sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4840, base_ring=CyclotomicField(44))
M = H._module
chi = DirichletCharacter(H, M([0,22,33,10]))
pari:[g,chi] = znchar(Mod(1253,4840))
Modulus: | 4840 | |
Conductor: | 4840 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 44 |
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)
|
χ4840(197,⋅)
χ4840(373,⋅)
χ4840(637,⋅)
χ4840(813,⋅)
χ4840(1077,⋅)
χ4840(1253,⋅)
χ4840(1517,⋅)
χ4840(1957,⋅)
χ4840(2133,⋅)
χ4840(2397,⋅)
χ4840(2573,⋅)
χ4840(2837,⋅)
χ4840(3013,⋅)
χ4840(3277,⋅)
χ4840(3453,⋅)
χ4840(3717,⋅)
χ4840(3893,⋅)
χ4840(4157,⋅)
χ4840(4333,⋅)
χ4840(4773,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(3631,2421,1937,4721) → (1,−1,−i,e(225))
a |
−1 | 1 | 3 | 7 | 9 | 13 | 17 | 19 | 21 | 23 | 27 | 29 |
χ4840(1253,a) |
1 | 1 | −i | e(4415) | −1 | e(4431) | e(4439) | e(2219) | e(111) | e(447) | i | e(2219) |
sage:chi.jacobi_sum(n)