![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([0,27,16,18]))
![Copy content]()
pari:[g,chi] = znchar(Mod(13,3024))
| Modulus: | \(3024\) | |
| Conductor: | \(3024\) |
![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: | odd |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{3024}(13,\cdot)\)
\(\chi_{3024}(349,\cdot)\)
\(\chi_{3024}(517,\cdot)\)
\(\chi_{3024}(853,\cdot)\)
\(\chi_{3024}(1021,\cdot)\)
\(\chi_{3024}(1357,\cdot)\)
\(\chi_{3024}(1525,\cdot)\)
\(\chi_{3024}(1861,\cdot)\)
\(\chi_{3024}(2029,\cdot)\)
\(\chi_{3024}(2365,\cdot)\)
\(\chi_{3024}(2533,\cdot)\)
\(\chi_{3024}(2869,\cdot)\)
![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 ]
\((1135,757,785,2593)\) → \((1,-i,e\left(\frac{4}{9}\right),-1)\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 3024 }(13, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
