sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, base_ring=CyclotomicField(156))
M = H._module
chi = DirichletCharacter(H, M([78,117,116]))
pari:[g,chi] = znchar(Mod(4598,7605))
χ7605(107,⋅)
χ7605(152,⋅)
χ7605(458,⋅)
χ7605(503,⋅)
χ7605(692,⋅)
χ7605(737,⋅)
χ7605(1043,⋅)
χ7605(1088,⋅)
χ7605(1277,⋅)
χ7605(1322,⋅)
χ7605(1628,⋅)
χ7605(1673,⋅)
χ7605(1862,⋅)
χ7605(1907,⋅)
χ7605(2213,⋅)
χ7605(2258,⋅)
χ7605(2447,⋅)
χ7605(2492,⋅)
χ7605(2798,⋅)
χ7605(2843,⋅)
χ7605(3032,⋅)
χ7605(3077,⋅)
χ7605(3383,⋅)
χ7605(3428,⋅)
χ7605(3617,⋅)
χ7605(3662,⋅)
χ7605(3968,⋅)
χ7605(4013,⋅)
χ7605(4553,⋅)
χ7605(4598,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(6761,1522,6931) → (−1,−i,e(3929))
a |
−1 | 1 | 2 | 4 | 7 | 8 | 11 | 14 | 16 | 17 | 19 | 22 |
χ7605(4598,a) |
1 | 1 | e(156155) | e(7877) | e(15649) | e(5251) | e(787) | e(134) | e(3938) | e(156127) | e(65) | e(121) |
sage:chi.jacobi_sum(n)