sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(529, base_ring=CyclotomicField(506))
M = H._module
chi = DirichletCharacter(H, M([310]))
pari:[g,chi] = znchar(Mod(48,529))
Modulus: | 529 | |
Conductor: | 529 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 253 |
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)
|
χ529(2,⋅)
χ529(3,⋅)
χ529(4,⋅)
χ529(6,⋅)
χ529(8,⋅)
χ529(9,⋅)
χ529(12,⋅)
χ529(13,⋅)
χ529(16,⋅)
χ529(18,⋅)
χ529(25,⋅)
χ529(26,⋅)
χ529(27,⋅)
χ529(29,⋅)
χ529(31,⋅)
χ529(32,⋅)
χ529(35,⋅)
χ529(36,⋅)
χ529(39,⋅)
χ529(41,⋅)
χ529(48,⋅)
χ529(49,⋅)
χ529(50,⋅)
χ529(52,⋅)
χ529(54,⋅)
χ529(55,⋅)
χ529(58,⋅)
χ529(59,⋅)
χ529(62,⋅)
χ529(64,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
5 → e(253155)
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
χ529(48,a) |
1 | 1 | e(253134) | e(253203) | e(25315) | e(253155) | e(25384) | e(2538) | e(253149) | e(253153) | e(25336) | e(25320) |
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)