# Properties

 Label 160.6.n Level 160 Weight 6 Character orbit n Rep. character $$\chi_{160}(63,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 60 Newform subspaces 4 Sturm bound 144 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 160.n (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$144$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(160, [\chi])$$.

Total New Old
Modular forms 256 60 196
Cusp forms 224 60 164
Eisenstein series 32 0 32

## Trace form

 $$60q + O(q^{10})$$ $$60q + 244q^{13} - 1212q^{17} + 3280q^{21} + 9348q^{25} + 18864q^{33} - 18820q^{37} - 19280q^{41} + 30780q^{45} + 37468q^{53} + 82592q^{57} + 5084q^{65} - 1972q^{73} + 241008q^{77} - 124620q^{81} - 118412q^{85} - 368880q^{93} - 155316q^{97} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(160, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
160.6.n.a $$14$$ $$25.661$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$-10$$ $$42$$ $$-66$$ $$q+(-1-\beta _{1}+\beta _{2})q^{3}+(3-4\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
160.6.n.b $$14$$ $$25.661$$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$0$$ $$10$$ $$42$$ $$66$$ $$q+(1+\beta _{1}-\beta _{2})q^{3}+(3-4\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
160.6.n.c $$16$$ $$25.661$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$-10$$ $$-42$$ $$86$$ $$q+(-1+\beta _{3}-\beta _{4})q^{3}+(-3+\beta _{4}-\beta _{8}+\cdots)q^{5}+\cdots$$
160.6.n.d $$16$$ $$25.661$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$10$$ $$-42$$ $$-86$$ $$q+(1-\beta _{3}+\beta _{4})q^{3}+(-3+\beta _{4}-\beta _{8}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(160, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(160, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ ($$1 + 10 T + 50 T^{2} + 254 T^{3} - 91369 T^{4} - 1354100 T^{5} - 8940292 T^{6} - 156709276 T^{7} + 3134936461 T^{8} + 38721912918 T^{9} + 290596015278 T^{10} + 2245195781154 T^{11} + 9414782746155 T^{12} + 473122978927848 T^{13} + 19255041373064328 T^{14} + 114968883879467064 T^{15} + 555933506377706595 T^{16} + 32216105460571098678 T^{17} +$$$$10\!\cdots\!78$$$$T^{18} +$$$$32\!\cdots\!74$$$$T^{19} +$$$$64\!\cdots\!89$$$$T^{20} -$$$$78\!\cdots\!32$$$$T^{21} -$$$$10\!\cdots\!92$$$$T^{22} -$$$$40\!\cdots\!00$$$$T^{23} -$$$$65\!\cdots\!81$$$$T^{24} +$$$$44\!\cdots\!78$$$$T^{25} +$$$$21\!\cdots\!50$$$$T^{26} +$$$$10\!\cdots\!30$$$$T^{27} +$$$$25\!\cdots\!49$$$$T^{28}$$)($$1 - 10 T + 50 T^{2} - 254 T^{3} - 91369 T^{4} + 1354100 T^{5} - 8940292 T^{6} + 156709276 T^{7} + 3134936461 T^{8} - 38721912918 T^{9} + 290596015278 T^{10} - 2245195781154 T^{11} + 9414782746155 T^{12} - 473122978927848 T^{13} + 19255041373064328 T^{14} - 114968883879467064 T^{15} + 555933506377706595 T^{16} - 32216105460571098678 T^{17} +$$$$10\!\cdots\!78$$$$T^{18} -$$$$32\!\cdots\!74$$$$T^{19} +$$$$64\!\cdots\!89$$$$T^{20} +$$$$78\!\cdots\!32$$$$T^{21} -$$$$10\!\cdots\!92$$$$T^{22} +$$$$40\!\cdots\!00$$$$T^{23} -$$$$65\!\cdots\!81$$$$T^{24} -$$$$44\!\cdots\!78$$$$T^{25} +$$$$21\!\cdots\!50$$$$T^{26} -$$$$10\!\cdots\!30$$$$T^{27} +$$$$25\!\cdots\!49$$$$T^{28}$$)($$1 + 10 T + 50 T^{2} - 3114 T^{3} - 71776 T^{4} - 1530706 T^{5} - 6869762 T^{6} - 282516126 T^{7} - 1414085636 T^{8} + 89177429938 T^{9} + 2520680189450 T^{10} + 49929440504142 T^{11} + 506618123321952 T^{12} - 709766597096154 T^{13} - 113295686701585050 T^{14} - 1816344389104634358 T^{15} - 43957043443472192442 T^{16} -$$$$44\!\cdots\!94$$$$T^{17} -$$$$66\!\cdots\!50$$$$T^{18} -$$$$10\!\cdots\!78$$$$T^{19} +$$$$17\!\cdots\!52$$$$T^{20} +$$$$42\!\cdots\!06$$$$T^{21} +$$$$51\!\cdots\!50$$$$T^{22} +$$$$44\!\cdots\!66$$$$T^{23} -$$$$17\!\cdots\!36$$$$T^{24} -$$$$83\!\cdots\!18$$$$T^{25} -$$$$49\!\cdots\!38$$$$T^{26} -$$$$26\!\cdots\!42$$$$T^{27} -$$$$30\!\cdots\!76$$$$T^{28} -$$$$32\!\cdots\!02$$$$T^{29} +$$$$12\!\cdots\!50$$$$T^{30} +$$$$60\!\cdots\!70$$$$T^{31} +$$$$14\!\cdots\!01$$$$T^{32}$$)($$1 - 10 T + 50 T^{2} + 3114 T^{3} - 71776 T^{4} + 1530706 T^{5} - 6869762 T^{6} + 282516126 T^{7} - 1414085636 T^{8} - 89177429938 T^{9} + 2520680189450 T^{10} - 49929440504142 T^{11} + 506618123321952 T^{12} + 709766597096154 T^{13} - 113295686701585050 T^{14} + 1816344389104634358 T^{15} - 43957043443472192442 T^{16} +$$$$44\!\cdots\!94$$$$T^{17} -$$$$66\!\cdots\!50$$$$T^{18} +$$$$10\!\cdots\!78$$$$T^{19} +$$$$17\!\cdots\!52$$$$T^{20} -$$$$42\!\cdots\!06$$$$T^{21} +$$$$51\!\cdots\!50$$$$T^{22} -$$$$44\!\cdots\!66$$$$T^{23} -$$$$17\!\cdots\!36$$$$T^{24} +$$$$83\!\cdots\!18$$$$T^{25} -$$$$49\!\cdots\!38$$$$T^{26} +$$$$26\!\cdots\!42$$$$T^{27} -$$$$30\!\cdots\!76$$$$T^{28} +$$$$32\!\cdots\!02$$$$T^{29} +$$$$12\!\cdots\!50$$$$T^{30} -$$$$60\!\cdots\!70$$$$T^{31} +$$$$14\!\cdots\!01$$$$T^{32}$$)
$5$ ($$1 - 42 T + 3115 T^{2} - 77660 T^{3} - 1600075 T^{4} + 15516250 T^{5} - 16330865625 T^{6} + 925536875000 T^{7} - 51033955078125 T^{8} + 151525878906250 T^{9} - 48830413818359375 T^{10} - 7406234741210937500 T^{11} +$$$$92\!\cdots\!75$$$$T^{12} -$$$$39\!\cdots\!50$$$$T^{13} +$$$$29\!\cdots\!25$$$$T^{14}$$)($$1 - 42 T + 3115 T^{2} - 77660 T^{3} - 1600075 T^{4} + 15516250 T^{5} - 16330865625 T^{6} + 925536875000 T^{7} - 51033955078125 T^{8} + 151525878906250 T^{9} - 48830413818359375 T^{10} - 7406234741210937500 T^{11} +$$$$92\!\cdots\!75$$$$T^{12} -$$$$39\!\cdots\!50$$$$T^{13} +$$$$29\!\cdots\!25$$$$T^{14}$$)($$1 + 42 T - 3688 T^{2} - 336370 T^{3} - 1345940 T^{4} + 732464050 T^{5} + 13329225000 T^{6} - 337978756250 T^{7} - 9350412656250 T^{8} - 1056183613281250 T^{9} + 130168212890625000 T^{10} + 22353028869628906250 T^{11} -$$$$12\!\cdots\!00$$$$T^{12} -$$$$10\!\cdots\!50$$$$T^{13} -$$$$34\!\cdots\!00$$$$T^{14} +$$$$12\!\cdots\!50$$$$T^{15} +$$$$90\!\cdots\!25$$$$T^{16}$$)($$1 + 42 T - 3688 T^{2} - 336370 T^{3} - 1345940 T^{4} + 732464050 T^{5} + 13329225000 T^{6} - 337978756250 T^{7} - 9350412656250 T^{8} - 1056183613281250 T^{9} + 130168212890625000 T^{10} + 22353028869628906250 T^{11} -$$$$12\!\cdots\!00$$$$T^{12} -$$$$10\!\cdots\!50$$$$T^{13} -$$$$34\!\cdots\!00$$$$T^{14} +$$$$12\!\cdots\!50$$$$T^{15} +$$$$90\!\cdots\!25$$$$T^{16}$$)
$7$ ($$1 + 66 T + 2178 T^{2} - 3104786 T^{3} - 390660977 T^{4} + 28598040732 T^{5} + 7558178349116 T^{6} + 730117525814980 T^{7} - 100452887411613603 T^{8} - 13091475719468548578 T^{9} +$$$$44\!\cdots\!50$$$$T^{10} +$$$$38\!\cdots\!06$$$$T^{11} +$$$$37\!\cdots\!31$$$$T^{12} -$$$$47\!\cdots\!84$$$$T^{13} -$$$$77\!\cdots\!76$$$$T^{14} -$$$$79\!\cdots\!88$$$$T^{15} +$$$$10\!\cdots\!19$$$$T^{16} +$$$$18\!\cdots\!58$$$$T^{17} +$$$$35\!\cdots\!50$$$$T^{18} -$$$$17\!\cdots\!46$$$$T^{19} -$$$$22\!\cdots\!47$$$$T^{20} +$$$$27\!\cdots\!40$$$$T^{21} +$$$$48\!\cdots\!16$$$$T^{22} +$$$$30\!\cdots\!24$$$$T^{23} -$$$$70\!\cdots\!73$$$$T^{24} -$$$$93\!\cdots\!98$$$$T^{25} +$$$$11\!\cdots\!78$$$$T^{26} +$$$$56\!\cdots\!62$$$$T^{27} +$$$$14\!\cdots\!49$$$$T^{28}$$)($$1 - 66 T + 2178 T^{2} + 3104786 T^{3} - 390660977 T^{4} - 28598040732 T^{5} + 7558178349116 T^{6} - 730117525814980 T^{7} - 100452887411613603 T^{8} + 13091475719468548578 T^{9} +$$$$44\!\cdots\!50$$$$T^{10} -$$$$38\!\cdots\!06$$$$T^{11} +$$$$37\!\cdots\!31$$$$T^{12} +$$$$47\!\cdots\!84$$$$T^{13} -$$$$77\!\cdots\!76$$$$T^{14} +$$$$79\!\cdots\!88$$$$T^{15} +$$$$10\!\cdots\!19$$$$T^{16} -$$$$18\!\cdots\!58$$$$T^{17} +$$$$35\!\cdots\!50$$$$T^{18} +$$$$17\!\cdots\!46$$$$T^{19} -$$$$22\!\cdots\!47$$$$T^{20} -$$$$27\!\cdots\!40$$$$T^{21} +$$$$48\!\cdots\!16$$$$T^{22} -$$$$30\!\cdots\!24$$$$T^{23} -$$$$70\!\cdots\!73$$$$T^{24} +$$$$93\!\cdots\!98$$$$T^{25} +$$$$11\!\cdots\!78$$$$T^{26} -$$$$56\!\cdots\!62$$$$T^{27} +$$$$14\!\cdots\!49$$$$T^{28}$$)($$1 - 86 T + 3698 T^{2} + 2808286 T^{3} - 810527584 T^{4} - 2504717314 T^{5} + 7155971823534 T^{6} - 2324030762443574 T^{7} + 166847822527644348 T^{8} + 29386477550704152562 T^{9} -$$$$38\!\cdots\!46$$$$T^{10} +$$$$51\!\cdots\!62$$$$T^{11} +$$$$38\!\cdots\!24$$$$T^{12} -$$$$97\!\cdots\!26$$$$T^{13} +$$$$45\!\cdots\!90$$$$T^{14} +$$$$35\!\cdots\!26$$$$T^{15} -$$$$24\!\cdots\!62$$$$T^{16} +$$$$60\!\cdots\!82$$$$T^{17} +$$$$12\!\cdots\!10$$$$T^{18} -$$$$46\!\cdots\!18$$$$T^{19} +$$$$30\!\cdots\!24$$$$T^{20} +$$$$69\!\cdots\!34$$$$T^{21} -$$$$87\!\cdots\!54$$$$T^{22} +$$$$11\!\cdots\!66$$$$T^{23} +$$$$10\!\cdots\!48$$$$T^{24} -$$$$24\!\cdots\!18$$$$T^{25} +$$$$12\!\cdots\!66$$$$T^{26} -$$$$75\!\cdots\!02$$$$T^{27} -$$$$41\!\cdots\!84$$$$T^{28} +$$$$23\!\cdots\!02$$$$T^{29} +$$$$53\!\cdots\!02$$$$T^{30} -$$$$20\!\cdots\!98$$$$T^{31} +$$$$40\!\cdots\!01$$$$T^{32}$$)($$1 + 86 T + 3698 T^{2} - 2808286 T^{3} - 810527584 T^{4} + 2504717314 T^{5} + 7155971823534 T^{6} + 2324030762443574 T^{7} + 166847822527644348 T^{8} - 29386477550704152562 T^{9} -$$$$38\!\cdots\!46$$$$T^{10} -$$$$51\!\cdots\!62$$$$T^{11} +$$$$38\!\cdots\!24$$$$T^{12} +$$$$97\!\cdots\!26$$$$T^{13} +$$$$45\!\cdots\!90$$$$T^{14} -$$$$35\!\cdots\!26$$$$T^{15} -$$$$24\!\cdots\!62$$$$T^{16} -$$$$60\!\cdots\!82$$$$T^{17} +$$$$12\!\cdots\!10$$$$T^{18} +$$$$46\!\cdots\!18$$$$T^{19} +$$$$30\!\cdots\!24$$$$T^{20} -$$$$69\!\cdots\!34$$$$T^{21} -$$$$87\!\cdots\!54$$$$T^{22} -$$$$11\!\cdots\!66$$$$T^{23} +$$$$10\!\cdots\!48$$$$T^{24} +$$$$24\!\cdots\!18$$$$T^{25} +$$$$12\!\cdots\!66$$$$T^{26} +$$$$75\!\cdots\!02$$$$T^{27} -$$$$41\!\cdots\!84$$$$T^{28} -$$$$23\!\cdots\!02$$$$T^{29} +$$$$53\!\cdots\!02$$$$T^{30} +$$$$20\!\cdots\!98$$$$T^{31} +$$$$40\!\cdots\!01$$$$T^{32}$$)
$11$ ($$1 - 1517670 T^{2} + 1118279059571 T^{4} - 531239593921187868 T^{6} +$$$$18\!\cdots\!61$$$$T^{8} -$$$$48\!\cdots\!18$$$$T^{10} +$$$$10\!\cdots\!67$$$$T^{12} -$$$$18\!\cdots\!88$$$$T^{14} +$$$$27\!\cdots\!67$$$$T^{16} -$$$$32\!\cdots\!18$$$$T^{18} +$$$$31\!\cdots\!61$$$$T^{20} -$$$$24\!\cdots\!68$$$$T^{22} +$$$$13\!\cdots\!71$$$$T^{24} -$$$$46\!\cdots\!70$$$$T^{26} +$$$$78\!\cdots\!01$$$$T^{28}$$)($$1 - 1517670 T^{2} + 1118279059571 T^{4} - 531239593921187868 T^{6} +$$$$18\!\cdots\!61$$$$T^{8} -$$$$48\!\cdots\!18$$$$T^{10} +$$$$10\!\cdots\!67$$$$T^{12} -$$$$18\!\cdots\!88$$$$T^{14} +$$$$27\!\cdots\!67$$$$T^{16} -$$$$32\!\cdots\!18$$$$T^{18} +$$$$31\!\cdots\!61$$$$T^{20} -$$$$24\!\cdots\!68$$$$T^{22} +$$$$13\!\cdots\!71$$$$T^{24} -$$$$46\!\cdots\!70$$$$T^{26} +$$$$78\!\cdots\!01$$$$T^{28}$$)($$1 - 580860 T^{2} + 233332093584 T^{4} - 74638580678134772 T^{6} +$$$$20\!\cdots\!20$$$$T^{8} -$$$$46\!\cdots\!24$$$$T^{10} +$$$$96\!\cdots\!08$$$$T^{12} -$$$$18\!\cdots\!84$$$$T^{14} +$$$$30\!\cdots\!54$$$$T^{16} -$$$$46\!\cdots\!84$$$$T^{18} +$$$$65\!\cdots\!08$$$$T^{20} -$$$$81\!\cdots\!24$$$$T^{22} +$$$$90\!\cdots\!20$$$$T^{24} -$$$$87\!\cdots\!72$$$$T^{26} +$$$$71\!\cdots\!84$$$$T^{28} -$$$$45\!\cdots\!60$$$$T^{30} +$$$$20\!\cdots\!01$$$$T^{32}$$)($$1 - 580860 T^{2} + 233332093584 T^{4} - 74638580678134772 T^{6} +$$$$20\!\cdots\!20$$$$T^{8} -$$$$46\!\cdots\!24$$$$T^{10} +$$$$96\!\cdots\!08$$$$T^{12} -$$$$18\!\cdots\!84$$$$T^{14} +$$$$30\!\cdots\!54$$$$T^{16} -$$$$46\!\cdots\!84$$$$T^{18} +$$$$65\!\cdots\!08$$$$T^{20} -$$$$81\!\cdots\!24$$$$T^{22} +$$$$90\!\cdots\!20$$$$T^{24} -$$$$87\!\cdots\!72$$$$T^{26} +$$$$71\!\cdots\!84$$$$T^{28} -$$$$45\!\cdots\!60$$$$T^{30} +$$$$20\!\cdots\!01$$$$T^{32}$$)
$13$ ($$1 + 414 T + 85698 T^{2} + 485371686 T^{3} + 407510115667 T^{4} - 25330305055892 T^{5} + 72383288599671444 T^{6} +$$$$13\!\cdots\!64$$$$T^{7} +$$$$19\!\cdots\!85$$$$T^{8} -$$$$26\!\cdots\!74$$$$T^{9} +$$$$24\!\cdots\!22$$$$T^{10} +$$$$12\!\cdots\!02$$$$T^{11} -$$$$99\!\cdots\!17$$$$T^{12} -$$$$27\!\cdots\!44$$$$T^{13} +$$$$44\!\cdots\!64$$$$T^{14} -$$$$10\!\cdots\!92$$$$T^{15} -$$$$13\!\cdots\!33$$$$T^{16} +$$$$63\!\cdots\!14$$$$T^{17} +$$$$45\!\cdots\!22$$$$T^{18} -$$$$18\!\cdots\!82$$$$T^{19} +$$$$49\!\cdots\!65$$$$T^{20} +$$$$13\!\cdots\!48$$$$T^{21} +$$$$26\!\cdots\!44$$$$T^{22} -$$$$33\!\cdots\!56$$$$T^{23} +$$$$20\!\cdots\!83$$$$T^{24} +$$$$89\!\cdots\!02$$$$T^{25} +$$$$58\!\cdots\!98$$$$T^{26} +$$$$10\!\cdots\!02$$$$T^{27} +$$$$94\!\cdots\!49$$$$T^{28}$$)($$1 + 414 T + 85698 T^{2} + 485371686 T^{3} + 407510115667 T^{4} - 25330305055892 T^{5} + 72383288599671444 T^{6} +$$$$13\!\cdots\!64$$$$T^{7} +$$$$19\!\cdots\!85$$$$T^{8} -$$$$26\!\cdots\!74$$$$T^{9} +$$$$24\!\cdots\!22$$$$T^{10} +$$$$12\!\cdots\!02$$$$T^{11} -$$$$99\!\cdots\!17$$$$T^{12} -$$$$27\!\cdots\!44$$$$T^{13} +$$$$44\!\cdots\!64$$$$T^{14} -$$$$10\!\cdots\!92$$$$T^{15} -$$$$13\!\cdots\!33$$$$T^{16} +$$$$63\!\cdots\!14$$$$T^{17} +$$$$45\!\cdots\!22$$$$T^{18} -$$$$18\!\cdots\!82$$$$T^{19} +$$$$49\!\cdots\!65$$$$T^{20} +$$$$13\!\cdots\!48$$$$T^{21} +$$$$26\!\cdots\!44$$$$T^{22} -$$$$33\!\cdots\!56$$$$T^{23} +$$$$20\!\cdots\!83$$$$T^{24} +$$$$89\!\cdots\!02$$$$T^{25} +$$$$58\!\cdots\!98$$$$T^{26} +$$$$10\!\cdots\!02$$$$T^{27} +$$$$94\!\cdots\!49$$$$T^{28}$$)($$1 - 536 T + 143648 T^{2} - 293170824 T^{3} - 185935117448 T^{4} + 112653613917608 T^{5} + 9301436713751904 T^{6} + 69204174166800470584 T^{7} +$$$$13\!\cdots\!60$$$$T^{8} -$$$$25\!\cdots\!64$$$$T^{9} -$$$$50\!\cdots\!68$$$$T^{10} -$$$$90\!\cdots\!08$$$$T^{11} +$$$$40\!\cdots\!76$$$$T^{12} +$$$$23\!\cdots\!68$$$$T^{13} +$$$$13\!\cdots\!08$$$$T^{14} +$$$$14\!\cdots\!44$$$$T^{15} -$$$$96\!\cdots\!10$$$$T^{16} +$$$$55\!\cdots\!92$$$$T^{17} +$$$$17\!\cdots\!92$$$$T^{18} +$$$$12\!\cdots\!76$$$$T^{19} +$$$$77\!\cdots\!76$$$$T^{20} -$$$$64\!\cdots\!44$$$$T^{21} -$$$$13\!\cdots\!32$$$$T^{22} -$$$$24\!\cdots\!48$$$$T^{23} +$$$$48\!\cdots\!60$$$$T^{24} +$$$$92\!\cdots\!12$$$$T^{25} +$$$$46\!\cdots\!96$$$$T^{26} +$$$$20\!\cdots\!56$$$$T^{27} -$$$$12\!\cdots\!48$$$$T^{28} -$$$$74\!\cdots\!32$$$$T^{29} +$$$$13\!\cdots\!52$$$$T^{30} -$$$$18\!\cdots\!52$$$$T^{31} +$$$$13\!\cdots\!01$$$$T^{32}$$)($$1 - 536 T + 143648 T^{2} - 293170824 T^{3} - 185935117448 T^{4} + 112653613917608 T^{5} + 9301436713751904 T^{6} + 69204174166800470584 T^{7} +$$$$13\!\cdots\!60$$$$T^{8} -$$$$25\!\cdots\!64$$$$T^{9} -$$$$50\!\cdots\!68$$$$T^{10} -$$$$90\!\cdots\!08$$$$T^{11} +$$$$40\!\cdots\!76$$$$T^{12} +$$$$23\!\cdots\!68$$$$T^{13} +$$$$13\!\cdots\!08$$$$T^{14} +$$$$14\!\cdots\!44$$$$T^{15} -$$$$96\!\cdots\!10$$$$T^{16} +$$$$55\!\cdots\!92$$$$T^{17} +$$$$17\!\cdots\!92$$$$T^{18} +$$$$12\!\cdots\!76$$$$T^{19} +$$$$77\!\cdots\!76$$$$T^{20} -$$$$64\!\cdots\!44$$$$T^{21} -$$$$13\!\cdots\!32$$$$T^{22} -$$$$24\!\cdots\!48$$$$T^{23} +$$$$48\!\cdots\!60$$$$T^{24} +$$$$92\!\cdots\!12$$$$T^{25} +$$$$46\!\cdots\!96$$$$T^{26} +$$$$20\!\cdots\!56$$$$T^{27} -$$$$12\!\cdots\!48$$$$T^{28} -$$$$74\!\cdots\!32$$$$T^{29} +$$$$13\!\cdots\!52$$$$T^{30} -$$$$18\!\cdots\!52$$$$T^{31} +$$$$13\!\cdots\!01$$$$T^{32}$$)
$17$ ($$1 - 1222 T + 746642 T^{2} - 1023656774 T^{3} - 7517818418661 T^{4} + 9805314295428420 T^{5} - 5845038493789599340 T^{6} +$$$$85\!\cdots\!80$$$$T^{7} +$$$$21\!\cdots\!05$$$$T^{8} -$$$$32\!\cdots\!70$$$$T^{9} +$$$$19\!\cdots\!70$$$$T^{10} -$$$$33\!\cdots\!50$$$$T^{11} -$$$$20\!\cdots\!37$$$$T^{12} +$$$$66\!\cdots\!24$$$$T^{13} -$$$$44\!\cdots\!04$$$$T^{14} +$$$$93\!\cdots\!68$$$$T^{15} -$$$$41\!\cdots\!13$$$$T^{16} -$$$$96\!\cdots\!50$$$$T^{17} +$$$$80\!\cdots\!70$$$$T^{18} -$$$$19\!\cdots\!90$$$$T^{19} +$$$$17\!\cdots\!45$$$$T^{20} +$$$$99\!\cdots\!40$$$$T^{21} -$$$$96\!\cdots\!40$$$$T^{22} +$$$$22\!\cdots\!40$$$$T^{23} -$$$$25\!\cdots\!89$$$$T^{24} -$$$$48\!\cdots\!82$$$$T^{25} +$$$$50\!\cdots\!42$$$$T^{26} -$$$$11\!\cdots\!54$$$$T^{27} +$$$$13\!\cdots\!49$$$$T^{28}$$)($$1 - 1222 T + 746642 T^{2} - 1023656774 T^{3} - 7517818418661 T^{4} + 9805314295428420 T^{5} - 5845038493789599340 T^{6} +$$$$85\!\cdots\!80$$$$T^{7} +$$$$21\!\cdots\!05$$$$T^{8} -$$$$32\!\cdots\!70$$$$T^{9} +$$$$19\!\cdots\!70$$$$T^{10} -$$$$33\!\cdots\!50$$$$T^{11} -$$$$20\!\cdots\!37$$$$T^{12} +$$$$66\!\cdots\!24$$$$T^{13} -$$$$44\!\cdots\!04$$$$T^{14} +$$$$93\!\cdots\!68$$$$T^{15} -$$$$41\!\cdots\!13$$$$T^{16} -$$$$96\!\cdots\!50$$$$T^{17} +$$$$80\!\cdots\!70$$$$T^{18} -$$$$19\!\cdots\!90$$$$T^{19} +$$$$17\!\cdots\!45$$$$T^{20} +$$$$99\!\cdots\!40$$$$T^{21} -$$$$96\!\cdots\!40$$$$T^{22} +$$$$22\!\cdots\!40$$$$T^{23} -$$$$25\!\cdots\!89$$$$T^{24} -$$$$48\!\cdots\!82$$$$T^{25} +$$$$50\!\cdots\!42$$$$T^{26} -$$$$11\!\cdots\!54$$$$T^{27} +$$$$13\!\cdots\!49$$$$T^{28}$$)($$1 + 1828 T + 1670792 T^{2} - 327758324 T^{3} + 3015753425928 T^{4} + 10493189333351412 T^{5} + 14196566162828930648 T^{6} +$$$$64\!\cdots\!44$$$$T^{7} +$$$$60\!\cdots\!96$$$$T^{8} +$$$$26\!\cdots\!20$$$$T^{9} +$$$$48\!\cdots\!00$$$$T^{10} +$$$$40\!\cdots\!40$$$$T^{11} +$$$$30\!\cdots\!88$$$$T^{12} +$$$$53\!\cdots\!44$$$$T^{13} +$$$$10\!\cdots\!76$$$$T^{14} +$$$$94\!\cdots\!68$$$$T^{15} +$$$$94\!\cdots\!74$$$$T^{16} +$$$$13\!\cdots\!76$$$$T^{17} +$$$$20\!\cdots\!24$$$$T^{18} +$$$$15\!\cdots\!92$$$$T^{19} +$$$$12\!\cdots\!88$$$$T^{20} +$$$$23\!\cdots\!80$$$$T^{21} +$$$$39\!\cdots\!00$$$$T^{22} +$$$$30\!\cdots\!60$$$$T^{23} +$$$$99\!\cdots\!96$$$$T^{24} +$$$$15\!\cdots\!08$$$$T^{25} +$$$$47\!\cdots\!52$$$$T^{26} +$$$$49\!\cdots\!16$$$$T^{27} +$$$$20\!\cdots\!28$$$$T^{28} -$$$$31\!\cdots\!68$$$$T^{29} +$$$$22\!\cdots\!08$$$$T^{30} +$$$$35\!\cdots\!04$$$$T^{31} +$$$$27\!\cdots\!01$$$$T^{32}$$)($$1 + 1828 T + 1670792 T^{2} - 327758324 T^{3} + 3015753425928 T^{4} + 10493189333351412 T^{5} + 14196566162828930648 T^{6} +$$$$64\!\cdots\!44$$$$T^{7} +$$$$60\!\cdots\!96$$$$T^{8} +$$$$26\!\cdots\!20$$$$T^{9} +$$$$48\!\cdots\!00$$$$T^{10} +$$$$40\!\cdots\!40$$$$T^{11} +$$$$30\!\cdots\!88$$$$T^{12} +$$$$53\!\cdots\!44$$$$T^{13} +$$$$10\!\cdots\!76$$$$T^{14} +$$$$94\!\cdots\!68$$$$T^{15} +$$$$94\!\cdots\!74$$$$T^{16} +$$$$13\!\cdots\!76$$$$T^{17} +$$$$20\!\cdots\!24$$$$T^{18} +$$$$15\!\cdots\!92$$$$T^{19} +$$$$12\!\cdots\!88$$$$T^{20} +$$$$23\!\cdots\!80$$$$T^{21} +$$$$39\!\cdots\!00$$$$T^{22} +$$$$30\!\cdots\!60$$$$T^{23} +$$$$99\!\cdots\!96$$$$T^{24} +$$$$15\!\cdots\!08$$$$T^{25} +$$$$47\!\cdots\!52$$$$T^{26} +$$$$49\!\cdots\!16$$$$T^{27} +$$$$20\!\cdots\!28$$$$T^{28} -$$$$31\!\cdots\!68$$$$T^{29} +$$$$22\!\cdots\!08$$$$T^{30} +$$$$35\!\cdots\!04$$$$T^{31} +$$$$27\!\cdots\!01$$$$T^{32}$$)
$19$ ($$( 1 + 2836 T + 12192485 T^{2} + 21773970856 T^{3} + 58437600122669 T^{4} + 77435325554759820 T^{5} +$$$$17\!\cdots\!85$$$$T^{6} +$$$$20\!\cdots\!00$$$$T^{7} +$$$$43\!\cdots\!15$$$$T^{8} +$$$$47\!\cdots\!20$$$$T^{9} +$$$$88\!\cdots\!31$$$$T^{10} +$$$$81\!\cdots\!56$$$$T^{11} +$$$$11\!\cdots\!15$$$$T^{12} +$$$$65\!\cdots\!36$$$$T^{13} +$$$$57\!\cdots\!99$$$$T^{14} )^{2}$$)($$( 1 - 2836 T + 12192485 T^{2} - 21773970856 T^{3} + 58437600122669 T^{4} - 77435325554759820 T^{5} +$$$$17\!\cdots\!85$$$$T^{6} -$$$$20\!\cdots\!00$$$$T^{7} +$$$$43\!\cdots\!15$$$$T^{8} -$$$$47\!\cdots\!20$$$$T^{9} +$$$$88\!\cdots\!31$$$$T^{10} -$$$$81\!\cdots\!56$$$$T^{11} +$$$$11\!\cdots\!15$$$$T^{12} -$$$$65\!\cdots\!36$$$$T^{13} +$$$$57\!\cdots\!99$$$$T^{14} )^{2}$$)($$( 1 + 1256 T + 11933496 T^{2} + 17157951112 T^{3} + 74779232061244 T^{4} + 104521619172501960 T^{5} +$$$$31\!\cdots\!88$$$$T^{6} +$$$$38\!\cdots\!64$$$$T^{7} +$$$$93\!\cdots\!18$$$$T^{8} +$$$$94\!\cdots\!36$$$$T^{9} +$$$$19\!\cdots\!88$$$$T^{10} +$$$$15\!\cdots\!40$$$$T^{11} +$$$$28\!\cdots\!44$$$$T^{12} +$$$$15\!\cdots\!88$$$$T^{13} +$$$$27\!\cdots\!96$$$$T^{14} +$$$$71\!\cdots\!44$$$$T^{15} +$$$$14\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 1256 T + 11933496 T^{2} - 17157951112 T^{3} + 74779232061244 T^{4} - 104521619172501960 T^{5} +$$$$31\!\cdots\!88$$$$T^{6} -$$$$38\!\cdots\!64$$$$T^{7} +$$$$93\!\cdots\!18$$$$T^{8} -$$$$94\!\cdots\!36$$$$T^{9} +$$$$19\!\cdots\!88$$$$T^{10} -$$$$15\!\cdots\!40$$$$T^{11} +$$$$28\!\cdots\!44$$$$T^{12} -$$$$15\!\cdots\!88$$$$T^{13} +$$$$27\!\cdots\!96$$$$T^{14} -$$$$71\!\cdots\!44$$$$T^{15} +$$$$14\!\cdots\!01$$$$T^{16} )^{2}$$)
$23$ ($$1 + 2902 T + 4210802 T^{2} - 8585545830 T^{3} - 77137172452561 T^{4} - 5298422918089420 T^{5} +$$$$34\!\cdots\!32$$$$T^{6} +$$$$17\!\cdots\!48$$$$T^{7} +$$$$43\!\cdots\!33$$$$T^{8} -$$$$14\!\cdots\!50$$$$T^{9} -$$$$10\!\cdots\!54$$$$T^{10} -$$$$57\!\cdots\!98$$$$T^{11} -$$$$19\!\cdots\!21$$$$T^{12} +$$$$51\!\cdots\!28$$$$T^{13} +$$$$13\!\cdots\!40$$$$T^{14} +$$$$33\!\cdots\!04$$$$T^{15} -$$$$79\!\cdots\!29$$$$T^{16} -$$$$15\!\cdots\!86$$$$T^{17} -$$$$18\!\cdots\!54$$$$T^{18} -$$$$15\!\cdots\!50$$$$T^{19} +$$$$30\!\cdots\!17$$$$T^{20} +$$$$81\!\cdots\!36$$$$T^{21} +$$$$10\!\cdots\!32$$$$T^{22} -$$$$10\!\cdots\!60$$$$T^{23} -$$$$94\!\cdots\!89$$$$T^{24} -$$$$67\!\cdots\!10$$$$T^{25} +$$$$21\!\cdots\!02$$$$T^{26} +$$$$94\!\cdots\!86$$$$T^{27} +$$$$20\!\cdots\!49$$$$T^{28}$$)($$1 - 2902 T + 4210802 T^{2} + 8585545830 T^{3} - 77137172452561 T^{4} + 5298422918089420 T^{5} +$$$$34\!\cdots\!32$$$$T^{6} -$$$$17\!\cdots\!48$$$$T^{7} +$$$$43\!\cdots\!33$$$$T^{8} +$$$$14\!\cdots\!50$$$$T^{9} -$$$$10\!\cdots\!54$$$$T^{10} +$$$$57\!\cdots\!98$$$$T^{11} -$$$$19\!\cdots\!21$$$$T^{12} -$$$$51\!\cdots\!28$$$$T^{13} +$$$$13\!\cdots\!40$$$$T^{14} -$$$$33\!\cdots\!04$$$$T^{15} -$$$$79\!\cdots\!29$$$$T^{16} +$$$$15\!\cdots\!86$$$$T^{17} -$$$$18\!\cdots\!54$$$$T^{18} +$$$$15\!\cdots\!50$$$$T^{19} +$$$$30\!\cdots\!17$$$$T^{20} -$$$$81\!\cdots\!36$$$$T^{21} +$$$$10\!\cdots\!32$$$$T^{22} +$$$$10\!\cdots\!60$$$$T^{23} -$$$$94\!\cdots\!89$$$$T^{24} +$$$$67\!\cdots\!10$$$$T^{25} +$$$$21\!\cdots\!02$$$$T^{26} -$$$$94\!\cdots\!86$$$$T^{27} +$$$$20\!\cdots\!49$$$$T^{28}$$)($$1 - 7642 T + 29200082 T^{2} - 114423930750 T^{3} + 421188911449792 T^{4} - 1070557300674963934 T^{5} +$$$$24\!\cdots\!34$$$$T^{6} -$$$$58\!\cdots\!94$$$$T^{7} +$$$$77\!\cdots\!36$$$$T^{8} +$$$$18\!\cdots\!62$$$$T^{9} -$$$$19\!\cdots\!06$$$$T^{10} +$$$$97\!\cdots\!06$$$$T^{11} -$$$$29\!\cdots\!68$$$$T^{12} +$$$$18\!\cdots\!70$$$$T^{13} +$$$$73\!\cdots\!74$$$$T^{14} -$$$$37\!\cdots\!54$$$$T^{15} +$$$$12\!\cdots\!78$$$$T^{16} -$$$$24\!\cdots\!22$$$$T^{17} +$$$$30\!\cdots\!26$$$$T^{18} +$$$$49\!\cdots\!90$$$$T^{19} -$$$$50\!\cdots\!68$$$$T^{20} +$$$$10\!\cdots\!58$$$$T^{21} -$$$$14\!\cdots\!94$$$$T^{22} +$$$$84\!\cdots\!34$$$$T^{23} +$$$$22\!\cdots\!36$$$$T^{24} -$$$$11\!\cdots\!42$$$$T^{25} +$$$$29\!\cdots\!66$$$$T^{26} -$$$$84\!\cdots\!38$$$$T^{27} +$$$$21\!\cdots\!92$$$$T^{28} -$$$$37\!\cdots\!50$$$$T^{29} +$$$$61\!\cdots\!18$$$$T^{30} -$$$$10\!\cdots\!94$$$$T^{31} +$$$$86\!\cdots\!01$$$$T^{32}$$)($$1 + 7642 T + 29200082 T^{2} + 114423930750 T^{3} + 421188911449792 T^{4} + 1070557300674963934 T^{5} +$$$$24\!\cdots\!34$$$$T^{6} +$$$$58\!\cdots\!94$$$$T^{7} +$$$$77\!\cdots\!36$$$$T^{8} -$$$$18\!\cdots\!62$$$$T^{9} -$$$$19\!\cdots\!06$$$$T^{10} -$$$$97\!\cdots\!06$$$$T^{11} -$$$$29\!\cdots\!68$$$$T^{12} -$$$$18\!\cdots\!70$$$$T^{13} +$$$$73\!\cdots\!74$$$$T^{14} +$$$$37\!\cdots\!54$$$$T^{15} +$$$$12\!\cdots\!78$$$$T^{16} +$$$$24\!\cdots\!22$$$$T^{17} +$$$$30\!\cdots\!26$$$$T^{18} -$$$$49\!\cdots\!90$$$$T^{19} -$$$$50\!\cdots\!68$$$$T^{20} -$$$$10\!\cdots\!58$$$$T^{21} -$$$$14\!\cdots\!94$$$$T^{22} -$$$$84\!\cdots\!34$$$$T^{23} +$$$$22\!\cdots\!36$$$$T^{24} +$$$$11\!\cdots\!42$$$$T^{25} +$$$$29\!\cdots\!66$$$$T^{26} +$$$$84\!\cdots\!38$$$$T^{27} +$$$$21\!\cdots\!92$$$$T^{28} +$$$$37\!\cdots\!50$$$$T^{29} +$$$$61\!\cdots\!18$$$$T^{30} +$$$$10\!\cdots\!94$$$$T^{31} +$$$$86\!\cdots\!01$$$$T^{32}$$)
$29$ ($$1 - 127109206 T^{2} + 8400089254893139 T^{4} -$$$$38\!\cdots\!76$$$$T^{6} +$$$$13\!\cdots\!57$$$$T^{8} -$$$$39\!\cdots\!02$$$$T^{10} +$$$$98\!\cdots\!23$$$$T^{12} -$$$$21\!\cdots\!92$$$$T^{14} +$$$$41\!\cdots\!23$$$$T^{16} -$$$$69\!\cdots\!02$$$$T^{18} +$$$$10\!\cdots\!57$$$$T^{20} -$$$$12\!\cdots\!76$$$$T^{22} +$$$$11\!\cdots\!39$$$$T^{24} -$$$$70\!\cdots\!06$$$$T^{26} +$$$$23\!\cdots\!01$$$$T^{28}$$)($$1 - 127109206 T^{2} + 8400089254893139 T^{4} -$$$$38\!\cdots\!76$$$$T^{6} +$$$$13\!\cdots\!57$$$$T^{8} -$$$$39\!\cdots\!02$$$$T^{10} +$$$$98\!\cdots\!23$$$$T^{12} -$$$$21\!\cdots\!92$$$$T^{14} +$$$$41\!\cdots\!23$$$$T^{16} -$$$$69\!\cdots\!02$$$$T^{18} +$$$$10\!\cdots\!57$$$$T^{20} -$$$$12\!\cdots\!76$$$$T^{22} +$$$$11\!\cdots\!39$$$$T^{24} -$$$$70\!\cdots\!06$$$$T^{26} +$$$$23\!\cdots\!01$$$$T^{28}$$)($$1 - 129450464 T^{2} + 9016787664231832 T^{4} -$$$$44\!\cdots\!56$$$$T^{6} +$$$$16\!\cdots\!60$$$$T^{8} -$$$$53\!\cdots\!48$$$$T^{10} +$$$$14\!\cdots\!16$$$$T^{12} -$$$$34\!\cdots\!32$$$$T^{14} +$$$$74\!\cdots\!82$$$$T^{16} -$$$$14\!\cdots\!32$$$$T^{18} +$$$$25\!\cdots\!16$$$$T^{20} -$$$$39\!\cdots\!48$$$$T^{22} +$$$$52\!\cdots\!60$$$$T^{24} -$$$$58\!\cdots\!56$$$$T^{26} +$$$$49\!\cdots\!32$$$$T^{28} -$$$$30\!\cdots\!64$$$$T^{30} +$$$$98\!\cdots\!01$$$$T^{32}$$)($$1 - 129450464 T^{2} + 9016787664231832 T^{4} -$$$$44\!\cdots\!56$$$$T^{6} +$$$$16\!\cdots\!60$$$$T^{8} -$$$$53\!\cdots\!48$$$$T^{10} +$$$$14\!\cdots\!16$$$$T^{12} -$$$$34\!\cdots\!32$$$$T^{14} +$$$$74\!\cdots\!82$$$$T^{16} -$$$$14\!\cdots\!32$$$$T^{18} +$$$$25\!\cdots\!16$$$$T^{20} -$$$$39\!\cdots\!48$$$$T^{22} +$$$$52\!\cdots\!60$$$$T^{24} -$$$$58\!\cdots\!56$$$$T^{26} +$$$$49\!\cdots\!32$$$$T^{28} -$$$$30\!\cdots\!64$$$$T^{30} +$$$$98\!\cdots\!01$$$$T^{32}$$)
$31$ ($$1 - 265679454 T^{2} + 34933996110970539 T^{4} -$$$$30\!\cdots\!64$$$$T^{6} +$$$$19\!\cdots\!17$$$$T^{8} -$$$$92\!\cdots\!38$$$$T^{10} +$$$$36\!\cdots\!43$$$$T^{12} -$$$$11\!\cdots\!88$$$$T^{14} +$$$$29\!\cdots\!43$$$$T^{16} -$$$$62\!\cdots\!38$$$$T^{18} +$$$$10\!\cdots\!17$$$$T^{20} -$$$$13\!\cdots\!64$$$$T^{22} +$$$$12\!\cdots\!39$$$$T^{24} -$$$$80\!\cdots\!54$$$$T^{26} +$$$$24\!\cdots\!01$$$$T^{28}$$)($$1 - 265679454 T^{2} + 34933996110970539 T^{4} -$$$$30\!\cdots\!64$$$$T^{6} +$$$$19\!\cdots\!17$$$$T^{8} -$$$$92\!\cdots\!38$$$$T^{10} +$$$$36\!\cdots\!43$$$$T^{12} -$$$$11\!\cdots\!88$$$$T^{14} +$$$$29\!\cdots\!43$$$$T^{16} -$$$$62\!\cdots\!38$$$$T^{18} +$$$$10\!\cdots\!17$$$$T^{20} -$$$$13\!\cdots\!64$$$$T^{22} +$$$$12\!\cdots\!39$$$$T^{24} -$$$$80\!\cdots\!54$$$$T^{26} +$$$$24\!\cdots\!01$$$$T^{28}$$)($$1 - 221015276 T^{2} + 25619057922480912 T^{4} -$$$$20\!\cdots\!04$$$$T^{6} +$$$$12\!\cdots\!00$$$$T^{8} -$$$$64\!\cdots\!72$$$$T^{10} +$$$$27\!\cdots\!96$$$$T^{12} -$$$$98\!\cdots\!48$$$$T^{14} +$$$$30\!\cdots\!82$$$$T^{16} -$$$$80\!\cdots\!48$$$$T^{18} +$$$$18\!\cdots\!96$$$$T^{20} -$$$$35\!\cdots\!72$$$$T^{22} +$$$$57\!\cdots\!00$$$$T^{24} -$$$$76\!\cdots\!04$$$$T^{26} +$$$$77\!\cdots\!12$$$$T^{28} -$$$$54\!\cdots\!76$$$$T^{30} +$$$$20\!\cdots\!01$$$$T^{32}$$)($$1 - 221015276 T^{2} + 25619057922480912 T^{4} -$$$$20\!\cdots\!04$$$$T^{6} +$$$$12\!\cdots\!00$$$$T^{8} -$$$$64\!\cdots\!72$$$$T^{10} +$$$$27\!\cdots\!96$$$$T^{12} -$$$$98\!\cdots\!48$$$$T^{14} +$$$$30\!\cdots\!82$$$$T^{16} -$$$$80\!\cdots\!48$$$$T^{18} +$$$$18\!\cdots\!96$$$$T^{20} -$$$$35\!\cdots\!72$$$$T^{22} +$$$$57\!\cdots\!00$$$$T^{24} -$$$$76\!\cdots\!04$$$$T^{26} +$$$$77\!\cdots\!12$$$$T^{28} -$$$$54\!\cdots\!76$$$$T^{30} +$$$$20\!\cdots\!01$$$$T^{32}$$)
$37$ ($$1 + 1790 T + 1602050 T^{2} - 1085215470730 T^{3} - 5589943426343837 T^{4} - 5189725886098796788 T^{5} +$$$$58\!\cdots\!80$$$$T^{6} +$$$$37\!\cdots\!60$$$$T^{7} +$$$$20\!\cdots\!01$$$$T^{8} -$$$$14\!\cdots\!14$$$$T^{9} -$$$$11\!\cdots\!78$$$$T^{10} -$$$$12\!\cdots\!50$$$$T^{11} -$$$$40\!\cdots\!45$$$$T^{12} +$$$$67\!\cdots\!72$$$$T^{13} +$$$$47\!\cdots\!96$$$$T^{14} +$$$$47\!\cdots\!04$$$$T^{15} -$$$$19\!\cdots\!05$$$$T^{16} -$$$$41\!\cdots\!50$$$$T^{17} -$$$$25\!\cdots\!78$$$$T^{18} -$$$$23\!\cdots\!98$$$$T^{19} +$$$$22\!\cdots\!49$$$$T^{20} +$$$$29\!\cdots\!80$$$$T^{21} +$$$$31\!\cdots\!80$$$$T^{22} -$$$$19\!\cdots\!16$$$$T^{23} -$$$$14\!\cdots\!13$$$$T^{24} -$$$$19\!\cdots\!90$$$$T^{25} +$$$$19\!\cdots\!50$$$$T^{26} +$$$$15\!\cdots\!30$$$$T^{27} +$$$$59\!\cdots\!49$$$$T^{28}$$)($$1 + 1790 T + 1602050 T^{2} - 1085215470730 T^{3} - 5589943426343837 T^{4} - 5189725886098796788 T^{5} +$$$$58\!\cdots\!80$$$$T^{6} +$$$$37\!\cdots\!60$$$$T^{7} +$$$$20\!\cdots\!01$$$$T^{8} -$$$$14\!\cdots\!14$$$$T^{9} -$$$$11\!\cdots\!78$$$$T^{10} -$$$$12\!\cdots\!50$$$$T^{11} -$$$$40\!\cdots\!45$$$$T^{12} +$$$$67\!\cdots\!72$$$$T^{13} +$$$$47\!\cdots\!96$$$$T^{14} +$$$$47\!\cdots\!04$$$$T^{15} -$$$$19\!\cdots\!05$$$$T^{16} -$$$$41\!\cdots\!50$$$$T^{17} -$$$$25\!\cdots\!78$$$$T^{18} -$$$$23\!\cdots\!98$$$$T^{19} +$$$$22\!\cdots\!49$$$$T^{20} +$$$$29\!\cdots\!80$$$$T^{21} +$$$$31\!\cdots\!80$$$$T^{22} -$$$$19\!\cdots\!16$$$$T^{23} -$$$$14\!\cdots\!13$$$$T^{24} -$$$$19\!\cdots\!90$$$$T^{25} +$$$$19\!\cdots\!50$$$$T^{26} +$$$$15\!\cdots\!30$$$$T^{27} +$$$$59\!\cdots\!49$$$$T^{28}$$)($$1 + 7620 T + 29032200 T^{2} + 1965688293660 T^{3} + 22987009602091912 T^{4} + 46723925283632703348 T^{5} +$$$$16\!\cdots\!60$$$$T^{6} +$$$$27\!\cdots\!40$$$$T^{7} +$$$$98\!\cdots\!88$$$$T^{8} +$$$$66\!\cdots\!16$$$$T^{9} +$$$$19\!\cdots\!52$$$$T^{10} +$$$$13\!\cdots\!00$$$$T^{11} +$$$$55\!\cdots\!44$$$$T^{12} +$$$$97\!\cdots\!64$$$$T^{13} +$$$$11\!\cdots\!44$$$$T^{14} +$$$$70\!\cdots\!36$$$$T^{15} +$$$$48\!\cdots\!10$$$$T^{16} +$$$$48\!\cdots\!52$$$$T^{17} +$$$$53\!\cdots\!56$$$$T^{18} +$$$$32\!\cdots\!52$$$$T^{19} +$$$$12\!\cdots\!44$$$$T^{20} +$$$$21\!\cdots\!00$$$$T^{21} +$$$$22\!\cdots\!48$$$$T^{22} +$$$$51\!\cdots\!88$$$$T^{23} +$$$$52\!\cdots\!88$$$$T^{24} +$$$$10\!\cdots\!80$$$$T^{25} +$$$$41\!\cdots\!40$$$$T^{26} +$$$$83\!\cdots\!64$$$$T^{27} +$$$$28\!\cdots\!12$$$$T^{28} +$$$$16\!\cdots\!20$$$$T^{29} +$$$$17\!\cdots\!00$$$$T^{30} +$$$$31\!\cdots\!60$$$$T^{31} +$$$$28\!\cdots\!01$$$$T^{32}$$)($$1 + 7620 T + 29032200 T^{2} + 1965688293660 T^{3} + 22987009602091912 T^{4} + 46723925283632703348 T^{5} +$$$$16\!\cdots\!60$$$$T^{6} +$$$$27\!\cdots\!40$$$$T^{7} +$$$$98\!\cdots\!88$$$$T^{8} +$$$$66\!\cdots\!16$$$$T^{9} +$$$$19\!\cdots\!52$$$$T^{10} +$$$$13\!\cdots\!00$$$$T^{11} +$$$$55\!\cdots\!44$$$$T^{12} +$$$$97\!\cdots\!64$$$$T^{13} +$$$$11\!\cdots\!44$$$$T^{14} +$$$$70\!\cdots\!36$$$$T^{15} +$$$$48\!\cdots\!10$$$$T^{16} +$$$$48\!\cdots\!52$$$$T^{17} +$$$$53\!\cdots\!56$$$$T^{18} +$$$$32\!\cdots\!52$$$$T^{19} +$$$$12\!\cdots\!44$$$$T^{20} +$$$$21\!\cdots\!00$$$$T^{21} +$$$$22\!\cdots\!48$$$$T^{22} +$$$$51\!\cdots\!88$$$$T^{23} +$$$$52\!\cdots\!88$$$$T^{24} +$$$$10\!\cdots\!80$$$$T^{25} +$$$$41\!\cdots\!40$$$$T^{26} +$$$$83\!\cdots\!64$$$$T^{27} +$$$$28\!\cdots\!12$$$$T^{28} +$$$$16\!\cdots\!20$$$$T^{29} +$$$$17\!\cdots\!00$$$$T^{30} +$$$$31\!\cdots\!60$$$$T^{31} +$$$$28\!\cdots\!01$$$$T^{32}$$)
$41$ ($$( 1 - 5822 T + 527400583 T^{2} - 3511555483012 T^{3} + 138605008918596701 T^{4} -$$$$95\!\cdots\!50$$$$T^{5} +$$$$23\!\cdots\!95$$$$T^{6} -$$$$14\!\cdots\!20$$$$T^{7} +$$$$26\!\cdots\!95$$$$T^{8} -$$$$12\!\cdots\!50$$$$T^{9} +$$$$21\!\cdots\!01$$$$T^{10} -$$$$63\!\cdots\!12$$$$T^{11} +$$$$11\!\cdots\!83$$$$T^{12} -$$$$14\!\cdots\!22$$$$T^{13} +$$$$28\!\cdots\!01$$$$T^{14} )^{2}$$)($$( 1 - 5822 T + 527400583 T^{2} - 3511555483012 T^{3} + 138605008918596701 T^{4} -$$$$95\!\cdots\!50$$$$T^{5} +$$$$23\!\cdots\!95$$$$T^{6} -$$$$14\!\cdots\!20$$$$T^{7} +$$$$26\!\cdots\!95$$$$T^{8} -$$$$12\!\cdots\!50$$$$T^{9} +$$$$21\!\cdots\!01$$$$T^{10} -$$$$63\!\cdots\!12$$$$T^{11} +$$$$11\!\cdots\!83$$$$T^{12} -$$$$14\!\cdots\!22$$$$T^{13} +$$$$28\!\cdots\!01$$$$T^{14} )^{2}$$)($$( 1 + 10642 T + 229001616 T^{2} + 2308310140798 T^{3} + 41488616565167196 T^{4} +$$$$33\!\cdots\!02$$$$T^{5} +$$$$55\!\cdots\!56$$$$T^{6} +$$$$38\!\cdots\!10$$$$T^{7} +$$$$61\!\cdots\!50$$$$T^{8} +$$$$44\!\cdots\!10$$$$T^{9} +$$$$74\!\cdots\!56$$$$T^{10} +$$$$52\!\cdots\!02$$$$T^{11} +$$$$74\!\cdots\!96$$$$T^{12} +$$$$48\!\cdots\!98$$$$T^{13} +$$$$55\!\cdots\!16$$$$T^{14} +$$$$29\!\cdots\!42$$$$T^{15} +$$$$32\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 + 10642 T + 229001616 T^{2} + 2308310140798 T^{3} + 41488616565167196 T^{4} +$$$$33\!\cdots\!02$$$$T^{5} +$$$$55\!\cdots\!56$$$$T^{6} +$$$$38\!\cdots\!10$$$$T^{7} +$$$$61\!\cdots\!50$$$$T^{8} +$$$$44\!\cdots\!10$$$$T^{9} +$$$$74\!\cdots\!56$$$$T^{10} +$$$$52\!\cdots\!02$$$$T^{11} +$$$$74\!\cdots\!96$$$$T^{12} +$$$$48\!\cdots\!98$$$$T^{13} +$$$$55\!\cdots\!16$$$$T^{14} +$$$$29\!\cdots\!42$$$$T^{15} +$$$$32\!\cdots\!01$$$$T^{16} )^{2}$$)
$43$ ($$1 - 3982 T + 7928162 T^{2} - 5090675647610 T^{3} + 44126507369726119 T^{4} - 95654814508201483332 T^{5} +$$$$12\!\cdots\!96$$$$T^{6} -$$$$15\!\cdots\!12$$$$T^{7} +$$$$46\!\cdots\!93$$$$T^{8} -$$$$33\!\cdots\!78$$$$T^{9} +$$$$35\!\cdots\!38$$$$T^{10} -$$$$10\!\cdots\!70$$$$T^{11} +$$$$78\!\cdots\!59$$$$T^{12} -$$$$84\!\cdots\!64$$$$T^{13} +$$$$18\!\cdots\!08$$$$T^{14} -$$$$12\!\cdots\!52$$$$T^{15} +$$$$16\!\cdots\!91$$$$T^{16} -$$$$34\!\cdots\!90$$$$T^{17} +$$$$16\!\cdots\!38$$$$T^{18} -$$$$22\!\cdots\!54$$$$T^{19} +$$$$47\!\cdots\!57$$$$T^{20} -$$$$23\!\cdots\!84$$$$T^{21} +$$$$28\!\cdots\!96$$$$T^{22} -$$$$30\!\cdots\!76$$$$T^{23} +$$$$20\!\cdots\!31$$$$T^{24} -$$$$35\!\cdots\!70$$$$T^{25} +$$$$80\!\cdots\!62$$$$T^{26} -$$$$59\!\cdots\!26$$$$T^{27} +$$$$22\!\cdots\!49$$$$T^{28}$$)($$1 + 3982 T + 7928162 T^{2} + 5090675647610 T^{3} + 44126507369726119 T^{4} + 95654814508201483332 T^{5} +$$$$12\!\cdots\!96$$$$T^{6} +$$$$15\!\cdots\!12$$$$T^{7} +$$$$46\!\cdots\!93$$$$T^{8} +$$$$33\!\cdots\!78$$$$T^{9} +$$$$35\!\cdots\!38$$$$T^{10} +$$$$10\!\cdots\!70$$$$T^{11} +$$$$78\!\cdots\!59$$$$T^{12} +$$$$84\!\cdots\!64$$$$T^{13} +$$$$18\!\cdots\!08$$$$T^{14} +$$$$12\!\cdots\!52$$$$T^{15} +$$$$16\!\cdots\!91$$$$T^{16} +$$$$34\!\cdots\!90$$$$T^{17} +$$$$16\!\cdots\!38$$$$T^{18} +$$$$22\!\cdots\!54$$$$T^{19} +$$$$47\!\cdots\!57$$$$T^{20} +$$$$23\!\cdots\!84$$$$T^{21} +$$$$28\!\cdots\!96$$$$T^{22} +$$$$30\!\cdots\!76$$$$T^{23} +$$$$20\!\cdots\!31$$$$T^{24} +$$$$35\!\cdots\!70$$$$T^{25} +$$$$80\!\cdots\!62$$$$T^{26} +$$$$59\!\cdots\!26$$$$T^{27} +$$$$22\!\cdots\!49$$$$T^{28}$$)($$1 + 20002 T + 200040002 T^{2} + 4643840984270 T^{3} + 57483685077584672 T^{4} - 83126825813520796778 T^{5} -$$$$23\!\cdots\!50$$$$T^{6} -$$$$76\!\cdots\!70$$$$T^{7} -$$$$32\!\cdots\!64$$$$T^{8} -$$$$35\!\cdots\!86$$$$T^{9} -$$$$28\!\cdots\!02$$$$T^{10} -$$$$51\!\cdots\!50$$$$T^{11} -$$$$19\!\cdots\!52$$$$T^{12} +$$$$54\!\cdots\!78$$$$T^{13} +$$$$53\!\cdots\!62$$$$T^{14} +$$$$11\!\cdots\!58$$$$T^{15} +$$$$24\!\cdots\!66$$$$T^{16} +$$$$17\!\cdots\!94$$$$T^{17} +$$$$11\!\cdots\!38$$$$T^{18} +$$$$17\!\cdots\!46$$$$T^{19} -$$$$89\!\cdots\!52$$$$T^{20} -$$$$35\!\cdots\!50$$$$T^{21} -$$$$28\!\cdots\!98$$$$T^{22} -$$$$53\!\cdots\!02$$$$T^{23} -$$$$70\!\cdots\!64$$$$T^{24} -$$$$24\!\cdots\!10$$$$T^{25} -$$$$11\!\cdots\!50$$$$T^{26} -$$$$57\!\cdots\!46$$$$T^{27} +$$$$58\!\cdots\!72$$$$T^{28} +$$$$69\!\cdots\!10$$$$T^{29} +$$$$44\!\cdots\!98$$$$T^{30} +$$$$64\!\cdots\!14$$$$T^{31} +$$$$47\!\cdots\!01$$$$T^{32}$$)($$1 - 20002 T + 200040002 T^{2} - 4643840984270 T^{3} + 57483685077584672 T^{4} + 83126825813520796778 T^{5} -$$$$23\!\cdots\!50$$$$T^{6} +$$$$76\!\cdots\!70$$$$T^{7} -$$$$32\!\cdots\!64$$$$T^{8} +$$$$35\!\cdots\!86$$$$T^{9} -$$$$28\!\cdots\!02$$$$T^{10} +$$$$51\!\cdots\!50$$$$T^{11} -$$$$19\!\cdots\!52$$$$T^{12} -$$$$54\!\cdots\!78$$$$T^{13} +$$$$53\!\cdots\!62$$$$T^{14} -$$$$11\!\cdots\!58$$$$T^{15} +$$$$24\!\cdots\!66$$$$T^{16} -$$$$17\!\cdots\!94$$$$T^{17} +$$$$11\!\cdots\!38$$$$T^{18} -$$$$17\!\cdots\!46$$$$T^{19} -$$$$89\!\cdots\!52$$$$T^{20} +$$$$35\!\cdots\!50$$$$T^{21} -$$$$28\!\cdots\!98$$$$T^{22} +$$$$53\!\cdots\!02$$$$T^{23} -$$$$70\!\cdots\!64$$$$T^{24} +$$$$24\!\cdots\!10$$$$T^{25} -$$$$11\!\cdots\!50$$$$T^{26} +$$$$57\!\cdots\!46$$$$T^{27} +$$$$58\!\cdots\!72$$$$T^{28} -$$$$69\!\cdots\!10$$$$T^{29} +$$$$44\!\cdots\!98$$$$T^{30} -$$$$64\!\cdots\!14$$$$T^{31} +$$$$47\!\cdots\!01$$$$T^{32}$$)
$47$ ($$1 - 1278 T + 816642 T^{2} - 351784473730 T^{3} + 13143771115043551 T^{4} + 55735540634425394844 T^{5} -$$$$20\!\cdots\!24$$$$T^{6} +$$$$35\!\cdots\!24$$$$T^{7} +$$$$21\!\cdots\!21$$$$T^{8} -$$$$27\!\cdots\!06$$$$T^{9} +$$$$23\!\cdots\!58$$$$T^{10} -$$$$14\!\cdots\!22$$$$T^{11} -$$$$33\!\cdots\!25$$$$T^{12} +$$$$57\!\cdots\!44$$$$T^{13} -$$$$35\!\cdots\!52$$$$T^{14} +$$$$13\!\cdots\!08$$$$T^{15} -$$$$17\!\cdots\!25$$$$T^{16} -$$$$16\!\cdots\!46$$$$T^{17} +$$$$64\!\cdots\!58$$$$T^{18} -$$$$17\!\cdots\!42$$$$T^{19} +$$$$31\!\cdots\!29$$$$T^{20} +$$$$11\!\cdots\!32$$$$T^{21} -$$$$15\!\cdots\!24$$$$T^{22} +$$$$97\!\cdots\!08$$$$T^{23} +$$$$52\!\cdots\!99$$$$T^{24} -$$$$32\!\cdots\!90$$$$T^{25} +$$$$17\!\cdots\!42$$$$T^{26} -$$$$62\!\cdots\!46$$$$T^{27} +$$$$11\!\cdots\!49$$$$T^{28}$$)($$1 + 1278 T + 816642 T^{2} + 351784473730 T^{3} + 13143771115043551 T^{4} - 55735540634425394844 T^{5} -$$$$20\!\cdots\!24$$$$T^{6} -$$$$35\!\cdots\!24$$$$T^{7} +$$$$21\!\cdots\!21$$$$T^{8} +$$$$27\!\cdots\!06$$$$T^{9} +$$$$23\!\cdots\!58$$$$T^{10} +$$$$14\!\cdots\!22$$$$T^{11} -$$$$33\!\cdots\!25$$$$T^{12} -$$$$57\!\cdots\!44$$$$T^{13} -$$$$35\!\cdots\!52$$$$T^{14} -$$$$13\!\cdots\!08$$$$T^{15} -$$$$17\!\cdots\!25$$$$T^{16} +$$$$16\!\cdots\!46$$$$T^{17} +$$$$64\!\cdots\!58$$$$T^{18} +$$$$17\!\cdots\!42$$$$T^{19} +$$$$31\!\cdots\!29$$$$T^{20} -$$$$11\!\cdots\!32$$$$T^{21} -$$$$15\!\cdots\!24$$$$T^{22} -$$$$97\!\cdots\!08$$$$T^{23} +$$$$52\!\cdots\!99$$$$T^{24} +$$$$32\!\cdots\!90$$$$T^{25} +$$$$17\!\cdots\!42$$$$T^{26} +$$$$62\!\cdots\!46$$$$T^{27} +$$$$11\!\cdots\!49$$$$T^{28}$$)($$1 + 25298 T + 319994402 T^{2} + 6541896537590 T^{3} - 11741966210019840 T^{4} -$$$$87\!\cdots\!98$$$$T^{5} +$$$$31\!\cdots\!26$$$$T^{6} -$$$$28\!\cdots\!26$$$$T^{7} +$$$$89\!\cdots\!80$$$$T^{8} +$$$$49\!\cdots\!50$$$$T^{9} -$$$$48\!\cdots\!58$$$$T^{10} +$$$$14\!\cdots\!46$$$$T^{11} +$$$$91\!\cdots\!24$$$$T^{12} -$$$$38\!\cdots\!50$$$$T^{13} +$$$$47\!\cdots\!30$$$$T^{14} +$$$$60\!\cdots\!90$$$$T^{15} +$$$$93\!\cdots\!70$$$$T^{16} +$$$$13\!\cdots\!30$$$$T^{17} +$$$$25\!\cdots\!70$$$$T^{18} -$$$$45\!\cdots\!50$$$$T^{19} +$$$$25\!\cdots\!24$$$$T^{20} +$$$$94\!\cdots\!22$$$$T^{21} -$$$$70\!\cdots\!42$$$$T^{22} +$$$$16\!\cdots\!50$$$$T^{23} +$$$$68\!\cdots\!80$$$$T^{24} -$$$$49\!\cdots\!82$$$$T^{25} +$$$$12\!\cdots\!74$$$$T^{26} -$$$$80\!\cdots\!14$$$$T^{27} -$$$$24\!\cdots\!40$$$$T^{28} +$$$$31\!\cdots\!30$$$$T^{29} +$$$$35\!\cdots\!98$$$$T^{30} +$$$$64\!\cdots\!14$$$$T^{31} +$$$$58\!\cdots\!01$$$$T^{32}$$)($$1 - 25298 T + 319994402 T^{2} - 6541896537590 T^{3} - 11741966210019840 T^{4} +$$$$87\!\cdots\!98$$$$T^{5} +$$$$31\!\cdots\!26$$$$T^{6} +$$$$28\!\cdots\!26$$$$T^{7} +$$$$89\!\cdots\!80$$$$T^{8} -$$$$49\!\cdots\!50$$$$T^{9} -$$$$48\!\cdots\!58$$$$T^{10} -$$$$14\!\cdots\!46$$$$T^{11} +$$$$91\!\cdots\!24$$$$T^{12} +$$$$38\!\cdots\!50$$$$T^{13} +$$$$47\!\cdots\!30$$$$T^{14} -$$$$60\!\cdots\!90$$$$T^{15} +$$$$93\!\cdots\!70$$$$T^{16} -$$$$13\!\cdots\!30$$$$T^{17} +$$$$25\!\cdots\!70$$$$T^{18} +$$$$45\!\cdots\!50$$$$T^{19} +$$$$25\!\cdots\!24$$$$T^{20} -$$$$94\!\cdots\!22$$$$T^{21} -$$$$70\!\cdots\!42$$$$T^{22} -$$$$16\!\cdots\!50$$$$T^{23} +$$$$68\!\cdots\!80$$$$T^{24} +$$$$49\!\cdots\!82$$$$T^{25} +$$$$12\!\cdots\!74$$$$T^{26} +$$$$80\!\cdots\!14$$$$T^{27} -$$$$24\!\cdots\!40$$$$T^{28} -$$$$31\!\cdots\!30$$$$T^{29} +$$$$35\!\cdots\!98$$$$T^{30} -$$$$64\!\cdots\!14$$$$T^{31} +$$$$58\!\cdots\!01$$$$T^{32}$$)
$53$ ($$1 - 5882 T + 17298962 T^{2} + 13844528488830 T^{3} - 174311180941592381 T^{4} -$$$$81\!\cdots\!52$$$$T^{5} +$$$$14\!\cdots\!36$$$$T^{6} -$$$$35\!\cdots\!12$$$$T^{7} -$$$$10\!\cdots\!67$$$$T^{8} +$$$$15\!\cdots\!82$$$$T^{9} +$$$$26\!\cdots\!38$$$$T^{10} -$$$$97\!\cdots\!30$$$$T^{11} +$$$$23\!\cdots\!39$$$$T^{12} +$$$$29\!\cdots\!36$$$$T^{13} -$$$$56\!\cdots\!72$$$$T^{14} +$$$$12\!\cdots\!48$$$$T^{15} +$$$$41\!\cdots\!11$$$$T^{16} -$$$$71\!\cdots\!10$$$$T^{17} +$$$$82\!\cdots\!38$$$$T^{18} +$$$$19\!\cdots\!26$$$$T^{19} -$$$$56\!\cdots\!83$$$$T^{20} -$$$$78\!\cdots\!84$$$$T^{21} +$$$$13\!\cdots\!36$$$$T^{22} -$$$$31\!\cdots\!36$$$$T^{23} -$$$$28\!\cdots\!69$$$$T^{24} +$$$$94\!\cdots\!10$$$$T^{25} +$$$$49\!\cdots\!62$$$$T^{26} -$$$$70\!\cdots\!26$$$$T^{27} +$$$$50\!\cdots\!49$$$$T^{28}$$)($$1 - 5882 T + 17298962 T^{2} + 13844528488830 T^{3} - 174311180941592381 T^{4} -$$$$81\!\cdots\!52$$$$T^{5} +$$$$14\!\cdots\!36$$$$T^{6} -$$$$35\!\cdots\!12$$$$T^{7} -$$$$10\!\cdots\!67$$$$T^{8} +$$$$15\!\cdots\!82$$$$T^{9} +$$$$26\!\cdots\!38$$$$T^{10} -$$$$97\!\cdots\!30$$$$T^{11} +$$$$23\!\cdots\!39$$$$T^{12} +$$$$29\!\cdots\!36$$$$T^{13} -$$$$56\!\cdots\!72$$$$T^{14} +$$$$12\!\cdots\!48$$$$T^{15} +$$$$41\!\cdots\!11$$$$T^{16} -$$$$71\!\cdots\!10$$$$T^{17} +$$$$82\!\cdots\!38$$$$T^{18} +$$$$19\!\cdots\!26$$$$T^{19} -$$$$56\!\cdots\!83$$$$T^{20} -$$$$78\!\cdots\!84$$$$T^{21} +$$$$13\!\cdots\!36$$$$T^{22} -$$$$31\!\cdots\!36$$$$T^{23} -$$$$28\!\cdots\!69$$$$T^{24} +$$$$94\!\cdots\!10$$$$T^{25} +$$$$49\!\cdots\!62$$$$T^{26} -$$$$70\!\cdots\!26$$$$T^{27} +$$$$50\!\cdots\!49$$$$T^{28}$$)($$1 - 12852 T + 82586952 T^{2} + 12779415797620 T^{3} - 141875027604640888 T^{4} -$$$$55\!\cdots\!72$$$$T^{5} +$$$$16\!\cdots\!20$$$$T^{6} -$$$$16\!\cdots\!60$$$$T^{7} -$$$$86\!\cdots\!84$$$$T^{8} +$$$$14\!\cdots\!16$$$$T^{9} +$$$$64\!\cdots\!88$$$$T^{10} -$$$$74\!\cdots\!80$$$$T^{11} +$$$$67\!\cdots\!08$$$$T^{12} +$$$$29\!\cdots\!72$$$$T^{13} -$$$$53\!\cdots\!88$$$$T^{14} -$$$$64\!\cdots\!48$$$$T^{15} +$$$$25\!\cdots\!06$$$$T^{16} -$$$$27\!\cdots\!64$$$$T^{17} -$$$$94\!\cdots\!12$$$$T^{18} +$$$$21\!\cdots\!04$$$$T^{19} +$$$$20\!\cdots\!08$$$$T^{20} -$$$$95\!\cdots\!40$$$$T^{21} +$$$$34\!\cdots\!12$$$$T^{22} +$$$$32\!\cdots\!12$$$$T^{23} -$$$$80\!\cdots\!84$$$$T^{24} -$$$$64\!\cdots\!80$$$$T^{25} +$$$$27\!\cdots\!80$$$$T^{26} -$$$$38\!\cdots\!04$$$$T^{27} -$$$$40\!\cdots\!88$$$$T^{28} +$$$$15\!\cdots\!60$$$$T^{29} +$$$$41\!\cdots\!48$$$$T^{30} -$$$$26\!\cdots\!64$$$$T^{31} +$$$$87\!\cdots\!01$$$$T^{32}$$)($$1 - 12852 T + 82586952 T^{2} + 12779415797620 T^{3} - 141875027604640888 T^{4} -$$$$55\!\cdots\!72$$$$T^{5} +$$$$16\!\cdots\!20$$$$T^{6} -$$$$16\!\cdots\!60$$$$T^{7} -$$$$86\!\cdots\!84$$$$T^{8} +$$$$14\!\cdots\!16$$$$T^{9} +$$$$64\!\cdots\!88$$$$T^{10} -$$$$74\!\cdots\!80$$$$T^{11} +$$$$67\!\cdots\!08$$$$T^{12} +$$$$29\!\cdots\!72$$$$T^{13} -$$$$53\!\cdots\!88$$$$T^{14} -$$$$64\!\cdots\!48$$$$T^{15} +$$$$25\!\cdots\!06$$$$T^{16} -$$$$27\!\cdots\!64$$$$T^{17} -$$$$94\!\cdots\!12$$$$T^{18} +$$$$21\!\cdots\!04$$$$T^{19} +$$$$20\!\cdots\!08$$$$T^{20} -$$$$95\!\cdots\!40$$$$T^{21} +$$$$34\!\cdots\!12$$$$T^{22} +$$$$32\!\cdots\!12$$$$T^{23} -$$$$80\!\cdots\!84$$$$T^{24} -$$$$64\!\cdots\!80$$$$T^{25} +$$$$27\!\cdots\!80$$$$T^{26} -$$$$38\!\cdots\!04$$$$T^{27} -$$$$40\!\cdots\!88$$$$T^{28} +$$$$15\!\cdots\!60$$$$T^{29} +$$$$41\!\cdots\!48$$$$T^{30} -$$$$26\!\cdots\!64$$$$T^{31} +$$$$87\!\cdots\!01$$$$T^{32}$$)
$59$ ($$( 1 - 4252 T + 2005910877 T^{2} - 20518241068280 T^{3} + 2395790088022200413 T^{4} -$$$$22\!\cdots\!48$$$$T^{5} +$$$$23\!\cdots\!29$$$$T^{6} -$$$$16\!\cdots\!28$$$$T^{7} +$$$$16\!\cdots\!71$$$$T^{8} -$$$$11\!\cdots\!48$$$$T^{9} +$$$$87\!\cdots\!87$$$$T^{10} -$$$$53\!\cdots\!80$$$$T^{11} +$$$$37\!\cdots\!23$$$$T^{12} -$$$$56\!\cdots\!52$$$$T^{13} +$$$$95\!\cdots\!99$$$$T^{14} )^{2}$$)($$( 1 + 4252 T + 2005910877 T^{2} + 20518241068280 T^{3} + 2395790088022200413 T^{4} +$$$$22\!\cdots\!48$$$$T^{5} +$$$$23\!\cdots\!29$$$$T^{6} +$$$$16\!\cdots\!28$$$$T^{7} +$$$$16\!\cdots\!71$$$$T^{8} +$$$$11\!\cdots\!48$$$$T^{9} +$$$$87\!\cdots\!87$$$$T^{10} +$$$$53\!\cdots\!80$$$$T^{11} +$$$$37\!\cdots\!23$$$$T^{12} +$$$$56\!\cdots\!52$$$$T^{13} +$$$$95\!\cdots\!99$$$$T^{14} )^{2}$$)($$( 1 - 71352 T + 5147553272 T^{2} - 263083260595160 T^{3} + 11526051017122699388 T^{4} -$$$$44\!\cdots\!28$$$$T^{5} +$$$$15\!\cdots\!16$$$$T^{6} -$$$$46\!\cdots\!12$$$$T^{7} +$$$$13\!\cdots\!10$$$$T^{8} -$$$$32\!\cdots\!88$$$$T^{9} +$$$$77\!\cdots\!16$$$$T^{10} -$$$$16\!\cdots\!72$$$$T^{11} +$$$$30\!\cdots\!88$$$$T^{12} -$$$$49\!\cdots\!40$$$$T^{13} +$$$$68\!\cdots\!72$$$$T^{14} -$$$$68\!\cdots\!48$$$$T^{15} +$$$$68\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 + 71352 T + 5147553272 T^{2} + 263083260595160 T^{3} + 11526051017122699388 T^{4} +$$$$44\!\cdots\!28$$$$T^{5} +$$$$15\!\cdots\!16$$$$T^{6} +$$$$46\!\cdots\!12$$$$T^{7} +$$$$13\!\cdots\!10$$$$T^{8} +$$$$32\!\cdots\!88$$$$T^{9} +$$$$77\!\cdots\!16$$$$T^{10} +$$$$16\!\cdots\!72$$$$T^{11} +$$$$30\!\cdots\!88$$$$T^{12} +$$$$49\!\cdots\!40$$$$T^{13} +$$$$68\!\cdots\!72$$$$T^{14} +$$$$68\!\cdots\!48$$$$T^{15} +$$$$68\!\cdots\!01$$$$T^{16} )^{2}$$)
$61$ ($$( 1 - 10282 T + 2916253203 T^{2} + 3083320715268 T^{3} + 3046127491767085861 T^{4} +$$$$70\!\cdots\!38$$$$T^{5} +$$$$15\!\cdots\!39$$$$T^{6} +$$$$10\!\cdots\!44$$$$T^{7} +$$$$12\!\cdots\!39$$$$T^{8} +$$$$50\!\cdots\!38$$$$T^{9} +$$$$18\!\cdots\!61$$$$T^{10} +$$$$15\!\cdots\!68$$$$T^{11} +$$$$12\!\cdots\!03$$$$T^{12} -$$$$37\!\cdots\!82$$$$T^{13} +$$$$30\!\cdots\!01$$$$T^{14} )^{2}$$)($$( 1 - 10282 T + 2916253203 T^{2} + 3083320715268 T^{3} + 3046127491767085861 T^{4} +$$$$70\!\cdots\!38$$$$T^{5} +$$$$15\!\cdots\!39$$$$T^{6} +$$$$10\!\cdots\!44$$$$T^{7} +$$$$12\!\cdots\!39$$$$T^{8} +$$$$50\!\cdots\!38$$$$T^{9} +$$$$18\!\cdots\!61$$$$T^{10} +$$$$15\!\cdots\!68$$$$T^{11} +$$$$12\!\cdots\!03$$$$T^{12} -$$$$37\!\cdots\!82$$$$T^{13} +$$$$30\!\cdots\!01$$$$T^{14} )^{2}$$)($$( 1 + 10282 T + 3727559576 T^{2} + 11244934877598 T^{3} + 6582098174228731436 T^{4} -$$$$31\!\cdots\!30$$$$T^{5} +$$$$74\!\cdots\!72$$$$T^{6} -$$$$78\!\cdots\!62$$$$T^{7} +$$$$66\!\cdots\!54$$$$T^{8} -$$$$66\!\cdots\!62$$$$T^{9} +$$$$52\!\cdots\!72$$$$T^{10} -$$$$18\!\cdots\!30$$$$T^{11} +$$$$33\!\cdots\!36$$$$T^{12} +$$$$48\!\cdots\!98$$$$T^{13} +$$$$13\!\cdots\!76$$$$T^{14} +$$$$31\!\cdots\!82$$$$T^{15} +$$$$25\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 + 10282 T + 3727559576 T^{2} + 11244934877598 T^{3} + 6582098174228731436 T^{4} -$$$$31\!\cdots\!30$$$$T^{5} +$$$$74\!\cdots\!72$$$$T^{6} -$$$$78\!\cdots\!62$$$$T^{7} +$$$$66\!\cdots\!54$$$$T^{8} -$$$$66\!\cdots\!62$$$$T^{9} +$$$$52\!\cdots\!72$$$$T^{10} -$$$$18\!\cdots\!30$$$$T^{11} +$$$$33\!\cdots\!36$$$$T^{12} +$$$$48\!\cdots\!98$$$$T^{13} +$$$$13\!\cdots\!76$$$$T^{14} +$$$$31\!\cdots\!82$$$$T^{15} +$$$$25\!\cdots\!01$$$$T^{16} )^{2}$$)
$67$ ($$1 + 107926 T + 5824010738 T^{2} + 286091118212770 T^{3} + 7910959270847152663 T^{4} -$$$$10\!\cdots\!32$$$$T^{5} -$$$$16\!\cdots\!76$$$$T^{6} -$$$$10\!\cdots\!52$$$$T^{7} -$$$$49\!\cdots\!51$$$$T^{8} -$$$$12\!\cdots\!38$$$$T^{9} -$$$$20\!\cdots\!90$$$$T^{10} +$$$$24\!\cdots\!26$$$$T^{11} +$$$$60\!\cdots\!11$$$$T^{12} +$$$$31\!\cdots\!32$$$$T^{13} +$$$$11\!\cdots\!96$$$$T^{14} +$$$$43\!\cdots\!24$$$$T^{15} +$$$$10\!\cdots\!39$$$$T^{16} +$$$$61\!\cdots\!18$$$$T^{17} -$$$$68\!\cdots\!90$$$$T^{18} -$$$$57\!\cdots\!66$$$$T^{19} -$$$$30\!\cdots\!99$$$$T^{20} -$$$$86\!\cdots\!36$$$$T^{21} -$$$$18\!\cdots\!76$$$$T^{22} -$$$$15\!\cdots\!24$$$$T^{23} +$$$$15\!\cdots\!87$$$$T^{24} +$$$$77\!\cdots\!10$$$$T^{25} +$$$$21\!\cdots\!38$$$$T^{26} +$$$$53\!\cdots\!82$$$$T^{27} +$$$$66\!\cdots\!49$$$$T^{28}$$)($$1 - 107926 T + 5824010738 T^{2} - 286091118212770 T^{3} + 7910959270847152663 T^{4} +$$$$10\!\cdots\!32$$$$T^{5} -$$$$16\!\cdots\!76$$$$T^{6} +$$$$10\!\cdots\!52$$$$T^{7} -$$$$49\!\cdots\!51$$$$T^{8} +$$$$12\!\cdots\!38$$$$T^{9} -$$$$20\!\cdots\!90$$$$T^{10} -$$$$24\!\cdots\!26$$$$T^{11} +$$$$60\!\cdots\!11$$$$T^{12} -$$$$31\!\cdots\!32$$$$T^{13} +$$$$11\!\cdots\!96$$$$T^{14} -$$$$43\!\cdots\!24$$$$T^{15} +$$$$10\!\cdots\!39$$$$T^{16} -$$$$61\!\cdots\!18$$$$T^{17} -$$$$68\!\cdots\!90$$$$T^{18} +$$$$57\!\cdots\!66$$$$T^{19} -$$$$30\!\cdots\!99$$$$T^{20} +$$$$86\!\cdots\!36$$$$T^{21} -$$$$18\!\cdots\!76$$$$T^{22} +$$$$15\!\cdots\!24$$$$T^{23} +$$$$15\!\cdots\!87$$$$T^{24} -$$$$77\!\cdots\!10$$$$T^{25} +$$$$21\!\cdots\!38$$$$T^{26} -$$$$53\!\cdots\!82$$$$T^{27} +$$$$66\!\cdots\!49$$$$T^{28}$$)($$1 - 10506 T + 55188018 T^{2} - 64685094733110 T^{3} - 1145101582269918112 T^{4} +$$$$11\!\cdots\!66$$$$T^{5} +$$$$90\!\cdots\!70$$$$T^{6} +$$$$13\!\cdots\!94$$$$T^{7} -$$$$58\!\cdots\!16$$$$T^{8} -$$$$10\!\cdots\!70$$$$T^{9} +$$$$57\!\cdots\!86$$$$T^{10} +$$$$37\!\cdots\!82$$$$T^{11} +$$$$12\!\cdots\!56$$$$T^{12} -$$$$51\!\cdots\!34$$$$T^{13} +$$$$11\!\cdots\!26$$$$T^{14} -$$$$28\!\cdots\!74$$$$T^{15} -$$$$82\!\cdots\!58$$$$T^{16} -$$$$38\!\cdots\!18$$$$T^{17} +$$$$21\!\cdots\!74$$$$T^{18} -$$$$12\!\cdots\!62$$$$T^{19} +$$$$40\!\cdots\!56$$$$T^{20} +$$$$16\!\cdots\!74$$$$T^{21} +$$$$34\!\cdots\!14$$$$T^{22} -$$$$89\!\cdots\!10$$$$T^{23} -$$$$64\!\cdots\!16$$$$T^{24} +$$$$20\!\cdots\!58$$$$T^{25} +$$$$18\!\cdots\!30$$$$T^{26} +$$$$32\!\cdots\!38$$$$T^{27} -$$$$42\!\cdots\!12$$$$T^{28} -$$$$32\!\cdots\!70$$$$T^{29} +$$$$36\!\cdots\!82$$$$T^{30} -$$$$94\!\cdots\!58$$$$T^{31} +$$$$12\!\cdots\!01$$$$T^{32}$$)($$1 + 10506 T + 55188018 T^{2} + 64685094733110 T^{3} - 1145101582269918112 T^{4} -$$$$11\!\cdots\!66$$$$T^{5} +$$$$90\!\cdots\!70$$$$T^{6} -$$$$13\!\cdots\!94$$$$T^{7} -$$$$58\!\cdots\!16$$$$T^{8} +$$$$10\!\cdots\!70$$$$T^{9} +$$$$57\!\cdots\!86$$$$T^{10} -$$$$37\!\cdots\!82$$$$T^{11} +$$$$12\!\cdots\!56$$$$T^{12} +$$$$51\!\cdots\!34$$$$T^{13} +$$$$11\!\cdots\!26$$$$T^{14} +$$$$28\!\cdots\!74$$$$T^{15} -$$$$82\!\cdots\!58$$$$T^{16} +$$$$38\!\cdots\!18$$$$T^{17} +$$$$21\!\cdots\!74$$$$T^{18} +$$$$12\!\cdots\!62$$$$T^{19} +$$$$40\!\cdots\!56$$$$T^{20} -$$$$16\!\cdots\!74$$$$T^{21} +$$$$34\!\cdots\!14$$$$T^{22} +$$$$89\!\cdots\!10$$$$T^{23} -$$$$64\!\cdots\!16$$$$T^{24} -$$$$20\!\cdots\!58$$$$T^{25} +$$$$18\!\cdots\!30$$$$T^{26} -$$$$32\!\cdots\!38$$$$T^{27} -$$$$42\!\cdots\!12$$$$T^{28} +$$$$32\!\cdots\!70$$$$T^{29} +$$$$36\!\cdots\!82$$$$T^{30} +$$$$94\!\cdots\!58$$$$T^{31} +$$$$12\!\cdots\!01$$$$T^{32}$$)
$71$ ($$1 - 12494857902 T^{2} + 77600272039468829243 T^{4} -$$$$32\!\cdots\!32$$$$T^{6} +$$$$99\!\cdots\!41$$$$T^{8} -$$$$25\!\cdots\!58$$$$T^{10} +$$$$55\!\cdots\!91$$$$T^{12} -$$$$10\!\cdots\!64$$$$T^{14} +$$$$17\!\cdots\!91$$$$T^{16} -$$$$26\!\cdots\!58$$$$T^{18} +$$$$34\!\cdots\!41$$$$T^{20} -$$$$35\!\cdots\!32$$$$T^{22} +$$$$28\!\cdots\!43$$$$T^{24} -$$$$14\!\cdots\!02$$$$T^{26} +$$$$38\!\cdots\!01$$$$T^{28}$$)($$1 - 12494857902 T^{2} + 77600272039468829243 T^{4} -$$$$32\!\cdots\!32$$$$T^{6} +$$$$99\!\cdots\!41$$$$T^{8} -$$$$25\!\cdots\!58$$$$T^{10} +$$$$55\!\cdots\!91$$$$T^{12} -$$$$10\!\cdots\!64$$$$T^{14} +$$$$17\!\cdots\!91$$$$T^{16} -$$$$26\!\cdots\!58$$$$T^{18} +$$$$34\!\cdots\!41$$$$T^{20} -$$$$35\!\cdots\!32$$$$T^{22} +$$$$28\!\cdots\!43$$$$T^{24} -$$$$14\!\cdots\!02$$$$T^{26} +$$$$38\!\cdots\!01$$$$T^{28}$$)($$1 - 13607740108 T^{2} + 94972263534983306896 T^{4} -$$$$45\!\cdots\!72$$$$T^{6} +$$$$16\!\cdots\!96$$$$T^{8} -$$$$50\!\cdots\!76$$$$T^{10} +$$$$12\!\cdots\!40$$$$T^{12} -$$$$27\!\cdots\!08$$$$T^{14} +$$$$53\!\cdots\!06$$$$T^{16} -$$$$90\!\cdots\!08$$$$T^{18} +$$$$13\!\cdots\!40$$$$T^{20} -$$$$17\!\cdots\!76$$$$T^{22} +$$$$18\!\cdots\!96$$$$T^{24} -$$$$16\!\cdots\!72$$$$T^{26} +$$$$11\!\cdots\!96$$$$T^{28} -$$$$52\!\cdots\!08$$$$T^{30} +$$$$12\!\cdots\!01$$$$T^{32}$$)($$1 - 13607740108 T^{2} + 94972263534983306896 T^{4} -$$$$45\!\cdots\!72$$$$T^{6} +$$$$16\!\cdots\!96$$$$T^{8} -$$$$50\!\cdots\!76$$$$T^{10} +$$$$12\!\cdots\!40$$$$T^{12} -$$$$27\!\cdots\!08$$$$T^{14} +$$$$53\!\cdots\!06$$$$T^{16} -$$$$90\!\cdots\!08$$$$T^{18} +$$$$13\!\cdots\!40$$$$T^{20} -$$$$17\!\cdots\!76$$$$T^{22} +$$$$18\!\cdots\!96$$$$T^{24} -$$$$16\!\cdots\!72$$$$T^{26} +$$$$11\!\cdots\!96$$$$T^{28} -$$$$52\!\cdots\!08$$$$T^{30} +$$$$12\!\cdots\!01$$$$T^{32}$$)
$73$ ($$1 + 16418 T + 134775362 T^{2} - 257655666175822 T^{3} - 4365114300655601877 T^{4} +$$$$39\!\cdots\!72$$$$T^{5} +$$$$40\!\cdots\!12$$$$T^{6} +$$$$72\!\cdots\!32$$$$T^{7} -$$$$10\!\cdots\!35$$$$T^{8} -$$$$45\!\cdots\!66$$$$T^{9} +$$$$74\!\cdots\!94$$$$T^{10} +$$$$14\!\cdots\!50$$$$T^{11} +$$$$46\!\cdots\!07$$$$T^{12} -$$$$13\!\cdots\!16$$$$T^{13} -$$$$14\!\cdots\!04$$$$T^{14} -$$$$27\!\cdots\!88$$$$T^{15} +$$$$20\!\cdots\!43$$$$T^{16} +$$$$12\!\cdots\!50$$$$T^{17} +$$$$13\!\cdots\!94$$$$T^{18} -$$$$17\!\cdots\!38$$$$T^{19} -$$$$80\!\cdots\!15$$$$T^{20} +$$$$11\!\cdots\!24$$$$T^{21} +$$$$13\!\cdots\!12$$$$T^{22} +$$$$28\!\cdots\!96$$$$T^{23} -$$$$63\!\cdots\!73$$$$T^{24} -$$$$78\!\cdots\!54$$$$T^{25} +$$$$84\!\cdots\!62$$$$T^{26} +$$$$21\!\cdots\!74$$$$T^{27} +$$$$27\!\cdots\!49$$$$T^{28}$$)($$1 + 16418 T + 134775362 T^{2} - 257655666175822 T^{3} - 4365114300655601877 T^{4} +$$$$39\!\cdots\!72$$$$T^{5} +$$$$40\!\cdots\!12$$$$T^{6} +$$$$72\!\cdots\!32$$$$T^{7} -$$$$10\!\cdots\!35$$$$T^{8} -$$$$45\!\cdots\!66$$$$T^{9} +$$$$74\!\cdots\!94$$$$T^{10} +$$$$14\!\cdots\!50$$$$T^{11} +$$$$46\!\cdots\!07$$$$T^{12} -$$$$13\!\cdots\!16$$$$T^{13} -$$$$14\!\cdots\!04$$$$T^{14} -$$$$27\!\cdots\!88$$$$T^{15} +$$$$20\!\cdots\!43$$$$T^{16} +$$$$12\!\cdots\!50$$$$T^{17} +$$$$13\!\cdots\!94$$$$T^{18} -$$$$17\!\cdots\!38$$$$T^{19} -$$$$80\!\cdots\!15$$$$T^{20} +$$$$11\!\cdots\!24$$$$T^{21} +$$$$13\!\cdots\!12$$$$T^{22} +$$$$28\!\cdots\!96$$$$T^{23} -$$$$63\!\cdots\!73$$$$T^{24} -$$$$78\!\cdots\!54$$$$T^{25} +$$$$84\!\cdots\!62$$$$T^{26} +$$$$21\!\cdots\!74$$$$T^{27} +$$$$27\!\cdots\!49$$$$T^{28}$$)($$1 - 15432 T + 119073312 T^{2} - 56032493808632 T^{3} + 4235186228799589816 T^{4} +$$$$61\!\cdots\!96$$$$T^{5} +$$$$12\!\cdots\!48$$$$T^{6} -$$$$11\!\cdots\!24$$$$T^{7} -$$$$89\!\cdots\!60$$$$T^{8} +$$$$71\!\cdots\!68$$$$T^{9} -$$$$22\!\cdots\!48$$$$T^{10} +$$$$11\!\cdots\!04$$$$T^{11} -$$$$29\!\cdots\!68$$$$T^{12} -$$$$26\!\cdots\!56$$$$T^{13} +$$$$53\!\cdots\!44$$$$T^{14} +$$$$14\!\cdots\!88$$$$T^{15} +$$$$30\!\cdots\!30$$$$T^{16} +$$$$29\!\cdots\!84$$$$T^{17} +$$$$22\!\cdots\!56$$$$T^{18} -$$$$23\!\cdots\!92$$$$T^{19} -$$$$54\!\cdots\!68$$$$T^{20} +$$$$42\!\cdots\!72$$$$T^{21} -$$$$17\!\cdots\!52$$$$T^{22} +$$$$11\!\cdots\!76$$$$T^{23} -$$$$30\!\cdots\!60$$$$T^{24} -$$$$80\!\cdots\!32$$$$T^{25} +$$$$18\!\cdots\!52$$$$T^{26} +$$$$18\!\cdots\!72$$$$T^{27} +$$$$26\!\cdots\!16$$$$T^{28} -$$$$73\!\cdots\!76$$$$T^{29} +$$$$32\!\cdots\!88$$$$T^{30} -$$$$86\!\cdots\!24$$$$T^{31} +$$$$11\!\cdots\!01$$$$T^{32}$$)($$1 - 15432 T + 119073312 T^{2} - 56032493808632 T^{3} + 4235186228799589816 T^{4} +$$$$61\!\cdots\!96$$$$T^{5} +$$$$12\!\cdots\!48$$$$T^{6} -$$$$11\!\cdots\!24$$$$T^{7} -$$$$89\!\cdots\!60$$$$T^{8} +$$$$71\!\cdots\!68$$$$T^{9} -$$$$22\!\cdots\!48$$$$T^{10} +$$$$11\!\cdots\!04$$$$T^{11} -$$$$29\!\cdots\!68$$$$T^{12} -$$$$26\!\cdots\!56$$$$T^{13} +$$$$53\!\cdots\!44$$$$T^{14} +$$$$14\!\cdots\!88$$$$T^{15} +$$$$30\!\cdots\!30$$$$T^{16} +$$$$29\!\cdots\!84$$$$T^{17} +$$$$22\!\cdots\!56$$$$T^{18} -$$$$23\!\cdots\!92$$$$T^{19} -$$$$54\!\cdots\!68$$$$T^{20} +$$$$42\!\cdots\!72$$$$T^{21} -$$$$17\!\cdots\!52$$$$T^{22} +$$$$11\!\cdots\!76$$$$T^{23} -$$$$30\!\cdots\!60$$$$T^{24} -$$$$80\!\cdots\!32$$$$T^{25} +$$$$18\!\cdots\!52$$$$T^{26} +$$$$18\!\cdots\!72$$$$T^{27} +$$$$26\!\cdots\!16$$$$T^{28} -$$$$73\!\cdots\!76$$$$T^{29} +$$$$32\!\cdots\!88$$$$T^{30} -$$$$86\!\cdots\!24$$$$T^{31} +$$$$11\!\cdots\!01$$$$T^{32}$$)
$79$ ($$( 1 - 73272 T + 14910422889 T^{2} - 713614712327088 T^{3} + 91878682859930077941 T^{4} -$$$$30\!\cdots\!92$$$$T^{5} +$$$$35\!\cdots\!29$$$$T^{6} -$$$$97\!\cdots\!08$$$$T^{7} +$$$$10\!\cdots\!71$$$$T^{8} -$$$$29\!\cdots\!92$$$$T^{9} +$$$$26\!\cdots\!59$$$$T^{10} -$$$$63\!\cdots\!88$$$$T^{11} +$$$$41\!\cdots\!11$$$$T^{12} -$$$$62\!\cdots\!72$$$$T^{13} +$$$$26\!\cdots\!99$$$$T^{14} )^{2}$$)($$( 1 + 73272 T + 14910422889 T^{2} + 713614712327088 T^{3} + 91878682859930077941 T^{4} +$$$$30\!\cdots\!92$$$$T^{5} +$$$$35\!\cdots\!29$$$$T^{6} +$$$$97\!\cdots\!08$$$$T^{7} +$$$$10\!\cdots\!71$$$$T^{8} +$$$$29\!\cdots\!92$$$$T^{9} +$$$$26\!\cdots\!59$$$$T^{10} +$$$$63\!\cdots\!88$$$$T^{11} +$$$$41\!\cdots\!11$$$$T^{12} +$$$$62\!\cdots\!72$$$$T^{13} +$$$$26\!\cdots\!99$$$$T^{14} )^{2}$$)($$( 1 - 79672 T + 15921600120 T^{2} - 883492472350200 T^{3} +$$$$11\!\cdots\!40$$$$T^{4} -$$$$53\!\cdots\!80$$$$T^{5} +$$$$56\!\cdots\!80$$$$T^{6} -$$$$23\!\cdots\!20$$$$T^{7} +$$$$20\!\cdots\!70$$$$T^{8} -$$$$71\!\cdots\!80$$$$T^{9} +$$$$53\!\cdots\!80$$$$T^{10} -$$$$15\!\cdots\!20$$$$T^{11} +$$$$10\!\cdots\!40$$$$T^{12} -$$$$24\!\cdots\!00$$$$T^{13} +$$$$13\!\cdots\!20$$$$T^{14} -$$$$20\!\cdots\!28$$$$T^{15} +$$$$80\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 + 79672 T + 15921600120 T^{2} + 883492472350200 T^{3} +$$$$11\!\cdots\!40$$$$T^{4} +$$$$53\!\cdots\!80$$$$T^{5} +$$$$56\!\cdots\!80$$$$T^{6} +$$$$23\!\cdots\!20$$$$T^{7} +$$$$20\!\cdots\!70$$$$T^{8} +$$$$71\!\cdots\!80$$$$T^{9} +$$$$53\!\cdots\!80$$$$T^{10} +$$$$15\!\cdots\!20$$$$T^{11} +$$$$10\!\cdots\!40$$$$T^{12} +$$$$24\!\cdots\!00$$$$T^{13} +$$$$13\!\cdots\!20$$$$T^{14} +$$$$20\!\cdots\!28$$$$T^{15} +$$$$80\!\cdots\!01$$$$T^{16} )^{2}$$)
$83$ ($$1 - 36398 T + 662407202 T^{2} + 351755925637942 T^{3} - 18959358682913357257 T^{4} -$$$$10\!\cdots\!44$$$$T^{5} +$$$$11\!\cdots\!08$$$$T^{6} -$$$$60\!\cdots\!36$$$$T^{7} +$$$$11\!\cdots\!21$$$$T^{8} +$$$$15\!\cdots\!90$$$$T^{9} -$$$$10\!\cdots\!50$$$$T^{10} +$$$$86\!\cdots\!90$$$$T^{11} -$$$$70\!\cdots\!85$$$$T^{12} -$$$$38\!\cdots\!20$$$$T^{13} +$$$$31\!\cdots\!80$$$$T^{14} -$$$$15\!\cdots\!60$$$$T^{15} -$$$$10\!\cdots\!65$$$$T^{16} +$$$$52\!\cdots\!30$$$$T^{17} -$$$$25\!\cdots\!50$$$$T^{18} +$$$$14\!\cdots\!70$$$$T^{19} +$$$$43\!\cdots\!29$$$$T^{20} -$$$$88\!\cdots\!52$$$$T^{21} +$$$$64\!\cdots\!08$$$$T^{22} -$$$$23\!\cdots\!92$$$$T^{23} -$$$$17\!\cdots\!93$$$$T^{24} +$$$$12\!\cdots\!94$$$$T^{25} +$$$$92\!\cdots\!02$$$$T^{26} -$$$$20\!\cdots\!14$$$$T^{27} +$$$$21\!\cdots\!49$$$$T^{28}$$)($$1 + 36398 T + 662407202 T^{2} - 351755925637942 T^{3} - 18959358682913357257 T^{4} +$$$$10\!\cdots\!44$$$$T^{5} +$$$$11\!\cdots\!08$$$$T^{6} +$$$$60\!\cdots\!36$$$$T^{7} +$$$$11\!\cdots\!21$$$$T^{8} -$$$$15\!\cdots\!90$$$$T^{9} -$$$$10\!\cdots\!50$$$$T^{10} -$$$$86\!\cdots\!90$$$$T^{11} -$$$$70\!\cdots\!85$$$$T^{12} +$$$$38\!\cdots\!20$$$$T^{13} +$$$$31\!\cdots\!80$$$$T^{14} +$$$$15\!\cdots\!60$$$$T^{15} -$$$$10\!\cdots\!65$$$$T^{16} -$$$$52\!\cdots\!30$$$$T^{17} -$$$$25\!\cdots\!50$$$$T^{18} -$$$$14\!\cdots\!70$$$$T^{19} +$$$$43\!\cdots\!29$$$$T^{20} +$$$$88\!\cdots\!52$$$$T^{21} +$$$$64\!\cdots\!08$$$$T^{22} +$$$$23\!\cdots\!92$$$$T^{23} -$$$$17\!\cdots\!93$$$$T^{24} -$$$$12\!\cdots\!94$$$$T^{25} +$$$$92\!\cdots\!02$$$$T^{26} +$$$$20\!\cdots\!14$$$$T^{27} +$$$$21\!\cdots\!49$$$$T^{28}$$)($$1 - 61222 T + 1874066642 T^{2} - 12255516798122 T^{3} - 16226769598202256704 T^{4} +$$$$11\!\cdots\!34$$$$T^{5} +$$$$23\!\cdots\!62$$$$T^{6} -$$$$43\!\cdots\!38$$$$T^{7} +$$$$11\!\cdots\!04$$$$T^{8} +$$$$19\!\cdots\!26$$$$T^{9} -$$$$94\!\cdots\!78$$$$T^{10} +$$$$75\!\cdots\!74$$$$T^{11} +$$$$22\!\cdots\!04$$$$T^{12} -$$$$26\!\cdots\!90$$$$T^{13} +$$$$45\!\cdots\!30$$$$T^{14} +$$$$37\!\cdots\!50$$$$T^{15} -$$$$11\!\cdots\!10$$$$T^{16} +$$$$14\!\cdots\!50$$$$T^{17} +$$$$70\!\cdots\!70$$$$T^{18} -$$$$16\!\cdots\!30$$$$T^{19} +$$$$53\!\cdots\!04$$$$T^{20} +$$$$72\!\cdots\!82$$$$T^{21} -$$$$35\!\cdots\!22$$$$T^{22} +$$$$27\!\cdots\!82$$$$T^{23} +$$$$68\!\cdots\!04$$$$T^{24} -$$$$98\!\cdots\!34$$$$T^{25} +$$$$21\!\cdots\!38$$$$T^{26} +$$$$39\!\cdots\!38$$$$T^{27} -$$$$22\!\cdots\!04$$$$T^{28} -$$$$67\!\cdots\!46$$$$T^{29} +$$$$40\!\cdots\!58$$$$T^{30} -$$$$52\!\cdots\!54$$$$T^{31} +$$$$33\!\cdots\!01$$$$T^{32}$$)($$1 + 61222 T + 1874066642 T^{2} + 12255516798122 T^{3} - 16226769598202256704 T^{4} -$$$$11\!\cdots\!34$$$$T^{5} +$$$$23\!\cdots\!62$$$$T^{6} +$$$$43\!\cdots\!38$$$$T^{7} +$$$$11\!\cdots\!04$$$$T^{8} -$$$$19\!\cdots\!26$$$$T^{9} -$$$$94\!\cdots\!78$$$$T^{10} -$$$$75\!\cdots\!74$$$$T^{11} +$$$$22\!\cdots\!04$$$$T^{12} +$$$$26\!\cdots\!90$$$$T^{13} +$$$$45\!\cdots\!30$$$$T^{14} -$$$$37\!\cdots\!50$$$$T^{15} -$$$$11\!\cdots\!10$$$$T^{16} -$$$$14\!\cdots\!50$$$$T^{17} +$$$$70\!\cdots\!70$$$$T^{18} +$$$$16\!\cdots\!30$$$$T^{19} +$$$$53\!\cdots\!04$$$$T^{20} -$$$$72\!\cdots\!82$$$$T^{21} -$$$$35\!\cdots\!22$$$$T^{22} -$$$$27\!\cdots\!82$$$$T^{23} +$$$$68\!\cdots\!04$$$$T^{24} +$$$$98\!\cdots\!34$$$$T^{25} +$$$$21\!\cdots\!38$$$$T^{26} -$$$$39\!\cdots\!38$$$$T^{27} -$$$$22\!\cdots\!04$$$$T^{28} +$$$$67\!\cdots\!46$$$$T^{29} +$$$$40\!\cdots\!58$$$$T^{30} +$$$$52\!\cdots\!54$$$$T^{31} +$$$$33\!\cdots\!01$$$$T^{32}$$)
$89$ ($$1 - 30334038558 T^{2} +$$$$36\!\cdots\!35$$$$T^{4} -$$$$20\!\cdots\!52$$$$T^{6} +$$$$39\!\cdots\!69$$$$T^{8} -$$$$12\!\cdots\!10$$$$T^{10} +$$$$42\!\cdots\!95$$$$T^{12} -$$$$38\!\cdots\!60$$$$T^{14} +$$$$13\!\cdots\!95$$$$T^{16} -$$$$11\!\cdots\!10$$$$T^{18} +$$$$12\!\cdots\!69$$$$T^{20} -$$$$19\!\cdots\!52$$$$T^{22} +$$$$10\!\cdots\!35$$$$T^{24} -$$$$27\!\cdots\!58$$$$T^{26} +$$$$28\!\cdots\!01$$$$T^{28}$$)($$1 - 30334038558 T^{2} +$$$$36\!\cdots\!35$$$$T^{4} -$$$$20\!\cdots\!52$$$$T^{6} +$$$$39\!\cdots\!69$$$$T^{8} -$$$$12\!\cdots\!10$$$$T^{10} +$$$$42\!\cdots\!95$$$$T^{12} -$$$$38\!\cdots\!60$$$$T^{14} +$$$$13\!\cdots\!95$$$$T^{16} -$$$$11\!\cdots\!10$$$$T^{18} +$$$$12\!\cdots\!69$$$$T^{20} -$$$$19\!\cdots\!52$$$$T^{22} +$$$$10\!\cdots\!35$$$$T^{24} -$$$$27\!\cdots\!58$$$$T^{26} +$$$$28\!\cdots\!01$$$$T^{28}$$)($$1 - 59849990032 T^{2} +$$$$17\!\cdots\!44$$$$T^{4} -$$$$33\!\cdots\!56$$$$T^{6} +$$$$45\!\cdots\!84$$$$T^{8} -$$$$48\!\cdots\!60$$$$T^{10} +$$$$42\!\cdots\!32$$$$T^{12} -$$$$30\!\cdots\!72$$$$T^{14} +$$$$18\!\cdots\!38$$$$T^{16} -$$$$94\!\cdots\!72$$$$T^{18} +$$$$40\!\cdots\!32$$$$T^{20} -$$$$14\!\cdots\!60$$$$T^{22} +$$$$43\!\cdots\!84$$$$T^{24} -$$$$97\!\cdots\!56$$$$T^{26} +$$$$16\!\cdots\!44$$$$T^{28} -$$$$17\!\cdots\!32$$$$T^{30} +$$$$89\!\cdots\!01$$$$T^{32}$$)($$1 - 59849990032 T^{2} +$$$$17\!\cdots\!44$$$$T^{4} -$$$$33\!\cdots\!56$$$$T^{6} +$$$$45\!\cdots\!84$$$$T^{8} -$$$$48\!\cdots\!60$$$$T^{10} +$$$$42\!\cdots\!32$$$$T^{12} -$$$$30\!\cdots\!72$$$$T^{14} +$$$$18\!\cdots\!38$$$$T^{16} -$$$$94\!\cdots\!72$$$$T^{18} +$$$$40\!\cdots\!32$$$$T^{20} -$$$$14\!\cdots\!60$$$$T^{22} +$$$$43\!\cdots\!84$$$$T^{24} -$$$$97\!\cdots\!56$$$$T^{26} +$$$$16\!\cdots\!44$$$$T^{28} -$$$$17\!\cdots\!32$$$$T^{30} +$$$$89\!\cdots\!01$$$$T^{32}$$)
$97$ ($$1 + 60314 T + 1818889298 T^{2} - 623535693824102 T^{3} -$$$$16\!\cdots\!77$$$$T^{4} -$$$$33\!\cdots\!64$$$$T^{5} +$$$$29\!\cdots\!52$$$$T^{6} +$$$$51\!\cdots\!52$$$$T^{7} +$$$$12\!\cdots\!01$$$$T^{8} -$$$$44\!\cdots\!50$$$$T^{9} +$$$$18\!\cdots\!50$$$$T^{10} +$$$$91\!\cdots\!50$$$$T^{11} +$$$$44\!\cdots\!75$$$$T^{12} -$$$$82\!\cdots\!00$$$$T^{13} -$$$$73\!\cdots\!00$$$$T^{14} -$$$$70\!\cdots\!00$$$$T^{15} +$$$$32\!\cdots\!75$$$$T^{16} +$$$$57\!\cdots\!50$$$$T^{17} +$$$$99\!\cdots\!50$$$$T^{18} -$$$$20\!\cdots\!50$$$$T^{19} +$$$$51\!\cdots\!49$$$$T^{20} +$$$$17\!\cdots\!36$$$$T^{21} +$$$$88\!\cdots\!52$$$$T^{22} -$$$$84\!\cdots\!48$$$$T^{23} -$$$$36\!\cdots\!73$$$$T^{24} -$$$$11\!\cdots\!86$$$$T^{25} +$$$$29\!\cdots\!98$$$$T^{26} +$$$$83\!\cdots\!98$$$$T^{27} +$$$$11\!\cdots\!49$$$$T^{28}$$)($$1 + 60314 T + 1818889298 T^{2} - 623535693824102 T^{3} -$$$$16\!\cdots\!77$$$$T^{4} -$$$$33\!\cdots\!64$$$$T^{5} +$$$$29\!\cdots\!52$$$$T^{6} +$$$$51\!\cdots\!52$$$$T^{7} +$$$$12\!\cdots\!01$$$$T^{8} -$$$$44\!\cdots\!50$$$$T^{9} +$$$$18\!\cdots\!50$$$$T^{10} +$$$$91\!\cdots\!50$$$$T^{11} +$$$$44\!\cdots\!75$$$$T^{12} -$$$$82\!\cdots\!00$$$$T^{13} -$$$$73\!\cdots\!00$$$$T^{14} -$$$$70\!\cdots\!00$$$$T^{15} +$$$$32\!\cdots\!75$$$$T^{16} +$$$$57\!\cdots\!50$$$$T^{17} +$$$$99\!\cdots\!50$$$$T^{18} -$$$$20\!\cdots\!50$$$$T^{19} +$$$$51\!\cdots\!49$$$$T^{20} +$$$$17\!\cdots\!36$$$$T^{21} +$$$$88\!\cdots\!52$$$$T^{22} -$$$$84\!\cdots\!48$$$$T^{23} -$$$$36\!\cdots\!73$$$$T^{24} -$$$$11\!\cdots\!86$$$$T^{25} +$$$$29\!\cdots\!98$$$$T^{26} +$$$$83\!\cdots\!98$$$$T^{27} +$$$$11\!\cdots\!49$$$$T^{28}$$)($$1 + 17344 T + 150407168 T^{2} - 246974906594432 T^{3} + 52594420471951685112 T^{4} +$$$$73\!\cdots\!08$$$$T^{5} +$$$$15\!\cdots\!48$$$$T^{6} +$$$$60\!\cdots\!32$$$$T^{7} +$$$$10\!\cdots\!36$$$$T^{8} +$$$$15\!\cdots\!56$$$$T^{9} +$$$$30\!\cdots\!48$$$$T^{10} -$$$$19\!\cdots\!76$$$$T^{11} +$$$$13\!\cdots\!92$$$$T^{12} +$$$$57\!\cdots\!52$$$$T^{13} +$$$$10\!\cdots\!20$$$$T^{14} +$$$$29\!\cdots\!16$$$$T^{15} +$$$$43\!\cdots\!78$$$$T^{16} +$$$$25\!\cdots\!12$$$$T^{17} +$$$$80\!\cdots\!80$$$$T^{18} +$$$$36\!\cdots\!36$$$$T^{19} +$$$$75\!\cdots\!92$$$$T^{20} -$$$$92\!\cdots\!32$$$$T^{21} +$$$$12\!\cdots\!52$$$$T^{22} +$$$$51\!\cdots\!08$$$$T^{23} +$$$$30\!\cdots\!36$$$$T^{24} +$$$$15\!\cdots\!24$$$$T^{25} +$$$$32\!\cdots\!52$$$$T^{26} +$$$$13\!\cdots\!44$$$$T^{27} +$$$$84\!\cdots\!12$$$$T^{28} -$$$$34\!\cdots\!24$$$$T^{29} +$$$$17\!\cdots\!32$$$$T^{30} +$$$$17\!\cdots\!92$$$$T^{31} +$$$$87\!\cdots\!01$$$$T^{32}$$)($$1 + 17344 T + 150407168 T^{2} - 246974906594432 T^{3} + 52594420471951685112 T^{4} +$$$$73\!\cdots\!08$$$$T^{5} +$$$$15\!\cdots\!48$$$$T^{6} +$$$$60\!\cdots\!32$$$$T^{7} +$$$$10\!\cdots\!36$$$$T^{8} +$$$$15\!\cdots\!56$$$$T^{9} +$$$$30\!\cdots\!48$$$$T^{10} -$$$$19\!\cdots\!76$$$$T^{11} +$$$$13\!\cdots\!92$$$$T^{12} +$$$$57\!\cdots\!52$$$$T^{13} +$$$$10\!\cdots\!20$$$$T^{14} +$$$$29\!\cdots\!16$$$$T^{15} +$$$$43\!\cdots\!78$$$$T^{16} +$$$$25\!\cdots\!12$$$$T^{17} +$$$$80\!\cdots\!80$$$$T^{18} +$$$$36\!\cdots\!36$$$$T^{19} +$$$$75\!\cdots\!92$$$$T^{20} -$$$$92\!\cdots\!32$$$$T^{21} +$$$$12\!\cdots\!52$$$$T^{22} +$$$$51\!\cdots\!08$$$$T^{23} +$$$$30\!\cdots\!36$$$$T^{24} +$$$$15\!\cdots\!24$$$$T^{25} +$$$$32\!\cdots\!52$$$$T^{26} +$$$$13\!\cdots\!44$$$$T^{27} +$$$$84\!\cdots\!12$$$$T^{28} -$$$$34\!\cdots\!24$$$$T^{29} +$$$$17\!\cdots\!32$$$$T^{30} +$$$$17\!\cdots\!92$$$$T^{31} +$$$$87\!\cdots\!01$$$$T^{32}$$)