Reconstruct the ten coefficients $a_i$ of these quadrics in a Galois orbit of size 168.
$x^{168} - 10014013832542203812872613924739x^{161} + 171047690745503707515328576627906817785436888130925209472262244x^{154} - 1268317331496745879603035032448157273146519836562713924560050631153969519297207668270922371313x^{147} + 23237703563539410755436556575134206593366430461423708193774287327245213403024087108979694756912313 \cdots$