# Properties

 Label 585.o Modulus $585$ Conductor $65$ Order $4$ Real no Primitive no Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(585, base_ring=CyclotomicField(4))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,3,2]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(298,585))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$585$$ Conductor: $$65$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 65.h sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\sqrt{-1})$$ Fixed field: 4.0.21125.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$11$$ $$14$$ $$16$$ $$17$$ $$19$$ $$22$$
$$\chi_{585}(298,\cdot)$$ $$-1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$1$$ $$-i$$ $$1$$ $$-i$$
$$\chi_{585}(532,\cdot)$$ $$-1$$ $$1$$ $$-i$$ $$-1$$ $$-i$$ $$i$$ $$-1$$ $$-1$$ $$1$$ $$i$$ $$1$$ $$i$$