Properties

Label 630.2.i
Level 630
Weight 2
Character orbit i
Rep. character \(\chi_{630}(121,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 64
Newform subspaces 9
Sturm bound 288
Trace bound 5

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 630.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 9 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(630, [\chi])\).

Total New Old
Modular forms 304 64 240
Cusp forms 272 64 208
Eisenstein series 32 0 32

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(630, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
630.2.i.a \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(-1\) \(-1\) \(q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.b \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(1\) \(-4\) \(q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.c \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-1\) \(-5\) \(q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.d \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(1\) \(-4\) \(q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.e \(4\) \(5.031\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(-6\) \(2\) \(-2\) \(q+q^{2}+(-2-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
630.2.i.f \(12\) \(5.031\) 12.0.\(\cdots\).1 None \(-12\) \(2\) \(-6\) \(4\) \(q-q^{2}+(\beta _{4}-\beta _{7})q^{3}+q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots\)
630.2.i.g \(12\) \(5.031\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(0\) \(-6\) \(4\) \(q+q^{2}-\beta _{8}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots\)
630.2.i.h \(12\) \(5.031\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(2\) \(6\) \(8\) \(q+q^{2}+(-\beta _{2}+\beta _{6})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
630.2.i.i \(16\) \(5.031\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(2\) \(8\) \(4\) \(q-q^{2}+(-\beta _{1}+\beta _{7})q^{3}+q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{12} \))(\( ( 1 - T )^{12} \))(\( ( 1 - T )^{12} \))(\( ( 1 + T )^{16} \))
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( ( 1 + 3 T + 3 T^{2} )^{2} \))(\( 1 - 2 T + 4 T^{2} - 9 T^{3} + 9 T^{4} - 9 T^{5} + 9 T^{6} - 27 T^{7} + 81 T^{8} - 243 T^{9} + 324 T^{10} - 486 T^{11} + 729 T^{12} \))(\( 1 - 2 T^{2} + 9 T^{3} - 11 T^{4} - 27 T^{5} + 51 T^{6} - 81 T^{7} - 99 T^{8} + 243 T^{9} - 162 T^{10} + 729 T^{12} \))(\( 1 - 2 T + 4 T^{2} - 9 T^{3} + 15 T^{4} - 39 T^{5} + 75 T^{6} - 117 T^{7} + 135 T^{8} - 243 T^{9} + 324 T^{10} - 486 T^{11} + 729 T^{12} \))(\( 1 - 2 T + 5 T^{2} - 5 T^{3} + 8 T^{4} - 8 T^{5} - 20 T^{6} + 51 T^{7} - 183 T^{8} + 153 T^{9} - 180 T^{10} - 216 T^{11} + 648 T^{12} - 1215 T^{13} + 3645 T^{14} - 4374 T^{15} + 6561 T^{16} \))
$5$ (\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{6} \))(\( ( 1 + T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{6} \))(\( ( 1 - T + T^{2} )^{8} \))
$7$ (\( 1 + T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 5 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( ( 1 - 2 T - 4 T^{2} + 31 T^{3} - 28 T^{4} - 98 T^{5} + 343 T^{6} )^{2} \))(\( ( 1 - 2 T + 2 T^{2} + 19 T^{3} + 14 T^{4} - 98 T^{5} + 343 T^{6} )^{2} \))(\( ( 1 - 4 T + 14 T^{2} - 55 T^{3} + 98 T^{4} - 196 T^{5} + 343 T^{6} )^{2} \))(\( 1 - 4 T + 15 T^{2} - 46 T^{3} + 85 T^{4} - 234 T^{5} + 295 T^{6} + 350 T^{7} - 39 T^{8} + 2450 T^{9} + 14455 T^{10} - 80262 T^{11} + 204085 T^{12} - 773122 T^{13} + 1764735 T^{14} - 3294172 T^{15} + 5764801 T^{16} \))
$11$ (\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 4 T^{2} - 105 T^{4} - 484 T^{6} + 14641 T^{8} \))(\( 1 + 7 T - 9 T^{2} - 100 T^{3} + 262 T^{4} + 640 T^{5} - 8115 T^{6} - 15798 T^{7} + 74164 T^{8} + 80949 T^{9} - 972110 T^{10} + 548862 T^{11} + 17010145 T^{12} + 6037482 T^{13} - 117625310 T^{14} + 107743119 T^{15} + 1085835124 T^{16} - 2544283698 T^{17} - 14376217515 T^{18} + 12471789440 T^{19} + 56162026822 T^{20} - 235794769100 T^{21} - 233436821409 T^{22} + 1997181694277 T^{23} + 3138428376721 T^{24} \))(\( 1 - 3 T - 13 T^{2} + 192 T^{3} - 332 T^{4} - 1956 T^{5} + 16237 T^{6} - 20670 T^{7} - 129674 T^{8} + 872529 T^{9} - 1117882 T^{10} - 4992144 T^{11} + 35318321 T^{12} - 54913584 T^{13} - 135263722 T^{14} + 1161336099 T^{15} - 1898557034 T^{16} - 3328924170 T^{17} + 28764835957 T^{18} - 38116906476 T^{19} - 71167148492 T^{20} + 452725956672 T^{21} - 337186519813 T^{22} - 855935011833 T^{23} + 3138428376721 T^{24} \))(\( 1 + 7 T - 5 T^{2} - 100 T^{3} + 96 T^{4} + 824 T^{5} - 2267 T^{6} - 5202 T^{7} + 18548 T^{8} - 3791 T^{9} - 96786 T^{10} + 475772 T^{11} + 2698025 T^{12} + 5233492 T^{13} - 11711106 T^{14} - 5045821 T^{15} + 271561268 T^{16} - 837787302 T^{17} - 4016128787 T^{18} + 16057428904 T^{19} + 20578452576 T^{20} - 235794769100 T^{21} - 129687123005 T^{22} + 1997181694277 T^{23} + 3138428376721 T^{24} \))(\( 1 - T - 35 T^{2} + 182 T^{3} + 577 T^{4} - 5289 T^{5} + 8314 T^{6} + 80986 T^{7} - 380701 T^{8} + 165840 T^{9} + 6417590 T^{10} - 21138520 T^{11} - 17857183 T^{12} + 372829025 T^{13} - 755353711 T^{14} - 1808389533 T^{15} + 15175368627 T^{16} - 19892284863 T^{17} - 91397799031 T^{18} + 496235432275 T^{19} - 261447016303 T^{20} - 3404379784520 T^{21} + 11369152157990 T^{22} + 3231752438640 T^{23} - 81606640355581 T^{24} + 190960751703326 T^{25} + 215643748132714 T^{26} - 1509013425861579 T^{27} + 1810873173368017 T^{28} + 6283133610195442 T^{29} - 13291244175413435 T^{30} - 4177248169415651 T^{31} + 45949729863572161 T^{32} \))
$13$ (\( ( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 + 4 T + 3 T^{2} + 52 T^{3} + 169 T^{4} \))(\( ( 1 - 7 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} ) \))(\( 1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4} \))(\( ( 1 - 5 T + 13 T^{2} )^{2}( 1 + 7 T + 13 T^{2} )^{2} \))(\( 1 + 2 T - 44 T^{2} - 132 T^{3} + 977 T^{4} + 3781 T^{5} - 11684 T^{6} - 65747 T^{7} + 50792 T^{8} + 714313 T^{9} + 868188 T^{10} - 3554073 T^{11} - 19510287 T^{12} - 46202949 T^{13} + 146723772 T^{14} + 1569345661 T^{15} + 1450670312 T^{16} - 24411400871 T^{17} - 56396436356 T^{18} + 237252142777 T^{19} + 796968914417 T^{20} - 1399793917236 T^{21} - 6065773641356 T^{22} + 3584320788074 T^{23} + 23298085122481 T^{24} \))(\( 1 + 2 T - 40 T^{2} - 80 T^{3} + 861 T^{4} + 1779 T^{5} - 10316 T^{6} - 26179 T^{7} + 43538 T^{8} + 287567 T^{9} + 1150280 T^{10} - 1429999 T^{11} - 24752599 T^{12} - 18589987 T^{13} + 194397320 T^{14} + 631784699 T^{15} + 1243488818 T^{16} - 9720079447 T^{17} - 49793361644 T^{18} + 111629611743 T^{19} + 702344150781 T^{20} - 848359949840 T^{21} - 5514339673960 T^{22} + 3584320788074 T^{23} + 23298085122481 T^{24} \))(\( 1 - 2 T - 36 T^{3} - 17 T^{4} - 371 T^{5} + 3240 T^{6} - 7131 T^{7} + 28438 T^{8} - 222777 T^{9} + 460892 T^{10} - 507411 T^{11} + 7449937 T^{12} - 6596343 T^{13} + 77890748 T^{14} - 489441069 T^{15} + 812217718 T^{16} - 2647690383 T^{17} + 15638861160 T^{18} - 23279699807 T^{19} - 13867422257 T^{20} - 381761977428 T^{21} - 3584320788074 T^{23} + 23298085122481 T^{24} \))(\( 1 - 2 T - 50 T^{2} + 148 T^{3} + 1054 T^{4} - 3995 T^{5} - 11532 T^{6} + 43443 T^{7} + 117342 T^{8} + 20138 T^{9} - 2880550 T^{10} - 3340678 T^{11} + 58331516 T^{12} - 10068559 T^{13} - 672470458 T^{14} + 306068259 T^{15} + 6775158987 T^{16} + 3978887367 T^{17} - 113647507402 T^{18} - 22120624123 T^{19} + 1666006428476 T^{20} - 1240370356654 T^{21} - 13903864664950 T^{22} + 1263629635346 T^{23} + 95719474263582 T^{24} + 460691266261239 T^{25} - 1589784128002668 T^{26} - 7159680774177815 T^{27} + 24556181719094974 T^{28} + 44825515775653444 T^{29} - 196868819284964450 T^{30} - 102371786028181514 T^{31} + 665416609183179841 T^{32} \))
$17$ (\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( ( 1 - 17 T^{2} + 289 T^{4} )^{2} \))(\( 1 - T - 30 T^{2} + 115 T^{3} - 5 T^{4} - 2674 T^{5} + 5895 T^{6} + 18453 T^{7} - 18224 T^{8} - 437961 T^{9} + 1559167 T^{10} + 7061088 T^{11} - 61824431 T^{12} + 120038496 T^{13} + 450599263 T^{14} - 2151702393 T^{15} - 1522086704 T^{16} + 26200621221 T^{17} + 142290969255 T^{18} - 1097245611602 T^{19} - 34878787205 T^{20} + 13637605797155 T^{21} - 60479817013470 T^{22} - 34271896307633 T^{23} + 582622237229761 T^{24} \))(\( 1 - T - 50 T^{2} + 211 T^{3} + 1359 T^{4} - 9716 T^{5} - 8711 T^{6} + 283281 T^{7} - 515860 T^{8} - 4710193 T^{9} + 23752041 T^{10} + 36045190 T^{11} - 503461927 T^{12} + 612768230 T^{13} + 6864339849 T^{14} - 23141178209 T^{15} - 43085143060 T^{16} + 402218510817 T^{17} - 210262363559 T^{18} - 3986850546868 T^{19} + 9480054362319 T^{20} + 25022041940867 T^{21} - 100799695022450 T^{22} - 34271896307633 T^{23} + 582622237229761 T^{24} \))(\( 1 - 7 T - 26 T^{2} + 253 T^{3} + 159 T^{4} - 2042 T^{5} - 15857 T^{6} + 20745 T^{7} + 626078 T^{8} - 1325347 T^{9} - 9319905 T^{10} + 15360616 T^{11} + 109941593 T^{12} + 261130472 T^{13} - 2693452545 T^{14} - 6511429811 T^{15} + 52290660638 T^{16} + 29454933465 T^{17} - 382749431633 T^{18} - 837911570266 T^{19} + 1109145433119 T^{20} + 30002732753741 T^{21} - 52415841411674 T^{22} - 239903274153431 T^{23} + 582622237229761 T^{24} \))(\( 1 - 11 T + 36 T^{2} + 123 T^{3} - 1898 T^{4} + 9669 T^{5} - 17977 T^{6} - 83870 T^{7} + 834166 T^{8} - 3577974 T^{9} + 6674756 T^{10} + 20040864 T^{11} - 226666002 T^{12} + 969820747 T^{13} - 1237622341 T^{14} - 9875829222 T^{15} + 67383134907 T^{16} - 167889096774 T^{17} - 357672856549 T^{18} + 4764729330011 T^{19} - 18931371153042 T^{20} + 28455161036448 T^{21} + 161112383508164 T^{22} - 1468181103188502 T^{23} + 5818939681529206 T^{24} - 9945965201803390 T^{25} - 36241522348371673 T^{26} + 331374965398503477 T^{27} - 1105817006262086378 T^{28} + 1218263098047430251 T^{29} + 6061601756138433444 T^{30} - 31486653566607973723 T^{31} + 48661191875666868481 T^{32} \))
$19$ (\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 - 19 T^{2} + 361 T^{4} \))(\( 1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 8 T^{2} - 56 T^{3} - 89 T^{4} - 1064 T^{5} - 2888 T^{6} + 27436 T^{7} + 130321 T^{8} \))(\( 1 + 2 T - 80 T^{2} - 180 T^{3} + 3449 T^{4} + 7837 T^{5} - 102176 T^{6} - 211409 T^{7} + 2371040 T^{8} + 3579469 T^{9} - 47864088 T^{10} - 27533469 T^{11} + 916901667 T^{12} - 523135911 T^{13} - 17278935768 T^{14} + 24551577871 T^{15} + 308996303840 T^{16} - 523469613491 T^{17} - 4806959937056 T^{18} + 7005272818543 T^{19} + 58576308928409 T^{20} - 58083785600220 T^{21} - 490485300624080 T^{22} + 232980517796438 T^{23} + 2213314919066161 T^{24} \))(\( 1 - 8 T - 16 T^{2} + 368 T^{3} - 525 T^{4} - 8817 T^{5} + 35926 T^{6} + 100093 T^{7} - 897124 T^{8} - 345797 T^{9} + 15630782 T^{10} - 3617369 T^{11} - 256926625 T^{12} - 68730011 T^{13} + 5642712302 T^{14} - 2371821623 T^{15} - 116914096804 T^{16} + 247840177207 T^{17} + 1690170320806 T^{18} - 7881267122763 T^{19} - 8916370596525 T^{20} + 118749072782672 T^{21} - 98097060124816 T^{22} - 931922071185752 T^{23} + 2213314919066161 T^{24} \))(\( 1 - 14 T + 66 T^{2} - 444 T^{3} + 4717 T^{4} - 22391 T^{5} + 98142 T^{6} - 823887 T^{7} + 3750856 T^{8} - 13240737 T^{9} + 95742878 T^{10} - 421689765 T^{11} + 1264726999 T^{12} - 8012105535 T^{13} + 34563178958 T^{14} - 90818215083 T^{15} + 488815304776 T^{16} - 2040025776813 T^{17} + 4617176853102 T^{18} - 20014682107949 T^{19} + 80111466864397 T^{20} - 143273337813876 T^{21} + 404650373014866 T^{22} - 1630863624575066 T^{23} + 2213314919066161 T^{24} \))(\( 1 + 2 T - 54 T^{2} + 52 T^{3} + 1522 T^{4} - 5531 T^{5} - 18356 T^{6} + 142945 T^{7} - 156428 T^{8} - 2136646 T^{9} + 5666688 T^{10} + 23411554 T^{11} - 135081014 T^{12} - 508657467 T^{13} + 5117825840 T^{14} + 6906391627 T^{15} - 121849980107 T^{16} + 131221440913 T^{17} + 1847535128240 T^{18} - 3488881566153 T^{19} - 17603892825494 T^{20} + 57969325447846 T^{21} + 266594329312128 T^{22} - 1909887475647394 T^{23} - 2656704799377548 T^{24} + 46126592959019155 T^{25} - 112541852228195156 T^{26} - 644307621966049289 T^{27} + 3368665306818697042 T^{28} + 2186755140037367068 T^{29} - 43146361032275742534 T^{30} + 30362254059749596598 T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))
$23$ (\( 1 - 23 T^{2} + 529 T^{4} \))(\( 1 - T - 22 T^{2} - 23 T^{3} + 529 T^{4} \))(\( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 3 T - 14 T^{2} - 69 T^{3} + 529 T^{4} \))(\( 1 + 26 T^{2} + 147 T^{4} + 13754 T^{6} + 279841 T^{8} \))(\( 1 + 9 T - 48 T^{2} - 477 T^{3} + 2766 T^{4} + 20637 T^{5} - 83191 T^{6} - 525717 T^{7} + 1781613 T^{8} + 8690382 T^{9} - 29166372 T^{10} - 91574172 T^{11} + 316597101 T^{12} - 2106205956 T^{13} - 15429010788 T^{14} + 105735877794 T^{15} + 498568363533 T^{16} - 3383694932931 T^{17} - 12315253641799 T^{18} + 70265382749739 T^{19} + 216608185287246 T^{20} - 859149819517851 T^{21} - 1988472538255152 T^{22} + 8575287821225343 T^{23} + 21914624432020321 T^{24} \))(\( 1 - 11 T - 2 T^{2} + 365 T^{3} - 216 T^{4} - 8719 T^{5} - 5111 T^{6} + 358923 T^{7} - 1003285 T^{8} - 4953998 T^{9} + 34134756 T^{10} - 5769328 T^{11} - 489517147 T^{12} - 132694544 T^{13} + 18057285924 T^{14} - 60275293666 T^{15} - 280760277685 T^{16} + 2310151538589 T^{17} - 756611428679 T^{18} - 29686673072393 T^{19} - 16915172820696 T^{20} + 657420721433995 T^{21} - 82853022427298 T^{22} - 10480907337053197 T^{23} + 21914624432020321 T^{24} \))(\( 1 + 9 T - 24 T^{2} - 45 T^{3} + 3480 T^{4} + 4437 T^{5} - 43177 T^{6} + 508653 T^{7} + 1537083 T^{8} - 6790500 T^{9} + 64602594 T^{10} + 262176318 T^{11} - 931869183 T^{12} + 6030055314 T^{13} + 34174772226 T^{14} - 82620013500 T^{15} + 430138843803 T^{16} + 3273865175979 T^{17} - 6391745579353 T^{18} + 15107210508339 T^{19} + 272522228777880 T^{20} - 81051869765835 T^{21} - 994236269127576 T^{22} + 8575287821225343 T^{23} + 21914624432020321 T^{24} \))(\( 1 - 11 T - 8 T^{2} + 511 T^{3} - 1175 T^{4} - 7314 T^{5} + 31375 T^{6} - 146176 T^{7} + 863162 T^{8} + 3529440 T^{9} - 34166005 T^{10} + 8815708 T^{11} + 134850764 T^{12} - 1234120523 T^{13} + 19738400159 T^{14} + 2588217123 T^{15} - 586357209291 T^{16} + 59528993829 T^{17} + 10441613684111 T^{18} - 15015544403341 T^{19} + 37736772648524 T^{20} + 56740920475844 T^{21} - 5057794923753445 T^{22} + 12017127125659680 T^{23} + 67595066677118522 T^{24} - 263285291442015488 T^{25} + 1299756789328237375 T^{26} - 6968850569382462078 T^{27} - 25749683707623877175 T^{28} + \)\(25\!\cdots\!13\)\( T^{29} - 92742690596309998472 T^{30} - \)\(29\!\cdots\!77\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))
$29$ (\( 1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - T - 28 T^{2} - 29 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 6 T - 13 T^{2} + 54 T^{3} + 516 T^{4} + 1566 T^{5} - 10933 T^{6} - 146334 T^{7} + 707281 T^{8} \))(\( 1 - 3 T - 87 T^{2} - 372 T^{3} + 6477 T^{4} + 37248 T^{5} - 116788 T^{6} - 2654523 T^{7} - 2866536 T^{8} + 76700583 T^{9} + 479807001 T^{10} - 1248956703 T^{11} - 16840293807 T^{12} - 36219744387 T^{13} + 403517687841 T^{14} + 1870650518787 T^{15} - 2027446448616 T^{16} - 54447316776927 T^{17} - 69468226012948 T^{18} + 642523392757632 T^{19} + 3240096016748397 T^{20} - 5396658303023268 T^{21} - 36601529297117487 T^{22} - 36601529297117487 T^{23} + 353814783205469041 T^{24} \))(\( 1 - 13 T - 33 T^{2} + 1042 T^{3} + 1159 T^{4} - 64528 T^{5} + 58386 T^{6} + 2236053 T^{7} - 3262784 T^{8} - 61621545 T^{9} + 189094723 T^{10} + 570853983 T^{11} - 5049474515 T^{12} + 16554765507 T^{13} + 159028662043 T^{14} - 1502887861005 T^{15} - 2307705130304 T^{16} + 45864016254897 T^{17} + 34729354419906 T^{18} - 1113100018467152 T^{19} + 579785592621799 T^{20} + 15116446106855498 T^{21} - 13883338698906633 T^{22} - 158606626954175777 T^{23} + 353814783205469041 T^{24} \))(\( 1 + 9 T - 69 T^{2} - 702 T^{3} + 3759 T^{4} + 34596 T^{5} - 143518 T^{6} - 1156437 T^{7} + 4050324 T^{8} + 25653105 T^{9} - 98719569 T^{10} - 302648535 T^{11} + 2262044085 T^{12} - 8776807515 T^{13} - 83023157529 T^{14} + 625653577845 T^{15} + 2864717209044 T^{16} - 23719851616113 T^{17} - 85367853383278 T^{18} + 596776720786164 T^{19} + 1880426266320399 T^{20} - 10184016475060038 T^{21} - 29028799097713869 T^{22} + 109804587891352461 T^{23} + 353814783205469041 T^{24} \))(\( 1 - 17 T + 46 T^{2} + 223 T^{3} + 3250 T^{4} - 18084 T^{5} - 204302 T^{6} + 750182 T^{7} + 3378518 T^{8} + 10195995 T^{9} - 165509581 T^{10} + 32483596 T^{11} + 4544588759 T^{12} - 14362280831 T^{13} - 142821670546 T^{14} + 116125876596 T^{15} + 6133655884938 T^{16} + 3367650421284 T^{17} - 120113024929186 T^{18} - 350281667187259 T^{19} + 3214301282054279 T^{20} + 666275877611804 T^{21} - 98448958627738501 T^{22} + 175879652597182455 T^{23} + 1690091510624171798 T^{24} + 10882999782469358158 T^{25} - 85951329177697664702 T^{26} - \)\(22\!\cdots\!36\)\( T^{27} + \)\(11\!\cdots\!50\)\( T^{28} + \)\(22\!\cdots\!47\)\( T^{29} + \)\(13\!\cdots\!26\)\( T^{30} - \)\(14\!\cdots\!33\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))
$31$ (\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 10 T + 31 T^{2} )^{2} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 48 T^{2} - 124 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 9 T + 150 T^{2} - 1087 T^{3} + 9609 T^{4} - 58170 T^{5} + 367149 T^{6} - 1803270 T^{7} + 9234249 T^{8} - 32382817 T^{9} + 138528150 T^{10} - 257662359 T^{11} + 887503681 T^{12} )^{2} \))(\( ( 1 + 21 T + 286 T^{2} + 2721 T^{3} + 22157 T^{4} + 151338 T^{5} + 918241 T^{6} + 4691478 T^{7} + 21292877 T^{8} + 81061311 T^{9} + 264127006 T^{10} + 601212171 T^{11} + 887503681 T^{12} )^{2} \))(\( ( 1 + 9 T + 96 T^{2} + 767 T^{3} + 5613 T^{4} + 34584 T^{5} + 205869 T^{6} + 1072104 T^{7} + 5394093 T^{8} + 22849697 T^{9} + 88658016 T^{10} + 257662359 T^{11} + 887503681 T^{12} )^{2} \))(\( ( 1 - 15 T + 294 T^{2} - 2963 T^{3} + 33518 T^{4} - 256035 T^{5} + 2103711 T^{6} - 12738397 T^{7} + 81705846 T^{8} - 394890307 T^{9} + 2021666271 T^{10} - 7627538685 T^{11} + 30954576878 T^{12} - 84828174413 T^{13} + 260926082214 T^{14} - 412689211665 T^{15} + 852891037441 T^{16} )^{2} \))
$37$ (\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( ( 1 - T + 37 T^{2} )( 1 + 11 T + 37 T^{2} ) \))(\( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 8 T - 8 T^{2} + 16 T^{3} + 1447 T^{4} + 592 T^{5} - 10952 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( 1 - 6 T - 111 T^{2} + 802 T^{3} + 5847 T^{4} - 49353 T^{5} - 218618 T^{6} + 1971477 T^{7} + 7114131 T^{8} - 58413395 T^{9} - 181224618 T^{10} + 875260311 T^{11} + 4536500245 T^{12} + 32384631507 T^{13} - 248096502042 T^{14} - 2958813696935 T^{15} + 13333026869091 T^{16} + 136710016314489 T^{17} - 560913976082762 T^{18} - 4685172932144949 T^{19} + 20537467367076087 T^{20} + 104229315315651754 T^{21} - 533752865338381239 T^{22} - 1067505730676762478 T^{23} + 6582952005840035281 T^{24} \))(\( 1 - 18 T + 119 T^{2} - 678 T^{3} + 7703 T^{4} - 69441 T^{5} + 533994 T^{6} - 4260171 T^{7} + 27103075 T^{8} - 158201349 T^{9} + 1165990240 T^{10} - 8176208427 T^{11} + 50154968893 T^{12} - 302519711799 T^{13} + 1596240638560 T^{14} - 8013372930897 T^{15} + 50795526145075 T^{16} - 295417114636647 T^{17} + 1370082508047546 T^{18} - 6592164479992653 T^{19} + 27056629233553463 T^{20} - 88114059581062206 T^{21} + 572221540317724031 T^{22} - 3202517192030287434 T^{23} + 6582952005840035281 T^{24} \))(\( 1 + 12 T - 75 T^{2} - 1124 T^{3} + 5793 T^{4} + 66639 T^{5} - 404162 T^{6} - 2798919 T^{7} + 24121197 T^{8} + 87063469 T^{9} - 1138257942 T^{10} - 1336271169 T^{11} + 44567264293 T^{12} - 49442033253 T^{13} - 1558275122598 T^{14} + 4410025895257 T^{15} + 45207006690717 T^{16} - 194088118782483 T^{17} - 1036969116914258 T^{18} + 6326165360265987 T^{19} + 20347793476564353 T^{20} - 146076995529666548 T^{21} - 360643827931338675 T^{22} + 2135011461353524956 T^{23} + 6582952005840035281 T^{24} \))(\( 1 + 2 T - 109 T^{2} - 494 T^{3} + 4396 T^{4} + 37709 T^{5} + 5949 T^{6} - 1192233 T^{7} - 6568281 T^{8} + 15849024 T^{9} + 180379971 T^{10} - 663666882 T^{11} - 2633817279 T^{12} + 62063414607 T^{13} + 300032298102 T^{14} - 1464225969303 T^{15} - 17940373399443 T^{16} - 54176360864211 T^{17} + 410744216101638 T^{18} + 3143698140088371 T^{19} - 4936197625427919 T^{20} - 46021287727732074 T^{21} + 462805655249354139 T^{22} + 1504577599045968192 T^{23} - 23070952060079679801 T^{24} - \)\(15\!\cdots\!41\)\( T^{25} + 28606268431513783701 T^{26} + \)\(67\!\cdots\!17\)\( T^{27} + \)\(28\!\cdots\!76\)\( T^{28} - \)\(12\!\cdots\!18\)\( T^{29} - \)\(98\!\cdots\!01\)\( T^{30} + \)\(66\!\cdots\!86\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))
$41$ (\( 1 - 3 T - 32 T^{2} - 123 T^{3} + 1681 T^{4} \))(\( 1 + 10 T + 59 T^{2} + 410 T^{3} + 1681 T^{4} \))(\( 1 + 5 T - 16 T^{2} + 205 T^{3} + 1681 T^{4} \))(\( 1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( ( 1 + 9 T + 40 T^{2} + 369 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 2 T + 118 T^{2} - 443 T^{3} + 5993 T^{4} - 38003 T^{5} + 232561 T^{6} - 1558123 T^{7} + 10074233 T^{8} - 30532003 T^{9} + 333439798 T^{10} - 231712402 T^{11} + 4750104241 T^{12} )( 1 + 13 T - 5 T^{2} - 1007 T^{3} - 5128 T^{4} + 21646 T^{5} + 337849 T^{6} + 887486 T^{7} - 8620168 T^{8} - 69403447 T^{9} - 14128805 T^{10} + 1506130613 T^{11} + 4750104241 T^{12} ) \))(\( 1 - 5 T - 189 T^{2} + 674 T^{3} + 21334 T^{4} - 51791 T^{5} - 1737525 T^{6} + 2754282 T^{7} + 111275218 T^{8} - 98774466 T^{9} - 5884736759 T^{10} + 1597606794 T^{11} + 262521605425 T^{12} + 65501878554 T^{13} - 9892242491879 T^{14} - 6807634971186 T^{15} + 314437171290898 T^{16} + 319100649002682 T^{17} - 8253424871343525 T^{18} - 10086518598570871 T^{19} + 170350394838067414 T^{20} + 220655423781529714 T^{21} - 2536882609618803789 T^{22} - 2751645158581242205 T^{23} + 22563490300366186081 T^{24} \))(\( 1 - T - 197 T^{2} + 250 T^{3} + 21102 T^{4} - 27179 T^{5} - 1633109 T^{6} + 1654722 T^{7} + 101292122 T^{8} - 62228170 T^{9} - 5261216175 T^{10} + 1034229106 T^{11} + 233114446817 T^{12} + 42403393346 T^{13} - 8844104390175 T^{14} - 4288827704570 T^{15} + 286227327954842 T^{16} + 191709804631122 T^{17} - 7757437986915269 T^{18} - 5293226409811699 T^{19} + 168497892184911342 T^{20} + 81845483598490250 T^{21} - 2644263884100022997 T^{22} - 550329031716248441 T^{23} + 22563490300366186081 T^{24} \))(\( 1 - 7 T - 58 T^{2} + 821 T^{3} - 5081 T^{4} + 3487 T^{5} + 202690 T^{6} - 2313484 T^{7} + 22320617 T^{8} - 84574319 T^{9} - 449228446 T^{10} + 8174132915 T^{11} - 61865466443 T^{12} + 229869969509 T^{13} + 311827818587 T^{14} - 13738704403974 T^{15} + 126160448679906 T^{16} - 563286880562934 T^{17} + 524182563044747 T^{18} + 15842868168529789 T^{19} - 174817022321438123 T^{20} + 947023986000955915 T^{21} - 2133881946522439486 T^{22} - 16471210085825062039 T^{23} + \)\(17\!\cdots\!57\)\( T^{24} - \)\(75\!\cdots\!24\)\( T^{25} + \)\(27\!\cdots\!90\)\( T^{26} + \)\(19\!\cdots\!67\)\( T^{27} - \)\(11\!\cdots\!61\)\( T^{28} + \)\(75\!\cdots\!41\)\( T^{29} - \)\(21\!\cdots\!38\)\( T^{30} - \)\(10\!\cdots\!07\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))
$43$ (\( ( 1 - 8 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( 1 - 3 T - 34 T^{2} - 129 T^{3} + 1849 T^{4} \))(\( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} \))(\( 1 + 11 T + 78 T^{2} + 473 T^{3} + 1849 T^{4} \))(\( ( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} )^{2} \))(\( 1 - 23 T + 113 T^{2} + 896 T^{3} - 1332 T^{4} - 148755 T^{5} + 870961 T^{6} + 3952150 T^{7} - 29247526 T^{8} - 288761288 T^{9} + 2809373309 T^{10} + 289322302 T^{11} - 86189636971 T^{12} + 12440858986 T^{13} + 5194531248341 T^{14} - 22958543725016 T^{15} - 99991471136326 T^{16} + 580999418002450 T^{17} + 5505660682520089 T^{18} - 40434377495221785 T^{19} - 15568682769764532 T^{20} + 450322980295411328 T^{21} + 2442097501401120137 T^{22} - 21373756007838122261 T^{23} + 39959630797262576401 T^{24} \))(\( 1 + 11 T - 47 T^{2} - 336 T^{3} + 4742 T^{4} - 6185 T^{5} - 265967 T^{6} + 524632 T^{7} + 3908504 T^{8} - 33033908 T^{9} - 58808445 T^{10} + 1188416940 T^{11} + 11051987505 T^{12} + 51101928420 T^{13} - 108736814805 T^{14} - 2626426923356 T^{15} + 13362397383704 T^{16} + 77125333467976 T^{17} - 1681273966053383 T^{18} - 1681198109696795 T^{19} + 55425445716383942 T^{20} - 168871117610779248 T^{21} - 1015739668724359703 T^{22} + 10222231134183449777 T^{23} + 39959630797262576401 T^{24} \))(\( 1 - 7 T - 61 T^{2} - 38 T^{3} + 2916 T^{4} + 23601 T^{5} + 1081 T^{6} - 108892 T^{7} - 5446372 T^{8} - 63105082 T^{9} - 148348975 T^{10} + 1479379556 T^{11} + 27501185741 T^{12} + 63613320908 T^{13} - 274297254775 T^{14} - 5017295754574 T^{15} - 18620062039972 T^{16} - 16008043375156 T^{17} + 6833393455969 T^{18} + 6415191040736307 T^{19} + 34082792009484516 T^{20} - 19098519253600034 T^{21} - 1318300421110339189 T^{22} - 6505056176298558949 T^{23} + 39959630797262576401 T^{24} \))(\( 1 + 13 T - 110 T^{2} - 1567 T^{3} + 10823 T^{4} + 109505 T^{5} - 883584 T^{6} - 5592870 T^{7} + 52864479 T^{8} + 206005533 T^{9} - 2766579456 T^{10} - 7286801151 T^{11} + 131529658809 T^{12} + 225678713547 T^{13} - 6233727820281 T^{14} - 3123476792046 T^{15} + 288754313221062 T^{16} - 134309502057978 T^{17} - 11526162739699569 T^{18} + 17943037477981329 T^{19} + 449673729065868009 T^{20} - 1071221291659117893 T^{21} - 17488553145280921344 T^{22} + 55996137860417255031 T^{23} + \)\(61\!\cdots\!79\)\( T^{24} - \)\(28\!\cdots\!10\)\( T^{25} - \)\(19\!\cdots\!16\)\( T^{26} + \)\(10\!\cdots\!35\)\( T^{27} + \)\(43\!\cdots\!23\)\( T^{28} - \)\(26\!\cdots\!81\)\( T^{29} - \)\(81\!\cdots\!90\)\( T^{30} + \)\(41\!\cdots\!91\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))
$47$ (\( ( 1 + 9 T + 47 T^{2} )^{2} \))(\( ( 1 + 7 T + 47 T^{2} )^{2} \))(\( ( 1 + 13 T + 47 T^{2} )^{2} \))(\( ( 1 - 3 T + 47 T^{2} )^{2} \))(\( ( 1 + 6 T + 85 T^{2} + 282 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + T + 220 T^{2} + 76 T^{3} + 21464 T^{4} - 167 T^{5} + 1253383 T^{6} - 7849 T^{7} + 47413976 T^{8} + 7890548 T^{9} + 1073529820 T^{10} + 229345007 T^{11} + 10779215329 T^{12} )^{2} \))(\( ( 1 - 23 T + 364 T^{2} - 4178 T^{3} + 41930 T^{4} - 349481 T^{5} + 2600287 T^{6} - 16425607 T^{7} + 92623370 T^{8} - 433772494 T^{9} + 1776203884 T^{10} - 5274935161 T^{11} + 10779215329 T^{12} )^{2} \))(\( ( 1 + 7 T + 192 T^{2} + 1490 T^{3} + 18046 T^{4} + 130951 T^{5} + 1054511 T^{6} + 6154697 T^{7} + 39863614 T^{8} + 154696270 T^{9} + 936898752 T^{10} + 1605415049 T^{11} + 10779215329 T^{12} )^{2} \))(\( ( 1 - 5 T + 167 T^{2} - 679 T^{3} + 12865 T^{4} - 55056 T^{5} + 721843 T^{6} - 3490742 T^{7} + 35510129 T^{8} - 164064874 T^{9} + 1594551187 T^{10} - 5716079088 T^{11} + 62777096065 T^{12} - 155725259753 T^{13} + 1800128959943 T^{14} - 2533115602315 T^{15} + 23811286661761 T^{16} )^{2} \))
$53$ (\( 1 + 12 T + 91 T^{2} + 636 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 12 T + 20 T^{2} + 216 T^{3} + 4935 T^{4} + 11448 T^{5} + 56180 T^{6} + 1786524 T^{7} + 7890481 T^{8} \))(\( 1 + 4 T - 69 T^{2} + 608 T^{3} + 3817 T^{4} - 53819 T^{5} + 247674 T^{6} + 1787013 T^{7} - 23754551 T^{8} + 62188347 T^{9} + 305246782 T^{10} - 5161623099 T^{11} + 3988104733 T^{12} - 273566024247 T^{13} + 857438210638 T^{14} + 9258414536319 T^{15} - 187434833329031 T^{16} + 747320782532409 T^{17} + 5489535978263946 T^{18} - 63221778834887503 T^{19} + 237645238300164937 T^{20} + 2006256263815696864 T^{21} - 12067235455220400381 T^{22} + 37076143717488766388 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - 2 T - 255 T^{2} + 422 T^{3} + 35953 T^{4} - 47393 T^{5} - 3605976 T^{6} + 3309969 T^{7} + 285580525 T^{8} - 148182909 T^{9} - 18913659452 T^{10} + 3090482955 T^{11} + 1076146210033 T^{12} + 163795596615 T^{13} - 53128469400668 T^{14} - 22061026943193 T^{15} + 2253367706482525 T^{16} + 1384214117769717 T^{17} - 79924154286506904 T^{18} - 55673085050294941 T^{19} + 2238422649359662033 T^{20} + 1392500235740500126 T^{21} - 44596304943205827495 T^{22} - 18538071858744383194 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - 2 T - 167 T^{2} + 1010 T^{3} + 13227 T^{4} - 131245 T^{5} - 429158 T^{6} + 9790659 T^{7} - 11991223 T^{8} - 447494225 T^{9} + 2419646052 T^{10} + 9239703395 T^{11} - 165502278643 T^{12} + 489704279935 T^{13} + 6796785760068 T^{14} - 66621597735325 T^{15} - 94616517248263 T^{16} + 4094409467299887 T^{17} - 9512012893399382 T^{18} - 154174963547907065 T^{19} + 823508925071071947 T^{20} + 3332761227720154330 T^{21} - 29206207551040679183 T^{22} - 18538071858744383194 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - 18 T - 25 T^{2} + 3094 T^{3} - 20382 T^{4} - 155341 T^{5} + 2463947 T^{6} - 2962263 T^{7} - 127200023 T^{8} + 760818902 T^{9} + 3333886647 T^{10} - 61667632700 T^{11} + 106780502839 T^{12} + 3773454519213 T^{13} - 28393687643164 T^{14} - 98984202945069 T^{15} + 2205152767325745 T^{16} - 5246162756088657 T^{17} - 79757868589647676 T^{18} + 561780588456873801 T^{19} + 842549528821575559 T^{20} - 25789126059119421100 T^{21} + 73893467607258944463 T^{22} + \)\(89\!\cdots\!74\)\( T^{23} - \)\(79\!\cdots\!03\)\( T^{24} - \)\(97\!\cdots\!79\)\( T^{25} + \)\(43\!\cdots\!03\)\( T^{26} - \)\(14\!\cdots\!77\)\( T^{27} - \)\(10\!\cdots\!62\)\( T^{28} + \)\(80\!\cdots\!62\)\( T^{29} - \)\(34\!\cdots\!25\)\( T^{30} - \)\(13\!\cdots\!26\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))
$59$ (\( ( 1 - 6 T + 59 T^{2} )^{2} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 136 T^{2} - 708 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 11 T + 151 T^{2} + 725 T^{3} + 10547 T^{4} + 66515 T^{5} + 880441 T^{6} + 3924385 T^{7} + 36714107 T^{8} + 148899775 T^{9} + 1829721511 T^{10} + 7864167289 T^{11} + 42180533641 T^{12} )^{2} \))(\( ( 1 + T + 181 T^{2} + 187 T^{3} + 17933 T^{4} + 24505 T^{5} + 1246183 T^{6} + 1445795 T^{7} + 62424773 T^{8} + 38405873 T^{9} + 2193242341 T^{10} + 714924299 T^{11} + 42180533641 T^{12} )^{2} \))(\( ( 1 + 29 T + 597 T^{2} + 8413 T^{3} + 99691 T^{4} + 952679 T^{5} + 8015939 T^{6} + 56208061 T^{7} + 347024371 T^{8} + 1727853527 T^{9} + 7234064517 T^{10} + 20732804671 T^{11} + 42180533641 T^{12} )^{2} \))(\( ( 1 + T + 317 T^{2} + 659 T^{3} + 48346 T^{4} + 123360 T^{5} + 4790140 T^{6} + 11791354 T^{7} + 334628690 T^{8} + 695689886 T^{9} + 16674477340 T^{10} + 25335553440 T^{11} + 585825934906 T^{12} + 471135113041 T^{13} + 13371229164197 T^{14} + 2488651484819 T^{15} + 146830437604321 T^{16} )^{2} \))
$61$ (\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 + 11 T + 61 T^{2} )^{2} \))(\( ( 1 + 6 T + 61 T^{2} )^{2} \))(\( ( 1 + 7 T + 61 T^{2} )^{2} \))(\( ( 1 + 8 T + 66 T^{2} + 488 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 25 T + 500 T^{2} - 6951 T^{3} + 82777 T^{4} - 796808 T^{5} + 6827935 T^{6} - 48605288 T^{7} + 308013217 T^{8} - 1577744931 T^{9} + 6922920500 T^{10} - 21114907525 T^{11} + 51520374361 T^{12} )^{2} \))(\( ( 1 - T - 16 T^{2} - 789 T^{3} - 2045 T^{4} + 26308 T^{5} + 419365 T^{6} + 1604788 T^{7} - 7609445 T^{8} - 179088009 T^{9} - 221533456 T^{10} - 844596301 T^{11} + 51520374361 T^{12} )^{2} \))(\( ( 1 - 11 T + 362 T^{2} - 3015 T^{3} + 54025 T^{4} - 347434 T^{5} + 4351741 T^{6} - 21193474 T^{7} + 201027025 T^{8} - 684347715 T^{9} + 5012194442 T^{10} - 9290559311 T^{11} + 51520374361 T^{12} )^{2} \))(\( ( 1 - 27 T + 644 T^{2} - 9523 T^{3} + 127396 T^{4} - 1294067 T^{5} + 12537951 T^{6} - 101639815 T^{7} + 845706468 T^{8} - 6200028715 T^{9} + 46653715671 T^{10} - 293728621727 T^{11} + 1763904760036 T^{12} - 8043090574423 T^{13} + 33179121088484 T^{14} - 84854056572567 T^{15} + 191707312997281 T^{16} )^{2} \))
$67$ (\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 + 9 T + 67 T^{2} )^{2} \))(\( ( 1 - 12 T + 67 T^{2} )^{2} \))(\( ( 1 + 7 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 66 T^{2} - 268 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 2 T + 177 T^{2} - 243 T^{3} + 18145 T^{4} - 40274 T^{5} + 1465189 T^{6} - 2698358 T^{7} + 81452905 T^{8} - 73085409 T^{9} + 3566748417 T^{10} - 2700250214 T^{11} + 90458382169 T^{12} )^{2} \))(\( ( 1 + 2 T + 121 T^{2} + 1039 T^{3} + 13819 T^{4} + 79592 T^{5} + 1283207 T^{6} + 5332664 T^{7} + 62033491 T^{8} + 312492757 T^{9} + 2438285641 T^{10} + 2700250214 T^{11} + 90458382169 T^{12} )^{2} \))(\( ( 1 - 22 T + 565 T^{2} - 7781 T^{3} + 110749 T^{4} - 1067896 T^{5} + 10367459 T^{6} - 71549032 T^{7} + 497152261 T^{8} - 2340236903 T^{9} + 11385383365 T^{10} - 29702752354 T^{11} + 90458382169 T^{12} )^{2} \))(\( ( 1 - 10 T + 183 T^{2} - 1911 T^{3} + 28302 T^{4} - 239130 T^{5} + 2683324 T^{6} - 21197185 T^{7} + 215653584 T^{8} - 1420211395 T^{9} + 12045441436 T^{10} - 71921456190 T^{11} + 570317026542 T^{12} - 2580089079477 T^{13} + 16553883936927 T^{14} - 60607116053230 T^{15} + 406067677556641 T^{16} )^{2} \))
$71$ (\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 124 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 11 T + 244 T^{2} - 2045 T^{3} + 18530 T^{4} - 153299 T^{5} + 887101 T^{6} - 10884229 T^{7} + 93409730 T^{8} - 731927995 T^{9} + 6200450164 T^{10} - 19846522861 T^{11} + 128100283921 T^{12} )^{2} \))(\( ( 1 + 15 T + 472 T^{2} + 5103 T^{3} + 87582 T^{4} + 709377 T^{5} + 8398649 T^{6} + 50365767 T^{7} + 441500862 T^{8} + 1826419833 T^{9} + 11994313432 T^{10} + 27063440265 T^{11} + 128100283921 T^{12} )^{2} \))(\( ( 1 - 5 T + 282 T^{2} - 1537 T^{3} + 40228 T^{4} - 200831 T^{5} + 3541613 T^{6} - 14259001 T^{7} + 202789348 T^{8} - 550109207 T^{9} + 7166094042 T^{10} - 9021146755 T^{11} + 128100283921 T^{12} )^{2} \))(\( ( 1 + 19 T + 400 T^{2} + 3773 T^{3} + 41473 T^{4} + 130458 T^{5} + 473407 T^{6} - 19694168 T^{7} - 122824232 T^{8} - 1398285928 T^{9} + 2386444687 T^{10} + 46692353238 T^{11} + 1053898646113 T^{12} + 6807357341323 T^{13} + 51240113568400 T^{14} + 172807283009429 T^{15} + 645753531245761 T^{16} )^{2} \))
$73$ (\( 1 + 8 T - 9 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( 1 - 14 T + 123 T^{2} - 1022 T^{3} + 5329 T^{4} \))(\( 1 - 73 T^{2} + 5329 T^{4} \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 - 8 T - 26 T^{2} + 448 T^{3} - 1901 T^{4} + 32704 T^{5} - 138554 T^{6} - 3112136 T^{7} + 28398241 T^{8} \))(\( 1 - 24 T + 42 T^{2} + 3412 T^{3} - 16221 T^{4} - 351231 T^{5} + 2912248 T^{6} + 10402335 T^{7} - 128561004 T^{8} + 12356683 T^{9} - 873975840 T^{10} - 31448077707 T^{11} + 794156097013 T^{12} - 2295709672611 T^{13} - 4657417251360 T^{14} + 4806959750611 T^{15} - 3650906374793964 T^{16} + 21564785189369655 T^{17} + 440722797841687672 T^{18} - 3880188829260958407 T^{19} - 13081589150613887901 T^{20} + \)\(20\!\cdots\!56\)\( T^{21} + \)\(18\!\cdots\!58\)\( T^{22} - \)\(75\!\cdots\!48\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 22 T - 46 T^{2} + 3256 T^{3} + 12483 T^{4} - 414879 T^{5} - 2110886 T^{6} + 33167477 T^{7} + 364001024 T^{8} - 2404017511 T^{9} - 35612367328 T^{10} + 55783713671 T^{11} + 3123892980185 T^{12} + 4072211097983 T^{13} - 189778305490912 T^{14} - 935203680076687 T^{15} + 10336988803798784 T^{16} + 68758554380180861 T^{17} - 319449299594282054 T^{18} - 4583333650204444263 T^{19} + 10067041327113813123 T^{20} + \)\(19\!\cdots\!28\)\( T^{21} - \)\(19\!\cdots\!54\)\( T^{22} - \)\(69\!\cdots\!94\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 6 T - 264 T^{2} + 676 T^{3} + 41379 T^{4} - 177 T^{5} - 4351292 T^{6} - 7764489 T^{7} + 350907786 T^{8} + 808896697 T^{9} - 24223821882 T^{10} - 30050609763 T^{11} + 1721091747949 T^{12} - 2193694512699 T^{13} - 129088746809178 T^{14} + 314674566376849 T^{15} + 9965163875604426 T^{16} - 16096341580060977 T^{17} - 658499408177515388 T^{18} - 1955389537880169 T^{19} + 33370512142485177699 T^{20} + 39797192614789109188 T^{21} - \)\(11\!\cdots\!36\)\( T^{22} - \)\(18\!\cdots\!62\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 + 8 T - 390 T^{2} - 908 T^{3} + 103150 T^{4} - 105353 T^{5} - 16697378 T^{6} + 75246967 T^{7} + 1927206172 T^{8} - 14189615254 T^{9} - 139595267550 T^{10} + 1686118517626 T^{11} + 5218854241786 T^{12} - 119151906708597 T^{13} + 190749604993352 T^{14} + 3821131738775017 T^{15} - 31483648169073569 T^{16} + 278942616930576241 T^{17} + 1016504645009572808 T^{18} - 46352117292058279149 T^{19} + \)\(14\!\cdots\!26\)\( T^{20} + \)\(34\!\cdots\!18\)\( T^{21} - \)\(21\!\cdots\!50\)\( T^{22} - \)\(15\!\cdots\!38\)\( T^{23} + \)\(15\!\cdots\!32\)\( T^{24} + \)\(44\!\cdots\!71\)\( T^{25} - \)\(71\!\cdots\!22\)\( T^{26} - \)\(33\!\cdots\!81\)\( T^{27} + \)\(23\!\cdots\!50\)\( T^{28} - \)\(15\!\cdots\!64\)\( T^{29} - \)\(47\!\cdots\!10\)\( T^{30} + \)\(71\!\cdots\!56\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))
$79$ (\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 10 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 - 4 T - 316 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - T + 179 T^{2} + 915 T^{3} + 21280 T^{4} + 88630 T^{5} + 2361307 T^{6} + 7001770 T^{7} + 132808480 T^{8} + 451130685 T^{9} + 6972064499 T^{10} - 3077056399 T^{11} + 243087455521 T^{12} )^{2} \))(\( ( 1 + 27 T + 763 T^{2} + 12207 T^{3} + 189134 T^{4} + 2055720 T^{5} + 21347467 T^{6} + 162401880 T^{7} + 1180385294 T^{8} + 6018527073 T^{9} + 29718911803 T^{10} + 83080522773 T^{11} + 243087455521 T^{12} )^{2} \))(\( ( 1 + T + 53 T^{2} - 531 T^{3} + 1360 T^{4} - 20890 T^{5} + 639331 T^{6} - 1650310 T^{7} + 8487760 T^{8} - 261803709 T^{9} + 2064354293 T^{10} + 3077056399 T^{11} + 243087455521 T^{12} )^{2} \))(\( ( 1 - 25 T + 807 T^{2} - 13099 T^{3} + 239467 T^{4} - 2871909 T^{5} + 37853854 T^{6} - 357554245 T^{7} + 3709340088 T^{8} - 28246785355 T^{9} + 236245902814 T^{10} - 1415963141451 T^{11} + 9327259046827 T^{12} - 40306361770501 T^{13} + 196171576605447 T^{14} - 480097724653975 T^{15} + 1517108809906561 T^{16} )^{2} \))
$83$ (\( 1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 - 5 T - 58 T^{2} - 415 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( ( 1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4} )^{2} \))(\( 1 - 4 T - 294 T^{2} + 1948 T^{3} + 44977 T^{4} - 398395 T^{5} - 3801708 T^{6} + 52335429 T^{7} + 120574846 T^{8} - 4218193263 T^{9} + 14917345312 T^{10} + 151178074263 T^{11} - 2170254522125 T^{12} + 12547780163829 T^{13} + 102765591854368 T^{14} - 2411908071270981 T^{15} + 5722279745993566 T^{16} + 206151381899840847 T^{17} - 1242931832959914252 T^{18} - 10810867034012448665 T^{19} + \)\(10\!\cdots\!57\)\( T^{20} + \)\(36\!\cdots\!44\)\( T^{21} - \)\(45\!\cdots\!06\)\( T^{22} - \)\(51\!\cdots\!68\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - 6 T - 330 T^{2} + 1740 T^{3} + 59559 T^{4} - 268053 T^{5} - 7813786 T^{6} + 31726179 T^{7} + 814223178 T^{8} - 2507023989 T^{9} - 75271442382 T^{10} + 84734329059 T^{11} + 6524490952095 T^{12} + 7032949311897 T^{13} - 518544966569598 T^{14} - 1433483725598343 T^{15} + 38641664947164138 T^{16} + 124970708528093097 T^{17} - 2554642112265465034 T^{18} - 7273899875922486231 T^{19} + \)\(13\!\cdots\!19\)\( T^{20} + \)\(32\!\cdots\!20\)\( T^{21} - \)\(51\!\cdots\!70\)\( T^{22} - \)\(77\!\cdots\!02\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + 26 T + 232 T^{2} + 1516 T^{3} + 11499 T^{4} - 94349 T^{5} - 2607716 T^{6} - 23093955 T^{7} - 195776338 T^{8} - 925613923 T^{9} + 9434947014 T^{10} + 206018004805 T^{11} + 2189491903883 T^{12} + 17099494398815 T^{13} + 64997349979446 T^{14} - 529254008190401 T^{15} - 9291216293008498 T^{16} - 90968027352613065 T^{17} - 852567642680315204 T^{18} - 2560259274820317823 T^{19} + 25899108377366832459 T^{20} + \)\(28\!\cdots\!48\)\( T^{21} + \)\(35\!\cdots\!68\)\( T^{22} + \)\(33\!\cdots\!42\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - 2 T - 379 T^{2} + 46 T^{3} + 71929 T^{4} + 111425 T^{5} - 9247598 T^{6} - 27250484 T^{7} + 925626125 T^{8} + 3684425840 T^{9} - 76460286955 T^{10} - 351032380757 T^{11} + 5350114348114 T^{12} + 23636419050310 T^{13} - 345108599067805 T^{14} - 759472537118196 T^{15} + 25092808099894680 T^{16} - 63036220580810268 T^{17} - 2377453138978108645 T^{18} + 13514997139519603970 T^{19} + \)\(25\!\cdots\!94\)\( T^{20} - \)\(13\!\cdots\!51\)\( T^{21} - \)\(24\!\cdots\!95\)\( T^{22} + \)\(99\!\cdots\!80\)\( T^{23} + \)\(20\!\cdots\!25\)\( T^{24} - \)\(50\!\cdots\!52\)\( T^{25} - \)\(14\!\cdots\!02\)\( T^{26} + \)\(14\!\cdots\!75\)\( T^{27} + \)\(76\!\cdots\!69\)\( T^{28} + \)\(40\!\cdots\!98\)\( T^{29} - \)\(27\!\cdots\!91\)\( T^{30} - \)\(12\!\cdots\!14\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))
$89$ (\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 + T - 88 T^{2} + 89 T^{3} + 7921 T^{4} \))(\( 1 - 14 T + 107 T^{2} - 1246 T^{3} + 7921 T^{4} \))(\( 1 - 15 T + 136 T^{2} - 1335 T^{3} + 7921 T^{4} \))(\( ( 1 - 89 T^{2} + 7921 T^{4} )^{2} \))(\( 1 - 2 T - 255 T^{2} + 326 T^{3} + 33115 T^{4} + 1237 T^{5} - 2035002 T^{6} - 10969065 T^{7} + 3238993 T^{8} + 1541883639 T^{9} + 12567967198 T^{10} - 74858833077 T^{11} - 1448697683687 T^{12} - 6662436143853 T^{13} + 99550868175358 T^{14} + 1086980167102191 T^{15} + 203221679403313 T^{16} - 61251911059945185 T^{17} - 1011357921068216922 T^{18} + 54714161265769373 T^{19} + \)\(13\!\cdots\!15\)\( T^{20} + \)\(11\!\cdots\!34\)\( T^{21} - \)\(79\!\cdots\!55\)\( T^{22} - \)\(55\!\cdots\!78\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 18 T - 115 T^{2} - 1950 T^{3} + 30919 T^{4} + 158145 T^{5} - 3931898 T^{6} + 1392867 T^{7} + 346157113 T^{8} - 979144353 T^{9} - 18572538958 T^{10} + 88654414143 T^{11} + 1705608497513 T^{12} + 7890242858727 T^{13} - 147113081086318 T^{14} - 690266415390057 T^{15} + 21718673007710233 T^{16} + 7777852132550283 T^{17} - 1954079743966973978 T^{18} + 6994964457053433705 T^{19} + \)\(12\!\cdots\!39\)\( T^{20} - \)\(68\!\cdots\!50\)\( T^{21} - \)\(35\!\cdots\!15\)\( T^{22} + \)\(49\!\cdots\!02\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 - 2 T - 131 T^{2} + 1310 T^{3} - 5289 T^{4} - 98935 T^{5} + 2008330 T^{6} - 7349421 T^{7} - 31479907 T^{8} + 1608975643 T^{9} - 11307686898 T^{10} - 57565868677 T^{11} + 1401967996337 T^{12} - 5123362312253 T^{13} - 89568187919058 T^{14} + 1134277950070067 T^{15} - 1975119911651587 T^{16} - 41039603779729029 T^{17} + 998102436075705130 T^{18} - 4376027117889161615 T^{19} - 20820618193358306409 T^{20} + \)\(45\!\cdots\!90\)\( T^{21} - \)\(40\!\cdots\!31\)\( T^{22} - \)\(55\!\cdots\!78\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 6 T - 361 T^{2} - 3094 T^{3} + 62940 T^{4} + 748723 T^{5} - 6298663 T^{6} - 119355885 T^{7} + 250393933 T^{8} + 13841837530 T^{9} + 33272999661 T^{10} - 1196873353342 T^{11} - 8138474562173 T^{12} + 74723700233589 T^{13} + 1028573157441158 T^{14} - 2348330140909041 T^{15} - 100635305983812723 T^{16} - 209001382540904649 T^{17} + 8147327980091412518 T^{18} + 52677892229973003741 T^{19} - \)\(51\!\cdots\!93\)\( T^{20} - \)\(66\!\cdots\!58\)\( T^{21} + \)\(16\!\cdots\!21\)\( T^{22} + \)\(61\!\cdots\!70\)\( T^{23} + \)\(98\!\cdots\!73\)\( T^{24} - \)\(41\!\cdots\!65\)\( T^{25} - \)\(19\!\cdots\!63\)\( T^{26} + \)\(20\!\cdots\!47\)\( T^{27} + \)\(15\!\cdots\!40\)\( T^{28} - \)\(68\!\cdots\!86\)\( T^{29} - \)\(70\!\cdots\!01\)\( T^{30} + \)\(10\!\cdots\!94\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))
$97$ (\( 1 - 10 T + 3 T^{2} - 970 T^{3} + 9409 T^{4} \))(\( 1 + 10 T + 3 T^{2} + 970 T^{3} + 9409 T^{4} \))(\( 1 + 2 T - 93 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 - 10 T + 3 T^{2} - 970 T^{3} + 9409 T^{4} \))(\( 1 + 4 T - 110 T^{2} - 272 T^{3} + 4915 T^{4} - 26384 T^{5} - 1034990 T^{6} + 3650692 T^{7} + 88529281 T^{8} \))(\( ( 1 + 18 T - 36 T^{2} - 490 T^{3} + 31950 T^{4} + 166842 T^{5} - 1649145 T^{6} + 16183674 T^{7} + 300617550 T^{8} - 447209770 T^{9} - 3187054116 T^{10} + 154572124626 T^{11} + 832972004929 T^{12} )^{2} \))(\( 1 + 4 T - 142 T^{2} - 1276 T^{3} - 1290 T^{4} + 122538 T^{5} + 421462 T^{6} - 4407458 T^{7} - 23869888 T^{8} + 1323819664 T^{9} + 17054431616 T^{10} - 120190432922 T^{11} - 2625924073873 T^{12} - 11658471993434 T^{13} + 160465147074944 T^{14} + 1208214464201872 T^{15} - 2113184022190528 T^{16} - 37848341514436706 T^{17} + 351066047141386198 T^{18} + 9900860183379010794 T^{19} - 10110289336746279690 T^{20} - \)\(97\!\cdots\!92\)\( T^{21} - \)\(10\!\cdots\!58\)\( T^{22} + \)\(28\!\cdots\!12\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 6 T - 168 T^{2} + 1492 T^{3} + 5214 T^{4} - 121578 T^{5} + 1943470 T^{6} - 2165256 T^{7} - 213568578 T^{8} + 1521589192 T^{9} - 5900408970 T^{10} - 81665164176 T^{11} + 2384863292767 T^{12} - 7921520925072 T^{13} - 55516947998730 T^{14} + 1388713372630216 T^{15} - 18907072654532418 T^{16} - 18593790015510792 T^{17} + 1618856102419363630 T^{18} - 9823293830280022314 T^{19} + 40864378761081474654 T^{20} + \)\(11\!\cdots\!64\)\( T^{21} - \)\(12\!\cdots\!32\)\( T^{22} - \)\(42\!\cdots\!18\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 26 T - 56 T^{2} + 2492 T^{3} + 90143 T^{4} - 817018 T^{5} - 11928114 T^{6} - 57652506 T^{7} + 2793757095 T^{8} + 11900406246 T^{9} - 106656506274 T^{10} - 4250712480600 T^{11} + 2907448664925 T^{12} + 284134319779998 T^{13} + 4080312688533132 T^{14} - 24204163500327996 T^{15} - 351229803717868731 T^{16} - 2347803859531815612 T^{17} + 38391662086408238988 T^{18} + \)\(25\!\cdots\!54\)\( T^{19} + \)\(25\!\cdots\!25\)\( T^{20} - \)\(36\!\cdots\!00\)\( T^{21} - \)\(88\!\cdots\!46\)\( T^{22} + \)\(96\!\cdots\!98\)\( T^{23} + \)\(21\!\cdots\!95\)\( T^{24} - \)\(43\!\cdots\!02\)\( T^{25} - \)\(87\!\cdots\!86\)\( T^{26} - \)\(58\!\cdots\!54\)\( T^{27} + \)\(62\!\cdots\!63\)\( T^{28} + \)\(16\!\cdots\!84\)\( T^{29} - \)\(36\!\cdots\!64\)\( T^{30} - \)\(16\!\cdots\!18\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))
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