from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4928, base_ring=CyclotomicField(40))
M = H._module
chi = DirichletCharacter(H, M([20,15,0,28]))
pari: [g,chi] = znchar(Mod(183,4928))
Basic properties
| Modulus: | \(4928\) | |
| Conductor: | \(352\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(40\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{352}(227,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4928.ej
\(\chi_{4928}(183,\cdot)\) \(\chi_{4928}(519,\cdot)\) \(\chi_{4928}(743,\cdot)\) \(\chi_{4928}(855,\cdot)\) \(\chi_{4928}(1415,\cdot)\) \(\chi_{4928}(1751,\cdot)\) \(\chi_{4928}(1975,\cdot)\) \(\chi_{4928}(2087,\cdot)\) \(\chi_{4928}(2647,\cdot)\) \(\chi_{4928}(2983,\cdot)\) \(\chi_{4928}(3207,\cdot)\) \(\chi_{4928}(3319,\cdot)\) \(\chi_{4928}(3879,\cdot)\) \(\chi_{4928}(4215,\cdot)\) \(\chi_{4928}(4439,\cdot)\) \(\chi_{4928}(4551,\cdot)\)
sage: chi.galois_orbit()
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Related number fields
| Field of values: | \(\Q(\zeta_{40})\) |
| Fixed field: | 40.40.1411841662908675517629776705295515492024702234241930698046194396081616318012166504448.1 |
Values on generators
\((4159,1541,2817,3137)\) → \((-1,e\left(\frac{3}{8}\right),1,e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 4928 }(183, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(-i\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{27}{40}\right)\) |
sage: chi.jacobi_sum(n)