![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([0,27,22]))
![Copy content]()
pari:[g,chi] = znchar(Mod(585,608))
\(\chi_{608}(41,\cdot)\)
\(\chi_{608}(89,\cdot)\)
\(\chi_{608}(105,\cdot)\)
\(\chi_{608}(185,\cdot)\)
\(\chi_{608}(249,\cdot)\)
\(\chi_{608}(281,\cdot)\)
\(\chi_{608}(345,\cdot)\)
\(\chi_{608}(393,\cdot)\)
\(\chi_{608}(409,\cdot)\)
\(\chi_{608}(489,\cdot)\)
\(\chi_{608}(553,\cdot)\)
\(\chi_{608}(585,\cdot)\)
![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 ]
\((191,229,97)\) → \((1,-i,e\left(\frac{11}{18}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 608 }(585, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
![Copy content]()
sage:chi.gauss_sum(a)
![Copy content]()
pari:znchargauss(g,chi,a)
![Copy content]()
sage:chi.jacobi_sum(n)
![Copy content]()
sage:chi.kloosterman_sum(a,b)
