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{'Lhash': 'dirichlet_L_4160.1309', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.1305261922200516, 0.9914448613738104], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.25881904510252074, -0.9659258262890683], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9659258262890683, 0.25881904510252074], 'algebraic': True, 'analytic_conductor': 19.31895878139701, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '4160.1309', 'coeff_info': ['x^48 - 1', '0.991444861373810 + 0.130526192220052*I', '\\\\zeta_{48}'], 'conductor': 4160, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_4160.1589', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^11', 0, 0, 0, 'a^82', 0, 'a^22', 0, 'a^53', 0, 0, 0, 0, 0, 'a^52', 0, 'a^55', 0, 'a^45', 0, 'a^38', 0, 0, 0, 'a^33', 0, 'a^59', 0, 'a^24', 0, 'a^64', 0, 0, 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.31895878139701, 'bad_primes': [2, 5, 13], 'central_character': '4160.1309', 'conductor': 4160, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4160/1309'], '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': '1-4160-4160.1309-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': '1-4160-4160.1309-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.31895878139701, 'root_angle': 0.2750211909703833, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.970606566304', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4160.1309', 'Lhash_array': ['dirichlet_L_4160.1309'], 'label': '1-4160-4160.1309-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4160/1309'}