this equation gave me a whole gamut of greek sybmols and imaginary numbers

the answer i got in maple was

-1/3+1/3*Psi(1/2+1/2*I*sqrt(3))-1/6*I*Pi*tanh(1/2*Pi*sqrt(3))+1/6*sqrt(3)*Pi*tanh(1/2*Pi*sqrt(3))+1/3*gamma

the answer is pretty long, but i suppose that most of you have some sort of symbolic math program that you can use to find this. The (I) is in the second and third terms. When I approximate the answer to decimal the imaginary part of the complex number is only .00003(I). Still you shouldnt get an imaginary number.

I also noticed that when i find the sum of the first 999 terms i get a huge fraction without greek symbols of (I), but when I add the first 1000 terms ( just one more term mind you) i get an answer with greek symbols and (i). when i list the first 1000 terms i dont get any greek symbols or imaginary numbers. could it just be a weird maple thing?