sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2681, base_ring=CyclotomicField(382))
M = H._module
chi = DirichletCharacter(H, M([191,296]))
pari:[g,chi] = znchar(Mod(412,2681))
Modulus: | 2681 | |
Conductor: | 2681 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 382 |
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)
|
χ2681(6,⋅)
χ2681(27,⋅)
χ2681(34,⋅)
χ2681(48,⋅)
χ2681(55,⋅)
χ2681(62,⋅)
χ2681(69,⋅)
χ2681(76,⋅)
χ2681(139,⋅)
χ2681(146,⋅)
χ2681(153,⋅)
χ2681(174,⋅)
χ2681(195,⋅)
χ2681(202,⋅)
χ2681(216,⋅)
χ2681(223,⋅)
χ2681(251,⋅)
χ2681(258,⋅)
χ2681(265,⋅)
χ2681(272,⋅)
χ2681(279,⋅)
χ2681(286,⋅)
χ2681(293,⋅)
χ2681(300,⋅)
χ2681(342,⋅)
χ2681(363,⋅)
χ2681(370,⋅)
χ2681(391,⋅)
χ2681(412,⋅)
χ2681(419,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(2299,771) → (−1,e(191148))
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 8 | 9 | 10 | 11 | 12 |
χ2681(412,a) |
−1 | 1 | e(191159) | e(382257) | e(191127) | e(382105) | e(382193) | e(19195) | e(19166) | e(38241) | e(191121) | e(382129) |
sage:chi.jacobi_sum(n)