Land Rover Repair: rough idle, diagnostic system, data stream

Question
when the  motor on my 2001 range rover is idling it causes a vibration and runs fine as soon as it is under load. Any ideas?
Bill
I HAVE JUST RECENTLY PURCHASED THE CAR AND IT HASE 113000 MILES ON IT AND HAS ALWAYS BEEN PROMPTLY SERVICED BY THE DEALERSHIP AND LOOKS NEW INSIDE AND OUT.

Answer
Your vehicle has a pretty sophisticated self diagnostic system.  First of all, it's hard to imagine it has a roughness you can feel without setting a check engine light.  If there is a light, its code should point to the next step.  If not, I would find a dealer or specialist with proper training and equipment and have them read the live data stream paying particular attention to the misfire and rough run data.  That should give some clues.

It's also possible you have a totally different issue, like a borken motor mount, but a good specialist should spot that too.