![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([27,0,4]))
![Copy content]()
pari:[g,chi] = znchar(Mod(23,1045))
\(\chi_{1045}(23,\cdot)\)
\(\chi_{1045}(177,\cdot)\)
\(\chi_{1045}(188,\cdot)\)
\(\chi_{1045}(232,\cdot)\)
\(\chi_{1045}(397,\cdot)\)
\(\chi_{1045}(408,\cdot)\)
\(\chi_{1045}(518,\cdot)\)
\(\chi_{1045}(617,\cdot)\)
\(\chi_{1045}(727,\cdot)\)
\(\chi_{1045}(738,\cdot)\)
\(\chi_{1045}(947,\cdot)\)
\(\chi_{1045}(1013,\cdot)\)
![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 ]
\((837,761,496)\) → \((-i,1,e\left(\frac{1}{9}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1045 }(23, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
