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lfunc_lfunctions • Show schema
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{'Lhash': '1369754779487918094575116558162', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.35027811608699, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]], [11, [1, -1]]], 'bad_primes': [2, 7, 11], 'central_character': '4928.1', 'coefficient_field': '1.1.1.1', 'conductor': 4928, 'conductor_radical': 154, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, 3, 5], [1, -1], [1, -1], [1, -4, 13], [1, 6, 17], [1, 2, 19], [1, -3, 23], [1, -6, 29], [1, -5, 31], [1, 11, 37], [1, -6, 41], [1, 8, 43], [1, 0, 47], [1, -6, 53], [1, -9, 59], [1, -10, 61], [1, 5, 67], [1, -9, 71], [1, -2, 73], [1, 10, 79], [1, 12, 83], [1, 3, 89], [1, 1, 97], [1, -12, 101], [1, 4, 103], [1, 6, 107], [1, 20, 109], [1, 3, 113]], 'euler_factors_factorization': [[1], [[[1, 1, 3], 1]], [[[1, 3, 5], 1]], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, -4, 13], 1]], [[[1, 6, 17], 1]], [[[1, 2, 19], 1]], [[[1, -3, 23], 1]], [[[1, -6, 29], 1]], [[[1, -5, 31], 1]], [[[1, 11, 37], 1]], [[[1, -6, 41], 1]], [[[1, 8, 43], 1]], [[[1, 0, 47], 1]], [[[1, -6, 53], 1]], [[[1, -9, 59], 1]], [[[1, -10, 61], 1]], [[[1, 5, 67], 1]], [[[1, -9, 71], 1]], [[[1, -2, 73], 1]], [[[1, 10, 79], 1]], [[[1, 12, 83], 1]], [[[1, 3, 89], 1]], [[[1, 1, 97], 1]], [[[1, -12, 101], 1]], [[[1, 4, 103], 1]], [[[1, 6, 107], 1]], [[[1, 20, 109], 1]], [[[1, 3, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 65, 'label': '2-4928-1.1-c1-0-65', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4928/2/a/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.7380687201838736e-61, 0.13007780851533376, 0.25877005275694, 0.38464821497823853, 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2.697963759167481, 3.0925887107067913, 3.376456303160607, 3.528392948074019, 3.5339114902250053, 3.3863460518517243, 3.087540420670387, 2.6480344758768966, 2.0867234622317477], 'positive_zeros': ['1.08054599527764648143837096247417', '2.47348180702840979174904080971078', '3.48528504268689712306029643360932', '4.20086015444217019855350266016546', '4.84767148577891784015091892690298', '5.70008544609539374844814353462292', '6.69227362449418376626075160667132', '6.89635932514915681940214174887586', '8.154848181833606301816411535200013'], 'prelabel': '2-4928-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.2729800028445, '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': 309715017200164778, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08054599527764648143837096247', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47348180702840979174904080971', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48528504268689712306029643361', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.35027811608699, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 4928, 'conductor_radical': 154, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -3, 0, 1, 0, -2, 0, 1, 0, 4, 0, 3, 0, -6, 0, -2, 0, -1, 0, 3, 0, 4, 0, 5, 0, 6, 0, 5, 0, -1, 0, -3, 0, -11, 0, -4, 0, 6, 0, -8, 0, 6, 0, 0, 0, 1, 0, 6, 0, 6, 0, -3, 0, 2, 0, 9, 0, 10, 0, -2, 0, -12, 0, -5, 0, -3, 0, 9, 0, 2, 0, -4, 0, 1, 0, -10, 0, 1, 0, -12, 0, 18, 0, -6, 0, -3, 0, 4, 0, -5, 0, 6, 0, -1, 0, -2, 0], 'euler11': [1, -1, 0], 'euler13': [1, -4, 13], 'euler17': [1, 6, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 3], 'euler31': [1, -5, 31], 'euler37': [1, 11, 37], 'euler41': [1, -6, 41], 'euler43': [1, 8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 3, 5], 'euler53': [1, -6, 53], 'euler59': [1, -9, 59], 'euler61': [1, -10, 61], 'euler67': [1, 5, 67], 'euler7': [1, -1, 0], 'euler71': [1, -9, 71], 'euler73': [1, -2, 73], 'euler79': [1, 10, 79], 'euler83': [1, 12, 83], 'euler89': [1, 3, 89], 'euler97': [1, 1, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 3, 5], [1, -1, 0], [1, -1, 0], [1, -4, 13], [1, 6, 17], [1, 2, 19], [1, -3, 23], [1, -6, 29], [1, -5, 31], [1, 11, 37], [1, -6, 41], [1, 8, 43], [1, 0, 47], [1, -6, 53], [1, -9, 59], [1, -10, 61], [1, 5, 67], [1, -9, 71], [1, -2, 73], [1, 10, 79], [1, 12, 83], [1, 3, 89], [1, 1, 97]], 'index': 65, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4928/i', 'ModularForm/GL2/Q/holomorphic/4928/2/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/4928/2/a/i'], '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': '2-4928-1.1-c1-0-65', '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': '2-4928-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.2729800028445, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 309715017200164778, 'z1': {'__RealLiteral__': 0, 'data': '1.08054599527764648143837096247', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20137124
{'Lhash': '1369754779487918094575116558162', 'Lhash_array': ['1369754779487918094575116558162'], 'label': '2-4928-1.1-c1-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4928/2/a/i'}
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id: 24568113
{'Lhash': '1369754779487918094575116558162', 'Lhash_array': ['1369754779487918094575116558162'], 'label': '2-4928-1.1-c1-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4928/2/a/i/1/1'}
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id: 34948
{'Lhash': '309715017200164778', 'Lhash_array': ['309715017200164778'], 'label': '2-4928-1.1-c1-0-65', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4928/i'}