sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(54))
M = H._module
chi = DirichletCharacter(H, M([37,18]))
pari:[g,chi] = znchar(Mod(191,567))
Modulus: | 567 | |
Conductor: | 567 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 54 |
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)
|
χ567(2,⋅)
χ567(32,⋅)
χ567(65,⋅)
χ567(95,⋅)
χ567(128,⋅)
χ567(158,⋅)
χ567(191,⋅)
χ567(221,⋅)
χ567(254,⋅)
χ567(284,⋅)
χ567(317,⋅)
χ567(347,⋅)
χ567(380,⋅)
χ567(410,⋅)
χ567(443,⋅)
χ567(473,⋅)
χ567(506,⋅)
χ567(536,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(407,325) → (e(5437),e(31))
a |
−1 | 1 | 2 | 4 | 5 | 8 | 10 | 11 | 13 | 16 | 17 | 19 |
χ567(191,a) |
−1 | 1 | e(5419) | e(2719) | e(5423) | e(181) | e(97) | e(5413) | e(2713) | e(2711) | e(1817) | e(95) |
sage:chi.jacobi_sum(n)
sage:chi.gauss_sum(a)
pari:znchargauss(g,chi,a)
sage:chi.jacobi_sum(n)
sage:chi.kloosterman_sum(a,b)