![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1081, base_ring=CyclotomicField(46))
M = H._module
chi = DirichletCharacter(H, M([0,20]))
![Copy content]()
pari:[g,chi] = znchar(Mod(990,1081))
\(\chi_{1081}(24,\cdot)\)
\(\chi_{1081}(162,\cdot)\)
\(\chi_{1081}(277,\cdot)\)
\(\chi_{1081}(300,\cdot)\)
\(\chi_{1081}(346,\cdot)\)
\(\chi_{1081}(392,\cdot)\)
\(\chi_{1081}(484,\cdot)\)
\(\chi_{1081}(507,\cdot)\)
\(\chi_{1081}(553,\cdot)\)
\(\chi_{1081}(576,\cdot)\)
\(\chi_{1081}(645,\cdot)\)
\(\chi_{1081}(714,\cdot)\)
\(\chi_{1081}(737,\cdot)\)
\(\chi_{1081}(760,\cdot)\)
\(\chi_{1081}(806,\cdot)\)
\(\chi_{1081}(852,\cdot)\)
\(\chi_{1081}(921,\cdot)\)
\(\chi_{1081}(944,\cdot)\)
\(\chi_{1081}(967,\cdot)\)
\(\chi_{1081}(990,\cdot)\)
\(\chi_{1081}(1036,\cdot)\)
\(\chi_{1081}(1059,\cdot)\)
![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 ]
\((189,898)\) → \((1,e\left(\frac{10}{23}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1081 }(990, a) \) |
\(1\) | \(1\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
