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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_896.445', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9469301294951057, 0.3214394653031616], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.8968727415326883, -0.4422886902190013], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.7933533402912352, -0.6087614290087207], 'algebraic': True, 'analytic_conductor': 4.161006506762433, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '896.445', 'coeff_info': ['x^96 - 1', '0.997858923238603 + 0.0654031292301431*I', '\\\\zeta_{96}'], 'conductor': 896, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_896.149', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^139', 0, 'a^89', 0, 0, 0, 'a^86', 0, 'a^109', 0, 'a^87', 0, 'a^36', 0, 'a^124', 0, 'a^95', 0, 0, 0, 'a^62', 0, 'a^82', 0, 'a^33', 0, 'a^3', 0, 'a^136', 0, 'a^56', 0, 0, 0, 'a^113', 0, 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{'__RealLiteral__': 0, 'data': '3.40791015583', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.161006506762433, 'bad_primes': [2, 7], 'central_character': '896.445', 'conductor': 896, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/896/445'], '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': '1-896-896.445-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': '1-896-896.445-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.161006506762433, 'root_angle': 0.02376769013969361, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02268177013', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_896.445', 'Lhash_array': ['dirichlet_L_896.445'], 'factors': ['1-896-896.445-r0-0-0'], 'label': '1-896-896.445-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/896/445'}