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 -7x3 + 4x2 + 10x - 5 with even exponents is (4) + (-5) = -1).
