Properties

Label 225.2.h
Level 225
Weight 2
Character orbit h
Rep. character \(\chi_{225}(46,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 44
Newform subspaces 5
Sturm bound 60
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 225.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 5 \)
Sturm bound: \(60\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(225, [\chi])\).

Total New Old
Modular forms 136 52 84
Cusp forms 104 44 60
Eisenstein series 32 8 24

Trace form

\( 44q + 4q^{2} - 12q^{4} + 11q^{5} - 10q^{7} - 7q^{8} + O(q^{10}) \) \( 44q + 4q^{2} - 12q^{4} + 11q^{5} - 10q^{7} - 7q^{8} - 4q^{10} - 4q^{11} - 3q^{13} + 11q^{14} + 8q^{16} + 2q^{17} + 7q^{19} - 21q^{20} - 14q^{22} - 25q^{23} - 11q^{25} + 44q^{26} + 5q^{28} - q^{29} + 15q^{31} - 30q^{32} - 20q^{34} + 25q^{35} - 5q^{37} + 21q^{38} + 7q^{40} - 2q^{41} - 54q^{43} - 32q^{44} - 3q^{46} + 18q^{47} - 14q^{49} - 76q^{50} - 12q^{52} - 45q^{53} - 36q^{55} + 18q^{58} - 12q^{59} + 25q^{61} - 20q^{62} - 7q^{64} - 12q^{65} - 42q^{67} + 128q^{68} - 20q^{70} - 16q^{71} + 45q^{73} + 66q^{74} - 36q^{76} + 60q^{77} + 31q^{79} + 169q^{80} + 120q^{82} + 17q^{83} - 22q^{85} - 39q^{86} + 82q^{88} - 28q^{89} - 8q^{91} - 10q^{92} - 27q^{94} - 91q^{95} + 48q^{97} - 53q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
225.2.h.a \(4\) \(1.797\) \(\Q(\zeta_{10})\) None \(1\) \(0\) \(-5\) \(0\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots\)
225.2.h.b \(4\) \(1.797\) \(\Q(\zeta_{10})\) None \(2\) \(0\) \(5\) \(-2\) \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}+\zeta_{10}^{3})q^{4}+\cdots\)
225.2.h.c \(8\) \(1.797\) 8.0.26265625.1 None \(1\) \(0\) \(5\) \(4\) \(q+(\beta _{3}+\beta _{7})q^{2}+(-1+2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
225.2.h.d \(12\) \(1.797\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(6\) \(-12\) \(q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{5}-2\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots\)
225.2.h.e \(16\) \(1.797\) 16.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{10}+\beta _{12}-\beta _{14})q^{2}+(-\beta _{8}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(225, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T - T^{2} + 3 T^{3} - T^{4} + 6 T^{5} - 4 T^{6} - 8 T^{7} + 16 T^{8} \))(\( 1 - 2 T + 2 T^{2} - 5 T^{3} + 11 T^{4} - 10 T^{5} + 8 T^{6} - 16 T^{7} + 16 T^{8} \))(\( ( 1 - 3 T + 2 T^{2} + T^{4} + 8 T^{6} - 24 T^{7} + 16 T^{8} )( 1 + 2 T + 2 T^{2} + 5 T^{3} + 11 T^{4} + 10 T^{5} + 8 T^{6} + 16 T^{7} + 16 T^{8} ) \))(\( 1 + 2 T^{2} + 3 T^{3} - 2 T^{4} + 2 T^{5} - 5 T^{6} - 10 T^{7} - 18 T^{8} - T^{9} - 2 T^{10} - 22 T^{11} + 121 T^{12} - 44 T^{13} - 8 T^{14} - 8 T^{15} - 288 T^{16} - 320 T^{17} - 320 T^{18} + 256 T^{19} - 512 T^{20} + 1536 T^{21} + 2048 T^{22} + 4096 T^{24} \))(\( 1 - 3 T^{2} + 15 T^{6} - 15 T^{8} - 99 T^{10} + 242 T^{12} + 105 T^{14} - 915 T^{16} + 420 T^{18} + 3872 T^{20} - 6336 T^{22} - 3840 T^{24} + 15360 T^{26} - 49152 T^{30} + 65536 T^{32} \))
$3$ 1
$5$ (\( 1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4} \))(\( 1 - 5 T + 15 T^{2} - 25 T^{3} + 25 T^{4} \))(\( 1 - 5 T + 20 T^{2} - 65 T^{3} + 155 T^{4} - 325 T^{5} + 500 T^{6} - 625 T^{7} + 625 T^{8} \))(\( 1 - 6 T + 16 T^{2} - 21 T^{3} - 4 T^{4} + 100 T^{5} - 285 T^{6} + 500 T^{7} - 100 T^{8} - 2625 T^{9} + 10000 T^{10} - 18750 T^{11} + 15625 T^{12} \))(\( 1 - 5 T^{2} + 50 T^{4} - 375 T^{6} + 1375 T^{8} - 9375 T^{10} + 31250 T^{12} - 78125 T^{14} + 390625 T^{16} \))
$7$ (\( ( 1 - 6 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 + T + 13 T^{2} + 7 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 - 2 T + 12 T^{2} - 15 T^{3} + 61 T^{4} - 105 T^{5} + 588 T^{6} - 686 T^{7} + 2401 T^{8} )^{2} \))(\( ( 1 + 6 T + 46 T^{2} + 185 T^{3} + 822 T^{4} + 2435 T^{5} + 7706 T^{6} + 17045 T^{7} + 40278 T^{8} + 63455 T^{9} + 110446 T^{10} + 100842 T^{11} + 117649 T^{12} )^{2} \))(\( ( 1 + 18 T^{2} + 5 T^{3} + 159 T^{4} + 35 T^{5} + 882 T^{6} + 2401 T^{8} )^{4} \))
$11$ (\( 1 - 6 T + 5 T^{2} + 6 T^{3} + 49 T^{4} + 66 T^{5} + 605 T^{6} - 7986 T^{7} + 14641 T^{8} \))(\( 1 - 2 T + 13 T^{2} - 34 T^{3} + 225 T^{4} - 374 T^{5} + 1573 T^{6} - 2662 T^{7} + 14641 T^{8} \))(\( 1 + 16 T + 105 T^{2} + 340 T^{3} + 390 T^{4} - 1332 T^{5} - 9707 T^{6} - 42730 T^{7} - 156045 T^{8} - 470030 T^{9} - 1174547 T^{10} - 1772892 T^{11} + 5709990 T^{12} + 54757340 T^{13} + 186013905 T^{14} + 311794736 T^{15} + 214358881 T^{16} \))(\( 1 - 4 T - 22 T^{2} + 120 T^{3} + 58 T^{4} - 900 T^{5} + 1437 T^{6} - 4466 T^{7} - 10704 T^{8} + 67762 T^{9} + 285698 T^{10} - 117068 T^{11} - 5557163 T^{12} - 1287748 T^{13} + 34569458 T^{14} + 90191222 T^{15} - 156717264 T^{16} - 719253766 T^{17} + 2545733157 T^{18} - 17538453900 T^{19} + 12432815098 T^{20} + 282953722920 T^{21} - 570623341222 T^{22} - 1141246682444 T^{23} + 3138428376721 T^{24} \))(\( 1 - 14 T^{2} + 255 T^{4} - 3590 T^{6} + 31630 T^{8} - 26672 T^{10} - 1618917 T^{12} + 54477410 T^{14} - 819034805 T^{16} + 6591766610 T^{18} - 23702563797 T^{20} - 47251074992 T^{22} + 6780171406030 T^{24} - 93115354317590 T^{26} + 800299236063855 T^{28} - 5316497670165374 T^{30} + 45949729863572161 T^{32} \))
$13$ (\( 1 + 2 T + 11 T^{2} + 16 T^{3} + 49 T^{4} + 208 T^{5} + 1859 T^{6} + 4394 T^{7} + 28561 T^{8} \))(\( 1 - 9 T + 23 T^{2} - 15 T^{3} + 16 T^{4} - 195 T^{5} + 3887 T^{6} - 19773 T^{7} + 28561 T^{8} \))(\( 1 + 8 T + 17 T^{2} + 14 T^{3} + 276 T^{4} + 578 T^{5} - 4815 T^{6} - 18048 T^{7} - 25061 T^{8} - 234624 T^{9} - 813735 T^{10} + 1269866 T^{11} + 7882836 T^{12} + 5198102 T^{13} + 82055753 T^{14} + 501988136 T^{15} + 815730721 T^{16} \))(\( 1 + 2 T - 20 T^{2} + 8 T^{3} + 236 T^{4} - 1188 T^{5} - 3563 T^{6} + 9192 T^{7} - 20810 T^{8} - 140028 T^{9} + 822700 T^{10} + 1862120 T^{11} - 6309151 T^{12} + 24207560 T^{13} + 139036300 T^{14} - 307641516 T^{15} - 594354410 T^{16} + 3412925256 T^{17} - 17197920467 T^{18} - 74545238196 T^{19} + 192512450156 T^{20} + 84835994984 T^{21} - 2757169836980 T^{22} + 3584320788074 T^{23} + 23298085122481 T^{24} \))(\( ( 1 - 31 T^{2} - 70 T^{3} + 232 T^{4} + 1950 T^{5} + 6617 T^{6} - 14700 T^{7} - 162685 T^{8} - 191100 T^{9} + 1118273 T^{10} + 4284150 T^{11} + 6626152 T^{12} - 25990510 T^{13} - 149631079 T^{14} + 815730721 T^{16} )^{2} \))
$17$ (\( 1 - 8 T + 17 T^{2} - 60 T^{3} + 461 T^{4} - 1020 T^{5} + 4913 T^{6} - 39304 T^{7} + 83521 T^{8} \))(\( 1 + 8 T + 7 T^{2} - 110 T^{3} - 579 T^{4} - 1870 T^{5} + 2023 T^{6} + 39304 T^{7} + 83521 T^{8} \))(\( 1 - T - 27 T^{2} + 38 T^{3} + 591 T^{4} - 456 T^{5} - 11720 T^{6} + 3109 T^{7} + 167979 T^{8} + 52853 T^{9} - 3387080 T^{10} - 2240328 T^{11} + 49360911 T^{12} + 53954566 T^{13} - 651714363 T^{14} - 410338673 T^{15} + 6975757441 T^{16} \))(\( 1 - T - 22 T^{2} - 27 T^{3} - 141 T^{4} + 1839 T^{5} + 11791 T^{6} + 5192 T^{7} - 114598 T^{8} - 1351839 T^{9} - 1459527 T^{10} + 15628812 T^{11} + 54801289 T^{12} + 265689804 T^{13} - 421803303 T^{14} - 6641585007 T^{15} - 9571339558 T^{16} + 7371897544 T^{17} + 284606076079 T^{18} + 754612819647 T^{19} - 983581799181 T^{20} - 3201872665419 T^{21} - 44351865809878 T^{22} - 34271896307633 T^{23} + 582622237229761 T^{24} \))(\( 1 - 53 T^{2} + 1125 T^{4} - 4010 T^{6} - 312365 T^{8} + 7565836 T^{10} - 61832928 T^{12} - 561210595 T^{14} + 22136734435 T^{16} - 162189861955 T^{18} - 5164347979488 T^{20} + 182620888492684 T^{22} - 2178982473057965 T^{24} - 8084135540800490 T^{26} + 655450016883481125 T^{28} - 8924024807648249237 T^{30} + 48661191875666868481 T^{32} \))
$19$ (\( 1 + 4 T - 3 T^{2} + 62 T^{3} + 605 T^{4} + 1178 T^{5} - 1083 T^{6} + 27436 T^{7} + 130321 T^{8} \))(\( 1 + 5 T + 21 T^{2} + 145 T^{3} + 956 T^{4} + 2755 T^{5} + 7581 T^{6} + 34295 T^{7} + 130321 T^{8} \))(\( 1 + 5 T - 33 T^{2} - 265 T^{3} - 47 T^{4} + 6980 T^{5} + 26814 T^{6} - 68150 T^{7} - 765695 T^{8} - 1294850 T^{9} + 9679854 T^{10} + 47875820 T^{11} - 6125087 T^{12} - 656166235 T^{13} - 1552514073 T^{14} + 4469358695 T^{15} + 16983563041 T^{16} \))(\( 1 - 7 T + 16 T^{2} - 122 T^{3} + 1071 T^{4} - 728 T^{5} - 5797 T^{6} - 36918 T^{7} + 65678 T^{8} + 636002 T^{9} + 4923209 T^{10} - 25899375 T^{11} + 44345259 T^{12} - 492088125 T^{13} + 1777278449 T^{14} + 4362337718 T^{15} + 8559222638 T^{16} - 91412622882 T^{17} - 272724972157 T^{18} - 650738625992 T^{19} + 18189396016911 T^{20} - 39367899129038 T^{21} + 98097060124816 T^{22} - 815431812287533 T^{23} + 2213314919066161 T^{24} \))(\( ( 1 - 7 T + 15 T^{2} - 45 T^{3} + 495 T^{4} - 1926 T^{5} + 4452 T^{6} - 54240 T^{7} + 359505 T^{8} - 1030560 T^{9} + 1607172 T^{10} - 13210434 T^{11} + 64508895 T^{12} - 111424455 T^{13} + 705688215 T^{14} - 6257102173 T^{15} + 16983563041 T^{16} )^{2} \))
$23$ (\( 1 + 10 T + 37 T^{2} + 200 T^{3} + 1389 T^{4} + 4600 T^{5} + 19573 T^{6} + 121670 T^{7} + 279841 T^{8} \))(\( 1 - 11 T + 28 T^{2} + 245 T^{3} - 2259 T^{4} + 5635 T^{5} + 14812 T^{6} - 133837 T^{7} + 279841 T^{8} \))(\( 1 + 7 T + 12 T^{2} + 31 T^{3} + 1026 T^{4} + 672 T^{5} - 34550 T^{6} - 127672 T^{7} - 3411 T^{8} - 2936456 T^{9} - 18276950 T^{10} + 8176224 T^{11} + 287116866 T^{12} + 199526633 T^{13} + 1776430668 T^{14} + 23833778129 T^{15} + 78310985281 T^{16} \))(\( 1 + 19 T + 87 T^{2} - 664 T^{3} - 8155 T^{4} - 10802 T^{5} + 276289 T^{6} + 1712486 T^{7} - 1232028 T^{8} - 57899808 T^{9} - 214047367 T^{10} + 649484443 T^{11} + 7850412157 T^{12} + 14938142189 T^{13} - 113231057143 T^{14} - 704466963936 T^{15} - 344771947548 T^{16} + 11022147278698 T^{17} + 40900687735921 T^{18} - 36778924478494 T^{19} - 638626084966555 T^{20} - 1195965367211432 T^{21} + 3604106475587463 T^{22} + 18103385400364613 T^{23} + 21914624432020321 T^{24} \))(\( 1 - 17 T^{2} + 180 T^{4} + 12295 T^{6} - 136670 T^{8} - 4324196 T^{10} + 92201472 T^{12} + 1128216050 T^{14} - 139454538005 T^{16} + 596826290450 T^{18} + 25801752125952 T^{20} - 640136199070244 T^{22} - 10702762358354270 T^{24} + 509338955371814455 T^{26} + 3944632397763657780 T^{28} - \)\(19\!\cdots\!53\)\( T^{30} + \)\(61\!\cdots\!61\)\( T^{32} \))
$29$ (\( 1 - 8 T + 5 T^{2} + 232 T^{3} - 1711 T^{4} + 6728 T^{5} + 4205 T^{6} - 195112 T^{7} + 707281 T^{8} \))(\( 1 + 5 T - 19 T^{2} - 145 T^{3} - 4 T^{4} - 4205 T^{5} - 15979 T^{6} + 121945 T^{7} + 707281 T^{8} \))(\( 1 + 5 T + 12 T^{2} - 110 T^{3} - 322 T^{4} - 4795 T^{5} - 5456 T^{6} - 22500 T^{7} + 487955 T^{8} - 652500 T^{9} - 4588496 T^{10} - 116945255 T^{11} - 227744482 T^{12} - 2256226390 T^{13} + 7137879852 T^{14} + 86249381545 T^{15} + 500246412961 T^{16} \))(\( 1 - T - 75 T^{2} + 3 T^{3} + 2691 T^{4} - 6800 T^{5} - 35703 T^{6} + 577442 T^{7} - 700036 T^{8} - 20501600 T^{9} + 54541649 T^{10} + 290598314 T^{11} - 2133422469 T^{12} + 8427351106 T^{13} + 45869526809 T^{14} - 500013522400 T^{15} - 495122162116 T^{16} + 11843998900858 T^{17} - 21236977029663 T^{18} - 117299158901200 T^{19} + 1346163097278051 T^{20} + 43521437927607 T^{21} - 31553042497515075 T^{22} - 12200509765705829 T^{23} + 353814783205469041 T^{24} \))(\( 1 + 39 T^{2} + 1290 T^{4} + 19350 T^{6} - 930210 T^{8} - 20945943 T^{10} - 6111982 T^{12} + 30999707520 T^{14} + 1820594900175 T^{16} + 26070754024320 T^{18} - 4322888740942 T^{20} - 12459135376736703 T^{22} - 465334215800451810 T^{24} + 8140684964358889350 T^{26} + \)\(45\!\cdots\!90\)\( T^{28} + \)\(11\!\cdots\!59\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))
$31$ (\( 1 + 9 T^{2} - 110 T^{3} + 741 T^{4} - 3410 T^{5} + 8649 T^{6} + 923521 T^{8} \))(\( 1 - 3 T - 22 T^{2} + 159 T^{3} + 205 T^{4} + 4929 T^{5} - 21142 T^{6} - 89373 T^{7} + 923521 T^{8} \))(\( 1 + 19 T + 110 T^{2} - 455 T^{3} - 10080 T^{4} - 55148 T^{5} - 24492 T^{6} + 1584870 T^{7} + 12593785 T^{8} + 49130970 T^{9} - 23536812 T^{10} - 1642914068 T^{11} - 9309091680 T^{12} - 13026263705 T^{13} + 97625404910 T^{14} + 522739668109 T^{15} + 852891037441 T^{16} \))(\( 1 - 13 T - 49 T^{2} + 1410 T^{3} - 4283 T^{4} - 42518 T^{5} + 442503 T^{6} - 1354402 T^{7} - 10366302 T^{8} + 126161252 T^{9} - 343254057 T^{10} - 2277200953 T^{11} + 23831716157 T^{12} - 70593229543 T^{13} - 329867148777 T^{14} + 3758469858332 T^{15} - 9573497589342 T^{16} - 38775379372702 T^{17} + 392723041353543 T^{18} - 1169781326771498 T^{19} - 3652932313359803 T^{20} + 37279867246546110 T^{21} - 40161786062059249 T^{22} - 330310199653262803 T^{23} + 787662783788549761 T^{24} \))(\( ( 1 - 9 T + 20 T^{2} + 35 T^{3} + 430 T^{4} - 19992 T^{5} + 129878 T^{6} - 181500 T^{7} - 383755 T^{8} - 5626500 T^{9} + 124812758 T^{10} - 595581672 T^{11} + 397114030 T^{12} + 1002020285 T^{13} + 17750073620 T^{14} - 247613526999 T^{15} + 852891037441 T^{16} )^{2} \))
$37$ (\( 1 + 15 T + 63 T^{2} + 65 T^{3} + 144 T^{4} + 2405 T^{5} + 86247 T^{6} + 759795 T^{7} + 1874161 T^{8} \))(\( 1 + 7 T - 18 T^{2} - 145 T^{3} + 371 T^{4} - 5365 T^{5} - 24642 T^{6} + 354571 T^{7} + 1874161 T^{8} \))(\( 1 + T + 3 T^{2} + 42 T^{3} + 2811 T^{4} + 3486 T^{5} - 59280 T^{6} + 126501 T^{7} + 3465939 T^{8} + 4680537 T^{9} - 81154320 T^{10} + 176576358 T^{11} + 5268266571 T^{12} + 2912446194 T^{13} + 7697179227 T^{14} + 94931877133 T^{15} + 3512479453921 T^{16} \))(\( 1 - 8 T - 67 T^{2} + 1147 T^{3} - 3085 T^{4} - 39031 T^{5} + 455721 T^{6} - 1535453 T^{7} - 11486553 T^{8} + 153908236 T^{9} - 464906763 T^{10} - 3103077939 T^{11} + 36758415492 T^{12} - 114813883743 T^{13} - 636457358547 T^{14} + 7795913878108 T^{15} - 21527649657033 T^{16} - 106474386807521 T^{17} + 1169255404835889 T^{18} - 3705286096378123 T^{19} - 10835999115346285 T^{20} + 149066115544953319 T^{21} - 322175152951995883 T^{22} - 1423340974235683304 T^{23} + 6582952005840035281 T^{24} \))(\( ( 1 - 5 T + 81 T^{2} - 230 T^{3} + 5257 T^{4} - 7670 T^{5} + 184608 T^{6} - 6325 T^{7} + 7711315 T^{8} - 234025 T^{9} + 252728352 T^{10} - 388508510 T^{11} + 9852464377 T^{12} - 15949110110 T^{13} + 207823839129 T^{14} - 474659385665 T^{15} + 3512479453921 T^{16} )^{2} \))
$41$ (\( 1 - 31 T^{2} - 180 T^{3} + 1501 T^{4} - 7380 T^{5} - 52111 T^{6} + 2825761 T^{8} \))(\( 1 + 8 T - 17 T^{2} - 254 T^{3} - 435 T^{4} - 10414 T^{5} - 28577 T^{6} + 551368 T^{7} + 2825761 T^{8} \))(\( ( 1 - 7 T + 28 T^{2} - 389 T^{3} + 3975 T^{4} - 15949 T^{5} + 47068 T^{6} - 482447 T^{7} + 2825761 T^{8} )^{2} \))(\( 1 + 8 T + 56 T^{2} + 840 T^{3} + 5172 T^{4} + 38968 T^{5} + 387993 T^{6} + 1909992 T^{7} + 12984488 T^{8} + 115425908 T^{9} + 544467188 T^{10} + 3312068648 T^{11} + 28013676237 T^{12} + 135794814568 T^{13} + 915249343028 T^{14} + 7955269005268 T^{15} + 36691059795368 T^{16} + 221284417060392 T^{17} + 1843007194778313 T^{18} + 7589184544594808 T^{19} + 41298033285013812 T^{20} + 275000824890927240 T^{21} + 751668921368534456 T^{22} + 4402632253729987528 T^{23} + 22563490300366186081 T^{24} \))(\( 1 - 104 T^{2} + 1575 T^{4} + 194440 T^{6} - 5957900 T^{8} - 330995792 T^{10} + 19929404133 T^{12} + 140417241800 T^{14} - 34203961093745 T^{16} + 236041383465800 T^{18} + 56315732952270213 T^{20} - 1572264515332353872 T^{22} - 47573386022580005900 T^{24} + \)\(26\!\cdots\!40\)\( T^{26} + \)\(35\!\cdots\!75\)\( T^{28} - \)\(39\!\cdots\!44\)\( T^{30} + \)\(63\!\cdots\!41\)\( T^{32} \))
$43$ (\( ( 1 - 2 T + 42 T^{2} - 86 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 3 T + 77 T^{2} + 129 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 16 T + 233 T^{2} - 2040 T^{3} + 16241 T^{4} - 87720 T^{5} + 430817 T^{6} - 1272112 T^{7} + 3418801 T^{8} )^{2} \))(\( ( 1 + 2 T + 167 T^{2} + 256 T^{3} + 13452 T^{4} + 15956 T^{5} + 692036 T^{6} + 686108 T^{7} + 24872748 T^{8} + 20353792 T^{9} + 570939767 T^{10} + 294016886 T^{11} + 6321363049 T^{12} )^{2} \))(\( ( 1 + 20 T + 287 T^{2} + 2730 T^{3} + 20939 T^{4} + 117390 T^{5} + 530663 T^{6} + 1590140 T^{7} + 3418801 T^{8} )^{4} \))
$47$ (\( 1 - 2 T - 23 T^{2} - 250 T^{3} + 2601 T^{4} - 11750 T^{5} - 50807 T^{6} - 207646 T^{7} + 4879681 T^{8} \))(\( 1 - 2 T - 43 T^{2} - 50 T^{3} + 2351 T^{4} - 2350 T^{5} - 94987 T^{6} - 207646 T^{7} + 4879681 T^{8} \))(\( 1 - T - 62 T^{2} + 78 T^{3} + 3466 T^{4} - 4691 T^{5} - 155900 T^{6} + 95604 T^{7} + 3265179 T^{8} + 4493388 T^{9} - 344383100 T^{10} - 487033693 T^{11} + 16912974346 T^{12} + 17888910546 T^{13} - 668311350398 T^{14} - 506623120463 T^{15} + 23811286661761 T^{16} \))(\( 1 - 13 T + 37 T^{2} - 325 T^{3} + 7867 T^{4} - 56088 T^{5} + 222715 T^{6} - 1098334 T^{7} + 12592498 T^{8} - 108988468 T^{9} + 281826965 T^{10} - 1078581014 T^{11} + 21055334183 T^{12} - 50693307658 T^{13} + 622555765685 T^{14} - 11315509713164 T^{15} + 61447373233138 T^{16} - 251897418918338 T^{17} + 2400692941998235 T^{18} - 28415477580528744 T^{19} + 187323392168073787 T^{20} - 363717403758399275 T^{21} + 1946167892725711813 T^{22} - 32138069796092159939 T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 - 213 T^{2} + 20670 T^{4} - 1200990 T^{6} + 43061190 T^{8} - 552221379 T^{10} - 52474967158 T^{12} + 5507563494060 T^{14} - 317764676162385 T^{16} + 12166207758378540 T^{18} - 256061100216516598 T^{20} - 5952513153518318691 T^{22} + \)\(10\!\cdots\!90\)\( T^{24} - \)\(63\!\cdots\!10\)\( T^{26} + \)\(24\!\cdots\!70\)\( T^{28} - \)\(54\!\cdots\!97\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))
$53$ (\( 1 - 5 T - 43 T^{2} + 265 T^{3} + 1244 T^{4} + 14045 T^{5} - 120787 T^{6} - 744385 T^{7} + 7890481 T^{8} \))(\( 1 + 9 T + 8 T^{2} + 315 T^{3} + 5131 T^{4} + 16695 T^{5} + 22472 T^{6} + 1339893 T^{7} + 7890481 T^{8} \))(\( 1 - 3 T - 63 T^{2} + 6 T^{3} + 4741 T^{4} + 3522 T^{5} - 240240 T^{6} + 209553 T^{7} + 7555219 T^{8} + 11106309 T^{9} - 674834160 T^{10} + 524344794 T^{11} + 37408770421 T^{12} + 2509172958 T^{13} - 1396354751127 T^{14} - 3524133419511 T^{15} + 62259690411361 T^{16} \))(\( 1 + 44 T + 817 T^{2} + 7511 T^{3} + 18675 T^{4} - 371047 T^{5} - 5505981 T^{6} - 45196759 T^{7} - 286840983 T^{8} - 1119924348 T^{9} + 5970507613 T^{10} + 163921234483 T^{11} + 1596195784652 T^{12} + 8687825427599 T^{13} + 16771155884917 T^{14} - 166730977157196 T^{15} - 2263313326382823 T^{16} - 18901080912007187 T^{17} - 122036551253412549 T^{18} - 435873044303099339 T^{19} + 1162699718432166675 T^{20} + 24784524338025820963 T^{21} + \)\(14\!\cdots\!33\)\( T^{22} + \)\(40\!\cdots\!68\)\( T^{23} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 + 43 T^{2} - 3135 T^{4} + 82870 T^{6} + 4231795 T^{8} - 1030728416 T^{10} + 14362866672 T^{12} + 1344642401885 T^{14} - 126528175677005 T^{16} + 3777100506894965 T^{18} + 113329926580949232 T^{20} - 22845436838146141664 T^{22} + \)\(26\!\cdots\!95\)\( T^{24} + \)\(14\!\cdots\!30\)\( T^{26} - \)\(15\!\cdots\!35\)\( T^{28} + \)\(59\!\cdots\!67\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))
$59$ (\( 1 + 4 T - 43 T^{2} - 408 T^{3} + 905 T^{4} - 24072 T^{5} - 149683 T^{6} + 821516 T^{7} + 12117361 T^{8} \))(\( 1 + 31 T^{2} - 210 T^{3} + 2851 T^{4} - 12390 T^{5} + 107911 T^{6} + 12117361 T^{8} \))(\( 1 + 30 T + 377 T^{2} + 2475 T^{3} + 8643 T^{4} + 1155 T^{5} - 582521 T^{6} - 10821600 T^{7} - 108687625 T^{8} - 638474400 T^{9} - 2027755601 T^{10} + 237212745 T^{11} + 104730351123 T^{12} + 1769437640025 T^{13} + 15902061182657 T^{14} + 74659544544570 T^{15} + 146830437604321 T^{16} \))(\( 1 - 22 T + 36 T^{2} + 2583 T^{3} - 16419 T^{4} - 137618 T^{5} + 1667358 T^{6} + 2698622 T^{7} - 107608927 T^{8} + 155893882 T^{9} + 5010588449 T^{10} - 10213783795 T^{11} - 198548784261 T^{12} - 602613243905 T^{13} + 17441858390969 T^{14} + 32017329591278 T^{15} - 1303936215281647 T^{16} + 1929310441615978 T^{17} + 70330050210590478 T^{18} - 342483240037821142 T^{19} - 2410808955025346499 T^{20} + 22376518199585707437 T^{21} + 18400203118823090436 T^{22} - \)\(66\!\cdots\!98\)\( T^{23} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 + 224 T^{2} + 24195 T^{4} + 2068305 T^{6} + 171667695 T^{8} + 11805210387 T^{10} + 664199677293 T^{12} + 39649746993960 T^{14} + 2482020647300265 T^{16} + 138020769285974760 T^{18} + 8048347265842783773 T^{20} + \)\(49\!\cdots\!67\)\( T^{22} + \)\(25\!\cdots\!95\)\( T^{24} + \)\(10\!\cdots\!05\)\( T^{26} + \)\(43\!\cdots\!95\)\( T^{28} + \)\(13\!\cdots\!64\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))
$61$ (\( 1 - 2 T - 57 T^{2} - 64 T^{3} + 3905 T^{4} - 3904 T^{5} - 212097 T^{6} - 453962 T^{7} + 13845841 T^{8} \))(\( 1 - 13 T + 78 T^{2} - 941 T^{3} + 11075 T^{4} - 57401 T^{5} + 290238 T^{6} - 2950753 T^{7} + 13845841 T^{8} \))(\( 1 + 14 T + 35 T^{2} + 110 T^{3} + 8070 T^{4} + 33812 T^{5} - 419217 T^{6} - 1871430 T^{7} + 12043555 T^{8} - 114157230 T^{9} - 1559906457 T^{10} + 7674681572 T^{11} + 111735936870 T^{12} + 92905593110 T^{13} + 1803213102635 T^{14} + 43998399704294 T^{15} + 191707312997281 T^{16} \))(\( 1 + 8 T - 130 T^{2} - 1358 T^{3} + 564 T^{4} + 21392 T^{5} + 487611 T^{6} + 8007850 T^{7} - 7109096 T^{8} - 542757032 T^{9} - 551554860 T^{10} + 10321250720 T^{11} + 3604709585 T^{12} + 629596293920 T^{13} - 2052335634060 T^{14} - 123195533880392 T^{15} - 98431412869736 T^{16} + 6763400488962850 T^{17} + 25121901262541571 T^{18} + 67229554748161232 T^{19} + 108122924530466484 T^{20} - 15880650394068763478 T^{21} - 92734578516174738130 T^{22} + \)\(34\!\cdots\!88\)\( T^{23} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 16 T + 15 T^{2} + 960 T^{3} - 3000 T^{4} - 9768 T^{5} - 217407 T^{6} + 637260 T^{7} + 14903655 T^{8} + 38872860 T^{9} - 808971447 T^{10} - 2217150408 T^{11} - 41537523000 T^{12} + 810812448960 T^{13} + 772805615415 T^{14} - 50283885376336 T^{15} + 191707312997281 T^{16} )^{2} \))
$67$ (\( 1 - 2 T - 43 T^{2} - 370 T^{3} + 5041 T^{4} - 24790 T^{5} - 193027 T^{6} - 601526 T^{7} + 20151121 T^{8} \))(\( 1 + 2 T - 3 T^{2} - 410 T^{3} + 1601 T^{4} - 27470 T^{5} - 13467 T^{6} + 601526 T^{7} + 20151121 T^{8} \))(\( 1 - 4 T - 97 T^{2} + 122 T^{3} + 9681 T^{4} - 8074 T^{5} - 723795 T^{6} + 600576 T^{7} + 39163204 T^{8} + 40238592 T^{9} - 3249115755 T^{10} - 2428360462 T^{11} + 195083002401 T^{12} + 164715263054 T^{13} - 8774463070393 T^{14} - 24242846421292 T^{15} + 406067677556641 T^{16} \))(\( 1 + 6 T - 172 T^{2} - 858 T^{3} + 11749 T^{4} + 57666 T^{5} - 232014 T^{6} - 4755072 T^{7} - 22912618 T^{8} + 467752054 T^{9} + 2928188158 T^{10} - 17377714672 T^{11} - 223143036976 T^{12} - 1164306883024 T^{13} + 13144636641262 T^{14} + 140682511017202 T^{15} - 461714937744778 T^{16} - 6419942092792704 T^{17} - 20987611080558366 T^{18} + 349496995432556118 T^{19} + 4770889143612975109 T^{20} - 23343206512021064526 T^{21} - \)\(31\!\cdots\!28\)\( T^{22} + \)\(73\!\cdots\!98\)\( T^{23} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( ( 1 + 20 T + 261 T^{2} + 3240 T^{3} + 34947 T^{4} + 325680 T^{5} + 3089343 T^{6} + 27153900 T^{7} + 224184240 T^{8} + 1819311300 T^{9} + 13868060727 T^{10} + 97952493840 T^{11} + 704221225587 T^{12} + 4374405346680 T^{13} + 23609637746109 T^{14} + 121214232106460 T^{15} + 406067677556641 T^{16} )^{2} \))
$71$ (\( 1 + 8 T - 47 T^{2} - 434 T^{3} + 1365 T^{4} - 30814 T^{5} - 236927 T^{6} + 2863288 T^{7} + 25411681 T^{8} \))(\( 1 + 8 T - 37 T^{2} - 694 T^{3} - 2425 T^{4} - 49274 T^{5} - 186517 T^{6} + 2863288 T^{7} + 25411681 T^{8} \))(\( 1 + 21 T + 305 T^{2} + 2480 T^{3} + 13165 T^{4} - 10682 T^{5} - 810942 T^{6} - 9320005 T^{7} - 80224815 T^{8} - 661720355 T^{9} - 4087958622 T^{10} - 3823205302 T^{11} + 334544780365 T^{12} + 4474488790480 T^{13} + 39070586595905 T^{14} + 190997523326211 T^{15} + 645753531245761 T^{16} \))(\( 1 - 21 T + 46 T^{2} + 1289 T^{3} + 2891 T^{4} - 230821 T^{5} + 1592921 T^{6} + 6954484 T^{7} - 90555524 T^{8} - 1177173511 T^{9} + 16628404231 T^{10} - 5732671986 T^{11} - 764574531549 T^{12} - 407019711006 T^{13} + 83823785728471 T^{14} - 421323348495521 T^{15} - 2301168088675844 T^{16} + 12547484153859884 T^{17} + 204053632363723241 T^{18} - 2099344730079969011 T^{19} + 1866873458831495051 T^{20} + 59098717426080800959 T^{21} + \)\(14\!\cdots\!46\)\( T^{22} - \)\(48\!\cdots\!91\)\( T^{23} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 + 141 T^{2} + 4485 T^{4} + 192330 T^{6} + 69422535 T^{8} + 3292611048 T^{10} - 213402155272 T^{12} - 5365589194005 T^{14} + 1200886789327035 T^{16} - 27047935126979205 T^{18} - 5422907494484532232 T^{20} + \)\(42\!\cdots\!08\)\( T^{22} + \)\(44\!\cdots\!35\)\( T^{24} + \)\(62\!\cdots\!30\)\( T^{26} + \)\(73\!\cdots\!85\)\( T^{28} + \)\(11\!\cdots\!21\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \))
$73$ (\( 1 + 10 T + 27 T^{2} + 740 T^{3} + 11429 T^{4} + 54020 T^{5} + 143883 T^{6} + 3890170 T^{7} + 28398241 T^{8} \))(\( 1 - 9 T + 8 T^{2} + 585 T^{3} - 5849 T^{4} + 42705 T^{5} + 42632 T^{6} - 3501153 T^{7} + 28398241 T^{8} \))(\( 1 - 2 T - 163 T^{2} - 986 T^{3} + 8481 T^{4} + 176518 T^{5} + 938895 T^{6} - 6925578 T^{7} - 156207836 T^{8} - 505567194 T^{9} + 5003371455 T^{10} + 68668502806 T^{11} + 240845481921 T^{12} - 2044048590698 T^{13} - 24667478885107 T^{14} - 22094797038194 T^{15} + 806460091894081 T^{16} \))(\( 1 + 16 T - 28 T^{2} - 506 T^{3} + 12385 T^{4} - 2328 T^{5} - 561526 T^{6} + 14932744 T^{7} + 69930462 T^{8} - 421338712 T^{9} + 9017966158 T^{10} + 43966609042 T^{11} - 621466327768 T^{12} + 3209562460066 T^{13} + 48056741655982 T^{14} - 163907921726104 T^{15} + 1985902113117342 T^{16} + 30956647391941192 T^{17} - 84978102751157014 T^{18} - 25718343752457816 T^{19} + 9988008238108193185 T^{20} - 29789022874383563978 T^{21} - \)\(12\!\cdots\!72\)\( T^{22} + \)\(50\!\cdots\!32\)\( T^{23} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 30 T + 569 T^{2} - 8290 T^{3} + 100537 T^{4} - 1081770 T^{5} + 10670867 T^{6} - 98572950 T^{7} + 862584500 T^{8} - 7195825350 T^{9} + 56865050243 T^{10} - 420826920090 T^{11} + 2855073955417 T^{12} - 17185763505970 T^{13} + 86109174758441 T^{14} - 331421955572910 T^{15} + 806460091894081 T^{16} )^{2} \))
$79$ (\( 1 - 79 T^{2} + 6241 T^{4} - 493039 T^{6} + 38950081 T^{8} \))(\( 1 - 15 T + 21 T^{2} + 145 T^{3} + 2916 T^{4} + 11455 T^{5} + 131061 T^{6} - 7395585 T^{7} + 38950081 T^{8} \))(\( 1 + 30 T + 447 T^{2} + 5690 T^{3} + 63618 T^{4} + 615980 T^{5} + 6355819 T^{6} + 63162750 T^{7} + 565067755 T^{8} + 4989857250 T^{9} + 39666666379 T^{10} + 303702163220 T^{11} + 2477926253058 T^{12} + 17508450910310 T^{13} + 108660092617887 T^{14} + 576117269584770 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 10 T - 272 T^{2} + 2840 T^{3} + 26866 T^{4} - 289420 T^{5} - 489675 T^{6} + 1858730 T^{7} - 91007200 T^{8} + 1966674780 T^{9} + 3705819298 T^{10} - 105092388950 T^{11} + 146277106069 T^{12} - 8302298727050 T^{13} + 23128018238818 T^{14} + 969647366856420 T^{15} - 3544737811583200 T^{16} + 5719417040513270 T^{17} - 119033849782245675 T^{18} - 5557995338774137780 T^{19} + 40758645286949667826 T^{20} + \)\(34\!\cdots\!60\)\( T^{21} - \)\(25\!\cdots\!72\)\( T^{22} - \)\(74\!\cdots\!90\)\( T^{23} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 18 T + 195 T^{2} - 2670 T^{3} + 31590 T^{4} - 298764 T^{5} + 3295307 T^{6} - 34117590 T^{7} + 300163995 T^{8} - 2695289610 T^{9} + 20566010987 T^{10} - 147302303796 T^{11} + 1230433058790 T^{12} - 8215740585330 T^{13} + 47402053826595 T^{14} - 345670361750862 T^{15} + 1517108809906561 T^{16} )^{2} \))
$83$ (\( 1 - 18 T + 41 T^{2} + 1416 T^{3} - 18731 T^{4} + 117528 T^{5} + 282449 T^{6} - 10292166 T^{7} + 47458321 T^{8} \))(\( 1 + 9 T - 52 T^{2} - 675 T^{3} + 121 T^{4} - 56025 T^{5} - 358228 T^{6} + 5146083 T^{7} + 47458321 T^{8} \))(\( 1 + 2 T - 123 T^{2} + 626 T^{3} + 1416 T^{4} - 170328 T^{5} + 1146775 T^{6} + 9202888 T^{7} - 131919081 T^{8} + 763839704 T^{9} + 7900132975 T^{10} - 97391336136 T^{11} + 67200982536 T^{12} + 2465839442518 T^{13} - 40213665924387 T^{14} + 54272101979254 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 10 T - 32 T^{2} + 586 T^{3} + 7028 T^{4} - 84104 T^{5} - 240235 T^{6} + 5165580 T^{7} + 16282512 T^{8} - 55940648 T^{9} - 5964955348 T^{10} + 18358343086 T^{11} + 292581600901 T^{12} + 1523742476138 T^{13} - 41092577392372 T^{14} - 31986135297976 T^{15} + 772740681182352 T^{16} + 20347429564667940 T^{17} - 78542520596301715 T^{18} - 2282250432431589208 T^{19} + 15829109807473180148 T^{20} + \)\(10\!\cdots\!58\)\( T^{21} - \)\(49\!\cdots\!68\)\( T^{22} - \)\(12\!\cdots\!70\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - 152 T^{2} + 24675 T^{4} - 2817320 T^{6} + 356430460 T^{8} - 31958826416 T^{10} + 3318429986817 T^{12} - 268566824475880 T^{14} + 24918932909158855 T^{16} - 1850156853814337320 T^{18} + \)\(15\!\cdots\!57\)\( T^{20} - \)\(10\!\cdots\!04\)\( T^{22} + \)\(80\!\cdots\!60\)\( T^{24} - \)\(43\!\cdots\!80\)\( T^{26} + \)\(26\!\cdots\!75\)\( T^{28} - \)\(11\!\cdots\!08\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))
$89$ (\( 1 - 9 T - 43 T^{2} + 993 T^{3} - 4460 T^{4} + 88377 T^{5} - 340603 T^{6} - 6344721 T^{7} + 62742241 T^{8} \))(\( 1 - 20 T + 151 T^{2} - 1600 T^{3} + 21441 T^{4} - 142400 T^{5} + 1196071 T^{6} - 14099380 T^{7} + 62742241 T^{8} \))(\( 1 + 77 T^{2} - 700 T^{3} + 12658 T^{4} - 121100 T^{5} + 1037049 T^{6} - 10883950 T^{7} + 150329955 T^{8} - 968671550 T^{9} + 8214465129 T^{10} - 85371745900 T^{11} + 794191286578 T^{12} - 3908841614300 T^{13} + 38267559403997 T^{14} + 3936588805702081 T^{16} \))(\( 1 + 57 T + 1416 T^{2} + 19412 T^{3} + 146681 T^{4} + 436608 T^{5} + 1888 T^{6} + 50698623 T^{7} + 1130538888 T^{8} + 10860338043 T^{9} + 55652919649 T^{10} + 136415194025 T^{11} + 148330818154 T^{12} + 12140952268225 T^{13} + 440826776539729 T^{14} + 7656201649835667 T^{15} + 70932543370768008 T^{16} + 283104124814438727 T^{17} + 938300677334368 T^{18} + 19311754666067125632 T^{19} + \)\(57\!\cdots\!61\)\( T^{20} + \)\(68\!\cdots\!08\)\( T^{21} + \)\(44\!\cdots\!16\)\( T^{22} + \)\(15\!\cdots\!73\)\( T^{23} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 + 94 T^{2} - 1665 T^{4} + 1016470 T^{6} + 167043310 T^{8} + 4324962352 T^{10} + 640161517323 T^{12} + 105517486987430 T^{14} + 7276045289401435 T^{16} + 835804014427433030 T^{18} + 40165168198805340843 T^{20} + \)\(21\!\cdots\!72\)\( T^{22} + \)\(65\!\cdots\!10\)\( T^{24} + \)\(31\!\cdots\!70\)\( T^{26} - \)\(41\!\cdots\!65\)\( T^{28} + \)\(18\!\cdots\!54\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))
$97$ (\( 1 - 2 T - 33 T^{2} - 820 T^{3} + 10061 T^{4} - 79540 T^{5} - 310497 T^{6} - 1825346 T^{7} + 88529281 T^{8} \))(\( 1 - 8 T - 63 T^{2} + 20 T^{3} + 9821 T^{4} + 1940 T^{5} - 592767 T^{6} - 7301384 T^{7} + 88529281 T^{8} \))(\( 1 + 6 T - 187 T^{2} - 1878 T^{3} + 3816 T^{4} + 286836 T^{5} + 2735335 T^{6} - 15219804 T^{7} - 421030321 T^{8} - 1476320988 T^{9} + 25736767015 T^{10} + 261787472628 T^{11} + 337827736296 T^{12} - 16127025002646 T^{13} - 155765764921723 T^{14} + 484789706868678 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 4 T - 152 T^{2} - 258 T^{3} + 15244 T^{4} + 16576 T^{5} - 519489 T^{6} - 1347552 T^{7} - 32374768 T^{8} + 207718764 T^{9} + 20086873388 T^{10} - 47224426932 T^{11} - 2473927275691 T^{12} - 4580769412404 T^{13} + 188997391707692 T^{14} + 189579307496172 T^{15} - 2866114933581808 T^{16} - 11571887538000864 T^{17} - 432719793868561281 T^{18} + 1339312363509201088 T^{19} + \)\(11\!\cdots\!84\)\( T^{20} - \)\(19\!\cdots\!86\)\( T^{21} - \)\(11\!\cdots\!48\)\( T^{22} - \)\(28\!\cdots\!12\)\( T^{23} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 20 T + 291 T^{2} - 4700 T^{3} + 64912 T^{4} - 730280 T^{5} + 8764653 T^{6} - 95559100 T^{7} + 946211815 T^{8} - 9269232700 T^{9} + 82466620077 T^{10} - 666506838440 T^{11} + 5746612688272 T^{12} - 40360499207900 T^{13} + 242394853434339 T^{14} - 1615965689562260 T^{15} + 7837433594376961 T^{16} )^{2} \))
show more
show less