Properties

 Label 630.2.l Level 630 Weight 2 Character orbit l Rep. character $$\chi_{630}(331,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 64 Newform subspaces 9 Sturm bound 288 Trace bound 3

Related objects

Defining parameters

 Level: $$N$$ = $$630 = 2 \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 630.l (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$63$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$9$$ Sturm bound: $$288$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$11$$, $$13$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(630, [\chi])$$.

Total New Old
Modular forms 304 64 240
Cusp forms 272 64 208
Eisenstein series 32 0 32

Trace form

 $$64q - 32q^{4} - 8q^{5} + 4q^{6} + 4q^{7} + 2q^{9} + O(q^{10})$$ $$64q - 32q^{4} - 8q^{5} + 4q^{6} + 4q^{7} + 2q^{9} + 8q^{11} - 4q^{13} - 2q^{14} + 4q^{15} - 32q^{16} + 16q^{17} - 8q^{18} + 8q^{19} + 4q^{20} + 18q^{21} - 24q^{23} - 2q^{24} + 64q^{25} + 8q^{26} - 12q^{27} + 4q^{28} + 10q^{29} + 4q^{30} - 4q^{31} + 16q^{33} + 8q^{36} - 4q^{37} - 48q^{38} + 20q^{39} - 22q^{41} - 16q^{42} - 4q^{43} - 4q^{44} - 2q^{45} + 6q^{46} + 12q^{47} + 16q^{49} + 8q^{52} - 8q^{53} - 8q^{54} + 4q^{56} - 52q^{57} + 20q^{59} - 8q^{60} - 22q^{61} - 64q^{62} + 64q^{64} - 4q^{65} - 28q^{67} - 32q^{68} - 56q^{69} - 6q^{70} - 88q^{71} - 8q^{72} + 56q^{73} - 24q^{74} + 8q^{76} + 20q^{77} - 48q^{78} - 16q^{79} + 4q^{80} - 22q^{81} + 24q^{83} - 18q^{84} - 12q^{85} + 40q^{86} + 24q^{87} + 2q^{89} + 32q^{91} + 12q^{92} + 24q^{93} - 12q^{94} - 2q^{96} - 4q^{97} + 64q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(630, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
630.2.l.a $$2$$ $$5.031$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-3$$ $$2$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
630.2.l.b $$2$$ $$5.031$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-2$$ $$5$$ $$q+(-1+\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
630.2.l.c $$2$$ $$5.031$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-2$$ $$-1$$ $$q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
630.2.l.d $$2$$ $$5.031$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$2$$ $$5$$ $$q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
630.2.l.e $$4$$ $$5.031$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$6$$ $$-4$$ $$-2$$ $$q+(-1-\beta _{1})q^{2}+(1-\beta _{1})q^{3}+\beta _{1}q^{4}+\cdots$$
630.2.l.f $$12$$ $$5.031$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-6$$ $$-7$$ $$-12$$ $$-4$$ $$q+(-1+\beta _{3})q^{2}+(-1+\beta _{1})q^{3}-\beta _{3}q^{4}+\cdots$$
630.2.l.g $$12$$ $$5.031$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-6$$ $$3$$ $$12$$ $$4$$ $$q+(-1-\beta _{6})q^{2}+\beta _{1}q^{3}+\beta _{6}q^{4}+q^{5}+\cdots$$
630.2.l.h $$12$$ $$5.031$$ 12.0.$$\cdots$$.1 None $$6$$ $$-1$$ $$12$$ $$-8$$ $$q+(1+\beta _{4})q^{2}-\beta _{3}q^{3}+\beta _{4}q^{4}+q^{5}+\cdots$$
630.2.l.i $$16$$ $$5.031$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$8$$ $$-1$$ $$-16$$ $$4$$ $$q+\beta _{4}q^{2}+\beta _{1}q^{3}+(-1+\beta _{4})q^{4}-q^{5}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(630, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(630, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 2}$$

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 + T + T^{2}$$)($$1 + T + T^{2}$$)($$1 - T + T^{2}$$)($$1 - T + T^{2}$$)($$( 1 + T + T^{2} )^{2}$$)($$( 1 + T + T^{2} )^{6}$$)($$( 1 + T + T^{2} )^{6}$$)($$( 1 - T + T^{2} )^{6}$$)($$( 1 - T + T^{2} )^{8}$$)
$3$ ($$1 + 3 T + 3 T^{2}$$)($$1 + 3 T^{2}$$)($$1 + 3 T^{2}$$)($$1 - 3 T + 3 T^{2}$$)($$( 1 - 3 T + 3 T^{2} )^{2}$$)($$1 + 7 T + 25 T^{2} + 57 T^{3} + 84 T^{4} + 78 T^{5} + 75 T^{6} + 234 T^{7} + 756 T^{8} + 1539 T^{9} + 2025 T^{10} + 1701 T^{11} + 729 T^{12}$$)($$1 - 3 T + 7 T^{2} - 3 T^{3} - 2 T^{4} + 24 T^{5} - 21 T^{6} + 72 T^{7} - 18 T^{8} - 81 T^{9} + 567 T^{10} - 729 T^{11} + 729 T^{12}$$)($$1 + T + T^{2} - 3 T^{3} + 9 T^{6} - 81 T^{9} + 81 T^{10} + 243 T^{11} + 729 T^{12}$$)($$1 + T - 4 T^{2} - 2 T^{3} + 8 T^{4} + 10 T^{5} - 32 T^{6} - 33 T^{7} + 123 T^{8} - 99 T^{9} - 288 T^{10} + 270 T^{11} + 648 T^{12} - 486 T^{13} - 2916 T^{14} + 2187 T^{15} + 6561 T^{16}$$)
$5$ ($$( 1 - T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 + T )^{4}$$)($$( 1 + T )^{12}$$)($$( 1 - T )^{12}$$)($$( 1 - T )^{12}$$)($$( 1 + T )^{16}$$)
$7$ ($$1 - T + 7 T^{2}$$)($$1 - 5 T + 7 T^{2}$$)($$1 + T + 7 T^{2}$$)($$1 - 5 T + 7 T^{2}$$)($$1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4}$$)($$( 1 + 2 T + 2 T^{2} - 19 T^{3} + 14 T^{4} + 98 T^{5} + 343 T^{6} )^{2}$$)($$( 1 - 2 T - 4 T^{2} + 31 T^{3} - 28 T^{4} - 98 T^{5} + 343 T^{6} )^{2}$$)($$( 1 + 4 T + 14 T^{2} + 55 T^{3} + 98 T^{4} + 196 T^{5} + 343 T^{6} )^{2}$$)($$1 - 4 T + 3 T^{2} + 2 T^{3} + 61 T^{4} - 126 T^{5} - 401 T^{6} + 806 T^{7} + 201 T^{8} + 5642 T^{9} - 19649 T^{10} - 43218 T^{11} + 146461 T^{12} + 33614 T^{13} + 352947 T^{14} - 3294172 T^{15} + 5764801 T^{16}$$)
$11$ ($$( 1 + 2 T + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 4 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 7 T + 54 T^{2} - 239 T^{3} + 1147 T^{4} - 3976 T^{5} + 15191 T^{6} - 43736 T^{7} + 138787 T^{8} - 318109 T^{9} + 790614 T^{10} - 1127357 T^{11} + 1771561 T^{12} )^{2}$$)($$( 1 + 3 T + 22 T^{2} + 129 T^{3} + 429 T^{4} + 1692 T^{5} + 7055 T^{6} + 18612 T^{7} + 51909 T^{8} + 171699 T^{9} + 322102 T^{10} + 483153 T^{11} + 1771561 T^{12} )^{2}$$)($$( 1 - 7 T + 58 T^{2} - 253 T^{3} + 1331 T^{4} - 4600 T^{5} + 18637 T^{6} - 50600 T^{7} + 161051 T^{8} - 336743 T^{9} + 849178 T^{10} - 1127357 T^{11} + 1771561 T^{12} )^{2}$$)($$( 1 + T + 36 T^{2} + 109 T^{3} + 610 T^{4} + 2585 T^{5} + 10489 T^{6} + 28155 T^{7} + 149742 T^{8} + 309705 T^{9} + 1269169 T^{10} + 3440635 T^{11} + 8931010 T^{12} + 17554559 T^{13} + 63776196 T^{14} + 19487171 T^{15} + 214358881 T^{16} )^{2}$$)
$13$ ($$( 1 - 7 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} )$$)($$1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4}$$)($$1 + 4 T + 3 T^{2} + 52 T^{3} + 169 T^{4}$$)($$( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} )$$)($$( 1 - 5 T + 13 T^{2} )^{2}( 1 + 7 T + 13 T^{2} )^{2}$$)($$1 - 2 T - 36 T^{3} - 17 T^{4} - 371 T^{5} + 3240 T^{6} - 7131 T^{7} + 28438 T^{8} - 222777 T^{9} + 460892 T^{10} - 507411 T^{11} + 7449937 T^{12} - 6596343 T^{13} + 77890748 T^{14} - 489441069 T^{15} + 812217718 T^{16} - 2647690383 T^{17} + 15638861160 T^{18} - 23279699807 T^{19} - 13867422257 T^{20} - 381761977428 T^{21} - 3584320788074 T^{23} + 23298085122481 T^{24}$$)($$1 + 2 T - 40 T^{2} - 80 T^{3} + 861 T^{4} + 1779 T^{5} - 10316 T^{6} - 26179 T^{7} + 43538 T^{8} + 287567 T^{9} + 1150280 T^{10} - 1429999 T^{11} - 24752599 T^{12} - 18589987 T^{13} + 194397320 T^{14} + 631784699 T^{15} + 1243488818 T^{16} - 9720079447 T^{17} - 49793361644 T^{18} + 111629611743 T^{19} + 702344150781 T^{20} - 848359949840 T^{21} - 5514339673960 T^{22} + 3584320788074 T^{23} + 23298085122481 T^{24}$$)($$1 + 2 T - 44 T^{2} - 132 T^{3} + 977 T^{4} + 3781 T^{5} - 11684 T^{6} - 65747 T^{7} + 50792 T^{8} + 714313 T^{9} + 868188 T^{10} - 3554073 T^{11} - 19510287 T^{12} - 46202949 T^{13} + 146723772 T^{14} + 1569345661 T^{15} + 1450670312 T^{16} - 24411400871 T^{17} - 56396436356 T^{18} + 237252142777 T^{19} + 796968914417 T^{20} - 1399793917236 T^{21} - 6065773641356 T^{22} + 3584320788074 T^{23} + 23298085122481 T^{24}$$)($$1 - 2 T - 50 T^{2} + 148 T^{3} + 1054 T^{4} - 3995 T^{5} - 11532 T^{6} + 43443 T^{7} + 117342 T^{8} + 20138 T^{9} - 2880550 T^{10} - 3340678 T^{11} + 58331516 T^{12} - 10068559 T^{13} - 672470458 T^{14} + 306068259 T^{15} + 6775158987 T^{16} + 3978887367 T^{17} - 113647507402 T^{18} - 22120624123 T^{19} + 1666006428476 T^{20} - 1240370356654 T^{21} - 13903864664950 T^{22} + 1263629635346 T^{23} + 95719474263582 T^{24} + 460691266261239 T^{25} - 1589784128002668 T^{26} - 7159680774177815 T^{27} + 24556181719094974 T^{28} + 44825515775653444 T^{29} - 196868819284964450 T^{30} - 102371786028181514 T^{31} + 665416609183179841 T^{32}$$)
$17$ ($$1 - 17 T^{2} + 289 T^{4}$$)($$1 - 17 T^{2} + 289 T^{4}$$)($$1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4}$$)($$1 - 17 T^{2} + 289 T^{4}$$)($$( 1 - 17 T^{2} + 289 T^{4} )^{2}$$)($$1 - 7 T - 26 T^{2} + 253 T^{3} + 159 T^{4} - 2042 T^{5} - 15857 T^{6} + 20745 T^{7} + 626078 T^{8} - 1325347 T^{9} - 9319905 T^{10} + 15360616 T^{11} + 109941593 T^{12} + 261130472 T^{13} - 2693452545 T^{14} - 6511429811 T^{15} + 52290660638 T^{16} + 29454933465 T^{17} - 382749431633 T^{18} - 837911570266 T^{19} + 1109145433119 T^{20} + 30002732753741 T^{21} - 52415841411674 T^{22} - 239903274153431 T^{23} + 582622237229761 T^{24}$$)($$1 - T - 50 T^{2} + 211 T^{3} + 1359 T^{4} - 9716 T^{5} - 8711 T^{6} + 283281 T^{7} - 515860 T^{8} - 4710193 T^{9} + 23752041 T^{10} + 36045190 T^{11} - 503461927 T^{12} + 612768230 T^{13} + 6864339849 T^{14} - 23141178209 T^{15} - 43085143060 T^{16} + 402218510817 T^{17} - 210262363559 T^{18} - 3986850546868 T^{19} + 9480054362319 T^{20} + 25022041940867 T^{21} - 100799695022450 T^{22} - 34271896307633 T^{23} + 582622237229761 T^{24}$$)($$1 - T - 30 T^{2} + 115 T^{3} - 5 T^{4} - 2674 T^{5} + 5895 T^{6} + 18453 T^{7} - 18224 T^{8} - 437961 T^{9} + 1559167 T^{10} + 7061088 T^{11} - 61824431 T^{12} + 120038496 T^{13} + 450599263 T^{14} - 2151702393 T^{15} - 1522086704 T^{16} + 26200621221 T^{17} + 142290969255 T^{18} - 1097245611602 T^{19} - 34878787205 T^{20} + 13637605797155 T^{21} - 60479817013470 T^{22} - 34271896307633 T^{23} + 582622237229761 T^{24}$$)($$1 - 11 T + 36 T^{2} + 123 T^{3} - 1898 T^{4} + 9669 T^{5} - 17977 T^{6} - 83870 T^{7} + 834166 T^{8} - 3577974 T^{9} + 6674756 T^{10} + 20040864 T^{11} - 226666002 T^{12} + 969820747 T^{13} - 1237622341 T^{14} - 9875829222 T^{15} + 67383134907 T^{16} - 167889096774 T^{17} - 357672856549 T^{18} + 4764729330011 T^{19} - 18931371153042 T^{20} + 28455161036448 T^{21} + 161112383508164 T^{22} - 1468181103188502 T^{23} + 5818939681529206 T^{24} - 9945965201803390 T^{25} - 36241522348371673 T^{26} + 331374965398503477 T^{27} - 1105817006262086378 T^{28} + 1218263098047430251 T^{29} + 6061601756138433444 T^{30} - 31486653566607973723 T^{31} + 48661191875666868481 T^{32}$$)
$19$ ($$1 - 19 T^{2} + 361 T^{4}$$)($$1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4}$$)($$1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4}$$)($$1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4}$$)($$1 + 4 T - 8 T^{2} - 56 T^{3} - 89 T^{4} - 1064 T^{5} - 2888 T^{6} + 27436 T^{7} + 130321 T^{8}$$)($$1 - 14 T + 66 T^{2} - 444 T^{3} + 4717 T^{4} - 22391 T^{5} + 98142 T^{6} - 823887 T^{7} + 3750856 T^{8} - 13240737 T^{9} + 95742878 T^{10} - 421689765 T^{11} + 1264726999 T^{12} - 8012105535 T^{13} + 34563178958 T^{14} - 90818215083 T^{15} + 488815304776 T^{16} - 2040025776813 T^{17} + 4617176853102 T^{18} - 20014682107949 T^{19} + 80111466864397 T^{20} - 143273337813876 T^{21} + 404650373014866 T^{22} - 1630863624575066 T^{23} + 2213314919066161 T^{24}$$)($$1 - 8 T - 16 T^{2} + 368 T^{3} - 525 T^{4} - 8817 T^{5} + 35926 T^{6} + 100093 T^{7} - 897124 T^{8} - 345797 T^{9} + 15630782 T^{10} - 3617369 T^{11} - 256926625 T^{12} - 68730011 T^{13} + 5642712302 T^{14} - 2371821623 T^{15} - 116914096804 T^{16} + 247840177207 T^{17} + 1690170320806 T^{18} - 7881267122763 T^{19} - 8916370596525 T^{20} + 118749072782672 T^{21} - 98097060124816 T^{22} - 931922071185752 T^{23} + 2213314919066161 T^{24}$$)($$1 + 2 T - 80 T^{2} - 180 T^{3} + 3449 T^{4} + 7837 T^{5} - 102176 T^{6} - 211409 T^{7} + 2371040 T^{8} + 3579469 T^{9} - 47864088 T^{10} - 27533469 T^{11} + 916901667 T^{12} - 523135911 T^{13} - 17278935768 T^{14} + 24551577871 T^{15} + 308996303840 T^{16} - 523469613491 T^{17} - 4806959937056 T^{18} + 7005272818543 T^{19} + 58576308928409 T^{20} - 58083785600220 T^{21} - 490485300624080 T^{22} + 232980517796438 T^{23} + 2213314919066161 T^{24}$$)($$1 + 2 T - 54 T^{2} + 52 T^{3} + 1522 T^{4} - 5531 T^{5} - 18356 T^{6} + 142945 T^{7} - 156428 T^{8} - 2136646 T^{9} + 5666688 T^{10} + 23411554 T^{11} - 135081014 T^{12} - 508657467 T^{13} + 5117825840 T^{14} + 6906391627 T^{15} - 121849980107 T^{16} + 131221440913 T^{17} + 1847535128240 T^{18} - 3488881566153 T^{19} - 17603892825494 T^{20} + 57969325447846 T^{21} + 266594329312128 T^{22} - 1909887475647394 T^{23} - 2656704799377548 T^{24} + 46126592959019155 T^{25} - 112541852228195156 T^{26} - 644307621966049289 T^{27} + 3368665306818697042 T^{28} + 2186755140037367068 T^{29} - 43146361032275742534 T^{30} + 30362254059749596598 T^{31} +$$$$28\!\cdots\!81$$$$T^{32}$$)
$23$ ($$( 1 + 4 T + 23 T^{2} )^{2}$$)($$( 1 + 3 T + 23 T^{2} )^{2}$$)($$( 1 + T + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 - 26 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 9 T + 105 T^{2} - 495 T^{3} + 3090 T^{4} - 8082 T^{5} + 54493 T^{6} - 185886 T^{7} + 1634610 T^{8} - 6022665 T^{9} + 29383305 T^{10} - 57927087 T^{11} + 148035889 T^{12} )^{2}$$)($$( 1 + 11 T + 123 T^{2} + 859 T^{3} + 5896 T^{4} + 32774 T^{5} + 171365 T^{6} + 753802 T^{7} + 3118984 T^{8} + 10451453 T^{9} + 34420443 T^{10} + 70799773 T^{11} + 148035889 T^{12} )^{2}$$)($$( 1 - 9 T + 129 T^{2} - 819 T^{3} + 6504 T^{4} - 32058 T^{5} + 186793 T^{6} - 737334 T^{7} + 3440616 T^{8} - 9964773 T^{9} + 36099489 T^{10} - 57927087 T^{11} + 148035889 T^{12} )^{2}$$)($$( 1 + 11 T + 129 T^{2} + 965 T^{3} + 7201 T^{4} + 41251 T^{5} + 241420 T^{6} + 1184349 T^{7} + 6096522 T^{8} + 27240027 T^{9} + 127711180 T^{10} + 501900917 T^{11} + 2015135041 T^{12} + 6211070995 T^{13} + 19096629681 T^{14} + 37453079917 T^{15} + 78310985281 T^{16} )^{2}$$)
$29$ ($$1 - T - 28 T^{2} - 29 T^{3} + 841 T^{4}$$)($$1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4}$$)($$1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4}$$)($$1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4}$$)($$1 - 6 T - 13 T^{2} + 54 T^{3} + 516 T^{4} + 1566 T^{5} - 10933 T^{6} - 146334 T^{7} + 707281 T^{8}$$)($$1 + 9 T - 69 T^{2} - 702 T^{3} + 3759 T^{4} + 34596 T^{5} - 143518 T^{6} - 1156437 T^{7} + 4050324 T^{8} + 25653105 T^{9} - 98719569 T^{10} - 302648535 T^{11} + 2262044085 T^{12} - 8776807515 T^{13} - 83023157529 T^{14} + 625653577845 T^{15} + 2864717209044 T^{16} - 23719851616113 T^{17} - 85367853383278 T^{18} + 596776720786164 T^{19} + 1880426266320399 T^{20} - 10184016475060038 T^{21} - 29028799097713869 T^{22} + 109804587891352461 T^{23} + 353814783205469041 T^{24}$$)($$1 - 13 T - 33 T^{2} + 1042 T^{3} + 1159 T^{4} - 64528 T^{5} + 58386 T^{6} + 2236053 T^{7} - 3262784 T^{8} - 61621545 T^{9} + 189094723 T^{10} + 570853983 T^{11} - 5049474515 T^{12} + 16554765507 T^{13} + 159028662043 T^{14} - 1502887861005 T^{15} - 2307705130304 T^{16} + 45864016254897 T^{17} + 34729354419906 T^{18} - 1113100018467152 T^{19} + 579785592621799 T^{20} + 15116446106855498 T^{21} - 13883338698906633 T^{22} - 158606626954175777 T^{23} + 353814783205469041 T^{24}$$)($$1 - 3 T - 87 T^{2} - 372 T^{3} + 6477 T^{4} + 37248 T^{5} - 116788 T^{6} - 2654523 T^{7} - 2866536 T^{8} + 76700583 T^{9} + 479807001 T^{10} - 1248956703 T^{11} - 16840293807 T^{12} - 36219744387 T^{13} + 403517687841 T^{14} + 1870650518787 T^{15} - 2027446448616 T^{16} - 54447316776927 T^{17} - 69468226012948 T^{18} + 642523392757632 T^{19} + 3240096016748397 T^{20} - 5396658303023268 T^{21} - 36601529297117487 T^{22} - 36601529297117487 T^{23} + 353814783205469041 T^{24}$$)($$1 - 17 T + 46 T^{2} + 223 T^{3} + 3250 T^{4} - 18084 T^{5} - 204302 T^{6} + 750182 T^{7} + 3378518 T^{8} + 10195995 T^{9} - 165509581 T^{10} + 32483596 T^{11} + 4544588759 T^{12} - 14362280831 T^{13} - 142821670546 T^{14} + 116125876596 T^{15} + 6133655884938 T^{16} + 3367650421284 T^{17} - 120113024929186 T^{18} - 350281667187259 T^{19} + 3214301282054279 T^{20} + 666275877611804 T^{21} - 98448958627738501 T^{22} + 175879652597182455 T^{23} + 1690091510624171798 T^{24} + 10882999782469358158 T^{25} - 85951329177697664702 T^{26} -$$$$22\!\cdots\!36$$$$T^{27} +$$$$11\!\cdots\!50$$$$T^{28} +$$$$22\!\cdots\!47$$$$T^{29} +$$$$13\!\cdots\!26$$$$T^{30} -$$$$14\!\cdots\!33$$$$T^{31} +$$$$25\!\cdots\!21$$$$T^{32}$$)
$31$ ($$1 + 10 T + 69 T^{2} + 310 T^{3} + 961 T^{4}$$)($$1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4}$$)($$1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4}$$)($$( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} )$$)($$1 + 4 T - 32 T^{2} - 56 T^{3} + 847 T^{4} - 1736 T^{5} - 30752 T^{6} + 119164 T^{7} + 923521 T^{8}$$)($$1 - 9 T - 15 T^{2} + 670 T^{3} - 3300 T^{4} - 7182 T^{5} + 149923 T^{6} - 589968 T^{7} - 879804 T^{8} + 15913627 T^{9} - 40432842 T^{10} - 76992306 T^{11} + 1023668209 T^{12} - 2386761486 T^{13} - 38855961162 T^{14} + 474082861957 T^{15} - 812517469884 T^{16} - 16890282957168 T^{17} + 133057214366563 T^{18} - 197595594545202 T^{19} - 2814540423555300 T^{20} + 17714546847649570 T^{21} - 12294424304712015 T^{22} - 228676292067643479 T^{23} + 787662783788549761 T^{24}$$)($$1 - 21 T + 155 T^{2} - 564 T^{3} + 2498 T^{4} + 1050 T^{5} - 274677 T^{6} + 2301600 T^{7} - 7725776 T^{8} + 17080953 T^{9} + 5323876 T^{10} - 1695931548 T^{11} + 16126243345 T^{12} - 52573877988 T^{13} + 5116244836 T^{14} + 508858670823 T^{15} - 7134916377296 T^{16} + 65892853941600 T^{17} - 243776848586037 T^{18} + 28888244816550 T^{19} + 2130521811527618 T^{20} - 14911946898618444 T^{21} + 127042384482024155 T^{22} - 533578014824501451 T^{23} + 787662783788549761 T^{24}$$)($$1 + 9 T - 69 T^{2} - 824 T^{3} + 3108 T^{4} + 48258 T^{5} - 49013 T^{6} - 1898406 T^{7} - 2745648 T^{8} + 49606711 T^{9} + 235960866 T^{10} - 638978658 T^{11} - 9752658551 T^{12} - 19808338398 T^{13} + 226758392226 T^{14} + 1477833527401 T^{15} - 2535663586608 T^{16} - 54349752033306 T^{17} - 43499217916853 T^{18} + 1327703731768638 T^{19} + 2650785344366628 T^{20} - 21786248660392904 T^{21} - 56554351801675269 T^{22} + 228676292067643479 T^{23} + 787662783788549761 T^{24}$$)($$1 + 15 T - 69 T^{2} - 1516 T^{3} + 8473 T^{4} + 121617 T^{5} - 708026 T^{6} - 6940684 T^{7} + 46779649 T^{8} + 296085538 T^{9} - 2604117812 T^{10} - 10137812896 T^{11} + 118754098487 T^{12} + 249077881849 T^{13} - 4617172050497 T^{14} - 2800322842103 T^{15} + 155907848900999 T^{16} - 86810008105193 T^{17} - 4437102340527617 T^{18} + 7420279178163559 T^{19} + 109671903788812727 T^{20} - 290236976209331296 T^{21} - 2311164143907665972 T^{22} + 8146087150841826718 T^{23} + 39897943366735838209 T^{24} -$$$$18\!\cdots\!64$$$$T^{25} -$$$$58\!\cdots\!26$$$$T^{26} +$$$$30\!\cdots\!27$$$$T^{27} +$$$$66\!\cdots\!53$$$$T^{28} -$$$$37\!\cdots\!56$$$$T^{29} -$$$$52\!\cdots\!49$$$$T^{30} +$$$$35\!\cdots\!65$$$$T^{31} +$$$$72\!\cdots\!81$$$$T^{32}$$)
$37$ ($$1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4}$$)($$1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4}$$)($$( 1 - T + 37 T^{2} )( 1 + 11 T + 37 T^{2} )$$)($$1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4}$$)($$1 - 8 T - 8 T^{2} + 16 T^{3} + 1447 T^{4} + 592 T^{5} - 10952 T^{6} - 405224 T^{7} + 1874161 T^{8}$$)($$1 + 12 T - 75 T^{2} - 1124 T^{3} + 5793 T^{4} + 66639 T^{5} - 404162 T^{6} - 2798919 T^{7} + 24121197 T^{8} + 87063469 T^{9} - 1138257942 T^{10} - 1336271169 T^{11} + 44567264293 T^{12} - 49442033253 T^{13} - 1558275122598 T^{14} + 4410025895257 T^{15} + 45207006690717 T^{16} - 194088118782483 T^{17} - 1036969116914258 T^{18} + 6326165360265987 T^{19} + 20347793476564353 T^{20} - 146076995529666548 T^{21} - 360643827931338675 T^{22} + 2135011461353524956 T^{23} + 6582952005840035281 T^{24}$$)($$1 - 18 T + 119 T^{2} - 678 T^{3} + 7703 T^{4} - 69441 T^{5} + 533994 T^{6} - 4260171 T^{7} + 27103075 T^{8} - 158201349 T^{9} + 1165990240 T^{10} - 8176208427 T^{11} + 50154968893 T^{12} - 302519711799 T^{13} + 1596240638560 T^{14} - 8013372930897 T^{15} + 50795526145075 T^{16} - 295417114636647 T^{17} + 1370082508047546 T^{18} - 6592164479992653 T^{19} + 27056629233553463 T^{20} - 88114059581062206 T^{21} + 572221540317724031 T^{22} - 3202517192030287434 T^{23} + 6582952005840035281 T^{24}$$)($$1 - 6 T - 111 T^{2} + 802 T^{3} + 5847 T^{4} - 49353 T^{5} - 218618 T^{6} + 1971477 T^{7} + 7114131 T^{8} - 58413395 T^{9} - 181224618 T^{10} + 875260311 T^{11} + 4536500245 T^{12} + 32384631507 T^{13} - 248096502042 T^{14} - 2958813696935 T^{15} + 13333026869091 T^{16} + 136710016314489 T^{17} - 560913976082762 T^{18} - 4685172932144949 T^{19} + 20537467367076087 T^{20} + 104229315315651754 T^{21} - 533752865338381239 T^{22} - 1067505730676762478 T^{23} + 6582952005840035281 T^{24}$$)($$1 + 2 T - 109 T^{2} - 494 T^{3} + 4396 T^{4} + 37709 T^{5} + 5949 T^{6} - 1192233 T^{7} - 6568281 T^{8} + 15849024 T^{9} + 180379971 T^{10} - 663666882 T^{11} - 2633817279 T^{12} + 62063414607 T^{13} + 300032298102 T^{14} - 1464225969303 T^{15} - 17940373399443 T^{16} - 54176360864211 T^{17} + 410744216101638 T^{18} + 3143698140088371 T^{19} - 4936197625427919 T^{20} - 46021287727732074 T^{21} + 462805655249354139 T^{22} + 1504577599045968192 T^{23} - 23070952060079679801 T^{24} -$$$$15\!\cdots\!41$$$$T^{25} + 28606268431513783701 T^{26} +$$$$67\!\cdots\!17$$$$T^{27} +$$$$28\!\cdots\!76$$$$T^{28} -$$$$12\!\cdots\!18$$$$T^{29} -$$$$98\!\cdots\!01$$$$T^{30} +$$$$66\!\cdots\!86$$$$T^{31} +$$$$12\!\cdots\!41$$$$T^{32}$$)
$41$ ($$1 + 5 T - 16 T^{2} + 205 T^{3} + 1681 T^{4}$$)($$1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4}$$)($$1 + 10 T + 59 T^{2} + 410 T^{3} + 1681 T^{4}$$)($$1 - 3 T - 32 T^{2} - 123 T^{3} + 1681 T^{4}$$)($$( 1 + 9 T + 40 T^{2} + 369 T^{3} + 1681 T^{4} )^{2}$$)($$1 - T - 197 T^{2} + 250 T^{3} + 21102 T^{4} - 27179 T^{5} - 1633109 T^{6} + 1654722 T^{7} + 101292122 T^{8} - 62228170 T^{9} - 5261216175 T^{10} + 1034229106 T^{11} + 233114446817 T^{12} + 42403393346 T^{13} - 8844104390175 T^{14} - 4288827704570 T^{15} + 286227327954842 T^{16} + 191709804631122 T^{17} - 7757437986915269 T^{18} - 5293226409811699 T^{19} + 168497892184911342 T^{20} + 81845483598490250 T^{21} - 2644263884100022997 T^{22} - 550329031716248441 T^{23} + 22563490300366186081 T^{24}$$)($$1 - 5 T - 189 T^{2} + 674 T^{3} + 21334 T^{4} - 51791 T^{5} - 1737525 T^{6} + 2754282 T^{7} + 111275218 T^{8} - 98774466 T^{9} - 5884736759 T^{10} + 1597606794 T^{11} + 262521605425 T^{12} + 65501878554 T^{13} - 9892242491879 T^{14} - 6807634971186 T^{15} + 314437171290898 T^{16} + 319100649002682 T^{17} - 8253424871343525 T^{18} - 10086518598570871 T^{19} + 170350394838067414 T^{20} + 220655423781529714 T^{21} - 2536882609618803789 T^{22} - 2751645158581242205 T^{23} + 22563490300366186081 T^{24}$$)($$( 1 - 2 T + 118 T^{2} - 443 T^{3} + 5993 T^{4} - 38003 T^{5} + 232561 T^{6} - 1558123 T^{7} + 10074233 T^{8} - 30532003 T^{9} + 333439798 T^{10} - 231712402 T^{11} + 4750104241 T^{12} )( 1 + 13 T - 5 T^{2} - 1007 T^{3} - 5128 T^{4} + 21646 T^{5} + 337849 T^{6} + 887486 T^{7} - 8620168 T^{8} - 69403447 T^{9} - 14128805 T^{10} + 1506130613 T^{11} + 4750104241 T^{12} )$$)($$1 - 7 T - 58 T^{2} + 821 T^{3} - 5081 T^{4} + 3487 T^{5} + 202690 T^{6} - 2313484 T^{7} + 22320617 T^{8} - 84574319 T^{9} - 449228446 T^{10} + 8174132915 T^{11} - 61865466443 T^{12} + 229869969509 T^{13} + 311827818587 T^{14} - 13738704403974 T^{15} + 126160448679906 T^{16} - 563286880562934 T^{17} + 524182563044747 T^{18} + 15842868168529789 T^{19} - 174817022321438123 T^{20} + 947023986000955915 T^{21} - 2133881946522439486 T^{22} - 16471210085825062039 T^{23} +$$$$17\!\cdots\!57$$$$T^{24} -$$$$75\!\cdots\!24$$$$T^{25} +$$$$27\!\cdots\!90$$$$T^{26} +$$$$19\!\cdots\!67$$$$T^{27} -$$$$11\!\cdots\!61$$$$T^{28} +$$$$75\!\cdots\!41$$$$T^{29} -$$$$21\!\cdots\!38$$$$T^{30} -$$$$10\!\cdots\!07$$$$T^{31} +$$$$63\!\cdots\!41$$$$T^{32}$$)
$43$ ($$1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4}$$)($$1 + 11 T + 78 T^{2} + 473 T^{3} + 1849 T^{4}$$)($$1 - 3 T - 34 T^{2} - 129 T^{3} + 1849 T^{4}$$)($$( 1 - 8 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} )$$)($$( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} )^{2}$$)($$1 - 7 T - 61 T^{2} - 38 T^{3} + 2916 T^{4} + 23601 T^{5} + 1081 T^{6} - 108892 T^{7} - 5446372 T^{8} - 63105082 T^{9} - 148348975 T^{10} + 1479379556 T^{11} + 27501185741 T^{12} + 63613320908 T^{13} - 274297254775 T^{14} - 5017295754574 T^{15} - 18620062039972 T^{16} - 16008043375156 T^{17} + 6833393455969 T^{18} + 6415191040736307 T^{19} + 34082792009484516 T^{20} - 19098519253600034 T^{21} - 1318300421110339189 T^{22} - 6505056176298558949 T^{23} + 39959630797262576401 T^{24}$$)($$1 + 11 T - 47 T^{2} - 336 T^{3} + 4742 T^{4} - 6185 T^{5} - 265967 T^{6} + 524632 T^{7} + 3908504 T^{8} - 33033908 T^{9} - 58808445 T^{10} + 1188416940 T^{11} + 11051987505 T^{12} + 51101928420 T^{13} - 108736814805 T^{14} - 2626426923356 T^{15} + 13362397383704 T^{16} + 77125333467976 T^{17} - 1681273966053383 T^{18} - 1681198109696795 T^{19} + 55425445716383942 T^{20} - 168871117610779248 T^{21} - 1015739668724359703 T^{22} + 10222231134183449777 T^{23} + 39959630797262576401 T^{24}$$)($$1 - 23 T + 113 T^{2} + 896 T^{3} - 1332 T^{4} - 148755 T^{5} + 870961 T^{6} + 3952150 T^{7} - 29247526 T^{8} - 288761288 T^{9} + 2809373309 T^{10} + 289322302 T^{11} - 86189636971 T^{12} + 12440858986 T^{13} + 5194531248341 T^{14} - 22958543725016 T^{15} - 99991471136326 T^{16} + 580999418002450 T^{17} + 5505660682520089 T^{18} - 40434377495221785 T^{19} - 15568682769764532 T^{20} + 450322980295411328 T^{21} + 2442097501401120137 T^{22} - 21373756007838122261 T^{23} + 39959630797262576401 T^{24}$$)($$1 + 13 T - 110 T^{2} - 1567 T^{3} + 10823 T^{4} + 109505 T^{5} - 883584 T^{6} - 5592870 T^{7} + 52864479 T^{8} + 206005533 T^{9} - 2766579456 T^{10} - 7286801151 T^{11} + 131529658809 T^{12} + 225678713547 T^{13} - 6233727820281 T^{14} - 3123476792046 T^{15} + 288754313221062 T^{16} - 134309502057978 T^{17} - 11526162739699569 T^{18} + 17943037477981329 T^{19} + 449673729065868009 T^{20} - 1071221291659117893 T^{21} - 17488553145280921344 T^{22} + 55996137860417255031 T^{23} +$$$$61\!\cdots\!79$$$$T^{24} -$$$$28\!\cdots\!10$$$$T^{25} -$$$$19\!\cdots\!16$$$$T^{26} +$$$$10\!\cdots\!35$$$$T^{27} +$$$$43\!\cdots\!23$$$$T^{28} -$$$$26\!\cdots\!81$$$$T^{29} -$$$$81\!\cdots\!90$$$$T^{30} +$$$$41\!\cdots\!91$$$$T^{31} +$$$$13\!\cdots\!01$$$$T^{32}$$)
$47$ ($$1 - 13 T + 122 T^{2} - 611 T^{3} + 2209 T^{4}$$)($$1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4}$$)($$1 - 7 T + 2 T^{2} - 329 T^{3} + 2209 T^{4}$$)($$1 - 9 T + 34 T^{2} - 423 T^{3} + 2209 T^{4}$$)($$1 - 6 T - 49 T^{2} + 54 T^{3} + 3324 T^{4} + 2538 T^{5} - 108241 T^{6} - 622938 T^{7} + 4879681 T^{8}$$)($$1 - 7 T - 143 T^{2} + 1636 T^{3} + 8388 T^{4} - 164387 T^{5} - 52367 T^{6} + 9860370 T^{7} - 25622842 T^{8} - 372053548 T^{9} + 2235815499 T^{10} + 6458752942 T^{11} - 121918206439 T^{12} + 303561388274 T^{13} + 4938916437291 T^{14} - 38627715514004 T^{15} - 125031295273402 T^{16} + 2261426626672590 T^{17} - 564475169133743 T^{18} - 83282254903551181 T^{19} + 199729072518851268 T^{20} + 1830897453996126812 T^{21} - 7521675909723697007 T^{22} - 17305114505588086121 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 + 23 T + 165 T^{2} + 16 T^{3} - 5528 T^{4} - 58507 T^{5} - 644325 T^{6} - 3006420 T^{7} + 14443366 T^{8} + 167453628 T^{9} + 157591519 T^{10} - 257317800 T^{11} + 15656686345 T^{12} - 12093936600 T^{13} + 348119665471 T^{14} + 17385538019844 T^{15} + 70479018646246 T^{16} - 689507415944940 T^{17} - 6945317916857925 T^{18} - 29640998908928741 T^{19} - 131628792666214808 T^{20} + 17906087569644272 T^{21} + 8678856818911958085 T^{22} + 56859661946932282969 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 - T - 219 T^{2} - 68 T^{3} + 26860 T^{4} + 26375 T^{5} - 2209371 T^{6} - 2950278 T^{7} + 137542054 T^{8} + 164192604 T^{9} - 7121259227 T^{10} - 3549295014 T^{11} + 339625941589 T^{12} - 166816865658 T^{13} - 15730861632443 T^{14} + 17046968725092 T^{15} + 671161347604774 T^{16} - 676631528561946 T^{17} - 23815285750648059 T^{18} + 13362184802211625 T^{19} + 639571159734900460 T^{20} - 76100872170988156 T^{21} - 11519209959646780731 T^{22} - 2472159215084012303 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 + 5 T - 142 T^{2} - 523 T^{3} + 11629 T^{4} + 39799 T^{5} - 519008 T^{6} - 2553412 T^{7} + 6974711 T^{8} + 160407457 T^{9} + 819946652 T^{10} - 8794224685 T^{11} - 74482937135 T^{12} + 363511537727 T^{13} + 3939718895363 T^{14} - 6885259823688 T^{15} - 181944181040538 T^{16} - 323607211713336 T^{17} + 8702839039856867 T^{18} + 37740858381430321 T^{19} - 363452973161853935 T^{20} - 2016911521940897795 T^{21} + 8838381520200628508 T^{22} + 81266126410874492591 T^{23} +$$$$16\!\cdots\!71$$$$T^{24} -$$$$28\!\cdots\!04$$$$T^{25} -$$$$27\!\cdots\!92$$$$T^{26} +$$$$98\!\cdots\!97$$$$T^{27} +$$$$13\!\cdots\!89$$$$T^{28} -$$$$28\!\cdots\!21$$$$T^{29} -$$$$36\!\cdots\!98$$$$T^{30} +$$$$60\!\cdots\!15$$$$T^{31} +$$$$56\!\cdots\!21$$$$T^{32}$$)
$53$ ($$1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4}$$)($$1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4}$$)($$1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4}$$)($$1 + 12 T + 91 T^{2} + 636 T^{3} + 2809 T^{4}$$)($$1 + 12 T + 20 T^{2} + 216 T^{3} + 4935 T^{4} + 11448 T^{5} + 56180 T^{6} + 1786524 T^{7} + 7890481 T^{8}$$)($$1 - 2 T - 167 T^{2} + 1010 T^{3} + 13227 T^{4} - 131245 T^{5} - 429158 T^{6} + 9790659 T^{7} - 11991223 T^{8} - 447494225 T^{9} + 2419646052 T^{10} + 9239703395 T^{11} - 165502278643 T^{12} + 489704279935 T^{13} + 6796785760068 T^{14} - 66621597735325 T^{15} - 94616517248263 T^{16} + 4094409467299887 T^{17} - 9512012893399382 T^{18} - 154174963547907065 T^{19} + 823508925071071947 T^{20} + 3332761227720154330 T^{21} - 29206207551040679183 T^{22} - 18538071858744383194 T^{23} +$$$$49\!\cdots\!41$$$$T^{24}$$)($$1 - 2 T - 255 T^{2} + 422 T^{3} + 35953 T^{4} - 47393 T^{5} - 3605976 T^{6} + 3309969 T^{7} + 285580525 T^{8} - 148182909 T^{9} - 18913659452 T^{10} + 3090482955 T^{11} + 1076146210033 T^{12} + 163795596615 T^{13} - 53128469400668 T^{14} - 22061026943193 T^{15} + 2253367706482525 T^{16} + 1384214117769717 T^{17} - 79924154286506904 T^{18} - 55673085050294941 T^{19} + 2238422649359662033 T^{20} + 1392500235740500126 T^{21} - 44596304943205827495 T^{22} - 18538071858744383194 T^{23} +$$$$49\!\cdots\!41$$$$T^{24}$$)($$1 + 4 T - 69 T^{2} + 608 T^{3} + 3817 T^{4} - 53819 T^{5} + 247674 T^{6} + 1787013 T^{7} - 23754551 T^{8} + 62188347 T^{9} + 305246782 T^{10} - 5161623099 T^{11} + 3988104733 T^{12} - 273566024247 T^{13} + 857438210638 T^{14} + 9258414536319 T^{15} - 187434833329031 T^{16} + 747320782532409 T^{17} + 5489535978263946 T^{18} - 63221778834887503 T^{19} + 237645238300164937 T^{20} + 2006256263815696864 T^{21} - 12067235455220400381 T^{22} + 37076143717488766388 T^{23} +$$$$49\!\cdots\!41$$$$T^{24}$$)($$1 - 18 T - 25 T^{2} + 3094 T^{3} - 20382 T^{4} - 155341 T^{5} + 2463947 T^{6} - 2962263 T^{7} - 127200023 T^{8} + 760818902 T^{9} + 3333886647 T^{10} - 61667632700 T^{11} + 106780502839 T^{12} + 3773454519213 T^{13} - 28393687643164 T^{14} - 98984202945069 T^{15} + 2205152767325745 T^{16} - 5246162756088657 T^{17} - 79757868589647676 T^{18} + 561780588456873801 T^{19} + 842549528821575559 T^{20} - 25789126059119421100 T^{21} + 73893467607258944463 T^{22} +$$$$89\!\cdots\!74$$$$T^{23} -$$$$79\!\cdots\!03$$$$T^{24} -$$$$97\!\cdots\!79$$$$T^{25} +$$$$43\!\cdots\!03$$$$T^{26} -$$$$14\!\cdots\!77$$$$T^{27} -$$$$10\!\cdots\!62$$$$T^{28} +$$$$80\!\cdots\!62$$$$T^{29} -$$$$34\!\cdots\!25$$$$T^{30} -$$$$13\!\cdots\!26$$$$T^{31} +$$$$38\!\cdots\!21$$$$T^{32}$$)
$59$ ($$1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4}$$)($$1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4}$$)($$1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4}$$)($$1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4}$$)($$1 + 12 T + 8 T^{2} + 216 T^{3} + 6519 T^{4} + 12744 T^{5} + 27848 T^{6} + 2464548 T^{7} + 12117361 T^{8}$$)($$1 - 29 T + 244 T^{2} - 487 T^{3} + 12741 T^{4} - 193162 T^{5} - 332771 T^{6} + 10128051 T^{7} + 50934638 T^{8} - 261544697 T^{9} - 7392832827 T^{10} + 18057216194 T^{11} + 349068797417 T^{12} + 1065375755446 T^{13} - 25734451070787 T^{14} - 53715788325163 T^{15} + 617193396050318 T^{16} + 7240789761411249 T^{17} - 14036458360249211 T^{18} - 480712898110607678 T^{19} + 1870766605516653861 T^{20} - 4218878963684955293 T^{21} +$$$$12\!\cdots\!44$$$$T^{22} -$$$$87\!\cdots\!11$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 - T - 180 T^{2} + 193 T^{3} + 14641 T^{4} - 22486 T^{5} - 743043 T^{6} + 2825361 T^{7} + 31917748 T^{8} - 220677645 T^{9} - 1651548767 T^{10} + 6363833874 T^{11} + 99112484569 T^{12} + 375466198566 T^{13} - 5749041257927 T^{14} - 45322554052455 T^{15} + 386758874823028 T^{16} + 2019919232346939 T^{17} - 31341950258209563 T^{18} - 55959817287640034 T^{19} + 2149744436964863761 T^{20} + 1671958193000403227 T^{21} - 92001015594115452180 T^{22} - 30155888444737842659 T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 - 11 T - 30 T^{2} - 211 T^{3} + 4279 T^{4} + 56044 T^{5} - 37755 T^{6} - 1168281 T^{7} - 20308394 T^{8} - 123532017 T^{9} - 86903849 T^{10} + 7506556428 T^{11} + 64394152369 T^{12} + 442886829252 T^{13} - 302512298369 T^{14} - 25370882119443 T^{15} - 246084141428234 T^{16} - 835232474960019 T^{17} - 1592526047615955 T^{18} + 139473983815196036 T^{19} + 628287442508889559 T^{20} - 1827892117736192129 T^{21} - 15333502599019242030 T^{22} -$$$$33\!\cdots\!49$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 - T - 316 T^{2} + 1001 T^{3} + 51484 T^{4} - 235571 T^{5} - 5434481 T^{6} + 29768732 T^{7} + 426521114 T^{8} - 2331666176 T^{9} - 29352498892 T^{10} + 116177331236 T^{11} + 2090327412760 T^{12} - 3539170015363 T^{13} - 152245895361241 T^{14} + 51717192606732 T^{15} + 9846162822911919 T^{16} + 3051314363797188 T^{17} - 529967961752479921 T^{18} - 726871198585237577 T^{19} + 25329251868608926360 T^{20} + 83057997093588103564 T^{21} -$$$$12\!\cdots\!72$$$$T^{22} -$$$$58\!\cdots\!44$$$$T^{23} +$$$$62\!\cdots\!94$$$$T^{24} +$$$$25\!\cdots\!48$$$$T^{25} -$$$$27\!\cdots\!81$$$$T^{26} -$$$$71\!\cdots\!89$$$$T^{27} +$$$$91\!\cdots\!04$$$$T^{28} +$$$$10\!\cdots\!79$$$$T^{29} -$$$$19\!\cdots\!76$$$$T^{30} -$$$$36\!\cdots\!99$$$$T^{31} +$$$$21\!\cdots\!41$$$$T^{32}$$)
$61$ ($$1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4}$$)($$1 - 7 T - 12 T^{2} - 427 T^{3} + 3721 T^{4}$$)($$1 - 11 T + 60 T^{2} - 671 T^{3} + 3721 T^{4}$$)($$1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4}$$)($$1 - 8 T - 2 T^{2} + 448 T^{3} - 3269 T^{4} + 27328 T^{5} - 7442 T^{6} - 1815848 T^{7} + 13845841 T^{8}$$)($$1 + 11 T - 241 T^{2} - 2048 T^{3} + 43854 T^{4} + 250314 T^{5} - 5585117 T^{6} - 19594216 T^{7} + 561086276 T^{8} + 1043763053 T^{9} - 45287200486 T^{10} - 25159448314 T^{11} + 3026878189487 T^{12} - 1534726347154 T^{13} - 168513673008406 T^{14} + 236914381532993 T^{15} + 7768711364778116 T^{16} - 16549202354595016 T^{17} - 287747318689985237 T^{18} + 786672530255760594 T^{19} + 8407132504182760974 T^{20} - 23949611198124320768 T^{21} -$$$$17\!\cdots\!41$$$$T^{22} +$$$$47\!\cdots\!71$$$$T^{23} +$$$$26\!\cdots\!21$$$$T^{24}$$)($$1 + T + 17 T^{2} - 1594 T^{3} + 1512 T^{4} - 34842 T^{5} + 1454839 T^{6} - 3640784 T^{7} + 36048746 T^{8} - 948066965 T^{9} + 3101837708 T^{10} - 25177834376 T^{11} + 499339420823 T^{12} - 1535847896936 T^{13} + 11541938111468 T^{14} - 215193187782665 T^{15} + 499125205365386 T^{16} - 3074992699139984 T^{17} + 74953849914982879 T^{18} - 109499445892643682 T^{19} + 289861457251888872 T^{20} - 18640468871977620754 T^{21} + 12126829498269004217 T^{22} + 43513917611435838661 T^{23} +$$$$26\!\cdots\!21$$$$T^{24}$$)($$1 + 25 T + 125 T^{2} - 1402 T^{3} - 6552 T^{4} + 133458 T^{5} + 663571 T^{6} - 2121410 T^{7} + 21703004 T^{8} - 117091991 T^{9} - 6501670294 T^{10} - 1405398680 T^{11} + 442721821271 T^{12} - 85729319480 T^{13} - 24192715163974 T^{14} - 26577657209171 T^{15} + 300496342606364 T^{16} - 1791735038904410 T^{17} + 34187426335103131 T^{18} + 419424173409690618 T^{19} - 1256066314758185112 T^{20} - 16395192822153465682 T^{21} + 89167863957860325125 T^{22} +$$$$10\!\cdots\!25$$$$T^{23} +$$$$26\!\cdots\!21$$$$T^{24}$$)($$1 + 27 T + 85 T^{2} - 1658 T^{3} + 30219 T^{4} + 547495 T^{5} - 1219402 T^{6} - 13401696 T^{7} + 474743873 T^{8} + 1951202852 T^{9} - 15375923544 T^{10} + 148846055954 T^{11} + 1569754350677 T^{12} - 2958396909555 T^{13} + 58982140939637 T^{14} + 589570294581029 T^{15} - 740131184661087 T^{16} + 35963787969442769 T^{17} + 219472546436389277 T^{18} - 671499888927703455 T^{19} + 21734569148531984357 T^{20} +$$$$12\!\cdots\!54$$$$T^{21} -$$$$79\!\cdots\!84$$$$T^{22} +$$$$61\!\cdots\!92$$$$T^{23} +$$$$91\!\cdots\!13$$$$T^{24} -$$$$15\!\cdots\!36$$$$T^{25} -$$$$86\!\cdots\!02$$$$T^{26} +$$$$23\!\cdots\!95$$$$T^{27} +$$$$80\!\cdots\!99$$$$T^{28} -$$$$26\!\cdots\!98$$$$T^{29} +$$$$83\!\cdots\!85$$$$T^{30} +$$$$16\!\cdots\!27$$$$T^{31} +$$$$36\!\cdots\!61$$$$T^{32}$$)
$67$ ($$1 + 12 T + 77 T^{2} + 804 T^{3} + 4489 T^{4}$$)($$1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4}$$)($$1 - 9 T + 14 T^{2} - 603 T^{3} + 4489 T^{4}$$)($$1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4}$$)($$1 + 4 T - 50 T^{2} - 272 T^{3} - 1205 T^{4} - 18224 T^{5} - 224450 T^{6} + 1203052 T^{7} + 20151121 T^{8}$$)($$1 + 22 T - 81 T^{2} - 3132 T^{3} + 37294 T^{4} + 591205 T^{5} - 4788018 T^{6} - 45351381 T^{7} + 749433037 T^{8} + 3612096162 T^{9} - 65595408268 T^{10} - 57278016342 T^{11} + 5531646582331 T^{12} - 3837627094914 T^{13} - 294457787715052 T^{14} + 1086384877971606 T^{15} + 15101915809984477 T^{16} - 61230038125222767 T^{17} - 433116362076051042 T^{18} + 3583123004624984215 T^{19} + 15143887966797369454 T^{20} - 85210865729195774004 T^{21} -$$$$14\!\cdots\!69$$$$T^{22} +$$$$26\!\cdots\!26$$$$T^{23} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 - 2 T - 117 T^{2} + 1836 T^{3} - 1256 T^{4} - 150035 T^{5} + 1814652 T^{6} - 2995755 T^{7} - 87702209 T^{8} + 1422288486 T^{9} - 4989555298 T^{10} - 49960372308 T^{11} + 894785650027 T^{12} - 3347344944636 T^{13} - 22398113732722 T^{14} + 427771751914818 T^{15} - 1767297825526289 T^{16} - 4044644039920785 T^{17} + 164150484119740188 T^{18} - 909318865704636305 T^{19} - 510021003011141096 T^{20} + 49951197151597522692 T^{21} -$$$$21\!\cdots\!33$$$$T^{22} -$$$$24\!\cdots\!66$$$$T^{23} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 + 2 T - 173 T^{2} - 132 T^{3} + 12698 T^{4} + 10705 T^{5} - 302786 T^{6} - 4219025 T^{7} - 10543483 T^{8} + 513034234 T^{9} - 498151188 T^{10} - 17751960180 T^{11} + 139863477279 T^{12} - 1189381332060 T^{13} - 2236200682932 T^{14} + 154301715320542 T^{15} - 212463001694443 T^{16} - 5696211579560675 T^{17} - 27389531703422834 T^{18} + 64879917734982715 T^{19} + 5156247369614227418 T^{20} - 3591262540310933004 T^{21} -$$$$31\!\cdots\!77$$$$T^{22} +$$$$24\!\cdots\!66$$$$T^{23} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 + 10 T - 83 T^{2} - 1992 T^{3} - 13923 T^{4} + 22803 T^{5} + 1448003 T^{6} + 14593967 T^{7} + 61267598 T^{8} - 292609163 T^{9} - 6586443125 T^{10} - 55156879841 T^{11} - 326931234356 T^{12} - 1085899976057 T^{13} + 6095209464340 T^{14} + 202150970450717 T^{15} + 2452238121492227 T^{16} + 13544115020198039 T^{17} + 27361395285422260 T^{18} - 326598534498831491 T^{19} - 6588030862187113076 T^{20} - 74468688297116267987 T^{21} -$$$$59\!\cdots\!25$$$$T^{22} -$$$$17\!\cdots\!49$$$$T^{23} +$$$$24\!\cdots\!18$$$$T^{24} +$$$$39\!\cdots\!49$$$$T^{25} +$$$$26\!\cdots\!47$$$$T^{26} +$$$$27\!\cdots\!49$$$$T^{27} -$$$$11\!\cdots\!03$$$$T^{28} -$$$$10\!\cdots\!04$$$$T^{29} -$$$$30\!\cdots\!07$$$$T^{30} +$$$$24\!\cdots\!30$$$$T^{31} +$$$$16\!\cdots\!81$$$$T^{32}$$)
$71$ ($$( 1 + 12 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 + 6 T + 71 T^{2} )^{2}$$)($$( 1 + 124 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 5 T + 282 T^{2} - 1537 T^{3} + 40228 T^{4} - 200831 T^{5} + 3541613 T^{6} - 14259001 T^{7} + 202789348 T^{8} - 550109207 T^{9} + 7166094042 T^{10} - 9021146755 T^{11} + 128100283921 T^{12} )^{2}$$)($$( 1 + 15 T + 472 T^{2} + 5103 T^{3} + 87582 T^{4} + 709377 T^{5} + 8398649 T^{6} + 50365767 T^{7} + 441500862 T^{8} + 1826419833 T^{9} + 11994313432 T^{10} + 27063440265 T^{11} + 128100283921 T^{12} )^{2}$$)($$( 1 - 11 T + 244 T^{2} - 2045 T^{3} + 18530 T^{4} - 153299 T^{5} + 887101 T^{6} - 10884229 T^{7} + 93409730 T^{8} - 731927995 T^{9} + 6200450164 T^{10} - 19846522861 T^{11} + 128100283921 T^{12} )^{2}$$)($$( 1 + 19 T + 400 T^{2} + 3773 T^{3} + 41473 T^{4} + 130458 T^{5} + 473407 T^{6} - 19694168 T^{7} - 122824232 T^{8} - 1398285928 T^{9} + 2386444687 T^{10} + 46692353238 T^{11} + 1053898646113 T^{12} + 6807357341323 T^{13} + 51240113568400 T^{14} + 172807283009429 T^{15} + 645753531245761 T^{16} )^{2}$$)
$73$ ($$1 - 73 T^{2} + 5329 T^{4}$$)($$1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4}$$)($$1 - 14 T + 123 T^{2} - 1022 T^{3} + 5329 T^{4}$$)($$1 + 8 T - 9 T^{2} + 584 T^{3} + 5329 T^{4}$$)($$1 - 8 T - 26 T^{2} + 448 T^{3} - 1901 T^{4} + 32704 T^{5} - 138554 T^{6} - 3112136 T^{7} + 28398241 T^{8}$$)($$1 - 6 T - 264 T^{2} + 676 T^{3} + 41379 T^{4} - 177 T^{5} - 4351292 T^{6} - 7764489 T^{7} + 350907786 T^{8} + 808896697 T^{9} - 24223821882 T^{10} - 30050609763 T^{11} + 1721091747949 T^{12} - 2193694512699 T^{13} - 129088746809178 T^{14} + 314674566376849 T^{15} + 9965163875604426 T^{16} - 16096341580060977 T^{17} - 658499408177515388 T^{18} - 1955389537880169 T^{19} + 33370512142485177699 T^{20} + 39797192614789109188 T^{21} -$$$$11\!\cdots\!36$$$$T^{22} -$$$$18\!\cdots\!62$$$$T^{23} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$1 - 22 T - 46 T^{2} + 3256 T^{3} + 12483 T^{4} - 414879 T^{5} - 2110886 T^{6} + 33167477 T^{7} + 364001024 T^{8} - 2404017511 T^{9} - 35612367328 T^{10} + 55783713671 T^{11} + 3123892980185 T^{12} + 4072211097983 T^{13} - 189778305490912 T^{14} - 935203680076687 T^{15} + 10336988803798784 T^{16} + 68758554380180861 T^{17} - 319449299594282054 T^{18} - 4583333650204444263 T^{19} + 10067041327113813123 T^{20} +$$$$19\!\cdots\!28$$$$T^{21} -$$$$19\!\cdots\!54$$$$T^{22} -$$$$69\!\cdots\!94$$$$T^{23} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$1 - 24 T + 42 T^{2} + 3412 T^{3} - 16221 T^{4} - 351231 T^{5} + 2912248 T^{6} + 10402335 T^{7} - 128561004 T^{8} + 12356683 T^{9} - 873975840 T^{10} - 31448077707 T^{11} + 794156097013 T^{12} - 2295709672611 T^{13} - 4657417251360 T^{14} + 4806959750611 T^{15} - 3650906374793964 T^{16} + 21564785189369655 T^{17} + 440722797841687672 T^{18} - 3880188829260958407 T^{19} - 13081589150613887901 T^{20} +$$$$20\!\cdots\!56$$$$T^{21} +$$$$18\!\cdots\!58$$$$T^{22} -$$$$75\!\cdots\!48$$$$T^{23} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$1 + 8 T - 390 T^{2} - 908 T^{3} + 103150 T^{4} - 105353 T^{5} - 16697378 T^{6} + 75246967 T^{7} + 1927206172 T^{8} - 14189615254 T^{9} - 139595267550 T^{10} + 1686118517626 T^{11} + 5218854241786 T^{12} - 119151906708597 T^{13} + 190749604993352 T^{14} + 3821131738775017 T^{15} - 31483648169073569 T^{16} + 278942616930576241 T^{17} + 1016504645009572808 T^{18} - 46352117292058279149 T^{19} +$$$$14\!\cdots\!26$$$$T^{20} +$$$$34\!\cdots\!18$$$$T^{21} -$$$$21\!\cdots\!50$$$$T^{22} -$$$$15\!\cdots\!38$$$$T^{23} +$$$$15\!\cdots\!32$$$$T^{24} +$$$$44\!\cdots\!71$$$$T^{25} -$$$$71\!\cdots\!22$$$$T^{26} -$$$$33\!\cdots\!81$$$$T^{27} +$$$$23\!\cdots\!50$$$$T^{28} -$$$$15\!\cdots\!64$$$$T^{29} -$$$$47\!\cdots\!10$$$$T^{30} +$$$$71\!\cdots\!56$$$$T^{31} +$$$$65\!\cdots\!61$$$$T^{32}$$)
$79$ ($$1 + 10 T + 21 T^{2} + 790 T^{3} + 6241 T^{4}$$)($$( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} )$$)($$1 - 79 T^{2} + 6241 T^{4}$$)($$1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4}$$)($$1 + 4 T + 16 T^{2} - 632 T^{3} - 7505 T^{4} - 49928 T^{5} + 99856 T^{6} + 1972156 T^{7} + 38950081 T^{8}$$)($$1 - T - 52 T^{2} - 1115 T^{3} + 1980 T^{4} + 51753 T^{5} + 1509433 T^{6} - 481201 T^{7} - 54915913 T^{8} - 1095187870 T^{9} - 2212260694 T^{10} + 28301030714 T^{11} + 1014448414133 T^{12} + 2235781426406 T^{13} - 13806718991254 T^{14} - 539970332236930 T^{15} - 2138979259538953 T^{16} - 1480682616255199 T^{17} + 366924227249429593 T^{18} + 993859901760686727 T^{19} + 3003875443614990780 T^{20} -$$$$13\!\cdots\!85$$$$T^{21} -$$$$49\!\cdots\!52$$$$T^{22} -$$$$74\!\cdots\!79$$$$T^{23} +$$$$59\!\cdots\!41$$$$T^{24}$$)($$1 - 27 T - 34 T^{2} + 3813 T^{3} + 63446 T^{4} - 1156425 T^{5} - 8107899 T^{6} + 89486493 T^{7} + 1978694821 T^{8} - 11375470374 T^{9} - 184938038468 T^{10} + 67660756632 T^{11} + 21114353417797 T^{12} + 5345199773928 T^{13} - 1154198298078788 T^{14} - 5608550537726586 T^{15} + 77070323552230501 T^{16} + 275354985909718707 T^{17} - 1970928537531260379 T^{18} - 22207880449318921575 T^{19} + 96254485553331669206 T^{20} +$$$$45\!\cdots\!47$$$$T^{21} -$$$$32\!\cdots\!34$$$$T^{22} -$$$$20\!\cdots\!33$$$$T^{23} +$$$$59\!\cdots\!41$$$$T^{24}$$)($$1 + T - 178 T^{2} + 2009 T^{3} + 11676 T^{4} - 294975 T^{5} + 1839349 T^{6} + 7617877 T^{7} - 197744023 T^{8} + 2216898430 T^{9} - 7775453584 T^{10} - 124426532624 T^{11} + 2189706881621 T^{12} - 9829696077296 T^{13} - 48526605817744 T^{14} + 1093017385028770 T^{15} - 7702145713115863 T^{16} + 23440637169644923 T^{17} + 447122668225095829 T^{18} - 5664673053192251025 T^{19} + 17713762464469006236 T^{20} +$$$$24\!\cdots\!71$$$$T^{21} -$$$$16\!\cdots\!78$$$$T^{22} +$$$$74\!\cdots\!79$$$$T^{23} +$$$$59\!\cdots\!41$$$$T^{24}$$)($$1 + 25 T - 182 T^{2} - 6023 T^{3} + 84307 T^{4} + 1469452 T^{5} - 17756085 T^{6} - 194582298 T^{7} + 3345620082 T^{8} + 20818372616 T^{9} - 456031241449 T^{10} - 1544591192596 T^{11} + 50400744313286 T^{12} + 75913178939879 T^{13} - 4799434602487981 T^{14} - 2540107477595451 T^{15} + 391220140859842245 T^{16} - 200668490730040629 T^{17} - 29953271354127489421 T^{18} + 37428157831339002281 T^{19} +$$$$19\!\cdots\!66$$$$T^{20} -$$$$47\!\cdots\!04$$$$T^{21} -$$$$11\!\cdots\!29$$$$T^{22} +$$$$39\!\cdots\!44$$$$T^{23} +$$$$50\!\cdots\!02$$$$T^{24} -$$$$23\!\cdots\!62$$$$T^{25} -$$$$16\!\cdots\!85$$$$T^{26} +$$$$10\!\cdots\!08$$$$T^{27} +$$$$49\!\cdots\!87$$$$T^{28} -$$$$28\!\cdots\!97$$$$T^{29} -$$$$67\!\cdots\!42$$$$T^{30} +$$$$72\!\cdots\!75$$$$T^{31} +$$$$23\!\cdots\!21$$$$T^{32}$$)
$83$ ($$1 - 5 T - 58 T^{2} - 415 T^{3} + 6889 T^{4}$$)($$1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4}$$)($$1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4}$$)($$1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4}$$)($$( 1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4} )^{2}$$)($$1 + 26 T + 232 T^{2} + 1516 T^{3} + 11499 T^{4} - 94349 T^{5} - 2607716 T^{6} - 23093955 T^{7} - 195776338 T^{8} - 925613923 T^{9} + 9434947014 T^{10} + 206018004805 T^{11} + 2189491903883 T^{12} + 17099494398815 T^{13} + 64997349979446 T^{14} - 529254008190401 T^{15} - 9291216293008498 T^{16} - 90968027352613065 T^{17} - 852567642680315204 T^{18} - 2560259274820317823 T^{19} + 25899108377366832459 T^{20} +$$$$28\!\cdots\!48$$$$T^{21} +$$$$35\!\cdots\!68$$$$T^{22} +$$$$33\!\cdots\!42$$$$T^{23} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 - 6 T - 330 T^{2} + 1740 T^{3} + 59559 T^{4} - 268053 T^{5} - 7813786 T^{6} + 31726179 T^{7} + 814223178 T^{8} - 2507023989 T^{9} - 75271442382 T^{10} + 84734329059 T^{11} + 6524490952095 T^{12} + 7032949311897 T^{13} - 518544966569598 T^{14} - 1433483725598343 T^{15} + 38641664947164138 T^{16} + 124970708528093097 T^{17} - 2554642112265465034 T^{18} - 7273899875922486231 T^{19} +$$$$13\!\cdots\!19$$$$T^{20} +$$$$32\!\cdots\!20$$$$T^{21} -$$$$51\!\cdots\!70$$$$T^{22} -$$$$77\!\cdots\!02$$$$T^{23} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 - 4 T - 294 T^{2} + 1948 T^{3} + 44977 T^{4} - 398395 T^{5} - 3801708 T^{6} + 52335429 T^{7} + 120574846 T^{8} - 4218193263 T^{9} + 14917345312 T^{10} + 151178074263 T^{11} - 2170254522125 T^{12} + 12547780163829 T^{13} + 102765591854368 T^{14} - 2411908071270981 T^{15} + 5722279745993566 T^{16} + 206151381899840847 T^{17} - 1242931832959914252 T^{18} - 10810867034012448665 T^{19} +$$$$10\!\cdots\!57$$$$T^{20} +$$$$36\!\cdots\!44$$$$T^{21} -$$$$45\!\cdots\!06$$$$T^{22} -$$$$51\!\cdots\!68$$$$T^{23} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 - 2 T - 379 T^{2} + 46 T^{3} + 71929 T^{4} + 111425 T^{5} - 9247598 T^{6} - 27250484 T^{7} + 925626125 T^{8} + 3684425840 T^{9} - 76460286955 T^{10} - 351032380757 T^{11} + 5350114348114 T^{12} + 23636419050310 T^{13} - 345108599067805 T^{14} - 759472537118196 T^{15} + 25092808099894680 T^{16} - 63036220580810268 T^{17} - 2377453138978108645 T^{18} + 13514997139519603970 T^{19} +$$$$25\!\cdots\!94$$$$T^{20} -$$$$13\!\cdots\!51$$$$T^{21} -$$$$24\!\cdots\!95$$$$T^{22} +$$$$99\!\cdots\!80$$$$T^{23} +$$$$20\!\cdots\!25$$$$T^{24} -$$$$50\!\cdots\!52$$$$T^{25} -$$$$14\!\cdots\!02$$$$T^{26} +$$$$14\!\cdots\!75$$$$T^{27} +$$$$76\!\cdots\!69$$$$T^{28} +$$$$40\!\cdots\!98$$$$T^{29} -$$$$27\!\cdots\!91$$$$T^{30} -$$$$12\!\cdots\!14$$$$T^{31} +$$$$50\!\cdots\!81$$$$T^{32}$$)
$89$ ($$1 - 14 T + 107 T^{2} - 1246 T^{3} + 7921 T^{4}$$)($$1 - 15 T + 136 T^{2} - 1335 T^{3} + 7921 T^{4}$$)($$1 + T - 88 T^{2} + 89 T^{3} + 7921 T^{4}$$)($$1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4}$$)($$( 1 - 89 T^{2} + 7921 T^{4} )^{2}$$)($$1 - 2 T - 131 T^{2} + 1310 T^{3} - 5289 T^{4} - 98935 T^{5} + 2008330 T^{6} - 7349421 T^{7} - 31479907 T^{8} + 1608975643 T^{9} - 11307686898 T^{10} - 57565868677 T^{11} + 1401967996337 T^{12} - 5123362312253 T^{13} - 89568187919058 T^{14} + 1134277950070067 T^{15} - 1975119911651587 T^{16} - 41039603779729029 T^{17} + 998102436075705130 T^{18} - 4376027117889161615 T^{19} - 20820618193358306409 T^{20} +$$$$45\!\cdots\!90$$$$T^{21} -$$$$40\!\cdots\!31$$$$T^{22} -$$$$55\!\cdots\!78$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$1 + 18 T - 115 T^{2} - 1950 T^{3} + 30919 T^{4} + 158145 T^{5} - 3931898 T^{6} + 1392867 T^{7} + 346157113 T^{8} - 979144353 T^{9} - 18572538958 T^{10} + 88654414143 T^{11} + 1705608497513 T^{12} + 7890242858727 T^{13} - 147113081086318 T^{14} - 690266415390057 T^{15} + 21718673007710233 T^{16} + 7777852132550283 T^{17} - 1954079743966973978 T^{18} + 6994964457053433705 T^{19} +$$$$12\!\cdots\!39$$$$T^{20} -$$$$68\!\cdots\!50$$$$T^{21} -$$$$35\!\cdots\!15$$$$T^{22} +$$$$49\!\cdots\!02$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$1 - 2 T - 255 T^{2} + 326 T^{3} + 33115 T^{4} + 1237 T^{5} - 2035002 T^{6} - 10969065 T^{7} + 3238993 T^{8} + 1541883639 T^{9} + 12567967198 T^{10} - 74858833077 T^{11} - 1448697683687 T^{12} - 6662436143853 T^{13} + 99550868175358 T^{14} + 1086980167102191 T^{15} + 203221679403313 T^{16} - 61251911059945185 T^{17} - 1011357921068216922 T^{18} + 54714161265769373 T^{19} +$$$$13\!\cdots\!15$$$$T^{20} +$$$$11\!\cdots\!34$$$$T^{21} -$$$$79\!\cdots\!55$$$$T^{22} -$$$$55\!\cdots\!78$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$1 + 6 T - 361 T^{2} - 3094 T^{3} + 62940 T^{4} + 748723 T^{5} - 6298663 T^{6} - 119355885 T^{7} + 250393933 T^{8} + 13841837530 T^{9} + 33272999661 T^{10} - 1196873353342 T^{11} - 8138474562173 T^{12} + 74723700233589 T^{13} + 1028573157441158 T^{14} - 2348330140909041 T^{15} - 100635305983812723 T^{16} - 209001382540904649 T^{17} + 8147327980091412518 T^{18} + 52677892229973003741 T^{19} -$$$$51\!\cdots\!93$$$$T^{20} -$$$$66\!\cdots\!58$$$$T^{21} +$$$$16\!\cdots\!21$$$$T^{22} +$$$$61\!\cdots\!70$$$$T^{23} +$$$$98\!\cdots\!73$$$$T^{24} -$$$$41\!\cdots\!65$$$$T^{25} -$$$$19\!\cdots\!63$$$$T^{26} +$$$$20\!\cdots\!47$$$$T^{27} +$$$$15\!\cdots\!40$$$$T^{28} -$$$$68\!\cdots\!86$$$$T^{29} -$$$$70\!\cdots\!01$$$$T^{30} +$$$$10\!\cdots\!94$$$$T^{31} +$$$$15\!\cdots\!61$$$$T^{32}$$)
$97$ ($$1 + 2 T - 93 T^{2} + 194 T^{3} + 9409 T^{4}$$)($$1 - 10 T + 3 T^{2} - 970 T^{3} + 9409 T^{4}$$)($$1 + 10 T + 3 T^{2} + 970 T^{3} + 9409 T^{4}$$)($$1 - 10 T + 3 T^{2} - 970 T^{3} + 9409 T^{4}$$)($$1 + 4 T - 110 T^{2} - 272 T^{3} + 4915 T^{4} - 26384 T^{5} - 1034990 T^{6} + 3650692 T^{7} + 88529281 T^{8}$$)($$1 - 6 T - 168 T^{2} + 1492 T^{3} + 5214 T^{4} - 121578 T^{5} + 1943470 T^{6} - 2165256 T^{7} - 213568578 T^{8} + 1521589192 T^{9} - 5900408970 T^{10} - 81665164176 T^{11} + 2384863292767 T^{12} - 7921520925072 T^{13} - 55516947998730 T^{14} + 1388713372630216 T^{15} - 18907072654532418 T^{16} - 18593790015510792 T^{17} + 1618856102419363630 T^{18} - 9823293830280022314 T^{19} + 40864378761081474654 T^{20} +$$$$11\!\cdots\!64$$$$T^{21} -$$$$12\!\cdots\!32$$$$T^{22} -$$$$42\!\cdots\!18$$$$T^{23} +$$$$69\!\cdots\!41$$$$T^{24}$$)($$1 + 4 T - 142 T^{2} - 1276 T^{3} - 1290 T^{4} + 122538 T^{5} + 421462 T^{6} - 4407458 T^{7} - 23869888 T^{8} + 1323819664 T^{9} + 17054431616 T^{10} - 120190432922 T^{11} - 2625924073873 T^{12} - 11658471993434 T^{13} + 160465147074944 T^{14} + 1208214464201872 T^{15} - 2113184022190528 T^{16} - 37848341514436706 T^{17} + 351066047141386198 T^{18} + 9900860183379010794 T^{19} - 10110289336746279690 T^{20} -$$$$97\!\cdots\!92$$$$T^{21} -$$$$10\!\cdots\!58$$$$T^{22} +$$$$28\!\cdots\!12$$$$T^{23} +$$$$69\!\cdots\!41$$$$T^{24}$$)($$( 1 + 18 T - 36 T^{2} - 490 T^{3} + 31950 T^{4} + 166842 T^{5} - 1649145 T^{6} + 16183674 T^{7} + 300617550 T^{8} - 447209770 T^{9} - 3187054116 T^{10} + 154572124626 T^{11} + 832972004929 T^{12} )^{2}$$)($$1 - 26 T - 56 T^{2} + 2492 T^{3} + 90143 T^{4} - 817018 T^{5} - 11928114 T^{6} - 57652506 T^{7} + 2793757095 T^{8} + 11900406246 T^{9} - 106656506274 T^{10} - 4250712480600 T^{11} + 2907448664925 T^{12} + 284134319779998 T^{13} + 4080312688533132 T^{14} - 24204163500327996 T^{15} - 351229803717868731 T^{16} - 2347803859531815612 T^{17} + 38391662086408238988 T^{18} +$$$$25\!\cdots\!54$$$$T^{19} +$$$$25\!\cdots\!25$$$$T^{20} -$$$$36\!\cdots\!00$$$$T^{21} -$$$$88\!\cdots\!46$$$$T^{22} +$$$$96\!\cdots\!98$$$$T^{23} +$$$$21\!\cdots\!95$$$$T^{24} -$$$$43\!\cdots\!02$$$$T^{25} -$$$$87\!\cdots\!86$$$$T^{26} -$$$$58\!\cdots\!54$$$$T^{27} +$$$$62\!\cdots\!63$$$$T^{28} +$$$$16\!\cdots\!84$$$$T^{29} -$$$$36\!\cdots\!64$$$$T^{30} -$$$$16\!\cdots\!18$$$$T^{31} +$$$$61\!\cdots\!21$$$$T^{32}$$)