![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([0,9,40]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1033,1050))
\(\chi_{1050}(37,\cdot)\)
\(\chi_{1050}(67,\cdot)\)
\(\chi_{1050}(163,\cdot)\)
\(\chi_{1050}(247,\cdot)\)
\(\chi_{1050}(277,\cdot)\)
\(\chi_{1050}(373,\cdot)\)
\(\chi_{1050}(403,\cdot)\)
\(\chi_{1050}(487,\cdot)\)
\(\chi_{1050}(583,\cdot)\)
\(\chi_{1050}(613,\cdot)\)
\(\chi_{1050}(667,\cdot)\)
\(\chi_{1050}(697,\cdot)\)
\(\chi_{1050}(823,\cdot)\)
\(\chi_{1050}(877,\cdot)\)
\(\chi_{1050}(1003,\cdot)\)
\(\chi_{1050}(1033,\cdot)\)
![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 ]
\((701,127,451)\) → \((1,e\left(\frac{3}{20}\right),e\left(\frac{2}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 1050 }(1033, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(i\) |
![Copy content]()
sage:chi.jacobi_sum(n)
