# classification of representations of $D_{1009}$

A follow-up of this question

To fix ideas, take $$n=1009$$.

$$D_n$$ has $$2$$ irreducible representations of degree $$1$$ and $$504$$ representations of degree $$2$$.

• Are the degree 1 representations all isomorphic?
• Are the degree 2 representations all isomorphic?