How do I interpolate between bins on an FFT in python?

I have four frequency peaks, which I have after applying FFT. Now I want to know precise values of these frequency peaks. there are different interpolation methods. How can I use this method of interpolation for four frequency peaks by using python

k=index of the max (possibly local) magnitude of an DFT
X[i]=bin "i" of an DFT
|X[i]|=magnitude of DFT at bin "i“
k'=the interpolated bin location