The best time to negotiate your salary for a new job is the moment AFTER they say they want you, and not before. Then it becomes a game of chicken for each side to name an amount first, but it is to your advantage to get them to give a number before you do.
The fact remains that getting people right is not what living is all about anyway. It’s getting them wrong that is living, getting them wrong and wrong and wrong and then, on careful reconsideration, getting them wrong again.