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lfunc_lfunctions • Show schema
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{'Lhash': '2133210570299080342534833975862', 'a10': [2.9365723645894013, -2.9365723645894013], 'a2': [0.0, -1.9497857669537408], 'a3': [-1.1009191607950657, -1.1009191607950657], 'a4': [-1.8016645370153879, 0.0], 'a5': [1.5061000107603473, 1.5061000107603473], 'a6': [-2.146556510284876, 2.146556510284876], 'a7': [0.0, 0.0], 'a8': [0.0, -0.38671166280957747], 'a9': [0.0, -0.5759540027885764], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.651538488372659, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-3.3943348007738234, 2.340617709122045]]]], 'bad_primes': [7, 17], 'central_character': '833.540', 'coefficient_field': 'CDF', 'conductor': 833, 'conductor_radical': 119, 'conjugate': '943364979496737299963958393151', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.9497857669537408], [-2.0, 0]], [[1.0, 0], [1.1009191607950657, 1.1009191607950657], [0, 3.0]], [[1.0, 0], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68280642151316335914492198812', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.70540983427784848485272063273', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.00208851135673391909041462480', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.651538488372659, 'bad_primes': [7, 17], 'central_character': '17.13', 'conductor': 833, 'conductor_radical': 119, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/833/2/g/g/540/2'], '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': '2-833-17.13-c1-0-41', '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': '2-833-17.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5790576744952136, 'root_angle': -0.49057485006001106, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68280642151316335914492198812', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2133210570299080342534833975862', 'Lhash_array': ['2133210570299080342534833975862'], 'label': '2-833-17.13-c1-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/833/2/g/g/540/2'}