![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12138, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([0,40,9]))
![Copy content]()
pari:[g,chi] = znchar(Mod(11485,12138))
\(\chi_{12138}(1081,\cdot)\)
\(\chi_{12138}(1405,\cdot)\)
\(\chi_{12138}(1669,\cdot)\)
\(\chi_{12138}(3139,\cdot)\)
\(\chi_{12138}(3337,\cdot)\)
\(\chi_{12138}(4177,\cdot)\)
\(\chi_{12138}(5071,\cdot)\)
\(\chi_{12138}(5911,\cdot)\)
\(\chi_{12138}(6109,\cdot)\)
\(\chi_{12138}(7579,\cdot)\)
\(\chi_{12138}(7843,\cdot)\)
\(\chi_{12138}(8167,\cdot)\)
\(\chi_{12138}(9313,\cdot)\)
\(\chi_{12138}(9901,\cdot)\)
\(\chi_{12138}(11485,\cdot)\)
\(\chi_{12138}(12073,\cdot)\)
![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 ]
\((8093,10405,9829)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{3}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 12138 }(11485, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(i\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{9}{16}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
