Quadratic residues mod $p$

Squares.
- $0^2=0$
- $1^2=1$
- $2^2=4$
- $3^2=9\equiv2$
- $4^2=16\equiv2$
- $5^2=25\equiv4$
- $6^2=36\equiv1$

Quadratic residues. $\{0,1,2,4\}$.

Non-residues. $\{3,5,6\}$.

Conclusion. The quadratic residues mod $7$ are $0,1,2,4$; the non-residues are $3,5,6$.