# Properties

 Label 430.2.k Level 430 Weight 2 Character orbit k Rep. character $$\chi_{430}(11,\cdot)$$ Character field $$\Q(\zeta_{7})$$ Dimension 72 Newform subspaces 4 Sturm bound 132 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$430 = 2 \cdot 5 \cdot 43$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 430.k (of order $$7$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$43$$ Character field: $$\Q(\zeta_{7})$$ Newform subspaces: $$4$$ Sturm bound: $$132$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(430, [\chi])$$.

Total New Old
Modular forms 420 72 348
Cusp forms 372 72 300
Eisenstein series 48 0 48

## Trace form

 $$72q + 2q^{2} + 8q^{3} - 12q^{4} + 2q^{5} + 8q^{6} + 16q^{7} + 2q^{8} - 10q^{9} + O(q^{10})$$ $$72q + 2q^{2} + 8q^{3} - 12q^{4} + 2q^{5} + 8q^{6} + 16q^{7} + 2q^{8} - 10q^{9} + 8q^{11} + 8q^{12} + 20q^{13} - 10q^{14} - 12q^{16} + 8q^{17} + 10q^{18} - 14q^{19} + 2q^{20} + 16q^{21} - 26q^{22} - 16q^{23} - 6q^{24} - 12q^{25} - 20q^{26} + 32q^{27} + 16q^{28} + 12q^{29} + 8q^{30} + 4q^{31} + 2q^{32} + 18q^{33} - 6q^{34} + 8q^{35} + 32q^{36} - 72q^{37} - 8q^{38} - 36q^{39} + 24q^{41} - 32q^{42} - 14q^{43} - 20q^{44} - 30q^{45} - 12q^{46} - 8q^{47} + 8q^{48} + 28q^{49} - 12q^{50} - 70q^{51} - 36q^{52} + 20q^{53} - 10q^{54} + 8q^{55} + 4q^{56} - 12q^{57} + 40q^{58} - 60q^{59} + 56q^{61} + 24q^{62} - 12q^{63} - 12q^{64} + 16q^{65} + 8q^{66} + 32q^{67} + 8q^{68} + 26q^{69} + 16q^{70} + 16q^{71} + 10q^{72} + 56q^{73} + 12q^{74} - 6q^{75} + 28q^{76} + 72q^{77} + 24q^{78} - 24q^{79} - 12q^{80} - 20q^{81} + 52q^{82} - 6q^{83} + 16q^{84} - 16q^{85} - 68q^{86} - 120q^{87} - 26q^{88} + 32q^{89} + 16q^{90} + 8q^{91} - 16q^{92} - 112q^{93} - 12q^{94} - 4q^{95} + 8q^{96} + 44q^{97} + 26q^{98} + 58q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(430, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
430.2.k.a $$12$$ $$3.434$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-2$$ $$-1$$ $$-2$$ $$4$$ $$q+(-1+\beta _{7}+\beta _{8}-\beta _{9}+\beta _{10}-\beta _{11})q^{2}+\cdots$$
430.2.k.b $$18$$ $$3.434$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$-3$$ $$2$$ $$3$$ $$6$$ $$q-\beta _{3}q^{2}+\beta _{5}q^{3}+\beta _{4}q^{4}-\beta _{10}q^{5}+\cdots$$
430.2.k.c $$18$$ $$3.434$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$3$$ $$5$$ $$-3$$ $$8$$ $$q-\beta _{12}q^{2}+\beta _{1}q^{3}+(-1+\beta _{3}-\beta _{7}+\cdots)q^{4}+\cdots$$
430.2.k.d $$24$$ $$3.434$$ None $$4$$ $$2$$ $$4$$ $$-2$$

## Decomposition of $$S_{2}^{\mathrm{old}}(430, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(430, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(43, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(86, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(215, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2}$$)($$( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{3}$$)($$( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{3}$$)
$3$ ($$1 + T - 6 T^{2} - 3 T^{3} + 19 T^{4} - 15 T^{5} - 26 T^{6} + 148 T^{7} - 103 T^{8} - 578 T^{9} + 737 T^{10} + 825 T^{11} - 2537 T^{12} + 2475 T^{13} + 6633 T^{14} - 15606 T^{15} - 8343 T^{16} + 35964 T^{17} - 18954 T^{18} - 32805 T^{19} + 124659 T^{20} - 59049 T^{21} - 354294 T^{22} + 177147 T^{23} + 531441 T^{24}$$)($$1 - 2 T + T^{2} - 3 T^{3} + T^{4} + 18 T^{6} + 64 T^{7} - 171 T^{8} + 290 T^{9} - 781 T^{10} + 709 T^{11} - 1029 T^{12} + 953 T^{13} + 2528 T^{14} + 38 T^{15} + 12474 T^{16} - 47133 T^{17} + 61948 T^{18} - 141399 T^{19} + 112266 T^{20} + 1026 T^{21} + 204768 T^{22} + 231579 T^{23} - 750141 T^{24} + 1550583 T^{25} - 5124141 T^{26} + 5708070 T^{27} - 10097379 T^{28} + 11337408 T^{29} + 9565938 T^{30} + 4782969 T^{32} - 43046721 T^{33} + 43046721 T^{34} - 258280326 T^{35} + 387420489 T^{36}$$)($$1 - 5 T + 11 T^{2} - 22 T^{3} + 64 T^{4} - 177 T^{5} + 364 T^{6} - 721 T^{7} + 1705 T^{8} - 3727 T^{9} + 6910 T^{10} - 13168 T^{11} + 27619 T^{12} - 53717 T^{13} + 95903 T^{14} - 176450 T^{15} + 331870 T^{16} - 581677 T^{17} + 983731 T^{18} - 1745031 T^{19} + 2986830 T^{20} - 4764150 T^{21} + 7768143 T^{22} - 13053231 T^{23} + 20134251 T^{24} - 28798416 T^{25} + 45336510 T^{26} - 73358541 T^{27} + 100678545 T^{28} - 127722987 T^{29} + 193444524 T^{30} - 282195171 T^{31} + 306110016 T^{32} - 315675954 T^{33} + 473513931 T^{34} - 645700815 T^{35} + 387420489 T^{36}$$)
$5$ ($$( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2}$$)($$( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{3}$$)($$( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{3}$$)
$7$ ($$( 1 - 2 T + 26 T^{2} - 35 T^{3} + 311 T^{4} - 323 T^{5} + 2521 T^{6} - 2261 T^{7} + 15239 T^{8} - 12005 T^{9} + 62426 T^{10} - 33614 T^{11} + 117649 T^{12} )^{2}$$)($$( 1 - 3 T + 35 T^{2} - 104 T^{3} + 659 T^{4} - 1784 T^{5} + 8247 T^{6} - 20223 T^{7} + 75730 T^{8} - 164555 T^{9} + 530110 T^{10} - 990927 T^{11} + 2828721 T^{12} - 4283384 T^{13} + 11075813 T^{14} - 12235496 T^{15} + 28824005 T^{16} - 17294403 T^{17} + 40353607 T^{18} )^{2}$$)($$( 1 - 4 T + 43 T^{2} - 165 T^{3} + 954 T^{4} - 3272 T^{5} + 13473 T^{6} - 40583 T^{7} + 131977 T^{8} - 340920 T^{9} + 923839 T^{10} - 1988567 T^{11} + 4621239 T^{12} - 7856072 T^{13} + 16033878 T^{14} - 19412085 T^{15} + 35412349 T^{16} - 23059204 T^{17} + 40353607 T^{18} )^{2}$$)
$11$ ($$1 - 3 T - 22 T^{2} + 35 T^{3} + 429 T^{4} - 597 T^{5} - 2700 T^{6} + 812 T^{7} - 9863 T^{8} - 2764 T^{9} + 826623 T^{10} - 223415 T^{11} - 11420881 T^{12} - 2457565 T^{13} + 100021383 T^{14} - 3678884 T^{15} - 144404183 T^{16} + 130773412 T^{17} - 4783214700 T^{18} - 11633841087 T^{19} + 91959959949 T^{20} + 82528169185 T^{21} - 570623341222 T^{22} - 855935011833 T^{23} + 3138428376721 T^{24}$$)($$1 - 9 T + 25 T^{2} - 12 T^{3} - 24 T^{4} - 91 T^{5} - 540 T^{6} + 7247 T^{7} - 3173 T^{8} - 124295 T^{9} + 349798 T^{10} - 201170 T^{11} - 267079 T^{12} + 5753101 T^{13} - 42575665 T^{14} + 100911028 T^{15} + 151819518 T^{16} - 1253904551 T^{17} + 3739030263 T^{18} - 13792950061 T^{19} + 18370161678 T^{20} + 134312578268 T^{21} - 623350311265 T^{22} + 926542669151 T^{23} - 473146740319 T^{24} - 3920234190070 T^{25} + 74982307856038 T^{26} - 293081108252845 T^{27} - 82299448258973 T^{28} + 2067653676917917 T^{29} - 1694751323429340 T^{30} - 3141566805097721 T^{31} - 9113996005997784 T^{32} - 50126978032987812 T^{33} + 1148743246589304025 T^{34} - 4549023256493643939 T^{35} + 5559917313492231481 T^{36}$$)($$1 - 5 T + 29 T^{2} - 2 T^{3} - 64 T^{4} + 1743 T^{5} - 258 T^{6} + 563 T^{7} + 93155 T^{8} - 93657 T^{9} + 443272 T^{10} + 1889454 T^{11} - 1463949 T^{12} + 6857689 T^{13} + 40881021 T^{14} - 138737432 T^{15} + 197538356 T^{16} - 688470581 T^{17} - 1743464851 T^{18} - 7573176391 T^{19} + 23902141076 T^{20} - 184659521992 T^{21} + 598539028461 T^{22} + 1104437671139 T^{23} - 2593474954389 T^{24} + 36820113194634 T^{25} + 95019289898632 T^{26} - 220838306895987 T^{27} + 2416200788706155 T^{28} + 160630470553993 T^{29} - 809714521194018 T^{30} + 60173087266871733 T^{31} - 24303989349327424 T^{32} - 8354496338831302 T^{33} + 1332542166043592669 T^{34} - 2527235142496468855 T^{35} + 5559917313492231481 T^{36}$$)
$13$ ($$( 1 + 2 T - 9 T^{2} - 44 T^{3} + 113 T^{4} - 126 T^{5} - 1637 T^{6} - 1638 T^{7} + 19097 T^{8} - 96668 T^{9} - 257049 T^{10} + 742586 T^{11} + 4826809 T^{12} )^{2}$$)($$1 - 4 T + 21 T^{2} + 56 T^{3} - 260 T^{4} + 1952 T^{5} + 3110 T^{6} - 2420 T^{7} + 66011 T^{8} + 439956 T^{9} - 292985 T^{10} + 2208328 T^{11} + 34844172 T^{12} - 36854292 T^{13} + 139942287 T^{14} + 1680146632 T^{15} - 929707432 T^{16} + 4297523544 T^{17} + 71524901083 T^{18} + 55867806072 T^{19} - 157120556008 T^{20} + 3691282150504 T^{21} + 3996891659007 T^{22} - 13683740639556 T^{23} + 168186163007148 T^{24} + 138569307049576 T^{25} - 238996865292185 T^{26} + 4665513126147588 T^{27} + 9100176905444339 T^{28} - 4337028153569540 T^{29} + 72457044730915910 T^{30} + 591212208068077856 T^{31} - 1023717860281815140 T^{32} + 2866410008789082392 T^{33} + 13973748792846776661 T^{34} - 34601663677525351732 T^{35} +$$$$11\!\cdots\!29$$$$T^{36}$$)($$1 - 22 T + 189 T^{2} - 776 T^{3} + 2016 T^{4} - 11560 T^{5} + 76130 T^{6} - 262662 T^{7} + 880343 T^{8} - 5919980 T^{9} + 28592867 T^{10} - 84734756 T^{11} + 312372760 T^{12} - 1531317100 T^{13} + 5382091707 T^{14} - 17490109252 T^{15} + 77239495484 T^{16} - 309727210712 T^{17} + 1082670643211 T^{18} - 4026453739256 T^{19} + 13053474736796 T^{20} - 38425770026644 T^{21} + 153717921243627 T^{22} - 568567320010300 T^{23} + 1507763649322840 T^{24} - 5316980277356852 T^{25} + 23324080013367107 T^{26} - 62778424198172540 T^{27} + 121362758289824207 T^{28} - 470732433418546494 T^{29} + 1773683220374478530 T^{30} - 3501236232206444680 T^{31} + 7937750793569766624 T^{32} - 39720252978934427432 T^{33} +$$$$12\!\cdots\!49$$$$T^{34} -$$$$19\!\cdots\!26$$$$T^{35} +$$$$11\!\cdots\!29$$$$T^{36}$$)
$17$ ($$1 + 5 T + 6 T^{2} - 50 T^{3} - 256 T^{4} - 61 T^{5} - 2524 T^{6} + 31036 T^{7} + 260014 T^{8} + 878434 T^{9} + 371178 T^{10} - 9204064 T^{11} - 16949749 T^{12} - 156469088 T^{13} + 107270442 T^{14} + 4315746242 T^{15} + 21716629294 T^{16} + 44066681852 T^{17} - 60923224156 T^{18} - 25030659053 T^{19} - 1785793904896 T^{20} - 5929393824850 T^{21} + 12095963402694 T^{22} + 171359481538165 T^{23} + 582622237229761 T^{24}$$)($$1 + T - 23 T^{2} - 61 T^{3} + 797 T^{4} + 882 T^{5} - 9111 T^{6} - 55466 T^{7} + 169817 T^{8} + 861950 T^{9} + 2044903 T^{10} - 27646324 T^{11} - 18677652 T^{12} + 301514042 T^{13} + 2189324221 T^{14} - 6752066729 T^{15} - 26803962017 T^{16} - 10192305047 T^{17} + 842845786937 T^{18} - 173269185799 T^{19} - 7746345022913 T^{20} - 33172903839577 T^{21} + 182854548262141 T^{22} + 428106823131994 T^{23} - 450833113907988 T^{24} - 11344355903488052 T^{25} + 14264747318373223 T^{26} + 102216820146589150 T^{27} + 342350036192547833 T^{28} - 1900925000599171978 T^{29} - 5308271203400352471 T^{30} + 8735837825023036434 T^{31} +$$$$13\!\cdots\!13$$$$T^{32} -$$$$17\!\cdots\!73$$$$T^{33} -$$$$11\!\cdots\!63$$$$T^{34} +$$$$82\!\cdots\!77$$$$T^{35} +$$$$14\!\cdots\!09$$$$T^{36}$$)($$1 - T + 17 T^{2} - 71 T^{3} + 163 T^{4} - 1386 T^{5} + 5859 T^{6} - 25092 T^{7} + 79275 T^{8} - 574216 T^{9} + 380351 T^{10} - 8959160 T^{11} + 10289590 T^{12} - 149888072 T^{13} + 943088259 T^{14} - 2036970771 T^{15} + 18923873831 T^{16} - 49782589785 T^{17} + 210671203633 T^{18} - 846304026345 T^{19} + 5468999537159 T^{20} - 10007637397923 T^{21} + 78767674479939 T^{22} - 212819628245704 T^{23} + 248365688606710 T^{24} - 3676289825594680 T^{25} + 2653236318441791 T^{26} - 68095056090601352 T^{27} + 159817916458094475 T^{28} - 859950422151127236 T^{29} + 3413583687929169699 T^{30} - 13727745153607628682 T^{31} + 27445585729182351427 T^{32} -$$$$20\!\cdots\!03$$$$T^{33} +$$$$82\!\cdots\!77$$$$T^{34} -$$$$82\!\cdots\!77$$$$T^{35} +$$$$14\!\cdots\!09$$$$T^{36}$$)
$19$ ($$1 + 2 T - 24 T^{2} - 52 T^{3} + 115 T^{4} + 52 T^{5} - 1076 T^{6} - 45484 T^{7} - 66401 T^{8} + 1006610 T^{9} + 2114774 T^{10} - 3943776 T^{11} + 1394383 T^{12} - 74931744 T^{13} + 763433414 T^{14} + 6904337990 T^{15} - 8653444721 T^{16} - 112622886916 T^{17} - 50621367956 T^{18} + 46481330428 T^{19} + 1953109749715 T^{20} - 16779760284508 T^{21} - 147145590187224 T^{22} + 232980517796438 T^{23} + 2213314919066161 T^{24}$$)($$1 + 2 T - 23 T^{2} - 24 T^{3} + 184 T^{4} + 1428 T^{5} + 12528 T^{6} + 12458 T^{7} - 294757 T^{8} - 220636 T^{9} + 6100277 T^{10} + 13014080 T^{11} + 26646360 T^{12} - 26340508 T^{13} - 628545959 T^{14} + 3968341152 T^{15} + 37315624628 T^{16} + 43754418476 T^{17} - 384806928499 T^{18} + 831333951044 T^{19} + 13470940490708 T^{20} + 27218851961568 T^{21} - 81912737922839 T^{22} - 65221705518292 T^{23} + 1253601481643160 T^{24} + 11632918321085120 T^{25} + 103604438997062357 T^{26} - 71196522887167444 T^{27} - 1807174696950649357 T^{28} + 1451235645354012302 T^{29} + 27728409306060865008 T^{30} + 60051660384103080252 T^{31} +$$$$14\!\cdots\!64$$$$T^{32} -$$$$36\!\cdots\!76$$$$T^{33} -$$$$66\!\cdots\!63$$$$T^{34} +$$$$10\!\cdots\!78$$$$T^{35} +$$$$10\!\cdots\!41$$$$T^{36}$$)($$1 + 7 T + 80 T^{2} + 528 T^{3} + 3734 T^{4} + 20920 T^{5} + 120996 T^{6} + 605461 T^{7} + 2904657 T^{8} + 13467676 T^{9} + 54757744 T^{10} + 216429928 T^{11} + 724355904 T^{12} + 2023912444 T^{13} + 3282662694 T^{14} - 10380996494 T^{15} - 115691998692 T^{16} - 856017011464 T^{17} - 3500283086684 T^{18} - 16264323217816 T^{19} - 41764811527812 T^{20} - 71203254952346 T^{21} + 427799884944774 T^{22} + 5011407578675956 T^{23} + 34077961661231424 T^{24} + 193460596113004792 T^{25} + 929981597206939504 T^{26} + 4345853362873491604 T^{27} + 17808644523185479257 T^{28} + 70530308642774573959 T^{29} +$$$$26\!\cdots\!56$$$$T^{30} +$$$$87\!\cdots\!80$$$$T^{31} +$$$$29\!\cdots\!14$$$$T^{32} +$$$$80\!\cdots\!72$$$$T^{33} +$$$$23\!\cdots\!80$$$$T^{34} +$$$$38\!\cdots\!73$$$$T^{35} +$$$$10\!\cdots\!41$$$$T^{36}$$)
$23$ ($$( 1 + 8 T - T^{2} - 318 T^{3} - 1135 T^{4} + 2980 T^{5} + 39361 T^{6} + 68540 T^{7} - 600415 T^{8} - 3869106 T^{9} - 279841 T^{10} + 51490744 T^{11} + 148035889 T^{12} )^{2}$$)($$1 + 19 T + 94 T^{2} - 364 T^{3} - 4934 T^{4} - 12944 T^{5} + 44670 T^{6} + 630217 T^{7} + 3232637 T^{8} + 217968 T^{9} - 91045708 T^{10} - 430615360 T^{11} + 84196748 T^{12} + 8365868928 T^{13} + 33581348290 T^{14} + 45796983038 T^{15} - 144611422188 T^{16} - 1864211343076 T^{17} - 11619108269332 T^{18} - 42876860890748 T^{19} - 76499442337452 T^{20} + 557211892623346 T^{21} + 9397438086821890 T^{22} + 53845601913650304 T^{23} + 12464140441088972 T^{24} - 1466170135597065920 T^{25} - 7129879099086223948 T^{26} + 392593643313767184 T^{27} +$$$$13\!\cdots\!13$$$$T^{28} +$$$$60\!\cdots\!59$$$$T^{29} +$$$$97\!\cdots\!70$$$$T^{30} -$$$$65\!\cdots\!52$$$$T^{31} -$$$$57\!\cdots\!06$$$$T^{32} -$$$$97\!\cdots\!48$$$$T^{33} +$$$$57\!\cdots\!34$$$$T^{34} +$$$$26\!\cdots\!57$$$$T^{35} +$$$$32\!\cdots\!69$$$$T^{36}$$)($$1 - 8 T + 13 T^{2} + 20 T^{3} + 794 T^{4} - 8894 T^{5} + 44620 T^{6} - 76030 T^{7} - 348697 T^{8} - 785090 T^{9} + 27523733 T^{10} - 101765222 T^{11} - 302476000 T^{12} + 4014732254 T^{13} - 12572137619 T^{14} - 14995597814 T^{15} + 64743711756 T^{16} + 2079662840830 T^{17} - 17083611139087 T^{18} + 47832245339090 T^{19} + 34249423518924 T^{20} - 182451438602938 T^{21} - 3518199563438579 T^{22} + 25840193839907122 T^{23} - 44777303561164000 T^{24} - 346492817485204234 T^{25} + 2155410649841173973 T^{26} - 1414066942987986670 T^{27} - 14445300180665765353 T^{28} - 72442125894195869810 T^{29} +$$$$97\!\cdots\!20$$$$T^{30} -$$$$44\!\cdots\!02$$$$T^{31} +$$$$92\!\cdots\!46$$$$T^{32} +$$$$53\!\cdots\!40$$$$T^{33} +$$$$79\!\cdots\!93$$$$T^{34} -$$$$11\!\cdots\!24$$$$T^{35} +$$$$32\!\cdots\!69$$$$T^{36}$$)
$29$ ($$1 - 2 T - 118 T^{2} - 61 T^{3} + 6359 T^{4} + 20645 T^{5} - 141187 T^{6} - 1423013 T^{7} - 2112377 T^{8} + 46855717 T^{9} + 277899604 T^{10} - 613421260 T^{11} - 10677579883 T^{12} - 17789216540 T^{13} + 233713566964 T^{14} + 1142764081913 T^{15} - 1494044116937 T^{16} - 29187631671937 T^{17} - 83981320222027 T^{18} + 356123696399305 T^{19} + 3181066940018999 T^{20} - 884935904528009 T^{21} - 49643453529423718 T^{22} - 24401019531411658 T^{23} + 353814783205469041 T^{24}$$)($$1 + 4 T - 51 T^{2} - 579 T^{3} - 1214 T^{4} + 26250 T^{5} + 148683 T^{6} - 209901 T^{7} - 4679822 T^{8} - 12680244 T^{9} + 95608714 T^{10} + 242480516 T^{11} - 2375176587 T^{12} - 7243939876 T^{13} + 48280620694 T^{14} + 562413939767 T^{15} + 693667484295 T^{16} - 10502405541311 T^{17} - 61444790128505 T^{18} - 304569760698019 T^{19} + 583374354292095 T^{20} + 13716713576977363 T^{21} + 34147965685073014 T^{22} - 148581530143677524 T^{23} - 1412810425440785427 T^{24} + 4182758908342495444 T^{25} + 47827916226314142154 T^{26} -$$$$18\!\cdots\!36$$$$T^{27} -$$$$19\!\cdots\!22$$$$T^{28} -$$$$25\!\cdots\!29$$$$T^{29} +$$$$52\!\cdots\!03$$$$T^{30} +$$$$26\!\cdots\!50$$$$T^{31} -$$$$36\!\cdots\!34$$$$T^{32} -$$$$49\!\cdots\!71$$$$T^{33} -$$$$12\!\cdots\!71$$$$T^{34} +$$$$29\!\cdots\!36$$$$T^{35} +$$$$21\!\cdots\!61$$$$T^{36}$$)($$1 + 6 T - 71 T^{2} - 679 T^{3} + 1326 T^{4} + 34252 T^{5} + 88405 T^{6} - 867289 T^{7} - 8027938 T^{8} - 681278 T^{9} + 325349830 T^{10} + 1194610606 T^{11} - 6989192779 T^{12} - 61491095320 T^{13} - 35442154336 T^{14} + 1740460758039 T^{15} + 9086251390251 T^{16} - 21170258850237 T^{17} - 364928839121169 T^{18} - 613937506656873 T^{19} + 7641537419201091 T^{20} + 42448097427813171 T^{21} - 25067562360920416 T^{22} - 1261253018281722680 T^{23} - 4157334859913999059 T^{24} + 20606885190919533254 T^{25} +$$$$16\!\cdots\!30$$$$T^{26} - 9883399396148080582 T^{27} -$$$$33\!\cdots\!38$$$$T^{28} -$$$$10\!\cdots\!81$$$$T^{29} +$$$$31\!\cdots\!05$$$$T^{30} +$$$$35\!\cdots\!28$$$$T^{31} +$$$$39\!\cdots\!06$$$$T^{32} -$$$$58\!\cdots\!71$$$$T^{33} -$$$$17\!\cdots\!91$$$$T^{34} +$$$$43\!\cdots\!54$$$$T^{35} +$$$$21\!\cdots\!61$$$$T^{36}$$)
$31$ ($$1 - 27 T + 253 T^{2} - 122 T^{3} - 18419 T^{4} + 174117 T^{5} - 494429 T^{6} - 4086333 T^{7} + 51528500 T^{8} - 237955904 T^{9} + 67393797 T^{10} + 6991353571 T^{11} - 55877035301 T^{12} + 216731960701 T^{13} + 64765438917 T^{14} - 7088944336064 T^{15} + 47587651848500 T^{16} - 116988244493283 T^{17} - 438807557493149 T^{18} + 4790413831164987 T^{19} - 15709400018625779 T^{20} - 3225633903601862 T^{21} + 207365956606142653 T^{22} - 686028876202930437 T^{23} + 787662783788549761 T^{24}$$)($$1 + 13 T + 82 T^{2} + 105 T^{3} - 1391 T^{4} - 5662 T^{5} + 25298 T^{6} + 405809 T^{7} + 2689426 T^{8} + 18321725 T^{9} + 105862757 T^{10} + 271821692 T^{11} - 314337076 T^{12} - 5345100555 T^{13} + 22049757012 T^{14} + 354024484218 T^{15} + 2321550409047 T^{16} + 12194450118645 T^{17} + 57150223625159 T^{18} + 378027953677995 T^{19} + 2231009943094167 T^{20} + 10546743409338438 T^{21} + 20363413645479252 T^{22} - 153025690899278805 T^{23} - 278975312024776756 T^{24} + 7478525318995095812 T^{25} + 90289396644094484837 T^{26} +$$$$48\!\cdots\!75$$$$T^{27} +$$$$22\!\cdots\!26$$$$T^{28} +$$$$10\!\cdots\!79$$$$T^{29} +$$$$19\!\cdots\!78$$$$T^{30} -$$$$13\!\cdots\!42$$$$T^{31} -$$$$10\!\cdots\!11$$$$T^{32} +$$$$24\!\cdots\!55$$$$T^{33} +$$$$59\!\cdots\!42$$$$T^{34} +$$$$29\!\cdots\!43$$$$T^{35} +$$$$69\!\cdots\!41$$$$T^{36}$$)($$1 + 5 T - 66 T^{2} - 503 T^{3} + 337 T^{4} + 12028 T^{5} + 33978 T^{6} + 406763 T^{7} + 2995682 T^{8} - 18538475 T^{9} - 206059741 T^{10} - 275557932 T^{11} + 1910953762 T^{12} + 11736742065 T^{13} + 105697996694 T^{14} + 712002834894 T^{15} - 316523157013 T^{16} - 20711586044207 T^{17} - 106673227770053 T^{18} - 642059167370417 T^{19} - 304178753889493 T^{20} + 21211276454327154 T^{21} + 97614319604839574 T^{22} + 336012960826936815 T^{23} + 1695978497995797922 T^{24} - 7581319048341178452 T^{25} -$$$$17\!\cdots\!81$$$$T^{26} -$$$$49\!\cdots\!25$$$$T^{27} +$$$$24\!\cdots\!82$$$$T^{28} +$$$$10\!\cdots\!53$$$$T^{29} +$$$$26\!\cdots\!58$$$$T^{30} +$$$$29\!\cdots\!48$$$$T^{31} +$$$$25\!\cdots\!77$$$$T^{32} -$$$$11\!\cdots\!53$$$$T^{33} -$$$$48\!\cdots\!46$$$$T^{34} +$$$$11\!\cdots\!55$$$$T^{35} +$$$$69\!\cdots\!41$$$$T^{36}$$)
$37$ ($$( 1 + 9 T + 165 T^{2} + 1279 T^{3} + 12099 T^{4} + 82177 T^{5} + 546535 T^{6} + 3040549 T^{7} + 16563531 T^{8} + 64785187 T^{9} + 309236565 T^{10} + 624095613 T^{11} + 2565726409 T^{12} )^{2}$$)($$( 1 - T + 154 T^{2} - 284 T^{3} + 12699 T^{4} - 29079 T^{5} + 767754 T^{6} - 1693550 T^{7} + 36154572 T^{8} - 70746236 T^{9} + 1337719164 T^{10} - 2318469950 T^{11} + 38889043362 T^{12} - 54498727719 T^{13} + 880598909943 T^{14} - 728666300156 T^{15} + 14619509078482 T^{16} - 3512479453921 T^{17} + 129961739795077 T^{18} )^{2}$$)($$( 1 + 9 T + 218 T^{2} + 1614 T^{3} + 23401 T^{4} + 151257 T^{5} + 1644298 T^{6} + 9291632 T^{7} + 82504230 T^{8} + 404531792 T^{9} + 3052656510 T^{10} + 12720244208 T^{11} + 83288626594 T^{12} + 283479970377 T^{13} + 1622717937757 T^{14} + 4141082424126 T^{15} + 20695149214994 T^{16} + 31612315085289 T^{17} + 129961739795077 T^{18} )^{2}$$)
$41$ ($$1 - 14 T - 71 T^{2} + 1449 T^{3} + 8085 T^{4} - 145075 T^{5} - 261043 T^{6} + 7055293 T^{7} + 15992640 T^{8} - 312930646 T^{9} - 102994633 T^{10} + 3464301323 T^{11} + 16362105383 T^{12} + 142036354243 T^{13} - 173133978073 T^{14} - 21567493052966 T^{15} + 45191378399040 T^{16} + 817399443921893 T^{17} - 1239981461383363 T^{18} - 28253976283286075 T^{19} + 64558120477443285 T^{20} + 474376422936849489 T^{21} - 953008811020820471 T^{22} - 7704606444027478174 T^{23} + 22563490300366186081 T^{24}$$)($$1 + 4 T - 76 T^{2} - 391 T^{3} + 1975 T^{4} + 9938 T^{5} - 26870 T^{6} + 433565 T^{7} + 4152628 T^{8} - 23937849 T^{9} - 280692273 T^{10} - 314064324 T^{11} + 5084566150 T^{12} + 15633564413 T^{13} + 29460875358 T^{14} + 1346278111323 T^{15} + 11524941557581 T^{16} - 48638796714869 T^{17} - 956776297373447 T^{18} - 1994190665309629 T^{19} + 19373426758293661 T^{20} + 92786833710492483 T^{21} + 83249392612497438 T^{22} + 1811245380978975013 T^{23} + 24152219232760042150 T^{24} - 61165369372547121444 T^{25} -$$$$22\!\cdots\!33$$$$T^{26} -$$$$78\!\cdots\!89$$$$T^{27} +$$$$55\!\cdots\!28$$$$T^{28} +$$$$23\!\cdots\!65$$$$T^{29} -$$$$60\!\cdots\!70$$$$T^{30} +$$$$91\!\cdots\!98$$$$T^{31} +$$$$74\!\cdots\!75$$$$T^{32} -$$$$60\!\cdots\!91$$$$T^{33} -$$$$48\!\cdots\!16$$$$T^{34} +$$$$10\!\cdots\!24$$$$T^{35} +$$$$10\!\cdots\!21$$$$T^{36}$$)($$1 - 16 T - 52 T^{2} + 2313 T^{3} - 7721 T^{4} - 117110 T^{5} + 860282 T^{6} + 1872521 T^{7} - 38916852 T^{8} + 82707819 T^{9} + 1144968899 T^{10} - 8680504064 T^{11} - 18775033826 T^{12} + 451896528557 T^{13} - 387529241846 T^{14} - 14990466569601 T^{15} + 45356087778625 T^{16} + 236151025913079 T^{17} - 2271300748262055 T^{18} + 9682192062436239 T^{19} + 76243583555868625 T^{20} - 1033157946443470521 T^{21} - 1095065017967994806 T^{22} + 52355015043702031957 T^{23} - 89183367801801056066 T^{24} -$$$$16\!\cdots\!84$$$$T^{25} +$$$$91\!\cdots\!79$$$$T^{26} +$$$$27\!\cdots\!59$$$$T^{27} -$$$$52\!\cdots\!52$$$$T^{28} +$$$$10\!\cdots\!61$$$$T^{29} +$$$$19\!\cdots\!42$$$$T^{30} -$$$$10\!\cdots\!10$$$$T^{31} -$$$$29\!\cdots\!81$$$$T^{32} +$$$$35\!\cdots\!13$$$$T^{33} -$$$$33\!\cdots\!32$$$$T^{34} -$$$$41\!\cdots\!96$$$$T^{35} +$$$$10\!\cdots\!21$$$$T^{36}$$)
$43$ ($$1 - 14 T + 134 T^{2} - 1176 T^{3} + 10648 T^{4} - 73696 T^{5} + 480257 T^{6} - 3168928 T^{7} + 19688152 T^{8} - 93500232 T^{9} + 458119334 T^{10} - 2058118202 T^{11} + 6321363049 T^{12}$$)($$1 + 13 T + 23 T^{2} + 341 T^{3} + 7465 T^{4} - 3559 T^{5} - 300996 T^{6} + 568061 T^{7} - 6089961 T^{8} - 178982555 T^{9} - 261868323 T^{10} + 1050344789 T^{11} - 23931288972 T^{12} - 12167512759 T^{13} + 1097418026995 T^{14} + 2155584799709 T^{15} + 6251828055461 T^{16} + 151946603608813 T^{17} + 502592611936843 T^{18}$$)($$1 + 13 T + 135 T^{2} + 173 T^{3} - 5485 T^{4} - 91815 T^{5} - 487924 T^{6} - 685681 T^{7} + 23032937 T^{8} + 203701481 T^{9} + 990416291 T^{10} - 1267824169 T^{11} - 38793373468 T^{12} - 313897213815 T^{13} - 806341309855 T^{14} + 1093595807477 T^{15} + 36695512499445 T^{16} + 151946603608813 T^{17} + 502592611936843 T^{18}$$)
$47$ ($$1 - 2 T + 95 T^{2} + 486 T^{3} + 4126 T^{4} + 57824 T^{5} + 308156 T^{6} + 3836880 T^{7} + 21611017 T^{8} + 212259114 T^{9} + 1535272757 T^{10} + 8731117266 T^{11} + 89844070544 T^{12} + 410362511502 T^{13} + 3391417520213 T^{14} + 22037377992822 T^{15} + 105454869045577 T^{16} + 879969270458160 T^{17} + 3321679878923324 T^{18} + 29294975317652512 T^{19} + 98245368766425886 T^{20} + 543897409927944762 T^{21} + 4996917562403854655 T^{22} - 4944318430168024606 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 - 16 T + 58 T^{2} + 132 T^{3} + 2174 T^{4} - 59622 T^{5} + 583964 T^{6} - 2362132 T^{7} - 6973035 T^{8} - 13171090 T^{9} + 1946977070 T^{10} - 15462631128 T^{11} + 23862188930 T^{12} + 232936464174 T^{13} + 476845081058 T^{14} - 35831178696668 T^{15} + 291005595210458 T^{16} - 336150127799338 T^{17} - 5856096864612524 T^{18} - 15799056006568886 T^{19} + 642831359819901722 T^{20} - 3720100465824161764 T^{21} + 2326851881982182498 T^{22} + 53422815006541279218 T^{23} +$$$$25\!\cdots\!70$$$$T^{24} -$$$$78\!\cdots\!64$$$$T^{25} +$$$$46\!\cdots\!70$$$$T^{26} -$$$$14\!\cdots\!30$$$$T^{27} -$$$$36\!\cdots\!15$$$$T^{28} -$$$$58\!\cdots\!96$$$$T^{29} +$$$$67\!\cdots\!24$$$$T^{30} -$$$$32\!\cdots\!94$$$$T^{31} +$$$$55\!\cdots\!06$$$$T^{32} +$$$$15\!\cdots\!76$$$$T^{33} +$$$$32\!\cdots\!18$$$$T^{34} -$$$$42\!\cdots\!92$$$$T^{35} +$$$$12\!\cdots\!89$$$$T^{36}$$)($$1 + 36 T + 612 T^{2} + 6578 T^{3} + 56686 T^{4} + 524814 T^{5} + 5385180 T^{6} + 49774124 T^{7} + 394711081 T^{8} + 3091549542 T^{9} + 26602209040 T^{10} + 226026429292 T^{11} + 1707793138576 T^{12} + 12049342225310 T^{13} + 89717535794078 T^{14} + 702257335176408 T^{15} + 5175913711157672 T^{16} + 34826239488864972 T^{17} + 232179354339637252 T^{18} + 1636833255976653684 T^{19} + 11433593387947297448 T^{20} + 72910463310020207784 T^{21} +$$$$43\!\cdots\!18$$$$T^{22} +$$$$27\!\cdots\!70$$$$T^{23} +$$$$18\!\cdots\!04$$$$T^{24} +$$$$11\!\cdots\!96$$$$T^{25} +$$$$63\!\cdots\!40$$$$T^{26} +$$$$34\!\cdots\!14$$$$T^{27} +$$$$20\!\cdots\!69$$$$T^{28} +$$$$12\!\cdots\!72$$$$T^{29} +$$$$62\!\cdots\!80$$$$T^{30} +$$$$28\!\cdots\!78$$$$T^{31} +$$$$14\!\cdots\!34$$$$T^{32} +$$$$79\!\cdots\!54$$$$T^{33} +$$$$34\!\cdots\!52$$$$T^{34} +$$$$95\!\cdots\!32$$$$T^{35} +$$$$12\!\cdots\!89$$$$T^{36}$$)
$53$ ($$1 - 2 T - 192 T^{2} + 831 T^{3} + 14431 T^{4} - 117825 T^{5} - 365313 T^{6} + 9752081 T^{7} - 30260439 T^{8} - 531160493 T^{9} + 4601458502 T^{10} + 12612277558 T^{11} - 319965750843 T^{12} + 668450710574 T^{13} + 12925496932118 T^{14} - 79077580716361 T^{15} - 238769418981159 T^{16} + 4078276321570933 T^{17} - 8096929257118377 T^{18} - 138410340051294525 T^{19} + 898469592326350591 T^{20} + 2742103544787572523 T^{21} - 33578394310178505408 T^{22} - 18538071858744383194 T^{23} +$$$$49\!\cdots\!41$$$$T^{24}$$)($$1 - 14 T + 153 T^{2} - 1705 T^{3} + 14214 T^{4} - 166466 T^{5} + 1703087 T^{6} - 15265377 T^{7} + 137855194 T^{8} - 1013052036 T^{9} + 8625510462 T^{10} - 71977968032 T^{11} + 565915051273 T^{12} - 4612841434870 T^{13} + 31009525649816 T^{14} - 229284034127169 T^{15} + 1720930523999681 T^{16} - 12770176509314833 T^{17} + 101981507436118171 T^{18} - 676819354993686149 T^{19} + 4834093841915103929 T^{20} - 34135119148750539213 T^{21} +$$$$24\!\cdots\!96$$$$T^{22} -$$$$19\!\cdots\!10$$$$T^{23} +$$$$12\!\cdots\!17$$$$T^{24} -$$$$84\!\cdots\!84$$$$T^{25} +$$$$53\!\cdots\!82$$$$T^{26} -$$$$33\!\cdots\!88$$$$T^{27} +$$$$24\!\cdots\!06$$$$T^{28} -$$$$14\!\cdots\!69$$$$T^{29} +$$$$83\!\cdots\!67$$$$T^{30} -$$$$43\!\cdots\!18$$$$T^{31} +$$$$19\!\cdots\!66$$$$T^{32} -$$$$12\!\cdots\!85$$$$T^{33} +$$$$59\!\cdots\!13$$$$T^{34} -$$$$28\!\cdots\!82$$$$T^{35} +$$$$10\!\cdots\!89$$$$T^{36}$$)($$1 + 18 T + 219 T^{2} + 1873 T^{3} + 21028 T^{4} + 191940 T^{5} + 1927031 T^{6} + 16691841 T^{7} + 157628752 T^{8} + 1143000974 T^{9} + 9987462820 T^{10} + 79427444768 T^{11} + 685958917601 T^{12} + 4783166371000 T^{13} + 40313855954708 T^{14} + 280316920456111 T^{15} + 2208536845954869 T^{16} + 15550871535373675 T^{17} + 128962261045140095 T^{18} + 824196191374804775 T^{19} + 6203780000287227021 T^{20} + 41732742166744437347 T^{21} +$$$$31\!\cdots\!48$$$$T^{22} +$$$$20\!\cdots\!00$$$$T^{23} +$$$$15\!\cdots\!29$$$$T^{24} +$$$$93\!\cdots\!16$$$$T^{25} +$$$$62\!\cdots\!20$$$$T^{26} +$$$$37\!\cdots\!42$$$$T^{27} +$$$$27\!\cdots\!48$$$$T^{28} +$$$$15\!\cdots\!77$$$$T^{29} +$$$$94\!\cdots\!71$$$$T^{30} +$$$$49\!\cdots\!20$$$$T^{31} +$$$$29\!\cdots\!32$$$$T^{32} +$$$$13\!\cdots\!61$$$$T^{33} +$$$$84\!\cdots\!99$$$$T^{34} +$$$$36\!\cdots\!34$$$$T^{35} +$$$$10\!\cdots\!89$$$$T^{36}$$)
$59$ ($$1 - 4 T - 111 T^{2} + 373 T^{3} + 10187 T^{4} - 53634 T^{5} - 308525 T^{6} + 3531028 T^{7} - 13046963 T^{8} - 215283643 T^{9} + 3379492827 T^{10} + 4284465948 T^{11} - 240376275189 T^{12} + 252783490932 T^{13} + 11764014530787 T^{14} - 44214739315697 T^{15} - 158094760624643 T^{16} + 2524417717649372 T^{17} - 13013749141589525 T^{18} - 133476333736782246 T^{19} + 1495761667875218027 T^{20} + 3231297440358292247 T^{21} - 56733959616371195511 T^{22} -$$$$12\!\cdots\!36$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 + 16 T + 110 T^{2} + 53 T^{3} - 9107 T^{4} - 138521 T^{5} - 1133458 T^{6} - 6642925 T^{7} - 15509483 T^{8} + 216413994 T^{9} + 3934924448 T^{10} + 39080271562 T^{11} + 325806014415 T^{12} + 2377170408214 T^{13} + 12590066317713 T^{14} - 2478684438573 T^{15} - 789252526438949 T^{16} - 11177472533604662 T^{17} - 102361406567292607 T^{18} - 659470879482675058 T^{19} - 2747388044533981469 T^{20} - 509069731309684167 T^{21} +$$$$15\!\cdots\!93$$$$T^{22} +$$$$16\!\cdots\!86$$$$T^{23} +$$$$13\!\cdots\!15$$$$T^{24} +$$$$97\!\cdots\!78$$$$T^{25} +$$$$57\!\cdots\!08$$$$T^{26} +$$$$18\!\cdots\!66$$$$T^{27} -$$$$79\!\cdots\!83$$$$T^{28} -$$$$20\!\cdots\!75$$$$T^{29} -$$$$20\!\cdots\!98$$$$T^{30} -$$$$14\!\cdots\!59$$$$T^{31} -$$$$56\!\cdots\!27$$$$T^{32} +$$$$19\!\cdots\!47$$$$T^{33} +$$$$23\!\cdots\!10$$$$T^{34} +$$$$20\!\cdots\!04$$$$T^{35} +$$$$75\!\cdots\!21$$$$T^{36}$$)($$1 + 4 T + 182 T^{2} + 889 T^{3} + 19535 T^{4} + 92775 T^{5} + 1403700 T^{6} + 3337697 T^{7} + 60900249 T^{8} - 100866924 T^{9} + 279379214 T^{10} - 22396990778 T^{11} - 136590509711 T^{12} - 1169980179938 T^{13} - 4940983425545 T^{14} + 7131058308663 T^{15} + 145810789722975 T^{16} + 5887152771171894 T^{17} + 24165780228834877 T^{18} + 347342013499141746 T^{19} + 507567359025675975 T^{20} + 1464569624374898277 T^{21} - 59871679862345386745 T^{22} -$$$$83\!\cdots\!62$$$$T^{23} -$$$$57\!\cdots\!51$$$$T^{24} -$$$$55\!\cdots\!82$$$$T^{25} +$$$$41\!\cdots\!94$$$$T^{26} -$$$$87\!\cdots\!36$$$$T^{27} +$$$$31\!\cdots\!49$$$$T^{28} +$$$$10\!\cdots\!23$$$$T^{29} +$$$$24\!\cdots\!00$$$$T^{30} +$$$$97\!\cdots\!25$$$$T^{31} +$$$$12\!\cdots\!35$$$$T^{32} +$$$$32\!\cdots\!11$$$$T^{33} +$$$$39\!\cdots\!62$$$$T^{34} +$$$$50\!\cdots\!76$$$$T^{35} +$$$$75\!\cdots\!21$$$$T^{36}$$)
$61$ ($$1 - 16 T - 66 T^{2} + 2397 T^{3} - 3126 T^{4} - 170243 T^{5} + 586028 T^{6} + 11035274 T^{7} - 81228727 T^{8} - 525242399 T^{9} + 7900192381 T^{10} + 10108936107 T^{11} - 527396641733 T^{12} + 616645102527 T^{13} + 29396615849701 T^{14} - 119220044967419 T^{15} - 1124680038674407 T^{16} + 9320351600921474 T^{17} + 30192381946028108 T^{18} - 535029968632723103 T^{19} - 599277060429500406 T^{20} + 28030868184523435977 T^{21} - 47080632169750251666 T^{22} -$$$$69\!\cdots\!76$$$$T^{23} +$$$$26\!\cdots\!21$$$$T^{24}$$)($$1 - 24 T + 193 T^{2} - 1023 T^{3} + 12269 T^{4} - 101120 T^{5} + 137341 T^{6} + 6279714 T^{7} - 66107156 T^{8} - 91531315 T^{9} + 3450816819 T^{10} - 8829436552 T^{11} + 246170019400 T^{12} - 4618272414559 T^{13} + 35328002089660 T^{14} - 91573533385944 T^{15} - 1045706406860373 T^{16} + 6388716443127935 T^{17} + 8003958918844677 T^{18} + 389711703030804035 T^{19} - 3891073539927447933 T^{20} - 20785452181474955064 T^{21} +$$$$48\!\cdots\!60$$$$T^{22} -$$$$39\!\cdots\!59$$$$T^{23} +$$$$12\!\cdots\!00$$$$T^{24} -$$$$27\!\cdots\!92$$$$T^{25} +$$$$66\!\cdots\!39$$$$T^{26} -$$$$10\!\cdots\!15$$$$T^{27} -$$$$47\!\cdots\!56$$$$T^{28} +$$$$27\!\cdots\!54$$$$T^{29} +$$$$36\!\cdots\!61$$$$T^{30} -$$$$16\!\cdots\!20$$$$T^{31} +$$$$12\!\cdots\!29$$$$T^{32} -$$$$61\!\cdots\!23$$$$T^{33} +$$$$70\!\cdots\!73$$$$T^{34} -$$$$53\!\cdots\!04$$$$T^{35} +$$$$13\!\cdots\!81$$$$T^{36}$$)($$1 - 42 T + 933 T^{2} - 14861 T^{3} + 192423 T^{4} - 2141538 T^{5} + 21336371 T^{6} - 196037772 T^{7} + 1665767448 T^{8} - 12759457459 T^{9} + 83761862657 T^{10} - 415805126156 T^{11} + 730146937632 T^{12} + 16028186575331 T^{13} - 292933998347776 T^{14} + 3505813369714012 T^{15} - 35535339534952817 T^{16} + 322709127419838593 T^{17} - 2650994802911766219 T^{18} + 19685256772610154173 T^{19} -$$$$13\!\cdots\!57$$$$T^{20} +$$$$79\!\cdots\!72$$$$T^{21} -$$$$40\!\cdots\!16$$$$T^{22} +$$$$13\!\cdots\!31$$$$T^{23} +$$$$37\!\cdots\!52$$$$T^{24} -$$$$13\!\cdots\!76$$$$T^{25} +$$$$16\!\cdots\!17$$$$T^{26} -$$$$14\!\cdots\!19$$$$T^{27} +$$$$11\!\cdots\!48$$$$T^{28} -$$$$85\!\cdots\!92$$$$T^{29} +$$$$56\!\cdots\!91$$$$T^{30} -$$$$34\!\cdots\!78$$$$T^{31} +$$$$19\!\cdots\!43$$$$T^{32} -$$$$89\!\cdots\!61$$$$T^{33} +$$$$34\!\cdots\!13$$$$T^{34} -$$$$94\!\cdots\!82$$$$T^{35} +$$$$13\!\cdots\!81$$$$T^{36}$$)
$67$ ($$1 - 9 T - 148 T^{2} + 2384 T^{3} + 2552 T^{4} - 283635 T^{5} + 1159511 T^{6} + 20567317 T^{7} - 175592461 T^{8} - 922488196 T^{9} + 15849512297 T^{10} + 19004289445 T^{11} - 1127214234705 T^{12} + 1273287392815 T^{13} + 71148460701233 T^{14} - 277450317293548 T^{15} - 3538384928298781 T^{16} + 27768451065327919 T^{17} + 104887489167159359 T^{18} - 1719029936175789105 T^{19} + 1036284713124547832 T^{20} + 64860378000767153648 T^{21} -$$$$26\!\cdots\!52$$$$T^{22} -$$$$10\!\cdots\!47$$$$T^{23} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 - 5 T - 243 T^{2} + 2637 T^{3} + 14043 T^{4} - 432442 T^{5} + 2109906 T^{6} + 27147279 T^{7} - 406935575 T^{8} + 400811603 T^{9} + 30519003442 T^{10} - 202859948048 T^{11} - 1206933969243 T^{12} + 21871443321101 T^{13} - 24381765716161 T^{14} - 1594432006027610 T^{15} + 11273924333523498 T^{16} + 50256293453176677 T^{17} - 1103332578696118791 T^{18} + 3367171661362837359 T^{19} + 50608646333186982522 T^{20} -$$$$47\!\cdots\!30$$$$T^{21} -$$$$49\!\cdots\!81$$$$T^{22} +$$$$29\!\cdots\!07$$$$T^{23} -$$$$10\!\cdots\!67$$$$T^{24} -$$$$12\!\cdots\!04$$$$T^{25} +$$$$12\!\cdots\!22$$$$T^{26} +$$$$10\!\cdots\!41$$$$T^{27} -$$$$74\!\cdots\!75$$$$T^{28} +$$$$33\!\cdots\!57$$$$T^{29} +$$$$17\!\cdots\!66$$$$T^{30} -$$$$23\!\cdots\!54$$$$T^{31} +$$$$51\!\cdots\!47$$$$T^{32} +$$$$64\!\cdots\!91$$$$T^{33} -$$$$40\!\cdots\!83$$$$T^{34} -$$$$55\!\cdots\!35$$$$T^{35} +$$$$74\!\cdots\!09$$$$T^{36}$$)($$1 + 19 T - 121 T^{2} - 3509 T^{3} + 17241 T^{4} + 454616 T^{5} - 1635832 T^{6} - 44808601 T^{7} + 41507781 T^{8} + 3267974565 T^{9} + 6835163934 T^{10} - 240159436956 T^{11} - 1558153168075 T^{12} + 15530120367369 T^{13} + 158968204106237 T^{14} - 817261224750396 T^{15} - 11907700881595164 T^{16} + 24442230601190901 T^{17} + 850574669249442709 T^{18} + 1637629450279790367 T^{19} - 53453669257480691196 T^{20} -$$$$24\!\cdots\!48$$$$T^{21} +$$$$32\!\cdots\!77$$$$T^{22} +$$$$20\!\cdots\!83$$$$T^{23} -$$$$14\!\cdots\!75$$$$T^{24} -$$$$14\!\cdots\!88$$$$T^{25} +$$$$27\!\cdots\!94$$$$T^{26} +$$$$88\!\cdots\!55$$$$T^{27} +$$$$75\!\cdots\!69$$$$T^{28} -$$$$54\!\cdots\!83$$$$T^{29} -$$$$13\!\cdots\!52$$$$T^{30} +$$$$24\!\cdots\!92$$$$T^{31} +$$$$63\!\cdots\!89$$$$T^{32} -$$$$86\!\cdots\!87$$$$T^{33} -$$$$19\!\cdots\!01$$$$T^{34} +$$$$20\!\cdots\!13$$$$T^{35} +$$$$74\!\cdots\!09$$$$T^{36}$$)
$71$ ($$1 - 27 T + 253 T^{2} + 79 T^{3} - 26059 T^{4} + 245632 T^{5} - 262147 T^{6} - 14158898 T^{7} + 170058639 T^{8} - 1116863367 T^{9} + 2185060299 T^{10} + 53608272881 T^{11} - 740263984961 T^{12} + 3806187374551 T^{13} + 11014888967259 T^{14} - 399737684546337 T^{15} + 4321475885562159 T^{16} - 25545899349415198 T^{17} - 33581105129038387 T^{18} + 2234052554745898112 T^{19} - 16827691270733285899 T^{20} + 3622031556757473449 T^{21} +$$$$82\!\cdots\!53$$$$T^{22} -$$$$62\!\cdots\!17$$$$T^{23} +$$$$16\!\cdots\!41$$$$T^{24}$$)($$1 + 3 T + 202 T^{2} - 152 T^{3} + 27691 T^{4} - 92044 T^{5} + 2694570 T^{6} - 19553968 T^{7} + 262197087 T^{8} - 2018099301 T^{9} + 27616454078 T^{10} - 171467755434 T^{11} + 2659217155551 T^{12} - 13109941104883 T^{13} + 220898323319547 T^{14} - 1195438763913623 T^{15} + 14974987479690423 T^{16} - 102503631929816908 T^{17} + 1048608441396878449 T^{18} - 7277757867017000468 T^{19} + 75488911885119422343 T^{20} -$$$$42\!\cdots\!53$$$$T^{21} +$$$$56\!\cdots\!07$$$$T^{22} -$$$$23\!\cdots\!33$$$$T^{23} +$$$$34\!\cdots\!71$$$$T^{24} -$$$$15\!\cdots\!94$$$$T^{25} +$$$$17\!\cdots\!58$$$$T^{26} -$$$$92\!\cdots\!31$$$$T^{27} +$$$$85\!\cdots\!87$$$$T^{28} -$$$$45\!\cdots\!28$$$$T^{29} +$$$$44\!\cdots\!70$$$$T^{30} -$$$$10\!\cdots\!84$$$$T^{31} +$$$$22\!\cdots\!71$$$$T^{32} -$$$$89\!\cdots\!52$$$$T^{33} +$$$$84\!\cdots\!42$$$$T^{34} +$$$$88\!\cdots\!73$$$$T^{35} +$$$$21\!\cdots\!61$$$$T^{36}$$)($$1 + 27 T + 192 T^{2} - 3064 T^{3} - 71457 T^{4} - 431170 T^{5} + 3006306 T^{6} + 66658940 T^{7} + 407727641 T^{8} - 36960119 T^{9} - 18346711662 T^{10} - 203539733210 T^{11} - 1941959274995 T^{12} - 10817050171315 T^{13} + 59547414301229 T^{14} + 1594397690229843 T^{15} + 9439982388216595 T^{16} - 39777894586305512 T^{17} - 893741411732820099 T^{18} - 2824230515627691352 T^{19} + 47586951218999855395 T^{20} +$$$$57\!\cdots\!73$$$$T^{21} +$$$$15\!\cdots\!49$$$$T^{22} -$$$$19\!\cdots\!65$$$$T^{23} -$$$$24\!\cdots\!95$$$$T^{24} -$$$$18\!\cdots\!10$$$$T^{25} -$$$$11\!\cdots\!82$$$$T^{26} -$$$$16\!\cdots\!89$$$$T^{27} +$$$$13\!\cdots\!41$$$$T^{28} +$$$$15\!\cdots\!40$$$$T^{29} +$$$$49\!\cdots\!46$$$$T^{30} -$$$$50\!\cdots\!70$$$$T^{31} -$$$$59\!\cdots\!17$$$$T^{32} -$$$$17\!\cdots\!64$$$$T^{33} +$$$$80\!\cdots\!32$$$$T^{34} +$$$$79\!\cdots\!57$$$$T^{35} +$$$$21\!\cdots\!61$$$$T^{36}$$)
$73$ ($$1 - 28 T + 505 T^{2} - 6083 T^{3} + 51071 T^{4} - 242501 T^{5} - 627567 T^{6} + 22785623 T^{7} - 200315116 T^{8} + 258559266 T^{9} + 17601898277 T^{10} - 299053047825 T^{11} + 3088299490395 T^{12} - 21830872491225 T^{13} + 93800515918133 T^{14} + 100583949981522 T^{15} - 5688596940110956 T^{16} + 47236227770107439 T^{17} - 94972366389508863 T^{18} - 2679005188279541597 T^{19} + 41186723353122610751 T^{20} -$$$$35\!\cdots\!79$$$$T^{21} +$$$$21\!\cdots\!45$$$$T^{22} -$$$$87\!\cdots\!56$$$$T^{23} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$1 + 22 T + 272 T^{2} + 2669 T^{3} + 31125 T^{4} + 309208 T^{5} + 1961900 T^{6} + 14213181 T^{7} + 190802684 T^{8} + 2015970959 T^{9} + 10963042915 T^{10} + 81525488566 T^{11} + 933068681880 T^{12} + 3934730546441 T^{13} - 34153795489790 T^{14} - 225081571812169 T^{15} + 1756036748972213 T^{16} - 803992448271191 T^{17} - 175608418784800179 T^{18} - 58691448723796943 T^{19} + 9357919835272923077 T^{20} - 87560557821654547873 T^{21} -$$$$96\!\cdots\!90$$$$T^{22} +$$$$81\!\cdots\!13$$$$T^{23} +$$$$14\!\cdots\!20$$$$T^{24} +$$$$90\!\cdots\!02$$$$T^{25} +$$$$88\!\cdots\!15$$$$T^{26} +$$$$11\!\cdots\!67$$$$T^{27} +$$$$81\!\cdots\!16$$$$T^{28} +$$$$44\!\cdots\!37$$$$T^{29} +$$$$44\!\cdots\!00$$$$T^{30} +$$$$51\!\cdots\!64$$$$T^{31} +$$$$37\!\cdots\!25$$$$T^{32} +$$$$23\!\cdots\!33$$$$T^{33} +$$$$17\!\cdots\!92$$$$T^{34} +$$$$10\!\cdots\!66$$$$T^{35} +$$$$34\!\cdots\!69$$$$T^{36}$$)($$1 - 28 T + 206 T^{2} + 1439 T^{3} - 30467 T^{4} + 115902 T^{5} + 1193696 T^{6} - 12456075 T^{7} - 52758690 T^{8} + 1181272439 T^{9} + 858716819 T^{10} - 81754299384 T^{11} - 22479646170 T^{12} + 7830326968241 T^{13} - 27470831061776 T^{14} - 692066597072037 T^{15} + 6983730927869749 T^{16} + 20546869285875433 T^{17} - 650284685443406899 T^{18} + 1499921457868906609 T^{19} + 37216302114617892421 T^{20} -$$$$26\!\cdots\!29$$$$T^{21} -$$$$78\!\cdots\!16$$$$T^{22} +$$$$16\!\cdots\!13$$$$T^{23} -$$$$34\!\cdots\!30$$$$T^{24} -$$$$90\!\cdots\!48$$$$T^{25} +$$$$69\!\cdots\!39$$$$T^{26} +$$$$69\!\cdots\!07$$$$T^{27} -$$$$22\!\cdots\!10$$$$T^{28} -$$$$39\!\cdots\!75$$$$T^{29} +$$$$27\!\cdots\!16$$$$T^{30} +$$$$19\!\cdots\!66$$$$T^{31} -$$$$37\!\cdots\!03$$$$T^{32} +$$$$12\!\cdots\!23$$$$T^{33} +$$$$13\!\cdots\!66$$$$T^{34} -$$$$13\!\cdots\!84$$$$T^{35} +$$$$34\!\cdots\!69$$$$T^{36}$$)
$79$ ($$( 1 - 5 T + 368 T^{2} - 975 T^{3} + 57067 T^{4} - 71424 T^{5} + 5407867 T^{6} - 5642496 T^{7} + 356155147 T^{8} - 480713025 T^{9} + 14333629808 T^{10} - 15385281995 T^{11} + 243087455521 T^{12} )^{2}$$)($$( 1 + 19 T + 531 T^{2} + 7400 T^{3} + 109592 T^{4} + 1180276 T^{5} + 11765861 T^{6} + 107015700 T^{7} + 850808559 T^{8} + 7993181266 T^{9} + 67213876161 T^{10} + 667884983700 T^{11} + 5801028341579 T^{12} + 45971845802356 T^{13} + 337220764879208 T^{14} + 1798847170855400 T^{15} + 10197275671650429 T^{16} + 28825067388224659 T^{17} + 119851595982618319 T^{18} )^{2}$$)($$( 1 + 13 T + 473 T^{2} + 3826 T^{3} + 90460 T^{4} + 498762 T^{5} + 11312861 T^{6} + 50578492 T^{7} + 1144441533 T^{8} + 4524834638 T^{9} + 90410881107 T^{10} + 315660368572 T^{11} + 5577681674579 T^{12} + 19426820299722 T^{13} + 278350521853540 T^{14} + 930052604823346 T^{15} + 9083448950453207 T^{16} + 19722414528785293 T^{17} + 119851595982618319 T^{18} )^{2}$$)
$83$ ($$1 + 31 T + 452 T^{2} + 2892 T^{3} - 8490 T^{4} - 345229 T^{5} - 2667420 T^{6} - 6265342 T^{7} + 19930908 T^{8} - 246940166 T^{9} + 1158607142 T^{10} + 136753954064 T^{11} + 2035262795035 T^{12} + 11350578187312 T^{13} + 7981644601238 T^{14} - 141197176696642 T^{15} + 945887429685468 T^{16} - 24679436780294906 T^{17} - 872087290731937980 T^{18} - 9368151747097939583 T^{19} - 19121961050860458090 T^{20} +$$$$54\!\cdots\!76$$$$T^{21} +$$$$70\!\cdots\!48$$$$T^{22} +$$$$39\!\cdots\!77$$$$T^{23} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 + 26 T + 41 T^{2} - 4688 T^{3} - 28457 T^{4} + 507415 T^{5} + 4946122 T^{6} - 38886347 T^{7} - 708143290 T^{8} - 839183842 T^{9} + 54673401155 T^{10} + 460215646841 T^{11} - 1917272402872 T^{12} - 58344829035493 T^{13} - 162190885833500 T^{14} + 4674551351114112 T^{15} + 42143643054278062 T^{16} - 154094583853300240 T^{17} - 4385792214629651212 T^{18} - 12789850459823919920 T^{19} +$$$$29\!\cdots\!18$$$$T^{20} +$$$$26\!\cdots\!44$$$$T^{21} -$$$$76\!\cdots\!00$$$$T^{22} -$$$$22\!\cdots\!99$$$$T^{23} -$$$$62\!\cdots\!68$$$$T^{24} +$$$$12\!\cdots\!07$$$$T^{25} +$$$$12\!\cdots\!55$$$$T^{26} -$$$$15\!\cdots\!26$$$$T^{27} -$$$$10\!\cdots\!10$$$$T^{28} -$$$$50\!\cdots\!49$$$$T^{29} +$$$$52\!\cdots\!42$$$$T^{30} +$$$$45\!\cdots\!45$$$$T^{31} -$$$$20\!\cdots\!53$$$$T^{32} -$$$$28\!\cdots\!16$$$$T^{33} +$$$$20\!\cdots\!21$$$$T^{34} +$$$$10\!\cdots\!98$$$$T^{35} +$$$$34\!\cdots\!09$$$$T^{36}$$)($$1 - 62 T + 1955 T^{2} - 43474 T^{3} + 791403 T^{4} - 12660991 T^{5} + 182312666 T^{6} - 2380818115 T^{7} + 28454173700 T^{8} - 313999851042 T^{9} + 3203343358059 T^{10} - 30029118019905 T^{11} + 256415447656186 T^{12} - 1966785367099865 T^{13} + 13121718252161262 T^{14} - 70231361214705904 T^{15} + 228113352519056074 T^{16} + 528279145154473206 T^{17} - 13256029529997156100 T^{18} + 43847169047821276098 T^{19} +$$$$15\!\cdots\!86$$$$T^{20} -$$$$40\!\cdots\!48$$$$T^{21} +$$$$62\!\cdots\!02$$$$T^{22} -$$$$77\!\cdots\!95$$$$T^{23} +$$$$83\!\cdots\!34$$$$T^{24} -$$$$81\!\cdots\!35$$$$T^{25} +$$$$72\!\cdots\!19$$$$T^{26} -$$$$58\!\cdots\!26$$$$T^{27} +$$$$44\!\cdots\!00$$$$T^{28} -$$$$30\!\cdots\!05$$$$T^{29} +$$$$19\!\cdots\!26$$$$T^{30} -$$$$11\!\cdots\!33$$$$T^{31} +$$$$58\!\cdots\!87$$$$T^{32} -$$$$26\!\cdots\!18$$$$T^{33} +$$$$99\!\cdots\!55$$$$T^{34} -$$$$26\!\cdots\!26$$$$T^{35} +$$$$34\!\cdots\!09$$$$T^{36}$$)
$89$ ($$1 + 38 T + 521 T^{2} + 2967 T^{3} + 18241 T^{4} + 334174 T^{5} + 2136543 T^{6} - 2477584 T^{7} + 111400957 T^{8} + 2189866865 T^{9} + 11128069385 T^{10} + 269872470160 T^{11} + 4501464216545 T^{12} + 24018649844240 T^{13} + 88145437598585 T^{14} + 1543788253952185 T^{15} + 6989545691724637 T^{16} - 13834976345891216 T^{17} + 1061821898333687823 T^{18} + 14780962107378508046 T^{19} + 71807316404811659521 T^{20} +$$$$10\!\cdots\!03$$$$T^{21} +$$$$16\!\cdots\!21$$$$T^{22} +$$$$10\!\cdots\!82$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$1 - 52 T + 1128 T^{2} - 13153 T^{3} + 81467 T^{4} + 68453 T^{5} - 9458026 T^{6} + 132595253 T^{7} - 801617131 T^{8} - 3309701708 T^{9} + 120931060118 T^{10} - 1201000189794 T^{11} + 3658479374927 T^{12} + 72912524472654 T^{13} - 1364925845819525 T^{14} + 10187321088410209 T^{15} + 12050739011899131 T^{16} - 1203687248326207182 T^{17} + 15537143357929513709 T^{18} -$$$$10\!\cdots\!98$$$$T^{19} + 95453903713253016651 T^{20} +$$$$71\!\cdots\!21$$$$T^{21} -$$$$85\!\cdots\!25$$$$T^{22} +$$$$40\!\cdots\!46$$$$T^{23} +$$$$18\!\cdots\!47$$$$T^{24} -$$$$53\!\cdots\!26$$$$T^{25} +$$$$47\!\cdots\!58$$$$T^{26} -$$$$11\!\cdots\!72$$$$T^{27} -$$$$24\!\cdots\!31$$$$T^{28} +$$$$36\!\cdots\!17$$$$T^{29} -$$$$23\!\cdots\!46$$$$T^{30} +$$$$15\!\cdots\!57$$$$T^{31} +$$$$15\!\cdots\!47$$$$T^{32} -$$$$22\!\cdots\!97$$$$T^{33} +$$$$17\!\cdots\!08$$$$T^{34} -$$$$71\!\cdots\!08$$$$T^{35} +$$$$12\!\cdots\!81$$$$T^{36}$$)($$1 + 12 T + 116 T^{2} + 1499 T^{3} + 3935 T^{4} - 42611 T^{5} - 1895934 T^{6} - 26145279 T^{7} - 209446975 T^{8} - 2196428168 T^{9} - 7262368198 T^{10} + 44027191578 T^{11} + 1289869174743 T^{12} + 22210109524986 T^{13} + 120472292193179 T^{14} + 920900716991509 T^{15} + 1767591597163055 T^{16} - 97723090524153866 T^{17} - 862701798538908603 T^{18} - 8697355056649694074 T^{19} + 14001093041128558655 T^{20} +$$$$64\!\cdots\!21$$$$T^{21} +$$$$75\!\cdots\!39$$$$T^{22} +$$$$12\!\cdots\!14$$$$T^{23} +$$$$64\!\cdots\!23$$$$T^{24} +$$$$19\!\cdots\!62$$$$T^{25} -$$$$28\!\cdots\!38$$$$T^{26} -$$$$76\!\cdots\!12$$$$T^{27} -$$$$65\!\cdots\!75$$$$T^{28} -$$$$72\!\cdots\!31$$$$T^{29} -$$$$46\!\cdots\!14$$$$T^{30} -$$$$93\!\cdots\!59$$$$T^{31} +$$$$76\!\cdots\!35$$$$T^{32} +$$$$26\!\cdots\!51$$$$T^{33} +$$$$17\!\cdots\!76$$$$T^{34} +$$$$16\!\cdots\!48$$$$T^{35} +$$$$12\!\cdots\!81$$$$T^{36}$$)
$97$ ($$1 + 15 T - 61 T^{2} - 908 T^{3} + 14954 T^{4} + 129879 T^{5} + 769775 T^{6} + 22467776 T^{7} + 57832976 T^{8} - 1013973842 T^{9} + 16680785489 T^{10} + 212073098570 T^{11} + 697406047257 T^{12} + 20571090561290 T^{13} + 156949510666001 T^{14} - 925426548299666 T^{15} + 5119911783370256 T^{16} + 192938437330058432 T^{17} + 641201025094220975 T^{18} + 10494000389732838327 T^{19} +$$$$11\!\cdots\!94$$$$T^{20} -$$$$69\!\cdots\!36$$$$T^{21} -$$$$44\!\cdots\!89$$$$T^{22} +$$$$10\!\cdots\!95$$$$T^{23} +$$$$69\!\cdots\!41$$$$T^{24}$$)($$1 - 27 T + 66 T^{2} + 6423 T^{3} - 102424 T^{4} + 202528 T^{5} + 13832941 T^{6} - 194404750 T^{7} + 369359831 T^{8} + 18779122634 T^{9} - 227205754104 T^{10} + 306742101966 T^{11} + 18629760587417 T^{12} - 187413939377042 T^{13} - 64509572163695 T^{14} + 16124698263546201 T^{15} - 117486606211482490 T^{16} - 549881906918518023 T^{17} + 14838596816271178503 T^{18} - 53338544971096248231 T^{19} -$$$$11\!\cdots\!10$$$$T^{20} +$$$$14\!\cdots\!73$$$$T^{21} -$$$$57\!\cdots\!95$$$$T^{22} -$$$$16\!\cdots\!94$$$$T^{23} +$$$$15\!\cdots\!93$$$$T^{24} +$$$$24\!\cdots\!58$$$$T^{25} -$$$$17\!\cdots\!44$$$$T^{26} +$$$$14\!\cdots\!78$$$$T^{27} +$$$$27\!\cdots\!19$$$$T^{28} -$$$$13\!\cdots\!50$$$$T^{29} +$$$$95\!\cdots\!81$$$$T^{30} +$$$$13\!\cdots\!56$$$$T^{31} -$$$$66\!\cdots\!56$$$$T^{32} +$$$$40\!\cdots\!39$$$$T^{33} +$$$$40\!\cdots\!86$$$$T^{34} -$$$$16\!\cdots\!99$$$$T^{35} +$$$$57\!\cdots\!89$$$$T^{36}$$)($$1 - 71 T + 2368 T^{2} - 50969 T^{3} + 836880 T^{4} - 11828308 T^{5} + 155370763 T^{6} - 1975485248 T^{7} + 25025905391 T^{8} - 318238582892 T^{9} + 3957848635408 T^{10} - 46785223241176 T^{11} + 523567041637077 T^{12} - 5637158848736682 T^{13} + 59668959182508043 T^{14} - 630662658429013549 T^{15} + 6659652238475527590 T^{16} - 69228635653545298441 T^{17} +$$$$69\!\cdots\!39$$$$T^{18} -$$$$67\!\cdots\!77$$$$T^{19} +$$$$62\!\cdots\!10$$$$T^{20} -$$$$57\!\cdots\!77$$$$T^{21} +$$$$52\!\cdots\!83$$$$T^{22} -$$$$48\!\cdots\!74$$$$T^{23} +$$$$43\!\cdots\!33$$$$T^{24} -$$$$37\!\cdots\!88$$$$T^{25} +$$$$31\!\cdots\!88$$$$T^{26} -$$$$24\!\cdots\!64$$$$T^{27} +$$$$18\!\cdots\!59$$$$T^{28} -$$$$14\!\cdots\!44$$$$T^{29} +$$$$10\!\cdots\!83$$$$T^{30} -$$$$79\!\cdots\!16$$$$T^{31} +$$$$54\!\cdots\!20$$$$T^{32} -$$$$32\!\cdots\!17$$$$T^{33} +$$$$14\!\cdots\!28$$$$T^{34} -$$$$42\!\cdots\!27$$$$T^{35} +$$$$57\!\cdots\!89$$$$T^{36}$$)