# Properties

 Label 24.h Modulus $24$ Conductor $24$ Order $2$ Real yes Primitive yes Minimal yes Parity odd

# Related objects

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

H = DirichletGroup(24, base_ring=CyclotomicField(2))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(5,24))

order = charorder(g,chi)

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

## Kronecker symbol representation

sage: kronecker_character(-24)

pari: znchartokronecker(g,chi)

$$\displaystyle\left(\frac{-24}{\bullet}\right)$$

## Basic properties

 Modulus: $$24$$ Conductor: $$24$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: yes 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: $$\Q$$ Fixed field: $$\Q(\sqrt{-6})$$

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$
$$\chi_{24}(5,\cdot)$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$