# Properties

 Label 75.b Modulus $75$ Conductor $5$ Order $2$ Real yes Primitive no Minimal no Parity even

# Learn more

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

H = DirichletGroup(75, base_ring=CyclotomicField(2))

M = H._module

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

chi.galois_orbit()

[g,chi] = znchar(Mod(49,75))

order = charorder(g,chi)

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

## Basic properties

 Modulus: $$75$$ Conductor: $$5$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from 5.b sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Related number fields

 Field of values: $$\Q$$ Fixed field: $$\Q(\sqrt{5})$$

## Characters in Galois orbit

Character $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$11$$ $$13$$ $$14$$ $$16$$ $$17$$ $$19$$
$$\chi_{75}(49,\cdot)$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$