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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1323.1222', 'a10': [0.6234898018587335, 0.7818314824680298], 'a2': [-0.9987569212189223, -0.04984588566069716], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9950307753654014, 0.09956784659581666], 'a5': [-0.6616858375968594, -0.7497812029677342], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9888308262251285, -0.14904226617617444], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 6.143986170141405, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '1323.1222', 'coeff_info': ['x^63 - 1', '0.995030775365401 + 0.0995678465958167*I', '\\\\zeta_{63}'], 'conductor': 1323, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_1323.1192', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^32', 0, 'a^1', 'a^40', 0, 0, 'a^33', 0, 'a^9', 'a^32', 0, 'a^25', 0, 0, 'a^2', 'a^27', 0, 'a^0', 'a^41', 0, 'a^1', 'a^43', 0, 'a^17', 'a^57', 0, 0, 'a^20', 0, 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'188.12865582030038923263388441751', '188.59710506214096733425650396676', '188.72420437896496582015322883971', '189.56600562588713376526256291951', '190.52773175195048293725703265982', '190.81461644118989167450392462878', '191.16879676159734183738119694869', '192.04710667461653906465960439351', '192.2972376857353539532715990151', '193.09007474669810150563738844611', '193.50123311518542255360257508194', '194.225553953382171120336533231561', '195.13307067864454796405949901133', '195.58891284784695432630552212002', '196.244840679735507048299961851064', '196.756534574020061100784792799892', '197.42023289922555304019959076605', '197.87728968715019058945321193234', '198.76850143077171042428839396180', '199.24394193040905620113566042500', '199.43684786663377657401180639055'], 'prelabel': '1-1323-1323.1222-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.143986170141405, 'root_angle': -0.08408919123204839, 'root_number': '0.863641048568571506702396480225-0.504107269564106079707925548695*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.084089191232', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(63)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.530841617114015611086452614731-0.0622850867494037329846498001900*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.520127057449', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.78260012741', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.66961080374', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.143986170141405, 'bad_primes': [3, 7], 'central_character': '1323.1222', 'conductor': 1323, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1323/1222'], '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': '1-1323-1323.1222-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': '1-1323-1323.1222-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.143986170141405, 'root_angle': -0.08408919123204839, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.520127057449', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1323.1222', 'Lhash_array': ['dirichlet_L_1323.1222'], 'factors': ['1-1323-1323.1222-r0-0-0'], 'label': '1-1323-1323.1222-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1323/1222'}
Lfunction data - 1-1323-1323.1222-r0-0-0