![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([18,0,9,8]))
![Copy content]()
pari:[g,chi] = znchar(Mod(5887,6080))
\(\chi_{6080}(63,\cdot)\)
\(\chi_{6080}(1023,\cdot)\)
\(\chi_{6080}(1087,\cdot)\)
\(\chi_{6080}(1727,\cdot)\)
\(\chi_{6080}(2303,\cdot)\)
\(\chi_{6080}(2943,\cdot)\)
\(\chi_{6080}(3007,\cdot)\)
\(\chi_{6080}(4223,\cdot)\)
\(\chi_{6080}(4607,\cdot)\)
\(\chi_{6080}(4927,\cdot)\)
\(\chi_{6080}(5823,\cdot)\)
\(\chi_{6080}(5887,\cdot)\)
![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 ]
\((191,5701,1217,1921)\) → \((-1,1,i,e\left(\frac{2}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6080 }(5887, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{18}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
