sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(85600, base_ring=CyclotomicField(2120))
M = H._module
chi = DirichletCharacter(H, M([1060,1855,1908,1560]))
pari:[g,chi] = znchar(Mod(19,85600))
Modulus: | 85600 | |
Conductor: | 85600 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 2120 |
sage:chi.multiplicative_order()
pari:charorder(g,chi)
|
Real: | no |
Primitive: | yes |
sage:chi.is_primitive()
pari:#znconreyconductor(g,chi)==1
|
Minimal: | yes |
Parity: | odd |
sage:chi.is_odd()
pari:zncharisodd(g,chi)
|
χ85600(19,⋅)
χ85600(539,⋅)
χ85600(579,⋅)
χ85600(779,⋅)
χ85600(859,⋅)
χ85600(939,⋅)
χ85600(979,⋅)
χ85600(1019,⋅)
χ85600(1139,⋅)
χ85600(1219,⋅)
χ85600(1539,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(26751,32101,82177,16801) → (−1,e(87),e(109),e(5339))
a |
−1 | 1 | 3 | 7 | 9 | 11 | 13 | 17 | 19 | 21 | 23 | 27 |
χ85600(19,a) |
−1 | 1 | e(21201981) | e(21283) | e(1060921) | e(2120983) | e(21201117) | e(265143) | e(2120469) | e(2120691) | e(1060289) | e(21201703) |
sage:chi.jacobi_sum(n)