![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(84))
M = H._module
chi = DirichletCharacter(H, M([42,0,63,76]))
![Copy content]()
pari:[g,chi] = znchar(Mod(23,1960))
\(\chi_{1960}(23,\cdot)\)
\(\chi_{1960}(207,\cdot)\)
\(\chi_{1960}(247,\cdot)\)
\(\chi_{1960}(303,\cdot)\)
\(\chi_{1960}(487,\cdot)\)
\(\chi_{1960}(527,\cdot)\)
\(\chi_{1960}(543,\cdot)\)
\(\chi_{1960}(583,\cdot)\)
\(\chi_{1960}(767,\cdot)\)
\(\chi_{1960}(807,\cdot)\)
\(\chi_{1960}(823,\cdot)\)
\(\chi_{1960}(1087,\cdot)\)
\(\chi_{1960}(1103,\cdot)\)
\(\chi_{1960}(1143,\cdot)\)
\(\chi_{1960}(1327,\cdot)\)
\(\chi_{1960}(1367,\cdot)\)
\(\chi_{1960}(1383,\cdot)\)
\(\chi_{1960}(1423,\cdot)\)
\(\chi_{1960}(1607,\cdot)\)
\(\chi_{1960}(1663,\cdot)\)
\(\chi_{1960}(1703,\cdot)\)
\(\chi_{1960}(1887,\cdot)\)
\(\chi_{1960}(1927,\cdot)\)
\(\chi_{1960}(1943,\cdot)\)
![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 ]
\((1471,981,1177,1081)\) → \((-1,1,-i,e\left(\frac{19}{21}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 1960 }(23, a) \) |
\(1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{31}{84}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
