Object spotted at 3600 feet, followed but a military jet.On March 19, 2009, at approximately 5:00 PM CST I was on Continental flight CO 1527 H. I was in the window seat (15A) on the left hand side of the plan sitting directly beside the wing. We were at cruising altitude of 3600 feet. We were above the clouds and the sky was clear.I was looking out the window and could see several planes in the distance and started to look all around to see if I could see more planes. I looked towards the rear of the plane and saw a dark object. It looked like a cigar. It may have been a disc but I could not tell for sure because it looked as if I was looking at a side profile of the object. The object appeared to be moving away from the plane I was on and was turning left. It was also above the cloud line and there was no tail as seen with planes.After watching it for about 30 seconds I took out my cell phone and tried to get a picture of the object. However, by the time I got my phone out the object was gone. It looked like the object had move so the plane was covering my view. I still took a picture and there appears to be an object like I seen in it, but I am not sure if it is the object or the tail wing of the plane.I continued to look out the window and about one minute later a jet fly by going in the same direct I seen the object go. I could not tell what kind of jet it was, but there was black smoke trailing it unlike the white trails I was seeing from the other planes I saw. I believe it to be a military jet and it was moving very, very fast!