-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1445593511236673447306199683700', 'a10': [0.0, 0.0], 'a2': [2.0, 0.0], 'a3': [-7.0710678118654755, 0.0], 'a4': [4.0, 0.0], 'a5': [0.0, 0.0], 'a6': [-14.142135623730951, 0.0], 'a7': [0.0, 0.0], 'a8': [8.0, 0.0], 'a9': [23.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 144.55467951406456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '2450.1', 'coefficient_field': 'CDF', 'conductor': 2450, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [7.0710678118654755, 0], [27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [14.0, 0], [1331.0, 0]], [[1.0, 0], [-50.91168824543142, 0], [2197.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [4913.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [6859.0, 0]], [[1.0, 0], [140.0, 0], [12167.0, 0]], [[1.0, 0], [286.0, 0], [24389.0, 0]], [[1.0, 0], [-93.33809511662427, 0], [29791.0, 0]], [[1.0, 0], [-38.0, 0], [50653.0, 0]], [[1.0, 0], [-125.86500705120545, 0], [68921.0, 0]], [[1.0, 0], [-34.0, 0], [79507.0, 0]], [[1.0, 0], [-523.2590180780452, 0], [103823.0, 0]], [[1.0, 0], [-74.0, 0], [148877.0, 0]], [[1.0, 0], [434.16356364854016, 0], [205379.0, 0]], [[1.0, 0], [14.142135623730951, 0], [226981.0, 0]], [[1.0, 0], [684.0, 0], [300763.0, 0]], [[1.0, 0], [-588.0, 0], [357911.0, 0]], [[1.0, 0], [270.1147904132612, 0], [389017.0, 0]], [[1.0, 0], [-1220.0, 0], [493039.0, 0]], [[1.0, 0], [-422.8498551495554, 0], [571787.0, 0]], [[1.0, 0], [618.0113267570425, 0], [704969.0, 0]], [[1.0, 0], [-1483.5100269293766, 0], [912673.0, 0]], [[1.0, 0], [1128.5424227737299, 0], [1030301.0, 0]], [[1.0, 0], [868.3271272970803, 0], [1092727.0, 0]], [[1.0, 0], [-1684.0, 0], [1225043.0, 0]], [[1.0, 0], [818.0, 0], [1295029.0, 0]], [[1.0, 0], [-540.0, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 134, 'label': '2-2450-1.1-c3-0-134', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2450/4/a/bx/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.2072257313663737e-60, 0.22905027278667683, 0.4548130630667908, 0.6740343692644462, 0.8835272073899598, 1.0802052419351558, 1.261116515838698, 1.423477235634139, 1.5647055062333766, 1.6824548378544157, 1.7746471685001521, 1.8395050626112535, 1.875582663755271, 1.8817949002799002, 1.857444371528855, 1.8022452821261739, 1.716343746353892, 1.600333756796699, 1.4552681037782258, 1.2826635467198708, 1.0844995768852328, 0.8632101738702092, 0.6216680458306038, 0.3631609552814544, 0.09135986712421368, -0.18972118857877796, -0.4757734722905215, -0.7622498529714825, -1.044428631593582, -1.3174842061872483, -1.5765637054360466, -1.8168685125305108, -2.0337394050439697, -2.2227438558501915, -2.379763880451225, -2.5010826832935105, -2.583468255215052, -2.6242520111383216, -2.621400535944968, -2.5735785308057637, -2.4802011248246565, -2.341473839340846, -2.1584186650604926, -1.9328849344897654, -1.66754394165374, -1.365866574119427, -1.032083573766378, -0.6711284260334606, -0.288563284660352, 0.10951123881836945, 0.5165611644686656, 0.9257374348349551, 1.3300053263792893, 1.7222825263525383, 2.0955830868090706, 2.443164186742302, 2.758672415668122, 3.0362861470017757, 3.2708505054238852, 3.458001455521709, 3.594275653675007, 3.6772029134671067, 3.7053784363487043, 3.6785123506972823, 3.5974545778796974, 3.4641935947701272, 3.28182827706602, 3.0545126728543956, 2.7873742551508203, 2.4864069176173125, 2.1583406899554074, 1.8104908381944396, 1.4505896594751782, 1.0866048603882312, 0.7265489027259083, 0.3782840923939726, 0.04932846008485807, -0.25333237723991797, -0.5234221870407446, -0.7555348878195028, -0.9452743770009925, -1.0893691353632486, -1.1857579145473294, -1.233643534944656, -1.23351265523167, -1.187120301403462, -1.0974389379156553, -0.9685728987848546, -0.805640041992725, -0.6146235143633171, -0.4021974835634429, -0.17553157660696098, 0.05792047084452404, 0.2906418316582062, 0.5152767013940459, 0.7248506856062549, 0.9129805898531272, 1.0740669124465767, 1.203462730017558, 1.297613271032836, 1.354161280609055, 1.372014272234542, 1.351370912305785, 1.293705059328414, 1.201707343279857, 1.0791855795226508, 0.9309267200607262, 0.7625244052593826, 0.5801774435157588, 0.39046566822068185, 0.20011055715359632, 0.01572871031290454, -0.15641326456702648, -0.31063373896300067, -0.4420523313707275, -0.5467792978458857, -0.6220706217837907, -0.6664424003816234, -0.6797394069016132, -0.663154214414726, -0.6191949528555354, -0.5516015834246377, -0.46521245242320874, -0.36578476548164196, -0.2597744351711533, -0.15408243214809678, -0.055776246372334415, 0.02820372074408291, 0.09134211444693735, 0.12783967958147135, 0.1328860112915386, 0.1029028802890521, 0.035747705112176724, -0.06913214792189515, -0.21060205997120646, -0.38580582840660826, -0.590198148797072, -0.8176453849334354, -1.0605935888047133, -1.3103001589111554, -1.5571229841793885, -1.7908585076986705, -2.0011179543268667, -2.1777290892931487, -2.3111493936340852, -2.3928755276202764, -2.4158334617096275, -2.3747337252016187, -2.2663768754399873, -2.089895523932007, -1.8469210471627155, -1.5416654144344004, -1.180911317024999, -0.773906897257166, -0.3321647507172204, 0.1308316058535898, 0.6000070701650105, 1.0591499364632702, 1.491429184945595, 1.8799579290296247, 2.2083845510650884, 2.4614913320726894, 2.6257793370593223, 2.690018017940678, 2.645738478927077, 2.4876506241135266, 2.2139664541808446, 1.8266145489783245, 1.331334186765095, 0.7376415034892917, 0.058664457233741, -0.6891520153668161, -1.4864645462843686, -2.3115628416660163, -3.1409990123887086, -3.9502956318646785, -4.714710043730786, -5.4100297905636365, -6.013372231524985, -6.503960553274033, -6.863848512896278, -7.078567405950342, -7.13767091070021, -7.035156566089273, -6.769746603188611, -6.34501553967457, -5.769357205116766, -5.055789506393354, -4.221601062979688, -3.287849624920996, -2.2787277120588865, -1.220815966444495, -0.142249089168704, 0.9281772419091487, 1.9619275565227696, 2.9316435603546864, 3.8120243610526976, 4.580638438415098, 5.218638060113571, 5.7113501945823115, 6.04872234583026, 6.225606976038253, 6.241874098982706, 6.102347998649709, 5.8165706092669165, 5.398400629546772, 4.865463677265076, 4.238474470796025, 3.5404569209461685, 2.7958919268466014, 2.029825428438372, 1.266970754487219, 0.5308394486600858, -0.15706645942821396, -0.7779703070125693, -1.316418105574734, -1.7607354762108582, -2.103328117753729, -2.340816101821794, -2.473999075724015, -2.507656358481853, -2.4501926497455964, -2.3131463532042225, -2.11058307897185, -1.8584014953716732, -1.5735821503309735, -1.2734120249204852, -0.9747183200896372, -0.693144275882333, -0.4424977060343247, -0.23419948729356474, -0.07685461818247351, 0.024037144710752276, 0.0662204096318605, 0.05066917310716274, -0.01857915114558356, -0.13473078075485745, -0.2886674187891816, -0.4694810319328285, -0.6650850634962283, -0.8628721994165696, -1.050386787963073, -1.2159794702737776, -1.3494125413024058, -1.442386992648333, -1.4889659855411388, -1.4858744954424978, -1.432660833800519, -1.3317124146394361, -1.1881251858332693, -1.0094332576485743, -0.8052120986837984, -0.5865749052016397, -0.36558708226907755, -0.1546279415204346, 0.034268489711679076, 0.19006038737009132], 'positive_zeros': ['1.14037220585578311664133561774259', '2.28411736587091172824019237618931', '3.56984457303778247217196761589267', '4.30091462727367112306503724482086', '5.20725043161734134037000453509660', '5.93622471832302949160875645891897', '6.20545877091659162545689375239713', '7.25251042351175463691371907291731', '7.972573588764912874047333041867701'], 'prelabel': '2-2450-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.023089433006167, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14037220585578311664133561774', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28411736587091172824019237619', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56984457303778247217196761589', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 144.55467951406456, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 2450, 'conductor_radical': 70, 'degree': 2, 'index': 134, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2450/4/a/bx/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-2450-1.1-c3-0-134', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-2450-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.023089433006167, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14037220585578311664133561774', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1445593511236673447306199683700', 'Lhash_array': ['1445593511236673447306199683700'], 'label': '2-2450-1.1-c3-0-134', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2450/4/a/bx/1/1'}