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lfunc_lfunctions • Show schema
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{'Lhash': '2029226106367690886123805387635', 'a10': [-26.92515228865521, 0.0], 'a2': [5.385030457731042, 0.0], 'a3': [0.0, 0.0], 'a4': [20.998553030690992, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [12.57019883508461, 0.0], 'a8': [69.99760397670313, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.89577355232496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.0, 0]]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-5.385030457731042, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [-12.57019883508461, 0], [343.0, 0]], [[1.0, 0], [-12.830687253728946, 0], [1331.0, 0]], [[1.0, 0], [-59.86449465991273, 0], [2197.0, 0]], [[1.0, 0], [110.01087434822539, 0], [4913.0, 0]], [[1.0, 0], [12.087170976446993, 0], [6859.0, 0]], 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'4.16463209098446068639553574113889', '4.63407213640431552555192754310032', '5.98832554641626732896442875770077', '6.61323815346549005315335532432926', '7.75568253154504959856833798973974', '8.772539296728125686840746225471626', '10.59374581461984949794635850554900', '11.16367822216126260023413695974042'], 'prelabel': '2-405-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60077714316732582054481276997', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93701824830953775772850386143', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16463209098446068639553574114', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/a/m/1/7'], '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': '2-405-1.1-c3-0-35', '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': '2-405-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60077714316732582054481276997', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2029226106367690886123805387635', 'Lhash_array': ['2029226106367690886123805387635'], 'label': '2-405-1.1-c3-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/a/m/1/7'}