Is this plot linear in the same way the Chebyshev function is linear?

Question

The Dirichlet generating function for the von Mangoldt function is: $$-\frac{\zeta '(s)}{\zeta (s)}=\lim_{c\to 1} \, \left(\frac{\zeta (c) \zeta (s)}{\zeta (c+s-1)}-\zeta (c)\right) \;\;\;\;\;\;\;\;\;(1)$$

where: $$\frac{\zeta (c) \zeta (s)}{\zeta (c+s-1)} \;\;\;\;\;\;\;\;\;(2)$$

is associated with a symmetric matrix recorded in the OEIS: https://oeis.org/A191898

Plotting $(2)$ on the critical line $s=1/2+it$ and close to the pole $c=1$ $$\frac{\zeta (1+1/10) \zeta (1/2+it)}{\zeta (1+1/10+1/2+it-1)} \;\;\;\;\;\;\;\;\;(3)$$

$c=1+1/10$ is regarded as close to the pole $c=1$.

This is a plot that looks like this:

Then plot the Fourier transform of it in Mathematica and notice that there are spikes at logarithms of prime powers:

What exactly that Fourier transform is I don't know. Instead I constructed a more pure plot that has spikes at prime powers.

So the first two plots are only the context to the question I want to ask.

When you accumulate the previous plot:

Is the plot linear like in the spirit of the Chebyshev function? With Chebyshev function I mean the summatory von Mangoldt function.

The definitions of the functions in the plots are a bit difficult to state but they are all given clearly by this Mathematica program which I essentially copied from Heike's answer here.

Mathematica program with definitions of the plots:

(*Mathematica start*)
Clear[s, c, t, n, g1, g2]
c = 1 + 1/10;

Print["The Fourier Transform of Re[Zeta[1/2+I*t]/Zeta[1/2+I*t+c-1]], \
where c=1+1/10 (i.e. a number c close to 1), is:"]
Plot[Re[Zeta[1/2 + I*t]*Zeta[c]/Zeta[1/2 + I*t + c - 1]], {t, 0, 60}, 
 PlotRange -> {-1, 20}, ImageSize -> Large]
c = 1 + 1/10;
g1 = ListLinePlot[
   FourierDCT[
     Table[Re[Zeta[1/2 + I*t]/Zeta[1/2 + I*t + c - 1]], {t, 1/1000, 
       600, N[1/60]}]][[1 ;; 700]], PlotRange -> {-1, 10}];
mm = 192;
g2 = Graphics[
   Table[Style[Text[n, {mm*Log[n], 4 + (-1)^n}], 
     FontFamily -> "Times New Roman", FontSize -> 14], {n, 1, 27}]];
Print["and gives spikes at logarithms of prime powers:"]
Show[g1, g2, ImageSize -> Large]
Clear[x, xx]
scale = 200;
xres = .001;
x = Exp[Range[0, Log[scale], xres]];
xx = Flatten[{0, Differences[Floor[Exp[Range[0, Log[scale], xres]]]]}];
yy = Accumulate[xx]*xx;
zz = Table[
   If[yy[[i]] == 0, 0, MangoldtLambda[yy[[i]]]], {i, 1, Length[yy]}];

Print["Construct the more pure, but not directly related sequence \
that has spikes at prime powers:"]
ListLinePlot[zz*x^(-1), PlotRange -> {-0.1, 0.8}, ImageSize -> Large]

Print["And accumulate it:"]
ListLinePlot[Accumulate[zz*x^(-1)], ImageSize -> Large]

Print["Is the plot linear?"]
(*End*)

This oneliner is the plot that I believe is linear on average.

ListLinePlot[Accumulate[zz*x^(-1)], ImageSize -> Large]