If the is idling at 400rpm, no wonder it's running rough. Did you get that from the tach (not accurate below 1000 or so) or from a live data reader?
Cold start idle is 1200 and warm idle is 750.

Has this car been running rough since you bought it or did the develop in the 1000 miles you've driven it? Rough idle and running can be caused by:

Flaky Crank sensor
Flaky Cam sensor
Bad gas
Injectors with gum or crap in them from bad or really old gas
Flaky Throttle body
Flaky MAF sensor
Bad plugs or coil pack (your car is too young for that, and you'd have misfire codes, at least you would if you ever "got on it" and opened the throttle for 15 seconds or so)
Rat's nest or other obstruction in the intake