![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8450, base_ring=CyclotomicField(26))
M = H._module
chi = DirichletCharacter(H, M([0,6]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1301,8450))
\(\chi_{8450}(651,\cdot)\)
\(\chi_{8450}(1301,\cdot)\)
\(\chi_{8450}(1951,\cdot)\)
\(\chi_{8450}(2601,\cdot)\)
\(\chi_{8450}(3251,\cdot)\)
\(\chi_{8450}(3901,\cdot)\)
\(\chi_{8450}(4551,\cdot)\)
\(\chi_{8450}(5201,\cdot)\)
\(\chi_{8450}(5851,\cdot)\)
\(\chi_{8450}(6501,\cdot)\)
\(\chi_{8450}(7151,\cdot)\)
\(\chi_{8450}(7801,\cdot)\)
![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 ]
\((677,3551)\) → \((1,e\left(\frac{3}{13}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8450 }(1301, a) \) |
\(1\) | \(1\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(1\) | \(e\left(\frac{4}{13}\right)\) | \(1\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
