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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 0, 'Lhash': '955989422685251105', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 925.6258602306826, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [7, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '115920.1', 'coefficient_field': '1.1.1.1', 'conductor': 115920, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, 1], [1, -4, 11], [1, -6, 13], [1, -6, 17], [1, 6, 19], [1, 1], [1, -2, 29], [1, -8, 31], [1, 8, 37], [1, -10, 41], [1, -4, 43], [1, 12, 47], [1, -6, 53], [1, -10, 59], [1, -6, 61], [1, -12, 67], [1, 2, 71], [1, -6, 73], [1, -2, 79], [1, -4, 83], [1, -14, 89], [1, -4, 97]], 'gamma_factors': [[], [0]], 'index': 76, 'label': '2-115920-1.1-c1-0-76', 'leading_term': '4.33802371818', '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/115920/dt', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.338023718175037, 3.604945904295018, 1.793395890621101, 0.03770583390206725, -0.3643742908854409, 0.7673739454911642, 1.914907749441531, 1.289967388357959, -0.8538238146677392, -2.013329645466152, -0.3378388972379178, 2.673240887037818, 3.666715900689513, 1.793102699235176, -0.0701775877475772, 0.4863627528682187, 1.665054235202083, 0.240622877353791, -2.875100377628331, -3.271585805926761, 0.2276575259682764, 3.202481497749885, 2.053170730655412, -0.7247028043371915, -1.032070319505979, 0.223443719935188, -0.2057272211698173, -1.061232123161814, 1.329532427098646, 5.177400569522498, 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0.8713314684418367, -4.643266752159925, -3.699354075606175, -0.08113546919896476, -0.3752179244221126, -0.6135844979653033, 1.162949323909828, -1.070330523023125, -5.459112303044928, -3.889411977751981, 0.3518162786342712, 0.006824349602937265, -0.962350771434826, 0.5343076941062473, -1.502065976760837, -5.505142912363761, -2.774788616599439, 2.573667859126839, 1.326157590304114, -1.539697557014183, 0.4038725863872314, 1.417176585468794, -0.8011086002405156, -0.5895579228779129, 0.2765005958494838, -1.412597129735799, 1.162544611419803, 8.367552380655958, 8.53190028254336, 1.634882805953327, -0.9520248483496709, 0.0973964530474508, -1.234607022728518, -0.786339727417569, 1.692437518549016, -1.513504279156972, -6.437781495147399, -4.066238782548779, -0.01919825465940079, -0.61691181070185, -0.3997669129492818], 'positive_zeros': ['0.7576964701976165', '1.109775334910532', '1.905733958578325', '2.528525433227388', '3.479456133453510', '3.651948062980905', '4.270245953788664', '4.986510960692274', '5.672478529571531', '6.191633440357163', '6.458757216977368', '6.906592308591180', '7.740152611650026', '8.346472212515611', '8.633343127073512', '9.139059345831409', '9.809774931664962', '10.10243587354054', '10.66142376101919', '11.18202813117249', '11.68106932294607', '12.18564665405070', '12.65214539278725', '13.13981526772653', '13.59987393310650', '14.14980660704638', '14.45575055596559', '14.86529421343013', '15.65684076429085', '15.92857319904299', '16.41991206766158', '16.92919586310812', '17.24471527271422', '17.87447657497563', '18.07645837031607', '18.94274303775977', '19.17384663236574', '19.36084031072290'], 'prelabel': '2-115920-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.424099990479302, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 955989422685251105, 'z1': {'__RealLiteral__': 0, 'data': '0.7576964701976165', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.109775334910532', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.905733958578325', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 925.6258602306826, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 115920, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 4, 0, 6, 0, 0, 0, 6, 0, -6, 0, 0, 0, -1, 0, 1, 0, 0, 0, 2, 0, 8, 0, 0, 0, -1, 0, -8, 0, 0, 0, 10, 0, 4, 0, 0, 0, -12, 0, 1, 0, 0, 0, 6, 0, 4, 0, 0, 0, 10, 0, 6, 0, 0, 0, 6, 0, 12, 0, 0, 0, -2, 0, 6, 0, 0, 0, -4, 0, 2, 0, 0, 0, 4, 0, 6, 0, 0, 0, 14, 0, -6, 0, 0, 0, -6, 0, 4, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, -6, 13], 'euler17': [1, -6, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 8, 37], 'euler41': [1, -10, 41], 'euler43': [1, -4, 43], 'euler47': [1, 12, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -10, 59], 'euler61': [1, -6, 61], 'euler67': [1, -12, 67], 'euler7': [1, 1, 0], 'euler71': [1, 2, 71], 'euler73': [1, -6, 73], 'euler79': [1, -2, 79], 'euler83': [1, -4, 83], 'euler89': [1, -14, 89], 'euler97': [1, -4, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -4, 11], [1, -6, 13], [1, -6, 17], [1, 6, 19], [1, 1, 0], [1, -2, 29], [1, -8, 31], [1, 8, 37], [1, -10, 41], [1, -4, 43], [1, 12, 47], [1, -6, 53], [1, -10, 59], [1, -6, 61], [1, -12, 67], [1, 2, 71], [1, -6, 73], [1, -2, 79], [1, -4, 83], [1, -14, 89], [1, -4, 97]], 'index': 76, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/115920/dt'], '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': '2-115920-1.1-c1-0-76', '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': '2-115920-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.424099990479302, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 955989422685251105, 'z1': {'__RealLiteral__': 0, 'data': '0.7576964701976165', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '955989422685251105', 'Lhash_array': ['955989422685251105'], 'label': '2-115920-1.1-c1-0-76', 'type': 'ECQ', 'url': 'EllipticCurve/Q/115920/dt'}