|          k |   z |                 ratio |
|    0.00025 | 2.0 |   0.24154385915845986 |
|    0.00075 | 2.0 |    0.2051623542020443 |
|    0.00125 | 2.0 |   0.11012183891119887 |
|    0.00175 | 2.0 |   0.09884270973673104 |
|    0.00225 | 2.0 |   0.06334478514533168 |
|    0.00275 | 2.0 |   0.08246543356052571 |
|    0.00325 | 2.0 |   0.06932954039595628 |
|    0.00375 | 2.0 |   0.06049104006694867 |
|    0.00425 | 2.0 |   0.08653460845864137 |
|    0.00475 | 2.0 |   0.04048932232848221 |
|    0.00525 | 2.0 |   0.04089750823812919 |
|    0.00575 | 2.0 |    0.0428746288950868 |
|    0.00625 | 2.0 |   0.04923353460230409 |
|    0.00675 | 2.0 |   0.04393965051093807 |
|    0.00725 | 2.0 |   0.05137840209943982 |
|    0.00775 | 2.0 |   0.06649832495339794 |
|    0.00825 | 2.0 |  0.041413453882651746 |
|    0.00875 | 2.0 |  0.034957993107167455 |
|    0.00925 | 2.0 |   0.08972537103000819 |
|    0.00975 | 2.0 |   0.09359338338563461 |
| 0.01061009 | 2.0 |   0.09578535098870986 |
| 0.01190472 | 2.0 |   0.10025386057896254 |
| 0.01335731 | 2.0 |   0.10870219393238727 |
| 0.01498715 | 2.0 |   0.09672994850794173 |
| 0.01681586 | 2.0 |    0.0873265811912814 |
| 0.01886771 | 2.0 |   0.10845347443652104 |
| 0.02116992 | 2.0 |   0.13278271468198227 |
| 0.02375304 | 2.0 |   0.17777444999014186 |
| 0.02665135 | 2.0 |    0.2736136389011975 |
|    0.00025 | 2.2 |   0.16761687761802208 |
|    0.00075 | 2.2 |   0.17932457369516372 |
|    0.00125 | 2.2 |   0.07742905535089044 |
|    0.00175 | 2.2 |   0.09091163440001952 |
|    0.00225 | 2.2 |   0.04984163961497734 |
|    0.00275 | 2.2 |   0.07313684948568945 |
|    0.00325 | 2.2 |   0.04933181451355113 |
|    0.00375 | 2.2 |   0.04433615049381512 |
|    0.00425 | 2.2 |   0.04200743308106136 |
|    0.00475 | 2.2 |    0.0162389150833509 |
|    0.00525 | 2.2 |   0.02474274738200749 |
|    0.00575 | 2.2 |  0.023638173930625637 |
|    0.00625 | 2.2 |    0.0381687140030587 |
|    0.00675 | 2.2 |   0.03235276630455122 |
|    0.00725 | 2.2 |   0.02599993436047088 |
|    0.00775 | 2.2 |  0.032403835478533746 |
|    0.00825 | 2.2 |  0.030641636109463074 |
|    0.00875 | 2.2 |   0.04127976167306072 |
|    0.00925 | 2.2 |   0.04828579515888322 |
|    0.00975 | 2.2 |  0.056346627297129824 |
| 0.01061009 | 2.2 |   0.06612965238204246 |
| 0.01190472 | 2.2 |     0.073228313094499 |
| 0.01335731 | 2.2 |   0.08295328180583184 |
| 0.01498715 | 2.2 |   0.04967149438275823 |
| 0.01681586 | 2.2 |   0.03886255648635035 |
| 0.01886771 | 2.2 |  0.023198101736878075 |
| 0.02116992 | 2.2 |  0.037269027113103176 |
| 0.02375304 | 2.2 |    0.0721528623658286 |
| 0.02665135 | 2.2 |   0.07092260452977726 |
|  0.0299033 | 2.2 |    0.0859874419145796 |
|    0.00025 | 2.4 |   0.11723103158732942 |
|    0.00075 | 2.4 |   0.15963361676350127 |
|    0.00125 | 2.4 |    0.0815935896389045 |
|    0.00175 | 2.4 |   0.07542639625454955 |
|    0.00225 | 2.4 |   0.04632600118420694 |
|    0.00275 | 2.4 |   0.07207590570334052 |
|    0.00325 | 2.4 |   0.05022990825091107 |
|    0.00375 | 2.4 |  0.048932307524588124 |
|    0.00425 | 2.4 |  0.051128788716892984 |
|    0.00475 | 2.4 |  0.022127012816286522 |
|    0.00525 | 2.4 |  0.022059204782022897 |
|    0.00575 | 2.4 |  0.021084377939985202 |
|    0.00625 | 2.4 |  0.027910171820902024 |
|    0.00675 | 2.4 |  0.028677845441863307 |
|    0.00725 | 2.4 |   0.02949291867296857 |
|    0.00775 | 2.4 |  0.028127252908986794 |
|    0.00825 | 2.4 |   0.02677254927742211 |
|    0.00875 | 2.4 |  0.039124989471232864 |
|    0.00925 | 2.4 |   0.07540469047086003 |
|    0.00975 | 2.4 |   0.05341988367082185 |
| 0.01061009 | 2.4 |   0.06517825465965951 |
| 0.01190472 | 2.4 |   0.07075907453307875 |
| 0.01335731 | 2.4 |   0.07748771412124085 |
| 0.01498715 | 2.4 |   0.05464611288531738 |
| 0.01681586 | 2.4 |   0.03944588880280933 |
| 0.01886771 | 2.4 |  0.015241000388742064 |
| 0.02116992 | 2.4 |  0.028955895156817908 |
| 0.02375304 | 2.4 |  0.059636584171025485 |
| 0.02665135 | 2.4 |   0.06509549878683916 |
|  0.0299033 | 2.4 |  0.042710192054395024 |
|    0.00025 | 2.6 |   0.17604146683411975 |
|    0.00075 | 2.6 |    0.1409883370006698 |
|    0.00125 | 2.6 |   0.08693466883120914 |
|    0.00175 | 2.6 |   0.08136242533416659 |
|    0.00225 | 2.6 |   0.04946169500167004 |
|    0.00275 | 2.6 |   0.06942578892705302 |
|    0.00325 | 2.6 |  0.050358926996198795 |
|    0.00375 | 2.6 |  0.043438920089761746 |
|    0.00425 | 2.6 |   0.04426503300406036 |
|    0.00475 | 2.6 |  0.025518632188415092 |
|    0.00525 | 2.6 |  0.026256492297941136 |
|    0.00575 | 2.6 |  0.024275336390819892 |
|    0.00625 | 2.6 |   0.03616125978496797 |
|    0.00675 | 2.6 |   0.02648752824292824 |
|    0.00725 | 2.6 |  0.031034924156235974 |
|    0.00775 | 2.6 |   0.03323232921159924 |
|    0.00825 | 2.6 |    0.0310731898427365 |
|    0.00875 | 2.6 |  0.036461632627722396 |
|    0.00925 | 2.6 |  0.057974889414097425 |
|    0.00975 | 2.6 |   0.05515460823403031 |
| 0.01061009 | 2.6 |   0.06245926077759819 |
| 0.01190472 | 2.6 |   0.06389206519163754 |
| 0.01335731 | 2.6 |   0.06726278312478143 |
| 0.01498715 | 2.6 |   0.04725558490015125 |
| 0.01681586 | 2.6 |   0.03211082753798548 |
| 0.01886771 | 2.6 |   0.01997381588219659 |
| 0.02116992 | 2.6 |   0.02270129103382789 |
| 0.02375304 | 2.6 |   0.05383362183913161 |
| 0.02665135 | 2.6 |   0.05724793971402728 |
|  0.0299033 | 2.6 |   0.03039160638244893 |
| 0.03355206 | 2.6 |   0.06487574268877229 |
|    0.00025 | 2.8 |   0.08375204093892467 |
|    0.00075 | 2.8 |    0.1401526161129232 |
|    0.00125 | 2.8 |   0.06546790739820008 |
|    0.00175 | 2.8 |    0.0618356273744464 |
|    0.00225 | 2.8 |   0.03138636289359634 |
|    0.00275 | 2.8 |   0.05328573309632609 |
|    0.00325 | 2.8 |   0.03841427521375891 |
|    0.00375 | 2.8 |    0.0298635135969905 |
|    0.00425 | 2.8 |   0.03683415605380753 |
|    0.00475 | 2.8 |   0.01873824034689174 |
|    0.00525 | 2.8 |  0.018601288244377064 |
|    0.00575 | 2.8 |  0.018653182707338612 |
|    0.00625 | 2.8 |  0.026008458618249127 |
|    0.00675 | 2.8 |   0.02523440383968999 |
|    0.00725 | 2.8 |  0.024744440641023328 |
|    0.00775 | 2.8 |  0.028597591910333897 |
|    0.00825 | 2.8 |  0.018945301402399053 |
|    0.00875 | 2.8 |  0.031223981267390594 |
|    0.00925 | 2.8 |  0.043988474903573695 |
|    0.00975 | 2.8 |    0.0433133528896204 |
| 0.01061009 | 2.8 |   0.05042446953413186 |
| 0.01190472 | 2.8 |  0.050937361421757865 |
| 0.01335731 | 2.8 |   0.05867270099765171 |
| 0.01498715 | 2.8 |  0.040340508274994226 |
| 0.01681586 | 2.8 |  0.030583694013194794 |
| 0.01886771 | 2.8 |   0.01060558479005147 |
| 0.02116992 | 2.8 |   0.02005474732995824 |
| 0.02375304 | 2.8 |   0.04121802484677605 |
| 0.02665135 | 2.8 |   0.04493329143031902 |
|  0.0299033 | 2.8 |  0.022378206770251746 |
| 0.03355206 | 2.8 |   0.02851301417275404 |
|    0.00025 | 3.0 |   0.24109875032785533 |
|    0.00075 | 3.0 |   0.10527793059002709 |
|    0.00125 | 3.0 |   0.07413770544714345 |
|    0.00175 | 3.0 |   0.05298261226223699 |
|    0.00225 | 3.0 |   0.03539930661775339 |
|    0.00275 | 3.0 |   0.05116730043601859 |
|    0.00325 | 3.0 |   0.03842348986382888 |
|    0.00375 | 3.0 |   0.03243350386135015 |
|    0.00425 | 3.0 |  0.028692679885919677 |
|    0.00475 | 3.0 |   0.01862219727010851 |
|    0.00525 | 3.0 |  0.017301566193849573 |
|    0.00575 | 3.0 |  0.021234043923572497 |
|    0.00625 | 3.0 |  0.028588134182757262 |
|    0.00675 | 3.0 |  0.022792094068937993 |
|    0.00725 | 3.0 |   0.02715395891341105 |
|    0.00775 | 3.0 |   0.02265825116814541 |
|    0.00825 | 3.0 |  0.023514061217438216 |
|    0.00875 | 3.0 |  0.026305391534048362 |
|    0.00925 | 3.0 |   0.04366651395050132 |
|    0.00975 | 3.0 |  0.039132663836051226 |
| 0.01061009 | 3.0 |   0.04510851200420808 |
| 0.01190472 | 3.0 |  0.044525063463087496 |
| 0.01335731 | 3.0 |   0.04786014378545598 |
| 0.01498715 | 3.0 |  0.033069096648155966 |
| 0.01681586 | 3.0 |   0.02745220596949682 |
| 0.01886771 | 3.0 |  0.013394412759239869 |
| 0.02116992 | 3.0 |  0.015501302562538377 |
| 0.02375304 | 3.0 |   0.03921341165212115 |
| 0.02665135 | 3.0 |   0.03162960275412075 |
|  0.0299033 | 3.0 |  0.013819170976261643 |
| 0.03355206 | 3.0 |  0.020335625217549974 |
| 0.03764603 | 3.0 |   0.03447639631539128 |
|    0.00025 | 3.2 |    1.0173023506474566 |
|    0.00075 | 3.2 |   0.07873659585396392 |
|    0.00125 | 3.2 |   0.05895819564989001 |
|    0.00175 | 3.2 |   0.04595579743922462 |
|    0.00225 | 3.2 |  0.025996290233118308 |
|    0.00275 | 3.2 |    0.0426031925256957 |
|    0.00325 | 3.2 |   0.03195982994526291 |
|    0.00375 | 3.2 |   0.02703321291591082 |
|    0.00425 | 3.2 |   0.02608414138598911 |
|    0.00475 | 3.2 |  0.017745734175245283 |
|    0.00525 | 3.2 |  0.013541754273599974 |
|    0.00575 | 3.2 |  0.017920270677375484 |
|    0.00625 | 3.2 |  0.019440809726945164 |
|    0.00675 | 3.2 |  0.019219286315396433 |
|    0.00725 | 3.2 |  0.022476603782863938 |
|    0.00775 | 3.2 |  0.020624667048925002 |
|    0.00825 | 3.2 |  0.016623420966163555 |
|    0.00875 | 3.2 |  0.024834534053846016 |
|    0.00925 | 3.2 |   0.03929389037919683 |
|    0.00975 | 3.2 |   0.03169794086361928 |
| 0.01061009 | 3.2 |  0.038046760251480675 |
| 0.01190472 | 3.2 |  0.040886489078138986 |
| 0.01335731 | 3.2 |    0.0431408375868037 |
| 0.01498715 | 3.2 |   0.03162074056906674 |
| 0.01681586 | 3.2 |  0.018619511242240032 |
| 0.01886771 | 3.2 |  0.011221482158842019 |
| 0.02116992 | 3.2 |  0.012106350255182193 |
| 0.02375304 | 3.2 |   0.02869783424319227 |
| 0.02665135 | 3.2 |  0.030470795939966235 |
|  0.0299033 | 3.2 |   0.01170135583241152 |
| 0.03355206 | 3.2 |  0.013379892164541314 |
| 0.03764603 | 3.2 |   0.04716921540356236 |
|    0.00025 | 3.4 |    0.8259943360316105 |
|    0.00075 | 3.4 |   0.07257170862132808 |
|    0.00125 | 3.4 |   0.06155632068630204 |
|    0.00175 | 3.4 |  0.037237115179317194 |
|    0.00225 | 3.4 |  0.025665130191480107 |
|    0.00275 | 3.4 |   0.03546193269856272 |
|    0.00325 | 3.4 |  0.029236017833389354 |
|    0.00375 | 3.4 |  0.026530823798685488 |
|    0.00425 | 3.4 |  0.023682775282167376 |
|    0.00475 | 3.4 |  0.014295379266784928 |
|    0.00525 | 3.4 |  0.014993187815656558 |
|    0.00575 | 3.4 |  0.016373915297952932 |
|    0.00625 | 3.4 |   0.01919982496324045 |
|    0.00675 | 3.4 |  0.023097571595909812 |
|    0.00725 | 3.4 |  0.021022428274264572 |
|    0.00775 | 3.4 |  0.018802602672427098 |
|    0.00825 | 3.4 |  0.023793008318791196 |
|    0.00875 | 3.4 |  0.022691387485004773 |
|    0.00925 | 3.4 |   0.03490045144844734 |
|    0.00975 | 3.4 |   0.03232381030619524 |
| 0.01061009 | 3.4 |  0.030235480466659068 |
| 0.01190472 | 3.4 |   0.03555377008966834 |
| 0.01335731 | 3.4 |  0.034190600880599574 |
| 0.01498715 | 3.4 |  0.022180291466341866 |
| 0.01681586 | 3.4 |   0.01579383968946452 |
| 0.01886771 | 3.4 |  0.008093868858697601 |
| 0.02116992 | 3.4 |   0.01305336184171461 |
| 0.02375304 | 3.4 |  0.027631583666832337 |
| 0.02665135 | 3.4 |   0.02292194730734766 |
|  0.0299033 | 3.4 |  0.012450493561811786 |
| 0.03355206 | 3.4 |  0.014749855777925255 |
| 0.03764603 | 3.4 |  0.026157574236367703 |
| 0.04223954 | 3.4 |   0.31749751655833924 |
|    0.00025 | 3.6 |     0.329840571304947 |
|    0.00075 | 3.6 |   0.05139283613178943 |
|    0.00125 | 3.6 |   0.04112784995295565 |
|    0.00175 | 3.6 |  0.030724214244050783 |
|    0.00225 | 3.6 |  0.023635615537756033 |
|    0.00275 | 3.6 |  0.026142901599675184 |
|    0.00325 | 3.6 |   0.02122946436359474 |
|    0.00375 | 3.6 |    0.0181804581485332 |
|    0.00425 | 3.6 |  0.023787544587117033 |
|    0.00475 | 3.6 |  0.013022052139737547 |
|    0.00525 | 3.6 |    0.0113956352911035 |
|    0.00575 | 3.6 |   0.00943361165625115 |
|    0.00625 | 3.6 |  0.016523012434709945 |
|    0.00675 | 3.6 |  0.014483403234322395 |
|    0.00725 | 3.6 |  0.019015611374003233 |
|    0.00775 | 3.6 |   0.01829051016441606 |
|    0.00825 | 3.6 |   0.01342095939757444 |
|    0.00875 | 3.6 |   0.01928680490867125 |
|    0.00925 | 3.6 |  0.036341126048800486 |
|    0.00975 | 3.6 |   0.01969937632815297 |
| 0.01061009 | 3.6 |  0.030014656974791522 |
| 0.01190472 | 3.6 |  0.025886782440223837 |
| 0.01335731 | 3.6 |  0.029930202279957265 |
| 0.01498715 | 3.6 |   0.02267260243199513 |
| 0.01681586 | 3.6 |  0.017827880542892027 |
| 0.01886771 | 3.6 |  0.006793715989921092 |
| 0.02116992 | 3.6 |  0.007110197137592635 |
| 0.02375304 | 3.6 |   0.02338164892716526 |
| 0.02665135 | 3.6 |  0.022596115834268404 |
|  0.0299033 | 3.6 |   0.00808967993488532 |
| 0.03355206 | 3.6 |  0.009415485907678935 |
| 0.03764603 | 3.6 |  0.026259510533429776 |
| 0.04223954 | 3.6 |  0.014966796041425125 |
|    0.00025 | 3.8 |  0.008066773105739979 |
|    0.00075 | 3.8 |   0.08014571224965587 |
|    0.00125 | 3.8 |  0.036505562585414535 |
|    0.00175 | 3.8 |   0.02639594816223056 |
|    0.00225 | 3.8 |  0.016824344320538906 |
|    0.00275 | 3.8 |   0.03400964084246963 |
|    0.00325 | 3.8 |  0.023244230787593294 |
|    0.00375 | 3.8 |  0.019302046169260116 |
|    0.00425 | 3.8 |  0.012485274915031668 |
|    0.00475 | 3.8 |   0.01148639764978577 |
|    0.00525 | 3.8 |  0.012799922699826285 |
|    0.00575 | 3.8 |  0.011105269143946137 |
|    0.00625 | 3.8 |    0.0174962873116576 |
|    0.00675 | 3.8 |  0.020770460665437192 |
|    0.00725 | 3.8 |  0.012248586712352155 |
|    0.00775 | 3.8 |  0.014745634384813971 |
|    0.00825 | 3.8 |  0.011196840298180508 |
|    0.00875 | 3.8 |  0.013458059513150076 |
|    0.00925 | 3.8 |   0.01998901092997277 |
|    0.00975 | 3.8 |  0.020904990872747085 |
| 0.01061009 | 3.8 |  0.022053882640601426 |
| 0.01190472 | 3.8 |  0.020798694234366328 |
| 0.01335731 | 3.8 |  0.023475439081372732 |
| 0.01498715 | 3.8 |   0.01575779413684568 |
| 0.01681586 | 3.8 |  0.010851115201370562 |
| 0.01886771 | 3.8 |  0.008940960554202184 |
| 0.02116992 | 3.8 |    0.0093403841363173 |
| 0.02375304 | 3.8 |  0.017489000607641053 |
| 0.02665135 | 3.8 |  0.011305565243255745 |
|  0.0299033 | 3.8 | 0.0065839984355334814 |
| 0.03355206 | 3.8 |  0.008799020005992628 |
| 0.03764603 | 3.8 |  0.012136534326549278 |
| 0.04223954 | 3.8 |  0.010928855985018443 |
