The pilot reported his engine began running rough after 1.7 hours of flight. After making a 180-degree turn toward an airport he just passed, the airplanes engine died and the pilot, who was unsure he could make it back to the airport without unduly endangering people on the ground, opted to set down the aircraft in an empty field. The landing was uneventful; however, the aircraft encountered a divot on the landing roll and nosed over on its back. After the aircraft was righted, the right wings fuel filler cap was missing and there were several blue stains aft of the filler port to the trailing edge of the wing. The fuel filler cap was found in the run-up area where the pilot had last refilled his tank. Further examination of the fuel system found it to be intact with just three tablespoons of fuel in the fuel sump and none in the main fuel lines to the injector when the boost pump was turned on.
