sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28900, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([0,8,1]))
pari:[g,chi] = znchar(Mod(7449,28900))
χ28900(249,⋅)
χ28900(4549,⋅)
χ28900(5649,⋅)
χ28900(7449,⋅)
χ28900(16249,⋅)
χ28900(18049,⋅)
χ28900(19149,⋅)
χ28900(23449,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(14451,24277,23701) → (1,−1,e(161))
a |
−1 | 1 | 3 | 7 | 9 | 11 | 13 | 19 | 21 | 23 | 27 | 29 |
χ28900(7449,a) |
−1 | 1 | e(169) | e(163) | e(81) | e(167) | −i | e(87) | −i | e(167) | e(1611) | e(1613) |
sage:chi.jacobi_sum(n)