Let \(Q(x) = a_0 + a_1x + a_2x^2 + \cdots + a_nx^n\) be a polynomial with integer coefficients, and \(0 \le a_i < 3\) for all \(0 \le i \le n\).

Given that \(Q\big(\sqrt 3\big) = 20 + 17\sqrt 3\), what is the value of \(Q(2)\)?

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