Square root of Möbius function asymptotic

(*Square root of Möbius function asymptotic*)
nn = 1000;
s = N[1/2 + 1/100];
Show[ListLinePlot[
  Re[Accumulate[Table[(MoebiusMu[n])^(1/2)/n^(s), {n, 1, nn}]]]],
 ListLinePlot[
  Table[Re[3/Pi^2*(Zeta[s] - k^(1 - s)/(s - 1) + (k^(-s))/2 + s)], {k,
     1, nn}], PlotStyle -> Red]]

s = 1/2 + 1/1000;
Show[ListLinePlot[
  Table[Sum[1/n^s, {n, 1, k}]*(3/Pi^2), {k, 1, 40, 1/10}]],
 ListLinePlot[
  Table[(Zeta[s] - k^(1 - s)/(s - 1))*(3/Pi^2), {k, 1, 40, 1/10}],
  PlotStyle -> Red]]