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Aims. The work is aimed at studying the circumstellar disk of the bright classical binary Be star π Aqr. Methods. We analysed variations of a double-peaked profile of the Hα emission line in the spectrum of π Aqr that was observed in many phases during ∼40 orbital cycles in 2004-2013. We applied the discrete Fourier transform (DFT) method to search for periodicity in the peak intensity ratio (V/R). Doppler tomography was used to study the structure of the disk around the primary. Results. The dominant frequency in the power spectrum of the Hα V/R ratio is 0.011873 day-1, which corresponds to a period of 84.2(2) days and agrees with the earlier determined orbital period of the system, Porb = 84.1 days. The V/R shows a sinusoidal variation that is phase-locked with the orbital period. Doppler maps of all our spectra show a non-uniform structure of the disk around the primary: a ring with the inner and outer radii at Vin ≈ 450 km s-1 and Vout ≈ 200 km s-1, respectively, along with an extended stable region (spot) at Vx ≈ 225 km s-1 and Vy ≈ 100 km s-1. The disk radius of ≈65 R☉ = 0.33 AU was estimated by assuming Keplerian motion of a particle on a circular orbit at the disk's outer edge. [ABSTRACT FROM AUTHOR]