Best size for Twitter avatar?

I'm working with a 300 dpi PNG image for a Twitter avatar that I can't seem to get looking clear. I thought maybe a graphic designer on the forums might know the exact specifications as the rest of the web is littered with suggestions that haven't worked for me.

For example, image #1 (300px) looks slightly blurred with the small text in it while image #2 (500px) has the small text almost unreadable. Both attached below.

Any ideas? I just want it to look professional. Thanks