Very interesting elaboration. I reached the point of the "root of unity filter" before and was hoping to stay away from a summation over congruence, but i was thinking that was not going to be the case. I also appreciate the link you provided as I have been working with multisections of power series and was happy to see some of that in there. Thanks again. I will award the bounty when overflow lets me grant it.

I can see your point. Perhaps a non-rational then.....

Sorry...will do