2018 Electra glide limited with three hundred miles on it has a shimmy around 30 to 35 mph. If coasting it will shake its angry head, have checked front tire pressure 40 lbs last week. What is everyone running on the front tire as I believe that's the right pressure

 

But, still shouldn't cause shimmy.

 

Agreed with RTFM. Or call a dealership or indie. Or Google it.

 

The pressure shown on the tire is the max pressure for that tire. For the correct number look at your owner's manual.
It's under warranty- get it to the dealer.

 

Sounds like you have the "death wobble". Lots of discussion about this in past threads.
I had it on an '09 FLHP I rode, it only happened if I let go of the handlebars at 35 mph. Dealer fixed the problem by telling me not to let go of the handlebars.

 

More like out of balance. Or bad tire. If it wasn't doing it before the new tire then it makes more sense that it's the tire

 

Sell the bike OP, before you get into real trouble.

 

It was alignment issues with my 2013 Electra Glide.

I don't know if your 2018 has the same set up as the 2013, but on mine when you would go to do the final torque to spec on the rear wheel, the adjuster cam on the rite side would turn just a little, this would make my ride exactly the way your describing.
I get a second person to work the torque wrench and i hold the adjuster cam with channel locks, the ride was night and day as one would expect, because the alignment was jacked!!!
look's like these pics are gonna be huge, sorry not real computer literate.

 

Get that check out its under warranty as soon as possible they should/may send someone to your house to get it. There a couple of thing a mentioned above amonst a few other things that can be a big problem also. If you have a lift lift it and check all bearingband neck bearings and bars atleast before attempting to drive it. Things that come loose or break normally happen soon after put together.

 

I trust you checked rear tire pressure. also a shimmy can come from a multitude of things. too soft damping of shocks will do it. alignment was mentioned.