![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3645, base_ring=CyclotomicField(108))
M = H._module
chi = DirichletCharacter(H, M([86,27]))
![Copy content]()
pari:[g,chi] = znchar(Mod(917,3645))
\(\chi_{3645}(53,\cdot)\)
\(\chi_{3645}(107,\cdot)\)
\(\chi_{3645}(188,\cdot)\)
\(\chi_{3645}(377,\cdot)\)
\(\chi_{3645}(458,\cdot)\)
\(\chi_{3645}(512,\cdot)\)
\(\chi_{3645}(593,\cdot)\)
\(\chi_{3645}(782,\cdot)\)
\(\chi_{3645}(863,\cdot)\)
\(\chi_{3645}(917,\cdot)\)
\(\chi_{3645}(998,\cdot)\)
\(\chi_{3645}(1187,\cdot)\)
\(\chi_{3645}(1268,\cdot)\)
\(\chi_{3645}(1322,\cdot)\)
\(\chi_{3645}(1403,\cdot)\)
\(\chi_{3645}(1592,\cdot)\)
\(\chi_{3645}(1673,\cdot)\)
\(\chi_{3645}(1727,\cdot)\)
\(\chi_{3645}(1808,\cdot)\)
\(\chi_{3645}(1997,\cdot)\)
\(\chi_{3645}(2078,\cdot)\)
\(\chi_{3645}(2132,\cdot)\)
\(\chi_{3645}(2213,\cdot)\)
\(\chi_{3645}(2402,\cdot)\)
\(\chi_{3645}(2483,\cdot)\)
\(\chi_{3645}(2537,\cdot)\)
\(\chi_{3645}(2618,\cdot)\)
\(\chi_{3645}(2807,\cdot)\)
\(\chi_{3645}(2888,\cdot)\)
\(\chi_{3645}(2942,\cdot)\)
...
![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 ]
\((731,2917)\) → \((e\left(\frac{43}{54}\right),i)\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3645 }(917, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{108}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
