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1+9694080*q^8+89754255360*q^12+10164979630080*q^14+639876527832960*q^16+
24647440237854720*q^18+646038471835975680*q^20+12399979575839293440*q^22+
184026095698230213120*q^24+2200347840694273966080*q^26+21889196776341251850240*q^28+
185813171532073386639360*q^30+1373979253438910041038720*q^32+
8998373669092683059036160*q^34+52930789703078794637475840*q^36+
282884460049422917440634880*q^38+O(q^40);
In terms of H1 = \theta_{D4} and H2 = (\eta(q)\eta(q^2))^8:
H1^16-384*H1^12*H2+38016*H1^8*H2^2-743424*H1^4*H2^3+9732096*H2^4.
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