number theory – Let a ≡ 1 mod (4) and p an odd prime. Show that the Legendre symbol (a/p) only depends on p mod (a)

Let $a equiv 1 pmod 4$ and let $p$ be an odd prime. Show that $left( frac{a}{p}right)$ only depends on $p pmod a$.

I know that $left(frac{a}{p}right)=left(frac{p}{a}right)$ because of the law of quadratic reciprocity. But I don’t know how to go on.

Can I use Euler’s criterion to prove this?