![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1925, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([15,10,6]))
![Copy content]()
pari:[g,chi] = znchar(Mod(118,1925))
\(\chi_{1925}(118,\cdot)\)
\(\chi_{1925}(293,\cdot)\)
\(\chi_{1925}(468,\cdot)\)
\(\chi_{1925}(657,\cdot)\)
\(\chi_{1925}(832,\cdot)\)
\(\chi_{1925}(1007,\cdot)\)
\(\chi_{1925}(1168,\cdot)\)
\(\chi_{1925}(1707,\cdot)\)
![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 ]
\((1002,276,1751)\) → \((-i,-1,e\left(\frac{3}{10}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 1925 }(118, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(i\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
