sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([0,0,3,0]))
pari:[g,chi] = znchar(Mod(8833,9200))
χ9200(737,⋅)
χ9200(1473,⋅)
χ9200(2577,⋅)
χ9200(3313,⋅)
χ9200(4417,⋅)
χ9200(5153,⋅)
χ9200(8097,⋅)
χ9200(8833,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1151,6901,2577,1201) → (1,1,e(203),1)
a |
−1 | 1 | 3 | 7 | 9 | 11 | 13 | 17 | 19 | 21 | 27 | 29 |
χ9200(8833,a) |
−1 | 1 | e(201) | −i | e(101) | e(52) | e(2017) | e(2019) | e(107) | e(54) | e(203) | e(103) |
sage:chi.jacobi_sum(n)