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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1441.292', 'a10': [-0.9895063994510511, -0.14448904956922132], 'a2': [0.39936458356569554, -0.9167921953165824], 'a3': [0.7796743540632224, 0.6261851975383137], 'a4': [-0.6810158587867972, -0.7322686665977736], 'a5': [-0.2627073781985869, -0.9648755533435515], 'a6': [0.8854560256532099, -0.46472317204376856], 'a7': [0.44319154559924134, 0.8964269372957038], 'a8': [-0.943311813257743, 0.33190785312852844], 'a9': [0.21578419676780614, 0.9764410788292721], 'algebraic': True, 'analytic_conductor': 6.691975866344493, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [131, [1]]], 'bad_primes': [11, 131], 'central_character': '1441.292', 'coeff_info': ['x^130 - 1', '0.998832226832327 + 0.0483133795255071*I', '\\\\zeta_{130}'], 'conductor': 1441, 'conductor_radical': 1441, 'conjugate': 'dirichlet_L_1441.607', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^106', 'a^14', 'a^82', 'a^92', 'a^120', 'a^23', 'a^58', 'a^28', 'a^68', 0, 'a^96', 'a^49', 'a^129', 'a^106', 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{'__RealLiteral__': 0, 'data': '2.77729885527', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.691975866344493, 'bad_primes': [11, 131], 'central_character': '1441.292', 'conductor': 1441, 'conductor_radical': 1441, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1441/292'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-1441-1441.292-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1441-1441.292-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': 0.0024986230308059265, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19001382174', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1441.292', 'Lhash_array': ['dirichlet_L_1441.292'], 'label': '1-1441-1441.292-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1441/292'}