Improved effective estimates of Pólya's Theorem for quadratic forms

Following de Loera and Santos, the Pólya exponent of a $n$-ary real form (i.e. a homogeneous polynomial in $n$ variables with real coefficients) $f$ is the infimum of the upward closed set of nonnegative integers $m$ such that $(x_1 + \cdots + x_n)^m f$ strictly has positive coefficients. By a theor