![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3600, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([0,0,40,57]))
![Copy content]()
pari:[g,chi] = znchar(Mod(2113,3600))
\(\chi_{3600}(97,\cdot)\)
\(\chi_{3600}(337,\cdot)\)
\(\chi_{3600}(673,\cdot)\)
\(\chi_{3600}(817,\cdot)\)
\(\chi_{3600}(913,\cdot)\)
\(\chi_{3600}(1537,\cdot)\)
\(\chi_{3600}(1633,\cdot)\)
\(\chi_{3600}(1777,\cdot)\)
\(\chi_{3600}(2113,\cdot)\)
\(\chi_{3600}(2353,\cdot)\)
\(\chi_{3600}(2497,\cdot)\)
\(\chi_{3600}(2833,\cdot)\)
\(\chi_{3600}(2977,\cdot)\)
\(\chi_{3600}(3073,\cdot)\)
\(\chi_{3600}(3217,\cdot)\)
\(\chi_{3600}(3553,\cdot)\)
![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 ]
\((3151,901,2801,577)\) → \((1,1,e\left(\frac{2}{3}\right),e\left(\frac{19}{20}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3600 }(2113, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{2}{15}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
