-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '318912376491701537667979273909', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.6016791318831545, 0], 'a4': [0, 0], 'a5': [0, 1.0], 'a6': [0, 0], 'a7': [0, 2.768734305276283], 'a8': [0, 0], 'a9': [3.768734305276283, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.304441810213165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [0.1670551733931289, -3.6016791318831545]]]], 'bad_primes': [2, 5, 13], 'central_character': '1040.961', 'coefficient_field': 'CDF', 'conductor': 1040, 'conductor_radical': 130, 'conjugate': '2155899747951236760336249843499', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.6016791318831545, 0], [3.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -2.768734305276283], [-7.0, 0]], [[1.0, 0], [0, -2.1670551733931287], [-11.0, 0]], [[1.0, 0], [0.1670551733931289, -3.6016791318831545]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [0, 5.036303090373179], [-19.0, 0]], [[1.0, 0], [-4.935789478669412, 0], [23.0, 0]], [[1.0, 0], [4.434623958490025, 0], [29.0, 0]], [[1.0, 0], [0, -3.370413437159437], [-31.0, 0]], [[1.0, 0], [0, -3.9720925690425917], [-37.0, 0]], [[1.0, 0], [0, 1.6658896532137422], [-41.0, 0]], [[1.0, 0], [9.805037395649462, 0], [43.0, 0]], [[1.0, 0], [0, -11.637982222256333], [-47.0, 0]], [[1.0, 0], [12.740826874318875, 0], [53.0, 0]], [[1.0, 0], [0, 8.167055173393129], [-59.0, 0]], [[1.0, 0], [10.30620291582885, 0], [61.0, 0]], [[1.0, 0], [0, -7.102844652062541], [-67.0, 0]], [[1.0, 0], [0, 16.111240311478312], [-71.0, 0]], [[1.0, 0], [0, 15.97209256904259], [-73.0, 0]], [[1.0, 0], [11.944185138085183, 0], [79.0, 0]], [[1.0, 0], [0, -3.9720925690425917], [-83.0, 0]], [[1.0, 0], [0, -7.944185138085183], [-89.0, 0]], [[1.0, 0], [0, -0.4625313894474337], [-97.0, 0]], [[1.0, 0], [-12.740826874318875, 0], [101.0, 0]], [[1.0, 0], [-4.13914774243572, 0], [103.0, 0]], [[1.0, 0], [7.064210521330588, 0], [107.0, 0]], [[1.0, 0], [0, -14.86924791698005], [-109.0, 0]], [[1.0, 0], [-3.1307520830199493, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-1040-13.12-c1-0-1', 'leading_term': '0.4192094316064049940363081961152398117866966511181671000', '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/1040/2/k/c/961/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.419209431606405, 0.31874598078698624, 0.21987085620706082, 0.12272233788394141, 0.027528318831230355, -0.06534877667919019, -0.15537477486742224, -0.24181594249948338, -0.32372158046983757, -0.39991738081064404, -0.4690094150423058, -0.5293982907798047, -0.5793028232407249, -0.6167924773886845, -0.6398277984986765, -0.6463080237997018, -0.6341250271503214, -0.6012226767761405, -0.5456605782767248, -0.4656810349144093, -0.35977789353373457, -0.2267657693108779, -0.06584796927807515, 0.12331872314671935, 0.3405643693960778, 0.5851533575952096, 0.8557411360677376, 1.150342264596998, 1.4663117559026615, 1.800341512123974, 2.148473416395322, 2.506130317468786, 2.86816574821674, 3.2289327521529314, 3.582371664332294, 3.9221161156889295, 4.241615917576734, 4.534274853263039, 4.793600775069617, 5.013364801366007, 5.187765849642965, 5.311596254003329, 5.3804038209987874, 5.390645399143633, 5.339826894977304, 5.226624679592122, 5.0509835075562135, 4.814186423822846, 4.518892666632807, 4.169140282472292, 3.770311043043906, 3.3290562772037107, 2.85318337923395, 2.3515039983122845, 1.833646216150309, 1.3098343388009928, 0.7906412187616538, 0.286719236212917, -0.19148284603100754, -0.6340090293123609, -1.031682414934662, -1.3763794911326572, -1.6612830057562284, -1.8811042549118282, -2.0322661521559375, -2.1130393193506234, -2.1236246495546927, -2.066177311360482, -1.9447689562358697, -1.7652869057744567, -1.5352712721240651, -1.2636932294302698, -0.9606799255830824, -0.6371937147736179, -0.30467541256977465, 0.025336962556621483, 0.3416010784978671, 0.6335609274837909, 0.8917208148264348, 1.1079883165905309, 1.2759724021554022, 1.3912240657975012, 1.4514085156292107, 1.456400190310683, 1.4082945519277559, 1.311333652591051, 1.1717457873642565, 0.997503004381339, 0.7980037085394617, 0.5836909238283605, 0.3656198245676356, 0.15499076469046347, -0.037333905960884206, -0.2013095646661532, -0.32816528834549524, -0.41081600327839957, -0.4442118234983684, -0.42560753568271414, -0.3547379555949822, -0.23388838916541618, -0.06785356295934253, 0.1362170069813337, 0.369084342235303, 0.6197881728212499, 0.8761052404300662, 1.1250805139164988, 1.353610156813761, 1.5490519192901806, 1.6998364116532834, 1.7960515982431773, 1.8299729315545414, 1.7965128790705955, 1.6935661770696118, 1.5222309163873422, 1.286890406717284, 0.9951465050699885, 0.6576015069721415, 0.2874925202061387, -0.09981082704608654, -0.4874277656078489, -0.8576830759019712, -1.1928899551690326, -1.476165695780325, -1.692243952512046, -1.8282460877470892, -1.8743744901001897, -1.8244929167713175, -1.6765627849219256, -1.4329098210652906, -1.1003023765507114, -0.6898307621648857, -0.21658580954859172, 0.3008558578035334, 0.8411230916436262, 1.3808924511001925, 1.8958478944586725, 2.3617177956339472, 2.7553441909343976, 3.05573617285311, 3.2450585451378386, 3.3095083542627046, 3.240035724956541, 3.032871446479161, 2.689831763996968, 2.2183805015645404, 1.6314395616346238, 0.9469505157887865, 0.18720187298584248, -0.6220518933203741, -1.4526429383334711, -2.2751686047117317, -3.060243256691174, -3.779766068842931, -4.408145522051835, -4.9234223065587575, -5.308236182334311, -5.550588982459517, -5.644365101260809, -5.589582084196537, -5.392356808777278, -5.064586595789721, -4.623358730693074, -4.090115585470564, -3.4896150939510506, -2.848737072558673, -2.1951941960209185, -1.5562118488646444, -0.9572432355259531, -0.4207848659083529, 0.034647160815702384, 0.3953275898700817, 0.6528774983100281, 0.8045363488194478, 0.8531369882936666, 0.8067857517742487, 0.6782656900609003, 0.4841960090755808, 0.2439942514036218, -0.02130120256030594, -0.2902827366576149, -0.542429170840543, -0.7592948660438634, -0.925564974004788, -1.0299167241153482, -1.0656373107389991, -1.030962561384385, -0.9291164035393668, -0.7680483380338662, -0.5598837052881063, -0.3201184901097682, -0.06660575694308671, 0.1816063816049735, 0.4055158797420941, 0.5874120424827352, 0.7120488833424924, 0.7676737850013154, 0.7468464153348581, 0.6469946037786651, 0.47066904860145414, 0.2254764707337853, -0.07630985265556328, -0.41844347663269743, -0.7816643674018428, -1.1448698022598558, -1.4864275580622133, -1.7855520938806266, -2.023658787929809, -2.185610713434497, -2.260777091661984, -2.243832288731345, -2.1352385597877626, -1.941373931065409, -1.674287634264321, -1.3510881557859473, -0.9929918915388805, -0.6240822089781014, -0.269848045254275, 0.04441323758739832, 0.29523321904627225, 0.46254926980229416, 0.5311209829246292, 0.4916932878762606, 0.3418262541018417, 0.08632976639566287, -0.2627362741383848, -0.6865100656926365, -1.1602111276198244, -1.6544184359933114, -2.1366780253327984, -2.5733526755184823, -2.931609122233273, -3.1814269768331815, -3.297509057684192, -3.2609755642293443, -3.0607344783915753, -2.6944373212800246, -2.168952063135019, -1.5003123312951891, -0.7131325169064702, 0.16048984988993228, 1.0825319222972511, 2.010982386288901, 2.9020518665037387, 3.7125330325226455, 4.402175323355107, 4.935935967109684, 5.285974063552902, 5.433267754724104, 5.368755256801216, 5.0939276097926465, 4.620832849455767, 3.9714860225965425, 3.1767149460955935, 2.2745056635582146, 1.3079420489357478, 0.3228590032984212, -0.634653432736363], 'positive_zeros': ['0.25157750600542780009122957912222', '1.31047403035555371636557785297459', '3.37451461165066725031040200520657', '4.38997021838414185833428904590252', '5.37864346065838155300787139110721', '5.87997788749276626716052060160922', '6.89907174082525367433432522481963', '7.70078450015180593900362688274177', '8.627084910889388566118439330891223', '9.897438732319476880749305858722884'], 'prelabel': '2-1040-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.881742842484937, 'root_angle': -0.9852465398397637, 'root_number': '-0.998926060597949270803022899660267379484404926049750150006 - 0.0463327687308041339350649725345606290691265202696280814*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.49262326991988187', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25157750600542780009122957912', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.31047403035555371636557785297', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37451461165066725031040200521', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.304441810213165, 'bad_primes': [2, 5, 13], 'central_character': '13.12', 'conductor': 1040, 'conductor_radical': 130, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1040/2/k/c/961/2'], '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': '2-1040-13.12-c1-0-1', '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': '2-1040-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.881742842484937, 'root_angle': -0.49262326991988187, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.25157750600542780009122957912', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '318912376491701537667979273909', 'Lhash_array': ['318912376491701537667979273909'], 'label': '2-1040-13.12-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1040/2/k/c/961/2'}