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lfunc_lfunctions • Show schema
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{'Lhash': '2423237204835556159458741300766', 'a10': -1, 'a2': 1, 'a3': 2, 'a4': 1, 'a5': -1, 'a6': 2, 'a7': 2, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.11785225802358, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [23, [1, 1]], [131, [1, -1]]], 'bad_primes': [2, 23, 131], 'central_character': '6026.1', 'coefficient_field': '1.1.1.1', 'conductor': 6026, 'conductor_radical': 6026, 'degree': 2, 'euler_factors': [[1, -1], [1, -2, 3], [1, 1, 5], [1, -2, 7], [1, 5, 11], [1, 2, 13], [1, 3, 17], [1, 6, 19], [1, 1], [1, 2, 29], [1, -4, 31], [1, -2, 37], [1, -7, 41], [1, 1, 43], [1, 6, 47], [1, -6, 53], [1, -10, 59], [1, 3, 61], [1, 10, 67], [1, 2, 71], [1, 16, 73], [1, -4, 79], [1, 12, 83], [1, 16, 89], [1, -10, 97], [1, -16, 101], [1, -1, 103], [1, -13, 107], [1, -1, 109], [1, 12, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -2, 3], 1]], [[[1, 1, 5], 1]], [[[1, -2, 7], 1]], [[[1, 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0.04043071353305911, -0.41982742574104337, -0.9424790076697533, -1.50124247303291, -2.068017884866363, -2.6143356693972617, -3.1128151402694013, -3.5385562080859585, -3.870391410890161, -4.091933037335675], 'positive_zeros': ['1.91159709497181123771052394535080', '2.44338517386560553379649909970626', '3.11604157674398979015951476784782', '4.18612527745841938002559454043557', '4.54663950261094573486040620748833', '5.46631210375278095549961792991025', '6.20984871688873478131419909737598', '7.33136092664972074183455072853478', '7.69306586890244365183550821205763'], 'prelabel': '2-6026-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.936703270143792, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1483822298029876412, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91159709497181123771052394535', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44338517386560553379649909971', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11604157674398979015951476785', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.11785225802358, 'bad_primes': [2, 23, 131], 'central_character': '1.1', 'conductor': 6026, 'conductor_radical': 6026, 'degree': 2, 'dirichlet_coefficients': [1, 1, 2, 1, -1, 2, 2, 1, 1, -1, -5, 2, -2, 2, -2, 1, -3, 1, -6, -1, 4, -5, -1, 2, -4, -2, -4, 2, -2, -2, 4, 1, -10, -3, -2, 1, 2, -6, -4, -1, 7, 4, -1, -5, -1, -1, -6, 2, -3, -4, -6, -2, 6, -4, 5, 2, -12, -2, 10, -2, -3, 4, 2, 1, 2, -10, -10, -3, -2, -2, -2, 1, -16, 2, -8, -6, -10, -4, 4, -1, -11, 7, -12, 4, 3, -1, -4, -5, -16, -1, -4, -1, 8, -6, 6, 2, 10, -3, -5, -4], 'euler11': [1, 5, 11], 'euler13': [1, 2, 13], 'euler17': [1, 3, 17], 'euler19': [1, 6, 19], 'euler2': [1, -1, 0], 'euler23': [1, 1, 0], 'euler29': [1, 2, 29], 'euler3': [1, -2, 3], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -7, 41], 'euler43': [1, 1, 43], 'euler47': [1, 6, 47], 'euler5': [1, 1, 5], 'euler53': [1, -6, 53], 'euler59': [1, -10, 59], 'euler61': [1, 3, 61], 'euler67': [1, 10, 67], 'euler7': [1, -2, 7], 'euler71': [1, 2, 71], 'euler73': [1, 16, 73], 'euler79': [1, -4, 79], 'euler83': [1, 12, 83], 'euler89': [1, 16, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, -1, 0], [1, -2, 3], [1, 1, 5], [1, -2, 7], [1, 5, 11], [1, 2, 13], [1, 3, 17], [1, 6, 19], [1, 1, 0], [1, 2, 29], [1, -4, 31], [1, -2, 37], [1, -7, 41], [1, 1, 43], [1, 6, 47], [1, -6, 53], [1, -10, 59], [1, 3, 61], [1, 10, 67], [1, 2, 71], [1, 16, 73], [1, -4, 79], [1, 12, 83], [1, 16, 89], [1, -10, 97]], 'index': 237, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6026/d', 'ModularForm/GL2/Q/holomorphic/6026/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/6026/2/a/d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-6026-1.1-c1-0-237', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6026-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.936703270143792, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1483822298029876412, 'z1': {'__RealLiteral__': 0, 'data': '1.91159709497181123771052394535', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21790331
{'Lhash': '2423237204835556159458741300766', 'Lhash_array': ['2423237204835556159458741300766'], 'label': '2-6026-1.1-c1-0-237', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6026/2/a/d'}
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id: 24573069
{'Lhash': '2423237204835556159458741300766', 'Lhash_array': ['2423237204835556159458741300766'], 'label': '2-6026-1.1-c1-0-237', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6026/2/a/d/1/1'}
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id: 90616
{'Lhash': '1483822298029876412', 'Lhash_array': ['1483822298029876412'], 'label': '2-6026-1.1-c1-0-237', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6026/d'}