# Properties

 Label 176.i Modulus $176$ Conductor $176$ Order $4$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

H = DirichletGroup(176, base_ring=CyclotomicField(4))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(43,176))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$176$$ Conductor: $$176$$ 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: 4.4.247808.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$13$$ $$15$$ $$17$$ $$19$$ $$21$$ $$23$$
$$\chi_{176}(43,\cdot)$$ $$1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-1$$ $$i$$ $$-1$$ $$-1$$ $$-i$$ $$-i$$ $$1$$
$$\chi_{176}(131,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$-1$$ $$-1$$ $$i$$ $$i$$ $$1$$