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lfunc_lfunctions • Show schema
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{'Lhash': '833381501149603572657254087463,1883470420657243282750087928046,1914265005438867454946313298300,2650707870057564512072092502109', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 8, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 82.99952890949935, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 2, 0, 1]], [3, [1]], [7, [1, -8, 30, -56, 49]]], 'bad_primes': [2, 3, 7], 'central_character': '378.1', 'coefficient_field': '1.1.1.1', 'conductor': 20415837456, 'conductor_radical': 42, 'degree': 8, 'euler_factors': [[1, 0, 2, 0, 1], [1], [1, 0, 14, 0, 99, 0, 350, 0, 625], [1, -8, 30, -56, 49], [1, 0, -26, 0, 411, 0, -3146, 0, 14641], [1, 0, -28, 0, 534, 0, -4732, 0, 28561], [1, 0, -28, 0, 774, 0, -8092, 0, 83521], [1, 0, -70, 0, 1947, 0, -25270, 0, 130321], [1, 0, -74, 0, 2427, 0, -39146, 0, 279841], [1, 0, -44, 0, 2166, 0, -37004, 0, 707281], [1, 0, -70, 0, 3147, 0, -67270, 0, 923521], 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{'algebraic': True, 'analytic_conductor': 82.99952890949935, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 20415837456, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28], 'euler11': [1, 0, -26, 0, 411, 0, -3146, 0, 14641], 'euler13': [1, 0, -28, 0, 534, 0, -4732, 0, 28561], 'euler17': [1, 0, -28, 0, 774, 0, -8092, 0, 83521], 'euler19': [1, 0, -70, 0, 1947, 0, -25270, 0, 130321], 'euler2': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, -74, 0, 2427, 0, -39146, 0, 279841], 'euler29': [1, 0, -44, 0, 2166, 0, -37004, 0, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -70, 0, 3147, 0, -67270, 0, 923521], 'euler37': [1, -28, 442, -4480, 32371, -165760, 605098, -1418284, 1874161], 'euler41': [1, 0, -130, 0, 7587, 0, -218530, 0, 2825761], 'euler43': [1, 8, 196, 1064, 13174, 45752, 362404, 636056, 3418801], 'euler47': [1, 0, 164, 0, 11142, 0, 362276, 0, 4879681], 'euler5': [1, 0, 14, 0, 99, 0, 350, 0, 625], 'euler53': [1, 0, 76, 0, 7062, 0, 213484, 0, 7890481], 'euler59': [1, 0, 212, 0, 18198, 0, 737972, 0, 12117361], 'euler61': [1, 0, -148, 0, 12918, 0, -550708, 0, 13845841], 'euler67': [1, -8, 292, -1640, 30166, -109880, 1310788, -2406104, 20151121], 'euler7': [1, -8, 30, -56, 49, 0, 0, 0, 0], 'euler71': [1, 0, -266, 0, 27771, 0, -1340906, 0, 25411681], 'euler73': [1, 0, -268, 0, 28614, 0, -1428172, 0, 28398241], 'euler79': [1, 40, 916, 13480, 142246, 1064920, 5716756, 19721560, 38950081], 'euler83': [1, 0, -268, 0, 31734, 0, -1846252, 0, 47458321], 'euler89': [1, 0, 302, 0, 38643, 0, 2392142, 0, 62742241], 'euler97': [1, 0, -4, 0, 18822, 0, -37636, 0, 88529281], 'euler_factors': [[1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 14, 0, 99, 0, 350, 0, 625], [1, -8, 30, -56, 49, 0, 0, 0, 0], [1, 0, -26, 0, 411, 0, -3146, 0, 14641], [1, 0, -28, 0, 534, 0, -4732, 0, 28561], [1, 0, -28, 0, 774, 0, -8092, 0, 83521], [1, 0, -70, 0, 1947, 0, -25270, 0, 130321], [1, 0, -74, 0, 2427, 0, -39146, 0, 279841], [1, 0, -44, 0, 2166, 0, -37004, 0, 707281], [1, 0, -70, 0, 3147, 0, -67270, 0, 923521], [1, -28, 442, -4480, 32371, -165760, 605098, -1418284, 1874161], [1, 0, -130, 0, 7587, 0, -218530, 0, 2825761], [1, 8, 196, 1064, 13174, 45752, 362404, 636056, 3418801], [1, 0, 164, 0, 11142, 0, 362276, 0, 4879681], [1, 0, 76, 0, 7062, 0, 213484, 0, 7890481], [1, 0, 212, 0, 18198, 0, 737972, 0, 12117361], [1, 0, -148, 0, 12918, 0, -550708, 0, 13845841], [1, -8, 292, -1640, 30166, -109880, 1310788, -2406104, 20151121], [1, 0, -266, 0, 27771, 0, -1340906, 0, 25411681], [1, 0, -268, 0, 28614, 0, -1428172, 0, 28398241], [1, 40, 916, 13480, 142246, 1064920, 5716756, 19721560, 38950081], [1, 0, -268, 0, 31734, 0, -1846252, 0, 47458321], [1, 0, 302, 0, 38643, 0, 2392142, 0, 62742241], [1, 0, -4, 0, 18822, 0, -37636, 0, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/d/b'], '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': '8-378e4-1.1-c1e4-0-4', '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': '8-378e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 312274510659437505, 'z1': {'__RealLiteral__': 0, 'data': '0.65742208539132196488344514468', 'prec': 103}}
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{'Lhash': '833381501149603572657254087463,1883470420657243282750087928046,1914265005438867454946313298300,2650707870057564512072092502109', 'Lhash_array': ['833381501149603572657254087463', '1883470420657243282750087928046', '1914265005438867454946313298300', '2650707870057564512072092502109'], 'label': '8-378e4-1.1-c1e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/d/b'}