sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3895, base_ring=CyclotomicField(120))
M = H._module
chi = DirichletCharacter(H, M([60,20,33]))
pari:[g,chi] = znchar(Mod(274,3895))
Modulus: | 3895 | |
Conductor: | 3895 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 120 |
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)
|
χ3895(69,⋅)
χ3895(179,⋅)
χ3895(259,⋅)
χ3895(274,⋅)
χ3895(354,⋅)
χ3895(464,⋅)
χ3895(544,⋅)
χ3895(559,⋅)
χ3895(639,⋅)
χ3895(749,⋅)
χ3895(844,⋅)
χ3895(924,⋅)
χ3895(1019,⋅)
χ3895(1114,⋅)
χ3895(1129,⋅)
χ3895(1224,⋅)
χ3895(1319,⋅)
χ3895(1874,⋅)
χ3895(2079,⋅)
χ3895(2349,⋅)
χ3895(2554,⋅)
χ3895(3109,⋅)
χ3895(3204,⋅)
χ3895(3299,⋅)
χ3895(3314,⋅)
χ3895(3409,⋅)
χ3895(3504,⋅)
χ3895(3584,⋅)
χ3895(3679,⋅)
χ3895(3789,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(3117,2871,1236) → (−1,e(61),e(4011))
a |
−1 | 1 | 2 | 3 | 4 | 6 | 7 | 8 | 9 | 11 | 12 | 13 |
χ3895(274,a) |
1 | 1 | e(6049) | e(2419) | e(3019) | e(12073) | e(409) | e(209) | e(127) | e(4033) | e(4017) | e(120103) |
sage:chi.jacobi_sum(n)