My nut is perfect, so there must be slight variance at factory. The stock strings are Ernie Ball 2849 105-45. I generally thought my jack socket was fine, I actually thought it looks good. I will check my P4 jack socket when I practice tomorrow. Hopefully the shop will sort the nut for you.
The only thing I will be doing is a setup to my preferences. Straighter neck, lower action, check intonation, and I think the strings sit a bit high in the nut, so I might order some nut files and sort that.