![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(54))
M = H._module
chi = DirichletCharacter(H, M([29,45]))
![Copy content]()
pari:[g,chi] = znchar(Mod(3155,3969))
\(\chi_{3969}(68,\cdot)\)
\(\chi_{3969}(227,\cdot)\)
\(\chi_{3969}(509,\cdot)\)
\(\chi_{3969}(668,\cdot)\)
\(\chi_{3969}(950,\cdot)\)
\(\chi_{3969}(1109,\cdot)\)
\(\chi_{3969}(1391,\cdot)\)
\(\chi_{3969}(1550,\cdot)\)
\(\chi_{3969}(1832,\cdot)\)
\(\chi_{3969}(1991,\cdot)\)
\(\chi_{3969}(2273,\cdot)\)
\(\chi_{3969}(2432,\cdot)\)
\(\chi_{3969}(2714,\cdot)\)
\(\chi_{3969}(2873,\cdot)\)
\(\chi_{3969}(3155,\cdot)\)
\(\chi_{3969}(3314,\cdot)\)
\(\chi_{3969}(3596,\cdot)\)
\(\chi_{3969}(3755,\cdot)\)
![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 ]
\((2108,3727)\) → \((e\left(\frac{29}{54}\right),e\left(\frac{5}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3969 }(3155, a) \) |
\(1\) | \(1\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
