![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2900, base_ring=CyclotomicField(28))
M = H._module
chi = DirichletCharacter(H, M([14,21,16]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1243,2900))
\(\chi_{2900}(7,\cdot)\)
\(\chi_{2900}(107,\cdot)\)
\(\chi_{2900}(343,\cdot)\)
\(\chi_{2900}(807,\cdot)\)
\(\chi_{2900}(1243,\cdot)\)
\(\chi_{2900}(1707,\cdot)\)
\(\chi_{2900}(1843,\cdot)\)
\(\chi_{2900}(2307,\cdot)\)
\(\chi_{2900}(2343,\cdot)\)
\(\chi_{2900}(2443,\cdot)\)
\(\chi_{2900}(2543,\cdot)\)
\(\chi_{2900}(2807,\cdot)\)
![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 ]
\((1451,1277,901)\) → \((-1,-i,e\left(\frac{4}{7}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2900 }(1243, a) \) |
\(1\) | \(1\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(-i\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{23}{28}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
