IFFT of analytic function

I'm trying to inverse Fourier transform 10/(.1+is) using ifft. The shape is correct but the amplitude is always off. My code is below:

N=128; %Number of points in frequency space
w=linspace(0,10,N); %grid in frequency space
f=10./(.1+j*w); %function values in frequency space
ws=w(2)-w(1); %increment in freq space
ts=2*pi/(ws); %increment in time space
F=N/(2*pi)*abs(ifft(f)); %Function in time space, where prefactor needed due to ifft settings.
Fp=F(1:N/2+1)*ws; %Take half of function and scale
T=ts*(0:N/2)/N; %grid in time space
N2=length(T);
Fa=10*exp(-1*T); %analytic function
plot(T,abs(Fa),'*',T,abs(Fp),'+'); %comparison