You can very likely compress the table and/or interpolate between entries. It's not like that those entries are totally random.
Edit: I think this is either Restrictive Pade's approximation or barycentric rational interpolation. Or both combined.
Normally instead division is approximated with Newton-Raphson iteration. I think 6 steps is enough for 16 bit.
In this application no rounding is needed either since the difference between rounding and truncation is also not significant.
You don't need the computer to do any of your multiplication or store any table.
You can start from a sufficiently low reference point, then add delta Y as you increment X.
Xref + deltaX = Yref + deltaY