sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1640, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([10,0,10,11]))
pari:[g,chi] = znchar(Mod(1399,1640))
χ1640(39,⋅)
χ1640(159,⋅)
χ1640(279,⋅)
χ1640(759,⋅)
χ1640(799,⋅)
χ1640(1279,⋅)
χ1640(1399,⋅)
χ1640(1519,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1231,821,657,1441) → (−1,1,−1,e(2011))
a |
−1 | 1 | 3 | 7 | 9 | 11 | 13 | 17 | 19 | 21 | 23 | 27 |
χ1640(1399,a) |
−1 | 1 | i | e(209) | −1 | e(203) | e(2011) | e(2013) | e(209) | e(107) | e(54) | −i |
sage:chi.jacobi_sum(n)