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lfunc_lfunctions • Show schema
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{'Lhash': '888275262594131247441502645823', 'a10': [2.4466691160689025, 0.18335250280402127], 'a2': [-1.163550846044013, 1.4590466117930752], 'a3': [0.006443160405205569, 0.042747576177145793], 'a4': [-0.3299245761424855, -1.4454940147753188], 'a5': [-0.740611616753511, -1.0862777309475762], 'a6': [-0.06986765092430516, -0.04033810706879439], 'a7': [-2.4088025184804946, 1.3907227824693622], 'a8': [-0.8698322116311203, -0.4188891157427664], 'a9': [2.8649325764054083, -0.8837146642522264], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.837064387755599, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [-4.0702542537124, -0.6580503857123066]]], [43, [[1.0, 0], [-5.042527849681783, -4.192005830766891]]]], 'bad_primes': [17, 43], 'central_character': '731.67', 'coefficient_field': 'CDF', 'conductor': 731, 'conductor_radical': 731, 'conjugate': '1472830566607929370266209958309', 'degree': 2, 'euler_factors': [[[1.0, 0], 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-0.6311315676839585, 'root_number': '-0.4004079228979428 - 0.9163369987513083*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.315565783842', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70072562773543834303398894059', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09190956141215211167679885938', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40868101463692699984581664593', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.837064387755599, 'bad_primes': [17, 43], 'central_character': '731.67', 'conductor': 731, 'conductor_radical': 731, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/731/2/z/a/67/14'], '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': '2-731-731.67-c1-0-12', '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': '2-731-731.67-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.416001735875949, 'root_angle': -0.31556578384197925, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70072562773543834303398894059', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '888275262594131247441502645823', 'Lhash_array': ['888275262594131247441502645823'], 'label': '2-731-731.67-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/731/2/z/a/67/14'}