![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(34272, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([12,15,8,12,0]))
![Copy content]()
pari:[g,chi] = znchar(Mod(20299,34272))
\(\chi_{34272}(3163,\cdot)\)
\(\chi_{34272}(6019,\cdot)\)
\(\chi_{34272}(11731,\cdot)\)
\(\chi_{34272}(14587,\cdot)\)
\(\chi_{34272}(20299,\cdot)\)
\(\chi_{34272}(23155,\cdot)\)
\(\chi_{34272}(28867,\cdot)\)
\(\chi_{34272}(31723,\cdot)\)
![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 ]
\((2143,29989,3809,14689,14113)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{1}{3}\right),-1,1)\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 34272 }(20299, a) \) |
\(1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{12}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
