![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2380, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([8,8,0,13]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1219,2380))
\(\chi_{2380}(99,\cdot)\)
\(\chi_{2380}(379,\cdot)\)
\(\chi_{2380}(1219,\cdot)\)
\(\chi_{2380}(1499,\cdot)\)
\(\chi_{2380}(1639,\cdot)\)
\(\chi_{2380}(1779,\cdot)\)
\(\chi_{2380}(2199,\cdot)\)
\(\chi_{2380}(2339,\cdot)\)
![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 ]
\((1191,477,1361,1261)\) → \((-1,-1,1,e\left(\frac{13}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(33\) |
| \( \chi_{ 2380 }(1219, a) \) |
\(1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(1\) |
![Copy content]()
sage:chi.jacobi_sum(n)
