Computing a fourier transform using FFT

Question

Say I wish to compute the expression $\hat{f}(k)=\frac{1}{L}\int_L f(x)e^{ikx}dx$ using a FFT, so a discrete version of this would be $\hat{f}(k)=\sum f(x)e^{ikx}$ over modes of $k$ defined by $L$. However, the convention Python uses for FFT is $\hat{f}(k)=\sum f(x)e^{2\pi ikx}$, and I realize that the two $\hat{f}(k)$ are not the same. So how does one relate the two? Is it just the same function but with $2\pi k$ ?