sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2664, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([0,9,6,7]))
pari:[g,chi] = znchar(Mod(733,2664))
Modulus: | 2664 | |
Conductor: | 2664 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 18 |
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)
|
χ2664(373,⋅)
χ2664(733,⋅)
χ2664(1357,⋅)
χ2664(1501,⋅)
χ2664(1669,⋅)
χ2664(2581,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1999,1333,2369,1297) → (1,−1,e(31),e(187))
a |
−1 | 1 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 25 | 29 | 31 |
χ2664(733,a) |
1 | 1 | e(91) | e(97) | −1 | e(94) | e(1813) | e(91) | −1 | e(92) | 1 | e(61) |
sage:chi.jacobi_sum(n)