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lfunc_lfunctions • Show schema
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{'Lhash': '1198706959236182859701337902131', 'a10': [-2.6771542682831586, 4.994978094186771], 'a2': [1.792120563399473, 1.792120563399473], 'a3': [0, 0], 'a4': [0, 4.423392227518488], 'a5': [0.646670729983404, 2.1405179202666655], 'a6': [0, 0], 'a7': [-0.3451440899586203, 0.3451440899586203], 'a8': [-4.343011044118338, 4.343011044118338], '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], [-0.646670729983404, -2.1405179202666655]]], [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': '3080482724088231899624950149311', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.792120563399473, -1.792120563399473], [0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.646670729983404, 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'-0.995928885330156797352797221860218523989511314656663264865 - 0.09014241712441148405213992764914435840828639235493942694*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.48563388807306784', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.945613056957781708669877538839', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.08556969540828333980536490965', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17010781733388873745102908528', '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': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1035/2/j/b/323/22'], '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-c1-0-17', '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': -0.48563388807306784, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.945613056957781708669877538839', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1198706959236182859701337902131', 'Lhash_array': ['1198706959236182859701337902131'], 'label': '2-1035-15.8-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1035/2/j/b/323/22'}