# Properties

 Label 324.5 Level 324 Weight 5 Dimension 5320 Nonzero newspaces 8 Sturm bound 29160 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$324\( 324 = 2^{2} \cdot 3^{4}$$ \) Weight: $$k$$ = $$5$$ Nonzero newspaces: $$8$$ Sturm bound: $$29160$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(324))$$.

Total New Old
Modular forms 11934 5432 6502
Cusp forms 11394 5320 6074
Eisenstein series 540 112 428

## Trace form

 $$5320q - 12q^{2} - 20q^{4} - 33q^{5} - 18q^{6} - 39q^{7} - 15q^{8} - 36q^{9} + O(q^{10})$$ $$5320q - 12q^{2} - 20q^{4} - 33q^{5} - 18q^{6} - 39q^{7} - 15q^{8} - 36q^{9} - 61q^{10} - 18q^{11} - 18q^{12} + 215q^{13} + 843q^{14} + 352q^{16} - 30q^{17} - 18q^{18} - 1332q^{19} - 1965q^{20} + 2259q^{21} - 1128q^{22} + 4275q^{23} - 18q^{24} + 411q^{25} + 4701q^{26} - 1431q^{27} - 105q^{28} - 4263q^{29} - 18q^{30} - 2781q^{31} - 4962q^{32} - 3249q^{33} - 1114q^{34} + 5346q^{35} - 18q^{36} + 2576q^{37} + 6066q^{38} + 9305q^{40} + 10560q^{41} + 18297q^{42} + 864q^{43} - 6063q^{44} - 11268q^{45} - 25497q^{46} - 23895q^{47} - 35163q^{48} - 1865q^{49} - 55122q^{50} - 12348q^{51} - 7021q^{52} + 6q^{53} + 13464q^{54} + 9414q^{55} + 72081q^{56} + 21132q^{57} + 36881q^{58} + 41940q^{59} + 58131q^{60} + 17039q^{61} + 51069q^{62} + 14040q^{63} - 4439q^{64} + 19911q^{65} - 34650q^{66} - 22878q^{67} - 115764q^{68} - 47484q^{69} - 23193q^{70} - 19764q^{71} - 18q^{72} - 7651q^{73} - 6801q^{74} - 56250q^{75} + 17070q^{76} - 39993q^{77} - 747q^{78} + 10353q^{79} + 63966q^{80} + 11556q^{81} + 37406q^{82} + 53973q^{83} - 747q^{84} - 12992q^{85} + 2544q^{86} + 126000q^{87} - 45444q^{88} + 149631q^{89} - 116757q^{90} + 10713q^{91} - 122187q^{92} + 33516q^{93} - 13767q^{94} - 115632q^{95} + 91359q^{96} - 36862q^{97} + 235965q^{98} - 169380q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(324))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
324.5.c $$\chi_{324}(161, \cdot)$$ 324.5.c.a 8 1
324.5.c.b 8
324.5.d $$\chi_{324}(163, \cdot)$$ 324.5.d.a 2 1
324.5.d.b 2
324.5.d.c 10
324.5.d.d 10
324.5.d.e 22
324.5.d.f 22
324.5.d.g 24
324.5.f $$\chi_{324}(55, \cdot)$$ n/a 188 2
324.5.g $$\chi_{324}(53, \cdot)$$ 324.5.g.a 2 2
324.5.g.b 2
324.5.g.c 4
324.5.g.d 4
324.5.g.e 4
324.5.g.f 16
324.5.j $$\chi_{324}(19, \cdot)$$ n/a 420 6
324.5.k $$\chi_{324}(17, \cdot)$$ 324.5.k.a 72 6
324.5.n $$\chi_{324}(7, \cdot)$$ n/a 3852 18
324.5.o $$\chi_{324}(5, \cdot)$$ n/a 648 18

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{5}^{\mathrm{old}}(\Gamma_1(324))$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(\Gamma_1(324)) \cong$$ $$S_{5}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 5}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 8}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 9}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 6}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 3}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 4}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 3}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 2}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$( 1 + 4 T )^{2}$$)($$( 1 - 4 T )^{2}$$)($$1 + 11 T + 78 T^{2} + 412 T^{3} + 1832 T^{4} + 7440 T^{5} + 29312 T^{6} + 105472 T^{7} + 319488 T^{8} + 720896 T^{9} + 1048576 T^{10}$$)($$1 - 11 T + 78 T^{2} - 412 T^{3} + 1832 T^{4} - 7440 T^{5} + 29312 T^{6} - 105472 T^{7} + 319488 T^{8} - 720896 T^{9} + 1048576 T^{10}$$)
$3$ 1
$5$ ($$1 - 2147 T^{2} + 2477509 T^{4} - 2147976218 T^{6} + 1511855308306 T^{8} - 839053210156250 T^{10} + 378037872314453125 T^{12} -$$$$12\!\cdots\!75$$$$T^{14} +$$$$23\!\cdots\!25$$$$T^{16}$$)($$1 - 2336 T^{2} + 3413950 T^{4} - 3293143040 T^{6} + 2404523790019 T^{8} - 1286384000000000 T^{10} + 520927429199218750 T^{12} -$$$$13\!\cdots\!00$$$$T^{14} +$$$$23\!\cdots\!25$$$$T^{16}$$)($$1 - 14 T - 429 T^{2} - 8750 T^{3} + 390625 T^{4}$$)($$1 + 14 T - 429 T^{2} + 8750 T^{3} + 390625 T^{4}$$)($$( 1 - T + 1659 T^{2} - 6218 T^{3} + 1302341 T^{4} - 7050267 T^{5} + 813963125 T^{6} - 2428906250 T^{7} + 405029296875 T^{8} - 152587890625 T^{9} + 95367431640625 T^{10} )^{2}$$)($$( 1 + T + 1659 T^{2} + 6218 T^{3} + 1302341 T^{4} + 7050267 T^{5} + 813963125 T^{6} + 2428906250 T^{7} + 405029296875 T^{8} + 152587890625 T^{9} + 95367431640625 T^{10} )^{2}$$)($$( 1 - 25 T + 625 T^{2} )( 1 + 25 T + 625 T^{2} )$$)($$( 1 - 25 T + 625 T^{2} )( 1 + 25 T + 625 T^{2} )$$)($$1 - 208 T^{2} - 347361 T^{4} - 81250000 T^{6} + 152587890625 T^{8}$$)($$1 + 1169 T^{2} + 975936 T^{4} + 456640625 T^{6} + 152587890625 T^{8}$$)($$1 - 694 T^{2} + 91011 T^{4} - 271093750 T^{6} + 152587890625 T^{8}$$)($$1 + 2336 T^{2} + 2042946 T^{4} + 1388701120 T^{6} + 1557748671041 T^{8} + 1295074534439232 T^{10} + 672728923363514050 T^{12} +$$$$49\!\cdots\!60$$$$T^{14} +$$$$39\!\cdots\!36$$$$T^{16} +$$$$19\!\cdots\!00$$$$T^{18} +$$$$10\!\cdots\!50$$$$T^{20} +$$$$77\!\cdots\!00$$$$T^{22} +$$$$36\!\cdots\!25$$$$T^{24} +$$$$12\!\cdots\!00$$$$T^{26} +$$$$72\!\cdots\!50$$$$T^{28} +$$$$32\!\cdots\!00$$$$T^{30} +$$$$54\!\cdots\!25$$$$T^{32}$$)
$7$ ($$( 1 + 13 T + 4723 T^{2} + 93076 T^{3} + 12134350 T^{4} + 223475476 T^{5} + 27227155123 T^{6} + 179936733613 T^{7} + 33232930569601 T^{8} )^{2}$$)($$( 1 - 26 T + 4282 T^{2} - 214310 T^{3} + 11854978 T^{4} - 514558310 T^{5} + 24684877882 T^{6} - 359873467226 T^{7} + 33232930569601 T^{8} )^{2}$$)($$( 1 - 49 T )^{2}( 1 + 49 T )^{2}$$)($$( 1 - 49 T )^{2}( 1 + 49 T )^{2}$$)($$1 - 8290 T^{2} + 44254557 T^{4} - 163560113592 T^{6} + 493650399199842 T^{8} - 1256885499793177548 T^{10} +$$$$28\!\cdots\!42$$$$T^{12} -$$$$54\!\cdots\!92$$$$T^{14} +$$$$84\!\cdots\!57$$$$T^{16} -$$$$91\!\cdots\!90$$$$T^{18} +$$$$63\!\cdots\!01$$$$T^{20}$$)($$1 - 8290 T^{2} + 44254557 T^{4} - 163560113592 T^{6} + 493650399199842 T^{8} - 1256885499793177548 T^{10} +$$$$28\!\cdots\!42$$$$T^{12} -$$$$54\!\cdots\!92$$$$T^{14} +$$$$84\!\cdots\!57$$$$T^{16} -$$$$91\!\cdots\!90$$$$T^{18} +$$$$63\!\cdots\!01$$$$T^{20}$$)($$( 1 - 71 T + 2401 T^{2} )( 1 + 94 T + 2401 T^{2} )$$)($$( 1 - 71 T + 2401 T^{2} )( 1 - 23 T + 2401 T^{2} )$$)($$( 1 + 68 T + 2223 T^{2} + 163268 T^{3} + 5764801 T^{4} )^{2}$$)($$( 1 + 5 T - 2376 T^{2} + 12005 T^{3} + 5764801 T^{4} )^{2}$$)($$( 1 - 31 T - 1440 T^{2} - 74431 T^{3} + 5764801 T^{4} )^{2}$$)($$( 1 + 26 T - 3606 T^{2} - 317288 T^{3} + 908486 T^{4} + 815774874 T^{5} + 31157000008 T^{6} - 864356739502 T^{7} - 89954645400189 T^{8} - 2075320531544302 T^{9} + 179613904803118408 T^{10} + 11291374322393587674 T^{11} + 30191652161454534086 T^{12} -$$$$25\!\cdots\!88$$$$T^{13} -$$$$69\!\cdots\!06$$$$T^{14} +$$$$11\!\cdots\!26$$$$T^{15} +$$$$11\!\cdots\!01$$$$T^{16} )^{2}$$)
$11$ ($$1 - 67376 T^{2} + 2511150250 T^{4} - 60712318203824 T^{6} + 1049763807787064539 T^{8} -$$$$13\!\cdots\!44$$$$T^{10} +$$$$11\!\cdots\!50$$$$T^{12} -$$$$66\!\cdots\!16$$$$T^{14} +$$$$21\!\cdots\!21$$$$T^{16}$$)($$1 - 51068 T^{2} + 1609814488 T^{4} - 35017149442772 T^{6} + 585430682946749806 T^{8} -$$$$75\!\cdots\!32$$$$T^{10} +$$$$73\!\cdots\!68$$$$T^{12} -$$$$50\!\cdots\!88$$$$T^{14} +$$$$21\!\cdots\!21$$$$T^{16}$$)($$( 1 - 121 T )^{2}( 1 + 121 T )^{2}$$)($$( 1 - 121 T )^{2}( 1 + 121 T )^{2}$$)($$1 - 54562 T^{2} + 1881197565 T^{4} - 46664469100728 T^{6} + 904347180647259234 T^{8} -$$$$14\!\cdots\!52$$$$T^{10} +$$$$19\!\cdots\!54$$$$T^{12} -$$$$21\!\cdots\!08$$$$T^{14} +$$$$18\!\cdots\!65$$$$T^{16} -$$$$11\!\cdots\!02$$$$T^{18} +$$$$45\!\cdots\!01$$$$T^{20}$$)($$1 - 54562 T^{2} + 1881197565 T^{4} - 46664469100728 T^{6} + 904347180647259234 T^{8} -$$$$14\!\cdots\!52$$$$T^{10} +$$$$19\!\cdots\!54$$$$T^{12} -$$$$21\!\cdots\!08$$$$T^{14} +$$$$18\!\cdots\!65$$$$T^{16} -$$$$11\!\cdots\!02$$$$T^{18} +$$$$45\!\cdots\!01$$$$T^{20}$$)($$( 1 - 121 T + 14641 T^{2} )( 1 + 121 T + 14641 T^{2} )$$)($$( 1 - 121 T + 14641 T^{2} )( 1 + 121 T + 14641 T^{2} )$$)($$1 + 5954 T^{2} - 178908765 T^{4} + 1276292777474 T^{6} + 45949729863572161 T^{8}$$)($$1 + 15593 T^{2} + 28782768 T^{4} + 3342498031433 T^{6} + 45949729863572161 T^{8}$$)($$1 - 19318 T^{2} + 158826243 T^{4} - 4140984863158 T^{6} + 45949729863572161 T^{8}$$)($$1 + 51068 T^{2} + 998126136 T^{4} + 12175707387640 T^{6} + 217816215084471842 T^{8} +$$$$40\!\cdots\!52$$$$T^{10} +$$$$48\!\cdots\!16$$$$T^{12} +$$$$61\!\cdots\!12$$$$T^{14} +$$$$10\!\cdots\!95$$$$T^{16} +$$$$13\!\cdots\!72$$$$T^{18} +$$$$22\!\cdots\!76$$$$T^{20} +$$$$40\!\cdots\!32$$$$T^{22} +$$$$45\!\cdots\!82$$$$T^{24} +$$$$55\!\cdots\!40$$$$T^{26} +$$$$96\!\cdots\!16$$$$T^{28} +$$$$10\!\cdots\!48$$$$T^{30} +$$$$44\!\cdots\!41$$$$T^{32}$$)
$13$ ($$( 1 - 5 T + 42079 T^{2} - 3738530 T^{3} + 1399773016 T^{4} - 106776155330 T^{5} + 34325133008959 T^{6} - 116490425612405 T^{7} + 665416609183179841 T^{8} )^{2}$$)($$( 1 - 110 T + 50350 T^{2} - 3749312 T^{3} + 1512180355 T^{4} - 107084100032 T^{5} + 41072041802350 T^{6} - 2562789363472910 T^{7} + 665416609183179841 T^{8} )^{2}$$)($$1 - 238 T + 28083 T^{2} - 6797518 T^{3} + 815730721 T^{4}$$)($$1 - 238 T + 28083 T^{2} - 6797518 T^{3} + 815730721 T^{4}$$)($$( 1 + 89 T + 64683 T^{2} + 4875402 T^{3} + 1741550373 T^{4} + 151839904563 T^{5} + 49740420203253 T^{6} + 3977015188624842 T^{7} + 1506990039977438523 T^{8} + 59222078217303005849 T^{9} +$$$$19\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 + 89 T + 64683 T^{2} + 4875402 T^{3} + 1741550373 T^{4} + 151839904563 T^{5} + 49740420203253 T^{6} + 3977015188624842 T^{7} + 1506990039977438523 T^{8} + 59222078217303005849 T^{9} +$$$$19\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 146 T + 28561 T^{2} )( 1 + 337 T + 28561 T^{2} )$$)($$( 1 - 191 T + 28561 T^{2} )( 1 + 337 T + 28561 T^{2} )$$)($$( 1 - 16 T - 28305 T^{2} - 456976 T^{3} + 815730721 T^{4} )^{2}$$)($$( 1 - 34 T - 27405 T^{2} - 971074 T^{3} + 815730721 T^{4} )^{2}$$)($$( 1 - 241 T + 29520 T^{2} - 6883201 T^{3} + 815730721 T^{4} )^{2}$$)($$( 1 + 110 T - 38250 T^{2} - 1960124 T^{3} + 610517825 T^{4} - 36817718868 T^{5} + 8283892200274 T^{6} + 1966981039674770 T^{7} - 284382529178714100 T^{8} + 56178945474151105970 T^{9} +$$$$67\!\cdots\!54$$$$T^{10} -$$$$85\!\cdots\!08$$$$T^{11} +$$$$40\!\cdots\!25$$$$T^{12} -$$$$37\!\cdots\!24$$$$T^{13} -$$$$20\!\cdots\!50$$$$T^{14} +$$$$17\!\cdots\!10$$$$T^{15} +$$$$44\!\cdots\!81$$$$T^{16} )^{2}$$)
$17$ ($$1 - 288125 T^{2} + 52320681154 T^{4} - 6759733382202755 T^{6} +$$$$63\!\cdots\!86$$$$T^{8} -$$$$47\!\cdots\!55$$$$T^{10} +$$$$25\!\cdots\!74$$$$T^{12} -$$$$97\!\cdots\!25$$$$T^{14} +$$$$23\!\cdots\!61$$$$T^{16}$$)($$1 - 581912 T^{2} + 154148002822 T^{4} - 24278327086299392 T^{6} +$$$$24\!\cdots\!83$$$$T^{8} -$$$$16\!\cdots\!72$$$$T^{10} +$$$$75\!\cdots\!82$$$$T^{12} -$$$$19\!\cdots\!52$$$$T^{14} +$$$$23\!\cdots\!61$$$$T^{16}$$)($$1 + 322 T + 20163 T^{2} + 26893762 T^{3} + 6975757441 T^{4}$$)($$1 - 322 T + 20163 T^{2} - 26893762 T^{3} + 6975757441 T^{4}$$)($$( 1 + 11 T + 230895 T^{2} + 8443618 T^{3} + 31163951597 T^{4} + 589404873693 T^{5} + 2602844401333037 T^{6} + 58900631092461538 T^{7} +$$$$13\!\cdots\!95$$$$T^{8} +$$$$53\!\cdots\!91$$$$T^{9} +$$$$40\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 11 T + 230895 T^{2} - 8443618 T^{3} + 31163951597 T^{4} - 589404873693 T^{5} + 2602844401333037 T^{6} - 58900631092461538 T^{7} +$$$$13\!\cdots\!95$$$$T^{8} -$$$$53\!\cdots\!91$$$$T^{9} +$$$$40\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 289 T )^{2}( 1 + 289 T )^{2}$$)($$( 1 - 289 T )^{2}( 1 + 289 T )^{2}$$)($$( 1 + 79360 T^{2} + 6975757441 T^{4} )^{2}$$)($$( 1 + 35458 T^{2} + 6975757441 T^{4} )^{2}$$)($$( 1 - 118442 T^{2} + 6975757441 T^{4} )^{2}$$)($$( 1 - 581912 T^{2} + 154148002822 T^{4} - 24278327086299392 T^{6} +$$$$24\!\cdots\!83$$$$T^{8} -$$$$16\!\cdots\!72$$$$T^{10} +$$$$75\!\cdots\!82$$$$T^{12} -$$$$19\!\cdots\!52$$$$T^{14} +$$$$23\!\cdots\!61$$$$T^{16} )^{2}$$)
$19$ ($$( 1 - 281 T + 110170 T^{2} + 68843041 T^{3} - 21846246566 T^{4} + 8971693946161 T^{5} + 1871079140226970 T^{6} - 621941492257591241 T^{7} +$$$$28\!\cdots\!81$$$$T^{8} )^{2}$$)($$( 1 + 154 T + 428050 T^{2} + 50927398 T^{3} + 78431447410 T^{4} + 6636909434758 T^{5} + 7269814159700050 T^{6} + 340850497536188794 T^{7} +$$$$28\!\cdots\!81$$$$T^{8} )^{2}$$)($$( 1 - 361 T )^{2}( 1 + 361 T )^{2}$$)($$( 1 - 361 T )^{2}( 1 + 361 T )^{2}$$)($$1 - 565858 T^{2} + 172733340861 T^{4} - 37140945268901304 T^{6} +$$$$62\!\cdots\!22$$$$T^{8} -$$$$87\!\cdots\!92$$$$T^{10} +$$$$10\!\cdots\!02$$$$T^{12} -$$$$10\!\cdots\!24$$$$T^{14} +$$$$84\!\cdots\!81$$$$T^{16} -$$$$47\!\cdots\!38$$$$T^{18} +$$$$14\!\cdots\!01$$$$T^{20}$$)($$1 - 565858 T^{2} + 172733340861 T^{4} - 37140945268901304 T^{6} +$$$$62\!\cdots\!22$$$$T^{8} -$$$$87\!\cdots\!92$$$$T^{10} +$$$$10\!\cdots\!02$$$$T^{12} -$$$$10\!\cdots\!24$$$$T^{14} +$$$$84\!\cdots\!81$$$$T^{16} -$$$$47\!\cdots\!38$$$$T^{18} +$$$$14\!\cdots\!01$$$$T^{20}$$)($$( 1 - 647 T + 130321 T^{2} )^{2}$$)($$( 1 + 46 T + 130321 T^{2} )^{2}$$)($$( 1 + 208 T + 130321 T^{2} )^{4}$$)($$( 1 + 64 T + 130321 T^{2} )^{4}$$)($$( 1 + 271 T + 130321 T^{2} )^{4}$$)($$( 1 + 154 T + 428050 T^{2} + 50927398 T^{3} + 78431447410 T^{4} + 6636909434758 T^{5} + 7269814159700050 T^{6} + 340850497536188794 T^{7} +$$$$28\!\cdots\!81$$$$T^{8} )^{4}$$)
$23$ ($$1 - 103955 T^{2} + 204060092029 T^{4} - 14985633296690750 T^{6} +$$$$21\!\cdots\!46$$$$T^{8} -$$$$11\!\cdots\!50$$$$T^{10} +$$$$12\!\cdots\!69$$$$T^{12} -$$$$49\!\cdots\!55$$$$T^{14} +$$$$37\!\cdots\!21$$$$T^{16}$$)($$1 - 1539572 T^{2} + 1071515224168 T^{4} - 464417540343703388 T^{6} +$$$$14\!\cdots\!66$$$$T^{8} -$$$$36\!\cdots\!28$$$$T^{10} +$$$$65\!\cdots\!48$$$$T^{12} -$$$$73\!\cdots\!52$$$$T^{14} +$$$$37\!\cdots\!21$$$$T^{16}$$)($$( 1 - 529 T )^{2}( 1 + 529 T )^{2}$$)($$( 1 - 529 T )^{2}( 1 + 529 T )^{2}$$)($$1 - 1697890 T^{2} + 1450407862749 T^{4} - 815636912959727544 T^{6} +$$$$33\!\cdots\!94$$$$T^{8} -$$$$10\!\cdots\!08$$$$T^{10} +$$$$26\!\cdots\!14$$$$T^{12} -$$$$50\!\cdots\!84$$$$T^{14} +$$$$69\!\cdots\!09$$$$T^{16} -$$$$63\!\cdots\!90$$$$T^{18} +$$$$29\!\cdots\!01$$$$T^{20}$$)($$1 - 1697890 T^{2} + 1450407862749 T^{4} - 815636912959727544 T^{6} +$$$$33\!\cdots\!94$$$$T^{8} -$$$$10\!\cdots\!08$$$$T^{10} +$$$$26\!\cdots\!14$$$$T^{12} -$$$$50\!\cdots\!84$$$$T^{14} +$$$$69\!\cdots\!09$$$$T^{16} -$$$$63\!\cdots\!90$$$$T^{18} +$$$$29\!\cdots\!01$$$$T^{20}$$)($$( 1 - 529 T + 279841 T^{2} )( 1 + 529 T + 279841 T^{2} )$$)($$( 1 - 529 T + 279841 T^{2} )( 1 + 529 T + 279841 T^{2} )$$)($$1 + 536354 T^{2} + 209364628035 T^{4} + 42002410199405474 T^{6} +$$$$61\!\cdots\!61$$$$T^{8}$$)($$1 + 185138 T^{2} - 44034906237 T^{4} + 14498339192953778 T^{6} +$$$$61\!\cdots\!61$$$$T^{8}$$)($$1 + 511082 T^{2} + 182893825443 T^{4} + 40023334979384042 T^{6} +$$$$61\!\cdots\!61$$$$T^{8}$$)($$1 + 1539572 T^{2} + 1298766719016 T^{4} + 720839756015369320 T^{6} +$$$$28\!\cdots\!22$$$$T^{8} +$$$$80\!\cdots\!08$$$$T^{10} +$$$$14\!\cdots\!36$$$$T^{12} +$$$$13\!\cdots\!08$$$$T^{14} +$$$$10\!\cdots\!95$$$$T^{16} +$$$$10\!\cdots\!48$$$$T^{18} +$$$$91\!\cdots\!96$$$$T^{20} +$$$$38\!\cdots\!28$$$$T^{22} +$$$$10\!\cdots\!62$$$$T^{24} +$$$$21\!\cdots\!20$$$$T^{26} +$$$$29\!\cdots\!96$$$$T^{28} +$$$$27\!\cdots\!92$$$$T^{30} +$$$$14\!\cdots\!41$$$$T^{32}$$)
$29$ ($$1 - 3708803 T^{2} + 6181658247973 T^{4} - 6420936064399980986 T^{6} +$$$$50\!\cdots\!30$$$$T^{8} -$$$$32\!\cdots\!46$$$$T^{10} +$$$$15\!\cdots\!33$$$$T^{12} -$$$$46\!\cdots\!43$$$$T^{14} +$$$$62\!\cdots\!41$$$$T^{16}$$)($$1 - 1716392 T^{2} + 2128658111734 T^{4} - 1990766770969759616 T^{6} +$$$$16\!\cdots\!35$$$$T^{8} -$$$$99\!\cdots\!76$$$$T^{10} +$$$$53\!\cdots\!14$$$$T^{12} -$$$$21\!\cdots\!52$$$$T^{14} +$$$$62\!\cdots\!41$$$$T^{16}$$)($$1 + 82 T - 700557 T^{2} + 57997042 T^{3} + 500246412961 T^{4}$$)($$1 - 82 T - 700557 T^{2} - 57997042 T^{3} + 500246412961 T^{4}$$)($$( 1 - 1033 T + 1999275 T^{2} - 1654294250 T^{3} + 2208839699237 T^{4} - 1496099818334019 T^{5} + 1562270351316044597 T^{6} -$$$$82\!\cdots\!50$$$$T^{7} +$$$$70\!\cdots\!75$$$$T^{8} -$$$$25\!\cdots\!93$$$$T^{9} +$$$$17\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 + 1033 T + 1999275 T^{2} + 1654294250 T^{3} + 2208839699237 T^{4} + 1496099818334019 T^{5} + 1562270351316044597 T^{6} +$$$$82\!\cdots\!50$$$$T^{7} +$$$$70\!\cdots\!75$$$$T^{8} +$$$$25\!\cdots\!93$$$$T^{9} +$$$$17\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 841 T + 707281 T^{2} )( 1 + 841 T + 707281 T^{2} )$$)($$( 1 - 841 T + 707281 T^{2} )( 1 + 841 T + 707281 T^{2} )$$)($$1 + 993200 T^{2} + 486199827039 T^{4} + 496844737352865200 T^{6} +$$$$25\!\cdots\!21$$$$T^{8}$$)($$1 + 286718 T^{2} - 418039201437 T^{4} + 143429651031351998 T^{6} +$$$$25\!\cdots\!21$$$$T^{8}$$)($$1 + 1220162 T^{2} + 988548893283 T^{4} + 610381663731319682 T^{6} +$$$$25\!\cdots\!21$$$$T^{8}$$)($$1 + 1716392 T^{2} + 817343385930 T^{4} - 327921788224175504 T^{6} -$$$$52\!\cdots\!51$$$$T^{8} -$$$$37\!\cdots\!20$$$$T^{10} -$$$$16\!\cdots\!98$$$$T^{12} +$$$$14\!\cdots\!32$$$$T^{14} +$$$$23\!\cdots\!60$$$$T^{16} +$$$$72\!\cdots\!52$$$$T^{18} -$$$$40\!\cdots\!58$$$$T^{20} -$$$$47\!\cdots\!20$$$$T^{22} -$$$$32\!\cdots\!91$$$$T^{24} -$$$$10\!\cdots\!04$$$$T^{26} +$$$$12\!\cdots\!30$$$$T^{28} +$$$$13\!\cdots\!32$$$$T^{30} +$$$$39\!\cdots\!81$$$$T^{32}$$)
$31$ ($$( 1 + 187 T + 2550973 T^{2} + 331939744 T^{3} + 3082958795560 T^{4} + 306553324318624 T^{5} + 2175702008453980093 T^{6} +$$$$14\!\cdots\!07$$$$T^{7} +$$$$72\!\cdots\!81$$$$T^{8} )^{2}$$)($$( 1 + 736 T + 1540120 T^{2} + 1931471584 T^{3} + 1422185749294 T^{4} + 1783754568727264 T^{5} + 1313554544583632920 T^{6} +$$$$57\!\cdots\!96$$$$T^{7} +$$$$72\!\cdots\!81$$$$T^{8} )^{2}$$)($$( 1 - 961 T )^{2}( 1 + 961 T )^{2}$$)($$( 1 - 961 T )^{2}( 1 + 961 T )^{2}$$)($$1 - 6281866 T^{2} + 18990861709101 T^{4} - 36759913337747332728 T^{6} +$$$$51\!\cdots\!10$$$$T^{8} -$$$$53\!\cdots\!24$$$$T^{10} +$$$$43\!\cdots\!10$$$$T^{12} -$$$$26\!\cdots\!68$$$$T^{14} +$$$$11\!\cdots\!21$$$$T^{16} -$$$$33\!\cdots\!26$$$$T^{18} +$$$$45\!\cdots\!01$$$$T^{20}$$)($$1 - 6281866 T^{2} + 18990861709101 T^{4} - 36759913337747332728 T^{6} +$$$$51\!\cdots\!10$$$$T^{8} -$$$$53\!\cdots\!24$$$$T^{10} +$$$$43\!\cdots\!10$$$$T^{12} -$$$$26\!\cdots\!68$$$$T^{14} +$$$$11\!\cdots\!21$$$$T^{16} -$$$$33\!\cdots\!26$$$$T^{18} +$$$$45\!\cdots\!01$$$$T^{20}$$)($$( 1 - 1559 T + 923521 T^{2} )( 1 + 1753 T + 923521 T^{2} )$$)($$( 1 - 1559 T + 923521 T^{2} )( 1 + 1753 T + 923521 T^{2} )$$)($$( 1 + 1652 T + 1805583 T^{2} + 1525656692 T^{3} + 852891037441 T^{4} )^{2}$$)($$( 1 - 697 T - 437712 T^{2} - 643694137 T^{3} + 852891037441 T^{4} )^{2}$$)($$( 1 - 778 T - 318237 T^{2} - 718499338 T^{3} + 852891037441 T^{4} )^{2}$$)($$( 1 - 736 T - 998424 T^{2} + 2729414848 T^{3} - 471779220718 T^{4} - 2664995161716576 T^{5} + 2854511490180793312 T^{6} +$$$$12\!\cdots\!48$$$$T^{7} -$$$$33\!\cdots\!09$$$$T^{8} +$$$$11\!\cdots\!08$$$$T^{9} +$$$$24\!\cdots\!92$$$$T^{10} -$$$$20\!\cdots\!36$$$$T^{11} -$$$$34\!\cdots\!58$$$$T^{12} +$$$$18\!\cdots\!48$$$$T^{13} -$$$$61\!\cdots\!04$$$$T^{14} -$$$$42\!\cdots\!76$$$$T^{15} +$$$$52\!\cdots\!61$$$$T^{16} )^{2}$$)
$37$ ($$( 1 - 8 T + 3611368 T^{2} + 1256575624 T^{3} + 6911619203950 T^{4} + 2355025028051464 T^{5} + 12684855900547773928 T^{6} - 52663616046720282248 T^{7} +$$$$12\!\cdots\!41$$$$T^{8} )^{2}$$)($$( 1 - 614 T + 4316302 T^{2} - 1557229880 T^{3} + 8895611838523 T^{4} - 2918499509130680 T^{5} + 15160922091918120142 T^{6} -$$$$40\!\cdots\!34$$$$T^{7} +$$$$12\!\cdots\!41$$$$T^{8} )^{2}$$)($$1 + 2162 T + 2800083 T^{2} + 4051936082 T^{3} + 3512479453921 T^{4}$$)($$1 + 2162 T + 2800083 T^{2} + 4051936082 T^{3} + 3512479453921 T^{4}$$)($$( 1 + 41 T + 4485627 T^{2} + 414188058 T^{3} + 11001613493061 T^{4} + 412173167971347 T^{5} + 20618794945768696821 T^{6} +$$$$14\!\cdots\!18$$$$T^{7} +$$$$29\!\cdots\!87$$$$T^{8} +$$$$50\!\cdots\!81$$$$T^{9} +$$$$23\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 + 41 T + 4485627 T^{2} + 414188058 T^{3} + 11001613493061 T^{4} + 412173167971347 T^{5} + 20618794945768696821 T^{6} +$$$$14\!\cdots\!18$$$$T^{7} +$$$$29\!\cdots\!87$$$$T^{8} +$$$$50\!\cdots\!81$$$$T^{9} +$$$$23\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 2591 T + 1874161 T^{2} )^{2}$$)($$( 1 + 2062 T + 1874161 T^{2} )^{2}$$)($$( 1 + 442 T + 1874161 T^{2} )^{4}$$)($$( 1 + 748 T + 1874161 T^{2} )^{4}$$)($$( 1 - 1079 T + 1874161 T^{2} )^{4}$$)($$( 1 - 614 T + 4316302 T^{2} - 1557229880 T^{3} + 8895611838523 T^{4} - 2918499509130680 T^{5} + 15160922091918120142 T^{6} -$$$$40\!\cdots\!34$$$$T^{7} +$$$$12\!\cdots\!41$$$$T^{8} )^{4}$$)
$41$ ($$1 - 12649388 T^{2} + 74446575673498 T^{4} -$$$$29\!\cdots\!76$$$$T^{6} +$$$$89\!\cdots\!55$$$$T^{8} -$$$$23\!\cdots\!96$$$$T^{10} +$$$$47\!\cdots\!18$$$$T^{12} -$$$$64\!\cdots\!68$$$$T^{14} +$$$$40\!\cdots\!81$$$$T^{16}$$)($$1 - 3947288 T^{2} - 3616850163692 T^{4} + 16457572376333935288 T^{6} +$$$$20\!\cdots\!26$$$$T^{8} +$$$$13\!\cdots\!48$$$$T^{10} -$$$$23\!\cdots\!72$$$$T^{12} -$$$$20\!\cdots\!68$$$$T^{14} +$$$$40\!\cdots\!81$$$$T^{16}$$)($$( 1 + 3038 T + 2825761 T^{2} )^{2}$$)($$( 1 - 3038 T + 2825761 T^{2} )^{2}$$)($$( 1 + 1826 T + 9958077 T^{2} + 13360693432 T^{3} + 45705921601634 T^{4} + 47268111294059340 T^{5} +$$$$12\!\cdots\!74$$$$T^{6} +$$$$10\!\cdots\!72$$$$T^{7} +$$$$22\!\cdots\!37$$$$T^{8} +$$$$11\!\cdots\!66$$$$T^{9} +$$$$18\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 1826 T + 9958077 T^{2} - 13360693432 T^{3} + 45705921601634 T^{4} - 47268111294059340 T^{5} +$$$$12\!\cdots\!74$$$$T^{6} -$$$$10\!\cdots\!72$$$$T^{7} +$$$$22\!\cdots\!37$$$$T^{8} -$$$$11\!\cdots\!66$$$$T^{9} +$$$$18\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 1681 T + 2825761 T^{2} )( 1 + 1681 T + 2825761 T^{2} )$$)($$( 1 - 1681 T + 2825761 T^{2} )( 1 + 1681 T + 2825761 T^{2} )$$)($$1 + 5405120 T^{2} + 21230396985279 T^{4} + 43159479054426499520 T^{6} +$$$$63\!\cdots\!41$$$$T^{8}$$)($$1 + 5183666 T^{2} + 18885467970435 T^{4} + 41391185422736737586 T^{6} +$$$$63\!\cdots\!41$$$$T^{8}$$)($$1 + 791522 T^{2} - 7358418152637 T^{4} + 6320243987204312162 T^{6} +$$$$63\!\cdots\!41$$$$T^{8}$$)($$1 + 3947288 T^{2} + 19197932718636 T^{4} + 18638395503728403280 T^{6} +$$$$57\!\cdots\!82$$$$T^{8} -$$$$23\!\cdots\!28$$$$T^{10} +$$$$40\!\cdots\!16$$$$T^{12} -$$$$19\!\cdots\!88$$$$T^{14} +$$$$92\!\cdots\!15$$$$T^{16} -$$$$15\!\cdots\!48$$$$T^{18} +$$$$25\!\cdots\!56$$$$T^{20} -$$$$12\!\cdots\!08$$$$T^{22} +$$$$23\!\cdots\!42$$$$T^{24} +$$$$60\!\cdots\!80$$$$T^{26} +$$$$49\!\cdots\!56$$$$T^{28} +$$$$81\!\cdots\!08$$$$T^{30} +$$$$16\!\cdots\!61$$$$T^{32}$$)
$43$ ($$( 1 - 68 T + 12955228 T^{2} - 545371076 T^{3} + 65226299853025 T^{4} - 1864515179999876 T^{5} +$$$$15\!\cdots\!28$$$$T^{6} -$$$$27\!\cdots\!68$$$$T^{7} +$$$$13\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 - 194 T + 5548210 T^{2} + 7089791362 T^{3} + 12339731626930 T^{4} + 24238585798196962 T^{5} + 64848589662188644210 T^{6} -$$$$77\!\cdots\!94$$$$T^{7} +$$$$13\!\cdots\!01$$$$T^{8} )^{2}$$)($$( 1 - 1849 T )^{2}( 1 + 1849 T )^{2}$$)($$( 1 - 1849 T )^{2}( 1 + 1849 T )^{2}$$)($$1 - 16085602 T^{2} + 146040634110717 T^{4} -$$$$92\!\cdots\!28$$$$T^{6} +$$$$44\!\cdots\!02$$$$T^{8} -$$$$17\!\cdots\!32$$$$T^{10} +$$$$52\!\cdots\!02$$$$T^{12} -$$$$12\!\cdots\!28$$$$T^{14} +$$$$23\!\cdots\!17$$$$T^{16} -$$$$30\!\cdots\!02$$$$T^{18} +$$$$21\!\cdots\!01$$$$T^{20}$$)($$1 - 16085602 T^{2} + 146040634110717 T^{4} -$$$$92\!\cdots\!28$$$$T^{6} +$$$$44\!\cdots\!02$$$$T^{8} -$$$$17\!\cdots\!32$$$$T^{10} +$$$$52\!\cdots\!02$$$$T^{12} -$$$$12\!\cdots\!28$$$$T^{14} +$$$$23\!\cdots\!17$$$$T^{16} -$$$$30\!\cdots\!02$$$$T^{18} +$$$$21\!\cdots\!01$$$$T^{20}$$)($$( 1 - 3191 T + 3418801 T^{2} )( 1 - 23 T + 3418801 T^{2} )$$)($$( 1 - 3191 T + 3418801 T^{2} )( 1 - 23 T + 3418801 T^{2} )$$)($$( 1 + 1160 T - 2073201 T^{2} + 3965809160 T^{3} + 11688200277601 T^{4} )^{2}$$)($$( 1 + 2618 T + 3435123 T^{2} + 8950421018 T^{3} + 11688200277601 T^{4} )^{2}$$)($$( 1 - 298 T - 3329997 T^{2} - 1018802698 T^{3} + 11688200277601 T^{4} )^{2}$$)($$( 1 + 194 T - 5510574 T^{2} + 15255935464 T^{3} + 19818322101398 T^{4} - 68362053002007822 T^{5} +$$$$11\!\cdots\!92$$$$T^{6} +$$$$20\!\cdots\!14$$$$T^{7} -$$$$51\!\cdots\!73$$$$T^{8} +$$$$68\!\cdots\!14$$$$T^{9} +$$$$13\!\cdots\!92$$$$T^{10} -$$$$27\!\cdots\!22$$$$T^{11} +$$$$27\!\cdots\!98$$$$T^{12} +$$$$71\!\cdots\!64$$$$T^{13} -$$$$87\!\cdots\!74$$$$T^{14} +$$$$10\!\cdots\!94$$$$T^{15} +$$$$18\!\cdots\!01$$$$T^{16} )^{2}$$)
$47$ ($$1 - 19981955 T^{2} + 227810016714829 T^{4} -$$$$17\!\cdots\!90$$$$T^{6} +$$$$10\!\cdots\!46$$$$T^{8} -$$$$42\!\cdots\!90$$$$T^{10} +$$$$12\!\cdots\!09$$$$T^{12} -$$$$26\!\cdots\!55$$$$T^{14} +$$$$32\!\cdots\!41$$$$T^{16}$$)($$1 - 4274840 T^{2} + 79909048264972 T^{4} -$$$$29\!\cdots\!36$$$$T^{6} +$$$$26\!\cdots\!10$$$$T^{8} -$$$$70\!\cdots\!96$$$$T^{10} +$$$$45\!\cdots\!12$$$$T^{12} -$$$$57\!\cdots\!40$$$$T^{14} +$$$$32\!\cdots\!41$$$$T^{16}$$)($$( 1 - 2209 T )^{2}( 1 + 2209 T )^{2}$$)($$( 1 - 2209 T )^{2}( 1 + 2209 T )^{2}$$)($$1 - 23221738 T^{2} + 319085795124909 T^{4} -$$$$30\!\cdots\!08$$$$T^{6} +$$$$21\!\cdots\!10$$$$T^{8} -$$$$11\!\cdots\!60$$$$T^{10} +$$$$50\!\cdots\!10$$$$T^{12} -$$$$17\!\cdots\!68$$$$T^{14} +$$$$43\!\cdots\!29$$$$T^{16} -$$$$74\!\cdots\!58$$$$T^{18} +$$$$76\!\cdots\!01$$$$T^{20}$$)($$1 - 23221738 T^{2} + 319085795124909 T^{4} -$$$$30\!\cdots\!08$$$$T^{6} +$$$$21\!\cdots\!10$$$$T^{8} -$$$$11\!\cdots\!60$$$$T^{10} +$$$$50\!\cdots\!10$$$$T^{12} -$$$$17\!\cdots\!68$$$$T^{14} +$$$$43\!\cdots\!29$$$$T^{16} -$$$$74\!\cdots\!58$$$$T^{18} +$$$$76\!\cdots\!01$$$$T^{20}$$)($$( 1 - 2209 T + 4879681 T^{2} )( 1 + 2209 T + 4879681 T^{2} )$$)($$( 1 - 2209 T + 4879681 T^{2} )( 1 + 2209 T + 4879681 T^{2} )$$)($$1 + 9549410 T^{2} + 67379944686339 T^{4} +$$$$22\!\cdots\!10$$$$T^{6} +$$$$56\!\cdots\!21$$$$T^{8}$$)($$1 + 2758046 T^{2} - 16204468923645 T^{4} + 65672623932323279006 T^{6} +$$$$56\!\cdots\!21$$$$T^{8}$$)($$1 - 1175638 T^{2} - 22429161954717 T^{4} - 27993453428459378518 T^{6} +$$$$56\!\cdots\!21$$$$T^{8}$$)($$1 + 4274840 T^{2} - 61634791239372 T^{4} -$$$$25\!\cdots\!92$$$$T^{6} +$$$$24\!\cdots\!34$$$$T^{8} +$$$$78\!\cdots\!88$$$$T^{10} -$$$$65\!\cdots\!40$$$$T^{12} -$$$$83\!\cdots\!44$$$$T^{14} +$$$$16\!\cdots\!39$$$$T^{16} -$$$$19\!\cdots\!84$$$$T^{18} -$$$$37\!\cdots\!40$$$$T^{20} +$$$$10\!\cdots\!28$$$$T^{22} +$$$$78\!\cdots\!94$$$$T^{24} -$$$$19\!\cdots\!92$$$$T^{26} -$$$$11\!\cdots\!92$$$$T^{28} +$$$$18\!\cdots\!40$$$$T^{30} +$$$$10\!\cdots\!81$$$$T^{32}$$)
$53$ ($$1 - 5145920 T^{2} + 115452291970684 T^{4} - 84051566001475463360 T^{6} +$$$$67\!\cdots\!26$$$$T^{8} -$$$$52\!\cdots\!60$$$$T^{10} +$$$$44\!\cdots\!64$$$$T^{12} -$$$$12\!\cdots\!20$$$$T^{14} +$$$$15\!\cdots\!41$$$$T^{16}$$)($$1 - 6401528 T^{2} + 78679698713236 T^{4} -$$$$35\!\cdots\!72$$$$T^{6} +$$$$43\!\cdots\!02$$$$T^{8} -$$$$21\!\cdots\!92$$$$T^{10} +$$$$30\!\cdots\!56$$$$T^{12} -$$$$15\!\cdots\!68$$$$T^{14} +$$$$15\!\cdots\!41$$$$T^{16}$$)($$( 1 - 2482 T + 7890481 T^{2} )^{2}$$)($$( 1 + 2482 T + 7890481 T^{2} )^{2}$$)($$( 1 - 3094 T + 32121309 T^{2} - 83277636872 T^{3} + 466311376063058 T^{4} - 928635509491035204 T^{5} +$$$$36\!\cdots\!98$$$$T^{6} -$$$$51\!\cdots\!92$$$$T^{7} +$$$$15\!\cdots\!69$$$$T^{8} -$$$$11\!\cdots\!74$$$$T^{9} +$$$$30\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 + 3094 T + 32121309 T^{2} + 83277636872 T^{3} + 466311376063058 T^{4} + 928635509491035204 T^{5} +$$$$36\!\cdots\!98$$$$T^{6} +$$$$51\!\cdots\!92$$$$T^{7} +$$$$15\!\cdots\!69$$$$T^{8} +$$$$11\!\cdots\!74$$$$T^{9} +$$$$30\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 2809 T )^{2}( 1 + 2809 T )^{2}$$)($$( 1 - 2809 T )^{2}( 1 + 2809 T )^{2}$$)($$( 1 - 9620912 T^{2} + 62259690411361 T^{4} )^{2}$$)($$( 1 - 14633921 T^{2} + 62259690411361 T^{4} )^{2}$$)($$( 1 - 6255362 T^{2} + 62259690411361 T^{4} )^{2}$$)($$( 1 - 6401528 T^{2} + 78679698713236 T^{4} -$$$$35\!\cdots\!72$$$$T^{6} +$$$$43\!\cdots\!02$$$$T^{8} -$$$$21\!\cdots\!92$$$$T^{10} +$$$$30\!\cdots\!56$$$$T^{12} -$$$$15\!\cdots\!68$$$$T^{14} +$$$$15\!\cdots\!41$$$$T^{16} )^{2}$$)
$59$ ($$1 - 31340696 T^{2} + 646808461063090 T^{4} -$$$$10\!\cdots\!44$$$$T^{6} +$$$$14\!\cdots\!19$$$$T^{8} -$$$$15\!\cdots\!24$$$$T^{10} +$$$$13\!\cdots\!90$$$$T^{12} -$$$$99\!\cdots\!56$$$$T^{14} +$$$$46\!\cdots\!81$$$$T^{16}$$)($$1 - 12582392 T^{2} + 342351109975372 T^{4} -$$$$46\!\cdots\!08$$$$T^{6} +$$$$57\!\cdots\!38$$$$T^{8} -$$$$68\!\cdots\!68$$$$T^{10} +$$$$73\!\cdots\!52$$$$T^{12} -$$$$39\!\cdots\!12$$$$T^{14} +$$$$46\!\cdots\!81$$$$T^{16}$$)($$( 1 - 3481 T )^{2}( 1 + 3481 T )^{2}$$)($$( 1 - 3481 T )^{2}( 1 + 3481 T )^{2}$$)($$1 - 8251594 T^{2} + 298370641474701 T^{4} +$$$$16\!\cdots\!28$$$$T^{6} +$$$$40\!\cdots\!74$$$$T^{8} +$$$$16\!\cdots\!40$$$$T^{10} +$$$$58\!\cdots\!54$$$$T^{12} +$$$$36\!\cdots\!48$$$$T^{14} +$$$$94\!\cdots\!61$$$$T^{16} -$$$$38\!\cdots\!14$$$$T^{18} +$$$$68\!\cdots\!01$$$$T^{20}$$)($$1 - 8251594 T^{2} + 298370641474701 T^{4} +$$$$16\!\cdots\!28$$$$T^{6} +$$$$40\!\cdots\!74$$$$T^{8} +$$$$16\!\cdots\!40$$$$T^{10} +$$$$58\!\cdots\!54$$$$T^{12} +$$$$36\!\cdots\!48$$$$T^{14} +$$$$94\!\cdots\!61$$$$T^{16} -$$$$38\!\cdots\!14$$$$T^{18} +$$$$68\!\cdots\!01$$$$T^{20}$$)($$( 1 - 3481 T + 12117361 T^{2} )( 1 + 3481 T + 12117361 T^{2} )$$)($$( 1 - 3481 T + 12117361 T^{2} )( 1 + 3481 T + 12117361 T^{2} )$$)($$1 + 12943970 T^{2} + 20715921756579 T^{4} +$$$$19\!\cdots\!70$$$$T^{6} +$$$$21\!\cdots\!41$$$$T^{8}$$)($$1 - 9567874 T^{2} - 55286224724445 T^{4} -$$$$14\!\cdots\!54$$$$T^{6} +$$$$21\!\cdots\!41$$$$T^{8}$$)($$1 + 16021322 T^{2} + 109852321023363 T^{4} +$$$$23\!\cdots\!62$$$$T^{6} +$$$$21\!\cdots\!41$$$$T^{8}$$)($$1 + 12582392 T^{2} - 184034521533708 T^{4} -$$$$49\!\cdots\!92$$$$T^{6} +$$$$14\!\cdots\!10$$$$T^{8} +$$$$82\!\cdots\!52$$$$T^{10} +$$$$80\!\cdots\!76$$$$T^{12} -$$$$67\!\cdots\!92$$$$T^{14} -$$$$18\!\cdots\!17$$$$T^{16} -$$$$98\!\cdots\!32$$$$T^{18} +$$$$17\!\cdots\!16$$$$T^{20} +$$$$26\!\cdots\!72$$$$T^{22} +$$$$67\!\cdots\!10$$$$T^{24} -$$$$33\!\cdots\!92$$$$T^{26} -$$$$18\!\cdots\!68$$$$T^{28} +$$$$18\!\cdots\!72$$$$T^{30} +$$$$21\!\cdots\!61$$$$T^{32}$$)
$61$ ($$( 1 - 1937 T + 14281603 T^{2} + 60991858006 T^{3} - 94182960283700 T^{4} + 844483568245653046 T^{5} +$$$$27\!\cdots\!43$$$$T^{6} -$$$$51\!\cdots\!77$$$$T^{7} +$$$$36\!\cdots\!61$$$$T^{8} )^{2}$$)($$( 1 - 902 T + 6189730 T^{2} + 29137234624 T^{3} - 232110610634705 T^{4} + 403429517783598784 T^{5} +$$$$11\!\cdots\!30$$$$T^{6} -$$$$23\!\cdots\!42$$$$T^{7} +$$$$36\!\cdots\!61$$$$T^{8} )^{2}$$)($$1 - 6958 T + 34567923 T^{2} - 96339361678 T^{3} + 191707312997281 T^{4}$$)($$1 - 6958 T + 34567923 T^{2} - 96339361678 T^{3} + 191707312997281 T^{4}$$)($$( 1 + 4841 T + 62450187 T^{2} + 246079372554 T^{3} + 1626496921541733 T^{4} + 4959056958308702403 T^{5} +$$$$22\!\cdots\!53$$$$T^{6} +$$$$47\!\cdots\!74$$$$T^{7} +$$$$16\!\cdots\!27$$$$T^{8} +$$$$17\!\cdots\!01$$$$T^{9} +$$$$50\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 + 4841 T + 62450187 T^{2} + 246079372554 T^{3} + 1626496921541733 T^{4} + 4959056958308702403 T^{5} +$$$$22\!\cdots\!53$$$$T^{6} +$$$$47\!\cdots\!74$$$$T^{7} +$$$$16\!\cdots\!27$$$$T^{8} +$$$$17\!\cdots\!01$$$$T^{9} +$$$$50\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 7199 T + 13845841 T^{2} )( 1 + 1966 T + 13845841 T^{2} )$$)($$( 1 - 7199 T + 13845841 T^{2} )( 1 + 5233 T + 13845841 T^{2} )$$)($$( 1 - 3910 T + 1442259 T^{2} - 54137238310 T^{3} + 191707312997281 T^{4} )^{2}$$)($$( 1 + 6404 T + 27165375 T^{2} + 88668765764 T^{3} + 191707312997281 T^{4} )^{2}$$)($$( 1 - 2641 T - 6870960 T^{2} - 36566866081 T^{3} + 191707312997281 T^{4} )^{2}$$)($$( 1 + 902 T - 5376126 T^{2} + 63857605708 T^{3} + 296705153738453 T^{4} - 165053591467802484 T^{5} +$$$$50\!\cdots\!54$$$$T^{6} +$$$$15\!\cdots\!62$$$$T^{7} +$$$$23\!\cdots\!16$$$$T^{8} +$$$$21\!\cdots\!42$$$$T^{9} +$$$$96\!\cdots\!74$$$$T^{10} -$$$$43\!\cdots\!64$$$$T^{11} +$$$$10\!\cdots\!33$$$$T^{12} +$$$$32\!\cdots\!08$$$$T^{13} -$$$$37\!\cdots\!66$$$$T^{14} +$$$$87\!\cdots\!62$$$$T^{15} +$$$$13\!\cdots\!21$$$$T^{16} )^{2}$$)
$67$ ($$( 1 + 154 T + 33859570 T^{2} - 10195927724 T^{3} + 608674748042419 T^{4} - 205459373273578604 T^{5} +$$$$13\!\cdots\!70$$$$T^{6} +$$$$12\!\cdots\!94$$$$T^{7} +$$$$16\!\cdots\!81$$$$T^{8} )^{2}$$)($$( 1 + 1090 T + 32366794 T^{2} + 11878062622 T^{3} + 477344036370850 T^{4} + 239356277141499262 T^{5} +$$$$13\!\cdots\!54$$$$T^{6} +$$$$89\!\cdots\!90$$$$T^{7} +$$$$16\!\cdots\!81$$$$T^{8} )^{2}$$)($$( 1 - 4489 T )^{2}( 1 + 4489 T )^{2}$$)($$( 1 - 4489 T )^{2}( 1 + 4489 T )^{2}$$)($$1 - 76181218 T^{2} + 3869991932462397 T^{4} -$$$$13\!\cdots\!00$$$$T^{6} +$$$$38\!\cdots\!18$$$$T^{8} -$$$$86\!\cdots\!64$$$$T^{10} +$$$$15\!\cdots\!38$$$$T^{12} -$$$$22\!\cdots\!00$$$$T^{14} +$$$$25\!\cdots\!37$$$$T^{16} -$$$$20\!\cdots\!98$$$$T^{18} +$$$$11\!\cdots\!01$$$$T^{20}$$)($$1 - 76181218 T^{2} + 3869991932462397 T^{4} -$$$$13\!\cdots\!00$$$$T^{6} +$$$$38\!\cdots\!18$$$$T^{8} -$$$$86\!\cdots\!64$$$$T^{10} +$$$$15\!\cdots\!38$$$$T^{12} -$$$$22\!\cdots\!00$$$$T^{14} +$$$$25\!\cdots\!37$$$$T^{16} -$$$$20\!\cdots\!98$$$$T^{18} +$$$$11\!\cdots\!01$$$$T^{20}$$)($$( 1 - 5906 T + 20151121 T^{2} )( 1 - 2903 T + 20151121 T^{2} )$$)($$( 1 - 2903 T + 20151121 T^{2} )( 1 + 8809 T + 20151121 T^{2} )$$)($$( 1 + 6392 T + 20706543 T^{2} + 128805965432 T^{3} + 406067677556641 T^{4} )^{2}$$)($$( 1 - 5218 T + 7076403 T^{2} - 105148549378 T^{3} + 406067677556641 T^{4} )^{2}$$)($$( 1 + 5609 T + 11309760 T^{2} + 113027637689 T^{3} + 406067677556641 T^{4} )^{2}$$)($$( 1 - 1090 T - 31178694 T^{2} - 11523680216 T^{3} + 557318229209606 T^{4} + 416798916141579870 T^{5} +$$$$10\!\cdots\!12$$$$T^{6} -$$$$13\!\cdots\!94$$$$T^{7} -$$$$34\!\cdots\!21$$$$T^{8} -$$$$27\!\cdots\!74$$$$T^{9} +$$$$43\!\cdots\!92$$$$T^{10} +$$$$34\!\cdots\!70$$$$T^{11} +$$$$91\!\cdots\!86$$$$T^{12} -$$$$38\!\cdots\!16$$$$T^{13} -$$$$20\!\cdots\!74$$$$T^{14} -$$$$14\!\cdots\!90$$$$T^{15} +$$$$27\!\cdots\!61$$$$T^{16} )^{2}$$)
$71$ ($$1 - 68871716 T^{2} + 3244147638477940 T^{4} -$$$$11\!\cdots\!24$$$$T^{6} +$$$$30\!\cdots\!74$$$$T^{8} -$$$$73\!\cdots\!64$$$$T^{10} +$$$$13\!\cdots\!40$$$$T^{12} -$$$$18\!\cdots\!96$$$$T^{14} +$$$$17\!\cdots\!41$$$$T^{16}$$)($$1 - 15796628 T^{2} + 1499316890690728 T^{4} -$$$$15\!\cdots\!88$$$$T^{6} +$$$$12\!\cdots\!18$$$$T^{8} -$$$$10\!\cdots\!68$$$$T^{10} +$$$$62\!\cdots\!88$$$$T^{12} -$$$$42\!\cdots\!68$$$$T^{14} +$$$$17\!\cdots\!41$$$$T^{16}$$)($$( 1 - 5041 T )^{2}( 1 + 5041 T )^{2}$$)($$( 1 - 5041 T )^{2}( 1 + 5041 T )^{2}$$)($$1 - 122025250 T^{2} + 8373374789851485 T^{4} -$$$$39\!\cdots\!44$$$$T^{6} +$$$$14\!\cdots\!70$$$$T^{8} -$$$$41\!\cdots\!44$$$$T^{10} +$$$$93\!\cdots\!70$$$$T^{12} -$$$$16\!\cdots\!24$$$$T^{14} +$$$$22\!\cdots\!85$$$$T^{16} -$$$$21\!\cdots\!50$$$$T^{18} +$$$$11\!\cdots\!01$$$$T^{20}$$)($$1 - 122025250 T^{2} + 8373374789851485 T^{4} -$$$$39\!\cdots\!44$$$$T^{6} +$$$$14\!\cdots\!70$$$$T^{8} -$$$$41\!\cdots\!44$$$$T^{10} +$$$$93\!\cdots\!70$$$$T^{12} -$$$$16\!\cdots\!24$$$$T^{14} +$$$$22\!\cdots\!85$$$$T^{16} -$$$$21\!\cdots\!50$$$$T^{18} +$$$$11\!\cdots\!01$$$$T^{20}$$)($$( 1 - 5041 T )^{2}( 1 + 5041 T )^{2}$$)($$( 1 - 5041 T )^{2}( 1 + 5041 T )^{2}$$)($$( 1 - 7689890 T^{2} + 645753531245761 T^{4} )^{2}$$)($$( 1 - 7658462 T^{2} + 645753531245761 T^{4} )^{2}$$)($$( 1 - 31383362 T^{2} + 645753531245761 T^{4} )^{2}$$)($$( 1 - 15796628 T^{2} + 1499316890690728 T^{4} -$$$$15\!\cdots\!88$$$$T^{6} +$$$$12\!\cdots\!18$$$$T^{8} -$$$$10\!\cdots\!68$$$$T^{10} +$$$$62\!\cdots\!88$$$$T^{12} -$$$$42\!\cdots\!68$$$$T^{14} +$$$$17\!\cdots\!41$$$$T^{16} )^{2}$$)
$73$ ($$( 1 + 3901 T + 59309470 T^{2} + 292589317519 T^{3} + 2279602007321194 T^{4} + 8309021952930084079 T^{5} +$$$$47\!\cdots\!70$$$$T^{6} +$$$$89\!\cdots\!21$$$$T^{7} +$$$$65\!\cdots\!61$$$$T^{8} )^{2}$$)($$( 1 + 2272 T + 39410902 T^{2} - 196772776832 T^{3} + 103134174803371 T^{4} - 5588000738714352512 T^{5} +$$$$31\!\cdots\!62$$$$T^{6} +$$$$52\!\cdots\!12$$$$T^{7} +$$$$65\!\cdots\!61$$$$T^{8} )^{2}$$)($$1 + 1442 T - 26318877 T^{2} + 40950263522 T^{3} + 806460091894081 T^{4}$$)($$1 + 1442 T - 26318877 T^{2} + 40950263522 T^{3} + 806460091894081 T^{4}$$)($$( 1 - 5011 T + 66413247 T^{2} - 215624587266 T^{3} + 2237408316811149 T^{4} - 7105191506898479877 T^{5} +$$$$63\!\cdots\!09$$$$T^{6} -$$$$17\!\cdots\!46$$$$T^{7} +$$$$15\!\cdots\!87$$$$T^{8} -$$$$32\!\cdots\!71$$$$T^{9} +$$$$18\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 5011 T + 66413247 T^{2} - 215624587266 T^{3} + 2237408316811149 T^{4} - 7105191506898479877 T^{5} +$$$$63\!\cdots\!09$$$$T^{6} -$$$$17\!\cdots\!46$$$$T^{7} +$$$$15\!\cdots\!87$$$$T^{8} -$$$$32\!\cdots\!71$$$$T^{9} +$$$$18\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 9791 T + 28398241 T^{2} )^{2}$$)($$( 1 + 8542 T + 28398241 T^{2} )^{2}$$)($$( 1 + 2224 T + 28398241 T^{2} )^{4}$$)($$( 1 + 4519 T + 28398241 T^{2} )^{4}$$)($$( 1 - 7199 T + 28398241 T^{2} )^{4}$$)($$( 1 + 2272 T + 39410902 T^{2} - 196772776832 T^{3} + 103134174803371 T^{4} - 5588000738714352512 T^{5} +$$$$31\!\cdots\!62$$$$T^{6} +$$$$52\!\cdots\!12$$$$T^{7} +$$$$65\!\cdots\!61$$$$T^{8} )^{4}$$)
$79$ ($$( 1 - 2195 T + 92542939 T^{2} - 195388180760 T^{3} + 5006999286743146 T^{4} - 7610385467044641560 T^{5} +$$$$14\!\cdots\!79$$$$T^{6} -$$$$12\!\cdots\!95$$$$T^{7} +$$$$23\!\cdots\!21$$$$T^{8} )^{2}$$)($$( 1 + 2506 T + 105092818 T^{2} + 227234889574 T^{3} + 5831277891584050 T^{4} + 8850817354933355494 T^{5} +$$$$15\!\cdots\!98$$$$T^{6} +$$$$14\!\cdots\!46$$$$T^{7} +$$$$23\!\cdots\!21$$$$T^{8} )^{2}$$)($$( 1 - 6241 T )^{2}( 1 + 6241 T )^{2}$$)($$( 1 - 6241 T )^{2}( 1 + 6241 T )^{2}$$)($$1 - 131940322 T^{2} + 7771849483972125 T^{4} -$$$$32\!\cdots\!44$$$$T^{6} +$$$$15\!\cdots\!18$$$$T^{8} -$$$$67\!\cdots\!64$$$$T^{10} +$$$$23\!\cdots\!98$$$$T^{12} -$$$$74\!\cdots\!24$$$$T^{14} +$$$$27\!\cdots\!25$$$$T^{16} -$$$$69\!\cdots\!02$$$$T^{18} +$$$$80\!\cdots\!01$$$$T^{20}$$)($$1 - 131940322 T^{2} + 7771849483972125 T^{4} -$$$$32\!\cdots\!44$$$$T^{6} +$$$$15\!\cdots\!18$$$$T^{8} -$$$$67\!\cdots\!64$$$$T^{10} +$$$$23\!\cdots\!98$$$$T^{12} -$$$$74\!\cdots\!24$$$$T^{14} +$$$$27\!\cdots\!25$$$$T^{16} -$$$$69\!\cdots\!02$$$$T^{18} +$$$$80\!\cdots\!01$$$$T^{20}$$)($$( 1 - 7682 T + 38950081 T^{2} )( 1 - 4679 T + 38950081 T^{2} )$$)($$( 1 - 4679 T + 38950081 T^{2} )( 1 + 12361 T + 38950081 T^{2} )$$)($$( 1 - 7060 T + 10893519 T^{2} - 274987571860 T^{3} + 1517108809906561 T^{4} )^{2}$$)($$( 1 + 7502 T + 17329923 T^{2} + 292203507662 T^{3} + 1517108809906561 T^{4} )^{2}$$)($$( 1 + 329 T - 38841840 T^{2} + 12814576649 T^{3} + 1517108809906561 T^{4} )^{2}$$)($$( 1 - 2506 T - 98812782 T^{2} + 191107177240 T^{3} + 4643771870324630 T^{4} - 3505207455564576426 T^{5} -$$$$26\!\cdots\!92$$$$T^{6} -$$$$12\!\cdots\!50$$$$T^{7} +$$$$13\!\cdots\!11$$$$T^{8} -$$$$48\!\cdots\!50$$$$T^{9} -$$$$40\!\cdots\!12$$$$T^{10} -$$$$20\!\cdots\!66$$$$T^{11} +$$$$10\!\cdots\!30$$$$T^{12} +$$$$17\!\cdots\!40$$$$T^{13} -$$$$34\!\cdots\!42$$$$T^{14} -$$$$34\!\cdots\!66$$$$T^{15} +$$$$52\!\cdots\!41$$$$T^{16} )^{2}$$)
$83$ ($$1 - 81188291 T^{2} + 8014262915096365 T^{4} -$$$$34\!\cdots\!54$$$$T^{6} +$$$$22\!\cdots\!34$$$$T^{8} -$$$$78\!\cdots\!14$$$$T^{10} +$$$$40\!\cdots\!65$$$$T^{12} -$$$$92\!\cdots\!11$$$$T^{14} +$$$$25\!\cdots\!61$$$$T^{16}$$)($$1 - 175659320 T^{2} + 14988116577681148 T^{4} -$$$$80\!\cdots\!00$$$$T^{6} +$$$$37\!\cdots\!38$$$$T^{8} -$$$$18\!\cdots\!00$$$$T^{10} +$$$$76\!\cdots\!88$$$$T^{12} -$$$$20\!\cdots\!20$$$$T^{14} +$$$$25\!\cdots\!61$$$$T^{16}$$)($$( 1 - 6889 T )^{2}( 1 + 6889 T )^{2}$$)($$( 1 - 6889 T )^{2}( 1 + 6889 T )^{2}$$)($$1 - 139018378 T^{2} + 9598127152975053 T^{4} -$$$$49\!\cdots\!52$$$$T^{6} +$$$$25\!\cdots\!46$$$$T^{8} -$$$$13\!\cdots\!28$$$$T^{10} +$$$$57\!\cdots\!86$$$$T^{12} -$$$$24\!\cdots\!12$$$$T^{14} +$$$$10\!\cdots\!13$$$$T^{16} -$$$$35\!\cdots\!58$$$$T^{18} +$$$$57\!\cdots\!01$$$$T^{20}$$)($$1 - 139018378 T^{2} + 9598127152975053 T^{4} -$$$$49\!\cdots\!52$$$$T^{6} +$$$$25\!\cdots\!46$$$$T^{8} -$$$$13\!\cdots\!28$$$$T^{10} +$$$$57\!\cdots\!86$$$$T^{12} -$$$$24\!\cdots\!12$$$$T^{14} +$$$$10\!\cdots\!13$$$$T^{16} -$$$$35\!\cdots\!58$$$$T^{18} +$$$$57\!\cdots\!01$$$$T^{20}$$)($$( 1 - 6889 T + 47458321 T^{2} )( 1 + 6889 T + 47458321 T^{2} )$$)($$( 1 - 6889 T + 47458321 T^{2} )( 1 + 6889 T + 47458321 T^{2} )$$)($$1 + 59434754 T^{2} + 1280197750901475 T^{4} +$$$$13\!\cdots\!14$$$$T^{6} +$$$$50\!\cdots\!81$$$$T^{8}$$)($$1 + 64875281 T^{2} + 1956509852689920 T^{4} +$$$$14\!\cdots\!21$$$$T^{6} +$$$$50\!\cdots\!81$$$$T^{8}$$)($$1 + 93167042 T^{2} + 6427805482890723 T^{4} +$$$$20\!\cdots\!22$$$$T^{6} +$$$$50\!\cdots\!81$$$$T^{8}$$)($$1 + 175659320 T^{2} + 15868080125181252 T^{4} +$$$$10\!\cdots\!60$$$$T^{6} +$$$$45\!\cdots\!66$$$$T^{8} +$$$$65\!\cdots\!80$$$$T^{10} -$$$$81\!\cdots\!48$$$$T^{12} -$$$$86\!\cdots\!20$$$$T^{14} -$$$$50\!\cdots\!41$$$$T^{16} -$$$$19\!\cdots\!20$$$$T^{18} -$$$$41\!\cdots\!88$$$$T^{20} +$$$$75\!\cdots\!80$$$$T^{22} +$$$$11\!\cdots\!26$$$$T^{24} +$$$$58\!\cdots\!60$$$$T^{26} +$$$$20\!\cdots\!32$$$$T^{28} +$$$$51\!\cdots\!20$$$$T^{30} +$$$$66\!\cdots\!21$$$$T^{32}$$)
$89$ ($$1 - 294759296 T^{2} + 46567064448316540 T^{4} -$$$$48\!\cdots\!04$$$$T^{6} +$$$$35\!\cdots\!14$$$$T^{8} -$$$$19\!\cdots\!24$$$$T^{10} +$$$$72\!\cdots\!40$$$$T^{12} -$$$$17\!\cdots\!36$$$$T^{14} +$$$$24\!\cdots\!21$$$$T^{16}$$)($$1 - 259833392 T^{2} + 39708026833239838 T^{4} -$$$$39\!\cdots\!88$$$$T^{6} +$$$$29\!\cdots\!31$$$$T^{8} -$$$$15\!\cdots\!28$$$$T^{10} +$$$$61\!\cdots\!18$$$$T^{12} -$$$$15\!\cdots\!72$$$$T^{14} +$$$$24\!\cdots\!21$$$$T^{16}$$)($$1 - 9758 T + 32476323 T^{2} - 612238787678 T^{3} + 3936588805702081 T^{4}$$)($$1 + 9758 T + 32476323 T^{2} + 612238787678 T^{3} + 3936588805702081 T^{4}$$)($$( 1 - 9637 T + 235493295 T^{2} - 2005374023198 T^{3} + 27250343853222509 T^{4} -$$$$17\!\cdots\!27$$$$T^{5} +$$$$17\!\cdots\!69$$$$T^{6} -$$$$78\!\cdots\!38$$$$T^{7} +$$$$58\!\cdots\!95$$$$T^{8} -$$$$14\!\cdots\!57$$$$T^{9} +$$$$97\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 + 9637 T + 235493295 T^{2} + 2005374023198 T^{3} + 27250343853222509 T^{4} +$$$$17\!\cdots\!27$$$$T^{5} +$$$$17\!\cdots\!69$$$$T^{6} +$$$$78\!\cdots\!38$$$$T^{7} +$$$$58\!\cdots\!95$$$$T^{8} +$$$$14\!\cdots\!57$$$$T^{9} +$$$$97\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 7921 T )^{2}( 1 + 7921 T )^{2}$$)($$( 1 - 7921 T )^{2}( 1 + 7921 T )^{2}$$)($$( 1 - 54274304 T^{2} + 3936588805702081 T^{4} )^{2}$$)($$( 1 - 46736606 T^{2} + 3936588805702081 T^{4} )^{2}$$)($$( 1 - 58951082 T^{2} + 3936588805702081 T^{4} )^{2}$$)($$( 1 - 259833392 T^{2} + 39708026833239838 T^{4} -$$$$39\!\cdots\!88$$$$T^{6} +$$$$29\!\cdots\!31$$$$T^{8} -$$$$15\!\cdots\!28$$$$T^{10} +$$$$61\!\cdots\!18$$$$T^{12} -$$$$15\!\cdots\!72$$$$T^{14} +$$$$24\!\cdots\!21$$$$T^{16} )^{2}$$)
$97$ ($$( 1 + 7282 T + 336254488 T^{2} + 1720884578884 T^{3} + 43500636050571385 T^{4} +$$$$15\!\cdots\!04$$$$T^{5} +$$$$26\!\cdots\!68$$$$T^{6} +$$$$50\!\cdots\!62$$$$T^{7} +$$$$61\!\cdots\!21$$$$T^{8} )^{2}$$)($$( 1 + 1264 T + 258571096 T^{2} + 226571051536 T^{3} + 31287418967396782 T^{4} + 20058172287896025616 T^{5} +$$$$20\!\cdots\!56$$$$T^{6} +$$$$87\!\cdots\!24$$$$T^{7} +$$$$61\!\cdots\!21$$$$T^{8} )^{2}$$)($$( 1 + 1918 T + 88529281 T^{2} )^{2}$$)($$( 1 + 1918 T + 88529281 T^{2} )^{2}$$)($$( 1 + 7886 T + 173503773 T^{2} + 1977141493128 T^{3} + 28364550451989858 T^{4} +$$$$18\!\cdots\!28$$$$T^{5} +$$$$25\!\cdots\!98$$$$T^{6} +$$$$15\!\cdots\!08$$$$T^{7} +$$$$12\!\cdots\!93$$$$T^{8} +$$$$48\!\cdots\!06$$$$T^{9} +$$$$54\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 + 7886 T + 173503773 T^{2} + 1977141493128 T^{3} + 28364550451989858 T^{4} +$$$$18\!\cdots\!28$$$$T^{5} +$$$$25\!\cdots\!98$$$$T^{6} +$$$$15\!\cdots\!08$$$$T^{7} +$$$$12\!\cdots\!93$$$$T^{8} +$$$$48\!\cdots\!06$$$$T^{9} +$$$$54\!\cdots\!01$$$$T^{10} )^{2}$$)($$( 1 - 9071 T + 88529281 T^{2} )( 1 + 18814 T + 88529281 T^{2} )$$)($$( 1 - 9743 T + 88529281 T^{2} )( 1 - 9071 T + 88529281 T^{2} )$$)($$( 1 + 4352 T - 69589377 T^{2} + 385279430912 T^{3} + 7837433594376961 T^{4} )^{2}$$)($$( 1 + 10571 T + 23216760 T^{2} + 935843029451 T^{3} + 7837433594376961 T^{4} )^{2}$$)($$( 1 - 15961 T + 166224240 T^{2} - 1413015854041 T^{3} + 7837433594376961 T^{4} )^{2}$$)($$( 1 - 1264 T - 256973400 T^{2} + 126308237728 T^{3} + 35285206910102930 T^{4} + 451697744147035824 T^{5} -$$$$40\!\cdots\!88$$$$T^{6} -$$$$15\!\cdots\!88$$$$T^{7} +$$$$39\!\cdots\!23$$$$T^{8} -$$$$13\!\cdots\!28$$$$T^{9} -$$$$31\!\cdots\!68$$$$T^{10} +$$$$31\!\cdots\!84$$$$T^{11} +$$$$21\!\cdots\!30$$$$T^{12} +$$$$68\!\cdots\!28$$$$T^{13} -$$$$12\!\cdots\!00$$$$T^{14} -$$$$53\!\cdots\!04$$$$T^{15} +$$$$37\!\cdots\!41$$$$T^{16} )^{2}$$)