|          k |   z |               ratio |
|    0.00025 | 2.0 |  0.4287062165956834 |
|    0.00075 | 2.0 |  0.6050383849681897 |
|    0.00125 | 2.0 |  0.9274771129678557 |
|    0.00175 | 2.0 |  0.9948035921510389 |
|    0.00225 | 2.0 |  0.9194063355345171 |
|    0.00275 | 2.0 |  0.9018579773843536 |
|    0.00325 | 2.0 |  1.0032890324449903 |
|    0.00375 | 2.0 |  1.2183009621286445 |
|    0.00425 | 2.0 |  1.3323577439191412 |
|    0.00475 | 2.0 |  1.1436571930285797 |
|    0.00525 | 2.0 |   1.224713451198451 |
|    0.00575 | 2.0 |   1.107877627409347 |
|    0.00625 | 2.0 |  1.2881176745668896 |
|    0.00675 | 2.0 |  1.4038195970693403 |
|    0.00725 | 2.0 |  1.6150042852698794 |
|    0.00775 | 2.0 |  1.1283768487746157 |
|    0.00825 | 2.0 |    1.23103797784459 |
|    0.00875 | 2.0 |  1.4121721115496477 |
|    0.00925 | 2.0 |   1.453982672046701 |
|    0.00975 | 2.0 |  1.6675067855102983 |
| 0.01061009 | 2.0 |  1.5515607395775564 |
| 0.01190472 | 2.0 |  1.6379044424186397 |
| 0.01335731 | 2.0 |  1.6868151767730861 |
| 0.01498715 | 2.0 |  1.9365912723513214 |
| 0.01681586 | 2.0 |  2.2417153962778538 |
| 0.01886771 | 2.0 |  2.6913733603045067 |
| 0.02116992 | 2.0 |  3.0330028864548146 |
| 0.02375304 | 2.0 |  3.4071691721790174 |
| 0.02665135 | 2.0 |   4.244948867437637 |
|    0.00025 | 2.2 | 0.22436159790039403 |
|    0.00075 | 2.2 | 0.41433094964229433 |
|    0.00125 | 2.2 |  0.4990306060592811 |
|    0.00175 | 2.2 |  0.5534413034310496 |
|    0.00225 | 2.2 |  0.5654388941996077 |
|    0.00275 | 2.2 |  0.5503960446415772 |
|    0.00325 | 2.2 |  0.5735279888258586 |
|    0.00375 | 2.2 |  0.7025900808181483 |
|    0.00425 | 2.2 |  0.7772325391833945 |
|    0.00475 | 2.2 |  0.7833880920019193 |
|    0.00525 | 2.2 |   0.674436522593413 |
|    0.00575 | 2.2 |  0.6568171153517283 |
|    0.00625 | 2.2 |   0.785353201664459 |
|    0.00675 | 2.2 |  0.8077154387153299 |
|    0.00725 | 2.2 |  0.8115350420682462 |
|    0.00775 | 2.2 |  0.7118828727341484 |
|    0.00825 | 2.2 |    0.69852078049392 |
|    0.00875 | 2.2 |  0.7973394371052752 |
|    0.00925 | 2.2 |  0.7813413912867646 |
|    0.00975 | 2.2 |  0.8300264779895404 |
| 0.01061009 | 2.2 |  0.8183701557168799 |
| 0.01190472 | 2.2 |  0.8912651073964912 |
| 0.01335731 | 2.2 |   0.958121601191356 |
| 0.01498715 | 2.2 |  1.0678827469265293 |
| 0.01681586 | 2.2 |   1.134638507512669 |
| 0.01886771 | 2.2 |   1.363125690862123 |
| 0.02116992 | 2.2 |   1.575322059460812 |
| 0.02375304 | 2.2 |  1.7888899129412872 |
| 0.02665135 | 2.2 |  2.1967920328598636 |
|  0.0299033 | 2.2 |   3.750831003990134 |
|    0.00025 | 2.4 | 0.18083233818576505 |
|    0.00075 | 2.4 |  0.3597205175961254 |
|    0.00125 | 2.4 |  0.4428768379358783 |
|    0.00175 | 2.4 |  0.5130505177914734 |
|    0.00225 | 2.4 | 0.48041269687578003 |
|    0.00275 | 2.4 |  0.4849985405358774 |
|    0.00325 | 2.4 |  0.5222262400651788 |
|    0.00375 | 2.4 |  0.6333598096732382 |
|    0.00425 | 2.4 |  0.6640927538775491 |
|    0.00475 | 2.4 |  0.6355999117174381 |
|    0.00525 | 2.4 |  0.6235579659260959 |
|    0.00575 | 2.4 |  0.5877165729875163 |
|    0.00625 | 2.4 |  0.6626881499576832 |
|    0.00675 | 2.4 |  0.7199864951251695 |
|    0.00725 | 2.4 |  0.6957672146656005 |
|    0.00775 | 2.4 |  0.6621090892520451 |
|    0.00825 | 2.4 |  0.6462337536242787 |
|    0.00875 | 2.4 |  0.6451111514983617 |
|    0.00925 | 2.4 |  0.7041964063742153 |
|    0.00975 | 2.4 |  0.7885050373149652 |
| 0.01061009 | 2.4 |  0.7071167361604295 |
| 0.01190472 | 2.4 |  0.7740358739669522 |
| 0.01335731 | 2.4 |  0.7979526187663115 |
| 0.01498715 | 2.4 |   0.911745270639751 |
| 0.01681586 | 2.4 |  0.9440824708787778 |
| 0.01886771 | 2.4 |  1.0595700537722144 |
| 0.02116992 | 2.4 |  1.1939212763404434 |
| 0.02375304 | 2.4 |   1.307576094305238 |
| 0.02665135 | 2.4 |  1.6064515549986942 |
|  0.0299033 | 2.4 |   2.017032386584013 |
|    0.00025 | 2.6 | 0.20091572777853464 |
|    0.00075 | 2.6 | 0.34328058806416434 |
|    0.00125 | 2.6 |  0.4263968862461724 |
|    0.00175 | 2.6 |  0.4805755257424303 |
|    0.00225 | 2.6 |  0.4600455468573981 |
|    0.00275 | 2.6 |  0.4751322807162359 |
|    0.00325 | 2.6 | 0.49017657124531533 |
|    0.00375 | 2.6 |  0.5846676033107233 |
|    0.00425 | 2.6 |  0.6306425244418326 |
|    0.00475 | 2.6 |  0.6104961858381313 |
|    0.00525 | 2.6 |  0.6131936455170025 |
|    0.00575 | 2.6 |  0.5876091416945716 |
|    0.00625 | 2.6 |  0.6086382464114414 |
|    0.00675 | 2.6 |  0.6761800578786248 |
|    0.00725 | 2.6 |  0.7013150945049353 |
|    0.00775 | 2.6 |  0.5752695850922714 |
|    0.00825 | 2.6 |  0.6335094221427346 |
|    0.00875 | 2.6 |  0.6912912477796996 |
|    0.00925 | 2.6 |  0.6196886037262467 |
|    0.00975 | 2.6 |  0.6742314392853758 |
| 0.01061009 | 2.6 |  0.6714207056033075 |
| 0.01190472 | 2.6 |  0.7179262741401086 |
| 0.01335731 | 2.6 |  0.7848867046786447 |
| 0.01498715 | 2.6 |  0.8021354372226241 |
| 0.01681586 | 2.6 |  0.9014525261321988 |
| 0.01886771 | 2.6 |  1.0014581633971653 |
| 0.02116992 | 2.6 |  1.1009144857046906 |
| 0.02375304 | 2.6 |  1.2248272588739106 |
| 0.02665135 | 2.6 |   1.410203739061997 |
|  0.0299033 | 2.6 |  1.8366176423413774 |
| 0.03355206 | 2.6 |   2.146411530302635 |
|    0.00025 | 2.8 | 0.13552711070794404 |
|    0.00075 | 2.8 |  0.2862176057451845 |
|    0.00125 | 2.8 | 0.35330096714399595 |
|    0.00175 | 2.8 |  0.4012784022728858 |
|    0.00225 | 2.8 |  0.3792916748896835 |
|    0.00275 | 2.8 | 0.40254980191735457 |
|    0.00325 | 2.8 |  0.4109818843467167 |
|    0.00375 | 2.8 |  0.4864596254988506 |
|    0.00425 | 2.8 |  0.5476375455644752 |
|    0.00475 | 2.8 |  0.4846197910163529 |
|    0.00525 | 2.8 |  0.4606858915164453 |
|    0.00575 | 2.8 |  0.4822422809424785 |
|    0.00625 | 2.8 |  0.5342803686585451 |
|    0.00675 | 2.8 |  0.5552408820348886 |
|    0.00725 | 2.8 |  0.5524629866518549 |
|    0.00775 | 2.8 |  0.5241606802992759 |
|    0.00825 | 2.8 |  0.5080578154012292 |
|    0.00875 | 2.8 |  0.5538783943914951 |
|    0.00925 | 2.8 |   0.564640002812507 |
|    0.00975 | 2.8 |   0.577552198384855 |
| 0.01061009 | 2.8 |  0.5801498315732155 |
| 0.01190472 | 2.8 |  0.6128336989907853 |
| 0.01335731 | 2.8 |  0.6477134848963116 |
| 0.01498715 | 2.8 |  0.7188507818685216 |
| 0.01681586 | 2.8 |  0.7370886041850362 |
| 0.01886771 | 2.8 |   0.805004624019741 |
| 0.02116992 | 2.8 |  0.9007568009364124 |
| 0.02375304 | 2.8 |  0.9561137277418089 |
| 0.02665135 | 2.8 |  1.1530269264593134 |
|  0.0299033 | 2.8 |   1.432041611879252 |
| 0.03355206 | 2.8 |  1.8241036325844633 |
|    0.00025 | 3.0 | 0.12433692044254836 |
|    0.00075 | 3.0 | 0.20429488174871965 |
|    0.00125 | 3.0 | 0.28531417315992696 |
|    0.00175 | 3.0 | 0.31525886091632727 |
|    0.00225 | 3.0 |  0.2867078712140798 |
|    0.00275 | 3.0 |  0.3208214383345169 |
|    0.00325 | 3.0 |  0.3445146665766775 |
|    0.00375 | 3.0 |  0.3927451846570878 |
|    0.00425 | 3.0 |  0.4046222938243321 |
|    0.00475 | 3.0 |  0.4015040297868127 |
|    0.00525 | 3.0 | 0.36898319119474915 |
|    0.00575 | 3.0 |  0.3781541586470862 |
|    0.00625 | 3.0 |  0.4138674610593692 |
|    0.00675 | 3.0 |  0.4515021831673558 |
|    0.00725 | 3.0 |  0.4490884782764492 |
|    0.00775 | 3.0 |  0.4283791379349568 |
|    0.00825 | 3.0 | 0.44387945786451927 |
|    0.00875 | 3.0 |  0.4294034238466432 |
|    0.00925 | 3.0 | 0.44910293990885747 |
|    0.00975 | 3.0 |  0.5199393638498772 |
| 0.01061009 | 3.0 | 0.46927827458180016 |
| 0.01190472 | 3.0 |   0.501622365985976 |
| 0.01335731 | 3.0 |  0.5129090887375952 |
| 0.01498715 | 3.0 |  0.5613865498818431 |
| 0.01681586 | 3.0 |  0.5945768491476693 |
| 0.01886771 | 3.0 |   0.685036012724314 |
| 0.02116992 | 3.0 |  0.7159895452736234 |
| 0.02375304 | 3.0 |  0.7998558813384054 |
| 0.02665135 | 3.0 |  0.8701401122321182 |
|  0.0299033 | 3.0 |  1.0585358692122782 |
| 0.03355206 | 3.0 |  1.4425832770641414 |
| 0.03764603 | 3.0 |  1.8037950224430401 |
|    0.00025 | 3.2 |   0.139976784405674 |
|    0.00075 | 3.2 | 0.20182700895875674 |
|    0.00125 | 3.2 | 0.22569736135987448 |
|    0.00175 | 3.2 | 0.25358358787086943 |
|    0.00225 | 3.2 |  0.2547959480677944 |
|    0.00275 | 3.2 |  0.2676336375545146 |
|    0.00325 | 3.2 |  0.2707906965419784 |
|    0.00375 | 3.2 |  0.3222168131096474 |
|    0.00425 | 3.2 | 0.32165195415723324 |
|    0.00475 | 3.2 | 0.32484069744065724 |
|    0.00525 | 3.2 | 0.31992290616189506 |
|    0.00575 | 3.2 | 0.32790885640133416 |
|    0.00625 | 3.2 |  0.3494431566208589 |
|    0.00675 | 3.2 |  0.3493589287802799 |
|    0.00725 | 3.2 | 0.36449742629005144 |
|    0.00775 | 3.2 |  0.3306805285877219 |
|    0.00825 | 3.2 | 0.33793573621828055 |
|    0.00875 | 3.2 |  0.3694362394244197 |
|    0.00925 | 3.2 | 0.38286081205258143 |
|    0.00975 | 3.2 |  0.3979711281537279 |
| 0.01061009 | 3.2 | 0.38856280094563433 |
| 0.01190472 | 3.2 |  0.4149547172479593 |
| 0.01335731 | 3.2 |  0.4516025651061858 |
| 0.01498715 | 3.2 |  0.5072234083574617 |
| 0.01681586 | 3.2 |  0.5014592958808949 |
| 0.01886771 | 3.2 |  0.5444736505246586 |
| 0.02116992 | 3.2 |  0.6075029547471964 |
| 0.02375304 | 3.2 |   0.662349092833719 |
| 0.02665135 | 3.2 |  0.8081189377193886 |
|  0.0299033 | 3.2 |  0.9191859099199514 |
| 0.03355206 | 3.2 |  1.1142838254091414 |
| 0.03764603 | 3.2 |  1.6067638402413784 |
|    0.00025 | 3.4 |  0.1352868786823126 |
|    0.00075 | 3.4 | 0.17874412562489161 |
|    0.00125 | 3.4 | 0.24589406241686057 |
|    0.00175 | 3.4 | 0.24079404364055115 |
|    0.00225 | 3.4 | 0.22074088860038177 |
|    0.00275 | 3.4 |  0.2406402024699638 |
|    0.00325 | 3.4 |  0.3255352147289391 |
|    0.00375 | 3.4 | 0.29420260425892053 |
|    0.00425 | 3.4 | 0.33291161420724263 |
|    0.00475 | 3.4 |  0.3035218601132679 |
|    0.00525 | 3.4 | 0.32823649327459153 |
|    0.00575 | 3.4 |  0.3151064067221567 |
|    0.00625 | 3.4 | 0.32741227947946694 |
|    0.00675 | 3.4 |  0.3755328788979756 |
|    0.00725 | 3.4 | 0.39189231300173477 |
|    0.00775 | 3.4 | 0.34885398886968116 |
|    0.00825 | 3.4 | 0.35114114038677025 |
|    0.00875 | 3.4 | 0.39126130440292445 |
|    0.00925 | 3.4 | 0.38401555962403106 |
|    0.00975 | 3.4 |  0.4219975614834651 |
| 0.01061009 | 3.4 | 0.38835832196404213 |
| 0.01190472 | 3.4 |  0.4313772121300898 |
| 0.01335731 | 3.4 |    0.43192535647381 |
| 0.01498715 | 3.4 |  0.4506933271444183 |
| 0.01681586 | 3.4 |  0.5209802919726583 |
| 0.01886771 | 3.4 |  0.5498256376159114 |
| 0.02116992 | 3.4 |  0.6049671778757814 |
| 0.02375304 | 3.4 |  0.6569955707160372 |
| 0.02665135 | 3.4 |  0.7248542423444998 |
|  0.0299033 | 3.4 |   0.849880821966067 |
| 0.03355206 | 3.4 |  0.9669309341520632 |
| 0.03764603 | 3.4 |  1.2858151828684017 |
| 0.04223954 | 3.4 |  0.7479722368697515 |
|    0.00025 | 3.6 | 0.14168078564871495 |
|    0.00075 | 3.6 | 0.22543732085974588 |
|    0.00125 | 3.6 |   0.204621165949895 |
|    0.00175 | 3.6 |  0.2854400429667609 |
|    0.00225 | 3.6 |  0.2744016004536751 |
|    0.00275 | 3.6 |  0.2939987746758396 |
|    0.00325 | 3.6 | 0.25666654151875673 |
|    0.00375 | 3.6 | 0.33575852042072535 |
|    0.00425 | 3.6 |  0.3955204952721972 |
|    0.00475 | 3.6 | 0.36990887203781486 |
|    0.00525 | 3.6 |   0.310388212898921 |
|    0.00575 | 3.6 | 0.36258665588109873 |
|    0.00625 | 3.6 |  0.3595909625853474 |
|    0.00675 | 3.6 | 0.39218760906305505 |
|    0.00725 | 3.6 |  0.4163791020652998 |
|    0.00775 | 3.6 |   0.380758773698986 |
|    0.00825 | 3.6 | 0.36752937149376563 |
|    0.00875 | 3.6 |  0.3533273168674103 |
|    0.00925 | 3.6 |  0.4403645778289471 |
|    0.00975 | 3.6 | 0.40293339368825565 |
| 0.01061009 | 3.6 | 0.45235355058586424 |
| 0.01190472 | 3.6 |  0.4417506292103941 |
| 0.01335731 | 3.6 | 0.49524480299367485 |
| 0.01498715 | 3.6 |  0.5338317892376148 |
| 0.01681586 | 3.6 |  0.5331253095536103 |
| 0.01886771 | 3.6 |  0.6137966394407843 |
| 0.02116992 | 3.6 |  0.6042959039563618 |
| 0.02375304 | 3.6 |  0.6467377026661361 |
| 0.02665135 | 3.6 |   0.702387316563267 |
|  0.0299033 | 3.6 |  0.9092889845466763 |
| 0.03355206 | 3.6 |  0.9646304332504504 |
| 0.03764603 | 3.6 |  1.1746348811370733 |
| 0.04223954 | 3.6 |  1.8067246824221845 |
|    0.00025 | 3.8 | 0.08841388466264401 |
|    0.00075 | 3.8 | 0.19392638508107984 |
|    0.00125 | 3.8 | 0.23339010063855284 |
|    0.00175 | 3.8 | 0.22602528120248738 |
|    0.00225 | 3.8 |  0.2636294267283554 |
|    0.00275 | 3.8 | 0.29102755242951267 |
|    0.00325 | 3.8 | 0.28866638129215233 |
|    0.00375 | 3.8 | 0.30588597731422507 |
|    0.00425 | 3.8 | 0.26724882057115973 |
|    0.00475 | 3.8 |  0.3207939949522417 |
|    0.00525 | 3.8 |  0.3549437471240362 |
|    0.00575 | 3.8 | 0.29361611287862616 |
|    0.00625 | 3.8 |    0.32908082465102 |
|    0.00675 | 3.8 | 0.43377445468989356 |
|    0.00725 | 3.8 | 0.31006813541447303 |
|    0.00775 | 3.8 |  0.3591401958103085 |
|    0.00825 | 3.8 | 0.31553495597586706 |
|    0.00875 | 3.8 | 0.35777677511351297 |
|    0.00925 | 3.8 |  0.4184476447927328 |
|    0.00975 | 3.8 |  0.4236617841747271 |
| 0.01061009 | 3.8 |  0.3805519930032624 |
| 0.01190472 | 3.8 |  0.4178054936891123 |
| 0.01335731 | 3.8 | 0.45417434737376117 |
| 0.01498715 | 3.8 |  0.4384649950521644 |
| 0.01681586 | 3.8 |  0.4372191324703735 |
| 0.01886771 | 3.8 |  0.4910103293537187 |
| 0.02116992 | 3.8 |  0.5580879241371934 |
| 0.02375304 | 3.8 |  0.5661633807300346 |
| 0.02665135 | 3.8 |  0.5640303808866215 |
|  0.0299033 | 3.8 |  0.6018436608497978 |
| 0.03355206 | 3.8 |  0.7552016400163193 |
| 0.03764603 | 3.8 |  0.8239814701127621 |
| 0.04223954 | 3.8 |   1.057593506268684 |
