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lfunc_lfunctions • Show schema
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{'Lhash': '1498665179158451409581690056701', 'a10': [-1.5, 2.598076211353316], 'a2': [0.8660254037844386, 0.5], 'a3': [0.5, -0.8660254037844386], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, 3.0], 'a6': [0.8660254037844386, -0.5], 'a7': [-2.598076211353316, 1.5], 'a8': [0.0, 1.0], 'a9': [1.0, 1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.6989435883192785, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 13], 'central_character': '338.147', 'coefficient_field': 'CDF', 'conductor': 338, 'conductor_radical': 26, 'conjugate': '3232543234239193666836379653789', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.5, 0.8660254037844386], [-1.5, -2.598076211353316]], [[1.0, 0], [0, -3.0], [-5.0, 0]], [[1.0, 0], [2.598076211353316, -1.5], [3.5, -6.06217782649107]], [[1.0, 0], [0, 0], [5.5, 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09173494102892783268122105548', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6989435883192785, 'bad_primes': [2, 13], 'central_character': '13.4', 'conductor': 338, 'conductor_radical': 26, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/338/2/e/c/147/2'], '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': '2-338-13.4-c1-0-5', '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': '2-338-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6428461852283307, 'root_angle': -0.20731285763704999, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18223836985414581431463868065', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1498665179158451409581690056701', 'Lhash_array': ['1498665179158451409581690056701'], 'label': '2-338-13.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/338/2/e/c/147/2'}