![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([0,35,12]))
![Copy content]()
pari:[g,chi] = znchar(Mod(869,1764))
\(\chi_{1764}(29,\cdot)\)
\(\chi_{1764}(113,\cdot)\)
\(\chi_{1764}(281,\cdot)\)
\(\chi_{1764}(365,\cdot)\)
\(\chi_{1764}(533,\cdot)\)
\(\chi_{1764}(617,\cdot)\)
\(\chi_{1764}(869,\cdot)\)
\(\chi_{1764}(1037,\cdot)\)
\(\chi_{1764}(1121,\cdot)\)
\(\chi_{1764}(1289,\cdot)\)
\(\chi_{1764}(1541,\cdot)\)
\(\chi_{1764}(1625,\cdot)\)
![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 ]
\((883,785,1081)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{2}{7}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 1764 }(869, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(1\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{7}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
