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  • lfunc_lfunctions • Show schema
    {'Lhash': '1341032623986647965509363064419', 'a10': [-3.1689260525637875e-61, -0.9110302710469612], 'a2': [-0.20489878127603442, -0.24418885870388926], 'a3': [0.0, 0.0], 'a4': [0.3296516671871569, -1.8695475069251908], 'a5': [2.1893484884792693, 1.8370815092014903], 'a6': [0.0, 0.0], 'a7': [0.4680068574684536, 2.604029489341951], 'a8': [-1.0761866593121274, 0.6213366574521408], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.4680068574684536, -2.604029489341951]]]], 'bad_primes': [3, 7], 'central_character': '567.341', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '2361362910405465376198398334799', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.20489878127603442, 0.24418885870388926], [-0.3472963553338607, 1.969615506024416]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'data': '2.78028129317611599279539498106', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00787608474881048705594774809', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '189.131', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/ba/a/341/10'], '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': '2-567-189.131-c1-0-5', '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': '2-567-189.131-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': -0.07745980817690114, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05788820968901586333144173400', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '1341032623986647965509363064419', 'Lhash_array': ['1341032623986647965509363064419'], 'factors': ['2-567-189.131-c1-0-5'], 'label': '2-567-189.131-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/ba/a/341/10'}