Confusion; Human-Machine Interface; Situational Awareness
ATC Issue All Types; Deviation - Track / Heading All Types
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Requested ATC Assistance / Clarification
Airspace Structure; Aircraft; ATC Equipment / Nav Facility / Buildings; Chart Or Publication
We flew at 37;000 feet for turbulence direct BIL direct to [an NRS waypoint] (a distance between the fixes of 156nm) and we were just maybe five to ten miles past KD84U [another NRS waypoint] when Center said that they showed us 5 miles south of course and that we couldn't go any further right of course. This totally caught us by surprise since we had just crossed over KD84U and the airplane was tracking the Navigation Display (ND) line to [fix] which was 489 miles in front of us. I immediately checked that we were in NAV on the PFD and the Flight Computer Plan (FCP) and we were. While the First Officer talked to Center I immediately double checked that I had typed in the correct waypoints; I had; and then I pulled KD84U and the next fix up to compare the Latitude and Longitude to the flight plan release. They all checked and on the GPS Position Monitor and we showed real close to the [fix] position. Everything said we were on course and where we were supposed to be. So I told Center that everything matched and we were; as far as we could tell; exactly where we were supposed to be. Center said that their computer had a predicted course for us and we were five miles south of the predicted course.I asked if she could verify how close we were to KD84U since we had just overflown it and she said those points were not in their computer. The wind was around 015 degrees at 65 knots; we were showing the airplane crabbing to the left. I asked for an assigned heading until we could straighten the course discrepancy out and she said our present heading would be fine but we couldn't fly any further to the right. This tracked us over the white line that we would have been flying anyways if we had not got into this discussion. We never could account for the difference. Shortly we changed to another frequency and went back on course with that controller's permission and there really wasn't any change in the track.UNKNOWN what lead to this discussion and Center did not say they were taking action; we are doing this report in case they do and because there wasn't anything that we could see wrong to fix. The problem was that the DEN [Center] computer was predicting us one place with its line and it did not include our fix of KD84U or I would guess [the next NRS waypoint].  So if it was predicting us from known fixes it may be possible that we were tracking differently. This sounds like an ATC computer software problem or company needs to be notified to change how they file us.Figure out if this was an ATC computer program/software issue.
An air carrier pilot reported ATC advised them they were 5 miles south of course. The pilot verified they had the correct route programmed and their instruments showed them on course.