# Properties

 Label 5520.cf Modulus $5520$ Conductor $5520$ Order $4$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(5520, base_ring=CyclotomicField(4))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([2,3,2,1,2]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(3587,5520))

pari: order = charorder(g,chi)

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

## Basic properties

 Modulus: $$5520$$ Conductor: $$5520$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q(\sqrt{-1})$$ Fixed field: 4.4.1218816000.2

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{5520}(3587,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$i$$ $$1$$ $$i$$ $$-i$$ $$i$$ $$-1$$ $$-1$$ $$1$$ $$-1$$
$$\chi_{5520}(5243,\cdot)$$ $$1$$ $$1$$ $$i$$ $$-i$$ $$1$$ $$-i$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$1$$ $$-1$$