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lfunc_lfunctions • Show schema
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{'Lhash': '59920009502918768031596927392', 'a10': [-6.254344303889397, -7.217898097283565], 'a2': [-0.7645815764181828, 1.1897121555241361], 'a3': [0.0, 0.0], 'a4': [-0.8308300260037729, -1.8192639907090367], 'a5': [-1.9026323381714767, 6.4797706744086145], 'a6': [0.0, 0.0], 'a7': [-7.741270436058252, 8.93390233029462], 'a8': [2.7996378148714145, 0.4025271488260269], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.280682944516293, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7645815764181828, -1.1897121555241361]]], [3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-21.744150537401353, 7.49612682702397]]]], 'bad_primes': [2, 3, 23], 'central_character': '414.71', 'coefficient_field': 'CDF', 'conductor': 414, 'conductor_radical': 138, 'conjugate': '3337216229326788313611221424309', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7645815764181828, -1.1897121555241361]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.04726855293732412897141862997', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.30332798666816139065936328697', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16564633880507869394943035508', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.280682944516293, 'bad_primes': [2, 3, 23], 'central_character': '69.2', 'conductor': 414, 'conductor_radical': 138, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/414/3/k/a/71/1'], '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': '2-414-69.2-c2-0-0', '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': '2-414-69.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.358672795095749, 'root_angle': 0.2659493381603262, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.04726855293732412897141862997', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '59920009502918768031596927392', 'Lhash_array': ['59920009502918768031596927392'], 'label': '2-414-69.2-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/414/3/k/a/71/1'}