![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2808, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([18,0,10,33]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1463,2808))
\(\chi_{2808}(119,\cdot)\)
\(\chi_{2808}(383,\cdot)\)
\(\chi_{2808}(479,\cdot)\)
\(\chi_{2808}(527,\cdot)\)
\(\chi_{2808}(1055,\cdot)\)
\(\chi_{2808}(1319,\cdot)\)
\(\chi_{2808}(1415,\cdot)\)
\(\chi_{2808}(1463,\cdot)\)
\(\chi_{2808}(1991,\cdot)\)
\(\chi_{2808}(2255,\cdot)\)
\(\chi_{2808}(2351,\cdot)\)
\(\chi_{2808}(2399,\cdot)\)
![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 ]
\((703,1405,2081,1081)\) → \((-1,1,e\left(\frac{5}{18}\right),e\left(\frac{11}{12}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2808 }(1463, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{2}{3}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
