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We present full-track high-resolution radio observations of the jet of the galaxy M87 at 8 and 15 GHz. These observations were taken over three consecutive days in 2009 May using the Very Long Baseline Array (VLBA), one antenna of the Very Large Array (VLA), and the Effelsberg 100 m telescope. Our produced images have dynamic ranges exceeding 20 000:1 and resolve linear scales down to approximately 100 Schwarzschild radii, revealing a limb-brightened jet and a faint, steep spectrum counter-jet. We performed jet-to-counter-jet analysis, which helped estimate the physical parameters of the flow. The rich internal structure of the jet is dominated by three helical threads, likely produced by the Kelvin–Helmholtz (KH) instability developing in a supersonic flow with a Mach number of approximately 20 and an enthalpy ratio of around 0.3. We produce a clean imaging bias-corrected 8–15 GHz spectral index image, which shows spectrum flattening in regions of helical thread intersections. This further supports the KH origin of the observed internal structure of the jet. We detect polarized emission in the jet at distances of approximately 20 milliarcseconds from the core and find Faraday rotation which follows a transverse gradient across the jet. We apply Faraday rotation correction to the polarization position angle and find that the position angle changes as a function of distance from the jet axis, which suggests the presence of a helical magnetic field.