Thanks dharr,

I did update my thread above, specifying that every monomial be multiplied by (exp(2k Pi i/3)^p.  Sorry for this but (exp(2 Pi I/3))^9=1 anyway.    There is a more definitive way of checking the conjugated series:  for example, by solving for theRoots=f(1/20,w)=0 and then confirming that three of these roots agree to a high precision with say 100 terms of the generator and two conjugated series (the radius of convergence of the series is about 0.167).  I'll work on confirming this also.  

Thanks everyone.  Very informative.  I had to use the curly braces because I'm investigating the algcurves.puiseux function which returns power series delimited by curly brackets.  Should have mentioned  that in my post.  Also very nice to be able to download your examples into Maple so that I can work on them.