sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1444, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([9,16]))
pari:[g,chi] = znchar(Mod(423,1444))
χ1444(99,⋅)
χ1444(415,⋅)
χ1444(423,⋅)
χ1444(595,⋅)
χ1444(967,⋅)
χ1444(1111,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(723,1085) → (−1,e(98))
a |
−1 | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 21 | 23 |
χ1444(423,a) |
−1 | 1 | e(181) | e(92) | e(65) | e(91) | e(61) | e(94) | e(185) | e(98) | e(98) | e(185) |
sage:chi.jacobi_sum(n)