function part1vsim2(N,L,numavg)
  
  alleigs = [];

  for (l=1:numavg) 
    l
    V = zeros(N,L);
    for (k=1:L) 
      V(:,k) = ((exp(2*pi*j*rand(1))).^(0:(N-1)))';
    end
    V = (1/N)*V'*V;
    alleigs = [ alleigs ; eig(V) ];
  end
  
  [ n , xout ] = hist(alleigs,200);
   n = n / ( numavg*L*(xout(2) - xout(1)) );
   bar(xout,n)
  axis([0 10 0 1])
  
