Trying to understand eta function

[spydrcom]

Good day and thanks for having a look... please see the attachment. the issue comes from reading up about eta and zeta and in particular the association eta = zeta * mu where mu(z) = 1 - 2/2^z. The plot of H takes evaluations from Anaconda mpmath.eta function on the critical line 0.5+i*x (the domain of all these plots). the plot of eta(z) computed from mpmath.zeta multiplied by mu shows the cyclic result one might expect seeing plots for zeta and mu. the mpmath.eta plot "H" show exponential decay one sees in the infinite series so maybe not a surprise.... BUT "H" and "n" seem like completely different animals. is this something I have failed to understand or is there insight you can offer? I appreciate any thoughts you care to share. Thanks again. Michael