What JtD said....
As for software, for many years a small program called X-Foil, done by the guys at MIT, has been a weapon of choice for simulating basic characteristics of any airfoil you wanted. It was created however, in the era when youngsters actually had a computer knowledge going above pushing an "on" button on their Playstation (early 2000, UNIX, communication through DOS console with no fancy UI whatsoever!), therefore today it might be considered "a bit" unfriendly... There is an Italian fella though, who created a small program called "Profili", which has an X-Foil module built-in and also has a nice'n easy Windows-style interface. Demo version is available for free, getting all functions requires some small donation though.
Below you'll find a few polars it calculated for Republic S-3 airfoil, at standard "reasonable" Re numbers (Cl(alpha): only linear range!). As you can see, they look smoother then the versions found by you. Remember though, that even these are the result of numerical simulation and therefore, far from perfect - NOTHING beats the empirical test results from the wind tunnel!
Cheers.
