sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2898, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([22,33,21]))
pari:[g,chi] = znchar(Mod(1903,2898))
χ2898(97,⋅)
χ2898(475,⋅)
χ2898(517,⋅)
χ2898(727,⋅)
χ2898(769,⋅)
χ2898(895,⋅)
χ2898(1147,⋅)
χ2898(1399,⋅)
χ2898(1483,⋅)
χ2898(1525,⋅)
χ2898(1735,⋅)
χ2898(1861,⋅)
χ2898(1903,⋅)
χ2898(2029,⋅)
χ2898(2113,⋅)
χ2898(2365,⋅)
χ2898(2407,⋅)
χ2898(2491,⋅)
χ2898(2659,⋅)
χ2898(2869,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1289,829,1891) → (e(31),−1,e(227))
a |
−1 | 1 | 5 | 11 | 13 | 17 | 19 | 25 | 29 | 31 | 37 | 41 |
χ2898(1903,a) |
1 | 1 | e(3316) | e(6613) | e(6641) | e(118) | e(113) | e(3332) | e(332) | e(665) | e(2215) | e(6665) |
sage:chi.jacobi_sum(n)