![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7056, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([0,0,28,12]))
![Copy content]()
pari:[g,chi] = znchar(Mod(673,7056))
\(\chi_{7056}(337,\cdot)\)
\(\chi_{7056}(673,\cdot)\)
\(\chi_{7056}(1345,\cdot)\)
\(\chi_{7056}(1681,\cdot)\)
\(\chi_{7056}(2689,\cdot)\)
\(\chi_{7056}(3361,\cdot)\)
\(\chi_{7056}(3697,\cdot)\)
\(\chi_{7056}(4369,\cdot)\)
\(\chi_{7056}(5377,\cdot)\)
\(\chi_{7056}(5713,\cdot)\)
\(\chi_{7056}(6385,\cdot)\)
\(\chi_{7056}(6721,\cdot)\)
![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 ]
\((6175,1765,785,4609)\) → \((1,1,e\left(\frac{2}{3}\right),e\left(\frac{2}{7}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 7056 }(673, a) \) |
\(1\) | \(1\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(1\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{7}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
