![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2700, base_ring=CyclotomicField(180))
M = H._module
chi = DirichletCharacter(H, M([0,160,117]))
![Copy content]()
pari:[g,chi] = znchar(Mod(817,2700))
\(\chi_{2700}(13,\cdot)\)
\(\chi_{2700}(97,\cdot)\)
\(\chi_{2700}(133,\cdot)\)
\(\chi_{2700}(277,\cdot)\)
\(\chi_{2700}(313,\cdot)\)
\(\chi_{2700}(337,\cdot)\)
\(\chi_{2700}(373,\cdot)\)
\(\chi_{2700}(517,\cdot)\)
\(\chi_{2700}(553,\cdot)\)
\(\chi_{2700}(637,\cdot)\)
\(\chi_{2700}(673,\cdot)\)
\(\chi_{2700}(697,\cdot)\)
\(\chi_{2700}(733,\cdot)\)
\(\chi_{2700}(817,\cdot)\)
\(\chi_{2700}(853,\cdot)\)
\(\chi_{2700}(877,\cdot)\)
\(\chi_{2700}(913,\cdot)\)
\(\chi_{2700}(997,\cdot)\)
\(\chi_{2700}(1033,\cdot)\)
\(\chi_{2700}(1177,\cdot)\)
\(\chi_{2700}(1213,\cdot)\)
\(\chi_{2700}(1237,\cdot)\)
\(\chi_{2700}(1273,\cdot)\)
\(\chi_{2700}(1417,\cdot)\)
\(\chi_{2700}(1453,\cdot)\)
\(\chi_{2700}(1537,\cdot)\)
\(\chi_{2700}(1573,\cdot)\)
\(\chi_{2700}(1597,\cdot)\)
\(\chi_{2700}(1633,\cdot)\)
\(\chi_{2700}(1717,\cdot)\)
...
![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 ]
\((1351,1001,2377)\) → \((1,e\left(\frac{8}{9}\right),e\left(\frac{13}{20}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 2700 }(817, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{83}{180}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{167}{180}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{32}{45}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
