Similarity in absolute value of nearby DFT coefficients Is there any approximate relation in FFT coefficients?

For example, consider time domain signal $x_n$. Its $N$ point (assume $N$ to be even) DFT is given as $X_0,X_1,...,X_{N-1}$

Can I say something about the nature of $abs(X_1)/abs(X_0)$? I am trying to see the variation in DFT coeffcients and for that I thught one can sonsider the ratio of successive coefficients. My motivation is to see how similar the magnitude spectrogram at frequency $f1$ is to spectrogram at frequency $f1+1$ and $f1-1$

I tried to simplify the expanded equation but got stuck after a step -

$abs(X_0) = \Sigma_0^{N-1} x_n$

$abs(X_1) = abs(x_0+x_{N/2}+2(x_1.e^{-j.2\pi/N} + x_2.e^{-j.2\pi.2/N}+..+x_{N/2-1}.e^{-j.2\pi.(N/2-1)/N}))$

How do I (approximately) simplify $abs(X_1)/abs(X_0)$?
Because the basis vectors for adjacent DFT bins are absolutely orthogonal, the values in the adjacent DFT result bins can be completely unrelated, and thus their ratio can be anything, depending on the data.

If you use a non-rectangular window function, then there will be some leakage of spectral peaks into adjacent bins due to convolution with the transform of the window.  But this depends on the window chosen.