Properties

Label 17.8.a
Level 17
Weight 8
Character orbit a
Rep. character \(\chi_{17}(1,\cdot)\)
Character field \(\Q\)
Dimension 10
Newform subspaces 3
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(17))\).

Total New Old
Modular forms 12 10 2
Cusp forms 10 10 0
Eisenstein series 2 0 2

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

\(17\)Dim.
\(+\)\(6\)
\(-\)\(4\)

Trace form

\( 10q + 14q^{2} - 28q^{3} + 586q^{4} - 392q^{5} + 322q^{6} - 396q^{7} + 2814q^{8} + 5082q^{9} + O(q^{10}) \) \( 10q + 14q^{2} - 28q^{3} + 586q^{4} - 392q^{5} + 322q^{6} - 396q^{7} + 2814q^{8} + 5082q^{9} + 466q^{10} - 1092q^{11} - 394q^{12} + 4516q^{13} - 19768q^{14} + 18360q^{15} + 15282q^{16} - 9826q^{17} - 5854q^{18} - 53664q^{19} - 131242q^{20} + 46736q^{21} + 37322q^{22} - 144716q^{23} + 89982q^{24} + 122238q^{25} + 250544q^{26} - 199720q^{27} - 238704q^{28} + 161112q^{29} - 456656q^{30} + 493292q^{31} + 760246q^{32} + 674104q^{33} - 78608q^{34} + 55000q^{35} - 344826q^{36} - 190528q^{37} - 199448q^{38} - 295992q^{39} - 2330858q^{40} + 23964q^{41} + 75672q^{42} + 1646064q^{43} - 1157106q^{44} - 629352q^{45} - 512540q^{46} - 717984q^{47} + 2983822q^{48} + 886778q^{49} - 417146q^{50} - 530604q^{51} + 938480q^{52} + 803220q^{53} - 2944340q^{54} + 2265992q^{55} + 1386144q^{56} - 53920q^{57} - 3586438q^{58} - 2281392q^{59} + 1789280q^{60} - 1922176q^{61} + 6003704q^{62} - 5770684q^{63} + 11273354q^{64} - 89600q^{65} - 1862932q^{66} + 909784q^{67} - 1886592q^{68} - 4111344q^{69} + 17308440q^{70} + 643868q^{71} - 5539878q^{72} + 2656244q^{73} + 5908694q^{74} - 19207316q^{75} - 17345880q^{76} - 1420128q^{77} - 13551036q^{78} + 10534932q^{79} - 26016226q^{80} + 14907522q^{81} + 20638064q^{82} - 239920q^{83} + 1099784q^{84} - 117912q^{85} - 19882012q^{86} + 41992440q^{87} - 4108970q^{88} - 5368028q^{89} + 47657786q^{90} - 6274200q^{91} - 56318332q^{92} - 38834816q^{93} + 7636896q^{94} - 16028656q^{95} + 30349998q^{96} - 27032980q^{97} + 39536286q^{98} + 26005388q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(17))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 17
17.8.a.a \(1\) \(5.311\) \(\Q\) None \(-2\) \(18\) \(-10\) \(-902\) \(-\) \(q-2q^{2}+18q^{3}-124q^{4}-10q^{5}+\cdots\)
17.8.a.b \(3\) \(5.311\) 3.3.694349.1 None \(1\) \(-86\) \(-198\) \(-1558\) \(-\) \(q+\beta _{2}q^{2}+(-28-\beta _{1}-2\beta _{2})q^{3}+(78+\cdots)q^{4}+\cdots\)
17.8.a.c \(6\) \(5.311\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(15\) \(40\) \(-184\) \(2064\) \(+\) \(q+(2+\beta _{1})q^{2}+(6+\beta _{1}+\beta _{4})q^{3}+(78+\cdots)q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 128 T^{2} \))(\( 1 - T + 80 T^{2} + 1436 T^{3} + 10240 T^{4} - 16384 T^{5} + 2097152 T^{6} \))(\( 1 - 15 T + 254 T^{2} - 4288 T^{3} + 66144 T^{4} - 840000 T^{5} + 8531328 T^{6} - 107520000 T^{7} + 1083703296 T^{8} - 8992587776 T^{9} + 68182605824 T^{10} - 515396075520 T^{11} + 4398046511104 T^{12} \))
$3$ (\( 1 - 18 T + 2187 T^{2} \))(\( 1 + 86 T + 6429 T^{2} + 362628 T^{3} + 14060223 T^{4} + 411335334 T^{5} + 10460353203 T^{6} \))(\( 1 - 40 T + 4438 T^{2} - 169200 T^{3} + 14834091 T^{4} - 497515896 T^{5} + 40304178396 T^{6} - 1088067264552 T^{7} + 70950997396179 T^{8} - 1769891761947600 T^{9} + 101527204915116918 T^{10} - 2001261803959988280 T^{11} + \)\(10\!\cdots\!09\)\( T^{12} \))
$5$ (\( 1 + 10 T + 78125 T^{2} \))(\( 1 + 198 T + 177571 T^{2} + 31262532 T^{3} + 13872734375 T^{4} + 1208496093750 T^{5} + 476837158203125 T^{6} \))(\( 1 + 184 T + 110390 T^{2} + 47291000 T^{3} + 16248140375 T^{4} + 4896511750000 T^{5} + 1476865196712500 T^{6} + 382539980468750000 T^{7} + 99170778656005859375 T^{8} + \)\(22\!\cdots\!00\)\( T^{9} + \)\(41\!\cdots\!50\)\( T^{10} + \)\(53\!\cdots\!00\)\( T^{11} + \)\(22\!\cdots\!25\)\( T^{12} \))
$7$ (\( 1 + 902 T + 823543 T^{2} \))(\( 1 + 1558 T + 2346921 T^{2} + 2034323780 T^{3} + 1932790361103 T^{4} + 1056671547498742 T^{5} + 558545864083284007 T^{6} \))(\( 1 - 2064 T + 4254394 T^{2} - 6038540328 T^{3} + 7896640383779 T^{4} - 8449064172757416 T^{5} + 8451666450678733348 T^{6} - \)\(69\!\cdots\!88\)\( T^{7} + \)\(53\!\cdots\!71\)\( T^{8} - \)\(33\!\cdots\!96\)\( T^{9} + \)\(19\!\cdots\!94\)\( T^{10} - \)\(78\!\cdots\!52\)\( T^{11} + \)\(31\!\cdots\!49\)\( T^{12} \))
$11$ (\( 1 + 8634 T + 19487171 T^{2} \))(\( 1 - 5542 T + 57697157 T^{2} - 214597222276 T^{3} + 1124354364672847 T^{4} - 2104573577718321622 T^{5} + \)\(74\!\cdots\!11\)\( T^{6} \))(\( 1 - 2000 T + 33863558 T^{2} + 27482771512 T^{3} + 893205987118267 T^{4} - 370008476246913128 T^{5} + \)\(26\!\cdots\!60\)\( T^{6} - \)\(72\!\cdots\!88\)\( T^{7} + \)\(33\!\cdots\!47\)\( T^{8} + \)\(20\!\cdots\!32\)\( T^{9} + \)\(48\!\cdots\!98\)\( T^{10} - \)\(56\!\cdots\!00\)\( T^{11} + \)\(54\!\cdots\!21\)\( T^{12} \))
$13$ (\( 1 - 10858 T + 62748517 T^{2} \))(\( 1 + 15050 T + 137098299 T^{2} + 918670965468 T^{3} + 8602714945472583 T^{4} + 59257514604774299450 T^{5} + \)\(24\!\cdots\!13\)\( T^{6} \))(\( 1 - 8708 T + 351653490 T^{2} - 2383795239108 T^{3} + 52313336757808263 T^{4} - \)\(27\!\cdots\!36\)\( T^{5} + \)\(42\!\cdots\!56\)\( T^{6} - \)\(17\!\cdots\!12\)\( T^{7} + \)\(20\!\cdots\!07\)\( T^{8} - \)\(58\!\cdots\!04\)\( T^{9} + \)\(54\!\cdots\!90\)\( T^{10} - \)\(84\!\cdots\!56\)\( T^{11} + \)\(61\!\cdots\!69\)\( T^{12} \))
$17$ (\( 1 - 4913 T \))(\( ( 1 - 4913 T )^{3} \))(\( ( 1 + 4913 T )^{6} \))
$19$ (\( 1 + 784 T + 893871739 T^{2} \))(\( 1 + 7480 T + 1302721905 T^{2} - 7827185642992 T^{3} + 1164466294655742795 T^{4} + \)\(59\!\cdots\!80\)\( T^{5} + \)\(71\!\cdots\!19\)\( T^{6} \))(\( 1 + 45400 T + 4412654226 T^{2} + 165091627653288 T^{3} + 8478947349974464759 T^{4} + \)\(26\!\cdots\!88\)\( T^{5} + \)\(95\!\cdots\!08\)\( T^{6} + \)\(23\!\cdots\!32\)\( T^{7} + \)\(67\!\cdots\!39\)\( T^{8} + \)\(11\!\cdots\!72\)\( T^{9} + \)\(28\!\cdots\!66\)\( T^{10} + \)\(25\!\cdots\!00\)\( T^{11} + \)\(51\!\cdots\!61\)\( T^{12} \))
$23$ (\( 1 - 77330 T + 3404825447 T^{2} \))(\( 1 + 194838 T + 22496187001 T^{2} + 1578686759869956 T^{3} + 76595589961475414447 T^{4} + \)\(22\!\cdots\!42\)\( T^{5} + \)\(39\!\cdots\!23\)\( T^{6} \))(\( 1 + 27208 T + 5229376298 T^{2} + 136067293705424 T^{3} + 17000935065147667619 T^{4} + \)\(49\!\cdots\!08\)\( T^{5} + \)\(47\!\cdots\!68\)\( T^{6} + \)\(16\!\cdots\!76\)\( T^{7} + \)\(19\!\cdots\!71\)\( T^{8} + \)\(53\!\cdots\!52\)\( T^{9} + \)\(70\!\cdots\!38\)\( T^{10} + \)\(12\!\cdots\!56\)\( T^{11} + \)\(15\!\cdots\!29\)\( T^{12} \))
$29$ (\( 1 + 18210 T + 17249876309 T^{2} \))(\( 1 + 225486 T + 12849146875 T^{2} - 1027649768743788 T^{3} + \)\(22\!\cdots\!75\)\( T^{4} + \)\(67\!\cdots\!66\)\( T^{5} + \)\(51\!\cdots\!29\)\( T^{6} \))(\( 1 - 404808 T + 159515553958 T^{2} - 37493507131648968 T^{3} + \)\(82\!\cdots\!03\)\( T^{4} - \)\(13\!\cdots\!96\)\( T^{5} + \)\(20\!\cdots\!16\)\( T^{6} - \)\(23\!\cdots\!64\)\( T^{7} + \)\(24\!\cdots\!43\)\( T^{8} - \)\(19\!\cdots\!72\)\( T^{9} + \)\(14\!\cdots\!38\)\( T^{10} - \)\(61\!\cdots\!92\)\( T^{11} + \)\(26\!\cdots\!41\)\( T^{12} \))
$31$ (\( 1 + 237002 T + 27512614111 T^{2} \))(\( 1 - 197310 T + 29970378577 T^{2} - 3455506190298868 T^{3} + \)\(82\!\cdots\!47\)\( T^{4} - \)\(14\!\cdots\!10\)\( T^{5} + \)\(20\!\cdots\!31\)\( T^{6} \))(\( 1 - 532984 T + 237248332026 T^{2} - 71247619377853248 T^{3} + \)\(18\!\cdots\!31\)\( T^{4} - \)\(38\!\cdots\!68\)\( T^{5} + \)\(70\!\cdots\!44\)\( T^{6} - \)\(10\!\cdots\!48\)\( T^{7} + \)\(14\!\cdots\!51\)\( T^{8} - \)\(14\!\cdots\!88\)\( T^{9} + \)\(13\!\cdots\!66\)\( T^{10} - \)\(84\!\cdots\!84\)\( T^{11} + \)\(43\!\cdots\!61\)\( T^{12} \))
$37$ (\( 1 - 230878 T + 94931877133 T^{2} \))(\( 1 + 859374 T + 505394549635 T^{2} + 179028252673028276 T^{3} + \)\(47\!\cdots\!55\)\( T^{4} + \)\(77\!\cdots\!86\)\( T^{5} + \)\(85\!\cdots\!37\)\( T^{6} \))(\( 1 - 437968 T + 231604016550 T^{2} - 65352965223357648 T^{3} + \)\(28\!\cdots\!95\)\( T^{4} - \)\(98\!\cdots\!44\)\( T^{5} + \)\(38\!\cdots\!68\)\( T^{6} - \)\(93\!\cdots\!52\)\( T^{7} + \)\(25\!\cdots\!55\)\( T^{8} - \)\(55\!\cdots\!76\)\( T^{9} + \)\(18\!\cdots\!50\)\( T^{10} - \)\(33\!\cdots\!24\)\( T^{11} + \)\(73\!\cdots\!69\)\( T^{12} \))
$41$ (\( 1 + 304182 T + 194754273881 T^{2} \))(\( 1 - 769806 T + 780191092279 T^{2} - 316324014016920036 T^{3} + \)\(15\!\cdots\!99\)\( T^{4} - \)\(29\!\cdots\!66\)\( T^{5} + \)\(73\!\cdots\!41\)\( T^{6} \))(\( 1 + 441660 T + 833389954642 T^{2} + 234417549053593452 T^{3} + \)\(29\!\cdots\!55\)\( T^{4} + \)\(60\!\cdots\!28\)\( T^{5} + \)\(68\!\cdots\!44\)\( T^{6} + \)\(11\!\cdots\!68\)\( T^{7} + \)\(11\!\cdots\!55\)\( T^{8} + \)\(17\!\cdots\!32\)\( T^{9} + \)\(11\!\cdots\!82\)\( T^{10} + \)\(12\!\cdots\!60\)\( T^{11} + \)\(54\!\cdots\!81\)\( T^{12} \))
$43$ (\( 1 + 525032 T + 271818611107 T^{2} \))(\( 1 - 1018856 T + 983875775817 T^{2} - 555398153170342192 T^{3} + \)\(26\!\cdots\!19\)\( T^{4} - \)\(75\!\cdots\!44\)\( T^{5} + \)\(20\!\cdots\!43\)\( T^{6} \))(\( 1 - 1152240 T + 1498924518994 T^{2} - 1094330124574004304 T^{3} + \)\(82\!\cdots\!67\)\( T^{4} - \)\(45\!\cdots\!96\)\( T^{5} + \)\(26\!\cdots\!48\)\( T^{6} - \)\(12\!\cdots\!72\)\( T^{7} + \)\(60\!\cdots\!83\)\( T^{8} - \)\(21\!\cdots\!72\)\( T^{9} + \)\(81\!\cdots\!94\)\( T^{10} - \)\(17\!\cdots\!80\)\( T^{11} + \)\(40\!\cdots\!49\)\( T^{12} \))
$47$ (\( 1 - 802752 T + 506623120463 T^{2} \))(\( 1 + 1430440 T + 1796808113837 T^{2} + 1298122931022223792 T^{3} + \)\(91\!\cdots\!31\)\( T^{4} + \)\(36\!\cdots\!60\)\( T^{5} + \)\(13\!\cdots\!47\)\( T^{6} \))(\( 1 + 90296 T + 552243509114 T^{2} + 231532476456892136 T^{3} + \)\(39\!\cdots\!99\)\( T^{4} + \)\(10\!\cdots\!68\)\( T^{5} + \)\(29\!\cdots\!76\)\( T^{6} + \)\(51\!\cdots\!84\)\( T^{7} + \)\(10\!\cdots\!31\)\( T^{8} + \)\(30\!\cdots\!92\)\( T^{9} + \)\(36\!\cdots\!54\)\( T^{10} + \)\(30\!\cdots\!28\)\( T^{11} + \)\(16\!\cdots\!09\)\( T^{12} \))
$53$ (\( 1 - 152862 T + 1174711139837 T^{2} \))(\( 1 - 788122 T + 3670919588291 T^{2} - 1859101340422767196 T^{3} + \)\(43\!\cdots\!67\)\( T^{4} - \)\(10\!\cdots\!18\)\( T^{5} + \)\(16\!\cdots\!53\)\( T^{6} \))(\( 1 + 137764 T + 3317163783242 T^{2} + 526480006837595332 T^{3} + \)\(61\!\cdots\!15\)\( T^{4} + \)\(97\!\cdots\!80\)\( T^{5} + \)\(80\!\cdots\!56\)\( T^{6} + \)\(11\!\cdots\!60\)\( T^{7} + \)\(84\!\cdots\!35\)\( T^{8} + \)\(85\!\cdots\!96\)\( T^{9} + \)\(63\!\cdots\!62\)\( T^{10} + \)\(30\!\cdots\!48\)\( T^{11} + \)\(26\!\cdots\!09\)\( T^{12} \))
$59$ (\( 1 + 1602408 T + 2488651484819 T^{2} \))(\( 1 - 1371096 T + 6441009631129 T^{2} - 6216633246850251216 T^{3} + \)\(16\!\cdots\!51\)\( T^{4} - \)\(84\!\cdots\!56\)\( T^{5} + \)\(15\!\cdots\!59\)\( T^{6} \))(\( 1 + 2050080 T + 10944850249714 T^{2} + 20812461435729649440 T^{3} + \)\(57\!\cdots\!35\)\( T^{4} + \)\(92\!\cdots\!28\)\( T^{5} + \)\(18\!\cdots\!20\)\( T^{6} + \)\(22\!\cdots\!32\)\( T^{7} + \)\(35\!\cdots\!35\)\( T^{8} + \)\(32\!\cdots\!60\)\( T^{9} + \)\(41\!\cdots\!94\)\( T^{10} + \)\(19\!\cdots\!20\)\( T^{11} + \)\(23\!\cdots\!81\)\( T^{12} \))
$61$ (\( 1 + 2601610 T + 3142742836021 T^{2} \))(\( 1 - 589626 T + 9478901919451 T^{2} - 3707040753816033436 T^{3} + \)\(29\!\cdots\!71\)\( T^{4} - \)\(58\!\cdots\!66\)\( T^{5} + \)\(31\!\cdots\!61\)\( T^{6} \))(\( 1 - 89808 T + 6795152628406 T^{2} - 553306889308888080 T^{3} + \)\(10\!\cdots\!03\)\( T^{4} + \)\(27\!\cdots\!00\)\( T^{5} - \)\(69\!\cdots\!44\)\( T^{6} + \)\(85\!\cdots\!00\)\( T^{7} + \)\(10\!\cdots\!23\)\( T^{8} - \)\(17\!\cdots\!80\)\( T^{9} + \)\(66\!\cdots\!86\)\( T^{10} - \)\(27\!\cdots\!08\)\( T^{11} + \)\(96\!\cdots\!21\)\( T^{12} \))
$67$ (\( 1 - 1074604 T + 6060711605323 T^{2} \))(\( 1 + 4851452 T + 23434724383889 T^{2} + 59980455854394377960 T^{3} + \)\(14\!\cdots\!47\)\( T^{4} + \)\(17\!\cdots\!08\)\( T^{5} + \)\(22\!\cdots\!67\)\( T^{6} \))(\( 1 - 4686632 T + 36688314339170 T^{2} - \)\(13\!\cdots\!40\)\( T^{3} + \)\(55\!\cdots\!95\)\( T^{4} - \)\(15\!\cdots\!16\)\( T^{5} + \)\(44\!\cdots\!08\)\( T^{6} - \)\(92\!\cdots\!68\)\( T^{7} + \)\(20\!\cdots\!55\)\( T^{8} - \)\(29\!\cdots\!80\)\( T^{9} + \)\(49\!\cdots\!70\)\( T^{10} - \)\(38\!\cdots\!76\)\( T^{11} + \)\(49\!\cdots\!89\)\( T^{12} \))
$71$ (\( 1 + 502298 T + 9095120158391 T^{2} \))(\( 1 - 6699398 T + 38387989298969 T^{2} - \)\(12\!\cdots\!32\)\( T^{3} + \)\(34\!\cdots\!79\)\( T^{4} - \)\(55\!\cdots\!38\)\( T^{5} + \)\(75\!\cdots\!71\)\( T^{6} \))(\( 1 + 5553232 T + 55159797104890 T^{2} + \)\(22\!\cdots\!76\)\( T^{3} + \)\(12\!\cdots\!31\)\( T^{4} + \)\(38\!\cdots\!96\)\( T^{5} + \)\(15\!\cdots\!68\)\( T^{6} + \)\(35\!\cdots\!36\)\( T^{7} + \)\(10\!\cdots\!11\)\( T^{8} + \)\(16\!\cdots\!96\)\( T^{9} + \)\(37\!\cdots\!90\)\( T^{10} + \)\(34\!\cdots\!32\)\( T^{11} + \)\(56\!\cdots\!41\)\( T^{12} \))
$73$ (\( 1 - 3648258 T + 11047398519097 T^{2} \))(\( 1 - 444438 T + 4415357786743 T^{2} - 61063221549199602964 T^{3} + \)\(48\!\cdots\!71\)\( T^{4} - \)\(54\!\cdots\!42\)\( T^{5} + \)\(13\!\cdots\!73\)\( T^{6} \))(\( 1 + 1436452 T + 48614119668658 T^{2} + 38142817132358351348 T^{3} + \)\(10\!\cdots\!11\)\( T^{4} + \)\(56\!\cdots\!56\)\( T^{5} + \)\(15\!\cdots\!60\)\( T^{6} + \)\(62\!\cdots\!32\)\( T^{7} + \)\(13\!\cdots\!99\)\( T^{8} + \)\(51\!\cdots\!04\)\( T^{9} + \)\(72\!\cdots\!98\)\( T^{10} + \)\(23\!\cdots\!64\)\( T^{11} + \)\(18\!\cdots\!29\)\( T^{12} \))
$79$ (\( 1 + 2892174 T + 19203908986159 T^{2} \))(\( 1 - 1039946 T + 21476622148593 T^{2} - 23830879537077150652 T^{3} + \)\(41\!\cdots\!87\)\( T^{4} - \)\(38\!\cdots\!26\)\( T^{5} + \)\(70\!\cdots\!79\)\( T^{6} \))(\( 1 - 12387160 T + 118120899087802 T^{2} - \)\(80\!\cdots\!16\)\( T^{3} + \)\(49\!\cdots\!07\)\( T^{4} - \)\(25\!\cdots\!24\)\( T^{5} + \)\(12\!\cdots\!20\)\( T^{6} - \)\(49\!\cdots\!16\)\( T^{7} + \)\(18\!\cdots\!67\)\( T^{8} - \)\(57\!\cdots\!64\)\( T^{9} + \)\(16\!\cdots\!22\)\( T^{10} - \)\(32\!\cdots\!40\)\( T^{11} + \)\(50\!\cdots\!41\)\( T^{12} \))
$83$ (\( 1 - 728104 T + 27136050989627 T^{2} \))(\( 1 - 909784 T + 28508520590609 T^{2} + 30234057398909173808 T^{3} + \)\(77\!\cdots\!43\)\( T^{4} - \)\(66\!\cdots\!36\)\( T^{5} + \)\(19\!\cdots\!83\)\( T^{6} \))(\( 1 + 1877808 T + 149272727601122 T^{2} + \)\(24\!\cdots\!36\)\( T^{3} + \)\(96\!\cdots\!23\)\( T^{4} + \)\(12\!\cdots\!64\)\( T^{5} + \)\(34\!\cdots\!36\)\( T^{6} + \)\(34\!\cdots\!28\)\( T^{7} + \)\(70\!\cdots\!67\)\( T^{8} + \)\(48\!\cdots\!88\)\( T^{9} + \)\(80\!\cdots\!02\)\( T^{10} + \)\(27\!\cdots\!56\)\( T^{11} + \)\(39\!\cdots\!89\)\( T^{12} \))
$89$ (\( 1 - 7931846 T + 44231334895529 T^{2} \))(\( 1 - 6024450 T + 95135983014343 T^{2} - \)\(51\!\cdots\!56\)\( T^{3} + \)\(42\!\cdots\!47\)\( T^{4} - \)\(11\!\cdots\!50\)\( T^{5} + \)\(86\!\cdots\!89\)\( T^{6} \))(\( 1 + 19324324 T + 348053151109850 T^{2} + \)\(37\!\cdots\!08\)\( T^{3} + \)\(39\!\cdots\!27\)\( T^{4} + \)\(30\!\cdots\!36\)\( T^{5} + \)\(23\!\cdots\!44\)\( T^{6} + \)\(13\!\cdots\!44\)\( T^{7} + \)\(77\!\cdots\!07\)\( T^{8} + \)\(32\!\cdots\!12\)\( T^{9} + \)\(13\!\cdots\!50\)\( T^{10} + \)\(32\!\cdots\!76\)\( T^{11} + \)\(74\!\cdots\!21\)\( T^{12} \))
$97$ (\( 1 + 6551038 T + 80798284478113 T^{2} \))(\( 1 + 12851130 T + 250793138509039 T^{2} + \)\(18\!\cdots\!80\)\( T^{3} + \)\(20\!\cdots\!07\)\( T^{4} + \)\(83\!\cdots\!70\)\( T^{5} + \)\(52\!\cdots\!97\)\( T^{6} \))(\( 1 + 7630812 T + 253559602322722 T^{2} + \)\(69\!\cdots\!48\)\( T^{3} + \)\(24\!\cdots\!43\)\( T^{4} - \)\(38\!\cdots\!68\)\( T^{5} + \)\(16\!\cdots\!76\)\( T^{6} - \)\(31\!\cdots\!84\)\( T^{7} + \)\(16\!\cdots\!67\)\( T^{8} + \)\(36\!\cdots\!56\)\( T^{9} + \)\(10\!\cdots\!42\)\( T^{10} + \)\(26\!\cdots\!16\)\( T^{11} + \)\(27\!\cdots\!09\)\( T^{12} \))
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