![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6384, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([0,27,18,6,8]))
![Copy content]()
pari:[g,chi] = znchar(Mod(605,6384))
| Modulus: | \(6384\) | |
| Conductor: | \(6384\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(36\) |
![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)
|
\(\chi_{6384}(605,\cdot)\)
\(\chi_{6384}(845,\cdot)\)
\(\chi_{6384}(1013,\cdot)\)
\(\chi_{6384}(1613,\cdot)\)
\(\chi_{6384}(2189,\cdot)\)
\(\chi_{6384}(2285,\cdot)\)
\(\chi_{6384}(3797,\cdot)\)
\(\chi_{6384}(4037,\cdot)\)
\(\chi_{6384}(4205,\cdot)\)
\(\chi_{6384}(4805,\cdot)\)
\(\chi_{6384}(5381,\cdot)\)
\(\chi_{6384}(5477,\cdot)\)
![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 ]
\((799,4789,2129,913,1009)\) → \((1,-i,-1,e\left(\frac{1}{6}\right),e\left(\frac{2}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6384 }(605, a) \) |
\(1\) | \(1\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(-1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{18}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
