Testing for quadratic residues

Question

Is $1487$ is a quadratic residue mod $2783$?

I believe $1487$ is not a quadratic residue mod $2783$, and I'm thinking about using Legendre's symbol.

Answer 1

$2783 = 11^2 \cdot 23$

$1487 \equiv 2 \bmod 11$

$x^2 \equiv 1487 \bmod 2783$ implies $x^2 \equiv 2 \bmod 11$

But $2$ is not a quadratic residue mod $11$ and so $1487$ cannot be a quadratic residue mod $2783$.