I would've bet bigger on the flop. Anyways AP I think it's safe to assume you have close to zero FE so to keep the math simple let's just go with that. Flatting is not an option so he basically just shoved for $358 total. Now it's $313 to call a pot of $473. Getting about 1.5 to 1 you need 40% equity.
You lose to nine set combos and three J9s combos.
Have you seen him GII with TPTK on a draw heavy flop before for $400? If you have, close your eyes and shove, especially since you don't have Q
. Vs AJ, the twelve combos that beat you, and a few combo draws you are nearly flipping. So it's safe to GII. Don't forget though, AA is a worse hand because it double blocks AJ. Based on Hold EQ we're AA is around 42% so it's almost BE. That's a HUGE difference! Shove AA anyways to desensitize yourself to the variance and also to show that you're not afraid to gamble for stacks with one pair in case there are aggro villains at your table looking for spots to bluff you.
Also this is somewhat important, do you think villain would 3 bet JJ? Because if he does, that's three less combos you lose to now which is huge. If we remove JJ from his range, now AA jumps to 48% and QQ is a 55% favourite.
Most importantly, it's how you think he plays AJ.
The above calculations assumes that he gets it in 100% of the time with AJ. If he flats AJ half the time and gets it in the other half, our equity is obviously going to suffer. A lot. QQ goes from near flipping to 40%. AA goes from 42% to a 2-1 dog! In other words, QQ goes from clearly +EV to break even, while AA goes from very slightly +EV to definitely -EV.