sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([33,55,33,42]))
pari:[g,chi] = znchar(Mod(59,4140))
Modulus: | 4140 | |
Conductor: | 4140 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 66 |
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)
|
χ4140(59,⋅)
χ4140(119,⋅)
χ4140(239,⋅)
χ4140(959,⋅)
χ4140(1139,⋅)
χ4140(1199,⋅)
χ4140(1319,⋅)
χ4140(1499,⋅)
χ4140(1559,⋅)
χ4140(2099,⋅)
χ4140(2279,⋅)
χ4140(2579,⋅)
χ4140(2819,⋅)
χ4140(2939,⋅)
χ4140(2999,⋅)
χ4140(3479,⋅)
χ4140(3659,⋅)
χ4140(3719,⋅)
χ4140(3899,⋅)
χ4140(4079,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(2071,461,1657,3961) → (−1,e(65),−1,e(117))
a |
−1 | 1 | 7 | 11 | 13 | 17 | 19 | 29 | 31 | 37 | 41 | 43 |
χ4140(59,a) |
1 | 1 | e(3314) | e(332) | e(665) | e(115) | e(221) | e(6619) | e(6665) | e(2219) | e(6653) | e(3317) |
sage:chi.jacobi_sum(n)