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lfunc_lfunctions • Show schema
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{'Lhash': '1880299004547161062915327380375', 'a10': [-5.854101966249685, 0.0], 'a2': [-2.618033988749895, 0.0], 'a3': [-2.23606797749979, 0.0], 'a4': [4.854101966249685, 0.0], 'a5': [2.23606797749979, 0.0], 'a6': [5.854101966249685, 0.0], 'a7': [0.0, 0.0], 'a8': [-7.47213595499958, 0.0], 'a9': [2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '1880299004547161062915327380375', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.618033988749895, 0], [2.0, 0]], [[1.0, 0], [2.23606797749979, 0], [3.0, 0]], [[1.0, 0], [-2.23606797749979, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.4721359549995794, 0], [17.0, 0]], 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'10.04739722696444408909984293124823'], 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48329437481324086898099118124', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72343313377748065226121554450', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.05312515101241452638497988149', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/a/f/1/1'], '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': '2-637-1.1-c1-0-17', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48329437481324086898099118124', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1880299004547161062915327380375', 'Lhash_array': ['1880299004547161062915327380375'], 'label': '2-637-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/f/1/1'}