![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([12,9,2]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1429,1710))
\(\chi_{1710}(499,\cdot)\)
\(\chi_{1710}(709,\cdot)\)
\(\chi_{1710}(1309,\cdot)\)
\(\chi_{1710}(1339,\cdot)\)
\(\chi_{1710}(1429,\cdot)\)
\(\chi_{1710}(1669,\cdot)\)
![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 ]
\((191,1027,1351)\) → \((e\left(\frac{2}{3}\right),-1,e\left(\frac{1}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 1710 }(1429, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
