Dear friends, I put together a jazz bass with various parts (vintage mod squire body, mexican standard replacement neck, cs60 pickups, vintage style bridge, road worn tort pickguard). I have a wide range of strings I like to use, including 3-4 kinds of flats, tapewounds, grounds, and GHS pressure wounds. I recently put on some DR sunbeams which I really like and which probably fit the bass best (I've avoided rounds my whole life but the sunbeams are making me rethink that). Unfortunately, I noticed that the left piece of the nut next to the E string has broken off. The string stays in place and at first I thought it wasn't making a difference, but I've noticed a vibration sound coming out of my amp when I play the E string. At first I thought it may have been an issue with the pickups or the amp, but the other strings don't have any problems. It is less when I solo with just one pickup, but otherwise the E string sounds almost like there are two notes being played slightly out of sync when I play the E. I was meaning to replace the nut anyway, but I guess I have a few questions: 1.) What kind of nut comes on a standard MIM neck? 2.) What is the preferred nut for a jazz? What are the good options? 3.) Does my E string noise issue sound like it's related to the broken nut? Thanks in advance for any help and advice.