![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1001, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([10,12,5]))
![Copy content]()
pari:[g,chi] = znchar(Mod(940,1001))
| Modulus: | \(1001\) | |
| Conductor: | \(1001\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(30\) |
![Copy content]()
sage:chi.multiplicative_order()
![Copy content]()
pari:charorder(g,chi)
|
| Real: | no |
| Primitive: | yes |
![Copy content]()
sage:chi.is_primitive()
![Copy content]()
pari:#znconreyconductor(g,chi)==1
|
| Minimal: | yes |
| Parity: | even |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{1001}(179,\cdot)\)
\(\chi_{1001}(212,\cdot)\)
\(\chi_{1001}(361,\cdot)\)
\(\chi_{1001}(394,\cdot)\)
\(\chi_{1001}(543,\cdot)\)
\(\chi_{1001}(576,\cdot)\)
\(\chi_{1001}(907,\cdot)\)
\(\chi_{1001}(940,\cdot)\)
![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 ]
\((430,365,925)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{2}{5}\right),e\left(\frac{1}{6}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(15\) |
| \( \chi_{ 1001 }(940, a) \) |
\(1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{29}{30}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
