![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3744, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([0,3,0,16]))
![Copy content]()
pari:[g,chi] = znchar(Mod(3493,3744))
\(\chi_{3744}(685,\cdot)\)
\(\chi_{3744}(757,\cdot)\)
\(\chi_{3744}(1621,\cdot)\)
\(\chi_{3744}(1693,\cdot)\)
\(\chi_{3744}(2557,\cdot)\)
\(\chi_{3744}(2629,\cdot)\)
\(\chi_{3744}(3493,\cdot)\)
\(\chi_{3744}(3565,\cdot)\)
![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 ]
\((703,2341,2081,2017)\) → \((1,e\left(\frac{1}{8}\right),1,e\left(\frac{2}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 3744 }(3493, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(i\) | \(e\left(\frac{1}{24}\right)\) | \(1\) | \(e\left(\frac{17}{24}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
