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  • lfunc_lfunctions • Show schema
    {'Lhash': '1022265727522697404642200966177', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.4029218007493631, 2.4299318379439176], 'a4': [0, 0], 'a5': [219.14090521049107, 379.56318184120585], 'a6': [0, 0], 'a7': [893.2818104209822, -159.9706447164994], 'a8': [0, 0], 'a9': [1089.5636208419644, 1887.1795493769944], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.98712285422165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-893.2818104209822, 159.9706447164994]]]], 'bad_primes': [2, 7], 'central_character': '112.81', 'coefficient_field': 'CDF', 'conductor': 112, 'conductor_radical': 14, 'conjugate': '2111890604140516033423883591063', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4029218007493631, -2.4299318379439176], [-1093.5, -1893.9975580765674]], [[1.0, 0], [-219.14090521049107, -379.56318184120585], [-39062.5, 67658.23467065927]], [[1.0, 0], [-893.2818104209822, 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'3.79938210199151210583213155026732', '5.26416026578023570100250404669659', '5.96236838076228912926223502571413', '7.85489616837917819192432296873780', '8.744177324759779041357662059553530', '9.648023349185256061879782117337183', '10.98083699351133545969571320899714', '12.09196270190158823691422505934590'], 'prelabel': '2-112-7.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.914991365523846, 'root_angle': -0.2681163449184862, 'root_number': '-0.1135827010981986604408265664880308131032398137718378951 - 0.9935285451416266483794872000219616696446271125589953488*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2681163449184862', 'prec': 54}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.806425467189971276717523388570', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.73064351829055000806950376415', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.79938210199151210583213155027', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 34.98712285422165, 'bad_primes': [2, 7], 'central_character': '7.4', 'conductor': 112, 'conductor_radical': 14, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/112/8/i/b/81/1'], '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': '2-112-7.4-c7-0-11', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-112-7.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.914991365523846, 'root_angle': -0.2681163449184862, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.806425467189971276717523388570', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1022265727522697404642200966177', 'Lhash_array': ['1022265727522697404642200966177'], 'factors': ['2-112-7.4-c7-0-11'], 'label': '2-112-7.4-c7-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/112/8/i/b/81/1'}