![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, base_ring=CyclotomicField(90))
M = H._module
chi = DirichletCharacter(H, M([0,9,25]))
![Copy content]()
pari:[g,chi] = znchar(Mod(2179,8550))
\(\chi_{8550}(109,\cdot)\)
\(\chi_{8550}(469,\cdot)\)
\(\chi_{8550}(1009,\cdot)\)
\(\chi_{8550}(1459,\cdot)\)
\(\chi_{8550}(1819,\cdot)\)
\(\chi_{8550}(2179,\cdot)\)
\(\chi_{8550}(2359,\cdot)\)
\(\chi_{8550}(2719,\cdot)\)
\(\chi_{8550}(3169,\cdot)\)
\(\chi_{8550}(3259,\cdot)\)
\(\chi_{8550}(3529,\cdot)\)
\(\chi_{8550}(3889,\cdot)\)
\(\chi_{8550}(4069,\cdot)\)
\(\chi_{8550}(4429,\cdot)\)
\(\chi_{8550}(4879,\cdot)\)
\(\chi_{8550}(4969,\cdot)\)
\(\chi_{8550}(5239,\cdot)\)
\(\chi_{8550}(5779,\cdot)\)
\(\chi_{8550}(6139,\cdot)\)
\(\chi_{8550}(6589,\cdot)\)
\(\chi_{8550}(6679,\cdot)\)
\(\chi_{8550}(7309,\cdot)\)
\(\chi_{8550}(7489,\cdot)\)
\(\chi_{8550}(8389,\cdot)\)
![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 ]
\((1901,1027,1351)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{5}{18}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8550 }(2179, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{17}{18}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
