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lfunc_lfunctions • Show schema
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{'Lhash': '3034597319537442858041262366652', 'a10': [2628726220179774500, 0.0], 'a2': [-262144.0, 0.0], 'a3': [1162182946.167981, 0.0], 'a4': [68719476736.0, 0.0], 'a5': [-10027794724196.527, 0.0], 'a6': [-304659286240259.2, 0.0], 'a7': [-3320613759263619.5, 0.0], 'a8': [-18014398509481984, 0.0], 'a9': [900385294472691000, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.342807624921097, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '18.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [262144.0, 0]]]], 'bad_primes': [2], 'central_character': '2.1', 'coefficient_field': 'CDF', 'conductor': 2, 'conductor_radical': 2, 'conjugate': '3034597319537442858041262366652', 'degree': 2, 'euler_factors': [[[1.0, 0], [262144.0, 0]], [[1.0, 0], [-1162182946.167981, 0], [450283905890997400, 0]], [[1.0, 0], [10027794724196.527, 0], [72759576141834256000000000, 0]], [[1.0, 0], [3320613759263619.5, 0], [18562115921017575000000000000000, 0]], [[1.0, 0], [22017924651487973000, 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'7.45753467676015678922558812795933', '8.422048796732566740039092975693149', '10.08123335997394365918979508618135', '12.71627125398104200115109036481139', '14.84506040264417134492511671913198', '16.01541736793047335697822960656420', '18.93681688401047451573014777199158'], 'prelabel': '2-2-1.1-c37-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.1644696691080725, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c37-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.39387518847156318666877916962', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.69410166133358014376711419365', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.45753467676015678922558812796', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.342807624921097, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 2, 'conductor_radical': 2, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2/38/a/a/1/2'], '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': '2-2-1.1-c37-0-3', 'motivic_weight': 37, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [37], 'order_of_vanishing': 1, 'prelabel': '2-2-1.1-c37-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.1644696691080725, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c37-0', 'z1': {'__RealLiteral__': 0, 'data': '2.39387518847156318666877916962', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3034597319537442858041262366652', 'Lhash_array': ['3034597319537442858041262366652'], 'label': '2-2-1.1-c37-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2/38/a/a/1/2'}