sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1037, base_ring=CyclotomicField(80))
M = H._module
chi = DirichletCharacter(H, M([15,68]))
pari:[g,chi] = znchar(Mod(333,1037))
Modulus: | 1037 | |
Conductor: | 1037 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 80 |
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)
|
χ1037(28,⋅)
χ1037(114,⋅)
χ1037(130,⋅)
χ1037(159,⋅)
χ1037(160,⋅)
χ1037(175,⋅)
χ1037(207,⋅)
χ1037(211,⋅)
χ1037(216,⋅)
χ1037(267,⋅)
χ1037(277,⋅)
χ1037(282,⋅)
χ1037(313,⋅)
χ1037(328,⋅)
χ1037(333,⋅)
χ1037(435,⋅)
χ1037(465,⋅)
χ1037(516,⋅)
χ1037(541,⋅)
χ1037(573,⋅)
χ1037(618,⋅)
χ1037(634,⋅)
χ1037(643,⋅)
χ1037(694,⋅)
χ1037(708,⋅)
χ1037(785,⋅)
χ1037(887,⋅)
χ1037(891,⋅)
χ1037(938,⋅)
χ1037(1000,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(428,307) → (e(163),e(2017))
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
χ1037(333,a) |
1 | 1 | e(4019) | e(8023) | e(2019) | e(8051) | e(8061) | e(8057) | e(4017) | e(4023) | e(809) | e(161) |
sage:chi.jacobi_sum(n)