One rule of thumb here is to raster the image at twice the printer's resolvable resolution of the sake of anti-aliasing. So in this case, raster at 800ppi and send to the printer just like any other photo. One way would be to raster a 800ppi TIFF out of IL. Another would be to raster IL's file in PS and send like any other photo. A third way would be to send the vector file to the printer and hope and pray that it rasters it well.
In these situations it's always informative to test all methods and see the printed results for yourself. The 2nd option - rastering in Photoshop - is a tried and true backup method that service bureaus and prepress depts have relied on for decades. Sans trapping, imposition nd other things, PS is a very capable basic RIP for Adobe's own data and you've got a full suite of reliable color management tools that you can trust, but it's important to raster at exactly the right resolution for your device. If you don't, you'll either get soft edges, poor antialiasing, or both. Do your own testing if you like but I'd suggest that 800ppi would be optimal for your Z.