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lfunc_lfunctions • Show schema
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{'Lhash': '1589373151830763932551196596827', 'a10': [0.8635727701915286, 0.0], 'a2': [0.4472782233464983, 0.0], 'a3': [0.0, 0.0], 'a4': [-7.79994219092, 0.0], 'a5': [1.9307284037446517, 0.0], 'a6': [0.0, 0.0], 'a7': [8.1453703243702, 0.0], 'a8': [-7.066970072132078, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.4472782233464983, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.9307284037446517, 0], [125.0, 0]], [[1.0, 0], [-8.1453703243702, 0], [343.0, 0]], [[1.0, 0], [-8.408415535098209, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-52.12713776882049, 0], [4913.0, 0]], [[1.0, 0], [48.83044013143488, 0], [6859.0, 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'4.24678647511237328495814579314193', '5.64009921029944032516287959024470', '5.77296479990981163294161835044205', '7.27244449784593615556648500648182', '7.944585491578587656740766884996790', '8.766072807263789432906937830021305'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25379434328718907243274242497', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48427927055281865006370487960', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.90621921499643429040701461373', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 129, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/bi/1/5'], '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': '2-39e2-1.1-c3-0-129', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25379434328718907243274242497', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1589373151830763932551196596827', 'Lhash_array': ['1589373151830763932551196596827'], 'label': '2-39e2-1.1-c3-0-129', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bi/1/5'}