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Had to resize the pic. Here it is. About an inch and a quarter past the nut.
Edit: I don't know where my other post went. This is a 35" scale bass with DR lo-riders but it's not through body. I'm guessing you should have around 1/2" left over past the nut.
I posted a similar ? with zero feedback. You may have to try elsewhere for an answer. On my Schecter the taper is partially on the nut groove relaxed so if the strings don't stretch under tension then they won't be long enough despite Dr and other xperts saying they would fit. My lo riders measure 37-3/4" from ball to taper.
If you want to make sure, make a mark on one of your existing strings just past the nut. Remove it, and measure from your mark to the start of the ball end. This is the winding length you need.
Here are the various winding lengths my manufacturer. Also, this the best place on the internet to buy strings, and as a TB user you will get a discount!