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lfunc_lfunctions • Show schema
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{'Lhash': '2138881259258193067119262607777', 'a10': [1.766668786066786, -1.3707229480596392], 'a2': [0.9396926207859084, -0.3420201433256687], 'a3': [-0.3623697706755305, 0.9956027624239698], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [2.1289404807948986, -0.6838219280140017], 'a6': [-3.0133044510018854e-61, 1.059498329987205], 'a7': [-1.0618539668965883, 0.18723350393618174], 'a8': [0.5, -0.8660254037844386], 'a9': [1.438220319510131, 1.2068101396526207], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9396926207859084, 0.3420201433256687]]], [5, [[1.0, 0], [-2.1289404807948986, 0.6838219280140017]]], [37, [[1.0, 0], [4.8663135626479095, 3.6495194628867247]]]], 'bad_primes': [2, 5, 37], 'central_character': '370.289', 'coefficient_field': 'CDF', 'conductor': 370, 'conductor_radical': 370, 'conjugate': 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'data': '-0.00129018522271', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68727980633867582026239196669', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12288765424161898488161071604', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.52097489333390051872455789509', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9544648747873756, 'bad_primes': [2, 5, 37], 'central_character': '185.104', 'conductor': 370, 'conductor_radical': 370, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/370/2/v/b/289/5'], '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': '2-370-185.104-c1-0-10', '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': '2-370-185.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7188556875978203, 'root_angle': -0.001290185222714487, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68727980633867582026239196669', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2138881259258193067119262607777', 'Lhash_array': ['2138881259258193067119262607777'], 'label': '2-370-185.104-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/370/2/v/b/289/5'}