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lfunc_lfunctions • Show schema
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{'Lhash': '3094016992210535036161386480711', 'a10': [-0.8660254037844386, 0.5], 'a2': [0.25881904510252074, -0.9659258262890683], 'a3': [0.0, 0.0], 'a4': [-0.8660254037844386, -0.5], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.808485320465464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, 0.9659258262890683]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.863', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '279350663224743420380600828627', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.25881904510252074, 0.9659258262890683]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 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'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.44074904524439490058349553075', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51370806710728590956459472029', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39884896669995591127354918611', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.808485320465464, 'bad_primes': [2, 3, 5], 'central_character': '180.23', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/1/w/a/863/2'], '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': '2-1620-180.23-c0-0-5', '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': '2-1620-180.23-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8991581176108371, 'root_angle': -0.35634034885705274, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.44074904524439490058349553075', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3094016992210535036161386480711', 'Lhash_array': ['3094016992210535036161386480711'], 'label': '2-1620-180.23-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/1/w/a/863/2'}