The power spectrum analysis of stochastic spectra has emerged as a powerful tool for studying both system-specific and universal properties of complex systems. In the context of complex quantum systems, it reveals whether the corresponding classical dynamics is regular or chaotic, or a mixture of both, and encodes a ‘degree of chaoticity’. In combination with other long- and short-range spectral fluctuation measures, it provides an effective way to identify system symmetries, determine a degree of incompleteness of experimentally measured spectra, and get the clues about systems’ internal structure. Yet, the theoretical foundations of the power spectrum analysis of stochastic spectra have not been settled. In this talk, I shall formulate a non-perturbative approach [Phys. Rev. Lett. 118, 204101 (2017)] to the power spectrum of energy level fluctuations in fully chaotic quantum structures. In the particular case of broken time-reversal symmetry, our theory produces a parameter-free prediction for the power spectrum expressed – in the domain of its universality – in terms of a fifth Painlevé transcendent. Finally, I shall present fair evidence that a universal Painlevé V curve can be observed in the spectrum of Riemannium.