# Properties

 Label 1045.j Modulus $1045$ Conductor $55$ Order $4$ Real no Primitive no Minimal yes Parity even

# Learn more

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

H = DirichletGroup(1045, base_ring=CyclotomicField(4))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(153,1045))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$1045$$ Conductor: $$55$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 55.e 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: 4.4.15125.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$12$$ $$13$$ $$14$$
$$\chi_{1045}(153,\cdot)$$ $$1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-1$$ $$i$$ $$-i$$ $$-1$$ $$-i$$ $$-i$$ $$-1$$
$$\chi_{1045}(362,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$-1$$