![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(44100, base_ring=CyclotomicField(210))
M = H._module
chi = DirichletCharacter(H, M([0,140,126,110]))
![Copy content]()
pari:[g,chi] = znchar(Mod(18421,44100))
\(\chi_{44100}(121,\cdot)\)
\(\chi_{44100}(781,\cdot)\)
\(\chi_{44100}(1381,\cdot)\)
\(\chi_{44100}(2041,\cdot)\)
\(\chi_{44100}(2641,\cdot)\)
\(\chi_{44100}(4561,\cdot)\)
\(\chi_{44100}(5161,\cdot)\)
\(\chi_{44100}(5821,\cdot)\)
\(\chi_{44100}(6421,\cdot)\)
\(\chi_{44100}(7081,\cdot)\)
\(\chi_{44100}(7681,\cdot)\)
\(\chi_{44100}(8341,\cdot)\)
\(\chi_{44100}(8941,\cdot)\)
\(\chi_{44100}(10861,\cdot)\)
\(\chi_{44100}(11461,\cdot)\)
\(\chi_{44100}(13381,\cdot)\)
\(\chi_{44100}(13981,\cdot)\)
\(\chi_{44100}(14641,\cdot)\)
\(\chi_{44100}(15241,\cdot)\)
\(\chi_{44100}(17161,\cdot)\)
\(\chi_{44100}(17761,\cdot)\)
\(\chi_{44100}(18421,\cdot)\)
\(\chi_{44100}(19021,\cdot)\)
\(\chi_{44100}(19681,\cdot)\)
\(\chi_{44100}(20281,\cdot)\)
\(\chi_{44100}(23461,\cdot)\)
\(\chi_{44100}(24061,\cdot)\)
\(\chi_{44100}(24721,\cdot)\)
\(\chi_{44100}(25321,\cdot)\)
\(\chi_{44100}(25981,\cdot)\)
...
![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 ]
\((22051,34301,15877,9901)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{3}{5}\right),e\left(\frac{11}{21}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 44100 }(18421, a) \) |
\(1\) | \(1\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{17}{21}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
