![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9900, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([0,5,3,21]))
![Copy content]()
pari:[g,chi] = znchar(Mod(29,9900))
\(\chi_{9900}(29,\cdot)\)
\(\chi_{9900}(569,\cdot)\)
\(\chi_{9900}(1289,\cdot)\)
\(\chi_{9900}(4109,\cdot)\)
\(\chi_{9900}(6629,\cdot)\)
\(\chi_{9900}(7169,\cdot)\)
\(\chi_{9900}(7409,\cdot)\)
\(\chi_{9900}(7889,\cdot)\)
![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 ]
\((4951,5501,2377,4501)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{1}{10}\right),e\left(\frac{7}{10}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 9900 }(29, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
