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lfunc_lfunctions • Show schema
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{'A10': -3, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 3, 'A6': 0, 'A7': 4, 'A8': -1, 'A9': 0, 'Lhash': '1602448177265215929', 'a10': [-0.9486832980505138, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 156.52275804211388, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [11, [1]]], 'bad_primes': [2, 3, 11], 'central_character': '19602.1', 'coefficient_field': '1.1.1.1', 'conductor': 19602, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -3, 5], [1, -4, 7], [1], [1, -1, 13], [1, 3, 17], [1, -4, 19], [1, 0, 23], [1, -9, 29], [1, 4, 31], [1, 1, 37], [1, -6, 41], [1, 8, 43], [1, -12, 47], [1, -6, 53], [1, 0, 59], [1, -1, 61], [1, 4, 67], [1, -12, 71], [1, 11, 73], [1, -16, 79], [1, 12, 83], [1, -3, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 14, 'label': '2-19602-1.1-c1-0-14', 'leading_term': '3.06059349218', '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/19602/p', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.060593492178062, 2.731980605648167, 1.808344835621884, 0.5699870243182527, -0.430244297632064, -0.6506217323614815, -0.0579429552485296, 0.6698422827411843, 0.6428289552126958, -0.2855824606562928, -1.03523406851502, -0.08646265583634918, 2.849023353446232, 5.904437151885611, 6.265753786245535, 2.85222096593647, -2.149683210904273, -4.919194941916895, -3.616169761492208, -0.2479518408824744, 1.500871845171858, 0.2971206435344766, -1.564284395362903, -1.235134326948776, 0.9908591668445863, 2.078686737317467, 0.3357692761651244, -2.181653200467143, -2.300254951254755, 0.007892978358657501, 1.571808677669097, 0.3529246102546026, -1.848540723459967, -2.11632569608409, -0.5778956885959164, 0.08959988910257705, -1.067728442767469, -1.857514738067523, -0.5881185321407812, 1.038629312550637, 0.5772793795519794, -1.12265033655222, -1.226069369023192, 0.2996258952446599, 0.4510586318946947, -1.595119628492237, -2.48782181633714, -0.1216722101688591, 1.971143327456635, -0.5727651538431664, -5.507810790135199, -6.184323212219409, -1.20171591976272, 3.263213529475868, 2.510004864163551, -0.2706674589704444, -0.1225105138331137, 1.494657726578176, 0.03747609725807174, -3.402326471353322, -3.413684714360912, 0.2985264096776134, 1.752006457206366, -1.613728752399437, -4.611424654302961, -2.73068733342612, 0.8770566933320296, 1.142370310528362, -0.977021615970853, -1.436980079988341, -0.2182329975934088, 0.08612119555608116, -0.1738940320445828, 0.6324910593844881, 0.7107975328927877, -2.027340126647383, -4.291481230527254, -1.632208612786336, 3.323353380019224, 4.152439468705469, 0.9895668018671756, -0.2720368830296758, 1.556227900420179, 1.912510404350165, -0.0689953600403525, -0.3052375613523643, 1.297157975077264, 0.4853938634426864, -1.422968350171569, 1.900590000162344, 8.87724139881646, 9.388564939008987, 1.185800863852889, -4.921807072109844, -1.857130519136384, 3.36917811109411, 2.804466406183314, -0.2292592401079605, 0.1128932717234715, 1.639815634773367, 0.6582750989578445, -0.1993657588455205, 1.432801474435102, 1.846153543811176, -1.02682100718481, -2.669211594406488, -0.643706856050094, 0.7766048953403442, -0.4628816559130703, -0.304397553621246, 2.286805322545596, 2.589234785797195, -0.1479631510839752, -0.921273208201379, 0.9073262792725337, 0.8013818486935348, -0.9286441705233561, 0.02806982522142261, 1.976240057168585, 0.2761352379898761, -2.220990417199674], 'positive_zeros': ['0.8750453045688398', '1.517564371792932', '2.185309175637112', '2.760204378497833', '3.889926445567422', '4.770552288191000', '5.284501482580921', '5.895166097956818', '6.530276199961455', '7.249223268602146', '7.787703194398690', '8.621262346420856', '8.789334258951279', '9.574239749431673', '10.08356491436524', '10.69970379187588', '11.07123165171086', '11.75953436967111', '12.21868497845610', '13.05096012380496', '13.71568821122412', '14.01733397890492', '14.50284837301708', '15.23016556917662', '15.65597630587806', '16.42546499803126', '16.88520180250543', '17.56178615562416', '17.80315226656564', '18.08972423029584', '18.59062325967232', '19.32810501154639'], 'prelabel': '2-19602-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.510905564431132, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1602448177265215929, 'z1': {'__RealLiteral__': 0, 'data': '0.8750453045688398', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.517564371792932', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.185309175637112', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 156.52275804211388, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 19602, 'conductor_radical': 66, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 3, 0, 4, -1, 0, -3, 0, 0, 1, -4, 0, 1, -3, 0, 4, 3, 0, 0, 0, 0, 4, -1, 0, 4, 9, 0, -4, -1, 0, 3, 12, 0, -1, -4, 0, -3, 6, 0, -8, 0, 0, 0, 12, 0, 9, -4, 0, 1, 6, 0, 0, -4, 0, -9, 0, 0, 1, 4, 0, 1, 3, 0, -4, -3, 0, -12, 12, 0, -11, 1, 0, 4, 0, 0, 16, 3, 0, -6, -12, 0, -9, 8, 0, 0, 3, 0, 4, 0, 0, -12, 12, 0, 2, -9, 0, 4], 'euler11': [1, 0, 0], 'euler13': [1, -1, 13], 'euler17': [1, 3, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -9, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 1, 37], 'euler41': [1, -6, 41], 'euler43': [1, 8, 43], 'euler47': [1, -12, 47], 'euler5': [1, -3, 5], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -1, 61], 'euler67': [1, 4, 67], 'euler7': [1, -4, 7], 'euler71': [1, -12, 71], 'euler73': [1, 11, 73], 'euler79': [1, -16, 79], 'euler83': [1, 12, 83], 'euler89': [1, -3, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -3, 5], [1, -4, 7], [1, 0, 0], [1, -1, 13], [1, 3, 17], [1, -4, 19], [1, 0, 23], [1, -9, 29], [1, 4, 31], [1, 1, 37], [1, -6, 41], [1, 8, 43], [1, -12, 47], [1, -6, 53], [1, 0, 59], [1, -1, 61], [1, 4, 67], [1, -12, 71], [1, 11, 73], [1, -16, 79], [1, 12, 83], [1, -3, 89], [1, -2, 97]], 'index': 14, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/19602/p'], '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': '2-19602-1.1-c1-0-14', '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': '2-19602-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.510905564431132, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1602448177265215929, 'z1': {'__RealLiteral__': 0, 'data': '0.8750453045688398', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1602448177265215929', 'Lhash_array': ['1602448177265215929'], 'factors': ['2-19602-1.1-c1-0-14'], 'label': '2-19602-1.1-c1-0-14', 'type': 'ECQ', 'url': 'EllipticCurve/Q/19602/p'}