![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([20,27,10]))
![Copy content]()
pari:[g,chi] = znchar(Mod(787,3150))
\(\chi_{3150}(187,\cdot)\)
\(\chi_{3150}(283,\cdot)\)
\(\chi_{3150}(313,\cdot)\)
\(\chi_{3150}(787,\cdot)\)
\(\chi_{3150}(817,\cdot)\)
\(\chi_{3150}(913,\cdot)\)
\(\chi_{3150}(1417,\cdot)\)
\(\chi_{3150}(1447,\cdot)\)
\(\chi_{3150}(1573,\cdot)\)
\(\chi_{3150}(2047,\cdot)\)
\(\chi_{3150}(2077,\cdot)\)
\(\chi_{3150}(2173,\cdot)\)
\(\chi_{3150}(2203,\cdot)\)
\(\chi_{3150}(2677,\cdot)\)
\(\chi_{3150}(2803,\cdot)\)
\(\chi_{3150}(2833,\cdot)\)
![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 ]
\((2801,127,451)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{9}{20}\right),e\left(\frac{1}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3150 }(787, a) \) |
\(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{12}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
