# Properties

 Modulus 4032 Conductor 112 Order 12 Real no Primitive no Minimal no Parity even Orbit label 4032.ek

# Related objects

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

sage: H = DirichletGroup(4032)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([6,9,0,2]))

pari: [g,chi] = znchar(Mod(1711,4032))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 4032 Conductor = 112 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 12 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 = 4032.ek Orbit index = 115

## 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

$$(127,3781,1793,577)$$ → $$(-1,-i,1,e\left(\frac{1}{6}\right))$$

## Values

 -1 1 5 11 13 17 19 23 25 29 31 37 $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{12})$$