Properties

Label 803.2.a
Level 803
Weight 2
Character orbit a
Rep. character \(\chi_{803}(1,\cdot)\)
Character field \(\Q\)
Dimension 61
Newform subspaces 6
Sturm bound 148
Trace bound 1

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Defining parameters

Level: \( N \) = \( 803 = 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 803.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(148\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(803))\).

Total New Old
Modular forms 76 61 15
Cusp forms 73 61 12
Eisenstein series 3 0 3

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

\(11\)\(73\)FrickeDim.
\(+\)\(+\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(21\)
\(-\)\(+\)\(-\)\(19\)
\(-\)\(-\)\(+\)\(10\)
Plus space\(+\)\(21\)
Minus space\(-\)\(40\)

Trace form

\( 61q + 3q^{2} + 2q^{3} + 59q^{4} - 4q^{6} + 8q^{7} + 3q^{8} + 63q^{9} + O(q^{10}) \) \( 61q + 3q^{2} + 2q^{3} + 59q^{4} - 4q^{6} + 8q^{7} + 3q^{8} + 63q^{9} - 2q^{10} - 3q^{11} + 14q^{13} - 24q^{14} - 22q^{15} + 67q^{16} + 6q^{17} + 3q^{18} + 4q^{19} + 10q^{20} - 12q^{21} + q^{22} + 2q^{23} - 8q^{24} + 85q^{25} + 6q^{26} - 10q^{27} + 24q^{28} - 2q^{29} + 24q^{30} - 14q^{31} - q^{32} - 2q^{33} - 2q^{34} - 36q^{35} + 87q^{36} + 24q^{37} + 8q^{38} + 40q^{39} - 22q^{40} + 22q^{41} - 4q^{42} + 8q^{43} - 3q^{44} - 18q^{45} - 68q^{46} - 32q^{47} + 12q^{48} + 77q^{49} - 39q^{50} - 44q^{51} + 22q^{52} + 18q^{53} - 40q^{54} - 48q^{56} - 24q^{57} + 58q^{58} + 2q^{59} - 72q^{60} + 2q^{61} - 20q^{62} + 71q^{64} + 16q^{65} + 4q^{66} - 2q^{67} - 38q^{68} - 30q^{69} - 48q^{70} + 34q^{71} - 9q^{72} + q^{73} + 26q^{74} - 4q^{75} + 8q^{76} + 8q^{77} - 4q^{78} + 48q^{79} + 66q^{80} + 21q^{81} - 58q^{82} - 12q^{83} - 52q^{84} + 32q^{85} + 28q^{86} - 8q^{87} + 9q^{88} - 40q^{89} - 46q^{90} + 40q^{91} - 16q^{92} + 82q^{93} + 24q^{94} - 48q^{95} - 52q^{96} + 16q^{97} + 123q^{98} - 9q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(803))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 11 73
803.2.a.a \(2\) \(6.412\) \(\Q(\sqrt{21}) \) None \(-2\) \(1\) \(-4\) \(-1\) \(+\) \(+\) \(q-q^{2}+\beta q^{3}-q^{4}-2q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)
803.2.a.b \(5\) \(6.412\) 5.5.3714917.1 None \(0\) \(2\) \(1\) \(-1\) \(+\) \(-\) \(q+\beta _{1}q^{3}-2q^{4}+\beta _{4}q^{5}-\beta _{3}q^{7}+(1+\cdots)q^{9}+\cdots\)
803.2.a.c \(9\) \(6.412\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(-5\) \(-1\) \(-1\) \(+\) \(+\) \(q-\beta _{2}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
803.2.a.d \(10\) \(6.412\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-5\) \(-3\) \(-2\) \(-8\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{6}+\cdots)q^{4}+\cdots\)
803.2.a.e \(16\) \(6.412\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(4\) \(4\) \(3\) \(+\) \(-\) \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(2+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
803.2.a.f \(19\) \(6.412\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(7\) \(3\) \(2\) \(16\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}-\beta _{15}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(803))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(803)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(73))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + T + 2 T^{2} )^{2} \))(\( ( 1 + 2 T^{2} )^{5} \))(\( 1 - 3 T + 11 T^{2} - 20 T^{3} + 47 T^{4} - 70 T^{5} + 145 T^{6} - 203 T^{7} + 377 T^{8} - 472 T^{9} + 754 T^{10} - 812 T^{11} + 1160 T^{12} - 1120 T^{13} + 1504 T^{14} - 1280 T^{15} + 1408 T^{16} - 768 T^{17} + 512 T^{18} \))(\( 1 + 5 T + 20 T^{2} + 59 T^{3} + 152 T^{4} + 338 T^{5} + 686 T^{6} + 1261 T^{7} + 2156 T^{8} + 3391 T^{9} + 4993 T^{10} + 6782 T^{11} + 8624 T^{12} + 10088 T^{13} + 10976 T^{14} + 10816 T^{15} + 9728 T^{16} + 7552 T^{17} + 5120 T^{18} + 2560 T^{19} + 1024 T^{20} \))(\( 1 - 3 T^{2} + T^{3} + 18 T^{4} - 45 T^{6} + 12 T^{7} + 166 T^{8} - T^{9} - 358 T^{10} + 72 T^{11} + 1021 T^{12} + 39 T^{13} - 1930 T^{14} + 219 T^{15} + 4670 T^{16} + 438 T^{17} - 7720 T^{18} + 312 T^{19} + 16336 T^{20} + 2304 T^{21} - 22912 T^{22} - 128 T^{23} + 42496 T^{24} + 6144 T^{25} - 46080 T^{26} + 73728 T^{28} + 8192 T^{29} - 49152 T^{30} + 65536 T^{32} \))(\( 1 - 7 T + 32 T^{2} - 111 T^{3} + 325 T^{4} - 835 T^{5} + 1940 T^{6} - 4142 T^{7} + 8248 T^{8} - 15493 T^{9} + 27741 T^{10} - 47767 T^{11} + 79706 T^{12} - 129675 T^{13} + 206533 T^{14} - 322578 T^{15} + 494042 T^{16} - 740948 T^{17} + 1086488 T^{18} - 1555408 T^{19} + 2172976 T^{20} - 2963792 T^{21} + 3952336 T^{22} - 5161248 T^{23} + 6609056 T^{24} - 8299200 T^{25} + 10202368 T^{26} - 12228352 T^{27} + 14203392 T^{28} - 15864832 T^{29} + 16891904 T^{30} - 16965632 T^{31} + 15892480 T^{32} - 13680640 T^{33} + 10649600 T^{34} - 7274496 T^{35} + 4194304 T^{36} - 1835008 T^{37} + 524288 T^{38} \))
$3$ (\( 1 - T + T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - 2 T + 6 T^{2} - 16 T^{3} + 34 T^{4} - 53 T^{5} + 102 T^{6} - 144 T^{7} + 162 T^{8} - 162 T^{9} + 243 T^{10} \))(\( 1 + 5 T + 27 T^{2} + 93 T^{3} + 305 T^{4} + 815 T^{5} + 2013 T^{6} + 4386 T^{7} + 8757 T^{8} + 15859 T^{9} + 26271 T^{10} + 39474 T^{11} + 54351 T^{12} + 66015 T^{13} + 74115 T^{14} + 67797 T^{15} + 59049 T^{16} + 32805 T^{17} + 19683 T^{18} \))(\( 1 + 3 T + 17 T^{2} + 46 T^{3} + 160 T^{4} + 373 T^{5} + 1014 T^{6} + 2041 T^{7} + 4633 T^{8} + 8180 T^{9} + 15925 T^{10} + 24540 T^{11} + 41697 T^{12} + 55107 T^{13} + 82134 T^{14} + 90639 T^{15} + 116640 T^{16} + 100602 T^{17} + 111537 T^{18} + 59049 T^{19} + 59049 T^{20} \))(\( 1 - 4 T + 19 T^{2} - 50 T^{3} + 149 T^{4} - 325 T^{5} + 845 T^{6} - 1714 T^{7} + 4104 T^{8} - 7614 T^{9} + 16649 T^{10} - 28785 T^{11} + 60007 T^{12} - 99680 T^{13} + 200515 T^{14} - 318597 T^{15} + 620554 T^{16} - 955791 T^{17} + 1804635 T^{18} - 2691360 T^{19} + 4860567 T^{20} - 6994755 T^{21} + 12137121 T^{22} - 16651818 T^{23} + 26926344 T^{24} - 33736662 T^{25} + 49896405 T^{26} - 57572775 T^{27} + 79184709 T^{28} - 79716150 T^{29} + 90876411 T^{30} - 57395628 T^{31} + 43046721 T^{32} \))(\( 1 - 3 T + 22 T^{2} - 51 T^{3} + 236 T^{4} - 461 T^{5} + 1709 T^{6} - 2893 T^{7} + 9420 T^{8} - 13939 T^{9} + 42048 T^{10} - 54061 T^{11} + 158140 T^{12} - 174165 T^{13} + 520036 T^{14} - 484544 T^{15} + 1568037 T^{16} - 1262232 T^{17} + 4604177 T^{18} - 3515971 T^{19} + 13812531 T^{20} - 11360088 T^{21} + 42336999 T^{22} - 39248064 T^{23} + 126368748 T^{24} - 126966285 T^{25} + 345852180 T^{26} - 354694221 T^{27} + 827630784 T^{28} - 823084011 T^{29} + 1668724740 T^{30} - 1537458813 T^{31} + 2724698007 T^{32} - 2204948709 T^{33} + 3386342052 T^{34} - 2195382771 T^{35} + 2841083586 T^{36} - 1162261467 T^{37} + 1162261467 T^{38} \))
$5$ (\( ( 1 + 2 T + 5 T^{2} )^{2} \))(\( 1 - T + 3 T^{2} + 8 T^{3} + 24 T^{4} - 14 T^{5} + 120 T^{6} + 200 T^{7} + 375 T^{8} - 625 T^{9} + 3125 T^{10} \))(\( 1 + T + 28 T^{2} + 36 T^{3} + 380 T^{4} + 542 T^{5} + 3397 T^{6} + 4789 T^{7} + 22317 T^{8} + 28541 T^{9} + 111585 T^{10} + 119725 T^{11} + 424625 T^{12} + 338750 T^{13} + 1187500 T^{14} + 562500 T^{15} + 2187500 T^{16} + 390625 T^{17} + 1953125 T^{18} \))(\( 1 + 2 T + 27 T^{2} + 39 T^{3} + 321 T^{4} + 231 T^{5} + 2127 T^{6} - 583 T^{7} + 8965 T^{8} - 14817 T^{9} + 36054 T^{10} - 74085 T^{11} + 224125 T^{12} - 72875 T^{13} + 1329375 T^{14} + 721875 T^{15} + 5015625 T^{16} + 3046875 T^{17} + 10546875 T^{18} + 3906250 T^{19} + 9765625 T^{20} \))(\( 1 - 4 T + 29 T^{2} - 103 T^{3} + 450 T^{4} - 1407 T^{5} + 4822 T^{6} - 13834 T^{7} + 41197 T^{8} - 111220 T^{9} + 302412 T^{10} - 771311 T^{11} + 1958458 T^{12} - 4713187 T^{13} + 11303337 T^{14} - 25819182 T^{15} + 59122988 T^{16} - 129095910 T^{17} + 282583425 T^{18} - 589148375 T^{19} + 1224036250 T^{20} - 2410346875 T^{21} + 4725187500 T^{22} - 8689062500 T^{23} + 16092578125 T^{24} - 27019531250 T^{25} + 47089843750 T^{26} - 68701171875 T^{27} + 109863281250 T^{28} - 125732421875 T^{29} + 177001953125 T^{30} - 122070312500 T^{31} + 152587890625 T^{32} \))(\( 1 - 2 T + 30 T^{2} - 43 T^{3} + 444 T^{4} - 374 T^{5} + 4558 T^{6} - 1542 T^{7} + 38890 T^{8} + 1358 T^{9} + 298739 T^{10} + 87528 T^{11} + 2089207 T^{12} + 960318 T^{13} + 13406812 T^{14} + 7285190 T^{15} + 79555763 T^{16} + 44682604 T^{17} + 434330920 T^{18} + 237253766 T^{19} + 2171654600 T^{20} + 1117065100 T^{21} + 9944470375 T^{22} + 4553243750 T^{23} + 41896287500 T^{24} + 15004968750 T^{25} + 163219296875 T^{26} + 34190625000 T^{27} + 583474609375 T^{28} + 13261718750 T^{29} + 1898925781250 T^{30} - 376464843750 T^{31} + 5563964843750 T^{32} - 2282714843750 T^{33} + 13549804687500 T^{34} - 6561279296875 T^{35} + 22888183593750 T^{36} - 7629394531250 T^{37} + 19073486328125 T^{38} \))
$7$ (\( 1 + T + 9 T^{2} + 7 T^{3} + 49 T^{4} \))(\( 1 + T + 11 T^{2} + 2 T^{3} + 109 T^{4} + 82 T^{5} + 763 T^{6} + 98 T^{7} + 3773 T^{8} + 2401 T^{9} + 16807 T^{10} \))(\( 1 + T + 30 T^{2} + 27 T^{3} + 433 T^{4} + 276 T^{5} + 4116 T^{6} + 1468 T^{7} + 30789 T^{8} + 7220 T^{9} + 215523 T^{10} + 71932 T^{11} + 1411788 T^{12} + 662676 T^{13} + 7277431 T^{14} + 3176523 T^{15} + 24706290 T^{16} + 5764801 T^{17} + 40353607 T^{18} \))(\( 1 + 8 T + 69 T^{2} + 383 T^{3} + 2023 T^{4} + 8744 T^{5} + 35117 T^{6} + 124540 T^{7} + 409037 T^{8} + 1220581 T^{9} + 3374955 T^{10} + 8544067 T^{11} + 20042813 T^{12} + 42717220 T^{13} + 84315917 T^{14} + 146960408 T^{15} + 238003927 T^{16} + 315416969 T^{17} + 397771269 T^{18} + 322828856 T^{19} + 282475249 T^{20} \))(\( 1 - 3 T + 44 T^{2} - 86 T^{3} + 903 T^{4} - 1130 T^{5} + 12570 T^{6} - 8787 T^{7} + 138242 T^{8} - 31368 T^{9} + 1295186 T^{10} + 192432 T^{11} + 10916581 T^{12} + 4202178 T^{13} + 85242287 T^{14} + 40845279 T^{15} + 619253588 T^{16} + 285916953 T^{17} + 4176872063 T^{18} + 1441347054 T^{19} + 26210710981 T^{20} + 3234204624 T^{21} + 152377337714 T^{22} - 25832896824 T^{23} + 796937619842 T^{24} - 354587144709 T^{25} + 3550713879930 T^{26} - 2234379219590 T^{27} + 12498682342503 T^{28} - 8332454895002 T^{29} + 29841815205356 T^{30} - 14242684529829 T^{31} + 33232930569601 T^{32} \))(\( 1 - 16 T + 178 T^{2} - 1455 T^{3} + 9955 T^{4} - 58108 T^{5} + 301714 T^{6} - 1407213 T^{7} + 6017422 T^{8} - 23726689 T^{9} + 87362225 T^{10} - 301542447 T^{11} + 985064946 T^{12} - 3056240490 T^{13} + 9088222378 T^{14} - 26014931076 T^{15} + 72409145846 T^{16} - 196959942893 T^{17} + 528636416832 T^{18} - 1403209213983 T^{19} + 3700454917824 T^{20} - 9651037201757 T^{21} + 24836337025178 T^{22} - 62461849513476 T^{23} + 152745753507046 T^{24} - 359563637408010 T^{25} + 811243340823678 T^{26} - 1738332200008047 T^{27} + 3525380894295575 T^{28} - 6702202383220561 T^{29} + 11898409444516546 T^{30} - 19477639285980813 T^{31} + 29232770885937598 T^{32} - 39410186317109692 T^{33} + 47261974831482565 T^{34} - 48353913978769455 T^{35} + 41408231489722846 T^{36} - 26054617566567184 T^{37} + 11398895185373143 T^{38} \))
$11$ (\( ( 1 + T )^{2} \))(\( ( 1 + T )^{5} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{10} \))(\( ( 1 + T )^{16} \))(\( ( 1 - T )^{19} \))
$13$ (\( 1 - T + 21 T^{2} - 13 T^{3} + 169 T^{4} \))(\( 1 - 3 T + 41 T^{2} - 70 T^{3} + 703 T^{4} - 798 T^{5} + 9139 T^{6} - 11830 T^{7} + 90077 T^{8} - 85683 T^{9} + 371293 T^{10} \))(\( 1 + 25 T + 362 T^{2} + 3720 T^{3} + 30023 T^{4} + 199644 T^{5} + 1129889 T^{6} + 5549539 T^{7} + 23973798 T^{8} + 91726004 T^{9} + 311659374 T^{10} + 937872091 T^{11} + 2482366133 T^{12} + 5702032284 T^{13} + 11147329739 T^{14} + 17955729480 T^{15} + 22714963154 T^{16} + 20393268025 T^{17} + 10604499373 T^{18} \))(\( 1 + 24 T + 345 T^{2} + 3604 T^{3} + 30106 T^{4} + 210394 T^{5} + 1267194 T^{6} + 6699727 T^{7} + 31500585 T^{8} + 132761141 T^{9} + 504025295 T^{10} + 1725894833 T^{11} + 5323598865 T^{12} + 14719300219 T^{13} + 36192327834 T^{14} + 78117819442 T^{15} + 145315911754 T^{16} + 226145655268 T^{17} + 281427098745 T^{18} + 254507984952 T^{19} + 137858491849 T^{20} \))(\( 1 - 29 T + 484 T^{2} - 5963 T^{3} + 60059 T^{4} - 519448 T^{5} + 3973622 T^{6} - 27395967 T^{7} + 172503648 T^{8} - 1001381681 T^{9} + 5396768570 T^{10} - 27142907692 T^{11} + 127903601819 T^{12} - 566339584778 T^{13} + 2361372454287 T^{14} - 9284604535603 T^{15} + 34453994850514 T^{16} - 120699858962839 T^{17} + 399071944774503 T^{18} - 1244248067757266 T^{19} + 3653054771552459 T^{20} - 10077971625685756 T^{21} + 26049171104593130 T^{22} - 62835215433717077 T^{23} + 140716525158170208 T^{24} - 290520514874228691 T^{25} + 547797536098007078 T^{26} - 930934132361731576 T^{27} + 1399259694371086379 T^{28} - 1806044260609604639 T^{29} + 1905690170678455876 T^{30} - 1484390897408631953 T^{31} + 665416609183179841 T^{32} \))(\( 1 - 30 T + 562 T^{2} - 7714 T^{3} + 86174 T^{4} - 816779 T^{5} + 6795338 T^{6} - 50594899 T^{7} + 342860613 T^{8} - 2138677004 T^{9} + 12404189646 T^{10} - 67375248943 T^{11} + 344918250238 T^{12} - 1671783799767 T^{13} + 7702252631421 T^{14} - 33821159225255 T^{15} + 141873476477144 T^{16} - 569319222093999 T^{17} + 2188114499121778 T^{18} - 8058239297022679 T^{19} + 28445488488583114 T^{20} - 96214948533885831 T^{21} + 311696027820285368 T^{22} - 965966128632508055 T^{23} + 2859792486278197353 T^{24} - 8069381090769553503 T^{25} + 21643108688669397046 T^{26} - 54960060397827877903 T^{27} + \)\(13\!\cdots\!58\)\( T^{28} - \)\(29\!\cdots\!96\)\( T^{29} + \)\(61\!\cdots\!81\)\( T^{30} - \)\(11\!\cdots\!19\)\( T^{31} + \)\(20\!\cdots\!14\)\( T^{32} - \)\(32\!\cdots\!31\)\( T^{33} + \)\(44\!\cdots\!18\)\( T^{34} - \)\(51\!\cdots\!74\)\( T^{35} + \)\(48\!\cdots\!46\)\( T^{36} - \)\(33\!\cdots\!70\)\( T^{37} + \)\(14\!\cdots\!77\)\( T^{38} \))
$17$ (\( 1 - T + 29 T^{2} - 17 T^{3} + 289 T^{4} \))(\( 1 - 9 T + 57 T^{2} - 198 T^{3} + 407 T^{4} - 774 T^{5} + 6919 T^{6} - 57222 T^{7} + 280041 T^{8} - 751689 T^{9} + 1419857 T^{10} \))(\( 1 + 104 T^{2} - 2 T^{3} + 5104 T^{4} - 71 T^{5} + 158983 T^{6} + 421 T^{7} + 3558613 T^{8} + 35476 T^{9} + 60496421 T^{10} + 121669 T^{11} + 781083479 T^{12} - 5929991 T^{13} + 7246950128 T^{14} - 48275138 T^{15} + 42675221992 T^{16} + 118587876497 T^{18} \))(\( 1 + 9 T + 110 T^{2} + 774 T^{3} + 6151 T^{4} + 35553 T^{5} + 218781 T^{6} + 1085060 T^{7} + 5614861 T^{8} + 24262528 T^{9} + 108678001 T^{10} + 412462976 T^{11} + 1622694829 T^{12} + 5330899780 T^{13} + 18272807901 T^{14} + 50480175921 T^{15} + 148470186919 T^{16} + 317602132902 T^{17} + 767333318510 T^{18} + 1067290888473 T^{19} + 2015993900449 T^{20} \))(\( 1 + 4 T + 148 T^{2} + 583 T^{3} + 10745 T^{4} + 43320 T^{5} + 515227 T^{6} + 2179124 T^{7} + 18526576 T^{8} + 82602469 T^{9} + 535894397 T^{10} + 2483086055 T^{11} + 13001121748 T^{12} + 60878470574 T^{13} + 271172527905 T^{14} + 1237750037190 T^{15} + 4928103545644 T^{16} + 21041750632230 T^{17} + 78368860564545 T^{18} + 299095925930062 T^{19} + 1085866689514708 T^{20} + 3525627116794135 T^{21} + 12935187984300893 T^{22} + 33894987515983637 T^{23} + 129236900388252016 T^{24} + 258417687783648628 T^{25} + 1038694489346636923 T^{26} + 1484658548046661560 T^{27} + 6260275939033781945 T^{28} + 5774368993184161271 T^{29} + 24919918330791337492 T^{30} + 11449692206039263172 T^{31} + 48661191875666868481 T^{32} \))(\( 1 - 9 T + 183 T^{2} - 1347 T^{3} + 15548 T^{4} - 98617 T^{5} + 846850 T^{6} - 4811733 T^{7} + 34286925 T^{8} - 179579748 T^{9} + 1125060593 T^{10} - 5525777697 T^{11} + 31418753186 T^{12} - 145657082652 T^{13} + 764547608321 T^{14} - 3348441748187 T^{15} + 16394259310095 T^{16} - 67844639509120 T^{17} + 312189799299291 T^{18} - 1221450751175355 T^{19} + 5307226588087947 T^{20} - 19607100818135680 T^{21} + 80544995990496735 T^{22} - 279665203250326427 T^{23} + 1085548273507830097 T^{24} - 3515807882851352988 T^{25} + 12892329489657762178 T^{26} - 38546484887159593377 T^{27} + \)\(13\!\cdots\!21\)\( T^{28} - \)\(36\!\cdots\!52\)\( T^{29} + \)\(11\!\cdots\!25\)\( T^{30} - \)\(28\!\cdots\!13\)\( T^{31} + \)\(83\!\cdots\!50\)\( T^{32} - \)\(16\!\cdots\!93\)\( T^{33} + \)\(44\!\cdots\!64\)\( T^{34} - \)\(65\!\cdots\!07\)\( T^{35} + \)\(15\!\cdots\!91\)\( T^{36} - \)\(12\!\cdots\!81\)\( T^{37} + \)\(23\!\cdots\!53\)\( T^{38} \))
$19$ (\( 1 - 2 T + 18 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 + 47 T^{2} - 40 T^{3} + 1018 T^{4} - 1584 T^{5} + 19342 T^{6} - 14440 T^{7} + 322373 T^{8} + 2476099 T^{10} \))(\( 1 + T + 43 T^{2} - 36 T^{3} + 1401 T^{4} - 2201 T^{5} + 37714 T^{6} - 57737 T^{7} + 844774 T^{8} - 1473978 T^{9} + 16050706 T^{10} - 20843057 T^{11} + 258680326 T^{12} - 286836521 T^{13} + 3469014699 T^{14} - 1693651716 T^{15} + 38436484777 T^{16} + 16983563041 T^{17} + 322687697779 T^{18} \))(\( 1 + 7 T + 174 T^{2} + 947 T^{3} + 13168 T^{4} + 57841 T^{5} + 590791 T^{6} + 2153726 T^{7} + 17956652 T^{8} + 55616555 T^{9} + 396040088 T^{10} + 1056714545 T^{11} + 6482351372 T^{12} + 14772406634 T^{13} + 76992473911 T^{14} + 143220042259 T^{15} + 619500161008 T^{16} + 846496536833 T^{17} + 2955139969134 T^{18} + 2258813884453 T^{19} + 6131066257801 T^{20} \))(\( 1 - 11 T + 256 T^{2} - 2155 T^{3} + 28703 T^{4} - 196874 T^{5} + 1946583 T^{6} - 11316493 T^{7} + 92103131 T^{8} - 467059445 T^{9} + 3311052519 T^{10} - 14983097012 T^{11} + 95731277525 T^{12} - 393470547945 T^{13} + 2309353137802 T^{14} - 8727038923427 T^{15} + 47415354856576 T^{16} - 165813739545113 T^{17} + 833676482746522 T^{18} - 2698814488354755 T^{19} + 12475795818335525 T^{20} - 37099631528316188 T^{21} + 155771382793624239 T^{22} - 417491238318524855 T^{23} + 1564239331611981371 T^{24} - 3651693073102169047 T^{25} + 11934629349309043983 T^{26} - 22933903230327967406 T^{27} + 63528778121956019183 T^{28} - 90624179361163962145 T^{29} + \)\(20\!\cdots\!76\)\( T^{30} - \)\(16\!\cdots\!89\)\( T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( 1 + T + 67 T^{2} + 184 T^{3} + 2966 T^{4} + 8824 T^{5} + 106255 T^{6} + 326177 T^{7} + 2966913 T^{8} + 9395989 T^{9} + 74654382 T^{10} + 214584734 T^{11} + 1667965012 T^{12} + 4563077375 T^{13} + 34167124375 T^{14} + 86816216559 T^{15} + 685386182044 T^{16} + 1611427061035 T^{17} + 13065531169745 T^{18} + 31178572194644 T^{19} + 248245092225155 T^{20} + 581725169033635 T^{21} + 4701063822639796 T^{22} + 11313976158185439 T^{23} + 84601182497813125 T^{24} + 214673995178042375 T^{25} + 1490946785867595868 T^{26} + 3644413357525216094 T^{27} + 24090050656694017578 T^{28} + 57607431116569360189 T^{29} + \)\(34\!\cdots\!47\)\( T^{30} + \)\(72\!\cdots\!97\)\( T^{31} + \)\(44\!\cdots\!45\)\( T^{32} + \)\(70\!\cdots\!04\)\( T^{33} + \)\(45\!\cdots\!34\)\( T^{34} + \)\(53\!\cdots\!04\)\( T^{35} + \)\(36\!\cdots\!13\)\( T^{36} + \)\(10\!\cdots\!41\)\( T^{37} + \)\(19\!\cdots\!79\)\( T^{38} \))
$23$ (\( 1 + T - T^{2} + 23 T^{3} + 529 T^{4} \))(\( 1 + 44 T^{2} + 120 T^{3} + 960 T^{4} + 5367 T^{5} + 22080 T^{6} + 63480 T^{7} + 535348 T^{8} + 6436343 T^{10} \))(\( 1 + 4 T + 138 T^{2} + 522 T^{3} + 9453 T^{4} + 33304 T^{5} + 420850 T^{6} + 1335524 T^{7} + 13258256 T^{8} + 36660141 T^{9} + 304939888 T^{10} + 706492196 T^{11} + 5120481950 T^{12} + 9319824664 T^{13} + 60842750379 T^{14} + 77274734058 T^{15} + 469865911686 T^{16} + 313243941124 T^{17} + 1801152661463 T^{18} \))(\( 1 + 8 T + 174 T^{2} + 1061 T^{3} + 13167 T^{4} + 62991 T^{5} + 590981 T^{6} + 2282245 T^{7} + 18545131 T^{8} + 61102613 T^{9} + 463710165 T^{10} + 1405360099 T^{11} + 9810374299 T^{12} + 27768074915 T^{13} + 165380714021 T^{14} + 405431681913 T^{15} + 1949188550463 T^{16} + 3612519799267 T^{17} + 13626111438894 T^{18} + 14409221291704 T^{19} + 41426511213649 T^{20} \))(\( 1 - 17 T + 281 T^{2} - 3083 T^{3} + 31442 T^{4} - 258509 T^{5} + 1980781 T^{6} - 12927771 T^{7} + 78580987 T^{8} - 409112769 T^{9} + 1950666600 T^{10} - 7477683240 T^{11} + 23386859678 T^{12} - 24219446630 T^{13} - 230677306737 T^{14} + 2585989568146 T^{15} - 13921455733514 T^{16} + 59477760067358 T^{17} - 122028295263873 T^{18} - 294678007147210 T^{19} + 6544602199151198 T^{20} - 48128934177991320 T^{21} + 288768664273607400 T^{22} - 1392957566583832743 T^{23} + 6153754516323452347 T^{24} - 23284889143434188973 T^{25} + 82056846308282879869 T^{26} - \)\(24\!\cdots\!43\)\( T^{27} + \)\(68\!\cdots\!82\)\( T^{28} - \)\(15\!\cdots\!89\)\( T^{29} + \)\(32\!\cdots\!29\)\( T^{30} - \)\(45\!\cdots\!19\)\( T^{31} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 + 2 T + 213 T^{2} + 669 T^{3} + 22392 T^{4} + 94543 T^{5} + 1593787 T^{6} + 8013638 T^{7} + 88423733 T^{8} + 476238400 T^{9} + 4091922977 T^{10} + 21832602474 T^{11} + 161858477319 T^{12} + 823760521084 T^{13} + 5513924152053 T^{14} + 26612656518727 T^{15} + 163066207801709 T^{16} + 748991437565441 T^{17} + 4234234118194577 T^{18} + 18427574037755267 T^{19} + 97387384718475271 T^{20} + 396216470472118289 T^{21} + 1984026550323393403 T^{22} + 7447312412857082407 T^{23} + 35489507118597262179 T^{24} + \)\(12\!\cdots\!76\)\( T^{25} + \)\(55\!\cdots\!93\)\( T^{26} + \)\(17\!\cdots\!94\)\( T^{27} + \)\(73\!\cdots\!51\)\( T^{28} + \)\(19\!\cdots\!00\)\( T^{29} + \)\(84\!\cdots\!91\)\( T^{30} + \)\(17\!\cdots\!98\)\( T^{31} + \)\(80\!\cdots\!21\)\( T^{32} + \)\(10\!\cdots\!87\)\( T^{33} + \)\(59\!\cdots\!44\)\( T^{34} + \)\(41\!\cdots\!09\)\( T^{35} + \)\(30\!\cdots\!39\)\( T^{36} + \)\(64\!\cdots\!38\)\( T^{37} + \)\(74\!\cdots\!87\)\( T^{38} \))
$29$ (\( 1 - 7 T + 65 T^{2} - 203 T^{3} + 841 T^{4} \))(\( 1 - 22 T + 294 T^{2} - 2758 T^{3} + 20514 T^{4} - 121826 T^{5} + 594906 T^{6} - 2319478 T^{7} + 7170366 T^{8} - 15560182 T^{9} + 20511149 T^{10} \))(\( 1 + 13 T + 214 T^{2} + 1943 T^{3} + 19002 T^{4} + 137760 T^{5} + 1039285 T^{6} + 6422685 T^{7} + 40684341 T^{8} + 217165996 T^{9} + 1179845889 T^{10} + 5401478085 T^{11} + 25347121865 T^{12} + 97435030560 T^{13} + 389752853298 T^{14} + 1155741712703 T^{15} + 3691473530126 T^{16} + 6503203368493 T^{17} + 14507145975869 T^{18} \))(\( 1 + 22 T + 391 T^{2} + 4871 T^{3} + 53072 T^{4} + 480345 T^{5} + 3945872 T^{6} + 28516522 T^{7} + 190877155 T^{8} + 1152628909 T^{9} + 6510592529 T^{10} + 33426238361 T^{11} + 160527687355 T^{12} + 695489455058 T^{13} + 2790840294032 T^{14} + 9852427866405 T^{15} + 31568463292112 T^{16} + 84024147501139 T^{17} + 195596347467751 T^{18} + 319157211469118 T^{19} + 420707233300201 T^{20} \))(\( 1 + 14 T + 334 T^{2} + 3621 T^{3} + 49661 T^{4} + 448206 T^{5} + 4564120 T^{6} + 35750417 T^{7} + 298333991 T^{8} + 2081479145 T^{9} + 15018732563 T^{10} + 95130596598 T^{11} + 615659230410 T^{12} + 3600942502746 T^{13} + 21492497746452 T^{14} + 117791679348169 T^{15} + 660271927861264 T^{16} + 3415958701096901 T^{17} + 18075190604766132 T^{18} + 87823386699472194 T^{19} + 435444076143615210 T^{20} + 1951237841280471102 T^{21} + 8933492380334501723 T^{22} + 35905257791013075805 T^{23} + \)\(14\!\cdots\!51\)\( T^{24} + \)\(51\!\cdots\!73\)\( T^{25} + \)\(19\!\cdots\!20\)\( T^{26} + \)\(54\!\cdots\!74\)\( T^{27} + \)\(17\!\cdots\!01\)\( T^{28} + \)\(37\!\cdots\!69\)\( T^{29} + \)\(99\!\cdots\!54\)\( T^{30} + \)\(12\!\cdots\!86\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 - 18 T + 462 T^{2} - 6061 T^{3} + 93604 T^{4} - 996900 T^{5} + 11759994 T^{6} - 107217792 T^{7} + 1054635061 T^{8} - 8487746999 T^{9} + 72764025456 T^{10} - 527227548218 T^{11} + 4043724207141 T^{12} - 26736431457334 T^{13} + 186581996265917 T^{14} - 1136275181185399 T^{15} + 7295544248697733 T^{16} - 41171691492631474 T^{17} + 244889820479080132 T^{18} - 1284583574588905064 T^{19} + 7101804793893323828 T^{20} - 34625392545303069634 T^{21} + \)\(17\!\cdots\!37\)\( T^{22} - \)\(80\!\cdots\!19\)\( T^{23} + \)\(38\!\cdots\!33\)\( T^{24} - \)\(15\!\cdots\!14\)\( T^{25} + \)\(69\!\cdots\!69\)\( T^{26} - \)\(26\!\cdots\!98\)\( T^{27} + \)\(10\!\cdots\!64\)\( T^{28} - \)\(35\!\cdots\!99\)\( T^{29} + \)\(12\!\cdots\!69\)\( T^{30} - \)\(37\!\cdots\!72\)\( T^{31} + \)\(12\!\cdots\!66\)\( T^{32} - \)\(29\!\cdots\!00\)\( T^{33} + \)\(80\!\cdots\!96\)\( T^{34} - \)\(15\!\cdots\!81\)\( T^{35} + \)\(33\!\cdots\!58\)\( T^{36} - \)\(37\!\cdots\!98\)\( T^{37} + \)\(61\!\cdots\!69\)\( T^{38} \))
$31$ (\( 1 + 10 T + 66 T^{2} + 310 T^{3} + 961 T^{4} \))(\( 1 + 9 T + 97 T^{2} + 532 T^{3} + 4776 T^{4} + 23574 T^{5} + 148056 T^{6} + 511252 T^{7} + 2889727 T^{8} + 8311689 T^{9} + 28629151 T^{10} \))(\( 1 + 6 T + 142 T^{2} + 687 T^{3} + 10475 T^{4} + 42011 T^{5} + 527755 T^{6} + 1849345 T^{7} + 20530776 T^{8} + 63843393 T^{9} + 636454056 T^{10} + 1777220545 T^{11} + 15722349205 T^{12} + 38798040731 T^{13} + 299890356725 T^{14} + 609715028847 T^{15} + 3906791203762 T^{16} + 5117346224646 T^{17} + 26439622160671 T^{18} \))(\( 1 + T + 208 T^{2} - 36 T^{3} + 19072 T^{4} - 31619 T^{5} + 1036266 T^{6} - 3527359 T^{7} + 39600618 T^{8} - 191932671 T^{9} + 1272956730 T^{10} - 5949912801 T^{11} + 38056193898 T^{12} - 105083551969 T^{13} + 957013412586 T^{14} - 905225125469 T^{15} + 16926470204032 T^{16} - 990454107996 T^{17} + 177401335787728 T^{18} + 26439622160671 T^{19} + 819628286980801 T^{20} \))(\( 1 - 7 T + 242 T^{2} - 1298 T^{3} + 27299 T^{4} - 113150 T^{5} + 1963020 T^{6} - 5826211 T^{7} + 100415825 T^{8} - 157573495 T^{9} + 3822862772 T^{10} + 1236593646 T^{11} + 112254972921 T^{12} + 344615751122 T^{13} + 2774684645630 T^{14} + 18116634165469 T^{15} + 74136043658692 T^{16} + 561615659129539 T^{17} + 2666471944450430 T^{18} + 10266447841675502 T^{19} + 103669824846974841 T^{20} + 35402626216974546 T^{21} + 3392804782107863732 T^{22} - 4335258762056587945 T^{23} + 85643757159743903825 T^{24} - \)\(15\!\cdots\!81\)\( T^{25} + \)\(16\!\cdots\!20\)\( T^{26} - \)\(28\!\cdots\!50\)\( T^{27} + \)\(21\!\cdots\!39\)\( T^{28} - \)\(31\!\cdots\!18\)\( T^{29} + \)\(18\!\cdots\!82\)\( T^{30} - \)\(16\!\cdots\!57\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 - 5 T + 343 T^{2} - 1413 T^{3} + 55786 T^{4} - 189873 T^{5} + 5803508 T^{6} - 16428794 T^{7} + 440482242 T^{8} - 1056585478 T^{9} + 26411005702 T^{10} - 55618027760 T^{11} + 1320762320572 T^{12} - 2555072969030 T^{13} + 57151273227112 T^{14} - 105370999317862 T^{15} + 2189710779889193 T^{16} - 3901159558766782 T^{17} + 75249116390597913 T^{18} - 128495348032862550 T^{19} + 2332722608108535303 T^{20} - 3749014335974877502 T^{21} + 65233673843678948663 T^{22} - 97312330661031232102 T^{23} + \)\(16\!\cdots\!12\)\( T^{24} - \)\(22\!\cdots\!30\)\( T^{25} + \)\(36\!\cdots\!92\)\( T^{26} - \)\(47\!\cdots\!60\)\( T^{27} + \)\(69\!\cdots\!42\)\( T^{28} - \)\(86\!\cdots\!78\)\( T^{29} + \)\(11\!\cdots\!02\)\( T^{30} - \)\(12\!\cdots\!34\)\( T^{31} + \)\(14\!\cdots\!28\)\( T^{32} - \)\(14\!\cdots\!33\)\( T^{33} + \)\(13\!\cdots\!86\)\( T^{34} - \)\(10\!\cdots\!53\)\( T^{35} + \)\(77\!\cdots\!73\)\( T^{36} - \)\(34\!\cdots\!05\)\( T^{37} + \)\(21\!\cdots\!71\)\( T^{38} \))
$37$ (\( 1 + 15 T + 125 T^{2} + 555 T^{3} + 1369 T^{4} \))(\( 1 - 21 T + 230 T^{2} - 1475 T^{3} + 6524 T^{4} - 28347 T^{5} + 241388 T^{6} - 2019275 T^{7} + 11650190 T^{8} - 39357381 T^{9} + 69343957 T^{10} \))(\( 1 + 28 T + 539 T^{2} + 7410 T^{3} + 83348 T^{4} + 782441 T^{5} + 6435198 T^{6} + 47194645 T^{7} + 318285492 T^{8} + 1995890935 T^{9} + 11776563204 T^{10} + 64609469005 T^{11} + 325962084294 T^{12} + 1466420407001 T^{13} + 5779680128036 T^{14} + 19012032690690 T^{15} + 51168281774687 T^{16} + 98349424709788 T^{17} + 129961739795077 T^{18} \))(\( 1 + 34 T + 793 T^{2} + 13175 T^{3} + 180762 T^{4} + 2066371 T^{5} + 20697909 T^{6} + 181841426 T^{7} + 1435620397 T^{8} + 10145304508 T^{9} + 65048327217 T^{10} + 375376266796 T^{11} + 1965364323493 T^{12} + 9210813751178 T^{13} + 38791213829349 T^{14} + 143290341770047 T^{15} + 463785837143658 T^{16} + 1250727481227275 T^{17} + 2785396206959353 T^{18} + 4418699153032618 T^{19} + 4808584372417849 T^{20} \))(\( 1 - 44 T + 1282 T^{2} - 27505 T^{3} + 486997 T^{4} - 7339584 T^{5} + 97519605 T^{6} - 1159199685 T^{7} + 12530208720 T^{8} - 124190621810 T^{9} + 1139015021895 T^{10} - 9715191946968 T^{11} + 77495349413570 T^{12} - 579786800975753 T^{13} + 4082036132940175 T^{14} - 27081251113013163 T^{15} + 169572375329145270 T^{16} - 1002006291181487031 T^{17} + 5588307465995099575 T^{18} - 29367940829824816709 T^{19} + \)\(14\!\cdots\!70\)\( T^{20} - \)\(67\!\cdots\!76\)\( T^{21} + \)\(29\!\cdots\!55\)\( T^{22} - \)\(11\!\cdots\!30\)\( T^{23} + \)\(44\!\cdots\!20\)\( T^{24} - \)\(15\!\cdots\!45\)\( T^{25} + \)\(46\!\cdots\!45\)\( T^{26} - \)\(13\!\cdots\!92\)\( T^{27} + \)\(32\!\cdots\!57\)\( T^{28} - \)\(66\!\cdots\!85\)\( T^{29} + \)\(11\!\cdots\!98\)\( T^{30} - \)\(14\!\cdots\!92\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 - 36 T + 1024 T^{2} - 21201 T^{3} + 380292 T^{4} - 5850328 T^{5} + 81254125 T^{6} - 1019788640 T^{7} + 11815554140 T^{8} - 126710332944 T^{9} + 1271257083467 T^{10} - 11960714406414 T^{11} + 106168333693028 T^{12} - 890687617162222 T^{13} + 7087850229456213 T^{14} - 53563561848469615 T^{15} + 385252627270101861 T^{16} - 2638734799035024948 T^{17} + 17233429911203201094 T^{18} - \)\(10\!\cdots\!98\)\( T^{19} + \)\(63\!\cdots\!78\)\( T^{20} - \)\(36\!\cdots\!12\)\( T^{21} + \)\(19\!\cdots\!33\)\( T^{22} - \)\(10\!\cdots\!15\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} - \)\(22\!\cdots\!98\)\( T^{25} + \)\(10\!\cdots\!24\)\( T^{26} - \)\(42\!\cdots\!94\)\( T^{27} + \)\(16\!\cdots\!59\)\( T^{28} - \)\(60\!\cdots\!56\)\( T^{29} + \)\(21\!\cdots\!20\)\( T^{30} - \)\(67\!\cdots\!40\)\( T^{31} + \)\(19\!\cdots\!25\)\( T^{32} - \)\(52\!\cdots\!92\)\( T^{33} + \)\(12\!\cdots\!56\)\( T^{34} - \)\(26\!\cdots\!41\)\( T^{35} + \)\(46\!\cdots\!08\)\( T^{36} - \)\(60\!\cdots\!44\)\( T^{37} + \)\(62\!\cdots\!73\)\( T^{38} \))
$41$ (\( 1 + 6 T + 70 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 - 2 T + 117 T^{2} - 104 T^{3} + 7650 T^{4} - 6412 T^{5} + 313650 T^{6} - 174824 T^{7} + 8063757 T^{8} - 5651522 T^{9} + 115856201 T^{10} \))(\( 1 - 11 T + 208 T^{2} - 1692 T^{3} + 19406 T^{4} - 134953 T^{5} + 1192139 T^{6} - 7482356 T^{7} + 56261965 T^{8} - 330580126 T^{9} + 2306740565 T^{10} - 12577840436 T^{11} + 82163412019 T^{12} - 381344924233 T^{13} + 2248305436606 T^{14} - 8037176375772 T^{15} + 40508888967248 T^{16} - 87834177520331 T^{17} + 327381934393961 T^{18} \))(\( 1 - 7 T + 213 T^{2} - 1495 T^{3} + 25030 T^{4} - 164735 T^{5} + 2009097 T^{6} - 12069775 T^{7} + 120803732 T^{8} - 649415110 T^{9} + 5603015678 T^{10} - 26626019510 T^{11} + 203071073492 T^{12} - 831860962775 T^{13} + 5677227947817 T^{14} - 19085571271735 T^{15} + 118895109152230 T^{16} - 291157639452095 T^{17} + 1700789073802773 T^{18} - 2291673540757727 T^{19} + 13422659310152401 T^{20} \))(\( 1 + T + 383 T^{2} + 97 T^{3} + 72133 T^{4} - 36484 T^{5} + 8940132 T^{6} - 11116576 T^{7} + 822288751 T^{8} - 1570001050 T^{9} + 59961068198 T^{10} - 146302329390 T^{11} + 3612517028175 T^{12} - 9999050115175 T^{13} + 184676178396423 T^{14} - 524503953856591 T^{15} + 8135607647569016 T^{16} - 21504662108120231 T^{17} + 310440655884387063 T^{18} - 689144532987976175 T^{19} + 10208109730052816175 T^{20} - 16950032080576047390 T^{21} + \)\(28\!\cdots\!18\)\( T^{22} - \)\(30\!\cdots\!50\)\( T^{23} + \)\(65\!\cdots\!71\)\( T^{24} - \)\(36\!\cdots\!36\)\( T^{25} + \)\(12\!\cdots\!32\)\( T^{26} - \)\(20\!\cdots\!44\)\( T^{27} + \)\(16\!\cdots\!73\)\( T^{28} + \)\(89\!\cdots\!37\)\( T^{29} + \)\(14\!\cdots\!63\)\( T^{30} + \)\(15\!\cdots\!01\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 9 T + 448 T^{2} - 4206 T^{3} + 103423 T^{4} - 969280 T^{5} + 16177747 T^{6} - 147258414 T^{7} + 1905871579 T^{8} - 16574130895 T^{9} + 178677845152 T^{10} - 1470061445528 T^{11} + 13779983008390 T^{12} - 106642503419401 T^{13} + 893165642362411 T^{14} - 6478101398666722 T^{15} + 49342013883210278 T^{16} - 334427836955579823 T^{17} + 2343431797311796339 T^{18} - 14793149713609808212 T^{19} + 96080703689783649899 T^{20} - \)\(56\!\cdots\!63\)\( T^{21} + \)\(34\!\cdots\!38\)\( T^{22} - \)\(18\!\cdots\!42\)\( T^{23} + \)\(10\!\cdots\!11\)\( T^{24} - \)\(50\!\cdots\!41\)\( T^{25} + \)\(26\!\cdots\!90\)\( T^{26} - \)\(11\!\cdots\!88\)\( T^{27} + \)\(58\!\cdots\!72\)\( T^{28} - \)\(22\!\cdots\!95\)\( T^{29} + \)\(10\!\cdots\!39\)\( T^{30} - \)\(33\!\cdots\!34\)\( T^{31} + \)\(14\!\cdots\!87\)\( T^{32} - \)\(36\!\cdots\!80\)\( T^{33} + \)\(16\!\cdots\!23\)\( T^{34} - \)\(26\!\cdots\!46\)\( T^{35} + \)\(11\!\cdots\!88\)\( T^{36} - \)\(96\!\cdots\!89\)\( T^{37} + \)\(43\!\cdots\!61\)\( T^{38} \))
$43$ (\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( 1 - 2 T + 81 T^{2} - 324 T^{3} + 3993 T^{4} - 25462 T^{5} + 171699 T^{6} - 599076 T^{7} + 6440067 T^{8} - 6837602 T^{9} + 147008443 T^{10} \))(\( 1 + 129 T^{2} - 60 T^{3} + 9553 T^{4} - 24733 T^{5} + 502325 T^{6} - 2549837 T^{7} + 20723009 T^{8} - 135963106 T^{9} + 891089387 T^{10} - 4714648613 T^{11} + 39938353775 T^{12} - 84557205133 T^{13} + 1404371655979 T^{14} - 379281782940 T^{15} + 35064600832803 T^{16} + 502592611936843 T^{18} \))(\( 1 + 26 T + 554 T^{2} + 8160 T^{3} + 105082 T^{4} + 1121945 T^{5} + 10880480 T^{6} + 93125636 T^{7} + 742271786 T^{8} + 5378615029 T^{9} + 36811222298 T^{10} + 231280446247 T^{11} + 1372460532314 T^{12} + 7404139941452 T^{13} + 37198195904480 T^{14} + 164935387581635 T^{15} + 664261471915018 T^{16} + 2218039866633120 T^{17} + 6475262953790954 T^{18} + 13067407910357918 T^{19} + 21611482313284249 T^{20} \))(\( 1 - 15 T + 448 T^{2} - 4823 T^{3} + 86525 T^{4} - 727779 T^{5} + 10205301 T^{6} - 69859008 T^{7} + 862098746 T^{8} - 4933869009 T^{9} + 57799274913 T^{10} - 283739397474 T^{11} + 3297704146195 T^{12} - 14310116513446 T^{13} + 166477097511490 T^{14} - 660993107014588 T^{15} + 7544949887158154 T^{16} - 28422703601627284 T^{17} + 307816153298745010 T^{18} - 1137754433634551122 T^{19} + 11274194232715612195 T^{20} - 41712087040410872982 T^{21} + \)\(36\!\cdots\!37\)\( T^{22} - \)\(13\!\cdots\!63\)\( T^{23} + \)\(10\!\cdots\!46\)\( T^{24} - \)\(35\!\cdots\!44\)\( T^{25} + \)\(22\!\cdots\!49\)\( T^{26} - \)\(67\!\cdots\!53\)\( T^{27} + \)\(34\!\cdots\!25\)\( T^{28} - \)\(82\!\cdots\!89\)\( T^{29} + \)\(33\!\cdots\!52\)\( T^{30} - \)\(47\!\cdots\!05\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 33 T + 1037 T^{2} - 21896 T^{3} + 424125 T^{4} - 6820060 T^{5} + 101347936 T^{6} - 1340516251 T^{7} + 16553669822 T^{8} - 187847728848 T^{9} + 2006813485354 T^{10} - 20043358983283 T^{11} + 189629607325842 T^{12} - 1694298724514145 T^{13} + 14402332515529400 T^{14} - 116323501465025519 T^{15} + 896401430449899433 T^{16} - 6586461170998808490 T^{17} + 46249378418886701836 T^{18} - \)\(31\!\cdots\!58\)\( T^{19} + \)\(19\!\cdots\!48\)\( T^{20} - \)\(12\!\cdots\!10\)\( T^{21} + \)\(71\!\cdots\!31\)\( T^{22} - \)\(39\!\cdots\!19\)\( T^{23} + \)\(21\!\cdots\!00\)\( T^{24} - \)\(10\!\cdots\!05\)\( T^{25} + \)\(51\!\cdots\!94\)\( T^{26} - \)\(23\!\cdots\!83\)\( T^{27} + \)\(10\!\cdots\!22\)\( T^{28} - \)\(40\!\cdots\!52\)\( T^{29} + \)\(15\!\cdots\!54\)\( T^{30} - \)\(53\!\cdots\!51\)\( T^{31} + \)\(17\!\cdots\!48\)\( T^{32} - \)\(50\!\cdots\!40\)\( T^{33} + \)\(13\!\cdots\!75\)\( T^{34} - \)\(29\!\cdots\!96\)\( T^{35} + \)\(60\!\cdots\!91\)\( T^{36} - \)\(83\!\cdots\!17\)\( T^{37} + \)\(10\!\cdots\!07\)\( T^{38} \))
$47$ (\( ( 1 + 2 T + 47 T^{2} )^{2} \))(\( 1 - 12 T + 123 T^{2} - 912 T^{3} + 9114 T^{4} - 63432 T^{5} + 428358 T^{6} - 2014608 T^{7} + 12770229 T^{8} - 58556172 T^{9} + 229345007 T^{10} \))(\( 1 + 8 T + 222 T^{2} + 1202 T^{3} + 22863 T^{4} + 97177 T^{5} + 1663930 T^{6} + 5924072 T^{7} + 94856161 T^{8} + 295769250 T^{9} + 4458239567 T^{10} + 13086275048 T^{11} + 172754204390 T^{12} + 474192760537 T^{13} + 5243514895041 T^{14} + 12956616825458 T^{15} + 112470332742786 T^{16} + 190490293294088 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 6 T + 269 T^{2} + 1304 T^{3} + 32931 T^{4} + 109153 T^{5} + 2420805 T^{6} + 3899537 T^{7} + 125950211 T^{8} + 28007566 T^{9} + 5815612042 T^{10} + 1316355602 T^{11} + 278224016099 T^{12} + 404861629951 T^{13} + 11812756163205 T^{14} + 25033695549071 T^{15} + 354970339999299 T^{16} + 660636549083752 T^{17} + 6405236112013709 T^{18} + 6714782838616602 T^{19} + 52599132235830049 T^{20} \))(\( 1 - 2 T + 345 T^{2} - 472 T^{3} + 59324 T^{4} - 69737 T^{5} + 6735408 T^{6} - 9348373 T^{7} + 564507457 T^{8} - 1149443645 T^{9} + 37301551166 T^{10} - 116061097357 T^{11} + 2055718093976 T^{12} - 9128366519924 T^{13} + 101022104014745 T^{14} - 554444374720290 T^{15} + 4762044711408724 T^{16} - 26058885611853630 T^{17} + 223157827768571705 T^{18} - 947734397198069452 T^{19} + 10031248524530901656 T^{20} - 26618033185768846499 T^{21} + \)\(40\!\cdots\!14\)\( T^{22} - \)\(58\!\cdots\!35\)\( T^{23} + \)\(13\!\cdots\!77\)\( T^{24} - \)\(10\!\cdots\!91\)\( T^{25} + \)\(35\!\cdots\!92\)\( T^{26} - \)\(17\!\cdots\!11\)\( T^{27} + \)\(68\!\cdots\!84\)\( T^{28} - \)\(25\!\cdots\!44\)\( T^{29} + \)\(88\!\cdots\!05\)\( T^{30} - \)\(24\!\cdots\!86\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 28 T + 898 T^{2} + 17922 T^{3} + 350426 T^{4} + 5544633 T^{5} + 83267306 T^{6} + 1104765804 T^{7} + 13844918890 T^{8} + 159324526669 T^{9} + 1735851110387 T^{10} + 17710505983964 T^{11} + 171751351753377 T^{12} + 1576732324978507 T^{13} + 13809808214961932 T^{14} + 115211050611593124 T^{15} + 919647267819215451 T^{16} + 7016401129647590803 T^{17} + 51309951838064008710 T^{18} + \)\(35\!\cdots\!64\)\( T^{19} + \)\(24\!\cdots\!70\)\( T^{20} + \)\(15\!\cdots\!27\)\( T^{21} + \)\(95\!\cdots\!73\)\( T^{22} + \)\(56\!\cdots\!44\)\( T^{23} + \)\(31\!\cdots\!24\)\( T^{24} + \)\(16\!\cdots\!03\)\( T^{25} + \)\(87\!\cdots\!51\)\( T^{26} + \)\(42\!\cdots\!04\)\( T^{27} + \)\(19\!\cdots\!29\)\( T^{28} + \)\(83\!\cdots\!81\)\( T^{29} + \)\(34\!\cdots\!70\)\( T^{30} + \)\(12\!\cdots\!64\)\( T^{31} + \)\(45\!\cdots\!62\)\( T^{32} + \)\(14\!\cdots\!77\)\( T^{33} + \)\(42\!\cdots\!18\)\( T^{34} + \)\(10\!\cdots\!62\)\( T^{35} + \)\(23\!\cdots\!26\)\( T^{36} + \)\(35\!\cdots\!92\)\( T^{37} + \)\(58\!\cdots\!83\)\( T^{38} \))
$53$ (\( 1 + 10 T + 110 T^{2} + 530 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 149 T^{2} - 864 T^{3} + 11198 T^{4} - 67480 T^{5} + 593494 T^{6} - 2426976 T^{7} + 22182673 T^{8} - 31561924 T^{9} + 418195493 T^{10} \))(\( 1 + 25 T + 502 T^{2} + 6504 T^{3} + 78574 T^{4} + 759789 T^{5} + 7306613 T^{6} + 59443048 T^{7} + 490031585 T^{8} + 3510456750 T^{9} + 25971674005 T^{10} + 166975521832 T^{11} + 1087786623601 T^{12} + 5995100668509 T^{13} + 32859292666982 T^{14} + 144157004783016 T^{15} + 589704992198174 T^{16} + 1556492260284025 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 19 T + 429 T^{2} + 5667 T^{3} + 79814 T^{4} + 841829 T^{5} + 9235601 T^{6} + 82489839 T^{7} + 758376410 T^{8} + 5859939628 T^{9} + 46341968186 T^{10} + 310576800284 T^{11} + 2130279335690 T^{12} + 12280839760803 T^{13} + 72873334214081 T^{14} + 352049093676697 T^{15} + 1769026319150006 T^{16} + 6657088029456279 T^{17} + 26709407186473869 T^{18} + 62695508244240527 T^{19} + 174887470365513049 T^{20} \))(\( 1 - 41 T + 1179 T^{2} - 24597 T^{3} + 433389 T^{4} - 6516744 T^{5} + 88128072 T^{6} - 1076613682 T^{7} + 12196093277 T^{8} - 128294894540 T^{9} + 1272879601678 T^{10} - 11906556496030 T^{11} + 106092089069919 T^{12} - 898960073088721 T^{13} + 7296345174701559 T^{14} - 56564459872830741 T^{15} + 421070152305745164 T^{16} - 2997916373260029273 T^{17} + 20495433595736679231 T^{18} - \)\(13\!\cdots\!17\)\( T^{19} + \)\(83\!\cdots\!39\)\( T^{20} - \)\(49\!\cdots\!90\)\( T^{21} + \)\(28\!\cdots\!62\)\( T^{22} - \)\(15\!\cdots\!80\)\( T^{23} + \)\(75\!\cdots\!97\)\( T^{24} - \)\(35\!\cdots\!06\)\( T^{25} + \)\(15\!\cdots\!28\)\( T^{26} - \)\(60\!\cdots\!68\)\( T^{27} + \)\(21\!\cdots\!49\)\( T^{28} - \)\(64\!\cdots\!81\)\( T^{29} + \)\(16\!\cdots\!51\)\( T^{30} - \)\(29\!\cdots\!37\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 - 27 T + 1028 T^{2} - 19464 T^{3} + 431181 T^{4} - 6344768 T^{5} + 104071701 T^{6} - 1254980464 T^{7} + 16725929881 T^{8} - 170827493887 T^{9} + 1950559616826 T^{10} - 17295196544596 T^{11} + 176000140197516 T^{12} - 1386067641522077 T^{13} + 13008824731724953 T^{14} - 93219118564243488 T^{15} + 830278999875427216 T^{16} - 5551401006996316929 T^{17} + 47731604406235507837 T^{18} - \)\(30\!\cdots\!20\)\( T^{19} + \)\(25\!\cdots\!61\)\( T^{20} - \)\(15\!\cdots\!61\)\( T^{21} + \)\(12\!\cdots\!32\)\( T^{22} - \)\(73\!\cdots\!28\)\( T^{23} + \)\(54\!\cdots\!29\)\( T^{24} - \)\(30\!\cdots\!33\)\( T^{25} + \)\(20\!\cdots\!92\)\( T^{26} - \)\(10\!\cdots\!56\)\( T^{27} + \)\(64\!\cdots\!58\)\( T^{28} - \)\(29\!\cdots\!63\)\( T^{29} + \)\(15\!\cdots\!57\)\( T^{30} - \)\(61\!\cdots\!24\)\( T^{31} + \)\(27\!\cdots\!73\)\( T^{32} - \)\(87\!\cdots\!92\)\( T^{33} + \)\(31\!\cdots\!17\)\( T^{34} - \)\(75\!\cdots\!44\)\( T^{35} + \)\(21\!\cdots\!64\)\( T^{36} - \)\(29\!\cdots\!03\)\( T^{37} + \)\(57\!\cdots\!17\)\( T^{38} \))
$59$ (\( 1 - 2 T + 98 T^{2} - 118 T^{3} + 3481 T^{4} \))(\( 1 + 3 T + 149 T^{2} + 292 T^{3} + 13592 T^{4} + 29650 T^{5} + 801928 T^{6} + 1016452 T^{7} + 30601471 T^{8} + 36352083 T^{9} + 714924299 T^{10} \))(\( 1 + 3 T + 157 T^{2} + 1009 T^{3} + 17205 T^{4} + 120169 T^{5} + 1650818 T^{6} + 10165708 T^{7} + 119438043 T^{8} + 694026305 T^{9} + 7046844537 T^{10} + 35386829548 T^{11} + 339043350022 T^{12} + 1456131154009 T^{13} + 12300272564295 T^{14} + 42560158443769 T^{15} + 390718283116583 T^{16} + 440491312812963 T^{17} + 8662995818654939 T^{18} \))(\( 1 - 12 T + 380 T^{2} - 4293 T^{3} + 71761 T^{4} - 735144 T^{5} + 8873766 T^{6} - 81228211 T^{7} + 792826177 T^{8} - 6446153990 T^{9} + 53471064586 T^{10} - 380323085410 T^{11} + 2759827922137 T^{12} - 16682568746969 T^{13} + 107526626051526 T^{14} - 525572308864056 T^{15} + 3026917274611801 T^{16} - 10683780824327967 T^{17} + 55795566289641980 T^{18} - 103955949823859268 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 22 T + 476 T^{2} - 6917 T^{3} + 103020 T^{4} - 1225974 T^{5} + 14820998 T^{6} - 154273648 T^{7} + 1644212393 T^{8} - 15578679104 T^{9} + 151319474918 T^{10} - 1332446420292 T^{11} + 12057633093040 T^{12} - 99738705194871 T^{13} + 847209888286840 T^{14} - 6612673774083646 T^{15} + 52987205193104244 T^{16} - 390147752670935114 T^{17} + 2949137621126490040 T^{18} - 20484235534217411109 T^{19} + \)\(14\!\cdots\!40\)\( T^{20} - \)\(95\!\cdots\!08\)\( T^{21} + \)\(63\!\cdots\!38\)\( T^{22} - \)\(38\!\cdots\!76\)\( T^{23} + \)\(24\!\cdots\!53\)\( T^{24} - \)\(13\!\cdots\!72\)\( T^{25} + \)\(75\!\cdots\!98\)\( T^{26} - \)\(36\!\cdots\!66\)\( T^{27} + \)\(18\!\cdots\!20\)\( T^{28} - \)\(72\!\cdots\!43\)\( T^{29} + \)\(29\!\cdots\!36\)\( T^{30} - \)\(80\!\cdots\!78\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 + 28 T + 983 T^{2} + 18979 T^{3} + 401671 T^{4} + 6093857 T^{5} + 98073559 T^{6} + 1243602829 T^{7} + 16604572545 T^{8} + 182442646897 T^{9} + 2117136541407 T^{10} + 20658893396598 T^{11} + 214862892141877 T^{12} + 1898894316474999 T^{13} + 18127576804372879 T^{14} + 147732806686592819 T^{15} + 1320440231601136556 T^{16} + 10094517636381442491 T^{17} + 85726799285930738470 T^{18} + \)\(62\!\cdots\!14\)\( T^{19} + \)\(50\!\cdots\!30\)\( T^{20} + \)\(35\!\cdots\!71\)\( T^{21} + \)\(27\!\cdots\!24\)\( T^{22} + \)\(17\!\cdots\!59\)\( T^{23} + \)\(12\!\cdots\!21\)\( T^{24} + \)\(80\!\cdots\!59\)\( T^{25} + \)\(53\!\cdots\!63\)\( T^{26} + \)\(30\!\cdots\!58\)\( T^{27} + \)\(18\!\cdots\!73\)\( T^{28} + \)\(93\!\cdots\!97\)\( T^{29} + \)\(50\!\cdots\!55\)\( T^{30} + \)\(22\!\cdots\!49\)\( T^{31} + \)\(10\!\cdots\!61\)\( T^{32} + \)\(37\!\cdots\!77\)\( T^{33} + \)\(14\!\cdots\!29\)\( T^{34} + \)\(40\!\cdots\!39\)\( T^{35} + \)\(12\!\cdots\!77\)\( T^{36} + \)\(21\!\cdots\!88\)\( T^{37} + \)\(44\!\cdots\!39\)\( T^{38} \))
$61$ (\( 1 - 4 T + 42 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 + 14 T + 185 T^{2} + 1488 T^{3} + 11602 T^{4} + 80004 T^{5} + 707722 T^{6} + 5536848 T^{7} + 41991485 T^{8} + 193841774 T^{9} + 844596301 T^{10} \))(\( 1 + 6 T + 284 T^{2} + 1705 T^{3} + 45496 T^{4} + 265377 T^{5} + 4959240 T^{6} + 26479610 T^{7} + 400085732 T^{8} + 1903026886 T^{9} + 24405229652 T^{10} + 98530628810 T^{11} + 1125653254440 T^{12} + 3674367747057 T^{13} + 38425753310296 T^{14} + 87842238285505 T^{15} + 892538965429964 T^{16} + 1150243877983686 T^{17} + 11694146092834141 T^{18} \))(\( 1 + 32 T + 837 T^{2} + 15799 T^{3} + 259250 T^{4} + 3579024 T^{5} + 44363174 T^{6} + 485251643 T^{7} + 4835921624 T^{8} + 43329832306 T^{9} + 356032850024 T^{10} + 2643119770666 T^{11} + 17994464362904 T^{12} + 110142903179783 T^{13} + 614245453459334 T^{14} + 3022830431590224 T^{15} + 13356657053089250 T^{16} + 49652194066295779 T^{17} + 160459020978724197 T^{18} + 374212674970692512 T^{19} + 713342911662882601 T^{20} \))(\( 1 - 46 T + 1755 T^{2} - 46981 T^{3} + 1095839 T^{4} - 21432728 T^{5} + 376915183 T^{6} - 5886865902 T^{7} + 84265615525 T^{8} - 1099887811078 T^{9} + 13316038082497 T^{10} - 149104000586418 T^{11} + 1560319873925829 T^{12} - 15222974583829437 T^{13} + 139426793736576133 T^{14} - 1195546681310819886 T^{15} + 9644100865853773580 T^{16} - 72928347559960013046 T^{17} + \)\(51\!\cdots\!93\)\( T^{18} - \)\(34\!\cdots\!97\)\( T^{19} + \)\(21\!\cdots\!89\)\( T^{20} - \)\(12\!\cdots\!18\)\( T^{21} + \)\(68\!\cdots\!17\)\( T^{22} - \)\(34\!\cdots\!38\)\( T^{23} + \)\(16\!\cdots\!25\)\( T^{24} - \)\(68\!\cdots\!82\)\( T^{25} + \)\(26\!\cdots\!83\)\( T^{26} - \)\(93\!\cdots\!08\)\( T^{27} + \)\(29\!\cdots\!19\)\( T^{28} - \)\(76\!\cdots\!61\)\( T^{29} + \)\(17\!\cdots\!55\)\( T^{30} - \)\(27\!\cdots\!46\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 - 4 T + 462 T^{2} - 1589 T^{3} + 106161 T^{4} - 286851 T^{5} + 16505902 T^{6} - 31611865 T^{7} + 1997613212 T^{8} - 2442529355 T^{9} + 204121073944 T^{10} - 147051406382 T^{11} + 18402514103318 T^{12} - 7535137580109 T^{13} + 1491171904170118 T^{14} - 339473884743527 T^{15} + 109390930429652943 T^{16} - 13565245791947137 T^{17} + 7303257162170949815 T^{18} - 633036368925137946 T^{19} + \)\(44\!\cdots\!15\)\( T^{20} - 50476279591835296777 T^{21} + \)\(24\!\cdots\!83\)\( T^{22} - \)\(47\!\cdots\!07\)\( T^{23} + \)\(12\!\cdots\!18\)\( T^{24} - \)\(38\!\cdots\!49\)\( T^{25} + \)\(57\!\cdots\!78\)\( T^{26} - \)\(28\!\cdots\!42\)\( T^{27} + \)\(23\!\cdots\!04\)\( T^{28} - \)\(17\!\cdots\!55\)\( T^{29} + \)\(86\!\cdots\!32\)\( T^{30} - \)\(83\!\cdots\!65\)\( T^{31} + \)\(26\!\cdots\!62\)\( T^{32} - \)\(28\!\cdots\!91\)\( T^{33} + \)\(63\!\cdots\!61\)\( T^{34} - \)\(58\!\cdots\!29\)\( T^{35} + \)\(10\!\cdots\!02\)\( T^{36} - \)\(54\!\cdots\!24\)\( T^{37} + \)\(83\!\cdots\!41\)\( T^{38} \))
$67$ (\( 1 - 11 T + 117 T^{2} - 737 T^{3} + 4489 T^{4} \))(\( 1 + 16 T + 376 T^{2} + 4128 T^{3} + 52584 T^{4} + 409437 T^{5} + 3523128 T^{6} + 18530592 T^{7} + 113086888 T^{8} + 322417936 T^{9} + 1350125107 T^{10} \))(\( 1 + 43 T + 1262 T^{2} + 26527 T^{3} + 456782 T^{4} + 6549400 T^{5} + 81564224 T^{6} + 888208395 T^{7} + 8615957535 T^{8} + 74442925137 T^{9} + 577269154845 T^{10} + 3987167485155 T^{11} + 24531500702912 T^{12} + 131977751877400 T^{13} + 616712846625674 T^{14} + 2399589503797063 T^{15} + 7648618045917626 T^{16} + 17460910134935563 T^{17} + 27206534396294947 T^{18} \))(\( 1 + 25 T + 720 T^{2} + 12804 T^{3} + 220301 T^{4} + 3031191 T^{5} + 39128865 T^{6} + 435888000 T^{7} + 4546496853 T^{8} + 42001027544 T^{9} + 364131033503 T^{10} + 2814068845448 T^{11} + 20409224373117 T^{12} + 131098982544000 T^{13} + 788490493207665 T^{14} + 4092487073212437 T^{15} + 19928072050212869 T^{16} + 77601351394555692 T^{17} + 292368727840781520 T^{18} + 680163359907373675 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 50 T + 1864 T^{2} - 50619 T^{3} + 1167949 T^{4} - 22965622 T^{5} + 403210939 T^{6} - 6351207880 T^{7} + 91603256974 T^{8} - 1214237541231 T^{9} + 14950862575813 T^{10} - 171419303534665 T^{11} + 1841322303910778 T^{12} - 18554621564588356 T^{13} + 176023032664469881 T^{14} - 1572591831394201438 T^{15} + 13256461714594297158 T^{16} - \)\(10\!\cdots\!46\)\( T^{17} + \)\(79\!\cdots\!09\)\( T^{18} - \)\(55\!\cdots\!28\)\( T^{19} + \)\(37\!\cdots\!38\)\( T^{20} - \)\(23\!\cdots\!55\)\( T^{21} + \)\(13\!\cdots\!97\)\( T^{22} - \)\(73\!\cdots\!13\)\( T^{23} + \)\(37\!\cdots\!34\)\( T^{24} - \)\(17\!\cdots\!60\)\( T^{25} + \)\(73\!\cdots\!11\)\( T^{26} - \)\(28\!\cdots\!26\)\( T^{27} + \)\(95\!\cdots\!89\)\( T^{28} - \)\(27\!\cdots\!53\)\( T^{29} + \)\(68\!\cdots\!56\)\( T^{30} - \)\(12\!\cdots\!50\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 21 T + 661 T^{2} - 9325 T^{3} + 178370 T^{4} - 1967469 T^{5} + 30120496 T^{6} - 285098211 T^{7} + 3903227307 T^{8} - 33322671880 T^{9} + 424474298875 T^{10} - 3333208470921 T^{11} + 40228883325968 T^{12} - 295340662952716 T^{13} + 3426383848267851 T^{14} - 23853805384374171 T^{15} + 267177610855284657 T^{16} - 1776067154865863160 T^{17} + 19227795342039394749 T^{18} - \)\(12\!\cdots\!97\)\( T^{19} + \)\(12\!\cdots\!83\)\( T^{20} - \)\(79\!\cdots\!40\)\( T^{21} + \)\(80\!\cdots\!91\)\( T^{22} - \)\(48\!\cdots\!91\)\( T^{23} + \)\(46\!\cdots\!57\)\( T^{24} - \)\(26\!\cdots\!04\)\( T^{25} + \)\(24\!\cdots\!64\)\( T^{26} - \)\(13\!\cdots\!61\)\( T^{27} + \)\(11\!\cdots\!25\)\( T^{28} - \)\(60\!\cdots\!20\)\( T^{29} + \)\(47\!\cdots\!81\)\( T^{30} - \)\(23\!\cdots\!71\)\( T^{31} + \)\(16\!\cdots\!52\)\( T^{32} - \)\(72\!\cdots\!01\)\( T^{33} + \)\(43\!\cdots\!10\)\( T^{34} - \)\(15\!\cdots\!25\)\( T^{35} + \)\(73\!\cdots\!47\)\( T^{36} - \)\(15\!\cdots\!89\)\( T^{37} + \)\(49\!\cdots\!03\)\( T^{38} \))
$71$ (\( 1 - 25 T + 293 T^{2} - 1775 T^{3} + 5041 T^{4} \))(\( 1 - 9 T + 280 T^{2} - 2441 T^{3} + 34620 T^{4} - 256121 T^{5} + 2458020 T^{6} - 12305081 T^{7} + 100215080 T^{8} - 228705129 T^{9} + 1804229351 T^{10} \))(\( 1 + 21 T + 761 T^{2} + 11725 T^{3} + 238208 T^{4} + 2871532 T^{5} + 41629142 T^{6} + 403913135 T^{7} + 4540774282 T^{8} + 35730297675 T^{9} + 322394974022 T^{10} + 2036126113535 T^{11} + 14899527842362 T^{12} + 72970455165292 T^{13} + 429781865243008 T^{14} + 1501975828973725 T^{15} + 6921386440535551 T^{16} + 13560824156160981 T^{17} + 45848500718449031 T^{18} \))(\( 1 - 23 T + 611 T^{2} - 9874 T^{3} + 165735 T^{4} - 2148716 T^{5} + 27790267 T^{6} - 300626327 T^{7} + 3201852917 T^{8} - 29495788596 T^{9} + 266112109567 T^{10} - 2094200990316 T^{11} + 16140540554597 T^{12} - 107597469322897 T^{13} + 706197399908827 T^{14} - 3876776474163316 T^{15} + 21230700555646935 T^{16} - 89805216443952734 T^{17} + 394555407591159971 T^{18} - 1054515516524327713 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - 5 T + 510 T^{2} - 2775 T^{3} + 130486 T^{4} - 768158 T^{5} + 22085764 T^{6} - 141822149 T^{7} + 2780362768 T^{8} - 19798489509 T^{9} + 279941094197 T^{10} - 2243121283515 T^{11} + 23926908285688 T^{12} - 214545234451890 T^{13} + 1837404331772738 T^{14} - 17632990653715603 T^{15} + 133018291970708992 T^{16} - 1251942336413807813 T^{17} + 9262355236466372258 T^{18} - 76788099407910401790 T^{19} + \)\(60\!\cdots\!28\)\( T^{20} - \)\(40\!\cdots\!65\)\( T^{21} + \)\(35\!\cdots\!37\)\( T^{22} - \)\(18\!\cdots\!19\)\( T^{23} + \)\(17\!\cdots\!48\)\( T^{24} - \)\(65\!\cdots\!19\)\( T^{25} + \)\(71\!\cdots\!64\)\( T^{26} - \)\(17\!\cdots\!18\)\( T^{27} + \)\(21\!\cdots\!26\)\( T^{28} - \)\(32\!\cdots\!25\)\( T^{29} + \)\(42\!\cdots\!10\)\( T^{30} - \)\(29\!\cdots\!55\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 + 7 T + 652 T^{2} + 5183 T^{3} + 218693 T^{4} + 1828445 T^{5} + 49973502 T^{6} + 418543382 T^{7} + 8683098275 T^{8} + 70698258218 T^{9} + 1216543267632 T^{10} + 9468288264572 T^{11} + 142691038653295 T^{12} + 1053716152181235 T^{13} + 14396517796428638 T^{14} + 100738122925142409 T^{15} + 1275631693844305165 T^{16} + 8468963142840226431 T^{17} + \)\(10\!\cdots\!34\)\( T^{18} + \)\(63\!\cdots\!36\)\( T^{19} + \)\(71\!\cdots\!14\)\( T^{20} + \)\(42\!\cdots\!71\)\( T^{21} + \)\(45\!\cdots\!15\)\( T^{22} + \)\(25\!\cdots\!29\)\( T^{23} + \)\(25\!\cdots\!38\)\( T^{24} + \)\(13\!\cdots\!35\)\( T^{25} + \)\(12\!\cdots\!45\)\( T^{26} + \)\(61\!\cdots\!92\)\( T^{27} + \)\(55\!\cdots\!92\)\( T^{28} + \)\(23\!\cdots\!18\)\( T^{29} + \)\(20\!\cdots\!25\)\( T^{30} + \)\(68\!\cdots\!62\)\( T^{31} + \)\(58\!\cdots\!22\)\( T^{32} + \)\(15\!\cdots\!45\)\( T^{33} + \)\(12\!\cdots\!43\)\( T^{34} + \)\(21\!\cdots\!43\)\( T^{35} + \)\(19\!\cdots\!32\)\( T^{36} + \)\(14\!\cdots\!27\)\( T^{37} + \)\(14\!\cdots\!31\)\( T^{38} \))
$73$ (\( ( 1 + T )^{2} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{10} \))(\( ( 1 - T )^{16} \))(\( ( 1 + T )^{19} \))
$79$ (\( 1 + 16 T + 138 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 223 T^{2} + 1104 T^{3} + 22910 T^{4} + 93456 T^{5} + 1809890 T^{6} + 6890064 T^{7} + 109947697 T^{8} + 311600648 T^{9} + 3077056399 T^{10} \))(\( 1 - 19 T + 416 T^{2} - 4607 T^{3} + 55294 T^{4} - 455388 T^{5} + 3678218 T^{6} - 24875092 T^{7} + 117963504 T^{8} - 1084543460 T^{9} + 9319116816 T^{10} - 155245449172 T^{11} + 1813504924502 T^{12} - 17737399486428 T^{13} + 170142756526306 T^{14} - 1119903907585247 T^{15} + 7988826138242144 T^{16} - 28825067388224659 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 3 T + 265 T^{2} - 84 T^{3} + 46718 T^{4} - 6005 T^{5} + 6313662 T^{6} - 5802746 T^{7} + 636481674 T^{8} - 569682608 T^{9} + 57351822948 T^{10} - 45004926032 T^{11} + 3972282127434 T^{12} - 2860980085094 T^{13} + 245917646306622 T^{14} - 18477723675995 T^{15} + 11356559747030078 T^{16} - 1613128354837356 T^{17} + 402033834625238665 T^{18} + 359554787947854957 T^{19} + 9468276082626847201 T^{20} \))(\( 1 - 31 T + 1161 T^{2} - 25586 T^{3} + 582605 T^{4} - 10234082 T^{5} + 178421349 T^{6} - 2643487988 T^{7} + 38361648091 T^{8} - 495407313206 T^{9} + 6239682265995 T^{10} - 71717983253762 T^{11} + 803217460265983 T^{12} - 8328189124944338 T^{13} + 84161401212213687 T^{14} - 793406915917704625 T^{15} + 7292511364083143248 T^{16} - 62679146357498665375 T^{17} + \)\(52\!\cdots\!67\)\( T^{18} - \)\(41\!\cdots\!82\)\( T^{19} + \)\(31\!\cdots\!23\)\( T^{20} - \)\(22\!\cdots\!38\)\( T^{21} + \)\(15\!\cdots\!95\)\( T^{22} - \)\(95\!\cdots\!54\)\( T^{23} + \)\(58\!\cdots\!51\)\( T^{24} - \)\(31\!\cdots\!72\)\( T^{25} + \)\(16\!\cdots\!49\)\( T^{26} - \)\(76\!\cdots\!78\)\( T^{27} + \)\(34\!\cdots\!05\)\( T^{28} - \)\(11\!\cdots\!54\)\( T^{29} + \)\(42\!\cdots\!41\)\( T^{30} - \)\(90\!\cdots\!69\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 - 25 T + 816 T^{2} - 16343 T^{3} + 343791 T^{4} - 5794457 T^{5} + 97446962 T^{6} - 1440478943 T^{7} + 20862704128 T^{8} - 277075133788 T^{9} + 3582544509416 T^{10} - 43415591446102 T^{11} + 511169473524614 T^{12} - 5710691746345308 T^{13} + 61953811967344406 T^{14} - 642292055416953377 T^{15} + 6466963142377604407 T^{16} - 62467819752841177462 T^{17} + \)\(58\!\cdots\!57\)\( T^{18} - \)\(52\!\cdots\!18\)\( T^{19} + \)\(46\!\cdots\!03\)\( T^{20} - \)\(38\!\cdots\!42\)\( T^{21} + \)\(31\!\cdots\!73\)\( T^{22} - \)\(25\!\cdots\!37\)\( T^{23} + \)\(19\!\cdots\!94\)\( T^{24} - \)\(13\!\cdots\!68\)\( T^{25} + \)\(98\!\cdots\!26\)\( T^{26} - \)\(65\!\cdots\!22\)\( T^{27} + \)\(42\!\cdots\!04\)\( T^{28} - \)\(26\!\cdots\!88\)\( T^{29} + \)\(15\!\cdots\!12\)\( T^{30} - \)\(85\!\cdots\!63\)\( T^{31} + \)\(45\!\cdots\!18\)\( T^{32} - \)\(21\!\cdots\!17\)\( T^{33} + \)\(10\!\cdots\!09\)\( T^{34} - \)\(37\!\cdots\!03\)\( T^{35} + \)\(14\!\cdots\!44\)\( T^{36} - \)\(35\!\cdots\!25\)\( T^{37} + \)\(11\!\cdots\!19\)\( T^{38} \))
$83$ (\( 1 + 9 T + 181 T^{2} + 747 T^{3} + 6889 T^{4} \))(\( 1 + 19 T + 345 T^{2} + 4234 T^{3} + 53207 T^{4} + 487832 T^{5} + 4416181 T^{6} + 29168026 T^{7} + 197266515 T^{8} + 901708099 T^{9} + 3939040643 T^{10} \))(\( 1 - 26 T + 710 T^{2} - 11499 T^{3} + 180092 T^{4} - 2101094 T^{5} + 23856985 T^{6} - 222621982 T^{7} + 2151080809 T^{8} - 18688706496 T^{9} + 178539707147 T^{10} - 1533642833998 T^{11} + 13641113882195 T^{12} - 99714393503174 T^{13} + 709389707479156 T^{14} - 3759487353370131 T^{15} + 19266596202635170 T^{16} - 58559598035615066 T^{17} + 186940255267540403 T^{18} \))(\( 1 + 13 T + 604 T^{2} + 6915 T^{3} + 168502 T^{4} + 1698152 T^{5} + 29226862 T^{6} + 259810954 T^{7} + 3594704920 T^{8} + 28325305822 T^{9} + 337276238727 T^{10} + 2351000383226 T^{11} + 24763922193880 T^{12} + 148556525954798 T^{13} + 1387057798618702 T^{14} + 6689089745991736 T^{15} + 55090106793423238 T^{16} + 187645792593270705 T^{17} + 1360384508211980764 T^{18} + 2430223318478025239 T^{19} + 15516041187205853449 T^{20} \))(\( 1 + 12 T + 974 T^{2} + 10306 T^{3} + 454129 T^{4} + 4298937 T^{5} + 135692136 T^{6} + 1162251374 T^{7} + 29297089202 T^{8} + 228939542736 T^{9} + 4876318945706 T^{10} + 34944716077601 T^{11} + 650341567411455 T^{12} + 4282447826649058 T^{13} + 71141973659717421 T^{14} + 429916964905352361 T^{15} + 6465215739979665508 T^{16} + 35683108087144245963 T^{17} + \)\(49\!\cdots\!69\)\( T^{18} + \)\(24\!\cdots\!46\)\( T^{19} + \)\(30\!\cdots\!55\)\( T^{20} + \)\(13\!\cdots\!43\)\( T^{21} + \)\(15\!\cdots\!14\)\( T^{22} + \)\(62\!\cdots\!72\)\( T^{23} + \)\(65\!\cdots\!82\)\( T^{24} + \)\(21\!\cdots\!22\)\( T^{25} + \)\(21\!\cdots\!64\)\( T^{26} + \)\(55\!\cdots\!79\)\( T^{27} + \)\(48\!\cdots\!69\)\( T^{28} + \)\(91\!\cdots\!78\)\( T^{29} + \)\(71\!\cdots\!46\)\( T^{30} + \)\(73\!\cdots\!84\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 15 T + 955 T^{2} - 11598 T^{3} + 431177 T^{4} - 4429079 T^{5} + 126273726 T^{6} - 1130213343 T^{7} + 27455872747 T^{8} - 218860098219 T^{9} + 4769761303806 T^{10} - 34427118346117 T^{11} + 691109031690600 T^{12} - 4573015935200845 T^{13} + 85672396331655016 T^{14} - 524480884139024109 T^{15} + 9224326593182985581 T^{16} - 52607950815201590384 T^{17} + \)\(87\!\cdots\!12\)\( T^{18} - \)\(46\!\cdots\!89\)\( T^{19} + \)\(72\!\cdots\!96\)\( T^{20} - \)\(36\!\cdots\!76\)\( T^{21} + \)\(52\!\cdots\!47\)\( T^{22} - \)\(24\!\cdots\!89\)\( T^{23} + \)\(33\!\cdots\!88\)\( T^{24} - \)\(14\!\cdots\!05\)\( T^{25} + \)\(18\!\cdots\!00\)\( T^{26} - \)\(77\!\cdots\!97\)\( T^{27} + \)\(89\!\cdots\!18\)\( T^{28} - \)\(33\!\cdots\!31\)\( T^{29} + \)\(35\!\cdots\!49\)\( T^{30} - \)\(12\!\cdots\!23\)\( T^{31} + \)\(11\!\cdots\!38\)\( T^{32} - \)\(32\!\cdots\!91\)\( T^{33} + \)\(26\!\cdots\!39\)\( T^{34} - \)\(58\!\cdots\!38\)\( T^{35} + \)\(40\!\cdots\!65\)\( T^{36} - \)\(52\!\cdots\!35\)\( T^{37} + \)\(29\!\cdots\!47\)\( T^{38} \))
$89$ (\( 1 - 7 T + 185 T^{2} - 623 T^{3} + 7921 T^{4} \))(\( 1 - T + 194 T^{2} - 187 T^{3} + 24648 T^{4} - 45635 T^{5} + 2193672 T^{6} - 1481227 T^{7} + 136763986 T^{8} - 62742241 T^{9} + 5584059449 T^{10} \))(\( 1 + 27 T + 666 T^{2} + 9076 T^{3} + 122152 T^{4} + 1110713 T^{5} + 12932351 T^{6} + 119182214 T^{7} + 1508326201 T^{8} + 13192247241 T^{9} + 134241031889 T^{10} + 944042317094 T^{11} + 9116906552119 T^{12} + 69688622727833 T^{13} + 682104029814248 T^{14} + 4510602196762036 T^{15} + 29458069040422314 T^{16} + 106287897753956187 T^{17} + 350356403707485209 T^{18} \))(\( 1 - 13 T + 434 T^{2} - 6663 T^{3} + 123355 T^{4} - 1622538 T^{5} + 23509945 T^{6} - 273567453 T^{7} + 3206480799 T^{8} - 32687103402 T^{9} + 331338861751 T^{10} - 2909152202778 T^{11} + 25398534408879 T^{12} - 192856573773957 T^{13} + 1475066635086745 T^{14} - 9060348650261562 T^{15} + 61305127146494155 T^{16} - 294713384408909727 T^{17} + 1708479541674703154 T^{18} - 4554633248197307717 T^{19} + 31181719929966183601 T^{20} \))(\( 1 + 13 T + 829 T^{2} + 9096 T^{3} + 337487 T^{4} + 3239523 T^{5} + 91152594 T^{6} + 783376893 T^{7} + 18442376530 T^{8} + 143957469373 T^{9} + 2975291450353 T^{10} + 21291244057831 T^{11} + 396767152435849 T^{12} + 2618767112746047 T^{13} + 44673889445784179 T^{14} + 272854952213802192 T^{15} + 4295126301397932612 T^{16} + 24284090747028395088 T^{17} + \)\(35\!\cdots\!59\)\( T^{18} + \)\(18\!\cdots\!43\)\( T^{19} + \)\(24\!\cdots\!09\)\( T^{20} + \)\(11\!\cdots\!19\)\( T^{21} + \)\(14\!\cdots\!33\)\( T^{22} + \)\(63\!\cdots\!17\)\( T^{23} + \)\(72\!\cdots\!30\)\( T^{24} + \)\(27\!\cdots\!37\)\( T^{25} + \)\(28\!\cdots\!94\)\( T^{26} + \)\(89\!\cdots\!47\)\( T^{27} + \)\(83\!\cdots\!27\)\( T^{28} + \)\(19\!\cdots\!24\)\( T^{29} + \)\(16\!\cdots\!89\)\( T^{30} + \)\(22\!\cdots\!37\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 + 21 T + 1279 T^{2} + 23126 T^{3} + 787496 T^{4} + 12590132 T^{5} + 312595405 T^{6} + 4497326129 T^{7} + 90124245100 T^{8} + 1180688936641 T^{9} + 20116823547687 T^{10} + 241859277173605 T^{11} + 3612959502131566 T^{12} + 40054980828483776 T^{13} + 535025442557004653 T^{14} + 5482682521170982344 T^{15} + 66352170108581228064 T^{16} + \)\(62\!\cdots\!59\)\( T^{17} + \)\(69\!\cdots\!98\)\( T^{18} + \)\(60\!\cdots\!16\)\( T^{19} + \)\(61\!\cdots\!22\)\( T^{20} + \)\(49\!\cdots\!39\)\( T^{21} + \)\(46\!\cdots\!16\)\( T^{22} + \)\(34\!\cdots\!04\)\( T^{23} + \)\(29\!\cdots\!97\)\( T^{24} + \)\(19\!\cdots\!36\)\( T^{25} + \)\(15\!\cdots\!14\)\( T^{26} + \)\(95\!\cdots\!05\)\( T^{27} + \)\(70\!\cdots\!83\)\( T^{28} + \)\(36\!\cdots\!41\)\( T^{29} + \)\(25\!\cdots\!00\)\( T^{30} + \)\(11\!\cdots\!09\)\( T^{31} + \)\(68\!\cdots\!45\)\( T^{32} + \)\(24\!\cdots\!12\)\( T^{33} + \)\(13\!\cdots\!04\)\( T^{34} + \)\(35\!\cdots\!86\)\( T^{35} + \)\(17\!\cdots\!91\)\( T^{36} + \)\(25\!\cdots\!01\)\( T^{37} + \)\(10\!\cdots\!09\)\( T^{38} \))
$97$ (\( 1 + 3 T + 149 T^{2} + 291 T^{3} + 9409 T^{4} \))(\( 1 + 9 T + 198 T^{2} - 873 T^{3} - 6728 T^{4} - 351325 T^{5} - 652616 T^{6} - 8214057 T^{7} + 180709254 T^{8} + 796763529 T^{9} + 8587340257 T^{10} \))(\( 1 - 4 T + 573 T^{2} - 1091 T^{3} + 152944 T^{4} - 35266 T^{5} + 25989738 T^{6} + 22324436 T^{7} + 3231119980 T^{8} + 3705655385 T^{9} + 313418638060 T^{10} + 210050618324 T^{11} + 23720132149674 T^{12} - 3122073623746 T^{13} + 1313382168266608 T^{14} - 908772457377539 T^{15} + 46297417005958749 T^{16} - 31349734377507844 T^{17} + 760231058654565217 T^{18} \))(\( 1 + 16 T + 685 T^{2} + 8652 T^{3} + 215324 T^{4} + 2247242 T^{5} + 42169630 T^{6} + 375491333 T^{7} + 5907580703 T^{8} + 46179097563 T^{9} + 641492518669 T^{10} + 4479372463611 T^{11} + 55584426834527 T^{12} + 342700801363109 T^{13} + 3733247023936030 T^{14} + 19297831693821194 T^{15} + 179358863989331996 T^{16} + 699066757304633676 T^{17} + 5368642012148218285 T^{18} + 12163696938473043472 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 22 T + 1254 T^{2} - 22662 T^{3} + 731201 T^{4} - 11305364 T^{5} + 268458754 T^{6} - 3641065077 T^{7} + 70295070387 T^{8} - 850100510992 T^{9} + 14036460014623 T^{10} - 153025688362066 T^{11} + 2225441924973862 T^{12} - 22025698753987498 T^{13} + 287224105126472428 T^{14} - 2589539825865702667 T^{15} + 30597682416536221340 T^{16} - \)\(25\!\cdots\!99\)\( T^{17} + \)\(27\!\cdots\!52\)\( T^{18} - \)\(20\!\cdots\!54\)\( T^{19} + \)\(19\!\cdots\!22\)\( T^{20} - \)\(13\!\cdots\!62\)\( T^{21} + \)\(11\!\cdots\!67\)\( T^{22} - \)\(68\!\cdots\!96\)\( T^{23} + \)\(55\!\cdots\!07\)\( T^{24} - \)\(27\!\cdots\!09\)\( T^{25} + \)\(19\!\cdots\!46\)\( T^{26} - \)\(80\!\cdots\!92\)\( T^{27} + \)\(50\!\cdots\!41\)\( T^{28} - \)\(15\!\cdots\!74\)\( T^{29} + \)\(81\!\cdots\!26\)\( T^{30} - \)\(13\!\cdots\!46\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 - 18 T + 668 T^{2} - 11162 T^{3} + 238344 T^{4} - 3512300 T^{5} + 57283946 T^{6} - 735036935 T^{7} + 10123424747 T^{8} - 114052706584 T^{9} + 1384656013460 T^{10} - 13864578809965 T^{11} + 152480875544583 T^{12} - 1373817415632980 T^{13} + 14110020118543071 T^{14} - 116342301633998684 T^{15} + 1174929141921114417 T^{16} - 9233545244713475744 T^{17} + 99115585922888000366 T^{18} - \)\(80\!\cdots\!66\)\( T^{19} + \)\(96\!\cdots\!02\)\( T^{20} - \)\(86\!\cdots\!96\)\( T^{21} + \)\(10\!\cdots\!41\)\( T^{22} - \)\(10\!\cdots\!04\)\( T^{23} + \)\(12\!\cdots\!47\)\( T^{24} - \)\(11\!\cdots\!20\)\( T^{25} + \)\(12\!\cdots\!79\)\( T^{26} - \)\(10\!\cdots\!65\)\( T^{27} + \)\(10\!\cdots\!20\)\( T^{28} - \)\(84\!\cdots\!16\)\( T^{29} + \)\(72\!\cdots\!91\)\( T^{30} - \)\(50\!\cdots\!35\)\( T^{31} + \)\(38\!\cdots\!42\)\( T^{32} - \)\(22\!\cdots\!00\)\( T^{33} + \)\(15\!\cdots\!92\)\( T^{34} - \)\(68\!\cdots\!02\)\( T^{35} + \)\(39\!\cdots\!16\)\( T^{36} - \)\(10\!\cdots\!02\)\( T^{37} + \)\(56\!\cdots\!33\)\( T^{38} \))
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