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lfunc_lfunctions • Show schema
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{'Lhash': '2085628698229737592419783144294', 'a10': [4.285528234643542, -1.827279063613462], 'a2': [1.4732515408526505, 1.4732515408526505], 'a3': [0, 0], 'a4': [0, 2.3409402052494173], 'a5': [0.8342937722662617, -2.074597286597505], 'a6': [0, 0], 'a7': [0.1888699416375637, -0.1888699416375637], 'a8': [-0.5022906827223231, 0.5022906827223231], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.264516609202524, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.8342937722662617, 2.074597286597505]]], [23, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [3, 5, 23], 'central_character': '1035.323', 'coefficient_field': 'CDF', 'conductor': 1035, 'conductor_radical': 345, 'conjugate': '1470776380474428831083190877988', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4732515408526505, -1.4732515408526505], [0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'0.89384517111261355184213292222988525806012406019003612358 - 0.44837574653259580603760240142656251362431756624085186336*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07399866999395548', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64527094284043125908305879272', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62164790122568314039909733894', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41314659984578841356763046565', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.264516609202524, 'bad_primes': [3, 5, 23], 'central_character': '15.8', 'conductor': 1035, 'conductor_radical': 345, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1035/2/j/b/323/18'], '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': '2-1035-15.8-c1-0-32', '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': '2-1035-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.874807229920386, 'root_angle': -0.07399866999395548, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64527094284043125908305879272', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2085628698229737592419783144294', 'Lhash_array': ['2085628698229737592419783144294'], 'label': '2-1035-15.8-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1035/2/j/b/323/18'}