We present a spectral analysis of the lobes and X-ray jets of Cygnus A, using more than 2 Ms of $textit{Chandra}$ observations. The X-ray jets are misaligned with the radio jets and significantly wider. We detect non-thermal emission components in both lobes and jets. For the eastern lobe and jet, we find 1 keV flux densities of $71_{-10}^{+10}$ nJy and $24_{-4}^{+4}$ nJy, and photon indices of $1.72_{-0.03}^{+0.03}$ and $1.64_{-0.04}^{+0.04}$ respectively. For the western lobe and jet, we find flux densities of $50_{-13}^{+12}$ nJy and $13_{-5}^{+5}$ nJy, and photon indices of $1.97_{-0.10}^{+0.23}$ and $1.86_{-0.12}^{+0.18}$ respectively. Using these results, we modeled the electron energy distributions of the lobes as broken power laws with age breaks. We find that a significant population of non-radiating particles is required to account for the total pressure of the eastern lobe. In the western lobe, no such population is required and the low energy cutoff to the electron distribution there needs to be raised to obtain pressures consistent with observations. This discrepancy is a consequence of the differing X-ray photon indices, which may indicate that the turnover in the inverse-Compton spectrum of the western lobe is at lower energies than in the eastern lobe. We modeled the emission from both jets as inverse-Compton emission. There is a narrow region of parameter space for which the X-ray jet can be a relic of an earlier active phase, although lack of knowledge about the jets electron distribution and particle content makes the modelling uncertain.
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