Lower than you might think!
Factory pressure for the front tyres are between 16-19psi and rears 23-25psi, depending on the years and exactly models. So that's the kind of ball park.
When I first got my 500 on the road, I thought 'thats way too low, let's put 26 front and rear and go from there', I'd had other vehicles where the owners consensus was to ignore the very low factory suggested pressures, as modern tyre technology made them irrelevant. But clearly this is not the case for the 500.
I can confirm that the handling was definitely worse at the higher pressure, the front end especially felt more wayward at speed. Dropping back to the factory pressures, was a good improvement.