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lfunc_lfunctions • Show schema
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{'Lhash': '4378351707816866814297211103581', 'a10': [-1.7768407681550857, 3.0775784874043204], 'a2': [-0.9396926207859084, -0.3420201433256687], 'a3': [-1.145171368693962, -1.2994547072997957], 'a4': [0.766044443118978, 0.6427876096865394], 'a5': [0.6170903227888787, -3.499693128694591], 'a6': [0.6316693994611238, 1.6127596751482918], 'a7': [-0.2447518819171296, 0.20537121384660864], 'a8': [-0.5, -0.8660254037844386], 'a9': [-0.3771650726471959, 2.9761966514286375], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4311921709149143, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9396926207859084, 0.3420201433256687]]], [3, [[1.0, 0], [1.145171368693962, 1.2994547072997957]]]], 'bad_primes': [2, 3], 'central_character': '54.31', 'coefficient_field': 'CDF', 'conductor': 54, 'conductor_radical': 6, 'conjugate': '1864658059888933730187943541639', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9396926207859084, 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.45391049160437654506309570118', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.95663554087565013889154636311', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.71241493544558731484101917092', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4311921709149143, 'bad_primes': [2, 3], 'central_character': '27.4', 'conductor': 54, 'conductor_radical': 6, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/54/2/e/b/31/1'], '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': '2-54-27.4-c1-0-2', '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': '2-54-27.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6566522450391183, 'root_angle': 0.2291675508156795, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.45391049160437654506309570118', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4378351707816866814297211103581', 'Lhash_array': ['4378351707816866814297211103581'], 'label': '2-54-27.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/54/2/e/b/31/1'}