![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1984, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([0,5,0]))
![Copy content]()
pari:[g,chi] = znchar(Mod(373,1984))
\(\chi_{1984}(125,\cdot)\)
\(\chi_{1984}(373,\cdot)\)
\(\chi_{1984}(621,\cdot)\)
\(\chi_{1984}(869,\cdot)\)
\(\chi_{1984}(1117,\cdot)\)
\(\chi_{1984}(1365,\cdot)\)
\(\chi_{1984}(1613,\cdot)\)
\(\chi_{1984}(1861,\cdot)\)
![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 ]
\((63,1861,65)\) → \((1,e\left(\frac{5}{16}\right),1)\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1984 }(373, a) \) |
\(1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(i\) | \(-i\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
