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lfunc_lfunctions • Show schema
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{'Lhash': '2396933824328890712054519080342', 'a10': [-0.3584407085710257, -0.6208375187460057], 'a2': [0.11878234922776941, -0.6736481776669303], 'a3': [0.0, 0.0], 'a4': [1.4396926207859084, 0.5240052604587699], 'a5': [0.8028226358791068, -0.6736481776669303], 'a6': [0.0, 0.0], 'a7': [0.11334079845283873, -0.04125267696479814], 'a8': [1.2080455471101075, -2.092396265452048], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.649', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1225126707578699022509965681364', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.11878234922776941, 0.6736481776669303], [-1.8793852415718169, -0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8028226358791068, 0.6736481776669303], [0.8682408883346517, 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103}, 'z3': {'__RealLiteral__': 0, 'data': '4.45599997355821570822878007332', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.25', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/q/649/2'], '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': '2-3e6-27.25-c1-0-27', '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': '2-3e6-27.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.23148148148148148, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89084738641495041672478950555', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2396933824328890712054519080342', 'Lhash_array': ['2396933824328890712054519080342'], 'label': '2-3e6-27.25-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/q/649/2'}