The chi function and its variants

(*start*)
nn=1;
Show[Graphics[
  RasterArray[
   Table[Hue[
     Mod[3 Pi/2 +
        Arg[Sum[(Total[
              MoebiusMu[Divisors[n]]*Divisors[n]^(1 - (sigma + I*t))]*
             Total[MoebiusMu[Divisors[n]]*
               Divisors[n]^(sigma + I*t)]   *   Pi^(-(sigma + I*t)/2)*
             Gamma[(sigma + I*t)/2]*Zeta[sigma + I*t])/n, {n, 1,
           nn}]], 2 Pi]/(2 Pi)], {t, -30, 30, .1}, {sigma, -30,
     30, .1}]]], AspectRatio -> Automatic]
nn=2;
Show[Graphics[
  RasterArray[
   Table[Hue[
     Mod[3 Pi/2 +
        Arg[Sum[(Total[
              MoebiusMu[Divisors[n]]*Divisors[n]^(1 - (sigma + I*t))]*
             Total[MoebiusMu[Divisors[n]]*
               Divisors[n]^(sigma + I*t)]   *   Pi^(-(sigma + I*t)/2)*
             Gamma[(sigma + I*t)/2]*Zeta[sigma + I*t])/n, {n, 1,
           nn}]], 2 Pi]/(2 Pi)], {t, -30, 30, .1}, {sigma, -30,
     30, .1}]]], AspectRatio -> Automatic]
nn=20;
Show[Graphics[
  RasterArray[
   Table[Hue[
     Mod[3 Pi/2 +
        Arg[Sum[(Total[
              MoebiusMu[Divisors[n]]*Divisors[n]^(1 - (sigma + I*t))]*
             Total[MoebiusMu[Divisors[n]]*
               Divisors[n]^(sigma + I*t)]   *   Pi^(-(sigma + I*t)/2)*
             Gamma[(sigma + I*t)/2]*Zeta[sigma + I*t])/n, {n, 1,
           nn}]], 2 Pi]/(2 Pi)], {t, -30, 30, .1}, {sigma, -30,
     30, .1}]]], AspectRatio -> Automatic]
(*end*)