not to bust a gut

I am not a fan of pop music.

It's not your business.

to not be all one/it is cracked up to be

not to kill oneself

not to over-exert oneself

I am not a piece of Lalique.

to not be as black as one is painted

I'm not going to do that!

I’m not taking any!

to not be exactly over the moon

I do not like this.

to not be feeling quite up to par

not too short

I am not under your orders!

I do not want to trespass on your valuable time [too much]

to not be feeling so hot

to not take a blind/the blindest bit of notice of somebody

I’m not going to help with your exam assignment. It would be of no benefit to you in the long run.

Not that I remember

Oh no, not that old chestnut again!

not to harm something

not to do wrong

not a lot

to not be got at