# Properties

 Label 3024.167 Modulus $3024$ Conductor $1512$ Order $18$ Real no Primitive no Minimal no Parity odd

# Related objects

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

sage: H = DirichletGroup(3024, base_ring=CyclotomicField(18))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([9,9,5,9]))

pari: [g,chi] = znchar(Mod(167,3024))

## Basic properties

 Modulus: $$3024$$ Conductor: $$1512$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$18$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{1512}(923,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3024.fm

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

$$(1135,757,785,2593)$$ → $$(-1,-1,e\left(\frac{5}{18}\right),-1)$$

## Values

 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$-1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $$\Q(\zeta_{9})$$ Fixed field: 18.0.16001058221486883031447445258662576128.1