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lfunc_lfunctions • Show schema
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{'Lhash': '2940882410556429695424905824864', 'a10': [0.9396926207859084, 1.6275953626987474], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [1.7232798302233832, 0.6272225635126262], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [-0.32635182233306964, -1.8508331567966467], 'a6': [-1.833876091079788, -2.804978665060675e-63], 'a7': [0.5984888042569352, 3.3941986748270985], 'a8': [-0.5, 0.8660254037844386], 'a9': [0.2781518997184476, 0.23339715646500916], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9396926207859084, -0.3420201433256687]]], [37, [[1.0, 0], [2.563680537885292, -5.516116577780801]]]], 'bad_primes': [2, 37], 'central_character': '74.7', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '3219913097137029656501749817575', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9396926207859084, 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.31994716054009641416243844545', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.98282362841921112276334608742', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.81210004841551863407061843341', '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': '37.7', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/f/b/7/2'], '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': '2-74-37.7-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': '2-74-37.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': -0.06045601550892638, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.31994716054009641416243844545', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2940882410556429695424905824864', 'Lhash_array': ['2940882410556429695424905824864'], 'label': '2-74-37.7-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/f/b/7/2'}