![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2442, base_ring=CyclotomicField(36))
M = H._module
chi = DirichletCharacter(H, M([0,18,7]))
![Copy content]()
pari:[g,chi] = znchar(Mod(2089,2442))
\(\chi_{2442}(109,\cdot)\)
\(\chi_{2442}(241,\cdot)\)
\(\chi_{2442}(439,\cdot)\)
\(\chi_{2442}(505,\cdot)\)
\(\chi_{2442}(901,\cdot)\)
\(\chi_{2442}(967,\cdot)\)
\(\chi_{2442}(1165,\cdot)\)
\(\chi_{2442}(1297,\cdot)\)
\(\chi_{2442}(1495,\cdot)\)
\(\chi_{2442}(1759,\cdot)\)
\(\chi_{2442}(2089,\cdot)\)
\(\chi_{2442}(2353,\cdot)\)
![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 ]
\((815,1333,1519)\) → \((1,-1,e\left(\frac{7}{36}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2442 }(2089, a) \) |
\(1\) | \(1\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-i\) | \(e\left(\frac{7}{36}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
