# Properties

 Label 1792.3 Level 1792 Weight 3 Dimension 105464 Nonzero newspaces 24 Sturm bound 589824 Trace bound 193

## Defining parameters

 Level: $$N$$ = $$1792 = 2^{8} \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$24$$ Sturm bound: $$589824$$ Trace bound: $$193$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(1792))$$.

Total New Old
Modular forms 198720 106504 92216
Cusp forms 194496 105464 89032
Eisenstein series 4224 1040 3184

## Trace form

 $$105464q - 128q^{2} - 96q^{3} - 128q^{4} - 128q^{5} - 128q^{6} - 120q^{7} - 320q^{8} - 160q^{9} + O(q^{10})$$ $$105464q - 128q^{2} - 96q^{3} - 128q^{4} - 128q^{5} - 128q^{6} - 120q^{7} - 320q^{8} - 160q^{9} - 128q^{10} - 96q^{11} - 128q^{12} - 128q^{13} - 160q^{14} - 240q^{15} - 128q^{16} - 192q^{17} - 128q^{18} - 96q^{19} - 128q^{20} - 160q^{21} - 320q^{22} - 96q^{23} - 128q^{24} - 160q^{25} - 128q^{26} - 96q^{27} - 160q^{28} - 320q^{29} - 128q^{30} - 112q^{31} - 128q^{32} - 224q^{33} - 128q^{34} - 120q^{35} - 320q^{36} - 128q^{37} - 128q^{38} - 96q^{39} - 128q^{40} - 160q^{41} - 160q^{42} - 240q^{43} - 128q^{44} - 272q^{45} - 128q^{46} - 96q^{47} - 128q^{48} - 240q^{49} - 320q^{50} - 864q^{51} - 128q^{52} - 768q^{53} - 128q^{54} - 1120q^{55} - 160q^{56} - 1168q^{57} - 128q^{58} - 608q^{59} - 128q^{60} - 384q^{61} - 128q^{62} - 112q^{63} - 320q^{64} - 32q^{65} - 128q^{66} + 544q^{67} - 128q^{68} + 640q^{69} - 160q^{70} + 784q^{71} - 128q^{72} + 1120q^{73} - 128q^{74} + 1440q^{75} - 128q^{76} + 288q^{77} - 320q^{78} + 928q^{79} - 128q^{80} + 456q^{81} - 128q^{82} - 96q^{83} - 160q^{84} + 80q^{85} - 128q^{86} - 96q^{87} - 128q^{88} - 160q^{89} - 128q^{90} - 120q^{91} - 320q^{92} + 160q^{93} - 128q^{94} - 112q^{95} - 128q^{96} - 224q^{97} - 160q^{98} - 96q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(1792))$$

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
1792.3.c $$\chi_{1792}(769, \cdot)$$ n/a 124 1
1792.3.d $$\chi_{1792}(1023, \cdot)$$ 1792.3.d.a 4 1
1792.3.d.b 4
1792.3.d.c 4
1792.3.d.d 6
1792.3.d.e 6
1792.3.d.f 8
1792.3.d.g 8
1792.3.d.h 12
1792.3.d.i 12
1792.3.d.j 16
1792.3.d.k 16
1792.3.g $$\chi_{1792}(127, \cdot)$$ 1792.3.g.a 4 1
1792.3.g.b 4
1792.3.g.c 4
1792.3.g.d 8
1792.3.g.e 8
1792.3.g.f 8
1792.3.g.g 12
1792.3.g.h 24
1792.3.g.i 24
1792.3.h $$\chi_{1792}(1665, \cdot)$$ n/a 124 1
1792.3.k $$\chi_{1792}(575, \cdot)$$ n/a 192 2
1792.3.l $$\chi_{1792}(321, \cdot)$$ n/a 256 2
1792.3.n $$\chi_{1792}(129, \cdot)$$ n/a 248 2
1792.3.o $$\chi_{1792}(639, \cdot)$$ n/a 248 2
1792.3.r $$\chi_{1792}(767, \cdot)$$ n/a 248 2
1792.3.s $$\chi_{1792}(257, \cdot)$$ n/a 248 2
1792.3.v $$\chi_{1792}(97, \cdot)$$ n/a 496 4
1792.3.w $$\chi_{1792}(351, \cdot)$$ n/a 384 4
1792.3.y $$\chi_{1792}(191, \cdot)$$ n/a 512 4
1792.3.bb $$\chi_{1792}(577, \cdot)$$ n/a 512 4
1792.3.be $$\chi_{1792}(15, \cdot)$$ n/a 768 8
1792.3.bf $$\chi_{1792}(209, \cdot)$$ n/a 1008 8
1792.3.bg $$\chi_{1792}(33, \cdot)$$ n/a 992 8
1792.3.bj $$\chi_{1792}(95, \cdot)$$ n/a 992 8
1792.3.bl $$\chi_{1792}(71, \cdot)$$ None 0 16
1792.3.bm $$\chi_{1792}(41, \cdot)$$ None 0 16
1792.3.bo $$\chi_{1792}(17, \cdot)$$ n/a 2016 16
1792.3.bp $$\chi_{1792}(79, \cdot)$$ n/a 2016 16
1792.3.bt $$\chi_{1792}(13, \cdot)$$ n/a 16320 32
1792.3.bu $$\chi_{1792}(43, \cdot)$$ n/a 12288 32
1792.3.bw $$\chi_{1792}(23, \cdot)$$ None 0 32
1792.3.bz $$\chi_{1792}(73, \cdot)$$ None 0 32
1792.3.ca $$\chi_{1792}(5, \cdot)$$ n/a 32640 64
1792.3.cd $$\chi_{1792}(11, \cdot)$$ n/a 32640 64

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(1792))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(1792)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 7}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(896))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ ($$1 - 20 T^{2} + 234 T^{4} - 1620 T^{6} + 6561 T^{8}$$)($$( 1 - 14 T^{2} + 81 T^{4} )^{2}$$)($$1 - 20 T^{2} + 234 T^{4} - 1620 T^{6} + 6561 T^{8}$$)($$1 - 22 T^{2} + 319 T^{4} - 3188 T^{6} + 25839 T^{8} - 144342 T^{10} + 531441 T^{12}$$)($$1 - 22 T^{2} + 319 T^{4} - 3188 T^{6} + 25839 T^{8} - 144342 T^{10} + 531441 T^{12}$$)($$( 1 - 2 T - 2 T^{2} - 18 T^{3} + 81 T^{4} )^{2}( 1 + 2 T - 2 T^{2} + 18 T^{3} + 81 T^{4} )^{2}$$)($$( 1 - 24 T^{2} + 274 T^{4} - 1944 T^{6} + 6561 T^{8} )^{2}$$)($$1 - 28 T^{2} + 434 T^{4} - 5740 T^{6} + 67151 T^{8} - 711480 T^{10} + 6862396 T^{12} - 57629880 T^{14} + 440577711 T^{16} - 3050471340 T^{18} + 18682276914 T^{20} - 97629963228 T^{22} + 282429536481 T^{24}$$)($$1 - 28 T^{2} + 434 T^{4} - 5740 T^{6} + 67151 T^{8} - 711480 T^{10} + 6862396 T^{12} - 57629880 T^{14} + 440577711 T^{16} - 3050471340 T^{18} + 18682276914 T^{20} - 97629963228 T^{22} + 282429536481 T^{24}$$)($$( 1 - 12 T^{2} + 168 T^{4} - 2212 T^{6} + 17038 T^{8} - 179172 T^{10} + 1102248 T^{12} - 6377292 T^{14} + 43046721 T^{16} )^{2}$$)($$( 1 - 16 T^{2} + 64 T^{4} - 288 T^{6} + 5598 T^{8} - 23328 T^{10} + 419904 T^{12} - 8503056 T^{14} + 43046721 T^{16} )^{2}$$)($$( 1 + 2 T + 9 T^{2} )^{4}$$)($$( 1 - 10 T^{2} + 81 T^{4} )^{2}$$)($$( 1 - 2 T + 9 T^{2} )^{4}$$)($$( 1 + 4 T + 16 T^{2} + 60 T^{3} + 158 T^{4} + 540 T^{5} + 1296 T^{6} + 2916 T^{7} + 6561 T^{8} )^{2}$$)($$( 1 + 16 T^{2} + 142 T^{4} + 1296 T^{6} + 6561 T^{8} )^{2}$$)($$( 1 - 4 T + 16 T^{2} - 60 T^{3} + 158 T^{4} - 540 T^{5} + 1296 T^{6} - 2916 T^{7} + 6561 T^{8} )^{2}$$)($$( 1 + 22 T^{2} + 319 T^{4} + 3188 T^{6} + 25839 T^{8} + 144342 T^{10} + 531441 T^{12} )^{2}$$)
$5$ ($$( 1 + 10 T + 68 T^{2} + 250 T^{3} + 625 T^{4} )^{2}$$)($$( 1 + 22 T^{2} + 625 T^{4} )^{2}$$)($$( 1 - 10 T + 68 T^{2} - 250 T^{3} + 625 T^{4} )^{2}$$)($$( 1 + 8 T + 67 T^{2} + 392 T^{3} + 1675 T^{4} + 5000 T^{5} + 15625 T^{6} )^{2}$$)($$( 1 - 8 T + 67 T^{2} - 392 T^{3} + 1675 T^{4} - 5000 T^{5} + 15625 T^{6} )^{2}$$)($$( 1 + 16 T^{2} + 558 T^{4} + 10000 T^{6} + 390625 T^{8} )^{2}$$)($$( 1 + 16 T^{2} - 254 T^{4} + 10000 T^{6} + 390625 T^{8} )^{2}$$)($$( 1 + 8 T + 86 T^{2} + 552 T^{3} + 3895 T^{4} + 20624 T^{5} + 121252 T^{6} + 515600 T^{7} + 2434375 T^{8} + 8625000 T^{9} + 33593750 T^{10} + 78125000 T^{11} + 244140625 T^{12} )^{2}$$)($$( 1 - 8 T + 86 T^{2} - 552 T^{3} + 3895 T^{4} - 20624 T^{5} + 121252 T^{6} - 515600 T^{7} + 2434375 T^{8} - 8625000 T^{9} + 33593750 T^{10} - 78125000 T^{11} + 244140625 T^{12} )^{2}$$)($$( 1 + 92 T^{2} + 5464 T^{4} + 211956 T^{6} + 6231214 T^{8} + 132472500 T^{10} + 2134375000 T^{12} + 22460937500 T^{14} + 152587890625 T^{16} )^{2}$$)($$( 1 + 120 T^{2} + 6656 T^{4} + 234840 T^{6} + 6399966 T^{8} + 146775000 T^{10} + 2600000000 T^{12} + 29296875000 T^{14} + 152587890625 T^{16} )^{2}$$)($$1 - 36 T^{2} + 1126 T^{4} - 22500 T^{6} + 390625 T^{8}$$)($$( 1 - 6 T + 25 T^{2} )^{2}( 1 + 6 T + 25 T^{2} )^{2}$$)($$1 - 36 T^{2} + 1126 T^{4} - 22500 T^{6} + 390625 T^{8}$$)($$1 - 48 T^{2} + 732 T^{4} + 16432 T^{6} - 1001466 T^{8} + 10270000 T^{10} + 285937500 T^{12} - 11718750000 T^{14} + 152587890625 T^{16}$$)($$( 1 - 56 T^{2} + 1950 T^{4} - 35000 T^{6} + 390625 T^{8} )^{2}$$)($$1 - 48 T^{2} + 732 T^{4} + 16432 T^{6} - 1001466 T^{8} + 10270000 T^{10} + 285937500 T^{12} - 11718750000 T^{14} + 152587890625 T^{16}$$)($$( 1 - 90 T^{2} + 4031 T^{4} - 119276 T^{6} + 2519375 T^{8} - 35156250 T^{10} + 244140625 T^{12} )^{2}$$)
$7$ ($$( 1 + 7 T^{2} )^{2}$$)($$( 1 + 7 T^{2} )^{2}$$)($$( 1 + 7 T^{2} )^{2}$$)($$( 1 + 7 T^{2} )^{3}$$)($$( 1 + 7 T^{2} )^{3}$$)($$( 1 + 7 T^{2} )^{4}$$)($$( 1 + 7 T^{2} )^{4}$$)($$( 1 + 7 T^{2} )^{6}$$)($$( 1 + 7 T^{2} )^{6}$$)($$( 1 + 7 T^{2} )^{8}$$)($$( 1 + 7 T^{2} )^{8}$$)($$( 1 + 7 T^{2} )^{2}$$)($$( 1 + 7 T^{2} )^{2}$$)($$( 1 + 7 T^{2} )^{2}$$)($$( 1 + 7 T^{2} )^{4}$$)($$( 1 + 7 T^{2} )^{4}$$)($$( 1 + 7 T^{2} )^{4}$$)($$( 1 + 7 T^{2} )^{6}$$)
$11$ ($$1 - 420 T^{2} + 72934 T^{4} - 6149220 T^{6} + 214358881 T^{8}$$)($$( 1 - 178 T^{2} + 14641 T^{4} )^{2}$$)($$1 - 420 T^{2} + 72934 T^{4} - 6149220 T^{6} + 214358881 T^{8}$$)($$1 - 246 T^{2} + 16223 T^{4} + 193036 T^{6} + 237520943 T^{8} - 52732284726 T^{10} + 3138428376721 T^{12}$$)($$1 - 246 T^{2} + 16223 T^{4} + 193036 T^{6} + 237520943 T^{8} - 52732284726 T^{10} + 3138428376721 T^{12}$$)($$( 1 - 36 T^{2} + 24230 T^{4} - 527076 T^{6} + 214358881 T^{8} )^{2}$$)($$( 1 - 308 T^{2} + 48390 T^{4} - 4509428 T^{6} + 214358881 T^{8} )^{2}$$)($$1 - 860 T^{2} + 372674 T^{4} - 107655724 T^{6} + 23102568975 T^{8} - 3878856590264 T^{10} + 522219976611356 T^{12} - 56790339338055224 T^{14} + 4952240833706316975 T^{16} -$$$$33\!\cdots\!04$$$$T^{18} +$$$$17\!\cdots\!14$$$$T^{20} -$$$$57\!\cdots\!60$$$$T^{22} +$$$$98\!\cdots\!41$$$$T^{24}$$)($$1 - 860 T^{2} + 372674 T^{4} - 107655724 T^{6} + 23102568975 T^{8} - 3878856590264 T^{10} + 522219976611356 T^{12} - 56790339338055224 T^{14} + 4952240833706316975 T^{16} -$$$$33\!\cdots\!04$$$$T^{18} +$$$$17\!\cdots\!14$$$$T^{20} -$$$$57\!\cdots\!60$$$$T^{22} +$$$$98\!\cdots\!41$$$$T^{24}$$)($$( 1 - 400 T^{2} + 47836 T^{4} + 1686928 T^{6} - 819692794 T^{8} + 24698312848 T^{10} + 10254071431516 T^{12} - 1255371350688400 T^{14} + 45949729863572161 T^{16} )^{2}$$)($$( 1 - 240 T^{2} + 51356 T^{4} - 7652880 T^{6} + 1127485830 T^{8} - 112045816080 T^{10} + 11008614692636 T^{12} - 753222810413040 T^{14} + 45949729863572161 T^{16} )^{2}$$)($$( 1 + 8 T + 146 T^{2} + 968 T^{3} + 14641 T^{4} )^{2}$$)($$( 1 + 130 T^{2} + 14641 T^{4} )^{2}$$)($$( 1 - 8 T + 146 T^{2} - 968 T^{3} + 14641 T^{4} )^{2}$$)($$( 1 + 16 T + 276 T^{2} + 1840 T^{3} + 27782 T^{4} + 222640 T^{5} + 4040916 T^{6} + 28344976 T^{7} + 214358881 T^{8} )^{2}$$)($$( 1 + 404 T^{2} + 68742 T^{4} + 5914964 T^{6} + 214358881 T^{8} )^{2}$$)($$( 1 - 16 T + 276 T^{2} - 1840 T^{3} + 27782 T^{4} - 222640 T^{5} + 4040916 T^{6} - 28344976 T^{7} + 214358881 T^{8} )^{2}$$)($$( 1 + 214 T^{2} + 51679 T^{4} + 6313780 T^{6} + 756632239 T^{8} + 45872800534 T^{10} + 3138428376721 T^{12} )^{2}$$)
$13$ ($$( 1 - 14 T + 380 T^{2} - 2366 T^{3} + 28561 T^{4} )^{2}$$)($$( 1 + 310 T^{2} + 28561 T^{4} )^{2}$$)($$( 1 + 14 T + 380 T^{2} + 2366 T^{3} + 28561 T^{4} )^{2}$$)($$( 1 + 243 T^{2} + 1384 T^{3} + 41067 T^{4} + 4826809 T^{6} )^{2}$$)($$( 1 + 243 T^{2} - 1384 T^{3} + 41067 T^{4} + 4826809 T^{6} )^{2}$$)($$( 1 + 144 T^{2} + 61550 T^{4} + 4112784 T^{6} + 815730721 T^{8} )^{2}$$)($$( 1 + 592 T^{2} + 143170 T^{4} + 16908112 T^{6} + 815730721 T^{8} )^{2}$$)($$( 1 + 40 T + 1366 T^{2} + 31752 T^{3} + 636951 T^{4} + 10347664 T^{5} + 147108644 T^{6} + 1748755216 T^{7} + 18191957511 T^{8} + 153260839368 T^{9} + 1114288164886 T^{10} + 5514339673960 T^{11} + 23298085122481 T^{12} )^{2}$$)($$( 1 - 40 T + 1366 T^{2} - 31752 T^{3} + 636951 T^{4} - 10347664 T^{5} + 147108644 T^{6} - 1748755216 T^{7} + 18191957511 T^{8} - 153260839368 T^{9} + 1114288164886 T^{10} - 5514339673960 T^{11} + 23298085122481 T^{12} )^{2}$$)($$( 1 + 444 T^{2} + 142936 T^{4} + 35361044 T^{6} + 6575436334 T^{8} + 1009946777684 T^{10} + 116597286336856 T^{12} + 10344349794381564 T^{14} + 665416609183179841 T^{16} )^{2}$$)($$( 1 + 72 T^{2} + 37376 T^{4} + 7051272 T^{6} + 512975454 T^{8} + 201391379592 T^{10} + 30488751428096 T^{12} + 1677462128818632 T^{14} + 665416609183179841 T^{16} )^{2}$$)($$1 - 164 T^{2} + 59814 T^{4} - 4684004 T^{6} + 815730721 T^{8}$$)($$( 1 - 322 T^{2} + 28561 T^{4} )^{2}$$)($$1 - 164 T^{2} + 59814 T^{4} - 4684004 T^{6} + 815730721 T^{8}$$)($$1 - 1136 T^{2} + 596060 T^{4} - 187756944 T^{6} + 38751742342 T^{8} - 5362526077584 T^{10} + 486224453559260 T^{12} - 26466624699138416 T^{14} + 665416609183179841 T^{16}$$)($$( 1 - 200 T^{2} + 30078 T^{4} - 5712200 T^{6} + 815730721 T^{8} )^{2}$$)($$1 - 1136 T^{2} + 596060 T^{4} - 187756944 T^{6} + 38751742342 T^{8} - 5362526077584 T^{10} + 486224453559260 T^{12} - 26466624699138416 T^{14} + 665416609183179841 T^{16}$$)($$( 1 - 250 T^{2} + 64991 T^{4} - 14409132 T^{6} + 1856207951 T^{8} - 203932680250 T^{10} + 23298085122481 T^{12} )^{2}$$)
$17$ ($$( 1 + 4 T + 470 T^{2} + 1156 T^{3} + 83521 T^{4} )^{2}$$)($$( 1 + 2 T + 289 T^{2} )^{4}$$)($$( 1 + 4 T + 470 T^{2} + 1156 T^{3} + 83521 T^{4} )^{2}$$)($$( 1 + 14 T + 591 T^{2} + 5444 T^{3} + 170799 T^{4} + 1169294 T^{5} + 24137569 T^{6} )^{2}$$)($$( 1 + 14 T + 591 T^{2} + 5444 T^{3} + 170799 T^{4} + 1169294 T^{5} + 24137569 T^{6} )^{2}$$)($$( 1 + 12 T + 278 T^{2} + 3468 T^{3} + 83521 T^{4} )^{4}$$)($$( 1 - 36 T + 870 T^{2} - 10404 T^{3} + 83521 T^{4} )^{4}$$)($$( 1 - 20 T + 642 T^{2} - 14148 T^{3} + 360367 T^{4} - 6576936 T^{5} + 110674460 T^{6} - 1900734504 T^{7} + 30098212207 T^{8} - 341498326212 T^{9} + 4478436277122 T^{10} - 40319878008980 T^{11} + 582622237229761 T^{12} )^{2}$$)($$( 1 - 20 T + 642 T^{2} - 14148 T^{3} + 360367 T^{4} - 6576936 T^{5} + 110674460 T^{6} - 1900734504 T^{7} + 30098212207 T^{8} - 341498326212 T^{9} + 4478436277122 T^{10} - 40319878008980 T^{11} + 582622237229761 T^{12} )^{2}$$)($$( 1 + 40 T + 1308 T^{2} + 31512 T^{3} + 588230 T^{4} + 9106968 T^{5} + 109245468 T^{6} + 965502760 T^{7} + 6975757441 T^{8} )^{4}$$)($$( 1 - 16 T + 428 T^{2} - 6192 T^{3} + 184742 T^{4} - 1789488 T^{5} + 35746988 T^{6} - 386201104 T^{7} + 6975757441 T^{8} )^{4}$$)($$( 1 + 28 T + 662 T^{2} + 8092 T^{3} + 83521 T^{4} )^{2}$$)($$( 1 + 2 T + 289 T^{2} )^{4}$$)($$( 1 + 28 T + 662 T^{2} + 8092 T^{3} + 83521 T^{4} )^{2}$$)($$( 1 + 8 T + 428 T^{2} - 1416 T^{3} + 75814 T^{4} - 409224 T^{5} + 35746988 T^{6} + 193100552 T^{7} + 6975757441 T^{8} )^{2}$$)($$( 1 - 32 T + 750 T^{2} - 9248 T^{3} + 83521 T^{4} )^{4}$$)($$( 1 + 8 T + 428 T^{2} - 1416 T^{3} + 75814 T^{4} - 409224 T^{5} + 35746988 T^{6} + 193100552 T^{7} + 6975757441 T^{8} )^{2}$$)($$( 1 + 2 T + 751 T^{2} + 668 T^{3} + 217039 T^{4} + 167042 T^{5} + 24137569 T^{6} )^{4}$$)
$19$ ($$1 - 1092 T^{2} + 554026 T^{4} - 142310532 T^{6} + 16983563041 T^{8}$$)($$( 1 - 238 T^{2} + 130321 T^{4} )^{2}$$)($$1 - 1092 T^{2} + 554026 T^{4} - 142310532 T^{6} + 16983563041 T^{8}$$)($$1 - 758 T^{2} + 249727 T^{4} - 71505332 T^{6} + 32544672367 T^{8} - 12873540785078 T^{10} + 2213314919066161 T^{12}$$)($$1 - 758 T^{2} + 249727 T^{4} - 71505332 T^{6} + 32544672367 T^{8} - 12873540785078 T^{10} + 2213314919066161 T^{12}$$)($$( 1 - 1416 T^{2} + 761822 T^{4} - 184534536 T^{6} + 16983563041 T^{8} )^{2}$$)($$( 1 + 8 T^{2} + 249106 T^{4} + 1042568 T^{6} + 16983563041 T^{8} )^{2}$$)($$1 - 1436 T^{2} + 1152050 T^{4} - 666723564 T^{6} + 325723784399 T^{8} - 141728641930296 T^{10} + 54804625031533372 T^{12} - 18470218344998105016 T^{14} +$$$$55\!\cdots\!59$$$$T^{16} -$$$$14\!\cdots\!04$$$$T^{18} +$$$$33\!\cdots\!50$$$$T^{20} -$$$$53\!\cdots\!36$$$$T^{22} +$$$$48\!\cdots\!21$$$$T^{24}$$)($$1 - 1436 T^{2} + 1152050 T^{4} - 666723564 T^{6} + 325723784399 T^{8} - 141728641930296 T^{10} + 54804625031533372 T^{12} - 18470218344998105016 T^{14} +$$$$55\!\cdots\!59$$$$T^{16} -$$$$14\!\cdots\!04$$$$T^{18} +$$$$33\!\cdots\!50$$$$T^{20} -$$$$53\!\cdots\!36$$$$T^{22} +$$$$48\!\cdots\!21$$$$T^{24}$$)($$( 1 - 2636 T^{2} + 3120040 T^{4} - 2166005604 T^{6} + 964702997902 T^{8} - 282276016318884 T^{10} + 52989396030441640 T^{12} - 5834298126658400396 T^{14} +$$$$28\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 1344 T^{2} + 939968 T^{4} - 470005872 T^{6} + 187852542174 T^{8} - 61251635244912 T^{10} + 15964005784522688 T^{12} - 2974695251224920384 T^{14} +$$$$28\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 20 T + 374 T^{2} - 7220 T^{3} + 130321 T^{4} )^{2}$$)($$( 1 + 22 T^{2} + 130321 T^{4} )^{2}$$)($$( 1 + 20 T + 374 T^{2} + 7220 T^{3} + 130321 T^{4} )^{2}$$)($$( 1 + 44 T + 1936 T^{2} + 47828 T^{3} + 1128094 T^{4} + 17265908 T^{5} + 252301456 T^{6} + 2070018764 T^{7} + 16983563041 T^{8} )^{2}$$)($$( 1 + 464 T^{2} + 112782 T^{4} + 60468944 T^{6} + 16983563041 T^{8} )^{2}$$)($$( 1 - 44 T + 1936 T^{2} - 47828 T^{3} + 1128094 T^{4} - 17265908 T^{5} + 252301456 T^{6} - 2070018764 T^{7} + 16983563041 T^{8} )^{2}$$)($$( 1 + 566 T^{2} + 358783 T^{4} + 123926324 T^{6} + 46756959343 T^{8} + 9612696681206 T^{10} + 2213314919066161 T^{12} )^{2}$$)
$23$ ($$1 - 1212 T^{2} + 919750 T^{4} - 339167292 T^{6} + 78310985281 T^{8}$$)($$( 1 - 946 T^{2} + 279841 T^{4} )^{2}$$)($$1 - 1212 T^{2} + 919750 T^{4} - 339167292 T^{6} + 78310985281 T^{8}$$)($$1 - 358 T^{2} + 221423 T^{4} - 249431508 T^{6} + 61963233743 T^{8} - 28035332730598 T^{10} + 21914624432020321 T^{12}$$)($$1 - 358 T^{2} + 221423 T^{4} - 249431508 T^{6} + 61963233743 T^{8} - 28035332730598 T^{10} + 21914624432020321 T^{12}$$)($$( 1 - 884 T^{2} + 689190 T^{4} - 247379444 T^{6} + 78310985281 T^{8} )^{2}$$)($$( 1 - 268 T^{2} + 477286 T^{4} - 74997388 T^{6} + 78310985281 T^{8} )^{2}$$)($$1 - 3436 T^{2} + 6171202 T^{4} - 7507951164 T^{6} + 6853799257263 T^{8} - 4944408358257112 T^{10} + 2892437896315721884 T^{12} -$$$$13\!\cdots\!92$$$$T^{14} +$$$$53\!\cdots\!03$$$$T^{16} -$$$$16\!\cdots\!44$$$$T^{18} +$$$$37\!\cdots\!22$$$$T^{20} -$$$$58\!\cdots\!36$$$$T^{22} +$$$$48\!\cdots\!41$$$$T^{24}$$)($$1 - 3436 T^{2} + 6171202 T^{4} - 7507951164 T^{6} + 6853799257263 T^{8} - 4944408358257112 T^{10} + 2892437896315721884 T^{12} -$$$$13\!\cdots\!92$$$$T^{14} +$$$$53\!\cdots\!03$$$$T^{16} -$$$$16\!\cdots\!44$$$$T^{18} +$$$$37\!\cdots\!22$$$$T^{20} -$$$$58\!\cdots\!36$$$$T^{22} +$$$$48\!\cdots\!41$$$$T^{24}$$)($$( 1 - 1744 T^{2} + 1272156 T^{4} - 412076080 T^{6} + 99307893702 T^{8} - 115315782303280 T^{10} + 99623789791135836 T^{12} - 38219105009443439824 T^{14} +$$$$61\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 - 2496 T^{2} + 3043580 T^{4} - 2415222336 T^{6} + 1439342865030 T^{8} - 675878233728576 T^{10} + 238345748581545980 T^{12} - 54698902582322721216 T^{14} +$$$$61\!\cdots\!61$$$$T^{16} )^{2}$$)($$1 - 1604 T^{2} + 1138374 T^{4} - 448864964 T^{6} + 78310985281 T^{8}$$)($$( 1 - 610 T^{2} + 279841 T^{4} )^{2}$$)($$1 - 1604 T^{2} + 1138374 T^{4} - 448864964 T^{6} + 78310985281 T^{8}$$)($$1 - 1928 T^{2} + 2366876 T^{4} - 1917103032 T^{6} + 1186521008582 T^{8} - 536484029577912 T^{10} + 185352391597952156 T^{12} - 42251395904935178888 T^{14} +$$$$61\!\cdots\!61$$$$T^{16}$$)($$( 1 - 1508 T^{2} + 1042182 T^{4} - 422000228 T^{6} + 78310985281 T^{8} )^{2}$$)($$1 - 1928 T^{2} + 2366876 T^{4} - 1917103032 T^{6} + 1186521008582 T^{8} - 536484029577912 T^{10} + 185352391597952156 T^{12} - 42251395904935178888 T^{14} +$$$$61\!\cdots\!61$$$$T^{16}$$)($$( 1 - 2246 T^{2} + 2391919 T^{4} - 1569561620 T^{6} + 669357004879 T^{8} - 175886472941126 T^{10} + 21914624432020321 T^{12} )^{2}$$)
$29$ ($$( 1 + 52 T + 1658 T^{2} + 43732 T^{3} + 707281 T^{4} )^{2}$$)($$( 1 + 1570 T^{2} + 707281 T^{4} )^{2}$$)($$( 1 - 52 T + 1658 T^{2} - 43732 T^{3} + 707281 T^{4} )^{2}$$)($$( 1 + 24 T + 1211 T^{2} + 36592 T^{3} + 1018451 T^{4} + 16974744 T^{5} + 594823321 T^{6} )^{2}$$)($$( 1 - 24 T + 1211 T^{2} - 36592 T^{3} + 1018451 T^{4} - 16974744 T^{5} + 594823321 T^{6} )^{2}$$)($$( 1 + 1236 T^{2} + 1784390 T^{4} + 874199316 T^{6} + 500246412961 T^{8} )^{2}$$)($$( 1 + 1178 T^{2} + 707281 T^{4} )^{4}$$)($$( 1 + 40 T + 3686 T^{2} + 112136 T^{3} + 6087551 T^{4} + 154554768 T^{5} + 6291990292 T^{6} + 129980559888 T^{7} + 4305609158831 T^{8} + 66701107923656 T^{9} + 1843908278174246 T^{10} + 16828289332008040 T^{11} + 353814783205469041 T^{12} )^{2}$$)($$( 1 - 40 T + 3686 T^{2} - 112136 T^{3} + 6087551 T^{4} - 154554768 T^{5} + 6291990292 T^{6} - 129980559888 T^{7} + 4305609158831 T^{8} - 66701107923656 T^{9} + 1843908278174246 T^{10} - 16828289332008040 T^{11} + 353814783205469041 T^{12} )^{2}$$)($$( 1 + 3384 T^{2} + 6555580 T^{4} + 8754768776 T^{6} + 8490907402822 T^{8} + 6192081614658056 T^{10} + 3279405379878872380 T^{12} +$$$$11\!\cdots\!44$$$$T^{14} +$$$$25\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 + 1320 T^{2} + 1724252 T^{4} + 1951314840 T^{6} + 1453224436998 T^{8} + 1380127911350040 T^{10} + 862550878040830172 T^{12} +$$$$46\!\cdots\!20$$$$T^{14} +$$$$25\!\cdots\!21$$$$T^{16} )^{2}$$)($$1 - 1148 T^{2} + 1340838 T^{4} - 811958588 T^{6} + 500246412961 T^{8}$$)($$( 1 - 1486 T^{2} + 707281 T^{4} )^{2}$$)($$1 - 1148 T^{2} + 1340838 T^{4} - 811958588 T^{6} + 500246412961 T^{8}$$)($$1 - 5720 T^{2} + 14827292 T^{4} - 22985018856 T^{6} + 23490964042630 T^{8} - 16256867121490536 T^{10} + 7417299636925331612 T^{12} -$$$$20\!\cdots\!20$$$$T^{14} +$$$$25\!\cdots\!21$$$$T^{16}$$)($$( 1 + 964 T^{2} + 1109286 T^{4} + 681818884 T^{6} + 500246412961 T^{8} )^{2}$$)($$1 - 5720 T^{2} + 14827292 T^{4} - 22985018856 T^{6} + 23490964042630 T^{8} - 16256867121490536 T^{10} + 7417299636925331612 T^{12} -$$$$20\!\cdots\!20$$$$T^{14} +$$$$25\!\cdots\!21$$$$T^{16}$$)($$( 1 - 2826 T^{2} + 3861567 T^{4} - 3662727820 T^{6} + 2731212969327 T^{8} - 1413696363027786 T^{10} + 353814783205469041 T^{12} )^{2}$$)
$31$ ($$1 - 2916 T^{2} + 3944134 T^{4} - 2692987236 T^{6} + 852891037441 T^{8}$$)($$( 1 - 130 T^{2} + 923521 T^{4} )^{2}$$)($$1 - 2916 T^{2} + 3944134 T^{4} - 2692987236 T^{6} + 852891037441 T^{8}$$)($$1 - 4166 T^{2} + 7919503 T^{4} - 9294175124 T^{6} + 7313827330063 T^{8} - 3553144061979206 T^{10} + 787662783788549761 T^{12}$$)($$1 - 4166 T^{2} + 7919503 T^{4} - 9294175124 T^{6} + 7313827330063 T^{8} - 3553144061979206 T^{10} + 787662783788549761 T^{12}$$)($$( 1 + 1084 T^{2} + 1087110 T^{4} + 1001096764 T^{6} + 852891037441 T^{8} )^{2}$$)($$( 1 - 1380 T^{2} + 1419974 T^{4} - 1274458980 T^{6} + 852891037441 T^{8} )^{2}$$)($$1 - 7180 T^{2} + 25730370 T^{4} - 60923195100 T^{6} + 106144916097775 T^{8} - 143341998035391256 T^{10} +$$$$15\!\cdots\!80$$$$T^{12} -$$$$13\!\cdots\!76$$$$T^{14} +$$$$90\!\cdots\!75$$$$T^{16} -$$$$47\!\cdots\!00$$$$T^{18} +$$$$18\!\cdots\!70$$$$T^{20} -$$$$48\!\cdots\!80$$$$T^{22} +$$$$62\!\cdots\!21$$$$T^{24}$$)($$1 - 7180 T^{2} + 25730370 T^{4} - 60923195100 T^{6} + 106144916097775 T^{8} - 143341998035391256 T^{10} +$$$$15\!\cdots\!80$$$$T^{12} -$$$$13\!\cdots\!76$$$$T^{14} +$$$$90\!\cdots\!75$$$$T^{16} -$$$$47\!\cdots\!00$$$$T^{18} +$$$$18\!\cdots\!70$$$$T^{20} -$$$$48\!\cdots\!80$$$$T^{22} +$$$$62\!\cdots\!21$$$$T^{24}$$)($$( 1 - 3944 T^{2} + 8438620 T^{4} - 12447428312 T^{6} + 13694235978694 T^{8} - 11495461442126552 T^{10} + 7197223366370371420 T^{12} -$$$$31\!\cdots\!84$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 3816 T^{2} + 7231580 T^{4} - 9186920280 T^{6} + 9404151345606 T^{8} - 8484313803905880 T^{10} + 6167749768537586780 T^{12} -$$$$30\!\cdots\!76$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 1906 T^{2} + 923521 T^{4} )^{2}$$)($$( 1 - 914 T^{2} + 923521 T^{4} )^{2}$$)($$( 1 - 1906 T^{2} + 923521 T^{4} )^{2}$$)($$1 - 3624 T^{2} + 5953500 T^{4} - 5905968152 T^{6} + 5172694104774 T^{8} - 5454285613703192 T^{10} + 5077686791404993500 T^{12} -$$$$28\!\cdots\!64$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16}$$)($$( 1 + 716 T^{2} - 69018 T^{4} + 661241036 T^{6} + 852891037441 T^{8} )^{2}$$)($$1 - 3624 T^{2} + 5953500 T^{4} - 5905968152 T^{6} + 5172694104774 T^{8} - 5454285613703192 T^{10} + 5077686791404993500 T^{12} -$$$$28\!\cdots\!64$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16}$$)($$( 1 - 3718 T^{2} + 6570127 T^{4} - 7534084372 T^{6} + 6067650257167 T^{8} - 3171048877205638 T^{10} + 787662783788549761 T^{12} )^{2}$$)
$37$ ($$( 1 + 4 T + 2042 T^{2} + 5476 T^{3} + 1874161 T^{4} )^{2}$$)($$( 1 - 62 T^{2} + 1874161 T^{4} )^{2}$$)($$( 1 - 4 T + 2042 T^{2} - 5476 T^{3} + 1874161 T^{4} )^{2}$$)($$( 1 + 8 T + 2667 T^{2} - 2992 T^{3} + 3651123 T^{4} + 14993288 T^{5} + 2565726409 T^{6} )^{2}$$)($$( 1 - 8 T + 2667 T^{2} + 2992 T^{3} + 3651123 T^{4} - 14993288 T^{5} + 2565726409 T^{6} )^{2}$$)($$( 1 + 2452 T^{2} + 4271622 T^{4} + 4595442772 T^{6} + 3512479453921 T^{8} )^{2}$$)($$( 1 + 1780 T^{2} + 2031622 T^{4} + 3336006580 T^{6} + 3512479453921 T^{8} )^{2}$$)($$( 1 - 24 T + 3910 T^{2} - 28856 T^{3} + 5520735 T^{4} + 92138768 T^{5} + 5499443668 T^{6} + 126137973392 T^{7} + 10346746228335 T^{8} - 74036601258104 T^{9} + 13733794664831110 T^{10} - 115406024938028376 T^{11} + 6582952005840035281 T^{12} )^{2}$$)($$( 1 + 24 T + 3910 T^{2} + 28856 T^{3} + 5520735 T^{4} - 92138768 T^{5} + 5499443668 T^{6} - 126137973392 T^{7} + 10346746228335 T^{8} + 74036601258104 T^{9} + 13733794664831110 T^{10} + 115406024938028376 T^{11} + 6582952005840035281 T^{12} )^{2}$$)($$( 1 + 3512 T^{2} + 9188668 T^{4} + 18622781448 T^{6} + 27544347275206 T^{8} + 34902090701365128 T^{10} + 32275007558901367228 T^{12} +$$$$23\!\cdots\!72$$$$T^{14} +$$$$12\!\cdots\!41$$$$T^{16} )^{2}$$)($$( 1 + 6504 T^{2} + 20629340 T^{4} + 42708434520 T^{6} + 66110417120646 T^{8} + 80042482348437720 T^{10} + 72460132897950642140 T^{12} +$$$$42\!\cdots\!24$$$$T^{14} +$$$$12\!\cdots\!41$$$$T^{16} )^{2}$$)($$1 - 2940 T^{2} + 5391334 T^{4} - 5510033340 T^{6} + 3512479453921 T^{8}$$)($$( 1 - 2542 T^{2} + 1874161 T^{4} )^{2}$$)($$1 - 2940 T^{2} + 5391334 T^{4} - 5510033340 T^{6} + 3512479453921 T^{8}$$)($$1 + 360 T^{2} + 3032604 T^{4} + 2655359320 T^{6} + 6705554738694 T^{8} + 4976570878530520 T^{10} + 10651959241878640284 T^{12} +$$$$23\!\cdots\!60$$$$T^{14} +$$$$12\!\cdots\!41$$$$T^{16}$$)($$( 1 - 5180 T^{2} + 10434918 T^{4} - 9708153980 T^{6} + 3512479453921 T^{8} )^{2}$$)($$1 + 360 T^{2} + 3032604 T^{4} + 2655359320 T^{6} + 6705554738694 T^{8} + 4976570878530520 T^{10} + 10651959241878640284 T^{12} +$$$$23\!\cdots\!60$$$$T^{14} +$$$$12\!\cdots\!41$$$$T^{16}$$)($$( 1 - 5418 T^{2} + 14370335 T^{4} - 24150289868 T^{6} + 26932321413935 T^{8} - 19030613681343978 T^{10} + 6582952005840035281 T^{12} )^{2}$$)
$41$ ($$( 1 + 4 T + 566 T^{2} + 6724 T^{3} + 2825761 T^{4} )^{2}$$)($$( 1 + 10 T + 1681 T^{2} )^{4}$$)($$( 1 + 4 T + 566 T^{2} + 6724 T^{3} + 2825761 T^{4} )^{2}$$)($$( 1 + 38 T + 3263 T^{2} + 92820 T^{3} + 5485103 T^{4} + 107378918 T^{5} + 4750104241 T^{6} )^{2}$$)($$( 1 + 38 T + 3263 T^{2} + 92820 T^{3} + 5485103 T^{4} + 107378918 T^{5} + 4750104241 T^{6} )^{2}$$)($$( 1 - 4 T + 3030 T^{2} - 6724 T^{3} + 2825761 T^{4} )^{4}$$)($$( 1 - 20 T + 3174 T^{2} - 33620 T^{3} + 2825761 T^{4} )^{4}$$)($$( 1 + 44 T + 4002 T^{2} + 68668 T^{3} + 3181775 T^{4} - 186466216 T^{5} - 1936661412 T^{6} - 313449709096 T^{7} + 8990935705775 T^{8} + 326180158020988 T^{9} + 31955670766942242 T^{10} + 590597009646705644 T^{11} + 22563490300366186081 T^{12} )^{2}$$)($$( 1 + 44 T + 4002 T^{2} + 68668 T^{3} + 3181775 T^{4} - 186466216 T^{5} - 1936661412 T^{6} - 313449709096 T^{7} + 8990935705775 T^{8} + 326180158020988 T^{9} + 31955670766942242 T^{10} + 590597009646705644 T^{11} + 22563490300366186081 T^{12} )^{2}$$)($$( 1 + 64 T + 4956 T^{2} + 221760 T^{3} + 11848326 T^{4} + 372778560 T^{5} + 14004471516 T^{6} + 304006671424 T^{7} + 7984925229121 T^{8} )^{4}$$)($$( 1 - 136 T + 12236 T^{2} - 754296 T^{3} + 35735462 T^{4} - 1267971576 T^{5} + 34576011596 T^{6} - 646014176776 T^{7} + 7984925229121 T^{8} )^{4}$$)($$( 1 - 60 T + 4150 T^{2} - 100860 T^{3} + 2825761 T^{4} )^{2}$$)($$( 1 + 46 T + 1681 T^{2} )^{4}$$)($$( 1 - 60 T + 4150 T^{2} - 100860 T^{3} + 2825761 T^{4} )^{2}$$)($$( 1 + 72 T + 4364 T^{2} + 180408 T^{3} + 8880422 T^{4} + 303265848 T^{5} + 12331621004 T^{6} + 342007505352 T^{7} + 7984925229121 T^{8} )^{2}$$)($$( 1 - 40 T + 3006 T^{2} - 67240 T^{3} + 2825761 T^{4} )^{4}$$)($$( 1 + 72 T + 4364 T^{2} + 180408 T^{3} + 8880422 T^{4} + 303265848 T^{5} + 12331621004 T^{6} + 342007505352 T^{7} + 7984925229121 T^{8} )^{2}$$)($$( 1 - 10 T + 3647 T^{2} - 18252 T^{3} + 6130607 T^{4} - 28257610 T^{5} + 4750104241 T^{6} )^{4}$$)
$43$ ($$1 + 2460 T^{2} + 7801702 T^{4} + 8410250460 T^{6} + 11688200277601 T^{8}$$)($$( 1 - 3442 T^{2} + 3418801 T^{4} )^{2}$$)($$1 + 2460 T^{2} + 7801702 T^{4} + 8410250460 T^{6} + 11688200277601 T^{8}$$)($$1 - 2742 T^{2} + 6748895 T^{4} - 9272578676 T^{6} + 23073128974895 T^{8} - 32049045161181942 T^{10} + 39959630797262576401 T^{12}$$)($$1 - 2742 T^{2} + 6748895 T^{4} - 9272578676 T^{6} + 23073128974895 T^{8} - 32049045161181942 T^{10} + 39959630797262576401 T^{12}$$)($$( 1 - 3364 T^{2} + 5747622 T^{4} - 11500846564 T^{6} + 11688200277601 T^{8} )^{2}$$)($$( 1 - 6580 T^{2} + 17648902 T^{4} - 22495710580 T^{6} + 11688200277601 T^{8} )^{2}$$)($$1 - 12636 T^{2} + 80008386 T^{4} - 338822584876 T^{6} + 1076022972788495 T^{8} - 2707884560676689848 T^{10} +$$$$55\!\cdots\!20$$$$T^{12} -$$$$92\!\cdots\!48$$$$T^{14} +$$$$12\!\cdots\!95$$$$T^{16} -$$$$13\!\cdots\!76$$$$T^{18} +$$$$10\!\cdots\!86$$$$T^{20} -$$$$59\!\cdots\!36$$$$T^{22} +$$$$15\!\cdots\!01$$$$T^{24}$$)($$1 - 12636 T^{2} + 80008386 T^{4} - 338822584876 T^{6} + 1076022972788495 T^{8} - 2707884560676689848 T^{10} +$$$$55\!\cdots\!20$$$$T^{12} -$$$$92\!\cdots\!48$$$$T^{14} +$$$$12\!\cdots\!95$$$$T^{16} -$$$$13\!\cdots\!76$$$$T^{18} +$$$$10\!\cdots\!86$$$$T^{20} -$$$$59\!\cdots\!36$$$$T^{22} +$$$$15\!\cdots\!01$$$$T^{24}$$)($$( 1 - 9360 T^{2} + 42404572 T^{4} - 124584286064 T^{6} + 265774122344710 T^{8} - 425928881779889264 T^{10} +$$$$49\!\cdots\!72$$$$T^{12} -$$$$37\!\cdots\!60$$$$T^{14} +$$$$13\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 8496 T^{2} + 26386460 T^{4} - 34876242384 T^{6} + 32588441897094 T^{8} - 119234932338661584 T^{10} +$$$$30\!\cdots\!60$$$$T^{12} -$$$$33\!\cdots\!96$$$$T^{14} +$$$$13\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 24 T + 1042 T^{2} - 44376 T^{3} + 3418801 T^{4} )^{2}$$)($$( 1 + 3586 T^{2} + 3418801 T^{4} )^{2}$$)($$( 1 + 24 T + 1042 T^{2} + 44376 T^{3} + 3418801 T^{4} )^{2}$$)($$( 1 - 112 T + 8468 T^{2} - 425040 T^{3} + 19578758 T^{4} - 785898960 T^{5} + 28950406868 T^{6} - 707992661488 T^{7} + 11688200277601 T^{8} )^{2}$$)($$( 1 + 1940 T^{2} + 7476102 T^{4} + 6632473940 T^{6} + 11688200277601 T^{8} )^{2}$$)($$( 1 + 112 T + 8468 T^{2} + 425040 T^{3} + 19578758 T^{4} + 785898960 T^{5} + 28950406868 T^{6} + 707992661488 T^{7} + 11688200277601 T^{8} )^{2}$$)($$( 1 + 6998 T^{2} + 25469023 T^{4} + 57500194868 T^{6} + 87073521301423 T^{8} + 81794025542651798 T^{10} + 39959630797262576401 T^{12} )^{2}$$)
$47$ ($$1 - 3204 T^{2} + 4985734 T^{4} - 15634497924 T^{6} + 23811286661761 T^{8}$$)($$( 1 - 386 T^{2} + 4879681 T^{4} )^{2}$$)($$1 - 3204 T^{2} + 4985734 T^{4} - 15634497924 T^{6} + 23811286661761 T^{8}$$)($$1 - 9862 T^{2} + 43497935 T^{4} - 117483644436 T^{6} + 212256046958735 T^{8} - 234826909058286982 T^{10} +$$$$11\!\cdots\!41$$$$T^{12}$$)($$1 - 9862 T^{2} + 43497935 T^{4} - 117483644436 T^{6} + 212256046958735 T^{8} - 234826909058286982 T^{10} +$$$$11\!\cdots\!41$$$$T^{12}$$)($$( 1 - 3970 T^{2} + 4879681 T^{4} )^{4}$$)($$( 1 - 7492 T^{2} + 23390470 T^{4} - 36558570052 T^{6} + 23811286661761 T^{8} )^{2}$$)($$1 - 8204 T^{2} + 36286402 T^{4} - 117012077532 T^{6} + 322140684114799 T^{8} - 799370927852095256 T^{10} +$$$$18\!\cdots\!76$$$$T^{12} -$$$$39\!\cdots\!36$$$$T^{14} +$$$$76\!\cdots\!39$$$$T^{16} -$$$$13\!\cdots\!12$$$$T^{18} +$$$$20\!\cdots\!42$$$$T^{20} -$$$$22\!\cdots\!04$$$$T^{22} +$$$$13\!\cdots\!81$$$$T^{24}$$)($$1 - 8204 T^{2} + 36286402 T^{4} - 117012077532 T^{6} + 322140684114799 T^{8} - 799370927852095256 T^{10} +$$$$18\!\cdots\!76$$$$T^{12} -$$$$39\!\cdots\!36$$$$T^{14} +$$$$76\!\cdots\!39$$$$T^{16} -$$$$13\!\cdots\!12$$$$T^{18} +$$$$20\!\cdots\!42$$$$T^{20} -$$$$22\!\cdots\!04$$$$T^{22} +$$$$13\!\cdots\!81$$$$T^{24}$$)($$( 1 - 8392 T^{2} + 39566748 T^{4} - 127207295352 T^{6} + 316693927920198 T^{8} - 620731022190542712 T^{10} +$$$$94\!\cdots\!28$$$$T^{12} -$$$$97\!\cdots\!72$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 4740 T^{2} + 12509062 T^{4} - 23129687940 T^{6} + 23811286661761 T^{8} )^{4}$$)($$1 - 5348 T^{2} + 14587206 T^{4} - 26096533988 T^{6} + 23811286661761 T^{8}$$)($$( 1 - 3410 T^{2} + 4879681 T^{4} )^{2}$$)($$1 - 5348 T^{2} + 14587206 T^{4} - 26096533988 T^{6} + 23811286661761 T^{8}$$)($$1 - 6696 T^{2} + 34041564 T^{4} - 108976927256 T^{6} + 286725887177670 T^{8} - 531772641369485336 T^{10} +$$$$81\!\cdots\!04$$$$T^{12} -$$$$77\!\cdots\!36$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16}$$)($$( 1 - 4084 T^{2} + 12949350 T^{4} - 19928617204 T^{6} + 23811286661761 T^{8} )^{2}$$)($$1 - 6696 T^{2} + 34041564 T^{4} - 108976927256 T^{6} + 286725887177670 T^{8} - 531772641369485336 T^{10} +$$$$81\!\cdots\!04$$$$T^{12} -$$$$77\!\cdots\!36$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16}$$)($$( 1 - 7814 T^{2} + 34231759 T^{4} - 91924200980 T^{6} + 167040063988879 T^{8} - 186061393975000454 T^{10} +$$$$11\!\cdots\!41$$$$T^{12} )^{2}$$)
$53$ ($$( 1 - 88 T + 4754 T^{2} - 247192 T^{3} + 7890481 T^{4} )^{2}$$)($$( 1 + 5170 T^{2} + 7890481 T^{4} )^{2}$$)($$( 1 + 88 T + 4754 T^{2} + 247192 T^{3} + 7890481 T^{4} )^{2}$$)($$( 1 - 88 T + 9131 T^{2} - 437040 T^{3} + 25648979 T^{4} - 694362328 T^{5} + 22164361129 T^{6} )^{2}$$)($$( 1 + 88 T + 9131 T^{2} + 437040 T^{3} + 25648979 T^{4} + 694362328 T^{5} + 22164361129 T^{6} )^{2}$$)($$( 1 + 2724 T^{2} - 448858 T^{4} + 21493670244 T^{6} + 62259690411361 T^{8} )^{2}$$)($$( 1 + 1604 T^{2} - 6155034 T^{4} + 12656331524 T^{6} + 62259690411361 T^{8} )^{2}$$)($$( 1 + 8 T + 11974 T^{2} + 126440 T^{3} + 67832223 T^{4} + 715535440 T^{5} + 236438856404 T^{6} + 2009939050960 T^{7} + 535228866769263 T^{8} + 2802461821150760 T^{9} + 745497532985636614 T^{10} + 1399099762924104392 T^{11} +$$$$49\!\cdots\!41$$$$T^{12} )^{2}$$)($$( 1 - 8 T + 11974 T^{2} - 126440 T^{3} + 67832223 T^{4} - 715535440 T^{5} + 236438856404 T^{6} - 2009939050960 T^{7} + 535228866769263 T^{8} - 2802461821150760 T^{9} + 745497532985636614 T^{10} - 1399099762924104392 T^{11} +$$$$49\!\cdots\!41$$$$T^{12} )^{2}$$)($$( 1 + 18920 T^{2} + 162796828 T^{4} + 840091728600 T^{6} + 2864724835962118 T^{8} + 6628727822775456600 T^{10} +$$$$10\!\cdots\!08$$$$T^{12} +$$$$92\!\cdots\!20$$$$T^{14} +$$$$38\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 + 11880 T^{2} + 80524316 T^{4} + 360963487320 T^{6} + 1184552464654086 T^{8} + 2848175538392200920 T^{10} +$$$$50\!\cdots\!76$$$$T^{12} +$$$$58\!\cdots\!80$$$$T^{14} +$$$$38\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 40 T + 530 T^{2} - 112360 T^{3} + 7890481 T^{4} )( 1 + 40 T + 530 T^{2} + 112360 T^{3} + 7890481 T^{4} )$$)($$( 1 - 5134 T^{2} + 7890481 T^{4} )^{2}$$)($$( 1 - 40 T + 530 T^{2} - 112360 T^{3} + 7890481 T^{4} )( 1 + 40 T + 530 T^{2} + 112360 T^{3} + 7890481 T^{4} )$$)($$1 - 11640 T^{2} + 63508956 T^{4} - 235884348872 T^{6} + 714590361466758 T^{8} - 1861240972971887432 T^{10} +$$$$39\!\cdots\!16$$$$T^{12} -$$$$57\!\cdots\!40$$$$T^{14} +$$$$38\!\cdots\!21$$$$T^{16}$$)($$( 1 - 3502 T^{2} + 7890481 T^{4} )^{4}$$)($$1 - 11640 T^{2} + 63508956 T^{4} - 235884348872 T^{6} + 714590361466758 T^{8} - 1861240972971887432 T^{10} +$$$$39\!\cdots\!16$$$$T^{12} -$$$$57\!\cdots\!40$$$$T^{14} +$$$$38\!\cdots\!21$$$$T^{16}$$)($$( 1 - 14570 T^{2} + 93486559 T^{4} - 339534731084 T^{6} + 737653917544879 T^{8} - 907123689293529770 T^{10} +$$$$49\!\cdots\!41$$$$T^{12} )^{2}$$)
$59$ ($$1 - 3268 T^{2} + 16106730 T^{4} - 39599535748 T^{6} + 146830437604321 T^{8}$$)($$( 1 - 6062 T^{2} + 12117361 T^{4} )^{2}$$)($$1 - 3268 T^{2} + 16106730 T^{4} - 39599535748 T^{6} + 146830437604321 T^{8}$$)($$1 - 10102 T^{2} + 64382623 T^{4} - 263853999412 T^{6} + 780147485017903 T^{8} - 1483281080678850742 T^{10} +$$$$17\!\cdots\!81$$$$T^{12}$$)($$1 - 10102 T^{2} + 64382623 T^{4} - 263853999412 T^{6} + 780147485017903 T^{8} - 1483281080678850742 T^{10} +$$$$17\!\cdots\!81$$$$T^{12}$$)($$( 1 - 10312 T^{2} + 48187422 T^{4} - 124954226632 T^{6} + 146830437604321 T^{8} )^{2}$$)($$( 1 - 9208 T^{2} + 43383250 T^{4} - 111576660088 T^{6} + 146830437604321 T^{8} )^{2}$$)($$1 - 22044 T^{2} + 264884594 T^{4} - 2185434980332 T^{6} + 13536601206908431 T^{8} - 65715772376485313336 T^{10} +$$$$25\!\cdots\!52$$$$T^{12} -$$$$79\!\cdots\!96$$$$T^{14} +$$$$19\!\cdots\!51$$$$T^{16} -$$$$38\!\cdots\!92$$$$T^{18} +$$$$57\!\cdots\!54$$$$T^{20} -$$$$57\!\cdots\!44$$$$T^{22} +$$$$31\!\cdots\!61$$$$T^{24}$$)($$1 - 22044 T^{2} + 264884594 T^{4} - 2185434980332 T^{6} + 13536601206908431 T^{8} - 65715772376485313336 T^{10} +$$$$25\!\cdots\!52$$$$T^{12} -$$$$79\!\cdots\!96$$$$T^{14} +$$$$19\!\cdots\!51$$$$T^{16} -$$$$38\!\cdots\!92$$$$T^{18} +$$$$57\!\cdots\!54$$$$T^{20} -$$$$57\!\cdots\!44$$$$T^{22} +$$$$31\!\cdots\!61$$$$T^{24}$$)($$( 1 - 1804 T^{2} - 12929112 T^{4} + 2548527324 T^{6} + 280743846121998 T^{8} + 30881425603271964 T^{10} -$$$$18\!\cdots\!52$$$$T^{12} -$$$$32\!\cdots\!24$$$$T^{14} +$$$$21\!\cdots\!41$$$$T^{16} )^{2}$$)($$( 1 - 19904 T^{2} + 195592000 T^{4} - 1201735802864 T^{6} + 5022454079325790 T^{8} - 14561866549927921904 T^{10} +$$$$28\!\cdots\!00$$$$T^{12} -$$$$35\!\cdots\!24$$$$T^{14} +$$$$21\!\cdots\!41$$$$T^{16} )^{2}$$)($$( 1 + 36 T + 5494 T^{2} + 125316 T^{3} + 12117361 T^{4} )^{2}$$)($$( 1 - 1130 T^{2} + 12117361 T^{4} )^{2}$$)($$( 1 - 36 T + 5494 T^{2} - 125316 T^{3} + 12117361 T^{4} )^{2}$$)($$( 1 + 116 T + 17424 T^{2} + 1222412 T^{3} + 96865118 T^{4} + 4255216172 T^{5} + 211132898064 T^{6} + 4892941902356 T^{7} + 146830437604321 T^{8} )^{2}$$)($$( 1 - 2032 T^{2} + 19804878 T^{4} - 24622477552 T^{6} + 146830437604321 T^{8} )^{2}$$)($$( 1 - 116 T + 17424 T^{2} - 1222412 T^{3} + 96865118 T^{4} - 4255216172 T^{5} + 211132898064 T^{6} - 4892941902356 T^{7} + 146830437604321 T^{8} )^{2}$$)($$( 1 + 15670 T^{2} + 117060767 T^{4} + 516019884468 T^{6} + 1418467572675887 T^{8} + 2300832957259710070 T^{10} +$$$$17\!\cdots\!81$$$$T^{12} )^{2}$$)
$61$ ($$( 1 - 30 T + 2564 T^{2} - 111630 T^{3} + 13845841 T^{4} )^{2}$$)($$( 1 + 2710 T^{2} + 13845841 T^{4} )^{2}$$)($$( 1 + 30 T + 2564 T^{2} + 111630 T^{3} + 13845841 T^{4} )^{2}$$)($$( 1 - 72 T + 6803 T^{2} - 586360 T^{3} + 25313963 T^{4} - 996900552 T^{5} + 51520374361 T^{6} )^{2}$$)($$( 1 + 72 T + 6803 T^{2} + 586360 T^{3} + 25313963 T^{4} + 996900552 T^{5} + 51520374361 T^{6} )^{2}$$)($$( 1 + 12336 T^{2} + 64250030 T^{4} + 170802294576 T^{6} + 191707312997281 T^{8} )^{2}$$)($$( 1 + 13232 T^{2} + 71110338 T^{4} + 183208168112 T^{6} + 191707312997281 T^{8} )^{2}$$)($$( 1 - 56 T + 12854 T^{2} - 706840 T^{3} + 88446423 T^{4} - 4166219632 T^{5} + 405467252580 T^{6} - 15502503250672 T^{7} + 1224615109876743 T^{8} - 36416661413329240 T^{9} + 2464205801267049974 T^{10} - 39947203053121425656 T^{11} +$$$$26\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 + 56 T + 12854 T^{2} + 706840 T^{3} + 88446423 T^{4} + 4166219632 T^{5} + 405467252580 T^{6} + 15502503250672 T^{7} + 1224615109876743 T^{8} + 36416661413329240 T^{9} + 2464205801267049974 T^{10} + 39947203053121425656 T^{11} +$$$$26\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 + 16316 T^{2} + 140172120 T^{4} + 816942037524 T^{6} + 3499102878259502 T^{8} + 11311249557773337684 T^{10} +$$$$26\!\cdots\!20$$$$T^{12} +$$$$43\!\cdots\!36$$$$T^{14} +$$$$36\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 + 13976 T^{2} + 89245888 T^{4} + 380830885688 T^{6} + 1421456386949854 T^{8} + 5272923891125223608 T^{10} +$$$$17\!\cdots\!28$$$$T^{12} +$$$$37\!\cdots\!96$$$$T^{14} +$$$$36\!\cdots\!61$$$$T^{16} )^{2}$$)($$1 - 14372 T^{2} + 79326246 T^{4} - 198992426852 T^{6} + 191707312997281 T^{8}$$)($$( 1 - 5138 T^{2} + 13845841 T^{4} )^{2}$$)($$1 - 14372 T^{2} + 79326246 T^{4} - 198992426852 T^{6} + 191707312997281 T^{8}$$)($$1 - 16240 T^{2} + 130126300 T^{4} - 693430250128 T^{6} + 2856274871188870 T^{8} - 9601124987862517648 T^{10} +$$$$24\!\cdots\!00$$$$T^{12} -$$$$43\!\cdots\!40$$$$T^{14} +$$$$36\!\cdots\!61$$$$T^{16}$$)($$( 1 - 8632 T^{2} + 40857438 T^{4} - 119517299512 T^{6} + 191707312997281 T^{8} )^{2}$$)($$1 - 16240 T^{2} + 130126300 T^{4} - 693430250128 T^{6} + 2856274871188870 T^{8} - 9601124987862517648 T^{10} +$$$$24\!\cdots\!00$$$$T^{12} -$$$$43\!\cdots\!40$$$$T^{14} +$$$$36\!\cdots\!61$$$$T^{16}$$)($$( 1 - 16762 T^{2} + 126447967 T^{4} - 579841512748 T^{6} + 1750778445855247 T^{8} - 3213397980460424122 T^{10} +$$$$26\!\cdots\!21$$$$T^{12} )^{2}$$)
$67$ ($$1 + 4572 T^{2} + 42660838 T^{4} + 92130925212 T^{6} + 406067677556641 T^{8}$$)($$( 1 - 1922 T^{2} + 20151121 T^{4} )^{2}$$)($$1 + 4572 T^{2} + 42660838 T^{4} + 92130925212 T^{6} + 406067677556641 T^{8}$$)($$1 - 7670 T^{2} + 66799807 T^{4} - 296460562292 T^{6} + 1346090993633647 T^{8} - 3114539086859436470 T^{10} +$$$$81\!\cdots\!61$$$$T^{12}$$)($$1 - 7670 T^{2} + 66799807 T^{4} - 296460562292 T^{6} + 1346090993633647 T^{8} - 3114539086859436470 T^{10} +$$$$81\!\cdots\!61$$$$T^{12}$$)($$( 1 - 15828 T^{2} + 102921542 T^{4} - 318951943188 T^{6} + 406067677556641 T^{8} )^{2}$$)($$( 1 - 10660 T^{2} + 62288614 T^{4} - 214810949860 T^{6} + 406067677556641 T^{8} )^{2}$$)($$1 - 31580 T^{2} + 461655938 T^{4} - 4209090810796 T^{6} + 27645634830134223 T^{8} -$$$$14\!\cdots\!48$$$$T^{10} +$$$$68\!\cdots\!72$$$$T^{12} -$$$$29\!\cdots\!08$$$$T^{14} +$$$$11\!\cdots\!43$$$$T^{16} -$$$$34\!\cdots\!56$$$$T^{18} +$$$$76\!\cdots\!78$$$$T^{20} -$$$$10\!\cdots\!80$$$$T^{22} +$$$$66\!\cdots\!21$$$$T^{24}$$)($$1 - 31580 T^{2} + 461655938 T^{4} - 4209090810796 T^{6} + 27645634830134223 T^{8} -$$$$14\!\cdots\!48$$$$T^{10} +$$$$68\!\cdots\!72$$$$T^{12} -$$$$29\!\cdots\!08$$$$T^{14} +$$$$11\!\cdots\!43$$$$T^{16} -$$$$34\!\cdots\!56$$$$T^{18} +$$$$76\!\cdots\!78$$$$T^{20} -$$$$10\!\cdots\!80$$$$T^{22} +$$$$66\!\cdots\!21$$$$T^{24}$$)($$( 1 - 21344 T^{2} + 191426940 T^{4} - 1006794243744 T^{6} + 4374042881960006 T^{8} - 20288032627788837024 T^{10} +$$$$77\!\cdots\!40$$$$T^{12} -$$$$17\!\cdots\!84$$$$T^{14} +$$$$16\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 17712 T^{2} + 180398684 T^{4} - 1231615425744 T^{6} + 6368769162861702 T^{8} - 24818431469633859024 T^{10} +$$$$73\!\cdots\!44$$$$T^{12} -$$$$14\!\cdots\!32$$$$T^{14} +$$$$16\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 + 48 T + 6754 T^{2} + 215472 T^{3} + 20151121 T^{4} )^{2}$$)($$( 1 + 4946 T^{2} + 20151121 T^{4} )^{2}$$)($$( 1 - 48 T + 6754 T^{2} - 215472 T^{3} + 20151121 T^{4} )^{2}$$)($$( 1 - 184 T + 25028 T^{2} - 2353896 T^{3} + 180133414 T^{4} - 10566639144 T^{5} + 504342256388 T^{6} - 16644342319096 T^{7} + 406067677556641 T^{8} )^{2}$$)($$( 1 - 572 T^{2} + 33416742 T^{4} - 11526441212 T^{6} + 406067677556641 T^{8} )^{2}$$)($$( 1 + 184 T + 25028 T^{2} + 2353896 T^{3} + 180133414 T^{4} + 10566639144 T^{5} + 504342256388 T^{6} + 16644342319096 T^{7} + 406067677556641 T^{8} )^{2}$$)($$( 1 + 6870 T^{2} + 51039551 T^{4} + 270200089268 T^{6} + 1028504167986671 T^{8} + 2789684944814123670 T^{10} +$$$$81\!\cdots\!61$$$$T^{12} )^{2}$$)
$71$ ($$1 - 15556 T^{2} + 106095174 T^{4} - 395304109636 T^{6} + 645753531245761 T^{8}$$)($$( 1 - 71 T )^{4}( 1 + 71 T )^{4}$$)($$1 - 15556 T^{2} + 106095174 T^{4} - 395304109636 T^{6} + 645753531245761 T^{8}$$)($$1 - 998 T^{2} - 8217425 T^{4} - 95318514644 T^{6} - 208818582741425 T^{8} - 644462024183269478 T^{10} +$$$$16\!\cdots\!41$$$$T^{12}$$)($$1 - 998 T^{2} - 8217425 T^{4} - 95318514644 T^{6} - 208818582741425 T^{8} - 644462024183269478 T^{10} +$$$$16\!\cdots\!41$$$$T^{12}$$)($$( 1 - 4484 T^{2} + 4218822 T^{4} - 113945977604 T^{6} + 645753531245761 T^{8} )^{2}$$)($$( 1 - 9412 T^{2} + 47279686 T^{4} - 239174741572 T^{6} + 645753531245761 T^{8} )^{2}$$)($$1 - 45388 T^{2} + 996102914 T^{4} - 13962644273052 T^{6} + 139159466340239663 T^{8} -$$$$10\!\cdots\!04$$$$T^{10} +$$$$59\!\cdots\!92$$$$T^{12} -$$$$26\!\cdots\!24$$$$T^{14} +$$$$89\!\cdots\!43$$$$T^{16} -$$$$22\!\cdots\!32$$$$T^{18} +$$$$41\!\cdots\!94$$$$T^{20} -$$$$48\!\cdots\!88$$$$T^{22} +$$$$26\!\cdots\!81$$$$T^{24}$$)($$1 - 45388 T^{2} + 996102914 T^{4} - 13962644273052 T^{6} + 139159466340239663 T^{8} -$$$$10\!\cdots\!04$$$$T^{10} +$$$$59\!\cdots\!92$$$$T^{12} -$$$$26\!\cdots\!24$$$$T^{14} +$$$$89\!\cdots\!43$$$$T^{16} -$$$$22\!\cdots\!32$$$$T^{18} +$$$$41\!\cdots\!94$$$$T^{20} -$$$$48\!\cdots\!88$$$$T^{22} +$$$$26\!\cdots\!81$$$$T^{24}$$)($$( 1 - 9864 T^{2} + 51888284 T^{4} - 294531431096 T^{6} + 1789421441990854 T^{8} - 7484538771485032376 T^{10} +$$$$33\!\cdots\!24$$$$T^{12} -$$$$16\!\cdots\!24$$$$T^{14} +$$$$41\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 28424 T^{2} + 396941212 T^{4} - 3486574139960 T^{6} + 21000930030289606 T^{8} - 88599709827512872760 T^{10} +$$$$25\!\cdots\!32$$$$T^{12} -$$$$46\!\cdots\!84$$$$T^{14} +$$$$41\!\cdots\!21$$$$T^{16} )^{2}$$)($$1 - 8388 T^{2} + 39052870 T^{4} - 213153180228 T^{6} + 645753531245761 T^{8}$$)($$( 1 - 114 T + 5041 T^{2} )^{2}( 1 + 114 T + 5041 T^{2} )^{2}$$)($$1 - 8388 T^{2} + 39052870 T^{4} - 213153180228 T^{6} + 645753531245761 T^{8}$$)($$1 - 21000 T^{2} + 247457180 T^{4} - 1991232124728 T^{6} + 11615880585488070 T^{8} - 50600555550540147768 T^{10} +$$$$15\!\cdots\!80$$$$T^{12} -$$$$34\!\cdots\!00$$$$T^{14} +$$$$41\!\cdots\!21$$$$T^{16}$$)($$( 1 - 13700 T^{2} + 92907462 T^{4} - 348140029700 T^{6} + 645753531245761 T^{8} )^{2}$$)($$1 - 21000 T^{2} + 247457180 T^{4} - 1991232124728 T^{6} + 11615880585488070 T^{8} - 50600555550540147768 T^{10} +$$$$15\!\cdots\!80$$$$T^{12} -$$$$34\!\cdots\!00$$$$T^{14} +$$$$41\!\cdots\!21$$$$T^{16}$$)($$( 1 - 25318 T^{2} + 288430255 T^{4} - 1875969873364 T^{6} + 7329497630808655 T^{8} - 16349187904080176998 T^{10} +$$$$16\!\cdots\!41$$$$T^{12} )^{2}$$)
$73$ ($$( 1 - 52 T + 10326 T^{2} - 277108 T^{3} + 28398241 T^{4} )^{2}$$)($$( 1 - 82 T + 5329 T^{2} )^{4}$$)($$( 1 - 52 T + 10326 T^{2} - 277108 T^{3} + 28398241 T^{4} )^{2}$$)($$( 1 - 78 T + 7391 T^{2} - 269060 T^{3} + 39386639 T^{4} - 2215062798 T^{5} + 151334226289 T^{6} )^{2}$$)($$( 1 - 78 T + 7391 T^{2} - 269060 T^{3} + 39386639 T^{4} - 2215062798 T^{5} + 151334226289 T^{6} )^{2}$$)($$( 1 + 100 T + 12822 T^{2} + 532900 T^{3} + 28398241 T^{4} )^{4}$$)($$( 1 + 116 T + 13894 T^{2} + 618164 T^{3} + 28398241 T^{4} )^{4}$$)($$( 1 - 12 T + 14306 T^{2} + 131172 T^{3} + 94457167 T^{4} + 3386669544 T^{5} + 497655287772 T^{6} + 18047561999976 T^{7} + 2682417392643247 T^{8} + 19850813130780708 T^{9} + 11537218074636722786 T^{10} - 51571509956442691788 T^{11} +$$$$22\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 - 12 T + 14306 T^{2} + 131172 T^{3} + 94457167 T^{4} + 3386669544 T^{5} + 497655287772 T^{6} + 18047561999976 T^{7} + 2682417392643247 T^{8} + 19850813130780708 T^{9} + 11537218074636722786 T^{10} - 51571509956442691788 T^{11} +$$$$22\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 - 56 T + 18460 T^{2} - 736008 T^{3} + 138223494 T^{4} - 3922186632 T^{5} + 524231528860 T^{6} - 8474716672184 T^{7} + 806460091894081 T^{8} )^{4}$$)($$( 1 + 16 T + 8044 T^{2} + 169264 T^{3} + 63798502 T^{4} + 902007856 T^{5} + 228435450604 T^{6} + 2421347620624 T^{7} + 806460091894081 T^{8} )^{4}$$)($$( 1 - 76 T + 4934 T^{2} - 405004 T^{3} + 28398241 T^{4} )^{2}$$)($$( 1 - 110 T + 5329 T^{2} )^{4}$$)($$( 1 - 76 T + 4934 T^{2} - 405004 T^{3} + 28398241 T^{4} )^{2}$$)($$( 1 + 136 T + 21660 T^{2} + 1811512 T^{3} + 170528390 T^{4} + 9653547448 T^{5} + 615105900060 T^{6} + 20581454775304 T^{7} + 806460091894081 T^{8} )^{2}$$)($$( 1 + 92 T + 4374 T^{2} + 490268 T^{3} + 28398241 T^{4} )^{4}$$)($$( 1 + 136 T + 21660 T^{2} + 1811512 T^{3} + 170528390 T^{4} + 9653547448 T^{5} + 615105900060 T^{6} + 20581454775304 T^{7} + 806460091894081 T^{8} )^{2}$$)($$( 1 - 66 T + 15647 T^{2} - 699740 T^{3} + 83382863 T^{4} - 1874283906 T^{5} + 151334226289 T^{6} )^{4}$$)
$79$ ($$1 - 19332 T^{2} + 170120326 T^{4} - 752982965892 T^{6} + 1517108809906561 T^{8}$$)($$( 1 - 94 T + 6241 T^{2} )^{2}( 1 + 94 T + 6241 T^{2} )^{2}$$)($$1 - 19332 T^{2} + 170120326 T^{4} - 752982965892 T^{6} + 1517108809906561 T^{8}$$)($$1 - 23046 T^{2} + 261506639 T^{4} - 1949259060500 T^{6} + 10185704771087759 T^{8} - 34963289633106604806 T^{10} +$$$$59\!\cdots\!41$$$$T^{12}$$)($$1 - 23046 T^{2} + 261506639 T^{4} - 1949259060500 T^{6} + 10185704771087759 T^{8} - 34963289633106604806 T^{10} +$$$$59\!\cdots\!41$$$$T^{12}$$)($$( 1 - 14660 T^{2} + 105286662 T^{4} - 571008187460 T^{6} + 1517108809906561 T^{8} )^{2}$$)($$( 1 - 16900 T^{2} + 142880134 T^{4} - 658256368900 T^{6} + 1517108809906561 T^{8} )^{2}$$)($$1 - 29836 T^{2} + 518234562 T^{4} - 6205818140764 T^{6} + 58141197450350703 T^{8} -$$$$44\!\cdots\!64$$$$T^{10} +$$$$29\!\cdots\!76$$$$T^{12} -$$$$17\!\cdots\!84$$$$T^{14} +$$$$88\!\cdots\!83$$$$T^{16} -$$$$36\!\cdots\!24$$$$T^{18} +$$$$11\!\cdots\!02$$$$T^{20} -$$$$26\!\cdots\!36$$$$T^{22} +$$$$34\!\cdots\!81$$$$T^{24}$$)($$1 - 29836 T^{2} + 518234562 T^{4} - 6205818140764 T^{6} + 58141197450350703 T^{8} -$$$$44\!\cdots\!64$$$$T^{10} +$$$$29\!\cdots\!76$$$$T^{12} -$$$$17\!\cdots\!84$$$$T^{14} +$$$$88\!\cdots\!83$$$$T^{16} -$$$$36\!\cdots\!24$$$$T^{18} +$$$$11\!\cdots\!02$$$$T^{20} -$$$$26\!\cdots\!36$$$$T^{22} +$$$$34\!\cdots\!81$$$$T^{24}$$)($$( 1 - 24968 T^{2} + 330869788 T^{4} - 3106127956152 T^{6} + 22189846569597766 T^{8} -$$$$12\!\cdots\!12$$$$T^{10} +$$$$50\!\cdots\!68$$$$T^{12} -$$$$14\!\cdots\!88$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 19464 T^{2} + 209739548 T^{4} - 1871174596152 T^{6} + 13514744462230854 T^{8} - 72882402085262688312 T^{10} +$$$$31\!\cdots\!28$$$$T^{12} -$$$$11\!\cdots\!24$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 1282 T^{2} + 38950081 T^{4} )^{2}$$)($$( 1 - 94 T + 6241 T^{2} )^{2}( 1 + 94 T + 6241 T^{2} )^{2}$$)($$( 1 - 1282 T^{2} + 38950081 T^{4} )^{2}$$)($$1 - 26248 T^{2} + 289540636 T^{4} - 1851543245752 T^{6} + 10296312398061382 T^{8} - 72117759397043305912 T^{10} +$$$$43\!\cdots\!96$$$$T^{12} -$$$$15\!\cdots\!68$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16}$$)($$( 1 - 22084 T^{2} + 198084102 T^{4} - 860173588804 T^{6} + 1517108809906561 T^{8} )^{2}$$)($$1 - 26248 T^{2} + 289540636 T^{4} - 1851543245752 T^{6} + 10296312398061382 T^{8} - 72117759397043305912 T^{10} +$$$$43\!\cdots\!96$$$$T^{12} -$$$$15\!\cdots\!68$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16}$$)($$( 1 - 31494 T^{2} + 446220879 T^{4} - 3596761635604 T^{6} + 17380339380941199 T^{8} - 47779824859197232134 T^{10} +$$$$59\!\cdots\!41$$$$T^{12} )^{2}$$)
$83$ ($$1 - 12084 T^{2} + 87882154 T^{4} - 573486350964 T^{6} + 2252292232139041 T^{8}$$)($$( 1 - 11662 T^{2} + 47458321 T^{4} )^{2}$$)($$1 - 12084 T^{2} + 87882154 T^{4} - 573486350964 T^{6} + 2252292232139041 T^{8}$$)($$1 - 29558 T^{2} + 421104895 T^{4} - 3637965181364 T^{6} + 19984931281581295 T^{8} - 66573253797565773878 T^{10} +$$$$10\!\cdots\!61$$$$T^{12}$$)($$1 - 29558 T^{2} + 421104895 T^{4} - 3637965181364 T^{6} + 19984931281581295 T^{8} - 66573253797565773878 T^{10} +$$$$10\!\cdots\!61$$$$T^{12}$$)($$( 1 - 10728 T^{2} + 57600542 T^{4} - 509132867688 T^{6} + 2252292232139041 T^{8} )^{2}$$)($$( 1 - 25912 T^{2} + 262120210 T^{4} - 1229740013752 T^{6} + 2252292232139041 T^{8} )^{2}$$)($$1 - 25436 T^{2} + 370879410 T^{4} - 3817459569068 T^{6} + 30147675209268431 T^{8} -$$$$20\!\cdots\!04$$$$T^{10} +$$$$13\!\cdots\!04$$$$T^{12} -$$$$96\!\cdots\!84$$$$T^{14} +$$$$67\!\cdots\!71$$$$T^{16} -$$$$40\!\cdots\!48$$$$T^{18} +$$$$18\!\cdots\!10$$$$T^{20} -$$$$61\!\cdots\!36$$$$T^{22} +$$$$11\!\cdots\!21$$$$T^{24}$$)($$1 - 25436 T^{2} + 370879410 T^{4} - 3817459569068 T^{6} + 30147675209268431 T^{8} -$$$$20\!\cdots\!04$$$$T^{10} +$$$$13\!\cdots\!04$$$$T^{12} -$$$$96\!\cdots\!84$$$$T^{14} +$$$$67\!\cdots\!71$$$$T^{16} -$$$$40\!\cdots\!48$$$$T^{18} +$$$$18\!\cdots\!10$$$$T^{20} -$$$$61\!\cdots\!36$$$$T^{22} +$$$$11\!\cdots\!21$$$$T^{24}$$)($$( 1 - 31660 T^{2} + 529313064 T^{4} - 5903046467332 T^{6} + 47298953549416590 T^{8} -$$$$28\!\cdots\!72$$$$T^{10} +$$$$11\!\cdots\!24$$$$T^{12} -$$$$33\!\cdots\!60$$$$T^{14} +$$$$50\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 30576 T^{2} + 509429120 T^{4} - 5646777044160 T^{6} + 45462865558564446 T^{8} -$$$$26\!\cdots\!60$$$$T^{10} +$$$$11\!\cdots\!20$$$$T^{12} -$$$$32\!\cdots\!36$$$$T^{14} +$$$$50\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 + 124 T + 13590 T^{2} + 854236 T^{3} + 47458321 T^{4} )^{2}$$)($$( 1 + 12406 T^{2} + 47458321 T^{4} )^{2}$$)($$( 1 - 124 T + 13590 T^{2} - 854236 T^{3} + 47458321 T^{4} )^{2}$$)($$( 1 - 212 T + 32112 T^{2} - 3651372 T^{3} + 342998878 T^{4} - 25154301708 T^{5} + 1523981603952 T^{6} - 69311359154228 T^{7} + 2252292232139041 T^{8} )^{2}$$)($$( 1 + 4016 T^{2} + 20075982 T^{4} + 190592617136 T^{6} + 2252292232139041 T^{8} )^{2}$$)($$( 1 + 212 T + 32112 T^{2} + 3651372 T^{3} + 342998878 T^{4} + 25154301708 T^{5} + 1523981603952 T^{6} + 69311359154228 T^{7} + 2252292232139041 T^{8} )^{2}$$)($$( 1 + 15734 T^{2} + 12104959 T^{4} - 672850782796 T^{6} + 574481029913839 T^{8} + 35437565980475671094 T^{10} +$$$$10\!\cdots\!61$$$$T^{12} )^{2}$$)
$89$ ($$( 1 + 188 T + 22886 T^{2} + 1489148 T^{3} + 62742241 T^{4} )^{2}$$)($$( 1 + 22 T + 7921 T^{2} )^{4}$$)($$( 1 + 188 T + 22886 T^{2} + 1489148 T^{3} + 62742241 T^{4} )^{2}$$)($$( 1 - 110 T + 20287 T^{2} - 1296452 T^{3} + 160693327 T^{4} - 6901646510 T^{5} + 496981290961 T^{6} )^{2}$$)($$( 1 - 110 T + 20287 T^{2} - 1296452 T^{3} + 160693327 T^{4} - 6901646510 T^{5} + 496981290961 T^{6} )^{2}$$)($$( 1 + 92 T + 16614 T^{2} + 728732 T^{3} + 62742241 T^{4} )^{4}$$)($$( 1 + 156 T + 20774 T^{2} + 1235676 T^{3} + 62742241 T^{4} )^{4}$$)($$( 1 + 116 T + 26594 T^{2} + 2305380 T^{3} + 321006095 T^{4} + 21356415720 T^{5} + 2729834914012 T^{6} + 169164168918120 T^{7} + 20140641774958895 T^{8} + 1145730728555670180 T^{9} +$$$$10\!\cdots\!14$$$$T^{10} +$$$$36\!\cdots\!16$$$$T^{11} +$$$$24\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 + 116 T + 26594 T^{2} + 2305380 T^{3} + 321006095 T^{4} + 21356415720 T^{5} + 2729834914012 T^{6} + 169164168918120 T^{7} + 20140641774958895 T^{8} + 1145730728555670180 T^{9} +$$$$10\!\cdots\!14$$$$T^{10} +$$$$36\!\cdots\!16$$$$T^{11} +$$$$24\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 - 256 T + 48252 T^{2} - 6269952 T^{3} + 638304966 T^{4} - 49664289792 T^{5} + 3027438612732 T^{6} - 127227210486016 T^{7} + 3936588805702081 T^{8} )^{4}$$)($$( 1 - 128 T + 28028 T^{2} - 2658432 T^{3} + 327913670 T^{4} - 21057439872 T^{5} + 1758539530748 T^{6} - 63613605243008 T^{7} + 3936588805702081 T^{8} )^{4}$$)($$( 1 + 68 T + 15206 T^{2} + 538628 T^{3} + 62742241 T^{4} )^{2}$$)($$( 1 - 134 T + 7921 T^{2} )^{4}$$)($$( 1 + 68 T + 15206 T^{2} + 538628 T^{3} + 62742241 T^{4} )^{2}$$)($$( 1 - 40 T + 25916 T^{2} - 837912 T^{3} + 285914566 T^{4} - 6637100952 T^{5} + 1626027917756 T^{6} - 19879251638440 T^{7} + 3936588805702081 T^{8} )^{2}$$)($$( 1 - 28 T + 10662 T^{2} - 221788 T^{3} + 62742241 T^{4} )^{4}$$)($$( 1 - 40 T + 25916 T^{2} - 837912 T^{3} + 285914566 T^{4} - 6637100952 T^{5} + 1626027917756 T^{6} - 19879251638440 T^{7} + 3936588805702081 T^{8} )^{2}$$)($$( 1 + 174 T + 24959 T^{2} + 2135620 T^{3} + 197700239 T^{4} + 10917149934 T^{5} + 496981290961 T^{6} )^{4}$$)
$97$ ($$( 1 - 76 T + 4134 T^{2} - 715084 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 - 38 T + 9409 T^{2} )^{4}$$)($$( 1 - 76 T + 4134 T^{2} - 715084 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 - 34 T + 15983 T^{2} - 495708 T^{3} + 150384047 T^{4} - 3009995554 T^{5} + 832972004929 T^{6} )^{2}$$)($$( 1 - 34 T + 15983 T^{2} - 495708 T^{3} + 150384047 T^{4} - 3009995554 T^{5} + 832972004929 T^{6} )^{2}$$)($$( 1 - 60 T + 18374 T^{2} - 564540 T^{3} + 88529281 T^{4} )^{4}$$)($$( 1 + 68 T + 3046 T^{2} + 639812 T^{3} + 88529281 T^{4} )^{4}$$)($$( 1 + 204 T + 59970 T^{2} + 8632220 T^{3} + 1423216239 T^{4} + 153783252120 T^{5} + 17852135544220 T^{6} + 1446946619197080 T^{7} + 125996310346194159 T^{8} + 7190397600388212380 T^{9} +$$$$47\!\cdots\!70$$$$T^{10} +$$$$15\!\cdots\!96$$$$T^{11} +$$$$69\!\cdots\!41$$$$T^{12} )^{2}$$)($$( 1 + 204 T + 59970 T^{2} + 8632220 T^{3} + 1423216239 T^{4} + 153783252120 T^{5} + 17852135544220 T^{6} + 1446946619197080 T^{7} + 125996310346194159 T^{8} + 7190397600388212380 T^{9} +$$$$47\!\cdots\!70$$$$T^{10} +$$$$15\!\cdots\!96$$$$T^{11} +$$$$69\!\cdots\!41$$$$T^{12} )^{2}$$)($$( 1 - 32 T + 19484 T^{2} - 1437536 T^{3} + 199130566 T^{4} - 13525776224 T^{5} + 1724904511004 T^{6} - 26655104157728 T^{7} + 7837433594376961 T^{8} )^{4}$$)($$( 1 - 32 T + 12988 T^{2} - 504800 T^{3} + 67508614 T^{4} - 4749663200 T^{5} + 1149818301628 T^{6} - 26655104157728 T^{7} + 7837433594376961 T^{8} )^{4}$$)($$( 1 + 300 T + 41206 T^{2} + 2822700 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 + 178 T + 9409 T^{2} )^{4}$$)($$( 1 + 300 T + 41206 T^{2} + 2822700 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 - 264 T + 52364 T^{2} - 7260024 T^{3} + 808802534 T^{4} - 68309565816 T^{5} + 4635747270284 T^{6} - 219904609301256 T^{7} + 7837433594376961 T^{8} )^{2}$$)($$( 1 - 16 T + 18798 T^{2} - 150544 T^{3} + 88529281 T^{4} )^{4}$$)($$( 1 - 264 T + 52364 T^{2} - 7260024 T^{3} + 808802534 T^{4} - 68309565816 T^{5} + 4635747270284 T^{6} - 219904609301256 T^{7} + 7837433594376961 T^{8} )^{2}$$)($$( 1 - 126 T + 29295 T^{2} - 2174884 T^{3} + 275636655 T^{4} - 11154689406 T^{5} + 832972004929 T^{6} )^{4}$$)