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but no way near her.
That's not a good mentality to go in with. The whole "she's out of my league" idea is all in the head. I'm not getting on you for it in any way, I just think that leagues are excuses to not go for a girl. You can talk yourself out of things before anything even happens that way.
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Do you think she's interested or just flirting friendly, or not even flirting?
Sounds like she is flirting to me. I'd flirt back and see what happens. Next time you have class, pat the seat next to you, smile, and say "Sit". More than likely she will, and then you can do your thing.