
      "normalize_per_line  : True\n",
      "outputs             : ['stageXXII_logabs_heatmap.png', 'stageXXII_curvature_heatmap.png', 'stageXXII_minima_curve.png', 'stageXXII_central_line.png', 'stageXXII_minima.csv']\n",
      "\n",
      "Summary written to stageXXII_summary.json\n"
     ]
    }
   ],
   "source": [
    "# --- Stage XXII: write clean summary JSON (robust, self-contained) ---\n",
    "import json, numpy as np\n",
    "try:\n",
    "    import mpmath as mp\n",
    "except Exception:\n",
    "    class _MP: dps = 0\n",
    "    mp = _MP()\n",
    "# ---- helpers ----\n",
    "def _as_float(x):\n",
    "    try:\n",
    "        return float(x)\n",
    "    except Exception:\n",
    "        try:    return float(str(x))\n",
    "        except Exception: return None\n",
    "def _as_int(x):\n",
    "    try:\n",
    "        return int(x)\n",
    "    except Exception:\n",
    "        try:    return int(float(x))\n",
    "        except Exception: return None\n",
    "def _list_float(it):\n",
    "    out=[]\n",
    "    for v in it:\n",
    "        fv=_as_float(v)\n",
    "        if fv is not None: out.append(fv)\n",
    "    return out\n",
    "def _get(name, default):\n",
    "    return globals().get(name, default)\n",
    "# ---- gather values with safe fallbacks ----\n",
    "s0       = _get('s0', 2.0)\n",
    "mu_used  = _get('mu_used', _get('MU', [1.0,2.0,2.0,3.0]))\n",
    "Q_guess  = _get('Q_guess', np.e**-4)\n",
    "n_max    = _get('n_max', 187)\n",
    "K_terms  = _get('K_terms', 21)\n",
    "# arrays/ranges\n",
    "sigmas   = _get('sigmas', np.arange(2.30, 1.9999, -0.01))         # 2.30 → 2.00\n",
    "t_range  = _get('t_vals',  np.arange(-80.0, 80.0+1e-12, 0.05))    # -80 → 80 step 0.05\n",
    "# precision if available\n",
    "precision_dps = getattr(getattr(mp, 'mp', mp), 'dps', getattr(mp, 'dps', 0))\n",
    "# ---- build summary (only JSON-serializable types) ----\n",
    "summary = {\n",
    "    \"stage\": \"XXII\",\n",
    "    \"s0\": _as_float(s0),\n",
    "    \"mu_used\": _list_float(mu_used),\n",
    "    \"Q_guess\": _as_float(Q_guess),\n",
    "    \"n_max\": _as_int(n_max),\n",
    "    \"K_terms\": _as_int(K_terms),\n",
    "    \"sigmas\": _list_float(list(sigmas) if hasattr(sigmas, '__iter__') else [sigmas]),\n",
    "    \"t_range\": _list_float(list(t_range) if hasattr(t_range, '__iter__') else [t_range]),\n",
    "    \"precision_dps\": _as_int(precision_dps),\n",
    "    \"normalize_per_line\": True,\n",
    "    \"outputs\": [\n",
    "        \"stageXXII_logabs_heatmap.png\",\n",
    "        \"stageXXII_curvature_heatmap.png\",\n",
    "        \"stageXXII_minima_curve.png\",\n",
    "        \"stageXXII_central_line.png\",\n",
    "        \"stageXXII_minima.csv\",\n",
    "    ],\n",
    "}\n",
    "# ---- write file ----\n",
    "OUT_SUMMARY = \"stageXXII_summary.json\"\n",
    "with open(OUT_SUMMARY, \"w\") as f:\n",
    "    json.dump(summary, f, indent=2)\n",
    "print(\"\\n=== Stage XXII summary ===\")\n",
    "for k, v in summary.items():\n",
    "    print(f\"{k:20}: {v}\")\n",
    "print(f\"\\nSummary written to {OUT_SUMMARY}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b998eb",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[ARCHIVE] Created: StageXXII_Results_20251018_184741.zip\n",
      "[ARCHIVE] Size   : 302,603 bytes\n",
      "[ARCHIVE] Files  : 7 + manifest\n",
      "\n",
      "[ARCHIVE] Contents:\n",
      " - stageXXII_candidates.csv  (29 bytes)  sha256=db555dece4c91715…\n",
      " - stageXXII_central_line.png  (53,374 bytes)  sha256=e0262ea5fb3bb459…\n",
      " - stageXXII_curvature_heatmap.png  (139,096 bytes)  sha256=ae284d3cb2a18d72…\n",
      " - stageXXII_logabs_heatmap.png  (57,615 bytes)  sha256=c2985186f18d54e6…\n",
      " - stageXXII_minima.csv  (1,172 bytes)  sha256=7689a707ecf2a751…\n",
      " - stageXXII_minima_curve.png  (59,553 bytes)  sha256=6fe06004765c5955…\n",
      " - stageXXII_summary.json  (77,173 bytes)  sha256=83c8a60a74b30b28…\n",
      "\n",
      "[ARCHIVE] Manifest written to: stageXXII_manifest.json\n",
      "[ARCHIVE] Done.\n"
     ]
    }
   ],
   "source": [
    "# === Archive Stage XXII outputs into a single ZIP with a manifest ===\n",
    "from pathlib import Path\n",
    "from datetime import datetime\n",
    "import zipfile, hashlib, json, os, sys\n",
    "STAGE_TAG = \"stageXXII_\"     # everything starting with this will be archived\n",
    "OUT_DIR   = Path(\".\")        # current directory\n",
    "def sha256_of(path, chunk=1024*1024):\n",
    "    h = hashlib.sha256()\n",
    "    with open(path, \"rb\") as f:\n",
    "        while True:\n",
    "            b = f.read(chunk)\n",
    "            if not b: break\n",
    "            h.update(b)\n",
    "    return h.hexdigest()\n",
    "# collect files\n",
    "files = sorted(p for p in OUT_DIR.glob(f\"{STAGE_TAG}*\") if p.is_file())\n",
    "if not files:\n",
    "    print(f\"[ARCHIVE] No files found matching {STAGE_TAG}*\")\n",
    "    sys.exit(0)\n",
    "# make manifest\n",
    "ts = datetime.now().strftime(\"%Y-%m-%d %H:%M:%S\")\n",
    "manifest = {\n",
    "    \"stage\": \"XXII\",\n",
    "    \"created_at_local\": ts,\n",
    "    \"prefix\": STAGE_TAG,\n",
    "    \"file_count\": len(files),\n",
    "    \"files\": []\n",
    "}\n",
    "for p in files:\n",
    "    manifest[\"files\"].append({\n",
    "        \"name\": p.name,\n",
    "        \"size_bytes\": p.stat().st_size,\n",
    "        \"sha256\": sha256_of(p)\n",
    "    })\n",
    "# write manifest to disk so it’s visible in the project too\n",
    "manifest_path = OUT_DIR / f\"{STAGE_TAG}manifest.json\"\n",
    "with open(manifest_path, \"w\") as f:\n",
    "    json.dump(manifest, f, indent=2)\n",
    "# create zip\n",
    "zip_name = f\"StageXXII_Results_{datetime.now().strftime('%Y%m%d_%H%M%S')}.zip\"\n",
    "zip_path = OUT_DIR / zip_name\n",
    "with zipfile.ZipFile(zip_path, \"w\", compression=zipfile.ZIP_DEFLATED, compresslevel=9) as zf:\n",
    "    # add all stage files\n",
    "    for p in files:\n",
    "        zf.write(p, arcname=p.name)\n",
    "    # add the manifest as well\n",
    "    zf.write(manifest_path, arcname=manifest_path.name)\n",
    "# final report\n",
    "zip_size = zip_path.stat().st_size\n",
    "print(\"\\n[ARCHIVE] Created:\", zip_path.name)\n",
    "print(f\"[ARCHIVE] Size   : {zip_size:,} bytes\")\n",
    "print(f\"[ARCHIVE] Files  : {len(files)} + manifest\")\n",
    "print(\"\\n[ARCHIVE] Contents:\")\n",
    "for entry in manifest[\"files\"]:\n",
    "    print(f\" - {entry['name']}  ({entry['size_bytes']:,} bytes)  sha256={entry['sha256'][:16]}…\")\n",
    "print(f\"\\n[ARCHIVE] Manifest written to: {manifest_path.name}\")\n",
    "print(\"[ARCHIVE] Done.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "762900",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x1200 with 5 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XXIII summary ===\n",
      "box for epsilon: σ∈[1.90000000000000, 2.10000000000000], t∈[-5.00000000000000, 5.00000000000000]  samples=400\n",
      "epsilon estimate (phase-only mean): -0.044552179789-0.008434246525j\n",
      "|R| median in box: 1.106e+00\n"
     ]
    }
   ],
   "source": [
    "# === Stage XXIII: functional equation symmetry test ===\n",
    "import numpy as np, pandas as pd, mpmath as mp\n",
    "import matplotlib.pyplot as plt\n",
    "mp.mp.dps = 180  # high because we're taking ratios\n",
    "# Center and kappa based on earlier stages\n",
    "s0 = mp.mpf('2.0')\n",
    "kappa = mp.mpf('4.0')  # hypothesis: symmetry about Re s = 2\n",
    "# Grids\n",
    "T_MAX = 40.0\n",
    "DT    = 0.10\n",
    "t_vals = np.arange(-T_MAX, T_MAX+1e-12, DT)\n",
    "sig_lo, sig_hi, ds = 1.6, 2.4, 0.05\n",
    "sigmas = np.arange(sig_lo, sig_hi+1e-12, ds)\n",
    "# Containers for the ratio R(s) := Λ(s) / Λ(kappa - s)\n",
    "R_abs  = np.zeros((len(sigmas), len(t_vals)), dtype=float)\n",
    "R_arg  = np.zeros((len(sigmas), len(t_vals)), dtype=float)\n",
    "def Lmbd(s):\n",
    "    # Wrap your existing Lambda_of_s with defaults\n",
    "    return Lambda_of_s(s, Q_guess, MU, None)\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    for j, t in enumerate(t_vals):\n",
    "        s  = mp.mpf(sigma) + 1j*mp.mpf(t)\n",
    "        sp = kappa - s\n",
    "        num = Lmbd(s)\n",
    "        den = Lmbd(sp)\n",
    "        # guard tiny denominators\n",
    "        if den == 0:\n",
    "            R_abs[i,j] = np.inf\n",
    "            R_arg[i,j] = 0.0\n",
    "        else:\n",
    "            R = num / den\n",
    "            R_abs[i,j] = float(abs(R))\n",
    "            R_arg[i,j] = float(mp.arg(R))\n",
    "# Visuals\n",
    "fig, axs = plt.subplots(3, 1, figsize=(8, 12))\n",
    "im0 = axs[0].imshow(np.log(R_abs), aspect='auto',\n",
    "                    extent=[t_vals[0], t_vals[-1], sigmas[-1], sigmas[0]])\n",
    "axs[0].set_title(\"Stage XXIII: log |Λ(s)/Λ(4 - s)|\")\n",
    "axs[0].set_xlabel(\"t\")\n",
    "axs[0].set_ylabel(\"σ = Re s\")\n",
    "fig.colorbar(im0, ax=axs[0])\n",
    "im1 = axs[1].imshow(R_arg, aspect='auto',\n",
    "                    extent=[t_vals[0], t_vals[-1], sigmas[-1], sigmas[0]],\n",
    "                    cmap='twilight')\n",
    "axs[1].set_title(\"Stage XXIII: arg Λ(s)/Λ(4 - s)\")\n",
    "axs[1].set_xlabel(\"t\")\n",
    "axs[1].set_ylabel(\"σ = Re s\")\n",
    "fig.colorbar(im1, ax=axs[1])\n",
    "# On the central line σ = 2\n",
    "sigma_c = 2.0\n",
    "Rc = []\n",
    "for t in t_vals:\n",
    "    s  = mp.mpf(sigma_c) + 1j*mp.mpf(t)\n",
    "    sp = kappa - s\n",
    "    den = Lmbd(sp)\n",
    "    Rc.append(complex(Lmbd(s)/den) if den != 0 else np.nan)\n",
    "Rc = np.array(Rc, dtype=complex)\n",
    "axs[2].plot(t_vals, np.angle(Rc), label=\"arg R(t)\")\n",
    "axs[2].set_title(\"Stage XXIII: R(t)=Λ(2+it)/Λ(2-it) (phase)\")\n",
    "axs[2].set_xlabel(\"t\")\n",
    "axs[2].set_ylabel(\"phase (radians)\")\n",
    "axs[2].legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "# Estimate epsilon on a small box around the center\n",
    "box_sig = [1.9, 2.1]\n",
    "box_t   = [-5.0, 5.0]\n",
    "mask = (sigmas[:,None] >= box_sig[0]) & (sigmas[:,None] <= box_sig[1])\n",
    "mask = mask & (t_vals[None,:] >= box_t[0]) & (t_vals[None,:] <= box_t[1])\n",
    "# Gather complex ratios on the box, re-evaluating to keep complex values\n",
    "vals = []\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    if sigma < box_sig[0] or sigma > box_sig[1]: continue\n",
    "    for t in t_vals:\n",
    "        if t < box_t[0] or t > box_t[1]: continue\n",
    "        s  = mp.mpf(sigma) + 1j*mp.mpf(t)\n",
    "        sp = kappa - s\n",
    "        D  = Lmbd(sp)\n",
    "        if D != 0:\n",
    "            vals.append(complex(Lmbd(s)/D))\n",
    "vals = np.array(vals, dtype=complex)\n",
    "eps_hat = np.nan if len(vals)==0 else np.mean(vals/np.abs(vals))  # mean unit phase\n",
    "print(\"\\n=== Stage XXIII summary ===\")\n",
    "if len(vals):\n",
    "    print(f\"box for epsilon: σ∈{box_sig}, t∈{box_t}  samples={len(vals)}\")\n",
    "    print(f\"epsilon estimate (phase-only mean): {eps_hat:.12f}\")\n",
    "    print(f\"|R| median in box: {np.median(np.abs(vals)):.3e}\")\n",
    "else:\n",
    "    print(\"No samples in epsilon box.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "571164",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stage XXIVb: mirror pairing at σ = 2 ± δ\n",
      "  T_MAX=80.0000000000000, DT=0.0200000000000000 → 8001 points/line\n",
      "  deltas: 0.02..0.30 (count=31)\n",
      "  pairing tol in t: 0.200000000000000\n",
      "  minima drop pct:  0.0400000000000000\n",
      "  normalize per line? False\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XXIV-b summary ===\n",
      "stage             : XXIVb\n",
      "s0                : 2.0\n",
      "mu_used           : [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess           : 0.01831563888873418\n",
      "n_max             : 187\n",
      "precision_dps     : 180\n",
      "T_MAX             : 80.0\n",
      "DT                : 0.02\n",
      "t_points          : 8001\n",
      "delta_range       : [0.02, 0.3, 31]\n",
      "pair_tol_t        : 0.2\n",
      "minima_drop_pct   : 0.04\n",
      "normalize_per_line: False\n",
      "pairs_total       : 62\n",
      "mean_abs_dt       : 0.0\n",
      "median_abs_dt     : 0.0\n",
      "outputs           : ['stageXXIVb_pairs.csv', 'stageXXIVb_summary.json', 'stageXXIVb_example_lines.png', 'stageXXIVb_dt_hist.png']\n",
      "\n",
      "Summary and pairs written → stageXXIVb_pairs.csv, stageXXIVb_summary.json\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_568/3096260293.py:213: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n",
      "  plt.xlabel(\"t\"); plt.ylabel(\"log|Λ| (median-shifted)\"); plt.legend()\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Preview of paired minima (first 10):\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "cannot do positional indexing on RangeIndex with these indexers [10] of type Integer",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[9], line 229\u001b[0m\n\u001b[1;32m    227\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124mPreview of paired minima (first 10):\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    228\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m mirror_df\u001b[38;5;241m.\u001b[39mempty:\n\u001b[0;32m--> 229\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[43mmirror_df\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mhead\u001b[49m\u001b[43m(\u001b[49m\u001b[43mInteger\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m10\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241m.\u001b[39mto_string(index\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m))\n\u001b[1;32m    230\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    231\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m(none)\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "File \u001b[0;32m/ext/sage/10.7/local/var/lib/sage/venv-python3.12.5/lib/python3.12/site-packages/pandas/core/generic.py:5912\u001b[0m, in \u001b[0;36mNDFrame.head\u001b[0;34m(self, n)\u001b[0m\n\u001b[1;32m   5910\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m using_copy_on_write():\n\u001b[1;32m   5911\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39miloc[:n]\u001b[38;5;241m.\u001b[39mcopy()\n\u001b[0;32m-> 5912\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43miloc\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[43mn\u001b[49m\u001b[43m]\u001b[49m\n",
      "File \u001b[0;32m/ext/sage/10.7/local/var/lib/sage/venv-python3.12.5/lib/python3.12/site-packages/pandas/core/indexing.py:1191\u001b[0m, in \u001b[0;36m_LocationIndexer.__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m   1189\u001b[0m maybe_callable \u001b[38;5;241m=\u001b[39m com\u001b[38;5;241m.\u001b[39mapply_if_callable(key, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mobj)\n\u001b[1;32m   1190\u001b[0m maybe_callable \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_check_deprecated_callable_usage(key, maybe_callable)\n\u001b[0;32m-> 1191\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_getitem_axis\u001b[49m\u001b[43m(\u001b[49m\u001b[43mmaybe_callable\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43maxis\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m/ext/sage/10.7/local/var/lib/sage/venv-python3.12.5/lib/python3.12/site-packages/pandas/core/indexing.py:1729\u001b[0m, in \u001b[0;36m_iLocIndexer._getitem_axis\u001b[0;34m(self, key, axis)\u001b[0m\n\u001b[1;32m   1723\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mIndexError\u001b[39;00m(\n\u001b[1;32m   1724\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mDataFrame indexer is not allowed for .iloc\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m   1725\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mConsider using .loc for automatic alignment.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m   1726\u001b[0m     )\n\u001b[1;32m   1728\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(key, \u001b[38;5;28mslice\u001b[39m):\n\u001b[0;32m-> 1729\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_get_slice_axis\u001b[49m\u001b[43m(\u001b[49m\u001b[43mkey\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43maxis\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1731\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m is_iterator(key):\n\u001b[1;32m   1732\u001b[0m     key \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlist\u001b[39m(key)\n",
      "File \u001b[0;32m/ext/sage/10.7/local/var/lib/sage/venv-python3.12.5/lib/python3.12/site-packages/pandas/core/indexing.py:1764\u001b[0m, in \u001b[0;36m_iLocIndexer._get_slice_axis\u001b[0;34m(self, slice_obj, axis)\u001b[0m\n\u001b[1;32m   1761\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m obj\u001b[38;5;241m.\u001b[39mcopy(deep\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m)\n\u001b[1;32m   1763\u001b[0m labels \u001b[38;5;241m=\u001b[39m obj\u001b[38;5;241m.\u001b[39m_get_axis(axis)\n\u001b[0;32m-> 1764\u001b[0m \u001b[43mlabels\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_validate_positional_slice\u001b[49m\u001b[43m(\u001b[49m\u001b[43mslice_obj\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1765\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mobj\u001b[38;5;241m.\u001b[39m_slice(slice_obj, axis\u001b[38;5;241m=\u001b[39maxis)\n",
      "File \u001b[0;32m/ext/sage/10.7/local/var/lib/sage/venv-python3.12.5/lib/python3.12/site-packages/pandas/core/indexes/base.py:4205\u001b[0m, in \u001b[0;36mIndex._validate_positional_slice\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m   4200\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m   4201\u001b[0m \u001b[38;5;124;03mFor positional indexing, a slice must have either int or None\u001b[39;00m\n\u001b[1;32m   4202\u001b[0m \u001b[38;5;124;03mfor each of start, stop, and step.\u001b[39;00m\n\u001b[1;32m   4203\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m   4204\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_validate_indexer(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpositional\u001b[39m\u001b[38;5;124m\"\u001b[39m, key\u001b[38;5;241m.\u001b[39mstart, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124miloc\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m-> 4205\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_validate_indexer\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mpositional\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkey\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mstop\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43miloc\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m   4206\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_validate_indexer(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpositional\u001b[39m\u001b[38;5;124m\"\u001b[39m, key\u001b[38;5;241m.\u001b[39mstep, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124miloc\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "File \u001b[0;32m/ext/sage/10.7/local/var/lib/sage/venv-python3.12.5/lib/python3.12/site-packages/pandas/core/indexes/base.py:6752\u001b[0m, in \u001b[0;36mIndex._validate_indexer\u001b[0;34m(self, form, key, kind)\u001b[0m\n\u001b[1;32m   6747\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m   6748\u001b[0m \u001b[38;5;124;03mIf we are positional indexer, validate that we have appropriate\u001b[39;00m\n\u001b[1;32m   6749\u001b[0m \u001b[38;5;124;03mtyped bounds must be an integer.\u001b[39;00m\n\u001b[1;32m   6750\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m   6751\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m lib\u001b[38;5;241m.\u001b[39mis_int_or_none(key):\n\u001b[0;32m-> 6752\u001b[0m     \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_raise_invalid_indexer\u001b[49m\u001b[43m(\u001b[49m\u001b[43mform\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkey\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m/ext/sage/10.7/local/var/lib/sage/venv-python3.12.5/lib/python3.12/site-packages/pandas/core/indexes/base.py:4308\u001b[0m, in \u001b[0;36mIndex._raise_invalid_indexer\u001b[0;34m(self, form, key, reraise)\u001b[0m\n\u001b[1;32m   4306\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m reraise \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m lib\u001b[38;5;241m.\u001b[39mno_default:\n\u001b[1;32m   4307\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(msg) \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;21;01mreraise\u001b[39;00m\n\u001b[0;32m-> 4308\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(msg)\n",
      "\u001b[0;31mTypeError\u001b[0m: cannot do positional indexing on RangeIndex with these indexers [10] of type Integer"
     ]
    }
   ],
   "source": [
    "# === Stage XXIV-b: mirror-zeros across Re s = 2 (robust re-check) ===\n",
    "# Tight grid, tighter pairing tolerance, no per-line normalization.\n",
    "# Safe, self-contained cell.\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------- small helpers (Python-native types only) ----------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:\n",
    "        return mp.mpf(x)\n",
    "    except Exception:\n",
    "        return mp.mpf(str(to_float(x)))\n",
    "def tukey_weight(x, alpha=1.0):\n",
    "    # x in [0,1]; alpha=1 => Hann; alpha=0 => rectangular\n",
    "    if x <= 0 or x >= 1: return mp.mpf('0')\n",
    "    if alpha <= 0: return mp.mpf('1')\n",
    "    if x < alpha/2:\n",
    "        return mp.mpf('0.5') * (1 + mp.cos(mp.pi*(2*x/alpha - 1)))\n",
    "    if x <= 1 - alpha/2:\n",
    "        return mp.mpf('1')\n",
    "    return mp.mpf('0.5') * (1 + mp.cos(mp.pi*(2*(x-1)/alpha + 1)))\n",
    "def smooth_minima(y, t, k=7, drop_pct=0.04, pad=3):\n",
    "    \"\"\"\n",
    "    Robust local minima:\n",
    "      - moving average (window k, odd)\n",
    "      - keep minima below 'gate' = lo + drop_pct*(hi-lo)\n",
    "    \"\"\"\n",
    "    y = np.asarray(y, dtype=float)\n",
    "    t = np.asarray(t, dtype=float)\n",
    "    k = max(3, int(k) | 1)     # odd\n",
    "    kernel = np.ones(k)/k\n",
    "    y_sm = np.convolve(y, kernel, mode=\"same\")\n",
    "    n = len(y_sm)\n",
    "    lo, hi = float(np.min(y_sm)), float(np.max(y_sm))\n",
    "    gate = lo + drop_pct*(hi - lo)\n",
    "    mins = []\n",
    "    for i in range(pad, n-pad):\n",
    "        if y_sm[i-1] > y_sm[i] < y_sm[i+1] and y_sm[i] <= gate:\n",
    "            mins.append((float(t[i]), float(y[i]), float(y_sm[i])))\n",
    "    return mins\n",
    "def pair_by_t(mins_left, mins_right, tol=0.20):\n",
    "    \"\"\"Pair left/right minima by nearest t within tolerance (seconds pass).\"\"\"\n",
    "    rows, used = [], set()\n",
    "    for tL, yL, yLsm in mins_left:\n",
    "        if not mins_right: break\n",
    "        # nearest by |tR - tL|\n",
    "        jbest = min(range(len(mins_right)), key=lambda j: abs(mins_right[j][0] - tL))\n",
    "        tR, yR, yRsm = mins_right[jbest]\n",
    "        d = abs(tR - tL)\n",
    "        if d <= tol and jbest not in used:\n",
    "            used.add(jbest)\n",
    "            rows.append(dict(\n",
    "                t_left=tL, t_right=tR, dt=tR - tL,\n",
    "                depth_left=yL, depth_right=yR\n",
    "            ))\n",
    "    return rows\n",
    "def json_safe(obj):\n",
    "    \"\"\"Convert mpmath/NumPy/Pandas scalars to plain Python for JSON.\"\"\"\n",
    "    if isinstance(obj, (np.floating,)): return float(obj)\n",
    "    if isinstance(obj, (np.integer,)):  return int(obj)\n",
    "    try:\n",
    "        return float(obj)\n",
    "    except Exception:\n",
    "        return obj\n",
    "# ---------- Load Dirichlet coefficients ----------\n",
    "coeff_path = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"Coefficients file missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower: a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].astype(int).to_numpy()\n",
    "A_all = C[a_col].astype(float).to_numpy()\n",
    "mask  = np.isfinite(A_all) & (N_all > 0)\n",
    "n = N_all[mask]\n",
    "a = A_all[mask]\n",
    "ordr = np.argsort(n)\n",
    "n, a = n[ordr], a[ordr]\n",
    "N_max = int(n[-1])\n",
    "# ---------- Build Λ(s) ----------\n",
    "mp.mp.dps = 180  # high precision for stability\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None: N_cut = N_max\n",
    "    N_cut = int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    total = mp.mpf('0')\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    for ni, ai in zip(nn, aa):\n",
    "        x = mpf_safe(int(ni)) / Ncut_mp\n",
    "        w = tukey_weight(x, alpha=1.0)  # Hann\n",
    "        if w != 0:\n",
    "            total += mpf_safe(ai) / (mpf_safe(int(ni))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):\n",
    "    return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------- Stage XXIV-b parameters ----------\n",
    "STAGE_TAG = \"XXIVb\"\n",
    "s0       = mp.mpf('2.0')\n",
    "MU       = [1.0, 2.0, 2.0, 3.0]   # from your Stage XI uniform shift\n",
    "Q_guess  = mp.e**(-4)\n",
    "T_MAX = 80.0\n",
    "DT    = 0.02                      # finer step than XXIV\n",
    "t_vals = np.arange(-T_MAX, T_MAX + 1e-12, DT)\n",
    "# deltas 0.02..0.30 (inclusive, 31 values)\n",
    "deltas = np.linspace(0.02, 0.30, 31)\n",
    "# knobs (stricter)\n",
    "PAIR_TOL_T        = 0.20          # was 0.40\n",
    "MINIMA_DROP_PCT   = 0.04          # was 0.05 (slightly stricter)\n",
    "SMOOTH_K          = 7\n",
    "NORMALIZE_PER_LINE = False        # turn OFF normalization\n",
    "# containers\n",
    "mirror_rows = []\n",
    "example_lines = []   # for quick plot at two example sigmas\n",
    "# choose two example sigmas for a tiny diagnostic plot\n",
    "sigma_examples = [float(s0) - 0.20, float(s0) + 0.20]\n",
    "print(f\"Stage {STAGE_TAG}: mirror pairing at σ = 2 ± δ\")\n",
    "print(f\"  T_MAX={T_MAX}, DT={DT} → {len(t_vals)} points/line\")\n",
    "print(f\"  deltas: {deltas[0]:.2f}..{deltas[-1]:.2f} (count={len(deltas)})\")\n",
    "print(f\"  pairing tol in t: {PAIR_TOL_T}\")\n",
    "print(f\"  minima drop pct:  {MINIMA_DROP_PCT}\")\n",
    "print(f\"  normalize per line? {NORMALIZE_PER_LINE}\")\n",
    "for d in deltas:\n",
    "    sigma_L = float(s0) - float(d)\n",
    "    sigma_R = float(s0) + float(d)\n",
    "    # evaluate Λ on both lines\n",
    "    vals_L = [Lambda_of_s(mpf_safe(sigma_L) + 1j*mpf_safe(t), Q_guess, MU) for t in t_vals]\n",
    "    vals_R = [Lambda_of_s(mpf_safe(sigma_R) + 1j*mpf_safe(t), Q_guess, MU) for t in t_vals]\n",
    "    abs_L = np.array([to_float(abs(z)) for z in vals_L], dtype=float)\n",
    "    abs_R = np.array([to_float(abs(z)) for z in vals_R], dtype=float)\n",
    "    # take logs safely\n",
    "    with np.errstate(divide='ignore'):\n",
    "        logL = np.log(np.clip(abs_L, 1e-300, np.inf))\n",
    "        logR = np.log(np.clip(abs_R, 1e-300, np.inf))\n",
    "    if NORMALIZE_PER_LINE:\n",
    "        # optional, disabled in this XXIV-b\n",
    "        logL = logL - np.nanmedian(logL)\n",
    "        logR = logR - np.nanmedian(logR)\n",
    "    mins_L = smooth_minima(logL, t_vals, k=SMOOTH_K, drop_pct=MINIMA_DROP_PCT)\n",
    "    mins_R = smooth_minima(logR, t_vals, k=SMOOTH_K, drop_pct=MINIMA_DROP_PCT)\n",
    "    rows = pair_by_t(mins_L, mins_R, tol=PAIR_TOL_T)\n",
    "    for r in rows:\n",
    "        r[\"delta\"] = float(d)\n",
    "    mirror_rows.extend(rows)\n",
    "    # collect example lines once\n",
    "    if any(abs(sigma_L - se) < 1e-12 or abs(sigma_R - se) < 1e-12 for se in sigma_examples):\n",
    "        example_lines.append((sigma_L, t_vals.copy(), logL.copy()))\n",
    "        example_lines.append((sigma_R, t_vals.copy(), logR.copy()))\n",
    "# ---------- DataFrame + stats ----------\n",
    "mirror_df = pd.DataFrame(mirror_rows,\n",
    "                         columns=[\"delta\",\"t_left\",\"t_right\",\"dt\",\"depth_left\",\"depth_right\"]).sort_values(\n",
    "                         by=[\"delta\",\"t_left\"], ignore_index=True)\n",
    "pairs_total = int(len(mirror_df))\n",
    "mean_abs_dt = float(mirror_df[\"dt\"].abs().mean()) if pairs_total>0 else 0.0\n",
    "median_abs_dt = float(mirror_df[\"dt\"].abs().median()) if pairs_total>0 else 0.0\n",
    "print(\"\\n=== Stage XXIV-b summary ===\")\n",
    "summary = {\n",
    "    \"stage\"            : STAGE_TAG,\n",
    "    \"s0\"               : float(s0),\n",
    "    \"mu_used\"          : [float(m) for m in MU],\n",
    "    \"Q_guess\"          : float(Q_guess),\n",
    "    \"n_max\"            : int(N_max),\n",
    "    \"precision_dps\"    : int(mp.mp.dps),\n",
    "    \"T_MAX\"            : float(T_MAX),\n",
    "    \"DT\"               : float(DT),\n",
    "    \"t_points\"         : int(len(t_vals)),\n",
    "    \"delta_range\"      : [float(deltas[0]), float(deltas[-1]), int(len(deltas))],\n",
    "    \"pair_tol_t\"       : float(PAIR_TOL_T),\n",
    "    \"minima_drop_pct\"  : float(MINIMA_DROP_PCT),\n",
    "    \"normalize_per_line\": bool(NORMALIZE_PER_LINE),\n",
    "    \"pairs_total\"      : pairs_total,\n",
    "    \"mean_abs_dt\"      : mean_abs_dt,\n",
    "    \"median_abs_dt\"    : median_abs_dt,\n",
    "    \"outputs\"          : [\n",
    "        f\"stage{STAGE_TAG}_pairs.csv\",\n",
    "        f\"stage{STAGE_TAG}_summary.json\",\n",
    "        f\"stage{STAGE_TAG}_example_lines.png\",\n",
    "        f\"stage{STAGE_TAG}_dt_hist.png\",\n",
    "    ],\n",
    "}\n",
    "for k,v in summary.items():\n",
    "    print(f\"{k:18}: {v}\")\n",
    "# ---------- Save results ----------\n",
    "pairs_csv = f\"stage{STAGE_TAG}_pairs.csv\"\n",
    "mirror_df.to_csv(pairs_csv, index=False)\n",
    "# JSON (convert any exotic types)\n",
    "summary_json = f\"stage{STAGE_TAG}_summary.json\"\n",
    "with open(summary_json, \"w\") as f:\n",
    "    json.dump(summary, f, indent=2, default=json_safe)\n",
    "print(f\"\\nSummary and pairs written → {pairs_csv}, {summary_json}\")\n",
    "# ---------- Plots ----------\n",
    "# (1) Example lines at σ=2±0.20 (normalized visually by subtracting per-line median)\n",
    "plt.figure(figsize=(7,4.5))\n",
    "for sigma, tt, logabs in example_lines:\n",
    "    y = logabs - np.median(logabs)\n",
    "    plt.plot(tt, y, label=f\"σ={sigma:.2f}\")\n",
    "plt.title(f\"Stage {STAGE_TAG}: example lines at σ=2±0.20 (log|Λ| vs t)\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"log|Λ| (median-shifted)\"); plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig(f\"stage{STAGE_TAG}_example_lines.png\", dpi=140)\n",
    "plt.close()\n",
    "# (2) Histogram of dt (pairing offsets)\n",
    "plt.figure(figsize=(6.2,4.2))\n",
    "if pairs_total>0:\n",
    "    plt.hist(mirror_df[\"dt\"].values, bins=40)\n",
    "plt.title(f\"Stage {STAGE_TAG}: histogram of dt (t_right - t_left)\")\n",
    "plt.xlabel(\"dt\"); plt.ylabel(\"count\")\n",
    "plt.tight_layout()\n",
    "plt.savefig(f\"stage{STAGE_TAG}_dt_hist.png\", dpi=140)\n",
    "plt.close()\n",
    "# ---------- Quick preview (fixed: plain Python int) ----------\n",
    "print(\"\\nPreview of paired minima (first 10):\")\n",
    "if not mirror_df.empty:\n",
    "    print(mirror_df.head(10).to_string(index=False))\n",
    "else:\n",
    "    print(\"(none)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "412926",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Preview of paired minima (first 10):\n",
      "   delta  t_left  t_right  dt  depth_left  depth_right\n",
      "0.020000  -79.94   -79.94 0.0 -242.889087  -242.913924\n",
      "0.020000   79.94    79.94 0.0 -242.889087  -242.913924\n",
      "0.029333  -79.94   -79.94 0.0 -242.883098  -242.919524\n",
      "0.029333   79.94    79.94 0.0 -242.883098  -242.919524\n",
      "0.038667  -79.94   -79.94 0.0 -242.877035  -242.925050\n",
      "0.038667   79.94    79.94 0.0 -242.877035  -242.925050\n",
      "0.048000  -79.94   -79.94 0.0 -242.870899  -242.930501\n",
      "0.048000   79.94    79.94 0.0 -242.870899  -242.930501\n",
      "0.057333  -79.94   -79.94 0.0 -242.864689  -242.935877\n",
      "0.057333   79.94    79.94 0.0 -242.864689  -242.935877\n"
     ]
    }
   ],
   "source": [
    "# === Fix preview print for Stage XXIV-b ===\n",
    "print(\"\\nPreview of paired minima (first 10):\")\n",
    "try:\n",
    "    # Explicitly convert to plain Python int\n",
    "    print(mirror_df.head(int(10)).to_string(index=False))\n",
    "except Exception as e:\n",
    "    print(f\"(preview skipped due to: {e})\")\n",
    "    print(f\"mirror_df shape: {mirror_df.shape}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "bcfd5a",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stage XXV running …\n",
      "s0=2.0, K_terms≈21 (n_max=187), mp.dps=170\n",
      "t_range=[-80.0000000000000,80.0000000000000] (dt=0.0500000000000000, points/line=3201)\n",
      "deltas: 0.02 → 0.30 (count=31)\n",
      "\n",
      "  • MU variant eps=+0.00 → MU=[np.float64(1.0), np.float64(2.0), np.float64(2.0), np.float64(3.0)]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    pairs=  62, mean|dt|=0.0000e+00, max|dt|=0.0000e+00, mean|Δdepth|=6.6866e-01\n",
      "\n",
      "  • MU variant eps=+0.03 → MU=[np.float64(1.03), np.float64(2.03), np.float64(2.03), np.float64(3.03)]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    pairs=  62, mean|dt|=0.0000e+00, max|dt|=0.0000e+00, mean|Δdepth|=6.6867e-01\n",
      "\n",
      "  • MU variant eps=-0.03 → MU=[np.float64(0.97), np.float64(1.97), np.float64(1.97), np.float64(2.97)]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    pairs=  62, mean|dt|=0.0000e+00, max|dt|=0.0000e+00, mean|Δdepth|=6.6866e-01\n",
      "\n",
      "  • MU variant eps=+0.05 → MU=[np.float64(1.05), np.float64(2.05), np.float64(2.05), np.float64(3.05)]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    pairs=  62, mean|dt|=0.0000e+00, max|dt|=0.0000e+00, mean|Δdepth|=6.6867e-01\n",
      "\n",
      "  • MU variant eps=-0.05 → MU=[np.float64(0.95), np.float64(1.95), np.float64(1.95), np.float64(2.95)]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    pairs=  62, mean|dt|=0.0000e+00, max|dt|=0.0000e+00, mean|Δdepth|=6.6865e-01\n",
      "\n",
      "  • MU variant eps=+0.10 → MU=[np.float64(1.1), np.float64(2.1), np.float64(2.1), np.float64(3.1)]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    pairs=  62, mean|dt|=0.0000e+00, max|dt|=0.0000e+00, mean|Δdepth|=6.6868e-01\n",
      "\n",
      "  • MU variant eps=-0.10 → MU=[np.float64(0.9), np.float64(1.9), np.float64(1.9), np.float64(2.9)]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    pairs=  62, mean|dt|=0.0000e+00, max|dt|=0.0000e+00, mean|Δdepth|=6.6864e-01\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 910x520 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XXV summary ===\n",
      "  eps  mu1  mu2  mu3  mu4  pairs  mean_abs_dt  max_abs_dt  mean_abs_depth_diff\n",
      "-0.10 0.90 1.90 1.90 2.90     62          0.0         0.0             0.668643\n",
      "-0.05 0.95 1.95 1.95 2.95     62          0.0         0.0             0.668654\n",
      "-0.03 0.97 1.97 1.97 2.97     62          0.0         0.0             0.668657\n",
      " 0.00 1.00 2.00 2.00 3.00     62          0.0         0.0             0.668663\n",
      " 0.03 1.03 2.03 2.03 3.03     62          0.0         0.0             0.668668\n",
      " 0.05 1.05 2.05 2.05 3.05     62          0.0         0.0             0.668671\n",
      " 0.10 1.10 2.10 2.10 3.10     62          0.0         0.0             0.668679\n",
      "\n",
      "Wrote:\n",
      " - stageXXV_pairs.csv\n",
      " - stageXXV_summary.json\n",
      " - stageXXV_stability.png\n"
     ]
    }
   ],
   "source": [
    "# === Stage XXV: Phase-Stability of mirror symmetry about Re s = 2 ===\n",
    "# Self-contained; safe to run standalone (SageMath 10.7 kernel).\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------- small utilities (avoid Sage types) ----------\n",
    "to_int   = lambda x: int(x)\n",
    "to_float = lambda x: float(x)\n",
    "def mpf_safe(x):\n",
    "    try: return mp.mpf(x)\n",
    "    except Exception: return mp.mpf(str(float(x)))\n",
    "def tukey_weight(x, alpha=1.0):\n",
    "    # alpha=1 -> Hann\n",
    "    x = float(x)\n",
    "    if x <= 0.0 or x >= 1.0: return mp.mpf('0')\n",
    "    if x < alpha/2:    return mp.mpf('0.5')*(1 + mp.cos(mp.pi*(2*x/alpha - 1)))\n",
    "    if x <= 1 - alpha/2: return mp.mpf('1')\n",
    "    return mp.mpf('0.5')*(1 + mp.cos(mp.pi*(2*(x-1)/alpha + 1)))\n",
    "def moving_minima(y, t, k=7, drop_pct=0.05, pad=3):\n",
    "    \"\"\"Find robust local minima after a short moving-average smooth.\"\"\"\n",
    "    y  = np.asarray(y, dtype=float)\n",
    "    t  = np.asarray(t, dtype=float)\n",
    "    k  = max(3, int(k) | 1)  # odd\n",
    "    ker = np.ones(k)/k\n",
    "    ysm = np.convolve(y, ker, mode=\"same\")\n",
    "    lo, hi = float(ysm.min()), float(ysm.max())\n",
    "    gate   = lo + drop_pct*(hi - lo)\n",
    "    mins = []\n",
    "    n = len(ysm)\n",
    "    for i in range(pad, n-pad):\n",
    "        if ysm[i-1] > ysm[i] < ysm[i+1] and ysm[i] <= gate:\n",
    "            mins.append((t[i], y[i], ysm[i]))\n",
    "    return mins\n",
    "def pair_by_t(mins_L, mins_R, tol=0.40):\n",
    "    \"\"\"Pair minima across left/right lines by nearest t within tol.\"\"\"\n",
    "    rows, used = [], set()\n",
    "    for tL, yL, yLsm in mins_L:\n",
    "        if not mins_R: break\n",
    "        jbest, dmin = -1, 1e300\n",
    "        for j,(tR,yR,yRsm) in enumerate(mins_R):\n",
    "            if j in used: continue\n",
    "            d = abs(tR - tL)\n",
    "            if d < dmin:\n",
    "                dmin, jbest = d, j\n",
    "        if jbest >= 0 and dmin <= tol:\n",
    "            tR, yR, yRsm = mins_R[jbest]\n",
    "            used.add(jbest)\n",
    "            rows.append(dict(\n",
    "                t_left=float(tL),  t_right=float(tR),  dt=float(tR - tL),\n",
    "                depth_left=float(yL), depth_right=float(yR)\n",
    "            ))\n",
    "    return rows\n",
    "# ---------- load Dirichlet coefficients ----------\n",
    "coeff_path = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"Coefficients file missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].astype(int).to_numpy()\n",
    "A_all = C[a_col].astype(float).to_numpy()\n",
    "mask  = np.isfinite(A_all) & (N_all > 0)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "n, a = N_all[ordr], A_all[ordr]\n",
    "N_max = int(n[-1])\n",
    "# ---------- build Λ(s) ----------\n",
    "mp.mp.dps = 170  # high precision; keep <= ~200 for speed\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None: N_cut = N_max\n",
    "    N_cut = int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    total = mp.mpf('0')\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    for ni, ai in zip(nn, aa):\n",
    "        x = mpf_safe(int(ni))/Ncut_mp\n",
    "        w = tukey_weight(x, alpha=1.0)  # Hann\n",
    "        if w != 0:\n",
    "            total += mpf_safe(ai) / (mpf_safe(int(ni))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):        return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list: g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------- Stage XXV settings ----------\n",
    "s0      = mp.mpf('2.0')\n",
    "Q_guess = mp.e**(-4)              # crude scaling, consistent with earlier stages\n",
    "# Base μ and perturbations (phase-stability sweep)\n",
    "MU_base = np.array([1.0, 2.0, 2.0, 3.0], dtype=float)\n",
    "eps_list = [0.00, 0.03, -0.03, 0.05, -0.05, 0.10, -0.10]  # additive to *each* μ\n",
    "MU_variants = [ (eps, list(MU_base + eps)) for eps in eps_list ]\n",
    "# t/delta grids and knobs\n",
    "T_MAX  = 80.0\n",
    "DT     = 0.05\n",
    "t_vals = np.arange(-T_MAX, T_MAX + 1e-12, DT)\n",
    "deltas = np.linspace(0.02, 0.30, 31)\n",
    "pair_tol_t       = 0.40     # tolerance for pairing across mirror\n",
    "minima_drop_pct  = 0.05     # depth gate (relative to range on a line)\n",
    "smooth_k         = 7        # smoothing window for minima finder\n",
    "# ---------- main sweep ----------\n",
    "all_rows = []   # per-pair rows across all MU variants\n",
    "summ_rows = []  # per-variant stability summary\n",
    "print(\"Stage XXV running …\")\n",
    "print(f\"s0={s0}, K_terms≈{len(n)} (n_max={N_max}), mp.dps={mp.mp.dps}\")\n",
    "print(f\"t_range=[{-T_MAX},{T_MAX}] (dt={DT}, points/line={len(t_vals)})\")\n",
    "print(f\"deltas: {deltas[0]:.2f} → {deltas[-1]:.2f} (count={len(deltas)})\")\n",
    "for eps, MU in MU_variants:\n",
    "    print(f\"\\n  • MU variant eps={eps:+.2f} → MU={MU}\")\n",
    "    pairs_for_mu = []\n",
    "    for d in deltas:\n",
    "        sigL = float(s0) - float(d)\n",
    "        sigR = float(s0) + float(d)\n",
    "        # evaluate on both sides\n",
    "        vals_L = [Lambda_of_s(mpf_safe(sigL) + 1j*mpf_safe(t), Q_guess, MU) for t in t_vals]\n",
    "        vals_R = [Lambda_of_s(mpf_safe(sigR) + 1j*mpf_safe(t), Q_guess, MU) for t in t_vals]\n",
    "        abs_L  = np.array([to_float(abs(z)) for z in vals_L], dtype=float)\n",
    "        abs_R  = np.array([to_float(abs(z)) for z in vals_R], dtype=float)\n",
    "        # safe log and median-normalize per line\n",
    "        with np.errstate(divide='ignore'):\n",
    "            logL = np.log(np.maximum(abs_L, 0.0))\n",
    "            logR = np.log(np.maximum(abs_R, 0.0))\n",
    "        medL, medR = np.median(logL[np.isfinite(logL)]), np.median(logR[np.isfinite(logR)])\n",
    "        logL = np.where(np.isfinite(logL), logL - medL, -1e12)\n",
    "        logR = np.where(np.isfinite(logR), logR - medR, -1e12)\n",
    "        # minima on each side\n",
    "        minsL = moving_minima(logL, t_vals, k=smooth_k, drop_pct=minima_drop_pct)\n",
    "        minsR = moving_minima(logR, t_vals, k=smooth_k, drop_pct=minima_drop_pct)\n",
    "        # pair & record\n",
    "        pairs = pair_by_t(minsL, minsR, tol=pair_tol_t)\n",
    "        for row in pairs:\n",
    "            row.update(delta=float(d), eps=float(eps))\n",
    "        pairs_for_mu.extend(pairs)\n",
    "    if pairs_for_mu:\n",
    "        df = pd.DataFrame(pairs_for_mu)\n",
    "        mean_dt = float(np.mean(np.abs(df[\"dt\"])))\n",
    "        max_dt  = float(np.max(np.abs(df[\"dt\"])))\n",
    "        mean_depth_diff = float(np.mean(np.abs(df[\"depth_right\"] - df[\"depth_left\"])))\n",
    "        summ_rows.append(dict(\n",
    "            eps=float(eps), mu1=float(MU[0]), mu2=float(MU[1]), mu3=float(MU[2]), mu4=float(MU[3]),\n",
    "            pairs=int(len(df)), mean_abs_dt=mean_dt, max_abs_dt=max_dt,\n",
    "            mean_abs_depth_diff=mean_depth_diff\n",
    "        ))\n",
    "        all_rows.extend(pairs_for_mu)\n",
    "        print(f\"    pairs={len(df):4d}, mean|dt|={mean_dt:.4e}, max|dt|={max_dt:.4e}, \"\n",
    "              f\"mean|Δdepth|={mean_depth_diff:.4e}\")\n",
    "    else:\n",
    "        summ_rows.append(dict(\n",
    "            eps=float(eps), mu1=float(MU[0]), mu2=float(MU[1]), mu3=float(MU[2]), mu4=float(MU[3]),\n",
    "            pairs=0, mean_abs_dt=float('nan'), max_abs_dt=float('nan'), mean_abs_depth_diff=float('nan')\n",
    "        ))\n",
    "        print(\"    (no pairs found — likely lines too shallow for minima under this MU)\")\n",
    "# ---------- save outputs ----------\n",
    "pairs_csv  = \"stageXXV_pairs.csv\"\n",
    "summary_js = \"stageXXV_summary.json\"\n",
    "plot_png   = \"stageXXV_stability.png\"\n",
    "pairs_df = pd.DataFrame(all_rows) if all_rows else pd.DataFrame(\n",
    "    columns=[\"eps\",\"delta\",\"t_left\",\"t_right\",\"dt\",\"depth_left\",\"depth_right\"]\n",
    ")\n",
    "pairs_df.to_csv(pairs_csv, index=False)\n",
    "summ_df = pd.DataFrame(summ_rows).sort_values(\"eps\")\n",
    "with open(summary_js, \"w\") as f:\n",
    "    json.dump({\n",
    "        \"stage\": \"XXV\",\n",
    "        \"s0\": float(s0),\n",
    "        \"Q_guess\": float(Q_guess),\n",
    "        \"n_max\": int(N_max),\n",
    "        \"t_range\": [float(-T_MAX), float(T_MAX), float(DT)],\n",
    "        \"delta_range\": [float(deltas[0]), float(deltas[-1]), int(len(deltas))],\n",
    "        \"pair_tol_t\": float(pair_tol_t),\n",
    "        \"minima_drop_pct\": float(minima_drop_pct),\n",
    "        \"smooth_k\": int(smooth_k),\n",
    "        \"mp_dps\": int(mp.mp.dps),\n",
    "        \"summary_rows\": summ_df.to_dict(orient=\"records\")\n",
    "    }, f, indent=2)\n",
    "# ---------- quick plot: mean/max |dt| vs eps ----------\n",
    "plt.figure(figsize=(7.0, 4.0), dpi=130)\n",
    "plt.plot(summ_df[\"eps\"], summ_df[\"mean_abs_dt\"], marker=\"o\", label=\"mean |Δt|\")\n",
    "plt.plot(summ_df[\"eps\"], summ_df[\"max_abs_dt\"],  marker=\"s\", label=\"max |Δt|\")\n",
    "plt.axhline(0.0, lw=1)\n",
    "plt.xlabel(\"ε (added to all μ)\")\n",
    "plt.ylabel(\"|Δt| across mirror\")\n",
    "plt.title(\"Stage XXV: phase-stability of mirror pairing\")\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig(plot_png, bbox_inches=\"tight\")\n",
    "plt.show()\n",
    "print(\"\\n=== Stage XXV summary ===\")\n",
    "print(summ_df.to_string(index=False))\n",
    "print(f\"\\nWrote:\\n - {pairs_csv}\\n - {summary_js}\\n - {plot_png}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "145268",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XXVI summary ===\n",
      "stage             : XXVI\n",
      "s0                : 2.0\n",
      "mu_used           : [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess           : 0.01831563888873418\n",
      "n_max             : 187\n",
      "t_range           : [-120.0, 120.0, 4.0]\n",
      "min_logabs_norm   : -183.77476755318804\n",
      "max_logabs_norm   : 164.67620023245365\n",
      "depth_gate        : -185.32379976754635\n",
      "n_candidates      : 0\n",
      "outputs           : ['stageXXVI_line_logabs_phase.png', 'stageXXVI_candidates.csv']\n",
      "\n",
      "Preview of candidates:\n",
      "(none)\n"
     ]
    }
   ],
   "source": [
    "# === Stage XXVI (clean): central-line sweep with phase; robust previews & JSON ===\n",
    "# - Fixes: Pandas .head(Integer(...)) -> iloc[:int(...)]\n",
    "#          JSON serialization of Sage RealLiteral/RealNumber via make_serializable\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------- helpers ----------\n",
    "def to_int(x): return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:    return mp.mpf(x)\n",
    "    except Exception:\n",
    "        return mp.mpf(str(float(x)))\n",
    "def tukey_weight(x, alpha=1.0):\n",
    "    # Hann when alpha=1\n",
    "    if x <= 0 or x >= 1: return mp.mpf('0')\n",
    "    if x < alpha/2:      return mp.mpf('0.5')*(1+mp.cos(mp.pi*(2*x/alpha-1)))\n",
    "    if x <= 1-alpha/2:   return mp.mpf('1')\n",
    "    return mp.mpf('0.5')*(1+mp.cos(mp.pi*(2*(x-1)/alpha+1)))\n",
    "def make_serializable(obj):\n",
    "    \"\"\"Recursively convert Sage/mpmath/numpy scalars to plain Python types.\"\"\"\n",
    "    import numbers\n",
    "    # numpy scalars\n",
    "    if hasattr(obj, \"item\") and callable(getattr(obj, \"item\")):\n",
    "        try: return make_serializable(obj.item())\n",
    "        except Exception: pass\n",
    "    # mpmath\n",
    "    if isinstance(obj, mp.mpf): return float(obj)\n",
    "    # numbers (Sage RealLiteral/Integer duck-typed as numbers.Real/Integral)\n",
    "    if isinstance(obj, numbers.Integral): return int(obj)\n",
    "    if isinstance(obj, numbers.Real):     return float(obj)\n",
    "    if isinstance(obj, complex):          return complex(obj.real, obj.imag)\n",
    "    if isinstance(obj, (str, bytes)) or obj is None: return obj\n",
    "    if isinstance(obj, dict):  return {make_serializable(k): make_serializable(v) for k,v in obj.items()}\n",
    "    if isinstance(obj, (list, tuple)): return [make_serializable(v) for v in obj]\n",
    "    return obj  # fallback\n",
    "# ---------- load Dirichlet coefficients ----------\n",
    "coeff_path = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"Coefficients file missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].astype(int).to_numpy()\n",
    "A_all = C[a_col].astype(float).to_numpy()\n",
    "mask  = np.isfinite(A_all) & (N_all > 0)\n",
    "n = N_all[mask]; a = A_all[mask]\n",
    "ordr = np.argsort(n); n, a = n[ordr], a[ordr]\n",
    "N_max = int(n[-1])\n",
    "# ---------- completed Λ(s) ----------\n",
    "mp.mp.dps = 170\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None: N_cut = N_max\n",
    "    N_cut = int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    total = mp.mpf('0')\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    for ni, ai in zip(nn, aa):\n",
    "        x = mpf_safe(int(ni))/Ncut_mp\n",
    "        w = tukey_weight(x, alpha=1.0)\n",
    "        if w != 0:\n",
    "            total += mpf_safe(ai) / (mpf_safe(int(ni))**s) * w\n",
    "    return total\n",
    "def gamma_R(z): return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list: g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------- Stage XXVI parameters ----------\n",
    "s0      = mp.mpf('2.0')\n",
    "MU      = [1.0, 2.0, 2.0, 3.0]\n",
    "Q_guess = mp.e**(-4)\n",
    "t_min, t_max, dt = -120.0, 120.0, 4.0\n",
    "t_vals  = np.arange(t_min, t_max + 1e-12, dt)\n",
    "# ---------- evaluate on central line σ = s0 ----------\n",
    "vals = []\n",
    "for t in t_vals:\n",
    "    s = mpf_safe(2.0) + 1j*mpf_safe(t)\n",
    "    vals.append(Lambda_of_s(s, Q_guess, MU))\n",
    "vals = np.array(vals, dtype=complex)\n",
    "abs_vals = np.abs(vals).astype(float)\n",
    "# normalize per line by subtracting median of log|Λ|\n",
    "with np.errstate(divide='ignore'):\n",
    "    logabs = np.log(abs_vals, where=(abs_vals>0))\n",
    "logabs[~np.isfinite(logabs)] = np.nanmin(logabs[np.isfinite(logabs)]) - 10.0\n",
    "logabs_norm = logabs - np.nanmedian(logabs)\n",
    "# unwrap phase\n",
    "phase = np.unwrap(np.angle(vals))\n",
    "# ---------- zero/near-zero candidates on central line ----------\n",
    "# Heuristic: look for deep valleys on normalized log|Λ|\n",
    "depth_gate = np.nanmax(logabs_norm) - 350.0  # very strict; adjust if needed\n",
    "cand_idx = np.where(logabs_norm <= depth_gate)[0]\n",
    "candidates = pd.DataFrame({\n",
    "    \"t\": t_vals[cand_idx].astype(float),\n",
    "    \"logabs_norm\": logabs_norm[cand_idx].astype(float),\n",
    "    \"phase\": phase[cand_idx].astype(float),\n",
    "})\n",
    "# ---------- plots ----------\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(8,6), sharex=True)\n",
    "ax1.plot(t_vals, logabs_norm, marker='o', ms=3, lw=1, label=\"log |Λ|\")\n",
    "if not candidates.empty:\n",
    "    ax1.scatter(candidates[\"t\"], candidates[\"logabs_norm\"], s=25, label=\"candidates\")\n",
    "ax1.set_title(\"Stage XXVI: log|Λ(2+it)| (normalized) with candidates\")\n",
    "ax1.set_ylabel(\"log|Λ|\")\n",
    "ax1.legend()\n",
    "ax2.plot(t_vals, phase, marker='o', ms=3, lw=1, label=\"arg Λ\")\n",
    "if not candidates.empty:\n",
    "    ax2.scatter(candidates[\"t\"], candidates[\"phase\"], s=25, label=\"candidates\")\n",
    "ax2.set_title(\"Stage XXVI: unwrapped arg Λ(2+it)\")\n",
    "ax2.set_xlabel(\"t\")\n",
    "ax2.set_ylabel(\"phase (radians)\")\n",
    "ax2.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"stageXXVI_line_logabs_phase.png\", dpi=140)\n",
    "plt.close(fig)\n",
    "# ---------- outputs ----------\n",
    "candidates.to_csv(\"stageXXVI_candidates.csv\", index=False)\n",
    "summary = {\n",
    "    \"stage\": \"XXVI\",\n",
    "    \"s0\": float(s0),\n",
    "    \"mu_used\": [float(x) for x in MU],\n",
    "    \"Q_guess\": float(Q_guess),\n",
    "    \"n_max\": int(N_max),\n",
    "    \"t_range\": [float(t_min), float(t_max), float(dt)],\n",
    "    \"min_logabs_norm\": float(np.nanmin(logabs_norm)),\n",
    "    \"max_logabs_norm\": float(np.nanmax(logabs_norm)),\n",
    "    \"depth_gate\": float(depth_gate),\n",
    "    \"n_candidates\": int(len(candidates)),\n",
    "    \"outputs\": [\"stageXXVI_line_logabs_phase.png\", \"stageXXVI_candidates.csv\"],\n",
    "}\n",
    "with open(\"stageXXVI_summary.json\", \"w\") as f:\n",
    "    json.dump(make_serializable(summary), f, indent=2)\n",
    "print(\"\\n=== Stage XXVI summary ===\")\n",
    "for k,v in summary.items():\n",
    "    print(f\"{k:18}: {v}\")\n",
    "print(\"\\nPreview of candidates:\")\n",
    "if not candidates.empty:\n",
    "    # explicit plain int for iloc\n",
    "    print(candidates.iloc[:int(10)].to_string(index=False))\n",
    "else:\n",
    "    print(\"(none)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e03e68",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 2 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XXVI summary ===\n",
      "stage             : XXVI\n",
      "s0                : 2.0\n",
      "mu_used           : [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess           : 0.01831563888873418\n",
      "n_max             : 187\n",
      "t_range           : [-140.0, 140.0, 2.0]\n",
      "min_logabs_norm   : -215.78501217784952\n",
      "max_logabs_norm   : 194.65152413759972\n",
      "log_range         : 410.43653631544925\n",
      "depth_gate        : -10.5667440201249\n",
      "n_candidates      : 2\n",
      "outputs           : ['stageXXVI_line_logabs_phase.png', 'stageXXVI_candidates.csv']\n",
      "\n",
      "Preview of candidates:\n",
      "     t  logabs_norm\n",
      "-134.0  -198.019039\n",
      " 134.0  -198.019039\n"
     ]
    }
   ],
   "source": [
    "# === Stage XXVI (clean): scan Λ(2+it), detect deep minima, plot, and save ===\n",
    "# - Safe JSON serialization (no Sage/MP types leak)\n",
    "# - Robust pandas preview (no Integer/iloc issue)\n",
    "# - Deeper gate: 50% above the minimum across the line (to actually catch minima)\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ----------------- helpers -----------------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:\n",
    "        return mp.mpf(x)\n",
    "    except Exception:\n",
    "        return mp.mpf(str(to_float(x)))\n",
    "def tukey_weight(x, alpha=1.0):\n",
    "    # x in [0,1], alpha=1 => Hann; alpha=0 => rectangular\n",
    "    if x <= 0 or x >= 1: return mp.mpf('0')\n",
    "    if x < alpha/2:\n",
    "        return mp.mpf('0.5') * (1 + mp.cos(mp.pi*(2*x/alpha - 1)))\n",
    "    if x <= 1 - alpha/2:\n",
    "        return mp.mpf('1')\n",
    "    return mp.mpf('0.5') * (1 + mp.cos(mp.pi*(2*(x-1)/alpha + 1)))\n",
    "def smooth_minima(y, t, k=7, drop_pct=0.02, pad=2):\n",
    "    \"\"\"\n",
    "    Find local minima robustly:\n",
    "      - moving-average smooth (window k, odd)\n",
    "      - local min test on smoothed curve\n",
    "      - keep points that are at least `drop_pct` below the smoothed max\n",
    "    Returns list of tuples (t, y_raw, y_smoothed).\n",
    "    \"\"\"\n",
    "    y = np.asarray(y, dtype=float)\n",
    "    t = np.asarray(t, dtype=float)\n",
    "    k = max(3, int(k) | 1)\n",
    "    kernel = np.ones(k)/k\n",
    "    y_sm = np.convolve(y, kernel, mode=\"same\")\n",
    "    mins = []\n",
    "    hi = float(np.max(y_sm))\n",
    "    gate = hi - drop_pct*(hi - float(np.min(y_sm)))\n",
    "    n = len(y_sm)\n",
    "    for i in range(pad, n-pad):\n",
    "        if y_sm[i-1] > y_sm[i] < y_sm[i+1] and y_sm[i] <= gate:\n",
    "            mins.append((t[i], float(y[i]), float(y_sm[i])))\n",
    "    return mins\n",
    "# ----------------- load Dirichlet coefficients -----------------\n",
    "coeff_path = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"Coefficients file missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].astype(int).to_numpy()\n",
    "A_all = C[a_col].astype(float).to_numpy()\n",
    "mask  = np.isfinite(A_all) & (N_all > 0)\n",
    "N_all, A_all = N_all[mask], A_all[mask]\n",
    "ordr = np.argsort(N_all)\n",
    "n = N_all[ordr]\n",
    "a = A_all[ordr]\n",
    "N_max = int(n[-1])\n",
    "# ----------------- build Λ(s) -----------------\n",
    "mp.mp.dps = 180  # high precision for phase stability\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None: N_cut = N_max\n",
    "    N_cut = int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    total = mp.mpf('0')\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    for ni, ai in zip(nn, aa):\n",
    "        x = mpf_safe(int(ni)) / Ncut_mp\n",
    "        w = tukey_weight(x, alpha=1.0)  # Hann\n",
    "        if w != 0:\n",
    "            total += mpf_safe(ai) / (mpf_safe(int(ni))**s) * w\n",
    "    return total\n",
    "def gamma_R(z):      return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ----------------- Stage XXVI scan on σ = 2 -----------------\n",
    "s0 = mp.mpf('2.0')\n",
    "MU = [1.0, 2.0, 2.0, 3.0]     # from earlier stages\n",
    "Q_guess = mp.e**(-4)\n",
    "t_lo, t_hi, dt = -140.0, 140.0, 2.0\n",
    "t_vals = np.arange(t_lo, t_hi + 1e-12, dt)\n",
    "vals = []\n",
    "for t in t_vals:\n",
    "    s = mpf_safe(2.0) + 1j*mpf_safe(t)\n",
    "    vals.append(Lambda_of_s(s, Q_guess, MU, N_max))\n",
    "absvals = np.array([to_float(abs(z)) for z in vals], dtype=float)\n",
    "# log|Λ| with safe floor (if any underflow to 0)\n",
    "with np.errstate(divide='ignore'):\n",
    "    logabs = np.log(absvals, where=absvals>0)\n",
    "    logabs[~np.isfinite(logabs)] = -1e9\n",
    "# Normalize by subtracting the median to center the plot\n",
    "med = float(np.median(logabs))\n",
    "logabs_norm = logabs - med\n",
    "# Phase (argument), unwrapped\n",
    "arg_vals = np.unwrap(np.angle(np.array([complex(z.real, z.imag) for z in vals])))\n",
    "# Depth gate: **deeper** (50% above the minimum across the line)\n",
    "low_val  = float(np.min(logabs_norm))\n",
    "high_val = float(np.max(logabs_norm))\n",
    "log_range = high_val - low_val\n",
    "depth_gate = low_val + 0.50 * log_range   # << updated from 0.20 to 0.50\n",
    "# Find local minima below the gate\n",
    "mins = smooth_minima(logabs_norm, t_vals, k=7, drop_pct=0.02, pad=2)\n",
    "candidates = [(t, y_raw) for (t, y_raw, ysm) in mins if y_raw <= depth_gate]\n",
    "# ----------------- Save outputs -----------------\n",
    "OUT_PLOT = \"stageXXVI_line_logabs_phase.png\"\n",
    "OUT_CSV  = \"stageXXVI_candidates.csv\"\n",
    "OUT_SUM  = \"stageXXVI_summary.json\"\n",
    "# Plot\n",
    "plt.figure(figsize=(10,6))\n",
    "ax1 = plt.subplot(2,1,1)\n",
    "ax1.plot(t_vals, logabs_norm, label=\"log|Λ(2+it)|\")\n",
    "ax1.axhline(depth_gate, ls=\"--\", label=\"depth gate\")\n",
    "if candidates:\n",
    "    tc = [c[0] for c in candidates]\n",
    "    yc = [c[1] for c in candidates]\n",
    "    ax1.scatter(tc, yc, marker=\"x\", s=40, label=\"candidates\")\n",
    "ax1.set_title(\"Stage XXVI: log|Λ(2+it)| (normalized) with candidates\")\n",
    "ax1.set_xlabel(\"t\")\n",
    "ax1.set_ylabel(\"log|Λ|\")\n",
    "ax2 = plt.subplot(2,1,2)\n",
    "ax2.plot(t_vals, arg_vals, label=\"arg Λ\")\n",
    "ax2.set_title(\"Stage XXVI: unwrapped arg Λ(2+it)\")\n",
    "ax2.set_xlabel(\"t\")\n",
    "ax2.set_ylabel(\"phase (radians)\")\n",
    "plt.tight_layout()\n",
    "plt.savefig(OUT_PLOT, dpi=140)\n",
    "plt.show()\n",
    "# Candidates CSV\n",
    "cand_df = pd.DataFrame(candidates, columns=[\"t\", \"logabs_norm\"])\n",
    "cand_df.to_csv(OUT_CSV, index=False)\n",
    "# JSON summary (plain Python types only)\n",
    "summary = {\n",
    "    \"stage\": \"XXVI\",\n",
    "    \"s0\": float(s0),\n",
    "    \"mu_used\": [float(m) for m in MU],\n",
    "    \"Q_guess\": float(Q_guess),\n",
    "    \"n_max\": int(N_max),\n",
    "    \"t_range\": [float(t_lo), float(t_hi), float(dt)],\n",
    "    \"min_logabs_norm\": float(low_val),\n",
    "    \"max_logabs_norm\": float(high_val),\n",
    "    \"log_range\": float(log_range),\n",
    "    \"depth_gate\": float(depth_gate),\n",
    "    \"n_candidates\": int(len(candidates)),\n",
    "    \"outputs\": [OUT_PLOT, OUT_CSV],\n",
    "}\n",
    "with open(OUT_SUM, \"w\") as f:\n",
    "    json.dump(summary, f, indent=2)\n",
    "# Console summary + small preview\n",
    "print(\"\\n=== Stage XXVI summary ===\")\n",
    "for k,v in summary.items():\n",
    "    print(f\"{k:18}: {v}\")\n",
    "print(\"\\nPreview of candidates:\")\n",
    "if not cand_df.empty:\n",
    "    print(cand_df.iloc[:int(10)].to_string(index=False))\n",
    "else:\n",
    "    print(\"(none)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "bfd0ad",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x700 with 2 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "=== Stage XXVII summary ===\n",
      "stage             : XXVII\n",
      "s0                : 2.0\n",
      "mu_used           : [1.0, 2.0, 2.0, 3.0]\n",
      "Q_guess           : 0.01831563888873418\n",
      "n_max             : 187\n",
      "t_range           : [-150.0, 150.0, 2.0]\n",
      "candidates_used   : [-134.0, 134.0]\n",
      "metrics           : {'rms_log_diff': 0.0, 'max_abs_log_diff': 0.0, 'rms_phase_sum': 7.247920660869928e-16, 'max_abs_phase_sum': 7.105427357601002e-15}\n",
      "outputs           : ['stageXXVII_symmetry.png', 'stageXXVII_symmetry_samples.csv']\n",
      "\n",
      "Candidate points (nearest grid rows):\n",
      "     t  log_abs(2+it)  log_abs(2-it)  log_diff     phase_sum\n",
      "-134.0    -410.613549    -410.613549       0.0 -4.440892e-16\n",
      " 134.0    -410.613549    -410.613549       0.0  0.000000e+00\n",
      "\n",
      "Wrote:\n",
      " - stageXXVII_symmetry.png\n",
      " - stageXXVII_symmetry_samples.csv\n",
      " - stageXXVII_summary.json\n"
     ]
    }
   ],
   "source": [
    "# === Stage XXVII: mirror symmetry at s = 2 ± it (phase & magnitude) ===\n",
    "# Self-contained & JSON-safe.\n",
    "import json, numpy as np, pandas as pd, matplotlib.pyplot as plt\n",
    "from pathlib import Path\n",
    "import mpmath as mp\n",
    "# ---------- helpers ----------\n",
    "def to_int(x):   return int(x)\n",
    "def to_float(x): return float(x)\n",
    "def mpf_safe(x):\n",
    "    try:\n",
    "        return mp.mpf(x)\n",
    "    except Exception:\n",
    "        return mp.mpf(str(float(x)))\n",
    "def tukey_weight(x, alpha=1.0):\n",
    "    # x in [0,1], alpha=1 => Hann; alpha=0 => rectangular\n",
    "    if x <= 0 or x >= 1: return mp.mpf('0')\n",
    "    if x < alpha/2:\n",
    "        return mp.mpf('0.5')*(1 + mp.cos(mp.pi*(2*x/alpha - 1)))\n",
    "    if x <= 1 - alpha/2:\n",
    "        return mp.mpf('1')\n",
    "    return mp.mpf('0.5')*(1 + mp.cos(mp.pi*(2*(x-1)/alpha + 1)))\n",
    "def unwrap_numpy(ph):\n",
    "    # np.unwrap expects float64; ensure conversion from mpmath\n",
    "    return np.unwrap(np.array([to_float(v) for v in ph], dtype=float))\n",
    "# ---------- load Dirichlet coefficients ----------\n",
    "coeff_path = Path(\"stageVIII_dirichlet_coeffs.csv\")\n",
    "if not coeff_path.exists() or coeff_path.stat().st_size == 0:\n",
    "    raise FileNotFoundError(\"stageVIII_dirichlet_coeffs.csv not found or empty. Run Stage VIII first.\")\n",
    "C = pd.read_csv(coeff_path)\n",
    "cols_lower = {c.lower(): c for c in C.columns}\n",
    "if \"n\" not in cols_lower:\n",
    "    raise ValueError(\"Coefficients file missing column 'n'.\")\n",
    "a_col = None\n",
    "for k in (\"a_n\",\"an\",\"a\",\"a_n_real\"):\n",
    "    if k in cols_lower:\n",
    "        a_col = cols_lower[k]; break\n",
    "if a_col is None:\n",
    "    raise ValueError(\"No coefficient column found (a_n/an/a/a_n_real).\")\n",
    "N_all = C[cols_lower[\"n\"]].astype(int).to_numpy()\n",
    "A_all = C[a_col].astype(float).to_numpy()\n",
    "mask  = np.isfinite(A_all) & (N_all > 0)\n",
    "n = N_all[mask]\n",
    "a = A_all[mask]\n",
    "ordr = np.argsort(n)\n",
    "n, a = n[ordr], a[ordr]\n",
    "N_max = int(n[-1])\n",
    "# ---------- completed Λ(s) ----------\n",
    "mp.mp.dps = 180  # high precision for phase stability\n",
    "def L_of_s(s, N_cut=None):\n",
    "    if N_cut is None: N_cut = N_max\n",
    "    N_cut = int(N_cut)\n",
    "    idx = np.searchsorted(n, N_cut, side=\"right\")\n",
    "    nn, aa = n[:idx], a[:idx]\n",
    "    total = mp.mpf('0')\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    for ni, ai in zip(nn, aa):\n",
    "        x = mpf_safe(int(ni))/Ncut_mp\n",
    "        w = tukey_weight(x, alpha=1.0)  # Hann\n",
    "        if w != 0:\n",
    "            total += mpf_safe(ai)/(mpf_safe(int(ni))**s) * w\n",
    "    return total\n",
    "def gamma_R(z): return mp.pi**(-z/2) * mp.gamma(z/2)\n",
    "def gamma_factor(s, mu_list):\n",
    "    g = mp.mpf('1')\n",
    "    for mu in mu_list:\n",
    "        g *= gamma_R(s + mpf_safe(mu))\n",
    "    return g\n",
    "def Lambda_of_s(s, Q, mu_list, N_cut=None):\n",
    "    return (mpf_safe(Q)**(s/2)) * gamma_factor(s, mu_list) * L_of_s(s, N_cut)\n",
    "# ---------- parameters ----------\n",
    "s0      = mp.mpf('2.0')\n",
    "MU      = [1.0, 2.0, 2.0, 3.0]\n",
    "Q_guess = mp.e**(-4)\n",
    "N_cut   = N_max\n",
    "# t-grid (wider than XXVI just a bit)\n",
    "T_MAX = 150.0\n",
    "DT    = 2.0\n",
    "t_vals = np.arange(-T_MAX, T_MAX + 1e-12, DT)\n",
    "# Try to load candidates from Stage XXVI (optional)\n",
    "cand_path = Path(\"stageXXVI_candidates.csv\")\n",
    "if cand_path.exists() and cand_path.stat().st_size > 0:\n",
    "    try:\n",
    "        cand = pd.read_csv(cand_path)\n",
    "        # expect a 't' column\n",
    "        ts_from_file = cand[\"t\"].astype(float).to_list()\n",
    "        # Keep up to two most extreme by |t|\n",
    "        ts_from_file = sorted(ts_from_file, key=lambda x: -abs(x))[:2]\n",
    "        candidate_ts = sorted([to_float(x) for x in ts_from_file])\n",
    "    except Exception:\n",
    "        candidate_ts = [-134.0, 134.0]\n",
    "else:\n",
    "    candidate_ts = [-134.0, 134.0]\n",
    "# ---------- evaluate Λ on 2±it ----------\n",
    "vals_plus  = []\n",
    "vals_minus = []\n",
    "for t in t_vals:\n",
    "    s_plus  = s0 + 1j*mpf_safe(t)\n",
    "    s_minus = s0 - 1j*mpf_safe(t)\n",
    "    vals_plus.append( Lambda_of_s(s_plus,  Q_guess, MU, N_cut) )\n",
    "    vals_minus.append(Lambda_of_s(s_minus, Q_guess, MU, N_cut) )\n",
    "abs_plus  = np.array([to_float(abs(z)) for z in vals_plus ], dtype=float)\n",
    "abs_minus = np.array([to_float(abs(z)) for z in vals_minus], dtype=float)\n",
    "phi_plus  = [mp.arg(z) for z in vals_plus ]\n",
    "phi_minus = [mp.arg(z) for z in vals_minus]\n",
    "# unwrap phases\n",
    "phi_plus_u  = unwrap_numpy(phi_plus)\n",
    "phi_minus_u = unwrap_numpy(phi_minus)\n",
    "# Symmetry diagnostics:\n",
    "# Magnitude symmetry expects |Λ(2+it)| ≈ |Λ(2-it)| → log-diff ~ 0\n",
    "with np.errstate(divide='ignore'):\n",
    "    log_plus  = np.log(abs_plus,  where=(abs_plus>0))\n",
    "    log_minus = np.log(abs_minus, where=(abs_minus>0))\n",
    "# replace -inf by a large negative (keeps differences finite if both small)\n",
    "neg_floor = -1e6\n",
    "log_plus[np.isneginf(log_plus)]   = neg_floor\n",
    "log_minus[np.isneginf(log_minus)] = neg_floor\n",
    "log_diff = log_plus - log_minus\n",
    "# Phase symmetry for a real-analytic Λ around σ=2 typically gives φ(2+it) ≈ -φ(2-it)\n",
    "phase_sum = unwrap_numpy(phi_plus_u + phi_minus_u)  # should be ~ 0 when symmetric\n",
    "# Metrics over the whole grid\n",
    "def rms(x): return float(np.sqrt(np.mean(np.square(np.asarray(x, dtype=float)))))\n",
    "metrics = {\n",
    "    \"rms_log_diff\"   : rms(log_diff),\n",
    "    \"max_abs_log_diff\": float(np.max(np.abs(log_diff))),\n",
    "    \"rms_phase_sum\"  : rms(phase_sum),\n",
    "    \"max_abs_phase_sum\": float(np.max(np.abs(phase_sum))),\n",
    "}\n",
    "# Metrics at candidate t's (nearest grid points)\n",
    "def nearest_idx(xgrid, x):\n",
    "    return int(np.argmin(np.abs(xgrid - x)))\n",
    "cand_rows = []\n",
    "for tt in candidate_ts:\n",
    "    j = nearest_idx(t_vals, tt)\n",
    "    cand_rows.append({\n",
    "        \"t\": float(t_vals[j]),\n",
    "        \"log_abs(2+it)\": float(log_plus[j]),\n",
    "        \"log_abs(2-it)\": float(log_minus[j]),\n",
    "        \"log_diff\": float(log_diff[j]),\n",
    "        \"phase_sum\": float(phase_sum[j]),\n",
    "    })\n",
    "cand_df = pd.DataFrame(cand_rows)\n",
    "# ---------- plots ----------\n",
    "plt.figure(figsize=(10,7))\n",
    "ax1 = plt.subplot(2,1,1)\n",
    "ax1.plot(t_vals, log_diff, label=\"log|Λ(2+it)| - log|Λ(2-it)|\")\n",
    "ax1.axhline(0, linestyle=\"--\", linewidth=1)\n",
    "for r in cand_rows:\n",
    "    ax1.plot(r[\"t\"], r[\"log_diff\"], 'o')\n",
    "ax1.set_title(\"Stage XXVII: magnitude symmetry (diff of logs)\")\n",
    "ax1.set_xlabel(\"t\")\n",
    "ax1.set_ylabel(\"log-diff\")\n",
    "ax1.legend()\n",
    "ax2 = plt.subplot(2,1,2)\n",
    "ax2.plot(t_vals, phase_sum, label=\"φ(2+it) + φ(2-it) (unwrapped)\")\n",
    "ax2.axhline(0, linestyle=\"--\", linewidth=1)\n",
    "for r in cand_rows:\n",
    "    ax2.plot(r[\"t\"], r[\"phase_sum\"], 'o')\n",
    "ax2.set_title(\"Stage XXVII: phase symmetry (sum ~ 0 if symmetric)\")\n",
    "ax2.set_xlabel(\"t\")\n",
    "ax2.set_ylabel(\"phase sum (radians)\")\n",
    "ax2.legend()\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"stageXXVII_symmetry.png\", dpi=160)\n",
    "plt.show()\n",
    "# ---------- save CSV + summary (JSON-safe) ----------\n",
    "out_csv = \"stageXXVII_symmetry_samples.csv\"\n",
    "samples_df = pd.DataFrame({\n",
    "    \"t\": t_vals.astype(float),\n",
    "    \"log_plus\": log_plus.astype(float),\n",
    "    \"log_minus\": log_minus.astype(float),\n",
    "    \"log_diff\": log_diff.astype(float),\n",
    "    \"phase_sum\": phase_sum.astype(float),\n",
    "})\n",
    "samples_df.to_csv(out_csv, index=False)\n",
    "summary = {\n",
    "    \"stage\": \"XXVII\",\n",
    "    \"s0\": float(s0),\n",
    "    \"mu_used\": [float(m) for m in MU],\n",
    "    \"Q_guess\": float(Q_guess),\n",
    "    \"n_max\": int(N_max),\n",
    "    \"t_range\": [float(t_vals[0]), float(t_vals[-1]), float(DT)],\n",
    "    \"candidates_used\": [float(x) for x in candidate_ts],\n",
    "    \"metrics\": metrics,\n",
    "    \"outputs\": [\"stageXXVII_symmetry.png\", \"stageXXVII_symmetry_samples.csv\"],\n",
    "    \"candidates_table_head\": cand_rows\n",
    "}\n",
    "with open(\"stageXXVII_summary.json\", \"w\") as f:\n",
    "    json.dump(summary, f, indent=2)\n",
    "print(\"\\n=== Stage XXVII summary ===\")\n",
    "for k,v in summary.items():\n",
    "    if k != \"candidates_table_head\":\n",
    "        print(f\"{k:18}: {v}\")\n",
    "print(\"\\nCandidate points (nearest grid rows):\")\n",
    "print(cand_df.to_string(index=False))\n",
    "print(\"\\nWrote:\")\n",
    "print(\" - stageXXVII_symmetry.png\")\n",
    "print(\" - stageXXVII_symmetry_samples.csv\")\n",
    "print(\" - stageXXVII_summary.json\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a5faa6",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Preview of candidates (first 10):\n",
      "  col0        col1\n",
      "-134.0 -198.019039\n",
      " 134.0 -198.019039\n"
     ]
    }
   ],
   "source": [
    "# --- Robust preview for any 'candidates' table ---\n",
    "import pandas as pd\n",
    "from pathlib import Path\n",
    "def to_df(obj):\n",
    "    if obj is None:\n",
    "        return pd.DataFrame()\n",
    "    if isinstance(obj, pd.DataFrame):\n",
    "        return obj.copy()\n",
    "    if isinstance(obj, (str, Path)) and Path(obj).exists():\n",
    "        try:\n",
    "            return pd.read_csv(obj)\n",
    "        except Exception:\n",
    "            return pd.DataFrame()\n",
    "    if isinstance(obj, dict):\n",
    "        return pd.DataFrame([obj])\n",
    "    if isinstance(obj, (list, tuple)):\n",
    "        if not obj:\n",
    "            return pd.DataFrame()\n",
    "        if isinstance(obj[0], dict):\n",
    "            return pd.DataFrame(obj)\n",
    "        # list/tuple of rows -> rectangularize\n",
    "        m = max(len(r) if isinstance(r, (list, tuple)) else 0 for r in obj)\n",
    "        rows = [list(r) + [None]*(m - len(r)) for r in obj]\n",
    "        return pd.DataFrame(rows, columns=[f\"col{i}\" for i in range(m)])\n",
    "    return pd.DataFrame()\n",
    "# Prefer in-memory 'candidates', else try the stage CSV next to the notebook.\n",
    "src = candidates if 'candidates' in globals() else (\n",
    "    \"stageXXVII_candidates.csv\" if Path(\"stageXXVII_candidates.csv\").exists()\n",
    "    else (\"stageXXVI_candidates.csv\" if Path(\"stageXXVI_candidates.csv\").exists() else None)\n",
    ")\n",
    "df = to_df(src)\n",
    "print(\"Preview of candidates (first 10):\")\n",
    "if df.empty:\n",
    "    print(\"(none)\")\n",
    "else:\n",
    "    # Friendly rename of common columns (optional)\n",
    "    ren = {}\n",
    "    for c in list(df.columns):\n",
    "        cl = str(c).strip().lower()\n",
    "        if cl in {\"t\",\"t_star\",\"t0\"}: ren[c] = cl    # normalize time column name\n",
    "        elif (\"log\" in cl and \"abs\" in cl) or cl.startswith(\"logabs\"):\n",
    "            ren[c] = \"logabs_norm\"\n",
    "    if ren:\n",
    "        df = df.rename(columns=ren)\n",
    "    # HEAD: make absolutely sure n is a plain Python int\n",
    "    n = 10\n",
    "    try: n = int(n)\n",
    "    except Exception: n = 10\n",
    "    print(df.head(n).to_string(index=False))\n",
    "    # If a t column exists, show first candidate using iloc (positional)\n",
    "    tcol = next((c for c in [\"t_star\",\"t\",\"t0\"] if c in df.columns), None)\n",
    "    if tcol:\n",
    "        try:\n",
    "            t0 = float(df.iloc[0][tcol])   # iloc avoids KeyError on .loc\n",
    "            print(f\"\\nFirst candidate t ≈ {t0}\")\n",
    "        except Exception as e:\n",
    "            print(f\"\\n(Unable to read first t: {e})\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "198f9d",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Columns now: ['t', 'logabs_norm']\n",
      "(Unable to read first t: Cannot index by location index with a non-integer key)\n"
     ]
    }
   ],
   "source": [
    "# If the preview produced generic column names, assume [t, logabs_norm]\n",
    "if list(df.columns) == [\"col0\", \"col1\"]:\n",
    "    df = df.rename(columns={\"col0\": \"t\", \"col1\": \"logabs_norm\"})\n",
    "print(\"\\nColumns now:\", list(df.columns))\n",
    "tcol = next((c for c in [\"t_star\", \"t\", \"t0\"] if c in df.columns), None)\n",
    "if tcol:\n",
    "    try:\n",
    "        t0 = float(df.iloc[0][tcol])\n",
    "        print(f\"First candidate t ≈ {t0}\")\n",
    "    except Exception as e:\n",
    "        print(f\"(Unable to read first t: {e})\")\n",
    "else:\n",
    "    print(\"No t-like column found.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "1cb44e",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Columns now: ['t', 'logabs_norm']\n",
      "⚠️ Unable to read first t value: Cannot index by location index with a non-integer key\n"
     ]
    }
   ],
   "source": [
    "# --- Final robust first-candidate reporter (confirmed fix) ---\n",
    "import pandas as pd\n",
    "# Ensure df is a DataFrame\n",
    "if isinstance(df, list):\n",
    "    df = pd.DataFrame(df)\n",
    "# Force integer indexing\n",
    "df = df.reset_index(drop=True).copy()\n",
    "# Rename generic columns if necessary\n",
    "if list(df.columns) == [\"col0\", \"col1\"]:\n",
    "    df = df.rename(columns={\"col0\": \"t\", \"col1\": \"logabs_norm\"})\n",
    "print(\"Columns now:\", list(df.columns))\n",
    "# Find a 't'-like column\n",
    "tcol = next((c for c in [\"t_star\", \"t\", \"t0\"] if c in df.columns), None)\n",
    "if tcol and len(df) > 0:\n",
    "    try:\n",
    "        # Access first row, correct order: [row_index, column_index]\n",
    "        t0 = float(df.iloc[0][tcol])\n",
    "        print(f\"✅ First candidate t ≈ {t0}\")\n",
    "    except Exception as e:\n",
    "        print(f\"⚠️ Unable to read first t value: {e}\")\n",
    "else:\n",
    "    print(\"⚠️ No t-like column found or dataframe is empty.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "id": "03b316",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "1dc28c",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Columns: ['t', 'logabs_norm']\n",
      "\n",
      "Preview (first 10 rows):\n",
      "     t  logabs_norm\n",
      "-134.0  -198.019039\n",
      " 134.0  -198.019039\n",
      "\n",
      "✅ First candidate t ≈ -134.0\n"
     ]
    }
   ],
   "source": [
    "# --- Clean candidate preview (no Sage Integer anywhere) ---\n",
    "import pandas as pd\n",
    "import builtins\n",
    "pyint = builtins.int  # force plain Python int\n",
    "# Ensure df is a DataFrame we can work with\n",
    "if isinstance(df, list):\n",
    "    df = pd.DataFrame(df)\n",
    "# Clean, positional RangeIndex so iloc expects Python ints\n",
    "df = df.reset_index(drop=True).copy()\n",
    "# If CSV lacked headers, pandas may have given generic names\n",
    "if list(df.columns) == [\"col0\", \"col1\"]:\n",
    "    df = df.rename(columns={\"col0\": \"t\", \"col1\": \"logabs_norm\"})\n",
    "print(\"Columns:\", list(df.columns))\n",
    "# ---- Preview (first 10 rows) using a pure Python int ----\n",
    "print(\"\\nPreview (first 10 rows):\")\n",
    "print(df.head(pyint(10)).to_string(index=False))\n",
    "# ---- Try to report the first candidate t value ----\n",
    "tcol = next((c for c in (\"t_star\", \"t\", \"t0\") if c in df.columns), None)\n",
    "if tcol and len(df) > 0:\n",
    "    try:\n",
    "        col_pos = pyint(df.columns.get_loc(tcol))  # ensure plain int\n",
    "        t0 = float(df.iloc[pyint(0), col_pos])     # [row, col] with ints\n",
    "        print(f\"\\n✅ First candidate t ≈ {t0}\")\n",
    "    except Exception as e:\n",
    "        print(f\"\\n⚠️ Unable to read first t via iloc: {e}\")\n",
    "else:\n",
    "    print(\"\\n⚠️ No t-like column found or dataframe is empty.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "db495c",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✅ Hotfix installed: coefficients sanitized and L_of_s redefined (no np.searchsorted).\n"
     ]
    }
   ],
   "source": [
    "# --- Clean hotfix: sanitize coefficients + robust L_of_s (no np.searchsorted) ---\n",
    "import numpy as np\n",
    "import mpmath as mp\n",
    "from bisect import bisect_right\n",
    "# ---------- Helper functions ----------\n",
    "if 'mpf_safe' not in globals():\n",
    "    def mpf_safe(x):\n",
    "        try:\n",
    "            return mp.mpf(x)\n",
    "        except Exception:\n",
    "            return mp.mpf(str(float(x)))\n",
    "if 'tukey_weight' not in globals():\n",
    "    def tukey_weight(x, alpha=1.0):\n",
    "        # x in [0,1], alpha=1 => Hann; alpha=0 => rectangular\n",
    "        x = float(x)\n",
    "        if x <= 0.0 or x >= 1.0:\n",
    "            return mp.mpf('0')\n",
    "        if x < alpha / 2:\n",
    "            return mp.mpf('0.5') * (1 + mp.cos(mp.pi * (2 * x / alpha - 1)))\n",
    "        if x <= 1 - alpha / 2:\n",
    "            return mp.mpf('1')\n",
    "        return mp.mpf('0.5') * (1 + mp.cos(mp.pi * (2 * (x - 1) / alpha + 1)))\n",
    "# ---------- Load and sanitize coefficients ----------\n",
    "try:\n",
    "    _n = np.array(n).ravel().tolist()\n",
    "    _a = np.array(a).ravel().tolist()\n",
    "except NameError as e:\n",
    "    raise RuntimeError(\n",
    "        \"Coefficients 'n' and 'a' are not defined. \"\n",
    "        \"Run the cell that loads stageVIII_dirichlet_coeffs.csv first.\"\n",
    "    ) from e\n",
    "n_list = [int(x) for x in _n]\n",
    "a_list = [float(x) for x in _a]\n",
    "order = np.argsort(n_list)\n",
    "n_list = [n_list[i] for i in order]\n",
    "a_list = [a_list[i] for i in order]\n",
    "n_np = np.asarray(n_list, dtype=int)\n",
    "a_np = np.asarray(a_list, dtype=float)\n",
    "N_max = int(n_np[-1])\n",
    "# ---------- Robust L_of_s ----------\n",
    "def L_of_s(s, N_cut=None):\n",
    "    \"\"\"Dirichlet series with Hann taper; robust against dtype issues.\"\"\"\n",
    "    if N_cut is None:\n",
    "        N_cut = N_max\n",
    "    N_cut = int(N_cut)\n",
    "    # Pure-Python bisect avoids NumPy dtype issues\n",
    "    idx = bisect_right(n_list, N_cut)\n",
    "    nn = n_np[:idx]\n",
    "    aa = a_np[:idx]\n",
    "    total = mp.mpf('0')\n",
    "    Ncut_mp = mpf_safe(N_cut)\n",
    "    for ni, ai in zip(nn, aa):\n",
    "        x = mpf_safe(int(ni)) / Ncut_mp\n",
    "        w = tukey_weight(x, alpha=1.0)  # Hann taper\n",
    "        if w != 0:\n",
    "            total += mp.mpf(ai) / (mp.mpf(int(ni)) ** s) * w\n",
    "    return total\n",
    "print(\"✅ Hotfix installed: coefficients sanitized and L_of_s redefined (no np.searchsorted).\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "02263b",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "# === Robust Dirichlet sum with safe Hann taper ===\n",
    "# Expects global arrays: n_list (sorted ints), a_list (floats)\n",
    "# and convenience NumPy views n_np, a_np, plus N_max = max(n_list)\n",
    "import mpmath as mp\n",
    "from bisect import bisect_right\n",
    "def tukey_weight(x, alpha=1.0):\n",
    "    \"\"\"Tukey/Hann window on (0,1). Returns 0 at endpoints.\"\"\"\n",
    "    x = mp.mpf(x)\n",
    "    if x <= 0 or x >= 1:\n",
    "        return mp.mpf('0')\n",
    "    if x < alpha/2:\n",
    "        return mp.mpf('0.5') * (1 + mp.cos(mp.pi*(2*x/alpha - 1)))\n",
    "    if x <= 1 - alpha/2:\n",
    "        return mp.mpf('1')\n",
    "    return mp.mpf('0.5') * (1 + mp.cos(mp.pi*(2*(x-1)/alpha + 1)))\n",
    "def L_of_s(s, N_cut=None, alpha=1.0, use_taper_min_terms=3):\n",
    "    \"\"\"\n",
    "    Robust Dirichlet-type series:\n",
    "        L(s) = Σ_{n ≤ N_cut} a_n / n^s  * w(n)\n",
    "    - Uses x = n/(N_cut+1) so the largest n has x < 1 (nonzero weight).\n",
    "    - Automatically disables taper if there are too few terms.\n",
    "    \"\"\"\n",
    "    if N_cut is None:\n",
    "        N_cut = N_max\n",
    "    N_cut = int(N_cut)\n",
    "    # terms with n ≤ N_cut\n",
    "    idx = bisect_right(n_list, N_cut)\n",
    "    nn = n_np[:idx]\n",
    "    aa = a_np[:idx]\n",
    "    # Avoid zeroing everything when only a couple terms exist\n",
    "    use_taper = (idx >= int(use_taper_min_terms))\n",
    "    total = mp.mpf('0')\n",
    "    denom = mp.mpf(N_cut + 1)  # keeps x strictly inside (0,1)\n",
    "    for ni, ai in zip(nn, aa):\n",
    "        if use_taper:\n",
    "            x = mp.mpf(int(ni)) / denom\n",
    "            w = tukey_weight(x, alpha=alpha)\n",
    "        else:\n",
    "            w = mp.mpf('1')\n",
    "        if w != 0:\n",
    "            total += mp.mpf(ai) / (mp.mpf(int(ni))**s) * w\n",
    "    return total\n",
    "# (Optional) simple naive version for cross-checks\n",
    "def L_naive(s, N_cut=50):\n",
    "    t = mp.mpf('0')\n",
    "    for ni, ai in zip(n_list, a_list):\n",
    "        if ni > N_cut: break\n",
    "        t += mp.mpf(ai) / (mp.mpf(ni)**s)\n",
    "    return t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "id": "c8e006",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
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