Properties

Label 9036.2.a
Level 9036
Weight 2
Character orbit a
Rep. character \(\chi_{9036}(1,\cdot)\)
Character field \(\Q\)
Dimension 103
Newform subspaces 15
Sturm bound 3024
Trace bound 17

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Defining parameters

Level: \( N \) \(=\) \( 9036 = 2^{2} \cdot 3^{2} \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9036.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(3024\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9036))\).

Total New Old
Modular forms 1524 103 1421
Cusp forms 1501 103 1398
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.

\(2\)\(3\)\(251\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(20\)
\(-\)\(+\)\(-\)\(+\)\(20\)
\(-\)\(-\)\(+\)\(+\)\(28\)
\(-\)\(-\)\(-\)\(-\)\(35\)
Plus space\(+\)\(48\)
Minus space\(-\)\(55\)

Trace form

\( 103q + 2q^{7} + O(q^{10}) \) \( 103q + 2q^{7} - 4q^{11} - 6q^{13} - 4q^{19} - 4q^{23} + 103q^{25} - 12q^{31} + 2q^{35} + 2q^{37} - 4q^{41} - 12q^{43} + 73q^{49} - 6q^{53} - 6q^{55} - 10q^{59} - 38q^{61} - 15q^{65} + 10q^{67} + 4q^{71} + 18q^{73} - 24q^{77} + 10q^{79} + 23q^{83} + 2q^{85} - 12q^{89} + 4q^{91} - 12q^{95} - 40q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9036))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 251
9036.2.a.a \(1\) \(72.153\) \(\Q\) None \(0\) \(0\) \(-3\) \(-3\) \(-\) \(-\) \(-\) \(q-3q^{5}-3q^{7}-6q^{13}+7q^{17}-6q^{19}+\cdots\)
9036.2.a.b \(1\) \(72.153\) \(\Q\) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(+\) \(q-2q^{5}+2q^{7}+2q^{11}-q^{13}-5q^{19}+\cdots\)
9036.2.a.c \(1\) \(72.153\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q-4q^{7}-q^{13}-6q^{17}+5q^{19}+9q^{23}+\cdots\)
9036.2.a.d \(1\) \(72.153\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q-4q^{7}-q^{13}+6q^{17}+5q^{19}-9q^{23}+\cdots\)
9036.2.a.e \(1\) \(72.153\) \(\Q\) None \(0\) \(0\) \(1\) \(5\) \(-\) \(-\) \(-\) \(q+q^{5}+5q^{7}+6q^{11}-2q^{13}+3q^{17}+\cdots\)
9036.2.a.f \(1\) \(72.153\) \(\Q\) None \(0\) \(0\) \(2\) \(2\) \(-\) \(-\) \(+\) \(q+2q^{5}+2q^{7}-6q^{11}+7q^{13}-8q^{17}+\cdots\)
9036.2.a.g \(1\) \(72.153\) \(\Q\) None \(0\) \(0\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q+3q^{5}+q^{7}+2q^{11}+2q^{13}+5q^{17}+\cdots\)
9036.2.a.h \(6\) \(72.153\) 6.6.4443861.1 None \(0\) \(0\) \(4\) \(-3\) \(-\) \(-\) \(-\) \(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
9036.2.a.i \(7\) \(72.153\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(2\) \(-6\) \(-\) \(-\) \(+\) \(q-\beta _{5}q^{5}+(-1-\beta _{6})q^{7}+(1-\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots\)
9036.2.a.j \(9\) \(72.153\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{5}q^{5}-\beta _{7}q^{7}+(-1-\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)
9036.2.a.k \(10\) \(72.153\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-5\) \(-4\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+\beta _{2}q^{11}+\cdots\)
9036.2.a.l \(12\) \(72.153\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-7\) \(0\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{5}+\beta _{6}q^{7}+(1+\beta _{4}-\beta _{6}+\cdots)q^{11}+\cdots\)
9036.2.a.m \(14\) \(72.153\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(2\) \(8\) \(-\) \(-\) \(-\) \(q-\beta _{4}q^{5}+(1-\beta _{9})q^{7}+(-1+\beta _{8})q^{11}+\cdots\)
9036.2.a.n \(19\) \(72.153\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{5}+\beta _{10}q^{7}+(-1+\beta _{4})q^{11}+\cdots\)
9036.2.a.o \(19\) \(72.153\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{5}+\beta _{10}q^{7}+(1-\beta _{4})q^{11}+\beta _{8}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9036))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9036)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(502))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(753))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1004))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1506))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2259))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3012))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4518))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( 1 + 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 4 T + 24 T^{2} - 72 T^{3} + 256 T^{4} - 592 T^{5} + 1613 T^{6} - 2960 T^{7} + 6400 T^{8} - 9000 T^{9} + 15000 T^{10} - 12500 T^{11} + 15625 T^{12} \))(\( 1 - 2 T + 24 T^{2} - 35 T^{3} + 276 T^{4} - 331 T^{5} + 2035 T^{6} - 2033 T^{7} + 10175 T^{8} - 8275 T^{9} + 34500 T^{10} - 21875 T^{11} + 75000 T^{12} - 31250 T^{13} + 78125 T^{14} \))(\( 1 - 3 T + 28 T^{2} - 85 T^{3} + 410 T^{4} - 1139 T^{5} + 3984 T^{6} - 9633 T^{7} + 27502 T^{8} - 56851 T^{9} + 137510 T^{10} - 240825 T^{11} + 498000 T^{12} - 711875 T^{13} + 1281250 T^{14} - 1328125 T^{15} + 2187500 T^{16} - 1171875 T^{17} + 1953125 T^{18} \))(\( 1 + 5 T + 25 T^{2} + 82 T^{3} + 262 T^{4} + 726 T^{5} + 1970 T^{6} + 4906 T^{7} + 11590 T^{8} + 26690 T^{9} + 58650 T^{10} + 133450 T^{11} + 289750 T^{12} + 613250 T^{13} + 1231250 T^{14} + 2268750 T^{15} + 4093750 T^{16} + 6406250 T^{17} + 9765625 T^{18} + 9765625 T^{19} + 9765625 T^{20} \))(\( 1 + 7 T + 45 T^{2} + 206 T^{3} + 891 T^{4} + 3287 T^{5} + 11407 T^{6} + 35784 T^{7} + 106032 T^{8} + 290916 T^{9} + 756166 T^{10} + 1839384 T^{11} + 4246100 T^{12} + 9196920 T^{13} + 18904150 T^{14} + 36364500 T^{15} + 66270000 T^{16} + 111825000 T^{17} + 178234375 T^{18} + 256796875 T^{19} + 348046875 T^{20} + 402343750 T^{21} + 439453125 T^{22} + 341796875 T^{23} + 244140625 T^{24} \))(\( 1 - 2 T + 24 T^{2} - 59 T^{3} + 320 T^{4} - 863 T^{5} + 3339 T^{6} - 8624 T^{7} + 28921 T^{8} - 68243 T^{9} + 207217 T^{10} - 458259 T^{11} + 1263673 T^{12} - 2658519 T^{13} + 6736137 T^{14} - 13292595 T^{15} + 31591825 T^{16} - 57282375 T^{17} + 129510625 T^{18} - 213259375 T^{19} + 451890625 T^{20} - 673750000 T^{21} + 1304296875 T^{22} - 1685546875 T^{23} + 3125000000 T^{24} - 2880859375 T^{25} + 5859375000 T^{26} - 2441406250 T^{27} + 6103515625 T^{28} \))(\( 1 + 34 T^{2} + 12 T^{3} + 613 T^{4} + 312 T^{5} + 7849 T^{6} + 4544 T^{7} + 79829 T^{8} + 49576 T^{9} + 687311 T^{10} + 450472 T^{11} + 5183313 T^{12} + 3542716 T^{13} + 34829697 T^{14} + 24231792 T^{15} + 210704093 T^{16} + 145027276 T^{17} + 1155914723 T^{18} + 768650796 T^{19} + 5779573615 T^{20} + 3625681900 T^{21} + 26338011625 T^{22} + 15144870000 T^{23} + 108842803125 T^{24} + 55354937500 T^{25} + 404946328125 T^{26} + 175965625000 T^{27} + 1342404296875 T^{28} + 484140625000 T^{29} + 3897900390625 T^{30} + 1109375000000 T^{31} + 9581298828125 T^{32} + 1904296875000 T^{33} + 18707275390625 T^{34} + 1831054687500 T^{35} + 25939941406250 T^{36} + 19073486328125 T^{38} \))(\( 1 + 34 T^{2} - 12 T^{3} + 613 T^{4} - 312 T^{5} + 7849 T^{6} - 4544 T^{7} + 79829 T^{8} - 49576 T^{9} + 687311 T^{10} - 450472 T^{11} + 5183313 T^{12} - 3542716 T^{13} + 34829697 T^{14} - 24231792 T^{15} + 210704093 T^{16} - 145027276 T^{17} + 1155914723 T^{18} - 768650796 T^{19} + 5779573615 T^{20} - 3625681900 T^{21} + 26338011625 T^{22} - 15144870000 T^{23} + 108842803125 T^{24} - 55354937500 T^{25} + 404946328125 T^{26} - 175965625000 T^{27} + 1342404296875 T^{28} - 484140625000 T^{29} + 3897900390625 T^{30} - 1109375000000 T^{31} + 9581298828125 T^{32} - 1904296875000 T^{33} + 18707275390625 T^{34} - 1831054687500 T^{35} + 25939941406250 T^{36} + 19073486328125 T^{38} \))
$7$ (\( 1 + 3 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 + 3 T + 35 T^{2} + 77 T^{3} + 519 T^{4} + 881 T^{5} + 4523 T^{6} + 6167 T^{7} + 25431 T^{8} + 26411 T^{9} + 84035 T^{10} + 50421 T^{11} + 117649 T^{12} \))(\( 1 + 6 T + 49 T^{2} + 217 T^{3} + 1012 T^{4} + 3486 T^{5} + 11665 T^{6} + 31629 T^{7} + 81655 T^{8} + 170814 T^{9} + 347116 T^{10} + 521017 T^{11} + 823543 T^{12} + 705894 T^{13} + 823543 T^{14} \))(\( 1 + 34 T^{2} + T^{3} + 547 T^{4} + 24 T^{5} + 5731 T^{6} + 197 T^{7} + 46577 T^{8} + 1163 T^{9} + 326039 T^{10} + 9653 T^{11} + 1965733 T^{12} + 57624 T^{13} + 9193429 T^{14} + 117649 T^{15} + 28000462 T^{16} + 40353607 T^{18} \))(\( 1 + 4 T + 29 T^{2} + 105 T^{3} + 533 T^{4} + 1663 T^{5} + 6684 T^{6} + 18777 T^{7} + 65342 T^{8} + 164302 T^{9} + 505486 T^{10} + 1150114 T^{11} + 3201758 T^{12} + 6440511 T^{13} + 16048284 T^{14} + 27950041 T^{15} + 62706917 T^{16} + 86472015 T^{17} + 167179229 T^{18} + 161414428 T^{19} + 282475249 T^{20} \))(\( 1 + 31 T^{2} - 23 T^{3} + 568 T^{4} - 531 T^{5} + 7755 T^{6} - 8068 T^{7} + 83695 T^{8} - 88185 T^{9} + 756850 T^{10} - 766081 T^{11} + 5735960 T^{12} - 5362567 T^{13} + 37085650 T^{14} - 30247455 T^{15} + 200951695 T^{16} - 135598876 T^{17} + 912367995 T^{18} - 437301333 T^{19} + 3274406968 T^{20} - 928132961 T^{21} + 8756732719 T^{22} + 13841287201 T^{24} \))(\( 1 - 8 T + 63 T^{2} - 299 T^{3} + 1414 T^{4} - 4980 T^{5} + 18363 T^{6} - 54402 T^{7} + 178145 T^{8} - 485063 T^{9} + 1521945 T^{10} - 4020493 T^{11} + 12333269 T^{12} - 31560379 T^{13} + 91881835 T^{14} - 220922653 T^{15} + 604330181 T^{16} - 1379029099 T^{17} + 3654189945 T^{18} - 8152453841 T^{19} + 20958581105 T^{20} - 44802386286 T^{21} + 105859040763 T^{22} - 200960962860 T^{23} + 399420002086 T^{24} - 591220696157 T^{25} + 872001093663 T^{26} - 775112083256 T^{27} + 678223072849 T^{28} \))(\( 1 - 4 T + 75 T^{2} - 278 T^{3} + 2810 T^{4} - 9622 T^{5} + 70125 T^{6} - 222440 T^{7} + 1312592 T^{8} - 3876804 T^{9} + 19657079 T^{10} - 54319606 T^{11} + 244837469 T^{12} - 634988872 T^{13} + 2597675766 T^{14} - 6330707748 T^{15} + 23823830986 T^{16} - 54534114122 T^{17} + 190499882582 T^{18} - 408768963436 T^{19} + 1333499178074 T^{20} - 2672171591978 T^{21} + 8171574028198 T^{22} - 15200029302948 T^{23} + 43659136599162 T^{24} - 74705805801928 T^{25} + 201634183732667 T^{26} - 313141718988406 T^{27} + 793234040733953 T^{28} - 1095101175224196 T^{29} + 2595423264247856 T^{30} - 3078855924990440 T^{31} + 6794341854790875 T^{32} - 6525862406953078 T^{33} + 13340647842939830 T^{34} - 9238754698349078 T^{35} + 17447288549040525 T^{36} - 6513654391641796 T^{37} + 11398895185373143 T^{38} \))(\( 1 - 4 T + 75 T^{2} - 278 T^{3} + 2810 T^{4} - 9622 T^{5} + 70125 T^{6} - 222440 T^{7} + 1312592 T^{8} - 3876804 T^{9} + 19657079 T^{10} - 54319606 T^{11} + 244837469 T^{12} - 634988872 T^{13} + 2597675766 T^{14} - 6330707748 T^{15} + 23823830986 T^{16} - 54534114122 T^{17} + 190499882582 T^{18} - 408768963436 T^{19} + 1333499178074 T^{20} - 2672171591978 T^{21} + 8171574028198 T^{22} - 15200029302948 T^{23} + 43659136599162 T^{24} - 74705805801928 T^{25} + 201634183732667 T^{26} - 313141718988406 T^{27} + 793234040733953 T^{28} - 1095101175224196 T^{29} + 2595423264247856 T^{30} - 3078855924990440 T^{31} + 6794341854790875 T^{32} - 6525862406953078 T^{33} + 13340647842939830 T^{34} - 9238754698349078 T^{35} + 17447288549040525 T^{36} - 6513654391641796 T^{37} + 11398895185373143 T^{38} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 5 T + 36 T^{2} - 104 T^{3} + 405 T^{4} - 568 T^{5} + 2873 T^{6} - 6248 T^{7} + 49005 T^{8} - 138424 T^{9} + 527076 T^{10} - 805255 T^{11} + 1771561 T^{12} \))(\( 1 - 5 T + 57 T^{2} - 246 T^{3} + 1548 T^{4} - 5621 T^{5} + 25904 T^{6} - 77368 T^{7} + 284944 T^{8} - 680141 T^{9} + 2060388 T^{10} - 3601686 T^{11} + 9179907 T^{12} - 8857805 T^{13} + 19487171 T^{14} \))(\( 1 + 5 T + 79 T^{2} + 289 T^{3} + 2680 T^{4} + 7539 T^{5} + 54443 T^{6} + 123131 T^{7} + 778449 T^{8} + 1507064 T^{9} + 8562939 T^{10} + 14898851 T^{11} + 72463633 T^{12} + 110378499 T^{13} + 431616680 T^{14} + 511981129 T^{15} + 1539486509 T^{16} + 1071794405 T^{17} + 2357947691 T^{18} \))(\( 1 + 5 T + 66 T^{2} + 302 T^{3} + 2201 T^{4} + 8642 T^{5} + 46803 T^{6} + 160758 T^{7} + 720038 T^{8} + 2213949 T^{9} + 8768246 T^{10} + 24353439 T^{11} + 87124598 T^{12} + 213968898 T^{13} + 685242723 T^{14} + 1391802742 T^{15} + 3899205761 T^{16} + 5885125642 T^{17} + 14147686146 T^{18} + 11789738455 T^{19} + 25937424601 T^{20} \))(\( 1 - T + 42 T^{2} - 36 T^{3} + 1216 T^{4} - 855 T^{5} + 24155 T^{6} - 13160 T^{7} + 397737 T^{8} - 163959 T^{9} + 5331891 T^{10} - 1772391 T^{11} + 63489516 T^{12} - 19496301 T^{13} + 645158811 T^{14} - 218229429 T^{15} + 5823267417 T^{16} - 2119431160 T^{17} + 42792055955 T^{18} - 16661531205 T^{19} + 260660399296 T^{20} - 84886116876 T^{21} + 1089371833242 T^{22} - 285311670611 T^{23} + 3138428376721 T^{24} \))(\( 1 + 9 T + 100 T^{2} + 687 T^{3} + 4884 T^{4} + 27546 T^{5} + 155686 T^{6} + 756862 T^{7} + 3649790 T^{8} + 15719595 T^{9} + 66852900 T^{10} + 258836085 T^{11} + 987952117 T^{12} + 3464423852 T^{13} + 11971213668 T^{14} + 38108662372 T^{15} + 119542206157 T^{16} + 344510829135 T^{17} + 978793308900 T^{18} + 2531656494345 T^{19} + 6465825622190 T^{20} + 14749099217402 T^{21} + 33372676747366 T^{22} + 64952027096286 T^{23} + 126678381751284 T^{24} + 196009117709757 T^{25} + 313842837672100 T^{26} + 310704409295379 T^{27} + 379749833583241 T^{28} \))(\( 1 + 14 T + 192 T^{2} + 1734 T^{3} + 14810 T^{4} + 103518 T^{5} + 687064 T^{6} + 4022502 T^{7} + 22523845 T^{8} + 115320604 T^{9} + 568218473 T^{10} + 2612275242 T^{11} + 11612964824 T^{12} + 48764054982 T^{13} + 198681748130 T^{14} + 770418018014 T^{15} + 2905001183624 T^{16} + 10470381352242 T^{17} + 36740297698157 T^{18} + 123474456470168 T^{19} + 404143274679727 T^{20} + 1266916143621282 T^{21} + 3866556575403544 T^{22} + 11279690201742974 T^{23} + 31997894218084630 T^{24} + 86388498007966902 T^{25} + 226303831342272904 T^{26} + 559964397739124202 T^{27} + 1339829436393895843 T^{28} + 2991119471191779004 T^{29} + 6426315845533219295 T^{30} + 12624334422216975942 T^{31} + 23719312696457808584 T^{32} + 39310943272869941838 T^{33} + 61865045389045791310 T^{34} + 79676831583434127174 T^{35} + 97045829471864404032 T^{36} + 77838842388891240734 T^{37} + 61159090448414546291 T^{38} \))(\( 1 - 14 T + 192 T^{2} - 1734 T^{3} + 14810 T^{4} - 103518 T^{5} + 687064 T^{6} - 4022502 T^{7} + 22523845 T^{8} - 115320604 T^{9} + 568218473 T^{10} - 2612275242 T^{11} + 11612964824 T^{12} - 48764054982 T^{13} + 198681748130 T^{14} - 770418018014 T^{15} + 2905001183624 T^{16} - 10470381352242 T^{17} + 36740297698157 T^{18} - 123474456470168 T^{19} + 404143274679727 T^{20} - 1266916143621282 T^{21} + 3866556575403544 T^{22} - 11279690201742974 T^{23} + 31997894218084630 T^{24} - 86388498007966902 T^{25} + 226303831342272904 T^{26} - 559964397739124202 T^{27} + 1339829436393895843 T^{28} - 2991119471191779004 T^{29} + 6426315845533219295 T^{30} - 12624334422216975942 T^{31} + 23719312696457808584 T^{32} - 39310943272869941838 T^{33} + 61865045389045791310 T^{34} - 79676831583434127174 T^{35} + 97045829471864404032 T^{36} - 77838842388891240734 T^{37} + 61159090448414546291 T^{38} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 7 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 9 T + 64 T^{2} + 356 T^{3} + 1742 T^{4} + 7647 T^{5} + 29193 T^{6} + 99411 T^{7} + 294398 T^{8} + 782132 T^{9} + 1827904 T^{10} + 3341637 T^{11} + 4826809 T^{12} \))(\( 1 + T + 49 T^{2} + 10 T^{3} + 1145 T^{4} - 534 T^{5} + 18318 T^{6} - 12855 T^{7} + 238134 T^{8} - 90246 T^{9} + 2515565 T^{10} + 285610 T^{11} + 18193357 T^{12} + 4826809 T^{13} + 62748517 T^{14} \))(\( 1 + 11 T + 145 T^{2} + 1059 T^{3} + 8145 T^{4} + 44976 T^{5} + 253176 T^{6} + 1116147 T^{7} + 4964037 T^{8} + 17842150 T^{9} + 64532481 T^{10} + 188628843 T^{11} + 556227672 T^{12} + 1284559536 T^{13} + 3024181485 T^{14} + 5111590731 T^{15} + 9098534965 T^{16} + 8973037931 T^{17} + 10604499373 T^{18} \))(\( 1 - 7 T + 92 T^{2} - 512 T^{3} + 3872 T^{4} - 18447 T^{5} + 103461 T^{6} - 434969 T^{7} + 1992019 T^{8} - 7451501 T^{9} + 29326630 T^{10} - 96869513 T^{11} + 336651211 T^{12} - 955626893 T^{13} + 2954949621 T^{14} - 6849241971 T^{15} + 18689404448 T^{16} - 32127240704 T^{17} + 75047226332 T^{18} - 74231495611 T^{19} + 137858491849 T^{20} \))(\( 1 - 17 T + 201 T^{2} - 1643 T^{3} + 11207 T^{4} - 63010 T^{5} + 320587 T^{6} - 1461260 T^{7} + 6403806 T^{8} - 26383063 T^{9} + 106951324 T^{10} - 408974279 T^{11} + 1524225908 T^{12} - 5316665627 T^{13} + 18074773756 T^{14} - 57963589411 T^{15} + 182899103166 T^{16} - 542555609180 T^{17} + 1547412216883 T^{18} - 3953784056170 T^{19} + 9141894190247 T^{20} - 17423192469839 T^{21} + 27709556861649 T^{22} - 30466726698629 T^{23} + 23298085122481 T^{24} \))(\( 1 + T + 77 T^{2} + 118 T^{3} + 3157 T^{4} + 5386 T^{5} + 92690 T^{6} + 150851 T^{7} + 2123696 T^{8} + 3170308 T^{9} + 39751641 T^{10} + 54234088 T^{11} + 633863833 T^{12} + 790255061 T^{13} + 8807951688 T^{14} + 10273315793 T^{15} + 107122987777 T^{16} + 119152291336 T^{17} + 1135346618601 T^{18} + 1177113168244 T^{19} + 10250674966064 T^{20} + 9465676537967 T^{21} + 75610080529490 T^{22} + 57115833622978 T^{23} + 435219258767293 T^{24} + 211474926496366 T^{25} + 1793952554431037 T^{26} + 302875106592253 T^{27} + 3937376385699289 T^{28} \))(\( 1 + 3 T + 118 T^{2} + 337 T^{3} + 6928 T^{4} + 19401 T^{5} + 274488 T^{6} + 765011 T^{7} + 8326468 T^{8} + 23166037 T^{9} + 206465831 T^{10} + 571728858 T^{11} + 4346355136 T^{12} + 11910181682 T^{13} + 79591200605 T^{14} + 214026005819 T^{15} + 1289056095790 T^{16} + 3362347031397 T^{17} + 18658780844975 T^{18} + 46521518540510 T^{19} + 242564150984675 T^{20} + 568236648306093 T^{21} + 2832056242450630 T^{22} + 6112796752196459 T^{23} + 29551655646232265 T^{24} + 57488172134312738 T^{25} + 272727339139333312 T^{26} + 466376793552846618 T^{27} + 2189466775385423963 T^{28} + 3193634922938132413 T^{29} + 14922366171816471316 T^{30} + 17823291397634312291 T^{31} + 83135582258294341464 T^{32} + 76389039258951905889 T^{33} + \)\(35\!\cdots\!96\)\( T^{34} + \)\(22\!\cdots\!17\)\( T^{35} + \)\(10\!\cdots\!94\)\( T^{36} + \)\(33\!\cdots\!87\)\( T^{37} + \)\(14\!\cdots\!77\)\( T^{38} \))(\( 1 + 3 T + 118 T^{2} + 337 T^{3} + 6928 T^{4} + 19401 T^{5} + 274488 T^{6} + 765011 T^{7} + 8326468 T^{8} + 23166037 T^{9} + 206465831 T^{10} + 571728858 T^{11} + 4346355136 T^{12} + 11910181682 T^{13} + 79591200605 T^{14} + 214026005819 T^{15} + 1289056095790 T^{16} + 3362347031397 T^{17} + 18658780844975 T^{18} + 46521518540510 T^{19} + 242564150984675 T^{20} + 568236648306093 T^{21} + 2832056242450630 T^{22} + 6112796752196459 T^{23} + 29551655646232265 T^{24} + 57488172134312738 T^{25} + 272727339139333312 T^{26} + 466376793552846618 T^{27} + 2189466775385423963 T^{28} + 3193634922938132413 T^{29} + 14922366171816471316 T^{30} + 17823291397634312291 T^{31} + 83135582258294341464 T^{32} + 76389039258951905889 T^{33} + \)\(35\!\cdots\!96\)\( T^{34} + \)\(22\!\cdots\!17\)\( T^{35} + \)\(10\!\cdots\!94\)\( T^{36} + \)\(33\!\cdots\!87\)\( T^{37} + \)\(14\!\cdots\!77\)\( T^{38} \))
$17$ (\( 1 - 7 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 5 T + 17 T^{2} \))(\( 1 - 6 T + 53 T^{2} - 230 T^{3} + 1161 T^{4} - 4518 T^{5} + 18899 T^{6} - 76806 T^{7} + 335529 T^{8} - 1129990 T^{9} + 4426613 T^{10} - 8519142 T^{11} + 24137569 T^{12} \))(\( 1 - 8 T + 112 T^{2} - 599 T^{3} + 4772 T^{4} - 19059 T^{5} + 115579 T^{6} - 380413 T^{7} + 1964843 T^{8} - 5508051 T^{9} + 23444836 T^{10} - 50029079 T^{11} + 159023984 T^{12} - 193100552 T^{13} + 410338673 T^{14} \))(\( 1 - 9 T + 117 T^{2} - 830 T^{3} + 6651 T^{4} - 38255 T^{5} + 234080 T^{6} - 1125083 T^{7} + 5622716 T^{8} - 22801813 T^{9} + 95586172 T^{10} - 325148987 T^{11} + 1150035040 T^{12} - 3195095855 T^{13} + 9443468907 T^{14} - 20034182270 T^{15} + 48009624741 T^{16} - 62781816969 T^{17} + 118587876497 T^{18} \))(\( 1 + 13 T + 188 T^{2} + 1637 T^{3} + 14282 T^{4} + 95591 T^{5} + 626825 T^{6} + 3416146 T^{7} + 18135940 T^{8} + 82615530 T^{9} + 366110162 T^{10} + 1404464010 T^{11} + 5241286660 T^{12} + 16783525298 T^{13} + 52353050825 T^{14} + 135725550487 T^{15} + 344732760458 T^{16} + 671724407701 T^{17} + 1311442398908 T^{18} + 1541642394461 T^{19} + 2015993900449 T^{20} \))(\( 1 + 17 T + 234 T^{2} + 2265 T^{3} + 19237 T^{4} + 137392 T^{5} + 898853 T^{6} + 5267119 T^{7} + 28960380 T^{8} + 146780169 T^{9} + 705706807 T^{10} + 3163000586 T^{11} + 13489960680 T^{12} + 53771009962 T^{13} + 203949267223 T^{14} + 721130970297 T^{15} + 2418799897980 T^{16} + 7478555781983 T^{17} + 21696126308357 T^{18} + 56377250960816 T^{19} + 134192645892517 T^{20} + 268601540265705 T^{21} + 471742572705066 T^{22} + 582622237229761 T^{23} + 582622237229761 T^{24} \))(\( 1 + 104 T^{2} - 19 T^{3} + 5532 T^{4} - 2047 T^{5} + 205715 T^{6} - 93642 T^{7} + 6080575 T^{8} - 2798407 T^{9} + 150481407 T^{10} - 68169151 T^{11} + 3176734263 T^{12} - 1420430387 T^{13} + 57926949651 T^{14} - 24147316579 T^{15} + 918076202007 T^{16} - 334915038863 T^{17} + 12568357594047 T^{18} - 3973337767799 T^{19} + 146770298622175 T^{20} - 38424934017066 T^{21} + 1435017941975315 T^{22} - 242749383189359 T^{23} + 11152478257283868 T^{24} - 651166029845027 T^{25} + 60592712671895144 T^{26} + 168377826559400929 T^{28} \))(\( 1 + 2 T + 164 T^{2} + 558 T^{3} + 13826 T^{4} + 61050 T^{5} + 821987 T^{6} + 4012856 T^{7} + 38439505 T^{8} + 189124454 T^{9} + 1467587962 T^{10} + 6984743110 T^{11} + 46599637237 T^{12} + 211243496784 T^{13} + 1249782417607 T^{14} + 5349169312606 T^{15} + 28644055021465 T^{16} + 114893506574728 T^{17} + 564689173156821 T^{18} + 2109622446424602 T^{19} + 9599715943665957 T^{20} + 33204223400096392 T^{21} + 140728242320457545 T^{22} + 446767970158165726 T^{23} + 1774512314116222199 T^{24} + 5098904479425078096 T^{25} + 19121633306111966501 T^{26} + 48723873723055981510 T^{27} + \)\(17\!\cdots\!14\)\( T^{28} + \)\(38\!\cdots\!46\)\( T^{29} + \)\(13\!\cdots\!65\)\( T^{30} + \)\(23\!\cdots\!16\)\( T^{31} + \)\(81\!\cdots\!19\)\( T^{32} + \)\(10\!\cdots\!50\)\( T^{33} + \)\(39\!\cdots\!18\)\( T^{34} + \)\(27\!\cdots\!98\)\( T^{35} + \)\(13\!\cdots\!28\)\( T^{36} + \)\(28\!\cdots\!18\)\( T^{37} + \)\(23\!\cdots\!53\)\( T^{38} \))(\( 1 - 2 T + 164 T^{2} - 558 T^{3} + 13826 T^{4} - 61050 T^{5} + 821987 T^{6} - 4012856 T^{7} + 38439505 T^{8} - 189124454 T^{9} + 1467587962 T^{10} - 6984743110 T^{11} + 46599637237 T^{12} - 211243496784 T^{13} + 1249782417607 T^{14} - 5349169312606 T^{15} + 28644055021465 T^{16} - 114893506574728 T^{17} + 564689173156821 T^{18} - 2109622446424602 T^{19} + 9599715943665957 T^{20} - 33204223400096392 T^{21} + 140728242320457545 T^{22} - 446767970158165726 T^{23} + 1774512314116222199 T^{24} - 5098904479425078096 T^{25} + 19121633306111966501 T^{26} - 48723873723055981510 T^{27} + \)\(17\!\cdots\!14\)\( T^{28} - \)\(38\!\cdots\!46\)\( T^{29} + \)\(13\!\cdots\!65\)\( T^{30} - \)\(23\!\cdots\!16\)\( T^{31} + \)\(81\!\cdots\!19\)\( T^{32} - \)\(10\!\cdots\!50\)\( T^{33} + \)\(39\!\cdots\!18\)\( T^{34} - \)\(27\!\cdots\!98\)\( T^{35} + \)\(13\!\cdots\!28\)\( T^{36} - \)\(28\!\cdots\!18\)\( T^{37} + \)\(23\!\cdots\!53\)\( T^{38} \))
$19$ (\( 1 + 6 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + T + 39 T^{2} - 11 T^{3} + 821 T^{4} - 1335 T^{5} + 12695 T^{6} - 25365 T^{7} + 296381 T^{8} - 75449 T^{9} + 5082519 T^{10} + 2476099 T^{11} + 47045881 T^{12} \))(\( 1 + 15 T + 198 T^{2} + 1705 T^{3} + 13153 T^{4} + 79977 T^{5} + 441300 T^{6} + 2015782 T^{7} + 8384700 T^{8} + 28871697 T^{9} + 90216427 T^{10} + 222197305 T^{11} + 490267602 T^{12} + 705688215 T^{13} + 893871739 T^{14} \))(\( 1 + 7 T + 102 T^{2} + 574 T^{3} + 4737 T^{4} + 22781 T^{5} + 135974 T^{6} + 590058 T^{7} + 2932716 T^{8} + 12098264 T^{9} + 55721604 T^{10} + 213010938 T^{11} + 932645666 T^{12} + 2968842701 T^{13} + 11729280963 T^{14} + 27004335694 T^{15} + 91174917378 T^{16} + 118884941287 T^{17} + 322687697779 T^{18} \))(\( 1 - 13 T + 183 T^{2} - 1377 T^{3} + 10933 T^{4} - 56361 T^{5} + 328663 T^{6} - 1281093 T^{7} + 6602298 T^{8} - 22381284 T^{9} + 120882188 T^{10} - 425244396 T^{11} + 2383429578 T^{12} - 8787016887 T^{13} + 42831690823 T^{14} - 139555415739 T^{15} + 514352616973 T^{16} - 1230861384603 T^{17} + 3107992036503 T^{18} - 4194940071127 T^{19} + 6131066257801 T^{20} \))(\( 1 - 3 T + 118 T^{2} - 354 T^{3} + 6367 T^{4} - 18339 T^{5} + 202805 T^{6} - 553837 T^{7} + 4111668 T^{8} - 11110434 T^{9} + 57039911 T^{10} - 180637625 T^{11} + 811731260 T^{12} - 3432114875 T^{13} + 20591407871 T^{14} - 76206466806 T^{15} + 535836685428 T^{16} - 1371355241863 T^{17} + 9541139896205 T^{18} - 16392713821521 T^{19} + 108134345882047 T^{20} - 114231445013766 T^{21} + 723465818420518 T^{22} - 349470776694657 T^{23} + 2213314919066161 T^{24} \))(\( 1 - 27 T + 441 T^{2} - 5254 T^{3} + 50682 T^{4} - 414675 T^{5} + 2979448 T^{6} - 19196965 T^{7} + 113021852 T^{8} - 616541144 T^{9} + 3160784719 T^{10} - 15400093521 T^{11} + 72100535921 T^{12} - 326801388214 T^{13} + 1442586078560 T^{14} - 6209226376066 T^{15} + 26028293467481 T^{16} - 105629241460539 T^{17} + 411916625364799 T^{18} - 1526616910117256 T^{19} + 5317212599591612 T^{20} - 17159624488072135 T^{21} + 50601642935381368 T^{22} - 133810521076506825 T^{23} + 310734700077870282 T^{24} - 612039820251242626 T^{25} + 976071879308177001 T^{26} - 1135430553480940593 T^{27} + 799006685782884121 T^{28} \))(\( 1 + 7 T + 226 T^{2} + 1463 T^{3} + 25161 T^{4} + 151710 T^{5} + 1838170 T^{6} + 10372558 T^{7} + 99005595 T^{8} + 524732907 T^{9} + 4189411564 T^{10} + 20913842891 T^{11} + 145004177773 T^{12} + 683116077882 T^{13} + 4221373237530 T^{14} + 18777746727740 T^{15} + 105431186946384 T^{16} + 442182643819714 T^{17} + 2289016957568664 T^{18} + 9014019018636812 T^{19} + 43491322193804616 T^{20} + 159627934418916754 T^{21} + 723152511265247856 T^{22} + 2447134731305804540 T^{23} + 10452538052074795470 T^{24} + 32137797709223304042 T^{25} + \)\(12\!\cdots\!47\)\( T^{26} + \)\(35\!\cdots\!31\)\( T^{27} + \)\(13\!\cdots\!56\)\( T^{28} + \)\(32\!\cdots\!07\)\( T^{29} + \)\(11\!\cdots\!05\)\( T^{30} + \)\(22\!\cdots\!38\)\( T^{31} + \)\(77\!\cdots\!30\)\( T^{32} + \)\(12\!\cdots\!10\)\( T^{33} + \)\(38\!\cdots\!39\)\( T^{34} + \)\(42\!\cdots\!03\)\( T^{35} + \)\(12\!\cdots\!14\)\( T^{36} + \)\(72\!\cdots\!87\)\( T^{37} + \)\(19\!\cdots\!79\)\( T^{38} \))(\( 1 + 7 T + 226 T^{2} + 1463 T^{3} + 25161 T^{4} + 151710 T^{5} + 1838170 T^{6} + 10372558 T^{7} + 99005595 T^{8} + 524732907 T^{9} + 4189411564 T^{10} + 20913842891 T^{11} + 145004177773 T^{12} + 683116077882 T^{13} + 4221373237530 T^{14} + 18777746727740 T^{15} + 105431186946384 T^{16} + 442182643819714 T^{17} + 2289016957568664 T^{18} + 9014019018636812 T^{19} + 43491322193804616 T^{20} + 159627934418916754 T^{21} + 723152511265247856 T^{22} + 2447134731305804540 T^{23} + 10452538052074795470 T^{24} + 32137797709223304042 T^{25} + \)\(12\!\cdots\!47\)\( T^{26} + \)\(35\!\cdots\!31\)\( T^{27} + \)\(13\!\cdots\!56\)\( T^{28} + \)\(32\!\cdots\!07\)\( T^{29} + \)\(11\!\cdots\!05\)\( T^{30} + \)\(22\!\cdots\!38\)\( T^{31} + \)\(77\!\cdots\!30\)\( T^{32} + \)\(12\!\cdots\!10\)\( T^{33} + \)\(38\!\cdots\!39\)\( T^{34} + \)\(42\!\cdots\!03\)\( T^{35} + \)\(12\!\cdots\!14\)\( T^{36} + \)\(72\!\cdots\!87\)\( T^{37} + \)\(19\!\cdots\!79\)\( T^{38} \))
$23$ (\( 1 + 9 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 7 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 21 T + 265 T^{2} - 2307 T^{3} + 15952 T^{4} - 91410 T^{5} + 465279 T^{6} - 2102430 T^{7} + 8438608 T^{8} - 28069269 T^{9} + 74157865 T^{10} - 135163203 T^{11} + 148035889 T^{12} \))(\( 1 - 5 T + 114 T^{2} - 562 T^{3} + 6547 T^{4} - 28211 T^{5} + 231026 T^{6} - 828297 T^{7} + 5313598 T^{8} - 14923619 T^{9} + 79657349 T^{10} - 157270642 T^{11} + 733743102 T^{12} - 740179445 T^{13} + 3404825447 T^{14} \))(\( 1 + 10 T + 134 T^{2} + 1099 T^{3} + 9450 T^{4} + 63094 T^{5} + 422678 T^{6} + 2397151 T^{7} + 13353378 T^{8} + 64511703 T^{9} + 307127694 T^{10} + 1268092879 T^{11} + 5142723226 T^{12} + 17656288054 T^{13} + 60823441350 T^{14} + 162691442011 T^{15} + 456246609898 T^{16} + 783109852810 T^{17} + 1801152661463 T^{18} \))(\( 1 + 12 T + 211 T^{2} + 1967 T^{3} + 20472 T^{4} + 154025 T^{5} + 1196304 T^{6} + 7461695 T^{7} + 46733896 T^{8} + 244926002 T^{9} + 1276808824 T^{10} + 5633298046 T^{11} + 24722230984 T^{12} + 90786443065 T^{13} + 334774907664 T^{14} + 991357730575 T^{15} + 3030590719608 T^{16} + 6697291654249 T^{17} + 16523617894291 T^{18} + 21613831937556 T^{19} + 41426511213649 T^{20} \))(\( 1 - 8 T + 204 T^{2} - 1221 T^{3} + 17826 T^{4} - 80106 T^{5} + 898289 T^{6} - 2899385 T^{7} + 29853816 T^{8} - 62599814 T^{9} + 744746866 T^{10} - 964408071 T^{11} + 16885024916 T^{12} - 22181385633 T^{13} + 393971092114 T^{14} - 761651936938 T^{15} + 8354321723256 T^{16} - 18661436349055 T^{17} + 132979010693921 T^{18} - 272746947257382 T^{19} + 1395971623619106 T^{20} - 2199207399646323 T^{21} + 8451008287584396 T^{22} - 7622478063311416 T^{23} + 21914624432020321 T^{24} \))(\( 1 + 13 T + 190 T^{2} + 1518 T^{3} + 13387 T^{4} + 77351 T^{5} + 513478 T^{6} + 2186676 T^{7} + 11981481 T^{8} + 31447409 T^{9} + 146114163 T^{10} - 206892093 T^{11} - 842453049 T^{12} - 23183395277 T^{13} - 66332617343 T^{14} - 533218091371 T^{15} - 445657662921 T^{16} - 2517256095531 T^{17} + 40888733488083 T^{18} + 202406310785287 T^{19} + 1773689191371609 T^{20} + 7445250089144172 T^{21} + 40210968100117318 T^{22} + 139320959516824513 T^{23} + 554576705617119163 T^{24} + 1446365212513341186 T^{25} + 4163778642083860990 T^{26} + 6552472705174075979 T^{27} + 11592836324538749809 T^{28} \))(\( 1 + 27 T + 593 T^{2} + 9306 T^{3} + 127662 T^{4} + 1490324 T^{5} + 15782195 T^{6} + 150624557 T^{7} + 1332003355 T^{8} + 10903967934 T^{9} + 83792343328 T^{10} + 604875834714 T^{11} + 4133126792436 T^{12} + 26761574134582 T^{13} + 164900149755521 T^{14} + 967929535226421 T^{15} + 5424941903281773 T^{16} + 29052731657510460 T^{17} + 148835571912743977 T^{18} + 729590235034550375 T^{19} + 3423218153993111471 T^{20} + 15368895046823033340 T^{21} + 66005268137229332091 T^{22} + \)\(27\!\cdots\!61\)\( T^{23} + \)\(10\!\cdots\!03\)\( T^{24} + \)\(39\!\cdots\!98\)\( T^{25} + \)\(14\!\cdots\!92\)\( T^{26} + \)\(47\!\cdots\!34\)\( T^{27} + \)\(15\!\cdots\!64\)\( T^{28} + \)\(45\!\cdots\!66\)\( T^{29} + \)\(12\!\cdots\!85\)\( T^{30} + \)\(33\!\cdots\!97\)\( T^{31} + \)\(79\!\cdots\!85\)\( T^{32} + \)\(17\!\cdots\!16\)\( T^{33} + \)\(34\!\cdots\!34\)\( T^{34} + \)\(57\!\cdots\!66\)\( T^{35} + \)\(83\!\cdots\!79\)\( T^{36} + \)\(87\!\cdots\!63\)\( T^{37} + \)\(74\!\cdots\!87\)\( T^{38} \))(\( 1 - 27 T + 593 T^{2} - 9306 T^{3} + 127662 T^{4} - 1490324 T^{5} + 15782195 T^{6} - 150624557 T^{7} + 1332003355 T^{8} - 10903967934 T^{9} + 83792343328 T^{10} - 604875834714 T^{11} + 4133126792436 T^{12} - 26761574134582 T^{13} + 164900149755521 T^{14} - 967929535226421 T^{15} + 5424941903281773 T^{16} - 29052731657510460 T^{17} + 148835571912743977 T^{18} - 729590235034550375 T^{19} + 3423218153993111471 T^{20} - 15368895046823033340 T^{21} + 66005268137229332091 T^{22} - \)\(27\!\cdots\!61\)\( T^{23} + \)\(10\!\cdots\!03\)\( T^{24} - \)\(39\!\cdots\!98\)\( T^{25} + \)\(14\!\cdots\!92\)\( T^{26} - \)\(47\!\cdots\!34\)\( T^{27} + \)\(15\!\cdots\!64\)\( T^{28} - \)\(45\!\cdots\!66\)\( T^{29} + \)\(12\!\cdots\!85\)\( T^{30} - \)\(33\!\cdots\!97\)\( T^{31} + \)\(79\!\cdots\!85\)\( T^{32} - \)\(17\!\cdots\!16\)\( T^{33} + \)\(34\!\cdots\!34\)\( T^{34} - \)\(57\!\cdots\!66\)\( T^{35} + \)\(83\!\cdots\!79\)\( T^{36} - \)\(87\!\cdots\!63\)\( T^{37} + \)\(74\!\cdots\!87\)\( T^{38} \))
$29$ (\( 1 + 2 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 19 T + 281 T^{2} - 2805 T^{3} + 24104 T^{4} - 163378 T^{5} + 975989 T^{6} - 4737962 T^{7} + 20271464 T^{8} - 68411145 T^{9} + 198745961 T^{10} - 389711831 T^{11} + 594823321 T^{12} \))(\( 1 + 132 T^{2} - 90 T^{3} + 8557 T^{4} - 8078 T^{5} + 357562 T^{6} - 322880 T^{7} + 10369298 T^{8} - 6793598 T^{9} + 208696673 T^{10} - 63655290 T^{11} + 2707471668 T^{12} + 17249876309 T^{14} \))(\( 1 - 9 T + 162 T^{2} - 1246 T^{3} + 13492 T^{4} - 89670 T^{5} + 737627 T^{6} - 4274392 T^{7} + 28947044 T^{8} - 145093038 T^{9} + 839464276 T^{10} - 3594763672 T^{11} + 17989984903 T^{12} - 63421887270 T^{13} + 276736422308 T^{14} - 741149857966 T^{15} + 2794479962058 T^{16} - 4502217716649 T^{17} + 14507145975869 T^{18} \))(\( 1 + 5 T + 103 T^{2} + 383 T^{3} + 6122 T^{4} + 22658 T^{5} + 297171 T^{6} + 1047682 T^{7} + 11321173 T^{8} + 36306888 T^{9} + 356091452 T^{10} + 1052899752 T^{11} + 9521106493 T^{12} + 25551916298 T^{13} + 210183402051 T^{14} + 464741614042 T^{15} + 3641508371162 T^{16} + 6606702626347 T^{17} + 51525380534983 T^{18} + 72535729879345 T^{19} + 420707233300201 T^{20} \))(\( 1 + 15 T + 322 T^{2} + 3312 T^{3} + 40692 T^{4} + 316638 T^{5} + 2839934 T^{6} + 17558747 T^{7} + 127727660 T^{8} + 655248228 T^{9} + 4241189978 T^{10} + 19529280148 T^{11} + 124135281138 T^{12} + 566349124292 T^{13} + 3566840771498 T^{14} + 15980849032692 T^{15} + 90339347092460 T^{16} + 360150075970303 T^{17} + 1689258973300814 T^{18} + 5461966334729142 T^{19} + 20356027036209012 T^{20} + 48047667472078128 T^{21} + 135467729122664722 T^{22} + 183007646485587435 T^{23} + 353814783205469041 T^{24} \))(\( 1 + 157 T^{2} - 192 T^{3} + 13404 T^{4} - 26074 T^{5} + 840016 T^{6} - 1985546 T^{7} + 42186822 T^{8} - 108389824 T^{9} + 1784428139 T^{10} - 4581335888 T^{11} + 64702247509 T^{12} - 158910539972 T^{13} + 2018754156720 T^{14} - 4608405659188 T^{15} + 54414590155069 T^{16} - 111734200972432 T^{17} + 1262092118580059 T^{18} - 2223199830147776 T^{19} + 25093705564475862 T^{20} - 34250422905829714 T^{21} + 420214990829847376 T^{22} - 378259324174808306 T^{23} + 5639159755155894204 T^{24} - 2342497875015519168 T^{25} + 55548920963258639437 T^{26} + \)\(29\!\cdots\!81\)\( T^{28} \))(\( 1 + 3 T + 288 T^{2} + 1011 T^{3} + 42177 T^{4} + 166402 T^{5} + 4158474 T^{6} + 17983276 T^{7} + 309322080 T^{8} + 1437669576 T^{9} + 18472069112 T^{10} + 90562337812 T^{11} + 920794917893 T^{12} + 4666588181925 T^{13} + 39317886158991 T^{14} + 201302548583530 T^{15} + 1462985988055118 T^{16} + 7371596379443790 T^{17} + 47937854553987646 T^{18} + 230881636574127154 T^{19} + 1390197782065641734 T^{20} + 6199512555112227390 T^{21} + 35680765262676272902 T^{22} + \)\(14\!\cdots\!30\)\( T^{23} + \)\(80\!\cdots\!59\)\( T^{24} + \)\(27\!\cdots\!25\)\( T^{25} + \)\(15\!\cdots\!37\)\( T^{26} + \)\(45\!\cdots\!32\)\( T^{27} + \)\(26\!\cdots\!28\)\( T^{28} + \)\(60\!\cdots\!76\)\( T^{29} + \)\(37\!\cdots\!20\)\( T^{30} + \)\(63\!\cdots\!16\)\( T^{31} + \)\(42\!\cdots\!86\)\( T^{32} + \)\(49\!\cdots\!62\)\( T^{33} + \)\(36\!\cdots\!73\)\( T^{34} + \)\(25\!\cdots\!31\)\( T^{35} + \)\(20\!\cdots\!92\)\( T^{36} + \)\(63\!\cdots\!83\)\( T^{37} + \)\(61\!\cdots\!69\)\( T^{38} \))(\( 1 - 3 T + 288 T^{2} - 1011 T^{3} + 42177 T^{4} - 166402 T^{5} + 4158474 T^{6} - 17983276 T^{7} + 309322080 T^{8} - 1437669576 T^{9} + 18472069112 T^{10} - 90562337812 T^{11} + 920794917893 T^{12} - 4666588181925 T^{13} + 39317886158991 T^{14} - 201302548583530 T^{15} + 1462985988055118 T^{16} - 7371596379443790 T^{17} + 47937854553987646 T^{18} - 230881636574127154 T^{19} + 1390197782065641734 T^{20} - 6199512555112227390 T^{21} + 35680765262676272902 T^{22} - \)\(14\!\cdots\!30\)\( T^{23} + \)\(80\!\cdots\!59\)\( T^{24} - \)\(27\!\cdots\!25\)\( T^{25} + \)\(15\!\cdots\!37\)\( T^{26} - \)\(45\!\cdots\!32\)\( T^{27} + \)\(26\!\cdots\!28\)\( T^{28} - \)\(60\!\cdots\!76\)\( T^{29} + \)\(37\!\cdots\!20\)\( T^{30} - \)\(63\!\cdots\!16\)\( T^{31} + \)\(42\!\cdots\!86\)\( T^{32} - \)\(49\!\cdots\!62\)\( T^{33} + \)\(36\!\cdots\!73\)\( T^{34} - \)\(25\!\cdots\!31\)\( T^{35} + \)\(20\!\cdots\!92\)\( T^{36} - \)\(63\!\cdots\!83\)\( T^{37} + \)\(61\!\cdots\!69\)\( T^{38} \))
$31$ (\( 1 + 3 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 - 7 T + 129 T^{2} - 643 T^{3} + 7468 T^{4} - 28890 T^{5} + 272013 T^{6} - 895590 T^{7} + 7176748 T^{8} - 19155613 T^{9} + 119134209 T^{10} - 200404057 T^{11} + 887503681 T^{12} \))(\( 1 + 21 T + 323 T^{2} + 3712 T^{3} + 34723 T^{4} + 275114 T^{5} + 1883364 T^{6} + 11173393 T^{7} + 58384284 T^{8} + 264384554 T^{9} + 1034432893 T^{10} + 3428109952 T^{11} + 9247215773 T^{12} + 18637577301 T^{13} + 27512614111 T^{14} \))(\( 1 + 2 T + 142 T^{2} + 407 T^{3} + 11026 T^{4} + 34260 T^{5} + 602380 T^{6} + 1786363 T^{7} + 24465508 T^{8} + 65380843 T^{9} + 758430748 T^{10} + 1716694843 T^{11} + 17945502580 T^{12} + 31639829460 T^{13} + 315665018926 T^{14} + 361213998167 T^{15} + 3906791203762 T^{16} + 1705782074882 T^{17} + 26439622160671 T^{18} \))(\( 1 + 10 T + 225 T^{2} + 1585 T^{3} + 21676 T^{4} + 121661 T^{5} + 1329822 T^{6} + 6413891 T^{7} + 60587636 T^{8} + 257715708 T^{9} + 2132976388 T^{10} + 7989186948 T^{11} + 58224718196 T^{12} + 191076226781 T^{13} + 1228118543262 T^{14} + 3483051139811 T^{15} + 19237529789356 T^{16} + 43607493365935 T^{17} + 191900483424225 T^{18} + 264396221606710 T^{19} + 819628286980801 T^{20} \))(\( 1 + 2 T + 191 T^{2} + 645 T^{3} + 17531 T^{4} + 71081 T^{5} + 1090695 T^{6} + 4239006 T^{7} + 51703656 T^{8} + 176281591 T^{9} + 1956678326 T^{10} + 6115319911 T^{11} + 63707039664 T^{12} + 189574917241 T^{13} + 1880367871286 T^{14} + 5251604877481 T^{15} + 47749412092776 T^{16} + 121359142863906 T^{17} + 967995827348295 T^{18} + 1955624123623991 T^{19} + 14952032777378171 T^{20} + 17053556293632795 T^{21} + 156549002813332991 T^{22} + 50816953792809662 T^{23} + 787662783788549761 T^{24} \))(\( 1 - 25 T + 503 T^{2} - 6946 T^{3} + 83553 T^{4} - 823630 T^{5} + 7364616 T^{6} - 57517098 T^{7} + 419903137 T^{8} - 2780464125 T^{9} + 17714198221 T^{10} - 105465364251 T^{11} + 621052204731 T^{12} - 3495835300725 T^{13} + 19820760784583 T^{14} - 108370894322475 T^{15} + 596831168746491 T^{16} - 3141918666401541 T^{17} + 16359434055256141 T^{18} - 79602327284707875 T^{19} + 372665579750947297 T^{20} - 1582445722058569878 T^{21} + 6281214980594587656 T^{22} - 21776466000193455730 T^{23} + 68482402262106865953 T^{24} - \)\(17\!\cdots\!26\)\( T^{25} + \)\(39\!\cdots\!83\)\( T^{26} - \)\(61\!\cdots\!75\)\( T^{27} + \)\(75\!\cdots\!21\)\( T^{28} \))(\( 1 + 259 T^{2} - 6 T^{3} + 33612 T^{4} - 3290 T^{5} + 2920397 T^{6} - 736010 T^{7} + 191902643 T^{8} - 95839056 T^{9} + 10225973710 T^{10} - 8478976352 T^{11} + 462793713236 T^{12} - 555264921514 T^{13} + 18400371098569 T^{14} - 28389038545082 T^{15} + 660495516450243 T^{16} - 1172576457476606 T^{17} + 21884802012393629 T^{18} - 39910819866076064 T^{19} + 678428862384202499 T^{20} - 1126845975635018366 T^{21} + 19676821930569189213 T^{22} - 26217873266192673722 T^{23} + \)\(52\!\cdots\!19\)\( T^{24} - \)\(49\!\cdots\!34\)\( T^{25} + \)\(12\!\cdots\!96\)\( T^{26} - \)\(72\!\cdots\!32\)\( T^{27} + \)\(27\!\cdots\!10\)\( T^{28} - \)\(78\!\cdots\!56\)\( T^{29} + \)\(48\!\cdots\!33\)\( T^{30} - \)\(57\!\cdots\!10\)\( T^{31} + \)\(71\!\cdots\!27\)\( T^{32} - \)\(24\!\cdots\!90\)\( T^{33} + \)\(78\!\cdots\!12\)\( T^{34} - \)\(43\!\cdots\!86\)\( T^{35} + \)\(58\!\cdots\!49\)\( T^{36} + \)\(21\!\cdots\!71\)\( T^{38} \))(\( 1 + 259 T^{2} - 6 T^{3} + 33612 T^{4} - 3290 T^{5} + 2920397 T^{6} - 736010 T^{7} + 191902643 T^{8} - 95839056 T^{9} + 10225973710 T^{10} - 8478976352 T^{11} + 462793713236 T^{12} - 555264921514 T^{13} + 18400371098569 T^{14} - 28389038545082 T^{15} + 660495516450243 T^{16} - 1172576457476606 T^{17} + 21884802012393629 T^{18} - 39910819866076064 T^{19} + 678428862384202499 T^{20} - 1126845975635018366 T^{21} + 19676821930569189213 T^{22} - 26217873266192673722 T^{23} + \)\(52\!\cdots\!19\)\( T^{24} - \)\(49\!\cdots\!34\)\( T^{25} + \)\(12\!\cdots\!96\)\( T^{26} - \)\(72\!\cdots\!32\)\( T^{27} + \)\(27\!\cdots\!10\)\( T^{28} - \)\(78\!\cdots\!56\)\( T^{29} + \)\(48\!\cdots\!33\)\( T^{30} - \)\(57\!\cdots\!10\)\( T^{31} + \)\(71\!\cdots\!27\)\( T^{32} - \)\(24\!\cdots\!90\)\( T^{33} + \)\(78\!\cdots\!12\)\( T^{34} - \)\(43\!\cdots\!86\)\( T^{35} + \)\(58\!\cdots\!49\)\( T^{36} + \)\(21\!\cdots\!71\)\( T^{38} \))
$37$ (\( 1 + 12 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 8 T + 129 T^{2} - 344 T^{3} + 3460 T^{4} + 18315 T^{5} + 4173 T^{6} + 677655 T^{7} + 4736740 T^{8} - 17424632 T^{9} + 241766769 T^{10} - 554751656 T^{11} + 2565726409 T^{12} \))(\( 1 + T + 107 T^{2} - 80 T^{3} + 5714 T^{4} - 14045 T^{5} + 214630 T^{6} - 801168 T^{7} + 7941310 T^{8} - 19227605 T^{9} + 289431242 T^{10} - 149932880 T^{11} + 7419803399 T^{12} + 2565726409 T^{13} + 94931877133 T^{14} \))(\( 1 + 10 T + 186 T^{2} + 1578 T^{3} + 17376 T^{4} + 130229 T^{5} + 1107955 T^{6} + 7364964 T^{7} + 52362504 T^{8} + 310533890 T^{9} + 1937412648 T^{10} + 10082635716 T^{11} + 56121244615 T^{12} + 244070112869 T^{13} + 1204920596832 T^{14} + 4048716273402 T^{15} + 17657329146738 T^{16} + 35124794539210 T^{17} + 129961739795077 T^{18} \))(\( 1 + 2 T + 233 T^{2} + 230 T^{3} + 26618 T^{4} + 10345 T^{5} + 2014617 T^{6} + 156879 T^{7} + 111518881 T^{8} - 5975720 T^{9} + 4698224076 T^{10} - 221101640 T^{11} + 152669348089 T^{12} + 7946391987 T^{13} + 3775716611337 T^{14} + 717363235165 T^{15} + 68294505554762 T^{16} + 21834331740590 T^{17} + 818407712763593 T^{18} + 259923479590154 T^{19} + 4808584372417849 T^{20} \))(\( 1 - 14 T + 377 T^{2} - 3746 T^{3} + 56817 T^{4} - 424173 T^{5} + 4713026 T^{6} - 26947853 T^{7} + 250003375 T^{8} - 1105562417 T^{9} + 9810759741 T^{10} - 36152170021 T^{11} + 353130249998 T^{12} - 1337630290777 T^{13} + 13430930085429 T^{14} - 56000053108301 T^{15} + 468546575293375 T^{16} - 1868670759674321 T^{17} + 12092335274503634 T^{18} - 40267539119136009 T^{19} + 199568545133429457 T^{20} - 486836677272358442 T^{21} + 1812836308401529073 T^{22} - 2490846704912445782 T^{23} + 6582952005840035281 T^{24} \))(\( 1 + T + 206 T^{2} + 417 T^{3} + 22954 T^{4} + 67484 T^{5} + 1814134 T^{6} + 6641756 T^{7} + 115182508 T^{8} + 460182755 T^{9} + 6224084362 T^{10} + 24574724091 T^{11} + 290341422433 T^{12} + 1073562144200 T^{13} + 11624734096484 T^{14} + 39721799335400 T^{15} + 397477407310777 T^{16} + 1244783499381423 T^{17} + 11664936171970282 T^{18} + 31910893174861535 T^{19} + 295526802630453772 T^{20} + 630514364539365548 T^{21} + 6372108401659519414 T^{22} + 8770338048330976268 T^{23} + \)\(11\!\cdots\!46\)\( T^{24} + 74191648282034992221 T^{25} + \)\(13\!\cdots\!86\)\( T^{26} + \)\(24\!\cdots\!97\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \))(\( 1 + 6 T + 419 T^{2} + 1970 T^{3} + 84924 T^{4} + 311596 T^{5} + 11281782 T^{6} + 32044200 T^{7} + 1117645702 T^{8} + 2439775320 T^{9} + 88522309049 T^{10} + 148271514036 T^{11} + 5835379370792 T^{12} + 7566761794838 T^{13} + 327798369610567 T^{14} + 337663037683796 T^{15} + 15913671000078712 T^{16} + 13679580506944708 T^{17} + 673152377653840940 T^{18} + 519371760132361844 T^{19} + 24906637973192114780 T^{20} + 18727345714007305252 T^{21} + \)\(80\!\cdots\!36\)\( T^{22} + \)\(63\!\cdots\!56\)\( T^{23} + \)\(22\!\cdots\!19\)\( T^{24} + \)\(19\!\cdots\!42\)\( T^{25} + \)\(55\!\cdots\!36\)\( T^{26} + \)\(52\!\cdots\!56\)\( T^{27} + \)\(11\!\cdots\!73\)\( T^{28} + \)\(11\!\cdots\!80\)\( T^{29} + \)\(19\!\cdots\!26\)\( T^{30} + \)\(21\!\cdots\!00\)\( T^{31} + \)\(27\!\cdots\!54\)\( T^{32} + \)\(28\!\cdots\!44\)\( T^{33} + \)\(28\!\cdots\!32\)\( T^{34} + \)\(24\!\cdots\!70\)\( T^{35} + \)\(19\!\cdots\!23\)\( T^{36} + \)\(10\!\cdots\!74\)\( T^{37} + \)\(62\!\cdots\!73\)\( T^{38} \))(\( 1 + 6 T + 419 T^{2} + 1970 T^{3} + 84924 T^{4} + 311596 T^{5} + 11281782 T^{6} + 32044200 T^{7} + 1117645702 T^{8} + 2439775320 T^{9} + 88522309049 T^{10} + 148271514036 T^{11} + 5835379370792 T^{12} + 7566761794838 T^{13} + 327798369610567 T^{14} + 337663037683796 T^{15} + 15913671000078712 T^{16} + 13679580506944708 T^{17} + 673152377653840940 T^{18} + 519371760132361844 T^{19} + 24906637973192114780 T^{20} + 18727345714007305252 T^{21} + \)\(80\!\cdots\!36\)\( T^{22} + \)\(63\!\cdots\!56\)\( T^{23} + \)\(22\!\cdots\!19\)\( T^{24} + \)\(19\!\cdots\!42\)\( T^{25} + \)\(55\!\cdots\!36\)\( T^{26} + \)\(52\!\cdots\!56\)\( T^{27} + \)\(11\!\cdots\!73\)\( T^{28} + \)\(11\!\cdots\!80\)\( T^{29} + \)\(19\!\cdots\!26\)\( T^{30} + \)\(21\!\cdots\!00\)\( T^{31} + \)\(27\!\cdots\!54\)\( T^{32} + \)\(28\!\cdots\!44\)\( T^{33} + \)\(28\!\cdots\!32\)\( T^{34} + \)\(24\!\cdots\!70\)\( T^{35} + \)\(19\!\cdots\!23\)\( T^{36} + \)\(10\!\cdots\!74\)\( T^{37} + \)\(62\!\cdots\!73\)\( T^{38} \))
$41$ (\( 1 + 3 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 + T + 41 T^{2} \))(\( 1 - 30 T + 609 T^{2} - 8420 T^{3} + 92486 T^{4} - 797141 T^{5} + 5683913 T^{6} - 32682781 T^{7} + 155468966 T^{8} - 580314820 T^{9} + 1720888449 T^{10} - 3475686030 T^{11} + 4750104241 T^{12} \))(\( 1 - 10 T + 183 T^{2} - 1925 T^{3} + 18522 T^{4} - 156974 T^{5} + 1223611 T^{6} - 7778621 T^{7} + 50168051 T^{8} - 263873294 T^{9} + 1276554762 T^{10} - 5439589925 T^{11} + 21201684783 T^{12} - 47501042410 T^{13} + 194754273881 T^{14} \))(\( 1 - 5 T + 137 T^{2} - 318 T^{3} + 8754 T^{4} - 7839 T^{5} + 496735 T^{6} - 518793 T^{7} + 26207463 T^{8} - 31606587 T^{9} + 1074505983 T^{10} - 872091033 T^{11} + 34235472935 T^{12} - 22151140479 T^{13} + 1014205183554 T^{14} - 1510533148638 T^{15} + 26681335521697 T^{16} - 39924626145605 T^{17} + 327381934393961 T^{18} \))(\( 1 + 11 T + 304 T^{2} + 2905 T^{3} + 45565 T^{4} + 375425 T^{5} + 4318661 T^{6} + 30778096 T^{7} + 284952272 T^{8} + 1754102716 T^{9} + 13635868384 T^{10} + 71918211356 T^{11} + 479004769232 T^{12} + 2121257154416 T^{13} + 12203503826021 T^{14} + 43495314260425 T^{15} + 216438499741165 T^{16} + 565761165624305 T^{17} + 2427417269652784 T^{18} + 3601201278333571 T^{19} + 13422659310152401 T^{20} \))(\( 1 + 5 T + 238 T^{2} + 649 T^{3} + 21308 T^{4} + 13918 T^{5} + 871065 T^{6} - 875013 T^{7} + 13357013 T^{8} + 46692813 T^{9} - 137880757 T^{10} + 9679686232 T^{11} - 10918413792 T^{12} + 396867135512 T^{13} - 231777552517 T^{14} + 3218115364773 T^{15} + 37743726411893 T^{16} - 101375682005613 T^{17} + 4137649550686665 T^{18} + 2710589983875758 T^{19} + 170142786782110268 T^{20} + 212470875421680689 T^{21} + 3194592915816271438 T^{22} + 2751645158581242205 T^{23} + 22563490300366186081 T^{24} \))(\( 1 + 10 T + 271 T^{2} + 2287 T^{3} + 35114 T^{4} + 272478 T^{5} + 3121403 T^{6} + 22996332 T^{7} + 218558009 T^{8} + 1529053321 T^{9} + 12761407637 T^{10} + 84350370261 T^{11} + 639294414953 T^{12} + 3977962213993 T^{13} + 27952401522009 T^{14} + 163096450773713 T^{15} + 1074653911535993 T^{16} + 5813511868758381 T^{17} + 36060688005736757 T^{18} + 177150308897493521 T^{19} + 1038173325455416169 T^{20} + 4478633940586404492 T^{21} + 24924169564953976763 T^{22} + 89204374719797705358 T^{23} + \)\(47\!\cdots\!14\)\( T^{24} + \)\(12\!\cdots\!67\)\( T^{25} + \)\(61\!\cdots\!51\)\( T^{26} + \)\(92\!\cdots\!10\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \))(\( 1 + 32 T + 946 T^{2} + 19232 T^{3} + 352968 T^{4} + 5435264 T^{5} + 76600293 T^{6} + 965083024 T^{7} + 11281674438 T^{8} + 121365504768 T^{9} + 1224776046431 T^{10} + 11562481837852 T^{11} + 103301535046434 T^{12} + 872737497448896 T^{13} + 7028487670728960 T^{14} + 53942868920750476 T^{15} + 396933115844171978 T^{16} + 2798723433138807368 T^{17} + 18993867105549159690 T^{18} + \)\(12\!\cdots\!52\)\( T^{19} + \)\(77\!\cdots\!90\)\( T^{20} + \)\(47\!\cdots\!08\)\( T^{21} + \)\(27\!\cdots\!38\)\( T^{22} + \)\(15\!\cdots\!36\)\( T^{23} + \)\(81\!\cdots\!60\)\( T^{24} + \)\(41\!\cdots\!36\)\( T^{25} + \)\(20\!\cdots\!54\)\( T^{26} + \)\(92\!\cdots\!92\)\( T^{27} + \)\(40\!\cdots\!91\)\( T^{28} + \)\(16\!\cdots\!68\)\( T^{29} + \)\(62\!\cdots\!58\)\( T^{30} + \)\(21\!\cdots\!44\)\( T^{31} + \)\(70\!\cdots\!53\)\( T^{32} + \)\(20\!\cdots\!04\)\( T^{33} + \)\(54\!\cdots\!68\)\( T^{34} + \)\(12\!\cdots\!12\)\( T^{35} + \)\(24\!\cdots\!26\)\( T^{36} + \)\(34\!\cdots\!72\)\( T^{37} + \)\(43\!\cdots\!61\)\( T^{38} \))(\( 1 - 32 T + 946 T^{2} - 19232 T^{3} + 352968 T^{4} - 5435264 T^{5} + 76600293 T^{6} - 965083024 T^{7} + 11281674438 T^{8} - 121365504768 T^{9} + 1224776046431 T^{10} - 11562481837852 T^{11} + 103301535046434 T^{12} - 872737497448896 T^{13} + 7028487670728960 T^{14} - 53942868920750476 T^{15} + 396933115844171978 T^{16} - 2798723433138807368 T^{17} + 18993867105549159690 T^{18} - \)\(12\!\cdots\!52\)\( T^{19} + \)\(77\!\cdots\!90\)\( T^{20} - \)\(47\!\cdots\!08\)\( T^{21} + \)\(27\!\cdots\!38\)\( T^{22} - \)\(15\!\cdots\!36\)\( T^{23} + \)\(81\!\cdots\!60\)\( T^{24} - \)\(41\!\cdots\!36\)\( T^{25} + \)\(20\!\cdots\!54\)\( T^{26} - \)\(92\!\cdots\!92\)\( T^{27} + \)\(40\!\cdots\!91\)\( T^{28} - \)\(16\!\cdots\!68\)\( T^{29} + \)\(62\!\cdots\!58\)\( T^{30} - \)\(21\!\cdots\!44\)\( T^{31} + \)\(70\!\cdots\!53\)\( T^{32} - \)\(20\!\cdots\!04\)\( T^{33} + \)\(54\!\cdots\!68\)\( T^{34} - \)\(12\!\cdots\!12\)\( T^{35} + \)\(24\!\cdots\!26\)\( T^{36} - \)\(34\!\cdots\!72\)\( T^{37} + \)\(43\!\cdots\!61\)\( T^{38} \))
$43$ (\( 1 + 2 T + 43 T^{2} \))(\( 1 - 9 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 3 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 23 T + 387 T^{2} + 4389 T^{3} + 42992 T^{4} + 339324 T^{5} + 2433499 T^{6} + 14590932 T^{7} + 79492208 T^{8} + 348956223 T^{9} + 1323075987 T^{10} + 3381194189 T^{11} + 6321363049 T^{12} \))(\( 1 + 23 T + 479 T^{2} + 6374 T^{3} + 76418 T^{4} + 709137 T^{5} + 5980176 T^{6} + 41069820 T^{7} + 257147568 T^{8} + 1311194313 T^{9} + 6075765926 T^{10} + 21791437574 T^{11} + 70417044197 T^{12} + 145391350127 T^{13} + 271818611107 T^{14} \))(\( 1 + 17 T + 296 T^{2} + 2964 T^{3} + 30412 T^{4} + 204488 T^{5} + 1500729 T^{6} + 6996402 T^{7} + 46431846 T^{8} + 200588410 T^{9} + 1996569378 T^{10} + 12936347298 T^{11} + 119318460603 T^{12} + 699103778888 T^{13} + 4470820768516 T^{14} + 18736520077236 T^{15} + 80458308887672 T^{16} + 198699404719217 T^{17} + 502592611936843 T^{18} \))(\( 1 + 5 T + 261 T^{2} + 1245 T^{3} + 35554 T^{4} + 156012 T^{5} + 3213081 T^{6} + 12782846 T^{7} + 210358865 T^{8} + 746239890 T^{9} + 10371652676 T^{10} + 32088315270 T^{11} + 388953541385 T^{12} + 1016325736922 T^{13} + 10984884535881 T^{14} + 22935081209316 T^{15} + 224749741844146 T^{16} + 338414170828215 T^{17} + 3050620272453861 T^{18} + 2512963059684215 T^{19} + 21611482313284249 T^{20} \))(\( 1 - 9 T + 250 T^{2} - 1582 T^{3} + 28850 T^{4} - 135120 T^{5} + 2196230 T^{6} - 7631733 T^{7} + 128983874 T^{8} - 332981628 T^{9} + 6455485150 T^{10} - 13493607454 T^{11} + 291017666658 T^{12} - 580225120522 T^{13} + 11936192042350 T^{14} - 26474370297396 T^{15} + 440970197415074 T^{16} - 1121929185721719 T^{17} + 13883167169105270 T^{18} - 36728130732777840 T^{19} + 337204578008788850 T^{20} - 795101512084085626 T^{21} + 5402870578321062250 T^{22} - 8363643655241004363 T^{23} + 39959630797262576401 T^{24} \))(\( 1 - 35 T + 948 T^{2} - 18609 T^{3} + 311924 T^{4} - 4456696 T^{5} + 56842554 T^{6} - 650599032 T^{7} + 6808036286 T^{8} - 65426928661 T^{9} + 582811610820 T^{10} - 4824699695991 T^{11} + 37308717328405 T^{12} - 269691818544208 T^{13} + 1827487675896028 T^{14} - 11596748197400944 T^{15} + 68983818340220845 T^{16} - 383597398729156437 T^{17} + 1992516917883026820 T^{18} - 9618310912725684823 T^{19} + 43036069014571596014 T^{20} - \)\(17\!\cdots\!24\)\( T^{21} + \)\(66\!\cdots\!54\)\( T^{22} - \)\(22\!\cdots\!28\)\( T^{23} + \)\(67\!\cdots\!76\)\( T^{24} - \)\(17\!\cdots\!63\)\( T^{25} + \)\(37\!\cdots\!48\)\( T^{26} - \)\(60\!\cdots\!05\)\( T^{27} + \)\(73\!\cdots\!49\)\( T^{28} \))(\( 1 + T + 344 T^{2} + 871 T^{3} + 63697 T^{4} + 219562 T^{5} + 8434802 T^{6} + 33110644 T^{7} + 878395244 T^{8} + 3640858528 T^{9} + 75425601946 T^{10} + 316938704678 T^{11} + 5495978507147 T^{12} + 22831627466285 T^{13} + 346175873937401 T^{14} + 1397438362729482 T^{15} + 19080219749635938 T^{16} + 73841556010605200 T^{17} + 927168548185330818 T^{18} + 3397972040413139358 T^{19} + 39868247571969225174 T^{20} + \)\(13\!\cdots\!00\)\( T^{21} + \)\(15\!\cdots\!66\)\( T^{22} + \)\(47\!\cdots\!82\)\( T^{23} + \)\(50\!\cdots\!43\)\( T^{24} + \)\(14\!\cdots\!65\)\( T^{25} + \)\(14\!\cdots\!29\)\( T^{26} + \)\(37\!\cdots\!78\)\( T^{27} + \)\(37\!\cdots\!78\)\( T^{28} + \)\(78\!\cdots\!72\)\( T^{29} + \)\(81\!\cdots\!08\)\( T^{30} + \)\(13\!\cdots\!44\)\( T^{31} + \)\(14\!\cdots\!86\)\( T^{32} + \)\(16\!\cdots\!38\)\( T^{33} + \)\(20\!\cdots\!79\)\( T^{34} + \)\(11\!\cdots\!71\)\( T^{35} + \)\(20\!\cdots\!92\)\( T^{36} + \)\(25\!\cdots\!49\)\( T^{37} + \)\(10\!\cdots\!07\)\( T^{38} \))(\( 1 + T + 344 T^{2} + 871 T^{3} + 63697 T^{4} + 219562 T^{5} + 8434802 T^{6} + 33110644 T^{7} + 878395244 T^{8} + 3640858528 T^{9} + 75425601946 T^{10} + 316938704678 T^{11} + 5495978507147 T^{12} + 22831627466285 T^{13} + 346175873937401 T^{14} + 1397438362729482 T^{15} + 19080219749635938 T^{16} + 73841556010605200 T^{17} + 927168548185330818 T^{18} + 3397972040413139358 T^{19} + 39868247571969225174 T^{20} + \)\(13\!\cdots\!00\)\( T^{21} + \)\(15\!\cdots\!66\)\( T^{22} + \)\(47\!\cdots\!82\)\( T^{23} + \)\(50\!\cdots\!43\)\( T^{24} + \)\(14\!\cdots\!65\)\( T^{25} + \)\(14\!\cdots\!29\)\( T^{26} + \)\(37\!\cdots\!78\)\( T^{27} + \)\(37\!\cdots\!78\)\( T^{28} + \)\(78\!\cdots\!72\)\( T^{29} + \)\(81\!\cdots\!08\)\( T^{30} + \)\(13\!\cdots\!44\)\( T^{31} + \)\(14\!\cdots\!86\)\( T^{32} + \)\(16\!\cdots\!38\)\( T^{33} + \)\(20\!\cdots\!79\)\( T^{34} + \)\(11\!\cdots\!71\)\( T^{35} + \)\(20\!\cdots\!92\)\( T^{36} + \)\(25\!\cdots\!49\)\( T^{37} + \)\(10\!\cdots\!07\)\( T^{38} \))
$47$ (\( 1 - 6 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 13 T + 179 T^{2} + 1149 T^{3} + 7700 T^{4} + 18850 T^{5} + 155063 T^{6} + 885950 T^{7} + 17009300 T^{8} + 119292627 T^{9} + 873462899 T^{10} + 2981485091 T^{11} + 10779215329 T^{12} \))(\( 1 - 10 T + 175 T^{2} - 1405 T^{3} + 16332 T^{4} - 102894 T^{5} + 981162 T^{6} - 5586582 T^{7} + 46114614 T^{8} - 227292846 T^{9} + 1695637236 T^{10} - 6855951805 T^{11} + 40135376225 T^{12} - 107792153290 T^{13} + 506623120463 T^{14} \))(\( 1 + 11 T + 294 T^{2} + 2746 T^{3} + 41588 T^{4} + 342626 T^{5} + 3795051 T^{6} + 27449520 T^{7} + 244456728 T^{8} + 1529271474 T^{9} + 11489466216 T^{10} + 60635989680 T^{11} + 394013579973 T^{12} + 1671905582306 T^{13} + 9538000151116 T^{14} + 29599725293434 T^{15} + 148947197416122 T^{16} + 261924153279371 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 3 T + 297 T^{2} + 569 T^{3} + 40016 T^{4} + 33182 T^{5} + 3326029 T^{6} - 635502 T^{7} + 201032939 T^{8} - 174090390 T^{9} + 10072202268 T^{10} - 8182248330 T^{11} + 444081762251 T^{12} - 65979724146 T^{13} + 16229960516749 T^{14} + 7610126022274 T^{15} + 431341080605264 T^{16} + 288268555543447 T^{17} + 7071952138543017 T^{18} + 3357391419308301 T^{19} + 52599132235830049 T^{20} \))(\( 1 - 5 T + 415 T^{2} - 1807 T^{3} + 82559 T^{4} - 319377 T^{5} + 10497212 T^{6} - 36483779 T^{7} + 954387597 T^{8} - 2987603102 T^{9} + 65511558741 T^{10} - 183656784354 T^{11} + 3484379811974 T^{12} - 8631868864638 T^{13} + 144715033258869 T^{14} - 310181916858946 T^{15} + 4657107023716557 T^{16} - 8367372550141453 T^{17} + 113151708502162748 T^{18} - 161803772344111551 T^{19} + 1965836015508326399 T^{20} - 2022268764896699969 T^{21} + 21828639877869470335 T^{22} - 12360796075420061515 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 6 T + 382 T^{2} + 1059 T^{3} + 61842 T^{4} - 36571 T^{5} + 5929810 T^{6} - 26059681 T^{7} + 432153524 T^{8} - 3250819243 T^{9} + 30303276714 T^{10} - 230841065832 T^{11} + 2036943202521 T^{12} - 12145587908550 T^{13} + 110601003501836 T^{14} - 570842631701850 T^{15} + 4499607534368889 T^{16} - 23966611977875736 T^{17} + 147870323619048234 T^{18} - 745559162041569701 T^{19} + 4658275890382169396 T^{20} - 13202436906490352303 T^{21} + \)\(14\!\cdots\!10\)\( T^{22} - 40927720531841291957 T^{23} + \)\(32\!\cdots\!58\)\( T^{24} + \)\(26\!\cdots\!77\)\( T^{25} + \)\(44\!\cdots\!62\)\( T^{26} + \)\(32\!\cdots\!62\)\( T^{27} + \)\(25\!\cdots\!69\)\( T^{28} \))(\( 1 + 16 T + 484 T^{2} + 6160 T^{3} + 109613 T^{4} + 1168912 T^{5} + 15718308 T^{6} + 145224672 T^{7} + 1627876934 T^{8} + 13355364480 T^{9} + 131952351916 T^{10} + 982478716304 T^{11} + 8902379674627 T^{12} + 61460733297054 T^{13} + 526276152172489 T^{14} + 3436429531049116 T^{15} + 28340890777410034 T^{16} + 177552252919214706 T^{17} + 1420668622772617420 T^{18} + 8603542516341208616 T^{19} + 66771425270313018740 T^{20} + \)\(39\!\cdots\!54\)\( T^{21} + \)\(29\!\cdots\!82\)\( T^{22} + \)\(16\!\cdots\!96\)\( T^{23} + \)\(12\!\cdots\!23\)\( T^{24} + \)\(66\!\cdots\!66\)\( T^{25} + \)\(45\!\cdots\!01\)\( T^{26} + \)\(23\!\cdots\!44\)\( T^{27} + \)\(14\!\cdots\!72\)\( T^{28} + \)\(70\!\cdots\!20\)\( T^{29} + \)\(40\!\cdots\!02\)\( T^{30} + \)\(16\!\cdots\!52\)\( T^{31} + \)\(85\!\cdots\!16\)\( T^{32} + \)\(30\!\cdots\!28\)\( T^{33} + \)\(13\!\cdots\!59\)\( T^{34} + \)\(34\!\cdots\!60\)\( T^{35} + \)\(12\!\cdots\!08\)\( T^{36} + \)\(20\!\cdots\!24\)\( T^{37} + \)\(58\!\cdots\!83\)\( T^{38} \))(\( 1 - 16 T + 484 T^{2} - 6160 T^{3} + 109613 T^{4} - 1168912 T^{5} + 15718308 T^{6} - 145224672 T^{7} + 1627876934 T^{8} - 13355364480 T^{9} + 131952351916 T^{10} - 982478716304 T^{11} + 8902379674627 T^{12} - 61460733297054 T^{13} + 526276152172489 T^{14} - 3436429531049116 T^{15} + 28340890777410034 T^{16} - 177552252919214706 T^{17} + 1420668622772617420 T^{18} - 8603542516341208616 T^{19} + 66771425270313018740 T^{20} - \)\(39\!\cdots\!54\)\( T^{21} + \)\(29\!\cdots\!82\)\( T^{22} - \)\(16\!\cdots\!96\)\( T^{23} + \)\(12\!\cdots\!23\)\( T^{24} - \)\(66\!\cdots\!66\)\( T^{25} + \)\(45\!\cdots\!01\)\( T^{26} - \)\(23\!\cdots\!44\)\( T^{27} + \)\(14\!\cdots\!72\)\( T^{28} - \)\(70\!\cdots\!20\)\( T^{29} + \)\(40\!\cdots\!02\)\( T^{30} - \)\(16\!\cdots\!52\)\( T^{31} + \)\(85\!\cdots\!16\)\( T^{32} - \)\(30\!\cdots\!28\)\( T^{33} + \)\(13\!\cdots\!59\)\( T^{34} - \)\(34\!\cdots\!60\)\( T^{35} + \)\(12\!\cdots\!08\)\( T^{36} - \)\(20\!\cdots\!24\)\( T^{37} + \)\(58\!\cdots\!83\)\( T^{38} \))
$53$ (\( 1 + 4 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 - 5 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 + 6 T + 180 T^{2} + 711 T^{3} + 15575 T^{4} + 43759 T^{5} + 941335 T^{6} + 2319227 T^{7} + 43750175 T^{8} + 105851547 T^{9} + 1420286580 T^{10} + 2509172958 T^{11} + 22164361129 T^{12} \))(\( 1 - T + 341 T^{2} - 296 T^{3} + 51270 T^{4} - 37529 T^{5} + 4404456 T^{6} - 2612924 T^{7} + 233436168 T^{8} - 105418961 T^{9} + 7632923790 T^{10} - 2335582376 T^{11} + 142604663113 T^{12} - 22164361129 T^{13} + 1174711139837 T^{14} \))(\( 1 - 12 T + 213 T^{2} - 1395 T^{3} + 14650 T^{4} - 46468 T^{5} + 520199 T^{6} - 737781 T^{7} + 25113787 T^{8} - 45490740 T^{9} + 1331030711 T^{10} - 2072426829 T^{11} + 77445666523 T^{12} - 366654871108 T^{13} + 6126563972450 T^{14} - 30919283774955 T^{15} + 250213472785281 T^{16} - 747116284936332 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 12 T + 400 T^{2} + 3917 T^{3} + 76415 T^{4} + 642181 T^{5} + 9256935 T^{6} + 67387863 T^{7} + 783260708 T^{8} + 4945323863 T^{9} + 48339661722 T^{10} + 262102164739 T^{11} + 2200179328772 T^{12} + 10032502879851 T^{13} + 73041669735735 T^{14} + 268557199890233 T^{15} + 1693689655672535 T^{16} + 4601343534741529 T^{17} + 24903876164544400 T^{18} + 39597163101625596 T^{19} + 174887470365513049 T^{20} \))(\( 1 + 20 T + 391 T^{2} + 5061 T^{3} + 66078 T^{4} + 688896 T^{5} + 7195370 T^{6} + 64055235 T^{7} + 576501890 T^{8} + 4575784579 T^{9} + 37263039957 T^{10} + 273998533065 T^{11} + 2092888845610 T^{12} + 14521922252445 T^{13} + 104671879239213 T^{14} + 681229080767783 T^{15} + 4548877209509090 T^{16} + 26787610580055855 T^{17} + 159480779136772730 T^{18} + 809253805389149952 T^{19} + 4113995823001912158 T^{20} + 16700103538110595113 T^{21} + 68381000912915602159 T^{22} + \)\(18\!\cdots\!40\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - T + 336 T^{2} - 657 T^{3} + 55960 T^{4} - 176338 T^{5} + 6430150 T^{6} - 27382410 T^{7} + 584794578 T^{8} - 2927367915 T^{9} + 44477723032 T^{10} - 239086649523 T^{11} + 2895999634685 T^{12} - 15648142913420 T^{13} + 164010413112036 T^{14} - 829351574411260 T^{15} + 8134862973830165 T^{16} - 35594503121035671 T^{17} + 350950628507258392 T^{18} - 1224212068405807095 T^{19} + 12961598213073158562 T^{20} - 32166422062584067170 T^{21} + \)\(40\!\cdots\!50\)\( T^{22} - \)\(58\!\cdots\!54\)\( T^{23} + \)\(97\!\cdots\!40\)\( T^{24} - \)\(60\!\cdots\!29\)\( T^{25} + \)\(16\!\cdots\!76\)\( T^{26} - \)\(26\!\cdots\!73\)\( T^{27} + \)\(13\!\cdots\!69\)\( T^{28} \))(\( 1 + 3 T + 567 T^{2} + 2502 T^{3} + 160981 T^{4} + 895883 T^{5} + 30788750 T^{6} + 196647553 T^{7} + 4470135169 T^{8} + 30664108806 T^{9} + 523233584274 T^{10} + 3674448291210 T^{11} + 51021444874293 T^{12} + 354473218824735 T^{13} + 4222402900290382 T^{14} + 28331651701927905 T^{15} + 299751829537727446 T^{16} + 1909196315586417497 T^{17} + 18362342764761491681 T^{18} + \)\(10\!\cdots\!32\)\( T^{19} + \)\(97\!\cdots\!93\)\( T^{20} + \)\(53\!\cdots\!73\)\( T^{21} + \)\(44\!\cdots\!42\)\( T^{22} + \)\(22\!\cdots\!05\)\( T^{23} + \)\(17\!\cdots\!26\)\( T^{24} + \)\(78\!\cdots\!15\)\( T^{25} + \)\(59\!\cdots\!41\)\( T^{26} + \)\(22\!\cdots\!10\)\( T^{27} + \)\(17\!\cdots\!42\)\( T^{28} + \)\(53\!\cdots\!94\)\( T^{29} + \)\(41\!\cdots\!93\)\( T^{30} + \)\(96\!\cdots\!73\)\( T^{31} + \)\(80\!\cdots\!50\)\( T^{32} + \)\(12\!\cdots\!27\)\( T^{33} + \)\(11\!\cdots\!17\)\( T^{34} + \)\(96\!\cdots\!42\)\( T^{35} + \)\(11\!\cdots\!71\)\( T^{36} + \)\(32\!\cdots\!67\)\( T^{37} + \)\(57\!\cdots\!17\)\( T^{38} \))(\( 1 - 3 T + 567 T^{2} - 2502 T^{3} + 160981 T^{4} - 895883 T^{5} + 30788750 T^{6} - 196647553 T^{7} + 4470135169 T^{8} - 30664108806 T^{9} + 523233584274 T^{10} - 3674448291210 T^{11} + 51021444874293 T^{12} - 354473218824735 T^{13} + 4222402900290382 T^{14} - 28331651701927905 T^{15} + 299751829537727446 T^{16} - 1909196315586417497 T^{17} + 18362342764761491681 T^{18} - \)\(10\!\cdots\!32\)\( T^{19} + \)\(97\!\cdots\!93\)\( T^{20} - \)\(53\!\cdots\!73\)\( T^{21} + \)\(44\!\cdots\!42\)\( T^{22} - \)\(22\!\cdots\!05\)\( T^{23} + \)\(17\!\cdots\!26\)\( T^{24} - \)\(78\!\cdots\!15\)\( T^{25} + \)\(59\!\cdots\!41\)\( T^{26} - \)\(22\!\cdots\!10\)\( T^{27} + \)\(17\!\cdots\!42\)\( T^{28} - \)\(53\!\cdots\!94\)\( T^{29} + \)\(41\!\cdots\!93\)\( T^{30} - \)\(96\!\cdots\!73\)\( T^{31} + \)\(80\!\cdots\!50\)\( T^{32} - \)\(12\!\cdots\!27\)\( T^{33} + \)\(11\!\cdots\!17\)\( T^{34} - \)\(96\!\cdots\!42\)\( T^{35} + \)\(11\!\cdots\!71\)\( T^{36} - \)\(32\!\cdots\!67\)\( T^{37} + \)\(57\!\cdots\!17\)\( T^{38} \))
$59$ (\( 1 - 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 2 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 - 23 T + 517 T^{2} - 7027 T^{3} + 89876 T^{4} - 843564 T^{5} + 7417047 T^{6} - 49770276 T^{7} + 312858356 T^{8} - 1443198233 T^{9} + 6264675637 T^{10} - 16443258877 T^{11} + 42180533641 T^{12} \))(\( 1 - 4 T + 192 T^{2} - 766 T^{3} + 17341 T^{4} - 80260 T^{5} + 1108838 T^{6} - 5770956 T^{7} + 65421442 T^{8} - 279385060 T^{9} + 3561477239 T^{10} - 9281898526 T^{11} + 137265465408 T^{12} - 168722134564 T^{13} + 2488651484819 T^{14} \))(\( 1 + 13 T + 322 T^{2} + 3340 T^{3} + 51330 T^{4} + 449070 T^{5} + 5322163 T^{6} + 40405236 T^{7} + 404985128 T^{8} + 2715863918 T^{9} + 23894122552 T^{10} + 140650626516 T^{11} + 1093060514777 T^{12} + 5441543304270 T^{13} + 36697064267670 T^{14} + 140882982360940 T^{15} + 801345778111718 T^{16} + 1908795688856173 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 21 T + 681 T^{2} + 10267 T^{3} + 190862 T^{4} + 2253932 T^{5} + 30521881 T^{6} + 294274000 T^{7} + 3158394645 T^{8} + 25325572642 T^{9} + 223520098228 T^{10} + 1494208785878 T^{11} + 10994371759245 T^{12} + 60437699846000 T^{13} + 369844650476041 T^{14} + 1611390755093668 T^{15} + 8050661011788542 T^{16} + 25550984794636673 T^{17} + 99991528008542601 T^{18} + 181922912191753719 T^{19} + 511116753300641401 T^{20} \))(\( 1 - T + 145 T^{2} - 185 T^{3} + 13595 T^{4} - 45839 T^{5} + 1031864 T^{6} - 5048697 T^{7} + 67176379 T^{8} - 468846228 T^{9} + 4088157703 T^{10} - 33569908242 T^{11} + 223918464210 T^{12} - 1980624586278 T^{13} + 14230876964143 T^{14} - 96291169460412 T^{15} + 814000435015819 T^{16} - 3609436163588403 T^{17} + 43524574164936824 T^{18} - 114077295412618141 T^{19} + 1996159799230743995 T^{20} - 1602654226451163715 T^{21} + 74111929228593003145 T^{22} - 30155888444737842659 T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 + 30 T + 779 T^{2} + 13424 T^{3} + 209000 T^{4} + 2609668 T^{5} + 30561096 T^{6} + 309458644 T^{7} + 3067074882 T^{8} + 27703864660 T^{9} + 254359244333 T^{10} + 2182190578586 T^{11} + 19036964650525 T^{12} + 153468834699824 T^{13} + 1232796925002464 T^{14} + 9054661247289616 T^{15} + 66267673948477525 T^{16} + 448176118839414094 T^{17} + 3082162787270165213 T^{18} + 19806166021641373340 T^{19} + \)\(12\!\cdots\!62\)\( T^{20} + \)\(77\!\cdots\!36\)\( T^{21} + \)\(44\!\cdots\!16\)\( T^{22} + \)\(22\!\cdots\!52\)\( T^{23} + \)\(10\!\cdots\!00\)\( T^{24} + \)\(40\!\cdots\!16\)\( T^{25} + \)\(13\!\cdots\!99\)\( T^{26} + \)\(31\!\cdots\!70\)\( T^{27} + \)\(61\!\cdots\!61\)\( T^{28} \))(\( 1 + 22 T + 856 T^{2} + 14476 T^{3} + 332289 T^{4} + 4698478 T^{5} + 81704742 T^{6} + 1010089898 T^{7} + 14593446476 T^{8} + 161821016520 T^{9} + 2033108581496 T^{10} + 20534797016812 T^{11} + 230305968632691 T^{12} + 2139115771638734 T^{13} + 21767359845197299 T^{14} + 186987122445937478 T^{15} + 1744555351273058604 T^{16} + 13900046084767866226 T^{17} + \)\(11\!\cdots\!16\)\( T^{18} + \)\(88\!\cdots\!88\)\( T^{19} + \)\(70\!\cdots\!44\)\( T^{20} + \)\(48\!\cdots\!06\)\( T^{21} + \)\(35\!\cdots\!16\)\( T^{22} + \)\(22\!\cdots\!58\)\( T^{23} + \)\(15\!\cdots\!01\)\( T^{24} + \)\(90\!\cdots\!94\)\( T^{25} + \)\(57\!\cdots\!29\)\( T^{26} + \)\(30\!\cdots\!52\)\( T^{27} + \)\(17\!\cdots\!44\)\( T^{28} + \)\(82\!\cdots\!20\)\( T^{29} + \)\(44\!\cdots\!84\)\( T^{30} + \)\(17\!\cdots\!38\)\( T^{31} + \)\(85\!\cdots\!18\)\( T^{32} + \)\(29\!\cdots\!58\)\( T^{33} + \)\(12\!\cdots\!11\)\( T^{34} + \)\(31\!\cdots\!16\)\( T^{35} + \)\(10\!\cdots\!64\)\( T^{36} + \)\(16\!\cdots\!62\)\( T^{37} + \)\(44\!\cdots\!39\)\( T^{38} \))(\( 1 - 22 T + 856 T^{2} - 14476 T^{3} + 332289 T^{4} - 4698478 T^{5} + 81704742 T^{6} - 1010089898 T^{7} + 14593446476 T^{8} - 161821016520 T^{9} + 2033108581496 T^{10} - 20534797016812 T^{11} + 230305968632691 T^{12} - 2139115771638734 T^{13} + 21767359845197299 T^{14} - 186987122445937478 T^{15} + 1744555351273058604 T^{16} - 13900046084767866226 T^{17} + \)\(11\!\cdots\!16\)\( T^{18} - \)\(88\!\cdots\!88\)\( T^{19} + \)\(70\!\cdots\!44\)\( T^{20} - \)\(48\!\cdots\!06\)\( T^{21} + \)\(35\!\cdots\!16\)\( T^{22} - \)\(22\!\cdots\!58\)\( T^{23} + \)\(15\!\cdots\!01\)\( T^{24} - \)\(90\!\cdots\!94\)\( T^{25} + \)\(57\!\cdots\!29\)\( T^{26} - \)\(30\!\cdots\!52\)\( T^{27} + \)\(17\!\cdots\!44\)\( T^{28} - \)\(82\!\cdots\!20\)\( T^{29} + \)\(44\!\cdots\!84\)\( T^{30} - \)\(17\!\cdots\!38\)\( T^{31} + \)\(85\!\cdots\!18\)\( T^{32} - \)\(29\!\cdots\!58\)\( T^{33} + \)\(12\!\cdots\!11\)\( T^{34} - \)\(31\!\cdots\!16\)\( T^{35} + \)\(10\!\cdots\!64\)\( T^{36} - \)\(16\!\cdots\!62\)\( T^{37} + \)\(44\!\cdots\!39\)\( T^{38} \))
$61$ (\( 1 + 12 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 17 T + 360 T^{2} + 3895 T^{3} + 48866 T^{4} + 394643 T^{5} + 3736755 T^{6} + 24073223 T^{7} + 181830386 T^{8} + 884090995 T^{9} + 4984502760 T^{10} + 14358137117 T^{11} + 51520374361 T^{12} \))(\( 1 - 3 T + 162 T^{2} + 61 T^{3} + 11799 T^{4} + 53561 T^{5} + 692826 T^{6} + 4721098 T^{7} + 42262386 T^{8} + 199300481 T^{9} + 2678148819 T^{10} + 844596301 T^{11} + 136824600762 T^{12} - 154561123083 T^{13} + 3142742836021 T^{14} \))(\( 1 + 23 T + 639 T^{2} + 9936 T^{3} + 162903 T^{4} + 1936183 T^{5} + 23410964 T^{6} + 223459838 T^{7} + 2143248067 T^{8} + 16725285500 T^{9} + 130738132087 T^{10} + 831494057198 T^{11} + 5313844019684 T^{12} + 26808081964903 T^{13} + 137587271221803 T^{14} + 511906439650896 T^{15} + 2008212672217419 T^{16} + 4409268198937463 T^{17} + 11694146092834141 T^{18} \))(\( 1 - 21 T + 574 T^{2} - 8285 T^{3} + 130622 T^{4} - 1430621 T^{5} + 16656811 T^{6} - 148114329 T^{7} + 1428377529 T^{8} - 11034985676 T^{9} + 95393666726 T^{10} - 673134126236 T^{11} + 5314992785409 T^{12} - 33619138510749 T^{13} + 230627556673051 T^{14} - 1208297204732921 T^{15} + 6729694339782542 T^{16} - 26037624396433985 T^{17} + 110039997660439294 T^{18} - 245577067949516961 T^{19} + 713342911662882601 T^{20} \))(\( 1 - 21 T + 518 T^{2} - 7501 T^{3} + 112665 T^{4} - 1279504 T^{5} + 14865165 T^{6} - 142744822 T^{7} + 1409215247 T^{8} - 11998030813 T^{9} + 106302314133 T^{10} - 833215395315 T^{11} + 6881799952526 T^{12} - 50826139114215 T^{13} + 395550910888893 T^{14} - 2723325031965553 T^{15} + 19511770244737727 T^{16} - 120561748648103422 T^{17} + 765858865738034565 T^{18} - 4021152029660213584 T^{19} + 21598704418838663865 T^{20} - 87717789842348891641 T^{21} + \)\(36\!\cdots\!18\)\( T^{22} - \)\(91\!\cdots\!81\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 3 T + 403 T^{2} - 1236 T^{3} + 82870 T^{4} - 256913 T^{5} + 11777036 T^{6} - 35236793 T^{7} + 1301617432 T^{8} - 3621165890 T^{9} + 118008463253 T^{10} - 302860230171 T^{11} + 9025363533113 T^{12} - 21515936469586 T^{13} + 592385566983864 T^{14} - 1312472124644746 T^{15} + 33583377706713473 T^{16} - 68743517904443751 T^{17} + 1633926418855380773 T^{18} - 3058423316001372890 T^{19} + 67059817371443460952 T^{20} - \)\(11\!\cdots\!53\)\( T^{21} + \)\(22\!\cdots\!16\)\( T^{22} - \)\(30\!\cdots\!33\)\( T^{23} + \)\(59\!\cdots\!70\)\( T^{24} - \)\(53\!\cdots\!96\)\( T^{25} + \)\(10\!\cdots\!63\)\( T^{26} - \)\(48\!\cdots\!43\)\( T^{27} + \)\(98\!\cdots\!41\)\( T^{28} \))(\( 1 + 10 T + 626 T^{2} + 5698 T^{3} + 190550 T^{4} + 1635166 T^{5} + 38304701 T^{6} + 317838308 T^{7} + 5796377505 T^{8} + 47102610816 T^{9} + 708748940180 T^{10} + 5648696348532 T^{11} + 72969293776809 T^{12} + 567193955198722 T^{13} + 6483700500012836 T^{14} + 48727868334365896 T^{15} + 504701130295649477 T^{16} + 3631648606711639594 T^{17} + 34711764327080423751 T^{18} + \)\(23\!\cdots\!80\)\( T^{19} + \)\(21\!\cdots\!11\)\( T^{20} + \)\(13\!\cdots\!74\)\( T^{21} + \)\(11\!\cdots\!37\)\( T^{22} + \)\(67\!\cdots\!36\)\( T^{23} + \)\(54\!\cdots\!36\)\( T^{24} + \)\(29\!\cdots\!42\)\( T^{25} + \)\(22\!\cdots\!89\)\( T^{26} + \)\(10\!\cdots\!92\)\( T^{27} + \)\(82\!\cdots\!80\)\( T^{28} + \)\(33\!\cdots\!16\)\( T^{29} + \)\(25\!\cdots\!05\)\( T^{30} + \)\(84\!\cdots\!68\)\( T^{31} + \)\(62\!\cdots\!81\)\( T^{32} + \)\(16\!\cdots\!06\)\( T^{33} + \)\(11\!\cdots\!50\)\( T^{34} + \)\(20\!\cdots\!78\)\( T^{35} + \)\(14\!\cdots\!46\)\( T^{36} + \)\(13\!\cdots\!10\)\( T^{37} + \)\(83\!\cdots\!41\)\( T^{38} \))(\( 1 + 10 T + 626 T^{2} + 5698 T^{3} + 190550 T^{4} + 1635166 T^{5} + 38304701 T^{6} + 317838308 T^{7} + 5796377505 T^{8} + 47102610816 T^{9} + 708748940180 T^{10} + 5648696348532 T^{11} + 72969293776809 T^{12} + 567193955198722 T^{13} + 6483700500012836 T^{14} + 48727868334365896 T^{15} + 504701130295649477 T^{16} + 3631648606711639594 T^{17} + 34711764327080423751 T^{18} + \)\(23\!\cdots\!80\)\( T^{19} + \)\(21\!\cdots\!11\)\( T^{20} + \)\(13\!\cdots\!74\)\( T^{21} + \)\(11\!\cdots\!37\)\( T^{22} + \)\(67\!\cdots\!36\)\( T^{23} + \)\(54\!\cdots\!36\)\( T^{24} + \)\(29\!\cdots\!42\)\( T^{25} + \)\(22\!\cdots\!89\)\( T^{26} + \)\(10\!\cdots\!92\)\( T^{27} + \)\(82\!\cdots\!80\)\( T^{28} + \)\(33\!\cdots\!16\)\( T^{29} + \)\(25\!\cdots\!05\)\( T^{30} + \)\(84\!\cdots\!68\)\( T^{31} + \)\(62\!\cdots\!81\)\( T^{32} + \)\(16\!\cdots\!06\)\( T^{33} + \)\(11\!\cdots\!50\)\( T^{34} + \)\(20\!\cdots\!78\)\( T^{35} + \)\(14\!\cdots\!46\)\( T^{36} + \)\(13\!\cdots\!10\)\( T^{37} + \)\(83\!\cdots\!41\)\( T^{38} \))
$67$ (\( 1 + 13 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 - 16 T + 136 T^{2} - 618 T^{3} + 6551 T^{4} - 107383 T^{5} + 1218805 T^{6} - 7194661 T^{7} + 29407439 T^{8} - 185871534 T^{9} + 2740552456 T^{10} - 21602001712 T^{11} + 90458382169 T^{12} \))(\( 1 + 28 T + 648 T^{2} + 9931 T^{3} + 135284 T^{4} + 1472821 T^{5} + 14791793 T^{6} + 125329735 T^{7} + 991050131 T^{8} + 6611493469 T^{9} + 40688421692 T^{10} + 200120782651 T^{11} + 874881069336 T^{12} + 2532834700732 T^{13} + 6060711605323 T^{14} \))(\( 1 + 7 T + 512 T^{2} + 3309 T^{3} + 121957 T^{4} + 709373 T^{5} + 17665941 T^{6} + 90079691 T^{7} + 1710168149 T^{8} + 7410244257 T^{9} + 114581265983 T^{10} + 404367732899 T^{11} + 5313261412983 T^{12} + 14294661157133 T^{13} + 164657207674399 T^{14} + 299326786597221 T^{15} + 3103084341925376 T^{16} + 2842473742896487 T^{17} + 27206534396294947 T^{18} \))(\( 1 - 25 T + 823 T^{2} - 14582 T^{3} + 277413 T^{4} - 3802804 T^{5} + 52742388 T^{6} - 583236206 T^{7} + 6383677852 T^{8} - 58042209474 T^{9} + 518294442246 T^{10} - 3888828034758 T^{11} + 28656329877628 T^{12} - 175415871025178 T^{13} + 1062818242416948 T^{14} - 5134261157400028 T^{15} + 25094331172648797 T^{16} - 88377296628819986 T^{17} + 334193698629115543 T^{18} - 680163359907373675 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 21 T + 497 T^{2} - 6780 T^{3} + 110140 T^{4} - 1283885 T^{5} + 16908065 T^{6} - 170443072 T^{7} + 1929071601 T^{8} - 17522688286 T^{9} + 176526224390 T^{10} - 1441791364400 T^{11} + 13026678692100 T^{12} - 96600021414800 T^{13} + 792426221286710 T^{14} - 5270176296962218 T^{15} + 38872955249414721 T^{16} - 230119470821408704 T^{17} + 1529476205508292985 T^{18} - 7781256719400119855 T^{19} + 44724294006088439740 T^{20} - \)\(18\!\cdots\!60\)\( T^{21} + \)\(90\!\cdots\!53\)\( T^{22} - \)\(25\!\cdots\!43\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 - 22 T + 694 T^{2} - 10439 T^{3} + 193492 T^{4} - 2285571 T^{5} + 32492463 T^{6} - 328286398 T^{7} + 3998651363 T^{8} - 36396393149 T^{9} + 399795726501 T^{10} - 3357364823787 T^{11} + 33894768425127 T^{12} - 263865853266971 T^{13} + 2457414462651723 T^{14} - 17679012168887057 T^{15} + 152153615460395103 T^{16} - 1009771116496649481 T^{17} + 8056332060004557621 T^{18} - 49139684194707691943 T^{19} + \)\(36\!\cdots\!47\)\( T^{20} - \)\(19\!\cdots\!54\)\( T^{21} + \)\(13\!\cdots\!83\)\( T^{22} - \)\(62\!\cdots\!37\)\( T^{23} + \)\(35\!\cdots\!08\)\( T^{24} - \)\(12\!\cdots\!37\)\( T^{25} + \)\(56\!\cdots\!34\)\( T^{26} - \)\(12\!\cdots\!14\)\( T^{27} + \)\(36\!\cdots\!29\)\( T^{28} \))(\( 1 + 16 T + 796 T^{2} + 11174 T^{3} + 308411 T^{4} + 3871830 T^{5} + 77929745 T^{6} + 887961160 T^{7} + 14507359854 T^{8} + 151770335876 T^{9} + 2129091057322 T^{10} + 20632309944852 T^{11} + 257044091804278 T^{12} + 2322130118823236 T^{13} + 26251828334139690 T^{14} + 221960997863784176 T^{15} + 2309276440782195440 T^{16} + 18302785098419669466 T^{17} + \)\(17\!\cdots\!16\)\( T^{18} + \)\(13\!\cdots\!62\)\( T^{19} + \)\(11\!\cdots\!72\)\( T^{20} + \)\(82\!\cdots\!74\)\( T^{21} + \)\(69\!\cdots\!20\)\( T^{22} + \)\(44\!\cdots\!96\)\( T^{23} + \)\(35\!\cdots\!30\)\( T^{24} + \)\(21\!\cdots\!84\)\( T^{25} + \)\(15\!\cdots\!94\)\( T^{26} + \)\(83\!\cdots\!32\)\( T^{27} + \)\(57\!\cdots\!34\)\( T^{28} + \)\(27\!\cdots\!24\)\( T^{29} + \)\(17\!\cdots\!82\)\( T^{30} + \)\(72\!\cdots\!60\)\( T^{31} + \)\(42\!\cdots\!15\)\( T^{32} + \)\(14\!\cdots\!70\)\( T^{33} + \)\(75\!\cdots\!73\)\( T^{34} + \)\(18\!\cdots\!94\)\( T^{35} + \)\(87\!\cdots\!92\)\( T^{36} + \)\(11\!\cdots\!44\)\( T^{37} + \)\(49\!\cdots\!03\)\( T^{38} \))(\( 1 + 16 T + 796 T^{2} + 11174 T^{3} + 308411 T^{4} + 3871830 T^{5} + 77929745 T^{6} + 887961160 T^{7} + 14507359854 T^{8} + 151770335876 T^{9} + 2129091057322 T^{10} + 20632309944852 T^{11} + 257044091804278 T^{12} + 2322130118823236 T^{13} + 26251828334139690 T^{14} + 221960997863784176 T^{15} + 2309276440782195440 T^{16} + 18302785098419669466 T^{17} + \)\(17\!\cdots\!16\)\( T^{18} + \)\(13\!\cdots\!62\)\( T^{19} + \)\(11\!\cdots\!72\)\( T^{20} + \)\(82\!\cdots\!74\)\( T^{21} + \)\(69\!\cdots\!20\)\( T^{22} + \)\(44\!\cdots\!96\)\( T^{23} + \)\(35\!\cdots\!30\)\( T^{24} + \)\(21\!\cdots\!84\)\( T^{25} + \)\(15\!\cdots\!94\)\( T^{26} + \)\(83\!\cdots\!32\)\( T^{27} + \)\(57\!\cdots\!34\)\( T^{28} + \)\(27\!\cdots\!24\)\( T^{29} + \)\(17\!\cdots\!82\)\( T^{30} + \)\(72\!\cdots\!60\)\( T^{31} + \)\(42\!\cdots\!15\)\( T^{32} + \)\(14\!\cdots\!70\)\( T^{33} + \)\(75\!\cdots\!73\)\( T^{34} + \)\(18\!\cdots\!94\)\( T^{35} + \)\(87\!\cdots\!92\)\( T^{36} + \)\(11\!\cdots\!44\)\( T^{37} + \)\(49\!\cdots\!03\)\( T^{38} \))
$71$ (\( 1 + 4 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 - 13 T + 278 T^{2} - 1823 T^{3} + 27298 T^{4} - 123741 T^{5} + 2037921 T^{6} - 8785611 T^{7} + 137609218 T^{8} - 652471753 T^{9} + 7064447318 T^{10} - 23454981563 T^{11} + 128100283921 T^{12} \))(\( 1 - 18 T + 509 T^{2} - 6143 T^{3} + 99682 T^{4} - 906794 T^{5} + 10907742 T^{6} - 79739874 T^{7} + 774449682 T^{8} - 4571148554 T^{9} + 35677284302 T^{10} - 156103956383 T^{11} + 918352739659 T^{12} - 2305805110578 T^{13} + 9095120158391 T^{14} \))(\( 1 + 15 T + 357 T^{2} + 3510 T^{3} + 49633 T^{4} + 417733 T^{5} + 4922778 T^{6} + 41726588 T^{7} + 429547987 T^{8} + 3410982944 T^{9} + 30497907077 T^{10} + 210343730108 T^{11} + 1761916396758 T^{12} + 10615297739173 T^{13} + 89549315378183 T^{14} + 449631996562710 T^{15} + 3246957896545587 T^{16} + 9686302968686415 T^{17} + 45848500718449031 T^{18} \))(\( 1 + 5 T + 494 T^{2} + 2409 T^{3} + 119368 T^{4} + 563747 T^{5} + 18532309 T^{6} + 82606289 T^{7} + 2044290799 T^{8} + 8287705582 T^{9} + 167399338138 T^{10} + 588427096322 T^{11} + 10305269917759 T^{12} + 29565699502279 T^{13} + 470937124501429 T^{14} + 1017128883938197 T^{15} + 15291074691081928 T^{16} + 21910144461563919 T^{17} + 319002244435405934 T^{18} + 229242503592245155 T^{19} + 3255243551009881201 T^{20} \))(\( 1 - 17 T + 616 T^{2} - 8749 T^{3} + 180925 T^{4} - 2197096 T^{5} + 33840105 T^{6} - 357489152 T^{7} + 4525059339 T^{8} - 42191830223 T^{9} + 459723529695 T^{10} - 3816711757819 T^{11} + 36652901427310 T^{12} - 270986534805149 T^{13} + 2317466313192495 T^{14} - 15100920146944153 T^{15} + 114989364428738859 T^{16} - 644992420702500352 T^{17} + 4334927058416451705 T^{18} - 19982852119520232536 T^{19} + \)\(11\!\cdots\!25\)\( T^{20} - \)\(40\!\cdots\!19\)\( T^{21} + \)\(20\!\cdots\!16\)\( T^{22} - \)\(39\!\cdots\!07\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 6 T + 440 T^{2} + 951 T^{3} + 96092 T^{4} - 58657 T^{5} + 14918598 T^{6} - 40123203 T^{7} + 1874503078 T^{8} - 7242827855 T^{9} + 200997151216 T^{10} - 842990815480 T^{11} + 18428438400077 T^{12} - 74289209148314 T^{13} + 1428760173206436 T^{14} - 5274533849530294 T^{15} + 92897757974788157 T^{16} - 301715685759262280 T^{17} + 5107675488609754096 T^{18} - 13067722600231372105 T^{19} + \)\(24\!\cdots\!38\)\( T^{20} - \)\(36\!\cdots\!73\)\( T^{21} + \)\(96\!\cdots\!78\)\( T^{22} - \)\(26\!\cdots\!67\)\( T^{23} + \)\(31\!\cdots\!92\)\( T^{24} + \)\(21\!\cdots\!21\)\( T^{25} + \)\(72\!\cdots\!40\)\( T^{26} + \)\(69\!\cdots\!66\)\( T^{27} + \)\(82\!\cdots\!81\)\( T^{28} \))(\( 1 + 36 T + 1224 T^{2} + 30188 T^{3} + 660774 T^{4} + 12677466 T^{5} + 220741665 T^{6} + 3530689216 T^{7} + 52426674841 T^{8} + 728218563854 T^{9} + 9526245318776 T^{10} + 117791243162970 T^{11} + 1383045789124161 T^{12} + 15455537183804776 T^{13} + 164815072538233572 T^{14} + 1680084351352328032 T^{15} + 16394028424198476515 T^{16} + \)\(15\!\cdots\!80\)\( T^{17} + \)\(13\!\cdots\!67\)\( T^{18} + \)\(11\!\cdots\!84\)\( T^{19} + \)\(97\!\cdots\!57\)\( T^{20} + \)\(77\!\cdots\!80\)\( T^{21} + \)\(58\!\cdots\!65\)\( T^{22} + \)\(42\!\cdots\!92\)\( T^{23} + \)\(29\!\cdots\!72\)\( T^{24} + \)\(19\!\cdots\!96\)\( T^{25} + \)\(12\!\cdots\!51\)\( T^{26} + \)\(76\!\cdots\!70\)\( T^{27} + \)\(43\!\cdots\!56\)\( T^{28} + \)\(23\!\cdots\!54\)\( T^{29} + \)\(12\!\cdots\!11\)\( T^{30} + \)\(57\!\cdots\!56\)\( T^{31} + \)\(25\!\cdots\!15\)\( T^{32} + \)\(10\!\cdots\!46\)\( T^{33} + \)\(38\!\cdots\!74\)\( T^{34} + \)\(12\!\cdots\!48\)\( T^{35} + \)\(36\!\cdots\!84\)\( T^{36} + \)\(75\!\cdots\!96\)\( T^{37} + \)\(14\!\cdots\!31\)\( T^{38} \))(\( 1 - 36 T + 1224 T^{2} - 30188 T^{3} + 660774 T^{4} - 12677466 T^{5} + 220741665 T^{6} - 3530689216 T^{7} + 52426674841 T^{8} - 728218563854 T^{9} + 9526245318776 T^{10} - 117791243162970 T^{11} + 1383045789124161 T^{12} - 15455537183804776 T^{13} + 164815072538233572 T^{14} - 1680084351352328032 T^{15} + 16394028424198476515 T^{16} - \)\(15\!\cdots\!80\)\( T^{17} + \)\(13\!\cdots\!67\)\( T^{18} - \)\(11\!\cdots\!84\)\( T^{19} + \)\(97\!\cdots\!57\)\( T^{20} - \)\(77\!\cdots\!80\)\( T^{21} + \)\(58\!\cdots\!65\)\( T^{22} - \)\(42\!\cdots\!92\)\( T^{23} + \)\(29\!\cdots\!72\)\( T^{24} - \)\(19\!\cdots\!96\)\( T^{25} + \)\(12\!\cdots\!51\)\( T^{26} - \)\(76\!\cdots\!70\)\( T^{27} + \)\(43\!\cdots\!56\)\( T^{28} - \)\(23\!\cdots\!54\)\( T^{29} + \)\(12\!\cdots\!11\)\( T^{30} - \)\(57\!\cdots\!56\)\( T^{31} + \)\(25\!\cdots\!15\)\( T^{32} - \)\(10\!\cdots\!46\)\( T^{33} + \)\(38\!\cdots\!74\)\( T^{34} - \)\(12\!\cdots\!48\)\( T^{35} + \)\(36\!\cdots\!84\)\( T^{36} - \)\(75\!\cdots\!96\)\( T^{37} + \)\(14\!\cdots\!31\)\( T^{38} \))
$73$ (\( 1 - 7 T + 73 T^{2} \))(\( 1 - T + 73 T^{2} \))(\( 1 - 5 T + 73 T^{2} \))(\( 1 - 5 T + 73 T^{2} \))(\( 1 - 7 T + 73 T^{2} \))(\( 1 - T + 73 T^{2} \))(\( 1 + 5 T + 73 T^{2} \))(\( 1 + 32 T + 698 T^{2} + 10897 T^{3} + 139781 T^{4} + 1495787 T^{5} + 13789779 T^{6} + 109192451 T^{7} + 744892949 T^{8} + 4239118249 T^{9} + 19821972218 T^{10} + 66338290976 T^{11} + 151334226289 T^{12} \))(\( 1 + 7 T + 277 T^{2} + 2034 T^{3} + 44471 T^{4} + 290456 T^{5} + 4664818 T^{6} + 26135103 T^{7} + 340531714 T^{8} + 1547840024 T^{9} + 17299975007 T^{10} + 57762022194 T^{11} + 574240831261 T^{12} + 1059339584023 T^{13} + 11047398519097 T^{14} \))(\( 1 + 35 T + 932 T^{2} + 16986 T^{3} + 265062 T^{4} + 3378629 T^{5} + 39072758 T^{6} + 396140013 T^{7} + 3795164784 T^{8} + 33070672341 T^{9} + 277047029232 T^{10} + 2111030129277 T^{11} + 15199967098886 T^{12} + 95947120591589 T^{13} + 549492502583766 T^{14} + 2570563167744954 T^{15} + 10296175419798404 T^{16} + 28226103216292835 T^{17} + 58871586708267913 T^{18} \))(\( 1 - 15 T + 639 T^{2} - 7523 T^{3} + 182674 T^{4} - 1782413 T^{5} + 31796166 T^{6} - 263720334 T^{7} + 3783852264 T^{8} - 26904873286 T^{9} + 323539040974 T^{10} - 1964055749878 T^{11} + 20164148714856 T^{12} - 102591693171678 T^{13} + 902955184944006 T^{14} - 3695069757293909 T^{15} + 27644828453116786 T^{16} - 83109579059166731 T^{17} + 515327998720317759 T^{18} - 883073800624018695 T^{19} + 4297625829703557649 T^{20} \))(\( 1 - 45 T + 1236 T^{2} - 25360 T^{3} + 437084 T^{4} - 6574931 T^{5} + 89104011 T^{6} - 1101390828 T^{7} + 12595816762 T^{8} - 133996824913 T^{9} + 1335728338560 T^{10} - 12495316519766 T^{11} + 110073378181218 T^{12} - 912158105942918 T^{13} + 7118096316186240 T^{14} - 52127042837180521 T^{15} + 357699039999115642 T^{16} - 2283262038317549004 T^{17} + 13484486563931545179 T^{18} - 72635882992564957307 T^{19} + \)\(35\!\cdots\!04\)\( T^{20} - \)\(14\!\cdots\!80\)\( T^{21} + \)\(53\!\cdots\!64\)\( T^{22} - \)\(14\!\cdots\!65\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 5 T + 509 T^{2} - 2246 T^{3} + 131047 T^{4} - 543096 T^{5} + 22785570 T^{6} - 92847232 T^{7} + 3016491029 T^{8} - 12396170995 T^{9} + 324499520677 T^{10} - 1340853514487 T^{11} + 29471947693033 T^{12} - 118946765135011 T^{13} + 2308572431873909 T^{14} - 8683113854855803 T^{15} + 157056009256172857 T^{16} - 521614811645189279 T^{17} + 9215215592569929157 T^{18} - 25698149951705045035 T^{19} + \)\(45\!\cdots\!81\)\( T^{20} - \)\(10\!\cdots\!04\)\( T^{21} + \)\(18\!\cdots\!70\)\( T^{22} - \)\(31\!\cdots\!48\)\( T^{23} + \)\(56\!\cdots\!03\)\( T^{24} - \)\(70\!\cdots\!42\)\( T^{25} + \)\(11\!\cdots\!89\)\( T^{26} - \)\(83\!\cdots\!65\)\( T^{27} + \)\(12\!\cdots\!09\)\( T^{28} \))(\( 1 - 3 T + 772 T^{2} - 2271 T^{3} + 305525 T^{4} - 891750 T^{5} + 81859648 T^{6} - 236912166 T^{7} + 16573074918 T^{8} - 47318147954 T^{9} + 2685363470607 T^{10} - 7507638358839 T^{11} + 360293894888549 T^{12} - 977615715307968 T^{13} + 40893701446345831 T^{14} - 106610380265782023 T^{15} + 3979989374650718193 T^{16} - 9857487772620536730 T^{17} + \)\(33\!\cdots\!87\)\( T^{18} - \)\(77\!\cdots\!81\)\( T^{19} + \)\(24\!\cdots\!51\)\( T^{20} - \)\(52\!\cdots\!70\)\( T^{21} + \)\(15\!\cdots\!81\)\( T^{22} - \)\(30\!\cdots\!43\)\( T^{23} + \)\(84\!\cdots\!83\)\( T^{24} - \)\(14\!\cdots\!52\)\( T^{25} + \)\(39\!\cdots\!53\)\( T^{26} - \)\(60\!\cdots\!59\)\( T^{27} + \)\(15\!\cdots\!91\)\( T^{28} - \)\(20\!\cdots\!46\)\( T^{29} + \)\(51\!\cdots\!86\)\( T^{30} - \)\(54\!\cdots\!86\)\( T^{31} + \)\(13\!\cdots\!84\)\( T^{32} - \)\(10\!\cdots\!50\)\( T^{33} + \)\(27\!\cdots\!25\)\( T^{34} - \)\(14\!\cdots\!31\)\( T^{35} + \)\(36\!\cdots\!16\)\( T^{36} - \)\(10\!\cdots\!07\)\( T^{37} + \)\(25\!\cdots\!37\)\( T^{38} \))(\( 1 - 3 T + 772 T^{2} - 2271 T^{3} + 305525 T^{4} - 891750 T^{5} + 81859648 T^{6} - 236912166 T^{7} + 16573074918 T^{8} - 47318147954 T^{9} + 2685363470607 T^{10} - 7507638358839 T^{11} + 360293894888549 T^{12} - 977615715307968 T^{13} + 40893701446345831 T^{14} - 106610380265782023 T^{15} + 3979989374650718193 T^{16} - 9857487772620536730 T^{17} + \)\(33\!\cdots\!87\)\( T^{18} - \)\(77\!\cdots\!81\)\( T^{19} + \)\(24\!\cdots\!51\)\( T^{20} - \)\(52\!\cdots\!70\)\( T^{21} + \)\(15\!\cdots\!81\)\( T^{22} - \)\(30\!\cdots\!43\)\( T^{23} + \)\(84\!\cdots\!83\)\( T^{24} - \)\(14\!\cdots\!52\)\( T^{25} + \)\(39\!\cdots\!53\)\( T^{26} - \)\(60\!\cdots\!59\)\( T^{27} + \)\(15\!\cdots\!91\)\( T^{28} - \)\(20\!\cdots\!46\)\( T^{29} + \)\(51\!\cdots\!86\)\( T^{30} - \)\(54\!\cdots\!86\)\( T^{31} + \)\(13\!\cdots\!84\)\( T^{32} - \)\(10\!\cdots\!50\)\( T^{33} + \)\(27\!\cdots\!25\)\( T^{34} - \)\(14\!\cdots\!31\)\( T^{35} + \)\(36\!\cdots\!16\)\( T^{36} - \)\(10\!\cdots\!07\)\( T^{37} + \)\(25\!\cdots\!37\)\( T^{38} \))
$79$ (\( 1 - 5 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 13 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 15 T + 79 T^{2} \))(\( 1 - 7 T + 48 T^{2} + 668 T^{3} - 1988 T^{4} + 22913 T^{5} + 556795 T^{6} + 1810127 T^{7} - 12407108 T^{8} + 329350052 T^{9} + 1869603888 T^{10} - 21539394793 T^{11} + 243087455521 T^{12} \))(\( 1 + 30 T + 864 T^{2} + 15277 T^{3} + 251870 T^{4} + 3126597 T^{5} + 36178295 T^{6} + 332923983 T^{7} + 2858085305 T^{8} + 19513091877 T^{9} + 124181732930 T^{10} + 595040387437 T^{11} + 2658576728736 T^{12} + 7292623665630 T^{13} + 19203908986159 T^{14} \))(\( 1 + 18 T + 401 T^{2} + 6077 T^{3} + 88501 T^{4} + 1108698 T^{5} + 12926144 T^{6} + 136656105 T^{7} + 1367007952 T^{8} + 12426119255 T^{9} + 107993628208 T^{10} + 852870751305 T^{11} + 6373093111616 T^{12} + 43183876904538 T^{13} + 272322568367899 T^{14} + 1477242467201117 T^{15} + 7700767503449759 T^{16} + 27307958578318098 T^{17} + 119851595982618319 T^{18} \))(\( 1 + 14 T + 500 T^{2} + 5191 T^{3} + 112620 T^{4} + 918193 T^{5} + 15761215 T^{6} + 105265099 T^{7} + 1625336720 T^{8} + 9420501826 T^{9} + 138160799724 T^{10} + 744219644254 T^{11} + 10143726469520 T^{12} + 51899799145861 T^{13} + 613900600908415 T^{14} + 2825331646167007 T^{15} + 27376509240775020 T^{16} + 99687491547151369 T^{17} + 758554404953280500 T^{18} + 1677922343756656466 T^{19} + 9468276082626847201 T^{20} \))(\( 1 - 6 T + 582 T^{2} - 3381 T^{3} + 169545 T^{4} - 943791 T^{5} + 32683087 T^{6} - 171479712 T^{7} + 4648149362 T^{8} - 22592239791 T^{9} + 513962658395 T^{10} - 2277380476923 T^{11} + 45305690610664 T^{12} - 179913057676917 T^{13} + 3207640951043195 T^{14} - 11138855314314849 T^{15} + 181045794149998322 T^{16} - 527652745108277088 T^{17} + 7944848457401473327 T^{18} - 18124476465955988769 T^{19} + \)\(25\!\cdots\!45\)\( T^{20} - \)\(40\!\cdots\!39\)\( T^{21} + \)\(55\!\cdots\!82\)\( T^{22} - \)\(44\!\cdots\!74\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 - 56 T + 2178 T^{2} - 61573 T^{3} + 1444638 T^{4} - 28678155 T^{5} + 502092413 T^{6} - 7837978292 T^{7} + 111253380003 T^{8} - 1445274307857 T^{9} + 17375055426959 T^{10} - 193997565121459 T^{11} + 2024946369538101 T^{12} - 19782596308792413 T^{13} + 181527502415863181 T^{14} - 1562825108394600627 T^{15} + 12637690292287288341 T^{16} - 95648365509919023901 T^{17} + \)\(67\!\cdots\!79\)\( T^{18} - \)\(44\!\cdots\!43\)\( T^{19} + \)\(27\!\cdots\!63\)\( T^{20} - \)\(15\!\cdots\!28\)\( T^{21} + \)\(76\!\cdots\!93\)\( T^{22} - \)\(34\!\cdots\!45\)\( T^{23} + \)\(13\!\cdots\!38\)\( T^{24} - \)\(46\!\cdots\!67\)\( T^{25} + \)\(12\!\cdots\!98\)\( T^{26} - \)\(26\!\cdots\!84\)\( T^{27} + \)\(36\!\cdots\!81\)\( T^{28} \))(\( 1 + 14 T + 881 T^{2} + 9630 T^{3} + 359449 T^{4} + 3150678 T^{5} + 93553204 T^{6} + 669689448 T^{7} + 18009494902 T^{8} + 107423450230 T^{9} + 2799425778981 T^{10} + 14265546505554 T^{11} + 369268826481152 T^{12} + 1647534319862910 T^{13} + 42296493481232283 T^{14} + 168499267836552426 T^{15} + 4250543558116233801 T^{16} + 15407763351699382208 T^{17} + \)\(37\!\cdots\!49\)\( T^{18} + \)\(12\!\cdots\!58\)\( T^{19} + \)\(29\!\cdots\!71\)\( T^{20} + \)\(96\!\cdots\!28\)\( T^{21} + \)\(20\!\cdots\!39\)\( T^{22} + \)\(65\!\cdots\!06\)\( T^{23} + \)\(13\!\cdots\!17\)\( T^{24} + \)\(40\!\cdots\!10\)\( T^{25} + \)\(70\!\cdots\!68\)\( T^{26} + \)\(21\!\cdots\!94\)\( T^{27} + \)\(33\!\cdots\!39\)\( T^{28} + \)\(10\!\cdots\!30\)\( T^{29} + \)\(13\!\cdots\!58\)\( T^{30} + \)\(39\!\cdots\!68\)\( T^{31} + \)\(43\!\cdots\!56\)\( T^{32} + \)\(11\!\cdots\!18\)\( T^{33} + \)\(10\!\cdots\!51\)\( T^{34} + \)\(22\!\cdots\!30\)\( T^{35} + \)\(16\!\cdots\!79\)\( T^{36} + \)\(20\!\cdots\!54\)\( T^{37} + \)\(11\!\cdots\!19\)\( T^{38} \))(\( 1 + 14 T + 881 T^{2} + 9630 T^{3} + 359449 T^{4} + 3150678 T^{5} + 93553204 T^{6} + 669689448 T^{7} + 18009494902 T^{8} + 107423450230 T^{9} + 2799425778981 T^{10} + 14265546505554 T^{11} + 369268826481152 T^{12} + 1647534319862910 T^{13} + 42296493481232283 T^{14} + 168499267836552426 T^{15} + 4250543558116233801 T^{16} + 15407763351699382208 T^{17} + \)\(37\!\cdots\!49\)\( T^{18} + \)\(12\!\cdots\!58\)\( T^{19} + \)\(29\!\cdots\!71\)\( T^{20} + \)\(96\!\cdots\!28\)\( T^{21} + \)\(20\!\cdots\!39\)\( T^{22} + \)\(65\!\cdots\!06\)\( T^{23} + \)\(13\!\cdots\!17\)\( T^{24} + \)\(40\!\cdots\!10\)\( T^{25} + \)\(70\!\cdots\!68\)\( T^{26} + \)\(21\!\cdots\!94\)\( T^{27} + \)\(33\!\cdots\!39\)\( T^{28} + \)\(10\!\cdots\!30\)\( T^{29} + \)\(13\!\cdots\!58\)\( T^{30} + \)\(39\!\cdots\!68\)\( T^{31} + \)\(43\!\cdots\!56\)\( T^{32} + \)\(11\!\cdots\!18\)\( T^{33} + \)\(10\!\cdots\!51\)\( T^{34} + \)\(22\!\cdots\!30\)\( T^{35} + \)\(16\!\cdots\!79\)\( T^{36} + \)\(20\!\cdots\!54\)\( T^{37} + \)\(11\!\cdots\!19\)\( T^{38} \))
$83$ (\( 1 + 7 T + 83 T^{2} \))(\( 1 - 13 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 + 15 T + 83 T^{2} \))(\( 1 + 11 T + 83 T^{2} \))(\( 1 - 15 T + 83 T^{2} \))(\( 1 - 32 T + 759 T^{2} - 12780 T^{3} + 181039 T^{4} - 2083586 T^{5} + 20798723 T^{6} - 172937638 T^{7} + 1247177671 T^{8} - 7307437860 T^{9} + 36020865639 T^{10} - 126049300576 T^{11} + 326940373369 T^{12} \))(\( 1 + 13 T + 485 T^{2} + 5360 T^{3} + 109330 T^{4} + 996823 T^{5} + 14416686 T^{6} + 106582888 T^{7} + 1196584938 T^{8} + 6867113647 T^{9} + 62513472710 T^{10} + 254376600560 T^{11} + 1910434711855 T^{12} + 4250224853797 T^{13} + 27136050989627 T^{14} \))(\( 1 - 15 T + 413 T^{2} - 3686 T^{3} + 66853 T^{4} - 432863 T^{5} + 7882688 T^{6} - 48515359 T^{7} + 857532618 T^{8} - 4883164587 T^{9} + 71175207294 T^{10} - 334222308151 T^{11} + 4507218523456 T^{12} - 20542951203023 T^{13} + 263336684106479 T^{14} - 1205102216238134 T^{15} + 11207189058715951 T^{16} - 33784383482085615 T^{17} + 186940255267540403 T^{18} \))(\( 1 + 35 T + 1214 T^{2} + 26521 T^{3} + 545056 T^{4} + 8774551 T^{5} + 132587365 T^{6} + 1684520714 T^{7} + 20146919256 T^{8} + 208409548218 T^{9} + 2033561761052 T^{10} + 17297992502094 T^{11} + 138792126754584 T^{12} + 963187045495918 T^{13} + 6292373728714165 T^{14} + 34563313013076293 T^{15} + 178200812147013664 T^{16} + 719675208295897667 T^{17} + 2734282769816795774 T^{18} + 6542908934363914105 T^{19} + 15516041187205853449 T^{20} \))(\( 1 - T + 389 T^{2} - 1198 T^{3} + 87177 T^{4} - 372265 T^{5} + 14562155 T^{6} - 70132740 T^{7} + 1927478677 T^{8} - 9544977639 T^{9} + 210088709769 T^{10} - 997874990444 T^{11} + 19097365203668 T^{12} - 82823624206852 T^{13} + 1447301121598641 T^{14} - 5457694129270893 T^{15} + 91474901773721317 T^{16} - 276255713264951820 T^{17} + 4760956392757250195 T^{18} - 10101802021653495155 T^{19} + \)\(19\!\cdots\!57\)\( T^{20} - \)\(22\!\cdots\!94\)\( T^{21} + \)\(60\!\cdots\!61\)\( T^{22} - \)\(12\!\cdots\!67\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - 28 T + 1194 T^{2} - 24258 T^{3} + 597660 T^{4} - 9577457 T^{5} + 174046785 T^{6} - 2306100582 T^{7} + 33960396380 T^{8} - 384505903734 T^{9} + 4841020526267 T^{10} - 48162250372593 T^{11} + 538120608580119 T^{12} - 4819591768627718 T^{13} + 48926682521657972 T^{14} - 400026116796100594 T^{15} + 3707112872508439791 T^{16} - 27538548653793833691 T^{17} + \)\(22\!\cdots\!07\)\( T^{18} - \)\(15\!\cdots\!62\)\( T^{19} + \)\(11\!\cdots\!20\)\( T^{20} - \)\(62\!\cdots\!14\)\( T^{21} + \)\(39\!\cdots\!85\)\( T^{22} - \)\(17\!\cdots\!71\)\( T^{23} + \)\(92\!\cdots\!40\)\( T^{24} - \)\(31\!\cdots\!86\)\( T^{25} + \)\(12\!\cdots\!34\)\( T^{26} - \)\(24\!\cdots\!64\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \))(\( 1 + 25 T + 1034 T^{2} + 17839 T^{3} + 416802 T^{4} + 5218353 T^{5} + 87478759 T^{6} + 755530524 T^{7} + 9936957087 T^{8} + 37697949991 T^{9} + 444370271320 T^{10} - 5162741859377 T^{11} - 25917443638697 T^{12} - 1054303397498994 T^{13} - 2560913058796617 T^{14} - 65346141684937671 T^{15} + 483249581099534901 T^{16} + 1674266552532337102 T^{17} + \)\(10\!\cdots\!81\)\( T^{18} + \)\(47\!\cdots\!47\)\( T^{19} + \)\(89\!\cdots\!23\)\( T^{20} + \)\(11\!\cdots\!78\)\( T^{21} + \)\(27\!\cdots\!87\)\( T^{22} - \)\(31\!\cdots\!91\)\( T^{23} - \)\(10\!\cdots\!31\)\( T^{24} - \)\(34\!\cdots\!86\)\( T^{25} - \)\(70\!\cdots\!19\)\( T^{26} - \)\(11\!\cdots\!57\)\( T^{27} + \)\(83\!\cdots\!60\)\( T^{28} + \)\(58\!\cdots\!59\)\( T^{29} + \)\(12\!\cdots\!29\)\( T^{30} + \)\(80\!\cdots\!64\)\( T^{31} + \)\(77\!\cdots\!17\)\( T^{32} + \)\(38\!\cdots\!37\)\( T^{33} + \)\(25\!\cdots\!14\)\( T^{34} + \)\(90\!\cdots\!59\)\( T^{35} + \)\(43\!\cdots\!82\)\( T^{36} + \)\(87\!\cdots\!25\)\( T^{37} + \)\(29\!\cdots\!47\)\( T^{38} \))(\( 1 - 25 T + 1034 T^{2} - 17839 T^{3} + 416802 T^{4} - 5218353 T^{5} + 87478759 T^{6} - 755530524 T^{7} + 9936957087 T^{8} - 37697949991 T^{9} + 444370271320 T^{10} + 5162741859377 T^{11} - 25917443638697 T^{12} + 1054303397498994 T^{13} - 2560913058796617 T^{14} + 65346141684937671 T^{15} + 483249581099534901 T^{16} - 1674266552532337102 T^{17} + \)\(10\!\cdots\!81\)\( T^{18} - \)\(47\!\cdots\!47\)\( T^{19} + \)\(89\!\cdots\!23\)\( T^{20} - \)\(11\!\cdots\!78\)\( T^{21} + \)\(27\!\cdots\!87\)\( T^{22} + \)\(31\!\cdots\!91\)\( T^{23} - \)\(10\!\cdots\!31\)\( T^{24} + \)\(34\!\cdots\!86\)\( T^{25} - \)\(70\!\cdots\!19\)\( T^{26} + \)\(11\!\cdots\!57\)\( T^{27} + \)\(83\!\cdots\!60\)\( T^{28} - \)\(58\!\cdots\!59\)\( T^{29} + \)\(12\!\cdots\!29\)\( T^{30} - \)\(80\!\cdots\!64\)\( T^{31} + \)\(77\!\cdots\!17\)\( T^{32} - \)\(38\!\cdots\!37\)\( T^{33} + \)\(25\!\cdots\!14\)\( T^{34} - \)\(90\!\cdots\!59\)\( T^{35} + \)\(43\!\cdots\!82\)\( T^{36} - \)\(87\!\cdots\!25\)\( T^{37} + \)\(29\!\cdots\!47\)\( T^{38} \))
$89$ (\( 1 + 18 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - 14 T + 357 T^{2} - 3330 T^{3} + 49061 T^{4} - 333810 T^{5} + 4490927 T^{6} - 29709090 T^{7} + 388612181 T^{8} - 2347546770 T^{9} + 22398980037 T^{10} - 78176832286 T^{11} + 496981290961 T^{12} \))(\( 1 + 109 T^{2} + 211 T^{3} + 18778 T^{4} - 41946 T^{5} + 1597555 T^{6} - 597701 T^{7} + 142182395 T^{8} - 332254266 T^{9} + 13237907882 T^{10} + 13238612851 T^{11} + 608662479941 T^{12} + 44231334895529 T^{14} \))(\( 1 - 8 T + 442 T^{2} - 4464 T^{3} + 106261 T^{4} - 1086280 T^{5} + 17754848 T^{6} - 163089398 T^{7} + 2155674004 T^{8} - 17093637388 T^{9} + 191854986356 T^{10} - 1291831121558 T^{11} + 12516617439712 T^{12} - 68155641553480 T^{13} + 593367741110189 T^{14} - 2218524482849904 T^{15} + 19550250023823818 T^{16} - 31492710445616648 T^{17} + 350356403707485209 T^{18} \))(\( 1 + 30 T + 993 T^{2} + 19386 T^{3} + 386207 T^{4} + 5772046 T^{5} + 86644393 T^{6} + 1058804326 T^{7} + 12928680268 T^{8} + 132791889316 T^{9} + 1359822891188 T^{10} + 11818478149124 T^{11} + 102408076402828 T^{12} + 746424226895894 T^{13} + 5436263386904713 T^{14} + 32231448006362654 T^{15} + 191937653438174927 T^{16} + 857468658284725194 T^{17} + 3909032684062166433 T^{18} + 10510692111224556270 T^{19} + 31181719929966183601 T^{20} \))(\( 1 + 22 T + 993 T^{2} + 17132 T^{3} + 434746 T^{4} + 6183372 T^{5} + 114445646 T^{6} + 1384856906 T^{7} + 20650783613 T^{8} + 216950897432 T^{9} + 2740116113841 T^{10} + 25269472540800 T^{11} + 277494322845008 T^{12} + 2248983056131200 T^{13} + 21704459737734561 T^{14} + 152943657211739608 T^{15} + 1295676442285696733 T^{16} + 7733123291462204794 T^{17} + 56877344893945605806 T^{18} + \)\(27\!\cdots\!88\)\( T^{19} + \)\(17\!\cdots\!26\)\( T^{20} + \)\(60\!\cdots\!88\)\( T^{21} + \)\(30\!\cdots\!93\)\( T^{22} + \)\(61\!\cdots\!58\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 - 24 T + 669 T^{2} - 10517 T^{3} + 185238 T^{4} - 2263722 T^{5} + 31585183 T^{6} - 325130743 T^{7} + 4027076643 T^{8} - 37730303200 T^{9} + 449488705240 T^{10} - 4053222457673 T^{11} + 47081758898733 T^{12} - 407899267298090 T^{13} + 4474499931731100 T^{14} - 36303034789530010 T^{15} + 372934612236864093 T^{16} - 2857396182763277137 T^{17} + 28201928670946042840 T^{18} - \)\(21\!\cdots\!00\)\( T^{19} + \)\(20\!\cdots\!23\)\( T^{20} - \)\(14\!\cdots\!47\)\( T^{21} + \)\(12\!\cdots\!23\)\( T^{22} - \)\(79\!\cdots\!98\)\( T^{23} + \)\(57\!\cdots\!38\)\( T^{24} - \)\(29\!\cdots\!13\)\( T^{25} + \)\(16\!\cdots\!49\)\( T^{26} - \)\(52\!\cdots\!56\)\( T^{27} + \)\(19\!\cdots\!41\)\( T^{28} \))(\( 1 + 42 T + 1647 T^{2} + 43788 T^{3} + 1083906 T^{4} + 22246876 T^{5} + 430436860 T^{6} + 7390316980 T^{7} + 120808795793 T^{8} + 1809371992886 T^{9} + 25988146717585 T^{10} + 348113968042716 T^{11} + 4495046720266244 T^{12} + 54714113237773252 T^{13} + 644340851547920014 T^{14} + 7200557062815060272 T^{15} + 78041547467239175304 T^{16} + \)\(80\!\cdots\!68\)\( T^{17} + \)\(80\!\cdots\!86\)\( T^{18} + \)\(77\!\cdots\!04\)\( T^{19} + \)\(71\!\cdots\!54\)\( T^{20} + \)\(63\!\cdots\!28\)\( T^{21} + \)\(55\!\cdots\!76\)\( T^{22} + \)\(45\!\cdots\!52\)\( T^{23} + \)\(35\!\cdots\!86\)\( T^{24} + \)\(27\!\cdots\!72\)\( T^{25} + \)\(19\!\cdots\!76\)\( T^{26} + \)\(13\!\cdots\!96\)\( T^{27} + \)\(91\!\cdots\!65\)\( T^{28} + \)\(56\!\cdots\!86\)\( T^{29} + \)\(33\!\cdots\!77\)\( T^{30} + \)\(18\!\cdots\!80\)\( T^{31} + \)\(94\!\cdots\!40\)\( T^{32} + \)\(43\!\cdots\!16\)\( T^{33} + \)\(18\!\cdots\!94\)\( T^{34} + \)\(67\!\cdots\!68\)\( T^{35} + \)\(22\!\cdots\!63\)\( T^{36} + \)\(51\!\cdots\!02\)\( T^{37} + \)\(10\!\cdots\!09\)\( T^{38} \))(\( 1 - 42 T + 1647 T^{2} - 43788 T^{3} + 1083906 T^{4} - 22246876 T^{5} + 430436860 T^{6} - 7390316980 T^{7} + 120808795793 T^{8} - 1809371992886 T^{9} + 25988146717585 T^{10} - 348113968042716 T^{11} + 4495046720266244 T^{12} - 54714113237773252 T^{13} + 644340851547920014 T^{14} - 7200557062815060272 T^{15} + 78041547467239175304 T^{16} - \)\(80\!\cdots\!68\)\( T^{17} + \)\(80\!\cdots\!86\)\( T^{18} - \)\(77\!\cdots\!04\)\( T^{19} + \)\(71\!\cdots\!54\)\( T^{20} - \)\(63\!\cdots\!28\)\( T^{21} + \)\(55\!\cdots\!76\)\( T^{22} - \)\(45\!\cdots\!52\)\( T^{23} + \)\(35\!\cdots\!86\)\( T^{24} - \)\(27\!\cdots\!72\)\( T^{25} + \)\(19\!\cdots\!76\)\( T^{26} - \)\(13\!\cdots\!96\)\( T^{27} + \)\(91\!\cdots\!65\)\( T^{28} - \)\(56\!\cdots\!86\)\( T^{29} + \)\(33\!\cdots\!77\)\( T^{30} - \)\(18\!\cdots\!80\)\( T^{31} + \)\(94\!\cdots\!40\)\( T^{32} - \)\(43\!\cdots\!16\)\( T^{33} + \)\(18\!\cdots\!94\)\( T^{34} - \)\(67\!\cdots\!68\)\( T^{35} + \)\(22\!\cdots\!63\)\( T^{36} - \)\(51\!\cdots\!02\)\( T^{37} + \)\(10\!\cdots\!09\)\( T^{38} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 12 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 29 T + 794 T^{2} + 13737 T^{3} + 217745 T^{4} + 2629266 T^{5} + 29134681 T^{6} + 255038802 T^{7} + 2048762705 T^{8} + 12537389001 T^{9} + 70292249114 T^{10} + 249032867453 T^{11} + 832972004929 T^{12} \))(\( 1 + 2 T + 455 T^{2} - 86 T^{3} + 89144 T^{4} - 192034 T^{5} + 10939992 T^{6} - 31982204 T^{7} + 1061179224 T^{8} - 1806847906 T^{9} + 81359321912 T^{10} - 7613518166 T^{11} + 3907239816935 T^{12} + 1665944009858 T^{13} + 80798284478113 T^{14} \))(\( 1 + 43 T + 1297 T^{2} + 28926 T^{3} + 545844 T^{4} + 8754196 T^{5} + 124772555 T^{6} + 1577863256 T^{7} + 18078712657 T^{8} + 186544972542 T^{9} + 1753635127729 T^{10} + 14846115375704 T^{11} + 113876542089515 T^{12} + 775002677613076 T^{13} + 4687348155241908 T^{14} + 24094548214576254 T^{15} + 104795374968112561 T^{16} + 337009644558209323 T^{17} + 760231058654565217 T^{18} \))(\( 1 - 31 T + 948 T^{2} - 17713 T^{3} + 322751 T^{4} - 4421250 T^{5} + 60248941 T^{6} - 663424636 T^{7} + 7579740116 T^{8} - 73397228310 T^{9} + 775634999502 T^{10} - 7119531146070 T^{11} + 71317774751444 T^{12} - 605489752812028 T^{13} + 5333795427741421 T^{14} - 37966778111261250 T^{15} + 268842547562839679 T^{16} - 1431180012960815569 T^{17} + 7429887047469359028 T^{18} - 23567162818291521727 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 29 T + 586 T^{2} - 5635 T^{3} + 16926 T^{4} + 576021 T^{5} - 7857755 T^{6} + 22560715 T^{7} + 935277491 T^{8} - 13454188022 T^{9} + 65540750049 T^{10} + 819726607062 T^{11} - 14053893735172 T^{12} + 79513480885014 T^{13} + 616672917211041 T^{14} - 12279274144602806 T^{15} + 82799443813713971 T^{16} + 193736536146203755 T^{17} - 6545289936590874395 T^{18} + 46541508623367128373 T^{19} + \)\(13\!\cdots\!86\)\( T^{20} - \)\(42\!\cdots\!95\)\( T^{21} + \)\(43\!\cdots\!14\)\( T^{22} - \)\(20\!\cdots\!37\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 6 T + 832 T^{2} - 5918 T^{3} + 341876 T^{4} - 2755486 T^{5} + 92593566 T^{6} - 810972134 T^{7} + 18572514318 T^{8} - 169569347650 T^{9} + 2931193224296 T^{10} - 26741162517482 T^{11} + 376439434844093 T^{12} - 3283902645684332 T^{13} + 40023991828359028 T^{14} - 318538556631380204 T^{15} + 3541918642448071037 T^{16} - 24405937018317849386 T^{17} + \)\(25\!\cdots\!76\)\( T^{18} - \)\(14\!\cdots\!50\)\( T^{19} + \)\(15\!\cdots\!22\)\( T^{20} - \)\(65\!\cdots\!42\)\( T^{21} + \)\(72\!\cdots\!26\)\( T^{22} - \)\(20\!\cdots\!62\)\( T^{23} + \)\(25\!\cdots\!24\)\( T^{24} - \)\(42\!\cdots\!54\)\( T^{25} + \)\(57\!\cdots\!12\)\( T^{26} - \)\(40\!\cdots\!62\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \))(\( 1 + 6 T + 984 T^{2} + 6272 T^{3} + 498210 T^{4} + 3238598 T^{5} + 171456717 T^{6} + 1109459176 T^{7} + 44779126774 T^{8} + 283905879590 T^{9} + 9402186963242 T^{10} + 57761996978052 T^{11} + 1642481809267899 T^{12} + 9693133530049972 T^{13} + 243930203817054337 T^{14} + 1372365202094554728 T^{15} + 31222003302133241475 T^{16} + \)\(16\!\cdots\!18\)\( T^{17} + \)\(34\!\cdots\!53\)\( T^{18} + \)\(17\!\cdots\!88\)\( T^{19} + \)\(33\!\cdots\!41\)\( T^{20} + \)\(15\!\cdots\!62\)\( T^{21} + \)\(28\!\cdots\!75\)\( T^{22} + \)\(12\!\cdots\!68\)\( T^{23} + \)\(20\!\cdots\!09\)\( T^{24} + \)\(80\!\cdots\!88\)\( T^{25} + \)\(13\!\cdots\!87\)\( T^{26} + \)\(45\!\cdots\!72\)\( T^{27} + \)\(71\!\cdots\!14\)\( T^{28} + \)\(20\!\cdots\!10\)\( T^{29} + \)\(32\!\cdots\!22\)\( T^{30} + \)\(76\!\cdots\!16\)\( T^{31} + \)\(11\!\cdots\!09\)\( T^{32} + \)\(21\!\cdots\!62\)\( T^{33} + \)\(31\!\cdots\!30\)\( T^{34} + \)\(38\!\cdots\!12\)\( T^{35} + \)\(58\!\cdots\!08\)\( T^{36} + \)\(34\!\cdots\!34\)\( T^{37} + \)\(56\!\cdots\!33\)\( T^{38} \))(\( 1 + 6 T + 984 T^{2} + 6272 T^{3} + 498210 T^{4} + 3238598 T^{5} + 171456717 T^{6} + 1109459176 T^{7} + 44779126774 T^{8} + 283905879590 T^{9} + 9402186963242 T^{10} + 57761996978052 T^{11} + 1642481809267899 T^{12} + 9693133530049972 T^{13} + 243930203817054337 T^{14} + 1372365202094554728 T^{15} + 31222003302133241475 T^{16} + \)\(16\!\cdots\!18\)\( T^{17} + \)\(34\!\cdots\!53\)\( T^{18} + \)\(17\!\cdots\!88\)\( T^{19} + \)\(33\!\cdots\!41\)\( T^{20} + \)\(15\!\cdots\!62\)\( T^{21} + \)\(28\!\cdots\!75\)\( T^{22} + \)\(12\!\cdots\!68\)\( T^{23} + \)\(20\!\cdots\!09\)\( T^{24} + \)\(80\!\cdots\!88\)\( T^{25} + \)\(13\!\cdots\!87\)\( T^{26} + \)\(45\!\cdots\!72\)\( T^{27} + \)\(71\!\cdots\!14\)\( T^{28} + \)\(20\!\cdots\!10\)\( T^{29} + \)\(32\!\cdots\!22\)\( T^{30} + \)\(76\!\cdots\!16\)\( T^{31} + \)\(11\!\cdots\!09\)\( T^{32} + \)\(21\!\cdots\!62\)\( T^{33} + \)\(31\!\cdots\!30\)\( T^{34} + \)\(38\!\cdots\!12\)\( T^{35} + \)\(58\!\cdots\!08\)\( T^{36} + \)\(34\!\cdots\!34\)\( T^{37} + \)\(56\!\cdots\!33\)\( T^{38} \))
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