Properties

Label 294.2
Level 294
Weight 2
Dimension 563
Nonzero newspaces 8
Newform subspaces 28
Sturm bound 9408
Trace bound 4

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Defining parameters

Level: \( N \) = \( 294\( 294 = 2 \cdot 3 \cdot 7^{2} \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 28 \)
Sturm bound: \(9408\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(294))\).

Total New Old
Modular forms 2592 563 2029
Cusp forms 2113 563 1550
Eisenstein series 479 0 479

Trace form

\( 563q - q^{2} + 3q^{3} + 7q^{4} + 18q^{5} + 11q^{6} + 16q^{7} - q^{8} + 15q^{9} + O(q^{10}) \) \( 563q - q^{2} + 3q^{3} + 7q^{4} + 18q^{5} + 11q^{6} + 16q^{7} - q^{8} + 15q^{9} + 18q^{10} + 36q^{11} + 3q^{12} + 18q^{13} - 6q^{15} - q^{16} + 6q^{17} - 25q^{18} + 12q^{19} - 6q^{20} - 10q^{21} - 12q^{22} - 13q^{24} + 17q^{25} + 10q^{26} + 3q^{27} + 12q^{28} + 18q^{29} + 18q^{30} + 48q^{31} - q^{32} + 36q^{33} + 30q^{34} + 48q^{35} + 15q^{36} - 38q^{37} - 32q^{38} - 56q^{39} - 66q^{40} - 114q^{41} - 54q^{42} - 52q^{43} - 48q^{44} - 66q^{45} - 180q^{46} - 144q^{47} - 11q^{48} - 288q^{49} - 103q^{50} - 210q^{51} - 58q^{52} - 150q^{53} - 37q^{54} - 420q^{55} - 72q^{56} - 48q^{57} - 222q^{58} - 132q^{59} - 72q^{60} - 178q^{61} - 68q^{62} - 30q^{63} + 7q^{64} + 84q^{65} - 12q^{66} - 20q^{67} + 6q^{68} + 24q^{69} + 72q^{71} + 23q^{72} + 30q^{73} + 34q^{74} + 45q^{75} + 12q^{76} + 108q^{77} + 34q^{78} + 160q^{79} + 18q^{80} + 27q^{81} + 102q^{82} - 12q^{83} + 26q^{84} + 108q^{85} + 76q^{86} - 78q^{87} + 12q^{88} - 66q^{89} + 18q^{90} - 56q^{91} + 24q^{92} - 228q^{93} + 96q^{94} - 240q^{95} - 13q^{96} - 66q^{97} + 24q^{98} - 180q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)

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
294.2.a \(\chi_{294}(1, \cdot)\) 294.2.a.a 1 1
294.2.a.b 1
294.2.a.c 1
294.2.a.d 1
294.2.a.e 1
294.2.a.f 1
294.2.a.g 1
294.2.d \(\chi_{294}(293, \cdot)\) 294.2.d.a 4 1
294.2.d.b 8
294.2.e \(\chi_{294}(67, \cdot)\) 294.2.e.a 2 2
294.2.e.b 2
294.2.e.c 2
294.2.e.d 2
294.2.e.e 2
294.2.e.f 2
294.2.f \(\chi_{294}(215, \cdot)\) 294.2.f.a 4 2
294.2.f.b 8
294.2.f.c 16
294.2.i \(\chi_{294}(43, \cdot)\) 294.2.i.a 6 6
294.2.i.b 12
294.2.i.c 12
294.2.i.d 18
294.2.j \(\chi_{294}(41, \cdot)\) 294.2.j.a 120 6
294.2.m \(\chi_{294}(25, \cdot)\) 294.2.m.a 24 12
294.2.m.b 24
294.2.m.c 36
294.2.m.d 36
294.2.p \(\chi_{294}(5, \cdot)\) 294.2.p.a 216 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(294))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(294)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T^{2} + T^{4} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{3} \))
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 - 3 T^{2} )^{2} \))(\( 1 + 8 T^{2} + 32 T^{4} + 72 T^{6} + 81 T^{8} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 - 9 T^{4} + 81 T^{8} \))(\( 1 - 8 T^{2} + 32 T^{4} - 112 T^{6} + 367 T^{8} - 1008 T^{10} + 2592 T^{12} - 5832 T^{14} + 6561 T^{16} \))(\( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{3} \))
$5$ (\( 1 + 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( ( 1 + 7 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 + 4 T^{2} + 22 T^{4} + 100 T^{6} + 625 T^{8} )^{2} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} \))(\( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} \))(\( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 - 7 T^{2} + 24 T^{4} - 175 T^{6} + 625 T^{8} \))(\( ( 1 - 4 T^{2} - 9 T^{4} - 100 T^{6} + 625 T^{8} )^{2} \))(\( ( 1 - 4 T^{2} - 6 T^{4} + 112 T^{6} - 541 T^{8} + 2800 T^{10} - 3750 T^{12} - 62500 T^{14} + 390625 T^{16} )^{2} \))(\( 1 - 5 T + 6 T^{2} + 2 T^{3} + 9 T^{4} - 13 T^{5} - 64 T^{6} - 65 T^{7} + 225 T^{8} + 250 T^{9} + 3750 T^{10} - 15625 T^{11} + 15625 T^{12} \))(\( 1 - T + 3 T^{2} - 17 T^{3} + 52 T^{4} - 76 T^{5} + 288 T^{6} - 995 T^{7} + 1533 T^{8} - 3651 T^{9} + 11471 T^{10} - 26420 T^{11} + 36936 T^{12} - 132100 T^{13} + 286775 T^{14} - 456375 T^{15} + 958125 T^{16} - 3109375 T^{17} + 4500000 T^{18} - 5937500 T^{19} + 20312500 T^{20} - 33203125 T^{21} + 29296875 T^{22} - 48828125 T^{23} + 244140625 T^{24} \))(\( 1 + T - 11 T^{2} - 11 T^{3} + 38 T^{4} + 20 T^{5} - 48 T^{6} - 83 T^{7} + 483 T^{8} + 2615 T^{9} - 1283 T^{10} - 10022 T^{11} - 4616 T^{12} - 50110 T^{13} - 32075 T^{14} + 326875 T^{15} + 301875 T^{16} - 259375 T^{17} - 750000 T^{18} + 1562500 T^{19} + 14843750 T^{20} - 21484375 T^{21} - 107421875 T^{22} + 48828125 T^{23} + 244140625 T^{24} \))(\( 1 - 3 T - 6 T^{2} + 16 T^{3} + 52 T^{4} - 48 T^{5} - 488 T^{6} + 635 T^{7} + 1823 T^{8} - 2030 T^{9} - 10568 T^{10} + 12216 T^{11} + 54088 T^{12} - 68562 T^{13} - 292136 T^{14} + 259156 T^{15} + 1891974 T^{16} - 1116080 T^{17} - 7929944 T^{18} - 5580400 T^{19} + 47299350 T^{20} + 32394500 T^{21} - 182585000 T^{22} - 214256250 T^{23} + 845125000 T^{24} + 954375000 T^{25} - 4128125000 T^{26} - 3964843750 T^{27} + 17802734375 T^{28} + 31005859375 T^{29} - 119140625000 T^{30} - 58593750000 T^{31} + 317382812500 T^{32} + 488281250000 T^{33} - 915527343750 T^{34} - 2288818359375 T^{35} + 3814697265625 T^{36} \))
$7$ (\( 1 - 7 T + 21 T^{2} - 49 T^{3} + 147 T^{4} - 343 T^{5} + 343 T^{6} \))(\( 1 - 7 T^{2} + 14 T^{3} - 49 T^{4} - 98 T^{5} + 735 T^{6} - 686 T^{7} - 2401 T^{8} + 4802 T^{9} - 16807 T^{10} + 117649 T^{12} \))(\( 1 - 7 T^{2} + 14 T^{3} - 49 T^{4} - 98 T^{5} + 735 T^{6} - 686 T^{7} - 2401 T^{8} + 4802 T^{9} - 16807 T^{10} + 117649 T^{12} \))(\( 1 - T + 22 T^{2} + 48 T^{3} + 113 T^{4} + 1287 T^{5} + 1408 T^{6} + 8407 T^{7} + 33096 T^{8} + 29351 T^{9} + 231672 T^{10} + 411943 T^{11} + 482944 T^{12} + 3090087 T^{13} + 1899191 T^{14} + 5647152 T^{15} + 18117946 T^{16} - 5764801 T^{17} + 40353607 T^{18} \))
$11$ (\( 1 - 3 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( ( 1 - 13 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 4 T + 8 T^{2} - 44 T^{3} + 121 T^{4} )^{2}( 1 + 4 T + 8 T^{2} + 44 T^{3} + 121 T^{4} )^{2} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + 13 T^{2} + 48 T^{4} + 1573 T^{6} + 14641 T^{8} \))(\( ( 1 + 11 T^{2} + 121 T^{4} )^{4} \))(\( ( 1 - 4 T + 8 T^{2} + 56 T^{3} - 233 T^{4} + 616 T^{5} + 968 T^{6} - 5324 T^{7} + 14641 T^{8} )^{2}( 1 + 4 T + 8 T^{2} - 56 T^{3} - 233 T^{4} - 616 T^{5} + 968 T^{6} + 5324 T^{7} + 14641 T^{8} )^{2} \))(\( 1 - 4 T + 5 T^{2} - 18 T^{3} + 227 T^{4} - 710 T^{5} + 1519 T^{6} - 7810 T^{7} + 27467 T^{8} - 23958 T^{9} + 73205 T^{10} - 644204 T^{11} + 1771561 T^{12} \))(\( ( 1 - 4 T + 33 T^{2} - 116 T^{3} + 633 T^{4} - 2012 T^{5} + 8141 T^{6} - 22132 T^{7} + 76593 T^{8} - 154396 T^{9} + 483153 T^{10} - 644204 T^{11} + 1771561 T^{12} )( 1 + 10 T + 47 T^{2} + 108 T^{3} - 39 T^{4} - 1326 T^{5} - 5873 T^{6} - 14586 T^{7} - 4719 T^{8} + 143748 T^{9} + 688127 T^{10} + 1610510 T^{11} + 1771561 T^{12} ) \))(\( 1 + 6 T + 12 T^{2} + 8 T^{3} + 91 T^{4} + 546 T^{5} + 378 T^{6} + 8028 T^{7} + 66333 T^{8} + 191606 T^{9} + 200332 T^{10} + 531188 T^{11} + 4415761 T^{12} + 5843068 T^{13} + 24240172 T^{14} + 255027586 T^{15} + 971181453 T^{16} + 1292917428 T^{17} + 669650058 T^{18} + 10639995366 T^{19} + 19506658171 T^{20} + 18863581528 T^{21} + 311249095212 T^{22} + 1711870023666 T^{23} + 3138428376721 T^{24} \))(\( 1 + 4 T - 21 T^{2} - 92 T^{3} + 114 T^{4} + 518 T^{5} + 552 T^{6} + 3314 T^{7} - 465 T^{8} - 17998 T^{9} - 282673 T^{10} - 616446 T^{11} + 5672708 T^{12} + 7461826 T^{13} - 41152837 T^{14} + 50201038 T^{15} + 151911488 T^{16} - 719392574 T^{17} - 1055908673 T^{18} - 7913318314 T^{19} + 18381290048 T^{20} + 66817581578 T^{21} - 602518686517 T^{22} + 1201734539126 T^{23} + 10049548257188 T^{24} - 12012788614266 T^{25} - 60593467968913 T^{26} - 42438342542618 T^{27} - 12060902439465 T^{28} + 945522876404854 T^{29} + 1732412463949992 T^{30} + 17882764890556258 T^{31} + 43291481028489474 T^{32} - 384306831586239892 T^{33} - 964944327135015381 T^{34} + 2021788113997175084 T^{35} + 5559917313492231481 T^{36} \))
$13$ (\( 1 - 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( ( 1 - 14 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 20 T^{2} + 310 T^{4} - 3380 T^{6} + 28561 T^{8} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 14 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 20 T^{2} + 169 T^{4} )^{4} \))(\( ( 1 - 20 T^{2} + 310 T^{4} - 3380 T^{6} + 28561 T^{8} )^{4} \))(\( 1 - 13 T + 72 T^{2} - 200 T^{3} - 79 T^{4} + 4173 T^{5} - 22100 T^{6} + 54249 T^{7} - 13351 T^{8} - 439400 T^{9} + 2056392 T^{10} - 4826809 T^{11} + 4826809 T^{12} \))(\( 1 - T + 15 T^{2} - 105 T^{3} + 390 T^{4} - 1228 T^{5} + 7898 T^{6} - 37509 T^{7} + 100851 T^{8} - 484985 T^{9} + 2276721 T^{10} - 7914572 T^{11} + 22873384 T^{12} - 102889436 T^{13} + 384765849 T^{14} - 1065512045 T^{15} + 2880405411 T^{16} - 13926829137 T^{17} + 38122137482 T^{18} - 77055178876 T^{19} + 318134981190 T^{20} - 1113472434165 T^{21} + 2067877377735 T^{22} - 1792160394037 T^{23} + 23298085122481 T^{24} \))(\( 1 + T + T^{2} - 7 T^{3} + 26 T^{4} - 592 T^{5} + 478 T^{6} + 3223 T^{7} + 14107 T^{8} - 54337 T^{9} + 206163 T^{10} - 983912 T^{11} - 5997248 T^{12} - 12790856 T^{13} + 34841547 T^{14} - 119378389 T^{15} + 402910027 T^{16} + 1196677339 T^{17} + 2307214702 T^{18} - 37147122064 T^{19} + 21208998746 T^{20} - 74231495611 T^{21} + 137858491849 T^{22} + 1792160394037 T^{23} + 23298085122481 T^{24} \))(\( 1 + 5 T - 8 T^{2} - 54 T^{3} + 194 T^{4} - 22 T^{5} - 6756 T^{6} - 1025 T^{7} + 120147 T^{8} + 128408 T^{9} - 675064 T^{10} + 2038560 T^{11} + 8636984 T^{12} - 56149632 T^{13} - 239607388 T^{14} - 15891968 T^{15} + 1155511444 T^{16} + 3700974820 T^{17} + 12224313708 T^{18} + 48112672660 T^{19} + 195281434036 T^{20} - 34914653696 T^{21} - 6843426608668 T^{22} - 20847965314176 T^{23} + 41689072104056 T^{24} + 127916616815520 T^{25} - 550670443441144 T^{26} + 1361702555488184 T^{27} + 16563284220181803 T^{28} - 1836964403887925 T^{29} - 157401863087481636 T^{30} - 6663252345029566 T^{31} + 763851018825662066 T^{32} - 2764038222760900878 T^{33} - 5323332873465438728 T^{34} + 43252079596906689665 T^{35} + \)\(11\!\cdots\!29\)\( T^{36} \))
$17$ (\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( ( 1 + 22 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 + 32 T^{2} + 672 T^{4} + 9248 T^{6} + 83521 T^{8} )^{2} \))(\( 1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 22 T^{2} + 195 T^{4} - 6358 T^{6} + 83521 T^{8} \))(\( ( 1 - 10 T^{2} - 189 T^{4} - 2890 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 - 32 T^{2} + 352 T^{4} - 3008 T^{6} + 72127 T^{8} - 869312 T^{10} + 29399392 T^{12} - 772402208 T^{14} + 6975757441 T^{16} )^{2} \))(\( 1 - 9 T + 29 T^{2} - 87 T^{3} + 766 T^{4} - 4120 T^{5} + 15945 T^{6} - 70040 T^{7} + 221374 T^{8} - 427431 T^{9} + 2422109 T^{10} - 12778713 T^{11} + 24137569 T^{12} \))(\( 1 + 7 T + 36 T^{2} + 42 T^{3} - 246 T^{4} - 1470 T^{5} + 3903 T^{6} + 15274 T^{7} - 37899 T^{8} - 1169945 T^{9} - 3246658 T^{10} + 1347402 T^{11} + 65397899 T^{12} + 22905834 T^{13} - 938284162 T^{14} - 5747939785 T^{15} - 3165362379 T^{16} + 21686895818 T^{17} + 94208931807 T^{18} - 603197849310 T^{19} - 1716036330486 T^{20} + 4980690812874 T^{21} + 72575780416164 T^{22} + 239903274153431 T^{23} + 582622237229761 T^{24} \))(\( 1 + 7 T + 36 T^{2} + 224 T^{3} + 762 T^{4} + 2296 T^{5} + 7571 T^{6} - 3178 T^{7} - 93339 T^{8} - 156233 T^{9} - 1502636 T^{10} - 7146748 T^{11} - 5058165 T^{12} - 121494716 T^{13} - 434261804 T^{14} - 767572729 T^{15} - 7795766619 T^{16} - 4512305546 T^{17} + 182745534899 T^{18} + 942137593208 T^{19} + 5315527170042 T^{20} + 26563684335328 T^{21} + 72575780416164 T^{22} + 239903274153431 T^{23} + 582622237229761 T^{24} \))(\( 1 + 7 T + 3 T^{2} - 51 T^{3} + 179 T^{4} + 471 T^{5} - 1720 T^{6} + 70463 T^{7} + 376515 T^{8} - 531880 T^{9} - 3336267 T^{10} + 12156538 T^{11} - 9937718 T^{12} - 236663816 T^{13} + 2112368907 T^{14} + 9364237386 T^{15} - 24286739612 T^{16} - 65535104700 T^{17} + 343189121853 T^{18} - 1114096779900 T^{19} - 7018867747868 T^{20} + 46006498277418 T^{21} + 176427163481547 T^{22} - 336028775794312 T^{23} - 239872353927542 T^{24} + 4988297671194074 T^{25} - 23272989350412747 T^{26} - 63074519751224360 T^{27} + 759051943427555235 T^{28} + 2414900629524744079 T^{29} - 1002110248035188920 T^{30} + 4665056253498696327 T^{31} + 30139630954132766291 T^{32} - \)\(14\!\cdots\!43\)\( T^{33} + \)\(14\!\cdots\!43\)\( T^{34} + \)\(57\!\cdots\!39\)\( T^{35} + \)\(14\!\cdots\!09\)\( T^{36} \))
$19$ (\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( ( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 - 72 T^{2} + 2016 T^{4} - 25992 T^{6} + 130321 T^{8} )^{2} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( ( 1 - 7 T + 19 T^{2} )( 1 - T + 19 T^{2} ) \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( ( 1 - T + 19 T^{2} )^{2}( 1 + 7 T + 19 T^{2} )^{2} \))(\( ( 1 + 32 T^{2} + 663 T^{4} + 11552 T^{6} + 130321 T^{8} )^{2} \))(\( ( 1 + 72 T^{2} + 3168 T^{4} + 93168 T^{6} + 2062511 T^{8} + 33633648 T^{10} + 412856928 T^{12} + 3387303432 T^{14} + 16983563041 T^{16} )^{2} \))(\( ( 1 + 9 T + 63 T^{2} + 313 T^{3} + 1197 T^{4} + 3249 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 - 11 T + 102 T^{2} - 612 T^{3} + 3499 T^{4} - 16697 T^{5} + 78308 T^{6} - 317243 T^{7} + 1263139 T^{8} - 4197708 T^{9} + 13292742 T^{10} - 27237089 T^{11} + 47045881 T^{12} )^{2} \))(\( ( 1 - 5 T + 63 T^{2} - 191 T^{3} + 1197 T^{4} - 1805 T^{5} + 6859 T^{6} )^{4} \))(\( ( 1 + 14 T + 146 T^{2} + 1002 T^{3} + 5943 T^{4} + 29558 T^{5} + 154690 T^{6} + 792382 T^{7} + 4151964 T^{8} + 18917264 T^{9} + 78887316 T^{10} + 286049902 T^{11} + 1061018710 T^{12} + 3852028118 T^{13} + 14715456357 T^{14} + 47139972762 T^{15} + 130505273894 T^{16} + 237769882574 T^{17} + 322687697779 T^{18} )^{2} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( ( 1 - 10 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 38 T^{2} + 529 T^{4} )^{4} \))(\( 1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4} \))(\( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 + 10 T^{2} - 429 T^{4} + 5290 T^{6} + 279841 T^{8} \))(\( ( 1 + 10 T^{2} - 429 T^{4} + 5290 T^{6} + 279841 T^{8} )^{2} \))(\( ( 1 + 38 T^{2} + 915 T^{4} + 20102 T^{6} + 279841 T^{8} )^{4} \))(\( 1 + T + 20 T^{2} + 81 T^{3} + 657 T^{4} + 2868 T^{5} + 2653 T^{6} + 65964 T^{7} + 347553 T^{8} + 985527 T^{9} + 5596820 T^{10} + 6436343 T^{11} + 148035889 T^{12} \))(\( 1 - 21 T + 199 T^{2} - 1344 T^{3} + 8426 T^{4} - 47054 T^{5} + 225067 T^{6} - 1070636 T^{7} + 5302370 T^{8} - 24392193 T^{9} + 105816848 T^{10} - 481632172 T^{11} + 2300498641 T^{12} - 11077539956 T^{13} + 55977112592 T^{14} - 296779812231 T^{15} + 1483820523170 T^{16} - 6890980524148 T^{17} + 33317993429563 T^{18} - 160210656583138 T^{19} + 659848361977706 T^{20} - 2420749177006272 T^{21} + 8243875731516151 T^{22} - 20009004916192467 T^{23} + 21914624432020321 T^{24} \))(\( 1 + 21 T + 213 T^{2} + 1470 T^{3} + 9350 T^{4} + 62384 T^{5} + 370569 T^{6} + 1781640 T^{7} + 8025048 T^{8} + 40971343 T^{9} + 205469954 T^{10} + 861657944 T^{11} + 3635431429 T^{12} + 19818132712 T^{13} + 108693605666 T^{14} + 498498330281 T^{15} + 2245737457368 T^{16} + 11467246142520 T^{17} + 54857511350841 T^{18} + 212406630685648 T^{19} + 732207712377350 T^{20} + 2647694412350610 T^{21} + 8823846888507237 T^{22} + 20009004916192467 T^{23} + 21914624432020321 T^{24} \))(\( 1 - 9 T + 40 T^{2} - 185 T^{3} + 730 T^{4} - 3341 T^{5} + 9531 T^{6} - 26655 T^{7} + 158809 T^{8} + 549254 T^{9} - 2603813 T^{10} + 4361626 T^{11} + 41899696 T^{12} - 338975562 T^{13} - 4996783871 T^{14} + 33018695530 T^{15} - 143460183152 T^{16} + 845706730684 T^{17} - 3731716043465 T^{18} + 19451254805732 T^{19} - 75890436887408 T^{20} + 401738468513510 T^{21} - 1398304995244511 T^{22} - 2181762985649766 T^{23} + 6202658746189744 T^{24} + 14850575195096822 T^{25} - 203907161517476453 T^{26} + 989290303919198602 T^{27} + 6578902819328384041 T^{28} - 25397144097195724185 T^{29} + \)\(20\!\cdots\!51\)\( T^{30} - \)\(16\!\cdots\!03\)\( T^{31} + \)\(84\!\cdots\!70\)\( T^{32} - \)\(49\!\cdots\!95\)\( T^{33} + \)\(24\!\cdots\!40\)\( T^{34} - \)\(12\!\cdots\!27\)\( T^{35} + \)\(32\!\cdots\!69\)\( T^{36} \))
$29$ (\( 1 - 9 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( ( 1 - 49 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 92 T^{2} + 3670 T^{4} - 77372 T^{6} + 707281 T^{8} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 5 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 9 T + 29 T^{2} )^{2} \))(\( ( 1 - 49 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 22 T^{2} + 841 T^{4} )^{4} \))(\( ( 1 - 92 T^{2} + 3670 T^{4} - 77372 T^{6} + 707281 T^{8} )^{4} \))(\( 1 - 23 T + 206 T^{2} - 739 T^{3} - 1913 T^{4} + 40244 T^{5} - 278607 T^{6} + 1167076 T^{7} - 1608833 T^{8} - 18023471 T^{9} + 145699886 T^{10} - 471756427 T^{11} + 594823321 T^{12} \))(\( 1 - 3 T - 11 T^{2} - 176 T^{3} + 588 T^{4} - 2884 T^{5} + 45829 T^{6} - 126136 T^{7} + 795804 T^{8} - 6804891 T^{9} + 12038050 T^{10} - 137122006 T^{11} + 1664050031 T^{12} - 3976538174 T^{13} + 10124000050 T^{14} - 165964486599 T^{15} + 562857048924 T^{16} - 2587194290264 T^{17} + 27260157978109 T^{18} - 49748643275156 T^{19} + 294144890821068 T^{20} - 2553257691752944 T^{21} - 4627779566302211 T^{22} - 36601529297117487 T^{23} + 353814783205469041 T^{24} \))(\( 1 - 3 T - 11 T^{2} + 90 T^{3} + 126 T^{4} + 3990 T^{5} - 41853 T^{6} + 170286 T^{7} + 725146 T^{8} + 756495 T^{9} - 4209706 T^{10} - 124453014 T^{11} + 1665132903 T^{12} - 3609137406 T^{13} - 3540362746 T^{14} + 18450156555 T^{15} + 512881988026 T^{16} + 3492761518614 T^{17} - 24895140453813 T^{18} + 68827006472910 T^{19} + 63031048033086 T^{20} + 1305643137828210 T^{21} - 4627779566302211 T^{22} - 36601529297117487 T^{23} + 353814783205469041 T^{24} \))(\( 1 + 5 T - 16 T^{2} + 69 T^{3} + 1288 T^{4} + 4033 T^{5} + 10761 T^{6} - 26967 T^{7} + 670805 T^{8} + 7675230 T^{9} + 9235189 T^{10} + 139494950 T^{11} + 1739415050 T^{12} + 3335361726 T^{13} + 6192996177 T^{14} + 214316706882 T^{15} + 1512925536710 T^{16} + 2988728041586 T^{17} - 6671123117169 T^{18} + 86673113205994 T^{19} + 1272370376373110 T^{20} + 5226970164145098 T^{21} + 4380188529064737 T^{22} + 68412101330883174 T^{23} + 1034644636638381050 T^{24} + 2406270633230139550 T^{25} + 4619870170266884629 T^{26} + \)\(11\!\cdots\!70\)\( T^{27} + \)\(28\!\cdots\!05\)\( T^{28} - \)\(32\!\cdots\!43\)\( T^{29} + \)\(38\!\cdots\!01\)\( T^{30} + \)\(41\!\cdots\!37\)\( T^{31} + \)\(38\!\cdots\!28\)\( T^{32} + \)\(59\!\cdots\!81\)\( T^{33} - \)\(40\!\cdots\!36\)\( T^{34} + \)\(36\!\cdots\!45\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))
$31$ (\( 1 - T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 - 3 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( ( 1 - 11 T + 31 T^{2} )^{2}( 1 + 11 T + 31 T^{2} )^{2} \))(\( ( 1 - 44 T^{2} + 2374 T^{4} - 42284 T^{6} + 923521 T^{8} )^{2} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 - 3 T - 22 T^{2} - 93 T^{3} + 961 T^{4} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} \))(\( ( 1 - 7 T + 31 T^{2} )^{2}( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} + 961 T^{4} )^{4} \))(\( ( 1 + 44 T^{2} - 438 T^{4} + 19888 T^{6} + 2851859 T^{8} + 19112368 T^{10} - 404502198 T^{12} + 39050161964 T^{14} + 852891037441 T^{16} )^{2} \))(\( ( 1 - 14 T + 142 T^{2} - 917 T^{3} + 4402 T^{4} - 13454 T^{5} + 29791 T^{6} )^{2} \))(\( ( 1 - T + 33 T^{2} + 180 T^{3} + 1114 T^{4} + 2126 T^{5} + 72911 T^{6} + 65906 T^{7} + 1070554 T^{8} + 5362380 T^{9} + 30476193 T^{10} - 28629151 T^{11} + 887503681 T^{12} )^{2} \))(\( ( 1 + T + 75 T^{2} - 26 T^{3} + 3284 T^{4} - 3134 T^{5} + 108107 T^{6} - 97154 T^{7} + 3155924 T^{8} - 774566 T^{9} + 69264075 T^{10} + 28629151 T^{11} + 887503681 T^{12} )^{2} \))(\( ( 1 - 2 T + 89 T^{2} - 229 T^{3} + 4867 T^{4} - 16117 T^{5} + 202818 T^{6} - 748417 T^{7} + 7406308 T^{8} - 27059003 T^{9} + 229595548 T^{10} - 719228737 T^{11} + 6042151038 T^{12} - 14884387957 T^{13} + 139338077917 T^{14} - 203238342949 T^{15} + 2448622655879 T^{16} - 1705782074882 T^{17} + 26439622160671 T^{18} )^{2} \))
$37$ (\( 1 - 8 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{4} \))(\( ( 1 + 2 T + 37 T^{2} )^{8} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( 1 - 4 T - 21 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( 1 - 6 T - T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 - 6 T - T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( ( 1 - 2 T - 33 T^{2} - 74 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 2 T - 33 T^{2} - 74 T^{3} + 1369 T^{4} )^{4} \))(\( ( 1 - 2 T - 33 T^{2} - 74 T^{3} + 1369 T^{4} )^{8} \))(\( 1 + 18 T + 119 T^{2} + 524 T^{3} + 3797 T^{4} + 24430 T^{5} + 124923 T^{6} + 903910 T^{7} + 5198093 T^{8} + 26542172 T^{9} + 223025159 T^{10} + 1248191226 T^{11} + 2565726409 T^{12} \))(\( 1 + 16 T + 62 T^{2} - 288 T^{3} - 2107 T^{4} + 966 T^{5} - 37814 T^{6} - 1118808 T^{7} - 7164167 T^{8} + 6473024 T^{9} + 291577494 T^{10} + 981489768 T^{11} - 154435981 T^{12} + 36315121416 T^{13} + 399169589286 T^{14} + 327878084672 T^{15} - 13426802388887 T^{16} - 77582573843256 T^{17} - 97020378429926 T^{18} + 91704193310478 T^{19} - 7400794209411547 T^{20} - 37428981060982176 T^{21} + 298132231089906638 T^{22} + 2846681948471366608 T^{23} + 6582952005840035281 T^{24} \))(\( 1 - 33 T + 419 T^{2} - 2017 T^{3} - 5656 T^{4} + 103628 T^{5} - 252672 T^{6} - 1606267 T^{7} + 2793137 T^{8} + 121636681 T^{9} - 776141753 T^{10} - 1894755184 T^{11} + 38363646888 T^{12} - 70105941808 T^{13} - 1062538059857 T^{14} + 6161262802693 T^{15} + 5234788433057 T^{16} - 111384909778519 T^{17} - 648287223214848 T^{18} + 9837600563538524 T^{19} - 19866583791377176 T^{20} - 262132829166670309 T^{21} + 2014796852043078731 T^{22} - 5871281518722193629 T^{23} + 6582952005840035281 T^{24} \))(\( 1 - 3 T - 16 T^{2} + 138 T^{3} + 178 T^{4} + 2354 T^{5} - 136028 T^{6} + 377983 T^{7} + 5788371 T^{8} - 13066504 T^{9} - 97106240 T^{10} - 44342936 T^{11} + 10449121232 T^{12} - 16870520576 T^{13} - 486599091684 T^{14} + 445892974392 T^{15} + 15530528080756 T^{16} + 17827963236428 T^{17} - 555759711740132 T^{18} + 659634639747836 T^{19} + 21261292942554964 T^{20} + 22585816831877976 T^{21} - 911965040269577124 T^{22} - 1169868653389759232 T^{23} + 26809586295785015888 T^{24} - 4209558152068482488 T^{25} - \)\(34\!\cdots\!40\)\( T^{26} - \)\(16\!\cdots\!08\)\( T^{27} + \)\(27\!\cdots\!79\)\( T^{28} + \)\(67\!\cdots\!79\)\( T^{29} - \)\(89\!\cdots\!68\)\( T^{30} + \)\(57\!\cdots\!38\)\( T^{31} + \)\(16\!\cdots\!42\)\( T^{32} + \)\(46\!\cdots\!34\)\( T^{33} - \)\(19\!\cdots\!56\)\( T^{34} - \)\(13\!\cdots\!51\)\( T^{35} + \)\(16\!\cdots\!29\)\( T^{36} \))
$41$ (\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( ( 1 + 34 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 + 64 T^{2} + 3136 T^{4} + 107584 T^{6} + 2825761 T^{8} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 34 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 + 58 T^{2} + 1681 T^{4} )^{4} \))(\( ( 1 + 64 T^{2} + 3136 T^{4} + 107584 T^{6} + 2825761 T^{8} )^{4} \))(\( 1 + 20 T + 212 T^{2} + 1593 T^{3} + 8811 T^{4} + 39339 T^{5} + 198337 T^{6} + 1612899 T^{7} + 14811291 T^{8} + 109791153 T^{9} + 599061332 T^{10} + 2317124020 T^{11} + 4750104241 T^{12} \))(\( 1 + 14 T + 205 T^{2} + 1687 T^{3} + 17440 T^{4} + 121982 T^{5} + 1059069 T^{6} + 5889233 T^{7} + 44119794 T^{8} + 201011440 T^{9} + 1524662502 T^{10} + 5979705984 T^{11} + 53707565779 T^{12} + 245167945344 T^{13} + 2562957665862 T^{14} + 13853909456240 T^{15} + 124671993213234 T^{16} + 682304162183833 T^{17} + 5030688148411629 T^{18} + 23756515836552142 T^{19} + 139257095995870240 T^{20} + 552293323322612207 T^{21} + 2751645158581242205 T^{22} + 7704606444027478174 T^{23} + 22563490300366186081 T^{24} \))(\( 1 + 14 T + 93 T^{2} + 903 T^{3} + 7906 T^{4} + 42602 T^{5} + 255945 T^{6} + 760207 T^{7} - 4651502 T^{8} - 53848144 T^{9} - 656483066 T^{10} - 6157780804 T^{11} - 39878765829 T^{12} - 252469012964 T^{13} - 1103548033946 T^{14} - 3711267932624 T^{15} - 13144032943022 T^{16} + 88074694993607 T^{17} + 1215765429962745 T^{18} + 8296921575878362 T^{19} + 63128818861430626 T^{20} + 295625886757746783 T^{21} + 1248307315844173293 T^{22} + 7704606444027478174 T^{23} + 22563490300366186081 T^{24} \))(\( 1 - 40 T + 706 T^{2} - 7443 T^{3} + 59064 T^{4} - 481935 T^{5} + 4382993 T^{6} - 36725546 T^{7} + 279484337 T^{8} - 2198499478 T^{9} + 17410472557 T^{10} - 123630729774 T^{11} + 819364899730 T^{12} - 5768850419038 T^{13} + 41536568646609 T^{14} - 274708625186638 T^{15} + 1752682367814724 T^{16} - 11852805049720898 T^{17} + 79312207102305539 T^{18} - 485965007038556818 T^{19} + 2946259060296551044 T^{20} - 18933193156488277598 T^{21} + \)\(11\!\cdots\!49\)\( T^{22} - \)\(66\!\cdots\!38\)\( T^{23} + \)\(38\!\cdots\!30\)\( T^{24} - \)\(24\!\cdots\!94\)\( T^{25} + \)\(13\!\cdots\!97\)\( T^{26} - \)\(71\!\cdots\!58\)\( T^{27} + \)\(37\!\cdots\!37\)\( T^{28} - \)\(20\!\cdots\!86\)\( T^{29} + \)\(98\!\cdots\!33\)\( T^{30} - \)\(44\!\cdots\!35\)\( T^{31} + \)\(22\!\cdots\!04\)\( T^{32} - \)\(11\!\cdots\!43\)\( T^{33} + \)\(45\!\cdots\!46\)\( T^{34} - \)\(10\!\cdots\!40\)\( T^{35} + \)\(10\!\cdots\!21\)\( T^{36} \))
$43$ (\( 1 + 10 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{4} \))(\( ( 1 + 4 T + 40 T^{2} + 172 T^{3} + 1849 T^{4} )^{4} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{4} \))(\( ( 1 - 4 T + 43 T^{2} )^{8} \))(\( ( 1 + 4 T + 40 T^{2} + 172 T^{3} + 1849 T^{4} )^{8} \))(\( 1 - 25 T + 302 T^{2} - 2464 T^{3} + 15140 T^{4} - 72859 T^{5} + 374751 T^{6} - 3132937 T^{7} + 27993860 T^{8} - 195905248 T^{9} + 1032477902 T^{10} - 3675211075 T^{11} + 6321363049 T^{12} \))(\( 1 - 13 T + 81 T^{2} - 167 T^{3} - 3529 T^{4} + 41564 T^{5} - 214082 T^{6} + 149741 T^{7} + 5788818 T^{8} - 49702479 T^{9} + 131599514 T^{10} + 1022557988 T^{11} - 10010627843 T^{12} + 43969993484 T^{13} + 243327501386 T^{14} - 3951694997853 T^{15} + 19790816767218 T^{16} + 22013191263263 T^{17} - 1353290044256018 T^{18} + 11297868752051348 T^{19} - 41247658779653929 T^{20} - 83932966193452781 T^{21} + 1750530067376024169 T^{22} - 12080818613125895191 T^{23} + 39959630797262576401 T^{24} \))(\( 1 - 13 T + 53 T^{2} - 27 T^{3} - 169 T^{4} - 12126 T^{5} + 99168 T^{6} - 83793 T^{7} + 3025694 T^{8} - 46119291 T^{9} + 281268558 T^{10} - 126632810 T^{11} - 8704933243 T^{12} - 5445210830 T^{13} + 520065563742 T^{14} - 3666806469537 T^{15} + 10344245672894 T^{16} - 12318278464299 T^{17} + 626876930843232 T^{18} - 3296072478283482 T^{19} - 1975305846914569 T^{20} - 13570000522294761 T^{21} + 1145408562604065197 T^{22} - 12080818613125895191 T^{23} + 39959630797262576401 T^{24} \))(\( 1 + 15 T + 68 T^{2} + 134 T^{3} + 4595 T^{4} + 45276 T^{5} + 173547 T^{6} + 934521 T^{7} + 6186781 T^{8} - 7812352 T^{9} - 6492035 T^{10} + 1088155662 T^{11} - 11134014802 T^{12} - 162364239292 T^{13} - 488079756415 T^{14} - 2385201497730 T^{15} - 38782775978908 T^{16} - 250877819889798 T^{17} - 1183778094362959 T^{18} - 10787746255261314 T^{19} - 71709352785000892 T^{20} - 189640215480019110 T^{21} - 1668647559311358415 T^{22} - 23868914017196342356 T^{23} - 70382149756381851298 T^{24} + \)\(29\!\cdots\!34\)\( T^{25} - 75880205289195408035 T^{26} - \)\(39\!\cdots\!36\)\( T^{27} + \)\(13\!\cdots\!69\)\( T^{28} + \)\(86\!\cdots\!47\)\( T^{29} + \)\(69\!\cdots\!47\)\( T^{30} + \)\(77\!\cdots\!68\)\( T^{31} + \)\(33\!\cdots\!55\)\( T^{32} + \)\(42\!\cdots\!38\)\( T^{33} + \)\(92\!\cdots\!68\)\( T^{34} + \)\(88\!\cdots\!45\)\( T^{35} + \)\(25\!\cdots\!49\)\( T^{36} \))
$47$ (\( 1 - 6 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( ( 1 + 46 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 + 172 T^{2} + 11782 T^{4} + 379948 T^{6} + 4879681 T^{8} )^{2} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 46 T^{2} - 93 T^{4} - 101614 T^{6} + 4879681 T^{8} \))(\( ( 1 - 70 T^{2} + 2691 T^{4} - 154630 T^{6} + 4879681 T^{8} )^{2} \))(\( ( 1 - 172 T^{2} + 17802 T^{4} - 1266608 T^{6} + 68584787 T^{8} - 2797937072 T^{10} + 86868081162 T^{12} - 1854025036588 T^{14} + 23811286661761 T^{16} )^{2} \))(\( 1 + 28 T + 345 T^{2} + 2198 T^{3} + 2307 T^{4} - 101458 T^{5} - 1072945 T^{6} - 4768526 T^{7} + 5096163 T^{8} + 228202954 T^{9} + 1683489945 T^{10} + 6421660196 T^{11} + 10779215329 T^{12} \))(\( 1 + 2 T - 42 T^{2} - 922 T^{3} - 2269 T^{4} + 17986 T^{5} + 408494 T^{6} + 1110886 T^{7} + 475627 T^{8} - 99943658 T^{9} - 224796956 T^{10} - 603131108 T^{11} + 22889002413 T^{12} - 28347162076 T^{13} - 496576475804 T^{14} - 10376450404534 T^{15} + 2320908034987 T^{16} + 254776157446202 T^{17} + 4403244786604526 T^{18} + 9112123444647518 T^{19} - 54027809435535709 T^{20} - 1031838296200751174 T^{21} - 2209163553904862058 T^{22} + 4944318430168024606 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 40 T + 854 T^{2} + 12486 T^{3} + 141441 T^{4} + 1323312 T^{5} + 10790488 T^{6} + 80197110 T^{7} + 568917571 T^{8} + 3943533856 T^{9} + 27054326272 T^{10} + 184228075800 T^{11} + 1260047713873 T^{12} + 8658719562600 T^{13} + 59763006734848 T^{14} + 409429515531488 T^{15} + 2776136261774851 T^{16} + 18392806754329770 T^{17} + 116312993656990552 T^{18} + 670420454786133456 T^{19} + 3367892196726137601 T^{20} + 13973463087161148762 T^{21} + 44919658929398861846 T^{22} + 98886368603360492120 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 22 T + 287 T^{2} + 2592 T^{3} + 12390 T^{4} - 50886 T^{5} - 1781800 T^{6} - 21162868 T^{7} - 161356693 T^{8} - 691561202 T^{9} + 1275794455 T^{10} + 56853488434 T^{11} + 621523445652 T^{12} + 4439634318702 T^{13} + 20590361912623 T^{14} + 20638489744166 T^{15} - 740566818937292 T^{16} - 9681683997812358 T^{17} - 78095284818493761 T^{18} - 455039147897180826 T^{19} - 1635912103032478028 T^{20} + 2142749920708546618 T^{21} + \)\(10\!\cdots\!63\)\( T^{22} + \)\(10\!\cdots\!14\)\( T^{23} + \)\(66\!\cdots\!08\)\( T^{24} + \)\(28\!\cdots\!42\)\( T^{25} + \)\(30\!\cdots\!55\)\( T^{26} - \)\(77\!\cdots\!34\)\( T^{27} - \)\(84\!\cdots\!57\)\( T^{28} - \)\(52\!\cdots\!04\)\( T^{29} - \)\(20\!\cdots\!00\)\( T^{30} - \)\(27\!\cdots\!22\)\( T^{31} + \)\(31\!\cdots\!10\)\( T^{32} + \)\(31\!\cdots\!56\)\( T^{33} + \)\(16\!\cdots\!27\)\( T^{34} + \)\(58\!\cdots\!14\)\( T^{35} + \)\(12\!\cdots\!89\)\( T^{36} \))
$53$ (\( 1 + 3 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( ( 1 - 25 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 60 T^{2} + 5366 T^{4} - 168540 T^{6} + 7890481 T^{8} )^{2} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 9 T + 28 T^{2} - 477 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 - 3 T - 44 T^{2} - 159 T^{3} + 2809 T^{4} \))(\( 1 + 25 T^{2} - 2184 T^{4} + 70225 T^{6} + 7890481 T^{8} \))(\( ( 1 + 70 T^{2} + 2091 T^{4} + 196630 T^{6} + 7890481 T^{8} )^{2} \))(\( ( 1 + 60 T^{2} - 1766 T^{4} - 15120 T^{6} + 10791075 T^{8} - 42472080 T^{10} - 13934589446 T^{12} + 1329861667740 T^{14} + 62259690411361 T^{16} )^{2} \))(\( 1 - 22 T + 249 T^{2} - 2198 T^{3} + 20865 T^{4} - 183650 T^{5} + 1427831 T^{6} - 9733450 T^{7} + 58609785 T^{8} - 327231646 T^{9} + 1964729769 T^{10} - 9200300846 T^{11} + 22164361129 T^{12} \))(\( 1 + 8 T - 44 T^{2} - 1086 T^{3} - 5691 T^{4} + 29274 T^{5} + 711466 T^{6} + 3879394 T^{7} - 19054181 T^{8} - 375687860 T^{9} - 1587296810 T^{10} + 10210133108 T^{11} + 151553170615 T^{12} + 541137054724 T^{13} - 4458716739290 T^{14} - 55931281533220 T^{15} - 150346653151061 T^{16} + 1622345086371242 T^{17} + 15769189355005114 T^{18} + 34388493907588338 T^{19} - 354319898131055451 T^{20} - 3583543260697116438 T^{21} - 7695048696082574156 T^{22} + 74152287434977532776 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 + 8 T - 44 T^{2} - 106 T^{3} + 8099 T^{4} + 16170 T^{5} - 188972 T^{6} + 664602 T^{7} - 6187761 T^{8} - 119506648 T^{9} + 1027620530 T^{10} - 2019024924 T^{11} - 127594471249 T^{12} - 107008320972 T^{13} + 2886586068770 T^{14} - 17791791234296 T^{15} - 48824410603041 T^{16} + 277933561038786 T^{17} - 4188443651269388 T^{18} + 18995079131164290 T^{19} + 504241232641612739 T^{20} - 349774940731026098 T^{21} - 7695048696082574156 T^{22} + 74152287434977532776 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 + 38 T + 559 T^{2} + 3146 T^{3} - 7592 T^{4} - 85480 T^{5} + 2426088 T^{6} + 42849708 T^{7} + 274722635 T^{8} + 169562126 T^{9} - 6859580173 T^{10} + 36925466446 T^{11} + 1480832620176 T^{12} + 12970691985902 T^{13} + 33443548411599 T^{14} - 209491552405150 T^{15} - 434467187831716 T^{16} + 28448062296391746 T^{17} + 333955538694386995 T^{18} + 1507747301708762538 T^{19} - 1220418330619290244 T^{20} - 31188473847421516550 T^{21} + \)\(26\!\cdots\!19\)\( T^{22} + \)\(54\!\cdots\!86\)\( T^{23} + \)\(32\!\cdots\!04\)\( T^{24} + \)\(43\!\cdots\!02\)\( T^{25} - \)\(42\!\cdots\!53\)\( T^{26} + \)\(55\!\cdots\!58\)\( T^{27} + \)\(48\!\cdots\!15\)\( T^{28} + \)\(39\!\cdots\!76\)\( T^{29} + \)\(11\!\cdots\!08\)\( T^{30} - \)\(22\!\cdots\!40\)\( T^{31} - \)\(10\!\cdots\!48\)\( T^{32} + \)\(23\!\cdots\!22\)\( T^{33} + \)\(21\!\cdots\!39\)\( T^{34} + \)\(78\!\cdots\!94\)\( T^{35} + \)\(10\!\cdots\!89\)\( T^{36} \))
$59$ (\( 1 + 3 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + 11 T + 59 T^{2} \))(\( 1 - 11 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( ( 1 + 115 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 216 T^{2} + 18528 T^{4} + 751896 T^{6} + 12117361 T^{8} )^{2} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 11 T + 62 T^{2} + 649 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4} \))(\( 1 - 115 T^{2} + 9744 T^{4} - 400315 T^{6} + 12117361 T^{8} \))(\( ( 1 + 32 T^{2} - 2457 T^{4} + 111392 T^{6} + 12117361 T^{8} )^{2} \))(\( ( 1 - 216 T^{2} + 28128 T^{4} - 2498256 T^{6} + 168759887 T^{8} - 8696429136 T^{10} + 340837130208 T^{12} - 9110995266456 T^{14} + 146830437604321 T^{16} )^{2} \))(\( 1 + 38 T + 601 T^{2} + 5364 T^{3} + 34323 T^{4} + 219716 T^{5} + 1624197 T^{6} + 12963244 T^{7} + 119478363 T^{8} + 1101652956 T^{9} + 7282533961 T^{10} + 27167123362 T^{11} + 42180533641 T^{12} \))(\( 1 + 20 T + 56 T^{2} - 2326 T^{3} - 32239 T^{4} - 150590 T^{5} + 1002962 T^{6} + 22309882 T^{7} + 157529459 T^{8} + 265697316 T^{9} - 4100747486 T^{10} - 49150416968 T^{11} - 398248757805 T^{12} - 2899874601112 T^{13} - 14274701998766 T^{14} + 54568649062764 T^{15} + 1908841322837699 T^{16} + 15949876749622718 T^{17} + 42305472381644642 T^{18} - 374766027098893210 T^{19} - 4733666477925704719 T^{20} - 20150128274191388114 T^{21} + 28622538184835918456 T^{22} + \)\(60\!\cdots\!80\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 - 6 T + 196 T^{2} - 1790 T^{3} + 25427 T^{4} - 240206 T^{5} + 2707112 T^{6} - 24908450 T^{7} + 229726647 T^{8} - 2110464030 T^{9} + 16809148542 T^{10} - 145372962712 T^{11} + 1069932786619 T^{12} - 8577004800008 T^{13} + 58512646074702 T^{14} - 433444992017370 T^{15} + 2783680713018567 T^{16} - 17807656155426550 T^{17} + 114187428785954792 T^{18} - 597789018562432714 T^{19} + 3733457536965070067 T^{20} - 15506762515392340810 T^{21} + \)\(10\!\cdots\!96\)\( T^{22} - \)\(18\!\cdots\!54\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 - 24 T + 219 T^{2} - 1222 T^{3} + 4234 T^{4} + 38368 T^{5} - 724198 T^{6} + 7790122 T^{7} - 58813081 T^{8} + 56429994 T^{9} + 2818693101 T^{10} - 38159897462 T^{11} + 385528337940 T^{12} - 2590739018566 T^{13} + 12757906676881 T^{14} - 33339608883518 T^{15} - 406112732959828 T^{16} + 6153054402462062 T^{17} - 50509287826422019 T^{18} + 363030209745261658 T^{19} - 1413678423433161268 T^{20} - 6847255532888043322 T^{21} + \)\(15\!\cdots\!41\)\( T^{22} - \)\(18\!\cdots\!34\)\( T^{23} + \)\(16\!\cdots\!40\)\( T^{24} - \)\(94\!\cdots\!78\)\( T^{25} + \)\(41\!\cdots\!21\)\( T^{26} + \)\(48\!\cdots\!66\)\( T^{27} - \)\(30\!\cdots\!81\)\( T^{28} + \)\(23\!\cdots\!98\)\( T^{29} - \)\(12\!\cdots\!38\)\( T^{30} + \)\(40\!\cdots\!72\)\( T^{31} + \)\(26\!\cdots\!74\)\( T^{32} - \)\(44\!\cdots\!78\)\( T^{33} + \)\(47\!\cdots\!79\)\( T^{34} - \)\(30\!\cdots\!56\)\( T^{35} + \)\(75\!\cdots\!21\)\( T^{36} \))
$61$ (\( 1 - 10 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( ( 1 - 164 T^{2} + 14134 T^{4} - 610244 T^{6} + 13845841 T^{8} )^{2} \))(\( 1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 + 6 T - 25 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 + 6 T - 25 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 + 4 T - 45 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 - 4 T - 45 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( ( 1 + 61 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 28 T^{2} - 2937 T^{4} - 104188 T^{6} + 13845841 T^{8} )^{2} \))(\( ( 1 + 164 T^{2} + 12762 T^{4} + 1097488 T^{6} + 85844099 T^{8} + 4083752848 T^{10} + 176700622842 T^{12} + 8449341395204 T^{14} + 191707312997281 T^{16} )^{2} \))(\( 1 + 15 T + 94 T^{2} + 376 T^{3} - 143 T^{4} - 51919 T^{5} - 704864 T^{6} - 3167059 T^{7} - 532103 T^{8} + 85344856 T^{9} + 1301509054 T^{10} + 12668944515 T^{11} + 51520374361 T^{12} \))(\( 1 + T - 11 T^{2} - 361 T^{3} + 3174 T^{4} - 9234 T^{5} + 306664 T^{6} + 1592403 T^{7} + 8046829 T^{8} - 144890707 T^{9} + 1034764645 T^{10} + 2186236306 T^{11} + 43231066596 T^{12} + 133360414666 T^{13} + 3850359244045 T^{14} - 32887437565567 T^{15} + 111415114888189 T^{16} + 1344937683501303 T^{17} + 15799444083041704 T^{18} - 29020087347817914 T^{19} + 608479011453369894 T^{20} - 4221586739513124901 T^{21} - 7846772028291708611 T^{22} + 43513917611435838661 T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 8 T - 25 T^{2} - 1060 T^{3} + 13786 T^{4} + 27028 T^{5} + 288254 T^{6} - 10855104 T^{7} - 6290795 T^{8} + 262482440 T^{9} + 4641466219 T^{10} - 14920387008 T^{11} - 238402008960 T^{12} - 910143607488 T^{13} + 17270895800899 T^{14} + 59578526713640 T^{15} - 87101347333595 T^{16} - 9168180685370304 T^{17} + 14850953991055694 T^{18} + 84942053371975588 T^{19} + 2642877016980515866 T^{20} - 12395794858404189460 T^{21} - 17833572791572065025 T^{22} - \)\(34\!\cdots\!88\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 22 T + 64 T^{2} + 2230 T^{3} - 30396 T^{4} + 215134 T^{5} - 105986 T^{6} - 21969284 T^{7} + 240219267 T^{8} - 1162605988 T^{9} + 1986948726 T^{10} + 72250187524 T^{11} - 1117811760698 T^{12} + 5954234331764 T^{13} - 13920922494828 T^{14} - 50092255290798 T^{15} + 2167151771048322 T^{16} - 14722713533239840 T^{17} + 40006343182019312 T^{18} - 898085525527630240 T^{19} + 8063971740070806162 T^{20} - 11369990198160620838 T^{21} - \)\(19\!\cdots\!48\)\( T^{22} + \)\(50\!\cdots\!64\)\( T^{23} - \)\(57\!\cdots\!78\)\( T^{24} + \)\(22\!\cdots\!04\)\( T^{25} + \)\(38\!\cdots\!06\)\( T^{26} - \)\(13\!\cdots\!08\)\( T^{27} + \)\(17\!\cdots\!67\)\( T^{28} - \)\(95\!\cdots\!24\)\( T^{29} - \)\(28\!\cdots\!06\)\( T^{30} + \)\(34\!\cdots\!54\)\( T^{31} - \)\(30\!\cdots\!36\)\( T^{32} + \)\(13\!\cdots\!30\)\( T^{33} + \)\(23\!\cdots\!04\)\( T^{34} - \)\(49\!\cdots\!62\)\( T^{35} + \)\(13\!\cdots\!81\)\( T^{36} \))
$67$ (\( 1 + 10 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( ( 1 - 2 T + 67 T^{2} )^{4} \))(\( ( 1 + 4 T + 66 T^{2} + 268 T^{3} + 4489 T^{4} )^{4} \))(\( 1 + 4 T - 51 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 - 2 T - 63 T^{2} - 134 T^{3} + 4489 T^{4} \))(\( 1 + 4 T - 51 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 + 4 T - 51 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 + 4 T - 51 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 - 10 T + 33 T^{2} - 670 T^{3} + 4489 T^{4} \))(\( ( 1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} )^{4} \))(\( ( 1 - 4 T - 50 T^{2} + 272 T^{3} - 1205 T^{4} + 18224 T^{5} - 224450 T^{6} - 1203052 T^{7} + 20151121 T^{8} )^{4} \))(\( ( 1 + 30 T + 473 T^{2} + 4684 T^{3} + 31691 T^{4} + 134670 T^{5} + 300763 T^{6} )^{2} \))(\( ( 1 - 38 T + 950 T^{2} - 16530 T^{3} + 227335 T^{4} - 2490324 T^{5} + 22546132 T^{6} - 166851708 T^{7} + 1020506815 T^{8} - 4971612390 T^{9} + 19143564950 T^{10} - 51304754066 T^{11} + 90458382169 T^{12} )^{2} \))(\( ( 1 + 39 T + 894 T^{2} + 14312 T^{3} + 179973 T^{4} + 1857173 T^{5} + 16408000 T^{6} + 124430591 T^{7} + 807898797 T^{8} + 4304520056 T^{9} + 18015102174 T^{10} + 52654879173 T^{11} + 90458382169 T^{12} )^{2} \))(\( ( 1 - 53 T + 1663 T^{2} - 37593 T^{3} + 674406 T^{4} - 10047098 T^{5} + 128058458 T^{6} - 1421701295 T^{7} + 13912778438 T^{8} - 120777429250 T^{9} + 932156155346 T^{10} - 6382017113255 T^{11} + 38515246003454 T^{12} - 202460287496858 T^{13} + 910532472911442 T^{14} - 3400601960879217 T^{15} + 10078963399652149 T^{16} - 21521586910501973 T^{17} + 27206534396294947 T^{18} )^{2} \))
$71$ (\( 1 + 6 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( ( 1 + 2 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 140 T^{2} + 12934 T^{4} - 705740 T^{6} + 25411681 T^{8} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 2 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 2 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 71 T^{2} )^{8} \))(\( ( 1 - 140 T^{2} + 12934 T^{4} - 705740 T^{6} + 25411681 T^{8} )^{4} \))(\( 1 - 6 T - 35 T^{2} + 258 T^{3} + 4381 T^{4} - 44842 T^{5} + 20567 T^{6} - 3183782 T^{7} + 22084621 T^{8} + 92341038 T^{9} - 889408835 T^{10} - 10825376106 T^{11} + 128100283921 T^{12} \))(\( 1 - 40 T + 736 T^{2} - 10390 T^{3} + 143657 T^{4} - 1783966 T^{5} + 20127152 T^{6} - 223458602 T^{7} + 2315935173 T^{8} - 22463817424 T^{9} + 214057178408 T^{10} - 1915402187380 T^{11} + 16200442968901 T^{12} - 135993555303980 T^{13} + 1079062236354728 T^{14} - 8040047358041264 T^{15} + 58851805832955813 T^{16} - 403170568461827302 T^{17} + 2578293885721122992 T^{18} - 16225385128484158706 T^{19} + 92767015038172287977 T^{20} - \)\(47\!\cdots\!90\)\( T^{21} + \)\(23\!\cdots\!36\)\( T^{22} - \)\(92\!\cdots\!40\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 2 T - 90 T^{2} + 880 T^{3} + 3559 T^{4} - 105660 T^{5} + 151854 T^{6} + 3042232 T^{7} - 21345605 T^{8} + 41540738 T^{9} + 893462328 T^{10} + 3630232148 T^{11} + 63853829545 T^{12} + 257746482508 T^{13} + 4503943595448 T^{14} + 14867887078318 T^{15} - 542427705012005 T^{16} + 5488884266951432 T^{17} + 19452540514539534 T^{18} - 960990395935593060 T^{19} + 2298236817703663399 T^{20} + 40346680632235147280 T^{21} - \)\(29\!\cdots\!90\)\( T^{22} + \)\(46\!\cdots\!42\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 4 T - 223 T^{2} - 970 T^{3} + 23234 T^{4} + 120642 T^{5} - 1219922 T^{6} - 10677348 T^{7} + 1325443 T^{8} + 890248228 T^{9} + 5212115899 T^{10} - 84464157116 T^{11} - 514144515364 T^{12} + 7682363045196 T^{13} + 45123132391715 T^{14} - 514775184234880 T^{15} - 4357061961125656 T^{16} + 15287731841412884 T^{17} + 355047512245873675 T^{18} + 1085428960740314764 T^{19} - 21963949346034431896 T^{20} - \)\(18\!\cdots\!80\)\( T^{21} + \)\(11\!\cdots\!15\)\( T^{22} + \)\(13\!\cdots\!96\)\( T^{23} - \)\(65\!\cdots\!44\)\( T^{24} - \)\(76\!\cdots\!56\)\( T^{25} + \)\(33\!\cdots\!39\)\( T^{26} + \)\(40\!\cdots\!68\)\( T^{27} + \)\(43\!\cdots\!43\)\( T^{28} - \)\(24\!\cdots\!08\)\( T^{29} - \)\(20\!\cdots\!02\)\( T^{30} + \)\(14\!\cdots\!62\)\( T^{31} + \)\(19\!\cdots\!54\)\( T^{32} - \)\(56\!\cdots\!70\)\( T^{33} - \)\(92\!\cdots\!83\)\( T^{34} + \)\(11\!\cdots\!64\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))
$73$ (\( 1 + 2 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( ( 1 - 98 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 288 T^{2} + 31392 T^{4} - 1534752 T^{6} + 28398241 T^{8} )^{2} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( ( 1 - 7 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 + 16 T + 183 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( 1 - 16 T + 183 T^{2} - 1168 T^{3} + 5329 T^{4} \))(\( 1 - 2 T - 69 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( ( 1 + 12 T + 121 T^{2} + 876 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 14 T + 123 T^{2} - 1022 T^{3} + 5329 T^{4} )^{2}( 1 + 14 T + 123 T^{2} + 1022 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 288 T^{2} + 51552 T^{4} + 5971392 T^{6} + 515050847 T^{8} + 31821547968 T^{10} + 1463986120032 T^{12} + 43584257171232 T^{14} + 806460091894081 T^{16} )^{2} \))(\( 1 - 17 T + 6 T^{2} + 2070 T^{3} - 15083 T^{4} - 58933 T^{5} + 1456680 T^{6} - 4302109 T^{7} - 80377307 T^{8} + 805265190 T^{9} + 170389446 T^{10} - 35242217081 T^{11} + 151334226289 T^{12} \))(\( 1 + 25 T + 223 T^{2} + 31 T^{3} - 23368 T^{4} - 240592 T^{5} + 55056 T^{6} + 16202729 T^{7} + 78532377 T^{8} - 595720121 T^{9} - 9041932145 T^{10} - 1742581816 T^{11} + 545718574944 T^{12} - 127208472568 T^{13} - 48184456400705 T^{14} - 231745254311057 T^{15} + 2230181368348857 T^{16} + 33589417218977297 T^{17} + 8331857162567184 T^{18} - 2657915704506585424 T^{19} - 18845359427380884808 T^{20} + 1825019187956305303 T^{21} + \)\(95\!\cdots\!27\)\( T^{22} + \)\(78\!\cdots\!25\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 11 T + 307 T^{2} - 3125 T^{3} + 44084 T^{4} - 383864 T^{5} + 3901276 T^{6} - 24936363 T^{7} + 200746189 T^{8} - 639756429 T^{9} + 3107574119 T^{10} + 27228233616 T^{11} - 184104039024 T^{12} + 1987661053968 T^{13} + 16560262480151 T^{14} - 248876126740293 T^{15} + 5700838655053549 T^{16} - 51694865768036259 T^{17} + 590396584999844764 T^{18} - 4240698585134650808 T^{19} + 35551986691058666804 T^{20} - \)\(18\!\cdots\!25\)\( T^{21} + \)\(13\!\cdots\!43\)\( T^{22} - \)\(34\!\cdots\!47\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 + 23 T + 416 T^{2} + 4544 T^{3} + 43712 T^{4} + 169368 T^{5} - 905136 T^{6} - 40074693 T^{7} - 467825947 T^{8} - 4725996160 T^{9} - 24958214168 T^{10} - 65896536464 T^{11} + 1604640555864 T^{12} + 20298517040864 T^{13} + 217780247993034 T^{14} + 927051452810342 T^{15} + 1364793396121648 T^{16} - 83840550622590488 T^{17} - 750774282550445408 T^{18} - 6120360195449105624 T^{19} + 7272984007932262192 T^{20} + \)\(36\!\cdots\!14\)\( T^{21} + \)\(61\!\cdots\!94\)\( T^{22} + \)\(42\!\cdots\!52\)\( T^{23} + \)\(24\!\cdots\!96\)\( T^{24} - \)\(72\!\cdots\!08\)\( T^{25} - \)\(20\!\cdots\!08\)\( T^{26} - \)\(27\!\cdots\!80\)\( T^{27} - \)\(20\!\cdots\!03\)\( T^{28} - \)\(12\!\cdots\!61\)\( T^{29} - \)\(20\!\cdots\!56\)\( T^{30} + \)\(28\!\cdots\!44\)\( T^{31} + \)\(53\!\cdots\!08\)\( T^{32} + \)\(40\!\cdots\!08\)\( T^{33} + \)\(27\!\cdots\!76\)\( T^{34} + \)\(10\!\cdots\!19\)\( T^{35} + \)\(34\!\cdots\!69\)\( T^{36} \))
$79$ (\( 1 + T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 - 3 T + 79 T^{2} \))(\( 1 - 3 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( ( 1 + T + 79 T^{2} )^{4} \))(\( ( 1 - 24 T + 294 T^{2} - 1896 T^{3} + 6241 T^{4} )^{4} \))(\( 1 - 79 T^{2} + 6241 T^{4} \))(\( 1 + 3 T - 70 T^{2} + 237 T^{3} + 6241 T^{4} \))(\( 1 - 79 T^{2} + 6241 T^{4} \))(\( 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 - 8 T - 15 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( ( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4} )^{4} \))(\( ( 1 + 24 T + 282 T^{2} + 3264 T^{3} + 34691 T^{4} + 257856 T^{5} + 1759962 T^{6} + 11832936 T^{7} + 38950081 T^{8} )^{4} \))(\( ( 1 + 21 T + 321 T^{2} + 3409 T^{3} + 25359 T^{4} + 131061 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 - 36 T + 769 T^{2} - 12618 T^{3} + 167943 T^{4} - 1886498 T^{5} + 18179147 T^{6} - 149033342 T^{7} + 1048132263 T^{8} - 6221166102 T^{9} + 29952612289 T^{10} - 110774030364 T^{11} + 243087455521 T^{12} )^{2} \))(\( ( 1 - 22 T + 461 T^{2} - 5982 T^{3} + 77013 T^{4} - 760366 T^{5} + 7556703 T^{6} - 60068914 T^{7} + 480638133 T^{8} - 2949359298 T^{9} + 17955987341 T^{10} - 67695240778 T^{11} + 243087455521 T^{12} )^{2} \))(\( ( 1 + 5 T + 444 T^{2} + 1740 T^{3} + 89709 T^{4} + 275637 T^{5} + 11294752 T^{6} + 27733297 T^{7} + 1059009140 T^{8} + 2270037573 T^{9} + 83661722060 T^{10} + 173083506577 T^{11} + 5568753231328 T^{12} + 10736083476597 T^{13} + 276039652497891 T^{14} + 422972172606540 T^{15} + 8526535589854596 T^{16} + 7585544049532805 T^{17} + 119851595982618319 T^{18} )^{2} \))
$83$ (\( 1 - 9 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 7 T + 83 T^{2} \))(\( 1 - 7 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( ( 1 + 91 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 216 T^{2} + 22080 T^{4} + 1488024 T^{6} + 47458321 T^{8} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 7 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 9 T + 83 T^{2} )^{2} \))(\( ( 1 + 91 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 160 T^{2} + 6889 T^{4} )^{4} \))(\( ( 1 + 216 T^{2} + 22080 T^{4} + 1488024 T^{6} + 47458321 T^{8} )^{4} \))(\( 1 + 18 T + 143 T^{2} + 618 T^{3} + 4351 T^{4} + 10084 T^{5} - 139875 T^{6} + 836972 T^{7} + 29974039 T^{8} + 353364366 T^{9} + 6786539903 T^{10} + 70902731574 T^{11} + 326940373369 T^{12} \))(\( 1 - 11 T + 133 T^{2} - 2347 T^{3} + 31596 T^{4} - 352364 T^{5} + 3694196 T^{6} - 39651059 T^{7} + 430314471 T^{8} - 4035443283 T^{9} + 35723120099 T^{10} - 356413624648 T^{11} + 3296332017472 T^{12} - 29582330845784 T^{13} + 246096574362011 T^{14} - 2307414008456721 T^{15} + 20422002295663191 T^{16} - 156187132938990937 T^{17} + 1207781819538266324 T^{18} - 9561767470908928228 T^{19} + 71163425366665139436 T^{20} - \)\(43\!\cdots\!41\)\( T^{21} + \)\(20\!\cdots\!17\)\( T^{22} - \)\(14\!\cdots\!37\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + 46 T + 770 T^{2} + 3222 T^{3} - 59229 T^{4} - 584040 T^{5} + 4786588 T^{6} + 92797446 T^{7} + 81423901 T^{8} - 7344250154 T^{9} - 53724829226 T^{10} + 109800250704 T^{11} + 3769461877087 T^{12} + 9113420808432 T^{13} - 370110348537914 T^{14} - 4199346762805198 T^{15} + 3864241630730221 T^{16} + 365532911360597778 T^{17} + 1564928867883574972 T^{18} - 15848539219981753080 T^{19} - \)\(13\!\cdots\!89\)\( T^{20} + \)\(60\!\cdots\!66\)\( T^{21} + \)\(11\!\cdots\!30\)\( T^{22} + \)\(59\!\cdots\!82\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - T - 236 T^{2} + 314 T^{3} + 35728 T^{4} + 55170 T^{5} - 4186796 T^{6} - 17101749 T^{7} + 380090743 T^{8} + 2765767140 T^{9} - 19881917724 T^{10} - 340289613732 T^{11} - 233243291612 T^{12} + 31041091728076 T^{13} + 212840882775104 T^{14} - 1964875857448552 T^{15} - 31935723242061712 T^{16} + 59936482782227272 T^{17} + 3119158978847159984 T^{18} + 4974728070924863576 T^{19} - \)\(22\!\cdots\!68\)\( T^{20} - \)\(11\!\cdots\!24\)\( T^{21} + \)\(10\!\cdots\!84\)\( T^{22} + \)\(12\!\cdots\!68\)\( T^{23} - \)\(76\!\cdots\!28\)\( T^{24} - \)\(92\!\cdots\!64\)\( T^{25} - \)\(44\!\cdots\!84\)\( T^{26} + \)\(51\!\cdots\!20\)\( T^{27} + \)\(58\!\cdots\!07\)\( T^{28} - \)\(22\!\cdots\!83\)\( T^{29} - \)\(44\!\cdots\!56\)\( T^{30} + \)\(48\!\cdots\!10\)\( T^{31} + \)\(26\!\cdots\!12\)\( T^{32} + \)\(19\!\cdots\!98\)\( T^{33} - \)\(11\!\cdots\!16\)\( T^{34} - \)\(42\!\cdots\!23\)\( T^{35} + \)\(34\!\cdots\!09\)\( T^{36} \))
$89$ (\( 1 + 6 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( ( 1 + 70 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 192 T^{2} + 23136 T^{4} + 1520832 T^{6} + 62742241 T^{8} )^{2} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 - 8 T - 25 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( 1 + 8 T - 25 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 - 70 T^{2} - 3021 T^{4} - 554470 T^{6} + 62742241 T^{8} \))(\( ( 1 - 89 T^{2} + 7921 T^{4} )^{4} \))(\( ( 1 - 192 T^{2} + 13728 T^{4} - 1400448 T^{6} + 180532511 T^{8} - 11092948608 T^{10} + 861325484448 T^{12} - 95420407864512 T^{14} + 3936588805702081 T^{16} )^{2} \))(\( 1 + 20 T + 59 T^{2} - 1272 T^{3} - 5589 T^{4} + 97398 T^{5} + 1357735 T^{6} + 8668422 T^{7} - 44270469 T^{8} - 896720568 T^{9} + 3701792219 T^{10} + 111681188980 T^{11} + 496981290961 T^{12} \))(\( 1 + 12 T - 336 T^{2} - 4566 T^{3} + 41159 T^{4} + 648470 T^{5} - 2070780 T^{6} - 27638562 T^{7} + 195715455 T^{8} - 2405953316 T^{9} - 57134230810 T^{10} + 195542463500 T^{11} + 7587050225563 T^{12} + 17403279251500 T^{13} - 452560242246010 T^{14} - 1696122503227204 T^{15} + 12279626245034655 T^{16} - 154335373292872338 T^{17} - 1029138917696219580 T^{18} + 28682693739703690630 T^{19} + \)\(16\!\cdots\!79\)\( T^{20} - \)\(15\!\cdots\!94\)\( T^{21} - \)\(10\!\cdots\!36\)\( T^{22} + \)\(33\!\cdots\!68\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 30 T + 322 T^{2} - 1202 T^{3} - 73641 T^{4} - 784886 T^{5} - 514008 T^{6} + 77295470 T^{7} + 910066225 T^{8} + 3945816830 T^{9} - 18477720078 T^{10} - 458976909768 T^{11} - 4923232592533 T^{12} - 40848944969352 T^{13} - 146362020737838 T^{14} + 2781678544828270 T^{15} + 57099594414910225 T^{16} + 431622499618396030 T^{17} - 255452359404281688 T^{18} - 34716555520812174694 T^{19} - \)\(28\!\cdots\!21\)\( T^{20} - \)\(42\!\cdots\!18\)\( T^{21} + \)\(10\!\cdots\!22\)\( T^{22} + \)\(83\!\cdots\!70\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 - 18 T + 159 T^{2} - 1450 T^{3} + 21106 T^{4} - 170560 T^{5} + 577604 T^{6} - 13263052 T^{7} + 190097239 T^{8} - 335355142 T^{9} - 6613938749 T^{10} + 13144221270 T^{11} - 501330516152 T^{12} + 12991910680226 T^{13} - 37665013149621 T^{14} - 71226566681710 T^{15} - 7692857532138696 T^{16} + 85478120811605238 T^{17} - 457293555371234025 T^{18} + 7607552752232866182 T^{19} - 60935124512070611016 T^{20} - 50212521487038416990 T^{21} - \)\(23\!\cdots\!61\)\( T^{22} + \)\(72\!\cdots\!74\)\( T^{23} - \)\(24\!\cdots\!72\)\( T^{24} + \)\(58\!\cdots\!30\)\( T^{25} - \)\(26\!\cdots\!69\)\( T^{26} - \)\(11\!\cdots\!78\)\( T^{27} + \)\(59\!\cdots\!39\)\( T^{28} - \)\(36\!\cdots\!28\)\( T^{29} + \)\(14\!\cdots\!84\)\( T^{30} - \)\(37\!\cdots\!40\)\( T^{31} + \)\(41\!\cdots\!46\)\( T^{32} - \)\(25\!\cdots\!50\)\( T^{33} + \)\(24\!\cdots\!99\)\( T^{34} - \)\(24\!\cdots\!22\)\( T^{35} + \)\(12\!\cdots\!81\)\( T^{36} \))
$97$ (\( 1 - T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( ( 1 - 19 T + 97 T^{2} )^{2}( 1 + 19 T + 97 T^{2} )^{2} \))(\( ( 1 - 288 T^{2} + 37632 T^{4} - 2709792 T^{6} + 88529281 T^{8} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 7 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 8 T + 97 T^{2} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 - T + 97 T^{2} )^{2} \))(\( ( 1 - 19 T + 97 T^{2} )^{2}( 1 + 19 T + 97 T^{2} )^{2} \))(\( ( 1 - 170 T^{2} + 9409 T^{4} )^{4} \))(\( ( 1 - 288 T^{2} + 37632 T^{4} - 2709792 T^{6} + 88529281 T^{8} )^{4} \))(\( ( 1 + 242 T^{2} + 91 T^{3} + 23474 T^{4} + 912673 T^{6} )^{2} \))(\( ( 1 + 13 T + 331 T^{2} + 1866 T^{3} + 30168 T^{4} - 25320 T^{5} + 1583189 T^{6} - 2456040 T^{7} + 283850712 T^{8} + 1703047818 T^{9} + 29303192011 T^{10} + 111635423341 T^{11} + 832972004929 T^{12} )^{2} \))(\( ( 1 + 15 T + 387 T^{2} + 3776 T^{3} + 68094 T^{4} + 573854 T^{5} + 8289259 T^{6} + 55663838 T^{7} + 640696446 T^{8} + 3446253248 T^{9} + 34260831747 T^{10} + 128810103855 T^{11} + 832972004929 T^{12} )^{2} \))(\( ( 1 + 28 T + 383 T^{2} + 3675 T^{3} + 47265 T^{4} + 643951 T^{5} + 6509902 T^{6} + 52597699 T^{7} + 546055790 T^{8} + 5887192871 T^{9} + 52967411630 T^{10} + 494891749891 T^{11} + 5941411788046 T^{12} + 57008519029231 T^{13} + 405880637247105 T^{14} + 3061172118114075 T^{15} + 30945742955117279 T^{16} + 219448140642554908 T^{17} + 760231058654565217 T^{18} )^{2} \))
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