If you're asking for a function to take a coverage like in the top row of your table and return a z-value from the bottom row of your table, you can do it from a function that returns an inverse normal cdf, also known as the normal quantile function (which this package calls the percentage point function).
Such a function doesn't do what you seem to be asking directly, but it's a simple calculation from that.
However, such a function doesn't exist in closed form; they're usually calculated via one of various accurate approximations.
With the knowledge of a few such search terms, there are a number examples readily located via use of a search engine -- for example here or here. I can't speak to the correctness of these implementations, but they're easy enough to check against Excel or R (or more extensive tables, also easily found via search engine). There are also a number of more extensive stats libraries like this one - but again I can't speak for accuracy.
Anyway, once you have an inverse-normal-cdf (quantile function), let's call it Q(x) say, then evaluating
should give you the functionality you mention above.