Yasuaki Honda at gmail dot com
[1] Conrey, The Riemann Hypothesis https://www.ams.org/notices/200303/fea-conrey-web.pdf
[2] The LMFDB Collaboration, The L-functions and Modular Forms Database, home page of the Zeros of zeta(s), https://www.lmfdb.org/zeros/zeta/?limit=200&N=1, 2020 , [Online; accessed 10 October 2020].
f(x)='realpart(sum(x^rho[j],j,1,inf));
/*
The LMFDB Collaboration, The L-functions and Modular Forms Database,
home page of the Zeros of zeta(s),
https://www.lmfdb.org/zeros/zeta/?limit=200&N=1, 2020 , [Online; accessed 10 October 2020].
*/
kill(img_rho);
img_rho:[
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]$
f(x):=-ev(realpart(sum(x^(1/2+%i*img_rho[j]),j,1,200)),numer);
pi1[n]:=if n<2 then 0 elseif primep(n) then pi1[n-1]+1 else pi1[n-1]$
pi(x):=if integerp(x) and primep(x) then pi1[x]-1/2 else pi1[floor(x)]$
plot2d([f(x),pi(x)*10],[x,1,100]);