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lfunc_lfunctions • Show schema
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{'Lhash': '1320229545652691671014863891277', 'a10': [-1.1019950895257504, 0.0], 'a2': [0.0, 1.0], 'a3': [1.3651005975246915, 1.3651005975246915], 'a4': [-1.0, 0.0], 'a5': [0.0, 1.1019950895257504], 'a6': [-1.3651005975246915, 1.3651005975246915], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [0.0, -1.0], 'a9': [0.0, 0.7269992827245388], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.583413076021496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [7, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [41, [[1.0, 0], [-2.0756898757981896, 6.05735185865151]]]], 'bad_primes': [2, 7, 41], 'central_character': '574.337', 'coefficient_field': 'CDF', 'conductor': 574, 'conductor_radical': 574, 'conjugate': '2697699002103040010526412514774', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [-1.3651005975246915, -1.3651005975246915], [0, 3.0]], [[1.0, 0], [0, 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50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04147747448310748272535530372', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18558420638471304622484682122', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42545956642293358588773340870', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.583413076021496, 'bad_primes': [2, 7, 41], 'central_character': '41.9', 'conductor': 574, 'conductor_radical': 574, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/574/2/f/a/337/9'], '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': '2-574-41.9-c1-0-5', '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': '2-574-41.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1408907202427443, 'root_angle': -0.37615197229636343, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04147747448310748272535530372', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1320229545652691671014863891277', 'Lhash_array': ['1320229545652691671014863891277'], 'label': '2-574-41.9-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/574/2/f/a/337/9'}