Your bike, as mentioned, came from the factory with Syn3. Just one of the advantages of a full synthetic oil is that thermal degradation begins at much higher oil temperatures than with dino oil. These are ballpark numbers, but for sake of discussion, lets say that dino oil begins breaking down at oil temps of 270 degrees. Synthetic oil begins breaking down at 350 degrees. A large air cooled engine, like a 110 CI Twin Cam, produces a lot of heat. I have personally seen oil temps in the crankcase of a 110 of 260 degrees (or more). So, you can decide which you'd rather have in your motor based on those rough numbers.
Discarding all the "old wives tales" of synthetic being "too slippery", causing leaks because it gets past sealing gaskets easier, blah, blah, blah, blah, blah...there is only one reason to use Dino oil over Synthetic oil: It costs less.