![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1122, base_ring=CyclotomicField(8))
M = H._module
chi = DirichletCharacter(H, M([4,4,3]))
![Copy content]()
pari:[g,chi] = znchar(Mod(593,1122))
\(\chi_{1122}(263,\cdot)\)
\(\chi_{1122}(461,\cdot)\)
\(\chi_{1122}(593,\cdot)\)
\(\chi_{1122}(791,\cdot)\)
![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 ]
\((749,409,1057)\) → \((-1,-1,e\left(\frac{3}{8}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 1122 }(593, a) \) |
\(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
