Simulation of Cauchy random variables and calculating empirical CDF followed by plotting them

Question: Simulated some Cauchy random variables (200) and calculate the empirical distribution function F_n and also make a vector F for the theoretical cdf. Plot F and Fn on the same figure.

Below is what I did and the output I got.

% Matlab HW for Advanced statistics

ULst = rand(200,1);
CauchyLst = tan(pi*(ULst-0.5));
SortCauchyLst = sort(CauchyLst);

plot(SortCauchyLst,'*') %middle step to get a quick picture

tLst = -20:0.01:15;
FnLst = [];
for t=-20:0.01:15
Fn = 1/100*sum(CauchyLst<=t);
FnLst = [FnLst,Fn];
end

FLst = [];
for t=-20:0.01:15
F = (1/pi)*atan(t)+0.5;
FLst = [FLst,F];
end

plot(tLst,FLst)
hold on
plot(tLst,FnLst,'r.')
hold on

[f,x] = ecdf(Fn);
ecdf(Fn)
hold on
[h,stats] = cdfplot(F);
cdfplot(F)
hold off

% End of script

Can someone please verify if this is correct or wrong? Kindly help me out if this is incorrect. Thanks in advance.