# Properties

 Label 1152.3.m Level $1152$ Weight $3$ Character orbit 1152.m Rep. character $\chi_{1152}(415,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $76$ Newform subspaces $6$ Sturm bound $576$ Trace bound $19$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1152.m (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$16$$ Character field: $$\Q(i)$$ Newform subspaces: $$6$$ Sturm bound: $$576$$ Trace bound: $$19$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(1152, [\chi])$$.

Total New Old
Modular forms 832 84 748
Cusp forms 704 76 628
Eisenstein series 128 8 120

## Trace form

 $$76q - 4q^{5} + O(q^{10})$$ $$76q - 4q^{5} + 4q^{13} + 8q^{17} + 28q^{29} - 92q^{37} + 356q^{49} - 164q^{53} + 68q^{61} + 40q^{65} + 24q^{77} - 216q^{85} - 8q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(1152, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1152.3.m.a $$6$$ $$31.390$$ 6.0.399424.1 None $$0$$ $$0$$ $$-2$$ $$-4$$ $$q+(-1+\beta _{1}-\beta _{2}-\beta _{4})q^{5}+(\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$$
1152.3.m.b $$6$$ $$31.390$$ 6.0.399424.1 None $$0$$ $$0$$ $$-2$$ $$4$$ $$q+(-1+\beta _{1}-\beta _{2}-\beta _{4})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$$
1152.3.m.c $$16$$ $$31.390$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{11}q^{5}-\beta _{3}q^{7}+(-2-2\beta _{2}+\beta _{5}+\cdots)q^{11}+\cdots$$
1152.3.m.d $$16$$ $$31.390$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}-\beta _{8}q^{7}+(\beta _{4}+\beta _{14})q^{11}+\cdots$$
1152.3.m.e $$16$$ $$31.390$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{5}+\beta _{8}q^{7}+(-\beta _{4}-\beta _{14})q^{11}+\cdots$$
1152.3.m.f $$16$$ $$31.390$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{11}q^{5}+\beta _{3}q^{7}+(2+2\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(1152, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(1152, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(16, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(384, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(576, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ ($$1 + 2 T + 2 T^{2} - 14 T^{3} - 369 T^{4} + 636 T^{5} + 2108 T^{6} + 15900 T^{7} - 230625 T^{8} - 218750 T^{9} + 781250 T^{10} + 19531250 T^{11} + 244140625 T^{12}$$)($$1 + 2 T + 2 T^{2} - 14 T^{3} - 369 T^{4} + 636 T^{5} + 2108 T^{6} + 15900 T^{7} - 230625 T^{8} - 218750 T^{9} + 781250 T^{10} + 19531250 T^{11} + 244140625 T^{12}$$)($$1 + 32 T^{3} - 344 T^{4} + 5664 T^{5} + 512 T^{6} + 145600 T^{7} + 223452 T^{8} - 2255168 T^{9} + 20875776 T^{10} - 67282720 T^{11} + 753060504 T^{12} + 1881828576 T^{13} + 2740220928 T^{14} + 75471830656 T^{15} - 399298967994 T^{16} + 1886795766400 T^{17} + 1712638080000 T^{18} + 29403571500000 T^{19} + 294164259375000 T^{20} - 657057812500000 T^{21} + 5096625000000000 T^{22} - 13764453125000000 T^{23} + 34096069335937500 T^{24} + 555419921875000000 T^{25} + 48828125000000000 T^{26} + 13504028320312500000 T^{27} - 20503997802734375000 T^{28} + 47683715820312500000 T^{29} +$$$$23\!\cdots\!25$$$$T^{32}$$)($$1 - 344 T^{4} - 8484 T^{8} + 258572952 T^{12} - 94198183354 T^{16} + 101005059375000 T^{20} - 1294555664062500 T^{24} - 20503997802734375000 T^{28} +$$$$23\!\cdots\!25$$$$T^{32}$$)($$1 - 344 T^{4} - 8484 T^{8} + 258572952 T^{12} - 94198183354 T^{16} + 101005059375000 T^{20} - 1294555664062500 T^{24} - 20503997802734375000 T^{28} +$$$$23\!\cdots\!25$$$$T^{32}$$)($$1 + 32 T^{3} - 344 T^{4} + 5664 T^{5} + 512 T^{6} + 145600 T^{7} + 223452 T^{8} - 2255168 T^{9} + 20875776 T^{10} - 67282720 T^{11} + 753060504 T^{12} + 1881828576 T^{13} + 2740220928 T^{14} + 75471830656 T^{15} - 399298967994 T^{16} + 1886795766400 T^{17} + 1712638080000 T^{18} + 29403571500000 T^{19} + 294164259375000 T^{20} - 657057812500000 T^{21} + 5096625000000000 T^{22} - 13764453125000000 T^{23} + 34096069335937500 T^{24} + 555419921875000000 T^{25} + 48828125000000000 T^{26} + 13504028320312500000 T^{27} - 20503997802734375000 T^{28} + 47683715820312500000 T^{29} +$$$$23\!\cdots\!25$$$$T^{32}$$)
$7$ ($$( 1 + 2 T + 87 T^{2} + 332 T^{3} + 4263 T^{4} + 4802 T^{5} + 117649 T^{6} )^{2}$$)($$( 1 - 2 T + 87 T^{2} - 332 T^{3} + 4263 T^{4} - 4802 T^{5} + 117649 T^{6} )^{2}$$)($$( 1 + 168 T^{2} + 448 T^{3} + 15076 T^{4} + 56512 T^{5} + 1070392 T^{6} + 3649664 T^{7} + 60103046 T^{8} + 178833536 T^{9} + 2570011192 T^{10} + 6648580288 T^{11} + 86910139876 T^{12} + 126548911552 T^{13} + 2325336249768 T^{14} + 33232930569601 T^{16} )^{2}$$)($$( 1 + 84 T^{2} - 352 T^{3} + 3530 T^{4} - 17248 T^{5} + 201684 T^{6} + 5764801 T^{8} )^{4}$$)($$( 1 + 84 T^{2} + 352 T^{3} + 3530 T^{4} + 17248 T^{5} + 201684 T^{6} + 5764801 T^{8} )^{4}$$)($$( 1 + 168 T^{2} - 448 T^{3} + 15076 T^{4} - 56512 T^{5} + 1070392 T^{6} - 3649664 T^{7} + 60103046 T^{8} - 178833536 T^{9} + 2570011192 T^{10} - 6648580288 T^{11} + 86910139876 T^{12} - 126548911552 T^{13} + 2325336249768 T^{14} + 33232930569601 T^{16} )^{2}$$)
$11$ ($$1 + 18 T + 162 T^{2} + 2146 T^{3} + 17759 T^{4} + 65756 T^{5} + 609308 T^{6} + 7956476 T^{7} + 260009519 T^{8} + 3801769906 T^{9} + 34726138722 T^{10} + 466873642818 T^{11} + 3138428376721 T^{12}$$)($$1 - 18 T + 162 T^{2} - 2146 T^{3} + 17759 T^{4} - 65756 T^{5} + 609308 T^{6} - 7956476 T^{7} + 260009519 T^{8} - 3801769906 T^{9} + 34726138722 T^{10} - 466873642818 T^{11} + 3138428376721 T^{12}$$)($$1 + 32 T + 512 T^{2} + 8480 T^{3} + 137032 T^{4} + 1636576 T^{5} + 18165248 T^{6} + 219655136 T^{7} + 2263228700 T^{8} + 21867108000 T^{9} + 253620152832 T^{10} + 2916953293728 T^{11} + 33797606438392 T^{12} + 431768458252384 T^{13} + 5293166227138048 T^{14} + 61910274521995104 T^{15} + 703855220885889990 T^{16} + 7491143217161407584 T^{17} + 77497246731528160768 T^{18} +$$$$76\!\cdots\!24$$$$T^{19} +$$$$72\!\cdots\!52$$$$T^{20} +$$$$75\!\cdots\!28$$$$T^{21} +$$$$79\!\cdots\!72$$$$T^{22} +$$$$83\!\cdots\!00$$$$T^{23} +$$$$10\!\cdots\!00$$$$T^{24} +$$$$12\!\cdots\!16$$$$T^{25} +$$$$12\!\cdots\!48$$$$T^{26} +$$$$13\!\cdots\!96$$$$T^{27} +$$$$13\!\cdots\!12$$$$T^{28} +$$$$10\!\cdots\!80$$$$T^{29} +$$$$73\!\cdots\!72$$$$T^{30} +$$$$55\!\cdots\!32$$$$T^{31} +$$$$21\!\cdots\!21$$$$T^{32}$$)($$1 - 27832 T^{4} + 345241884 T^{8} - 1221720802824 T^{12} - 7510669490883642 T^{16} -$$$$26\!\cdots\!44$$$$T^{20} +$$$$15\!\cdots\!24$$$$T^{24} -$$$$27\!\cdots\!12$$$$T^{28} +$$$$21\!\cdots\!21$$$$T^{32}$$)($$1 - 27832 T^{4} + 345241884 T^{8} - 1221720802824 T^{12} - 7510669490883642 T^{16} -$$$$26\!\cdots\!44$$$$T^{20} +$$$$15\!\cdots\!24$$$$T^{24} -$$$$27\!\cdots\!12$$$$T^{28} +$$$$21\!\cdots\!21$$$$T^{32}$$)($$1 - 32 T + 512 T^{2} - 8480 T^{3} + 137032 T^{4} - 1636576 T^{5} + 18165248 T^{6} - 219655136 T^{7} + 2263228700 T^{8} - 21867108000 T^{9} + 253620152832 T^{10} - 2916953293728 T^{11} + 33797606438392 T^{12} - 431768458252384 T^{13} + 5293166227138048 T^{14} - 61910274521995104 T^{15} + 703855220885889990 T^{16} - 7491143217161407584 T^{17} + 77497246731528160768 T^{18} -$$$$76\!\cdots\!24$$$$T^{19} +$$$$72\!\cdots\!52$$$$T^{20} -$$$$75\!\cdots\!28$$$$T^{21} +$$$$79\!\cdots\!72$$$$T^{22} -$$$$83\!\cdots\!00$$$$T^{23} +$$$$10\!\cdots\!00$$$$T^{24} -$$$$12\!\cdots\!16$$$$T^{25} +$$$$12\!\cdots\!48$$$$T^{26} -$$$$13\!\cdots\!96$$$$T^{27} +$$$$13\!\cdots\!12$$$$T^{28} -$$$$10\!\cdots\!80$$$$T^{29} +$$$$73\!\cdots\!72$$$$T^{30} -$$$$55\!\cdots\!32$$$$T^{31} +$$$$21\!\cdots\!21$$$$T^{32}$$)
$13$ ($$1 - 2 T + 2 T^{2} - 1554 T^{3} - 7825 T^{4} + 453380 T^{5} + 316348 T^{6} + 76621220 T^{7} - 223489825 T^{8} - 7500861186 T^{9} + 1631461442 T^{10} - 275716983698 T^{11} + 23298085122481 T^{12}$$)($$1 - 2 T + 2 T^{2} - 1554 T^{3} - 7825 T^{4} + 453380 T^{5} + 316348 T^{6} + 76621220 T^{7} - 223489825 T^{8} - 7500861186 T^{9} + 1631461442 T^{10} - 275716983698 T^{11} + 23298085122481 T^{12}$$)($$1 - 3200 T^{3} + 7608 T^{4} - 95360 T^{5} + 5120000 T^{6} - 68335872 T^{7} + 2004669468 T^{8} - 7270355200 T^{9} + 184268595200 T^{10} - 4889456013184 T^{11} + 5354592144136 T^{12} - 669839496880000 T^{13} + 7008632866619392 T^{14} - 70586941744778752 T^{15} + 2398056097119178950 T^{16} - 11929193154867609088 T^{17} +$$$$20\!\cdots\!12$$$$T^{18} -$$$$32\!\cdots\!00$$$$T^{19} +$$$$43\!\cdots\!56$$$$T^{20} -$$$$67\!\cdots\!16$$$$T^{21} +$$$$42\!\cdots\!00$$$$T^{22} -$$$$28\!\cdots\!00$$$$T^{23} +$$$$13\!\cdots\!88$$$$T^{24} -$$$$76\!\cdots\!88$$$$T^{25} +$$$$97\!\cdots\!00$$$$T^{26} -$$$$30\!\cdots\!40$$$$T^{27} +$$$$41\!\cdots\!88$$$$T^{28} -$$$$29\!\cdots\!00$$$$T^{29} +$$$$44\!\cdots\!81$$$$T^{32}$$)($$( 1 + 4352 T^{3} + 12636 T^{4} - 622336 T^{5} + 9469952 T^{6} + 45147648 T^{7} - 2135161210 T^{8} + 7629952512 T^{9} + 270471299072 T^{10} - 3003897005824 T^{11} + 10307573390556 T^{12} + 599960156526848 T^{13} + 665416609183179841 T^{16} )^{2}$$)($$( 1 + 4352 T^{3} + 12636 T^{4} - 622336 T^{5} + 9469952 T^{6} + 45147648 T^{7} - 2135161210 T^{8} + 7629952512 T^{9} + 270471299072 T^{10} - 3003897005824 T^{11} + 10307573390556 T^{12} + 599960156526848 T^{13} + 665416609183179841 T^{16} )^{2}$$)($$1 - 3200 T^{3} + 7608 T^{4} - 95360 T^{5} + 5120000 T^{6} - 68335872 T^{7} + 2004669468 T^{8} - 7270355200 T^{9} + 184268595200 T^{10} - 4889456013184 T^{11} + 5354592144136 T^{12} - 669839496880000 T^{13} + 7008632866619392 T^{14} - 70586941744778752 T^{15} + 2398056097119178950 T^{16} - 11929193154867609088 T^{17} +$$$$20\!\cdots\!12$$$$T^{18} -$$$$32\!\cdots\!00$$$$T^{19} +$$$$43\!\cdots\!56$$$$T^{20} -$$$$67\!\cdots\!16$$$$T^{21} +$$$$42\!\cdots\!00$$$$T^{22} -$$$$28\!\cdots\!00$$$$T^{23} +$$$$13\!\cdots\!88$$$$T^{24} -$$$$76\!\cdots\!88$$$$T^{25} +$$$$97\!\cdots\!00$$$$T^{26} -$$$$30\!\cdots\!40$$$$T^{27} +$$$$41\!\cdots\!88$$$$T^{28} -$$$$29\!\cdots\!00$$$$T^{29} +$$$$44\!\cdots\!81$$$$T^{32}$$)
$17$ ($$( 1 - 2 T + 607 T^{2} + 388 T^{3} + 175423 T^{4} - 167042 T^{5} + 24137569 T^{6} )^{2}$$)($$( 1 - 2 T + 607 T^{2} + 388 T^{3} + 175423 T^{4} - 167042 T^{5} + 24137569 T^{6} )^{2}$$)($$( 1 + 968 T^{2} + 2944 T^{3} + 516540 T^{4} + 3209600 T^{5} + 201700088 T^{6} + 1543904000 T^{7} + 63894476806 T^{8} + 446188256000 T^{9} + 16846193049848 T^{10} + 77471941462400 T^{11} + 3603257748574140 T^{12} + 5935086042921856 T^{13} + 563978325638408648 T^{14} + 48661191875666868481 T^{16} )^{2}$$)($$( 1 + 1208 T^{2} + 806844 T^{4} + 368107656 T^{6} + 122826347526 T^{8} + 30744719536776 T^{10} + 5628348036726204 T^{12} + 703807662573551288 T^{14} + 48661191875666868481 T^{16} )^{2}$$)($$( 1 + 1208 T^{2} + 806844 T^{4} + 368107656 T^{6} + 122826347526 T^{8} + 30744719536776 T^{10} + 5628348036726204 T^{12} + 703807662573551288 T^{14} + 48661191875666868481 T^{16} )^{2}$$)($$( 1 + 968 T^{2} + 2944 T^{3} + 516540 T^{4} + 3209600 T^{5} + 201700088 T^{6} + 1543904000 T^{7} + 63894476806 T^{8} + 446188256000 T^{9} + 16846193049848 T^{10} + 77471941462400 T^{11} + 3603257748574140 T^{12} + 5935086042921856 T^{13} + 563978325638408648 T^{14} + 48661191875666868481 T^{16} )^{2}$$)
$19$ ($$1 + 30 T + 450 T^{2} + 12014 T^{3} + 441215 T^{4} + 8004292 T^{5} + 113750108 T^{6} + 2889549412 T^{7} + 57499580015 T^{8} + 565209214334 T^{9} + 7642603368450 T^{10} + 183931987734030 T^{11} + 2213314919066161 T^{12}$$)($$1 - 30 T + 450 T^{2} - 12014 T^{3} + 441215 T^{4} - 8004292 T^{5} + 113750108 T^{6} - 2889549412 T^{7} + 57499580015 T^{8} - 565209214334 T^{9} + 7642603368450 T^{10} - 183931987734030 T^{11} + 2213314919066161 T^{12}$$)($$1 + 32 T + 512 T^{2} - 2656 T^{3} - 523448 T^{4} - 8424608 T^{5} + 1945088 T^{6} + 4454446304 T^{7} + 107916937244 T^{8} - 703649376 T^{9} - 30601835632128 T^{10} - 698985761087712 T^{11} + 998616856187896 T^{12} + 253693358084547040 T^{13} + 3161998119961945600 T^{14} - 30474951661580761248 T^{15} -$$$$19\!\cdots\!42$$$$T^{16} -$$$$11\!\cdots\!28$$$$T^{17} +$$$$41\!\cdots\!00$$$$T^{18} +$$$$11\!\cdots\!40$$$$T^{19} +$$$$16\!\cdots\!36$$$$T^{20} -$$$$42\!\cdots\!12$$$$T^{21} -$$$$67\!\cdots\!08$$$$T^{22} -$$$$56\!\cdots\!96$$$$T^{23} +$$$$31\!\cdots\!64$$$$T^{24} +$$$$46\!\cdots\!64$$$$T^{25} +$$$$73\!\cdots\!88$$$$T^{26} -$$$$11\!\cdots\!88$$$$T^{27} -$$$$25\!\cdots\!08$$$$T^{28} -$$$$46\!\cdots\!36$$$$T^{29} +$$$$32\!\cdots\!92$$$$T^{30} +$$$$73\!\cdots\!32$$$$T^{31} +$$$$83\!\cdots\!61$$$$T^{32}$$)($$( 1 + 16 T + 128 T^{2} - 7984 T^{3} - 156764 T^{4} + 603504 T^{5} + 61593984 T^{6} + 384035120 T^{7} + 7522568070 T^{8} + 138636678320 T^{9} + 8026989588864 T^{10} + 28392377367024 T^{11} - 2662411276559324 T^{12} - 48950433002283184 T^{13} + 283304309640468608 T^{14} + 12784106972526145936 T^{15} +$$$$28\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 16 T + 128 T^{2} + 7984 T^{3} - 156764 T^{4} - 603504 T^{5} + 61593984 T^{6} - 384035120 T^{7} + 7522568070 T^{8} - 138636678320 T^{9} + 8026989588864 T^{10} - 28392377367024 T^{11} - 2662411276559324 T^{12} + 48950433002283184 T^{13} + 283304309640468608 T^{14} - 12784106972526145936 T^{15} +$$$$28\!\cdots\!81$$$$T^{16} )^{2}$$)($$1 - 32 T + 512 T^{2} + 2656 T^{3} - 523448 T^{4} + 8424608 T^{5} + 1945088 T^{6} - 4454446304 T^{7} + 107916937244 T^{8} + 703649376 T^{9} - 30601835632128 T^{10} + 698985761087712 T^{11} + 998616856187896 T^{12} - 253693358084547040 T^{13} + 3161998119961945600 T^{14} + 30474951661580761248 T^{15} -$$$$19\!\cdots\!42$$$$T^{16} +$$$$11\!\cdots\!28$$$$T^{17} +$$$$41\!\cdots\!00$$$$T^{18} -$$$$11\!\cdots\!40$$$$T^{19} +$$$$16\!\cdots\!36$$$$T^{20} +$$$$42\!\cdots\!12$$$$T^{21} -$$$$67\!\cdots\!08$$$$T^{22} +$$$$56\!\cdots\!96$$$$T^{23} +$$$$31\!\cdots\!64$$$$T^{24} -$$$$46\!\cdots\!64$$$$T^{25} +$$$$73\!\cdots\!88$$$$T^{26} +$$$$11\!\cdots\!88$$$$T^{27} -$$$$25\!\cdots\!08$$$$T^{28} +$$$$46\!\cdots\!36$$$$T^{29} +$$$$32\!\cdots\!92$$$$T^{30} -$$$$73\!\cdots\!32$$$$T^{31} +$$$$83\!\cdots\!61$$$$T^{32}$$)
$23$ ($$( 1 + 30 T + 1751 T^{2} + 30772 T^{3} + 926279 T^{4} + 8395230 T^{5} + 148035889 T^{6} )^{2}$$)($$( 1 - 30 T + 1751 T^{2} - 30772 T^{3} + 926279 T^{4} - 8395230 T^{5} + 148035889 T^{6} )^{2}$$)($$( 1 + 64 T + 3496 T^{2} + 127936 T^{3} + 4410332 T^{4} + 130001728 T^{5} + 3673719192 T^{6} + 94049622208 T^{7} + 2261818535238 T^{8} + 49752250148032 T^{9} + 1028057252408472 T^{10} + 19244921376016192 T^{11} + 345377444336323292 T^{12} + 5299942138629398464 T^{13} + 76613527014343042216 T^{14} +$$$$74\!\cdots\!76$$$$T^{15} +$$$$61\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 + 2600 T^{2} + 3157852 T^{4} + 2464614168 T^{6} + 1453801462342 T^{8} + 689700093387288 T^{10} + 247294501491576412 T^{12} + 56978023523252834600 T^{14} +$$$$61\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 + 2600 T^{2} + 3157852 T^{4} + 2464614168 T^{6} + 1453801462342 T^{8} + 689700093387288 T^{10} + 247294501491576412 T^{12} + 56978023523252834600 T^{14} +$$$$61\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 - 64 T + 3496 T^{2} - 127936 T^{3} + 4410332 T^{4} - 130001728 T^{5} + 3673719192 T^{6} - 94049622208 T^{7} + 2261818535238 T^{8} - 49752250148032 T^{9} + 1028057252408472 T^{10} - 19244921376016192 T^{11} + 345377444336323292 T^{12} - 5299942138629398464 T^{13} + 76613527014343042216 T^{14} -$$$$74\!\cdots\!76$$$$T^{15} +$$$$61\!\cdots\!61$$$$T^{16} )^{2}$$)
$29$ ($$1 + 18 T + 162 T^{2} - 4894 T^{3} + 124463 T^{4} + 24625372 T^{5} + 435069308 T^{6} + 20709937852 T^{7} + 88030315103 T^{8} - 2911065332974 T^{9} + 81039918899682 T^{10} + 7572730199403618 T^{11} + 353814783205469041 T^{12}$$)($$1 + 18 T + 162 T^{2} - 4894 T^{3} + 124463 T^{4} + 24625372 T^{5} + 435069308 T^{6} + 20709937852 T^{7} + 88030315103 T^{8} - 2911065332974 T^{9} + 81039918899682 T^{10} + 7572730199403618 T^{11} + 353814783205469041 T^{12}$$)($$1 - 32 T + 512 T^{2} + 18368 T^{3} - 1552984 T^{4} + 20596992 T^{5} + 304715776 T^{6} - 25469097376 T^{7} + 491466517980 T^{8} + 9791032230816 T^{9} - 347423504794624 T^{10} + 2649303176415616 T^{11} + 694517140133881240 T^{12} - 20658732330776531008 T^{13} +$$$$19\!\cdots\!28$$$$T^{14} +$$$$11\!\cdots\!40$$$$T^{15} -$$$$82\!\cdots\!10$$$$T^{16} +$$$$96\!\cdots\!40$$$$T^{17} +$$$$13\!\cdots\!68$$$$T^{18} -$$$$12\!\cdots\!68$$$$T^{19} +$$$$34\!\cdots\!40$$$$T^{20} +$$$$11\!\cdots\!16$$$$T^{21} -$$$$12\!\cdots\!84$$$$T^{22} +$$$$29\!\cdots\!96$$$$T^{23} +$$$$12\!\cdots\!80$$$$T^{24} -$$$$53\!\cdots\!36$$$$T^{25} +$$$$53\!\cdots\!76$$$$T^{26} +$$$$30\!\cdots\!72$$$$T^{27} -$$$$19\!\cdots\!04$$$$T^{28} +$$$$19\!\cdots\!28$$$$T^{29} +$$$$45\!\cdots\!32$$$$T^{30} -$$$$23\!\cdots\!32$$$$T^{31} +$$$$62\!\cdots\!41$$$$T^{32}$$)($$1 - 1812568 T^{4} + 855482597340 T^{8} + 905028609054258072 T^{12} -$$$$12\!\cdots\!34$$$$T^{16} +$$$$45\!\cdots\!92$$$$T^{20} +$$$$21\!\cdots\!40$$$$T^{24} -$$$$22\!\cdots\!08$$$$T^{28} +$$$$62\!\cdots\!41$$$$T^{32}$$)($$1 - 1812568 T^{4} + 855482597340 T^{8} + 905028609054258072 T^{12} -$$$$12\!\cdots\!34$$$$T^{16} +$$$$45\!\cdots\!92$$$$T^{20} +$$$$21\!\cdots\!40$$$$T^{24} -$$$$22\!\cdots\!08$$$$T^{28} +$$$$62\!\cdots\!41$$$$T^{32}$$)($$1 - 32 T + 512 T^{2} + 18368 T^{3} - 1552984 T^{4} + 20596992 T^{5} + 304715776 T^{6} - 25469097376 T^{7} + 491466517980 T^{8} + 9791032230816 T^{9} - 347423504794624 T^{10} + 2649303176415616 T^{11} + 694517140133881240 T^{12} - 20658732330776531008 T^{13} +$$$$19\!\cdots\!28$$$$T^{14} +$$$$11\!\cdots\!40$$$$T^{15} -$$$$82\!\cdots\!10$$$$T^{16} +$$$$96\!\cdots\!40$$$$T^{17} +$$$$13\!\cdots\!68$$$$T^{18} -$$$$12\!\cdots\!68$$$$T^{19} +$$$$34\!\cdots\!40$$$$T^{20} +$$$$11\!\cdots\!16$$$$T^{21} -$$$$12\!\cdots\!84$$$$T^{22} +$$$$29\!\cdots\!96$$$$T^{23} +$$$$12\!\cdots\!80$$$$T^{24} -$$$$53\!\cdots\!36$$$$T^{25} +$$$$53\!\cdots\!76$$$$T^{26} +$$$$30\!\cdots\!72$$$$T^{27} -$$$$19\!\cdots\!04$$$$T^{28} +$$$$19\!\cdots\!28$$$$T^{29} +$$$$45\!\cdots\!32$$$$T^{30} -$$$$23\!\cdots\!32$$$$T^{31} +$$$$62\!\cdots\!41$$$$T^{32}$$)
$31$ ($$1 - 3846 T^{2} + 7131791 T^{4} - 8361808916 T^{6} + 6586358756111 T^{8} - 3280218929998086 T^{10} + 787662783788549761 T^{12}$$)($$1 - 3846 T^{2} + 7131791 T^{4} - 8361808916 T^{6} + 6586358756111 T^{8} - 3280218929998086 T^{10} + 787662783788549761 T^{12}$$)($$1 - 7312 T^{2} + 29025544 T^{4} - 80335806576 T^{6} + 171125889681052 T^{8} - 295006946315669072 T^{10} +$$$$42\!\cdots\!64$$$$T^{12} -$$$$51\!\cdots\!00$$$$T^{14} +$$$$53\!\cdots\!38$$$$T^{16} -$$$$47\!\cdots\!00$$$$T^{18} +$$$$36\!\cdots\!24$$$$T^{20} -$$$$23\!\cdots\!92$$$$T^{22} +$$$$12\!\cdots\!12$$$$T^{24} -$$$$53\!\cdots\!76$$$$T^{26} +$$$$18\!\cdots\!24$$$$T^{28} -$$$$41\!\cdots\!92$$$$T^{30} +$$$$52\!\cdots\!61$$$$T^{32}$$)($$( 1 - 3656 T^{2} + 7444644 T^{4} - 10749322008 T^{6} + 11704860550022 T^{8} - 9927224610150168 T^{10} + 6349470144538916004 T^{12} -$$$$28\!\cdots\!16$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 3656 T^{2} + 7444644 T^{4} - 10749322008 T^{6} + 11704860550022 T^{8} - 9927224610150168 T^{10} + 6349470144538916004 T^{12} -$$$$28\!\cdots\!16$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16} )^{2}$$)($$1 - 7312 T^{2} + 29025544 T^{4} - 80335806576 T^{6} + 171125889681052 T^{8} - 295006946315669072 T^{10} +$$$$42\!\cdots\!64$$$$T^{12} -$$$$51\!\cdots\!00$$$$T^{14} +$$$$53\!\cdots\!38$$$$T^{16} -$$$$47\!\cdots\!00$$$$T^{18} +$$$$36\!\cdots\!24$$$$T^{20} -$$$$23\!\cdots\!92$$$$T^{22} +$$$$12\!\cdots\!12$$$$T^{24} -$$$$53\!\cdots\!76$$$$T^{26} +$$$$18\!\cdots\!24$$$$T^{28} -$$$$41\!\cdots\!92$$$$T^{30} +$$$$52\!\cdots\!61$$$$T^{32}$$)
$37$ ($$1 + 46 T + 1058 T^{2} - 6594 T^{3} - 356337 T^{4} + 78343460 T^{5} + 4002544124 T^{6} + 107252196740 T^{7} - 667832908257 T^{8} - 16918399940946 T^{9} + 3716203262248418 T^{10} + 221194881131221054 T^{11} + 6582952005840035281 T^{12}$$)($$1 + 46 T + 1058 T^{2} - 6594 T^{3} - 356337 T^{4} + 78343460 T^{5} + 4002544124 T^{6} + 107252196740 T^{7} - 667832908257 T^{8} - 16918399940946 T^{9} + 3716203262248418 T^{10} + 221194881131221054 T^{11} + 6582952005840035281 T^{12}$$)($$1 - 96 T + 4608 T^{2} - 145952 T^{3} + 4040888 T^{4} - 217733344 T^{5} + 12932982272 T^{6} - 602883756192 T^{7} + 21839639792924 T^{8} - 655265530977504 T^{9} + 21703692469355008 T^{10} - 815191556064282016 T^{11} + 35433653736114978312 T^{12} -$$$$14\!\cdots\!40$$$$T^{13} +$$$$50\!\cdots\!52$$$$T^{14} -$$$$14\!\cdots\!84$$$$T^{15} +$$$$43\!\cdots\!90$$$$T^{16} -$$$$20\!\cdots\!96$$$$T^{17} +$$$$95\!\cdots\!72$$$$T^{18} -$$$$37\!\cdots\!60$$$$T^{19} +$$$$12\!\cdots\!52$$$$T^{20} -$$$$39\!\cdots\!84$$$$T^{21} +$$$$14\!\cdots\!48$$$$T^{22} -$$$$59\!\cdots\!56$$$$T^{23} +$$$$26\!\cdots\!84$$$$T^{24} -$$$$10\!\cdots\!68$$$$T^{25} +$$$$29\!\cdots\!72$$$$T^{26} -$$$$68\!\cdots\!36$$$$T^{27} +$$$$17\!\cdots\!68$$$$T^{28} -$$$$86\!\cdots\!68$$$$T^{29} +$$$$37\!\cdots\!68$$$$T^{30} -$$$$10\!\cdots\!04$$$$T^{31} +$$$$15\!\cdots\!81$$$$T^{32}$$)($$( 1 + 48 T + 1152 T^{2} + 50960 T^{3} - 719780 T^{4} - 84286160 T^{5} - 1918088320 T^{6} - 86111407472 T^{7} - 3715717913082 T^{8} - 117886516829168 T^{9} - 3594806323899520 T^{10} - 216255226625199440 T^{11} - 2528212461343257380 T^{12} +$$$$24\!\cdots\!40$$$$T^{13} +$$$$75\!\cdots\!12$$$$T^{14} +$$$$43\!\cdots\!72$$$$T^{15} +$$$$12\!\cdots\!41$$$$T^{16} )^{2}$$)($$( 1 + 48 T + 1152 T^{2} + 50960 T^{3} - 719780 T^{4} - 84286160 T^{5} - 1918088320 T^{6} - 86111407472 T^{7} - 3715717913082 T^{8} - 117886516829168 T^{9} - 3594806323899520 T^{10} - 216255226625199440 T^{11} - 2528212461343257380 T^{12} +$$$$24\!\cdots\!40$$$$T^{13} +$$$$75\!\cdots\!12$$$$T^{14} +$$$$43\!\cdots\!72$$$$T^{15} +$$$$12\!\cdots\!41$$$$T^{16} )^{2}$$)($$1 - 96 T + 4608 T^{2} - 145952 T^{3} + 4040888 T^{4} - 217733344 T^{5} + 12932982272 T^{6} - 602883756192 T^{7} + 21839639792924 T^{8} - 655265530977504 T^{9} + 21703692469355008 T^{10} - 815191556064282016 T^{11} + 35433653736114978312 T^{12} -$$$$14\!\cdots\!40$$$$T^{13} +$$$$50\!\cdots\!52$$$$T^{14} -$$$$14\!\cdots\!84$$$$T^{15} +$$$$43\!\cdots\!90$$$$T^{16} -$$$$20\!\cdots\!96$$$$T^{17} +$$$$95\!\cdots\!72$$$$T^{18} -$$$$37\!\cdots\!60$$$$T^{19} +$$$$12\!\cdots\!52$$$$T^{20} -$$$$39\!\cdots\!84$$$$T^{21} +$$$$14\!\cdots\!48$$$$T^{22} -$$$$59\!\cdots\!56$$$$T^{23} +$$$$26\!\cdots\!84$$$$T^{24} -$$$$10\!\cdots\!68$$$$T^{25} +$$$$29\!\cdots\!72$$$$T^{26} -$$$$68\!\cdots\!36$$$$T^{27} +$$$$17\!\cdots\!68$$$$T^{28} -$$$$86\!\cdots\!68$$$$T^{29} +$$$$37\!\cdots\!68$$$$T^{30} -$$$$10\!\cdots\!04$$$$T^{31} +$$$$15\!\cdots\!81$$$$T^{32}$$)
$41$ ($$1 - 5094 T^{2} + 15050223 T^{4} - 31243096276 T^{6} + 42528333194703 T^{8} - 40675209117142374 T^{10} + 22563490300366186081 T^{12}$$)($$1 - 5094 T^{2} + 15050223 T^{4} - 31243096276 T^{6} + 42528333194703 T^{8} - 40675209117142374 T^{10} + 22563490300366186081 T^{12}$$)($$1 - 13840 T^{2} + 102706104 T^{4} - 524939980080 T^{6} + 2044068651261084 T^{8} - 6376104819902485008 T^{10} +$$$$16\!\cdots\!68$$$$T^{12} -$$$$35\!\cdots\!72$$$$T^{14} +$$$$64\!\cdots\!06$$$$T^{16} -$$$$99\!\cdots\!92$$$$T^{18} +$$$$13\!\cdots\!28$$$$T^{20} -$$$$14\!\cdots\!48$$$$T^{22} +$$$$13\!\cdots\!44$$$$T^{24} -$$$$94\!\cdots\!80$$$$T^{26} +$$$$52\!\cdots\!44$$$$T^{28} -$$$$19\!\cdots\!40$$$$T^{30} +$$$$40\!\cdots\!81$$$$T^{32}$$)($$( 1 - 6200 T^{2} + 18860092 T^{4} - 40121913352 T^{6} + 71431934605958 T^{8} - 113374937995460872 T^{10} +$$$$15\!\cdots\!32$$$$T^{12} -$$$$13\!\cdots\!00$$$$T^{14} +$$$$63\!\cdots\!41$$$$T^{16} )^{2}$$)($$( 1 - 6200 T^{2} + 18860092 T^{4} - 40121913352 T^{6} + 71431934605958 T^{8} - 113374937995460872 T^{10} +$$$$15\!\cdots\!32$$$$T^{12} -$$$$13\!\cdots\!00$$$$T^{14} +$$$$63\!\cdots\!41$$$$T^{16} )^{2}$$)($$1 - 13840 T^{2} + 102706104 T^{4} - 524939980080 T^{6} + 2044068651261084 T^{8} - 6376104819902485008 T^{10} +$$$$16\!\cdots\!68$$$$T^{12} -$$$$35\!\cdots\!72$$$$T^{14} +$$$$64\!\cdots\!06$$$$T^{16} -$$$$99\!\cdots\!92$$$$T^{18} +$$$$13\!\cdots\!28$$$$T^{20} -$$$$14\!\cdots\!48$$$$T^{22} +$$$$13\!\cdots\!44$$$$T^{24} -$$$$94\!\cdots\!80$$$$T^{26} +$$$$52\!\cdots\!44$$$$T^{28} -$$$$19\!\cdots\!40$$$$T^{30} +$$$$40\!\cdots\!81$$$$T^{32}$$)
$43$ ($$1 - 114 T + 6498 T^{2} - 241730 T^{3} + 12357983 T^{4} - 838941724 T^{5} + 44553879452 T^{6} - 1551203247676 T^{7} + 42249484638383 T^{8} - 1528063089834770 T^{9} + 75949925403851298 T^{10} - 2463708983714404386 T^{11} + 39959630797262576401 T^{12}$$)($$1 + 114 T + 6498 T^{2} + 241730 T^{3} + 12357983 T^{4} + 838941724 T^{5} + 44553879452 T^{6} + 1551203247676 T^{7} + 42249484638383 T^{8} + 1528063089834770 T^{9} + 75949925403851298 T^{10} + 2463708983714404386 T^{11} + 39959630797262576401 T^{12}$$)($$1 - 160 T + 12800 T^{2} - 978464 T^{3} + 71106632 T^{4} - 3813053664 T^{5} + 178619596288 T^{6} - 8719368905312 T^{7} + 336417491247900 T^{8} - 9339737479444512 T^{9} + 288453906337733120 T^{10} - 7137460469658328480 T^{11} -$$$$12\!\cdots\!76$$$$T^{12} +$$$$13\!\cdots\!84$$$$T^{13} -$$$$44\!\cdots\!20$$$$T^{14} +$$$$28\!\cdots\!76$$$$T^{15} -$$$$17\!\cdots\!30$$$$T^{16} +$$$$53\!\cdots\!24$$$$T^{17} -$$$$15\!\cdots\!20$$$$T^{18} +$$$$83\!\cdots\!16$$$$T^{19} -$$$$15\!\cdots\!76$$$$T^{20} -$$$$15\!\cdots\!20$$$$T^{21} +$$$$11\!\cdots\!20$$$$T^{22} -$$$$69\!\cdots\!88$$$$T^{23} +$$$$45\!\cdots\!00$$$$T^{24} -$$$$22\!\cdots\!88$$$$T^{25} +$$$$83\!\cdots\!88$$$$T^{26} -$$$$32\!\cdots\!36$$$$T^{27} +$$$$11\!\cdots\!32$$$$T^{28} -$$$$28\!\cdots\!36$$$$T^{29} +$$$$69\!\cdots\!00$$$$T^{30} -$$$$16\!\cdots\!40$$$$T^{31} +$$$$18\!\cdots\!01$$$$T^{32}$$)($$( 1 + 16 T + 128 T^{2} + 120528 T^{3} - 217180 T^{4} - 199455632 T^{5} + 4100008320 T^{6} - 63109389264 T^{7} - 21163084456442 T^{8} - 116689260749136 T^{9} + 14017112544424320 T^{10} - 1260831462039741968 T^{11} - 2538443336289385180 T^{12} +$$$$26\!\cdots\!72$$$$T^{13} +$$$$51\!\cdots\!28$$$$T^{14} +$$$$11\!\cdots\!84$$$$T^{15} +$$$$13\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 16 T + 128 T^{2} - 120528 T^{3} - 217180 T^{4} + 199455632 T^{5} + 4100008320 T^{6} + 63109389264 T^{7} - 21163084456442 T^{8} + 116689260749136 T^{9} + 14017112544424320 T^{10} + 1260831462039741968 T^{11} - 2538443336289385180 T^{12} -$$$$26\!\cdots\!72$$$$T^{13} +$$$$51\!\cdots\!28$$$$T^{14} -$$$$11\!\cdots\!84$$$$T^{15} +$$$$13\!\cdots\!01$$$$T^{16} )^{2}$$)($$1 + 160 T + 12800 T^{2} + 978464 T^{3} + 71106632 T^{4} + 3813053664 T^{5} + 178619596288 T^{6} + 8719368905312 T^{7} + 336417491247900 T^{8} + 9339737479444512 T^{9} + 288453906337733120 T^{10} + 7137460469658328480 T^{11} -$$$$12\!\cdots\!76$$$$T^{12} -$$$$13\!\cdots\!84$$$$T^{13} -$$$$44\!\cdots\!20$$$$T^{14} -$$$$28\!\cdots\!76$$$$T^{15} -$$$$17\!\cdots\!30$$$$T^{16} -$$$$53\!\cdots\!24$$$$T^{17} -$$$$15\!\cdots\!20$$$$T^{18} -$$$$83\!\cdots\!16$$$$T^{19} -$$$$15\!\cdots\!76$$$$T^{20} +$$$$15\!\cdots\!20$$$$T^{21} +$$$$11\!\cdots\!20$$$$T^{22} +$$$$69\!\cdots\!88$$$$T^{23} +$$$$45\!\cdots\!00$$$$T^{24} +$$$$22\!\cdots\!88$$$$T^{25} +$$$$83\!\cdots\!88$$$$T^{26} +$$$$32\!\cdots\!36$$$$T^{27} +$$$$11\!\cdots\!32$$$$T^{28} +$$$$28\!\cdots\!36$$$$T^{29} +$$$$69\!\cdots\!00$$$$T^{30} +$$$$16\!\cdots\!40$$$$T^{31} +$$$$18\!\cdots\!01$$$$T^{32}$$)
$47$ ($$1 - 4678 T^{2} + 12462287 T^{4} - 24905944212 T^{6} + 60811985090447 T^{8} - 111389199003717958 T^{10} +$$$$11\!\cdots\!41$$$$T^{12}$$)($$1 - 4678 T^{2} + 12462287 T^{4} - 24905944212 T^{6} + 60811985090447 T^{8} - 111389199003717958 T^{10} +$$$$11\!\cdots\!41$$$$T^{12}$$)($$1 - 24144 T^{2} + 280869112 T^{4} - 2097883923184 T^{6} + 11327375509374492 T^{8} - 47271044690493269328 T^{10} +$$$$15\!\cdots\!16$$$$T^{12} -$$$$44\!\cdots\!04$$$$T^{14} +$$$$10\!\cdots\!58$$$$T^{16} -$$$$21\!\cdots\!24$$$$T^{18} +$$$$37\!\cdots\!76$$$$T^{20} -$$$$54\!\cdots\!48$$$$T^{22} +$$$$64\!\cdots\!32$$$$T^{24} -$$$$58\!\cdots\!84$$$$T^{26} +$$$$37\!\cdots\!72$$$$T^{28} -$$$$15\!\cdots\!84$$$$T^{30} +$$$$32\!\cdots\!41$$$$T^{32}$$)($$( 1 - 6312 T^{2} + 26526428 T^{4} - 83137920920 T^{6} + 212859158930374 T^{8} - 405686533092826520 T^{10} +$$$$63\!\cdots\!08$$$$T^{12} -$$$$73\!\cdots\!92$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 6312 T^{2} + 26526428 T^{4} - 83137920920 T^{6} + 212859158930374 T^{8} - 405686533092826520 T^{10} +$$$$63\!\cdots\!08$$$$T^{12} -$$$$73\!\cdots\!92$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16} )^{2}$$)($$1 - 24144 T^{2} + 280869112 T^{4} - 2097883923184 T^{6} + 11327375509374492 T^{8} - 47271044690493269328 T^{10} +$$$$15\!\cdots\!16$$$$T^{12} -$$$$44\!\cdots\!04$$$$T^{14} +$$$$10\!\cdots\!58$$$$T^{16} -$$$$21\!\cdots\!24$$$$T^{18} +$$$$37\!\cdots\!76$$$$T^{20} -$$$$54\!\cdots\!48$$$$T^{22} +$$$$64\!\cdots\!32$$$$T^{24} -$$$$58\!\cdots\!84$$$$T^{26} +$$$$37\!\cdots\!72$$$$T^{28} -$$$$15\!\cdots\!84$$$$T^{30} +$$$$32\!\cdots\!41$$$$T^{32}$$)
$53$ ($$1 - 78 T + 3042 T^{2} - 270110 T^{3} + 31648463 T^{4} - 1389102820 T^{5} + 48555101564 T^{6} - 3901989821380 T^{7} + 249721595980703 T^{8} - 5986815584554190 T^{9} + 189393978231360162 T^{10} - 13641222688510017822 T^{11} +$$$$49\!\cdots\!41$$$$T^{12}$$)($$1 - 78 T + 3042 T^{2} - 270110 T^{3} + 31648463 T^{4} - 1389102820 T^{5} + 48555101564 T^{6} - 3901989821380 T^{7} + 249721595980703 T^{8} - 5986815584554190 T^{9} + 189393978231360162 T^{10} - 13641222688510017822 T^{11} +$$$$49\!\cdots\!41$$$$T^{12}$$)($$1 + 160 T + 12800 T^{2} + 602944 T^{3} + 3948712 T^{4} - 1481707264 T^{5} - 105845942272 T^{6} - 3791430241760 T^{7} + 34861972067036 T^{8} + 14471440004155872 T^{9} + 1098860393015073792 T^{10} + 54880211634179791488 T^{11} +$$$$13\!\cdots\!12$$$$T^{12} -$$$$17\!\cdots\!00$$$$T^{13} -$$$$18\!\cdots\!48$$$$T^{14} +$$$$16\!\cdots\!08$$$$T^{15} +$$$$51\!\cdots\!54$$$$T^{16} +$$$$46\!\cdots\!72$$$$T^{17} -$$$$14\!\cdots\!88$$$$T^{18} -$$$$38\!\cdots\!00$$$$T^{19} +$$$$84\!\cdots\!32$$$$T^{20} +$$$$95\!\cdots\!12$$$$T^{21} +$$$$53\!\cdots\!72$$$$T^{22} +$$$$19\!\cdots\!68$$$$T^{23} +$$$$13\!\cdots\!56$$$$T^{24} -$$$$41\!\cdots\!40$$$$T^{25} -$$$$32\!\cdots\!72$$$$T^{26} -$$$$12\!\cdots\!76$$$$T^{27} +$$$$95\!\cdots\!72$$$$T^{28} +$$$$40\!\cdots\!76$$$$T^{29} +$$$$24\!\cdots\!00$$$$T^{30} +$$$$85\!\cdots\!40$$$$T^{31} +$$$$15\!\cdots\!41$$$$T^{32}$$)($$1 - 41116504 T^{4} + 844846897443036 T^{8} -$$$$11\!\cdots\!20$$$$T^{12} +$$$$10\!\cdots\!98$$$$T^{16} -$$$$69\!\cdots\!20$$$$T^{20} +$$$$32\!\cdots\!56$$$$T^{24} -$$$$99\!\cdots\!24$$$$T^{28} +$$$$15\!\cdots\!41$$$$T^{32}$$)($$1 - 41116504 T^{4} + 844846897443036 T^{8} -$$$$11\!\cdots\!20$$$$T^{12} +$$$$10\!\cdots\!98$$$$T^{16} -$$$$69\!\cdots\!20$$$$T^{20} +$$$$32\!\cdots\!56$$$$T^{24} -$$$$99\!\cdots\!24$$$$T^{28} +$$$$15\!\cdots\!41$$$$T^{32}$$)($$1 + 160 T + 12800 T^{2} + 602944 T^{3} + 3948712 T^{4} - 1481707264 T^{5} - 105845942272 T^{6} - 3791430241760 T^{7} + 34861972067036 T^{8} + 14471440004155872 T^{9} + 1098860393015073792 T^{10} + 54880211634179791488 T^{11} +$$$$13\!\cdots\!12$$$$T^{12} -$$$$17\!\cdots\!00$$$$T^{13} -$$$$18\!\cdots\!48$$$$T^{14} +$$$$16\!\cdots\!08$$$$T^{15} +$$$$51\!\cdots\!54$$$$T^{16} +$$$$46\!\cdots\!72$$$$T^{17} -$$$$14\!\cdots\!88$$$$T^{18} -$$$$38\!\cdots\!00$$$$T^{19} +$$$$84\!\cdots\!32$$$$T^{20} +$$$$95\!\cdots\!12$$$$T^{21} +$$$$53\!\cdots\!72$$$$T^{22} +$$$$19\!\cdots\!68$$$$T^{23} +$$$$13\!\cdots\!56$$$$T^{24} -$$$$41\!\cdots\!40$$$$T^{25} -$$$$32\!\cdots\!72$$$$T^{26} -$$$$12\!\cdots\!76$$$$T^{27} +$$$$95\!\cdots\!72$$$$T^{28} +$$$$40\!\cdots\!76$$$$T^{29} +$$$$24\!\cdots\!00$$$$T^{30} +$$$$85\!\cdots\!40$$$$T^{31} +$$$$15\!\cdots\!41$$$$T^{32}$$)
$59$ ($$1 - 206 T + 21218 T^{2} - 1942462 T^{3} + 171214239 T^{4} - 11916831972 T^{5} + 708622973852 T^{6} - 41482492094532 T^{7} + 2074664742303279 T^{8} - 81934083737364142 T^{9} + 3115448225088482978 T^{10} -$$$$10\!\cdots\!06$$$$T^{11} +$$$$17\!\cdots\!81$$$$T^{12}$$)($$1 + 206 T + 21218 T^{2} + 1942462 T^{3} + 171214239 T^{4} + 11916831972 T^{5} + 708622973852 T^{6} + 41482492094532 T^{7} + 2074664742303279 T^{8} + 81934083737364142 T^{9} + 3115448225088482978 T^{10} +$$$$10\!\cdots\!06$$$$T^{11} +$$$$17\!\cdots\!81$$$$T^{12}$$)($$1 - 128 T + 8192 T^{2} - 1121408 T^{3} + 136226184 T^{4} - 9279937408 T^{5} + 700645040128 T^{6} - 71627082366848 T^{7} + 5234572115355804 T^{8} - 316007889653226112 T^{9} + 25502997282495045632 T^{10} -$$$$19\!\cdots\!80$$$$T^{11} +$$$$10\!\cdots\!40$$$$T^{12} -$$$$69\!\cdots\!16$$$$T^{13} +$$$$51\!\cdots\!56$$$$T^{14} -$$$$29\!\cdots\!24$$$$T^{15} +$$$$15\!\cdots\!38$$$$T^{16} -$$$$10\!\cdots\!44$$$$T^{17} +$$$$62\!\cdots\!16$$$$T^{18} -$$$$29\!\cdots\!56$$$$T^{19} +$$$$16\!\cdots\!40$$$$T^{20} -$$$$98\!\cdots\!80$$$$T^{21} +$$$$45\!\cdots\!92$$$$T^{22} -$$$$19\!\cdots\!32$$$$T^{23} +$$$$11\!\cdots\!64$$$$T^{24} -$$$$53\!\cdots\!08$$$$T^{25} +$$$$18\!\cdots\!28$$$$T^{26} -$$$$84\!\cdots\!48$$$$T^{27} +$$$$43\!\cdots\!24$$$$T^{28} -$$$$12\!\cdots\!28$$$$T^{29} +$$$$31\!\cdots\!32$$$$T^{30} -$$$$17\!\cdots\!28$$$$T^{31} +$$$$46\!\cdots\!81$$$$T^{32}$$)($$1 - 11621240 T^{4} - 131007530650980 T^{8} +$$$$57\!\cdots\!44$$$$T^{12} +$$$$25\!\cdots\!66$$$$T^{16} +$$$$84\!\cdots\!24$$$$T^{20} -$$$$28\!\cdots\!80$$$$T^{24} -$$$$36\!\cdots\!40$$$$T^{28} +$$$$46\!\cdots\!81$$$$T^{32}$$)($$1 - 11621240 T^{4} - 131007530650980 T^{8} +$$$$57\!\cdots\!44$$$$T^{12} +$$$$25\!\cdots\!66$$$$T^{16} +$$$$84\!\cdots\!24$$$$T^{20} -$$$$28\!\cdots\!80$$$$T^{24} -$$$$36\!\cdots\!40$$$$T^{28} +$$$$46\!\cdots\!81$$$$T^{32}$$)($$1 + 128 T + 8192 T^{2} + 1121408 T^{3} + 136226184 T^{4} + 9279937408 T^{5} + 700645040128 T^{6} + 71627082366848 T^{7} + 5234572115355804 T^{8} + 316007889653226112 T^{9} + 25502997282495045632 T^{10} +$$$$19\!\cdots\!80$$$$T^{11} +$$$$10\!\cdots\!40$$$$T^{12} +$$$$69\!\cdots\!16$$$$T^{13} +$$$$51\!\cdots\!56$$$$T^{14} +$$$$29\!\cdots\!24$$$$T^{15} +$$$$15\!\cdots\!38$$$$T^{16} +$$$$10\!\cdots\!44$$$$T^{17} +$$$$62\!\cdots\!16$$$$T^{18} +$$$$29\!\cdots\!56$$$$T^{19} +$$$$16\!\cdots\!40$$$$T^{20} +$$$$98\!\cdots\!80$$$$T^{21} +$$$$45\!\cdots\!92$$$$T^{22} +$$$$19\!\cdots\!32$$$$T^{23} +$$$$11\!\cdots\!64$$$$T^{24} +$$$$53\!\cdots\!08$$$$T^{25} +$$$$18\!\cdots\!28$$$$T^{26} +$$$$84\!\cdots\!48$$$$T^{27} +$$$$43\!\cdots\!24$$$$T^{28} +$$$$12\!\cdots\!28$$$$T^{29} +$$$$31\!\cdots\!32$$$$T^{30} +$$$$17\!\cdots\!28$$$$T^{31} +$$$$46\!\cdots\!81$$$$T^{32}$$)
$61$ ($$1 + 30 T + 450 T^{2} + 111694 T^{3} + 33268655 T^{4} + 582006980 T^{5} + 8727089468 T^{6} + 2165647972580 T^{7} + 460632507413855 T^{8} + 5754516693877534 T^{9} + 86268290848776450 T^{10} + 21400287349886478030 T^{11} +$$$$26\!\cdots\!21$$$$T^{12}$$)($$1 + 30 T + 450 T^{2} + 111694 T^{3} + 33268655 T^{4} + 582006980 T^{5} + 8727089468 T^{6} + 2165647972580 T^{7} + 460632507413855 T^{8} + 5754516693877534 T^{9} + 86268290848776450 T^{10} + 21400287349886478030 T^{11} +$$$$26\!\cdots\!21$$$$T^{12}$$)($$1 - 32 T + 512 T^{2} + 38048 T^{3} - 60439624 T^{4} + 1520787552 T^{5} - 16996289024 T^{6} - 2981900088544 T^{7} + 2018049968078364 T^{8} - 40394929489472928 T^{9} + 275088896591278592 T^{10} +$$$$10\!\cdots\!56$$$$T^{11} -$$$$45\!\cdots\!20$$$$T^{12} +$$$$71\!\cdots\!16$$$$T^{13} -$$$$18\!\cdots\!28$$$$T^{14} -$$$$23\!\cdots\!64$$$$T^{15} +$$$$72\!\cdots\!42$$$$T^{16} -$$$$88\!\cdots\!44$$$$T^{17} -$$$$26\!\cdots\!48$$$$T^{18} +$$$$36\!\cdots\!76$$$$T^{19} -$$$$86\!\cdots\!20$$$$T^{20} +$$$$75\!\cdots\!56$$$$T^{21} +$$$$73\!\cdots\!32$$$$T^{22} -$$$$39\!\cdots\!48$$$$T^{23} +$$$$74\!\cdots\!04$$$$T^{24} -$$$$40\!\cdots\!64$$$$T^{25} -$$$$86\!\cdots\!24$$$$T^{26} +$$$$28\!\cdots\!92$$$$T^{27} -$$$$42\!\cdots\!84$$$$T^{28} +$$$$99\!\cdots\!28$$$$T^{29} +$$$$49\!\cdots\!72$$$$T^{30} -$$$$11\!\cdots\!32$$$$T^{31} +$$$$13\!\cdots\!21$$$$T^{32}$$)($$( 1 - 16 T + 128 T^{2} - 6576 T^{3} - 8849956 T^{4} + 175483376 T^{5} - 1653317760 T^{6} + 420993646800 T^{7} - 32622960575354 T^{8} + 1566517359742800 T^{9} - 22891574827436160 T^{10} + 9040969225652122736 T^{11} -$$$$16\!\cdots\!36$$$$T^{12} -$$$$46\!\cdots\!76$$$$T^{13} +$$$$33\!\cdots\!88$$$$T^{14} -$$$$15\!\cdots\!56$$$$T^{15} +$$$$36\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 - 16 T + 128 T^{2} - 6576 T^{3} - 8849956 T^{4} + 175483376 T^{5} - 1653317760 T^{6} + 420993646800 T^{7} - 32622960575354 T^{8} + 1566517359742800 T^{9} - 22891574827436160 T^{10} + 9040969225652122736 T^{11} -$$$$16\!\cdots\!36$$$$T^{12} -$$$$46\!\cdots\!76$$$$T^{13} +$$$$33\!\cdots\!88$$$$T^{14} -$$$$15\!\cdots\!56$$$$T^{15} +$$$$36\!\cdots\!61$$$$T^{16} )^{2}$$)($$1 - 32 T + 512 T^{2} + 38048 T^{3} - 60439624 T^{4} + 1520787552 T^{5} - 16996289024 T^{6} - 2981900088544 T^{7} + 2018049968078364 T^{8} - 40394929489472928 T^{9} + 275088896591278592 T^{10} +$$$$10\!\cdots\!56$$$$T^{11} -$$$$45\!\cdots\!20$$$$T^{12} +$$$$71\!\cdots\!16$$$$T^{13} -$$$$18\!\cdots\!28$$$$T^{14} -$$$$23\!\cdots\!64$$$$T^{15} +$$$$72\!\cdots\!42$$$$T^{16} -$$$$88\!\cdots\!44$$$$T^{17} -$$$$26\!\cdots\!48$$$$T^{18} +$$$$36\!\cdots\!76$$$$T^{19} -$$$$86\!\cdots\!20$$$$T^{20} +$$$$75\!\cdots\!56$$$$T^{21} +$$$$73\!\cdots\!32$$$$T^{22} -$$$$39\!\cdots\!48$$$$T^{23} +$$$$74\!\cdots\!04$$$$T^{24} -$$$$40\!\cdots\!64$$$$T^{25} -$$$$86\!\cdots\!24$$$$T^{26} +$$$$28\!\cdots\!92$$$$T^{27} -$$$$42\!\cdots\!84$$$$T^{28} +$$$$99\!\cdots\!28$$$$T^{29} +$$$$49\!\cdots\!72$$$$T^{30} -$$$$11\!\cdots\!32$$$$T^{31} +$$$$13\!\cdots\!21$$$$T^{32}$$)
$67$ ($$1 - 226 T + 25538 T^{2} - 2083538 T^{3} + 120508479 T^{4} - 5203289532 T^{5} + 268963196252 T^{6} - 23357566709148 T^{7} + 2428380941854959 T^{8} - 188473476667633922 T^{9} + 10370156349441497858 T^{10} -$$$$41\!\cdots\!74$$$$T^{11} +$$$$81\!\cdots\!61$$$$T^{12}$$)($$1 + 226 T + 25538 T^{2} + 2083538 T^{3} + 120508479 T^{4} + 5203289532 T^{5} + 268963196252 T^{6} + 23357566709148 T^{7} + 2428380941854959 T^{8} + 188473476667633922 T^{9} + 10370156349441497858 T^{10} +$$$$41\!\cdots\!74$$$$T^{11} +$$$$81\!\cdots\!61$$$$T^{12}$$)($$1 - 320 T + 51200 T^{2} - 6047552 T^{3} + 641735304 T^{4} - 64228593856 T^{5} + 5982745065472 T^{6} - 525110406070976 T^{7} + 43992629224199580 T^{8} - 3502096836597496384 T^{9} +$$$$26\!\cdots\!12$$$$T^{10} -$$$$19\!\cdots\!80$$$$T^{11} +$$$$14\!\cdots\!20$$$$T^{12} -$$$$10\!\cdots\!88$$$$T^{13} +$$$$71\!\cdots\!04$$$$T^{14} -$$$$48\!\cdots\!52$$$$T^{15} +$$$$32\!\cdots\!74$$$$T^{16} -$$$$21\!\cdots\!28$$$$T^{17} +$$$$14\!\cdots\!84$$$$T^{18} -$$$$93\!\cdots\!72$$$$T^{19} +$$$$58\!\cdots\!20$$$$T^{20} -$$$$36\!\cdots\!20$$$$T^{21} +$$$$21\!\cdots\!32$$$$T^{22} -$$$$12\!\cdots\!36$$$$T^{23} +$$$$72\!\cdots\!80$$$$T^{24} -$$$$38\!\cdots\!84$$$$T^{25} +$$$$19\!\cdots\!72$$$$T^{26} -$$$$95\!\cdots\!84$$$$T^{27} +$$$$42\!\cdots\!84$$$$T^{28} -$$$$18\!\cdots\!88$$$$T^{29} +$$$$69\!\cdots\!00$$$$T^{30} -$$$$19\!\cdots\!80$$$$T^{31} +$$$$27\!\cdots\!61$$$$T^{32}$$)($$( 1 + 128 T + 8192 T^{2} + 693376 T^{3} + 50920004 T^{4} + 2251590016 T^{5} + 111451987968 T^{6} + 7277319415168 T^{7} + 468898776356806 T^{8} + 32667886854689152 T^{9} + 2245882495233712128 T^{10} +$$$$20\!\cdots\!04$$$$T^{11} +$$$$20\!\cdots\!64$$$$T^{12} +$$$$12\!\cdots\!24$$$$T^{13} +$$$$67\!\cdots\!12$$$$T^{14} +$$$$47\!\cdots\!12$$$$T^{15} +$$$$16\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 128 T + 8192 T^{2} - 693376 T^{3} + 50920004 T^{4} - 2251590016 T^{5} + 111451987968 T^{6} - 7277319415168 T^{7} + 468898776356806 T^{8} - 32667886854689152 T^{9} + 2245882495233712128 T^{10} -$$$$20\!\cdots\!04$$$$T^{11} +$$$$20\!\cdots\!64$$$$T^{12} -$$$$12\!\cdots\!24$$$$T^{13} +$$$$67\!\cdots\!12$$$$T^{14} -$$$$47\!\cdots\!12$$$$T^{15} +$$$$16\!\cdots\!81$$$$T^{16} )^{2}$$)($$1 + 320 T + 51200 T^{2} + 6047552 T^{3} + 641735304 T^{4} + 64228593856 T^{5} + 5982745065472 T^{6} + 525110406070976 T^{7} + 43992629224199580 T^{8} + 3502096836597496384 T^{9} +$$$$26\!\cdots\!12$$$$T^{10} +$$$$19\!\cdots\!80$$$$T^{11} +$$$$14\!\cdots\!20$$$$T^{12} +$$$$10\!\cdots\!88$$$$T^{13} +$$$$71\!\cdots\!04$$$$T^{14} +$$$$48\!\cdots\!52$$$$T^{15} +$$$$32\!\cdots\!74$$$$T^{16} +$$$$21\!\cdots\!28$$$$T^{17} +$$$$14\!\cdots\!84$$$$T^{18} +$$$$93\!\cdots\!72$$$$T^{19} +$$$$58\!\cdots\!20$$$$T^{20} +$$$$36\!\cdots\!20$$$$T^{21} +$$$$21\!\cdots\!32$$$$T^{22} +$$$$12\!\cdots\!36$$$$T^{23} +$$$$72\!\cdots\!80$$$$T^{24} +$$$$38\!\cdots\!84$$$$T^{25} +$$$$19\!\cdots\!72$$$$T^{26} +$$$$95\!\cdots\!84$$$$T^{27} +$$$$42\!\cdots\!84$$$$T^{28} +$$$$18\!\cdots\!88$$$$T^{29} +$$$$69\!\cdots\!00$$$$T^{30} +$$$$19\!\cdots\!80$$$$T^{31} +$$$$27\!\cdots\!61$$$$T^{32}$$)
$71$ ($$( 1 - 130 T + 11575 T^{2} - 918796 T^{3} + 58349575 T^{4} - 3303518530 T^{5} + 128100283921 T^{6} )^{2}$$)($$( 1 + 130 T + 11575 T^{2} + 918796 T^{3} + 58349575 T^{4} + 3303518530 T^{5} + 128100283921 T^{6} )^{2}$$)($$( 1 - 256 T + 68104 T^{2} - 10692864 T^{3} + 1610923548 T^{4} - 179723087616 T^{5} + 18972832358712 T^{6} - 1588998739085056 T^{7} + 125568612540426694 T^{8} - 8010142643727767296 T^{9} +$$$$48\!\cdots\!72$$$$T^{10} -$$$$23\!\cdots\!36$$$$T^{11} +$$$$10\!\cdots\!28$$$$T^{12} -$$$$34\!\cdots\!64$$$$T^{13} +$$$$11\!\cdots\!64$$$$T^{14} -$$$$21\!\cdots\!36$$$$T^{15} +$$$$41\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 + 776 T^{2} + 40385436 T^{4} - 127559387592 T^{6} + 690614216465094 T^{8} - 3241498466043262152 T^{10} +$$$$26\!\cdots\!96$$$$T^{12} +$$$$12\!\cdots\!16$$$$T^{14} +$$$$41\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 + 776 T^{2} + 40385436 T^{4} - 127559387592 T^{6} + 690614216465094 T^{8} - 3241498466043262152 T^{10} +$$$$26\!\cdots\!96$$$$T^{12} +$$$$12\!\cdots\!16$$$$T^{14} +$$$$41\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 + 256 T + 68104 T^{2} + 10692864 T^{3} + 1610923548 T^{4} + 179723087616 T^{5} + 18972832358712 T^{6} + 1588998739085056 T^{7} + 125568612540426694 T^{8} + 8010142643727767296 T^{9} +$$$$48\!\cdots\!72$$$$T^{10} +$$$$23\!\cdots\!36$$$$T^{11} +$$$$10\!\cdots\!28$$$$T^{12} +$$$$34\!\cdots\!64$$$$T^{13} +$$$$11\!\cdots\!64$$$$T^{14} +$$$$21\!\cdots\!36$$$$T^{15} +$$$$41\!\cdots\!21$$$$T^{16} )^{2}$$)
$73$ ($$1 - 13126 T^{2} + 103571951 T^{4} - 653716749588 T^{6} + 2941261225338191 T^{8} - 10585595166201707206 T^{10} +$$$$22\!\cdots\!21$$$$T^{12}$$)($$1 - 13126 T^{2} + 103571951 T^{4} - 653716749588 T^{6} + 2941261225338191 T^{8} - 10585595166201707206 T^{10} +$$$$22\!\cdots\!21$$$$T^{12}$$)($$1 - 42768 T^{2} + 946714744 T^{4} - 14391245893936 T^{6} + 167549428359087132 T^{8} -$$$$15\!\cdots\!24$$$$T^{10} +$$$$12\!\cdots\!76$$$$T^{12} -$$$$83\!\cdots\!96$$$$T^{14} +$$$$47\!\cdots\!22$$$$T^{16} -$$$$23\!\cdots\!36$$$$T^{18} +$$$$10\!\cdots\!56$$$$T^{20} -$$$$36\!\cdots\!04$$$$T^{22} +$$$$10\!\cdots\!52$$$$T^{24} -$$$$26\!\cdots\!36$$$$T^{26} +$$$$49\!\cdots\!04$$$$T^{28} -$$$$63\!\cdots\!08$$$$T^{30} +$$$$42\!\cdots\!21$$$$T^{32}$$)($$( 1 - 22536 T^{2} + 300646172 T^{4} - 2600139782456 T^{6} + 16379358145749190 T^{8} - 73839396175873059896 T^{10} +$$$$24\!\cdots\!32$$$$T^{12} -$$$$51\!\cdots\!56$$$$T^{14} +$$$$65\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 - 22536 T^{2} + 300646172 T^{4} - 2600139782456 T^{6} + 16379358145749190 T^{8} - 73839396175873059896 T^{10} +$$$$24\!\cdots\!32$$$$T^{12} -$$$$51\!\cdots\!56$$$$T^{14} +$$$$65\!\cdots\!61$$$$T^{16} )^{2}$$)($$1 - 42768 T^{2} + 946714744 T^{4} - 14391245893936 T^{6} + 167549428359087132 T^{8} -$$$$15\!\cdots\!24$$$$T^{10} +$$$$12\!\cdots\!76$$$$T^{12} -$$$$83\!\cdots\!96$$$$T^{14} +$$$$47\!\cdots\!22$$$$T^{16} -$$$$23\!\cdots\!36$$$$T^{18} +$$$$10\!\cdots\!56$$$$T^{20} -$$$$36\!\cdots\!04$$$$T^{22} +$$$$10\!\cdots\!52$$$$T^{24} -$$$$26\!\cdots\!36$$$$T^{26} +$$$$49\!\cdots\!04$$$$T^{28} -$$$$63\!\cdots\!08$$$$T^{30} +$$$$42\!\cdots\!21$$$$T^{32}$$)
$79$ ($$1 - 70 T^{2} + 84324175 T^{4} + 17226941804 T^{6} + 3284433446508175 T^{8} - 106197616693459270 T^{10} +$$$$59\!\cdots\!41$$$$T^{12}$$)($$1 - 70 T^{2} + 84324175 T^{4} + 17226941804 T^{6} + 3284433446508175 T^{8} - 106197616693459270 T^{10} +$$$$59\!\cdots\!41$$$$T^{12}$$)($$1 - 62928 T^{2} + 1905826568 T^{4} - 37296559235888 T^{6} + 534425714020543644 T^{8} -$$$$60\!\cdots\!08$$$$T^{10} +$$$$55\!\cdots\!96$$$$T^{12} -$$$$43\!\cdots\!36$$$$T^{14} +$$$$29\!\cdots\!62$$$$T^{16} -$$$$16\!\cdots\!16$$$$T^{18} +$$$$84\!\cdots\!56$$$$T^{20} -$$$$35\!\cdots\!28$$$$T^{22} +$$$$12\!\cdots\!24$$$$T^{24} -$$$$33\!\cdots\!88$$$$T^{26} +$$$$66\!\cdots\!08$$$$T^{28} -$$$$85\!\cdots\!08$$$$T^{30} +$$$$52\!\cdots\!41$$$$T^{32}$$)($$( 1 - 35304 T^{2} + 608675620 T^{4} - 6614894483704 T^{6} + 49280941921260934 T^{8} -$$$$25\!\cdots\!24$$$$T^{10} +$$$$92\!\cdots\!20$$$$T^{12} -$$$$20\!\cdots\!64$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 35304 T^{2} + 608675620 T^{4} - 6614894483704 T^{6} + 49280941921260934 T^{8} -$$$$25\!\cdots\!24$$$$T^{10} +$$$$92\!\cdots\!20$$$$T^{12} -$$$$20\!\cdots\!64$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16} )^{2}$$)($$1 - 62928 T^{2} + 1905826568 T^{4} - 37296559235888 T^{6} + 534425714020543644 T^{8} -$$$$60\!\cdots\!08$$$$T^{10} +$$$$55\!\cdots\!96$$$$T^{12} -$$$$43\!\cdots\!36$$$$T^{14} +$$$$29\!\cdots\!62$$$$T^{16} -$$$$16\!\cdots\!16$$$$T^{18} +$$$$84\!\cdots\!56$$$$T^{20} -$$$$35\!\cdots\!28$$$$T^{22} +$$$$12\!\cdots\!24$$$$T^{24} -$$$$33\!\cdots\!88$$$$T^{26} +$$$$66\!\cdots\!08$$$$T^{28} -$$$$85\!\cdots\!08$$$$T^{30} +$$$$52\!\cdots\!41$$$$T^{32}$$)
$83$ ($$1 - 318 T + 50562 T^{2} - 6712846 T^{3} + 819490815 T^{4} - 81203275140 T^{5} + 6918697616348 T^{6} - 559409362439460 T^{7} + 38891658154821615 T^{8} - 2194700377608598174 T^{9} +$$$$11\!\cdots\!42$$$$T^{10} -$$$$49\!\cdots\!82$$$$T^{11} +$$$$10\!\cdots\!61$$$$T^{12}$$)($$1 + 318 T + 50562 T^{2} + 6712846 T^{3} + 819490815 T^{4} + 81203275140 T^{5} + 6918697616348 T^{6} + 559409362439460 T^{7} + 38891658154821615 T^{8} + 2194700377608598174 T^{9} +$$$$11\!\cdots\!42$$$$T^{10} +$$$$49\!\cdots\!82$$$$T^{11} +$$$$10\!\cdots\!61$$$$T^{12}$$)($$1 - 160 T + 12800 T^{2} - 895904 T^{3} + 107479624 T^{4} - 16432771168 T^{5} + 1654826188288 T^{6} - 174484645067104 T^{7} + 18280323695716892 T^{8} - 1483531366054758688 T^{9} +$$$$11\!\cdots\!96$$$$T^{10} -$$$$11\!\cdots\!36$$$$T^{11} +$$$$13\!\cdots\!00$$$$T^{12} -$$$$12\!\cdots\!44$$$$T^{13} +$$$$89\!\cdots\!76$$$$T^{14} -$$$$74\!\cdots\!76$$$$T^{15} +$$$$61\!\cdots\!66$$$$T^{16} -$$$$51\!\cdots\!64$$$$T^{17} +$$$$42\!\cdots\!96$$$$T^{18} -$$$$39\!\cdots\!36$$$$T^{19} +$$$$30\!\cdots\!00$$$$T^{20} -$$$$17\!\cdots\!64$$$$T^{21} +$$$$12\!\cdots\!56$$$$T^{22} -$$$$10\!\cdots\!52$$$$T^{23} +$$$$92\!\cdots\!52$$$$T^{24} -$$$$60\!\cdots\!36$$$$T^{25} +$$$$39\!\cdots\!88$$$$T^{26} -$$$$27\!\cdots\!52$$$$T^{27} +$$$$12\!\cdots\!04$$$$T^{28} -$$$$70\!\cdots\!76$$$$T^{29} +$$$$69\!\cdots\!00$$$$T^{30} -$$$$59\!\cdots\!40$$$$T^{31} +$$$$25\!\cdots\!61$$$$T^{32}$$)($$1 - 47654840 T^{4} - 1328477750370788 T^{8} +$$$$67\!\cdots\!96$$$$T^{12} +$$$$24\!\cdots\!06$$$$T^{16} +$$$$15\!\cdots\!36$$$$T^{20} -$$$$67\!\cdots\!28$$$$T^{24} -$$$$54\!\cdots\!40$$$$T^{28} +$$$$25\!\cdots\!61$$$$T^{32}$$)($$1 - 47654840 T^{4} - 1328477750370788 T^{8} +$$$$67\!\cdots\!96$$$$T^{12} +$$$$24\!\cdots\!06$$$$T^{16} +$$$$15\!\cdots\!36$$$$T^{20} -$$$$67\!\cdots\!28$$$$T^{24} -$$$$54\!\cdots\!40$$$$T^{28} +$$$$25\!\cdots\!61$$$$T^{32}$$)($$1 + 160 T + 12800 T^{2} + 895904 T^{3} + 107479624 T^{4} + 16432771168 T^{5} + 1654826188288 T^{6} + 174484645067104 T^{7} + 18280323695716892 T^{8} + 1483531366054758688 T^{9} +$$$$11\!\cdots\!96$$$$T^{10} +$$$$11\!\cdots\!36$$$$T^{11} +$$$$13\!\cdots\!00$$$$T^{12} +$$$$12\!\cdots\!44$$$$T^{13} +$$$$89\!\cdots\!76$$$$T^{14} +$$$$74\!\cdots\!76$$$$T^{15} +$$$$61\!\cdots\!66$$$$T^{16} +$$$$51\!\cdots\!64$$$$T^{17} +$$$$42\!\cdots\!96$$$$T^{18} +$$$$39\!\cdots\!36$$$$T^{19} +$$$$30\!\cdots\!00$$$$T^{20} +$$$$17\!\cdots\!64$$$$T^{21} +$$$$12\!\cdots\!56$$$$T^{22} +$$$$10\!\cdots\!52$$$$T^{23} +$$$$92\!\cdots\!52$$$$T^{24} +$$$$60\!\cdots\!36$$$$T^{25} +$$$$39\!\cdots\!88$$$$T^{26} +$$$$27\!\cdots\!52$$$$T^{27} +$$$$12\!\cdots\!04$$$$T^{28} +$$$$70\!\cdots\!76$$$$T^{29} +$$$$69\!\cdots\!00$$$$T^{30} +$$$$59\!\cdots\!40$$$$T^{31} +$$$$25\!\cdots\!61$$$$T^{32}$$)
$89$ ($$1 - 31238 T^{2} + 466178479 T^{4} - 4433595811988 T^{6} + 29249082478431439 T^{8} -$$$$12\!\cdots\!78$$$$T^{10} +$$$$24\!\cdots\!21$$$$T^{12}$$)($$1 - 31238 T^{2} + 466178479 T^{4} - 4433595811988 T^{6} + 29249082478431439 T^{8} -$$$$12\!\cdots\!78$$$$T^{10} +$$$$24\!\cdots\!21$$$$T^{12}$$)($$1 - 81008 T^{2} + 3201135736 T^{4} - 82544801381712 T^{6} + 1567286911309649436 T^{8} -$$$$23\!\cdots\!04$$$$T^{10} +$$$$28\!\cdots\!72$$$$T^{12} -$$$$29\!\cdots\!36$$$$T^{14} +$$$$25\!\cdots\!10$$$$T^{16} -$$$$18\!\cdots\!76$$$$T^{18} +$$$$11\!\cdots\!32$$$$T^{20} -$$$$57\!\cdots\!84$$$$T^{22} +$$$$24\!\cdots\!96$$$$T^{24} -$$$$80\!\cdots\!12$$$$T^{26} +$$$$19\!\cdots\!76$$$$T^{28} -$$$$31\!\cdots\!48$$$$T^{30} +$$$$24\!\cdots\!21$$$$T^{32}$$)($$( 1 - 17608 T^{2} + 140263452 T^{4} - 1652317947000 T^{6} + 18439815418282950 T^{8} -$$$$10\!\cdots\!00$$$$T^{10} +$$$$55\!\cdots\!12$$$$T^{12} -$$$$43\!\cdots\!68$$$$T^{14} +$$$$15\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 - 17608 T^{2} + 140263452 T^{4} - 1652317947000 T^{6} + 18439815418282950 T^{8} -$$$$10\!\cdots\!00$$$$T^{10} +$$$$55\!\cdots\!12$$$$T^{12} -$$$$43\!\cdots\!68$$$$T^{14} +$$$$15\!\cdots\!61$$$$T^{16} )^{2}$$)($$1 - 81008 T^{2} + 3201135736 T^{4} - 82544801381712 T^{6} + 1567286911309649436 T^{8} -$$$$23\!\cdots\!04$$$$T^{10} +$$$$28\!\cdots\!72$$$$T^{12} -$$$$29\!\cdots\!36$$$$T^{14} +$$$$25\!\cdots\!10$$$$T^{16} -$$$$18\!\cdots\!76$$$$T^{18} +$$$$11\!\cdots\!32$$$$T^{20} -$$$$57\!\cdots\!84$$$$T^{22} +$$$$24\!\cdots\!96$$$$T^{24} -$$$$80\!\cdots\!12$$$$T^{26} +$$$$19\!\cdots\!76$$$$T^{28} -$$$$31\!\cdots\!48$$$$T^{30} +$$$$24\!\cdots\!21$$$$T^{32}$$)
$97$ ($$( 1 + 2 T + 10687 T^{2} + 557564 T^{3} + 100553983 T^{4} + 177058562 T^{5} + 832972004929 T^{6} )^{2}$$)($$( 1 + 2 T + 10687 T^{2} + 557564 T^{3} + 100553983 T^{4} + 177058562 T^{5} + 832972004929 T^{6} )^{2}$$)($$( 1 + 38216 T^{2} + 116224 T^{3} + 770481564 T^{4} + 3485408768 T^{5} + 10857255215864 T^{6} + 49274039499776 T^{7} + 116292098553803590 T^{8} + 463619437653392384 T^{9} +$$$$96\!\cdots\!84$$$$T^{10} +$$$$29\!\cdots\!72$$$$T^{11} +$$$$60\!\cdots\!04$$$$T^{12} +$$$$85\!\cdots\!76$$$$T^{13} +$$$$26\!\cdots\!56$$$$T^{14} +$$$$61\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 + 25252 T^{2} - 77824 T^{3} + 327999814 T^{4} - 732246016 T^{5} + 2235541403812 T^{6} + 7837433594376961 T^{8} )^{4}$$)($$( 1 + 25252 T^{2} - 77824 T^{3} + 327999814 T^{4} - 732246016 T^{5} + 2235541403812 T^{6} + 7837433594376961 T^{8} )^{4}$$)($$( 1 + 38216 T^{2} + 116224 T^{3} + 770481564 T^{4} + 3485408768 T^{5} + 10857255215864 T^{6} + 49274039499776 T^{7} + 116292098553803590 T^{8} + 463619437653392384 T^{9} +$$$$96\!\cdots\!84$$$$T^{10} +$$$$29\!\cdots\!72$$$$T^{11} +$$$$60\!\cdots\!04$$$$T^{12} +$$$$85\!\cdots\!76$$$$T^{13} +$$$$26\!\cdots\!56$$$$T^{14} +$$$$61\!\cdots\!21$$$$T^{16} )^{2}$$)