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lfunc_lfunctions • Show schema
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{'Lhash': '353405849218858458173431785617', 'a10': [0, 0], 'a2': [0.25881904510252074, 0.9659258262890683], 'a3': [0.9659258262890683, 0.25881904510252074], 'a4': [-0.8660254037844386, 0.5], 'a5': [0, 0], 'a6': [0, 1.0], 'a7': [-2.5275619505805045, -0.7819402700831285], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [3, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.5275619505805045, 0.7819402700831285]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.943', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '2547957229103794547379183805898', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.25881904510252074, 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'2.76414312045829987727362706418', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.384292212234444, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.33', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/2/bc/h/943/3'], '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': '2-1050-35.33-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': '2-1050-35.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.47981957784717744, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.27878805812518909116052307650', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '353405849218858458173431785617', 'Lhash_array': ['353405849218858458173431785617'], 'label': '2-1050-35.33-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/2/bc/h/943/3'}