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lfunc_lfunctions • Show schema
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{'Lhash': '1151397196759950864127660734998,1675849215608793235490477252269,2584917476311069174712857700446,2945406564618413495096366175617', 'a10': -18, 'a2': 6, 'a3': 3, 'a4': 17, 'a5': -3, 'a6': 18, 'a7': 0, 'a8': 30, 'a9': 7, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 669.3698663148037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1]], [13, [1, 10, 51, 130, 169]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': '1.1.1.1', 'conductor': 164648481361, 'conductor_radical': 91, 'degree': 8, 'euler_factors': [[1, -6, 19, -42, 69, -84, 76, -48, 16], [1, -3, 2, -3, 13, -9, 18, -81, 81], [1, 3, -2, 3, 51, 15, -50, 375, 625], [1], [1, -3, -4, 27, -51, 297, -484, -3993, 14641], [1, 10, 51, 130, 169], [1, -12, 82, -480, 2331, -8160, 23698, -58956, 83521], [1, 3, -20, -27, 309, -513, -7220, 20577, 130321], [1, 0, 52, 0, 1734, 0, 27508, 0, 279841], [1, 3, -20, -87, -261, -2523, -16820, 73167, 707281], 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'10.94414540142417443506037448172253', '10.94433054022492507375361283342126'], 'prelabel': '8-637e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 1612316625493919041, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.908292234904990279633198491028', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.32201192923907521844642456413', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.03914034028436336896142654439', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 669.3698663148037, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 164648481361, 'conductor_radical': 91, 'degree': 8, 'dirichlet_coefficients': [1, 6, 3, 17, -3, 18, 0, 30, 7, -18, 3, 51, -10, 0, -9, 40, 12, 42, -3, -51, 0, 18, 0, 90, 11, -60, 18, 0, -3, -54, -4, 54, 9, 72, 0, 119, 16, -18, -30, -90, -6, 0, -5, 51, -21, 0, 0, 120, 0, 66, 36, -170, -12, 108, -9, 0, -9, -18, 0, -153, 12, -24, 0, 79, 30, 54, 12, 204, 0, 0, 6, 210, 4, 96, 33, -51, 0, -180, -8, -120, 36, -36, 0, 0, -36, -30, -9, 90, 42, -126, 0, 0, -12, 0, 9, 162, -31, 0, 21, 187], 'euler11': [1, -3, -4, 27, -51, 297, -484, -3993, 14641], 'euler13': [1, 10, 51, 130, 169, 0, 0, 0, 0], 'euler17': [1, -12, 82, -480, 2331, -8160, 23698, -58956, 83521], 'euler19': [1, 3, -20, -27, 309, -513, -7220, 20577, 130321], 'euler2': [1, -6, 19, -42, 69, -84, 76, -48, 16], 'euler23': [1, 0, 52, 0, 1734, 0, 27508, 0, 279841], 'euler29': [1, 3, -20, -87, -261, -2523, -16820, 73167, 707281], 'euler3': [1, -3, 2, -3, 13, -9, 18, -81, 81], 'euler31': [1, 4, -5, -164, -1016, -5084, -4805, 119164, 923521], 'euler37': [1, -16, 244, -2032, 15574, -75184, 334036, -810448, 1874161], 'euler41': [1, 6, -50, 24, 4239, 984, -84050, 413526, 2825761], 'euler43': [1, 5, 34, -475, -2843, -20425, 62866, 397535, 3418801], 'euler47': [1, 0, -89, 0, 5712, 0, -196601, 0, 4879681], 'euler5': [1, 3, -2, 3, 51, 15, -50, 375, 625], 'euler53': [1, 12, 7, 372, 8328, 19716, 19663, 1786524, 7890481], 'euler59': [1, 0, 226, 0, 19731, 0, 786706, 0, 12117361], 'euler61': [1, -12, -14, -432, 12459, -26352, -52094, -2723772, 13845841], 'euler67': [1, -12, 19, 108, 1488, 7236, 85291, -3609156, 20151121], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, -6, 10, 696, -6921, 49416, 50410, -2147466, 25411681], 'euler73': [1, -4, -134, -16, 16003, -1168, -714086, -1556068, 28398241], 'euler79': [1, 8, -110, 128, 18979, 10112, -686510, 3944312, 38950081], 'euler83': [1, 0, 242, 0, 28419, 0, 1667138, 0, 47458321], 'euler89': [1, -42, 955, -14532, 160389, -1293348, 7564555, -29608698, 62742241], 'euler97': [1, 31, 538, 7099, 76303, 688603, 5062042, 28292863, 88529281], 'euler_factors': [[1, -6, 19, -42, 69, -84, 76, -48, 16], [1, -3, 2, -3, 13, -9, 18, -81, 81], [1, 3, -2, 3, 51, 15, -50, 375, 625], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -3, -4, 27, -51, 297, -484, -3993, 14641], [1, 10, 51, 130, 169, 0, 0, 0, 0], [1, -12, 82, -480, 2331, -8160, 23698, -58956, 83521], [1, 3, -20, -27, 309, -513, -7220, 20577, 130321], [1, 0, 52, 0, 1734, 0, 27508, 0, 279841], [1, 3, -20, -87, -261, -2523, -16820, 73167, 707281], [1, 4, -5, -164, -1016, -5084, -4805, 119164, 923521], [1, -16, 244, -2032, 15574, -75184, 334036, -810448, 1874161], [1, 6, -50, 24, 4239, 984, -84050, 413526, 2825761], [1, 5, 34, -475, -2843, -20425, 62866, 397535, 3418801], [1, 0, -89, 0, 5712, 0, -196601, 0, 4879681], [1, 12, 7, 372, 8328, 19716, 19663, 1786524, 7890481], [1, 0, 226, 0, 19731, 0, 786706, 0, 12117361], [1, -12, -14, -432, 12459, -26352, -52094, -2723772, 13845841], [1, -12, 19, 108, 1488, 7236, 85291, -3609156, 20151121], [1, -6, 10, 696, -6921, 49416, 50410, -2147466, 25411681], [1, -4, -134, -16, 16003, -1168, -714086, -1556068, 28398241], [1, 8, -110, 128, 18979, 10112, -686510, 3944312, 38950081], [1, 0, 242, 0, 28419, 0, 1667138, 0, 47458321], [1, -42, 955, -14532, 160389, -1293348, 7564555, -29608698, 62742241], [1, 31, 538, 7099, 76303, 688603, 5062042, 28292863, 88529281]], 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/h/g'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '8-637e4-1.1-c1e4-0-23', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-637e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1612316625493919041, 'z1': {'__RealLiteral__': 0, 'data': '0.908292234904990279633198491028', 'prec': 107}}
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{'Lhash': '1151397196759950864127660734998,1675849215608793235490477252269,2584917476311069174712857700446,2945406564618413495096366175617', 'Lhash_array': ['1151397196759950864127660734998', '1675849215608793235490477252269', '2584917476311069174712857700446', '2945406564618413495096366175617'], 'label': '8-637e4-1.1-c1e4-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/h/g'}