sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4160, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([0,9,6,2]))
pari:[g,chi] = znchar(Mod(457,4160))
χ4160(457,⋅)
χ4160(617,⋅)
χ4160(1593,⋅)
χ4160(1753,⋅)
χ4160(2537,⋅)
χ4160(2697,⋅)
χ4160(3673,⋅)
χ4160(3833,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(4031,261,2497,1601) → (1,e(83),i,e(121))
a |
−1 | 1 | 3 | 7 | 9 | 11 | 17 | 19 | 21 | 23 | 27 | 29 |
χ4160(457,a) |
1 | 1 | e(245) | e(1211) | e(125) | e(2411) | e(1211) | e(2413) | e(81) | e(65) | e(85) | e(2423) |
sage:chi.jacobi_sum(n)