Properties

Label 114.2
Level 114
Weight 2
Dimension 91
Nonzero newspaces 6
Newform subspaces 21
Sturm bound 1440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 21 \)
Sturm bound: \(1440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(114))\).

Total New Old
Modular forms 432 91 341
Cusp forms 289 91 198
Eisenstein series 143 0 143

Trace form

\( 91q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 91q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + 6q^{10} + 12q^{11} - 5q^{12} - 34q^{13} - 28q^{14} - 30q^{15} + q^{16} - 18q^{17} + q^{18} - 65q^{19} - 30q^{20} - 34q^{21} - 42q^{22} - 12q^{23} + q^{24} - 41q^{25} - 22q^{26} - 14q^{27} - 4q^{28} - 6q^{29} + 6q^{30} - 4q^{31} + q^{32} - 42q^{33} + 18q^{34} - 24q^{35} + q^{36} + 2q^{37} + 19q^{38} - 40q^{39} + 6q^{40} + 6q^{41} + 8q^{42} - 28q^{43} + 12q^{44} + 6q^{45} + 24q^{46} + 12q^{47} + 10q^{48} + 21q^{49} + 31q^{50} + 99q^{51} + 14q^{52} + 54q^{53} + 55q^{54} + 72q^{55} + 8q^{56} + 109q^{57} + 30q^{58} + 60q^{59} + 42q^{60} + 50q^{61} + 32q^{62} + 74q^{63} + q^{64} + 48q^{65} + 84q^{66} - 4q^{67} + 18q^{68} + 78q^{69} + 48q^{70} + 36q^{71} + 10q^{72} + 20q^{73} + 38q^{74} - 11q^{75} + 19q^{76} + 24q^{77} - 22q^{78} - 76q^{79} + 6q^{80} - 71q^{81} - 30q^{82} - 60q^{83} - 46q^{84} - 36q^{85} - 28q^{86} - 150q^{87} + 12q^{88} - 54q^{89} - 84q^{90} - 80q^{91} - 48q^{92} - 118q^{93} - 96q^{94} + 6q^{95} + q^{96} - 10q^{97} - 87q^{98} - 69q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)

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
114.2.a \(\chi_{114}(1, \cdot)\) 114.2.a.a 1 1
114.2.a.b 1
114.2.a.c 1
114.2.b \(\chi_{114}(113, \cdot)\) 114.2.b.a 2 1
114.2.b.b 2
114.2.b.c 2
114.2.b.d 2
114.2.e \(\chi_{114}(7, \cdot)\) 114.2.e.a 2 2
114.2.e.b 2
114.2.h \(\chi_{114}(65, \cdot)\) 114.2.h.a 2 2
114.2.h.b 2
114.2.h.c 2
114.2.h.d 2
114.2.h.e 4
114.2.h.f 4
114.2.i \(\chi_{114}(25, \cdot)\) 114.2.i.a 6 6
114.2.i.b 6
114.2.i.c 6
114.2.i.d 6
114.2.l \(\chi_{114}(29, \cdot)\) 114.2.l.a 18 6
114.2.l.b 18

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(114))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(114)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( 1 - T^{3} + T^{6} \))(\( 1 + T^{3} + T^{6} \))(\( 1 + T^{3} + T^{6} \))(\( 1 - T^{3} + T^{6} \))(\( ( 1 - T^{3} + T^{6} )^{3} \))(\( ( 1 + T^{3} + T^{6} )^{3} \))
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( ( 1 - 2 T + 3 T^{2} )^{2} \))(\( 1 - 2 T + T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 + T^{3} + T^{6} \))(\( 1 + T^{3} + T^{6} \))(\( 1 - T^{3} + T^{6} \))(\( 1 - T^{3} + T^{6} \))(\( 1 + T^{3} + 18 T^{5} + 10 T^{6} + 18 T^{7} + 90 T^{8} - 81 T^{9} + 270 T^{10} + 162 T^{11} + 270 T^{12} + 1458 T^{13} + 729 T^{15} + 19683 T^{18} \))(\( 1 - 3 T + 6 T^{2} - 7 T^{3} + 6 T^{4} - 3 T^{5} - 8 T^{6} + 27 T^{7} - 9 T^{9} + 243 T^{11} - 216 T^{12} - 243 T^{13} + 1458 T^{14} - 5103 T^{15} + 13122 T^{16} - 19683 T^{17} + 19683 T^{18} \))
$5$ (\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 8 T^{2} + 25 T^{4} \))(\( 1 + 2 T^{2} + 25 T^{4} \))(\( 1 + 2 T^{2} + 25 T^{4} \))(\( 1 - 8 T^{2} + 25 T^{4} \))(\( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 + 6 T + 17 T^{2} + 30 T^{3} + 25 T^{4} \))(\( 1 - 6 T + 17 T^{2} - 30 T^{3} + 25 T^{4} \))(\( 1 + 6 T + 17 T^{2} + 30 T^{3} + 25 T^{4} \))(\( 1 - 6 T + 17 T^{2} - 30 T^{3} + 25 T^{4} \))(\( 1 + 8 T^{2} + 39 T^{4} + 200 T^{6} + 625 T^{8} \))(\( 1 + 8 T^{2} + 39 T^{4} + 200 T^{6} + 625 T^{8} \))(\( 1 + 9 T + 36 T^{2} + 90 T^{3} + 207 T^{4} + 567 T^{5} + 1441 T^{6} + 2835 T^{7} + 5175 T^{8} + 11250 T^{9} + 22500 T^{10} + 28125 T^{11} + 15625 T^{12} \))(\( 1 + 3 T - 9 T^{4} - 15 T^{5} + 109 T^{6} - 75 T^{7} - 225 T^{8} + 9375 T^{11} + 15625 T^{12} \))(\( 1 - 3 T + 12 T^{2} - 16 T^{3} + 75 T^{4} - 153 T^{5} + 581 T^{6} - 765 T^{7} + 1875 T^{8} - 2000 T^{9} + 7500 T^{10} - 9375 T^{11} + 15625 T^{12} \))(\( 1 - 9 T + 36 T^{2} - 90 T^{3} + 207 T^{4} - 567 T^{5} + 1441 T^{6} - 2835 T^{7} + 5175 T^{8} - 11250 T^{9} + 22500 T^{10} - 28125 T^{11} + 15625 T^{12} \))(\( 1 + 9 T^{2} + 18 T^{4} - 108 T^{5} - 89 T^{6} - 954 T^{7} - 558 T^{8} - 1782 T^{9} + 4617 T^{10} + 17298 T^{11} + 52688 T^{12} + 161568 T^{13} + 85149 T^{14} + 403848 T^{15} - 1430298 T^{16} - 1525608 T^{17} - 12164327 T^{18} - 7628040 T^{19} - 35757450 T^{20} + 50481000 T^{21} + 53218125 T^{22} + 504900000 T^{23} + 823250000 T^{24} + 1351406250 T^{25} + 1803515625 T^{26} - 3480468750 T^{27} - 5449218750 T^{28} - 46582031250 T^{29} - 21728515625 T^{30} - 131835937500 T^{31} + 109863281250 T^{32} + 1373291015625 T^{34} + 3814697265625 T^{36} \))(\( 1 + 9 T^{2} + 18 T^{4} + 108 T^{5} - 89 T^{6} + 954 T^{7} - 558 T^{8} + 1782 T^{9} + 4617 T^{10} - 17298 T^{11} + 52688 T^{12} - 161568 T^{13} + 85149 T^{14} - 403848 T^{15} - 1430298 T^{16} + 1525608 T^{17} - 12164327 T^{18} + 7628040 T^{19} - 35757450 T^{20} - 50481000 T^{21} + 53218125 T^{22} - 504900000 T^{23} + 823250000 T^{24} - 1351406250 T^{25} + 1803515625 T^{26} + 3480468750 T^{27} - 5449218750 T^{28} + 46582031250 T^{29} - 21728515625 T^{30} + 131835937500 T^{31} + 109863281250 T^{32} + 1373291015625 T^{34} + 3814697265625 T^{36} \))
$7$ (\( 1 - 4 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 - T + 7 T^{2} )^{2} \))(\( ( 1 - T + 7 T^{2} )^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 + 3 T + 7 T^{2} )^{2} \))(\( ( 1 - T + 7 T^{2} )^{2} \))(\( ( 1 + 2 T + 7 T^{2} )^{2} \))(\( ( 1 - T + 7 T^{2} )^{2} \))(\( ( 1 - T + 7 T^{2} )^{2} \))(\( ( 1 + 2 T + 7 T^{2} )^{2} \))(\( ( 1 - 4 T + 12 T^{2} - 28 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 - 4 T + 12 T^{2} - 28 T^{3} + 49 T^{4} )^{2} \))(\( 1 - 9 T + 36 T^{2} - 115 T^{3} + 405 T^{4} - 1296 T^{5} + 3567 T^{6} - 9072 T^{7} + 19845 T^{8} - 39445 T^{9} + 86436 T^{10} - 151263 T^{11} + 117649 T^{12} \))(\( 1 - 3 T - 6 T^{2} + 41 T^{3} - 9 T^{4} - 162 T^{5} + 519 T^{6} - 1134 T^{7} - 441 T^{8} + 14063 T^{9} - 14406 T^{10} - 50421 T^{11} + 117649 T^{12} \))(\( 1 + 3 T + 6 T^{2} + 39 T^{3} + 33 T^{4} - 24 T^{5} + 407 T^{6} - 168 T^{7} + 1617 T^{8} + 13377 T^{9} + 14406 T^{10} + 50421 T^{11} + 117649 T^{12} \))(\( 1 - 3 T - 12 T^{2} + 19 T^{3} + 171 T^{4} - 126 T^{5} - 1161 T^{6} - 882 T^{7} + 8379 T^{8} + 6517 T^{9} - 28812 T^{10} - 50421 T^{11} + 117649 T^{12} \))(\( 1 - 42 T^{2} - 4 T^{3} + 885 T^{4} + 120 T^{5} - 13234 T^{6} - 906 T^{7} + 162387 T^{8} - 5772 T^{9} - 1713330 T^{10} + 145500 T^{11} + 15871186 T^{12} - 1406388 T^{13} - 132726909 T^{14} + 10232980 T^{15} + 1026357738 T^{16} - 34303050 T^{17} - 7420332713 T^{18} - 240121350 T^{19} + 50291529162 T^{20} + 3509912140 T^{21} - 318677308509 T^{22} - 23637163116 T^{23} + 1867229161714 T^{24} + 119825506500 T^{25} - 9877006497330 T^{26} - 232921019604 T^{27} + 45870308259363 T^{28} - 1791458029158 T^{29} - 183175594818034 T^{30} + 11626681248840 T^{31} + 600227419471365 T^{32} - 18990246039772 T^{33} - 1395783083923242 T^{34} + 1628413597910449 T^{36} \))(\( 1 - 42 T^{2} - 4 T^{3} + 885 T^{4} + 120 T^{5} - 13234 T^{6} - 906 T^{7} + 162387 T^{8} - 5772 T^{9} - 1713330 T^{10} + 145500 T^{11} + 15871186 T^{12} - 1406388 T^{13} - 132726909 T^{14} + 10232980 T^{15} + 1026357738 T^{16} - 34303050 T^{17} - 7420332713 T^{18} - 240121350 T^{19} + 50291529162 T^{20} + 3509912140 T^{21} - 318677308509 T^{22} - 23637163116 T^{23} + 1867229161714 T^{24} + 119825506500 T^{25} - 9877006497330 T^{26} - 232921019604 T^{27} + 45870308259363 T^{28} - 1791458029158 T^{29} - 183175594818034 T^{30} + 11626681248840 T^{31} + 600227419471365 T^{32} - 18990246039772 T^{33} - 1395783083923242 T^{34} + 1628413597910449 T^{36} \))
$11$ (\( 1 - 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 10 T^{2} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 + 10 T^{2} + 121 T^{4} \))(\( ( 1 - 2 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( 1 - 19 T^{2} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 - 19 T^{2} + 121 T^{4} \))(\( 1 - 34 T^{2} + 507 T^{4} - 4114 T^{6} + 14641 T^{8} \))(\( 1 - 34 T^{2} + 507 T^{4} - 4114 T^{6} + 14641 T^{8} \))(\( 1 - 24 T^{2} + 18 T^{3} + 312 T^{4} - 216 T^{5} - 3593 T^{6} - 2376 T^{7} + 37752 T^{8} + 23958 T^{9} - 351384 T^{10} + 1771561 T^{12} \))(\( 1 - 12 T + 66 T^{2} - 306 T^{3} + 1446 T^{4} - 5430 T^{5} + 17539 T^{6} - 59730 T^{7} + 174966 T^{8} - 407286 T^{9} + 966306 T^{10} - 1932612 T^{11} + 1771561 T^{12} \))(\( 1 - 12 T^{2} + 74 T^{3} + 12 T^{4} - 444 T^{5} + 2447 T^{6} - 4884 T^{7} + 1452 T^{8} + 98494 T^{9} - 175692 T^{10} + 1771561 T^{12} \))(\( 1 - 30 T^{2} - 2 T^{3} + 570 T^{4} + 30 T^{5} - 7237 T^{6} + 330 T^{7} + 68970 T^{8} - 2662 T^{9} - 439230 T^{10} + 1771561 T^{12} \))(\( 1 + 48 T^{2} + 1158 T^{4} - 1314 T^{5} + 20983 T^{6} - 59130 T^{7} + 321210 T^{8} - 1332396 T^{9} + 4917732 T^{10} - 22608792 T^{11} + 79556150 T^{12} - 318259620 T^{13} + 1177125408 T^{14} - 3883011912 T^{15} + 15730008942 T^{16} - 45082464102 T^{17} + 187351494091 T^{18} - 495907105122 T^{19} + 1903331081982 T^{20} - 5168288854872 T^{21} + 17234293098528 T^{22} - 51256030060620 T^{23} + 140938572650150 T^{24} - 440581395807432 T^{25} + 1054159528577892 T^{26} - 3141720071697636 T^{27} + 8331360156087210 T^{28} - 16870479083228430 T^{29} + 65853642628736743 T^{30} - 45362843757125334 T^{31} + 439750307289393078 T^{32} + 2205587033451463728 T^{34} + 5559917313492231481 T^{36} \))(\( 1 + 48 T^{2} + 1158 T^{4} + 1314 T^{5} + 20983 T^{6} + 59130 T^{7} + 321210 T^{8} + 1332396 T^{9} + 4917732 T^{10} + 22608792 T^{11} + 79556150 T^{12} + 318259620 T^{13} + 1177125408 T^{14} + 3883011912 T^{15} + 15730008942 T^{16} + 45082464102 T^{17} + 187351494091 T^{18} + 495907105122 T^{19} + 1903331081982 T^{20} + 5168288854872 T^{21} + 17234293098528 T^{22} + 51256030060620 T^{23} + 140938572650150 T^{24} + 440581395807432 T^{25} + 1054159528577892 T^{26} + 3141720071697636 T^{27} + 8331360156087210 T^{28} + 16870479083228430 T^{29} + 65853642628736743 T^{30} + 45362843757125334 T^{31} + 439750307289393078 T^{32} + 2205587033451463728 T^{34} + 5559917313492231481 T^{36} \))
$13$ (\( 1 + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 8 T^{2} + 169 T^{4} \))(\( ( 1 - 7 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( ( 1 - 7 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 - 8 T^{2} + 169 T^{4} \))(\( ( 1 - 5 T + 13 T^{2} )( 1 - 2 T + 13 T^{2} ) \))(\( 1 - 3 T - 4 T^{2} - 39 T^{3} + 169 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 78 T^{3} + 169 T^{4} \))(\( ( 1 - 7 T + 13 T^{2} )( 1 - 2 T + 13 T^{2} ) \))(\( ( 1 - 7 T + 13 T^{2} )( 1 - 2 T + 13 T^{2} ) \))(\( 1 + 6 T + 25 T^{2} + 78 T^{3} + 169 T^{4} \))(\( ( 1 + 6 T + 25 T^{2} + 78 T^{3} + 169 T^{4} )^{2} \))(\( ( 1 + 6 T + 25 T^{2} + 78 T^{3} + 169 T^{4} )^{2} \))(\( 1 - 15 T + 96 T^{2} - 352 T^{3} + 963 T^{4} - 2925 T^{5} + 10521 T^{6} - 38025 T^{7} + 162747 T^{8} - 773344 T^{9} + 2741856 T^{10} - 5569395 T^{11} + 4826809 T^{12} \))(\( ( 1 + 7 T + 13 T^{2} )^{3}( 1 - 89 T^{3} + 2197 T^{6} ) \))(\( 1 - 9 T + 36 T^{2} - 106 T^{3} + 27 T^{4} + 1161 T^{5} - 4731 T^{6} + 15093 T^{7} + 4563 T^{8} - 232882 T^{9} + 1028196 T^{10} - 3341637 T^{11} + 4826809 T^{12} \))(\( 1 + 3 T + 18 T^{2} + 102 T^{3} + 477 T^{4} + 1533 T^{5} + 6821 T^{6} + 19929 T^{7} + 80613 T^{8} + 224094 T^{9} + 514098 T^{10} + 1113879 T^{11} + 4826809 T^{12} \))(\( 1 + 12 T + 27 T^{2} - 318 T^{3} - 2016 T^{4} + 276 T^{5} + 34311 T^{6} + 68124 T^{7} - 228906 T^{8} - 626832 T^{9} + 876177 T^{10} - 7168332 T^{11} - 44288472 T^{12} + 168933792 T^{13} + 1227937095 T^{14} - 492511650 T^{15} - 15317424756 T^{16} - 4905480720 T^{17} + 155037380533 T^{18} - 63771249360 T^{19} - 2588644783764 T^{20} - 1082048095050 T^{21} + 35071111370295 T^{22} + 62723934433056 T^{23} - 213771995245848 T^{24} - 449802202363644 T^{25} + 714724495933617 T^{26} - 6647239550976336 T^{27} - 31556635935187194 T^{28} + 122089134683376588 T^{29} + 799380598637445591 T^{30} + 83593529419461828 T^{31} - 7937750793569766624 T^{32} - 16277113978480860726 T^{33} + 17966248447945855707 T^{34} + \)\(10\!\cdots\!96\)\( T^{35} + \)\(11\!\cdots\!29\)\( T^{36} \))(\( 1 + 12 T + 27 T^{2} - 318 T^{3} - 2016 T^{4} + 276 T^{5} + 34311 T^{6} + 68124 T^{7} - 228906 T^{8} - 626832 T^{9} + 876177 T^{10} - 7168332 T^{11} - 44288472 T^{12} + 168933792 T^{13} + 1227937095 T^{14} - 492511650 T^{15} - 15317424756 T^{16} - 4905480720 T^{17} + 155037380533 T^{18} - 63771249360 T^{19} - 2588644783764 T^{20} - 1082048095050 T^{21} + 35071111370295 T^{22} + 62723934433056 T^{23} - 213771995245848 T^{24} - 449802202363644 T^{25} + 714724495933617 T^{26} - 6647239550976336 T^{27} - 31556635935187194 T^{28} + 122089134683376588 T^{29} + 799380598637445591 T^{30} + 83593529419461828 T^{31} - 7937750793569766624 T^{32} - 16277113978480860726 T^{33} + 17966248447945855707 T^{34} + \)\(10\!\cdots\!96\)\( T^{35} + \)\(11\!\cdots\!29\)\( T^{36} \))
$17$ (\( 1 + 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 26 T^{2} + 289 T^{4} \))(\( 1 - 31 T^{2} + 289 T^{4} \))(\( 1 - 31 T^{2} + 289 T^{4} \))(\( 1 - 26 T^{2} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 + 12 T + 65 T^{2} + 204 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 29 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 29 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - 12 T + 65 T^{2} - 204 T^{3} + 289 T^{4} \))(\( 1 - 12 T + 86 T^{2} - 456 T^{3} + 1971 T^{4} - 7752 T^{5} + 24854 T^{6} - 58956 T^{7} + 83521 T^{8} \))(\( 1 + 12 T + 86 T^{2} + 456 T^{3} + 1971 T^{4} + 7752 T^{5} + 24854 T^{6} + 58956 T^{7} + 83521 T^{8} \))(\( 1 + 9 T + 36 T^{2} + 72 T^{3} - 225 T^{4} - 3897 T^{5} - 21815 T^{6} - 66249 T^{7} - 65025 T^{8} + 353736 T^{9} + 3006756 T^{10} + 12778713 T^{11} + 24137569 T^{12} \))(\( 1 - 3 T - 18 T^{2} + 180 T^{3} - 423 T^{4} - 1785 T^{5} + 18649 T^{6} - 30345 T^{7} - 122247 T^{8} + 884340 T^{9} - 1503378 T^{10} - 4259571 T^{11} + 24137569 T^{12} \))(\( 1 + 3 T + 18 T^{2} + 126 T^{3} + 621 T^{4} + 2217 T^{5} + 10549 T^{6} + 37689 T^{7} + 179469 T^{8} + 619038 T^{9} + 1503378 T^{10} + 4259571 T^{11} + 24137569 T^{12} \))(\( 1 + 3 T + 48 T^{2} + 142 T^{3} + 1407 T^{4} + 3825 T^{5} + 27149 T^{6} + 65025 T^{7} + 406623 T^{8} + 697646 T^{9} + 4009008 T^{10} + 4259571 T^{11} + 24137569 T^{12} \))(\( 1 + 6 T + 21 T^{2} - 150 T^{3} - 1122 T^{4} - 6402 T^{5} - 527 T^{6} + 57612 T^{7} + 635322 T^{8} + 954660 T^{9} + 3233433 T^{10} - 27099996 T^{11} - 24215494 T^{12} - 454155294 T^{13} + 806325141 T^{14} - 4532483178 T^{15} + 24436771518 T^{16} - 62821812054 T^{17} + 452385711361 T^{18} - 1067970804918 T^{19} + 7062226968702 T^{20} - 22268089853514 T^{21} + 67345082101461 T^{22} - 644835573272958 T^{23} - 584503157294086 T^{24} - 11120176396945308 T^{25} + 22555644309724953 T^{26} + 113211102176626020 T^{27} + 1280805276821059578 T^{28} + 1974472490075352396 T^{29} - 307041919020084047 T^{30} - 63409108566663808674 T^{31} - \)\(18\!\cdots\!38\)\( T^{32} - \)\(42\!\cdots\!50\)\( T^{33} + \)\(10\!\cdots\!01\)\( T^{34} + \)\(49\!\cdots\!62\)\( T^{35} + \)\(14\!\cdots\!09\)\( T^{36} \))(\( 1 - 6 T + 21 T^{2} + 150 T^{3} - 1122 T^{4} + 6402 T^{5} - 527 T^{6} - 57612 T^{7} + 635322 T^{8} - 954660 T^{9} + 3233433 T^{10} + 27099996 T^{11} - 24215494 T^{12} + 454155294 T^{13} + 806325141 T^{14} + 4532483178 T^{15} + 24436771518 T^{16} + 62821812054 T^{17} + 452385711361 T^{18} + 1067970804918 T^{19} + 7062226968702 T^{20} + 22268089853514 T^{21} + 67345082101461 T^{22} + 644835573272958 T^{23} - 584503157294086 T^{24} + 11120176396945308 T^{25} + 22555644309724953 T^{26} - 113211102176626020 T^{27} + 1280805276821059578 T^{28} - 1974472490075352396 T^{29} - 307041919020084047 T^{30} + 63409108566663808674 T^{31} - \)\(18\!\cdots\!38\)\( T^{32} + \)\(42\!\cdots\!50\)\( T^{33} + \)\(10\!\cdots\!01\)\( T^{34} - \)\(49\!\cdots\!62\)\( T^{35} + \)\(14\!\cdots\!09\)\( T^{36} \))
$19$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 12 T + 78 T^{2} + 385 T^{3} + 1482 T^{4} + 4332 T^{5} + 6859 T^{6} \))(\( 1 - 6 T - 12 T^{2} + 169 T^{3} - 228 T^{4} - 2166 T^{5} + 6859 T^{6} \))(\( 1 + 107 T^{3} + 6859 T^{6} \))(\( 1 + 18 T + 162 T^{2} + 883 T^{3} + 3078 T^{4} + 6498 T^{5} + 6859 T^{6} \))(\( 1 + 6 T - 30 T^{2} - 275 T^{3} + 306 T^{4} + 6408 T^{5} - 4006 T^{6} - 139704 T^{7} + 47316 T^{8} + 2942011 T^{9} + 899004 T^{10} - 50433144 T^{11} - 27477154 T^{12} + 835096968 T^{13} + 757686294 T^{14} - 12937617275 T^{15} - 26816152170 T^{16} + 101901378246 T^{17} + 322687697779 T^{18} \))(\( 1 + 6 T - 30 T^{2} - 275 T^{3} + 306 T^{4} + 6408 T^{5} - 4006 T^{6} - 139704 T^{7} + 47316 T^{8} + 2942011 T^{9} + 899004 T^{10} - 50433144 T^{11} - 27477154 T^{12} + 835096968 T^{13} + 757686294 T^{14} - 12937617275 T^{15} - 26816152170 T^{16} + 101901378246 T^{17} + 322687697779 T^{18} \))
$23$ (\( 1 + 2 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 44 T^{2} + 529 T^{4} \))(\( 1 - 19 T^{2} + 529 T^{4} \))(\( 1 - 19 T^{2} + 529 T^{4} \))(\( 1 - 44 T^{2} + 529 T^{4} \))(\( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 23 T^{2} + 529 T^{4} \))(\( 1 + 23 T^{2} + 529 T^{4} \))(\( 1 + 23 T^{2} + 529 T^{4} \))(\( 1 + 23 T^{2} + 529 T^{4} \))(\( 1 - 4 T^{2} - 513 T^{4} - 2116 T^{6} + 279841 T^{8} \))(\( 1 - 4 T^{2} - 513 T^{4} - 2116 T^{6} + 279841 T^{8} \))(\( 1 - 9 T + 36 T^{2} - 90 T^{3} + 369 T^{4} - 2025 T^{5} + 5923 T^{6} - 46575 T^{7} + 195201 T^{8} - 1095030 T^{9} + 10074276 T^{10} - 57927087 T^{11} + 148035889 T^{12} \))(\( 1 + 15 T + 108 T^{2} + 522 T^{3} + 1881 T^{4} + 6855 T^{5} + 32347 T^{6} + 157665 T^{7} + 995049 T^{8} + 6351174 T^{9} + 30222828 T^{10} + 96545145 T^{11} + 148035889 T^{12} \))(\( 1 - 27 T + 378 T^{2} - 3694 T^{3} + 28215 T^{4} - 177039 T^{5} + 927971 T^{6} - 4071897 T^{7} + 14925735 T^{8} - 44944898 T^{9} + 105779898 T^{10} - 173781261 T^{11} + 148035889 T^{12} \))(\( 1 + 21 T + 210 T^{2} + 1258 T^{3} + 4431 T^{4} + 6129 T^{5} - 7357 T^{6} + 140967 T^{7} + 2343999 T^{8} + 15306086 T^{9} + 58766610 T^{10} + 135163203 T^{11} + 148035889 T^{12} \))(\( 1 - 105 T^{2} - 306 T^{3} + 6486 T^{4} + 30186 T^{5} - 243515 T^{6} - 1820970 T^{7} + 5972118 T^{8} + 75696948 T^{9} - 45593781 T^{10} - 2436071598 T^{11} - 3368630716 T^{12} + 59621322114 T^{13} + 211038011391 T^{14} - 1068936440778 T^{15} - 7352150061234 T^{16} + 9132576534612 T^{17} + 192674644050967 T^{18} + 210049260296076 T^{19} - 3889287382392786 T^{20} - 13005749674945926 T^{21} + 59057088145668831 T^{22} + 383743279239189102 T^{23} - 498678242755766524 T^{24} - 8294398567584354306 T^{25} - 3570493912796137461 T^{26} + \)\(13\!\cdots\!24\)\( T^{27} + \)\(24\!\cdots\!82\)\( T^{28} - \)\(17\!\cdots\!90\)\( T^{29} - \)\(53\!\cdots\!15\)\( T^{30} + \)\(15\!\cdots\!38\)\( T^{31} + \)\(75\!\cdots\!74\)\( T^{32} - \)\(81\!\cdots\!42\)\( T^{33} - \)\(64\!\cdots\!05\)\( T^{34} + \)\(32\!\cdots\!69\)\( T^{36} \))(\( 1 - 105 T^{2} + 306 T^{3} + 6486 T^{4} - 30186 T^{5} - 243515 T^{6} + 1820970 T^{7} + 5972118 T^{8} - 75696948 T^{9} - 45593781 T^{10} + 2436071598 T^{11} - 3368630716 T^{12} - 59621322114 T^{13} + 211038011391 T^{14} + 1068936440778 T^{15} - 7352150061234 T^{16} - 9132576534612 T^{17} + 192674644050967 T^{18} - 210049260296076 T^{19} - 3889287382392786 T^{20} + 13005749674945926 T^{21} + 59057088145668831 T^{22} - 383743279239189102 T^{23} - 498678242755766524 T^{24} + 8294398567584354306 T^{25} - 3570493912796137461 T^{26} - \)\(13\!\cdots\!24\)\( T^{27} + \)\(24\!\cdots\!82\)\( T^{28} + \)\(17\!\cdots\!90\)\( T^{29} - \)\(53\!\cdots\!15\)\( T^{30} - \)\(15\!\cdots\!38\)\( T^{31} + \)\(75\!\cdots\!74\)\( T^{32} + \)\(81\!\cdots\!42\)\( T^{33} - \)\(64\!\cdots\!05\)\( T^{34} + \)\(32\!\cdots\!69\)\( T^{36} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 9 T + 29 T^{2} )^{2} \))(\( ( 1 - 9 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( 1 + 4 T - 13 T^{2} + 116 T^{3} + 841 T^{4} \))(\( 1 - 29 T^{2} + 841 T^{4} \))(\( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 52 T^{2} + 1863 T^{4} - 43732 T^{6} + 707281 T^{8} \))(\( 1 - 52 T^{2} + 1863 T^{4} - 43732 T^{6} + 707281 T^{8} \))(\( 1 + 9 T - 18 T^{2} - 594 T^{3} - 2331 T^{4} + 10287 T^{5} + 126217 T^{6} + 298323 T^{7} - 1960371 T^{8} - 14487066 T^{9} - 12731058 T^{10} + 184600341 T^{11} + 594823321 T^{12} \))(\( 1 - 15 T + 72 T^{2} + 36 T^{3} - 729 T^{4} - 13389 T^{5} + 142381 T^{6} - 388281 T^{7} - 613089 T^{8} + 878004 T^{9} + 50924232 T^{10} - 307667235 T^{11} + 594823321 T^{12} \))(\( 1 + 3 T + 12 T^{2} - 128 T^{3} + 147 T^{4} - 3231 T^{5} - 1507 T^{6} - 93699 T^{7} + 123627 T^{8} - 3121792 T^{9} + 8487372 T^{10} + 61533447 T^{11} + 594823321 T^{12} \))(\( 1 + 3 T + 18 T^{2} + 90 T^{3} + 81 T^{4} + 4413 T^{5} + 19153 T^{6} + 127977 T^{7} + 68121 T^{8} + 2195010 T^{9} + 12731058 T^{10} + 61533447 T^{11} + 594823321 T^{12} \))(\( 1 - 6 T + 111 T^{2} - 432 T^{3} + 6756 T^{4} - 25854 T^{5} + 359037 T^{6} - 1347846 T^{7} + 15292992 T^{8} - 52656642 T^{9} + 547390905 T^{10} - 1907356866 T^{11} + 18071986176 T^{12} - 62454734718 T^{13} + 526205563113 T^{14} - 1810034045028 T^{15} + 14839402855758 T^{16} - 54064521051522 T^{17} + 433746062243863 T^{18} - 1567871110494138 T^{19} + 12479937801692478 T^{20} - 44144920324187892 T^{21} + 372175196884125753 T^{22} - 1281018369556370982 T^{23} + 10749638834274410496 T^{24} - 32901670015621887594 T^{25} + \)\(27\!\cdots\!05\)\( T^{26} - \)\(76\!\cdots\!98\)\( T^{27} + \)\(64\!\cdots\!92\)\( T^{28} - \)\(16\!\cdots\!34\)\( T^{29} + \)\(12\!\cdots\!17\)\( T^{30} - \)\(26\!\cdots\!06\)\( T^{31} + \)\(20\!\cdots\!36\)\( T^{32} - \)\(37\!\cdots\!68\)\( T^{33} + \)\(27\!\cdots\!31\)\( T^{34} - \)\(43\!\cdots\!54\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))(\( 1 + 6 T + 111 T^{2} + 432 T^{3} + 6756 T^{4} + 25854 T^{5} + 359037 T^{6} + 1347846 T^{7} + 15292992 T^{8} + 52656642 T^{9} + 547390905 T^{10} + 1907356866 T^{11} + 18071986176 T^{12} + 62454734718 T^{13} + 526205563113 T^{14} + 1810034045028 T^{15} + 14839402855758 T^{16} + 54064521051522 T^{17} + 433746062243863 T^{18} + 1567871110494138 T^{19} + 12479937801692478 T^{20} + 44144920324187892 T^{21} + 372175196884125753 T^{22} + 1281018369556370982 T^{23} + 10749638834274410496 T^{24} + 32901670015621887594 T^{25} + \)\(27\!\cdots\!05\)\( T^{26} + \)\(76\!\cdots\!98\)\( T^{27} + \)\(64\!\cdots\!92\)\( T^{28} + \)\(16\!\cdots\!34\)\( T^{29} + \)\(12\!\cdots\!17\)\( T^{30} + \)\(26\!\cdots\!06\)\( T^{31} + \)\(20\!\cdots\!36\)\( T^{32} + \)\(37\!\cdots\!68\)\( T^{33} + \)\(27\!\cdots\!31\)\( T^{34} + \)\(43\!\cdots\!54\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))
$31$ (\( 1 - 6 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 44 T^{2} + 961 T^{4} \))(\( ( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( ( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 - 44 T^{2} + 961 T^{4} \))(\( ( 1 - T + 31 T^{2} )^{2} \))(\( ( 1 + 3 T + 31 T^{2} )^{2} \))(\( 1 - 14 T^{2} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( 1 - 14 T^{2} + 961 T^{4} \))(\( ( 1 - 44 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 44 T^{2} + 961 T^{4} )^{2} \))(\( 1 + 9 T + 54 T^{2} + 209 T^{3} - 261 T^{4} - 5958 T^{5} - 40569 T^{6} - 184698 T^{7} - 250821 T^{8} + 6226319 T^{9} + 49870134 T^{10} + 257662359 T^{11} + 887503681 T^{12} \))(\( 1 - 3 T - 78 T^{2} + 77 T^{3} + 4365 T^{4} - 1404 T^{5} - 155145 T^{6} - 43524 T^{7} + 4194765 T^{8} + 2293907 T^{9} - 72034638 T^{10} - 85887453 T^{11} + 887503681 T^{12} \))(\( 1 + 15 T + 60 T^{2} + 397 T^{3} + 6525 T^{4} + 32400 T^{5} + 78903 T^{6} + 1004400 T^{7} + 6270525 T^{8} + 11827027 T^{9} + 55411260 T^{10} + 429437265 T^{11} + 887503681 T^{12} \))(\( 1 - 9 T - 12 T^{2} + 225 T^{3} + 987 T^{4} - 6138 T^{5} - 4417 T^{6} - 190278 T^{7} + 948507 T^{8} + 6702975 T^{9} - 11082252 T^{10} - 257662359 T^{11} + 887503681 T^{12} \))(\( 1 + 114 T^{2} + 5601 T^{4} - 9990 T^{5} + 219930 T^{6} - 696546 T^{7} + 9357981 T^{8} - 5530194 T^{9} + 364518102 T^{10} + 294224670 T^{11} + 9695245116 T^{12} + 2532085866 T^{13} + 120281065773 T^{14} + 583374247038 T^{15} + 3558442900152 T^{16} + 45311738657760 T^{17} + 205885978276165 T^{18} + 1404663898390560 T^{19} + 3419663627046072 T^{20} + 17379302193509058 T^{21} + 111082090143746733 T^{22} + 72491468602679766 T^{23} + 8604565728647271996 T^{24} + 8094889807646318370 T^{25} + \)\(31\!\cdots\!82\)\( T^{26} - \)\(14\!\cdots\!74\)\( T^{27} + \)\(76\!\cdots\!81\)\( T^{28} - \)\(17\!\cdots\!26\)\( T^{29} + \)\(17\!\cdots\!30\)\( T^{30} - \)\(24\!\cdots\!90\)\( T^{31} + \)\(42\!\cdots\!21\)\( T^{32} + \)\(82\!\cdots\!34\)\( T^{34} + \)\(69\!\cdots\!41\)\( T^{36} \))(\( 1 + 114 T^{2} + 5601 T^{4} - 9990 T^{5} + 219930 T^{6} - 696546 T^{7} + 9357981 T^{8} - 5530194 T^{9} + 364518102 T^{10} + 294224670 T^{11} + 9695245116 T^{12} + 2532085866 T^{13} + 120281065773 T^{14} + 583374247038 T^{15} + 3558442900152 T^{16} + 45311738657760 T^{17} + 205885978276165 T^{18} + 1404663898390560 T^{19} + 3419663627046072 T^{20} + 17379302193509058 T^{21} + 111082090143746733 T^{22} + 72491468602679766 T^{23} + 8604565728647271996 T^{24} + 8094889807646318370 T^{25} + \)\(31\!\cdots\!82\)\( T^{26} - \)\(14\!\cdots\!74\)\( T^{27} + \)\(76\!\cdots\!81\)\( T^{28} - \)\(17\!\cdots\!26\)\( T^{29} + \)\(17\!\cdots\!30\)\( T^{30} - \)\(24\!\cdots\!90\)\( T^{31} + \)\(42\!\cdots\!21\)\( T^{32} + \)\(82\!\cdots\!34\)\( T^{34} + \)\(69\!\cdots\!41\)\( T^{36} \))
$37$ (\( 1 + 8 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - 56 T^{2} + 1369 T^{4} \))(\( ( 1 - 10 T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( ( 1 - 10 T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 - 56 T^{2} + 1369 T^{4} \))(\( ( 1 - 7 T + 37 T^{2} )^{2} \))(\( ( 1 + 5 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + 11 T + 37 T^{2} ) \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + 11 T + 37 T^{2} ) \))(\( ( 1 - 10 T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 - 88 T^{2} + 3810 T^{4} - 120472 T^{6} + 1874161 T^{8} \))(\( 1 - 88 T^{2} + 3810 T^{4} - 120472 T^{6} + 1874161 T^{8} \))(\( ( 1 - 9 T + 126 T^{2} - 665 T^{3} + 4662 T^{4} - 12321 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 - 3 T + 102 T^{2} - 203 T^{3} + 3774 T^{4} - 4107 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 3 T + 66 T^{2} + 239 T^{3} + 2442 T^{4} + 4107 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 9 T + 54 T^{2} + 305 T^{3} + 1998 T^{4} + 12321 T^{5} + 50653 T^{6} )^{2} \))(\( 1 - 324 T^{2} + 51984 T^{4} - 5307594 T^{6} + 373443840 T^{8} - 18097521588 T^{10} + 530319518007 T^{12} - 1456970393160 T^{14} - 747058665149136 T^{16} + 40979990975507188 T^{18} - 1022723312589167184 T^{20} - 2730597089015138760 T^{22} + \)\(13\!\cdots\!63\)\( T^{24} - \)\(63\!\cdots\!48\)\( T^{26} + \)\(17\!\cdots\!60\)\( T^{28} - \)\(34\!\cdots\!14\)\( T^{30} + \)\(46\!\cdots\!76\)\( T^{32} - \)\(39\!\cdots\!84\)\( T^{34} + \)\(16\!\cdots\!29\)\( T^{36} \))(\( 1 - 324 T^{2} + 51984 T^{4} - 5307594 T^{6} + 373443840 T^{8} - 18097521588 T^{10} + 530319518007 T^{12} - 1456970393160 T^{14} - 747058665149136 T^{16} + 40979990975507188 T^{18} - 1022723312589167184 T^{20} - 2730597089015138760 T^{22} + \)\(13\!\cdots\!63\)\( T^{24} - \)\(63\!\cdots\!48\)\( T^{26} + \)\(17\!\cdots\!60\)\( T^{28} - \)\(34\!\cdots\!14\)\( T^{30} + \)\(46\!\cdots\!76\)\( T^{32} - \)\(39\!\cdots\!84\)\( T^{34} + \)\(16\!\cdots\!29\)\( T^{36} \))
$41$ (\( 1 - 10 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( 1 + 4 T - 25 T^{2} + 164 T^{3} + 1681 T^{4} \))(\( 1 + 4 T - 25 T^{2} + 164 T^{3} + 1681 T^{4} \))(\( 1 - 3 T - 32 T^{2} - 123 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 103 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 103 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 + 3 T - 32 T^{2} + 123 T^{3} + 1681 T^{4} \))(\( ( 1 - 3 T - 32 T^{2} - 123 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 3 T - 32 T^{2} + 123 T^{3} + 1681 T^{4} )^{2} \))(\( 1 - 27 T + 405 T^{2} - 4473 T^{3} + 40986 T^{4} - 320760 T^{5} + 2190817 T^{6} - 13151160 T^{7} + 68897466 T^{8} - 308283633 T^{9} + 1144433205 T^{10} - 3128117427 T^{11} + 4750104241 T^{12} \))(\( 1 + 9 T + 27 T^{2} + 153 T^{3} - 1728 T^{4} - 21024 T^{5} - 78155 T^{6} - 861984 T^{7} - 2904768 T^{8} + 10544913 T^{9} + 76295547 T^{10} + 1042705809 T^{11} + 4750104241 T^{12} \))(\( 1 + 15 T + 87 T^{2} - 53 T^{3} - 2874 T^{4} - 20052 T^{5} - 101167 T^{6} - 822132 T^{7} - 4831194 T^{8} - 3652813 T^{9} + 245841207 T^{10} + 1737843015 T^{11} + 4750104241 T^{12} \))(\( 1 + 15 T + 177 T^{2} + 1657 T^{3} + 15216 T^{4} + 110376 T^{5} + 759557 T^{6} + 4525416 T^{7} + 25578096 T^{8} + 114202097 T^{9} + 500159697 T^{10} + 1737843015 T^{11} + 4750104241 T^{12} \))(\( 1 + 3 T - 81 T^{2} - 729 T^{3} + 3150 T^{4} + 51888 T^{5} + 65235 T^{6} - 1923639 T^{7} - 9379107 T^{8} + 27894240 T^{9} + 443543373 T^{10} + 1209767853 T^{11} - 11724901572 T^{12} - 125864370879 T^{13} - 126907771644 T^{14} + 6812152423767 T^{15} + 40936056170904 T^{16} - 121589755652562 T^{17} - 2550730175210513 T^{18} - 4985179981755042 T^{19} + 68813510423289624 T^{20} + 469500357198445407 T^{21} - 358611031708521084 T^{22} - 14582167851295970679 T^{23} - 55694504682464766852 T^{24} + \)\(23\!\cdots\!93\)\( T^{25} + \)\(35\!\cdots\!33\)\( T^{26} + \)\(91\!\cdots\!40\)\( T^{27} - \)\(12\!\cdots\!07\)\( T^{28} - \)\(10\!\cdots\!99\)\( T^{29} + \)\(14\!\cdots\!35\)\( T^{30} + \)\(48\!\cdots\!48\)\( T^{31} + \)\(11\!\cdots\!50\)\( T^{32} - \)\(11\!\cdots\!29\)\( T^{33} - \)\(51\!\cdots\!21\)\( T^{34} + \)\(78\!\cdots\!43\)\( T^{35} + \)\(10\!\cdots\!21\)\( T^{36} \))(\( 1 - 3 T - 81 T^{2} + 729 T^{3} + 3150 T^{4} - 51888 T^{5} + 65235 T^{6} + 1923639 T^{7} - 9379107 T^{8} - 27894240 T^{9} + 443543373 T^{10} - 1209767853 T^{11} - 11724901572 T^{12} + 125864370879 T^{13} - 126907771644 T^{14} - 6812152423767 T^{15} + 40936056170904 T^{16} + 121589755652562 T^{17} - 2550730175210513 T^{18} + 4985179981755042 T^{19} + 68813510423289624 T^{20} - 469500357198445407 T^{21} - 358611031708521084 T^{22} + 14582167851295970679 T^{23} - 55694504682464766852 T^{24} - \)\(23\!\cdots\!93\)\( T^{25} + \)\(35\!\cdots\!33\)\( T^{26} - \)\(91\!\cdots\!40\)\( T^{27} - \)\(12\!\cdots\!07\)\( T^{28} + \)\(10\!\cdots\!99\)\( T^{29} + \)\(14\!\cdots\!35\)\( T^{30} - \)\(48\!\cdots\!48\)\( T^{31} + \)\(11\!\cdots\!50\)\( T^{32} + \)\(11\!\cdots\!29\)\( T^{33} - \)\(51\!\cdots\!21\)\( T^{34} - \)\(78\!\cdots\!43\)\( T^{35} + \)\(10\!\cdots\!21\)\( T^{36} \))
$43$ (\( 1 + 12 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( 1 + 7 T + 6 T^{2} + 301 T^{3} + 1849 T^{4} \))(\( 1 - 9 T + 38 T^{2} - 387 T^{3} + 1849 T^{4} \))(\( ( 1 - 5 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} \))(\( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} \))(\( ( 1 - 5 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( 1 - 8 T - 14 T^{2} + 64 T^{3} + 1483 T^{4} + 2752 T^{5} - 25886 T^{6} - 636056 T^{7} + 3418801 T^{8} \))(\( 1 - 8 T - 14 T^{2} + 64 T^{3} + 1483 T^{4} + 2752 T^{5} - 25886 T^{6} - 636056 T^{7} + 3418801 T^{8} \))(\( 1 + 21 T + 231 T^{2} + 1979 T^{3} + 14112 T^{4} + 84366 T^{5} + 511749 T^{6} + 3627738 T^{7} + 26093088 T^{8} + 157344353 T^{9} + 789743031 T^{10} + 3087177303 T^{11} + 6321363049 T^{12} \))(\( 1 + 9 T + 45 T^{2} + 209 T^{3} - 972 T^{4} - 25110 T^{5} - 174579 T^{6} - 1079730 T^{7} - 1797228 T^{8} + 16616963 T^{9} + 153846045 T^{10} + 1323075987 T^{11} + 6321363049 T^{12} \))(\( 1 - 3 T - 3 T^{2} - 107 T^{3} - 1206 T^{4} + 3258 T^{5} + 55089 T^{6} + 140094 T^{7} - 2229894 T^{8} - 8507249 T^{9} - 10256403 T^{10} - 441025329 T^{11} + 6321363049 T^{12} \))(\( 1 - 3 T + 99 T^{2} - 561 T^{3} + 8010 T^{4} - 34446 T^{5} + 422585 T^{6} - 1481178 T^{7} + 14810490 T^{8} - 44603427 T^{9} + 338461299 T^{10} - 441025329 T^{11} + 6321363049 T^{12} \))(\( 1 + 6 T - 21 T^{2} - 186 T^{3} + 189 T^{4} + 33264 T^{5} + 209640 T^{6} - 423348 T^{7} - 6295659 T^{8} + 1746038 T^{9} + 448365285 T^{10} + 3074511312 T^{11} + 241045917 T^{12} - 69848346114 T^{13} + 174658804875 T^{14} + 3378420352086 T^{15} + 24837189432183 T^{16} + 79669539140166 T^{17} - 556166859942453 T^{18} + 3425790183027138 T^{19} + 45923963260106367 T^{20} + 268608066933301602 T^{21} + 597123696765454875 T^{22} - 10268296608344240502 T^{23} + 1523738752836120933 T^{24} + \)\(83\!\cdots\!84\)\( T^{25} + \)\(52\!\cdots\!85\)\( T^{26} + \)\(87\!\cdots\!34\)\( T^{27} - \)\(13\!\cdots\!91\)\( T^{28} - \)\(39\!\cdots\!36\)\( T^{29} + \)\(83\!\cdots\!40\)\( T^{30} + \)\(57\!\cdots\!52\)\( T^{31} + \)\(13\!\cdots\!61\)\( T^{32} - \)\(59\!\cdots\!02\)\( T^{33} - \)\(28\!\cdots\!21\)\( T^{34} + \)\(35\!\cdots\!58\)\( T^{35} + \)\(25\!\cdots\!49\)\( T^{36} \))(\( 1 + 6 T - 21 T^{2} - 186 T^{3} + 189 T^{4} + 33264 T^{5} + 209640 T^{6} - 423348 T^{7} - 6295659 T^{8} + 1746038 T^{9} + 448365285 T^{10} + 3074511312 T^{11} + 241045917 T^{12} - 69848346114 T^{13} + 174658804875 T^{14} + 3378420352086 T^{15} + 24837189432183 T^{16} + 79669539140166 T^{17} - 556166859942453 T^{18} + 3425790183027138 T^{19} + 45923963260106367 T^{20} + 268608066933301602 T^{21} + 597123696765454875 T^{22} - 10268296608344240502 T^{23} + 1523738752836120933 T^{24} + \)\(83\!\cdots\!84\)\( T^{25} + \)\(52\!\cdots\!85\)\( T^{26} + \)\(87\!\cdots\!34\)\( T^{27} - \)\(13\!\cdots\!91\)\( T^{28} - \)\(39\!\cdots\!36\)\( T^{29} + \)\(83\!\cdots\!40\)\( T^{30} + \)\(57\!\cdots\!52\)\( T^{31} + \)\(13\!\cdots\!61\)\( T^{32} - \)\(59\!\cdots\!02\)\( T^{33} - \)\(28\!\cdots\!21\)\( T^{34} + \)\(35\!\cdots\!58\)\( T^{35} + \)\(25\!\cdots\!49\)\( T^{36} \))
$47$ (\( 1 - 10 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 92 T^{2} + 2209 T^{4} \))(\( 1 - 82 T^{2} + 2209 T^{4} \))(\( 1 - 82 T^{2} + 2209 T^{4} \))(\( 1 - 92 T^{2} + 2209 T^{4} \))(\( 1 + 2 T - 43 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( 1 + 10 T + 53 T^{2} + 470 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 59 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 95 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 95 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 + 6 T + 59 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 56 T^{2} + 96 T^{3} + 111 T^{4} + 4512 T^{5} + 123704 T^{6} + 1245876 T^{7} + 4879681 T^{8} \))(\( 1 - 12 T + 56 T^{2} - 96 T^{3} + 111 T^{4} - 4512 T^{5} + 123704 T^{6} - 1245876 T^{7} + 4879681 T^{8} \))(\( 1 - 27 T + 333 T^{2} - 2439 T^{3} + 8496 T^{4} + 28422 T^{5} - 477611 T^{6} + 1335834 T^{7} + 18767664 T^{8} - 253224297 T^{9} + 1624933773 T^{10} - 6192315189 T^{11} + 10779215329 T^{12} \))(\( 1 + 21 T + 261 T^{2} + 2673 T^{3} + 22680 T^{4} + 170022 T^{5} + 1202725 T^{6} + 7991034 T^{7} + 50100120 T^{8} + 277518879 T^{9} + 1273596741 T^{10} + 4816245147 T^{11} + 10779215329 T^{12} \))(\( 1 - 15 T + 51 T^{2} + 503 T^{3} - 4224 T^{4} - 24030 T^{5} + 424469 T^{6} - 1129410 T^{7} - 9330816 T^{8} + 52222969 T^{9} + 248863731 T^{10} - 3440175105 T^{11} + 10779215329 T^{12} \))(\( 1 + 9 T + 63 T^{2} + 211 T^{3} + 684 T^{4} - 19926 T^{5} - 157555 T^{6} - 936522 T^{7} + 1510956 T^{8} + 21906653 T^{9} + 307419903 T^{10} + 2064105063 T^{11} + 10779215329 T^{12} \))(\( 1 + 30 T + 513 T^{2} + 7080 T^{3} + 82653 T^{4} + 839658 T^{5} + 7834750 T^{6} + 68409582 T^{7} + 564354339 T^{8} + 4487696358 T^{9} + 34855810623 T^{10} + 265959739158 T^{11} + 2009262496811 T^{12} + 15134745403848 T^{13} + 113276083053393 T^{14} + 839189032735482 T^{15} + 6142918374289473 T^{16} + 43955605156298646 T^{17} + 305538102586585597 T^{18} + 2065913442346036362 T^{19} + 13569706688805445857 T^{20} + 87127122945695947686 T^{21} + \)\(55\!\cdots\!33\)\( T^{22} + \)\(34\!\cdots\!36\)\( T^{23} + \)\(21\!\cdots\!19\)\( T^{24} + \)\(13\!\cdots\!54\)\( T^{25} + \)\(82\!\cdots\!03\)\( T^{26} + \)\(50\!\cdots\!86\)\( T^{27} + \)\(29\!\cdots\!11\)\( T^{28} + \)\(16\!\cdots\!46\)\( T^{29} + \)\(91\!\cdots\!50\)\( T^{30} + \)\(45\!\cdots\!66\)\( T^{31} + \)\(21\!\cdots\!57\)\( T^{32} + \)\(85\!\cdots\!40\)\( T^{33} + \)\(29\!\cdots\!73\)\( T^{34} + \)\(79\!\cdots\!10\)\( T^{35} + \)\(12\!\cdots\!89\)\( T^{36} \))(\( 1 - 30 T + 513 T^{2} - 7080 T^{3} + 82653 T^{4} - 839658 T^{5} + 7834750 T^{6} - 68409582 T^{7} + 564354339 T^{8} - 4487696358 T^{9} + 34855810623 T^{10} - 265959739158 T^{11} + 2009262496811 T^{12} - 15134745403848 T^{13} + 113276083053393 T^{14} - 839189032735482 T^{15} + 6142918374289473 T^{16} - 43955605156298646 T^{17} + 305538102586585597 T^{18} - 2065913442346036362 T^{19} + 13569706688805445857 T^{20} - 87127122945695947686 T^{21} + \)\(55\!\cdots\!33\)\( T^{22} - \)\(34\!\cdots\!36\)\( T^{23} + \)\(21\!\cdots\!19\)\( T^{24} - \)\(13\!\cdots\!54\)\( T^{25} + \)\(82\!\cdots\!03\)\( T^{26} - \)\(50\!\cdots\!86\)\( T^{27} + \)\(29\!\cdots\!11\)\( T^{28} - \)\(16\!\cdots\!46\)\( T^{29} + \)\(91\!\cdots\!50\)\( T^{30} - \)\(45\!\cdots\!66\)\( T^{31} + \)\(21\!\cdots\!57\)\( T^{32} - \)\(85\!\cdots\!40\)\( T^{33} + \)\(29\!\cdots\!73\)\( T^{34} - \)\(79\!\cdots\!10\)\( T^{35} + \)\(12\!\cdots\!89\)\( T^{36} \))
$53$ (\( 1 - 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 9 T + 53 T^{2} )^{2} \))(\( ( 1 + 9 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( 1 - 4 T - 37 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 - 4 T - 37 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 12 T + 91 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( 1 - 12 T + 91 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 - 12 T + 26 T^{2} - 144 T^{3} + 3483 T^{4} - 7632 T^{5} + 73034 T^{6} - 1786524 T^{7} + 7890481 T^{8} \))(\( 1 + 12 T + 26 T^{2} + 144 T^{3} + 3483 T^{4} + 7632 T^{5} + 73034 T^{6} + 1786524 T^{7} + 7890481 T^{8} \))(\( 1 + 90 T^{2} - 162 T^{3} + 8118 T^{4} - 15894 T^{5} + 425035 T^{6} - 842382 T^{7} + 22803462 T^{8} - 24118074 T^{9} + 710143290 T^{10} + 22164361129 T^{12} \))(\( 1 - 30 T + 378 T^{2} - 2214 T^{3} - 3276 T^{4} + 201552 T^{5} - 2070449 T^{6} + 10682256 T^{7} - 9202284 T^{8} - 329613678 T^{9} + 2982601818 T^{10} - 12545864790 T^{11} + 22164361129 T^{12} \))(\( 1 - 6 T - 30 T^{2} - 226 T^{3} + 2688 T^{4} - 11340 T^{5} + 185231 T^{6} - 601020 T^{7} + 7550592 T^{8} - 33646202 T^{9} - 236714430 T^{10} - 2509172958 T^{11} + 22164361129 T^{12} \))(\( 1 - 12 T + 174 T^{2} - 1510 T^{3} + 13782 T^{4} - 123426 T^{5} + 886811 T^{6} - 6541578 T^{7} + 38713638 T^{8} - 224804270 T^{9} + 1372943694 T^{10} - 5018345916 T^{11} + 22164361129 T^{12} \))(\( 1 - 60 T + 1650 T^{2} - 27432 T^{3} + 301668 T^{4} - 2105628 T^{5} + 4281813 T^{6} + 119664084 T^{7} - 2040984564 T^{8} + 18553996944 T^{9} - 97195599030 T^{10} - 6711373824 T^{11} + 6282268912998 T^{12} - 76409942308296 T^{13} + 541422906597858 T^{14} - 1929763576020600 T^{15} - 8353932299807628 T^{16} + 204027698698036896 T^{17} - 1895432192029963487 T^{18} + 10813468030995955488 T^{19} - 23466195830159627052 T^{20} - \)\(28\!\cdots\!00\)\( T^{21} + \)\(42\!\cdots\!98\)\( T^{22} - \)\(31\!\cdots\!28\)\( T^{23} + \)\(13\!\cdots\!42\)\( T^{24} - \)\(78\!\cdots\!88\)\( T^{25} - \)\(60\!\cdots\!30\)\( T^{26} + \)\(61\!\cdots\!52\)\( T^{27} - \)\(35\!\cdots\!36\)\( T^{28} + \)\(11\!\cdots\!48\)\( T^{29} + \)\(21\!\cdots\!33\)\( T^{30} - \)\(54\!\cdots\!44\)\( T^{31} + \)\(41\!\cdots\!92\)\( T^{32} - \)\(20\!\cdots\!24\)\( T^{33} + \)\(63\!\cdots\!50\)\( T^{34} - \)\(12\!\cdots\!80\)\( T^{35} + \)\(10\!\cdots\!89\)\( T^{36} \))(\( 1 + 60 T + 1650 T^{2} + 27432 T^{3} + 301668 T^{4} + 2105628 T^{5} + 4281813 T^{6} - 119664084 T^{7} - 2040984564 T^{8} - 18553996944 T^{9} - 97195599030 T^{10} + 6711373824 T^{11} + 6282268912998 T^{12} + 76409942308296 T^{13} + 541422906597858 T^{14} + 1929763576020600 T^{15} - 8353932299807628 T^{16} - 204027698698036896 T^{17} - 1895432192029963487 T^{18} - 10813468030995955488 T^{19} - 23466195830159627052 T^{20} + \)\(28\!\cdots\!00\)\( T^{21} + \)\(42\!\cdots\!98\)\( T^{22} + \)\(31\!\cdots\!28\)\( T^{23} + \)\(13\!\cdots\!42\)\( T^{24} + \)\(78\!\cdots\!88\)\( T^{25} - \)\(60\!\cdots\!30\)\( T^{26} - \)\(61\!\cdots\!52\)\( T^{27} - \)\(35\!\cdots\!36\)\( T^{28} - \)\(11\!\cdots\!48\)\( T^{29} + \)\(21\!\cdots\!33\)\( T^{30} + \)\(54\!\cdots\!44\)\( T^{31} + \)\(41\!\cdots\!92\)\( T^{32} + \)\(20\!\cdots\!24\)\( T^{33} + \)\(63\!\cdots\!50\)\( T^{34} + \)\(12\!\cdots\!80\)\( T^{35} + \)\(10\!\cdots\!89\)\( T^{36} \))
$59$ (\( 1 - 4 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 3 T + 59 T^{2} )^{2} \))(\( ( 1 + 3 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( 1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 - 14 T + 137 T^{2} - 826 T^{3} + 3481 T^{4} \))(\( 1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4} \))(\( 1 + 18 T + 131 T^{2} + 1350 T^{3} + 14652 T^{4} + 79650 T^{5} + 456011 T^{6} + 3696822 T^{7} + 12117361 T^{8} \))(\( 1 - 18 T + 131 T^{2} - 1350 T^{3} + 14652 T^{4} - 79650 T^{5} + 456011 T^{6} - 3696822 T^{7} + 12117361 T^{8} \))(\( 1 - 9 T + 162 T^{2} - 1710 T^{3} + 19845 T^{4} - 153801 T^{5} + 1449937 T^{6} - 9074259 T^{7} + 69080445 T^{8} - 351198090 T^{9} + 1963012482 T^{10} - 6434318691 T^{11} + 42180533641 T^{12} \))(\( 1 - 27 T + 360 T^{2} - 3312 T^{3} + 30879 T^{4} - 316287 T^{5} + 2798533 T^{6} - 18660933 T^{7} + 107489799 T^{8} - 680215248 T^{9} + 4362249960 T^{10} - 19302956073 T^{11} + 42180533641 T^{12} \))(\( 1 + 27 T + 198 T^{2} - 1134 T^{3} - 21663 T^{4} - 27117 T^{5} + 768025 T^{6} - 1599903 T^{7} - 75408903 T^{8} - 232899786 T^{9} + 2399237478 T^{10} + 19302956073 T^{11} + 42180533641 T^{12} \))(\( 1 - 27 T + 324 T^{2} - 1940 T^{3} - 1485 T^{4} + 146097 T^{5} - 1529227 T^{6} + 8619723 T^{7} - 5169285 T^{8} - 398435260 T^{9} + 3926024964 T^{10} - 19302956073 T^{11} + 42180533641 T^{12} \))(\( 1 + 3 T + 147 T^{2} + 171 T^{3} + 14145 T^{4} - 20985 T^{5} + 1008486 T^{6} - 2985972 T^{7} + 69846681 T^{8} - 198304002 T^{9} + 4259411502 T^{10} - 13599227022 T^{11} + 172659954987 T^{12} - 1030334779743 T^{13} + 3618940408428 T^{14} - 63172843841151 T^{15} + 36030527777310 T^{16} - 2630542860701457 T^{17} + 552420470270473 T^{18} - 155202028781385963 T^{19} + 125422267192816110 T^{20} - 12974375495251751229 T^{21} + 43852007366409518508 T^{22} - \)\(73\!\cdots\!57\)\( T^{23} + \)\(72\!\cdots\!67\)\( T^{24} - \)\(33\!\cdots\!18\)\( T^{25} + \)\(62\!\cdots\!42\)\( T^{26} - \)\(17\!\cdots\!78\)\( T^{27} + \)\(35\!\cdots\!81\)\( T^{28} - \)\(90\!\cdots\!48\)\( T^{29} + \)\(17\!\cdots\!66\)\( T^{30} - \)\(22\!\cdots\!15\)\( T^{31} + \)\(87\!\cdots\!45\)\( T^{32} + \)\(62\!\cdots\!29\)\( T^{33} + \)\(31\!\cdots\!27\)\( T^{34} + \)\(38\!\cdots\!57\)\( T^{35} + \)\(75\!\cdots\!21\)\( T^{36} \))(\( 1 - 3 T + 147 T^{2} - 171 T^{3} + 14145 T^{4} + 20985 T^{5} + 1008486 T^{6} + 2985972 T^{7} + 69846681 T^{8} + 198304002 T^{9} + 4259411502 T^{10} + 13599227022 T^{11} + 172659954987 T^{12} + 1030334779743 T^{13} + 3618940408428 T^{14} + 63172843841151 T^{15} + 36030527777310 T^{16} + 2630542860701457 T^{17} + 552420470270473 T^{18} + 155202028781385963 T^{19} + 125422267192816110 T^{20} + 12974375495251751229 T^{21} + 43852007366409518508 T^{22} + \)\(73\!\cdots\!57\)\( T^{23} + \)\(72\!\cdots\!67\)\( T^{24} + \)\(33\!\cdots\!18\)\( T^{25} + \)\(62\!\cdots\!42\)\( T^{26} + \)\(17\!\cdots\!78\)\( T^{27} + \)\(35\!\cdots\!81\)\( T^{28} + \)\(90\!\cdots\!48\)\( T^{29} + \)\(17\!\cdots\!66\)\( T^{30} + \)\(22\!\cdots\!15\)\( T^{31} + \)\(87\!\cdots\!45\)\( T^{32} - \)\(62\!\cdots\!29\)\( T^{33} + \)\(31\!\cdots\!27\)\( T^{34} - \)\(38\!\cdots\!57\)\( T^{35} + \)\(75\!\cdots\!21\)\( T^{36} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 8 T + 61 T^{2} )^{2} \))(\( ( 1 + 8 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( 1 + 11 T + 60 T^{2} + 671 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4} \))(\( 1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 - 8 T - 68 T^{2} - 80 T^{3} + 9799 T^{4} - 4880 T^{5} - 253028 T^{6} - 1815848 T^{7} + 13845841 T^{8} \))(\( 1 - 8 T - 68 T^{2} - 80 T^{3} + 9799 T^{4} - 4880 T^{5} - 253028 T^{6} - 1815848 T^{7} + 13845841 T^{8} \))(\( 1 + 3 T - 12 T^{2} - 388 T^{3} - 2754 T^{4} + 24057 T^{5} + 363015 T^{6} + 1467477 T^{7} - 10247634 T^{8} - 88068628 T^{9} - 166150092 T^{10} + 2533788903 T^{11} + 51520374361 T^{12} \))(\( 1 + 9 T + 72 T^{2} + 506 T^{3} + 6588 T^{4} + 59805 T^{5} + 418827 T^{6} + 3648105 T^{7} + 24513948 T^{8} + 114852386 T^{9} + 996900552 T^{10} + 7601366709 T^{11} + 51520374361 T^{12} \))(\( 1 + 15 T + 84 T^{2} + 32 T^{3} - 1638 T^{4} - 9657 T^{5} - 118173 T^{6} - 589077 T^{7} - 6094998 T^{8} + 7263392 T^{9} + 1163050644 T^{10} + 12668944515 T^{11} + 51520374361 T^{12} \))(\( 1 - 3 T - 60 T^{2} + 806 T^{3} - 720 T^{4} - 27153 T^{5} + 261519 T^{6} - 1656333 T^{7} - 2679120 T^{8} + 182946686 T^{9} - 830750460 T^{10} - 2533788903 T^{11} + 51520374361 T^{12} \))(\( 1 - 54 T + 1419 T^{2} - 24196 T^{3} + 298188 T^{4} - 2773170 T^{5} + 19625393 T^{6} - 102502452 T^{7} + 335429073 T^{8} + 12010950 T^{9} - 5870177721 T^{10} - 27572569602 T^{11} + 1258817150338 T^{12} - 15125142990834 T^{13} + 94725395808498 T^{14} - 97890584096768 T^{15} - 4855539132950343 T^{16} + 66754071035652906 T^{17} - 593552957411241911 T^{18} + 4071998333174827266 T^{19} - 18067461113708226303 T^{20} - 22219302668868497408 T^{21} + \)\(13\!\cdots\!18\)\( T^{22} - \)\(12\!\cdots\!34\)\( T^{23} + \)\(64\!\cdots\!18\)\( T^{24} - \)\(86\!\cdots\!42\)\( T^{25} - \)\(11\!\cdots\!01\)\( T^{26} + \)\(14\!\cdots\!50\)\( T^{27} + \)\(23\!\cdots\!73\)\( T^{28} - \)\(44\!\cdots\!72\)\( T^{29} + \)\(52\!\cdots\!53\)\( T^{30} - \)\(44\!\cdots\!70\)\( T^{31} + \)\(29\!\cdots\!08\)\( T^{32} - \)\(14\!\cdots\!96\)\( T^{33} + \)\(52\!\cdots\!59\)\( T^{34} - \)\(12\!\cdots\!34\)\( T^{35} + \)\(13\!\cdots\!81\)\( T^{36} \))(\( 1 - 54 T + 1419 T^{2} - 24196 T^{3} + 298188 T^{4} - 2773170 T^{5} + 19625393 T^{6} - 102502452 T^{7} + 335429073 T^{8} + 12010950 T^{9} - 5870177721 T^{10} - 27572569602 T^{11} + 1258817150338 T^{12} - 15125142990834 T^{13} + 94725395808498 T^{14} - 97890584096768 T^{15} - 4855539132950343 T^{16} + 66754071035652906 T^{17} - 593552957411241911 T^{18} + 4071998333174827266 T^{19} - 18067461113708226303 T^{20} - 22219302668868497408 T^{21} + \)\(13\!\cdots\!18\)\( T^{22} - \)\(12\!\cdots\!34\)\( T^{23} + \)\(64\!\cdots\!18\)\( T^{24} - \)\(86\!\cdots\!42\)\( T^{25} - \)\(11\!\cdots\!01\)\( T^{26} + \)\(14\!\cdots\!50\)\( T^{27} + \)\(23\!\cdots\!73\)\( T^{28} - \)\(44\!\cdots\!72\)\( T^{29} + \)\(52\!\cdots\!53\)\( T^{30} - \)\(44\!\cdots\!70\)\( T^{31} + \)\(29\!\cdots\!08\)\( T^{32} - \)\(14\!\cdots\!96\)\( T^{33} + \)\(52\!\cdots\!59\)\( T^{34} - \)\(12\!\cdots\!34\)\( T^{35} + \)\(13\!\cdots\!81\)\( T^{36} \))
$67$ (\( 1 + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( ( 1 - 67 T^{2} )^{2} \))(\( 1 - 59 T^{2} + 4489 T^{4} \))(\( 1 - 59 T^{2} + 4489 T^{4} \))(\( ( 1 - 67 T^{2} )^{2} \))(\( 1 + 3 T - 58 T^{2} + 201 T^{3} + 4489 T^{4} \))(\( 1 + 3 T - 58 T^{2} + 201 T^{3} + 4489 T^{4} \))(\( 1 - 9 T + 94 T^{2} - 603 T^{3} + 4489 T^{4} \))(\( 1 - 15 T + 142 T^{2} - 1005 T^{3} + 4489 T^{4} \))(\( 1 - 15 T + 142 T^{2} - 1005 T^{3} + 4489 T^{4} \))(\( 1 - 9 T + 94 T^{2} - 603 T^{3} + 4489 T^{4} \))(\( 1 + 6 T + 131 T^{2} + 714 T^{3} + 10476 T^{4} + 47838 T^{5} + 588059 T^{6} + 1804578 T^{7} + 20151121 T^{8} \))(\( 1 + 6 T + 131 T^{2} + 714 T^{3} + 10476 T^{4} + 47838 T^{5} + 588059 T^{6} + 1804578 T^{7} + 20151121 T^{8} \))(\( 1 + 3 T - 66 T^{2} - 982 T^{3} - 5553 T^{4} + 45963 T^{5} + 880911 T^{6} + 3079521 T^{7} - 24927417 T^{8} - 295349266 T^{9} - 1329973986 T^{10} + 4050375321 T^{11} + 90458382169 T^{12} \))(\( 1 + 15 T + 156 T^{2} + 1472 T^{3} + 16461 T^{4} + 143415 T^{5} + 1174659 T^{6} + 9608805 T^{7} + 73893429 T^{8} + 442723136 T^{9} + 3143574876 T^{10} + 20251876605 T^{11} + 90458382169 T^{12} \))(\( 1 + 3 T + 72 T^{2} + 30 T^{3} + 4257 T^{4} - 9465 T^{5} + 51479 T^{6} - 634155 T^{7} + 19109673 T^{8} + 9022890 T^{9} + 1450880712 T^{10} + 4050375321 T^{11} + 90458382169 T^{12} \))(\( 1 - 21 T + 126 T^{2} + 780 T^{3} - 13725 T^{4} + 32307 T^{5} + 306467 T^{6} + 2164569 T^{7} - 61611525 T^{8} + 234595140 T^{9} + 2539041246 T^{10} - 28352627247 T^{11} + 90458382169 T^{12} \))(\( 1 + 15 T + 261 T^{2} - 141 T^{3} - 10899 T^{4} - 414861 T^{5} - 707334 T^{6} + 127626 T^{7} + 366702183 T^{8} + 1265766858 T^{9} + 7693768710 T^{10} - 157969256568 T^{11} - 934704180705 T^{12} - 3849388888953 T^{13} + 21174817187466 T^{14} + 571406655639057 T^{15} - 239625722079108 T^{16} + 15635582643657549 T^{17} - 283713925369319687 T^{18} + 1047584037125055783 T^{19} - 1075679866413115812 T^{20} + \)\(17\!\cdots\!91\)\( T^{21} + \)\(42\!\cdots\!86\)\( T^{22} - \)\(51\!\cdots\!71\)\( T^{23} - \)\(84\!\cdots\!45\)\( T^{24} - \)\(95\!\cdots\!64\)\( T^{25} + \)\(31\!\cdots\!10\)\( T^{26} + \)\(34\!\cdots\!26\)\( T^{27} + \)\(66\!\cdots\!67\)\( T^{28} + \)\(15\!\cdots\!58\)\( T^{29} - \)\(57\!\cdots\!74\)\( T^{30} - \)\(22\!\cdots\!07\)\( T^{31} - \)\(40\!\cdots\!71\)\( T^{32} - \)\(34\!\cdots\!63\)\( T^{33} + \)\(43\!\cdots\!41\)\( T^{34} + \)\(16\!\cdots\!05\)\( T^{35} + \)\(74\!\cdots\!09\)\( T^{36} \))(\( 1 + 15 T + 261 T^{2} - 141 T^{3} - 10899 T^{4} - 414861 T^{5} - 707334 T^{6} + 127626 T^{7} + 366702183 T^{8} + 1265766858 T^{9} + 7693768710 T^{10} - 157969256568 T^{11} - 934704180705 T^{12} - 3849388888953 T^{13} + 21174817187466 T^{14} + 571406655639057 T^{15} - 239625722079108 T^{16} + 15635582643657549 T^{17} - 283713925369319687 T^{18} + 1047584037125055783 T^{19} - 1075679866413115812 T^{20} + \)\(17\!\cdots\!91\)\( T^{21} + \)\(42\!\cdots\!86\)\( T^{22} - \)\(51\!\cdots\!71\)\( T^{23} - \)\(84\!\cdots\!45\)\( T^{24} - \)\(95\!\cdots\!64\)\( T^{25} + \)\(31\!\cdots\!10\)\( T^{26} + \)\(34\!\cdots\!26\)\( T^{27} + \)\(66\!\cdots\!67\)\( T^{28} + \)\(15\!\cdots\!58\)\( T^{29} - \)\(57\!\cdots\!74\)\( T^{30} - \)\(22\!\cdots\!07\)\( T^{31} - \)\(40\!\cdots\!71\)\( T^{32} - \)\(34\!\cdots\!63\)\( T^{33} + \)\(43\!\cdots\!41\)\( T^{34} + \)\(16\!\cdots\!05\)\( T^{35} + \)\(74\!\cdots\!09\)\( T^{36} \))
$71$ (\( 1 + 16 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( 1 + 2 T - 67 T^{2} + 142 T^{3} + 5041 T^{4} \))(\( 1 + 14 T + 125 T^{2} + 994 T^{3} + 5041 T^{4} \))(\( 1 + 6 T - 35 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 + 6 T - 35 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 - 6 T - 35 T^{2} - 426 T^{3} + 5041 T^{4} \))(\( 1 - 6 T - 35 T^{2} - 426 T^{3} + 5041 T^{4} \))(\( ( 1 + 6 T - 35 T^{2} + 426 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 6 T - 35 T^{2} - 426 T^{3} + 5041 T^{4} )^{2} \))(\( 1 - 9 T - 27 T^{2} - 189 T^{3} + 2052 T^{4} - 16182 T^{5} + 532117 T^{6} - 1148922 T^{7} + 10344132 T^{8} - 67645179 T^{9} - 686115387 T^{10} - 16238064159 T^{11} + 128100283921 T^{12} \))(\( 1 - 9 T + 81 T^{2} - 9 T^{3} + 2916 T^{4} + 32418 T^{5} - 92555 T^{6} + 2301678 T^{7} + 14699556 T^{8} - 3221199 T^{9} + 2058346161 T^{10} - 16238064159 T^{11} + 128100283921 T^{12} \))(\( 1 - 3 T - 87 T^{2} - 187 T^{3} - 2094 T^{4} + 26118 T^{5} + 499145 T^{6} + 1854378 T^{7} - 10555854 T^{8} - 66929357 T^{9} - 2210816247 T^{10} - 5412688053 T^{11} + 128100283921 T^{12} \))(\( 1 - 39 T + 561 T^{2} - 2527 T^{3} - 21102 T^{4} + 349974 T^{5} - 2934895 T^{6} + 24848154 T^{7} - 106375182 T^{8} - 904441097 T^{9} + 14255953041 T^{10} - 70364944689 T^{11} + 128100283921 T^{12} \))(\( 1 + 36 T + 783 T^{2} + 12294 T^{3} + 151929 T^{4} + 1490724 T^{5} + 11252010 T^{6} + 56430666 T^{7} + 21405141 T^{8} - 2944849464 T^{9} - 32608974411 T^{10} - 144013019832 T^{11} + 788706469095 T^{12} + 19730660420844 T^{13} + 146027357453205 T^{14} - 296958247957530 T^{15} - 22225401167018517 T^{16} - 338162280479965170 T^{17} - 3347740106755531157 T^{18} - 24009521914077527070 T^{19} - \)\(11\!\cdots\!97\)\( T^{20} - \)\(10\!\cdots\!30\)\( T^{21} + \)\(37\!\cdots\!05\)\( T^{22} + \)\(35\!\cdots\!44\)\( T^{23} + \)\(10\!\cdots\!95\)\( T^{24} - \)\(13\!\cdots\!12\)\( T^{25} - \)\(21\!\cdots\!71\)\( T^{26} - \)\(13\!\cdots\!84\)\( T^{27} + \)\(69\!\cdots\!41\)\( T^{28} + \)\(13\!\cdots\!86\)\( T^{29} + \)\(18\!\cdots\!10\)\( T^{30} + \)\(17\!\cdots\!64\)\( T^{31} + \)\(12\!\cdots\!49\)\( T^{32} + \)\(72\!\cdots\!94\)\( T^{33} + \)\(32\!\cdots\!43\)\( T^{34} + \)\(10\!\cdots\!76\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))(\( 1 - 36 T + 783 T^{2} - 12294 T^{3} + 151929 T^{4} - 1490724 T^{5} + 11252010 T^{6} - 56430666 T^{7} + 21405141 T^{8} + 2944849464 T^{9} - 32608974411 T^{10} + 144013019832 T^{11} + 788706469095 T^{12} - 19730660420844 T^{13} + 146027357453205 T^{14} + 296958247957530 T^{15} - 22225401167018517 T^{16} + 338162280479965170 T^{17} - 3347740106755531157 T^{18} + 24009521914077527070 T^{19} - \)\(11\!\cdots\!97\)\( T^{20} + \)\(10\!\cdots\!30\)\( T^{21} + \)\(37\!\cdots\!05\)\( T^{22} - \)\(35\!\cdots\!44\)\( T^{23} + \)\(10\!\cdots\!95\)\( T^{24} + \)\(13\!\cdots\!12\)\( T^{25} - \)\(21\!\cdots\!71\)\( T^{26} + \)\(13\!\cdots\!84\)\( T^{27} + \)\(69\!\cdots\!41\)\( T^{28} - \)\(13\!\cdots\!86\)\( T^{29} + \)\(18\!\cdots\!10\)\( T^{30} - \)\(17\!\cdots\!64\)\( T^{31} + \)\(12\!\cdots\!49\)\( T^{32} - \)\(72\!\cdots\!94\)\( T^{33} + \)\(32\!\cdots\!43\)\( T^{34} - \)\(10\!\cdots\!76\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))
$73$ (\( 1 + 2 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( ( 1 + 4 T + 73 T^{2} )^{2} \))(\( ( 1 - 11 T + 73 T^{2} )^{2} \))(\( ( 1 - 11 T + 73 T^{2} )^{2} \))(\( ( 1 + 4 T + 73 T^{2} )^{2} \))(\( 1 - 3 T - 64 T^{2} - 219 T^{3} + 5329 T^{4} \))(\( 1 - 11 T + 48 T^{2} - 803 T^{3} + 5329 T^{4} \))(\( 1 + 5 T - 48 T^{2} + 365 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 10 T + 73 T^{2} ) \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 10 T + 73 T^{2} ) \))(\( 1 + 5 T - 48 T^{2} + 365 T^{3} + 5329 T^{4} \))(\( 1 - 2 T - 47 T^{2} + 190 T^{3} - 3020 T^{4} + 13870 T^{5} - 250463 T^{6} - 778034 T^{7} + 28398241 T^{8} \))(\( 1 - 2 T - 47 T^{2} + 190 T^{3} - 3020 T^{4} + 13870 T^{5} - 250463 T^{6} - 778034 T^{7} + 28398241 T^{8} \))(\( 1 + 12 T + 78 T^{2} + 413 T^{3} - 3663 T^{4} - 50373 T^{5} - 323559 T^{6} - 3677229 T^{7} - 19520127 T^{8} + 160664021 T^{9} + 2215062798 T^{10} + 24876859116 T^{11} + 151334226289 T^{12} \))(\( 1 - 12 T + 246 T^{2} - 2623 T^{3} + 30177 T^{4} - 326385 T^{5} + 2687649 T^{6} - 23826105 T^{7} + 160813233 T^{8} - 1020391591 T^{9} + 6985967286 T^{10} - 24876859116 T^{11} + 151334226289 T^{12} \))(\( 1 - 12 T + 54 T^{2} - 795 T^{3} - 135 T^{4} + 40083 T^{5} + 66905 T^{6} + 2926059 T^{7} - 719415 T^{8} - 309268515 T^{9} + 1533505014 T^{10} - 24876859116 T^{11} + 151334226289 T^{12} \))(\( 1 - 36 T + 558 T^{2} - 4367 T^{3} + 1161 T^{4} + 426735 T^{5} - 5460783 T^{6} + 31151655 T^{7} + 6186969 T^{8} - 1698837239 T^{9} + 15846218478 T^{10} - 74630577348 T^{11} + 151334226289 T^{12} \))(\( 1 + 42 T + 987 T^{2} + 18237 T^{3} + 294471 T^{4} + 4232547 T^{5} + 54899301 T^{6} + 657717267 T^{7} + 7388296041 T^{8} + 78246890120 T^{9} + 786613667418 T^{10} + 7581280265856 T^{11} + 70571415355692 T^{12} + 637318813879413 T^{13} + 5622272403642198 T^{14} + 48866439365813094 T^{15} + 420712573911451605 T^{16} + 3599514157362254064 T^{17} + 30740101302597031740 T^{18} + \)\(26\!\cdots\!72\)\( T^{19} + \)\(22\!\cdots\!45\)\( T^{20} + \)\(19\!\cdots\!98\)\( T^{21} + \)\(15\!\cdots\!18\)\( T^{22} + \)\(13\!\cdots\!09\)\( T^{23} + \)\(10\!\cdots\!88\)\( T^{24} + \)\(83\!\cdots\!32\)\( T^{25} + \)\(63\!\cdots\!58\)\( T^{26} + \)\(46\!\cdots\!60\)\( T^{27} + \)\(31\!\cdots\!09\)\( T^{28} + \)\(20\!\cdots\!59\)\( T^{29} + \)\(12\!\cdots\!21\)\( T^{30} + \)\(70\!\cdots\!51\)\( T^{31} + \)\(35\!\cdots\!39\)\( T^{32} + \)\(16\!\cdots\!09\)\( T^{33} + \)\(64\!\cdots\!07\)\( T^{34} + \)\(19\!\cdots\!26\)\( T^{35} + \)\(34\!\cdots\!69\)\( T^{36} \))(\( 1 + 42 T + 987 T^{2} + 18237 T^{3} + 294471 T^{4} + 4232547 T^{5} + 54899301 T^{6} + 657717267 T^{7} + 7388296041 T^{8} + 78246890120 T^{9} + 786613667418 T^{10} + 7581280265856 T^{11} + 70571415355692 T^{12} + 637318813879413 T^{13} + 5622272403642198 T^{14} + 48866439365813094 T^{15} + 420712573911451605 T^{16} + 3599514157362254064 T^{17} + 30740101302597031740 T^{18} + \)\(26\!\cdots\!72\)\( T^{19} + \)\(22\!\cdots\!45\)\( T^{20} + \)\(19\!\cdots\!98\)\( T^{21} + \)\(15\!\cdots\!18\)\( T^{22} + \)\(13\!\cdots\!09\)\( T^{23} + \)\(10\!\cdots\!88\)\( T^{24} + \)\(83\!\cdots\!32\)\( T^{25} + \)\(63\!\cdots\!58\)\( T^{26} + \)\(46\!\cdots\!60\)\( T^{27} + \)\(31\!\cdots\!09\)\( T^{28} + \)\(20\!\cdots\!59\)\( T^{29} + \)\(12\!\cdots\!21\)\( T^{30} + \)\(70\!\cdots\!51\)\( T^{31} + \)\(35\!\cdots\!39\)\( T^{32} + \)\(16\!\cdots\!09\)\( T^{33} + \)\(64\!\cdots\!07\)\( T^{34} + \)\(19\!\cdots\!26\)\( T^{35} + \)\(34\!\cdots\!69\)\( T^{36} \))
$79$ (\( 1 - 10 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 140 T^{2} + 6241 T^{4} \))(\( 1 - 110 T^{2} + 6241 T^{4} \))(\( 1 - 110 T^{2} + 6241 T^{4} \))(\( 1 - 140 T^{2} + 6241 T^{4} \))(\( 1 + 5 T - 54 T^{2} + 395 T^{3} + 6241 T^{4} \))(\( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 + 24 T + 271 T^{2} + 1896 T^{3} + 6241 T^{4} \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} ) \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} ) \))(\( 1 + 24 T + 271 T^{2} + 1896 T^{3} + 6241 T^{4} \))(\( 1 + 86 T^{2} + 1155 T^{4} + 536726 T^{6} + 38950081 T^{8} \))(\( 1 + 86 T^{2} + 1155 T^{4} + 536726 T^{6} + 38950081 T^{8} \))(\( 1 + 21 T + 231 T^{2} + 1223 T^{3} + 10710 T^{4} + 207918 T^{5} + 2599065 T^{6} + 16425522 T^{7} + 66841110 T^{8} + 602986697 T^{9} + 8997468711 T^{10} + 64618184379 T^{11} + 243087455521 T^{12} \))(\( 1 - 15 T + 105 T^{2} - 559 T^{3} - 6300 T^{4} + 127350 T^{5} - 1087083 T^{6} + 10060650 T^{7} - 39318300 T^{8} - 275608801 T^{9} + 4089758505 T^{10} - 46155845985 T^{11} + 243087455521 T^{12} \))(\( 1 - 27 T + 351 T^{2} - 3337 T^{3} + 19872 T^{4} - 49734 T^{5} + 58989 T^{6} - 3928986 T^{7} + 124021152 T^{8} - 1645271143 T^{9} + 13671478431 T^{10} - 83080522773 T^{11} + 243087455521 T^{12} \))(\( 1 + 45 T + 1125 T^{2} + 20185 T^{3} + 284850 T^{4} + 3300750 T^{5} + 32006361 T^{6} + 260759250 T^{7} + 1777748850 T^{8} + 9951992215 T^{9} + 43818841125 T^{10} + 138467537955 T^{11} + 243087455521 T^{12} \))(\( 1 + 6 T + 105 T^{2} + 12 T^{3} - 7521 T^{4} - 174786 T^{5} - 1839648 T^{6} - 15531168 T^{7} - 84472401 T^{8} + 500721516 T^{9} + 9828562413 T^{10} + 183247507110 T^{11} + 1703096733405 T^{12} + 13936667143614 T^{13} + 70953323686269 T^{14} - 63562841678010 T^{15} - 6626064358334913 T^{16} - 117320535019130334 T^{17} - 1023587231020301171 T^{18} - 9268322266511296386 T^{19} - 41353267660368192033 T^{20} - 31338959898084372390 T^{21} + \)\(27\!\cdots\!89\)\( T^{22} + \)\(42\!\cdots\!86\)\( T^{23} + \)\(41\!\cdots\!05\)\( T^{24} + \)\(35\!\cdots\!90\)\( T^{25} + \)\(14\!\cdots\!93\)\( T^{26} + \)\(60\!\cdots\!04\)\( T^{27} - \)\(79\!\cdots\!01\)\( T^{28} - \)\(11\!\cdots\!72\)\( T^{29} - \)\(10\!\cdots\!68\)\( T^{30} - \)\(81\!\cdots\!54\)\( T^{31} - \)\(27\!\cdots\!01\)\( T^{32} + \)\(34\!\cdots\!88\)\( T^{33} + \)\(24\!\cdots\!05\)\( T^{34} + \)\(10\!\cdots\!54\)\( T^{35} + \)\(14\!\cdots\!61\)\( T^{36} \))(\( 1 + 6 T + 105 T^{2} + 12 T^{3} - 7521 T^{4} - 174786 T^{5} - 1839648 T^{6} - 15531168 T^{7} - 84472401 T^{8} + 500721516 T^{9} + 9828562413 T^{10} + 183247507110 T^{11} + 1703096733405 T^{12} + 13936667143614 T^{13} + 70953323686269 T^{14} - 63562841678010 T^{15} - 6626064358334913 T^{16} - 117320535019130334 T^{17} - 1023587231020301171 T^{18} - 9268322266511296386 T^{19} - 41353267660368192033 T^{20} - 31338959898084372390 T^{21} + \)\(27\!\cdots\!89\)\( T^{22} + \)\(42\!\cdots\!86\)\( T^{23} + \)\(41\!\cdots\!05\)\( T^{24} + \)\(35\!\cdots\!90\)\( T^{25} + \)\(14\!\cdots\!93\)\( T^{26} + \)\(60\!\cdots\!04\)\( T^{27} - \)\(79\!\cdots\!01\)\( T^{28} - \)\(11\!\cdots\!72\)\( T^{29} - \)\(10\!\cdots\!68\)\( T^{30} - \)\(81\!\cdots\!54\)\( T^{31} - \)\(27\!\cdots\!01\)\( T^{32} + \)\(34\!\cdots\!88\)\( T^{33} + \)\(24\!\cdots\!05\)\( T^{34} + \)\(10\!\cdots\!54\)\( T^{35} + \)\(14\!\cdots\!61\)\( T^{36} \))
$83$ (\( 1 + 16 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( ( 1 - 18 T + 83 T^{2} )( 1 + 18 T + 83 T^{2} ) \))(\( 1 - 58 T^{2} + 6889 T^{4} \))(\( 1 - 58 T^{2} + 6889 T^{4} \))(\( ( 1 - 18 T + 83 T^{2} )( 1 + 18 T + 83 T^{2} ) \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 8 T + 83 T^{2} )^{2} \))(\( 1 - 139 T^{2} + 6889 T^{4} \))(\( 1 - 58 T^{2} + 6889 T^{4} \))(\( 1 - 58 T^{2} + 6889 T^{4} \))(\( 1 - 139 T^{2} + 6889 T^{4} \))(\( ( 1 - 18 T + 241 T^{2} - 1494 T^{3} + 6889 T^{4} )( 1 + 18 T + 241 T^{2} + 1494 T^{3} + 6889 T^{4} ) \))(\( ( 1 - 18 T + 241 T^{2} - 1494 T^{3} + 6889 T^{4} )( 1 + 18 T + 241 T^{2} + 1494 T^{3} + 6889 T^{4} ) \))(\( 1 + 9 T - 24 T^{2} - 765 T^{3} - 5385 T^{4} - 5094 T^{5} + 401515 T^{6} - 422802 T^{7} - 37097265 T^{8} - 437417055 T^{9} - 1138999704 T^{10} + 35451365787 T^{11} + 326940373369 T^{12} \))(\( 1 + 3 T + 30 T^{2} + 2727 T^{3} + 6369 T^{4} + 60420 T^{5} + 2990995 T^{6} + 5014860 T^{7} + 43876041 T^{8} + 1559263149 T^{9} + 1423749630 T^{10} + 11817121929 T^{11} + 326940373369 T^{12} \))(\( 1 - 3 T - 204 T^{2} + 459 T^{3} + 26043 T^{4} - 31530 T^{5} - 2382653 T^{6} - 2616990 T^{7} + 179410227 T^{8} + 262450233 T^{9} - 9681497484 T^{10} - 11817121929 T^{11} + 326940373369 T^{12} \))(\( 1 + 27 T + 258 T^{2} + 2747 T^{3} + 48153 T^{4} + 422916 T^{5} + 2558915 T^{6} + 35102028 T^{7} + 331726017 T^{8} + 1570698889 T^{9} + 12244246818 T^{10} + 106354097361 T^{11} + 326940373369 T^{12} \))(\( 1 + 36 T + 933 T^{2} + 18036 T^{3} + 288726 T^{4} + 3894066 T^{5} + 44585626 T^{6} + 427832820 T^{7} + 3238148952 T^{8} + 15314831406 T^{9} - 41770983672 T^{10} - 2031136646670 T^{11} - 28546456613887 T^{12} - 267157369918080 T^{13} - 1619051199635544 T^{14} - 1166445387626454 T^{15} + 131515615370951265 T^{16} + 2209564952357871564 T^{17} + 23659712196432683167 T^{18} + \)\(18\!\cdots\!12\)\( T^{19} + \)\(90\!\cdots\!85\)\( T^{20} - \)\(66\!\cdots\!98\)\( T^{21} - \)\(76\!\cdots\!24\)\( T^{22} - \)\(10\!\cdots\!40\)\( T^{23} - \)\(93\!\cdots\!03\)\( T^{24} - \)\(55\!\cdots\!90\)\( T^{25} - \)\(94\!\cdots\!52\)\( T^{26} + \)\(28\!\cdots\!18\)\( T^{27} + \)\(50\!\cdots\!48\)\( T^{28} + \)\(55\!\cdots\!40\)\( T^{29} + \)\(47\!\cdots\!86\)\( T^{30} + \)\(34\!\cdots\!58\)\( T^{31} + \)\(21\!\cdots\!54\)\( T^{32} + \)\(11\!\cdots\!52\)\( T^{33} + \)\(47\!\cdots\!73\)\( T^{34} + \)\(15\!\cdots\!28\)\( T^{35} + \)\(34\!\cdots\!09\)\( T^{36} \))(\( 1 - 36 T + 933 T^{2} - 18036 T^{3} + 288726 T^{4} - 3894066 T^{5} + 44585626 T^{6} - 427832820 T^{7} + 3238148952 T^{8} - 15314831406 T^{9} - 41770983672 T^{10} + 2031136646670 T^{11} - 28546456613887 T^{12} + 267157369918080 T^{13} - 1619051199635544 T^{14} + 1166445387626454 T^{15} + 131515615370951265 T^{16} - 2209564952357871564 T^{17} + 23659712196432683167 T^{18} - \)\(18\!\cdots\!12\)\( T^{19} + \)\(90\!\cdots\!85\)\( T^{20} + \)\(66\!\cdots\!98\)\( T^{21} - \)\(76\!\cdots\!24\)\( T^{22} + \)\(10\!\cdots\!40\)\( T^{23} - \)\(93\!\cdots\!03\)\( T^{24} + \)\(55\!\cdots\!90\)\( T^{25} - \)\(94\!\cdots\!52\)\( T^{26} - \)\(28\!\cdots\!18\)\( T^{27} + \)\(50\!\cdots\!48\)\( T^{28} - \)\(55\!\cdots\!40\)\( T^{29} + \)\(47\!\cdots\!86\)\( T^{30} - \)\(34\!\cdots\!58\)\( T^{31} + \)\(21\!\cdots\!54\)\( T^{32} - \)\(11\!\cdots\!52\)\( T^{33} + \)\(47\!\cdots\!73\)\( T^{34} - \)\(15\!\cdots\!28\)\( T^{35} + \)\(34\!\cdots\!09\)\( T^{36} \))
$89$ (\( 1 + 2 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( 1 + 18 T + 235 T^{2} + 1602 T^{3} + 7921 T^{4} \))(\( 1 - 14 T + 107 T^{2} - 1246 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 + 24 T + 278 T^{2} + 2880 T^{3} + 29619 T^{4} + 256320 T^{5} + 2202038 T^{6} + 16919256 T^{7} + 62742241 T^{8} \))(\( 1 - 24 T + 278 T^{2} - 2880 T^{3} + 29619 T^{4} - 256320 T^{5} + 2202038 T^{6} - 16919256 T^{7} + 62742241 T^{8} \))(\( 1 + 90 T^{2} - 1503 T^{3} + 10845 T^{4} - 69993 T^{5} + 2290681 T^{6} - 6229377 T^{7} + 85903245 T^{8} - 1059568407 T^{9} + 5646801690 T^{10} + 496981290961 T^{12} \))(\( 1 + 48 T + 1044 T^{2} + 11907 T^{3} + 43551 T^{4} - 760371 T^{5} - 12833135 T^{6} - 67673019 T^{7} + 344967471 T^{8} + 8394065883 T^{9} + 65502899604 T^{10} + 268034853552 T^{11} + 496981290961 T^{12} \))(\( 1 - 42 T + 756 T^{2} - 7371 T^{3} + 29799 T^{4} + 258951 T^{5} - 4921811 T^{6} + 23046639 T^{7} + 236037879 T^{8} - 5196326499 T^{9} + 47433134196 T^{10} - 234530496858 T^{11} + 496981290961 T^{12} \))(\( 1 + 30 T + 246 T^{2} - 1397 T^{3} - 27591 T^{4} + 122913 T^{5} + 4060949 T^{6} + 10939257 T^{7} - 218548311 T^{8} - 984841693 T^{9} + 15434591286 T^{10} + 167521783470 T^{11} + 496981290961 T^{12} \))(\( 1 - 60 T + 1776 T^{2} - 34614 T^{3} + 496338 T^{4} - 5534214 T^{5} + 49734306 T^{6} - 369669372 T^{7} + 2296624737 T^{8} - 12045834756 T^{9} + 64847325075 T^{10} - 666977776530 T^{11} + 10435284988407 T^{12} - 129666784460280 T^{13} + 947893176853536 T^{14} + 915051609860724 T^{15} - 142365550113566094 T^{16} + 2442885993414165792 T^{17} - 27130214352755261423 T^{18} + \)\(21\!\cdots\!88\)\( T^{19} - \)\(11\!\cdots\!74\)\( T^{20} + \)\(64\!\cdots\!56\)\( T^{21} + \)\(59\!\cdots\!76\)\( T^{22} - \)\(72\!\cdots\!20\)\( T^{23} + \)\(51\!\cdots\!27\)\( T^{24} - \)\(29\!\cdots\!70\)\( T^{25} + \)\(25\!\cdots\!75\)\( T^{26} - \)\(42\!\cdots\!04\)\( T^{27} + \)\(71\!\cdots\!37\)\( T^{28} - \)\(10\!\cdots\!08\)\( T^{29} + \)\(12\!\cdots\!26\)\( T^{30} - \)\(12\!\cdots\!66\)\( T^{31} + \)\(97\!\cdots\!58\)\( T^{32} - \)\(60\!\cdots\!86\)\( T^{33} + \)\(27\!\cdots\!36\)\( T^{34} - \)\(82\!\cdots\!40\)\( T^{35} + \)\(12\!\cdots\!81\)\( T^{36} \))(\( 1 + 60 T + 1776 T^{2} + 34614 T^{3} + 496338 T^{4} + 5534214 T^{5} + 49734306 T^{6} + 369669372 T^{7} + 2296624737 T^{8} + 12045834756 T^{9} + 64847325075 T^{10} + 666977776530 T^{11} + 10435284988407 T^{12} + 129666784460280 T^{13} + 947893176853536 T^{14} - 915051609860724 T^{15} - 142365550113566094 T^{16} - 2442885993414165792 T^{17} - 27130214352755261423 T^{18} - \)\(21\!\cdots\!88\)\( T^{19} - \)\(11\!\cdots\!74\)\( T^{20} - \)\(64\!\cdots\!56\)\( T^{21} + \)\(59\!\cdots\!76\)\( T^{22} + \)\(72\!\cdots\!20\)\( T^{23} + \)\(51\!\cdots\!27\)\( T^{24} + \)\(29\!\cdots\!70\)\( T^{25} + \)\(25\!\cdots\!75\)\( T^{26} + \)\(42\!\cdots\!04\)\( T^{27} + \)\(71\!\cdots\!37\)\( T^{28} + \)\(10\!\cdots\!08\)\( T^{29} + \)\(12\!\cdots\!26\)\( T^{30} + \)\(12\!\cdots\!66\)\( T^{31} + \)\(97\!\cdots\!58\)\( T^{32} + \)\(60\!\cdots\!86\)\( T^{33} + \)\(27\!\cdots\!36\)\( T^{34} + \)\(82\!\cdots\!40\)\( T^{35} + \)\(12\!\cdots\!81\)\( T^{36} \))
$97$ (\( 1 + 10 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 122 T^{2} + 9409 T^{4} \))(\( ( 1 - 14 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))(\( ( 1 - 14 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))(\( 1 - 122 T^{2} + 9409 T^{4} \))(\( 1 + 10 T + 3 T^{2} + 970 T^{3} + 9409 T^{4} \))(\( 1 + 2 T - 93 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 - 15 T + 172 T^{2} - 1455 T^{3} + 9409 T^{4} \))(\( 1 - 12 T + 145 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( 1 - 12 T + 145 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( 1 - 15 T + 172 T^{2} - 1455 T^{3} + 9409 T^{4} \))(\( 1 + 18 T + 257 T^{2} + 2682 T^{3} + 23268 T^{4} + 260154 T^{5} + 2418113 T^{6} + 16428114 T^{7} + 88529281 T^{8} \))(\( 1 + 18 T + 257 T^{2} + 2682 T^{3} + 23268 T^{4} + 260154 T^{5} + 2418113 T^{6} + 16428114 T^{7} + 88529281 T^{8} \))(\( 1 + 54 T + 1323 T^{2} + 18839 T^{3} + 159489 T^{4} + 678051 T^{5} + 1700166 T^{6} + 65770947 T^{7} + 1500632001 T^{8} + 17193846647 T^{9} + 117124238763 T^{10} + 463716373878 T^{11} + 832972004929 T^{12} \))(\( 1 - 18 T + 99 T^{2} + 551 T^{3} - 5967 T^{4} - 122661 T^{5} + 2662518 T^{6} - 11898117 T^{7} - 56143503 T^{8} + 502882823 T^{9} + 8764398819 T^{10} - 154572124626 T^{11} + 832972004929 T^{12} \))(\( 1 - 18 T + 171 T^{2} - 713 T^{3} - 4239 T^{4} + 76491 T^{5} - 635802 T^{6} + 7419627 T^{7} - 39884751 T^{8} - 650735849 T^{9} + 15138507051 T^{10} - 154572124626 T^{11} + 832972004929 T^{12} \))(\( 1 + 6 T + 3 T^{2} - 1129 T^{3} - 4671 T^{4} - 9261 T^{5} + 257046 T^{6} - 898317 T^{7} - 43949439 T^{8} - 1030407817 T^{9} + 265587843 T^{10} + 51524041542 T^{11} + 832972004929 T^{12} \))(\( 1 - 9 T - 144 T^{2} + 738 T^{3} + 24876 T^{4} - 33426 T^{5} - 3312222 T^{6} + 7543458 T^{7} + 194381685 T^{8} + 180299952 T^{9} - 17434826145 T^{10} + 30673420866 T^{11} + 1593626340066 T^{12} - 12345639540786 T^{13} - 123372283755096 T^{14} + 798341631533874 T^{15} + 21902978789430156 T^{16} - 35315966793092571 T^{17} - 2473083691139187794 T^{18} - 3425648778929979387 T^{19} + \)\(20\!\cdots\!04\)\( T^{20} + \)\(72\!\cdots\!02\)\( T^{21} - \)\(10\!\cdots\!76\)\( T^{22} - \)\(10\!\cdots\!02\)\( T^{23} + \)\(13\!\cdots\!14\)\( T^{24} + \)\(24\!\cdots\!58\)\( T^{25} - \)\(13\!\cdots\!45\)\( T^{26} + \)\(13\!\cdots\!84\)\( T^{27} + \)\(14\!\cdots\!65\)\( T^{28} + \)\(53\!\cdots\!74\)\( T^{29} - \)\(22\!\cdots\!02\)\( T^{30} - \)\(22\!\cdots\!02\)\( T^{31} + \)\(16\!\cdots\!44\)\( T^{32} + \)\(46\!\cdots\!34\)\( T^{33} - \)\(88\!\cdots\!24\)\( T^{34} - \)\(53\!\cdots\!33\)\( T^{35} + \)\(57\!\cdots\!89\)\( T^{36} \))(\( 1 - 9 T - 144 T^{2} + 738 T^{3} + 24876 T^{4} - 33426 T^{5} - 3312222 T^{6} + 7543458 T^{7} + 194381685 T^{8} + 180299952 T^{9} - 17434826145 T^{10} + 30673420866 T^{11} + 1593626340066 T^{12} - 12345639540786 T^{13} - 123372283755096 T^{14} + 798341631533874 T^{15} + 21902978789430156 T^{16} - 35315966793092571 T^{17} - 2473083691139187794 T^{18} - 3425648778929979387 T^{19} + \)\(20\!\cdots\!04\)\( T^{20} + \)\(72\!\cdots\!02\)\( T^{21} - \)\(10\!\cdots\!76\)\( T^{22} - \)\(10\!\cdots\!02\)\( T^{23} + \)\(13\!\cdots\!14\)\( T^{24} + \)\(24\!\cdots\!58\)\( T^{25} - \)\(13\!\cdots\!45\)\( T^{26} + \)\(13\!\cdots\!84\)\( T^{27} + \)\(14\!\cdots\!65\)\( T^{28} + \)\(53\!\cdots\!74\)\( T^{29} - \)\(22\!\cdots\!02\)\( T^{30} - \)\(22\!\cdots\!02\)\( T^{31} + \)\(16\!\cdots\!44\)\( T^{32} + \)\(46\!\cdots\!34\)\( T^{33} - \)\(88\!\cdots\!24\)\( T^{34} - \)\(53\!\cdots\!33\)\( T^{35} + \)\(57\!\cdots\!89\)\( T^{36} \))
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