Properties

Label 160.6
Level 160
Weight 6
Dimension 1950
Nonzero newspaces 10
Sturm bound 9216
Trace bound 7

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Defining parameters

Level: \( N \) = \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(9216\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(160))\).

Total New Old
Modular forms 3968 2010 1958
Cusp forms 3712 1950 1762
Eisenstein series 256 60 196

Trace form

\( 1950q - 8q^{2} - 4q^{3} - 8q^{4} - 50q^{5} - 24q^{6} + 188q^{7} - 8q^{8} - 586q^{9} + O(q^{10}) \) \( 1950q - 8q^{2} - 4q^{3} - 8q^{4} - 50q^{5} - 24q^{6} + 188q^{7} - 8q^{8} - 586q^{9} + 188q^{10} - 16q^{11} + 3160q^{12} - 228q^{13} - 4968q^{14} - 428q^{15} - 8384q^{16} - 3628q^{17} + 3232q^{18} - 8q^{19} + 7588q^{20} + 11752q^{21} + 24752q^{22} + 1324q^{23} - 42928q^{24} + 5826q^{25} - 25984q^{26} + 13952q^{27} + 4352q^{28} - 24492q^{29} + 32300q^{30} - 57672q^{31} + 37152q^{32} + 16040q^{33} + 12496q^{34} + 9544q^{35} - 131200q^{36} - 23132q^{37} - 824q^{38} + 111344q^{39} + 28936q^{40} + 32068q^{41} + 107232q^{42} - 65460q^{43} - 7448q^{44} - 2638q^{45} - 126680q^{46} - 44196q^{47} - 224752q^{48} - 61674q^{49} + 4508q^{50} + 18920q^{51} - 36952q^{52} + 171396q^{53} - 2640q^{54} - 37084q^{55} + 161936q^{56} + 271976q^{57} + 169136q^{58} + 57912q^{59} + 62456q^{60} - 409364q^{61} - 126976q^{62} + 76900q^{63} + 651376q^{64} + 47484q^{65} + 220232q^{66} + 33060q^{67} - 304512q^{68} - 27752q^{69} - 742776q^{70} - 18160q^{71} - 773960q^{72} + 80092q^{73} - 329240q^{74} - 65520q^{75} - 24984q^{76} + 121144q^{77} + 1611672q^{78} - 246096q^{79} + 1082840q^{80} + 117998q^{81} - 135848q^{82} + 784916q^{83} - 775136q^{84} + 55348q^{85} - 903968q^{86} + 896952q^{87} - 846240q^{88} - 43204q^{89} - 1676136q^{90} - 729680q^{91} - 84496q^{92} - 1034640q^{93} + 76400q^{94} - 811424q^{95} + 2219360q^{96} + 123076q^{97} + 2413200q^{98} - 677104q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(160))\)

We only show spaces with even 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
160.6.a \(\chi_{160}(1, \cdot)\) 160.6.a.a 2 1
160.6.a.b 2
160.6.a.c 2
160.6.a.d 2
160.6.a.e 2
160.6.a.f 3
160.6.a.g 3
160.6.a.h 4
160.6.c \(\chi_{160}(129, \cdot)\) 160.6.c.a 2 1
160.6.c.b 4
160.6.c.c 12
160.6.c.d 12
160.6.d \(\chi_{160}(81, \cdot)\) 160.6.d.a 20 1
160.6.f \(\chi_{160}(49, \cdot)\) 160.6.f.a 28 1
160.6.j \(\chi_{160}(87, \cdot)\) None 0 2
160.6.l \(\chi_{160}(41, \cdot)\) None 0 2
160.6.n \(\chi_{160}(63, \cdot)\) 160.6.n.a 14 2
160.6.n.b 14
160.6.n.c 16
160.6.n.d 16
160.6.o \(\chi_{160}(47, \cdot)\) 160.6.o.a 56 2
160.6.q \(\chi_{160}(9, \cdot)\) None 0 2
160.6.s \(\chi_{160}(7, \cdot)\) None 0 2
160.6.u \(\chi_{160}(43, \cdot)\) n/a 472 4
160.6.x \(\chi_{160}(21, \cdot)\) n/a 320 4
160.6.z \(\chi_{160}(29, \cdot)\) n/a 472 4
160.6.ba \(\chi_{160}(3, \cdot)\) n/a 472 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(160)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 8 T + 222 T^{2} + 1944 T^{3} + 59049 T^{4} \))(\( 1 + 306 T^{2} + 59049 T^{4} \))(\( 1 + 146 T^{2} + 59049 T^{4} \))(\( 1 + 446 T^{2} + 59049 T^{4} \))(\( 1 - 8 T + 222 T^{2} - 1944 T^{3} + 59049 T^{4} \))(\( 1 + 10 T + 181 T^{2} + 5268 T^{3} + 43983 T^{4} + 590490 T^{5} + 14348907 T^{6} \))(\( 1 - 10 T + 181 T^{2} - 5268 T^{3} + 43983 T^{4} - 590490 T^{5} + 14348907 T^{6} \))(\( 1 + 124 T^{2} + 25686 T^{4} + 7322076 T^{6} + 3486784401 T^{8} \))(\( ( 1 - 243 T^{2} )^{2} \))(\( ( 1 - 38 T + 722 T^{2} - 9234 T^{3} + 59049 T^{4} )( 1 + 38 T + 722 T^{2} + 9234 T^{3} + 59049 T^{4} ) \))(\( ( 1 - 310 T^{2} + 120679 T^{4} - 26699028 T^{6} + 7125974271 T^{8} - 1080903164310 T^{10} + 205891132094649 T^{12} )^{2} \))(\( ( 1 - 662 T^{2} + 270567 T^{4} - 78508116 T^{6} + 15976710783 T^{8} - 2308251273462 T^{10} + 205891132094649 T^{12} )^{2} \))(\( 1 - 1620 T^{2} + 1394322 T^{4} - 834927892 T^{6} + 392823148221 T^{8} - 155295909553872 T^{10} + 53814329151823576 T^{12} - 16772396183204761872 T^{14} + \)\(47\!\cdots\!30\)\( T^{16} - \)\(12\!\cdots\!00\)\( T^{18} + \)\(31\!\cdots\!00\)\( T^{20} - \)\(75\!\cdots\!00\)\( T^{22} + \)\(16\!\cdots\!30\)\( T^{24} - \)\(34\!\cdots\!28\)\( T^{26} + \)\(65\!\cdots\!76\)\( T^{28} - \)\(11\!\cdots\!28\)\( T^{30} + \)\(16\!\cdots\!21\)\( T^{32} - \)\(20\!\cdots\!08\)\( T^{34} + \)\(20\!\cdots\!22\)\( T^{36} - \)\(14\!\cdots\!80\)\( T^{38} + \)\(51\!\cdots\!01\)\( T^{40} \))(\( 1 + 10 T + 50 T^{2} + 254 T^{3} - 91369 T^{4} - 1354100 T^{5} - 8940292 T^{6} - 156709276 T^{7} + 3134936461 T^{8} + 38721912918 T^{9} + 290596015278 T^{10} + 2245195781154 T^{11} + 9414782746155 T^{12} + 473122978927848 T^{13} + 19255041373064328 T^{14} + 114968883879467064 T^{15} + 555933506377706595 T^{16} + 32216105460571098678 T^{17} + \)\(10\!\cdots\!78\)\( T^{18} + \)\(32\!\cdots\!74\)\( T^{19} + \)\(64\!\cdots\!89\)\( T^{20} - \)\(78\!\cdots\!32\)\( T^{21} - \)\(10\!\cdots\!92\)\( T^{22} - \)\(40\!\cdots\!00\)\( T^{23} - \)\(65\!\cdots\!81\)\( T^{24} + \)\(44\!\cdots\!78\)\( T^{25} + \)\(21\!\cdots\!50\)\( T^{26} + \)\(10\!\cdots\!30\)\( T^{27} + \)\(25\!\cdots\!49\)\( T^{28} \))(\( 1 - 10 T + 50 T^{2} - 254 T^{3} - 91369 T^{4} + 1354100 T^{5} - 8940292 T^{6} + 156709276 T^{7} + 3134936461 T^{8} - 38721912918 T^{9} + 290596015278 T^{10} - 2245195781154 T^{11} + 9414782746155 T^{12} - 473122978927848 T^{13} + 19255041373064328 T^{14} - 114968883879467064 T^{15} + 555933506377706595 T^{16} - 32216105460571098678 T^{17} + \)\(10\!\cdots\!78\)\( T^{18} - \)\(32\!\cdots\!74\)\( T^{19} + \)\(64\!\cdots\!89\)\( T^{20} + \)\(78\!\cdots\!32\)\( T^{21} - \)\(10\!\cdots\!92\)\( T^{22} + \)\(40\!\cdots\!00\)\( T^{23} - \)\(65\!\cdots\!81\)\( T^{24} - \)\(44\!\cdots\!78\)\( T^{25} + \)\(21\!\cdots\!50\)\( T^{26} - \)\(10\!\cdots\!30\)\( T^{27} + \)\(25\!\cdots\!49\)\( T^{28} \))(\( 1 + 10 T + 50 T^{2} - 3114 T^{3} - 71776 T^{4} - 1530706 T^{5} - 6869762 T^{6} - 282516126 T^{7} - 1414085636 T^{8} + 89177429938 T^{9} + 2520680189450 T^{10} + 49929440504142 T^{11} + 506618123321952 T^{12} - 709766597096154 T^{13} - 113295686701585050 T^{14} - 1816344389104634358 T^{15} - 43957043443472192442 T^{16} - \)\(44\!\cdots\!94\)\( T^{17} - \)\(66\!\cdots\!50\)\( T^{18} - \)\(10\!\cdots\!78\)\( T^{19} + \)\(17\!\cdots\!52\)\( T^{20} + \)\(42\!\cdots\!06\)\( T^{21} + \)\(51\!\cdots\!50\)\( T^{22} + \)\(44\!\cdots\!66\)\( T^{23} - \)\(17\!\cdots\!36\)\( T^{24} - \)\(83\!\cdots\!18\)\( T^{25} - \)\(49\!\cdots\!38\)\( T^{26} - \)\(26\!\cdots\!42\)\( T^{27} - \)\(30\!\cdots\!76\)\( T^{28} - \)\(32\!\cdots\!02\)\( T^{29} + \)\(12\!\cdots\!50\)\( T^{30} + \)\(60\!\cdots\!70\)\( T^{31} + \)\(14\!\cdots\!01\)\( T^{32} \))(\( 1 - 10 T + 50 T^{2} + 3114 T^{3} - 71776 T^{4} + 1530706 T^{5} - 6869762 T^{6} + 282516126 T^{7} - 1414085636 T^{8} - 89177429938 T^{9} + 2520680189450 T^{10} - 49929440504142 T^{11} + 506618123321952 T^{12} + 709766597096154 T^{13} - 113295686701585050 T^{14} + 1816344389104634358 T^{15} - 43957043443472192442 T^{16} + \)\(44\!\cdots\!94\)\( T^{17} - \)\(66\!\cdots\!50\)\( T^{18} + \)\(10\!\cdots\!78\)\( T^{19} + \)\(17\!\cdots\!52\)\( T^{20} - \)\(42\!\cdots\!06\)\( T^{21} + \)\(51\!\cdots\!50\)\( T^{22} - \)\(44\!\cdots\!66\)\( T^{23} - \)\(17\!\cdots\!36\)\( T^{24} + \)\(83\!\cdots\!18\)\( T^{25} - \)\(49\!\cdots\!38\)\( T^{26} + \)\(26\!\cdots\!42\)\( T^{27} - \)\(30\!\cdots\!76\)\( T^{28} + \)\(32\!\cdots\!02\)\( T^{29} + \)\(12\!\cdots\!50\)\( T^{30} - \)\(60\!\cdots\!70\)\( T^{31} + \)\(14\!\cdots\!01\)\( T^{32} \))
$5$ (\( ( 1 - 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 - 25 T )^{2} \))(\( ( 1 - 25 T )^{2} \))(\( ( 1 + 25 T )^{3} \))(\( ( 1 + 25 T )^{3} \))(\( ( 1 - 25 T )^{4} \))(\( 1 - 82 T + 3125 T^{2} \))(\( ( 1 - 3125 T^{2} )^{2} \))(\( ( 1 + 30 T + 75 T^{2} - 123500 T^{3} + 234375 T^{4} + 292968750 T^{5} + 30517578125 T^{6} )^{2} \))(\( ( 1 + 30 T + 4555 T^{2} + 273300 T^{3} + 14234375 T^{4} + 292968750 T^{5} + 30517578125 T^{6} )^{2} \))(\( ( 1 + 625 T^{2} )^{10} \))(\( 1 - 42 T + 3115 T^{2} - 77660 T^{3} - 1600075 T^{4} + 15516250 T^{5} - 16330865625 T^{6} + 925536875000 T^{7} - 51033955078125 T^{8} + 151525878906250 T^{9} - 48830413818359375 T^{10} - 7406234741210937500 T^{11} + \)\(92\!\cdots\!75\)\( T^{12} - \)\(39\!\cdots\!50\)\( T^{13} + \)\(29\!\cdots\!25\)\( T^{14} \))(\( 1 - 42 T + 3115 T^{2} - 77660 T^{3} - 1600075 T^{4} + 15516250 T^{5} - 16330865625 T^{6} + 925536875000 T^{7} - 51033955078125 T^{8} + 151525878906250 T^{9} - 48830413818359375 T^{10} - 7406234741210937500 T^{11} + \)\(92\!\cdots\!75\)\( T^{12} - \)\(39\!\cdots\!50\)\( T^{13} + \)\(29\!\cdots\!25\)\( T^{14} \))(\( 1 + 42 T - 3688 T^{2} - 336370 T^{3} - 1345940 T^{4} + 732464050 T^{5} + 13329225000 T^{6} - 337978756250 T^{7} - 9350412656250 T^{8} - 1056183613281250 T^{9} + 130168212890625000 T^{10} + 22353028869628906250 T^{11} - \)\(12\!\cdots\!00\)\( T^{12} - \)\(10\!\cdots\!50\)\( T^{13} - \)\(34\!\cdots\!00\)\( T^{14} + \)\(12\!\cdots\!50\)\( T^{15} + \)\(90\!\cdots\!25\)\( T^{16} \))(\( 1 + 42 T - 3688 T^{2} - 336370 T^{3} - 1345940 T^{4} + 732464050 T^{5} + 13329225000 T^{6} - 337978756250 T^{7} - 9350412656250 T^{8} - 1056183613281250 T^{9} + 130168212890625000 T^{10} + 22353028869628906250 T^{11} - \)\(12\!\cdots\!00\)\( T^{12} - \)\(10\!\cdots\!50\)\( T^{13} - \)\(34\!\cdots\!00\)\( T^{14} + \)\(12\!\cdots\!50\)\( T^{15} + \)\(90\!\cdots\!25\)\( T^{16} \))
$7$ (\( 1 + 104 T + 36038 T^{2} + 1747928 T^{3} + 282475249 T^{4} \))(\( 1 + 14394 T^{2} + 282475249 T^{4} \))(\( 1 + 30554 T^{2} + 282475249 T^{4} \))(\( 1 + 31654 T^{2} + 282475249 T^{4} \))(\( 1 - 104 T + 36038 T^{2} - 1747928 T^{3} + 282475249 T^{4} \))(\( 1 - 6 T + 27153 T^{2} - 1137532 T^{3} + 456360471 T^{4} - 1694851494 T^{5} + 4747561509943 T^{6} \))(\( 1 + 6 T + 27153 T^{2} + 1137532 T^{3} + 456360471 T^{4} + 1694851494 T^{5} + 4747561509943 T^{6} \))(\( 1 - 27060 T^{2} + 497649542 T^{4} - 7643780237940 T^{6} + 79792266297612001 T^{8} \))(\( ( 1 - 16807 T^{2} )^{2} \))(\( ( 1 - 366 T + 66978 T^{2} - 6151362 T^{3} + 282475249 T^{4} )( 1 + 366 T + 66978 T^{2} + 6151362 T^{3} + 282475249 T^{4} ) \))(\( ( 1 - 42334 T^{2} + 748334111 T^{4} - 10497411086308 T^{6} + 211385864339918639 T^{8} - \)\(33\!\cdots\!34\)\( T^{10} + \)\(22\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 54910 T^{2} + 1199559327 T^{4} - 18786317442980 T^{6} + 338845819584597423 T^{8} - \)\(43\!\cdots\!10\)\( T^{10} + \)\(22\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 98 T + 84148 T^{2} - 8017214 T^{3} + 3556570901 T^{4} - 345044190776 T^{5} + 103920201897616 T^{6} - 10159390994080936 T^{7} + 2363994840482709802 T^{8} - \)\(22\!\cdots\!76\)\( T^{9} + \)\(43\!\cdots\!72\)\( T^{10} - \)\(37\!\cdots\!32\)\( T^{11} + \)\(66\!\cdots\!98\)\( T^{12} - \)\(48\!\cdots\!48\)\( T^{13} + \)\(82\!\cdots\!16\)\( T^{14} - \)\(46\!\cdots\!32\)\( T^{15} + \)\(80\!\cdots\!49\)\( T^{16} - \)\(30\!\cdots\!02\)\( T^{17} + \)\(53\!\cdots\!48\)\( T^{18} - \)\(10\!\cdots\!86\)\( T^{19} + \)\(17\!\cdots\!49\)\( T^{20} )^{2} \))(\( 1 + 66 T + 2178 T^{2} - 3104786 T^{3} - 390660977 T^{4} + 28598040732 T^{5} + 7558178349116 T^{6} + 730117525814980 T^{7} - 100452887411613603 T^{8} - 13091475719468548578 T^{9} + \)\(44\!\cdots\!50\)\( T^{10} + \)\(38\!\cdots\!06\)\( T^{11} + \)\(37\!\cdots\!31\)\( T^{12} - \)\(47\!\cdots\!84\)\( T^{13} - \)\(77\!\cdots\!76\)\( T^{14} - \)\(79\!\cdots\!88\)\( T^{15} + \)\(10\!\cdots\!19\)\( T^{16} + \)\(18\!\cdots\!58\)\( T^{17} + \)\(35\!\cdots\!50\)\( T^{18} - \)\(17\!\cdots\!46\)\( T^{19} - \)\(22\!\cdots\!47\)\( T^{20} + \)\(27\!\cdots\!40\)\( T^{21} + \)\(48\!\cdots\!16\)\( T^{22} + \)\(30\!\cdots\!24\)\( T^{23} - \)\(70\!\cdots\!73\)\( T^{24} - \)\(93\!\cdots\!98\)\( T^{25} + \)\(11\!\cdots\!78\)\( T^{26} + \)\(56\!\cdots\!62\)\( T^{27} + \)\(14\!\cdots\!49\)\( T^{28} \))(\( 1 - 66 T + 2178 T^{2} + 3104786 T^{3} - 390660977 T^{4} - 28598040732 T^{5} + 7558178349116 T^{6} - 730117525814980 T^{7} - 100452887411613603 T^{8} + 13091475719468548578 T^{9} + \)\(44\!\cdots\!50\)\( T^{10} - \)\(38\!\cdots\!06\)\( T^{11} + \)\(37\!\cdots\!31\)\( T^{12} + \)\(47\!\cdots\!84\)\( T^{13} - \)\(77\!\cdots\!76\)\( T^{14} + \)\(79\!\cdots\!88\)\( T^{15} + \)\(10\!\cdots\!19\)\( T^{16} - \)\(18\!\cdots\!58\)\( T^{17} + \)\(35\!\cdots\!50\)\( T^{18} + \)\(17\!\cdots\!46\)\( T^{19} - \)\(22\!\cdots\!47\)\( T^{20} - \)\(27\!\cdots\!40\)\( T^{21} + \)\(48\!\cdots\!16\)\( T^{22} - \)\(30\!\cdots\!24\)\( T^{23} - \)\(70\!\cdots\!73\)\( T^{24} + \)\(93\!\cdots\!98\)\( T^{25} + \)\(11\!\cdots\!78\)\( T^{26} - \)\(56\!\cdots\!62\)\( T^{27} + \)\(14\!\cdots\!49\)\( T^{28} \))(\( 1 - 86 T + 3698 T^{2} + 2808286 T^{3} - 810527584 T^{4} - 2504717314 T^{5} + 7155971823534 T^{6} - 2324030762443574 T^{7} + 166847822527644348 T^{8} + 29386477550704152562 T^{9} - \)\(38\!\cdots\!46\)\( T^{10} + \)\(51\!\cdots\!62\)\( T^{11} + \)\(38\!\cdots\!24\)\( T^{12} - \)\(97\!\cdots\!26\)\( T^{13} + \)\(45\!\cdots\!90\)\( T^{14} + \)\(35\!\cdots\!26\)\( T^{15} - \)\(24\!\cdots\!62\)\( T^{16} + \)\(60\!\cdots\!82\)\( T^{17} + \)\(12\!\cdots\!10\)\( T^{18} - \)\(46\!\cdots\!18\)\( T^{19} + \)\(30\!\cdots\!24\)\( T^{20} + \)\(69\!\cdots\!34\)\( T^{21} - \)\(87\!\cdots\!54\)\( T^{22} + \)\(11\!\cdots\!66\)\( T^{23} + \)\(10\!\cdots\!48\)\( T^{24} - \)\(24\!\cdots\!18\)\( T^{25} + \)\(12\!\cdots\!66\)\( T^{26} - \)\(75\!\cdots\!02\)\( T^{27} - \)\(41\!\cdots\!84\)\( T^{28} + \)\(23\!\cdots\!02\)\( T^{29} + \)\(53\!\cdots\!02\)\( T^{30} - \)\(20\!\cdots\!98\)\( T^{31} + \)\(40\!\cdots\!01\)\( T^{32} \))(\( 1 + 86 T + 3698 T^{2} - 2808286 T^{3} - 810527584 T^{4} + 2504717314 T^{5} + 7155971823534 T^{6} + 2324030762443574 T^{7} + 166847822527644348 T^{8} - 29386477550704152562 T^{9} - \)\(38\!\cdots\!46\)\( T^{10} - \)\(51\!\cdots\!62\)\( T^{11} + \)\(38\!\cdots\!24\)\( T^{12} + \)\(97\!\cdots\!26\)\( T^{13} + \)\(45\!\cdots\!90\)\( T^{14} - \)\(35\!\cdots\!26\)\( T^{15} - \)\(24\!\cdots\!62\)\( T^{16} - \)\(60\!\cdots\!82\)\( T^{17} + \)\(12\!\cdots\!10\)\( T^{18} + \)\(46\!\cdots\!18\)\( T^{19} + \)\(30\!\cdots\!24\)\( T^{20} - \)\(69\!\cdots\!34\)\( T^{21} - \)\(87\!\cdots\!54\)\( T^{22} - \)\(11\!\cdots\!66\)\( T^{23} + \)\(10\!\cdots\!48\)\( T^{24} + \)\(24\!\cdots\!18\)\( T^{25} + \)\(12\!\cdots\!66\)\( T^{26} + \)\(75\!\cdots\!02\)\( T^{27} - \)\(41\!\cdots\!84\)\( T^{28} - \)\(23\!\cdots\!02\)\( T^{29} + \)\(53\!\cdots\!02\)\( T^{30} + \)\(20\!\cdots\!98\)\( T^{31} + \)\(40\!\cdots\!01\)\( T^{32} \))
$11$ (\( 1 + 320 T + 319702 T^{2} + 51536320 T^{3} + 25937424601 T^{4} \))(\( 1 + 254822 T^{2} + 25937424601 T^{4} \))(\( 1 + 92262 T^{2} + 25937424601 T^{4} \))(\( 1 - 197738 T^{2} + 25937424601 T^{4} \))(\( 1 - 320 T + 319702 T^{2} - 51536320 T^{3} + 25937424601 T^{4} \))(\( 1 - 396 T + 327873 T^{2} - 67617992 T^{3} + 52804274523 T^{4} - 10271220141996 T^{5} + 4177248169415651 T^{6} \))(\( 1 + 396 T + 327873 T^{2} + 67617992 T^{3} + 52804274523 T^{4} + 10271220141996 T^{5} + 4177248169415651 T^{6} \))(\( 1 + 382252 T^{2} + 87516901782 T^{4} + 9914632428581452 T^{6} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 161051 T^{2} )^{2} \))(\( ( 1 + 161051 T^{2} )^{4} \))(\( ( 1 + 220194 T^{2} + 46554422967 T^{4} + 4986677846505148 T^{6} + \)\(12\!\cdots\!67\)\( T^{8} + \)\(14\!\cdots\!94\)\( T^{10} + \)\(17\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 311650 T^{2} + 88422679991 T^{4} + 16030422126529084 T^{6} + \)\(22\!\cdots\!91\)\( T^{8} + \)\(20\!\cdots\!50\)\( T^{10} + \)\(17\!\cdots\!01\)\( T^{12} )^{2} \))(\( 1 - 1510004 T^{2} + 1155249727726 T^{4} - 592766540112799924 T^{6} + \)\(22\!\cdots\!17\)\( T^{8} - \)\(70\!\cdots\!04\)\( T^{10} + \)\(18\!\cdots\!36\)\( T^{12} - \)\(40\!\cdots\!64\)\( T^{14} + \)\(79\!\cdots\!82\)\( T^{16} - \)\(14\!\cdots\!04\)\( T^{18} + \)\(23\!\cdots\!76\)\( T^{20} - \)\(36\!\cdots\!04\)\( T^{22} + \)\(53\!\cdots\!82\)\( T^{24} - \)\(70\!\cdots\!64\)\( T^{26} + \)\(82\!\cdots\!36\)\( T^{28} - \)\(82\!\cdots\!04\)\( T^{30} + \)\(69\!\cdots\!17\)\( T^{32} - \)\(46\!\cdots\!24\)\( T^{34} + \)\(23\!\cdots\!26\)\( T^{36} - \)\(80\!\cdots\!04\)\( T^{38} + \)\(13\!\cdots\!01\)\( T^{40} \))(\( 1 - 1517670 T^{2} + 1118279059571 T^{4} - 531239593921187868 T^{6} + \)\(18\!\cdots\!61\)\( T^{8} - \)\(48\!\cdots\!18\)\( T^{10} + \)\(10\!\cdots\!67\)\( T^{12} - \)\(18\!\cdots\!88\)\( T^{14} + \)\(27\!\cdots\!67\)\( T^{16} - \)\(32\!\cdots\!18\)\( T^{18} + \)\(31\!\cdots\!61\)\( T^{20} - \)\(24\!\cdots\!68\)\( T^{22} + \)\(13\!\cdots\!71\)\( T^{24} - \)\(46\!\cdots\!70\)\( T^{26} + \)\(78\!\cdots\!01\)\( T^{28} \))(\( 1 - 1517670 T^{2} + 1118279059571 T^{4} - 531239593921187868 T^{6} + \)\(18\!\cdots\!61\)\( T^{8} - \)\(48\!\cdots\!18\)\( T^{10} + \)\(10\!\cdots\!67\)\( T^{12} - \)\(18\!\cdots\!88\)\( T^{14} + \)\(27\!\cdots\!67\)\( T^{16} - \)\(32\!\cdots\!18\)\( T^{18} + \)\(31\!\cdots\!61\)\( T^{20} - \)\(24\!\cdots\!68\)\( T^{22} + \)\(13\!\cdots\!71\)\( T^{24} - \)\(46\!\cdots\!70\)\( T^{26} + \)\(78\!\cdots\!01\)\( T^{28} \))(\( 1 - 580860 T^{2} + 233332093584 T^{4} - 74638580678134772 T^{6} + \)\(20\!\cdots\!20\)\( T^{8} - \)\(46\!\cdots\!24\)\( T^{10} + \)\(96\!\cdots\!08\)\( T^{12} - \)\(18\!\cdots\!84\)\( T^{14} + \)\(30\!\cdots\!54\)\( T^{16} - \)\(46\!\cdots\!84\)\( T^{18} + \)\(65\!\cdots\!08\)\( T^{20} - \)\(81\!\cdots\!24\)\( T^{22} + \)\(90\!\cdots\!20\)\( T^{24} - \)\(87\!\cdots\!72\)\( T^{26} + \)\(71\!\cdots\!84\)\( T^{28} - \)\(45\!\cdots\!60\)\( T^{30} + \)\(20\!\cdots\!01\)\( T^{32} \))(\( 1 - 580860 T^{2} + 233332093584 T^{4} - 74638580678134772 T^{6} + \)\(20\!\cdots\!20\)\( T^{8} - \)\(46\!\cdots\!24\)\( T^{10} + \)\(96\!\cdots\!08\)\( T^{12} - \)\(18\!\cdots\!84\)\( T^{14} + \)\(30\!\cdots\!54\)\( T^{16} - \)\(46\!\cdots\!84\)\( T^{18} + \)\(65\!\cdots\!08\)\( T^{20} - \)\(81\!\cdots\!24\)\( T^{22} + \)\(90\!\cdots\!20\)\( T^{24} - \)\(87\!\cdots\!72\)\( T^{26} + \)\(71\!\cdots\!84\)\( T^{28} - \)\(45\!\cdots\!60\)\( T^{30} + \)\(20\!\cdots\!01\)\( T^{32} \))
$13$ (\( 1 + 100 T + 297086 T^{2} + 37129300 T^{3} + 137858491849 T^{4} \))(\( ( 1 - 154 T + 371293 T^{2} )^{2} \))(\( ( 1 - 506 T + 371293 T^{2} )^{2} \))(\( ( 1 + 146 T + 371293 T^{2} )^{2} \))(\( 1 + 100 T + 297086 T^{2} + 37129300 T^{3} + 137858491849 T^{4} \))(\( 1 + 354 T + 845379 T^{2} + 291738444 T^{3} + 313883305047 T^{4} + 48801906114546 T^{5} + 51185893014090757 T^{6} \))(\( 1 + 354 T + 845379 T^{2} + 291738444 T^{3} + 313883305047 T^{4} + 48801906114546 T^{5} + 51185893014090757 T^{6} \))(\( ( 1 + 292 T - 102402 T^{2} + 108417556 T^{3} + 137858491849 T^{4} )^{2} \))(\( ( 1 - 1194 T + 371293 T^{2} )( 1 + 1194 T + 371293 T^{2} ) \))(\( ( 1 - 371293 T^{2} )^{4} \))(\( ( 1 - 921822 T^{2} + 378030377607 T^{4} - 125995996576493956 T^{6} + \)\(52\!\cdots\!43\)\( T^{8} - \)\(17\!\cdots\!22\)\( T^{10} + \)\(26\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 183262 T^{2} + 260173900423 T^{4} - 19831011157232516 T^{6} + \)\(35\!\cdots\!27\)\( T^{8} - \)\(34\!\cdots\!62\)\( T^{10} + \)\(26\!\cdots\!49\)\( T^{12} )^{2} \))(\( 1 - 3520332 T^{2} + 6227853839054 T^{4} - 7441447313525468748 T^{6} + \)\(67\!\cdots\!57\)\( T^{8} - \)\(50\!\cdots\!12\)\( T^{10} + \)\(32\!\cdots\!64\)\( T^{12} - \)\(17\!\cdots\!28\)\( T^{14} + \)\(87\!\cdots\!42\)\( T^{16} - \)\(38\!\cdots\!32\)\( T^{18} + \)\(14\!\cdots\!64\)\( T^{20} - \)\(52\!\cdots\!68\)\( T^{22} + \)\(16\!\cdots\!42\)\( T^{24} - \)\(46\!\cdots\!72\)\( T^{26} + \)\(11\!\cdots\!64\)\( T^{28} - \)\(25\!\cdots\!88\)\( T^{30} + \)\(46\!\cdots\!57\)\( T^{32} - \)\(70\!\cdots\!52\)\( T^{34} + \)\(81\!\cdots\!54\)\( T^{36} - \)\(63\!\cdots\!68\)\( T^{38} + \)\(24\!\cdots\!01\)\( T^{40} \))(\( 1 + 414 T + 85698 T^{2} + 485371686 T^{3} + 407510115667 T^{4} - 25330305055892 T^{5} + 72383288599671444 T^{6} + \)\(13\!\cdots\!64\)\( T^{7} + \)\(19\!\cdots\!85\)\( T^{8} - \)\(26\!\cdots\!74\)\( T^{9} + \)\(24\!\cdots\!22\)\( T^{10} + \)\(12\!\cdots\!02\)\( T^{11} - \)\(99\!\cdots\!17\)\( T^{12} - \)\(27\!\cdots\!44\)\( T^{13} + \)\(44\!\cdots\!64\)\( T^{14} - \)\(10\!\cdots\!92\)\( T^{15} - \)\(13\!\cdots\!33\)\( T^{16} + \)\(63\!\cdots\!14\)\( T^{17} + \)\(45\!\cdots\!22\)\( T^{18} - \)\(18\!\cdots\!82\)\( T^{19} + \)\(49\!\cdots\!65\)\( T^{20} + \)\(13\!\cdots\!48\)\( T^{21} + \)\(26\!\cdots\!44\)\( T^{22} - \)\(33\!\cdots\!56\)\( T^{23} + \)\(20\!\cdots\!83\)\( T^{24} + \)\(89\!\cdots\!02\)\( T^{25} + \)\(58\!\cdots\!98\)\( T^{26} + \)\(10\!\cdots\!02\)\( T^{27} + \)\(94\!\cdots\!49\)\( T^{28} \))(\( 1 + 414 T + 85698 T^{2} + 485371686 T^{3} + 407510115667 T^{4} - 25330305055892 T^{5} + 72383288599671444 T^{6} + \)\(13\!\cdots\!64\)\( T^{7} + \)\(19\!\cdots\!85\)\( T^{8} - \)\(26\!\cdots\!74\)\( T^{9} + \)\(24\!\cdots\!22\)\( T^{10} + \)\(12\!\cdots\!02\)\( T^{11} - \)\(99\!\cdots\!17\)\( T^{12} - \)\(27\!\cdots\!44\)\( T^{13} + \)\(44\!\cdots\!64\)\( T^{14} - \)\(10\!\cdots\!92\)\( T^{15} - \)\(13\!\cdots\!33\)\( T^{16} + \)\(63\!\cdots\!14\)\( T^{17} + \)\(45\!\cdots\!22\)\( T^{18} - \)\(18\!\cdots\!82\)\( T^{19} + \)\(49\!\cdots\!65\)\( T^{20} + \)\(13\!\cdots\!48\)\( T^{21} + \)\(26\!\cdots\!44\)\( T^{22} - \)\(33\!\cdots\!56\)\( T^{23} + \)\(20\!\cdots\!83\)\( T^{24} + \)\(89\!\cdots\!02\)\( T^{25} + \)\(58\!\cdots\!98\)\( T^{26} + \)\(10\!\cdots\!02\)\( T^{27} + \)\(94\!\cdots\!49\)\( T^{28} \))(\( 1 - 536 T + 143648 T^{2} - 293170824 T^{3} - 185935117448 T^{4} + 112653613917608 T^{5} + 9301436713751904 T^{6} + 69204174166800470584 T^{7} + \)\(13\!\cdots\!60\)\( T^{8} - \)\(25\!\cdots\!64\)\( T^{9} - \)\(50\!\cdots\!68\)\( T^{10} - \)\(90\!\cdots\!08\)\( T^{11} + \)\(40\!\cdots\!76\)\( T^{12} + \)\(23\!\cdots\!68\)\( T^{13} + \)\(13\!\cdots\!08\)\( T^{14} + \)\(14\!\cdots\!44\)\( T^{15} - \)\(96\!\cdots\!10\)\( T^{16} + \)\(55\!\cdots\!92\)\( T^{17} + \)\(17\!\cdots\!92\)\( T^{18} + \)\(12\!\cdots\!76\)\( T^{19} + \)\(77\!\cdots\!76\)\( T^{20} - \)\(64\!\cdots\!44\)\( T^{21} - \)\(13\!\cdots\!32\)\( T^{22} - \)\(24\!\cdots\!48\)\( T^{23} + \)\(48\!\cdots\!60\)\( T^{24} + \)\(92\!\cdots\!12\)\( T^{25} + \)\(46\!\cdots\!96\)\( T^{26} + \)\(20\!\cdots\!56\)\( T^{27} - \)\(12\!\cdots\!48\)\( T^{28} - \)\(74\!\cdots\!32\)\( T^{29} + \)\(13\!\cdots\!52\)\( T^{30} - \)\(18\!\cdots\!52\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 536 T + 143648 T^{2} - 293170824 T^{3} - 185935117448 T^{4} + 112653613917608 T^{5} + 9301436713751904 T^{6} + 69204174166800470584 T^{7} + \)\(13\!\cdots\!60\)\( T^{8} - \)\(25\!\cdots\!64\)\( T^{9} - \)\(50\!\cdots\!68\)\( T^{10} - \)\(90\!\cdots\!08\)\( T^{11} + \)\(40\!\cdots\!76\)\( T^{12} + \)\(23\!\cdots\!68\)\( T^{13} + \)\(13\!\cdots\!08\)\( T^{14} + \)\(14\!\cdots\!44\)\( T^{15} - \)\(96\!\cdots\!10\)\( T^{16} + \)\(55\!\cdots\!92\)\( T^{17} + \)\(17\!\cdots\!92\)\( T^{18} + \)\(12\!\cdots\!76\)\( T^{19} + \)\(77\!\cdots\!76\)\( T^{20} - \)\(64\!\cdots\!44\)\( T^{21} - \)\(13\!\cdots\!32\)\( T^{22} - \)\(24\!\cdots\!48\)\( T^{23} + \)\(48\!\cdots\!60\)\( T^{24} + \)\(92\!\cdots\!12\)\( T^{25} + \)\(46\!\cdots\!96\)\( T^{26} + \)\(20\!\cdots\!56\)\( T^{27} - \)\(12\!\cdots\!48\)\( T^{28} - \)\(74\!\cdots\!32\)\( T^{29} + \)\(13\!\cdots\!52\)\( T^{30} - \)\(18\!\cdots\!52\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))
$17$ (\( 1 - 580 T + 2475814 T^{2} - 823517060 T^{3} + 2015993900449 T^{4} \))(\( ( 1 - 178 T + 1419857 T^{2} )^{2} \))(\( ( 1 + 1838 T + 1419857 T^{2} )^{2} \))(\( ( 1 + 702 T + 1419857 T^{2} )^{2} \))(\( 1 - 580 T + 2475814 T^{2} - 823517060 T^{3} + 2015993900449 T^{4} \))(\( 1 - 1158 T + 1914111 T^{2} - 544550612 T^{3} + 2717763902127 T^{4} - 2334520936719942 T^{5} + 2862423051509815793 T^{6} \))(\( 1 - 1158 T + 1914111 T^{2} - 544550612 T^{3} + 2717763902127 T^{4} - 2334520936719942 T^{5} + 2862423051509815793 T^{6} \))(\( ( 1 + 380 T + 2009510 T^{2} + 539545660 T^{3} + 2015993900449 T^{4} )^{2} \))(\( ( 1 - 2242 T + 1419857 T^{2} )( 1 + 2242 T + 1419857 T^{2} ) \))(\( ( 1 - 1419857 T^{2} )^{4} \))(\( ( 1 - 7508390 T^{2} + 24616526523247 T^{4} - 45351621021996027220 T^{6} + \)\(49\!\cdots\!03\)\( T^{8} - \)\(30\!\cdots\!90\)\( T^{10} + \)\(81\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 + 1156442 T^{2} + 502148271983 T^{4} - 1980542974409409364 T^{6} + \)\(10\!\cdots\!67\)\( T^{8} + \)\(47\!\cdots\!42\)\( T^{10} + \)\(81\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 + 5447662 T^{2} + 1859072000 T^{3} + 15317572824845 T^{4} + 7413542230528000 T^{5} + 32518332783929091752 T^{6} + \)\(14\!\cdots\!00\)\( T^{7} + \)\(56\!\cdots\!10\)\( T^{8} + \)\(21\!\cdots\!00\)\( T^{9} + \)\(84\!\cdots\!72\)\( T^{10} + \)\(31\!\cdots\!00\)\( T^{11} + \)\(11\!\cdots\!90\)\( T^{12} + \)\(41\!\cdots\!00\)\( T^{13} + \)\(13\!\cdots\!52\)\( T^{14} + \)\(42\!\cdots\!00\)\( T^{15} + \)\(12\!\cdots\!05\)\( T^{16} + \)\(21\!\cdots\!00\)\( T^{17} + \)\(89\!\cdots\!62\)\( T^{18} + \)\(33\!\cdots\!49\)\( T^{20} )^{2} \))(\( 1 - 1222 T + 746642 T^{2} - 1023656774 T^{3} - 7517818418661 T^{4} + 9805314295428420 T^{5} - 5845038493789599340 T^{6} + \)\(85\!\cdots\!80\)\( T^{7} + \)\(21\!\cdots\!05\)\( T^{8} - \)\(32\!\cdots\!70\)\( T^{9} + \)\(19\!\cdots\!70\)\( T^{10} - \)\(33\!\cdots\!50\)\( T^{11} - \)\(20\!\cdots\!37\)\( T^{12} + \)\(66\!\cdots\!24\)\( T^{13} - \)\(44\!\cdots\!04\)\( T^{14} + \)\(93\!\cdots\!68\)\( T^{15} - \)\(41\!\cdots\!13\)\( T^{16} - \)\(96\!\cdots\!50\)\( T^{17} + \)\(80\!\cdots\!70\)\( T^{18} - \)\(19\!\cdots\!90\)\( T^{19} + \)\(17\!\cdots\!45\)\( T^{20} + \)\(99\!\cdots\!40\)\( T^{21} - \)\(96\!\cdots\!40\)\( T^{22} + \)\(22\!\cdots\!40\)\( T^{23} - \)\(25\!\cdots\!89\)\( T^{24} - \)\(48\!\cdots\!82\)\( T^{25} + \)\(50\!\cdots\!42\)\( T^{26} - \)\(11\!\cdots\!54\)\( T^{27} + \)\(13\!\cdots\!49\)\( T^{28} \))(\( 1 - 1222 T + 746642 T^{2} - 1023656774 T^{3} - 7517818418661 T^{4} + 9805314295428420 T^{5} - 5845038493789599340 T^{6} + \)\(85\!\cdots\!80\)\( T^{7} + \)\(21\!\cdots\!05\)\( T^{8} - \)\(32\!\cdots\!70\)\( T^{9} + \)\(19\!\cdots\!70\)\( T^{10} - \)\(33\!\cdots\!50\)\( T^{11} - \)\(20\!\cdots\!37\)\( T^{12} + \)\(66\!\cdots\!24\)\( T^{13} - \)\(44\!\cdots\!04\)\( T^{14} + \)\(93\!\cdots\!68\)\( T^{15} - \)\(41\!\cdots\!13\)\( T^{16} - \)\(96\!\cdots\!50\)\( T^{17} + \)\(80\!\cdots\!70\)\( T^{18} - \)\(19\!\cdots\!90\)\( T^{19} + \)\(17\!\cdots\!45\)\( T^{20} + \)\(99\!\cdots\!40\)\( T^{21} - \)\(96\!\cdots\!40\)\( T^{22} + \)\(22\!\cdots\!40\)\( T^{23} - \)\(25\!\cdots\!89\)\( T^{24} - \)\(48\!\cdots\!82\)\( T^{25} + \)\(50\!\cdots\!42\)\( T^{26} - \)\(11\!\cdots\!54\)\( T^{27} + \)\(13\!\cdots\!49\)\( T^{28} \))(\( 1 + 1828 T + 1670792 T^{2} - 327758324 T^{3} + 3015753425928 T^{4} + 10493189333351412 T^{5} + 14196566162828930648 T^{6} + \)\(64\!\cdots\!44\)\( T^{7} + \)\(60\!\cdots\!96\)\( T^{8} + \)\(26\!\cdots\!20\)\( T^{9} + \)\(48\!\cdots\!00\)\( T^{10} + \)\(40\!\cdots\!40\)\( T^{11} + \)\(30\!\cdots\!88\)\( T^{12} + \)\(53\!\cdots\!44\)\( T^{13} + \)\(10\!\cdots\!76\)\( T^{14} + \)\(94\!\cdots\!68\)\( T^{15} + \)\(94\!\cdots\!74\)\( T^{16} + \)\(13\!\cdots\!76\)\( T^{17} + \)\(20\!\cdots\!24\)\( T^{18} + \)\(15\!\cdots\!92\)\( T^{19} + \)\(12\!\cdots\!88\)\( T^{20} + \)\(23\!\cdots\!80\)\( T^{21} + \)\(39\!\cdots\!00\)\( T^{22} + \)\(30\!\cdots\!60\)\( T^{23} + \)\(99\!\cdots\!96\)\( T^{24} + \)\(15\!\cdots\!08\)\( T^{25} + \)\(47\!\cdots\!52\)\( T^{26} + \)\(49\!\cdots\!16\)\( T^{27} + \)\(20\!\cdots\!28\)\( T^{28} - \)\(31\!\cdots\!68\)\( T^{29} + \)\(22\!\cdots\!08\)\( T^{30} + \)\(35\!\cdots\!04\)\( T^{31} + \)\(27\!\cdots\!01\)\( T^{32} \))(\( 1 + 1828 T + 1670792 T^{2} - 327758324 T^{3} + 3015753425928 T^{4} + 10493189333351412 T^{5} + 14196566162828930648 T^{6} + \)\(64\!\cdots\!44\)\( T^{7} + \)\(60\!\cdots\!96\)\( T^{8} + \)\(26\!\cdots\!20\)\( T^{9} + \)\(48\!\cdots\!00\)\( T^{10} + \)\(40\!\cdots\!40\)\( T^{11} + \)\(30\!\cdots\!88\)\( T^{12} + \)\(53\!\cdots\!44\)\( T^{13} + \)\(10\!\cdots\!76\)\( T^{14} + \)\(94\!\cdots\!68\)\( T^{15} + \)\(94\!\cdots\!74\)\( T^{16} + \)\(13\!\cdots\!76\)\( T^{17} + \)\(20\!\cdots\!24\)\( T^{18} + \)\(15\!\cdots\!92\)\( T^{19} + \)\(12\!\cdots\!88\)\( T^{20} + \)\(23\!\cdots\!80\)\( T^{21} + \)\(39\!\cdots\!00\)\( T^{22} + \)\(30\!\cdots\!60\)\( T^{23} + \)\(99\!\cdots\!96\)\( T^{24} + \)\(15\!\cdots\!08\)\( T^{25} + \)\(47\!\cdots\!52\)\( T^{26} + \)\(49\!\cdots\!16\)\( T^{27} + \)\(20\!\cdots\!28\)\( T^{28} - \)\(31\!\cdots\!68\)\( T^{29} + \)\(22\!\cdots\!08\)\( T^{30} + \)\(35\!\cdots\!04\)\( T^{31} + \)\(27\!\cdots\!01\)\( T^{32} \))
$19$ (\( 1 + 720 T + 4633798 T^{2} + 1782791280 T^{3} + 6131066257801 T^{4} \))(\( 1 + 4019078 T^{2} + 6131066257801 T^{4} \))(\( 1 + 687238 T^{2} + 6131066257801 T^{4} \))(\( 1 - 2512762 T^{2} + 6131066257801 T^{4} \))(\( 1 - 720 T + 4633798 T^{2} - 1782791280 T^{3} + 6131066257801 T^{4} \))(\( 1 + 3192 T + 9330057 T^{2} + 15933739216 T^{3} + 23102144807643 T^{4} + 19570363494900792 T^{5} + 15181127029874798299 T^{6} \))(\( 1 - 3192 T + 9330057 T^{2} - 15933739216 T^{3} + 23102144807643 T^{4} - 19570363494900792 T^{5} + 15181127029874798299 T^{6} \))(\( 1 + 1633036 T^{2} + 154661897526 T^{4} + 10012251917374313836 T^{6} + \)\(37\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 2476099 T^{2} )^{2} \))(\( ( 1 + 2476099 T^{2} )^{4} \))(\( ( 1 + 8862994 T^{2} + 40251921150215 T^{4} + \)\(12\!\cdots\!80\)\( T^{6} + \)\(24\!\cdots\!15\)\( T^{8} + \)\(33\!\cdots\!94\)\( T^{10} + \)\(23\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 3143250 T^{2} + 17341223849991 T^{4} + 36134402435803900316 T^{6} + \)\(10\!\cdots\!91\)\( T^{8} + \)\(11\!\cdots\!50\)\( T^{10} + \)\(23\!\cdots\!01\)\( T^{12} )^{2} \))(\( 1 - 23638692 T^{2} + 296336418074734 T^{4} - \)\(25\!\cdots\!32\)\( T^{6} + \)\(17\!\cdots\!97\)\( T^{8} - \)\(93\!\cdots\!80\)\( T^{10} + \)\(42\!\cdots\!52\)\( T^{12} - \)\(16\!\cdots\!48\)\( T^{14} + \)\(56\!\cdots\!66\)\( T^{16} - \)\(16\!\cdots\!12\)\( T^{18} + \)\(44\!\cdots\!28\)\( T^{20} - \)\(10\!\cdots\!12\)\( T^{22} + \)\(21\!\cdots\!66\)\( T^{24} - \)\(38\!\cdots\!48\)\( T^{26} + \)\(60\!\cdots\!52\)\( T^{28} - \)\(80\!\cdots\!80\)\( T^{30} + \)\(91\!\cdots\!97\)\( T^{32} - \)\(83\!\cdots\!32\)\( T^{34} + \)\(59\!\cdots\!34\)\( T^{36} - \)\(28\!\cdots\!92\)\( T^{38} + \)\(75\!\cdots\!01\)\( T^{40} \))(\( ( 1 + 2836 T + 12192485 T^{2} + 21773970856 T^{3} + 58437600122669 T^{4} + 77435325554759820 T^{5} + \)\(17\!\cdots\!85\)\( T^{6} + \)\(20\!\cdots\!00\)\( T^{7} + \)\(43\!\cdots\!15\)\( T^{8} + \)\(47\!\cdots\!20\)\( T^{9} + \)\(88\!\cdots\!31\)\( T^{10} + \)\(81\!\cdots\!56\)\( T^{11} + \)\(11\!\cdots\!15\)\( T^{12} + \)\(65\!\cdots\!36\)\( T^{13} + \)\(57\!\cdots\!99\)\( T^{14} )^{2} \))(\( ( 1 - 2836 T + 12192485 T^{2} - 21773970856 T^{3} + 58437600122669 T^{4} - 77435325554759820 T^{5} + \)\(17\!\cdots\!85\)\( T^{6} - \)\(20\!\cdots\!00\)\( T^{7} + \)\(43\!\cdots\!15\)\( T^{8} - \)\(47\!\cdots\!20\)\( T^{9} + \)\(88\!\cdots\!31\)\( T^{10} - \)\(81\!\cdots\!56\)\( T^{11} + \)\(11\!\cdots\!15\)\( T^{12} - \)\(65\!\cdots\!36\)\( T^{13} + \)\(57\!\cdots\!99\)\( T^{14} )^{2} \))(\( ( 1 + 1256 T + 11933496 T^{2} + 17157951112 T^{3} + 74779232061244 T^{4} + 104521619172501960 T^{5} + \)\(31\!\cdots\!88\)\( T^{6} + \)\(38\!\cdots\!64\)\( T^{7} + \)\(93\!\cdots\!18\)\( T^{8} + \)\(94\!\cdots\!36\)\( T^{9} + \)\(19\!\cdots\!88\)\( T^{10} + \)\(15\!\cdots\!40\)\( T^{11} + \)\(28\!\cdots\!44\)\( T^{12} + \)\(15\!\cdots\!88\)\( T^{13} + \)\(27\!\cdots\!96\)\( T^{14} + \)\(71\!\cdots\!44\)\( T^{15} + \)\(14\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 1256 T + 11933496 T^{2} - 17157951112 T^{3} + 74779232061244 T^{4} - 104521619172501960 T^{5} + \)\(31\!\cdots\!88\)\( T^{6} - \)\(38\!\cdots\!64\)\( T^{7} + \)\(93\!\cdots\!18\)\( T^{8} - \)\(94\!\cdots\!36\)\( T^{9} + \)\(19\!\cdots\!88\)\( T^{10} - \)\(15\!\cdots\!40\)\( T^{11} + \)\(28\!\cdots\!44\)\( T^{12} - \)\(15\!\cdots\!88\)\( T^{13} + \)\(27\!\cdots\!96\)\( T^{14} - \)\(71\!\cdots\!44\)\( T^{15} + \)\(14\!\cdots\!01\)\( T^{16} )^{2} \))
$23$ (\( 1 + 1688 T + 10950502 T^{2} + 10864546984 T^{3} + 41426511213649 T^{4} \))(\( 1 + 5934266 T^{2} + 41426511213649 T^{4} \))(\( 1 + 9265626 T^{2} + 41426511213649 T^{4} \))(\( 1 - 3871674 T^{2} + 41426511213649 T^{4} \))(\( 1 - 1688 T + 10950502 T^{2} - 10864546984 T^{3} + 41426511213649 T^{4} \))(\( 1 + 6126 T + 29722593 T^{2} + 84141222540 T^{3} + 191304803397399 T^{4} + 253778807694813774 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 - 6126 T + 29722593 T^{2} - 84141222540 T^{3} + 191304803397399 T^{4} - 253778807694813774 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 + 25651084 T^{2} + 247347299659206 T^{4} + \)\(10\!\cdots\!16\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 6436343 T^{2} )^{2} \))(\( ( 1 - 4838 T + 11703122 T^{2} - 31139027434 T^{3} + 41426511213649 T^{4} )( 1 + 4838 T + 11703122 T^{2} + 31139027434 T^{3} + 41426511213649 T^{4} ) \))(\( ( 1 - 27906430 T^{2} + 367961637958719 T^{4} - \)\(29\!\cdots\!08\)\( T^{6} + \)\(15\!\cdots\!31\)\( T^{8} - \)\(47\!\cdots\!30\)\( T^{10} + \)\(71\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 2071710 T^{2} + 29683977204927 T^{4} - \)\(44\!\cdots\!80\)\( T^{6} + \)\(12\!\cdots\!23\)\( T^{8} - \)\(35\!\cdots\!10\)\( T^{10} + \)\(71\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 2338 T + 35997660 T^{2} - 45007042654 T^{3} + 520972471777845 T^{4} - 50426407997609208 T^{5} + \)\(39\!\cdots\!60\)\( T^{6} + \)\(66\!\cdots\!96\)\( T^{7} + \)\(17\!\cdots\!10\)\( T^{8} + \)\(91\!\cdots\!52\)\( T^{9} + \)\(76\!\cdots\!60\)\( T^{10} + \)\(58\!\cdots\!36\)\( T^{11} + \)\(74\!\cdots\!90\)\( T^{12} + \)\(17\!\cdots\!72\)\( T^{13} + \)\(68\!\cdots\!60\)\( T^{14} - \)\(55\!\cdots\!44\)\( T^{15} + \)\(37\!\cdots\!05\)\( T^{16} - \)\(20\!\cdots\!78\)\( T^{17} + \)\(10\!\cdots\!60\)\( T^{18} - \)\(44\!\cdots\!34\)\( T^{19} + \)\(12\!\cdots\!49\)\( T^{20} )^{2} \))(\( 1 + 2902 T + 4210802 T^{2} - 8585545830 T^{3} - 77137172452561 T^{4} - 5298422918089420 T^{5} + \)\(34\!\cdots\!32\)\( T^{6} + \)\(17\!\cdots\!48\)\( T^{7} + \)\(43\!\cdots\!33\)\( T^{8} - \)\(14\!\cdots\!50\)\( T^{9} - \)\(10\!\cdots\!54\)\( T^{10} - \)\(57\!\cdots\!98\)\( T^{11} - \)\(19\!\cdots\!21\)\( T^{12} + \)\(51\!\cdots\!28\)\( T^{13} + \)\(13\!\cdots\!40\)\( T^{14} + \)\(33\!\cdots\!04\)\( T^{15} - \)\(79\!\cdots\!29\)\( T^{16} - \)\(15\!\cdots\!86\)\( T^{17} - \)\(18\!\cdots\!54\)\( T^{18} - \)\(15\!\cdots\!50\)\( T^{19} + \)\(30\!\cdots\!17\)\( T^{20} + \)\(81\!\cdots\!36\)\( T^{21} + \)\(10\!\cdots\!32\)\( T^{22} - \)\(10\!\cdots\!60\)\( T^{23} - \)\(94\!\cdots\!89\)\( T^{24} - \)\(67\!\cdots\!10\)\( T^{25} + \)\(21\!\cdots\!02\)\( T^{26} + \)\(94\!\cdots\!86\)\( T^{27} + \)\(20\!\cdots\!49\)\( T^{28} \))(\( 1 - 2902 T + 4210802 T^{2} + 8585545830 T^{3} - 77137172452561 T^{4} + 5298422918089420 T^{5} + \)\(34\!\cdots\!32\)\( T^{6} - \)\(17\!\cdots\!48\)\( T^{7} + \)\(43\!\cdots\!33\)\( T^{8} + \)\(14\!\cdots\!50\)\( T^{9} - \)\(10\!\cdots\!54\)\( T^{10} + \)\(57\!\cdots\!98\)\( T^{11} - \)\(19\!\cdots\!21\)\( T^{12} - \)\(51\!\cdots\!28\)\( T^{13} + \)\(13\!\cdots\!40\)\( T^{14} - \)\(33\!\cdots\!04\)\( T^{15} - \)\(79\!\cdots\!29\)\( T^{16} + \)\(15\!\cdots\!86\)\( T^{17} - \)\(18\!\cdots\!54\)\( T^{18} + \)\(15\!\cdots\!50\)\( T^{19} + \)\(30\!\cdots\!17\)\( T^{20} - \)\(81\!\cdots\!36\)\( T^{21} + \)\(10\!\cdots\!32\)\( T^{22} + \)\(10\!\cdots\!60\)\( T^{23} - \)\(94\!\cdots\!89\)\( T^{24} + \)\(67\!\cdots\!10\)\( T^{25} + \)\(21\!\cdots\!02\)\( T^{26} - \)\(94\!\cdots\!86\)\( T^{27} + \)\(20\!\cdots\!49\)\( T^{28} \))(\( 1 - 7642 T + 29200082 T^{2} - 114423930750 T^{3} + 421188911449792 T^{4} - 1070557300674963934 T^{5} + \)\(24\!\cdots\!34\)\( T^{6} - \)\(58\!\cdots\!94\)\( T^{7} + \)\(77\!\cdots\!36\)\( T^{8} + \)\(18\!\cdots\!62\)\( T^{9} - \)\(19\!\cdots\!06\)\( T^{10} + \)\(97\!\cdots\!06\)\( T^{11} - \)\(29\!\cdots\!68\)\( T^{12} + \)\(18\!\cdots\!70\)\( T^{13} + \)\(73\!\cdots\!74\)\( T^{14} - \)\(37\!\cdots\!54\)\( T^{15} + \)\(12\!\cdots\!78\)\( T^{16} - \)\(24\!\cdots\!22\)\( T^{17} + \)\(30\!\cdots\!26\)\( T^{18} + \)\(49\!\cdots\!90\)\( T^{19} - \)\(50\!\cdots\!68\)\( T^{20} + \)\(10\!\cdots\!58\)\( T^{21} - \)\(14\!\cdots\!94\)\( T^{22} + \)\(84\!\cdots\!34\)\( T^{23} + \)\(22\!\cdots\!36\)\( T^{24} - \)\(11\!\cdots\!42\)\( T^{25} + \)\(29\!\cdots\!66\)\( T^{26} - \)\(84\!\cdots\!38\)\( T^{27} + \)\(21\!\cdots\!92\)\( T^{28} - \)\(37\!\cdots\!50\)\( T^{29} + \)\(61\!\cdots\!18\)\( T^{30} - \)\(10\!\cdots\!94\)\( T^{31} + \)\(86\!\cdots\!01\)\( T^{32} \))(\( 1 + 7642 T + 29200082 T^{2} + 114423930750 T^{3} + 421188911449792 T^{4} + 1070557300674963934 T^{5} + \)\(24\!\cdots\!34\)\( T^{6} + \)\(58\!\cdots\!94\)\( T^{7} + \)\(77\!\cdots\!36\)\( T^{8} - \)\(18\!\cdots\!62\)\( T^{9} - \)\(19\!\cdots\!06\)\( T^{10} - \)\(97\!\cdots\!06\)\( T^{11} - \)\(29\!\cdots\!68\)\( T^{12} - \)\(18\!\cdots\!70\)\( T^{13} + \)\(73\!\cdots\!74\)\( T^{14} + \)\(37\!\cdots\!54\)\( T^{15} + \)\(12\!\cdots\!78\)\( T^{16} + \)\(24\!\cdots\!22\)\( T^{17} + \)\(30\!\cdots\!26\)\( T^{18} - \)\(49\!\cdots\!90\)\( T^{19} - \)\(50\!\cdots\!68\)\( T^{20} - \)\(10\!\cdots\!58\)\( T^{21} - \)\(14\!\cdots\!94\)\( T^{22} - \)\(84\!\cdots\!34\)\( T^{23} + \)\(22\!\cdots\!36\)\( T^{24} + \)\(11\!\cdots\!42\)\( T^{25} + \)\(29\!\cdots\!66\)\( T^{26} + \)\(84\!\cdots\!38\)\( T^{27} + \)\(21\!\cdots\!92\)\( T^{28} + \)\(37\!\cdots\!50\)\( T^{29} + \)\(61\!\cdots\!18\)\( T^{30} + \)\(10\!\cdots\!94\)\( T^{31} + \)\(86\!\cdots\!01\)\( T^{32} \))
$29$ (\( 1 - 108 T + 39233214 T^{2} - 2215204092 T^{3} + 420707233300201 T^{4} \))(\( ( 1 - 4110 T + 20511149 T^{2} )^{2} \))(\( ( 1 + 4530 T + 20511149 T^{2} )^{2} \))(\( ( 1 + 4010 T + 20511149 T^{2} )^{2} \))(\( 1 - 108 T + 39233214 T^{2} - 2215204092 T^{3} + 420707233300201 T^{4} \))(\( 1 - 426 T - 939693 T^{2} + 141773503364 T^{3} - 19274183137257 T^{4} - 179221281385885626 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( 1 - 426 T - 939693 T^{2} + 141773503364 T^{3} - 19274183137257 T^{4} - 179221281385885626 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( ( 1 + 84 T + 9837118 T^{2} + 1722936516 T^{3} + 420707233300201 T^{4} )^{2} \))(\( ( 1 - 2950 T + 20511149 T^{2} )^{2} \))(\( ( 1 - 1686 T + 20511149 T^{2} )^{4} \))(\( ( 1 + 5326 T + 46243827 T^{2} + 133362268948 T^{3} + 948514025927223 T^{4} + 2240686724556870526 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} )^{4} \))(\( ( 1 + 1966 T + 38511987 T^{2} + 51339089236 T^{3} + 789925103643063 T^{4} + 827110420668195166 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} )^{4} \))(\( 1 - 215092900 T^{2} + 23243889276296494 T^{4} - \)\(16\!\cdots\!00\)\( T^{6} + \)\(90\!\cdots\!13\)\( T^{8} - \)\(38\!\cdots\!00\)\( T^{10} + \)\(13\!\cdots\!92\)\( T^{12} - \)\(42\!\cdots\!00\)\( T^{14} + \)\(11\!\cdots\!86\)\( T^{16} - \)\(27\!\cdots\!00\)\( T^{18} + \)\(58\!\cdots\!28\)\( T^{20} - \)\(11\!\cdots\!00\)\( T^{22} + \)\(20\!\cdots\!86\)\( T^{24} - \)\(31\!\cdots\!00\)\( T^{26} + \)\(43\!\cdots\!92\)\( T^{28} - \)\(51\!\cdots\!00\)\( T^{30} + \)\(50\!\cdots\!13\)\( T^{32} - \)\(39\!\cdots\!00\)\( T^{34} + \)\(22\!\cdots\!94\)\( T^{36} - \)\(88\!\cdots\!00\)\( T^{38} + \)\(17\!\cdots\!01\)\( T^{40} \))(\( 1 - 127109206 T^{2} + 8400089254893139 T^{4} - \)\(38\!\cdots\!76\)\( T^{6} + \)\(13\!\cdots\!57\)\( T^{8} - \)\(39\!\cdots\!02\)\( T^{10} + \)\(98\!\cdots\!23\)\( T^{12} - \)\(21\!\cdots\!92\)\( T^{14} + \)\(41\!\cdots\!23\)\( T^{16} - \)\(69\!\cdots\!02\)\( T^{18} + \)\(10\!\cdots\!57\)\( T^{20} - \)\(12\!\cdots\!76\)\( T^{22} + \)\(11\!\cdots\!39\)\( T^{24} - \)\(70\!\cdots\!06\)\( T^{26} + \)\(23\!\cdots\!01\)\( T^{28} \))(\( 1 - 127109206 T^{2} + 8400089254893139 T^{4} - \)\(38\!\cdots\!76\)\( T^{6} + \)\(13\!\cdots\!57\)\( T^{8} - \)\(39\!\cdots\!02\)\( T^{10} + \)\(98\!\cdots\!23\)\( T^{12} - \)\(21\!\cdots\!92\)\( T^{14} + \)\(41\!\cdots\!23\)\( T^{16} - \)\(69\!\cdots\!02\)\( T^{18} + \)\(10\!\cdots\!57\)\( T^{20} - \)\(12\!\cdots\!76\)\( T^{22} + \)\(11\!\cdots\!39\)\( T^{24} - \)\(70\!\cdots\!06\)\( T^{26} + \)\(23\!\cdots\!01\)\( T^{28} \))(\( 1 - 129450464 T^{2} + 9016787664231832 T^{4} - \)\(44\!\cdots\!56\)\( T^{6} + \)\(16\!\cdots\!60\)\( T^{8} - \)\(53\!\cdots\!48\)\( T^{10} + \)\(14\!\cdots\!16\)\( T^{12} - \)\(34\!\cdots\!32\)\( T^{14} + \)\(74\!\cdots\!82\)\( T^{16} - \)\(14\!\cdots\!32\)\( T^{18} + \)\(25\!\cdots\!16\)\( T^{20} - \)\(39\!\cdots\!48\)\( T^{22} + \)\(52\!\cdots\!60\)\( T^{24} - \)\(58\!\cdots\!56\)\( T^{26} + \)\(49\!\cdots\!32\)\( T^{28} - \)\(30\!\cdots\!64\)\( T^{30} + \)\(98\!\cdots\!01\)\( T^{32} \))(\( 1 - 129450464 T^{2} + 9016787664231832 T^{4} - \)\(44\!\cdots\!56\)\( T^{6} + \)\(16\!\cdots\!60\)\( T^{8} - \)\(53\!\cdots\!48\)\( T^{10} + \)\(14\!\cdots\!16\)\( T^{12} - \)\(34\!\cdots\!32\)\( T^{14} + \)\(74\!\cdots\!82\)\( T^{16} - \)\(14\!\cdots\!32\)\( T^{18} + \)\(25\!\cdots\!16\)\( T^{20} - \)\(39\!\cdots\!48\)\( T^{22} + \)\(52\!\cdots\!60\)\( T^{24} - \)\(58\!\cdots\!56\)\( T^{26} + \)\(49\!\cdots\!32\)\( T^{28} - \)\(30\!\cdots\!64\)\( T^{30} + \)\(98\!\cdots\!01\)\( T^{32} \))
$31$ (\( 1 + 9840 T + 76732702 T^{2} + 281710845840 T^{3} + 819628286980801 T^{4} \))(\( 1 + 47289582 T^{2} + 819628286980801 T^{4} \))(\( 1 + 43928942 T^{2} + 819628286980801 T^{4} \))(\( 1 + 36406942 T^{2} + 819628286980801 T^{4} \))(\( 1 - 9840 T + 76732702 T^{2} - 281710845840 T^{3} + 819628286980801 T^{4} \))(\( 1 + 3276 T + 2292813 T^{2} - 41639420248 T^{3} + 65641289591763 T^{4} + 2685102268149104076 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( 1 - 3276 T + 2292813 T^{2} + 41639420248 T^{3} + 65641289591763 T^{4} - 2685102268149104076 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( 1 + 24283452 T^{2} + 1637830022018822 T^{4} + \)\(19\!\cdots\!52\)\( T^{6} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 28629151 T^{2} )^{2} \))(\( ( 1 + 28629151 T^{2} )^{4} \))(\( ( 1 + 10594234 T^{2} - 153174449706673 T^{4} + \)\(19\!\cdots\!88\)\( T^{6} - \)\(12\!\cdots\!73\)\( T^{8} + \)\(71\!\cdots\!34\)\( T^{10} + \)\(55\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 47574970 T^{2} + 2163796989249871 T^{4} + \)\(78\!\cdots\!04\)\( T^{6} + \)\(17\!\cdots\!71\)\( T^{8} + \)\(31\!\cdots\!70\)\( T^{10} + \)\(55\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 3580 T + 132421614 T^{2} + 484936307876 T^{3} + 8983138546835629 T^{4} + 33755686429634218608 T^{5} + \)\(43\!\cdots\!88\)\( T^{6} + \)\(16\!\cdots\!96\)\( T^{7} + \)\(17\!\cdots\!38\)\( T^{8} + \)\(60\!\cdots\!32\)\( T^{9} + \)\(54\!\cdots\!44\)\( T^{10} + \)\(17\!\cdots\!32\)\( T^{11} + \)\(13\!\cdots\!38\)\( T^{12} + \)\(38\!\cdots\!96\)\( T^{13} + \)\(29\!\cdots\!88\)\( T^{14} + \)\(64\!\cdots\!08\)\( T^{15} + \)\(49\!\cdots\!29\)\( T^{16} + \)\(76\!\cdots\!76\)\( T^{17} + \)\(59\!\cdots\!14\)\( T^{18} + \)\(46\!\cdots\!80\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} )^{2} \))(\( 1 - 265679454 T^{2} + 34933996110970539 T^{4} - \)\(30\!\cdots\!64\)\( T^{6} + \)\(19\!\cdots\!17\)\( T^{8} - \)\(92\!\cdots\!38\)\( T^{10} + \)\(36\!\cdots\!43\)\( T^{12} - \)\(11\!\cdots\!88\)\( T^{14} + \)\(29\!\cdots\!43\)\( T^{16} - \)\(62\!\cdots\!38\)\( T^{18} + \)\(10\!\cdots\!17\)\( T^{20} - \)\(13\!\cdots\!64\)\( T^{22} + \)\(12\!\cdots\!39\)\( T^{24} - \)\(80\!\cdots\!54\)\( T^{26} + \)\(24\!\cdots\!01\)\( T^{28} \))(\( 1 - 265679454 T^{2} + 34933996110970539 T^{4} - \)\(30\!\cdots\!64\)\( T^{6} + \)\(19\!\cdots\!17\)\( T^{8} - \)\(92\!\cdots\!38\)\( T^{10} + \)\(36\!\cdots\!43\)\( T^{12} - \)\(11\!\cdots\!88\)\( T^{14} + \)\(29\!\cdots\!43\)\( T^{16} - \)\(62\!\cdots\!38\)\( T^{18} + \)\(10\!\cdots\!17\)\( T^{20} - \)\(13\!\cdots\!64\)\( T^{22} + \)\(12\!\cdots\!39\)\( T^{24} - \)\(80\!\cdots\!54\)\( T^{26} + \)\(24\!\cdots\!01\)\( T^{28} \))(\( 1 - 221015276 T^{2} + 25619057922480912 T^{4} - \)\(20\!\cdots\!04\)\( T^{6} + \)\(12\!\cdots\!00\)\( T^{8} - \)\(64\!\cdots\!72\)\( T^{10} + \)\(27\!\cdots\!96\)\( T^{12} - \)\(98\!\cdots\!48\)\( T^{14} + \)\(30\!\cdots\!82\)\( T^{16} - \)\(80\!\cdots\!48\)\( T^{18} + \)\(18\!\cdots\!96\)\( T^{20} - \)\(35\!\cdots\!72\)\( T^{22} + \)\(57\!\cdots\!00\)\( T^{24} - \)\(76\!\cdots\!04\)\( T^{26} + \)\(77\!\cdots\!12\)\( T^{28} - \)\(54\!\cdots\!76\)\( T^{30} + \)\(20\!\cdots\!01\)\( T^{32} \))(\( 1 - 221015276 T^{2} + 25619057922480912 T^{4} - \)\(20\!\cdots\!04\)\( T^{6} + \)\(12\!\cdots\!00\)\( T^{8} - \)\(64\!\cdots\!72\)\( T^{10} + \)\(27\!\cdots\!96\)\( T^{12} - \)\(98\!\cdots\!48\)\( T^{14} + \)\(30\!\cdots\!82\)\( T^{16} - \)\(80\!\cdots\!48\)\( T^{18} + \)\(18\!\cdots\!96\)\( T^{20} - \)\(35\!\cdots\!72\)\( T^{22} + \)\(57\!\cdots\!00\)\( T^{24} - \)\(76\!\cdots\!04\)\( T^{26} + \)\(77\!\cdots\!12\)\( T^{28} - \)\(54\!\cdots\!76\)\( T^{30} + \)\(20\!\cdots\!01\)\( T^{32} \))
$37$ (\( 1 - 6540 T + 61572814 T^{2} - 453509478780 T^{3} + 4808584372417849 T^{4} \))(\( ( 1 - 7442 T + 69343957 T^{2} )^{2} \))(\( ( 1 - 338 T + 69343957 T^{2} )^{2} \))(\( ( 1 + 14778 T + 69343957 T^{2} )^{2} \))(\( 1 - 6540 T + 61572814 T^{2} - 453509478780 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 11562 T + 90623691 T^{2} + 525372493468 T^{3} + 6284205331885287 T^{4} + 55596852513895170138 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( 1 + 11562 T + 90623691 T^{2} + 525372493468 T^{3} + 6284205331885287 T^{4} + 55596852513895170138 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( ( 1 - 9868 T + 159567054 T^{2} - 684286167676 T^{3} + 4808584372417849 T^{4} )^{2} \))(\( ( 1 - 12242 T + 69343957 T^{2} )( 1 + 12242 T + 69343957 T^{2} ) \))(\( ( 1 - 69343957 T^{2} )^{4} \))(\( ( 1 - 234974254 T^{2} + 32080895329334807 T^{4} - \)\(26\!\cdots\!92\)\( T^{6} + \)\(15\!\cdots\!43\)\( T^{8} - \)\(54\!\cdots\!54\)\( T^{10} + \)\(11\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 301201198 T^{2} + 42883739211630103 T^{4} - \)\(37\!\cdots\!24\)\( T^{6} + \)\(20\!\cdots\!47\)\( T^{8} - \)\(69\!\cdots\!98\)\( T^{10} + \)\(11\!\cdots\!49\)\( T^{12} )^{2} \))(\( 1 - 565372668 T^{2} + 171401952644913934 T^{4} - \)\(36\!\cdots\!00\)\( T^{6} + \)\(59\!\cdots\!09\)\( T^{8} - \)\(80\!\cdots\!44\)\( T^{10} + \)\(93\!\cdots\!16\)\( T^{12} - \)\(93\!\cdots\!40\)\( T^{14} + \)\(83\!\cdots\!86\)\( T^{16} - \)\(67\!\cdots\!48\)\( T^{18} + \)\(48\!\cdots\!08\)\( T^{20} - \)\(32\!\cdots\!52\)\( T^{22} + \)\(19\!\cdots\!86\)\( T^{24} - \)\(10\!\cdots\!60\)\( T^{26} + \)\(49\!\cdots\!16\)\( T^{28} - \)\(20\!\cdots\!56\)\( T^{30} + \)\(73\!\cdots\!09\)\( T^{32} - \)\(21\!\cdots\!00\)\( T^{34} + \)\(48\!\cdots\!34\)\( T^{36} - \)\(77\!\cdots\!32\)\( T^{38} + \)\(66\!\cdots\!01\)\( T^{40} \))(\( 1 + 1790 T + 1602050 T^{2} - 1085215470730 T^{3} - 5589943426343837 T^{4} - 5189725886098796788 T^{5} + \)\(58\!\cdots\!80\)\( T^{6} + \)\(37\!\cdots\!60\)\( T^{7} + \)\(20\!\cdots\!01\)\( T^{8} - \)\(14\!\cdots\!14\)\( T^{9} - \)\(11\!\cdots\!78\)\( T^{10} - \)\(12\!\cdots\!50\)\( T^{11} - \)\(40\!\cdots\!45\)\( T^{12} + \)\(67\!\cdots\!72\)\( T^{13} + \)\(47\!\cdots\!96\)\( T^{14} + \)\(47\!\cdots\!04\)\( T^{15} - \)\(19\!\cdots\!05\)\( T^{16} - \)\(41\!\cdots\!50\)\( T^{17} - \)\(25\!\cdots\!78\)\( T^{18} - \)\(23\!\cdots\!98\)\( T^{19} + \)\(22\!\cdots\!49\)\( T^{20} + \)\(29\!\cdots\!80\)\( T^{21} + \)\(31\!\cdots\!80\)\( T^{22} - \)\(19\!\cdots\!16\)\( T^{23} - \)\(14\!\cdots\!13\)\( T^{24} - \)\(19\!\cdots\!90\)\( T^{25} + \)\(19\!\cdots\!50\)\( T^{26} + \)\(15\!\cdots\!30\)\( T^{27} + \)\(59\!\cdots\!49\)\( T^{28} \))(\( 1 + 1790 T + 1602050 T^{2} - 1085215470730 T^{3} - 5589943426343837 T^{4} - 5189725886098796788 T^{5} + \)\(58\!\cdots\!80\)\( T^{6} + \)\(37\!\cdots\!60\)\( T^{7} + \)\(20\!\cdots\!01\)\( T^{8} - \)\(14\!\cdots\!14\)\( T^{9} - \)\(11\!\cdots\!78\)\( T^{10} - \)\(12\!\cdots\!50\)\( T^{11} - \)\(40\!\cdots\!45\)\( T^{12} + \)\(67\!\cdots\!72\)\( T^{13} + \)\(47\!\cdots\!96\)\( T^{14} + \)\(47\!\cdots\!04\)\( T^{15} - \)\(19\!\cdots\!05\)\( T^{16} - \)\(41\!\cdots\!50\)\( T^{17} - \)\(25\!\cdots\!78\)\( T^{18} - \)\(23\!\cdots\!98\)\( T^{19} + \)\(22\!\cdots\!49\)\( T^{20} + \)\(29\!\cdots\!80\)\( T^{21} + \)\(31\!\cdots\!80\)\( T^{22} - \)\(19\!\cdots\!16\)\( T^{23} - \)\(14\!\cdots\!13\)\( T^{24} - \)\(19\!\cdots\!90\)\( T^{25} + \)\(19\!\cdots\!50\)\( T^{26} + \)\(15\!\cdots\!30\)\( T^{27} + \)\(59\!\cdots\!49\)\( T^{28} \))(\( 1 + 7620 T + 29032200 T^{2} + 1965688293660 T^{3} + 22987009602091912 T^{4} + 46723925283632703348 T^{5} + \)\(16\!\cdots\!60\)\( T^{6} + \)\(27\!\cdots\!40\)\( T^{7} + \)\(98\!\cdots\!88\)\( T^{8} + \)\(66\!\cdots\!16\)\( T^{9} + \)\(19\!\cdots\!52\)\( T^{10} + \)\(13\!\cdots\!00\)\( T^{11} + \)\(55\!\cdots\!44\)\( T^{12} + \)\(97\!\cdots\!64\)\( T^{13} + \)\(11\!\cdots\!44\)\( T^{14} + \)\(70\!\cdots\!36\)\( T^{15} + \)\(48\!\cdots\!10\)\( T^{16} + \)\(48\!\cdots\!52\)\( T^{17} + \)\(53\!\cdots\!56\)\( T^{18} + \)\(32\!\cdots\!52\)\( T^{19} + \)\(12\!\cdots\!44\)\( T^{20} + \)\(21\!\cdots\!00\)\( T^{21} + \)\(22\!\cdots\!48\)\( T^{22} + \)\(51\!\cdots\!88\)\( T^{23} + \)\(52\!\cdots\!88\)\( T^{24} + \)\(10\!\cdots\!80\)\( T^{25} + \)\(41\!\cdots\!40\)\( T^{26} + \)\(83\!\cdots\!64\)\( T^{27} + \)\(28\!\cdots\!12\)\( T^{28} + \)\(16\!\cdots\!20\)\( T^{29} + \)\(17\!\cdots\!00\)\( T^{30} + \)\(31\!\cdots\!60\)\( T^{31} + \)\(28\!\cdots\!01\)\( T^{32} \))(\( 1 + 7620 T + 29032200 T^{2} + 1965688293660 T^{3} + 22987009602091912 T^{4} + 46723925283632703348 T^{5} + \)\(16\!\cdots\!60\)\( T^{6} + \)\(27\!\cdots\!40\)\( T^{7} + \)\(98\!\cdots\!88\)\( T^{8} + \)\(66\!\cdots\!16\)\( T^{9} + \)\(19\!\cdots\!52\)\( T^{10} + \)\(13\!\cdots\!00\)\( T^{11} + \)\(55\!\cdots\!44\)\( T^{12} + \)\(97\!\cdots\!64\)\( T^{13} + \)\(11\!\cdots\!44\)\( T^{14} + \)\(70\!\cdots\!36\)\( T^{15} + \)\(48\!\cdots\!10\)\( T^{16} + \)\(48\!\cdots\!52\)\( T^{17} + \)\(53\!\cdots\!56\)\( T^{18} + \)\(32\!\cdots\!52\)\( T^{19} + \)\(12\!\cdots\!44\)\( T^{20} + \)\(21\!\cdots\!00\)\( T^{21} + \)\(22\!\cdots\!48\)\( T^{22} + \)\(51\!\cdots\!88\)\( T^{23} + \)\(52\!\cdots\!88\)\( T^{24} + \)\(10\!\cdots\!80\)\( T^{25} + \)\(41\!\cdots\!40\)\( T^{26} + \)\(83\!\cdots\!64\)\( T^{27} + \)\(28\!\cdots\!12\)\( T^{28} + \)\(16\!\cdots\!20\)\( T^{29} + \)\(17\!\cdots\!00\)\( T^{30} + \)\(31\!\cdots\!60\)\( T^{31} + \)\(28\!\cdots\!01\)\( T^{32} \))
$41$ (\( 1 + 10620 T + 77106582 T^{2} + 1230392854620 T^{3} + 13422659310152401 T^{4} \))(\( ( 1 - 7270 T + 115856201 T^{2} )^{2} \))(\( ( 1 + 6330 T + 115856201 T^{2} )^{2} \))(\( ( 1 + 4350 T + 115856201 T^{2} )^{2} \))(\( 1 + 10620 T + 77106582 T^{2} + 1230392854620 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 12450 T + 384843783 T^{2} - 2886023186300 T^{3} + 44586538676848383 T^{4} - \)\(16\!\cdots\!50\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( 1 - 12450 T + 384843783 T^{2} - 2886023186300 T^{3} + 44586538676848383 T^{4} - \)\(16\!\cdots\!50\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( ( 1 - 23812 T + 331016342 T^{2} - 2758767858212 T^{3} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 - 20950 T + 115856201 T^{2} )^{2} \))(\( ( 1 - 211028098 T^{2} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 + 27418 T + 531273543 T^{2} + 6402679071436 T^{3} + 61551334383790143 T^{4} + \)\(36\!\cdots\!18\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} )^{4} \))(\( ( 1 - 16390 T + 318388423 T^{2} - 3510238606580 T^{3} + 36887273131161023 T^{4} - \)\(21\!\cdots\!90\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} )^{4} \))(\( ( 1 - 5804 T + 580737234 T^{2} - 4176614475628 T^{3} + 181136735899530493 T^{4} - \)\(13\!\cdots\!48\)\( T^{5} + \)\(39\!\cdots\!40\)\( T^{6} - \)\(28\!\cdots\!68\)\( T^{7} + \)\(63\!\cdots\!42\)\( T^{8} - \)\(43\!\cdots\!24\)\( T^{9} + \)\(82\!\cdots\!24\)\( T^{10} - \)\(49\!\cdots\!24\)\( T^{11} + \)\(85\!\cdots\!42\)\( T^{12} - \)\(44\!\cdots\!68\)\( T^{13} + \)\(70\!\cdots\!40\)\( T^{14} - \)\(28\!\cdots\!48\)\( T^{15} + \)\(43\!\cdots\!93\)\( T^{16} - \)\(11\!\cdots\!28\)\( T^{17} + \)\(18\!\cdots\!34\)\( T^{18} - \)\(21\!\cdots\!04\)\( T^{19} + \)\(43\!\cdots\!01\)\( T^{20} )^{2} \))(\( ( 1 - 5822 T + 527400583 T^{2} - 3511555483012 T^{3} + 138605008918596701 T^{4} - \)\(95\!\cdots\!50\)\( T^{5} + \)\(23\!\cdots\!95\)\( T^{6} - \)\(14\!\cdots\!20\)\( T^{7} + \)\(26\!\cdots\!95\)\( T^{8} - \)\(12\!\cdots\!50\)\( T^{9} + \)\(21\!\cdots\!01\)\( T^{10} - \)\(63\!\cdots\!12\)\( T^{11} + \)\(11\!\cdots\!83\)\( T^{12} - \)\(14\!\cdots\!22\)\( T^{13} + \)\(28\!\cdots\!01\)\( T^{14} )^{2} \))(\( ( 1 - 5822 T + 527400583 T^{2} - 3511555483012 T^{3} + 138605008918596701 T^{4} - \)\(95\!\cdots\!50\)\( T^{5} + \)\(23\!\cdots\!95\)\( T^{6} - \)\(14\!\cdots\!20\)\( T^{7} + \)\(26\!\cdots\!95\)\( T^{8} - \)\(12\!\cdots\!50\)\( T^{9} + \)\(21\!\cdots\!01\)\( T^{10} - \)\(63\!\cdots\!12\)\( T^{11} + \)\(11\!\cdots\!83\)\( T^{12} - \)\(14\!\cdots\!22\)\( T^{13} + \)\(28\!\cdots\!01\)\( T^{14} )^{2} \))(\( ( 1 + 10642 T + 229001616 T^{2} + 2308310140798 T^{3} + 41488616565167196 T^{4} + \)\(33\!\cdots\!02\)\( T^{5} + \)\(55\!\cdots\!56\)\( T^{6} + \)\(38\!\cdots\!10\)\( T^{7} + \)\(61\!\cdots\!50\)\( T^{8} + \)\(44\!\cdots\!10\)\( T^{9} + \)\(74\!\cdots\!56\)\( T^{10} + \)\(52\!\cdots\!02\)\( T^{11} + \)\(74\!\cdots\!96\)\( T^{12} + \)\(48\!\cdots\!98\)\( T^{13} + \)\(55\!\cdots\!16\)\( T^{14} + \)\(29\!\cdots\!42\)\( T^{15} + \)\(32\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 10642 T + 229001616 T^{2} + 2308310140798 T^{3} + 41488616565167196 T^{4} + \)\(33\!\cdots\!02\)\( T^{5} + \)\(55\!\cdots\!56\)\( T^{6} + \)\(38\!\cdots\!10\)\( T^{7} + \)\(61\!\cdots\!50\)\( T^{8} + \)\(44\!\cdots\!10\)\( T^{9} + \)\(74\!\cdots\!56\)\( T^{10} + \)\(52\!\cdots\!02\)\( T^{11} + \)\(74\!\cdots\!96\)\( T^{12} + \)\(48\!\cdots\!98\)\( T^{13} + \)\(55\!\cdots\!16\)\( T^{14} + \)\(29\!\cdots\!42\)\( T^{15} + \)\(32\!\cdots\!01\)\( T^{16} )^{2} \))
$43$ (\( 1 + 25672 T + 364912302 T^{2} + 3774000748696 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 26783614 T^{2} + 21611482313284249 T^{4} \))(\( 1 - 35859614 T^{2} + 21611482313284249 T^{4} \))(\( 1 + 139567886 T^{2} + 21611482313284249 T^{4} \))(\( 1 - 25672 T + 364912302 T^{2} - 3774000748696 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 26346 T + 640605069 T^{2} + 8098987233524 T^{3} + 94174353771597567 T^{4} + \)\(56\!\cdots\!54\)\( T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( 1 - 26346 T + 640605069 T^{2} - 8098987233524 T^{3} + 94174353771597567 T^{4} - \)\(56\!\cdots\!54\)\( T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( 1 + 385757980 T^{2} + 71059469286049782 T^{4} + \)\(83\!\cdots\!20\)\( T^{6} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 147008443 T^{2} )^{2} \))(\( ( 1 - 11862 T + 70353522 T^{2} - 1743814150866 T^{3} + 21611482313284249 T^{4} )( 1 + 11862 T + 70353522 T^{2} + 1743814150866 T^{3} + 21611482313284249 T^{4} ) \))(\( ( 1 - 613900486 T^{2} + 182904754783784951 T^{4} - \)\(33\!\cdots\!72\)\( T^{6} + \)\(39\!\cdots\!99\)\( T^{8} - \)\(28\!\cdots\!86\)\( T^{10} + \)\(10\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 640358182 T^{2} + 187647756282389367 T^{4} - \)\(33\!\cdots\!76\)\( T^{6} + \)\(40\!\cdots\!83\)\( T^{8} - \)\(29\!\cdots\!82\)\( T^{10} + \)\(10\!\cdots\!49\)\( T^{12} )^{2} \))(\( 1 - 1208126740 T^{2} + 787740581508660018 T^{4} - \)\(36\!\cdots\!96\)\( T^{6} + \)\(12\!\cdots\!73\)\( T^{8} - \)\(37\!\cdots\!80\)\( T^{10} + \)\(95\!\cdots\!40\)\( T^{12} - \)\(20\!\cdots\!56\)\( T^{14} + \)\(40\!\cdots\!70\)\( T^{16} - \)\(70\!\cdots\!00\)\( T^{18} + \)\(10\!\cdots\!96\)\( T^{20} - \)\(15\!\cdots\!00\)\( T^{22} + \)\(18\!\cdots\!70\)\( T^{24} - \)\(21\!\cdots\!44\)\( T^{26} + \)\(20\!\cdots\!40\)\( T^{28} - \)\(17\!\cdots\!20\)\( T^{30} + \)\(13\!\cdots\!73\)\( T^{32} - \)\(79\!\cdots\!04\)\( T^{34} + \)\(37\!\cdots\!18\)\( T^{36} - \)\(12\!\cdots\!60\)\( T^{38} + \)\(22\!\cdots\!01\)\( T^{40} \))(\( 1 - 3982 T + 7928162 T^{2} - 5090675647610 T^{3} + 44126507369726119 T^{4} - 95654814508201483332 T^{5} + \)\(12\!\cdots\!96\)\( T^{6} - \)\(15\!\cdots\!12\)\( T^{7} + \)\(46\!\cdots\!93\)\( T^{8} - \)\(33\!\cdots\!78\)\( T^{9} + \)\(35\!\cdots\!38\)\( T^{10} - \)\(10\!\cdots\!70\)\( T^{11} + \)\(78\!\cdots\!59\)\( T^{12} - \)\(84\!\cdots\!64\)\( T^{13} + \)\(18\!\cdots\!08\)\( T^{14} - \)\(12\!\cdots\!52\)\( T^{15} + \)\(16\!\cdots\!91\)\( T^{16} - \)\(34\!\cdots\!90\)\( T^{17} + \)\(16\!\cdots\!38\)\( T^{18} - \)\(22\!\cdots\!54\)\( T^{19} + \)\(47\!\cdots\!57\)\( T^{20} - \)\(23\!\cdots\!84\)\( T^{21} + \)\(28\!\cdots\!96\)\( T^{22} - \)\(30\!\cdots\!76\)\( T^{23} + \)\(20\!\cdots\!31\)\( T^{24} - \)\(35\!\cdots\!70\)\( T^{25} + \)\(80\!\cdots\!62\)\( T^{26} - \)\(59\!\cdots\!26\)\( T^{27} + \)\(22\!\cdots\!49\)\( T^{28} \))(\( 1 + 3982 T + 7928162 T^{2} + 5090675647610 T^{3} + 44126507369726119 T^{4} + 95654814508201483332 T^{5} + \)\(12\!\cdots\!96\)\( T^{6} + \)\(15\!\cdots\!12\)\( T^{7} + \)\(46\!\cdots\!93\)\( T^{8} + \)\(33\!\cdots\!78\)\( T^{9} + \)\(35\!\cdots\!38\)\( T^{10} + \)\(10\!\cdots\!70\)\( T^{11} + \)\(78\!\cdots\!59\)\( T^{12} + \)\(84\!\cdots\!64\)\( T^{13} + \)\(18\!\cdots\!08\)\( T^{14} + \)\(12\!\cdots\!52\)\( T^{15} + \)\(16\!\cdots\!91\)\( T^{16} + \)\(34\!\cdots\!90\)\( T^{17} + \)\(16\!\cdots\!38\)\( T^{18} + \)\(22\!\cdots\!54\)\( T^{19} + \)\(47\!\cdots\!57\)\( T^{20} + \)\(23\!\cdots\!84\)\( T^{21} + \)\(28\!\cdots\!96\)\( T^{22} + \)\(30\!\cdots\!76\)\( T^{23} + \)\(20\!\cdots\!31\)\( T^{24} + \)\(35\!\cdots\!70\)\( T^{25} + \)\(80\!\cdots\!62\)\( T^{26} + \)\(59\!\cdots\!26\)\( T^{27} + \)\(22\!\cdots\!49\)\( T^{28} \))(\( 1 + 20002 T + 200040002 T^{2} + 4643840984270 T^{3} + 57483685077584672 T^{4} - 83126825813520796778 T^{5} - \)\(23\!\cdots\!50\)\( T^{6} - \)\(76\!\cdots\!70\)\( T^{7} - \)\(32\!\cdots\!64\)\( T^{8} - \)\(35\!\cdots\!86\)\( T^{9} - \)\(28\!\cdots\!02\)\( T^{10} - \)\(51\!\cdots\!50\)\( T^{11} - \)\(19\!\cdots\!52\)\( T^{12} + \)\(54\!\cdots\!78\)\( T^{13} + \)\(53\!\cdots\!62\)\( T^{14} + \)\(11\!\cdots\!58\)\( T^{15} + \)\(24\!\cdots\!66\)\( T^{16} + \)\(17\!\cdots\!94\)\( T^{17} + \)\(11\!\cdots\!38\)\( T^{18} + \)\(17\!\cdots\!46\)\( T^{19} - \)\(89\!\cdots\!52\)\( T^{20} - \)\(35\!\cdots\!50\)\( T^{21} - \)\(28\!\cdots\!98\)\( T^{22} - \)\(53\!\cdots\!02\)\( T^{23} - \)\(70\!\cdots\!64\)\( T^{24} - \)\(24\!\cdots\!10\)\( T^{25} - \)\(11\!\cdots\!50\)\( T^{26} - \)\(57\!\cdots\!46\)\( T^{27} + \)\(58\!\cdots\!72\)\( T^{28} + \)\(69\!\cdots\!10\)\( T^{29} + \)\(44\!\cdots\!98\)\( T^{30} + \)\(64\!\cdots\!14\)\( T^{31} + \)\(47\!\cdots\!01\)\( T^{32} \))(\( 1 - 20002 T + 200040002 T^{2} - 4643840984270 T^{3} + 57483685077584672 T^{4} + 83126825813520796778 T^{5} - \)\(23\!\cdots\!50\)\( T^{6} + \)\(76\!\cdots\!70\)\( T^{7} - \)\(32\!\cdots\!64\)\( T^{8} + \)\(35\!\cdots\!86\)\( T^{9} - \)\(28\!\cdots\!02\)\( T^{10} + \)\(51\!\cdots\!50\)\( T^{11} - \)\(19\!\cdots\!52\)\( T^{12} - \)\(54\!\cdots\!78\)\( T^{13} + \)\(53\!\cdots\!62\)\( T^{14} - \)\(11\!\cdots\!58\)\( T^{15} + \)\(24\!\cdots\!66\)\( T^{16} - \)\(17\!\cdots\!94\)\( T^{17} + \)\(11\!\cdots\!38\)\( T^{18} - \)\(17\!\cdots\!46\)\( T^{19} - \)\(89\!\cdots\!52\)\( T^{20} + \)\(35\!\cdots\!50\)\( T^{21} - \)\(28\!\cdots\!98\)\( T^{22} + \)\(53\!\cdots\!02\)\( T^{23} - \)\(70\!\cdots\!64\)\( T^{24} + \)\(24\!\cdots\!10\)\( T^{25} - \)\(11\!\cdots\!50\)\( T^{26} + \)\(57\!\cdots\!46\)\( T^{27} + \)\(58\!\cdots\!72\)\( T^{28} - \)\(69\!\cdots\!10\)\( T^{29} + \)\(44\!\cdots\!98\)\( T^{30} - \)\(64\!\cdots\!14\)\( T^{31} + \)\(47\!\cdots\!01\)\( T^{32} \))
$47$ (\( 1 + 28296 T + 617782998 T^{2} + 6489546318072 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 403777034 T^{2} + 52599132235830049 T^{4} \))(\( 1 + 442383274 T^{2} + 52599132235830049 T^{4} \))(\( 1 + 422513974 T^{2} + 52599132235830049 T^{4} \))(\( 1 - 28296 T + 617782998 T^{2} - 6489546318072 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 36762 T + 1119958377 T^{2} + 18490559326820 T^{3} + 256856861812773639 T^{4} + \)\(19\!\cdots\!38\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 - 36762 T + 1119958377 T^{2} - 18490559326820 T^{3} + 256856861812773639 T^{4} - \)\(19\!\cdots\!38\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 + 353765740 T^{2} + 66158288717340582 T^{4} + \)\(18\!\cdots\!60\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 229345007 T^{2} )^{2} \))(\( ( 1 - 33334 T + 555577778 T^{2} - 7644986463338 T^{3} + 52599132235830049 T^{4} )( 1 + 33334 T + 555577778 T^{2} + 7644986463338 T^{3} + 52599132235830049 T^{4} ) \))(\( ( 1 - 579920494 T^{2} + 165136673035562991 T^{4} - \)\(38\!\cdots\!48\)\( T^{6} + \)\(86\!\cdots\!59\)\( T^{8} - \)\(16\!\cdots\!94\)\( T^{10} + \)\(14\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 764642190 T^{2} + 310900354010297967 T^{4} - \)\(85\!\cdots\!20\)\( T^{6} + \)\(16\!\cdots\!83\)\( T^{8} - \)\(21\!\cdots\!90\)\( T^{10} + \)\(14\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 + 22090 T + 1548510076 T^{2} + 25779450599270 T^{3} + 1065218725316011845 T^{4} + \)\(14\!\cdots\!20\)\( T^{5} + \)\(45\!\cdots\!96\)\( T^{6} + \)\(51\!\cdots\!60\)\( T^{7} + \)\(14\!\cdots\!10\)\( T^{8} + \)\(14\!\cdots\!00\)\( T^{9} + \)\(36\!\cdots\!56\)\( T^{10} + \)\(32\!\cdots\!00\)\( T^{11} + \)\(76\!\cdots\!90\)\( T^{12} + \)\(62\!\cdots\!80\)\( T^{13} + \)\(12\!\cdots\!96\)\( T^{14} + \)\(90\!\cdots\!40\)\( T^{15} + \)\(15\!\cdots\!05\)\( T^{16} + \)\(86\!\cdots\!10\)\( T^{17} + \)\(11\!\cdots\!76\)\( T^{18} + \)\(38\!\cdots\!30\)\( T^{19} + \)\(40\!\cdots\!49\)\( T^{20} )^{2} \))(\( 1 - 1278 T + 816642 T^{2} - 351784473730 T^{3} + 13143771115043551 T^{4} + 55735540634425394844 T^{5} - \)\(20\!\cdots\!24\)\( T^{6} + \)\(35\!\cdots\!24\)\( T^{7} + \)\(21\!\cdots\!21\)\( T^{8} - \)\(27\!\cdots\!06\)\( T^{9} + \)\(23\!\cdots\!58\)\( T^{10} - \)\(14\!\cdots\!22\)\( T^{11} - \)\(33\!\cdots\!25\)\( T^{12} + \)\(57\!\cdots\!44\)\( T^{13} - \)\(35\!\cdots\!52\)\( T^{14} + \)\(13\!\cdots\!08\)\( T^{15} - \)\(17\!\cdots\!25\)\( T^{16} - \)\(16\!\cdots\!46\)\( T^{17} + \)\(64\!\cdots\!58\)\( T^{18} - \)\(17\!\cdots\!42\)\( T^{19} + \)\(31\!\cdots\!29\)\( T^{20} + \)\(11\!\cdots\!32\)\( T^{21} - \)\(15\!\cdots\!24\)\( T^{22} + \)\(97\!\cdots\!08\)\( T^{23} + \)\(52\!\cdots\!99\)\( T^{24} - \)\(32\!\cdots\!90\)\( T^{25} + \)\(17\!\cdots\!42\)\( T^{26} - \)\(62\!\cdots\!46\)\( T^{27} + \)\(11\!\cdots\!49\)\( T^{28} \))(\( 1 + 1278 T + 816642 T^{2} + 351784473730 T^{3} + 13143771115043551 T^{4} - 55735540634425394844 T^{5} - \)\(20\!\cdots\!24\)\( T^{6} - \)\(35\!\cdots\!24\)\( T^{7} + \)\(21\!\cdots\!21\)\( T^{8} + \)\(27\!\cdots\!06\)\( T^{9} + \)\(23\!\cdots\!58\)\( T^{10} + \)\(14\!\cdots\!22\)\( T^{11} - \)\(33\!\cdots\!25\)\( T^{12} - \)\(57\!\cdots\!44\)\( T^{13} - \)\(35\!\cdots\!52\)\( T^{14} - \)\(13\!\cdots\!08\)\( T^{15} - \)\(17\!\cdots\!25\)\( T^{16} + \)\(16\!\cdots\!46\)\( T^{17} + \)\(64\!\cdots\!58\)\( T^{18} + \)\(17\!\cdots\!42\)\( T^{19} + \)\(31\!\cdots\!29\)\( T^{20} - \)\(11\!\cdots\!32\)\( T^{21} - \)\(15\!\cdots\!24\)\( T^{22} - \)\(97\!\cdots\!08\)\( T^{23} + \)\(52\!\cdots\!99\)\( T^{24} + \)\(32\!\cdots\!90\)\( T^{25} + \)\(17\!\cdots\!42\)\( T^{26} + \)\(62\!\cdots\!46\)\( T^{27} + \)\(11\!\cdots\!49\)\( T^{28} \))(\( 1 + 25298 T + 319994402 T^{2} + 6541896537590 T^{3} - 11741966210019840 T^{4} - \)\(87\!\cdots\!98\)\( T^{5} + \)\(31\!\cdots\!26\)\( T^{6} - \)\(28\!\cdots\!26\)\( T^{7} + \)\(89\!\cdots\!80\)\( T^{8} + \)\(49\!\cdots\!50\)\( T^{9} - \)\(48\!\cdots\!58\)\( T^{10} + \)\(14\!\cdots\!46\)\( T^{11} + \)\(91\!\cdots\!24\)\( T^{12} - \)\(38\!\cdots\!50\)\( T^{13} + \)\(47\!\cdots\!30\)\( T^{14} + \)\(60\!\cdots\!90\)\( T^{15} + \)\(93\!\cdots\!70\)\( T^{16} + \)\(13\!\cdots\!30\)\( T^{17} + \)\(25\!\cdots\!70\)\( T^{18} - \)\(45\!\cdots\!50\)\( T^{19} + \)\(25\!\cdots\!24\)\( T^{20} + \)\(94\!\cdots\!22\)\( T^{21} - \)\(70\!\cdots\!42\)\( T^{22} + \)\(16\!\cdots\!50\)\( T^{23} + \)\(68\!\cdots\!80\)\( T^{24} - \)\(49\!\cdots\!82\)\( T^{25} + \)\(12\!\cdots\!74\)\( T^{26} - \)\(80\!\cdots\!14\)\( T^{27} - \)\(24\!\cdots\!40\)\( T^{28} + \)\(31\!\cdots\!30\)\( T^{29} + \)\(35\!\cdots\!98\)\( T^{30} + \)\(64\!\cdots\!14\)\( T^{31} + \)\(58\!\cdots\!01\)\( T^{32} \))(\( 1 - 25298 T + 319994402 T^{2} - 6541896537590 T^{3} - 11741966210019840 T^{4} + \)\(87\!\cdots\!98\)\( T^{5} + \)\(31\!\cdots\!26\)\( T^{6} + \)\(28\!\cdots\!26\)\( T^{7} + \)\(89\!\cdots\!80\)\( T^{8} - \)\(49\!\cdots\!50\)\( T^{9} - \)\(48\!\cdots\!58\)\( T^{10} - \)\(14\!\cdots\!46\)\( T^{11} + \)\(91\!\cdots\!24\)\( T^{12} + \)\(38\!\cdots\!50\)\( T^{13} + \)\(47\!\cdots\!30\)\( T^{14} - \)\(60\!\cdots\!90\)\( T^{15} + \)\(93\!\cdots\!70\)\( T^{16} - \)\(13\!\cdots\!30\)\( T^{17} + \)\(25\!\cdots\!70\)\( T^{18} + \)\(45\!\cdots\!50\)\( T^{19} + \)\(25\!\cdots\!24\)\( T^{20} - \)\(94\!\cdots\!22\)\( T^{21} - \)\(70\!\cdots\!42\)\( T^{22} - \)\(16\!\cdots\!50\)\( T^{23} + \)\(68\!\cdots\!80\)\( T^{24} + \)\(49\!\cdots\!82\)\( T^{25} + \)\(12\!\cdots\!74\)\( T^{26} + \)\(80\!\cdots\!14\)\( T^{27} - \)\(24\!\cdots\!40\)\( T^{28} - \)\(31\!\cdots\!30\)\( T^{29} + \)\(35\!\cdots\!98\)\( T^{30} - \)\(64\!\cdots\!14\)\( T^{31} + \)\(58\!\cdots\!01\)\( T^{32} \))
$53$ (\( 1 - 31340 T + 755347886 T^{2} - 13106246750620 T^{3} + 174887470365513049 T^{4} \))(\( ( 1 - 32226 T + 418195493 T^{2} )^{2} \))(\( ( 1 + 15486 T + 418195493 T^{2} )^{2} \))(\( ( 1 + 18154 T + 418195493 T^{2} )^{2} \))(\( 1 - 31340 T + 755347886 T^{2} - 13106246750620 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 21162 T + 395789499 T^{2} - 881498066468 T^{3} + 165517384658528007 T^{4} + \)\(37\!\cdots\!38\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( 1 + 21162 T + 395789499 T^{2} - 881498066468 T^{3} + 165517384658528007 T^{4} + \)\(37\!\cdots\!38\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( ( 1 - 8748 T + 833865262 T^{2} - 3658374172764 T^{3} + 174887470365513049 T^{4} )^{2} \))(\( ( 1 - 7294 T + 418195493 T^{2} )( 1 + 7294 T + 418195493 T^{2} ) \))(\( ( 1 - 418195493 T^{2} )^{4} \))(\( ( 1 - 2026325390 T^{2} + 1866514545072595447 T^{4} - \)\(99\!\cdots\!20\)\( T^{6} + \)\(32\!\cdots\!03\)\( T^{8} - \)\(61\!\cdots\!90\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 1611835534 T^{2} + 1232324270520828407 T^{4} - \)\(61\!\cdots\!84\)\( T^{6} + \)\(21\!\cdots\!43\)\( T^{8} - \)\(49\!\cdots\!34\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} )^{2} \))(\( 1 - 4003669356 T^{2} + 7954725909905649454 T^{4} - \)\(10\!\cdots\!60\)\( T^{6} + \)\(10\!\cdots\!77\)\( T^{8} - \)\(91\!\cdots\!76\)\( T^{10} + \)\(65\!\cdots\!16\)\( T^{12} - \)\(40\!\cdots\!80\)\( T^{14} + \)\(22\!\cdots\!54\)\( T^{16} - \)\(11\!\cdots\!56\)\( T^{18} + \)\(48\!\cdots\!96\)\( T^{20} - \)\(19\!\cdots\!44\)\( T^{22} + \)\(68\!\cdots\!54\)\( T^{24} - \)\(21\!\cdots\!20\)\( T^{26} + \)\(61\!\cdots\!16\)\( T^{28} - \)\(14\!\cdots\!24\)\( T^{30} + \)\(31\!\cdots\!77\)\( T^{32} - \)\(53\!\cdots\!40\)\( T^{34} + \)\(69\!\cdots\!54\)\( T^{36} - \)\(61\!\cdots\!44\)\( T^{38} + \)\(26\!\cdots\!01\)\( T^{40} \))(\( 1 - 5882 T + 17298962 T^{2} + 13844528488830 T^{3} - 174311180941592381 T^{4} - \)\(81\!\cdots\!52\)\( T^{5} + \)\(14\!\cdots\!36\)\( T^{6} - \)\(35\!\cdots\!12\)\( T^{7} - \)\(10\!\cdots\!67\)\( T^{8} + \)\(15\!\cdots\!82\)\( T^{9} + \)\(26\!\cdots\!38\)\( T^{10} - \)\(97\!\cdots\!30\)\( T^{11} + \)\(23\!\cdots\!39\)\( T^{12} + \)\(29\!\cdots\!36\)\( T^{13} - \)\(56\!\cdots\!72\)\( T^{14} + \)\(12\!\cdots\!48\)\( T^{15} + \)\(41\!\cdots\!11\)\( T^{16} - \)\(71\!\cdots\!10\)\( T^{17} + \)\(82\!\cdots\!38\)\( T^{18} + \)\(19\!\cdots\!26\)\( T^{19} - \)\(56\!\cdots\!83\)\( T^{20} - \)\(78\!\cdots\!84\)\( T^{21} + \)\(13\!\cdots\!36\)\( T^{22} - \)\(31\!\cdots\!36\)\( T^{23} - \)\(28\!\cdots\!69\)\( T^{24} + \)\(94\!\cdots\!10\)\( T^{25} + \)\(49\!\cdots\!62\)\( T^{26} - \)\(70\!\cdots\!26\)\( T^{27} + \)\(50\!\cdots\!49\)\( T^{28} \))(\( 1 - 5882 T + 17298962 T^{2} + 13844528488830 T^{3} - 174311180941592381 T^{4} - \)\(81\!\cdots\!52\)\( T^{5} + \)\(14\!\cdots\!36\)\( T^{6} - \)\(35\!\cdots\!12\)\( T^{7} - \)\(10\!\cdots\!67\)\( T^{8} + \)\(15\!\cdots\!82\)\( T^{9} + \)\(26\!\cdots\!38\)\( T^{10} - \)\(97\!\cdots\!30\)\( T^{11} + \)\(23\!\cdots\!39\)\( T^{12} + \)\(29\!\cdots\!36\)\( T^{13} - \)\(56\!\cdots\!72\)\( T^{14} + \)\(12\!\cdots\!48\)\( T^{15} + \)\(41\!\cdots\!11\)\( T^{16} - \)\(71\!\cdots\!10\)\( T^{17} + \)\(82\!\cdots\!38\)\( T^{18} + \)\(19\!\cdots\!26\)\( T^{19} - \)\(56\!\cdots\!83\)\( T^{20} - \)\(78\!\cdots\!84\)\( T^{21} + \)\(13\!\cdots\!36\)\( T^{22} - \)\(31\!\cdots\!36\)\( T^{23} - \)\(28\!\cdots\!69\)\( T^{24} + \)\(94\!\cdots\!10\)\( T^{25} + \)\(49\!\cdots\!62\)\( T^{26} - \)\(70\!\cdots\!26\)\( T^{27} + \)\(50\!\cdots\!49\)\( T^{28} \))(\( 1 - 12852 T + 82586952 T^{2} + 12779415797620 T^{3} - 141875027604640888 T^{4} - \)\(55\!\cdots\!72\)\( T^{5} + \)\(16\!\cdots\!20\)\( T^{6} - \)\(16\!\cdots\!60\)\( T^{7} - \)\(86\!\cdots\!84\)\( T^{8} + \)\(14\!\cdots\!16\)\( T^{9} + \)\(64\!\cdots\!88\)\( T^{10} - \)\(74\!\cdots\!80\)\( T^{11} + \)\(67\!\cdots\!08\)\( T^{12} + \)\(29\!\cdots\!72\)\( T^{13} - \)\(53\!\cdots\!88\)\( T^{14} - \)\(64\!\cdots\!48\)\( T^{15} + \)\(25\!\cdots\!06\)\( T^{16} - \)\(27\!\cdots\!64\)\( T^{17} - \)\(94\!\cdots\!12\)\( T^{18} + \)\(21\!\cdots\!04\)\( T^{19} + \)\(20\!\cdots\!08\)\( T^{20} - \)\(95\!\cdots\!40\)\( T^{21} + \)\(34\!\cdots\!12\)\( T^{22} + \)\(32\!\cdots\!12\)\( T^{23} - \)\(80\!\cdots\!84\)\( T^{24} - \)\(64\!\cdots\!80\)\( T^{25} + \)\(27\!\cdots\!80\)\( T^{26} - \)\(38\!\cdots\!04\)\( T^{27} - \)\(40\!\cdots\!88\)\( T^{28} + \)\(15\!\cdots\!60\)\( T^{29} + \)\(41\!\cdots\!48\)\( T^{30} - \)\(26\!\cdots\!64\)\( T^{31} + \)\(87\!\cdots\!01\)\( T^{32} \))(\( 1 - 12852 T + 82586952 T^{2} + 12779415797620 T^{3} - 141875027604640888 T^{4} - \)\(55\!\cdots\!72\)\( T^{5} + \)\(16\!\cdots\!20\)\( T^{6} - \)\(16\!\cdots\!60\)\( T^{7} - \)\(86\!\cdots\!84\)\( T^{8} + \)\(14\!\cdots\!16\)\( T^{9} + \)\(64\!\cdots\!88\)\( T^{10} - \)\(74\!\cdots\!80\)\( T^{11} + \)\(67\!\cdots\!08\)\( T^{12} + \)\(29\!\cdots\!72\)\( T^{13} - \)\(53\!\cdots\!88\)\( T^{14} - \)\(64\!\cdots\!48\)\( T^{15} + \)\(25\!\cdots\!06\)\( T^{16} - \)\(27\!\cdots\!64\)\( T^{17} - \)\(94\!\cdots\!12\)\( T^{18} + \)\(21\!\cdots\!04\)\( T^{19} + \)\(20\!\cdots\!08\)\( T^{20} - \)\(95\!\cdots\!40\)\( T^{21} + \)\(34\!\cdots\!12\)\( T^{22} + \)\(32\!\cdots\!12\)\( T^{23} - \)\(80\!\cdots\!84\)\( T^{24} - \)\(64\!\cdots\!80\)\( T^{25} + \)\(27\!\cdots\!80\)\( T^{26} - \)\(38\!\cdots\!04\)\( T^{27} - \)\(40\!\cdots\!88\)\( T^{28} + \)\(15\!\cdots\!60\)\( T^{29} + \)\(41\!\cdots\!48\)\( T^{30} - \)\(26\!\cdots\!64\)\( T^{31} + \)\(87\!\cdots\!01\)\( T^{32} \))
$59$ (\( 1 + 30800 T + 1666896598 T^{2} + 22019668409200 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 270997718 T^{2} + 511116753300641401 T^{4} \))(\( 1 + 1376531158 T^{2} + 511116753300641401 T^{4} \))(\( 1 + 1041470358 T^{2} + 511116753300641401 T^{4} \))(\( 1 - 30800 T + 1666896598 T^{2} - 22019668409200 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 35040 T + 1757220897 T^{2} + 50989349593920 T^{3} + 1256279917975876203 T^{4} + \)\(17\!\cdots\!40\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( 1 - 35040 T + 1757220897 T^{2} - 50989349593920 T^{3} + 1256279917975876203 T^{4} - \)\(17\!\cdots\!40\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( 1 + 488747308 T^{2} + 896846029819225302 T^{4} + \)\(24\!\cdots\!08\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 714924299 T^{2} )^{2} \))(\( ( 1 + 714924299 T^{2} )^{4} \))(\( ( 1 + 55950786 T^{2} + 253972763776609047 T^{4} - \)\(45\!\cdots\!68\)\( T^{6} + \)\(12\!\cdots\!47\)\( T^{8} + \)\(14\!\cdots\!86\)\( T^{10} + \)\(13\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 2333761794 T^{2} + 3044701823751957015 T^{4} + \)\(26\!\cdots\!80\)\( T^{6} + \)\(15\!\cdots\!15\)\( T^{8} + \)\(60\!\cdots\!94\)\( T^{10} + \)\(13\!\cdots\!01\)\( T^{12} )^{2} \))(\( 1 - 9996949828 T^{2} + 49650800837889885966 T^{4} - \)\(16\!\cdots\!20\)\( T^{6} + \)\(39\!\cdots\!17\)\( T^{8} - \)\(73\!\cdots\!28\)\( T^{10} + \)\(11\!\cdots\!44\)\( T^{12} - \)\(14\!\cdots\!80\)\( T^{14} + \)\(15\!\cdots\!54\)\( T^{16} - \)\(13\!\cdots\!88\)\( T^{18} + \)\(10\!\cdots\!24\)\( T^{20} - \)\(70\!\cdots\!88\)\( T^{22} + \)\(39\!\cdots\!54\)\( T^{24} - \)\(19\!\cdots\!80\)\( T^{26} + \)\(77\!\cdots\!44\)\( T^{28} - \)\(25\!\cdots\!28\)\( T^{30} + \)\(69\!\cdots\!17\)\( T^{32} - \)\(14\!\cdots\!20\)\( T^{34} + \)\(23\!\cdots\!66\)\( T^{36} - \)\(23\!\cdots\!28\)\( T^{38} + \)\(12\!\cdots\!01\)\( T^{40} \))(\( ( 1 - 4252 T + 2005910877 T^{2} - 20518241068280 T^{3} + 2395790088022200413 T^{4} - \)\(22\!\cdots\!48\)\( T^{5} + \)\(23\!\cdots\!29\)\( T^{6} - \)\(16\!\cdots\!28\)\( T^{7} + \)\(16\!\cdots\!71\)\( T^{8} - \)\(11\!\cdots\!48\)\( T^{9} + \)\(87\!\cdots\!87\)\( T^{10} - \)\(53\!\cdots\!80\)\( T^{11} + \)\(37\!\cdots\!23\)\( T^{12} - \)\(56\!\cdots\!52\)\( T^{13} + \)\(95\!\cdots\!99\)\( T^{14} )^{2} \))(\( ( 1 + 4252 T + 2005910877 T^{2} + 20518241068280 T^{3} + 2395790088022200413 T^{4} + \)\(22\!\cdots\!48\)\( T^{5} + \)\(23\!\cdots\!29\)\( T^{6} + \)\(16\!\cdots\!28\)\( T^{7} + \)\(16\!\cdots\!71\)\( T^{8} + \)\(11\!\cdots\!48\)\( T^{9} + \)\(87\!\cdots\!87\)\( T^{10} + \)\(53\!\cdots\!80\)\( T^{11} + \)\(37\!\cdots\!23\)\( T^{12} + \)\(56\!\cdots\!52\)\( T^{13} + \)\(95\!\cdots\!99\)\( T^{14} )^{2} \))(\( ( 1 - 71352 T + 5147553272 T^{2} - 263083260595160 T^{3} + 11526051017122699388 T^{4} - \)\(44\!\cdots\!28\)\( T^{5} + \)\(15\!\cdots\!16\)\( T^{6} - \)\(46\!\cdots\!12\)\( T^{7} + \)\(13\!\cdots\!10\)\( T^{8} - \)\(32\!\cdots\!88\)\( T^{9} + \)\(77\!\cdots\!16\)\( T^{10} - \)\(16\!\cdots\!72\)\( T^{11} + \)\(30\!\cdots\!88\)\( T^{12} - \)\(49\!\cdots\!40\)\( T^{13} + \)\(68\!\cdots\!72\)\( T^{14} - \)\(68\!\cdots\!48\)\( T^{15} + \)\(68\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 71352 T + 5147553272 T^{2} + 263083260595160 T^{3} + 11526051017122699388 T^{4} + \)\(44\!\cdots\!28\)\( T^{5} + \)\(15\!\cdots\!16\)\( T^{6} + \)\(46\!\cdots\!12\)\( T^{7} + \)\(13\!\cdots\!10\)\( T^{8} + \)\(32\!\cdots\!88\)\( T^{9} + \)\(77\!\cdots\!16\)\( T^{10} + \)\(16\!\cdots\!72\)\( T^{11} + \)\(30\!\cdots\!88\)\( T^{12} + \)\(49\!\cdots\!40\)\( T^{13} + \)\(68\!\cdots\!72\)\( T^{14} + \)\(68\!\cdots\!48\)\( T^{15} + \)\(68\!\cdots\!01\)\( T^{16} )^{2} \))
$61$ (\( 1 - 24540 T + 1447225822 T^{2} - 20726393226540 T^{3} + 713342911662882601 T^{4} \))(\( ( 1 - 26770 T + 844596301 T^{2} )^{2} \))(\( ( 1 + 16750 T + 844596301 T^{2} )^{2} \))(\( ( 1 + 42130 T + 844596301 T^{2} )^{2} \))(\( 1 - 24540 T + 1447225822 T^{2} - 20726393226540 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 24138 T + 393086643 T^{2} - 6904061162564 T^{3} + 331999524650307543 T^{4} + \)\(17\!\cdots\!38\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( 1 + 24138 T + 393086643 T^{2} - 6904061162564 T^{3} + 331999524650307543 T^{4} + \)\(17\!\cdots\!38\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( ( 1 + 31012 T + 1250446302 T^{2} + 26192620486612 T^{3} + 713342911662882601 T^{4} )^{2} \))(\( ( 1 + 18950 T + 844596301 T^{2} )^{2} \))(\( ( 1 - 1041591898 T^{2} + 713342911662882601 T^{4} )^{2} \))(\( ( 1 - 16138 T + 744681843 T^{2} - 29097452426876 T^{3} + 628955530019662743 T^{4} - \)\(11\!\cdots\!38\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} )^{4} \))(\( ( 1 + 29558 T + 2350852083 T^{2} + 48603849831556 T^{3} + 1985520973499944983 T^{4} + \)\(21\!\cdots\!58\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} )^{4} \))(\( 1 - 7152852348 T^{2} + 26523669582205677166 T^{4} - \)\(67\!\cdots\!00\)\( T^{6} + \)\(13\!\cdots\!17\)\( T^{8} - \)\(22\!\cdots\!48\)\( T^{10} + \)\(31\!\cdots\!84\)\( T^{12} - \)\(38\!\cdots\!60\)\( T^{14} + \)\(42\!\cdots\!14\)\( T^{16} - \)\(41\!\cdots\!08\)\( T^{18} + \)\(36\!\cdots\!64\)\( T^{20} - \)\(29\!\cdots\!08\)\( T^{22} + \)\(21\!\cdots\!14\)\( T^{24} - \)\(13\!\cdots\!60\)\( T^{26} + \)\(81\!\cdots\!84\)\( T^{28} - \)\(41\!\cdots\!48\)\( T^{30} + \)\(17\!\cdots\!17\)\( T^{32} - \)\(63\!\cdots\!00\)\( T^{34} + \)\(17\!\cdots\!66\)\( T^{36} - \)\(34\!\cdots\!48\)\( T^{38} + \)\(34\!\cdots\!01\)\( T^{40} \))(\( ( 1 - 10282 T + 2916253203 T^{2} + 3083320715268 T^{3} + 3046127491767085861 T^{4} + \)\(70\!\cdots\!38\)\( T^{5} + \)\(15\!\cdots\!39\)\( T^{6} + \)\(10\!\cdots\!44\)\( T^{7} + \)\(12\!\cdots\!39\)\( T^{8} + \)\(50\!\cdots\!38\)\( T^{9} + \)\(18\!\cdots\!61\)\( T^{10} + \)\(15\!\cdots\!68\)\( T^{11} + \)\(12\!\cdots\!03\)\( T^{12} - \)\(37\!\cdots\!82\)\( T^{13} + \)\(30\!\cdots\!01\)\( T^{14} )^{2} \))(\( ( 1 - 10282 T + 2916253203 T^{2} + 3083320715268 T^{3} + 3046127491767085861 T^{4} + \)\(70\!\cdots\!38\)\( T^{5} + \)\(15\!\cdots\!39\)\( T^{6} + \)\(10\!\cdots\!44\)\( T^{7} + \)\(12\!\cdots\!39\)\( T^{8} + \)\(50\!\cdots\!38\)\( T^{9} + \)\(18\!\cdots\!61\)\( T^{10} + \)\(15\!\cdots\!68\)\( T^{11} + \)\(12\!\cdots\!03\)\( T^{12} - \)\(37\!\cdots\!82\)\( T^{13} + \)\(30\!\cdots\!01\)\( T^{14} )^{2} \))(\( ( 1 + 10282 T + 3727559576 T^{2} + 11244934877598 T^{3} + 6582098174228731436 T^{4} - \)\(31\!\cdots\!30\)\( T^{5} + \)\(74\!\cdots\!72\)\( T^{6} - \)\(78\!\cdots\!62\)\( T^{7} + \)\(66\!\cdots\!54\)\( T^{8} - \)\(66\!\cdots\!62\)\( T^{9} + \)\(52\!\cdots\!72\)\( T^{10} - \)\(18\!\cdots\!30\)\( T^{11} + \)\(33\!\cdots\!36\)\( T^{12} + \)\(48\!\cdots\!98\)\( T^{13} + \)\(13\!\cdots\!76\)\( T^{14} + \)\(31\!\cdots\!82\)\( T^{15} + \)\(25\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 10282 T + 3727559576 T^{2} + 11244934877598 T^{3} + 6582098174228731436 T^{4} - \)\(31\!\cdots\!30\)\( T^{5} + \)\(74\!\cdots\!72\)\( T^{6} - \)\(78\!\cdots\!62\)\( T^{7} + \)\(66\!\cdots\!54\)\( T^{8} - \)\(66\!\cdots\!62\)\( T^{9} + \)\(52\!\cdots\!72\)\( T^{10} - \)\(18\!\cdots\!30\)\( T^{11} + \)\(33\!\cdots\!36\)\( T^{12} + \)\(48\!\cdots\!98\)\( T^{13} + \)\(13\!\cdots\!76\)\( T^{14} + \)\(31\!\cdots\!82\)\( T^{15} + \)\(25\!\cdots\!01\)\( T^{16} )^{2} \))
$67$ (\( 1 + 34584 T + 2930656478 T^{2} + 46692726700488 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 219594834 T^{2} + 1822837804551761449 T^{4} \))(\( 1 + 2513562674 T^{2} + 1822837804551761449 T^{4} \))(\( 1 + 2438310974 T^{2} + 1822837804551761449 T^{4} \))(\( 1 - 34584 T + 2930656478 T^{2} - 46692726700488 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 9570 T + 659335509 T^{2} - 83080838420484 T^{3} + 890185424637524463 T^{4} - \)\(17\!\cdots\!30\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( 1 + 9570 T + 659335509 T^{2} + 83080838420484 T^{3} + 890185424637524463 T^{4} + \)\(17\!\cdots\!30\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( 1 + 3336863100 T^{2} + 6361754088145172822 T^{4} + \)\(60\!\cdots\!00\)\( T^{6} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 1350125107 T^{2} )^{2} \))(\( ( 1 - 100434 T + 5043494178 T^{2} - 135598464996438 T^{3} + 1822837804551761449 T^{4} )( 1 + 100434 T + 5043494178 T^{2} + 135598464996438 T^{3} + 1822837804551761449 T^{4} ) \))(\( ( 1 - 2173336374 T^{2} + 6882868324909910631 T^{4} - \)\(82\!\cdots\!68\)\( T^{6} + \)\(12\!\cdots\!19\)\( T^{8} - \)\(72\!\cdots\!74\)\( T^{10} + \)\(60\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 3741380758 T^{2} + 9572756841213379047 T^{4} - \)\(14\!\cdots\!84\)\( T^{6} + \)\(17\!\cdots\!03\)\( T^{8} - \)\(12\!\cdots\!58\)\( T^{10} + \)\(60\!\cdots\!49\)\( T^{12} )^{2} \))(\( 1 - 11828518964 T^{2} + 68669252417166303634 T^{4} - \)\(26\!\cdots\!60\)\( T^{6} + \)\(76\!\cdots\!57\)\( T^{8} - \)\(18\!\cdots\!04\)\( T^{10} + \)\(38\!\cdots\!16\)\( T^{12} - \)\(70\!\cdots\!40\)\( T^{14} + \)\(11\!\cdots\!54\)\( T^{16} - \)\(18\!\cdots\!64\)\( T^{18} + \)\(25\!\cdots\!76\)\( T^{20} - \)\(33\!\cdots\!36\)\( T^{22} + \)\(39\!\cdots\!54\)\( T^{24} - \)\(42\!\cdots\!60\)\( T^{26} + \)\(42\!\cdots\!16\)\( T^{28} - \)\(36\!\cdots\!96\)\( T^{30} + \)\(28\!\cdots\!57\)\( T^{32} - \)\(17\!\cdots\!40\)\( T^{34} + \)\(83\!\cdots\!34\)\( T^{36} - \)\(26\!\cdots\!36\)\( T^{38} + \)\(40\!\cdots\!01\)\( T^{40} \))(\( 1 + 107926 T + 5824010738 T^{2} + 286091118212770 T^{3} + 7910959270847152663 T^{4} - \)\(10\!\cdots\!32\)\( T^{5} - \)\(16\!\cdots\!76\)\( T^{6} - \)\(10\!\cdots\!52\)\( T^{7} - \)\(49\!\cdots\!51\)\( T^{8} - \)\(12\!\cdots\!38\)\( T^{9} - \)\(20\!\cdots\!90\)\( T^{10} + \)\(24\!\cdots\!26\)\( T^{11} + \)\(60\!\cdots\!11\)\( T^{12} + \)\(31\!\cdots\!32\)\( T^{13} + \)\(11\!\cdots\!96\)\( T^{14} + \)\(43\!\cdots\!24\)\( T^{15} + \)\(10\!\cdots\!39\)\( T^{16} + \)\(61\!\cdots\!18\)\( T^{17} - \)\(68\!\cdots\!90\)\( T^{18} - \)\(57\!\cdots\!66\)\( T^{19} - \)\(30\!\cdots\!99\)\( T^{20} - \)\(86\!\cdots\!36\)\( T^{21} - \)\(18\!\cdots\!76\)\( T^{22} - \)\(15\!\cdots\!24\)\( T^{23} + \)\(15\!\cdots\!87\)\( T^{24} + \)\(77\!\cdots\!10\)\( T^{25} + \)\(21\!\cdots\!38\)\( T^{26} + \)\(53\!\cdots\!82\)\( T^{27} + \)\(66\!\cdots\!49\)\( T^{28} \))(\( 1 - 107926 T + 5824010738 T^{2} - 286091118212770 T^{3} + 7910959270847152663 T^{4} + \)\(10\!\cdots\!32\)\( T^{5} - \)\(16\!\cdots\!76\)\( T^{6} + \)\(10\!\cdots\!52\)\( T^{7} - \)\(49\!\cdots\!51\)\( T^{8} + \)\(12\!\cdots\!38\)\( T^{9} - \)\(20\!\cdots\!90\)\( T^{10} - \)\(24\!\cdots\!26\)\( T^{11} + \)\(60\!\cdots\!11\)\( T^{12} - \)\(31\!\cdots\!32\)\( T^{13} + \)\(11\!\cdots\!96\)\( T^{14} - \)\(43\!\cdots\!24\)\( T^{15} + \)\(10\!\cdots\!39\)\( T^{16} - \)\(61\!\cdots\!18\)\( T^{17} - \)\(68\!\cdots\!90\)\( T^{18} + \)\(57\!\cdots\!66\)\( T^{19} - \)\(30\!\cdots\!99\)\( T^{20} + \)\(86\!\cdots\!36\)\( T^{21} - \)\(18\!\cdots\!76\)\( T^{22} + \)\(15\!\cdots\!24\)\( T^{23} + \)\(15\!\cdots\!87\)\( T^{24} - \)\(77\!\cdots\!10\)\( T^{25} + \)\(21\!\cdots\!38\)\( T^{26} - \)\(53\!\cdots\!82\)\( T^{27} + \)\(66\!\cdots\!49\)\( T^{28} \))(\( 1 - 10506 T + 55188018 T^{2} - 64685094733110 T^{3} - 1145101582269918112 T^{4} + \)\(11\!\cdots\!66\)\( T^{5} + \)\(90\!\cdots\!70\)\( T^{6} + \)\(13\!\cdots\!94\)\( T^{7} - \)\(58\!\cdots\!16\)\( T^{8} - \)\(10\!\cdots\!70\)\( T^{9} + \)\(57\!\cdots\!86\)\( T^{10} + \)\(37\!\cdots\!82\)\( T^{11} + \)\(12\!\cdots\!56\)\( T^{12} - \)\(51\!\cdots\!34\)\( T^{13} + \)\(11\!\cdots\!26\)\( T^{14} - \)\(28\!\cdots\!74\)\( T^{15} - \)\(82\!\cdots\!58\)\( T^{16} - \)\(38\!\cdots\!18\)\( T^{17} + \)\(21\!\cdots\!74\)\( T^{18} - \)\(12\!\cdots\!62\)\( T^{19} + \)\(40\!\cdots\!56\)\( T^{20} + \)\(16\!\cdots\!74\)\( T^{21} + \)\(34\!\cdots\!14\)\( T^{22} - \)\(89\!\cdots\!10\)\( T^{23} - \)\(64\!\cdots\!16\)\( T^{24} + \)\(20\!\cdots\!58\)\( T^{25} + \)\(18\!\cdots\!30\)\( T^{26} + \)\(32\!\cdots\!38\)\( T^{27} - \)\(42\!\cdots\!12\)\( T^{28} - \)\(32\!\cdots\!70\)\( T^{29} + \)\(36\!\cdots\!82\)\( T^{30} - \)\(94\!\cdots\!58\)\( T^{31} + \)\(12\!\cdots\!01\)\( T^{32} \))(\( 1 + 10506 T + 55188018 T^{2} + 64685094733110 T^{3} - 1145101582269918112 T^{4} - \)\(11\!\cdots\!66\)\( T^{5} + \)\(90\!\cdots\!70\)\( T^{6} - \)\(13\!\cdots\!94\)\( T^{7} - \)\(58\!\cdots\!16\)\( T^{8} + \)\(10\!\cdots\!70\)\( T^{9} + \)\(57\!\cdots\!86\)\( T^{10} - \)\(37\!\cdots\!82\)\( T^{11} + \)\(12\!\cdots\!56\)\( T^{12} + \)\(51\!\cdots\!34\)\( T^{13} + \)\(11\!\cdots\!26\)\( T^{14} + \)\(28\!\cdots\!74\)\( T^{15} - \)\(82\!\cdots\!58\)\( T^{16} + \)\(38\!\cdots\!18\)\( T^{17} + \)\(21\!\cdots\!74\)\( T^{18} + \)\(12\!\cdots\!62\)\( T^{19} + \)\(40\!\cdots\!56\)\( T^{20} - \)\(16\!\cdots\!74\)\( T^{21} + \)\(34\!\cdots\!14\)\( T^{22} + \)\(89\!\cdots\!10\)\( T^{23} - \)\(64\!\cdots\!16\)\( T^{24} - \)\(20\!\cdots\!58\)\( T^{25} + \)\(18\!\cdots\!30\)\( T^{26} - \)\(32\!\cdots\!38\)\( T^{27} - \)\(42\!\cdots\!12\)\( T^{28} + \)\(32\!\cdots\!70\)\( T^{29} + \)\(36\!\cdots\!82\)\( T^{30} + \)\(94\!\cdots\!58\)\( T^{31} + \)\(12\!\cdots\!01\)\( T^{32} \))
$71$ (\( 1 - 12400 T + 1143670702 T^{2} - 22372443952400 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 681226622 T^{2} + 3255243551009881201 T^{4} \))(\( 1 + 1737195262 T^{2} + 3255243551009881201 T^{4} \))(\( 1 + 1542914862 T^{2} + 3255243551009881201 T^{4} \))(\( 1 + 12400 T + 1143670702 T^{2} + 22372443952400 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 88092 T + 7289446053 T^{2} + 329541325840584 T^{3} + 13151832521353701603 T^{4} + \)\(28\!\cdots\!92\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( 1 - 88092 T + 7289446053 T^{2} - 329541325840584 T^{3} + 13151832521353701603 T^{4} - \)\(28\!\cdots\!92\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( 1 + 6374750812 T^{2} + 16622748841310481702 T^{4} + \)\(20\!\cdots\!12\)\( T^{6} + \)\(10\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 1804229351 T^{2} )^{2} \))(\( ( 1 + 1804229351 T^{2} )^{4} \))(\( ( 1 + 942628714 T^{2} + 4622069102042239647 T^{4} + \)\(48\!\cdots\!68\)\( T^{6} + \)\(15\!\cdots\!47\)\( T^{8} + \)\(99\!\cdots\!14\)\( T^{10} + \)\(34\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 9793576042 T^{2} + 41626938509482688159 T^{4} + \)\(98\!\cdots\!36\)\( T^{6} + \)\(13\!\cdots\!59\)\( T^{8} + \)\(10\!\cdots\!42\)\( T^{10} + \)\(34\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 - 100156 T + 13448448446 T^{2} - 957445823975748 T^{3} + 76873855601451932317 T^{4} - \)\(43\!\cdots\!20\)\( T^{5} + \)\(26\!\cdots\!28\)\( T^{6} - \)\(12\!\cdots\!92\)\( T^{7} + \)\(67\!\cdots\!74\)\( T^{8} - \)\(28\!\cdots\!84\)\( T^{9} + \)\(13\!\cdots\!68\)\( T^{10} - \)\(51\!\cdots\!84\)\( T^{11} + \)\(21\!\cdots\!74\)\( T^{12} - \)\(74\!\cdots\!92\)\( T^{13} + \)\(28\!\cdots\!28\)\( T^{14} - \)\(82\!\cdots\!20\)\( T^{15} + \)\(26\!\cdots\!17\)\( T^{16} - \)\(59\!\cdots\!48\)\( T^{17} + \)\(15\!\cdots\!46\)\( T^{18} - \)\(20\!\cdots\!56\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} )^{2} \))(\( 1 - 12494857902 T^{2} + 77600272039468829243 T^{4} - \)\(32\!\cdots\!32\)\( T^{6} + \)\(99\!\cdots\!41\)\( T^{8} - \)\(25\!\cdots\!58\)\( T^{10} + \)\(55\!\cdots\!91\)\( T^{12} - \)\(10\!\cdots\!64\)\( T^{14} + \)\(17\!\cdots\!91\)\( T^{16} - \)\(26\!\cdots\!58\)\( T^{18} + \)\(34\!\cdots\!41\)\( T^{20} - \)\(35\!\cdots\!32\)\( T^{22} + \)\(28\!\cdots\!43\)\( T^{24} - \)\(14\!\cdots\!02\)\( T^{26} + \)\(38\!\cdots\!01\)\( T^{28} \))(\( 1 - 12494857902 T^{2} + 77600272039468829243 T^{4} - \)\(32\!\cdots\!32\)\( T^{6} + \)\(99\!\cdots\!41\)\( T^{8} - \)\(25\!\cdots\!58\)\( T^{10} + \)\(55\!\cdots\!91\)\( T^{12} - \)\(10\!\cdots\!64\)\( T^{14} + \)\(17\!\cdots\!91\)\( T^{16} - \)\(26\!\cdots\!58\)\( T^{18} + \)\(34\!\cdots\!41\)\( T^{20} - \)\(35\!\cdots\!32\)\( T^{22} + \)\(28\!\cdots\!43\)\( T^{24} - \)\(14\!\cdots\!02\)\( T^{26} + \)\(38\!\cdots\!01\)\( T^{28} \))(\( 1 - 13607740108 T^{2} + 94972263534983306896 T^{4} - \)\(45\!\cdots\!72\)\( T^{6} + \)\(16\!\cdots\!96\)\( T^{8} - \)\(50\!\cdots\!76\)\( T^{10} + \)\(12\!\cdots\!40\)\( T^{12} - \)\(27\!\cdots\!08\)\( T^{14} + \)\(53\!\cdots\!06\)\( T^{16} - \)\(90\!\cdots\!08\)\( T^{18} + \)\(13\!\cdots\!40\)\( T^{20} - \)\(17\!\cdots\!76\)\( T^{22} + \)\(18\!\cdots\!96\)\( T^{24} - \)\(16\!\cdots\!72\)\( T^{26} + \)\(11\!\cdots\!96\)\( T^{28} - \)\(52\!\cdots\!08\)\( T^{30} + \)\(12\!\cdots\!01\)\( T^{32} \))(\( 1 - 13607740108 T^{2} + 94972263534983306896 T^{4} - \)\(45\!\cdots\!72\)\( T^{6} + \)\(16\!\cdots\!96\)\( T^{8} - \)\(50\!\cdots\!76\)\( T^{10} + \)\(12\!\cdots\!40\)\( T^{12} - \)\(27\!\cdots\!08\)\( T^{14} + \)\(53\!\cdots\!06\)\( T^{16} - \)\(90\!\cdots\!08\)\( T^{18} + \)\(13\!\cdots\!40\)\( T^{20} - \)\(17\!\cdots\!76\)\( T^{22} + \)\(18\!\cdots\!96\)\( T^{24} - \)\(16\!\cdots\!72\)\( T^{26} + \)\(11\!\cdots\!96\)\( T^{28} - \)\(52\!\cdots\!08\)\( T^{30} + \)\(12\!\cdots\!01\)\( T^{32} \))
$73$ (\( 1 + 7180 T + 284279286 T^{2} + 14884654037740 T^{3} + 4297625829703557649 T^{4} \))(\( ( 1 + 18534 T + 2073071593 T^{2} )^{2} \))(\( ( 1 + 20806 T + 2073071593 T^{2} )^{2} \))(\( ( 1 - 26266 T + 2073071593 T^{2} )^{2} \))(\( 1 + 7180 T + 284279286 T^{2} + 14884654037740 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 66750 T + 3875077479 T^{2} - 111360074258500 T^{3} + 8033313042388954047 T^{4} - \)\(28\!\cdots\!50\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( 1 - 66750 T + 3875077479 T^{2} - 111360074258500 T^{3} + 8033313042388954047 T^{4} - \)\(28\!\cdots\!50\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( ( 1 - 59700 T + 5029368950 T^{2} - 123762374102100 T^{3} + 4297625829703557649 T^{4} )^{2} \))(\( ( 1 - 88806 T + 2073071593 T^{2} )( 1 + 88806 T + 2073071593 T^{2} ) \))(\( ( 1 - 2073071593 T^{2} )^{4} \))(\( ( 1 - 4736672630 T^{2} + 15959781190221205247 T^{4} - \)\(37\!\cdots\!40\)\( T^{6} + \)\(68\!\cdots\!03\)\( T^{8} - \)\(87\!\cdots\!30\)\( T^{10} + \)\(79\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 5477783158 T^{2} + 15527894807038343935 T^{4} - \)\(34\!\cdots\!40\)\( T^{6} + \)\(66\!\cdots\!15\)\( T^{8} - \)\(10\!\cdots\!58\)\( T^{10} + \)\(79\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 + 52568 T + 9379342894 T^{2} + 374528688123736 T^{3} + 37721970904921608509 T^{4} + \)\(11\!\cdots\!56\)\( T^{5} + \)\(82\!\cdots\!04\)\( T^{6} + \)\(19\!\cdots\!04\)\( T^{7} + \)\(11\!\cdots\!58\)\( T^{8} + \)\(24\!\cdots\!96\)\( T^{9} + \)\(16\!\cdots\!04\)\( T^{10} + \)\(51\!\cdots\!28\)\( T^{11} + \)\(49\!\cdots\!42\)\( T^{12} + \)\(17\!\cdots\!28\)\( T^{13} + \)\(15\!\cdots\!04\)\( T^{14} + \)\(44\!\cdots\!08\)\( T^{15} + \)\(29\!\cdots\!41\)\( T^{16} + \)\(61\!\cdots\!52\)\( T^{17} + \)\(31\!\cdots\!94\)\( T^{18} + \)\(37\!\cdots\!24\)\( T^{19} + \)\(14\!\cdots\!49\)\( T^{20} )^{2} \))(\( 1 + 16418 T + 134775362 T^{2} - 257655666175822 T^{3} - 4365114300655601877 T^{4} + \)\(39\!\cdots\!72\)\( T^{5} + \)\(40\!\cdots\!12\)\( T^{6} + \)\(72\!\cdots\!32\)\( T^{7} - \)\(10\!\cdots\!35\)\( T^{8} - \)\(45\!\cdots\!66\)\( T^{9} + \)\(74\!\cdots\!94\)\( T^{10} + \)\(14\!\cdots\!50\)\( T^{11} + \)\(46\!\cdots\!07\)\( T^{12} - \)\(13\!\cdots\!16\)\( T^{13} - \)\(14\!\cdots\!04\)\( T^{14} - \)\(27\!\cdots\!88\)\( T^{15} + \)\(20\!\cdots\!43\)\( T^{16} + \)\(12\!\cdots\!50\)\( T^{17} + \)\(13\!\cdots\!94\)\( T^{18} - \)\(17\!\cdots\!38\)\( T^{19} - \)\(80\!\cdots\!15\)\( T^{20} + \)\(11\!\cdots\!24\)\( T^{21} + \)\(13\!\cdots\!12\)\( T^{22} + \)\(28\!\cdots\!96\)\( T^{23} - \)\(63\!\cdots\!73\)\( T^{24} - \)\(78\!\cdots\!54\)\( T^{25} + \)\(84\!\cdots\!62\)\( T^{26} + \)\(21\!\cdots\!74\)\( T^{27} + \)\(27\!\cdots\!49\)\( T^{28} \))(\( 1 + 16418 T + 134775362 T^{2} - 257655666175822 T^{3} - 4365114300655601877 T^{4} + \)\(39\!\cdots\!72\)\( T^{5} + \)\(40\!\cdots\!12\)\( T^{6} + \)\(72\!\cdots\!32\)\( T^{7} - \)\(10\!\cdots\!35\)\( T^{8} - \)\(45\!\cdots\!66\)\( T^{9} + \)\(74\!\cdots\!94\)\( T^{10} + \)\(14\!\cdots\!50\)\( T^{11} + \)\(46\!\cdots\!07\)\( T^{12} - \)\(13\!\cdots\!16\)\( T^{13} - \)\(14\!\cdots\!04\)\( T^{14} - \)\(27\!\cdots\!88\)\( T^{15} + \)\(20\!\cdots\!43\)\( T^{16} + \)\(12\!\cdots\!50\)\( T^{17} + \)\(13\!\cdots\!94\)\( T^{18} - \)\(17\!\cdots\!38\)\( T^{19} - \)\(80\!\cdots\!15\)\( T^{20} + \)\(11\!\cdots\!24\)\( T^{21} + \)\(13\!\cdots\!12\)\( T^{22} + \)\(28\!\cdots\!96\)\( T^{23} - \)\(63\!\cdots\!73\)\( T^{24} - \)\(78\!\cdots\!54\)\( T^{25} + \)\(84\!\cdots\!62\)\( T^{26} + \)\(21\!\cdots\!74\)\( T^{27} + \)\(27\!\cdots\!49\)\( T^{28} \))(\( 1 - 15432 T + 119073312 T^{2} - 56032493808632 T^{3} + 4235186228799589816 T^{4} + \)\(61\!\cdots\!96\)\( T^{5} + \)\(12\!\cdots\!48\)\( T^{6} - \)\(11\!\cdots\!24\)\( T^{7} - \)\(89\!\cdots\!60\)\( T^{8} + \)\(71\!\cdots\!68\)\( T^{9} - \)\(22\!\cdots\!48\)\( T^{10} + \)\(11\!\cdots\!04\)\( T^{11} - \)\(29\!\cdots\!68\)\( T^{12} - \)\(26\!\cdots\!56\)\( T^{13} + \)\(53\!\cdots\!44\)\( T^{14} + \)\(14\!\cdots\!88\)\( T^{15} + \)\(30\!\cdots\!30\)\( T^{16} + \)\(29\!\cdots\!84\)\( T^{17} + \)\(22\!\cdots\!56\)\( T^{18} - \)\(23\!\cdots\!92\)\( T^{19} - \)\(54\!\cdots\!68\)\( T^{20} + \)\(42\!\cdots\!72\)\( T^{21} - \)\(17\!\cdots\!52\)\( T^{22} + \)\(11\!\cdots\!76\)\( T^{23} - \)\(30\!\cdots\!60\)\( T^{24} - \)\(80\!\cdots\!32\)\( T^{25} + \)\(18\!\cdots\!52\)\( T^{26} + \)\(18\!\cdots\!72\)\( T^{27} + \)\(26\!\cdots\!16\)\( T^{28} - \)\(73\!\cdots\!76\)\( T^{29} + \)\(32\!\cdots\!88\)\( T^{30} - \)\(86\!\cdots\!24\)\( T^{31} + \)\(11\!\cdots\!01\)\( T^{32} \))(\( 1 - 15432 T + 119073312 T^{2} - 56032493808632 T^{3} + 4235186228799589816 T^{4} + \)\(61\!\cdots\!96\)\( T^{5} + \)\(12\!\cdots\!48\)\( T^{6} - \)\(11\!\cdots\!24\)\( T^{7} - \)\(89\!\cdots\!60\)\( T^{8} + \)\(71\!\cdots\!68\)\( T^{9} - \)\(22\!\cdots\!48\)\( T^{10} + \)\(11\!\cdots\!04\)\( T^{11} - \)\(29\!\cdots\!68\)\( T^{12} - \)\(26\!\cdots\!56\)\( T^{13} + \)\(53\!\cdots\!44\)\( T^{14} + \)\(14\!\cdots\!88\)\( T^{15} + \)\(30\!\cdots\!30\)\( T^{16} + \)\(29\!\cdots\!84\)\( T^{17} + \)\(22\!\cdots\!56\)\( T^{18} - \)\(23\!\cdots\!92\)\( T^{19} - \)\(54\!\cdots\!68\)\( T^{20} + \)\(42\!\cdots\!72\)\( T^{21} - \)\(17\!\cdots\!52\)\( T^{22} + \)\(11\!\cdots\!76\)\( T^{23} - \)\(30\!\cdots\!60\)\( T^{24} - \)\(80\!\cdots\!32\)\( T^{25} + \)\(18\!\cdots\!52\)\( T^{26} + \)\(18\!\cdots\!72\)\( T^{27} + \)\(26\!\cdots\!16\)\( T^{28} - \)\(73\!\cdots\!76\)\( T^{29} + \)\(32\!\cdots\!88\)\( T^{30} - \)\(86\!\cdots\!24\)\( T^{31} + \)\(11\!\cdots\!01\)\( T^{32} \))
$79$ (\( 1 + 71840 T + 7430807198 T^{2} + 221055731704160 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 1369983522 T^{2} + 9468276082626847201 T^{4} \))(\( 1 + 1275471838 T^{2} + 9468276082626847201 T^{4} \))(\( 1 + 6078817438 T^{2} + 9468276082626847201 T^{4} \))(\( 1 - 71840 T + 7430807198 T^{2} - 221055731704160 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 92952 T + 11164448877 T^{2} - 573846024396496 T^{3} + 34353638858281213923 T^{4} - \)\(88\!\cdots\!52\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( 1 + 92952 T + 11164448877 T^{2} + 573846024396496 T^{3} + 34353638858281213923 T^{4} + \)\(88\!\cdots\!52\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( 1 + 10884258108 T^{2} + 48452581383610561862 T^{4} + \)\(10\!\cdots\!08\)\( T^{6} + \)\(89\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 3077056399 T^{2} )^{2} \))(\( ( 1 + 3077056399 T^{2} )^{4} \))(\( ( 1 + 454164826 T^{2} + 18487132928554429487 T^{4} - \)\(50\!\cdots\!28\)\( T^{6} + \)\(17\!\cdots\!87\)\( T^{8} + \)\(40\!\cdots\!26\)\( T^{10} + \)\(84\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 8854539610 T^{2} + 48426464203018517551 T^{4} + \)\(17\!\cdots\!76\)\( T^{6} + \)\(45\!\cdots\!51\)\( T^{8} + \)\(79\!\cdots\!10\)\( T^{10} + \)\(84\!\cdots\!01\)\( T^{12} )^{2} \))(\( ( 1 + 141040 T + 30508439526 T^{2} + 3027236690742416 T^{3} + \)\(38\!\cdots\!93\)\( T^{4} + \)\(29\!\cdots\!88\)\( T^{5} + \)\(27\!\cdots\!48\)\( T^{6} + \)\(17\!\cdots\!16\)\( T^{7} + \)\(13\!\cdots\!30\)\( T^{8} + \)\(73\!\cdots\!40\)\( T^{9} + \)\(47\!\cdots\!04\)\( T^{10} + \)\(22\!\cdots\!60\)\( T^{11} + \)\(12\!\cdots\!30\)\( T^{12} + \)\(51\!\cdots\!84\)\( T^{13} + \)\(24\!\cdots\!48\)\( T^{14} + \)\(81\!\cdots\!12\)\( T^{15} + \)\(32\!\cdots\!93\)\( T^{16} + \)\(79\!\cdots\!84\)\( T^{17} + \)\(24\!\cdots\!26\)\( T^{18} + \)\(34\!\cdots\!60\)\( T^{19} + \)\(76\!\cdots\!01\)\( T^{20} )^{2} \))(\( ( 1 - 73272 T + 14910422889 T^{2} - 713614712327088 T^{3} + 91878682859930077941 T^{4} - \)\(30\!\cdots\!92\)\( T^{5} + \)\(35\!\cdots\!29\)\( T^{6} - \)\(97\!\cdots\!08\)\( T^{7} + \)\(10\!\cdots\!71\)\( T^{8} - \)\(29\!\cdots\!92\)\( T^{9} + \)\(26\!\cdots\!59\)\( T^{10} - \)\(63\!\cdots\!88\)\( T^{11} + \)\(41\!\cdots\!11\)\( T^{12} - \)\(62\!\cdots\!72\)\( T^{13} + \)\(26\!\cdots\!99\)\( T^{14} )^{2} \))(\( ( 1 + 73272 T + 14910422889 T^{2} + 713614712327088 T^{3} + 91878682859930077941 T^{4} + \)\(30\!\cdots\!92\)\( T^{5} + \)\(35\!\cdots\!29\)\( T^{6} + \)\(97\!\cdots\!08\)\( T^{7} + \)\(10\!\cdots\!71\)\( T^{8} + \)\(29\!\cdots\!92\)\( T^{9} + \)\(26\!\cdots\!59\)\( T^{10} + \)\(63\!\cdots\!88\)\( T^{11} + \)\(41\!\cdots\!11\)\( T^{12} + \)\(62\!\cdots\!72\)\( T^{13} + \)\(26\!\cdots\!99\)\( T^{14} )^{2} \))(\( ( 1 - 79672 T + 15921600120 T^{2} - 883492472350200 T^{3} + \)\(11\!\cdots\!40\)\( T^{4} - \)\(53\!\cdots\!80\)\( T^{5} + \)\(56\!\cdots\!80\)\( T^{6} - \)\(23\!\cdots\!20\)\( T^{7} + \)\(20\!\cdots\!70\)\( T^{8} - \)\(71\!\cdots\!80\)\( T^{9} + \)\(53\!\cdots\!80\)\( T^{10} - \)\(15\!\cdots\!20\)\( T^{11} + \)\(10\!\cdots\!40\)\( T^{12} - \)\(24\!\cdots\!00\)\( T^{13} + \)\(13\!\cdots\!20\)\( T^{14} - \)\(20\!\cdots\!28\)\( T^{15} + \)\(80\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 79672 T + 15921600120 T^{2} + 883492472350200 T^{3} + \)\(11\!\cdots\!40\)\( T^{4} + \)\(53\!\cdots\!80\)\( T^{5} + \)\(56\!\cdots\!80\)\( T^{6} + \)\(23\!\cdots\!20\)\( T^{7} + \)\(20\!\cdots\!70\)\( T^{8} + \)\(71\!\cdots\!80\)\( T^{9} + \)\(53\!\cdots\!80\)\( T^{10} + \)\(15\!\cdots\!20\)\( T^{11} + \)\(10\!\cdots\!40\)\( T^{12} + \)\(24\!\cdots\!00\)\( T^{13} + \)\(13\!\cdots\!20\)\( T^{14} + \)\(20\!\cdots\!28\)\( T^{15} + \)\(80\!\cdots\!01\)\( T^{16} )^{2} \))
$83$ (\( 1 - 31928 T + 5910993662 T^{2} - 125765689649704 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 1693436786 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 3421895214 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 1875047714 T^{2} + 15516041187205853449 T^{4} \))(\( 1 + 31928 T + 5910993662 T^{2} + 125765689649704 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 30258 T + 4293702405 T^{2} + 426012342532708 T^{3} + 16913068282241846415 T^{4} + \)\(46\!\cdots\!42\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 - 30258 T + 4293702405 T^{2} - 426012342532708 T^{3} + 16913068282241846415 T^{4} - \)\(46\!\cdots\!42\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 + 7906443964 T^{2} + 42876570344126662806 T^{4} + \)\(12\!\cdots\!36\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 3939040643 T^{2} )^{2} \))(\( ( 1 - 163262 T + 13327240322 T^{2} - 643095653457466 T^{3} + 15516041187205853449 T^{4} )( 1 + 163262 T + 13327240322 T^{2} + 643095653457466 T^{3} + 15516041187205853449 T^{4} ) \))(\( ( 1 - 11599602390 T^{2} + 72197091204656028039 T^{4} - \)\(31\!\cdots\!48\)\( T^{6} + \)\(11\!\cdots\!11\)\( T^{8} - \)\(27\!\cdots\!90\)\( T^{10} + \)\(37\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 17886738486 T^{2} + \)\(14\!\cdots\!27\)\( T^{4} - \)\(73\!\cdots\!08\)\( T^{6} + \)\(22\!\cdots\!23\)\( T^{8} - \)\(43\!\cdots\!86\)\( T^{10} + \)\(37\!\cdots\!49\)\( T^{12} )^{2} \))(\( 1 - 34768653380 T^{2} + \)\(55\!\cdots\!58\)\( T^{4} - \)\(53\!\cdots\!56\)\( T^{6} + \)\(34\!\cdots\!33\)\( T^{8} - \)\(15\!\cdots\!20\)\( T^{10} + \)\(44\!\cdots\!40\)\( T^{12} - \)\(24\!\cdots\!36\)\( T^{14} - \)\(64\!\cdots\!10\)\( T^{16} + \)\(49\!\cdots\!20\)\( T^{18} - \)\(23\!\cdots\!44\)\( T^{20} + \)\(76\!\cdots\!80\)\( T^{22} - \)\(15\!\cdots\!10\)\( T^{24} - \)\(90\!\cdots\!64\)\( T^{26} + \)\(25\!\cdots\!40\)\( T^{28} - \)\(14\!\cdots\!80\)\( T^{30} + \)\(48\!\cdots\!33\)\( T^{32} - \)\(11\!\cdots\!44\)\( T^{34} + \)\(18\!\cdots\!58\)\( T^{36} - \)\(18\!\cdots\!20\)\( T^{38} + \)\(80\!\cdots\!01\)\( T^{40} \))(\( 1 - 36398 T + 662407202 T^{2} + 351755925637942 T^{3} - 18959358682913357257 T^{4} - \)\(10\!\cdots\!44\)\( T^{5} + \)\(11\!\cdots\!08\)\( T^{6} - \)\(60\!\cdots\!36\)\( T^{7} + \)\(11\!\cdots\!21\)\( T^{8} + \)\(15\!\cdots\!90\)\( T^{9} - \)\(10\!\cdots\!50\)\( T^{10} + \)\(86\!\cdots\!90\)\( T^{11} - \)\(70\!\cdots\!85\)\( T^{12} - \)\(38\!\cdots\!20\)\( T^{13} + \)\(31\!\cdots\!80\)\( T^{14} - \)\(15\!\cdots\!60\)\( T^{15} - \)\(10\!\cdots\!65\)\( T^{16} + \)\(52\!\cdots\!30\)\( T^{17} - \)\(25\!\cdots\!50\)\( T^{18} + \)\(14\!\cdots\!70\)\( T^{19} + \)\(43\!\cdots\!29\)\( T^{20} - \)\(88\!\cdots\!52\)\( T^{21} + \)\(64\!\cdots\!08\)\( T^{22} - \)\(23\!\cdots\!92\)\( T^{23} - \)\(17\!\cdots\!93\)\( T^{24} + \)\(12\!\cdots\!94\)\( T^{25} + \)\(92\!\cdots\!02\)\( T^{26} - \)\(20\!\cdots\!14\)\( T^{27} + \)\(21\!\cdots\!49\)\( T^{28} \))(\( 1 + 36398 T + 662407202 T^{2} - 351755925637942 T^{3} - 18959358682913357257 T^{4} + \)\(10\!\cdots\!44\)\( T^{5} + \)\(11\!\cdots\!08\)\( T^{6} + \)\(60\!\cdots\!36\)\( T^{7} + \)\(11\!\cdots\!21\)\( T^{8} - \)\(15\!\cdots\!90\)\( T^{9} - \)\(10\!\cdots\!50\)\( T^{10} - \)\(86\!\cdots\!90\)\( T^{11} - \)\(70\!\cdots\!85\)\( T^{12} + \)\(38\!\cdots\!20\)\( T^{13} + \)\(31\!\cdots\!80\)\( T^{14} + \)\(15\!\cdots\!60\)\( T^{15} - \)\(10\!\cdots\!65\)\( T^{16} - \)\(52\!\cdots\!30\)\( T^{17} - \)\(25\!\cdots\!50\)\( T^{18} - \)\(14\!\cdots\!70\)\( T^{19} + \)\(43\!\cdots\!29\)\( T^{20} + \)\(88\!\cdots\!52\)\( T^{21} + \)\(64\!\cdots\!08\)\( T^{22} + \)\(23\!\cdots\!92\)\( T^{23} - \)\(17\!\cdots\!93\)\( T^{24} - \)\(12\!\cdots\!94\)\( T^{25} + \)\(92\!\cdots\!02\)\( T^{26} + \)\(20\!\cdots\!14\)\( T^{27} + \)\(21\!\cdots\!49\)\( T^{28} \))(\( 1 - 61222 T + 1874066642 T^{2} - 12255516798122 T^{3} - 16226769598202256704 T^{4} + \)\(11\!\cdots\!34\)\( T^{5} + \)\(23\!\cdots\!62\)\( T^{6} - \)\(43\!\cdots\!38\)\( T^{7} + \)\(11\!\cdots\!04\)\( T^{8} + \)\(19\!\cdots\!26\)\( T^{9} - \)\(94\!\cdots\!78\)\( T^{10} + \)\(75\!\cdots\!74\)\( T^{11} + \)\(22\!\cdots\!04\)\( T^{12} - \)\(26\!\cdots\!90\)\( T^{13} + \)\(45\!\cdots\!30\)\( T^{14} + \)\(37\!\cdots\!50\)\( T^{15} - \)\(11\!\cdots\!10\)\( T^{16} + \)\(14\!\cdots\!50\)\( T^{17} + \)\(70\!\cdots\!70\)\( T^{18} - \)\(16\!\cdots\!30\)\( T^{19} + \)\(53\!\cdots\!04\)\( T^{20} + \)\(72\!\cdots\!82\)\( T^{21} - \)\(35\!\cdots\!22\)\( T^{22} + \)\(27\!\cdots\!82\)\( T^{23} + \)\(68\!\cdots\!04\)\( T^{24} - \)\(98\!\cdots\!34\)\( T^{25} + \)\(21\!\cdots\!38\)\( T^{26} + \)\(39\!\cdots\!38\)\( T^{27} - \)\(22\!\cdots\!04\)\( T^{28} - \)\(67\!\cdots\!46\)\( T^{29} + \)\(40\!\cdots\!58\)\( T^{30} - \)\(52\!\cdots\!54\)\( T^{31} + \)\(33\!\cdots\!01\)\( T^{32} \))(\( 1 + 61222 T + 1874066642 T^{2} + 12255516798122 T^{3} - 16226769598202256704 T^{4} - \)\(11\!\cdots\!34\)\( T^{5} + \)\(23\!\cdots\!62\)\( T^{6} + \)\(43\!\cdots\!38\)\( T^{7} + \)\(11\!\cdots\!04\)\( T^{8} - \)\(19\!\cdots\!26\)\( T^{9} - \)\(94\!\cdots\!78\)\( T^{10} - \)\(75\!\cdots\!74\)\( T^{11} + \)\(22\!\cdots\!04\)\( T^{12} + \)\(26\!\cdots\!90\)\( T^{13} + \)\(45\!\cdots\!30\)\( T^{14} - \)\(37\!\cdots\!50\)\( T^{15} - \)\(11\!\cdots\!10\)\( T^{16} - \)\(14\!\cdots\!50\)\( T^{17} + \)\(70\!\cdots\!70\)\( T^{18} + \)\(16\!\cdots\!30\)\( T^{19} + \)\(53\!\cdots\!04\)\( T^{20} - \)\(72\!\cdots\!82\)\( T^{21} - \)\(35\!\cdots\!22\)\( T^{22} - \)\(27\!\cdots\!82\)\( T^{23} + \)\(68\!\cdots\!04\)\( T^{24} + \)\(98\!\cdots\!34\)\( T^{25} + \)\(21\!\cdots\!38\)\( T^{26} - \)\(39\!\cdots\!38\)\( T^{27} - \)\(22\!\cdots\!04\)\( T^{28} + \)\(67\!\cdots\!46\)\( T^{29} + \)\(40\!\cdots\!58\)\( T^{30} + \)\(52\!\cdots\!54\)\( T^{31} + \)\(33\!\cdots\!01\)\( T^{32} \))
$89$ (\( 1 + 40748 T + 8570866774 T^{2} + 227539254427852 T^{3} + 31181719929966183601 T^{4} \))(\( ( 1 + 107590 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 18310 T + 5584059449 T^{2} )^{2} \))(\( ( 1 - 30570 T + 5584059449 T^{2} )^{2} \))(\( 1 + 40748 T + 8570866774 T^{2} + 227539254427852 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 172686 T + 26445328791 T^{2} - 2103593815517412 T^{3} + \)\(14\!\cdots\!59\)\( T^{4} - \)\(53\!\cdots\!86\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( 1 - 172686 T + 26445328791 T^{2} - 2103593815517412 T^{3} + \)\(14\!\cdots\!59\)\( T^{4} - \)\(53\!\cdots\!86\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( ( 1 - 104660 T + 13126874198 T^{2} - 584427661932340 T^{3} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 - 51050 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 149286 T + 5584059449 T^{2} )^{4} \))(\( ( 1 + 930 T + 9446079447 T^{2} + 231471892494140 T^{3} + 52747469192025044703 T^{4} + \)\(28\!\cdots\!30\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{4} \))(\( ( 1 - 88734 T + 11682221271 T^{2} - 581994460142148 T^{3} + 65234218073636339679 T^{4} - \)\(27\!\cdots\!34\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{4} \))(\( ( 1 + 1580 T + 27398194046 T^{2} + 460040940498284 T^{3} + \)\(38\!\cdots\!93\)\( T^{4} + \)\(90\!\cdots\!72\)\( T^{5} + \)\(38\!\cdots\!08\)\( T^{6} + \)\(95\!\cdots\!24\)\( T^{7} + \)\(29\!\cdots\!70\)\( T^{8} + \)\(73\!\cdots\!60\)\( T^{9} + \)\(18\!\cdots\!64\)\( T^{10} + \)\(40\!\cdots\!40\)\( T^{11} + \)\(91\!\cdots\!70\)\( T^{12} + \)\(16\!\cdots\!76\)\( T^{13} + \)\(37\!\cdots\!08\)\( T^{14} + \)\(49\!\cdots\!28\)\( T^{15} + \)\(11\!\cdots\!93\)\( T^{16} + \)\(77\!\cdots\!16\)\( T^{17} + \)\(25\!\cdots\!46\)\( T^{18} + \)\(83\!\cdots\!20\)\( T^{19} + \)\(29\!\cdots\!01\)\( T^{20} )^{2} \))(\( 1 - 30334038558 T^{2} + \)\(36\!\cdots\!35\)\( T^{4} - \)\(20\!\cdots\!52\)\( T^{6} + \)\(39\!\cdots\!69\)\( T^{8} - \)\(12\!\cdots\!10\)\( T^{10} + \)\(42\!\cdots\!95\)\( T^{12} - \)\(38\!\cdots\!60\)\( T^{14} + \)\(13\!\cdots\!95\)\( T^{16} - \)\(11\!\cdots\!10\)\( T^{18} + \)\(12\!\cdots\!69\)\( T^{20} - \)\(19\!\cdots\!52\)\( T^{22} + \)\(10\!\cdots\!35\)\( T^{24} - \)\(27\!\cdots\!58\)\( T^{26} + \)\(28\!\cdots\!01\)\( T^{28} \))(\( 1 - 30334038558 T^{2} + \)\(36\!\cdots\!35\)\( T^{4} - \)\(20\!\cdots\!52\)\( T^{6} + \)\(39\!\cdots\!69\)\( T^{8} - \)\(12\!\cdots\!10\)\( T^{10} + \)\(42\!\cdots\!95\)\( T^{12} - \)\(38\!\cdots\!60\)\( T^{14} + \)\(13\!\cdots\!95\)\( T^{16} - \)\(11\!\cdots\!10\)\( T^{18} + \)\(12\!\cdots\!69\)\( T^{20} - \)\(19\!\cdots\!52\)\( T^{22} + \)\(10\!\cdots\!35\)\( T^{24} - \)\(27\!\cdots\!58\)\( T^{26} + \)\(28\!\cdots\!01\)\( T^{28} \))(\( 1 - 59849990032 T^{2} + \)\(17\!\cdots\!44\)\( T^{4} - \)\(33\!\cdots\!56\)\( T^{6} + \)\(45\!\cdots\!84\)\( T^{8} - \)\(48\!\cdots\!60\)\( T^{10} + \)\(42\!\cdots\!32\)\( T^{12} - \)\(30\!\cdots\!72\)\( T^{14} + \)\(18\!\cdots\!38\)\( T^{16} - \)\(94\!\cdots\!72\)\( T^{18} + \)\(40\!\cdots\!32\)\( T^{20} - \)\(14\!\cdots\!60\)\( T^{22} + \)\(43\!\cdots\!84\)\( T^{24} - \)\(97\!\cdots\!56\)\( T^{26} + \)\(16\!\cdots\!44\)\( T^{28} - \)\(17\!\cdots\!32\)\( T^{30} + \)\(89\!\cdots\!01\)\( T^{32} \))(\( 1 - 59849990032 T^{2} + \)\(17\!\cdots\!44\)\( T^{4} - \)\(33\!\cdots\!56\)\( T^{6} + \)\(45\!\cdots\!84\)\( T^{8} - \)\(48\!\cdots\!60\)\( T^{10} + \)\(42\!\cdots\!32\)\( T^{12} - \)\(30\!\cdots\!72\)\( T^{14} + \)\(18\!\cdots\!38\)\( T^{16} - \)\(94\!\cdots\!72\)\( T^{18} + \)\(40\!\cdots\!32\)\( T^{20} - \)\(14\!\cdots\!60\)\( T^{22} + \)\(43\!\cdots\!84\)\( T^{24} - \)\(97\!\cdots\!56\)\( T^{26} + \)\(16\!\cdots\!44\)\( T^{28} - \)\(17\!\cdots\!32\)\( T^{30} + \)\(89\!\cdots\!01\)\( T^{32} \))
$97$ (\( 1 + 190140 T + 19653817414 T^{2} + 1632796876465980 T^{3} + 73742412689492826049 T^{4} \))(\( ( 1 + 108838 T + 8587340257 T^{2} )^{2} \))(\( ( 1 - 49978 T + 8587340257 T^{2} )^{2} \))(\( ( 1 - 66882 T + 8587340257 T^{2} )^{2} \))(\( 1 + 190140 T + 19653817414 T^{2} + 1632796876465980 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 170910 T + 30283966671 T^{2} - 2852314667192740 T^{3} + \)\(26\!\cdots\!47\)\( T^{4} - \)\(12\!\cdots\!90\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( 1 - 170910 T + 30283966671 T^{2} - 2852314667192740 T^{3} + \)\(26\!\cdots\!47\)\( T^{4} - \)\(12\!\cdots\!90\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( ( 1 + 29564 T + 14772618438 T^{2} + 253876127357948 T^{3} + 73742412689492826049 T^{4} )^{2} \))(\( ( 1 - 92142 T + 8587340257 T^{2} )( 1 + 92142 T + 8587340257 T^{2} ) \))(\( ( 1 - 8587340257 T^{2} )^{4} \))(\( ( 1 - 35609466630 T^{2} + \)\(64\!\cdots\!47\)\( T^{4} - \)\(68\!\cdots\!40\)\( T^{6} + \)\(47\!\cdots\!03\)\( T^{8} - \)\(19\!\cdots\!30\)\( T^{10} + \)\(40\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 22620660742 T^{2} + \)\(25\!\cdots\!35\)\( T^{4} - \)\(22\!\cdots\!60\)\( T^{6} + \)\(18\!\cdots\!15\)\( T^{8} - \)\(12\!\cdots\!42\)\( T^{10} + \)\(40\!\cdots\!49\)\( T^{12} )^{2} \))(\( ( 1 - 73688 T + 43672916862 T^{2} - 2817316775448856 T^{3} + \)\(98\!\cdots\!25\)\( T^{4} - \)\(59\!\cdots\!28\)\( T^{5} + \)\(15\!\cdots\!52\)\( T^{6} - \)\(87\!\cdots\!16\)\( T^{7} + \)\(18\!\cdots\!70\)\( T^{8} - \)\(96\!\cdots\!88\)\( T^{9} + \)\(17\!\cdots\!72\)\( T^{10} - \)\(82\!\cdots\!16\)\( T^{11} + \)\(13\!\cdots\!30\)\( T^{12} - \)\(55\!\cdots\!88\)\( T^{13} + \)\(84\!\cdots\!52\)\( T^{14} - \)\(27\!\cdots\!96\)\( T^{15} + \)\(39\!\cdots\!25\)\( T^{16} - \)\(97\!\cdots\!08\)\( T^{17} + \)\(12\!\cdots\!62\)\( T^{18} - \)\(18\!\cdots\!16\)\( T^{19} + \)\(21\!\cdots\!49\)\( T^{20} )^{2} \))(\( 1 + 60314 T + 1818889298 T^{2} - 623535693824102 T^{3} - \)\(16\!\cdots\!77\)\( T^{4} - \)\(33\!\cdots\!64\)\( T^{5} + \)\(29\!\cdots\!52\)\( T^{6} + \)\(51\!\cdots\!52\)\( T^{7} + \)\(12\!\cdots\!01\)\( T^{8} - \)\(44\!\cdots\!50\)\( T^{9} + \)\(18\!\cdots\!50\)\( T^{10} + \)\(91\!\cdots\!50\)\( T^{11} + \)\(44\!\cdots\!75\)\( T^{12} - \)\(82\!\cdots\!00\)\( T^{13} - \)\(73\!\cdots\!00\)\( T^{14} - \)\(70\!\cdots\!00\)\( T^{15} + \)\(32\!\cdots\!75\)\( T^{16} + \)\(57\!\cdots\!50\)\( T^{17} + \)\(99\!\cdots\!50\)\( T^{18} - \)\(20\!\cdots\!50\)\( T^{19} + \)\(51\!\cdots\!49\)\( T^{20} + \)\(17\!\cdots\!36\)\( T^{21} + \)\(88\!\cdots\!52\)\( T^{22} - \)\(84\!\cdots\!48\)\( T^{23} - \)\(36\!\cdots\!73\)\( T^{24} - \)\(11\!\cdots\!86\)\( T^{25} + \)\(29\!\cdots\!98\)\( T^{26} + \)\(83\!\cdots\!98\)\( T^{27} + \)\(11\!\cdots\!49\)\( T^{28} \))(\( 1 + 60314 T + 1818889298 T^{2} - 623535693824102 T^{3} - \)\(16\!\cdots\!77\)\( T^{4} - \)\(33\!\cdots\!64\)\( T^{5} + \)\(29\!\cdots\!52\)\( T^{6} + \)\(51\!\cdots\!52\)\( T^{7} + \)\(12\!\cdots\!01\)\( T^{8} - \)\(44\!\cdots\!50\)\( T^{9} + \)\(18\!\cdots\!50\)\( T^{10} + \)\(91\!\cdots\!50\)\( T^{11} + \)\(44\!\cdots\!75\)\( T^{12} - \)\(82\!\cdots\!00\)\( T^{13} - \)\(73\!\cdots\!00\)\( T^{14} - \)\(70\!\cdots\!00\)\( T^{15} + \)\(32\!\cdots\!75\)\( T^{16} + \)\(57\!\cdots\!50\)\( T^{17} + \)\(99\!\cdots\!50\)\( T^{18} - \)\(20\!\cdots\!50\)\( T^{19} + \)\(51\!\cdots\!49\)\( T^{20} + \)\(17\!\cdots\!36\)\( T^{21} + \)\(88\!\cdots\!52\)\( T^{22} - \)\(84\!\cdots\!48\)\( T^{23} - \)\(36\!\cdots\!73\)\( T^{24} - \)\(11\!\cdots\!86\)\( T^{25} + \)\(29\!\cdots\!98\)\( T^{26} + \)\(83\!\cdots\!98\)\( T^{27} + \)\(11\!\cdots\!49\)\( T^{28} \))(\( 1 + 17344 T + 150407168 T^{2} - 246974906594432 T^{3} + 52594420471951685112 T^{4} + \)\(73\!\cdots\!08\)\( T^{5} + \)\(15\!\cdots\!48\)\( T^{6} + \)\(60\!\cdots\!32\)\( T^{7} + \)\(10\!\cdots\!36\)\( T^{8} + \)\(15\!\cdots\!56\)\( T^{9} + \)\(30\!\cdots\!48\)\( T^{10} - \)\(19\!\cdots\!76\)\( T^{11} + \)\(13\!\cdots\!92\)\( T^{12} + \)\(57\!\cdots\!52\)\( T^{13} + \)\(10\!\cdots\!20\)\( T^{14} + \)\(29\!\cdots\!16\)\( T^{15} + \)\(43\!\cdots\!78\)\( T^{16} + \)\(25\!\cdots\!12\)\( T^{17} + \)\(80\!\cdots\!80\)\( T^{18} + \)\(36\!\cdots\!36\)\( T^{19} + \)\(75\!\cdots\!92\)\( T^{20} - \)\(92\!\cdots\!32\)\( T^{21} + \)\(12\!\cdots\!52\)\( T^{22} + \)\(51\!\cdots\!08\)\( T^{23} + \)\(30\!\cdots\!36\)\( T^{24} + \)\(15\!\cdots\!24\)\( T^{25} + \)\(32\!\cdots\!52\)\( T^{26} + \)\(13\!\cdots\!44\)\( T^{27} + \)\(84\!\cdots\!12\)\( T^{28} - \)\(34\!\cdots\!24\)\( T^{29} + \)\(17\!\cdots\!32\)\( T^{30} + \)\(17\!\cdots\!92\)\( T^{31} + \)\(87\!\cdots\!01\)\( T^{32} \))(\( 1 + 17344 T + 150407168 T^{2} - 246974906594432 T^{3} + 52594420471951685112 T^{4} + \)\(73\!\cdots\!08\)\( T^{5} + \)\(15\!\cdots\!48\)\( T^{6} + \)\(60\!\cdots\!32\)\( T^{7} + \)\(10\!\cdots\!36\)\( T^{8} + \)\(15\!\cdots\!56\)\( T^{9} + \)\(30\!\cdots\!48\)\( T^{10} - \)\(19\!\cdots\!76\)\( T^{11} + \)\(13\!\cdots\!92\)\( T^{12} + \)\(57\!\cdots\!52\)\( T^{13} + \)\(10\!\cdots\!20\)\( T^{14} + \)\(29\!\cdots\!16\)\( T^{15} + \)\(43\!\cdots\!78\)\( T^{16} + \)\(25\!\cdots\!12\)\( T^{17} + \)\(80\!\cdots\!80\)\( T^{18} + \)\(36\!\cdots\!36\)\( T^{19} + \)\(75\!\cdots\!92\)\( T^{20} - \)\(92\!\cdots\!32\)\( T^{21} + \)\(12\!\cdots\!52\)\( T^{22} + \)\(51\!\cdots\!08\)\( T^{23} + \)\(30\!\cdots\!36\)\( T^{24} + \)\(15\!\cdots\!24\)\( T^{25} + \)\(32\!\cdots\!52\)\( T^{26} + \)\(13\!\cdots\!44\)\( T^{27} + \)\(84\!\cdots\!12\)\( T^{28} - \)\(34\!\cdots\!24\)\( T^{29} + \)\(17\!\cdots\!32\)\( T^{30} + \)\(17\!\cdots\!92\)\( T^{31} + \)\(87\!\cdots\!01\)\( T^{32} \))
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