![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8712, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([0,0,10,6]))
![Copy content]()
pari:[g,chi] = znchar(Mod(7825,8712))
\(\chi_{8712}(2689,\cdot)\)
\(\chi_{8712}(4849,\cdot)\)
\(\chi_{8712}(4921,\cdot)\)
\(\chi_{8712}(5569,\cdot)\)
\(\chi_{8712}(5593,\cdot)\)
\(\chi_{8712}(7753,\cdot)\)
\(\chi_{8712}(7825,\cdot)\)
\(\chi_{8712}(8473,\cdot)\)
![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 ]
\((6535,4357,1937,5689)\) → \((1,1,e\left(\frac{1}{3}\right),e\left(\frac{1}{5}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8712 }(7825, a) \) |
\(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
