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lfunc_lfunctions • Show schema
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{'Lhash': '1571458183207068826341542253409', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 4.301691043097465], 'a4': [0.0, 0.0], 'a5': [8.58257569495584, 7.16515138991168], 'a6': [0.0, 0.0], 'a7': [0.0, -28.31620690750261], 'a8': [0.0, 0.0], 'a9': [8.49545416973504, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.440305600918503, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-8.58257569495584, -7.16515138991168]]]], 'bad_primes': [2, 5], 'central_character': '160.129', 'coefficient_field': 'CDF', 'conductor': 160, 'conductor_radical': 10, 'conjugate': '1979983349460698398341626503566', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -4.301691043097465], [-27.0, 0]], [[1.0, 0], [-8.58257569495584, -7.16515138991168]], [[1.0, 0], [0, 28.31620690750261], [-343.0, 0]], [[1.0, 0], [-65.23579590120015, 0], [1331.0, 0]], [[1.0, 0], [0, -33.66969722017664], [-2197.0, 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['1.23966192492169492694470605436268', '2.48600369849055589303356204426210', '4.64008319903868148717623633520951', '6.01327237379624715361047431653169', '6.68896330492514016541639423111243', '8.374677045455460130359117812570925', '9.037935095013584841341932593066544', '10.05150361930136669543305855543673', '11.78719477915906677016778557223816', '12.27462208942282877977934992218362'], 'prelabel': '2-160-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.072508031058422, 'root_angle': -0.27857349808488796, 'root_number': '0.6408706230767846 - 0.7676489070383504*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.139286749042', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23966192492169492694470605436', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48600369849055589303356204426', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.64008319903868148717623633521', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.440305600918503, 'bad_primes': [2, 5], 'central_character': '5.4', 'conductor': 160, 'conductor_radical': 10, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/160/4/c/d/129/6'], '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': '2-160-5.4-c3-0-9', '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': '2-160-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.072508031058422, 'root_angle': -0.13928674904244398, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23966192492169492694470605436', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1571458183207068826341542253409', 'Lhash_array': ['1571458183207068826341542253409'], 'label': '2-160-5.4-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/160/4/c/d/129/6'}