Properties

Label 170.2
Level 170
Weight 2
Dimension 265
Nonzero newspaces 10
Newform subspaces 30
Sturm bound 3456
Trace bound 10

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Defining parameters

Level: \( N \) = \( 170\( 170 = 2 \cdot 5 \cdot 17 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 30 \)
Sturm bound: \(3456\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(170))\).

Total New Old
Modular forms 992 265 727
Cusp forms 737 265 472
Eisenstein series 255 0 255

Trace form

\( 265q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + O(q^{10}) \) \( 265q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} - 3q^{10} - 20q^{11} - 12q^{12} - 18q^{13} - 24q^{14} - 44q^{15} - 7q^{16} - 15q^{17} - 51q^{18} - 12q^{19} - 3q^{20} - 64q^{21} - 20q^{22} - 8q^{23} - 12q^{24} - 35q^{25} + 6q^{26} - 8q^{27} + 8q^{28} - 10q^{29} + 4q^{30} - 32q^{31} + q^{32} - 16q^{33} + 17q^{34} - 24q^{35} + 13q^{36} - 26q^{37} + 4q^{38} - 72q^{39} + q^{40} - 94q^{41} - 64q^{42} - 68q^{43} - 52q^{44} - 71q^{45} - 40q^{46} - 112q^{47} + 4q^{48} - 71q^{49} - 15q^{50} - 60q^{51} - 50q^{52} - 82q^{53} - 72q^{54} - 68q^{55} + 8q^{56} - 96q^{57} - 34q^{58} - 100q^{59} - 28q^{60} - 34q^{61} - 64q^{62} - 88q^{63} + q^{64} - 22q^{65} + 32q^{66} + 36q^{67} + 25q^{68} + 96q^{69} + 104q^{70} + 104q^{71} + 53q^{72} + 226q^{73} + 110q^{74} + 148q^{75} + 20q^{76} + 192q^{77} + 184q^{78} + 176q^{79} + 49q^{80} + 297q^{81} + 178q^{82} + 132q^{83} + 96q^{84} + 269q^{85} + 108q^{86} + 216q^{87} + 76q^{88} + 90q^{89} + 217q^{90} + 176q^{91} + 56q^{92} + 128q^{93} + 176q^{94} + 132q^{95} + 4q^{96} + 162q^{97} + 129q^{98} + 108q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)

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

Label \(\chi\) Newforms Dimension \(\chi\) degree
170.2.a \(\chi_{170}(1, \cdot)\) 170.2.a.a 1 1
170.2.a.b 1
170.2.a.c 1
170.2.a.d 1
170.2.a.e 1
170.2.a.f 2
170.2.b \(\chi_{170}(101, \cdot)\) 170.2.b.a 2 1
170.2.b.b 2
170.2.b.c 2
170.2.c \(\chi_{170}(69, \cdot)\) 170.2.c.a 2 1
170.2.c.b 6
170.2.d \(\chi_{170}(169, \cdot)\) 170.2.d.a 2 1
170.2.d.b 2
170.2.d.c 4
170.2.g \(\chi_{170}(89, \cdot)\) 170.2.g.a 2 2
170.2.g.b 2
170.2.g.c 2
170.2.g.d 2
170.2.g.e 4
170.2.g.f 4
170.2.h \(\chi_{170}(21, \cdot)\) 170.2.h.a 4 2
170.2.h.b 8
170.2.k \(\chi_{170}(111, \cdot)\) 170.2.k.a 8 4
170.2.k.b 16
170.2.n \(\chi_{170}(9, \cdot)\) 170.2.n.a 20 4
170.2.n.b 20
170.2.o \(\chi_{170}(3, \cdot)\) 170.2.o.a 32 8
170.2.o.b 40
170.2.r \(\chi_{170}(23, \cdot)\) 170.2.r.a 32 8
170.2.r.b 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(170))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(170)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{3} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{4} \))(\( ( 1 + T^{4} )^{5} \))(\( ( 1 + T^{4} )^{5} \))
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 + T + 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 - 5 T^{2} + 9 T^{4} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( 1 - 5 T^{2} + 9 T^{4} \))(\( 1 - T^{2} + 3 T^{4} - 38 T^{6} + 27 T^{8} - 81 T^{10} + 729 T^{12} \))(\( ( 1 + T + 3 T^{2} )^{2} \))(\( ( 1 - T + 3 T^{2} )^{2} \))(\( ( 1 - 2 T^{2} + 9 T^{4} )^{2} \))(\( 1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 16 T^{3} + 31 T^{4} + 48 T^{5} + 72 T^{6} + 108 T^{7} + 81 T^{8} \))(\( 1 - 4 T + 8 T^{2} - 16 T^{3} + 31 T^{4} - 48 T^{5} + 72 T^{6} - 108 T^{7} + 81 T^{8} \))(\( 1 - 4 T + 8 T^{2} - 16 T^{3} + 31 T^{4} - 48 T^{5} + 72 T^{6} - 108 T^{7} + 81 T^{8} \))(\( 1 - 4 T^{3} - 19 T^{4} - 16 T^{5} + 8 T^{6} + 52 T^{7} + 244 T^{8} + 156 T^{9} + 72 T^{10} - 432 T^{11} - 1539 T^{12} - 972 T^{13} + 6561 T^{16} \))(\( 1 - 4 T^{2} - 8 T^{3} + 8 T^{4} + 32 T^{5} + 8 T^{6} - 24 T^{7} - 137 T^{8} - 72 T^{9} + 72 T^{10} + 864 T^{11} + 648 T^{12} - 1944 T^{13} - 2916 T^{14} + 6561 T^{16} \))(\( 1 + 8 T^{3} + 16 T^{5} + 84 T^{6} + 24 T^{7} + 213 T^{8} + 344 T^{9} + 408 T^{10} + 1600 T^{11} + 2312 T^{12} + 4504 T^{13} + 9380 T^{14} + 11040 T^{15} + 26884 T^{16} + 33120 T^{17} + 84420 T^{18} + 121608 T^{19} + 187272 T^{20} + 388800 T^{21} + 297432 T^{22} + 752328 T^{23} + 1397493 T^{24} + 472392 T^{25} + 4960116 T^{26} + 2834352 T^{27} + 12754584 T^{29} + 43046721 T^{32} \))(\( 1 - 8 T^{3} + 32 T^{5} + 28 T^{6} - 72 T^{7} - 234 T^{8} - 24 T^{9} + 1224 T^{10} + 728 T^{11} - 2488 T^{12} - 6728 T^{13} + 1256 T^{14} + 27240 T^{15} + 14713 T^{16} - 60616 T^{17} - 122316 T^{18} + 66920 T^{19} + 485264 T^{20} + 200760 T^{21} - 1100844 T^{22} - 1636632 T^{23} + 1191753 T^{24} + 6619320 T^{25} + 915624 T^{26} - 14714136 T^{27} - 16323768 T^{28} + 14329224 T^{29} + 72275976 T^{30} - 4251528 T^{31} - 124357194 T^{32} - 114791256 T^{33} + 133923132 T^{34} + 459165024 T^{35} - 1033121304 T^{37} + 3486784401 T^{40} \))(\( 1 + 8 T^{3} - 32 T^{5} + 28 T^{6} + 72 T^{7} - 234 T^{8} + 24 T^{9} + 1224 T^{10} - 728 T^{11} - 2488 T^{12} + 6728 T^{13} + 1256 T^{14} - 27240 T^{15} + 14713 T^{16} + 60616 T^{17} - 122316 T^{18} - 66920 T^{19} + 485264 T^{20} - 200760 T^{21} - 1100844 T^{22} + 1636632 T^{23} + 1191753 T^{24} - 6619320 T^{25} + 915624 T^{26} + 14714136 T^{27} - 16323768 T^{28} - 14329224 T^{29} + 72275976 T^{30} + 4251528 T^{31} - 124357194 T^{32} + 114791256 T^{33} + 133923132 T^{34} - 459165024 T^{35} + 1033121304 T^{37} + 3486784401 T^{40} \))
$5$ (\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T - 3 T^{2} + 24 T^{3} - 15 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 8 T^{2} + 25 T^{4} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 - 8 T^{2} + 25 T^{4} \))(\( 1 + 8 T^{2} + 25 T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( 1 + T^{8} \))(\( ( 1 + T^{8} )^{2} \))(\( 1 + 4 T + 14 T^{2} + 28 T^{3} + 41 T^{4} + 32 T^{5} - 72 T^{6} - 416 T^{7} - 1550 T^{8} - 4944 T^{9} - 10916 T^{10} - 24720 T^{11} - 38750 T^{12} - 52000 T^{13} - 45000 T^{14} + 100000 T^{15} + 640625 T^{16} + 2187500 T^{17} + 5468750 T^{18} + 7812500 T^{19} + 9765625 T^{20} \))(\( 1 + 4 T + 4 T^{2} - 4 T^{3} + T^{4} + 32 T^{5} + 24 T^{6} + 224 T^{7} + 906 T^{8} - 752 T^{9} - 7288 T^{10} - 3760 T^{11} + 22650 T^{12} + 28000 T^{13} + 15000 T^{14} + 100000 T^{15} + 15625 T^{16} - 312500 T^{17} + 1562500 T^{18} + 7812500 T^{19} + 9765625 T^{20} \))
$7$ (\( 1 - 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T - 2 T^{2} - 14 T^{3} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 275 T^{4} - 2316 T^{6} + 13475 T^{8} - 52822 T^{10} + 117649 T^{12} \))(\( ( 1 + 2 T + 7 T^{2} )^{2} \))(\( ( 1 - 2 T + 7 T^{2} )^{2} \))(\( ( 1 - 4 T^{2} + 49 T^{4} )^{2} \))(\( 1 + 6 T + 18 T^{2} + 42 T^{3} + 49 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 42 T^{3} + 49 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4} \))(\( ( 1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4} )^{2} \))(\( 1 - 4 T + 8 T^{2} - 20 T^{3} + 46 T^{4} - 140 T^{5} + 392 T^{6} - 1372 T^{7} + 2401 T^{8} \))(\( 1 + 4 T + 8 T^{2} - 12 T^{3} - 208 T^{4} - 524 T^{5} - 360 T^{6} + 3076 T^{7} + 16158 T^{8} + 21532 T^{9} - 17640 T^{10} - 179732 T^{11} - 499408 T^{12} - 201684 T^{13} + 941192 T^{14} + 3294172 T^{15} + 5764801 T^{16} \))(\( 1 + 4 T^{2} - 32 T^{3} + 8 T^{4} - 160 T^{5} + 572 T^{6} - 576 T^{7} + 4414 T^{8} - 4032 T^{9} + 28028 T^{10} - 54880 T^{11} + 19208 T^{12} - 537824 T^{13} + 470596 T^{14} + 5764801 T^{16} \))(\( 1 + 4 T^{2} + 32 T^{3} + 8 T^{4} + 288 T^{5} + 380 T^{6} + 832 T^{7} + 9984 T^{8} + 3264 T^{9} + 37700 T^{10} + 200992 T^{11} + 77592 T^{12} + 1542176 T^{13} + 2426812 T^{14} + 2781312 T^{15} + 37848190 T^{16} + 19469184 T^{17} + 118913788 T^{18} + 528966368 T^{19} + 186298392 T^{20} + 3378072544 T^{21} + 4435367300 T^{22} + 2688044352 T^{23} + 57555773184 T^{24} + 33574201024 T^{25} + 107340594620 T^{26} + 569470101984 T^{27} + 110730297608 T^{28} + 3100448333024 T^{29} + 2712892291396 T^{30} + 33232930569601 T^{32} \))(\( 1 + 28 T^{2} + 72 T^{3} + 392 T^{4} + 2152 T^{5} + 5636 T^{6} + 31696 T^{7} + 93057 T^{8} + 321232 T^{9} + 1251096 T^{10} + 3073136 T^{11} + 11857952 T^{12} + 32094064 T^{13} + 87528552 T^{14} + 298482128 T^{15} + 656393822 T^{16} + 2152770768 T^{17} + 5629095584 T^{18} + 13238676192 T^{19} + 44114872624 T^{20} + 92670733344 T^{21} + 275825683616 T^{22} + 738400373424 T^{23} + 1576001566622 T^{24} + 5016589125296 T^{25} + 10297646614248 T^{26} + 26430841748752 T^{27} + 68358733547552 T^{28} + 124012122401552 T^{29} + 353403654122904 T^{30} + 635180624307376 T^{31} + 1288028663063457 T^{32} + 3070994073860272 T^{33} + 3822465238576964 T^{34} + 10216752369397336 T^{35} + 13027308783283592 T^{36} + 16749397007078904 T^{37} + 45595580741492572 T^{38} + 79792266297612001 T^{40} \))(\( 1 + 28 T^{2} - 72 T^{3} + 392 T^{4} - 2152 T^{5} + 5636 T^{6} - 31696 T^{7} + 93057 T^{8} - 321232 T^{9} + 1251096 T^{10} - 3073136 T^{11} + 11857952 T^{12} - 32094064 T^{13} + 87528552 T^{14} - 298482128 T^{15} + 656393822 T^{16} - 2152770768 T^{17} + 5629095584 T^{18} - 13238676192 T^{19} + 44114872624 T^{20} - 92670733344 T^{21} + 275825683616 T^{22} - 738400373424 T^{23} + 1576001566622 T^{24} - 5016589125296 T^{25} + 10297646614248 T^{26} - 26430841748752 T^{27} + 68358733547552 T^{28} - 124012122401552 T^{29} + 353403654122904 T^{30} - 635180624307376 T^{31} + 1288028663063457 T^{32} - 3070994073860272 T^{33} + 3822465238576964 T^{34} - 10216752369397336 T^{35} + 13027308783283592 T^{36} - 16749397007078904 T^{37} + 45595580741492572 T^{38} + 79792266297612001 T^{40} \))
$11$ (\( 1 - 6 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( ( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 - 2 T + 11 T^{2} )^{6} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 11 T^{2} )^{4} \))(\( 1 - 2 T + 2 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 22 T^{3} + 121 T^{4} \))(\( ( 1 + 6 T + 11 T^{2} )^{2}( 1 + 14 T^{2} + 121 T^{4} ) \))(\( ( 1 + 6 T + 11 T^{2} )^{2}( 1 + 14 T^{2} + 121 T^{4} ) \))(\( ( 1 - 2 T + 2 T^{2} - 22 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 4 T + 8 T^{2} + 12 T^{3} - 178 T^{4} + 132 T^{5} + 968 T^{6} - 5324 T^{7} + 14641 T^{8} )^{2} \))(\( 1 - 16 T + 116 T^{2} - 464 T^{3} + 840 T^{4} + 1136 T^{5} - 10068 T^{6} + 22384 T^{7} - 37474 T^{8} + 246224 T^{9} - 1218228 T^{10} + 1512016 T^{11} + 12298440 T^{12} - 74727664 T^{13} + 205501076 T^{14} - 311794736 T^{15} + 214358881 T^{16} \))(\( 1 + 8 T - 16 T^{2} - 328 T^{3} - 448 T^{4} + 6040 T^{5} + 19712 T^{6} - 66008 T^{7} - 364948 T^{8} + 553512 T^{9} + 5007584 T^{10} - 4614824 T^{11} - 63537600 T^{12} + 36387768 T^{13} + 784865968 T^{14} - 147622328 T^{15} - 9020633882 T^{16} - 1623845608 T^{17} + 94968782128 T^{18} + 48432119208 T^{19} - 930254001600 T^{20} - 743222020024 T^{21} + 8871240518624 T^{22} + 10786382994552 T^{23} - 78229844903188 T^{24} - 155643411187528 T^{25} + 511278513734912 T^{26} + 1723282490490440 T^{27} - 1406015912771008 T^{28} - 11323449583209368 T^{29} - 6075997337331856 T^{30} + 33417985355325208 T^{31} + 45949729863572161 T^{32} \))(\( 1 + 8 T + 32 T^{2} + 88 T^{3} + 192 T^{4} + 1336 T^{5} + 8272 T^{6} + 31784 T^{7} + 74909 T^{8} + 75696 T^{9} + 299120 T^{10} + 2946256 T^{11} + 14548096 T^{12} + 38626064 T^{13} + 40847888 T^{14} + 70277616 T^{15} + 1208780434 T^{16} + 7630937792 T^{17} + 25235168784 T^{18} + 46671777024 T^{19} + 75581355904 T^{20} + 513389547264 T^{21} + 3053455422864 T^{22} + 10156778201152 T^{23} + 17697754334194 T^{24} + 11318280334416 T^{25} + 72364525313168 T^{26} + 752712714224944 T^{27} + 3118513579240576 T^{28} + 6947117532294896 T^{29} + 7758402446651120 T^{30} + 21596952218570256 T^{31} + 235096531271793389 T^{32} + 1097269882782702904 T^{33} + 3141290623400569552 T^{34} + 5580803554339309736 T^{35} + 8822348133805854912 T^{36} + 44479338507937851848 T^{37} + \)\(17\!\cdots\!92\)\( T^{38} + \)\(48\!\cdots\!28\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))(\( 1 + 8 T + 32 T^{2} + 88 T^{3} + 192 T^{4} + 1336 T^{5} + 8272 T^{6} + 31784 T^{7} + 74909 T^{8} + 75696 T^{9} + 299120 T^{10} + 2946256 T^{11} + 14548096 T^{12} + 38626064 T^{13} + 40847888 T^{14} + 70277616 T^{15} + 1208780434 T^{16} + 7630937792 T^{17} + 25235168784 T^{18} + 46671777024 T^{19} + 75581355904 T^{20} + 513389547264 T^{21} + 3053455422864 T^{22} + 10156778201152 T^{23} + 17697754334194 T^{24} + 11318280334416 T^{25} + 72364525313168 T^{26} + 752712714224944 T^{27} + 3118513579240576 T^{28} + 6947117532294896 T^{29} + 7758402446651120 T^{30} + 21596952218570256 T^{31} + 235096531271793389 T^{32} + 1097269882782702904 T^{33} + 3141290623400569552 T^{34} + 5580803554339309736 T^{35} + 8822348133805854912 T^{36} + 44479338507937851848 T^{37} + \)\(17\!\cdots\!92\)\( T^{38} + \)\(48\!\cdots\!28\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))
$13$ (\( 1 - 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 3 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 5 T + 28 T^{2} - 65 T^{3} + 169 T^{4} \))(\( ( 1 + 5 T + 13 T^{2} )^{2} \))(\( ( 1 - T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( 1 - 17 T^{2} + 169 T^{4} \))(\( 1 - 61 T^{2} + 1723 T^{4} - 28558 T^{6} + 291187 T^{8} - 1742221 T^{10} + 4826809 T^{12} \))(\( 1 - 25 T^{2} + 169 T^{4} \))(\( 1 - 25 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )^{2}( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 17 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 17 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - T + 13 T^{2} )^{4} \))(\( ( 1 + 6 T + 49 T^{2} + 206 T^{3} + 932 T^{4} + 2678 T^{5} + 8281 T^{6} + 13182 T^{7} + 28561 T^{8} )^{2} \))(\( 1 - 52 T^{2} + 1386 T^{4} - 26096 T^{6} + 381683 T^{8} - 4410224 T^{10} + 39585546 T^{12} - 250994068 T^{14} + 815730721 T^{16} \))(\( 1 - 76 T^{2} + 3430 T^{4} - 111192 T^{6} + 2863025 T^{8} - 61251048 T^{10} + 1119763510 T^{12} - 17768536788 T^{14} + 246624737540 T^{16} - 3002882717172 T^{18} + 31981565609110 T^{20} - 295647109745832 T^{22} + 2335457447491025 T^{24} - 15328761425674008 T^{26} + 79912431970109830 T^{28} - 299240605313145964 T^{30} + 665416609183179841 T^{32} \))(\( ( 1 + 12 T + 126 T^{2} + 944 T^{3} + 6370 T^{4} + 36804 T^{5} + 195036 T^{6} + 930636 T^{7} + 4101389 T^{8} + 16591780 T^{9} + 62248284 T^{10} + 215693140 T^{11} + 693134741 T^{12} + 2044607292 T^{13} + 5570423196 T^{14} + 13665067572 T^{15} + 30746773330 T^{16} + 59234600048 T^{17} + 102782070846 T^{18} + 127253992476 T^{19} + 137858491849 T^{20} )^{2} \))(\( ( 1 - 12 T + 126 T^{2} - 944 T^{3} + 6370 T^{4} - 36804 T^{5} + 195036 T^{6} - 930636 T^{7} + 4101389 T^{8} - 16591780 T^{9} + 62248284 T^{10} - 215693140 T^{11} + 693134741 T^{12} - 2044607292 T^{13} + 5570423196 T^{14} - 13665067572 T^{15} + 30746773330 T^{16} - 59234600048 T^{17} + 102782070846 T^{18} - 127253992476 T^{19} + 137858491849 T^{20} )^{2} \))
$17$ (\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{3} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T^{2} + 289 T^{4} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 16 T^{2} + 289 T^{4} \))(\( 1 + 16 T^{2} + 289 T^{4} \))(\( 1 + 8 T + 32 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 + 8 T + 66 T^{2} + 344 T^{3} + 1730 T^{4} + 5848 T^{5} + 19074 T^{6} + 39304 T^{7} + 83521 T^{8} \))(\( 1 - 48 T^{2} + 1152 T^{4} - 13872 T^{6} + 83521 T^{8} \))(\( 1 - 16 T^{2} + 642 T^{4} - 160 T^{5} - 15280 T^{6} - 2848 T^{7} + 207874 T^{8} - 48416 T^{9} - 4415920 T^{10} - 786080 T^{11} + 53620482 T^{12} - 386201104 T^{14} + 6975757441 T^{16} \))(\( 1 + 18 T^{2} - 16 T^{3} + 803 T^{4} - 1696 T^{5} + 11588 T^{6} - 48032 T^{7} + 238596 T^{8} - 1229744 T^{9} + 3632100 T^{10} - 20905648 T^{11} + 68954244 T^{12} - 235981216 T^{13} + 967841348 T^{14} - 2408077472 T^{15} + 19382467907 T^{16} - 6565418768 T^{17} + 125563633938 T^{18} + 2015993900449 T^{20} \))(\( 1 + 18 T^{2} + 16 T^{3} + 803 T^{4} + 1696 T^{5} + 11588 T^{6} + 48032 T^{7} + 238596 T^{8} + 1229744 T^{9} + 3632100 T^{10} + 20905648 T^{11} + 68954244 T^{12} + 235981216 T^{13} + 967841348 T^{14} + 2408077472 T^{15} + 19382467907 T^{16} + 6565418768 T^{17} + 125563633938 T^{18} + 2015993900449 T^{20} \))
$19$ (\( 1 - 8 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + T + 34 T^{2} + 19 T^{3} + 361 T^{4} \))(\( ( 1 - 3 T + 19 T^{2} )^{2} \))(\( ( 1 - 7 T + 19 T^{2} )^{2} \))(\( ( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 - 7 T + 19 T^{2} )^{2} \))(\( ( 1 + T + 33 T^{2} + 58 T^{3} + 627 T^{4} + 361 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 + 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 5 T + 19 T^{2} )^{2} \))(\( ( 1 - 2 T + 19 T^{2} )^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 195 T^{4} - 7942 T^{6} + 130321 T^{8} \))(\( 1 - 22 T^{2} + 195 T^{4} - 7942 T^{6} + 130321 T^{8} \))(\( 1 - 70 T^{2} + 1939 T^{4} - 25270 T^{6} + 130321 T^{8} \))(\( 1 - 66 T^{2} + 2465 T^{4} - 63130 T^{6} + 1314132 T^{8} - 22789930 T^{10} + 321241265 T^{12} - 3105028146 T^{14} + 16983563041 T^{16} \))(\( 1 + 16 T + 128 T^{2} + 808 T^{3} + 3650 T^{4} + 8088 T^{5} - 11360 T^{6} - 251240 T^{7} - 1571141 T^{8} - 4773560 T^{9} - 4100960 T^{10} + 55475592 T^{11} + 475671650 T^{12} + 2000687992 T^{13} + 6021872768 T^{14} + 14301947824 T^{15} + 16983563041 T^{16} \))(\( 1 + 88 T^{3} + 102 T^{4} + 264 T^{5} + 3872 T^{6} + 34312 T^{7} + 146153 T^{8} + 250536 T^{9} + 2659360 T^{10} + 13384312 T^{11} + 30672606 T^{12} + 263275656 T^{13} + 995458496 T^{14} + 4638677568 T^{15} + 27904305492 T^{16} + 88134873792 T^{17} + 359360517056 T^{18} + 1805807724504 T^{19} + 3997284686526 T^{20} + 33140881558888 T^{21} + 125111934096160 T^{22} + 223947050002104 T^{23} + 2482198689131273 T^{24} + 11072060286193048 T^{25} + 23739488550205472 T^{26} + 30753428349129816 T^{27} + 225758121744748422 T^{28} + 3700662544678621192 T^{29} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( 1 - 104 T^{3} - 440 T^{4} - 1768 T^{5} + 5408 T^{6} - 5432 T^{7} + 242710 T^{8} + 738648 T^{9} + 4507360 T^{10} + 7934112 T^{11} + 6690854 T^{12} - 462658112 T^{13} - 1445661280 T^{14} - 8971090888 T^{15} - 40777542279 T^{16} - 43430694488 T^{17} + 214418884704 T^{18} + 3590696280576 T^{19} + 25541206222212 T^{20} + 68223229330944 T^{21} + 77405217378144 T^{22} - 297891133493192 T^{23} - 5314170087341559 T^{24} - 22213309176685912 T^{25} - 68012408545187680 T^{26} - 413557011135896768 T^{27} + 113634540707127014 T^{28} + 2560240335200737248 T^{29} + 27634922807761915360 T^{30} + 86045296754651667912 T^{31} + \)\(53\!\cdots\!10\)\( T^{32} - \)\(22\!\cdots\!88\)\( T^{33} + \)\(43\!\cdots\!68\)\( T^{34} - \)\(26\!\cdots\!32\)\( T^{35} - \)\(12\!\cdots\!40\)\( T^{36} - \)\(56\!\cdots\!56\)\( T^{37} + \)\(37\!\cdots\!01\)\( T^{40} \))(\( 1 - 104 T^{3} - 440 T^{4} - 1768 T^{5} + 5408 T^{6} - 5432 T^{7} + 242710 T^{8} + 738648 T^{9} + 4507360 T^{10} + 7934112 T^{11} + 6690854 T^{12} - 462658112 T^{13} - 1445661280 T^{14} - 8971090888 T^{15} - 40777542279 T^{16} - 43430694488 T^{17} + 214418884704 T^{18} + 3590696280576 T^{19} + 25541206222212 T^{20} + 68223229330944 T^{21} + 77405217378144 T^{22} - 297891133493192 T^{23} - 5314170087341559 T^{24} - 22213309176685912 T^{25} - 68012408545187680 T^{26} - 413557011135896768 T^{27} + 113634540707127014 T^{28} + 2560240335200737248 T^{29} + 27634922807761915360 T^{30} + 86045296754651667912 T^{31} + \)\(53\!\cdots\!10\)\( T^{32} - \)\(22\!\cdots\!88\)\( T^{33} + \)\(43\!\cdots\!68\)\( T^{34} - \)\(26\!\cdots\!32\)\( T^{35} - \)\(12\!\cdots\!40\)\( T^{36} - \)\(56\!\cdots\!56\)\( T^{37} + \)\(37\!\cdots\!01\)\( T^{40} \))
$23$ (\( 1 + 6 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 2 T + 30 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 - 42 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 + 18 T^{2} + 529 T^{4} \))(\( 1 - 70 T^{2} + 2355 T^{4} - 57580 T^{6} + 1245795 T^{8} - 19588870 T^{10} + 148035889 T^{12} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 44 T^{2} + 529 T^{4} )^{2} \))(\( 1 - 10 T + 50 T^{2} - 230 T^{3} + 529 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 + 10 T + 50 T^{2} + 230 T^{3} + 529 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 - 158 T^{4} + 279841 T^{8} \))(\( 1 - 158 T^{4} + 279841 T^{8} \))(\( 1 + 8 T + 32 T^{2} - 40 T^{3} - 734 T^{4} - 920 T^{5} + 16928 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( ( 1 + 8 T + 32 T^{2} + 216 T^{3} + 1442 T^{4} + 4968 T^{5} + 16928 T^{6} + 97336 T^{7} + 279841 T^{8} )^{2} \))(\( 1 - 24 T + 296 T^{2} - 2376 T^{3} + 13280 T^{4} - 49720 T^{5} + 88072 T^{6} + 294104 T^{7} - 2824990 T^{8} + 6764392 T^{9} + 46590088 T^{10} - 604943240 T^{11} + 3716288480 T^{12} - 15292750968 T^{13} + 43818623144 T^{14} - 81715810728 T^{15} + 78310985281 T^{16} \))(\( 1 - 8 T + 120 T^{2} - 872 T^{3} + 7520 T^{4} - 47768 T^{5} + 313496 T^{6} - 1818424 T^{7} + 10176164 T^{8} - 56108568 T^{9} + 291322632 T^{10} - 1563982584 T^{11} + 7887703072 T^{12} - 40951922824 T^{13} + 203064358952 T^{14} - 1008566309288 T^{15} + 4857811804614 T^{16} - 23197025113624 T^{17} + 107421045885608 T^{18} - 498262044999608 T^{19} + 2207302715371552 T^{20} - 10066328356650312 T^{21} + 43126204813939848 T^{22} - 191039880121129896 T^{23} + 796905429221042084 T^{24} - 3275259227268194312 T^{25} + 12987045559434106904 T^{26} - 45513816516032464936 T^{27} + \)\(16\!\cdots\!20\)\( T^{28} - \)\(43\!\cdots\!76\)\( T^{29} + \)\(13\!\cdots\!80\)\( T^{30} - \)\(21\!\cdots\!56\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 - 16 T + 56 T^{2} + 376 T^{3} - 2400 T^{4} - 7256 T^{5} + 72440 T^{6} + 121072 T^{7} - 2621531 T^{8} + 4314208 T^{9} + 70866208 T^{10} - 388785408 T^{11} - 779461504 T^{12} + 12408165568 T^{13} - 8863476320 T^{14} - 287308681888 T^{15} + 756303717514 T^{16} + 5606916061312 T^{17} - 30507258885872 T^{18} - 66054575985616 T^{19} + 960733835992000 T^{20} - 1519255247669168 T^{21} - 16138339950626288 T^{22} + 68219347717983104 T^{23} + 211644788612835274 T^{24} - 1849217223509055584 T^{25} - 1312112596661648480 T^{26} + 42247637876515608896 T^{27} - 61040398366850122624 T^{28} - \)\(70\!\cdots\!04\)\( T^{29} + \)\(29\!\cdots\!92\)\( T^{30} + \)\(41\!\cdots\!16\)\( T^{31} - \)\(57\!\cdots\!51\)\( T^{32} + \)\(61\!\cdots\!76\)\( T^{33} + \)\(83\!\cdots\!60\)\( T^{34} - \)\(19\!\cdots\!92\)\( T^{35} - \)\(14\!\cdots\!00\)\( T^{36} + \)\(53\!\cdots\!28\)\( T^{37} + \)\(18\!\cdots\!64\)\( T^{38} - \)\(11\!\cdots\!92\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))(\( 1 + 16 T + 56 T^{2} - 376 T^{3} - 2400 T^{4} + 7256 T^{5} + 72440 T^{6} - 121072 T^{7} - 2621531 T^{8} - 4314208 T^{9} + 70866208 T^{10} + 388785408 T^{11} - 779461504 T^{12} - 12408165568 T^{13} - 8863476320 T^{14} + 287308681888 T^{15} + 756303717514 T^{16} - 5606916061312 T^{17} - 30507258885872 T^{18} + 66054575985616 T^{19} + 960733835992000 T^{20} + 1519255247669168 T^{21} - 16138339950626288 T^{22} - 68219347717983104 T^{23} + 211644788612835274 T^{24} + 1849217223509055584 T^{25} - 1312112596661648480 T^{26} - 42247637876515608896 T^{27} - 61040398366850122624 T^{28} + \)\(70\!\cdots\!04\)\( T^{29} + \)\(29\!\cdots\!92\)\( T^{30} - \)\(41\!\cdots\!16\)\( T^{31} - \)\(57\!\cdots\!51\)\( T^{32} - \)\(61\!\cdots\!76\)\( T^{33} + \)\(83\!\cdots\!60\)\( T^{34} + \)\(19\!\cdots\!92\)\( T^{35} - \)\(14\!\cdots\!00\)\( T^{36} - \)\(53\!\cdots\!28\)\( T^{37} + \)\(18\!\cdots\!64\)\( T^{38} + \)\(11\!\cdots\!92\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - T + 20 T^{2} - 29 T^{3} + 841 T^{4} \))(\( 1 - 57 T^{2} + 841 T^{4} \))(\( 1 - 49 T^{2} + 841 T^{4} \))(\( 1 - 22 T^{2} + 841 T^{4} \))(\( ( 1 - 5 T + 29 T^{2} )^{2} \))(\( ( 1 + 17 T + 153 T^{2} + 936 T^{3} + 4437 T^{4} + 14297 T^{5} + 24389 T^{6} )^{2} \))(\( 1 + 23 T^{2} + 841 T^{4} \))(\( 1 + 23 T^{2} + 841 T^{4} \))(\( ( 1 - 40 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 10 T + 29 T^{2} )( 1 - 4 T + 29 T^{2} ) \))(\( 1 + 10 T + 50 T^{2} + 290 T^{3} + 841 T^{4} \))(\( ( 1 - 10 T + 29 T^{2} )( 1 - 4 T + 29 T^{2} ) \))(\( 1 + 10 T + 50 T^{2} + 290 T^{3} + 841 T^{4} \))(\( 1 + 1567 T^{4} + 707281 T^{8} \))(\( 1 + 1567 T^{4} + 707281 T^{8} \))(\( 1 + 8 T + 32 T^{2} - 96 T^{3} - 1393 T^{4} - 2784 T^{5} + 26912 T^{6} + 195112 T^{7} + 707281 T^{8} \))(\( 1 - 24 T + 288 T^{2} - 2640 T^{3} + 22065 T^{4} - 164976 T^{5} + 1089504 T^{6} - 6624840 T^{7} + 37336208 T^{8} - 192120360 T^{9} + 916272864 T^{10} - 4023599664 T^{11} + 15606155265 T^{12} - 54149433360 T^{13} + 171309116448 T^{14} - 413997031416 T^{15} + 500246412961 T^{16} \))(\( 1 - 8 T + 304 T^{3} - 1408 T^{4} - 824 T^{5} + 41632 T^{6} - 43752 T^{7} - 672337 T^{8} - 1268808 T^{9} + 35012512 T^{10} - 20096536 T^{11} - 995851648 T^{12} + 6235389296 T^{13} - 137999010472 T^{15} + 500246412961 T^{16} \))(\( 1 - 8 T + 32 T^{2} + 416 T^{3} - 3840 T^{4} + 29384 T^{5} - 11840 T^{6} - 651048 T^{7} + 10221809 T^{8} - 36975912 T^{9} + 79144480 T^{10} + 1605711096 T^{11} - 10517929216 T^{12} + 61516520128 T^{13} + 44651055680 T^{14} - 1220613560392 T^{15} + 13350264496192 T^{16} - 35397793251368 T^{17} + 37551537826880 T^{18} + 1500326409401792 T^{19} - 7439131493821696 T^{20} + 32934979541009304 T^{21} + 47076982432418080 T^{22} - 637829908412468808 T^{23} + 5113423286222466449 T^{24} - 9444848373297560712 T^{25} - 4981173642274379840 T^{26} + \)\(35\!\cdots\!36\)\( T^{27} - \)\(13\!\cdots\!40\)\( T^{28} + \)\(42\!\cdots\!24\)\( T^{29} + \)\(95\!\cdots\!92\)\( T^{30} - \)\(69\!\cdots\!92\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 + 12 T + 38 T^{2} + 212 T^{3} + 2978 T^{4} + 17140 T^{5} + 92422 T^{6} + 571116 T^{7} + 2331938 T^{8} + 14922092 T^{9} + 130048102 T^{10} + 770925860 T^{11} + 3851687522 T^{12} + 19564235252 T^{13} + 133504284918 T^{14} + 966299457452 T^{15} + 4642708862081 T^{16} + 19643962031712 T^{17} + 123559244554608 T^{18} + 710977606960016 T^{19} + 3560114011124736 T^{20} + 20618350601840464 T^{21} + 103913324670425328 T^{22} + 479096589991423968 T^{23} + 3283699766681511761 T^{24} + 19819912150417132348 T^{25} + 79411462122654972678 T^{26} + \)\(33\!\cdots\!68\)\( T^{27} + \)\(19\!\cdots\!42\)\( T^{28} + \)\(11\!\cdots\!40\)\( T^{29} + \)\(54\!\cdots\!02\)\( T^{30} + \)\(18\!\cdots\!68\)\( T^{31} + \)\(82\!\cdots\!58\)\( T^{32} + \)\(58\!\cdots\!24\)\( T^{33} + \)\(27\!\cdots\!82\)\( T^{34} + \)\(14\!\cdots\!60\)\( T^{35} + \)\(74\!\cdots\!38\)\( T^{36} + \)\(15\!\cdots\!08\)\( T^{37} + \)\(79\!\cdots\!18\)\( T^{38} + \)\(73\!\cdots\!28\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))(\( 1 + 12 T + 38 T^{2} + 212 T^{3} + 2978 T^{4} + 17140 T^{5} + 92422 T^{6} + 571116 T^{7} + 2331938 T^{8} + 14922092 T^{9} + 130048102 T^{10} + 770925860 T^{11} + 3851687522 T^{12} + 19564235252 T^{13} + 133504284918 T^{14} + 966299457452 T^{15} + 4642708862081 T^{16} + 19643962031712 T^{17} + 123559244554608 T^{18} + 710977606960016 T^{19} + 3560114011124736 T^{20} + 20618350601840464 T^{21} + 103913324670425328 T^{22} + 479096589991423968 T^{23} + 3283699766681511761 T^{24} + 19819912150417132348 T^{25} + 79411462122654972678 T^{26} + \)\(33\!\cdots\!68\)\( T^{27} + \)\(19\!\cdots\!42\)\( T^{28} + \)\(11\!\cdots\!40\)\( T^{29} + \)\(54\!\cdots\!02\)\( T^{30} + \)\(18\!\cdots\!68\)\( T^{31} + \)\(82\!\cdots\!58\)\( T^{32} + \)\(58\!\cdots\!24\)\( T^{33} + \)\(27\!\cdots\!82\)\( T^{34} + \)\(14\!\cdots\!60\)\( T^{35} + \)\(74\!\cdots\!38\)\( T^{36} + \)\(15\!\cdots\!08\)\( T^{37} + \)\(79\!\cdots\!18\)\( T^{38} + \)\(73\!\cdots\!28\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))
$31$ (\( 1 - 2 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 9 T + 78 T^{2} + 279 T^{3} + 961 T^{4} \))(\( 1 - 13 T^{2} + 961 T^{4} \))(\( 1 - 13 T^{2} + 961 T^{4} \))(\( 1 + 38 T^{2} + 961 T^{4} \))(\( ( 1 - 5 T + 31 T^{2} )^{2} \))(\( ( 1 - 3 T + 47 T^{2} - 260 T^{3} + 1457 T^{4} - 2883 T^{5} + 29791 T^{6} )^{2} \))(\( 1 - 37 T^{2} + 961 T^{4} \))(\( 1 - 37 T^{2} + 961 T^{4} \))(\( ( 1 - 44 T^{2} + 961 T^{4} )^{2} \))(\( 1 - 2 T + 2 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 8 T^{2} + 192 T^{3} - 1633 T^{4} + 5952 T^{5} + 7688 T^{6} - 119164 T^{7} + 923521 T^{8} \))(\( 1 - 4 T + 8 T^{2} + 192 T^{3} - 1633 T^{4} + 5952 T^{5} + 7688 T^{6} - 119164 T^{7} + 923521 T^{8} \))(\( 1 + 12 T + 72 T^{2} + 576 T^{3} + 4319 T^{4} + 17856 T^{5} + 69192 T^{6} + 357492 T^{7} + 923521 T^{8} \))(\( 1 - 4 T + 8 T^{2} + 240 T^{3} + 257 T^{4} - 12200 T^{5} + 75544 T^{6} + 16212 T^{7} - 1964000 T^{8} + 502572 T^{9} + 72597784 T^{10} - 363450200 T^{11} + 237344897 T^{12} + 6870996240 T^{13} + 7100029448 T^{14} - 110050456444 T^{15} + 852891037441 T^{16} \))(\( 1 + 16 T + 68 T^{2} - 152 T^{3} - 1144 T^{4} + 5584 T^{5} + 19224 T^{6} - 453096 T^{7} - 4328313 T^{8} - 14045976 T^{9} + 18474264 T^{10} + 166352944 T^{11} - 1056508024 T^{12} - 4351630952 T^{13} + 60350250308 T^{14} + 440201825776 T^{15} + 852891037441 T^{16} \))(\( 1 - 32 T + 548 T^{2} - 6808 T^{3} + 69000 T^{4} - 608640 T^{5} + 4865496 T^{6} - 35869848 T^{7} + 246301929 T^{8} - 1595242696 T^{9} + 9882803936 T^{10} - 59393372880 T^{11} + 349673282200 T^{12} - 2025742485832 T^{13} + 11589796641940 T^{14} - 65585046187504 T^{15} + 367102777561424 T^{16} - 2033136431812624 T^{17} + 11137794572904340 T^{18} - 60348894395421112 T^{19} + 322930619250626200 T^{20} - 1700381840580824880 T^{21} + 8771024871801288416 T^{22} - 43889296708439283256 T^{23} + \)\(21\!\cdots\!89\)\( T^{24} - \)\(94\!\cdots\!08\)\( T^{25} + \)\(39\!\cdots\!96\)\( T^{26} - \)\(15\!\cdots\!40\)\( T^{27} + \)\(54\!\cdots\!00\)\( T^{28} - \)\(16\!\cdots\!28\)\( T^{29} + \)\(41\!\cdots\!08\)\( T^{30} - \)\(75\!\cdots\!32\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 - 8 T + 4 T^{2} + 384 T^{3} - 2296 T^{4} + 6096 T^{5} + 40040 T^{6} - 153440 T^{7} + 1584090 T^{8} - 14476232 T^{9} + 89328068 T^{10} + 315411224 T^{11} - 3760050272 T^{12} + 22889881832 T^{13} + 17254141740 T^{14} - 332815622952 T^{15} + 2990654769257 T^{16} - 6114910723832 T^{17} + 38570348356996 T^{18} + 367744608569728 T^{19} - 1791803809774288 T^{20} + 11400082865661568 T^{21} + 37066104771073156 T^{22} - 182169305373679112 T^{23} + 2761932483158993897 T^{24} - 9528228724651873752 T^{25} + 15313114306745744940 T^{26} + \)\(62\!\cdots\!52\)\( T^{27} - \)\(32\!\cdots\!52\)\( T^{28} + \)\(83\!\cdots\!04\)\( T^{29} + \)\(73\!\cdots\!68\)\( T^{30} - \)\(36\!\cdots\!92\)\( T^{31} + \)\(12\!\cdots\!90\)\( T^{32} - \)\(37\!\cdots\!40\)\( T^{33} + \)\(30\!\cdots\!40\)\( T^{34} + \)\(14\!\cdots\!96\)\( T^{35} - \)\(16\!\cdots\!76\)\( T^{36} + \)\(86\!\cdots\!24\)\( T^{37} + \)\(27\!\cdots\!64\)\( T^{38} - \)\(17\!\cdots\!68\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))(\( 1 - 8 T + 4 T^{2} + 384 T^{3} - 2296 T^{4} + 6096 T^{5} + 40040 T^{6} - 153440 T^{7} + 1584090 T^{8} - 14476232 T^{9} + 89328068 T^{10} + 315411224 T^{11} - 3760050272 T^{12} + 22889881832 T^{13} + 17254141740 T^{14} - 332815622952 T^{15} + 2990654769257 T^{16} - 6114910723832 T^{17} + 38570348356996 T^{18} + 367744608569728 T^{19} - 1791803809774288 T^{20} + 11400082865661568 T^{21} + 37066104771073156 T^{22} - 182169305373679112 T^{23} + 2761932483158993897 T^{24} - 9528228724651873752 T^{25} + 15313114306745744940 T^{26} + \)\(62\!\cdots\!52\)\( T^{27} - \)\(32\!\cdots\!52\)\( T^{28} + \)\(83\!\cdots\!04\)\( T^{29} + \)\(73\!\cdots\!68\)\( T^{30} - \)\(36\!\cdots\!92\)\( T^{31} + \)\(12\!\cdots\!90\)\( T^{32} - \)\(37\!\cdots\!40\)\( T^{33} + \)\(30\!\cdots\!40\)\( T^{34} + \)\(14\!\cdots\!96\)\( T^{35} - \)\(16\!\cdots\!76\)\( T^{36} + \)\(86\!\cdots\!24\)\( T^{37} + \)\(27\!\cdots\!64\)\( T^{38} - \)\(17\!\cdots\!68\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))
$37$ (\( 1 - 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 6 T + 66 T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 + 26 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( ( 1 - 10 T + 93 T^{2} - 472 T^{3} + 3441 T^{4} - 13690 T^{5} + 50653 T^{6} )( 1 + 10 T + 93 T^{2} + 472 T^{3} + 3441 T^{4} + 13690 T^{5} + 50653 T^{6} ) \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 56 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 + 2 T + 2 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 2 T + 37 T^{2} ) \))(\( 1 - 2 T + 2 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 8 T^{2} - 12 T^{3} - 1138 T^{4} - 444 T^{5} + 10952 T^{6} - 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 4 T + 8 T^{2} + 12 T^{3} - 1138 T^{4} + 444 T^{5} + 10952 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( 1 - 12 T + 72 T^{2} - 612 T^{3} + 5006 T^{4} - 22644 T^{5} + 98568 T^{6} - 607836 T^{7} + 1874161 T^{8} \))(\( 1 + 20 T + 200 T^{2} + 1484 T^{3} + 9888 T^{4} + 60164 T^{5} + 326808 T^{6} + 1410492 T^{7} + 6339550 T^{8} + 52188204 T^{9} + 447400152 T^{10} + 3047487092 T^{11} + 18531703968 T^{12} + 102906432188 T^{13} + 513145281800 T^{14} + 1898637542660 T^{15} + 3512479453921 T^{16} \))(\( ( 1 + 4 T + 54 T^{2} + 452 T^{3} + 2466 T^{4} + 16724 T^{5} + 73926 T^{6} + 202612 T^{7} + 1874161 T^{8} )^{2} \))(\( 1 + 8 T + 12 T^{2} + 200 T^{3} + 1928 T^{4} + 12312 T^{5} + 148644 T^{6} + 711608 T^{7} + 3174928 T^{8} + 34103656 T^{9} + 148373724 T^{10} + 1112598856 T^{11} + 10158573080 T^{12} + 40152417688 T^{13} + 300897419892 T^{14} + 1928212146840 T^{15} + 6429418423390 T^{16} + 71343849433080 T^{17} + 411928567832148 T^{18} + 2033840413150264 T^{19} + 19038801482185880 T^{20} + 77152007228713192 T^{21} + 380686382068477116 T^{22} + 3237524081178098248 T^{23} + 11151869367678492688 T^{24} + 92481813732095153816 T^{25} + \)\(71\!\cdots\!56\)\( T^{26} + \)\(21\!\cdots\!56\)\( T^{27} + \)\(12\!\cdots\!68\)\( T^{28} + \)\(48\!\cdots\!00\)\( T^{29} + \)\(10\!\cdots\!68\)\( T^{30} + \)\(26\!\cdots\!44\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 + 8 T + 118 T^{2} + 960 T^{3} + 8114 T^{4} + 50464 T^{5} + 338982 T^{6} + 1440600 T^{7} + 4335441 T^{8} - 9800336 T^{9} - 346829856 T^{10} - 3402505696 T^{11} - 26710359232 T^{12} - 167815912224 T^{13} - 904985189600 T^{14} - 3602804409392 T^{15} - 5581747209506 T^{16} + 63717621771584 T^{17} + 1054915539916916 T^{18} + 8107624670209056 T^{19} + 59840742028993692 T^{20} + 299982112797735072 T^{21} + 1444179374146258004 T^{22} + 3227488695596044352 T^{23} - 10461092931914974466 T^{24} - \)\(24\!\cdots\!44\)\( T^{25} - \)\(23\!\cdots\!00\)\( T^{26} - \)\(15\!\cdots\!92\)\( T^{27} - \)\(93\!\cdots\!72\)\( T^{28} - \)\(44\!\cdots\!92\)\( T^{29} - \)\(16\!\cdots\!44\)\( T^{30} - \)\(17\!\cdots\!68\)\( T^{31} + \)\(28\!\cdots\!21\)\( T^{32} + \)\(35\!\cdots\!00\)\( T^{33} + \)\(30\!\cdots\!98\)\( T^{34} + \)\(16\!\cdots\!52\)\( T^{35} + \)\(10\!\cdots\!74\)\( T^{36} + \)\(43\!\cdots\!20\)\( T^{37} + \)\(19\!\cdots\!22\)\( T^{38} + \)\(49\!\cdots\!84\)\( T^{39} + \)\(23\!\cdots\!01\)\( T^{40} \))(\( 1 - 8 T + 118 T^{2} - 960 T^{3} + 8114 T^{4} - 50464 T^{5} + 338982 T^{6} - 1440600 T^{7} + 4335441 T^{8} + 9800336 T^{9} - 346829856 T^{10} + 3402505696 T^{11} - 26710359232 T^{12} + 167815912224 T^{13} - 904985189600 T^{14} + 3602804409392 T^{15} - 5581747209506 T^{16} - 63717621771584 T^{17} + 1054915539916916 T^{18} - 8107624670209056 T^{19} + 59840742028993692 T^{20} - 299982112797735072 T^{21} + 1444179374146258004 T^{22} - 3227488695596044352 T^{23} - 10461092931914974466 T^{24} + \)\(24\!\cdots\!44\)\( T^{25} - \)\(23\!\cdots\!00\)\( T^{26} + \)\(15\!\cdots\!92\)\( T^{27} - \)\(93\!\cdots\!72\)\( T^{28} + \)\(44\!\cdots\!92\)\( T^{29} - \)\(16\!\cdots\!44\)\( T^{30} + \)\(17\!\cdots\!68\)\( T^{31} + \)\(28\!\cdots\!21\)\( T^{32} - \)\(35\!\cdots\!00\)\( T^{33} + \)\(30\!\cdots\!98\)\( T^{34} - \)\(16\!\cdots\!52\)\( T^{35} + \)\(10\!\cdots\!74\)\( T^{36} - \)\(43\!\cdots\!20\)\( T^{37} + \)\(19\!\cdots\!22\)\( T^{38} - \)\(49\!\cdots\!84\)\( T^{39} + \)\(23\!\cdots\!01\)\( T^{40} \))
$41$ (\( 1 + 6 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 8 T + 30 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( 1 + 62 T^{2} + 1681 T^{4} \))(\( ( 1 - 10 T + 41 T^{2} )( 1 + 10 T + 41 T^{2} ) \))(\( 1 - 66 T^{2} + 1681 T^{4} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 - 16 T + 183 T^{2} - 1296 T^{3} + 7503 T^{4} - 26896 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 - 8 T + 41 T^{2} )( 1 + 8 T + 41 T^{2} ) \))(\( ( 1 - 8 T + 41 T^{2} )( 1 + 8 T + 41 T^{2} ) \))(\( ( 1 - 10 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 10 T + 41 T^{2} )( 1 + 8 T + 41 T^{2} ) \))(\( 1 + 14 T + 98 T^{2} + 574 T^{3} + 1681 T^{4} \))(\( ( 1 - 10 T + 41 T^{2} )( 1 + 8 T + 41 T^{2} ) \))(\( 1 + 14 T + 98 T^{2} + 574 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 72 T^{2} - 660 T^{3} + 5854 T^{4} - 27060 T^{5} + 121032 T^{6} - 827052 T^{7} + 2825761 T^{8} \))(\( 1 - 12 T + 72 T^{2} - 660 T^{3} + 5854 T^{4} - 27060 T^{5} + 121032 T^{6} - 827052 T^{7} + 2825761 T^{8} \))(\( 1 + 4 T + 8 T^{2} - 84 T^{3} - 2962 T^{4} - 3444 T^{5} + 13448 T^{6} + 275684 T^{7} + 2825761 T^{8} \))(\( 1 - 4420 T^{4} + 10011334 T^{8} - 12489863620 T^{12} + 7984925229121 T^{16} \))(\( 1 + 68 T^{2} + 2312 T^{4} - 9856 T^{5} - 31220 T^{6} - 939904 T^{7} - 3008818 T^{8} - 38536064 T^{9} - 52480820 T^{10} - 679285376 T^{11} + 6533159432 T^{12} + 323007088388 T^{14} + 7984925229121 T^{16} \))(\( 1 + 32 T + 520 T^{2} + 5088 T^{3} + 27680 T^{4} - 17248 T^{5} - 2012456 T^{6} - 22724256 T^{7} - 145472452 T^{8} - 382619616 T^{9} + 3679213384 T^{10} + 59763425248 T^{11} + 446162317792 T^{12} + 1726334249376 T^{13} - 2696546863400 T^{14} - 100460662345632 T^{15} - 856449502946298 T^{16} - 4118887156170912 T^{17} - 4532895277375400 T^{18} + 118980682801243296 T^{19} + 1260748077286239712 T^{20} + 6923963407980762848 T^{21} + 17476647098882361544 T^{22} - 74516805486707049696 T^{23} - \)\(11\!\cdots\!92\)\( T^{24} - \)\(74\!\cdots\!16\)\( T^{25} - \)\(27\!\cdots\!56\)\( T^{26} - \)\(94\!\cdots\!68\)\( T^{27} + \)\(62\!\cdots\!80\)\( T^{28} + \)\(47\!\cdots\!48\)\( T^{29} + \)\(19\!\cdots\!20\)\( T^{30} + \)\(49\!\cdots\!32\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 4 T + 30 T^{2} + 92 T^{3} - 334 T^{4} - 10116 T^{5} + 85854 T^{6} - 842916 T^{7} - 2808099 T^{8} + 21400784 T^{9} - 13842264 T^{10} - 1079831088 T^{11} + 13460410040 T^{12} + 2388153040 T^{13} - 195580560792 T^{14} + 2644046148048 T^{15} + 10500427183938 T^{16} - 192141210610008 T^{17} + 664554433081812 T^{18} - 1101475111191192 T^{19} - 30298126262993364 T^{20} - 45160479558838872 T^{21} + 1117116002010525972 T^{22} - 13242564376452361368 T^{23} + 29671697619711826818 T^{24} + \)\(30\!\cdots\!48\)\( T^{25} - \)\(92\!\cdots\!72\)\( T^{26} + \)\(46\!\cdots\!40\)\( T^{27} + \)\(10\!\cdots\!40\)\( T^{28} - \)\(35\!\cdots\!68\)\( T^{29} - \)\(18\!\cdots\!64\)\( T^{30} + \)\(11\!\cdots\!44\)\( T^{31} - \)\(63\!\cdots\!19\)\( T^{32} - \)\(77\!\cdots\!36\)\( T^{33} + \)\(32\!\cdots\!94\)\( T^{34} - \)\(15\!\cdots\!16\)\( T^{35} - \)\(21\!\cdots\!94\)\( T^{36} + \)\(24\!\cdots\!52\)\( T^{37} + \)\(32\!\cdots\!30\)\( T^{38} - \)\(17\!\cdots\!44\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))(\( 1 - 4 T + 30 T^{2} + 92 T^{3} - 334 T^{4} - 10116 T^{5} + 85854 T^{6} - 842916 T^{7} - 2808099 T^{8} + 21400784 T^{9} - 13842264 T^{10} - 1079831088 T^{11} + 13460410040 T^{12} + 2388153040 T^{13} - 195580560792 T^{14} + 2644046148048 T^{15} + 10500427183938 T^{16} - 192141210610008 T^{17} + 664554433081812 T^{18} - 1101475111191192 T^{19} - 30298126262993364 T^{20} - 45160479558838872 T^{21} + 1117116002010525972 T^{22} - 13242564376452361368 T^{23} + 29671697619711826818 T^{24} + \)\(30\!\cdots\!48\)\( T^{25} - \)\(92\!\cdots\!72\)\( T^{26} + \)\(46\!\cdots\!40\)\( T^{27} + \)\(10\!\cdots\!40\)\( T^{28} - \)\(35\!\cdots\!68\)\( T^{29} - \)\(18\!\cdots\!64\)\( T^{30} + \)\(11\!\cdots\!44\)\( T^{31} - \)\(63\!\cdots\!19\)\( T^{32} - \)\(77\!\cdots\!36\)\( T^{33} + \)\(32\!\cdots\!94\)\( T^{34} - \)\(15\!\cdots\!16\)\( T^{35} - \)\(21\!\cdots\!94\)\( T^{36} + \)\(24\!\cdots\!52\)\( T^{37} + \)\(32\!\cdots\!30\)\( T^{38} - \)\(17\!\cdots\!44\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 6 T + 78 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 186 T^{2} + 16391 T^{4} - 879788 T^{6} + 30306959 T^{8} - 635896986 T^{10} + 6321363049 T^{12} \))(\( 1 - 50 T^{2} + 1849 T^{4} \))(\( 1 - 50 T^{2} + 1849 T^{4} \))(\( ( 1 - 50 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 16 T + 132 T^{2} - 688 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 16 T + 132 T^{2} + 688 T^{3} + 1849 T^{4} )^{2} \))(\( 1 - 64 T^{2} + 2130 T^{4} - 118336 T^{6} + 3418801 T^{8} \))(\( 1 - 228 T^{2} + 25352 T^{4} - 1829068 T^{6} + 92968878 T^{8} - 3381946732 T^{10} + 86673442952 T^{12} - 1441270775172 T^{14} + 11688200277601 T^{16} \))(\( 1 + 8 T + 32 T^{2} + 200 T^{3} + 4904 T^{4} + 40696 T^{5} + 188640 T^{6} + 1480888 T^{7} + 11243730 T^{8} + 63678184 T^{9} + 348795360 T^{10} + 3235616872 T^{11} + 16765800104 T^{12} + 29401688600 T^{13} + 202283617568 T^{14} + 2174548888856 T^{15} + 11688200277601 T^{16} \))(\( 1 + 16 T + 128 T^{2} + 720 T^{3} + 2756 T^{4} + 21120 T^{5} + 244352 T^{6} + 1810176 T^{7} + 7254104 T^{8} + 17393920 T^{9} + 202697216 T^{10} + 2477751552 T^{11} + 22372983660 T^{12} + 124397766416 T^{13} + 585143289600 T^{14} + 4267259599952 T^{15} + 28438813484718 T^{16} + 183492162797936 T^{17} + 1081929942470400 T^{18} + 9890493214436912 T^{19} + 76488778909791660 T^{20} + 364250397800353536 T^{21} + 1281322691357571584 T^{22} + 4727991176106269440 T^{23} + 84787420386546524504 T^{24} + \)\(90\!\cdots\!68\)\( T^{25} + \)\(52\!\cdots\!48\)\( T^{26} + \)\(19\!\cdots\!40\)\( T^{27} + \)\(11\!\cdots\!56\)\( T^{28} + \)\(12\!\cdots\!60\)\( T^{29} + \)\(94\!\cdots\!72\)\( T^{30} + \)\(50\!\cdots\!12\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 16 T + 128 T^{2} - 1488 T^{3} + 20694 T^{4} - 176960 T^{5} + 1289600 T^{6} - 12374208 T^{7} + 114689745 T^{8} - 816890480 T^{9} + 5773220224 T^{10} - 47396668080 T^{11} + 376357329952 T^{12} - 2558318885360 T^{13} + 17028142721920 T^{14} - 127218542416432 T^{15} + 963177088145694 T^{16} - 6226032087351344 T^{17} + 38642451157210368 T^{18} - 278587214299949552 T^{19} + 2002378843515302292 T^{20} - 11979250214897830736 T^{21} + 71449892189681970432 T^{22} - \)\(49\!\cdots\!08\)\( T^{23} + \)\(32\!\cdots\!94\)\( T^{24} - \)\(18\!\cdots\!76\)\( T^{25} + \)\(10\!\cdots\!80\)\( T^{26} - \)\(69\!\cdots\!20\)\( T^{27} + \)\(43\!\cdots\!52\)\( T^{28} - \)\(23\!\cdots\!40\)\( T^{29} + \)\(12\!\cdots\!76\)\( T^{30} - \)\(75\!\cdots\!60\)\( T^{31} + \)\(45\!\cdots\!45\)\( T^{32} - \)\(21\!\cdots\!44\)\( T^{33} + \)\(95\!\cdots\!00\)\( T^{34} - \)\(56\!\cdots\!20\)\( T^{35} + \)\(28\!\cdots\!94\)\( T^{36} - \)\(87\!\cdots\!84\)\( T^{37} + \)\(32\!\cdots\!72\)\( T^{38} - \)\(17\!\cdots\!12\)\( T^{39} + \)\(46\!\cdots\!01\)\( T^{40} \))(\( 1 + 16 T + 128 T^{2} + 1488 T^{3} + 20694 T^{4} + 176960 T^{5} + 1289600 T^{6} + 12374208 T^{7} + 114689745 T^{8} + 816890480 T^{9} + 5773220224 T^{10} + 47396668080 T^{11} + 376357329952 T^{12} + 2558318885360 T^{13} + 17028142721920 T^{14} + 127218542416432 T^{15} + 963177088145694 T^{16} + 6226032087351344 T^{17} + 38642451157210368 T^{18} + 278587214299949552 T^{19} + 2002378843515302292 T^{20} + 11979250214897830736 T^{21} + 71449892189681970432 T^{22} + \)\(49\!\cdots\!08\)\( T^{23} + \)\(32\!\cdots\!94\)\( T^{24} + \)\(18\!\cdots\!76\)\( T^{25} + \)\(10\!\cdots\!80\)\( T^{26} + \)\(69\!\cdots\!20\)\( T^{27} + \)\(43\!\cdots\!52\)\( T^{28} + \)\(23\!\cdots\!40\)\( T^{29} + \)\(12\!\cdots\!76\)\( T^{30} + \)\(75\!\cdots\!60\)\( T^{31} + \)\(45\!\cdots\!45\)\( T^{32} + \)\(21\!\cdots\!44\)\( T^{33} + \)\(95\!\cdots\!00\)\( T^{34} + \)\(56\!\cdots\!20\)\( T^{35} + \)\(28\!\cdots\!94\)\( T^{36} + \)\(87\!\cdots\!84\)\( T^{37} + \)\(32\!\cdots\!72\)\( T^{38} + \)\(17\!\cdots\!12\)\( T^{39} + \)\(46\!\cdots\!01\)\( T^{40} \))
$47$ (\( 1 - 12 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 + 13 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 - 9 T + 110 T^{2} - 423 T^{3} + 2209 T^{4} \))(\( ( 1 - 7 T + 47 T^{2} )^{2} \))(\( ( 1 - 9 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( 1 - 85 T^{2} + 2209 T^{4} \))(\( 1 - 25 T^{2} + 4995 T^{4} - 125830 T^{6} + 11033955 T^{8} - 121992025 T^{10} + 10779215329 T^{12} \))(\( 1 - 45 T^{2} + 2209 T^{4} \))(\( 1 - 45 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 166 T^{2} + 11235 T^{4} - 366694 T^{6} + 4879681 T^{8} \))(\( 1 - 166 T^{2} + 11235 T^{4} - 366694 T^{6} + 4879681 T^{8} \))(\( ( 1 + 2 T + 77 T^{2} + 94 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 - 10 T + 179 T^{2} - 1178 T^{3} + 12016 T^{4} - 55366 T^{5} + 395411 T^{6} - 1038230 T^{7} + 4879681 T^{8} )^{2} \))(\( 1 - 292 T^{2} + 40470 T^{4} - 3443528 T^{6} + 195768731 T^{8} - 7606753352 T^{10} + 197480690070 T^{12} - 3147530876068 T^{14} + 23811286661761 T^{16} \))(\( 1 - 188 T^{2} + 22642 T^{4} - 1768080 T^{6} + 95073161 T^{8} - 2786921184 T^{10} - 46621754966 T^{12} + 10885491892716 T^{14} - 693159078792268 T^{16} + 24046051591009644 T^{18} - 227499291894245846 T^{20} - 30040823547287629536 T^{22} + \)\(22\!\cdots\!21\)\( T^{24} - \)\(92\!\cdots\!20\)\( T^{26} + \)\(26\!\cdots\!22\)\( T^{28} - \)\(48\!\cdots\!72\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 20 T + 388 T^{2} - 4976 T^{3} + 62092 T^{4} - 635100 T^{5} + 6214238 T^{6} - 53431788 T^{7} + 439450571 T^{8} - 3289992044 T^{9} + 23554230924 T^{10} - 154629626068 T^{11} + 970746311339 T^{12} - 5547448525524 T^{13} + 30323499098078 T^{14} - 145657013945700 T^{15} + 669303038208268 T^{16} - 2520956647423888 T^{17} + 9238779224763268 T^{18} - 22382609462055340 T^{19} + 52599132235830049 T^{20} )^{2} \))(\( ( 1 + 20 T + 388 T^{2} + 4976 T^{3} + 62092 T^{4} + 635100 T^{5} + 6214238 T^{6} + 53431788 T^{7} + 439450571 T^{8} + 3289992044 T^{9} + 23554230924 T^{10} + 154629626068 T^{11} + 970746311339 T^{12} + 5547448525524 T^{13} + 30323499098078 T^{14} + 145657013945700 T^{15} + 669303038208268 T^{16} + 2520956647423888 T^{17} + 9238779224763268 T^{18} + 22382609462055340 T^{19} + 52599132235830049 T^{20} )^{2} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 3 T + 104 T^{2} - 159 T^{3} + 2809 T^{4} \))(\( ( 1 + T + 53 T^{2} )^{2} \))(\( ( 1 + 11 T + 53 T^{2} )^{2} \))(\( ( 1 - 10 T + 53 T^{2} )^{2} \))(\( 1 - 25 T^{2} + 2809 T^{4} \))(\( 1 - 53 T^{2} + 7995 T^{4} - 263774 T^{6} + 22457955 T^{8} - 418195493 T^{10} + 22164361129 T^{12} \))(\( 1 - 105 T^{2} + 2809 T^{4} \))(\( 1 - 105 T^{2} + 2809 T^{4} \))(\( ( 1 - 70 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 10 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 10 T + 53 T^{2} )^{2} \))(\( ( 1 + 3 T + 53 T^{2} )^{4} \))(\( ( 1 - 3 T + 53 T^{2} )^{4} \))(\( 1 - 18 T^{2} - 1501 T^{4} - 50562 T^{6} + 7890481 T^{8} \))(\( 1 - 366 T^{2} + 60833 T^{4} - 6024462 T^{6} + 390030964 T^{8} - 16922713758 T^{10} + 480001630673 T^{12} - 8112156173214 T^{14} + 62259690411361 T^{16} \))(\( 1 + 8 T + 32 T^{2} + 224 T^{3} + 5774 T^{4} + 49528 T^{5} + 236544 T^{6} + 2064840 T^{7} + 16695955 T^{8} + 109436520 T^{9} + 664452096 T^{10} + 7373580056 T^{11} + 45559637294 T^{12} + 93675790432 T^{13} + 709259556128 T^{14} + 9397689118696 T^{15} + 62259690411361 T^{16} \))(\( 1 + 40 T + 800 T^{2} + 11344 T^{3} + 124562 T^{4} + 1010264 T^{5} + 5104128 T^{6} - 5461208 T^{7} - 516663727 T^{8} - 7410897016 T^{9} - 70520559680 T^{10} - 498940491896 T^{11} - 2294252808206 T^{12} + 424322361200 T^{13} + 141643884807200 T^{14} + 1827245915743464 T^{15} + 15562066579376068 T^{16} + 96844033534403592 T^{17} + 397877672423424800 T^{18} + 63171840168372400 T^{19} - 18102758192346087086 T^{20} - \)\(20\!\cdots\!28\)\( T^{21} - \)\(15\!\cdots\!20\)\( T^{22} - \)\(87\!\cdots\!92\)\( T^{23} - \)\(32\!\cdots\!47\)\( T^{24} - \)\(18\!\cdots\!64\)\( T^{25} + \)\(89\!\cdots\!72\)\( T^{26} + \)\(93\!\cdots\!08\)\( T^{27} + \)\(61\!\cdots\!42\)\( T^{28} + \)\(29\!\cdots\!12\)\( T^{29} + \)\(11\!\cdots\!00\)\( T^{30} + \)\(29\!\cdots\!80\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 - 44 T + 968 T^{2} - 14204 T^{3} + 153360 T^{4} - 1253852 T^{5} + 7593816 T^{6} - 29525844 T^{7} + 21121854 T^{8} + 436104500 T^{9} + 1235332696 T^{10} - 80090622156 T^{11} + 970719706210 T^{12} - 6135983063340 T^{13} + 7164913588248 T^{14} + 319649478179492 T^{15} - 4261370408835583 T^{16} + 31329479689545576 T^{17} - 136710820885404048 T^{18} + 162474207458147632 T^{19} + 1532805880285790428 T^{20} + 8611132995281824496 T^{21} - \)\(38\!\cdots\!32\)\( T^{22} + \)\(46\!\cdots\!52\)\( T^{23} - \)\(33\!\cdots\!23\)\( T^{24} + \)\(13\!\cdots\!56\)\( T^{25} + \)\(15\!\cdots\!92\)\( T^{26} - \)\(72\!\cdots\!80\)\( T^{27} + \)\(60\!\cdots\!10\)\( T^{28} - \)\(26\!\cdots\!48\)\( T^{29} + \)\(21\!\cdots\!04\)\( T^{30} + \)\(40\!\cdots\!00\)\( T^{31} + \)\(10\!\cdots\!14\)\( T^{32} - \)\(76\!\cdots\!12\)\( T^{33} + \)\(10\!\cdots\!04\)\( T^{34} - \)\(91\!\cdots\!64\)\( T^{35} + \)\(59\!\cdots\!60\)\( T^{36} - \)\(29\!\cdots\!52\)\( T^{37} + \)\(10\!\cdots\!52\)\( T^{38} - \)\(25\!\cdots\!48\)\( T^{39} + \)\(30\!\cdots\!01\)\( T^{40} \))(\( 1 + 44 T + 968 T^{2} + 14204 T^{3} + 153360 T^{4} + 1253852 T^{5} + 7593816 T^{6} + 29525844 T^{7} + 21121854 T^{8} - 436104500 T^{9} + 1235332696 T^{10} + 80090622156 T^{11} + 970719706210 T^{12} + 6135983063340 T^{13} + 7164913588248 T^{14} - 319649478179492 T^{15} - 4261370408835583 T^{16} - 31329479689545576 T^{17} - 136710820885404048 T^{18} - 162474207458147632 T^{19} + 1532805880285790428 T^{20} - 8611132995281824496 T^{21} - \)\(38\!\cdots\!32\)\( T^{22} - \)\(46\!\cdots\!52\)\( T^{23} - \)\(33\!\cdots\!23\)\( T^{24} - \)\(13\!\cdots\!56\)\( T^{25} + \)\(15\!\cdots\!92\)\( T^{26} + \)\(72\!\cdots\!80\)\( T^{27} + \)\(60\!\cdots\!10\)\( T^{28} + \)\(26\!\cdots\!48\)\( T^{29} + \)\(21\!\cdots\!04\)\( T^{30} - \)\(40\!\cdots\!00\)\( T^{31} + \)\(10\!\cdots\!14\)\( T^{32} + \)\(76\!\cdots\!12\)\( T^{33} + \)\(10\!\cdots\!04\)\( T^{34} + \)\(91\!\cdots\!64\)\( T^{35} + \)\(59\!\cdots\!60\)\( T^{36} + \)\(29\!\cdots\!52\)\( T^{37} + \)\(10\!\cdots\!52\)\( T^{38} + \)\(25\!\cdots\!48\)\( T^{39} + \)\(30\!\cdots\!01\)\( T^{40} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 - 15 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + 13 T + 122 T^{2} + 767 T^{3} + 3481 T^{4} \))(\( ( 1 + 9 T + 59 T^{2} )^{2} \))(\( ( 1 + 5 T + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 5 T + 59 T^{2} )^{2} \))(\( ( 1 + 9 T + 161 T^{2} + 902 T^{3} + 9499 T^{4} + 31329 T^{5} + 205379 T^{6} )^{2} \))(\( ( 1 + 5 T + 59 T^{2} )^{2} \))(\( ( 1 + 5 T + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 22 T^{2} + 3555 T^{4} - 76582 T^{6} + 12117361 T^{8} \))(\( 1 - 22 T^{2} + 3555 T^{4} - 76582 T^{6} + 12117361 T^{8} \))(\( 1 - 38 T^{2} + 6931 T^{4} - 132278 T^{6} + 12117361 T^{8} \))(\( 1 - 250 T^{2} + 33137 T^{4} - 3007930 T^{6} + 202771380 T^{8} - 10470604330 T^{10} + 401532991457 T^{12} - 10545133410250 T^{14} + 146830437604321 T^{16} \))(\( 1 + 40 T + 800 T^{2} + 11768 T^{3} + 145074 T^{4} + 1520128 T^{5} + 13988832 T^{6} + 118894256 T^{7} + 946277099 T^{8} + 7014761104 T^{9} + 48695124192 T^{10} + 312202368512 T^{11} + 1757914029714 T^{12} + 8413229150632 T^{13} + 33744426912800 T^{14} + 99546059392760 T^{15} + 146830437604321 T^{16} \))(\( 1 - 16 T + 128 T^{2} - 896 T^{3} + 15118 T^{4} - 208456 T^{5} + 1801600 T^{6} - 14575512 T^{7} + 140518089 T^{8} - 1408025728 T^{9} + 12092118176 T^{10} - 107459276400 T^{11} + 935469995214 T^{12} - 7129230334024 T^{13} + 54379192071264 T^{14} - 476400349233432 T^{15} + 4096460971629972 T^{16} - 28107620604772488 T^{17} + 189293967600069984 T^{18} - 1464194196771515096 T^{19} + 11335427636676310254 T^{20} - 76825247851317243600 T^{21} + \)\(51\!\cdots\!16\)\( T^{22} - \)\(35\!\cdots\!32\)\( T^{23} + \)\(20\!\cdots\!69\)\( T^{24} - \)\(12\!\cdots\!68\)\( T^{25} + \)\(92\!\cdots\!00\)\( T^{26} - \)\(62\!\cdots\!04\)\( T^{27} + \)\(26\!\cdots\!58\)\( T^{28} - \)\(94\!\cdots\!84\)\( T^{29} + \)\(79\!\cdots\!08\)\( T^{30} - \)\(58\!\cdots\!84\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 - 16 T + 128 T^{2} - 640 T^{3} + 6032 T^{4} - 73144 T^{5} + 603008 T^{6} - 4225576 T^{7} + 33076134 T^{8} - 244311232 T^{9} + 1417281312 T^{10} - 16887395168 T^{11} + 211053947230 T^{12} - 1522774288880 T^{13} + 6460849018400 T^{14} - 56720710039568 T^{15} + 808791885028057 T^{16} - 6447237579834824 T^{17} + 35399211288359360 T^{18} - 220142009338344872 T^{19} + 1853897520463942116 T^{20} - 12988378550962347448 T^{21} + \)\(12\!\cdots\!60\)\( T^{22} - \)\(13\!\cdots\!96\)\( T^{23} + \)\(98\!\cdots\!77\)\( T^{24} - \)\(40\!\cdots\!32\)\( T^{25} + \)\(27\!\cdots\!00\)\( T^{26} - \)\(37\!\cdots\!20\)\( T^{27} + \)\(30\!\cdots\!30\)\( T^{28} - \)\(14\!\cdots\!52\)\( T^{29} + \)\(72\!\cdots\!12\)\( T^{30} - \)\(73\!\cdots\!88\)\( T^{31} + \)\(58\!\cdots\!54\)\( T^{32} - \)\(44\!\cdots\!04\)\( T^{33} + \)\(37\!\cdots\!88\)\( T^{34} - \)\(26\!\cdots\!56\)\( T^{35} + \)\(13\!\cdots\!12\)\( T^{36} - \)\(81\!\cdots\!60\)\( T^{37} + \)\(96\!\cdots\!88\)\( T^{38} - \)\(70\!\cdots\!24\)\( T^{39} + \)\(26\!\cdots\!01\)\( T^{40} \))(\( 1 - 16 T + 128 T^{2} - 640 T^{3} + 6032 T^{4} - 73144 T^{5} + 603008 T^{6} - 4225576 T^{7} + 33076134 T^{8} - 244311232 T^{9} + 1417281312 T^{10} - 16887395168 T^{11} + 211053947230 T^{12} - 1522774288880 T^{13} + 6460849018400 T^{14} - 56720710039568 T^{15} + 808791885028057 T^{16} - 6447237579834824 T^{17} + 35399211288359360 T^{18} - 220142009338344872 T^{19} + 1853897520463942116 T^{20} - 12988378550962347448 T^{21} + \)\(12\!\cdots\!60\)\( T^{22} - \)\(13\!\cdots\!96\)\( T^{23} + \)\(98\!\cdots\!77\)\( T^{24} - \)\(40\!\cdots\!32\)\( T^{25} + \)\(27\!\cdots\!00\)\( T^{26} - \)\(37\!\cdots\!20\)\( T^{27} + \)\(30\!\cdots\!30\)\( T^{28} - \)\(14\!\cdots\!52\)\( T^{29} + \)\(72\!\cdots\!12\)\( T^{30} - \)\(73\!\cdots\!88\)\( T^{31} + \)\(58\!\cdots\!54\)\( T^{32} - \)\(44\!\cdots\!04\)\( T^{33} + \)\(37\!\cdots\!88\)\( T^{34} - \)\(26\!\cdots\!56\)\( T^{35} + \)\(13\!\cdots\!12\)\( T^{36} - \)\(81\!\cdots\!60\)\( T^{37} + \)\(96\!\cdots\!88\)\( T^{38} - \)\(70\!\cdots\!24\)\( T^{39} + \)\(26\!\cdots\!01\)\( T^{40} \))
$61$ (\( 1 - 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 7 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 - 11 T + 61 T^{2} \))(\( 1 - 19 T + 208 T^{2} - 1159 T^{3} + 3721 T^{4} \))(\( 1 - 113 T^{2} + 3721 T^{4} \))(\( 1 - 121 T^{2} + 3721 T^{4} \))(\( ( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( ( 1 + 3 T + 61 T^{2} )^{2} \))(\( ( 1 + 9 T + 153 T^{2} + 1064 T^{3} + 9333 T^{4} + 33489 T^{5} + 226981 T^{6} )^{2} \))(\( 1 - 97 T^{2} + 3721 T^{4} \))(\( 1 - 97 T^{2} + 3721 T^{4} \))(\( ( 1 - 104 T^{2} + 3721 T^{4} )^{2} \))(\( 1 + 18 T + 162 T^{2} + 1098 T^{3} + 3721 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 + 18 T + 162 T^{2} + 1098 T^{3} + 3721 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 - 16 T + 128 T^{2} - 1344 T^{3} + 13583 T^{4} - 81984 T^{5} + 476288 T^{6} - 3631696 T^{7} + 13845841 T^{8} \))(\( 1 - 16 T + 128 T^{2} - 1344 T^{3} + 13583 T^{4} - 81984 T^{5} + 476288 T^{6} - 3631696 T^{7} + 13845841 T^{8} \))(\( 1 - 8 T + 32 T^{2} + 416 T^{3} - 7361 T^{4} + 25376 T^{5} + 119072 T^{6} - 1815848 T^{7} + 13845841 T^{8} \))(\( 1 + 16 T + 128 T^{2} + 616 T^{3} + 2273 T^{4} + 43536 T^{5} + 595360 T^{6} + 5565640 T^{7} + 48746896 T^{8} + 339504040 T^{9} + 2215334560 T^{10} + 9881844816 T^{11} + 31471596593 T^{12} + 520271321416 T^{13} + 6594607918208 T^{14} + 50283885376336 T^{15} + 191707312997281 T^{16} \))(\( 1 + 24 T + 184 T^{2} - 1312 T^{3} - 37600 T^{4} - 293048 T^{5} - 205024 T^{6} + 17255496 T^{7} + 194698687 T^{8} + 1052585256 T^{9} - 762894304 T^{10} - 66516328088 T^{11} - 520603621600 T^{12} - 1108110346912 T^{13} + 9479748882424 T^{14} + 75425828064504 T^{15} + 191707312997281 T^{16} \))(\( 1 + 24 T + 552 T^{2} + 8160 T^{3} + 113184 T^{4} + 1253720 T^{5} + 13166416 T^{6} + 120528168 T^{7} + 1064498753 T^{8} + 8752960904 T^{9} + 71172146896 T^{10} + 573728005752 T^{11} + 4644413938400 T^{12} + 38440204280720 T^{13} + 313043743583352 T^{14} + 2568662577433176 T^{15} + 20124775252425440 T^{16} + 156688417223423736 T^{17} + 1164835769873652792 T^{18} + 8725196007842106320 T^{19} + 64305816929270194400 T^{20} + \)\(48\!\cdots\!52\)\( T^{21} + \)\(36\!\cdots\!56\)\( T^{22} + \)\(27\!\cdots\!84\)\( T^{23} + \)\(20\!\cdots\!93\)\( T^{24} + \)\(14\!\cdots\!88\)\( T^{25} + \)\(93\!\cdots\!16\)\( T^{26} + \)\(54\!\cdots\!20\)\( T^{27} + \)\(30\!\cdots\!64\)\( T^{28} + \)\(13\!\cdots\!60\)\( T^{29} + \)\(54\!\cdots\!32\)\( T^{30} + \)\(14\!\cdots\!24\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 - 8 T + 10 T^{2} + 320 T^{3} - 2126 T^{4} - 27296 T^{5} - 72510 T^{6} + 8840 T^{7} - 3520990 T^{8} - 69652728 T^{9} + 659172698 T^{10} + 1929507872 T^{11} + 77537561570 T^{12} + 128446570208 T^{13} + 1861119756730 T^{14} + 37614663351992 T^{15} - 71694040127423 T^{16} - 1493114370031936 T^{17} + 3398743476006728 T^{18} - 110814064642641248 T^{19} - 1163583925604399136 T^{20} - 6759657943201116128 T^{21} + 12646724474221034888 T^{22} - \)\(33\!\cdots\!16\)\( T^{23} - \)\(99\!\cdots\!43\)\( T^{24} + \)\(31\!\cdots\!92\)\( T^{25} + \)\(95\!\cdots\!30\)\( T^{26} + \)\(40\!\cdots\!68\)\( T^{27} + \)\(14\!\cdots\!70\)\( T^{28} + \)\(22\!\cdots\!52\)\( T^{29} + \)\(47\!\cdots\!98\)\( T^{30} - \)\(30\!\cdots\!08\)\( T^{31} - \)\(93\!\cdots\!90\)\( T^{32} + \)\(14\!\cdots\!40\)\( T^{33} - \)\(71\!\cdots\!10\)\( T^{34} - \)\(16\!\cdots\!96\)\( T^{35} - \)\(78\!\cdots\!86\)\( T^{36} + \)\(71\!\cdots\!20\)\( T^{37} + \)\(13\!\cdots\!10\)\( T^{38} - \)\(66\!\cdots\!28\)\( T^{39} + \)\(50\!\cdots\!01\)\( T^{40} \))(\( 1 - 8 T + 10 T^{2} + 320 T^{3} - 2126 T^{4} - 27296 T^{5} - 72510 T^{6} + 8840 T^{7} - 3520990 T^{8} - 69652728 T^{9} + 659172698 T^{10} + 1929507872 T^{11} + 77537561570 T^{12} + 128446570208 T^{13} + 1861119756730 T^{14} + 37614663351992 T^{15} - 71694040127423 T^{16} - 1493114370031936 T^{17} + 3398743476006728 T^{18} - 110814064642641248 T^{19} - 1163583925604399136 T^{20} - 6759657943201116128 T^{21} + 12646724474221034888 T^{22} - \)\(33\!\cdots\!16\)\( T^{23} - \)\(99\!\cdots\!43\)\( T^{24} + \)\(31\!\cdots\!92\)\( T^{25} + \)\(95\!\cdots\!30\)\( T^{26} + \)\(40\!\cdots\!68\)\( T^{27} + \)\(14\!\cdots\!70\)\( T^{28} + \)\(22\!\cdots\!52\)\( T^{29} + \)\(47\!\cdots\!98\)\( T^{30} - \)\(30\!\cdots\!08\)\( T^{31} - \)\(93\!\cdots\!90\)\( T^{32} + \)\(14\!\cdots\!40\)\( T^{33} - \)\(71\!\cdots\!10\)\( T^{34} - \)\(16\!\cdots\!96\)\( T^{35} - \)\(78\!\cdots\!86\)\( T^{36} + \)\(71\!\cdots\!20\)\( T^{37} + \)\(13\!\cdots\!10\)\( T^{38} - \)\(66\!\cdots\!28\)\( T^{39} + \)\(50\!\cdots\!01\)\( T^{40} \))
$67$ (\( 1 - 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 10 T + 142 T^{2} + 670 T^{3} + 4489 T^{4} \))(\( ( 1 - 10 T + 67 T^{2} )^{2} \))(\( ( 1 + 10 T + 67 T^{2} )^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 270 T^{2} + 34775 T^{4} - 2833220 T^{6} + 156104975 T^{8} - 5440802670 T^{10} + 90458382169 T^{12} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( ( 1 + 10 T^{2} + 4489 T^{4} )^{2} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 52 T^{2} - 714 T^{4} - 233428 T^{6} + 20151121 T^{8} \))(\( 1 - 52 T^{2} - 714 T^{4} - 233428 T^{6} + 20151121 T^{8} \))(\( ( 1 - 12 T + 162 T^{2} - 804 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 8 T + 156 T^{2} + 1288 T^{3} + 12678 T^{4} + 86296 T^{5} + 700284 T^{6} + 2406104 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 + 212 T^{2} - 224 T^{3} + 19182 T^{4} - 15008 T^{5} + 951668 T^{6} + 20151121 T^{8} )^{2} \))(\( ( 1 - 8 T + 276 T^{2} - 2456 T^{3} + 40224 T^{4} - 383416 T^{5} + 4011676 T^{6} - 37708968 T^{7} + 303284510 T^{8} - 2526500856 T^{9} + 18008413564 T^{10} - 115317346408 T^{11} + 810558691104 T^{12} - 3315907262792 T^{13} + 24966513478644 T^{14} - 48485692842584 T^{15} + 406067677556641 T^{16} )^{2} \))(\( 1 - 532 T^{2} + 148646 T^{4} - 29200180 T^{6} + 4500891213 T^{8} - 575578725168 T^{10} + 63179028972648 T^{12} - 6089051557526448 T^{14} + 523435323978922754 T^{16} - 40558419543281652984 T^{18} + \)\(28\!\cdots\!68\)\( T^{20} - \)\(18\!\cdots\!76\)\( T^{22} + \)\(10\!\cdots\!34\)\( T^{24} - \)\(55\!\cdots\!12\)\( T^{26} + \)\(25\!\cdots\!68\)\( T^{28} - \)\(10\!\cdots\!32\)\( T^{30} + \)\(36\!\cdots\!93\)\( T^{32} - \)\(10\!\cdots\!20\)\( T^{34} + \)\(24\!\cdots\!26\)\( T^{36} - \)\(39\!\cdots\!88\)\( T^{38} + \)\(33\!\cdots\!01\)\( T^{40} \))(\( 1 - 532 T^{2} + 148646 T^{4} - 29200180 T^{6} + 4500891213 T^{8} - 575578725168 T^{10} + 63179028972648 T^{12} - 6089051557526448 T^{14} + 523435323978922754 T^{16} - 40558419543281652984 T^{18} + \)\(28\!\cdots\!68\)\( T^{20} - \)\(18\!\cdots\!76\)\( T^{22} + \)\(10\!\cdots\!34\)\( T^{24} - \)\(55\!\cdots\!12\)\( T^{26} + \)\(25\!\cdots\!68\)\( T^{28} - \)\(10\!\cdots\!32\)\( T^{30} + \)\(36\!\cdots\!93\)\( T^{32} - \)\(10\!\cdots\!20\)\( T^{34} + \)\(24\!\cdots\!26\)\( T^{36} - \)\(39\!\cdots\!88\)\( T^{38} + \)\(33\!\cdots\!01\)\( T^{40} \))
$71$ (\( 1 + 6 T + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 + 21 T + 214 T^{2} + 1491 T^{3} + 5041 T^{4} \))(\( 1 - 61 T^{2} + 5041 T^{4} \))(\( 1 - 141 T^{2} + 5041 T^{4} \))(\( 1 - 42 T^{2} + 5041 T^{4} \))(\( ( 1 + 15 T + 71 T^{2} )^{2} \))(\( ( 1 + T + 95 T^{2} + 476 T^{3} + 6745 T^{4} + 5041 T^{5} + 357911 T^{6} )^{2} \))(\( 1 - 117 T^{2} + 5041 T^{4} \))(\( 1 - 117 T^{2} + 5041 T^{4} \))(\( ( 1 - 124 T^{2} + 5041 T^{4} )^{2} \))(\( 1 - 2 T + 2 T^{2} - 142 T^{3} + 5041 T^{4} \))(\( 1 - 10 T + 50 T^{2} - 710 T^{3} + 5041 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 142 T^{3} + 5041 T^{4} \))(\( 1 - 10 T + 50 T^{2} - 710 T^{3} + 5041 T^{4} \))(\( 1 - 12 T + 72 T^{2} - 1056 T^{3} + 15199 T^{4} - 74976 T^{5} + 362952 T^{6} - 4294932 T^{7} + 25411681 T^{8} \))(\( 1 - 12 T + 72 T^{2} - 1056 T^{3} + 15199 T^{4} - 74976 T^{5} + 362952 T^{6} - 4294932 T^{7} + 25411681 T^{8} \))(\( 1 + 36 T + 648 T^{2} + 8352 T^{3} + 81727 T^{4} + 592992 T^{5} + 3266568 T^{6} + 12884796 T^{7} + 25411681 T^{8} \))(\( 1 - 4 T + 8 T^{2} + 488 T^{3} - 2335 T^{4} - 45368 T^{5} + 319224 T^{6} - 1238244 T^{7} - 10911776 T^{8} - 87915324 T^{9} + 1609208184 T^{10} - 16237706248 T^{11} - 59336275135 T^{12} + 880463923288 T^{13} + 1024802271368 T^{14} - 36380480633564 T^{15} + 645753531245761 T^{16} \))(\( 1 - 24 T + 372 T^{2} - 5176 T^{3} + 62088 T^{4} - 669672 T^{5} + 6915064 T^{6} - 65111408 T^{7} + 558097111 T^{8} - 4622909968 T^{9} + 34858837624 T^{10} - 239682975192 T^{11} + 1577760449928 T^{12} - 9338691120776 T^{13} + 47653305618612 T^{14} - 218282883801384 T^{15} + 645753531245761 T^{16} \))(\( 1 - 8 T + 324 T^{2} - 1992 T^{3} + 48712 T^{4} - 250440 T^{5} + 4639528 T^{6} - 25517088 T^{7} + 393483513 T^{8} - 2953677392 T^{9} + 37946061664 T^{10} - 310693631608 T^{11} + 3558244901336 T^{12} - 23908134462744 T^{13} + 277605488611268 T^{14} - 1477081706701080 T^{15} + 19716719812522288 T^{16} - 104872801175776680 T^{17} + 1399409268089401988 T^{18} - 8556984313695167784 T^{19} + 90420984352626905816 T^{20} - \)\(56\!\cdots\!08\)\( T^{21} + \)\(48\!\cdots\!44\)\( T^{22} - \)\(26\!\cdots\!72\)\( T^{23} + \)\(25\!\cdots\!93\)\( T^{24} - \)\(11\!\cdots\!28\)\( T^{25} + \)\(15\!\cdots\!28\)\( T^{26} - \)\(57\!\cdots\!40\)\( T^{27} + \)\(79\!\cdots\!92\)\( T^{28} - \)\(23\!\cdots\!12\)\( T^{29} + \)\(26\!\cdots\!44\)\( T^{30} - \)\(46\!\cdots\!08\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 - 8 T + 4 T^{2} + 1064 T^{3} - 7736 T^{4} + 33056 T^{5} + 411864 T^{6} - 3498384 T^{7} + 43320906 T^{8} - 175160784 T^{9} + 1711157444 T^{10} + 23184409480 T^{11} - 282606722400 T^{12} + 2190349172904 T^{13} + 5955655055116 T^{14} - 92105865793280 T^{15} + 1484388456856825 T^{16} - 5521262001586648 T^{17} + 13570667323190324 T^{18} + 605072991295826840 T^{19} - 4474880001515114064 T^{20} + 42960182382003705640 T^{21} + 68409733976202423284 T^{22} - \)\(19\!\cdots\!28\)\( T^{23} + \)\(37\!\cdots\!25\)\( T^{24} - \)\(16\!\cdots\!80\)\( T^{25} + \)\(76\!\cdots\!36\)\( T^{26} + \)\(19\!\cdots\!64\)\( T^{27} - \)\(18\!\cdots\!00\)\( T^{28} + \)\(10\!\cdots\!80\)\( T^{29} + \)\(55\!\cdots\!44\)\( T^{30} - \)\(40\!\cdots\!64\)\( T^{31} + \)\(71\!\cdots\!46\)\( T^{32} - \)\(40\!\cdots\!24\)\( T^{33} + \)\(34\!\cdots\!84\)\( T^{34} + \)\(19\!\cdots\!56\)\( T^{35} - \)\(32\!\cdots\!56\)\( T^{36} + \)\(31\!\cdots\!24\)\( T^{37} + \)\(84\!\cdots\!44\)\( T^{38} - \)\(11\!\cdots\!48\)\( T^{39} + \)\(10\!\cdots\!01\)\( T^{40} \))(\( 1 - 8 T + 4 T^{2} + 1064 T^{3} - 7736 T^{4} + 33056 T^{5} + 411864 T^{6} - 3498384 T^{7} + 43320906 T^{8} - 175160784 T^{9} + 1711157444 T^{10} + 23184409480 T^{11} - 282606722400 T^{12} + 2190349172904 T^{13} + 5955655055116 T^{14} - 92105865793280 T^{15} + 1484388456856825 T^{16} - 5521262001586648 T^{17} + 13570667323190324 T^{18} + 605072991295826840 T^{19} - 4474880001515114064 T^{20} + 42960182382003705640 T^{21} + 68409733976202423284 T^{22} - \)\(19\!\cdots\!28\)\( T^{23} + \)\(37\!\cdots\!25\)\( T^{24} - \)\(16\!\cdots\!80\)\( T^{25} + \)\(76\!\cdots\!36\)\( T^{26} + \)\(19\!\cdots\!64\)\( T^{27} - \)\(18\!\cdots\!00\)\( T^{28} + \)\(10\!\cdots\!80\)\( T^{29} + \)\(55\!\cdots\!44\)\( T^{30} - \)\(40\!\cdots\!64\)\( T^{31} + \)\(71\!\cdots\!46\)\( T^{32} - \)\(40\!\cdots\!24\)\( T^{33} + \)\(34\!\cdots\!84\)\( T^{34} + \)\(19\!\cdots\!56\)\( T^{35} - \)\(32\!\cdots\!56\)\( T^{36} + \)\(31\!\cdots\!24\)\( T^{37} + \)\(84\!\cdots\!44\)\( T^{38} - \)\(11\!\cdots\!48\)\( T^{39} + \)\(10\!\cdots\!01\)\( T^{40} \))
$73$ (\( 1 - 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 + 3 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 - 7 T + 52 T^{2} - 511 T^{3} + 5329 T^{4} \))(\( 1 - 97 T^{2} + 5329 T^{4} \))(\( 1 - 65 T^{2} + 5329 T^{4} \))(\( 1 - 2 T^{2} + 5329 T^{4} \))(\( 1 - 25 T^{2} + 5329 T^{4} \))(\( 1 - 421 T^{2} + 75043 T^{4} - 7247278 T^{6} + 399904147 T^{8} - 11955659461 T^{10} + 151334226289 T^{12} \))(\( ( 1 + 11 T + 73 T^{2} )^{2} \))(\( ( 1 - 11 T + 73 T^{2} )^{2} \))(\( ( 1 + 74 T^{2} + 5329 T^{4} )^{2} \))(\( 1 - 2 T + 2 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 8 T + 32 T^{2} - 5329 T^{4} + 170528 T^{6} + 3112136 T^{7} + 28398241 T^{8} \))(\( 1 - 8 T + 32 T^{2} - 5329 T^{4} + 170528 T^{6} - 3112136 T^{7} + 28398241 T^{8} \))(\( 1 - 8 T + 32 T^{2} - 448 T^{3} + 5983 T^{4} - 32704 T^{5} + 170528 T^{6} - 3112136 T^{7} + 28398241 T^{8} \))(\( 1 - 28 T + 392 T^{2} - 4460 T^{3} + 37581 T^{4} - 178712 T^{5} + 217984 T^{6} + 8414576 T^{7} - 122737516 T^{8} + 614264048 T^{9} + 1161636736 T^{10} - 69522006104 T^{11} + 1067234295021 T^{12} - 9245899304780 T^{13} + 59323016705288 T^{14} - 309327158534716 T^{15} + 806460091894081 T^{16} \))(\( 1 + 16 T + 144 T^{2} + 1920 T^{3} + 20608 T^{4} + 212848 T^{5} + 2145152 T^{6} + 18530416 T^{7} + 161770079 T^{8} + 1352720368 T^{9} + 11431515008 T^{10} + 82801490416 T^{11} + 585230950528 T^{12} + 3980297458560 T^{13} + 21792128585616 T^{14} + 176758376305552 T^{15} + 806460091894081 T^{16} \))(\( 1 - 16 T + 276 T^{2} - 2640 T^{3} + 26056 T^{4} - 186192 T^{5} + 1574636 T^{6} - 10818544 T^{7} + 75908205 T^{8} - 182870688 T^{9} + 855139432 T^{10} - 3726715264 T^{11} + 432868265920 T^{12} - 6285826956000 T^{13} + 78502153457000 T^{14} - 718659174458976 T^{15} + 6327370177850484 T^{16} - 52462119735505248 T^{17} + 418337975772353000 T^{18} - 2445293544942252000 T^{19} + 12292697336848246720 T^{20} - 7725747548997895552 T^{21} + \)\(12\!\cdots\!48\)\( T^{22} - \)\(20\!\cdots\!36\)\( T^{23} + \)\(61\!\cdots\!05\)\( T^{24} - \)\(63\!\cdots\!72\)\( T^{25} + \)\(67\!\cdots\!64\)\( T^{26} - \)\(58\!\cdots\!84\)\( T^{27} + \)\(59\!\cdots\!76\)\( T^{28} - \)\(44\!\cdots\!20\)\( T^{29} + \)\(33\!\cdots\!84\)\( T^{30} - \)\(14\!\cdots\!12\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 + 60 T + 1682 T^{2} + 29988 T^{3} + 398642 T^{4} + 4449180 T^{5} + 44616114 T^{6} + 400755436 T^{7} + 3146402174 T^{8} + 22577269012 T^{9} + 172416257546 T^{10} + 1548661495372 T^{11} + 15112755685578 T^{12} + 149613932704668 T^{13} + 1492299482027146 T^{14} + 14514912884993716 T^{15} + 131595396462860353 T^{16} + 1114942726481802512 T^{17} + 9296763449815475432 T^{18} + 79328198294011301400 T^{19} + \)\(68\!\cdots\!92\)\( T^{20} + \)\(57\!\cdots\!00\)\( T^{21} + \)\(49\!\cdots\!28\)\( T^{22} + \)\(43\!\cdots\!04\)\( T^{23} + \)\(37\!\cdots\!73\)\( T^{24} + \)\(30\!\cdots\!88\)\( T^{25} + \)\(22\!\cdots\!94\)\( T^{26} + \)\(16\!\cdots\!96\)\( T^{27} + \)\(12\!\cdots\!18\)\( T^{28} + \)\(91\!\cdots\!36\)\( T^{29} + \)\(74\!\cdots\!54\)\( T^{30} + \)\(70\!\cdots\!24\)\( T^{31} + \)\(72\!\cdots\!54\)\( T^{32} + \)\(67\!\cdots\!88\)\( T^{33} + \)\(54\!\cdots\!26\)\( T^{34} + \)\(39\!\cdots\!60\)\( T^{35} + \)\(25\!\cdots\!62\)\( T^{36} + \)\(14\!\cdots\!64\)\( T^{37} + \)\(58\!\cdots\!58\)\( T^{38} + \)\(15\!\cdots\!20\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))(\( 1 - 60 T + 1682 T^{2} - 29988 T^{3} + 398642 T^{4} - 4449180 T^{5} + 44616114 T^{6} - 400755436 T^{7} + 3146402174 T^{8} - 22577269012 T^{9} + 172416257546 T^{10} - 1548661495372 T^{11} + 15112755685578 T^{12} - 149613932704668 T^{13} + 1492299482027146 T^{14} - 14514912884993716 T^{15} + 131595396462860353 T^{16} - 1114942726481802512 T^{17} + 9296763449815475432 T^{18} - 79328198294011301400 T^{19} + \)\(68\!\cdots\!92\)\( T^{20} - \)\(57\!\cdots\!00\)\( T^{21} + \)\(49\!\cdots\!28\)\( T^{22} - \)\(43\!\cdots\!04\)\( T^{23} + \)\(37\!\cdots\!73\)\( T^{24} - \)\(30\!\cdots\!88\)\( T^{25} + \)\(22\!\cdots\!94\)\( T^{26} - \)\(16\!\cdots\!96\)\( T^{27} + \)\(12\!\cdots\!18\)\( T^{28} - \)\(91\!\cdots\!36\)\( T^{29} + \)\(74\!\cdots\!54\)\( T^{30} - \)\(70\!\cdots\!24\)\( T^{31} + \)\(72\!\cdots\!54\)\( T^{32} - \)\(67\!\cdots\!88\)\( T^{33} + \)\(54\!\cdots\!26\)\( T^{34} - \)\(39\!\cdots\!60\)\( T^{35} + \)\(25\!\cdots\!62\)\( T^{36} - \)\(14\!\cdots\!64\)\( T^{37} + \)\(58\!\cdots\!58\)\( T^{38} - \)\(15\!\cdots\!20\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))
$79$ (\( 1 + 10 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( 1 - 94 T^{2} + 6241 T^{4} \))(\( ( 1 - 79 T^{2} )^{2} \))(\( 1 - 122 T^{2} + 6241 T^{4} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 163 T^{2} + 472 T^{3} + 12877 T^{4} + 24964 T^{5} + 493039 T^{6} )^{2} \))(\( 1 + 98 T^{2} + 6241 T^{4} \))(\( 1 + 98 T^{2} + 6241 T^{4} \))(\( ( 1 - 140 T^{2} + 6241 T^{4} )^{2} \))(\( 1 - 6 T + 18 T^{2} - 474 T^{3} + 6241 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 158 T^{3} + 6241 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 474 T^{3} + 6241 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 158 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 128 T^{2} - 1200 T^{3} + 11234 T^{4} - 94800 T^{5} + 798848 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 - 16 T + 128 T^{2} - 1200 T^{3} + 11234 T^{4} - 94800 T^{5} + 798848 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 - 16 T + 128 T^{2} - 1200 T^{3} + 11234 T^{4} - 94800 T^{5} + 798848 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 - 8 T + 32 T^{2} + 232 T^{3} + 548 T^{4} + 19080 T^{5} - 143264 T^{6} + 3853144 T^{7} - 12081722 T^{8} + 304398376 T^{9} - 894110624 T^{10} + 9407184120 T^{11} + 21344644388 T^{12} + 713877084568 T^{13} + 7778798576672 T^{14} - 153631271889272 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 8 T - 40 T^{2} - 1240 T^{3} - 5536 T^{4} + 71320 T^{5} + 838872 T^{6} - 1864712 T^{7} - 47211870 T^{8} - 147312248 T^{9} + 5235400152 T^{10} + 35163541480 T^{11} - 215627648416 T^{12} - 3815549934760 T^{13} - 9723498220840 T^{14} + 153631271889272 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 40 T + 648 T^{2} - 2776 T^{3} - 75808 T^{4} + 1522712 T^{5} - 10404792 T^{6} - 39728344 T^{7} + 1478270884 T^{8} - 13459659000 T^{9} + 34995603032 T^{10} + 626696970424 T^{11} - 10252604611680 T^{12} + 77663922396552 T^{13} - 116715903085032 T^{14} - 5158833680727816 T^{15} + 70986929291924038 T^{16} - 407547860777497464 T^{17} - 728423951153684712 T^{18} + 38291342634473601528 T^{19} - \)\(39\!\cdots\!80\)\( T^{20} + \)\(19\!\cdots\!76\)\( T^{21} + \)\(85\!\cdots\!72\)\( T^{22} - \)\(25\!\cdots\!00\)\( T^{23} + \)\(22\!\cdots\!24\)\( T^{24} - \)\(47\!\cdots\!36\)\( T^{25} - \)\(98\!\cdots\!92\)\( T^{26} + \)\(11\!\cdots\!48\)\( T^{27} - \)\(44\!\cdots\!28\)\( T^{28} - \)\(12\!\cdots\!64\)\( T^{29} + \)\(23\!\cdots\!88\)\( T^{30} - \)\(11\!\cdots\!60\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 - 56 T + 1608 T^{2} - 32544 T^{3} + 531232 T^{4} - 7502656 T^{5} + 94723432 T^{6} - 1079876968 T^{7} + 11152309445 T^{8} - 104467318464 T^{9} + 885876705344 T^{10} - 6748309500960 T^{11} + 45237704790656 T^{12} - 254352077824672 T^{13} + 1043944393809024 T^{14} - 1173550884529024 T^{15} - 28330582069716470 T^{16} + 326793601144278544 T^{17} - 2173623899474329584 T^{18} + 10801150466444693600 T^{19} - 64674172953547878720 T^{20} + \)\(85\!\cdots\!00\)\( T^{21} - \)\(13\!\cdots\!44\)\( T^{22} + \)\(16\!\cdots\!16\)\( T^{23} - \)\(11\!\cdots\!70\)\( T^{24} - \)\(36\!\cdots\!76\)\( T^{25} + \)\(25\!\cdots\!04\)\( T^{26} - \)\(48\!\cdots\!48\)\( T^{27} + \)\(68\!\cdots\!16\)\( T^{28} - \)\(80\!\cdots\!40\)\( T^{29} + \)\(83\!\cdots\!44\)\( T^{30} - \)\(78\!\cdots\!56\)\( T^{31} + \)\(65\!\cdots\!45\)\( T^{32} - \)\(50\!\cdots\!52\)\( T^{33} + \)\(34\!\cdots\!92\)\( T^{34} - \)\(21\!\cdots\!44\)\( T^{35} + \)\(12\!\cdots\!72\)\( T^{36} - \)\(59\!\cdots\!96\)\( T^{37} + \)\(23\!\cdots\!88\)\( T^{38} - \)\(63\!\cdots\!64\)\( T^{39} + \)\(89\!\cdots\!01\)\( T^{40} \))(\( 1 - 56 T + 1608 T^{2} - 32544 T^{3} + 531232 T^{4} - 7502656 T^{5} + 94723432 T^{6} - 1079876968 T^{7} + 11152309445 T^{8} - 104467318464 T^{9} + 885876705344 T^{10} - 6748309500960 T^{11} + 45237704790656 T^{12} - 254352077824672 T^{13} + 1043944393809024 T^{14} - 1173550884529024 T^{15} - 28330582069716470 T^{16} + 326793601144278544 T^{17} - 2173623899474329584 T^{18} + 10801150466444693600 T^{19} - 64674172953547878720 T^{20} + \)\(85\!\cdots\!00\)\( T^{21} - \)\(13\!\cdots\!44\)\( T^{22} + \)\(16\!\cdots\!16\)\( T^{23} - \)\(11\!\cdots\!70\)\( T^{24} - \)\(36\!\cdots\!76\)\( T^{25} + \)\(25\!\cdots\!04\)\( T^{26} - \)\(48\!\cdots\!48\)\( T^{27} + \)\(68\!\cdots\!16\)\( T^{28} - \)\(80\!\cdots\!40\)\( T^{29} + \)\(83\!\cdots\!44\)\( T^{30} - \)\(78\!\cdots\!56\)\( T^{31} + \)\(65\!\cdots\!45\)\( T^{32} - \)\(50\!\cdots\!52\)\( T^{33} + \)\(34\!\cdots\!92\)\( T^{34} - \)\(21\!\cdots\!44\)\( T^{35} + \)\(12\!\cdots\!72\)\( T^{36} - \)\(59\!\cdots\!96\)\( T^{37} + \)\(23\!\cdots\!88\)\( T^{38} - \)\(63\!\cdots\!64\)\( T^{39} + \)\(89\!\cdots\!01\)\( T^{40} \))
$83$ (\( 1 - 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 4 T + 102 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( ( 1 - 2 T + 83 T^{2} )^{2} \))(\( ( 1 - 6 T + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( 1 - 170 T^{2} + 855 T^{4} + 1073140 T^{6} + 5890095 T^{8} - 8067914570 T^{10} + 326940373369 T^{12} \))(\( 1 - 130 T^{2} + 6889 T^{4} \))(\( 1 - 130 T^{2} + 6889 T^{4} \))(\( ( 1 - 130 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 148 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 148 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 68 T^{2} + 6889 T^{4} )^{2} \))(\( 1 - 300 T^{2} + 56408 T^{4} - 7222532 T^{6} + 693023310 T^{8} - 49756022948 T^{10} + 2677028970968 T^{12} - 98082112010700 T^{14} + 2252292232139041 T^{16} \))(\( 1 - 8 T + 32 T^{2} - 568 T^{3} + 16072 T^{4} - 92744 T^{5} + 388960 T^{6} - 6798072 T^{7} + 117032466 T^{8} - 564239976 T^{9} + 2679545440 T^{10} - 53029813528 T^{11} + 762750135112 T^{12} - 2237375085224 T^{13} + 10462091947808 T^{14} - 217088407917016 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 32 T + 512 T^{2} - 4240 T^{3} + 32036 T^{4} - 651488 T^{5} + 13433984 T^{6} - 155605072 T^{7} + 1085940056 T^{8} - 7946115088 T^{9} + 139887075072 T^{10} - 2116082672992 T^{11} + 19160857300876 T^{12} - 111249085447120 T^{13} + 935146497989248 T^{14} - 14927162026453792 T^{15} + 176840852970889006 T^{16} - 1238954448195664736 T^{17} + 6442224224647929472 T^{18} - 63610780820552403440 T^{19} + \)\(90\!\cdots\!96\)\( T^{20} - \)\(83\!\cdots\!56\)\( T^{21} + \)\(45\!\cdots\!68\)\( T^{22} - \)\(21\!\cdots\!76\)\( T^{23} + \)\(24\!\cdots\!96\)\( T^{24} - \)\(29\!\cdots\!16\)\( T^{25} + \)\(20\!\cdots\!16\)\( T^{26} - \)\(83\!\cdots\!96\)\( T^{27} + \)\(34\!\cdots\!96\)\( T^{28} - \)\(37\!\cdots\!20\)\( T^{29} + \)\(37\!\cdots\!48\)\( T^{30} - \)\(19\!\cdots\!24\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 544 T^{3} - 1354 T^{4} + 59152 T^{5} + 147968 T^{6} + 546160 T^{7} - 31611727 T^{8} + 119552016 T^{9} + 1652717184 T^{10} - 6405201136 T^{11} + 252699874336 T^{12} + 937926276176 T^{13} + 17620618729088 T^{14} - 121733300402992 T^{15} - 1091081305080034 T^{16} + 10833819307749168 T^{17} + 164063275302237440 T^{18} + 183331162121083376 T^{19} - 10465764546854435628 T^{20} + 15216486456049920208 T^{21} + \)\(11\!\cdots\!60\)\( T^{22} + \)\(61\!\cdots\!16\)\( T^{23} - \)\(51\!\cdots\!14\)\( T^{24} - \)\(47\!\cdots\!56\)\( T^{25} + \)\(57\!\cdots\!72\)\( T^{26} + \)\(25\!\cdots\!52\)\( T^{27} + \)\(56\!\cdots\!76\)\( T^{28} - \)\(11\!\cdots\!08\)\( T^{29} + \)\(25\!\cdots\!16\)\( T^{30} + \)\(15\!\cdots\!72\)\( T^{31} - \)\(33\!\cdots\!47\)\( T^{32} + \)\(48\!\cdots\!80\)\( T^{33} + \)\(10\!\cdots\!72\)\( T^{34} + \)\(36\!\cdots\!64\)\( T^{35} - \)\(68\!\cdots\!74\)\( T^{36} - \)\(22\!\cdots\!12\)\( T^{37} + \)\(24\!\cdots\!01\)\( T^{40} \))(\( 1 + 544 T^{3} - 1354 T^{4} - 59152 T^{5} + 147968 T^{6} - 546160 T^{7} - 31611727 T^{8} - 119552016 T^{9} + 1652717184 T^{10} + 6405201136 T^{11} + 252699874336 T^{12} - 937926276176 T^{13} + 17620618729088 T^{14} + 121733300402992 T^{15} - 1091081305080034 T^{16} - 10833819307749168 T^{17} + 164063275302237440 T^{18} - 183331162121083376 T^{19} - 10465764546854435628 T^{20} - 15216486456049920208 T^{21} + \)\(11\!\cdots\!60\)\( T^{22} - \)\(61\!\cdots\!16\)\( T^{23} - \)\(51\!\cdots\!14\)\( T^{24} + \)\(47\!\cdots\!56\)\( T^{25} + \)\(57\!\cdots\!72\)\( T^{26} - \)\(25\!\cdots\!52\)\( T^{27} + \)\(56\!\cdots\!76\)\( T^{28} + \)\(11\!\cdots\!08\)\( T^{29} + \)\(25\!\cdots\!16\)\( T^{30} - \)\(15\!\cdots\!72\)\( T^{31} - \)\(33\!\cdots\!47\)\( T^{32} - \)\(48\!\cdots\!80\)\( T^{33} + \)\(10\!\cdots\!72\)\( T^{34} - \)\(36\!\cdots\!64\)\( T^{35} - \)\(68\!\cdots\!74\)\( T^{36} + \)\(22\!\cdots\!12\)\( T^{37} + \)\(24\!\cdots\!01\)\( T^{40} \))
$89$ (\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 9 T + 89 T^{2} \))(\( 1 + 9 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 7 T + 152 T^{2} + 623 T^{3} + 7921 T^{4} \))(\( ( 1 + T + 89 T^{2} )^{2} \))(\( ( 1 + T + 89 T^{2} )^{2} \))(\( ( 1 - 2 T + 89 T^{2} )^{2} \))(\( ( 1 - T + 89 T^{2} )^{2} \))(\( ( 1 - 9 T + 251 T^{2} - 1442 T^{3} + 22339 T^{4} - 71289 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 - 5 T + 89 T^{2} )^{2} \))(\( ( 1 - 5 T + 89 T^{2} )^{2} \))(\( ( 1 - 12 T + 89 T^{2} )^{4} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 115 T^{2} - 534 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 6 T + 115 T^{2} - 534 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 18 T + 227 T^{2} - 1602 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 22 T + 213 T^{2} + 26 T^{3} - 10296 T^{4} + 2314 T^{5} + 1687173 T^{6} + 15509318 T^{7} + 62742241 T^{8} )^{2} \))(\( 1 - 452 T^{2} + 101642 T^{4} - 14938576 T^{6} + 1561986259 T^{8} - 118328460496 T^{10} + 6377246859722 T^{12} - 224635543514372 T^{14} + 3936588805702081 T^{16} \))(\( 1 - 452 T^{2} + 117710 T^{4} - 22520544 T^{6} + 3445383617 T^{8} - 447835564456 T^{10} + 51066923538006 T^{12} - 5226847939440180 T^{14} + 487096621627460484 T^{16} - 41401862528305665780 T^{18} + \)\(32\!\cdots\!46\)\( T^{20} - \)\(22\!\cdots\!16\)\( T^{22} + \)\(13\!\cdots\!77\)\( T^{24} - \)\(70\!\cdots\!44\)\( T^{26} + \)\(29\!\cdots\!10\)\( T^{28} - \)\(88\!\cdots\!32\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 - 948 T^{2} + 453936 T^{4} - 146353496 T^{6} + 35701988702 T^{8} - 7013810546556 T^{10} + 1152109743195558 T^{12} - 162048052656574324 T^{14} + 19816119477140894897 T^{16} - \)\(21\!\cdots\!68\)\( T^{18} + \)\(20\!\cdots\!84\)\( T^{20} - \)\(16\!\cdots\!28\)\( T^{22} + \)\(12\!\cdots\!77\)\( T^{24} - \)\(80\!\cdots\!64\)\( T^{26} + \)\(45\!\cdots\!98\)\( T^{28} - \)\(21\!\cdots\!56\)\( T^{30} + \)\(88\!\cdots\!42\)\( T^{32} - \)\(28\!\cdots\!36\)\( T^{34} + \)\(70\!\cdots\!96\)\( T^{36} - \)\(11\!\cdots\!88\)\( T^{38} + \)\(97\!\cdots\!01\)\( T^{40} \))(\( 1 - 948 T^{2} + 453936 T^{4} - 146353496 T^{6} + 35701988702 T^{8} - 7013810546556 T^{10} + 1152109743195558 T^{12} - 162048052656574324 T^{14} + 19816119477140894897 T^{16} - \)\(21\!\cdots\!68\)\( T^{18} + \)\(20\!\cdots\!84\)\( T^{20} - \)\(16\!\cdots\!28\)\( T^{22} + \)\(12\!\cdots\!77\)\( T^{24} - \)\(80\!\cdots\!64\)\( T^{26} + \)\(45\!\cdots\!98\)\( T^{28} - \)\(21\!\cdots\!56\)\( T^{30} + \)\(88\!\cdots\!42\)\( T^{32} - \)\(28\!\cdots\!36\)\( T^{34} + \)\(70\!\cdots\!96\)\( T^{36} - \)\(11\!\cdots\!88\)\( T^{38} + \)\(97\!\cdots\!01\)\( T^{40} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 9 T + 176 T^{2} - 873 T^{3} + 9409 T^{4} \))(\( 1 - 193 T^{2} + 9409 T^{4} \))(\( 1 - 193 T^{2} + 9409 T^{4} \))(\( 1 + 62 T^{2} + 9409 T^{4} \))(\( 1 - 113 T^{2} + 9409 T^{4} \))(\( 1 - 493 T^{2} + 108803 T^{4} - 13645854 T^{6} + 1023727427 T^{8} - 43644935533 T^{10} + 832972004929 T^{12} \))(\( ( 1 + 7 T + 97 T^{2} )^{2} \))(\( ( 1 - 7 T + 97 T^{2} )^{2} \))(\( ( 1 + 97 T^{2} )^{4} \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 8 T + 97 T^{2} ) \))(\( 1 + 6 T + 18 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( ( 1 - 8 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( 1 - 6 T + 18 T^{2} - 582 T^{3} + 9409 T^{4} \))(\( 1 + 8 T + 32 T^{2} + 768 T^{3} + 18431 T^{4} + 74496 T^{5} + 301088 T^{6} + 7301384 T^{7} + 88529281 T^{8} \))(\( 1 - 8 T + 32 T^{2} - 768 T^{3} + 18431 T^{4} - 74496 T^{5} + 301088 T^{6} - 7301384 T^{7} + 88529281 T^{8} \))(\( 1 - 32 T + 512 T^{2} - 6912 T^{3} + 79151 T^{4} - 670464 T^{5} + 4817408 T^{6} - 29205536 T^{7} + 88529281 T^{8} \))(\( 1 - 20 T + 200 T^{2} - 1676 T^{3} + 9693 T^{4} - 76136 T^{5} + 988608 T^{6} - 10834248 T^{7} + 115952980 T^{8} - 1050922056 T^{9} + 9301812672 T^{10} - 69487271528 T^{11} + 858114320733 T^{12} - 14392382270732 T^{13} + 166594400985800 T^{14} - 1615965689562260 T^{15} + 7837433594376961 T^{16} \))(\( 1 + 32 T + 464 T^{2} + 4544 T^{3} + 40064 T^{4} + 365264 T^{5} + 2561856 T^{6} + 1123488 T^{7} - 134491233 T^{8} + 108978336 T^{9} + 24104503104 T^{10} + 333366590672 T^{11} + 3546837113984 T^{12} + 39020874127808 T^{13} + 386499010287056 T^{14} + 2585545103299616 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 24 T + 620 T^{2} - 11256 T^{3} + 188168 T^{4} - 2644552 T^{5} + 33137396 T^{6} - 363116776 T^{7} + 3495879981 T^{8} - 27290302688 T^{9} + 151068862808 T^{10} + 49701229232 T^{11} - 16205192405056 T^{12} + 307163155178640 T^{13} - 4139600928735048 T^{14} + 47878710235684832 T^{15} - 491134601735993292 T^{16} + 4644234892861428704 T^{17} - 38949505138468066632 T^{18} + \)\(28\!\cdots\!20\)\( T^{19} - \)\(14\!\cdots\!36\)\( T^{20} + \)\(42\!\cdots\!24\)\( T^{21} + \)\(12\!\cdots\!32\)\( T^{22} - \)\(22\!\cdots\!44\)\( T^{23} + \)\(27\!\cdots\!41\)\( T^{24} - \)\(27\!\cdots\!92\)\( T^{25} + \)\(24\!\cdots\!04\)\( T^{26} - \)\(18\!\cdots\!56\)\( T^{27} + \)\(13\!\cdots\!88\)\( T^{28} - \)\(75\!\cdots\!12\)\( T^{29} + \)\(40\!\cdots\!80\)\( T^{30} - \)\(15\!\cdots\!32\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 - 48 T + 1142 T^{2} - 16936 T^{3} + 160946 T^{4} - 603200 T^{5} - 12193658 T^{6} + 329836064 T^{7} - 4766618146 T^{8} + 48871055912 T^{9} - 342706004482 T^{10} + 607199068352 T^{11} + 28990974681866 T^{12} - 605921738623824 T^{13} + 7806367455647038 T^{14} - 74491245978555832 T^{15} + 484575109311053409 T^{16} - 549564314450980192 T^{17} - 41722742455227040440 T^{18} + \)\(77\!\cdots\!16\)\( T^{19} - \)\(90\!\cdots\!40\)\( T^{20} + \)\(75\!\cdots\!52\)\( T^{21} - \)\(39\!\cdots\!60\)\( T^{22} - \)\(50\!\cdots\!16\)\( T^{23} + \)\(42\!\cdots\!29\)\( T^{24} - \)\(63\!\cdots\!24\)\( T^{25} + \)\(65\!\cdots\!02\)\( T^{26} - \)\(48\!\cdots\!12\)\( T^{27} + \)\(22\!\cdots\!26\)\( T^{28} + \)\(46\!\cdots\!84\)\( T^{29} - \)\(25\!\cdots\!18\)\( T^{30} + \)\(34\!\cdots\!36\)\( T^{31} - \)\(33\!\cdots\!86\)\( T^{32} + \)\(22\!\cdots\!28\)\( T^{33} - \)\(79\!\cdots\!02\)\( T^{34} - \)\(38\!\cdots\!00\)\( T^{35} + \)\(98\!\cdots\!66\)\( T^{36} - \)\(10\!\cdots\!32\)\( T^{37} + \)\(66\!\cdots\!38\)\( T^{38} - \)\(26\!\cdots\!84\)\( T^{39} + \)\(54\!\cdots\!01\)\( T^{40} \))(\( 1 + 48 T + 1142 T^{2} + 16936 T^{3} + 160946 T^{4} + 603200 T^{5} - 12193658 T^{6} - 329836064 T^{7} - 4766618146 T^{8} - 48871055912 T^{9} - 342706004482 T^{10} - 607199068352 T^{11} + 28990974681866 T^{12} + 605921738623824 T^{13} + 7806367455647038 T^{14} + 74491245978555832 T^{15} + 484575109311053409 T^{16} + 549564314450980192 T^{17} - 41722742455227040440 T^{18} - \)\(77\!\cdots\!16\)\( T^{19} - \)\(90\!\cdots\!40\)\( T^{20} - \)\(75\!\cdots\!52\)\( T^{21} - \)\(39\!\cdots\!60\)\( T^{22} + \)\(50\!\cdots\!16\)\( T^{23} + \)\(42\!\cdots\!29\)\( T^{24} + \)\(63\!\cdots\!24\)\( T^{25} + \)\(65\!\cdots\!02\)\( T^{26} + \)\(48\!\cdots\!12\)\( T^{27} + \)\(22\!\cdots\!26\)\( T^{28} - \)\(46\!\cdots\!84\)\( T^{29} - \)\(25\!\cdots\!18\)\( T^{30} - \)\(34\!\cdots\!36\)\( T^{31} - \)\(33\!\cdots\!86\)\( T^{32} - \)\(22\!\cdots\!28\)\( T^{33} - \)\(79\!\cdots\!02\)\( T^{34} + \)\(38\!\cdots\!00\)\( T^{35} + \)\(98\!\cdots\!66\)\( T^{36} + \)\(10\!\cdots\!32\)\( T^{37} + \)\(66\!\cdots\!38\)\( T^{38} + \)\(26\!\cdots\!84\)\( T^{39} + \)\(54\!\cdots\!01\)\( T^{40} \))
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