![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(305760, base_ring=CyclotomicField(84))
M = H._module
chi = DirichletCharacter(H, M([0,21,0,21,34,63]))
![Copy content]()
pari:[g,chi] = znchar(Mod(270457,305760))
\(\chi_{305760}(73,\cdot)\)
\(\chi_{305760}(8377,\cdot)\)
\(\chi_{305760}(18793,\cdot)\)
\(\chi_{305760}(33337,\cdot)\)
\(\chi_{305760}(43753,\cdot)\)
\(\chi_{305760}(62473,\cdot)\)
\(\chi_{305760}(77017,\cdot)\)
\(\chi_{305760}(87433,\cdot)\)
\(\chi_{305760}(95737,\cdot)\)
\(\chi_{305760}(120697,\cdot)\)
\(\chi_{305760}(131113,\cdot)\)
\(\chi_{305760}(139417,\cdot)\)
\(\chi_{305760}(149833,\cdot)\)
\(\chi_{305760}(174793,\cdot)\)
\(\chi_{305760}(183097,\cdot)\)
\(\chi_{305760}(193513,\cdot)\)
\(\chi_{305760}(208057,\cdot)\)
\(\chi_{305760}(226777,\cdot)\)
\(\chi_{305760}(237193,\cdot)\)
\(\chi_{305760}(251737,\cdot)\)
\(\chi_{305760}(262153,\cdot)\)
\(\chi_{305760}(270457,\cdot)\)
\(\chi_{305760}(280873,\cdot)\)
\(\chi_{305760}(295417,\cdot)\)
![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 ]
\((95551,114661,101921,183457,18721,211681)\) → \((1,i,1,i,e\left(\frac{17}{42}\right),-i)\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 305760 }(270457, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{11}{21}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
