![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([12,21,0,10]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1111,2496))
\(\chi_{2496}(7,\cdot)\)
\(\chi_{2496}(535,\cdot)\)
\(\chi_{2496}(583,\cdot)\)
\(\chi_{2496}(1111,\cdot)\)
\(\chi_{2496}(1255,\cdot)\)
\(\chi_{2496}(1783,\cdot)\)
\(\chi_{2496}(1831,\cdot)\)
\(\chi_{2496}(2359,\cdot)\)
![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 ]
\((703,1093,833,769)\) → \((-1,e\left(\frac{7}{8}\right),1,e\left(\frac{5}{12}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2496 }(1111, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(i\) | \(e\left(\frac{7}{24}\right)\) | \(i\) | \(e\left(\frac{11}{24}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
