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lfunc_lfunctions • Show schema
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{'Lhash': '1490482376474838076750721303754', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.3722813232690143, 0.0], 'a4': [0.0, 0.0], 'a5': [2.5243377989621387, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.3166247903554, 0.0], 'a8': [0.0, 0.0], 'a9': [8.372281323269014, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.8392355431508, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 19], 'central_character': '4864.1', 'coefficient_field': 'CDF', 'conductor': 4864, 'conductor_radical': 38, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.3722813232690143, 0], [3.0, 0]], [[1.0, 0], [-2.5243377989621387, 0], [5.0, 0]], [[1.0, 0], [3.3166247903554, 0], [7.0, 0]], [[1.0, 0], [-2.3722813232690143, 0], [11.0, 0]], [[1.0, 0], [5.840962589317538, 0], [13.0, 0]], [[1.0, 0], [-5.0, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.7922869913932613, 0], [23.0, 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'6.37573089069668888238124057017442', '6.87940282784754454027124823130875', '7.65929808528468218639895046861307', '8.302107843454249583018874885906373'], 'prelabel': '2-4864-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.23211324858196, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17578327672190567591310113795', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32234543097201405185811266083', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.68830220642473865910340592535', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 38.8392355431508, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 4864, 'conductor_radical': 38, 'degree': 2, 'index': 77, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4864/2/a/bl/1/4'], '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': '2-4864-1.1-c1-0-77', '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': '2-4864-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.23211324858196, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17578327672190567591310113795', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1490482376474838076750721303754', 'Lhash_array': ['1490482376474838076750721303754'], 'label': '2-4864-1.1-c1-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4864/2/a/bl/1/4'}