Roots of the Dirichlet eta function plotted

https://oeis.org/draft/A348702

(*start*)
(*Mathematica 8*)
(*Dirichlet eta function*)
Clear[m, s, n, k];
n = 100;(*Increase k=100 for better precision*)$MaxRootDegree =
 Round[Log[n]*n] + 10;
Monitor[s =
   Table[n*(-Log[
        Root[Sum[(-1)^(k + 1)*#1^Round[Log[k]*n], {k, 1, n}] &,
         m]]), {m, 1, Round[Log[n]*n]}];, n]
"Real parts of zeros:"
ListPlot[Re[N[s]]]
"Real parts of zeros sorted:"
Show[ListLinePlot[Sort[Re[N[s]]], PlotRange -> {Min[Re[N[s]]] - 1, 2},
   PlotStyle -> Thickness[0.004]],
 Graphics[Line[{{0, 1/2}, {150, 1/2}}]], ImageSize -> Large]
"Imaginary parts of zeros:"
ListLinePlot[Im[N[s]]]
"Imaginary parts of zeros sorted:"
ListLinePlot[Sort[Im[N[s]]]]
"Plot of the zeros in the complex plane:"
ListPlot[Table[{Re[s[[n]]], Im[s[[n]]]}, {n, 1, Length[s]}]]
(*end*)

(*shorter program*)
(*start*)(*Mathematica 8*)(*Dirichlet eta function*)
Clear[m, s, n, k];
n = 100;(*Increase k=100 for better precision*)$MaxRootDegree =
 Round[Log[n]*n] + 10;
Monitor[s =
   Table[-n*(Log[
       Root[Sum[(-1)^(k + 1)*#1^Round[Log[k]*n], {k, 1, n}] &,
        m]]), {m, Round[Log[n]*n*3/4], Round[Log[n]*n]}];, n]
"Plot of the zeros in the complex plane:"
ListPlot[Table[{Re[s[[n]]], Im[s[[n]]]}, {n, 1, Length[s]}]]
(*end*)

(*start*)
Clear[s, k, number]
number = 1;
s = 11;
k = 5;
FullSimplify[Exp[-s/number]^(Log[k]*number)]
1/k^s
(*end*)