nMax = 1024;
   magScale = 2/3;
imagePixels = 600;
randomizeMoebiusSign = False;
If[
  randomizeMoebiusSign,
(*** True: define a filter that randomizes the sign of the Moebius function ***)
    theRandomSeed = 6; (* chosen for its (accidental) good hue match! *)
    RandomSeed[theRandomSeed];
    moebiusFilter := (#*Table[2*RandomInteger[]-1,{Length[#]}])&;
    titleDescriptor = "random-sign Moebius function";
    fileNameSuffix = "randomized";,
(*** False: use the canonical Moebius function ***)
    moebiusFilter := Identity;
    titleDescriptor = "canonical Moebius function";
    fileNameSuffix = "canonical";
];

(*** compute the Moebius function and (if desired) randomize its signs ***)
Table[MoebiusMu[i],{i,nMax}]//moebiusFilter//
(*** compute a table of Kalai-normed fourier coefficients ***)
 Table[
   Take[#,n]//
    (* compute k<=n values by fast transform *)
    Fourier[#,FourierParameters->{-1,1}]&//
     (#*Sqrt[n])&//
      (* extend to k>n values by periodicity *)
      Table[#[[Mod[i,n,1]]],{i,1,nMax}]&,
   {n,1,nMax}
 ]&//Transpose//Reverse//
(*** print a few statistics ***)
  (#//Flatten//Abs//Max//Print["   max |\[Mu]|*Sqrt[n] =  ",#]&;#)&//
  (#//Flatten//Abs//Median//Print["median |\[Mu]|*Sqrt[n] =  ",#]&;#)&//
  (#//Flatten//Abs//Mean//Print["  mean |\[Mu]|*Sqrt[n] =  ",#]&;#)&//
  (#//Flatten//Abs//StandardDeviation//Print["  sdev |\[Mu]|*Sqrt[n] = \[PlusMinus]",#]&;#)&//
(*** plot the table ***)
   ArrayPlot[#,
     PlotLabel->Style[
       "|\[Mu](k,n)| * Sqrt[n]\n"<>titleDescriptor,
       FontSize->16,FontFamily -> "Helvetica"
     ],
     LabelStyle -> Directive[Bold,FontSize->14,FontFamily -> "Helvetica"],
     FrameLabel->{"1 \[LeftArrow] k -> "<>(nMax//ToString),"1 \[LeftArrow] n -> "<>(nMax//ToString)},
     ColorFunctionScaling -> False,
     ColorFunction -> Function[
       {x},
       Hue[
         x//Arg//(#/(2*Pi))&//Mod[#+1/2,1]&,
         (x/magScale//Abs)//Sqrt//Min[#,1]&,
         (x/magScale//Abs)//Sqrt//Min[#,1]&
       ]
     ]
   ]&//
(*** rasterize the plot ***)
    Rasterize[#,
      RasterSize->imagePixels,
      Background->White
    ]&//(
(*** export the figure  ***)
       Export["~/Desktop/Moebius_"<>"_"<>(nMax//ToString)<>"_"<>
         fileNameSuffix<>".png",
         #,"png",
         ImageSize -> imagePixels
       ];
       #
     )&