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lfunc_lfunctions • Show schema
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{'Lhash': '2676768506041801098804728767188', 'a10': [-2.183483026494543, 0.4820807743627935], 'a2': [-0.8660254037844386, -0.5], 'a3': [0.9659258262890683, -0.25881904510252074], 'a4': [0.5, 0.8660254037844386], 'a5': [1.649911382495008, -1.5092357105215246], 'a6': [-0.9659258262890683, -0.25881904510252074], 'a7': [-1.5604613790093056, -2.7027983916931118], 'a8': [0.0, -1.0], 'a9': [0.8660254037844386, -0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [-0.9659258262890683, 0.25881904510252074]]], [5, [[1.0, 0], [-1.649911382495008, 1.5092357105215246]]], [13, [[1.0, 0], [3.131147593679725, 1.787712154289294]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.253', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '1228818563574407346576918271448', 'degree': 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'4.86255608339410565344452880213224', '6.15532433494367660226896008412020', '6.75853327067023159897647382950876', '7.969958690335186330444253804484079', '8.947581812776139326364711342315721', '9.719944904925127036462147976650592', '10.16455774493394015763813594623413', '11.45967626246842961358054721038472'], 'prelabel': '2-390-65.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.5344640733674721, 'root_number': '-0.10806066089389497 + 0.9941443021851378*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.267232036684', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.11159802674323062282264667645', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02205165488721833084930689013', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.86255608339410565344452880213', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.58', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bd/b/253/4'], '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': '2-390-65.58-c1-0-13', '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': '2-390-65.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.2672320366837361, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.11159802674323062282264667645', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2676768506041801098804728767188', 'Lhash_array': ['2676768506041801098804728767188'], 'label': '2-390-65.58-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bd/b/253/4'}