# Properties

 Label 380.l Modulus $380$ Conductor $95$ Order $4$ Real no Primitive no Minimal yes Parity even

# Related objects

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

H = DirichletGroup(380, base_ring=CyclotomicField(4))

M = H._module

chi = DirichletCharacter(H, M([0,1,2]))

chi.galois_orbit()

[g,chi] = znchar(Mod(37,380))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$380$$ Conductor: $$95$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 95.g 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: 4.4.45125.1

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$21$$ $$23$$ $$27$$ $$29$$
$$\chi_{380}(37,\cdot)$$ $$1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$-i$$ $$1$$
$$\chi_{380}(113,\cdot)$$ $$1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$i$$ $$i$$ $$1$$