sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([10,1]))
pari:[g,chi] = znchar(Mod(118,287))
Modulus: | 287 | |
Conductor: | 287 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 20 |
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)
|
χ287(20,⋅)
χ287(62,⋅)
χ287(90,⋅)
χ287(118,⋅)
χ287(125,⋅)
χ287(244,⋅)
χ287(251,⋅)
χ287(279,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(206,211) → (−1,e(201))
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 8 | 9 | 10 | 11 | 12 |
χ287(118,a) |
−1 | 1 | e(103) | i | e(53) | e(53) | e(2011) | e(109) | −1 | e(109) | e(203) | e(2017) |
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)