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lfunc_lfunctions • Show schema
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{'Lhash': '2363102408354030434463202670770', 'a10': [-22.308785684274596, 39.61235540137381], 'a2': [-3.521494528592919, 2.033135814032916], 'a3': [-3.936602072686167, -2.2727982663577975], 'a4': [4.267282476606577, -7.39115005973094], 'a5': [9.622119821213742, -5.693400578407041], 'a6': [18.483630213615843, 3.253731710136552e-60], 'a7': [17.06623416463123, 7.193306015871548], 'a8': [0.0, 2.173686302608985], 'a9': [-3.168776080881982, -5.488481169896579], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0650668502009224, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-9.622119821213742, 5.693400578407041]]], [7, [[1.0, 0], [-17.06623416463123, -7.193306015871548]]]], 'bad_primes': [5, 7], 'central_character': '35.4', 'coefficient_field': 'CDF', 'conductor': 35, 'conductor_radical': 35, 'conjugate': '1293967060075684274215750555246', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.521494528592919, 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'4.99895808554948595513167567828681', '7.05905891382657512250595366470089', '8.891056254891177648581537541181983', '10.09053946416319517097871309511829', '10.91563835941103038945632084353363', '11.75988065151440276857504228875920', '13.75988451750009756856221710564693', '15.05661467609123127629466333606592', '16.94264107481819654995233925253838'], 'prelabel': '2-35-35.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4370340462915006, 'root_angle': 0.14374148485822202, 'root_number': '0.8997599581605097 + 0.4363851712547046*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0718707424291', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.86415910498411353857131335762', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.99895808554948595513167567829', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.05905891382657512250595366470', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.0650668502009224, 'bad_primes': [5, 7], 'central_character': '35.4', 'conductor': 35, 'conductor_radical': 35, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/35/4/j/a/4/2'], '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': '2-35-35.4-c3-0-3', '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': '2-35-35.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4370340462915006, 'root_angle': 0.07187074242911101, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.86415910498411353857131335762', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2363102408354030434463202670770', 'Lhash_array': ['2363102408354030434463202670770'], 'label': '2-35-35.4-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/4/j/a/4/2'}