![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3360, base_ring=CyclotomicField(8))
M = H._module
chi = DirichletCharacter(H, M([4,1,4,6,4]))
![Copy content]()
pari:[g,chi] = znchar(Mod(923,3360))
| Modulus: | \(3360\) | |
| Conductor: | \(3360\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(8\) |
![Copy content]()
sage:chi.multiplicative_order()
![Copy content]()
pari:charorder(g,chi)
|
| Real: | no |
| Primitive: | yes |
![Copy content]()
sage:chi.is_primitive()
![Copy content]()
pari:#znconreyconductor(g,chi)==1
|
| Minimal: | yes |
| Parity: | even |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{3360}(923,\cdot)\)
\(\chi_{3360}(1427,\cdot)\)
\(\chi_{3360}(2603,\cdot)\)
\(\chi_{3360}(3107,\cdot)\)
![Copy content]()
sage:chi.galois_orbit()
![Copy content]()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((1471,421,1121,2017,1921)\) → \((-1,e\left(\frac{1}{8}\right),-1,-i,-1)\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3360 }(923, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{3}{8}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
