sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(173, base_ring=CyclotomicField(86))
M = H._module
chi = DirichletCharacter(H, M([36]))
pari:[g,chi] = znchar(Mod(95,173))
Modulus: | 173 | |
Conductor: | 173 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 43 |
sage:chi.multiplicative_order()
pari:charorder(g,chi)
|
Real: | no |
Primitive: | yes |
sage:chi.is_primitive()
pari:#znconreyconductor(g,chi)==1
|
Minimal: | yes |
Parity: | even |
sage:chi.is_odd()
pari:zncharisodd(g,chi)
|
χ173(6,⋅)
χ173(10,⋅)
χ173(14,⋅)
χ173(16,⋅)
χ173(22,⋅)
χ173(23,⋅)
χ173(29,⋅)
χ173(36,⋅)
χ173(43,⋅)
χ173(47,⋅)
χ173(51,⋅)
χ173(52,⋅)
χ173(57,⋅)
χ173(60,⋅)
χ173(81,⋅)
χ173(83,⋅)
χ173(84,⋅)
χ173(85,⋅)
χ173(95,⋅)
χ173(96,⋅)
χ173(100,⋅)
χ173(106,⋅)
χ173(109,⋅)
χ173(117,⋅)
χ173(118,⋅)
χ173(119,⋅)
χ173(124,⋅)
χ173(132,⋅)
χ173(133,⋅)
χ173(135,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
2 → e(4318)
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
χ173(95,a) |
1 | 1 | e(4318) | e(4313) | e(4336) | e(4314) | e(4331) | e(4333) | e(4311) | e(4326) | e(4332) | e(4327) |
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)