![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3025, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([11,6]))
![Copy content]()
pari:[g,chi] = znchar(Mod(723,3025))
\(\chi_{3025}(602,\cdot)\)
\(\chi_{3025}(723,\cdot)\)
\(\chi_{3025}(887,\cdot)\)
\(\chi_{3025}(1183,\cdot)\)
\(\chi_{3025}(1322,\cdot)\)
\(\chi_{3025}(1613,\cdot)\)
\(\chi_{3025}(1667,\cdot)\)
\(\chi_{3025}(2653,\cdot)\)
![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 ]
\((727,2301)\) → \((e\left(\frac{11}{20}\right),e\left(\frac{3}{10}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 3025 }(723, a) \) |
\(1\) | \(1\) | \(e\left(\frac{17}{20}\right)\) | \(i\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(-1\) | \(e\left(\frac{19}{20}\right)\) | \(-i\) | \(e\left(\frac{7}{10}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
