# Properties

 Label 432.6.i Level 432 Weight 6 Character orbit i Rep. character $$\chi_{432}(145,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 58 Newform subspaces 6 Sturm bound 432 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$432 = 2^{4} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 432.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$6$$ Sturm bound: $$432$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(432, [\chi])$$.

Total New Old
Modular forms 756 62 694
Cusp forms 684 58 626
Eisenstein series 72 4 68

## Trace form

 $$58q + q^{5} + q^{7} + O(q^{10})$$ $$58q + q^{5} + q^{7} - 727q^{11} - q^{13} - 1000q^{17} + 4q^{19} + 3173q^{23} - 15626q^{25} + 3981q^{29} - 1625q^{31} + 35646q^{35} - 4q^{37} - 2901q^{41} - 13865q^{43} + 37935q^{47} - 55224q^{49} + 4q^{53} - 6246q^{55} - 55033q^{59} - q^{61} + 5743q^{65} + q^{67} - 23672q^{71} - 53632q^{73} - 24885q^{77} + q^{79} - 41693q^{83} - 3126q^{85} - 207948q^{89} - 80758q^{91} - 61748q^{95} - 58147q^{97} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(432, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
432.6.i.a $$4$$ $$69.286$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$54$$ $$-74$$ $$q+(3^{3}\beta _{1}+2\beta _{2})q^{5}+(-37+37\beta _{1}+\cdots)q^{7}+\cdots$$
432.6.i.b $$6$$ $$69.286$$ 6.0.$$\cdots$$.3 None $$0$$ $$0$$ $$54$$ $$132$$ $$q+(18-18\beta _{1}-\beta _{5})q^{5}+(44\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots$$
432.6.i.c $$8$$ $$69.286$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$-78$$ $$-28$$ $$q+(-1-19\beta _{1}+\beta _{2}-\beta _{6}+\beta _{7})q^{5}+\cdots$$
432.6.i.d $$10$$ $$69.286$$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$21$$ $$-29$$ $$q+(4-4\beta _{1}+\beta _{7})q^{5}+(-6\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
432.6.i.e $$14$$ $$69.286$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$0$$ $$-25$$ $$-93$$ $$q+(-4+4\beta _{1}-\beta _{3}+\beta _{6})q^{5}+(-13\beta _{1}+\cdots)q^{7}+\cdots$$
432.6.i.f $$16$$ $$69.286$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$-25$$ $$93$$ $$q+(-3\beta _{8}-\beta _{10})q^{5}+(12-\beta _{2}-12\beta _{8}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(432, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(432, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(9, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ ($$1 - 54 T - 3199 T^{2} + 7290 T^{3} + 18515100 T^{4} + 22781250 T^{5} - 31240234375 T^{6} - 1647949218750 T^{7} + 95367431640625 T^{8}$$)($$1 - 54 T - 1788 T^{2} - 10584 T^{3} + 854952 T^{4} + 487704186 T^{5} - 21775421594 T^{6} + 1524075581250 T^{7} + 8349140625000 T^{8} - 322998046875000 T^{9} - 170516967773437500 T^{10} - 16093254089355468750 T^{11} +$$$$93\!\cdots\!25$$$$T^{12}$$)($$1 + 78 T - 2381 T^{2} - 191094 T^{3} + 7253005 T^{4} + 66450636 T^{5} - 21330994286 T^{6} - 411629383632 T^{7} - 16622006693174 T^{8} - 1286341823850000 T^{9} - 208310491074218750 T^{10} + 2027912475585937500 T^{11} +$$$$69\!\cdots\!25$$$$T^{12} -$$$$56\!\cdots\!50$$$$T^{13} -$$$$22\!\cdots\!25$$$$T^{14} +$$$$22\!\cdots\!50$$$$T^{15} +$$$$90\!\cdots\!25$$$$T^{16}$$)($$1 - 21 T - 5203 T^{2} + 519930 T^{3} + 14035794 T^{4} - 2854822770 T^{5} + 76722872007 T^{6} + 9761967315441 T^{7} - 599011867854189 T^{8} - 11924309583255600 T^{9} + 2533145723872694124 T^{10} - 37263467447673750000 T^{11} -$$$$58\!\cdots\!25$$$$T^{12} +$$$$29\!\cdots\!25$$$$T^{13} +$$$$73\!\cdots\!75$$$$T^{14} -$$$$85\!\cdots\!50$$$$T^{15} +$$$$13\!\cdots\!50$$$$T^{16} +$$$$15\!\cdots\!50$$$$T^{17} -$$$$47\!\cdots\!75$$$$T^{18} -$$$$59\!\cdots\!25$$$$T^{19} +$$$$88\!\cdots\!25$$$$T^{20}$$)($$1 + 25 T - 8164 T^{2} - 318611 T^{3} + 27932517 T^{4} + 1565127556 T^{5} - 45270335220 T^{6} - 3251191238312 T^{7} - 19378417944440 T^{8} + 8065656641221992 T^{9} + 579169791252842788 T^{10} - 38380584781304890100 T^{11} -$$$$47\!\cdots\!26$$$$T^{12} +$$$$63\!\cdots\!18$$$$T^{13} +$$$$21\!\cdots\!84$$$$T^{14} +$$$$19\!\cdots\!50$$$$T^{15} -$$$$46\!\cdots\!50$$$$T^{16} -$$$$11\!\cdots\!00$$$$T^{17} +$$$$55\!\cdots\!00$$$$T^{18} +$$$$24\!\cdots\!00$$$$T^{19} -$$$$18\!\cdots\!00$$$$T^{20} -$$$$94\!\cdots\!00$$$$T^{21} -$$$$41\!\cdots\!00$$$$T^{22} +$$$$44\!\cdots\!00$$$$T^{23} +$$$$24\!\cdots\!25$$$$T^{24} -$$$$88\!\cdots\!75$$$$T^{25} -$$$$70\!\cdots\!00$$$$T^{26} +$$$$67\!\cdots\!25$$$$T^{27} +$$$$84\!\cdots\!25$$$$T^{28}$$)($$1 + 25 T - 9961 T^{2} - 355120 T^{3} + 41317970 T^{4} + 1924368340 T^{5} - 44885115889 T^{6} - 3607801829815 T^{7} - 229629274018871 T^{8} - 5266430289086380 T^{9} + 772909460585629736 T^{10} + 22637800967616144220 T^{11} +$$$$27\!\cdots\!70$$$$T^{12} +$$$$55\!\cdots\!50$$$$T^{13} -$$$$57\!\cdots\!86$$$$T^{14} -$$$$19\!\cdots\!40$$$$T^{15} +$$$$19\!\cdots\!76$$$$T^{16} -$$$$59\!\cdots\!00$$$$T^{17} -$$$$55\!\cdots\!50$$$$T^{18} +$$$$16\!\cdots\!50$$$$T^{19} +$$$$26\!\cdots\!50$$$$T^{20} +$$$$67\!\cdots\!00$$$$T^{21} +$$$$71\!\cdots\!00$$$$T^{22} -$$$$15\!\cdots\!00$$$$T^{23} -$$$$20\!\cdots\!75$$$$T^{24} -$$$$10\!\cdots\!75$$$$T^{25} -$$$$39\!\cdots\!25$$$$T^{26} +$$$$53\!\cdots\!00$$$$T^{27} +$$$$35\!\cdots\!50$$$$T^{28} -$$$$96\!\cdots\!00$$$$T^{29} -$$$$84\!\cdots\!25$$$$T^{30} +$$$$66\!\cdots\!25$$$$T^{31} +$$$$82\!\cdots\!25$$$$T^{32}$$)
$7$ ($$1 + 74 T - 29291 T^{2} + 85322 T^{3} + 834233908 T^{4} + 1434006854 T^{5} - 8273982518459 T^{6} + 351319551735782 T^{7} + 79792266297612001 T^{8}$$)($$1 - 132 T + 9930 T^{2} - 2383268 T^{3} + 22216338 T^{4} + 1188047664 T^{5} + 4115243377158 T^{6} + 19967517088848 T^{7} + 6275565608418162 T^{8} - 11314711424678833724 T^{9} +$$$$79\!\cdots\!30$$$$T^{10} -$$$$17\!\cdots\!24$$$$T^{11} +$$$$22\!\cdots\!49$$$$T^{12}$$)($$1 + 28 T - 37767 T^{2} + 688508 T^{3} + 752155661 T^{4} - 29978584680 T^{5} - 6360743348222 T^{6} + 326958516789136 T^{7} + 37987499418745374 T^{8} + 5495191791675008752 T^{9} -$$$$17\!\cdots\!78$$$$T^{10} -$$$$14\!\cdots\!40$$$$T^{11} +$$$$60\!\cdots\!61$$$$T^{12} +$$$$92\!\cdots\!56$$$$T^{13} -$$$$85\!\cdots\!83$$$$T^{14} +$$$$10\!\cdots\!04$$$$T^{15} +$$$$63\!\cdots\!01$$$$T^{16}$$)($$1 + 29 T - 39569 T^{2} - 3762444 T^{3} + 440397336 T^{4} + 77352503496 T^{5} - 2769093584103 T^{6} + 560172784984473 T^{7} + 238615372451780007 T^{8} - 16031898530170676332 T^{9} -$$$$69\!\cdots\!60$$$$T^{10} -$$$$26\!\cdots\!24$$$$T^{11} +$$$$67\!\cdots\!43$$$$T^{12} +$$$$26\!\cdots\!39$$$$T^{13} -$$$$22\!\cdots\!03$$$$T^{14} +$$$$10\!\cdots\!72$$$$T^{15} +$$$$99\!\cdots\!64$$$$T^{16} -$$$$14\!\cdots\!92$$$$T^{17} -$$$$25\!\cdots\!69$$$$T^{18} +$$$$31\!\cdots\!03$$$$T^{19} +$$$$17\!\cdots\!49$$$$T^{20}$$)($$1 + 93 T - 47014 T^{2} - 4171389 T^{3} + 1494556117 T^{4} + 156294715500 T^{5} - 27659965511228 T^{6} - 3955572741308496 T^{7} + 262751253492307760 T^{8} + 78744340598713966992 T^{9} +$$$$41\!\cdots\!80$$$$T^{10} -$$$$10\!\cdots\!20$$$$T^{11} -$$$$20\!\cdots\!70$$$$T^{12} +$$$$73\!\cdots\!26$$$$T^{13} +$$$$46\!\cdots\!88$$$$T^{14} +$$$$12\!\cdots\!82$$$$T^{15} -$$$$58\!\cdots\!30$$$$T^{16} -$$$$50\!\cdots\!60$$$$T^{17} +$$$$33\!\cdots\!80$$$$T^{18} +$$$$10\!\cdots\!44$$$$T^{19} +$$$$59\!\cdots\!40$$$$T^{20} -$$$$14\!\cdots\!28$$$$T^{21} -$$$$17\!\cdots\!28$$$$T^{22} +$$$$16\!\cdots\!00$$$$T^{23} +$$$$26\!\cdots\!33$$$$T^{24} -$$$$12\!\cdots\!27$$$$T^{25} -$$$$23\!\cdots\!14$$$$T^{26} +$$$$79\!\cdots\!51$$$$T^{27} +$$$$14\!\cdots\!49$$$$T^{28}$$)($$1 - 93 T - 51467 T^{2} + 1139634 T^{3} + 1413276300 T^{4} + 65493773442 T^{5} - 18530034778363 T^{6} - 2277040599077847 T^{7} - 8935217953801423 T^{8} + 25357782238509171204 T^{9} +$$$$28\!\cdots\!76$$$$T^{10} -$$$$16\!\cdots\!28$$$$T^{11} +$$$$24\!\cdots\!90$$$$T^{12} -$$$$20\!\cdots\!38$$$$T^{13} -$$$$98\!\cdots\!14$$$$T^{14} +$$$$83\!\cdots\!40$$$$T^{15} +$$$$21\!\cdots\!24$$$$T^{16} +$$$$14\!\cdots\!80$$$$T^{17} -$$$$27\!\cdots\!86$$$$T^{18} -$$$$99\!\cdots\!34$$$$T^{19} +$$$$19\!\cdots\!90$$$$T^{20} -$$$$21\!\cdots\!96$$$$T^{21} +$$$$64\!\cdots\!24$$$$T^{22} +$$$$96\!\cdots\!72$$$$T^{23} -$$$$56\!\cdots\!23$$$$T^{24} -$$$$24\!\cdots\!29$$$$T^{25} -$$$$33\!\cdots\!87$$$$T^{26} +$$$$19\!\cdots\!06$$$$T^{27} +$$$$71\!\cdots\!00$$$$T^{28} +$$$$97\!\cdots\!38$$$$T^{29} -$$$$73\!\cdots\!83$$$$T^{30} -$$$$22\!\cdots\!99$$$$T^{31} +$$$$40\!\cdots\!01$$$$T^{32}$$)
$11$ ($$1 + 78 T + 81845 T^{2} - 31033314 T^{3} - 21177529764 T^{4} - 4997946253014 T^{5} + 2122848516468845 T^{6} + 325825357214420778 T^{7} +$$$$67\!\cdots\!01$$$$T^{8}$$)($$1 + 315 T - 222063 T^{2} - 18182214 T^{3} + 32678625651 T^{4} - 5249320804629 T^{5} - 7280422055915978 T^{6} - 845408364906305079 T^{7} +$$$$84\!\cdots\!51$$$$T^{8} -$$$$75\!\cdots\!14$$$$T^{9} -$$$$14\!\cdots\!63$$$$T^{10} +$$$$34\!\cdots\!65$$$$T^{11} +$$$$17\!\cdots\!01$$$$T^{12}$$)($$1 - 444 T - 421874 T^{2} + 122372328 T^{3} + 147603288625 T^{4} - 24043789512072 T^{5} - 33881306185300610 T^{6} + 1343287267601416260 T^{7} +$$$$64\!\cdots\!56$$$$T^{8} +$$$$21\!\cdots\!60$$$$T^{9} -$$$$87\!\cdots\!10$$$$T^{10} -$$$$10\!\cdots\!72$$$$T^{11} +$$$$99\!\cdots\!25$$$$T^{12} +$$$$13\!\cdots\!28$$$$T^{13} -$$$$73\!\cdots\!74$$$$T^{14} -$$$$12\!\cdots\!44$$$$T^{15} +$$$$45\!\cdots\!01$$$$T^{16}$$)($$1 - 177 T - 396232 T^{2} - 71434269 T^{3} + 104816625882 T^{4} + 33726096455301 T^{5} - 6913987980717606 T^{6} - 8552599160812456257 T^{7} -$$$$10\!\cdots\!51$$$$T^{8} +$$$$50\!\cdots\!82$$$$T^{9} +$$$$47\!\cdots\!16$$$$T^{10} +$$$$81\!\cdots\!82$$$$T^{11} -$$$$27\!\cdots\!51$$$$T^{12} -$$$$35\!\cdots\!07$$$$T^{13} -$$$$46\!\cdots\!06$$$$T^{14} +$$$$36\!\cdots\!51$$$$T^{15} +$$$$18\!\cdots\!82$$$$T^{16} -$$$$20\!\cdots\!19$$$$T^{17} -$$$$17\!\cdots\!32$$$$T^{18} -$$$$12\!\cdots\!27$$$$T^{19} +$$$$11\!\cdots\!01$$$$T^{20}$$)($$1 + 359 T - 713557 T^{2} - 159433936 T^{3} + 305969114322 T^{4} + 33381105701438 T^{5} - 91317280089255693 T^{6} - 2170736290619808613 T^{7} +$$$$21\!\cdots\!56$$$$T^{8} -$$$$58\!\cdots\!73$$$$T^{9} -$$$$39\!\cdots\!79$$$$T^{10} +$$$$17\!\cdots\!14$$$$T^{11} +$$$$67\!\cdots\!61$$$$T^{12} -$$$$13\!\cdots\!75$$$$T^{13} -$$$$10\!\cdots\!94$$$$T^{14} -$$$$21\!\cdots\!25$$$$T^{15} +$$$$17\!\cdots\!61$$$$T^{16} +$$$$72\!\cdots\!14$$$$T^{17} -$$$$26\!\cdots\!79$$$$T^{18} -$$$$63\!\cdots\!23$$$$T^{19} +$$$$36\!\cdots\!56$$$$T^{20} -$$$$61\!\cdots\!63$$$$T^{21} -$$$$41\!\cdots\!93$$$$T^{22} +$$$$24\!\cdots\!38$$$$T^{23} +$$$$35\!\cdots\!22$$$$T^{24} -$$$$30\!\cdots\!36$$$$T^{25} -$$$$21\!\cdots\!57$$$$T^{26} +$$$$17\!\cdots\!09$$$$T^{27} +$$$$78\!\cdots\!01$$$$T^{28}$$)($$1 + 596 T - 61060 T^{2} - 455883968 T^{3} - 218809782778 T^{4} + 19952947552364 T^{5} + 92717220800303336 T^{6} + 39432028403284968532 T^{7} -$$$$21\!\cdots\!99$$$$T^{8} -$$$$11\!\cdots\!92$$$$T^{9} -$$$$46\!\cdots\!52$$$$T^{10} -$$$$75\!\cdots\!32$$$$T^{11} +$$$$88\!\cdots\!86$$$$T^{12} +$$$$40\!\cdots\!20$$$$T^{13} +$$$$51\!\cdots\!24$$$$T^{14} -$$$$45\!\cdots\!20$$$$T^{15} -$$$$29\!\cdots\!60$$$$T^{16} -$$$$72\!\cdots\!20$$$$T^{17} +$$$$13\!\cdots\!24$$$$T^{18} +$$$$17\!\cdots\!20$$$$T^{19} +$$$$59\!\cdots\!86$$$$T^{20} -$$$$82\!\cdots\!32$$$$T^{21} -$$$$81\!\cdots\!52$$$$T^{22} -$$$$31\!\cdots\!92$$$$T^{23} -$$$$98\!\cdots\!99$$$$T^{24} +$$$$28\!\cdots\!32$$$$T^{25} +$$$$10\!\cdots\!36$$$$T^{26} +$$$$37\!\cdots\!64$$$$T^{27} -$$$$66\!\cdots\!78$$$$T^{28} -$$$$22\!\cdots\!68$$$$T^{29} -$$$$48\!\cdots\!60$$$$T^{30} +$$$$75\!\cdots\!96$$$$T^{31} +$$$$20\!\cdots\!01$$$$T^{32}$$)
$13$ ($$1 - 1106 T + 261241 T^{2} - 242666354 T^{3} + 333396924028 T^{4} - 90100318575722 T^{5} + 36014290269124609 T^{6} - 56611597673584377242 T^{7} +$$$$19\!\cdots\!01$$$$T^{8}$$)($$1 + 744 T + 110316 T^{2} - 5563444 T^{3} - 92859229188 T^{4} - 67995162383184 T^{5} - 18766393745055906 T^{6} - 25246127826739536912 T^{7} -$$$$12\!\cdots\!12$$$$T^{8} -$$$$28\!\cdots\!08$$$$T^{9} +$$$$20\!\cdots\!16$$$$T^{10} +$$$$52\!\cdots\!92$$$$T^{11} +$$$$26\!\cdots\!49$$$$T^{12}$$)($$1 + 182 T - 1009641 T^{2} - 162494414 T^{3} + 553084541681 T^{4} + 66263508549516 T^{5} - 217064082764017418 T^{6} - 12452829446314121656 T^{7} +$$$$75\!\cdots\!98$$$$T^{8} -$$$$46\!\cdots\!08$$$$T^{9} -$$$$29\!\cdots\!82$$$$T^{10} +$$$$33\!\cdots\!12$$$$T^{11} +$$$$10\!\cdots\!81$$$$T^{12} -$$$$11\!\cdots\!02$$$$T^{13} -$$$$26\!\cdots\!09$$$$T^{14} +$$$$17\!\cdots\!74$$$$T^{15} +$$$$36\!\cdots\!01$$$$T^{16}$$)($$1 + 181 T - 1012331 T^{2} + 14482182 T^{3} + 446454243174 T^{4} - 84043375137762 T^{5} - 192479505557683773 T^{6} - 802846347498861897 T^{7} +$$$$98\!\cdots\!51$$$$T^{8} +$$$$77\!\cdots\!72$$$$T^{9} -$$$$41\!\cdots\!24$$$$T^{10} +$$$$28\!\cdots\!96$$$$T^{11} +$$$$13\!\cdots\!99$$$$T^{12} -$$$$41\!\cdots\!29$$$$T^{13} -$$$$36\!\cdots\!73$$$$T^{14} -$$$$59\!\cdots\!66$$$$T^{15} +$$$$11\!\cdots\!26$$$$T^{16} +$$$$14\!\cdots\!74$$$$T^{17} -$$$$36\!\cdots\!31$$$$T^{18} +$$$$24\!\cdots\!33$$$$T^{19} +$$$$49\!\cdots\!49$$$$T^{20}$$)($$1 - 89 T - 2058636 T^{2} + 219178995 T^{3} + 2268011875089 T^{4} - 247134469996752 T^{5} - 1792198711390521660 T^{6} +$$$$16\!\cdots\!80$$$$T^{7} +$$$$11\!\cdots\!60$$$$T^{8} -$$$$77\!\cdots\!20$$$$T^{9} -$$$$60\!\cdots\!88$$$$T^{10} +$$$$23\!\cdots\!36$$$$T^{11} +$$$$27\!\cdots\!94$$$$T^{12} -$$$$33\!\cdots\!42$$$$T^{13} -$$$$10\!\cdots\!88$$$$T^{14} -$$$$12\!\cdots\!06$$$$T^{15} +$$$$38\!\cdots\!06$$$$T^{16} +$$$$12\!\cdots\!52$$$$T^{17} -$$$$11\!\cdots\!88$$$$T^{18} -$$$$54\!\cdots\!60$$$$T^{19} +$$$$29\!\cdots\!40$$$$T^{20} +$$$$16\!\cdots\!60$$$$T^{21} -$$$$64\!\cdots\!60$$$$T^{22} -$$$$33\!\cdots\!36$$$$T^{23} +$$$$11\!\cdots\!61$$$$T^{24} +$$$$40\!\cdots\!15$$$$T^{25} -$$$$14\!\cdots\!36$$$$T^{26} -$$$$22\!\cdots\!77$$$$T^{27} +$$$$94\!\cdots\!49$$$$T^{28}$$)($$1 + 89 T - 502679 T^{2} + 47151622 T^{3} + 82535103458 T^{4} - 71526474077762 T^{5} + 4174495306830045 T^{6} + 31969473411078931545 T^{7} -$$$$49\!\cdots\!67$$$$T^{8} -$$$$31\!\cdots\!60$$$$T^{9} -$$$$11\!\cdots\!64$$$$T^{10} -$$$$29\!\cdots\!76$$$$T^{11} +$$$$33\!\cdots\!06$$$$T^{12} +$$$$18\!\cdots\!02$$$$T^{13} -$$$$13\!\cdots\!26$$$$T^{14} -$$$$38\!\cdots\!56$$$$T^{15} +$$$$33\!\cdots\!84$$$$T^{16} -$$$$14\!\cdots\!08$$$$T^{17} -$$$$18\!\cdots\!74$$$$T^{18} +$$$$95\!\cdots\!14$$$$T^{19} +$$$$64\!\cdots\!06$$$$T^{20} -$$$$20\!\cdots\!68$$$$T^{21} -$$$$30\!\cdots\!36$$$$T^{22} -$$$$30\!\cdots\!20$$$$T^{23} -$$$$18\!\cdots\!67$$$$T^{24} +$$$$42\!\cdots\!85$$$$T^{25} +$$$$20\!\cdots\!05$$$$T^{26} -$$$$13\!\cdots\!34$$$$T^{27} +$$$$56\!\cdots\!58$$$$T^{28} +$$$$12\!\cdots\!46$$$$T^{29} -$$$$47\!\cdots\!71$$$$T^{30} +$$$$31\!\cdots\!73$$$$T^{31} +$$$$13\!\cdots\!01$$$$T^{32}$$)
$17$ ($$( 1 + 492 T + 991654 T^{2} + 698569644 T^{3} + 2015993900449 T^{4} )^{2}$$)($$( 1 + 1449 T + 3759531 T^{2} + 3184553142 T^{3} + 5337996407067 T^{4} + 2921175161750601 T^{5} + 2862423051509815793 T^{6} )^{2}$$)($$( 1 - 2178 T + 4502417 T^{2} - 6473305458 T^{3} + 7835841277908 T^{4} - 9191168067679506 T^{5} + 9076845209277885233 T^{6} -$$$$62\!\cdots\!54$$$$T^{7} +$$$$40\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 + 1140 T + 4980550 T^{2} + 3443850354 T^{3} + 10068870522169 T^{4} + 5069379208548852 T^{5} + 14296356292995309833 T^{6} +$$$$69\!\cdots\!46$$$$T^{7} +$$$$14\!\cdots\!50$$$$T^{8} +$$$$46\!\cdots\!40$$$$T^{9} +$$$$57\!\cdots\!57$$$$T^{10} )^{2}$$)($$( 1 - 680 T + 5575556 T^{2} - 4650824578 T^{3} + 14317451937038 T^{4} - 15537252897814160 T^{5} + 24941954641724178845 T^{6} -$$$$29\!\cdots\!52$$$$T^{7} +$$$$35\!\cdots\!65$$$$T^{8} -$$$$31\!\cdots\!40$$$$T^{9} +$$$$40\!\cdots\!34$$$$T^{10} -$$$$18\!\cdots\!78$$$$T^{11} +$$$$32\!\cdots\!92$$$$T^{12} -$$$$55\!\cdots\!20$$$$T^{13} +$$$$11\!\cdots\!93$$$$T^{14} )^{2}$$)($$( 1 + 277 T + 4457165 T^{2} + 28004106 T^{3} + 10361936287448 T^{4} - 2191806006139228 T^{5} + 19212285035261150395 T^{6} -$$$$42\!\cdots\!75$$$$T^{7} +$$$$30\!\cdots\!06$$$$T^{8} -$$$$59\!\cdots\!75$$$$T^{9} +$$$$38\!\cdots\!55$$$$T^{10} -$$$$62\!\cdots\!04$$$$T^{11} +$$$$42\!\cdots\!48$$$$T^{12} +$$$$16\!\cdots\!42$$$$T^{13} +$$$$36\!\cdots\!85$$$$T^{14} +$$$$32\!\cdots\!61$$$$T^{15} +$$$$16\!\cdots\!01$$$$T^{16} )^{2}$$)
$19$ ($$( 1 - 1640 T + 2303382 T^{2} - 4060802360 T^{3} + 6131066257801 T^{4} )^{2}$$)($$( 1 + 1131 T + 5928369 T^{2} + 5953391858 T^{3} + 14679228552531 T^{4} + 6934235937572931 T^{5} + 15181127029874798299 T^{6} )^{2}$$)($$( 1 + 476 T + 5379895 T^{2} + 1785507140 T^{3} + 16120413258280 T^{4} + 4421092443846860 T^{5} + 32984492705012310895 T^{6} +$$$$72\!\cdots\!24$$$$T^{7} +$$$$37\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 - 416 T + 5046258 T^{2} - 6215761044 T^{3} + 20272296121125 T^{4} - 15898268281316088 T^{5} + 50196212153221491375 T^{6} -$$$$38\!\cdots\!44$$$$T^{7} +$$$$76\!\cdots\!42$$$$T^{8} -$$$$15\!\cdots\!16$$$$T^{9} +$$$$93\!\cdots\!99$$$$T^{10} )^{2}$$)($$( 1 + 884 T + 7442692 T^{2} + 897057820 T^{3} + 25796998037726 T^{4} - 13937022580183268 T^{5} + 60547133087281518999 T^{6} -$$$$65\!\cdots\!88$$$$T^{7} +$$$$14\!\cdots\!01$$$$T^{8} -$$$$85\!\cdots\!68$$$$T^{9} +$$$$39\!\cdots\!74$$$$T^{10} +$$$$33\!\cdots\!20$$$$T^{11} +$$$$69\!\cdots\!08$$$$T^{12} +$$$$20\!\cdots\!84$$$$T^{13} +$$$$57\!\cdots\!99$$$$T^{14} )^{2}$$)($$( 1 - 437 T + 12400611 T^{2} + 1289091140 T^{3} + 65043737194094 T^{4} + 47486032667071602 T^{5} +$$$$20\!\cdots\!77$$$$T^{6} +$$$$26\!\cdots\!73$$$$T^{7} +$$$$51\!\cdots\!34$$$$T^{8} +$$$$66\!\cdots\!27$$$$T^{9} +$$$$12\!\cdots\!77$$$$T^{10} +$$$$72\!\cdots\!98$$$$T^{11} +$$$$24\!\cdots\!94$$$$T^{12} +$$$$11\!\cdots\!60$$$$T^{13} +$$$$28\!\cdots\!11$$$$T^{14} -$$$$24\!\cdots\!63$$$$T^{15} +$$$$14\!\cdots\!01$$$$T^{16} )^{2}$$)
$23$ ($$1 + 5538 T + 10264397 T^{2} + 41714215218 T^{3} + 177540370655268 T^{4} + 268486997118867774 T^{5} +$$$$42\!\cdots\!53$$$$T^{6} +$$$$14\!\cdots\!66$$$$T^{7} +$$$$17\!\cdots\!01$$$$T^{8}$$)($$1 + 3168 T - 11449086 T^{2} - 14347077444 T^{3} + 192790258568754 T^{4} + 140383346504289372 T^{5} -$$$$11\!\cdots\!18$$$$T^{6} +$$$$90\!\cdots\!96$$$$T^{7} +$$$$79\!\cdots\!46$$$$T^{8} -$$$$38\!\cdots\!08$$$$T^{9} -$$$$19\!\cdots\!86$$$$T^{10} +$$$$34\!\cdots\!24$$$$T^{11} +$$$$71\!\cdots\!49$$$$T^{12}$$)($$1 - 8844 T + 29643313 T^{2} - 58247545548 T^{3} + 172348926961837 T^{4} - 574153269020383320 T^{5} +$$$$14\!\cdots\!02$$$$T^{6} -$$$$52\!\cdots\!88$$$$T^{7} +$$$$17\!\cdots\!06$$$$T^{8} -$$$$33\!\cdots\!84$$$$T^{9} +$$$$60\!\cdots\!98$$$$T^{10} -$$$$15\!\cdots\!40$$$$T^{11} +$$$$29\!\cdots\!37$$$$T^{12} -$$$$64\!\cdots\!64$$$$T^{13} +$$$$21\!\cdots\!37$$$$T^{14} -$$$$40\!\cdots\!08$$$$T^{15} +$$$$29\!\cdots\!01$$$$T^{16}$$)($$1 - 399 T - 16077241 T^{2} - 38108825820 T^{3} + 155650662506976 T^{4} + 562944417983120520 T^{5} - 48522958516353490863 T^{6} -$$$$48\!\cdots\!51$$$$T^{7} -$$$$71\!\cdots\!41$$$$T^{8} +$$$$11\!\cdots\!52$$$$T^{9} +$$$$81\!\cdots\!80$$$$T^{10} +$$$$74\!\cdots\!36$$$$T^{11} -$$$$29\!\cdots\!09$$$$T^{12} -$$$$12\!\cdots\!57$$$$T^{13} -$$$$83\!\cdots\!63$$$$T^{14} +$$$$62\!\cdots\!60$$$$T^{15} +$$$$11\!\cdots\!24$$$$T^{16} -$$$$17\!\cdots\!40$$$$T^{17} -$$$$47\!\cdots\!41$$$$T^{18} -$$$$75\!\cdots\!57$$$$T^{19} +$$$$12\!\cdots\!49$$$$T^{20}$$)($$1 - 2503 T - 11606062 T^{2} + 65361494759 T^{3} + 1401913886037 T^{4} - 570601291483651060 T^{5} +$$$$16\!\cdots\!72$$$$T^{6} +$$$$65\!\cdots\!36$$$$T^{7} -$$$$16\!\cdots\!68$$$$T^{8} +$$$$42\!\cdots\!28$$$$T^{9} +$$$$49\!\cdots\!08$$$$T^{10} -$$$$41\!\cdots\!32$$$$T^{11} +$$$$62\!\cdots\!34$$$$T^{12} +$$$$13\!\cdots\!54$$$$T^{13} -$$$$68\!\cdots\!68$$$$T^{14} +$$$$90\!\cdots\!22$$$$T^{15} +$$$$25\!\cdots\!66$$$$T^{16} -$$$$11\!\cdots\!24$$$$T^{17} +$$$$84\!\cdots\!08$$$$T^{18} +$$$$46\!\cdots\!04$$$$T^{19} -$$$$11\!\cdots\!32$$$$T^{20} +$$$$30\!\cdots\!52$$$$T^{21} +$$$$48\!\cdots\!72$$$$T^{22} -$$$$10\!\cdots\!80$$$$T^{23} +$$$$17\!\cdots\!13$$$$T^{24} +$$$$51\!\cdots\!13$$$$T^{25} -$$$$58\!\cdots\!62$$$$T^{26} -$$$$81\!\cdots\!29$$$$T^{27} +$$$$20\!\cdots\!49$$$$T^{28}$$)($$1 - 133 T - 32014591 T^{2} - 33173095682 T^{3} + 531881681603900 T^{4} + 1020363968296714982 T^{5} -$$$$56\!\cdots\!27$$$$T^{6} -$$$$15\!\cdots\!95$$$$T^{7} +$$$$42\!\cdots\!41$$$$T^{8} +$$$$16\!\cdots\!84$$$$T^{9} -$$$$21\!\cdots\!08$$$$T^{10} -$$$$12\!\cdots\!92$$$$T^{11} +$$$$51\!\cdots\!78$$$$T^{12} +$$$$65\!\cdots\!46$$$$T^{13} +$$$$28\!\cdots\!54$$$$T^{14} -$$$$16\!\cdots\!16$$$$T^{15} -$$$$35\!\cdots\!20$$$$T^{16} -$$$$10\!\cdots\!88$$$$T^{17} +$$$$11\!\cdots\!46$$$$T^{18} +$$$$17\!\cdots\!22$$$$T^{19} +$$$$88\!\cdots\!78$$$$T^{20} -$$$$13\!\cdots\!56$$$$T^{21} -$$$$15\!\cdots\!92$$$$T^{22} +$$$$73\!\cdots\!88$$$$T^{23} +$$$$12\!\cdots\!41$$$$T^{24} -$$$$29\!\cdots\!85$$$$T^{25} -$$$$68\!\cdots\!23$$$$T^{26} +$$$$80\!\cdots\!74$$$$T^{27} +$$$$26\!\cdots\!00$$$$T^{28} -$$$$10\!\cdots\!26$$$$T^{29} -$$$$67\!\cdots\!59$$$$T^{30} -$$$$17\!\cdots\!31$$$$T^{31} +$$$$86\!\cdots\!01$$$$T^{32}$$)
$29$ ($$1 - 3894 T - 26328655 T^{2} - 1828595142 T^{3} + 989854392537516 T^{4} - 37506587418238158 T^{5} -$$$$11\!\cdots\!55$$$$T^{6} -$$$$33\!\cdots\!06$$$$T^{7} +$$$$17\!\cdots\!01$$$$T^{8}$$)($$1 - 5148 T - 22104564 T^{2} + 185150934252 T^{3} + 244953744801108 T^{4} - 2482021182847364820 T^{5} +$$$$50\!\cdots\!82$$$$T^{6} -$$$$50\!\cdots\!80$$$$T^{7} +$$$$10\!\cdots\!08$$$$T^{8} +$$$$15\!\cdots\!48$$$$T^{9} -$$$$39\!\cdots\!64$$$$T^{10} -$$$$18\!\cdots\!52$$$$T^{11} +$$$$74\!\cdots\!01$$$$T^{12}$$)($$1 + 12018 T + 15291415 T^{2} - 58796364810 T^{3} + 2512265879646529 T^{4} + 12711396421291774644 T^{5} -$$$$20\!\cdots\!74$$$$T^{6} +$$$$10\!\cdots\!36$$$$T^{7} +$$$$21\!\cdots\!82$$$$T^{8} +$$$$21\!\cdots\!64$$$$T^{9} -$$$$86\!\cdots\!74$$$$T^{10} +$$$$10\!\cdots\!56$$$$T^{11} +$$$$44\!\cdots\!29$$$$T^{12} -$$$$21\!\cdots\!90$$$$T^{13} +$$$$11\!\cdots\!15$$$$T^{14} +$$$$18\!\cdots\!82$$$$T^{15} +$$$$31\!\cdots\!01$$$$T^{16}$$)($$1 - 6033 T + 3652157 T^{2} - 31641196734 T^{3} + 283528398607854 T^{4} - 668469168127712358 T^{5} +$$$$64\!\cdots\!39$$$$T^{6} -$$$$82\!\cdots\!55$$$$T^{7} -$$$$90\!\cdots\!17$$$$T^{8} -$$$$14\!\cdots\!60$$$$T^{9} +$$$$58\!\cdots\!16$$$$T^{10} -$$$$29\!\cdots\!40$$$$T^{11} -$$$$38\!\cdots\!17$$$$T^{12} -$$$$71\!\cdots\!95$$$$T^{13} +$$$$11\!\cdots\!39$$$$T^{14} -$$$$24\!\cdots\!42$$$$T^{15} +$$$$21\!\cdots\!54$$$$T^{16} -$$$$48\!\cdots\!66$$$$T^{17} +$$$$11\!\cdots\!57$$$$T^{18} -$$$$38\!\cdots\!17$$$$T^{19} +$$$$13\!\cdots\!01$$$$T^{20}$$)($$1 + 165 T - 98986676 T^{2} + 155484594393 T^{3} + 5359192977256801 T^{4} - 14410108625728925088 T^{5} -$$$$18\!\cdots\!24$$$$T^{6} +$$$$72\!\cdots\!60$$$$T^{7} +$$$$43\!\cdots\!24$$$$T^{8} -$$$$22\!\cdots\!20$$$$T^{9} -$$$$64\!\cdots\!56$$$$T^{10} +$$$$44\!\cdots\!72$$$$T^{11} +$$$$50\!\cdots\!38$$$$T^{12} -$$$$37\!\cdots\!62$$$$T^{13} -$$$$16\!\cdots\!16$$$$T^{14} -$$$$77\!\cdots\!38$$$$T^{15} +$$$$21\!\cdots\!38$$$$T^{16} +$$$$38\!\cdots\!28$$$$T^{17} -$$$$11\!\cdots\!56$$$$T^{18} -$$$$81\!\cdots\!80$$$$T^{19} +$$$$32\!\cdots\!24$$$$T^{20} +$$$$11\!\cdots\!40$$$$T^{21} -$$$$57\!\cdots\!24$$$$T^{22} -$$$$92\!\cdots\!12$$$$T^{23} +$$$$70\!\cdots\!01$$$$T^{24} +$$$$42\!\cdots\!57$$$$T^{25} -$$$$54\!\cdots\!76$$$$T^{26} +$$$$18\!\cdots\!85$$$$T^{27} +$$$$23\!\cdots\!01$$$$T^{28}$$)($$1 - 1089 T - 54506731 T^{2} + 126985273830 T^{3} + 816212017726146 T^{4} - 2783742130150557714 T^{5} +$$$$15\!\cdots\!53$$$$T^{6} -$$$$92\!\cdots\!29$$$$T^{7} -$$$$39\!\cdots\!51$$$$T^{8} +$$$$45\!\cdots\!64$$$$T^{9} -$$$$11\!\cdots\!08$$$$T^{10} -$$$$10\!\cdots\!44$$$$T^{11} +$$$$45\!\cdots\!50$$$$T^{12} -$$$$25\!\cdots\!46$$$$T^{13} +$$$$11\!\cdots\!34$$$$T^{14} +$$$$35\!\cdots\!88$$$$T^{15} -$$$$15\!\cdots\!20$$$$T^{16} +$$$$73\!\cdots\!12$$$$T^{17} +$$$$48\!\cdots\!34$$$$T^{18} -$$$$21\!\cdots\!54$$$$T^{19} +$$$$79\!\cdots\!50$$$$T^{20} -$$$$39\!\cdots\!56$$$$T^{21} -$$$$88\!\cdots\!08$$$$T^{22} +$$$$70\!\cdots\!36$$$$T^{23} -$$$$12\!\cdots\!51$$$$T^{24} -$$$$59\!\cdots\!21$$$$T^{25} +$$$$20\!\cdots\!53$$$$T^{26} -$$$$75\!\cdots\!86$$$$T^{27} +$$$$45\!\cdots\!46$$$$T^{28} +$$$$14\!\cdots\!70$$$$T^{29} -$$$$12\!\cdots\!31$$$$T^{30} -$$$$52\!\cdots\!61$$$$T^{31} +$$$$98\!\cdots\!01$$$$T^{32}$$)
$31$ ($$1 + 4718 T + 308941 T^{2} - 166581818242 T^{3} - 975071466725036 T^{4} - 4769096028304772542 T^{5} +$$$$25\!\cdots\!41$$$$T^{6} +$$$$11\!\cdots\!18$$$$T^{7} +$$$$67\!\cdots\!01$$$$T^{8}$$)($$1 - 8610 T - 10689342 T^{2} + 137042221612 T^{3} + 1032348577619862 T^{4} - 2025683261171583642 T^{5} -$$$$31\!\cdots\!06$$$$T^{6} -$$$$57\!\cdots\!42$$$$T^{7} +$$$$84\!\cdots\!62$$$$T^{8} +$$$$32\!\cdots\!12$$$$T^{9} -$$$$71\!\cdots\!42$$$$T^{10} -$$$$16\!\cdots\!10$$$$T^{11} +$$$$55\!\cdots\!01$$$$T^{12}$$)($$1 + 1132 T - 60658635 T^{2} - 62431167700 T^{3} + 1166392900733297 T^{4} + 126919079777751576 T^{5} -$$$$56\!\cdots\!38$$$$T^{6} +$$$$20\!\cdots\!72$$$$T^{7} +$$$$28\!\cdots\!06$$$$T^{8} +$$$$60\!\cdots\!72$$$$T^{9} -$$$$46\!\cdots\!38$$$$T^{10} +$$$$29\!\cdots\!76$$$$T^{11} +$$$$78\!\cdots\!97$$$$T^{12} -$$$$12\!\cdots\!00$$$$T^{13} -$$$$33\!\cdots\!35$$$$T^{14} +$$$$17\!\cdots\!32$$$$T^{15} +$$$$45\!\cdots\!01$$$$T^{16}$$)($$1 + 2759 T - 54902477 T^{2} + 189444651072 T^{3} + 2052158291804100 T^{4} - 13274031992302596720 T^{5} -$$$$32\!\cdots\!47$$$$T^{6} +$$$$42\!\cdots\!39$$$$T^{7} -$$$$13\!\cdots\!49$$$$T^{8} -$$$$36\!\cdots\!48$$$$T^{9} +$$$$63\!\cdots\!24$$$$T^{10} -$$$$10\!\cdots\!48$$$$T^{11} -$$$$11\!\cdots\!49$$$$T^{12} +$$$$99\!\cdots\!89$$$$T^{13} -$$$$21\!\cdots\!47$$$$T^{14} -$$$$25\!\cdots\!20$$$$T^{15} +$$$$11\!\cdots\!00$$$$T^{16} +$$$$29\!\cdots\!72$$$$T^{17} -$$$$24\!\cdots\!77$$$$T^{18} +$$$$35\!\cdots\!09$$$$T^{19} +$$$$36\!\cdots\!01$$$$T^{20}$$)($$1 + 5143 T - 109681746 T^{2} - 315878935347 T^{3} + 7000666428159981 T^{4} + 4942120298051414760 T^{5} -$$$$34\!\cdots\!12$$$$T^{6} -$$$$60\!\cdots\!20$$$$T^{7} +$$$$13\!\cdots\!84$$$$T^{8} +$$$$51\!\cdots\!84$$$$T^{9} -$$$$48\!\cdots\!52$$$$T^{10} -$$$$16\!\cdots\!28$$$$T^{11} +$$$$16\!\cdots\!90$$$$T^{12} +$$$$19\!\cdots\!30$$$$T^{13} -$$$$52\!\cdots\!92$$$$T^{14} +$$$$54\!\cdots\!30$$$$T^{15} +$$$$13\!\cdots\!90$$$$T^{16} -$$$$39\!\cdots\!28$$$$T^{17} -$$$$32\!\cdots\!52$$$$T^{18} +$$$$98\!\cdots\!84$$$$T^{19} +$$$$74\!\cdots\!84$$$$T^{20} -$$$$94\!\cdots\!20$$$$T^{21} -$$$$15\!\cdots\!12$$$$T^{22} +$$$$63\!\cdots\!60$$$$T^{23} +$$$$25\!\cdots\!81$$$$T^{24} -$$$$33\!\cdots\!97$$$$T^{25} -$$$$33\!\cdots\!46$$$$T^{26} +$$$$44\!\cdots\!93$$$$T^{27} +$$$$24\!\cdots\!01$$$$T^{28}$$)($$1 - 3517 T - 115326029 T^{2} + 863095735936 T^{3} + 5493586170208052 T^{4} - 74258762006207563328 T^{5} -$$$$68\!\cdots\!97$$$$T^{6} +$$$$36\!\cdots\!17$$$$T^{7} -$$$$60\!\cdots\!31$$$$T^{8} -$$$$13\!\cdots\!68$$$$T^{9} +$$$$46\!\cdots\!88$$$$T^{10} +$$$$38\!\cdots\!04$$$$T^{11} -$$$$22\!\cdots\!10$$$$T^{12} -$$$$90\!\cdots\!98$$$$T^{13} +$$$$91\!\cdots\!30$$$$T^{14} +$$$$10\!\cdots\!20$$$$T^{15} -$$$$29\!\cdots\!76$$$$T^{16} +$$$$30\!\cdots\!20$$$$T^{17} +$$$$75\!\cdots\!30$$$$T^{18} -$$$$21\!\cdots\!98$$$$T^{19} -$$$$15\!\cdots\!10$$$$T^{20} +$$$$73\!\cdots\!04$$$$T^{21} +$$$$25\!\cdots\!88$$$$T^{22} -$$$$20\!\cdots\!68$$$$T^{23} -$$$$27\!\cdots\!31$$$$T^{24} +$$$$47\!\cdots\!67$$$$T^{25} -$$$$25\!\cdots\!97$$$$T^{26} -$$$$78\!\cdots\!28$$$$T^{27} +$$$$16\!\cdots\!52$$$$T^{28} +$$$$74\!\cdots\!36$$$$T^{29} -$$$$28\!\cdots\!29$$$$T^{30} -$$$$25\!\cdots\!67$$$$T^{31} +$$$$20\!\cdots\!01$$$$T^{32}$$)
$37$ ($$( 1 + 4796 T - 2933298 T^{2} + 332573617772 T^{3} + 4808584372417849 T^{4} )^{2}$$)($$( 1 - 19968 T + 327446979 T^{2} - 2957339330768 T^{3} + 22706469231555903 T^{4} - 96017812748439608832 T^{5} +$$$$33\!\cdots\!93$$$$T^{6} )^{2}$$)($$( 1 + 7588 T + 181007992 T^{2} + 1702118220604 T^{3} + 15462039197985406 T^{4} +$$$$11\!\cdots\!28$$$$T^{5} +$$$$87\!\cdots\!08$$$$T^{6} +$$$$25\!\cdots\!84$$$$T^{7} +$$$$23\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 + 7586 T + 201201093 T^{2} + 803146672896 T^{3} + 19241810738464926 T^{4} + 60351714230064941916 T^{5} +$$$$13\!\cdots\!82$$$$T^{6} +$$$$38\!\cdots\!04$$$$T^{7} +$$$$67\!\cdots\!49$$$$T^{8} +$$$$17\!\cdots\!86$$$$T^{9} +$$$$16\!\cdots\!57$$$$T^{10} )^{2}$$)($$( 1 + 9942 T + 332201371 T^{2} + 2693330117316 T^{3} + 50133814193692869 T^{4} +$$$$32\!\cdots\!94$$$$T^{5} +$$$$47\!\cdots\!35$$$$T^{6} +$$$$26\!\cdots\!44$$$$T^{7} +$$$$33\!\cdots\!95$$$$T^{8} +$$$$15\!\cdots\!06$$$$T^{9} +$$$$16\!\cdots\!17$$$$T^{10} +$$$$62\!\cdots\!16$$$$T^{11} +$$$$53\!\cdots\!47$$$$T^{12} +$$$$11\!\cdots\!58$$$$T^{13} +$$$$77\!\cdots\!93$$$$T^{14} )^{2}$$)($$( 1 - 9942 T + 392275880 T^{2} - 2850674667090 T^{3} + 67740517235106316 T^{4} -$$$$36\!\cdots\!18$$$$T^{5} +$$$$71\!\cdots\!20$$$$T^{6} -$$$$30\!\cdots\!02$$$$T^{7} +$$$$56\!\cdots\!54$$$$T^{8} -$$$$21\!\cdots\!14$$$$T^{9} +$$$$34\!\cdots\!80$$$$T^{10} -$$$$12\!\cdots\!74$$$$T^{11} +$$$$15\!\cdots\!16$$$$T^{12} -$$$$45\!\cdots\!30$$$$T^{13} +$$$$43\!\cdots\!20$$$$T^{14} -$$$$76\!\cdots\!06$$$$T^{15} +$$$$53\!\cdots\!01$$$$T^{16} )^{2}$$)
$41$ ($$1 + 15354 T - 54861079 T^{2} + 904258368522 T^{3} + 43716860789439108 T^{4} +$$$$10\!\cdots\!22$$$$T^{5} -$$$$73\!\cdots\!79$$$$T^{6} +$$$$23\!\cdots\!54$$$$T^{7} +$$$$18\!\cdots\!01$$$$T^{8}$$)($$1 + 5049 T - 49911369 T^{2} + 2355608603160 T^{3} + 1935356544736665 T^{4} - 94902326907305939361 T^{5} +$$$$30\!\cdots\!26$$$$T^{6} -$$$$10\!\cdots\!61$$$$T^{7} +$$$$25\!\cdots\!65$$$$T^{8} +$$$$36\!\cdots\!60$$$$T^{9} -$$$$89\!\cdots\!69$$$$T^{10} +$$$$10\!\cdots\!49$$$$T^{11} +$$$$24\!\cdots\!01$$$$T^{12}$$)($$1 + 1248 T - 412882754 T^{2} - 256860139200 T^{3} + 101750473497083809 T^{4} + 31706402029277721984 T^{5} -$$$$17\!\cdots\!98$$$$T^{6} -$$$$13\!\cdots\!52$$$$T^{7} +$$$$23\!\cdots\!00$$$$T^{8} -$$$$15\!\cdots\!52$$$$T^{9} -$$$$23\!\cdots\!98$$$$T^{10} +$$$$49\!\cdots\!84$$$$T^{11} +$$$$18\!\cdots\!09$$$$T^{12} -$$$$53\!\cdots\!00$$$$T^{13} -$$$$99\!\cdots\!54$$$$T^{14} +$$$$34\!\cdots\!48$$$$T^{15} +$$$$32\!\cdots\!01$$$$T^{16}$$)($$1 - 18435 T - 117679042 T^{2} + 4344492069675 T^{3} - 505249106564622 T^{4} -$$$$52\!\cdots\!97$$$$T^{5} +$$$$16\!\cdots\!40$$$$T^{6} +$$$$39\!\cdots\!43$$$$T^{7} -$$$$31\!\cdots\!03$$$$T^{8} -$$$$10\!\cdots\!42$$$$T^{9} +$$$$29\!\cdots\!40$$$$T^{10} -$$$$11\!\cdots\!42$$$$T^{11} -$$$$41\!\cdots\!03$$$$T^{12} +$$$$62\!\cdots\!43$$$$T^{13} +$$$$30\!\cdots\!40$$$$T^{14} -$$$$10\!\cdots\!97$$$$T^{15} -$$$$12\!\cdots\!22$$$$T^{16} +$$$$12\!\cdots\!75$$$$T^{17} -$$$$38\!\cdots\!42$$$$T^{18} -$$$$69\!\cdots\!35$$$$T^{19} +$$$$43\!\cdots\!01$$$$T^{20}$$)($$1 - 12273 T - 357178727 T^{2} + 1235021514918 T^{3} + 100489810504965844 T^{4} +$$$$23\!\cdots\!88$$$$T^{5} -$$$$15\!\cdots\!23$$$$T^{6} -$$$$93\!\cdots\!83$$$$T^{7} +$$$$13\!\cdots\!56$$$$T^{8} +$$$$12\!\cdots\!51$$$$T^{9} -$$$$10\!\cdots\!21$$$$T^{10} -$$$$47\!\cdots\!72$$$$T^{11} +$$$$13\!\cdots\!15$$$$T^{12} -$$$$15\!\cdots\!01$$$$T^{13} -$$$$20\!\cdots\!10$$$$T^{14} -$$$$18\!\cdots\!01$$$$T^{15} +$$$$18\!\cdots\!15$$$$T^{16} -$$$$73\!\cdots\!72$$$$T^{17} -$$$$18\!\cdots\!21$$$$T^{18} +$$$$25\!\cdots\!51$$$$T^{19} +$$$$32\!\cdots\!56$$$$T^{20} -$$$$26\!\cdots\!83$$$$T^{21} -$$$$50\!\cdots\!23$$$$T^{22} +$$$$88\!\cdots\!88$$$$T^{23} +$$$$43\!\cdots\!44$$$$T^{24} +$$$$62\!\cdots\!18$$$$T^{25} -$$$$20\!\cdots\!27$$$$T^{26} -$$$$83\!\cdots\!73$$$$T^{27} +$$$$78\!\cdots\!01$$$$T^{28}$$)($$1 + 11958 T - 317542966 T^{2} - 2880044533908 T^{3} + 50829316389696744 T^{4} +$$$$13\!\cdots\!06$$$$T^{5} -$$$$51\!\cdots\!28$$$$T^{6} +$$$$41\!\cdots\!78$$$$T^{7} +$$$$48\!\cdots\!75$$$$T^{8} -$$$$45\!\cdots\!38$$$$T^{9} -$$$$38\!\cdots\!36$$$$T^{10} -$$$$37\!\cdots\!06$$$$T^{11} +$$$$55\!\cdots\!00$$$$T^{12} +$$$$11\!\cdots\!04$$$$T^{13} -$$$$14\!\cdots\!90$$$$T^{14} -$$$$63\!\cdots\!74$$$$T^{15} +$$$$23\!\cdots\!56$$$$T^{16} -$$$$73\!\cdots\!74$$$$T^{17} -$$$$18\!\cdots\!90$$$$T^{18} +$$$$17\!\cdots\!04$$$$T^{19} +$$$$10\!\cdots\!00$$$$T^{20} -$$$$78\!\cdots\!06$$$$T^{21} -$$$$93\!\cdots\!36$$$$T^{22} -$$$$12\!\cdots\!38$$$$T^{23} +$$$$15\!\cdots\!75$$$$T^{24} +$$$$15\!\cdots\!78$$$$T^{25} -$$$$22\!\cdots\!28$$$$T^{26} +$$$$67\!\cdots\!06$$$$T^{27} +$$$$29\!\cdots\!44$$$$T^{28} -$$$$19\!\cdots\!08$$$$T^{29} -$$$$24\!\cdots\!66$$$$T^{30} +$$$$10\!\cdots\!58$$$$T^{31} +$$$$10\!\cdots\!01$$$$T^{32}$$)
$43$ ($$1 + 32858 T + 531117661 T^{2} + 8362808427386 T^{3} + 120556834830700108 T^{4} +$$$$12\!\cdots\!98$$$$T^{5} +$$$$11\!\cdots\!89$$$$T^{6} +$$$$10\!\cdots\!06$$$$T^{7} +$$$$46\!\cdots\!01$$$$T^{8}$$)($$1 - 31389 T + 371875485 T^{2} - 1823349120818 T^{3} + 12515413892662971 T^{4} -$$$$36\!\cdots\!65$$$$T^{5} +$$$$57\!\cdots\!06$$$$T^{6} -$$$$53\!\cdots\!95$$$$T^{7} +$$$$27\!\cdots\!79$$$$T^{8} -$$$$57\!\cdots\!26$$$$T^{9} +$$$$17\!\cdots\!85$$$$T^{10} -$$$$21\!\cdots\!27$$$$T^{11} +$$$$10\!\cdots\!49$$$$T^{12}$$)($$1 - 6092 T - 493633434 T^{2} + 1717030281896 T^{3} + 152938627936979465 T^{4} -$$$$29\!\cdots\!88$$$$T^{5} -$$$$33\!\cdots\!22$$$$T^{6} +$$$$15\!\cdots\!68$$$$T^{7} +$$$$57\!\cdots\!20$$$$T^{8} +$$$$23\!\cdots\!24$$$$T^{9} -$$$$72\!\cdots\!78$$$$T^{10} -$$$$92\!\cdots\!16$$$$T^{11} +$$$$71\!\cdots\!65$$$$T^{12} +$$$$11\!\cdots\!28$$$$T^{13} -$$$$49\!\cdots\!66$$$$T^{14} -$$$$90\!\cdots\!44$$$$T^{15} +$$$$21\!\cdots\!01$$$$T^{16}$$)($$1 + 1469 T - 271863536 T^{2} - 4016430594327 T^{3} + 12129147672135834 T^{4} +$$$$75\!\cdots\!27$$$$T^{5} +$$$$55\!\cdots\!62$$$$T^{6} +$$$$12\!\cdots\!57$$$$T^{7} -$$$$29\!\cdots\!39$$$$T^{8} -$$$$61\!\cdots\!62$$$$T^{9} -$$$$11\!\cdots\!84$$$$T^{10} -$$$$90\!\cdots\!66$$$$T^{11} -$$$$64\!\cdots\!11$$$$T^{12} +$$$$38\!\cdots\!99$$$$T^{13} +$$$$26\!\cdots\!62$$$$T^{14} +$$$$52\!\cdots\!61$$$$T^{15} +$$$$12\!\cdots\!66$$$$T^{16} -$$$$59\!\cdots\!89$$$$T^{17} -$$$$59\!\cdots\!36$$$$T^{18} +$$$$47\!\cdots\!67$$$$T^{19} +$$$$47\!\cdots\!49$$$$T^{20}$$)($$1 + 10661 T - 623773965 T^{2} - 4644578579856 T^{3} + 217495733901369402 T^{4} +$$$$91\!\cdots\!58$$$$T^{5} -$$$$57\!\cdots\!73$$$$T^{6} -$$$$14\!\cdots\!15$$$$T^{7} +$$$$12\!\cdots\!76$$$$T^{8} +$$$$22\!\cdots\!93$$$$T^{9} -$$$$24\!\cdots\!03$$$$T^{10} -$$$$28\!\cdots\!30$$$$T^{11} +$$$$42\!\cdots\!69$$$$T^{12} +$$$$17\!\cdots\!71$$$$T^{13} -$$$$65\!\cdots\!62$$$$T^{14} +$$$$25\!\cdots\!53$$$$T^{15} +$$$$90\!\cdots\!81$$$$T^{16} -$$$$90\!\cdots\!10$$$$T^{17} -$$$$11\!\cdots\!03$$$$T^{18} +$$$$15\!\cdots\!99$$$$T^{19} +$$$$12\!\cdots\!24$$$$T^{20} -$$$$21\!\cdots\!05$$$$T^{21} -$$$$12\!\cdots\!73$$$$T^{22} +$$$$29\!\cdots\!94$$$$T^{23} +$$$$10\!\cdots\!98$$$$T^{24} -$$$$32\!\cdots\!92$$$$T^{25} -$$$$63\!\cdots\!65$$$$T^{26} +$$$$15\!\cdots\!23$$$$T^{27} +$$$$22\!\cdots\!49$$$$T^{28}$$)($$1 + 6358 T - 605632010 T^{2} + 3590184015404 T^{3} + 251121895055192660 T^{4} -$$$$32\!\cdots\!58$$$$T^{5} -$$$$55\!\cdots\!56$$$$T^{6} +$$$$13\!\cdots\!46$$$$T^{7} +$$$$54\!\cdots\!11$$$$T^{8} -$$$$37\!\cdots\!86$$$$T^{9} +$$$$12\!\cdots\!00$$$$T^{10} +$$$$71\!\cdots\!02$$$$T^{11} -$$$$67\!\cdots\!48$$$$T^{12} -$$$$91\!\cdots\!08$$$$T^{13} +$$$$17\!\cdots\!98$$$$T^{14} +$$$$54\!\cdots\!18$$$$T^{15} -$$$$29\!\cdots\!68$$$$T^{16} +$$$$80\!\cdots\!74$$$$T^{17} +$$$$37\!\cdots\!02$$$$T^{18} -$$$$29\!\cdots\!56$$$$T^{19} -$$$$31\!\cdots\!48$$$$T^{20} +$$$$49\!\cdots\!86$$$$T^{21} +$$$$12\!\cdots\!00$$$$T^{22} -$$$$54\!\cdots\!02$$$$T^{23} +$$$$11\!\cdots\!11$$$$T^{24} +$$$$44\!\cdots\!78$$$$T^{25} -$$$$26\!\cdots\!44$$$$T^{26} -$$$$22\!\cdots\!06$$$$T^{27} +$$$$25\!\cdots\!60$$$$T^{28} +$$$$53\!\cdots\!72$$$$T^{29} -$$$$13\!\cdots\!90$$$$T^{30} +$$$$20\!\cdots\!06$$$$T^{31} +$$$$47\!\cdots\!01$$$$T^{32}$$)
$47$ ($$1 - 24954 T + 21728789 T^{2} - 3550537792602 T^{3} + 165756186376684068 T^{4} -$$$$81\!\cdots\!14$$$$T^{5} +$$$$11\!\cdots\!61$$$$T^{6} -$$$$30\!\cdots\!22$$$$T^{7} +$$$$27\!\cdots\!01$$$$T^{8}$$)($$1 - 12924 T - 448629342 T^{2} + 4068633746340 T^{3} + 160129591294416234 T^{4} -$$$$73\!\cdots\!76$$$$T^{5} -$$$$35\!\cdots\!10$$$$T^{6} -$$$$16\!\cdots\!32$$$$T^{7} +$$$$84\!\cdots\!66$$$$T^{8} +$$$$49\!\cdots\!20$$$$T^{9} -$$$$12\!\cdots\!42$$$$T^{10} -$$$$82\!\cdots\!68$$$$T^{11} +$$$$14\!\cdots\!49$$$$T^{12}$$)($$1 + 60 T - 695011823 T^{2} + 3293074754652 T^{3} + 272693815319492413 T^{4} -$$$$15\!\cdots\!00$$$$T^{5} -$$$$70\!\cdots\!78$$$$T^{6} +$$$$17\!\cdots\!56$$$$T^{7} +$$$$15\!\cdots\!82$$$$T^{8} +$$$$41\!\cdots\!92$$$$T^{9} -$$$$37\!\cdots\!22$$$$T^{10} -$$$$18\!\cdots\!00$$$$T^{11} +$$$$75\!\cdots\!13$$$$T^{12} +$$$$20\!\cdots\!64$$$$T^{13} -$$$$10\!\cdots\!27$$$$T^{14} +$$$$20\!\cdots\!80$$$$T^{15} +$$$$76\!\cdots\!01$$$$T^{16}$$)($$1 + 25155 T - 401246233 T^{2} - 14349179861244 T^{3} + 97557609874842960 T^{4} +$$$$41\!\cdots\!12$$$$T^{5} -$$$$25\!\cdots\!27$$$$T^{6} -$$$$55\!\cdots\!85$$$$T^{7} +$$$$12\!\cdots\!11$$$$T^{8} +$$$$42\!\cdots\!56$$$$T^{9} -$$$$37\!\cdots\!60$$$$T^{10} +$$$$96\!\cdots\!92$$$$T^{11} +$$$$67\!\cdots\!39$$$$T^{12} -$$$$67\!\cdots\!55$$$$T^{13} -$$$$71\!\cdots\!27$$$$T^{14} +$$$$26\!\cdots\!84$$$$T^{15} +$$$$14\!\cdots\!40$$$$T^{16} -$$$$47\!\cdots\!92$$$$T^{17} -$$$$30\!\cdots\!33$$$$T^{18} +$$$$44\!\cdots\!85$$$$T^{19} +$$$$40\!\cdots\!49$$$$T^{20}$$)($$1 - 6621 T - 533369894 T^{2} + 17569640679837 T^{3} + 64218296273974477 T^{4} -$$$$74\!\cdots\!44$$$$T^{5} +$$$$13\!\cdots\!88$$$$T^{6} +$$$$10\!\cdots\!80$$$$T^{7} -$$$$55\!\cdots\!48$$$$T^{8} +$$$$75\!\cdots\!08$$$$T^{9} +$$$$79\!\cdots\!48$$$$T^{10} -$$$$29\!\cdots\!32$$$$T^{11} +$$$$30\!\cdots\!94$$$$T^{12} +$$$$42\!\cdots\!86$$$$T^{13} -$$$$11\!\cdots\!24$$$$T^{14} +$$$$96\!\cdots\!02$$$$T^{15} +$$$$16\!\cdots\!06$$$$T^{16} -$$$$36\!\cdots\!76$$$$T^{17} +$$$$21\!\cdots\!48$$$$T^{18} +$$$$47\!\cdots\!56$$$$T^{19} -$$$$80\!\cdots\!52$$$$T^{20} +$$$$33\!\cdots\!40$$$$T^{21} +$$$$10\!\cdots\!88$$$$T^{22} -$$$$13\!\cdots\!08$$$$T^{23} +$$$$25\!\cdots\!73$$$$T^{24} +$$$$16\!\cdots\!91$$$$T^{25} -$$$$11\!\cdots\!94$$$$T^{26} -$$$$32\!\cdots\!47$$$$T^{27} +$$$$11\!\cdots\!49$$$$T^{28}$$)($$1 - 18651 T - 478342651 T^{2} + 16725616433838 T^{3} - 33307495516308636 T^{4} -$$$$54\!\cdots\!54$$$$T^{5} +$$$$55\!\cdots\!09$$$$T^{6} +$$$$88\!\cdots\!55$$$$T^{7} -$$$$14\!\cdots\!23$$$$T^{8} -$$$$20\!\cdots\!40$$$$T^{9} +$$$$46\!\cdots\!92$$$$T^{10} +$$$$52\!\cdots\!36$$$$T^{11} -$$$$16\!\cdots\!66$$$$T^{12} -$$$$76\!\cdots\!58$$$$T^{13} +$$$$33\!\cdots\!34$$$$T^{14} -$$$$94\!\cdots\!12$$$$T^{15} -$$$$52\!\cdots\!12$$$$T^{16} -$$$$21\!\cdots\!84$$$$T^{17} +$$$$17\!\cdots\!66$$$$T^{18} -$$$$92\!\cdots\!94$$$$T^{19} -$$$$46\!\cdots\!66$$$$T^{20} +$$$$33\!\cdots\!52$$$$T^{21} +$$$$67\!\cdots\!08$$$$T^{22} -$$$$68\!\cdots\!20$$$$T^{23} -$$$$11\!\cdots\!23$$$$T^{24} +$$$$15\!\cdots\!85$$$$T^{25} +$$$$22\!\cdots\!41$$$$T^{26} -$$$$49\!\cdots\!22$$$$T^{27} -$$$$70\!\cdots\!36$$$$T^{28} +$$$$81\!\cdots\!66$$$$T^{29} -$$$$53\!\cdots\!99$$$$T^{30} -$$$$47\!\cdots\!93$$$$T^{31} +$$$$58\!\cdots\!01$$$$T^{32}$$)
$53$ ($$( 1 - 16332 T + 896230798 T^{2} - 6829968791676 T^{3} + 174887470365513049 T^{4} )^{2}$$)($$( 1 - 48024 T + 1811738067 T^{2} - 41931353529216 T^{3} + 757660694115932031 T^{4} -$$$$83\!\cdots\!76$$$$T^{5} +$$$$73\!\cdots\!57$$$$T^{6} )^{2}$$)($$( 1 + 10476 T + 1064413976 T^{2} + 16431260960628 T^{3} + 549720542476264830 T^{4} +$$$$68\!\cdots\!04$$$$T^{5} +$$$$18\!\cdots\!24$$$$T^{6} +$$$$76\!\cdots\!32$$$$T^{7} +$$$$30\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 + 58422 T + 3354568213 T^{2} + 110313236959296 T^{3} + 3390725554692289246 T^{4} +$$$$71\!\cdots\!28$$$$T^{5} +$$$$14\!\cdots\!78$$$$T^{6} +$$$$19\!\cdots\!04$$$$T^{7} +$$$$24\!\cdots\!41$$$$T^{8} +$$$$17\!\cdots\!22$$$$T^{9} +$$$$12\!\cdots\!93$$$$T^{10} )^{2}$$)($$( 1 - 18118 T + 1311642011 T^{2} - 23787594499172 T^{3} + 1115922058804459445 T^{4} -$$$$18\!\cdots\!66$$$$T^{5} +$$$$63\!\cdots\!59$$$$T^{6} -$$$$93\!\cdots\!04$$$$T^{7} +$$$$26\!\cdots\!87$$$$T^{8} -$$$$33\!\cdots\!34$$$$T^{9} +$$$$81\!\cdots\!65$$$$T^{10} -$$$$72\!\cdots\!72$$$$T^{11} +$$$$16\!\cdots\!23$$$$T^{12} -$$$$96\!\cdots\!82$$$$T^{13} +$$$$22\!\cdots\!57$$$$T^{14} )^{2}$$)($$( 1 + 13574 T + 1121284472 T^{2} + 17073561025410 T^{3} + 432137755729592684 T^{4} +$$$$60\!\cdots\!98$$$$T^{5} +$$$$60\!\cdots\!56$$$$T^{6} -$$$$70\!\cdots\!50$$$$T^{7} +$$$$23\!\cdots\!86$$$$T^{8} -$$$$29\!\cdots\!50$$$$T^{9} +$$$$10\!\cdots\!44$$$$T^{10} +$$$$44\!\cdots\!86$$$$T^{11} +$$$$13\!\cdots\!84$$$$T^{12} +$$$$21\!\cdots\!30$$$$T^{13} +$$$$59\!\cdots\!28$$$$T^{14} +$$$$30\!\cdots\!18$$$$T^{15} +$$$$93\!\cdots\!01$$$$T^{16} )^{2}$$)
$59$ ($$1 - 21966 T - 1047077995 T^{2} - 2190769191198 T^{3} + 1483553202105261756 T^{4} -$$$$15\!\cdots\!02$$$$T^{5} -$$$$53\!\cdots\!95$$$$T^{6} -$$$$80\!\cdots\!34$$$$T^{7} +$$$$26\!\cdots\!01$$$$T^{8}$$)($$1 - 62955 T + 1128633393 T^{2} - 9982647295866 T^{3} + 705724247444789571 T^{4} -$$$$15\!\cdots\!79$$$$T^{5} +$$$$56\!\cdots\!06$$$$T^{6} -$$$$11\!\cdots\!21$$$$T^{7} +$$$$36\!\cdots\!71$$$$T^{8} -$$$$36\!\cdots\!34$$$$T^{9} +$$$$29\!\cdots\!93$$$$T^{10} -$$$$11\!\cdots\!45$$$$T^{11} +$$$$13\!\cdots\!01$$$$T^{12}$$)($$1 - 2076 T - 2248193858 T^{2} + 15695201332392 T^{3} + 2863253985413117089 T^{4} -$$$$21\!\cdots\!96$$$$T^{5} -$$$$25\!\cdots\!86$$$$T^{6} +$$$$73\!\cdots\!56$$$$T^{7} +$$$$18\!\cdots\!76$$$$T^{8} +$$$$52\!\cdots\!44$$$$T^{9} -$$$$12\!\cdots\!86$$$$T^{10} -$$$$77\!\cdots\!04$$$$T^{11} +$$$$74\!\cdots\!89$$$$T^{12} +$$$$29\!\cdots\!08$$$$T^{13} -$$$$30\!\cdots\!58$$$$T^{14} -$$$$19\!\cdots\!24$$$$T^{15} +$$$$68\!\cdots\!01$$$$T^{16}$$)($$1 + 90537 T + 2831117840 T^{2} + 13805150996349 T^{3} - 966660594685472478 T^{4} -$$$$10\!\cdots\!09$$$$T^{5} +$$$$69\!\cdots\!78$$$$T^{6} +$$$$39\!\cdots\!93$$$$T^{7} +$$$$84\!\cdots\!01$$$$T^{8} -$$$$17\!\cdots\!74$$$$T^{9} -$$$$12\!\cdots\!20$$$$T^{10} -$$$$12\!\cdots\!26$$$$T^{11} +$$$$42\!\cdots\!01$$$$T^{12} +$$$$14\!\cdots\!07$$$$T^{13} +$$$$18\!\cdots\!78$$$$T^{14} -$$$$19\!\cdots\!91$$$$T^{15} -$$$$12\!\cdots\!78$$$$T^{16} +$$$$13\!\cdots\!51$$$$T^{17} +$$$$19\!\cdots\!40$$$$T^{18} +$$$$44\!\cdots\!63$$$$T^{19} +$$$$34\!\cdots\!01$$$$T^{20}$$)($$1 + 46241 T + 243574211 T^{2} + 61572307402616 T^{3} + 2814190939651890498 T^{4} -$$$$37\!\cdots\!42$$$$T^{5} +$$$$18\!\cdots\!11$$$$T^{6} +$$$$96\!\cdots\!49$$$$T^{7} -$$$$46\!\cdots\!68$$$$T^{8} +$$$$41\!\cdots\!49$$$$T^{9} +$$$$20\!\cdots\!33$$$$T^{10} -$$$$21\!\cdots\!78$$$$T^{11} +$$$$88\!\cdots\!93$$$$T^{12} +$$$$32\!\cdots\!11$$$$T^{13} -$$$$49\!\cdots\!54$$$$T^{14} +$$$$23\!\cdots\!89$$$$T^{15} +$$$$45\!\cdots\!93$$$$T^{16} -$$$$78\!\cdots\!22$$$$T^{17} +$$$$54\!\cdots\!33$$$$T^{18} +$$$$77\!\cdots\!51$$$$T^{19} -$$$$62\!\cdots\!68$$$$T^{20} +$$$$92\!\cdots\!51$$$$T^{21} +$$$$12\!\cdots\!11$$$$T^{22} -$$$$18\!\cdots\!58$$$$T^{23} +$$$$98\!\cdots\!98$$$$T^{24} +$$$$15\!\cdots\!84$$$$T^{25} +$$$$43\!\cdots\!11$$$$T^{26} +$$$$58\!\cdots\!59$$$$T^{27} +$$$$91\!\cdots\!01$$$$T^{28}$$)($$1 + 5252 T - 3858271396 T^{2} - 10135261277120 T^{3} + 7800958924504670150 T^{4} +$$$$52\!\cdots\!36$$$$T^{5} -$$$$10\!\cdots\!40$$$$T^{6} +$$$$63\!\cdots\!24$$$$T^{7} +$$$$11\!\cdots\!89$$$$T^{8} -$$$$15\!\cdots\!68$$$$T^{9} -$$$$10\!\cdots\!96$$$$T^{10} +$$$$16\!\cdots\!36$$$$T^{11} +$$$$79\!\cdots\!46$$$$T^{12} -$$$$11\!\cdots\!36$$$$T^{13} -$$$$55\!\cdots\!28$$$$T^{14} +$$$$33\!\cdots\!52$$$$T^{15} +$$$$38\!\cdots\!20$$$$T^{16} +$$$$23\!\cdots\!48$$$$T^{17} -$$$$28\!\cdots\!28$$$$T^{18} -$$$$41\!\cdots\!64$$$$T^{19} +$$$$20\!\cdots\!46$$$$T^{20} +$$$$30\!\cdots\!64$$$$T^{21} -$$$$13\!\cdots\!96$$$$T^{22} -$$$$14\!\cdots\!32$$$$T^{23} +$$$$80\!\cdots\!89$$$$T^{24} +$$$$31\!\cdots\!76$$$$T^{25} -$$$$38\!\cdots\!40$$$$T^{26} +$$$$13\!\cdots\!64$$$$T^{27} +$$$$13\!\cdots\!50$$$$T^{28} -$$$$12\!\cdots\!80$$$$T^{29} -$$$$35\!\cdots\!96$$$$T^{30} +$$$$34\!\cdots\!48$$$$T^{31} +$$$$46\!\cdots\!01$$$$T^{32}$$)
$61$ ($$1 - 3050 T - 1573942703 T^{2} + 323139566950 T^{3} + 1785465604069576108 T^{4} +$$$$27\!\cdots\!50$$$$T^{5} -$$$$11\!\cdots\!03$$$$T^{6} -$$$$18\!\cdots\!50$$$$T^{7} +$$$$50\!\cdots\!01$$$$T^{8}$$)($$1 + 75966 T + 1651965492 T^{2} + 45532183560440 T^{3} + 3331090328104364760 T^{4} +$$$$76\!\cdots\!06$$$$T^{5} +$$$$63\!\cdots\!14$$$$T^{6} +$$$$64\!\cdots\!06$$$$T^{7} +$$$$23\!\cdots\!60$$$$T^{8} +$$$$27\!\cdots\!40$$$$T^{9} +$$$$84\!\cdots\!92$$$$T^{10} +$$$$32\!\cdots\!66$$$$T^{11} +$$$$36\!\cdots\!01$$$$T^{12}$$)($$1 - 48142 T - 755431725 T^{2} + 43590251951830 T^{3} + 1116615498545065565 T^{4} -$$$$17\!\cdots\!08$$$$T^{5} -$$$$17\!\cdots\!86$$$$T^{6} +$$$$66\!\cdots\!20$$$$T^{7} +$$$$16\!\cdots\!34$$$$T^{8} +$$$$56\!\cdots\!20$$$$T^{9} -$$$$12\!\cdots\!86$$$$T^{10} -$$$$10\!\cdots\!08$$$$T^{11} +$$$$56\!\cdots\!65$$$$T^{12} +$$$$18\!\cdots\!30$$$$T^{13} -$$$$27\!\cdots\!25$$$$T^{14} -$$$$14\!\cdots\!42$$$$T^{15} +$$$$25\!\cdots\!01$$$$T^{16}$$)($$1 - 1403 T - 3536905883 T^{2} - 452840008146 T^{3} + 7065863261737144698 T^{4} +$$$$54\!\cdots\!90$$$$T^{5} -$$$$10\!\cdots\!33$$$$T^{6} -$$$$70\!\cdots\!89$$$$T^{7} +$$$$11\!\cdots\!67$$$$T^{8} +$$$$32\!\cdots\!04$$$$T^{9} -$$$$10\!\cdots\!12$$$$T^{10} +$$$$27\!\cdots\!04$$$$T^{11} +$$$$80\!\cdots\!67$$$$T^{12} -$$$$42\!\cdots\!89$$$$T^{13} -$$$$51\!\cdots\!33$$$$T^{14} +$$$$23\!\cdots\!90$$$$T^{15} +$$$$25\!\cdots\!98$$$$T^{16} -$$$$13\!\cdots\!46$$$$T^{17} -$$$$91\!\cdots\!83$$$$T^{18} -$$$$30\!\cdots\!03$$$$T^{19} +$$$$18\!\cdots\!01$$$$T^{20}$$)($$1 - 52097 T + 863578572 T^{2} + 1263331168971 T^{3} - 2127122959172469747 T^{4} +$$$$11\!\cdots\!84$$$$T^{5} -$$$$25\!\cdots\!08$$$$T^{6} +$$$$32\!\cdots\!76$$$$T^{7} +$$$$19\!\cdots\!80$$$$T^{8} -$$$$13\!\cdots\!64$$$$T^{9} +$$$$37\!\cdots\!40$$$$T^{10} -$$$$73\!\cdots\!96$$$$T^{11} -$$$$62\!\cdots\!66$$$$T^{12} +$$$$98\!\cdots\!54$$$$T^{13} -$$$$34\!\cdots\!84$$$$T^{14} +$$$$82\!\cdots\!54$$$$T^{15} -$$$$44\!\cdots\!66$$$$T^{16} -$$$$44\!\cdots\!96$$$$T^{17} +$$$$19\!\cdots\!40$$$$T^{18} -$$$$56\!\cdots\!64$$$$T^{19} +$$$$69\!\cdots\!80$$$$T^{20} +$$$$99\!\cdots\!76$$$$T^{21} -$$$$65\!\cdots\!08$$$$T^{22} +$$$$24\!\cdots\!84$$$$T^{23} -$$$$39\!\cdots\!47$$$$T^{24} +$$$$19\!\cdots\!71$$$$T^{25} +$$$$11\!\cdots\!72$$$$T^{26} -$$$$57\!\cdots\!97$$$$T^{27} +$$$$93\!\cdots\!01$$$$T^{28}$$)($$1 + 28727 T - 3368554313 T^{2} - 158770267526528 T^{3} + 4307631856591137578 T^{4} +$$$$35\!\cdots\!96$$$$T^{5} -$$$$12\!\cdots\!85$$$$T^{6} -$$$$45\!\cdots\!13$$$$T^{7} -$$$$31\!\cdots\!19$$$$T^{8} +$$$$42\!\cdots\!32$$$$T^{9} +$$$$54\!\cdots\!40$$$$T^{10} -$$$$33\!\cdots\!68$$$$T^{11} -$$$$66\!\cdots\!14$$$$T^{12} +$$$$23\!\cdots\!30$$$$T^{13} +$$$$79\!\cdots\!66$$$$T^{14} -$$$$80\!\cdots\!56$$$$T^{15} -$$$$78\!\cdots\!12$$$$T^{16} -$$$$68\!\cdots\!56$$$$T^{17} +$$$$56\!\cdots\!66$$$$T^{18} +$$$$13\!\cdots\!30$$$$T^{19} -$$$$33\!\cdots\!14$$$$T^{20} -$$$$14\!\cdots\!68$$$$T^{21} +$$$$19\!\cdots\!40$$$$T^{22} +$$$$12\!\cdots\!32$$$$T^{23} -$$$$82\!\cdots\!19$$$$T^{24} -$$$$99\!\cdots\!13$$$$T^{25} -$$$$23\!\cdots\!85$$$$T^{26} +$$$$55\!\cdots\!96$$$$T^{27} +$$$$56\!\cdots\!78$$$$T^{28} -$$$$17\!\cdots\!28$$$$T^{29} -$$$$31\!\cdots\!13$$$$T^{30} +$$$$22\!\cdots\!27$$$$T^{31} +$$$$67\!\cdots\!01$$$$T^{32}$$)
$67$ ($$1 + 36758 T - 1083763235 T^{2} - 9753235942570 T^{3} + 2281745104215240604 T^{4} -$$$$13\!\cdots\!90$$$$T^{5} -$$$$19\!\cdots\!15$$$$T^{6} +$$$$90\!\cdots\!94$$$$T^{7} +$$$$33\!\cdots\!01$$$$T^{8}$$)($$1 - 32991 T - 1801789179 T^{2} + 76747890991738 T^{3} + 1612255572283172571 T^{4} -$$$$51\!\cdots\!59$$$$T^{5} -$$$$93\!\cdots\!82$$$$T^{6} -$$$$69\!\cdots\!13$$$$T^{7} +$$$$29\!\cdots\!79$$$$T^{8} +$$$$18\!\cdots\!34$$$$T^{9} -$$$$59\!\cdots\!79$$$$T^{10} -$$$$14\!\cdots\!37$$$$T^{11} +$$$$60\!\cdots\!49$$$$T^{12}$$)($$1 - 7148 T - 3268771122 T^{2} + 16753922588168 T^{3} + 4825996342110423185 T^{4} -$$$$80\!\cdots\!92$$$$T^{5} -$$$$77\!\cdots\!58$$$$T^{6} -$$$$18\!\cdots\!60$$$$T^{7} +$$$$12\!\cdots\!20$$$$T^{8} -$$$$25\!\cdots\!20$$$$T^{9} -$$$$14\!\cdots\!42$$$$T^{10} -$$$$19\!\cdots\!56$$$$T^{11} +$$$$16\!\cdots\!85$$$$T^{12} +$$$$75\!\cdots\!76$$$$T^{13} -$$$$19\!\cdots\!78$$$$T^{14} -$$$$58\!\cdots\!64$$$$T^{15} +$$$$11\!\cdots\!01$$$$T^{16}$$)($$1 + 13907 T - 3876685544 T^{2} + 77425491657903 T^{3} + 10014688417385231130 T^{4} -$$$$30\!\cdots\!39$$$$T^{5} -$$$$79\!\cdots\!54$$$$T^{6} +$$$$69\!\cdots\!51$$$$T^{7} -$$$$33\!\cdots\!67$$$$T^{8} -$$$$37\!\cdots\!46$$$$T^{9} +$$$$22\!\cdots\!76$$$$T^{10} -$$$$51\!\cdots\!22$$$$T^{11} -$$$$60\!\cdots\!83$$$$T^{12} +$$$$16\!\cdots\!93$$$$T^{13} -$$$$26\!\cdots\!54$$$$T^{14} -$$$$13\!\cdots\!73$$$$T^{15} +$$$$60\!\cdots\!70$$$$T^{16} +$$$$63\!\cdots\!29$$$$T^{17} -$$$$42\!\cdots\!44$$$$T^{18} +$$$$20\!\cdots\!49$$$$T^{19} +$$$$20\!\cdots\!49$$$$T^{20}$$)($$1 + 65899 T - 2734869621 T^{2} - 160857140751480 T^{3} + 10983488420604054306 T^{4} +$$$$38\!\cdots\!26$$$$T^{5} -$$$$16\!\cdots\!29$$$$T^{6} -$$$$90\!\cdots\!73$$$$T^{7} +$$$$25\!\cdots\!88$$$$T^{8} -$$$$26\!\cdots\!89$$$$T^{9} +$$$$95\!\cdots\!41$$$$T^{10} +$$$$14\!\cdots\!98$$$$T^{11} -$$$$49\!\cdots\!87$$$$T^{12} -$$$$37\!\cdots\!23$$$$T^{13} +$$$$13\!\cdots\!66$$$$T^{14} -$$$$50\!\cdots\!61$$$$T^{15} -$$$$90\!\cdots\!63$$$$T^{16} +$$$$34\!\cdots\!14$$$$T^{17} +$$$$31\!\cdots\!41$$$$T^{18} -$$$$11\!\cdots\!23$$$$T^{19} +$$$$15\!\cdots\!12$$$$T^{20} -$$$$74\!\cdots\!39$$$$T^{21} -$$$$18\!\cdots\!29$$$$T^{22} +$$$$57\!\cdots\!82$$$$T^{23} +$$$$22\!\cdots\!94$$$$T^{24} -$$$$43\!\cdots\!40$$$$T^{25} -$$$$10\!\cdots\!21$$$$T^{26} +$$$$32\!\cdots\!93$$$$T^{27} +$$$$66\!\cdots\!49$$$$T^{28}$$)($$1 - 76426 T - 596311166 T^{2} + 99165605625028 T^{3} + 5511021538454671736 T^{4} -$$$$28\!\cdots\!26$$$$T^{5} -$$$$57\!\cdots\!92$$$$T^{6} +$$$$15\!\cdots\!34$$$$T^{7} +$$$$14\!\cdots\!59$$$$T^{8} -$$$$20\!\cdots\!70$$$$T^{9} -$$$$17\!\cdots\!80$$$$T^{10} +$$$$20\!\cdots\!14$$$$T^{11} +$$$$11\!\cdots\!80$$$$T^{12} +$$$$13\!\cdots\!96$$$$T^{13} -$$$$21\!\cdots\!78$$$$T^{14} +$$$$48\!\cdots\!02$$$$T^{15} -$$$$86\!\cdots\!24$$$$T^{16} +$$$$65\!\cdots\!14$$$$T^{17} -$$$$39\!\cdots\!22$$$$T^{18} +$$$$33\!\cdots\!28$$$$T^{19} +$$$$38\!\cdots\!80$$$$T^{20} +$$$$90\!\cdots\!98$$$$T^{21} -$$$$10\!\cdots\!20$$$$T^{22} -$$$$17\!\cdots\!10$$$$T^{23} +$$$$16\!\cdots\!59$$$$T^{24} +$$$$23\!\cdots\!38$$$$T^{25} -$$$$11\!\cdots\!08$$$$T^{26} -$$$$76\!\cdots\!18$$$$T^{27} +$$$$20\!\cdots\!36$$$$T^{28} +$$$$49\!\cdots\!96$$$$T^{29} -$$$$39\!\cdots\!34$$$$T^{30} -$$$$69\!\cdots\!18$$$$T^{31} +$$$$12\!\cdots\!01$$$$T^{32}$$)
$71$ ($$( 1 + 73848 T + 4273554814 T^{2} + 133238729112648 T^{3} + 3255243551009881201 T^{4} )^{2}$$)($$( 1 + 64836 T + 5330360517 T^{2} + 233818077065976 T^{3} + 9617192896182934467 T^{4} +$$$$21\!\cdots\!36$$$$T^{5} +$$$$58\!\cdots\!51$$$$T^{6} )^{2}$$)($$( 1 + 35928 T + 5285725772 T^{2} + 127659705990840 T^{3} + 12554595869440882758 T^{4} +$$$$23\!\cdots\!40$$$$T^{5} +$$$$17\!\cdots\!72$$$$T^{6} +$$$$21\!\cdots\!28$$$$T^{7} +$$$$10\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 - 114684 T + 7758380659 T^{2} - 426246123888336 T^{3} + 19260501229393543450 T^{4} -$$$$77\!\cdots\!40$$$$T^{5} +$$$$34\!\cdots\!50$$$$T^{6} -$$$$13\!\cdots\!36$$$$T^{7} +$$$$45\!\cdots\!09$$$$T^{8} -$$$$12\!\cdots\!84$$$$T^{9} +$$$$19\!\cdots\!51$$$$T^{10} )^{2}$$)($$( 1 - 19540 T + 3633668465 T^{2} - 12132114903560 T^{3} + 11913806947274641829 T^{4} -$$$$94\!\cdots\!48$$$$T^{5} +$$$$27\!\cdots\!29$$$$T^{6} -$$$$78\!\cdots\!40$$$$T^{7} +$$$$49\!\cdots\!79$$$$T^{8} -$$$$30\!\cdots\!48$$$$T^{9} +$$$$69\!\cdots\!79$$$$T^{10} -$$$$12\!\cdots\!60$$$$T^{11} +$$$$69\!\cdots\!15$$$$T^{12} -$$$$67\!\cdots\!40$$$$T^{13} +$$$$62\!\cdots\!51$$$$T^{14} )^{2}$$)($$( 1 - 28552 T + 12272552360 T^{2} - 340583707445064 T^{3} + 69214592054837903036 T^{4} -$$$$17\!\cdots\!16$$$$T^{5} +$$$$23\!\cdots\!48$$$$T^{6} -$$$$51\!\cdots\!56$$$$T^{7} +$$$$51\!\cdots\!30$$$$T^{8} -$$$$93\!\cdots\!56$$$$T^{9} +$$$$76\!\cdots\!48$$$$T^{10} -$$$$10\!\cdots\!16$$$$T^{11} +$$$$73\!\cdots\!36$$$$T^{12} -$$$$65\!\cdots\!64$$$$T^{13} +$$$$42\!\cdots\!60$$$$T^{14} -$$$$17\!\cdots\!52$$$$T^{15} +$$$$11\!\cdots\!01$$$$T^{16} )^{2}$$)
$73$ ($$( 1 + 51188 T + 4637705622 T^{2} + 106116388702484 T^{3} + 4297625829703557649 T^{4} )^{2}$$)($$( 1 + 4233 T + 1481704827 T^{2} + 31872982860070 T^{3} + 3071680186064679411 T^{4} +$$$$18\!\cdots\!17$$$$T^{5} +$$$$89\!\cdots\!57$$$$T^{6} )^{2}$$)($$( 1 - 61226 T + 6621012721 T^{2} - 212085627051026 T^{3} + 16124371439127547300 T^{4} -$$$$43\!\cdots\!18$$$$T^{5} +$$$$28\!\cdots\!29$$$$T^{6} -$$$$54\!\cdots\!82$$$$T^{7} +$$$$18\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 - 7600 T + 3606834246 T^{2} - 31056473559714 T^{3} + 12288417972789256281 T^{4} -$$$$80\!\cdots\!84$$$$T^{5} +$$$$25\!\cdots\!33$$$$T^{6} -$$$$13\!\cdots\!86$$$$T^{7} +$$$$32\!\cdots\!22$$$$T^{8} -$$$$14\!\cdots\!00$$$$T^{9} +$$$$38\!\cdots\!93$$$$T^{10} )^{2}$$)($$( 1 + 119756 T + 12665001844 T^{2} + 840674059831786 T^{3} + 54000925751576970494 T^{4} +$$$$26\!\cdots\!20$$$$T^{5} +$$$$13\!\cdots\!21$$$$T^{6} +$$$$60\!\cdots\!00$$$$T^{7} +$$$$28\!\cdots\!53$$$$T^{8} +$$$$11\!\cdots\!80$$$$T^{9} +$$$$48\!\cdots\!58$$$$T^{10} +$$$$15\!\cdots\!86$$$$T^{11} +$$$$48\!\cdots\!92$$$$T^{12} +$$$$95\!\cdots\!44$$$$T^{13} +$$$$16\!\cdots\!57$$$$T^{14} )^{2}$$)($$( 1 - 79535 T + 13865713689 T^{2} - 726558675410662 T^{3} + 76497322497906218852 T^{4} -$$$$30\!\cdots\!44$$$$T^{5} +$$$$25\!\cdots\!79$$$$T^{6} -$$$$84\!\cdots\!51$$$$T^{7} +$$$$62\!\cdots\!22$$$$T^{8} -$$$$17\!\cdots\!43$$$$T^{9} +$$$$11\!\cdots\!71$$$$T^{10} -$$$$26\!\cdots\!08$$$$T^{11} +$$$$14\!\cdots\!52$$$$T^{12} -$$$$27\!\cdots\!66$$$$T^{13} +$$$$11\!\cdots\!61$$$$T^{14} -$$$$13\!\cdots\!95$$$$T^{15} +$$$$34\!\cdots\!01$$$$T^{16} )^{2}$$)
$79$ ($$1 - 14926 T - 5879056307 T^{2} + 780197169890 T^{3} + 27078673587607710964 T^{4} +$$$$24\!\cdots\!10$$$$T^{5} -$$$$55\!\cdots\!07$$$$T^{6} -$$$$43\!\cdots\!74$$$$T^{7} +$$$$89\!\cdots\!01$$$$T^{8}$$)($$1 + 89202 T - 946471758 T^{2} - 73104980305676 T^{3} + 13192286849737226406 T^{4} -$$$$18\!\cdots\!50$$$$T^{5} -$$$$72\!\cdots\!62$$$$T^{6} -$$$$56\!\cdots\!50$$$$T^{7} +$$$$12\!\cdots\!06$$$$T^{8} -$$$$21\!\cdots\!24$$$$T^{9} -$$$$84\!\cdots\!58$$$$T^{10} +$$$$24\!\cdots\!98$$$$T^{11} +$$$$84\!\cdots\!01$$$$T^{12}$$)($$1 - 59516 T - 3717013179 T^{2} + 374196053042180 T^{3} - 3765094998545504239 T^{4} -$$$$30\!\cdots\!72$$$$T^{5} -$$$$95\!\cdots\!50$$$$T^{6} -$$$$90\!\cdots\!24$$$$T^{7} +$$$$17\!\cdots\!98$$$$T^{8} -$$$$27\!\cdots\!76$$$$T^{9} -$$$$90\!\cdots\!50$$$$T^{10} -$$$$87\!\cdots\!28$$$$T^{11} -$$$$33\!\cdots\!39$$$$T^{12} +$$$$10\!\cdots\!20$$$$T^{13} -$$$$31\!\cdots\!79$$$$T^{14} -$$$$15\!\cdots\!84$$$$T^{15} +$$$$80\!\cdots\!01$$$$T^{16}$$)($$1 + 29993 T - 5352351629 T^{2} + 358913063028768 T^{3} + 26234825811851125236 T^{4} -$$$$21\!\cdots\!52$$$$T^{5} +$$$$27\!\cdots\!85$$$$T^{6} +$$$$84\!\cdots\!45$$$$T^{7} -$$$$35\!\cdots\!45$$$$T^{8} -$$$$81\!\cdots\!80$$$$T^{9} +$$$$16\!\cdots\!00$$$$T^{10} -$$$$25\!\cdots\!20$$$$T^{11} -$$$$33\!\cdots\!45$$$$T^{12} +$$$$24\!\cdots\!55$$$$T^{13} +$$$$24\!\cdots\!85$$$$T^{14} -$$$$60\!\cdots\!48$$$$T^{15} +$$$$22\!\cdots\!36$$$$T^{16} +$$$$93\!\cdots\!32$$$$T^{17} -$$$$43\!\cdots\!29$$$$T^{18} +$$$$74\!\cdots\!07$$$$T^{19} +$$$$76\!\cdots\!01$$$$T^{20}$$)($$1 + 52289 T - 10254865914 T^{2} - 445080895598253 T^{3} + 55928397506183270997 T^{4} +$$$$18\!\cdots\!20$$$$T^{5} -$$$$20\!\cdots\!84$$$$T^{6} -$$$$57\!\cdots\!20$$$$T^{7} +$$$$55\!\cdots\!84$$$$T^{8} +$$$$16\!\cdots\!96$$$$T^{9} -$$$$17\!\cdots\!76$$$$T^{10} -$$$$42\!\cdots\!92$$$$T^{11} +$$$$72\!\cdots\!86$$$$T^{12} +$$$$59\!\cdots\!70$$$$T^{13} -$$$$25\!\cdots\!92$$$$T^{14} +$$$$18\!\cdots\!30$$$$T^{15} +$$$$68\!\cdots\!86$$$$T^{16} -$$$$12\!\cdots\!08$$$$T^{17} -$$$$15\!\cdots\!76$$$$T^{18} +$$$$44\!\cdots\!04$$$$T^{19} +$$$$47\!\cdots\!84$$$$T^{20} -$$$$14\!\cdots\!80$$$$T^{21} -$$$$16\!\cdots\!84$$$$T^{22} +$$$$44\!\cdots\!80$$$$T^{23} +$$$$42\!\cdots\!97$$$$T^{24} -$$$$10\!\cdots\!47$$$$T^{25} -$$$$73\!\cdots\!14$$$$T^{26} +$$$$11\!\cdots\!11$$$$T^{27} +$$$$68\!\cdots\!01$$$$T^{28}$$)($$1 - 97043 T - 6981685421 T^{2} + 727810639417952 T^{3} + 35972102294414959172 T^{4} -$$$$22\!\cdots\!20$$$$T^{5} -$$$$18\!\cdots\!45$$$$T^{6} -$$$$12\!\cdots\!65$$$$T^{7} +$$$$98\!\cdots\!05$$$$T^{8} +$$$$21\!\cdots\!64$$$$T^{9} -$$$$29\!\cdots\!24$$$$T^{10} -$$$$11\!\cdots\!12$$$$T^{11} +$$$$37\!\cdots\!46$$$$T^{12} +$$$$37\!\cdots\!06$$$$T^{13} +$$$$76\!\cdots\!82$$$$T^{14} -$$$$56\!\cdots\!68$$$$T^{15} -$$$$41\!\cdots\!08$$$$T^{16} -$$$$17\!\cdots\!32$$$$T^{17} +$$$$72\!\cdots\!82$$$$T^{18} +$$$$10\!\cdots\!94$$$$T^{19} +$$$$33\!\cdots\!46$$$$T^{20} -$$$$32\!\cdots\!88$$$$T^{21} -$$$$24\!\cdots\!24$$$$T^{22} +$$$$57\!\cdots\!36$$$$T^{23} +$$$$78\!\cdots\!05$$$$T^{24} -$$$$31\!\cdots\!35$$$$T^{25} -$$$$14\!\cdots\!45$$$$T^{26} -$$$$53\!\cdots\!80$$$$T^{27} +$$$$25\!\cdots\!72$$$$T^{28} +$$$$16\!\cdots\!48$$$$T^{29} -$$$$47\!\cdots\!21$$$$T^{30} -$$$$20\!\cdots\!57$$$$T^{31} +$$$$64\!\cdots\!01$$$$T^{32}$$)
$83$ ($$1 - 90762 T - 1695108259 T^{2} - 186494818454154 T^{3} + 50696650939413455868 T^{4} -$$$$73\!\cdots\!22$$$$T^{5} -$$$$26\!\cdots\!91$$$$T^{6} -$$$$55\!\cdots\!34$$$$T^{7} +$$$$24\!\cdots\!01$$$$T^{8}$$)($$1 - 32634 T - 7761884658 T^{2} + 19287559006164 T^{3} + 38129210867128845714 T^{4} +$$$$40\!\cdots\!90$$$$T^{5} -$$$$17\!\cdots\!58$$$$T^{6} +$$$$16\!\cdots\!70$$$$T^{7} +$$$$59\!\cdots\!86$$$$T^{8} +$$$$11\!\cdots\!48$$$$T^{9} -$$$$18\!\cdots\!58$$$$T^{10} -$$$$30\!\cdots\!62$$$$T^{11} +$$$$37\!\cdots\!49$$$$T^{12}$$)($$1 - 117696 T - 5262215903 T^{2} + 507938387214576 T^{3} + 83906673955765181161 T^{4} -$$$$37\!\cdots\!00$$$$T^{5} -$$$$42\!\cdots\!38$$$$T^{6} +$$$$12\!\cdots\!52$$$$T^{7} +$$$$24\!\cdots\!34$$$$T^{8} +$$$$47\!\cdots\!36$$$$T^{9} -$$$$65\!\cdots\!62$$$$T^{10} -$$$$22\!\cdots\!00$$$$T^{11} +$$$$20\!\cdots\!61$$$$T^{12} +$$$$48\!\cdots\!68$$$$T^{13} -$$$$19\!\cdots\!47$$$$T^{14} -$$$$17\!\cdots\!72$$$$T^{15} +$$$$57\!\cdots\!01$$$$T^{16}$$)($$1 + 228951 T + 21403431983 T^{2} + 1202282302650156 T^{3} + 62567029919071222368 T^{4} +$$$$36\!\cdots\!68$$$$T^{5} +$$$$11\!\cdots\!01$$$$T^{6} -$$$$11\!\cdots\!41$$$$T^{7} -$$$$18\!\cdots\!73$$$$T^{8} -$$$$14\!\cdots\!84$$$$T^{9} -$$$$88\!\cdots\!72$$$$T^{10} -$$$$55\!\cdots\!12$$$$T^{11} -$$$$28\!\cdots\!77$$$$T^{12} -$$$$67\!\cdots\!87$$$$T^{13} +$$$$28\!\cdots\!01$$$$T^{14} +$$$$34\!\cdots\!24$$$$T^{15} +$$$$23\!\cdots\!32$$$$T^{16} +$$$$17\!\cdots\!92$$$$T^{17} +$$$$12\!\cdots\!83$$$$T^{18} +$$$$52\!\cdots\!93$$$$T^{19} +$$$$89\!\cdots\!49$$$$T^{20}$$)($$1 - 33317 T - 8432560942 T^{2} + 477533729480965 T^{3} + 20105513085767342373 T^{4} -$$$$28\!\cdots\!40$$$$T^{5} +$$$$34\!\cdots\!76$$$$T^{6} +$$$$10\!\cdots\!32$$$$T^{7} -$$$$48\!\cdots\!72$$$$T^{8} -$$$$29\!\cdots\!04$$$$T^{9} +$$$$27\!\cdots\!12$$$$T^{10} +$$$$59\!\cdots\!36$$$$T^{11} -$$$$12\!\cdots\!94$$$$T^{12} -$$$$60\!\cdots\!34$$$$T^{13} +$$$$48\!\cdots\!92$$$$T^{14} -$$$$23\!\cdots\!62$$$$T^{15} -$$$$18\!\cdots\!06$$$$T^{16} +$$$$36\!\cdots\!52$$$$T^{17} +$$$$66\!\cdots\!12$$$$T^{18} -$$$$28\!\cdots\!72$$$$T^{19} -$$$$17\!\cdots\!28$$$$T^{20} +$$$$15\!\cdots\!24$$$$T^{21} +$$$$20\!\cdots\!76$$$$T^{22} -$$$$65\!\cdots\!20$$$$T^{23} +$$$$18\!\cdots\!77$$$$T^{24} +$$$$16\!\cdots\!55$$$$T^{25} -$$$$11\!\cdots\!42$$$$T^{26} -$$$$18\!\cdots\!31$$$$T^{27} +$$$$21\!\cdots\!49$$$$T^{28}$$)($$1 + 87151 T - 10575830677 T^{2} - 176442258235768 T^{3} +$$$$13\!\cdots\!72$$$$T^{4} -$$$$27\!\cdots\!28$$$$T^{5} -$$$$80\!\cdots\!21$$$$T^{6} +$$$$54\!\cdots\!01$$$$T^{7} +$$$$29\!\cdots\!85$$$$T^{8} -$$$$41\!\cdots\!40$$$$T^{9} +$$$$85\!\cdots\!16$$$$T^{10} +$$$$21\!\cdots\!84$$$$T^{11} -$$$$76\!\cdots\!26$$$$T^{12} -$$$$72\!\cdots\!06$$$$T^{13} +$$$$59\!\cdots\!62$$$$T^{14} +$$$$11\!\cdots\!04$$$$T^{15} -$$$$27\!\cdots\!08$$$$T^{16} +$$$$46\!\cdots\!72$$$$T^{17} +$$$$92\!\cdots\!38$$$$T^{18} -$$$$44\!\cdots\!42$$$$T^{19} -$$$$18\!\cdots\!26$$$$T^{20} +$$$$20\!\cdots\!12$$$$T^{21} +$$$$31\!\cdots\!84$$$$T^{22} -$$$$61\!\cdots\!80$$$$T^{23} +$$$$16\!\cdots\!85$$$$T^{24} +$$$$12\!\cdots\!43$$$$T^{25} -$$$$72\!\cdots\!29$$$$T^{26} -$$$$96\!\cdots\!96$$$$T^{27} +$$$$18\!\cdots\!72$$$$T^{28} -$$$$96\!\cdots\!24$$$$T^{29} -$$$$22\!\cdots\!73$$$$T^{30} +$$$$74\!\cdots\!57$$$$T^{31} +$$$$33\!\cdots\!01$$$$T^{32}$$)
$89$ ($$( 1 - 9300 T + 3189231862 T^{2} - 51931752875700 T^{3} + 31181719929966183601 T^{4} )^{2}$$)($$( 1 + 33066 T + 16131261399 T^{2} + 360180435327660 T^{3} + 90077922639374909151 T^{4} +$$$$10\!\cdots\!66$$$$T^{5} +$$$$17\!\cdots\!49$$$$T^{6} )^{2}$$)($$( 1 - 225864 T + 38022042668 T^{2} - 4189883418729720 T^{3} +$$$$36\!\cdots\!22$$$$T^{4} -$$$$23\!\cdots\!80$$$$T^{5} +$$$$11\!\cdots\!68$$$$T^{6} -$$$$39\!\cdots\!36$$$$T^{7} +$$$$97\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 + 299166 T + 52616244181 T^{2} + 6660261403977288 T^{3} +$$$$67\!\cdots\!10$$$$T^{4} +$$$$55\!\cdots\!64$$$$T^{5} +$$$$37\!\cdots\!90$$$$T^{6} +$$$$20\!\cdots\!88$$$$T^{7} +$$$$91\!\cdots\!69$$$$T^{8} +$$$$29\!\cdots\!66$$$$T^{9} +$$$$54\!\cdots\!49$$$$T^{10} )^{2}$$)($$( 1 + 17418 T + 22938251123 T^{2} + 54792061641540 T^{3} +$$$$25\!\cdots\!13$$$$T^{4} -$$$$20\!\cdots\!02$$$$T^{5} +$$$$18\!\cdots\!91$$$$T^{6} -$$$$20\!\cdots\!48$$$$T^{7} +$$$$10\!\cdots\!59$$$$T^{8} -$$$$62\!\cdots\!02$$$$T^{9} +$$$$44\!\cdots\!37$$$$T^{10} +$$$$53\!\cdots\!40$$$$T^{11} +$$$$12\!\cdots\!27$$$$T^{12} +$$$$52\!\cdots\!18$$$$T^{13} +$$$$16\!\cdots\!49$$$$T^{14} )^{2}$$)($$( 1 - 10512 T + 19793459944 T^{2} + 278250638401872 T^{3} +$$$$22\!\cdots\!64$$$$T^{4} +$$$$51\!\cdots\!76$$$$T^{5} +$$$$19\!\cdots\!56$$$$T^{6} +$$$$41\!\cdots\!96$$$$T^{7} +$$$$12\!\cdots\!46$$$$T^{8} +$$$$23\!\cdots\!04$$$$T^{9} +$$$$60\!\cdots\!56$$$$T^{10} +$$$$89\!\cdots\!24$$$$T^{11} +$$$$22\!\cdots\!64$$$$T^{12} +$$$$15\!\cdots\!28$$$$T^{13} +$$$$60\!\cdots\!44$$$$T^{14} -$$$$17\!\cdots\!88$$$$T^{15} +$$$$94\!\cdots\!01$$$$T^{16} )^{2}$$)
$97$ ($$1 + 30262 T - 7152864215 T^{2} - 275566608895610 T^{3} - 16503442419968593676 T^{4} -$$$$23\!\cdots\!70$$$$T^{5} -$$$$52\!\cdots\!35$$$$T^{6} +$$$$19\!\cdots\!66$$$$T^{7} +$$$$54\!\cdots\!01$$$$T^{8}$$)($$1 - 46245 T - 17067186177 T^{2} + 116084978368376 T^{3} +$$$$18\!\cdots\!05$$$$T^{4} +$$$$22\!\cdots\!89$$$$T^{5} -$$$$18\!\cdots\!78$$$$T^{6} +$$$$18\!\cdots\!73$$$$T^{7} +$$$$13\!\cdots\!45$$$$T^{8} +$$$$73\!\cdots\!68$$$$T^{9} -$$$$92\!\cdots\!77$$$$T^{10} -$$$$21\!\cdots\!65$$$$T^{11} +$$$$40\!\cdots\!49$$$$T^{12}$$)($$1 - 33976 T - 11979920730 T^{2} + 1870850391619312 T^{3} + 3904959771682438313 T^{4} -$$$$16\!\cdots\!64$$$$T^{5} +$$$$12\!\cdots\!22$$$$T^{6} +$$$$57\!\cdots\!68$$$$T^{7} -$$$$11\!\cdots\!00$$$$T^{8} +$$$$49\!\cdots\!76$$$$T^{9} +$$$$91\!\cdots\!78$$$$T^{10} -$$$$10\!\cdots\!52$$$$T^{11} +$$$$21\!\cdots\!13$$$$T^{12} +$$$$87\!\cdots\!84$$$$T^{13} -$$$$48\!\cdots\!70$$$$T^{14} -$$$$11\!\cdots\!68$$$$T^{15} +$$$$29\!\cdots\!01$$$$T^{16}$$)($$1 - 40541 T - 17893496138 T^{2} + 2263333692661293 T^{3} + 99710157551726941410 T^{4} -$$$$30\!\cdots\!95$$$$T^{5} +$$$$10\!\cdots\!20$$$$T^{6} +$$$$21\!\cdots\!29$$$$T^{7} -$$$$20\!\cdots\!15$$$$T^{8} -$$$$65\!\cdots\!06$$$$T^{9} +$$$$19\!\cdots\!00$$$$T^{10} -$$$$56\!\cdots\!42$$$$T^{11} -$$$$15\!\cdots\!35$$$$T^{12} +$$$$13\!\cdots\!97$$$$T^{13} +$$$$56\!\cdots\!20$$$$T^{14} -$$$$14\!\cdots\!15$$$$T^{15} +$$$$39\!\cdots\!90$$$$T^{16} +$$$$77\!\cdots\!49$$$$T^{17} -$$$$52\!\cdots\!38$$$$T^{18} -$$$$10\!\cdots\!37$$$$T^{19} +$$$$21\!\cdots\!49$$$$T^{20}$$)($$1 - 143167 T - 11385949647 T^{2} + 1605240582289122 T^{3} + 72062857810158958812 T^{4} +$$$$63\!\cdots\!68$$$$T^{5} -$$$$11\!\cdots\!23$$$$T^{6} +$$$$18\!\cdots\!83$$$$T^{7} +$$$$54\!\cdots\!84$$$$T^{8} -$$$$13\!\cdots\!39$$$$T^{9} +$$$$92\!\cdots\!23$$$$T^{10} +$$$$39\!\cdots\!32$$$$T^{11} -$$$$23\!\cdots\!89$$$$T^{12} +$$$$26\!\cdots\!01$$$$T^{13} -$$$$75\!\cdots\!38$$$$T^{14} +$$$$22\!\cdots\!57$$$$T^{15} -$$$$17\!\cdots\!61$$$$T^{16} +$$$$24\!\cdots\!76$$$$T^{17} +$$$$50\!\cdots\!23$$$$T^{18} -$$$$62\!\cdots\!23$$$$T^{19} +$$$$21\!\cdots\!16$$$$T^{20} +$$$$64\!\cdots\!19$$$$T^{21} -$$$$34\!\cdots\!23$$$$T^{22} +$$$$16\!\cdots\!76$$$$T^{23} +$$$$15\!\cdots\!88$$$$T^{24} +$$$$30\!\cdots\!46$$$$T^{25} -$$$$18\!\cdots\!47$$$$T^{26} -$$$$19\!\cdots\!19$$$$T^{27} +$$$$11\!\cdots\!49$$$$T^{28}$$)($$1 + 291814 T + 3048369358 T^{2} - 2374481152502668 T^{3} +$$$$84\!\cdots\!84$$$$T^{4} +$$$$10\!\cdots\!50$$$$T^{5} -$$$$98\!\cdots\!52$$$$T^{6} +$$$$68\!\cdots\!82$$$$T^{7} +$$$$26\!\cdots\!07$$$$T^{8} -$$$$16\!\cdots\!50$$$$T^{9} -$$$$15\!\cdots\!80$$$$T^{10} +$$$$23\!\cdots\!78$$$$T^{11} +$$$$13\!\cdots\!28$$$$T^{12} -$$$$13\!\cdots\!96$$$$T^{13} +$$$$11\!\cdots\!78$$$$T^{14} +$$$$12\!\cdots\!42$$$$T^{15} -$$$$59\!\cdots\!92$$$$T^{16} +$$$$10\!\cdots\!94$$$$T^{17} +$$$$84\!\cdots\!22$$$$T^{18} -$$$$82\!\cdots\!28$$$$T^{19} +$$$$75\!\cdots\!28$$$$T^{20} +$$$$10\!\cdots\!46$$$$T^{21} -$$$$60\!\cdots\!20$$$$T^{22} -$$$$55\!\cdots\!50$$$$T^{23} +$$$$78\!\cdots\!07$$$$T^{24} +$$$$17\!\cdots\!74$$$$T^{25} -$$$$21\!\cdots\!48$$$$T^{26} +$$$$19\!\cdots\!50$$$$T^{27} +$$$$13\!\cdots\!84$$$$T^{28} -$$$$32\!\cdots\!76$$$$T^{29} +$$$$36\!\cdots\!42$$$$T^{30} +$$$$29\!\cdots\!02$$$$T^{31} +$$$$87\!\cdots\!01$$$$T^{32}$$)