![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1140, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([9,9,9,2]))
![Copy content]()
pari:[g,chi] = znchar(Mod(479,1140))
| Modulus: | \(1140\) | |
| Conductor: | \(1140\) |
![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)
|
\(\chi_{1140}(119,\cdot)\)
\(\chi_{1140}(359,\cdot)\)
\(\chi_{1140}(479,\cdot)\)
\(\chi_{1140}(719,\cdot)\)
\(\chi_{1140}(899,\cdot)\)
\(\chi_{1140}(959,\cdot)\)
![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 ]
\((571,761,457,781)\) → \((-1,-1,-1,e\left(\frac{1}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 1140 }(479, a) \) |
\(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
