![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22848, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([0,24,0,40,27]))
![Copy content]()
pari:[g,chi] = znchar(Mod(12577,22848))
\(\chi_{22848}(481,\cdot)\)
\(\chi_{22848}(1825,\cdot)\)
\(\chi_{22848}(3169,\cdot)\)
\(\chi_{22848}(3937,\cdot)\)
\(\chi_{22848}(5281,\cdot)\)
\(\chi_{22848}(6625,\cdot)\)
\(\chi_{22848}(7201,\cdot)\)
\(\chi_{22848}(8545,\cdot)\)
\(\chi_{22848}(9313,\cdot)\)
\(\chi_{22848}(9889,\cdot)\)
\(\chi_{22848}(12577,\cdot)\)
\(\chi_{22848}(17377,\cdot)\)
\(\chi_{22848}(20065,\cdot)\)
\(\chi_{22848}(20641,\cdot)\)
\(\chi_{22848}(21409,\cdot)\)
\(\chi_{22848}(22753,\cdot)\)
![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 ]
\((13567,18565,15233,3265,2689)\) → \((1,-1,1,e\left(\frac{5}{6}\right),e\left(\frac{9}{16}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 22848 }(12577, a) \) |
\(1\) | \(1\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(i\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{11}{16}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
