![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([0,9,10]))
![Copy content]()
pari:[g,chi] = znchar(Mod(337,1300))
\(\chi_{1300}(77,\cdot)\)
\(\chi_{1300}(233,\cdot)\)
\(\chi_{1300}(337,\cdot)\)
\(\chi_{1300}(597,\cdot)\)
\(\chi_{1300}(753,\cdot)\)
\(\chi_{1300}(1013,\cdot)\)
\(\chi_{1300}(1117,\cdot)\)
\(\chi_{1300}(1273,\cdot)\)
![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 ]
\((651,677,301)\) → \((1,e\left(\frac{9}{20}\right),-1)\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1300 }(337, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{3}{20}\right)\) | \(-i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
