![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([0,15,3,5]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1529,2100))
\(\chi_{2100}(89,\cdot)\)
\(\chi_{2100}(269,\cdot)\)
\(\chi_{2100}(509,\cdot)\)
\(\chi_{2100}(689,\cdot)\)
\(\chi_{2100}(929,\cdot)\)
\(\chi_{2100}(1109,\cdot)\)
\(\chi_{2100}(1529,\cdot)\)
\(\chi_{2100}(1769,\cdot)\)
![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 ]
\((1051,701,1177,1501)\) → \((1,-1,e\left(\frac{1}{10}\right),e\left(\frac{1}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 2100 }(1529, a) \) |
\(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) |
![Copy content]()
sage:chi.jacobi_sum(n)
