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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1053.2', 'a10': [-0.17364817766693036, 0.984807753012208], 'a2': [0.8021231927550437, 0.5971585917027862], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.28680323271109026, 0.9579895123154889], 'a5': [0.44879918020046217, 0.8936326403234123], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.23061587074244017, 0.9730448705798238], 'a8': [-0.3420201433256687, 0.9396926207859084], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 4.890111441541118, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1053.2', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 1053, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_1053.527', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 0, 'a^22', 'a^19', 0, 'a^23', 'a^33', 0, 'a^30', 'a^89', 0, 0, 'a^34', 0, 'a^44', 'a^84', 0, 'a^33', 'a^41', 0, 'a^100', 'a^4', 0, 'a^38', 0, 0, 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'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.38513889128513566215626836046+1.18239994693691839556131213003*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.71666003625', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.9406748146', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.25736101109', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.890111441541118, 'bad_primes': [3, 13], 'central_character': '1053.2', 'conductor': 1053, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1053/2'], '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': '1-1053-1053.2-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': '1-1053-1053.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.890111441541118, 'root_angle': 0.3816978510460028, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71666003625', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1053.2', 'Lhash_array': ['dirichlet_L_1053.2'], 'label': '1-1053-1053.2-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1053/2'}
Lfunction data - 1-1053-1053.2-r0-0-0