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We present here the microwave surface impedance of a high purity crystal of Y Ba2Cu3O6.99 measured at 5 frequencies between 1 and 75 GHz. This data set reveals the main features of the conductivity spectrum of the thermally excited quasiparticles in the superconducting state. Below 20 K there is a regime of extremely long quasiparticle lifetimes, due to both the collapse of inelastic scattering below Tc and the very weak impurity scattering in the high purity BaZrO3-grown crystal used in this study. Above 20 K, the scattering increases dramatically, initially at least as fast as T 4 .74.25.Nf,74.25.Fy