![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10890, base_ring=CyclotomicField(330))
M = H._module
chi = DirichletCharacter(H, M([220,0,192]))
![Copy content]()
pari:[g,chi] = znchar(Mod(3481,10890))
\(\chi_{10890}(31,\cdot)\)
\(\chi_{10890}(301,\cdot)\)
\(\chi_{10890}(421,\cdot)\)
\(\chi_{10890}(691,\cdot)\)
\(\chi_{10890}(751,\cdot)\)
\(\chi_{10890}(841,\cdot)\)
\(\chi_{10890}(961,\cdot)\)
\(\chi_{10890}(1021,\cdot)\)
\(\chi_{10890}(1411,\cdot)\)
\(\chi_{10890}(1501,\cdot)\)
\(\chi_{10890}(1681,\cdot)\)
\(\chi_{10890}(1741,\cdot)\)
\(\chi_{10890}(1831,\cdot)\)
\(\chi_{10890}(1951,\cdot)\)
\(\chi_{10890}(2011,\cdot)\)
\(\chi_{10890}(2281,\cdot)\)
\(\chi_{10890}(2401,\cdot)\)
\(\chi_{10890}(2491,\cdot)\)
\(\chi_{10890}(2731,\cdot)\)
\(\chi_{10890}(2821,\cdot)\)
\(\chi_{10890}(2941,\cdot)\)
\(\chi_{10890}(3001,\cdot)\)
\(\chi_{10890}(3271,\cdot)\)
\(\chi_{10890}(3481,\cdot)\)
\(\chi_{10890}(3661,\cdot)\)
\(\chi_{10890}(3721,\cdot)\)
\(\chi_{10890}(3811,\cdot)\)
\(\chi_{10890}(3931,\cdot)\)
\(\chi_{10890}(3991,\cdot)\)
\(\chi_{10890}(4261,\cdot)\)
...
![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 ]
\((8471,4357,3511)\) → \((e\left(\frac{2}{3}\right),1,e\left(\frac{32}{55}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 10890 }(3481, a) \) |
\(1\) | \(1\) | \(e\left(\frac{122}{165}\right)\) | \(e\left(\frac{16}{165}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{61}{165}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{7}{33}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
