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lfunc_lfunctions • Show schema
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{'Lhash': '1054258242736841698375737171936', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.6133350255036207, 0.0], 'a4': [0.0, 0.0], 'a5': [10.53217905261227, 0.0], 'a6': [0.0, 0.0], 'a7': [13.741808578543763, 0.0], 'a8': [0.0, 0.0], 'a9': [-24.39715009548323, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 109.50754497065464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [29.0, 0]]]], 'bad_primes': [2, 29], 'central_character': '1856.1', 'coefficient_field': 'CDF', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.6133350255036207, 0], [27.0, 0]], [[1.0, 0], [-10.53217905261227, 0], [125.0, 0]], [[1.0, 0], [-13.741808578543763, 0], [343.0, 0]], [[1.0, 0], [-30.294778704885122, 0], [1331.0, 0]], [[1.0, 0], [19.928637756177082, 0], [2197.0, 0]], [[1.0, 0], [-105.49781658185738, 0], [4913.0, 0]], [[1.0, 0], 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'2.83872342743203284801242329785934', '3.88420325100670890257028654418978', '5.16411820057230947720006156766005', '5.55486923826456731393456313211936', '6.30623115255850652551200504521909', '7.35926621455780660907844684068388', '8.063704705204508760238993998909312', '9.020404463800279731506718531306815'], 'prelabel': '2-1856-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.464585274661134, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.831663111702098136619886812972', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.76654340347678687381151072374', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83872342743203284801242329786', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 109.50754497065464, 'bad_primes': [2, 29], 'central_character': '1.1', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'index': 72, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1856/4/a/bj/1/6'], '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': '2-1856-1.1-c3-0-72', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1856-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.464585274661134, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.831663111702098136619886812972', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1054258242736841698375737171936', 'Lhash_array': ['1054258242736841698375737171936'], 'label': '2-1856-1.1-c3-0-72', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1856/4/a/bj/1/6'}