![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2808, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([0,9,10,6]))
![Copy content]()
pari:[g,chi] = znchar(Mod(133,2808))
| Modulus: | \(2808\) | |
| Conductor: | \(2808\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(18\) |
![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)
|
\(\chi_{2808}(133,\cdot)\)
\(\chi_{2808}(373,\cdot)\)
\(\chi_{2808}(1069,\cdot)\)
\(\chi_{2808}(1309,\cdot)\)
\(\chi_{2808}(2005,\cdot)\)
\(\chi_{2808}(2245,\cdot)\)
![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 ]
\((703,1405,2081,1081)\) → \((1,-1,e\left(\frac{5}{9}\right),e\left(\frac{1}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2808 }(133, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
