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lfunc_lfunctions • Show schema
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{'Lhash': '4270034276510467691425361337513', 'a10': [-12.792169499530035, -39.37024947345899], 'a2': [2.8053646048948266, -2.038216692017048], 'a3': [0.0, -1.5409812459463033], 'a4': [1.2436073277802104, -3.827429799419663], 'a5': [3.6890329698989883, -11.353676039554848], 'a6': [-3.1408536975729833, -4.323014244184489], 'a7': [-3.258578131919631, 4.485048027216911], 'a8': [4.260072100913057, 13.111153772159708], 'a9': [24.625376799641778, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.419078310235366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[41, [[1.0, 0], [-38.9192319351313, 259.6272200397706]]]], 'bad_primes': [41], 'central_character': '41.4', 'coefficient_field': 'CDF', 'conductor': 41, 'conductor_radical': 41, 'conjugate': '2623806390776959280818531476488', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.8053646048948266, 2.038216692017048], [2.4721359549995796, -7.608452130361228]], [[1.0, 0], [0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.419078310235366, 'bad_primes': [41], 'central_character': '41.4', 'conductor': 41, 'conductor_radical': 41, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/41/4/f/a/4/8'], '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': '2-41-41.4-c3-0-7', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-41-41.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5553386480877296, 'root_angle': 0.18431765602245698, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.36846310469279576965261393691', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4270034276510467691425361337513', 'Lhash_array': ['4270034276510467691425361337513'], 'label': '2-41-41.4-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/41/4/f/a/4/8'}