LMFDB - Space of Modular Forms of Level 320 and Weight 6

Defining parameters

Level:	$ N $	=	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	=	$ 6 $
Nonzero newspaces:			$ 14 $
Sturm bound:			$36864$
Trace bound:			$12$

Dimensions

The following table gives the dimensions of various subspaces of $M_{6}(\Gamma_1(320))$.

	Total	New	Old
Modular forms	15648	7986	7662
Cusp forms	15072	7854	7218
Eisenstein series	576	132	444

Trace form

$ 7854q - 16q^{2} - 12q^{3} - 16q^{4} - 24q^{5} - 48q^{6} - 8q^{7} - 16q^{8} + 466q^{9} + O(q^{10}) $

\( 7854q - 16q^{2} - 12q^{3} - 16q^{4} - 24q^{5} - 48q^{6} - 8q^{7} - 16q^{8} + 466q^{9} - 24q^{10} - 1244q^{11} - 16q^{12} + 448q^{13} - 16q^{14} + 1780q^{15} - 48q^{16} + 1588q^{17} - 16q^{18} - 4732q^{19} - 24q^{20} - 10488q^{21} - 27200q^{22} - 8q^{23} + 44064q^{24} + 12434q^{25} + 51872q^{26} + 8424q^{27} - 8736q^{28} - 16304q^{29} - 64904q^{30} - 23120q^{31} - 74336q^{32} - 44416q^{33} - 25536q^{34} + 8620q^{35} + 124592q^{36} + 46880q^{37} + 139264q^{38} - 16q^{39} + 62336q^{40} - 26684q^{41} - 92736q^{42} - 30772q^{43} - 131040q^{44} + 23500q^{45} - 48q^{46} + 88344q^{47} - 16q^{48} + 24886q^{49} + 137040q^{50} - 89048q^{51} - 146992q^{52} - 77728q^{53} - 466576q^{54} + 220080q^{55} - 301888q^{56} - 72672q^{57} - 52000q^{58} - 175316q^{59} + 197832q^{60} + 100256q^{61} + 350736q^{62} - 793800q^{63} + 749744q^{64} - 155296q^{65} + 509200q^{66} - 216556q^{67} + 14288q^{68} + 283112q^{69} - 286968q^{70} + 863008q^{71} - 828160q^{72} + 250540q^{73} - 755456q^{74} + 291984q^{75} - 537008q^{76} - 375480q^{77} - 665344q^{78} - 1315728q^{79} + 299840q^{80} - 306266q^{81} + 1006224q^{82} + 202788q^{83} + 1970064q^{84} + 312224q^{85} + 1443680q^{86} + 564360q^{87} + 446544q^{88} + 331468q^{89} - 284424q^{90} + 196520q^{91} - 1842560q^{92} + 8768q^{93} - 1642576q^{94} - 327252q^{95} - 2428736q^{96} - 1673788q^{97} - 1914624q^{98} - 1069828q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of $S_{6}^{\mathrm{new}}(\Gamma_1(320))$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $ S_k^{\mathrm{new}}(N, \chi) $ we list the newforms together with their dimension.

Label	$\chi$	Newforms	Dimension	$\chi$ degree
320.6.a	$\chi_{320}(1, \cdot)$	320.6.a.a	1	1
		320.6.a.b	1
		320.6.a.c	1
		320.6.a.d	1
		320.6.a.e	1
		320.6.a.f	1
		320.6.a.g	1
		320.6.a.h	1
		320.6.a.i	1
		320.6.a.j	1
		320.6.a.k	1
		320.6.a.l	1
		320.6.a.m	1
		320.6.a.n	1
		320.6.a.o	1
		320.6.a.p	1
		320.6.a.q	2
		320.6.a.r	2
		320.6.a.s	2
		320.6.a.t	2
		320.6.a.u	2
		320.6.a.v	2
		320.6.a.w	2
		320.6.a.x	3
		320.6.a.y	3
		320.6.a.z	4
320.6.c	$\chi_{320}(129, \cdot)$	320.6.c.a	2	1
		320.6.c.b	2
		320.6.c.c	2
		320.6.c.d	2
		320.6.c.e	2
		320.6.c.f	2
		320.6.c.g	2
		320.6.c.h	4
		320.6.c.i	8
		320.6.c.j	8
		320.6.c.k	12
		320.6.c.l	12
320.6.d	$\chi_{320}(161, \cdot)$	320.6.d.a	8	1
		320.6.d.b	8
		320.6.d.c	12
		320.6.d.d	12
320.6.f	$\chi_{320}(289, \cdot)$	320.6.f.a	4	1
		320.6.f.b	8
		320.6.f.c	16
		320.6.f.d	32
320.6.j	$\chi_{320}(47, \cdot)$	n/a	116	2
320.6.l	$\chi_{320}(81, \cdot)$	320.6.l.a	80	2
320.6.n	$\chi_{320}(63, \cdot)$	n/a	116	2
320.6.o	$\chi_{320}(223, \cdot)$	n/a	120	2
320.6.q	$\chi_{320}(49, \cdot)$	n/a	116	2
320.6.s	$\chi_{320}(207, \cdot)$	n/a	116	2
320.6.u	$\chi_{320}(87, \cdot)$	None	0	4
320.6.x	$\chi_{320}(41, \cdot)$	None	0	4
320.6.z	$\chi_{320}(9, \cdot)$	None	0	4
320.6.ba	$\chi_{320}(7, \cdot)$	None	0	4
320.6.bd	$\chi_{320}(43, \cdot)$	n/a	1904	8
320.6.be	$\chi_{320}(21, \cdot)$	n/a	1280	8
320.6.bf	$\chi_{320}(29, \cdot)$	n/a	1904	8
320.6.bj	$\chi_{320}(3, \cdot)$	n/a	1904	8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of $S_{6}^{\mathrm{old}}(\Gamma_1(320))$ into lower level spaces

Hecke Characteristic Polynomials

$p$	$F_p(T)$
$2$	1
$3$	($ 1 + 26 T + 243 T^{2} $)($ 1 + 24 T + 243 T^{2} $)($ 1 + 22 T + 243 T^{2} $)($ 1 + 18 T + 243 T^{2} $)($ 1 + 8 T + 243 T^{2} $)($ 1 + 6 T + 243 T^{2} $)($ 1 + 4 T + 243 T^{2} $)($ 1 + 2 T + 243 T^{2} $)($ 1 - 2 T + 243 T^{2} $)($ 1 - 4 T + 243 T^{2} $)($ 1 - 6 T + 243 T^{2} $)($ 1 - 8 T + 243 T^{2} $)($ 1 - 18 T + 243 T^{2} $)($ 1 - 22 T + 243 T^{2} $)($ 1 - 24 T + 243 T^{2} $)($ 1 - 26 T + 243 T^{2} $)($ 1 + 12 T + 6 T^{2} + 2916 T^{3} + 59049 T^{4} $)($ 1 + 8 T + 222 T^{2} + 1944 T^{3} + 59049 T^{4} $)($ 1 + 446 T^{2} + 59049 T^{4} $)($ 1 + 306 T^{2} + 59049 T^{4} $)($ 1 + 146 T^{2} + 59049 T^{4} $)($ 1 - 8 T + 222 T^{2} - 1944 T^{3} + 59049 T^{4} $)($ 1 - 12 T + 6 T^{2} - 2916 T^{3} + 59049 T^{4} $)($ 1 + 10 T + 181 T^{2} + 5268 T^{3} + 43983 T^{4} + 590490 T^{5} + 14348907 T^{6} $)($ 1 - 10 T + 181 T^{2} - 5268 T^{3} + 43983 T^{4} - 590490 T^{5} + 14348907 T^{6} $)($ 1 + 124 T^{2} + 25686 T^{4} + 7322076 T^{6} + 3486784401 T^{8} $)($ 1 - 290 T^{2} + 59049 T^{4} $)($ 1 - 290 T^{2} + 59049 T^{4} $)($ ( 1 - 243 T^{2} )^{2} $)($ 1 - 362 T^{2} + 59049 T^{4} $)($ 1 - 362 T^{2} + 59049 T^{4} $)($ ( 1 - 24 T + 243 T^{2} )( 1 + 24 T + 243 T^{2} ) $)($ ( 1 - 24 T + 243 T^{2} )( 1 + 24 T + 243 T^{2} ) $)($ ( 1 - 38 T + 722 T^{2} - 9234 T^{3} + 59049 T^{4} )( 1 + 38 T + 722 T^{2} + 9234 T^{3} + 59049 T^{4} ) $)($ 1 - 472 T^{2} + 69724 T^{4} - 20119464 T^{6} + 8439593958 T^{8} - 1188034229736 T^{10} + 243112555575324 T^{12} - 97180614348674328 T^{14} + 12157665459056928801 T^{16} $)($ 1 - 472 T^{2} + 69724 T^{4} - 20119464 T^{6} + 8439593958 T^{8} - 1188034229736 T^{10} + 243112555575324 T^{12} - 97180614348674328 T^{14} + 12157665459056928801 T^{16} $)($ ( 1 - 310 T^{2} + 120679 T^{4} - 26699028 T^{6} + 7125974271 T^{8} - 1080903164310 T^{10} + 205891132094649 T^{12} )^{2} $)($ ( 1 - 662 T^{2} + 270567 T^{4} - 78508116 T^{6} + 15976710783 T^{8} - 2308251273462 T^{10} + 205891132094649 T^{12} )^{2} $)($ 1 - 376 T^{2} + 163684 T^{4} - 39360744 T^{6} + 11878187814 T^{8} - 2324212572456 T^{10} + 570730817893284 T^{12} - 77415065667588024 T^{14} + 12157665459056928801 T^{16} $)($ 1 - 376 T^{2} + 163684 T^{4} - 39360744 T^{6} + 11878187814 T^{8} - 2324212572456 T^{10} + 570730817893284 T^{12} - 77415065667588024 T^{14} + 12157665459056928801 T^{16} $)($ 1 - 1244 T^{2} + 696846 T^{4} - 230065580 T^{6} + 47479013407 T^{8} - 5765072774040 T^{10} + 634724537410692 T^{12} - 340421782234287960 T^{14} + $$16\!\cdots\!07$$ T^{16} - $$47\!\cdots\!20$$ T^{18} + $$84\!\cdots\!46$$ T^{20} - $$89\!\cdots\!56$$ T^{22} + $$42\!\cdots\!01$$ T^{24} $)($ 1 - 1244 T^{2} + 696846 T^{4} - 230065580 T^{6} + 47479013407 T^{8} - 5765072774040 T^{10} + 634724537410692 T^{12} - 340421782234287960 T^{14} + $$16\!\cdots\!07$$ T^{16} - $$47\!\cdots\!20$$ T^{18} + $$84\!\cdots\!46$$ T^{20} - $$89\!\cdots\!56$$ T^{22} + $$42\!\cdots\!01$$ T^{24} $)($ ( 1 + 243 T^{2} )^{4} $)($ ( 1 + 120 T^{2} + 59049 T^{4} )^{4} $)($ ( 1 + 248 T^{2} + 69330 T^{4} + 14644152 T^{6} + 3486784401 T^{8} )^{4} $)
$5$	($ 1 - 25 T $)($ 1 + 25 T $)($ 1 - 25 T $)($ 1 - 25 T $)($ 1 + 25 T $)($ 1 - 25 T $)($ 1 + 25 T $)($ 1 - 25 T $)($ 1 - 25 T $)($ 1 + 25 T $)($ 1 - 25 T $)($ 1 + 25 T $)($ 1 - 25 T $)($ 1 - 25 T $)($ 1 + 25 T $)($ 1 - 25 T $)($ ( 1 + 25 T )^{2} $)($ ( 1 + 25 T )^{2} $)($ ( 1 + 25 T )^{2} $)($ ( 1 - 25 T )^{2} $)($ ( 1 - 25 T )^{2} $)($ ( 1 + 25 T )^{2} $)($ ( 1 + 25 T )^{2} $)($ ( 1 - 25 T )^{3} $)($ ( 1 - 25 T )^{3} $)($ ( 1 + 25 T )^{4} $)($ 1 + 110 T + 3125 T^{2} $)($ 1 + 110 T + 3125 T^{2} $)($ 1 + 82 T + 3125 T^{2} $)($ 1 - 10 T + 3125 T^{2} $)($ 1 - 10 T + 3125 T^{2} $)($ 1 - 90 T + 3125 T^{2} $)($ 1 - 90 T + 3125 T^{2} $)($ ( 1 - 3125 T^{2} )^{2} $)($ 1 + 8 T + 1100 T^{2} - 113000 T^{3} - 438250 T^{4} - 353125000 T^{5} + 10742187500 T^{6} + 244140625000 T^{7} + 95367431640625 T^{8} $)($ 1 + 8 T + 1100 T^{2} - 113000 T^{3} - 438250 T^{4} - 353125000 T^{5} + 10742187500 T^{6} + 244140625000 T^{7} + 95367431640625 T^{8} $)($ ( 1 - 30 T + 75 T^{2} + 123500 T^{3} + 234375 T^{4} - 292968750 T^{5} + 30517578125 T^{6} )^{2} $)($ ( 1 - 30 T + 4555 T^{2} - 273300 T^{3} + 14234375 T^{4} - 292968750 T^{5} + 30517578125 T^{6} )^{2} $)($ ( 1 + 625 T^{2} )^{4} $)($ ( 1 + 625 T^{2} )^{4} $)($ ( 1 + 625 T^{2} )^{6} $)($ ( 1 + 625 T^{2} )^{6} $)($ ( 1 - 3125 T^{2} )^{2} $)($ ( 1 - 5950 T^{2} + 9765625 T^{4} )^{2} $)($ ( 1 - 220 T^{2} - 6114250 T^{4} - 2148437500 T^{6} + 95367431640625 T^{8} )^{2} $)
$7$	($ 1 - 22 T + 16807 T^{2} $)($ 1 + 172 T + 16807 T^{2} $)($ 1 - 218 T + 16807 T^{2} $)($ 1 + 242 T + 16807 T^{2} $)($ 1 - 108 T + 16807 T^{2} $)($ 1 + 118 T + 16807 T^{2} $)($ 1 + 192 T + 16807 T^{2} $)($ 1 - 62 T + 16807 T^{2} $)($ 1 + 62 T + 16807 T^{2} $)($ 1 - 192 T + 16807 T^{2} $)($ 1 - 118 T + 16807 T^{2} $)($ 1 + 108 T + 16807 T^{2} $)($ 1 - 242 T + 16807 T^{2} $)($ 1 + 218 T + 16807 T^{2} $)($ 1 - 172 T + 16807 T^{2} $)($ 1 + 22 T + 16807 T^{2} $)($ 1 + 52 T + 29646 T^{2} + 873964 T^{3} + 282475249 T^{4} $)($ 1 - 104 T + 36038 T^{2} - 1747928 T^{3} + 282475249 T^{4} $)($ 1 + 31654 T^{2} + 282475249 T^{4} $)($ 1 + 14394 T^{2} + 282475249 T^{4} $)($ 1 + 30554 T^{2} + 282475249 T^{4} $)($ 1 + 104 T + 36038 T^{2} + 1747928 T^{3} + 282475249 T^{4} $)($ 1 - 52 T + 29646 T^{2} - 873964 T^{3} + 282475249 T^{4} $)($ 1 + 6 T + 27153 T^{2} + 1137532 T^{3} + 456360471 T^{4} + 1694851494 T^{5} + 4747561509943 T^{6} $)($ 1 - 6 T + 27153 T^{2} - 1137532 T^{3} + 456360471 T^{4} - 1694851494 T^{5} + 4747561509943 T^{6} $)($ 1 - 27060 T^{2} + 497649542 T^{4} - 7643780237940 T^{6} + 79792266297612001 T^{8} $)($ 1 - 8650 T^{2} + 282475249 T^{4} $)($ 1 - 8650 T^{2} + 282475249 T^{4} $)($ ( 1 - 16807 T^{2} )^{2} $)($ 1 - 18610 T^{2} + 282475249 T^{4} $)($ 1 - 18610 T^{2} + 282475249 T^{4} $)($ 1 - 30050 T^{2} + 282475249 T^{4} $)($ 1 - 30050 T^{2} + 282475249 T^{4} $)($ ( 1 - 366 T + 66978 T^{2} - 6151362 T^{3} + 282475249 T^{4} )( 1 + 366 T + 66978 T^{2} + 6151362 T^{3} + 282475249 T^{4} ) $)($ 1 - 44728 T^{2} + 1493128636 T^{4} - 37445733732616 T^{6} + 682894235558230726 T^{8} - $$10\!\cdots\!84$$ T^{10} + $$11\!\cdots\!36$$ T^{12} - $$10\!\cdots\!72$$ T^{14} + $$63\!\cdots\!01$$ T^{16} $)($ 1 - 44728 T^{2} + 1493128636 T^{4} - 37445733732616 T^{6} + 682894235558230726 T^{8} - $$10\!\cdots\!84$$ T^{10} + $$11\!\cdots\!36$$ T^{12} - $$10\!\cdots\!72$$ T^{14} + $$63\!\cdots\!01$$ T^{16} $)($ ( 1 - 42334 T^{2} + 748334111 T^{4} - 10497411086308 T^{6} + 211385864339918639 T^{8} - $$33\!\cdots\!34$$ T^{10} + $$22\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 54910 T^{2} + 1199559327 T^{4} - 18786317442980 T^{6} + 338845819584597423 T^{8} - $$43\!\cdots\!10$$ T^{10} + $$22\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 + 160 T + 25708 T^{2} + 3666960 T^{3} + 699810714 T^{4} + 61630596720 T^{5} + 7261873701292 T^{6} + 759609841590880 T^{7} + 79792266297612001 T^{8} )^{2} $)($ ( 1 - 160 T + 25708 T^{2} - 3666960 T^{3} + 699810714 T^{4} - 61630596720 T^{5} + 7261873701292 T^{6} - 759609841590880 T^{7} + 79792266297612001 T^{8} )^{2} $)($ ( 1 + 134 T + 60784 T^{2} + 9725794 T^{3} + 1872794971 T^{4} + 305623921700 T^{5} + 37504003751552 T^{6} + 5136621252011900 T^{7} + 529018225759172779 T^{8} + 46173805248034569742 T^{9} + $$48\!\cdots\!84$$ T^{10} + $$17\!\cdots\!38$$ T^{11} + $$22\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 134 T + 60784 T^{2} - 9725794 T^{3} + 1872794971 T^{4} - 305623921700 T^{5} + 37504003751552 T^{6} - 5136621252011900 T^{7} + 529018225759172779 T^{8} - 46173805248034569742 T^{9} + $$48\!\cdots\!84$$ T^{10} - $$17\!\cdots\!38$$ T^{11} + $$22\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 + 26886 T^{2} + 282475249 T^{4} )^{2} $)($ ( 1 - 18852 T^{2} + 282475249 T^{4} )^{4} $)($ ( 1 - 49648 T^{2} + 1179577874 T^{4} - 14024331162352 T^{6} + 79792266297612001 T^{8} )^{4} $)
$11$	($ 1 + 768 T + 161051 T^{2} $)($ 1 + 132 T + 161051 T^{2} $)($ 1 - 480 T + 161051 T^{2} $)($ 1 - 656 T + 161051 T^{2} $)($ 1 + 604 T + 161051 T^{2} $)($ 1 + 192 T + 161051 T^{2} $)($ 1 + 148 T + 161051 T^{2} $)($ 1 + 144 T + 161051 T^{2} $)($ 1 - 144 T + 161051 T^{2} $)($ 1 - 148 T + 161051 T^{2} $)($ 1 - 192 T + 161051 T^{2} $)($ 1 - 604 T + 161051 T^{2} $)($ 1 + 656 T + 161051 T^{2} $)($ 1 + 480 T + 161051 T^{2} $)($ 1 - 132 T + 161051 T^{2} $)($ 1 - 768 T + 161051 T^{2} $)($ 1 - 560 T + 381926 T^{2} - 90188560 T^{3} + 25937424601 T^{4} $)($ 1 + 320 T + 319702 T^{2} + 51536320 T^{3} + 25937424601 T^{4} $)($ 1 - 197738 T^{2} + 25937424601 T^{4} $)($ 1 + 254822 T^{2} + 25937424601 T^{4} $)($ 1 + 92262 T^{2} + 25937424601 T^{4} $)($ 1 - 320 T + 319702 T^{2} - 51536320 T^{3} + 25937424601 T^{4} $)($ 1 + 560 T + 381926 T^{2} + 90188560 T^{3} + 25937424601 T^{4} $)($ 1 - 396 T + 327873 T^{2} - 67617992 T^{3} + 52804274523 T^{4} - 10271220141996 T^{5} + 4177248169415651 T^{6} $)($ 1 + 396 T + 327873 T^{2} + 67617992 T^{3} + 52804274523 T^{4} + 10271220141996 T^{5} + 4177248169415651 T^{6} $)($ 1 + 382252 T^{2} + 87516901782 T^{4} + 9914632428581452 T^{6} + $$67\!\cdots\!01$$ T^{8} $)($ ( 1 + 148 T + 161051 T^{2} )^{2} $)($ ( 1 - 148 T + 161051 T^{2} )^{2} $)($ ( 1 + 161051 T^{2} )^{2} $)($ ( 1 + 100 T + 161051 T^{2} )^{2} $)($ ( 1 - 100 T + 161051 T^{2} )^{2} $)($ ( 1 + 252 T + 161051 T^{2} )^{2} $)($ ( 1 - 252 T + 161051 T^{2} )^{2} $)($ ( 1 + 161051 T^{2} )^{4} $)($ ( 1 + 368 T + 176204 T^{2} + 51158896 T^{3} + 42277949270 T^{4} + 8239191359696 T^{5} + 4570277964394604 T^{6} + 1537227326344959568 T^{7} + $$67\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 - 368 T + 176204 T^{2} - 51158896 T^{3} + 42277949270 T^{4} - 8239191359696 T^{5} + 4570277964394604 T^{6} - 1537227326344959568 T^{7} + $$67\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 220194 T^{2} + 46554422967 T^{4} + 4986677846505148 T^{6} + $$12\!\cdots\!67$$ T^{8} + $$14\!\cdots\!94$$ T^{10} + $$17\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 + 311650 T^{2} + 88422679991 T^{4} + 16030422126529084 T^{6} + $$22\!\cdots\!91$$ T^{8} + $$20\!\cdots\!50$$ T^{10} + $$17\!\cdots\!01$$ T^{12} )^{2} $)($ 1 - 461928 T^{2} + 80897449276 T^{4} - 9751521734727448 T^{6} + $$14\!\cdots\!94$$ T^{8} - $$25\!\cdots\!48$$ T^{10} + $$54\!\cdots\!76$$ T^{12} - $$80\!\cdots\!28$$ T^{14} + $$45\!\cdots\!01$$ T^{16} $)($ 1 - 461928 T^{2} + 80897449276 T^{4} - 9751521734727448 T^{6} + $$14\!\cdots\!94$$ T^{8} - $$25\!\cdots\!48$$ T^{10} + $$54\!\cdots\!76$$ T^{12} - $$80\!\cdots\!28$$ T^{14} + $$45\!\cdots\!01$$ T^{16} $)($ 1 - 1002172 T^{2} + 493219533810 T^{4} - 163075311940514028 T^{6} + $$41\!\cdots\!27$$ T^{8} - $$86\!\cdots\!44$$ T^{10} + $$15\!\cdots\!36$$ T^{12} - $$22\!\cdots\!44$$ T^{14} + $$27\!\cdots\!27$$ T^{16} - $$28\!\cdots\!28$$ T^{18} + $$22\!\cdots\!10$$ T^{20} - $$11\!\cdots\!72$$ T^{22} + $$30\!\cdots\!01$$ T^{24} $)($ 1 - 1002172 T^{2} + 493219533810 T^{4} - 163075311940514028 T^{6} + $$41\!\cdots\!27$$ T^{8} - $$86\!\cdots\!44$$ T^{10} + $$15\!\cdots\!36$$ T^{12} - $$22\!\cdots\!44$$ T^{14} + $$27\!\cdots\!27$$ T^{16} - $$28\!\cdots\!28$$ T^{18} + $$22\!\cdots\!10$$ T^{20} - $$11\!\cdots\!72$$ T^{22} + $$30\!\cdots\!01$$ T^{24} $)($ ( 1 + 321102 T^{2} + 25937424601 T^{4} )^{2} $)($ ( 1 - 233298 T^{2} + 25937424601 T^{4} )^{4} $)($ ( 1 - 577284 T^{2} + 134071408310 T^{4} - 14973260223363684 T^{6} + $$67\!\cdots\!01$$ T^{8} )^{4} $)
$13$	($ 1 - 46 T + 371293 T^{2} $)($ 1 - 946 T + 371293 T^{2} $)($ 1 - 622 T + 371293 T^{2} $)($ 1 - 206 T + 371293 T^{2} $)($ 1 - 306 T + 371293 T^{2} $)($ 1 + 1106 T + 371293 T^{2} $)($ 1 + 286 T + 371293 T^{2} $)($ 1 - 654 T + 371293 T^{2} $)($ 1 - 654 T + 371293 T^{2} $)($ 1 + 286 T + 371293 T^{2} $)($ 1 + 1106 T + 371293 T^{2} $)($ 1 - 306 T + 371293 T^{2} $)($ 1 - 206 T + 371293 T^{2} $)($ 1 - 622 T + 371293 T^{2} $)($ 1 - 946 T + 371293 T^{2} $)($ 1 - 46 T + 371293 T^{2} $)($ 1 + 1388 T + 1149918 T^{2} + 515354684 T^{3} + 137858491849 T^{4} $)($ 1 - 100 T + 297086 T^{2} - 37129300 T^{3} + 137858491849 T^{4} $)($ ( 1 - 146 T + 371293 T^{2} )^{2} $)($ ( 1 + 154 T + 371293 T^{2} )^{2} $)($ ( 1 + 506 T + 371293 T^{2} )^{2} $)($ 1 - 100 T + 297086 T^{2} - 37129300 T^{3} + 137858491849 T^{4} $)($ 1 + 1388 T + 1149918 T^{2} + 515354684 T^{3} + 137858491849 T^{4} $)($ 1 - 354 T + 845379 T^{2} - 291738444 T^{3} + 313883305047 T^{4} - 48801906114546 T^{5} + 51185893014090757 T^{6} $)($ 1 - 354 T + 845379 T^{2} - 291738444 T^{3} + 313883305047 T^{4} - 48801906114546 T^{5} + 51185893014090757 T^{6} $)($ ( 1 - 292 T - 102402 T^{2} - 108417556 T^{3} + 137858491849 T^{4} )^{2} $)($ 1 - 274730 T^{2} + 137858491849 T^{4} $)($ 1 - 274730 T^{2} + 137858491849 T^{4} $)($ ( 1 - 1194 T + 371293 T^{2} )( 1 + 1194 T + 371293 T^{2} ) $)($ 1 - 202442 T^{2} + 137858491849 T^{4} $)($ 1 - 202442 T^{2} + 137858491849 T^{4} $)($ 1 - 728330 T^{2} + 137858491849 T^{4} $)($ 1 - 728330 T^{2} + 137858491849 T^{4} $)($ ( 1 - 371293 T^{2} )^{4} $)($ 1 - 1578472 T^{2} + 1074189263356 T^{4} - 437549632721743384 T^{6} + $$15\!\cdots\!86$$ T^{8} - $$60\!\cdots\!16$$ T^{10} + $$20\!\cdots\!56$$ T^{12} - $$41\!\cdots\!28$$ T^{14} + $$36\!\cdots\!01$$ T^{16} $)($ 1 - 1578472 T^{2} + 1074189263356 T^{4} - 437549632721743384 T^{6} + $$15\!\cdots\!86$$ T^{8} - $$60\!\cdots\!16$$ T^{10} + $$20\!\cdots\!56$$ T^{12} - $$41\!\cdots\!28$$ T^{14} + $$36\!\cdots\!01$$ T^{16} $)($ ( 1 - 921822 T^{2} + 378030377607 T^{4} - 125995996576493956 T^{6} + $$52\!\cdots\!43$$ T^{8} - $$17\!\cdots\!22$$ T^{10} + $$26\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 183262 T^{2} + 260173900423 T^{4} - 19831011157232516 T^{6} + $$35\!\cdots\!27$$ T^{8} - $$34\!\cdots\!62$$ T^{10} + $$26\!\cdots\!49$$ T^{12} )^{2} $)($ 1 - 1173304 T^{2} + 912998161852 T^{4} - 514796045425358792 T^{6} + $$21\!\cdots\!70$$ T^{8} - $$70\!\cdots\!08$$ T^{10} + $$17\!\cdots\!52$$ T^{12} - $$30\!\cdots\!96$$ T^{14} + $$36\!\cdots\!01$$ T^{16} $)($ 1 - 1173304 T^{2} + 912998161852 T^{4} - 514796045425358792 T^{6} + $$21\!\cdots\!70$$ T^{8} - $$70\!\cdots\!08$$ T^{10} + $$17\!\cdots\!52$$ T^{12} - $$30\!\cdots\!96$$ T^{14} + $$36\!\cdots\!01$$ T^{16} $)($ 1 - 2253844 T^{2} + 2609423635634 T^{4} - 2090949123359826660 T^{6} + $$12\!\cdots\!95$$ T^{8} - $$64\!\cdots\!44$$ T^{10} + $$26\!\cdots\!16$$ T^{12} - $$88\!\cdots\!56$$ T^{14} + $$24\!\cdots\!95$$ T^{16} - $$54\!\cdots\!40$$ T^{18} + $$94\!\cdots\!34$$ T^{20} - $$11\!\cdots\!56$$ T^{22} + $$68\!\cdots\!01$$ T^{24} $)($ 1 - 2253844 T^{2} + 2609423635634 T^{4} - 2090949123359826660 T^{6} + $$12\!\cdots\!95$$ T^{8} - $$64\!\cdots\!44$$ T^{10} + $$26\!\cdots\!16$$ T^{12} - $$88\!\cdots\!56$$ T^{14} + $$24\!\cdots\!95$$ T^{16} - $$54\!\cdots\!40$$ T^{18} + $$94\!\cdots\!34$$ T^{20} - $$11\!\cdots\!56$$ T^{22} + $$68\!\cdots\!01$$ T^{24} $)($ ( 1 + 682086 T^{2} + 137858491849 T^{4} )^{2} $)($ ( 1 + 506394 T^{2} + 137858491849 T^{4} )^{4} $)($ ( 1 + 1011892 T^{2} + 531287817014 T^{4} + 139497905034068308 T^{6} + $$19\!\cdots\!01$$ T^{8} )^{4} $)
$17$	($ 1 - 378 T + 1419857 T^{2} $)($ 1 + 222 T + 1419857 T^{2} $)($ 1 - 186 T + 1419857 T^{2} $)($ 1 - 1690 T + 1419857 T^{2} $)($ 1 - 930 T + 1419857 T^{2} $)($ 1 - 762 T + 1419857 T^{2} $)($ 1 + 1678 T + 1419857 T^{2} $)($ 1 + 1190 T + 1419857 T^{2} $)($ 1 + 1190 T + 1419857 T^{2} $)($ 1 + 1678 T + 1419857 T^{2} $)($ 1 - 762 T + 1419857 T^{2} $)($ 1 - 930 T + 1419857 T^{2} $)($ 1 - 1690 T + 1419857 T^{2} $)($ 1 - 186 T + 1419857 T^{2} $)($ 1 + 222 T + 1419857 T^{2} $)($ 1 - 378 T + 1419857 T^{2} $)($ 1 - 148 T - 795706 T^{2} - 210138836 T^{3} + 2015993900449 T^{4} $)($ 1 - 580 T + 2475814 T^{2} - 823517060 T^{3} + 2015993900449 T^{4} $)($ ( 1 + 702 T + 1419857 T^{2} )^{2} $)($ ( 1 - 178 T + 1419857 T^{2} )^{2} $)($ ( 1 + 1838 T + 1419857 T^{2} )^{2} $)($ 1 - 580 T + 2475814 T^{2} - 823517060 T^{3} + 2015993900449 T^{4} $)($ 1 - 148 T - 795706 T^{2} - 210138836 T^{3} + 2015993900449 T^{4} $)($ 1 - 1158 T + 1914111 T^{2} - 544550612 T^{3} + 2717763902127 T^{4} - 2334520936719942 T^{5} + 2862423051509815793 T^{6} $)($ 1 - 1158 T + 1914111 T^{2} - 544550612 T^{3} + 2717763902127 T^{4} - 2334520936719942 T^{5} + 2862423051509815793 T^{6} $)($ ( 1 + 380 T + 2009510 T^{2} + 539545660 T^{3} + 2015993900449 T^{4} )^{2} $)($ 1 + 1354590 T^{2} + 2015993900449 T^{4} $)($ 1 + 1354590 T^{2} + 2015993900449 T^{4} $)($ ( 1 - 2242 T + 1419857 T^{2} )( 1 + 2242 T + 1419857 T^{2} ) $)($ 1 - 1879458 T^{2} + 2015993900449 T^{4} $)($ 1 - 1879458 T^{2} + 2015993900449 T^{4} $)($ 1 - 2363810 T^{2} + 2015993900449 T^{4} $)($ 1 - 2363810 T^{2} + 2015993900449 T^{4} $)($ ( 1 - 1419857 T^{2} )^{4} $)($ 1 - 6260872 T^{2} + 17547242668444 T^{4} - 31297293718759478968 T^{6} + $$45\!\cdots\!30$$ T^{8} - $$63\!\cdots\!32$$ T^{10} + $$71\!\cdots\!44$$ T^{12} - $$51\!\cdots\!28$$ T^{14} + $$16\!\cdots\!01$$ T^{16} $)($ 1 - 6260872 T^{2} + 17547242668444 T^{4} - 31297293718759478968 T^{6} + $$45\!\cdots\!30$$ T^{8} - $$63\!\cdots\!32$$ T^{10} + $$71\!\cdots\!44$$ T^{12} - $$51\!\cdots\!28$$ T^{14} + $$16\!\cdots\!01$$ T^{16} $)($ ( 1 - 7508390 T^{2} + 24616526523247 T^{4} - 45351621021996027220 T^{6} + $$49\!\cdots\!03$$ T^{8} - $$30\!\cdots\!90$$ T^{10} + $$81\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 + 1156442 T^{2} + 502148271983 T^{4} - 1980542974409409364 T^{6} + $$10\!\cdots\!67$$ T^{8} + $$47\!\cdots\!42$$ T^{10} + $$81\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 + 1200 T + 4842092 T^{2} + 4006103760 T^{3} + 9533675124390 T^{4} + 5688094466362320 T^{5} + 9761627937412899308 T^{6} + $$34\!\cdots\!00$$ T^{7} + $$40\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 1200 T + 4842092 T^{2} + 4006103760 T^{3} + 9533675124390 T^{4} + 5688094466362320 T^{5} + 9761627937412899308 T^{6} + $$34\!\cdots\!00$$ T^{7} + $$40\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 - 1200 T + 5829762 T^{2} - 7194221040 T^{3} + 17474250252687 T^{4} - 17877633531638880 T^{5} + 31833151505919656476 T^{6} - $$25\!\cdots\!60$$ T^{7} + $$35\!\cdots\!63$$ T^{8} - $$20\!\cdots\!20$$ T^{9} + $$23\!\cdots\!62$$ T^{10} - $$69\!\cdots\!00$$ T^{11} + $$81\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 1200 T + 5829762 T^{2} - 7194221040 T^{3} + 17474250252687 T^{4} - 17877633531638880 T^{5} + 31833151505919656476 T^{6} - $$25\!\cdots\!60$$ T^{7} + $$35\!\cdots\!63$$ T^{8} - $$20\!\cdots\!20$$ T^{9} + $$23\!\cdots\!62$$ T^{10} - $$69\!\cdots\!00$$ T^{11} + $$81\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 1419857 T^{2} )^{4} $)($ ( 1 - 2662570 T^{2} + 2015993900449 T^{4} )^{4} $)($ ( 1 + 554828 T^{2} + 3105096833510 T^{4} + 1118529863798317772 T^{6} + $$40\!\cdots\!01$$ T^{8} )^{4} $)
$19$	($ 1 - 1100 T + 2476099 T^{2} $)($ 1 + 500 T + 2476099 T^{2} $)($ 1 - 1204 T + 2476099 T^{2} $)($ 1 + 1364 T + 2476099 T^{2} $)($ 1 + 1324 T + 2476099 T^{2} $)($ 1 - 2740 T + 2476099 T^{2} $)($ 1 - 1060 T + 2476099 T^{2} $)($ 1 - 556 T + 2476099 T^{2} $)($ 1 + 556 T + 2476099 T^{2} $)($ 1 + 1060 T + 2476099 T^{2} $)($ 1 + 2740 T + 2476099 T^{2} $)($ 1 - 1324 T + 2476099 T^{2} $)($ 1 - 1364 T + 2476099 T^{2} $)($ 1 + 1204 T + 2476099 T^{2} $)($ 1 - 500 T + 2476099 T^{2} $)($ 1 + 1100 T + 2476099 T^{2} $)($ 1 + 1000 T + 4533462 T^{2} + 2476099000 T^{3} + 6131066257801 T^{4} $)($ 1 + 720 T + 4633798 T^{2} + 1782791280 T^{3} + 6131066257801 T^{4} $)($ 1 - 2512762 T^{2} + 6131066257801 T^{4} $)($ 1 + 4019078 T^{2} + 6131066257801 T^{4} $)($ 1 + 687238 T^{2} + 6131066257801 T^{4} $)($ 1 - 720 T + 4633798 T^{2} - 1782791280 T^{3} + 6131066257801 T^{4} $)($ 1 - 1000 T + 4533462 T^{2} - 2476099000 T^{3} + 6131066257801 T^{4} $)($ 1 + 3192 T + 9330057 T^{2} + 15933739216 T^{3} + 23102144807643 T^{4} + 19570363494900792 T^{5} + 15181127029874798299 T^{6} $)($ 1 - 3192 T + 9330057 T^{2} - 15933739216 T^{3} + 23102144807643 T^{4} - 19570363494900792 T^{5} + 15181127029874798299 T^{6} $)($ 1 + 1633036 T^{2} + 154661897526 T^{4} + 10012251917374313836 T^{6} + $$37\!\cdots\!01$$ T^{8} $)($ ( 1 + 2220 T + 2476099 T^{2} )^{2} $)($ ( 1 - 2220 T + 2476099 T^{2} )^{2} $)($ ( 1 + 2476099 T^{2} )^{2} $)($ ( 1 - 2244 T + 2476099 T^{2} )^{2} $)($ ( 1 + 2244 T + 2476099 T^{2} )^{2} $)($ ( 1 - 220 T + 2476099 T^{2} )^{2} $)($ ( 1 + 220 T + 2476099 T^{2} )^{2} $)($ ( 1 + 2476099 T^{2} )^{4} $)($ ( 1 - 688 T + 5308396 T^{2} - 6058136368 T^{3} + 15069081422710 T^{4} - 15000545402668432 T^{5} + 32546127598645797196 T^{6} - $$10\!\cdots\!12$$ T^{7} + $$37\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 688 T + 5308396 T^{2} + 6058136368 T^{3} + 15069081422710 T^{4} + 15000545402668432 T^{5} + 32546127598645797196 T^{6} + $$10\!\cdots\!12$$ T^{7} + $$37\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 8862994 T^{2} + 40251921150215 T^{4} + $$12\!\cdots\!80$$ T^{6} + $$24\!\cdots\!15$$ T^{8} + $$33\!\cdots\!94$$ T^{10} + $$23\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 + 3143250 T^{2} + 17341223849991 T^{4} + 36134402435803900316 T^{6} + $$10\!\cdots\!91$$ T^{8} + $$11\!\cdots\!50$$ T^{10} + $$23\!\cdots\!01$$ T^{12} )^{2} $)($ 1 - 4628552 T^{2} + 15129915669436 T^{4} - 43933554813794877112 T^{6} + $$13\!\cdots\!54$$ T^{8} - $$26\!\cdots\!12$$ T^{10} + $$56\!\cdots\!36$$ T^{12} - $$10\!\cdots\!52$$ T^{14} + $$14\!\cdots\!01$$ T^{16} $)($ 1 - 4628552 T^{2} + 15129915669436 T^{4} - 43933554813794877112 T^{6} + $$13\!\cdots\!54$$ T^{8} - $$26\!\cdots\!12$$ T^{10} + $$56\!\cdots\!36$$ T^{12} - $$10\!\cdots\!52$$ T^{14} + $$14\!\cdots\!01$$ T^{16} $)($ 1 - 19893836 T^{2} + 197127587113970 T^{4} - $$12\!\cdots\!52$$ T^{6} + $$60\!\cdots\!07$$ T^{8} - $$21\!\cdots\!16$$ T^{10} + $$60\!\cdots\!52$$ T^{12} - $$13\!\cdots\!16$$ T^{14} + $$22\!\cdots\!07$$ T^{16} - $$29\!\cdots\!52$$ T^{18} + $$27\!\cdots\!70$$ T^{20} - $$17\!\cdots\!36$$ T^{22} + $$53\!\cdots\!01$$ T^{24} $)($ 1 - 19893836 T^{2} + 197127587113970 T^{4} - $$12\!\cdots\!52$$ T^{6} + $$60\!\cdots\!07$$ T^{8} - $$21\!\cdots\!16$$ T^{10} + $$60\!\cdots\!52$$ T^{12} - $$13\!\cdots\!16$$ T^{14} + $$22\!\cdots\!07$$ T^{16} - $$29\!\cdots\!52$$ T^{18} + $$27\!\cdots\!70$$ T^{20} - $$17\!\cdots\!36$$ T^{22} + $$53\!\cdots\!01$$ T^{24} $)($ ( 1 - 1288802 T^{2} + 6131066257801 T^{4} )^{2} $)($ ( 1 + 1673278 T^{2} + 6131066257801 T^{4} )^{4} $)($ ( 1 - 8279076 T^{2} + 29313371734870 T^{4} - 50759563509370071876 T^{6} + $$37\!\cdots\!01$$ T^{8} )^{4} $)
$23$	($ 1 - 1986 T + 6436343 T^{2} $)($ 1 - 3564 T + 6436343 T^{2} $)($ 1 + 3186 T + 6436343 T^{2} $)($ 1 + 2198 T + 6436343 T^{2} $)($ 1 - 852 T + 6436343 T^{2} $)($ 1 - 1566 T + 6436343 T^{2} $)($ 1 + 2976 T + 6436343 T^{2} $)($ 1 + 2182 T + 6436343 T^{2} $)($ 1 - 2182 T + 6436343 T^{2} $)($ 1 - 2976 T + 6436343 T^{2} $)($ 1 + 1566 T + 6436343 T^{2} $)($ 1 + 852 T + 6436343 T^{2} $)($ 1 - 2198 T + 6436343 T^{2} $)($ 1 - 3186 T + 6436343 T^{2} $)($ 1 + 3564 T + 6436343 T^{2} $)($ 1 + 1986 T + 6436343 T^{2} $)($ 1 - 2452 T + 6569198 T^{2} - 15781913036 T^{3} + 41426511213649 T^{4} $)($ 1 - 1688 T + 10950502 T^{2} - 10864546984 T^{3} + 41426511213649 T^{4} $)($ 1 - 3871674 T^{2} + 41426511213649 T^{4} $)($ 1 + 5934266 T^{2} + 41426511213649 T^{4} $)($ 1 + 9265626 T^{2} + 41426511213649 T^{4} $)($ 1 + 1688 T + 10950502 T^{2} + 10864546984 T^{3} + 41426511213649 T^{4} $)($ 1 + 2452 T + 6569198 T^{2} + 15781913036 T^{3} + 41426511213649 T^{4} $)($ 1 - 6126 T + 29722593 T^{2} - 84141222540 T^{3} + 191304803397399 T^{4} - 253778807694813774 T^{5} + $$26\!\cdots\!07$$ T^{6} $)($ 1 + 6126 T + 29722593 T^{2} + 84141222540 T^{3} + 191304803397399 T^{4} + 253778807694813774 T^{5} + $$26\!\cdots\!07$$ T^{6} $)($ 1 + 25651084 T^{2} + 247347299659206 T^{4} + $$10\!\cdots\!16$$ T^{6} + $$17\!\cdots\!01$$ T^{8} $)($ 1 - 11320170 T^{2} + 41426511213649 T^{4} $)($ 1 - 11320170 T^{2} + 41426511213649 T^{4} $)($ ( 1 - 6436343 T^{2} )^{2} $)($ 1 - 1185810 T^{2} + 41426511213649 T^{4} $)($ 1 - 1185810 T^{2} + 41426511213649 T^{4} $)($ 1 - 6946370 T^{2} + 41426511213649 T^{4} $)($ 1 - 6946370 T^{2} + 41426511213649 T^{4} $)($ ( 1 - 4838 T + 11703122 T^{2} - 31139027434 T^{3} + 41426511213649 T^{4} )( 1 + 4838 T + 11703122 T^{2} + 31139027434 T^{3} + 41426511213649 T^{4} ) $)($ 1 - 34675896 T^{2} + 569897415616828 T^{4} - $$59\!\cdots\!20$$ T^{6} + $$44\!\cdots\!82$$ T^{8} - $$24\!\cdots\!80$$ T^{10} + $$97\!\cdots\!28$$ T^{12} - $$24\!\cdots\!04$$ T^{14} + $$29\!\cdots\!01$$ T^{16} $)($ 1 - 34675896 T^{2} + 569897415616828 T^{4} - $$59\!\cdots\!20$$ T^{6} + $$44\!\cdots\!82$$ T^{8} - $$24\!\cdots\!80$$ T^{10} + $$97\!\cdots\!28$$ T^{12} - $$24\!\cdots\!04$$ T^{14} + $$29\!\cdots\!01$$ T^{16} $)($ ( 1 - 27906430 T^{2} + 367961637958719 T^{4} - $$29\!\cdots\!08$$ T^{6} + $$15\!\cdots\!31$$ T^{8} - $$47\!\cdots\!30$$ T^{10} + $$71\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 2071710 T^{2} + 29683977204927 T^{4} - $$44\!\cdots\!80$$ T^{6} + $$12\!\cdots\!23$$ T^{8} - $$35\!\cdots\!10$$ T^{10} + $$71\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 880 T + 8141852 T^{2} - 31216146720 T^{3} + 19333174339674 T^{4} - 200917827428244960 T^{5} + $$33\!\cdots\!48$$ T^{6} - $$23\!\cdots\!60$$ T^{7} + $$17\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 880 T + 8141852 T^{2} + 31216146720 T^{3} + 19333174339674 T^{4} + 200917827428244960 T^{5} + $$33\!\cdots\!48$$ T^{6} + $$23\!\cdots\!60$$ T^{7} + $$17\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 4054 T + 24767560 T^{2} + 85869926290 T^{3} + 327319542066779 T^{4} + 869764424865766180 T^{5} + $$26\!\cdots\!28$$ T^{6} + $$55\!\cdots\!40$$ T^{7} + $$13\!\cdots\!71$$ T^{8} + $$22\!\cdots\!30$$ T^{9} + $$42\!\cdots\!60$$ T^{10} + $$44\!\cdots\!22$$ T^{11} + $$71\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 4054 T + 24767560 T^{2} - 85869926290 T^{3} + 327319542066779 T^{4} - 869764424865766180 T^{5} + $$26\!\cdots\!28$$ T^{6} - $$55\!\cdots\!40$$ T^{7} + $$13\!\cdots\!71$$ T^{8} - $$22\!\cdots\!30$$ T^{9} + $$42\!\cdots\!60$$ T^{10} - $$44\!\cdots\!22$$ T^{11} + $$71\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 1772186 T^{2} + 41426511213649 T^{4} )^{2} $)($ ( 1 - 12357236 T^{2} + 41426511213649 T^{4} )^{4} $)($ ( 1 - 265392 T^{2} + 72532989580114 T^{4} - 10994264664012735408 T^{6} + $$17\!\cdots\!01$$ T^{8} )^{4} $)
$29$	($ 1 - 5610 T + 20511149 T^{2} $)($ 1 + 2190 T + 20511149 T^{2} $)($ 1 + 5526 T + 20511149 T^{2} $)($ 1 - 2218 T + 20511149 T^{2} $)($ 1 + 5902 T + 20511149 T^{2} $)($ 1 + 5910 T + 20511149 T^{2} $)($ 1 - 3410 T + 20511149 T^{2} $)($ 1 - 1578 T + 20511149 T^{2} $)($ 1 - 1578 T + 20511149 T^{2} $)($ 1 - 3410 T + 20511149 T^{2} $)($ 1 + 5910 T + 20511149 T^{2} $)($ 1 + 5902 T + 20511149 T^{2} $)($ 1 - 2218 T + 20511149 T^{2} $)($ 1 + 5526 T + 20511149 T^{2} $)($ 1 + 2190 T + 20511149 T^{2} $)($ 1 - 5610 T + 20511149 T^{2} $)($ 1 + 1340 T - 8758306 T^{2} + 27484939660 T^{3} + 420707233300201 T^{4} $)($ 1 + 108 T + 39233214 T^{2} + 2215204092 T^{3} + 420707233300201 T^{4} $)($ ( 1 - 4010 T + 20511149 T^{2} )^{2} $)($ ( 1 + 4110 T + 20511149 T^{2} )^{2} $)($ ( 1 - 4530 T + 20511149 T^{2} )^{2} $)($ 1 + 108 T + 39233214 T^{2} + 2215204092 T^{3} + 420707233300201 T^{4} $)($ 1 + 1340 T - 8758306 T^{2} + 27484939660 T^{3} + 420707233300201 T^{4} $)($ 1 + 426 T - 939693 T^{2} - 141773503364 T^{3} - 19274183137257 T^{4} + 179221281385885626 T^{5} + $$86\!\cdots\!49$$ T^{6} $)($ 1 + 426 T - 939693 T^{2} - 141773503364 T^{3} - 19274183137257 T^{4} + 179221281385885626 T^{5} + $$86\!\cdots\!49$$ T^{6} $)($ ( 1 - 84 T + 9837118 T^{2} - 1722936516 T^{3} + 420707233300201 T^{4} )^{2} $)($ ( 1 + 270 T + 20511149 T^{2} )^{2} $)($ ( 1 + 270 T + 20511149 T^{2} )^{2} $)($ ( 1 + 2950 T + 20511149 T^{2} )^{2} $)($ ( 1 + 7854 T + 20511149 T^{2} )^{2} $)($ ( 1 + 7854 T + 20511149 T^{2} )^{2} $)($ ( 1 - 6930 T + 20511149 T^{2} )^{2} $)($ ( 1 - 6930 T + 20511149 T^{2} )^{2} $)($ ( 1 + 1686 T + 20511149 T^{2} )^{4} $)($ ( 1 + 2936 T + 58625996 T^{2} + 77951973928 T^{3} + 1466411094282230 T^{4} + 1598884552081323272 T^{5} + $$24\!\cdots\!96$$ T^{6} + $$25\!\cdots\!64$$ T^{7} + $$17\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 2936 T + 58625996 T^{2} + 77951973928 T^{3} + 1466411094282230 T^{4} + 1598884552081323272 T^{5} + $$24\!\cdots\!96$$ T^{6} + $$25\!\cdots\!64$$ T^{7} + $$17\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 - 5326 T + 46243827 T^{2} - 133362268948 T^{3} + 948514025927223 T^{4} - 2240686724556870526 T^{5} + $$86\!\cdots\!49$$ T^{6} )^{4} $)($ ( 1 - 1966 T + 38511987 T^{2} - 51339089236 T^{3} + 789925103643063 T^{4} - 827110420668195166 T^{5} + $$86\!\cdots\!49$$ T^{6} )^{4} $)($ 1 - 57762792 T^{2} + 1773990452604028 T^{4} - $$43\!\cdots\!44$$ T^{6} + $$95\!\cdots\!70$$ T^{8} - $$18\!\cdots\!44$$ T^{10} + $$31\!\cdots\!28$$ T^{12} - $$43\!\cdots\!92$$ T^{14} + $$31\!\cdots\!01$$ T^{16} $)($ 1 - 57762792 T^{2} + 1773990452604028 T^{4} - $$43\!\cdots\!44$$ T^{6} + $$95\!\cdots\!70$$ T^{8} - $$18\!\cdots\!44$$ T^{10} + $$31\!\cdots\!28$$ T^{12} - $$43\!\cdots\!92$$ T^{14} + $$31\!\cdots\!01$$ T^{16} $)($ 1 - 118766236 T^{2} + 8086517092300050 T^{4} - $$38\!\cdots\!40$$ T^{6} + $$13\!\cdots\!91$$ T^{8} - $$38\!\cdots\!40$$ T^{10} + $$88\!\cdots\!84$$ T^{12} - $$16\!\cdots\!40$$ T^{14} + $$24\!\cdots\!91$$ T^{16} - $$28\!\cdots\!40$$ T^{18} + $$25\!\cdots\!50$$ T^{20} - $$15\!\cdots\!36$$ T^{22} + $$55\!\cdots\!01$$ T^{24} $)($ 1 - 118766236 T^{2} + 8086517092300050 T^{4} - $$38\!\cdots\!40$$ T^{6} + $$13\!\cdots\!91$$ T^{8} - $$38\!\cdots\!40$$ T^{10} + $$88\!\cdots\!84$$ T^{12} - $$16\!\cdots\!40$$ T^{14} + $$24\!\cdots\!91$$ T^{16} - $$28\!\cdots\!40$$ T^{18} + $$25\!\cdots\!50$$ T^{20} - $$15\!\cdots\!36$$ T^{22} + $$55\!\cdots\!01$$ T^{24} $)($ ( 1 - 20511149 T^{2} )^{4} $)($ ( 1 - 27077290 T^{2} + 420707233300201 T^{4} )^{4} $)($ ( 1 - 18262996 T^{2} + 467877918484406 T^{4} - $$76\!\cdots\!96$$ T^{6} + $$17\!\cdots\!01$$ T^{8} )^{4} $)
$31$	($ 1 - 3988 T + 28629151 T^{2} $)($ 1 - 2312 T + 28629151 T^{2} $)($ 1 - 9356 T + 28629151 T^{2} $)($ 1 - 1700 T + 28629151 T^{2} $)($ 1 - 3320 T + 28629151 T^{2} $)($ 1 + 6868 T + 28629151 T^{2} $)($ 1 - 2448 T + 28629151 T^{2} $)($ 1 + 9660 T + 28629151 T^{2} $)($ 1 - 9660 T + 28629151 T^{2} $)($ 1 + 2448 T + 28629151 T^{2} $)($ 1 - 6868 T + 28629151 T^{2} $)($ 1 + 3320 T + 28629151 T^{2} $)($ 1 + 1700 T + 28629151 T^{2} $)($ 1 + 9356 T + 28629151 T^{2} $)($ 1 + 2312 T + 28629151 T^{2} $)($ 1 + 3988 T + 28629151 T^{2} $)($ 1 - 2248 T + 57017022 T^{2} - 64358331448 T^{3} + 819628286980801 T^{4} $)($ 1 - 9840 T + 76732702 T^{2} - 281710845840 T^{3} + 819628286980801 T^{4} $)($ 1 + 36406942 T^{2} + 819628286980801 T^{4} $)($ 1 + 47289582 T^{2} + 819628286980801 T^{4} $)($ 1 + 43928942 T^{2} + 819628286980801 T^{4} $)($ 1 + 9840 T + 76732702 T^{2} + 281710845840 T^{3} + 819628286980801 T^{4} $)($ 1 + 2248 T + 57017022 T^{2} + 64358331448 T^{3} + 819628286980801 T^{4} $)($ 1 - 3276 T + 2292813 T^{2} + 41639420248 T^{3} + 65641289591763 T^{4} - 2685102268149104076 T^{5} + $$23\!\cdots\!51$$ T^{6} $)($ 1 + 3276 T + 2292813 T^{2} - 41639420248 T^{3} + 65641289591763 T^{4} + 2685102268149104076 T^{5} + $$23\!\cdots\!51$$ T^{6} $)($ 1 + 24283452 T^{2} + 1637830022018822 T^{4} + $$19\!\cdots\!52$$ T^{6} + $$67\!\cdots\!01$$ T^{8} $)($ ( 1 - 2048 T + 28629151 T^{2} )^{2} $)($ ( 1 + 2048 T + 28629151 T^{2} )^{2} $)($ ( 1 + 28629151 T^{2} )^{2} $)($ ( 1 - 2144 T + 28629151 T^{2} )^{2} $)($ ( 1 + 2144 T + 28629151 T^{2} )^{2} $)($ ( 1 - 6752 T + 28629151 T^{2} )^{2} $)($ ( 1 + 6752 T + 28629151 T^{2} )^{2} $)($ ( 1 + 28629151 T^{2} )^{4} $)($ ( 1 + 2112 T + 80187004 T^{2} + 163080265536 T^{3} + 3196344720873606 T^{4} + 4668849547150239936 T^{5} + $$65\!\cdots\!04$$ T^{6} + $$49\!\cdots\!12$$ T^{7} + $$67\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 - 2112 T + 80187004 T^{2} - 163080265536 T^{3} + 3196344720873606 T^{4} - 4668849547150239936 T^{5} + $$65\!\cdots\!04$$ T^{6} - $$49\!\cdots\!12$$ T^{7} + $$67\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 10594234 T^{2} - 153174449706673 T^{4} + $$19\!\cdots\!88$$ T^{6} - $$12\!\cdots\!73$$ T^{8} + $$71\!\cdots\!34$$ T^{10} + $$55\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 + 47574970 T^{2} + 2163796989249871 T^{4} + $$78\!\cdots\!04$$ T^{6} + $$17\!\cdots\!71$$ T^{8} + $$31\!\cdots\!70$$ T^{10} + $$55\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 - 15520 T + 133260604 T^{2} - 763025830560 T^{3} + 3983065379572806 T^{4} - 21844781720002654560 T^{5} + $$10\!\cdots\!04$$ T^{6} - $$36\!\cdots\!20$$ T^{7} + $$67\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 15520 T + 133260604 T^{2} + 763025830560 T^{3} + 3983065379572806 T^{4} + 21844781720002654560 T^{5} + $$10\!\cdots\!04$$ T^{6} + $$36\!\cdots\!20$$ T^{7} + $$67\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 3988 T + 109571794 T^{2} + 302364450332 T^{3} + 5668865865566767 T^{4} + 12320621141215714888 T^{5} + $$19\!\cdots\!04$$ T^{6} + $$35\!\cdots\!88$$ T^{7} + $$46\!\cdots\!67$$ T^{8} + $$70\!\cdots\!32$$ T^{9} + $$73\!\cdots\!94$$ T^{10} + $$76\!\cdots\!88$$ T^{11} + $$55\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 - 3988 T + 109571794 T^{2} - 302364450332 T^{3} + 5668865865566767 T^{4} - 12320621141215714888 T^{5} + $$19\!\cdots\!04$$ T^{6} - $$35\!\cdots\!88$$ T^{7} + $$46\!\cdots\!67$$ T^{8} - $$70\!\cdots\!32$$ T^{9} + $$73\!\cdots\!94$$ T^{10} - $$76\!\cdots\!88$$ T^{11} + $$55\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 + 28629151 T^{2} )^{4} $)($ ( 1 + 18464654 T^{2} + 819628286980801 T^{4} )^{4} $)($ ( 1 + 39407004 T^{2} + 689994929185606 T^{4} + $$32\!\cdots\!04$$ T^{6} + $$67\!\cdots\!01$$ T^{8} )^{4} $)
$37$	($ 1 - 142 T + 69343957 T^{2} $)($ 1 - 11242 T + 69343957 T^{2} $)($ 1 + 5618 T + 69343957 T^{2} $)($ 1 - 846 T + 69343957 T^{2} $)($ 1 + 10774 T + 69343957 T^{2} $)($ 1 - 5518 T + 69343957 T^{2} $)($ 1 + 182 T + 69343957 T^{2} $)($ 1 - 3534 T + 69343957 T^{2} $)($ 1 - 3534 T + 69343957 T^{2} $)($ 1 + 182 T + 69343957 T^{2} $)($ 1 - 5518 T + 69343957 T^{2} $)($ 1 + 10774 T + 69343957 T^{2} $)($ 1 - 846 T + 69343957 T^{2} $)($ 1 + 5618 T + 69343957 T^{2} $)($ 1 - 11242 T + 69343957 T^{2} $)($ 1 - 142 T + 69343957 T^{2} $)($ 1 - 5940 T + 123434318 T^{2} - 411903104580 T^{3} + 4808584372417849 T^{4} $)($ 1 + 6540 T + 61572814 T^{2} + 453509478780 T^{3} + 4808584372417849 T^{4} $)($ ( 1 - 14778 T + 69343957 T^{2} )^{2} $)($ ( 1 + 7442 T + 69343957 T^{2} )^{2} $)($ ( 1 + 338 T + 69343957 T^{2} )^{2} $)($ 1 + 6540 T + 61572814 T^{2} + 453509478780 T^{3} + 4808584372417849 T^{4} $)($ 1 - 5940 T + 123434318 T^{2} - 411903104580 T^{3} + 4808584372417849 T^{4} $)($ 1 - 11562 T + 90623691 T^{2} - 525372493468 T^{3} + 6284205331885287 T^{4} - 55596852513895170138 T^{5} + $$33\!\cdots\!93$$ T^{6} $)($ 1 - 11562 T + 90623691 T^{2} - 525372493468 T^{3} + 6284205331885287 T^{4} - 55596852513895170138 T^{5} + $$33\!\cdots\!93$$ T^{6} $)($ ( 1 + 9868 T + 159567054 T^{2} + 684286167676 T^{3} + 4808584372417849 T^{4} )^{2} $)($ 1 - 119573530 T^{2} + 4808584372417849 T^{4} $)($ 1 - 119573530 T^{2} + 4808584372417849 T^{4} $)($ ( 1 - 12242 T + 69343957 T^{2} )( 1 + 12242 T + 69343957 T^{2} ) $)($ 1 - 30515770 T^{2} + 4808584372417849 T^{4} $)($ 1 - 30515770 T^{2} + 4808584372417849 T^{4} $)($ 1 + 56462470 T^{2} + 4808584372417849 T^{4} $)($ 1 + 56462470 T^{2} + 4808584372417849 T^{4} $)($ ( 1 - 69343957 T^{2} )^{4} $)($ 1 - 251774632 T^{2} + 38631208311838780 T^{4} - $$41\!\cdots\!52$$ T^{6} + $$32\!\cdots\!34$$ T^{8} - $$19\!\cdots\!48$$ T^{10} + $$89\!\cdots\!80$$ T^{12} - $$27\!\cdots\!68$$ T^{14} + $$53\!\cdots\!01$$ T^{16} $)($ 1 - 251774632 T^{2} + 38631208311838780 T^{4} - $$41\!\cdots\!52$$ T^{6} + $$32\!\cdots\!34$$ T^{8} - $$19\!\cdots\!48$$ T^{10} + $$89\!\cdots\!80$$ T^{12} - $$27\!\cdots\!68$$ T^{14} + $$53\!\cdots\!01$$ T^{16} $)($ ( 1 - 234974254 T^{2} + 32080895329334807 T^{4} - $$26\!\cdots\!92$$ T^{6} + $$15\!\cdots\!43$$ T^{8} - $$54\!\cdots\!54$$ T^{10} + $$11\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 301201198 T^{2} + 42883739211630103 T^{4} - $$37\!\cdots\!24$$ T^{6} + $$20\!\cdots\!47$$ T^{8} - $$69\!\cdots\!98$$ T^{10} + $$11\!\cdots\!49$$ T^{12} )^{2} $)($ 1 - 301131416 T^{2} + 47822074973756092 T^{4} - $$50\!\cdots\!08$$ T^{6} + $$40\!\cdots\!70$$ T^{8} - $$24\!\cdots\!92$$ T^{10} + $$11\!\cdots\!92$$ T^{12} - $$33\!\cdots\!84$$ T^{14} + $$53\!\cdots\!01$$ T^{16} $)($ 1 - 301131416 T^{2} + 47822074973756092 T^{4} - $$50\!\cdots\!08$$ T^{6} + $$40\!\cdots\!70$$ T^{8} - $$24\!\cdots\!92$$ T^{10} + $$11\!\cdots\!92$$ T^{12} - $$33\!\cdots\!84$$ T^{14} + $$53\!\cdots\!01$$ T^{16} $)($ 1 - 298070820 T^{2} + 53469062376708978 T^{4} - $$69\!\cdots\!56$$ T^{6} + $$71\!\cdots\!03$$ T^{8} - $$61\!\cdots\!04$$ T^{10} + $$45\!\cdots\!00$$ T^{12} - $$29\!\cdots\!96$$ T^{14} + $$16\!\cdots\!03$$ T^{16} - $$77\!\cdots\!44$$ T^{18} + $$28\!\cdots\!78$$ T^{20} - $$76\!\cdots\!80$$ T^{22} + $$12\!\cdots\!01$$ T^{24} $)($ 1 - 298070820 T^{2} + 53469062376708978 T^{4} - $$69\!\cdots\!56$$ T^{6} + $$71\!\cdots\!03$$ T^{8} - $$61\!\cdots\!04$$ T^{10} + $$45\!\cdots\!00$$ T^{12} - $$29\!\cdots\!96$$ T^{14} + $$16\!\cdots\!03$$ T^{16} - $$77\!\cdots\!44$$ T^{18} + $$28\!\cdots\!78$$ T^{20} - $$76\!\cdots\!80$$ T^{22} + $$12\!\cdots\!01$$ T^{24} $)($ ( 1 - 112652586 T^{2} + 4808584372417849 T^{4} )^{2} $)($ ( 1 + 105952386 T^{2} + 4808584372417849 T^{4} )^{4} $)($ ( 1 + 171738148 T^{2} + 16366808202619574 T^{4} + $$82\!\cdots\!52$$ T^{6} + $$23\!\cdots\!01$$ T^{8} )^{4} $)
$41$	($ 1 - 1542 T + 115856201 T^{2} $)($ 1 - 1242 T + 115856201 T^{2} $)($ 1 + 14394 T + 115856201 T^{2} $)($ 1 + 1818 T + 115856201 T^{2} $)($ 1 + 17958 T + 115856201 T^{2} $)($ 1 + 378 T + 115856201 T^{2} $)($ 1 + 9398 T + 115856201 T^{2} $)($ 1 - 7462 T + 115856201 T^{2} $)($ 1 - 7462 T + 115856201 T^{2} $)($ 1 + 9398 T + 115856201 T^{2} $)($ 1 + 378 T + 115856201 T^{2} $)($ 1 + 17958 T + 115856201 T^{2} $)($ 1 + 1818 T + 115856201 T^{2} $)($ 1 + 14394 T + 115856201 T^{2} $)($ 1 - 1242 T + 115856201 T^{2} $)($ 1 - 1542 T + 115856201 T^{2} $)($ 1 - 23076 T + 352280470 T^{2} - 2673497694276 T^{3} + 13422659310152401 T^{4} $)($ 1 + 10620 T + 77106582 T^{2} + 1230392854620 T^{3} + 13422659310152401 T^{4} $)($ ( 1 + 4350 T + 115856201 T^{2} )^{2} $)($ ( 1 - 7270 T + 115856201 T^{2} )^{2} $)($ ( 1 + 6330 T + 115856201 T^{2} )^{2} $)($ 1 + 10620 T + 77106582 T^{2} + 1230392854620 T^{3} + 13422659310152401 T^{4} $)($ 1 - 23076 T + 352280470 T^{2} - 2673497694276 T^{3} + 13422659310152401 T^{4} $)($ 1 - 12450 T + 384843783 T^{2} - 2886023186300 T^{3} + 44586538676848383 T^{4} - $$16\!\cdots\!50$$ T^{5} + $$15\!\cdots\!01$$ T^{6} $)($ 1 - 12450 T + 384843783 T^{2} - 2886023186300 T^{3} + 44586538676848383 T^{4} - $$16\!\cdots\!50$$ T^{5} + $$15\!\cdots\!01$$ T^{6} $)($ ( 1 - 23812 T + 331016342 T^{2} - 2758767858212 T^{3} + 13422659310152401 T^{4} )^{2} $)($ ( 1 + 2398 T + 115856201 T^{2} )^{2} $)($ ( 1 + 2398 T + 115856201 T^{2} )^{2} $)($ ( 1 - 20950 T + 115856201 T^{2} )^{2} $)($ ( 1 + 7414 T + 115856201 T^{2} )^{2} $)($ ( 1 + 7414 T + 115856201 T^{2} )^{2} $)($ ( 1 + 198 T + 115856201 T^{2} )^{2} $)($ ( 1 + 198 T + 115856201 T^{2} )^{2} $)($ ( 1 - 211028098 T^{2} + 13422659310152401 T^{4} )^{2} $)($ ( 1 - 11800 T + 337909340 T^{2} - 2943020124776 T^{3} + 51155654972384870 T^{4} - $$34\!\cdots\!76$$ T^{5} + $$45\!\cdots\!40$$ T^{6} - $$18\!\cdots\!00$$ T^{7} + $$18\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 - 11800 T + 337909340 T^{2} - 2943020124776 T^{3} + 51155654972384870 T^{4} - $$34\!\cdots\!76$$ T^{5} + $$45\!\cdots\!40$$ T^{6} - $$18\!\cdots\!00$$ T^{7} + $$18\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 27418 T + 531273543 T^{2} + 6402679071436 T^{3} + 61551334383790143 T^{4} + $$36\!\cdots\!18$$ T^{5} + $$15\!\cdots\!01$$ T^{6} )^{4} $)($ ( 1 - 16390 T + 318388423 T^{2} - 3510238606580 T^{3} + 36887273131161023 T^{4} - $$21\!\cdots\!90$$ T^{5} + $$15\!\cdots\!01$$ T^{6} )^{4} $)($ ( 1 - 10792 T + 381689636 T^{2} - 2595640517112 T^{3} + 58822716652823334 T^{4} - $$30\!\cdots\!12$$ T^{5} + $$51\!\cdots\!36$$ T^{6} - $$16\!\cdots\!92$$ T^{7} + $$18\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 - 10792 T + 381689636 T^{2} - 2595640517112 T^{3} + 58822716652823334 T^{4} - $$30\!\cdots\!12$$ T^{5} + $$51\!\cdots\!36$$ T^{6} - $$16\!\cdots\!92$$ T^{7} + $$18\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 28204 T + 645547054 T^{2} + 9891921342268 T^{3} + 144344267066611295 T^{4} + $$17\!\cdots\!96$$ T^{5} + $$20\!\cdots\!08$$ T^{6} + $$19\!\cdots\!96$$ T^{7} + $$19\!\cdots\!95$$ T^{8} + $$15\!\cdots\!68$$ T^{9} + $$11\!\cdots\!54$$ T^{10} + $$58\!\cdots\!04$$ T^{11} + $$24\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 + 28204 T + 645547054 T^{2} + 9891921342268 T^{3} + 144344267066611295 T^{4} + $$17\!\cdots\!96$$ T^{5} + $$20\!\cdots\!08$$ T^{6} + $$19\!\cdots\!96$$ T^{7} + $$19\!\cdots\!95$$ T^{8} + $$15\!\cdots\!68$$ T^{9} + $$11\!\cdots\!54$$ T^{10} + $$58\!\cdots\!04$$ T^{11} + $$24\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 - 15202 T + 115856201 T^{2} )^{4} $)($ ( 1 - 11396 T + 115856201 T^{2} )^{8} $)($ ( 1 + 12544 T + 129356290 T^{2} + 1453300185344 T^{3} + 13422659310152401 T^{4} )^{8} $)
$43$	($ 1 + 5026 T + 147008443 T^{2} $)($ 1 + 20624 T + 147008443 T^{2} $)($ 1 - 370 T + 147008443 T^{2} $)($ 1 - 10534 T + 147008443 T^{2} $)($ 1 - 9264 T + 147008443 T^{2} $)($ 1 - 2434 T + 147008443 T^{2} $)($ 1 + 1244 T + 147008443 T^{2} $)($ 1 + 7114 T + 147008443 T^{2} $)($ 1 - 7114 T + 147008443 T^{2} $)($ 1 - 1244 T + 147008443 T^{2} $)($ 1 + 2434 T + 147008443 T^{2} $)($ 1 + 9264 T + 147008443 T^{2} $)($ 1 + 10534 T + 147008443 T^{2} $)($ 1 + 370 T + 147008443 T^{2} $)($ 1 - 20624 T + 147008443 T^{2} $)($ 1 - 5026 T + 147008443 T^{2} $)($ 1 - 17684 T + 312898614 T^{2} - 2599697306012 T^{3} + 21611482313284249 T^{4} $)($ 1 + 25672 T + 364912302 T^{2} + 3774000748696 T^{3} + 21611482313284249 T^{4} $)($ 1 + 139567886 T^{2} + 21611482313284249 T^{4} $)($ 1 - 26783614 T^{2} + 21611482313284249 T^{4} $)($ 1 - 35859614 T^{2} + 21611482313284249 T^{4} $)($ 1 - 25672 T + 364912302 T^{2} - 3774000748696 T^{3} + 21611482313284249 T^{4} $)($ 1 + 17684 T + 312898614 T^{2} + 2599697306012 T^{3} + 21611482313284249 T^{4} $)($ 1 + 26346 T + 640605069 T^{2} + 8098987233524 T^{3} + 94174353771597567 T^{4} + $$56\!\cdots\!54$$ T^{5} + $$31\!\cdots\!07$$ T^{6} $)($ 1 - 26346 T + 640605069 T^{2} - 8098987233524 T^{3} + 94174353771597567 T^{4} - $$56\!\cdots\!54$$ T^{5} + $$31\!\cdots\!07$$ T^{6} $)($ 1 + 385757980 T^{2} + 71059469286049782 T^{4} + $$83\!\cdots\!20$$ T^{6} + $$46\!\cdots\!01$$ T^{8} $)($ 1 - 288754450 T^{2} + 21611482313284249 T^{4} $)($ 1 - 288754450 T^{2} + 21611482313284249 T^{4} $)($ ( 1 - 147008443 T^{2} )^{2} $)($ 1 + 21442214 T^{2} + 21611482313284249 T^{4} $)($ 1 + 21442214 T^{2} + 21611482313284249 T^{4} $)($ 1 - 293842250 T^{2} + 21611482313284249 T^{4} $)($ 1 - 293842250 T^{2} + 21611482313284249 T^{4} $)($ ( 1 - 11862 T + 70353522 T^{2} - 1743814150866 T^{3} + 21611482313284249 T^{4} )( 1 + 11862 T + 70353522 T^{2} + 1743814150866 T^{3} + 21611482313284249 T^{4} ) $)($ 1 - 283211672 T^{2} + 48021567531024796 T^{4} - $$54\!\cdots\!84$$ T^{6} + $$43\!\cdots\!06$$ T^{8} - $$11\!\cdots\!16$$ T^{10} + $$22\!\cdots\!96$$ T^{12} - $$28\!\cdots\!28$$ T^{14} + $$21\!\cdots\!01$$ T^{16} $)($ 1 - 283211672 T^{2} + 48021567531024796 T^{4} - $$54\!\cdots\!84$$ T^{6} + $$43\!\cdots\!06$$ T^{8} - $$11\!\cdots\!16$$ T^{10} + $$22\!\cdots\!96$$ T^{12} - $$28\!\cdots\!28$$ T^{14} + $$21\!\cdots\!01$$ T^{16} $)($ ( 1 - 613900486 T^{2} + 182904754783784951 T^{4} - $$33\!\cdots\!72$$ T^{6} + $$39\!\cdots\!99$$ T^{8} - $$28\!\cdots\!86$$ T^{10} + $$10\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 640358182 T^{2} + 187647756282389367 T^{4} - $$33\!\cdots\!76$$ T^{6} + $$40\!\cdots\!83$$ T^{8} - $$29\!\cdots\!82$$ T^{10} + $$10\!\cdots\!49$$ T^{12} )^{2} $)($ 1 - 542148344 T^{2} + 153567024284830372 T^{4} - $$32\!\cdots\!92$$ T^{6} + $$53\!\cdots\!70$$ T^{8} - $$69\!\cdots\!08$$ T^{10} + $$71\!\cdots\!72$$ T^{12} - $$54\!\cdots\!56$$ T^{14} + $$21\!\cdots\!01$$ T^{16} $)($ 1 - 542148344 T^{2} + 153567024284830372 T^{4} - $$32\!\cdots\!92$$ T^{6} + $$53\!\cdots\!70$$ T^{8} - $$69\!\cdots\!08$$ T^{10} + $$71\!\cdots\!72$$ T^{12} - $$54\!\cdots\!56$$ T^{14} + $$21\!\cdots\!01$$ T^{16} $)($ 1 - 854218268 T^{2} + 379569874740918830 T^{4} - $$11\!\cdots\!80$$ T^{6} + $$26\!\cdots\!71$$ T^{8} - $$50\!\cdots\!20$$ T^{10} + $$79\!\cdots\!96$$ T^{12} - $$10\!\cdots\!80$$ T^{14} + $$12\!\cdots\!71$$ T^{16} - $$11\!\cdots\!20$$ T^{18} + $$82\!\cdots\!30$$ T^{20} - $$40\!\cdots\!32$$ T^{22} + $$10\!\cdots\!01$$ T^{24} $)($ 1 - 854218268 T^{2} + 379569874740918830 T^{4} - $$11\!\cdots\!80$$ T^{6} + $$26\!\cdots\!71$$ T^{8} - $$50\!\cdots\!20$$ T^{10} + $$79\!\cdots\!96$$ T^{12} - $$10\!\cdots\!80$$ T^{14} + $$12\!\cdots\!71$$ T^{16} - $$11\!\cdots\!20$$ T^{18} + $$82\!\cdots\!30$$ T^{20} - $$40\!\cdots\!32$$ T^{22} + $$10\!\cdots\!01$$ T^{24} $)($ ( 1 + 147008443 T^{2} )^{4} $)($ ( 1 - 72715480 T^{2} + 21611482313284249 T^{4} )^{4} $)($ ( 1 + 515310072 T^{2} + 108506205300479794 T^{4} + $$11\!\cdots\!28$$ T^{6} + $$46\!\cdots\!01$$ T^{8} )^{4} $)
$47$	($ 1 + 24738 T + 229345007 T^{2} $)($ 1 - 6588 T + 229345007 T^{2} $)($ 1 - 16146 T + 229345007 T^{2} $)($ 1 + 12074 T + 229345007 T^{2} $)($ 1 - 9796 T + 229345007 T^{2} $)($ 1 - 13122 T + 229345007 T^{2} $)($ 1 - 12088 T + 229345007 T^{2} $)($ 1 - 28294 T + 229345007 T^{2} $)($ 1 + 28294 T + 229345007 T^{2} $)($ 1 + 12088 T + 229345007 T^{2} $)($ 1 + 13122 T + 229345007 T^{2} $)($ 1 + 9796 T + 229345007 T^{2} $)($ 1 - 12074 T + 229345007 T^{2} $)($ 1 + 16146 T + 229345007 T^{2} $)($ 1 + 6588 T + 229345007 T^{2} $)($ 1 - 24738 T + 229345007 T^{2} $)($ 1 - 2908 T + 56660030 T^{2} - 666935280356 T^{3} + 52599132235830049 T^{4} $)($ 1 - 28296 T + 617782998 T^{2} - 6489546318072 T^{3} + 52599132235830049 T^{4} $)($ 1 + 422513974 T^{2} + 52599132235830049 T^{4} $)($ 1 + 403777034 T^{2} + 52599132235830049 T^{4} $)($ 1 + 442383274 T^{2} + 52599132235830049 T^{4} $)($ 1 + 28296 T + 617782998 T^{2} + 6489546318072 T^{3} + 52599132235830049 T^{4} $)($ 1 + 2908 T + 56660030 T^{2} + 666935280356 T^{3} + 52599132235830049 T^{4} $)($ 1 - 36762 T + 1119958377 T^{2} - 18490559326820 T^{3} + 256856861812773639 T^{4} - $$19\!\cdots\!38$$ T^{5} + $$12\!\cdots\!43$$ T^{6} $)($ 1 + 36762 T + 1119958377 T^{2} + 18490559326820 T^{3} + 256856861812773639 T^{4} + $$19\!\cdots\!38$$ T^{5} + $$12\!\cdots\!43$$ T^{6} $)($ 1 + 353765740 T^{2} + 66158288717340582 T^{4} + $$18\!\cdots\!60$$ T^{6} + $$27\!\cdots\!01$$ T^{8} $)($ 1 - 344584890 T^{2} + 52599132235830049 T^{4} $)($ 1 - 344584890 T^{2} + 52599132235830049 T^{4} $)($ ( 1 - 229345007 T^{2} )^{2} $)($ 1 - 369731298 T^{2} + 52599132235830049 T^{4} $)($ 1 - 369731298 T^{2} + 52599132235830049 T^{4} $)($ 1 - 347593490 T^{2} + 52599132235830049 T^{4} $)($ 1 - 347593490 T^{2} + 52599132235830049 T^{4} $)($ ( 1 - 33334 T + 555577778 T^{2} - 7644986463338 T^{3} + 52599132235830049 T^{4} )( 1 + 33334 T + 555577778 T^{2} + 7644986463338 T^{3} + 52599132235830049 T^{4} ) $)($ 1 - 963352312 T^{2} + 473832864723586300 T^{4} - $$15\!\cdots\!72$$ T^{6} + $$40\!\cdots\!54$$ T^{8} - $$83\!\cdots\!28$$ T^{10} + $$13\!\cdots\!00$$ T^{12} - $$14\!\cdots\!88$$ T^{14} + $$76\!\cdots\!01$$ T^{16} $)($ 1 - 963352312 T^{2} + 473832864723586300 T^{4} - $$15\!\cdots\!72$$ T^{6} + $$40\!\cdots\!54$$ T^{8} - $$83\!\cdots\!28$$ T^{10} + $$13\!\cdots\!00$$ T^{12} - $$14\!\cdots\!88$$ T^{14} + $$76\!\cdots\!01$$ T^{16} $)($ ( 1 - 579920494 T^{2} + 165136673035562991 T^{4} - $$38\!\cdots\!48$$ T^{6} + $$86\!\cdots\!59$$ T^{8} - $$16\!\cdots\!94$$ T^{10} + $$14\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 764642190 T^{2} + 310900354010297967 T^{4} - $$85\!\cdots\!20$$ T^{6} + $$16\!\cdots\!83$$ T^{8} - $$21\!\cdots\!90$$ T^{10} + $$14\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 23840 T + 811201148 T^{2} - 13600000745040 T^{3} + 275458842496788474 T^{4} - $$31\!\cdots\!80$$ T^{5} + $$42\!\cdots\!52$$ T^{6} - $$28\!\cdots\!20$$ T^{7} + $$27\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 23840 T + 811201148 T^{2} + 13600000745040 T^{3} + 275458842496788474 T^{4} + $$31\!\cdots\!80$$ T^{5} + $$42\!\cdots\!52$$ T^{6} + $$28\!\cdots\!20$$ T^{7} + $$27\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 10586 T + 559351288 T^{2} + 141995130734 T^{3} + 85696824820019915 T^{4} - $$20\!\cdots\!52$$ T^{5} + $$41\!\cdots\!80$$ T^{6} - $$45\!\cdots\!64$$ T^{7} + $$45\!\cdots\!35$$ T^{8} + $$17\!\cdots\!62$$ T^{9} + $$15\!\cdots\!88$$ T^{10} + $$67\!\cdots\!02$$ T^{11} + $$14\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 10586 T + 559351288 T^{2} - 141995130734 T^{3} + 85696824820019915 T^{4} + $$20\!\cdots\!52$$ T^{5} + $$41\!\cdots\!80$$ T^{6} + $$45\!\cdots\!64$$ T^{7} + $$45\!\cdots\!35$$ T^{8} - $$17\!\cdots\!62$$ T^{9} + $$15\!\cdots\!88$$ T^{10} - $$67\!\cdots\!02$$ T^{11} + $$14\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 222705514 T^{2} + 52599132235830049 T^{4} )^{2} $)($ ( 1 - 453462436 T^{2} + 52599132235830049 T^{4} )^{4} $)($ ( 1 - 112031408 T^{2} + 100831510268064114 T^{4} - $$58\!\cdots\!92$$ T^{6} + $$27\!\cdots\!01$$ T^{8} )^{4} $)
$53$	($ 1 - 14166 T + 418195493 T^{2} $)($ 1 - 21066 T + 418195493 T^{2} $)($ 1 - 4374 T + 418195493 T^{2} $)($ 1 + 32586 T + 418195493 T^{2} $)($ 1 - 31434 T + 418195493 T^{2} $)($ 1 - 9174 T + 418195493 T^{2} $)($ 1 + 23846 T + 418195493 T^{2} $)($ 1 - 13046 T + 418195493 T^{2} $)($ 1 - 13046 T + 418195493 T^{2} $)($ 1 + 23846 T + 418195493 T^{2} $)($ 1 - 9174 T + 418195493 T^{2} $)($ 1 - 31434 T + 418195493 T^{2} $)($ 1 + 32586 T + 418195493 T^{2} $)($ 1 - 4374 T + 418195493 T^{2} $)($ 1 - 21066 T + 418195493 T^{2} $)($ 1 - 14166 T + 418195493 T^{2} $)($ 1 - 5412 T + 693247822 T^{2} - 2263274008116 T^{3} + 174887470365513049 T^{4} $)($ 1 + 31340 T + 755347886 T^{2} + 13106246750620 T^{3} + 174887470365513049 T^{4} $)($ ( 1 - 18154 T + 418195493 T^{2} )^{2} $)($ ( 1 + 32226 T + 418195493 T^{2} )^{2} $)($ ( 1 - 15486 T + 418195493 T^{2} )^{2} $)($ 1 + 31340 T + 755347886 T^{2} + 13106246750620 T^{3} + 174887470365513049 T^{4} $)($ 1 - 5412 T + 693247822 T^{2} - 2263274008116 T^{3} + 174887470365513049 T^{4} $)($ 1 - 21162 T + 395789499 T^{2} + 881498066468 T^{3} + 165517384658528007 T^{4} - $$37\!\cdots\!38$$ T^{5} + $$73\!\cdots\!57$$ T^{6} $)($ 1 - 21162 T + 395789499 T^{2} + 881498066468 T^{3} + 165517384658528007 T^{4} - $$37\!\cdots\!38$$ T^{5} + $$73\!\cdots\!57$$ T^{6} $)($ ( 1 + 8748 T + 833865262 T^{2} + 3658374172764 T^{3} + 174887470365513049 T^{4} )^{2} $)($ 1 - 827605690 T^{2} + 174887470365513049 T^{4} $)($ 1 - 827605690 T^{2} + 174887470365513049 T^{4} $)($ ( 1 - 7294 T + 418195493 T^{2} )( 1 + 7294 T + 418195493 T^{2} ) $)($ 1 - 248174170 T^{2} + 174887470365513049 T^{4} $)($ 1 - 248174170 T^{2} + 174887470365513049 T^{4} $)($ 1 - 802472090 T^{2} + 174887470365513049 T^{4} $)($ 1 - 802472090 T^{2} + 174887470365513049 T^{4} $)($ ( 1 - 418195493 T^{2} )^{4} $)($ 1 - 1183385640 T^{2} + 874785099161623996 T^{4} - $$49\!\cdots\!80$$ T^{6} + $$23\!\cdots\!06$$ T^{8} - $$86\!\cdots\!20$$ T^{10} + $$26\!\cdots\!96$$ T^{12} - $$63\!\cdots\!60$$ T^{14} + $$93\!\cdots\!01$$ T^{16} $)($ 1 - 1183385640 T^{2} + 874785099161623996 T^{4} - $$49\!\cdots\!80$$ T^{6} + $$23\!\cdots\!06$$ T^{8} - $$86\!\cdots\!20$$ T^{10} + $$26\!\cdots\!96$$ T^{12} - $$63\!\cdots\!60$$ T^{14} + $$93\!\cdots\!01$$ T^{16} $)($ ( 1 - 2026325390 T^{2} + 1866514545072595447 T^{4} - $$99\!\cdots\!20$$ T^{6} + $$32\!\cdots\!03$$ T^{8} - $$61\!\cdots\!90$$ T^{10} + $$53\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 1611835534 T^{2} + 1232324270520828407 T^{4} - $$61\!\cdots\!84$$ T^{6} + $$21\!\cdots\!43$$ T^{8} - $$49\!\cdots\!34$$ T^{10} + $$53\!\cdots\!49$$ T^{12} )^{2} $)($ 1 - 984292984 T^{2} + 650040420165524092 T^{4} - $$31\!\cdots\!92$$ T^{6} + $$12\!\cdots\!70$$ T^{8} - $$55\!\cdots\!08$$ T^{10} + $$19\!\cdots\!92$$ T^{12} - $$52\!\cdots\!16$$ T^{14} + $$93\!\cdots\!01$$ T^{16} $)($ 1 - 984292984 T^{2} + 650040420165524092 T^{4} - $$31\!\cdots\!92$$ T^{6} + $$12\!\cdots\!70$$ T^{8} - $$55\!\cdots\!08$$ T^{10} + $$19\!\cdots\!92$$ T^{12} - $$52\!\cdots\!16$$ T^{14} + $$93\!\cdots\!01$$ T^{16} $)($ 1 - 2472111540 T^{2} + 3272109664551065298 T^{4} - $$29\!\cdots\!96$$ T^{6} + $$20\!\cdots\!23$$ T^{8} - $$11\!\cdots\!44$$ T^{10} + $$51\!\cdots\!20$$ T^{12} - $$19\!\cdots\!56$$ T^{14} + $$62\!\cdots\!23$$ T^{16} - $$15\!\cdots\!04$$ T^{18} + $$30\!\cdots\!98$$ T^{20} - $$40\!\cdots\!60$$ T^{22} + $$28\!\cdots\!01$$ T^{24} $)($ 1 - 2472111540 T^{2} + 3272109664551065298 T^{4} - $$29\!\cdots\!96$$ T^{6} + $$20\!\cdots\!23$$ T^{8} - $$11\!\cdots\!44$$ T^{10} + $$51\!\cdots\!20$$ T^{12} - $$19\!\cdots\!56$$ T^{14} + $$62\!\cdots\!23$$ T^{16} - $$15\!\cdots\!04$$ T^{18} + $$30\!\cdots\!98$$ T^{20} - $$40\!\cdots\!60$$ T^{22} + $$28\!\cdots\!01$$ T^{24} $)($ ( 1 + 552886486 T^{2} + 174887470365513049 T^{4} )^{2} $)($ ( 1 + 539491786 T^{2} + 174887470365513049 T^{4} )^{4} $)($ ( 1 + 823212052 T^{2} + 458582260389137174 T^{4} + $$14\!\cdots\!48$$ T^{6} + $$30\!\cdots\!01$$ T^{8} )^{4} $)
$59$	($ 1 - 28380 T + 714924299 T^{2} $)($ 1 + 7980 T + 714924299 T^{2} $)($ 1 - 11748 T + 714924299 T^{2} $)($ 1 - 8668 T + 714924299 T^{2} $)($ 1 - 33228 T + 714924299 T^{2} $)($ 1 - 34980 T + 714924299 T^{2} $)($ 1 + 20020 T + 714924299 T^{2} $)($ 1 + 37092 T + 714924299 T^{2} $)($ 1 - 37092 T + 714924299 T^{2} $)($ 1 - 20020 T + 714924299 T^{2} $)($ 1 + 34980 T + 714924299 T^{2} $)($ 1 + 33228 T + 714924299 T^{2} $)($ 1 + 8668 T + 714924299 T^{2} $)($ 1 + 11748 T + 714924299 T^{2} $)($ 1 - 7980 T + 714924299 T^{2} $)($ 1 + 28380 T + 714924299 T^{2} $)($ 1 - 62584 T + 2277965606 T^{2} - 44742822328616 T^{3} + 511116753300641401 T^{4} $)($ 1 + 30800 T + 1666896598 T^{2} + 22019668409200 T^{3} + 511116753300641401 T^{4} $)($ 1 + 1041470358 T^{2} + 511116753300641401 T^{4} $)($ 1 + 270997718 T^{2} + 511116753300641401 T^{4} $)($ 1 + 1376531158 T^{2} + 511116753300641401 T^{4} $)($ 1 - 30800 T + 1666896598 T^{2} - 22019668409200 T^{3} + 511116753300641401 T^{4} $)($ 1 + 62584 T + 2277965606 T^{2} + 44742822328616 T^{3} + 511116753300641401 T^{4} $)($ 1 + 35040 T + 1757220897 T^{2} + 50989349593920 T^{3} + 1256279917975876203 T^{4} + $$17\!\cdots\!40$$ T^{5} + $$36\!\cdots\!99$$ T^{6} $)($ 1 - 35040 T + 1757220897 T^{2} - 50989349593920 T^{3} + 1256279917975876203 T^{4} - $$17\!\cdots\!40$$ T^{5} + $$36\!\cdots\!99$$ T^{6} $)($ 1 + 488747308 T^{2} + 896846029819225302 T^{4} + $$24\!\cdots\!08$$ T^{6} + $$26\!\cdots\!01$$ T^{8} $)($ ( 1 - 39740 T + 714924299 T^{2} )^{2} $)($ ( 1 + 39740 T + 714924299 T^{2} )^{2} $)($ ( 1 + 714924299 T^{2} )^{2} $)($ ( 1 + 25972 T + 714924299 T^{2} )^{2} $)($ ( 1 - 25972 T + 714924299 T^{2} )^{2} $)($ ( 1 - 24660 T + 714924299 T^{2} )^{2} $)($ ( 1 + 24660 T + 714924299 T^{2} )^{2} $)($ ( 1 + 714924299 T^{2} )^{4} $)($ ( 1 - 45840 T + 3064286732 T^{2} - 94721285480976 T^{3} + 3348109683185502486 T^{4} - $$67\!\cdots\!24$$ T^{5} + $$15\!\cdots\!32$$ T^{6} - $$16\!\cdots\!60$$ T^{7} + $$26\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 45840 T + 3064286732 T^{2} + 94721285480976 T^{3} + 3348109683185502486 T^{4} + $$67\!\cdots\!24$$ T^{5} + $$15\!\cdots\!32$$ T^{6} + $$16\!\cdots\!60$$ T^{7} + $$26\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 55950786 T^{2} + 253972763776609047 T^{4} - $$45\!\cdots\!68$$ T^{6} + $$12\!\cdots\!47$$ T^{8} + $$14\!\cdots\!86$$ T^{10} + $$13\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 + 2333761794 T^{2} + 3044701823751957015 T^{4} + $$26\!\cdots\!80$$ T^{6} + $$15\!\cdots\!15$$ T^{8} + $$60\!\cdots\!94$$ T^{10} + $$13\!\cdots\!01$$ T^{12} )^{2} $)($ 1 - 3042039688 T^{2} + 4949915655184301308 T^{4} - $$54\!\cdots\!56$$ T^{6} + $$44\!\cdots\!70$$ T^{8} - $$27\!\cdots\!56$$ T^{10} + $$12\!\cdots\!08$$ T^{12} - $$40\!\cdots\!88$$ T^{14} + $$68\!\cdots\!01$$ T^{16} $)($ 1 - 3042039688 T^{2} + 4949915655184301308 T^{4} - $$54\!\cdots\!56$$ T^{6} + $$44\!\cdots\!70$$ T^{8} - $$27\!\cdots\!56$$ T^{10} + $$12\!\cdots\!08$$ T^{12} - $$40\!\cdots\!88$$ T^{14} + $$68\!\cdots\!01$$ T^{16} $)($ 1 - 3285269100 T^{2} + 3759201793217414610 T^{4} - $$13\!\cdots\!44$$ T^{6} + $$12\!\cdots\!35$$ T^{8} - $$13\!\cdots\!20$$ T^{10} + $$18\!\cdots\!36$$ T^{12} - $$70\!\cdots\!20$$ T^{14} + $$33\!\cdots\!35$$ T^{16} - $$18\!\cdots\!44$$ T^{18} + $$25\!\cdots\!10$$ T^{20} - $$11\!\cdots\!00$$ T^{22} + $$17\!\cdots\!01$$ T^{24} $)($ 1 - 3285269100 T^{2} + 3759201793217414610 T^{4} - $$13\!\cdots\!44$$ T^{6} + $$12\!\cdots\!35$$ T^{8} - $$13\!\cdots\!20$$ T^{10} + $$18\!\cdots\!36$$ T^{12} - $$70\!\cdots\!20$$ T^{14} + $$33\!\cdots\!35$$ T^{16} - $$18\!\cdots\!44$$ T^{18} + $$25\!\cdots\!10$$ T^{20} - $$11\!\cdots\!00$$ T^{22} + $$17\!\cdots\!01$$ T^{24} $)($ ( 1 - 646632402 T^{2} + 511116753300641401 T^{4} )^{2} $)($ ( 1 - 1161609714 T^{2} + 511116753300641401 T^{4} )^{4} $)($ ( 1 - 2409567364 T^{2} + 2462718757251169526 T^{4} - $$12\!\cdots\!64$$ T^{6} + $$26\!\cdots\!01$$ T^{8} )^{4} $)
$61$	($ 1 + 5522 T + 844596301 T^{2} $)($ 1 + 16622 T + 844596301 T^{2} $)($ 1 + 13202 T + 844596301 T^{2} $)($ 1 - 34670 T + 844596301 T^{2} $)($ 1 - 40210 T + 844596301 T^{2} $)($ 1 - 9838 T + 844596301 T^{2} $)($ 1 + 32302 T + 844596301 T^{2} $)($ 1 + 39570 T + 844596301 T^{2} $)($ 1 + 39570 T + 844596301 T^{2} $)($ 1 + 32302 T + 844596301 T^{2} $)($ 1 - 9838 T + 844596301 T^{2} $)($ 1 - 40210 T + 844596301 T^{2} $)($ 1 - 34670 T + 844596301 T^{2} $)($ 1 + 13202 T + 844596301 T^{2} $)($ 1 + 16622 T + 844596301 T^{2} $)($ 1 + 5522 T + 844596301 T^{2} $)($ 1 + 14108 T + 1110042462 T^{2} + 11915564614508 T^{3} + 713342911662882601 T^{4} $)($ 1 + 24540 T + 1447225822 T^{2} + 20726393226540 T^{3} + 713342911662882601 T^{4} $)($ ( 1 - 42130 T + 844596301 T^{2} )^{2} $)($ ( 1 + 26770 T + 844596301 T^{2} )^{2} $)($ ( 1 - 16750 T + 844596301 T^{2} )^{2} $)($ 1 + 24540 T + 1447225822 T^{2} + 20726393226540 T^{3} + 713342911662882601 T^{4} $)($ 1 + 14108 T + 1110042462 T^{2} + 11915564614508 T^{3} + 713342911662882601 T^{4} $)($ 1 - 24138 T + 393086643 T^{2} + 6904061162564 T^{3} + 331999524650307543 T^{4} - $$17\!\cdots\!38$$ T^{5} + $$60\!\cdots\!01$$ T^{6} $)($ 1 - 24138 T + 393086643 T^{2} + 6904061162564 T^{3} + 331999524650307543 T^{4} - $$17\!\cdots\!38$$ T^{5} + $$60\!\cdots\!01$$ T^{6} $)($ ( 1 - 31012 T + 1250446302 T^{2} - 26192620486612 T^{3} + 713342911662882601 T^{4} )^{2} $)($ ( 1 - 42298 T + 844596301 T^{2} )^{2} $)($ ( 1 - 42298 T + 844596301 T^{2} )^{2} $)($ ( 1 - 18950 T + 844596301 T^{2} )^{2} $)($ ( 1 - 3058 T + 844596301 T^{2} )^{2} $)($ ( 1 - 3058 T + 844596301 T^{2} )^{2} $)($ ( 1 - 5698 T + 844596301 T^{2} )^{2} $)($ ( 1 - 5698 T + 844596301 T^{2} )^{2} $)($ ( 1 - 1041591898 T^{2} + 713342911662882601 T^{4} )^{2} $)($ ( 1 + 61928 T + 3903014764 T^{2} + 145287706763384 T^{3} + 5198153942066716726 T^{4} + $$12\!\cdots\!84$$ T^{5} + $$27\!\cdots\!64$$ T^{6} + $$37\!\cdots\!28$$ T^{7} + $$50\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 61928 T + 3903014764 T^{2} + 145287706763384 T^{3} + 5198153942066716726 T^{4} + $$12\!\cdots\!84$$ T^{5} + $$27\!\cdots\!64$$ T^{6} + $$37\!\cdots\!28$$ T^{7} + $$50\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 16138 T + 744681843 T^{2} + 29097452426876 T^{3} + 628955530019662743 T^{4} + $$11\!\cdots\!38$$ T^{5} + $$60\!\cdots\!01$$ T^{6} )^{4} $)($ ( 1 - 29558 T + 2350852083 T^{2} - 48603849831556 T^{3} + 1985520973499944983 T^{4} - $$21\!\cdots\!58$$ T^{5} + $$60\!\cdots\!01$$ T^{6} )^{4} $)($ 1 - 2582224408 T^{2} + 4867570283316136828 T^{4} - $$60\!\cdots\!56$$ T^{6} + $$59\!\cdots\!70$$ T^{8} - $$42\!\cdots\!56$$ T^{10} + $$24\!\cdots\!28$$ T^{12} - $$93\!\cdots\!08$$ T^{14} + $$25\!\cdots\!01$$ T^{16} $)($ 1 - 2582224408 T^{2} + 4867570283316136828 T^{4} - $$60\!\cdots\!56$$ T^{6} + $$59\!\cdots\!70$$ T^{8} - $$42\!\cdots\!56$$ T^{10} + $$24\!\cdots\!28$$ T^{12} - $$93\!\cdots\!08$$ T^{14} + $$25\!\cdots\!01$$ T^{16} $)($ 1 - 9275968036 T^{2} + 40037810273961512978 T^{4} - $$10\!\cdots\!60$$ T^{6} + $$19\!\cdots\!03$$ T^{8} - $$25\!\cdots\!00$$ T^{10} + $$24\!\cdots\!52$$ T^{12} - $$18\!\cdots\!00$$ T^{14} + $$98\!\cdots\!03$$ T^{16} - $$38\!\cdots\!60$$ T^{18} + $$10\!\cdots\!78$$ T^{20} - $$17\!\cdots\!36$$ T^{22} + $$13\!\cdots\!01$$ T^{24} $)($ 1 - 9275968036 T^{2} + 40037810273961512978 T^{4} - $$10\!\cdots\!60$$ T^{6} + $$19\!\cdots\!03$$ T^{8} - $$25\!\cdots\!00$$ T^{10} + $$24\!\cdots\!52$$ T^{12} - $$18\!\cdots\!00$$ T^{14} + $$98\!\cdots\!03$$ T^{16} - $$38\!\cdots\!60$$ T^{18} + $$10\!\cdots\!78$$ T^{20} - $$17\!\cdots\!36$$ T^{22} + $$13\!\cdots\!01$$ T^{24} $)($ ( 1 - 844596301 T^{2} )^{4} $)($ ( 1 + 686048530 T^{2} + 713342911662882601 T^{4} )^{4} $)($ ( 1 - 2000262204 T^{2} + 2103804668157499606 T^{4} - $$14\!\cdots\!04$$ T^{6} + $$50\!\cdots\!01$$ T^{8} )^{4} $)
$67$	($ 1 + 24742 T + 1350125107 T^{2} $)($ 1 + 1808 T + 1350125107 T^{2} $)($ 1 - 11542 T + 1350125107 T^{2} $)($ 1 + 47566 T + 1350125107 T^{2} $)($ 1 - 58864 T + 1350125107 T^{2} $)($ 1 + 33722 T + 1350125107 T^{2} $)($ 1 - 60972 T + 1350125107 T^{2} $)($ 1 + 56734 T + 1350125107 T^{2} $)($ 1 - 56734 T + 1350125107 T^{2} $)($ 1 + 60972 T + 1350125107 T^{2} $)($ 1 - 33722 T + 1350125107 T^{2} $)($ 1 + 58864 T + 1350125107 T^{2} $)($ 1 - 47566 T + 1350125107 T^{2} $)($ 1 + 11542 T + 1350125107 T^{2} $)($ 1 - 1808 T + 1350125107 T^{2} $)($ 1 - 24742 T + 1350125107 T^{2} $)($ 1 + 85412 T + 4371910566 T^{2} + 115316885639084 T^{3} + 1822837804551761449 T^{4} $)($ 1 + 34584 T + 2930656478 T^{2} + 46692726700488 T^{3} + 1822837804551761449 T^{4} $)($ 1 + 2438310974 T^{2} + 1822837804551761449 T^{4} $)($ 1 + 219594834 T^{2} + 1822837804551761449 T^{4} $)($ 1 + 2513562674 T^{2} + 1822837804551761449 T^{4} $)($ 1 - 34584 T + 2930656478 T^{2} - 46692726700488 T^{3} + 1822837804551761449 T^{4} $)($ 1 - 85412 T + 4371910566 T^{2} - 115316885639084 T^{3} + 1822837804551761449 T^{4} $)($ 1 - 9570 T + 659335509 T^{2} - 83080838420484 T^{3} + 890185424637524463 T^{4} - $$17\!\cdots\!30$$ T^{5} + $$24\!\cdots\!43$$ T^{6} $)($ 1 + 9570 T + 659335509 T^{2} + 83080838420484 T^{3} + 890185424637524463 T^{4} + $$17\!\cdots\!30$$ T^{5} + $$24\!\cdots\!43$$ T^{6} $)($ 1 + 3336863100 T^{2} + 6361754088145172822 T^{4} + $$60\!\cdots\!00$$ T^{6} + $$33\!\cdots\!01$$ T^{8} $)($ 1 - 1669968610 T^{2} + 1822837804551761449 T^{4} $)($ 1 - 1669968610 T^{2} + 1822837804551761449 T^{4} $)($ ( 1 - 1350125107 T^{2} )^{2} $)($ 1 + 755362070 T^{2} + 1822837804551761449 T^{4} $)($ 1 + 755362070 T^{2} + 1822837804551761449 T^{4} $)($ 1 - 795787610 T^{2} + 1822837804551761449 T^{4} $)($ 1 - 795787610 T^{2} + 1822837804551761449 T^{4} $)($ ( 1 - 100434 T + 5043494178 T^{2} - 135598464996438 T^{3} + 1822837804551761449 T^{4} )( 1 + 100434 T + 5043494178 T^{2} + 135598464996438 T^{3} + 1822837804551761449 T^{4} ) $)($ 1 - 9281919064 T^{2} + 39492482666681482588 T^{4} - $$10\!\cdots\!40$$ T^{6} + $$16\!\cdots\!62$$ T^{8} - $$18\!\cdots\!60$$ T^{10} + $$13\!\cdots\!88$$ T^{12} - $$56\!\cdots\!36$$ T^{14} + $$11\!\cdots\!01$$ T^{16} $)($ 1 - 9281919064 T^{2} + 39492482666681482588 T^{4} - $$10\!\cdots\!40$$ T^{6} + $$16\!\cdots\!62$$ T^{8} - $$18\!\cdots\!60$$ T^{10} + $$13\!\cdots\!88$$ T^{12} - $$56\!\cdots\!36$$ T^{14} + $$11\!\cdots\!01$$ T^{16} $)($ ( 1 - 2173336374 T^{2} + 6882868324909910631 T^{4} - $$82\!\cdots\!68$$ T^{6} + $$12\!\cdots\!19$$ T^{8} - $$72\!\cdots\!74$$ T^{10} + $$60\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 3741380758 T^{2} + 9572756841213379047 T^{4} - $$14\!\cdots\!84$$ T^{6} + $$17\!\cdots\!03$$ T^{8} - $$12\!\cdots\!58$$ T^{10} + $$60\!\cdots\!49$$ T^{12} )^{2} $)($ 1 - 7537851704 T^{2} + 25204334234273950564 T^{4} - $$51\!\cdots\!16$$ T^{6} + $$78\!\cdots\!94$$ T^{8} - $$94\!\cdots\!84$$ T^{10} + $$83\!\cdots\!64$$ T^{12} - $$45\!\cdots\!96$$ T^{14} + $$11\!\cdots\!01$$ T^{16} $)($ 1 - 7537851704 T^{2} + 25204334234273950564 T^{4} - $$51\!\cdots\!16$$ T^{6} + $$78\!\cdots\!94$$ T^{8} - $$94\!\cdots\!84$$ T^{10} + $$83\!\cdots\!64$$ T^{12} - $$45\!\cdots\!96$$ T^{14} + $$11\!\cdots\!01$$ T^{16} $)($ 1 - 7932747836 T^{2} + 31498024738605168590 T^{4} - $$85\!\cdots\!12$$ T^{6} + $$17\!\cdots\!55$$ T^{8} - $$30\!\cdots\!40$$ T^{10} + $$44\!\cdots\!12$$ T^{12} - $$55\!\cdots\!60$$ T^{14} + $$59\!\cdots\!55$$ T^{16} - $$51\!\cdots\!88$$ T^{18} + $$34\!\cdots\!90$$ T^{20} - $$15\!\cdots\!64$$ T^{22} + $$36\!\cdots\!01$$ T^{24} $)($ 1 - 7932747836 T^{2} + 31498024738605168590 T^{4} - $$85\!\cdots\!12$$ T^{6} + $$17\!\cdots\!55$$ T^{8} - $$30\!\cdots\!40$$ T^{10} + $$44\!\cdots\!12$$ T^{12} - $$55\!\cdots\!60$$ T^{14} + $$59\!\cdots\!55$$ T^{16} - $$51\!\cdots\!88$$ T^{18} + $$34\!\cdots\!90$$ T^{20} - $$15\!\cdots\!64$$ T^{22} + $$36\!\cdots\!01$$ T^{24} $)($ ( 1 + 1350125107 T^{2} )^{4} $)($ ( 1 + 2629714328 T^{2} + 1822837804551761449 T^{4} )^{4} $)($ ( 1 + 3461519512 T^{2} + 6000732802449327570 T^{4} + $$63\!\cdots\!88$$ T^{6} + $$33\!\cdots\!01$$ T^{8} )^{4} $)
$71$	($ 1 + 42372 T + 1804229351 T^{2} $)($ 1 + 24528 T + 1804229351 T^{2} $)($ 1 + 29532 T + 1804229351 T^{2} $)($ 1 + 948 T + 1804229351 T^{2} $)($ 1 - 55312 T + 1804229351 T^{2} $)($ 1 - 70212 T + 1804229351 T^{2} $)($ 1 - 32648 T + 1804229351 T^{2} $)($ 1 + 45588 T + 1804229351 T^{2} $)($ 1 - 45588 T + 1804229351 T^{2} $)($ 1 + 32648 T + 1804229351 T^{2} $)($ 1 + 70212 T + 1804229351 T^{2} $)($ 1 + 55312 T + 1804229351 T^{2} $)($ 1 - 948 T + 1804229351 T^{2} $)($ 1 - 29532 T + 1804229351 T^{2} $)($ 1 - 24528 T + 1804229351 T^{2} $)($ 1 - 42372 T + 1804229351 T^{2} $)($ 1 + 47208 T + 4011779662 T^{2} + 85174059202008 T^{3} + 3255243551009881201 T^{4} $)($ 1 + 12400 T + 1143670702 T^{2} + 22372443952400 T^{3} + 3255243551009881201 T^{4} $)($ 1 + 1542914862 T^{2} + 3255243551009881201 T^{4} $)($ 1 + 681226622 T^{2} + 3255243551009881201 T^{4} $)($ 1 + 1737195262 T^{2} + 3255243551009881201 T^{4} $)($ 1 - 12400 T + 1143670702 T^{2} - 22372443952400 T^{3} + 3255243551009881201 T^{4} $)($ 1 - 47208 T + 4011779662 T^{2} - 85174059202008 T^{3} + 3255243551009881201 T^{4} $)($ 1 - 88092 T + 7289446053 T^{2} - 329541325840584 T^{3} + 13151832521353701603 T^{4} - $$28\!\cdots\!92$$ T^{5} + $$58\!\cdots\!51$$ T^{6} $)($ 1 + 88092 T + 7289446053 T^{2} + 329541325840584 T^{3} + 13151832521353701603 T^{4} + $$28\!\cdots\!92$$ T^{5} + $$58\!\cdots\!51$$ T^{6} $)($ 1 + 6374750812 T^{2} + 16622748841310481702 T^{4} + $$20\!\cdots\!12$$ T^{6} + $$10\!\cdots\!01$$ T^{8} $)($ ( 1 - 4248 T + 1804229351 T^{2} )^{2} $)($ ( 1 + 4248 T + 1804229351 T^{2} )^{2} $)($ ( 1 + 1804229351 T^{2} )^{2} $)($ ( 1 + 37608 T + 1804229351 T^{2} )^{2} $)($ ( 1 - 37608 T + 1804229351 T^{2} )^{2} $)($ ( 1 - 53352 T + 1804229351 T^{2} )^{2} $)($ ( 1 + 53352 T + 1804229351 T^{2} )^{2} $)($ ( 1 + 1804229351 T^{2} )^{4} $)($ ( 1 - 62816 T + 3398787356 T^{2} - 184024084124896 T^{3} + 8353296562609817510 T^{4} - $$33\!\cdots\!96$$ T^{5} + $$11\!\cdots\!56$$ T^{6} - $$36\!\cdots\!16$$ T^{7} + $$10\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 62816 T + 3398787356 T^{2} + 184024084124896 T^{3} + 8353296562609817510 T^{4} + $$33\!\cdots\!96$$ T^{5} + $$11\!\cdots\!56$$ T^{6} + $$36\!\cdots\!16$$ T^{7} + $$10\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 942628714 T^{2} + 4622069102042239647 T^{4} + $$48\!\cdots\!68$$ T^{6} + $$15\!\cdots\!47$$ T^{8} + $$99\!\cdots\!14$$ T^{10} + $$34\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 + 9793576042 T^{2} + 41626938509482688159 T^{4} + $$98\!\cdots\!36$$ T^{6} + $$13\!\cdots\!59$$ T^{8} + $$10\!\cdots\!42$$ T^{10} + $$34\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 - 123360 T + 10006413404 T^{2} - 529309926298080 T^{3} + 24936343678058479206 T^{4} - $$95\!\cdots\!80$$ T^{5} + $$32\!\cdots\!04$$ T^{6} - $$72\!\cdots\!60$$ T^{7} + $$10\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 123360 T + 10006413404 T^{2} + 529309926298080 T^{3} + 24936343678058479206 T^{4} + $$95\!\cdots\!80$$ T^{5} + $$32\!\cdots\!04$$ T^{6} + $$72\!\cdots\!60$$ T^{7} + $$10\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 183852 T + 22719949218 T^{2} + 1935102444145668 T^{3} + $$13\!\cdots\!79$$ T^{4} + $$73\!\cdots\!52$$ T^{5} + $$34\!\cdots\!16$$ T^{6} + $$13\!\cdots\!52$$ T^{7} + $$43\!\cdots\!79$$ T^{8} + $$11\!\cdots\!68$$ T^{9} + $$24\!\cdots\!18$$ T^{10} + $$35\!\cdots\!52$$ T^{11} + $$34\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 - 183852 T + 22719949218 T^{2} - 1935102444145668 T^{3} + $$13\!\cdots\!79$$ T^{4} - $$73\!\cdots\!52$$ T^{5} + $$34\!\cdots\!16$$ T^{6} - $$13\!\cdots\!52$$ T^{7} + $$43\!\cdots\!79$$ T^{8} - $$11\!\cdots\!68$$ T^{9} + $$24\!\cdots\!18$$ T^{10} - $$35\!\cdots\!52$$ T^{11} + $$34\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 + 1804229351 T^{2} )^{4} $)($ ( 1 + 2762141854 T^{2} + 3255243551009881201 T^{4} )^{4} $)($ ( 1 + 823411004 T^{2} + 3069578968927394406 T^{4} + $$26\!\cdots\!04$$ T^{6} + $$10\!\cdots\!01$$ T^{8} )^{4} $)
$73$	($ 1 + 52126 T + 2073071593 T^{2} $)($ 1 - 20474 T + 2073071593 T^{2} $)($ 1 - 33698 T + 2073071593 T^{2} $)($ 1 + 63102 T + 2073071593 T^{2} $)($ 1 - 27258 T + 2073071593 T^{2} $)($ 1 - 21986 T + 2073071593 T^{2} $)($ 1 + 38774 T + 2073071593 T^{2} $)($ 1 - 11842 T + 2073071593 T^{2} $)($ 1 - 11842 T + 2073071593 T^{2} $)($ 1 + 38774 T + 2073071593 T^{2} $)($ 1 - 21986 T + 2073071593 T^{2} $)($ 1 - 27258 T + 2073071593 T^{2} $)($ 1 + 63102 T + 2073071593 T^{2} $)($ 1 - 33698 T + 2073071593 T^{2} $)($ 1 - 20474 T + 2073071593 T^{2} $)($ 1 + 52126 T + 2073071593 T^{2} $)($ 1 + 67452 T + 4400780438 T^{2} + 139832825091036 T^{3} + 4297625829703557649 T^{4} $)($ 1 + 7180 T + 284279286 T^{2} + 14884654037740 T^{3} + 4297625829703557649 T^{4} $)($ ( 1 - 26266 T + 2073071593 T^{2} )^{2} $)($ ( 1 + 18534 T + 2073071593 T^{2} )^{2} $)($ ( 1 + 20806 T + 2073071593 T^{2} )^{2} $)($ 1 + 7180 T + 284279286 T^{2} + 14884654037740 T^{3} + 4297625829703557649 T^{4} $)($ 1 + 67452 T + 4400780438 T^{2} + 139832825091036 T^{3} + 4297625829703557649 T^{4} $)($ 1 - 66750 T + 3875077479 T^{2} - 111360074258500 T^{3} + 8033313042388954047 T^{4} - $$28\!\cdots\!50$$ T^{5} + $$89\!\cdots\!57$$ T^{6} $)($ 1 - 66750 T + 3875077479 T^{2} - 111360074258500 T^{3} + 8033313042388954047 T^{4} - $$28\!\cdots\!50$$ T^{5} + $$89\!\cdots\!57$$ T^{6} $)($ ( 1 - 59700 T + 5029368950 T^{2} - 123762374102100 T^{3} + 4297625829703557649 T^{4} )^{2} $)($ 1 - 3239892370 T^{2} + 4297625829703557649 T^{4} $)($ 1 - 3239892370 T^{2} + 4297625829703557649 T^{4} $)($ ( 1 - 88806 T + 2073071593 T^{2} )( 1 + 88806 T + 2073071593 T^{2} ) $)($ 1 - 3569749522 T^{2} + 4297625829703557649 T^{4} $)($ 1 - 3569749522 T^{2} + 4297625829703557649 T^{4} $)($ 1 + 883886830 T^{2} + 4297625829703557649 T^{4} $)($ 1 + 883886830 T^{2} + 4297625829703557649 T^{4} $)($ ( 1 - 2073071593 T^{2} )^{4} $)($ 1 - 9140679496 T^{2} + 46078306824990298588 T^{4} - $$15\!\cdots\!60$$ T^{6} + $$37\!\cdots\!02$$ T^{8} - $$66\!\cdots\!40$$ T^{10} + $$85\!\cdots\!88$$ T^{12} - $$72\!\cdots\!04$$ T^{14} + $$34\!\cdots\!01$$ T^{16} $)($ 1 - 9140679496 T^{2} + 46078306824990298588 T^{4} - $$15\!\cdots\!60$$ T^{6} + $$37\!\cdots\!02$$ T^{8} - $$66\!\cdots\!40$$ T^{10} + $$85\!\cdots\!88$$ T^{12} - $$72\!\cdots\!04$$ T^{14} + $$34\!\cdots\!01$$ T^{16} $)($ ( 1 - 4736672630 T^{2} + 15959781190221205247 T^{4} - $$37\!\cdots\!40$$ T^{6} + $$68\!\cdots\!03$$ T^{8} - $$87\!\cdots\!30$$ T^{10} + $$79\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 5477783158 T^{2} + 15527894807038343935 T^{4} - $$34\!\cdots\!40$$ T^{6} + $$66\!\cdots\!15$$ T^{8} - $$10\!\cdots\!58$$ T^{10} + $$79\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 23200 T + 7007019628 T^{2} - 115342151623520 T^{3} + 20469715216228479110 T^{4} - $$23\!\cdots\!60$$ T^{5} + $$30\!\cdots\!72$$ T^{6} - $$20\!\cdots\!00$$ T^{7} + $$18\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 - 23200 T + 7007019628 T^{2} - 115342151623520 T^{3} + 20469715216228479110 T^{4} - $$23\!\cdots\!60$$ T^{5} + $$30\!\cdots\!72$$ T^{6} - $$20\!\cdots\!00$$ T^{7} + $$18\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 - 29368 T + 4461233378 T^{2} - 258540669925656 T^{3} + 16168785780639245407 T^{4} - $$68\!\cdots\!32$$ T^{5} + $$45\!\cdots\!60$$ T^{6} - $$14\!\cdots\!76$$ T^{7} + $$69\!\cdots\!43$$ T^{8} - $$23\!\cdots\!92$$ T^{9} + $$82\!\cdots\!78$$ T^{10} - $$11\!\cdots\!24$$ T^{11} + $$79\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 29368 T + 4461233378 T^{2} - 258540669925656 T^{3} + 16168785780639245407 T^{4} - $$68\!\cdots\!32$$ T^{5} + $$45\!\cdots\!60$$ T^{6} - $$14\!\cdots\!76$$ T^{7} + $$69\!\cdots\!43$$ T^{8} - $$23\!\cdots\!92$$ T^{9} + $$82\!\cdots\!78$$ T^{10} - $$11\!\cdots\!24$$ T^{11} + $$79\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 2073071593 T^{2} )^{4} $)($ ( 1 - 4145966042 T^{2} + 4297625829703557649 T^{4} )^{4} $)($ ( 1 - 4148991508 T^{2} + 8650887997979942790 T^{4} - $$17\!\cdots\!92$$ T^{6} + $$18\!\cdots\!01$$ T^{8} )^{4} $)
$79$	($ 1 - 39640 T + 3077056399 T^{2} $)($ 1 + 46240 T + 3077056399 T^{2} $)($ 1 - 31208 T + 3077056399 T^{2} $)($ 1 + 46536 T + 3077056399 T^{2} $)($ 1 + 31456 T + 3077056399 T^{2} $)($ 1 - 4520 T + 3077056399 T^{2} $)($ 1 - 33360 T + 3077056399 T^{2} $)($ 1 + 94216 T + 3077056399 T^{2} $)($ 1 - 94216 T + 3077056399 T^{2} $)($ 1 + 33360 T + 3077056399 T^{2} $)($ 1 + 4520 T + 3077056399 T^{2} $)($ 1 - 31456 T + 3077056399 T^{2} $)($ 1 - 46536 T + 3077056399 T^{2} $)($ 1 + 31208 T + 3077056399 T^{2} $)($ 1 - 46240 T + 3077056399 T^{2} $)($ 1 + 39640 T + 3077056399 T^{2} $)($ 1 - 65904 T + 3994274078 T^{2} - 202790324919696 T^{3} + 9468276082626847201 T^{4} $)($ 1 - 71840 T + 7430807198 T^{2} - 221055731704160 T^{3} + 9468276082626847201 T^{4} $)($ 1 + 6078817438 T^{2} + 9468276082626847201 T^{4} $)($ 1 - 1369983522 T^{2} + 9468276082626847201 T^{4} $)($ 1 + 1275471838 T^{2} + 9468276082626847201 T^{4} $)($ 1 + 71840 T + 7430807198 T^{2} + 221055731704160 T^{3} + 9468276082626847201 T^{4} $)($ 1 + 65904 T + 3994274078 T^{2} + 202790324919696 T^{3} + 9468276082626847201 T^{4} $)($ 1 + 92952 T + 11164448877 T^{2} + 573846024396496 T^{3} + 34353638858281213923 T^{4} + $$88\!\cdots\!52$$ T^{5} + $$29\!\cdots\!99$$ T^{6} $)($ 1 - 92952 T + 11164448877 T^{2} - 573846024396496 T^{3} + 34353638858281213923 T^{4} - $$88\!\cdots\!52$$ T^{5} + $$29\!\cdots\!99$$ T^{6} $)($ 1 + 10884258108 T^{2} + 48452581383610561862 T^{4} + $$10\!\cdots\!08$$ T^{6} + $$89\!\cdots\!01$$ T^{8} $)($ ( 1 - 35280 T + 3077056399 T^{2} )^{2} $)($ ( 1 + 35280 T + 3077056399 T^{2} )^{2} $)($ ( 1 + 3077056399 T^{2} )^{2} $)($ ( 1 - 79728 T + 3077056399 T^{2} )^{2} $)($ ( 1 + 79728 T + 3077056399 T^{2} )^{2} $)($ ( 1 - 51920 T + 3077056399 T^{2} )^{2} $)($ ( 1 + 51920 T + 3077056399 T^{2} )^{2} $)($ ( 1 + 3077056399 T^{2} )^{4} $)($ ( 1 + 21632 T + 7152876604 T^{2} + 332616618908288 T^{3} + 24121899620797566790 T^{4} + $$10\!\cdots\!12$$ T^{5} + $$67\!\cdots\!04$$ T^{6} + $$63\!\cdots\!68$$ T^{7} + $$89\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 - 21632 T + 7152876604 T^{2} - 332616618908288 T^{3} + 24121899620797566790 T^{4} - $$10\!\cdots\!12$$ T^{5} + $$67\!\cdots\!04$$ T^{6} - $$63\!\cdots\!68$$ T^{7} + $$89\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 454164826 T^{2} + 18487132928554429487 T^{4} - $$50\!\cdots\!28$$ T^{6} + $$17\!\cdots\!87$$ T^{8} + $$40\!\cdots\!26$$ T^{10} + $$84\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 + 8854539610 T^{2} + 48426464203018517551 T^{4} + $$17\!\cdots\!76$$ T^{6} + $$45\!\cdots\!51$$ T^{8} + $$79\!\cdots\!10$$ T^{10} + $$84\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 - 162880 T + 14181869596 T^{2} - 858599705367360 T^{3} + 48361267115636995206 T^{4} - $$26\!\cdots\!40$$ T^{5} + $$13\!\cdots\!96$$ T^{6} - $$47\!\cdots\!20$$ T^{7} + $$89\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 162880 T + 14181869596 T^{2} + 858599705367360 T^{3} + 48361267115636995206 T^{4} + $$26\!\cdots\!40$$ T^{5} + $$13\!\cdots\!96$$ T^{6} + $$47\!\cdots\!20$$ T^{7} + $$89\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 13096 T + 12178064842 T^{2} - 46215677031496 T^{3} + 67636133741719889263 T^{4} - $$78\!\cdots\!08$$ T^{5} + $$24\!\cdots\!84$$ T^{6} - $$24\!\cdots\!92$$ T^{7} + $$64\!\cdots\!63$$ T^{8} - $$13\!\cdots\!04$$ T^{9} + $$10\!\cdots\!42$$ T^{10} + $$36\!\cdots\!04$$ T^{11} + $$84\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 - 13096 T + 12178064842 T^{2} + 46215677031496 T^{3} + 67636133741719889263 T^{4} + $$78\!\cdots\!08$$ T^{5} + $$24\!\cdots\!84$$ T^{6} + $$24\!\cdots\!92$$ T^{7} + $$64\!\cdots\!63$$ T^{8} + $$13\!\cdots\!04$$ T^{9} + $$10\!\cdots\!42$$ T^{10} - $$36\!\cdots\!04$$ T^{11} + $$84\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 + 3077056399 T^{2} )^{4} $)($ ( 1 + 5182544750 T^{2} + 9468276082626847201 T^{4} )^{4} $)($ ( 1 + 2847963996 T^{2} + 15373907451301926406 T^{4} + $$26\!\cdots\!96$$ T^{6} + $$89\!\cdots\!01$$ T^{8} )^{4} $)
$83$	($ 1 + 59826 T + 3939040643 T^{2} $)($ 1 - 51576 T + 3939040643 T^{2} $)($ 1 - 38466 T + 3939040643 T^{2} $)($ 1 + 88778 T + 3939040643 T^{2} $)($ 1 - 24552 T + 3939040643 T^{2} $)($ 1 - 109074 T + 3939040643 T^{2} $)($ 1 - 16716 T + 3939040643 T^{2} $)($ 1 + 31482 T + 3939040643 T^{2} $)($ 1 - 31482 T + 3939040643 T^{2} $)($ 1 + 16716 T + 3939040643 T^{2} $)($ 1 + 109074 T + 3939040643 T^{2} $)($ 1 + 24552 T + 3939040643 T^{2} $)($ 1 - 88778 T + 3939040643 T^{2} $)($ 1 + 38466 T + 3939040643 T^{2} $)($ 1 + 51576 T + 3939040643 T^{2} $)($ 1 - 59826 T + 3939040643 T^{2} $)($ 1 - 108724 T + 10572459494 T^{2} - 428268254869532 T^{3} + 15516041187205853449 T^{4} $)($ 1 - 31928 T + 5910993662 T^{2} - 125765689649704 T^{3} + 15516041187205853449 T^{4} $)($ 1 - 1875047714 T^{2} + 15516041187205853449 T^{4} $)($ 1 + 1693436786 T^{2} + 15516041187205853449 T^{4} $)($ 1 - 3421895214 T^{2} + 15516041187205853449 T^{4} $)($ 1 + 31928 T + 5910993662 T^{2} + 125765689649704 T^{3} + 15516041187205853449 T^{4} $)($ 1 + 108724 T + 10572459494 T^{2} + 428268254869532 T^{3} + 15516041187205853449 T^{4} $)($ 1 + 30258 T + 4293702405 T^{2} + 426012342532708 T^{3} + 16913068282241846415 T^{4} + $$46\!\cdots\!42$$ T^{5} + $$61\!\cdots\!07$$ T^{6} $)($ 1 - 30258 T + 4293702405 T^{2} - 426012342532708 T^{3} + 16913068282241846415 T^{4} - $$46\!\cdots\!42$$ T^{5} + $$61\!\cdots\!07$$ T^{6} $)($ 1 + 7906443964 T^{2} + 42876570344126662806 T^{4} + $$12\!\cdots\!36$$ T^{6} + $$24\!\cdots\!01$$ T^{8} $)($ 1 - 7103795010 T^{2} + 15516041187205853449 T^{4} $)($ 1 - 7103795010 T^{2} + 15516041187205853449 T^{4} $)($ ( 1 - 3939040643 T^{2} )^{2} $)($ 1 - 7612675530 T^{2} + 15516041187205853449 T^{4} $)($ 1 - 7612675530 T^{2} + 15516041187205853449 T^{4} $)($ 1 - 4053674810 T^{2} + 15516041187205853449 T^{4} $)($ 1 - 4053674810 T^{2} + 15516041187205853449 T^{4} $)($ ( 1 - 163262 T + 13327240322 T^{2} - 643095653457466 T^{3} + 15516041187205853449 T^{4} )( 1 + 163262 T + 13327240322 T^{2} + 643095653457466 T^{3} + 15516041187205853449 T^{4} ) $)($ 1 - 6759897816 T^{2} + 40943120759345365468 T^{4} - $$86\!\cdots\!80$$ T^{6} + $$39\!\cdots\!42$$ T^{8} - $$13\!\cdots\!20$$ T^{10} + $$98\!\cdots\!68$$ T^{12} - $$25\!\cdots\!84$$ T^{14} + $$57\!\cdots\!01$$ T^{16} $)($ 1 - 6759897816 T^{2} + 40943120759345365468 T^{4} - $$86\!\cdots\!80$$ T^{6} + $$39\!\cdots\!42$$ T^{8} - $$13\!\cdots\!20$$ T^{10} + $$98\!\cdots\!68$$ T^{12} - $$25\!\cdots\!84$$ T^{14} + $$57\!\cdots\!01$$ T^{16} $)($ ( 1 - 11599602390 T^{2} + 72197091204656028039 T^{4} - $$31\!\cdots\!48$$ T^{6} + $$11\!\cdots\!11$$ T^{8} - $$27\!\cdots\!90$$ T^{10} + $$37\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 17886738486 T^{2} + $$14\!\cdots\!27$$ T^{4} - $$73\!\cdots\!08$$ T^{6} + $$22\!\cdots\!23$$ T^{8} - $$43\!\cdots\!86$$ T^{10} + $$37\!\cdots\!49$$ T^{12} )^{2} $)($ 1 - 29848826136 T^{2} + $$39\!\cdots\!24$$ T^{4} - $$30\!\cdots\!64$$ T^{6} + $$14\!\cdots\!54$$ T^{8} - $$47\!\cdots\!36$$ T^{10} + $$95\!\cdots\!24$$ T^{12} - $$11\!\cdots\!64$$ T^{14} + $$57\!\cdots\!01$$ T^{16} $)($ 1 - 29848826136 T^{2} + $$39\!\cdots\!24$$ T^{4} - $$30\!\cdots\!64$$ T^{6} + $$14\!\cdots\!54$$ T^{8} - $$47\!\cdots\!36$$ T^{10} + $$95\!\cdots\!24$$ T^{12} - $$11\!\cdots\!64$$ T^{14} + $$57\!\cdots\!01$$ T^{16} $)($ 1 - 15441152812 T^{2} + $$13\!\cdots\!30$$ T^{4} - $$79\!\cdots\!24$$ T^{6} + $$37\!\cdots\!87$$ T^{8} - $$15\!\cdots\!88$$ T^{10} + $$63\!\cdots\!52$$ T^{12} - $$24\!\cdots\!12$$ T^{14} + $$91\!\cdots\!87$$ T^{16} - $$29\!\cdots\!76$$ T^{18} + $$77\!\cdots\!30$$ T^{20} - $$13\!\cdots\!88$$ T^{22} + $$13\!\cdots\!01$$ T^{24} $)($ 1 - 15441152812 T^{2} + $$13\!\cdots\!30$$ T^{4} - $$79\!\cdots\!24$$ T^{6} + $$37\!\cdots\!87$$ T^{8} - $$15\!\cdots\!88$$ T^{10} + $$63\!\cdots\!52$$ T^{12} - $$24\!\cdots\!12$$ T^{14} + $$91\!\cdots\!87$$ T^{16} - $$29\!\cdots\!76$$ T^{18} + $$77\!\cdots\!30$$ T^{20} - $$13\!\cdots\!88$$ T^{22} + $$13\!\cdots\!01$$ T^{24} $)($ ( 1 + 3939040643 T^{2} )^{4} $)($ ( 1 - 3415955864 T^{2} + 15516041187205853449 T^{4} )^{4} $)($ ( 1 + 7032005368 T^{2} + 39846447958779448850 T^{4} + $$10\!\cdots\!32$$ T^{6} + $$24\!\cdots\!01$$ T^{8} )^{4} $)
$89$	($ 1 - 57690 T + 5584059449 T^{2} $)($ 1 + 110310 T + 5584059449 T^{2} $)($ 1 - 119514 T + 5584059449 T^{2} $)($ 1 + 104934 T + 5584059449 T^{2} $)($ 1 + 90854 T + 5584059449 T^{2} $)($ 1 - 38490 T + 5584059449 T^{2} $)($ 1 - 101370 T + 5584059449 T^{2} $)($ 1 + 94054 T + 5584059449 T^{2} $)($ 1 + 94054 T + 5584059449 T^{2} $)($ 1 - 101370 T + 5584059449 T^{2} $)($ 1 - 38490 T + 5584059449 T^{2} $)($ 1 + 90854 T + 5584059449 T^{2} $)($ 1 + 104934 T + 5584059449 T^{2} $)($ 1 - 119514 T + 5584059449 T^{2} $)($ 1 + 110310 T + 5584059449 T^{2} $)($ 1 - 57690 T + 5584059449 T^{2} $)($ 1 + 55020 T + 10818978262 T^{2} + 307234950883980 T^{3} + 31181719929966183601 T^{4} $)($ 1 + 40748 T + 8570866774 T^{2} + 227539254427852 T^{3} + 31181719929966183601 T^{4} $)($ ( 1 - 30570 T + 5584059449 T^{2} )^{2} $)($ ( 1 + 107590 T + 5584059449 T^{2} )^{2} $)($ ( 1 + 18310 T + 5584059449 T^{2} )^{2} $)($ 1 + 40748 T + 8570866774 T^{2} + 227539254427852 T^{3} + 31181719929966183601 T^{4} $)($ 1 + 55020 T + 10818978262 T^{2} + 307234950883980 T^{3} + 31181719929966183601 T^{4} $)($ 1 - 172686 T + 26445328791 T^{2} - 2103593815517412 T^{3} + $$14\!\cdots\!59$$ T^{4} - $$53\!\cdots\!86$$ T^{5} + $$17\!\cdots\!49$$ T^{6} $)($ 1 - 172686 T + 26445328791 T^{2} - 2103593815517412 T^{3} + $$14\!\cdots\!59$$ T^{4} - $$53\!\cdots\!86$$ T^{5} + $$17\!\cdots\!49$$ T^{6} $)($ ( 1 - 104660 T + 13126874198 T^{2} - 584427661932340 T^{3} + 31181719929966183601 T^{4} )^{2} $)($ ( 1 - 85210 T + 5584059449 T^{2} )^{2} $)($ ( 1 - 85210 T + 5584059449 T^{2} )^{2} $)($ ( 1 - 51050 T + 5584059449 T^{2} )^{2} $)($ ( 1 - 826 T + 5584059449 T^{2} )^{2} $)($ ( 1 - 826 T + 5584059449 T^{2} )^{2} $)($ ( 1 + 9990 T + 5584059449 T^{2} )^{2} $)($ ( 1 + 9990 T + 5584059449 T^{2} )^{2} $)($ ( 1 + 149286 T + 5584059449 T^{2} )^{4} $)($ ( 1 + 20952 T + 16118164796 T^{2} + 497915996461992 T^{3} + $$11\!\cdots\!30$$ T^{4} + $$27\!\cdots\!08$$ T^{5} + $$50\!\cdots\!96$$ T^{6} + $$36\!\cdots\!48$$ T^{7} + $$97\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 20952 T + 16118164796 T^{2} + 497915996461992 T^{3} + $$11\!\cdots\!30$$ T^{4} + $$27\!\cdots\!08$$ T^{5} + $$50\!\cdots\!96$$ T^{6} + $$36\!\cdots\!48$$ T^{7} + $$97\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 930 T + 9446079447 T^{2} + 231471892494140 T^{3} + 52747469192025044703 T^{4} + $$28\!\cdots\!30$$ T^{5} + $$17\!\cdots\!49$$ T^{6} )^{4} $)($ ( 1 - 88734 T + 11682221271 T^{2} - 581994460142148 T^{3} + 65234218073636339679 T^{4} - $$27\!\cdots\!34$$ T^{5} + $$17\!\cdots\!49$$ T^{6} )^{4} $)($ ( 1 + 39096 T + 18076226204 T^{2} + 489497603288904 T^{3} + $$13\!\cdots\!94$$ T^{4} + $$27\!\cdots\!96$$ T^{5} + $$56\!\cdots\!04$$ T^{6} + $$68\!\cdots\!04$$ T^{7} + $$97\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 39096 T + 18076226204 T^{2} + 489497603288904 T^{3} + $$13\!\cdots\!94$$ T^{4} + $$27\!\cdots\!96$$ T^{5} + $$56\!\cdots\!04$$ T^{6} + $$68\!\cdots\!04$$ T^{7} + $$97\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 - 43836 T + 13171715490 T^{2} - 211972966345068 T^{3} + 95738414377062864255 T^{4} - $$28\!\cdots\!20$$ T^{5} + $$69\!\cdots\!56$$ T^{6} - $$16\!\cdots\!80$$ T^{7} + $$29\!\cdots\!55$$ T^{8} - $$36\!\cdots\!32$$ T^{9} + $$12\!\cdots\!90$$ T^{10} - $$23\!\cdots\!64$$ T^{11} + $$30\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 - 43836 T + 13171715490 T^{2} - 211972966345068 T^{3} + 95738414377062864255 T^{4} - $$28\!\cdots\!20$$ T^{5} + $$69\!\cdots\!56$$ T^{6} - $$16\!\cdots\!80$$ T^{7} + $$29\!\cdots\!55$$ T^{8} - $$36\!\cdots\!32$$ T^{9} + $$12\!\cdots\!90$$ T^{10} - $$23\!\cdots\!64$$ T^{11} + $$30\!\cdots\!01$$ T^{12} )^{2} $)($ ( 1 - 128786 T + 5584059449 T^{2} )^{4} $)($ ( 1 + 99362 T + 5584059449 T^{2} )^{8} $)($ ( 1 + 57412 T + 10662063350 T^{2} + 320592021085988 T^{3} + 31181719929966183601 T^{4} )^{8} $)
$97$	($ 1 + 144382 T + 8587340257 T^{2} $)($ 1 + 78382 T + 8587340257 T^{2} $)($ 1 - 94658 T + 8587340257 T^{2} $)($ 1 + 36254 T + 8587340257 T^{2} $)($ 1 - 154706 T + 8587340257 T^{2} $)($ 1 + 1918 T + 8587340257 T^{2} $)($ 1 + 119038 T + 8587340257 T^{2} $)($ 1 - 23714 T + 8587340257 T^{2} $)($ 1 - 23714 T + 8587340257 T^{2} $)($ 1 + 119038 T + 8587340257 T^{2} $)($ 1 + 1918 T + 8587340257 T^{2} $)($ 1 - 154706 T + 8587340257 T^{2} $)($ 1 + 36254 T + 8587340257 T^{2} $)($ 1 - 94658 T + 8587340257 T^{2} $)($ 1 + 78382 T + 8587340257 T^{2} $)($ 1 + 144382 T + 8587340257 T^{2} $)($ 1 - 147668 T + 11612429670 T^{2} - 1268075361070676 T^{3} + 73742412689492826049 T^{4} $)($ 1 + 190140 T + 19653817414 T^{2} + 1632796876465980 T^{3} + 73742412689492826049 T^{4} $)($ ( 1 - 66882 T + 8587340257 T^{2} )^{2} $)($ ( 1 + 108838 T + 8587340257 T^{2} )^{2} $)($ ( 1 - 49978 T + 8587340257 T^{2} )^{2} $)($ 1 + 190140 T + 19653817414 T^{2} + 1632796876465980 T^{3} + 73742412689492826049 T^{4} $)($ 1 - 147668 T + 11612429670 T^{2} - 1268075361070676 T^{3} + 73742412689492826049 T^{4} $)($ 1 - 170910 T + 30283966671 T^{2} - 2852314667192740 T^{3} + $$26\!\cdots\!47$$ T^{4} - $$12\!\cdots\!90$$ T^{5} + $$63\!\cdots\!93$$ T^{6} $)($ 1 - 170910 T + 30283966671 T^{2} - 2852314667192740 T^{3} + $$26\!\cdots\!47$$ T^{4} - $$12\!\cdots\!90$$ T^{5} + $$63\!\cdots\!93$$ T^{6} $)($ ( 1 + 29564 T + 14772618438 T^{2} + 253876127357948 T^{3} + 73742412689492826049 T^{4} )^{2} $)($ 1 - 7720618690 T^{2} + 73742412689492826049 T^{4} $)($ 1 - 7720618690 T^{2} + 73742412689492826049 T^{4} $)($ ( 1 - 92142 T + 8587340257 T^{2} )( 1 + 92142 T + 8587340257 T^{2} ) $)($ 1 - 15761405890 T^{2} + 73742412689492826049 T^{4} $)($ 1 - 15761405890 T^{2} + 73742412689492826049 T^{4} $)($ 1 - 6923133890 T^{2} + 73742412689492826049 T^{4} $)($ 1 - 6923133890 T^{2} + 73742412689492826049 T^{4} $)($ ( 1 - 8587340257 T^{2} )^{4} $)($ 1 - 45263915272 T^{2} + $$10\!\cdots\!40$$ T^{4} - $$14\!\cdots\!12$$ T^{6} + $$15\!\cdots\!94$$ T^{8} - $$11\!\cdots\!88$$ T^{10} + $$55\!\cdots\!40$$ T^{12} - $$18\!\cdots\!28$$ T^{14} + $$29\!\cdots\!01$$ T^{16} $)($ 1 - 45263915272 T^{2} + $$10\!\cdots\!40$$ T^{4} - $$14\!\cdots\!12$$ T^{6} + $$15\!\cdots\!94$$ T^{8} - $$11\!\cdots\!88$$ T^{10} + $$55\!\cdots\!40$$ T^{12} - $$18\!\cdots\!28$$ T^{14} + $$29\!\cdots\!01$$ T^{16} $)($ ( 1 - 35609466630 T^{2} + $$64\!\cdots\!47$$ T^{4} - $$68\!\cdots\!40$$ T^{6} + $$47\!\cdots\!03$$ T^{8} - $$19\!\cdots\!30$$ T^{10} + $$40\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 22620660742 T^{2} + $$25\!\cdots\!35$$ T^{4} - $$22\!\cdots\!60$$ T^{6} + $$18\!\cdots\!15$$ T^{8} - $$12\!\cdots\!42$$ T^{10} + $$40\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 12480 T + 14325999628 T^{2} - 824172284150080 T^{3} + 95392462085617046694 T^{4} - $$70\!\cdots\!60$$ T^{5} + $$10\!\cdots\!72$$ T^{6} - $$79\!\cdots\!40$$ T^{7} + $$54\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 - 12480 T + 14325999628 T^{2} - 824172284150080 T^{3} + 95392462085617046694 T^{4} - $$70\!\cdots\!60$$ T^{5} + $$10\!\cdots\!72$$ T^{6} - $$79\!\cdots\!40$$ T^{7} + $$54\!\cdots\!01$$ T^{8} )^{2} $)($ ( 1 + 86168 T + 30789268338 T^{2} + 1787720936745144 T^{3} + $$45\!\cdots\!83$$ T^{4} + $$19\!\cdots\!32$$ T^{5} + $$44\!\cdots\!92$$ T^{6} + $$16\!\cdots\!24$$ T^{7} + $$33\!\cdots\!67$$ T^{8} + $$11\!\cdots\!92$$ T^{9} + $$16\!\cdots\!38$$ T^{10} + $$40\!\cdots\!76$$ T^{11} + $$40\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 + 86168 T + 30789268338 T^{2} + 1787720936745144 T^{3} + $$45\!\cdots\!83$$ T^{4} + $$19\!\cdots\!32$$ T^{5} + $$44\!\cdots\!92$$ T^{6} + $$16\!\cdots\!24$$ T^{7} + $$33\!\cdots\!67$$ T^{8} + $$11\!\cdots\!92$$ T^{9} + $$16\!\cdots\!38$$ T^{10} + $$40\!\cdots\!76$$ T^{11} + $$40\!\cdots\!49$$ T^{12} )^{2} $)($ ( 1 - 8587340257 T^{2} )^{4} $)($ ( 1 + 15344227702 T^{2} + 73742412689492826049 T^{4} )^{4} $)($ ( 1 - 31837059828 T^{2} + $$40\!\cdots\!94$$ T^{4} - $$23\!\cdots\!72$$ T^{6} + $$54\!\cdots\!01$$ T^{8} )^{4} $)
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Introduction	Features
Universe	News

Level:	\( N \)	=	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 14 \)
Sturm bound:			\(36864\)
Trace bound:			\(12\)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(320))\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

Hecke Characteristic Polynomials

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	320.6

Level	320
Weight	6
Dimension	7854
Nonzero newspaces	14
Sturm bound	36864
Trace bound	12

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
320.6.a	\(\chi_{320}(1, \cdot)\)	320.6.a.a	1	1
		320.6.a.b	1
		320.6.a.c	1
		320.6.a.d	1
		320.6.a.e	1
		320.6.a.f	1
		320.6.a.g	1
		320.6.a.h	1
		320.6.a.i	1
		320.6.a.j	1
		320.6.a.k	1
		320.6.a.l	1
		320.6.a.m	1
		320.6.a.n	1
		320.6.a.o	1
		320.6.a.p	1
		320.6.a.q	2
		320.6.a.r	2
		320.6.a.s	2
		320.6.a.t	2
		320.6.a.u	2
		320.6.a.v	2
		320.6.a.w	2
		320.6.a.x	3
		320.6.a.y	3
		320.6.a.z	4
320.6.c	\(\chi_{320}(129, \cdot)\)	320.6.c.a	2	1
		320.6.c.b	2
		320.6.c.c	2
		320.6.c.d	2
		320.6.c.e	2
		320.6.c.f	2
		320.6.c.g	2
		320.6.c.h	4
		320.6.c.i	8
		320.6.c.j	8
		320.6.c.k	12
		320.6.c.l	12
320.6.d	\(\chi_{320}(161, \cdot)\)	320.6.d.a	8	1
		320.6.d.b	8
		320.6.d.c	12
		320.6.d.d	12
320.6.f	\(\chi_{320}(289, \cdot)\)	320.6.f.a	4	1
		320.6.f.b	8
		320.6.f.c	16
		320.6.f.d	32
320.6.j	\(\chi_{320}(47, \cdot)\)	n/a	116	2
320.6.l	\(\chi_{320}(81, \cdot)\)	320.6.l.a	80	2
320.6.n	\(\chi_{320}(63, \cdot)\)	n/a	116	2
320.6.o	\(\chi_{320}(223, \cdot)\)	n/a	120	2
320.6.q	\(\chi_{320}(49, \cdot)\)	n/a	116	2
320.6.s	\(\chi_{320}(207, \cdot)\)	n/a	116	2
320.6.u	\(\chi_{320}(87, \cdot)\)	None	0	4
320.6.x	\(\chi_{320}(41, \cdot)\)	None	0	4
320.6.z	\(\chi_{320}(9, \cdot)\)	None	0	4
320.6.ba	\(\chi_{320}(7, \cdot)\)	None	0	4
320.6.bd	\(\chi_{320}(43, \cdot)\)	n/a	1904	8
320.6.be	\(\chi_{320}(21, \cdot)\)	n/a	1280	8
320.6.bf	\(\chi_{320}(29, \cdot)\)	n/a	1904	8
320.6.bj	\(\chi_{320}(3, \cdot)\)	n/a	1904	8