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lfunc_lfunctions • Show schema
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{'Lhash': '655418569531432265361791572553', 'a10': [4863.403171335926, 0.0], 'a2': [-10.763006219231926, 0.0], 'a3': [0.0, 0.0], 'a4': [-12.157697124774902, 0.0], 'a5': [-451.86289706362265, 0.0], 'a6': [0.0, 0.0], 'a7': [-504.67210094618554, 0.0], 'a8': [1508.5181658271767, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 165.87644853206874, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [59, [[1.0, 0], [-205379.0, 0]]]], 'bad_primes': [3, 59], 'central_character': '531.1', 'coefficient_field': 'CDF', 'conductor': 531, 'conductor_radical': 177, 'degree': 2, 'euler_factors': [[[1.0, 0], [10.763006219231926, 0], [128.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [451.86289706362265, 0], [78125.0, 0]], [[1.0, 0], [504.67210094618554, 0], [823543.0, 0]], [[1.0, 0], [-8070.716823402113, 0], [19487171.0, 0]], [[1.0, 0], [4674.685829851152, 0], [62748517.0, 0]], [[1.0, 0], [-13498.963541266945, 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'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 165.87644853206874, 'bad_primes': [3, 59], 'central_character': '1.1', 'conductor': 531, 'conductor_radical': 177, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/531/8/a/d/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': '2-531-1.1-c7-0-36', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-531-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.87930310739167, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51703408605922632415201744884', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '655418569531432265361791572553', 'Lhash_array': ['655418569531432265361791572553'], 'label': '2-531-1.1-c7-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/531/8/a/d/1/5'}