#! /usr/bin/env python # def legendre_theta ( l, k ): #*****************************************************************************80 # ## LEGENDRE_THETA returns the K-th theta coordinate in an L point rule. # # Discussion: # # The X coordinate is simply cos ( THETA ). # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 06 January 2016 # # Author: # # Original C++ version by Ignace Bogaert. # Python version by John Burkardt. # # Reference: # # Ignace Bogaert, # Iteration-free computation of Gauss-Legendre quadrature nodes and weights, # SIAM Journal on Scientific Computing, # Volume 36, Number 3, 2014, pages A1008-1026. # # Parameters: # # Input, integer L, the number of points in the given rule. # 1 <= L. # # Input, integer K, the index of the point to be returned. # 1 <= K <= L. # # Output, real THETA, the theta coordinate of the point. # import numpy as np from sys import exit EvenThetaZero1 = np.array ( [ \ 0.9553166181245092781638573E+00 ] ) EvenThetaZero2 = np.array ( [ \ 0.1223899586470372591854100E+01, \ 0.5332956802491269896325121E+00 ] ) EvenThetaZero3 = np.array ( [ \ 0.1329852612388110166006182E+01, \ 0.8483666264874876548310910E+00, \ 0.3696066519448289481138796E+00 ] ) EvenThetaZero4 = np.array ( [ \ 0.1386317078892131346282665E+01, \ 0.1017455539490153431016397E+01, \ 0.6490365804607796100719162E+00, \ 0.2827570635937967783987981E+00 ] ) EvenThetaZero5 = np.array ( [ \ 0.1421366498439524924081833E+01, \ 0.1122539327631709474018620E+01, \ 0.8238386589997556048023640E+00, \ 0.5255196555285001171749362E+00, \ 0.2289442988470260178701589E+00 ] ) EvenThetaZero6 = np.array ( [ \ 0.1445233238471440081118261E+01, \ 0.1194120375947706635968399E+01, \ 0.9430552870605735796668951E+00, \ 0.6921076988818410126677201E+00, \ 0.4414870814893317611922530E+00, \ 0.1923346793046672033050762E+00 ] ) EvenThetaZero7 = np.array ( [ \ 0.1462529992921481833498746E+01, \ 0.1246003586776677662375070E+01, \ 0.1029498592525136749641068E+01, \ 0.8130407055389454598609888E+00, \ 0.5966877608172733931509619E+00, \ 0.3806189306666775272453522E+00, \ 0.1658171411523664030454318E+00 ] ) EvenThetaZero8 = np.array ( [ \ 0.1475640280808194256470687E+01, \ 0.1285331444322965257106517E+01, \ 0.1095033401803444343034890E+01, \ 0.9047575323895165085030778E+00, \ 0.7145252532340252146626998E+00, \ 0.5243866409035941583262629E+00, \ 0.3344986386876292124968005E+00, \ 0.1457246820036738335698855E+00 ] ) EvenThetaZero9 = np.array ( [ \ 0.1485919440392653014379727E+01, \ 0.1316167494718022699851110E+01, \ 0.1146421481056642228295923E+01, \ 0.9766871104439832694094465E+00, \ 0.8069738930788195349918620E+00, \ 0.6373005058706191519531139E+00, \ 0.4677113145328286263205134E+00, \ 0.2983460782092324727528346E+00, \ 0.1299747364196768405406564E+00 ] ) EvenThetaZero10 = np.array ( [ \ 0.1494194914310399553510039E+01, \ 0.1340993178589955138305166E+01, \ 0.1187794926634098887711586E+01, \ 0.1034603297590104231043189E+01, \ 0.8814230742890135843662021E+00, \ 0.7282625848696072912405713E+00, \ 0.5751385026314284688366450E+00, \ 0.4220907301111166004529037E+00, \ 0.2692452880289302424376614E+00, \ 0.1172969277059561308491253E+00 ] ) EvenThetaZero11 = np.array ( [ \ 0.1501000399130816063282492E+01, \ 0.1361409225664372117193308E+01, \ 0.1221820208990359866348145E+01, \ 0.1082235198111836788818162E+01, \ 0.9426568273796608630446470E+00, \ 0.8030892957063359443650460E+00, \ 0.6635400754448062852164288E+00, \ 0.5240242709487281141128643E+00, \ 0.3845781703583910933413978E+00, \ 0.2453165389983612942439953E+00, \ 0.1068723357985259945018899E+00 ] ) EvenThetaZero12 = np.array ( [ \ 0.1506695545558101030878728E+01, \ 0.1378494427506219143960887E+01, \ 0.1250294703417272987066314E+01, \ 0.1122097523267250692925104E+01, \ 0.9939044422989454674968570E+00, \ 0.8657177770401081355080608E+00, \ 0.7375413075437535618804594E+00, \ 0.6093818382449565759195927E+00, \ 0.4812531951313686873528891E+00, \ 0.3531886675690780704072227E+00, \ 0.2252936226353075734690198E+00, \ 0.9814932949793685067733311E-01 ] ) EvenThetaZero13 = np.array ( [ \ 0.1511531546703289231944719E+01, \ 0.1393002286179807923400254E+01, \ 0.1274473959424494104852958E+01, \ 0.1155947313793812040125722E+01, \ 0.1037423319077439147088755E+01, \ 0.9189033445598992550553862E+00, \ 0.8003894803353296871788647E+00, \ 0.6818851814129298518332401E+00, \ 0.5633967073169293284500428E+00, \ 0.4449368152119130526034289E+00, \ 0.3265362611165358134766736E+00, \ 0.2082924425598466358987549E+00, \ 0.9074274842993199730441784E-01 ] ) EvenThetaZero14 = np.array ( [ \ 0.1515689149557281132993364E+01, \ 0.1405475003062348722192382E+01, \ 0.1295261501292316172835393E+01, \ 0.1185049147889021579229406E+01, \ 0.1074838574917869281769567E+01, \ 0.9646306371285440922680794E+00, \ 0.8544265718392254369377945E+00, \ 0.7442282945111358297916378E+00, \ 0.6340389954584301734412433E+00, \ 0.5238644768825679339859620E+00, \ 0.4137165857369637683488098E+00, \ 0.3036239070914333637971179E+00, \ 0.1936769929947376175341314E+00, \ 0.8437551461511597225722252E-01 ] ) EvenThetaZero15 = np.array ( [ \ 0.1519301729274526620713294E+01, \ 0.1416312682230741743401738E+01, \ 0.1313324092045794720169874E+01, \ 0.1210336308624476413072722E+01, \ 0.1107349759228459143499061E+01, \ 0.1004365001539081003659288E+01, \ 0.9013828087667156388167226E+00, \ 0.7984043170121235411718744E+00, \ 0.6954313000299367256853883E+00, \ 0.5924667257887385542924194E+00, \ 0.4895160050896970092628705E+00, \ 0.3865901987860504829542802E+00, \ 0.2837160095793466884313556E+00, \ 0.1809780449917272162574031E+00, \ 0.7884320726554945051322849E-01 ] ) EvenThetaZero16 = np.array ( [ \ 0.1522469852641529230282387E+01, \ 0.1425817011963825344615095E+01, \ 0.1329164502391080681347666E+01, \ 0.1232512573416362994802398E+01, \ 0.1135861522840293704616614E+01, \ 0.1039211728068951568003361E+01, \ 0.9425636940046777101926515E+00, \ 0.8459181315837993237739032E+00, \ 0.7492760951181414487254243E+00, \ 0.6526392394594561548023681E+00, \ 0.5560103418005302722406995E+00, \ 0.4593944730762095704649700E+00, \ 0.3628020075350028174968692E+00, \ 0.2662579994723859636910796E+00, \ 0.1698418454282150179319973E+00, \ 0.7399171309970959768773072E-01 ] ) EvenThetaZero17 = np.array ( [ \ 0.1525270780617194430047563E+01, \ 0.1434219768045409606267345E+01, \ 0.1343169000217435981125683E+01, \ 0.1252118659062444379491066E+01, \ 0.1161068957629157748792749E+01, \ 0.1070020159291475075961444E+01, \ 0.9789726059789103169325141E+00, \ 0.8879267623988119819560021E+00, \ 0.7968832893748414870413015E+00, \ 0.7058431727509840105946884E+00, \ 0.6148079652926100198490992E+00, \ 0.5237802779694730663856110E+00, \ 0.4327648832448234459097574E+00, \ 0.3417715500266717765568488E+00, \ 0.2508238767288223767569849E+00, \ 0.1599966542668327644694431E+00, \ 0.6970264809814094464033170E-01 ] ) EvenThetaZero18 = np.array ( [ \ 0.1527764849261740485876940E+01, \ 0.1441701954349064743573367E+01, \ 0.1355639243522655042028688E+01, \ 0.1269576852063768424508476E+01, \ 0.1183514935851550608323947E+01, \ 0.1097453683555812711123880E+01, \ 0.1011393333949027021740881E+01, \ 0.9253342019812867059380523E+00, \ 0.8392767201322475821509486E+00, \ 0.7532215073977623159515351E+00, \ 0.6671694908788198522546767E+00, \ 0.5811221342350705406265672E+00, \ 0.4950819018993074588093747E+00, \ 0.4090533017972007314666814E+00, \ 0.3230455648729987995657071E+00, \ 0.2370809940997936908335290E+00, \ 0.1512302802537625099602687E+00, \ 0.6588357082399222649528476E-01 ] ) EvenThetaZero19 = np.array ( [ \ 0.1529999863223206659623262E+01, \ 0.1448406982124841835685420E+01, \ 0.1366814241651488684482888E+01, \ 0.1285221744143731581870833E+01, \ 0.1203629605904952775544878E+01, \ 0.1122037965173751996510051E+01, \ 0.1040446993107623345153211E+01, \ 0.9588569097730895525404200E+00, \ 0.8772680085516152329147030E+00, \ 0.7956806951062012653043722E+00, \ 0.7140955526031660805347356E+00, \ 0.6325134568448222221560326E+00, \ 0.5509357927460004487348532E+00, \ 0.4693648943475422765864580E+00, \ 0.3878050333015201414955289E+00, \ 0.3062649591511896679168503E+00, \ 0.2247658146033686460963295E+00, \ 0.1433746167818849555570557E+00, \ 0.6246124541276674097388211E-01 ] ) EvenThetaZero20 = np.array ( [ \ 0.1532014188279762793560699E+01, \ 0.1454449946977268522285131E+01, \ 0.1376885814601482670609845E+01, \ 0.1299321869764876494939757E+01, \ 0.1221758200747475205847413E+01, \ 0.1144194910846247537582396E+01, \ 0.1066632125552939823863593E+01, \ 0.9890700026972186303565530E+00, \ 0.9115087474225932692070479E+00, \ 0.8339486352158799520695092E+00, \ 0.7563900488174808348719219E+00, \ 0.6788335401193977027577509E+00, \ 0.6012799395312684623216685E+00, \ 0.5237305617022755897200291E+00, \ 0.4461876237541810478131970E+00, \ 0.3686551849119556335824055E+00, \ 0.2911415613085158758589405E+00, \ 0.2136668503694680525340165E+00, \ 0.1362947587312224822844743E+00, \ 0.5937690028966411906487257E-01 ] ) EvenThetaZero21 = np.array ( [ \ 0.1533838971193864306068338E+01, \ 0.1459924288056445029654271E+01, \ 0.1386009690354996919044862E+01, \ 0.1312095239305276612560739E+01, \ 0.1238181002944535867235042E+01, \ 0.1164267059803796726229370E+01, \ 0.1090353503721897748980095E+01, \ 0.1016440450472067349837507E+01, \ 0.9425280472651469176638349E+00, \ 0.8686164868955467866176243E+00, \ 0.7947060295895204342519786E+00, \ 0.7207970381018823842440224E+00, \ 0.6468900366403721167107352E+00, \ 0.5729858150363658839291287E+00, \ 0.4990856247464946058899833E+00, \ 0.4251915773724379089467945E+00, \ 0.3513075400485981451355368E+00, \ 0.2774414365914335857735201E+00, \ 0.2036124177925793565507033E+00, \ 0.1298811916061515892914930E+00, \ 0.5658282534660210272754152E-01 ] ) EvenThetaZero22 = np.array ( [ \ 0.1535499761264077326499892E+01, \ 0.1464906652494521470377318E+01, \ 0.1394313611500109323616335E+01, \ 0.1323720686538524176057236E+01, \ 0.1253127930763390908996314E+01, \ 0.1182535404796980113294400E+01, \ 0.1111943180033868679273393E+01, \ 0.1041351343083674290731439E+01, \ 0.9707600019805773720746280E+00, \ 0.9001692951667510715040632E+00, \ 0.8295794049297955988640329E+00, \ 0.7589905782114329186155957E+00, \ 0.6884031600807736268672129E+00, \ 0.6178176499732537480601935E+00, \ 0.5472348011493452159473826E+00, \ 0.4766558078624760377875119E+00, \ 0.4060826859477620301047824E+00, \ 0.3355191279517093844978473E+00, \ 0.2649727008485465487101933E+00, \ 0.1944616940738156405895778E+00, \ 0.1240440866043499301839465E+00, \ 0.5403988657613871827831605E-01 ] ) EvenThetaZero23 = np.array ( [ \ 0.1537017713608809830855653E+01, \ 0.1469460505124226636602925E+01, \ 0.1401903350962364703169699E+01, \ 0.1334346289590505369693957E+01, \ 0.1266789363044399933941254E+01, \ 0.1199232618763735058848455E+01, \ 0.1131676111906105521856066E+01, \ 0.1064119908394702657537061E+01, \ 0.9965640890815034701957497E+00, \ 0.9290087556203499065939494E+00, \ 0.8614540390091103102510609E+00, \ 0.7939001124053586164046432E+00, \ 0.7263472110048245091518914E+00, \ 0.6587956640463586742461796E+00, \ 0.5912459486086227271608064E+00, \ 0.5236987847717837556177452E+00, \ 0.4561553147193391989386660E+00, \ 0.3886174669444433167860783E+00, \ 0.3210887745896478259115420E+00, \ 0.2535764786314617292100029E+00, \ 0.1860980813776342452540915E+00, \ 0.1187090676924131329841811E+00, \ 0.5171568198966901682810573E-01 ] ) EvenThetaZero24 = np.array ( [ \ 0.1538410494858190444190279E+01, \ 0.1473638845472165977392911E+01, \ 0.1408867240039222913928858E+01, \ 0.1344095709533508756473909E+01, \ 0.1279324287566779722061664E+01, \ 0.1214553011719528935181709E+01, \ 0.1149781925191718586091000E+01, \ 0.1085011078936665906275419E+01, \ 0.1020240534516704208782618E+01, \ 0.9554703680422404498752066E+00, \ 0.8907006757608306209160649E+00, \ 0.8259315822134856671969566E+00, \ 0.7611632524946588128425351E+00, \ 0.6963959112887657683892237E+00, \ 0.6316298735371143844913976E+00, \ 0.5668655960010826255149266E+00, \ 0.5021037684870694065589284E+00, \ 0.4373454855522296089897130E+00, \ 0.3725925956833896735786860E+00, \ 0.3078484858841616878136371E+00, \ 0.2431200981264999375962973E+00, \ 0.1784242126043536701754986E+00, \ 0.1138140258514833068653307E+00, \ 0.4958315373802413441075340E-01 ] ) EvenThetaZero25 = np.array ( [ \ 0.1539692973716708504412697E+01, \ 0.1477486279394502338589519E+01, \ 0.1415279620944410339318226E+01, \ 0.1353073023537942666830874E+01, \ 0.1290866514321280958405103E+01, \ 0.1228660123395079609266898E+01, \ 0.1166453885011658611362850E+01, \ 0.1104247839096738022319035E+01, \ 0.1042042033248543055386770E+01, \ 0.9798365254403234947595400E+00, \ 0.9176313877712591840677176E+00, \ 0.8554267118081827231209625E+00, \ 0.7932226163976800550406599E+00, \ 0.7310192594231560707888939E+00, \ 0.6688168560730805146438886E+00, \ 0.6066157082814543103941755E+00, \ 0.5444162542389049922529553E+00, \ 0.4822191559963931133878621E+00, \ 0.4200254643636986308379697E+00, \ 0.3578369542536859435571624E+00, \ 0.2956568781922605524959448E+00, \ 0.2334919029083292837123583E+00, \ 0.1713581437497397360313735E+00, \ 0.1093066902335822942650053E+00, \ 0.4761952998197036029817629E-01 ] ) EvenThetaZero26 = np.array ( [ \ 0.1540877753740080417345045E+01, \ 0.1481040617373741365390254E+01, \ 0.1421203510518656600018143E+01, \ 0.1361366453804322852131292E+01, \ 0.1301529469356044341206877E+01, \ 0.1241692581525935716830402E+01, \ 0.1181855817774264617619371E+01, \ 0.1122019209772750368801179E+01, \ 0.1062182794829879659341536E+01, \ 0.1002346617783007482854908E+01, \ 0.9425107335729934538419206E+00, \ 0.8826752108319277463183701E+00, \ 0.8228401370047382776784725E+00, \ 0.7630056258499810562932058E+00, \ 0.7031718287376427885875898E+00, \ 0.6433389522119553277924537E+00, \ 0.5835072863023426715977658E+00, \ 0.5236772521416453354847559E+00, \ 0.4638494862268433259444639E+00, \ 0.4040249990308909882616381E+00, \ 0.3442054975680110060507306E+00, \ 0.2843941101955779333389742E+00, \ 0.2245972494281051799602510E+00, \ 0.1648304164747050021714385E+00, \ 0.1051427544146599992432949E+00, \ 0.4580550859172367960799915E-01 ] ) EvenThetaZero27 = np.array ( [ \ 0.1541975588842621898865181E+01, \ 0.1484334121018556567335167E+01, \ 0.1426692677652358867201800E+01, \ 0.1369051275783071487471360E+01, \ 0.1311409933595114953831618E+01, \ 0.1253768670970438091691833E+01, \ 0.1196127510146226323327062E+01, \ 0.1138486476526912406867032E+01, \ 0.1080845599717322003702293E+01, \ 0.1023204914871722785830020E+01, \ 0.9655644644970043364617272E+00, \ 0.9079243009168822510582606E+00, \ 0.8502844897148263889326479E+00, \ 0.7926451146568312828354346E+00, \ 0.7350062849078710810840430E+00, \ 0.6773681459074923011631400E+00, \ 0.6197308962817025162722438E+00, \ 0.5620948151095422609589585E+00, \ 0.5044603077892199488064657E+00, \ 0.4468279872027509013135997E+00, \ 0.3891988265038338944044115E+00, \ 0.3315744698431505326770711E+00, \ 0.2739579305700525818998611E+00, \ 0.2163553856859193758294342E+00, \ 0.1587817673749480300092784E+00, \ 0.1012844151694839452028589E+00, \ 0.4412462056235422293371300E-01 ] ) EvenThetaZero28 = np.array ( [ \ 0.1542995710582548837472073E+01, \ 0.1487394484904746766220933E+01, \ 0.1431793279635669382208875E+01, \ 0.1376192108950239363921811E+01, \ 0.1320590987909222553912422E+01, \ 0.1264989932881031519687125E+01, \ 0.1209388962038683919740547E+01, \ 0.1153788095965648154683658E+01, \ 0.1098187358416032947576489E+01, \ 0.1042586777292402877200408E+01, \ 0.9869863859317282394719449E+00, \ 0.9313862248321055503829503E+00, \ 0.8757863440192765677772914E+00, \ 0.8201868063589761051746975E+00, \ 0.7645876922981545448147078E+00, \ 0.7089891068198449136125464E+00, \ 0.6533911899285832425290628E+00, \ 0.5977941329592257586198087E+00, \ 0.5421982048745539015834188E+00, \ 0.4866037965045890355211229E+00, \ 0.4310114988353693539492225E+00, \ 0.3754222503860499120445385E+00, \ 0.3198376369331602148544626E+00, \ 0.2642605649958747239907310E+00, \ 0.2086969927688100977274751E+00, \ 0.1531613237261629042774314E+00, \ 0.9769922156300582041279299E-01, \ 0.4256272861907242306694832E-01 ] ) EvenThetaZero29 = np.array ( [ \ 0.1543946088331101630230404E+01, \ 0.1490245617072432741470241E+01, \ 0.1436545162952171175361532E+01, \ 0.1382844737841275627385236E+01, \ 0.1329144354302189376680665E+01, \ 0.1275444025914442882448630E+01, \ 0.1221743767654456436125309E+01, \ 0.1168043596353244531685999E+01, \ 0.1114343531263457295536939E+01, \ 0.1060643594778787047442989E+01, \ 0.1006943813366184678568021E+01, \ 0.9532442187977767941200107E+00, \ 0.8995448498101763729640445E+00, \ 0.8458457543830885615091264E+00, \ 0.7921469929325243736682034E+00, \ 0.7384486428849507503612470E+00, \ 0.6847508053901545384892447E+00, \ 0.6310536154445759741044291E+00, \ 0.5773572576394624029563656E+00, \ 0.5236619915567428835581025E+00, \ 0.4699681944935857341529219E+00, \ 0.4162764370726533962791279E+00, \ 0.3625876255789859906927245E+00, \ 0.3089032914359211154562848E+00, \ 0.2552262416643531728802047E+00, \ 0.2015622306384971766058615E+00, \ 0.1479251692966707827334002E+00, \ 0.9435916010280739398532997E-01, \ 0.4110762866287674188292735E-01 ] ) EvenThetaZero30 = np.array ( [ \ 0.1544833637851665335244669E+01, \ 0.1492908264756388370493025E+01, \ 0.1440982906138650837480037E+01, \ 0.1389057572001580364167786E+01, \ 0.1337132272892735072773304E+01, \ 0.1285207020157876647295968E+01, \ 0.1233281826234298389291217E+01, \ 0.1181356705000596722238457E+01, \ 0.1129431672204958843918638E+01, \ 0.1077506746001711267258715E+01, \ 0.1025581947637229234301640E+01, \ 0.9736573023432582093437126E+00, \ 0.9217328405213548692702866E+00, \ 0.8698085993416727107979968E+00, \ 0.8178846249414537373941032E+00, \ 0.7659609755086193214466010E+00, \ 0.7140377257012462393241274E+00, \ 0.6621149731355525426273686E+00, \ 0.6101928481720243483360470E+00, \ 0.5582715291407654489802101E+00, \ 0.5063512668959282414914789E+00, \ 0.4544324261262307197237056E+00, \ 0.4025155584642650335664553E+00, \ 0.3506015401168133792671488E+00, \ 0.2986918517703509333332016E+00, \ 0.2467892075469457255751440E+00, \ 0.1948991714956708008247732E+00, \ 0.1430351946011564171352354E+00, \ 0.9123992133264713232350199E-01, \ 0.3974873026126591246235829E-01 ] ) EvenThetaZero31 = np.array ( [ \ 0.1545664389841685834178882E+01, \ 0.1495400520006868605194165E+01, \ 0.1445136662469633349524466E+01, \ 0.1394872825707861196682996E+01, \ 0.1344609018631531661347402E+01, \ 0.1294345250782284139500904E+01, \ 0.1244081532562166402923175E+01, \ 0.1193817875503760392032898E+01, \ 0.1143554292597402872188167E+01, \ 0.1093290798696377946301336E+01, \ 0.1043027411028491785799717E+01, \ 0.9927641498535133311947588E+00, \ 0.9425010393224361375194941E+00, \ 0.8922381086194002226900769E+00, \ 0.8419753935054036625982058E+00, \ 0.7917129384431112475049142E+00, \ 0.7414507995789214800057706E+00, \ 0.6911890490185720721582180E+00, \ 0.6409277811053987947460976E+00, \ 0.5906671218914768219060599E+00, \ 0.5404072438741681591850965E+00, \ 0.4901483897634232956856935E+00, \ 0.4398909124691513811974471E+00, \ 0.3896353458699818240468259E+00, \ 0.3393825380385224469051922E+00, \ 0.2891339221891949677776928E+00, \ 0.2388921255071779766209942E+00, \ 0.1886625339124777570188312E+00, \ 0.1384581678870181657476050E+00, \ 0.8832030722827102577102185E-01, \ 0.3847679847963676404657822E-01 ] ) EvenThetaZero32 = np.array ( [ \ 0.1546443627125265521960044E+01, \ 0.1497738231263909315513507E+01, \ 0.1449032845902631477147772E+01, \ 0.1400327478265391242178337E+01, \ 0.1351622135921668846451224E+01, \ 0.1302916826944702448727527E+01, \ 0.1254211560091483702838765E+01, \ 0.1205506345013417018443405E+01, \ 0.1156801192508980685500292E+01, \ 0.1108096114833249453312212E+01, \ 0.1059391126084216587933501E+01, \ 0.1010686242693213908544820E+01, \ 0.9619814840575052973573711E+00, \ 0.9132768733691264344256970E+00, \ 0.8645724387181842642305406E+00, \ 0.8158682145859558652971026E+00, \ 0.7671642439014559105969752E+00, \ 0.7184605809290069459742089E+00, \ 0.6697572954095121564500879E+00, \ 0.6210544786425143220264938E+00, \ 0.5723522526623283741373995E+00, \ 0.5236507845164779831804685E+00, \ 0.4749503092950064087413842E+00, \ 0.4262511688770346357064771E+00, \ 0.3775538805043668894422883E+00, \ 0.3288592658750793954850446E+00, \ 0.2801687136893753887834348E+00, \ 0.2314847695998852605184853E+00, \ 0.1828126524563463299986617E+00, \ 0.1341649789468091132459783E+00, \ 0.8558174883654483804697753E-01, \ 0.3728374374031613183399036E-01 ] ) EvenThetaZero33 = np.array ( [ \ 0.1547175997094614757138430E+01, \ 0.1499935340679181525271649E+01, \ 0.1452694693272706215568985E+01, \ 0.1405454061061768876728643E+01, \ 0.1358213450511184239883293E+01, \ 0.1310972868490444296079765E+01, \ 0.1263732322416537730871712E+01, \ 0.1216491820419724046503073E+01, \ 0.1169251371540540180758674E+01, \ 0.1122010985968754004469355E+01, \ 0.1074770675338453464761893E+01, \ 0.1027530453098431393666936E+01, \ 0.9802903349842005856557204E+00, \ 0.9330503396284544173873149E+00, \ 0.8858104893623263267477775E+00, \ 0.8385708112832335506864354E+00, \ 0.7913313387011139500976360E+00, \ 0.7440921131314510897906335E+00, \ 0.6968531870945337206139839E+00, \ 0.6496146281309018959581539E+00, \ 0.6023765246993705639765525E+00, \ 0.5551389950762090311242875E+00, \ 0.5079022012032895030848024E+00, \ 0.4606663710240282967569630E+00, \ 0.4134318360639670775957014E+00, \ 0.3661990979414348851212686E+00, \ 0.3189689535781378596191439E+00, \ 0.2717427498485401725509746E+00, \ 0.2245229557871702595200694E+00, \ 0.1773146332323969343091350E+00, \ 0.1301300193754780766338959E+00, \ 0.8300791095077070533235660E-01, \ 0.3616244959900389221395842E-01 ] ) EvenThetaZero34 = np.array ( [ \ 0.1547865604457777747119921E+01, \ 0.1502004162357357213441384E+01, \ 0.1456142728021903760325049E+01, \ 0.1410281306774684706589738E+01, \ 0.1364419904164498130803254E+01, \ 0.1318558526067441138200403E+01, \ 0.1272697178801115154796514E+01, \ 0.1226835869256177571730448E+01, \ 0.1180974605051351016009903E+01, \ 0.1135113394719709026888693E+01, \ 0.1089252247936466574864114E+01, \ 0.1043391175801911243726755E+01, \ 0.9975301911979639874925565E+00, \ 0.9516693092438447484954432E+00, \ 0.9058085478865097428655118E+00, \ 0.8599479286766250282572181E+00, \ 0.8140874778035996603018790E+00, \ 0.7682272274981820559251592E+00, \ 0.7223672179660643783333797E+00, \ 0.6765075001043380283085699E+00, \ 0.6306481393987597674748178E+00, \ 0.5847892216487432573582268E+00, \ 0.5389308616059791284685642E+00, \ 0.4930732164176132508179420E+00, \ 0.4472165073094733435432890E+00, \ 0.4013610560689043520551232E+00, \ 0.3555073496130768130758891E+00, \ 0.3096561615434305328219637E+00, \ 0.2638087993597793691714182E+00, \ 0.2179676599607749036552390E+00, \ 0.1721376573496165890967450E+00, \ 0.1263306713881449555499955E+00, \ 0.8058436603519718986295825E-01, \ 0.3510663068970053260227480E-01 ] ) EvenThetaZero35 = np.array ( [ \ 0.1548516088202564202943238E+01, \ 0.1503955613246577879586994E+01, \ 0.1459395145012190281751360E+01, \ 0.1414834688100222735099866E+01, \ 0.1370274247295441414922756E+01, \ 0.1325713827649021532002630E+01, \ 0.1281153434570536124285912E+01, \ 0.1236593073933169034954499E+01, \ 0.1192032752196710979323473E+01, \ 0.1147472476554108430135576E+01, \ 0.1102912255109027578275434E+01, \ 0.1058352097094263144928973E+01, \ 0.1013792013144153206047048E+01, \ 0.9692320156388929821870602E+00, \ 0.9246721191454417746654622E+00, \ 0.8801123409896300773149632E+00, \ 0.8355527020087518049947413E+00, \ 0.7909932275560464363973909E+00, \ 0.7464339488624693592395086E+00, \ 0.7018749049145358048463504E+00, \ 0.6573161450929179933243905E+00, \ 0.6127577329584494909986789E+00, \ 0.5681997518140860838771656E+00, \ 0.5236423130979094957496400E+00, \ 0.4790855694444512920982626E+00, \ 0.4345297357523596151738496E+00, \ 0.3899751246318782591316393E+00, \ 0.3454222091410984787772492E+00, \ 0.3008717408917773811461237E+00, \ 0.2563249902500918978614004E+00, \ 0.2117842860782107775954396E+00, \ 0.1672544029381415755198150E+00, \ 0.1227468836419337342946123E+00, \ 0.7829832364814667171382217E-01, \ 0.3411071484766340151578357E-01 ] ) EvenThetaZero36 = np.array ( [ \ 0.1549130685823945998342524E+01, \ 0.1505799405819664254557106E+01, \ 0.1462468131657470292685966E+01, \ 0.1419136867330461353369368E+01, \ 0.1375805616982638895139986E+01, \ 0.1332474384976155365522566E+01, \ 0.1289143175965912901391449E+01, \ 0.1245811994984327181800398E+01, \ 0.1202480847539690438616688E+01, \ 0.1159149739732435788417226E+01, \ 0.1115818678394807971862305E+01, \ 0.1072487671261111519215409E+01, \ 0.1029156727178025494814510E+01, \ 0.9858258563677261466814511E+00, \ 0.9424950707611702085500992E+00, \ 0.8991643844255133860018485E+00, \ 0.8558338141192845596532563E+00, \ 0.8125033800232146117493243E+00, \ 0.7691731067161328174004981E+00, \ 0.7258430244984030733808537E+00, \ 0.6825131712172895509836733E+00, \ 0.6391835948321685576634513E+00, \ 0.5958543570955633038336902E+00, \ 0.5525255389612023677479152E+00, \ 0.5091972487450747080139606E+00, \ 0.4658696348260689008126722E+00, \ 0.4225429061321313393543928E+00, \ 0.3792173666095906812269559E+00, \ 0.3358934762285008809293807E+00, \ 0.2925719658301625547639832E+00, \ 0.2492540707015179370724365E+00, \ 0.2059420554273186332219697E+00, \ 0.1626405628266886976038507E+00, \ 0.1193608172622853851645011E+00, \ 0.7613840464754681957544313E-01, \ 0.3316974474186058622824911E-01 ] ) EvenThetaZero37 = np.array ( [ \ 0.1549712287207882890839045E+01, \ 0.1507544209724862511636878E+01, \ 0.1465376137339015815734558E+01, \ 0.1423208073529702865859582E+01, \ 0.1381040021900765225468989E+01, \ 0.1338871986235691269778498E+01, \ 0.1296703970558498635765633E+01, \ 0.1254535979202491212629656E+01, \ 0.1212368016889500927716256E+01, \ 0.1170200088822853513468851E+01, \ 0.1128032200798161849314963E+01, \ 0.1085864359337236600941540E+01, \ 0.1043696571852037437540940E+01, \ 0.1001528846847853898635169E+01, \ 0.9593611941780778060127795E+00, \ 0.9171936253674231737318512E+00, \ 0.8750261540268988114426643E+00, \ 0.8328587963932301252176965E+00, \ 0.7906915720393251716472997E+00, \ 0.7485245048233193695739358E+00, \ 0.7063576241759074809548715E+00, \ 0.6641909668761970070284373E+00, \ 0.6220245795476036586681135E+00, \ 0.5798585222396645710869275E+00, \ 0.5376928736905555113005422E+00, \ 0.4955277392687366749125653E+00, \ 0.4533632633323484070376718E+00, \ 0.4111996491651493998151895E+00, \ 0.3690371925202636251212886E+00, \ 0.3268763409876008462653069E+00, \ 0.2847178057580674399826003E+00, \ 0.2425627889274157106498810E+00, \ 0.2004134942584602007834507E+00, \ 0.1582744399049656648660257E+00, \ 0.1161565488818554609430574E+00, \ 0.7409445176394481360104851E-01, \ 0.3227929535095246410912398E-01 ] ) EvenThetaZero38 = np.array ( [ \ 0.1550263480064160377720298E+01, \ 0.1509197788083808185665328E+01, \ 0.1468132100566875710992083E+01, \ 0.1427066420556418463513913E+01, \ 0.1386000751198712817289420E+01, \ 0.1344935095788765217267069E+01, \ 0.1303869457820298477498722E+01, \ 0.1262803841041882838326682E+01, \ 0.1221738249521212843639205E+01, \ 0.1180672687719991159061894E+01, \ 0.1139607160582508034089119E+01, \ 0.1098541673641858946868449E+01, \ 0.1057476233148907719560749E+01, \ 0.1016410846230700992453501E+01, \ 0.9753455210872527645472818E+00, \ 0.9342802672387126698703291E+00, \ 0.8932150958393123732306518E+00, \ 0.8521500200807685012223049E+00, \ 0.8110850557169691024167180E+00, \ 0.7700202217553081279468270E+00, \ 0.7289555413804262510029339E+00, \ 0.6878910432074509889956044E+00, \ 0.6468267630110350344178276E+00, \ 0.6057627461556542068727688E+00, \ 0.5646990510834698732732127E+00, \ 0.5236357544389875315454201E+00, \ 0.4825729588028297682338108E+00, \ 0.4415108047277878179738561E+00, \ 0.4004494901533595099830119E+00, \ 0.3593893030723592157150581E+00, \ 0.3183306793460978083354355E+00, \ 0.2772743115465352362860883E+00, \ 0.2362213703174823832436869E+00, \ 0.1951740017836102296584907E+00, \ 0.1541366059551230775894261E+00, \ 0.1131198202589878992052369E+00, \ 0.7215736988593890187079586E-01, \ 0.3143540438351454384152236E-01 ] ) EvenThetaZero39 = np.array ( [ \ 0.1550786588415152297375587E+01, \ 0.1510767112957397367780716E+01, \ 0.1470747641421582916022579E+01, \ 0.1430728176478592843861361E+01, \ 0.1390708720885325111445925E+01, \ 0.1350689277522434511387126E+01, \ 0.1310669849435604714836514E+01, \ 0.1270650439881648370588402E+01, \ 0.1230631052380981613091250E+01, \ 0.1190611690778358944744052E+01, \ 0.1150592359314214516523625E+01, \ 0.1110573062709576809284752E+01, \ 0.1070553806268363352417161E+01, \ 0.1030534596002003296175373E+01, \ 0.9905154387828984834423913E+00, \ 0.9504963425353941517573974E+00, \ 0.9104773164759498161192732E+00, \ 0.8704583714184727086854142E+00, \ 0.8304395201669023270865304E+00, \ 0.7904207780260519973626051E+00, \ 0.7504021634749074983118715E+00, \ 0.7103836990664583264642972E+00, \ 0.6703654126486745769832673E+00, \ 0.6303473390491956215820085E+00, \ 0.5903295224434431765765323E+00, \ 0.5503120197533818815098408E+00, \ 0.5102949056413983084126817E+00, \ 0.4702782800468414863285692E+00, \ 0.4302622799152491769326599E+00, \ 0.3902470981180917254123191E+00, \ 0.3502330152869736207185960E+00, \ 0.3102204561556976356809728E+00, \ 0.2702100956292792195263915E+00, \ 0.2302030745053307298726703E+00, \ 0.1902014842102915167005070E+00, \ 0.1502096126336221315300686E+00, \ 0.1102378261690820867329259E+00, \ 0.7031899075931525095025389E-01, \ 0.3063451333411226493032265E-01 ] ) EvenThetaZero40 = np.array ( [ \ 0.1551283705347968314195100E+01, \ 0.1512258463601911009913297E+01, \ 0.1473233225313284690780287E+01, \ 0.1434207992834186122366616E+01, \ 0.1395182768588723275108301E+01, \ 0.1356157555104474252423723E+01, \ 0.1317132355046745793679891E+01, \ 0.1278107171256650000336432E+01, \ 0.1239082006794203284097135E+01, \ 0.1200056864987904389011051E+01, \ 0.1161031749492588664002624E+01, \ 0.1122006664357811755961100E+01, \ 0.1082981614109627397900573E+01, \ 0.1043956603849447575483550E+01, \ 0.1004931639374790125389322E+01, \ 0.9659067273282460489273148E+00, \ 0.9268818753831082867718635E+00, \ 0.8878570924770502938457708E+00, \ 0.8488323891094102606331406E+00, \ 0.8098077777236123075833052E+00, \ 0.7707832732049530424809748E+00, \ 0.7317588935368492604710264E+00, \ 0.6927346606780251833003950E+00, \ 0.6537106017528970872810663E+00, \ 0.6146867506941756306797580E+00, \ 0.5756631505519364744300804E+00, \ 0.5366398568077528417370132E+00, \ 0.4976169422443344500752625E+00, \ 0.4585945042946725387136724E+00, \ 0.4195726764797194195007418E+00, \ 0.3805516468579533335376469E+00, \ 0.3415316890685593880011997E+00, \ 0.3025132172735989410463832E+00, \ 0.2634968895917008761291809E+00, \ 0.2244838184598823563259898E+00, \ 0.1854760433267094750424413E+00, \ 0.1464777455344068532549101E+00, \ 0.1074990339130794792907032E+00, \ 0.6857195785426972961368108E-01, \ 0.2987341732561906608807860E-01 ] ) EvenThetaZero41 = np.array ( [ \ 0.1551756721003315464043007E+01, \ 0.1513677510435354867644006E+01, \ 0.1475598302924814895692182E+01, \ 0.1437519100549654116408972E+01, \ 0.1399439905448387106945081E+01, \ 0.1361360719846430407096351E+01, \ 0.1323281546084682430842605E+01, \ 0.1285202386651141609385598E+01, \ 0.1247123244216506877361870E+01, \ 0.1209044121674894401873626E+01, \ 0.1170965022191058363946285E+01, \ 0.1132885949255841486220662E+01, \ 0.1094806906752030657845562E+01, \ 0.1056727899033393535018723E+01, \ 0.1018648931020478788570327E+01, \ 0.9805700083178549567966928E+00, \ 0.9424911373589552049711100E+00, \ 0.9044123255867553868253384E+00, \ 0.8663335816813894348633149E+00, \ 0.8282549158498738099497389E+00, \ 0.7901763401989443875774432E+00, \ 0.7520978692204962458482329E+00, \ 0.7140195204316730003387055E+00, \ 0.6759413152305656820841666E+00, \ 0.6378632800575392064866756E+00, \ 0.5997854479978337579981629E+00, \ 0.5617078610344953281799357E+00, \ 0.5236305732820186728652802E+00, \ 0.4855536557378012985520074E+00, \ 0.4474772034530068342865487E+00, \ 0.4094013466928584958758982E+00, \ 0.3713262689388439070717808E+00, \ 0.3332522371792479009733062E+00, \ 0.2951796555193184134657530E+00, \ 0.2571091661074227554417865E+00, \ 0.2190418543971735546480404E+00, \ 0.1809797103814301725822348E+00, \ 0.1429268140230164119614409E+00, \ 0.1048930290780323497410212E+00, \ 0.6690962797843649866645769E-01, \ 0.2914922224685900914817542E-01 ] ) EvenThetaZero42 = np.array ( [ \ 0.1552207346590136182648920E+01, \ 0.1515029387081184115266415E+01, \ 0.1477851430283927973458023E+01, \ 0.1440673478039699629370259E+01, \ 0.1403495532240969264030648E+01, \ 0.1366317594853508812224152E+01, \ 0.1329139667940348087929429E+01, \ 0.1291961753688162615428688E+01, \ 0.1254783854436838464182091E+01, \ 0.1217605972713102930414639E+01, \ 0.1180428111269300876868432E+01, \ 0.1143250273128649048802100E+01, \ 0.1106072461638634327789036E+01, \ 0.1068894680534663975270023E+01, \ 0.1031716934016664760314029E+01, \ 0.9945392268421176498894610E+00, \ 0.9573615644400829018748874E+00, \ 0.9201839530522288586731642E+00, \ 0.8830063999088902711516820E+00, \ 0.8458289134509915302518266E+00, \ 0.8086515036126424512848147E+00, \ 0.7714741821849085841225787E+00, \ 0.7342969632895448309937051E+00, \ 0.6971198640037406540069491E+00, \ 0.6599429051953912854163132E+00, \ 0.6227661126567800124770610E+00, \ 0.5855895186691062254659102E+00, \ 0.5484131642019636734351025E+00, \ 0.5112371020703309674589504E+00, \ 0.4740614015734592960802666E+00, \ 0.4368861554959151187817336E+00, \ 0.3997114910036376358365916E+00, \ 0.3625375872199777754435892E+00, \ 0.3253647047992267079974806E+00, \ 0.2881932382678453273830096E+00, \ 0.2510238145617968753500674E+00, \ 0.2138574934303919974438356E+00, \ 0.1766962177535783269128215E+00, \ 0.1395439709154010255199071E+00, \ 0.1024103832005221866954023E+00, \ 0.6532598686141261097119747E-01, \ 0.2845930797694291389393445E-01 ] ) EvenThetaZero43 = np.array ( [ \ 0.1552637135069155811491072E+01, \ 0.1516318752418798211357541E+01, \ 0.1480000372180291690418989E+01, \ 0.1443681995989991700140976E+01, \ 0.1407363625527612735973164E+01, \ 0.1371045262534953065860219E+01, \ 0.1334726908836065747097909E+01, \ 0.1298408566359386697763653E+01, \ 0.1262090237162411913706886E+01, \ 0.1225771923459625279363960E+01, \ 0.1189453627654523146514386E+01, \ 0.1153135352376772077918208E+01, \ 0.1116817100525785826106551E+01, \ 0.1080498875322336017099434E+01, \ 0.1044180680370244915946738E+01, \ 0.1007862519730785566833872E+01, \ 0.9715443980131875264637689E+00, \ 0.9352263204856910439167915E+00, \ 0.8989082932130182550456316E+00, \ 0.8625903232280967802521182E+00, \ 0.8262724187486163930514201E+00, \ 0.7899545894528804342126058E+00, \ 0.7536368468349768085155075E+00, \ 0.7173192046673890278545072E+00, \ 0.6810016796111441673128480E+00, \ 0.6446842920316340773745262E+00, \ 0.6083670671059611518530899E+00, \ 0.5720500363511797523369558E+00, \ 0.5357332397728172506411618E+00, \ 0.4994167289487775362163415E+00, \ 0.4631005715608865274454686E+00, \ 0.4267848582339839676363509E+00, \ 0.3904697131799790288672503E+00, \ 0.3541553113674441557740819E+00, \ 0.3178419074113077198829473E+00, \ 0.2815298867038369044519273E+00, \ 0.2452198616736214006194288E+00, \ 0.2089128675558041239775998E+00, \ 0.1726108022974787183994402E+00, \ 0.1363175571713249458600521E+00, \ 0.1000425397881322914313825E+00, \ 0.6381557644960651200944222E-01, \ 0.2780129671121636039734655E-01 ] ) EvenThetaZero44 = np.array ( [ \ 0.1553047499032218401181962E+01, \ 0.1517549844221432542461907E+01, \ 0.1482052191561582448658478E+01, \ 0.1446554542510861055782865E+01, \ 0.1411056898564365493121105E+01, \ 0.1375559261269981001734724E+01, \ 0.1340061632245437638964436E+01, \ 0.1304564013196950335363525E+01, \ 0.1269066405939915513649123E+01, \ 0.1233568812422221364483924E+01, \ 0.1198071234750839346739124E+01, \ 0.1162573675222508872274463E+01, \ 0.1127076136359515473862368E+01, \ 0.1091578620951808778363231E+01, \ 0.1056081132107029235444226E+01, \ 0.1020583673310438024843461E+01, \ 0.9850862484973095869616622E+00, \ 0.9495888621411026369897815E+00, \ 0.9140915193617473526041913E+00, \ 0.8785942260597805964360395E+00, \ 0.8430969890839839780181254E+00, \ 0.8075998164428632814935249E+00, \ 0.7721027175741014967901450E+00, \ 0.7366057036915554827257553E+00, \ 0.7011087882372792641869964E+00, \ 0.6656119874777629720186974E+00, \ 0.6301153213012084608241887E+00, \ 0.5946188142997514629085459E+00, \ 0.5591224972630766104664894E+00, \ 0.5236264092783024624074546E+00, \ 0.4881306007441175888503326E+00, \ 0.4526351377998500905914452E+00, \ 0.4171401090099414677462070E+00, \ 0.3816456357674021470057899E+00, \ 0.3461518890753412856675063E+00, \ 0.3106591177837409768492156E+00, \ 0.2751676985649013361686770E+00, \ 0.2396782299970584002479842E+00, \ 0.2041917239104339765549482E+00, \ 0.1687100353513348647833163E+00, \ 0.1332369676454340307348264E+00, \ 0.9778171579501174586520881E-01, \ 0.6237343205901608270979365E-01, \ 0.2717302558182235133513210E-01 ] ) EvenThetaZero45 = np.array ( [ \ 0.1553439726211153891540573E+01, \ 0.1518726525682668668950427E+01, \ 0.1484013327077361052080319E+01, \ 0.1449300131698066374929113E+01, \ 0.1414586940879145218883617E+01, \ 0.1379873756000009717714844E+01, \ 0.1345160578499605494109603E+01, \ 0.1310447409892181029407508E+01, \ 0.1275734251784724823396464E+01, \ 0.1241021105896515467487132E+01, \ 0.1206307974081314658309029E+01, \ 0.1171594858352843571506531E+01, \ 0.1136881760914326165420300E+01, \ 0.1102168684193068774494217E+01, \ 0.1067455630881287279906518E+01, \ 0.1032742603984709761582283E+01, \ 0.9980296068808995413713835E+00, \ 0.9633166433897968474836258E+00, \ 0.9286037178597176902839922E+00, \ 0.8938908352730483454962679E+00, \ 0.8591780013772376740585140E+00, \ 0.8244652228485703565016715E+00, \ 0.7897525074988288740747291E+00, \ 0.7550398645386622329842600E+00, \ 0.7203273049167972965433221E+00, \ 0.6856148417619669061621766E+00, \ 0.6509024909658764678789680E+00, \ 0.6161902719627732109904446E+00, \ 0.5814782087876726421060849E+00, \ 0.5467663315368932859708410E+00, \ 0.5120546784214694424751802E+00, \ 0.4773432987146161851453875E+00, \ 0.4426322570828636775769209E+00, \ 0.4079216401227574252826633E+00, \ 0.3732115665343573673240355E+00, \ 0.3385022035318641142927744E+00, \ 0.3037937944563405612019789E+00, \ 0.2690867076466992914990193E+00, \ 0.2343815284441088285495466E+00, \ 0.1996792463094099012688324E+00, \ 0.1649816752853099621072722E+00, \ 0.1302925346385956500837770E+00, \ 0.9562081616094948269905207E-01, \ 0.6099502786102040135198395E-01, \ 0.2657252290854776665952679E-01 ] ) EvenThetaZero46 = np.array ( [ \ 0.1553814992974904767594241E+01, \ 0.1519852325907741898557817E+01, \ 0.1485889660564341242674032E+01, \ 0.1451926998111647785152899E+01, \ 0.1417964339743630985906479E+01, \ 0.1384001686692845945859686E+01, \ 0.1350039040242776872946770E+01, \ 0.1316076401741232369348729E+01, \ 0.1282113772615099921371445E+01, \ 0.1248151154386817288949698E+01, \ 0.1214188548692984168143550E+01, \ 0.1180225957305622474388020E+01, \ 0.1146263382156703179022046E+01, \ 0.1112300825366698998613230E+01, \ 0.1078338289278105103916832E+01, \ 0.1044375776495107627552926E+01, \ 0.1010413289930890288650173E+01, \ 0.9764508328644780886953041E+00, \ 0.9424884090095589354132202E+00, \ 0.9085260225984488659490189E+00, \ 0.8745636784853451215455853E+00, \ 0.8406013822743460048537475E+00, \ 0.8066391404795569177534715E+00, \ 0.7726769607271702244889884E+00, \ 0.7387148520130367387469271E+00, \ 0.7047528250344497011443004E+00, \ 0.6707908926224332706815892E+00, \ 0.6368290703120276715090693E+00, \ 0.6028673771049329733376093E+00, \ 0.5689058365047911420524623E+00, \ 0.5349444779460832748774921E+00, \ 0.5009833388030907720537138E+00, \ 0.4670224672735823328060142E+00, \ 0.4330619266162571710985599E+00, \ 0.3991018015460700850326972E+00, \ 0.3651422081877256344485503E+00, \ 0.3311833101314466311103548E+00, \ 0.2972253454486352538763297E+00, \ 0.2632686745061683534910424E+00, \ 0.2293138699815081215985284E+00, \ 0.1953618999343470689252174E+00, \ 0.1614145391777897730914718E+00, \ 0.1274754265555317105245073E+00, \ 0.9355335943686297111639257E-01, \ 0.5967622944002585907962555E-01, \ 0.2599798753052849047032580E-01 ] ) EvenThetaZero47 = np.array ( [ \ 0.1554174376112911655131098E+01, \ 0.1520930475263640362170511E+01, \ 0.1487686575963027013435604E+01, \ 0.1454442679258803180913942E+01, \ 0.1421198786221944168258440E+01, \ 0.1387954897956585365296993E+01, \ 0.1354711015610581847809736E+01, \ 0.1321467140386931222410853E+01, \ 0.1288223273556309404505081E+01, \ 0.1254979416471008337267759E+01, \ 0.1221735570580615776412743E+01, \ 0.1188491737449843097435062E+01, \ 0.1155247918778991542491874E+01, \ 0.1122004116427655660730083E+01, \ 0.1088760332442401967089102E+01, \ 0.1055516569089340593777585E+01, \ 0.1022272828892740925095715E+01, \ 0.9890291146811467076264609E+00, \ 0.9557854296428465678959260E+00, \ 0.9225417773930866874628226E+00, \ 0.8892981620561221868061383E+00, \ 0.8560545883661619186153440E+00, \ 0.8228110617925680415850631E+00, \ 0.7895675886964734656602191E+00, \ 0.7563241765284943282959446E+00, \ 0.7230808340807681383862155E+00, \ 0.6898375718116413059811978E+00, \ 0.6565944022687408111136058E+00, \ 0.6233513406471279431598408E+00, \ 0.5901084055357449335782332E+00, \ 0.5568656199307345199294838E+00, \ 0.5236230126340485109018232E+00, \ 0.4903806202198476810807501E+00, \ 0.4571384898571183050552302E+00, \ 0.4238966834573972483152713E+00, \ 0.3906552839347125500730013E+00, \ 0.3574144049483910279156003E+00, \ 0.3241742066189948531421192E+00, \ 0.2909349219721993995636414E+00, \ 0.2576969037411283384416169E+00, \ 0.2244607124763750082606152E+00, \ 0.1912272957431274569912962E+00, \ 0.1579983907861406744991899E+00, \ 0.1247775594308675650267811E+00, \ 0.9157341285433675818728635E-01, \ 0.5841325237532701385812948E-01, \ 0.2544777076240816313972829E-01 ] ) EvenThetaZero48 = np.array ( [ \ 0.1554518863153354618809409E+01, \ 0.1521963936333782670214978E+01, \ 0.1489409010908686292228052E+01, \ 0.1456854087820918568482631E+01, \ 0.1424299168033388494075931E+01, \ 0.1391744252537595165009714E+01, \ 0.1359189342362693116905575E+01, \ 0.1326634438585269225516707E+01, \ 0.1294079542340034988016159E+01, \ 0.1261524654831668904330407E+01, \ 0.1228969777348083696352705E+01, \ 0.1196414911275444418157033E+01, \ 0.1163860058115329026827193E+01, \ 0.1131305219504506571098859E+01, \ 0.1098750397237914982841550E+01, \ 0.1066195593295557461150055E+01, \ 0.1033640809874212986016967E+01, \ 0.1001086049425085324651032E+01, \ 0.9685313146988134601280153E+00, \ 0.9359766087996588330547245E+00, \ 0.9034219352512048766203636E+00, \ 0.8708672980765996496647291E+00, \ 0.8383127018973108640833295E+00, \ 0.8057581520556423644789438E+00, \ 0.7732036547680256450048242E+00, \ 0.7406492173185620802637676E+00, \ 0.7080948483057714882525616E+00, \ 0.6755405579604902654406567E+00, \ 0.6429863585601198571817691E+00, \ 0.6104322649751623629236805E+00, \ 0.5778782954001507969801437E+00, \ 0.5453244723459250134170285E+00, \ 0.5127708240092147734858477E+00, \ 0.4802173861982495342372455E+00, \ 0.4476642050968422792532389E+00, \ 0.4151113413261211455132671E+00, \ 0.3825588760747025757978563E+00, \ 0.3500069206395502661556462E+00, \ 0.3174556318161704671189642E+00, \ 0.2849052377944113082878058E+00, \ 0.2523560839907875626097181E+00, \ 0.2198087193323827316322426E+00, \ 0.1872640717400572601243546E+00, \ 0.1547238424480887172335593E+00, \ 0.1221915194567498709631299E+00, \ 0.8967553546914315204781840E-01, \ 0.5720262597323678474637133E-01, \ 0.2492036059421555107245208E-01 ] ) EvenThetaZero49 = np.array ( [ \ 0.1554849361424470843090118E+01, \ 0.1522955431101933730645303E+01, \ 0.1491061502037751976297424E+01, \ 0.1459167575082261894770634E+01, \ 0.1427273651103158170602525E+01, \ 0.1395379730992862183093282E+01, \ 0.1363485815676330697886480E+01, \ 0.1331591906119453530640248E+01, \ 0.1299698003338207337770238E+01, \ 0.1267804108408757103237650E+01, \ 0.1235910222478728395590872E+01, \ 0.1204016346779913703159712E+01, \ 0.1172122482642727288439229E+01, \ 0.1140228631512787910483320E+01, \ 0.1108334794970091261912531E+01, \ 0.1076440974751339138680154E+01, \ 0.1044547172776127017814204E+01, \ 0.1012653391177865049408482E+01, \ 0.9807596323405319627306720E+00, \ 0.9488658989426541583823449E+00, \ 0.9169721940102869797082899E+00, \ 0.8850785209812848825432963E+00, \ 0.8531848837838285971960304E+00, \ 0.8212912869330969580404013E+00, \ 0.7893977356512249782795147E+00, \ 0.7575042360174185552669765E+00, \ 0.7256107951575083863622461E+00, \ 0.6937174214856350398887716E+00, \ 0.6618241250156435481462849E+00, \ 0.6299309177668761147121611E+00, \ 0.5980378142995696297245189E+00, \ 0.5661448324309071185385071E+00, \ 0.5342519942071113461815355E+00, \ 0.5023593272451872220760104E+00, \ 0.4704668666194035162003700E+00, \ 0.4385746575692260390945883E+00, \ 0.4066827594785525726660483E+00, \ 0.3747912518813925812276922E+00, \ 0.3429002438089823350625543E+00, \ 0.3110098888674705209106637E+00, \ 0.2791204106078991711912441E+00, \ 0.2472321474279120600810915E+00, \ 0.2153456371036966567922014E+00, \ 0.1834617887100953140198272E+00, \ 0.1515822689338083535939382E+00, \ 0.1197104949484175660714864E+00, \ 0.8785472823121690639967810E-01, \ 0.5604116141749524467628553E-01, \ 0.2441436781606819510490200E-01 ] ) EvenThetaZero50 = np.array ( [ \ 0.1555166706034023842787706E+01, \ 0.1523907464890582273398300E+01, \ 0.1492648224885016483409279E+01, \ 0.1461388986785839210767990E+01, \ 0.1430129751376631035251350E+01, \ 0.1398870519462421720845393E+01, \ 0.1367611291876438076975682E+01, \ 0.1336352069487341263827064E+01, \ 0.1305092853207091240256110E+01, \ 0.1273833643999595441027728E+01, \ 0.1242574442890323705495464E+01, \ 0.1211315250977103200801981E+01, \ 0.1180056069442347222927677E+01, \ 0.1148796899567022469820701E+01, \ 0.1117537742746723499546780E+01, \ 0.1086278600510304367969825E+01, \ 0.1055019474541620880304106E+01, \ 0.1023760366705069175705639E+01, \ 0.9925012790757765081567637E+00, \ 0.9612422139755203374385844E+00, \ 0.9299831740157389822411293E+00, \ 0.8987241621493743180375722E+00, \ 0.8674651817337867269827651E+00, \ 0.8362062366076504452859926E+00, \ 0.8049473311856388413561914E+00, \ 0.7736884705759381993127359E+00, \ 0.7424296607273230664538510E+00, \ 0.7111709086148904840060001E+00, \ 0.6799122224768919982385331E+00, \ 0.6486536121198915829209739E+00, \ 0.6173950893164463798129595E+00, \ 0.5861366683298159921278400E+00, \ 0.5548783666157332634604655E+00, \ 0.5236202057751242467455922E+00, \ 0.4923622128691229579358494E+00, \ 0.4611044222679868504944176E+00, \ 0.4298468783051183048132298E+00, \ 0.3985896391770900735176252E+00, \ 0.3673327828297899556279530E+00, \ 0.3360764161195064368209114E+00, \ 0.3048206895905456571224703E+00, \ 0.2735658223403245791263072E+00, \ 0.2423121460275046288225596E+00, \ 0.2110601877217048587999889E+00, \ 0.1798108384023314561549010E+00, \ 0.1485657315840060835766576E+00, \ 0.1173282164330337207824850E+00, \ 0.8610639001623934211634967E-01, \ 0.5492592372249737419414775E-01, \ 0.2392851379957687254895331E-01 ] ) OddThetaZero1 = np.array ( [ \ 0.6847192030022829138880982E+00 ] ) OddThetaZero2 = np.array ( [ \ 0.1002176803643121641749915E+01, \ 0.4366349492255221620374655E+00 ] ) OddThetaZero3 = np.array ( [ \ 0.1152892953722227341986065E+01, \ 0.7354466143229520469385622E+00, \ 0.3204050902900619825355950E+00 ] ) OddThetaZero4 = np.array ( [ \ 0.1240573923404363422789550E+01, \ 0.9104740292261473250358755E+00, \ 0.5807869795060065580284919E+00, \ 0.2530224166119306882187233E+00 ] ) OddThetaZero5 = np.array ( [ \ 0.1297877729331450368298142E+01, \ 0.1025003226369574843297844E+01, \ 0.7522519395990821317003373E+00, \ 0.4798534223256743217333579E+00, \ 0.2090492874137409414071522E+00 ] ) OddThetaZero6 = np.array ( [ \ 0.1338247676100454369194835E+01, \ 0.1105718066248490075175419E+01, \ 0.8732366099401630367220948E+00, \ 0.6408663264733867770811230E+00, \ 0.4088002373420211722955679E+00, \ 0.1780944581262765470585931E+00 ] ) OddThetaZero7 = np.array ( [ \ 0.1368219536992351783359098E+01, \ 0.1165652065603030148723847E+01, \ 0.9631067821301481995711685E+00, \ 0.7606069572889918619145483E+00, \ 0.5582062109125313357140248E+00, \ 0.3560718303314725022788878E+00, \ 0.1551231069747375098418591E+00 ] ) OddThetaZero8 = np.array ( [ \ 0.1391350647015287461874435E+01, \ 0.1211909966211469688151240E+01, \ 0.1032480728417239563449772E+01, \ 0.8530732514258505686069670E+00, \ 0.6737074594242522259878462E+00, \ 0.4944303818194983217354808E+00, \ 0.3153898594929282395996014E+00, \ 0.1373998952992547671039022E+00 ] ) OddThetaZero9 = np.array ( [ \ 0.1409742336767428999667236E+01, \ 0.1248691224331339221187704E+01, \ 0.1087646521650454938943641E+01, \ 0.9266134127998189551499083E+00, \ 0.7656007620508340547558669E+00, \ 0.6046261769405451549818494E+00, \ 0.4437316659960951760051408E+00, \ 0.2830497588453068048261493E+00, \ 0.1233108673082312764916251E+00 ] ) OddThetaZero10 = np.array ( [ \ 0.1424715475176742734932665E+01, \ 0.1278636375242898727771561E+01, \ 0.1132561101012537613667002E+01, \ 0.9864925055883793730483278E+00, \ 0.8404350520135058972624775E+00, \ 0.6943966110110701016065380E+00, \ 0.5483930281810389839680525E+00, \ 0.4024623099018152227701990E+00, \ 0.2567245837448891192759858E+00, \ 0.1118422651428890834760883E+00 ] ) OddThetaZero11 = np.array ( [ \ 0.1437141935303526306632113E+01, \ 0.1303488659735581140681362E+01, \ 0.1169837785762829821262819E+01, \ 0.1036190996404462300207004E+01, \ 0.9025507517347875930425807E+00, \ 0.7689210263823624893974324E+00, \ 0.6353089402976822861185532E+00, \ 0.5017289283414202278167583E+00, \ 0.3682157131008289798868520E+00, \ 0.2348791589702580223688923E+00, \ 0.1023252788872632487579640E+00 ] ) OddThetaZero12 = np.array ( [ \ 0.1447620393135667144403507E+01, \ 0.1324445197736386798102445E+01, \ 0.1201271573324181312770120E+01, \ 0.1078100568411879956441542E+01, \ 0.9549336362382321811515336E+00, \ 0.8317729718814276781352878E+00, \ 0.7086221837538611370849622E+00, \ 0.5854877911108011727748238E+00, \ 0.4623830630132757357909198E+00, \ 0.3393399712563371486343129E+00, \ 0.2164597408964339264361902E+00, \ 0.9430083986305519349231898E-01 ] ) OddThetaZero13 = np.array ( [ \ 0.1456575541704195839944967E+01, \ 0.1342355260834552126304154E+01, \ 0.1228136043468909663499174E+01, \ 0.1113918572282611841378549E+01, \ 0.9997037539874953933323299E+00, \ 0.8854928869950799998575862E+00, \ 0.7712879690777516856072467E+00, \ 0.6570923167092416238233585E+00, \ 0.5429119513798658239789812E+00, \ 0.4287591577660783587509129E+00, \ 0.3146635662674373982102762E+00, \ 0.2007190266590380629766487E+00, \ 0.8744338280630300217927750E-01 ] ) OddThetaZero14 = np.array ( [ \ 0.1464317002991565219979113E+01, \ 0.1357838033080061766980173E+01, \ 0.1251359804334884770836945E+01, \ 0.1144882777708662655968171E+01, \ 0.1038407544520296695714932E+01, \ 0.9319349156915986836657782E+00, \ 0.8254660749671546663859351E+00, \ 0.7190028636037068047812305E+00, \ 0.6125483562383020473196681E+00, \ 0.5061081521562999836102547E+00, \ 0.3996936914666951732317457E+00, \ 0.2933325857619472952507468E+00, \ 0.1871123137498061864373407E+00, \ 0.8151560650977882057817999E-01 ] ) OddThetaZero15 = np.array ( [ \ 0.1471075823713997440657641E+01, \ 0.1371355574944658989649887E+01, \ 0.1271635855736122280723838E+01, \ 0.1171916986981363820797100E+01, \ 0.1072199368669106404814915E+01, \ 0.9724835301003496870596165E+00, \ 0.8727702114891848603047954E+00, \ 0.7730605060747958359120755E+00, \ 0.6733561257504194406005404E+00, \ 0.5736599396529727772420934E+00, \ 0.4739771829190733570809765E+00, \ 0.3743185619229329461021810E+00, \ 0.2747099287638327553949437E+00, \ 0.1752332025619508475799133E+00, \ 0.7634046205384429302353073E-01 ] ) OddThetaZero16 = np.array ( [ \ 0.1477027911291552393547878E+01, \ 0.1383259682348271685979143E+01, \ 0.1289491840051302622319481E+01, \ 0.1195724613675799550484673E+01, \ 0.1101958282220461402990667E+01, \ 0.1008193204014774090964219E+01, \ 0.9144298626454031699590564E+00, \ 0.8206689427646120483710056E+00, \ 0.7269114630504563073034288E+00, \ 0.6331590254855162126233733E+00, \ 0.5394143214244183829842424E+00, \ 0.4456822679082866369288652E+00, \ 0.3519729273095236644049666E+00, \ 0.2583106041071417718760275E+00, \ 0.1647723231643112502628240E+00, \ 0.7178317184275122449502857E-01 ] ) OddThetaZero17 = np.array ( [ \ 0.1482309554825692463999299E+01, \ 0.1393822922226542123661077E+01, \ 0.1305336577335833571381699E+01, \ 0.1216850687682353365944624E+01, \ 0.1128365453024608460982204E+01, \ 0.1039881123511957522668140E+01, \ 0.9513980267579228357946521E+00, \ 0.8629166105524045911461307E+00, \ 0.7744375139383604902604254E+00, \ 0.6859616923374368587817328E+00, \ 0.5974906525247623278123711E+00, \ 0.5090269299866796725116786E+00, \ 0.4205751610647263669405267E+00, \ 0.3321448379994943116084719E+00, \ 0.2437588931448048912587688E+00, \ 0.1554900095178924564386865E+00, \ 0.6773932498157585698088354E-01 ] ) OddThetaZero18 = np.array ( [ \ 0.1487027983239550912222135E+01, \ 0.1403259745496922270264564E+01, \ 0.1319491725464661433609663E+01, \ 0.1235724047968681189212364E+01, \ 0.1151956859289811446164825E+01, \ 0.1068190338689553494802072E+01, \ 0.9844247150109837231349622E+00, \ 0.9006602918737365182850484E+00, \ 0.8168974877846821404275069E+00, \ 0.7331369031796229223580227E+00, \ 0.6493794386888650054486281E+00, \ 0.5656265174356596757139537E+00, \ 0.4818805368222631487731579E+00, \ 0.3981458834052590173509113E+00, \ 0.3144315409387123154212535E+00, \ 0.2307592167302372059759857E+00, \ 0.1471977156945989772472748E+00, \ 0.6412678117309944052403703E-01 ] ) OddThetaZero19 = np.array ( [ \ 0.1491268718102344688271411E+01, \ 0.1411741190914640487505771E+01, \ 0.1332213830951015404441941E+01, \ 0.1252686732830809999680267E+01, \ 0.1173160005794509313174730E+01, \ 0.1093633781237958896879965E+01, \ 0.1014108223243148393065201E+01, \ 0.9345835440325075907377330E+00, \ 0.8550600276575269107773349E+00, \ 0.7755380679025248517258532E+00, \ 0.6960182317959841585145109E+00, \ 0.6165013717819833504477346E+00, \ 0.5369888366794912945318079E+00, \ 0.4574829005269902932408889E+00, \ 0.3779877260196973978940863E+00, \ 0.2985118404618624984946326E+00, \ 0.2190758506462427957069113E+00, \ 0.1397450765119767349146353E+00, \ 0.6088003363863534825005464E-01 ] ) OddThetaZero20 = np.array ( [ \ 0.1495100801651051409999732E+01, \ 0.1419405340110198552778393E+01, \ 0.1343710008748627892724810E+01, \ 0.1268014880389353000310414E+01, \ 0.1192320038028903827079750E+01, \ 0.1116625579891689469044026E+01, \ 0.1040931626310454794079799E+01, \ 0.9652383295306942866661884E+00, \ 0.8895458882533946571137358E+00, \ 0.8138545700535261740447950E+00, \ 0.7381647473570304814395029E+00, \ 0.6624769578126105498149624E+00, \ 0.5867920109947446493391737E+00, \ 0.5111111891461744489290992E+00, \ 0.4354366553151050147918632E+00, \ 0.3597723703299625354660452E+00, \ 0.2841264494060559943920389E+00, \ 0.2085185052177154996230005E+00, \ 0.1330107089065635461375419E+00, \ 0.5794620170990797798650123E-01 ] ) OddThetaZero21 = np.array ( [ \ 0.1498580583401444174317386E+01, \ 0.1426364890228584522673414E+01, \ 0.1354149299629923281192036E+01, \ 0.1281933868420423988034246E+01, \ 0.1209718660626713399048551E+01, \ 0.1137503750956414845248481E+01, \ 0.1065289229411733880607916E+01, \ 0.9930752076949068878557126E+00, \ 0.9208618284397049456535757E+00, \ 0.8486492789905562098591586E+00, \ 0.7764378127156926158031943E+00, \ 0.7042277832708635930867344E+00, \ 0.6320197021480767602848178E+00, \ 0.5598143404345395912377042E+00, \ 0.4876129202946139420188428E+00, \ 0.4154175043169533365541148E+00, \ 0.3432318703096418027524597E+00, \ 0.2710637595435203246492797E+00, \ 0.1989318822110657561806962E+00, \ 0.1268955503926593166308254E+00, \ 0.5528212871240371048241379E-01 ] ) OddThetaZero22 = np.array ( [ \ 0.1501754508594837337089856E+01, \ 0.1432712730475143340404518E+01, \ 0.1363671034069754274950592E+01, \ 0.1294629464249430679064317E+01, \ 0.1225588071083248538559259E+01, \ 0.1156546912269029268686830E+01, \ 0.1087506056298747798071893E+01, \ 0.1018465586752840651469411E+01, \ 0.9494256083335850798964741E+00, \ 0.8803862556198167553278643E+00, \ 0.8113477061841624760598814E+00, \ 0.7423102009244498727845341E+00, \ 0.6732740767851639064676858E+00, \ 0.6042398217472142478598295E+00, \ 0.5352081720899522889584566E+00, \ 0.4661802954366277026594659E+00, \ 0.3971581629712621730826920E+00, \ 0.3281453857685808451825081E+00, \ 0.2591493642052661979197670E+00, \ 0.1901879854885491785792565E+00, \ 0.1213179541186130699071317E+00, \ 0.5285224511635143601147552E-01 ] ) OddThetaZero23 = np.array ( [ \ 0.1504661202517196460191540E+01, \ 0.1438526110541037227495230E+01, \ 0.1372391084315255737540026E+01, \ 0.1306256159670931796771616E+01, \ 0.1240121376243315949825014E+01, \ 0.1173986779205849344923421E+01, \ 0.1107852421486856229076325E+01, \ 0.1041718366715156747157745E+01, \ 0.9755846932657442605621389E+00, \ 0.9094514999854931965227238E+00, \ 0.8433189145364798253029042E+00, \ 0.7771871059265138564989363E+00, \ 0.7110563039566125173946002E+00, \ 0.6449268305419475123120585E+00, \ 0.5787991523675322133651034E+00, \ 0.5126739740395088296453592E+00, \ 0.4465524134105889084933393E+00, \ 0.3804363581140941600870992E+00, \ 0.3143292666717729726674543E+00, \ 0.2482382273986418438740754E+00, \ 0.1821803739336923550363257E+00, \ 0.1162100228791666307841708E+00, \ 0.5062697144246344520692308E-01 ] ) OddThetaZero24 = np.array ( [ \ 0.1507333049739684406957329E+01, \ 0.1443869798951040686809862E+01, \ 0.1380406601553595646811530E+01, \ 0.1316943486448336467960940E+01, \ 0.1253480485358734060913055E+01, \ 0.1190017634088428795118215E+01, \ 0.1126554974102287077081806E+01, \ 0.1063092554588577221978254E+01, \ 0.9996304352342330000643921E+00, \ 0.9361686900661624628632729E+00, \ 0.8727074129127595264965883E+00, \ 0.8092467253835331800652228E+00, \ 0.7457867888716805068068402E+00, \ 0.6823278231980088937854296E+00, \ 0.6188701366516795329577182E+00, \ 0.5554141765061554178407906E+00, \ 0.4919606183965743300387332E+00, \ 0.4285105345527885639657014E+00, \ 0.3650657359209552112046854E+00, \ 0.3016295408979540017854803E+00, \ 0.2382087510453128743250072E+00, \ 0.1748198074104535338147956E+00, \ 0.1115148317291502081079519E+00, \ 0.4858150828905663931389750E-01 ] ) OddThetaZero25 = np.array ( [ \ 0.1509797405521643600800862E+01, \ 0.1448798505784201776188819E+01, \ 0.1387799649767640868379247E+01, \ 0.1326800860997572277878513E+01, \ 0.1265802165120213614545418E+01, \ 0.1204803590828283748583827E+01, \ 0.1143805171007496028164312E+01, \ 0.1082806944206958485218487E+01, \ 0.1021808956582037259849130E+01, \ 0.9608112645303606832220554E+00, \ 0.8998139383584991342974664E+00, \ 0.8388170675106567024157190E+00, \ 0.7778207682214244793380700E+00, \ 0.7168251950382156442798800E+00, \ 0.6558305587295081487906238E+00, \ 0.5948371551492265376377962E+00, \ 0.5338454137827292925154468E+00, \ 0.4728559836463229599006206E+00, \ 0.4118698949811841042358258E+00, \ 0.3508888880839026413717319E+00, \ 0.2899161521835467942607342E+00, \ 0.2289582244272697168835150E+00, \ 0.1680309071251709912058722E+00, \ 0.1071842976730454709494914E+00, \ 0.4669490825917857848258897E-01 ] ) OddThetaZero26 = np.array ( [ \ 0.1512077535592702651885542E+01, \ 0.1453358762182399391553360E+01, \ 0.1394640024852448295479492E+01, \ 0.1335921342914185177270306E+01, \ 0.1277202737290683500323248E+01, \ 0.1218484231207691826029908E+01, \ 0.1159765851037557179133987E+01, \ 0.1101047627365156083369632E+01, \ 0.1042329596373083545617043E+01, \ 0.9836118016874520301049009E+00, \ 0.9248942968954766185908511E+00, \ 0.8661771490588063053774554E+00, \ 0.8074604437333368789787031E+00, \ 0.7487442923247565105494255E+00, \ 0.6900288431709550365296138E+00, \ 0.6313142987730108226833704E+00, \ 0.5726009435739572428629866E+00, \ 0.5138891906843943809444838E+00, \ 0.4551796645660731149033106E+00, \ 0.3964733566771858874923011E+00, \ 0.3377719420068963817561906E+00, \ 0.2790784903284342592940125E+00, \ 0.2203992941938221111139898E+00, \ 0.1617495649772923108686624E+00, \ 0.1031775271253784724197264E+00, \ 0.4494935602951385601335598E-01 ] ) OddThetaZero27 = np.array ( [ \ 0.1514193352804819997509006E+01, \ 0.1457590393617468793209691E+01, \ 0.1400987464419153080392546E+01, \ 0.1344384581184662080889348E+01, \ 0.1287781761126833878758488E+01, \ 0.1231179023218584237510462E+01, \ 0.1174576388822640925688125E+01, \ 0.1117973882475943676285829E+01, \ 0.1061371532893653466992815E+01, \ 0.1004769374285310770780417E+01, \ 0.9481674481184788854172919E+00, \ 0.8915658055327279211293483E+00, \ 0.8349645107156934027761499E+00, \ 0.7783636457331086848148917E+00, \ 0.7217633176118399859733190E+00, \ 0.6651636690166557413471029E+00, \ 0.6085648948549621671933311E+00, \ 0.5519672690500084950513985E+00, \ 0.4953711895788266953367288E+00, \ 0.4387772581729219934583483E+00, \ 0.3821864303519236078766179E+00, \ 0.3256003205491779498477363E+00, \ 0.2690218877324958059454348E+00, \ 0.2124571975249336244841297E+00, \ 0.1559209129891515317090843E+00, \ 0.9945952063842375053227931E-01, \ 0.4332960406341033436157524E-01 ] ) OddThetaZero28 = np.array ( [ \ 0.1516162000094549207021851E+01, \ 0.1461527685790782385188426E+01, \ 0.1406893396579229558427657E+01, \ 0.1352259145769086826235918E+01, \ 0.1297624947629923059740243E+01, \ 0.1242990817790597917328601E+01, \ 0.1188356773715062198539162E+01, \ 0.1133722835287525783953663E+01, \ 0.1079089025551156002698850E+01, \ 0.1024455371662101389801169E+01, \ 0.9698219061474760364582928E+00, \ 0.9151886685974009713577537E+00, \ 0.8605557079864861100238346E+00, \ 0.8059230859253162466918892E+00, \ 0.7512908813164713594661588E+00, \ 0.6966591971861112012613682E+00, \ 0.6420281709850565965229799E+00, \ 0.5873979906122764301937499E+00, \ 0.5327689202536826556885353E+00, \ 0.4781413438508069051295597E+00, \ 0.4235158420269503798571552E+00, \ 0.3688933369002844229314675E+00, \ 0.3142753865947702189467806E+00, \ 0.2596648470121556361200229E+00, \ 0.2050675726616484232653526E+00, \ 0.1504977164639767777858359E+00, \ 0.9600014792058154736462106E-01, \ 0.4182252607645932321862773E-01 ] ) OddThetaZero29 = np.array ( [ \ 0.1517998315905975681819213E+01, \ 0.1465200315462026532129551E+01, \ 0.1412402336143180968579639E+01, \ 0.1359604389111228213837104E+01, \ 0.1306806486279734731351497E+01, \ 0.1254008640622089183072742E+01, \ 0.1201210866535131048800458E+01, \ 0.1148413180281179970113571E+01, \ 0.1095615600538999408768381E+01, \ 0.1042818149105710558651372E+01, \ 0.9900208518088600875617620E+00, \ 0.9372237397138955502862203E+00, \ 0.8844268507524555199840381E+00, \ 0.8316302319600398731649744E+00, \ 0.7788339426133210890795576E+00, \ 0.7260380587255163256281298E+00, \ 0.6732426796448045921910045E+00, \ 0.6204479380061240544867289E+00, \ 0.5676540152134466427854705E+00, \ 0.5148611664077887834613451E+00, \ 0.4620697624728053757183766E+00, \ 0.4092803643735033357684553E+00, \ 0.3564938631002461237979451E+00, \ 0.3037117642790043703921396E+00, \ 0.2509368276982060978106092E+00, \ 0.1981747109679032915697317E+00, \ 0.1454390911823840643137232E+00, \ 0.9277332955453467429763451E-01, \ 0.4041676055113025684436480E-01 ] ) OddThetaZero30 = np.array ( [ \ 0.1519715208823086817411929E+01, \ 0.1468634099702062550682430E+01, \ 0.1417553008469014674939490E+01, \ 0.1366471944542347269659860E+01, \ 0.1315390917933946912760115E+01, \ 0.1264309939489363760018555E+01, \ 0.1213229021168654147755139E+01, \ 0.1162148176384137345494752E+01, \ 0.1111067420416500738111992E+01, \ 0.1059986770938296676746064E+01, \ 0.1008906248685091746434581E+01, \ 0.9578258783312407255956784E+00, \ 0.9067456896525242756445150E+00, \ 0.8556657190967860708153477E+00, \ 0.8045860119448479090873824E+00, \ 0.7535066253423996943740445E+00, \ 0.7024276326462752642452137E+00, \ 0.6513491298057893513225544E+00, \ 0.6002712449887427739045163E+00, \ 0.5491941535583390603837715E+00, \ 0.4981181022276018128369963E+00, \ 0.4470434496975185070560821E+00, \ 0.3959707385770101868486847E+00, \ 0.3449008307748737032772825E+00, \ 0.2938351828535981363494671E+00, \ 0.2427764647581323719392653E+00, \ 0.1917301500230701193408602E+00, \ 0.1407094708800750523796875E+00, \ 0.8975637836633630394302762E-01, \ 0.3910242380354419363081899E-01 ] ) OddThetaZero31 = np.array ( [ \ 0.1521323961422700444944464E+01, \ 0.1471851603590422118622546E+01, \ 0.1422379260986849454727777E+01, \ 0.1372906941604798453293218E+01, \ 0.1323434653909307929892118E+01, \ 0.1273962407026590487708892E+01, \ 0.1224490210963055761921526E+01, \ 0.1175018076866133593082748E+01, \ 0.1125546017342156230227131E+01, \ 0.1076074046851682267877939E+01, \ 0.1026602182210094558879809E+01, \ 0.9771304432322302018639612E+00, \ 0.9276588535760335871906045E+00, \ 0.8781874418647315968408864E+00, \ 0.8287162432047307488040550E+00, \ 0.7792453012756761070555010E+00, \ 0.7297746712644485550469075E+00, \ 0.6803044240724808212528033E+00, \ 0.6308346524943159683026367E+00, \ 0.5813654805388740483542438E+00, \ 0.5318970779332963132260134E+00, \ 0.4824296835154055410257004E+00, \ 0.4329636445908698102350729E+00, \ 0.3834994865870752458854056E+00, \ 0.3340380441799942088370002E+00, \ 0.2845807279748544733570760E+00, \ 0.2351301237470960623526672E+00, \ 0.1856915325646991222655151E+00, \ 0.1362777698319134965765757E+00, \ 0.8692946525012054120187353E-01, \ 0.3787087726949234365520114E-01 ] ) OddThetaZero32 = np.array ( [ \ 0.1522834478472358672931947E+01, \ 0.1474872636605138418026177E+01, \ 0.1426910807768284322082436E+01, \ 0.1378948998781055367310047E+01, \ 0.1330987216841224680164684E+01, \ 0.1283025469674968454386883E+01, \ 0.1235063765709222885799986E+01, \ 0.1187102114275073728898860E+01, \ 0.1139140525853183114841234E+01, \ 0.1091179012375759666645271E+01, \ 0.1043217587604604879578741E+01, \ 0.9952562676120370548458597E+00, \ 0.9472950714021223337048082E+00, \ 0.8993340217254078241758816E+00, \ 0.8513731461641338285808219E+00, \ 0.8034124786014693431693904E+00, \ 0.7554520612457602368887930E+00, \ 0.7074919474732165281510693E+00, \ 0.6595322059052657580628641E+00, \ 0.6115729263971504325174172E+00, \ 0.5636142290734363894767612E+00, \ 0.5156562783879918167717991E+00, \ 0.4676993058012953469089537E+00, \ 0.4197436479350834076514896E+00, \ 0.3717898140987174444032373E+00, \ 0.3238386134116156886828960E+00, \ 0.2758914133405791810724762E+00, \ 0.2279507206431424610498769E+00, \ 0.1800216744637006612298520E+00, \ 0.1321166988439841543825694E+00, \ 0.8427518284958235696897899E-01, \ 0.3671453742186897322954009E-01 ] ) OddThetaZero33 = np.array ( [ \ 0.1524255491013576804195881E+01, \ 0.1477714660784952783237945E+01, \ 0.1431173841758652772349485E+01, \ 0.1384633039781787069436630E+01, \ 0.1338092261006965672253841E+01, \ 0.1291551512012124788593875E+01, \ 0.1245010799937299944123195E+01, \ 0.1198470132644670409416924E+01, \ 0.1151929518909907204916554E+01, \ 0.1105388968655282680015213E+01, \ 0.1058848493238442193822372E+01, \ 0.1012308105815651361079674E+01, \ 0.9657678218054126734684090E+00, \ 0.9192276594886802366068293E+00, \ 0.8726876407972167893294764E+00, \ 0.8261477923647281669131478E+00, \ 0.7796081469509049827753598E+00, \ 0.7330687454042532567721262E+00, \ 0.6865296394193009886613469E+00, \ 0.6399908954920466591029822E+00, \ 0.5934526007301573325059582E+00, \ 0.5469148716199143611697357E+00, \ 0.5003778676688561814362271E+00, \ 0.4538418134105091550464446E+00, \ 0.4073070354279485829740435E+00, \ 0.3607740278788822846227453E+00, \ 0.3142435758510728338330843E+00, \ 0.2677170062389944640113953E+00, \ 0.2211967514739567668334169E+00, \ 0.1746877983807874325844051E+00, \ 0.1282022028383479964348629E+00, \ 0.8177818680168764430245080E-01, \ 0.3562671947817428176226631E-01 ] ) OddThetaZero34 = np.array ( [ \ 0.1525594725214770881206476E+01, \ 0.1480393128432045740356817E+01, \ 0.1435191541323085582529217E+01, \ 0.1389989968924959812091252E+01, \ 0.1344788416522907866060817E+01, \ 0.1299586889746827997174554E+01, \ 0.1254385394680661996389736E+01, \ 0.1209183937989395175829969E+01, \ 0.1163982527069600127515982E+01, \ 0.1118781170231154762473596E+01, \ 0.1073579876920155012130433E+01, \ 0.1028378657996412636748477E+01, \ 0.9831775260837211038023103E+00, \ 0.9379764960179657076015136E+00, \ 0.8927755854282048597997986E+00, \ 0.8475748155007347757967789E+00, \ 0.8023742119985848209905761E+00, \ 0.7571738066433708695662393E+00, \ 0.7119736390205872251796930E+00, \ 0.6667737592565460745639184E+00, \ 0.6215742318591892056934095E+00, \ 0.5763751413603713322640298E+00, \ 0.5311766008298875656047892E+00, \ 0.4859787651249621588538330E+00, \ 0.4407818522612533891543536E+00, \ 0.3955861793705505114602136E+00, \ 0.3503922263398633798966312E+00, \ 0.3052007556167344348049303E+00, \ 0.2600130558662051177480644E+00, \ 0.2148314894784555841956251E+00, \ 0.1696608997322034095150907E+00, \ 0.1245129955389270002683579E+00, \ 0.7942489891978153749097006E-01, \ 0.3460150809198016850782325E-01 ] ) OddThetaZero35 = np.array ( [ \ 0.1526859042890589526378487E+01, \ 0.1482921763148403842276533E+01, \ 0.1438984491795164536567108E+01, \ 0.1395047233189252525231459E+01, \ 0.1351109991891878034957302E+01, \ 0.1307172772745304669260382E+01, \ 0.1263235580960968906699379E+01, \ 0.1219298422221050703835127E+01, \ 0.1175361302797916700875697E+01, \ 0.1131424229697065895207730E+01, \ 0.1087487210830887883186060E+01, \ 0.1043550255232887174273672E+01, \ 0.9996133733253190253881393E+00, \ 0.9556765772578535710715874E+00, \ 0.9117398813415957196221754E+00, \ 0.8678033026125661948850687E+00, \ 0.8238668615732247310812836E+00, \ 0.7799305831824293601507400E+00, \ 0.7359944981977457886183921E+00, \ 0.6920586450266629333858465E+00, \ 0.6481230723279649663476697E+00, \ 0.6041878427445000852182582E+00, \ 0.5602530383870993537615272E+00, \ 0.5163187691099712879003757E+00, \ 0.4723851853891499571797438E+00, \ 0.4284524990953311047063058E+00, \ 0.3845210184454249891341793E+00, \ 0.3405912098612419399584605E+00, \ 0.2966638144233703899038032E+00, \ 0.2527400847124078576715667E+00, \ 0.2088223170017057788708674E+00, \ 0.1649152190599722827308055E+00, \ 0.1210301722471160155498167E+00, \ 0.7720326018898817828206987E-01, \ 0.3363364974516995102167462E-01 ] ) OddThetaZero36 = np.array ( [ \ 0.1528054559083405137047563E+01, \ 0.1485312794997097705446883E+01, \ 0.1442571038214470776579613E+01, \ 0.1399829292522320013570493E+01, \ 0.1357087561874166765548658E+01, \ 0.1314345850454078759228779E+01, \ 0.1271604162748143389685638E+01, \ 0.1228862503626296926524085E+01, \ 0.1186120878437839368895715E+01, \ 0.1143379293124832099340074E+01, \ 0.1100637754358770795248912E+01, \ 0.1057896269707576280860569E+01, \ 0.1015154847842238156769126E+01, \ 0.9724134987956584339974640E+00, \ 0.9296722342907946818431047E+00, \ 0.8869310681617368097575324E+00, \ 0.8441900169008687429295884E+00, \ 0.8014491003793523040286325E+00, \ 0.7587083428093935362576859E+00, \ 0.7159677740493625646700975E+00, \ 0.6732274314040501413860867E+00, \ 0.6304873621547357085895928E+00, \ 0.5877476271899241333221832E+00, \ 0.5450083063396327078463020E+00, \ 0.5022695064252395155059223E+00, \ 0.4595313737871711838065652E+00, \ 0.4167941144922007176438387E+00, \ 0.3740580283336802289311736E+00, \ 0.3313235690067746553700419E+00, \ 0.2885914573933480330041531E+00, \ 0.2458629119584249278750153E+00, \ 0.2031401664615301668533461E+00, \ 0.1604278005405711652039491E+00, \ 0.1177368858339244458607172E+00, \ 0.7510252408650086658441596E-01, \ 0.3271846270775478856070884E-01 ] ) OddThetaZero37 = np.array ( [ \ 0.1529186740959505109653289E+01, \ 0.1487577158293388707508111E+01, \ 0.1445967582009979387718202E+01, \ 0.1404358015412336440816745E+01, \ 0.1362748461941311565399969E+01, \ 0.1321138925227929972823825E+01, \ 0.1279529409151733277951100E+01, \ 0.1237919917907156982173977E+01, \ 0.1196310456080472987418488E+01, \ 0.1154701028740456700905269E+01, \ 0.1113091641546798022997704E+01, \ 0.1071482300881451340842721E+01, \ 0.1029873014009735917989475E+01, \ 0.9882637892802373569245916E+00, \ 0.9466546363756944528310758E+00, \ 0.9050455666314926033869497E+00, \ 0.8634365934447506520344540E+00, \ 0.8218277328062565148449433E+00, \ 0.7802190040012226850703573E+00, \ 0.7386104305454957746359112E+00, \ 0.6970020414556031913861513E+00, \ 0.6553938730008771105113861E+00, \ 0.6137859711661063914322283E+00, \ 0.5721783951857430999179669E+00, \ 0.5305712227365694155165922E+00, \ 0.4889645577740232855661796E+00, \ 0.4473585427277744403333139E+00, \ 0.4057533781735039172217875E+00, \ 0.3641493559322687127223795E+00, \ 0.3225469176515179389138545E+00, \ 0.2809467650889194227770571E+00, \ 0.2393500844055270891104500E+00, \ 0.1977590501629603151642330E+00, \ 0.1561781206604067112364815E+00, \ 0.1146180742271483316267615E+00, \ 0.7311308274978660184520447E-01, \ 0.3185176130791400787169333E-01 ] ) OddThetaZero38 = np.array ( [ \ 0.1530260491394766313570510E+01, \ 0.1489724658775115137266557E+01, \ 0.1449188831753177403184250E+01, \ 0.1408653013220734918131897E+01, \ 0.1368117206184034069757975E+01, \ 0.1327581413807020172726043E+01, \ 0.1287045639459248683416470E+01, \ 0.1246509886770075360771330E+01, \ 0.1205974159691064843702080E+01, \ 0.1165438462569017837684371E+01, \ 0.1124902800232641860108690E+01, \ 0.1084367178096737546333982E+01, \ 0.1043831602288925654461738E+01, \ 0.1003296079805520648394589E+01, \ 0.9627606187053432591598275E+00, \ 0.9222252283533212928777294E+00, \ 0.8816899197300536544215117E+00, \ 0.8411547058297167490229198E+00, \ 0.8006196021777239861105672E+00, \ 0.7600846275129127849719743E+00, \ 0.7195498046991648764002008E+00, \ 0.6790151619622966197448464E+00, \ 0.6384807345966275863946969E+00, \ 0.5979465673637771458800754E+00, \ 0.5574127179353942966481713E+00, \ 0.5168792619515766918187819E+00, \ 0.4763463006547495614450433E+00, \ 0.4358139727703203523144583E+00, \ 0.3952824736706231680817472E+00, \ 0.3547520876199503791717895E+00, \ 0.3142232448436673832093046E+00, \ 0.2736966289659020439688229E+00, \ 0.2331733955144496369946707E+00, \ 0.1926556629116315949109922E+00, \ 0.1521477743835989472840536E+00, \ 0.1116602300918232453371161E+00, \ 0.7122632005925390425640031E-01, \ 0.3102979192734513847869512E-01 ] ) OddThetaZero39 = np.array ( [ \ 0.1531280219945530918862887E+01, \ 0.1491764115543711582608611E+01, \ 0.1452248016067723206269747E+01, \ 0.1412731924058150689920340E+01, \ 0.1373215842151127100608219E+01, \ 0.1333699773114208203180680E+01, \ 0.1294183719885939986844436E+01, \ 0.1254667685620366764206205E+01, \ 0.1215151673737978313041594E+01, \ 0.1175635687984935008823566E+01, \ 0.1136119732502868295328130E+01, \ 0.1096603811912170337964094E+01, \ 0.1057087931412518476253055E+01, \ 0.1017572096905509113863513E+01, \ 0.9780563151458206514020694E+00, \ 0.9385405939294598498464432E+00, \ 0.8990249423306286659734381E+00, \ 0.8595093710029676968794279E+00, \ 0.8199938925669823205931282E+00, \ 0.7804785221142635001130339E+00, \ 0.7409632778721439753645470E+00, \ 0.7014481820920565808095373E+00, \ 0.6619332622550151160558599E+00, \ 0.6224185527349885679868616E+00, \ 0.5829040971371158016902326E+00, \ 0.5433899516536147244946347E+00, \ 0.5038761899947552937603140E+00, \ 0.4643629108305196256509391E+00, \ 0.4248502493722176391609139E+00, \ 0.3853383960541810555628366E+00, \ 0.3458276279674767760058527E+00, \ 0.3063183644932167228808922E+00, \ 0.2668112720373341483108662E+00, \ 0.2273074770384765519559169E+00, \ 0.1878090446069578429818381E+00, \ 0.1483202086882449059764783E+00, \ 0.1088512052741322662621244E+00, \ 0.6943448689600673838300180E-01, \ 0.3024917865720923179577363E-01 ] ) OddThetaZero40 = np.array ( [ \ 0.1532249903371281818085917E+01, \ 0.1493703482108998740614827E+01, \ 0.1455157065195200346809599E+01, \ 0.1416610654869340270223431E+01, \ 0.1378064253450997606022340E+01, \ 0.1339517863369794055919890E+01, \ 0.1300971487198245305453001E+01, \ 0.1262425127688525048786896E+01, \ 0.1223878787814308166546501E+01, \ 0.1185332470819113339105535E+01, \ 0.1146786180272904774996439E+01, \ 0.1108239920139165765487189E+01, \ 0.1069693694855262920629379E+01, \ 0.1031147509429735196850587E+01, \ 0.9926013695612463310882198E+00, \ 0.9540552817854489715123326E+00, \ 0.9155092536580933534978986E+00, \ 0.8769632939856246206308699E+00, \ 0.8384174131186299393233148E+00, \ 0.7998716233293992826192237E+00, \ 0.7613259393034545837300323E+00, \ 0.7227803787876118667749166E+00, \ 0.6842349634562860931661901E+00, \ 0.6456897200871628101751519E+00, \ 0.6071446821835496233813653E+00, \ 0.5685998922550279415939221E+00, \ 0.5300554050908430047380815E+00, \ 0.4915112925697217767572364E+00, \ 0.4529676509187802579380104E+00, \ 0.4144246120108054286121629E+00, \ 0.3758823615873930314093573E+00, \ 0.3373411699211847213003570E+00, \ 0.2988014460838619282843952E+00, \ 0.2602638401106843145315994E+00, \ 0.2217294507811754336425535E+00, \ 0.1832002925124018168986342E+00, \ 0.1446804953347050655563166E+00, \ 0.1061800440374660771048480E+00, \ 0.6773059476567831336488402E-01, \ 0.2950687695527422224851832E-01 ] ) OddThetaZero41 = np.array ( [ \ 0.1533173137460634461235066E+01, \ 0.1495549950040734249895393E+01, \ 0.1457926766471340970762709E+01, \ 0.1420303588732694442267846E+01, \ 0.1382680418872520759663065E+01, \ 0.1345057259031099988676433E+01, \ 0.1307434111468678960501903E+01, \ 0.1269810978596001635506341E+01, \ 0.1232187863008871596257323E+01, \ 0.1194564767527851916244615E+01, \ 0.1156941695244461089553108E+01, \ 0.1119318649575559636172662E+01, \ 0.1081695634328067979412755E+01, \ 0.1044072653776750930510111E+01, \ 0.1006449712758602402124214E+01, \ 0.9688268167884441336521039E+00, \ 0.9312039722018274751677424E+00, \ 0.8935811863333633591901354E+00, \ 0.8559584677414483220357356E+00, \ 0.8183358264943738874932307E+00, \ 0.7807132745385688213392421E+00, \ 0.7430908261781095392995681E+00, \ 0.7054684987070400358784448E+00, \ 0.6678463132547297820965882E+00, \ 0.6302242959332082940279826E+00, \ 0.5926024794204980683238426E+00, \ 0.5549809051864955237054951E+00, \ 0.5173596266878257139037738E+00, \ 0.4797387140623364241772428E+00, \ 0.4421182612140318859822955E+00, \ 0.4044983968396638104610711E+00, \ 0.3668793022152994411560368E+00, \ 0.3292612411240570212440856E+00, \ 0.2916446128242035199998930E+00, \ 0.2540300517665934607689814E+00, \ 0.2164186303985620085027010E+00, \ 0.1788123148742007754778852E+00, \ 0.1412151362884411752920148E+00, \ 0.1036368402634645114775150E+00, \ 0.6610832470916409695729856E-01, \ 0.2880013396280840229218334E-01 ] ) OddThetaZero42 = np.array ( [ \ 0.1534053181584449084854269E+01, \ 0.1497310038074501005766978E+01, \ 0.1460566897984002644464183E+01, \ 0.1423823763069232867789940E+01, \ 0.1387080635143547965139117E+01, \ 0.1350337516098480646600889E+01, \ 0.1313594407926723776707731E+01, \ 0.1276851312747612578778902E+01, \ 0.1240108232835827171448969E+01, \ 0.1203365170654181674634873E+01, \ 0.1166622128891556900019450E+01, \ 0.1129879110507284864268762E+01, \ 0.1093136118783624474731954E+01, \ 0.1056393157388405786003046E+01, \ 0.1019650230450503114577901E+01, \ 0.9829073426515786199715451E+00, \ 0.9461644993385942743541994E+00, \ 0.9094217066630320811486021E+00, \ 0.8726789717547518480094350E+00, \ 0.8359363029411928866147184E+00, \ 0.7991937100265521402467844E+00, \ 0.7624512046511992388808212E+00, \ 0.7257088007597790982554974E+00, \ 0.6889665152185689899094400E+00, \ 0.6522243686409073299342467E+00, \ 0.6154823865075504175164916E+00, \ 0.5787406007128420496638175E+00, \ 0.5419990517384125648087865E+00, \ 0.5052577917731960988645056E+00, \ 0.4685168892980173635234519E+00, \ 0.4317764360047099160222576E+00, \ 0.3950365575646972937604113E+00, \ 0.3582974309994310205507555E+00, \ 0.3215593139080007759227897E+00, \ 0.2848225961961619069649047E+00, \ 0.2480878974611689122432227E+00, \ 0.2113562650517154915467591E+00, \ 0.1746296191183898065201571E+00, \ 0.1379118964507339113271975E+00, \ 0.1012126146941469342401701E+00, \ 0.6456194899726137278760257E-01, \ 0.2812645439079299219187419E-01 ] ) OddThetaZero43 = np.array ( [ \ 0.1534892997139557227614279E+01, \ 0.1498989668998897501276994E+01, \ 0.1463086343903285773505644E+01, \ 0.1427183023414814244376429E+01, \ 0.1391279709144040438287602E+01, \ 0.1355376402767821814937864E+01, \ 0.1319473106048673173924451E+01, \ 0.1283569820856137399848247E+01, \ 0.1247666549190742942502495E+01, \ 0.1211763293211231530413995E+01, \ 0.1175860055265884319525693E+01, \ 0.1139956837928964066704190E+01, \ 0.1104053644043538840797350E+01, \ 0.1068150476772278342447444E+01, \ 0.1032247339658243608912598E+01, \ 0.9963442366982618328585493E+00, \ 0.9604411724322426430586723E+00, \ 0.9245381520528253319358567E+00, \ 0.8886351815411563067305273E+00, \ 0.8527322678365406966379400E+00, \ 0.8168294190504262166761188E+00, \ 0.7809266447390142664026016E+00, \ 0.7450239562542930157586944E+00, \ 0.7091213672012904985883029E+00, \ 0.6732188940411854039055226E+00, \ 0.6373165568977466866717861E+00, \ 0.6014143806519714388063208E+00, \ 0.5655123964528129857845238E+00, \ 0.5296106438411039715966193E+00, \ 0.4937091737981756577948229E+00, \ 0.4578080532255782153525438E+00, \ 0.4219073717059785387344039E+00, \ 0.3860072520255396095683859E+00, \ 0.3501078671472635990145335E+00, \ 0.3142094687704932495909488E+00, \ 0.2783124378775218384923333E+00, \ 0.2424173798924625361874772E+00, \ 0.2065253182141071551836492E+00, \ 0.1706381290938671641708352E+00, \ 0.1347596593282315198612592E+00, \ 0.9889920900871122533586553E-01, \ 0.6308626356388784057588631E-01, \ 0.2748357108440508277394892E-01 ] ) OddThetaZero44 = np.array ( [ \ 0.1535695280838629983064694E+01, \ 0.1500594236235067817656313E+01, \ 0.1465493194350303789230585E+01, \ 0.1430392156577492526495371E+01, \ 0.1395291124351096810858349E+01, \ 0.1360190099162024176252063E+01, \ 0.1325089082574000089379322E+01, \ 0.1289988076241572027256558E+01, \ 0.1254887081930202663795858E+01, \ 0.1219786101538994920367859E+01, \ 0.1184685137126702182946916E+01, \ 0.1149584190941820846004092E+01, \ 0.1114483265457749469332035E+01, \ 0.1079382363414242848588494E+01, \ 0.1044281487866708939888712E+01, \ 0.1009180642245317812316634E+01, \ 0.9740798304264509422659935E+00, \ 0.9389790568197674899837757E+00, \ 0.9038783264751749171405213E+00, \ 0.8687776452153701566068907E+00, \ 0.8336770198015192229270720E+00, \ 0.7985764581422970742698971E+00, \ 0.7634759695602610192254430E+00, \ 0.7283755651349081311799055E+00, \ 0.6932752581495918103871962E+00, \ 0.6581750646810479477537782E+00, \ 0.6230750043877162525265513E+00, \ 0.5879751015798285374141491E+00, \ 0.5528753866962970290878822E+00, \ 0.5177758983811020490994086E+00, \ 0.4826766864637186565865902E+00, \ 0.4475778163386701445336738E+00, \ 0.4124793755752883735361361E+00, \ 0.3773814842049053432591527E+00, \ 0.3422843113148581639684411E+00, \ 0.3071881029697497767338606E+00, \ 0.2720932316284942932084102E+00, \ 0.2370002891767127567222407E+00, \ 0.2019102761348421810146637E+00, \ 0.1668250268181992892198073E+00, \ 0.1317483020532982541977987E+00, \ 0.9668919410176593344830717E-01, \ 0.6167652949817792358742135E-01, \ 0.2686941953400762687915995E-01 ] ) OddThetaZero45 = np.array ( [ \ 0.1536462493634653558154673E+01, \ 0.1502128661685489464262068E+01, \ 0.1467794832169950298839286E+01, \ 0.1433461006333747476463744E+01, \ 0.1399127185457927306909792E+01, \ 0.1364793370871767472755746E+01, \ 0.1330459563966682507229700E+01, \ 0.1296125766211456950047804E+01, \ 0.1261791979169174443914592E+01, \ 0.1227458204516276373551266E+01, \ 0.1193124444064268679881601E+01, \ 0.1158790699784705540565424E+01, \ 0.1124456973838220917338613E+01, \ 0.1090123268608563332983681E+01, \ 0.1055789586742829027889885E+01, \ 0.1021455931199402224481903E+01, \ 0.9871223053055240306873772E+00, \ 0.9527887128269590857605072E+00, \ 0.9184551580529615732874848E+00, \ 0.8841216459007313197085517E+00, \ 0.8497881820448998068986446E+00, \ 0.8154547730794463756650640E+00, \ 0.7811214267220410983907210E+00, \ 0.7467881520744805288579630E+00, \ 0.7124549599581423848996086E+00, \ 0.6781218633510390484774053E+00, \ 0.6437888779643722276961833E+00, \ 0.6094560230135452763170614E+00, \ 0.5751233222647905281576305E+00, \ 0.5407908054797110156395425E+00, \ 0.5064585104462232763044121E+00, \ 0.4721264858937837018545325E+00, \ 0.4377947957771643018072936E+00, \ 0.4034635257416918872885646E+00, \ 0.3691327931855416440777167E+00, \ 0.3348027634909946151567752E+00, \ 0.3004736773353657517478163E+00, \ 0.2661458990278703974149616E+00, \ 0.2318200075085118064771005E+00, \ 0.1974969814205034596217949E+00, \ 0.1631786149772797106698111E+00, \ 0.1288685867945150272796250E+00, \ 0.9457579039019365184018477E-01, \ 0.6032842220945916819748797E-01, \ 0.2628211572883546008386342E-01 ] ) OddThetaZero46 = np.array ( [ \ 0.1537196885933572311910085E+01, \ 0.1503597446159129663218426E+01, \ 0.1469998008568304160871417E+01, \ 0.1436398574277729377094190E+01, \ 0.1402799144434368418084898E+01, \ 0.1369199720226542342210552E+01, \ 0.1335600302895785666466344E+01, \ 0.1302000893749787833197270E+01, \ 0.1268401494176718217187838E+01, \ 0.1234802105661283063077015E+01, \ 0.1201202729802928570677208E+01, \ 0.1167603368336689119731474E+01, \ 0.1134004023157288628212183E+01, \ 0.1100404696347243386055709E+01, \ 0.1066805390209896030700280E+01, \ 0.1033206107308545748870827E+01, \ 0.9996068505131472996246808E+00, \ 0.9660076230564559666956844E+00, \ 0.9324084286020318648375284E+00, \ 0.8988092713272342656758064E+00, \ 0.8652101560253048754543914E+00, \ 0.8316110882319595313175680E+00, \ 0.7980120743837286767240920E+00, \ 0.7644131220178278512956878E+00, \ 0.7308142400269308414762795E+00, \ 0.6972154389873656296775555E+00, \ 0.6636167315867435235683334E+00, \ 0.6300181331881122315700717E+00, \ 0.5964196625844131090385918E+00, \ 0.5628213430226633060114218E+00, \ 0.5292232036175455988770345E+00, \ 0.4956252813388603291268380E+00, \ 0.4620276238643496856689332E+00, \ 0.4284302937718012609061760E+00, \ 0.3948333748659561479104270E+00, \ 0.3612369820255324850503899E+00, \ 0.3276412770872600895283016E+00, \ 0.2940464955725917238672137E+00, \ 0.2604529939906062681054034E+00, \ 0.2268613388903867245835696E+00, \ 0.1932724879746856807613294E+00, \ 0.1596881970714452359218090E+00, \ 0.1261120661032951679792394E+00, \ 0.9255279834764232165670211E-01, \ 0.5903798711627596210077655E-01, \ 0.2571993685288741305807485E-01 ] ) OddThetaZero47 = np.array ( [ \ 0.1537900519639177351485509E+01, \ 0.1505004713461118831562885E+01, \ 0.1472108909246876714959093E+01, \ 0.1439213107999753788389740E+01, \ 0.1406317310749171844429399E+01, \ 0.1373421518560135827011261E+01, \ 0.1340525732543378926238078E+01, \ 0.1307629953866399941713193E+01, \ 0.1274734183765634621652739E+01, \ 0.1241838423560042429086765E+01, \ 0.1208942674666441461574345E+01, \ 0.1176046938616989970936899E+01, \ 0.1143151217079296988032361E+01, \ 0.1110255511879752164142939E+01, \ 0.1077359825030803093319347E+01, \ 0.1044464158763086533573607E+01, \ 0.1011568515563550961534623E+01, \ 0.9786728982210094134846821E+00, \ 0.9457773098809579873452675E+00, \ 0.9128817541120207886160886E+00, \ 0.8799862349870845994262022E+00, \ 0.8470907571831347751008168E+00, \ 0.8141953261050969543263697E+00, \ 0.7812999480407721032432037E+00, \ 0.7484046303564402266425896E+00, \ 0.7155093817462244075628281E+00, \ 0.6826142125533466396520346E+00, \ 0.6497191351887403950357432E+00, \ 0.6168241646833332909207560E+00, \ 0.5839293194266532352434130E+00, \ 0.5510346221695150324949297E+00, \ 0.5181401014079633610544426E+00, \ 0.4852457933290632607369490E+00, \ 0.4523517446039431388003505E+00, \ 0.4194580164920722423612656E+00, \ 0.3865646910356375140534892E+00, \ 0.3536718807003189971969294E+00, \ 0.3207797439266498255416416E+00, \ 0.2878885112969848452450724E+00, \ 0.2549985318477515756044100E+00, \ 0.2221103602568508117102717E+00, \ 0.1892249341643785313168465E+00, \ 0.1563439726212394862316010E+00, \ 0.1234710001537068179882843E+00, \ 0.9061453776736619019094845E-01, \ 0.5780160090309369034797044E-01, \ 0.2518130440638251656980999E-01 ] ) OddThetaZero48 = np.array ( [ \ 0.1538575287485045780713568E+01, \ 0.1506354249056545799167351E+01, \ 0.1474133212398093554231315E+01, \ 0.1441912178413208451704314E+01, \ 0.1409691148027973881079186E+01, \ 0.1377470122199186272616473E+01, \ 0.1345249101923067139210221E+01, \ 0.1313028088244711409410919E+01, \ 0.1280807082268469343020428E+01, \ 0.1248586085169490583375238E+01, \ 0.1216365098206699074213627E+01, \ 0.1184144122737518830558069E+01, \ 0.1151923160234735793613503E+01, \ 0.1119702212305964062886069E+01, \ 0.1087481280716290811591462E+01, \ 0.1055260367414810028339009E+01, \ 0.1023039474565930165787482E+01, \ 0.9908186045865674272211987E+00, \ 0.9585977601906320722299056E+00, \ 0.9263769444426036830464570E+00, \ 0.8941561608225061952846411E+00, \ 0.8619354133052817812042663E+00, \ 0.8297147064584916186566054E+00, \ 0.7974940455635382827549679E+00, \ 0.7652734367673509855003551E+00, \ 0.7330528872739117793257283E+00, \ 0.7008324055884451343305450E+00, \ 0.6686120018320298047193041E+00, \ 0.6363916881515750209117372E+00, \ 0.6041714792607289968809847E+00, \ 0.5719513931632926368357825E+00, \ 0.5397314521353000325496229E+00, \ 0.5075116840805377280486923E+00, \ 0.4752921244363891783961832E+00, \ 0.4430728189095547215892704E+00, \ 0.4108538274961112658763390E+00, \ 0.3786352305487998074788803E+00, \ 0.3464171382200184643128623E+00, \ 0.3141997056941599156198233E+00, \ 0.2819831588178046655599196E+00, \ 0.2497678394619649260592757E+00, \ 0.2175542909210219972765731E+00, \ 0.1853434315961135904158300E+00, \ 0.1531369452704970394027659E+00, \ 0.1209382841678252589048669E+00, \ 0.8875579450016283173293810E-01, \ 0.5661593754525190873771522E-01, \ 0.2466476940450737058975552E-01 ] ) OddThetaZero49 = np.array ( [ \ 0.1539222930035210331902410E+01, \ 0.1507649534071729882214386E+01, \ 0.1476076139707032453353232E+01, \ 0.1444502747756546556830706E+01, \ 0.1412929359055252480197337E+01, \ 0.1381355974464721552102928E+01, \ 0.1349782594880622732927647E+01, \ 0.1318209221240839295255046E+01, \ 0.1286635854534357387243172E+01, \ 0.1255062495811112994872428E+01, \ 0.1223489146193015470717893E+01, \ 0.1191915806886406014313715E+01, \ 0.1160342479196260434661502E+01, \ 0.1128769164542510055952304E+01, \ 0.1097195864478936528824546E+01, \ 0.1065622580715200621234508E+01, \ 0.1034049315142698534418744E+01, \ 0.1002476069865111021377467E+01, \ 0.9709028472347329448081481E+00, \ 0.9393296498959608456620406E+00, \ 0.9077564808376970380335442E+00, \ 0.8761833434569334264096395E+00, \ 0.8446102416364528348063321E+00, \ 0.8130371798404960344077378E+00, \ 0.7814641632334840064334645E+00, \ 0.7498911978285964532098456E+00, \ 0.7183182906753955596314298E+00, \ 0.6867454500990591398232408E+00, \ 0.6551726860086246453663390E+00, \ 0.6236000102986843027011345E+00, \ 0.5920274373793840619034224E+00, \ 0.5604549848852622707385612E+00, \ 0.5288826746375584896948472E+00, \ 0.4973105339724571989307663E+00, \ 0.4657385976085971045914307E+00, \ 0.4341669103277770901346174E+00, \ 0.4025955309141879357899857E+00, \ 0.3710245380997234377015025E+00, \ 0.3394540398171456073906403E+00, \ 0.3078841881262277508367562E+00, \ 0.2763152043287541015913350E+00, \ 0.2447474234189502677044064E+00, \ 0.2131813777658572006989977E+00, \ 0.1816179673056091210434906E+00, \ 0.1500588419721174291665790E+00, \ 0.1185073845935281602210493E+00, \ 0.8697177361567243680812898E-01, \ 0.5547793843128156580348541E-01, \ 0.2416899936118312040170588E-01 ] ) if ( l < 1 or 100 < l ): print ( '' ) print ( 'LEGENDRE_THETA - Fatal error!' ) print ( ' 1 <= L <= 100 is required.' ) exit ( 'LEGENDRE_THETA - Fatal error!' ) lhalf = ( ( l + 1 ) // 2 ) if ( ( l % 2 ) == 1 ): if ( lhalf < k ): kcopy = k - lhalf elif ( lhalf == k ): kcopy = lhalf else: kcopy = lhalf - k else: if ( lhalf < k ): kcopy = k - lhalf else: kcopy = lhalf + 1 - k if ( kcopy < 1 or lhalf < kcopy ): print ( '' ) print ( 'LEGENDRE_THETA - Fatal error!' ) print ( ' 1 <= K <= (L+1)/2 is required.' ) exit ( 'LEGENDRE_THETA - Fatal error!' ) # # If L is odd, and K = ( L - 1 ) / 2, then it's easy. # if ( ( l % 2 ) == 1 and kcopy == lhalf ): theta = np.pi / 2.0 elif ( l == 2 ): theta = EvenThetaZero1[kcopy-1] elif ( l == 3 ): theta = OddThetaZero1[kcopy-1] elif ( l == 4 ): theta = EvenThetaZero2[kcopy-1] elif ( l == 5 ): theta = OddThetaZero2[kcopy-1] elif ( l == 6 ): theta = EvenThetaZero3[kcopy-1] elif ( l == 7 ): theta = OddThetaZero3[kcopy-1] elif ( l == 8 ): theta = EvenThetaZero4[kcopy-1] elif ( l == 9 ): theta = OddThetaZero4[kcopy-1] elif ( l == 10 ): theta = EvenThetaZero5[kcopy-1] elif ( l == 11 ): theta = OddThetaZero5[kcopy-1] elif ( l == 12 ): theta = EvenThetaZero6[kcopy-1] elif ( l == 13 ): theta = OddThetaZero6[kcopy-1] elif ( l == 14 ): theta = EvenThetaZero7[kcopy-1] elif ( l == 15 ): theta = OddThetaZero7[kcopy-1] elif ( l == 16 ): theta = EvenThetaZero8[kcopy-1] elif ( l == 17 ): theta = OddThetaZero8[kcopy-1] elif ( l == 18 ): theta = EvenThetaZero9[kcopy-1] elif ( l == 19 ): theta = OddThetaZero9[kcopy-1] elif ( l == 20 ): theta = EvenThetaZero10[kcopy-1] elif ( l == 21 ): theta = OddThetaZero10[kcopy-1] elif ( l == 22 ): theta = EvenThetaZero11[kcopy-1] elif ( l == 23 ): theta = OddThetaZero11[kcopy-1] elif ( l == 24 ): theta = EvenThetaZero12[kcopy-1] elif ( l == 25 ): theta = OddThetaZero12[kcopy-1] elif ( l == 26 ): theta = EvenThetaZero13[kcopy-1] elif ( l == 27 ): theta = OddThetaZero13[kcopy-1] elif ( l == 28 ): theta = EvenThetaZero14[kcopy-1] elif ( l == 29 ): theta = OddThetaZero14[kcopy-1] elif ( l == 30 ): theta = EvenThetaZero15[kcopy-1] elif ( l == 31 ): theta = OddThetaZero15[kcopy-1] elif ( l == 32 ): theta = EvenThetaZero16[kcopy-1] elif ( l == 33 ): theta = OddThetaZero16[kcopy-1] elif ( l == 34 ): theta = EvenThetaZero17[kcopy-1] elif ( l == 35 ): theta = OddThetaZero17[kcopy-1] elif ( l == 36 ): theta = EvenThetaZero18[kcopy-1] elif ( l == 37 ): theta = OddThetaZero18[kcopy-1] elif ( l == 38 ): theta = EvenThetaZero19[kcopy-1] elif ( l == 39 ): theta = OddThetaZero19[kcopy-1] elif ( l == 40 ): theta = EvenThetaZero20[kcopy-1] elif ( l == 41 ): theta = OddThetaZero20[kcopy-1] elif ( l == 42 ): theta = EvenThetaZero21[kcopy-1] elif ( l == 43 ): theta = OddThetaZero21[kcopy-1] elif ( l == 44 ): theta = EvenThetaZero22[kcopy-1] elif ( l == 45 ): theta = OddThetaZero22[kcopy-1] elif ( l == 46 ): theta = EvenThetaZero23[kcopy-1] elif ( l == 47 ): theta = OddThetaZero23[kcopy-1] elif ( l == 48 ): theta = EvenThetaZero24[kcopy-1] elif ( l == 49 ): theta = OddThetaZero24[kcopy-1] elif ( l == 50 ): theta = EvenThetaZero25[kcopy-1] elif ( l == 51 ): theta = OddThetaZero25[kcopy-1] elif ( l == 52 ): theta = EvenThetaZero26[kcopy-1] elif ( l == 53 ): theta = OddThetaZero26[kcopy-1] elif ( l == 54 ): theta = EvenThetaZero27[kcopy-1] elif ( l == 55 ): theta = OddThetaZero27[kcopy-1] elif ( l == 56 ): theta = EvenThetaZero28[kcopy-1] elif ( l == 57 ): theta = OddThetaZero28[kcopy-1] elif ( l == 58 ): theta = EvenThetaZero29[kcopy-1] elif ( l == 59 ): theta = OddThetaZero29[kcopy-1] elif ( l == 60 ): theta = EvenThetaZero30[kcopy-1] elif ( l == 61 ): theta = OddThetaZero30[kcopy-1] elif ( l == 62 ): theta = EvenThetaZero31[kcopy-1] elif ( l == 63 ): theta = OddThetaZero31[kcopy-1] elif ( l == 64 ): theta = EvenThetaZero32[kcopy-1] elif ( l == 65 ): theta = OddThetaZero32[kcopy-1] elif ( l == 66 ): theta = EvenThetaZero33[kcopy-1] elif ( l == 67 ): theta = OddThetaZero33[kcopy-1] elif ( l == 68 ): theta = EvenThetaZero34[kcopy-1] elif ( l == 69 ): theta = OddThetaZero34[kcopy-1] elif ( l == 70 ): theta = EvenThetaZero35[kcopy-1] elif ( l == 71 ): theta = OddThetaZero35[kcopy-1] elif ( l == 72 ): theta = EvenThetaZero36[kcopy-1] elif ( l == 73 ): theta = OddThetaZero36[kcopy-1] elif ( l == 74 ): theta = EvenThetaZero37[kcopy-1] elif ( l == 75 ): theta = OddThetaZero37[kcopy-1] elif ( l == 76 ): theta = EvenThetaZero38[kcopy-1] elif ( l == 77 ): theta = OddThetaZero38[kcopy-1] elif ( l == 78 ): theta = EvenThetaZero39[kcopy-1] elif ( l == 79 ): theta = OddThetaZero39[kcopy-1] elif ( l == 80 ): theta = EvenThetaZero40[kcopy-1] elif ( l == 81 ): theta = OddThetaZero40[kcopy-1] elif ( l == 82 ): theta = EvenThetaZero41[kcopy-1] elif ( l == 83 ): theta = OddThetaZero41[kcopy-1] elif ( l == 84 ): theta = EvenThetaZero42[kcopy-1] elif ( l == 85 ): theta = OddThetaZero42[kcopy-1] elif ( l == 86 ): theta = EvenThetaZero43[kcopy-1] elif ( l == 87 ): theta = OddThetaZero43[kcopy-1] elif ( l == 88 ): theta = EvenThetaZero44[kcopy-1] elif ( l == 89 ): theta = OddThetaZero44[kcopy-1] elif ( l == 90 ): theta = EvenThetaZero45[kcopy-1] elif ( l == 91 ): theta = OddThetaZero45[kcopy-1] elif ( l == 92 ): theta = EvenThetaZero46[kcopy-1] elif ( l == 93 ): theta = OddThetaZero46[kcopy-1] elif ( l == 94 ): theta = EvenThetaZero47[kcopy-1] elif ( l == 95 ): theta = OddThetaZero47[kcopy-1] elif ( l == 96 ): theta = EvenThetaZero48[kcopy-1] elif ( l == 97 ): theta = OddThetaZero48[kcopy-1] elif ( l == 98 ): theta = EvenThetaZero49[kcopy-1] elif ( l == 99 ): theta = OddThetaZero49[kcopy-1] elif ( l == 100 ): theta = EvenThetaZero50[kcopy-1] if ( ( 2 * k - 1 ) <= l ): theta = np.pi - theta return theta def legendre_theta_test ( ): #*****************************************************************************80 # ## LEGENDRE_THETA_TEST tests LEGENDRE_THETA. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 06 January 2016 # # Author: # # John Burkardt # # Reference: # # Ignace Bogaert, # Iteration-free computation of Gauss-Legendre quadrature nodes and weights, # SIAM Journal on Scientific Computing, # Volume 36, Number 3, 2014, pages A1008-1026. # import numpy as np import platform print ( '' ) print ( 'LEGENDRE_THETA_TEST:' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' LEGENDRE_THETA returns the K-th theta value for' ) print ( ' a Gauss Legendre rule of order L.' ) for l in range ( 1, 11 ): print ( '' ) print ( ' Gauss Legendre rule of order %d' % ( l ) ) print ( '' ) print ( ' K Theta Cos(Theta)' ) print ( '' ) for k in range ( 1, l + 1 ): theta = legendre_theta ( l, k ) print ( ' %2d %14.6g %14.6g' % ( k, theta, np.cos ( theta ) ) ) # # Terminate. # print ( '' ) print ( 'LEGENDRE_THETA_TEST:' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) legendre_theta_test ( ) timestamp ( )