I take it the 0.397" is the clear hole diameter. Sharp V double depth for 24tpi is 0.0722", so the o.d. ought to be 0.4692. For standard thread, the double depth is 0.0541", giving an o.d. of 0.4511". Neither of those sounds like anything rational. I'm guessing the 0.397" dimension is somewhat larger than the actual root diameter. I'm with JCHannum -- try 7/16"-24 and see what kind of fit your get.
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