sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1480, base_ring=CyclotomicField(12))
M = H._module
chi = DirichletCharacter(H, M([0,0,3,4]))
pari:[g,chi] = znchar(Mod(137,1480))
χ1480(137,⋅)
χ1480(417,⋅)
χ1480(433,⋅)
χ1480(713,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1111,741,297,1001) → (1,1,i,e(31))
a |
−1 | 1 | 3 | 7 | 9 | 11 | 13 | 17 | 19 | 21 | 23 | 27 |
χ1480(137,a) |
−1 | 1 | e(125) | e(1211) | e(65) | 1 | e(125) | e(127) | e(61) | e(31) | −i | i |
sage:chi.jacobi_sum(n)