Degree \(6\) hyperbolic polynomials and orders of moduli

We consider real univariate degree \(d\) real-rooted polynomials with non-vanishing coefficients. Descartes' rule of signs implies that such a polynomial has \(\tilde{c}\) positive and \(\tilde{p}\) negative roots counted with multiplicity, where \(\tilde{c}\) and \(\tilde{p}\) are the numbers of sign changes and sign preservations in the sequence of its coefficients, \(\tilde{c}+\tilde{p}=d\). For \(d=6\), we give the exhaustive answer to the question: When the moduli of all \(6\) roots are distinct and arranged on the real positive half-axis, in which positions can the moduli of the negative roots be depending on the signs of the coefficients?