sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1920, base_ring=CyclotomicField(32))
M = H._module
chi = DirichletCharacter(H, M([16,27,0,24]))
pari:[g,chi] = znchar(Mod(1123,1920))
χ1920(163,⋅)
χ1920(187,⋅)
χ1920(403,⋅)
χ1920(427,⋅)
χ1920(643,⋅)
χ1920(667,⋅)
χ1920(883,⋅)
χ1920(907,⋅)
χ1920(1123,⋅)
χ1920(1147,⋅)
χ1920(1363,⋅)
χ1920(1387,⋅)
χ1920(1603,⋅)
χ1920(1627,⋅)
χ1920(1843,⋅)
χ1920(1867,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(511,901,641,1537) → (−1,e(3227),1,−i)
a |
−1 | 1 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 |
χ1920(1123,a) |
1 | 1 | e(1611) | e(327) | e(3229) | e(83) | e(3213) | e(169) | e(329) | i | e(3227) | e(165) |
sage:chi.jacobi_sum(n)