sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1053, base_ring=CyclotomicField(108))
M = H._module
chi = DirichletCharacter(H, M([46,45]))
pari:[g,chi] = znchar(Mod(734,1053))
Modulus: | 1053 | |
Conductor: | 1053 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 108 |
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)
|
χ1053(2,⋅)
χ1053(11,⋅)
χ1053(32,⋅)
χ1053(59,⋅)
χ1053(119,⋅)
χ1053(128,⋅)
χ1053(149,⋅)
χ1053(176,⋅)
χ1053(236,⋅)
χ1053(245,⋅)
χ1053(266,⋅)
χ1053(293,⋅)
χ1053(353,⋅)
χ1053(362,⋅)
χ1053(383,⋅)
χ1053(410,⋅)
χ1053(470,⋅)
χ1053(479,⋅)
χ1053(500,⋅)
χ1053(527,⋅)
χ1053(587,⋅)
χ1053(596,⋅)
χ1053(617,⋅)
χ1053(644,⋅)
χ1053(704,⋅)
χ1053(713,⋅)
χ1053(734,⋅)
χ1053(761,⋅)
χ1053(821,⋅)
χ1053(830,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(326,730) → (e(5423),e(125))
a |
−1 | 1 | 2 | 4 | 5 | 7 | 8 | 10 | 11 | 14 | 16 | 17 |
χ1053(734,a) |
1 | 1 | e(10891) | e(5437) | e(10859) | e(10843) | e(3619) | e(187) | e(10849) | e(5413) | e(2710) | e(98) |
sage:chi.jacobi_sum(n)