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lfunc_lfunctions • Show schema
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{'Lhash': '3550562876152344068180686297547', 'a10': [-1.5, -0.8660254037844386], 'a2': [0.9659258262890683, -0.25881904510252074], 'a3': [0.0, 0.0], 'a4': [0.8660254037844386, -0.5], 'a5': [-1.224744871391589, -1.224744871391589], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.23356242591224513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9659258262890683, 0.25881904510252074]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 13], 'central_character': '468.71', 'coefficient_field': 'CDF', 'conductor': 468, 'conductor_radical': 78, 'conjugate': '2038339789418894322355778895120', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9659258262890683, 0.25881904510252074]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.224744871391589, 1.224744871391589], [0, 1.0]], [[1.0, 0], [0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.23356242591224513, 'bad_primes': [2, 3, 13], 'central_character': '156.71', 'conductor': 468, 'conductor_radical': 78, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/468/1/bx/a/71/2'], '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': '2-468-156.71-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-468-156.71-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.48328296671023396, 'root_angle': 0.15818893147471458, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.80090024452565737098268707264', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3550562876152344068180686297547', 'Lhash_array': ['3550562876152344068180686297547'], 'factors': ['2-468-156.71-c0-0-1'], 'label': '2-468-156.71-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/468/1/bx/a/71/2'}