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lfunc_lfunctions • Show schema
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{'Lhash': '192044817604610074445234200554', 'a10': [-0.8780933200460308, 0.0], 'a2': [0.2205863862586966, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.9513416461973292, 0.0], 'a5': [-3.9807230851328756, 0.0], 'a6': [0.0, 0.0], 'a7': [0.11395966312987937, 0.0], 'a8': [-0.871612174608158, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.26137902105694, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '9801.1', 'coefficient_field': 'CDF', 'conductor': 9801, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.2205863862586966, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.9807230851328756, 0], [5.0, 0]], [[1.0, 0], [-0.11395966312987937, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.38792786386003, 0], [13.0, 0]], [[1.0, 0], [-5.392514418714723, 0], [17.0, 0]], [[1.0, 0], [4.997914018577864, 0], [19.0, 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'4.26489308796121353912411724957992', '4.73496154064792023250658777759529', '5.35884751334812490343548177527981', '6.36713839546595193023969281996479', '7.16385171190339187489419458842198', '7.86756806823180797638411455385280'], 'prelabel': '2-99e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846546163393764, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.15149664865857680735774581048', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.56038004682967233897071865579', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00332801802038508101939060454', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.26137902105694, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 9801, 'conductor_radical': 33, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9801/2/a/by/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': '2-99e2-1.1-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-99e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846546163393764, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.15149664865857680735774581048', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '192044817604610074445234200554', 'Lhash_array': ['192044817604610074445234200554'], 'label': '2-99e2-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9801/2/a/by/1/5'}