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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_104.45', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.5, 0.8660254037844386], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-5.8869658587496495e-30, 1.0], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, -0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 11.176352178641002, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [13, [1]]], 'bad_primes': [2, 13], 'central_character': '104.45', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 104, 'conductor_radical': 26, 'conjugate': 'dirichlet_L_104.37', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^14', 0, 'a^15', 0, 'a^7', 0, 'a^4', 0, 'a^17', 0, 0, 0, 'a^5', 0, 'a^10', 0, 'a^7', 0, 'a^9', 0, 'a^2', 0, 'a^6', 0, 'a^6', 0, 'a^14', 0, 'a^9', 0, 'a^7', 0, 'a^10', 0, 'a^17', 0, 0, 0, 'a^5', 0, 'a^16', 0, 'a^7', 0, 'a^3', 0, 'a^2', 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'187.35806147157593903389644491277', '187.79733933551568567287045084982', '188.75013026149969007037516878179', '189.83591764331567891830572666337', '190.60331514667602599138410429311', '191.29908613866203384669609498680', '191.77070094954150036390536762988', '193.03446817746927222780493121760', '193.65100094235905945713633802196', '194.057833612885640063844661293624', '194.82822093205818911929604892774', '196.15560464109595417520853114129', '196.78776491189479470991300766773', '197.68472111944577509847095101894', '198.12399877620117966169879805839', '198.84207292394939196890267117469', '199.63292700327750354788302843789'], 'prelabel': '1-104-104.45-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.176352178641002, 'root_angle': 0.4938544305176336, 'root_number': '-0.999254581709519099972048691413+0.0386041569333409557940348872511*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.493854430518', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.779119756439372728716110185639+0.503871315391654905581829658833*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.61330071019', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.52865722331', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.0251868633', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 11.176352178641002, 'bad_primes': [2, 13], 'central_character': '104.45', 'conductor': 104, 'conductor_radical': 26, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/104/45'], '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': '1-104-104.45-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-104-104.45-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.176352178641002, 'root_angle': 0.4938544305176336, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.61330071019', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_104.45', 'Lhash_array': ['dirichlet_L_104.45'], 'factors': ['1-104-104.45-r1-0-0'], 'label': '1-104-104.45-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/104/45'}
Lfunction data - 1-104-104.45-r1-0-0