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lfunc_lfunctions • Show schema
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{'Lhash': '970874230951246366977068630142', 'a10': [0.0, 0.0], 'a2': [-13.360724644064579, 0.0], 'a3': [-163.41455809235057, 0.0], 'a4': [-333.49103698548544, 0.0], 'a5': [0.0, 0.0], 'a6': [2183.3369135033913, 0.0], 'a7': [-2401.0, 0.0], 'a8': [11296.372934187691, 0.0], 'a9': [7021.317796518225, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 90.13127132867783, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2401.0, 0]]]], 'bad_primes': [5, 7], 'central_character': '175.1', 'coefficient_field': 'CDF', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'euler_factors': [[[1.0, 0], [13.360724644064579, 0], [512.0, 0]], [[1.0, 0], [163.41455809235057, 0], [19683.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2401.0, 0]], [[1.0, 0], [90199.89342761417, 0], [2357947691.0, 0]], [[1.0, 0], [-3199.885397692782, 0], [10604499373.0, 0]], [[1.0, 0], [116494.27048088214, 0], [118587876497.0, 0]], 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'4.32909173481365273822846362323', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 90.13127132867783, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/10/a/d/1/2'], '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': '2-175-1.1-c9-0-29', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 1, 'prelabel': '2-175-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.493749066026435, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76588472468395388654175095457', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '970874230951246366977068630142', 'Lhash_array': ['970874230951246366977068630142'], 'factors': ['2-175-1.1-c9-0-29'], 'label': '2-175-1.1-c9-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/10/a/d/1/2'}