# Properties

 Label 1728.j Modulus $1728$ Conductor $48$ Order $4$ Real no Primitive no Minimal no Parity odd

# Related objects

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

H = DirichletGroup(1728, base_ring=CyclotomicField(4))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(593,1728))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$1728$$ Conductor: $$48$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 48.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: $$\Q(\sqrt{-1})$$ Fixed field: 4.0.18432.2

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$
$$\chi_{1728}(593,\cdot)$$ $$-1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$i$$ $$1$$ $$-1$$ $$-i$$ $$1$$
$$\chi_{1728}(1457,\cdot)$$ $$-1$$ $$1$$ $$-i$$ $$-1$$ $$-i$$ $$-i$$ $$-1$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$1$$