# Properties

 Label 400.s Modulus $400$ Conductor $80$ Order $4$ Real no Primitive no Minimal yes Parity even

# Related objects

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

H = DirichletGroup(400, base_ring=CyclotomicField(4))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(107,400))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$400$$ Conductor: $$80$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 80.s 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: $$\mathbb{Q}(i)$$ Fixed field: 4.4.256000.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$
$$\chi_{400}(107,\cdot)$$ $$1$$ $$1$$ $$1$$ $$i$$ $$1$$ $$-i$$ $$-1$$ $$i$$ $$-i$$ $$i$$ $$-i$$ $$1$$
$$\chi_{400}(243,\cdot)$$ $$1$$ $$1$$ $$1$$ $$-i$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$i$$ $$-i$$ $$i$$ $$1$$