sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(431, base_ring=CyclotomicField(86))
M = H._module
chi = DirichletCharacter(H, M([68]))
pari:[g,chi] = znchar(Mod(220,431))
Modulus: | 431 | |
Conductor: | 431 |
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)
|
χ431(2,⋅)
χ431(3,⋅)
χ431(4,⋅)
χ431(6,⋅)
χ431(8,⋅)
χ431(9,⋅)
χ431(12,⋅)
χ431(16,⋅)
χ431(18,⋅)
χ431(24,⋅)
χ431(27,⋅)
χ431(32,⋅)
χ431(36,⋅)
χ431(48,⋅)
χ431(54,⋅)
χ431(55,⋅)
χ431(64,⋅)
χ431(72,⋅)
χ431(81,⋅)
χ431(96,⋅)
χ431(108,⋅)
χ431(110,⋅)
χ431(128,⋅)
χ431(144,⋅)
χ431(145,⋅)
χ431(149,⋅)
χ431(162,⋅)
χ431(165,⋅)
χ431(192,⋅)
χ431(216,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
7 → e(4334)
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
χ431(220,a) |
1 | 1 | e(4341) | e(4317) | e(4339) | e(4318) | e(4315) | e(4334) | e(4337) | e(4334) | e(4316) | e(4322) |
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)