![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1020, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([8,8,8,13]))
![Copy content]()
pari:[g,chi] = znchar(Mod(539,1020))
| Modulus: | \(1020\) | |
| Conductor: | \(1020\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(16\) |
![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)
|
\(\chi_{1020}(299,\cdot)\)
\(\chi_{1020}(419,\cdot)\)
\(\chi_{1020}(479,\cdot)\)
\(\chi_{1020}(539,\cdot)\)
\(\chi_{1020}(719,\cdot)\)
\(\chi_{1020}(779,\cdot)\)
\(\chi_{1020}(839,\cdot)\)
\(\chi_{1020}(959,\cdot)\)
![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 ]
\((511,341,817,241)\) → \((-1,-1,-1,e\left(\frac{13}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 1020 }(539, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
