![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1012, base_ring=CyclotomicField(22))
M = H._module
chi = DirichletCharacter(H, M([0,0,4]))
![Copy content]()
pari:[g,chi] = znchar(Mod(441,1012))
\(\chi_{1012}(133,\cdot)\)
\(\chi_{1012}(177,\cdot)\)
\(\chi_{1012}(265,\cdot)\)
\(\chi_{1012}(353,\cdot)\)
\(\chi_{1012}(397,\cdot)\)
\(\chi_{1012}(441,\cdot)\)
\(\chi_{1012}(485,\cdot)\)
\(\chi_{1012}(749,\cdot)\)
\(\chi_{1012}(837,\cdot)\)
\(\chi_{1012}(969,\cdot)\)
![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 ]
\((507,277,925)\) → \((1,1,e\left(\frac{2}{11}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(25\) |
| \( \chi_{ 1012 }(441, a) \) |
\(1\) | \(1\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
