I’m mainly a jazz bass man but I’ve had quite a few precisions over the last couple of years and the necks vary so much, my 71 is 40mm nut and very slim front to back which is nothing like the reissues, shame they didn’t copy those, I’ve recently bought a AVRI 62 P which has the 44mm nut but it’s very slim front to back, you might like them Linus,
I haven’t got a 57 but here is the spec for a US one ,
Body Material: Alder
Body Details: Solid alder body
Neck Material: Maple
Fingerboard Material: Maple
Neck Profile: Medium "C"
Neck Thickness (IN): 1st- .81" 12th- .94"
Fingerboard Radius: 7.25"
Nut Width: 1-3/4"
Scale Length: 34"
Neck Details: Maple neck with unbound maple fingerboard
Electronics: Original; Fender pickup, master volume, master tone
Weight: 8lbs 14oz