from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(243675, base_ring=CyclotomicField(684))
M = H._module
chi = DirichletCharacter(H, M([152,513,104]))
pari: [g,chi] = znchar(Mod(43,243675))
χ243675(43,⋅)
χ243675(682,⋅)
χ243675(1582,⋅)
χ243675(6343,⋅)
χ243675(7882,⋅)
χ243675(8293,⋅)
χ243675(8518,⋅)
χ243675(9832,⋅)
χ243675(10057,⋅)
χ243675(10093,⋅)
χ243675(11632,⋅)
χ243675(11968,⋅)
χ243675(12868,⋅)
χ243675(13507,⋅)
χ243675(14407,⋅)
χ243675(19168,⋅)
χ243675(20707,⋅)
χ243675(21118,⋅)
χ243675(21343,⋅)
χ243675(22657,⋅)
χ243675(22882,⋅)
χ243675(22918,⋅)
χ243675(24457,⋅)
χ243675(26332,⋅)
χ243675(27232,⋅)
χ243675(31993,⋅)
χ243675(33532,⋅)
χ243675(33943,⋅)
χ243675(35482,⋅)
χ243675(35707,⋅)
...
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(36101,77977,129601) → (e(92),−i,e(17126))
a |
−1 | 1 | 2 | 4 | 7 | 8 | 11 | 13 | 14 | 16 | 17 | 22 |
χ243675(43,a) |
−1 | 1 | e(68485) | e(34285) | e(68477) | e(22885) | e(17168) | e(68435) | e(389) | e(17185) | e(684305) | e(228119) |