![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7260, base_ring=CyclotomicField(220))
M = H._module
chi = DirichletCharacter(H, M([0,110,55,112]))
![Copy content]()
pari:[g,chi] = znchar(Mod(2297,7260))
\(\chi_{7260}(53,\cdot)\)
\(\chi_{7260}(113,\cdot)\)
\(\chi_{7260}(137,\cdot)\)
\(\chi_{7260}(257,\cdot)\)
\(\chi_{7260}(317,\cdot)\)
\(\chi_{7260}(377,\cdot)\)
\(\chi_{7260}(533,\cdot)\)
\(\chi_{7260}(653,\cdot)\)
\(\chi_{7260}(713,\cdot)\)
\(\chi_{7260}(773,\cdot)\)
\(\chi_{7260}(797,\cdot)\)
\(\chi_{7260}(917,\cdot)\)
\(\chi_{7260}(1037,\cdot)\)
\(\chi_{7260}(1193,\cdot)\)
\(\chi_{7260}(1313,\cdot)\)
\(\chi_{7260}(1373,\cdot)\)
\(\chi_{7260}(1433,\cdot)\)
\(\chi_{7260}(1457,\cdot)\)
\(\chi_{7260}(1577,\cdot)\)
\(\chi_{7260}(1637,\cdot)\)
\(\chi_{7260}(1853,\cdot)\)
\(\chi_{7260}(1973,\cdot)\)
\(\chi_{7260}(2033,\cdot)\)
\(\chi_{7260}(2093,\cdot)\)
\(\chi_{7260}(2117,\cdot)\)
\(\chi_{7260}(2237,\cdot)\)
\(\chi_{7260}(2297,\cdot)\)
\(\chi_{7260}(2357,\cdot)\)
\(\chi_{7260}(2513,\cdot)\)
\(\chi_{7260}(2633,\cdot)\)
...
![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 ]
\((3631,4841,4357,7141)\) → \((1,-1,i,e\left(\frac{28}{55}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 7260 }(2297, a) \) |
\(1\) | \(1\) | \(e\left(\frac{179}{220}\right)\) | \(e\left(\frac{37}{220}\right)\) | \(e\left(\frac{153}{220}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{139}{220}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{21}{44}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
