sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1920, base_ring=CyclotomicField(32))
M = H._module
chi = DirichletCharacter(H, M([0,19,0,16]))
pari:[g,chi] = znchar(Mod(829,1920))
χ1920(109,⋅)
χ1920(229,⋅)
χ1920(349,⋅)
χ1920(469,⋅)
χ1920(589,⋅)
χ1920(709,⋅)
χ1920(829,⋅)
χ1920(949,⋅)
χ1920(1069,⋅)
χ1920(1189,⋅)
χ1920(1309,⋅)
χ1920(1429,⋅)
χ1920(1549,⋅)
χ1920(1669,⋅)
χ1920(1789,⋅)
χ1920(1909,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(511,901,641,1537) → (1,e(3219),1,−1)
a |
−1 | 1 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 |
χ1920(829,a) |
1 | 1 | e(167) | e(3215) | e(3213) | e(81) | e(3221) | e(1613) | e(321) | −i | e(3211) | e(1613) |
sage:chi.jacobi_sum(n)