ln(5)*g(1)-zeta'(s,1/5)=f(1)*g(1)+f(3)*g(2)+f(2)*g(3)+f(4)*g(4),
ln(5)*g(2)-zeta'(s,2/5)=f(2)*g(1)+f(1)*g(2)+f(4)*g(3)+f(3)*g(4),
ln(5)g(3)-zeta'(s,3/5)=f(3)*g(1)+f(4)*g(2)+f(1)*g(3)+f(2)*g(4),
ln(5)g(4)-zeta'(s,4/5)=f(4)*g(1)+f(2)*g(2)+f(3)*g(3)+f(1)*g(4),
solve for f(1),f(2),f(3),f(4)
in terms of anything but other f(x)'s