![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2580, base_ring=CyclotomicField(14))
M = H._module
chi = DirichletCharacter(H, M([7,7,7,4]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1079,2580))
| Modulus: | \(2580\) | |
| Conductor: | \(2580\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(14\) |
![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)
|
\(\chi_{2580}(59,\cdot)\)
\(\chi_{2580}(299,\cdot)\)
\(\chi_{2580}(1079,\cdot)\)
\(\chi_{2580}(1139,\cdot)\)
\(\chi_{2580}(1559,\cdot)\)
\(\chi_{2580}(2099,\cdot)\)
![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 ]
\((1291,1721,517,1981)\) → \((-1,-1,-1,e\left(\frac{2}{7}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 2580 }(1079, a) \) |
\(1\) | \(1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(-1\) | \(e\left(\frac{3}{14}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
