Properties

Label 3021.2.a
Level 3021
Weight 2
Character orbit a
Rep. character \(\chi_{3021}(1,\cdot)\)
Character field \(\Q\)
Dimension 155
Newform subspaces 11
Sturm bound 720
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 3021 = 3 \cdot 19 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3021.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(720\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3021))\).

Total New Old
Modular forms 364 155 209
Cusp forms 357 155 202
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(19\)\(53\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(19\)
\(+\)\(+\)\(-\)\(-\)\(18\)
\(+\)\(-\)\(+\)\(-\)\(25\)
\(+\)\(-\)\(-\)\(+\)\(16\)
\(-\)\(+\)\(+\)\(-\)\(18\)
\(-\)\(+\)\(-\)\(+\)\(19\)
\(-\)\(-\)\(+\)\(+\)\(16\)
\(-\)\(-\)\(-\)\(-\)\(24\)
Plus space\(+\)\(70\)
Minus space\(-\)\(85\)

Trace form

\( 155q - 3q^{2} - q^{3} + 149q^{4} - 2q^{5} - 3q^{6} - 4q^{7} - 15q^{8} + 155q^{9} + O(q^{10}) \) \( 155q - 3q^{2} - q^{3} + 149q^{4} - 2q^{5} - 3q^{6} - 4q^{7} - 15q^{8} + 155q^{9} - 2q^{10} - 8q^{11} + 9q^{12} - 14q^{13} + 8q^{14} - 6q^{15} + 173q^{16} - 14q^{17} - 3q^{18} + 7q^{19} + 6q^{20} - 8q^{21} + 4q^{22} - 8q^{23} + 9q^{24} + 129q^{25} - 10q^{26} - q^{27} + 16q^{28} - 30q^{29} + 38q^{30} - 16q^{31} - 63q^{32} - 12q^{33} + 50q^{34} - 4q^{35} + 149q^{36} - 14q^{37} - 3q^{38} + 18q^{39} + 10q^{40} - 18q^{41} + 20q^{42} - 8q^{43} - 36q^{44} - 2q^{45} - 36q^{46} - 20q^{47} + 33q^{48} + 103q^{49} - 93q^{50} - 18q^{51} - 38q^{52} - q^{53} - 3q^{54} + 52q^{55} - 24q^{56} - q^{57} - 50q^{58} + 36q^{59} - 22q^{60} - 18q^{61} - 8q^{62} - 4q^{63} + 173q^{64} + 4q^{65} - 4q^{66} - 44q^{67} - 86q^{68} - 16q^{69} - 12q^{70} + 32q^{71} - 15q^{72} - 6q^{73} - 42q^{74} + 17q^{75} + 13q^{76} + 76q^{77} - 18q^{78} - 24q^{79} - 82q^{80} + 155q^{81} - 34q^{82} - 28q^{83} - 24q^{84} - 8q^{85} - 20q^{86} + 26q^{87} - 84q^{88} - 10q^{89} - 2q^{90} + 72q^{91} - 104q^{92} - 16q^{93} - 40q^{94} - 2q^{95} + 5q^{96} - 18q^{97} - 27q^{98} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3021))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 19 53
3021.2.a.a \(1\) \(24.123\) \(\Q\) None \(-2\) \(1\) \(1\) \(3\) \(-\) \(+\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
3021.2.a.b \(1\) \(24.123\) \(\Q\) None \(1\) \(1\) \(4\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}-q^{4}+4q^{5}+q^{6}-3q^{8}+\cdots\)
3021.2.a.c \(2\) \(24.123\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(2\) \(6\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
3021.2.a.d \(14\) \(24.123\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(3\) \(14\) \(3\) \(-4\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
3021.2.a.e \(16\) \(24.123\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-7\) \(16\) \(-13\) \(-8\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
3021.2.a.f \(16\) \(24.123\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(3\) \(-16\) \(-5\) \(-8\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots\)
3021.2.a.g \(18\) \(24.123\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-18\) \(2\) \(5\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
3021.2.a.h \(19\) \(24.123\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(-6\) \(19\) \(-14\) \(-7\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{9}+\cdots)q^{5}+\cdots\)
3021.2.a.i \(19\) \(24.123\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(2\) \(-19\) \(2\) \(-7\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
3021.2.a.j \(24\) \(24.123\) None \(6\) \(24\) \(13\) \(4\) \(-\) \(-\) \(-\)
3021.2.a.k \(25\) \(24.123\) None \(-5\) \(-25\) \(3\) \(12\) \(+\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3021))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3021)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(159))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1007))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - 2 T + 3 T^{2} - 4 T^{3} + 4 T^{4} \))(\( 1 - 3 T + 10 T^{2} - 22 T^{3} + 47 T^{4} - 81 T^{5} + 138 T^{6} - 202 T^{7} + 300 T^{8} - 392 T^{9} + 547 T^{10} - 687 T^{11} + 980 T^{12} - 1245 T^{13} + 1907 T^{14} - 2490 T^{15} + 3920 T^{16} - 5496 T^{17} + 8752 T^{18} - 12544 T^{19} + 19200 T^{20} - 25856 T^{21} + 35328 T^{22} - 41472 T^{23} + 48128 T^{24} - 45056 T^{25} + 40960 T^{26} - 24576 T^{27} + 16384 T^{28} \))(\( 1 + 7 T + 34 T^{2} + 124 T^{3} + 383 T^{4} + 1031 T^{5} + 2512 T^{6} + 5616 T^{7} + 11722 T^{8} + 22994 T^{9} + 42781 T^{10} + 75729 T^{11} + 128228 T^{12} + 207969 T^{13} + 324113 T^{14} + 485438 T^{15} + 699960 T^{16} + 970876 T^{17} + 1296452 T^{18} + 1663752 T^{19} + 2051648 T^{20} + 2423328 T^{21} + 2737984 T^{22} + 2943232 T^{23} + 3000832 T^{24} + 2875392 T^{25} + 2572288 T^{26} + 2111488 T^{27} + 1568768 T^{28} + 1015808 T^{29} + 557056 T^{30} + 229376 T^{31} + 65536 T^{32} \))(\( 1 - 3 T + 16 T^{2} - 40 T^{3} + 129 T^{4} - 283 T^{5} + 706 T^{6} - 1398 T^{7} + 2952 T^{8} - 5372 T^{9} + 10047 T^{10} - 16989 T^{11} + 28854 T^{12} - 45573 T^{13} + 71285 T^{14} - 105250 T^{15} + 152848 T^{16} - 210500 T^{17} + 285140 T^{18} - 364584 T^{19} + 461664 T^{20} - 543648 T^{21} + 643008 T^{22} - 687616 T^{23} + 755712 T^{24} - 715776 T^{25} + 722944 T^{26} - 579584 T^{27} + 528384 T^{28} - 327680 T^{29} + 262144 T^{30} - 98304 T^{31} + 65536 T^{32} \))(\( 1 + 10 T^{2} + 2 T^{3} + 54 T^{4} + 16 T^{5} + 208 T^{6} + 66 T^{7} + 627 T^{8} + 192 T^{9} + 1571 T^{10} + 452 T^{11} + 3454 T^{12} + 967 T^{13} + 7049 T^{14} + 2042 T^{15} + 14024 T^{16} + 4253 T^{17} + 27930 T^{18} + 8506 T^{19} + 56096 T^{20} + 16336 T^{21} + 112784 T^{22} + 30944 T^{23} + 221056 T^{24} + 57856 T^{25} + 402176 T^{26} + 98304 T^{27} + 642048 T^{28} + 135168 T^{29} + 851968 T^{30} + 131072 T^{31} + 884736 T^{32} + 65536 T^{33} + 655360 T^{34} + 262144 T^{36} \))(\( 1 + 6 T + 28 T^{2} + 98 T^{3} + 299 T^{4} + 799 T^{5} + 1950 T^{6} + 4376 T^{7} + 9180 T^{8} + 18103 T^{9} + 33845 T^{10} + 60284 T^{11} + 102888 T^{12} + 169015 T^{13} + 268566 T^{14} + 414439 T^{15} + 624080 T^{16} + 919822 T^{17} + 1332175 T^{18} + 1897910 T^{19} + 2664350 T^{20} + 3679288 T^{21} + 4992640 T^{22} + 6631024 T^{23} + 8594112 T^{24} + 10816960 T^{25} + 13169664 T^{26} + 15432704 T^{27} + 17328640 T^{28} + 18537472 T^{29} + 18800640 T^{30} + 17924096 T^{31} + 15974400 T^{32} + 13090816 T^{33} + 9797632 T^{34} + 6422528 T^{35} + 3670016 T^{36} + 1572864 T^{37} + 524288 T^{38} \))(\( 1 - 2 T + 14 T^{2} - 24 T^{3} + 99 T^{4} - 151 T^{5} + 484 T^{6} - 682 T^{7} + 1888 T^{8} - 2531 T^{9} + 6323 T^{10} - 8160 T^{11} + 18756 T^{12} - 23305 T^{13} + 49890 T^{14} - 59521 T^{15} + 119958 T^{16} - 137170 T^{17} + 262519 T^{18} - 287330 T^{19} + 525038 T^{20} - 548680 T^{21} + 959664 T^{22} - 952336 T^{23} + 1596480 T^{24} - 1491520 T^{25} + 2400768 T^{26} - 2088960 T^{27} + 3237376 T^{28} - 2591744 T^{29} + 3866624 T^{30} - 2793472 T^{31} + 3964928 T^{32} - 2473984 T^{33} + 3244032 T^{34} - 1572864 T^{35} + 1835008 T^{36} - 524288 T^{37} + 524288 T^{38} \))
$3$ (\( 1 - T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{14} \))(\( ( 1 - T )^{16} \))(\( ( 1 + T )^{16} \))(\( ( 1 + T )^{18} \))(\( ( 1 - T )^{19} \))(\( ( 1 + T )^{19} \))
$5$ (\( 1 - T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( ( 1 - T + 5 T^{2} )^{2} \))(\( 1 - 3 T + 31 T^{2} - 93 T^{3} + 567 T^{4} - 1597 T^{5} + 7332 T^{6} - 19141 T^{7} + 73016 T^{8} - 176232 T^{9} + 583702 T^{10} - 1299517 T^{11} + 3836923 T^{12} - 7852619 T^{13} + 20993350 T^{14} - 39263095 T^{15} + 95923075 T^{16} - 162439625 T^{17} + 364813750 T^{18} - 550725000 T^{19} + 1140875000 T^{20} - 1495390625 T^{21} + 2864062500 T^{22} - 3119140625 T^{23} + 5537109375 T^{24} - 4541015625 T^{25} + 7568359375 T^{26} - 3662109375 T^{27} + 6103515625 T^{28} \))(\( 1 + 13 T + 119 T^{2} + 801 T^{3} + 4549 T^{4} + 22139 T^{5} + 96562 T^{6} + 380487 T^{7} + 1383583 T^{8} + 4662291 T^{9} + 14733235 T^{10} + 43740658 T^{11} + 122894353 T^{12} + 326870281 T^{13} + 826938287 T^{14} + 1988293377 T^{15} + 4557663681 T^{16} + 9941466885 T^{17} + 20673457175 T^{18} + 40858785125 T^{19} + 76808970625 T^{20} + 136689556250 T^{21} + 230206796875 T^{22} + 364241484375 T^{23} + 540462109375 T^{24} + 743138671875 T^{25} + 942988281250 T^{26} + 1081005859375 T^{27} + 1110595703125 T^{28} + 977783203125 T^{29} + 726318359375 T^{30} + 396728515625 T^{31} + 152587890625 T^{32} \))(\( 1 + 5 T + 53 T^{2} + 213 T^{3} + 1293 T^{4} + 4363 T^{5} + 19782 T^{6} + 57937 T^{7} + 217929 T^{8} + 569187 T^{9} + 1880175 T^{10} + 4475978 T^{11} + 13432353 T^{12} + 29604827 T^{13} + 82256737 T^{14} + 169290069 T^{15} + 439313471 T^{16} + 846450345 T^{17} + 2056418425 T^{18} + 3700603375 T^{19} + 8395220625 T^{20} + 13987431250 T^{21} + 29377734375 T^{22} + 44467734375 T^{23} + 85128515625 T^{24} + 113158203125 T^{25} + 193183593750 T^{26} + 213037109375 T^{27} + 315673828125 T^{28} + 260009765625 T^{29} + 323486328125 T^{30} + 152587890625 T^{31} + 152587890625 T^{32} \))(\( 1 - 2 T + 45 T^{2} - 87 T^{3} + 1015 T^{4} - 1909 T^{5} + 15331 T^{6} - 28146 T^{7} + 174972 T^{8} - 313694 T^{9} + 1615655 T^{10} - 2820982 T^{11} + 12606498 T^{12} - 21312439 T^{13} + 85415871 T^{14} - 138701453 T^{15} + 510226470 T^{16} - 788724186 T^{17} + 2705351712 T^{18} - 3943620930 T^{19} + 12755661750 T^{20} - 17337681625 T^{21} + 53384919375 T^{22} - 66601371875 T^{23} + 196976531250 T^{24} - 220389218750 T^{25} + 631115234375 T^{26} - 612683593750 T^{27} + 1708710937500 T^{28} - 1374316406250 T^{29} + 3742919921875 T^{30} - 2330322265625 T^{31} + 6195068359375 T^{32} - 2655029296875 T^{33} + 6866455078125 T^{34} - 1525878906250 T^{35} + 3814697265625 T^{36} \))(\( 1 + 14 T + 135 T^{2} + 975 T^{3} + 5885 T^{4} + 30591 T^{5} + 141377 T^{6} + 589552 T^{7} + 2250725 T^{8} + 7934862 T^{9} + 26053625 T^{10} + 80158715 T^{11} + 232559538 T^{12} + 639677273 T^{13} + 1678190641 T^{14} + 4223589102 T^{15} + 10262392024 T^{16} + 24214989608 T^{17} + 55788568631 T^{18} + 125933565031 T^{19} + 278942843155 T^{20} + 605374740200 T^{21} + 1282799003000 T^{22} + 2639743188750 T^{23} + 5244345753125 T^{24} + 9994957390625 T^{25} + 18168713906250 T^{26} + 31311998046875 T^{27} + 50885986328125 T^{28} + 77488886718750 T^{29} + 109898681640625 T^{30} + 143933593750000 T^{31} + 172579345703125 T^{32} + 186712646484375 T^{33} + 179595947265625 T^{34} + 148773193359375 T^{35} + 102996826171875 T^{36} + 53405761718750 T^{37} + 19073486328125 T^{38} \))(\( 1 - 2 T + 45 T^{2} - 75 T^{3} + 995 T^{4} - 1361 T^{5} + 14501 T^{6} - 15854 T^{7} + 158419 T^{8} - 133924 T^{9} + 1403725 T^{10} - 888653 T^{11} + 10644328 T^{12} - 4962941 T^{13} + 71473465 T^{14} - 24964380 T^{15} + 432640664 T^{16} - 120779816 T^{17} + 2377730393 T^{18} - 592961787 T^{19} + 11888651965 T^{20} - 3019495400 T^{21} + 54080083000 T^{22} - 15602737500 T^{23} + 223354578125 T^{24} - 77545953125 T^{25} + 831588125000 T^{26} - 347130078125 T^{27} + 2741650390625 T^{28} - 1307851562500 T^{29} + 7735302734375 T^{30} - 3870605468750 T^{31} + 17701416015625 T^{32} - 8306884765625 T^{33} + 30364990234375 T^{34} - 11444091796875 T^{35} + 34332275390625 T^{36} - 7629394531250 T^{37} + 19073486328125 T^{38} \))
$7$ (\( 1 - 3 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( ( 1 - 3 T + 7 T^{2} )^{2} \))(\( 1 + 4 T + 51 T^{2} + 148 T^{3} + 1239 T^{4} + 2834 T^{5} + 19847 T^{6} + 35569 T^{7} + 235638 T^{8} + 325450 T^{9} + 2247162 T^{10} + 2365773 T^{11} + 18289129 T^{12} + 15624462 T^{13} + 133788090 T^{14} + 109371234 T^{15} + 896167321 T^{16} + 811460139 T^{17} + 5395435962 T^{18} + 5469838150 T^{19} + 27722575062 T^{20} + 29292600967 T^{21} + 114414005447 T^{22} + 114362122238 T^{23} + 349986833511 T^{24} + 292644357964 T^{25} + 705905647251 T^{26} + 387556041628 T^{27} + 678223072849 T^{28} \))(\( 1 + 8 T + 87 T^{2} + 512 T^{3} + 3273 T^{4} + 15478 T^{5} + 74699 T^{6} + 300105 T^{7} + 1208153 T^{8} + 4291578 T^{9} + 15223879 T^{10} + 49143071 T^{11} + 158393421 T^{12} + 471413830 T^{13} + 1399332196 T^{14} + 3856028723 T^{15} + 10582693957 T^{16} + 26992201061 T^{17} + 68567277604 T^{18} + 161694943690 T^{19} + 380302603821 T^{20} + 825947594297 T^{21} + 1791074140471 T^{22} + 3534299020854 T^{23} + 6964761622553 T^{24} + 12110319228735 T^{25} + 21100618625051 T^{26} + 30605063328154 T^{27} + 45302533008873 T^{28} + 49607173328384 T^{29} + 59005407337863 T^{30} + 37980492079544 T^{31} + 33232930569601 T^{32} \))(\( 1 + 8 T + 95 T^{2} + 572 T^{3} + 4041 T^{4} + 19958 T^{5} + 106835 T^{6} + 453105 T^{7} + 2008489 T^{8} + 7515950 T^{9} + 28830023 T^{10} + 96777931 T^{11} + 329297793 T^{12} + 1001244834 T^{13} + 3066228260 T^{14} + 8483966423 T^{15} + 23573894689 T^{16} + 59387764961 T^{17} + 150245184740 T^{18} + 343426978062 T^{19} + 790644000993 T^{20} + 1626546686317 T^{21} + 3391823375927 T^{22} + 6189708010850 T^{23} + 11578539395689 T^{24} + 18284421099735 T^{25} + 30178243226915 T^{26} + 39463487136794 T^{27} + 55932641579241 T^{28} + 55420513952804 T^{29} + 64431191920655 T^{30} + 37980492079544 T^{31} + 33232930569601 T^{32} \))(\( 1 - 5 T + 70 T^{2} - 303 T^{3} + 2428 T^{4} - 9325 T^{5} + 55573 T^{6} - 193139 T^{7} + 947872 T^{8} - 3026106 T^{9} + 12906298 T^{10} - 38285614 T^{11} + 146575232 T^{12} - 407122584 T^{13} + 1427727285 T^{14} - 3727417129 T^{15} + 12122540611 T^{16} - 29761399241 T^{17} + 90431136428 T^{18} - 208329794687 T^{19} + 594004489939 T^{20} - 1278504075247 T^{21} + 3427973211285 T^{22} - 6842509269288 T^{23} + 17244429469568 T^{24} - 31529849410402 T^{25} + 74402239616698 T^{26} - 122114292264342 T^{27} + 267750379220128 T^{28} - 381898909816277 T^{29} + 769201853621173 T^{30} - 903490022045275 T^{31} + 1646725620877372 T^{32} - 1438511137512729 T^{33} + 2326305139872070 T^{34} - 1163152569936035 T^{35} + 1628413597910449 T^{36} \))(\( 1 + 7 T + 78 T^{2} + 429 T^{3} + 2858 T^{4} + 13277 T^{5} + 68133 T^{6} + 278267 T^{7} + 1207471 T^{8} + 4442709 T^{9} + 17061489 T^{10} + 57512460 T^{11} + 200685310 T^{12} + 627611536 T^{13} + 2024122490 T^{14} + 5927112893 T^{15} + 17872403623 T^{16} + 49306099137 T^{17} + 140031384147 T^{18} + 365143880517 T^{19} + 980219689029 T^{20} + 2415998857713 T^{21} + 6130234442689 T^{22} + 14230998056093 T^{23} + 34019426689430 T^{24} + 73837869598864 T^{25} + 165272982253330 T^{26} + 331547886920460 T^{27} + 688492621940823 T^{28} + 1254955331009541 T^{29} + 2387564699696953 T^{30} + 3851573465560667 T^{31} + 6601338946060131 T^{32} + 9004767738216173 T^{33} + 13568530795417094 T^{34} + 14256927214358829 T^{35} + 18145180091002146 T^{36} + 11398895185373143 T^{37} + 11398895185373143 T^{38} \))(\( 1 + 7 T + 94 T^{2} + 529 T^{3} + 4110 T^{4} + 19593 T^{5} + 113989 T^{6} + 476179 T^{7} + 2287871 T^{8} + 8571941 T^{9} + 35770785 T^{10} + 122192744 T^{11} + 456370198 T^{12} + 1437907760 T^{13} + 4899345110 T^{14} + 14349060865 T^{15} + 45156666743 T^{16} + 123495951305 T^{17} + 361686127635 T^{18} + 925200925593 T^{19} + 2531802893445 T^{20} + 6051301613945 T^{21} + 15488736692849 T^{22} + 34452095136865 T^{23} + 82343293263770 T^{24} + 169168410056240 T^{25} + 375840481971514 T^{26} + 704416852803944 T^{27} + 1443480199971495 T^{28} + 2421361168388309 T^{29} + 4523868512834153 T^{30} + 6590930298084979 T^{31} + 11044281407283523 T^{32} + 13288424666330457 T^{33} + 19512477805865730 T^{34} + 17580220271318929 T^{35} + 21867268314797458 T^{36} + 11398895185373143 T^{37} + 11398895185373143 T^{38} \))
$11$ (\( 1 - 5 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( 1 - 15 T + 188 T^{2} - 1587 T^{3} + 11878 T^{4} - 72354 T^{5} + 406114 T^{6} - 1993262 T^{7} + 9303093 T^{8} - 39585210 T^{9} + 163863554 T^{10} - 631582747 T^{11} + 2383281425 T^{12} - 8396426431 T^{13} + 28849006572 T^{14} - 92360690741 T^{15} + 288377052425 T^{16} - 840636636257 T^{17} + 2399126294114 T^{18} - 6375237655710 T^{19} + 16480996738173 T^{20} - 38843037441802 T^{21} + 87054142598434 T^{22} - 170606947234614 T^{23} + 308084729410678 T^{24} - 452789621259657 T^{25} + 590024534823548 T^{26} - 517840682158965 T^{27} + 379749833583241 T^{28} \))(\( 1 + 27 T + 445 T^{2} + 5366 T^{3} + 52395 T^{4} + 433202 T^{5} + 3132966 T^{6} + 20216115 T^{7} + 118227223 T^{8} + 633528776 T^{9} + 3138600045 T^{10} + 14470808233 T^{11} + 62430383096 T^{12} + 253026997700 T^{13} + 966418404545 T^{14} + 3485537584639 T^{15} + 11886483560996 T^{16} + 38340913431029 T^{17} + 116936626949945 T^{18} + 336778933938700 T^{19} + 914043238908536 T^{20} + 2330538136732883 T^{21} + 5560221434320245 T^{22} + 12345683591332696 T^{23} + 25343055226017463 T^{24} + 47668541685240465 T^{25} + 81261069402496566 T^{26} + 123597586332026422 T^{27} + 164437954798296795 T^{28} + 185248873364333746 T^{29} + 168988675944542245 T^{30} + 112785700574222577 T^{31} + 45949729863572161 T^{32} \))(\( 1 + 15 T + 209 T^{2} + 2016 T^{3} + 17625 T^{4} + 129990 T^{5} + 879302 T^{6} + 5338755 T^{7} + 30080231 T^{8} + 156297510 T^{9} + 760112309 T^{10} + 3456530007 T^{11} + 14796135512 T^{12} + 59668440226 T^{13} + 227302482439 T^{14} + 818839932659 T^{15} + 2791093473596 T^{16} + 9007239259249 T^{17} + 27503600375119 T^{18} + 79418693940806 T^{19} + 216630220031192 T^{20} + 556677614157357 T^{21} + 1346585322244349 T^{22} + 3045796304244210 T^{23} + 6447964657381511 T^{24} + 12588505025064705 T^{25} + 22806829326508502 T^{26} + 37087664062723890 T^{27} + 55314800139707625 T^{28} + 69597787682164896 T^{29} + 79367715218897369 T^{30} + 62658722541234765 T^{31} + 45949729863572161 T^{32} \))(\( 1 - 6 T + 111 T^{2} - 630 T^{3} + 6082 T^{4} - 32249 T^{5} + 220364 T^{6} - 1079363 T^{7} + 5958924 T^{8} - 26775430 T^{9} + 128370127 T^{10} - 529411569 T^{11} + 2292689808 T^{12} - 8746815667 T^{13} + 34891815734 T^{14} - 124459881709 T^{15} + 461908589593 T^{16} - 1551451523507 T^{17} + 5395150563760 T^{18} - 17065966758577 T^{19} + 55890939340753 T^{20} - 165656102554679 T^{21} + 510851074161494 T^{22} - 1408683409986017 T^{23} + 4061639848950288 T^{24} - 10316733774481299 T^{25} + 27517276777547887 T^{26} - 63135063344032130 T^{27} + 154559141953089324 T^{28} - 307954860725700793 T^{29} + 691596630807746444 T^{30} - 1113322943929630819 T^{31} + 2309638487853271762 T^{32} - 2631666346731860130 T^{33} + 5100420014856509871 T^{34} - 3032682170995762626 T^{35} + 5559917313492231481 T^{36} \))(\( 1 + 22 T + 330 T^{2} + 3666 T^{3} + 34109 T^{4} + 273035 T^{5} + 1952404 T^{6} + 12638438 T^{7} + 75332328 T^{8} + 416644837 T^{9} + 2158409637 T^{10} + 10524300313 T^{11} + 48582916141 T^{12} + 213004911890 T^{13} + 890394164740 T^{14} + 3555884879836 T^{15} + 13601365511475 T^{16} + 49885091492992 T^{17} + 175696427716423 T^{18} + 594390457629446 T^{19} + 1932660704880653 T^{20} + 6036096070652032 T^{21} + 18103417495773225 T^{22} + 52061710525678876 T^{23} + 143398870625541740 T^{24} + 377351194712760290 T^{25} + 946743594518327111 T^{26} + 2255977238402629753 T^{27} + 5089417019796298167 T^{28} + 10806694045083435037 T^{29} + 21493192352695812408 T^{30} + 39664832456629001798 T^{31} + 67402281280659460124 T^{32} + \)\(10\!\cdots\!35\)\( T^{33} + \)\(14\!\cdots\!59\)\( T^{34} + \)\(16\!\cdots\!26\)\( T^{35} + \)\(16\!\cdots\!30\)\( T^{36} + \)\(12\!\cdots\!82\)\( T^{37} + 61159090448414546291 T^{38} \))(\( 1 + 10 T + 146 T^{2} + 1140 T^{3} + 9909 T^{4} + 65009 T^{5} + 432822 T^{6} + 2482702 T^{7} + 13904658 T^{8} + 71351553 T^{9} + 351992147 T^{10} + 1638529487 T^{11} + 7303362819 T^{12} + 31124006144 T^{13} + 127202149730 T^{14} + 499481226648 T^{15} + 1887396969337 T^{16} + 6859995600124 T^{17} + 24064731951063 T^{18} + 81196194416974 T^{19} + 264712051461693 T^{20} + 830059467615004 T^{21} + 2512125366187547 T^{22} + 7312904639353368 T^{23} + 20486033416166230 T^{24} + 55138075448470784 T^{25} + 142321880128895049 T^{26} + 351233347318824047 T^{27} + 829979070268782577 T^{28} + 1850675526101755353 T^{29} + 3967161203254606038 T^{30} + 7791782407741980142 T^{31} + 14942189315560503282 T^{32} + 24687156931412914169 T^{33} + 41392352110739685759 T^{34} + 52382692044472263540 T^{35} + 73795266160896890566 T^{36} + 55599173134922314810 T^{37} + 61159090448414546291 T^{38} \))
$13$ (\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( 1 + 100 T^{2} - 63 T^{3} + 4917 T^{4} - 6150 T^{5} + 159627 T^{6} - 290658 T^{7} + 3889567 T^{8} - 8809633 T^{9} + 76439714 T^{10} - 191941014 T^{11} + 1259675648 T^{12} - 3187426690 T^{13} + 17699033276 T^{14} - 41436546970 T^{15} + 212885184512 T^{16} - 421694407758 T^{17} + 2183194671554 T^{18} - 3270955065469 T^{19} + 18774197001703 T^{20} - 18238358454186 T^{21} + 130212647801067 T^{22} - 65217671143950 T^{23} + 677850204421533 T^{24} - 112906104824331 T^{25} + 2329808512248100 T^{26} + 3937376385699289 T^{28} \))(\( 1 + 108 T^{2} - 87 T^{3} + 5736 T^{4} - 8470 T^{5} + 206085 T^{6} - 395245 T^{7} + 5725974 T^{8} - 12054593 T^{9} + 130339181 T^{10} - 276478822 T^{11} + 2486138623 T^{12} - 5133383407 T^{13} + 40307154056 T^{14} - 79501603248 T^{15} + 562887320192 T^{16} - 1033520842224 T^{17} + 6811909035464 T^{18} - 11278043345179 T^{19} + 71006605211503 T^{20} - 102654651256846 T^{21} + 629122331903429 T^{22} - 756407833788581 T^{23} + 4670852899447254 T^{24} - 4191375354681385 T^{25} + 28410567292701165 T^{26} - 15179598537493390 T^{27} + 133637816262551016 T^{28} - 26350134273526011 T^{29} + 425236649655523212 T^{30} + 665416609183179841 T^{32} \))(\( 1 + 8 T + 120 T^{2} + 801 T^{3} + 6724 T^{4} + 37158 T^{5} + 226065 T^{6} + 1023007 T^{7} + 4849172 T^{8} + 17180299 T^{9} + 61860181 T^{10} + 135028630 T^{11} + 218214101 T^{12} - 1151890365 T^{13} - 8192533780 T^{14} - 48741621050 T^{15} - 175552315792 T^{16} - 633641073650 T^{17} - 1384538208820 T^{18} - 2530703131905 T^{19} + 6232412938661 T^{20} + 50135185118590 T^{21} + 298587278392429 T^{22} + 1078038283866583 T^{23} + 3955618571813012 T^{24} + 10848477090074611 T^{25} + 31164979959844185 T^{26} + 66593095921626846 T^{27} + 156656324363562244 T^{28} + 242602960380394653 T^{29} + 472485166283914680 T^{30} + 409487144112726056 T^{31} + 665416609183179841 T^{32} \))(\( 1 + 124 T^{2} + 33 T^{3} + 7575 T^{4} + 4510 T^{5} + 305315 T^{6} + 300632 T^{7} + 9160052 T^{8} + 13006979 T^{9} + 218821252 T^{10} + 409457543 T^{11} + 4354128659 T^{12} + 9953332912 T^{13} + 74659809035 T^{14} + 193314670278 T^{15} + 1132495066209 T^{16} + 3058234966673 T^{17} + 15466669843748 T^{18} + 39757054566749 T^{19} + 191391666189321 T^{20} + 424712330600766 T^{21} + 2132358805848635 T^{22} + 3695602836895216 T^{23} + 21016547398419131 T^{24} + 25692853597713731 T^{25} + 178499217664082692 T^{26} + 137932500650124167 T^{27} + 1262790953978416148 T^{28} + 538780763580131384 T^{29} + 7113254859170286515 T^{30} + 1365966730731061030 T^{31} + 29825626121672114175 T^{32} + 1689134469464994981 T^{33} + 82511659538714300284 T^{34} + \)\(11\!\cdots\!29\)\( T^{36} \))(\( 1 + 6 T + 114 T^{2} + 655 T^{3} + 6637 T^{4} + 35288 T^{5} + 256505 T^{6} + 1250888 T^{7} + 7290571 T^{8} + 32590545 T^{9} + 161321133 T^{10} + 661733326 T^{11} + 2889751842 T^{12} + 10923226923 T^{13} + 43515495961 T^{14} + 153500937686 T^{15} + 580359983049 T^{16} + 1966418275670 T^{17} + 7386002744699 T^{18} + 25053564381578 T^{19} + 96018035681087 T^{20} + 332324688588230 T^{21} + 1275050882758653 T^{22} + 4384140281249846 T^{23} + 16156999041847573 T^{24} + 52724330020978707 T^{25} + 181327642583518314 T^{26} + 539796203127708046 T^{27} + 1710729853750149609 T^{28} + 4492883382236967705 T^{29} + 13065872596114725127 T^{30} + 29143295102690013128 T^{31} + 77688979216445855765 T^{32} + \)\(13\!\cdots\!32\)\( T^{33} + \)\(33\!\cdots\!09\)\( T^{34} + \)\(43\!\cdots\!55\)\( T^{35} + \)\(98\!\cdots\!62\)\( T^{36} + \)\(67\!\cdots\!74\)\( T^{37} + \)\(14\!\cdots\!77\)\( T^{38} \))(\( 1 + 14 T + 254 T^{2} + 2527 T^{3} + 27473 T^{4} + 217760 T^{5} + 1795701 T^{6} + 12001548 T^{7} + 81864613 T^{8} + 476856097 T^{9} + 2810928421 T^{10} + 14574574886 T^{11} + 76176989766 T^{12} + 356579260753 T^{13} + 1679673313121 T^{14} + 7165577304056 T^{15} + 30741387649349 T^{16} + 120230385507610 T^{17} + 472782954147217 T^{18} + 1700056042572866 T^{19} + 6146178403913821 T^{20} + 20318935150786090 T^{21} + 67538828665619753 T^{22} + 204656053381143416 T^{23} + 623650943448635453 T^{24} + 1721139985015927177 T^{25} + 4779993137340677022 T^{26} + 11888928480025272806 T^{27} + 29808488678042380033 T^{28} + 65738662361420453353 T^{29} + \)\(14\!\cdots\!81\)\( T^{30} + \)\(27\!\cdots\!88\)\( T^{31} + \)\(54\!\cdots\!53\)\( T^{32} + \)\(85\!\cdots\!40\)\( T^{33} + \)\(14\!\cdots\!61\)\( T^{34} + \)\(16\!\cdots\!07\)\( T^{35} + \)\(21\!\cdots\!82\)\( T^{36} + \)\(15\!\cdots\!06\)\( T^{37} + \)\(14\!\cdots\!77\)\( T^{38} \))
$17$ (\( 1 + 5 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( 1 - 16 T + 281 T^{2} - 3129 T^{3} + 33211 T^{4} - 287532 T^{5} + 2312893 T^{6} - 16463319 T^{7} + 108606638 T^{8} - 656000797 T^{9} + 3681765194 T^{10} - 19222582465 T^{11} + 93521153351 T^{12} - 426335359962 T^{13} + 1814042590046 T^{14} - 7247701119354 T^{15} + 27027613318439 T^{16} - 94440547650545 T^{17} + 307504710768074 T^{18} - 931427323626029 T^{19} + 2621500218583022 T^{20} - 6755536471635687 T^{21} + 16134180554986813 T^{22} - 34097809304935404 T^{23} + 66953173427811739 T^{24} - 107236763546583657 T^{25} + 163716848661562841 T^{26} - 158473248526494992 T^{27} + 168377826559400929 T^{28} \))(\( 1 + 28 T + 530 T^{2} + 7477 T^{3} + 87779 T^{4} + 884533 T^{5} + 7899811 T^{6} + 63466792 T^{7} + 465173210 T^{8} + 3136066378 T^{9} + 19592096137 T^{10} + 113967842235 T^{11} + 619889294537 T^{12} + 3161305683930 T^{13} + 15150961320227 T^{14} + 68329410425895 T^{15} + 290261813994020 T^{16} + 1161599977240215 T^{17} + 4378627821545603 T^{18} + 15531494825148090 T^{19} + 51773773769024777 T^{20} + 161818038572260395 T^{21} + 472905572361470953 T^{22} + 1286849315988436394 T^{23} + 3244935481011355610 T^{24} + 7526392091356787624 T^{25} + 15925970790699915139 T^{26} + 30314623256679540389 T^{27} + 51141997361791190819 T^{28} + 74056529952037690949 T^{29} + 89240248076482492370 T^{30} + 80147845442274842204 T^{31} + 48661191875666868481 T^{32} \))(\( 1 - 6 T + 184 T^{2} - 919 T^{3} + 16151 T^{4} - 69901 T^{5} + 919717 T^{6} - 3540016 T^{7} + 38485332 T^{8} - 133844852 T^{9} + 1261255131 T^{10} - 4001270691 T^{11} + 33570191697 T^{12} - 97668403914 T^{13} + 741281010655 T^{14} - 1981613564705 T^{15} + 13733502993728 T^{16} - 33687430599985 T^{17} + 214230212079295 T^{18} - 479844868429482 T^{19} + 2803815980725137 T^{20} - 5681232199511187 T^{21} + 30443632751116539 T^{22} - 54921718957561396 T^{23} + 268464341068355412 T^{24} - 419802980205403952 T^{25} + 1854143862139252933 T^{26} - 2395639823799854333 T^{27} + 9409931753497869911 T^{28} - 9102307212240556103 T^{29} + 30981520086929770936 T^{30} - 17174538309058894758 T^{31} + 48661191875666868481 T^{32} \))(\( 1 + 17 T + 295 T^{2} + 3347 T^{3} + 35366 T^{4} + 305715 T^{5} + 2441342 T^{6} + 17089627 T^{7} + 110909755 T^{8} + 648551686 T^{9} + 3530018870 T^{10} + 17512080144 T^{11} + 81134189491 T^{12} + 344561679822 T^{13} + 1378539670408 T^{14} + 5133230998194 T^{15} + 18758184967483 T^{16} + 68220280474264 T^{17} + 270786907865114 T^{18} + 1159744768062488 T^{19} + 5421115455602587 T^{20} + 25219563894127122 T^{21} + 115137011812146568 T^{22} + 489228313027025454 T^{23} + 1958382097098087379 T^{24} + 7185883727758608912 T^{25} + 24624555399272911670 T^{26} + 76910367241289123942 T^{27} + \)\(22\!\cdots\!95\)\( T^{28} + \)\(58\!\cdots\!91\)\( T^{29} + \)\(14\!\cdots\!62\)\( T^{30} + \)\(30\!\cdots\!55\)\( T^{31} + \)\(59\!\cdots\!14\)\( T^{32} + \)\(95\!\cdots\!71\)\( T^{33} + \)\(14\!\cdots\!95\)\( T^{34} + \)\(14\!\cdots\!09\)\( T^{35} + \)\(14\!\cdots\!09\)\( T^{36} \))(\( 1 + 19 T + 308 T^{2} + 3438 T^{3} + 34121 T^{4} + 280888 T^{5} + 2118052 T^{6} + 14130020 T^{7} + 88229949 T^{8} + 504285811 T^{9} + 2746395667 T^{10} + 14011303470 T^{11} + 69202447723 T^{12} + 325864886190 T^{13} + 1505323513891 T^{14} + 6712176991882 T^{15} + 29610735110535 T^{16} + 126880295229828 T^{17} + 539599402877577 T^{18} + 2232722230583820 T^{19} + 9173189848918809 T^{20} + 36668405321420292 T^{21} + 145477541598058455 T^{22} + 560607734538976522 T^{23} + 2137344128462733587 T^{24} + 7865586175088272110 T^{25} + 28396440567007691579 T^{26} + 97739454438961620270 T^{27} + \)\(32\!\cdots\!99\)\( T^{28} + \)\(10\!\cdots\!39\)\( T^{29} + \)\(30\!\cdots\!17\)\( T^{30} + \)\(82\!\cdots\!20\)\( T^{31} + \)\(20\!\cdots\!24\)\( T^{32} + \)\(47\!\cdots\!52\)\( T^{33} + \)\(97\!\cdots\!53\)\( T^{34} + \)\(16\!\cdots\!78\)\( T^{35} + \)\(25\!\cdots\!16\)\( T^{36} + \)\(26\!\cdots\!71\)\( T^{37} + \)\(23\!\cdots\!53\)\( T^{38} \))(\( 1 - 11 T + 200 T^{2} - 1840 T^{3} + 19535 T^{4} - 153690 T^{5} + 1244598 T^{6} - 8568612 T^{7} + 58396117 T^{8} - 359332833 T^{9} + 2160980571 T^{10} - 12091362948 T^{11} + 65878821433 T^{12} - 339435702584 T^{13} + 1701994566529 T^{14} - 8143553639838 T^{15} + 37929955068375 T^{16} - 169387080059506 T^{17} + 736588826262913 T^{18} - 3077535580932724 T^{19} + 12522010046469521 T^{20} - 48952866137197234 T^{21} + 186349869250926375 T^{22} - 680157743552909598 T^{23} + 2416588899248166353 T^{24} - 8193152692184778296 T^{25} + 27032628165621178409 T^{26} - 84346415056342696068 T^{27} + \)\(25\!\cdots\!87\)\( T^{28} - \)\(72\!\cdots\!17\)\( T^{29} + \)\(20\!\cdots\!61\)\( T^{30} - \)\(49\!\cdots\!32\)\( T^{31} + \)\(12\!\cdots\!26\)\( T^{32} - \)\(25\!\cdots\!10\)\( T^{33} + \)\(55\!\cdots\!55\)\( T^{34} - \)\(89\!\cdots\!40\)\( T^{35} + \)\(16\!\cdots\!00\)\( T^{36} - \)\(15\!\cdots\!99\)\( T^{37} + \)\(23\!\cdots\!53\)\( T^{38} \))
$19$ (\( 1 + T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{14} \))(\( ( 1 - T )^{16} \))(\( ( 1 - T )^{16} \))(\( ( 1 + T )^{18} \))(\( ( 1 + T )^{19} \))(\( ( 1 + T )^{19} \))
$23$ (\( 1 - 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 2 T + 15 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 - T + 221 T^{2} - 13 T^{3} + 23318 T^{4} + 17250 T^{5} + 1586561 T^{6} + 2154195 T^{7} + 78917915 T^{8} + 138563380 T^{9} + 3059524868 T^{10} + 5891387852 T^{11} + 95426069459 T^{12} + 181036424341 T^{13} + 2426583490898 T^{14} + 4163837759843 T^{15} + 50480390743811 T^{16} + 71680515995284 T^{17} + 856180498585988 T^{18} + 891841440919340 T^{19} + 11682683705051435 T^{20} + 7334657953800165 T^{21} + 124245155118408641 T^{22} + 31069883410236750 T^{23} + 965983388479867382 T^{24} - 12386526852881051 T^{25} + 4843131999476490941 T^{26} - 504036361936467383 T^{27} + 11592836324538749809 T^{28} \))(\( 1 + 11 T + 212 T^{2} + 1602 T^{3} + 18498 T^{4} + 106940 T^{5} + 985432 T^{6} + 4750350 T^{7} + 40348710 T^{8} + 176707523 T^{9} + 1448449902 T^{10} + 5950017429 T^{11} + 45781925102 T^{12} + 173492457085 T^{13} + 1244660981805 T^{14} + 4370028980722 T^{15} + 29975225956240 T^{16} + 100510666556606 T^{17} + 658425659374845 T^{18} + 2110882725353195 T^{19} + 12811659702468782 T^{20} + 38296353029022147 T^{21} + 214422568914532878 T^{22} + 601658270986737781 T^{23} + 3159747234917337510 T^{24} + 8556105545380762050 T^{25} + 40823009798288561368 T^{26} + \)\(10\!\cdots\!80\)\( T^{27} + \)\(40\!\cdots\!58\)\( T^{28} + \)\(80\!\cdots\!66\)\( T^{29} + \)\(24\!\cdots\!08\)\( T^{30} + \)\(29\!\cdots\!77\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 + 5 T + 210 T^{2} + 1028 T^{3} + 22180 T^{4} + 106222 T^{5} + 1573196 T^{6} + 7304878 T^{7} + 83913964 T^{8} + 373942345 T^{9} + 3565492464 T^{10} + 15109686267 T^{11} + 124732775180 T^{12} + 498307153311 T^{13} + 3663748705023 T^{14} + 13666063493826 T^{15} + 91320510215280 T^{16} + 314319460357998 T^{17} + 1938123064957167 T^{18} + 6062903134334937 T^{19} + 34905344539146380 T^{20} + 97251123436801581 T^{21} + 527820846631040496 T^{22} + 1273208411966853215 T^{23} + 6571385199674363884 T^{24} + 13157200451362516514 T^{25} + 65172021735267752204 T^{26} + \)\(10\!\cdots\!94\)\( T^{27} + \)\(48\!\cdots\!80\)\( T^{28} + \)\(51\!\cdots\!24\)\( T^{29} + \)\(24\!\cdots\!90\)\( T^{30} + \)\(13\!\cdots\!35\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 + 3 T + 234 T^{2} + 676 T^{3} + 26949 T^{4} + 77781 T^{5} + 2049886 T^{6} + 6030524 T^{7} + 116410704 T^{8} + 350249943 T^{9} + 5281546972 T^{10} + 16096446059 T^{11} + 199618722400 T^{12} + 605557844316 T^{13} + 6451503344425 T^{14} + 19086247757769 T^{15} + 181051775978782 T^{16} + 511844187731017 T^{17} + 4446297548175166 T^{18} + 11772416317813391 T^{19} + 95776389492775678 T^{20} + 232222376468775423 T^{21} + 1805395147407236425 T^{22} + 3897577992358376388 T^{23} + 29550735031528213600 T^{24} + 54805589147946063373 T^{25} + \)\(41\!\cdots\!32\)\( T^{26} + \)\(63\!\cdots\!09\)\( T^{27} + \)\(48\!\cdots\!96\)\( T^{28} + \)\(57\!\cdots\!48\)\( T^{29} + \)\(44\!\cdots\!06\)\( T^{30} + \)\(39\!\cdots\!23\)\( T^{31} + \)\(31\!\cdots\!41\)\( T^{32} + \)\(18\!\cdots\!32\)\( T^{33} + \)\(14\!\cdots\!74\)\( T^{34} + \)\(42\!\cdots\!09\)\( T^{35} + \)\(32\!\cdots\!69\)\( T^{36} \))(\( 1 + 29 T + 616 T^{2} + 9368 T^{3} + 119779 T^{4} + 1291191 T^{5} + 12372304 T^{6} + 106073232 T^{7} + 835421121 T^{8} + 6086041302 T^{9} + 41670460521 T^{10} + 269711287902 T^{11} + 1666938182301 T^{12} + 9875436938545 T^{13} + 56414693115036 T^{14} + 311284609059156 T^{15} + 1664078337656527 T^{16} + 8617898864314219 T^{17} + 43295169543110401 T^{18} + 210808762190115960 T^{19} + 995788899491539223 T^{20} + 4558868499222221851 T^{21} + 20246841134266964009 T^{22} + 87110196283723274196 T^{23} + \)\(36\!\cdots\!48\)\( T^{24} + \)\(14\!\cdots\!05\)\( T^{25} + \)\(56\!\cdots\!47\)\( T^{26} + \)\(21\!\cdots\!62\)\( T^{27} + \)\(75\!\cdots\!23\)\( T^{28} + \)\(25\!\cdots\!98\)\( T^{29} + \)\(79\!\cdots\!67\)\( T^{30} + \)\(23\!\cdots\!72\)\( T^{31} + \)\(62\!\cdots\!32\)\( T^{32} + \)\(14\!\cdots\!19\)\( T^{33} + \)\(31\!\cdots\!53\)\( T^{34} + \)\(57\!\cdots\!48\)\( T^{35} + \)\(86\!\cdots\!48\)\( T^{36} + \)\(94\!\cdots\!01\)\( T^{37} + \)\(74\!\cdots\!87\)\( T^{38} \))(\( 1 - 13 T + 266 T^{2} - 2658 T^{3} + 32997 T^{4} - 277209 T^{5} + 2662566 T^{6} - 19608386 T^{7} + 158978761 T^{8} - 1051416104 T^{9} + 7518490349 T^{10} - 45409533272 T^{11} + 294076939485 T^{12} - 1642553968137 T^{13} + 9807062908540 T^{14} - 51158708345468 T^{15} + 285182325950267 T^{16} - 1399614648394315 T^{17} + 7345037695810517 T^{18} - 34058603555057856 T^{19} + 168935867003641891 T^{20} - 740396149000592635 T^{21} + 3469813359836898589 T^{22} - 14316304102104110588 T^{23} + 63121620701941069220 T^{24} - \)\(24\!\cdots\!93\)\( T^{25} + \)\(10\!\cdots\!95\)\( T^{26} - \)\(35\!\cdots\!32\)\( T^{27} + \)\(13\!\cdots\!87\)\( T^{28} - \)\(43\!\cdots\!96\)\( T^{29} + \)\(15\!\cdots\!47\)\( T^{30} - \)\(42\!\cdots\!06\)\( T^{31} + \)\(13\!\cdots\!78\)\( T^{32} - \)\(32\!\cdots\!81\)\( T^{33} + \)\(87\!\cdots\!79\)\( T^{34} - \)\(16\!\cdots\!38\)\( T^{35} + \)\(37\!\cdots\!98\)\( T^{36} - \)\(42\!\cdots\!97\)\( T^{37} + \)\(74\!\cdots\!87\)\( T^{38} \))
$29$ (\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 10 T + 75 T^{2} - 290 T^{3} + 841 T^{4} \))(\( 1 + 2 T + 194 T^{2} + 542 T^{3} + 19351 T^{4} + 68968 T^{5} + 1336951 T^{6} + 5539984 T^{7} + 71861249 T^{8} + 320038052 T^{9} + 3167514404 T^{10} + 14263027652 T^{11} + 117271485538 T^{12} + 508813651936 T^{13} + 3685580690260 T^{14} + 14755595906144 T^{15} + 98625319337458 T^{16} + 347860981404628 T^{17} + 2240322755175524 T^{18} + 6564348170241748 T^{19} + 42744746781387929 T^{20} + 95564038753839056 T^{21} + 668804942054621911 T^{22} + 1000528843663733192 T^{23} + 8141105671592189551 T^{24} + 6612676293012559318 T^{25} + 68640067941860993954 T^{26} + 20521257425917204378 T^{27} + \)\(29\!\cdots\!81\)\( T^{28} \))(\( 1 + 14 T + 305 T^{2} + 2894 T^{3} + 38696 T^{4} + 293398 T^{5} + 3143474 T^{6} + 20669070 T^{7} + 193545935 T^{8} + 1139671372 T^{9} + 9641189890 T^{10} + 51696096664 T^{11} + 402869076107 T^{12} + 1991951161406 T^{13} + 14441818937028 T^{14} + 66334729234054 T^{15} + 448938206638552 T^{16} + 1923707147787566 T^{17} + 12145569726040548 T^{18} + 48581696875530934 T^{19} + 284941643018035067 T^{20} + 1060346341393706936 T^{21} + 5734804588761424690 T^{22} + 19659190199908325948 T^{23} + 96820659726932863535 T^{24} + \)\(29\!\cdots\!30\)\( T^{25} + \)\(13\!\cdots\!74\)\( T^{26} + \)\(35\!\cdots\!42\)\( T^{27} + \)\(13\!\cdots\!36\)\( T^{28} + \)\(29\!\cdots\!66\)\( T^{29} + \)\(90\!\cdots\!05\)\( T^{30} + \)\(12\!\cdots\!86\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 + 265 T^{2} - 134 T^{3} + 33234 T^{4} - 32688 T^{5} + 2650270 T^{6} - 3683790 T^{7} + 153339527 T^{8} - 254559244 T^{9} + 7010203100 T^{10} - 12195811774 T^{11} + 269873303187 T^{12} - 445025917312 T^{13} + 9139942353748 T^{14} - 13782689900614 T^{15} + 278550568825296 T^{16} - 399698007117806 T^{17} + 7686691519502068 T^{18} - 10853737097322368 T^{19} + 190876259751404547 T^{20} - 250150112472468326 T^{21} + 4169832288826495100 T^{22} - 4391115472312550396 T^{23} + 76707548346886409447 T^{24} - 53441279274446463510 T^{25} + \)\(11\!\cdots\!70\)\( T^{26} - \)\(39\!\cdots\!52\)\( T^{27} + \)\(11\!\cdots\!94\)\( T^{28} - \)\(13\!\cdots\!26\)\( T^{29} + \)\(78\!\cdots\!65\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 + 6 T + 287 T^{2} + 1214 T^{3} + 38135 T^{4} + 106846 T^{5} + 3240447 T^{6} + 5190596 T^{7} + 205653397 T^{8} + 131968408 T^{9} + 10705589152 T^{10} - 443467206 T^{11} + 479547678480 T^{12} - 226940721730 T^{13} + 18787696807312 T^{14} - 13589839278860 T^{15} + 648449066671843 T^{16} - 535794317469034 T^{17} + 19895707538343140 T^{18} - 15538035206601986 T^{19} + 545345665071019963 T^{20} - 331442590172116540 T^{21} + 13288180985572438672 T^{22} - 4654814957571567770 T^{23} + \)\(28\!\cdots\!80\)\( T^{24} - 7649754450597822654 T^{25} + \)\(53\!\cdots\!72\)\( T^{26} + \)\(19\!\cdots\!52\)\( T^{27} + \)\(86\!\cdots\!97\)\( T^{28} + \)\(63\!\cdots\!84\)\( T^{29} + \)\(11\!\cdots\!27\)\( T^{30} + \)\(10\!\cdots\!94\)\( T^{31} + \)\(11\!\cdots\!35\)\( T^{32} + \)\(10\!\cdots\!86\)\( T^{33} + \)\(71\!\cdots\!27\)\( T^{34} + \)\(43\!\cdots\!54\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))(\( 1 + 16 T + 384 T^{2} + 4494 T^{3} + 64416 T^{4} + 613868 T^{5} + 6728012 T^{6} + 55302928 T^{7} + 509022350 T^{8} + 3737817668 T^{9} + 30315933099 T^{10} + 203415874146 T^{11} + 1495235191238 T^{12} + 9303644369540 T^{13} + 63079159128376 T^{14} + 367428508230202 T^{15} + 2324040458719563 T^{16} + 12744145461981164 T^{17} + 75735839056351713 T^{18} + 391903487718029996 T^{19} + 2196339332634199677 T^{20} + 10717826333526158924 T^{21} + 56681022747711422007 T^{22} + \)\(25\!\cdots\!62\)\( T^{23} + \)\(12\!\cdots\!24\)\( T^{24} + \)\(55\!\cdots\!40\)\( T^{25} + \)\(25\!\cdots\!42\)\( T^{26} + \)\(10\!\cdots\!06\)\( T^{27} + \)\(43\!\cdots\!31\)\( T^{28} + \)\(15\!\cdots\!68\)\( T^{29} + \)\(62\!\cdots\!50\)\( T^{30} + \)\(19\!\cdots\!48\)\( T^{31} + \)\(69\!\cdots\!68\)\( T^{32} + \)\(18\!\cdots\!08\)\( T^{33} + \)\(55\!\cdots\!84\)\( T^{34} + \)\(11\!\cdots\!74\)\( T^{35} + \)\(27\!\cdots\!56\)\( T^{36} + \)\(33\!\cdots\!76\)\( T^{37} + \)\(61\!\cdots\!69\)\( T^{38} \))(\( 1 + 18 T + 404 T^{2} + 5016 T^{3} + 68366 T^{4} + 665144 T^{5} + 6882362 T^{6} + 55136092 T^{7} + 466852704 T^{8} + 3123380646 T^{9} + 22264558839 T^{10} + 121999788002 T^{11} + 730389418304 T^{12} + 2959505815320 T^{13} + 13875365843970 T^{14} + 16443358330330 T^{15} - 26921203010987 T^{16} - 1980033671993176 T^{17} - 11076919902801515 T^{18} - 89730299414037696 T^{19} - 321230677181243935 T^{20} - 1665208318146261016 T^{21} - 656581220234961943 T^{22} + 11630074923234132730 T^{23} + \)\(28\!\cdots\!30\)\( T^{24} + \)\(17\!\cdots\!20\)\( T^{25} + \)\(12\!\cdots\!36\)\( T^{26} + \)\(61\!\cdots\!22\)\( T^{27} + \)\(32\!\cdots\!91\)\( T^{28} + \)\(13\!\cdots\!46\)\( T^{29} + \)\(56\!\cdots\!16\)\( T^{30} + \)\(19\!\cdots\!72\)\( T^{31} + \)\(70\!\cdots\!18\)\( T^{32} + \)\(19\!\cdots\!64\)\( T^{33} + \)\(58\!\cdots\!34\)\( T^{34} + \)\(12\!\cdots\!36\)\( T^{35} + \)\(29\!\cdots\!36\)\( T^{36} + \)\(37\!\cdots\!98\)\( T^{37} + \)\(61\!\cdots\!69\)\( T^{38} \))
$31$ (\( 1 - 2 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 6 T + 63 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 - 11 T + 305 T^{2} - 2544 T^{3} + 40054 T^{4} - 267951 T^{5} + 3162974 T^{6} - 17820622 T^{7} + 178752727 T^{8} - 895779012 T^{9} + 8165531047 T^{10} - 38032628385 T^{11} + 320250054151 T^{12} - 1396184824593 T^{13} + 10776719467218 T^{14} - 43281729562383 T^{15} + 307760302039111 T^{16} - 1133030032217535 T^{17} + 7541039398056487 T^{18} - 25645392597178812 T^{19} + 158643703201288087 T^{20} - 490291896303997042 T^{21} + 2697672176258909534 T^{22} - 7084523197573955121 T^{23} + 32829391406729003254 T^{24} - 64639165224453890064 T^{25} + \)\(24\!\cdots\!05\)\( T^{26} - \)\(26\!\cdots\!01\)\( T^{27} + \)\(75\!\cdots\!21\)\( T^{28} \))(\( 1 + 13 T + 418 T^{2} + 4345 T^{3} + 79362 T^{4} + 694572 T^{5} + 9352475 T^{6} + 71179299 T^{7} + 780656709 T^{8} + 5279797461 T^{9} + 49625415588 T^{10} + 302536421763 T^{11} + 2508518440079 T^{12} + 13898223683172 T^{13} + 103398167014096 T^{14} + 522230180654919 T^{15} + 3520123336306084 T^{16} + 16189135600302489 T^{17} + 99365638500546256 T^{18} + 414041981745377052 T^{19} + 2316669458300198159 T^{20} + 8661360901652613213 T^{21} + 44042739005504779428 T^{22} + \)\(14\!\cdots\!71\)\( T^{23} + \)\(66\!\cdots\!69\)\( T^{24} + \)\(18\!\cdots\!29\)\( T^{25} + \)\(76\!\cdots\!75\)\( T^{26} + \)\(17\!\cdots\!32\)\( T^{27} + \)\(62\!\cdots\!82\)\( T^{28} + \)\(10\!\cdots\!95\)\( T^{29} + \)\(31\!\cdots\!78\)\( T^{30} + \)\(30\!\cdots\!63\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 + 35 T + 782 T^{2} + 12829 T^{3} + 173780 T^{4} + 2021978 T^{5} + 21006019 T^{6} + 198255809 T^{7} + 1729955717 T^{8} + 14071859457 T^{9} + 107675193438 T^{10} + 778296544165 T^{11} + 5342081251881 T^{12} + 34890985852536 T^{13} + 217504770889594 T^{14} + 1294902535924527 T^{15} + 7373713876191948 T^{16} + 40141978613660337 T^{17} + 209022084824899834 T^{18} + 1039437359532899976 T^{19} + 4933524219818393001 T^{20} + 22281969285677953915 T^{21} + 95562130528612045278 T^{22} + \)\(38\!\cdots\!27\)\( T^{23} + \)\(14\!\cdots\!97\)\( T^{24} + \)\(52\!\cdots\!39\)\( T^{25} + \)\(17\!\cdots\!19\)\( T^{26} + \)\(51\!\cdots\!18\)\( T^{27} + \)\(13\!\cdots\!80\)\( T^{28} + \)\(31\!\cdots\!39\)\( T^{29} + \)\(59\!\cdots\!22\)\( T^{30} + \)\(82\!\cdots\!85\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 - 41 T + 1050 T^{2} - 20113 T^{3} + 319011 T^{4} - 4364971 T^{5} + 53127219 T^{6} - 585198196 T^{7} + 5916357595 T^{8} - 55403376247 T^{9} + 484290621317 T^{10} - 3972744218706 T^{11} + 30725365563404 T^{12} - 224770150627499 T^{13} + 1559680351298428 T^{14} - 10285239494239452 T^{15} + 64561335680358305 T^{16} - 386108991980853013 T^{17} + 2201547884054460172 T^{18} - 11969378751406443403 T^{19} + 62043443588824331105 T^{20} - \)\(30\!\cdots\!32\)\( T^{21} + \)\(14\!\cdots\!88\)\( T^{22} - \)\(64\!\cdots\!49\)\( T^{23} + \)\(27\!\cdots\!24\)\( T^{24} - \)\(10\!\cdots\!66\)\( T^{25} + \)\(41\!\cdots\!97\)\( T^{26} - \)\(14\!\cdots\!37\)\( T^{27} + \)\(48\!\cdots\!95\)\( T^{28} - \)\(14\!\cdots\!76\)\( T^{29} + \)\(41\!\cdots\!59\)\( T^{30} - \)\(10\!\cdots\!61\)\( T^{31} + \)\(24\!\cdots\!31\)\( T^{32} - \)\(47\!\cdots\!63\)\( T^{33} + \)\(76\!\cdots\!50\)\( T^{34} - \)\(92\!\cdots\!51\)\( T^{35} + \)\(69\!\cdots\!41\)\( T^{36} \))(\( 1 + 35 T + 751 T^{2} + 11848 T^{3} + 157361 T^{4} + 1838348 T^{5} + 19613440 T^{6} + 192849399 T^{7} + 1772884190 T^{8} + 15315188489 T^{9} + 125483068424 T^{10} + 977581449715 T^{11} + 7278901532393 T^{12} + 51852657976619 T^{13} + 354713362860532 T^{14} + 2331346327212777 T^{15} + 14758002424766395 T^{16} + 89955655048314557 T^{17} + 528871583231843609 T^{18} + 2997362211679781418 T^{19} + 16395019080187151879 T^{20} + 86447384501430289277 T^{21} + \)\(43\!\cdots\!45\)\( T^{22} + \)\(21\!\cdots\!17\)\( T^{23} + \)\(10\!\cdots\!32\)\( T^{24} + \)\(46\!\cdots\!39\)\( T^{25} + \)\(20\!\cdots\!23\)\( T^{26} + \)\(83\!\cdots\!15\)\( T^{27} + \)\(33\!\cdots\!04\)\( T^{28} + \)\(12\!\cdots\!89\)\( T^{29} + \)\(45\!\cdots\!90\)\( T^{30} + \)\(15\!\cdots\!39\)\( T^{31} + \)\(47\!\cdots\!40\)\( T^{32} + \)\(13\!\cdots\!08\)\( T^{33} + \)\(36\!\cdots\!11\)\( T^{34} + \)\(86\!\cdots\!88\)\( T^{35} + \)\(16\!\cdots\!61\)\( T^{36} + \)\(24\!\cdots\!35\)\( T^{37} + \)\(21\!\cdots\!71\)\( T^{38} \))(\( 1 + 21 T + 563 T^{2} + 8362 T^{3} + 135215 T^{4} + 1602624 T^{5} + 19782574 T^{6} + 198566577 T^{7} + 2040631864 T^{8} + 17948484897 T^{9} + 160389456840 T^{10} + 1262673662405 T^{11} + 10060376500821 T^{12} + 71861573200275 T^{13} + 518429724003846 T^{14} + 3389243263643967 T^{15} + 22353041954691857 T^{16} + 134432594536070407 T^{17} + 815167322229980463 T^{18} + 4520414352752147970 T^{19} + 25270186989129394353 T^{20} + \)\(12\!\cdots\!27\)\( T^{21} + \)\(66\!\cdots\!87\)\( T^{22} + \)\(31\!\cdots\!07\)\( T^{23} + \)\(14\!\cdots\!46\)\( T^{24} + \)\(63\!\cdots\!75\)\( T^{25} + \)\(27\!\cdots\!31\)\( T^{26} + \)\(10\!\cdots\!05\)\( T^{27} + \)\(42\!\cdots\!40\)\( T^{28} + \)\(14\!\cdots\!97\)\( T^{29} + \)\(51\!\cdots\!84\)\( T^{30} + \)\(15\!\cdots\!97\)\( T^{31} + \)\(48\!\cdots\!34\)\( T^{32} + \)\(12\!\cdots\!04\)\( T^{33} + \)\(31\!\cdots\!65\)\( T^{34} + \)\(60\!\cdots\!22\)\( T^{35} + \)\(12\!\cdots\!93\)\( T^{36} + \)\(14\!\cdots\!61\)\( T^{37} + \)\(21\!\cdots\!71\)\( T^{38} \))
$37$ (\( 1 - 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 66 T^{2} + 1369 T^{4} \))(\( 1 - 2 T + 229 T^{2} - 337 T^{3} + 29016 T^{4} - 37440 T^{5} + 2610789 T^{6} - 3103668 T^{7} + 182395791 T^{8} - 204498204 T^{9} + 10376633026 T^{10} - 11009297734 T^{11} + 492787765363 T^{12} - 489712923207 T^{13} + 19788146760282 T^{14} - 18119378158659 T^{15} + 674626450781947 T^{16} - 557653958120302 T^{17} + 19447480928641186 T^{18} - 14180714664753228 T^{19} + 467977697859144519 T^{20} - 294637029237623844 T^{21} + 9170342721022953669 T^{22} - 4865767537927682880 T^{23} + \)\(13\!\cdots\!84\)\( T^{24} - 59958238539678159181 T^{25} + \)\(15\!\cdots\!49\)\( T^{26} - \)\(48\!\cdots\!94\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \))(\( 1 + 297 T^{2} - 263 T^{3} + 43721 T^{4} - 77430 T^{5} + 4277640 T^{6} - 11289099 T^{7} + 315723581 T^{8} - 1078721214 T^{9} + 18933564715 T^{10} - 75745474874 T^{11} + 966201715410 T^{12} - 4163215210511 T^{13} + 43048515929700 T^{14} - 186003314873709 T^{15} + 1693053028837982 T^{16} - 6882122650327233 T^{17} + 58933418307759300 T^{18} - 210879340058013683 T^{19} + 1810817573154521010 T^{20} - 5252490952607236418 T^{21} + 48578347005786058435 T^{22} - \)\(10\!\cdots\!62\)\( T^{23} + \)\(11\!\cdots\!01\)\( T^{24} - \)\(14\!\cdots\!23\)\( T^{25} + \)\(20\!\cdots\!60\)\( T^{26} - \)\(13\!\cdots\!90\)\( T^{27} + \)\(28\!\cdots\!01\)\( T^{28} - \)\(64\!\cdots\!11\)\( T^{29} + \)\(26\!\cdots\!33\)\( T^{30} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 + 6 T + 351 T^{2} + 1867 T^{3} + 58475 T^{4} + 286638 T^{5} + 6246000 T^{6} + 29478577 T^{7} + 487940633 T^{8} + 2309339158 T^{9} + 30155009969 T^{10} + 146666261358 T^{11} + 1554576393426 T^{12} + 7747893976107 T^{13} + 69261728556340 T^{14} + 342595910280261 T^{15} + 2720662800589770 T^{16} + 12676048680369657 T^{17} + 94819306393629460 T^{18} + 392454073571747871 T^{19} + 2913526448079665586 T^{20} + 10170418920959913606 T^{21} + 77369505441121571321 T^{22} + \)\(21\!\cdots\!14\)\( T^{23} + \)\(17\!\cdots\!93\)\( T^{24} + \)\(38\!\cdots\!29\)\( T^{25} + \)\(30\!\cdots\!00\)\( T^{26} + \)\(50\!\cdots\!94\)\( T^{27} + \)\(38\!\cdots\!75\)\( T^{28} + \)\(45\!\cdots\!99\)\( T^{29} + \)\(31\!\cdots\!39\)\( T^{30} + \)\(20\!\cdots\!58\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 - 6 T + 371 T^{2} - 2399 T^{3} + 71694 T^{4} - 486210 T^{5} + 9430943 T^{6} - 65601330 T^{7} + 938364076 T^{8} - 6564101248 T^{9} + 74555045417 T^{10} - 515219791923 T^{11} + 4881605550981 T^{12} - 32780178773427 T^{13} + 268507800036943 T^{14} - 1724471852050117 T^{15} + 12551124110069944 T^{16} - 75879688682538176 T^{17} + 501695512443067788 T^{18} - 2807548481253912512 T^{19} + 17182488906685753336 T^{20} - 87349672721894576401 T^{21} + \)\(50\!\cdots\!23\)\( T^{22} - \)\(22\!\cdots\!39\)\( T^{23} + \)\(12\!\cdots\!29\)\( T^{24} - \)\(48\!\cdots\!59\)\( T^{25} + \)\(26\!\cdots\!57\)\( T^{26} - \)\(85\!\cdots\!96\)\( T^{27} + \)\(45\!\cdots\!24\)\( T^{28} - \)\(11\!\cdots\!90\)\( T^{29} + \)\(62\!\cdots\!83\)\( T^{30} - \)\(11\!\cdots\!70\)\( T^{31} + \)\(64\!\cdots\!66\)\( T^{32} - \)\(79\!\cdots\!07\)\( T^{33} + \)\(45\!\cdots\!11\)\( T^{34} - \)\(27\!\cdots\!02\)\( T^{35} + \)\(16\!\cdots\!29\)\( T^{36} \))(\( 1 + 8 T + 351 T^{2} + 2665 T^{3} + 63818 T^{4} + 466112 T^{5} + 7901813 T^{6} + 55766412 T^{7} + 743209943 T^{8} + 5078429836 T^{9} + 56312220867 T^{10} + 372574928186 T^{11} + 3565873183926 T^{12} + 22804445562612 T^{13} + 193488069652502 T^{14} + 1191347637950749 T^{15} + 9154054776703100 T^{16} + 53913085964727772 T^{17} + 381911703772589067 T^{18} + 2131304073279141408 T^{19} + 14130733039585795479 T^{20} + 73807014685712319868 T^{21} + \)\(46\!\cdots\!00\)\( T^{22} + \)\(22\!\cdots\!89\)\( T^{23} + \)\(13\!\cdots\!14\)\( T^{24} + \)\(58\!\cdots\!08\)\( T^{25} + \)\(33\!\cdots\!58\)\( T^{26} + \)\(13\!\cdots\!06\)\( T^{27} + \)\(73\!\cdots\!59\)\( T^{28} + \)\(24\!\cdots\!64\)\( T^{29} + \)\(13\!\cdots\!59\)\( T^{30} + \)\(36\!\cdots\!72\)\( T^{31} + \)\(19\!\cdots\!61\)\( T^{32} + \)\(42\!\cdots\!68\)\( T^{33} + \)\(21\!\cdots\!74\)\( T^{34} + \)\(32\!\cdots\!65\)\( T^{35} + \)\(16\!\cdots\!67\)\( T^{36} + \)\(13\!\cdots\!32\)\( T^{37} + \)\(62\!\cdots\!73\)\( T^{38} \))(\( 1 + 26 T + 605 T^{2} + 9947 T^{3} + 147708 T^{4} + 1858834 T^{5} + 21593971 T^{6} + 225461398 T^{7} + 2207938897 T^{8} + 19986338202 T^{9} + 171725727243 T^{10} + 1387121843010 T^{11} + 10739740128202 T^{12} + 79124656552330 T^{13} + 563596226974572 T^{14} + 3856755695312307 T^{15} + 25708124444903544 T^{16} + 165841920138847884 T^{17} + 1047812175034196753 T^{18} + 6433650747266988700 T^{19} + 38769050476265279861 T^{20} + \)\(22\!\cdots\!96\)\( T^{21} + \)\(13\!\cdots\!32\)\( T^{22} + \)\(72\!\cdots\!27\)\( T^{23} + \)\(39\!\cdots\!04\)\( T^{24} + \)\(20\!\cdots\!70\)\( T^{25} + \)\(10\!\cdots\!66\)\( T^{26} + \)\(48\!\cdots\!10\)\( T^{27} + \)\(22\!\cdots\!11\)\( T^{28} + \)\(96\!\cdots\!98\)\( T^{29} + \)\(39\!\cdots\!61\)\( T^{30} + \)\(14\!\cdots\!38\)\( T^{31} + \)\(52\!\cdots\!87\)\( T^{32} + \)\(16\!\cdots\!26\)\( T^{33} + \)\(49\!\cdots\!44\)\( T^{34} + \)\(12\!\cdots\!27\)\( T^{35} + \)\(27\!\cdots\!85\)\( T^{36} + \)\(43\!\cdots\!54\)\( T^{37} + \)\(62\!\cdots\!73\)\( T^{38} \))
$41$ (\( 1 + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 4 T + 54 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 - 35 T + 943 T^{2} - 18253 T^{3} + 303851 T^{4} - 4280604 T^{5} + 54138892 T^{6} - 610970924 T^{7} + 6325374682 T^{8} - 59853680535 T^{9} + 525848649165 T^{10} - 4274807360663 T^{11} + 32479025896757 T^{12} - 229728035521614 T^{13} + 1523148100400282 T^{14} - 9418849456386174 T^{15} + 54597242532448517 T^{16} - 294623998104254623 T^{17} + 1485922604713139565 T^{18} - 6934420042652747535 T^{19} + 30046189102882226362 T^{20} - \)\(11\!\cdots\!44\)\( T^{21} + \)\(43\!\cdots\!32\)\( T^{22} - \)\(14\!\cdots\!44\)\( T^{23} + \)\(40\!\cdots\!51\)\( T^{24} - \)\(10\!\cdots\!73\)\( T^{25} + \)\(21\!\cdots\!83\)\( T^{26} - \)\(32\!\cdots\!35\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \))(\( 1 + 21 T + 513 T^{2} + 7903 T^{3} + 118656 T^{4} + 1474067 T^{5} + 17275591 T^{6} + 182185289 T^{7} + 1813360279 T^{8} + 16756745703 T^{9} + 147176669395 T^{10} + 1216484565293 T^{11} + 9610607341819 T^{12} + 71982916571667 T^{13} + 516729582647499 T^{14} + 3532179929414785 T^{15} + 23159367622327654 T^{16} + 144819377106006185 T^{17} + 868622428430445819 T^{18} + 4961134593035861307 T^{19} + 27157279412825799259 T^{20} + \)\(14\!\cdots\!93\)\( T^{21} + \)\(69\!\cdots\!95\)\( T^{22} + \)\(32\!\cdots\!43\)\( T^{23} + \)\(14\!\cdots\!59\)\( T^{24} + \)\(59\!\cdots\!29\)\( T^{25} + \)\(23\!\cdots\!91\)\( T^{26} + \)\(81\!\cdots\!47\)\( T^{27} + \)\(26\!\cdots\!36\)\( T^{28} + \)\(73\!\cdots\!63\)\( T^{29} + \)\(19\!\cdots\!93\)\( T^{30} + \)\(32\!\cdots\!21\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 + 7 T + 301 T^{2} + 1671 T^{3} + 42588 T^{4} + 173787 T^{5} + 3804761 T^{6} + 9809435 T^{7} + 248936845 T^{8} + 276776993 T^{9} + 13550353151 T^{10} - 870585365 T^{11} + 681564231035 T^{12} - 437877889061 T^{13} + 32536145358261 T^{14} - 23765509019075 T^{15} + 1415757801184690 T^{16} - 974385869782075 T^{17} + 54693260347236741 T^{18} - 30178981991973181 T^{19} + 1925937623053692635 T^{20} - 100862713035098365 T^{21} + 64365589969612813391 T^{22} + 53903502298681619833 T^{23} + \)\(19\!\cdots\!45\)\( T^{24} + \)\(32\!\cdots\!35\)\( T^{25} + \)\(51\!\cdots\!61\)\( T^{26} + \)\(95\!\cdots\!67\)\( T^{27} + \)\(96\!\cdots\!28\)\( T^{28} + \)\(15\!\cdots\!91\)\( T^{29} + \)\(11\!\cdots\!61\)\( T^{30} + \)\(10\!\cdots\!07\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 3 T + 325 T^{2} - 425 T^{3} + 55097 T^{4} - 6722 T^{5} + 6541896 T^{6} + 5224094 T^{7} + 605364423 T^{8} + 901783884 T^{9} + 46299541394 T^{10} + 90235858084 T^{11} + 3021881232790 T^{12} + 6653828685222 T^{13} + 171309952558130 T^{14} + 391204275754318 T^{15} + 8510865839417913 T^{16} + 19056104914949444 T^{17} + 371863168438913566 T^{18} + 781300301512927204 T^{19} + 14306765476061511753 T^{20} + 26962189889263350878 T^{21} + \)\(48\!\cdots\!30\)\( T^{22} + \)\(77\!\cdots\!22\)\( T^{23} + \)\(14\!\cdots\!90\)\( T^{24} + \)\(17\!\cdots\!04\)\( T^{25} + \)\(36\!\cdots\!74\)\( T^{26} + \)\(29\!\cdots\!24\)\( T^{27} + \)\(81\!\cdots\!23\)\( T^{28} + \)\(28\!\cdots\!54\)\( T^{29} + \)\(14\!\cdots\!76\)\( T^{30} - \)\(62\!\cdots\!62\)\( T^{31} + \)\(20\!\cdots\!17\)\( T^{32} - \)\(66\!\cdots\!25\)\( T^{33} + \)\(20\!\cdots\!25\)\( T^{34} - \)\(78\!\cdots\!43\)\( T^{35} + \)\(10\!\cdots\!21\)\( T^{36} \))(\( 1 + 17 T + 503 T^{2} + 6687 T^{3} + 114747 T^{4} + 1270866 T^{5} + 16345518 T^{6} + 156796712 T^{7} + 1666218172 T^{8} + 14211451579 T^{9} + 131307048334 T^{10} + 1015723268844 T^{11} + 8433326990462 T^{12} + 60195905575009 T^{13} + 460663340252829 T^{14} + 3085026555196134 T^{15} + 22231879271326629 T^{16} + 141885131948163815 T^{17} + 979152069280955533 T^{18} + 6022585039401746850 T^{19} + 40145234840519176853 T^{20} + \)\(23\!\cdots\!15\)\( T^{21} + \)\(15\!\cdots\!09\)\( T^{22} + \)\(87\!\cdots\!74\)\( T^{23} + \)\(53\!\cdots\!29\)\( T^{24} + \)\(28\!\cdots\!69\)\( T^{25} + \)\(16\!\cdots\!22\)\( T^{26} + \)\(81\!\cdots\!24\)\( T^{27} + \)\(42\!\cdots\!74\)\( T^{28} + \)\(19\!\cdots\!79\)\( T^{29} + \)\(91\!\cdots\!52\)\( T^{30} + \)\(35\!\cdots\!72\)\( T^{31} + \)\(15\!\cdots\!78\)\( T^{32} + \)\(48\!\cdots\!26\)\( T^{33} + \)\(17\!\cdots\!47\)\( T^{34} + \)\(42\!\cdots\!67\)\( T^{35} + \)\(13\!\cdots\!43\)\( T^{36} + \)\(18\!\cdots\!57\)\( T^{37} + \)\(43\!\cdots\!61\)\( T^{38} \))(\( 1 + 7 T + 411 T^{2} + 2875 T^{3} + 83159 T^{4} + 578676 T^{5} + 11101840 T^{6} + 76050670 T^{7} + 1104843334 T^{8} + 7352333799 T^{9} + 87758197228 T^{10} + 560279118366 T^{11} + 5816083067580 T^{12} + 35322210638261 T^{13} + 331994125869413 T^{14} + 1912405917278604 T^{15} + 16720242774545857 T^{16} + 91497834939927537 T^{17} + 756119819117856349 T^{18} + 3940967140013332618 T^{19} + 31000912583832110309 T^{20} + \)\(15\!\cdots\!97\)\( T^{21} + \)\(11\!\cdots\!97\)\( T^{22} + \)\(54\!\cdots\!44\)\( T^{23} + \)\(38\!\cdots\!13\)\( T^{24} + \)\(16\!\cdots\!01\)\( T^{25} + \)\(11\!\cdots\!80\)\( T^{26} + \)\(44\!\cdots\!86\)\( T^{27} + \)\(28\!\cdots\!08\)\( T^{28} + \)\(98\!\cdots\!99\)\( T^{29} + \)\(60\!\cdots\!94\)\( T^{30} + \)\(17\!\cdots\!70\)\( T^{31} + \)\(10\!\cdots\!40\)\( T^{32} + \)\(21\!\cdots\!36\)\( T^{33} + \)\(12\!\cdots\!59\)\( T^{34} + \)\(18\!\cdots\!75\)\( T^{35} + \)\(10\!\cdots\!91\)\( T^{36} + \)\(75\!\cdots\!47\)\( T^{37} + \)\(43\!\cdots\!61\)\( T^{38} \))
$43$ (\( 1 + T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( ( 1 + T + 43 T^{2} )^{2} \))(\( 1 - 22 T + 477 T^{2} - 7203 T^{3} + 98656 T^{4} - 1165548 T^{5} + 12625983 T^{6} - 125141369 T^{7} + 1158499967 T^{8} - 10032400477 T^{9} + 82212720109 T^{10} - 636990895181 T^{11} + 4705186912091 T^{12} - 33047804640562 T^{13} + 222029032283712 T^{14} - 1421055599544166 T^{15} + 8699890600456259 T^{16} - 50645235103155767 T^{17} + 281068929721369309 T^{18} - 1474847573676227311 T^{19} + 7323298883661519383 T^{20} - 34015753113608585483 T^{21} + \)\(14\!\cdots\!83\)\( T^{22} - \)\(58\!\cdots\!64\)\( T^{23} + \)\(21\!\cdots\!44\)\( T^{24} - \)\(66\!\cdots\!21\)\( T^{25} + \)\(19\!\cdots\!77\)\( T^{26} - \)\(37\!\cdots\!46\)\( T^{27} + \)\(73\!\cdots\!49\)\( T^{28} \))(\( 1 + 6 T + 397 T^{2} + 2345 T^{3} + 78078 T^{4} + 456324 T^{5} + 10142163 T^{6} + 58814105 T^{7} + 979176840 T^{8} + 5631176011 T^{9} + 74991343870 T^{10} + 425274445648 T^{11} + 4745890496312 T^{12} + 26211861409524 T^{13} + 254774101201188 T^{14} + 1343701478987212 T^{15} + 11777016177664349 T^{16} + 57779163596450116 T^{17} + 471077313120996612 T^{18} + 2084026465087024668 T^{19} + 16225255174681961912 T^{20} + 62518934102400606064 T^{21} + \)\(47\!\cdots\!30\)\( T^{22} + \)\(15\!\cdots\!77\)\( T^{23} + \)\(11\!\cdots\!40\)\( T^{24} + \)\(29\!\cdots\!15\)\( T^{25} + \)\(21\!\cdots\!87\)\( T^{26} + \)\(42\!\cdots\!68\)\( T^{27} + \)\(31\!\cdots\!78\)\( T^{28} + \)\(40\!\cdots\!35\)\( T^{29} + \)\(29\!\cdots\!53\)\( T^{30} + \)\(19\!\cdots\!42\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 + 22 T + 529 T^{2} + 7205 T^{3} + 104170 T^{4} + 1074012 T^{5} + 12042999 T^{6} + 103907757 T^{7} + 1005870800 T^{8} + 7687409599 T^{9} + 67665987034 T^{10} + 471426071332 T^{11} + 3866326255848 T^{12} + 24977486864692 T^{13} + 193806816942052 T^{14} + 1179587937271536 T^{15} + 8740232196609237 T^{16} + 50722281302676048 T^{17} + 358348804525854148 T^{18} + 1985885048151066844 T^{19} + 13218200069819398248 T^{20} + 69303612736124256076 T^{21} + \)\(42\!\cdots\!66\)\( T^{22} + \)\(20\!\cdots\!93\)\( T^{23} + \)\(11\!\cdots\!00\)\( T^{24} + \)\(52\!\cdots\!51\)\( T^{25} + \)\(26\!\cdots\!51\)\( T^{26} + \)\(99\!\cdots\!84\)\( T^{27} + \)\(41\!\cdots\!70\)\( T^{28} + \)\(12\!\cdots\!15\)\( T^{29} + \)\(39\!\cdots\!21\)\( T^{30} + \)\(69\!\cdots\!54\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 + T + 442 T^{2} + 202 T^{3} + 95474 T^{4} - 4405 T^{5} + 13540262 T^{6} - 6556297 T^{7} + 1429731631 T^{8} - 1190883209 T^{9} + 120630408909 T^{10} - 130112817880 T^{11} + 8491278428576 T^{12} - 10383595409408 T^{13} + 511837840600098 T^{14} - 654347047357465 T^{15} + 26817838838421098 T^{16} - 33801277627458231 T^{17} + 1230722678240197002 T^{18} - 1453454937980703933 T^{19} + 49586184012240610202 T^{20} - 52025170694249969755 T^{21} + \)\(17\!\cdots\!98\)\( T^{22} - \)\(15\!\cdots\!44\)\( T^{23} + \)\(53\!\cdots\!24\)\( T^{24} - \)\(35\!\cdots\!60\)\( T^{25} + \)\(14\!\cdots\!09\)\( T^{26} - \)\(59\!\cdots\!87\)\( T^{27} + \)\(30\!\cdots\!19\)\( T^{28} - \)\(60\!\cdots\!79\)\( T^{29} + \)\(54\!\cdots\!62\)\( T^{30} - \)\(75\!\cdots\!15\)\( T^{31} + \)\(70\!\cdots\!26\)\( T^{32} + \)\(64\!\cdots\!14\)\( T^{33} + \)\(60\!\cdots\!42\)\( T^{34} + \)\(58\!\cdots\!43\)\( T^{35} + \)\(25\!\cdots\!49\)\( T^{36} \))(\( 1 + 9 T + 310 T^{2} + 3182 T^{3} + 52768 T^{4} + 539801 T^{5} + 6543746 T^{6} + 61367199 T^{7} + 634744790 T^{8} + 5421366616 T^{9} + 49920548386 T^{10} + 397109909507 T^{11} + 3319225983894 T^{12} + 24832584986629 T^{13} + 193098678503558 T^{14} + 1362214299736319 T^{15} + 10016266426876086 T^{16} + 67270665198751324 T^{17} + 469988440548066801 T^{18} + 3027501946677962067 T^{19} + 20209502943566872443 T^{20} + \)\(12\!\cdots\!76\)\( T^{21} + \)\(79\!\cdots\!02\)\( T^{22} + \)\(46\!\cdots\!19\)\( T^{23} + \)\(28\!\cdots\!94\)\( T^{24} + \)\(15\!\cdots\!21\)\( T^{25} + \)\(90\!\cdots\!58\)\( T^{26} + \)\(46\!\cdots\!07\)\( T^{27} + \)\(25\!\cdots\!98\)\( T^{28} + \)\(11\!\cdots\!84\)\( T^{29} + \)\(58\!\cdots\!30\)\( T^{30} + \)\(24\!\cdots\!99\)\( T^{31} + \)\(11\!\cdots\!78\)\( T^{32} + \)\(39\!\cdots\!49\)\( T^{33} + \)\(16\!\cdots\!76\)\( T^{34} + \)\(43\!\cdots\!82\)\( T^{35} + \)\(18\!\cdots\!30\)\( T^{36} + \)\(22\!\cdots\!41\)\( T^{37} + \)\(10\!\cdots\!07\)\( T^{38} \))(\( 1 + 25 T + 794 T^{2} + 14222 T^{3} + 273476 T^{4} + 3926713 T^{5} + 57742610 T^{6} + 702725143 T^{7} + 8602217946 T^{8} + 91617402032 T^{9} + 973620460142 T^{10} + 9256731577559 T^{11} + 87471322543242 T^{12} + 751930151809849 T^{13} + 6411444643949502 T^{14} + 50240846688870899 T^{15} + 390097193554991782 T^{16} + 2800104291460779600 T^{17} + 19905527941406424841 T^{18} + \)\(13\!\cdots\!55\)\( T^{19} + \)\(85\!\cdots\!63\)\( T^{20} + \)\(51\!\cdots\!00\)\( T^{21} + \)\(31\!\cdots\!74\)\( T^{22} + \)\(17\!\cdots\!99\)\( T^{23} + \)\(94\!\cdots\!86\)\( T^{24} + \)\(47\!\cdots\!01\)\( T^{25} + \)\(23\!\cdots\!94\)\( T^{26} + \)\(10\!\cdots\!59\)\( T^{27} + \)\(48\!\cdots\!06\)\( T^{28} + \)\(19\!\cdots\!68\)\( T^{29} + \)\(79\!\cdots\!22\)\( T^{30} + \)\(28\!\cdots\!43\)\( T^{31} + \)\(99\!\cdots\!30\)\( T^{32} + \)\(29\!\cdots\!37\)\( T^{33} + \)\(86\!\cdots\!32\)\( T^{34} + \)\(19\!\cdots\!22\)\( T^{35} + \)\(46\!\cdots\!42\)\( T^{36} + \)\(63\!\cdots\!25\)\( T^{37} + \)\(10\!\cdots\!07\)\( T^{38} \))
$47$ (\( 1 - 11 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 - 4 T + 66 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 - 7 T + 434 T^{2} - 2715 T^{3} + 93041 T^{4} - 524016 T^{5} + 13054398 T^{6} - 66567832 T^{7} + 1341204456 T^{8} - 6215921286 T^{9} + 106898916295 T^{10} - 450992213595 T^{11} + 6823742365831 T^{12} - 26170968029647 T^{13} + 354577079278690 T^{14} - 1230035497393409 T^{15} + 15073646886120679 T^{16} - 46823364592073685 T^{17} + 521632610765301895 T^{18} - 1425590510849119002 T^{19} + 14457131631438306024 T^{20} - 33724802770296746216 T^{21} + \)\(31\!\cdots\!78\)\( T^{22} - \)\(58\!\cdots\!72\)\( T^{23} + \)\(48\!\cdots\!09\)\( T^{24} - \)\(67\!\cdots\!45\)\( T^{25} + \)\(50\!\cdots\!94\)\( T^{26} - \)\(38\!\cdots\!89\)\( T^{27} + \)\(25\!\cdots\!69\)\( T^{28} \))(\( 1 + 21 T + 459 T^{2} + 6100 T^{3} + 83888 T^{4} + 880584 T^{5} + 9674245 T^{6} + 88036341 T^{7} + 846263459 T^{8} + 7014307648 T^{9} + 61634111245 T^{10} + 477241160851 T^{11} + 3913329652134 T^{12} + 28614815991532 T^{13} + 220539423999162 T^{14} + 1522354742969681 T^{15} + 11023623968728814 T^{16} + 71550672919575007 T^{17} + 487171587614148858 T^{18} + 2970876040688826836 T^{19} + 19095800350254889254 T^{20} + \)\(10\!\cdots\!57\)\( T^{21} + \)\(66\!\cdots\!05\)\( T^{22} + \)\(35\!\cdots\!24\)\( T^{23} + \)\(20\!\cdots\!99\)\( T^{24} + \)\(98\!\cdots\!47\)\( T^{25} + \)\(50\!\cdots\!05\)\( T^{26} + \)\(21\!\cdots\!52\)\( T^{27} + \)\(97\!\cdots\!08\)\( T^{28} + \)\(33\!\cdots\!00\)\( T^{29} + \)\(11\!\cdots\!71\)\( T^{30} + \)\(25\!\cdots\!03\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 - 11 T + 447 T^{2} - 4062 T^{3} + 91980 T^{4} - 710556 T^{5} + 11832573 T^{6} - 79311793 T^{7} + 1091146971 T^{8} - 6467489894 T^{9} + 78796407393 T^{10} - 422058236657 T^{11} + 4772713411494 T^{12} - 23671300852912 T^{13} + 255589970977676 T^{14} - 1200194733020113 T^{15} + 12502316441787110 T^{16} - 56409152451945311 T^{17} + 564598245889686284 T^{18} - 2457625468451882576 T^{19} + 23289318952512453414 T^{20} - 96796949240507321599 T^{21} + \)\(84\!\cdots\!97\)\( T^{22} - \)\(32\!\cdots\!22\)\( T^{23} + \)\(25\!\cdots\!31\)\( T^{24} - \)\(88\!\cdots\!31\)\( T^{25} + \)\(62\!\cdots\!77\)\( T^{26} - \)\(17\!\cdots\!68\)\( T^{27} + \)\(10\!\cdots\!80\)\( T^{28} - \)\(22\!\cdots\!74\)\( T^{29} + \)\(11\!\cdots\!43\)\( T^{30} - \)\(13\!\cdots\!73\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 16 T + 495 T^{2} + 6050 T^{3} + 113951 T^{4} + 1171780 T^{5} + 17167034 T^{6} + 155235590 T^{7} + 1932250763 T^{8} + 15737356112 T^{9} + 173997774810 T^{10} + 1296350731136 T^{11} + 13071897808589 T^{12} + 90097411752159 T^{13} + 842650925264916 T^{14} + 5420034606233581 T^{15} + 47507784898926120 T^{16} + 286983344644693594 T^{17} + 2369437030521116818 T^{18} + 13488217198300598918 T^{19} + \)\(10\!\cdots\!80\)\( T^{20} + \)\(56\!\cdots\!63\)\( T^{21} + \)\(41\!\cdots\!96\)\( T^{22} + \)\(20\!\cdots\!13\)\( T^{23} + \)\(14\!\cdots\!81\)\( T^{24} + \)\(65\!\cdots\!68\)\( T^{25} + \)\(41\!\cdots\!10\)\( T^{26} + \)\(17\!\cdots\!04\)\( T^{27} + \)\(10\!\cdots\!87\)\( T^{28} + \)\(38\!\cdots\!70\)\( T^{29} + \)\(19\!\cdots\!94\)\( T^{30} + \)\(63\!\cdots\!60\)\( T^{31} + \)\(29\!\cdots\!19\)\( T^{32} + \)\(72\!\cdots\!50\)\( T^{33} + \)\(28\!\cdots\!95\)\( T^{34} + \)\(42\!\cdots\!92\)\( T^{35} + \)\(12\!\cdots\!89\)\( T^{36} \))(\( 1 + 38 T + 1150 T^{2} + 25010 T^{3} + 476870 T^{4} + 7731940 T^{5} + 114293441 T^{6} + 1519708722 T^{7} + 18818039723 T^{8} + 215305702324 T^{9} + 2323928628495 T^{10} + 23529641975810 T^{11} + 226609949988761 T^{12} + 2065996834845383 T^{13} + 18011794803701307 T^{14} + 149485335899560340 T^{15} + 1190273264976725636 T^{16} + 9051430963910545387 T^{17} + 66157013579661449878 T^{18} + \)\(46\!\cdots\!68\)\( T^{19} + \)\(31\!\cdots\!66\)\( T^{20} + \)\(19\!\cdots\!83\)\( T^{21} + \)\(12\!\cdots\!28\)\( T^{22} + \)\(72\!\cdots\!40\)\( T^{23} + \)\(41\!\cdots\!49\)\( T^{24} + \)\(22\!\cdots\!07\)\( T^{25} + \)\(11\!\cdots\!43\)\( T^{26} + \)\(56\!\cdots\!10\)\( T^{27} + \)\(26\!\cdots\!65\)\( T^{28} + \)\(11\!\cdots\!76\)\( T^{29} + \)\(46\!\cdots\!69\)\( T^{30} + \)\(17\!\cdots\!02\)\( T^{31} + \)\(62\!\cdots\!07\)\( T^{32} + \)\(19\!\cdots\!60\)\( T^{33} + \)\(57\!\cdots\!10\)\( T^{34} + \)\(14\!\cdots\!10\)\( T^{35} + \)\(30\!\cdots\!50\)\( T^{36} + \)\(47\!\cdots\!82\)\( T^{37} + \)\(58\!\cdots\!83\)\( T^{38} \))(\( 1 + 10 T + 410 T^{2} + 2924 T^{3} + 74508 T^{4} + 369564 T^{5} + 8337951 T^{6} + 25410798 T^{7} + 676920009 T^{8} + 823102432 T^{9} + 44871366433 T^{10} - 22008800274 T^{11} + 2666805696119 T^{12} - 4779578098735 T^{13} + 151310027132785 T^{14} - 361224089366832 T^{15} + 8326064608873626 T^{16} - 19746803414345255 T^{17} + 431107512539224492 T^{18} - 950654574966556240 T^{19} + 20262053089343551124 T^{20} - 43620688742288668295 T^{21} + \)\(86\!\cdots\!98\)\( T^{22} - \)\(17\!\cdots\!92\)\( T^{23} + \)\(34\!\cdots\!95\)\( T^{24} - \)\(51\!\cdots\!15\)\( T^{25} + \)\(13\!\cdots\!97\)\( T^{26} - \)\(52\!\cdots\!14\)\( T^{27} + \)\(50\!\cdots\!11\)\( T^{28} + \)\(43\!\cdots\!68\)\( T^{29} + \)\(16\!\cdots\!27\)\( T^{30} + \)\(29\!\cdots\!18\)\( T^{31} + \)\(45\!\cdots\!77\)\( T^{32} + \)\(94\!\cdots\!16\)\( T^{33} + \)\(89\!\cdots\!44\)\( T^{34} + \)\(16\!\cdots\!04\)\( T^{35} + \)\(10\!\cdots\!70\)\( T^{36} + \)\(12\!\cdots\!90\)\( T^{37} + \)\(58\!\cdots\!83\)\( T^{38} \))
$53$ (\( 1 + T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{14} \))(\( ( 1 + T )^{16} \))(\( ( 1 - T )^{16} \))(\( ( 1 - T )^{18} \))(\( ( 1 - T )^{19} \))(\( ( 1 + T )^{19} \))
$59$ (\( 1 - 8 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 10 T + 135 T^{2} + 590 T^{3} + 3481 T^{4} \))(\( 1 - 40 T + 1337 T^{2} - 30818 T^{3} + 623097 T^{4} - 10457218 T^{5} + 158684633 T^{6} - 2126833635 T^{7} + 26258052370 T^{8} - 294811360877 T^{9} + 3084677672388 T^{10} - 29811027754937 T^{11} + 270372327110233 T^{12} - 2283000111108231 T^{13} + 18151553370670570 T^{14} - 134697006555385629 T^{15} + 941166070670721073 T^{16} - 6122559069281206123 T^{17} + 37378152924965128068 T^{18} - \)\(21\!\cdots\!23\)\( T^{19} + \)\(11\!\cdots\!70\)\( T^{20} - \)\(52\!\cdots\!65\)\( T^{21} + \)\(23\!\cdots\!93\)\( T^{22} - \)\(90\!\cdots\!02\)\( T^{23} + \)\(31\!\cdots\!97\)\( T^{24} - \)\(92\!\cdots\!62\)\( T^{25} + \)\(23\!\cdots\!97\)\( T^{26} - \)\(41\!\cdots\!60\)\( T^{27} + \)\(61\!\cdots\!61\)\( T^{28} \))(\( 1 + 68 T + 2766 T^{2} + 82428 T^{3} + 1983729 T^{4} + 40423560 T^{5} + 719330689 T^{6} + 11402423009 T^{7} + 163334932928 T^{8} + 2136236367158 T^{9} + 25709749259625 T^{10} + 286390529115165 T^{11} + 2966000129602981 T^{12} + 28653217237533355 T^{13} + 258833866143745351 T^{14} + 2189891353297886489 T^{15} + 17369869595881923446 T^{16} + \)\(12\!\cdots\!51\)\( T^{17} + \)\(90\!\cdots\!31\)\( T^{18} + \)\(58\!\cdots\!45\)\( T^{19} + \)\(35\!\cdots\!41\)\( T^{20} + \)\(20\!\cdots\!35\)\( T^{21} + \)\(10\!\cdots\!25\)\( T^{22} + \)\(53\!\cdots\!02\)\( T^{23} + \)\(23\!\cdots\!88\)\( T^{24} + \)\(98\!\cdots\!51\)\( T^{25} + \)\(36\!\cdots\!89\)\( T^{26} + \)\(12\!\cdots\!40\)\( T^{27} + \)\(35\!\cdots\!49\)\( T^{28} + \)\(86\!\cdots\!12\)\( T^{29} + \)\(17\!\cdots\!26\)\( T^{30} + \)\(24\!\cdots\!32\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 + 16 T + 688 T^{2} + 8902 T^{3} + 216711 T^{4} + 2383244 T^{5} + 42883293 T^{6} + 414761855 T^{7} + 6117495852 T^{8} + 53282453600 T^{9} + 679031458405 T^{10} + 5406492775417 T^{11} + 61340081364763 T^{12} + 450064503602175 T^{13} + 4629401546281479 T^{14} + 31388899078298105 T^{15} + 296046936753445626 T^{16} + 1851945045619588195 T^{17} + 16114946782605828399 T^{18} + 92433797685311099325 T^{19} + \)\(74\!\cdots\!43\)\( T^{20} + \)\(38\!\cdots\!83\)\( T^{21} + \)\(28\!\cdots\!05\)\( T^{22} + \)\(13\!\cdots\!00\)\( T^{23} + \)\(89\!\cdots\!92\)\( T^{24} + \)\(35\!\cdots\!45\)\( T^{25} + \)\(21\!\cdots\!93\)\( T^{26} + \)\(71\!\cdots\!96\)\( T^{27} + \)\(38\!\cdots\!91\)\( T^{28} + \)\(93\!\cdots\!58\)\( T^{29} + \)\(42\!\cdots\!68\)\( T^{30} + \)\(58\!\cdots\!84\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 - 62 T + 2328 T^{2} - 64324 T^{3} + 1446736 T^{4} - 27727366 T^{5} + 467586789 T^{6} - 7077224537 T^{7} + 97638557969 T^{8} - 1241377903222 T^{9} + 14677589069572 T^{10} - 162515357910088 T^{11} + 1695157313655979 T^{12} - 16735815744791123 T^{13} + 157022668756943006 T^{14} - 1404475678972057166 T^{15} + 12006335652128876231 T^{16} - 98264701195289252354 T^{17} + \)\(77\!\cdots\!66\)\( T^{18} - \)\(57\!\cdots\!86\)\( T^{19} + \)\(41\!\cdots\!11\)\( T^{20} - \)\(28\!\cdots\!14\)\( T^{21} + \)\(19\!\cdots\!66\)\( T^{22} - \)\(11\!\cdots\!77\)\( T^{23} + \)\(71\!\cdots\!39\)\( T^{24} - \)\(40\!\cdots\!72\)\( T^{25} + \)\(21\!\cdots\!12\)\( T^{26} - \)\(10\!\cdots\!58\)\( T^{27} + \)\(49\!\cdots\!69\)\( T^{28} - \)\(21\!\cdots\!83\)\( T^{29} + \)\(83\!\cdots\!09\)\( T^{30} - \)\(29\!\cdots\!14\)\( T^{31} + \)\(89\!\cdots\!96\)\( T^{32} - \)\(23\!\cdots\!76\)\( T^{33} + \)\(50\!\cdots\!48\)\( T^{34} - \)\(78\!\cdots\!78\)\( T^{35} + \)\(75\!\cdots\!21\)\( T^{36} \))(\( 1 + 42 T + 1479 T^{2} + 36470 T^{3} + 788052 T^{4} + 14233878 T^{5} + 231817749 T^{6} + 3336861869 T^{7} + 44031717326 T^{8} + 526100064035 T^{9} + 5817876603913 T^{10} + 58942689911138 T^{11} + 555997444994989 T^{12} + 4836778904898425 T^{13} + 39447908528521659 T^{14} + 299650495262015145 T^{15} + 2179074027701053279 T^{16} + 15273599798588304300 T^{17} + \)\(10\!\cdots\!39\)\( T^{18} + \)\(80\!\cdots\!88\)\( T^{19} + \)\(64\!\cdots\!01\)\( T^{20} + \)\(53\!\cdots\!00\)\( T^{21} + \)\(44\!\cdots\!41\)\( T^{22} + \)\(36\!\cdots\!45\)\( T^{23} + \)\(28\!\cdots\!41\)\( T^{24} + \)\(20\!\cdots\!25\)\( T^{25} + \)\(13\!\cdots\!91\)\( T^{26} + \)\(86\!\cdots\!98\)\( T^{27} + \)\(50\!\cdots\!07\)\( T^{28} + \)\(26\!\cdots\!35\)\( T^{29} + \)\(13\!\cdots\!34\)\( T^{30} + \)\(59\!\cdots\!89\)\( T^{31} + \)\(24\!\cdots\!71\)\( T^{32} + \)\(88\!\cdots\!58\)\( T^{33} + \)\(28\!\cdots\!48\)\( T^{34} + \)\(78\!\cdots\!70\)\( T^{35} + \)\(18\!\cdots\!01\)\( T^{36} + \)\(31\!\cdots\!82\)\( T^{37} + \)\(44\!\cdots\!39\)\( T^{38} \))(\( 1 + 42 T + 1437 T^{2} + 35908 T^{3} + 783688 T^{4} + 14704520 T^{5} + 250264581 T^{6} + 3855349225 T^{7} + 55029098010 T^{8} + 728050236353 T^{9} + 9040055859219 T^{10} + 105417674152482 T^{11} + 1163146363340167 T^{12} + 12148061315642921 T^{13} + 120680398523771101 T^{14} + 1140304185354700839 T^{15} + 10282191490511778065 T^{16} + 88437089706176717756 T^{17} + \)\(72\!\cdots\!01\)\( T^{18} + \)\(57\!\cdots\!12\)\( T^{19} + \)\(42\!\cdots\!59\)\( T^{20} + \)\(30\!\cdots\!36\)\( T^{21} + \)\(21\!\cdots\!35\)\( T^{22} + \)\(13\!\cdots\!79\)\( T^{23} + \)\(86\!\cdots\!99\)\( T^{24} + \)\(51\!\cdots\!61\)\( T^{25} + \)\(28\!\cdots\!73\)\( T^{26} + \)\(15\!\cdots\!22\)\( T^{27} + \)\(78\!\cdots\!41\)\( T^{28} + \)\(37\!\cdots\!53\)\( T^{29} + \)\(16\!\cdots\!90\)\( T^{30} + \)\(68\!\cdots\!25\)\( T^{31} + \)\(26\!\cdots\!99\)\( T^{32} + \)\(91\!\cdots\!20\)\( T^{33} + \)\(28\!\cdots\!12\)\( T^{34} + \)\(77\!\cdots\!28\)\( T^{35} + \)\(18\!\cdots\!03\)\( T^{36} + \)\(31\!\cdots\!82\)\( T^{37} + \)\(44\!\cdots\!39\)\( T^{38} \))
$61$ (\( 1 + T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 114 T^{2} + 3721 T^{4} \))(\( 1 + 17 T + 563 T^{2} + 8418 T^{3} + 159611 T^{4} + 2068214 T^{5} + 29652654 T^{6} + 336374103 T^{7} + 4014598774 T^{8} + 40439625170 T^{9} + 419447219459 T^{10} + 3791142201655 T^{11} + 34939881581887 T^{12} + 284942480536235 T^{13} + 2360372703586278 T^{14} + 17381491312710335 T^{15} + 130011299366201527 T^{16} + 860517248073853555 T^{17} + 5807599508521420019 T^{18} + 34155157832408496170 T^{19} + \)\(20\!\cdots\!14\)\( T^{20} + \)\(10\!\cdots\!63\)\( T^{21} + \)\(56\!\cdots\!74\)\( T^{22} + \)\(24\!\cdots\!74\)\( T^{23} + \)\(11\!\cdots\!11\)\( T^{24} + \)\(36\!\cdots\!98\)\( T^{25} + \)\(14\!\cdots\!23\)\( T^{26} + \)\(27\!\cdots\!77\)\( T^{27} + \)\(98\!\cdots\!41\)\( T^{28} \))(\( 1 + 31 T + 990 T^{2} + 19721 T^{3} + 380219 T^{4} + 5813991 T^{5} + 85505650 T^{6} + 1090934191 T^{7} + 13396447401 T^{8} + 149418376457 T^{9} + 1603867822527 T^{10} + 16052005400782 T^{11} + 154366331852934 T^{12} + 1405259312368136 T^{13} + 12269877985390876 T^{14} + 102244431492827627 T^{15} + 816352635357819980 T^{16} + 6236910321062485247 T^{17} + 45656215983639449596 T^{18} + \)\(31\!\cdots\!16\)\( T^{19} + \)\(21\!\cdots\!94\)\( T^{20} + \)\(13\!\cdots\!82\)\( T^{21} + \)\(82\!\cdots\!47\)\( T^{22} + \)\(46\!\cdots\!97\)\( T^{23} + \)\(25\!\cdots\!81\)\( T^{24} + \)\(12\!\cdots\!31\)\( T^{25} + \)\(60\!\cdots\!50\)\( T^{26} + \)\(25\!\cdots\!51\)\( T^{27} + \)\(10\!\cdots\!99\)\( T^{28} + \)\(31\!\cdots\!01\)\( T^{29} + \)\(97\!\cdots\!90\)\( T^{30} + \)\(18\!\cdots\!31\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 + 37 T + 1242 T^{2} + 28229 T^{3} + 583225 T^{4} + 9979253 T^{5} + 157808714 T^{6} + 2210489625 T^{7} + 28982695259 T^{8} + 347233840585 T^{9} + 3928601646587 T^{10} + 41297497234622 T^{11} + 412406675333858 T^{12} + 3862460069335186 T^{13} + 34492525411224920 T^{14} + 290293904710737579 T^{15} + 2333710352764141040 T^{16} + 17707928187354992319 T^{17} + \)\(12\!\cdots\!20\)\( T^{18} + \)\(87\!\cdots\!66\)\( T^{19} + \)\(57\!\cdots\!78\)\( T^{20} + \)\(34\!\cdots\!22\)\( T^{21} + \)\(20\!\cdots\!07\)\( T^{22} + \)\(10\!\cdots\!85\)\( T^{23} + \)\(55\!\cdots\!79\)\( T^{24} + \)\(25\!\cdots\!25\)\( T^{25} + \)\(11\!\cdots\!14\)\( T^{26} + \)\(43\!\cdots\!33\)\( T^{27} + \)\(15\!\cdots\!25\)\( T^{28} + \)\(45\!\cdots\!49\)\( T^{29} + \)\(12\!\cdots\!22\)\( T^{30} + \)\(22\!\cdots\!37\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 - 6 T + 554 T^{2} - 1816 T^{3} + 148300 T^{4} - 153091 T^{5} + 26668389 T^{6} + 22312782 T^{7} + 3715675085 T^{8} + 8404463533 T^{9} + 430176393115 T^{10} + 1374951844003 T^{11} + 42687110995306 T^{12} + 157342704810381 T^{13} + 3674167989748531 T^{14} + 14091791239068026 T^{15} + 275391395691850404 T^{16} + 1032528715192896256 T^{17} + 17992335698313827830 T^{18} + 62984251626766671616 T^{19} + \)\(10\!\cdots\!84\)\( T^{20} + \)\(31\!\cdots\!06\)\( T^{21} + \)\(50\!\cdots\!71\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{23} + \)\(21\!\cdots\!66\)\( T^{24} + \)\(43\!\cdots\!63\)\( T^{25} + \)\(82\!\cdots\!15\)\( T^{26} + \)\(98\!\cdots\!53\)\( T^{27} + \)\(26\!\cdots\!85\)\( T^{28} + \)\(97\!\cdots\!02\)\( T^{29} + \)\(70\!\cdots\!69\)\( T^{30} - \)\(24\!\cdots\!71\)\( T^{31} + \)\(14\!\cdots\!00\)\( T^{32} - \)\(10\!\cdots\!16\)\( T^{33} + \)\(20\!\cdots\!94\)\( T^{34} - \)\(13\!\cdots\!26\)\( T^{35} + \)\(13\!\cdots\!81\)\( T^{36} \))(\( 1 - 10 T + 543 T^{2} - 5548 T^{3} + 153096 T^{4} - 1498681 T^{5} + 29122543 T^{6} - 266283727 T^{7} + 4141325224 T^{8} - 35118407575 T^{9} + 467534822796 T^{10} - 3676048919452 T^{11} + 43755404517805 T^{12} - 320268103345016 T^{13} + 3519574826729115 T^{14} - 24184785158723479 T^{15} + 251611674491655029 T^{16} - 1643166156184010454 T^{17} + 16463818166473937916 T^{18} - \)\(10\!\cdots\!00\)\( T^{19} + \)\(10\!\cdots\!76\)\( T^{20} - \)\(61\!\cdots\!34\)\( T^{21} + \)\(57\!\cdots\!49\)\( T^{22} - \)\(33\!\cdots\!39\)\( T^{23} + \)\(29\!\cdots\!15\)\( T^{24} - \)\(16\!\cdots\!76\)\( T^{25} + \)\(13\!\cdots\!05\)\( T^{26} - \)\(70\!\cdots\!12\)\( T^{27} + \)\(54\!\cdots\!36\)\( T^{28} - \)\(25\!\cdots\!75\)\( T^{29} + \)\(18\!\cdots\!64\)\( T^{30} - \)\(70\!\cdots\!67\)\( T^{31} + \)\(47\!\cdots\!83\)\( T^{32} - \)\(14\!\cdots\!21\)\( T^{33} + \)\(92\!\cdots\!96\)\( T^{34} - \)\(20\!\cdots\!28\)\( T^{35} + \)\(12\!\cdots\!03\)\( T^{36} - \)\(13\!\cdots\!10\)\( T^{37} + \)\(83\!\cdots\!41\)\( T^{38} \))(\( 1 + 16 T + 889 T^{2} + 11688 T^{3} + 363492 T^{4} + 4051921 T^{5} + 92617529 T^{6} + 893575483 T^{7} + 16741910902 T^{8} + 141844013523 T^{9} + 2312963750440 T^{10} + 17405541022862 T^{11} + 256709771629249 T^{12} + 1734192513547734 T^{13} + 23740667487063313 T^{14} + 145679062239043683 T^{15} + 1880435277192588223 T^{16} + 10625141993427481710 T^{17} + \)\(13\!\cdots\!94\)\( T^{18} + \)\(68\!\cdots\!00\)\( T^{19} + \)\(79\!\cdots\!34\)\( T^{20} + \)\(39\!\cdots\!10\)\( T^{21} + \)\(42\!\cdots\!63\)\( T^{22} + \)\(20\!\cdots\!03\)\( T^{23} + \)\(20\!\cdots\!13\)\( T^{24} + \)\(89\!\cdots\!74\)\( T^{25} + \)\(80\!\cdots\!29\)\( T^{26} + \)\(33\!\cdots\!22\)\( T^{27} + \)\(27\!\cdots\!40\)\( T^{28} + \)\(10\!\cdots\!23\)\( T^{29} + \)\(72\!\cdots\!22\)\( T^{30} + \)\(23\!\cdots\!43\)\( T^{31} + \)\(14\!\cdots\!49\)\( T^{32} + \)\(40\!\cdots\!61\)\( T^{33} + \)\(21\!\cdots\!92\)\( T^{34} + \)\(42\!\cdots\!68\)\( T^{35} + \)\(19\!\cdots\!69\)\( T^{36} + \)\(21\!\cdots\!96\)\( T^{37} + \)\(83\!\cdots\!41\)\( T^{38} \))
$67$ (\( 1 + 8 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 18 T + 207 T^{2} + 1206 T^{3} + 4489 T^{4} \))(\( 1 - 44 T + 1544 T^{2} - 38444 T^{3} + 828968 T^{4} - 15051986 T^{5} + 245688394 T^{6} - 3569176505 T^{7} + 47552884333 T^{8} - 578173590581 T^{9} + 6521426050967 T^{10} - 67992582975052 T^{11} + 661864939553547 T^{12} - 5993105759666806 T^{13} + 50814237020853780 T^{14} - 401538085897676002 T^{15} + 2971111713655872483 T^{16} - 20449653233325564676 T^{17} + \)\(13\!\cdots\!07\)\( T^{18} - \)\(78\!\cdots\!67\)\( T^{19} + \)\(43\!\cdots\!77\)\( T^{20} - \)\(21\!\cdots\!15\)\( T^{21} + \)\(99\!\cdots\!54\)\( T^{22} - \)\(40\!\cdots\!42\)\( T^{23} + \)\(15\!\cdots\!32\)\( T^{24} - \)\(46\!\cdots\!52\)\( T^{25} + \)\(12\!\cdots\!84\)\( T^{26} - \)\(24\!\cdots\!28\)\( T^{27} + \)\(36\!\cdots\!29\)\( T^{28} \))(\( 1 + 6 T + 529 T^{2} + 2000 T^{3} + 130957 T^{4} + 254178 T^{5} + 20838386 T^{6} + 7567779 T^{7} + 2461030461 T^{8} - 2246275218 T^{9} + 236880153410 T^{10} - 413297710318 T^{11} + 19914285994877 T^{12} - 41179261038717 T^{13} + 1520317794779488 T^{14} - 3133541728212964 T^{15} + 106413318865108718 T^{16} - 209947295790268588 T^{17} + 6824706580765121632 T^{18} - 12385198087787641071 T^{19} + \)\(40\!\cdots\!17\)\( T^{20} - \)\(55\!\cdots\!26\)\( T^{21} + \)\(21\!\cdots\!90\)\( T^{22} - \)\(13\!\cdots\!14\)\( T^{23} + \)\(99\!\cdots\!01\)\( T^{24} + \)\(20\!\cdots\!13\)\( T^{25} + \)\(37\!\cdots\!14\)\( T^{26} + \)\(31\!\cdots\!74\)\( T^{27} + \)\(10\!\cdots\!77\)\( T^{28} + \)\(10\!\cdots\!00\)\( T^{29} + \)\(19\!\cdots\!41\)\( T^{30} + \)\(14\!\cdots\!58\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 + 32 T + 1221 T^{2} + 26072 T^{3} + 582739 T^{4} + 9419168 T^{5} + 154904030 T^{6} + 2006807079 T^{7} + 26383268251 T^{8} + 282440229040 T^{9} + 3105779439812 T^{10} + 28081456257818 T^{11} + 269023273477425 T^{12} + 2122868858362433 T^{13} + 18845754609835294 T^{14} + 139223776748651360 T^{15} + 1241782896620657294 T^{16} + 9327993042159641120 T^{17} + 84598592443550634766 T^{18} + \)\(63\!\cdots\!79\)\( T^{19} + \)\(54\!\cdots\!25\)\( T^{20} + \)\(37\!\cdots\!26\)\( T^{21} + \)\(28\!\cdots\!28\)\( T^{22} + \)\(17\!\cdots\!20\)\( T^{23} + \)\(10\!\cdots\!91\)\( T^{24} + \)\(54\!\cdots\!13\)\( T^{25} + \)\(28\!\cdots\!70\)\( T^{26} + \)\(11\!\cdots\!44\)\( T^{27} + \)\(47\!\cdots\!79\)\( T^{28} + \)\(14\!\cdots\!64\)\( T^{29} + \)\(44\!\cdots\!09\)\( T^{30} + \)\(78\!\cdots\!76\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 28 T + 1041 T^{2} - 21246 T^{3} + 474574 T^{4} - 7810632 T^{5} + 133153719 T^{6} - 1863988157 T^{7} + 26482597386 T^{8} - 325627918416 T^{9} + 4030120974158 T^{10} - 44447128232127 T^{11} + 491784920347906 T^{12} - 4933875059791447 T^{13} + 49604696680863378 T^{14} - 456938731184534620 T^{15} + 4217131436822658593 T^{16} - 35860313996308275203 T^{17} + \)\(30\!\cdots\!84\)\( T^{18} - \)\(24\!\cdots\!01\)\( T^{19} + \)\(18\!\cdots\!77\)\( T^{20} - \)\(13\!\cdots\!60\)\( T^{21} + \)\(99\!\cdots\!38\)\( T^{22} - \)\(66\!\cdots\!29\)\( T^{23} + \)\(44\!\cdots\!14\)\( T^{24} - \)\(26\!\cdots\!21\)\( T^{25} + \)\(16\!\cdots\!78\)\( T^{26} - \)\(88\!\cdots\!52\)\( T^{27} + \)\(48\!\cdots\!14\)\( T^{28} - \)\(22\!\cdots\!31\)\( T^{29} + \)\(10\!\cdots\!59\)\( T^{30} - \)\(42\!\cdots\!84\)\( T^{31} + \)\(17\!\cdots\!46\)\( T^{32} - \)\(52\!\cdots\!78\)\( T^{33} + \)\(17\!\cdots\!21\)\( T^{34} - \)\(30\!\cdots\!56\)\( T^{35} + \)\(74\!\cdots\!09\)\( T^{36} \))(\( 1 + 30 T + 940 T^{2} + 19278 T^{3} + 375839 T^{4} + 6008120 T^{5} + 90536521 T^{6} + 1198811701 T^{7} + 15021362785 T^{8} + 170146259377 T^{9} + 1832283292152 T^{10} + 18070441562637 T^{11} + 170223290053988 T^{12} + 1478033727414392 T^{13} + 12363463303405120 T^{14} + 96102583859729261 T^{15} + 737716712083277145 T^{16} + 5411483302613204793 T^{17} + 41675008474750816185 T^{18} + \)\(32\!\cdots\!30\)\( T^{19} + \)\(27\!\cdots\!95\)\( T^{20} + \)\(24\!\cdots\!77\)\( T^{21} + \)\(22\!\cdots\!35\)\( T^{22} + \)\(19\!\cdots\!81\)\( T^{23} + \)\(16\!\cdots\!40\)\( T^{24} + \)\(13\!\cdots\!48\)\( T^{25} + \)\(10\!\cdots\!24\)\( T^{26} + \)\(73\!\cdots\!17\)\( T^{27} + \)\(49\!\cdots\!44\)\( T^{28} + \)\(31\!\cdots\!73\)\( T^{29} + \)\(18\!\cdots\!55\)\( T^{30} + \)\(98\!\cdots\!61\)\( T^{31} + \)\(49\!\cdots\!27\)\( T^{32} + \)\(22\!\cdots\!80\)\( T^{33} + \)\(92\!\cdots\!77\)\( T^{34} + \)\(31\!\cdots\!18\)\( T^{35} + \)\(10\!\cdots\!80\)\( T^{36} + \)\(22\!\cdots\!70\)\( T^{37} + \)\(49\!\cdots\!03\)\( T^{38} \))(\( 1 + 40 T + 1404 T^{2} + 33412 T^{3} + 717037 T^{4} + 12706444 T^{5} + 208734735 T^{6} + 3036141557 T^{7} + 41764576545 T^{8} + 526758541117 T^{9} + 6367146355938 T^{10} + 71954807174033 T^{11} + 785655419135568 T^{12} + 8110990685116428 T^{13} + 81301548448579178 T^{14} + 775724963262417161 T^{15} + 7207486990379313001 T^{16} + 63987960543377212971 T^{17} + \)\(55\!\cdots\!49\)\( T^{18} + \)\(45\!\cdots\!02\)\( T^{19} + \)\(37\!\cdots\!83\)\( T^{20} + \)\(28\!\cdots\!19\)\( T^{21} + \)\(21\!\cdots\!63\)\( T^{22} + \)\(15\!\cdots\!81\)\( T^{23} + \)\(10\!\cdots\!46\)\( T^{24} + \)\(73\!\cdots\!32\)\( T^{25} + \)\(47\!\cdots\!64\)\( T^{26} + \)\(29\!\cdots\!53\)\( T^{27} + \)\(17\!\cdots\!86\)\( T^{28} + \)\(96\!\cdots\!33\)\( T^{29} + \)\(51\!\cdots\!35\)\( T^{30} + \)\(24\!\cdots\!77\)\( T^{31} + \)\(11\!\cdots\!45\)\( T^{32} + \)\(46\!\cdots\!76\)\( T^{33} + \)\(17\!\cdots\!91\)\( T^{34} + \)\(55\!\cdots\!72\)\( T^{35} + \)\(15\!\cdots\!08\)\( T^{36} + \)\(29\!\cdots\!60\)\( T^{37} + \)\(49\!\cdots\!03\)\( T^{38} \))
$71$ (\( 1 + 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 16 T + 198 T^{2} - 1136 T^{3} + 5041 T^{4} \))(\( 1 - 15 T + 773 T^{2} - 9412 T^{3} + 268131 T^{4} - 2734949 T^{5} + 56634770 T^{6} - 494882779 T^{7} + 8334485402 T^{8} - 63604728984 T^{9} + 929947034542 T^{10} - 6328264130415 T^{11} + 83891015907275 T^{12} - 520949969918046 T^{13} + 6412123471948672 T^{14} - 36987447864181266 T^{15} + 422894611188573275 T^{16} - 2264955343180963065 T^{17} + 23631517388677285102 T^{18} - \)\(11\!\cdots\!84\)\( T^{19} + \)\(10\!\cdots\!42\)\( T^{20} - \)\(45\!\cdots\!89\)\( T^{21} + \)\(36\!\cdots\!70\)\( T^{22} - \)\(12\!\cdots\!19\)\( T^{23} + \)\(87\!\cdots\!31\)\( T^{24} - \)\(21\!\cdots\!52\)\( T^{25} + \)\(12\!\cdots\!93\)\( T^{26} - \)\(17\!\cdots\!65\)\( T^{27} + \)\(82\!\cdots\!81\)\( T^{28} \))(\( 1 + 25 T + 639 T^{2} + 9334 T^{3} + 141556 T^{4} + 1527624 T^{5} + 18690949 T^{6} + 175454279 T^{7} + 2008716051 T^{8} + 17614257165 T^{9} + 192675802684 T^{10} + 1577549542334 T^{11} + 16468959666765 T^{12} + 126281116122362 T^{13} + 1268819185096366 T^{14} + 9253524118031829 T^{15} + 91445198043105346 T^{16} + 657000212380259859 T^{17} + 6396117512070781006 T^{18} + 45197400552470705782 T^{19} + \)\(41\!\cdots\!65\)\( T^{20} + \)\(28\!\cdots\!34\)\( T^{21} + \)\(24\!\cdots\!64\)\( T^{22} + \)\(16\!\cdots\!15\)\( T^{23} + \)\(12\!\cdots\!11\)\( T^{24} + \)\(80\!\cdots\!49\)\( T^{25} + \)\(60\!\cdots\!49\)\( T^{26} + \)\(35\!\cdots\!04\)\( T^{27} + \)\(23\!\cdots\!96\)\( T^{28} + \)\(10\!\cdots\!74\)\( T^{29} + \)\(52\!\cdots\!59\)\( T^{30} + \)\(14\!\cdots\!75\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 + 3 T + 633 T^{2} + 2314 T^{3} + 201588 T^{4} + 825112 T^{5} + 43165687 T^{6} + 186897489 T^{7} + 6972216401 T^{8} + 30702713341 T^{9} + 900770964750 T^{10} + 3920726315338 T^{11} + 96233812172181 T^{12} + 404635889044416 T^{13} + 8669764567677772 T^{14} + 34474424892425443 T^{15} + 665655056726287302 T^{16} + 2447684167362206453 T^{17} + 43704283185663648652 T^{18} + \)\(14\!\cdots\!76\)\( T^{19} + \)\(24\!\cdots\!61\)\( T^{20} + \)\(70\!\cdots\!38\)\( T^{21} + \)\(11\!\cdots\!50\)\( T^{22} + \)\(27\!\cdots\!31\)\( T^{23} + \)\(45\!\cdots\!61\)\( T^{24} + \)\(85\!\cdots\!59\)\( T^{25} + \)\(14\!\cdots\!87\)\( T^{26} + \)\(19\!\cdots\!52\)\( T^{27} + \)\(33\!\cdots\!08\)\( T^{28} + \)\(26\!\cdots\!54\)\( T^{29} + \)\(52\!\cdots\!73\)\( T^{30} + \)\(17\!\cdots\!53\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 - 37 T + 1123 T^{2} - 23396 T^{3} + 434101 T^{4} - 6711453 T^{5} + 97394048 T^{6} - 1271367825 T^{7} + 16068133539 T^{8} - 188895317661 T^{9} + 2168422804739 T^{10} - 23403209518319 T^{11} + 246866604036180 T^{12} - 2465584429896605 T^{13} + 24157829569582502 T^{14} - 225631860051124005 T^{15} + 2072742352725685667 T^{16} - 18188347415371237013 T^{17} + \)\(15\!\cdots\!84\)\( T^{18} - \)\(12\!\cdots\!23\)\( T^{19} + \)\(10\!\cdots\!47\)\( T^{20} - \)\(80\!\cdots\!55\)\( T^{21} + \)\(61\!\cdots\!62\)\( T^{22} - \)\(44\!\cdots\!55\)\( T^{23} + \)\(31\!\cdots\!80\)\( T^{24} - \)\(21\!\cdots\!29\)\( T^{25} + \)\(14\!\cdots\!79\)\( T^{26} - \)\(86\!\cdots\!91\)\( T^{27} + \)\(52\!\cdots\!39\)\( T^{28} - \)\(29\!\cdots\!75\)\( T^{29} + \)\(15\!\cdots\!68\)\( T^{30} - \)\(78\!\cdots\!83\)\( T^{31} + \)\(35\!\cdots\!81\)\( T^{32} - \)\(13\!\cdots\!96\)\( T^{33} + \)\(46\!\cdots\!83\)\( T^{34} - \)\(10\!\cdots\!67\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))(\( 1 + 41 T + 1509 T^{2} + 39082 T^{3} + 907735 T^{4} + 17903899 T^{5} + 323694718 T^{6} + 5270762793 T^{7} + 79988192556 T^{8} + 1122936425000 T^{9} + 14860939024353 T^{10} + 184654216179074 T^{11} + 2179927604128140 T^{12} + 24384099640530480 T^{13} + 260555430054062731 T^{14} + 2653335411637183915 T^{15} + 25905058653312917017 T^{16} + \)\(24\!\cdots\!90\)\( T^{17} + \)\(21\!\cdots\!42\)\( T^{18} + \)\(18\!\cdots\!72\)\( T^{19} + \)\(15\!\cdots\!82\)\( T^{20} + \)\(12\!\cdots\!90\)\( T^{21} + \)\(92\!\cdots\!87\)\( T^{22} + \)\(67\!\cdots\!15\)\( T^{23} + \)\(47\!\cdots\!81\)\( T^{24} + \)\(31\!\cdots\!80\)\( T^{25} + \)\(19\!\cdots\!40\)\( T^{26} + \)\(11\!\cdots\!14\)\( T^{27} + \)\(68\!\cdots\!43\)\( T^{28} + \)\(36\!\cdots\!00\)\( T^{29} + \)\(18\!\cdots\!76\)\( T^{30} + \)\(86\!\cdots\!13\)\( T^{31} + \)\(37\!\cdots\!98\)\( T^{32} + \)\(14\!\cdots\!19\)\( T^{33} + \)\(53\!\cdots\!85\)\( T^{34} + \)\(16\!\cdots\!22\)\( T^{35} + \)\(44\!\cdots\!19\)\( T^{36} + \)\(86\!\cdots\!01\)\( T^{37} + \)\(14\!\cdots\!31\)\( T^{38} \))(\( 1 + 23 T + 955 T^{2} + 17618 T^{3} + 422599 T^{4} + 6499629 T^{5} + 116480658 T^{6} + 1540461399 T^{7} + 22746261430 T^{8} + 265401098902 T^{9} + 3405264418039 T^{10} + 35855042136230 T^{11} + 414052400443396 T^{12} + 4012010402572428 T^{13} + 42718793295009279 T^{14} + 386506322943583533 T^{15} + 3849532999740285227 T^{16} + 32777280079344729930 T^{17} + \)\(30\!\cdots\!54\)\( T^{18} + \)\(24\!\cdots\!96\)\( T^{19} + \)\(21\!\cdots\!34\)\( T^{20} + \)\(16\!\cdots\!30\)\( T^{21} + \)\(13\!\cdots\!97\)\( T^{22} + \)\(98\!\cdots\!73\)\( T^{23} + \)\(77\!\cdots\!29\)\( T^{24} + \)\(51\!\cdots\!88\)\( T^{25} + \)\(37\!\cdots\!36\)\( T^{26} + \)\(23\!\cdots\!30\)\( T^{27} + \)\(15\!\cdots\!09\)\( T^{28} + \)\(86\!\cdots\!02\)\( T^{29} + \)\(52\!\cdots\!30\)\( T^{30} + \)\(25\!\cdots\!59\)\( T^{31} + \)\(13\!\cdots\!38\)\( T^{32} + \)\(53\!\cdots\!49\)\( T^{33} + \)\(24\!\cdots\!49\)\( T^{34} + \)\(73\!\cdots\!78\)\( T^{35} + \)\(28\!\cdots\!05\)\( T^{36} + \)\(48\!\cdots\!03\)\( T^{37} + \)\(14\!\cdots\!31\)\( T^{38} \))
$73$ (\( 1 + 3 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 74 T^{2} + 5329 T^{4} \))(\( 1 - 4 T + 695 T^{2} - 2019 T^{3} + 226838 T^{4} - 394577 T^{5} + 46322446 T^{6} - 23376477 T^{7} + 6689652549 T^{8} + 4951730685 T^{9} + 739089649796 T^{10} + 1345783032182 T^{11} + 66703273074867 T^{12} + 161806140788374 T^{13} + 5187528896272664 T^{14} + 11811848277551302 T^{15} + 355461742215966243 T^{16} + 523532477830345094 T^{17} + 20988845995512408836 T^{18} + 10265292219259931205 T^{19} + \)\(10\!\cdots\!61\)\( T^{20} - \)\(25\!\cdots\!69\)\( T^{21} + \)\(37\!\cdots\!26\)\( T^{22} - \)\(23\!\cdots\!01\)\( T^{23} + \)\(97\!\cdots\!62\)\( T^{24} - \)\(63\!\cdots\!63\)\( T^{25} + \)\(15\!\cdots\!95\)\( T^{26} - \)\(66\!\cdots\!32\)\( T^{27} + \)\(12\!\cdots\!09\)\( T^{28} \))(\( 1 - 2 T + 670 T^{2} - 1481 T^{3} + 209514 T^{4} - 532594 T^{5} + 40763773 T^{6} - 124208957 T^{7} + 5553617171 T^{8} - 21124442243 T^{9} + 567442474445 T^{10} - 2788616165432 T^{11} + 46181184823616 T^{12} - 296573288631319 T^{13} + 3271416692301613 T^{14} - 25988343877536040 T^{15} + 230281145016089434 T^{16} - 1897149103060130920 T^{17} + 17433379553275295677 T^{18} - \)\(11\!\cdots\!23\)\( T^{19} + \)\(13\!\cdots\!56\)\( T^{20} - \)\(57\!\cdots\!76\)\( T^{21} + \)\(85\!\cdots\!05\)\( T^{22} - \)\(23\!\cdots\!71\)\( T^{23} + \)\(44\!\cdots\!51\)\( T^{24} - \)\(73\!\cdots\!41\)\( T^{25} + \)\(17\!\cdots\!77\)\( T^{26} - \)\(16\!\cdots\!38\)\( T^{27} + \)\(47\!\cdots\!94\)\( T^{28} - \)\(24\!\cdots\!73\)\( T^{29} + \)\(81\!\cdots\!30\)\( T^{30} - \)\(17\!\cdots\!14\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 + 44 T + 1602 T^{2} + 40541 T^{3} + 888110 T^{4} + 16120166 T^{5} + 260118297 T^{6} + 3668819955 T^{7} + 46601489237 T^{8} + 528047201365 T^{9} + 5409495860729 T^{10} + 49765166620146 T^{11} + 414005720410020 T^{12} + 3123478835330113 T^{13} + 21940378118253457 T^{14} + 153426054724900966 T^{15} + 1196261067711484530 T^{16} + 11200101994917770518 T^{17} + \)\(11\!\cdots\!53\)\( T^{18} + \)\(12\!\cdots\!21\)\( T^{19} + \)\(11\!\cdots\!20\)\( T^{20} + \)\(10\!\cdots\!78\)\( T^{21} + \)\(81\!\cdots\!81\)\( T^{22} + \)\(58\!\cdots\!05\)\( T^{23} + \)\(37\!\cdots\!97\)\( T^{24} + \)\(21\!\cdots\!15\)\( T^{25} + \)\(11\!\cdots\!53\)\( T^{26} + \)\(50\!\cdots\!82\)\( T^{27} + \)\(20\!\cdots\!10\)\( T^{28} + \)\(67\!\cdots\!53\)\( T^{29} + \)\(19\!\cdots\!18\)\( T^{30} + \)\(39\!\cdots\!08\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 - 5 T + 647 T^{2} - 4261 T^{3} + 218097 T^{4} - 1716183 T^{5} + 50795828 T^{6} - 444627129 T^{7} + 9136992715 T^{8} - 84184954193 T^{9} + 1341315004731 T^{10} - 12469025915868 T^{11} + 165496845805492 T^{12} - 1504620655562629 T^{13} + 17437942540489868 T^{14} - 151681527292031405 T^{15} + 1582318992948052183 T^{16} - 12966593350367749599 T^{17} + \)\(12\!\cdots\!28\)\( T^{18} - \)\(94\!\cdots\!27\)\( T^{19} + \)\(84\!\cdots\!07\)\( T^{20} - \)\(59\!\cdots\!85\)\( T^{21} + \)\(49\!\cdots\!88\)\( T^{22} - \)\(31\!\cdots\!97\)\( T^{23} + \)\(25\!\cdots\!88\)\( T^{24} - \)\(13\!\cdots\!96\)\( T^{25} + \)\(10\!\cdots\!11\)\( T^{26} - \)\(49\!\cdots\!09\)\( T^{27} + \)\(39\!\cdots\!35\)\( T^{28} - \)\(13\!\cdots\!33\)\( T^{29} + \)\(11\!\cdots\!88\)\( T^{30} - \)\(28\!\cdots\!39\)\( T^{31} + \)\(26\!\cdots\!73\)\( T^{32} - \)\(37\!\cdots\!77\)\( T^{33} + \)\(42\!\cdots\!67\)\( T^{34} - \)\(23\!\cdots\!65\)\( T^{35} + \)\(34\!\cdots\!69\)\( T^{36} \))(\( 1 + 3 T + 508 T^{2} + 1130 T^{3} + 135886 T^{4} + 201474 T^{5} + 25196761 T^{6} + 18203876 T^{7} + 3621505577 T^{8} - 101844580 T^{9} + 429902923808 T^{10} - 323089370187 T^{11} + 43922189503839 T^{12} - 62530181001407 T^{13} + 3985026514732594 T^{14} - 7952365220430734 T^{15} + 329660140991120663 T^{16} - 785458672419478066 T^{17} + 25437222388167312475 T^{18} - 63168332724952083242 T^{19} + \)\(18\!\cdots\!75\)\( T^{20} - \)\(41\!\cdots\!14\)\( T^{21} + \)\(12\!\cdots\!71\)\( T^{22} - \)\(22\!\cdots\!94\)\( T^{23} + \)\(82\!\cdots\!42\)\( T^{24} - \)\(94\!\cdots\!23\)\( T^{25} + \)\(48\!\cdots\!83\)\( T^{26} - \)\(26\!\cdots\!47\)\( T^{27} + \)\(25\!\cdots\!04\)\( T^{28} - \)\(43\!\cdots\!20\)\( T^{29} + \)\(11\!\cdots\!29\)\( T^{30} + \)\(41\!\cdots\!96\)\( T^{31} + \)\(42\!\cdots\!13\)\( T^{32} + \)\(24\!\cdots\!66\)\( T^{33} + \)\(12\!\cdots\!02\)\( T^{34} + \)\(73\!\cdots\!30\)\( T^{35} + \)\(24\!\cdots\!24\)\( T^{36} + \)\(10\!\cdots\!07\)\( T^{37} + \)\(25\!\cdots\!37\)\( T^{38} \))(\( 1 - 7 T + 810 T^{2} - 5864 T^{3} + 329614 T^{4} - 2415428 T^{5} + 89797227 T^{6} - 653767388 T^{7} + 18366628685 T^{8} - 130915428434 T^{9} + 2994497590830 T^{10} - 20666321682775 T^{11} + 403239182830053 T^{12} - 2670753703464469 T^{13} + 45862155481527614 T^{14} - 289202339469784394 T^{15} + 4468419516871308693 T^{16} - 26612180908135758830 T^{17} + \)\(37\!\cdots\!09\)\( T^{18} - \)\(20\!\cdots\!98\)\( T^{19} + \)\(27\!\cdots\!57\)\( T^{20} - \)\(14\!\cdots\!70\)\( T^{21} + \)\(17\!\cdots\!81\)\( T^{22} - \)\(82\!\cdots\!54\)\( T^{23} + \)\(95\!\cdots\!02\)\( T^{24} - \)\(40\!\cdots\!41\)\( T^{25} + \)\(44\!\cdots\!41\)\( T^{26} - \)\(16\!\cdots\!75\)\( T^{27} + \)\(17\!\cdots\!90\)\( T^{28} - \)\(56\!\cdots\!66\)\( T^{29} + \)\(57\!\cdots\!45\)\( T^{30} - \)\(14\!\cdots\!48\)\( T^{31} + \)\(15\!\cdots\!91\)\( T^{32} - \)\(29\!\cdots\!52\)\( T^{33} + \)\(29\!\cdots\!98\)\( T^{34} - \)\(38\!\cdots\!04\)\( T^{35} + \)\(38\!\cdots\!30\)\( T^{36} - \)\(24\!\cdots\!83\)\( T^{37} + \)\(25\!\cdots\!37\)\( T^{38} \))
$79$ (\( 1 + 8 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 795 T^{2} + 6719 T^{3} + 308779 T^{4} + 2670969 T^{5} + 77904441 T^{6} + 667441798 T^{7} + 14267899735 T^{8} + 117411468054 T^{9} + 2002494344780 T^{10} + 15413427981531 T^{11} + 221413641160684 T^{12} + 1558512534202665 T^{13} + 19540873909827874 T^{14} + 123122490202010535 T^{15} + 1381842534483828844 T^{16} + 7599421118586062709 T^{17} + 77997316931222927180 T^{18} + \)\(36\!\cdots\!46\)\( T^{19} + \)\(34\!\cdots\!35\)\( T^{20} + \)\(12\!\cdots\!82\)\( T^{21} + \)\(11\!\cdots\!01\)\( T^{22} + \)\(32\!\cdots\!11\)\( T^{23} + \)\(29\!\cdots\!79\)\( T^{24} + \)\(50\!\cdots\!01\)\( T^{25} + \)\(46\!\cdots\!95\)\( T^{26} + \)\(37\!\cdots\!12\)\( T^{27} + \)\(36\!\cdots\!81\)\( T^{28} \))(\( 1 - 8 T + 921 T^{2} - 6357 T^{3} + 403178 T^{4} - 2381465 T^{5} + 112282302 T^{6} - 563955419 T^{7} + 22489972304 T^{8} - 95899071533 T^{9} + 3471905246311 T^{10} - 12651379101643 T^{11} + 431343158277833 T^{12} - 1365848189821101 T^{13} + 44291214145067272 T^{14} - 125021027995904552 T^{15} + 3812905738021803180 T^{16} - 9876661211676459608 T^{17} + \)\(27\!\cdots\!52\)\( T^{18} - \)\(67\!\cdots\!39\)\( T^{19} + \)\(16\!\cdots\!73\)\( T^{20} - \)\(38\!\cdots\!57\)\( T^{21} + \)\(84\!\cdots\!31\)\( T^{22} - \)\(18\!\cdots\!47\)\( T^{23} + \)\(34\!\cdots\!44\)\( T^{24} - \)\(67\!\cdots\!61\)\( T^{25} + \)\(10\!\cdots\!02\)\( T^{26} - \)\(17\!\cdots\!35\)\( T^{27} + \)\(23\!\cdots\!98\)\( T^{28} - \)\(29\!\cdots\!23\)\( T^{29} + \)\(33\!\cdots\!01\)\( T^{30} - \)\(23\!\cdots\!92\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 + 36 T + 1121 T^{2} + 24397 T^{3} + 477052 T^{4} + 7913113 T^{5} + 121717384 T^{6} + 1697299405 T^{7} + 22390352214 T^{8} + 275874381223 T^{9} + 3249758780987 T^{10} + 36242676003265 T^{11} + 388358346375551 T^{12} + 3965124160758541 T^{13} + 39012793937862718 T^{14} + 367044045373016358 T^{15} + 3334011710482810584 T^{16} + 28996479584468292282 T^{17} + \)\(24\!\cdots\!38\)\( T^{18} + \)\(19\!\cdots\!99\)\( T^{19} + \)\(15\!\cdots\!31\)\( T^{20} + \)\(11\!\cdots\!35\)\( T^{21} + \)\(78\!\cdots\!27\)\( T^{22} + \)\(52\!\cdots\!57\)\( T^{23} + \)\(33\!\cdots\!54\)\( T^{24} + \)\(20\!\cdots\!95\)\( T^{25} + \)\(11\!\cdots\!84\)\( T^{26} + \)\(59\!\cdots\!27\)\( T^{27} + \)\(28\!\cdots\!32\)\( T^{28} + \)\(11\!\cdots\!83\)\( T^{29} + \)\(41\!\cdots\!01\)\( T^{30} + \)\(10\!\cdots\!64\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 - 20 T + 1055 T^{2} - 17819 T^{3} + 524615 T^{4} - 7685377 T^{5} + 165252117 T^{6} - 2140541910 T^{7} + 37308150950 T^{8} - 433591877250 T^{9} + 6470477807087 T^{10} - 68266271595290 T^{11} + 902132050262153 T^{12} - 8725367881839196 T^{13} + 104440986860396941 T^{14} - 933498715026758963 T^{15} + 10276341641744837241 T^{16} - 85356188270670561419 T^{17} + \)\(87\!\cdots\!56\)\( T^{18} - \)\(67\!\cdots\!01\)\( T^{19} + \)\(64\!\cdots\!81\)\( T^{20} - \)\(46\!\cdots\!57\)\( T^{21} + \)\(40\!\cdots\!21\)\( T^{22} - \)\(26\!\cdots\!04\)\( T^{23} + \)\(21\!\cdots\!13\)\( T^{24} - \)\(13\!\cdots\!10\)\( T^{25} + \)\(98\!\cdots\!07\)\( T^{26} - \)\(51\!\cdots\!50\)\( T^{27} + \)\(35\!\cdots\!50\)\( T^{28} - \)\(16\!\cdots\!90\)\( T^{29} + \)\(97\!\cdots\!97\)\( T^{30} - \)\(35\!\cdots\!03\)\( T^{31} + \)\(19\!\cdots\!15\)\( T^{32} - \)\(51\!\cdots\!81\)\( T^{33} + \)\(24\!\cdots\!55\)\( T^{34} - \)\(36\!\cdots\!80\)\( T^{35} + \)\(14\!\cdots\!61\)\( T^{36} \))(\( 1 + 30 T + 936 T^{2} + 18563 T^{3} + 360490 T^{4} + 5650238 T^{5} + 86053686 T^{6} + 1149109169 T^{7} + 14944538221 T^{8} + 177527581172 T^{9} + 2070542662777 T^{10} + 22619148560490 T^{11} + 244831346781784 T^{12} + 2520653570407164 T^{13} + 25857865337046842 T^{14} + 254105323698799871 T^{15} + 2487966597675702302 T^{16} + 23353273468311437076 T^{17} + \)\(21\!\cdots\!45\)\( T^{18} + \)\(19\!\cdots\!94\)\( T^{19} + \)\(17\!\cdots\!55\)\( T^{20} + \)\(14\!\cdots\!16\)\( T^{21} + \)\(12\!\cdots\!78\)\( T^{22} + \)\(98\!\cdots\!51\)\( T^{23} + \)\(79\!\cdots\!58\)\( T^{24} + \)\(61\!\cdots\!44\)\( T^{25} + \)\(47\!\cdots\!56\)\( T^{26} + \)\(34\!\cdots\!90\)\( T^{27} + \)\(24\!\cdots\!63\)\( T^{28} + \)\(16\!\cdots\!72\)\( T^{29} + \)\(11\!\cdots\!59\)\( T^{30} + \)\(67\!\cdots\!29\)\( T^{31} + \)\(40\!\cdots\!54\)\( T^{32} + \)\(20\!\cdots\!78\)\( T^{33} + \)\(10\!\cdots\!10\)\( T^{34} + \)\(42\!\cdots\!23\)\( T^{35} + \)\(17\!\cdots\!24\)\( T^{36} + \)\(43\!\cdots\!30\)\( T^{37} + \)\(11\!\cdots\!19\)\( T^{38} \))(\( 1 + 26 T + 1256 T^{2} + 25357 T^{3} + 709436 T^{4} + 11927346 T^{5} + 249163962 T^{6} + 3633901085 T^{7} + 62391395351 T^{8} + 810033433452 T^{9} + 12003209106751 T^{10} + 141104439864044 T^{11} + 1856988832357390 T^{12} + 19987606235481294 T^{13} + 237856274128541756 T^{14} + 2360562042463873663 T^{15} + 25697387844345105186 T^{16} + \)\(23\!\cdots\!74\)\( T^{17} + \)\(23\!\cdots\!03\)\( T^{18} + \)\(20\!\cdots\!54\)\( T^{19} + \)\(18\!\cdots\!37\)\( T^{20} + \)\(14\!\cdots\!34\)\( T^{21} + \)\(12\!\cdots\!54\)\( T^{22} + \)\(91\!\cdots\!03\)\( T^{23} + \)\(73\!\cdots\!44\)\( T^{24} + \)\(48\!\cdots\!74\)\( T^{25} + \)\(35\!\cdots\!10\)\( T^{26} + \)\(21\!\cdots\!84\)\( T^{27} + \)\(14\!\cdots\!69\)\( T^{28} + \)\(76\!\cdots\!52\)\( T^{29} + \)\(46\!\cdots\!29\)\( T^{30} + \)\(21\!\cdots\!85\)\( T^{31} + \)\(11\!\cdots\!18\)\( T^{32} + \)\(43\!\cdots\!26\)\( T^{33} + \)\(20\!\cdots\!64\)\( T^{34} + \)\(58\!\cdots\!97\)\( T^{35} + \)\(22\!\cdots\!04\)\( T^{36} + \)\(37\!\cdots\!86\)\( T^{37} + \)\(11\!\cdots\!19\)\( T^{38} \))
$83$ (\( 1 + 12 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 8 T + 150 T^{2} - 664 T^{3} + 6889 T^{4} \))(\( 1 - 26 T + 1175 T^{2} - 24394 T^{3} + 626392 T^{4} - 10788509 T^{5} + 203533220 T^{6} - 2981579458 T^{7} + 45398111715 T^{8} - 575044445870 T^{9} + 7390510102163 T^{10} - 81790282008123 T^{11} + 908376918217845 T^{12} - 8830604869904466 T^{13} + 85782259984007162 T^{14} - 732940204202070678 T^{15} + 6257808589602734205 T^{16} - 46766619978578625801 T^{17} + \)\(35\!\cdots\!23\)\( T^{18} - \)\(22\!\cdots\!10\)\( T^{19} + \)\(14\!\cdots\!35\)\( T^{20} - \)\(80\!\cdots\!66\)\( T^{21} + \)\(45\!\cdots\!20\)\( T^{22} - \)\(20\!\cdots\!27\)\( T^{23} + \)\(97\!\cdots\!08\)\( T^{24} - \)\(31\!\cdots\!98\)\( T^{25} + \)\(12\!\cdots\!75\)\( T^{26} - \)\(23\!\cdots\!38\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \))(\( 1 + 18 T + 629 T^{2} + 8030 T^{3} + 180343 T^{4} + 1831189 T^{5} + 33314901 T^{6} + 273187286 T^{7} + 4477153251 T^{8} + 29076814975 T^{9} + 471269082809 T^{10} + 2293093474629 T^{11} + 41504448730080 T^{12} + 138616733882824 T^{13} + 3324246241769917 T^{14} + 7664660182901613 T^{15} + 268089537536409786 T^{16} + 636166795180833879 T^{17} + 22900732359552958213 T^{18} + 79259246416658286488 T^{19} + \)\(19\!\cdots\!80\)\( T^{20} + \)\(90\!\cdots\!47\)\( T^{21} + \)\(15\!\cdots\!21\)\( T^{22} + \)\(78\!\cdots\!25\)\( T^{23} + \)\(10\!\cdots\!91\)\( T^{24} + \)\(51\!\cdots\!58\)\( T^{25} + \)\(51\!\cdots\!49\)\( T^{26} + \)\(23\!\cdots\!63\)\( T^{27} + \)\(19\!\cdots\!23\)\( T^{28} + \)\(71\!\cdots\!90\)\( T^{29} + \)\(46\!\cdots\!41\)\( T^{30} + \)\(11\!\cdots\!26\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 + 8 T + 621 T^{2} + 5760 T^{3} + 205821 T^{4} + 2064349 T^{5} + 47676039 T^{6} + 492577542 T^{7} + 8574581643 T^{8} + 87855361871 T^{9} + 1260108602351 T^{10} + 12451569058079 T^{11} + 155347165484976 T^{12} + 1452654851437056 T^{13} + 16281269375111317 T^{14} + 142303558227244703 T^{15} + 1459732637166242190 T^{16} + 11811195332861310349 T^{17} + \)\(11\!\cdots\!13\)\( T^{18} + \)\(83\!\cdots\!72\)\( T^{19} + \)\(73\!\cdots\!96\)\( T^{20} + \)\(49\!\cdots\!97\)\( T^{21} + \)\(41\!\cdots\!19\)\( T^{22} + \)\(23\!\cdots\!17\)\( T^{23} + \)\(19\!\cdots\!63\)\( T^{24} + \)\(92\!\cdots\!26\)\( T^{25} + \)\(73\!\cdots\!11\)\( T^{26} + \)\(26\!\cdots\!83\)\( T^{27} + \)\(22\!\cdots\!81\)\( T^{28} + \)\(51\!\cdots\!80\)\( T^{29} + \)\(45\!\cdots\!09\)\( T^{30} + \)\(48\!\cdots\!56\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 8 T + 935 T^{2} - 6316 T^{3} + 418516 T^{4} - 2278771 T^{5} + 118991136 T^{6} - 478156584 T^{7} + 24070092250 T^{8} - 58197451990 T^{9} + 3688197029406 T^{10} - 2179268406887 T^{11} + 448012791942575 T^{12} + 651482952233025 T^{13} + 45209322874553430 T^{14} + 158320150271278426 T^{15} + 4026224333473262106 T^{16} + 19818896413044005259 T^{17} + \)\(33\!\cdots\!30\)\( T^{18} + \)\(16\!\cdots\!97\)\( T^{19} + \)\(27\!\cdots\!34\)\( T^{20} + \)\(90\!\cdots\!62\)\( T^{21} + \)\(21\!\cdots\!30\)\( T^{22} + \)\(25\!\cdots\!75\)\( T^{23} + \)\(14\!\cdots\!75\)\( T^{24} - \)\(59\!\cdots\!49\)\( T^{25} + \)\(83\!\cdots\!46\)\( T^{26} - \)\(10\!\cdots\!70\)\( T^{27} + \)\(37\!\cdots\!50\)\( T^{28} - \)\(61\!\cdots\!28\)\( T^{29} + \)\(12\!\cdots\!96\)\( T^{30} - \)\(20\!\cdots\!73\)\( T^{31} + \)\(30\!\cdots\!64\)\( T^{32} - \)\(38\!\cdots\!12\)\( T^{33} + \)\(47\!\cdots\!35\)\( T^{34} - \)\(33\!\cdots\!84\)\( T^{35} + \)\(34\!\cdots\!09\)\( T^{36} \))(\( 1 + 88 T + 4709 T^{2} + 184622 T^{3} + 5852448 T^{4} + 156993087 T^{5} + 3677099132 T^{6} + 76714423246 T^{7} + 1447235050999 T^{8} + 24961494068514 T^{9} + 397083614622066 T^{10} + 5866179594583439 T^{11} + 80936320758645778 T^{12} + 1047677571069126156 T^{13} + 12771721590866798024 T^{14} + \)\(14\!\cdots\!81\)\( T^{15} + \)\(16\!\cdots\!47\)\( T^{16} + \)\(16\!\cdots\!23\)\( T^{17} + \)\(16\!\cdots\!50\)\( T^{18} + \)\(15\!\cdots\!12\)\( T^{19} + \)\(13\!\cdots\!50\)\( T^{20} + \)\(11\!\cdots\!47\)\( T^{21} + \)\(91\!\cdots\!89\)\( T^{22} + \)\(69\!\cdots\!01\)\( T^{23} + \)\(50\!\cdots\!32\)\( T^{24} + \)\(34\!\cdots\!64\)\( T^{25} + \)\(21\!\cdots\!06\)\( T^{26} + \)\(13\!\cdots\!99\)\( T^{27} + \)\(74\!\cdots\!98\)\( T^{28} + \)\(38\!\cdots\!86\)\( T^{29} + \)\(18\!\cdots\!33\)\( T^{30} + \)\(82\!\cdots\!06\)\( T^{31} + \)\(32\!\cdots\!16\)\( T^{32} + \)\(11\!\cdots\!23\)\( T^{33} + \)\(35\!\cdots\!36\)\( T^{34} + \)\(93\!\cdots\!82\)\( T^{35} + \)\(19\!\cdots\!07\)\( T^{36} + \)\(30\!\cdots\!92\)\( T^{37} + \)\(29\!\cdots\!47\)\( T^{38} \))(\( 1 + 14 T + 953 T^{2} + 12396 T^{3} + 452982 T^{4} + 5556945 T^{5} + 142650218 T^{6} + 1663578304 T^{7} + 33361210893 T^{8} + 371563591036 T^{9} + 6163132369110 T^{10} + 65692972759961 T^{11} + 934751326038860 T^{12} + 9532144484025736 T^{13} + 119458512097622942 T^{14} + 1161944894810100533 T^{15} + 13095228819283953919 T^{16} + \)\(12\!\cdots\!73\)\( T^{17} + \)\(12\!\cdots\!28\)\( T^{18} + \)\(10\!\cdots\!24\)\( T^{19} + \)\(10\!\cdots\!24\)\( T^{20} + \)\(83\!\cdots\!97\)\( T^{21} + \)\(74\!\cdots\!53\)\( T^{22} + \)\(55\!\cdots\!93\)\( T^{23} + \)\(47\!\cdots\!06\)\( T^{24} + \)\(31\!\cdots\!84\)\( T^{25} + \)\(25\!\cdots\!20\)\( T^{26} + \)\(14\!\cdots\!01\)\( T^{27} + \)\(11\!\cdots\!30\)\( T^{28} + \)\(57\!\cdots\!64\)\( T^{29} + \)\(42\!\cdots\!31\)\( T^{30} + \)\(17\!\cdots\!44\)\( T^{31} + \)\(12\!\cdots\!34\)\( T^{32} + \)\(40\!\cdots\!05\)\( T^{33} + \)\(27\!\cdots\!74\)\( T^{34} + \)\(62\!\cdots\!76\)\( T^{35} + \)\(40\!\cdots\!19\)\( T^{36} + \)\(48\!\cdots\!26\)\( T^{37} + \)\(29\!\cdots\!47\)\( T^{38} \))
$89$ (\( 1 - 2 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 22 T + 291 T^{2} + 1958 T^{3} + 7921 T^{4} \))(\( 1 - 61 T + 2630 T^{2} - 81769 T^{3} + 2113582 T^{4} - 45969997 T^{5} + 879946778 T^{6} - 14940232541 T^{7} + 229837154316 T^{8} - 3220312799435 T^{9} + 41607188383666 T^{10} - 497310728149783 T^{11} + 5541712254783296 T^{12} - 57638406605878562 T^{13} + 561999215836289582 T^{14} - 5129818187923192018 T^{15} + 43895902770138487616 T^{16} - \)\(35\!\cdots\!27\)\( T^{17} + \)\(26\!\cdots\!06\)\( T^{18} - \)\(17\!\cdots\!15\)\( T^{19} + \)\(11\!\cdots\!76\)\( T^{20} - \)\(66\!\cdots\!89\)\( T^{21} + \)\(34\!\cdots\!18\)\( T^{22} - \)\(16\!\cdots\!73\)\( T^{23} + \)\(65\!\cdots\!82\)\( T^{24} - \)\(22\!\cdots\!41\)\( T^{25} + \)\(64\!\cdots\!30\)\( T^{26} - \)\(13\!\cdots\!09\)\( T^{27} + \)\(19\!\cdots\!41\)\( T^{28} \))(\( 1 + 47 T + 1615 T^{2} + 39214 T^{3} + 799541 T^{4} + 13714407 T^{5} + 210861034 T^{6} + 2940793961 T^{7} + 38474158370 T^{8} + 476882713545 T^{9} + 5670524165050 T^{10} + 64782581865315 T^{11} + 711530381771648 T^{12} + 7521156041974340 T^{13} + 76607298868430600 T^{14} + 755455833392383949 T^{15} + 7226437587606430756 T^{16} + 67235569171922171461 T^{17} + \)\(60\!\cdots\!00\)\( T^{18} + \)\(53\!\cdots\!60\)\( T^{19} + \)\(44\!\cdots\!68\)\( T^{20} + \)\(36\!\cdots\!35\)\( T^{21} + \)\(28\!\cdots\!50\)\( T^{22} + \)\(21\!\cdots\!05\)\( T^{23} + \)\(15\!\cdots\!70\)\( T^{24} + \)\(10\!\cdots\!49\)\( T^{25} + \)\(65\!\cdots\!34\)\( T^{26} + \)\(38\!\cdots\!23\)\( T^{27} + \)\(19\!\cdots\!61\)\( T^{28} + \)\(86\!\cdots\!66\)\( T^{29} + \)\(31\!\cdots\!15\)\( T^{30} + \)\(81\!\cdots\!03\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 - T + 753 T^{2} - 474 T^{3} + 277043 T^{4} - 120757 T^{5} + 66487514 T^{6} - 30135605 T^{7} + 11746074374 T^{8} - 7973189023 T^{9} + 1639730151328 T^{10} - 1729073563053 T^{11} + 190747384556740 T^{12} - 277622840616284 T^{13} + 19397053949703726 T^{14} - 32990729540578911 T^{15} + 1794732244061734208 T^{16} - 2936174929111523079 T^{17} + \)\(15\!\cdots\!46\)\( T^{18} - \)\(19\!\cdots\!96\)\( T^{19} + \)\(11\!\cdots\!40\)\( T^{20} - \)\(96\!\cdots\!97\)\( T^{21} + \)\(81\!\cdots\!08\)\( T^{22} - \)\(35\!\cdots\!67\)\( T^{23} + \)\(46\!\cdots\!94\)\( T^{24} - \)\(10\!\cdots\!45\)\( T^{25} + \)\(20\!\cdots\!14\)\( T^{26} - \)\(33\!\cdots\!73\)\( T^{27} + \)\(68\!\cdots\!03\)\( T^{28} - \)\(10\!\cdots\!06\)\( T^{29} + \)\(14\!\cdots\!73\)\( T^{30} - \)\(17\!\cdots\!49\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 - 11 T + 971 T^{2} - 8308 T^{3} + 442198 T^{4} - 3016104 T^{5} + 129192677 T^{6} - 719036635 T^{7} + 27745974919 T^{8} - 129775175182 T^{9} + 4728164377340 T^{10} - 19260375028154 T^{11} + 670012237562458 T^{12} - 2460549018811463 T^{13} + 81377073740665062 T^{14} - 276418531705302104 T^{15} + 8648762698908307848 T^{16} - 27574445033126943279 T^{17} + \)\(81\!\cdots\!24\)\( T^{18} - \)\(24\!\cdots\!31\)\( T^{19} + \)\(68\!\cdots\!08\)\( T^{20} - \)\(19\!\cdots\!76\)\( T^{21} + \)\(51\!\cdots\!42\)\( T^{22} - \)\(13\!\cdots\!87\)\( T^{23} + \)\(33\!\cdots\!38\)\( T^{24} - \)\(85\!\cdots\!66\)\( T^{25} + \)\(18\!\cdots\!40\)\( T^{26} - \)\(45\!\cdots\!38\)\( T^{27} + \)\(86\!\cdots\!19\)\( T^{28} - \)\(19\!\cdots\!15\)\( T^{29} + \)\(31\!\cdots\!17\)\( T^{30} - \)\(66\!\cdots\!76\)\( T^{31} + \)\(86\!\cdots\!18\)\( T^{32} - \)\(14\!\cdots\!92\)\( T^{33} + \)\(15\!\cdots\!31\)\( T^{34} - \)\(15\!\cdots\!19\)\( T^{35} + \)\(12\!\cdots\!81\)\( T^{36} \))(\( 1 + 71 T + 3464 T^{2} + 123299 T^{3} + 3647563 T^{4} + 91671120 T^{5} + 2039252889 T^{6} + 40634143411 T^{7} + 739413615092 T^{8} + 12377603820257 T^{9} + 192720555386659 T^{10} + 2804203725321642 T^{11} + 38397028161636936 T^{12} + 496254043721371803 T^{13} + 6081489188847392728 T^{14} + 70792993567170496879 T^{15} + \)\(78\!\cdots\!36\)\( T^{16} + \)\(83\!\cdots\!09\)\( T^{17} + \)\(83\!\cdots\!76\)\( T^{18} + \)\(80\!\cdots\!66\)\( T^{19} + \)\(74\!\cdots\!64\)\( T^{20} + \)\(65\!\cdots\!89\)\( T^{21} + \)\(55\!\cdots\!84\)\( T^{22} + \)\(44\!\cdots\!39\)\( T^{23} + \)\(33\!\cdots\!72\)\( T^{24} + \)\(24\!\cdots\!83\)\( T^{25} + \)\(16\!\cdots\!44\)\( T^{26} + \)\(11\!\cdots\!02\)\( T^{27} + \)\(67\!\cdots\!31\)\( T^{28} + \)\(38\!\cdots\!57\)\( T^{29} + \)\(20\!\cdots\!88\)\( T^{30} + \)\(10\!\cdots\!31\)\( T^{31} + \)\(44\!\cdots\!41\)\( T^{32} + \)\(17\!\cdots\!20\)\( T^{33} + \)\(63\!\cdots\!87\)\( T^{34} + \)\(19\!\cdots\!39\)\( T^{35} + \)\(47\!\cdots\!56\)\( T^{36} + \)\(87\!\cdots\!51\)\( T^{37} + \)\(10\!\cdots\!09\)\( T^{38} \))(\( 1 + 3 T + 822 T^{2} + 2435 T^{3} + 333911 T^{4} + 1107960 T^{5} + 89547357 T^{6} + 358573733 T^{7} + 17945216224 T^{8} + 88347214695 T^{9} + 2897632217951 T^{10} + 17109516368240 T^{11} + 397713025907834 T^{12} + 2673626934607585 T^{13} + 48138908539832644 T^{14} + 346117668010991559 T^{15} + 5240347115607206152 T^{16} + 38068354510404465053 T^{17} + \)\(51\!\cdots\!52\)\( T^{18} + \)\(36\!\cdots\!50\)\( T^{19} + \)\(45\!\cdots\!28\)\( T^{20} + \)\(30\!\cdots\!13\)\( T^{21} + \)\(36\!\cdots\!88\)\( T^{22} + \)\(21\!\cdots\!19\)\( T^{23} + \)\(26\!\cdots\!56\)\( T^{24} + \)\(13\!\cdots\!85\)\( T^{25} + \)\(17\!\cdots\!86\)\( T^{26} + \)\(67\!\cdots\!40\)\( T^{27} + \)\(10\!\cdots\!59\)\( T^{28} + \)\(27\!\cdots\!95\)\( T^{29} + \)\(49\!\cdots\!36\)\( T^{30} + \)\(88\!\cdots\!93\)\( T^{31} + \)\(19\!\cdots\!33\)\( T^{32} + \)\(21\!\cdots\!60\)\( T^{33} + \)\(58\!\cdots\!39\)\( T^{34} + \)\(37\!\cdots\!35\)\( T^{35} + \)\(11\!\cdots\!38\)\( T^{36} + \)\(36\!\cdots\!43\)\( T^{37} + \)\(10\!\cdots\!09\)\( T^{38} \))
$97$ (\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 20 T + 286 T^{2} + 1940 T^{3} + 9409 T^{4} \))(\( 1 - 36 T + 1428 T^{2} - 35074 T^{3} + 841393 T^{4} - 16019261 T^{5} + 291681521 T^{6} - 4590810735 T^{7} + 68974278874 T^{8} - 932296234154 T^{9} + 12061337517534 T^{10} - 143397627966848 T^{11} + 1636785135994691 T^{12} - 17357919179788632 T^{13} + 177056566818495596 T^{14} - 1683718160439497304 T^{15} + 15400511344574047619 T^{16} - \)\(13\!\cdots\!04\)\( T^{17} + \)\(10\!\cdots\!54\)\( T^{18} - \)\(80\!\cdots\!78\)\( T^{19} + \)\(57\!\cdots\!46\)\( T^{20} - \)\(37\!\cdots\!55\)\( T^{21} + \)\(22\!\cdots\!81\)\( T^{22} - \)\(12\!\cdots\!37\)\( T^{23} + \)\(62\!\cdots\!57\)\( T^{24} - \)\(25\!\cdots\!22\)\( T^{25} + \)\(99\!\cdots\!48\)\( T^{26} - \)\(24\!\cdots\!72\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \))(\( 1 + 20 T + 1082 T^{2} + 20528 T^{3} + 595038 T^{4} + 10205783 T^{5} + 215127797 T^{6} + 3291937871 T^{7} + 56454749653 T^{8} + 773047502175 T^{9} + 11364009424639 T^{10} + 140176049308909 T^{11} + 1817036137259531 T^{12} + 20304376336380040 T^{13} + 235925903301557222 T^{14} + 2395864309258765282 T^{15} + 25186716646381525274 T^{16} + \)\(23\!\cdots\!54\)\( T^{17} + \)\(22\!\cdots\!98\)\( T^{18} + \)\(18\!\cdots\!20\)\( T^{19} + \)\(16\!\cdots\!11\)\( T^{20} + \)\(12\!\cdots\!13\)\( T^{21} + \)\(94\!\cdots\!31\)\( T^{22} + \)\(62\!\cdots\!75\)\( T^{23} + \)\(44\!\cdots\!33\)\( T^{24} + \)\(25\!\cdots\!07\)\( T^{25} + \)\(15\!\cdots\!53\)\( T^{26} + \)\(73\!\cdots\!99\)\( T^{27} + \)\(41\!\cdots\!58\)\( T^{28} + \)\(13\!\cdots\!56\)\( T^{29} + \)\(70\!\cdots\!58\)\( T^{30} + \)\(12\!\cdots\!60\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 + 12 T + 848 T^{2} + 9434 T^{3} + 358356 T^{4} + 3799081 T^{5} + 100909421 T^{6} + 1039733163 T^{7} + 21321436351 T^{8} + 215707716863 T^{9} + 3603954167435 T^{10} + 35826836718213 T^{11} + 506972643177963 T^{12} + 4908623316356328 T^{13} + 60871115653377700 T^{14} + 563852945194123322 T^{15} + 6329562068774879466 T^{16} + 54693735683829962234 T^{17} + \)\(57\!\cdots\!00\)\( T^{18} + \)\(44\!\cdots\!44\)\( T^{19} + \)\(44\!\cdots\!03\)\( T^{20} + \)\(30\!\cdots\!41\)\( T^{21} + \)\(30\!\cdots\!15\)\( T^{22} + \)\(17\!\cdots\!19\)\( T^{23} + \)\(16\!\cdots\!11\)\( T^{24} + \)\(79\!\cdots\!71\)\( T^{25} + \)\(74\!\cdots\!29\)\( T^{26} + \)\(27\!\cdots\!93\)\( T^{27} + \)\(24\!\cdots\!96\)\( T^{28} + \)\(63\!\cdots\!18\)\( T^{29} + \)\(55\!\cdots\!12\)\( T^{30} + \)\(75\!\cdots\!16\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 - 20 T + 1154 T^{2} - 20744 T^{3} + 654665 T^{4} - 10747627 T^{5} + 243941167 T^{6} - 3692126989 T^{7} + 67090082641 T^{8} - 941398201854 T^{9} + 14483414923280 T^{10} - 188970069476496 T^{11} + 2545395920037086 T^{12} - 30908658866636369 T^{13} + 372482889702150459 T^{14} - 4205889558362409511 T^{15} + 46013508647191889975 T^{16} - \)\(48\!\cdots\!58\)\( T^{17} + \)\(48\!\cdots\!20\)\( T^{18} - \)\(46\!\cdots\!26\)\( T^{19} + \)\(43\!\cdots\!75\)\( T^{20} - \)\(38\!\cdots\!03\)\( T^{21} + \)\(32\!\cdots\!79\)\( T^{22} - \)\(26\!\cdots\!33\)\( T^{23} + \)\(21\!\cdots\!94\)\( T^{24} - \)\(15\!\cdots\!48\)\( T^{25} + \)\(11\!\cdots\!80\)\( T^{26} - \)\(71\!\cdots\!18\)\( T^{27} + \)\(49\!\cdots\!09\)\( T^{28} - \)\(26\!\cdots\!17\)\( T^{29} + \)\(16\!\cdots\!47\)\( T^{30} - \)\(72\!\cdots\!79\)\( T^{31} + \)\(42\!\cdots\!85\)\( T^{32} - \)\(13\!\cdots\!92\)\( T^{33} + \)\(70\!\cdots\!34\)\( T^{34} - \)\(11\!\cdots\!40\)\( T^{35} + \)\(57\!\cdots\!89\)\( T^{36} \))(\( 1 - 4 T + 864 T^{2} - 3040 T^{3} + 388737 T^{4} - 1086385 T^{5} + 119176073 T^{6} - 233744651 T^{7} + 27744332012 T^{8} - 29782744910 T^{9} + 5206361563529 T^{10} - 955508282872 T^{11} + 818935317412189 T^{12} + 524084450335366 T^{13} + 111124745019724541 T^{14} + 145178355741966597 T^{15} + 13300123795126985510 T^{16} + 22836788846187349895 T^{17} + \)\(14\!\cdots\!88\)\( T^{18} + \)\(25\!\cdots\!36\)\( T^{19} + \)\(13\!\cdots\!36\)\( T^{20} + \)\(21\!\cdots\!55\)\( T^{21} + \)\(12\!\cdots\!30\)\( T^{22} + \)\(12\!\cdots\!57\)\( T^{23} + \)\(95\!\cdots\!37\)\( T^{24} + \)\(43\!\cdots\!14\)\( T^{25} + \)\(66\!\cdots\!57\)\( T^{26} - \)\(74\!\cdots\!92\)\( T^{27} + \)\(39\!\cdots\!93\)\( T^{28} - \)\(21\!\cdots\!90\)\( T^{29} + \)\(19\!\cdots\!36\)\( T^{30} - \)\(16\!\cdots\!91\)\( T^{31} + \)\(80\!\cdots\!21\)\( T^{32} - \)\(70\!\cdots\!65\)\( T^{33} + \)\(24\!\cdots\!41\)\( T^{34} - \)\(18\!\cdots\!40\)\( T^{35} + \)\(51\!\cdots\!68\)\( T^{36} - \)\(23\!\cdots\!56\)\( T^{37} + \)\(56\!\cdots\!33\)\( T^{38} \))(\( 1 + 44 T + 1574 T^{2} + 38350 T^{3} + 842091 T^{4} + 15161345 T^{5} + 256786823 T^{6} + 3802885911 T^{7} + 54513499256 T^{8} + 706957216528 T^{9} + 9082703640615 T^{10} + 107617696325286 T^{11} + 1283323632089203 T^{12} + 14225828008196842 T^{13} + 160113898328750203 T^{14} + 1678557750530784425 T^{15} + 17993226297381504212 T^{16} + \)\(18\!\cdots\!35\)\( T^{17} + \)\(18\!\cdots\!82\)\( T^{18} + \)\(17\!\cdots\!72\)\( T^{19} + \)\(18\!\cdots\!54\)\( T^{20} + \)\(16\!\cdots\!15\)\( T^{21} + \)\(16\!\cdots\!76\)\( T^{22} + \)\(14\!\cdots\!25\)\( T^{23} + \)\(13\!\cdots\!71\)\( T^{24} + \)\(11\!\cdots\!18\)\( T^{25} + \)\(10\!\cdots\!39\)\( T^{26} + \)\(84\!\cdots\!46\)\( T^{27} + \)\(69\!\cdots\!55\)\( T^{28} + \)\(52\!\cdots\!72\)\( T^{29} + \)\(38\!\cdots\!68\)\( T^{30} + \)\(26\!\cdots\!51\)\( T^{31} + \)\(17\!\cdots\!71\)\( T^{32} + \)\(98\!\cdots\!05\)\( T^{33} + \)\(53\!\cdots\!63\)\( T^{34} + \)\(23\!\cdots\!50\)\( T^{35} + \)\(93\!\cdots\!38\)\( T^{36} + \)\(25\!\cdots\!16\)\( T^{37} + \)\(56\!\cdots\!33\)\( T^{38} \))
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