from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4096, base_ring=CyclotomicField(1024))
M = H._module
chi = DirichletCharacter(H, M([0,1]))
pari: [g,chi] = znchar(Mod(5,4096))
χ4096(5,⋅)
χ4096(13,⋅)
χ4096(21,⋅)
χ4096(29,⋅)
χ4096(37,⋅)
χ4096(45,⋅)
χ4096(53,⋅)
χ4096(61,⋅)
χ4096(69,⋅)
χ4096(77,⋅)
χ4096(85,⋅)
χ4096(93,⋅)
χ4096(101,⋅)
χ4096(109,⋅)
χ4096(117,⋅)
χ4096(125,⋅)
χ4096(133,⋅)
χ4096(141,⋅)
χ4096(149,⋅)
χ4096(157,⋅)
χ4096(165,⋅)
χ4096(173,⋅)
χ4096(181,⋅)
χ4096(189,⋅)
χ4096(197,⋅)
χ4096(205,⋅)
χ4096(213,⋅)
χ4096(221,⋅)
χ4096(229,⋅)
χ4096(237,⋅)
...
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(4095,5) → (1,e(10241))
a |
−1 | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 |
χ4096(5,a) |
1 | 1 | e(1024675) | e(10241) | e(512357) | e(512163) | e(1024213) | e(10241007) | e(256169) | e(256103) | e(1024919) | e(1024365) |