TurboFan notes a good thing with the synthetic oils. It's not recommended to use full synthetics until you've gone about 3000 miles. Using it before then will greatly increase break-in time and can cause problems later.
At the 500 mile service, your dealer or you should be changing to standard or semi-synthetic 10W40 oil. My dealer just uses the Honda stuff for Goldwings and such. Then at 3000 miles you switch to the full synthetic, which many of us use the Triumph branded Mobil 1 4T Race oil, though there are other good brands out there.