A rough answer, plus the assumptions behind it — because your real number depends on your full financial picture.
Using an illustrative 6.75% 30-year rate, a 20% down payment ($100,000), and estimated Denver-area property tax and insurance, a $500,000 home runs approximately $2,900–$3,000 per month for principal, interest, taxes and insurance (before any HOA dues).
Lenders typically want your total housing payment (plus other debts) to fall within roughly 28%–36% of gross monthly income, depending on the loan program and your overall profile. Applying that range to the payment above suggests a gross income of roughly $98,000 to $126,000 per year — narrower if you carry significant other debt, wider if you don't.
Put less down and the required income shifts: a smaller down payment means a larger loan and added PMI, which raises the qualifying income somewhat even at the same home price.