Face the Complexity

We are all aware of the floor function but we don't have any concept on floor function of complex numbers. So, let's assume floor function of $z$ like this

$\large \lfloor z \rfloor = \lfloor \Re(z) \rfloor + i \lfloor \Im(z) \rfloor$

If you give some trials on $\lfloor z \rfloor$ you will see it is a point in the complex plane. For some particular complex numbers it will maps to a single point.

Find number of all distinct values of $\lfloor z \rfloor$ for every $|z| \leq 8$

Notations: $\Re(z)$ and $\Im(z)$ is the real part and complex part of $z$ .