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lfunc_lfunctions • Show schema
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{'Lhash': '2371732654531372289833672742315', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.029061382345502, -1.1714791352994498], 'a4': [0.0, 0.0], 'a5': [-2.4367686074289225, 0.0], 'a6': [0.0, 0.0], 'a7': [0.9847475681106149, -0.5685442735324928], 'a8': [0.0, 0.0], 'a9': [-1.7552732711161072, -3.0402224867407184], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.335178997388352, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-7.057421802093887, 10.917545397539223]]]], 'bad_primes': [2, 13], 'central_character': '416.191', 'coefficient_field': 'CDF', 'conductor': 416, 'conductor_radical': 26, 'conjugate': '154339912409399057174100328783', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.029061382345502, 1.1714791352994498], [4.5, 7.794228634059948]], [[1.0, 0], [2.4367686074289225, 0], [25.0, 0]], [[1.0, 0], [-0.9847475681106149, 0.5685442735324928], [24.5, 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'10.86278259337773023795695408623335', '11.49051324831798185707519512676594'], 'prelabel': '2-416-52.35-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3667757569206107, 'root_angle': -0.49098004244760834, 'root_number': '-0.9983944550046913 - 0.05664373059646982*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.490980042448', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.87096716879585161138204348096', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.89632006855211318516541072334', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.37073204759588699729468293824', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.335178997388352, 'bad_primes': [2, 13], 'central_character': '52.35', 'conductor': 416, 'conductor_radical': 26, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/416/3/bb/c/191/6'], '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': '2-416-52.35-c2-0-25', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-416-52.35-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3667757569206107, 'root_angle': -0.49098004244760834, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.87096716879585161138204348096', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2371732654531372289833672742315', 'Lhash_array': ['2371732654531372289833672742315'], 'factors': ['2-416-52.35-c2-0-25'], 'label': '2-416-52.35-c2-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/416/3/bb/c/191/6'}