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We prove that $\\ind M<\\infty$ if and only if $\\ind\\H^{n}_\\fa(M)<\\infty$ and that $\\ind\\H^{n}_\\fa(M)=\\ind M-n$. We also prove that if $R$ has a dualizing complex and $\\Gid_{R} M<\\infty$, then $\\Gid_{R}\\H^{n}_\\fa(M)<\\infty$ and $\\Gid_{R}\\H^{n}_\\fa(M)=\\Gid_{R} M-n$. Moreover if $R$ and $M$ are Cohen-Macaulay, then it is proved that $\\Gid_{R} M<\\infty$ whenever $\\Gid_{R}\\H^{n}_\\fa(M)<\\infty$. 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