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lfunc_lfunctions • Show schema
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{'Lhash': '732510056034467105384722359189', 'a10': [2.0, 0], 'a2': [-0.5, -0.8660254037844386], 'a3': [0, 0], 'a4': [0.5, -0.8660254037844386], 'a5': [-1.0, 1.7320508075688772], 'a6': [0, 0], 'a7': [2.0, 3.4641016151377544], 'a8': [-3.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.408247332840828, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [3, 13], 'central_character': '1053.352', 'coefficient_field': 'CDF', 'conductor': 1053, 'conductor_radical': 39, 'conjugate': '1781387652041126682469690625673', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, -1.7320508075688772], [-2.5, -4.330127018922194]], [[1.0, 0], [-2.0, -3.4641016151377544], [-3.5, 6.06217782649107]], [[1.0, 0], [2.0, 3.4641016151377544], [-5.5, 9.526279441628825]], [[1.0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.408247332840828, 'bad_primes': [3, 13], 'central_character': '9.4', 'conductor': 1053, 'conductor_radical': 39, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1053/2/e/b/352/1'], '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': '2-1053-9.4-c1-0-7', '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': '2-1053-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8996978002614044, 'root_angle': -0.11111111111111113, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57784854588684380191294648504', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '732510056034467105384722359189', 'Lhash_array': ['732510056034467105384722359189'], 'label': '2-1053-9.4-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1053/2/e/b/352/1'}