![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18225, base_ring=CyclotomicField(1620))
M = H._module
chi = DirichletCharacter(H, M([10,243]))
![Copy content]()
pari:[g,chi] = znchar(Mod(8,18225))
\(\chi_{18225}(8,\cdot)\)
\(\chi_{18225}(17,\cdot)\)
\(\chi_{18225}(62,\cdot)\)
\(\chi_{18225}(98,\cdot)\)
\(\chi_{18225}(152,\cdot)\)
\(\chi_{18225}(197,\cdot)\)
\(\chi_{18225}(233,\cdot)\)
\(\chi_{18225}(278,\cdot)\)
\(\chi_{18225}(287,\cdot)\)
\(\chi_{18225}(413,\cdot)\)
\(\chi_{18225}(422,\cdot)\)
\(\chi_{18225}(467,\cdot)\)
\(\chi_{18225}(503,\cdot)\)
\(\chi_{18225}(548,\cdot)\)
\(\chi_{18225}(602,\cdot)\)
\(\chi_{18225}(638,\cdot)\)
\(\chi_{18225}(683,\cdot)\)
\(\chi_{18225}(692,\cdot)\)
\(\chi_{18225}(737,\cdot)\)
\(\chi_{18225}(773,\cdot)\)
\(\chi_{18225}(827,\cdot)\)
\(\chi_{18225}(872,\cdot)\)
\(\chi_{18225}(908,\cdot)\)
\(\chi_{18225}(953,\cdot)\)
\(\chi_{18225}(962,\cdot)\)
\(\chi_{18225}(1088,\cdot)\)
\(\chi_{18225}(1097,\cdot)\)
\(\chi_{18225}(1142,\cdot)\)
\(\chi_{18225}(1178,\cdot)\)
\(\chi_{18225}(1223,\cdot)\)
...
![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 ]
\((4376,13852)\) → \((e\left(\frac{1}{162}\right),e\left(\frac{3}{20}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 18225 }(8, a) \) |
\(1\) | \(1\) | \(e\left(\frac{253}{1620}\right)\) | \(e\left(\frac{253}{810}\right)\) | \(e\left(\frac{59}{324}\right)\) | \(e\left(\frac{253}{540}\right)\) | \(e\left(\frac{119}{810}\right)\) | \(e\left(\frac{1457}{1620}\right)\) | \(e\left(\frac{137}{405}\right)\) | \(e\left(\frac{253}{405}\right)\) | \(e\left(\frac{83}{540}\right)\) | \(e\left(\frac{179}{270}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
