sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2835, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([17,9,0]))
pari:[g,chi] = znchar(Mod(2339,2835))
χ2835(449,⋅)
χ2835(764,⋅)
χ2835(1394,⋅)
χ2835(1709,⋅)
χ2835(2339,⋅)
χ2835(2654,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1541,1702,2026) → (e(1817),−1,1)
a |
−1 | 1 | 2 | 4 | 8 | 11 | 13 | 16 | 17 | 19 | 22 | 23 |
χ2835(2339,a) |
−1 | 1 | e(94) | e(98) | e(31) | e(185) | e(181) | e(97) | e(32) | e(31) | e(1813) | e(98) |
sage:chi.jacobi_sum(n)