![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45120, base_ring=CyclotomicField(92))
M = H._module
chi = DirichletCharacter(H, M([0,69,0,46,24]))
![Copy content]()
pari:[g,chi] = znchar(Mod(5329,45120))
\(\chi_{45120}(49,\cdot)\)
\(\chi_{45120}(529,\cdot)\)
\(\chi_{45120}(1489,\cdot)\)
\(\chi_{45120}(1969,\cdot)\)
\(\chi_{45120}(3409,\cdot)\)
\(\chi_{45120}(4849,\cdot)\)
\(\chi_{45120}(5329,\cdot)\)
\(\chi_{45120}(5809,\cdot)\)
\(\chi_{45120}(7729,\cdot)\)
\(\chi_{45120}(9169,\cdot)\)
\(\chi_{45120}(9649,\cdot)\)
\(\chi_{45120}(10129,\cdot)\)
\(\chi_{45120}(10609,\cdot)\)
\(\chi_{45120}(11569,\cdot)\)
\(\chi_{45120}(12049,\cdot)\)
\(\chi_{45120}(12529,\cdot)\)
\(\chi_{45120}(13009,\cdot)\)
\(\chi_{45120}(15889,\cdot)\)
\(\chi_{45120}(18289,\cdot)\)
\(\chi_{45120}(18769,\cdot)\)
\(\chi_{45120}(19729,\cdot)\)
\(\chi_{45120}(20689,\cdot)\)
\(\chi_{45120}(22609,\cdot)\)
\(\chi_{45120}(23089,\cdot)\)
\(\chi_{45120}(24049,\cdot)\)
\(\chi_{45120}(24529,\cdot)\)
\(\chi_{45120}(25969,\cdot)\)
\(\chi_{45120}(27409,\cdot)\)
\(\chi_{45120}(27889,\cdot)\)
\(\chi_{45120}(28369,\cdot)\)
...
![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 ]
\((43711,2821,15041,36097,18241)\) → \((1,-i,1,-1,e\left(\frac{6}{23}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 45120 }(5329, a) \) |
\(1\) | \(1\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{57}{92}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{91}{92}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{35}{92}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{19}{92}\right)\) | \(e\left(\frac{19}{46}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
