i^x+i^y... (x.y) pairs

i^x+i^y... (x.y) pairs

Question :" Find the number of ordered pairs $(x,y)$ with $1 \le x < y \le
100$ and $1^x+1^y$ is real."
My work so far:
I tried using casework on $x$ when taken mod 4 to get the following cases
$x \equiv 1 \pmod 4$, I got a total of 325 $(x,y)$ pairs.
$x \equiv 3 \pmod 4$, I got a total of 276 $(x,y)$ pairs.
$x \equiv 2,4 \pmod 4$, I got a total of 1225 $(x,y)$ pairs.
Can anybody check that my numbers are right?...