Help me to solve a modular equation of 43rd degree of Dedekind's $\eta$ function.

Regarding the Post Additional values of Dedekind's $\eta$ function in radical form I wrote the equation that has as root the value $\frac{\eta(43i)}{\eta(i)}$ that is missing. Can someone help me solve /in radical form) the following equation, whose solution is the value of Dedekind's modular $\frac{\eta(43i)}{\eta(i)}$ function?

$x^{88} -\frac{ 2}{43}x^{84} +\frac{ 474}{43^{3}}x^{80} -\frac{ 40066}{43^{5}}x^{76} +\frac{ 2786563}{43^{7}}x^{72} -\frac{ 159280164}{43^{9}}x^{68} +\frac{ 7812993705}{43^{11}}x^{64} -\frac{ 326607759402}{43^{13}}x^{60} +\frac{ 11820655665054}{43^{15}}x^{56} -\frac{ 365197507792944}{43^{17}}x^{52} +\frac{ 9640297075587225}{43^{19}}x^{48} -\frac{ 2124009496000996632}{43^{21}}x^{44} +\frac{ 3860823722808209061}{43^{23}}x^{40} -\frac{ 55897428244220321520}{43^{25}}x^{36} +\frac{ 640672327975602215862}{43^{27}}x^{32} -\frac{ 5889591050734068070602}{43^{29}}x^{28} +\frac{ 44167587553062189465285}{43^{31}}x^{24} -\frac{ 146840771490012863115012}{43^{33}}x^{20} +\frac{ 924488130151563712081295}{43^{35}}x^{16} -\frac{ 137705932016249214612290}{43^{37}}x^{12} +\frac{ 15316355993702167693074}{43^{39}}x^{8} +\frac{ 6777645659773468}{43^{41}}x^{4} -\frac{ 1}{43^{43}}=0$

This equation comes from the work of J. Antoniadis and specializes for the value reported in the title of application. My intent is to find the solution in closed form.