The grid line at the center of a zone, is the only one that is aligned with true north.
The UTM grid lines are aligned with true north at the center of each utm zone, which would have an easting value of 500km. As you move away from the central meridian, grid north, will vary a bit from true north. Most USGS topo maps will show the value for grid north (labeled GN) on their declination diagram. Usually it's less than a degree off of true north, and many folks ignore the difference and use the UTM grid lines as true north reference for plotting compass bearings.