![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2664, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([9,9,3,17]))
![Copy content]()
pari:[g,chi] = znchar(Mod(731,2664))
| Modulus: | \(2664\) | |
| Conductor: | \(2664\) |
![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)
|
\(\chi_{2664}(707,\cdot)\)
\(\chi_{2664}(731,\cdot)\)
\(\chi_{2664}(2075,\cdot)\)
\(\chi_{2664}(2171,\cdot)\)
\(\chi_{2664}(2315,\cdot)\)
\(\chi_{2664}(2435,\cdot)\)
![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 ]
\((1999,1333,2369,1297)\) → \((-1,-1,e\left(\frac{1}{6}\right),e\left(\frac{17}{18}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 2664 }(731, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(-1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(-1\) | \(e\left(\frac{1}{9}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
