Properties

Label 430.2
Level 430
Weight 2
Dimension 1695
Nonzero newspaces 12
Newform subspaces 33
Sturm bound 22176
Trace bound 4

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Defining parameters

Level: \( N \) = \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 33 \)
Sturm bound: \(22176\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(430))\).

Total New Old
Modular forms 5880 1695 4185
Cusp forms 5209 1695 3514
Eisenstein series 671 0 671

Trace form

\( 1695q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + O(q^{10}) \) \( 1695q + q^{2} + 4q^{3} + q^{4} + q^{5} + 4q^{6} + 8q^{7} + q^{8} + 13q^{9} + q^{10} + 12q^{11} + 4q^{12} + 14q^{13} + 8q^{14} + 4q^{15} + q^{16} + 18q^{17} + 13q^{18} + 20q^{19} + q^{20} + 32q^{21} + 12q^{22} + 24q^{23} + 4q^{24} + q^{25} + 14q^{26} + 40q^{27} + 8q^{28} + 30q^{29} + 4q^{30} + 4q^{31} + q^{32} - 120q^{33} - 108q^{34} - 76q^{35} - 99q^{36} - 130q^{37} - 148q^{38} - 140q^{39} + q^{40} - 42q^{41} - 136q^{42} - 377q^{43} - 72q^{44} - 197q^{45} - 144q^{46} - 36q^{47} + 4q^{48} - 139q^{49} - 83q^{50} - 96q^{51} - 98q^{52} - 114q^{53} - 86q^{54} - 72q^{55} + 8q^{56} + 52q^{57} + 30q^{58} + 60q^{59} + 4q^{60} + 62q^{61} + 32q^{62} + 104q^{63} + q^{64} + 14q^{65} + 48q^{66} + 68q^{67} + 18q^{68} + 12q^{69} + 8q^{70} - 12q^{71} + 13q^{72} - 10q^{73} + 38q^{74} - 38q^{75} + 20q^{76} - 156q^{77} + 56q^{78} - 88q^{79} + q^{80} - 215q^{81} + 42q^{82} - 84q^{83} + 32q^{84} - 66q^{85} + 43q^{86} - 300q^{87} + 12q^{88} - 78q^{89} + 13q^{90} - 56q^{91} + 24q^{92} - 208q^{93} + 48q^{94} - 64q^{95} + 4q^{96} - 154q^{97} + 57q^{98} - 138q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(430))\)

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
430.2.a \(\chi_{430}(1, \cdot)\) 430.2.a.a 1 1
430.2.a.b 1
430.2.a.c 1
430.2.a.d 1
430.2.a.e 2
430.2.a.f 2
430.2.a.g 2
430.2.a.h 3
430.2.b \(\chi_{430}(259, \cdot)\) 430.2.b.a 6 1
430.2.b.b 16
430.2.e \(\chi_{430}(221, \cdot)\) 430.2.e.a 2 2
430.2.e.b 2
430.2.e.c 2
430.2.e.d 4
430.2.e.e 6
430.2.e.f 6
430.2.e.g 10
430.2.g \(\chi_{430}(257, \cdot)\) 430.2.g.a 4 2
430.2.g.b 40
430.2.j \(\chi_{430}(49, \cdot)\) 430.2.j.a 44 2
430.2.k \(\chi_{430}(11, \cdot)\) 430.2.k.a 12 6
430.2.k.b 18
430.2.k.c 18
430.2.k.d 24
430.2.l \(\chi_{430}(7, \cdot)\) 430.2.l.a 88 4
430.2.p \(\chi_{430}(59, \cdot)\) 430.2.p.a 132 6
430.2.q \(\chi_{430}(31, \cdot)\) 430.2.q.a 36 12
430.2.q.b 48
430.2.q.c 48
430.2.q.d 60
430.2.r \(\chi_{430}(27, \cdot)\) 430.2.r.a 264 12
430.2.t \(\chi_{430}(9, \cdot)\) 430.2.t.a 264 12
430.2.x \(\chi_{430}(3, \cdot)\) 430.2.x.a 528 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(430))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(430)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(215))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 + T^{2} )^{8} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{10} \))(\( 1 + T^{4} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{3} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{3} \))
$3$ (\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 - 2 T + 4 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 + 9 T^{4} \))(\( 1 + 4 T^{2} + 9 T^{4} \))(\( 1 + 2 T + 3 T^{2} + 4 T^{3} + 9 T^{4} + 18 T^{5} + 27 T^{6} \))(\( 1 - 10 T^{2} + 51 T^{4} - 176 T^{6} + 459 T^{8} - 810 T^{10} + 729 T^{12} \))(\( 1 - 10 T^{2} + 51 T^{4} - 176 T^{6} + 667 T^{8} - 3040 T^{10} + 11605 T^{12} - 33410 T^{14} + 91072 T^{16} - 300690 T^{18} + 940005 T^{20} - 2216160 T^{22} + 4376187 T^{24} - 10392624 T^{26} + 27103491 T^{28} - 47829690 T^{30} + 43046721 T^{32} \))(\( ( 1 + 3 T^{2} )( 1 + 3 T + 3 T^{2} ) \))(\( 1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( ( 1 - 3 T + 3 T^{2} )( 1 + 3 T + 3 T^{2} ) \))(\( ( 1 - 2 T + T^{2} - 6 T^{3} + 9 T^{4} )^{2} \))(\( ( 1 - 2 T + T^{2} + 3 T^{4} - 18 T^{5} + 27 T^{6} )( 1 + T - 2 T^{2} - 3 T^{3} - 6 T^{4} + 9 T^{5} + 27 T^{6} ) \))(\( 1 - 2 T + 8 T^{3} - 12 T^{4} - 2 T^{5} + 34 T^{6} - 6 T^{7} - 108 T^{8} + 216 T^{9} - 486 T^{11} + 729 T^{12} \))(\( 1 - T - 3 T^{2} + 10 T^{3} - 2 T^{4} - 42 T^{5} + 35 T^{6} + 115 T^{7} - 245 T^{8} - 132 T^{9} + 1032 T^{10} - 396 T^{11} - 2205 T^{12} + 3105 T^{13} + 2835 T^{14} - 10206 T^{15} - 1458 T^{16} + 21870 T^{17} - 19683 T^{18} - 19683 T^{19} + 59049 T^{20} \))(\( ( 1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4} )( 1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4} ) \))(\( 1 + T - 6 T^{2} - 3 T^{3} + 19 T^{4} - 15 T^{5} - 26 T^{6} + 148 T^{7} - 103 T^{8} - 578 T^{9} + 737 T^{10} + 825 T^{11} - 2537 T^{12} + 2475 T^{13} + 6633 T^{14} - 15606 T^{15} - 8343 T^{16} + 35964 T^{17} - 18954 T^{18} - 32805 T^{19} + 124659 T^{20} - 59049 T^{21} - 354294 T^{22} + 177147 T^{23} + 531441 T^{24} \))(\( 1 - 2 T + T^{2} - 3 T^{3} + T^{4} + 18 T^{6} + 64 T^{7} - 171 T^{8} + 290 T^{9} - 781 T^{10} + 709 T^{11} - 1029 T^{12} + 953 T^{13} + 2528 T^{14} + 38 T^{15} + 12474 T^{16} - 47133 T^{17} + 61948 T^{18} - 141399 T^{19} + 112266 T^{20} + 1026 T^{21} + 204768 T^{22} + 231579 T^{23} - 750141 T^{24} + 1550583 T^{25} - 5124141 T^{26} + 5708070 T^{27} - 10097379 T^{28} + 11337408 T^{29} + 9565938 T^{30} + 4782969 T^{32} - 43046721 T^{33} + 43046721 T^{34} - 258280326 T^{35} + 387420489 T^{36} \))(\( 1 - 5 T + 11 T^{2} - 22 T^{3} + 64 T^{4} - 177 T^{5} + 364 T^{6} - 721 T^{7} + 1705 T^{8} - 3727 T^{9} + 6910 T^{10} - 13168 T^{11} + 27619 T^{12} - 53717 T^{13} + 95903 T^{14} - 176450 T^{15} + 331870 T^{16} - 581677 T^{17} + 983731 T^{18} - 1745031 T^{19} + 2986830 T^{20} - 4764150 T^{21} + 7768143 T^{22} - 13053231 T^{23} + 20134251 T^{24} - 28798416 T^{25} + 45336510 T^{26} - 73358541 T^{27} + 100678545 T^{28} - 127722987 T^{29} + 193444524 T^{30} - 282195171 T^{31} + 306110016 T^{32} - 315675954 T^{33} + 473513931 T^{34} - 645700815 T^{35} + 387420489 T^{36} \))
$5$ (\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( 1 - 2 T + 3 T^{2} - 12 T^{3} + 15 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 - 2 T + 7 T^{2} - 37 T^{4} + 98 T^{5} - 159 T^{6} - 176 T^{7} + 728 T^{8} - 880 T^{9} - 3975 T^{10} + 12250 T^{11} - 23125 T^{12} + 109375 T^{14} - 156250 T^{15} + 390625 T^{16} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{3} \))(\( ( 1 - T + T^{2} )^{5} \))(\( 1 + 8 T^{2} + 25 T^{4} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{3} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{3} \))
$7$ (\( 1 - T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + 5 T + 7 T^{2} \))(\( 1 - 2 T + 3 T^{2} - 14 T^{3} + 49 T^{4} \))(\( ( 1 - T + 7 T^{2} )^{2} \))(\( ( 1 - T + 7 T^{2} )^{2} \))(\( 1 + 6 T + 26 T^{2} + 76 T^{3} + 182 T^{4} + 294 T^{5} + 343 T^{6} \))(\( 1 - 31 T^{2} + 454 T^{4} - 4003 T^{6} + 22246 T^{8} - 74431 T^{10} + 117649 T^{12} \))(\( 1 - 37 T^{2} + 669 T^{4} - 8530 T^{6} + 93904 T^{8} - 954556 T^{10} + 8661035 T^{12} - 68886013 T^{14} + 498263182 T^{16} - 3375414637 T^{18} + 20795145035 T^{20} - 112302558844 T^{22} + 541337873104 T^{24} - 2409513873970 T^{26} + 9259821137469 T^{28} - 25094253695413 T^{30} + 33232930569601 T^{32} \))(\( 1 - 7 T^{2} + 49 T^{4} \))(\( ( 1 - T + 7 T^{2} )( 1 + 5 T + 7 T^{2} ) \))(\( ( 1 - T + 7 T^{2} )( 1 + 5 T + 7 T^{2} ) \))(\( 1 - 4 T^{2} - 33 T^{4} - 196 T^{6} + 2401 T^{8} \))(\( 1 - 4 T - T^{2} + 36 T^{3} - 38 T^{4} - 128 T^{5} + 583 T^{6} - 896 T^{7} - 1862 T^{8} + 12348 T^{9} - 2401 T^{10} - 67228 T^{11} + 117649 T^{12} \))(\( ( 1 - 2 T - 3 T^{2} - 14 T^{3} + 49 T^{4} )^{3} \))(\( 1 - 6 T + 3 T^{2} + 50 T^{3} - 95 T^{4} - 16 T^{5} - 208 T^{6} + 348 T^{7} + 4257 T^{8} - 5530 T^{9} - 15197 T^{10} - 38710 T^{11} + 208593 T^{12} + 119364 T^{13} - 499408 T^{14} - 268912 T^{15} - 11176655 T^{16} + 41177150 T^{17} + 17294403 T^{18} - 242121642 T^{19} + 282475249 T^{20} \))(\( 1 - 94 T^{4} + 2401 T^{8} \))(\( ( 1 - 2 T + 26 T^{2} - 35 T^{3} + 311 T^{4} - 323 T^{5} + 2521 T^{6} - 2261 T^{7} + 15239 T^{8} - 12005 T^{9} + 62426 T^{10} - 33614 T^{11} + 117649 T^{12} )^{2} \))(\( ( 1 - 3 T + 35 T^{2} - 104 T^{3} + 659 T^{4} - 1784 T^{5} + 8247 T^{6} - 20223 T^{7} + 75730 T^{8} - 164555 T^{9} + 530110 T^{10} - 990927 T^{11} + 2828721 T^{12} - 4283384 T^{13} + 11075813 T^{14} - 12235496 T^{15} + 28824005 T^{16} - 17294403 T^{17} + 40353607 T^{18} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} - 165 T^{3} + 954 T^{4} - 3272 T^{5} + 13473 T^{6} - 40583 T^{7} + 131977 T^{8} - 340920 T^{9} + 923839 T^{10} - 1988567 T^{11} + 4621239 T^{12} - 7856072 T^{13} + 16033878 T^{14} - 19412085 T^{15} + 35412349 T^{16} - 23059204 T^{17} + 40353607 T^{18} )^{2} \))
$11$ (\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 - 2 T + 20 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 20 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 6 T + 11 T^{2} + 4 T^{3} + 121 T^{4} - 726 T^{5} + 1331 T^{6} \))(\( ( 1 + 6 T + 41 T^{2} + 130 T^{3} + 451 T^{4} + 726 T^{5} + 1331 T^{6} )^{2} \))(\( ( 1 - 2 T + 28 T^{2} - 88 T^{3} + 612 T^{4} - 1532 T^{5} + 9668 T^{6} - 22990 T^{7} + 112406 T^{8} - 252890 T^{9} + 1169828 T^{10} - 2039092 T^{11} + 8960292 T^{12} - 14172488 T^{13} + 49603708 T^{14} - 38974342 T^{15} + 214358881 T^{16} )^{2} \))(\( ( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 - 5 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} + 22 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 + 4 T + 33 T^{2} + 82 T^{3} + 363 T^{4} + 484 T^{5} + 1331 T^{6} )^{2} \))(\( ( 1 + T + 27 T^{2} + 20 T^{3} + 297 T^{4} + 121 T^{5} + 1331 T^{6} )^{2} \))(\( ( 1 - 2 T + 18 T^{2} - 76 T^{3} + 371 T^{4} - 702 T^{5} + 4081 T^{6} - 9196 T^{7} + 23958 T^{8} - 29282 T^{9} + 161051 T^{10} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{4} \))(\( 1 - 3 T - 22 T^{2} + 35 T^{3} + 429 T^{4} - 597 T^{5} - 2700 T^{6} + 812 T^{7} - 9863 T^{8} - 2764 T^{9} + 826623 T^{10} - 223415 T^{11} - 11420881 T^{12} - 2457565 T^{13} + 100021383 T^{14} - 3678884 T^{15} - 144404183 T^{16} + 130773412 T^{17} - 4783214700 T^{18} - 11633841087 T^{19} + 91959959949 T^{20} + 82528169185 T^{21} - 570623341222 T^{22} - 855935011833 T^{23} + 3138428376721 T^{24} \))(\( 1 - 9 T + 25 T^{2} - 12 T^{3} - 24 T^{4} - 91 T^{5} - 540 T^{6} + 7247 T^{7} - 3173 T^{8} - 124295 T^{9} + 349798 T^{10} - 201170 T^{11} - 267079 T^{12} + 5753101 T^{13} - 42575665 T^{14} + 100911028 T^{15} + 151819518 T^{16} - 1253904551 T^{17} + 3739030263 T^{18} - 13792950061 T^{19} + 18370161678 T^{20} + 134312578268 T^{21} - 623350311265 T^{22} + 926542669151 T^{23} - 473146740319 T^{24} - 3920234190070 T^{25} + 74982307856038 T^{26} - 293081108252845 T^{27} - 82299448258973 T^{28} + 2067653676917917 T^{29} - 1694751323429340 T^{30} - 3141566805097721 T^{31} - 9113996005997784 T^{32} - 50126978032987812 T^{33} + 1148743246589304025 T^{34} - 4549023256493643939 T^{35} + 5559917313492231481 T^{36} \))(\( 1 - 5 T + 29 T^{2} - 2 T^{3} - 64 T^{4} + 1743 T^{5} - 258 T^{6} + 563 T^{7} + 93155 T^{8} - 93657 T^{9} + 443272 T^{10} + 1889454 T^{11} - 1463949 T^{12} + 6857689 T^{13} + 40881021 T^{14} - 138737432 T^{15} + 197538356 T^{16} - 688470581 T^{17} - 1743464851 T^{18} - 7573176391 T^{19} + 23902141076 T^{20} - 184659521992 T^{21} + 598539028461 T^{22} + 1104437671139 T^{23} - 2593474954389 T^{24} + 36820113194634 T^{25} + 95019289898632 T^{26} - 220838306895987 T^{27} + 2416200788706155 T^{28} + 160630470553993 T^{29} - 809714521194018 T^{30} + 60173087266871733 T^{31} - 24303989349327424 T^{32} - 8354496338831302 T^{33} + 1332542166043592669 T^{34} - 2527235142496468855 T^{35} + 5559917313492231481 T^{36} \))
$13$ (\( 1 + T + 13 T^{2} \))(\( 1 + 3 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 2 T + 15 T^{2} - 26 T^{3} + 169 T^{4} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( 1 - 2 T + 19 T^{2} - 26 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 12 T^{2} - 2 T^{3} + 156 T^{4} + 676 T^{5} + 2197 T^{6} \))(\( 1 - 43 T^{2} + 878 T^{4} - 12687 T^{6} + 148382 T^{8} - 1228123 T^{10} + 4826809 T^{12} \))(\( 1 - 57 T^{2} + 2221 T^{4} - 63010 T^{6} + 1470096 T^{8} - 29164612 T^{10} + 504883051 T^{12} - 7776883625 T^{14} + 106613731662 T^{16} - 1314293332625 T^{18} + 14419964819611 T^{20} - 140772011683108 T^{22} + 1199202470019216 T^{24} - 8686463571405490 T^{26} + 51745047057030301 T^{28} - 224430453984859473 T^{30} + 665416609183179841 T^{32} \))(\( 1 - 13 T^{2} + 169 T^{4} \))(\( ( 1 - 7 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} ) \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 - 16 T^{2} + 87 T^{4} - 2704 T^{6} + 28561 T^{8} \))(\( 1 - 6 T + 21 T^{2} - 70 T^{3} - 30 T^{4} + 1176 T^{5} - 4515 T^{6} + 15288 T^{7} - 5070 T^{8} - 153790 T^{9} + 599781 T^{10} - 2227758 T^{11} + 4826809 T^{12} \))(\( 1 - 25 T^{2} + 32 T^{3} + 300 T^{4} - 400 T^{5} - 3475 T^{6} - 5200 T^{7} + 50700 T^{8} + 70304 T^{9} - 714025 T^{10} + 4826809 T^{12} \))(\( 1 + 6 T - 5 T^{2} + 18 T^{3} + 467 T^{4} - 554 T^{5} - 1746 T^{6} + 28202 T^{7} + 10477 T^{8} + 16676 T^{9} + 1420225 T^{10} + 216788 T^{11} + 1770613 T^{12} + 61959794 T^{13} - 49867506 T^{14} - 205696322 T^{15} + 2254119803 T^{16} + 1129473306 T^{17} - 4078653605 T^{18} + 63626996238 T^{19} + 137858491849 T^{20} \))(\( ( 1 - 4 T + 8 T^{2} - 52 T^{3} + 169 T^{4} )^{2} \))(\( ( 1 + 2 T - 9 T^{2} - 44 T^{3} + 113 T^{4} - 126 T^{5} - 1637 T^{6} - 1638 T^{7} + 19097 T^{8} - 96668 T^{9} - 257049 T^{10} + 742586 T^{11} + 4826809 T^{12} )^{2} \))(\( 1 - 4 T + 21 T^{2} + 56 T^{3} - 260 T^{4} + 1952 T^{5} + 3110 T^{6} - 2420 T^{7} + 66011 T^{8} + 439956 T^{9} - 292985 T^{10} + 2208328 T^{11} + 34844172 T^{12} - 36854292 T^{13} + 139942287 T^{14} + 1680146632 T^{15} - 929707432 T^{16} + 4297523544 T^{17} + 71524901083 T^{18} + 55867806072 T^{19} - 157120556008 T^{20} + 3691282150504 T^{21} + 3996891659007 T^{22} - 13683740639556 T^{23} + 168186163007148 T^{24} + 138569307049576 T^{25} - 238996865292185 T^{26} + 4665513126147588 T^{27} + 9100176905444339 T^{28} - 4337028153569540 T^{29} + 72457044730915910 T^{30} + 591212208068077856 T^{31} - 1023717860281815140 T^{32} + 2866410008789082392 T^{33} + 13973748792846776661 T^{34} - 34601663677525351732 T^{35} + \)\(11\!\cdots\!29\)\( T^{36} \))(\( 1 - 22 T + 189 T^{2} - 776 T^{3} + 2016 T^{4} - 11560 T^{5} + 76130 T^{6} - 262662 T^{7} + 880343 T^{8} - 5919980 T^{9} + 28592867 T^{10} - 84734756 T^{11} + 312372760 T^{12} - 1531317100 T^{13} + 5382091707 T^{14} - 17490109252 T^{15} + 77239495484 T^{16} - 309727210712 T^{17} + 1082670643211 T^{18} - 4026453739256 T^{19} + 13053474736796 T^{20} - 38425770026644 T^{21} + 153717921243627 T^{22} - 568567320010300 T^{23} + 1507763649322840 T^{24} - 5316980277356852 T^{25} + 23324080013367107 T^{26} - 62778424198172540 T^{27} + 121362758289824207 T^{28} - 470732433418546494 T^{29} + 1773683220374478530 T^{30} - 3501236232206444680 T^{31} + 7937750793569766624 T^{32} - 39720252978934427432 T^{33} + \)\(12\!\cdots\!49\)\( T^{34} - \)\(19\!\cdots\!26\)\( T^{35} + \)\(11\!\cdots\!29\)\( T^{36} \))
$17$ (\( 1 + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 10 T + 56 T^{2} - 170 T^{3} + 289 T^{4} \))(\( 1 + 28 T^{2} + 289 T^{4} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 - 8 T + 57 T^{2} - 228 T^{3} + 969 T^{4} - 2312 T^{5} + 4913 T^{6} \))(\( 1 - 42 T^{2} + 1155 T^{4} - 24816 T^{6} + 333795 T^{8} - 3507882 T^{10} + 24137569 T^{12} \))(\( 1 - 82 T^{2} + 3475 T^{4} - 100800 T^{6} + 2208355 T^{8} - 36519332 T^{10} + 437841909 T^{12} - 3747068150 T^{14} + 36785708160 T^{16} - 1082902695350 T^{18} + 36568994081589 T^{20} - 881487895983908 T^{22} + 15404948823619555 T^{24} - 203212185165259200 T^{26} + 2024612274373419475 T^{28} - 13806981777870876178 T^{30} + 48661191875666868481 T^{32} \))(\( 1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + 2 T - 21 T^{2} - 18 T^{3} + 268 T^{4} - 306 T^{5} - 6069 T^{6} + 9826 T^{7} + 83521 T^{8} \))(\( ( 1 - 17 T^{2} + 289 T^{4} )^{3} \))(\( 1 + 5 T - 18 T^{2} - 93 T^{3} + 348 T^{4} + 757 T^{5} - 5116 T^{6} + 12869 T^{7} + 100572 T^{8} - 456909 T^{9} - 1503378 T^{10} + 7099285 T^{11} + 24137569 T^{12} \))(\( 1 - 4 T - 6 T^{2} + 280 T^{3} - 1081 T^{4} - 208 T^{5} + 32636 T^{6} - 139236 T^{7} + 180789 T^{8} + 1937608 T^{9} - 11672626 T^{10} + 32939336 T^{11} + 52248021 T^{12} - 684066468 T^{13} + 2725791356 T^{14} - 295330256 T^{15} - 26092712089 T^{16} + 114894828440 T^{17} - 41854544646 T^{18} - 474351505988 T^{19} + 2015993900449 T^{20} \))(\( ( 1 - 8 T + 17 T^{2} )^{2}( 1 - 2 T + 17 T^{2} )^{2} \))(\( 1 + 5 T + 6 T^{2} - 50 T^{3} - 256 T^{4} - 61 T^{5} - 2524 T^{6} + 31036 T^{7} + 260014 T^{8} + 878434 T^{9} + 371178 T^{10} - 9204064 T^{11} - 16949749 T^{12} - 156469088 T^{13} + 107270442 T^{14} + 4315746242 T^{15} + 21716629294 T^{16} + 44066681852 T^{17} - 60923224156 T^{18} - 25030659053 T^{19} - 1785793904896 T^{20} - 5929393824850 T^{21} + 12095963402694 T^{22} + 171359481538165 T^{23} + 582622237229761 T^{24} \))(\( 1 + T - 23 T^{2} - 61 T^{3} + 797 T^{4} + 882 T^{5} - 9111 T^{6} - 55466 T^{7} + 169817 T^{8} + 861950 T^{9} + 2044903 T^{10} - 27646324 T^{11} - 18677652 T^{12} + 301514042 T^{13} + 2189324221 T^{14} - 6752066729 T^{15} - 26803962017 T^{16} - 10192305047 T^{17} + 842845786937 T^{18} - 173269185799 T^{19} - 7746345022913 T^{20} - 33172903839577 T^{21} + 182854548262141 T^{22} + 428106823131994 T^{23} - 450833113907988 T^{24} - 11344355903488052 T^{25} + 14264747318373223 T^{26} + 102216820146589150 T^{27} + 342350036192547833 T^{28} - 1900925000599171978 T^{29} - 5308271203400352471 T^{30} + 8735837825023036434 T^{31} + \)\(13\!\cdots\!13\)\( T^{32} - \)\(17\!\cdots\!73\)\( T^{33} - \)\(11\!\cdots\!63\)\( T^{34} + \)\(82\!\cdots\!77\)\( T^{35} + \)\(14\!\cdots\!09\)\( T^{36} \))(\( 1 - T + 17 T^{2} - 71 T^{3} + 163 T^{4} - 1386 T^{5} + 5859 T^{6} - 25092 T^{7} + 79275 T^{8} - 574216 T^{9} + 380351 T^{10} - 8959160 T^{11} + 10289590 T^{12} - 149888072 T^{13} + 943088259 T^{14} - 2036970771 T^{15} + 18923873831 T^{16} - 49782589785 T^{17} + 210671203633 T^{18} - 846304026345 T^{19} + 5468999537159 T^{20} - 10007637397923 T^{21} + 78767674479939 T^{22} - 212819628245704 T^{23} + 248365688606710 T^{24} - 3676289825594680 T^{25} + 2653236318441791 T^{26} - 68095056090601352 T^{27} + 159817916458094475 T^{28} - 859950422151127236 T^{29} + 3413583687929169699 T^{30} - 13727745153607628682 T^{31} + 27445585729182351427 T^{32} - \)\(20\!\cdots\!03\)\( T^{33} + \)\(82\!\cdots\!77\)\( T^{34} - \)\(82\!\cdots\!77\)\( T^{35} + \)\(14\!\cdots\!09\)\( T^{36} \))
$19$ (\( 1 - T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 + 6 T + 35 T^{2} + 114 T^{3} + 361 T^{4} \))(\( 1 - 2 T + 15 T^{2} - 38 T^{3} + 361 T^{4} \))(\( ( 1 + T + 19 T^{2} )^{2} \))(\( 1 - 2 T + 42 T^{2} - 44 T^{3} + 798 T^{4} - 722 T^{5} + 6859 T^{6} \))(\( ( 1 - 17 T + 148 T^{2} - 797 T^{3} + 2812 T^{4} - 6137 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 + 15 T + 200 T^{2} + 1733 T^{3} + 13726 T^{4} + 86371 T^{5} + 508275 T^{6} + 2529942 T^{7} + 11896286 T^{8} + 48068898 T^{9} + 183487275 T^{10} + 592418689 T^{11} + 1788786046 T^{12} + 4291079567 T^{13} + 9409176200 T^{14} + 13408076085 T^{15} + 16983563041 T^{16} )^{2} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 6 T + 17 T^{2} + 114 T^{3} + 361 T^{4} \))(\( ( 1 - 7 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 + 2 T - 25 T^{2} - 18 T^{3} + 404 T^{4} - 342 T^{5} - 9025 T^{6} + 13718 T^{7} + 130321 T^{8} \))(\( 1 + 2 T - 49 T^{2} - 42 T^{3} + 1654 T^{4} + 616 T^{5} - 35621 T^{6} + 11704 T^{7} + 597094 T^{8} - 288078 T^{9} - 6385729 T^{10} + 4952198 T^{11} + 47045881 T^{12} \))(\( 1 + 7 T + 30 T^{2} + 117 T^{3} - 56 T^{4} - 2375 T^{5} - 10766 T^{6} - 45125 T^{7} - 20216 T^{8} + 802503 T^{9} + 3909630 T^{10} + 17332693 T^{11} + 47045881 T^{12} \))(\( 1 - 4 T - 30 T^{2} + 180 T^{3} + 97 T^{4} - 2250 T^{5} + 5972 T^{6} - 11828 T^{7} - 17043 T^{8} + 256830 T^{9} - 1468214 T^{10} + 4879770 T^{11} - 6152523 T^{12} - 81128252 T^{13} + 778277012 T^{14} - 5571222750 T^{15} + 4563450457 T^{16} + 160896913020 T^{17} - 509506891230 T^{18} - 1290750791116 T^{19} + 6131066257801 T^{20} \))(\( ( 1 + 20 T^{2} + 361 T^{4} )^{2} \))(\( 1 + 2 T - 24 T^{2} - 52 T^{3} + 115 T^{4} + 52 T^{5} - 1076 T^{6} - 45484 T^{7} - 66401 T^{8} + 1006610 T^{9} + 2114774 T^{10} - 3943776 T^{11} + 1394383 T^{12} - 74931744 T^{13} + 763433414 T^{14} + 6904337990 T^{15} - 8653444721 T^{16} - 112622886916 T^{17} - 50621367956 T^{18} + 46481330428 T^{19} + 1953109749715 T^{20} - 16779760284508 T^{21} - 147145590187224 T^{22} + 232980517796438 T^{23} + 2213314919066161 T^{24} \))(\( 1 + 2 T - 23 T^{2} - 24 T^{3} + 184 T^{4} + 1428 T^{5} + 12528 T^{6} + 12458 T^{7} - 294757 T^{8} - 220636 T^{9} + 6100277 T^{10} + 13014080 T^{11} + 26646360 T^{12} - 26340508 T^{13} - 628545959 T^{14} + 3968341152 T^{15} + 37315624628 T^{16} + 43754418476 T^{17} - 384806928499 T^{18} + 831333951044 T^{19} + 13470940490708 T^{20} + 27218851961568 T^{21} - 81912737922839 T^{22} - 65221705518292 T^{23} + 1253601481643160 T^{24} + 11632918321085120 T^{25} + 103604438997062357 T^{26} - 71196522887167444 T^{27} - 1807174696950649357 T^{28} + 1451235645354012302 T^{29} + 27728409306060865008 T^{30} + 60051660384103080252 T^{31} + \)\(14\!\cdots\!64\)\( T^{32} - \)\(36\!\cdots\!76\)\( T^{33} - \)\(66\!\cdots\!63\)\( T^{34} + \)\(10\!\cdots\!78\)\( T^{35} + \)\(10\!\cdots\!41\)\( T^{36} \))(\( 1 + 7 T + 80 T^{2} + 528 T^{3} + 3734 T^{4} + 20920 T^{5} + 120996 T^{6} + 605461 T^{7} + 2904657 T^{8} + 13467676 T^{9} + 54757744 T^{10} + 216429928 T^{11} + 724355904 T^{12} + 2023912444 T^{13} + 3282662694 T^{14} - 10380996494 T^{15} - 115691998692 T^{16} - 856017011464 T^{17} - 3500283086684 T^{18} - 16264323217816 T^{19} - 41764811527812 T^{20} - 71203254952346 T^{21} + 427799884944774 T^{22} + 5011407578675956 T^{23} + 34077961661231424 T^{24} + 193460596113004792 T^{25} + 929981597206939504 T^{26} + 4345853362873491604 T^{27} + 17808644523185479257 T^{28} + 70530308642774573959 T^{29} + \)\(26\!\cdots\!56\)\( T^{30} + \)\(87\!\cdots\!80\)\( T^{31} + \)\(29\!\cdots\!14\)\( T^{32} + \)\(80\!\cdots\!72\)\( T^{33} + \)\(23\!\cdots\!80\)\( T^{34} + \)\(38\!\cdots\!73\)\( T^{35} + \)\(10\!\cdots\!41\)\( T^{36} \))
$23$ (\( 1 + 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 6 T + 28 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 44 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T - 92 T^{3} + 529 T^{4} \))(\( 1 - 14 T + 119 T^{2} - 652 T^{3} + 2737 T^{4} - 7406 T^{5} + 12167 T^{6} \))(\( 1 - 118 T^{2} + 6135 T^{4} - 181696 T^{6} + 3245415 T^{8} - 33021238 T^{10} + 148035889 T^{12} \))(\( 1 - 214 T^{2} + 22679 T^{4} - 1596744 T^{6} + 84184463 T^{8} - 3537581064 T^{10} + 122756878141 T^{12} - 3589213546070 T^{14} + 89334432012112 T^{16} - 1898693965871030 T^{18} + 34352407535855581 T^{20} - 523688957718805896 T^{22} + 6592568242881889103 T^{24} - 66147533221326758856 T^{26} + \)\(49\!\cdots\!59\)\( T^{28} - \)\(24\!\cdots\!26\)\( T^{30} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} \))(\( ( 1 - 23 T^{2} + 529 T^{4} )^{2} \))(\( 1 + 8 T - 17 T^{2} - 64 T^{3} + 1850 T^{4} + 3260 T^{5} - 33689 T^{6} + 74980 T^{7} + 978650 T^{8} - 778688 T^{9} - 4757297 T^{10} + 51490744 T^{11} + 148035889 T^{12} \))(\( 1 - 8 T - T^{2} + 120 T^{3} + 170 T^{4} - 1112 T^{5} - 4297 T^{6} - 25576 T^{7} + 89930 T^{8} + 1460040 T^{9} - 279841 T^{10} - 51490744 T^{11} + 148035889 T^{12} \))(\( 1 - 8 T - 27 T^{2} + 192 T^{3} + 1575 T^{4} - 5756 T^{5} - 23066 T^{6} + 48700 T^{7} - 54019 T^{8} + 249988 T^{9} + 6209083 T^{10} + 5749724 T^{11} - 28576051 T^{12} + 592532900 T^{13} - 6454812506 T^{14} - 37047590308 T^{15} + 233156525175 T^{16} + 653726485824 T^{17} - 2114396602587 T^{18} - 14409221291704 T^{19} + 41426511213649 T^{20} \))(\( ( 1 + 10 T + 50 T^{2} + 230 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 8 T - T^{2} - 318 T^{3} - 1135 T^{4} + 2980 T^{5} + 39361 T^{6} + 68540 T^{7} - 600415 T^{8} - 3869106 T^{9} - 279841 T^{10} + 51490744 T^{11} + 148035889 T^{12} )^{2} \))(\( 1 + 19 T + 94 T^{2} - 364 T^{3} - 4934 T^{4} - 12944 T^{5} + 44670 T^{6} + 630217 T^{7} + 3232637 T^{8} + 217968 T^{9} - 91045708 T^{10} - 430615360 T^{11} + 84196748 T^{12} + 8365868928 T^{13} + 33581348290 T^{14} + 45796983038 T^{15} - 144611422188 T^{16} - 1864211343076 T^{17} - 11619108269332 T^{18} - 42876860890748 T^{19} - 76499442337452 T^{20} + 557211892623346 T^{21} + 9397438086821890 T^{22} + 53845601913650304 T^{23} + 12464140441088972 T^{24} - 1466170135597065920 T^{25} - 7129879099086223948 T^{26} + 392593643313767184 T^{27} + \)\(13\!\cdots\!13\)\( T^{28} + \)\(60\!\cdots\!59\)\( T^{29} + \)\(97\!\cdots\!70\)\( T^{30} - \)\(65\!\cdots\!52\)\( T^{31} - \)\(57\!\cdots\!06\)\( T^{32} - \)\(97\!\cdots\!48\)\( T^{33} + \)\(57\!\cdots\!34\)\( T^{34} + \)\(26\!\cdots\!57\)\( T^{35} + \)\(32\!\cdots\!69\)\( T^{36} \))(\( 1 - 8 T + 13 T^{2} + 20 T^{3} + 794 T^{4} - 8894 T^{5} + 44620 T^{6} - 76030 T^{7} - 348697 T^{8} - 785090 T^{9} + 27523733 T^{10} - 101765222 T^{11} - 302476000 T^{12} + 4014732254 T^{13} - 12572137619 T^{14} - 14995597814 T^{15} + 64743711756 T^{16} + 2079662840830 T^{17} - 17083611139087 T^{18} + 47832245339090 T^{19} + 34249423518924 T^{20} - 182451438602938 T^{21} - 3518199563438579 T^{22} + 25840193839907122 T^{23} - 44777303561164000 T^{24} - 346492817485204234 T^{25} + 2155410649841173973 T^{26} - 1414066942987986670 T^{27} - 14445300180665765353 T^{28} - 72442125894195869810 T^{29} + \)\(97\!\cdots\!20\)\( T^{30} - \)\(44\!\cdots\!02\)\( T^{31} + \)\(92\!\cdots\!46\)\( T^{32} + \)\(53\!\cdots\!40\)\( T^{33} + \)\(79\!\cdots\!93\)\( T^{34} - \)\(11\!\cdots\!24\)\( T^{35} + \)\(32\!\cdots\!69\)\( T^{36} \))
$29$ (\( 1 + 5 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 - 16 T + 119 T^{2} - 464 T^{3} + 841 T^{4} \))(\( 1 - 14 T + 101 T^{2} - 406 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 49 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 6 T - 4 T^{2} + 194 T^{3} - 116 T^{4} - 5046 T^{5} + 24389 T^{6} \))(\( ( 1 - 5 T + 82 T^{2} - 291 T^{3} + 2378 T^{4} - 4205 T^{5} + 24389 T^{6} )^{2} \))(\( ( 1 - 3 T + 78 T^{2} - 569 T^{3} + 3594 T^{4} - 31051 T^{5} + 181717 T^{6} - 931820 T^{7} + 6832480 T^{8} - 27022780 T^{9} + 152823997 T^{10} - 757302839 T^{11} + 2541967914 T^{12} - 11670843781 T^{13} + 46396219038 T^{14} - 51749628927 T^{15} + 500246412961 T^{16} )^{2} \))(\( 1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4} \))(\( 1 - T - 28 T^{2} - 29 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 35 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 30 T^{2} - 192 T^{3} - 1541 T^{4} - 5568 T^{5} + 25230 T^{6} + 195112 T^{7} + 707281 T^{8} \))(\( 1 + 7 T + 13 T^{2} + 46 T^{3} - 469 T^{4} - 5021 T^{5} - 19406 T^{6} - 145609 T^{7} - 394429 T^{8} + 1121894 T^{9} + 9194653 T^{10} + 143578043 T^{11} + 594823321 T^{12} \))(\( 1 - 10 T + 34 T^{2} - 76 T^{3} - 478 T^{4} + 10598 T^{5} - 76382 T^{6} + 307342 T^{7} - 401998 T^{8} - 1853564 T^{9} + 24047554 T^{10} - 205111490 T^{11} + 594823321 T^{12} \))(\( 1 + T - 95 T^{2} - 82 T^{3} + 4736 T^{4} + 3458 T^{5} - 162633 T^{6} - 116645 T^{7} + 4535747 T^{8} + 1675080 T^{9} - 123827076 T^{10} + 48577320 T^{11} + 3814563227 T^{12} - 2844854905 T^{13} - 115027230873 T^{14} + 70927553242 T^{15} + 2817083248256 T^{16} - 1414489857338 T^{17} - 47523409231295 T^{18} + 14507145975869 T^{19} + 420707233300201 T^{20} \))(\( ( 1 + 40 T^{2} + 841 T^{4} )^{2} \))(\( 1 - 2 T - 118 T^{2} - 61 T^{3} + 6359 T^{4} + 20645 T^{5} - 141187 T^{6} - 1423013 T^{7} - 2112377 T^{8} + 46855717 T^{9} + 277899604 T^{10} - 613421260 T^{11} - 10677579883 T^{12} - 17789216540 T^{13} + 233713566964 T^{14} + 1142764081913 T^{15} - 1494044116937 T^{16} - 29187631671937 T^{17} - 83981320222027 T^{18} + 356123696399305 T^{19} + 3181066940018999 T^{20} - 884935904528009 T^{21} - 49643453529423718 T^{22} - 24401019531411658 T^{23} + 353814783205469041 T^{24} \))(\( 1 + 4 T - 51 T^{2} - 579 T^{3} - 1214 T^{4} + 26250 T^{5} + 148683 T^{6} - 209901 T^{7} - 4679822 T^{8} - 12680244 T^{9} + 95608714 T^{10} + 242480516 T^{11} - 2375176587 T^{12} - 7243939876 T^{13} + 48280620694 T^{14} + 562413939767 T^{15} + 693667484295 T^{16} - 10502405541311 T^{17} - 61444790128505 T^{18} - 304569760698019 T^{19} + 583374354292095 T^{20} + 13716713576977363 T^{21} + 34147965685073014 T^{22} - 148581530143677524 T^{23} - 1412810425440785427 T^{24} + 4182758908342495444 T^{25} + 47827916226314142154 T^{26} - \)\(18\!\cdots\!36\)\( T^{27} - \)\(19\!\cdots\!22\)\( T^{28} - \)\(25\!\cdots\!29\)\( T^{29} + \)\(52\!\cdots\!03\)\( T^{30} + \)\(26\!\cdots\!50\)\( T^{31} - \)\(36\!\cdots\!34\)\( T^{32} - \)\(49\!\cdots\!71\)\( T^{33} - \)\(12\!\cdots\!71\)\( T^{34} + \)\(29\!\cdots\!36\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))(\( 1 + 6 T - 71 T^{2} - 679 T^{3} + 1326 T^{4} + 34252 T^{5} + 88405 T^{6} - 867289 T^{7} - 8027938 T^{8} - 681278 T^{9} + 325349830 T^{10} + 1194610606 T^{11} - 6989192779 T^{12} - 61491095320 T^{13} - 35442154336 T^{14} + 1740460758039 T^{15} + 9086251390251 T^{16} - 21170258850237 T^{17} - 364928839121169 T^{18} - 613937506656873 T^{19} + 7641537419201091 T^{20} + 42448097427813171 T^{21} - 25067562360920416 T^{22} - 1261253018281722680 T^{23} - 4157334859913999059 T^{24} + 20606885190919533254 T^{25} + \)\(16\!\cdots\!30\)\( T^{26} - 9883399396148080582 T^{27} - \)\(33\!\cdots\!38\)\( T^{28} - \)\(10\!\cdots\!81\)\( T^{29} + \)\(31\!\cdots\!05\)\( T^{30} + \)\(35\!\cdots\!28\)\( T^{31} + \)\(39\!\cdots\!06\)\( T^{32} - \)\(58\!\cdots\!71\)\( T^{33} - \)\(17\!\cdots\!91\)\( T^{34} + \)\(43\!\cdots\!54\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))
$31$ (\( 1 + 9 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 11 T + 31 T^{2} \))(\( 1 + 16 T + 123 T^{2} + 496 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 65 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 - 2 T + 61 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 + 54 T^{2} - 16 T^{3} + 1674 T^{4} + 29791 T^{6} \))(\( ( 1 + 9 T + 84 T^{2} + 423 T^{3} + 2604 T^{4} + 8649 T^{5} + 29791 T^{6} )^{2} \))(\( ( 1 - 25 T + 452 T^{2} - 5865 T^{3} + 63046 T^{4} - 563375 T^{5} + 4370993 T^{6} - 29418450 T^{7} + 174910256 T^{8} - 911971950 T^{9} + 4200524273 T^{10} - 16783504625 T^{11} + 58224304966 T^{12} - 167909970615 T^{13} + 401151663812 T^{14} - 687815352775 T^{15} + 852891037441 T^{16} )^{2} \))(\( ( 1 - 7 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( 1 + 10 T + 69 T^{2} + 310 T^{3} + 961 T^{4} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 - 12 T + 56 T^{2} - 312 T^{3} + 2319 T^{4} - 9672 T^{5} + 53816 T^{6} - 357492 T^{7} + 923521 T^{8} \))(\( 1 - 8 T - 39 T^{2} + 156 T^{3} + 3496 T^{4} - 7070 T^{5} - 90701 T^{6} - 219170 T^{7} + 3359656 T^{8} + 4647396 T^{9} - 36017319 T^{10} - 229033208 T^{11} + 887503681 T^{12} \))(\( 1 + 6 T - 55 T^{2} - 190 T^{3} + 3252 T^{4} + 5402 T^{5} - 96301 T^{6} + 167462 T^{7} + 3125172 T^{8} - 5660290 T^{9} - 50793655 T^{10} + 171774906 T^{11} + 887503681 T^{12} \))(\( 1 + 8 T - 13 T^{2} + 388 T^{3} + 4345 T^{4} - 8230 T^{5} + 52964 T^{6} + 1316242 T^{7} - 980339 T^{8} + 3056850 T^{9} + 278176459 T^{10} + 94762350 T^{11} - 942105779 T^{12} + 39212165422 T^{13} + 48913366244 T^{14} - 235617912730 T^{15} + 3856203493945 T^{16} + 10674894275068 T^{17} - 11087583486733 T^{18} + 211516977285368 T^{19} + 819628286980801 T^{20} \))(\( ( 1 - 8 T + 31 T^{2} )^{4} \))(\( 1 - 27 T + 253 T^{2} - 122 T^{3} - 18419 T^{4} + 174117 T^{5} - 494429 T^{6} - 4086333 T^{7} + 51528500 T^{8} - 237955904 T^{9} + 67393797 T^{10} + 6991353571 T^{11} - 55877035301 T^{12} + 216731960701 T^{13} + 64765438917 T^{14} - 7088944336064 T^{15} + 47587651848500 T^{16} - 116988244493283 T^{17} - 438807557493149 T^{18} + 4790413831164987 T^{19} - 15709400018625779 T^{20} - 3225633903601862 T^{21} + 207365956606142653 T^{22} - 686028876202930437 T^{23} + 787662783788549761 T^{24} \))(\( 1 + 13 T + 82 T^{2} + 105 T^{3} - 1391 T^{4} - 5662 T^{5} + 25298 T^{6} + 405809 T^{7} + 2689426 T^{8} + 18321725 T^{9} + 105862757 T^{10} + 271821692 T^{11} - 314337076 T^{12} - 5345100555 T^{13} + 22049757012 T^{14} + 354024484218 T^{15} + 2321550409047 T^{16} + 12194450118645 T^{17} + 57150223625159 T^{18} + 378027953677995 T^{19} + 2231009943094167 T^{20} + 10546743409338438 T^{21} + 20363413645479252 T^{22} - 153025690899278805 T^{23} - 278975312024776756 T^{24} + 7478525318995095812 T^{25} + 90289396644094484837 T^{26} + \)\(48\!\cdots\!75\)\( T^{27} + \)\(22\!\cdots\!26\)\( T^{28} + \)\(10\!\cdots\!79\)\( T^{29} + \)\(19\!\cdots\!78\)\( T^{30} - \)\(13\!\cdots\!42\)\( T^{31} - \)\(10\!\cdots\!11\)\( T^{32} + \)\(24\!\cdots\!55\)\( T^{33} + \)\(59\!\cdots\!42\)\( T^{34} + \)\(29\!\cdots\!43\)\( T^{35} + \)\(69\!\cdots\!41\)\( T^{36} \))(\( 1 + 5 T - 66 T^{2} - 503 T^{3} + 337 T^{4} + 12028 T^{5} + 33978 T^{6} + 406763 T^{7} + 2995682 T^{8} - 18538475 T^{9} - 206059741 T^{10} - 275557932 T^{11} + 1910953762 T^{12} + 11736742065 T^{13} + 105697996694 T^{14} + 712002834894 T^{15} - 316523157013 T^{16} - 20711586044207 T^{17} - 106673227770053 T^{18} - 642059167370417 T^{19} - 304178753889493 T^{20} + 21211276454327154 T^{21} + 97614319604839574 T^{22} + 336012960826936815 T^{23} + 1695978497995797922 T^{24} - 7581319048341178452 T^{25} - \)\(17\!\cdots\!81\)\( T^{26} - \)\(49\!\cdots\!25\)\( T^{27} + \)\(24\!\cdots\!82\)\( T^{28} + \)\(10\!\cdots\!53\)\( T^{29} + \)\(26\!\cdots\!58\)\( T^{30} + \)\(29\!\cdots\!48\)\( T^{31} + \)\(25\!\cdots\!77\)\( T^{32} - \)\(11\!\cdots\!53\)\( T^{33} - \)\(48\!\cdots\!46\)\( T^{34} + \)\(11\!\cdots\!55\)\( T^{35} + \)\(69\!\cdots\!41\)\( T^{36} \))
$37$ (\( 1 - 4 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 2 T + 48 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 72 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 60 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 53 T^{2} + 300 T^{3} + 1961 T^{4} + 10952 T^{5} + 50653 T^{6} \))(\( 1 - 82 T^{2} + 4015 T^{4} - 159016 T^{6} + 5496535 T^{8} - 153681202 T^{10} + 2565726409 T^{12} \))(\( 1 - 394 T^{2} + 77383 T^{4} - 10014624 T^{6} + 953289279 T^{8} - 70658881624 T^{10} + 4214634576301 T^{12} - 206262118894570 T^{14} + 8368262409986752 T^{16} - 282372840766666330 T^{18} + 7898903752154858461 T^{20} - \)\(18\!\cdots\!16\)\( T^{22} + \)\(33\!\cdots\!59\)\( T^{24} - \)\(48\!\cdots\!76\)\( T^{26} + \)\(50\!\cdots\!23\)\( T^{28} - \)\(35\!\cdots\!66\)\( T^{30} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 - 8 T + 27 T^{2} - 296 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( ( 1 - T + 37 T^{2} )( 1 + 11 T + 37 T^{2} ) \))(\( ( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} )^{2} \))(\( 1 - 16 T + 65 T^{2} - 444 T^{3} + 8518 T^{4} - 45206 T^{5} + 106681 T^{6} - 1672622 T^{7} + 11661142 T^{8} - 22489932 T^{9} + 121820465 T^{10} - 1109503312 T^{11} + 2565726409 T^{12} \))(\( 1 + 10 T - 13 T^{2} - 102 T^{3} + 2428 T^{4} - 322 T^{5} - 128591 T^{6} - 11914 T^{7} + 3323932 T^{8} - 5166606 T^{9} - 24364093 T^{10} + 693439570 T^{11} + 2565726409 T^{12} \))(\( 1 - 14 T + 49 T^{2} + 226 T^{3} - 2811 T^{4} + 16774 T^{5} - 31644 T^{6} - 434806 T^{7} + 2812513 T^{8} - 2824952 T^{9} - 16711059 T^{10} - 104523224 T^{11} + 3850330297 T^{12} - 22024228318 T^{13} - 59305950684 T^{14} + 1163175534718 T^{15} - 7212256935699 T^{16} + 21454604232058 T^{17} + 172111493242129 T^{18} - 1819464357131078 T^{19} + 4808584372417849 T^{20} \))(\( 1 - 1294 T^{4} + 1874161 T^{8} \))(\( ( 1 + 9 T + 165 T^{2} + 1279 T^{3} + 12099 T^{4} + 82177 T^{5} + 546535 T^{6} + 3040549 T^{7} + 16563531 T^{8} + 64785187 T^{9} + 309236565 T^{10} + 624095613 T^{11} + 2565726409 T^{12} )^{2} \))(\( ( 1 - T + 154 T^{2} - 284 T^{3} + 12699 T^{4} - 29079 T^{5} + 767754 T^{6} - 1693550 T^{7} + 36154572 T^{8} - 70746236 T^{9} + 1337719164 T^{10} - 2318469950 T^{11} + 38889043362 T^{12} - 54498727719 T^{13} + 880598909943 T^{14} - 728666300156 T^{15} + 14619509078482 T^{16} - 3512479453921 T^{17} + 129961739795077 T^{18} )^{2} \))(\( ( 1 + 9 T + 218 T^{2} + 1614 T^{3} + 23401 T^{4} + 151257 T^{5} + 1644298 T^{6} + 9291632 T^{7} + 82504230 T^{8} + 404531792 T^{9} + 3052656510 T^{10} + 12720244208 T^{11} + 83288626594 T^{12} + 283479970377 T^{13} + 1622717937757 T^{14} + 4141082424126 T^{15} + 20695149214994 T^{16} + 31612315085289 T^{17} + 129961739795077 T^{18} )^{2} \))
$41$ (\( 1 + 7 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( 1 + 2 T + 71 T^{2} + 82 T^{3} + 1681 T^{4} \))(\( 1 + 14 T + 107 T^{2} + 574 T^{3} + 1681 T^{4} \))(\( 1 - 2 T + 75 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 - 16 T + 148 T^{2} - 978 T^{3} + 6068 T^{4} - 26896 T^{5} + 68921 T^{6} \))(\( ( 1 + 5 T + 46 T^{2} + 225 T^{3} + 1886 T^{4} + 8405 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 - 19 T + 406 T^{2} - 5039 T^{3} + 63478 T^{4} - 587281 T^{5} + 5386299 T^{6} - 39029276 T^{7} + 278582162 T^{8} - 1600200316 T^{9} + 9054368619 T^{10} - 40475993801 T^{11} + 179373656758 T^{12} - 583799396839 T^{13} + 1928542321846 T^{14} - 3700331203739 T^{15} + 7984925229121 T^{16} )^{2} \))(\( ( 1 - 5 T + 41 T^{2} )^{2} \))(\( ( 1 - 5 T + 41 T^{2} )^{2} \))(\( ( 1 + 7 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 67 T^{2} + 410 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + T + 78 T^{2} + 109 T^{3} + 3198 T^{4} + 1681 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 + 5 T + 30 T^{2} + 241 T^{3} + 1230 T^{4} + 8405 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 + 3 T + 163 T^{2} + 398 T^{3} + 11909 T^{4} + 22481 T^{5} + 488269 T^{6} + 669038 T^{7} + 11234123 T^{8} + 8477283 T^{9} + 115856201 T^{10} )^{2} \))(\( ( 1 + 12 T + 41 T^{2} )^{4} \))(\( 1 - 14 T - 71 T^{2} + 1449 T^{3} + 8085 T^{4} - 145075 T^{5} - 261043 T^{6} + 7055293 T^{7} + 15992640 T^{8} - 312930646 T^{9} - 102994633 T^{10} + 3464301323 T^{11} + 16362105383 T^{12} + 142036354243 T^{13} - 173133978073 T^{14} - 21567493052966 T^{15} + 45191378399040 T^{16} + 817399443921893 T^{17} - 1239981461383363 T^{18} - 28253976283286075 T^{19} + 64558120477443285 T^{20} + 474376422936849489 T^{21} - 953008811020820471 T^{22} - 7704606444027478174 T^{23} + 22563490300366186081 T^{24} \))(\( 1 + 4 T - 76 T^{2} - 391 T^{3} + 1975 T^{4} + 9938 T^{5} - 26870 T^{6} + 433565 T^{7} + 4152628 T^{8} - 23937849 T^{9} - 280692273 T^{10} - 314064324 T^{11} + 5084566150 T^{12} + 15633564413 T^{13} + 29460875358 T^{14} + 1346278111323 T^{15} + 11524941557581 T^{16} - 48638796714869 T^{17} - 956776297373447 T^{18} - 1994190665309629 T^{19} + 19373426758293661 T^{20} + 92786833710492483 T^{21} + 83249392612497438 T^{22} + 1811245380978975013 T^{23} + 24152219232760042150 T^{24} - 61165369372547121444 T^{25} - \)\(22\!\cdots\!33\)\( T^{26} - \)\(78\!\cdots\!89\)\( T^{27} + \)\(55\!\cdots\!28\)\( T^{28} + \)\(23\!\cdots\!65\)\( T^{29} - \)\(60\!\cdots\!70\)\( T^{30} + \)\(91\!\cdots\!98\)\( T^{31} + \)\(74\!\cdots\!75\)\( T^{32} - \)\(60\!\cdots\!91\)\( T^{33} - \)\(48\!\cdots\!16\)\( T^{34} + \)\(10\!\cdots\!24\)\( T^{35} + \)\(10\!\cdots\!21\)\( T^{36} \))(\( 1 - 16 T - 52 T^{2} + 2313 T^{3} - 7721 T^{4} - 117110 T^{5} + 860282 T^{6} + 1872521 T^{7} - 38916852 T^{8} + 82707819 T^{9} + 1144968899 T^{10} - 8680504064 T^{11} - 18775033826 T^{12} + 451896528557 T^{13} - 387529241846 T^{14} - 14990466569601 T^{15} + 45356087778625 T^{16} + 236151025913079 T^{17} - 2271300748262055 T^{18} + 9682192062436239 T^{19} + 76243583555868625 T^{20} - 1033157946443470521 T^{21} - 1095065017967994806 T^{22} + 52355015043702031957 T^{23} - 89183367801801056066 T^{24} - \)\(16\!\cdots\!84\)\( T^{25} + \)\(91\!\cdots\!79\)\( T^{26} + \)\(27\!\cdots\!59\)\( T^{27} - \)\(52\!\cdots\!52\)\( T^{28} + \)\(10\!\cdots\!61\)\( T^{29} + \)\(19\!\cdots\!42\)\( T^{30} - \)\(10\!\cdots\!10\)\( T^{31} - \)\(29\!\cdots\!81\)\( T^{32} + \)\(35\!\cdots\!13\)\( T^{33} - \)\(33\!\cdots\!32\)\( T^{34} - \)\(41\!\cdots\!96\)\( T^{35} + \)\(10\!\cdots\!21\)\( T^{36} \))
$43$ (\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 + T^{2} )^{8} \))(\( 1 + 13 T + 43 T^{2} \))(\( 1 - 13 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + 6 T + 55 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 - 5 T - 22 T^{2} + 163 T^{3} - 946 T^{4} - 9245 T^{5} + 79507 T^{6} \))(\( 1 + 7 T + 14 T^{2} - 167 T^{3} + 602 T^{4} + 12943 T^{5} + 79507 T^{6} \))(\( 1 - 15 T + 13 T^{2} + 604 T^{3} + 2365 T^{4} - 59039 T^{5} + 101695 T^{6} + 1116796 T^{7} + 1033591 T^{8} - 51282015 T^{9} + 147008443 T^{10} \))(\( 1 + 12 T + 72 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 - 14 T + 134 T^{2} - 1176 T^{3} + 10648 T^{4} - 73696 T^{5} + 480257 T^{6} - 3168928 T^{7} + 19688152 T^{8} - 93500232 T^{9} + 458119334 T^{10} - 2058118202 T^{11} + 6321363049 T^{12} \))(\( 1 + 13 T + 23 T^{2} + 341 T^{3} + 7465 T^{4} - 3559 T^{5} - 300996 T^{6} + 568061 T^{7} - 6089961 T^{8} - 178982555 T^{9} - 261868323 T^{10} + 1050344789 T^{11} - 23931288972 T^{12} - 12167512759 T^{13} + 1097418026995 T^{14} + 2155584799709 T^{15} + 6251828055461 T^{16} + 151946603608813 T^{17} + 502592611936843 T^{18} \))(\( 1 + 13 T + 135 T^{2} + 173 T^{3} - 5485 T^{4} - 91815 T^{5} - 487924 T^{6} - 685681 T^{7} + 23032937 T^{8} + 203701481 T^{9} + 990416291 T^{10} - 1267824169 T^{11} - 38793373468 T^{12} - 313897213815 T^{13} - 806341309855 T^{14} + 1093595807477 T^{15} + 36695512499445 T^{16} + 151946603608813 T^{17} + 502592611936843 T^{18} \))
$47$ (\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 14 T + 140 T^{2} - 658 T^{3} + 2209 T^{4} \))(\( 1 + 88 T^{2} + 2209 T^{4} \))(\( 1 + 44 T^{2} + 2209 T^{4} \))(\( 1 + 2 T + 135 T^{2} + 180 T^{3} + 6345 T^{4} + 4418 T^{5} + 103823 T^{6} \))(\( 1 - 170 T^{2} + 15279 T^{4} - 888968 T^{6} + 33751311 T^{8} - 829545770 T^{10} + 10779215329 T^{12} \))(\( 1 - 482 T^{2} + 116711 T^{4} - 18746928 T^{6} + 2228078775 T^{8} - 207244774732 T^{10} + 15578128441725 T^{12} - 964122051100670 T^{14} + 49615909496598816 T^{16} - 2129745610881380030 T^{18} + 76016297372645089725 T^{20} - \)\(22\!\cdots\!28\)\( T^{22} + \)\(53\!\cdots\!75\)\( T^{24} - \)\(98\!\cdots\!72\)\( T^{26} + \)\(13\!\cdots\!51\)\( T^{28} - \)\(12\!\cdots\!58\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( ( 1 + 3 T + 47 T^{2} )^{2} \))(\( ( 1 - T + 47 T^{2} )^{2} \))(\( ( 1 - 6 T + 47 T^{2} )^{2} \))(\( ( 1 - 4 T + 58 T^{2} - 188 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 9 T + 72 T^{2} + 297 T^{3} + 3384 T^{4} + 19881 T^{5} + 103823 T^{6} )^{2} \))(\( ( 1 - 4 T + 130 T^{2} - 350 T^{3} + 6110 T^{4} - 8836 T^{5} + 103823 T^{6} )^{2} \))(\( ( 1 + 11 T + 106 T^{2} + 41 T^{3} - 3215 T^{4} - 52196 T^{5} - 151105 T^{6} + 90569 T^{7} + 11005238 T^{8} + 53676491 T^{9} + 229345007 T^{10} )^{2} \))(\( ( 1 + 10 T + 50 T^{2} + 470 T^{3} + 2209 T^{4} )^{2} \))(\( 1 - 2 T + 95 T^{2} + 486 T^{3} + 4126 T^{4} + 57824 T^{5} + 308156 T^{6} + 3836880 T^{7} + 21611017 T^{8} + 212259114 T^{9} + 1535272757 T^{10} + 8731117266 T^{11} + 89844070544 T^{12} + 410362511502 T^{13} + 3391417520213 T^{14} + 22037377992822 T^{15} + 105454869045577 T^{16} + 879969270458160 T^{17} + 3321679878923324 T^{18} + 29294975317652512 T^{19} + 98245368766425886 T^{20} + 543897409927944762 T^{21} + 4996917562403854655 T^{22} - 4944318430168024606 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 - 16 T + 58 T^{2} + 132 T^{3} + 2174 T^{4} - 59622 T^{5} + 583964 T^{6} - 2362132 T^{7} - 6973035 T^{8} - 13171090 T^{9} + 1946977070 T^{10} - 15462631128 T^{11} + 23862188930 T^{12} + 232936464174 T^{13} + 476845081058 T^{14} - 35831178696668 T^{15} + 291005595210458 T^{16} - 336150127799338 T^{17} - 5856096864612524 T^{18} - 15799056006568886 T^{19} + 642831359819901722 T^{20} - 3720100465824161764 T^{21} + 2326851881982182498 T^{22} + 53422815006541279218 T^{23} + \)\(25\!\cdots\!70\)\( T^{24} - \)\(78\!\cdots\!64\)\( T^{25} + \)\(46\!\cdots\!70\)\( T^{26} - \)\(14\!\cdots\!30\)\( T^{27} - \)\(36\!\cdots\!15\)\( T^{28} - \)\(58\!\cdots\!96\)\( T^{29} + \)\(67\!\cdots\!24\)\( T^{30} - \)\(32\!\cdots\!94\)\( T^{31} + \)\(55\!\cdots\!06\)\( T^{32} + \)\(15\!\cdots\!76\)\( T^{33} + \)\(32\!\cdots\!18\)\( T^{34} - \)\(42\!\cdots\!92\)\( T^{35} + \)\(12\!\cdots\!89\)\( T^{36} \))(\( 1 + 36 T + 612 T^{2} + 6578 T^{3} + 56686 T^{4} + 524814 T^{5} + 5385180 T^{6} + 49774124 T^{7} + 394711081 T^{8} + 3091549542 T^{9} + 26602209040 T^{10} + 226026429292 T^{11} + 1707793138576 T^{12} + 12049342225310 T^{13} + 89717535794078 T^{14} + 702257335176408 T^{15} + 5175913711157672 T^{16} + 34826239488864972 T^{17} + 232179354339637252 T^{18} + 1636833255976653684 T^{19} + 11433593387947297448 T^{20} + 72910463310020207784 T^{21} + \)\(43\!\cdots\!18\)\( T^{22} + \)\(27\!\cdots\!70\)\( T^{23} + \)\(18\!\cdots\!04\)\( T^{24} + \)\(11\!\cdots\!96\)\( T^{25} + \)\(63\!\cdots\!40\)\( T^{26} + \)\(34\!\cdots\!14\)\( T^{27} + \)\(20\!\cdots\!69\)\( T^{28} + \)\(12\!\cdots\!72\)\( T^{29} + \)\(62\!\cdots\!80\)\( T^{30} + \)\(28\!\cdots\!78\)\( T^{31} + \)\(14\!\cdots\!34\)\( T^{32} + \)\(79\!\cdots\!54\)\( T^{33} + \)\(34\!\cdots\!52\)\( T^{34} + \)\(95\!\cdots\!32\)\( T^{35} + \)\(12\!\cdots\!89\)\( T^{36} \))
$53$ (\( 1 + 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 4 T + 98 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 - 8 T + 26 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( 1 + 74 T^{2} + 2809 T^{4} \))(\( 1 - 22 T + 223 T^{2} - 1644 T^{3} + 11819 T^{4} - 61798 T^{5} + 148877 T^{6} \))(\( 1 - 138 T^{2} + 14295 T^{4} - 854556 T^{6} + 40154655 T^{8} - 1088886378 T^{10} + 22164361129 T^{12} \))(\( 1 - 576 T^{2} + 154696 T^{4} - 25836080 T^{6} + 3031271836 T^{8} - 269432012400 T^{10} + 19302108479096 T^{12} - 1183214040569248 T^{14} + 65349852889172742 T^{16} - 3323648239959017632 T^{18} + \)\(15\!\cdots\!76\)\( T^{20} - \)\(59\!\cdots\!00\)\( T^{22} + \)\(18\!\cdots\!96\)\( T^{24} - \)\(45\!\cdots\!20\)\( T^{26} + \)\(75\!\cdots\!36\)\( T^{28} - \)\(79\!\cdots\!44\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 10 T + 47 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 + 4 T - 37 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 - 8 T - 18 T^{2} + 192 T^{3} + 523 T^{4} + 10176 T^{5} - 50562 T^{6} - 1191016 T^{7} + 7890481 T^{8} \))(\( 1 - 8 T - 71 T^{2} + 328 T^{3} + 5438 T^{4} - 3032 T^{5} - 352331 T^{6} - 160696 T^{7} + 15275342 T^{8} + 48831656 T^{9} - 560224151 T^{10} - 3345563944 T^{11} + 22164361129 T^{12} \))(\( 1 - 8 T - 51 T^{2} + 360 T^{3} + 2010 T^{4} + 1448 T^{5} - 173347 T^{6} + 76744 T^{7} + 5646090 T^{8} + 53595720 T^{9} - 402414531 T^{10} - 3345563944 T^{11} + 22164361129 T^{12} \))(\( 1 + 8 T + 31 T^{2} + 520 T^{3} + 3871 T^{4} - 2352 T^{5} + 98098 T^{6} + 852976 T^{7} - 7861235 T^{8} - 76503880 T^{9} - 119377183 T^{10} - 4054705640 T^{11} - 22082209115 T^{12} + 126988507952 T^{13} + 774040405138 T^{14} - 983595799536 T^{15} + 85798241930359 T^{16} + 610849792715240 T^{17} + 1930050402752191 T^{18} + 26398108734417064 T^{19} + 174887470365513049 T^{20} \))(\( ( 1 + 2809 T^{4} )^{2} \))(\( 1 - 2 T - 192 T^{2} + 831 T^{3} + 14431 T^{4} - 117825 T^{5} - 365313 T^{6} + 9752081 T^{7} - 30260439 T^{8} - 531160493 T^{9} + 4601458502 T^{10} + 12612277558 T^{11} - 319965750843 T^{12} + 668450710574 T^{13} + 12925496932118 T^{14} - 79077580716361 T^{15} - 238769418981159 T^{16} + 4078276321570933 T^{17} - 8096929257118377 T^{18} - 138410340051294525 T^{19} + 898469592326350591 T^{20} + 2742103544787572523 T^{21} - 33578394310178505408 T^{22} - 18538071858744383194 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - 14 T + 153 T^{2} - 1705 T^{3} + 14214 T^{4} - 166466 T^{5} + 1703087 T^{6} - 15265377 T^{7} + 137855194 T^{8} - 1013052036 T^{9} + 8625510462 T^{10} - 71977968032 T^{11} + 565915051273 T^{12} - 4612841434870 T^{13} + 31009525649816 T^{14} - 229284034127169 T^{15} + 1720930523999681 T^{16} - 12770176509314833 T^{17} + 101981507436118171 T^{18} - 676819354993686149 T^{19} + 4834093841915103929 T^{20} - 34135119148750539213 T^{21} + \)\(24\!\cdots\!96\)\( T^{22} - \)\(19\!\cdots\!10\)\( T^{23} + \)\(12\!\cdots\!17\)\( T^{24} - \)\(84\!\cdots\!84\)\( T^{25} + \)\(53\!\cdots\!82\)\( T^{26} - \)\(33\!\cdots\!88\)\( T^{27} + \)\(24\!\cdots\!06\)\( T^{28} - \)\(14\!\cdots\!69\)\( T^{29} + \)\(83\!\cdots\!67\)\( T^{30} - \)\(43\!\cdots\!18\)\( T^{31} + \)\(19\!\cdots\!66\)\( T^{32} - \)\(12\!\cdots\!85\)\( T^{33} + \)\(59\!\cdots\!13\)\( T^{34} - \)\(28\!\cdots\!82\)\( T^{35} + \)\(10\!\cdots\!89\)\( T^{36} \))(\( 1 + 18 T + 219 T^{2} + 1873 T^{3} + 21028 T^{4} + 191940 T^{5} + 1927031 T^{6} + 16691841 T^{7} + 157628752 T^{8} + 1143000974 T^{9} + 9987462820 T^{10} + 79427444768 T^{11} + 685958917601 T^{12} + 4783166371000 T^{13} + 40313855954708 T^{14} + 280316920456111 T^{15} + 2208536845954869 T^{16} + 15550871535373675 T^{17} + 128962261045140095 T^{18} + 824196191374804775 T^{19} + 6203780000287227021 T^{20} + 41732742166744437347 T^{21} + \)\(31\!\cdots\!48\)\( T^{22} + \)\(20\!\cdots\!00\)\( T^{23} + \)\(15\!\cdots\!29\)\( T^{24} + \)\(93\!\cdots\!16\)\( T^{25} + \)\(62\!\cdots\!20\)\( T^{26} + \)\(37\!\cdots\!42\)\( T^{27} + \)\(27\!\cdots\!48\)\( T^{28} + \)\(15\!\cdots\!77\)\( T^{29} + \)\(94\!\cdots\!71\)\( T^{30} + \)\(49\!\cdots\!20\)\( T^{31} + \)\(29\!\cdots\!32\)\( T^{32} + \)\(13\!\cdots\!61\)\( T^{33} + \)\(84\!\cdots\!99\)\( T^{34} + \)\(36\!\cdots\!34\)\( T^{35} + \)\(10\!\cdots\!89\)\( T^{36} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 20 T + 206 T^{2} + 1180 T^{3} + 3481 T^{4} \))(\( 1 + 94 T^{2} + 3481 T^{4} \))(\( 1 + 8 T + 126 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 16 T + 201 T^{2} - 1536 T^{3} + 11859 T^{4} - 55696 T^{5} + 205379 T^{6} \))(\( ( 1 + 20 T + 249 T^{2} + 2088 T^{3} + 14691 T^{4} + 69620 T^{5} + 205379 T^{6} )^{2} \))(\( ( 1 - 12 T + 376 T^{2} - 3324 T^{3} + 61004 T^{4} - 432892 T^{5} + 6064456 T^{6} - 36188204 T^{7} + 421065286 T^{8} - 2135104036 T^{9} + 21110371336 T^{10} - 88906926068 T^{11} + 739207490444 T^{12} - 2376408369876 T^{13} + 15859880649016 T^{14} - 29863817817828 T^{15} + 146830437604321 T^{16} )^{2} \))(\( ( 1 - 2 T + 59 T^{2} )^{2} \))(\( ( 1 - 14 T + 59 T^{2} )^{2} \))(\( ( 1 + 3 T + 59 T^{2} )^{2} \))(\( ( 1 - 14 T + 157 T^{2} - 826 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 12 T + 153 T^{2} + 984 T^{3} + 9027 T^{4} + 41772 T^{5} + 205379 T^{6} )^{2} \))(\( ( 1 - 3 T + 97 T^{2} + 2 T^{3} + 5723 T^{4} - 10443 T^{5} + 205379 T^{6} )^{2} \))(\( ( 1 - 4 T + 232 T^{2} - 856 T^{3} + 24811 T^{4} - 72008 T^{5} + 1463849 T^{6} - 2979736 T^{7} + 47647928 T^{8} - 48469444 T^{9} + 714924299 T^{10} )^{2} \))(\( ( 1 - 59 T^{2} )^{4} \))(\( 1 - 4 T - 111 T^{2} + 373 T^{3} + 10187 T^{4} - 53634 T^{5} - 308525 T^{6} + 3531028 T^{7} - 13046963 T^{8} - 215283643 T^{9} + 3379492827 T^{10} + 4284465948 T^{11} - 240376275189 T^{12} + 252783490932 T^{13} + 11764014530787 T^{14} - 44214739315697 T^{15} - 158094760624643 T^{16} + 2524417717649372 T^{17} - 13013749141589525 T^{18} - 133476333736782246 T^{19} + 1495761667875218027 T^{20} + 3231297440358292247 T^{21} - 56733959616371195511 T^{22} - \)\(12\!\cdots\!36\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 + 16 T + 110 T^{2} + 53 T^{3} - 9107 T^{4} - 138521 T^{5} - 1133458 T^{6} - 6642925 T^{7} - 15509483 T^{8} + 216413994 T^{9} + 3934924448 T^{10} + 39080271562 T^{11} + 325806014415 T^{12} + 2377170408214 T^{13} + 12590066317713 T^{14} - 2478684438573 T^{15} - 789252526438949 T^{16} - 11177472533604662 T^{17} - 102361406567292607 T^{18} - 659470879482675058 T^{19} - 2747388044533981469 T^{20} - 509069731309684167 T^{21} + \)\(15\!\cdots\!93\)\( T^{22} + \)\(16\!\cdots\!86\)\( T^{23} + \)\(13\!\cdots\!15\)\( T^{24} + \)\(97\!\cdots\!78\)\( T^{25} + \)\(57\!\cdots\!08\)\( T^{26} + \)\(18\!\cdots\!66\)\( T^{27} - \)\(79\!\cdots\!83\)\( T^{28} - \)\(20\!\cdots\!75\)\( T^{29} - \)\(20\!\cdots\!98\)\( T^{30} - \)\(14\!\cdots\!59\)\( T^{31} - \)\(56\!\cdots\!27\)\( T^{32} + \)\(19\!\cdots\!47\)\( T^{33} + \)\(23\!\cdots\!10\)\( T^{34} + \)\(20\!\cdots\!04\)\( T^{35} + \)\(75\!\cdots\!21\)\( T^{36} \))(\( 1 + 4 T + 182 T^{2} + 889 T^{3} + 19535 T^{4} + 92775 T^{5} + 1403700 T^{6} + 3337697 T^{7} + 60900249 T^{8} - 100866924 T^{9} + 279379214 T^{10} - 22396990778 T^{11} - 136590509711 T^{12} - 1169980179938 T^{13} - 4940983425545 T^{14} + 7131058308663 T^{15} + 145810789722975 T^{16} + 5887152771171894 T^{17} + 24165780228834877 T^{18} + 347342013499141746 T^{19} + 507567359025675975 T^{20} + 1464569624374898277 T^{21} - 59871679862345386745 T^{22} - \)\(83\!\cdots\!62\)\( T^{23} - \)\(57\!\cdots\!51\)\( T^{24} - \)\(55\!\cdots\!82\)\( T^{25} + \)\(41\!\cdots\!94\)\( T^{26} - \)\(87\!\cdots\!36\)\( T^{27} + \)\(31\!\cdots\!49\)\( T^{28} + \)\(10\!\cdots\!23\)\( T^{29} + \)\(24\!\cdots\!00\)\( T^{30} + \)\(97\!\cdots\!25\)\( T^{31} + \)\(12\!\cdots\!35\)\( T^{32} + \)\(32\!\cdots\!11\)\( T^{33} + \)\(39\!\cdots\!62\)\( T^{34} + \)\(50\!\cdots\!76\)\( T^{35} + \)\(75\!\cdots\!21\)\( T^{36} \))
$61$ (\( 1 + 7 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 + 3 T + 61 T^{2} \))(\( 1 + 119 T^{2} + 3721 T^{4} \))(\( 1 + 2 T + 117 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( 1 + 14 T + 121 T^{2} + 854 T^{3} + 3721 T^{4} \))(\( 1 + 2 T + 84 T^{2} - 118 T^{3} + 5124 T^{4} + 7442 T^{5} + 226981 T^{6} \))(\( ( 1 + 21 T + 272 T^{2} + 2329 T^{3} + 16592 T^{4} + 78141 T^{5} + 226981 T^{6} )^{2} \))(\( ( 1 - 29 T + 693 T^{2} - 10726 T^{3} + 148982 T^{4} - 1635184 T^{5} + 16908739 T^{6} - 147864185 T^{7} + 1244942418 T^{8} - 9019715285 T^{9} + 62917417819 T^{10} - 371155699504 T^{11} + 2062781083862 T^{12} - 9059139924526 T^{13} + 35703619432173 T^{14} - 91139542244609 T^{15} + 191707312997281 T^{16} )^{2} \))(\( 1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( 1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( ( 1 + T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 - 4 T - 100 T^{2} + 24 T^{3} + 8759 T^{4} + 1464 T^{5} - 372100 T^{6} - 907924 T^{7} + 13845841 T^{8} \))(\( 1 - 12 T - 63 T^{2} + 308 T^{3} + 13470 T^{4} - 30576 T^{5} - 746835 T^{6} - 1865136 T^{7} + 50121870 T^{8} + 69910148 T^{9} - 872287983 T^{10} - 10135155612 T^{11} + 51520374361 T^{12} \))(\( 1 + 4 T + 17 T^{2} + 1516 T^{3} + 3102 T^{4} + 16132 T^{5} + 971965 T^{6} + 984052 T^{7} + 11542542 T^{8} + 344103196 T^{9} + 235379297 T^{10} + 3378385204 T^{11} + 51520374361 T^{12} \))(\( 1 + 14 T + 45 T^{2} - 806 T^{3} - 8787 T^{4} - 17696 T^{5} + 772476 T^{6} + 8884756 T^{7} + 31411545 T^{8} - 248377590 T^{9} - 3246005175 T^{10} - 15151032990 T^{11} + 116882358945 T^{12} + 2016670801636 T^{13} + 10695579872316 T^{14} - 14945976142496 T^{15} - 452709529510107 T^{16} - 2533050725832926 T^{17} + 8626829084877645 T^{18} + 163718045299677974 T^{19} + 713342911662882601 T^{20} \))(\( ( 1 - 104 T^{2} + 3721 T^{4} )^{2} \))(\( 1 - 16 T - 66 T^{2} + 2397 T^{3} - 3126 T^{4} - 170243 T^{5} + 586028 T^{6} + 11035274 T^{7} - 81228727 T^{8} - 525242399 T^{9} + 7900192381 T^{10} + 10108936107 T^{11} - 527396641733 T^{12} + 616645102527 T^{13} + 29396615849701 T^{14} - 119220044967419 T^{15} - 1124680038674407 T^{16} + 9320351600921474 T^{17} + 30192381946028108 T^{18} - 535029968632723103 T^{19} - 599277060429500406 T^{20} + 28030868184523435977 T^{21} - 47080632169750251666 T^{22} - \)\(69\!\cdots\!76\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 24 T + 193 T^{2} - 1023 T^{3} + 12269 T^{4} - 101120 T^{5} + 137341 T^{6} + 6279714 T^{7} - 66107156 T^{8} - 91531315 T^{9} + 3450816819 T^{10} - 8829436552 T^{11} + 246170019400 T^{12} - 4618272414559 T^{13} + 35328002089660 T^{14} - 91573533385944 T^{15} - 1045706406860373 T^{16} + 6388716443127935 T^{17} + 8003958918844677 T^{18} + 389711703030804035 T^{19} - 3891073539927447933 T^{20} - 20785452181474955064 T^{21} + \)\(48\!\cdots\!60\)\( T^{22} - \)\(39\!\cdots\!59\)\( T^{23} + \)\(12\!\cdots\!00\)\( T^{24} - \)\(27\!\cdots\!92\)\( T^{25} + \)\(66\!\cdots\!39\)\( T^{26} - \)\(10\!\cdots\!15\)\( T^{27} - \)\(47\!\cdots\!56\)\( T^{28} + \)\(27\!\cdots\!54\)\( T^{29} + \)\(36\!\cdots\!61\)\( T^{30} - \)\(16\!\cdots\!20\)\( T^{31} + \)\(12\!\cdots\!29\)\( T^{32} - \)\(61\!\cdots\!23\)\( T^{33} + \)\(70\!\cdots\!73\)\( T^{34} - \)\(53\!\cdots\!04\)\( T^{35} + \)\(13\!\cdots\!81\)\( T^{36} \))(\( 1 - 42 T + 933 T^{2} - 14861 T^{3} + 192423 T^{4} - 2141538 T^{5} + 21336371 T^{6} - 196037772 T^{7} + 1665767448 T^{8} - 12759457459 T^{9} + 83761862657 T^{10} - 415805126156 T^{11} + 730146937632 T^{12} + 16028186575331 T^{13} - 292933998347776 T^{14} + 3505813369714012 T^{15} - 35535339534952817 T^{16} + 322709127419838593 T^{17} - 2650994802911766219 T^{18} + 19685256772610154173 T^{19} - \)\(13\!\cdots\!57\)\( T^{20} + \)\(79\!\cdots\!72\)\( T^{21} - \)\(40\!\cdots\!16\)\( T^{22} + \)\(13\!\cdots\!31\)\( T^{23} + \)\(37\!\cdots\!52\)\( T^{24} - \)\(13\!\cdots\!76\)\( T^{25} + \)\(16\!\cdots\!17\)\( T^{26} - \)\(14\!\cdots\!19\)\( T^{27} + \)\(11\!\cdots\!48\)\( T^{28} - \)\(85\!\cdots\!92\)\( T^{29} + \)\(56\!\cdots\!91\)\( T^{30} - \)\(34\!\cdots\!78\)\( T^{31} + \)\(19\!\cdots\!43\)\( T^{32} - \)\(89\!\cdots\!61\)\( T^{33} + \)\(34\!\cdots\!13\)\( T^{34} - \)\(94\!\cdots\!82\)\( T^{35} + \)\(13\!\cdots\!81\)\( T^{36} \))
$67$ (\( 1 - 15 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 + 107 T^{2} + 4489 T^{4} \))(\( 1 + 6 T + 137 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 - 6 T + 125 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 + 24 T + 350 T^{2} + 3340 T^{3} + 23450 T^{4} + 107736 T^{5} + 300763 T^{6} \))(\( 1 - 87 T^{2} + 978 T^{4} + 259189 T^{6} + 4390242 T^{8} - 1753147527 T^{10} + 90458382169 T^{12} \))(\( 1 - 461 T^{2} + 124889 T^{4} - 23767026 T^{6} + 3523375680 T^{8} - 423196090940 T^{10} + 42444100674783 T^{12} - 3599926920976653 T^{14} + 260857140941399214 T^{16} - 16160071948264195317 T^{18} + \)\(85\!\cdots\!43\)\( T^{20} - \)\(38\!\cdots\!60\)\( T^{22} + \)\(14\!\cdots\!80\)\( T^{24} - \)\(43\!\cdots\!74\)\( T^{26} + \)\(10\!\cdots\!29\)\( T^{28} - \)\(16\!\cdots\!69\)\( T^{30} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 5 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( 1 - 3 T - 58 T^{2} - 201 T^{3} + 4489 T^{4} \))(\( 1 - 3 T - 58 T^{2} - 201 T^{3} + 4489 T^{4} \))(\( 1 + 2 T + 29 T^{2} - 318 T^{3} - 4132 T^{4} - 21306 T^{5} + 130181 T^{6} + 601526 T^{7} + 20151121 T^{8} \))(\( 1 + 7 T - 27 T^{2} + 474 T^{3} + 481 T^{4} - 37661 T^{5} - 4586 T^{6} - 2523287 T^{7} + 2159209 T^{8} + 142561662 T^{9} - 544080267 T^{10} + 9450875749 T^{11} + 90458382169 T^{12} \))(\( 1 - 9 T - 21 T^{2} - 72 T^{3} - 237 T^{4} + 39465 T^{5} - 280222 T^{6} + 2644155 T^{7} - 1063893 T^{8} - 21654936 T^{9} - 423173541 T^{10} - 12151125963 T^{11} + 90458382169 T^{12} \))(\( 1 - 19 T + 54 T^{2} - 221 T^{3} + 14098 T^{4} - 32577 T^{5} - 397044 T^{6} - 4826483 T^{7} + 18752721 T^{8} + 110914612 T^{9} + 927211540 T^{10} + 7431279004 T^{11} + 84180964569 T^{12} - 1451627506529 T^{13} - 8000881686324 T^{14} - 43983025610739 T^{15} + 1275282271818562 T^{16} - 1339417264776383 T^{17} + 21927654588058614 T^{18} - 516924153529603993 T^{19} + 1822837804551761449 T^{20} \))(\( ( 1 + 4 T + 8 T^{2} + 268 T^{3} + 4489 T^{4} )^{2} \))(\( 1 - 9 T - 148 T^{2} + 2384 T^{3} + 2552 T^{4} - 283635 T^{5} + 1159511 T^{6} + 20567317 T^{7} - 175592461 T^{8} - 922488196 T^{9} + 15849512297 T^{10} + 19004289445 T^{11} - 1127214234705 T^{12} + 1273287392815 T^{13} + 71148460701233 T^{14} - 277450317293548 T^{15} - 3538384928298781 T^{16} + 27768451065327919 T^{17} + 104887489167159359 T^{18} - 1719029936175789105 T^{19} + 1036284713124547832 T^{20} + 64860378000767153648 T^{21} - \)\(26\!\cdots\!52\)\( T^{22} - \)\(10\!\cdots\!47\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 - 5 T - 243 T^{2} + 2637 T^{3} + 14043 T^{4} - 432442 T^{5} + 2109906 T^{6} + 27147279 T^{7} - 406935575 T^{8} + 400811603 T^{9} + 30519003442 T^{10} - 202859948048 T^{11} - 1206933969243 T^{12} + 21871443321101 T^{13} - 24381765716161 T^{14} - 1594432006027610 T^{15} + 11273924333523498 T^{16} + 50256293453176677 T^{17} - 1103332578696118791 T^{18} + 3367171661362837359 T^{19} + 50608646333186982522 T^{20} - \)\(47\!\cdots\!30\)\( T^{21} - \)\(49\!\cdots\!81\)\( T^{22} + \)\(29\!\cdots\!07\)\( T^{23} - \)\(10\!\cdots\!67\)\( T^{24} - \)\(12\!\cdots\!04\)\( T^{25} + \)\(12\!\cdots\!22\)\( T^{26} + \)\(10\!\cdots\!41\)\( T^{27} - \)\(74\!\cdots\!75\)\( T^{28} + \)\(33\!\cdots\!57\)\( T^{29} + \)\(17\!\cdots\!66\)\( T^{30} - \)\(23\!\cdots\!54\)\( T^{31} + \)\(51\!\cdots\!47\)\( T^{32} + \)\(64\!\cdots\!91\)\( T^{33} - \)\(40\!\cdots\!83\)\( T^{34} - \)\(55\!\cdots\!35\)\( T^{35} + \)\(74\!\cdots\!09\)\( T^{36} \))(\( 1 + 19 T - 121 T^{2} - 3509 T^{3} + 17241 T^{4} + 454616 T^{5} - 1635832 T^{6} - 44808601 T^{7} + 41507781 T^{8} + 3267974565 T^{9} + 6835163934 T^{10} - 240159436956 T^{11} - 1558153168075 T^{12} + 15530120367369 T^{13} + 158968204106237 T^{14} - 817261224750396 T^{15} - 11907700881595164 T^{16} + 24442230601190901 T^{17} + 850574669249442709 T^{18} + 1637629450279790367 T^{19} - 53453669257480691196 T^{20} - \)\(24\!\cdots\!48\)\( T^{21} + \)\(32\!\cdots\!77\)\( T^{22} + \)\(20\!\cdots\!83\)\( T^{23} - \)\(14\!\cdots\!75\)\( T^{24} - \)\(14\!\cdots\!88\)\( T^{25} + \)\(27\!\cdots\!94\)\( T^{26} + \)\(88\!\cdots\!55\)\( T^{27} + \)\(75\!\cdots\!69\)\( T^{28} - \)\(54\!\cdots\!83\)\( T^{29} - \)\(13\!\cdots\!52\)\( T^{30} + \)\(24\!\cdots\!92\)\( T^{31} + \)\(63\!\cdots\!89\)\( T^{32} - \)\(86\!\cdots\!87\)\( T^{33} - \)\(19\!\cdots\!01\)\( T^{34} + \)\(20\!\cdots\!13\)\( T^{35} + \)\(74\!\cdots\!09\)\( T^{36} \))
$71$ (\( 1 + 6 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 10 T + 164 T^{2} + 710 T^{3} + 5041 T^{4} \))(\( 1 - 12 T + 124 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( 1 - 4 T + 48 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 + 6 T + 191 T^{2} + 868 T^{3} + 13561 T^{4} + 30246 T^{5} + 357911 T^{6} \))(\( ( 1 + 8 T + 159 T^{2} + 930 T^{3} + 11289 T^{4} + 40328 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 - 12 T + 350 T^{2} - 3178 T^{3} + 57608 T^{4} - 469734 T^{5} + 6497602 T^{6} - 47379416 T^{7} + 534124718 T^{8} - 3363938536 T^{9} + 32754411682 T^{10} - 168122965674 T^{11} + 1463916119048 T^{12} - 5733840877478 T^{13} + 44835099372350 T^{14} - 109141441900692 T^{15} + 645753531245761 T^{16} )^{2} \))(\( 1 + 8 T - 7 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 + 10 T + 29 T^{2} + 710 T^{3} + 5041 T^{4} \))(\( 1 + 6 T - 35 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 + 16 T + 60 T^{2} + 864 T^{3} + 15199 T^{4} + 61344 T^{5} + 302460 T^{6} + 5726576 T^{7} + 25411681 T^{8} \))(\( 1 + 12 T - 99 T^{2} - 528 T^{3} + 21132 T^{4} + 64866 T^{5} - 1237277 T^{6} + 4605486 T^{7} + 106526412 T^{8} - 188977008 T^{9} - 2515756419 T^{10} + 21650752212 T^{11} + 128100283921 T^{12} \))(\( 1 - 4 T - 155 T^{2} + 580 T^{3} + 14572 T^{4} - 31108 T^{5} - 1041521 T^{6} - 2208668 T^{7} + 73457452 T^{8} + 207588380 T^{9} - 3938810555 T^{10} - 7216917404 T^{11} + 128100283921 T^{12} \))(\( 1 - 36 T + 567 T^{2} - 5968 T^{3} + 54917 T^{4} - 373762 T^{5} + 748760 T^{6} + 12952414 T^{7} - 202612107 T^{8} + 2525412690 T^{9} - 25391593021 T^{10} + 179304300990 T^{11} - 1021367631387 T^{12} + 4635811447154 T^{13} + 19027250265560 T^{14} - 674352370688462 T^{15} + 7034883292089557 T^{16} - 54279677105277488 T^{17} + 366142252216346487 T^{18} - 1650546025864165116 T^{19} + 3255243551009881201 T^{20} \))(\( ( 1 - 110 T^{2} + 5041 T^{4} )^{2} \))(\( 1 - 27 T + 253 T^{2} + 79 T^{3} - 26059 T^{4} + 245632 T^{5} - 262147 T^{6} - 14158898 T^{7} + 170058639 T^{8} - 1116863367 T^{9} + 2185060299 T^{10} + 53608272881 T^{11} - 740263984961 T^{12} + 3806187374551 T^{13} + 11014888967259 T^{14} - 399737684546337 T^{15} + 4321475885562159 T^{16} - 25545899349415198 T^{17} - 33581105129038387 T^{18} + 2234052554745898112 T^{19} - 16827691270733285899 T^{20} + 3622031556757473449 T^{21} + \)\(82\!\cdots\!53\)\( T^{22} - \)\(62\!\cdots\!17\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 3 T + 202 T^{2} - 152 T^{3} + 27691 T^{4} - 92044 T^{5} + 2694570 T^{6} - 19553968 T^{7} + 262197087 T^{8} - 2018099301 T^{9} + 27616454078 T^{10} - 171467755434 T^{11} + 2659217155551 T^{12} - 13109941104883 T^{13} + 220898323319547 T^{14} - 1195438763913623 T^{15} + 14974987479690423 T^{16} - 102503631929816908 T^{17} + 1048608441396878449 T^{18} - 7277757867017000468 T^{19} + 75488911885119422343 T^{20} - \)\(42\!\cdots\!53\)\( T^{21} + \)\(56\!\cdots\!07\)\( T^{22} - \)\(23\!\cdots\!33\)\( T^{23} + \)\(34\!\cdots\!71\)\( T^{24} - \)\(15\!\cdots\!94\)\( T^{25} + \)\(17\!\cdots\!58\)\( T^{26} - \)\(92\!\cdots\!31\)\( T^{27} + \)\(85\!\cdots\!87\)\( T^{28} - \)\(45\!\cdots\!28\)\( T^{29} + \)\(44\!\cdots\!70\)\( T^{30} - \)\(10\!\cdots\!84\)\( T^{31} + \)\(22\!\cdots\!71\)\( T^{32} - \)\(89\!\cdots\!52\)\( T^{33} + \)\(84\!\cdots\!42\)\( T^{34} + \)\(88\!\cdots\!73\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))(\( 1 + 27 T + 192 T^{2} - 3064 T^{3} - 71457 T^{4} - 431170 T^{5} + 3006306 T^{6} + 66658940 T^{7} + 407727641 T^{8} - 36960119 T^{9} - 18346711662 T^{10} - 203539733210 T^{11} - 1941959274995 T^{12} - 10817050171315 T^{13} + 59547414301229 T^{14} + 1594397690229843 T^{15} + 9439982388216595 T^{16} - 39777894586305512 T^{17} - 893741411732820099 T^{18} - 2824230515627691352 T^{19} + 47586951218999855395 T^{20} + \)\(57\!\cdots\!73\)\( T^{21} + \)\(15\!\cdots\!49\)\( T^{22} - \)\(19\!\cdots\!65\)\( T^{23} - \)\(24\!\cdots\!95\)\( T^{24} - \)\(18\!\cdots\!10\)\( T^{25} - \)\(11\!\cdots\!82\)\( T^{26} - \)\(16\!\cdots\!89\)\( T^{27} + \)\(13\!\cdots\!41\)\( T^{28} + \)\(15\!\cdots\!40\)\( T^{29} + \)\(49\!\cdots\!46\)\( T^{30} - \)\(50\!\cdots\!70\)\( T^{31} - \)\(59\!\cdots\!17\)\( T^{32} - \)\(17\!\cdots\!64\)\( T^{33} + \)\(80\!\cdots\!32\)\( T^{34} + \)\(79\!\cdots\!57\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))
$73$ (\( 1 + 5 T + 73 T^{2} \))(\( 1 + T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 - 7 T + 73 T^{2} \))(\( 1 - 8 T + 135 T^{2} - 584 T^{3} + 5329 T^{4} \))(\( 1 + 10 T + 165 T^{2} + 730 T^{3} + 5329 T^{4} \))(\( 1 + 10 T + 153 T^{2} + 730 T^{3} + 5329 T^{4} \))(\( 1 + 10 T + 68 T^{2} - 42 T^{3} + 4964 T^{4} + 53290 T^{5} + 389017 T^{6} \))(\( 1 - 51 T^{2} + 5858 T^{4} - 385823 T^{6} + 31217282 T^{8} - 1448310291 T^{10} + 151334226289 T^{12} \))(\( 1 - 905 T^{2} + 395545 T^{4} - 111083010 T^{6} + 22471297760 T^{8} - 3475557609012 T^{10} + 425393441711119 T^{12} - 42042952532589265 T^{14} + 3391469041132093230 T^{16} - \)\(22\!\cdots\!85\)\( T^{18} + \)\(12\!\cdots\!79\)\( T^{20} - \)\(52\!\cdots\!68\)\( T^{22} + \)\(18\!\cdots\!60\)\( T^{24} - \)\(47\!\cdots\!90\)\( T^{26} + \)\(90\!\cdots\!45\)\( T^{28} - \)\(11\!\cdots\!45\)\( T^{30} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 + 8 T - 9 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( 1 - 14 T + 123 T^{2} - 1022 T^{3} + 5329 T^{4} \))(\( 1 - 11 T + 48 T^{2} - 803 T^{3} + 5329 T^{4} \))(\( 1 + 6 T - 109 T^{2} - 6 T^{3} + 13068 T^{4} - 438 T^{5} - 580861 T^{6} + 2334102 T^{7} + 28398241 T^{8} \))(\( 1 + 14 T + 11 T^{2} - 702 T^{3} - 2324 T^{4} + 976 T^{5} - 55559 T^{6} + 71248 T^{7} - 12384596 T^{8} - 273089934 T^{9} + 312380651 T^{10} + 29023002302 T^{11} + 151334226289 T^{12} \))(\( 1 - 21 T + 132 T^{2} - 473 T^{3} + 9756 T^{4} - 93987 T^{5} + 505896 T^{6} - 6861051 T^{7} + 51989724 T^{8} - 184005041 T^{9} + 3748567812 T^{10} - 43534503453 T^{11} + 151334226289 T^{12} \))(\( 1 - 28 T + 130 T^{2} + 788 T^{3} + 40731 T^{4} - 647242 T^{5} - 299136 T^{6} - 781424 T^{7} + 698093137 T^{8} - 3419792278 T^{9} - 15252313914 T^{10} - 249644836294 T^{11} + 3720138327073 T^{12} - 303987220208 T^{13} - 8494936219776 T^{14} - 1341779003996506 T^{15} + 6163994370977259 T^{16} + 8705350033048436 T^{17} + 104839811946230530 T^{18} - 1648404427831501564 T^{19} + 4297625829703557649 T^{20} \))(\( ( 1 - 24 T + 288 T^{2} - 1752 T^{3} + 5329 T^{4} )( 1 + 24 T + 288 T^{2} + 1752 T^{3} + 5329 T^{4} ) \))(\( 1 - 28 T + 505 T^{2} - 6083 T^{3} + 51071 T^{4} - 242501 T^{5} - 627567 T^{6} + 22785623 T^{7} - 200315116 T^{8} + 258559266 T^{9} + 17601898277 T^{10} - 299053047825 T^{11} + 3088299490395 T^{12} - 21830872491225 T^{13} + 93800515918133 T^{14} + 100583949981522 T^{15} - 5688596940110956 T^{16} + 47236227770107439 T^{17} - 94972366389508863 T^{18} - 2679005188279541597 T^{19} + 41186723353122610751 T^{20} - \)\(35\!\cdots\!79\)\( T^{21} + \)\(21\!\cdots\!45\)\( T^{22} - \)\(87\!\cdots\!56\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 + 22 T + 272 T^{2} + 2669 T^{3} + 31125 T^{4} + 309208 T^{5} + 1961900 T^{6} + 14213181 T^{7} + 190802684 T^{8} + 2015970959 T^{9} + 10963042915 T^{10} + 81525488566 T^{11} + 933068681880 T^{12} + 3934730546441 T^{13} - 34153795489790 T^{14} - 225081571812169 T^{15} + 1756036748972213 T^{16} - 803992448271191 T^{17} - 175608418784800179 T^{18} - 58691448723796943 T^{19} + 9357919835272923077 T^{20} - 87560557821654547873 T^{21} - \)\(96\!\cdots\!90\)\( T^{22} + \)\(81\!\cdots\!13\)\( T^{23} + \)\(14\!\cdots\!20\)\( T^{24} + \)\(90\!\cdots\!02\)\( T^{25} + \)\(88\!\cdots\!15\)\( T^{26} + \)\(11\!\cdots\!67\)\( T^{27} + \)\(81\!\cdots\!16\)\( T^{28} + \)\(44\!\cdots\!37\)\( T^{29} + \)\(44\!\cdots\!00\)\( T^{30} + \)\(51\!\cdots\!64\)\( T^{31} + \)\(37\!\cdots\!25\)\( T^{32} + \)\(23\!\cdots\!33\)\( T^{33} + \)\(17\!\cdots\!92\)\( T^{34} + \)\(10\!\cdots\!66\)\( T^{35} + \)\(34\!\cdots\!69\)\( T^{36} \))(\( 1 - 28 T + 206 T^{2} + 1439 T^{3} - 30467 T^{4} + 115902 T^{5} + 1193696 T^{6} - 12456075 T^{7} - 52758690 T^{8} + 1181272439 T^{9} + 858716819 T^{10} - 81754299384 T^{11} - 22479646170 T^{12} + 7830326968241 T^{13} - 27470831061776 T^{14} - 692066597072037 T^{15} + 6983730927869749 T^{16} + 20546869285875433 T^{17} - 650284685443406899 T^{18} + 1499921457868906609 T^{19} + 37216302114617892421 T^{20} - \)\(26\!\cdots\!29\)\( T^{21} - \)\(78\!\cdots\!16\)\( T^{22} + \)\(16\!\cdots\!13\)\( T^{23} - \)\(34\!\cdots\!30\)\( T^{24} - \)\(90\!\cdots\!48\)\( T^{25} + \)\(69\!\cdots\!39\)\( T^{26} + \)\(69\!\cdots\!07\)\( T^{27} - \)\(22\!\cdots\!10\)\( T^{28} - \)\(39\!\cdots\!75\)\( T^{29} + \)\(27\!\cdots\!16\)\( T^{30} + \)\(19\!\cdots\!66\)\( T^{31} - \)\(37\!\cdots\!03\)\( T^{32} + \)\(12\!\cdots\!23\)\( T^{33} + \)\(13\!\cdots\!66\)\( T^{34} - \)\(13\!\cdots\!84\)\( T^{35} + \)\(34\!\cdots\!69\)\( T^{36} \))
$79$ (\( 1 - 9 T + 79 T^{2} \))(\( 1 - 9 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 - 7 T + 79 T^{2} \))(\( 1 + 4 T + 15 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 - 18 T + 233 T^{2} - 1422 T^{3} + 6241 T^{4} \))(\( 1 + 14 T + 205 T^{2} + 1106 T^{3} + 6241 T^{4} \))(\( 1 + 4 T + 202 T^{2} + 640 T^{3} + 15958 T^{4} + 24964 T^{5} + 493039 T^{6} \))(\( ( 1 - 9 T + 234 T^{2} - 1361 T^{3} + 18486 T^{4} - 56169 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 + 5 T + 234 T^{2} + 995 T^{3} + 29332 T^{4} + 88335 T^{5} + 2715965 T^{6} + 3567410 T^{7} + 217842536 T^{8} + 281825390 T^{9} + 16950337565 T^{10} + 43552600065 T^{11} + 1142483775892 T^{12} + 3061671117005 T^{13} + 56882464591914 T^{14} + 96019544930795 T^{15} + 1517108809906561 T^{16} )^{2} \))(\( 1 - 79 T^{2} + 6241 T^{4} \))(\( 1 + 16 T + 177 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 - 6 T - 43 T^{2} - 474 T^{3} + 6241 T^{4} \))(\( 1 - 148 T^{2} + 15663 T^{4} - 923668 T^{6} + 38950081 T^{8} \))(\( 1 + 4 T - 45 T^{2} + 132 T^{3} - 1322 T^{4} - 10172 T^{5} + 595399 T^{6} - 803588 T^{7} - 8250602 T^{8} + 65081148 T^{9} - 1752753645 T^{10} + 12308225596 T^{11} + 243087455521 T^{12} \))(\( 1 - 4 T - 125 T^{2} + 444 T^{3} + 6726 T^{4} - 6916 T^{5} - 430361 T^{6} - 546364 T^{7} + 41976966 T^{8} + 218909316 T^{9} - 4868760125 T^{10} - 12308225596 T^{11} + 243087455521 T^{12} \))(\( 1 + 10 T + 3 T^{2} - 790 T^{3} - 11175 T^{4} + 7900 T^{5} - 88976 T^{6} - 5523320 T^{7} - 28654919 T^{8} + 457995090 T^{9} + 11536331579 T^{10} + 36181612110 T^{11} - 178835349479 T^{12} - 2723212169480 T^{13} - 3465622407056 T^{14} + 24308745552100 T^{15} - 2716502315447175 T^{16} - 15171088099065610 T^{17} + 4551326429719683 T^{18} + 1198515959826183190 T^{19} + 9468276082626847201 T^{20} \))(\( ( 1 - 58 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 - 5 T + 368 T^{2} - 975 T^{3} + 57067 T^{4} - 71424 T^{5} + 5407867 T^{6} - 5642496 T^{7} + 356155147 T^{8} - 480713025 T^{9} + 14333629808 T^{10} - 15385281995 T^{11} + 243087455521 T^{12} )^{2} \))(\( ( 1 + 19 T + 531 T^{2} + 7400 T^{3} + 109592 T^{4} + 1180276 T^{5} + 11765861 T^{6} + 107015700 T^{7} + 850808559 T^{8} + 7993181266 T^{9} + 67213876161 T^{10} + 667884983700 T^{11} + 5801028341579 T^{12} + 45971845802356 T^{13} + 337220764879208 T^{14} + 1798847170855400 T^{15} + 10197275671650429 T^{16} + 28825067388224659 T^{17} + 119851595982618319 T^{18} )^{2} \))(\( ( 1 + 13 T + 473 T^{2} + 3826 T^{3} + 90460 T^{4} + 498762 T^{5} + 11312861 T^{6} + 50578492 T^{7} + 1144441533 T^{8} + 4524834638 T^{9} + 90410881107 T^{10} + 315660368572 T^{11} + 5577681674579 T^{12} + 19426820299722 T^{13} + 278350521853540 T^{14} + 930052604823346 T^{15} + 9083448950453207 T^{16} + 19722414528785293 T^{17} + 119851595982618319 T^{18} )^{2} \))
$83$ (\( 1 + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 154 T^{2} + 6889 T^{4} \))(\( ( 1 - 6 T + 83 T^{2} )^{2} \))(\( 1 + 4 T + 138 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 - 4 T + 157 T^{2} - 168 T^{3} + 13031 T^{4} - 27556 T^{5} + 571787 T^{6} \))(\( 1 + 34 T^{2} + 7719 T^{4} + 448204 T^{6} + 53176191 T^{8} + 1613582914 T^{10} + 326940373369 T^{12} \))(\( 1 - 580 T^{2} + 173632 T^{4} - 35649596 T^{6} + 5673283660 T^{8} - 749699370772 T^{10} + 85546383012736 T^{12} - 8573159301594284 T^{14} + 757692623249501222 T^{16} - 59060494428683022476 T^{18} + \)\(40\!\cdots\!56\)\( T^{20} - \)\(24\!\cdots\!68\)\( T^{22} + \)\(12\!\cdots\!60\)\( T^{24} - \)\(55\!\cdots\!04\)\( T^{26} + \)\(18\!\cdots\!52\)\( T^{28} - \)\(42\!\cdots\!20\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 + 11 T + 38 T^{2} + 913 T^{3} + 6889 T^{4} \))(\( 1 - 15 T + 142 T^{2} - 1245 T^{3} + 6889 T^{4} \))(\( 1 + 12 T + 61 T^{2} + 996 T^{3} + 6889 T^{4} \))(\( ( 1 + 6 T - 47 T^{2} + 498 T^{3} + 6889 T^{4} )^{2} \))(\( 1 - 15 T + 3 T^{2} + 1164 T^{3} - 2847 T^{4} - 49389 T^{5} + 551986 T^{6} - 4099287 T^{7} - 19612983 T^{8} + 665560068 T^{9} + 142374963 T^{10} - 59085609645 T^{11} + 326940373369 T^{12} \))(\( 1 - 10 T - 112 T^{2} + 816 T^{3} + 12668 T^{4} - 28186 T^{5} - 1120654 T^{6} - 2339438 T^{7} + 87269852 T^{8} + 466578192 T^{9} - 5315331952 T^{10} - 39390406430 T^{11} + 326940373369 T^{12} \))(\( 1 + 25 T + 191 T^{2} + 240 T^{3} + 2762 T^{4} + 155288 T^{5} + 1413133 T^{6} - 7730059 T^{7} - 182939905 T^{8} - 397129048 T^{9} + 6416763512 T^{10} - 32961710984 T^{11} - 1260273005545 T^{12} - 4419947245433 T^{13} + 67064919529693 T^{14} + 611685743370184 T^{15} + 903009311245178 T^{16} + 6512652237510480 T^{17} + 430187816338556831 T^{18} + 4673506381688510075 T^{19} + 15516041187205853449 T^{20} \))(\( ( 1 - 12 T + 72 T^{2} - 996 T^{3} + 6889 T^{4} )^{2} \))(\( 1 + 31 T + 452 T^{2} + 2892 T^{3} - 8490 T^{4} - 345229 T^{5} - 2667420 T^{6} - 6265342 T^{7} + 19930908 T^{8} - 246940166 T^{9} + 1158607142 T^{10} + 136753954064 T^{11} + 2035262795035 T^{12} + 11350578187312 T^{13} + 7981644601238 T^{14} - 141197176696642 T^{15} + 945887429685468 T^{16} - 24679436780294906 T^{17} - 872087290731937980 T^{18} - 9368151747097939583 T^{19} - 19121961050860458090 T^{20} + \)\(54\!\cdots\!76\)\( T^{21} + \)\(70\!\cdots\!48\)\( T^{22} + \)\(39\!\cdots\!77\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + 26 T + 41 T^{2} - 4688 T^{3} - 28457 T^{4} + 507415 T^{5} + 4946122 T^{6} - 38886347 T^{7} - 708143290 T^{8} - 839183842 T^{9} + 54673401155 T^{10} + 460215646841 T^{11} - 1917272402872 T^{12} - 58344829035493 T^{13} - 162190885833500 T^{14} + 4674551351114112 T^{15} + 42143643054278062 T^{16} - 154094583853300240 T^{17} - 4385792214629651212 T^{18} - 12789850459823919920 T^{19} + \)\(29\!\cdots\!18\)\( T^{20} + \)\(26\!\cdots\!44\)\( T^{21} - \)\(76\!\cdots\!00\)\( T^{22} - \)\(22\!\cdots\!99\)\( T^{23} - \)\(62\!\cdots\!68\)\( T^{24} + \)\(12\!\cdots\!07\)\( T^{25} + \)\(12\!\cdots\!55\)\( T^{26} - \)\(15\!\cdots\!26\)\( T^{27} - \)\(10\!\cdots\!10\)\( T^{28} - \)\(50\!\cdots\!49\)\( T^{29} + \)\(52\!\cdots\!42\)\( T^{30} + \)\(45\!\cdots\!45\)\( T^{31} - \)\(20\!\cdots\!53\)\( T^{32} - \)\(28\!\cdots\!16\)\( T^{33} + \)\(20\!\cdots\!21\)\( T^{34} + \)\(10\!\cdots\!98\)\( T^{35} + \)\(34\!\cdots\!09\)\( T^{36} \))(\( 1 - 62 T + 1955 T^{2} - 43474 T^{3} + 791403 T^{4} - 12660991 T^{5} + 182312666 T^{6} - 2380818115 T^{7} + 28454173700 T^{8} - 313999851042 T^{9} + 3203343358059 T^{10} - 30029118019905 T^{11} + 256415447656186 T^{12} - 1966785367099865 T^{13} + 13121718252161262 T^{14} - 70231361214705904 T^{15} + 228113352519056074 T^{16} + 528279145154473206 T^{17} - 13256029529997156100 T^{18} + 43847169047821276098 T^{19} + \)\(15\!\cdots\!86\)\( T^{20} - \)\(40\!\cdots\!48\)\( T^{21} + \)\(62\!\cdots\!02\)\( T^{22} - \)\(77\!\cdots\!95\)\( T^{23} + \)\(83\!\cdots\!34\)\( T^{24} - \)\(81\!\cdots\!35\)\( T^{25} + \)\(72\!\cdots\!19\)\( T^{26} - \)\(58\!\cdots\!26\)\( T^{27} + \)\(44\!\cdots\!00\)\( T^{28} - \)\(30\!\cdots\!05\)\( T^{29} + \)\(19\!\cdots\!26\)\( T^{30} - \)\(11\!\cdots\!33\)\( T^{31} + \)\(58\!\cdots\!87\)\( T^{32} - \)\(26\!\cdots\!18\)\( T^{33} + \)\(99\!\cdots\!55\)\( T^{34} - \)\(26\!\cdots\!26\)\( T^{35} + \)\(34\!\cdots\!09\)\( T^{36} \))
$89$ (\( 1 + 89 T^{2} \))(\( 1 - 4 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 40 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 64 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 + 4 T + 132 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 + 16 T + 121 T^{2} + 444 T^{3} + 10769 T^{4} + 126736 T^{5} + 704969 T^{6} \))(\( ( 1 - 14 T - T^{2} + 1286 T^{3} - 89 T^{4} - 110894 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 - 20 T + 460 T^{2} - 5698 T^{3} + 87296 T^{4} - 929226 T^{5} + 12020020 T^{6} - 113397072 T^{7} + 1243372926 T^{8} - 10092339408 T^{9} + 95210578420 T^{10} - 655075523994 T^{11} + 5477146670336 T^{12} - 31817970740402 T^{13} + 228611393842060 T^{14} - 884626697910580 T^{15} + 3936588805702081 T^{16} )^{2} \))(\( 1 + 13 T + 80 T^{2} + 1157 T^{3} + 7921 T^{4} \))(\( 1 - 3 T - 80 T^{2} - 267 T^{3} + 7921 T^{4} \))(\( 1 + 15 T + 136 T^{2} + 1335 T^{3} + 7921 T^{4} \))(\( ( 1 + 3 T - 80 T^{2} + 267 T^{3} + 7921 T^{4} )^{2} \))(\( 1 + 15 T + 75 T^{2} - 876 T^{3} - 14295 T^{4} - 47235 T^{5} + 68182 T^{6} - 4203915 T^{7} - 113230695 T^{8} - 617552844 T^{9} + 4705668075 T^{10} + 83760891735 T^{11} + 496981290961 T^{12} \))(\( 1 - 7 T - 169 T^{2} + 792 T^{3} + 20009 T^{4} - 36481 T^{5} - 1864546 T^{6} - 3246809 T^{7} + 158491289 T^{8} + 558335448 T^{9} - 10603438729 T^{10} - 39088416143 T^{11} + 496981290961 T^{12} \))(\( 1 - 19 T + 62 T^{2} - 165 T^{3} + 5234 T^{4} + 112771 T^{5} - 1360484 T^{6} - 1913717 T^{7} + 39369557 T^{8} - 1124166758 T^{9} + 20476807868 T^{10} - 100050841462 T^{11} + 311846260997 T^{12} - 1349111159773 T^{13} - 85359815004644 T^{14} + 629719968123179 T^{15} + 2601200076889874 T^{16} - 7298170257762285 T^{17} + 244068505953529022 T^{18} - 6656771670442218971 T^{19} + 31181719929966183601 T^{20} \))(\( ( 1 - 22 T^{2} + 7921 T^{4} )^{2} \))(\( 1 + 38 T + 521 T^{2} + 2967 T^{3} + 18241 T^{4} + 334174 T^{5} + 2136543 T^{6} - 2477584 T^{7} + 111400957 T^{8} + 2189866865 T^{9} + 11128069385 T^{10} + 269872470160 T^{11} + 4501464216545 T^{12} + 24018649844240 T^{13} + 88145437598585 T^{14} + 1543788253952185 T^{15} + 6989545691724637 T^{16} - 13834976345891216 T^{17} + 1061821898333687823 T^{18} + 14780962107378508046 T^{19} + 71807316404811659521 T^{20} + \)\(10\!\cdots\!03\)\( T^{21} + \)\(16\!\cdots\!21\)\( T^{22} + \)\(10\!\cdots\!82\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 - 52 T + 1128 T^{2} - 13153 T^{3} + 81467 T^{4} + 68453 T^{5} - 9458026 T^{6} + 132595253 T^{7} - 801617131 T^{8} - 3309701708 T^{9} + 120931060118 T^{10} - 1201000189794 T^{11} + 3658479374927 T^{12} + 72912524472654 T^{13} - 1364925845819525 T^{14} + 10187321088410209 T^{15} + 12050739011899131 T^{16} - 1203687248326207182 T^{17} + 15537143357929513709 T^{18} - \)\(10\!\cdots\!98\)\( T^{19} + 95453903713253016651 T^{20} + \)\(71\!\cdots\!21\)\( T^{21} - \)\(85\!\cdots\!25\)\( T^{22} + \)\(40\!\cdots\!46\)\( T^{23} + \)\(18\!\cdots\!47\)\( T^{24} - \)\(53\!\cdots\!26\)\( T^{25} + \)\(47\!\cdots\!58\)\( T^{26} - \)\(11\!\cdots\!72\)\( T^{27} - \)\(24\!\cdots\!31\)\( T^{28} + \)\(36\!\cdots\!17\)\( T^{29} - \)\(23\!\cdots\!46\)\( T^{30} + \)\(15\!\cdots\!57\)\( T^{31} + \)\(15\!\cdots\!47\)\( T^{32} - \)\(22\!\cdots\!97\)\( T^{33} + \)\(17\!\cdots\!08\)\( T^{34} - \)\(71\!\cdots\!08\)\( T^{35} + \)\(12\!\cdots\!81\)\( T^{36} \))(\( 1 + 12 T + 116 T^{2} + 1499 T^{3} + 3935 T^{4} - 42611 T^{5} - 1895934 T^{6} - 26145279 T^{7} - 209446975 T^{8} - 2196428168 T^{9} - 7262368198 T^{10} + 44027191578 T^{11} + 1289869174743 T^{12} + 22210109524986 T^{13} + 120472292193179 T^{14} + 920900716991509 T^{15} + 1767591597163055 T^{16} - 97723090524153866 T^{17} - 862701798538908603 T^{18} - 8697355056649694074 T^{19} + 14001093041128558655 T^{20} + \)\(64\!\cdots\!21\)\( T^{21} + \)\(75\!\cdots\!39\)\( T^{22} + \)\(12\!\cdots\!14\)\( T^{23} + \)\(64\!\cdots\!23\)\( T^{24} + \)\(19\!\cdots\!62\)\( T^{25} - \)\(28\!\cdots\!38\)\( T^{26} - \)\(76\!\cdots\!12\)\( T^{27} - \)\(65\!\cdots\!75\)\( T^{28} - \)\(72\!\cdots\!31\)\( T^{29} - \)\(46\!\cdots\!14\)\( T^{30} - \)\(93\!\cdots\!59\)\( T^{31} + \)\(76\!\cdots\!35\)\( T^{32} + \)\(26\!\cdots\!51\)\( T^{33} + \)\(17\!\cdots\!76\)\( T^{34} + \)\(16\!\cdots\!48\)\( T^{35} + \)\(12\!\cdots\!81\)\( T^{36} \))
$97$ (\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 + 6 T - 40 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( 1 + 28 T + 384 T^{2} + 2716 T^{3} + 9409 T^{4} \))(\( 1 + 4 T - 44 T^{2} + 388 T^{3} + 9409 T^{4} \))(\( 1 + 8 T + 233 T^{2} + 1260 T^{3} + 22601 T^{4} + 75272 T^{5} + 912673 T^{6} \))(\( 1 - 510 T^{2} + 114171 T^{4} - 14374424 T^{6} + 1074234939 T^{8} - 45149933310 T^{10} + 832972004929 T^{12} \))(\( 1 - 774 T^{2} + 301691 T^{4} - 79641640 T^{6} + 16078651115 T^{8} - 2644465230904 T^{10} + 367166336275261 T^{12} - 43893175395348070 T^{14} + 4560761585591764624 T^{16} - \)\(41\!\cdots\!30\)\( T^{18} + \)\(32\!\cdots\!41\)\( T^{20} - \)\(22\!\cdots\!16\)\( T^{22} + \)\(12\!\cdots\!15\)\( T^{24} - \)\(58\!\cdots\!60\)\( T^{26} + \)\(20\!\cdots\!31\)\( T^{28} - \)\(50\!\cdots\!06\)\( T^{30} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( ( 1 + 8 T + 97 T^{2} )^{2} \))(\( ( 1 + 12 T + 97 T^{2} )^{2} \))(\( ( 1 - 7 T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 233 T^{2} - 1358 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 10 T + 239 T^{2} + 1612 T^{3} + 23183 T^{4} + 94090 T^{5} + 912673 T^{6} )^{2} \))(\( ( 1 - 5 T + 155 T^{2} - 538 T^{3} + 15035 T^{4} - 47045 T^{5} + 912673 T^{6} )^{2} \))(\( ( 1 - 10 T + 318 T^{2} - 2434 T^{3} + 47465 T^{4} - 293384 T^{5} + 4604105 T^{6} - 22901506 T^{7} + 290230014 T^{8} - 885292810 T^{9} + 8587340257 T^{10} )^{2} \))(\( ( 1 - 18 T + 162 T^{2} - 1746 T^{3} + 9409 T^{4} )^{2} \))(\( 1 + 15 T - 61 T^{2} - 908 T^{3} + 14954 T^{4} + 129879 T^{5} + 769775 T^{6} + 22467776 T^{7} + 57832976 T^{8} - 1013973842 T^{9} + 16680785489 T^{10} + 212073098570 T^{11} + 697406047257 T^{12} + 20571090561290 T^{13} + 156949510666001 T^{14} - 925426548299666 T^{15} + 5119911783370256 T^{16} + 192938437330058432 T^{17} + 641201025094220975 T^{18} + 10494000389732838327 T^{19} + \)\(11\!\cdots\!94\)\( T^{20} - \)\(69\!\cdots\!36\)\( T^{21} - \)\(44\!\cdots\!89\)\( T^{22} + \)\(10\!\cdots\!95\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 27 T + 66 T^{2} + 6423 T^{3} - 102424 T^{4} + 202528 T^{5} + 13832941 T^{6} - 194404750 T^{7} + 369359831 T^{8} + 18779122634 T^{9} - 227205754104 T^{10} + 306742101966 T^{11} + 18629760587417 T^{12} - 187413939377042 T^{13} - 64509572163695 T^{14} + 16124698263546201 T^{15} - 117486606211482490 T^{16} - 549881906918518023 T^{17} + 14838596816271178503 T^{18} - 53338544971096248231 T^{19} - \)\(11\!\cdots\!10\)\( T^{20} + \)\(14\!\cdots\!73\)\( T^{21} - \)\(57\!\cdots\!95\)\( T^{22} - \)\(16\!\cdots\!94\)\( T^{23} + \)\(15\!\cdots\!93\)\( T^{24} + \)\(24\!\cdots\!58\)\( T^{25} - \)\(17\!\cdots\!44\)\( T^{26} + \)\(14\!\cdots\!78\)\( T^{27} + \)\(27\!\cdots\!19\)\( T^{28} - \)\(13\!\cdots\!50\)\( T^{29} + \)\(95\!\cdots\!81\)\( T^{30} + \)\(13\!\cdots\!56\)\( T^{31} - \)\(66\!\cdots\!56\)\( T^{32} + \)\(40\!\cdots\!39\)\( T^{33} + \)\(40\!\cdots\!86\)\( T^{34} - \)\(16\!\cdots\!99\)\( T^{35} + \)\(57\!\cdots\!89\)\( T^{36} \))(\( 1 - 71 T + 2368 T^{2} - 50969 T^{3} + 836880 T^{4} - 11828308 T^{5} + 155370763 T^{6} - 1975485248 T^{7} + 25025905391 T^{8} - 318238582892 T^{9} + 3957848635408 T^{10} - 46785223241176 T^{11} + 523567041637077 T^{12} - 5637158848736682 T^{13} + 59668959182508043 T^{14} - 630662658429013549 T^{15} + 6659652238475527590 T^{16} - 69228635653545298441 T^{17} + \)\(69\!\cdots\!39\)\( T^{18} - \)\(67\!\cdots\!77\)\( T^{19} + \)\(62\!\cdots\!10\)\( T^{20} - \)\(57\!\cdots\!77\)\( T^{21} + \)\(52\!\cdots\!83\)\( T^{22} - \)\(48\!\cdots\!74\)\( T^{23} + \)\(43\!\cdots\!33\)\( T^{24} - \)\(37\!\cdots\!88\)\( T^{25} + \)\(31\!\cdots\!88\)\( T^{26} - \)\(24\!\cdots\!64\)\( T^{27} + \)\(18\!\cdots\!59\)\( T^{28} - \)\(14\!\cdots\!44\)\( T^{29} + \)\(10\!\cdots\!83\)\( T^{30} - \)\(79\!\cdots\!16\)\( T^{31} + \)\(54\!\cdots\!20\)\( T^{32} - \)\(32\!\cdots\!17\)\( T^{33} + \)\(14\!\cdots\!28\)\( T^{34} - \)\(42\!\cdots\!27\)\( T^{35} + \)\(57\!\cdots\!89\)\( T^{36} \))
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