Properties

Label 8028.2.a
Level 8028
Weight 2
Character orbit a
Rep. character \(\chi_{8028}(1,\cdot)\)
Character field \(\Q\)
Dimension 92
Newform subspaces 16
Sturm bound 2688
Trace bound 7

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Defining parameters

Level: \( N \) \(=\) \( 8028 = 2^{2} \cdot 3^{2} \cdot 223 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8028.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(2688\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8028))\).

Total New Old
Modular forms 1356 92 1264
Cusp forms 1333 92 1241
Eisenstein series 23 0 23

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

\(2\)\(3\)\(223\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(18\)
\(-\)\(+\)\(-\)\(+\)\(18\)
\(-\)\(-\)\(+\)\(+\)\(28\)
\(-\)\(-\)\(-\)\(-\)\(28\)
Plus space\(+\)\(46\)
Minus space\(-\)\(46\)

Trace form

\( 92q + 2q^{7} + O(q^{10}) \) \( 92q + 2q^{7} + 6q^{11} + 8q^{17} - 8q^{19} + 90q^{25} + 4q^{29} + 14q^{31} - 10q^{35} + 10q^{37} + 6q^{41} - 14q^{43} + 6q^{47} + 102q^{49} - 10q^{53} + 18q^{55} - 2q^{59} - 4q^{61} + 12q^{65} + 16q^{67} + 26q^{71} + 6q^{73} + 2q^{77} + 4q^{79} - 4q^{83} - 18q^{85} + 16q^{91} + 10q^{95} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8028))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 223
8028.2.a.a \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(-3\) \(-2\) \(-\) \(+\) \(+\) \(q-3q^{5}-2q^{7}-4q^{11}-6q^{17}-8q^{23}+\cdots\)
8028.2.a.b \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(-\) \(q-2q^{5}-2q^{7}+3q^{11}+6q^{13}+7q^{17}+\cdots\)
8028.2.a.c \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(-\) \(-\) \(q-q^{5}-2q^{7}-6q^{11}-6q^{13}-4q^{17}+\cdots\)
8028.2.a.d \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q-4q^{7}-3q^{11}-4q^{13}+3q^{17}+2q^{19}+\cdots\)
8028.2.a.e \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(-\) \(+\) \(q+4q^{7}-q^{11}+3q^{17}-6q^{19}+q^{23}+\cdots\)
8028.2.a.f \(1\) \(64.104\) \(\Q\) None \(0\) \(0\) \(3\) \(-2\) \(-\) \(+\) \(+\) \(q+3q^{5}-2q^{7}+4q^{11}+6q^{17}+8q^{23}+\cdots\)
8028.2.a.g \(2\) \(64.104\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-8\) \(-\) \(+\) \(-\) \(q+\beta q^{5}-4q^{7}-2\beta q^{11}+2q^{13}+2q^{19}+\cdots\)
8028.2.a.h \(2\) \(64.104\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+(1-2\beta )q^{5}+2\beta q^{7}+(4+\beta )q^{11}+\cdots\)
8028.2.a.i \(5\) \(64.104\) 5.5.1710888.1 None \(0\) \(0\) \(6\) \(3\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1}+\beta _{2})q^{5}+(1-\beta _{4})q^{7}+(3+\cdots)q^{17}+\cdots\)
8028.2.a.j \(7\) \(64.104\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(7\) \(-1\) \(-\) \(-\) \(-\) \(q+(1+\beta _{1}+\beta _{6})q^{5}+(\beta _{3}+\beta _{6})q^{7}+(1+\cdots)q^{11}+\cdots\)
8028.2.a.k \(8\) \(64.104\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-5\) \(5\) \(-\) \(-\) \(+\) \(q+(-\beta _{2}+\beta _{3}+\beta _{6}+\beta _{7})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
8028.2.a.l \(8\) \(64.104\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(5\) \(-13\) \(-\) \(-\) \(+\) \(q+(\beta _{4}-\beta _{5})q^{5}+(-2+\beta _{2})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots\)
8028.2.a.m \(11\) \(64.104\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(0\) \(-5\) \(-5\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{5}-\beta _{10}q^{7}+\beta _{7}q^{11}+(-1+\cdots)q^{13}+\cdots\)
8028.2.a.n \(11\) \(64.104\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(0\) \(-5\) \(11\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{5}+(1+\beta _{9})q^{7}-\beta _{5}q^{11}+(1+\cdots)q^{13}+\cdots\)
8028.2.a.o \(16\) \(64.104\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-6\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{5}-\beta _{4}q^{7}+\beta _{15}q^{11}+(-1+\cdots)q^{13}+\cdots\)
8028.2.a.p \(16\) \(64.104\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(22\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{5}+(1-\beta _{7})q^{7}+\beta _{9}q^{11}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(223))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(446))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(669))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(892))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2007))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4014))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( 1 + 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 7 T^{2} + 25 T^{4} \))(\( 1 + 5 T^{2} + 25 T^{4} \))(\( 1 - 6 T + 28 T^{2} - 100 T^{3} + 291 T^{4} - 708 T^{5} + 1455 T^{6} - 2500 T^{7} + 3500 T^{8} - 3750 T^{9} + 3125 T^{10} \))(\( 1 - 7 T + 36 T^{2} - 127 T^{3} + 379 T^{4} - 935 T^{5} + 2172 T^{6} - 4790 T^{7} + 10860 T^{8} - 23375 T^{9} + 47375 T^{10} - 79375 T^{11} + 112500 T^{12} - 109375 T^{13} + 78125 T^{14} \))(\( 1 + 5 T + 27 T^{2} + 82 T^{3} + 309 T^{4} + 802 T^{5} + 2477 T^{6} + 5435 T^{7} + 14196 T^{8} + 27175 T^{9} + 61925 T^{10} + 100250 T^{11} + 193125 T^{12} + 256250 T^{13} + 421875 T^{14} + 390625 T^{15} + 390625 T^{16} \))(\( 1 - 5 T + 30 T^{2} - 101 T^{3} + 359 T^{4} - 936 T^{5} + 2632 T^{6} - 5866 T^{7} + 14628 T^{8} - 29330 T^{9} + 65800 T^{10} - 117000 T^{11} + 224375 T^{12} - 315625 T^{13} + 468750 T^{14} - 390625 T^{15} + 390625 T^{16} \))(\( 1 + 5 T + 32 T^{2} + 131 T^{3} + 537 T^{4} + 1854 T^{5} + 6075 T^{6} + 18039 T^{7} + 50548 T^{8} + 131661 T^{9} + 322735 T^{10} + 744316 T^{11} + 1613675 T^{12} + 3291525 T^{13} + 6318500 T^{14} + 11274375 T^{15} + 18984375 T^{16} + 28968750 T^{17} + 41953125 T^{18} + 51171875 T^{19} + 62500000 T^{20} + 48828125 T^{21} + 48828125 T^{22} \))(\( 1 + 5 T + 30 T^{2} + 101 T^{3} + 393 T^{4} + 1082 T^{5} + 3531 T^{6} + 8737 T^{7} + 25606 T^{8} + 58561 T^{9} + 156031 T^{10} + 325124 T^{11} + 780155 T^{12} + 1464025 T^{13} + 3200750 T^{14} + 5460625 T^{15} + 11034375 T^{16} + 16906250 T^{17} + 30703125 T^{18} + 39453125 T^{19} + 58593750 T^{20} + 48828125 T^{21} + 48828125 T^{22} \))(\( 1 + 29 T^{2} + 424 T^{4} + 4323 T^{6} + 35429 T^{8} + 251384 T^{10} + 1603002 T^{12} + 9290336 T^{14} + 48832208 T^{16} + 232258400 T^{18} + 1001876250 T^{20} + 3927875000 T^{22} + 13839453125 T^{24} + 42216796875 T^{26} + 103515625000 T^{28} + 177001953125 T^{30} + 152587890625 T^{32} \))(\( 1 + 35 T^{2} + 632 T^{4} + 7613 T^{6} + 68045 T^{8} + 480640 T^{10} + 2837354 T^{12} + 14936664 T^{14} + 75149664 T^{16} + 373416600 T^{18} + 1773346250 T^{20} + 7510000000 T^{22} + 26580078125 T^{24} + 74345703125 T^{26} + 154296875000 T^{28} + 213623046875 T^{30} + 152587890625 T^{32} \))
$7$ (\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( 1 - 2 T + 10 T^{2} - 14 T^{3} + 49 T^{4} \))(\( 1 - 3 T + 23 T^{2} - 49 T^{3} + 262 T^{4} - 464 T^{5} + 1834 T^{6} - 2401 T^{7} + 7889 T^{8} - 7203 T^{9} + 16807 T^{10} \))(\( 1 + T + 23 T^{2} + 22 T^{3} + 337 T^{4} + 316 T^{5} + 3272 T^{6} + 2535 T^{7} + 22904 T^{8} + 15484 T^{9} + 115591 T^{10} + 52822 T^{11} + 386561 T^{12} + 117649 T^{13} + 823543 T^{14} \))(\( 1 - 5 T + 40 T^{2} - 173 T^{3} + 754 T^{4} - 2744 T^{5} + 8927 T^{6} - 27193 T^{7} + 73718 T^{8} - 190351 T^{9} + 437423 T^{10} - 941192 T^{11} + 1810354 T^{12} - 2907611 T^{13} + 4705960 T^{14} - 4117715 T^{15} + 5764801 T^{16} \))(\( 1 + 13 T + 112 T^{2} + 716 T^{3} + 3696 T^{4} + 16018 T^{5} + 59548 T^{6} + 192211 T^{7} + 543510 T^{8} + 1345477 T^{9} + 2917852 T^{10} + 5494174 T^{11} + 8874096 T^{12} + 12033812 T^{13} + 13176688 T^{14} + 10706059 T^{15} + 5764801 T^{16} \))(\( 1 + 5 T + 41 T^{2} + 185 T^{3} + 903 T^{4} + 3453 T^{5} + 13519 T^{6} + 44700 T^{7} + 151170 T^{8} + 445366 T^{9} + 1326114 T^{10} + 3503366 T^{11} + 9282798 T^{12} + 21822934 T^{13} + 51851310 T^{14} + 107324700 T^{15} + 227213833 T^{16} + 406241997 T^{17} + 743659329 T^{18} + 1066488185 T^{19} + 1654497887 T^{20} + 1412376245 T^{21} + 1977326743 T^{22} \))(\( 1 - 11 T + 85 T^{2} - 475 T^{3} + 2287 T^{4} - 9423 T^{5} + 35743 T^{6} - 123100 T^{7} + 401082 T^{8} - 1213406 T^{9} + 3505798 T^{10} - 9478018 T^{11} + 24540586 T^{12} - 59456894 T^{13} + 137571126 T^{14} - 295563100 T^{15} + 600732601 T^{16} - 1108606527 T^{17} + 1883442841 T^{18} - 2738280475 T^{19} + 3430056595 T^{20} - 3107227739 T^{21} + 1977326743 T^{22} \))(\( ( 1 + 3 T + 32 T^{2} + 102 T^{3} + 494 T^{4} + 1540 T^{5} + 5114 T^{6} + 14561 T^{7} + 40342 T^{8} + 101927 T^{9} + 250586 T^{10} + 528220 T^{11} + 1186094 T^{12} + 1714314 T^{13} + 3764768 T^{14} + 2470629 T^{15} + 5764801 T^{16} )^{2} \))(\( ( 1 - 11 T + 82 T^{2} - 452 T^{3} + 2104 T^{4} - 8342 T^{5} + 29372 T^{6} - 91333 T^{7} + 255866 T^{8} - 639331 T^{9} + 1439228 T^{10} - 2861306 T^{11} + 5051704 T^{12} - 7596764 T^{13} + 9647218 T^{14} - 9058973 T^{15} + 5764801 T^{16} )^{2} \))
$11$ (\( 1 + 4 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 10 T^{2} + 121 T^{4} \))(\( 1 - 9 T + 41 T^{2} - 99 T^{3} + 121 T^{4} \))(\( ( 1 + 11 T^{2} )^{5} \))(\( 1 - 12 T + 89 T^{2} - 439 T^{3} + 1806 T^{4} - 6588 T^{5} + 24106 T^{6} - 81946 T^{7} + 265166 T^{8} - 797148 T^{9} + 2403786 T^{10} - 6427399 T^{11} + 14333539 T^{12} - 21258732 T^{13} + 19487171 T^{14} \))(\( 1 + 13 T + 134 T^{2} + 952 T^{3} + 5878 T^{4} + 29707 T^{5} + 134864 T^{6} + 526688 T^{7} + 1871422 T^{8} + 5793568 T^{9} + 16318544 T^{10} + 39540017 T^{11} + 86059798 T^{12} + 153320552 T^{13} + 237389174 T^{14} + 253333223 T^{15} + 214358881 T^{16} \))(\( 1 - T + 55 T^{2} - 41 T^{3} + 1410 T^{4} - 909 T^{5} + 23505 T^{6} - 14397 T^{7} + 292986 T^{8} - 158367 T^{9} + 2844105 T^{10} - 1209879 T^{11} + 20643810 T^{12} - 6603091 T^{13} + 97435855 T^{14} - 19487171 T^{15} + 214358881 T^{16} \))(\( 1 - 3 T + 50 T^{2} - 150 T^{3} + 1192 T^{4} - 3079 T^{5} + 15909 T^{6} - 29796 T^{7} + 104800 T^{8} - 46110 T^{9} + 84766 T^{10} + 1419124 T^{11} + 932426 T^{12} - 5579310 T^{13} + 139488800 T^{14} - 436243236 T^{15} + 2562160359 T^{16} - 5454636319 T^{17} + 23228707832 T^{18} - 32153832150 T^{19} + 117897384550 T^{20} - 77812273803 T^{21} + 285311670611 T^{22} \))(\( 1 - T + 52 T^{2} - 44 T^{3} + 1534 T^{4} - 1197 T^{5} + 32229 T^{6} - 23884 T^{7} + 529120 T^{8} - 376346 T^{9} + 7057530 T^{10} - 4646064 T^{11} + 77632830 T^{12} - 45537866 T^{13} + 704258720 T^{14} - 349685644 T^{15} + 5190512679 T^{16} - 2120558517 T^{17} + 29893320314 T^{18} - 9431790764 T^{19} + 122613279932 T^{20} - 25937424601 T^{21} + 285311670611 T^{22} \))(\( 1 + 71 T^{2} + 2343 T^{4} + 48579 T^{6} + 750106 T^{8} + 10207905 T^{10} + 138237521 T^{12} + 1826999349 T^{14} + 21633679674 T^{16} + 221066921229 T^{18} + 2023935544961 T^{20} + 18083926389705 T^{22} + 160791882791386 T^{24} + 1260014149691979 T^{26} + 7353337686657303 T^{28} + 26962238184410111 T^{30} + 45949729863572161 T^{32} \))(\( 1 + 75 T^{2} + 3019 T^{4} + 83279 T^{6} + 1750730 T^{8} + 29779421 T^{10} + 429204381 T^{12} + 5443903145 T^{14} + 62567694842 T^{16} + 658712280545 T^{18} + 6283981342221 T^{20} + 52756060846181 T^{22} + 375284523733130 T^{24} + 2160042783346679 T^{26} + 9474915269320699 T^{28} + 28481237518743075 T^{30} + 45949729863572161 T^{32} \))
$13$ (\( 1 + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( 1 - 2 T + 7 T^{2} - 26 T^{3} + 169 T^{4} \))(\( ( 1 + 13 T^{2} )^{5} \))(\( 1 + 9 T + 86 T^{2} + 467 T^{3} + 2703 T^{4} + 11051 T^{5} + 49602 T^{6} + 168810 T^{7} + 644826 T^{8} + 1867619 T^{9} + 5938491 T^{10} + 13337987 T^{11} + 31931198 T^{12} + 43441281 T^{13} + 62748517 T^{14} \))(\( 1 - 3 T + 85 T^{2} - 212 T^{3} + 3325 T^{4} - 6928 T^{5} + 78603 T^{6} - 136901 T^{7} + 1236404 T^{8} - 1779713 T^{9} + 13283907 T^{10} - 15220816 T^{11} + 94965325 T^{12} - 78714116 T^{13} + 410278765 T^{14} - 188245551 T^{15} + 815730721 T^{16} \))(\( 1 + 10 T + 83 T^{2} + 456 T^{3} + 2598 T^{4} + 12232 T^{5} + 57413 T^{6} + 221918 T^{7} + 859826 T^{8} + 2884934 T^{9} + 9702797 T^{10} + 26873704 T^{11} + 74201478 T^{12} + 169309608 T^{13} + 400625147 T^{14} + 627485170 T^{15} + 815730721 T^{16} \))(\( 1 + 42 T^{2} + 40 T^{3} + 1186 T^{4} + 2020 T^{5} + 22941 T^{6} + 65916 T^{7} + 364910 T^{8} + 1355260 T^{9} + 5004852 T^{10} + 20915000 T^{11} + 65063076 T^{12} + 229038940 T^{13} + 801707270 T^{14} + 1882626876 T^{15} + 8517832713 T^{16} + 9750154180 T^{17} + 74419741162 T^{18} + 32629228840 T^{19} + 445388973666 T^{20} + 1792160394037 T^{22} \))(\( 1 - 14 T + 156 T^{2} - 1180 T^{3} + 7604 T^{4} - 38806 T^{5} + 171253 T^{6} - 606076 T^{7} + 1806854 T^{8} - 3905404 T^{9} + 6719832 T^{10} - 10225392 T^{11} + 87357816 T^{12} - 660013276 T^{13} + 3969658238 T^{14} - 17310136636 T^{15} + 63585040129 T^{16} - 187309150054 T^{17} + 477139723268 T^{18} - 962562250780 T^{19} + 1654301902188 T^{20} - 1930018885886 T^{21} + 1792160394037 T^{22} \))(\( ( 1 + 6 T + 75 T^{2} + 368 T^{3} + 2588 T^{4} + 10618 T^{5} + 55269 T^{6} + 194720 T^{7} + 834534 T^{8} + 2531360 T^{9} + 9340461 T^{10} + 23327746 T^{11} + 73915868 T^{12} + 136635824 T^{13} + 362010675 T^{14} + 376491102 T^{15} + 815730721 T^{16} )^{2} \))(\( ( 1 - 6 T + 49 T^{2} - 206 T^{3} + 1168 T^{4} - 3748 T^{5} + 18303 T^{6} - 52472 T^{7} + 246446 T^{8} - 682136 T^{9} + 3093207 T^{10} - 8234356 T^{11} + 33359248 T^{12} - 76486358 T^{13} + 236513641 T^{14} - 376491102 T^{15} + 815730721 T^{16} )^{2} \))
$17$ (\( 1 + 6 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( 1 - T + 33 T^{2} - 17 T^{3} + 289 T^{4} \))(\( 1 - 13 T + 117 T^{2} - 689 T^{3} + 3502 T^{4} - 14660 T^{5} + 59534 T^{6} - 199121 T^{7} + 574821 T^{8} - 1085773 T^{9} + 1419857 T^{10} \))(\( 1 + 8 T + 98 T^{2} + 603 T^{3} + 4160 T^{4} + 21377 T^{5} + 107227 T^{6} + 458085 T^{7} + 1822859 T^{8} + 6177953 T^{9} + 20438080 T^{10} + 50363163 T^{11} + 139145986 T^{12} + 193100552 T^{13} + 410338673 T^{14} \))(\( 1 + T + 79 T^{2} - 11 T^{3} + 2945 T^{4} - 2988 T^{5} + 73324 T^{6} - 105027 T^{7} + 1398435 T^{8} - 1785459 T^{9} + 21190636 T^{10} - 14680044 T^{11} + 245969345 T^{12} - 15618427 T^{13} + 1906867951 T^{14} + 410338673 T^{15} + 6975757441 T^{16} \))(\( 1 - 10 T + 108 T^{2} - 558 T^{3} + 3021 T^{4} - 6399 T^{5} + 12954 T^{6} + 118715 T^{7} - 402700 T^{8} + 2018155 T^{9} + 3743706 T^{10} - 31438287 T^{11} + 252316941 T^{12} - 792280206 T^{13} + 2606857452 T^{14} - 4103386730 T^{15} + 6975757441 T^{16} \))(\( 1 + 8 T + 115 T^{2} + 814 T^{3} + 6876 T^{4} + 41147 T^{5} + 269394 T^{6} + 1390496 T^{7} + 7628177 T^{8} + 34702581 T^{9} + 165405097 T^{10} + 667245148 T^{11} + 2811886649 T^{12} + 10029045909 T^{13} + 37477233601 T^{14} + 116135616416 T^{15} + 382500956658 T^{16} + 993188551643 T^{17} + 2821488715548 T^{18} + 5678266556974 T^{19} + 13637605797155 T^{20} + 16127951203592 T^{21} + 34271896307633 T^{22} \))(\( 1 + 8 T + 119 T^{2} + 646 T^{3} + 5820 T^{4} + 23677 T^{5} + 174996 T^{6} + 585816 T^{7} + 4101835 T^{8} + 12324963 T^{9} + 82726321 T^{10} + 227915308 T^{11} + 1406347457 T^{12} + 3561914307 T^{13} + 20152315355 T^{14} + 48927938136 T^{15} + 248469295572 T^{16} + 571505221213 T^{17} + 2388171076860 T^{18} + 4506339306886 T^{19} + 14111957303143 T^{20} + 16127951203592 T^{21} + 34271896307633 T^{22} \))(\( 1 + 96 T^{2} + 4866 T^{4} + 173330 T^{6} + 4834895 T^{8} + 112170679 T^{10} + 2268239142 T^{12} + 41779044911 T^{14} + 726178837308 T^{16} + 12074143979279 T^{18} + 189445601378982 T^{20} + 2707527504139351 T^{22} + 33727054772703695 T^{24} + 349432222764825170 T^{26} + 2835039806360017026 T^{28} + 16164271349702489184 T^{30} + 48661191875666868481 T^{32} \))(\( 1 + 112 T^{2} + 5790 T^{4} + 179858 T^{6} + 3829395 T^{8} + 68317167 T^{10} + 1390056730 T^{12} + 31871878383 T^{14} + 621140964972 T^{16} + 9210972852687 T^{18} + 116098928146330 T^{20} + 1649010332347023 T^{22} + 26712930665778195 T^{24} + 362592630946956242 T^{26} + 3373382753560316190 T^{28} + 18858316574652904048 T^{30} + 48661191875666868481 T^{32} \))
$19$ (\( 1 + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( ( 1 - 7 T + 19 T^{2} )^{2} \))(\( 1 + T + 49 T^{2} + 133 T^{3} + 1324 T^{4} + 3756 T^{5} + 25156 T^{6} + 48013 T^{7} + 336091 T^{8} + 130321 T^{9} + 2476099 T^{10} \))(\( 1 + 12 T + 162 T^{2} + 1287 T^{3} + 10068 T^{4} + 58701 T^{5} + 329605 T^{6} + 1466121 T^{7} + 6262495 T^{8} + 21191061 T^{9} + 69056412 T^{10} + 167723127 T^{11} + 401128038 T^{12} + 564550572 T^{13} + 893871739 T^{14} \))(\( 1 - 8 T + 101 T^{2} - 541 T^{3} + 4234 T^{4} - 17538 T^{5} + 114149 T^{6} - 410056 T^{7} + 2404142 T^{8} - 7791064 T^{9} + 41207789 T^{10} - 120293142 T^{11} + 551779114 T^{12} - 1339569559 T^{13} + 4751633981 T^{14} - 7150973912 T^{15} + 16983563041 T^{16} \))(\( 1 + 5 T + 83 T^{2} + 389 T^{3} + 3914 T^{4} + 16250 T^{5} + 122087 T^{6} + 441190 T^{7} + 2730658 T^{8} + 8382610 T^{9} + 44073407 T^{10} + 111458750 T^{11} + 510076394 T^{12} + 963202511 T^{13} + 3904808123 T^{14} + 4469358695 T^{15} + 16983563041 T^{16} \))(\( 1 + 5 T + 136 T^{2} + 558 T^{3} + 8676 T^{4} + 29830 T^{5} + 352557 T^{6} + 1032918 T^{7} + 10424520 T^{8} + 26575017 T^{9} + 242151960 T^{10} + 552619952 T^{11} + 4600887240 T^{12} + 9593581137 T^{13} + 71501782680 T^{14} + 134610906678 T^{15} + 872966035143 T^{16} + 1403378630230 T^{17} + 7755231207564 T^{18} + 9476828176878 T^{19} + 43885526897944 T^{20} + 30655331289005 T^{21} + 116490258898219 T^{22} \))(\( 1 - 7 T + 124 T^{2} - 674 T^{3} + 7248 T^{4} - 32514 T^{5} + 272057 T^{6} - 1034822 T^{7} + 7497696 T^{8} - 24963723 T^{9} + 166710364 T^{10} - 506538600 T^{11} + 3167496916 T^{12} - 9011904003 T^{13} + 51426696864 T^{14} - 134859037862 T^{15} + 673640065643 T^{16} - 1529649774834 T^{17} + 6478782364272 T^{18} - 11446921489634 T^{19} + 40013274524596 T^{20} - 42917463804607 T^{21} + 116490258898219 T^{22} \))(\( ( 1 + 9 T + 97 T^{2} + 429 T^{3} + 2706 T^{4} + 5916 T^{5} + 35761 T^{6} - 3474 T^{7} + 405044 T^{8} - 66006 T^{9} + 12909721 T^{10} + 40577844 T^{11} + 352648626 T^{12} + 1062246471 T^{13} + 4563450457 T^{14} + 8044845651 T^{15} + 16983563041 T^{16} )^{2} \))(\( ( 1 - 5 T + 95 T^{2} - 463 T^{3} + 4846 T^{4} - 20652 T^{5} + 159341 T^{6} - 584056 T^{7} + 3601136 T^{8} - 11097064 T^{9} + 57522101 T^{10} - 141652068 T^{11} + 631535566 T^{12} - 1146433837 T^{13} + 4469358695 T^{14} - 4469358695 T^{15} + 16983563041 T^{16} )^{2} \))
$23$ (\( 1 + 8 T + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 34 T^{2} + 529 T^{4} \))(\( 1 - 11 T + 75 T^{2} - 253 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 59 T^{2} + 296 T^{3} + 2242 T^{4} + 8520 T^{5} + 51566 T^{6} + 156584 T^{7} + 717853 T^{8} + 1119364 T^{9} + 6436343 T^{10} \))(\( 1 - 12 T + 177 T^{2} - 1506 T^{3} + 12772 T^{4} - 82126 T^{5} + 498368 T^{6} - 2475808 T^{7} + 11462464 T^{8} - 43444654 T^{9} + 155396924 T^{10} - 421440546 T^{11} + 1139232711 T^{12} - 1776430668 T^{13} + 3404825447 T^{14} \))(\( 1 + 21 T + 298 T^{2} + 2923 T^{3} + 23181 T^{4} + 150180 T^{5} + 856682 T^{6} + 4396734 T^{7} + 21591348 T^{8} + 101124882 T^{9} + 453184778 T^{10} + 1827240060 T^{11} + 6486994221 T^{12} + 18813430589 T^{13} + 44114694922 T^{14} + 71501334387 T^{15} + 78310985281 T^{16} \))(\( 1 + T + 49 T^{2} + 237 T^{3} + 2226 T^{4} + 7181 T^{5} + 82855 T^{6} + 277089 T^{7} + 1786858 T^{8} + 6373047 T^{9} + 43830295 T^{10} + 87371227 T^{11} + 622926066 T^{12} + 1525413291 T^{13} + 7253758561 T^{14} + 3404825447 T^{15} + 78310985281 T^{16} \))(\( 1 + T + 124 T^{2} + 362 T^{3} + 8130 T^{4} + 31969 T^{5} + 393549 T^{6} + 1583780 T^{7} + 14690292 T^{8} + 55955166 T^{9} + 424988598 T^{10} + 1486183940 T^{11} + 9774737754 T^{12} + 29600282814 T^{13} + 178736782764 T^{14} + 443206578980 T^{15} + 2533016351307 T^{16} + 4732559335441 T^{17} + 27681230884110 T^{18} + 28348576671722 T^{19} + 223342930021412 T^{20} + 41426511213649 T^{21} + 952809757913927 T^{22} \))(\( 1 + 9 T + 180 T^{2} + 1206 T^{3} + 14310 T^{4} + 80149 T^{5} + 732713 T^{6} + 3624660 T^{7} + 27623256 T^{8} + 121913490 T^{9} + 802797642 T^{10} + 3163952812 T^{11} + 18464345766 T^{12} + 64492236210 T^{13} + 336092155752 T^{14} + 1014328479060 T^{15} + 4715992188559 T^{16} + 11864928467461 T^{17} + 48723052146570 T^{18} + 94443048248886 T^{19} + 324207479063340 T^{20} + 372838600922841 T^{21} + 952809757913927 T^{22} \))(\( 1 + 169 T^{2} + 15111 T^{4} + 949209 T^{6} + 46427418 T^{8} + 1856705579 T^{10} + 62422260209 T^{12} + 1793083653203 T^{14} + 44375066453018 T^{16} + 948541252544387 T^{18} + 17468307719146769 T^{20} + 274859060998524731 T^{22} + 3635776847632834458 T^{24} + 39322417282596553641 T^{26} + \)\(33\!\cdots\!31\)\( T^{28} + \)\(19\!\cdots\!21\)\( T^{30} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 + 221 T^{2} + 23599 T^{4} + 1618809 T^{6} + 80302546 T^{8} + 3091082779 T^{10} + 97454259881 T^{12} + 2639431294031 T^{14} + 63781505390570 T^{16} + 1396259154542399 T^{18} + 27271697539358921 T^{20} + 457591187161855531 T^{22} + 6288571497832825426 T^{24} + 67061609191255924041 T^{26} + \)\(51\!\cdots\!79\)\( T^{28} + \)\(25\!\cdots\!89\)\( T^{30} + \)\(61\!\cdots\!61\)\( T^{32} \))
$29$ (\( 1 + 4 T + 29 T^{2} \))(\( 1 + 7 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 5 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 + 10 T^{2} + 841 T^{4} \))(\( 1 - 19 T + 147 T^{2} - 551 T^{3} + 841 T^{4} \))(\( 1 + 11 T + 115 T^{2} + 811 T^{3} + 6024 T^{4} + 33304 T^{5} + 174696 T^{6} + 682051 T^{7} + 2804735 T^{8} + 7780091 T^{9} + 20511149 T^{10} \))(\( 1 - 24 T + 414 T^{2} - 4965 T^{3} + 49050 T^{4} - 392097 T^{5} + 2692081 T^{6} - 15558729 T^{7} + 78070349 T^{8} - 329753577 T^{9} + 1196280450 T^{10} - 3511650165 T^{11} + 8491615686 T^{12} - 14275759704 T^{13} + 17249876309 T^{14} \))(\( 1 + 11 T + 167 T^{2} + 1097 T^{3} + 9173 T^{4} + 35360 T^{5} + 217188 T^{6} + 349509 T^{7} + 3873143 T^{8} + 10135761 T^{9} + 182655108 T^{10} + 862395040 T^{11} + 6487888613 T^{12} + 22500730453 T^{13} + 99335494607 T^{14} + 189748639399 T^{15} + 500246412961 T^{16} \))(\( 1 - 14 T + 224 T^{2} - 1994 T^{3} + 19393 T^{4} - 134555 T^{5} + 1008624 T^{6} - 5792797 T^{7} + 35381532 T^{8} - 167991113 T^{9} + 848252784 T^{10} - 3281661895 T^{11} + 13716300433 T^{12} - 40899231106 T^{13} + 133240423904 T^{14} - 241498268326 T^{15} + 500246412961 T^{16} \))(\( 1 + 16 T + 283 T^{2} + 2866 T^{3} + 30626 T^{4} + 236869 T^{5} + 1961338 T^{6} + 12821850 T^{7} + 91205265 T^{8} + 529593539 T^{9} + 3340798743 T^{10} + 17306165672 T^{11} + 96883163547 T^{12} + 445388166299 T^{13} + 2224405208085 T^{14} + 9068650889850 T^{15} + 40229295957362 T^{16} + 140895205221949 T^{17} + 528294711839434 T^{18} + 1433706219546226 T^{19} + 4105522311170927 T^{20} + 6731315732803216 T^{21} + 12200509765705829 T^{22} \))(\( 1 + 14 T + 273 T^{2} + 2846 T^{3} + 31536 T^{4} + 260091 T^{5} + 2121970 T^{6} + 14462138 T^{7} + 97155057 T^{8} + 571965551 T^{9} + 3401371363 T^{10} + 18083881904 T^{11} + 98639769527 T^{12} + 481023028391 T^{13} + 2369514685173 T^{14} + 10228795426778 T^{15} + 43524042843530 T^{16} + 154708192382211 T^{17} + 543992099280624 T^{18} + 1423701291287006 T^{19} + 3960450851412237 T^{20} + 5889901266202814 T^{21} + 12200509765705829 T^{22} \))(\( 1 + 132 T^{2} + 9340 T^{4} + 524990 T^{6} + 24990469 T^{8} + 1020065729 T^{10} + 37490753330 T^{12} + 1249507114925 T^{14} + 37796704716920 T^{16} + 1050835483651925 T^{18} + 26516497505995730 T^{20} + 606758884562066009 T^{22} + 12501392475463068709 T^{24} + \)\(22\!\cdots\!90\)\( T^{26} + \)\(33\!\cdots\!40\)\( T^{28} + \)\(39\!\cdots\!92\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 + 324 T^{2} + 52524 T^{4} + 5595806 T^{6} + 436033713 T^{8} + 26253249121 T^{10} + 1260412630946 T^{12} + 49144293297901 T^{14} + 1571389612611712 T^{16} + 41330350663534741 T^{18} + 891465906028117826 T^{20} + 15616044829193550841 T^{22} + \)\(21\!\cdots\!93\)\( T^{24} + \)\(23\!\cdots\!06\)\( T^{26} + \)\(18\!\cdots\!84\)\( T^{28} + \)\(96\!\cdots\!44\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))
$31$ (\( 1 + 2 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( 1 - 2 T - 17 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 + 3 T + 125 T^{2} + 337 T^{3} + 7024 T^{4} + 15164 T^{5} + 217744 T^{6} + 323857 T^{7} + 3723875 T^{8} + 2770563 T^{9} + 28629151 T^{10} \))(\( 1 - T + 111 T^{2} - 256 T^{3} + 5963 T^{4} - 16622 T^{5} + 235568 T^{6} - 596825 T^{7} + 7302608 T^{8} - 15973742 T^{9} + 177643733 T^{10} - 236421376 T^{11} + 3177835761 T^{12} - 887503681 T^{13} + 27512614111 T^{14} \))(\( 1 - 13 T + 250 T^{2} - 2243 T^{3} + 24996 T^{4} - 172450 T^{5} + 1422665 T^{6} - 7980315 T^{7} + 53213832 T^{8} - 247389765 T^{9} + 1367181065 T^{10} - 5137457950 T^{11} + 23084330916 T^{12} - 64215185693 T^{13} + 221875920250 T^{14} - 357663983443 T^{15} + 852891037441 T^{16} \))(\( 1 + 21 T + 289 T^{2} + 2861 T^{3} + 25850 T^{4} + 205006 T^{5} + 1485675 T^{6} + 9336450 T^{7} + 54588270 T^{8} + 289429950 T^{9} + 1427733675 T^{10} + 6107333746 T^{11} + 23873017850 T^{12} + 81908001011 T^{13} + 256488563809 T^{14} + 577764896331 T^{15} + 852891037441 T^{16} \))(\( 1 - 7 T + 102 T^{2} - 550 T^{3} + 6026 T^{4} - 32074 T^{5} + 316311 T^{6} - 1571546 T^{7} + 13743210 T^{8} - 62551483 T^{9} + 482293076 T^{10} - 2049502120 T^{11} + 14951085356 T^{12} - 60111975163 T^{13} + 409423969110 T^{14} - 1451355733466 T^{15} + 9055715381961 T^{16} - 28465793064394 T^{17} + 165791012632886 T^{18} - 469090070592550 T^{19} + 2696841460388442 T^{20} - 5737398008865607 T^{21} + 25408476896404831 T^{22} \))(\( 1 - 15 T + 302 T^{2} - 3230 T^{3} + 37578 T^{4} - 312334 T^{5} + 2682611 T^{6} - 18365254 T^{7} + 129246562 T^{8} - 769189671 T^{9} + 4771201896 T^{10} - 25894157680 T^{11} + 147907258776 T^{12} - 739191273831 T^{13} + 3850384328542 T^{14} - 16960697739334 T^{15} + 76800875393261 T^{16} - 277197574701454 T^{17} + 1033869013063158 T^{18} - 2754838050934430 T^{19} + 7984765892522642 T^{20} - 12294424304712015 T^{21} + 25408476896404831 T^{22} \))(\( ( 1 - 3 T + 111 T^{2} - 317 T^{3} + 7600 T^{4} - 19582 T^{5} + 349085 T^{6} - 819998 T^{7} + 12474908 T^{8} - 25419938 T^{9} + 335470685 T^{10} - 583367362 T^{11} + 7018759600 T^{12} - 9075440867 T^{13} + 98512908591 T^{14} - 82537842333 T^{15} + 852891037441 T^{16} )^{2} \))(\( ( 1 - 13 T + 229 T^{2} - 1913 T^{3} + 20112 T^{4} - 128470 T^{5} + 1042661 T^{6} - 5533272 T^{7} + 37781400 T^{8} - 171531432 T^{9} + 1001997221 T^{10} - 3827249770 T^{11} + 18573854352 T^{12} - 54767565863 T^{13} + 203238342949 T^{14} - 357663983443 T^{15} + 852891037441 T^{16} )^{2} \))
$37$ (\( 1 + T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( ( 1 - 11 T + 37 T^{2} )^{2} \))(\( 1 + 7 T + 75 T^{2} + 259 T^{3} + 1369 T^{4} \))(\( 1 - 7 T + 166 T^{2} - 852 T^{3} + 11493 T^{4} - 44453 T^{5} + 425241 T^{6} - 1166388 T^{7} + 8408398 T^{8} - 13119127 T^{9} + 69343957 T^{10} \))(\( 1 + 13 T + 183 T^{2} + 1068 T^{3} + 5487 T^{4} - 16984 T^{5} - 283428 T^{6} - 2841185 T^{7} - 10486836 T^{8} - 23251096 T^{9} + 277933011 T^{10} + 2001603948 T^{11} + 12689944131 T^{12} + 33354443317 T^{13} + 94931877133 T^{14} \))(\( 1 - 6 T + 145 T^{2} - 344 T^{3} + 8062 T^{4} + 1995 T^{5} + 349463 T^{6} + 331435 T^{7} + 14756951 T^{8} + 12263095 T^{9} + 478414847 T^{10} + 101052735 T^{11} + 15109485982 T^{12} - 23854321208 T^{13} + 372030329305 T^{14} - 569591262798 T^{15} + 3512479453921 T^{16} \))(\( 1 + 21 T + 317 T^{2} + 3724 T^{3} + 35983 T^{4} + 308260 T^{5} + 2355447 T^{6} + 16331091 T^{7} + 104208025 T^{8} + 604250367 T^{9} + 3224606943 T^{10} + 15614293780 T^{11} + 67437935263 T^{12} + 258236895868 T^{13} + 813335271653 T^{14} + 1993569419793 T^{15} + 3512479453921 T^{16} \))(\( 1 - 3 T + 137 T^{2} - 562 T^{3} + 10881 T^{4} - 46942 T^{5} + 661944 T^{6} - 2841318 T^{7} + 32893818 T^{8} - 142115471 T^{9} + 1400259548 T^{10} - 5807833846 T^{11} + 51809603276 T^{12} - 194556079799 T^{13} + 1666170563154 T^{14} - 5325087384198 T^{15} + 45901816272408 T^{16} - 120440329091278 T^{17} + 1032953755084173 T^{18} - 1974013453103602 T^{19} + 17804758351925549 T^{20} - 14425753117253547 T^{21} + 177917621779460413 T^{22} \))(\( 1 - 23 T + 489 T^{2} - 7114 T^{3} + 93901 T^{4} - 1030282 T^{5} + 10358512 T^{6} - 91933454 T^{7} + 754651694 T^{8} - 5601927219 T^{9} + 38677033168 T^{10} - 243720248214 T^{11} + 1431050227216 T^{12} - 7669038362811 T^{13} + 38225372256182 T^{14} - 172298094082094 T^{15} + 718300210711984 T^{16} - 2643421736117338 T^{17} + 8914198194665833 T^{18} - 24987778835193994 T^{19} + 63551290759792653 T^{20} - 110597440565610527 T^{21} + 177917621779460413 T^{22} \))(\( ( 1 + 17 T + 317 T^{2} + 3286 T^{3} + 35541 T^{4} + 268340 T^{5} + 2173007 T^{6} + 13355805 T^{7} + 91867303 T^{8} + 494164785 T^{9} + 2974846583 T^{10} + 13592226020 T^{11} + 66609556101 T^{12} + 227864242702 T^{13} + 813335271653 T^{14} + 1613841911261 T^{15} + 3512479453921 T^{16} )^{2} \))(\( ( 1 - 15 T + 289 T^{2} - 3086 T^{3} + 35173 T^{4} - 290520 T^{5} + 2467199 T^{6} - 16446263 T^{7} + 111797663 T^{8} - 608511731 T^{9} + 3377595431 T^{10} - 14715709560 T^{11} + 65919864853 T^{12} - 213995451302 T^{13} + 741494932201 T^{14} - 1423978156995 T^{15} + 3512479453921 T^{16} )^{2} \))
$41$ (\( 1 + 2 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 11 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 26 T^{2} + 1681 T^{4} \))(\( 1 - 4 T + 81 T^{2} - 164 T^{3} + 1681 T^{4} \))(\( 1 - 17 T + 305 T^{2} - 3031 T^{3} + 29350 T^{4} - 191460 T^{5} + 1203350 T^{6} - 5095111 T^{7} + 21020905 T^{8} - 48037937 T^{9} + 115856201 T^{10} \))(\( 1 + 5 T + 264 T^{2} + 1158 T^{3} + 30717 T^{4} + 114497 T^{5} + 2041496 T^{6} + 6184759 T^{7} + 83701336 T^{8} + 192469457 T^{9} + 2117046357 T^{10} + 3272231238 T^{11} + 30586037064 T^{12} + 23750521205 T^{13} + 194754273881 T^{14} \))(\( 1 - 12 T + 112 T^{2} - 837 T^{3} + 7115 T^{4} - 50582 T^{5} + 356144 T^{6} - 2512364 T^{7} + 17725429 T^{8} - 103006924 T^{9} + 598678064 T^{10} - 3486162022 T^{11} + 20105289515 T^{12} - 96971640237 T^{13} + 532011674992 T^{14} - 2337051286572 T^{15} + 7984925229121 T^{16} \))(\( 1 - 31 T + 529 T^{2} - 6543 T^{3} + 65990 T^{4} - 576298 T^{5} + 4523223 T^{6} - 32547204 T^{7} + 216517746 T^{8} - 1334435364 T^{9} + 7603537863 T^{10} - 39719034458 T^{11} + 186471968390 T^{12} - 758047123143 T^{13} + 2512805143489 T^{14} - 6037382490311 T^{15} + 7984925229121 T^{16} \))(\( 1 + 29 T + 638 T^{2} + 10028 T^{3} + 136516 T^{4} + 1566978 T^{5} + 16283645 T^{6} + 150451998 T^{7} + 1283619166 T^{8} + 9954859025 T^{9} + 71931461786 T^{10} + 476547263756 T^{11} + 2949189933226 T^{12} + 16734118021025 T^{13} + 88468316539886 T^{14} + 425141388320478 T^{15} + 1886561248132645 T^{16} + 7443308843353698 T^{17} + 26587074453138596 T^{18} + 80072830197625388 T^{19} + 208869674143347118 T^{20} + 389257119994419629 T^{21} + 550329031716248441 T^{22} \))(\( 1 + 19 T + 432 T^{2} + 5672 T^{3} + 77682 T^{4} + 799740 T^{5} + 8327929 T^{6} + 71550830 T^{7} + 615562594 T^{8} + 4548097409 T^{9} + 33483376266 T^{10} + 214974965236 T^{11} + 1372818426906 T^{12} + 7645351744529 T^{13} + 42425189541074 T^{14} + 202185544931630 T^{15} + 964842216137729 T^{16} + 3798848365697340 T^{17} + 15128901503623842 T^{18} + 45290495899574312 T^{19} + 141428995658191152 T^{20} + 255030526892895619 T^{21} + 550329031716248441 T^{22} \))(\( 1 + 297 T^{2} + 43899 T^{4} + 4375303 T^{6} + 332416512 T^{8} + 20566091136 T^{10} + 1085706332611 T^{12} + 50820945868848 T^{14} + 2169861279009570 T^{16} + 85430010005533488 T^{18} + 3067946612145191971 T^{20} + 97691076725906107776 T^{22} + \)\(26\!\cdots\!52\)\( T^{24} + \)\(58\!\cdots\!03\)\( T^{26} + \)\(99\!\cdots\!19\)\( T^{28} + \)\(11\!\cdots\!17\)\( T^{30} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 + 317 T^{2} + 51599 T^{4} + 5654891 T^{6} + 465619192 T^{8} + 30692289628 T^{10} + 1696441305383 T^{12} + 81657695477692 T^{14} + 3519402244241026 T^{16} + 137266586098000252 T^{18} + 4793737679540371463 T^{20} + \)\(14\!\cdots\!48\)\( T^{22} + \)\(37\!\cdots\!32\)\( T^{24} + \)\(75\!\cdots\!91\)\( T^{26} + \)\(11\!\cdots\!19\)\( T^{28} + \)\(12\!\cdots\!37\)\( T^{30} + \)\(63\!\cdots\!41\)\( T^{32} \))
$43$ (\( 1 + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( 1 - 5 T + 91 T^{2} - 215 T^{3} + 1849 T^{4} \))(\( 1 - 15 T + 129 T^{2} - 969 T^{3} + 8260 T^{4} - 59832 T^{5} + 355180 T^{6} - 1791681 T^{7} + 10256403 T^{8} - 51282015 T^{9} + 147008443 T^{10} \))(\( 1 + 13 T + 210 T^{2} + 1334 T^{3} + 13059 T^{4} + 51311 T^{5} + 553438 T^{6} + 1937621 T^{7} + 23797834 T^{8} + 94874039 T^{9} + 1038281913 T^{10} + 4560680534 T^{11} + 30871773030 T^{12} + 82177719637 T^{13} + 271818611107 T^{14} \))(\( 1 - 23 T + 461 T^{2} - 6103 T^{3} + 73653 T^{4} - 707951 T^{5} + 6332791 T^{6} - 47787990 T^{7} + 338721832 T^{8} - 2054883570 T^{9} + 11709330559 T^{10} - 56287060157 T^{11} + 251804950053 T^{12} - 897192527629 T^{13} + 2914148365589 T^{14} - 6251828055461 T^{15} + 11688200277601 T^{16} \))(\( 1 + 18 T + 290 T^{2} + 3392 T^{3} + 34087 T^{4} + 306841 T^{5} + 2498008 T^{6} + 18492099 T^{7} + 128152936 T^{8} + 795160257 T^{9} + 4618816792 T^{10} + 24396007387 T^{11} + 116536669687 T^{12} + 498652638656 T^{13} + 1833195284210 T^{14} + 4892734999926 T^{15} + 11688200277601 T^{16} \))(\( 1 + 14 T + 399 T^{2} + 4518 T^{3} + 73364 T^{4} + 695379 T^{5} + 8318828 T^{6} + 67449906 T^{7} + 652760479 T^{8} + 4582892039 T^{9} + 37470185637 T^{10} + 228494038256 T^{11} + 1611217982391 T^{12} + 8473767380111 T^{13} + 51899027403853 T^{14} + 230597806082706 T^{15} + 1222937951864804 T^{16} + 4395743115650571 T^{17} + 19941700585253948 T^{18} + 52807288854201318 T^{19} + 200534452162800357 T^{20} + 302560752385979486 T^{21} + 929293739471222707 T^{22} \))(\( 1 - 22 T + 511 T^{2} - 7638 T^{3} + 108652 T^{4} - 1248793 T^{5} + 13499812 T^{6} - 126649222 T^{7} + 1119369859 T^{8} - 8841440961 T^{9} + 65960000953 T^{10} - 444828100728 T^{11} + 2836280040979 T^{12} - 16347824336889 T^{13} + 88997739379513 T^{14} - 432988486822822 T^{15} + 1984586342912716 T^{16} - 7894073926049857 T^{17} + 29533635733997764 T^{18} - 89274473720316438 T^{19} + 256824824699726773 T^{20} - 475452610892253478 T^{21} + 929293739471222707 T^{22} \))(\( ( 1 + 28 T + 424 T^{2} + 4272 T^{3} + 33555 T^{4} + 233239 T^{5} + 1639618 T^{6} + 11703343 T^{7} + 80150210 T^{8} + 503243749 T^{9} + 3031653682 T^{10} + 18544133173 T^{11} + 114717867555 T^{12} + 628020068496 T^{13} + 2680257932776 T^{14} + 7610921110996 T^{15} + 11688200277601 T^{16} )^{2} \))(\( ( 1 - 14 T + 308 T^{2} - 3238 T^{3} + 41175 T^{4} - 346937 T^{5} + 3271000 T^{6} - 22648557 T^{7} + 171184054 T^{8} - 973887951 T^{9} + 6048079000 T^{10} - 27583920059 T^{11} + 140769131175 T^{12} - 476013338434 T^{13} + 1946979819092 T^{14} - 3805460555498 T^{15} + 11688200277601 T^{16} )^{2} \))
$47$ (\( 1 - T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 11 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + T + 47 T^{2} \))(\( 1 + 91 T^{2} + 2209 T^{4} \))(\( 1 + 6 T + 58 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 25 T + 424 T^{2} - 5078 T^{3} + 48429 T^{4} - 365921 T^{5} + 2276163 T^{6} - 11217302 T^{7} + 44020952 T^{8} - 121992025 T^{9} + 229345007 T^{10} \))(\( 1 - 21 T + 426 T^{2} - 5556 T^{3} + 66591 T^{4} - 628257 T^{5} + 5425594 T^{6} - 38875515 T^{7} + 255002918 T^{8} - 1387819713 T^{9} + 6913677393 T^{10} - 27111507636 T^{11} + 97700972982 T^{12} - 226363521909 T^{13} + 506623120463 T^{14} \))(\( 1 + 23 T + 465 T^{2} + 6161 T^{3} + 75349 T^{4} + 737235 T^{5} + 6820303 T^{6} + 53370750 T^{7} + 395724972 T^{8} + 2508425250 T^{9} + 15066049327 T^{10} + 76541949405 T^{11} + 367679083669 T^{12} + 1412994588127 T^{13} + 5012335127985 T^{14} + 11652331770649 T^{15} + 23811286661761 T^{16} \))(\( 1 - 10 T + 226 T^{2} - 1979 T^{3} + 24748 T^{4} - 202646 T^{5} + 1815079 T^{6} - 13538111 T^{7} + 97818600 T^{8} - 636291217 T^{9} + 4009509511 T^{10} - 21039315658 T^{11} + 120762345388 T^{12} - 453873768853 T^{13} + 2436102664354 T^{14} - 5066231204630 T^{15} + 23811286661761 T^{16} \))(\( 1 + 6 T + 340 T^{2} + 1655 T^{3} + 56404 T^{4} + 231454 T^{5} + 6098142 T^{6} + 21514795 T^{7} + 479145198 T^{8} + 1475334020 T^{9} + 28807708461 T^{10} + 78284200452 T^{11} + 1353962297667 T^{12} + 3259012850180 T^{13} + 49746291891954 T^{14} + 104985336380395 T^{15} + 1398578419676994 T^{16} + 2494892504758366 T^{17} + 28575570486595052 T^{18} + 39407679425214455 T^{19} + 380504360854940780 T^{20} + 315594793414980294 T^{21} + 2472159215084012303 T^{22} \))(\( 1 + 4 T + 236 T^{2} + 1143 T^{3} + 28926 T^{4} + 153714 T^{5} + 2456162 T^{6} + 13572971 T^{7} + 164364346 T^{8} + 892107870 T^{9} + 9154599263 T^{10} + 46602983244 T^{11} + 430266165361 T^{12} + 1970666284830 T^{13} + 17064799494758 T^{14} + 66231768702251 T^{15} + 563308491083134 T^{16} + 1656916305081906 T^{17} + 14654580382512738 T^{18} + 27216300654392823 T^{19} + 264114791652253012 T^{20} + 210396528943320196 T^{21} + 2472159215084012303 T^{22} \))(\( 1 + 156 T^{2} + 12466 T^{4} + 751205 T^{6} + 43914736 T^{8} + 2652916196 T^{10} + 153658052909 T^{12} + 7777460687591 T^{14} + 366175291552760 T^{16} + 17180410658888519 T^{18} + 749802281277042029 T^{20} + 28596354926475568484 T^{22} + \)\(10\!\cdots\!96\)\( T^{24} + \)\(39\!\cdots\!45\)\( T^{26} + \)\(14\!\cdots\!06\)\( T^{28} + \)\(40\!\cdots\!64\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 446 T^{2} + 102912 T^{4} + 15989089 T^{6} + 1856126860 T^{8} + 169801471108 T^{10} + 12622248462849 T^{12} + 776165563934353 T^{14} + 39859201160382028 T^{16} + 1714549730730985777 T^{18} + 61592546001443471169 T^{20} + \)\(18\!\cdots\!32\)\( T^{22} + \)\(44\!\cdots\!60\)\( T^{24} + \)\(84\!\cdots\!61\)\( T^{26} + \)\(11\!\cdots\!92\)\( T^{28} + \)\(11\!\cdots\!74\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))
$53$ (\( 1 + 53 T^{2} \))(\( 1 + T + 53 T^{2} \))(\( 1 + 8 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 94 T^{2} + 2809 T^{4} \))(\( 1 - 7 T + 117 T^{2} - 371 T^{3} + 2809 T^{4} \))(\( 1 - 3 T + 61 T^{2} - 323 T^{3} + 5370 T^{4} - 25908 T^{5} + 284610 T^{6} - 907307 T^{7} + 9081497 T^{8} - 23671443 T^{9} + 418195493 T^{10} \))(\( 1 - 35 T + 807 T^{2} - 13478 T^{3} + 180093 T^{4} - 1977592 T^{5} + 18343012 T^{6} - 144325621 T^{7} + 972179636 T^{8} - 5555055928 T^{9} + 26811705561 T^{10} - 106347902918 T^{11} + 337483762851 T^{12} - 775752639515 T^{13} + 1174711139837 T^{14} \))(\( 1 + 14 T + 321 T^{2} + 3546 T^{3} + 46930 T^{4} + 435447 T^{5} + 4278457 T^{6} + 33928855 T^{7} + 269639007 T^{8} + 1798229315 T^{9} + 12018185713 T^{10} + 64828043019 T^{11} + 370300273330 T^{12} + 1482921218178 T^{13} + 7114759922409 T^{14} + 16445955957718 T^{15} + 62259690411361 T^{16} \))(\( 1 - 12 T + 230 T^{2} - 1960 T^{3} + 24687 T^{4} - 192703 T^{5} + 1926168 T^{6} - 13529797 T^{7} + 113704456 T^{8} - 717079241 T^{9} + 5410605912 T^{10} - 28689044531 T^{11} + 194792304447 T^{12} - 819663166280 T^{13} + 5097803059670 T^{14} - 14096533678044 T^{15} + 62259690411361 T^{16} \))(\( 1 + 18 T + 503 T^{2} + 6190 T^{3} + 103572 T^{4} + 1010689 T^{5} + 13081296 T^{6} + 108611228 T^{7} + 1181559175 T^{8} + 8565254009 T^{9} + 80807415505 T^{10} + 515989902348 T^{11} + 4282793021765 T^{12} + 24059798511281 T^{13} + 175906985296475 T^{14} + 856994830920668 T^{15} + 5470539029798928 T^{16} + 22401275985107881 T^{17} + 121667182175197764 T^{18} + 385387483646324590 T^{19} + 1659781086676472899 T^{20} + 3147974466579234882 T^{21} + 9269035929372191597 T^{22} \))(\( 1 + 8 T + 281 T^{2} + 1746 T^{3} + 36600 T^{4} + 182857 T^{5} + 3207208 T^{6} + 13749624 T^{7} + 227160395 T^{8} + 892920835 T^{9} + 13873315175 T^{10} + 50966893036 T^{11} + 735285704275 T^{12} + 2508214625515 T^{13} + 33818958126415 T^{14} + 108491146929144 T^{15} + 1341239930713544 T^{16} + 4052908582965553 T^{17} + 42994427718034200 T^{18} + 108705419458236306 T^{19} + 927233569296399373 T^{20} + 1399099762924104392 T^{21} + 9269035929372191597 T^{22} \))(\( 1 + 518 T^{2} + 138536 T^{4} + 24861716 T^{6} + 3321072741 T^{8} + 348158100789 T^{10} + 29527726759192 T^{12} + 2062100430261205 T^{14} + 119700809280640648 T^{16} + 5792440108603724845 T^{18} + \)\(23\!\cdots\!52\)\( T^{20} + \)\(77\!\cdots\!81\)\( T^{22} + \)\(20\!\cdots\!01\)\( T^{24} + \)\(43\!\cdots\!84\)\( T^{26} + \)\(68\!\cdots\!76\)\( T^{28} + \)\(71\!\cdots\!42\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 + 266 T^{2} + 44312 T^{4} + 5355560 T^{6} + 526992525 T^{8} + 43604475977 T^{10} + 3137519745672 T^{12} + 198239003457745 T^{14} + 11144774947407952 T^{16} + 556853360712805705 T^{18} + 24756539940349748232 T^{20} + \)\(96\!\cdots\!33\)\( T^{22} + \)\(32\!\cdots\!25\)\( T^{24} + \)\(93\!\cdots\!40\)\( T^{26} + \)\(21\!\cdots\!92\)\( T^{28} + \)\(36\!\cdots\!54\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))
$59$ (\( 1 + 14 T + 59 T^{2} \))(\( 1 - 9 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 9 T + 59 T^{2} \))(\( 1 + 11 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 10 T^{2} + 3481 T^{4} \))(\( ( 1 + 9 T + 59 T^{2} )^{2} \))(\( 1 - 14 T + 251 T^{2} - 2848 T^{3} + 26542 T^{4} - 239172 T^{5} + 1565978 T^{6} - 9913888 T^{7} + 51550129 T^{8} - 169643054 T^{9} + 714924299 T^{10} \))(\( 1 - 23 T + 523 T^{2} - 6868 T^{3} + 88042 T^{4} - 816213 T^{5} + 7731924 T^{6} - 57785640 T^{7} + 456183516 T^{8} - 2841237453 T^{9} + 18081977918 T^{10} - 83222035348 T^{11} + 373905408377 T^{12} - 970152273743 T^{13} + 2488651484819 T^{14} \))(\( 1 + 2 T + 109 T^{2} + 1256 T^{3} + 10161 T^{4} + 100953 T^{5} + 1071207 T^{6} + 7504655 T^{7} + 62733660 T^{8} + 442774645 T^{9} + 3728871567 T^{10} + 20733626187 T^{11} + 123124505121 T^{12} + 897944919544 T^{13} + 4597678166869 T^{14} + 4977302969638 T^{15} + 146830437604321 T^{16} \))(\( 1 + 2 T + 265 T^{2} + 342 T^{3} + 34642 T^{4} + 29142 T^{5} + 3061055 T^{6} + 1769250 T^{7} + 204478938 T^{8} + 104385750 T^{9} + 10655532455 T^{10} + 5985154818 T^{11} + 419769619762 T^{12} + 244504110258 T^{13} + 11177841414865 T^{14} + 4977302969638 T^{15} + 146830437604321 T^{16} \))(\( 1 + 14 T + 368 T^{2} + 4486 T^{3} + 65688 T^{4} + 709918 T^{5} + 7718943 T^{6} + 75369224 T^{7} + 686289922 T^{8} + 6108307044 T^{9} + 49221922368 T^{10} + 398885245732 T^{11} + 2904093419712 T^{12} + 21263016820164 T^{13} + 140949537890438 T^{14} + 913276095497864 T^{15} + 5518459913295957 T^{16} + 29944720081351438 T^{17} + 163474538734790472 T^{18} + 658681343092984006 T^{19} + 3187982461265017552 T^{20} + 7155634546208979614 T^{21} + 30155888444737842659 T^{22} \))(\( 1 - 8 T + 444 T^{2} - 3320 T^{3} + 94664 T^{4} - 662232 T^{5} + 13025563 T^{6} - 84265776 T^{7} + 1296855262 T^{8} - 7625726816 T^{9} + 98371043156 T^{10} - 516174086064 T^{11} + 5803891546204 T^{12} - 26545155046496 T^{13} + 266346836854298 T^{14} - 1021078827737136 T^{15} + 9312291496855337 T^{16} - 27933299154146712 T^{17} + 235585704158905816 T^{18} - 487477052846345720 T^{19} + 3846370143482792916 T^{20} - 4088934026405131208 T^{21} + 30155888444737842659 T^{22} \))(\( 1 + 740 T^{2} + 262711 T^{4} + 59545600 T^{6} + 9673224754 T^{8} + 1198157284632 T^{10} + 117435409078473 T^{12} + 9317406977692324 T^{14} + 605961638191101178 T^{16} + 32433893689346979844 T^{18} + \)\(14\!\cdots\!53\)\( T^{20} + \)\(50\!\cdots\!12\)\( T^{22} + \)\(14\!\cdots\!34\)\( T^{24} + \)\(30\!\cdots\!00\)\( T^{26} + \)\(46\!\cdots\!91\)\( T^{28} + \)\(45\!\cdots\!40\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 + 604 T^{2} + 181067 T^{4} + 35803892 T^{6} + 5229666946 T^{8} + 598620240396 T^{10} + 55583997739733 T^{12} + 4273511582559972 T^{14} + 275078878024939162 T^{16} + 14876093818891262532 T^{18} + \)\(67\!\cdots\!13\)\( T^{20} + \)\(25\!\cdots\!36\)\( T^{22} + \)\(76\!\cdots\!66\)\( T^{24} + \)\(18\!\cdots\!92\)\( T^{26} + \)\(32\!\cdots\!27\)\( T^{28} + \)\(37\!\cdots\!44\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( 1 + 4 T + 81 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 18 T + 297 T^{2} + 3552 T^{3} + 33826 T^{4} + 301116 T^{5} + 2063386 T^{6} + 13216992 T^{7} + 67413357 T^{8} + 249225138 T^{9} + 844596301 T^{10} \))(\( 1 + 17 T + 255 T^{2} + 2266 T^{3} + 14546 T^{4} + 19609 T^{5} - 426962 T^{6} - 6727784 T^{7} - 26044682 T^{8} + 72965089 T^{9} + 3301665626 T^{10} + 31374675706 T^{11} + 215372056755 T^{12} + 875846364137 T^{13} + 3142742836021 T^{14} \))(\( 1 + 13 T + 376 T^{2} + 3705 T^{3} + 65499 T^{4} + 537507 T^{5} + 7117372 T^{6} + 48827335 T^{7} + 521005360 T^{8} + 2978467435 T^{9} + 26483741212 T^{10} + 122003876367 T^{11} + 906888739659 T^{12} + 3129229295205 T^{13} + 19371660759736 T^{14} + 40855656868273 T^{15} + 191707312997281 T^{16} \))(\( 1 + 32 T + 749 T^{2} + 12362 T^{3} + 174494 T^{4} + 2051410 T^{5} + 21570827 T^{6} + 197747644 T^{7} + 1644692610 T^{8} + 12062606284 T^{9} + 80265047267 T^{10} + 465631093210 T^{11} + 2416016179454 T^{12} + 10440899472962 T^{13} + 38588760396389 T^{14} + 100567770752672 T^{15} + 191707312997281 T^{16} \))(\( 1 - 30 T + 840 T^{2} - 15684 T^{3} + 266348 T^{4} - 3722118 T^{5} + 47768893 T^{6} - 540068496 T^{7} + 5657801038 T^{8} - 53691866316 T^{9} + 474422184212 T^{10} - 3837270312664 T^{11} + 28939753236932 T^{12} - 199787434561836 T^{13} + 1284213337406278 T^{14} - 7477702524725136 T^{15} + 40345430330664793 T^{16} - 191764912775816598 T^{17} + 837063268888521308 T^{18} - 3006737497049355204 T^{19} + 9823082717980678440 T^{20} - 21400287349886478030 T^{21} + 43513917611435838661 T^{22} \))(\( 1 - 32 T + 982 T^{2} - 19520 T^{3} + 359814 T^{4} - 5301288 T^{5} + 72644305 T^{6} - 851856880 T^{7} + 9337544970 T^{8} - 90127698424 T^{9} + 815839854436 T^{10} - 6576156120992 T^{11} + 49766231120596 T^{12} - 335365165835704 T^{13} + 2119445294835570 T^{14} - 11794674915236080 T^{15} + 61355111291715805 T^{16} - 273124342355476968 T^{17} + 1130802870800060094 T^{18} - 3742126749706925120 T^{19} + 11483651463163126462 T^{20} - 22826973173212243232 T^{21} + 43513917611435838661 T^{22} \))(\( ( 1 + 2 T + 133 T^{2} - 150 T^{3} + 15902 T^{4} - 3490 T^{5} + 1446627 T^{6} - 1142890 T^{7} + 91818914 T^{8} - 69716290 T^{9} + 5382899067 T^{10} - 792163690 T^{11} + 220176563582 T^{12} - 126689445150 T^{13} + 6852209790013 T^{14} + 6285485672042 T^{15} + 191707312997281 T^{16} )^{2} \))(\( ( 1 - 20 T + 523 T^{2} - 7608 T^{3} + 115182 T^{4} - 1296264 T^{5} + 14229421 T^{6} - 127320956 T^{7} + 1088661250 T^{8} - 7766578316 T^{9} + 52947675541 T^{10} - 294227298984 T^{11} + 1594791658062 T^{12} - 6425688658008 T^{13} + 26945155790803 T^{14} - 62854856720420 T^{15} + 191707312997281 T^{16} )^{2} \))
$67$ (\( 1 + T + 67 T^{2} \))(\( 1 + 11 T + 67 T^{2} \))(\( 1 - T + 67 T^{2} \))(\( 1 - 11 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 + T + 67 T^{2} \))(\( ( 1 - 5 T + 67 T^{2} )^{2} \))(\( 1 - 2 T + 90 T^{2} - 134 T^{3} + 4489 T^{4} \))(\( 1 - 24 T + 396 T^{2} - 5014 T^{3} + 54055 T^{4} - 476220 T^{5} + 3621685 T^{6} - 22507846 T^{7} + 119102148 T^{8} - 483626904 T^{9} + 1350125107 T^{10} \))(\( 1 + 18 T + 559 T^{2} + 7233 T^{3} + 123736 T^{4} + 1211288 T^{5} + 14430462 T^{6} + 108201986 T^{7} + 966840954 T^{8} + 5437471832 T^{9} + 37215210568 T^{10} + 145753058193 T^{11} + 754719934813 T^{12} + 1628250879042 T^{13} + 6060711605323 T^{14} \))(\( 1 - 9 T + 332 T^{2} - 2424 T^{3} + 53604 T^{4} - 328469 T^{5} + 5666488 T^{6} - 29703222 T^{7} + 436787686 T^{8} - 1990115874 T^{9} + 25436864632 T^{10} - 98791321847 T^{11} + 1080180690084 T^{12} - 3272703259368 T^{13} + 30032182880108 T^{14} - 54546404447907 T^{15} + 406067677556641 T^{16} \))(\( 1 + 25 T + 525 T^{2} + 6780 T^{3} + 76820 T^{4} + 636082 T^{5} + 4955955 T^{6} + 31715563 T^{7} + 253871590 T^{8} + 2124942721 T^{9} + 22247281995 T^{10} + 191309930566 T^{11} + 1548009115220 T^{12} + 9153848225460 T^{13} + 47490650638725 T^{14} + 151517790133075 T^{15} + 406067677556641 T^{16} \))(\( 1 + 23 T + 673 T^{2} + 11028 T^{3} + 195432 T^{4} + 2551230 T^{5} + 34415498 T^{6} + 377105890 T^{7} + 4191230889 T^{8} + 39490194379 T^{9} + 374254106095 T^{10} + 3058308077044 T^{11} + 25075025108365 T^{12} + 177271482567331 T^{13} + 1260567175868307 T^{14} + 7599106419202690 T^{15} + 46465227919708286 T^{16} + 230780138341017870 T^{17} + 1184456990451484536 T^{18} + 4478114348094636948 T^{19} + 18309997648706499331 T^{20} + 41925269504690513327 T^{21} + \)\(12\!\cdots\!83\)\( T^{22} \))(\( 1 - 25 T + 603 T^{2} - 9000 T^{3} + 131314 T^{4} - 1453074 T^{5} + 16070968 T^{6} - 144028082 T^{7} + 1343304227 T^{8} - 10559434901 T^{9} + 92006625403 T^{10} - 700687867244 T^{11} + 6164443902001 T^{12} - 47401303270589 T^{13} + 404016209225201 T^{14} - 2902327307779922 T^{15} + 21697817390593576 T^{16} - 131442723211837506 T^{17} + 795856283741384422 T^{18} - 3654609098009769000 T^{19} + 16405540240965853041 T^{20} - 45570945113794036225 T^{21} + \)\(12\!\cdots\!83\)\( T^{22} \))(\( ( 1 + 23 T + 587 T^{2} + 9464 T^{3} + 145178 T^{4} + 1758118 T^{5} + 19918829 T^{6} + 189440377 T^{7} + 1678529002 T^{8} + 12692505259 T^{9} + 89415623381 T^{10} + 528776844034 T^{11} + 2925499444538 T^{12} + 12777584012648 T^{13} + 53099070333203 T^{14} + 139396366922429 T^{15} + 406067677556641 T^{16} )^{2} \))(\( ( 1 - 33 T + 569 T^{2} - 6792 T^{3} + 66120 T^{4} - 554330 T^{5} + 4083151 T^{6} - 27091935 T^{7} + 196813870 T^{8} - 1815159645 T^{9} + 18329264839 T^{10} - 166721953790 T^{11} + 1332392120520 T^{12} - 9170049726744 T^{13} + 51470819454161 T^{14} - 200003482975659 T^{15} + 406067677556641 T^{16} )^{2} \))
$71$ (\( 1 + 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 130 T^{2} + 5041 T^{4} \))(\( 1 - 9 T + 161 T^{2} - 639 T^{3} + 5041 T^{4} \))(\( 1 - 14 T + 251 T^{2} - 2464 T^{3} + 24802 T^{4} - 210468 T^{5} + 1760942 T^{6} - 12421024 T^{7} + 89835661 T^{8} - 355763534 T^{9} + 1804229351 T^{10} \))(\( 1 - 4 T + 279 T^{2} - 717 T^{3} + 39326 T^{4} - 65034 T^{5} + 3736292 T^{6} - 4506226 T^{7} + 265276732 T^{8} - 327836394 T^{9} + 14075207986 T^{10} - 18220175277 T^{11} + 503379988929 T^{12} - 512401135684 T^{13} + 9095120158391 T^{14} \))(\( 1 + 38 T + 934 T^{2} + 16547 T^{3} + 242819 T^{4} + 3022017 T^{5} + 33424686 T^{6} + 328500284 T^{7} + 2923207536 T^{8} + 23323520164 T^{9} + 168493842126 T^{10} + 1081613126487 T^{11} + 6170438968739 T^{12} + 29854583070997 T^{13} + 119645665182214 T^{14} + 345614566018858 T^{15} + 645753531245761 T^{16} \))(\( 1 - 11 T + 373 T^{2} - 3085 T^{3} + 60638 T^{4} - 381893 T^{5} + 6068747 T^{6} - 30759971 T^{7} + 466104290 T^{8} - 2183957941 T^{9} + 30592553627 T^{10} - 136683705523 T^{11} + 1540913512478 T^{12} - 5566047547835 T^{13} + 47781405902533 T^{14} - 100046321742301 T^{15} + 645753531245761 T^{16} \))(\( 1 + 7 T + 412 T^{2} + 1708 T^{3} + 73328 T^{4} + 115635 T^{5} + 8055271 T^{6} - 6998816 T^{7} + 675632342 T^{8} - 1949630058 T^{9} + 50181856476 T^{10} - 185064313880 T^{11} + 3562911809796 T^{12} - 9828085122378 T^{13} + 241816247157562 T^{14} - 177851679569696 T^{15} + 14533556368459121 T^{16} + 14812876331204835 T^{17} + 666926970974495248 T^{18} + 1102947031367759788 T^{19} + 18889582296001000772 T^{20} + 22786704857069168407 T^{21} + \)\(23\!\cdots\!71\)\( T^{22} \))(\( 1 + 3 T + 512 T^{2} + 1464 T^{3} + 131164 T^{4} + 363087 T^{5} + 22034791 T^{6} + 57906256 T^{7} + 2679149942 T^{8} + 6503463998 T^{9} + 246675272932 T^{10} + 536012733936 T^{11} + 17513944378172 T^{12} + 32783962013918 T^{13} + 958897234891162 T^{14} + 1471495305376336 T^{15} + 39755816665350641 T^{16} + 46511547788024127 T^{17} + 1192952340455197124 T^{18} + 945383169743794104 T^{19} + 23474432367845903872 T^{20} + 9765730653029643603 T^{21} + \)\(23\!\cdots\!71\)\( T^{22} \))(\( 1 + 315 T^{2} + 52537 T^{4} + 6092617 T^{6} + 521400102 T^{8} + 33864037107 T^{10} + 1680347320951 T^{12} + 65536782413673 T^{14} + 3071275202257810 T^{16} + 330370920147325593 T^{18} + 42700450089211428631 T^{20} + \)\(43\!\cdots\!47\)\( T^{22} + \)\(33\!\cdots\!22\)\( T^{24} + \)\(19\!\cdots\!17\)\( T^{26} + \)\(86\!\cdots\!17\)\( T^{28} + \)\(26\!\cdots\!15\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 + 595 T^{2} + 182709 T^{4} + 38112561 T^{6} + 6030610430 T^{8} + 766981313067 T^{10} + 81067778027067 T^{12} + 7259798859612721 T^{14} + 556343316141763170 T^{16} + 36596646051307726561 T^{18} + \)\(20\!\cdots\!27\)\( T^{20} + \)\(98\!\cdots\!07\)\( T^{22} + \)\(38\!\cdots\!30\)\( T^{24} + \)\(12\!\cdots\!61\)\( T^{26} + \)\(29\!\cdots\!69\)\( T^{28} + \)\(49\!\cdots\!95\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \))
$73$ (\( 1 + 11 T + 73 T^{2} \))(\( 1 + 5 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 + 13 T + 73 T^{2} \))(\( 1 + 5 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( ( 1 - 5 T + 73 T^{2} )^{2} \))(\( 1 - 4 T + 70 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( 1 + 23 T + 418 T^{2} + 4984 T^{3} + 52457 T^{4} + 458897 T^{5} + 3829361 T^{6} + 26559736 T^{7} + 162609106 T^{8} + 653159543 T^{9} + 2073071593 T^{10} \))(\( 1 - 23 T + 449 T^{2} - 5492 T^{3} + 66321 T^{4} - 645516 T^{5} + 6685720 T^{6} - 56509181 T^{7} + 488057560 T^{8} - 3439954764 T^{9} + 25799996457 T^{10} - 155963139572 T^{11} + 930809145257 T^{12} - 3480687204647 T^{13} + 11047398519097 T^{14} \))(\( 1 + 6 T + 347 T^{2} + 2546 T^{3} + 62734 T^{4} + 460045 T^{5} + 7722149 T^{6} + 49354079 T^{7} + 672054175 T^{8} + 3602847767 T^{9} + 41151332021 T^{10} + 178965325765 T^{11} + 1781535250894 T^{12} + 5278040275778 T^{13} + 52512976522283 T^{14} + 66284391114582 T^{15} + 806460091894081 T^{16} \))(\( 1 + 14 T + 434 T^{2} + 5525 T^{3} + 95216 T^{4} + 1011912 T^{5} + 12819531 T^{6} + 113320225 T^{7} + 1137285260 T^{8} + 8272376425 T^{9} + 68315280699 T^{10} + 393650970504 T^{11} + 2703966915056 T^{12} + 11453720551325 T^{13} + 65679054209426 T^{14} + 154663579267358 T^{15} + 806460091894081 T^{16} \))(\( 1 - 22 T + 602 T^{2} - 9725 T^{3} + 165032 T^{4} - 2209992 T^{5} + 28959690 T^{6} - 334292093 T^{7} + 3643512454 T^{8} - 36833838240 T^{9} + 345540785653 T^{10} - 3072587157072 T^{11} + 25224477352669 T^{12} - 196287523980960 T^{13} + 1417388284317718 T^{14} - 9493307421408413 T^{15} + 60035510681086170 T^{16} - 334447429424879688 T^{17} + 1823174272403616104 T^{18} - 7842824393669937725 T^{19} + 35440695198377283626 T^{20} - 94547768253478268278 T^{21} + \)\(31\!\cdots\!77\)\( T^{22} \))(\( 1 - 22 T + 646 T^{2} - 10301 T^{3} + 177656 T^{4} - 2247560 T^{5} + 29319642 T^{6} - 311242109 T^{7} + 3396250362 T^{8} - 31539539296 T^{9} + 304031013781 T^{10} - 2542416665424 T^{11} + 22194264006013 T^{12} - 168074204908384 T^{13} + 1321199127074154 T^{14} - 8838728420730269 T^{15} + 60781716947129706 T^{16} - 340132753638104840 T^{17} + 1962636631308696632 T^{18} - 8307345406600928381 T^{19} + 38031045013541071798 T^{20} - 94547768253478268278 T^{21} + \)\(31\!\cdots\!77\)\( T^{22} \))(\( ( 1 + 6 T + 434 T^{2} + 2691 T^{3} + 89992 T^{4} + 538840 T^{5} + 11602219 T^{6} + 62699067 T^{7} + 1015672012 T^{8} + 4577031891 T^{9} + 61828225051 T^{10} + 209617920280 T^{11} + 2555614504072 T^{12} + 5578635656763 T^{13} + 65679054209426 T^{14} + 66284391114582 T^{15} + 806460091894081 T^{16} )^{2} \))(\( ( 1 - 18 T + 266 T^{2} - 1861 T^{3} + 12124 T^{4} - 16136 T^{5} + 728399 T^{6} - 8728189 T^{7} + 129271132 T^{8} - 637157797 T^{9} + 3881638271 T^{10} - 6277178312 T^{11} + 344300273884 T^{12} - 3857986234573 T^{13} + 40254904192874 T^{14} - 198853173343746 T^{15} + 806460091894081 T^{16} )^{2} \))
$79$ (\( 1 - 11 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 11 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))(\( ( 1 + T + 79 T^{2} )^{2} \))(\( 1 + 18 T + 194 T^{2} + 1422 T^{3} + 6241 T^{4} \))(\( 1 - 14 T + 256 T^{2} - 1080 T^{3} + 10167 T^{4} + 39908 T^{5} + 803193 T^{6} - 6740280 T^{7} + 126217984 T^{8} - 545301134 T^{9} + 3077056399 T^{10} \))(\( 1 - 4 T + 227 T^{2} - 55 T^{3} + 27208 T^{4} + 17596 T^{5} + 2811774 T^{6} + 1054342 T^{7} + 222130146 T^{8} + 109816636 T^{9} + 13414605112 T^{10} - 2142254455 T^{11} + 698491802573 T^{12} - 972349822084 T^{13} + 19203908986159 T^{14} \))(\( 1 + 12 T + 364 T^{2} + 4003 T^{3} + 69703 T^{4} + 726945 T^{5} + 8992472 T^{6} + 83871466 T^{7} + 826480808 T^{8} + 6625845814 T^{9} + 56122017752 T^{10} + 358412235855 T^{11} + 2714937495943 T^{12} + 12317456765197 T^{13} + 88483833809644 T^{14} + 230446907833908 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 9 T + 189 T^{2} + 2128 T^{3} + 34396 T^{4} + 337898 T^{5} + 3743563 T^{6} + 35902435 T^{7} + 356457174 T^{8} + 2836292365 T^{9} + 23363576683 T^{10} + 166596892022 T^{11} + 1339726986076 T^{12} + 6547976017072 T^{13} + 45943529093469 T^{14} + 172835180875431 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 13 T + 525 T^{2} - 5456 T^{3} + 119728 T^{4} - 934414 T^{5} + 15315890 T^{6} - 78602050 T^{7} + 1217743257 T^{8} - 2744498133 T^{9} + 73670741675 T^{10} - 28917997180 T^{11} + 5819988592325 T^{12} - 17128412848053 T^{13} + 600394917688023 T^{14} - 3061556214266050 T^{15} + 47127857330880110 T^{16} - 227144321663199694 T^{17} + 2299245615094844752 T^{18} - 8277345666850196816 T^{19} + 62922087890874617475 T^{20} - \)\(12\!\cdots\!13\)\( T^{21} + \)\(74\!\cdots\!79\)\( T^{22} \))(\( 1 - 27 T + 889 T^{2} - 17384 T^{3} + 347704 T^{4} - 5335154 T^{5} + 80671646 T^{6} - 1017671510 T^{7} + 12502027941 T^{8} - 132782267235 T^{9} + 1367826059623 T^{10} - 12349850628132 T^{11} + 108058258710217 T^{12} - 828694129813635 T^{13} + 6163987354002699 T^{14} - 39638387745892310 T^{15} + 248231204542162754 T^{16} - 1296909010672685234 T^{17} + 6677275970123428936 T^{18} - 26373419551415656424 T^{19} + \)\(10\!\cdots\!91\)\( T^{20} - \)\(25\!\cdots\!27\)\( T^{21} + \)\(74\!\cdots\!79\)\( T^{22} \))(\( ( 1 + 25 T + 571 T^{2} + 8594 T^{3} + 123790 T^{4} + 1438268 T^{5} + 16380573 T^{6} + 159861395 T^{7} + 1528262642 T^{8} + 12629050205 T^{9} + 102231156093 T^{10} + 709122216452 T^{11} + 4821630526990 T^{12} + 26444222693006 T^{13} + 138802937102491 T^{14} + 480097724653975 T^{15} + 1517108809906561 T^{16} )^{2} \))(\( ( 1 - 15 T + 559 T^{2} - 6710 T^{3} + 137950 T^{4} - 1366644 T^{5} + 20137433 T^{6} - 166220285 T^{7} + 1933129586 T^{8} - 13131402515 T^{9} + 125677719353 T^{10} - 673808791116 T^{11} + 5373163673950 T^{12} - 20647048437290 T^{13} + 135885887636239 T^{14} - 288058634792385 T^{15} + 1517108809906561 T^{16} )^{2} \))
$83$ (\( 1 + 3 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 163 T^{2} + 6889 T^{4} \))(\( 1 + 9 T + 175 T^{2} + 747 T^{3} + 6889 T^{4} \))(\( 1 - 15 T + 250 T^{2} - 1848 T^{3} + 22837 T^{4} - 146349 T^{5} + 1895471 T^{6} - 12730872 T^{7} + 142946750 T^{8} - 711874815 T^{9} + 3939040643 T^{10} \))(\( 1 - 44 T + 1113 T^{2} - 20987 T^{3} + 324266 T^{4} - 4227976 T^{5} + 47361143 T^{6} - 461372423 T^{7} + 3930974869 T^{8} - 29126526664 T^{9} + 185411083342 T^{10} - 996007782827 T^{11} + 4384152235659 T^{12} - 14385376428236 T^{13} + 27136050989627 T^{14} \))(\( 1 + 28 T + 504 T^{2} + 7273 T^{3} + 99833 T^{4} + 1227119 T^{5} + 13816785 T^{6} + 138049897 T^{7} + 1299861514 T^{8} + 11458141451 T^{9} + 95183831865 T^{10} + 701650691653 T^{11} + 4737906560393 T^{12} + 28648642596539 T^{13} + 164777948177976 T^{14} + 759809427709556 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 25 T + 573 T^{2} + 9002 T^{3} + 134789 T^{4} + 1650666 T^{5} + 19348375 T^{6} + 195648613 T^{7} + 1902337721 T^{8} + 16238834879 T^{9} + 133290955375 T^{10} + 943829360142 T^{11} + 6396859629269 T^{12} + 35459243868286 T^{13} + 187336833940437 T^{14} + 678401274740675 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 13 T + 727 T^{2} + 8394 T^{3} + 251691 T^{4} + 2586526 T^{5} + 54790998 T^{6} + 499552992 T^{7} + 8324254426 T^{8} + 66885861345 T^{9} + 925683440764 T^{10} + 6483706847714 T^{11} + 76831725583412 T^{12} + 460776698805705 T^{13} + 4759700465479262 T^{14} + 23707946250846432 T^{15} + 215823967992531714 T^{16} + 845639776168626094 T^{17} + 6829899809630209257 T^{18} + 18905740996575110154 T^{19} + \)\(13\!\cdots\!81\)\( T^{20} + \)\(20\!\cdots\!37\)\( T^{21} + \)\(12\!\cdots\!67\)\( T^{22} \))(\( 1 - 3 T + 645 T^{2} - 2160 T^{3} + 202527 T^{4} - 707980 T^{5} + 40949704 T^{6} - 141398056 T^{7} + 5922872882 T^{8} - 19244924901 T^{9} + 642709856398 T^{10} - 1874720208494 T^{11} + 53344918081034 T^{12} - 132578287642989 T^{13} + 3386621716580134 T^{14} - 6710514330423976 T^{15} + 161302548374819672 T^{16} - 231467245537784620 T^{17} + 5495782998776187429 T^{18} - 4864951221420328560 T^{19} + \)\(12\!\cdots\!35\)\( T^{20} - 46548123561617560347 T^{21} + \)\(12\!\cdots\!67\)\( T^{22} \))(\( 1 + 567 T^{2} + 178091 T^{4} + 38633928 T^{6} + 6444658291 T^{8} + 872518825706 T^{10} + 99862021188253 T^{12} + 9923838133725723 T^{14} + 873057976545549799 T^{16} + 68365320903236505747 T^{18} + \)\(47\!\cdots\!13\)\( T^{20} + \)\(28\!\cdots\!14\)\( T^{22} + \)\(14\!\cdots\!31\)\( T^{24} + \)\(59\!\cdots\!72\)\( T^{26} + \)\(19\!\cdots\!51\)\( T^{28} + \)\(41\!\cdots\!43\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 + 761 T^{2} + 285839 T^{4} + 70977052 T^{6} + 13168713639 T^{8} + 1952091601664 T^{10} + 240379111111531 T^{12} + 25116679433447025 T^{14} + 2248911383834364457 T^{16} + \)\(17\!\cdots\!25\)\( T^{18} + \)\(11\!\cdots\!51\)\( T^{20} + \)\(63\!\cdots\!16\)\( T^{22} + \)\(29\!\cdots\!99\)\( T^{24} + \)\(11\!\cdots\!48\)\( T^{26} + \)\(30\!\cdots\!79\)\( T^{28} + \)\(56\!\cdots\!69\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))
$89$ (\( 1 - 12 T + 89 T^{2} \))(\( 1 - 9 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 - 9 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 - 14 T^{2} + 7921 T^{4} \))(\( 1 + 173 T^{2} + 7921 T^{4} \))(\( 1 - 25 T + 489 T^{2} - 6623 T^{3} + 80278 T^{4} - 793644 T^{5} + 7144742 T^{6} - 52460783 T^{7} + 344729841 T^{8} - 1568556025 T^{9} + 5584059449 T^{10} \))(\( 1 + 281 T^{2} + 803 T^{3} + 38846 T^{4} + 142510 T^{5} + 4407403 T^{6} + 12547239 T^{7} + 392258867 T^{8} + 1128821710 T^{9} + 27385225774 T^{10} + 50382019523 T^{11} + 1569120705169 T^{12} + 44231334895529 T^{14} \))(\( 1 - 9 T + 494 T^{2} - 4382 T^{3} + 120896 T^{4} - 984537 T^{5} + 18842103 T^{6} - 133392394 T^{7} + 2010163131 T^{8} - 11871923066 T^{9} + 149248297863 T^{10} - 694068064353 T^{11} + 7585285967936 T^{12} - 24469348505518 T^{13} + 245508757734734 T^{14} - 398082014059761 T^{15} + 3936588805702081 T^{16} \))(\( 1 - 23 T + 637 T^{2} - 10127 T^{3} + 171614 T^{4} - 2116722 T^{5} + 27197943 T^{6} - 275440868 T^{7} + 2897150346 T^{8} - 24514237252 T^{9} + 215434906503 T^{10} - 1492223391618 T^{11} + 10767446946974 T^{12} - 56549770040023 T^{13} + 316577082342157 T^{14} - 1017320702597167 T^{15} + 3936588805702081 T^{16} \))(\( 1 + 53 T + 1774 T^{2} + 42300 T^{3} + 824792 T^{4} + 13580878 T^{5} + 198984697 T^{6} + 2624179670 T^{7} + 31939405010 T^{8} + 358681454413 T^{9} + 3763131300342 T^{10} + 36685055849660 T^{11} + 334918685730438 T^{12} + 2841115800405373 T^{13} + 22516290410494690 T^{14} + 164646913282440470 T^{15} + 1111142377489251953 T^{16} + 6749442280823843758 T^{17} + 36481651171153154968 T^{18} + \)\(16\!\cdots\!00\)\( T^{19} + \)\(62\!\cdots\!66\)\( T^{20} + \)\(16\!\cdots\!53\)\( T^{21} + \)\(27\!\cdots\!89\)\( T^{22} \))(\( 1 + 19 T + 960 T^{2} + 14792 T^{3} + 412674 T^{4} + 5321628 T^{5} + 106399657 T^{6} + 1168153742 T^{7} + 18435766786 T^{8} + 173533597985 T^{9} + 2264179760970 T^{10} + 18242282205172 T^{11} + 201511998726330 T^{12} + 1374559629639185 T^{13} + 12996644075359634 T^{14} + 73292583605615822 T^{15} + 594142010041208993 T^{16} + 2644749553454204508 T^{17} + 18253121896677534546 T^{18} + 58230021613945182152 T^{19} + \)\(33\!\cdots\!40\)\( T^{20} + \)\(59\!\cdots\!19\)\( T^{21} + \)\(27\!\cdots\!89\)\( T^{22} \))(\( 1 + 569 T^{2} + 169363 T^{4} + 35825223 T^{6} + 6036555352 T^{8} + 852913669656 T^{10} + 104008876677755 T^{12} + 11130500668467816 T^{14} + 1052817161526366418 T^{16} + 88164695794933570536 T^{18} + \)\(65\!\cdots\!55\)\( T^{20} + \)\(42\!\cdots\!16\)\( T^{22} + \)\(23\!\cdots\!12\)\( T^{24} + \)\(11\!\cdots\!23\)\( T^{26} + \)\(41\!\cdots\!23\)\( T^{28} + \)\(11\!\cdots\!29\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 + 997 T^{2} + 487271 T^{4} + 155015155 T^{6} + 35962752808 T^{8} + 6459151607228 T^{10} + 930182074542431 T^{12} + 109675892833483148 T^{14} + 10707824476386441346 T^{16} + \)\(86\!\cdots\!08\)\( T^{18} + \)\(58\!\cdots\!71\)\( T^{20} + \)\(32\!\cdots\!08\)\( T^{22} + \)\(14\!\cdots\!48\)\( T^{24} + \)\(48\!\cdots\!55\)\( T^{26} + \)\(12\!\cdots\!91\)\( T^{28} + \)\(19\!\cdots\!77\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))
$97$ (\( 1 + 6 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( 1 + 19 T + 253 T^{2} + 1843 T^{3} + 9409 T^{4} \))(\( 1 + 12 T + 189 T^{2} + 1680 T^{3} + 12562 T^{4} + 113928 T^{5} + 1218514 T^{6} + 15807120 T^{7} + 172495197 T^{8} + 1062351372 T^{9} + 8587340257 T^{10} \))(\( 1 - 32 T + 985 T^{2} - 19467 T^{3} + 345002 T^{4} - 4837170 T^{5} + 60439928 T^{6} - 630492262 T^{7} + 5862673016 T^{8} - 45512932530 T^{9} + 314874010346 T^{10} - 1723399513227 T^{11} + 8458530153145 T^{12} - 26655104157728 T^{13} + 80798284478113 T^{14} \))(\( 1 + 14 T + 586 T^{2} + 6005 T^{3} + 148509 T^{4} + 1173735 T^{5} + 22820670 T^{6} + 147635470 T^{7} + 2523582628 T^{8} + 14320640590 T^{9} + 214719684030 T^{10} + 1071236243655 T^{11} + 13147394992029 T^{12} + 51566978243285 T^{13} + 488121594888394 T^{14} + 1131175982693582 T^{15} + 7837433594376961 T^{16} \))(\( 1 + 11 T + 541 T^{2} + 3845 T^{3} + 127598 T^{4} + 634135 T^{5} + 19241763 T^{6} + 73630137 T^{7} + 2136662818 T^{8} + 7142123289 T^{9} + 181045748067 T^{10} + 578757892855 T^{11} + 11296159197038 T^{12} + 33018323288165 T^{13} + 450637854666589 T^{14} + 888781129259243 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 27 T + 1058 T^{2} - 21360 T^{3} + 484854 T^{4} - 7856527 T^{5} + 131973169 T^{6} - 1783597584 T^{7} + 24218505542 T^{8} - 278885307030 T^{9} + 3188071731280 T^{10} - 31562730811392 T^{11} + 309242957934160 T^{12} - 2624031853845270 T^{13} + 22103576108533766 T^{14} - 157900611704857104 T^{15} + 1133298506997564433 T^{16} - 6544267046968821583 T^{17} + 39175371422351000502 T^{18} - \)\(16\!\cdots\!60\)\( T^{19} + \)\(80\!\cdots\!86\)\( T^{20} - \)\(19\!\cdots\!23\)\( T^{21} + \)\(71\!\cdots\!53\)\( T^{22} \))(\( 1 - 11 T + 656 T^{2} - 8452 T^{3} + 230104 T^{4} - 2900063 T^{5} + 55014325 T^{6} - 623749952 T^{7} + 9474454562 T^{8} - 95215603350 T^{9} + 1211228350432 T^{10} - 10720272095480 T^{11} + 117489149991904 T^{12} - 895883611920150 T^{13} + 8647078868464226 T^{14} - 55220134774344512 T^{15} + 472426727784181525 T^{16} - 2415671291530410527 T^{17} + 18592008451551713752 T^{18} - 66241988739674074372 T^{19} + \)\(49\!\cdots\!52\)\( T^{20} - \)\(81\!\cdots\!39\)\( T^{21} + \)\(71\!\cdots\!53\)\( T^{22} \))(\( ( 1 + T + 293 T^{2} + 709 T^{3} + 44202 T^{4} + 151047 T^{5} + 5952907 T^{6} + 17464307 T^{7} + 680888938 T^{8} + 1694037779 T^{9} + 56010901963 T^{10} + 137856518631 T^{11} + 3913171278762 T^{12} + 6088424242213 T^{13} + 244060797444197 T^{14} + 80798284478113 T^{15} + 7837433594376961 T^{16} )^{2} \))(\( ( 1 - 19 T + 475 T^{2} - 5959 T^{3} + 95634 T^{4} - 949437 T^{5} + 12629829 T^{6} - 110114201 T^{7} + 1339442842 T^{8} - 10681077497 T^{9} + 118834061061 T^{10} - 866525515101 T^{11} + 8466409259154 T^{12} - 51171960591463 T^{13} + 395661702341275 T^{14} - 1535167405084147 T^{15} + 7837433594376961 T^{16} )^{2} \))
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