sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2898, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([55,44,48]))
pari:[g,chi] = znchar(Mod(95,2898))
χ2898(95,⋅)
χ2898(317,⋅)
χ2898(347,⋅)
χ2898(443,⋅)
χ2898(473,⋅)
χ2898(725,⋅)
χ2898(821,⋅)
χ2898(947,⋅)
χ2898(1199,⋅)
χ2898(1451,⋅)
χ2898(1481,⋅)
χ2898(1577,⋅)
χ2898(1733,⋅)
χ2898(1829,⋅)
χ2898(2111,⋅)
χ2898(2237,⋅)
χ2898(2585,⋅)
χ2898(2615,⋅)
χ2898(2741,⋅)
χ2898(2837,⋅)
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(65),e(32),e(118))
a |
−1 | 1 | 5 | 11 | 13 | 17 | 19 | 25 | 29 | 31 | 37 | 41 |
χ2898(95,a) |
−1 | 1 | e(225) | e(221) | e(3328) | e(6617) | e(338) | e(115) | e(6661) | e(3323) | e(3320) | e(6659) |
sage:chi.jacobi_sum(n)