Screen coordinates for scene capture

I have a scene capture 2d rendering into a 256x256 image. It uses a blendable post process material where I’d like to display an image which fills the entire “screen” of the capture. Weirdly the mapping UVs have to be multiplied by roughly (5.325, 2.29) to more or less cover the entire area. I eyeballed these values but I’d really like to know what’s going on and how I could get the precise values.

This magic number seems to change every once in a while which really complicates things.