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lfunc_lfunctions • Show schema
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{'Lhash': '917951864507839733389644063065', 'a10': [4.905637596031533, 0.0], 'a2': [-2.1936148961434374, 0.0], 'a3': [-1.7123535617838699, 0.0], 'a4': [2.8119463125823843, 0.0], 'a5': [-2.236325803884749, 0.0], 'a6': [3.756244280593369, 0.0], 'a7': [-3.047203290652544, 0.0], 'a8': [-1.7810975261494537, 0.0], 'a9': [-0.06784527944609413, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.18769705477814, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[29, [[1.0, 0], [-1.0, 0]]], [139, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [29, 139], 'central_character': '4031.1', 'coefficient_field': 'CDF', 'conductor': 4031, 'conductor_radical': 4031, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1936148961434374, 0], [2.0, 0]], [[1.0, 0], [1.7123535617838699, 0], [3.0, 0]], [[1.0, 0], [2.236325803884749, 0], [5.0, 0]], [[1.0, 0], [3.047203290652544, 0], [7.0, 0]], [[1.0, 0], [1.236145688427317, 0], [11.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.18769705477814, 'bad_primes': [29, 139], 'central_character': '1.1', 'conductor': 4031, 'conductor_radical': 4031, 'degree': 2, 'index': 105, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4031/2/a/b/1/8'], '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': '2-4031-1.1-c1-0-105', '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': '2-4031-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.673420225470536, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72413633878497003053265343352', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '917951864507839733389644063065', 'Lhash_array': ['917951864507839733389644063065'], 'label': '2-4031-1.1-c1-0-105', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4031/2/a/b/1/8'}