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lfunc_lfunctions • Show schema
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{'Lhash': '2608752339905474783459212633315', 'a10': [1.5, -2.598076211353316], 'a2': [0.0, -1.7320508075688772], 'a3': [0.0, 1.7320508075688772], 'a4': [-1.0, 0.0], 'a5': [1.5, 0.8660254037844386], 'a6': [3.0, 0.0], 'a7': [1.5, 0.8660254037844386], 'a8': [0.0, -1.7320508075688772], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.934249703648981, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.7320508075688772]]], [13, [[1.0, 0], [1.0, -3.4641016151377544]]]], 'bad_primes': [3, 13], 'central_character': '117.4', 'coefficient_field': 'CDF', 'conductor': 117, 'conductor_radical': 39, 'conjugate': '2878522357429453563530549766943', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.7320508075688772], [-2.0, 0]], [[1.0, 0], [0, -1.7320508075688772]], [[1.0, 0], [-1.5, -0.8660254037844386], [2.5, 4.330127018922194]], [[1.0, 0], [-1.5, -0.8660254037844386], [3.5, 6.06217782649107]], [[1.0, 0], [0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.934249703648981, 'bad_primes': [3, 13], 'central_character': '117.4', 'conductor': 117, 'conductor_radical': 39, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/117/2/l/a/4/1'], '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': '2-117-117.4-c1-0-4', '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': '2-117-117.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9665659334204681, 'root_angle': 0.09824269791850555, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.05794273235526551664889387787', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2608752339905474783459212633315', 'Lhash_array': ['2608752339905474783459212633315'], 'factors': ['2-117-117.4-c1-0-4'], 'label': '2-117-117.4-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/117/2/l/a/4/1'}