![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2900, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([10,6,15]))
![Copy content]()
pari:[g,chi] = znchar(Mod(539,2900))
| Modulus: | \(2900\) | |
| Conductor: | \(2900\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(20\) |
![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)
|
\(\chi_{2900}(539,\cdot)\)
\(\chi_{2900}(679,\cdot)\)
\(\chi_{2900}(1119,\cdot)\)
\(\chi_{2900}(1259,\cdot)\)
\(\chi_{2900}(1839,\cdot)\)
\(\chi_{2900}(2279,\cdot)\)
\(\chi_{2900}(2419,\cdot)\)
\(\chi_{2900}(2859,\cdot)\)
![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 ]
\((1451,1277,901)\) → \((-1,e\left(\frac{3}{10}\right),-i)\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2900 }(539, a) \) |
\(1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
