I now know how find up to as many roots as I need to any precision I want. Instead of Reduce I have used SetPrecsion with NSolve however it will only solve 64 roots at a time with precision 30 so I have set up six NSolve lines and used the Join function to combine all the roots into one list each element with precision 30.
After a lot of trial and error I was actually able to use these roots in a generic trigonometric series.
There has to be an easier way. It's awkward to use. Again I've looked through the documentation and came up empty. My answer is in the attached Notebook.
I'm an oldtimer and had an easier time with Fortran with all due respect.