![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6800, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([8,8,8,9]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1799,6800))
\(\chi_{6800}(199,\cdot)\)
\(\chi_{6800}(1399,\cdot)\)
\(\chi_{6800}(1799,\cdot)\)
\(\chi_{6800}(2199,\cdot)\)
\(\chi_{6800}(2999,\cdot)\)
\(\chi_{6800}(5399,\cdot)\)
\(\chi_{6800}(6199,\cdot)\)
\(\chi_{6800}(6599,\cdot)\)
![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 ]
\((5951,1701,2177,1601)\) → \((-1,-1,-1,e\left(\frac{9}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6800 }(1799, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
