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lfunc_lfunctions • Show schema
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{'Lhash': '2211276769262842814737509466758', 'a10': [1.5782130769786642, -3.455804593899396], 'a2': [-0.9594929736144974, -0.28173255684142967], 'a3': [-0.7497367425841662, -0.6496505855579487], 'a4': [0.8412535328311812, 0.5406408174555976], 'a5': [-0.5406716940439088, 3.7604542314489513], 'a6': [0.5363394160473558, 0.8345604215935977], 'a7': [-2.618558180231006, 0.3783557277817849], 'a8': [-0.6548607339452851, -0.7557495743542583], 'a9': [-0.28688521495492464, -1.995330497974573], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9594929736144974, 0.28173255684142967]]], [7, [[1.0, 0], [2.618558180231006, -0.3783557277817849]]], [23, [[1.0, 0], [-2.1386124898274814, 4.292590898088694]]]], 'bad_primes': [2, 7, 23], 'central_character': '322.97', 'coefficient_field': 'CDF', 'conductor': 322, 'conductor_radical': 322, 'conjugate': 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0.7322717686095267, 'root_number': '-0.666648498917963 + 0.7453722418298301*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.366135884305', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74438979389488063674637427696', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.00671596997136985062404372915', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.09395230606645246415857302701', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'bad_primes': [2, 7, 23], 'central_character': '161.97', 'conductor': 322, 'conductor_radical': 322, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/322/2/k/a/97/3'], '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': '2-322-161.97-c1-0-8', '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': '2-322-161.97-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6034908621770283, 'root_angle': 0.36613588430476335, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74438979389488063674637427696', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2211276769262842814737509466758', 'Lhash_array': ['2211276769262842814737509466758'], 'label': '2-322-161.97-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/322/2/k/a/97/3'}