# Properties

 Modulus 6048 Conductor 3024 Order 36 Real no Primitive no Minimal no Parity even Orbit label 6048.ia

# Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(6048)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([18,9,28,30]))

pari: [g,chi] = znchar(Mod(103,6048))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 6048 Conductor = 3024 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 36 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = no sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 6048.ia Orbit index = 209

## Galois orbit

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Values on generators

$$(4159,3781,3809,2593)$$ → $$(-1,i,e\left(\frac{7}{9}\right),e\left(\frac{5}{6}\right))$$

## Values

 -1 1 5 11 13 17 19 23 25 29 31 37 $$1$$ $$1$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{36})$$