![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5200, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([0,30,33,25]))
![Copy content]()
pari:[g,chi] = znchar(Mod(2073,5200))
\(\chi_{5200}(137,\cdot)\)
\(\chi_{5200}(297,\cdot)\)
\(\chi_{5200}(873,\cdot)\)
\(\chi_{5200}(1033,\cdot)\)
\(\chi_{5200}(1177,\cdot)\)
\(\chi_{5200}(1337,\cdot)\)
\(\chi_{5200}(1913,\cdot)\)
\(\chi_{5200}(2073,\cdot)\)
\(\chi_{5200}(2217,\cdot)\)
\(\chi_{5200}(2377,\cdot)\)
\(\chi_{5200}(2953,\cdot)\)
\(\chi_{5200}(3113,\cdot)\)
\(\chi_{5200}(3417,\cdot)\)
\(\chi_{5200}(4153,\cdot)\)
\(\chi_{5200}(4297,\cdot)\)
\(\chi_{5200}(5033,\cdot)\)
![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 ]
\((1951,1301,4577,1601)\) → \((1,-1,e\left(\frac{11}{20}\right),e\left(\frac{5}{12}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 5200 }(2073, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{4}{15}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
