Easy.

You're actually taking your 9 bit byte and multiplying it by 29.28600715

If you decompose your table of 512 possible bytes and the desired result, you can see that you merely need to multiply the result by 29 or 30 and then add or subtract from a very regular adjustment series from that product and the desired true result.

The spreadsheet suggests that the adjustment series alters by 3 then 4 sets per accumulating increment. This is easily converted into a quick algorithm fed off of your input byte.

You could decompose the mapping even better through the spreadsheet, but I don't want to get into hard math. I don't even know how many here would understand what a number series is and how to compute it.