![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(34272, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([8,8,0,0,5]))
![Copy content]()
pari:[g,chi] = znchar(Mod(13231,34272))
\(\chi_{34272}(3151,\cdot)\)
\(\chi_{34272}(11215,\cdot)\)
\(\chi_{34272}(13231,\cdot)\)
\(\chi_{34272}(21295,\cdot)\)
\(\chi_{34272}(25327,\cdot)\)
\(\chi_{34272}(27343,\cdot)\)
\(\chi_{34272}(31375,\cdot)\)
\(\chi_{34272}(33391,\cdot)\)
![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 ]
\((2143,29989,3809,14689,14113)\) → \((-1,-1,1,1,e\left(\frac{5}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 34272 }(13231, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
