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lfunc_lfunctions • Show schema
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{'Lhash': '32488650996262090298685239517', 'a10': [0.8305782845945928, 2.0760875976605377], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [-0.8305782845945928, -0.8305782845945928], 'a4': [0.0, 1.0], 'a5': [-2.0553231559861818, -0.8807080812999284], 'a6': [0.0, 1.1746150746862534], 'a7': [0.0, 0.0], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [0.0, -1.6202794263198073], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.9126696990427408, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [2.0553231559861818, 0.8807080812999284]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '490.97', 'coefficient_field': 'CDF', 'conductor': 490, 'conductor_radical': 70, 'conjugate': '1904970111986802780927000182150', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], 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'-0.28508026992', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.02562902663432083958228799685', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.46249042916843609400826222463', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.22688579921651283834851925644', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.9126696990427408, 'bad_primes': [2, 5, 7], 'central_character': '35.27', 'conductor': 490, 'conductor_radical': 70, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/490/2/g/c/97/2'], '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': '2-490-35.27-c1-0-0', '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': '2-490-35.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9780469405559467, 'root_angle': -0.28508026992007596, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.02562902663432083958228799685', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '32488650996262090298685239517', 'Lhash_array': ['32488650996262090298685239517'], 'label': '2-490-35.27-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/490/2/g/c/97/2'}