from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2000, base_ring=CyclotomicField(100))
M = H._module
chi = DirichletCharacter(H, M([50,25,51]))
pari: [g,chi] = znchar(Mod(123,2000))
χ2000(67,⋅)
χ2000(123,⋅)
χ2000(147,⋅)
χ2000(203,⋅)
χ2000(227,⋅)
χ2000(283,⋅)
χ2000(363,⋅)
χ2000(387,⋅)
χ2000(467,⋅)
χ2000(523,⋅)
χ2000(547,⋅)
χ2000(603,⋅)
χ2000(627,⋅)
χ2000(683,⋅)
χ2000(763,⋅)
χ2000(787,⋅)
χ2000(867,⋅)
χ2000(923,⋅)
χ2000(947,⋅)
χ2000(1003,⋅)
χ2000(1027,⋅)
χ2000(1083,⋅)
χ2000(1163,⋅)
χ2000(1187,⋅)
χ2000(1267,⋅)
χ2000(1323,⋅)
χ2000(1347,⋅)
χ2000(1403,⋅)
χ2000(1427,⋅)
χ2000(1483,⋅)
...
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(751,501,1377) → (−1,i,e(10051))
a |
−1 | 1 | 3 | 7 | 9 | 11 | 13 | 17 | 19 | 21 | 23 | 27 |
χ2000(123,a) |
1 | 1 | e(5041) | e(207) | e(2516) | e(10051) | e(2516) | e(10023) | e(10043) | e(10017) | e(10081) | e(5023) |