sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2898, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([33,55,15]))
pari:[g,chi] = znchar(Mod(89,2898))
χ2898(17,⋅)
χ2898(89,⋅)
χ2898(143,⋅)
χ2898(341,⋅)
χ2898(467,⋅)
χ2898(521,⋅)
χ2898(773,⋅)
χ2898(845,⋅)
χ2898(971,⋅)
χ2898(1349,⋅)
χ2898(1529,⋅)
χ2898(1601,⋅)
χ2898(1781,⋅)
χ2898(1907,⋅)
χ2898(2159,⋅)
χ2898(2357,⋅)
χ2898(2411,⋅)
χ2898(2537,⋅)
χ2898(2609,⋅)
χ2898(2735,⋅)
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) → (−1,e(65),e(225))
a |
−1 | 1 | 5 | 11 | 13 | 17 | 19 | 25 | 29 | 31 | 37 | 41 |
χ2898(89,a) |
−1 | 1 | e(6659) | e(3329) | e(2215) | e(6661) | e(3319) | e(3326) | e(2213) | e(6613) | e(6629) | e(118) |
sage:chi.jacobi_sum(n)