Let $A = \left[ \begin{array} { c c } \frac { 1 } { \sqrt { 2 } } & - 2 \\ 0 & 1 \end{array} \right]$ and $P = \left[ \begin{array} { c c } \cos \theta & - \sin \theta \\ \sin \theta & \cos \theta \end{array} \right] , \theta > 0$. If $\mathrm { B } = \mathrm { PAP } ^ { \mathrm { T } } , \mathrm { C } = \mathrm { P } ^ { \mathrm { T } } \mathrm { B } ^ { 10 } \mathrm { P }$ and the sum of the diagonal elements of $C$ is $\frac { \mathrm { m } } { \mathrm { n } }$, where $\operatorname { gcd } ( \mathrm { m } , \mathrm { n } ) = 1$, then $\mathrm { m } + \mathrm { n }$ is :\\
(1) 127\\
(2) 258\\
(3) 65\\
(4) 2049