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lfunc_lfunctions • Show schema
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{'Lhash': '3374088473851339450078015697099', 'a10': [2.999187871608545, 1.002433095421438], 'a2': [-0.5331774248503404, 1.3098556537382124], 'a3': [0.6673045986041588, -1.5983443223166098], 'a4': [-1.4314436672599193, -1.3967709287715981], 'a5': [-0.14302830424727483, -2.231488943325543], 'a6': [1.7378085997322275, 1.7262738110440983], 'a7': [0.5827719754125508, -0.5827719754125508], 'a8': [2.592781746356623, -1.130257853659907], 'a9': [-2.1094091453634847, -2.133165032869443], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5331774248503404, -1.3098556537382124]]], [3, [[1.0, 0], [-0.6673045986041588, 1.5983443223166098]]], [5, [[1.0, 0], [0.14302830424727483, 2.231488943325543]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': 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'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': 0.15087177967716928, 'root_number': '0.8897598054999628 + 0.4564290618668671*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0754358898386', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.66168648777814985927553422342', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.72413545649241715614996623974', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.24157860483126280691610950354', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/w/c/53/6'], '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': '2-120-120.53-c1-0-14', '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': '2-120-120.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': 0.07543588983858464, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.66168648777814985927553422342', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3374088473851339450078015697099', 'Lhash_array': ['3374088473851339450078015697099'], 'label': '2-120-120.53-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/53/6'}