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lfunc_lfunctions • Show schema
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{'Lhash': '1234388552615976120236097524636', 'a10': [0.0, 0.0], 'a2': [0.0, 1.0], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, -1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8983170227394044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.451', 'coefficient_field': 'CDF', 'conductor': 1800, 'conductor_radical': 30, 'conjugate': '1636699414509477983711983922116', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [1.0, 0]], [[1.0, 0], [0, -2.0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 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'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.973760871011093482261064088893', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.33506781760078880709984307303', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19218900977646907267409218565', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8983170227394044, 'bad_primes': [2, 3, 5], 'central_character': '8.3', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/1/g/c/451/2', 'ArtinRepresentation/2.1800.8t11.c.b'], 'is_instance_Artin': True, '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': '2-1800-8.3-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1800-8.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9477958760932674, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.973760871011093482261064088893', 'prec': 107}}
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lfunc_instances • Show schema
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id: 19833690
{'Lhash': '1234388552615976120236097524636', 'Lhash_array': ['1234388552615976120236097524636'], 'label': '2-1800-8.3-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/1/g/c/451/2'}
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id: 24598930
{'Lhash': '1234388552615976120236097524636', 'Lhash_array': ['1234388552615976120236097524636'], 'label': '2-1800-8.3-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1800.8t11.c.b'}