CORRECTED OBSTRUCTION NOTE VERIFICATION
MOD=107
|V_840|=24
fiber sizes=[6, 6, 6, 6]
powers of 289 modulo 840=[1, 289, 361, 169, 121, 529]

Weighted defects D_k in row order r=0,1,2 and columns +,-:
k=0: [[0, 3], [0, 0], [0, 0]]; arm=[3, 0, 0]; sign=[0, 3]
k=1: [[0, 1], [0, 0], [2, 0]]; arm=[1, 0, 2]; sign=[2, 1]
k=2: [[0, 1], [0, 2], [0, 0]]; arm=[1, 2, 0]; sign=[0, 3]
k=3: [[2, 1], [0, 0], [0, 0]]; arm=[3, 0, 0]; sign=[2, 1]
k=4: [[0, 1], [0, 0], [0, 2]]; arm=[1, 0, 2]; sign=[0, 3]
k=5: [[0, 1], [2, 0], [0, 0]]; arm=[1, 2, 0]; sign=[2, 1]

Circulant multiplication matrices C(D_k): determinants and characteristic polynomials over Z:
k=0: det=-729; chi=(X - 3)**3*(X + 3)**3
k=1: det=63; chi=(X - 3)*(X - 1)*(X**2 + 3)*(X**2 + 4*X + 7)
k=2: det=-81; chi=(X - 3)*(X + 3)*(X**2 + 3)**2
k=3: det=27; chi=(X - 3)**3*(X - 1)**3
k=4: det=-81; chi=(X - 3)*(X + 3)*(X**2 + 3)**2
k=5: det=63; chi=(X - 3)*(X - 1)*(X**2 + 3)*(X**2 + 4*X + 7)

Champion shell ladder:
R=27; a=2200849; factorization=[(7, 1), (314407, 1)]; targets=[26, 17]; state=('tau', 'tau'); counts=[0, 0]; witnesses=[]
R=43; a=2200853; factorization=[(379, 1), (5807, 1)]; targets=[42, 41]; state=('0_Z', '0_Z'); counts=[0, 0]; witnesses=[]
R=107; a=2200869; factorization=[(3, 2), (11, 2), (43, 1), (47, 1)]; targets=[106, 86]; state=('2', '0_Z'); counts=[2, 0]; witnesses=[[(-2, 0, -1, -1), (2, 0, 1, 1)]]

Eta-sheet coefficients modulo 107 on n=744,747,750:
n=744: T6=34, F6=19, J6=16, Y6=52, f6=67; T9=0, I9=35, J9=35, Y9=72, f9=89
n=747: T6=83, F6=77, J6=1, Y6=58, f6=48; T9=0, I9=31, J9=31, Y9=76, f9=45
n=750: T6=101, F6=106, J6=2, Y6=93, f6=21; T9=0, I9=42, J9=42, Y9=65, f9=52

Resolvent and transport matrices modulo 107:
det M9=103 (-4)
det M6,1=82 (-25)
det M6,2=25 (25)
P9to6_1=[[32, 67, 44], [98, 72, 41], [51, 81, 71]]
P9to6_2=[[3, 28, 46], [106, 64, 81], [38, 47, 84]]
charpoly P1 coeffs mod107=[1, 39, 18, 74]; factor=X**3 + 39*X**2 + 18*X - 33
charpoly P2 coeffs mod107=[1, 63, 79, 33]; factor=(X + 17)*(X**2 + 46*X + 46)
