+185 Let \(f(x)\) be a quadratic polynomial such that \(f(-4) = -22,\) \(f(-1)=2\), and \(f(2)=-1.\) Let \(g(x) = f(x)^{16}.\) Find the sum of the coefficients of the terms in \(g(x)\)with even exponents. (For example, the sum of the coefficients of the terms in \(-7x^3 + 4x^2 + 10x - 5\) with even exponents is \((4) + (-5) = -1.\))
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