Formats: - HTML - YAML - JSON - 2025-11-09T09:13:12.894354
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '1006199468595403662416564076045', 'a10': [1579.8107130496396, 0], 'a2': [0, 8.0], 'a3': [0, 0], 'a4': [-64.0, 0], 'a5': [0, -197.47633913120495], 'a6': [0, 0], 'a7': [0, -828.309101482155], 'a8': [0, -512.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 73.09809596328452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -8.0]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [239.8271173700478, -7917.764833194655]]]], 'bad_primes': [2, 3, 13], 'central_character': '234.181', 'coefficient_field': 'CDF', 'conductor': 234, 'conductor_radical': 78, 'conjugate': '723034214379950158390852337180', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -8.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 197.47633913120495], [-78125.0, 0]], [[1.0, 0], [0, 828.309101482155], [-823543.0, 0]], [[1.0, 0], [0, -2526.9848192839704], [-19487171.0, 0]], [[1.0, 0], [239.8271173700478, -7917.764833194655]], [[1.0, 0], [16738.238427881388, 0], [410338673.0, 0]], [[1.0, 0], [0, -45175.72962390322], [-893871739.0, 0]], [[1.0, 0], [53685.61386554573, 0], [3404825447.0, 0]], [[1.0, 0], [-157722.51861695404, 0], [17249876309.0, 0]], [[1.0, 0], [0, 128295.02084375966], [-27512614111.0, 0]], [[1.0, 0], [0, 95626.05180647247], [-94931877133.0, 0]], [[1.0, 0], [0, 844950.2915919662], [-194754273881.0, 0]], [[1.0, 0], [-917123.6639751451, 0], [271818611107.0, 0]], [[1.0, 0], [0, -597630.3751950588], [-506623120463.0, 0]], [[1.0, 0], [576838.8864178354, 0], [1174711139837.0, 0]], [[1.0, 0], [0, 1630549.3776329875], [-2488651484819.0, 0]], [[1.0, 0], [-1559493.8092048226, 0], [3142742836021.0, 0]], [[1.0, 0], [0, 824691.5201337207], [-6060711605323.0, 0]], [[1.0, 0], [0, 5632878.739015636], [-9095120158391.0, 0]], [[1.0, 0], [0, -2728941.960195859], [-11047398519097.0, 0]], [[1.0, 0], [3759533.8648416945, 0], [19203908986159.0, 0]], [[1.0, 0], [0, -1520248.8457640116], [-27136050989627.0, 0]], [[1.0, 0], [0, 1743286.8515715664], [-44231334895529.0, 0]], [[1.0, 0], [0, 10622902.97741275], [-80798284478113.0, 0]], [[1.0, 0], [2902463.398641599, 0], [107213535210701.0, 0]], [[1.0, 0], [-5244818.296982566, 0], [122987386542487.0, 0]], [[1.0, 0], [-15168925.989205722, 0], [160578147647843.0, 0]], [[1.0, 0], [0, -9533730.95532069], [-182803912081669.0, 0]], [[1.0, 0], [11570280.110743726, 0], [235260548044817.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23131245, 'index': 21, 'label': '2-234-13.12-c7-0-21', 'leading_term': '1.697419626332232962657517996199169000177143130578666314', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/234/8/b/c/181/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.697419626332233, 1.7376275982230631, 1.7427542665588065, 1.7129349073030304, 1.648920111635557, 1.5520576778602373, 1.424265245470532, 1.2679940315324614, 1.0861841372121364, 0.8822119996280201, 0.6598306708115167, 0.4231037107147922, 0.17633358392499945, -0.07601445125813894, -0.3293918790361698, -0.5792487187650694, -0.8211163279978372, -1.0506899043184301, -1.263909322966912, -1.4570369125831413, -1.626730756042588, -1.770112109828024, -1.8848255659977982, -1.9690906376135378, -2.021743533126045, -2.042267998843519, -2.030814251784011, -1.9882051978234823, -1.9159293312075965, -1.816119939486863, -1.6915204901740175, -1.545436348424242, -1.381673264419623, -1.204463369645574, -1.018379726811784, -0.8282407820000874, -0.6390063623140186, -0.4556671399958857, -0.2831297365178939, -0.12609985931188186, 0.01103395851331201, 0.12431331661437184, 0.21031683291048084, 0.2662581751988112, 0.2900725155610749, 0.2804888128947114, 0.2370855305974719, 0.16032767131189188, 0.051583356846729544, -0.08688140503170202, -0.25193065045660457, -0.4396094418266849, -0.6452176884913888, -0.8634059916034408, -1.0882920833953558, -1.3135958157279202, -1.5327900545294153, -1.739264273466494, -1.9264971299399183, -2.088233867149636, -2.218664034629342, -2.3125947720776985, -2.365614771359818, -2.3742440305805905, -2.3360646504822546, -2.249828201931252, -2.1155356148607916, -1.9344861004241771, -1.7092923115523038, -1.4438597603427648, -1.143329427024277, -0.8139834936716247, -0.46311519153047964, -0.09886483550168293, 0.2699747979407436, 0.6341795452644797, 0.9843361996106097, 1.3111000641241188, 1.6054609143518386, 1.859009994331859, 2.0642002894374114, 2.2145921535056012, 2.3050764355192133, 2.3320675629381125, 2.2936595983268573, 2.1897390890637314, 2.022049564393133, 1.7942037794304266, 1.5116412334335552, 1.1815300636205115, 0.8126140931001127, 0.4150075433534654, -5.834509502914509e-05, -0.42053086186734073, -0.8338660578701191, -1.2273847736632275, -1.588644406864532, -1.9058154597847257, -2.1680513236575227, -2.3658395212394985, -2.4913227695206066, -2.5385787515928104, -2.5038484015366396, -2.3857037953654383, -2.18514837791956, -1.9056442000968827, -1.553063040289802, -1.1355606743104327, -0.6633760656469448, -0.14855979125076954, 0.3953614891877946, 0.9537753589374403, 1.511417476625615, 2.052835810721442, 2.5628707416896983, 3.0271355198239562, 3.4324810936447894, 3.7674293913566306, 4.022559764407868, 4.190834486334289, 4.267850920005104, 4.252010179811909, 4.144594760038135, 3.9497505959764534, 3.6743722734656585, 3.3278934952745787, 2.921988329385225, 2.4701920794224046, 1.9874537049820853, 1.4896344570055187, 0.9929696669217992, 0.5135123377934522, 0.06657824880463134, -0.33378735938268145, -0.675301837053726, -0.9478773708155538, -1.1439767430830465, -1.2588784722799342, -1.2908403469190113, -1.2411540098034948, -1.114087260488767, -0.9167149783136653, -0.65864386454611, -0.3516403925832009, -0.009175270615821138, 0.35409880171909724, 0.7229164133216601, 1.0819939220183041, 1.4166259597609512, 1.7132603510950182, 1.9600283420085642, 2.1472084930176467, 2.267604959534818, 2.316824089585772, 2.293437201985823, 2.199021921648075, 2.0380793685628036, 1.8178296267091516, 1.5478930476736799, 1.239869853937062, 0.9068349846037804, 0.5627689701458741, 0.22194865239874645, -0.10167636847369882, -0.39509468952931365, -0.64680474927979, -0.8473217696137041, -0.9895970635366578, -1.069330291498469, -1.085159689601213, -1.0387204850549738, -0.9345674452209528, -0.7799635337968269, -0.5845427084455943, -0.3598607168883298, -0.11885306476554262, 0.12477611456658014, 0.357206986277892, 0.5651690344762794, 0.7365873858004869, 0.8611799493044604, 0.9309766038228188, 0.940734752191933, 0.8882299115057574, 0.7744054499331576, 0.6033718878444816, 0.38225308162823995, 0.1208837946638823, -0.16862969866206645, -0.47246757068548495, -0.7757485065702334, -1.0632463933128087, -1.3201383956159325, -1.5327489258857088, -1.6892534000290673, -1.7803067695499624, -1.7995646270795533, -1.7440691083242676, -1.614477689555838, -1.4151200625910603, -1.153876249844819, -0.8418776392497144, -0.4930412748783611, -0.12345611789899139, 0.24935232072342403, 0.6072459728080125, 0.9323486633075904, 1.2079294153033855, 1.4192515157179117, 1.554344828727998, 1.6046615254350178, 1.565580107150732, 1.4367291603237087, 1.22211042191115, 0.9300100972385369, 0.5726975296150694, 0.16592079199790422, -0.2717809538020731, -0.7199189201051385, -1.1570122080062513, -1.561616895696204, -1.9133775465966962, -2.194049627298991, -2.3884414693405516, -2.485227113585732, -2.4775865753526833, -2.3636375694746823, -2.146632223304024, -1.834903359758074, -1.4415570389562313, -0.9839206258126224, -0.4827680825094994, 0.03864415989158034, 0.5556871240035811, 1.043563039489622, 1.4785450325789937, 1.8391916909150068, 2.1074752709412583, 2.2697652198958194, 2.31761459449988, 2.248305647046343, 2.0651219429115093, 1.777327365594384, 1.3998466408304016, 0.9526568741031615, 0.4599143031423637, -0.05114573377915544, -0.5514854453303317, -1.0116578024719571, -1.4032492361275033, -1.7003009557099455, -1.880637773745247, -1.9270366758561241, -1.8281742366734866, -1.579302067048486, -1.1826123293961335, -0.6472703662375562], 'positive_zeros': ['0.793751423629071173132837265746730', '2.49456389513205205612119693509340', '3.02481915747946150820317717286250', '4.57926514130120446325305835511089', '5.74999131417956477282142670907750', '6.82983587027317691980176951808956', '8.259857707877860120937311554938795', '9.001612413426898609134828398437151', '10.16734257403743022827289175157234', '10.96785367649612617708674962736380'], 'prelabel': '2-234-13.12-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.549742450114186, 'root_angle': 0.004819289948573495, 'root_number': '0.99954158093725382797997889441192433812655991827662461212 + 0.030275864602935040891186019135967964093373916928639709*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.004819289948573495', 'prec': 67}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.793751423629071173132837265747', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.49456389513205205612119693509', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02481915747946150820317717286', 'prec': 103}}