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lfunc_lfunctions • Show schema
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{'Lhash': '3411520179963440843682016016284', 'a10': [3.5, 6.06217782649107], 'a2': [0.5, 0.8660254037844386], 'a3': [-1.5, -2.598076211353316], 'a4': [3.5, -6.06217782649107], 'a5': [7.0, 0.0], 'a6': [1.5, -2.598076211353316], 'a7': [5.0, -8.660254037844387], 'a8': [15.0, 0.0], 'a9': [-4.5, 7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.301074490223885, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5, 2.598076211353316]]], [13, [[1.0, 0], [45.5, -11.258330249197702]]]], 'bad_primes': [3, 13], 'central_character': '39.16', 'coefficient_field': 'CDF', 'conductor': 39, 'conductor_radical': 39, 'conjugate': '2204983443050339549427312125038', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386], [-4.0, 6.928203230275509]], [[1.0, 0], [1.5, 2.598076211353316]], [[1.0, 0], [-7.0, 0], [125.0, 0]], [[1.0, 0], [-5.0, 8.660254037844387], [-171.5, -297.04671349806245]], [[1.0, 0], 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'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.69121489734570904503322389083', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.74113648188002584159266979691', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.51087938510444781682605443790', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.301074490223885, 'bad_primes': [3, 13], 'central_character': '13.3', 'conductor': 39, 'conductor_radical': 39, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/39/4/e/b/16/1'], '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': '2-39-13.3-c3-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-39-13.3-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': 0.08537428472590003, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.69121489734570904503322389083', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3411520179963440843682016016284', 'Lhash_array': ['3411520179963440843682016016284'], 'label': '2-39-13.3-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/39/4/e/b/16/1'}