Properties

Label 360.6
Level 360
Weight 6
Dimension 6999
Nonzero newspaces 18
Sturm bound 41472
Trace bound 10

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Defining parameters

Level: \( N \) = \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(41472\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(360))\).

Total New Old
Modular forms 17664 7107 10557
Cusp forms 16896 6999 9897
Eisenstein series 768 108 660

Trace form

\( 6999q - 4q^{2} + 14q^{3} - 48q^{4} - 67q^{5} + 104q^{6} - 172q^{7} - 1216q^{8} + 298q^{9} + O(q^{10}) \) \( 6999q - 4q^{2} + 14q^{3} - 48q^{4} - 67q^{5} + 104q^{6} - 172q^{7} - 1216q^{8} + 298q^{9} + 476q^{10} + 2166q^{11} + 2172q^{12} + 1250q^{13} - 2284q^{14} - 472q^{15} - 10004q^{16} - 2550q^{17} + 8960q^{18} - 6528q^{19} + 7934q^{20} - 496q^{21} - 9172q^{22} + 5964q^{23} - 18112q^{24} - 41493q^{25} - 37448q^{26} + 16712q^{27} + 10344q^{28} + 17562q^{29} + 38650q^{30} - 19536q^{31} + 12756q^{32} + 6894q^{33} + 21064q^{34} - 36372q^{35} - 133668q^{36} - 9910q^{37} - 20500q^{38} + 36168q^{39} - 30654q^{40} - 9012q^{41} + 190180q^{42} - 45062q^{43} + 72100q^{44} - 4490q^{45} - 171424q^{46} - 237700q^{47} - 255664q^{48} + 221125q^{49} + 256898q^{50} + 122422q^{51} + 140992q^{52} - 4366q^{53} + 141912q^{54} + 14948q^{55} + 203072q^{56} - 168430q^{57} - 5912q^{58} + 22266q^{59} - 473350q^{60} + 34334q^{61} - 712256q^{62} - 728q^{63} + 158952q^{64} + 133384q^{65} + 199720q^{66} + 353670q^{67} + 923620q^{68} + 76828q^{69} + 560626q^{70} - 553864q^{71} + 389196q^{72} - 67126q^{73} - 698072q^{74} - 488090q^{75} - 821884q^{76} + 329736q^{77} - 558596q^{78} - 168216q^{79} - 198704q^{80} + 495858q^{81} + 1530340q^{82} + 1167532q^{83} + 364928q^{84} + 6938q^{85} + 1224340q^{86} + 47604q^{87} + 209596q^{88} - 599162q^{89} - 319166q^{90} - 236640q^{91} - 1279780q^{92} - 203692q^{93} - 1010504q^{94} - 535500q^{95} - 73280q^{96} + 189428q^{97} - 480056q^{98} + 156156q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(360))\)

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
360.6.a \(\chi_{360}(1, \cdot)\) 360.6.a.a 1 1
360.6.a.b 1
360.6.a.c 1
360.6.a.d 1
360.6.a.e 1
360.6.a.f 1
360.6.a.g 1
360.6.a.h 1
360.6.a.i 1
360.6.a.j 2
360.6.a.k 2
360.6.a.l 2
360.6.a.m 2
360.6.a.n 2
360.6.a.o 3
360.6.a.p 3
360.6.b \(\chi_{360}(251, \cdot)\) 360.6.b.a 40 1
360.6.b.b 40
360.6.d \(\chi_{360}(109, \cdot)\) n/a 148 1
360.6.f \(\chi_{360}(289, \cdot)\) 360.6.f.a 6 1
360.6.f.b 8
360.6.f.c 8
360.6.f.d 16
360.6.h \(\chi_{360}(71, \cdot)\) None 0 1
360.6.k \(\chi_{360}(181, \cdot)\) 360.6.k.a 18 1
360.6.k.b 20
360.6.k.c 22
360.6.k.d 40
360.6.m \(\chi_{360}(179, \cdot)\) n/a 120 1
360.6.o \(\chi_{360}(359, \cdot)\) None 0 1
360.6.q \(\chi_{360}(121, \cdot)\) n/a 120 2
360.6.s \(\chi_{360}(17, \cdot)\) 360.6.s.a 28 2
360.6.s.b 32
360.6.t \(\chi_{360}(127, \cdot)\) None 0 2
360.6.w \(\chi_{360}(163, \cdot)\) n/a 296 2
360.6.x \(\chi_{360}(53, \cdot)\) n/a 240 2
360.6.bb \(\chi_{360}(119, \cdot)\) None 0 2
360.6.bd \(\chi_{360}(59, \cdot)\) n/a 712 2
360.6.bf \(\chi_{360}(61, \cdot)\) n/a 480 2
360.6.bg \(\chi_{360}(191, \cdot)\) None 0 2
360.6.bi \(\chi_{360}(49, \cdot)\) n/a 180 2
360.6.bk \(\chi_{360}(229, \cdot)\) n/a 712 2
360.6.bm \(\chi_{360}(11, \cdot)\) n/a 480 2
360.6.bo \(\chi_{360}(43, \cdot)\) n/a 1424 4
360.6.br \(\chi_{360}(77, \cdot)\) n/a 1424 4
360.6.bs \(\chi_{360}(113, \cdot)\) n/a 360 4
360.6.bv \(\chi_{360}(7, \cdot)\) None 0 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(360))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(360)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 2 T - 42 T^{2} + 288 T^{3} + 216 T^{4} - 11168 T^{5} + 50624 T^{6} + 27648 T^{7} - 979968 T^{8} + 7741440 T^{9} - 31358976 T^{10} + 28311552 T^{11} + 1658847232 T^{12} - 11710496768 T^{13} + 7247757312 T^{14} + 309237645312 T^{15} - 1443109011456 T^{16} - 2199023255552 T^{17} + 35184372088832 T^{18} \))(\( 1 + 2 T + 18 T^{2} + 116 T^{3} - 444 T^{4} + 1584 T^{5} - 2144 T^{6} - 186496 T^{7} - 497408 T^{8} - 567296 T^{9} - 25550848 T^{10} - 18153472 T^{11} - 509345792 T^{12} - 6111100928 T^{13} - 2248146944 T^{14} + 53150220288 T^{15} - 476741369856 T^{16} + 3985729650688 T^{17} + 19791209299968 T^{18} + 70368744177664 T^{19} + 1125899906842624 T^{20} \))
$3$ 1
$5$ (\( 1 + 25 T \))(\( 1 + 25 T \))(\( 1 + 25 T \))(\( 1 + 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 - 25 T )^{2} \))(\( ( 1 - 25 T )^{2} \))(\( ( 1 + 25 T )^{3} \))(\( ( 1 - 25 T )^{3} \))(\( 1 + 50 T - 625 T^{2} - 283500 T^{3} - 1953125 T^{4} + 488281250 T^{5} + 30517578125 T^{6} \))(\( 1 + 8 T + 1100 T^{2} - 113000 T^{3} - 438250 T^{4} - 353125000 T^{5} + 10742187500 T^{6} + 244140625000 T^{7} + 95367431640625 T^{8} \))(\( 1 - 66 T + 2460 T^{2} + 290850 T^{3} - 22572250 T^{4} + 908906250 T^{5} + 24023437500 T^{6} - 2014160156250 T^{7} + 95367431640625 T^{8} \))(\( 1 + 744 T^{2} - 15109700 T^{4} + 4853295000 T^{6} + 205682850843750 T^{8} + 47395458984375000 T^{10} - \)\(14\!\cdots\!00\)\( T^{12} + \)\(69\!\cdots\!00\)\( T^{14} + \)\(90\!\cdots\!25\)\( T^{16} \))(\( ( 1 + 625 T^{2} )^{9} \))(\( ( 1 + 625 T^{2} )^{10} \))
$7$ (\( 1 + 160 T + 16807 T^{2} \))(\( 1 + 108 T + 16807 T^{2} \))(\( 1 + 80 T + 16807 T^{2} \))(\( 1 - 128 T + 16807 T^{2} \))(\( 1 + 100 T + 16807 T^{2} \))(\( 1 + 62 T + 16807 T^{2} \))(\( 1 + 28 T + 16807 T^{2} \))(\( 1 - 108 T + 16807 T^{2} \))(\( 1 - 242 T + 16807 T^{2} \))(\( 1 + 80 T + 22058 T^{2} + 1344560 T^{3} + 282475249 T^{4} \))(\( 1 + 8 T - 946 T^{2} + 134456 T^{3} + 282475249 T^{4} \))(\( 1 - 52 T + 29646 T^{2} - 873964 T^{3} + 282475249 T^{4} \))(\( 1 + 80 T + 22058 T^{2} + 1344560 T^{3} + 282475249 T^{4} \))(\( 1 - 16 T + 9854 T^{2} - 268912 T^{3} + 282475249 T^{4} \))(\( 1 - 18 T + 945 T^{2} + 157516 T^{3} + 15882615 T^{4} - 5084554482 T^{5} + 4747561509943 T^{6} \))(\( 1 - 18 T + 945 T^{2} + 157516 T^{3} + 15882615 T^{4} - 5084554482 T^{5} + 4747561509943 T^{6} \))(\( 1 - 64626 T^{2} + 2028003087 T^{4} - 41058323262556 T^{6} + 572860676973093663 T^{8} - \)\(51\!\cdots\!26\)\( T^{10} + \)\(22\!\cdots\!49\)\( T^{12} \))(\( 1 - 44728 T^{2} + 1493128636 T^{4} - 37445733732616 T^{6} + 682894235558230726 T^{8} - \)\(10\!\cdots\!84\)\( T^{10} + \)\(11\!\cdots\!36\)\( T^{12} - \)\(10\!\cdots\!72\)\( T^{14} + \)\(63\!\cdots\!01\)\( T^{16} \))(\( 1 - 50044 T^{2} + 1063808116 T^{4} - 10453791123268 T^{6} + 72544565734839766 T^{8} - \)\(29\!\cdots\!32\)\( T^{10} + \)\(84\!\cdots\!16\)\( T^{12} - \)\(11\!\cdots\!56\)\( T^{14} + \)\(63\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 64504 T^{2} + 2303344348 T^{4} - 55653835395400 T^{6} + 1050929443294374022 T^{8} - \)\(15\!\cdots\!00\)\( T^{10} + \)\(18\!\cdots\!48\)\( T^{12} - \)\(14\!\cdots\!96\)\( T^{14} + \)\(63\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 98 T + 75575 T^{2} - 8345344 T^{3} + 2638517836 T^{4} - 315011006200 T^{5} + 56021877390964 T^{6} - 7518109467053312 T^{7} + 909223441762833686 T^{8} - \)\(13\!\cdots\!04\)\( T^{9} + \)\(15\!\cdots\!02\)\( T^{10} - \)\(21\!\cdots\!88\)\( T^{11} + \)\(26\!\cdots\!52\)\( T^{12} - \)\(25\!\cdots\!00\)\( T^{13} + \)\(35\!\cdots\!52\)\( T^{14} - \)\(18\!\cdots\!56\)\( T^{15} + \)\(28\!\cdots\!25\)\( T^{16} - \)\(62\!\cdots\!98\)\( T^{17} + \)\(10\!\cdots\!07\)\( T^{18} )^{2} \))(\( ( 1 + 98 T + 84148 T^{2} + 8017214 T^{3} + 3556570901 T^{4} + 345044190776 T^{5} + 103920201897616 T^{6} + 10159390994080936 T^{7} + 2363994840482709802 T^{8} + \)\(22\!\cdots\!76\)\( T^{9} + \)\(43\!\cdots\!72\)\( T^{10} + \)\(37\!\cdots\!32\)\( T^{11} + \)\(66\!\cdots\!98\)\( T^{12} + \)\(48\!\cdots\!48\)\( T^{13} + \)\(82\!\cdots\!16\)\( T^{14} + \)\(46\!\cdots\!32\)\( T^{15} + \)\(80\!\cdots\!49\)\( T^{16} + \)\(30\!\cdots\!02\)\( T^{17} + \)\(53\!\cdots\!48\)\( T^{18} + \)\(10\!\cdots\!86\)\( T^{19} + \)\(17\!\cdots\!49\)\( T^{20} )^{2} \))
$11$ (\( 1 - 596 T + 161051 T^{2} \))(\( 1 - 604 T + 161051 T^{2} \))(\( 1 + 684 T + 161051 T^{2} \))(\( 1 - 308 T + 161051 T^{2} \))(\( 1 - 136 T + 161051 T^{2} \))(\( 1 - 144 T + 161051 T^{2} \))(\( 1 - 208 T + 161051 T^{2} \))(\( 1 - 8 T + 161051 T^{2} \))(\( 1 + 656 T + 161051 T^{2} \))(\( 1 - 280 T + 328546 T^{2} - 45094280 T^{3} + 25937424601 T^{4} \))(\( 1 + 488 T + 243334 T^{2} + 78592888 T^{3} + 25937424601 T^{4} \))(\( 1 + 560 T + 381926 T^{2} + 90188560 T^{3} + 25937424601 T^{4} \))(\( 1 + 280 T + 328546 T^{2} + 45094280 T^{3} + 25937424601 T^{4} \))(\( 1 + 64 T - 58058 T^{2} + 10307264 T^{3} + 25937424601 T^{4} \))(\( 1 + 558 T + 216237 T^{2} + 56677948 T^{3} + 34825185087 T^{4} + 14473082927358 T^{5} + 4177248169415651 T^{6} \))(\( 1 - 558 T + 216237 T^{2} - 56677948 T^{3} + 34825185087 T^{4} - 14473082927358 T^{5} + 4177248169415651 T^{6} \))(\( ( 1 - 332 T + 408509 T^{2} - 107689464 T^{3} + 65790782959 T^{4} - 8611224967532 T^{5} + 4177248169415651 T^{6} )^{2} \))(\( ( 1 - 368 T + 176204 T^{2} - 51158896 T^{3} + 42277949270 T^{4} - 8239191359696 T^{5} + 4570277964394604 T^{6} - 1537227326344959568 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 342 T + 443712 T^{2} + 76803486 T^{3} + 83091304430 T^{4} + 12369278223786 T^{5} + 11508746544558912 T^{6} + 1428618873940152642 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 644376 T^{2} + 191792302396 T^{4} + 37148595807242088 T^{6} + \)\(60\!\cdots\!58\)\( T^{8} + \)\(96\!\cdots\!88\)\( T^{10} + \)\(12\!\cdots\!96\)\( T^{12} + \)\(11\!\cdots\!76\)\( T^{14} + \)\(45\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 1447478 T^{2} + 1009190764593 T^{4} - 441998694754773008 T^{6} + \)\(13\!\cdots\!08\)\( T^{8} - \)\(27\!\cdots\!60\)\( T^{10} + \)\(34\!\cdots\!68\)\( T^{12} - \)\(69\!\cdots\!72\)\( T^{14} - \)\(80\!\cdots\!22\)\( T^{16} + \)\(19\!\cdots\!40\)\( T^{18} - \)\(20\!\cdots\!22\)\( T^{20} - \)\(46\!\cdots\!72\)\( T^{22} + \)\(60\!\cdots\!68\)\( T^{24} - \)\(12\!\cdots\!60\)\( T^{26} + \)\(15\!\cdots\!08\)\( T^{28} - \)\(13\!\cdots\!08\)\( T^{30} + \)\(79\!\cdots\!93\)\( T^{32} - \)\(29\!\cdots\!78\)\( T^{34} + \)\(53\!\cdots\!01\)\( T^{36} \))(\( 1 - 1510004 T^{2} + 1155249727726 T^{4} - 592766540112799924 T^{6} + \)\(22\!\cdots\!17\)\( T^{8} - \)\(70\!\cdots\!04\)\( T^{10} + \)\(18\!\cdots\!36\)\( T^{12} - \)\(40\!\cdots\!64\)\( T^{14} + \)\(79\!\cdots\!82\)\( T^{16} - \)\(14\!\cdots\!04\)\( T^{18} + \)\(23\!\cdots\!76\)\( T^{20} - \)\(36\!\cdots\!04\)\( T^{22} + \)\(53\!\cdots\!82\)\( T^{24} - \)\(70\!\cdots\!64\)\( T^{26} + \)\(82\!\cdots\!36\)\( T^{28} - \)\(82\!\cdots\!04\)\( T^{30} + \)\(69\!\cdots\!17\)\( T^{32} - \)\(46\!\cdots\!24\)\( T^{34} + \)\(23\!\cdots\!26\)\( T^{36} - \)\(80\!\cdots\!04\)\( T^{38} + \)\(13\!\cdots\!01\)\( T^{40} \))
$13$ (\( 1 + 122 T + 371293 T^{2} \))(\( 1 + 306 T + 371293 T^{2} \))(\( 1 + 978 T + 371293 T^{2} \))(\( 1 + 1058 T + 371293 T^{2} \))(\( 1 - 82 T + 371293 T^{2} \))(\( 1 + 654 T + 371293 T^{2} \))(\( 1 + 422 T + 371293 T^{2} \))(\( 1 - 162 T + 371293 T^{2} \))(\( 1 + 206 T + 371293 T^{2} \))(\( 1 - 480 T + 326570 T^{2} - 178220640 T^{3} + 137858491849 T^{4} \))(\( 1 - 612 T + 525038 T^{2} - 227231316 T^{3} + 137858491849 T^{4} \))(\( 1 - 1388 T + 1149918 T^{2} - 515354684 T^{3} + 137858491849 T^{4} \))(\( 1 - 480 T + 326570 T^{2} - 178220640 T^{3} + 137858491849 T^{4} \))(\( 1 - 1164 T + 866894 T^{2} - 432185052 T^{3} + 137858491849 T^{4} \))(\( 1 + 84 T + 484743 T^{2} + 138297800 T^{3} + 179981682699 T^{4} + 11580113315316 T^{5} + 51185893014090757 T^{6} \))(\( 1 + 84 T + 484743 T^{2} + 138297800 T^{3} + 179981682699 T^{4} + 11580113315316 T^{5} + 51185893014090757 T^{6} \))(\( 1 - 2165574 T^{2} + 1976112655671 T^{4} - 972719104225889812 T^{6} + \)\(27\!\cdots\!79\)\( T^{8} - \)\(41\!\cdots\!74\)\( T^{10} + \)\(26\!\cdots\!49\)\( T^{12} \))(\( 1 - 1578472 T^{2} + 1074189263356 T^{4} - 437549632721743384 T^{6} + \)\(15\!\cdots\!86\)\( T^{8} - \)\(60\!\cdots\!16\)\( T^{10} + \)\(20\!\cdots\!56\)\( T^{12} - \)\(41\!\cdots\!28\)\( T^{14} + \)\(36\!\cdots\!01\)\( T^{16} \))(\( 1 + 78884 T^{2} + 436289293828 T^{4} + 45956706983246780 T^{6} + \)\(82\!\cdots\!62\)\( T^{8} + \)\(63\!\cdots\!20\)\( T^{10} + \)\(82\!\cdots\!28\)\( T^{12} + \)\(20\!\cdots\!16\)\( T^{14} + \)\(36\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 1315240 T^{2} + 1109046819196 T^{4} - 629758658597256280 T^{6} + \)\(27\!\cdots\!06\)\( T^{8} - \)\(86\!\cdots\!20\)\( T^{10} + \)\(21\!\cdots\!96\)\( T^{12} - \)\(34\!\cdots\!60\)\( T^{14} + \)\(36\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 3461146 T^{2} + 5772157343873 T^{4} - 6165622694747855536 T^{6} + \)\(47\!\cdots\!20\)\( T^{8} - \)\(28\!\cdots\!72\)\( T^{10} + \)\(13\!\cdots\!36\)\( T^{12} - \)\(55\!\cdots\!28\)\( T^{14} + \)\(20\!\cdots\!42\)\( T^{16} - \)\(75\!\cdots\!36\)\( T^{18} + \)\(28\!\cdots\!58\)\( T^{20} - \)\(10\!\cdots\!28\)\( T^{22} + \)\(35\!\cdots\!64\)\( T^{24} - \)\(10\!\cdots\!72\)\( T^{26} + \)\(23\!\cdots\!80\)\( T^{28} - \)\(42\!\cdots\!36\)\( T^{30} + \)\(54\!\cdots\!77\)\( T^{32} - \)\(45\!\cdots\!46\)\( T^{34} + \)\(17\!\cdots\!49\)\( T^{36} \))(\( 1 - 3520332 T^{2} + 6227853839054 T^{4} - 7441447313525468748 T^{6} + \)\(67\!\cdots\!57\)\( T^{8} - \)\(50\!\cdots\!12\)\( T^{10} + \)\(32\!\cdots\!64\)\( T^{12} - \)\(17\!\cdots\!28\)\( T^{14} + \)\(87\!\cdots\!42\)\( T^{16} - \)\(38\!\cdots\!32\)\( T^{18} + \)\(14\!\cdots\!64\)\( T^{20} - \)\(52\!\cdots\!68\)\( T^{22} + \)\(16\!\cdots\!42\)\( T^{24} - \)\(46\!\cdots\!72\)\( T^{26} + \)\(11\!\cdots\!64\)\( T^{28} - \)\(25\!\cdots\!88\)\( T^{30} + \)\(46\!\cdots\!57\)\( T^{32} - \)\(70\!\cdots\!52\)\( T^{34} + \)\(81\!\cdots\!54\)\( T^{36} - \)\(63\!\cdots\!68\)\( T^{38} + \)\(24\!\cdots\!01\)\( T^{40} \))
$17$ (\( 1 - 1078 T + 1419857 T^{2} \))(\( 1 + 930 T + 1419857 T^{2} \))(\( 1 - 862 T + 1419857 T^{2} \))(\( 1 + 1586 T + 1419857 T^{2} \))(\( 1 + 358 T + 1419857 T^{2} \))(\( 1 - 1190 T + 1419857 T^{2} \))(\( 1 - 146 T + 1419857 T^{2} \))(\( 1 - 714 T + 1419857 T^{2} \))(\( 1 + 1690 T + 1419857 T^{2} \))(\( 1 - 148 T + 1529590 T^{2} - 210138836 T^{3} + 2015993900449 T^{4} \))(\( 1 + 860 T + 2990038 T^{2} + 1221077020 T^{3} + 2015993900449 T^{4} \))(\( 1 + 148 T - 795706 T^{2} + 210138836 T^{3} + 2015993900449 T^{4} \))(\( 1 + 148 T + 1529590 T^{2} + 210138836 T^{3} + 2015993900449 T^{4} \))(\( 1 + 2164 T + 3414838 T^{2} + 3072570548 T^{3} + 2015993900449 T^{4} \))(\( 1 + 726 T + 3953151 T^{2} + 1935854132 T^{3} + 5612909119407 T^{4} + 1463611571725974 T^{5} + 2862423051509815793 T^{6} \))(\( 1 - 726 T + 3953151 T^{2} - 1935854132 T^{3} + 5612909119407 T^{4} - 1463611571725974 T^{5} + 2862423051509815793 T^{6} \))(\( 1 - 6393390 T^{2} + 19617942041247 T^{4} - 35338776492878157220 T^{6} + \)\(39\!\cdots\!03\)\( T^{8} - \)\(25\!\cdots\!90\)\( T^{10} + \)\(81\!\cdots\!49\)\( T^{12} \))(\( 1 - 6260872 T^{2} + 17547242668444 T^{4} - 31297293718759478968 T^{6} + \)\(45\!\cdots\!30\)\( T^{8} - \)\(63\!\cdots\!32\)\( T^{10} + \)\(71\!\cdots\!44\)\( T^{12} - \)\(51\!\cdots\!28\)\( T^{14} + \)\(16\!\cdots\!01\)\( T^{16} \))(\( 1 - 3560332 T^{2} + 5896843750180 T^{4} - 4412996604518385652 T^{6} + \)\(28\!\cdots\!34\)\( T^{8} - \)\(88\!\cdots\!48\)\( T^{10} + \)\(23\!\cdots\!80\)\( T^{12} - \)\(29\!\cdots\!68\)\( T^{14} + \)\(16\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 4000504 T^{2} + 8522048810908 T^{4} - 14167372887863087560 T^{6} + \)\(21\!\cdots\!42\)\( T^{8} - \)\(28\!\cdots\!40\)\( T^{10} + \)\(34\!\cdots\!08\)\( T^{12} - \)\(32\!\cdots\!96\)\( T^{14} + \)\(16\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 1734 T + 7191473 T^{2} - 10893129664 T^{3} + 27927047893276 T^{4} - 38861822453543016 T^{5} + 72745110756697826076 T^{6} - \)\(90\!\cdots\!32\)\( T^{7} + \)\(13\!\cdots\!66\)\( T^{8} - \)\(15\!\cdots\!20\)\( T^{9} + \)\(19\!\cdots\!62\)\( T^{10} - \)\(18\!\cdots\!68\)\( T^{11} + \)\(20\!\cdots\!68\)\( T^{12} - \)\(15\!\cdots\!16\)\( T^{13} + \)\(16\!\cdots\!32\)\( T^{14} - \)\(89\!\cdots\!36\)\( T^{15} + \)\(83\!\cdots\!89\)\( T^{16} - \)\(28\!\cdots\!34\)\( T^{17} + \)\(23\!\cdots\!57\)\( T^{18} )^{2} \))(\( ( 1 + 5447662 T^{2} - 1859072000 T^{3} + 15317572824845 T^{4} - 7413542230528000 T^{5} + 32518332783929091752 T^{6} - \)\(14\!\cdots\!00\)\( T^{7} + \)\(56\!\cdots\!10\)\( T^{8} - \)\(21\!\cdots\!00\)\( T^{9} + \)\(84\!\cdots\!72\)\( T^{10} - \)\(31\!\cdots\!00\)\( T^{11} + \)\(11\!\cdots\!90\)\( T^{12} - \)\(41\!\cdots\!00\)\( T^{13} + \)\(13\!\cdots\!52\)\( T^{14} - \)\(42\!\cdots\!00\)\( T^{15} + \)\(12\!\cdots\!05\)\( T^{16} - \)\(21\!\cdots\!00\)\( T^{17} + \)\(89\!\cdots\!62\)\( T^{18} + \)\(33\!\cdots\!49\)\( T^{20} )^{2} \))
$19$ (\( 1 - 796 T + 2476099 T^{2} \))(\( 1 + 1324 T + 2476099 T^{2} \))(\( 1 - 916 T + 2476099 T^{2} \))(\( 1 - 2308 T + 2476099 T^{2} \))(\( 1 - 796 T + 2476099 T^{2} \))(\( 1 - 556 T + 2476099 T^{2} \))(\( 1 + 2012 T + 2476099 T^{2} \))(\( 1 + 532 T + 2476099 T^{2} \))(\( 1 + 1364 T + 2476099 T^{2} \))(\( 1 + 48 T + 3637174 T^{2} + 118852752 T^{3} + 6131066257801 T^{4} \))(\( 1 + 96 T + 770806 T^{2} + 237705504 T^{3} + 6131066257801 T^{4} \))(\( 1 + 1000 T + 4533462 T^{2} + 2476099000 T^{3} + 6131066257801 T^{4} \))(\( 1 + 48 T + 3637174 T^{2} + 118852752 T^{3} + 6131066257801 T^{4} \))(\( 1 - 2640 T + 5527222 T^{2} - 6536901360 T^{3} + 6131066257801 T^{4} \))(\( 1 - 876 T + 3345081 T^{2} - 3724581832 T^{3} + 8282751719019 T^{4} - 5370814041833676 T^{5} + 15181127029874798299 T^{6} \))(\( 1 - 876 T + 3345081 T^{2} - 3724581832 T^{3} + 8282751719019 T^{4} - 5370814041833676 T^{5} + 15181127029874798299 T^{6} \))(\( ( 1 - 144 T + 1911561 T^{2} + 1871015072 T^{3} + 4733214280539 T^{4} - 882873541123344 T^{5} + 15181127029874798299 T^{6} )^{2} \))(\( ( 1 - 688 T + 5308396 T^{2} - 6058136368 T^{3} + 15069081422710 T^{4} - 15000545402668432 T^{5} + 32546127598645797196 T^{6} - \)\(10\!\cdots\!12\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 1520 T + 8017612 T^{2} + 7503400304 T^{3} + 25990277114806 T^{4} + 18579161989334096 T^{5} + 49156510401340391212 T^{6} + \)\(23\!\cdots\!80\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 688 T + 4775596 T^{2} - 1378597168 T^{3} + 11860428984310 T^{4} - 3413543069087632 T^{5} + 29279495496489424396 T^{6} - \)\(10\!\cdots\!12\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} )^{4} \))(\( 1 - 23419574 T^{2} + 264457379180353 T^{4} - \)\(18\!\cdots\!60\)\( T^{6} + \)\(93\!\cdots\!44\)\( T^{8} - \)\(33\!\cdots\!12\)\( T^{10} + \)\(81\!\cdots\!52\)\( T^{12} - \)\(11\!\cdots\!16\)\( T^{14} + \)\(14\!\cdots\!06\)\( T^{16} + \)\(28\!\cdots\!12\)\( T^{18} + \)\(89\!\cdots\!06\)\( T^{20} - \)\(44\!\cdots\!16\)\( T^{22} + \)\(18\!\cdots\!52\)\( T^{24} - \)\(46\!\cdots\!12\)\( T^{26} + \)\(81\!\cdots\!44\)\( T^{28} - \)\(10\!\cdots\!60\)\( T^{30} + \)\(86\!\cdots\!53\)\( T^{32} - \)\(46\!\cdots\!74\)\( T^{34} + \)\(12\!\cdots\!01\)\( T^{36} \))(\( 1 - 23638692 T^{2} + 296336418074734 T^{4} - \)\(25\!\cdots\!32\)\( T^{6} + \)\(17\!\cdots\!97\)\( T^{8} - \)\(93\!\cdots\!80\)\( T^{10} + \)\(42\!\cdots\!52\)\( T^{12} - \)\(16\!\cdots\!48\)\( T^{14} + \)\(56\!\cdots\!66\)\( T^{16} - \)\(16\!\cdots\!12\)\( T^{18} + \)\(44\!\cdots\!28\)\( T^{20} - \)\(10\!\cdots\!12\)\( T^{22} + \)\(21\!\cdots\!66\)\( T^{24} - \)\(38\!\cdots\!48\)\( T^{26} + \)\(60\!\cdots\!52\)\( T^{28} - \)\(80\!\cdots\!80\)\( T^{30} + \)\(91\!\cdots\!97\)\( T^{32} - \)\(83\!\cdots\!32\)\( T^{34} + \)\(59\!\cdots\!34\)\( T^{36} - \)\(28\!\cdots\!92\)\( T^{38} + \)\(75\!\cdots\!01\)\( T^{40} \))
$23$ (\( 1 - 1088 T + 6436343 T^{2} \))(\( 1 - 852 T + 6436343 T^{2} \))(\( 1 - 1552 T + 6436343 T^{2} \))(\( 1 + 2656 T + 6436343 T^{2} \))(\( 1 + 488 T + 6436343 T^{2} \))(\( 1 + 2182 T + 6436343 T^{2} \))(\( 1 - 1096 T + 6436343 T^{2} \))(\( 1 - 4584 T + 6436343 T^{2} \))(\( 1 + 2198 T + 6436343 T^{2} \))(\( 1 - 3232 T + 10221742 T^{2} - 20802260576 T^{3} + 41426511213649 T^{4} \))(\( 1 + 2984 T + 9255406 T^{2} + 19206047512 T^{3} + 41426511213649 T^{4} \))(\( 1 - 2452 T + 6569198 T^{2} - 15781913036 T^{3} + 41426511213649 T^{4} \))(\( 1 + 3232 T + 10221742 T^{2} + 20802260576 T^{3} + 41426511213649 T^{4} \))(\( 1 + 40 T - 10021778 T^{2} + 257453720 T^{3} + 41426511213649 T^{4} \))(\( 1 + 960 T + 15148581 T^{2} + 10843596928 T^{3} + 97501463279283 T^{4} + 39769450765103040 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 - 960 T + 15148581 T^{2} - 10843596928 T^{3} + 97501463279283 T^{4} - 39769450765103040 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 - 12847386 T^{2} + 119828345726079 T^{4} - \)\(79\!\cdots\!56\)\( T^{6} + \)\(49\!\cdots\!71\)\( T^{8} - \)\(22\!\cdots\!86\)\( T^{10} + \)\(71\!\cdots\!49\)\( T^{12} \))(\( 1 - 34675896 T^{2} + 569897415616828 T^{4} - \)\(59\!\cdots\!20\)\( T^{6} + \)\(44\!\cdots\!82\)\( T^{8} - \)\(24\!\cdots\!80\)\( T^{10} + \)\(97\!\cdots\!28\)\( T^{12} - \)\(24\!\cdots\!04\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} \))(\( 1 - 37462776 T^{2} + 688226025523036 T^{4} - \)\(78\!\cdots\!72\)\( T^{6} + \)\(60\!\cdots\!26\)\( T^{8} - \)\(32\!\cdots\!28\)\( T^{10} + \)\(11\!\cdots\!36\)\( T^{12} - \)\(26\!\cdots\!24\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 14927352 T^{2} + 114641830602076 T^{4} - \)\(53\!\cdots\!44\)\( T^{6} + \)\(24\!\cdots\!46\)\( T^{8} - \)\(22\!\cdots\!56\)\( T^{10} + \)\(19\!\cdots\!76\)\( T^{12} - \)\(10\!\cdots\!48\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 836 T + 34331319 T^{2} - 25687862976 T^{3} + 594523019931132 T^{4} - 377763847022935664 T^{5} + \)\(68\!\cdots\!08\)\( T^{6} - \)\(36\!\cdots\!76\)\( T^{7} + \)\(57\!\cdots\!78\)\( T^{8} - \)\(26\!\cdots\!00\)\( T^{9} + \)\(37\!\cdots\!54\)\( T^{10} - \)\(15\!\cdots\!24\)\( T^{11} + \)\(18\!\cdots\!56\)\( T^{12} - \)\(64\!\cdots\!64\)\( T^{13} + \)\(65\!\cdots\!76\)\( T^{14} - \)\(18\!\cdots\!24\)\( T^{15} + \)\(15\!\cdots\!33\)\( T^{16} - \)\(24\!\cdots\!36\)\( T^{17} + \)\(18\!\cdots\!43\)\( T^{18} )^{2} \))(\( ( 1 - 2338 T + 35997660 T^{2} - 45007042654 T^{3} + 520972471777845 T^{4} - 50426407997609208 T^{5} + \)\(39\!\cdots\!60\)\( T^{6} + \)\(66\!\cdots\!96\)\( T^{7} + \)\(17\!\cdots\!10\)\( T^{8} + \)\(91\!\cdots\!52\)\( T^{9} + \)\(76\!\cdots\!60\)\( T^{10} + \)\(58\!\cdots\!36\)\( T^{11} + \)\(74\!\cdots\!90\)\( T^{12} + \)\(17\!\cdots\!72\)\( T^{13} + \)\(68\!\cdots\!60\)\( T^{14} - \)\(55\!\cdots\!44\)\( T^{15} + \)\(37\!\cdots\!05\)\( T^{16} - \)\(20\!\cdots\!78\)\( T^{17} + \)\(10\!\cdots\!60\)\( T^{18} - \)\(44\!\cdots\!34\)\( T^{19} + \)\(12\!\cdots\!49\)\( T^{20} )^{2} \))
$29$ (\( 1 + 46 T + 20511149 T^{2} \))(\( 1 + 5902 T + 20511149 T^{2} \))(\( 1 - 7314 T + 20511149 T^{2} \))(\( 1 + 1198 T + 20511149 T^{2} \))(\( 1 + 7466 T + 20511149 T^{2} \))(\( 1 - 1578 T + 20511149 T^{2} \))(\( 1 - 1462 T + 20511149 T^{2} \))(\( 1 + 938 T + 20511149 T^{2} \))(\( 1 - 2218 T + 20511149 T^{2} \))(\( 1 - 1340 T + 41260702 T^{2} - 27484939660 T^{3} + 420707233300201 T^{4} \))(\( 1 + 2236 T + 28441822 T^{2} + 45862929164 T^{3} + 420707233300201 T^{4} \))(\( 1 + 1340 T - 8758306 T^{2} + 27484939660 T^{3} + 420707233300201 T^{4} \))(\( 1 + 1340 T + 41260702 T^{2} + 27484939660 T^{3} + 420707233300201 T^{4} \))(\( 1 + 1940 T + 17567422 T^{2} + 39791629060 T^{3} + 420707233300201 T^{4} \))(\( 1 + 1710 T + 42734451 T^{2} + 37260127060 T^{3} + 876532691894199 T^{4} + 719409368943343710 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( 1 - 1710 T + 42734451 T^{2} - 37260127060 T^{3} + 876532691894199 T^{4} - 719409368943343710 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( ( 1 - 946 T + 36417431 T^{2} - 76110228372 T^{3} + 746963353438219 T^{4} - 397989042701990146 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 + 2936 T + 58625996 T^{2} + 77951973928 T^{3} + 1466411094282230 T^{4} + 1598884552081323272 T^{5} + \)\(24\!\cdots\!96\)\( T^{6} + \)\(25\!\cdots\!64\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 4002 T + 41245860 T^{2} - 2052028782 T^{3} + 531865053741014 T^{4} - 42089468099890518 T^{5} + \)\(17\!\cdots\!60\)\( T^{6} - \)\(34\!\cdots\!98\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 50036904 T^{2} + 1677424685662204 T^{4} + \)\(36\!\cdots\!96\)\( T^{6} + \)\(78\!\cdots\!90\)\( T^{8} + \)\(15\!\cdots\!96\)\( T^{10} + \)\(29\!\cdots\!04\)\( T^{12} + \)\(37\!\cdots\!04\)\( T^{14} + \)\(31\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 243887718 T^{2} + 29230821756838977 T^{4} - \)\(22\!\cdots\!60\)\( T^{6} + \)\(13\!\cdots\!44\)\( T^{8} - \)\(60\!\cdots\!68\)\( T^{10} + \)\(22\!\cdots\!32\)\( T^{12} - \)\(68\!\cdots\!56\)\( T^{14} + \)\(17\!\cdots\!82\)\( T^{16} - \)\(39\!\cdots\!68\)\( T^{18} + \)\(74\!\cdots\!82\)\( T^{20} - \)\(12\!\cdots\!56\)\( T^{22} + \)\(16\!\cdots\!32\)\( T^{24} - \)\(18\!\cdots\!68\)\( T^{26} + \)\(17\!\cdots\!44\)\( T^{28} - \)\(12\!\cdots\!60\)\( T^{30} + \)\(68\!\cdots\!77\)\( T^{32} - \)\(23\!\cdots\!18\)\( T^{34} + \)\(41\!\cdots\!01\)\( T^{36} \))(\( 1 - 215092900 T^{2} + 23243889276296494 T^{4} - \)\(16\!\cdots\!00\)\( T^{6} + \)\(90\!\cdots\!13\)\( T^{8} - \)\(38\!\cdots\!00\)\( T^{10} + \)\(13\!\cdots\!92\)\( T^{12} - \)\(42\!\cdots\!00\)\( T^{14} + \)\(11\!\cdots\!86\)\( T^{16} - \)\(27\!\cdots\!00\)\( T^{18} + \)\(58\!\cdots\!28\)\( T^{20} - \)\(11\!\cdots\!00\)\( T^{22} + \)\(20\!\cdots\!86\)\( T^{24} - \)\(31\!\cdots\!00\)\( T^{26} + \)\(43\!\cdots\!92\)\( T^{28} - \)\(51\!\cdots\!00\)\( T^{30} + \)\(50\!\cdots\!13\)\( T^{32} - \)\(39\!\cdots\!00\)\( T^{34} + \)\(22\!\cdots\!94\)\( T^{36} - \)\(88\!\cdots\!00\)\( T^{38} + \)\(17\!\cdots\!01\)\( T^{40} \))
$31$ (\( 1 + 4952 T + 28629151 T^{2} \))(\( 1 + 3320 T + 28629151 T^{2} \))(\( 1 + 9312 T + 28629151 T^{2} \))(\( 1 - 9520 T + 28629151 T^{2} \))(\( 1 - 2728 T + 28629151 T^{2} \))(\( 1 - 9660 T + 28629151 T^{2} \))(\( 1 + 80 T + 28629151 T^{2} \))(\( 1 + 8360 T + 28629151 T^{2} \))(\( 1 + 1700 T + 28629151 T^{2} \))(\( 1 + 6440 T + 62364302 T^{2} + 184371732440 T^{3} + 819628286980801 T^{4} \))(\( 1 - 9352 T + 45895742 T^{2} - 267739820152 T^{3} + 819628286980801 T^{4} \))(\( 1 + 2248 T + 57017022 T^{2} + 64358331448 T^{3} + 819628286980801 T^{4} \))(\( 1 + 6440 T + 62364302 T^{2} + 184371732440 T^{3} + 819628286980801 T^{4} \))(\( 1 - 6328 T + 63242942 T^{2} - 181165267528 T^{3} + 819628286980801 T^{4} \))(\( 1 - 324 T + 78872013 T^{2} - 13928801848 T^{3} + 2258038769850963 T^{4} - 265559564981779524 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( 1 - 324 T + 78872013 T^{2} - 13928801848 T^{3} + 2258038769850963 T^{4} - 265559564981779524 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( ( 1 + 5124 T + 61295997 T^{2} + 221905216248 T^{3} + 1754852353808547 T^{4} + 4199775342489624324 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 - 2112 T + 80187004 T^{2} - 163080265536 T^{3} + 3196344720873606 T^{4} - 4668849547150239936 T^{5} + \)\(65\!\cdots\!04\)\( T^{6} - \)\(49\!\cdots\!12\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 3012 T + 64375804 T^{2} - 104976522036 T^{3} + 1995658050211206 T^{4} - 3005388700823471436 T^{5} + \)\(52\!\cdots\!04\)\( T^{6} - \)\(70\!\cdots\!12\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 1056 T + 33747004 T^{2} + 123082635168 T^{3} + 293348622009606 T^{4} + 3523751347702582368 T^{5} + \)\(27\!\cdots\!04\)\( T^{6} + \)\(24\!\cdots\!56\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} )^{4} \))(\( ( 1 + 9942 T + 230756015 T^{2} + 1980287460384 T^{3} + 24452379679898252 T^{4} + \)\(17\!\cdots\!00\)\( T^{5} + \)\(15\!\cdots\!16\)\( T^{6} + \)\(97\!\cdots\!40\)\( T^{7} + \)\(65\!\cdots\!18\)\( T^{8} + \)\(34\!\cdots\!64\)\( T^{9} + \)\(18\!\cdots\!18\)\( T^{10} + \)\(79\!\cdots\!40\)\( T^{11} + \)\(36\!\cdots\!16\)\( T^{12} + \)\(12\!\cdots\!00\)\( T^{13} + \)\(47\!\cdots\!52\)\( T^{14} + \)\(10\!\cdots\!84\)\( T^{15} + \)\(36\!\cdots\!65\)\( T^{16} + \)\(44\!\cdots\!42\)\( T^{17} + \)\(12\!\cdots\!51\)\( T^{18} )^{2} \))(\( ( 1 - 3580 T + 132421614 T^{2} - 484936307876 T^{3} + 8983138546835629 T^{4} - 33755686429634218608 T^{5} + \)\(43\!\cdots\!88\)\( T^{6} - \)\(16\!\cdots\!96\)\( T^{7} + \)\(17\!\cdots\!38\)\( T^{8} - \)\(60\!\cdots\!32\)\( T^{9} + \)\(54\!\cdots\!44\)\( T^{10} - \)\(17\!\cdots\!32\)\( T^{11} + \)\(13\!\cdots\!38\)\( T^{12} - \)\(38\!\cdots\!96\)\( T^{13} + \)\(29\!\cdots\!88\)\( T^{14} - \)\(64\!\cdots\!08\)\( T^{15} + \)\(49\!\cdots\!29\)\( T^{16} - \)\(76\!\cdots\!76\)\( T^{17} + \)\(59\!\cdots\!14\)\( T^{18} - \)\(46\!\cdots\!80\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} )^{2} \))
$37$ (\( 1 + 6114 T + 69343957 T^{2} \))(\( 1 - 10774 T + 69343957 T^{2} \))(\( 1 + 8826 T + 69343957 T^{2} \))(\( 1 - 4470 T + 69343957 T^{2} \))(\( 1 - 7794 T + 69343957 T^{2} \))(\( 1 + 3534 T + 69343957 T^{2} \))(\( 1 + 15750 T + 69343957 T^{2} \))(\( 1 - 1090 T + 69343957 T^{2} \))(\( 1 + 846 T + 69343957 T^{2} \))(\( 1 + 6440 T + 77014058 T^{2} + 446575083080 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 10612 T + 133614014 T^{2} - 735878071684 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 5940 T + 123434318 T^{2} + 411903104580 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 6440 T + 77014058 T^{2} + 446575083080 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 3532 T + 112622270 T^{2} - 244922856124 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 10320 T + 189184575 T^{2} - 1131781251360 T^{3} + 13118807033863275 T^{4} - 49624590723352201680 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( 1 - 10320 T + 189184575 T^{2} - 1131781251360 T^{3} + 13118807033863275 T^{4} - 49624590723352201680 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( 1 - 290752854 T^{2} + 38769784471186119 T^{4} - \)\(32\!\cdots\!24\)\( T^{6} + \)\(18\!\cdots\!31\)\( T^{8} - \)\(67\!\cdots\!54\)\( T^{10} + \)\(11\!\cdots\!49\)\( T^{12} \))(\( 1 - 251774632 T^{2} + 38631208311838780 T^{4} - \)\(41\!\cdots\!52\)\( T^{6} + \)\(32\!\cdots\!34\)\( T^{8} - \)\(19\!\cdots\!48\)\( T^{10} + \)\(89\!\cdots\!80\)\( T^{12} - \)\(27\!\cdots\!68\)\( T^{14} + \)\(53\!\cdots\!01\)\( T^{16} \))(\( 1 - 335599612 T^{2} + 58713287095888324 T^{4} - \)\(67\!\cdots\!68\)\( T^{6} + \)\(54\!\cdots\!30\)\( T^{8} - \)\(32\!\cdots\!32\)\( T^{10} + \)\(13\!\cdots\!24\)\( T^{12} - \)\(37\!\cdots\!88\)\( T^{14} + \)\(53\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 156602728 T^{2} + 10376850454113724 T^{4} - \)\(10\!\cdots\!36\)\( T^{6} + \)\(10\!\cdots\!58\)\( T^{8} - \)\(52\!\cdots\!64\)\( T^{10} + \)\(23\!\cdots\!24\)\( T^{12} - \)\(17\!\cdots\!72\)\( T^{14} + \)\(53\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 815917754 T^{2} + 325595650442279281 T^{4} - \)\(84\!\cdots\!44\)\( T^{6} + \)\(16\!\cdots\!20\)\( T^{8} - \)\(24\!\cdots\!52\)\( T^{10} + \)\(29\!\cdots\!52\)\( T^{12} - \)\(29\!\cdots\!04\)\( T^{14} + \)\(25\!\cdots\!98\)\( T^{16} - \)\(19\!\cdots\!92\)\( T^{18} + \)\(12\!\cdots\!02\)\( T^{20} - \)\(68\!\cdots\!04\)\( T^{22} + \)\(32\!\cdots\!48\)\( T^{24} - \)\(12\!\cdots\!52\)\( T^{26} + \)\(41\!\cdots\!80\)\( T^{28} - \)\(10\!\cdots\!44\)\( T^{30} + \)\(19\!\cdots\!69\)\( T^{32} - \)\(23\!\cdots\!54\)\( T^{34} + \)\(13\!\cdots\!49\)\( T^{36} \))(\( 1 - 565372668 T^{2} + 171401952644913934 T^{4} - \)\(36\!\cdots\!00\)\( T^{6} + \)\(59\!\cdots\!09\)\( T^{8} - \)\(80\!\cdots\!44\)\( T^{10} + \)\(93\!\cdots\!16\)\( T^{12} - \)\(93\!\cdots\!40\)\( T^{14} + \)\(83\!\cdots\!86\)\( T^{16} - \)\(67\!\cdots\!48\)\( T^{18} + \)\(48\!\cdots\!08\)\( T^{20} - \)\(32\!\cdots\!52\)\( T^{22} + \)\(19\!\cdots\!86\)\( T^{24} - \)\(10\!\cdots\!60\)\( T^{26} + \)\(49\!\cdots\!16\)\( T^{28} - \)\(20\!\cdots\!56\)\( T^{30} + \)\(73\!\cdots\!09\)\( T^{32} - \)\(21\!\cdots\!00\)\( T^{34} + \)\(48\!\cdots\!34\)\( T^{36} - \)\(77\!\cdots\!32\)\( T^{38} + \)\(66\!\cdots\!01\)\( T^{40} \))
$41$ (\( 1 - 6 T + 115856201 T^{2} \))(\( 1 - 17958 T + 115856201 T^{2} \))(\( 1 - 3286 T + 115856201 T^{2} \))(\( 1 - 6198 T + 115856201 T^{2} \))(\( 1 + 18234 T + 115856201 T^{2} \))(\( 1 + 7462 T + 115856201 T^{2} \))(\( 1 - 2358 T + 115856201 T^{2} \))(\( 1 - 11238 T + 115856201 T^{2} \))(\( 1 - 1818 T + 115856201 T^{2} \))(\( 1 + 9680 T + 219564178 T^{2} + 1121488025680 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 17156 T + 298517590 T^{2} + 1987628984356 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 23076 T + 352280470 T^{2} + 2673497694276 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 9680 T + 219564178 T^{2} - 1121488025680 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 2404 T - 34529258 T^{2} + 278518307204 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 4080 T + 108883419 T^{2} + 42537842400 T^{3} + 12614819277231219 T^{4} + 54764449985421796080 T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( 1 - 4080 T + 108883419 T^{2} - 42537842400 T^{3} + 12614819277231219 T^{4} - 54764449985421796080 T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( ( 1 - 662 T + 143511479 T^{2} - 442940770164 T^{3} + 16626694756831279 T^{4} - 8885800463320889462 T^{5} + \)\(15\!\cdots\!01\)\( T^{6} )^{2} \))(\( ( 1 + 11800 T + 337909340 T^{2} + 2943020124776 T^{3} + 51155654972384870 T^{4} + \)\(34\!\cdots\!76\)\( T^{5} + \)\(45\!\cdots\!40\)\( T^{6} + \)\(18\!\cdots\!00\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 18900 T + 417574740 T^{2} - 5341513264524 T^{3} + 73890473527486070 T^{4} - \)\(61\!\cdots\!24\)\( T^{5} + \)\(56\!\cdots\!40\)\( T^{6} - \)\(29\!\cdots\!00\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 458567496 T^{2} + 120108387972394204 T^{4} + \)\(21\!\cdots\!04\)\( T^{6} + \)\(28\!\cdots\!90\)\( T^{8} + \)\(28\!\cdots\!04\)\( T^{10} + \)\(21\!\cdots\!04\)\( T^{12} + \)\(11\!\cdots\!96\)\( T^{14} + \)\(32\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 16810 T + 762815361 T^{2} + 10738212065328 T^{3} + 276974282122259412 T^{4} + \)\(33\!\cdots\!56\)\( T^{5} + \)\(63\!\cdots\!68\)\( T^{6} + \)\(65\!\cdots\!76\)\( T^{7} + \)\(10\!\cdots\!46\)\( T^{8} + \)\(89\!\cdots\!36\)\( T^{9} + \)\(11\!\cdots\!46\)\( T^{10} + \)\(87\!\cdots\!76\)\( T^{11} + \)\(98\!\cdots\!68\)\( T^{12} + \)\(59\!\cdots\!56\)\( T^{13} + \)\(57\!\cdots\!12\)\( T^{14} + \)\(25\!\cdots\!28\)\( T^{15} + \)\(21\!\cdots\!61\)\( T^{16} + \)\(54\!\cdots\!10\)\( T^{17} + \)\(37\!\cdots\!01\)\( T^{18} )^{2} \))(\( ( 1 + 5804 T + 580737234 T^{2} + 4176614475628 T^{3} + 181136735899530493 T^{4} + \)\(13\!\cdots\!48\)\( T^{5} + \)\(39\!\cdots\!40\)\( T^{6} + \)\(28\!\cdots\!68\)\( T^{7} + \)\(63\!\cdots\!42\)\( T^{8} + \)\(43\!\cdots\!24\)\( T^{9} + \)\(82\!\cdots\!24\)\( T^{10} + \)\(49\!\cdots\!24\)\( T^{11} + \)\(85\!\cdots\!42\)\( T^{12} + \)\(44\!\cdots\!68\)\( T^{13} + \)\(70\!\cdots\!40\)\( T^{14} + \)\(28\!\cdots\!48\)\( T^{15} + \)\(43\!\cdots\!93\)\( T^{16} + \)\(11\!\cdots\!28\)\( T^{17} + \)\(18\!\cdots\!34\)\( T^{18} + \)\(21\!\cdots\!04\)\( T^{19} + \)\(43\!\cdots\!01\)\( T^{20} )^{2} \))
$43$ (\( 1 + 24116 T + 147008443 T^{2} \))(\( 1 - 9264 T + 147008443 T^{2} \))(\( 1 - 7556 T + 147008443 T^{2} \))(\( 1 + 6332 T + 147008443 T^{2} \))(\( 1 + 2444 T + 147008443 T^{2} \))(\( 1 + 7114 T + 147008443 T^{2} \))(\( 1 - 2812 T + 147008443 T^{2} \))(\( 1 + 7692 T + 147008443 T^{2} \))(\( 1 - 10534 T + 147008443 T^{2} \))(\( 1 + 19360 T + 382456886 T^{2} + 2846083456480 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 440 T + 1414022 T^{2} - 64683714920 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 17684 T + 312898614 T^{2} - 2599697306012 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 19360 T + 382456886 T^{2} + 2846083456480 T^{3} + 21611482313284249 T^{4} \))(\( 1 - 31928 T + 510747782 T^{2} - 4693685568104 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 1752 T + 208706289 T^{2} + 626926262672 T^{3} + 30681586590198027 T^{4} + 37863317012874004248 T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( 1 + 1752 T + 208706289 T^{2} + 626926262672 T^{3} + 30681586590198027 T^{4} + 37863317012874004248 T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( 1 - 502572210 T^{2} + 127464803683947447 T^{4} - \)\(22\!\cdots\!80\)\( T^{6} + \)\(27\!\cdots\!03\)\( T^{8} - \)\(23\!\cdots\!10\)\( T^{10} + \)\(10\!\cdots\!49\)\( T^{12} \))(\( 1 - 283211672 T^{2} + 48021567531024796 T^{4} - \)\(54\!\cdots\!84\)\( T^{6} + \)\(43\!\cdots\!06\)\( T^{8} - \)\(11\!\cdots\!16\)\( T^{10} + \)\(22\!\cdots\!96\)\( T^{12} - \)\(28\!\cdots\!28\)\( T^{14} + \)\(21\!\cdots\!01\)\( T^{16} \))(\( 1 - 780729368 T^{2} + 303614042895665980 T^{4} - \)\(75\!\cdots\!48\)\( T^{6} + \)\(13\!\cdots\!34\)\( T^{8} - \)\(16\!\cdots\!52\)\( T^{10} + \)\(14\!\cdots\!80\)\( T^{12} - \)\(78\!\cdots\!32\)\( T^{14} + \)\(21\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 624453080 T^{2} + 189664879587817660 T^{4} - \)\(38\!\cdots\!52\)\( T^{6} + \)\(61\!\cdots\!10\)\( T^{8} - \)\(83\!\cdots\!48\)\( T^{10} + \)\(88\!\cdots\!60\)\( T^{12} - \)\(63\!\cdots\!20\)\( T^{14} + \)\(21\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 1192764630 T^{2} + 663095466157584497 T^{4} - \)\(23\!\cdots\!36\)\( T^{6} + \)\(60\!\cdots\!88\)\( T^{8} - \)\(13\!\cdots\!92\)\( T^{10} + \)\(25\!\cdots\!56\)\( T^{12} - \)\(45\!\cdots\!88\)\( T^{14} + \)\(72\!\cdots\!54\)\( T^{16} - \)\(10\!\cdots\!08\)\( T^{18} + \)\(15\!\cdots\!46\)\( T^{20} - \)\(21\!\cdots\!88\)\( T^{22} + \)\(26\!\cdots\!44\)\( T^{24} - \)\(28\!\cdots\!92\)\( T^{26} + \)\(28\!\cdots\!12\)\( T^{28} - \)\(23\!\cdots\!36\)\( T^{30} + \)\(14\!\cdots\!53\)\( T^{32} - \)\(56\!\cdots\!30\)\( T^{34} + \)\(10\!\cdots\!49\)\( T^{36} \))(\( 1 - 1208126740 T^{2} + 787740581508660018 T^{4} - \)\(36\!\cdots\!96\)\( T^{6} + \)\(12\!\cdots\!73\)\( T^{8} - \)\(37\!\cdots\!80\)\( T^{10} + \)\(95\!\cdots\!40\)\( T^{12} - \)\(20\!\cdots\!56\)\( T^{14} + \)\(40\!\cdots\!70\)\( T^{16} - \)\(70\!\cdots\!00\)\( T^{18} + \)\(10\!\cdots\!96\)\( T^{20} - \)\(15\!\cdots\!00\)\( T^{22} + \)\(18\!\cdots\!70\)\( T^{24} - \)\(21\!\cdots\!44\)\( T^{26} + \)\(20\!\cdots\!40\)\( T^{28} - \)\(17\!\cdots\!20\)\( T^{30} + \)\(13\!\cdots\!73\)\( T^{32} - \)\(79\!\cdots\!04\)\( T^{34} + \)\(37\!\cdots\!18\)\( T^{36} - \)\(12\!\cdots\!60\)\( T^{38} + \)\(22\!\cdots\!01\)\( T^{40} \))
$47$ (\( 1 + 13480 T + 229345007 T^{2} \))(\( 1 - 9796 T + 229345007 T^{2} \))(\( 1 - 5960 T + 229345007 T^{2} \))(\( 1 + 14920 T + 229345007 T^{2} \))(\( 1 - 2200 T + 229345007 T^{2} \))(\( 1 - 28294 T + 229345007 T^{2} \))(\( 1 - 7960 T + 229345007 T^{2} \))(\( 1 - 13640 T + 229345007 T^{2} \))(\( 1 + 12074 T + 229345007 T^{2} \))(\( 1 + 15024 T + 178326558 T^{2} + 3445679385168 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 16728 T + 499568094 T^{2} - 3836483277096 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 2908 T + 56660030 T^{2} - 666935280356 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 15024 T + 178326558 T^{2} - 3445679385168 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 38232 T + 811508574 T^{2} + 8768318307624 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 8976 T + 403529613 T^{2} - 2395450153952 T^{3} + 92547501918192291 T^{4} - \)\(47\!\cdots\!24\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 + 8976 T + 403529613 T^{2} + 2395450153952 T^{3} + 92547501918192291 T^{4} + \)\(47\!\cdots\!24\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 - 288722058 T^{2} + 116437215277524783 T^{4} - \)\(17\!\cdots\!64\)\( T^{6} + \)\(61\!\cdots\!67\)\( T^{8} - \)\(79\!\cdots\!58\)\( T^{10} + \)\(14\!\cdots\!49\)\( T^{12} \))(\( 1 - 963352312 T^{2} + 473832864723586300 T^{4} - \)\(15\!\cdots\!72\)\( T^{6} + \)\(40\!\cdots\!54\)\( T^{8} - \)\(83\!\cdots\!28\)\( T^{10} + \)\(13\!\cdots\!00\)\( T^{12} - \)\(14\!\cdots\!88\)\( T^{14} + \)\(76\!\cdots\!01\)\( T^{16} \))(\( 1 - 948364072 T^{2} + 448732834702283644 T^{4} - \)\(14\!\cdots\!68\)\( T^{6} + \)\(38\!\cdots\!30\)\( T^{8} - \)\(78\!\cdots\!32\)\( T^{10} + \)\(12\!\cdots\!44\)\( T^{12} - \)\(13\!\cdots\!28\)\( T^{14} + \)\(76\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 1310013880 T^{2} + 842382244428730396 T^{4} - \)\(33\!\cdots\!60\)\( T^{6} + \)\(93\!\cdots\!06\)\( T^{8} - \)\(17\!\cdots\!40\)\( T^{10} + \)\(23\!\cdots\!96\)\( T^{12} - \)\(19\!\cdots\!20\)\( T^{14} + \)\(76\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 10604 T + 600456079 T^{2} + 135384893568 T^{3} + 106843221577975580 T^{4} - \)\(15\!\cdots\!76\)\( T^{5} + \)\(13\!\cdots\!84\)\( T^{6} - \)\(33\!\cdots\!72\)\( T^{7} + \)\(49\!\cdots\!10\)\( T^{8} - \)\(39\!\cdots\!16\)\( T^{9} + \)\(11\!\cdots\!70\)\( T^{10} - \)\(17\!\cdots\!28\)\( T^{11} + \)\(16\!\cdots\!12\)\( T^{12} - \)\(42\!\cdots\!76\)\( T^{13} + \)\(67\!\cdots\!60\)\( T^{14} + \)\(19\!\cdots\!32\)\( T^{15} + \)\(20\!\cdots\!97\)\( T^{16} + \)\(81\!\cdots\!04\)\( T^{17} + \)\(17\!\cdots\!07\)\( T^{18} )^{2} \))(\( ( 1 + 22090 T + 1548510076 T^{2} + 25779450599270 T^{3} + 1065218725316011845 T^{4} + \)\(14\!\cdots\!20\)\( T^{5} + \)\(45\!\cdots\!96\)\( T^{6} + \)\(51\!\cdots\!60\)\( T^{7} + \)\(14\!\cdots\!10\)\( T^{8} + \)\(14\!\cdots\!00\)\( T^{9} + \)\(36\!\cdots\!56\)\( T^{10} + \)\(32\!\cdots\!00\)\( T^{11} + \)\(76\!\cdots\!90\)\( T^{12} + \)\(62\!\cdots\!80\)\( T^{13} + \)\(12\!\cdots\!96\)\( T^{14} + \)\(90\!\cdots\!40\)\( T^{15} + \)\(15\!\cdots\!05\)\( T^{16} + \)\(86\!\cdots\!10\)\( T^{17} + \)\(11\!\cdots\!76\)\( T^{18} + \)\(38\!\cdots\!30\)\( T^{19} + \)\(40\!\cdots\!49\)\( T^{20} )^{2} \))
$53$ (\( 1 + 20598 T + 418195493 T^{2} \))(\( 1 - 31434 T + 418195493 T^{2} \))(\( 1 - 8698 T + 418195493 T^{2} \))(\( 1 + 38310 T + 418195493 T^{2} \))(\( 1 + 10122 T + 418195493 T^{2} \))(\( 1 - 13046 T + 418195493 T^{2} \))(\( 1 - 7590 T + 418195493 T^{2} \))(\( 1 + 19050 T + 418195493 T^{2} \))(\( 1 + 32586 T + 418195493 T^{2} \))(\( 1 + 1844 T + 311001070 T^{2} + 771152489092 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 31484 T + 851712526 T^{2} + 13166466901612 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 5412 T + 693247822 T^{2} - 2263274008116 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 1844 T + 311001070 T^{2} - 771152489092 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 24572 T + 952934926 T^{2} - 10275899653996 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 16098 T + 974021019 T^{2} - 9312300047724 T^{3} + 407331200233067367 T^{4} - \)\(28\!\cdots\!02\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( 1 + 16098 T + 974021019 T^{2} + 9312300047724 T^{3} + 407331200233067367 T^{4} + \)\(28\!\cdots\!02\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( 1 - 1963456710 T^{2} + 1786491383741543655 T^{4} - \)\(95\!\cdots\!64\)\( T^{6} + \)\(31\!\cdots\!95\)\( T^{8} - \)\(60\!\cdots\!10\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} \))(\( 1 - 1183385640 T^{2} + 874785099161623996 T^{4} - \)\(49\!\cdots\!80\)\( T^{6} + \)\(23\!\cdots\!06\)\( T^{8} - \)\(86\!\cdots\!20\)\( T^{10} + \)\(26\!\cdots\!96\)\( T^{12} - \)\(63\!\cdots\!60\)\( T^{14} + \)\(93\!\cdots\!01\)\( T^{16} \))(\( 1 - 383978028 T^{2} + 680329857618443044 T^{4} - \)\(19\!\cdots\!32\)\( T^{6} + \)\(17\!\cdots\!30\)\( T^{8} - \)\(34\!\cdots\!68\)\( T^{10} + \)\(20\!\cdots\!44\)\( T^{12} - \)\(20\!\cdots\!72\)\( T^{14} + \)\(93\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 2574268056 T^{2} + 3122678417422540348 T^{4} - \)\(23\!\cdots\!00\)\( T^{6} + \)\(11\!\cdots\!62\)\( T^{8} - \)\(40\!\cdots\!00\)\( T^{10} + \)\(95\!\cdots\!48\)\( T^{12} - \)\(13\!\cdots\!44\)\( T^{14} + \)\(93\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 2240205462 T^{2} + 2391370605827121969 T^{4} - \)\(16\!\cdots\!36\)\( T^{6} + \)\(94\!\cdots\!64\)\( T^{8} - \)\(48\!\cdots\!32\)\( T^{10} + \)\(23\!\cdots\!92\)\( T^{12} - \)\(11\!\cdots\!60\)\( T^{14} + \)\(55\!\cdots\!02\)\( T^{16} - \)\(24\!\cdots\!20\)\( T^{18} + \)\(97\!\cdots\!98\)\( T^{20} - \)\(35\!\cdots\!60\)\( T^{22} + \)\(12\!\cdots\!08\)\( T^{24} - \)\(45\!\cdots\!32\)\( T^{26} + \)\(15\!\cdots\!36\)\( T^{28} - \)\(48\!\cdots\!36\)\( T^{30} + \)\(11\!\cdots\!81\)\( T^{32} - \)\(19\!\cdots\!62\)\( T^{34} + \)\(15\!\cdots\!49\)\( T^{36} \))(\( 1 - 4003669356 T^{2} + 7954725909905649454 T^{4} - \)\(10\!\cdots\!60\)\( T^{6} + \)\(10\!\cdots\!77\)\( T^{8} - \)\(91\!\cdots\!76\)\( T^{10} + \)\(65\!\cdots\!16\)\( T^{12} - \)\(40\!\cdots\!80\)\( T^{14} + \)\(22\!\cdots\!54\)\( T^{16} - \)\(11\!\cdots\!56\)\( T^{18} + \)\(48\!\cdots\!96\)\( T^{20} - \)\(19\!\cdots\!44\)\( T^{22} + \)\(68\!\cdots\!54\)\( T^{24} - \)\(21\!\cdots\!20\)\( T^{26} + \)\(61\!\cdots\!16\)\( T^{28} - \)\(14\!\cdots\!24\)\( T^{30} + \)\(31\!\cdots\!77\)\( T^{32} - \)\(53\!\cdots\!40\)\( T^{34} + \)\(69\!\cdots\!54\)\( T^{36} - \)\(61\!\cdots\!44\)\( T^{38} + \)\(26\!\cdots\!01\)\( T^{40} \))
$59$ (\( 1 - 46756 T + 714924299 T^{2} \))(\( 1 + 33228 T + 714924299 T^{2} \))(\( 1 - 42036 T + 714924299 T^{2} \))(\( 1 + 11564 T + 714924299 T^{2} \))(\( 1 - 6776 T + 714924299 T^{2} \))(\( 1 - 37092 T + 714924299 T^{2} \))(\( 1 + 18064 T + 714924299 T^{2} \))(\( 1 - 18936 T + 714924299 T^{2} \))(\( 1 + 8668 T + 714924299 T^{2} \))(\( 1 - 12840 T + 732105634 T^{2} - 9179627999160 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 61464 T + 2273480806 T^{2} - 43942107113736 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 62584 T + 2277965606 T^{2} + 44742822328616 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 12840 T + 732105634 T^{2} + 9179627999160 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 5184 T + 1405691158 T^{2} + 3706167566016 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 23106 T + 1088276733 T^{2} - 11148915546724 T^{3} + 778035480458035167 T^{4} - \)\(11\!\cdots\!06\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( 1 + 23106 T + 1088276733 T^{2} + 11148915546724 T^{3} + 778035480458035167 T^{4} + \)\(11\!\cdots\!06\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( ( 1 - 5148 T + 597505773 T^{2} - 370643378904 T^{3} + 427171395910478127 T^{4} - \)\(26\!\cdots\!48\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} )^{2} \))(\( ( 1 + 45840 T + 3064286732 T^{2} + 94721285480976 T^{3} + 3348109683185502486 T^{4} + \)\(67\!\cdots\!24\)\( T^{5} + \)\(15\!\cdots\!32\)\( T^{6} + \)\(16\!\cdots\!60\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 43014 T + 3138923408 T^{2} - 85511244344238 T^{3} + 3396429745251891150 T^{4} - \)\(61\!\cdots\!62\)\( T^{5} + \)\(16\!\cdots\!08\)\( T^{6} - \)\(15\!\cdots\!86\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 3407992984 T^{2} + 4568722822719661756 T^{4} + \)\(32\!\cdots\!92\)\( T^{6} + \)\(19\!\cdots\!58\)\( T^{8} + \)\(16\!\cdots\!92\)\( T^{10} + \)\(11\!\cdots\!56\)\( T^{12} + \)\(45\!\cdots\!84\)\( T^{14} + \)\(68\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 3764975974 T^{2} + 7761343813098743249 T^{4} - \)\(11\!\cdots\!40\)\( T^{6} + \)\(12\!\cdots\!92\)\( T^{8} - \)\(11\!\cdots\!56\)\( T^{10} + \)\(95\!\cdots\!60\)\( T^{12} - \)\(69\!\cdots\!48\)\( T^{14} + \)\(47\!\cdots\!62\)\( T^{16} - \)\(32\!\cdots\!92\)\( T^{18} + \)\(24\!\cdots\!62\)\( T^{20} - \)\(18\!\cdots\!48\)\( T^{22} + \)\(12\!\cdots\!60\)\( T^{24} - \)\(80\!\cdots\!56\)\( T^{26} + \)\(44\!\cdots\!92\)\( T^{28} - \)\(19\!\cdots\!40\)\( T^{30} + \)\(70\!\cdots\!49\)\( T^{32} - \)\(17\!\cdots\!74\)\( T^{34} + \)\(23\!\cdots\!01\)\( T^{36} \))(\( 1 - 9996949828 T^{2} + 49650800837889885966 T^{4} - \)\(16\!\cdots\!20\)\( T^{6} + \)\(39\!\cdots\!17\)\( T^{8} - \)\(73\!\cdots\!28\)\( T^{10} + \)\(11\!\cdots\!44\)\( T^{12} - \)\(14\!\cdots\!80\)\( T^{14} + \)\(15\!\cdots\!54\)\( T^{16} - \)\(13\!\cdots\!88\)\( T^{18} + \)\(10\!\cdots\!24\)\( T^{20} - \)\(70\!\cdots\!88\)\( T^{22} + \)\(39\!\cdots\!54\)\( T^{24} - \)\(19\!\cdots\!80\)\( T^{26} + \)\(77\!\cdots\!44\)\( T^{28} - \)\(25\!\cdots\!28\)\( T^{30} + \)\(69\!\cdots\!17\)\( T^{32} - \)\(14\!\cdots\!20\)\( T^{34} + \)\(23\!\cdots\!66\)\( T^{36} - \)\(23\!\cdots\!28\)\( T^{38} + \)\(12\!\cdots\!01\)\( T^{40} \))
$61$ (\( 1 + 9602 T + 844596301 T^{2} \))(\( 1 + 40210 T + 844596301 T^{2} \))(\( 1 - 37518 T + 844596301 T^{2} \))(\( 1 + 48338 T + 844596301 T^{2} \))(\( 1 - 23398 T + 844596301 T^{2} \))(\( 1 - 39570 T + 844596301 T^{2} \))(\( 1 + 19658 T + 844596301 T^{2} \))(\( 1 + 1978 T + 844596301 T^{2} \))(\( 1 + 34670 T + 844596301 T^{2} \))(\( 1 + 24076 T + 1576248446 T^{2} + 20334500542876 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 51596 T + 2049215870 T^{2} - 43577790746396 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 14108 T + 1110042462 T^{2} - 11915564614508 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 24076 T + 1576248446 T^{2} + 20334500542876 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 53956 T + 1627858910 T^{2} + 45571038016756 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 51270 T + 2305394931 T^{2} - 70676310393124 T^{3} + 1947128031066750231 T^{4} - \)\(36\!\cdots\!70\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( 1 - 51270 T + 2305394931 T^{2} - 70676310393124 T^{3} + 1947128031066750231 T^{4} - \)\(36\!\cdots\!70\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( ( 1 + 26058 T + 886088883 T^{2} + 13089282520252 T^{3} + 748387392939021783 T^{4} + \)\(18\!\cdots\!58\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} )^{2} \))(\( ( 1 - 61928 T + 3903014764 T^{2} - 145287706763384 T^{3} + 5198153942066716726 T^{4} - \)\(12\!\cdots\!84\)\( T^{5} + \)\(27\!\cdots\!64\)\( T^{6} - \)\(37\!\cdots\!28\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 19480 T + 1818982540 T^{2} + 11177939991304 T^{3} + 1488458395242824950 T^{4} + \)\(94\!\cdots\!04\)\( T^{5} + \)\(12\!\cdots\!40\)\( T^{6} + \)\(11\!\cdots\!80\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 9032 T + 1492239052 T^{2} - 26562418349336 T^{3} + 1618346221688627830 T^{4} - \)\(22\!\cdots\!36\)\( T^{5} + \)\(10\!\cdots\!52\)\( T^{6} - \)\(54\!\cdots\!32\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} )^{4} \))(\( 1 - 7277488682 T^{2} + 27202119676896502657 T^{4} - \)\(69\!\cdots\!40\)\( T^{6} + \)\(13\!\cdots\!96\)\( T^{8} - \)\(20\!\cdots\!92\)\( T^{10} + \)\(27\!\cdots\!36\)\( T^{12} - \)\(30\!\cdots\!72\)\( T^{14} + \)\(30\!\cdots\!50\)\( T^{16} - \)\(27\!\cdots\!08\)\( T^{18} + \)\(21\!\cdots\!50\)\( T^{20} - \)\(15\!\cdots\!72\)\( T^{22} + \)\(98\!\cdots\!36\)\( T^{24} - \)\(53\!\cdots\!92\)\( T^{26} + \)\(24\!\cdots\!96\)\( T^{28} - \)\(91\!\cdots\!40\)\( T^{30} + \)\(25\!\cdots\!57\)\( T^{32} - \)\(48\!\cdots\!82\)\( T^{34} + \)\(47\!\cdots\!01\)\( T^{36} \))(\( 1 - 7152852348 T^{2} + 26523669582205677166 T^{4} - \)\(67\!\cdots\!00\)\( T^{6} + \)\(13\!\cdots\!17\)\( T^{8} - \)\(22\!\cdots\!48\)\( T^{10} + \)\(31\!\cdots\!84\)\( T^{12} - \)\(38\!\cdots\!60\)\( T^{14} + \)\(42\!\cdots\!14\)\( T^{16} - \)\(41\!\cdots\!08\)\( T^{18} + \)\(36\!\cdots\!64\)\( T^{20} - \)\(29\!\cdots\!08\)\( T^{22} + \)\(21\!\cdots\!14\)\( T^{24} - \)\(13\!\cdots\!60\)\( T^{26} + \)\(81\!\cdots\!84\)\( T^{28} - \)\(41\!\cdots\!48\)\( T^{30} + \)\(17\!\cdots\!17\)\( T^{32} - \)\(63\!\cdots\!00\)\( T^{34} + \)\(17\!\cdots\!66\)\( T^{36} - \)\(34\!\cdots\!48\)\( T^{38} + \)\(34\!\cdots\!01\)\( T^{40} \))
$67$ (\( 1 + 17404 T + 1350125107 T^{2} \))(\( 1 - 58864 T + 1350125107 T^{2} \))(\( 1 - 29324 T + 1350125107 T^{2} \))(\( 1 - 56972 T + 1350125107 T^{2} \))(\( 1 + 9676 T + 1350125107 T^{2} \))(\( 1 + 56734 T + 1350125107 T^{2} \))(\( 1 - 31868 T + 1350125107 T^{2} \))(\( 1 - 44212 T + 1350125107 T^{2} \))(\( 1 + 47566 T + 1350125107 T^{2} \))(\( 1 + 42240 T + 1422289750 T^{2} + 57029284519680 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 45816 T + 1490141302 T^{2} + 61857331902312 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 85412 T + 4371910566 T^{2} + 115316885639084 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 42240 T + 1422289750 T^{2} + 57029284519680 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 95160 T + 4779613558 T^{2} - 128477905182120 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 69084 T + 4950834057 T^{2} - 182092399391720 T^{3} + 6684245360946369099 T^{4} - \)\(12\!\cdots\!16\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( 1 - 69084 T + 4950834057 T^{2} - 182092399391720 T^{3} + 6684245360946369099 T^{4} - \)\(12\!\cdots\!16\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( 1 - 7507145634 T^{2} + 24155236685124504999 T^{4} - \)\(42\!\cdots\!84\)\( T^{6} + \)\(44\!\cdots\!51\)\( T^{8} - \)\(24\!\cdots\!34\)\( T^{10} + \)\(60\!\cdots\!49\)\( T^{12} \))(\( 1 - 9281919064 T^{2} + 39492482666681482588 T^{4} - \)\(10\!\cdots\!40\)\( T^{6} + \)\(16\!\cdots\!62\)\( T^{8} - \)\(18\!\cdots\!60\)\( T^{10} + \)\(13\!\cdots\!88\)\( T^{12} - \)\(56\!\cdots\!36\)\( T^{14} + \)\(11\!\cdots\!01\)\( T^{16} \))(\( 1 - 689670088 T^{2} + 6395411832810982876 T^{4} - \)\(31\!\cdots\!36\)\( T^{6} + \)\(16\!\cdots\!46\)\( T^{8} - \)\(56\!\cdots\!64\)\( T^{10} + \)\(21\!\cdots\!76\)\( T^{12} - \)\(41\!\cdots\!12\)\( T^{14} + \)\(11\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 4302504088 T^{2} + 12320798508402903676 T^{4} - \)\(23\!\cdots\!36\)\( T^{6} + \)\(36\!\cdots\!46\)\( T^{8} - \)\(43\!\cdots\!64\)\( T^{10} + \)\(40\!\cdots\!76\)\( T^{12} - \)\(26\!\cdots\!12\)\( T^{14} + \)\(11\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 18719793798 T^{2} + \)\(16\!\cdots\!17\)\( T^{4} - \)\(97\!\cdots\!44\)\( T^{6} + \)\(41\!\cdots\!36\)\( T^{8} - \)\(13\!\cdots\!16\)\( T^{10} + \)\(34\!\cdots\!48\)\( T^{12} - \)\(71\!\cdots\!12\)\( T^{14} + \)\(12\!\cdots\!98\)\( T^{16} - \)\(18\!\cdots\!60\)\( T^{18} + \)\(23\!\cdots\!02\)\( T^{20} - \)\(23\!\cdots\!12\)\( T^{22} + \)\(20\!\cdots\!52\)\( T^{24} - \)\(14\!\cdots\!16\)\( T^{26} + \)\(82\!\cdots\!64\)\( T^{28} - \)\(35\!\cdots\!44\)\( T^{30} + \)\(11\!\cdots\!33\)\( T^{32} - \)\(22\!\cdots\!98\)\( T^{34} + \)\(22\!\cdots\!49\)\( T^{36} \))(\( 1 - 11828518964 T^{2} + 68669252417166303634 T^{4} - \)\(26\!\cdots\!60\)\( T^{6} + \)\(76\!\cdots\!57\)\( T^{8} - \)\(18\!\cdots\!04\)\( T^{10} + \)\(38\!\cdots\!16\)\( T^{12} - \)\(70\!\cdots\!40\)\( T^{14} + \)\(11\!\cdots\!54\)\( T^{16} - \)\(18\!\cdots\!64\)\( T^{18} + \)\(25\!\cdots\!76\)\( T^{20} - \)\(33\!\cdots\!36\)\( T^{22} + \)\(39\!\cdots\!54\)\( T^{24} - \)\(42\!\cdots\!60\)\( T^{26} + \)\(42\!\cdots\!16\)\( T^{28} - \)\(36\!\cdots\!96\)\( T^{30} + \)\(28\!\cdots\!57\)\( T^{32} - \)\(17\!\cdots\!40\)\( T^{34} + \)\(83\!\cdots\!34\)\( T^{36} - \)\(26\!\cdots\!36\)\( T^{38} + \)\(40\!\cdots\!01\)\( T^{40} \))
$71$ (\( 1 + 26568 T + 1804229351 T^{2} \))(\( 1 - 55312 T + 1804229351 T^{2} \))(\( 1 + 84408 T + 1804229351 T^{2} \))(\( 1 + 44856 T + 1804229351 T^{2} \))(\( 1 + 13728 T + 1804229351 T^{2} \))(\( 1 + 45588 T + 1804229351 T^{2} \))(\( 1 + 57216 T + 1804229351 T^{2} \))(\( 1 - 59744 T + 1804229351 T^{2} \))(\( 1 + 948 T + 1804229351 T^{2} \))(\( 1 - 12880 T + 3454118398 T^{2} - 23238474040880 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 97456 T + 5874446350 T^{2} - 175832975631056 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 47208 T + 4011779662 T^{2} + 85174059202008 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 12880 T + 3454118398 T^{2} + 23238474040880 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 71552 T + 3857659342 T^{2} - 129096218522752 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 55932 T + 3009690789 T^{2} - 141554371038216 T^{3} + 5430172458948147939 T^{4} - \)\(18\!\cdots\!32\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( 1 + 55932 T + 3009690789 T^{2} + 141554371038216 T^{3} + 5430172458948147939 T^{4} + \)\(18\!\cdots\!32\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( ( 1 - 14144 T + 2246377637 T^{2} - 13852014127488 T^{3} + 4052980466105423587 T^{4} - \)\(46\!\cdots\!44\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 - 62816 T + 3398787356 T^{2} - 184024084124896 T^{3} + 8353296562609817510 T^{4} - \)\(33\!\cdots\!96\)\( T^{5} + \)\(11\!\cdots\!56\)\( T^{6} - \)\(36\!\cdots\!16\)\( T^{7} + \)\(10\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 81036 T + 8128543116 T^{2} + 379257248199228 T^{3} + 21602305876831289798 T^{4} + \)\(68\!\cdots\!28\)\( T^{5} + \)\(26\!\cdots\!16\)\( T^{6} + \)\(47\!\cdots\!36\)\( T^{7} + \)\(10\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 2871156792 T^{2} + 5431095844251854428 T^{4} + \)\(74\!\cdots\!44\)\( T^{6} + \)\(66\!\cdots\!70\)\( T^{8} + \)\(24\!\cdots\!44\)\( T^{10} + \)\(57\!\cdots\!28\)\( T^{12} + \)\(99\!\cdots\!92\)\( T^{14} + \)\(11\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 100156 T + 16182553631 T^{2} + 1230069155511584 T^{3} + \)\(11\!\cdots\!28\)\( T^{4} + \)\(69\!\cdots\!52\)\( T^{5} + \)\(46\!\cdots\!52\)\( T^{6} + \)\(23\!\cdots\!36\)\( T^{7} + \)\(12\!\cdots\!26\)\( T^{8} + \)\(51\!\cdots\!20\)\( T^{9} + \)\(22\!\cdots\!26\)\( T^{10} + \)\(76\!\cdots\!36\)\( T^{11} + \)\(27\!\cdots\!52\)\( T^{12} + \)\(73\!\cdots\!52\)\( T^{13} + \)\(21\!\cdots\!28\)\( T^{14} + \)\(42\!\cdots\!84\)\( T^{15} + \)\(10\!\cdots\!81\)\( T^{16} + \)\(11\!\cdots\!56\)\( T^{17} + \)\(20\!\cdots\!51\)\( T^{18} )^{2} \))(\( ( 1 - 100156 T + 13448448446 T^{2} - 957445823975748 T^{3} + 76873855601451932317 T^{4} - \)\(43\!\cdots\!20\)\( T^{5} + \)\(26\!\cdots\!28\)\( T^{6} - \)\(12\!\cdots\!92\)\( T^{7} + \)\(67\!\cdots\!74\)\( T^{8} - \)\(28\!\cdots\!84\)\( T^{9} + \)\(13\!\cdots\!68\)\( T^{10} - \)\(51\!\cdots\!84\)\( T^{11} + \)\(21\!\cdots\!74\)\( T^{12} - \)\(74\!\cdots\!92\)\( T^{13} + \)\(28\!\cdots\!28\)\( T^{14} - \)\(82\!\cdots\!20\)\( T^{15} + \)\(26\!\cdots\!17\)\( T^{16} - \)\(59\!\cdots\!48\)\( T^{17} + \)\(15\!\cdots\!46\)\( T^{18} - \)\(20\!\cdots\!56\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} )^{2} \))
$73$ (\( 1 - 75450 T + 2073071593 T^{2} \))(\( 1 - 27258 T + 2073071593 T^{2} \))(\( 1 + 46550 T + 2073071593 T^{2} \))(\( 1 + 19446 T + 2073071593 T^{2} \))(\( 1 + 27390 T + 2073071593 T^{2} \))(\( 1 - 11842 T + 2073071593 T^{2} \))(\( 1 - 9906 T + 2073071593 T^{2} \))(\( 1 - 56994 T + 2073071593 T^{2} \))(\( 1 + 63102 T + 2073071593 T^{2} \))(\( 1 + 96260 T + 5679384470 T^{2} + 199553871542180 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 58852 T + 4427698262 T^{2} - 122004409391236 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 67452 T + 4400780438 T^{2} + 139832825091036 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 96260 T + 5679384470 T^{2} + 199553871542180 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 96236 T + 6445380086 T^{2} + 199504117823948 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 100914 T + 9222632103 T^{2} - 440423264194140 T^{3} + 19119176625419150079 T^{4} - \)\(43\!\cdots\!86\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( 1 - 100914 T + 9222632103 T^{2} - 440423264194140 T^{3} + 19119176625419150079 T^{4} - \)\(43\!\cdots\!86\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( 1 - 2138297622 T^{2} + 9645229369668502143 T^{4} - \)\(18\!\cdots\!56\)\( T^{6} + \)\(41\!\cdots\!07\)\( T^{8} - \)\(39\!\cdots\!22\)\( T^{10} + \)\(79\!\cdots\!49\)\( T^{12} \))(\( 1 - 9140679496 T^{2} + 46078306824990298588 T^{4} - \)\(15\!\cdots\!60\)\( T^{6} + \)\(37\!\cdots\!02\)\( T^{8} - \)\(66\!\cdots\!40\)\( T^{10} + \)\(85\!\cdots\!88\)\( T^{12} - \)\(72\!\cdots\!04\)\( T^{14} + \)\(34\!\cdots\!01\)\( T^{16} \))(\( 1 - 11933853400 T^{2} + 67221911930035246396 T^{4} - \)\(23\!\cdots\!00\)\( T^{6} + \)\(58\!\cdots\!06\)\( T^{8} - \)\(10\!\cdots\!00\)\( T^{10} + \)\(12\!\cdots\!96\)\( T^{12} - \)\(94\!\cdots\!00\)\( T^{14} + \)\(34\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 4559473480 T^{2} + 20323547981168722396 T^{4} - \)\(57\!\cdots\!60\)\( T^{6} + \)\(13\!\cdots\!06\)\( T^{8} - \)\(24\!\cdots\!40\)\( T^{10} + \)\(37\!\cdots\!96\)\( T^{12} - \)\(36\!\cdots\!20\)\( T^{14} + \)\(34\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 100890 T + 17920655937 T^{2} - 1400613951954800 T^{3} + \)\(14\!\cdots\!68\)\( T^{4} - \)\(90\!\cdots\!60\)\( T^{5} + \)\(67\!\cdots\!44\)\( T^{6} - \)\(35\!\cdots\!40\)\( T^{7} + \)\(20\!\cdots\!74\)\( T^{8} - \)\(88\!\cdots\!80\)\( T^{9} + \)\(43\!\cdots\!82\)\( T^{10} - \)\(15\!\cdots\!60\)\( T^{11} + \)\(60\!\cdots\!08\)\( T^{12} - \)\(16\!\cdots\!60\)\( T^{13} + \)\(55\!\cdots\!24\)\( T^{14} - \)\(11\!\cdots\!00\)\( T^{15} + \)\(29\!\cdots\!09\)\( T^{16} - \)\(34\!\cdots\!90\)\( T^{17} + \)\(70\!\cdots\!93\)\( T^{18} )^{2} \))(\( ( 1 + 52568 T + 9379342894 T^{2} + 374528688123736 T^{3} + 37721970904921608509 T^{4} + \)\(11\!\cdots\!56\)\( T^{5} + \)\(82\!\cdots\!04\)\( T^{6} + \)\(19\!\cdots\!04\)\( T^{7} + \)\(11\!\cdots\!58\)\( T^{8} + \)\(24\!\cdots\!96\)\( T^{9} + \)\(16\!\cdots\!04\)\( T^{10} + \)\(51\!\cdots\!28\)\( T^{11} + \)\(49\!\cdots\!42\)\( T^{12} + \)\(17\!\cdots\!28\)\( T^{13} + \)\(15\!\cdots\!04\)\( T^{14} + \)\(44\!\cdots\!08\)\( T^{15} + \)\(29\!\cdots\!41\)\( T^{16} + \)\(61\!\cdots\!52\)\( T^{17} + \)\(31\!\cdots\!94\)\( T^{18} + \)\(37\!\cdots\!24\)\( T^{19} + \)\(14\!\cdots\!49\)\( T^{20} )^{2} \))
$79$ (\( 1 - 50472 T + 3077056399 T^{2} \))(\( 1 - 31456 T + 3077056399 T^{2} \))(\( 1 - 26752 T + 3077056399 T^{2} \))(\( 1 + 77328 T + 3077056399 T^{2} \))(\( 1 + 93288 T + 3077056399 T^{2} \))(\( 1 - 94216 T + 3077056399 T^{2} \))(\( 1 - 7872 T + 3077056399 T^{2} \))(\( 1 + 15128 T + 3077056399 T^{2} \))(\( 1 - 46536 T + 3077056399 T^{2} \))(\( 1 + 89896 T + 6990395502 T^{2} + 276615062044504 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 116776 T + 8933123742 T^{2} + 359326338049624 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 65904 T + 3994274078 T^{2} + 202790324919696 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 89896 T + 6990395502 T^{2} + 276615062044504 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 29288 T + 5671921950 T^{2} - 90120827813912 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 159492 T + 15447781533 T^{2} - 970158382454328 T^{3} + 47533695016471679667 T^{4} - \)\(15\!\cdots\!92\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( 1 - 159492 T + 15447781533 T^{2} - 970158382454328 T^{3} + 47533695016471679667 T^{4} - \)\(15\!\cdots\!92\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( ( 1 - 110100 T + 12028730445 T^{2} - 673264081259096 T^{3} + 37013081987633367555 T^{4} - \)\(10\!\cdots\!00\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} )^{2} \))(\( ( 1 - 21632 T + 7152876604 T^{2} - 332616618908288 T^{3} + 24121899620797566790 T^{4} - \)\(10\!\cdots\!12\)\( T^{5} + \)\(67\!\cdots\!04\)\( T^{6} - \)\(63\!\cdots\!68\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 84988 T + 5906431900 T^{2} + 410334793182028 T^{3} + 30047763404998661254 T^{4} + \)\(12\!\cdots\!72\)\( T^{5} + \)\(55\!\cdots\!00\)\( T^{6} + \)\(24\!\cdots\!12\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 8576 T + 5537482876 T^{2} - 173910727899008 T^{3} + 17190185901357317830 T^{4} - \)\(53\!\cdots\!92\)\( T^{5} + \)\(52\!\cdots\!76\)\( T^{6} - \)\(24\!\cdots\!24\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} )^{4} \))(\( ( 1 - 28530 T + 10831868831 T^{2} - 10488896625888 T^{3} + 58748015931898431500 T^{4} + \)\(66\!\cdots\!28\)\( T^{5} + \)\(27\!\cdots\!40\)\( T^{6} + \)\(29\!\cdots\!44\)\( T^{7} + \)\(10\!\cdots\!94\)\( T^{8} + \)\(10\!\cdots\!92\)\( T^{9} + \)\(32\!\cdots\!06\)\( T^{10} + \)\(28\!\cdots\!44\)\( T^{11} + \)\(80\!\cdots\!60\)\( T^{12} + \)\(59\!\cdots\!28\)\( T^{13} + \)\(16\!\cdots\!00\)\( T^{14} - \)\(89\!\cdots\!88\)\( T^{15} + \)\(28\!\cdots\!69\)\( T^{16} - \)\(22\!\cdots\!30\)\( T^{17} + \)\(24\!\cdots\!99\)\( T^{18} )^{2} \))(\( ( 1 - 141040 T + 30508439526 T^{2} - 3027236690742416 T^{3} + \)\(38\!\cdots\!93\)\( T^{4} - \)\(29\!\cdots\!88\)\( T^{5} + \)\(27\!\cdots\!48\)\( T^{6} - \)\(17\!\cdots\!16\)\( T^{7} + \)\(13\!\cdots\!30\)\( T^{8} - \)\(73\!\cdots\!40\)\( T^{9} + \)\(47\!\cdots\!04\)\( T^{10} - \)\(22\!\cdots\!60\)\( T^{11} + \)\(12\!\cdots\!30\)\( T^{12} - \)\(51\!\cdots\!84\)\( T^{13} + \)\(24\!\cdots\!48\)\( T^{14} - \)\(81\!\cdots\!12\)\( T^{15} + \)\(32\!\cdots\!93\)\( T^{16} - \)\(79\!\cdots\!84\)\( T^{17} + \)\(24\!\cdots\!26\)\( T^{18} - \)\(34\!\cdots\!60\)\( T^{19} + \)\(76\!\cdots\!01\)\( T^{20} )^{2} \))
$83$ (\( 1 + 33236 T + 3939040643 T^{2} \))(\( 1 + 24552 T + 3939040643 T^{2} \))(\( 1 - 7956 T + 3939040643 T^{2} \))(\( 1 + 40364 T + 3939040643 T^{2} \))(\( 1 - 23276 T + 3939040643 T^{2} \))(\( 1 - 31482 T + 3939040643 T^{2} \))(\( 1 + 109996 T + 3939040643 T^{2} \))(\( 1 - 21996 T + 3939040643 T^{2} \))(\( 1 - 88778 T + 3939040643 T^{2} \))(\( 1 - 57024 T + 8584451830 T^{2} - 224619853626432 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 136632 T + 12540178198 T^{2} - 538199001134376 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 108724 T + 10572459494 T^{2} + 428268254869532 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 57024 T + 8584451830 T^{2} + 224619853626432 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 143016 T + 12113227414 T^{2} - 563345836599288 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 16428 T + 4008885369 T^{2} + 134680015872584 T^{3} + 15791162401619052267 T^{4} + \)\(25\!\cdots\!72\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 - 16428 T + 4008885369 T^{2} - 134680015872584 T^{3} + 15791162401619052267 T^{4} - \)\(25\!\cdots\!72\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 - 5878219362 T^{2} + 30391064056477835847 T^{4} - \)\(17\!\cdots\!76\)\( T^{6} + \)\(47\!\cdots\!03\)\( T^{8} - \)\(14\!\cdots\!62\)\( T^{10} + \)\(37\!\cdots\!49\)\( T^{12} \))(\( 1 - 6759897816 T^{2} + 40943120759345365468 T^{4} - \)\(86\!\cdots\!80\)\( T^{6} + \)\(39\!\cdots\!42\)\( T^{8} - \)\(13\!\cdots\!20\)\( T^{10} + \)\(98\!\cdots\!68\)\( T^{12} - \)\(25\!\cdots\!84\)\( T^{14} + \)\(57\!\cdots\!01\)\( T^{16} \))(\( 1 - 21233018712 T^{2} + \)\(22\!\cdots\!96\)\( T^{4} - \)\(15\!\cdots\!64\)\( T^{6} + \)\(70\!\cdots\!06\)\( T^{8} - \)\(23\!\cdots\!36\)\( T^{10} + \)\(53\!\cdots\!96\)\( T^{12} - \)\(79\!\cdots\!88\)\( T^{14} + \)\(57\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 26022519576 T^{2} + \)\(31\!\cdots\!88\)\( T^{4} - \)\(22\!\cdots\!60\)\( T^{6} + \)\(10\!\cdots\!22\)\( T^{8} - \)\(34\!\cdots\!40\)\( T^{10} + \)\(74\!\cdots\!88\)\( T^{12} - \)\(97\!\cdots\!24\)\( T^{14} + \)\(57\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 24696311158 T^{2} + \)\(33\!\cdots\!25\)\( T^{4} - \)\(32\!\cdots\!12\)\( T^{6} + \)\(24\!\cdots\!64\)\( T^{8} - \)\(16\!\cdots\!04\)\( T^{10} + \)\(90\!\cdots\!20\)\( T^{12} - \)\(45\!\cdots\!64\)\( T^{14} + \)\(20\!\cdots\!66\)\( T^{16} - \)\(85\!\cdots\!24\)\( T^{18} + \)\(32\!\cdots\!34\)\( T^{20} - \)\(10\!\cdots\!64\)\( T^{22} + \)\(33\!\cdots\!80\)\( T^{24} - \)\(92\!\cdots\!04\)\( T^{26} + \)\(22\!\cdots\!36\)\( T^{28} - \)\(45\!\cdots\!12\)\( T^{30} + \)\(72\!\cdots\!25\)\( T^{32} - \)\(82\!\cdots\!58\)\( T^{34} + \)\(52\!\cdots\!49\)\( T^{36} \))(\( 1 - 34768653380 T^{2} + \)\(55\!\cdots\!58\)\( T^{4} - \)\(53\!\cdots\!56\)\( T^{6} + \)\(34\!\cdots\!33\)\( T^{8} - \)\(15\!\cdots\!20\)\( T^{10} + \)\(44\!\cdots\!40\)\( T^{12} - \)\(24\!\cdots\!36\)\( T^{14} - \)\(64\!\cdots\!10\)\( T^{16} + \)\(49\!\cdots\!20\)\( T^{18} - \)\(23\!\cdots\!44\)\( T^{20} + \)\(76\!\cdots\!80\)\( T^{22} - \)\(15\!\cdots\!10\)\( T^{24} - \)\(90\!\cdots\!64\)\( T^{26} + \)\(25\!\cdots\!40\)\( T^{28} - \)\(14\!\cdots\!80\)\( T^{30} + \)\(48\!\cdots\!33\)\( T^{32} - \)\(11\!\cdots\!44\)\( T^{34} + \)\(18\!\cdots\!58\)\( T^{36} - \)\(18\!\cdots\!20\)\( T^{38} + \)\(80\!\cdots\!01\)\( T^{40} \))
$89$ (\( 1 + 133194 T + 5584059449 T^{2} \))(\( 1 - 90854 T + 5584059449 T^{2} \))(\( 1 + 59674 T + 5584059449 T^{2} \))(\( 1 + 35706 T + 5584059449 T^{2} \))(\( 1 + 102354 T + 5584059449 T^{2} \))(\( 1 - 94054 T + 5584059449 T^{2} \))(\( 1 + 62466 T + 5584059449 T^{2} \))(\( 1 + 14066 T + 5584059449 T^{2} \))(\( 1 - 104934 T + 5584059449 T^{2} \))(\( 1 - 25240 T + 10143343298 T^{2} - 140941660492760 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 124924 T + 13365576758 T^{2} - 697583042606876 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 55020 T + 10818978262 T^{2} - 307234950883980 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 25240 T + 10143343298 T^{2} + 140941660492760 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 139724 T + 16006792406 T^{2} - 780227122452076 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 120852 T + 12302174427 T^{2} + 1026615424009896 T^{3} + 68696073352335510723 T^{4} + \)\(37\!\cdots\!52\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( 1 - 120852 T + 12302174427 T^{2} - 1026615424009896 T^{3} + 68696073352335510723 T^{4} - \)\(37\!\cdots\!52\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( ( 1 + 175710 T + 24190100439 T^{2} + 1951044010529988 T^{3} + \)\(13\!\cdots\!11\)\( T^{4} + \)\(54\!\cdots\!10\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 - 20952 T + 16118164796 T^{2} - 497915996461992 T^{3} + \)\(11\!\cdots\!30\)\( T^{4} - \)\(27\!\cdots\!08\)\( T^{5} + \)\(50\!\cdots\!96\)\( T^{6} - \)\(36\!\cdots\!48\)\( T^{7} + \)\(97\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 226488 T + 18828868604 T^{2} - 357850805109192 T^{3} - 29854343234341882650 T^{4} - \)\(19\!\cdots\!08\)\( T^{5} + \)\(58\!\cdots\!04\)\( T^{6} - \)\(39\!\cdots\!12\)\( T^{7} + \)\(97\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 10511122888 T^{2} + 32812007833496994652 T^{4} - \)\(11\!\cdots\!16\)\( T^{6} - \)\(28\!\cdots\!50\)\( T^{8} - \)\(34\!\cdots\!16\)\( T^{10} + \)\(31\!\cdots\!52\)\( T^{12} + \)\(31\!\cdots\!88\)\( T^{14} + \)\(94\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 110894 T + 30658222193 T^{2} + 2258172211882768 T^{3} + \)\(40\!\cdots\!56\)\( T^{4} + \)\(21\!\cdots\!88\)\( T^{5} + \)\(32\!\cdots\!52\)\( T^{6} + \)\(12\!\cdots\!96\)\( T^{7} + \)\(20\!\cdots\!54\)\( T^{8} + \)\(69\!\cdots\!08\)\( T^{9} + \)\(11\!\cdots\!46\)\( T^{10} + \)\(40\!\cdots\!96\)\( T^{11} + \)\(57\!\cdots\!48\)\( T^{12} + \)\(20\!\cdots\!88\)\( T^{13} + \)\(21\!\cdots\!44\)\( T^{14} + \)\(68\!\cdots\!68\)\( T^{15} + \)\(51\!\cdots\!57\)\( T^{16} + \)\(10\!\cdots\!94\)\( T^{17} + \)\(52\!\cdots\!49\)\( T^{18} )^{2} \))(\( ( 1 - 1580 T + 27398194046 T^{2} - 460040940498284 T^{3} + \)\(38\!\cdots\!93\)\( T^{4} - \)\(90\!\cdots\!72\)\( T^{5} + \)\(38\!\cdots\!08\)\( T^{6} - \)\(95\!\cdots\!24\)\( T^{7} + \)\(29\!\cdots\!70\)\( T^{8} - \)\(73\!\cdots\!60\)\( T^{9} + \)\(18\!\cdots\!64\)\( T^{10} - \)\(40\!\cdots\!40\)\( T^{11} + \)\(91\!\cdots\!70\)\( T^{12} - \)\(16\!\cdots\!76\)\( T^{13} + \)\(37\!\cdots\!08\)\( T^{14} - \)\(49\!\cdots\!28\)\( T^{15} + \)\(11\!\cdots\!93\)\( T^{16} - \)\(77\!\cdots\!16\)\( T^{17} + \)\(25\!\cdots\!46\)\( T^{18} - \)\(83\!\cdots\!20\)\( T^{19} + \)\(29\!\cdots\!01\)\( T^{20} )^{2} \))
$97$ (\( 1 + 42878 T + 8587340257 T^{2} \))(\( 1 - 154706 T + 8587340257 T^{2} \))(\( 1 - 136898 T + 8587340257 T^{2} \))(\( 1 + 97022 T + 8587340257 T^{2} \))(\( 1 + 49502 T + 8587340257 T^{2} \))(\( 1 - 23714 T + 8587340257 T^{2} \))(\( 1 + 97598 T + 8587340257 T^{2} \))(\( 1 - 75938 T + 8587340257 T^{2} \))(\( 1 + 36254 T + 8587340257 T^{2} \))(\( 1 + 229100 T + 28475803110 T^{2} + 1967359652878700 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 39260 T + 9987043590 T^{2} + 337138978489820 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 147668 T + 11612429670 T^{2} - 1268075361070676 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 229100 T + 28475803110 T^{2} + 1967359652878700 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 36860 T + 14824711110 T^{2} + 316529361873020 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 223734 T + 38248594287 T^{2} - 3912864163619380 T^{3} + \)\(32\!\cdots\!59\)\( T^{4} - \)\(16\!\cdots\!66\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( 1 - 223734 T + 38248594287 T^{2} - 3912864163619380 T^{3} + \)\(32\!\cdots\!59\)\( T^{4} - \)\(16\!\cdots\!66\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( 1 - 18122177670 T^{2} + \)\(22\!\cdots\!47\)\( T^{4} - \)\(21\!\cdots\!60\)\( T^{6} + \)\(16\!\cdots\!03\)\( T^{8} - \)\(98\!\cdots\!70\)\( T^{10} + \)\(40\!\cdots\!49\)\( T^{12} \))(\( 1 - 45263915272 T^{2} + \)\(10\!\cdots\!40\)\( T^{4} - \)\(14\!\cdots\!12\)\( T^{6} + \)\(15\!\cdots\!94\)\( T^{8} - \)\(11\!\cdots\!88\)\( T^{10} + \)\(55\!\cdots\!40\)\( T^{12} - \)\(18\!\cdots\!28\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} \))(\( 1 - 58225283080 T^{2} + \)\(15\!\cdots\!96\)\( T^{4} - \)\(24\!\cdots\!60\)\( T^{6} + \)\(25\!\cdots\!06\)\( T^{8} - \)\(18\!\cdots\!40\)\( T^{10} + \)\(84\!\cdots\!96\)\( T^{12} - \)\(23\!\cdots\!20\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} \))(\( ( 1 + 2457095672 T^{2} + \)\(27\!\cdots\!16\)\( T^{4} + \)\(49\!\cdots\!84\)\( T^{6} + \)\(29\!\cdots\!66\)\( T^{8} + \)\(36\!\cdots\!16\)\( T^{10} + \)\(14\!\cdots\!16\)\( T^{12} + \)\(98\!\cdots\!28\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 168570 T + 60455638553 T^{2} + 7637493399918000 T^{3} + \)\(15\!\cdots\!04\)\( T^{4} + \)\(15\!\cdots\!40\)\( T^{5} + \)\(23\!\cdots\!44\)\( T^{6} + \)\(20\!\cdots\!60\)\( T^{7} + \)\(26\!\cdots\!34\)\( T^{8} + \)\(19\!\cdots\!60\)\( T^{9} + \)\(22\!\cdots\!38\)\( T^{10} + \)\(14\!\cdots\!40\)\( T^{11} + \)\(15\!\cdots\!92\)\( T^{12} + \)\(84\!\cdots\!40\)\( T^{13} + \)\(72\!\cdots\!28\)\( T^{14} + \)\(30\!\cdots\!00\)\( T^{15} + \)\(20\!\cdots\!29\)\( T^{16} + \)\(49\!\cdots\!70\)\( T^{17} + \)\(25\!\cdots\!57\)\( T^{18} )^{2} \))(\( ( 1 - 73688 T + 43672916862 T^{2} - 2817316775448856 T^{3} + \)\(98\!\cdots\!25\)\( T^{4} - \)\(59\!\cdots\!28\)\( T^{5} + \)\(15\!\cdots\!52\)\( T^{6} - \)\(87\!\cdots\!16\)\( T^{7} + \)\(18\!\cdots\!70\)\( T^{8} - \)\(96\!\cdots\!88\)\( T^{9} + \)\(17\!\cdots\!72\)\( T^{10} - \)\(82\!\cdots\!16\)\( T^{11} + \)\(13\!\cdots\!30\)\( T^{12} - \)\(55\!\cdots\!88\)\( T^{13} + \)\(84\!\cdots\!52\)\( T^{14} - \)\(27\!\cdots\!96\)\( T^{15} + \)\(39\!\cdots\!25\)\( T^{16} - \)\(97\!\cdots\!08\)\( T^{17} + \)\(12\!\cdots\!62\)\( T^{18} - \)\(18\!\cdots\!16\)\( T^{19} + \)\(21\!\cdots\!49\)\( T^{20} )^{2} \))
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