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lfunc_lfunctions • Show schema
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{'Lhash': '2620109864203985957120094537489', 'a10': [0.5, -0.8660254037844386], 'a2': [0.8660254037844386, 0.5], 'a3': [0.5, -0.8660254037844386], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, -1.0], 'a6': [0.8660254037844386, -0.5], 'a7': [0.0, 0.0], 'a8': [3.9689140359382235e-80, 1.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0, 1.0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1109', 'coefficient_field': 'CDF', 'conductor': 1560, 'conductor_radical': 390, 'conjugate': '1731756680369770539688745589275', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [-0.5, 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{'__RealLiteral__': 0, 'data': '3.72485575481078228146443938005', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.1109', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/1/dk/b/1109/2'], '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': '2-1560-1560.1109-c0-0-3', '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': '2-1560-1560.1109-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.08129238194076664, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.06690223925445867820585087038', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2620109864203985957120094537489', 'Lhash_array': ['2620109864203985957120094537489'], 'label': '2-1560-1560.1109-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/1/dk/b/1109/2'}