Great fun
Symmetricals run deep downwind, perfectly balanced side-to-side, hence the symetry. If it comes with a tacker, I suspect it may instead be an assymetrical spin, which flies much like a giant genoa, tacked to the bow and sheeted back like a jib sheet. Since your jib is on a furler, it's not practical to use that halyard for the spin. See if you have a separate halyard line. It may have just a thin string as a sender for installing a real 3/8-inch line, which is easy. If so, try raising the thing in the chute and open it up while in the dock on a calm day. Then you can see if it's symmetrial or assymetrical. Regardless, you've made a great discovery.