sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3528, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([0,0,35,10]))
pari:[g,chi] = znchar(Mod(2993,3528))
χ3528(65,⋅)
χ3528(473,⋅)
χ3528(977,⋅)
χ3528(1073,⋅)
χ3528(1481,⋅)
χ3528(1577,⋅)
χ3528(1985,⋅)
χ3528(2081,⋅)
χ3528(2489,⋅)
χ3528(2585,⋅)
χ3528(2993,⋅)
χ3528(3089,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(2647,1765,785,1081) → (1,1,e(65),e(215))
a |
−1 | 1 | 5 | 11 | 13 | 17 | 19 | 23 | 25 | 29 | 31 | 37 |
χ3528(2993,a) |
−1 | 1 | e(141) | e(145) | e(2111) | e(4219) | e(31) | e(143) | e(71) | e(425) | e(31) | e(2113) |
sage:chi.jacobi_sum(n)