![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([24,27,24,8]))
![Copy content]()
pari:[g,chi] = znchar(Mod(3419,4032))
\(\chi_{4032}(395,\cdot)\)
\(\chi_{4032}(467,\cdot)\)
\(\chi_{4032}(899,\cdot)\)
\(\chi_{4032}(971,\cdot)\)
\(\chi_{4032}(1403,\cdot)\)
\(\chi_{4032}(1475,\cdot)\)
\(\chi_{4032}(1907,\cdot)\)
\(\chi_{4032}(1979,\cdot)\)
\(\chi_{4032}(2411,\cdot)\)
\(\chi_{4032}(2483,\cdot)\)
\(\chi_{4032}(2915,\cdot)\)
\(\chi_{4032}(2987,\cdot)\)
\(\chi_{4032}(3419,\cdot)\)
\(\chi_{4032}(3491,\cdot)\)
\(\chi_{4032}(3923,\cdot)\)
\(\chi_{4032}(3995,\cdot)\)
![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 ]
\((127,3781,1793,577)\) → \((-1,e\left(\frac{9}{16}\right),-1,e\left(\frac{1}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 4032 }(3419, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{48}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
