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lfunc_lfunctions • Show schema
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{'Lhash': '1884084642089719692655527814285', 'a10': [-0.766044443118978, -1.3268278963378768], 'a2': [0.766044443118978, 0.6427876096865394], 'a3': [-2.4126177261252173, 2.0244266441634378], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [-1.4396926207859084, -0.5240052604587699], 'a6': [-3.1494487660561257, -1.4104536630172788e-60], 'a7': [4.534238148034289, 1.6503277209587917], 'a8': [-0.5, 0.8660254037844386], 'a9': [1.2014765218139845, -6.813911954861171], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.766044443118978, -0.6427876096865394]]], [37, [[1.0, 0], [-5.840378677317959, 1.699993207495172]]]], 'bad_primes': [2, 37], 'central_character': '74.71', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '5339908103140470782695552631175', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.766044443118978, 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50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48628071627190231624132091261', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.46444877350296453794281036012', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.64784939369976856170397718391', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.34', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/f/b/71/1'], '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': '2-74-37.34-c1-0-0', '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': '2-74-37.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': -0.2778112815665586, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48628071627190231624132091261', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1884084642089719692655527814285', 'Lhash_array': ['1884084642089719692655527814285'], 'label': '2-74-37.34-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/f/b/71/1'}