??? so ... ??? we should pick a "ramification index" x over the gaussian integers ... ??? ...

(?? should x be invariant under the aut gp of the gaussian integers?? ...)

?? and then ... ???we should try to calculate according to artin reciprocity theorem what's the galois group of the x-maximal abelian extension of the gaussian integers, ... ?? and then we should try to connect that up with jugendtraum ideas, by identifying that extension as being generated by the values of certain lemniscatic functions at certain torsion points of the lemniscate ... and identifying how that galois group acts on those values .... ???? ......