Properties

Label 387.3
Level 387
Weight 3
Dimension 8585
Nonzero newspaces 20
Newform subspaces 36
Sturm bound 33264
Trace bound 5

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 387\( 387 = 3^{2} \cdot 43 \) \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 36 \)
Sturm bound: \(33264\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(387))\).

Total New Old
Modular forms 11424 8955 2469
Cusp forms 10752 8585 2167
Eisenstein series 672 370 302

Trace form

\( 8585q - 57q^{2} - 78q^{3} - 61q^{4} - 75q^{5} - 102q^{6} - 59q^{7} - 63q^{8} - 66q^{9} + O(q^{10}) \) \( 8585q - 57q^{2} - 78q^{3} - 61q^{4} - 75q^{5} - 102q^{6} - 59q^{7} - 63q^{8} - 66q^{9} - 165q^{10} - 57q^{11} - 96q^{12} - 71q^{13} - 75q^{14} - 84q^{15} - 85q^{16} - 63q^{17} - 84q^{18} - 233q^{19} - 51q^{20} - 72q^{21} - 69q^{22} + 33q^{23} + 6q^{24} - 37q^{25} - 63q^{26} - 192q^{27} - 197q^{28} - 219q^{29} - 120q^{30} + 78q^{31} + 303q^{32} - 102q^{33} + 495q^{34} + 231q^{35} - 66q^{36} + 157q^{37} + 339q^{38} - 36q^{39} + 213q^{40} - 84q^{42} - 229q^{43} - 294q^{44} + 24q^{45} - 717q^{46} - 150q^{48} - 496q^{49} - 813q^{50} - 246q^{51} - 1191q^{52} - 525q^{53} + 78q^{54} - 711q^{55} - 591q^{56} - 18q^{57} + 93q^{58} - 237q^{59} - 120q^{60} + 49q^{61} - 63q^{62} - 156q^{63} + 95q^{64} - 111q^{65} - 48q^{66} - 125q^{67} - 9q^{68} - 84q^{69} + 1173q^{70} + 525q^{71} - 354q^{72} + 55q^{73} + 1350q^{74} - 6q^{75} + 1282q^{76} + 933q^{77} - 156q^{78} + 517q^{79} + 777q^{80} + 78q^{81} + 357q^{82} + 273q^{83} - 240q^{84} + 66q^{85} - 48q^{86} + 300q^{87} - 681q^{88} - 399q^{89} - 192q^{90} - 661q^{91} - 1629q^{92} - 468q^{93} - 1743q^{94} - 1035q^{95} - 84q^{96} - 1805q^{97} - 1974q^{98} - 84q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(387))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
387.3.b \(\chi_{387}(343, \cdot)\) 387.3.b.a 1 1
387.3.b.b 2
387.3.b.c 6
387.3.b.d 12
387.3.b.e 14
387.3.c \(\chi_{387}(44, \cdot)\) 387.3.c.a 28 1
387.3.i \(\chi_{387}(251, \cdot)\) 387.3.i.a 60 2
387.3.j \(\chi_{387}(37, \cdot)\) 387.3.j.a 2 2
387.3.j.b 2
387.3.j.c 12
387.3.j.d 14
387.3.j.e 14
387.3.j.f 28
387.3.n \(\chi_{387}(265, \cdot)\) 387.3.n.a 172 2
387.3.o \(\chi_{387}(92, \cdot)\) 387.3.o.a 172 2
387.3.p \(\chi_{387}(221, \cdot)\) 387.3.p.a 172 2
387.3.q \(\chi_{387}(173, \cdot)\) 387.3.q.a 168 2
387.3.r \(\chi_{387}(7, \cdot)\) 387.3.r.a 172 2
387.3.s \(\chi_{387}(85, \cdot)\) 387.3.s.a 172 2
387.3.w \(\chi_{387}(82, \cdot)\) 387.3.w.a 12 6
387.3.w.b 42
387.3.w.c 72
387.3.w.d 84
387.3.x \(\chi_{387}(35, \cdot)\) 387.3.x.a 168 6
387.3.bd \(\chi_{387}(11, \cdot)\) 387.3.bd.a 1032 12
387.3.be \(\chi_{387}(23, \cdot)\) 387.3.be.a 1032 12
387.3.bf \(\chi_{387}(22, \cdot)\) 387.3.bf.a 1032 12
387.3.bg \(\chi_{387}(34, \cdot)\) 387.3.bg.a 1032 12
387.3.bh \(\chi_{387}(106, \cdot)\) 387.3.bh.a 1032 12
387.3.bi \(\chi_{387}(14, \cdot)\) 387.3.bi.a 1032 12
387.3.bm \(\chi_{387}(17, \cdot)\) 387.3.bm.a 360 12
387.3.bn \(\chi_{387}(19, \cdot)\) 387.3.bn.a 12 12
387.3.bn.b 72
387.3.bn.c 84
387.3.bn.d 96
387.3.bn.e 168

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(387))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(387)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(129))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 2 T )( 1 + 2 T ) \))(\( ( 1 - 2 T )^{2}( 1 + 2 T )^{2} \))(\( 1 - 4 T^{2} + 41 T^{4} - 114 T^{6} + 656 T^{8} - 1024 T^{10} + 4096 T^{12} \))(\( ( 1 - 7 T^{2} + 41 T^{4} - 147 T^{6} + 656 T^{8} - 1792 T^{10} + 4096 T^{12} )^{2} \))(\( 1 - 10 T^{2} + 43 T^{4} - 148 T^{6} + 603 T^{8} - 2066 T^{10} + 7025 T^{12} - 30360 T^{14} + 112400 T^{16} - 528896 T^{18} + 2469888 T^{20} - 9699328 T^{22} + 45088768 T^{24} - 167772160 T^{26} + 268435456 T^{28} \))(\( 1 - 5 T^{2} + 16 T^{4} \))(\( ( 1 - 2 T )^{2}( 1 + 2 T )^{2} \))(\( 1 - 11 T^{2} + 59 T^{4} - 178 T^{6} + 635 T^{8} - 4155 T^{10} + 21681 T^{12} - 66480 T^{14} + 162560 T^{16} - 729088 T^{18} + 3866624 T^{20} - 11534336 T^{22} + 16777216 T^{24} \))(\( 1 - 13 T^{2} + 112 T^{4} - 823 T^{6} + 4893 T^{8} - 25871 T^{10} + 122522 T^{12} - 512373 T^{14} + 1960352 T^{16} - 6622976 T^{18} + 20041728 T^{20} - 53936128 T^{22} + 117440512 T^{24} - 218103808 T^{26} + 268435456 T^{28} \))(\( 1 - 16 T^{2} + 148 T^{4} - 1075 T^{6} + 6618 T^{8} - 35501 T^{10} + 168269 T^{12} - 711516 T^{14} + 2692304 T^{16} - 9088256 T^{18} + 27107328 T^{20} - 70451200 T^{22} + 155189248 T^{24} - 268435456 T^{26} + 268435456 T^{28} \))(\( 1 + 21 T^{2} + 215 T^{4} + 1519 T^{6} + 8705 T^{8} + 43085 T^{10} + 185289 T^{12} + 689360 T^{14} + 2228480 T^{16} + 6221824 T^{18} + 14090240 T^{20} + 22020096 T^{22} + 16777216 T^{24} \))(\( ( 1 - 2 T + 4 T^{2} - 8 T^{3} + 16 T^{4} - 32 T^{5} + 64 T^{6} )^{2}( 1 + 2 T + 4 T^{2} + 8 T^{3} + 16 T^{4} + 32 T^{5} + 64 T^{6} )^{2} \))
$3$ 1
$5$ (\( ( 1 - 5 T )( 1 + 5 T ) \))(\( ( 1 - 5 T )^{2}( 1 + 5 T )^{2} \))(\( 1 - 33 T^{2} + 1538 T^{4} - 41006 T^{6} + 961250 T^{8} - 12890625 T^{10} + 244140625 T^{12} \))(\( ( 1 - 60 T^{2} + 2522 T^{4} - 76910 T^{6} + 1576250 T^{8} - 23437500 T^{10} + 244140625 T^{12} )^{2} \))(\( 1 - 158 T^{2} + 12245 T^{4} - 646152 T^{6} + 26887244 T^{8} - 946961944 T^{10} + 29003099582 T^{12} - 776091411812 T^{14} + 18126937238750 T^{16} - 369907009375000 T^{18} + 6564268554687500 T^{20} - 98594970703125000 T^{22} + 1167774200439453125 T^{24} - 9417533874511718750 T^{26} + 37252902984619140625 T^{28} \))(\( ( 1 - 5 T + 25 T^{2} )( 1 + 5 T + 25 T^{2} ) \))(\( ( 1 - 5 T + 25 T^{2} )( 1 + 5 T + 25 T^{2} ) \))(\( 1 - 3 T + 90 T^{2} - 261 T^{3} + 3868 T^{4} - 16263 T^{5} + 135026 T^{6} - 750009 T^{7} + 4440152 T^{8} - 24002067 T^{9} + 135845122 T^{10} - 636745773 T^{11} + 3708044426 T^{12} - 15918644325 T^{13} + 84903201250 T^{14} - 375032296875 T^{15} + 1734434375000 T^{16} - 7324306640625 T^{17} + 32965332031250 T^{18} - 99261474609375 T^{19} + 590209960937500 T^{20} - 995635986328125 T^{21} + 8583068847656250 T^{22} - 7152557373046875 T^{23} + 59604644775390625 T^{24} \))(\( 1 - 3 T + 70 T^{2} - 201 T^{3} + 1793 T^{4} - 6552 T^{5} + 37425 T^{6} - 268560 T^{7} + 1531274 T^{8} - 10260270 T^{9} + 50417000 T^{10} - 273059766 T^{11} + 1097052338 T^{12} - 6874224138 T^{13} + 23458274557 T^{14} - 171855603450 T^{15} + 685657711250 T^{16} - 4266558843750 T^{17} + 19694140625000 T^{18} - 100197949218750 T^{19} + 373846191406250 T^{20} - 1639160156250000 T^{21} + 5710601806640625 T^{22} - 24993896484375000 T^{23} + 170993804931640625 T^{24} - 479221343994140625 T^{25} + 4172325134277343750 T^{26} - 4470348358154296875 T^{27} + 37252902984619140625 T^{28} \))(\( 1 + 3 T + 46 T^{2} + 129 T^{3} + 545 T^{4} + 1242 T^{5} + 615 T^{6} + 582 T^{7} + 102428 T^{8} + 411882 T^{9} + 4666706 T^{10} - 11790090 T^{11} - 34013866 T^{12} - 1780412652 T^{13} - 4938268403 T^{14} - 44510316300 T^{15} - 21258666250 T^{16} - 184220156250 T^{17} + 1822932031250 T^{18} + 4022285156250 T^{19} + 25006835937500 T^{20} + 3552246093750 T^{21} + 93841552734375 T^{22} + 4737854003906250 T^{23} + 51975250244140625 T^{24} + 307559967041015625 T^{25} + 2741813659667968750 T^{26} + 4470348358154296875 T^{27} + 37252902984619140625 T^{28} \))(\( 1 + 48 T^{2} + 2008 T^{4} + 38377 T^{6} - 30857 T^{8} - 26673253 T^{10} - 1119438551 T^{12} - 16670783125 T^{14} - 12053515625 T^{16} + 9369384765625 T^{18} + 306396484375000 T^{20} + 4577636718750000 T^{22} + 59604644775390625 T^{24} \))(\( ( 1 - 5 T + 125 T^{3} - 625 T^{4} + 15625 T^{6} - 390625 T^{8} + 1953125 T^{9} - 48828125 T^{11} + 244140625 T^{12} )( 1 + 5 T - 125 T^{3} - 625 T^{4} + 15625 T^{6} - 390625 T^{8} - 1953125 T^{9} + 48828125 T^{11} + 244140625 T^{12} ) \))
$7$ (\( ( 1 - 7 T )( 1 + 7 T ) \))(\( ( 1 - 7 T )^{2}( 1 + 7 T )^{2} \))(\( 1 - 144 T^{2} + 11511 T^{4} - 668464 T^{6} + 27637911 T^{8} - 830131344 T^{10} + 13841287201 T^{12} \))(\( ( 1 - 84 T^{2} + 8232 T^{4} - 386386 T^{6} + 19765032 T^{8} - 484243284 T^{10} + 13841287201 T^{12} )^{2} \))(\( 1 - 338 T^{2} + 58561 T^{4} - 6653660 T^{6} + 554265016 T^{8} - 36391844060 T^{10} + 2025986266086 T^{12} - 102453858581484 T^{14} + 4864393024872486 T^{16} - 209791739028932060 T^{18} + 7671741271922860216 T^{20} - \)\(22\!\cdots\!60\)\( T^{22} + \)\(46\!\cdots\!61\)\( T^{24} - \)\(64\!\cdots\!38\)\( T^{26} + \)\(45\!\cdots\!01\)\( T^{28} \))(\( 1 - 18 T + 157 T^{2} - 882 T^{3} + 2401 T^{4} \))(\( ( 1 - 2 T + 49 T^{2} )( 1 + 11 T + 49 T^{2} ) \))(\( 1 - 9 T + 237 T^{2} - 1890 T^{3} + 29841 T^{4} - 211941 T^{5} + 2317384 T^{6} - 15083235 T^{7} + 123904335 T^{8} - 778414590 T^{9} + 4927316019 T^{10} - 34388074575 T^{11} + 204998231790 T^{12} - 1685015654175 T^{13} + 11830485761619 T^{14} - 91579698098910 T^{15} + 714283834312335 T^{16} - 4260640562350515 T^{17} + 32075577499002184 T^{18} - 143743276282689909 T^{19} + 991703881127463441 T^{20} - 3077701700050748610 T^{21} + 18910767112534044237 T^{22} - 35188389437246892441 T^{23} + \)\(19\!\cdots\!01\)\( T^{24} \))(\( 1 - 15 T + 286 T^{2} - 3165 T^{3} + 37819 T^{4} - 362844 T^{5} + 3600427 T^{6} - 32430336 T^{7} + 289032214 T^{8} - 2449147758 T^{9} + 20072535910 T^{10} - 157426321554 T^{11} + 1196392191768 T^{12} - 8709154930818 T^{13} + 62145047390781 T^{14} - 426748591610082 T^{15} + 2872537652434968 T^{16} - 18521049304506546 T^{17} + 115714175086503910 T^{18} - 691823622778841742 T^{19} + 4000577884314893014 T^{20} - 21995002135445547264 T^{21} + \)\(11\!\cdots\!27\)\( T^{22} - \)\(59\!\cdots\!56\)\( T^{23} + \)\(30\!\cdots\!19\)\( T^{24} - \)\(12\!\cdots\!85\)\( T^{25} + \)\(54\!\cdots\!86\)\( T^{26} - \)\(14\!\cdots\!35\)\( T^{27} + \)\(45\!\cdots\!01\)\( T^{28} \))(\( 1 + 36 T + 766 T^{2} + 12024 T^{3} + 151861 T^{4} + 1644948 T^{5} + 16044865 T^{6} + 146801961 T^{7} + 1295763397 T^{8} + 11119565754 T^{9} + 92264914843 T^{10} + 733730314923 T^{11} + 5583331591560 T^{12} + 40868183932695 T^{13} + 289971834292812 T^{14} + 2002541012702055 T^{15} + 13405579151335560 T^{16} + 86322637820376027 T^{17} + 531888873351841243 T^{18} + 3141002105133022746 T^{19} + 17935033322420381797 T^{20} + 99564477089679056889 T^{21} + \)\(53\!\cdots\!65\)\( T^{22} + \)\(26\!\cdots\!52\)\( T^{23} + \)\(12\!\cdots\!61\)\( T^{24} + \)\(47\!\cdots\!76\)\( T^{25} + \)\(14\!\cdots\!66\)\( T^{26} + \)\(33\!\cdots\!64\)\( T^{27} + \)\(45\!\cdots\!01\)\( T^{28} \))(\( ( 1 - 112 T^{2} + 9212 T^{4} - 542283 T^{6} + 22118012 T^{8} - 645657712 T^{10} + 13841287201 T^{12} )^{2} \))(\( ( 1 - 11 T + 72 T^{2} - 253 T^{3} - 745 T^{4} + 20592 T^{5} - 190007 T^{6} + 1009008 T^{7} - 1788745 T^{8} - 29765197 T^{9} + 415065672 T^{10} - 3107227739 T^{11} + 13841287201 T^{12} )( 1 + 2 T - 45 T^{2} - 188 T^{3} + 1829 T^{4} + 12870 T^{5} - 63881 T^{6} + 630630 T^{7} + 4391429 T^{8} - 22118012 T^{9} - 259416045 T^{10} + 564950498 T^{11} + 13841287201 T^{12} ) \))
$11$ (\( 1 - 21 T + 121 T^{2} \))(\( 1 + 199 T^{2} + 14641 T^{4} \))(\( ( 1 + 19 T + 411 T^{2} + 4354 T^{3} + 49731 T^{4} + 278179 T^{5} + 1771561 T^{6} )^{2} \))(\( ( 1 + 236 T^{2} + 31210 T^{4} + 3995438 T^{6} + 456945610 T^{8} + 50588695916 T^{10} + 3138428376721 T^{12} )^{2} \))(\( ( 1 - 7 T + 543 T^{2} - 3942 T^{3} + 146986 T^{4} - 1007864 T^{5} + 25813058 T^{6} - 153013646 T^{7} + 3123380018 T^{8} - 14756136824 T^{9} + 260394665146 T^{10} - 845002708902 T^{11} + 14084021558343 T^{12} - 21968998637047 T^{13} + 379749833583241 T^{14} )^{2} \))(\( ( 1 + T + 121 T^{2} )^{2} \))(\( ( 1 + 121 T^{2} )^{2} \))(\( ( 1 + 14 T + 430 T^{2} + 6047 T^{3} + 101321 T^{4} + 1177595 T^{5} + 15292736 T^{6} + 142488995 T^{7} + 1483440761 T^{8} + 10712629367 T^{9} + 92174318830 T^{10} + 363123944414 T^{11} + 3138428376721 T^{12} )^{2} \))(\( ( 1 - 28 T + 762 T^{2} - 13767 T^{3} + 233305 T^{4} - 3291392 T^{5} + 43215575 T^{6} - 495095879 T^{7} + 5229084575 T^{8} - 48189270272 T^{9} + 413314039105 T^{10} - 2951078714727 T^{11} + 19764317545962 T^{12} - 87875994548188 T^{13} + 379749833583241 T^{14} )^{2} \))(\( ( 1 - 17 T + 527 T^{2} - 5695 T^{3} + 98145 T^{4} - 704203 T^{5} + 10074874 T^{6} - 63066400 T^{7} + 1219059754 T^{8} - 10310236123 T^{9} + 173869854345 T^{10} - 1220773827295 T^{11} + 13669022764727 T^{12} - 53353282404257 T^{13} + 379749833583241 T^{14} )^{2} \))(\( 1 + 59 T^{2} + 43440 T^{4} + 5909746 T^{6} + 918391484 T^{8} + 175146212175 T^{10} + 14855763462631 T^{12} + 2564315692454175 T^{14} + 196865370830169404 T^{16} + 18547314545613422866 T^{18} + \)\(19\!\cdots\!40\)\( T^{20} + \)\(39\!\cdots\!59\)\( T^{22} + \)\(98\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 121 T^{2} + 14641 T^{4} - 1771561 T^{6} + 214358881 T^{8} - 25937424601 T^{10} + 3138428376721 T^{12} )^{2} \))
$13$ (\( 1 + 17 T + 169 T^{2} \))(\( ( 1 - 17 T + 169 T^{2} )^{2} \))(\( ( 1 - 15 T + 257 T^{2} - 1570 T^{3} + 43433 T^{4} - 428415 T^{5} + 4826809 T^{6} )^{2} \))(\( ( 1 + 12 T + 506 T^{2} + 4022 T^{3} + 85514 T^{4} + 342732 T^{5} + 4826809 T^{6} )^{4} \))(\( ( 1 + T + 617 T^{2} + 1916 T^{3} + 199528 T^{4} + 976928 T^{5} + 43815810 T^{6} + 223819278 T^{7} + 7404871890 T^{8} + 27902040608 T^{9} + 963083546152 T^{10} + 1562940061436 T^{11} + 85058689470833 T^{12} + 23298085122481 T^{13} + 3937376385699289 T^{14} )^{2} \))(\( 1 - 16 T + 87 T^{2} - 2704 T^{3} + 28561 T^{4} \))(\( ( 1 - 22 T + 169 T^{2} )( 1 - T + 169 T^{2} ) \))(\( 1 - 24 T - 211 T^{2} + 7466 T^{3} + 36644 T^{4} - 1139421 T^{5} - 11023890 T^{6} + 164450517 T^{7} + 1885659940 T^{8} - 21544092258 T^{9} - 166029500453 T^{10} + 1118804167120 T^{11} + 20761074178322 T^{12} + 189077904243280 T^{13} - 4741968562438133 T^{14} - 103989218407744722 T^{15} + 1538190742417016740 T^{16} + 22670900257408335933 T^{17} - \)\(25\!\cdots\!90\)\( T^{18} - \)\(44\!\cdots\!69\)\( T^{19} + \)\(24\!\cdots\!04\)\( T^{20} + \)\(83\!\cdots\!14\)\( T^{21} - \)\(40\!\cdots\!11\)\( T^{22} - \)\(77\!\cdots\!56\)\( T^{23} + \)\(54\!\cdots\!61\)\( T^{24} \))(\( 1 + 5 T - 736 T^{2} - 5221 T^{3} + 280219 T^{4} + 2376662 T^{5} - 67978209 T^{6} - 655697502 T^{7} + 11663466252 T^{8} + 119470405478 T^{9} - 1571690478380 T^{10} - 14381249946166 T^{11} + 199411953448652 T^{12} + 850749279449392 T^{13} - 29717470049487117 T^{14} + 143776628226947248 T^{15} + 5695404802446949772 T^{16} - 69415546671403564294 T^{17} - \)\(12\!\cdots\!80\)\( T^{18} + \)\(16\!\cdots\!22\)\( T^{19} + \)\(27\!\cdots\!12\)\( T^{20} - \)\(25\!\cdots\!78\)\( T^{21} - \)\(45\!\cdots\!69\)\( T^{22} + \)\(26\!\cdots\!98\)\( T^{23} + \)\(53\!\cdots\!19\)\( T^{24} - \)\(16\!\cdots\!49\)\( T^{25} - \)\(39\!\cdots\!96\)\( T^{26} + \)\(45\!\cdots\!45\)\( T^{27} + \)\(15\!\cdots\!21\)\( T^{28} \))(\( 1 + 34 T + 266 T^{2} + 26 T^{3} + 17573 T^{4} - 368798 T^{5} - 10103705 T^{6} - 28124213 T^{7} - 1171007631 T^{8} - 8865567680 T^{9} + 128644520845 T^{10} - 837230647839 T^{11} + 23543174940148 T^{12} + 372154748655175 T^{13} - 3877540036302488 T^{14} + 62894152522724575 T^{15} + 672416619465567028 T^{16} - 4041152426065115751 T^{17} + \)\(10\!\cdots\!45\)\( T^{18} - \)\(12\!\cdots\!20\)\( T^{19} - \)\(27\!\cdots\!11\)\( T^{20} - \)\(11\!\cdots\!57\)\( T^{21} - \)\(67\!\cdots\!05\)\( T^{22} - \)\(41\!\cdots\!42\)\( T^{23} + \)\(33\!\cdots\!73\)\( T^{24} + \)\(83\!\cdots\!94\)\( T^{25} + \)\(14\!\cdots\!26\)\( T^{26} + \)\(31\!\cdots\!06\)\( T^{27} + \)\(15\!\cdots\!21\)\( T^{28} \))(\( ( 1 + 3 T - 160 T^{2} - 5292 T^{3} - 18110 T^{4} + 415545 T^{5} + 15970331 T^{6} + 70227105 T^{7} - 517239710 T^{8} - 25543473228 T^{9} - 130516915360 T^{10} + 413575475547 T^{11} + 23298085122481 T^{12} )^{2} \))(\( ( 1 + T - 168 T^{2} - 337 T^{3} + 28055 T^{4} + 85008 T^{5} - 4656287 T^{6} + 14366352 T^{7} + 801278855 T^{8} - 1626634633 T^{9} - 137042761128 T^{10} + 137858491849 T^{11} + 23298085122481 T^{12} )( 1 + 22 T + 315 T^{2} + 3212 T^{3} + 17429 T^{4} - 159390 T^{5} - 6452081 T^{6} - 26936910 T^{7} + 497789669 T^{8} + 15503710508 T^{9} + 256955177115 T^{10} + 3032886820678 T^{11} + 23298085122481 T^{12} ) \))
$17$ (\( 1 - 9 T + 289 T^{2} \))(\( 1 - 497 T^{2} + 83521 T^{4} \))(\( ( 1 - 10 T + 767 T^{2} - 5655 T^{3} + 221663 T^{4} - 835210 T^{5} + 24137569 T^{6} )^{2} \))(\( ( 1 + 978 T^{2} + 505355 T^{4} + 175816052 T^{6} + 42207754955 T^{8} + 6822290777298 T^{10} + 582622237229761 T^{12} )^{2} \))(\( ( 1 - 9 T + 683 T^{2} - 5314 T^{3} + 315413 T^{4} - 2502531 T^{5} + 123338639 T^{6} - 787992708 T^{7} + 35644866671 T^{8} - 209013891651 T^{9} + 7613303050997 T^{10} - 37069175041474 T^{11} + 1376923834006667 T^{12} - 5243600135067849 T^{13} + 168377826559400929 T^{14} )^{2} \))(\( 1 - T - 288 T^{2} - 289 T^{3} + 83521 T^{4} \))(\( 1 - 289 T^{2} + 83521 T^{4} \))(\( 1 - 7 T - 910 T^{2} + 8453 T^{3} + 343548 T^{4} - 3893616 T^{5} - 110794242 T^{6} + 1195653416 T^{7} + 42885403526 T^{8} - 359068799653 T^{9} - 11658350660948 T^{10} + 53405218008175 T^{11} + 2646840415582786 T^{12} + 15434108004362575 T^{13} - 973717105553037908 T^{14} - 8667047927371463557 T^{15} + \)\(29\!\cdots\!66\)\( T^{16} + \)\(24\!\cdots\!84\)\( T^{17} - \)\(64\!\cdots\!62\)\( T^{18} - \)\(65\!\cdots\!64\)\( T^{19} + \)\(16\!\cdots\!88\)\( T^{20} + \)\(11\!\cdots\!77\)\( T^{21} - \)\(36\!\cdots\!10\)\( T^{22} - \)\(82\!\cdots\!23\)\( T^{23} + \)\(33\!\cdots\!21\)\( T^{24} \))(\( 1 - 12 T - 746 T^{2} + 23494 T^{3} + 126827 T^{4} - 13683790 T^{5} + 122412493 T^{6} + 3633705890 T^{7} - 79947454124 T^{8} - 311511093544 T^{9} + 22793036494499 T^{10} - 61181982218682 T^{11} - 4393320561835620 T^{12} + 13710025541945428 T^{13} + 1006664847307683772 T^{14} + 3962197381622228692 T^{15} - \)\(36\!\cdots\!20\)\( T^{16} - \)\(14\!\cdots\!58\)\( T^{17} + \)\(15\!\cdots\!59\)\( T^{18} - \)\(62\!\cdots\!56\)\( T^{19} - \)\(46\!\cdots\!64\)\( T^{20} + \)\(61\!\cdots\!10\)\( T^{21} + \)\(59\!\cdots\!33\)\( T^{22} - \)\(19\!\cdots\!10\)\( T^{23} + \)\(51\!\cdots\!27\)\( T^{24} + \)\(27\!\cdots\!66\)\( T^{25} - \)\(25\!\cdots\!66\)\( T^{26} - \)\(11\!\cdots\!28\)\( T^{27} + \)\(28\!\cdots\!41\)\( T^{28} \))(\( 1 - 11 T - 1166 T^{2} + 8553 T^{3} + 722357 T^{4} - 3268182 T^{5} - 312814057 T^{6} + 1389801743 T^{7} + 104627138864 T^{8} - 618890447745 T^{9} - 32337056866297 T^{10} + 193248629650838 T^{11} + 10280505101113772 T^{12} - 25691297459452652 T^{13} - 3113220021406055492 T^{14} - 7424784965781816428 T^{15} + \)\(85\!\cdots\!12\)\( T^{16} + \)\(46\!\cdots\!22\)\( T^{17} - \)\(22\!\cdots\!77\)\( T^{18} - \)\(12\!\cdots\!05\)\( T^{19} + \)\(60\!\cdots\!04\)\( T^{20} + \)\(23\!\cdots\!47\)\( T^{21} - \)\(15\!\cdots\!17\)\( T^{22} - \)\(45\!\cdots\!38\)\( T^{23} + \)\(29\!\cdots\!57\)\( T^{24} + \)\(10\!\cdots\!17\)\( T^{25} - \)\(39\!\cdots\!86\)\( T^{26} - \)\(10\!\cdots\!59\)\( T^{27} + \)\(28\!\cdots\!41\)\( T^{28} \))(\( 1 + 318 T^{2} + 19395 T^{4} + 2458172 T^{6} + 2011864837 T^{8} - 1914684768902 T^{10} - 1108464441450681 T^{12} - 159916386583463942 T^{14} + 14034281106989002117 T^{16} + \)\(14\!\cdots\!92\)\( T^{18} + \)\(94\!\cdots\!95\)\( T^{20} + \)\(12\!\cdots\!18\)\( T^{22} + \)\(33\!\cdots\!21\)\( T^{24} \))(\( 1 + 289 T^{2} - 24137569 T^{6} - 6975757441 T^{8} + 582622237229761 T^{12} - 48661191875666868481 T^{16} - \)\(14\!\cdots\!09\)\( T^{18} + \)\(11\!\cdots\!89\)\( T^{22} + \)\(33\!\cdots\!21\)\( T^{24} \))
$19$ (\( ( 1 - 19 T )( 1 + 19 T ) \))(\( ( 1 - 19 T )^{2}( 1 + 19 T )^{2} \))(\( 1 - 691 T^{2} + 378040 T^{4} - 133433020 T^{6} + 49266550840 T^{8} - 11735642061331 T^{10} + 2213314919066161 T^{12} \))(\( ( 1 - 220 T^{2} + 218248 T^{4} - 72222058 T^{6} + 28442297608 T^{8} - 3736383869020 T^{10} + 2213314919066161 T^{12} )^{2} \))(\( 1 - 3106 T^{2} + 4764233 T^{4} - 4822168116 T^{6} + 3619085950600 T^{8} - 2137515640209476 T^{10} + 1025890729835393262 T^{12} - \)\(40\!\cdots\!08\)\( T^{14} + \)\(13\!\cdots\!02\)\( T^{16} - \)\(36\!\cdots\!16\)\( T^{18} + \)\(80\!\cdots\!00\)\( T^{20} - \)\(13\!\cdots\!96\)\( T^{22} + \)\(17\!\cdots\!33\)\( T^{24} - \)\(15\!\cdots\!26\)\( T^{26} + \)\(63\!\cdots\!41\)\( T^{28} \))(\( 1 - 21 T + 508 T^{2} - 7581 T^{3} + 130321 T^{4} \))(\( ( 1 - 37 T + 361 T^{2} )( 1 - 11 T + 361 T^{2} ) \))(\( 1 - 66 T + 2608 T^{2} - 76296 T^{3} + 1836036 T^{4} - 38733966 T^{5} + 734123972 T^{6} - 14185527162 T^{7} + 292458472820 T^{8} - 6360444714264 T^{9} + 137883926411448 T^{10} - 2871978163512918 T^{11} + 56971930639346710 T^{12} - 1036784117028163398 T^{13} + 17969171173866314808 T^{14} - \)\(29\!\cdots\!84\)\( T^{15} + \)\(49\!\cdots\!20\)\( T^{16} - \)\(86\!\cdots\!62\)\( T^{17} + \)\(16\!\cdots\!92\)\( T^{18} - \)\(30\!\cdots\!86\)\( T^{19} + \)\(52\!\cdots\!16\)\( T^{20} - \)\(79\!\cdots\!36\)\( T^{21} + \)\(98\!\cdots\!08\)\( T^{22} - \)\(89\!\cdots\!26\)\( T^{23} + \)\(48\!\cdots\!21\)\( T^{24} \))(\( 1 - 21 T + 1526 T^{2} - 28959 T^{3} + 1151150 T^{4} - 26875377 T^{5} + 712056027 T^{6} - 19153701333 T^{7} + 391347719284 T^{8} - 10222926320733 T^{9} + 200124856604845 T^{10} - 4523563439936607 T^{11} + 93215209529454273 T^{12} - 1754653170005040450 T^{13} + 36708774521893792636 T^{14} - \)\(63\!\cdots\!50\)\( T^{15} + \)\(12\!\cdots\!33\)\( T^{16} - \)\(21\!\cdots\!67\)\( T^{17} + \)\(33\!\cdots\!45\)\( T^{18} - \)\(62\!\cdots\!33\)\( T^{19} + \)\(86\!\cdots\!24\)\( T^{20} - \)\(15\!\cdots\!93\)\( T^{21} + \)\(20\!\cdots\!87\)\( T^{22} - \)\(27\!\cdots\!57\)\( T^{23} + \)\(43\!\cdots\!50\)\( T^{24} - \)\(39\!\cdots\!99\)\( T^{25} + \)\(74\!\cdots\!46\)\( T^{26} - \)\(37\!\cdots\!01\)\( T^{27} + \)\(63\!\cdots\!41\)\( T^{28} \))(\( 1 + 72 T + 3143 T^{2} + 101880 T^{3} + 2700560 T^{4} + 62024958 T^{5} + 1204768074 T^{6} + 19072454901 T^{7} + 203588076148 T^{8} - 194307346203 T^{9} - 82762126437140 T^{10} - 2881214915971662 T^{11} - 73476647827834935 T^{12} - 1631111651319556434 T^{13} - 32602547253899654678 T^{14} - \)\(58\!\cdots\!74\)\( T^{15} - \)\(95\!\cdots\!35\)\( T^{16} - \)\(13\!\cdots\!22\)\( T^{17} - \)\(14\!\cdots\!40\)\( T^{18} - \)\(11\!\cdots\!03\)\( T^{19} + \)\(45\!\cdots\!28\)\( T^{20} + \)\(15\!\cdots\!21\)\( T^{21} + \)\(34\!\cdots\!94\)\( T^{22} + \)\(64\!\cdots\!78\)\( T^{23} + \)\(10\!\cdots\!60\)\( T^{24} + \)\(13\!\cdots\!80\)\( T^{25} + \)\(15\!\cdots\!03\)\( T^{26} + \)\(12\!\cdots\!32\)\( T^{27} + \)\(63\!\cdots\!41\)\( T^{28} \))(\( ( 1 + 35 T + 676 T^{2} - 5040 T^{3} - 228695 T^{4} - 4604579 T^{5} - 21586844 T^{6} - 1662253019 T^{7} - 29803761095 T^{8} - 237111240240 T^{9} + 11480888615716 T^{10} + 214587319023035 T^{11} + 2213314919066161 T^{12} )^{2} \))(\( ( 1 + 11 T - 240 T^{2} - 6611 T^{3} + 13919 T^{4} + 2539680 T^{5} + 22911721 T^{6} + 916824480 T^{7} + 1813937999 T^{8} - 311020319291 T^{9} - 4076055129840 T^{10} + 67441728835811 T^{11} + 2213314919066161 T^{12} )( 1 + 37 T + 1008 T^{2} + 23939 T^{3} + 521855 T^{4} + 10666656 T^{5} + 206276617 T^{6} + 3850662816 T^{7} + 68008665455 T^{8} + 1126231345259 T^{9} + 17119431545328 T^{10} + 226849451538637 T^{11} + 2213314919066161 T^{12} ) \))
$23$ (\( 1 + 3 T + 529 T^{2} \))(\( 1 - 1049 T^{2} + 279841 T^{4} \))(\( ( 1 - 40 T + 1387 T^{2} - 28195 T^{3} + 733723 T^{4} - 11193640 T^{5} + 148035889 T^{6} )^{2} \))(\( ( 1 + 1186 T^{2} + 999595 T^{4} + 548809204 T^{6} + 279727664395 T^{8} + 92876828543266 T^{10} + 21914624432020321 T^{12} )^{2} \))(\( ( 1 + 75 T + 5463 T^{2} + 247242 T^{3} + 10318521 T^{4} + 330847929 T^{5} + 9750023775 T^{6} + 233835070804 T^{7} + 5157762576975 T^{8} + 92584815299289 T^{9} + 1527511429400169 T^{10} + 19361764622845002 T^{11} + 226313030760164487 T^{12} + 1643596832401524075 T^{13} + 11592836324538749809 T^{14} )^{2} \))(\( 1 - 4 T - 513 T^{2} - 2116 T^{3} + 279841 T^{4} \))(\( 1 - 529 T^{2} + 279841 T^{4} \))(\( 1 - 16 T - 995 T^{2} + 970 T^{3} + 448208 T^{4} + 9378727 T^{5} + 41040474 T^{6} - 4400241755 T^{7} - 92523779140 T^{8} - 750281486226 T^{9} - 30397457804233 T^{10} + 745325850079516 T^{11} + 45354493455383514 T^{12} + 394277374692063964 T^{13} - 8506454989394366953 T^{14} - \)\(11\!\cdots\!14\)\( T^{15} - \)\(72\!\cdots\!40\)\( T^{16} - \)\(18\!\cdots\!95\)\( T^{17} + \)\(89\!\cdots\!54\)\( T^{18} + \)\(10\!\cdots\!43\)\( T^{19} + \)\(27\!\cdots\!88\)\( T^{20} + \)\(31\!\cdots\!30\)\( T^{21} - \)\(17\!\cdots\!95\)\( T^{22} - \)\(14\!\cdots\!64\)\( T^{23} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( 1 + 24 T - 2238 T^{2} - 34854 T^{3} + 3179244 T^{4} + 25583562 T^{5} - 3115897461 T^{6} - 6372594622 T^{7} + 2338251310905 T^{8} - 3698626581762 T^{9} - 1383489760177506 T^{10} + 4225344309228318 T^{11} + 714142904440708821 T^{12} - 1093513934245048626 T^{13} - \)\(36\!\cdots\!43\)\( T^{14} - \)\(57\!\cdots\!54\)\( T^{15} + \)\(19\!\cdots\!61\)\( T^{16} + \)\(62\!\cdots\!02\)\( T^{17} - \)\(10\!\cdots\!86\)\( T^{18} - \)\(15\!\cdots\!38\)\( T^{19} + \)\(51\!\cdots\!05\)\( T^{20} - \)\(73\!\cdots\!98\)\( T^{21} - \)\(19\!\cdots\!21\)\( T^{22} + \)\(82\!\cdots\!78\)\( T^{23} + \)\(54\!\cdots\!44\)\( T^{24} - \)\(31\!\cdots\!66\)\( T^{25} - \)\(10\!\cdots\!58\)\( T^{26} + \)\(60\!\cdots\!36\)\( T^{27} + \)\(13\!\cdots\!81\)\( T^{28} \))(\( 1 + 10 T - 1608 T^{2} + 2434 T^{3} + 1183484 T^{4} - 18061106 T^{5} - 586180393 T^{6} + 14236206998 T^{7} + 251588995837 T^{8} - 7510850544060 T^{9} - 83304804661218 T^{10} + 4203158109582796 T^{11} - 14276874273447195 T^{12} - 1124997355248805746 T^{13} + 28734586910175101821 T^{14} - \)\(59\!\cdots\!34\)\( T^{15} - \)\(39\!\cdots\!95\)\( T^{16} + \)\(62\!\cdots\!44\)\( T^{17} - \)\(65\!\cdots\!58\)\( T^{18} - \)\(31\!\cdots\!40\)\( T^{19} + \)\(55\!\cdots\!77\)\( T^{20} + \)\(16\!\cdots\!82\)\( T^{21} - \)\(35\!\cdots\!73\)\( T^{22} - \)\(58\!\cdots\!14\)\( T^{23} + \)\(20\!\cdots\!84\)\( T^{24} + \)\(22\!\cdots\!86\)\( T^{25} - \)\(77\!\cdots\!28\)\( T^{26} + \)\(25\!\cdots\!90\)\( T^{27} + \)\(13\!\cdots\!81\)\( T^{28} \))(\( 1 + 398 T^{2} - 133407 T^{4} + 101332038 T^{6} - 35424805823 T^{8} - 29080927325294 T^{10} + 29552213459104623 T^{12} - 8138035783637598254 T^{14} - \)\(27\!\cdots\!63\)\( T^{16} + \)\(22\!\cdots\!98\)\( T^{18} - \)\(81\!\cdots\!27\)\( T^{20} + \)\(68\!\cdots\!98\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( 1 + 529 T^{2} - 148035889 T^{6} - 78310985281 T^{8} + 21914624432020321 T^{12} - \)\(61\!\cdots\!61\)\( T^{16} - \)\(32\!\cdots\!69\)\( T^{18} + \)\(90\!\cdots\!29\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))
$29$ (\( ( 1 - 29 T )( 1 + 29 T ) \))(\( ( 1 - 29 T )^{2}( 1 + 29 T )^{2} \))(\( 1 - 1621 T^{2} + 1946890 T^{4} - 2007466870 T^{6} + 1376998306090 T^{8} - 810899435409781 T^{10} + 353814783205469041 T^{12} \))(\( ( 1 - 4648 T^{2} + 9308386 T^{4} - 10271462278 T^{6} + 6583644558466 T^{8} - 2325145327442728 T^{10} + 353814783205469041 T^{12} )^{2} \))(\( 1 - 5734 T^{2} + 16275365 T^{4} - 31011157008 T^{6} + 45539850410092 T^{8} - 55656176891335376 T^{10} + 58467585466871243502 T^{12} - \)\(52\!\cdots\!56\)\( T^{14} + \)\(41\!\cdots\!62\)\( T^{16} - \)\(27\!\cdots\!36\)\( T^{18} + \)\(16\!\cdots\!72\)\( T^{20} - \)\(77\!\cdots\!68\)\( T^{22} + \)\(28\!\cdots\!65\)\( T^{24} - \)\(71\!\cdots\!54\)\( T^{26} + \)\(88\!\cdots\!61\)\( T^{28} \))(\( ( 1 - 29 T + 841 T^{2} )( 1 + 29 T + 841 T^{2} ) \))(\( ( 1 - 29 T + 841 T^{2} )( 1 + 29 T + 841 T^{2} ) \))(\( 1 - 111 T + 7375 T^{2} - 362748 T^{3} + 14016537 T^{4} - 490234341 T^{5} + 16991400860 T^{6} - 618781423887 T^{7} + 22589952693419 T^{8} - 755597311945764 T^{9} + 22852874993878941 T^{10} - 643686573544215837 T^{11} + 18176844555197488294 T^{12} - \)\(54\!\cdots\!17\)\( T^{13} + \)\(16\!\cdots\!21\)\( T^{14} - \)\(44\!\cdots\!44\)\( T^{15} + \)\(11\!\cdots\!59\)\( T^{16} - \)\(26\!\cdots\!87\)\( T^{17} + \)\(60\!\cdots\!60\)\( T^{18} - \)\(14\!\cdots\!21\)\( T^{19} + \)\(35\!\cdots\!77\)\( T^{20} - \)\(76\!\cdots\!28\)\( T^{21} + \)\(13\!\cdots\!75\)\( T^{22} - \)\(16\!\cdots\!51\)\( T^{23} + \)\(12\!\cdots\!81\)\( T^{24} \))(\( 1 - 18 T + 3464 T^{2} - 60408 T^{3} + 6058934 T^{4} - 101207610 T^{5} + 6992585577 T^{6} - 83833922724 T^{7} + 5374748960167 T^{8} + 6411943288446 T^{9} + 1902305111762422 T^{10} + 108046604545002660 T^{11} - 1300611566011889073 T^{12} + \)\(15\!\cdots\!60\)\( T^{13} - \)\(22\!\cdots\!49\)\( T^{14} + \)\(13\!\cdots\!60\)\( T^{15} - \)\(91\!\cdots\!13\)\( T^{16} + \)\(64\!\cdots\!60\)\( T^{17} + \)\(95\!\cdots\!42\)\( T^{18} + \)\(26\!\cdots\!46\)\( T^{19} + \)\(19\!\cdots\!47\)\( T^{20} - \)\(24\!\cdots\!44\)\( T^{21} + \)\(17\!\cdots\!17\)\( T^{22} - \)\(21\!\cdots\!10\)\( T^{23} + \)\(10\!\cdots\!34\)\( T^{24} - \)\(89\!\cdots\!28\)\( T^{25} + \)\(43\!\cdots\!84\)\( T^{26} - \)\(18\!\cdots\!78\)\( T^{27} + \)\(88\!\cdots\!61\)\( T^{28} \))(\( 1 + 18 T + 3902 T^{2} + 68292 T^{3} + 8182538 T^{4} + 120430488 T^{5} + 10892286357 T^{6} + 102125483304 T^{7} + 9437734005715 T^{8} - 18449630748030 T^{9} + 4212226269136690 T^{10} - 174475664408519118 T^{11} - 947017306420087125 T^{12} - \)\(25\!\cdots\!24\)\( T^{13} - \)\(26\!\cdots\!53\)\( T^{14} - \)\(21\!\cdots\!84\)\( T^{15} - \)\(66\!\cdots\!25\)\( T^{16} - \)\(10\!\cdots\!78\)\( T^{17} + \)\(21\!\cdots\!90\)\( T^{18} - \)\(77\!\cdots\!30\)\( T^{19} + \)\(33\!\cdots\!15\)\( T^{20} + \)\(30\!\cdots\!24\)\( T^{21} + \)\(27\!\cdots\!97\)\( T^{22} + \)\(25\!\cdots\!68\)\( T^{23} + \)\(14\!\cdots\!38\)\( T^{24} + \)\(10\!\cdots\!72\)\( T^{25} + \)\(48\!\cdots\!62\)\( T^{26} + \)\(18\!\cdots\!78\)\( T^{27} + \)\(88\!\cdots\!61\)\( T^{28} \))(\( 1 + 2058 T^{2} + 1581593 T^{4} - 403130 T^{6} - 777117740419 T^{8} - 231757574604430 T^{10} + 215484913398254415 T^{12} - \)\(16\!\cdots\!30\)\( T^{14} - \)\(38\!\cdots\!59\)\( T^{16} - \)\(14\!\cdots\!30\)\( T^{18} + \)\(39\!\cdots\!53\)\( T^{20} + \)\(36\!\cdots\!58\)\( T^{22} + \)\(12\!\cdots\!81\)\( T^{24} \))(\( ( 1 - 29 T + 24389 T^{3} - 707281 T^{4} + 594823321 T^{6} - 500246412961 T^{8} + 14507145975869 T^{9} - 12200509765705829 T^{11} + 353814783205469041 T^{12} )( 1 + 29 T - 24389 T^{3} - 707281 T^{4} + 594823321 T^{6} - 500246412961 T^{8} - 14507145975869 T^{9} + 12200509765705829 T^{11} + 353814783205469041 T^{12} ) \))
$31$ (\( 1 - 19 T + 961 T^{2} \))(\( ( 1 + 19 T + 961 T^{2} )^{2} \))(\( ( 1 + 56 T + 2591 T^{2} + 96591 T^{3} + 2489951 T^{4} + 51717176 T^{5} + 887503681 T^{6} )^{2} \))(\( ( 1 - 22 T + 1565 T^{2} - 52440 T^{3} + 1503965 T^{4} - 20317462 T^{5} + 887503681 T^{6} )^{4} \))(\( ( 1 - 31 T + 3679 T^{2} - 95614 T^{3} + 6776409 T^{4} - 169871117 T^{5} + 8879136119 T^{6} - 201888437196 T^{7} + 8532849810359 T^{8} - 156879543842957 T^{9} + 6014087931461529 T^{10} - 81548323653883774 T^{11} + 3015412467802366879 T^{12} - 24417546297445042591 T^{13} + \)\(75\!\cdots\!21\)\( T^{14} )^{2} \))(\( 1 - 28 T - 177 T^{2} - 26908 T^{3} + 923521 T^{4} \))(\( ( 1 - 46 T + 961 T^{2} )( 1 + 59 T + 961 T^{2} ) \))(\( 1 + 29 T - 2854 T^{2} - 122293 T^{3} + 3710916 T^{4} + 236687409 T^{5} - 1692705294 T^{6} - 282476528401 T^{7} - 2178393607912 T^{8} + 217078922116565 T^{9} + 5420523596702458 T^{10} - 78231274595814749 T^{11} - 6486151840040562614 T^{12} - 75180254886577973789 T^{13} + \)\(50\!\cdots\!18\)\( T^{14} + \)\(19\!\cdots\!65\)\( T^{15} - \)\(18\!\cdots\!92\)\( T^{16} - \)\(23\!\cdots\!01\)\( T^{17} - \)\(13\!\cdots\!34\)\( T^{18} + \)\(17\!\cdots\!89\)\( T^{19} + \)\(26\!\cdots\!96\)\( T^{20} - \)\(85\!\cdots\!13\)\( T^{21} - \)\(19\!\cdots\!54\)\( T^{22} + \)\(18\!\cdots\!69\)\( T^{23} + \)\(62\!\cdots\!21\)\( T^{24} \))(\( 1 - 59 T + 690 T^{2} - 32071 T^{3} + 2636709 T^{4} - 74016768 T^{5} + 2040901047 T^{6} - 50725980140 T^{7} + 1665807585558 T^{8} - 57638718699348 T^{9} + 58125365091000 T^{10} + 1773322890220992 T^{11} + 610299658517634726 T^{12} + 14531871664541692354 T^{13} - \)\(11\!\cdots\!73\)\( T^{14} + \)\(13\!\cdots\!94\)\( T^{15} + \)\(56\!\cdots\!46\)\( T^{16} + \)\(15\!\cdots\!52\)\( T^{17} + \)\(49\!\cdots\!00\)\( T^{18} - \)\(47\!\cdots\!48\)\( T^{19} + \)\(13\!\cdots\!38\)\( T^{20} - \)\(38\!\cdots\!40\)\( T^{21} + \)\(14\!\cdots\!07\)\( T^{22} - \)\(51\!\cdots\!88\)\( T^{23} + \)\(17\!\cdots\!09\)\( T^{24} - \)\(20\!\cdots\!31\)\( T^{25} + \)\(42\!\cdots\!90\)\( T^{26} - \)\(35\!\cdots\!79\)\( T^{27} + \)\(57\!\cdots\!41\)\( T^{28} \))(\( 1 + 42 T - 3092 T^{2} - 179422 T^{3} + 3666047 T^{4} + 334197868 T^{5} - 2556078839 T^{6} - 381310846301 T^{7} + 3254825000977 T^{8} + 370958420136016 T^{9} - 4712874884690341 T^{10} - 332905521300848601 T^{11} + 3046664335265954274 T^{12} + \)\(14\!\cdots\!15\)\( T^{13} - \)\(11\!\cdots\!44\)\( T^{14} + \)\(13\!\cdots\!15\)\( T^{15} + \)\(28\!\cdots\!54\)\( T^{16} - \)\(29\!\cdots\!81\)\( T^{17} - \)\(40\!\cdots\!81\)\( T^{18} + \)\(30\!\cdots\!16\)\( T^{19} + \)\(25\!\cdots\!97\)\( T^{20} - \)\(28\!\cdots\!21\)\( T^{21} - \)\(18\!\cdots\!59\)\( T^{22} + \)\(23\!\cdots\!88\)\( T^{23} + \)\(24\!\cdots\!47\)\( T^{24} - \)\(11\!\cdots\!42\)\( T^{25} - \)\(19\!\cdots\!32\)\( T^{26} + \)\(25\!\cdots\!02\)\( T^{27} + \)\(57\!\cdots\!41\)\( T^{28} \))(\( ( 1 - 37 T + 142 T^{2} + 15302 T^{3} - 865099 T^{4} + 13227215 T^{5} + 518609048 T^{6} + 12711353615 T^{7} - 798937093579 T^{8} + 13580581326662 T^{9} + 121110527316622 T^{10} - 30326246618289637 T^{11} + 787662783788549761 T^{12} )^{2} \))(\( ( 1 + 59 T + 961 T^{2} )^{6}( 1 + 46 T + 1155 T^{2} + 8924 T^{3} - 699451 T^{4} - 40750710 T^{5} - 1202360249 T^{6} - 39161432310 T^{7} - 645957686971 T^{8} + 7920082849244 T^{9} + 985089148244355 T^{10} + 37702901201116846 T^{11} + 787662783788549761 T^{12} ) \))
$37$ (\( ( 1 - 37 T )( 1 + 37 T ) \))(\( ( 1 - 37 T )^{2}( 1 + 37 T )^{2} \))(\( 1 - 5259 T^{2} + 14237096 T^{4} - 24083763884 T^{6} + 26682610076456 T^{8} - 18472129448170539 T^{10} + 6582952005840035281 T^{12} \))(\( ( 1 - 5274 T^{2} + 14176787 T^{4} - 23887209716 T^{6} + 26569581300707 T^{8} - 18524816639979354 T^{10} + 6582952005840035281 T^{12} )^{2} \))(\( 1 - 4790 T^{2} + 17457059 T^{4} - 43407304428 T^{6} + 95846122850417 T^{8} - 174019995659920522 T^{10} + \)\(29\!\cdots\!39\)\( T^{12} - \)\(41\!\cdots\!96\)\( T^{14} + \)\(54\!\cdots\!79\)\( T^{16} - \)\(61\!\cdots\!62\)\( T^{18} + \)\(63\!\cdots\!77\)\( T^{20} - \)\(53\!\cdots\!48\)\( T^{22} + \)\(40\!\cdots\!59\)\( T^{24} - \)\(20\!\cdots\!90\)\( T^{26} + \)\(81\!\cdots\!21\)\( T^{28} \))(\( 1 + 42 T + 1957 T^{2} + 57498 T^{3} + 1874161 T^{4} \))(\( ( 1 - 73 T + 1369 T^{2} )( 1 - 26 T + 1369 T^{2} ) \))(\( 1 - 120 T + 13269 T^{2} - 1016280 T^{3} + 71816674 T^{4} - 4159036083 T^{5} + 226460485550 T^{6} - 10769149077249 T^{7} + 489905206154870 T^{8} - 20187174180639120 T^{9} + 817471660147259059 T^{10} - 30887683233450226884 T^{11} + \)\(11\!\cdots\!42\)\( T^{12} - \)\(42\!\cdots\!96\)\( T^{13} + \)\(15\!\cdots\!99\)\( T^{14} - \)\(51\!\cdots\!80\)\( T^{15} + \)\(17\!\cdots\!70\)\( T^{16} - \)\(51\!\cdots\!01\)\( T^{17} + \)\(14\!\cdots\!50\)\( T^{18} - \)\(37\!\cdots\!87\)\( T^{19} + \)\(88\!\cdots\!34\)\( T^{20} - \)\(17\!\cdots\!20\)\( T^{21} + \)\(30\!\cdots\!69\)\( T^{22} - \)\(37\!\cdots\!80\)\( T^{23} + \)\(43\!\cdots\!61\)\( T^{24} \))(\( 1 + 123 T + 12556 T^{2} + 924099 T^{3} + 60442577 T^{4} + 3361572552 T^{5} + 171326571705 T^{6} + 7978305928680 T^{7} + 350695618363934 T^{8} + 14777052689678016 T^{9} + 605408488394869628 T^{10} + 24437124328781814912 T^{11} + \)\(96\!\cdots\!66\)\( T^{12} + \)\(37\!\cdots\!62\)\( T^{13} + \)\(13\!\cdots\!33\)\( T^{14} + \)\(51\!\cdots\!78\)\( T^{15} + \)\(18\!\cdots\!26\)\( T^{16} + \)\(62\!\cdots\!08\)\( T^{17} + \)\(21\!\cdots\!88\)\( T^{18} + \)\(71\!\cdots\!84\)\( T^{19} + \)\(23\!\cdots\!54\)\( T^{20} + \)\(71\!\cdots\!20\)\( T^{21} + \)\(21\!\cdots\!05\)\( T^{22} + \)\(56\!\cdots\!08\)\( T^{23} + \)\(13\!\cdots\!77\)\( T^{24} + \)\(29\!\cdots\!31\)\( T^{25} + \)\(54\!\cdots\!16\)\( T^{26} + \)\(72\!\cdots\!07\)\( T^{27} + \)\(81\!\cdots\!21\)\( T^{28} \))(\( 1 - 42 T + 5206 T^{2} - 193956 T^{3} + 13053521 T^{4} - 390259872 T^{5} + 20336265249 T^{6} - 359046080067 T^{7} + 17577990155915 T^{8} + 179723702338170 T^{9} + 552340497682571 T^{10} + 1192483823725915263 T^{11} - 23261024090983040836 T^{12} + \)\(23\!\cdots\!13\)\( T^{13} - \)\(43\!\cdots\!36\)\( T^{14} + \)\(31\!\cdots\!97\)\( T^{15} - \)\(43\!\cdots\!96\)\( T^{16} + \)\(30\!\cdots\!67\)\( T^{17} + \)\(19\!\cdots\!91\)\( T^{18} + \)\(86\!\cdots\!30\)\( T^{19} + \)\(11\!\cdots\!15\)\( T^{20} - \)\(32\!\cdots\!63\)\( T^{21} + \)\(25\!\cdots\!09\)\( T^{22} - \)\(65\!\cdots\!88\)\( T^{23} + \)\(30\!\cdots\!21\)\( T^{24} - \)\(61\!\cdots\!64\)\( T^{25} + \)\(22\!\cdots\!66\)\( T^{26} - \)\(24\!\cdots\!78\)\( T^{27} + \)\(81\!\cdots\!21\)\( T^{28} \))(\( ( 1 - 4609 T^{2} + 9786814 T^{4} - 14651180725 T^{6} + 18342065113054 T^{8} - 16189017803121889 T^{10} + 6582952005840035281 T^{12} )^{2} \))(\( ( 1 + 26 T - 693 T^{2} - 53612 T^{3} - 445195 T^{4} + 61819758 T^{5} + 2216785663 T^{6} + 84631248702 T^{7} - 834367106395 T^{8} - 137553724239308 T^{9} - 2434148261567253 T^{10} + 125023193682864074 T^{11} + 6582952005840035281 T^{12} )( 1 + 73 T + 3960 T^{2} + 189143 T^{3} + 8386199 T^{4} + 353255760 T^{5} + 14306964049 T^{6} + 483607135440 T^{7} + 15717087104039 T^{8} + 485289190177487 T^{9} + 13909418637527160 T^{10} + 351026659186502977 T^{11} + 6582952005840035281 T^{12} ) \))
$41$ (\( 1 + 39 T + 1681 T^{2} \))(\( 1 - 1841 T^{2} + 2825761 T^{4} \))(\( ( 1 - 86 T + 6451 T^{2} - 292121 T^{3} + 10844131 T^{4} - 243015446 T^{5} + 4750104241 T^{6} )^{2} \))(\( ( 1 + 7678 T^{2} + 28068223 T^{4} + 59998308292 T^{6} + 79314089892703 T^{8} + 61308255909191038 T^{10} + 22563490300366186081 T^{12} )^{2} \))(\( ( 1 - 25 T + 6491 T^{2} - 125490 T^{3} + 20823001 T^{4} - 270807191 T^{5} + 44179722027 T^{6} - 449185257596 T^{7} + 74266112727387 T^{8} - 765236398847351 T^{9} + 98911425360447241 T^{10} - 1002028267002394290 T^{11} + 87126481582199234891 T^{12} - \)\(56\!\cdots\!25\)\( T^{13} + \)\(37\!\cdots\!61\)\( T^{14} )^{2} \))(\( ( 1 - 29 T + 1681 T^{2} )^{2} \))(\( ( 1 + 1681 T^{2} )^{2} \))(\( ( 1 + 47 T + 6771 T^{2} + 336496 T^{3} + 24096797 T^{4} + 992715921 T^{5} + 52240608766 T^{6} + 1668755463201 T^{7} + 68091789187517 T^{8} + 1598391076679536 T^{9} + 54065928726378291 T^{10} + 630864987577162847 T^{11} + 22563490300366186081 T^{12} )^{2} \))(\( ( 1 - 22 T + 4040 T^{2} - 155127 T^{3} + 13511983 T^{4} - 399614648 T^{5} + 29183019837 T^{6} - 896906912315 T^{7} + 49056656345997 T^{8} - 1129215487347128 T^{9} + 64183327752619903 T^{10} - 1238677496017853367 T^{11} + 54227543613015700040 T^{12} - \)\(49\!\cdots\!82\)\( T^{13} + \)\(37\!\cdots\!61\)\( T^{14} )^{2} \))(\( ( 1 + 37 T + 6295 T^{2} + 211149 T^{3} + 18523319 T^{4} + 492883229 T^{5} + 37572170886 T^{6} + 815194833264 T^{7} + 63158819259366 T^{8} + 1392770206062269 T^{9} + 87987696139295879 T^{10} + 1686008977203670029 T^{11} + 84495640357409364295 T^{12} + \)\(83\!\cdots\!97\)\( T^{13} + \)\(37\!\cdots\!61\)\( T^{14} )^{2} \))(\( 1 + 7418 T^{2} + 32473612 T^{4} + 101178274627 T^{6} + 251042861558711 T^{8} + 522790752188224045 T^{10} + \)\(94\!\cdots\!93\)\( T^{12} + \)\(14\!\cdots\!45\)\( T^{14} + \)\(20\!\cdots\!31\)\( T^{16} + \)\(22\!\cdots\!87\)\( T^{18} + \)\(20\!\cdots\!92\)\( T^{20} + \)\(13\!\cdots\!18\)\( T^{22} + \)\(50\!\cdots\!61\)\( T^{24} \))(\( ( 1 - 1681 T^{2} + 2825761 T^{4} - 4750104241 T^{6} + 7984925229121 T^{8} - 13422659310152401 T^{10} + 22563490300366186081 T^{12} )^{2} \))
$43$ (\( 1 + 43 T \))(\( ( 1 - 43 T )^{2} \))(\( 1 - 10 T + 147 T^{2} + 135020 T^{3} + 271803 T^{4} - 34188010 T^{5} + 6321363049 T^{6} \))(\( ( 1 + 50 T + 3123 T^{2} + 206228 T^{3} + 5774427 T^{4} + 170940050 T^{5} + 6321363049 T^{6} )^{2} \))(\( 1 - 46 T + 4923 T^{2} - 127548 T^{3} + 8944129 T^{4} - 175732658 T^{5} + 11683156115 T^{6} - 256027169288 T^{7} + 21602155656635 T^{8} - 600794986903058 T^{9} + 56539086566089321 T^{10} - 1490806569007452348 T^{11} + \)\(10\!\cdots\!27\)\( T^{12} - \)\(18\!\cdots\!46\)\( T^{13} + \)\(73\!\cdots\!49\)\( T^{14} \))(\( 1 + 43 T + 1849 T^{2} \))(\( 1 - 22 T + 1849 T^{2} \))(\( 1 - 5 T + 235 T^{2} + 31132 T^{3} + 5312177 T^{4} + 54939337 T^{5} + 786324230 T^{6} + 101582834113 T^{7} + 18161276039777 T^{8} + 196796674441468 T^{9} + 2746727065236235 T^{10} - 108057411566421245 T^{11} + 39959630797262576401 T^{12} \))(\( 1 - 52 T - 1452 T^{2} - 57573 T^{3} + 7915213 T^{4} + 220759162 T^{5} - 5898138043 T^{6} - 633358566011 T^{7} - 10905657241507 T^{8} + 754731643804762 T^{9} + 50034934983164437 T^{10} - 672924754582322373 T^{11} - 31379872318888729548 T^{12} - \)\(20\!\cdots\!52\)\( T^{13} + \)\(73\!\cdots\!49\)\( T^{14} \))(\( 1 - 57 T + 1891 T^{2} - 129821 T^{3} + 3430871 T^{4} - 72298833 T^{5} + 908453862 T^{6} + 187890868440 T^{7} + 1679731190838 T^{8} - 247175322559233 T^{9} + 21687781165285679 T^{10} - 1517373848238439421 T^{11} + 40867313054420514859 T^{12} - \)\(22\!\cdots\!57\)\( T^{13} + \)\(73\!\cdots\!49\)\( T^{14} \))(\( ( 1 - 13 T + 43 T^{2} - 101695 T^{3} + 79507 T^{4} - 44444413 T^{5} + 6321363049 T^{6} )^{2} \))(\( 1 + 22 T - 1365 T^{2} - 70708 T^{3} + 968309 T^{4} + 152041890 T^{5} + 1554518239 T^{6} + 281125454610 T^{7} + 3310455777509 T^{8} - 446970938468692 T^{9} - 15954393378925365 T^{10} + 475452610892253478 T^{11} + 39959630797262576401 T^{12} \))
$47$ (\( 1 - 78 T + 2209 T^{2} \))(\( 1 + 1666 T^{2} + 4879681 T^{4} \))(\( ( 1 + 15 T + 5052 T^{2} + 79770 T^{3} + 11159868 T^{4} + 73195215 T^{5} + 10779215329 T^{6} )^{2} \))(\( ( 1 + 7584 T^{2} + 28835970 T^{4} + 73363427822 T^{6} + 140710334925570 T^{8} + 180584798042795424 T^{10} + \)\(11\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 76 T + 9421 T^{2} + 486558 T^{3} + 37453290 T^{4} + 1772397162 T^{5} + 112478821196 T^{6} + 4844498862752 T^{7} + 248465716021964 T^{8} + 8648732755865322 T^{9} + 403717077689482410 T^{10} + 11585572015573108638 T^{11} + \)\(49\!\cdots\!29\)\( T^{12} + \)\(88\!\cdots\!16\)\( T^{13} + \)\(25\!\cdots\!69\)\( T^{14} )^{2} \))(\( ( 1 + 10 T + 2209 T^{2} )^{2} \))(\( ( 1 + 2209 T^{2} )^{2} \))(\( ( 1 - 9 T + 7161 T^{2} + 54567 T^{3} + 24318411 T^{4} + 403881570 T^{5} + 60415020470 T^{6} + 892174388130 T^{7} + 118666088106891 T^{8} + 588189442857543 T^{9} + 170512623784870521 T^{10} - 473392190122470441 T^{11} + \)\(11\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 70 T + 10420 T^{2} + 404997 T^{3} + 37631400 T^{4} + 681596286 T^{5} + 73985106875 T^{6} + 532924160126 T^{7} + 163433101086875 T^{8} + 3325972446464766 T^{9} + 405636963731730600 T^{10} + 9643499664153219717 T^{11} + \)\(54\!\cdots\!80\)\( T^{12} + \)\(81\!\cdots\!70\)\( T^{13} + \)\(25\!\cdots\!69\)\( T^{14} )^{2} \))(\( ( 1 - 96 T + 14326 T^{2} - 919089 T^{3} + 77763480 T^{4} - 3775661352 T^{5} + 241644889121 T^{6} - 9790891306734 T^{7} + 533793560068289 T^{8} - 18424022961788712 T^{9} + 838229295652384920 T^{10} - 21884691646671255729 T^{11} + \)\(75\!\cdots\!74\)\( T^{12} - \)\(11\!\cdots\!36\)\( T^{13} + \)\(25\!\cdots\!69\)\( T^{14} )^{2} \))(\( 1 - 1282 T^{2} + 272733 T^{4} - 18361406774 T^{6} + 50562855153425 T^{8} - 66167854383681006 T^{10} + \)\(18\!\cdots\!67\)\( T^{12} - \)\(32\!\cdots\!86\)\( T^{14} + \)\(12\!\cdots\!25\)\( T^{16} - \)\(21\!\cdots\!34\)\( T^{18} + \)\(15\!\cdots\!93\)\( T^{20} - \)\(35\!\cdots\!82\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( ( 1 - 2209 T^{2} + 4879681 T^{4} - 10779215329 T^{6} + 23811286661761 T^{8} - 52599132235830049 T^{10} + \)\(11\!\cdots\!41\)\( T^{12} )^{2} \))
$53$ (\( 1 + 63 T + 2809 T^{2} \))(\( 1 - 1649 T^{2} + 7890481 T^{4} \))(\( ( 1 - 55 T + 4677 T^{2} - 168490 T^{3} + 13137693 T^{4} - 433976455 T^{5} + 22164361129 T^{6} )^{2} \))(\( ( 1 + 11870 T^{2} + 67173439 T^{4} + 233080504292 T^{6} + 530030744134159 T^{8} + 739022525182855070 T^{10} + \)\(49\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 135 T + 19255 T^{2} + 1740194 T^{3} + 149657933 T^{4} + 10173177849 T^{5} + 659267373483 T^{6} + 35658979252380 T^{7} + 1851882052113747 T^{8} + 80271266527155369 T^{9} + 3317072472831686357 T^{10} + \)\(10\!\cdots\!34\)\( T^{11} + \)\(33\!\cdots\!95\)\( T^{12} + \)\(66\!\cdots\!35\)\( T^{13} + \)\(13\!\cdots\!69\)\( T^{14} )^{2} \))(\( 1 + 80 T + 3591 T^{2} + 224720 T^{3} + 7890481 T^{4} \))(\( 1 - 2809 T^{2} + 7890481 T^{4} \))(\( 1 - 58 T - 10011 T^{2} + 489700 T^{3} + 62208382 T^{4} - 2298288439 T^{5} - 284627569714 T^{6} + 7541357242599 T^{7} + 1029571029628954 T^{8} - 16839043965386300 T^{9} - 3214742139372951389 T^{10} + 18444106212599549754 T^{11} + \)\(92\!\cdots\!42\)\( T^{12} + \)\(51\!\cdots\!86\)\( T^{13} - \)\(25\!\cdots\!09\)\( T^{14} - \)\(37\!\cdots\!00\)\( T^{15} + \)\(64\!\cdots\!94\)\( T^{16} + \)\(13\!\cdots\!51\)\( T^{17} - \)\(13\!\cdots\!74\)\( T^{18} - \)\(31\!\cdots\!91\)\( T^{19} + \)\(24\!\cdots\!22\)\( T^{20} + \)\(53\!\cdots\!00\)\( T^{21} - \)\(30\!\cdots\!11\)\( T^{22} - \)\(49\!\cdots\!22\)\( T^{23} + \)\(24\!\cdots\!81\)\( T^{24} \))(\( 1 - 99 T - 5722 T^{2} + 406129 T^{3} + 47906195 T^{4} - 840940814 T^{5} - 245767092973 T^{6} + 2293646826398 T^{7} + 638023672196476 T^{8} - 162191044968228 T^{9} - 2249249303987897876 T^{10} + 24848301573533124640 T^{11} + \)\(86\!\cdots\!72\)\( T^{12} - \)\(89\!\cdots\!92\)\( T^{13} - \)\(24\!\cdots\!49\)\( T^{14} - \)\(25\!\cdots\!28\)\( T^{15} + \)\(67\!\cdots\!32\)\( T^{16} + \)\(55\!\cdots\!60\)\( T^{17} - \)\(14\!\cdots\!36\)\( T^{18} - \)\(28\!\cdots\!72\)\( T^{19} + \)\(31\!\cdots\!16\)\( T^{20} + \)\(31\!\cdots\!62\)\( T^{21} - \)\(95\!\cdots\!33\)\( T^{22} - \)\(91\!\cdots\!46\)\( T^{23} + \)\(14\!\cdots\!95\)\( T^{24} + \)\(34\!\cdots\!61\)\( T^{25} - \)\(13\!\cdots\!82\)\( T^{26} - \)\(67\!\cdots\!71\)\( T^{27} + \)\(19\!\cdots\!61\)\( T^{28} \))(\( 1 - 47 T - 3130 T^{2} + 36661 T^{3} + 8099129 T^{4} - 134196090 T^{5} - 14572817255 T^{6} + 1409306264806 T^{7} - 391354793772 T^{8} - 3782419425656352 T^{9} + 153272499218814590 T^{10} + 9760704232654711648 T^{11} - \)\(11\!\cdots\!02\)\( T^{12} - \)\(27\!\cdots\!00\)\( T^{13} + \)\(31\!\cdots\!27\)\( T^{14} - \)\(76\!\cdots\!00\)\( T^{15} - \)\(89\!\cdots\!62\)\( T^{16} + \)\(21\!\cdots\!92\)\( T^{17} + \)\(95\!\cdots\!90\)\( T^{18} - \)\(66\!\cdots\!48\)\( T^{19} - \)\(19\!\cdots\!52\)\( T^{20} + \)\(19\!\cdots\!14\)\( T^{21} - \)\(56\!\cdots\!55\)\( T^{22} - \)\(14\!\cdots\!10\)\( T^{23} + \)\(24\!\cdots\!29\)\( T^{24} + \)\(31\!\cdots\!49\)\( T^{25} - \)\(75\!\cdots\!30\)\( T^{26} - \)\(31\!\cdots\!63\)\( T^{27} + \)\(19\!\cdots\!61\)\( T^{28} \))(\( 1 - 11659 T^{2} + 80274885 T^{4} - 406839716133 T^{6} + 1632897384142762 T^{8} - 5537435466454687400 T^{10} + \)\(16\!\cdots\!89\)\( T^{12} - \)\(43\!\cdots\!00\)\( T^{14} + \)\(10\!\cdots\!82\)\( T^{16} - \)\(19\!\cdots\!53\)\( T^{18} + \)\(31\!\cdots\!85\)\( T^{20} - \)\(35\!\cdots\!59\)\( T^{22} + \)\(24\!\cdots\!81\)\( T^{24} \))(\( 1 + 2809 T^{2} - 22164361129 T^{6} - 62259690411361 T^{8} + \)\(49\!\cdots\!41\)\( T^{12} - \)\(38\!\cdots\!21\)\( T^{16} - \)\(10\!\cdots\!89\)\( T^{18} + \)\(85\!\cdots\!09\)\( T^{22} + \)\(24\!\cdots\!81\)\( T^{24} \))
$59$ (\( 1 - 54 T + 3481 T^{2} \))(\( 1 - 4046 T^{2} + 12117361 T^{4} \))(\( ( 1 - 6 T + 4271 T^{2} - 147196 T^{3} + 14867351 T^{4} - 72704166 T^{5} + 42180533641 T^{6} )^{2} \))(\( ( 1 + 8314 T^{2} + 57506075 T^{4} + 216996472356 T^{6} + 696821870468075 T^{8} + 1220748258242324794 T^{10} + \)\(17\!\cdots\!81\)\( T^{12} )^{2} \))(\( ( 1 - 122 T + 17963 T^{2} - 1308828 T^{3} + 126371597 T^{4} - 7649411134 T^{5} + 623982716663 T^{6} - 32425945779992 T^{7} + 2172083836703903 T^{8} - 92690676148097374 T^{9} + 5330421398525394677 T^{10} - \)\(19\!\cdots\!88\)\( T^{11} + \)\(91\!\cdots\!63\)\( T^{12} - \)\(21\!\cdots\!82\)\( T^{13} + \)\(61\!\cdots\!61\)\( T^{14} )^{2} \))(\( ( 1 - 41 T + 3481 T^{2} )^{2} \))(\( ( 1 + 3481 T^{2} )^{2} \))(\( ( 1 + 168 T + 29086 T^{2} + 3029785 T^{3} + 294619625 T^{4} + 21440752319 T^{5} + 1430753245424 T^{6} + 74635258822439 T^{7} + 3570012353809625 T^{8} + 127797948117497185 T^{9} + 4270710108159280606 T^{10} + 85867614554507755368 T^{11} + \)\(17\!\cdots\!81\)\( T^{12} )^{2} \))(\( ( 1 - 137 T + 27149 T^{2} - 2473053 T^{3} + 279838466 T^{4} - 19123508968 T^{5} + 1574351354774 T^{6} - 84825006951467 T^{7} + 5480317065968294 T^{8} - 231726461751993448 T^{9} + 11803735829158834706 T^{10} - \)\(36\!\cdots\!13\)\( T^{11} + \)\(13\!\cdots\!49\)\( T^{12} - \)\(24\!\cdots\!97\)\( T^{13} + \)\(61\!\cdots\!61\)\( T^{14} )^{2} \))(\( ( 1 + 24 T + 9431 T^{2} + 604769 T^{3} + 57739713 T^{4} + 3760396779 T^{5} + 317970703018 T^{6} + 14159712058412 T^{7} + 1106856017205658 T^{8} + 45566085274380219 T^{9} + 2435491906618185033 T^{10} + 88798496919527606849 T^{11} + \)\(48\!\cdots\!31\)\( T^{12} + \)\(42\!\cdots\!44\)\( T^{13} + \)\(61\!\cdots\!61\)\( T^{14} )^{2} \))(\( 1 - 11617 T^{2} + 71638992 T^{4} - 297119365904 T^{6} + 1048451854320398 T^{8} - 3652628127143740167 T^{10} + \)\(12\!\cdots\!43\)\( T^{12} - \)\(44\!\cdots\!87\)\( T^{14} + \)\(15\!\cdots\!58\)\( T^{16} - \)\(52\!\cdots\!24\)\( T^{18} + \)\(15\!\cdots\!72\)\( T^{20} - \)\(30\!\cdots\!17\)\( T^{22} + \)\(31\!\cdots\!61\)\( T^{24} \))(\( ( 1 - 3481 T^{2} + 12117361 T^{4} - 42180533641 T^{6} + 146830437604321 T^{8} - 511116753300641401 T^{10} + \)\(17\!\cdots\!81\)\( T^{12} )^{2} \))
$61$ (\( ( 1 - 61 T )( 1 + 61 T ) \))(\( ( 1 - 61 T )^{2}( 1 + 61 T )^{2} \))(\( 1 - 6176 T^{2} + 53251015 T^{4} - 178029474320 T^{6} + 737305086778615 T^{8} - 1183984365071207456 T^{10} + \)\(26\!\cdots\!21\)\( T^{12} \))(\( ( 1 + 298 T^{2} + 31588111 T^{4} + 19337532460 T^{6} + 437363962396351 T^{8} + 57128779273189738 T^{10} + \)\(26\!\cdots\!21\)\( T^{12} )^{2} \))(\( 1 - 33798 T^{2} + 564994107 T^{4} - 6205944738108 T^{6} + 50113713323620665 T^{8} - \)\(31\!\cdots\!30\)\( T^{10} + \)\(15\!\cdots\!07\)\( T^{12} - \)\(65\!\cdots\!80\)\( T^{14} + \)\(21\!\cdots\!87\)\( T^{16} - \)\(60\!\cdots\!30\)\( T^{18} + \)\(13\!\cdots\!65\)\( T^{20} - \)\(22\!\cdots\!88\)\( T^{22} + \)\(28\!\cdots\!07\)\( T^{24} - \)\(23\!\cdots\!18\)\( T^{26} + \)\(97\!\cdots\!81\)\( T^{28} \))(\( 1 + 180 T + 14521 T^{2} + 669780 T^{3} + 13845841 T^{4} \))(\( ( 1 - 121 T + 3721 T^{2} )( 1 - 47 T + 3721 T^{2} ) \))(\( 1 - 204 T + 33131 T^{2} - 3928836 T^{3} + 396166698 T^{4} - 36077954385 T^{5} + 3074787876040 T^{6} - 249044419787289 T^{7} + 19373960824471256 T^{8} - 1402697797539370524 T^{9} + 96292769362924730019 T^{10} - \)\(62\!\cdots\!62\)\( T^{11} + \)\(38\!\cdots\!74\)\( T^{12} - \)\(23\!\cdots\!02\)\( T^{13} + \)\(13\!\cdots\!79\)\( T^{14} - \)\(72\!\cdots\!64\)\( T^{15} + \)\(37\!\cdots\!36\)\( T^{16} - \)\(17\!\cdots\!89\)\( T^{17} + \)\(81\!\cdots\!40\)\( T^{18} - \)\(35\!\cdots\!85\)\( T^{19} + \)\(14\!\cdots\!78\)\( T^{20} - \)\(53\!\cdots\!16\)\( T^{21} + \)\(16\!\cdots\!31\)\( T^{22} - \)\(38\!\cdots\!84\)\( T^{23} + \)\(70\!\cdots\!41\)\( T^{24} \))(\( 1 + 75 T + 14670 T^{2} + 959625 T^{3} + 93492711 T^{4} + 6523470534 T^{5} + 516447473013 T^{6} + 40955289016050 T^{7} + 3099475009068240 T^{8} + 221454327856274874 T^{9} + 15041836352358228060 T^{10} + \)\(99\!\cdots\!66\)\( T^{11} + \)\(61\!\cdots\!12\)\( T^{12} + \)\(42\!\cdots\!16\)\( T^{13} + \)\(24\!\cdots\!33\)\( T^{14} + \)\(15\!\cdots\!36\)\( T^{15} + \)\(85\!\cdots\!92\)\( T^{16} + \)\(51\!\cdots\!26\)\( T^{17} + \)\(28\!\cdots\!60\)\( T^{18} + \)\(15\!\cdots\!74\)\( T^{19} + \)\(82\!\cdots\!40\)\( T^{20} + \)\(40\!\cdots\!50\)\( T^{21} + \)\(18\!\cdots\!93\)\( T^{22} + \)\(89\!\cdots\!54\)\( T^{23} + \)\(47\!\cdots\!11\)\( T^{24} + \)\(18\!\cdots\!25\)\( T^{25} + \)\(10\!\cdots\!70\)\( T^{26} + \)\(19\!\cdots\!75\)\( T^{27} + \)\(97\!\cdots\!81\)\( T^{28} \))(\( 1 + 27 T + 22782 T^{2} + 608553 T^{3} + 283942971 T^{4} + 7239195210 T^{5} + 2498669221221 T^{6} + 59872846528242 T^{7} + 17147330537242428 T^{8} + 380996725289528430 T^{9} + 96228236921075990724 T^{10} + \)\(19\!\cdots\!10\)\( T^{11} + \)\(45\!\cdots\!12\)\( T^{12} + \)\(86\!\cdots\!28\)\( T^{13} + \)\(18\!\cdots\!89\)\( T^{14} + \)\(32\!\cdots\!88\)\( T^{15} + \)\(62\!\cdots\!92\)\( T^{16} + \)\(10\!\cdots\!10\)\( T^{17} + \)\(18\!\cdots\!44\)\( T^{18} + \)\(27\!\cdots\!30\)\( T^{19} + \)\(45\!\cdots\!88\)\( T^{20} + \)\(59\!\cdots\!22\)\( T^{21} + \)\(91\!\cdots\!81\)\( T^{22} + \)\(98\!\cdots\!10\)\( T^{23} + \)\(14\!\cdots\!71\)\( T^{24} + \)\(11\!\cdots\!13\)\( T^{25} + \)\(16\!\cdots\!62\)\( T^{26} + \)\(70\!\cdots\!47\)\( T^{27} + \)\(97\!\cdots\!81\)\( T^{28} \))(\( ( 1 - 175 T + 18022 T^{2} - 970578 T^{3} + 3591233 T^{4} + 4115703697 T^{5} - 381741433072 T^{6} + 15314533456537 T^{7} + 49723641111953 T^{8} - 50004541906550658 T^{9} + 3454949194836998182 T^{10} - \)\(12\!\cdots\!75\)\( T^{11} + \)\(26\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 + 47 T - 1512 T^{2} - 245951 T^{3} - 5933545 T^{4} + 636307056 T^{5} + 51985152577 T^{6} + 2367698555376 T^{7} - 82154920636345 T^{8} - 12671487594462311 T^{9} - 289861457251888872 T^{10} + 33527116848155482247 T^{11} + \)\(26\!\cdots\!21\)\( T^{12} )( 1 + 121 T + 10920 T^{2} + 871079 T^{3} + 64767239 T^{4} + 4595550960 T^{5} + 315062769841 T^{6} + 17100045122160 T^{7} + 896756893202999 T^{8} + 44878316178005519 T^{9} + 2093443857930308520 T^{10} + 86314492311208794721 T^{11} + \)\(26\!\cdots\!21\)\( T^{12} ) \))
$67$ (\( 1 - 91 T + 4489 T^{2} \))(\( ( 1 + 91 T + 4489 T^{2} )^{2} \))(\( ( 1 + 35 T + 9017 T^{2} + 350730 T^{3} + 40477313 T^{4} + 705289235 T^{5} + 90458382169 T^{6} )^{2} \))(\( ( 1 - 94 T + 12035 T^{2} - 629964 T^{3} + 54025115 T^{4} - 1894205374 T^{5} + 90458382169 T^{6} )^{4} \))(\( ( 1 - 67 T + 20995 T^{2} - 909910 T^{3} + 195521481 T^{4} - 6071498237 T^{5} + 1189501163939 T^{6} - 30048384588084 T^{7} + 5339670724922171 T^{8} - 122347495625073677 T^{9} + 17686556850546872289 T^{10} - \)\(36\!\cdots\!10\)\( T^{11} + \)\(38\!\cdots\!55\)\( T^{12} - \)\(54\!\cdots\!87\)\( T^{13} + \)\(36\!\cdots\!29\)\( T^{14} )^{2} \))(\( 1 + 59 T - 1008 T^{2} + 264851 T^{3} + 20151121 T^{4} \))(\( ( 1 - 13 T + 4489 T^{2} )( 1 + 122 T + 4489 T^{2} ) \))(\( 1 - 115 T - 7960 T^{2} + 1601411 T^{3} + 12878544 T^{4} - 11631792126 T^{5} + 264032039310 T^{6} + 51372624149438 T^{7} - 2607440286917038 T^{8} - 136422464608902859 T^{9} + 13476394220383696006 T^{10} + \)\(18\!\cdots\!27\)\( T^{11} - \)\(61\!\cdots\!22\)\( T^{12} + \)\(84\!\cdots\!03\)\( T^{13} + \)\(27\!\cdots\!26\)\( T^{14} - \)\(12\!\cdots\!71\)\( T^{15} - \)\(10\!\cdots\!58\)\( T^{16} + \)\(93\!\cdots\!62\)\( T^{17} + \)\(21\!\cdots\!10\)\( T^{18} - \)\(42\!\cdots\!54\)\( T^{19} + \)\(21\!\cdots\!64\)\( T^{20} + \)\(11\!\cdots\!99\)\( T^{21} - \)\(26\!\cdots\!60\)\( T^{22} - \)\(17\!\cdots\!35\)\( T^{23} + \)\(66\!\cdots\!21\)\( T^{24} \))(\( 1 + 37 T - 24324 T^{2} - 1134721 T^{3} + 323364408 T^{4} + 16672839567 T^{5} - 2895733881225 T^{6} - 154918549203893 T^{7} + 19598134711042428 T^{8} + 975963875416802919 T^{9} - \)\(10\!\cdots\!63\)\( T^{10} - \)\(40\!\cdots\!87\)\( T^{11} + \)\(51\!\cdots\!75\)\( T^{12} + \)\(74\!\cdots\!82\)\( T^{13} - \)\(23\!\cdots\!92\)\( T^{14} + \)\(33\!\cdots\!98\)\( T^{15} + \)\(10\!\cdots\!75\)\( T^{16} - \)\(36\!\cdots\!03\)\( T^{17} - \)\(43\!\cdots\!83\)\( T^{18} + \)\(17\!\cdots\!31\)\( T^{19} + \)\(16\!\cdots\!08\)\( T^{20} - \)\(56\!\cdots\!97\)\( T^{21} - \)\(47\!\cdots\!25\)\( T^{22} + \)\(12\!\cdots\!03\)\( T^{23} + \)\(10\!\cdots\!08\)\( T^{24} - \)\(16\!\cdots\!69\)\( T^{25} - \)\(16\!\cdots\!04\)\( T^{26} + \)\(11\!\cdots\!53\)\( T^{27} + \)\(13\!\cdots\!41\)\( T^{28} \))(\( 1 - 21 T - 3872 T^{2} + 757577 T^{3} - 10344232 T^{4} - 3101690039 T^{5} + 396692197123 T^{6} + 3328477569223 T^{7} - 1909259543514542 T^{8} + 161992405027979041 T^{9} + 3839942574791564099 T^{10} - \)\(86\!\cdots\!37\)\( T^{11} + \)\(49\!\cdots\!37\)\( T^{12} + \)\(23\!\cdots\!32\)\( T^{13} - \)\(28\!\cdots\!56\)\( T^{14} + \)\(10\!\cdots\!48\)\( T^{15} + \)\(99\!\cdots\!77\)\( T^{16} - \)\(78\!\cdots\!53\)\( T^{17} + \)\(15\!\cdots\!59\)\( T^{18} + \)\(29\!\cdots\!09\)\( T^{19} - \)\(15\!\cdots\!62\)\( T^{20} + \)\(12\!\cdots\!67\)\( T^{21} + \)\(65\!\cdots\!63\)\( T^{22} - \)\(22\!\cdots\!51\)\( T^{23} - \)\(34\!\cdots\!32\)\( T^{24} + \)\(11\!\cdots\!53\)\( T^{25} - \)\(25\!\cdots\!12\)\( T^{26} - \)\(63\!\cdots\!49\)\( T^{27} + \)\(13\!\cdots\!41\)\( T^{28} \))(\( ( 1 + 22 T - 4369 T^{2} - 166064 T^{3} + 17233817 T^{4} + 618720814 T^{5} - 65229499377 T^{6} + 2777437734046 T^{7} + 347280731658857 T^{8} - 15021880776512816 T^{9} - 1774109683244964529 T^{10} + 40102431700138751878 T^{11} + \)\(81\!\cdots\!61\)\( T^{12} )^{2} \))(\( ( 1 - 122 T + 10395 T^{2} - 720532 T^{3} + 41241749 T^{4} - 1797025230 T^{5} + 34102866799 T^{6} - 8066846257470 T^{7} + 831067474350629 T^{8} - 65178159020993908 T^{9} + 4221073508201283195 T^{10} - \)\(22\!\cdots\!78\)\( T^{11} + \)\(81\!\cdots\!61\)\( T^{12} )( 1 + 13 T - 4320 T^{2} - 114517 T^{3} + 17903759 T^{4} + 746815680 T^{5} - 70661370311 T^{6} + 3352455587520 T^{7} + 360780813963839 T^{8} - 10359022550847373 T^{9} - 1754212367044689120 T^{10} + 23696891459172898837 T^{11} + \)\(81\!\cdots\!61\)\( T^{12} ) \))
$71$ (\( ( 1 - 71 T )( 1 + 71 T ) \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( 1 - 22246 T^{2} + 239223215 T^{4} - 1523736510420 T^{6} + 6079064027374415 T^{8} - 14365433056093199206 T^{10} + \)\(16\!\cdots\!41\)\( T^{12} \))(\( ( 1 - 8554 T^{2} + 44826155 T^{4} - 144692605764 T^{6} + 1139107951316555 T^{8} - 5523775706276239594 T^{10} + \)\(16\!\cdots\!41\)\( T^{12} )^{2} \))(\( 1 - 35326 T^{2} + 656197363 T^{4} - 8235510824956 T^{6} + 77924894067415761 T^{8} - \)\(59\!\cdots\!06\)\( T^{10} + \)\(37\!\cdots\!79\)\( T^{12} - \)\(20\!\cdots\!40\)\( T^{14} + \)\(95\!\cdots\!99\)\( T^{16} - \)\(38\!\cdots\!66\)\( T^{18} + \)\(12\!\cdots\!01\)\( T^{20} - \)\(34\!\cdots\!76\)\( T^{22} + \)\(69\!\cdots\!63\)\( T^{24} - \)\(95\!\cdots\!06\)\( T^{26} + \)\(68\!\cdots\!61\)\( T^{28} \))(\( 1 - 138 T + 11389 T^{2} - 695658 T^{3} + 25411681 T^{4} \))(\( ( 1 - 71 T + 5041 T^{2} )( 1 + 71 T + 5041 T^{2} ) \))(\( 1 - 66 T + 8383 T^{2} - 457446 T^{3} + 22253522 T^{4} - 2686038483 T^{5} - 142137724894 T^{6} - 6765531085149 T^{7} - 469326810763006 T^{8} - 20521634467403010 T^{9} + 5562036689541880365 T^{10} - \)\(10\!\cdots\!58\)\( T^{11} + \)\(64\!\cdots\!18\)\( T^{12} - \)\(54\!\cdots\!78\)\( T^{13} + \)\(14\!\cdots\!65\)\( T^{14} - \)\(26\!\cdots\!10\)\( T^{15} - \)\(30\!\cdots\!66\)\( T^{16} - \)\(22\!\cdots\!49\)\( T^{17} - \)\(23\!\cdots\!54\)\( T^{18} - \)\(22\!\cdots\!23\)\( T^{19} + \)\(92\!\cdots\!62\)\( T^{20} - \)\(96\!\cdots\!06\)\( T^{21} + \)\(88\!\cdots\!83\)\( T^{22} - \)\(35\!\cdots\!06\)\( T^{23} + \)\(26\!\cdots\!81\)\( T^{24} \))(\( 1 - 198 T + 48419 T^{2} - 6999498 T^{3} + 1080889108 T^{4} - 128379432066 T^{5} + 15610060908905 T^{6} - 1603453114300074 T^{7} + 165831642404318745 T^{8} - 15137112505446719976 T^{9} + \)\(13\!\cdots\!18\)\( T^{10} - \)\(11\!\cdots\!44\)\( T^{11} + \)\(92\!\cdots\!77\)\( T^{12} - \)\(69\!\cdots\!54\)\( T^{13} + \)\(51\!\cdots\!97\)\( T^{14} - \)\(35\!\cdots\!14\)\( T^{15} + \)\(23\!\cdots\!37\)\( T^{16} - \)\(14\!\cdots\!24\)\( T^{17} + \)\(89\!\cdots\!98\)\( T^{18} - \)\(49\!\cdots\!76\)\( T^{19} + \)\(27\!\cdots\!45\)\( T^{20} - \)\(13\!\cdots\!94\)\( T^{21} + \)\(65\!\cdots\!05\)\( T^{22} - \)\(26\!\cdots\!26\)\( T^{23} + \)\(11\!\cdots\!08\)\( T^{24} - \)\(37\!\cdots\!18\)\( T^{25} + \)\(13\!\cdots\!39\)\( T^{26} - \)\(26\!\cdots\!58\)\( T^{27} + \)\(68\!\cdots\!61\)\( T^{28} \))(\( 1 + 750 T + 293147 T^{2} + 79235250 T^{3} + 16600762060 T^{4} + 2869575797778 T^{5} + 425681397118169 T^{6} + 55659160239288282 T^{7} + 6536306404760344785 T^{8} + \)\(69\!\cdots\!32\)\( T^{9} + \)\(68\!\cdots\!22\)\( T^{10} + \)\(62\!\cdots\!00\)\( T^{11} + \)\(52\!\cdots\!49\)\( T^{12} + \)\(41\!\cdots\!58\)\( T^{13} + \)\(30\!\cdots\!77\)\( T^{14} + \)\(20\!\cdots\!78\)\( T^{15} + \)\(13\!\cdots\!69\)\( T^{16} + \)\(79\!\cdots\!00\)\( T^{17} + \)\(44\!\cdots\!42\)\( T^{18} + \)\(22\!\cdots\!32\)\( T^{19} + \)\(10\!\cdots\!85\)\( T^{20} + \)\(46\!\cdots\!42\)\( T^{21} + \)\(17\!\cdots\!49\)\( T^{22} + \)\(60\!\cdots\!58\)\( T^{23} + \)\(17\!\cdots\!60\)\( T^{24} + \)\(42\!\cdots\!50\)\( T^{25} + \)\(78\!\cdots\!07\)\( T^{26} + \)\(10\!\cdots\!50\)\( T^{27} + \)\(68\!\cdots\!61\)\( T^{28} \))(\( 1 + 16492 T^{2} + 49176413 T^{4} - 703845491426 T^{6} - 5042711533416745 T^{8} + 9446007259836530866 T^{10} + \)\(18\!\cdots\!47\)\( T^{12} + \)\(24\!\cdots\!46\)\( T^{14} - \)\(32\!\cdots\!45\)\( T^{16} - \)\(11\!\cdots\!66\)\( T^{18} + \)\(20\!\cdots\!73\)\( T^{20} + \)\(17\!\cdots\!92\)\( T^{22} + \)\(26\!\cdots\!81\)\( T^{24} \))(\( ( 1 - 71 T + 357911 T^{3} - 25411681 T^{4} + 128100283921 T^{6} - 645753531245761 T^{8} + 45848500718449031 T^{9} - \)\(23\!\cdots\!71\)\( T^{11} + \)\(16\!\cdots\!41\)\( T^{12} )( 1 + 71 T - 357911 T^{3} - 25411681 T^{4} + 128100283921 T^{6} - 645753531245761 T^{8} - 45848500718449031 T^{9} + \)\(23\!\cdots\!71\)\( T^{11} + \)\(16\!\cdots\!41\)\( T^{12} ) \))
$73$ (\( ( 1 - 73 T )( 1 + 73 T ) \))(\( ( 1 - 73 T )^{2}( 1 + 73 T )^{2} \))(\( 1 - 24604 T^{2} + 277197791 T^{4} - 1859020745064 T^{6} + 7871929673485631 T^{8} - 19842144100961968924 T^{10} + \)\(22\!\cdots\!21\)\( T^{12} \))(\( ( 1 - 23266 T^{2} + 242784035 T^{4} - 1568732835396 T^{6} + 6894639536882435 T^{8} - 18763100498007688546 T^{10} + \)\(22\!\cdots\!21\)\( T^{12} )^{2} \))(\( 1 - 39502 T^{2} + 752139715 T^{4} - 9087927750076 T^{6} + 78026579614304289 T^{8} - \)\(51\!\cdots\!58\)\( T^{10} + \)\(28\!\cdots\!55\)\( T^{12} - \)\(15\!\cdots\!36\)\( T^{14} + \)\(81\!\cdots\!55\)\( T^{16} - \)\(41\!\cdots\!98\)\( T^{18} + \)\(17\!\cdots\!69\)\( T^{20} - \)\(59\!\cdots\!36\)\( T^{22} + \)\(13\!\cdots\!15\)\( T^{24} - \)\(20\!\cdots\!82\)\( T^{26} + \)\(14\!\cdots\!81\)\( T^{28} \))(\( 1 - 21 T + 5476 T^{2} - 111909 T^{3} + 28398241 T^{4} \))(\( ( 1 + 46 T + 5329 T^{2} )( 1 + 143 T + 5329 T^{2} ) \))(\( 1 - 249 T + 47836 T^{2} - 6765081 T^{3} + 836510852 T^{4} - 87998072508 T^{5} + 8327492192822 T^{6} - 712665936231156 T^{7} + 56395869792302342 T^{8} - 4210361193162399351 T^{9} + \)\(30\!\cdots\!94\)\( T^{10} - \)\(21\!\cdots\!91\)\( T^{11} + \)\(15\!\cdots\!38\)\( T^{12} - \)\(11\!\cdots\!39\)\( T^{13} + \)\(85\!\cdots\!54\)\( T^{14} - \)\(63\!\cdots\!39\)\( T^{15} + \)\(45\!\cdots\!02\)\( T^{16} - \)\(30\!\cdots\!44\)\( T^{17} + \)\(19\!\cdots\!62\)\( T^{18} - \)\(10\!\cdots\!72\)\( T^{19} + \)\(54\!\cdots\!72\)\( T^{20} - \)\(23\!\cdots\!89\)\( T^{21} + \)\(88\!\cdots\!36\)\( T^{22} - \)\(24\!\cdots\!21\)\( T^{23} + \)\(52\!\cdots\!41\)\( T^{24} \))(\( 1 + 87 T + 26516 T^{2} + 2087391 T^{3} + 335859244 T^{4} + 20866673985 T^{5} + 2724790957817 T^{6} + 124663395901863 T^{7} + 16962440885567664 T^{8} + 618622607953760499 T^{9} + 99399901796104821355 T^{10} + \)\(33\!\cdots\!87\)\( T^{11} + \)\(59\!\cdots\!79\)\( T^{12} + \)\(19\!\cdots\!08\)\( T^{13} + \)\(33\!\cdots\!00\)\( T^{14} + \)\(10\!\cdots\!32\)\( T^{15} + \)\(16\!\cdots\!39\)\( T^{16} + \)\(50\!\cdots\!43\)\( T^{17} + \)\(80\!\cdots\!55\)\( T^{18} + \)\(26\!\cdots\!51\)\( T^{19} + \)\(38\!\cdots\!44\)\( T^{20} + \)\(15\!\cdots\!67\)\( T^{21} + \)\(17\!\cdots\!37\)\( T^{22} + \)\(72\!\cdots\!65\)\( T^{23} + \)\(62\!\cdots\!44\)\( T^{24} + \)\(20\!\cdots\!39\)\( T^{25} + \)\(13\!\cdots\!56\)\( T^{26} + \)\(24\!\cdots\!43\)\( T^{27} + \)\(14\!\cdots\!81\)\( T^{28} \))(\( 1 + 393 T + 93104 T^{2} + 16357053 T^{3} + 2335256692 T^{4} + 283208705367 T^{5} + 29841242718749 T^{6} + 2774460041494083 T^{7} + 229392579227160798 T^{8} + 16967373229729202241 T^{9} + \)\(11\!\cdots\!37\)\( T^{10} + \)\(67\!\cdots\!05\)\( T^{11} + \)\(36\!\cdots\!01\)\( T^{12} + \)\(20\!\cdots\!62\)\( T^{13} + \)\(12\!\cdots\!24\)\( T^{14} + \)\(10\!\cdots\!98\)\( T^{15} + \)\(10\!\cdots\!41\)\( T^{16} + \)\(10\!\cdots\!45\)\( T^{17} + \)\(90\!\cdots\!97\)\( T^{18} + \)\(72\!\cdots\!09\)\( T^{19} + \)\(52\!\cdots\!58\)\( T^{20} + \)\(33\!\cdots\!47\)\( T^{21} + \)\(19\!\cdots\!89\)\( T^{22} + \)\(98\!\cdots\!23\)\( T^{23} + \)\(43\!\cdots\!92\)\( T^{24} + \)\(16\!\cdots\!37\)\( T^{25} + \)\(48\!\cdots\!64\)\( T^{26} + \)\(10\!\cdots\!77\)\( T^{27} + \)\(14\!\cdots\!81\)\( T^{28} \))(\( ( 1 - 357 T + 54672 T^{2} - 4840381 T^{3} + 329887667 T^{4} - 25145445164 T^{5} + 1994675042179 T^{6} - 134000077278956 T^{7} + 9368229470393747 T^{8} - 732515313578976109 T^{9} + 44090786144033196432 T^{10} - \)\(15\!\cdots\!93\)\( T^{11} + \)\(22\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 143 T + 15120 T^{2} - 1400113 T^{3} + 119641679 T^{4} - 9647557920 T^{5} + 742030275169 T^{6} - 51411836155680 T^{7} + 3397613233886639 T^{8} - 211885017572170657 T^{9} + 12193676589438504720 T^{10} - \)\(61\!\cdots\!07\)\( T^{11} + \)\(22\!\cdots\!21\)\( T^{12} )( 1 - 46 T - 3213 T^{2} + 392932 T^{3} - 952795 T^{4} - 2050106058 T^{5} + 99382323223 T^{6} - 10925015183082 T^{7} - 27057702033595 T^{8} + 59464060204189348 T^{9} - 2591156275255682253 T^{10} - \)\(19\!\cdots\!54\)\( T^{11} + \)\(22\!\cdots\!21\)\( T^{12} ) \))
$79$ (\( 1 + 14 T + 6241 T^{2} \))(\( ( 1 - 14 T + 6241 T^{2} )^{2} \))(\( ( 1 - 89 T + 20896 T^{2} - 1122134 T^{3} + 130411936 T^{4} - 3466557209 T^{5} + 243087455521 T^{6} )^{2} \))(\( ( 1 - 2 T + 6073 T^{2} - 530216 T^{3} + 37901593 T^{4} - 77900162 T^{5} + 243087455521 T^{6} )^{4} \))(\( ( 1 + 30 T + 15435 T^{2} + 932364 T^{3} + 166994349 T^{4} + 8589161514 T^{5} + 1387372139847 T^{6} + 61448902589272 T^{7} + 8658589524785127 T^{8} + 334548536692382634 T^{9} + 40594231384795850829 T^{10} + \)\(14\!\cdots\!04\)\( T^{11} + \)\(14\!\cdots\!35\)\( T^{12} + \)\(17\!\cdots\!30\)\( T^{13} + \)\(36\!\cdots\!81\)\( T^{14} )^{2} \))(\( 1 - 52 T - 3537 T^{2} - 324532 T^{3} + 38950081 T^{4} \))(\( ( 1 + 11 T + 6241 T^{2} )( 1 + 131 T + 6241 T^{2} ) \))(\( 1 - 236 T + 6211 T^{2} + 1816934 T^{3} + 15618410 T^{4} - 18039764431 T^{5} - 862854134850 T^{6} + 144012352794143 T^{7} + 12282532151020286 T^{8} - 938070438536680854 T^{9} - 93564616453312180819 T^{10} + \)\(13\!\cdots\!72\)\( T^{11} + \)\(78\!\cdots\!82\)\( T^{12} + \)\(84\!\cdots\!52\)\( T^{13} - \)\(36\!\cdots\!39\)\( T^{14} - \)\(22\!\cdots\!34\)\( T^{15} + \)\(18\!\cdots\!46\)\( T^{16} + \)\(13\!\cdots\!43\)\( T^{17} - \)\(50\!\cdots\!50\)\( T^{18} - \)\(66\!\cdots\!11\)\( T^{19} + \)\(35\!\cdots\!10\)\( T^{20} + \)\(26\!\cdots\!74\)\( T^{21} + \)\(55\!\cdots\!11\)\( T^{22} - \)\(13\!\cdots\!76\)\( T^{23} + \)\(34\!\cdots\!81\)\( T^{24} \))(\( 1 - 30 T - 33252 T^{2} + 156498 T^{3} + 625487556 T^{4} + 6507450678 T^{5} - 7960741142745 T^{6} - 159820391002474 T^{7} + 76670493837333753 T^{8} + 1784859901358274780 T^{9} - \)\(59\!\cdots\!54\)\( T^{10} - \)\(11\!\cdots\!24\)\( T^{11} + \)\(40\!\cdots\!13\)\( T^{12} + \)\(31\!\cdots\!42\)\( T^{13} - \)\(25\!\cdots\!55\)\( T^{14} + \)\(19\!\cdots\!22\)\( T^{15} + \)\(15\!\cdots\!53\)\( T^{16} - \)\(28\!\cdots\!04\)\( T^{17} - \)\(90\!\cdots\!94\)\( T^{18} + \)\(16\!\cdots\!80\)\( T^{19} + \)\(45\!\cdots\!73\)\( T^{20} - \)\(58\!\cdots\!94\)\( T^{21} - \)\(18\!\cdots\!45\)\( T^{22} + \)\(93\!\cdots\!58\)\( T^{23} + \)\(56\!\cdots\!56\)\( T^{24} + \)\(87\!\cdots\!18\)\( T^{25} - \)\(11\!\cdots\!12\)\( T^{26} - \)\(65\!\cdots\!30\)\( T^{27} + \)\(13\!\cdots\!61\)\( T^{28} \))(\( 1 + 248 T + 23012 T^{2} + 2975878 T^{3} + 514218504 T^{4} + 41153248248 T^{5} + 2692670052575 T^{6} + 420619335390246 T^{7} + 34743730418077541 T^{8} + 1295972738284049338 T^{9} + \)\(20\!\cdots\!94\)\( T^{10} + \)\(22\!\cdots\!96\)\( T^{11} + \)\(71\!\cdots\!53\)\( T^{12} + \)\(80\!\cdots\!82\)\( T^{13} + \)\(12\!\cdots\!37\)\( T^{14} + \)\(49\!\cdots\!62\)\( T^{15} + \)\(27\!\cdots\!93\)\( T^{16} + \)\(54\!\cdots\!16\)\( T^{17} + \)\(31\!\cdots\!34\)\( T^{18} + \)\(12\!\cdots\!38\)\( T^{19} + \)\(20\!\cdots\!81\)\( T^{20} + \)\(15\!\cdots\!26\)\( T^{21} + \)\(61\!\cdots\!75\)\( T^{22} + \)\(59\!\cdots\!28\)\( T^{23} + \)\(46\!\cdots\!04\)\( T^{24} + \)\(16\!\cdots\!98\)\( T^{25} + \)\(80\!\cdots\!72\)\( T^{26} + \)\(54\!\cdots\!08\)\( T^{27} + \)\(13\!\cdots\!61\)\( T^{28} \))(\( ( 1 - 2 T + 6934 T^{2} - 401003 T^{3} + 43275094 T^{4} - 77900162 T^{5} + 243087455521 T^{6} )^{4} \))(\( ( 1 - 131 T + 10920 T^{2} - 612949 T^{3} + 12144599 T^{4} + 2234472240 T^{5} - 368510305799 T^{6} + 13945341249840 T^{7} + 473033114762519 T^{8} - 149000212774141429 T^{9} + 16566828204179646120 T^{10} - \)\(12\!\cdots\!31\)\( T^{11} + \)\(59\!\cdots\!41\)\( T^{12} )( 1 - 11 T - 6120 T^{2} + 135971 T^{3} + 36699239 T^{4} - 1252286640 T^{5} - 215264797559 T^{6} - 7815520920240 T^{7} + 1429438331688359 T^{8} + 33052844414645891 T^{9} - 9284705916628153320 T^{10} - \)\(10\!\cdots\!11\)\( T^{11} + \)\(59\!\cdots\!41\)\( T^{12} ) \))
$83$ (\( 1 + 123 T + 6889 T^{2} \))(\( 1 + 1351 T^{2} + 47458321 T^{4} \))(\( ( 1 + 5 T + 14767 T^{2} + 128390 T^{3} + 101729863 T^{4} + 237291605 T^{5} + 326940373369 T^{6} )^{2} \))(\( ( 1 + 29896 T^{2} + 438236338 T^{4} + 3805686578182 T^{6} + 20797960802668498 T^{8} + 67334528572028769736 T^{10} + \)\(10\!\cdots\!61\)\( T^{12} )^{2} \))(\( ( 1 - 147 T + 32295 T^{2} - 3413526 T^{3} + 469160262 T^{4} - 40188269148 T^{5} + 4362001508118 T^{6} - 322962400211822 T^{7} + 30049828389424902 T^{8} - 1907267777660180508 T^{9} + \)\(15\!\cdots\!78\)\( T^{10} - \)\(76\!\cdots\!66\)\( T^{11} + \)\(50\!\cdots\!55\)\( T^{12} - \)\(15\!\cdots\!67\)\( T^{13} + \)\(73\!\cdots\!29\)\( T^{14} )^{2} \))(\( 1 - 46 T - 4773 T^{2} - 316894 T^{3} + 47458321 T^{4} \))(\( 1 - 6889 T^{2} + 47458321 T^{4} \))(\( 1 - 4 T - 21815 T^{2} - 1032278 T^{3} + 256215014 T^{4} + 22099127125 T^{5} - 1301303064984 T^{6} - 269522473356119 T^{7} - 2312375630136352 T^{8} + 1824448248468292326 T^{9} + \)\(11\!\cdots\!01\)\( T^{10} - \)\(55\!\cdots\!10\)\( T^{11} - \)\(10\!\cdots\!42\)\( T^{12} - \)\(37\!\cdots\!90\)\( T^{13} + \)\(54\!\cdots\!21\)\( T^{14} + \)\(59\!\cdots\!94\)\( T^{15} - \)\(52\!\cdots\!32\)\( T^{16} - \)\(41\!\cdots\!31\)\( T^{17} - \)\(13\!\cdots\!24\)\( T^{18} + \)\(16\!\cdots\!25\)\( T^{19} + \)\(12\!\cdots\!34\)\( T^{20} - \)\(36\!\cdots\!02\)\( T^{21} - \)\(52\!\cdots\!15\)\( T^{22} - \)\(66\!\cdots\!56\)\( T^{23} + \)\(11\!\cdots\!21\)\( T^{24} \))(\( 1 + 219 T + 5826 T^{2} - 990009 T^{3} + 28290867 T^{4} + 2590022760 T^{5} - 1100763057351 T^{6} - 96614237152684 T^{7} - 4904323726399182 T^{8} - 260026319335969800 T^{9} - 26082269372837148762 T^{10} - \)\(13\!\cdots\!28\)\( T^{11} + \)\(50\!\cdots\!72\)\( T^{12} + \)\(41\!\cdots\!94\)\( T^{13} + \)\(32\!\cdots\!95\)\( T^{14} + \)\(28\!\cdots\!66\)\( T^{15} + \)\(24\!\cdots\!12\)\( T^{16} - \)\(44\!\cdots\!32\)\( T^{17} - \)\(58\!\cdots\!42\)\( T^{18} - \)\(40\!\cdots\!00\)\( T^{19} - \)\(52\!\cdots\!02\)\( T^{20} - \)\(71\!\cdots\!36\)\( T^{21} - \)\(55\!\cdots\!31\)\( T^{22} + \)\(90\!\cdots\!40\)\( T^{23} + \)\(68\!\cdots\!67\)\( T^{24} - \)\(16\!\cdots\!01\)\( T^{25} + \)\(66\!\cdots\!46\)\( T^{26} + \)\(17\!\cdots\!11\)\( T^{27} + \)\(54\!\cdots\!41\)\( T^{28} \))(\( 1 - 71 T - 29406 T^{2} + 1816393 T^{3} + 471275075 T^{4} - 23818829078 T^{5} - 5557177748389 T^{6} + 227782185944258 T^{7} + 52936010703161668 T^{8} - 1696386457028348844 T^{9} - \)\(43\!\cdots\!76\)\( T^{10} + \)\(90\!\cdots\!08\)\( T^{11} + \)\(32\!\cdots\!28\)\( T^{12} - \)\(23\!\cdots\!08\)\( T^{13} - \)\(22\!\cdots\!45\)\( T^{14} - \)\(15\!\cdots\!12\)\( T^{15} + \)\(15\!\cdots\!88\)\( T^{16} + \)\(29\!\cdots\!52\)\( T^{17} - \)\(97\!\cdots\!16\)\( T^{18} - \)\(26\!\cdots\!56\)\( T^{19} + \)\(56\!\cdots\!48\)\( T^{20} + \)\(16\!\cdots\!82\)\( T^{21} - \)\(28\!\cdots\!09\)\( T^{22} - \)\(83\!\cdots\!02\)\( T^{23} + \)\(11\!\cdots\!75\)\( T^{24} + \)\(30\!\cdots\!77\)\( T^{25} - \)\(33\!\cdots\!26\)\( T^{26} - \)\(55\!\cdots\!99\)\( T^{27} + \)\(54\!\cdots\!41\)\( T^{28} \))(\( 1 + 6914 T^{2} - 17464269 T^{4} - 60939336224 T^{6} + 1092183701655149 T^{8} - 13483612583858610150 T^{10} - \)\(19\!\cdots\!01\)\( T^{12} - \)\(63\!\cdots\!50\)\( T^{14} + \)\(24\!\cdots\!09\)\( T^{16} - \)\(65\!\cdots\!64\)\( T^{18} - \)\(88\!\cdots\!89\)\( T^{20} + \)\(16\!\cdots\!14\)\( T^{22} + \)\(11\!\cdots\!21\)\( T^{24} \))(\( 1 + 6889 T^{2} - 326940373369 T^{6} - 2252292232139041 T^{8} + \)\(10\!\cdots\!61\)\( T^{12} - \)\(50\!\cdots\!81\)\( T^{16} - \)\(34\!\cdots\!09\)\( T^{18} + \)\(16\!\cdots\!89\)\( T^{22} + \)\(11\!\cdots\!21\)\( T^{24} \))
$89$ (\( ( 1 - 89 T )( 1 + 89 T ) \))(\( ( 1 - 89 T )^{2}( 1 + 89 T )^{2} \))(\( 1 - 38876 T^{2} + 668902015 T^{4} - 6712320081320 T^{6} + 41968411430515615 T^{8} - \)\(15\!\cdots\!56\)\( T^{10} + \)\(24\!\cdots\!21\)\( T^{12} \))(\( ( 1 - 29354 T^{2} + 401491435 T^{4} - 3655307590724 T^{6} + 25190472374205835 T^{8} - \)\(11\!\cdots\!74\)\( T^{10} + \)\(24\!\cdots\!21\)\( T^{12} )^{2} \))(\( 1 - 55518 T^{2} + 1593591987 T^{4} - 31321862328060 T^{6} + 472577821360946961 T^{8} - \)\(57\!\cdots\!22\)\( T^{10} + \)\(58\!\cdots\!91\)\( T^{12} - \)\(50\!\cdots\!52\)\( T^{14} + \)\(36\!\cdots\!31\)\( T^{16} - \)\(22\!\cdots\!82\)\( T^{18} + \)\(11\!\cdots\!81\)\( T^{20} - \)\(48\!\cdots\!60\)\( T^{22} + \)\(15\!\cdots\!87\)\( T^{24} - \)\(33\!\cdots\!38\)\( T^{26} + \)\(38\!\cdots\!81\)\( T^{28} \))(\( 1 - 291 T + 36148 T^{2} - 2305011 T^{3} + 62742241 T^{4} \))(\( ( 1 - 89 T + 7921 T^{2} )( 1 + 89 T + 7921 T^{2} ) \))(\( 1 - 45 T + 19568 T^{2} - 850185 T^{3} + 135178944 T^{4} - 15768566256 T^{5} + 877991398306 T^{6} - 230067075716784 T^{7} + 11948725877253974 T^{8} - 1772692905496764327 T^{9} + \)\(15\!\cdots\!42\)\( T^{10} - \)\(84\!\cdots\!51\)\( T^{11} + \)\(14\!\cdots\!90\)\( T^{12} - \)\(67\!\cdots\!71\)\( T^{13} + \)\(96\!\cdots\!22\)\( T^{14} - \)\(88\!\cdots\!47\)\( T^{15} + \)\(47\!\cdots\!94\)\( T^{16} - \)\(71\!\cdots\!84\)\( T^{17} + \)\(21\!\cdots\!26\)\( T^{18} - \)\(30\!\cdots\!96\)\( T^{19} + \)\(20\!\cdots\!84\)\( T^{20} - \)\(10\!\cdots\!85\)\( T^{21} + \)\(19\!\cdots\!68\)\( T^{22} - \)\(34\!\cdots\!45\)\( T^{23} + \)\(61\!\cdots\!41\)\( T^{24} \))(\( 1 + 282 T + 86103 T^{2} + 16805790 T^{3} + 3273548421 T^{4} + 505119464988 T^{5} + 76892748843720 T^{6} + 10018740982670988 T^{7} + 1287691319201733708 T^{8} + \)\(14\!\cdots\!32\)\( T^{9} + \)\(16\!\cdots\!56\)\( T^{10} + \)\(17\!\cdots\!48\)\( T^{11} + \)\(17\!\cdots\!18\)\( T^{12} + \)\(16\!\cdots\!52\)\( T^{13} + \)\(14\!\cdots\!74\)\( T^{14} + \)\(12\!\cdots\!92\)\( T^{15} + \)\(10\!\cdots\!38\)\( T^{16} + \)\(84\!\cdots\!28\)\( T^{17} + \)\(65\!\cdots\!36\)\( T^{18} + \)\(45\!\cdots\!32\)\( T^{19} + \)\(31\!\cdots\!68\)\( T^{20} + \)\(19\!\cdots\!08\)\( T^{21} + \)\(11\!\cdots\!20\)\( T^{22} + \)\(62\!\cdots\!28\)\( T^{23} + \)\(31\!\cdots\!21\)\( T^{24} + \)\(12\!\cdots\!90\)\( T^{25} + \)\(52\!\cdots\!23\)\( T^{26} + \)\(13\!\cdots\!02\)\( T^{27} + \)\(38\!\cdots\!81\)\( T^{28} \))(\( 1 - 87 T + 38307 T^{2} - 3113208 T^{3} + 704200071 T^{4} - 58400274615 T^{5} + 9786288777084 T^{6} - 825887224050825 T^{7} + 121244295093606978 T^{8} - 9641110698515524023 T^{9} + \)\(13\!\cdots\!36\)\( T^{10} - \)\(97\!\cdots\!85\)\( T^{11} + \)\(12\!\cdots\!32\)\( T^{12} - \)\(89\!\cdots\!17\)\( T^{13} + \)\(10\!\cdots\!54\)\( T^{14} - \)\(70\!\cdots\!57\)\( T^{15} + \)\(76\!\cdots\!12\)\( T^{16} - \)\(48\!\cdots\!85\)\( T^{17} + \)\(51\!\cdots\!16\)\( T^{18} - \)\(30\!\cdots\!23\)\( T^{19} + \)\(29\!\cdots\!38\)\( T^{20} - \)\(16\!\cdots\!25\)\( T^{21} + \)\(15\!\cdots\!24\)\( T^{22} - \)\(71\!\cdots\!15\)\( T^{23} + \)\(68\!\cdots\!71\)\( T^{24} - \)\(23\!\cdots\!68\)\( T^{25} + \)\(23\!\cdots\!87\)\( T^{26} - \)\(42\!\cdots\!07\)\( T^{27} + \)\(38\!\cdots\!81\)\( T^{28} \))(\( 1 + 24893 T^{2} + 346264722 T^{4} + 2549513396497 T^{6} + 1418454053377871 T^{8} - \)\(18\!\cdots\!80\)\( T^{10} - \)\(22\!\cdots\!47\)\( T^{12} - \)\(11\!\cdots\!80\)\( T^{14} + \)\(55\!\cdots\!51\)\( T^{16} + \)\(62\!\cdots\!37\)\( T^{18} + \)\(53\!\cdots\!42\)\( T^{20} + \)\(24\!\cdots\!93\)\( T^{22} + \)\(61\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 89 T + 704969 T^{3} - 62742241 T^{4} + 496981290961 T^{6} - 3936588805702081 T^{8} + 350356403707485209 T^{9} - \)\(27\!\cdots\!89\)\( T^{11} + \)\(24\!\cdots\!21\)\( T^{12} )( 1 + 89 T - 704969 T^{3} - 62742241 T^{4} + 496981290961 T^{6} - 3936588805702081 T^{8} - 350356403707485209 T^{9} + \)\(27\!\cdots\!89\)\( T^{11} + \)\(24\!\cdots\!21\)\( T^{12} ) \))
$97$ (\( 1 + 193 T + 9409 T^{2} \))(\( ( 1 + 193 T + 9409 T^{2} )^{2} \))(\( ( 1 + 190 T + 26827 T^{2} + 2529295 T^{3} + 252415243 T^{4} + 16820563390 T^{5} + 832972004929 T^{6} )^{2} \))(\( ( 1 - 128 T + 30130 T^{2} - 2323646 T^{3} + 283493170 T^{4} - 11331747968 T^{5} + 832972004929 T^{6} )^{4} \))(\( ( 1 - 267 T + 83769 T^{2} - 14712948 T^{3} + 2641758456 T^{4} - 339877882320 T^{5} + 43330018949466 T^{6} - 4235858138068682 T^{7} + 407692148295525594 T^{8} - 30089144549592211920 T^{9} + \)\(22\!\cdots\!24\)\( T^{10} - \)\(11\!\cdots\!28\)\( T^{11} + \)\(61\!\cdots\!81\)\( T^{12} - \)\(18\!\cdots\!47\)\( T^{13} + \)\(65\!\cdots\!69\)\( T^{14} )^{2} \))(\( ( 1 + T + 9409 T^{2} )^{2} \))(\( ( 1 - 2 T + 9409 T^{2} )^{2} \))(\( ( 1 + 185 T + 45810 T^{2} + 6039385 T^{3} + 922201559 T^{4} + 96415612878 T^{5} + 11078943083116 T^{6} + 907174501569102 T^{7} + 81641840955349079 T^{8} + 5030638631988128665 T^{9} + \)\(35\!\cdots\!10\)\( T^{10} + \)\(13\!\cdots\!65\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 156 T + 51078 T^{2} - 5764413 T^{3} + 1070108259 T^{4} - 94802948610 T^{5} + 13483570113543 T^{6} - 1022689750529663 T^{7} + 126866911198326087 T^{8} - 8392836877123249410 T^{9} + \)\(89\!\cdots\!11\)\( T^{10} - \)\(45\!\cdots\!93\)\( T^{11} + \)\(37\!\cdots\!22\)\( T^{12} - \)\(10\!\cdots\!96\)\( T^{13} + \)\(65\!\cdots\!69\)\( T^{14} )^{2} \))(\( ( 1 - 267 T + 67713 T^{2} - 11214963 T^{3} + 1757194425 T^{4} - 220943514711 T^{5} + 26319520863132 T^{6} - 2630055446345096 T^{7} + 247640371801208988 T^{8} - 19559970498977752791 T^{9} + \)\(14\!\cdots\!25\)\( T^{10} - \)\(87\!\cdots\!43\)\( T^{11} + \)\(49\!\cdots\!37\)\( T^{12} - \)\(18\!\cdots\!47\)\( T^{13} + \)\(65\!\cdots\!69\)\( T^{14} )^{2} \))(\( ( 1 + 24 T - 8665 T^{2} + 321804 T^{3} - 78849569 T^{4} - 4605968874 T^{5} + 1700603651879 T^{6} - 43337561135466 T^{7} - 6980495650729889 T^{8} + 268053723074171916 T^{9} - 67911362095276367065 T^{10} + \)\(17\!\cdots\!76\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 2 T - 9405 T^{2} - 37628 T^{3} + 88416389 T^{4} + 530874630 T^{5} - 830848054841 T^{6} + 4994999393670 T^{7} + 7827439346786309 T^{8} - 31343070601468412 T^{9} - 73711062955115318205 T^{10} + \)\(14\!\cdots\!98\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} )^{2} \))
show more
show less