Let,

\( \large S_n = a_1^n + a_2^n + a_3^n + a_4^n + a_5^n + a_6^n + a_7^n + a_8^n + a_9^n + a_{10}^n + a_{11}^n + a_{12}^n \)

Given that,

\( \large S_1 = S_2 = S_3 = S_4 = S_6 = S_8 = S_9 = S_{11} = 0 \)

\( \large S_5 = 35 \) , \( \large S_7 = 14 \) , \( \large S_{10} = 245 \) , \( \large S_{12} = 168 \)

Find the largest value of \(n\) for which \( \large S_n = 0 \)

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