# Properties

 Label 8.c Modulus $8$ Conductor $4$ Order $2$ Real yes Primitive no Minimal no Parity odd

# Related objects

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

H = DirichletGroup(8, base_ring=CyclotomicField(2))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(7,8))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$8$$ Conductor: $$4$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from 4.b 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: $$\Q(\sqrt{-1})$$

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$
$$\chi_{8}(7,\cdot)$$ $$-1$$ $$1$$ $$-1$$ $$1$$