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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '161282477717238675', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1721.574667578806, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]], [11, [1, -1]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '215600.1', 'coefficient_field': '1.1.1.1', 'conductor': 215600, 'conductor_radical': 770, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1], [1], [1, -1], [1, -2, 13], [1, 6, 17], [1, -2, 19], [1, 6, 23], [1, 0, 29], [1, -8, 31], [1, -4, 37], [1, 12, 41], [1, 4, 43], [1, 12, 47], [1, 0, 53], [1, 0, 59], [1, 2, 61], [1, -8, 67], [1, 12, 71], [1, -2, 73], [1, 14, 79], [1, 12, 83], [1, 6, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 35, 'label': '2-215600-1.1-c1-0-35', 'leading_term': '2.28457630375', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/215600/ho', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.284576303751983, 1.139610748165888, -1.604737185031078, -4.043171812059463, -4.195049954154691, -1.979878976047754, 0.3070573058874019, 0.431059117112941, -1.007521190743454, -1.4025334797845, 0.08052587806823455, 1.231693828211247, 0.3496683830193115, -0.8047682214580257, 0.108577584247319, 1.687683535833755, 0.8922742987322226, -1.224704160692192, -0.644793286347875, 2.13271733112799, 1.508454647232712, -3.839374346279605, -7.232818393146611, -4.115578281811464, 0.2920634224905692, -0.2933770972621002, -2.857560246677235, -1.456456617304137, 1.589975774172763, 0.4387403097182027, -3.025366906161463, -2.933464240876837, -0.2427925218971281, 0.3605799687770938, -0.2256412794465928, 0.8425620205707207, 1.130821075835874, -1.2909136246803, -2.244659606620219, -0.07440345343628921, 0.001931422177015904, -2.517941149016806, -0.5189212538068679, 5.739230405922085, 6.720236741530671, 1.545256145343927, -0.6149096474754283, 0.558599064051057, -2.981882165091045, -8.681601367983394, -7.010651443422469, -0.7349087442835117, 0.7170643697167804, -1.055225172960866, -0.09763697625034636, 1.067289514869955, -0.01346733174253996, 0.6306394989904569, 2.575565739085034, 1.121923504831376, -0.9101380890477732, 0.734318323085935, 1.517428407731175, -0.5019949559237352, 0.8676923548443524, 3.721790516239865, -0.4815807846644843, -6.553089191325114, -4.174764020989645, 0.02960224908925817, -3.083277240327688, -5.611467640955139, -1.383813318489356, 0.892841891234348, -1.214735712319388, 0.5456085963033322, 4.376335508848682, 2.853990248276142, -0.00945788849330691, 0.6019401281346842, 0.6588679743605269, 0.002731030946998038, 1.727250541537745, 1.604474880925616, -1.117197936413416, 0.6422255372239256, 4.110666358703187, 1.640928938330053, -0.314371391559763, 3.551195129985215, 3.641675155993418, -0.7813822957524278, 1.598865104780351, 6.141535368942858, 1.642740809039001, -3.36257704112385, -0.1456323775173208, 2.035387328202571, -0.3662129378260122, 0.1943646370795334, 1.54582486580734, -0.5939891666780145, -0.6409962223129944, 1.455145717706873, 0.2177786515874464, -0.6847286203621809, 0.8664550048320125, 0.07355345350870314, 0.6749073715429565, 5.602770961198663, 4.883810676300384, -1.076461231170027, 0.2501256679848807, 4.150715893582669, 0.9274438325798764, -0.3845053593889218, 2.897455857685653, -1.229013600946178, -7.802625586770148, -4.478481995618166, 0.2271199140519344], 'positive_zeros': ['0.3634785447444082', '1.452563236194468', '1.834173605975854', '2.488930889231368', '3.056104354972018', '3.484855685749981', '4.096761298586483', '4.560081280578665', '5.084953049875918', '5.972165763213458', '6.222547874678279', '6.852319153353786', '7.281009458334523', '8.031281859822501', '8.359958630547078', '8.595182306455428', '9.133764139565962', '9.759133159027958', '10.00022912780551', '10.52302346524287', '11.34478901027772', '11.60983126850380', '11.84441380323384', '12.79319918351607', '13.09318319271983', '13.51203714457603', '13.99643750105500', '14.15564215783657', '14.84810181789139', '15.17461681020119', '15.67953461100248', '15.93299057115354', '16.48355541062375', '17.24103854064564', '17.29387916635583', '18.07797055465606', '18.36245681657768', '18.71709039858160', '19.49766304857331', '19.62120017382201'], 'prelabel': '2-215600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.49186266701949, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 161282477717238675, 'z1': {'__RealLiteral__': 0, 'data': '0.3634785447444082', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.452563236194468', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.834173605975854', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1721.574667578806, 'bad_primes': [2, 5, 7, 11], 'central_character': '1.1', 'conductor': 215600, 'conductor_radical': 770, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, -6, 0, 2, 0, 0, 0, -6, 0, 0, 0, -4, 0, 0, 0, 8, 0, 2, 0, 0, 0, 4, 0, 4, 0, -12, 0, -4, 0, 0, 0, -12, 0, 0, 0, -12, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, -12, 0, -12, 0, 2, 0, 0, 0, 0, 0, -14, 0, -11, 0, -12, 0, 0, 0, 0, 0, -6, 0, 0, 0, 16, 0, 0, 0, 8, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, 0, 29], 'euler3': [1, -2, 3], 'euler31': [1, -8, 31], 'euler37': [1, -4, 37], 'euler41': [1, 12, 41], 'euler43': [1, 4, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, 0, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, -2, 73], 'euler79': [1, 14, 79], 'euler83': [1, 12, 83], 'euler89': [1, 6, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 0, 0], [1, 0, 0], [1, -1, 0], [1, -2, 13], [1, 6, 17], [1, -2, 19], [1, 6, 23], [1, 0, 29], [1, -8, 31], [1, -4, 37], [1, 12, 41], [1, 4, 43], [1, 12, 47], [1, 0, 53], [1, 0, 59], [1, 2, 61], [1, -8, 67], [1, 12, 71], [1, -2, 73], [1, 14, 79], [1, 12, 83], [1, 6, 89], [1, -8, 97]], 'index': 35, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/215600/ho'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-215600-1.1-c1-0-35', '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': '2-215600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.49186266701949, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 161282477717238675, 'z1': {'__RealLiteral__': 0, 'data': '0.3634785447444082', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '161282477717238675', 'Lhash_array': ['161282477717238675'], 'factors': ['2-215600-1.1-c1-0-35'], 'label': '2-215600-1.1-c1-0-35', 'type': 'ECQ', 'url': 'EllipticCurve/Q/215600/ho'}