![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1984, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([10,5,6]))
![Copy content]()
pari:[g,chi] = znchar(Mod(463,1984))
\(\chi_{1984}(15,\cdot)\)
\(\chi_{1984}(271,\cdot)\)
\(\chi_{1984}(399,\cdot)\)
\(\chi_{1984}(463,\cdot)\)
\(\chi_{1984}(1007,\cdot)\)
\(\chi_{1984}(1263,\cdot)\)
\(\chi_{1984}(1391,\cdot)\)
\(\chi_{1984}(1455,\cdot)\)
![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 ]
\((63,1861,65)\) → \((-1,i,e\left(\frac{3}{10}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1984 }(463, a) \) |
\(1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(i\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
