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lfunc_lfunctions • Show schema
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{'Lhash': '408728178293497046404247556363', 'a10': [2.024458669761153, 3.5064652738496194], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [-4.048917339522306, 0], 'a6': [-0.5, 0.8660254037844386], 'a7': [0.34601073581504793, -0.5993081743959552], 'a8': [1.0, 0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.096830764957835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '1014.991', 'coefficient_field': 'CDF', 'conductor': 1014, 'conductor_radical': 78, 'conjugate': '1033619499947043887605384675366', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [4.048917339522306, 0], [5.0, 0]], [[1.0, 0], 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'8.181772681188123113590626667461859', '9.039724008567746920369068107234430', '9.830619882369048892991652409019535'], 'prelabel': '2-1014-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.845493061836179, 'root_angle': -0.023676072911058554, 'root_number': '0.997235040010757801502775337825030169479559152354711287343 - 0.0743120109722667024530575929380022754720741354361444469*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.011838036455529277', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.32242968071794318824857439158', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61321101798368069192324880189', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08723601219882637699709604046', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.096830764957835, 'bad_primes': [2, 3, 13], 'central_character': '13.3', 'conductor': 1014, 'conductor_radical': 78, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1014/2/e/k/991/1'], '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': '2-1014-13.3-c1-0-2', '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': '2-1014-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.845493061836179, 'root_angle': -0.011838036455529277, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.32242968071794318824857439158', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '408728178293497046404247556363', 'Lhash_array': ['408728178293497046404247556363'], 'label': '2-1014-13.3-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1014/2/e/k/991/1'}