-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '613129829126229871310311844126', 'a10': [70.42533913271853, 0.0], 'a2': [-4.108506877617775, 0.0], 'a3': [3.0, 0.0], 'a4': [8.87982876343256, 0.0], 'a5': [-17.14134629209945, 0.0], 'a6': [-12.325520632853324, 0.0], 'a7': [-4.949502709480102, 0.0], 'a8': [-3.614782525688614, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 93.6360311791104, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [23, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 23], 'central_character': '1587.1', 'coefficient_field': 'CDF', 'conductor': 1587, 'conductor_radical': 69, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.108506877617775, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [17.14134629209945, 0], [125.0, 0]], [[1.0, 0], [4.949502709480102, 0], [343.0, 0]], [[1.0, 0], [3.963140970355203, 0], [1331.0, 0]], [[1.0, 0], [-87.89815201301306, 0], [2197.0, 0]], [[1.0, 0], [129.4386651859432, 0], [4913.0, 0]], [[1.0, 0], [-37.74441416662778, 0], [6859.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.2043772904877805, 0], [24389.0, 0]], [[1.0, 0], [-134.07663078428172, 0], [29791.0, 0]], [[1.0, 0], [278.6188065978736, 0], [50653.0, 0]], [[1.0, 0], [-201.73991290555, 0], [68921.0, 0]], [[1.0, 0], [-505.04818581708247, 0], [79507.0, 0]], [[1.0, 0], [276.80488142338197, 0], [103823.0, 0]], [[1.0, 0], [228.28420264236553, 0], [148877.0, 0]], [[1.0, 0], [147.37136752022565, 0], [205379.0, 0]], [[1.0, 0], [518.2560701175155, 0], [226981.0, 0]], [[1.0, 0], [207.70902095759533, 0], [300763.0, 0]], [[1.0, 0], [-757.1598523806041, 0], [357911.0, 0]], [[1.0, 0], [259.21320057373265, 0], [389017.0, 0]], [[1.0, 0], [174.04454748748918, 0], [493039.0, 0]], [[1.0, 0], [136.93328534843397, 0], [571787.0, 0]], [[1.0, 0], [1028.0435354472204, 0], [704969.0, 0]], [[1.0, 0], [1145.7466373878417, 0], [912673.0, 0]], [[1.0, 0], [1343.1760451592172, 0], [1030301.0, 0]], [[1.0, 0], [-1732.0244679564692, 0], [1092727.0, 0]], [[1.0, 0], [-2078.944501650903, 0], [1225043.0, 0]], [[1.0, 0], [422.8804368622176, 0], [1295029.0, 0]], [[1.0, 0], [-244.4560992284618, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 41, 'label': '2-1587-1.1-c3-0-41', 'leading_term': '0.62861121344747192872663595193167', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1587/4/a/o/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.628611213447472, 0.6207385861148236, 0.5972495237130612, 0.5585296218302098, 0.5052186274499607, 0.43820595007378876, 0.35862414399134135, 0.26784014550932744, 0.1674440108434221, 0.05923487869540932, -0.05479612145959267, -0.17248627712818573, -0.2915252401445572, -0.40948267800360494, -0.5238397142968368, -0.6320241455333061, -0.7314493075280183, -0.8195563371064725, -0.893859437612201, -0.9519936136113768, -0.9917641956633519, -1.011197334772587, -1.0085905130630768, -0.9825619973221097, -0.9320980603243684, -0.8565967161020528, -0.7559066641273803, -0.6303601178634766, -0.4807982089094957, -0.30858771191489615, -0.1156279296360551, 0.09565328693353778, 0.3223152314768263, 0.5609323792268779, 0.8076351436657361, 1.0581634397150987, 1.3079328217644555, 1.552112623762394, 1.7857151722387143, 2.003694780220297, 2.2010548702232944, 2.37296122830234, 2.5148590695118513, 2.62259130934712, 2.6925151969953465, 2.7216142853577283, 2.7076025998662865, 2.6490178320483366, 2.545300432022834, 2.396855612223902, 2.205095506025521, 1.9724590504928794, 1.7024075803928427, 1.3993946261430672, 1.0688089938548613, 0.7168908603091679, 0.3506213259527384, -0.02241338157502899, -0.39418109111958394, -0.7563835274559307, -1.1006533289703506, -1.4187640665385757, -1.7028484574880864, -1.945619433388892, -2.140588301562903, -2.282273958081839, -2.36639698238161, -2.3900524847423497, -2.3518557978907055, -2.2520555082141067, -2.092608910580822, -1.877215737908798, -1.6113069509055906, -1.3019864573653528, -0.9579248408303683, -0.5892054866477142, -0.20712486594372012, 0.17604986285551733, 0.5473613904480336, 0.8934750587680305, 1.201016829647228, 1.4569282380544142, 1.648829250368083, 1.765379273590255, 1.796626142780043, 1.734332777917058, 1.572271367051905, 1.3064754105612182, 0.9354407527937699, 0.46026782358904056, -0.11526130596567256, -0.7846758108290941, -1.5388818438513474, -2.366301988471718, -3.2530871698920323, -4.183397572572656, -5.139746938093457, -6.1034025293365035, -7.054831114790585, -7.974179618871844, -8.841777664526463, -9.638648160376277, -10.347011404678966, -10.95076792976355, -11.4359455179106, -11.791096493164092, -12.007632528331177, -12.0800857817388, -12.006287157745353, -11.787454816999373, -11.428188681480759, -10.936369507690294, -10.322964051193885, -9.601740821981563, -8.78890383342768, -7.902654477818201, -6.962694120883983, -5.989682105237343, -5.004665506506985, -4.028498127814418, -3.0812667955477058, -2.1817429981529983, -1.3468772762216477, -0.5913525343883596, 0.07278936665988738, 0.6364357149661078, 1.093596512104842, 1.4414974084490573, 1.6805693216496829, 1.8143355905630738, 1.8492010676274782, 1.794150985335652, 1.6603706189058778, 1.4607995856994542, 1.2096369616522413, 0.9218151609412155, 0.6124616420421364, 0.29636791925207967, -0.012514952439097287, -0.30153628800908294, -0.5597446799959782, -0.7782118750378767, -0.9502705161544012, -1.0716580190101732, -1.1405625411484497, -1.1575708706599834, -1.1255219525686202, -1.0492735311312213, -0.9353928604705671, -0.7917854795155129, -0.6272785301641111, -0.4511769107354694, -0.2728116167745591, -0.10109987468228805, 0.05586390009758679, 0.19116867552142855, 0.29938341257272305, 0.3767770522090051, 0.421452622542274, 0.4333900414630423, 0.41439629079143836, 0.36796583174976616, 0.29905823485964994, 0.21380382736292056, 0.11915154340646648, 0.0224759382426812, -0.06883763702156034, -0.1478095133995914, -0.20826337158521338, -0.24518530239503752, -0.2550260597704241, -0.23593077698188145, -0.18788366579585772, -0.11275911141877962, -0.014274946129258753, 0.10215166119785885, 0.2296405346558143, 0.36016729292393757, 0.48495065781508273, 0.5948906572914711, 0.6810372195493788, 0.735066675484306, 0.7497427359754024, 0.7193386596929056, 0.6399985985412009, 0.5100184711891983, 0.3300300878289921, 0.10307649869348846, -0.1654285130501816, -0.46785844299499507, -0.7946455636833891, -1.134656251837331, -1.4756551465455603, -1.8048383635350622, -2.109412024109122, -2.377189416426813, -2.597178364661133, -2.7601299594622626, -2.85902076297943, -2.889442941128774, -2.8498804262643667, -2.7418540411996357, -2.569924326021283, -2.3415473541233176, -2.066785811667309, -1.7578847226090335, -1.4287280903993467, -1.0941990576030751, -0.7694716316906344, -0.4692662965475609, -0.20710467907383584, 0.005400316865222342, 0.15918297514855603, 0.24825813128181784, 0.2701196782183428, 0.2259799743899459, 0.12083279399740496, -0.0366695842393281, -0.23452586863442526, -0.45787352560066813, -0.6896375991409871, -0.9113149403697629, -1.1038607473580686, -1.2486381918322154, -1.328387463115474, -1.3281680616679847, -1.2362278101514772, -1.0447539078830799, -0.750465419402855, -0.35501273736602973, 0.1348424326181997, 0.7072834757538439, 1.3457379025199692, 2.0294139358193766, 2.7340581224657736, 3.432906404088577, 4.097791000759213, 4.70035684545269, 5.213334615751225, 5.611813019216861, 5.874451179538822, 5.984572905072417, 5.931088335846713, 5.709194863145665, 5.320818069336451, 4.774764392358597, 4.086569816054125, 3.278042569755446, 2.376511966647931, 1.413809460042969, 0.4250210817264087, -0.5529379966986864, -1.482866557490889, -2.328870979327508, -3.05793842388514, -3.641417902563725, -4.0563402444851455], 'positive_zeros': ['0.48367415202252198600685883877089', '1.55172934809755235616672184031299', '2.89148636731390881043642962702944', '3.88673500995973002134932193986546', '4.56079381207717773147320973032362', '6.29092319620870334919138608469105', '7.00570352507590956559711068259618', '7.80153223136463856505364955720552', '8.390984706901342935855393838071981', '8.842548667066658322524408808473174'], 'prelabel': '2-1587-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.676571251177268, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48367415202252198600685883877', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.55172934809755235616672184031', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89148636731390881043642962703', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 93.6360311791104, 'bad_primes': [3, 23], 'central_character': '1.1', 'conductor': 1587, 'conductor_radical': 69, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1587/4/a/o/1/2'], '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': '2-1587-1.1-c3-0-41', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1587-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.676571251177268, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48367415202252198600685883877', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '613129829126229871310311844126', 'Lhash_array': ['613129829126229871310311844126'], 'factors': ['2-1587-1.1-c3-0-41'], 'label': '2-1587-1.1-c3-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1587/4/a/o/1/2'}