sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([21,41,35]))
pari:[g,chi] = znchar(Mod(1895,3822))
χ3822(17,⋅)
χ3822(257,⋅)
χ3822(563,⋅)
χ3822(1349,⋅)
χ3822(1655,⋅)
χ3822(1895,⋅)
χ3822(2201,⋅)
χ3822(2441,⋅)
χ3822(2747,⋅)
χ3822(2987,⋅)
χ3822(3293,⋅)
χ3822(3533,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(2549,3433,1471) → (−1,e(4241),e(65))
a |
−1 | 1 | 5 | 11 | 17 | 19 | 23 | 25 | 29 | 31 | 37 | 41 |
χ3822(1895,a) |
1 | 1 | e(4213) | e(218) | e(74) | e(31) | e(1413) | e(2113) | e(4217) | e(31) | e(141) | e(4241) |
sage:chi.jacobi_sum(n)