sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([0,21,26]))
pari:[g,chi] = znchar(Mod(1129,1470))
χ1470(109,⋅)
χ1470(289,⋅)
χ1470(319,⋅)
χ1470(499,⋅)
χ1470(529,⋅)
χ1470(709,⋅)
χ1470(739,⋅)
χ1470(919,⋅)
χ1470(1129,⋅)
χ1470(1159,⋅)
χ1470(1339,⋅)
χ1470(1369,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(491,1177,1081) → (1,−1,e(2113))
a |
−1 | 1 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 |
χ1470(1129,a) |
1 | 1 | e(2116) | e(1413) | e(4241) | e(32) | e(421) | e(71) | e(31) | e(4213) | e(72) | e(143) |
sage:chi.jacobi_sum(n)