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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5160.1109', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, -0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 23.96293925769437, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [43, [1]]], 'bad_primes': [2, 3, 5, 43], 'central_character': '5160.1109', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 5160, 'conductor_radical': 1290, 'conjugate': 'dirichlet_L_5160.3029', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^28', 0, 0, 0, 'a^60', 0, 'a^22', 0, 0, 0, 'a^34', 0, 'a^38', 0, 0, 0, 'a^32', 0, 0, 0, 0, 0, 'a^61', 0, 'a^26', 0, 0, 0, 0, 0, 'a^35', 0, 0, 0, 'a^33', 0, 0, 0, 0, 0, 'a^24', 0, 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{'__RealLiteral__': 0, 'data': '2.17716288316', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 23.96293925769437, 'bad_primes': [2, 3, 5, 43], 'central_character': '5160.1109', 'conductor': 5160, 'conductor_radical': 1290, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5160/1109'], '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': '1-5160-5160.1109-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': '1-5160-5160.1109-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 23.96293925769437, 'root_angle': 0.40244040719111135, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0841917902081', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5160.1109', 'Lhash_array': ['dirichlet_L_5160.1109'], 'factors': ['1-5160-5160.1109-r0-0-0'], 'label': '1-5160-5160.1109-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5160/1109'}
Lfunction data - 1-5160-5160.1109-r0-0-0