sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, base_ring=CyclotomicField(110))
M = H._module
chi = DirichletCharacter(H, M([0,55,44,60]))
pari:[g,chi] = znchar(Mod(1881,9200))
χ9200(41,⋅)
χ9200(121,⋅)
χ9200(361,⋅)
χ9200(441,⋅)
χ9200(761,⋅)
χ9200(841,⋅)
χ9200(1481,⋅)
χ9200(1641,⋅)
χ9200(1881,⋅)
χ9200(1961,⋅)
χ9200(2281,⋅)
χ9200(2441,⋅)
χ9200(2681,⋅)
χ9200(2841,⋅)
χ9200(3321,⋅)
χ9200(3481,⋅)
χ9200(3721,⋅)
χ9200(4041,⋅)
χ9200(4121,⋅)
χ9200(4281,⋅)
χ9200(4441,⋅)
χ9200(4521,⋅)
χ9200(4681,⋅)
χ9200(5161,⋅)
χ9200(5321,⋅)
χ9200(5561,⋅)
χ9200(5641,⋅)
χ9200(5881,⋅)
χ9200(5961,⋅)
χ9200(6121,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1151,6901,2577,1201) → (1,−1,e(52),e(116))
a |
−1 | 1 | 3 | 7 | 9 | 11 | 13 | 17 | 19 | 21 | 27 | 29 |
χ9200(1881,a) |
1 | 1 | e(1103) | e(114) | e(553) | e(11089) | e(11081) | e(551) | e(11097) | e(11043) | e(1109) | e(11013) |
sage:chi.jacobi_sum(n)