Properties

Label 8004.2.a
Level 8004
Weight 2
Character orbit a
Rep. character \(\chi_{8004}(1,\cdot)\)
Character field \(\Q\)
Dimension 104
Newform subspaces 11
Sturm bound 2880
Trace bound 7

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Defining parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(2880\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8004))\).

Total New Old
Modular forms 1452 104 1348
Cusp forms 1429 104 1325
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.

\(2\)\(3\)\(23\)\(29\)FrickeDim.
\(-\)\(+\)\(+\)\(+\)\(-\)\(14\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(10\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(16\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(10\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(18\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(16\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(40\)
Minus space\(-\)\(64\)

Trace form

\( 104q + 104q^{9} + O(q^{10}) \) \( 104q + 104q^{9} + 8q^{19} + 8q^{21} + 112q^{25} + 8q^{31} + 8q^{37} + 16q^{39} + 8q^{41} + 16q^{43} - 8q^{47} + 120q^{49} + 32q^{53} + 8q^{55} + 8q^{57} + 16q^{59} + 16q^{61} + 56q^{65} + 32q^{67} - 8q^{69} - 8q^{71} - 8q^{73} + 24q^{77} - 16q^{79} + 104q^{81} + 72q^{83} + 24q^{85} - 16q^{89} + 8q^{91} + 24q^{93} + 32q^{95} + 48q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8004))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 23 29
8004.2.a.a \(1\) \(63.912\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-5\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{5}-5q^{7}+q^{9}-3q^{11}+\cdots\)
8004.2.a.b \(1\) \(63.912\) \(\Q\) None \(0\) \(-1\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
8004.2.a.c \(1\) \(63.912\) \(\Q\) None \(0\) \(1\) \(-2\) \(3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-2q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
8004.2.a.d \(8\) \(63.912\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(-5\) \(-4\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+(-1-\beta _{7})q^{5}+(\beta _{6}+\beta _{7})q^{7}+\cdots\)
8004.2.a.e \(9\) \(63.912\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(-3\) \(7\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+\beta _{1}q^{5}+(1-\beta _{3})q^{7}+q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots\)
8004.2.a.f \(9\) \(63.912\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(9\) \(-1\) \(-5\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{6})q^{7}+q^{9}+\cdots\)
8004.2.a.g \(12\) \(63.912\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-12\) \(-3\) \(4\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
8004.2.a.h \(13\) \(63.912\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-13\) \(5\) \(-8\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}+\beta _{1}q^{5}+(-1+\beta _{12})q^{7}+q^{9}+\cdots\)
8004.2.a.i \(16\) \(63.912\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-16\) \(5\) \(-4\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+\beta _{1}q^{5}-\beta _{12}q^{7}+q^{9}-\beta _{4}q^{11}+\cdots\)
8004.2.a.j \(16\) \(63.912\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(16\) \(3\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+\beta _{1}q^{5}-\beta _{7}q^{7}+q^{9}-\beta _{6}q^{11}+\cdots\)
8004.2.a.k \(18\) \(63.912\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(18\) \(5\) \(6\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}-\beta _{9}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8004))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(174))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(348))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(667))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2001))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2668))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4002))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 - T )^{8} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{12} \))(\( ( 1 + T )^{13} \))(\( ( 1 + T )^{16} \))(\( ( 1 - T )^{16} \))(\( ( 1 - T )^{18} \))
$5$ (\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T + 35 T^{2} + 123 T^{3} + 515 T^{4} + 1432 T^{5} + 4547 T^{6} + 10490 T^{7} + 27216 T^{8} + 52450 T^{9} + 113675 T^{10} + 179000 T^{11} + 321875 T^{12} + 384375 T^{13} + 546875 T^{14} + 390625 T^{15} + 390625 T^{16} \))(\( 1 + 3 T + 26 T^{2} + 76 T^{3} + 352 T^{4} + 897 T^{5} + 3136 T^{6} + 6906 T^{7} + 20281 T^{8} + 39416 T^{9} + 101405 T^{10} + 172650 T^{11} + 392000 T^{12} + 560625 T^{13} + 1100000 T^{14} + 1187500 T^{15} + 2031250 T^{16} + 1171875 T^{17} + 1953125 T^{18} \))(\( 1 + T + 28 T^{2} + 36 T^{3} + 380 T^{4} + 579 T^{5} + 3332 T^{6} + 5506 T^{7} + 21415 T^{8} + 33836 T^{9} + 107075 T^{10} + 137650 T^{11} + 416500 T^{12} + 361875 T^{13} + 1187500 T^{14} + 562500 T^{15} + 2187500 T^{16} + 390625 T^{17} + 1953125 T^{18} \))(\( 1 + 3 T + 29 T^{2} + 85 T^{3} + 447 T^{4} + 1222 T^{5} + 4791 T^{6} + 12124 T^{7} + 39159 T^{8} + 92181 T^{9} + 257964 T^{10} + 561329 T^{11} + 1410706 T^{12} + 2806645 T^{13} + 6449100 T^{14} + 11522625 T^{15} + 24474375 T^{16} + 37887500 T^{17} + 74859375 T^{18} + 95468750 T^{19} + 174609375 T^{20} + 166015625 T^{21} + 283203125 T^{22} + 146484375 T^{23} + 244140625 T^{24} \))(\( 1 - 5 T + 38 T^{2} - 142 T^{3} + 645 T^{4} - 2002 T^{5} + 6790 T^{6} - 18442 T^{7} + 51016 T^{8} - 127080 T^{9} + 303607 T^{10} - 724798 T^{11} + 1588171 T^{12} - 3739062 T^{13} + 7940855 T^{14} - 18119950 T^{15} + 37950875 T^{16} - 79425000 T^{17} + 159425000 T^{18} - 288156250 T^{19} + 530468750 T^{20} - 782031250 T^{21} + 1259765625 T^{22} - 1386718750 T^{23} + 1855468750 T^{24} - 1220703125 T^{25} + 1220703125 T^{26} \))(\( 1 - 5 T + 37 T^{2} - 141 T^{3} + 624 T^{4} - 1963 T^{5} + 6732 T^{6} - 18203 T^{7} + 52813 T^{8} - 124750 T^{9} + 319438 T^{10} - 668382 T^{11} + 1576116 T^{12} - 3007394 T^{13} + 6973497 T^{14} - 13024338 T^{15} + 32347212 T^{16} - 65121690 T^{17} + 174337425 T^{18} - 375924250 T^{19} + 985072500 T^{20} - 2088693750 T^{21} + 4991218750 T^{22} - 9746093750 T^{23} + 20630078125 T^{24} - 35552734375 T^{25} + 65742187500 T^{26} - 95849609375 T^{27} + 152343750000 T^{28} - 172119140625 T^{29} + 225830078125 T^{30} - 152587890625 T^{31} + 152587890625 T^{32} \))(\( 1 - 3 T + 31 T^{2} - 95 T^{3} + 502 T^{4} - 1453 T^{5} + 5480 T^{6} - 14265 T^{7} + 43779 T^{8} - 99922 T^{9} + 265306 T^{10} - 525742 T^{11} + 1264458 T^{12} - 2188838 T^{13} + 5201327 T^{14} - 8479994 T^{15} + 23022008 T^{16} - 42399970 T^{17} + 130033175 T^{18} - 273604750 T^{19} + 790286250 T^{20} - 1642943750 T^{21} + 4145406250 T^{22} - 7806406250 T^{23} + 17101171875 T^{24} - 27861328125 T^{25} + 53515625000 T^{26} - 70947265625 T^{27} + 122558593750 T^{28} - 115966796875 T^{29} + 189208984375 T^{30} - 91552734375 T^{31} + 152587890625 T^{32} \))(\( 1 - 5 T + 35 T^{2} - 137 T^{3} + 647 T^{4} - 2288 T^{5} + 8795 T^{6} - 28286 T^{7} + 94421 T^{8} - 281023 T^{9} + 848246 T^{10} - 2357997 T^{11} + 6543329 T^{12} - 17066296 T^{13} + 44122205 T^{14} - 108511970 T^{15} + 263137154 T^{16} - 610300998 T^{17} + 1393614302 T^{18} - 3051504990 T^{19} + 6578428850 T^{20} - 13563996250 T^{21} + 27576378125 T^{22} - 53332175000 T^{23} + 102239515625 T^{24} - 184218515625 T^{25} + 331346093750 T^{26} - 548873046875 T^{27} + 922080078125 T^{28} - 1381152343750 T^{29} + 2147216796875 T^{30} - 2792968750000 T^{31} + 3948974609375 T^{32} - 4180908203125 T^{33} + 5340576171875 T^{34} - 3814697265625 T^{35} + 3814697265625 T^{36} \))
$7$ (\( 1 + 5 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 + 4 T + 45 T^{2} + 155 T^{3} + 966 T^{4} + 2785 T^{5} + 12546 T^{6} + 30168 T^{7} + 107038 T^{8} + 211176 T^{9} + 614754 T^{10} + 955255 T^{11} + 2319366 T^{12} + 2605085 T^{13} + 5294205 T^{14} + 3294172 T^{15} + 5764801 T^{16} \))(\( 1 - 7 T + 65 T^{2} - 327 T^{3} + 1809 T^{4} - 7119 T^{5} + 29153 T^{6} - 93123 T^{7} + 303428 T^{8} - 796948 T^{9} + 2123996 T^{10} - 4563027 T^{11} + 9999479 T^{12} - 17092719 T^{13} + 30403863 T^{14} - 38471223 T^{15} + 53530295 T^{16} - 40353607 T^{17} + 40353607 T^{18} \))(\( 1 + 5 T + 47 T^{2} + 179 T^{3} + 987 T^{4} + 3081 T^{5} + 12739 T^{6} + 33935 T^{7} + 116730 T^{8} + 272488 T^{9} + 817110 T^{10} + 1662815 T^{11} + 4369477 T^{12} + 7397481 T^{13} + 16588509 T^{14} + 21059171 T^{15} + 38706521 T^{16} + 28824005 T^{17} + 40353607 T^{18} \))(\( 1 - 4 T + 51 T^{2} - 181 T^{3} + 1306 T^{4} - 4099 T^{5} + 21910 T^{6} - 61538 T^{7} + 269911 T^{8} - 683906 T^{9} + 2595787 T^{10} - 5956898 T^{11} + 20127548 T^{12} - 41698286 T^{13} + 127193563 T^{14} - 234579758 T^{15} + 648056311 T^{16} - 1034269166 T^{17} + 2577689590 T^{18} - 3375702757 T^{19} + 7528830106 T^{20} - 7304002867 T^{21} + 14406237699 T^{22} - 7909306972 T^{23} + 13841287201 T^{24} \))(\( 1 + 8 T + 68 T^{2} + 389 T^{3} + 2071 T^{4} + 9380 T^{5} + 39452 T^{6} + 150731 T^{7} + 541715 T^{8} + 1811420 T^{9} + 5758228 T^{10} + 17212944 T^{11} + 49216305 T^{12} + 133014208 T^{13} + 344514135 T^{14} + 843434256 T^{15} + 1975072204 T^{16} + 4349219420 T^{17} + 9104604005 T^{18} + 17733351419 T^{19} + 32490418436 T^{20} + 54073833380 T^{21} + 83572320097 T^{22} + 109882871861 T^{23} + 134458218524 T^{24} + 110730297608 T^{25} + 96889010407 T^{26} \))(\( 1 + 4 T + 49 T^{2} + 143 T^{3} + 1146 T^{4} + 2617 T^{5} + 17824 T^{6} + 31512 T^{7} + 209140 T^{8} + 272508 T^{9} + 1998130 T^{10} + 1731837 T^{11} + 16456118 T^{12} + 8189843 T^{13} + 123459485 T^{14} + 33939848 T^{15} + 879401590 T^{16} + 237578936 T^{17} + 6049514765 T^{18} + 2809116149 T^{19} + 39511139318 T^{20} + 29106984459 T^{21} + 235077996370 T^{22} + 224422055844 T^{23} + 1205650481140 T^{24} + 1271622863784 T^{25} + 5034838838176 T^{26} + 5174664086431 T^{27} + 15862115132346 T^{28} + 13855128488201 T^{29} + 33232930569601 T^{30} + 18990246039772 T^{31} + 33232930569601 T^{32} \))(\( 1 - 4 T + 47 T^{2} - 137 T^{3} + 972 T^{4} - 1999 T^{5} + 12134 T^{6} - 16308 T^{7} + 112920 T^{8} - 92052 T^{9} + 974324 T^{10} - 611743 T^{11} + 8628020 T^{12} - 6093673 T^{13} + 73145687 T^{14} - 56106964 T^{15} + 549676366 T^{16} - 392748748 T^{17} + 3584138663 T^{18} - 2090129839 T^{19} + 20715876020 T^{20} - 10281564601 T^{21} + 114628244276 T^{22} - 75808780236 T^{23} + 650961328920 T^{24} - 658086622956 T^{25} + 3427554671366 T^{26} - 3952676159257 T^{27} + 13453731159372 T^{28} - 13273794425759 T^{29} + 31876484423903 T^{30} - 18990246039772 T^{31} + 33232930569601 T^{32} \))(\( 1 - 6 T + 49 T^{2} - 231 T^{3} + 1229 T^{4} - 4975 T^{5} + 21563 T^{6} - 78759 T^{7} + 300034 T^{8} - 1009905 T^{9} + 3503978 T^{10} - 11021565 T^{11} + 35529538 T^{12} - 105544067 T^{13} + 320041957 T^{14} - 902568507 T^{15} + 2592704414 T^{16} - 6963281997 T^{17} + 19034710858 T^{18} - 48742973979 T^{19} + 127042516286 T^{20} - 309580997901 T^{21} + 768420738757 T^{22} - 1773879134069 T^{23} + 4180014616162 T^{24} - 9076732704795 T^{25} + 20199735878378 T^{26} - 40753309477335 T^{27} + 84752178858466 T^{28} - 155732276951937 T^{29} + 298459675915163 T^{30} - 482022826774825 T^{31} + 833536156531421 T^{32} - 1096686708796833 T^{33} + 1628413597910449 T^{34} - 1395783083923242 T^{35} + 1628413597910449 T^{36} \))
$11$ (\( 1 + 3 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 5 T + 76 T^{2} + 294 T^{3} + 2545 T^{4} + 7973 T^{5} + 50715 T^{6} + 131560 T^{7} + 672774 T^{8} + 1447160 T^{9} + 6136515 T^{10} + 10612063 T^{11} + 37261345 T^{12} + 47348994 T^{13} + 134638636 T^{14} + 97435855 T^{15} + 214358881 T^{16} \))(\( 1 + 2 T + 49 T^{2} + 95 T^{3} + 1244 T^{4} + 2309 T^{5} + 22092 T^{6} + 37857 T^{7} + 303948 T^{8} + 467906 T^{9} + 3343428 T^{10} + 4580697 T^{11} + 29404452 T^{12} + 33806069 T^{13} + 200347444 T^{14} + 168298295 T^{15} + 954871379 T^{16} + 428717762 T^{17} + 2357947691 T^{18} \))(\( 1 + 8 T + 95 T^{2} + 557 T^{3} + 3888 T^{4} + 18097 T^{5} + 93740 T^{6} + 359179 T^{7} + 1493566 T^{8} + 4770750 T^{9} + 16429226 T^{10} + 43460659 T^{11} + 124767940 T^{12} + 264958177 T^{13} + 626166288 T^{14} + 986759477 T^{15} + 1851281245 T^{16} + 1714871048 T^{17} + 2357947691 T^{18} \))(\( 1 + 5 T + 84 T^{2} + 394 T^{3} + 3529 T^{4} + 15213 T^{5} + 98145 T^{6} + 382998 T^{7} + 2001529 T^{8} + 7024517 T^{9} + 31392867 T^{10} + 98769211 T^{11} + 387711866 T^{12} + 1086461321 T^{13} + 3798536907 T^{14} + 9349632127 T^{15} + 29304386089 T^{16} + 61682210898 T^{17} + 173869854345 T^{18} + 296458332423 T^{19} + 756472491049 T^{20} + 929031390254 T^{21} + 2178743666484 T^{22} + 1426558353055 T^{23} + 3138428376721 T^{24} \))(\( 1 - T + 49 T^{2} - 135 T^{3} + 1568 T^{4} - 4900 T^{5} + 39847 T^{6} - 121776 T^{7} + 778305 T^{8} - 2335858 T^{9} + 12413304 T^{10} - 35012001 T^{11} + 164522468 T^{12} - 425615898 T^{13} + 1809747148 T^{14} - 4236452121 T^{15} + 16522107624 T^{16} - 34199296978 T^{17} + 125346798555 T^{18} - 215733612336 T^{19} + 776505302837 T^{20} - 1050358516900 T^{21} + 3697261979488 T^{22} - 3501552321135 T^{23} + 13980271859939 T^{24} - 3138428376721 T^{25} + 34522712143931 T^{26} \))(\( 1 - 5 T + 86 T^{2} - 332 T^{3} + 3444 T^{4} - 10852 T^{5} + 89725 T^{6} - 239870 T^{7} + 1769895 T^{8} - 4176547 T^{9} + 29063850 T^{10} - 63510903 T^{11} + 421824120 T^{12} - 883388327 T^{13} + 5513061075 T^{14} - 11073438454 T^{15} + 64368763384 T^{16} - 121807822994 T^{17} + 667080390075 T^{18} - 1175789863237 T^{19} + 6175926940920 T^{20} - 10228494439053 T^{21} + 51488383169850 T^{22} - 81389085578537 T^{23} + 379392711687495 T^{24} - 565600912640170 T^{25} + 2327235422324725 T^{26} - 3096202249470572 T^{27} + 10808747329427124 T^{28} - 11461540431785092 T^{29} + 32658485688158726 T^{30} - 20886240847078255 T^{31} + 45949729863572161 T^{32} \))(\( 1 - 5 T + 90 T^{2} - 368 T^{3} + 3750 T^{4} - 12402 T^{5} + 96387 T^{6} - 248512 T^{7} + 1715621 T^{8} - 3107483 T^{9} + 22553162 T^{10} - 20117519 T^{11} + 231881226 T^{12} + 67176915 T^{13} + 2074874657 T^{14} + 3224397132 T^{15} + 20170399972 T^{16} + 35468368452 T^{17} + 251059833497 T^{18} + 89412473865 T^{19} + 3394973029866 T^{20} - 3239946552469 T^{21} + 39954302225882 T^{22} - 60556052600593 T^{23} + 367758597780101 T^{24} - 585978296585792 T^{25} + 2500030545016587 T^{26} - 3538435338917622 T^{27} + 11769106412703750 T^{28} - 12704358068966608 T^{29} + 34177485022491690 T^{30} - 20886240847078255 T^{31} + 45949729863572161 T^{32} \))(\( 1 - 5 T + 68 T^{2} - 270 T^{3} + 2411 T^{4} - 9009 T^{5} + 64049 T^{6} - 225538 T^{7} + 1358293 T^{8} - 4545879 T^{9} + 24509219 T^{10} - 78775999 T^{11} + 387479707 T^{12} - 1194609864 T^{13} + 5460456679 T^{14} - 16199392563 T^{15} + 69561546004 T^{16} - 197395222517 T^{17} + 802354008898 T^{18} - 2171347447687 T^{19} + 8416947066484 T^{20} - 21561391501353 T^{21} + 79946546237239 T^{22} - 192393113207064 T^{23} + 686443937212627 T^{24} - 1535121363208829 T^{25} + 5253768759023939 T^{26} - 10718944891615389 T^{27} + 35230622273566093 T^{28} - 64348623566263718 T^{29} + 201013199100603329 T^{30} - 311015113704674379 T^{31} + 915576848769194051 T^{32} - 1127857005742225770 T^{33} + 3124581630722906948 T^{34} - 2527235142496468855 T^{35} + 5559917313492231481 T^{36} \))
$13$ (\( 1 - T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 4 T + 90 T^{2} + 319 T^{3} + 3697 T^{4} + 11374 T^{5} + 90515 T^{6} + 235529 T^{7} + 1442141 T^{8} + 3061877 T^{9} + 15297035 T^{10} + 24988678 T^{11} + 105590017 T^{12} + 118442467 T^{13} + 434412810 T^{14} + 250994068 T^{15} + 815730721 T^{16} \))(\( 1 + 7 T + 87 T^{2} + 469 T^{3} + 3480 T^{4} + 15664 T^{5} + 87354 T^{6} + 337444 T^{7} + 1543139 T^{8} + 5151761 T^{9} + 20060807 T^{10} + 57028036 T^{11} + 191916738 T^{12} + 447379504 T^{13} + 1292099640 T^{14} + 2263773421 T^{15} + 5459120979 T^{16} + 5710115047 T^{17} + 10604499373 T^{18} \))(\( 1 + T + 64 T^{2} + 22 T^{3} + 2056 T^{4} - 466 T^{5} + 44369 T^{6} - 24869 T^{7} + 727482 T^{8} - 452444 T^{9} + 9457266 T^{10} - 4202861 T^{11} + 97478693 T^{12} - 13309426 T^{13} + 763378408 T^{14} + 106189798 T^{15} + 4015905088 T^{16} + 815730721 T^{17} + 10604499373 T^{18} \))(\( 1 + 6 T + 103 T^{2} + 545 T^{3} + 4809 T^{4} + 22421 T^{5} + 135951 T^{6} + 557101 T^{7} + 2662315 T^{8} + 9670399 T^{9} + 40531145 T^{10} + 135620044 T^{11} + 543448756 T^{12} + 1763060572 T^{13} + 6849763505 T^{14} + 21245866603 T^{15} + 76038378715 T^{16} + 206847701593 T^{17} + 656209510359 T^{18} + 1406884499657 T^{19} + 3922849037289 T^{20} + 5779452158285 T^{21} + 14199424660447 T^{22} + 10752962364222 T^{23} + 23298085122481 T^{24} \))(\( 1 - T + 102 T^{2} - 190 T^{3} + 5113 T^{4} - 13325 T^{5} + 170101 T^{6} - 532119 T^{7} + 4244995 T^{8} - 14250969 T^{9} + 83981695 T^{10} - 277909764 T^{11} + 1343812157 T^{12} - 4117201856 T^{13} + 17469558041 T^{14} - 46966750116 T^{15} + 184507783915 T^{16} - 407021925609 T^{17} + 1576136928535 T^{18} - 2568436778271 T^{19} + 10673585490217 T^{20} - 10869611857325 T^{21} + 54220805294149 T^{22} - 26193113451310 T^{23} + 182800360191774 T^{24} - 23298085122481 T^{25} + 302875106592253 T^{26} \))(\( 1 - 8 T + 88 T^{2} - 521 T^{3} + 3554 T^{4} - 17904 T^{5} + 95493 T^{6} - 419436 T^{7} + 1852540 T^{8} - 7049837 T^{9} + 26303780 T^{10} - 86286315 T^{11} + 274232175 T^{12} - 769412620 T^{13} + 2146397951 T^{14} - 5657924955 T^{15} + 18836760148 T^{16} - 73553024415 T^{17} + 362741253719 T^{18} - 1690399526140 T^{19} + 7832345150175 T^{20} - 32037504755295 T^{21} + 126963322038020 T^{22} - 442366816841729 T^{23} + 1511173789881340 T^{24} - 4447908799013628 T^{25} + 13164520962136557 T^{26} - 32086839694838448 T^{27} + 82801394525297474 T^{28} - 157797930534563813 T^{29} + 346489121941537432 T^{30} - 409487144112726056 T^{31} + 665416609183179841 T^{32} \))(\( 1 - 6 T + 97 T^{2} - 359 T^{3} + 3862 T^{4} - 8739 T^{5} + 97576 T^{6} - 109826 T^{7} + 1948915 T^{8} - 237632 T^{9} + 34316745 T^{10} + 20907884 T^{11} + 569527538 T^{12} + 521147076 T^{13} + 8794275353 T^{14} + 8484394754 T^{15} + 121320902098 T^{16} + 110297131802 T^{17} + 1486232534657 T^{18} + 1144960125972 T^{19} + 16266276012818 T^{20} + 7762950974012 T^{21} + 165640373616705 T^{22} - 14911055591744 T^{23} + 1589789838117715 T^{24} - 1164649748139098 T^{25} + 13451680200658024 T^{26} - 15661689683489343 T^{27} + 89977204743021622 T^{28} - 108732163266618827 T^{29} + 381925509412831033 T^{30} - 307115358084544542 T^{31} + 665416609183179841 T^{32} \))(\( 1 - 6 T + 99 T^{2} - 519 T^{3} + 5281 T^{4} - 25427 T^{5} + 197841 T^{6} - 884791 T^{7} + 5767401 T^{8} - 24228303 T^{9} + 138499447 T^{10} - 549141354 T^{11} + 2830721103 T^{12} - 10626758320 T^{13} + 50276567054 T^{14} - 178667142246 T^{15} + 784917029510 T^{16} - 2635910494658 T^{17} + 10840622258686 T^{18} - 34266836430554 T^{19} + 132650977987190 T^{20} - 392531711514462 T^{21} + 1435949031629294 T^{22} - 3945640976907760 T^{23} + 13663350096450327 T^{24} - 34457805586872018 T^{25} + 112978253759411287 T^{26} - 256929023972354019 T^{27} + 795085203748414449 T^{28} - 1585687387200391267 T^{29} + 4609316458716763521 T^{30} - 7701205335321217031 T^{31} + 20793284692877945209 T^{32} - 26565478474313102883 T^{33} + 65876244309134804259 T^{34} - 51902495516288027598 T^{35} + \)\(11\!\cdots\!29\)\( T^{36} \))
$17$ (\( 1 + 3 T + 17 T^{2} \))(\( 1 - 5 T + 17 T^{2} \))(\( 1 + 5 T + 17 T^{2} \))(\( 1 + 3 T + 102 T^{2} + 230 T^{3} + 4831 T^{4} + 8730 T^{5} + 143335 T^{6} + 216129 T^{7} + 2915821 T^{8} + 3674193 T^{9} + 41423815 T^{10} + 42890490 T^{11} + 403489951 T^{12} + 326567110 T^{13} + 2462032038 T^{14} + 1231016019 T^{15} + 6975757441 T^{16} \))(\( 1 + 98 T^{2} - 115 T^{3} + 4525 T^{4} - 8601 T^{5} + 140632 T^{6} - 281898 T^{7} + 3253471 T^{8} - 5743037 T^{9} + 55309007 T^{10} - 81468522 T^{11} + 690925016 T^{12} - 718364121 T^{13} + 6424852925 T^{14} - 2775820435 T^{15} + 40213189954 T^{16} + 118587876497 T^{18} \))(\( 1 + 2 T + 89 T^{2} + 229 T^{3} + 4280 T^{4} + 11246 T^{5} + 136975 T^{6} + 341214 T^{7} + 3152871 T^{8} + 6956984 T^{9} + 53598807 T^{10} + 98610846 T^{11} + 672958175 T^{12} + 939277166 T^{13} + 6076987960 T^{14} + 5527503301 T^{15} + 36520141897 T^{16} + 13951514882 T^{17} + 118587876497 T^{18} \))(\( 1 + 7 T + 135 T^{2} + 779 T^{3} + 8739 T^{4} + 43410 T^{5} + 367973 T^{6} + 1616106 T^{7} + 11359339 T^{8} + 44687859 T^{9} + 271762001 T^{10} + 960357097 T^{11} + 5165105850 T^{12} + 16326070649 T^{13} + 78539218289 T^{14} + 219551451267 T^{15} + 948743352619 T^{16} + 2294639416842 T^{17} + 8881973677637 T^{18} + 17812801794930 T^{19} + 60961144276899 T^{20} + 92379955791163 T^{21} + 272159176560615 T^{22} + 239903274153431 T^{23} + 582622237229761 T^{24} \))(\( 1 + 2 T + 101 T^{2} + 209 T^{3} + 5508 T^{4} + 10724 T^{5} + 210093 T^{6} + 382984 T^{7} + 6192510 T^{8} + 10565848 T^{9} + 148878000 T^{10} + 236439927 T^{11} + 2991472795 T^{12} + 4400855588 T^{13} + 50855037515 T^{14} + 68331138903 T^{15} + 731437614000 T^{16} + 882470190808 T^{17} + 8792478671070 T^{18} + 9244302725896 T^{19} + 86209282826589 T^{20} + 74808022797284 T^{21} + 653182023745476 T^{22} + 421342725193841 T^{23} + 3461461527070933 T^{24} + 1165244474459522 T^{25} + 9904578032905937 T^{26} \))(\( 1 - 7 T + 94 T^{2} - 516 T^{3} + 4635 T^{4} - 21224 T^{5} + 155819 T^{6} - 616477 T^{7} + 4125685 T^{8} - 14665513 T^{9} + 95186233 T^{10} - 319182182 T^{11} + 2045014477 T^{12} - 6632736614 T^{13} + 40922908606 T^{14} - 127330577499 T^{15} + 739039136132 T^{16} - 2164619817483 T^{17} + 11826720587134 T^{18} - 32586634984582 T^{19} + 170801654133517 T^{20} - 453193055387974 T^{21} + 2297564266887577 T^{22} - 6017827143284249 T^{23} + 28779777837972085 T^{24} - 73106698339241069 T^{25} + 314130153574062731 T^{26} - 727386727233202792 T^{27} + 2700454069559942235 T^{28} - 5110762264979463492 T^{29} + 15827515696583687326 T^{30} - 20036961360568710551 T^{31} + 48661191875666868481 T^{32} \))(\( 1 - 3 T + 83 T^{2} - 125 T^{3} + 2861 T^{4} - 992 T^{5} + 69519 T^{6} - 20198 T^{7} + 1771472 T^{8} - 1756390 T^{9} + 39865506 T^{10} - 38769572 T^{11} + 711027721 T^{12} - 699954287 T^{13} + 13151255436 T^{14} - 19625255617 T^{15} + 245439220562 T^{16} - 333629345489 T^{17} + 3800712821004 T^{18} - 3438875412031 T^{19} + 59385746285641 T^{20} - 55047248191204 T^{21} + 962256401794914 T^{22} - 720714741870470 T^{23} + 12357358985523152 T^{24} - 2395237929486406 T^{25} + 140149879965314031 T^{26} - 33997721137171936 T^{27} + 1666882220714346221 T^{28} - 1238072254113242125 T^{29} + 13975359604430277107 T^{30} - 8587269154529447379 T^{31} + 48661191875666868481 T^{32} \))(\( 1 - 7 T + 159 T^{2} - 785 T^{3} + 10794 T^{4} - 37203 T^{5} + 434346 T^{6} - 925093 T^{7} + 12134253 T^{8} - 9173784 T^{9} + 263701825 T^{10} + 211750906 T^{11} + 4937195025 T^{12} + 12179734203 T^{13} + 87221693398 T^{14} + 334899000309 T^{15} + 1528270903255 T^{16} + 6881765927694 T^{17} + 26377674361600 T^{18} + 116990020770798 T^{19} + 441670291040695 T^{20} + 1645358788518117 T^{21} + 7284843054294358 T^{22} + 17293480866268971 T^{23} + 119171885582394225 T^{24} + 86889585774587738 T^{25} + 1839519967949029825 T^{26} - 1087899564002154648 T^{27} + 24462580034504979597 T^{28} - 31704691370917134869 T^{29} + \)\(25\!\cdots\!06\)\( T^{30} - \)\(36\!\cdots\!11\)\( T^{31} + \)\(18\!\cdots\!26\)\( T^{32} - \)\(22\!\cdots\!05\)\( T^{33} + \)\(77\!\cdots\!79\)\( T^{34} - \)\(57\!\cdots\!39\)\( T^{35} + \)\(14\!\cdots\!09\)\( T^{36} \))
$19$ (\( 1 - 6 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 5 T + 107 T^{2} + 478 T^{3} + 5359 T^{4} + 21939 T^{5} + 169074 T^{6} + 622661 T^{7} + 3759380 T^{8} + 11830559 T^{9} + 61035714 T^{10} + 150479601 T^{11} + 698390239 T^{12} + 1183575322 T^{13} + 5033909267 T^{14} + 4469358695 T^{15} + 16983563041 T^{16} \))(\( 1 + T + 97 T^{2} + 114 T^{3} + 4774 T^{4} + 6136 T^{5} + 160280 T^{6} + 198588 T^{7} + 4006913 T^{8} + 4421409 T^{9} + 76131347 T^{10} + 71690268 T^{11} + 1099360520 T^{12} + 799649656 T^{13} + 11820896626 T^{14} + 5363230434 T^{15} + 86705558683 T^{16} + 16983563041 T^{17} + 322687697779 T^{18} \))(\( 1 + 11 T + 152 T^{2} + 1069 T^{3} + 8804 T^{4} + 47609 T^{5} + 305389 T^{6} + 1397998 T^{7} + 7647564 T^{8} + 30527568 T^{9} + 145303716 T^{10} + 504677278 T^{11} + 2094663151 T^{12} + 6204452489 T^{13} + 21799575596 T^{14} + 50292046789 T^{15} + 135868504328 T^{16} + 186819193451 T^{17} + 322687697779 T^{18} \))(\( 1 + 3 T + 158 T^{2} + 469 T^{3} + 12128 T^{4} + 35189 T^{5} + 600218 T^{6} + 1677275 T^{7} + 21423184 T^{8} + 56533655 T^{9} + 583298614 T^{10} + 1416071249 T^{11} + 12458946078 T^{12} + 26905353731 T^{13} + 210570799654 T^{14} + 387764339645 T^{15} + 2791890762064 T^{16} + 4153098950225 T^{17} + 28237784602058 T^{18} + 31454452623671 T^{19} + 205976652561248 T^{20} + 151340530258351 T^{21} + 968708468732558 T^{22} + 349470776694657 T^{23} + 2213314919066161 T^{24} \))(\( 1 + 10 T + 156 T^{2} + 1238 T^{3} + 11666 T^{4} + 78774 T^{5} + 578073 T^{6} + 3424880 T^{7} + 21301761 T^{8} + 112578218 T^{9} + 615273202 T^{10} + 2931667482 T^{11} + 14328540623 T^{12} + 61762568300 T^{13} + 272242271837 T^{14} + 1058331961002 T^{15} + 4220158892518 T^{16} + 14671305947978 T^{17} + 52745269110339 T^{18} + 161126496919280 T^{19} + 516723117778947 T^{20} + 1337863194991734 T^{21} + 3764474682289814 T^{22} + 7590260027157638 T^{23} + 18172480388122164 T^{24} + 22133149190661610 T^{25} + 42052983462257059 T^{26} \))(\( 1 - T + 99 T^{2} - 272 T^{3} + 5907 T^{4} - 19503 T^{5} + 274410 T^{6} - 938905 T^{7} + 10142726 T^{8} - 35268703 T^{9} + 315815220 T^{10} - 1072284791 T^{11} + 8440406005 T^{12} - 27601647452 T^{13} + 195584026583 T^{14} - 607609573255 T^{15} + 3971249033986 T^{16} - 11544581891845 T^{17} + 70605833596463 T^{18} - 189319699873268 T^{19} + 1099962150977605 T^{20} - 2655083298710309 T^{21} + 14857805258108820 T^{22} - 31525696882884517 T^{23} + 172259626428589766 T^{24} - 302973092883191995 T^{25} + 1682425891803172410 T^{26} - 2271909519291965157 T^{27} + 13074051226923813027 T^{28} - 11438411501733920048 T^{29} + 79101661892505527979 T^{30} - 15181127029874798299 T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( 1 - 11 T + 210 T^{2} - 1815 T^{3} + 20282 T^{4} - 145097 T^{5} + 1217138 T^{6} - 7441281 T^{7} + 51415617 T^{8} - 274818036 T^{9} + 1645993344 T^{10} - 7853002292 T^{11} + 42366418590 T^{12} - 184882176290 T^{13} + 930230079980 T^{14} - 3820111749718 T^{15} + 18399434920492 T^{16} - 72582123244642 T^{17} + 335813058872780 T^{18} - 1268106847173110 T^{19} + 5521234037067390 T^{20} - 19444811122218908 T^{21} + 77437206988616064 T^{22} - 245652075747884604 T^{23} + 873220372611411297 T^{24} - 2401209834416614899 T^{25} + 7462353722887393538 T^{26} - 16902387095354882243 T^{27} + 44890453188499877402 T^{28} - 76326164983996562085 T^{29} + \)\(16\!\cdots\!10\)\( T^{30} - \)\(16\!\cdots\!89\)\( T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( 1 - 15 T + 194 T^{2} - 1629 T^{3} + 13365 T^{4} - 86800 T^{5} + 578834 T^{6} - 3251414 T^{7} + 19422911 T^{8} - 100337395 T^{9} + 562475888 T^{10} - 2744269883 T^{11} + 14653878255 T^{12} - 68067395616 T^{13} + 347181900070 T^{14} - 1539095520458 T^{15} + 7513161625244 T^{16} - 31873728193990 T^{17} + 149061665262828 T^{18} - 605600835685810 T^{19} + 2712251346713084 T^{20} - 10556656174821422 T^{21} + 45245092399022470 T^{22} - 168541610217381984 T^{23} + 689404612573217655 T^{24} - 2453025292602536537 T^{25} + 9552844702890455408 T^{26} - 32377642993692145705 T^{27} + \)\(11\!\cdots\!11\)\( T^{28} - \)\(37\!\cdots\!66\)\( T^{29} + \)\(12\!\cdots\!74\)\( T^{30} - \)\(36\!\cdots\!00\)\( T^{31} + \)\(10\!\cdots\!65\)\( T^{32} - \)\(24\!\cdots\!71\)\( T^{33} + \)\(55\!\cdots\!14\)\( T^{34} - \)\(82\!\cdots\!85\)\( T^{35} + \)\(10\!\cdots\!41\)\( T^{36} \))
$23$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( ( 1 - T )^{8} \))(\( ( 1 + T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 - T )^{12} \))(\( ( 1 + T )^{13} \))(\( ( 1 - T )^{16} \))(\( ( 1 - T )^{16} \))(\( ( 1 + T )^{18} \))
$29$ (\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( ( 1 - T )^{8} \))(\( ( 1 - T )^{9} \))(\( ( 1 + T )^{9} \))(\( ( 1 + T )^{12} \))(\( ( 1 + T )^{13} \))(\( ( 1 - T )^{16} \))(\( ( 1 + T )^{16} \))(\( ( 1 - T )^{18} \))
$31$ (\( 1 - 2 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 2 T + 104 T^{2} + 429 T^{3} + 5928 T^{4} + 32756 T^{5} + 261266 T^{6} + 1458383 T^{7} + 9221706 T^{8} + 45209873 T^{9} + 251076626 T^{10} + 975833996 T^{11} + 5474632488 T^{12} + 12281905779 T^{13} + 92300382824 T^{14} + 55025228222 T^{15} + 852891037441 T^{16} \))(\( 1 - 8 T + 153 T^{2} - 1097 T^{3} + 12326 T^{4} - 78609 T^{5} + 662686 T^{6} - 3844949 T^{7} + 26675000 T^{8} - 137552206 T^{9} + 826925000 T^{10} - 3694995989 T^{11} + 19742078626 T^{12} - 72597062289 T^{13} + 352882915226 T^{14} - 973591538057 T^{15} + 4209429958983 T^{16} - 6823128299528 T^{17} + 26439622160671 T^{18} \))(\( 1 + 199 T^{2} + 101 T^{3} + 18680 T^{4} + 15967 T^{5} + 1110738 T^{6} + 1111403 T^{7} + 46725240 T^{8} + 44236770 T^{9} + 1448482440 T^{10} + 1068058283 T^{11} + 33089995758 T^{12} + 14745859807 T^{13} + 534792540680 T^{14} + 89637871781 T^{15} + 5475010208089 T^{16} + 26439622160671 T^{18} \))(\( 1 - 2 T + 170 T^{2} - 137 T^{3} + 15770 T^{4} - 5574 T^{5} + 1044154 T^{6} - 101845 T^{7} + 53100647 T^{8} + 2363693 T^{9} + 2184198652 T^{10} + 201912019 T^{11} + 74253191996 T^{12} + 6259272589 T^{13} + 2099014904572 T^{14} + 70416778163 T^{15} + 49039562618087 T^{16} - 2915735883595 T^{17} + 926690518530874 T^{18} - 153355311054714 T^{19} + 13450091660444570 T^{20} - 3622228236011927 T^{21} + 139336808786736170 T^{22} - 50816953792809662 T^{23} + 787662783788549761 T^{24} \))(\( 1 + 26 T + 527 T^{2} + 7673 T^{3} + 96387 T^{4} + 1027543 T^{5} + 9885803 T^{6} + 85326852 T^{7} + 681250157 T^{8} + 5009963473 T^{9} + 34569088815 T^{10} + 222722534499 T^{11} + 1356392384024 T^{12} + 7758869905212 T^{13} + 42048163904744 T^{14} + 214036355653539 T^{15} + 1029847724887665 T^{16} + 4626806476548433 T^{17} + 19503613613526707 T^{18} + 75727895238142212 T^{19} + 271984283116366133 T^{20} + 876382215285237463 T^{21} + 2548435861200595677 T^{22} + 6289007846003686073 T^{23} + 13390267324405345937 T^{24} + 20479232378502293786 T^{25} + 24417546297445042591 T^{26} \))(\( 1 + 2 T + 304 T^{2} + 245 T^{3} + 44623 T^{4} - 11084 T^{5} + 4288800 T^{6} - 4847444 T^{7} + 307009964 T^{8} - 552289079 T^{9} + 17496878574 T^{10} - 39110100451 T^{11} + 822507319129 T^{12} - 2011025006762 T^{13} + 32509986488770 T^{14} - 79475439576393 T^{15} + 1091583949781846 T^{16} - 2463738626868183 T^{17} + 31242097015707970 T^{18} - 59910445976446742 T^{19} + 759602781869333209 T^{20} - 1119688971436847101 T^{21} + 15528544140435030894 T^{22} - 15194916308246593769 T^{23} + \)\(26\!\cdots\!24\)\( T^{24} - \)\(12\!\cdots\!24\)\( T^{25} + \)\(35\!\cdots\!00\)\( T^{26} - \)\(28\!\cdots\!04\)\( T^{27} + \)\(35\!\cdots\!03\)\( T^{28} + \)\(59\!\cdots\!95\)\( T^{29} + \)\(23\!\cdots\!84\)\( T^{30} + \)\(46\!\cdots\!02\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 - 14 T + 294 T^{2} - 3265 T^{3} + 42055 T^{4} - 395598 T^{5} + 3968314 T^{6} - 32714604 T^{7} + 278210372 T^{8} - 2057052635 T^{9} + 15470768158 T^{10} - 104234601543 T^{11} + 710239861465 T^{12} - 4407340071450 T^{13} + 27603613889578 T^{14} - 158782070053245 T^{15} + 921279848105094 T^{16} - 4922244171650595 T^{17} + 26527072947884458 T^{18} - 131299068068566950 T^{19} + 655921427100018265 T^{20} - 2984148146999379993 T^{21} + 13730363688122589598 T^{22} - 56594895352770732485 T^{23} + \)\(23\!\cdots\!52\)\( T^{24} - \)\(86\!\cdots\!84\)\( T^{25} + \)\(32\!\cdots\!14\)\( T^{26} - \)\(10\!\cdots\!38\)\( T^{27} + \)\(33\!\cdots\!55\)\( T^{28} - \)\(79\!\cdots\!15\)\( T^{29} + \)\(22\!\cdots\!74\)\( T^{30} - \)\(32\!\cdots\!14\)\( T^{31} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 - 10 T + 220 T^{2} - 2059 T^{3} + 25190 T^{4} - 209880 T^{5} + 1969292 T^{6} - 14621191 T^{7} + 118650675 T^{8} - 807402691 T^{9} + 5973810954 T^{10} - 38303626701 T^{11} + 264412591241 T^{12} - 1617356416067 T^{13} + 10519517391980 T^{14} - 61380661649932 T^{15} + 378422030380189 T^{16} - 2101315113464291 T^{17} + 12325973345746244 T^{18} - 65140768517393021 T^{19} + 363663571195361629 T^{20} - 1828591291213124212 T^{21} + 9714995221358761580 T^{22} - 46303541056400969117 T^{23} + \)\(23\!\cdots\!21\)\( T^{24} - \)\(10\!\cdots\!11\)\( T^{25} + \)\(50\!\cdots\!14\)\( T^{26} - \)\(21\!\cdots\!61\)\( T^{27} + \)\(97\!\cdots\!75\)\( T^{28} - \)\(37\!\cdots\!21\)\( T^{29} + \)\(15\!\cdots\!12\)\( T^{30} - \)\(51\!\cdots\!80\)\( T^{31} + \)\(19\!\cdots\!90\)\( T^{32} - \)\(48\!\cdots\!09\)\( T^{33} + \)\(16\!\cdots\!20\)\( T^{34} - \)\(22\!\cdots\!10\)\( T^{35} + \)\(69\!\cdots\!41\)\( T^{36} \))
$37$ (\( 1 - 6 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 10 T + 251 T^{2} + 1913 T^{3} + 27402 T^{4} + 167849 T^{5} + 1781631 T^{6} + 9069749 T^{7} + 78490558 T^{8} + 335580713 T^{9} + 2439052839 T^{10} + 8502055397 T^{11} + 51355759722 T^{12} + 132654989741 T^{13} + 643997328659 T^{14} + 949318771330 T^{15} + 3512479453921 T^{16} \))(\( 1 + 8 T + 253 T^{2} + 1765 T^{3} + 30221 T^{4} + 186187 T^{5} + 2251317 T^{6} + 12189502 T^{7} + 115890110 T^{8} + 541298595 T^{9} + 4287934070 T^{10} + 16687428238 T^{11} + 114035960001 T^{12} + 348944414107 T^{13} + 2095643724497 T^{14} + 4528507111885 T^{15} + 24017764914649 T^{16} + 28099835631368 T^{17} + 129961739795077 T^{18} \))(\( 1 + 2 T + 156 T^{2} + 477 T^{3} + 13177 T^{4} + 43010 T^{5} + 802457 T^{6} + 2429458 T^{7} + 37726953 T^{8} + 101904822 T^{9} + 1395897261 T^{10} + 3325928002 T^{11} + 40646854421 T^{12} + 80607664610 T^{13} + 913745321389 T^{14} + 1223851497093 T^{15} + 14809372832748 T^{16} + 7024958907842 T^{17} + 129961739795077 T^{18} \))(\( 1 + 20 T + 446 T^{2} + 5603 T^{3} + 73349 T^{4} + 690156 T^{5} + 6833206 T^{6} + 53316724 T^{7} + 447546425 T^{8} + 3088469653 T^{9} + 23080086808 T^{10} + 143320744868 T^{11} + 956581799354 T^{12} + 5302867560116 T^{13} + 31596638840152 T^{14} + 156440253333409 T^{15} + 838774055424425 T^{16} + 3697192616436868 T^{17} + 17532137092337254 T^{18} + 65517804594602748 T^{19} + 257636855465651429 T^{20} + 728175628071816431 T^{21} + 2144628630098360654 T^{22} + 3558352435589208260 T^{23} + 6582952005840035281 T^{24} \))(\( 1 - 15 T + 323 T^{2} - 3595 T^{3} + 46106 T^{4} - 402682 T^{5} + 3841163 T^{6} - 27094870 T^{7} + 208977761 T^{8} - 1209082646 T^{9} + 8072331658 T^{10} - 40119979535 T^{11} + 263483217970 T^{12} - 1315268236370 T^{13} + 9748879064890 T^{14} - 54924251983415 T^{15} + 408887815472674 T^{16} - 2266015540910006 T^{17} + 14491344872740277 T^{18} - 69518023507421830 T^{19} + 364648813963825679 T^{20} - 1414412251463816122 T^{21} + 5992015974991820162 T^{22} - 17286860818842167155 T^{23} + 57467391834765713399 T^{24} - 98744280087600529215 T^{25} + \)\(24\!\cdots\!97\)\( T^{26} \))(\( 1 - 14 T + 433 T^{2} - 4927 T^{3} + 86193 T^{4} - 831169 T^{5} + 10708358 T^{6} - 89834264 T^{7} + 944503836 T^{8} - 7025048824 T^{9} + 63718267980 T^{10} - 427096455754 T^{11} + 3465679544791 T^{12} - 21266913245502 T^{13} + 158399291355657 T^{14} - 902356988343606 T^{15} + 6265265623498270 T^{16} - 33387208568713422 T^{17} + 216848629865894433 T^{18} - 1077232956624412806 T^{19} + 6495241441345045351 T^{20} - 29616558262657778578 T^{21} + \)\(16\!\cdots\!20\)\( T^{22} - \)\(66\!\cdots\!92\)\( T^{23} + \)\(33\!\cdots\!56\)\( T^{24} - \)\(11\!\cdots\!28\)\( T^{25} + \)\(51\!\cdots\!42\)\( T^{26} - \)\(14\!\cdots\!97\)\( T^{27} + \)\(56\!\cdots\!33\)\( T^{28} - \)\(12\!\cdots\!19\)\( T^{29} + \)\(39\!\cdots\!37\)\( T^{30} - \)\(46\!\cdots\!02\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 - 4 T + 348 T^{2} - 1381 T^{3} + 60800 T^{4} - 246520 T^{5} + 7069922 T^{6} - 29586173 T^{7} + 612259255 T^{8} - 2635710207 T^{9} + 41930613664 T^{10} - 183054493959 T^{11} + 2355141441220 T^{12} - 10182672001961 T^{13} + 110988909462834 T^{14} - 460428621018917 T^{15} + 4445235835686068 T^{16} - 17035858977699929 T^{17} + 151943817054619746 T^{18} - 515782884915330533 T^{19} + 4413914238618316420 T^{20} - 12693722957749655763 T^{21} + \)\(10\!\cdots\!76\)\( T^{22} - \)\(25\!\cdots\!31\)\( T^{23} + \)\(21\!\cdots\!55\)\( T^{24} - \)\(38\!\cdots\!21\)\( T^{25} + \)\(33\!\cdots\!78\)\( T^{26} - \)\(43\!\cdots\!60\)\( T^{27} + \)\(40\!\cdots\!00\)\( T^{28} - \)\(33\!\cdots\!57\)\( T^{29} + \)\(31\!\cdots\!72\)\( T^{30} - \)\(13\!\cdots\!72\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 - 22 T + 432 T^{2} - 6005 T^{3} + 74365 T^{4} - 778108 T^{5} + 7449074 T^{6} - 63670560 T^{7} + 506182689 T^{8} - 3670614045 T^{9} + 24901854340 T^{10} - 154356904120 T^{11} + 889513407463 T^{12} - 4595058515322 T^{13} + 21504485481876 T^{14} - 84401410513930 T^{15} + 275971158874834 T^{16} - 582172153877556 T^{17} + 1636758100918108 T^{18} - 21540369693469572 T^{19} + 377804516499647746 T^{20} - 4275184646762096290 T^{21} + 40302868015198206036 T^{22} - \)\(31\!\cdots\!54\)\( T^{23} + \)\(22\!\cdots\!67\)\( T^{24} - \)\(14\!\cdots\!60\)\( T^{25} + \)\(87\!\cdots\!40\)\( T^{26} - \)\(47\!\cdots\!65\)\( T^{27} + \)\(24\!\cdots\!61\)\( T^{28} - \)\(11\!\cdots\!80\)\( T^{29} + \)\(49\!\cdots\!94\)\( T^{30} - \)\(18\!\cdots\!76\)\( T^{31} + \)\(67\!\cdots\!85\)\( T^{32} - \)\(20\!\cdots\!65\)\( T^{33} + \)\(53\!\cdots\!12\)\( T^{34} - \)\(10\!\cdots\!74\)\( T^{35} + \)\(16\!\cdots\!29\)\( T^{36} \))
$41$ (\( 1 + 2 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 11 T + 217 T^{2} + 2015 T^{3} + 24755 T^{4} + 190244 T^{5} + 1764337 T^{6} + 11438832 T^{7} + 86678840 T^{8} + 468992112 T^{9} + 2965850497 T^{10} + 13111806724 T^{11} + 69951713555 T^{12} + 233450245015 T^{13} + 1030772620297 T^{14} + 2142297012691 T^{15} + 7984925229121 T^{16} \))(\( 1 + 19 T + 400 T^{2} + 4888 T^{3} + 60100 T^{4} + 550873 T^{5} + 5032972 T^{6} + 37539398 T^{7} + 281599251 T^{8} + 1792540472 T^{9} + 11545569291 T^{10} + 63103728038 T^{11} + 346877463212 T^{12} + 1556635439353 T^{13} + 6962957680100 T^{14} + 23218509530008 T^{15} + 77901709552400 T^{16} + 151713579353299 T^{17} + 327381934393961 T^{18} \))(\( 1 + 3 T + 248 T^{2} + 652 T^{3} + 30406 T^{4} + 70619 T^{5} + 2398670 T^{6} + 4904464 T^{7} + 134000435 T^{8} + 237983212 T^{9} + 5494017835 T^{10} + 8244403984 T^{11} + 165318735070 T^{12} + 199552416059 T^{13} + 3522723647606 T^{14} + 3097067965132 T^{15} + 48299059922488 T^{16} + 23954775687363 T^{17} + 327381934393961 T^{18} \))(\( 1 + 3 T + 205 T^{2} + 307 T^{3} + 18175 T^{4} + 340 T^{5} + 936847 T^{6} - 738690 T^{7} + 37490859 T^{8} + 33321383 T^{9} + 1662380140 T^{10} + 6442561697 T^{11} + 74723330234 T^{12} + 264145029577 T^{13} + 2794461015340 T^{14} + 2296543037743 T^{15} + 105940207218699 T^{16} - 85581817116690 T^{17} + 4450120907868127 T^{18} + 66216453119540 T^{19} + 145126016039274175 T^{20} + 100506253858946027 T^{21} + 2751645158581242205 T^{22} + 1650987095148745323 T^{23} + 22563490300366186081 T^{24} \))(\( 1 - 21 T + 536 T^{2} - 7904 T^{3} + 120189 T^{4} - 1396862 T^{5} + 15981830 T^{6} - 155034404 T^{7} + 1454522612 T^{8} - 12175501078 T^{9} + 97839685059 T^{10} - 720902220548 T^{11} + 5084126750293 T^{12} - 33287754900734 T^{13} + 208449196762013 T^{14} - 1211836632741188 T^{15} + 6743208933951339 T^{16} - 34405056101670358 T^{17} + 168515464094917012 T^{18} - 736429579941307364 T^{19} + 3112529696939582230 T^{20} - 11153838625400418302 T^{21} + 39347707312875778629 T^{22} - \)\(10\!\cdots\!04\)\( T^{23} + \)\(29\!\cdots\!76\)\( T^{24} - \)\(47\!\cdots\!01\)\( T^{25} + \)\(92\!\cdots\!21\)\( T^{26} \))(\( 1 + T + 291 T^{2} - 41 T^{3} + 44852 T^{4} - 49667 T^{5} + 4812456 T^{6} - 9136611 T^{7} + 402888069 T^{8} - 986573010 T^{9} + 27907113690 T^{10} - 76364900726 T^{11} + 1647328324588 T^{12} - 4609023514894 T^{13} + 83871311547675 T^{14} - 226887864044812 T^{15} + 3695605203382292 T^{16} - 9302402425837292 T^{17} + 140987674711641675 T^{18} - 317658509670009374 T^{19} + 4654956133816111468 T^{20} - 8847347287856501926 T^{21} + \)\(13\!\cdots\!90\)\( T^{22} - \)\(19\!\cdots\!10\)\( T^{23} + \)\(32\!\cdots\!49\)\( T^{24} - \)\(29\!\cdots\!71\)\( T^{25} + \)\(64\!\cdots\!56\)\( T^{26} - \)\(27\!\cdots\!47\)\( T^{27} + \)\(10\!\cdots\!12\)\( T^{28} - \)\(37\!\cdots\!61\)\( T^{29} + \)\(11\!\cdots\!51\)\( T^{30} + \)\(15\!\cdots\!01\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 11 T + 351 T^{2} - 3509 T^{3} + 64654 T^{4} - 576009 T^{5} + 7980108 T^{6} - 64037115 T^{7} + 735336275 T^{8} - 5364634568 T^{9} + 53746803598 T^{10} - 359761312208 T^{11} + 3241410212330 T^{12} - 20060735863402 T^{13} + 165714106021951 T^{14} - 953277968669194 T^{15} + 7299109474364504 T^{16} - 39084396715436954 T^{17} + 278565412222899631 T^{18} - 1382605976441529242 T^{19} + 9159450563003833130 T^{20} - 41680578899193801808 T^{21} + \)\(25\!\cdots\!18\)\( T^{22} - \)\(10\!\cdots\!08\)\( T^{23} + \)\(58\!\cdots\!75\)\( T^{24} - \)\(20\!\cdots\!15\)\( T^{25} + \)\(10\!\cdots\!08\)\( T^{26} - \)\(31\!\cdots\!69\)\( T^{27} + \)\(14\!\cdots\!74\)\( T^{28} - \)\(32\!\cdots\!89\)\( T^{29} + \)\(13\!\cdots\!11\)\( T^{30} - \)\(17\!\cdots\!11\)\( T^{31} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 17 T + 385 T^{2} - 4809 T^{3} + 66837 T^{4} - 678550 T^{5} + 7284425 T^{6} - 62777172 T^{7} + 561214009 T^{8} - 4169234003 T^{9} + 31952105430 T^{10} - 203684025601 T^{11} + 1348465458429 T^{12} - 7160327734618 T^{13} + 40784297555839 T^{14} - 166752502229572 T^{15} + 846406185960820 T^{16} - 2409238990014298 T^{17} + 18963357153993154 T^{18} - 98778798590586218 T^{19} + 1422808798600138420 T^{20} - 11492749206164331812 T^{21} + \)\(11\!\cdots\!79\)\( T^{22} - \)\(82\!\cdots\!18\)\( T^{23} + \)\(64\!\cdots\!89\)\( T^{24} - \)\(39\!\cdots\!81\)\( T^{25} + \)\(25\!\cdots\!30\)\( T^{26} - \)\(13\!\cdots\!83\)\( T^{27} + \)\(75\!\cdots\!09\)\( T^{28} - \)\(34\!\cdots\!52\)\( T^{29} + \)\(16\!\cdots\!25\)\( T^{30} - \)\(62\!\cdots\!50\)\( T^{31} + \)\(25\!\cdots\!57\)\( T^{32} - \)\(74\!\cdots\!09\)\( T^{33} + \)\(24\!\cdots\!85\)\( T^{34} - \)\(44\!\cdots\!77\)\( T^{35} + \)\(10\!\cdots\!21\)\( T^{36} \))
$43$ (\( 1 - 6 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 7 T + 258 T^{2} + 1386 T^{3} + 30118 T^{4} + 127901 T^{5} + 2161035 T^{6} + 7532761 T^{7} + 108671872 T^{8} + 323908723 T^{9} + 3995753715 T^{10} + 10169024807 T^{11} + 102967448518 T^{12} + 203753701998 T^{13} + 1630911666642 T^{14} + 1902730277749 T^{15} + 11688200277601 T^{16} \))(\( 1 + 3 T + 120 T^{2} + 800 T^{3} + 10631 T^{4} + 70060 T^{5} + 768666 T^{6} + 4485320 T^{7} + 39922183 T^{8} + 230952547 T^{9} + 1716653869 T^{10} + 8293356680 T^{11} + 61114327662 T^{12} + 239521198060 T^{13} + 1562846757533 T^{14} + 5057090439200 T^{15} + 32618233332840 T^{16} + 35064600832803 T^{17} + 502592611936843 T^{18} \))(\( 1 + 19 T + 425 T^{2} + 5251 T^{3} + 67970 T^{4} + 626243 T^{5} + 5981877 T^{6} + 44535666 T^{7} + 349092239 T^{8} + 2219303996 T^{9} + 15010966277 T^{10} + 82346446434 T^{11} + 475601094639 T^{12} + 2141000194643 T^{13} + 9992163870710 T^{14} + 33193477370299 T^{15} + 115522909720475 T^{16} + 222075805274419 T^{17} + 502592611936843 T^{18} \))(\( 1 - 5 T + 227 T^{2} - 391 T^{3} + 21416 T^{4} + 29505 T^{5} + 1334662 T^{6} + 5130395 T^{7} + 78487526 T^{8} + 307723151 T^{9} + 4639561771 T^{10} + 12327703765 T^{11} + 228789635290 T^{12} + 530091261895 T^{13} + 8578549714579 T^{14} + 24466144566557 T^{15} + 268333232376326 T^{16} + 754211380924985 T^{17} + 8436883049704438 T^{18} + 8020008120712035 T^{19} + 250314497145103016 T^{20} - 196513711267305613 T^{21} + 4905806485115524523 T^{22} - 4646468697356113535 T^{23} + 39959630797262576401 T^{24} \))(\( 1 + 6 T + 275 T^{2} + 1841 T^{3} + 41567 T^{4} + 277558 T^{5} + 4371642 T^{6} + 28190285 T^{7} + 349706752 T^{8} + 2137278226 T^{9} + 22328956702 T^{10} + 127130429306 T^{11} + 1163701808431 T^{12} + 6079207214948 T^{13} + 50039177762533 T^{14} + 235064163786794 T^{15} + 1775308360505914 T^{16} + 7306928936327026 T^{17} + 51409845118107136 T^{18} + 178201025939778965 T^{19} + 1188293656697027694 T^{20} + 3244153492650378358 T^{21} + 20891267100378752981 T^{22} + 39786738938756302409 T^{23} + \)\(25\!\cdots\!25\)\( T^{24} + \)\(23\!\cdots\!06\)\( T^{25} + \)\(17\!\cdots\!43\)\( T^{26} \))(\( 1 + 13 T + 476 T^{2} + 5598 T^{3} + 110710 T^{4} + 1176341 T^{5} + 16654857 T^{6} + 160084609 T^{7} + 1816376364 T^{8} + 15837049807 T^{9} + 152933525073 T^{10} + 1214207439677 T^{11} + 10347972361250 T^{12} + 75132582499762 T^{13} + 577883827649346 T^{14} + 3850381644712395 T^{15} + 27062667776285686 T^{16} + 165566410722632985 T^{17} + 1068507197323640754 T^{18} + 5973566236808577334 T^{19} + 35377658256613861250 T^{20} + \)\(17\!\cdots\!11\)\( T^{21} + \)\(96\!\cdots\!77\)\( T^{22} + \)\(43\!\cdots\!49\)\( T^{23} + \)\(21\!\cdots\!64\)\( T^{24} + \)\(80\!\cdots\!87\)\( T^{25} + \)\(35\!\cdots\!93\)\( T^{26} + \)\(10\!\cdots\!87\)\( T^{27} + \)\(44\!\cdots\!10\)\( T^{28} + \)\(96\!\cdots\!14\)\( T^{29} + \)\(35\!\cdots\!24\)\( T^{30} + \)\(41\!\cdots\!91\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 23 T + 621 T^{2} - 10629 T^{3} + 176736 T^{4} - 2424625 T^{5} + 31250850 T^{6} - 360299505 T^{7} + 3893683705 T^{8} - 38882456890 T^{9} + 365372984754 T^{10} - 3221700793654 T^{11} + 26840051705792 T^{12} - 211481434110410 T^{13} + 1578864928177479 T^{14} - 11191510143979808 T^{15} + 75271909946487532 T^{16} - 481234936191131744 T^{17} + 2919321252200158671 T^{18} - 16814254381816367870 T^{19} + 91760795611813395392 T^{20} - \)\(47\!\cdots\!22\)\( T^{21} + \)\(23\!\cdots\!46\)\( T^{22} - \)\(10\!\cdots\!30\)\( T^{23} + \)\(45\!\cdots\!05\)\( T^{24} - \)\(18\!\cdots\!15\)\( T^{25} + \)\(67\!\cdots\!50\)\( T^{26} - \)\(22\!\cdots\!75\)\( T^{27} + \)\(70\!\cdots\!36\)\( T^{28} - \)\(18\!\cdots\!47\)\( T^{29} + \)\(45\!\cdots\!29\)\( T^{30} - \)\(73\!\cdots\!61\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 25 T + 555 T^{2} - 8401 T^{3} + 117237 T^{4} - 1332208 T^{5} + 14263327 T^{6} - 131585176 T^{7} + 1158918175 T^{8} - 8943458487 T^{9} + 66353481444 T^{10} - 425711080623 T^{11} + 2618819366795 T^{12} - 12921392425538 T^{13} + 58296943834281 T^{14} - 116343822432866 T^{15} - 323962269186112 T^{16} + 10098541961796656 T^{17} - 68535624694658702 T^{18} + 434237304357256208 T^{19} - 599006235725121088 T^{20} - 9250148290169877062 T^{21} + \)\(19\!\cdots\!81\)\( T^{22} - \)\(18\!\cdots\!34\)\( T^{23} + \)\(16\!\cdots\!55\)\( T^{24} - \)\(11\!\cdots\!61\)\( T^{25} + \)\(77\!\cdots\!44\)\( T^{26} - \)\(44\!\cdots\!41\)\( T^{27} + \)\(25\!\cdots\!75\)\( T^{28} - \)\(12\!\cdots\!32\)\( T^{29} + \)\(56\!\cdots\!27\)\( T^{30} - \)\(22\!\cdots\!44\)\( T^{31} + \)\(86\!\cdots\!13\)\( T^{32} - \)\(26\!\cdots\!07\)\( T^{33} + \)\(75\!\cdots\!55\)\( T^{34} - \)\(14\!\cdots\!75\)\( T^{35} + \)\(25\!\cdots\!49\)\( T^{36} \))
$47$ (\( 1 - 7 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 14 T + 330 T^{2} + 3314 T^{3} + 42963 T^{4} + 335929 T^{5} + 3171577 T^{6} + 20936253 T^{7} + 167081468 T^{8} + 984003891 T^{9} + 7006013593 T^{10} + 34877156567 T^{11} + 209645734803 T^{12} + 760049353198 T^{13} + 3557141058570 T^{14} + 7092723686482 T^{15} + 23811286661761 T^{16} \))(\( 1 + 3 T + 278 T^{2} + 977 T^{3} + 36995 T^{4} + 144455 T^{5} + 3167707 T^{6} + 12728693 T^{7} + 196210413 T^{8} + 731862316 T^{9} + 9221889411 T^{10} + 28117682837 T^{11} + 328880843861 T^{12} + 704894318855 T^{13} + 8484618533965 T^{14} + 10531293376433 T^{15} + 140841227488714 T^{16} + 71433859985283 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 3 T + 236 T^{2} + 887 T^{3} + 29987 T^{4} + 119173 T^{5} + 2564809 T^{6} + 9903133 T^{7} + 160339521 T^{8} + 557577112 T^{9} + 7535957487 T^{10} + 21876020797 T^{11} + 266286164807 T^{12} + 581526223813 T^{13} + 6877368724909 T^{14} + 9561163996823 T^{15} + 119563056429268 T^{16} + 71433859985283 T^{17} + 1119130473102767 T^{18} \))(\( 1 + 302 T^{2} + 722 T^{3} + 45483 T^{4} + 191777 T^{5} + 4737251 T^{6} + 24986927 T^{7} + 382331725 T^{8} + 2126276463 T^{9} + 24783876435 T^{10} + 131567343855 T^{11} + 1297056605334 T^{12} + 6183665161185 T^{13} + 54747583044915 T^{14} + 220756401218049 T^{15} + 1865656854179725 T^{16} + 5730626947723489 T^{17} + 51063848596520579 T^{18} + 97158662173032751 T^{19} + 1083008751236875563 T^{20} + 808012201580197774 T^{21} + 15884937935220674798 T^{22} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 - 16 T + 441 T^{2} - 5694 T^{3} + 95129 T^{4} - 1040385 T^{5} + 13257484 T^{6} - 126031950 T^{7} + 1330331990 T^{8} - 11155846284 T^{9} + 101375778530 T^{10} - 755526454964 T^{11} + 6030730212679 T^{12} - 40020248761926 T^{13} + 283444319995913 T^{14} - 1668957939015476 T^{15} + 10525137454320190 T^{16} - 54436971150955404 T^{17} + 305104999558873930 T^{18} - 1358525527383761550 T^{19} + 6716547913568295092 T^{20} - 24772905473596217985 T^{21} + \)\(10\!\cdots\!43\)\( T^{22} - \)\(29\!\cdots\!06\)\( T^{23} + \)\(10\!\cdots\!23\)\( T^{24} - \)\(18\!\cdots\!56\)\( T^{25} + \)\(54\!\cdots\!27\)\( T^{26} \))(\( 1 + 4 T + 350 T^{2} + 1492 T^{3} + 62253 T^{4} + 255333 T^{5} + 7303915 T^{6} + 26468619 T^{7} + 624450494 T^{8} + 1794433697 T^{9} + 41128444707 T^{10} + 77527415663 T^{11} + 2197732514771 T^{12} + 1679668521838 T^{13} + 103068758802868 T^{14} - 11943252911510 T^{15} + 4740210975040514 T^{16} - 561332886840970 T^{17} + 227678888195535412 T^{18} + 174388224942786674 T^{19} + 10724233595410268051 T^{20} + 17780525687922644641 T^{21} + \)\(44\!\cdots\!03\)\( T^{22} + \)\(90\!\cdots\!11\)\( T^{23} + \)\(14\!\cdots\!34\)\( T^{24} + \)\(29\!\cdots\!73\)\( T^{25} + \)\(38\!\cdots\!35\)\( T^{26} + \)\(63\!\cdots\!99\)\( T^{27} + \)\(72\!\cdots\!73\)\( T^{28} + \)\(81\!\cdots\!84\)\( T^{29} + \)\(89\!\cdots\!50\)\( T^{30} + \)\(48\!\cdots\!72\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 2 T + 318 T^{2} - 4 T^{3} + 50079 T^{4} - 77447 T^{5} + 5344865 T^{6} - 14968679 T^{7} + 432946692 T^{8} - 1678285661 T^{9} + 28484569213 T^{10} - 136345336793 T^{11} + 1603599668977 T^{12} - 8855144414230 T^{13} + 81258028210116 T^{14} - 483256164976500 T^{15} + 3890208356154710 T^{16} - 22713039753895500 T^{17} + 179498984316146244 T^{18} - 919367658518601290 T^{19} + 7825054836313356337 T^{20} - 31270122221207942551 T^{21} + \)\(30\!\cdots\!77\)\( T^{22} - \)\(85\!\cdots\!43\)\( T^{23} + \)\(10\!\cdots\!12\)\( T^{24} - \)\(16\!\cdots\!93\)\( T^{25} + \)\(28\!\cdots\!85\)\( T^{26} - \)\(19\!\cdots\!41\)\( T^{27} + \)\(58\!\cdots\!39\)\( T^{28} - \)\(21\!\cdots\!08\)\( T^{29} + \)\(81\!\cdots\!42\)\( T^{30} + \)\(24\!\cdots\!86\)\( T^{31} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 6 T + 444 T^{2} + 1846 T^{3} + 92028 T^{4} + 220155 T^{5} + 12055757 T^{6} + 6856313 T^{7} + 1146853619 T^{8} - 1556067342 T^{9} + 87012428474 T^{10} - 284763298666 T^{11} + 5668906356293 T^{12} - 27649741057343 T^{13} + 333425220559427 T^{14} - 1948942847217533 T^{15} + 18012808394762603 T^{16} - 109979944720479212 T^{17} + 888559270448993140 T^{18} - 5169057401862522964 T^{19} + 39790293744030590027 T^{20} - \)\(20\!\cdots\!59\)\( T^{21} + \)\(16\!\cdots\!87\)\( T^{22} - \)\(63\!\cdots\!01\)\( T^{23} + \)\(61\!\cdots\!97\)\( T^{24} - \)\(14\!\cdots\!58\)\( T^{25} + \)\(20\!\cdots\!14\)\( T^{26} - \)\(17\!\cdots\!14\)\( T^{27} + \)\(60\!\cdots\!31\)\( T^{28} + \)\(16\!\cdots\!39\)\( T^{29} + \)\(14\!\cdots\!37\)\( T^{30} + \)\(12\!\cdots\!85\)\( T^{31} + \)\(23\!\cdots\!32\)\( T^{32} + \)\(22\!\cdots\!78\)\( T^{33} + \)\(25\!\cdots\!24\)\( T^{34} + \)\(15\!\cdots\!22\)\( T^{35} + \)\(12\!\cdots\!89\)\( T^{36} \))
$53$ (\( 1 + 4 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 + 15 T + 297 T^{2} + 2791 T^{3} + 29831 T^{4} + 178666 T^{5} + 1370849 T^{6} + 5070700 T^{7} + 50414860 T^{8} + 268747100 T^{9} + 3850714841 T^{10} + 26599258082 T^{11} + 235380938711 T^{12} + 1167183620963 T^{13} + 6582815255313 T^{14} + 17620667097555 T^{15} + 62259690411361 T^{16} \))(\( 1 + 17 T + 398 T^{2} + 4052 T^{3} + 52736 T^{4} + 348193 T^{5} + 3384098 T^{6} + 14443272 T^{7} + 145879247 T^{8} + 516370164 T^{9} + 7731600091 T^{10} + 40571151048 T^{11} + 503814357946 T^{12} + 2747410250833 T^{13} + 22053957518848 T^{14} + 89809991294708 T^{15} + 467535033655126 T^{16} + 1058414736993137 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 9 T + 338 T^{2} + 2726 T^{3} + 56502 T^{4} + 400121 T^{5} + 5994720 T^{6} + 36962368 T^{7} + 441826927 T^{8} + 2340190448 T^{9} + 23416827131 T^{10} + 103827291712 T^{11} + 892475929440 T^{12} + 3157147148201 T^{13} + 23628881745486 T^{14} + 60420048437654 T^{15} + 397052365264906 T^{16} + 560337213702249 T^{17} + 3299763591802133 T^{18} \))(\( 1 + 3 T + 369 T^{2} + 869 T^{3} + 68815 T^{4} + 142618 T^{5} + 8630531 T^{6} + 16558800 T^{7} + 805876379 T^{8} + 1442902733 T^{9} + 58986949764 T^{10} + 97648128425 T^{11} + 3473322956874 T^{12} + 5175350806525 T^{13} + 165694341887076 T^{14} + 214815030180841 T^{15} + 6358752256848299 T^{16} + 6924815529488400 T^{17} + 191290205819029499 T^{18} + 167534953341273266 T^{19} + 4284400595657807215 T^{20} + 2867494561276053577 T^{21} + 64533476564874315081 T^{22} + 27807107788116574791 T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - 7 T + 422 T^{2} - 2902 T^{3} + 89166 T^{4} - 591009 T^{5} + 12527460 T^{6} - 78730236 T^{7} + 1305356898 T^{8} - 7665746709 T^{9} + 106334052251 T^{10} - 575474571078 T^{11} + 6949796047182 T^{12} - 34166597550230 T^{13} + 368339190500646 T^{14} - 1616508070158102 T^{15} + 15830694696972127 T^{16} - 60486428758177029 T^{17} + 545894371500060714 T^{18} - 1745005382475396444 T^{19} + 14716146815862424020 T^{20} - 36796037370328053249 T^{21} + \)\(29\!\cdots\!78\)\( T^{22} - \)\(50\!\cdots\!98\)\( T^{23} + \)\(39\!\cdots\!34\)\( T^{24} - \)\(34\!\cdots\!87\)\( T^{25} + \)\(26\!\cdots\!73\)\( T^{26} \))(\( 1 - 19 T + 375 T^{2} - 3609 T^{3} + 41181 T^{4} - 228676 T^{5} + 2170379 T^{6} - 3229288 T^{7} + 70602930 T^{8} + 333959474 T^{9} + 4519420709 T^{10} + 13237540954 T^{11} + 461465245523 T^{12} + 36740101119 T^{13} + 31624213422425 T^{14} + 1919664742309 T^{15} + 1732957206033114 T^{16} + 101742231342377 T^{17} + 88832415503591825 T^{18} + 5469756034293363 T^{19} + 3641182751959566563 T^{20} + 5535879965365720322 T^{21} + \)\(10\!\cdots\!61\)\( T^{22} + \)\(39\!\cdots\!38\)\( T^{23} + \)\(43\!\cdots\!30\)\( T^{24} - \)\(10\!\cdots\!04\)\( T^{25} + \)\(37\!\cdots\!71\)\( T^{26} - \)\(21\!\cdots\!72\)\( T^{27} + \)\(20\!\cdots\!21\)\( T^{28} - \)\(93\!\cdots\!57\)\( T^{29} + \)\(51\!\cdots\!75\)\( T^{30} - \)\(13\!\cdots\!83\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 - 19 T + 431 T^{2} - 5819 T^{3} + 85523 T^{4} - 950502 T^{5} + 11164835 T^{6} - 107392850 T^{7} + 1081832710 T^{8} - 9255764980 T^{9} + 83301576533 T^{10} - 649451637176 T^{11} + 5397180784669 T^{12} - 39327106176827 T^{13} + 311239365622937 T^{14} - 2179312691515715 T^{15} + 16832485566076786 T^{16} - 115503572650332895 T^{17} + 874271378034830033 T^{18} - 5854901586287473279 T^{19} + 42586352434995835789 T^{20} - \)\(27\!\cdots\!68\)\( T^{21} + \)\(18\!\cdots\!57\)\( T^{22} - \)\(10\!\cdots\!60\)\( T^{23} + \)\(67\!\cdots\!10\)\( T^{24} - \)\(35\!\cdots\!50\)\( T^{25} + \)\(19\!\cdots\!15\)\( T^{26} - \)\(88\!\cdots\!94\)\( T^{27} + \)\(42\!\cdots\!43\)\( T^{28} - \)\(15\!\cdots\!87\)\( T^{29} + \)\(59\!\cdots\!39\)\( T^{30} - \)\(13\!\cdots\!83\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 - 21 T + 765 T^{2} - 12287 T^{3} + 262000 T^{4} - 3481543 T^{5} + 55884154 T^{6} - 642391263 T^{7} + 8533845817 T^{8} - 87245805320 T^{9} + 1006500959160 T^{10} - 9317795439884 T^{11} + 95983203269123 T^{12} - 813936198489013 T^{13} + 7614204397772838 T^{14} - 59544464099103381 T^{15} + 511036759316648027 T^{16} - 3696786186801501028 T^{17} + 29276374909113093590 T^{18} - \)\(19\!\cdots\!84\)\( T^{19} + \)\(14\!\cdots\!43\)\( T^{20} - \)\(88\!\cdots\!37\)\( T^{21} + \)\(60\!\cdots\!78\)\( T^{22} - \)\(34\!\cdots\!09\)\( T^{23} + \)\(21\!\cdots\!67\)\( T^{24} - \)\(10\!\cdots\!08\)\( T^{25} + \)\(62\!\cdots\!60\)\( T^{26} - \)\(28\!\cdots\!60\)\( T^{27} + \)\(14\!\cdots\!33\)\( T^{28} - \)\(59\!\cdots\!11\)\( T^{29} + \)\(27\!\cdots\!14\)\( T^{30} - \)\(90\!\cdots\!39\)\( T^{31} + \)\(36\!\cdots\!00\)\( T^{32} - \)\(89\!\cdots\!59\)\( T^{33} + \)\(29\!\cdots\!65\)\( T^{34} - \)\(43\!\cdots\!73\)\( T^{35} + \)\(10\!\cdots\!89\)\( T^{36} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 - 9 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 245 T^{2} - 1104 T^{3} + 32870 T^{4} - 142016 T^{5} + 3010387 T^{6} - 11639812 T^{7} + 205110130 T^{8} - 686748908 T^{9} + 10479157147 T^{10} - 29167104064 T^{11} + 398297656070 T^{12} - 789276426096 T^{13} + 10334230742045 T^{14} - 9954605939276 T^{15} + 146830437604321 T^{16} \))(\( 1 + 10 T + 427 T^{2} + 3704 T^{3} + 86119 T^{4} + 648418 T^{5} + 10694205 T^{6} + 69416192 T^{7} + 899209120 T^{8} + 4957696952 T^{9} + 53053338080 T^{10} + 241637764352 T^{11} + 2196365128695 T^{12} + 7857114984898 T^{13} + 61568565705581 T^{14} + 156236696606264 T^{15} + 1062654184017713 T^{16} + 1468304376043210 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 2 T + 358 T^{2} + 678 T^{3} + 64211 T^{4} + 112668 T^{5} + 7411179 T^{6} + 11665706 T^{7} + 601636249 T^{8} + 825027460 T^{9} + 35496538691 T^{10} + 40608322586 T^{11} + 1522100531841 T^{12} + 1365238829148 T^{13} + 45906004163089 T^{14} + 28598401808598 T^{15} + 890937231565202 T^{16} + 293660875208642 T^{17} + 8662995818654939 T^{18} \))(\( 1 + 20 T + 494 T^{2} + 5912 T^{3} + 87243 T^{4} + 765416 T^{5} + 9306170 T^{6} + 70130916 T^{7} + 812437859 T^{8} + 5683683792 T^{9} + 61995753224 T^{10} + 398433959328 T^{11} + 3990056201442 T^{12} + 23507603600352 T^{13} + 215807216972744 T^{14} + 1167309293517168 T^{15} + 9844602827570099 T^{16} + 50138295959527884 T^{17} + 392539216753864970 T^{18} + 1904853664904219704 T^{19} + 12809927867913777003 T^{20} + 51215631279887999368 T^{21} + \)\(25\!\cdots\!94\)\( T^{22} + \)\(60\!\cdots\!80\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 + 11 T + 437 T^{2} + 3606 T^{3} + 78841 T^{4} + 509173 T^{5} + 8104683 T^{6} + 45821906 T^{7} + 592630313 T^{8} + 3727282305 T^{9} + 39470909973 T^{10} + 308161110792 T^{11} + 2613609868782 T^{12} + 21123747141182 T^{13} + 154202982258138 T^{14} + 1072708826666952 T^{15} + 8106496019344767 T^{16} + 45164825238597105 T^{17} + 423685811087675587 T^{18} + 1932792447527739746 T^{19} + 20169731381937307377 T^{20} + 74762094406304936533 T^{21} + \)\(68\!\cdots\!99\)\( T^{22} + \)\(18\!\cdots\!06\)\( T^{23} + \)\(13\!\cdots\!83\)\( T^{24} + \)\(19\!\cdots\!91\)\( T^{25} + \)\(10\!\cdots\!79\)\( T^{26} \))(\( 1 - 12 T + 525 T^{2} - 5770 T^{3} + 134425 T^{4} - 1331890 T^{5} + 22452546 T^{6} - 200163974 T^{7} + 2774131676 T^{8} - 22471902618 T^{9} + 273551901484 T^{10} - 2043185035018 T^{11} + 22645172402319 T^{12} - 157768996900930 T^{13} + 1622357406111901 T^{14} - 10599336953451256 T^{15} + 101998757649670230 T^{16} - 625360880253624104 T^{17} + 5647426130675527381 T^{18} - 32402438814516102470 T^{19} + \)\(27\!\cdots\!59\)\( T^{20} - \)\(14\!\cdots\!82\)\( T^{21} + \)\(11\!\cdots\!44\)\( T^{22} - \)\(55\!\cdots\!42\)\( T^{23} + \)\(40\!\cdots\!96\)\( T^{24} - \)\(17\!\cdots\!86\)\( T^{25} + \)\(11\!\cdots\!46\)\( T^{26} - \)\(40\!\cdots\!10\)\( T^{27} + \)\(23\!\cdots\!25\)\( T^{28} - \)\(60\!\cdots\!30\)\( T^{29} + \)\(32\!\cdots\!25\)\( T^{30} - \)\(43\!\cdots\!88\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 - 32 T + 822 T^{2} - 16290 T^{3} + 280616 T^{4} - 4266252 T^{5} + 59002420 T^{6} - 750388520 T^{7} + 8889961715 T^{8} - 98683415146 T^{9} + 1034078840112 T^{10} - 10260068417802 T^{11} + 96817508417900 T^{12} - 870380894105704 T^{13} + 7473128002490358 T^{14} - 61327399691512338 T^{15} + 481586259456684752 T^{16} - 3618316581799227942 T^{17} + 26013958576668936198 T^{18} - \)\(17\!\cdots\!16\)\( T^{19} + \)\(11\!\cdots\!00\)\( T^{20} - \)\(73\!\cdots\!98\)\( T^{21} + \)\(43\!\cdots\!92\)\( T^{22} - \)\(24\!\cdots\!74\)\( T^{23} + \)\(13\!\cdots\!15\)\( T^{24} - \)\(65\!\cdots\!80\)\( T^{25} + \)\(30\!\cdots\!20\)\( T^{26} - \)\(12\!\cdots\!68\)\( T^{27} + \)\(49\!\cdots\!96\)\( T^{28} - \)\(17\!\cdots\!10\)\( T^{29} + \)\(50\!\cdots\!42\)\( T^{30} - \)\(11\!\cdots\!68\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 - 6 T + 602 T^{2} - 2840 T^{3} + 175935 T^{4} - 621824 T^{5} + 33381056 T^{6} - 79166462 T^{7} + 4633724943 T^{8} - 5513657964 T^{9} + 503555352078 T^{10} + 3150746104 T^{11} + 44932740723991 T^{12} + 51596596438966 T^{13} + 3426355639143624 T^{14} + 7127898060029932 T^{15} + 231418232337110026 T^{16} + 596784711522518418 T^{17} + 14231710827703345888 T^{18} + 35210297979828586662 T^{19} + \)\(80\!\cdots\!06\)\( T^{20} + \)\(14\!\cdots\!28\)\( T^{21} + \)\(41\!\cdots\!64\)\( T^{22} + \)\(36\!\cdots\!34\)\( T^{23} + \)\(18\!\cdots\!31\)\( T^{24} + \)\(78\!\cdots\!76\)\( T^{25} + \)\(73\!\cdots\!38\)\( T^{26} - \)\(47\!\cdots\!96\)\( T^{27} + \)\(23\!\cdots\!43\)\( T^{28} - \)\(23\!\cdots\!58\)\( T^{29} + \)\(59\!\cdots\!36\)\( T^{30} - \)\(65\!\cdots\!96\)\( T^{31} + \)\(10\!\cdots\!35\)\( T^{32} - \)\(10\!\cdots\!60\)\( T^{33} + \)\(12\!\cdots\!82\)\( T^{34} - \)\(76\!\cdots\!14\)\( T^{35} + \)\(75\!\cdots\!21\)\( T^{36} \))
$61$ (\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - T + 282 T^{2} - 746 T^{3} + 40915 T^{4} - 129123 T^{5} + 4080190 T^{6} - 11958870 T^{7} + 292906840 T^{8} - 729491070 T^{9} + 15182386990 T^{10} - 29308467663 T^{11} + 566502584515 T^{12} - 630068840546 T^{13} + 14528745569802 T^{14} - 3142742836021 T^{15} + 191707312997281 T^{16} \))(\( 1 - T + 415 T^{2} - 281 T^{3} + 79991 T^{4} - 31893 T^{5} + 9569195 T^{6} - 1981755 T^{7} + 797704854 T^{8} - 104297468 T^{9} + 48659996094 T^{10} - 7374110355 T^{11} + 2172025450295 T^{12} - 441585407013 T^{13} + 67560102713291 T^{14} - 14477225195441 T^{15} + 1304238276948715 T^{16} - 191707312997281 T^{17} + 11694146092834141 T^{18} \))(\( 1 + 25 T + 651 T^{2} + 10695 T^{3} + 168445 T^{4} + 2084217 T^{5} + 24446885 T^{6} + 240989729 T^{7} + 2248681682 T^{8} + 18052608588 T^{9} + 137169582602 T^{10} + 896722781609 T^{11} + 5548978404185 T^{12} + 28857737191497 T^{13} + 142268023921945 T^{14} + 551010403790895 T^{15} + 2045925586249671 T^{16} + 4792682824932025 T^{17} + 11694146092834141 T^{18} \))(\( 1 + 17 T + 510 T^{2} + 6804 T^{3} + 120491 T^{4} + 1365399 T^{5} + 18372002 T^{6} + 183570674 T^{7} + 2050230403 T^{8} + 18314912721 T^{9} + 176756642032 T^{10} + 1415754289261 T^{11} + 12068026256610 T^{12} + 86361011644921 T^{13} + 657711465001072 T^{14} + 4157137204325301 T^{15} + 28387164173303923 T^{16} + 155043112232476874 T^{17} + 946532420801040722 T^{18} + 4291097925560237379 T^{19} + 23099005850355384971 T^{20} + 79566970015643495364 T^{21} + \)\(36\!\cdots\!10\)\( T^{22} + \)\(73\!\cdots\!37\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 19 T + 317 T^{2} - 1867 T^{3} + 12038 T^{4} + 30492 T^{5} + 1260478 T^{6} - 12706580 T^{7} + 200106142 T^{8} - 230230178 T^{9} + 2318037344 T^{10} + 23131149713 T^{11} + 744618234568 T^{12} - 4420821249002 T^{13} + 45421712308648 T^{14} + 86071008082073 T^{15} + 526150434378464 T^{16} - 3187730437989698 T^{17} + 169008907340580742 T^{18} - 654647758447995380 T^{19} + 3961358204462078038 T^{20} + 5845539387913092252 T^{21} + \)\(14\!\cdots\!58\)\( T^{22} - \)\(13\!\cdots\!67\)\( T^{23} + \)\(13\!\cdots\!37\)\( T^{24} - \)\(50\!\cdots\!99\)\( T^{25} + \)\(16\!\cdots\!81\)\( T^{26} \))(\( 1 - 21 T + 688 T^{2} - 10896 T^{3} + 204244 T^{4} - 2587358 T^{5} + 35323540 T^{6} - 370244264 T^{7} + 3999665515 T^{8} - 35396717507 T^{9} + 313490113918 T^{10} - 2378948179079 T^{11} + 17605136800576 T^{12} - 118427419531199 T^{13} + 770078149745886 T^{14} - 5245687475473816 T^{15} + 37051046350245696 T^{16} - 319986936003902776 T^{17} + 2865460795204441806 T^{18} - 26880774112611080219 T^{19} + \)\(24\!\cdots\!16\)\( T^{20} - \)\(20\!\cdots\!79\)\( T^{21} + \)\(16\!\cdots\!98\)\( T^{22} - \)\(11\!\cdots\!47\)\( T^{23} + \)\(76\!\cdots\!15\)\( T^{24} - \)\(43\!\cdots\!24\)\( T^{25} + \)\(25\!\cdots\!40\)\( T^{26} - \)\(11\!\cdots\!38\)\( T^{27} + \)\(54\!\cdots\!24\)\( T^{28} - \)\(17\!\cdots\!76\)\( T^{29} + \)\(67\!\cdots\!08\)\( T^{30} - \)\(12\!\cdots\!21\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 - 19 T + 724 T^{2} - 12046 T^{3} + 257102 T^{4} - 3745752 T^{5} + 59115952 T^{6} - 758558610 T^{7} + 9828612801 T^{8} - 112001359983 T^{9} + 1252735431022 T^{10} - 12783502348115 T^{11} + 126737259090406 T^{12} - 1166087086221651 T^{13} + 10393498646127598 T^{14} - 86613947283856460 T^{15} + 698885105370952532 T^{16} - 5283450784315244060 T^{17} + 38674208462240792158 T^{18} - \)\(26\!\cdots\!31\)\( T^{19} + \)\(17\!\cdots\!46\)\( T^{20} - \)\(10\!\cdots\!15\)\( T^{21} + \)\(64\!\cdots\!42\)\( T^{22} - \)\(35\!\cdots\!43\)\( T^{23} + \)\(18\!\cdots\!81\)\( T^{24} - \)\(88\!\cdots\!10\)\( T^{25} + \)\(42\!\cdots\!52\)\( T^{26} - \)\(16\!\cdots\!72\)\( T^{27} + \)\(68\!\cdots\!42\)\( T^{28} - \)\(19\!\cdots\!26\)\( T^{29} + \)\(71\!\cdots\!84\)\( T^{30} - \)\(11\!\cdots\!19\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( 1 - 7 T + 416 T^{2} - 2906 T^{3} + 92225 T^{4} - 662265 T^{5} + 14647264 T^{6} - 106697872 T^{7} + 1859573595 T^{8} - 13416052303 T^{9} + 198998697654 T^{10} - 1395731332087 T^{11} + 18442288745535 T^{12} - 124512015673048 T^{13} + 1501976409302808 T^{14} - 9717496997468787 T^{15} + 108518883485535428 T^{16} - 669528158433631589 T^{17} + 6998571870052211492 T^{18} - 40841217664451526929 T^{19} + \)\(40\!\cdots\!88\)\( T^{20} - \)\(22\!\cdots\!47\)\( T^{21} + \)\(20\!\cdots\!28\)\( T^{22} - \)\(10\!\cdots\!48\)\( T^{23} + \)\(95\!\cdots\!35\)\( T^{24} - \)\(43\!\cdots\!27\)\( T^{25} + \)\(38\!\cdots\!74\)\( T^{26} - \)\(15\!\cdots\!23\)\( T^{27} + \)\(13\!\cdots\!95\)\( T^{28} - \)\(46\!\cdots\!92\)\( T^{29} + \)\(38\!\cdots\!44\)\( T^{30} - \)\(10\!\cdots\!65\)\( T^{31} + \)\(91\!\cdots\!25\)\( T^{32} - \)\(17\!\cdots\!06\)\( T^{33} + \)\(15\!\cdots\!76\)\( T^{34} - \)\(15\!\cdots\!47\)\( T^{35} + \)\(13\!\cdots\!81\)\( T^{36} \))
$67$ (\( 1 - 9 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 + 5 T + 367 T^{2} + 2067 T^{3} + 65226 T^{4} + 359097 T^{5} + 7477626 T^{6} + 36309399 T^{7} + 596860648 T^{8} + 2432729733 T^{9} + 33567063114 T^{10} + 108003091011 T^{11} + 1314377018346 T^{12} + 2790708596169 T^{13} + 33198226256023 T^{14} + 30303558026615 T^{15} + 406067677556641 T^{16} \))(\( 1 - 12 T + 274 T^{2} - 3235 T^{3} + 47142 T^{4} - 446605 T^{5} + 5204776 T^{6} - 44226721 T^{7} + 436542763 T^{8} - 3279783782 T^{9} + 29248365121 T^{10} - 198533750569 T^{11} + 1565404044088 T^{12} - 8999591394205 T^{13} + 63647597794194 T^{14} - 292632866316715 T^{15} + 1660634979858502 T^{16} - 4872812130679692 T^{17} + 27206534396294947 T^{18} \))(\( 1 + 20 T + 542 T^{2} + 7475 T^{3} + 119860 T^{4} + 1291619 T^{5} + 15632406 T^{6} + 140272099 T^{7} + 1408424239 T^{8} + 10890441078 T^{9} + 94364424013 T^{10} + 629681452411 T^{11} + 4701649325778 T^{12} + 26027570754899 T^{13} + 161825995325020 T^{14} + 676176406713275 T^{15} + 3284905690085066 T^{16} + 8121353551132820 T^{17} + 27206534396294947 T^{18} \))(\( 1 + 9 T + 563 T^{2} + 4525 T^{3} + 147688 T^{4} + 1072099 T^{5} + 24581492 T^{6} + 162558481 T^{7} + 2972408127 T^{8} + 17933807816 T^{9} + 279171589761 T^{10} + 1526212276726 T^{11} + 20896286012256 T^{12} + 102256222540642 T^{13} + 1253201266437129 T^{14} + 5393825840163608 T^{15} + 59897355828560367 T^{16} + 219474286553882467 T^{17} + 2223601997620216148 T^{18} + 6497682851355182977 T^{19} + 59971323162985196008 T^{20} + \)\(12\!\cdots\!75\)\( T^{21} + \)\(10\!\cdots\!87\)\( T^{22} + \)\(10\!\cdots\!47\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 + 13 T + 468 T^{2} + 5852 T^{3} + 113142 T^{4} + 1320189 T^{5} + 18690760 T^{6} + 200509452 T^{7} + 2346598500 T^{8} + 22930691151 T^{9} + 234656483334 T^{10} + 2081615689262 T^{11} + 19108101224933 T^{12} + 153914054113794 T^{13} + 1280242782070511 T^{14} + 9344372829097118 T^{15} + 70575987896983842 T^{16} + 462079131997430271 T^{17} + 3168201550898539500 T^{18} + 18137760637512761388 T^{19} + \)\(11\!\cdots\!80\)\( T^{20} + \)\(53\!\cdots\!49\)\( T^{21} + \)\(30\!\cdots\!74\)\( T^{22} + \)\(10\!\cdots\!48\)\( T^{23} + \)\(57\!\cdots\!44\)\( T^{24} + \)\(10\!\cdots\!93\)\( T^{25} + \)\(54\!\cdots\!87\)\( T^{26} \))(\( 1 + 11 T + 677 T^{2} + 6253 T^{3} + 213651 T^{4} + 1742696 T^{5} + 42942399 T^{6} + 324003214 T^{7} + 6291846370 T^{8} + 45580026226 T^{9} + 724929048128 T^{10} + 5157895783324 T^{11} + 69004839961067 T^{12} + 484256922674237 T^{13} + 5621118295889744 T^{14} + 38295076389901251 T^{15} + 400888800091719174 T^{16} + 2565770118123383817 T^{17} + 25233200030249060816 T^{18} + \)\(14\!\cdots\!31\)\( T^{19} + \)\(13\!\cdots\!07\)\( T^{20} + \)\(69\!\cdots\!68\)\( T^{21} + \)\(65\!\cdots\!32\)\( T^{22} + \)\(27\!\cdots\!98\)\( T^{23} + \)\(25\!\cdots\!70\)\( T^{24} + \)\(88\!\cdots\!58\)\( T^{25} + \)\(78\!\cdots\!51\)\( T^{26} + \)\(21\!\cdots\!68\)\( T^{27} + \)\(17\!\cdots\!11\)\( T^{28} + \)\(34\!\cdots\!11\)\( T^{29} + \)\(24\!\cdots\!33\)\( T^{30} + \)\(27\!\cdots\!73\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 33 T + 949 T^{2} - 18749 T^{3} + 341207 T^{4} - 5197800 T^{5} + 75073803 T^{6} - 969967468 T^{7} + 12034150648 T^{8} - 137435325418 T^{9} + 1515871577664 T^{10} - 15620337250128 T^{11} + 156015993236885 T^{12} - 1468272486068645 T^{13} + 13422503694450576 T^{14} - 116108234925557999 T^{15} + 976415923955764262 T^{16} - 7779251740012385933 T^{17} + 60253619084388635664 T^{18} - \)\(44\!\cdots\!35\)\( T^{19} + \)\(31\!\cdots\!85\)\( T^{20} - \)\(21\!\cdots\!96\)\( T^{21} + \)\(13\!\cdots\!16\)\( T^{22} - \)\(83\!\cdots\!14\)\( T^{23} + \)\(48\!\cdots\!68\)\( T^{24} - \)\(26\!\cdots\!96\)\( T^{25} + \)\(13\!\cdots\!47\)\( T^{26} - \)\(63\!\cdots\!00\)\( T^{27} + \)\(27\!\cdots\!27\)\( T^{28} - \)\(10\!\cdots\!63\)\( T^{29} + \)\(34\!\cdots\!21\)\( T^{30} - \)\(81\!\cdots\!19\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 35 T + 1159 T^{2} - 25899 T^{3} + 531712 T^{4} - 9069989 T^{5} + 143662628 T^{6} - 2025970703 T^{7} + 26855417427 T^{8} - 327410306262 T^{9} + 3790710120337 T^{10} - 41126839671406 T^{11} + 427455848624801 T^{12} - 4215959944706251 T^{13} + 40144372509170156 T^{14} - 366106440699841969 T^{15} + 3244085772839912291 T^{16} - 27702438934694870276 T^{17} + \)\(23\!\cdots\!88\)\( T^{18} - \)\(18\!\cdots\!92\)\( T^{19} + \)\(14\!\cdots\!99\)\( T^{20} - \)\(11\!\cdots\!47\)\( T^{21} + \)\(80\!\cdots\!76\)\( T^{22} - \)\(56\!\cdots\!57\)\( T^{23} + \)\(38\!\cdots\!69\)\( T^{24} - \)\(24\!\cdots\!38\)\( T^{25} + \)\(15\!\cdots\!17\)\( T^{26} - \)\(89\!\cdots\!14\)\( T^{27} + \)\(48\!\cdots\!23\)\( T^{28} - \)\(24\!\cdots\!49\)\( T^{29} + \)\(11\!\cdots\!08\)\( T^{30} - \)\(49\!\cdots\!43\)\( T^{31} + \)\(19\!\cdots\!48\)\( T^{32} - \)\(63\!\cdots\!57\)\( T^{33} + \)\(19\!\cdots\!79\)\( T^{34} - \)\(38\!\cdots\!45\)\( T^{35} + \)\(74\!\cdots\!09\)\( T^{36} \))
$71$ (\( 1 + 71 T^{2} \))(\( 1 + 7 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + T + 309 T^{2} - 403 T^{3} + 50633 T^{4} - 107515 T^{5} + 5709802 T^{6} - 13531994 T^{7} + 465330730 T^{8} - 960771574 T^{9} + 28783111882 T^{10} - 38480801165 T^{11} + 1286669644073 T^{12} - 727104428453 T^{13} + 39582987731589 T^{14} + 9095120158391 T^{15} + 645753531245761 T^{16} \))(\( 1 + 7 T + 533 T^{2} + 3329 T^{3} + 132072 T^{4} + 728958 T^{5} + 19985738 T^{6} + 95991266 T^{7} + 2034708327 T^{8} + 8308609245 T^{9} + 144464291217 T^{10} + 483891971906 T^{11} + 7153115473318 T^{12} + 18524048158398 T^{13} + 238288178845272 T^{14} + 426445845173009 T^{15} + 4847699044422403 T^{16} + 4520274718720327 T^{17} + 45848500718449031 T^{18} \))(\( 1 - 9 T + 162 T^{2} - 624 T^{3} + 13976 T^{4} - 35278 T^{5} + 1370561 T^{6} - 4013065 T^{7} + 111571406 T^{8} - 203499152 T^{9} + 7921569826 T^{10} - 20229860665 T^{11} + 490538858071 T^{12} - 896473282318 T^{13} + 25215909409576 T^{14} - 79934577166704 T^{15} + 1473409465659342 T^{16} - 5811781781211849 T^{17} + 45848500718449031 T^{18} \))(\( 1 - 7 T + 476 T^{2} - 1492 T^{3} + 95284 T^{4} + 66242 T^{5} + 11768912 T^{6} + 49115224 T^{7} + 1226805976 T^{8} + 6523649352 T^{9} + 122762751080 T^{10} + 519837843019 T^{11} + 10106802962142 T^{12} + 36908486854349 T^{13} + 618847028194280 T^{14} + 2334885863223672 T^{15} + 31175202111005656 T^{16} + 88615128721739624 T^{17} + 1507600968641263952 T^{18} + 602478949532136622 T^{19} + 61529979471221091124 T^{20} - 68405963071925954252 T^{21} + \)\(15\!\cdots\!76\)\( T^{22} - \)\(16\!\cdots\!97\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 506 T^{2} - 433 T^{3} + 127600 T^{4} - 200994 T^{5} + 21378494 T^{6} - 47206286 T^{7} + 2677446032 T^{8} - 7252511852 T^{9} + 268048678584 T^{10} - 798191345505 T^{11} + 22359626877963 T^{12} - 65363504425892 T^{13} + 1587533508335373 T^{14} - 4023682572690705 T^{15} + 95937570600678024 T^{16} - 184298517631743212 T^{17} + 4830726716652885232 T^{18} - 6047138639455927406 T^{19} + \)\(19\!\cdots\!54\)\( T^{20} - \)\(12\!\cdots\!34\)\( T^{21} + \)\(58\!\cdots\!00\)\( T^{22} - \)\(14\!\cdots\!33\)\( T^{23} + \)\(11\!\cdots\!26\)\( T^{24} + \)\(11\!\cdots\!11\)\( T^{26} \))(\( 1 - 7 T + 117 T^{2} - 291 T^{3} + 21452 T^{4} - 136910 T^{5} + 2415623 T^{6} - 7185203 T^{7} + 230286309 T^{8} - 1493262365 T^{9} + 24972357372 T^{10} - 94846172137 T^{11} + 1702596997046 T^{12} - 10893914862268 T^{13} + 169597232593544 T^{14} - 750168218524879 T^{15} + 9606859347730640 T^{16} - 53261943515266409 T^{17} + 854939649504055304 T^{18} - 3899051962269202148 T^{19} + 43265851760490894326 T^{20} - \)\(17\!\cdots\!87\)\( T^{21} + \)\(31\!\cdots\!12\)\( T^{22} - \)\(13\!\cdots\!15\)\( T^{23} + \)\(14\!\cdots\!49\)\( T^{24} - \)\(32\!\cdots\!93\)\( T^{25} + \)\(78\!\cdots\!23\)\( T^{26} - \)\(31\!\cdots\!10\)\( T^{27} + \)\(35\!\cdots\!32\)\( T^{28} - \)\(33\!\cdots\!01\)\( T^{29} + \)\(96\!\cdots\!77\)\( T^{30} - \)\(41\!\cdots\!57\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 + 5 T + 524 T^{2} + 2352 T^{3} + 149201 T^{4} + 595217 T^{5} + 29572318 T^{6} + 103995194 T^{7} + 4508719255 T^{8} + 13939173581 T^{9} + 557562404560 T^{10} + 1520509439145 T^{11} + 57725098788352 T^{12} + 140465013275417 T^{13} + 5102567896652094 T^{14} + 11293730464414365 T^{15} + 389271182680022622 T^{16} + 801854862973419915 T^{17} + 25722044767023205854 T^{18} + 50273973366417773887 T^{19} + \)\(14\!\cdots\!12\)\( T^{20} + \)\(27\!\cdots\!95\)\( T^{21} + \)\(71\!\cdots\!60\)\( T^{22} + \)\(12\!\cdots\!71\)\( T^{23} + \)\(29\!\cdots\!55\)\( T^{24} + \)\(47\!\cdots\!14\)\( T^{25} + \)\(96\!\cdots\!18\)\( T^{26} + \)\(13\!\cdots\!07\)\( T^{27} + \)\(24\!\cdots\!41\)\( T^{28} + \)\(27\!\cdots\!72\)\( T^{29} + \)\(43\!\cdots\!44\)\( T^{30} + \)\(29\!\cdots\!55\)\( T^{31} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 - T + 768 T^{2} - 1178 T^{3} + 288190 T^{4} - 605112 T^{5} + 70658140 T^{6} - 190584652 T^{7} + 12763987732 T^{8} - 42239122638 T^{9} + 1816034671326 T^{10} - 7069912501439 T^{11} + 212488617436367 T^{12} - 930314706320830 T^{13} + 21081636369140130 T^{14} - 98555395087236676 T^{15} + 1812789095971482766 T^{16} - 8520689462239692892 T^{17} + \)\(13\!\cdots\!36\)\( T^{18} - \)\(60\!\cdots\!32\)\( T^{19} + \)\(91\!\cdots\!06\)\( T^{20} - \)\(35\!\cdots\!36\)\( T^{21} + \)\(53\!\cdots\!30\)\( T^{22} - \)\(16\!\cdots\!30\)\( T^{23} + \)\(27\!\cdots\!07\)\( T^{24} - \)\(64\!\cdots\!49\)\( T^{25} + \)\(11\!\cdots\!86\)\( T^{26} - \)\(19\!\cdots\!78\)\( T^{27} + \)\(41\!\cdots\!32\)\( T^{28} - \)\(44\!\cdots\!92\)\( T^{29} + \)\(11\!\cdots\!40\)\( T^{30} - \)\(70\!\cdots\!32\)\( T^{31} + \)\(23\!\cdots\!90\)\( T^{32} - \)\(69\!\cdots\!78\)\( T^{33} + \)\(32\!\cdots\!28\)\( T^{34} - \)\(29\!\cdots\!91\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))
$73$ (\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 21 T + 479 T^{2} + 6828 T^{3} + 103348 T^{4} + 1162895 T^{5} + 13471003 T^{6} + 125077854 T^{7} + 1189125482 T^{8} + 9130683342 T^{9} + 71786974987 T^{10} + 452385924215 T^{11} + 2934901410868 T^{12} + 14154932837004 T^{13} + 72489094392431 T^{14} + 231995368901037 T^{15} + 806460091894081 T^{16} \))(\( 1 - 13 T + 506 T^{2} - 4747 T^{3} + 107167 T^{4} - 734909 T^{5} + 13144645 T^{6} - 67606851 T^{7} + 1145412177 T^{8} - 4992931436 T^{9} + 83615088921 T^{10} - 360276908979 T^{11} + 5113490363965 T^{12} - 20870122895069 T^{13} + 222164863407031 T^{14} - 718383572193883 T^{15} + 5589983650663082 T^{16} - 10483981194623053 T^{17} + 58871586708267913 T^{18} \))(\( 1 + 11 T + 216 T^{2} + 783 T^{3} + 18999 T^{4} + 100595 T^{5} + 2714667 T^{6} + 13756013 T^{7} + 196354509 T^{8} + 632886124 T^{9} + 14333879157 T^{10} + 73305793277 T^{11} + 1056051612339 T^{12} + 2856721053395 T^{13} + 39386287195407 T^{14} + 118494699184287 T^{15} + 2386238080124952 T^{16} + 8871061010834891 T^{17} + 58871586708267913 T^{18} \))(\( 1 + 9 T + 709 T^{2} + 4662 T^{3} + 220376 T^{4} + 965723 T^{5} + 40155885 T^{6} + 92349544 T^{7} + 4908938519 T^{8} + 2009273495 T^{9} + 450446125726 T^{10} - 377142877857 T^{11} + 34808677030176 T^{12} - 27531430083561 T^{13} + 2400427403993854 T^{14} + 781641547204415 T^{15} + 139405219116745079 T^{16} + 191447216292903592 T^{17} + 6076959787425060765 T^{18} + 10668726840057912131 T^{19} + \)\(17\!\cdots\!56\)\( T^{20} + \)\(27\!\cdots\!06\)\( T^{21} + \)\(30\!\cdots\!41\)\( T^{22} + \)\(28\!\cdots\!93\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 9 T + 592 T^{2} - 4879 T^{3} + 173821 T^{4} - 1296931 T^{5} + 33546379 T^{6} - 226656351 T^{7} + 4771079224 T^{8} - 29281227419 T^{9} + 530220917047 T^{10} - 2959799841666 T^{11} + 47454331217192 T^{12} - 240237702532082 T^{13} + 3464166178855016 T^{14} - 15772773356238114 T^{15} + 206264950486872799 T^{16} - 831535353020569979 T^{17} + 9890788807226883832 T^{18} - 34300863512073011439 T^{19} + \)\(37\!\cdots\!63\)\( T^{20} - \)\(10\!\cdots\!11\)\( T^{21} + \)\(10\!\cdots\!73\)\( T^{22} - \)\(20\!\cdots\!71\)\( T^{23} + \)\(18\!\cdots\!84\)\( T^{24} - \)\(20\!\cdots\!89\)\( T^{25} + \)\(16\!\cdots\!33\)\( T^{26} \))(\( 1 + 13 T + 591 T^{2} + 6898 T^{3} + 182372 T^{4} + 1956529 T^{5} + 38630719 T^{6} + 383102958 T^{7} + 6243144468 T^{8} + 57513478640 T^{9} + 813550203641 T^{10} + 6978310738401 T^{11} + 88227180423132 T^{12} + 705198286076836 T^{13} + 8114168841062969 T^{14} + 60341860895801245 T^{15} + 639064450484286678 T^{16} + 4404955845393490885 T^{17} + 43240405754024561801 T^{18} + \)\(27\!\cdots\!12\)\( T^{19} + \)\(25\!\cdots\!12\)\( T^{20} + \)\(14\!\cdots\!93\)\( T^{21} + \)\(12\!\cdots\!49\)\( T^{22} + \)\(63\!\cdots\!80\)\( T^{23} + \)\(50\!\cdots\!08\)\( T^{24} + \)\(22\!\cdots\!54\)\( T^{25} + \)\(16\!\cdots\!31\)\( T^{26} + \)\(61\!\cdots\!33\)\( T^{27} + \)\(41\!\cdots\!12\)\( T^{28} + \)\(11\!\cdots\!34\)\( T^{29} + \)\(72\!\cdots\!19\)\( T^{30} + \)\(11\!\cdots\!41\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 - 23 T + 1033 T^{2} - 19008 T^{3} + 492054 T^{4} - 7612833 T^{5} + 146285379 T^{6} - 1961092652 T^{7} + 30725787368 T^{8} - 363799575798 T^{9} + 4869148361641 T^{10} - 51538421046465 T^{11} + 604954307644026 T^{12} - 5765014485858262 T^{13} + 60276142525015787 T^{14} - 518759265856954575 T^{15} + 4874762472412736270 T^{16} - 37869426407557683975 T^{17} + \)\(32\!\cdots\!23\)\( T^{18} - \)\(22\!\cdots\!54\)\( T^{19} + \)\(17\!\cdots\!66\)\( T^{20} - \)\(10\!\cdots\!45\)\( T^{21} + \)\(73\!\cdots\!49\)\( T^{22} - \)\(40\!\cdots\!06\)\( T^{23} + \)\(24\!\cdots\!08\)\( T^{24} - \)\(11\!\cdots\!76\)\( T^{25} + \)\(62\!\cdots\!71\)\( T^{26} - \)\(23\!\cdots\!41\)\( T^{27} + \)\(11\!\cdots\!34\)\( T^{28} - \)\(31\!\cdots\!64\)\( T^{29} + \)\(12\!\cdots\!97\)\( T^{30} - \)\(20\!\cdots\!11\)\( T^{31} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 - 27 T + 1113 T^{2} - 22162 T^{3} + 539955 T^{4} - 8713048 T^{5} + 160605638 T^{6} - 2214330912 T^{7} + 33912386930 T^{8} - 412922246141 T^{9} + 5511221171400 T^{10} - 60528148882991 T^{11} + 723445734893166 T^{12} - 7261286937206408 T^{13} + 78979019762562714 T^{14} - 730071423185508768 T^{15} + 7295455193711314876 T^{16} - 62353494883396706767 T^{17} + \)\(57\!\cdots\!82\)\( T^{18} - \)\(45\!\cdots\!91\)\( T^{19} + \)\(38\!\cdots\!04\)\( T^{20} - \)\(28\!\cdots\!56\)\( T^{21} + \)\(22\!\cdots\!74\)\( T^{22} - \)\(15\!\cdots\!44\)\( T^{23} + \)\(10\!\cdots\!74\)\( T^{24} - \)\(66\!\cdots\!27\)\( T^{25} + \)\(44\!\cdots\!00\)\( T^{26} - \)\(24\!\cdots\!33\)\( T^{27} + \)\(14\!\cdots\!70\)\( T^{28} - \)\(69\!\cdots\!24\)\( T^{29} + \)\(36\!\cdots\!98\)\( T^{30} - \)\(14\!\cdots\!84\)\( T^{31} + \)\(65\!\cdots\!95\)\( T^{32} - \)\(19\!\cdots\!34\)\( T^{33} + \)\(72\!\cdots\!93\)\( T^{34} - \)\(12\!\cdots\!31\)\( T^{35} + \)\(34\!\cdots\!69\)\( T^{36} \))
$79$ (\( 1 + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 441 T^{2} + 3855 T^{3} + 87828 T^{4} + 828813 T^{5} + 10853967 T^{6} + 103733333 T^{7} + 975633828 T^{8} + 8194933307 T^{9} + 67739608047 T^{10} + 408637132707 T^{11} + 3420907714068 T^{12} + 11862052418145 T^{13} + 107201567884761 T^{14} + 153631271889272 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 10 T + 425 T^{2} + 2715 T^{3} + 76957 T^{4} + 321871 T^{5} + 9247137 T^{6} + 29782950 T^{7} + 906879556 T^{8} + 2586333853 T^{9} + 71643484924 T^{10} + 185875390950 T^{11} + 4559199179343 T^{12} + 12536901521551 T^{13} + 236801029297843 T^{14} + 659982441739515 T^{15} + 8161661319117575 T^{16} + 15171088099065610 T^{17} + 119851595982618319 T^{18} \))(\( 1 - 4 T + 142 T^{2} - 1027 T^{3} + 18895 T^{4} - 127472 T^{5} + 2128855 T^{6} - 13201936 T^{7} + 196561307 T^{8} - 1316269664 T^{9} + 15528343253 T^{10} - 82393282576 T^{11} + 1049608540345 T^{12} - 4965044725232 T^{13} + 58140980659105 T^{14} - 249650816820067 T^{15} + 2726955076034578 T^{16} - 6068435239626244 T^{17} + 119851595982618319 T^{18} \))(\( 1 - 14 T + 410 T^{2} - 4613 T^{3} + 78351 T^{4} - 792764 T^{5} + 11062290 T^{6} - 109467202 T^{7} + 1344986159 T^{8} - 12514380775 T^{9} + 133618743464 T^{10} - 1142424924076 T^{11} + 11165347207894 T^{12} - 90251569002004 T^{13} + 833914577958824 T^{14} - 6170077782925225 T^{15} + 52387319836928879 T^{16} - 336836754394725598 T^{17} + 2689103928335403090 T^{18} - 15224167703503353476 T^{19} + \)\(11\!\cdots\!11\)\( T^{20} - \)\(55\!\cdots\!47\)\( T^{21} + \)\(38\!\cdots\!10\)\( T^{22} - \)\(10\!\cdots\!06\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 + 25 T + 703 T^{2} + 11777 T^{3} + 211285 T^{4} + 2877963 T^{5} + 41329810 T^{6} + 488515051 T^{7} + 6037309806 T^{8} + 63838024407 T^{9} + 702720850788 T^{10} + 6740512704916 T^{11} + 67046675840065 T^{12} + 585502883933898 T^{13} + 5296687391365135 T^{14} + 42067539791380756 T^{15} + 346468785551664732 T^{16} + 2486496221532626967 T^{17} + 18577142771297748594 T^{18} + \)\(11\!\cdots\!71\)\( T^{19} + \)\(79\!\cdots\!90\)\( T^{20} + \)\(43\!\cdots\!43\)\( T^{21} + \)\(25\!\cdots\!15\)\( T^{22} + \)\(11\!\cdots\!77\)\( T^{23} + \)\(52\!\cdots\!37\)\( T^{24} + \)\(14\!\cdots\!25\)\( T^{25} + \)\(46\!\cdots\!39\)\( T^{26} \))(\( 1 + 18 T + 579 T^{2} + 7553 T^{3} + 148040 T^{4} + 1700431 T^{5} + 26248023 T^{6} + 288677003 T^{7} + 3732561742 T^{8} + 39699718571 T^{9} + 446773746969 T^{10} + 4618561571973 T^{11} + 47031233415920 T^{12} + 468957869663831 T^{13} + 4404948383830349 T^{14} + 41771965462510402 T^{15} + 367448687940717810 T^{16} + 3299985271538321758 T^{17} + 27491282863485208109 T^{18} + \)\(23\!\cdots\!09\)\( T^{19} + \)\(18\!\cdots\!20\)\( T^{20} + \)\(14\!\cdots\!27\)\( T^{21} + \)\(10\!\cdots\!49\)\( T^{22} + \)\(76\!\cdots\!89\)\( T^{23} + \)\(56\!\cdots\!62\)\( T^{24} + \)\(34\!\cdots\!57\)\( T^{25} + \)\(24\!\cdots\!23\)\( T^{26} + \)\(12\!\cdots\!49\)\( T^{27} + \)\(87\!\cdots\!40\)\( T^{28} + \)\(35\!\cdots\!67\)\( T^{29} + \)\(21\!\cdots\!99\)\( T^{30} + \)\(52\!\cdots\!82\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 - 24 T + 976 T^{2} - 17809 T^{3} + 423439 T^{4} - 6352844 T^{5} + 113351534 T^{6} - 1460320242 T^{7} + 21484645028 T^{8} - 244361185721 T^{9} + 3116047394294 T^{10} - 31936971160069 T^{11} + 364590920008457 T^{12} - 3423996579040382 T^{13} + 35802802462447500 T^{14} - 311998492413383683 T^{15} + 3031192079903180294 T^{16} - 24647880900657310957 T^{17} + \)\(22\!\cdots\!00\)\( T^{18} - \)\(16\!\cdots\!98\)\( T^{19} + \)\(14\!\cdots\!17\)\( T^{20} - \)\(98\!\cdots\!31\)\( T^{21} + \)\(75\!\cdots\!74\)\( T^{22} - \)\(46\!\cdots\!39\)\( T^{23} + \)\(32\!\cdots\!08\)\( T^{24} - \)\(17\!\cdots\!98\)\( T^{25} + \)\(10\!\cdots\!34\)\( T^{26} - \)\(47\!\cdots\!76\)\( T^{27} + \)\(25\!\cdots\!99\)\( T^{28} - \)\(83\!\cdots\!51\)\( T^{29} + \)\(35\!\cdots\!56\)\( T^{30} - \)\(69\!\cdots\!76\)\( T^{31} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 + 450 T^{2} - 191 T^{3} + 101102 T^{4} + 12530 T^{5} + 15405842 T^{6} + 20487525 T^{7} + 1812676105 T^{8} + 4743655923 T^{9} + 180282508704 T^{10} + 640007554877 T^{11} + 16287138332491 T^{12} + 65813717933749 T^{13} + 1371642330107830 T^{14} + 5969059450311506 T^{15} + 108829832490163421 T^{16} + 506558353811562091 T^{17} + 8512316107946360620 T^{18} + 40018109951113405189 T^{19} + \)\(67\!\cdots\!61\)\( T^{20} + \)\(29\!\cdots\!34\)\( T^{21} + \)\(53\!\cdots\!30\)\( T^{22} + \)\(20\!\cdots\!51\)\( T^{23} + \)\(39\!\cdots\!11\)\( T^{24} + \)\(12\!\cdots\!43\)\( T^{25} + \)\(27\!\cdots\!44\)\( T^{26} + \)\(56\!\cdots\!37\)\( T^{27} + \)\(17\!\cdots\!05\)\( T^{28} + \)\(15\!\cdots\!75\)\( T^{29} + \)\(91\!\cdots\!22\)\( T^{30} + \)\(58\!\cdots\!70\)\( T^{31} + \)\(37\!\cdots\!62\)\( T^{32} - \)\(55\!\cdots\!09\)\( T^{33} + \)\(10\!\cdots\!50\)\( T^{34} + \)\(14\!\cdots\!61\)\( T^{36} \))
$83$ (\( 1 - 2 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 - 3 T + 339 T^{2} - 265 T^{3} + 59257 T^{4} + 2766 T^{5} + 7528439 T^{6} + 900678 T^{7} + 722055524 T^{8} + 74756274 T^{9} + 51863416271 T^{10} + 1581562842 T^{11} + 2812237727497 T^{12} - 1043845770395 T^{13} + 110832786572091 T^{14} - 81408152968881 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 9 T + 422 T^{2} - 4342 T^{3} + 86772 T^{4} - 940635 T^{5} + 11854664 T^{6} - 126639668 T^{7} + 1224295309 T^{8} - 12173194872 T^{9} + 101616510647 T^{10} - 872420672852 T^{11} + 6778342764568 T^{12} - 44640957773835 T^{13} + 341798434674396 T^{14} - 1419575101168198 T^{15} + 11451413517622594 T^{16} - 20270630089251369 T^{17} + 186940255267540403 T^{18} \))(\( 1 + 9 T + 464 T^{2} + 3538 T^{3} + 104322 T^{4} + 688973 T^{5} + 15400354 T^{6} + 89528422 T^{7} + 1673708815 T^{8} + 8563628116 T^{9} + 138917831645 T^{10} + 616761299158 T^{11} + 8805722212598 T^{12} + 32697501794333 T^{13} + 410928597959046 T^{14} + 1156715040979522 T^{15} + 12591127659186928 T^{16} + 20270630089251369 T^{17} + 186940255267540403 T^{18} \))(\( 1 - 5 T + 565 T^{2} - 923 T^{3} + 151223 T^{4} + 97770 T^{5} + 28057219 T^{6} + 49140288 T^{7} + 4066956867 T^{8} + 8728187813 T^{9} + 465226469736 T^{10} + 1049244370717 T^{11} + 42722631463610 T^{12} + 87087282769511 T^{13} + 3204945150011304 T^{14} + 4990664325031831 T^{15} + 193010944487240307 T^{16} + 193565591640725184 T^{17} + 9173037655555800811 T^{18} + 2653091705255831790 T^{19} + \)\(34\!\cdots\!43\)\( T^{20} - \)\(17\!\cdots\!69\)\( T^{21} + \)\(87\!\cdots\!85\)\( T^{22} - \)\(64\!\cdots\!35\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - 3 T + 574 T^{2} - 1332 T^{3} + 161638 T^{4} - 308151 T^{5} + 29839616 T^{6} - 50480444 T^{7} + 4089176250 T^{8} - 6571547881 T^{9} + 449863515713 T^{10} - 708368567536 T^{11} + 42184475233194 T^{12} - 64063681249978 T^{13} + 3501311444355102 T^{14} - 4879951061755504 T^{15} + 257226110058989131 T^{16} - 311874628803367801 T^{17} + 16107431445140328750 T^{18} - 16504095209192895836 T^{19} + \)\(80\!\cdots\!32\)\( T^{20} - \)\(69\!\cdots\!91\)\( T^{21} + \)\(30\!\cdots\!14\)\( T^{22} - \)\(20\!\cdots\!68\)\( T^{23} + \)\(73\!\cdots\!58\)\( T^{24} - \)\(32\!\cdots\!83\)\( T^{25} + \)\(88\!\cdots\!63\)\( T^{26} \))(\( 1 - 25 T + 819 T^{2} - 14447 T^{3} + 292981 T^{4} - 4179204 T^{5} + 66556473 T^{6} - 823298784 T^{7} + 11268998106 T^{8} - 125689558730 T^{9} + 1544698676427 T^{10} - 15870363430370 T^{11} + 179127412519771 T^{12} - 1714485105914409 T^{13} + 18000417951575385 T^{14} - 161522367046609711 T^{15} + 1589621530804707978 T^{16} - 13406356464868606013 T^{17} + \)\(12\!\cdots\!65\)\( T^{18} - \)\(98\!\cdots\!83\)\( T^{19} + \)\(85\!\cdots\!91\)\( T^{20} - \)\(62\!\cdots\!10\)\( T^{21} + \)\(50\!\cdots\!63\)\( T^{22} - \)\(34\!\cdots\!10\)\( T^{23} + \)\(25\!\cdots\!46\)\( T^{24} - \)\(15\!\cdots\!52\)\( T^{25} + \)\(10\!\cdots\!77\)\( T^{26} - \)\(53\!\cdots\!68\)\( T^{27} + \)\(31\!\cdots\!41\)\( T^{28} - \)\(12\!\cdots\!61\)\( T^{29} + \)\(60\!\cdots\!51\)\( T^{30} - \)\(15\!\cdots\!75\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 7 T + 721 T^{2} - 5329 T^{3} + 268417 T^{4} - 1996258 T^{5} + 67821703 T^{6} - 490771140 T^{7} + 12924366426 T^{8} - 89194290838 T^{9} + 1962515432901 T^{10} - 12771659562060 T^{11} + 245541472047935 T^{12} - 1496562645439495 T^{13} + 25858985819788019 T^{14} - 146790708985858061 T^{15} + 2320478010739533098 T^{16} - 12183628845826219063 T^{17} + \)\(17\!\cdots\!91\)\( T^{18} - \)\(85\!\cdots\!65\)\( T^{19} + \)\(11\!\cdots\!35\)\( T^{20} - \)\(50\!\cdots\!80\)\( T^{21} + \)\(64\!\cdots\!69\)\( T^{22} - \)\(24\!\cdots\!26\)\( T^{23} + \)\(29\!\cdots\!66\)\( T^{24} - \)\(91\!\cdots\!20\)\( T^{25} + \)\(10\!\cdots\!47\)\( T^{26} - \)\(25\!\cdots\!86\)\( T^{27} + \)\(28\!\cdots\!37\)\( T^{28} - \)\(47\!\cdots\!27\)\( T^{29} + \)\(53\!\cdots\!09\)\( T^{30} - \)\(42\!\cdots\!49\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 13 T + 523 T^{2} - 5687 T^{3} + 157302 T^{4} - 1568269 T^{5} + 34450764 T^{6} - 317090853 T^{7} + 6003054555 T^{8} - 51755651536 T^{9} + 876203423748 T^{10} - 7108215968376 T^{11} + 110169941030601 T^{12} - 844695319069285 T^{13} + 12163828081876180 T^{14} - 88311585850547653 T^{15} + 1192991069645811357 T^{16} - 8206675993683902158 T^{17} + \)\(10\!\cdots\!94\)\( T^{18} - \)\(68\!\cdots\!14\)\( T^{19} + \)\(82\!\cdots\!73\)\( T^{20} - \)\(50\!\cdots\!11\)\( T^{21} + \)\(57\!\cdots\!80\)\( T^{22} - \)\(33\!\cdots\!55\)\( T^{23} + \)\(36\!\cdots\!69\)\( T^{24} - \)\(19\!\cdots\!52\)\( T^{25} + \)\(19\!\cdots\!68\)\( T^{26} - \)\(96\!\cdots\!08\)\( T^{27} + \)\(93\!\cdots\!95\)\( T^{28} - \)\(40\!\cdots\!51\)\( T^{29} + \)\(36\!\cdots\!04\)\( T^{30} - \)\(13\!\cdots\!47\)\( T^{31} + \)\(11\!\cdots\!58\)\( T^{32} - \)\(34\!\cdots\!09\)\( T^{33} + \)\(26\!\cdots\!63\)\( T^{34} - \)\(54\!\cdots\!99\)\( T^{35} + \)\(34\!\cdots\!09\)\( T^{36} \))
$89$ (\( 1 + 9 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))(\( 1 - 9 T + 89 T^{2} \))(\( 1 + 20 T + 264 T^{2} + 3299 T^{3} + 52221 T^{4} + 576266 T^{5} + 5870883 T^{6} + 60574359 T^{7} + 659088331 T^{8} + 5391117951 T^{9} + 46503264243 T^{10} + 406249665754 T^{11} + 3276462567261 T^{12} + 18421812122251 T^{13} + 131203060813704 T^{14} + 884626697910580 T^{15} + 3936588805702081 T^{16} \))(\( 1 + 5 T + 291 T^{2} + 2317 T^{3} + 51986 T^{4} + 466616 T^{5} + 7203344 T^{6} + 61936092 T^{7} + 797299301 T^{8} + 6209910283 T^{9} + 70959637789 T^{10} + 490595784732 T^{11} + 5078134216336 T^{12} + 29276533526456 T^{13} + 290292914515714 T^{14} + 1151505651156637 T^{15} + 12871318454598939 T^{16} + 19682944028510405 T^{17} + 350356403707485209 T^{18} \))(\( 1 + 29 T + 820 T^{2} + 15028 T^{3} + 260838 T^{4} + 3659454 T^{5} + 48835451 T^{6} + 561496779 T^{7} + 6163562054 T^{8} + 59456950122 T^{9} + 548557022806 T^{10} + 4447615986459 T^{11} + 34427479056019 T^{12} + 229602344796414 T^{13} + 1456534898558262 T^{14} + 7468634840561908 T^{15} + 36269694614333780 T^{16} + 114161075365360349 T^{17} + 350356403707485209 T^{18} \))(\( 1 + 22 T + 911 T^{2} + 16895 T^{3} + 390631 T^{4} + 6201311 T^{5} + 104449155 T^{6} + 1434798065 T^{7} + 19412628579 T^{8} + 232283103135 T^{9} + 2643023184249 T^{10} + 27607421552446 T^{11} + 270352082987194 T^{12} + 2457060518167694 T^{13} + 20935386642436329 T^{14} + 163752386933977815 T^{15} + 1217991820747105539 T^{16} + 8011997692270166185 T^{17} + 51909275891685587955 T^{18} + \)\(27\!\cdots\!19\)\( T^{19} + \)\(15\!\cdots\!11\)\( T^{20} + \)\(59\!\cdots\!55\)\( T^{21} + \)\(28\!\cdots\!11\)\( T^{22} + \)\(61\!\cdots\!58\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 - 23 T + 734 T^{2} - 10984 T^{3} + 214778 T^{4} - 2453650 T^{5} + 38218673 T^{6} - 357909203 T^{7} + 4953149789 T^{8} - 39253786003 T^{9} + 517455741160 T^{10} - 3609114795061 T^{11} + 47987616741913 T^{12} - 317117604590984 T^{13} + 4270897890030257 T^{14} - 28587798291678181 T^{15} + 364790256389824040 T^{16} - 2462870501562652723 T^{17} + 27658682881577806261 T^{18} - \)\(17\!\cdots\!83\)\( T^{19} + \)\(16\!\cdots\!17\)\( T^{20} - \)\(96\!\cdots\!50\)\( T^{21} + \)\(75\!\cdots\!02\)\( T^{22} - \)\(34\!\cdots\!84\)\( T^{23} + \)\(20\!\cdots\!26\)\( T^{24} - \)\(56\!\cdots\!83\)\( T^{25} + \)\(21\!\cdots\!69\)\( T^{26} \))(\( 1 - 12 T + 646 T^{2} - 4091 T^{3} + 177301 T^{4} - 406466 T^{5} + 32347743 T^{6} + 27803907 T^{7} + 4909962075 T^{8} + 13752862353 T^{9} + 670323428561 T^{10} + 2421001814046 T^{11} + 80440456506451 T^{12} + 327695186971247 T^{13} + 8347803991668250 T^{14} + 36640041474876984 T^{15} + 775716976754939256 T^{16} + 3260963691264051576 T^{17} + 66122955418004208250 T^{18} + \)\(23\!\cdots\!43\)\( T^{19} + \)\(50\!\cdots\!91\)\( T^{20} + \)\(13\!\cdots\!54\)\( T^{21} + \)\(33\!\cdots\!21\)\( T^{22} + \)\(60\!\cdots\!37\)\( T^{23} + \)\(19\!\cdots\!75\)\( T^{24} + \)\(97\!\cdots\!63\)\( T^{25} + \)\(10\!\cdots\!43\)\( T^{26} - \)\(11\!\cdots\!74\)\( T^{27} + \)\(43\!\cdots\!21\)\( T^{28} - \)\(89\!\cdots\!79\)\( T^{29} + \)\(12\!\cdots\!86\)\( T^{30} - \)\(20\!\cdots\!88\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 + 2 T + 737 T^{2} + 1433 T^{3} + 278119 T^{4} + 460613 T^{5} + 71322669 T^{6} + 92702047 T^{7} + 13910198950 T^{8} + 13584922067 T^{9} + 2189781117450 T^{10} + 1600640366051 T^{11} + 287863420852619 T^{12} + 164145436153087 T^{13} + 32189395580626840 T^{14} + 15491547806714788 T^{15} + 3088744141027715150 T^{16} + 1378747754797616132 T^{17} + \)\(25\!\cdots\!40\)\( T^{18} + \)\(11\!\cdots\!03\)\( T^{19} + \)\(18\!\cdots\!79\)\( T^{20} + \)\(89\!\cdots\!99\)\( T^{21} + \)\(10\!\cdots\!50\)\( T^{22} + \)\(60\!\cdots\!43\)\( T^{23} + \)\(54\!\cdots\!50\)\( T^{24} + \)\(32\!\cdots\!23\)\( T^{25} + \)\(22\!\cdots\!69\)\( T^{26} + \)\(12\!\cdots\!57\)\( T^{27} + \)\(68\!\cdots\!99\)\( T^{28} + \)\(31\!\cdots\!77\)\( T^{29} + \)\(14\!\cdots\!17\)\( T^{30} + \)\(34\!\cdots\!98\)\( T^{31} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 - 30 T + 1383 T^{2} - 29997 T^{3} + 817328 T^{4} - 14225535 T^{5} + 293182588 T^{6} - 4330064250 T^{7} + 74159134945 T^{8} - 961812567150 T^{9} + 14371083074919 T^{10} - 167407403925238 T^{11} + 2245918032219621 T^{12} - 23863181941478078 T^{13} + 292651259909817476 T^{14} - 2866080056153776905 T^{15} + 32480424138163041145 T^{16} - \)\(29\!\cdots\!53\)\( T^{17} + \)\(31\!\cdots\!48\)\( T^{18} - \)\(26\!\cdots\!17\)\( T^{19} + \)\(25\!\cdots\!45\)\( T^{20} - \)\(20\!\cdots\!45\)\( T^{21} + \)\(18\!\cdots\!16\)\( T^{22} - \)\(13\!\cdots\!22\)\( T^{23} + \)\(11\!\cdots\!81\)\( T^{24} - \)\(74\!\cdots\!02\)\( T^{25} + \)\(56\!\cdots\!39\)\( T^{26} - \)\(33\!\cdots\!50\)\( T^{27} + \)\(23\!\cdots\!45\)\( T^{28} - \)\(12\!\cdots\!50\)\( T^{29} + \)\(72\!\cdots\!48\)\( T^{30} - \)\(31\!\cdots\!15\)\( T^{31} + \)\(15\!\cdots\!48\)\( T^{32} - \)\(52\!\cdots\!53\)\( T^{33} + \)\(21\!\cdots\!63\)\( T^{34} - \)\(41\!\cdots\!70\)\( T^{35} + \)\(12\!\cdots\!81\)\( T^{36} \))
$97$ (\( 1 - 6 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 + 7 T + 592 T^{2} + 3692 T^{3} + 165275 T^{4} + 908555 T^{5} + 28552838 T^{6} + 135175014 T^{7} + 3332566836 T^{8} + 13111976358 T^{9} + 268653652742 T^{10} + 829213617515 T^{11} + 14631676917275 T^{12} + 31704460228844 T^{13} + 493119426917968 T^{14} + 565587991346791 T^{15} + 7837433594376961 T^{16} \))(\( 1 + 7 T + 269 T^{2} + 2553 T^{3} + 38361 T^{4} + 294733 T^{5} + 3831941 T^{6} + 15532083 T^{7} + 260082212 T^{8} + 872400240 T^{9} + 25227974564 T^{10} + 146141368947 T^{11} + 3497309088293 T^{12} + 26092500576973 T^{13} + 329418959598777 T^{14} + 2126577528583737 T^{15} + 21734738524612397 T^{16} + 54862035160638727 T^{17} + 760231058654565217 T^{18} \))(\( 1 + 43 T + 1419 T^{2} + 33653 T^{3} + 675911 T^{4} + 11386603 T^{5} + 168876851 T^{6} + 2198016667 T^{7} + 25611739306 T^{8} + 265951175060 T^{9} + 2484338712682 T^{10} + 20681138819803 T^{11} + 154129342232723 T^{12} + 1008047776622443 T^{13} + 5804277740449127 T^{14} + 28032006881875637 T^{15} + 114652765674442347 T^{16} + 337009644558209323 T^{17} + 760231058654565217 T^{18} \))(\( 1 - 17 T + 774 T^{2} - 9880 T^{3} + 253537 T^{4} - 2584489 T^{5} + 48860064 T^{6} - 416211196 T^{7} + 6515305215 T^{8} - 48877804967 T^{9} + 691371657370 T^{10} - 4897327112811 T^{11} + 67453204211902 T^{12} - 475040729942667 T^{13} + 6505115924194330 T^{14} - 44609452892646791 T^{15} + 576795286179500415 T^{16} - 3574147158824917372 T^{17} + 40699065471039255456 T^{18} - \)\(20\!\cdots\!57\)\( T^{19} + \)\(19\!\cdots\!57\)\( T^{20} - \)\(75\!\cdots\!60\)\( T^{21} + \)\(57\!\cdots\!26\)\( T^{22} - \)\(12\!\cdots\!01\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 25 T + 785 T^{2} - 13985 T^{3} + 282257 T^{4} - 4177581 T^{5} + 67542647 T^{6} - 876415887 T^{7} + 12182328445 T^{8} - 141818177539 T^{9} + 1749460665473 T^{10} - 18459410214568 T^{11} + 205234105334120 T^{12} - 1970584379822462 T^{13} + 19907708217409640 T^{14} - 173684590708870312 T^{15} + 1596685513939239329 T^{16} - 12555061290258019459 T^{17} + \)\(10\!\cdots\!65\)\( T^{18} - \)\(73\!\cdots\!23\)\( T^{19} + \)\(54\!\cdots\!11\)\( T^{20} - \)\(32\!\cdots\!41\)\( T^{21} + \)\(21\!\cdots\!69\)\( T^{22} - \)\(10\!\cdots\!65\)\( T^{23} + \)\(56\!\cdots\!05\)\( T^{24} - \)\(17\!\cdots\!25\)\( T^{25} + \)\(67\!\cdots\!77\)\( T^{26} \))(\( 1 - 5 T + 746 T^{2} - 578 T^{3} + 251833 T^{4} + 959647 T^{5} + 54904494 T^{6} + 469001690 T^{7} + 9616658962 T^{8} + 114862667852 T^{9} + 1527018625282 T^{10} + 19504016809643 T^{11} + 218535622457863 T^{12} + 2629684761523704 T^{13} + 26972873110330406 T^{14} + 298659612495176735 T^{15} + 2833262019648399578 T^{16} + 28969982412032143295 T^{17} + \)\(25\!\cdots\!54\)\( T^{18} + \)\(24\!\cdots\!92\)\( T^{19} + \)\(19\!\cdots\!03\)\( T^{20} + \)\(16\!\cdots\!51\)\( T^{21} + \)\(12\!\cdots\!78\)\( T^{22} + \)\(92\!\cdots\!76\)\( T^{23} + \)\(75\!\cdots\!82\)\( T^{24} + \)\(35\!\cdots\!30\)\( T^{25} + \)\(40\!\cdots\!06\)\( T^{26} + \)\(68\!\cdots\!91\)\( T^{27} + \)\(17\!\cdots\!53\)\( T^{28} - \)\(38\!\cdots\!06\)\( T^{29} + \)\(48\!\cdots\!74\)\( T^{30} - \)\(31\!\cdots\!65\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 - 33 T + 1684 T^{2} - 42506 T^{3} + 1258657 T^{4} - 25952915 T^{5} + 570633520 T^{6} - 9975451732 T^{7} + 178170946482 T^{8} - 2701117024970 T^{9} + 40944616452912 T^{10} - 545983773475415 T^{11} + 7196188837938271 T^{12} - 85124759399088460 T^{13} + 989278876034505676 T^{14} - 10425323056413780161 T^{15} + \)\(10\!\cdots\!10\)\( T^{16} - \)\(10\!\cdots\!17\)\( T^{17} + \)\(93\!\cdots\!84\)\( T^{18} - \)\(77\!\cdots\!80\)\( T^{19} + \)\(63\!\cdots\!51\)\( T^{20} - \)\(46\!\cdots\!55\)\( T^{21} + \)\(34\!\cdots\!48\)\( T^{22} - \)\(21\!\cdots\!10\)\( T^{23} + \)\(13\!\cdots\!02\)\( T^{24} - \)\(75\!\cdots\!44\)\( T^{25} + \)\(42\!\cdots\!80\)\( T^{26} - \)\(18\!\cdots\!95\)\( T^{27} + \)\(87\!\cdots\!37\)\( T^{28} - \)\(28\!\cdots\!62\)\( T^{29} + \)\(10\!\cdots\!96\)\( T^{30} - \)\(20\!\cdots\!69\)\( T^{31} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 - 27 T + 930 T^{2} - 19476 T^{3} + 421102 T^{4} - 7342640 T^{5} + 126962594 T^{6} - 1934712124 T^{7} + 29031613151 T^{8} - 398709233423 T^{9} + 5384835329756 T^{10} - 67867534418253 T^{11} + 841013281490069 T^{12} - 9835457185330380 T^{13} + 113117954876260126 T^{14} - 1236010776401504776 T^{15} + 13285743797512469469 T^{16} - \)\(13\!\cdots\!89\)\( T^{17} + \)\(13\!\cdots\!48\)\( T^{18} - \)\(13\!\cdots\!33\)\( T^{19} + \)\(12\!\cdots\!21\)\( T^{20} - \)\(11\!\cdots\!48\)\( T^{21} + \)\(10\!\cdots\!06\)\( T^{22} - \)\(84\!\cdots\!60\)\( T^{23} + \)\(70\!\cdots\!01\)\( T^{24} - \)\(54\!\cdots\!89\)\( T^{25} + \)\(42\!\cdots\!16\)\( T^{26} - \)\(30\!\cdots\!91\)\( T^{27} + \)\(21\!\cdots\!99\)\( T^{28} - \)\(13\!\cdots\!72\)\( T^{29} + \)\(88\!\cdots\!54\)\( T^{30} - \)\(49\!\cdots\!80\)\( T^{31} + \)\(27\!\cdots\!38\)\( T^{32} - \)\(12\!\cdots\!68\)\( T^{33} + \)\(57\!\cdots\!30\)\( T^{34} - \)\(16\!\cdots\!99\)\( T^{35} + \)\(57\!\cdots\!89\)\( T^{36} \))
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