# Properties

 Label 240.i Modulus $240$ Conductor $120$ Order $2$ Real yes Primitive no Minimal no Parity odd

# Related objects

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

sage: H = DirichletGroup(240, base_ring=CyclotomicField(2))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,1,1,1]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(89,240))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$240$$ Conductor: $$120$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from 120.i sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q$$ Fixed field: $$\Q(\sqrt{-30})$$

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{240}(89,\cdot)$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$