# Properties

 Label 11.5.d Level 11 Weight 5 Character orbit d Rep. character $$\chi_{11}(2,\cdot)$$ Character field $$\Q(\zeta_{10})$$ Dimension 12 Newform subspaces 1 Sturm bound 5 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$11$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 11.d (of order $$10$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{10})$$ Newform subspaces: $$1$$ Sturm bound: $$5$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(11, [\chi])$$.

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

## Trace form

 $$12q - 5q^{2} - 6q^{3} + 7q^{4} - 18q^{5} + 75q^{6} - 80q^{7} - 245q^{8} + q^{9} + O(q^{10})$$ $$12q - 5q^{2} - 6q^{3} + 7q^{4} - 18q^{5} + 75q^{6} - 80q^{7} - 245q^{8} + q^{9} - 43q^{11} + 594q^{12} + 250q^{13} + 610q^{14} + 1134q^{15} - 633q^{16} - 1250q^{17} - 3150q^{18} - 1025q^{19} + 752q^{20} - 35q^{22} + 1684q^{23} + 5345q^{24} + 197q^{25} + 3490q^{26} - 687q^{27} - 3580q^{28} - 2690q^{29} - 6740q^{30} - 1136q^{31} + 5939q^{33} + 2370q^{34} + 3610q^{35} - 514q^{36} - 336q^{37} + 1900q^{38} - 6880q^{39} - 2340q^{40} - 4550q^{41} + 1310q^{42} - 6268q^{44} + 5136q^{45} + 4150q^{46} + 24q^{47} + 344q^{48} + 827q^{49} + 8895q^{50} + 13155q^{51} + 14070q^{52} + 414q^{53} - 2738q^{55} - 21340q^{56} - 26925q^{57} + 2980q^{58} - 10011q^{59} - 6856q^{60} + 9460q^{61} - 6200q^{62} + 9150q^{63} - 2633q^{64} - 3210q^{66} + 12154q^{67} - 9400q^{68} - 9022q^{69} - 9380q^{70} + 17574q^{71} + 43045q^{72} + 27950q^{73} + 43270q^{74} - 1761q^{75} + 4090q^{77} - 42920q^{78} - 41540q^{79} - 2308q^{80} - 21080q^{81} - 28175q^{82} - 18665q^{83} + 26250q^{84} - 4230q^{85} - 10125q^{86} - 15125q^{88} + 5554q^{89} + 18400q^{90} + 7390q^{91} + 3904q^{92} + 36898q^{93} + 18920q^{94} + 14110q^{95} - 21140q^{96} + 20769q^{97} - 3269q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(11, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
11.5.d.a $$12$$ $$1.137$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$-5$$ $$-6$$ $$-18$$ $$-80$$ $$q+(-1-\beta _{2}-2\beta _{3}-\beta _{4}+\beta _{7})q^{2}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + 5 T + 33 T^{2} + 125 T^{3} + 551 T^{4} + 1810 T^{5} + 8610 T^{6} + 50940 T^{7} + 233740 T^{8} + 1132840 T^{9} + 4354088 T^{10} + 17654480 T^{11} + 63726544 T^{12} + 282471680 T^{13} + 1114646528 T^{14} + 4640112640 T^{15} + 15318384640 T^{16} + 53414461440 T^{17} + 144451829760 T^{18} + 485868175360 T^{19} + 2366526980096 T^{20} + 8589934592000 T^{21} + 36283883716608 T^{22} + 87960930222080 T^{23} + 281474976710656 T^{24}$$
$3$ $$1 + 6 T - 104 T^{2} + 46 T^{3} + 10081 T^{4} - 91194 T^{5} - 1472814 T^{6} + 5513616 T^{7} + 56745846 T^{8} - 574747974 T^{9} + 106590006 T^{10} + 40654029276 T^{11} + 197200145376 T^{12} + 3292976371356 T^{13} + 699337029366 T^{14} - 305444638050534 T^{15} + 2442722600670966 T^{16} + 19224790261904016 T^{17} - 415966175342727534 T^{18} - 2086226211137713434 T^{19} + 18680296523815409121 T^{20} + 6904353223661959566 T^{21} -$$$$12\!\cdots\!04$$$$T^{22} +$$$$59\!\cdots\!86$$$$T^{23} +$$$$79\!\cdots\!61$$$$T^{24}$$
$5$ $$1 + 18 T - 874 T^{2} - 8990 T^{3} + 924345 T^{4} - 2498082 T^{5} - 756868316 T^{6} + 6088380428 T^{7} + 472540127940 T^{8} - 4427489398370 T^{9} - 231003059512494 T^{10} + 256199910578148 T^{11} + 91821549616068396 T^{12} + 160124944111342500 T^{13} - 90235570122067968750 T^{14} -$$$$10\!\cdots\!50$$$$T^{15} +$$$$72\!\cdots\!00$$$$T^{16} +$$$$58\!\cdots\!00$$$$T^{17} -$$$$45\!\cdots\!00$$$$T^{18} -$$$$93\!\cdots\!50$$$$T^{19} +$$$$21\!\cdots\!25$$$$T^{20} -$$$$13\!\cdots\!50$$$$T^{21} -$$$$79\!\cdots\!50$$$$T^{22} +$$$$10\!\cdots\!50$$$$T^{23} +$$$$35\!\cdots\!25$$$$T^{24}$$
$7$ $$1 + 80 T + 6388 T^{2} + 701930 T^{3} + 49215681 T^{4} + 3279603800 T^{5} + 239232786210 T^{6} + 14513581978500 T^{7} + 843606939238690 T^{8} + 50663633663881700 T^{9} + 2671940584129639018 T^{10} +$$$$13\!\cdots\!90$$$$T^{11} +$$$$72\!\cdots\!24$$$$T^{12} +$$$$33\!\cdots\!90$$$$T^{13} +$$$$15\!\cdots\!18$$$$T^{14} +$$$$70\!\cdots\!00$$$$T^{15} +$$$$28\!\cdots\!90$$$$T^{16} +$$$$11\!\cdots\!00$$$$T^{17} +$$$$45\!\cdots\!10$$$$T^{18} +$$$$15\!\cdots\!00$$$$T^{19} +$$$$54\!\cdots\!81$$$$T^{20} +$$$$18\!\cdots\!30$$$$T^{21} +$$$$40\!\cdots\!88$$$$T^{22} +$$$$12\!\cdots\!80$$$$T^{23} +$$$$36\!\cdots\!01$$$$T^{24}$$
$11$ $$1 + 43 T + 18931 T^{2} - 249865 T^{3} + 113135 T^{4} - 53668078882 T^{5} - 2617669162966 T^{6} - 785754342911362 T^{7} + 24251492001935 T^{8} - 784183406349392665 T^{9} +$$$$86\!\cdots\!91$$$$T^{10} +$$$$28\!\cdots\!43$$$$T^{11} +$$$$98\!\cdots\!41$$$$T^{12}$$
$13$ $$1 - 250 T + 98548 T^{2} - 25239340 T^{3} + 4920135411 T^{4} - 1056434505070 T^{5} + 134058098615820 T^{6} - 14343324685617900 T^{7} + 158785723907559280 T^{8} +$$$$58\!\cdots\!50$$$$T^{9} -$$$$16\!\cdots\!92$$$$T^{10} +$$$$38\!\cdots\!10$$$$T^{11} -$$$$73\!\cdots\!16$$$$T^{12} +$$$$11\!\cdots\!10$$$$T^{13} -$$$$13\!\cdots\!32$$$$T^{14} +$$$$13\!\cdots\!50$$$$T^{15} +$$$$10\!\cdots\!80$$$$T^{16} -$$$$27\!\cdots\!00$$$$T^{17} +$$$$72\!\cdots\!20$$$$T^{18} -$$$$16\!\cdots\!70$$$$T^{19} +$$$$21\!\cdots\!91$$$$T^{20} -$$$$31\!\cdots\!40$$$$T^{21} +$$$$35\!\cdots\!48$$$$T^{22} -$$$$25\!\cdots\!50$$$$T^{23} +$$$$29\!\cdots\!21$$$$T^{24}$$
$17$ $$1 + 1250 T + 992428 T^{2} + 582264010 T^{3} + 283914863531 T^{4} + 119803876725030 T^{5} + 46223383217047820 T^{6} + 16729167329461506640 T^{7} +$$$$58\!\cdots\!20$$$$T^{8} +$$$$19\!\cdots\!90$$$$T^{9} +$$$$62\!\cdots\!28$$$$T^{10} +$$$$19\!\cdots\!80$$$$T^{11} +$$$$56\!\cdots\!04$$$$T^{12} +$$$$16\!\cdots\!80$$$$T^{13} +$$$$43\!\cdots\!48$$$$T^{14} +$$$$11\!\cdots\!90$$$$T^{15} +$$$$28\!\cdots\!20$$$$T^{16} +$$$$67\!\cdots\!40$$$$T^{17} +$$$$15\!\cdots\!20$$$$T^{18} +$$$$33\!\cdots\!30$$$$T^{19} +$$$$67\!\cdots\!91$$$$T^{20} +$$$$11\!\cdots\!10$$$$T^{21} +$$$$16\!\cdots\!28$$$$T^{22} +$$$$17\!\cdots\!50$$$$T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$
$19$ $$1 + 1025 T + 619378 T^{2} + 353530160 T^{3} + 166899801006 T^{4} + 66114359518655 T^{5} + 21592456954609665 T^{6} + 5902640524678934610 T^{7} +$$$$15\!\cdots\!25$$$$T^{8} +$$$$24\!\cdots\!45$$$$T^{9} -$$$$10\!\cdots\!67$$$$T^{10} -$$$$11\!\cdots\!95$$$$T^{11} -$$$$61\!\cdots\!56$$$$T^{12} -$$$$15\!\cdots\!95$$$$T^{13} -$$$$17\!\cdots\!47$$$$T^{14} +$$$$53\!\cdots\!45$$$$T^{15} +$$$$46\!\cdots\!25$$$$T^{16} +$$$$22\!\cdots\!10$$$$T^{17} +$$$$10\!\cdots\!65$$$$T^{18} +$$$$42\!\cdots\!55$$$$T^{19} +$$$$13\!\cdots\!66$$$$T^{20} +$$$$38\!\cdots\!60$$$$T^{21} +$$$$87\!\cdots\!78$$$$T^{22} +$$$$18\!\cdots\!25$$$$T^{23} +$$$$23\!\cdots\!41$$$$T^{24}$$
$23$ $$( 1 - 842 T + 1237966 T^{2} - 916714810 T^{3} + 731144219855 T^{4} - 446744415652252 T^{5} + 258141193233856964 T^{6} -$$$$12\!\cdots\!32$$$$T^{7} +$$$$57\!\cdots\!55$$$$T^{8} -$$$$20\!\cdots\!10$$$$T^{9} +$$$$75\!\cdots\!26$$$$T^{10} -$$$$14\!\cdots\!42$$$$T^{11} +$$$$48\!\cdots\!41$$$$T^{12} )^{2}$$
$29$ $$1 + 2690 T + 5931748 T^{2} + 10598261380 T^{3} + 16033149600451 T^{4} + 21947778968733670 T^{5} + 27405046849774036980 T^{6} +$$$$31\!\cdots\!20$$$$T^{7} +$$$$34\!\cdots\!60$$$$T^{8} +$$$$34\!\cdots\!50$$$$T^{9} +$$$$33\!\cdots\!68$$$$T^{10} +$$$$30\!\cdots\!90$$$$T^{11} +$$$$26\!\cdots\!84$$$$T^{12} +$$$$21\!\cdots\!90$$$$T^{13} +$$$$16\!\cdots\!48$$$$T^{14} +$$$$12\!\cdots\!50$$$$T^{15} +$$$$85\!\cdots\!60$$$$T^{16} +$$$$56\!\cdots\!20$$$$T^{17} +$$$$34\!\cdots\!80$$$$T^{18} +$$$$19\!\cdots\!70$$$$T^{19} +$$$$10\!\cdots\!91$$$$T^{20} +$$$$46\!\cdots\!80$$$$T^{21} +$$$$18\!\cdots\!48$$$$T^{22} +$$$$59\!\cdots\!90$$$$T^{23} +$$$$15\!\cdots\!61$$$$T^{24}$$
$31$ $$1 + 1136 T - 230384 T^{2} - 239729514 T^{3} + 1267435488321 T^{4} + 2677537350048516 T^{5} + 1095876078080394266 T^{6} -$$$$12\!\cdots\!44$$$$T^{7} +$$$$51\!\cdots\!26$$$$T^{8} +$$$$24\!\cdots\!96$$$$T^{9} +$$$$25\!\cdots\!46$$$$T^{10} +$$$$85\!\cdots\!26$$$$T^{11} -$$$$77\!\cdots\!44$$$$T^{12} +$$$$78\!\cdots\!46$$$$T^{13} +$$$$21\!\cdots\!86$$$$T^{14} +$$$$19\!\cdots\!56$$$$T^{15} +$$$$37\!\cdots\!06$$$$T^{16} -$$$$81\!\cdots\!44$$$$T^{17} +$$$$67\!\cdots\!86$$$$T^{18} +$$$$15\!\cdots\!56$$$$T^{19} +$$$$67\!\cdots\!81$$$$T^{20} -$$$$11\!\cdots\!34$$$$T^{21} -$$$$10\!\cdots\!84$$$$T^{22} +$$$$47\!\cdots\!56$$$$T^{23} +$$$$38\!\cdots\!41$$$$T^{24}$$
$37$ $$1 + 336 T + 72946 T^{2} - 4475893024 T^{3} + 1626992896581 T^{4} - 4706417114238944 T^{5} + 10320605504003112056 T^{6} -$$$$11\!\cdots\!84$$$$T^{7} +$$$$22\!\cdots\!56$$$$T^{8} -$$$$44\!\cdots\!44$$$$T^{9} +$$$$30\!\cdots\!46$$$$T^{10} -$$$$47\!\cdots\!04$$$$T^{11} +$$$$15\!\cdots\!76$$$$T^{12} -$$$$89\!\cdots\!44$$$$T^{13} +$$$$10\!\cdots\!66$$$$T^{14} -$$$$29\!\cdots\!64$$$$T^{15} +$$$$27\!\cdots\!96$$$$T^{16} -$$$$26\!\cdots\!84$$$$T^{17} +$$$$44\!\cdots\!16$$$$T^{18} -$$$$38\!\cdots\!24$$$$T^{19} +$$$$24\!\cdots\!61$$$$T^{20} -$$$$12\!\cdots\!84$$$$T^{21} +$$$$39\!\cdots\!46$$$$T^{22} +$$$$33\!\cdots\!96$$$$T^{23} +$$$$18\!\cdots\!21$$$$T^{24}$$
$41$ $$1 + 4550 T + 14401928 T^{2} + 23922427770 T^{3} + 36931794819271 T^{4} + 40163345738311410 T^{5} +$$$$12\!\cdots\!20$$$$T^{6} +$$$$30\!\cdots\!20$$$$T^{7} +$$$$86\!\cdots\!60$$$$T^{8} +$$$$14\!\cdots\!70$$$$T^{9} +$$$$24\!\cdots\!68$$$$T^{10} +$$$$25\!\cdots\!80$$$$T^{11} +$$$$43\!\cdots\!24$$$$T^{12} +$$$$71\!\cdots\!80$$$$T^{13} +$$$$19\!\cdots\!28$$$$T^{14} +$$$$32\!\cdots\!70$$$$T^{15} +$$$$54\!\cdots\!60$$$$T^{16} +$$$$54\!\cdots\!20$$$$T^{17} +$$$$65\!\cdots\!20$$$$T^{18} +$$$$57\!\cdots\!10$$$$T^{19} +$$$$15\!\cdots\!51$$$$T^{20} +$$$$27\!\cdots\!70$$$$T^{21} +$$$$46\!\cdots\!28$$$$T^{22} +$$$$41\!\cdots\!50$$$$T^{23} +$$$$25\!\cdots\!21$$$$T^{24}$$
$43$ $$1 - 23356307 T^{2} + 286833712371781 T^{4} -$$$$23\!\cdots\!15$$$$T^{6} +$$$$14\!\cdots\!15$$$$T^{8} -$$$$69\!\cdots\!82$$$$T^{10} +$$$$26\!\cdots\!14$$$$T^{12} -$$$$81\!\cdots\!82$$$$T^{14} +$$$$19\!\cdots\!15$$$$T^{16} -$$$$37\!\cdots\!15$$$$T^{18} +$$$$53\!\cdots\!81$$$$T^{20} -$$$$50\!\cdots\!07$$$$T^{22} +$$$$25\!\cdots\!01$$$$T^{24}$$
$47$ $$1 - 24 T - 10068774 T^{2} - 8140867214 T^{3} + 53779050778611 T^{4} + 233185473449483776 T^{5} - 81521520124710716194 T^{6} -$$$$19\!\cdots\!44$$$$T^{7} -$$$$12\!\cdots\!74$$$$T^{8} +$$$$86\!\cdots\!36$$$$T^{9} +$$$$22\!\cdots\!96$$$$T^{10} -$$$$14\!\cdots\!34$$$$T^{11} -$$$$15\!\cdots\!64$$$$T^{12} -$$$$69\!\cdots\!54$$$$T^{13} +$$$$54\!\cdots\!56$$$$T^{14} +$$$$10\!\cdots\!76$$$$T^{15} -$$$$72\!\cdots\!54$$$$T^{16} -$$$$54\!\cdots\!44$$$$T^{17} -$$$$11\!\cdots\!14$$$$T^{18} +$$$$15\!\cdots\!36$$$$T^{19} +$$$$17\!\cdots\!51$$$$T^{20} -$$$$12\!\cdots\!94$$$$T^{21} -$$$$77\!\cdots\!74$$$$T^{22} -$$$$89\!\cdots\!44$$$$T^{23} +$$$$18\!\cdots\!61$$$$T^{24}$$
$53$ $$1 - 414 T - 13725134 T^{2} - 7014732824 T^{3} + 165958055930181 T^{4} + 208417442032136246 T^{5} -$$$$14\!\cdots\!44$$$$T^{6} -$$$$22\!\cdots\!24$$$$T^{7} +$$$$12\!\cdots\!16$$$$T^{8} +$$$$14\!\cdots\!66$$$$T^{9} -$$$$76\!\cdots\!74$$$$T^{10} -$$$$33\!\cdots\!74$$$$T^{11} +$$$$54\!\cdots\!16$$$$T^{12} -$$$$26\!\cdots\!94$$$$T^{13} -$$$$47\!\cdots\!14$$$$T^{14} +$$$$71\!\cdots\!06$$$$T^{15} +$$$$47\!\cdots\!36$$$$T^{16} -$$$$69\!\cdots\!24$$$$T^{17} -$$$$34\!\cdots\!64$$$$T^{18} +$$$$39\!\cdots\!06$$$$T^{19} +$$$$24\!\cdots\!21$$$$T^{20} -$$$$83\!\cdots\!04$$$$T^{21} -$$$$12\!\cdots\!34$$$$T^{22} -$$$$30\!\cdots\!34$$$$T^{23} +$$$$58\!\cdots\!61$$$$T^{24}$$
$59$ $$1 + 10011 T + 24606746 T^{2} - 48335046044 T^{3} - 85055058906234 T^{4} + 1848432652355091201 T^{5} +$$$$68\!\cdots\!21$$$$T^{6} -$$$$10\!\cdots\!34$$$$T^{7} -$$$$82\!\cdots\!39$$$$T^{8} +$$$$15\!\cdots\!31$$$$T^{9} +$$$$13\!\cdots\!41$$$$T^{10} -$$$$16\!\cdots\!29$$$$T^{11} -$$$$23\!\cdots\!24$$$$T^{12} -$$$$19\!\cdots\!69$$$$T^{13} +$$$$19\!\cdots\!61$$$$T^{14} +$$$$27\!\cdots\!11$$$$T^{15} -$$$$17\!\cdots\!99$$$$T^{16} -$$$$26\!\cdots\!34$$$$T^{17} +$$$$21\!\cdots\!81$$$$T^{18} +$$$$70\!\cdots\!21$$$$T^{19} -$$$$39\!\cdots\!54$$$$T^{20} -$$$$27\!\cdots\!04$$$$T^{21} +$$$$16\!\cdots\!46$$$$T^{22} +$$$$82\!\cdots\!71$$$$T^{23} +$$$$10\!\cdots\!21$$$$T^{24}$$
$61$ $$1 - 9460 T + 57744648 T^{2} - 309062215210 T^{3} + 1619001804085751 T^{4} - 7693654169306140700 T^{5} +$$$$35\!\cdots\!40$$$$T^{6} -$$$$16\!\cdots\!00$$$$T^{7} +$$$$77\!\cdots\!60$$$$T^{8} -$$$$32\!\cdots\!20$$$$T^{9} +$$$$12\!\cdots\!28$$$$T^{10} -$$$$48\!\cdots\!10$$$$T^{11} +$$$$18\!\cdots\!84$$$$T^{12} -$$$$67\!\cdots\!10$$$$T^{13} +$$$$24\!\cdots\!68$$$$T^{14} -$$$$86\!\cdots\!20$$$$T^{15} +$$$$28\!\cdots\!60$$$$T^{16} -$$$$85\!\cdots\!00$$$$T^{17} +$$$$25\!\cdots\!40$$$$T^{18} -$$$$75\!\cdots\!00$$$$T^{19} +$$$$21\!\cdots\!71$$$$T^{20} -$$$$57\!\cdots\!10$$$$T^{21} +$$$$14\!\cdots\!48$$$$T^{22} -$$$$33\!\cdots\!60$$$$T^{23} +$$$$49\!\cdots\!81$$$$T^{24}$$
$67$ $$( 1 - 6077 T + 35718991 T^{2} - 18219600105 T^{3} + 122534918608155 T^{4} + 2701855134548306278 T^{5} -$$$$61\!\cdots\!46$$$$T^{6} +$$$$54\!\cdots\!38$$$$T^{7} +$$$$49\!\cdots\!55$$$$T^{8} -$$$$14\!\cdots\!05$$$$T^{9} +$$$$58\!\cdots\!71$$$$T^{10} -$$$$20\!\cdots\!77$$$$T^{11} +$$$$66\!\cdots\!21$$$$T^{12} )^{2}$$
$71$ $$1 - 17574 T + 104286776 T^{2} - 424728504824 T^{3} + 5029513991381961 T^{4} - 44618257451712179514 T^{5} +$$$$20\!\cdots\!06$$$$T^{6} -$$$$10\!\cdots\!44$$$$T^{7} +$$$$80\!\cdots\!46$$$$T^{8} -$$$$47\!\cdots\!54$$$$T^{9} +$$$$20\!\cdots\!26$$$$T^{10} -$$$$11\!\cdots\!94$$$$T^{11} +$$$$68\!\cdots\!36$$$$T^{12} -$$$$29\!\cdots\!14$$$$T^{13} +$$$$13\!\cdots\!86$$$$T^{14} -$$$$77\!\cdots\!14$$$$T^{15} +$$$$33\!\cdots\!66$$$$T^{16} -$$$$11\!\cdots\!44$$$$T^{17} +$$$$56\!\cdots\!86$$$$T^{18} -$$$$30\!\cdots\!54$$$$T^{19} +$$$$87\!\cdots\!01$$$$T^{20} -$$$$18\!\cdots\!04$$$$T^{21} +$$$$11\!\cdots\!76$$$$T^{22} -$$$$50\!\cdots\!94$$$$T^{23} +$$$$72\!\cdots\!61$$$$T^{24}$$
$73$ $$1 - 27950 T + 454822888 T^{2} - 5337429236470 T^{3} + 50136942858006191 T^{4} -$$$$39\!\cdots\!10$$$$T^{5} +$$$$27\!\cdots\!20$$$$T^{6} -$$$$17\!\cdots\!80$$$$T^{7} +$$$$99\!\cdots\!60$$$$T^{8} -$$$$54\!\cdots\!10$$$$T^{9} +$$$$29\!\cdots\!08$$$$T^{10} -$$$$15\!\cdots\!80$$$$T^{11} +$$$$84\!\cdots\!04$$$$T^{12} -$$$$44\!\cdots\!80$$$$T^{13} +$$$$23\!\cdots\!48$$$$T^{14} -$$$$12\!\cdots\!10$$$$T^{15} +$$$$64\!\cdots\!60$$$$T^{16} -$$$$31\!\cdots\!80$$$$T^{17} +$$$$14\!\cdots\!20$$$$T^{18} -$$$$59\!\cdots\!10$$$$T^{19} +$$$$21\!\cdots\!11$$$$T^{20} -$$$$64\!\cdots\!70$$$$T^{21} +$$$$15\!\cdots\!88$$$$T^{22} -$$$$27\!\cdots\!50$$$$T^{23} +$$$$27\!\cdots\!81$$$$T^{24}$$
$79$ $$1 + 41540 T + 884578158 T^{2} + 13528269571760 T^{3} + 171031570391119991 T^{4} +$$$$18\!\cdots\!60$$$$T^{5} +$$$$18\!\cdots\!10$$$$T^{6} +$$$$17\!\cdots\!80$$$$T^{7} +$$$$14\!\cdots\!70$$$$T^{8} +$$$$11\!\cdots\!40$$$$T^{9} +$$$$82\!\cdots\!08$$$$T^{10} +$$$$56\!\cdots\!20$$$$T^{11} +$$$$36\!\cdots\!24$$$$T^{12} +$$$$21\!\cdots\!20$$$$T^{13} +$$$$12\!\cdots\!88$$$$T^{14} +$$$$66\!\cdots\!40$$$$T^{15} +$$$$33\!\cdots\!70$$$$T^{16} +$$$$15\!\cdots\!80$$$$T^{17} +$$$$65\!\cdots\!10$$$$T^{18} +$$$$25\!\cdots\!60$$$$T^{19} +$$$$90\!\cdots\!31$$$$T^{20} +$$$$27\!\cdots\!60$$$$T^{21} +$$$$71\!\cdots\!58$$$$T^{22} +$$$$13\!\cdots\!40$$$$T^{23} +$$$$12\!\cdots\!61$$$$T^{24}$$
$83$ $$1 + 18665 T + 224643628 T^{2} + 792700664890 T^{3} - 7907731388500564 T^{4} -$$$$17\!\cdots\!75$$$$T^{5} -$$$$12\!\cdots\!65$$$$T^{6} -$$$$28\!\cdots\!70$$$$T^{7} +$$$$49\!\cdots\!05$$$$T^{8} +$$$$50\!\cdots\!25$$$$T^{9} +$$$$19\!\cdots\!53$$$$T^{10} -$$$$10\!\cdots\!35$$$$T^{11} -$$$$13\!\cdots\!56$$$$T^{12} -$$$$49\!\cdots\!35$$$$T^{13} +$$$$44\!\cdots\!73$$$$T^{14} +$$$$53\!\cdots\!25$$$$T^{15} +$$$$25\!\cdots\!05$$$$T^{16} -$$$$67\!\cdots\!70$$$$T^{17} -$$$$14\!\cdots\!65$$$$T^{18} -$$$$97\!\cdots\!75$$$$T^{19} -$$$$20\!\cdots\!04$$$$T^{20} +$$$$96\!\cdots\!90$$$$T^{21} +$$$$13\!\cdots\!28$$$$T^{22} +$$$$51\!\cdots\!65$$$$T^{23} +$$$$13\!\cdots\!41$$$$T^{24}$$
$89$ $$( 1 - 2777 T + 289401541 T^{2} - 984806913445 T^{3} + 37686355645869335 T^{4} -$$$$12\!\cdots\!62$$$$T^{5} +$$$$29\!\cdots\!14$$$$T^{6} -$$$$81\!\cdots\!42$$$$T^{7} +$$$$14\!\cdots\!35$$$$T^{8} -$$$$24\!\cdots\!45$$$$T^{9} +$$$$44\!\cdots\!01$$$$T^{10} -$$$$27\!\cdots\!77$$$$T^{11} +$$$$61\!\cdots\!41$$$$T^{12} )^{2}$$
$97$ $$1 - 20769 T + 424679856 T^{2} - 8132949547004 T^{3} + 119819968442578026 T^{4} -$$$$16\!\cdots\!09$$$$T^{5} +$$$$21\!\cdots\!91$$$$T^{6} -$$$$25\!\cdots\!44$$$$T^{7} +$$$$28\!\cdots\!01$$$$T^{8} -$$$$31\!\cdots\!79$$$$T^{9} +$$$$31\!\cdots\!81$$$$T^{10} -$$$$31\!\cdots\!59$$$$T^{11} +$$$$30\!\cdots\!76$$$$T^{12} -$$$$27\!\cdots\!79$$$$T^{13} +$$$$24\!\cdots\!41$$$$T^{14} -$$$$21\!\cdots\!39$$$$T^{15} +$$$$17\!\cdots\!21$$$$T^{16} -$$$$13\!\cdots\!44$$$$T^{17} +$$$$10\!\cdots\!71$$$$T^{18} -$$$$70\!\cdots\!49$$$$T^{19} +$$$$45\!\cdots\!66$$$$T^{20} -$$$$27\!\cdots\!84$$$$T^{21} +$$$$12\!\cdots\!56$$$$T^{22} -$$$$54\!\cdots\!89$$$$T^{23} +$$$$23\!\cdots\!61$$$$T^{24}$$