Floor log polynomial Abs value Histogram close to Abs Exp -zeta zeros

(*start*)
Clear[rr, j, x]
c = 300;
Sum[(-1)^(n - 1)*x^Floor[Log[n]*c], {n, 1, 100}]
rr = DeleteCases[roots = N[x /. NSolve[Total[%] == 0, x]],
   Indeterminate];
Histogram[Abs[rr]];
Graphics[{Pink,
   Line[{{Abs[Exp[-(1/2 + I*1)/c]], 0}, {Abs[Exp[-(1/2 + I*1)/c]],
      800}}]}];
Show[%%, %]
ListPlot[Table[{Re[rr[[j]]], Im[rr[[j]]]}, {j, 1, Length[rr]}],
 AspectRatio -> 1]
g1 = ListLinePlot[Sort[N[Abs[rr]]]];
rr = N[Exp[-Table[1/2 + I*t, {t, 1, 1400}]/c]];
g2 = ListLinePlot[N[Abs[rr]], PlotStyle -> Pink];
Show[g1, g2]
(*end*)


(*version 2, logarithms approximated by von Mangoldt function matrix*)
(*start*)
Clear[rr, j, x]
c = 500;

nn = c;
a[n_] := Total[Divisors[n]*MoebiusMu[Divisors[n]]];
TableForm[
  b = Table[
    Sum[If[n == 1, 0, a[GCD[n, k]]/k], {k, 1, nn}], {n, 1, nn}]];
log = Table[
   Sum[If[Mod[n, k] == 0, b[[n/k]], 0], {k, 1, n}], {n, 1, nn}];
Show[ListLinePlot[log], Plot[Log[n], {n, 1, nn}, PlotStyle -> Pink]]


polynomial = Sum[(-1)^(n - 1)*x^Floor[log[[n]]*c], {n, 1, nn}]
rr = DeleteCases[roots = N[x /. NSolve[Total[%] == 0, x]],
   Indeterminate];
ListPlot[Table[{Re[rr[[j]]], Im[rr[[j]]]}, {j, 1, Length[rr]}],
 AspectRatio -> 1]
Histogram[Abs[rr]];
Graphics[{Pink,
   Line[{{Abs[Exp[-(1/2 + I*1)/c]], 0}, {Abs[Exp[-(1/2 + I*1)/c]],
      2000}}]}];
Show[%%, %]
g1 = ListLinePlot[Sort[N[Abs[rr]]]];
rr = N[Exp[-Table[1/2 + I*t, {t, 1, 3000}]/c]];
g2 = ListLinePlot[N[Abs[rr]], PlotStyle -> Pink];
Show[g1, g2]
(*end*)