sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1171, base_ring=CyclotomicField(234))
M = H._module
chi = DirichletCharacter(H, M([211]))
pari:[g,chi] = znchar(Mod(307,1171))
Modulus: | 1171 | |
Conductor: | 1171 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 234 |
sage:chi.multiplicative_order()
pari:charorder(g,chi)
|
Real: | no |
Primitive: | yes |
sage:chi.is_primitive()
pari:#znconreyconductor(g,chi)==1
|
Minimal: | yes |
Parity: | odd |
sage:chi.is_odd()
pari:zncharisodd(g,chi)
|
χ1171(3,⋅)
χ1171(7,⋅)
χ1171(29,⋅)
χ1171(32,⋅)
χ1171(60,⋅)
χ1171(63,⋅)
χ1171(89,⋅)
χ1171(130,⋅)
χ1171(140,⋅)
χ1171(142,⋅)
χ1171(147,⋅)
χ1171(152,⋅)
χ1171(176,⋅)
χ1171(183,⋅)
χ1171(243,⋅)
χ1171(248,⋅)
χ1171(250,⋅)
χ1171(258,⋅)
χ1171(276,⋅)
χ1171(285,⋅)
χ1171(307,⋅)
χ1171(316,⋅)
χ1171(326,⋅)
χ1171(330,⋅)
χ1171(397,⋅)
χ1171(410,⋅)
χ1171(413,⋅)
χ1171(419,⋅)
χ1171(422,⋅)
χ1171(458,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
2 → e(234211)
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
χ1171(307,a) |
−1 | 1 | e(234211) | e(234179) | e(11794) | e(92) | e(32) | e(234205) | e(7855) | e(11762) | e(23429) | e(7819) |
sage:chi.jacobi_sum(n)