![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(738, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([20,24]))
![Copy content]()
pari:[g,chi] = znchar(Mod(529,738))
\(\chi_{738}(133,\cdot)\)
\(\chi_{738}(139,\cdot)\)
\(\chi_{738}(223,\cdot)\)
\(\chi_{738}(283,\cdot)\)
\(\chi_{738}(385,\cdot)\)
\(\chi_{738}(529,\cdot)\)
\(\chi_{738}(625,\cdot)\)
\(\chi_{738}(715,\cdot)\)
![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 ]
\((83,703)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{4}{5}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 738 }(529, a) \) |
\(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) |
![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)
