sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(2))
M = H._module
chi = DirichletCharacter(H, M([0,0,1,0]))
pari:[g,chi] = znchar(Mod(449,1120))
χ1120(449,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(351,421,897,801) → (1,1,−1,1)
a |
−1 | 1 | 3 | 9 | 11 | 13 | 17 | 19 | 23 | 27 | 29 | 31 |
χ1120(449,a) |
1 | 1 | −1 | 1 | 1 | −1 | −1 | 1 | −1 | −1 | 1 | 1 |
sage:chi.jacobi_sum(n)