Think about using the Despain algorithm, derived by recursively decomposing an N-point FFT into FFTs of size sqrt(N). You end up with a bunch of 4-point FFTs w

Think about using the Despain algorithm, derived by recursively decomposing an N-point FFT into FFTs of size sqrt(N). You end up with a bunch of 4-point FFTs where the twiddle factors are rotations by multiples of pi/2, which can be implemented with swapping of real/imaginary parts and a change of sign. Non-degenerate twiddle factors still occur between those 4-point FFTs In this way the number of maths operations can be reduced. The cost is that the input and output are both in a weird order.