![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([24,27,32]))
![Copy content]()
pari:[g,chi] = znchar(Mod(43,8550))
\(\chi_{8550}(43,\cdot)\)
\(\chi_{8550}(1507,\cdot)\)
\(\chi_{8550}(1543,\cdot)\)
\(\chi_{8550}(3607,\cdot)\)
\(\chi_{8550}(4243,\cdot)\)
\(\chi_{8550}(4957,\cdot)\)
\(\chi_{8550}(5557,\cdot)\)
\(\chi_{8550}(5857,\cdot)\)
\(\chi_{8550}(6343,\cdot)\)
\(\chi_{8550}(7357,\cdot)\)
\(\chi_{8550}(7693,\cdot)\)
\(\chi_{8550}(8293,\cdot)\)
![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 ]
\((1901,1027,1351)\) → \((e\left(\frac{2}{3}\right),-i,e\left(\frac{8}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8550 }(43, a) \) |
\(-1\) | \(1\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-i\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{36}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
