-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '608248036551574206114822907669', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.739646484782567, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.2935231424704, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '6048.1', 'coefficient_field': 'CDF', 'conductor': 6048, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.739646484782567, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.2453093463640443, 0], [11.0, 0]], [[1.0, 0], [0.45868511740730356, 0], [13.0, 0]], [[1.0, 0], [7.443640948553915, 0], [17.0, 0]], [[1.0, 0], [-4.245309346364044, 0], [19.0, 0]], [[1.0, 0], [4.703994463771347, 0], [23.0, 0]], [[1.0, 0], [1.7396464847825672, 0], [29.0, 0]], [[1.0, 0], [1.7396464847825672, 0], [31.0, 0]], [[1.0, 0], [-2.494337138418523, 0], [37.0, 0]], [[1.0, 0], [4.7396464847825674, 0], [41.0, 0]], [[1.0, 0], [1.9643479789887806, 0], [43.0, 0]], [[1.0, 0], [-9.90232606596122, 0], [47.0, 0]], [[1.0, 0], [-5.423033096396084, 0], [53.0, 0]], [[1.0, 0], [-6.479292969565134, 0], [59.0, 0]], [[1.0, 0], [-5.23398362320109, 0], [61.0, 0]], [[1.0, 0], [2.7752985057937867, 0], [67.0, 0]], [[1.0, 0], [-0.7039944637713477, 0], [71.0, 0]], [[1.0, 0], [7.969911662293223, 0], [73.0, 0]], [[1.0, 0], [6.668342442760128, 0], [79.0, 0]], [[1.0, 0], [-3.505662861581477, 0], [83.0, 0]], [[1.0, 0], [1.7866242289567407, 0], [89.0, 0]], [[1.0, 0], [-13.16267958117865, 0], [97.0, 0]], [[1.0, 0], [2.4906186927280882, 0], [101.0, 0]], [[1.0, 0], [10.381619035526352, 0], [103.0, 0]], [[1.0, 0], [4.0, 0], [107.0, 0]], [[1.0, 0], [-8.494337138418523, 0], [109.0, 0]], [[1.0, 0], [1.7546906536359559, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-6048-1.1-c1-0-8', 'leading_term': '0.90397660228733397345285799032548', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/6048/2/a/bt/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.903976602287334, 0.893774310636401, 0.8631560034860031, 0.8120959463589903, 0.7405791435317405, 0.6486409908368876, 0.5364186438904999, 0.404210455723168, 0.2525394053901397, 0.08221631378595184, -0.10560122155537743, -0.3093579091437392, -0.5270611386724082, -0.7562553883641737, -0.9940128349563039, -1.2369417561468183, -1.4812137326648955, -1.722610073006991, -1.9565872951878087, -2.1783609038286835, -2.3830060978916214, -2.5655734393242544, -2.7212169158457784, -2.8453312568934783, -2.9336948291555305, -2.98261396878772, -2.9890642245669907, -2.9508237132920123, -2.86659364793881, -2.7361011101281396, -2.5601793172659377, -2.3408209922120653, -2.0812009844573907, -1.7856650146635422, -1.4596823097337088, -1.1097609462593965, -0.7433259013410142, -0.3685610889988367, 0.005782001634213971, 0.37060509865097574, 0.7167080873874333, 1.0350515892739014, 1.3170295877884097, 1.5547436229107092, 1.7412694342425867, 1.8709065813681456, 1.9394015441650536, 1.94413513165441, 1.8842657195993975, 1.7608208948545714, 1.5767314941326378, 1.3368037567760944, 1.0476273203599629, 0.7174190149130253, 0.35580478331887055, -0.026455512149913485, -0.41779323700088006, -0.806196655342021, -1.1796056544582627, -1.5263223406442437, -1.8354230287611892, -2.0971563496483703, -2.303311961592939, -2.447544719023921, -2.525640145418927, -2.5357086750475073, -2.478298339964587, -2.3564183278185595, -2.175469039270878, -1.9430778232408847, -1.6688433343823412, -1.3639952935268498, -1.0409801797720488, -0.7129868782903269, -0.39342938791009574, -0.09540620280120536, 0.16884221508495295, 0.3884554769014204, 0.5544323543291092, 0.6600453342631233, 0.7011709176468321, 0.6765187318809465, 0.5877461793581402, 0.4394497399724234, 0.23902902488507405, -0.003574950293301001, -0.27626026285819044, -0.5652508675416609, -0.8556720288308076, -1.132192169804099, -1.379705111900126, -1.5840238917106708, -1.732555730941105, -1.814927430493992, -1.8235315312928122, -1.7539660445838146, -1.6053443505575244, -1.3804568789142762, -1.0857722386721336, -0.7312723202822329, -0.33012326568063166, 0.10180823122347825, 0.5465764159476425, 0.9848919695601691, 1.3969416638585301, 1.7632574419178673, 2.065596749861301, 2.2877941720139088, 2.4165444628000445, 2.4420789914397774, 2.358701397958512, 2.165153788386825, 1.8647918709526272, 1.465555767906943, 0.9797324710559753, 0.4235156268567207, -0.18362191675641454, -0.8197180690938075, -1.461240843215897, -2.084096944382201, -2.6646841733535034, -3.180938999578371, -3.6133297291923254, -3.9457471677769886, -4.166248558237924, -4.267616738762888, -4.247704673647356, -4.109545408057832, -3.8612186360849376, -3.515476921297373, -3.0891465886405896, -2.6023298090604223, -2.0774448224498974, -1.538150026422711, -1.0082043020418, -0.5103200533794967, -0.06506672670799457, 0.3101190923418202, 0.601765517334592, 0.8009950380297692, 0.9039177852812322, 0.9117659786747249, 0.8307604172444407, 0.6717138884716866, 0.4493904052370265, 0.1816524833245224, -0.11155948904375104, -0.40936203681755584, -0.6911167981864685, -0.9376075680232793, -1.1321412243621842, -1.2615107324008732, -1.3167650305601586, -1.293740386874935, -1.1933203071161878, -1.0214056518128927, -0.7885925186628384, -0.509571816704476, -0.20228039712863263, 0.11315178903069258, 0.41560161481564994, 0.6842334049199754, 0.8997879426444633, 1.0458055472031647, 1.109711097634885, 1.0836952124852202, 0.965336016403009, 0.7579195492083296, 0.4704332065151756, 0.11722477751546034, -0.28266132900877305, -0.7064402734319535, -1.1287874887516782, -1.5232208349450231, -1.863589243913811, -2.1255850288037563, -2.288193745828478, -2.3349970898783847, -2.2552508004783065, -2.0446706915585975, -1.705875160395172, -1.2484510893733516, -0.6886309280341789, -0.0485907721628962, 0.644598813576394, 1.3603169314633643, 2.065961201376099, 2.7286568457272633, 3.3170119097483237, 3.8028201766456458, 4.162614634133562, 4.378981320891569, 4.441555730164902, 4.347641049625088, 4.102408453094486, 3.7186632651796288, 3.2161857459058187, 2.620680034925766, 1.9623879789246983, 1.2744447343400083, 0.5910689374904168, -0.05430915405820316, -0.6308735413459174, -1.1120961517029169, -1.4771602031511393, -1.7120492883065352, -1.8102375193071738, -1.772939501416397, -1.60890506916077, -1.3337710668841931, -0.9690093285645572, -0.5405347546871125, -0.07705844638402805, 0.3917131089145513, 0.8369218579353627, 1.232330899336749, 1.5559158893068714, 1.7911757371726402, 1.9280803283224042, 1.963595474758279, 1.9017517377603943, 1.753252573238091, 1.5346466242599732, 1.2671170687223818, 0.9749659177231883, 0.6838914154337518, 0.41917085405096294, 0.20386819621379285, 0.05718533929273091, -0.006932409362562953, 0.019158375144180714, 0.13617626844097613, 0.3377604701663298, 0.6108004810860614, 0.9362339508085943, 1.2902654715550383, 1.6459305548725667, 1.9749050510749182, 2.2494424988575608, 2.4443115905640744, 2.538603905050847, 2.517288564595437, 2.372405228408271, 2.103809009102397, 1.719409153155319, 1.2348759009748735, 0.6728247596898498, 0.061522220486225035, -0.5668105682961688, -1.1779916888102797, -1.7380438815912898, -2.215391927389378, -2.58294783662001, -2.819944601158062, -2.9133934605314318, -2.859062342963571, -2.6619029966274836], 'positive_zeros': ['0.47982309671297790410679821516883', '1.92889648426033721430511828439597', '2.78951034116507858121468846127809', '3.82608333537007061913668484015290', '4.31570696992215995681891220498705', '5.11715136489752782023161574460654', '5.87560489995100177750862077293197', '6.91436579278990664140837084522149', '7.39503012121939899724682770947421', '8.055940450473674886832702337749833'], 'prelabel': '2-6048-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.949354152903016, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47982309671297790410679821517', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92889648426033721430511828440', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.78951034116507858121468846128', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 48.2935231424704, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 6048, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6048/2/a/bt/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': '2-6048-1.1-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6048-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.949354152903016, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.47982309671297790410679821517', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '608248036551574206114822907669', 'Lhash_array': ['608248036551574206114822907669'], 'label': '2-6048-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6048/2/a/bt/1/1'}