My 46K mile, 6 speed coupe has developed an alarming issue which occurs when coasting in 1st gear (that is, removing one's foot from the accelerator while still in gear). A slight shuddering as well as an audible humming/groaning sound occurs immediately and lasts as long as I coast. This effect is also present in 2nd gear, although less obviously, but is not noticeable in any other gear. I can feel the vibration through the seat, although I can't quite tell what part of the car it is coming from. It happens with the A/C on or off.

Any ideas?