|          k |   z |              ratio |
|    0.00025 | 2.0 |  2.613989867846787 |
|    0.00075 | 2.0 |  2.381670225907207 |
|    0.00125 | 2.0 | 1.3770054509264644 |
|    0.00175 | 2.0 |  1.404039931797173 |
|    0.00225 | 2.0 | 1.3644777980274803 |
|    0.00275 | 2.0 | 1.3095773448798433 |
|    0.00325 | 2.0 | 1.3002242599114986 |
|    0.00375 | 2.0 | 1.1900992051786456 |
|    0.00425 | 2.0 | 1.2110585634823952 |
|    0.00475 | 2.0 | 1.2207591099551447 |
|    0.00525 | 2.0 |  1.148995262138697 |
|    0.00575 | 2.0 | 1.2888058526960544 |
|    0.00625 | 2.0 |  1.264383661015674 |
|    0.00675 | 2.0 |  1.098394409276325 |
|    0.00725 | 2.0 |  1.160901544248252 |
|    0.00775 | 2.0 | 1.2139644150506994 |
|    0.00825 | 2.0 | 1.2738487722325662 |
|    0.00875 | 2.0 |  1.230230129851663 |
|    0.00925 | 2.0 | 1.1498453848036878 |
|    0.00975 | 2.0 |   1.00416791294169 |
| 0.01061009 | 2.0 | 1.2090122141622905 |
| 0.01190472 | 2.0 | 1.2776266634315732 |
| 0.01335731 | 2.0 |  1.234734918856166 |
| 0.01498715 | 2.0 | 1.1922328546867451 |
| 0.01681586 | 2.0 | 1.2151380528069993 |
| 0.01886771 | 2.0 |   1.21261612982722 |
| 0.02116992 | 2.0 |  1.157844665250035 |
| 0.02375304 | 2.0 | 1.2816564004735855 |
| 0.02665135 | 2.0 | 1.2038336568537773 |
|    0.00025 | 2.2 | 2.8169045916777087 |
|    0.00075 | 2.2 | 2.0854626683522537 |
|    0.00125 | 2.2 | 1.5139370641581387 |
|    0.00175 | 2.2 |  1.382733354507509 |
|    0.00225 | 2.2 | 1.3240308150175393 |
|    0.00275 | 2.2 | 1.3779957272302967 |
|    0.00325 | 2.2 | 1.3536925482455573 |
|    0.00375 | 2.2 |  1.196393514021511 |
|    0.00425 | 2.2 | 1.0420131643633899 |
|    0.00475 | 2.2 |  1.075938104396108 |
|    0.00525 | 2.2 | 1.1740451809581303 |
|    0.00575 | 2.2 | 1.2517500643167165 |
|    0.00625 | 2.2 | 1.0896394358725932 |
|    0.00675 | 2.2 | 1.1700599984065971 |
|    0.00725 | 2.2 | 1.1180903640126805 |
|    0.00775 | 2.2 |  1.240230469809214 |
|    0.00825 | 2.2 | 1.3034116470320025 |
|    0.00875 | 2.2 | 1.2685774400378365 |
|    0.00925 | 2.2 | 1.1936517139093041 |
|    0.00975 | 2.2 | 1.0181060689878318 |
| 0.01061009 | 2.2 | 1.2080620439400913 |
| 0.01190472 | 2.2 | 1.2766020966324945 |
| 0.01335731 | 2.2 | 1.2828092660858479 |
| 0.01498715 | 2.2 |  1.136180556014882 |
| 0.01681586 | 2.2 |  1.315531546392726 |
| 0.01886771 | 2.2 |  1.155814128127132 |
| 0.02116992 | 2.2 | 1.0714854326541152 |
| 0.02375304 | 2.2 | 1.1745073152397774 |
| 0.02665135 | 2.2 |  1.272858268158798 |
|  0.0299033 | 2.2 | 1.1888011755836272 |
|    0.00025 | 2.4 |  2.381660021828616 |
|    0.00075 | 2.4 | 1.9378955966991256 |
|    0.00125 | 2.4 | 1.4070343253975817 |
|    0.00175 | 2.4 |  1.161652678799729 |
|    0.00225 | 2.4 |  1.271121479816002 |
|    0.00275 | 2.4 | 1.2333924001437413 |
|    0.00325 | 2.4 | 1.2701024580407894 |
|    0.00375 | 2.4 |  1.081211483197064 |
|    0.00425 | 2.4 |  1.055456500547346 |
|    0.00475 | 2.4 | 1.0358741898842738 |
|    0.00525 | 2.4 | 1.1379293224893585 |
|    0.00575 | 2.4 | 1.1448433599257375 |
|    0.00625 | 2.4 |  1.056587538150337 |
|    0.00675 | 2.4 | 1.0520896229438537 |
|    0.00725 | 2.4 | 1.0876824409655839 |
|    0.00775 | 2.4 | 1.1265782174825607 |
|    0.00825 | 2.4 | 1.1808318565884361 |
|    0.00875 | 2.4 | 1.2846389440360282 |
|    0.00925 | 2.4 |  1.198726026550351 |
|    0.00975 | 2.4 |  1.049946629648884 |
| 0.01061009 | 2.4 |  1.217926832383295 |
| 0.01190472 | 2.4 | 1.1761202272375693 |
| 0.01335731 | 2.4 | 1.1849956965217336 |
| 0.01498715 | 2.4 | 1.2081126526190105 |
| 0.01681586 | 2.4 | 1.2471810177621265 |
| 0.01886771 | 2.4 | 1.2578215069637366 |
| 0.02116992 | 2.4 | 1.2770351055940996 |
| 0.02375304 | 2.4 | 1.1888378233473686 |
| 0.02665135 | 2.4 | 1.2033952502271732 |
|  0.0299033 | 2.4 | 1.1440696166698199 |
|    0.00025 | 2.6 |  2.426302015654183 |
|    0.00075 | 2.6 | 1.9780184404460661 |
|    0.00125 | 2.6 | 1.4461091653703004 |
|    0.00175 | 2.6 | 1.2517979522626514 |
|    0.00225 | 2.6 | 1.2823812912676447 |
|    0.00275 | 2.6 | 1.2205957165416859 |
|    0.00325 | 2.6 | 1.2117301674830674 |
|    0.00375 | 2.6 |   1.05645765174765 |
|    0.00425 | 2.6 | 1.0460066351905857 |
|    0.00475 | 2.6 | 0.9883492973618694 |
|    0.00525 | 2.6 | 1.1052604686129142 |
|    0.00575 | 2.6 |  1.080960573143869 |
|    0.00625 | 2.6 |  1.065582915339191 |
|    0.00675 | 2.6 |  1.110781675180294 |
|    0.00725 | 2.6 |  1.076668660591532 |
|    0.00775 | 2.6 | 1.1639866591902468 |
|    0.00825 | 2.6 |  1.107642015361531 |
|    0.00875 | 2.6 | 1.1393816709633326 |
|    0.00925 | 2.6 | 1.0525495719748021 |
|    0.00975 | 2.6 | 1.1050240698212772 |
| 0.01061009 | 2.6 | 1.2537329625167772 |
| 0.01190472 | 2.6 | 1.1494308285248247 |
| 0.01335731 | 2.6 | 1.1625765990985562 |
| 0.01498715 | 2.6 | 1.2537572962908734 |
| 0.01681586 | 2.6 |  1.192859630937254 |
| 0.01886771 | 2.6 |  1.239406466524371 |
| 0.02116992 | 2.6 | 1.3213429914727843 |
| 0.02375304 | 2.6 | 1.2645641135447725 |
| 0.02665135 | 2.6 |  1.287006536628432 |
|  0.0299033 | 2.6 | 1.3428206707719952 |
| 0.03355206 | 2.6 | 1.3751812749421413 |
|    0.00025 | 2.8 | 2.3475204909080083 |
|    0.00075 | 2.8 |  1.961629098272187 |
|    0.00125 | 2.8 | 1.4761344495155273 |
|    0.00175 | 2.8 | 1.2006367968141656 |
|    0.00225 | 2.8 |  1.353876506181656 |
|    0.00275 | 2.8 | 1.1388727546501909 |
|    0.00325 | 2.8 | 1.2188467041660613 |
|    0.00375 | 2.8 | 0.9731497378891377 |
|    0.00425 | 2.8 | 1.0330132894536377 |
|    0.00475 | 2.8 | 1.1253861540495593 |
|    0.00525 | 2.8 | 1.1869943153574285 |
|    0.00575 | 2.8 | 1.1404865443397871 |
|    0.00625 | 2.8 | 1.0227477265203313 |
|    0.00675 | 2.8 |  1.051615160439942 |
|    0.00725 | 2.8 | 1.0215649813282353 |
|    0.00775 | 2.8 | 1.0174111443705272 |
|    0.00825 | 2.8 |  1.074592195999552 |
|    0.00875 | 2.8 | 1.1052320885371891 |
|    0.00925 | 2.8 | 1.1508685942989827 |
|    0.00975 | 2.8 | 1.1092884074016949 |
| 0.01061009 | 2.8 |  1.112261202693878 |
| 0.01190472 | 2.8 | 1.1715240649507364 |
| 0.01335731 | 2.8 | 1.2106544665414884 |
| 0.01498715 | 2.8 | 1.1595791846971637 |
| 0.01681586 | 2.8 | 1.2759318119880916 |
| 0.01886771 | 2.8 | 1.2225104551365849 |
| 0.02116992 | 2.8 | 1.2288575338963734 |
| 0.02375304 | 2.8 | 1.2376712424226428 |
| 0.02665135 | 2.8 |  1.359215993786871 |
|  0.0299033 | 2.8 | 1.1907820149200237 |
| 0.03355206 | 2.8 | 1.2161388180533788 |
|    0.00025 | 3.0 | 2.2084080028643154 |
|    0.00075 | 3.0 | 1.8865323109350516 |
|    0.00125 | 3.0 | 1.3626686358400268 |
|    0.00175 | 3.0 | 1.2456421193611822 |
|    0.00225 | 3.0 | 1.2359891648226402 |
|    0.00275 | 3.0 | 1.2062704084248985 |
|    0.00325 | 3.0 | 1.0750622798587273 |
|    0.00375 | 3.0 | 0.9719389550734292 |
|    0.00425 | 3.0 | 1.0076542108886115 |
|    0.00475 | 3.0 | 1.1130351378052952 |
|    0.00525 | 3.0 | 1.1004258110297642 |
|    0.00575 | 3.0 | 1.1564287819544656 |
|    0.00625 | 3.0 |  1.060418303907985 |
|    0.00675 | 3.0 | 0.9460641349188318 |
|    0.00725 | 3.0 | 1.0048788513059719 |
|    0.00775 | 3.0 | 1.0271938245020782 |
|    0.00825 | 3.0 | 1.1222455318291609 |
|    0.00875 | 3.0 | 1.2178148841341043 |
|    0.00925 | 3.0 | 1.0063509112017643 |
|    0.00975 | 3.0 | 0.9486194790718218 |
| 0.01061009 | 3.0 |  1.049143719996839 |
| 0.01190472 | 3.0 | 1.1600881341957288 |
| 0.01335731 | 3.0 | 1.1645418285748905 |
| 0.01498715 | 3.0 | 1.1718354268359323 |
| 0.01681586 | 3.0 | 1.2397168845876327 |
| 0.01886771 | 3.0 | 1.1944729085988448 |
| 0.02116992 | 3.0 | 1.2632518335133744 |
| 0.02375304 | 3.0 | 1.3782338960191183 |
| 0.02665135 | 3.0 |  1.348122478300612 |
|  0.0299033 | 3.0 |  1.355045563318385 |
| 0.03355206 | 3.0 | 1.1949227137758065 |
| 0.03764603 | 3.0 | 1.1094088594760112 |
|    0.00025 | 3.2 | 1.9096842545314265 |
|    0.00075 | 3.2 | 1.5102050544249455 |
|    0.00125 | 3.2 | 1.3142645070225019 |
|    0.00175 | 3.2 |   1.17471814702645 |
|    0.00225 | 3.2 | 1.1994139653907179 |
|    0.00275 | 3.2 | 1.2726424919766213 |
|    0.00325 | 3.2 | 1.1096263021095518 |
|    0.00375 | 3.2 | 1.0231822492668405 |
|    0.00425 | 3.2 | 1.0460156142682948 |
|    0.00475 | 3.2 | 1.0224332557493223 |
|    0.00525 | 3.2 | 0.9998653325847627 |
|    0.00575 | 3.2 |  1.082912377121542 |
|    0.00625 | 3.2 | 1.0717623938402334 |
|    0.00675 | 3.2 | 1.0644113589016804 |
|    0.00725 | 3.2 | 1.0148379784982913 |
|    0.00775 | 3.2 | 1.1754738282689479 |
|    0.00825 | 3.2 |  1.153360618067374 |
|    0.00875 | 3.2 | 1.0415899794216563 |
|    0.00925 | 3.2 |  1.148059660843056 |
|    0.00975 | 3.2 |  1.104074091318912 |
| 0.01061009 | 3.2 |  1.159769575401726 |
| 0.01190472 | 3.2 | 1.0713152658553295 |
| 0.01335731 | 3.2 | 1.0921994339469867 |
| 0.01498715 | 3.2 | 1.0743521664112043 |
| 0.01681586 | 3.2 | 1.3326279142310509 |
| 0.01886771 | 3.2 |  1.229332756415133 |
| 0.02116992 | 3.2 |  1.369325668830939 |
| 0.02375304 | 3.2 |  1.230539642120681 |
| 0.02665135 | 3.2 | 1.3003438729213275 |
|  0.0299033 | 3.2 | 1.3273391321235182 |
| 0.03355206 | 3.2 | 1.4325498399094916 |
| 0.03764603 | 3.2 | 1.2735754443921736 |
|    0.00025 | 3.4 | 1.9329744934920012 |
|    0.00075 | 3.4 | 1.6667823169333291 |
|    0.00125 | 3.4 | 1.2581017566936068 |
|    0.00175 | 3.4 | 1.1167794345344326 |
|    0.00225 | 3.4 | 1.2807665316362018 |
|    0.00275 | 3.4 | 1.1480244855789403 |
|    0.00325 | 3.4 | 0.9683925008954114 |
|    0.00375 | 3.4 | 0.9703377328523578 |
|    0.00425 | 3.4 |   0.95505327302678 |
|    0.00475 | 3.4 | 1.0309236778211988 |
|    0.00525 | 3.4 | 1.0319884793270522 |
|    0.00575 | 3.4 |   1.09794717535651 |
|    0.00625 | 3.4 | 0.9793912604279689 |
|    0.00675 | 3.4 | 1.1481998940611124 |
|    0.00725 | 3.4 |   0.98177517728828 |
|    0.00775 | 3.4 | 1.0341376267901228 |
|    0.00825 | 3.4 | 1.0872957329776598 |
|    0.00875 | 3.4 | 1.0397093305591762 |
|    0.00925 | 3.4 |  1.047873086160627 |
|    0.00975 | 3.4 | 1.0967980084729643 |
| 0.01061009 | 3.4 | 1.1305630034384773 |
| 0.01190472 | 3.4 | 1.1246574215861116 |
| 0.01335731 | 3.4 | 1.1527500702563118 |
| 0.01498715 | 3.4 | 1.2167097882968176 |
| 0.01681586 | 3.4 | 1.2749977853851402 |
| 0.01886771 | 3.4 | 1.2925712976706205 |
| 0.02116992 | 3.4 | 1.2910408065730232 |
| 0.02375304 | 3.4 |  1.355440172598677 |
| 0.02665135 | 3.4 | 1.2550984858488439 |
|  0.0299033 | 3.4 | 1.4335663788808726 |
| 0.03355206 | 3.4 | 1.3854687191733932 |
| 0.03764603 | 3.4 |  1.372334560535534 |
| 0.04223954 | 3.4 | 1.4701254524602525 |
|    0.00025 | 3.6 |  2.132124493500385 |
|    0.00075 | 3.6 | 1.7505100369293405 |
|    0.00125 | 3.6 | 1.4921539501990153 |
|    0.00175 | 3.6 | 1.2470963459391478 |
|    0.00225 | 3.6 | 1.1977591479855079 |
|    0.00275 | 3.6 |  1.092801330062083 |
|    0.00325 | 3.6 | 1.1202946651372947 |
|    0.00375 | 3.6 | 1.0662576151798404 |
|    0.00425 | 3.6 | 0.9538146983602493 |
|    0.00475 | 3.6 | 1.0453986980247767 |
|    0.00525 | 3.6 | 1.1064145383076756 |
|    0.00575 | 3.6 | 1.0329279949420995 |
|    0.00625 | 3.6 | 1.0830261979742217 |
|    0.00675 | 3.6 | 1.1387580455522144 |
|    0.00725 | 3.6 | 0.9758414478523995 |
|    0.00775 | 3.6 | 1.0932299410424848 |
|    0.00825 | 3.6 | 1.1803405675307617 |
|    0.00875 | 3.6 | 1.1445082305816678 |
|    0.00925 | 3.6 | 1.1022039781095625 |
|    0.00975 | 3.6 |  1.164330231683797 |
| 0.01061009 | 3.6 | 1.1638784970085785 |
| 0.01190472 | 3.6 | 1.1535856757794887 |
| 0.01335731 | 3.6 | 1.1917827838171287 |
| 0.01498715 | 3.6 | 1.1661820443170439 |
| 0.01681586 | 3.6 | 1.2955492477844237 |
| 0.01886771 | 3.6 | 1.1858632842310388 |
| 0.02116992 | 3.6 | 1.3753415489893082 |
| 0.02375304 | 3.6 |  1.415796060477363 |
| 0.02665135 | 3.6 | 1.4173385014734659 |
|  0.0299033 | 3.6 | 1.2119408504194846 |
| 0.03355206 | 3.6 | 1.5941062489541455 |
| 0.03764603 | 3.6 |  1.672179080362235 |
| 0.04223954 | 3.6 |   1.29123898544005 |
|    0.00025 | 3.8 | 2.4548866880686226 |
|    0.00075 | 3.8 |   1.71848490684129 |
|    0.00125 | 3.8 |  1.327709619361229 |
|    0.00175 | 3.8 | 1.3698901991111505 |
|    0.00225 | 3.8 | 1.2619273906648667 |
|    0.00275 | 3.8 | 1.1093892009125477 |
|    0.00325 | 3.8 | 1.1403077481476114 |
|    0.00375 | 3.8 | 1.0888984773455743 |
|    0.00425 | 3.8 | 1.1928499817569869 |
|    0.00475 | 3.8 |   0.96429532641352 |
|    0.00525 | 3.8 | 1.0211589466798645 |
|    0.00575 | 3.8 |  1.257533212505282 |
|    0.00625 | 3.8 |   1.16145204245332 |
|    0.00675 | 3.8 | 0.9546359712324036 |
|    0.00725 | 3.8 | 1.1360351406889677 |
|    0.00775 | 3.8 | 1.3460099365683005 |
|    0.00825 | 3.8 | 1.3899101748609624 |
|    0.00875 | 3.8 | 1.1258862746525455 |
|    0.00925 | 3.8 | 1.1359798542828328 |
|    0.00975 | 3.8 | 1.0045273678989297 |
| 0.01061009 | 3.8 | 1.1575187066612647 |
| 0.01190472 | 3.8 | 1.1656587374726561 |
| 0.01335731 | 3.8 | 1.1655056648778435 |
| 0.01498715 | 3.8 | 1.1802408854856832 |
| 0.01681586 | 3.8 | 1.3694347249340044 |
| 0.01886771 | 3.8 | 1.4593305815065287 |
| 0.02116992 | 3.8 | 1.1984292589459293 |
| 0.02375304 | 3.8 | 1.4761856181537247 |
| 0.02665135 | 3.8 |  1.419024665487798 |
|  0.0299033 | 3.8 | 1.5486782623203241 |
| 0.03355206 | 3.8 | 1.3905682862798545 |
| 0.03764603 | 3.8 | 1.5456636621836513 |
| 0.04223954 | 3.8 | 1.4093300544586849 |
