Assume that x_{1}, x_{2}, \ldots, x_{7} are real numbers such that
\begin{aligned}
x_{1}+4 x_{2}+9 x_{3}+16 x_{4}+25 x_{5}+36 x_{6}+49 x_{7}= & 1 \\
4 x_{1}+9 x_{2}+16 x_{3}+25 x_{4}+36 x_{5}+49 x_{6}+64 x_{7}= & 12 \\
9 x_{1}+16 x_{2}+25 x_{3}+36 x_{4}+49 x_{5}+64 x_{6}+81 x_{7}= & 123 .
\end{aligned}
Find the value of
16 x_{1}+25 x_{2}+36 x_{3}+49 x_{4}+64 x_{5}+81 x_{6}+100 x_{7} .