![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1760, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([10,15,5,12]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1527,1760))
\(\chi_{1760}(103,\cdot)\)
\(\chi_{1760}(247,\cdot)\)
\(\chi_{1760}(423,\cdot)\)
\(\chi_{1760}(1367,\cdot)\)
\(\chi_{1760}(1527,\cdot)\)
\(\chi_{1760}(1543,\cdot)\)
\(\chi_{1760}(1687,\cdot)\)
\(\chi_{1760}(1703,\cdot)\)
![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 ]
\((991,1541,1057,321)\) → \((-1,-i,i,e\left(\frac{3}{5}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1760 }(1527, a) \) |
\(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(-i\) | \(-i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
