![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28665, base_ring=CyclotomicField(28))
M = H._module
chi = DirichletCharacter(H, M([14,21,8,14]))
![Copy content]()
pari:[g,chi] = znchar(Mod(19538,28665))
\(\chi_{28665}(3158,\cdot)\)
\(\chi_{28665}(3977,\cdot)\)
\(\chi_{28665}(8072,\cdot)\)
\(\chi_{28665}(11348,\cdot)\)
\(\chi_{28665}(12167,\cdot)\)
\(\chi_{28665}(15443,\cdot)\)
\(\chi_{28665}(16262,\cdot)\)
\(\chi_{28665}(19538,\cdot)\)
\(\chi_{28665}(20357,\cdot)\)
\(\chi_{28665}(23633,\cdot)\)
\(\chi_{28665}(27728,\cdot)\)
\(\chi_{28665}(28547,\cdot)\)
![Copy content]()
sage:chi.galois_orbit()
![Copy content]()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((25481,11467,18721,11026)\) → \((-1,-i,e\left(\frac{2}{7}\right),-1)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) | \(29\) |
| \( \chi_{ 28665 }(19538, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(1\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
