from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, base_ring=CyclotomicField(24))
M = H._module
chi = DirichletCharacter(H, M([4,21]))
pari: [g,chi] = znchar(Mod(325,4018))
Basic properties
| Modulus: | \(4018\) | |
| Conductor: | \(287\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(24\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{287}(38,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4018.ba
\(\chi_{4018}(325,\cdot)\) \(\chi_{4018}(1011,\cdot)\) \(\chi_{4018}(1391,\cdot)\) \(\chi_{4018}(2077,\cdot)\) \(\chi_{4018}(2187,\cdot)\) \(\chi_{4018}(2873,\cdot)\) \(\chi_{4018}(3253,\cdot)\) \(\chi_{4018}(3939,\cdot)\)
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: | \(\Q(\zeta_{24})\) |
| Fixed field: | 24.24.589415824352273084266952490343550409844469452348841.1 |
Values on generators
\((493,785)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{7}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4018 }(325, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
sage: chi.jacobi_sum(n)