![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1275, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([0,0,3]))
![Copy content]()
pari:[g,chi] = znchar(Mod(826,1275))
\(\chi_{1275}(226,\cdot)\)
\(\chi_{1275}(301,\cdot)\)
\(\chi_{1275}(601,\cdot)\)
\(\chi_{1275}(751,\cdot)\)
\(\chi_{1275}(826,\cdot)\)
\(\chi_{1275}(976,\cdot)\)
\(\chi_{1275}(1051,\cdot)\)
\(\chi_{1275}(1201,\cdot)\)
![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 ]
\((851,52,751)\) → \((1,1,e\left(\frac{3}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(19\) | \(22\) |
| \( \chi_{ 1275 }(826, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(-i\) | \(e\left(\frac{11}{16}\right)\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
