LMFDB - Space of Modular Forms of Level 432 and Weight 2

Defining parameters

Level:	$ N $	=	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	=	$ 2 $
Nonzero newspaces:			$ 12 $
Newform subspaces:			$ 43 $
Sturm bound:			$20736$
Trace bound:			$10$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(432))$.

	Total	New	Old
Modular forms	5604	2376	3228
Cusp forms	4765	2232	2533
Eisenstein series	839	144	695

Trace form

$ 2232q - 16q^{2} - 18q^{3} - 28q^{4} - 21q^{5} - 24q^{6} - 23q^{7} - 16q^{8} - 6q^{9} + O(q^{10}) $

\( 2232q - 16q^{2} - 18q^{3} - 28q^{4} - 21q^{5} - 24q^{6} - 23q^{7} - 16q^{8} - 6q^{9} - 28q^{10} - 17q^{11} - 24q^{12} - 39q^{13} - 8q^{14} - 18q^{15} - 20q^{16} - 27q^{17} - 24q^{18} - 19q^{19} + 12q^{20} - 30q^{21} - 4q^{22} - q^{23} - 24q^{24} + 14q^{25} + 16q^{26} - 40q^{28} + 35q^{29} - 24q^{30} + 5q^{31} + 4q^{32} - 30q^{33} - 20q^{34} + 73q^{35} - 24q^{36} + q^{37} - 44q^{38} + 18q^{39} - 60q^{40} + 39q^{41} - 24q^{42} + 41q^{43} - 60q^{44} - 6q^{45} - 76q^{46} + 59q^{47} - 24q^{48} - 64q^{49} - 60q^{50} - 27q^{51} - 60q^{52} - 24q^{53} - 24q^{54} - 30q^{55} - 196q^{56} - 21q^{57} - 124q^{58} - 29q^{59} - 144q^{60} - 103q^{61} - 256q^{62} - 48q^{63} - 100q^{64} - 223q^{65} - 204q^{66} - 67q^{67} - 292q^{68} - 126q^{69} - 220q^{70} - 131q^{71} - 192q^{72} - 71q^{73} - 296q^{74} - 60q^{75} - 220q^{76} - 183q^{77} - 180q^{78} - 79q^{79} - 348q^{80} - 150q^{81} - 176q^{82} - 109q^{83} - 156q^{84} - 81q^{85} - 268q^{86} - 36q^{87} - 132q^{88} - 63q^{89} - 132q^{90} - 81q^{91} - 76q^{92} - 102q^{93} - 60q^{94} - 173q^{95} - 24q^{96} - 39q^{97} - 64q^{98} - 126q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(432))$

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
432.2.a	$\chi_{432}(1, \cdot)$	432.2.a.a	1	1
		432.2.a.b	1
		432.2.a.c	1
		432.2.a.d	1
		432.2.a.e	1
		432.2.a.f	1
		432.2.a.g	1
		432.2.a.h	1
432.2.c	$\chi_{432}(431, \cdot)$	432.2.c.a	2	1
		432.2.c.b	2
		432.2.c.c	4
432.2.d	$\chi_{432}(217, \cdot)$	None	0	1
432.2.f	$\chi_{432}(215, \cdot)$	None	0	1
432.2.i	$\chi_{432}(145, \cdot)$	432.2.i.a	2	2
		432.2.i.b	2
		432.2.i.c	2
		432.2.i.d	4
432.2.k	$\chi_{432}(109, \cdot)$	432.2.k.a	4	2
		432.2.k.b	4
		432.2.k.c	24
		432.2.k.d	32
432.2.l	$\chi_{432}(107, \cdot)$	432.2.l.a	32	2
432.2.l	$\chi_{432}(107, \cdot)$	432.2.l.b	32	2
432.2.p	$\chi_{432}(71, \cdot)$	None	0	2
432.2.r	$\chi_{432}(73, \cdot)$	None	0	2
432.2.s	$\chi_{432}(143, \cdot)$	432.2.s.a	2	2
		432.2.s.b	2
		432.2.s.c	2
		432.2.s.d	2
		432.2.s.e	4
432.2.u	$\chi_{432}(49, \cdot)$	432.2.u.a	6	6
		432.2.u.b	12
		432.2.u.c	12
		432.2.u.d	18
		432.2.u.e	24
		432.2.u.f	30
432.2.v	$\chi_{432}(35, \cdot)$	432.2.v.a	88	4
432.2.y	$\chi_{432}(37, \cdot)$	432.2.y.a	4	4
		432.2.y.b	4
		432.2.y.c	4
		432.2.y.d	4
		432.2.y.e	72
432.2.bb	$\chi_{432}(25, \cdot)$	None	0	6
432.2.bd	$\chi_{432}(23, \cdot)$	None	0	6
432.2.be	$\chi_{432}(47, \cdot)$	432.2.be.a	36	6
		432.2.be.b	36
		432.2.be.c	36
432.2.bg	$\chi_{432}(13, \cdot)$	432.2.bg.a	840	12
432.2.bj	$\chi_{432}(11, \cdot)$	432.2.bj.a	840	12

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(432))$ into lower level spaces

Hecke Characteristic Polynomials

$p$	$F_p(T)$
$2$	()()()()()()()()()()()()()()()($ ( 1 + 2 T^{2} )^{2} $)($ ( 1 + 2 T^{2} )^{2} $)()()()()()()()()()($ 1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4} $)($ 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} $)($ 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} $)($ ( 1 - 2 T + 2 T^{2} )^{2} $)
$3$	()()()()()()()()()()()()()()()()()()()()()()($ 1 + 9 T^{3} + 27 T^{6} $)($ 1 + 6 T^{2} + 18 T^{4} + 18 T^{5} + 57 T^{6} + 54 T^{7} + 162 T^{8} + 486 T^{10} + 729 T^{12} $)($ 1 - 6 T + 18 T^{2} - 39 T^{3} + 63 T^{4} - 81 T^{5} + 117 T^{6} - 243 T^{7} + 567 T^{8} - 1053 T^{9} + 1458 T^{10} - 1458 T^{11} + 729 T^{12} $)($ 1 - 3 T^{2} - 9 T^{3} + 18 T^{4} + 18 T^{5} + 3 T^{6} - 135 T^{7} + 81 T^{8} + 108 T^{9} + 243 T^{10} - 1215 T^{11} + 81 T^{12} + 1458 T^{13} + 4374 T^{14} - 6561 T^{15} - 6561 T^{16} + 19683 T^{18} $)()()()()
$5$	($ 1 + 4 T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 + T + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 - 3 T + 5 T^{2} $)($ 1 - 4 T + 5 T^{2} $)($ ( 1 - 5 T^{2} )^{2} $)($ ( 1 - 5 T^{2} )^{2} $)($ ( 1 - T^{2} + 25 T^{4} )^{2} $)($ 1 + T - 4 T^{2} + 5 T^{3} + 25 T^{4} $)($ 1 - 5 T^{2} + 25 T^{4} $)($ 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} $)($ 1 + T - T^{2} - 8 T^{3} - 26 T^{4} - 40 T^{5} - 25 T^{6} + 125 T^{7} + 625 T^{8} $)($ 1 + 31 T^{4} + 625 T^{8} $)($ 1 + 31 T^{4} + 625 T^{8} $)($ 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} $)($ 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} $)($ 1 - 6 T + 17 T^{2} - 30 T^{3} + 25 T^{4} $)($ 1 - 6 T + 17 T^{2} - 30 T^{3} + 25 T^{4} $)($ ( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} )^{2} $)($ 1 + 3 T + 9 T^{2} + 9 T^{3} + 36 T^{4} + 12 T^{5} + 109 T^{6} + 60 T^{7} + 900 T^{8} + 1125 T^{9} + 5625 T^{10} + 9375 T^{11} + 15625 T^{12} $)($ 1 + 3 T + 9 T^{2} + 9 T^{3} - 18 T^{4} - 42 T^{5} - 142 T^{6} + 9 T^{7} - 171 T^{8} - 702 T^{9} - 603 T^{10} - 1791 T^{11} + 8049 T^{12} - 8955 T^{13} - 15075 T^{14} - 87750 T^{15} - 106875 T^{16} + 28125 T^{17} - 2218750 T^{18} - 3281250 T^{19} - 7031250 T^{20} + 17578125 T^{21} + 87890625 T^{22} + 146484375 T^{23} + 244140625 T^{24} $)($ 1 + 3 T + 3 T^{2} + 18 T^{3} + 87 T^{4} + 147 T^{5} + 323 T^{6} + 1368 T^{7} + 3096 T^{8} + 5562 T^{9} + 16272 T^{10} + 41310 T^{11} + 82629 T^{12} + 206550 T^{13} + 406800 T^{14} + 695250 T^{15} + 1935000 T^{16} + 4275000 T^{17} + 5046875 T^{18} + 11484375 T^{19} + 33984375 T^{20} + 35156250 T^{21} + 29296875 T^{22} + 146484375 T^{23} + 244140625 T^{24} $)($ 1 - 3 T + 18 T^{3} - 36 T^{4} + 42 T^{5} + 12 T^{6} - 66 T^{7} + 207 T^{8} - 306 T^{9} - 1881 T^{10} + 8988 T^{11} + 3777 T^{12} - 51780 T^{13} + 130257 T^{14} - 141489 T^{15} - 166455 T^{16} + 864168 T^{17} - 1249796 T^{18} + 4320840 T^{19} - 4161375 T^{20} - 17686125 T^{21} + 81410625 T^{22} - 161812500 T^{23} + 59015625 T^{24} + 702187500 T^{25} - 734765625 T^{26} - 597656250 T^{27} + 2021484375 T^{28} - 3222656250 T^{29} + 2929687500 T^{30} + 51269531250 T^{31} - 219726562500 T^{32} + 549316406250 T^{33} - 2288818359375 T^{35} + 3814697265625 T^{36} $)($ 1 + 2 T + 5 T^{2} + 14 T^{3} + 16 T^{4} + 70 T^{5} + 125 T^{6} + 250 T^{7} + 625 T^{8} $)($ 1 + 4 T + 20 T^{2} + 52 T^{3} + 151 T^{4} + 260 T^{5} + 500 T^{6} + 500 T^{7} + 625 T^{8} $)($ 1 - 8 T + 20 T^{2} + 4 T^{3} - 89 T^{4} + 20 T^{5} + 500 T^{6} - 1000 T^{7} + 625 T^{8} $)($ 1 - 4 T + 5 T^{2} + 8 T^{3} - 44 T^{4} + 40 T^{5} + 125 T^{6} - 500 T^{7} + 625 T^{8} $)
$7$	($ 1 - 3 T + 7 T^{2} $)($ 1 - T + 7 T^{2} $)($ 1 + 3 T + 7 T^{2} $)($ 1 + 5 T + 7 T^{2} $)($ 1 - T + 7 T^{2} $)($ 1 + 3 T + 7 T^{2} $)($ 1 - T + 7 T^{2} $)($ 1 - 3 T + 7 T^{2} $)($ ( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} ) $)($ ( 1 - 5 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} ) $)($ ( 1 - 5 T + 7 T^{2} )^{2}( 1 + 5 T + 7 T^{2} )^{2} $)($ 1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4} $)($ 1 - 2 T - 3 T^{2} - 14 T^{3} + 49 T^{4} $)($ ( 1 - 4 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} ) $)($ 1 - 3 T + T^{2} + 18 T^{3} - 48 T^{4} + 126 T^{5} + 49 T^{6} - 1029 T^{7} + 2401 T^{8} $)($ ( 1 - 5 T^{2} + 49 T^{4} )^{2} $)($ ( 1 - 5 T^{2} + 49 T^{4} )^{2} $)($ ( 1 - T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) $)($ ( 1 - 4 T + 7 T^{2} )( 1 + T + 7 T^{2} ) $)($ ( 1 + T + 7 T^{2} )( 1 + 5 T + 7 T^{2} ) $)($ ( 1 - 5 T + 7 T^{2} )( 1 - T + 7 T^{2} ) $)($ 1 + 5 T^{2} - 24 T^{4} + 245 T^{6} + 2401 T^{8} $)($ 1 + 3 T - 6 T^{2} - 50 T^{3} - 99 T^{4} + 207 T^{5} + 1401 T^{6} + 1449 T^{7} - 4851 T^{8} - 17150 T^{9} - 14406 T^{10} + 50421 T^{11} + 117649 T^{12} $)($ 1 - 3 T + 24 T^{2} - 46 T^{3} + 321 T^{4} - 561 T^{5} + 3304 T^{6} - 4068 T^{7} + 25767 T^{8} - 26386 T^{9} + 193845 T^{10} - 149838 T^{11} + 1294315 T^{12} - 1048866 T^{13} + 9498405 T^{14} - 9050398 T^{15} + 61866567 T^{16} - 68370876 T^{17} + 388712296 T^{18} - 462007623 T^{19} + 1850501121 T^{20} - 1856265922 T^{21} + 6779405976 T^{22} - 5931980229 T^{23} + 13841287201 T^{24} $)($ 1 - 6 T + 12 T^{2} + 11 T^{3} - 213 T^{4} + 678 T^{5} - 224 T^{6} - 3942 T^{7} + 15255 T^{8} - 25135 T^{9} - 22044 T^{10} + 210732 T^{11} - 647141 T^{12} + 1475124 T^{13} - 1080156 T^{14} - 8621305 T^{15} + 36627255 T^{16} - 66253194 T^{17} - 26353376 T^{18} + 558362154 T^{19} - 1227902613 T^{20} + 443889677 T^{21} + 3389702988 T^{22} - 11863960458 T^{23} + 13841287201 T^{24} $)($ 1 + 9 T^{2} - 6 T^{3} + 90 T^{4} + 144 T^{5} + 642 T^{6} + 1305 T^{7} + 3294 T^{8} + 16123 T^{9} + 41769 T^{10} + 164808 T^{11} + 268632 T^{12} + 1051596 T^{13} + 2182869 T^{14} + 10020276 T^{15} + 22667607 T^{16} + 57261276 T^{17} + 121068222 T^{18} + 400828932 T^{19} + 1110712743 T^{20} + 3436954668 T^{21} + 5241068469 T^{22} + 17674173972 T^{23} + 31604286168 T^{24} + 135726474744 T^{25} + 240789972969 T^{26} + 650621205661 T^{27} + 930473470206 T^{28} + 2580411399615 T^{29} + 8886106383042 T^{30} + 13952017498608 T^{31} + 61040076556410 T^{32} - 28485369059658 T^{33} + 299096375126409 T^{34} + 1628413597910449 T^{36} $)($ 1 + 12 T + 73 T^{2} + 300 T^{3} + 912 T^{4} + 2100 T^{5} + 3577 T^{6} + 4116 T^{7} + 2401 T^{8} $)($ 1 - 6 T + 28 T^{2} - 96 T^{3} + 291 T^{4} - 672 T^{5} + 1372 T^{6} - 2058 T^{7} + 2401 T^{8} $)($ 1 + 6 T + 28 T^{2} + 96 T^{3} + 291 T^{4} + 672 T^{5} + 1372 T^{6} + 2058 T^{7} + 2401 T^{8} $)($ 1 - 12 T + 73 T^{2} - 300 T^{3} + 912 T^{4} - 2100 T^{5} + 3577 T^{6} - 4116 T^{7} + 2401 T^{8} $)
$11$	($ 1 - 4 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 - 5 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)($ ( 1 + 11 T^{2} )^{2} $)($ ( 1 + 11 T^{2} )^{2} $)($ ( 1 - 5 T^{2} + 121 T^{4} )^{2} $)($ 1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4} $)($ 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} $)($ 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} $)($ ( 1 + T - 10 T^{2} + 11 T^{3} + 121 T^{4} )^{2} $)($ 1 + 199 T^{4} + 14641 T^{8} $)($ 1 - 233 T^{4} + 14641 T^{8} $)($ 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} $)($ 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} $)($ 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} $)($ 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} $)($ 1 + 5 T^{2} - 96 T^{4} + 605 T^{6} + 14641 T^{8} $)($ 1 - 3 T + 9 T^{2} + 9 T^{3} - 18 T^{4} + 114 T^{5} + 1225 T^{6} + 1254 T^{7} - 2178 T^{8} + 11979 T^{9} + 131769 T^{10} - 483153 T^{11} + 1771561 T^{12} $)($ 1 - 12 T + 90 T^{2} - 504 T^{3} + 2628 T^{4} - 12720 T^{5} + 57872 T^{6} - 239643 T^{7} + 957330 T^{8} - 3660336 T^{9} + 13502205 T^{10} - 46654983 T^{11} + 157089783 T^{12} - 513204813 T^{13} + 1633766805 T^{14} - 4871907216 T^{15} + 14016268530 T^{16} - 38594744793 T^{17} + 102523778192 T^{18} - 247876815120 T^{19} + 563335139268 T^{20} - 1188405636264 T^{21} + 2334368214090 T^{22} - 3423740047332 T^{23} + 3138428376721 T^{24} $)($ 1 + 3 T - 15 T^{2} - 126 T^{3} - 201 T^{4} + 1488 T^{5} + 7145 T^{6} + 1530 T^{7} - 61974 T^{8} - 202716 T^{9} - 19692 T^{10} + 1304451 T^{11} + 4526883 T^{12} + 14348961 T^{13} - 2382732 T^{14} - 269814996 T^{15} - 907361334 T^{16} + 246408030 T^{17} + 12657803345 T^{18} + 28996910448 T^{19} - 43086135081 T^{20} - 297101409066 T^{21} - 389061369015 T^{22} + 855935011833 T^{23} + 3138428376721 T^{24} $)($ 1 + 3 T - 36 T^{3} - 252 T^{4} + 183 T^{5} + 3414 T^{6} + 14331 T^{7} + 19242 T^{8} - 82413 T^{9} - 362790 T^{10} - 885057 T^{11} + 3067980 T^{12} + 12803547 T^{13} + 53216793 T^{14} + 119847402 T^{15} - 27497151 T^{16} - 185418060 T^{17} - 3750422330 T^{18} - 2039598660 T^{19} - 3327155271 T^{20} + 159516892062 T^{21} + 779147066313 T^{22} + 2062024047897 T^{23} + 5435113716780 T^{24} - 17247257103747 T^{25} - 77767258437990 T^{26} - 194325543058383 T^{27} + 499087924172442 T^{28} + 4088801551526241 T^{29} + 10714594478125494 T^{30} + 6317656322339373 T^{31} - 95696958062976732 T^{32} - 150380934098963436 T^{33} + 1516341085497881313 T^{35} + 5559917313492231481 T^{36} $)($ 1 + 4 T + 5 T^{2} - 20 T^{3} - 164 T^{4} - 220 T^{5} + 605 T^{6} + 5324 T^{7} + 14641 T^{8} $)($ 1 + 8 T + 41 T^{2} + 152 T^{3} + 532 T^{4} + 1672 T^{5} + 4961 T^{6} + 10648 T^{7} + 14641 T^{8} $)($ 1 - 10 T + 41 T^{2} - 82 T^{3} + 136 T^{4} - 902 T^{5} + 4961 T^{6} - 13310 T^{7} + 14641 T^{8} $)($ 1 - 2 T + 5 T^{2} - 26 T^{3} - 32 T^{4} - 286 T^{5} + 605 T^{6} - 2662 T^{7} + 14641 T^{8} $)
$13$	($ 1 - T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 7 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ ( 1 + 5 T + 13 T^{2} )^{2} $)($ ( 1 - 7 T + 13 T^{2} )^{2} $)($ ( 1 + 2 T + 13 T^{2} )^{4} $)($ ( 1 - 7 T + 13 T^{2} )( 1 + 2 T + 13 T^{2} ) $)($ ( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) $)($ 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} $)($ 1 + 5 T + T^{2} - 10 T^{3} + 82 T^{4} - 130 T^{5} + 169 T^{6} + 10985 T^{7} + 28561 T^{8} $)($ ( 1 + 4 T + 13 T^{2} )^{2}( 1 + 6 T + 13 T^{2} )^{2} $)($ ( 1 - 6 T + 13 T^{2} )^{2}( 1 + 4 T + 13 T^{2} )^{2} $)($ ( 1 - 7 T + 13 T^{2} )( 1 + 2 T + 13 T^{2} ) $)($ ( 1 - 7 T + 13 T^{2} )( 1 + 2 T + 13 T^{2} ) $)($ 1 + 4 T + 3 T^{2} + 52 T^{3} + 169 T^{4} $)($ 1 + 4 T + 3 T^{2} + 52 T^{3} + 169 T^{4} $)($ ( 1 + T - 12 T^{2} + 13 T^{3} + 169 T^{4} )^{2} $)($ 1 + 12 T + 78 T^{2} + 386 T^{3} + 1566 T^{4} + 5886 T^{5} + 21843 T^{6} + 76518 T^{7} + 264654 T^{8} + 848042 T^{9} + 2227758 T^{10} + 4455516 T^{11} + 4826809 T^{12} $)($ 1 - 12 T + 48 T^{2} - 74 T^{3} + 246 T^{4} - 1974 T^{5} + 8974 T^{6} - 33102 T^{7} + 94338 T^{8} - 225668 T^{9} + 896478 T^{10} - 3069618 T^{11} + 8300191 T^{12} - 39905034 T^{13} + 151504782 T^{14} - 495792596 T^{15} + 2694387618 T^{16} - 12290540886 T^{17} + 43315783966 T^{18} - 123865572558 T^{19} + 200669757366 T^{20} - 784732953602 T^{21} + 6617207608752 T^{22} - 21505924728444 T^{23} + 23298085122481 T^{24} $)($ 1 + 6 T + 48 T^{2} + 214 T^{3} + 1488 T^{4} + 5928 T^{5} + 32329 T^{6} + 112023 T^{7} + 560277 T^{8} + 1799710 T^{9} + 8467593 T^{10} + 25055985 T^{11} + 112181629 T^{12} + 325727805 T^{13} + 1431023217 T^{14} + 3953962870 T^{15} + 16002071397 T^{16} + 41593355739 T^{17} + 156045908161 T^{18} + 371973208776 T^{19} + 1213807312848 T^{20} + 2269362865822 T^{21} + 6617207608752 T^{22} + 10752962364222 T^{23} + 23298085122481 T^{24} $)($ 1 - 45 T^{2} + 33 T^{3} + 819 T^{4} - 2223 T^{5} - 6621 T^{6} + 67680 T^{7} + 2295 T^{8} - 1105627 T^{9} + 769527 T^{10} + 10632708 T^{11} - 24128055 T^{12} - 87782535 T^{13} + 521321076 T^{14} + 1050449085 T^{15} - 7341713262 T^{16} - 6958867761 T^{17} + 89217898098 T^{18} - 90465280893 T^{19} - 1240749541278 T^{20} + 2307836639745 T^{21} + 14889451251636 T^{22} - 32593040767755 T^{23} - 116461513026495 T^{24} + 667186658694036 T^{25} + 627726814538967 T^{26} - 11724620828271871 T^{27} + 316385238793455 T^{28} + 121293415468424160 T^{29} - 154256621595946701 T^{30} - 673291361954578419 T^{31} + 3224711259887717691 T^{32} + 1689134469464994981 T^{33} - 29943747413243092845 T^{34} + $$11\!\cdots\!29$$ T^{36} $)($ ( 1 - 4 T + 13 T^{2} )^{2}( 1 + 6 T + 23 T^{2} + 78 T^{3} + 169 T^{4} ) $)($ ( 1 - 7 T + 13 T^{2} )^{2}( 1 - T^{2} + 169 T^{4} ) $)($ ( 1 + 5 T + 13 T^{2} )^{2}( 1 + 23 T^{2} + 169 T^{4} ) $)($ ( 1 - 6 T + 13 T^{2} )^{2}( 1 + 4 T + 3 T^{2} + 52 T^{3} + 169 T^{4} ) $)
$17$	($ 1 - 4 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 8 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 8 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ ( 1 - 17 T^{2} )^{2} $)($ ( 1 - 17 T^{2} )^{2} $)($ ( 1 + 2 T^{2} + 289 T^{4} )^{2} $)($ ( 1 - 2 T + 17 T^{2} )^{2} $)($ ( 1 - 3 T + 17 T^{2} )^{2} $)($ ( 1 + 6 T + 17 T^{2} )^{2} $)($ ( 1 - 5 T + 32 T^{2} - 85 T^{3} + 289 T^{4} )^{2} $)($ ( 1 + 16 T^{2} + 289 T^{4} )^{2} $)($ ( 1 + 16 T^{2} + 289 T^{4} )^{2} $)($ 1 + 14 T^{2} + 289 T^{4} $)($ 1 + 14 T^{2} + 289 T^{4} $)($ 1 - 31 T^{2} + 289 T^{4} $)($ 1 - 31 T^{2} + 289 T^{4} $)($ ( 1 - 22 T^{2} + 289 T^{4} )^{2} $)($ 1 + 6 T + 12 T^{2} + 54 T^{3} - 102 T^{4} - 2082 T^{5} - 8345 T^{6} - 35394 T^{7} - 29478 T^{8} + 265302 T^{9} + 1002252 T^{10} + 8519142 T^{11} + 24137569 T^{12} $)($ 1 + 6 T - 48 T^{2} - 252 T^{3} + 1722 T^{4} + 5946 T^{5} - 48874 T^{6} - 104832 T^{7} + 1071234 T^{8} + 1189944 T^{9} - 21101022 T^{10} - 6521976 T^{11} + 379698279 T^{12} - 110873592 T^{13} - 6098195358 T^{14} + 5846194872 T^{15} + 89470534914 T^{16} - 148846449024 T^{17} - 1179699547306 T^{18} + 2439873749658 T^{19} + 12012254313402 T^{20} - 29884144877244 T^{21} - 96767707221552 T^{22} + 205631377845798 T^{23} + 582622237229761 T^{24} $)($ 1 - 9 T - 30 T^{2} + 423 T^{3} + 1029 T^{4} - 14184 T^{5} - 23521 T^{6} + 296649 T^{7} + 637560 T^{8} - 4620213 T^{9} - 12537675 T^{10} + 28264410 T^{11} + 250681641 T^{12} + 480494970 T^{13} - 3623388075 T^{14} - 22699106469 T^{15} + 53249648760 T^{16} + 421199159193 T^{17} - 567739760449 T^{18} - 5820243737832 T^{19} + 7178054406789 T^{20} + 50162671758231 T^{21} - 60479817013470 T^{22} - 308447066768697 T^{23} + 582622237229761 T^{24} $)($ 1 + 12 T - 630 T^{3} - 2493 T^{4} + 9264 T^{5} + 71715 T^{6} - 20382 T^{7} - 663750 T^{8} + 1631844 T^{9} + 5926023 T^{10} - 55869558 T^{11} - 116813226 T^{12} + 478010541 T^{13} - 1415343366 T^{14} - 8092973394 T^{15} + 53937481662 T^{16} + 118392015135 T^{17} - 620668817804 T^{18} + 2012664257295 T^{19} + 15587932200318 T^{20} - 39760778284722 T^{21} - 118210893271686 T^{22} + 678706612712637 T^{23} - 2819587302687594 T^{24} - 22925440290816534 T^{25} + 41338499037787143 T^{26} + 193516914734370468 T^{27} - 1338115951423023750 T^{28} - 698529790542175806 T^{29} + 41782753742932310115 T^{30} + 91756010896840600368 T^{31} - $$41\!\cdots\!97$$ T^{32} - $$18\!\cdots\!90$$ T^{33} + $$99\!\cdots\!24$$ T^{35} + $$14\!\cdots\!09$$ T^{36} $)($ ( 1 + 4 T + 17 T^{2} )^{4} $)($ ( 1 - 8 T + 47 T^{2} - 136 T^{3} + 289 T^{4} )^{2} $)($ ( 1 - 8 T + 47 T^{2} - 136 T^{3} + 289 T^{4} )^{2} $)($ ( 1 + 4 T + 17 T^{2} )^{4} $)
$19$	($ 1 - T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 - T + 19 T^{2} $)($ 1 - 7 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 - T + 19 T^{2} $)($ ( 1 - 7 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) $)($ ( 1 - T + 19 T^{2} )( 1 + T + 19 T^{2} ) $)($ ( 1 + 10 T^{2} + 361 T^{4} )^{2} $)($ ( 1 - 4 T + 19 T^{2} )^{2} $)($ ( 1 - T + 19 T^{2} )^{2} $)($ ( 1 - 4 T + 19 T^{2} )^{2} $)($ ( 1 + 7 T + 42 T^{2} + 133 T^{3} + 361 T^{4} )^{2} $)($ ( 1 + 4 T + 8 T^{2} + 76 T^{3} + 361 T^{4} )^{2} $)($ ( 1 - 8 T + 32 T^{2} - 152 T^{3} + 361 T^{4} )^{2} $)($ ( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) $)($ ( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) $)($ 1 - 35 T^{2} + 361 T^{4} $)($ 1 - 35 T^{2} + 361 T^{4} $)($ ( 1 - 2 T^{2} + 361 T^{4} )^{2} $)($ 1 + 9 T + 36 T^{2} + 79 T^{3} - 297 T^{4} - 4806 T^{5} - 27429 T^{6} - 91314 T^{7} - 107217 T^{8} + 541861 T^{9} + 4691556 T^{10} + 22284891 T^{11} + 47045881 T^{12} $)($ 1 - 9 T - 36 T^{2} + 419 T^{3} + 1611 T^{4} - 13806 T^{5} - 55610 T^{6} + 315819 T^{7} + 1580067 T^{8} - 4822864 T^{9} - 38744127 T^{10} + 34656777 T^{11} + 805313071 T^{12} + 658478763 T^{13} - 13986629847 T^{14} - 33080024176 T^{15} + 205915911507 T^{16} + 781999110081 T^{17} - 2616221442410 T^{18} - 12340793228634 T^{19} + 27360520059051 T^{20} + 135206145369401 T^{21} - 220718385280836 T^{22} - 1048412330083971 T^{23} + 2213314919066161 T^{24} $)($ 1 - 3 T - 75 T^{2} + 242 T^{3} + 3012 T^{4} - 9714 T^{5} - 85589 T^{6} + 257166 T^{7} + 1946502 T^{8} - 4391737 T^{9} - 39399504 T^{10} + 33490578 T^{11} + 763159453 T^{12} + 636320982 T^{13} - 14223220944 T^{14} - 30122924083 T^{15} + 253670087142 T^{16} + 636768475434 T^{17} - 4026609908909 T^{18} - 8683070072646 T^{19} + 51154491879492 T^{20} + 78090422862518 T^{21} - 459829969335075 T^{22} - 349470776694657 T^{23} + 2213314919066161 T^{24} $)($ 1 - 81 T^{2} + 12 T^{3} + 2916 T^{4} - 378 T^{5} - 63789 T^{6} - 26217 T^{7} + 1135107 T^{8} + 2182495 T^{9} - 24267384 T^{10} - 68364540 T^{11} + 564078960 T^{12} + 1060991325 T^{13} - 9783469926 T^{14} - 6143751819 T^{15} + 107000768556 T^{16} - 9549612666 T^{17} - 1139182247424 T^{18} - 181442640654 T^{19} + 38627277448716 T^{20} - 42139993726521 T^{21} - 1274991584226246 T^{22} + 2627119558841175 T^{23} + 26537591626763760 T^{24} - 61109130255735060 T^{25} - 412146646004154744 T^{26} + 704264286964178605 T^{27} + 6959416226693719707 T^{28} - 3054025117534607523 T^{29} - $$14\!\cdots\!29$$ T^{30} - 15896027748733168302 T^{31} + $$23\!\cdots\!36$$ T^{32} + $$18\!\cdots\!88$$ T^{33} - $$23\!\cdots\!61$$ T^{34} + $$10\!\cdots\!41$$ T^{36} $)($ ( 1 + 6 T + 18 T^{2} + 114 T^{3} + 361 T^{4} )^{2} $)($ 1 + 6 T + 18 T^{2} + 132 T^{3} + 959 T^{4} + 2508 T^{5} + 6498 T^{6} + 41154 T^{7} + 130321 T^{8} $)($ 1 + 6 T + 18 T^{2} + 132 T^{3} + 959 T^{4} + 2508 T^{5} + 6498 T^{6} + 41154 T^{7} + 130321 T^{8} $)($ ( 1 + 6 T + 18 T^{2} + 114 T^{3} + 361 T^{4} )^{2} $)
$23$	($ 1 - 4 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 2 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 2 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ ( 1 + 23 T^{2} )^{2} $)($ ( 1 + 23 T^{2} )^{2} $)($ ( 1 + 23 T^{2} )^{4} $)($ 1 - T - 22 T^{2} - 23 T^{3} + 529 T^{4} $)($ 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} $)($ 1 - 3 T - 14 T^{2} - 69 T^{3} + 529 T^{4} $)($ 1 + 5 T - 19 T^{2} - 10 T^{3} + 832 T^{4} - 230 T^{5} - 10051 T^{6} + 60835 T^{7} + 279841 T^{8} $)($ ( 1 - 14 T^{2} + 529 T^{4} )^{2} $)($ ( 1 - 38 T^{2} + 529 T^{4} )^{2} $)($ 1 + 9 T + 58 T^{2} + 207 T^{3} + 529 T^{4} $)($ 1 - 9 T + 58 T^{2} - 207 T^{3} + 529 T^{4} $)($ 1 - 23 T^{2} + 529 T^{4} $)($ 1 - 23 T^{2} + 529 T^{4} $)($ 1 - 19 T^{2} - 168 T^{4} - 10051 T^{6} + 279841 T^{8} $)($ 1 - 6 T + 36 T^{2} - 180 T^{3} + 1386 T^{4} - 6954 T^{5} + 33589 T^{6} - 159942 T^{7} + 733194 T^{8} - 2190060 T^{9} + 10074276 T^{10} - 38618058 T^{11} + 148035889 T^{12} $)($ 1 + 30 T + 414 T^{2} + 3222 T^{3} + 12348 T^{4} - 19608 T^{5} - 550618 T^{6} - 3222558 T^{7} - 7146234 T^{8} + 22769856 T^{9} + 232883658 T^{10} + 864182466 T^{11} + 2884098855 T^{12} + 19876196718 T^{13} + 123195455082 T^{14} + 277040837952 T^{15} - 1999809268794 T^{16} - 20741488625394 T^{17} - 81511225129402 T^{18} - 66761817364776 T^{19} + 966984046249788 T^{20} + 5803313875233786 T^{21} + 17150575642450686 T^{22} + 28584292737417810 T^{23} + 21914624432020321 T^{24} $)($ 1 - 12 T + 48 T^{2} - 153 T^{3} - 336 T^{4} + 12228 T^{5} - 51922 T^{6} + 116820 T^{7} - 165330 T^{8} - 4324509 T^{9} + 14509764 T^{10} + 2453454 T^{11} + 107316369 T^{12} + 56429442 T^{13} + 7675665156 T^{14} - 52616301003 T^{15} - 46266112530 T^{16} + 751893589260 T^{17} - 7686319428658 T^{18} + 41634205565916 T^{19} - 26312491054416 T^{20} - 275576357203839 T^{21} + 1988472538255152 T^{22} - 11433717094967124 T^{23} + 21914624432020321 T^{24} $)($ 1 - 30 T + 459 T^{2} - 4716 T^{3} + 35739 T^{4} - 203682 T^{5} + 823269 T^{6} - 1638444 T^{7} - 6429924 T^{8} + 76742136 T^{9} - 307889172 T^{10} - 367007538 T^{11} + 14732471886 T^{12} - 121578320496 T^{13} + 628848268830 T^{14} - 2040092984925 T^{15} + 1341049467978 T^{16} + 31755560848485 T^{17} - 226915587058772 T^{18} + 730377899515155 T^{19} + 709415168560362 T^{20} - 24821811347582475 T^{21} + 175977528397656030 T^{22} - 782519772076186128 T^{23} + 2180934572811516654 T^{24} - 1249596604623219486 T^{25} - 24111104416671277332 T^{26} + $$13\!\cdots\!68$$ T^{27} - $$26\!\cdots\!76$$ T^{28} - $$15\!\cdots\!88$$ T^{29} + $$18\!\cdots\!49$$ T^{30} - $$10\!\cdots\!06$$ T^{31} + $$41\!\cdots\!51$$ T^{32} - $$12\!\cdots\!12$$ T^{33} + $$28\!\cdots\!99$$ T^{34} - $$42\!\cdots\!90$$ T^{35} + $$32\!\cdots\!69$$ T^{36} $)($ 1 + 12 T + 97 T^{2} + 588 T^{3} + 2976 T^{4} + 13524 T^{5} + 51313 T^{6} + 146004 T^{7} + 279841 T^{8} $)($ 1 - 6 T + 52 T^{2} - 240 T^{3} + 1347 T^{4} - 5520 T^{5} + 27508 T^{6} - 73002 T^{7} + 279841 T^{8} $)($ 1 + 6 T + 52 T^{2} + 240 T^{3} + 1347 T^{4} + 5520 T^{5} + 27508 T^{6} + 73002 T^{7} + 279841 T^{8} $)($ 1 - 12 T + 97 T^{2} - 588 T^{3} + 2976 T^{4} - 13524 T^{5} + 51313 T^{6} - 146004 T^{7} + 279841 T^{8} $)
$29$	($ 1 + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 + 29 T^{2} $)($ 1 + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 + 29 T^{2} $)($ ( 1 - 29 T^{2} )^{2} $)($ ( 1 - 29 T^{2} )^{2} $)($ ( 1 - 22 T^{2} + 841 T^{4} )^{2} $)($ 1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4} $)($ 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} $)($ 1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4} $)($ 1 + 3 T - 43 T^{2} - 18 T^{3} + 1602 T^{4} - 522 T^{5} - 36163 T^{6} + 73167 T^{7} + 707281 T^{8} $)($ 1 - 1646 T^{4} + 707281 T^{8} $)($ ( 1 - 40 T^{2} + 841 T^{4} )( 1 + 40 T^{2} + 841 T^{4} ) $)($ 1 + 3 T + 32 T^{2} + 87 T^{3} + 841 T^{4} $)($ 1 + 3 T + 32 T^{2} + 87 T^{3} + 841 T^{4} $)($ 1 - 6 T + 41 T^{2} - 174 T^{3} + 841 T^{4} $)($ 1 - 6 T + 41 T^{2} - 174 T^{3} + 841 T^{4} $)($ ( 1 - 15 T + 104 T^{2} - 435 T^{3} + 841 T^{4} )^{2} $)($ 1 - 15 T + 99 T^{2} - 387 T^{3} - 162 T^{4} + 17112 T^{5} - 132695 T^{6} + 496248 T^{7} - 136242 T^{8} - 9438543 T^{9} + 70020819 T^{10} - 307667235 T^{11} + 594823321 T^{12} $)($ 1 - 15 T + 81 T^{2} + 45 T^{3} - 4518 T^{4} + 31692 T^{5} - 51964 T^{6} - 564705 T^{7} + 4930839 T^{8} - 14676930 T^{9} - 17187291 T^{10} + 338065677 T^{11} - 2175351603 T^{12} + 9803904633 T^{13} - 14454511731 T^{14} - 357955645770 T^{15} + 3487488738759 T^{16} - 11582748396045 T^{17} - 30909399052444 T^{18} + 546683079984828 T^{19} - 2260113293757798 T^{20} + 652821568914105 T^{21} + 34077285897316281 T^{22} - 183007646485587435 T^{23} + 353814783205469041 T^{24} $)($ 1 + 6 T + 21 T^{2} + 252 T^{3} + 249 T^{4} - 984 T^{5} + 18431 T^{6} + 29592 T^{7} + 680634 T^{8} + 5882274 T^{9} + 10161684 T^{10} + 17557326 T^{11} + 254066229 T^{12} + 509162454 T^{13} + 8545976244 T^{14} + 143462780586 T^{15} + 481399496154 T^{16} + 606965921208 T^{17} + 10963188629351 T^{18} - 16973878288056 T^{19} + 124561356827289 T^{20} + 3655800785918988 T^{21} + 8834851899304221 T^{22} + 73203058594234974 T^{23} + 353814783205469041 T^{24} $)($ 1 + 24 T + 216 T^{2} + 513 T^{3} - 5085 T^{4} - 38622 T^{5} - 39165 T^{6} + 335661 T^{7} - 972927 T^{8} - 15344370 T^{9} + 17037873 T^{10} + 849699627 T^{11} + 5794706544 T^{12} + 21856511310 T^{13} + 65301140610 T^{14} + 312703277274 T^{15} + 367683018633 T^{16} - 19987658397597 T^{17} - 182924253089192 T^{18} - 579642093530313 T^{19} + 309221418670353 T^{20} + 7626520229435586 T^{21} + 46186256031781410 T^{22} + 448302160099595190 T^{23} + 3446826590722512624 T^{24} + 14657213465553436743 T^{25} + 8523134852735071953 T^{26} - $$22\!\cdots\!30$$ T^{27} - $$40\!\cdots\!27$$ T^{28} + $$40\!\cdots\!69$$ T^{29} - $$13\!\cdots\!65$$ T^{30} - $$39\!\cdots\!58$$ T^{31} - $$15\!\cdots\!85$$ T^{32} + $$44\!\cdots\!37$$ T^{33} + $$54\!\cdots\!36$$ T^{34} + $$17\!\cdots\!16$$ T^{35} + $$21\!\cdots\!61$$ T^{36} $)($ 1 - 6 T + 9 T^{2} + 174 T^{3} - 1528 T^{4} + 5046 T^{5} + 7569 T^{6} - 146334 T^{7} + 707281 T^{8} $)($ 1 + 6 T + 18 T^{2} + 36 T^{3} - 457 T^{4} + 1044 T^{5} + 15138 T^{6} + 146334 T^{7} + 707281 T^{8} $)($ 1 - 6 T + 18 T^{2} - 36 T^{3} - 457 T^{4} - 1044 T^{5} + 15138 T^{6} - 146334 T^{7} + 707281 T^{8} $)($ 1 + 9 T^{2} + 156 T^{3} - 484 T^{4} + 4524 T^{5} + 7569 T^{6} + 707281 T^{8} $)
$31$	($ 1 - 4 T + 31 T^{2} $)($ 1 + 5 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 + 5 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ ( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) $)($ ( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) $)($ ( 1 - 35 T^{2} + 961 T^{4} )^{2} $)($ 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} $)($ ( 1 - 7 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) $)($ 1 - 5 T - 6 T^{2} - 155 T^{3} + 961 T^{4} $)($ 1 - 7 T - 17 T^{2} - 28 T^{3} + 1876 T^{4} - 868 T^{5} - 16337 T^{6} - 208537 T^{7} + 923521 T^{8} $)($ ( 1 + T + 31 T^{2} )^{4} $)($ ( 1 + 7 T + 31 T^{2} )^{4} $)($ 1 + 9 T + 58 T^{2} + 279 T^{3} + 961 T^{4} $)($ 1 - 9 T + 58 T^{2} - 279 T^{3} + 961 T^{4} $)($ 1 + 31 T^{2} + 961 T^{4} $)($ 1 + 31 T^{2} + 961 T^{4} $)($ 1 + 53 T^{2} + 1848 T^{4} + 50933 T^{6} + 923521 T^{8} $)($ 1 - 18 T + 171 T^{2} - 1253 T^{3} + 7263 T^{4} - 37719 T^{5} + 206634 T^{6} - 1169289 T^{7} + 6979743 T^{8} - 37328123 T^{9} + 157922091 T^{10} - 515324718 T^{11} + 887503681 T^{12} $)($ 1 + 81 T^{2} - 49 T^{3} + 4023 T^{4} + 2565 T^{5} + 163531 T^{6} + 464805 T^{7} + 4701186 T^{8} + 27482744 T^{9} + 112711716 T^{10} + 1250347077 T^{11} + 3229099084 T^{12} + 38760759387 T^{13} + 108315959076 T^{14} + 818738426504 T^{15} + 4341643995906 T^{16} + 13306972530555 T^{17} + 145134364457611 T^{18} + 70569855194715 T^{19} + 3431180643625143 T^{20} - 1295541485872879 T^{21} + 66389891245444881 T^{22} + 787662783788549761 T^{24} $)($ 1 + 3 T + 84 T^{2} + 434 T^{3} + 5601 T^{4} + 30963 T^{5} + 266473 T^{6} + 1627992 T^{7} + 11453211 T^{8} + 69240287 T^{9} + 408317577 T^{10} + 2527882269 T^{11} + 13547586181 T^{12} + 78364350339 T^{13} + 392393191497 T^{14} + 2062737390017 T^{15} + 10577280875931 T^{16} + 46608028794792 T^{17} + 236495768387113 T^{18} + 851873070718893 T^{19} + 4777042700707041 T^{20} + 11474796017731214 T^{21} + 68848776106387284 T^{22} + 76225430689214493 T^{23} + 787662783788549761 T^{24} $)($ 1 + 9 T - 45 T^{2} - 816 T^{3} - 1629 T^{4} + 21807 T^{5} + 131943 T^{6} - 1719 T^{7} - 1559916 T^{8} + 2236900 T^{9} - 3018924 T^{10} - 598265892 T^{11} - 3251038833 T^{12} + 8698989627 T^{13} + 152835071832 T^{14} + 400071404862 T^{15} - 1915318217007 T^{16} - 9512206426008 T^{17} - 6801570693948 T^{18} - 294878399206248 T^{19} - 1840620806543727 T^{20} + 11918527222243842 T^{21} + 141146398373360472 T^{22} + 249044687578816677 T^{23} - 2885308931361444273 T^{24} - 16459858622369202012 T^{25} - 2574813222315533484 T^{26} + 59142790811204959900 T^{27} - $$12\!\cdots\!16$$ T^{28} - 43677171784919904489 T^{29} + $$10\!\cdots\!23$$ T^{30} + $$53\!\cdots\!37$$ T^{31} - $$12\!\cdots\!09$$ T^{32} - $$19\!\cdots\!16$$ T^{33} - $$32\!\cdots\!45$$ T^{34} + $$20\!\cdots\!99$$ T^{35} + $$69\!\cdots\!41$$ T^{36} $)($ 1 + 8 T + 13 T^{2} - 88 T^{3} - 344 T^{4} - 2728 T^{5} + 12493 T^{6} + 238328 T^{7} + 923521 T^{8} $)($ 1 + 8 T - 2 T^{2} + 32 T^{3} + 1411 T^{4} + 992 T^{5} - 1922 T^{6} + 238328 T^{7} + 923521 T^{8} $)($ 1 + 8 T - 2 T^{2} + 32 T^{3} + 1411 T^{4} + 992 T^{5} - 1922 T^{6} + 238328 T^{7} + 923521 T^{8} $)($ 1 + 8 T + 13 T^{2} - 88 T^{3} - 344 T^{4} - 2728 T^{5} + 12493 T^{6} + 238328 T^{7} + 923521 T^{8} $)
$37$	($ 1 + 9 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + T + 37 T^{2} $)($ 1 - 11 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 + 9 T + 37 T^{2} $)($ ( 1 - 11 T + 37 T^{2} )^{2} $)($ ( 1 + T + 37 T^{2} )^{2} $)($ ( 1 - 8 T + 37 T^{2} )^{4} $)($ ( 1 + 6 T + 37 T^{2} )^{2} $)($ ( 1 + 4 T + 37 T^{2} )^{2} $)($ ( 1 - 2 T + 37 T^{2} )^{2} $)($ ( 1 - 6 T + 50 T^{2} - 222 T^{3} + 1369 T^{4} )^{2} $)($ ( 1 - 8 T + 32 T^{2} - 296 T^{3} + 1369 T^{4} )^{2} $)($ ( 1 + 4 T + 8 T^{2} + 148 T^{3} + 1369 T^{4} )^{2} $)($ ( 1 - 2 T + 37 T^{2} )^{2} $)($ ( 1 - 2 T + 37 T^{2} )^{2} $)($ ( 1 - 2 T + 37 T^{2} )^{2} $)($ ( 1 - 2 T + 37 T^{2} )^{2} $)($ ( 1 + 4 T + 37 T^{2} )^{4} $)($ 1 - 15 T + 60 T^{2} - 289 T^{3} + 4725 T^{4} - 17730 T^{5} - 19395 T^{6} - 656010 T^{7} + 6468525 T^{8} - 14638717 T^{9} + 112449660 T^{10} - 1040159355 T^{11} + 2565726409 T^{12} $)($ 1 + 15 T + 3 T^{2} - 578 T^{3} + 2505 T^{4} + 24945 T^{5} - 192167 T^{6} - 791163 T^{7} + 6816672 T^{8} + 1096072 T^{9} - 278194485 T^{10} + 271278831 T^{11} + 11925628483 T^{12} + 10037316747 T^{13} - 380848249965 T^{14} + 55519335016 T^{15} + 12775540812192 T^{16} - 54862373051991 T^{17} - 493047946838303 T^{18} + 2368075675082685 T^{19} + 8798761032072105 T^{20} - 75117885601554506 T^{21} + 14425753117253547 T^{22} + 2668764326691906195 T^{23} + 6582952005840035281 T^{24} $)($ 1 + 3 T - 156 T^{2} - 107 T^{3} + 13731 T^{4} - 9132 T^{5} - 864755 T^{6} + 641043 T^{7} + 43249536 T^{8} - 18536771 T^{9} - 1953626739 T^{10} + 269355786 T^{11} + 78884071369 T^{12} + 9966164082 T^{13} - 2674515005691 T^{14} - 938943061463 T^{15} + 81056593639296 T^{16} + 44452458227151 T^{17} - 2218724740814795 T^{18} - 866917901978556 T^{19} + 48229855381789251 T^{20} - 13905906158073239 T^{21} - 750139162097184444 T^{22} + 533752865338381239 T^{23} + 6582952005840035281 T^{24} $)($ 1 - 162 T^{2} - 498 T^{3} + 12069 T^{4} + 69120 T^{5} - 436659 T^{6} - 3993678 T^{7} + 5314518 T^{8} + 92943608 T^{9} - 67375773 T^{10} + 822064248 T^{11} + 22823309772 T^{12} - 67304973087 T^{13} - 1588732176582 T^{14} - 666327415302 T^{15} + 53054144866422 T^{16} + 47616232092741 T^{17} - 1542710676723420 T^{18} + 1761800587431417 T^{19} + 72631124322131718 T^{20} - 33751482567292206 T^{21} - 2977539884795097702 T^{22} - 4667193159631085259 T^{23} + 58558368622808168748 T^{24} + 78040102186568040984 T^{25} - $$23\!\cdots\!33$$ T^{26} + $$12\!\cdots\!16$$ T^{27} + $$25\!\cdots\!82$$ T^{28} - $$71\!\cdots\!14$$ T^{29} - $$28\!\cdots\!79$$ T^{30} + $$16\!\cdots\!40$$ T^{31} + $$10\!\cdots\!41$$ T^{32} - $$16\!\cdots\!14$$ T^{33} - $$19\!\cdots\!42$$ T^{34} + $$16\!\cdots\!29$$ T^{36} $)($ 1 + 24 T + 288 T^{2} + 2472 T^{3} + 16862 T^{4} + 91464 T^{5} + 394272 T^{6} + 1215672 T^{7} + 1874161 T^{8} $)($ 1 - 12 T + 72 T^{2} - 588 T^{3} + 4658 T^{4} - 21756 T^{5} + 98568 T^{6} - 607836 T^{7} + 1874161 T^{8} $)($ 1 - 12 T + 72 T^{2} - 588 T^{3} + 4658 T^{4} - 21756 T^{5} + 98568 T^{6} - 607836 T^{7} + 1874161 T^{8} $)($ 1 + 24 T + 288 T^{2} + 2472 T^{3} + 16862 T^{4} + 91464 T^{5} + 394272 T^{6} + 1215672 T^{7} + 1874161 T^{8} $)
$41$	($ 1 + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ ( 1 - 41 T^{2} )^{2} $)($ ( 1 - 41 T^{2} )^{2} $)($ ( 1 - 41 T^{2} )^{4} $)($ 1 - 3 T - 32 T^{2} - 123 T^{3} + 1681 T^{4} $)($ 1 - 9 T + 40 T^{2} - 369 T^{3} + 1681 T^{4} $)($ 1 - 3 T - 32 T^{2} - 123 T^{3} + 1681 T^{4} $)($ 1 + 12 T + 59 T^{2} + 36 T^{3} - 360 T^{4} + 1476 T^{5} + 99179 T^{6} + 827052 T^{7} + 2825761 T^{8} $)($ ( 1 - 74 T^{2} + 1681 T^{4} )^{2} $)($ ( 1 - 50 T^{2} + 1681 T^{4} )^{2} $)($ 1 - 9 T + 68 T^{2} - 369 T^{3} + 1681 T^{4} $)($ 1 - 9 T + 68 T^{2} - 369 T^{3} + 1681 T^{4} $)($ 1 - 9 T + 68 T^{2} - 369 T^{3} + 1681 T^{4} $)($ 1 - 9 T + 68 T^{2} - 369 T^{3} + 1681 T^{4} $)($ ( 1 + 9 T + 68 T^{2} + 369 T^{3} + 1681 T^{4} )^{2} $)($ 1 + 3 T + 36 T^{2} - 72 T^{3} + 738 T^{4} + 1119 T^{5} + 93799 T^{6} + 45879 T^{7} + 1240578 T^{8} - 4962312 T^{9} + 101727396 T^{10} + 347568603 T^{11} + 4750104241 T^{12} $)($ 1 + 12 T + 117 T^{2} + 630 T^{3} + 5031 T^{4} + 23943 T^{5} + 171524 T^{6} + 408330 T^{7} + 3551247 T^{8} - 22823100 T^{9} - 180203112 T^{10} - 2500776837 T^{11} - 9745515051 T^{12} - 102531850317 T^{13} - 302921431272 T^{14} - 1572990875100 T^{15} + 10034975273967 T^{16} + 47307562554330 T^{17} + 814756879833284 T^{18} + 4663001579532783 T^{19} + 40172158827707751 T^{20} + 206250618668195430 T^{21} + 1570451139287830917 T^{22} + 6603948380594981292 T^{23} + 22563490300366186081 T^{24} $)($ 1 - 15 T + 93 T^{2} - 90 T^{3} - 2460 T^{4} + 12513 T^{5} + 27971 T^{6} - 441396 T^{7} + 3206862 T^{8} - 12736494 T^{9} - 41813613 T^{10} + 1731506832 T^{11} - 16389887967 T^{12} + 70991780112 T^{13} - 70288683453 T^{14} - 877811902974 T^{15} + 9061825571982 T^{16} - 51138463696596 T^{17} + 132865165725011 T^{18} + 2436960229072953 T^{19} - 19642916063637660 T^{20} - 29464374095456490 T^{21} + 1248307315844173293 T^{22} - 8254935475743726615 T^{23} + 22563490300366186081 T^{24} $)($ 1 - 21 T + 270 T^{2} - 2844 T^{3} + 28449 T^{4} - 225534 T^{5} + 1364187 T^{6} - 5783241 T^{7} + 7120458 T^{8} + 266586381 T^{9} - 3961333476 T^{10} + 35030856111 T^{11} - 226766681787 T^{12} + 1184373682962 T^{13} - 3751533361044 T^{14} - 14056953699150 T^{15} + 350489698231473 T^{16} - 3267580417540392 T^{17} + 22906077409966138 T^{18} - 133970797119156072 T^{19} + 589173182727106113 T^{20} - 968819305899117150 T^{21} - 10600936661837054484 T^{22} + $$13\!\cdots\!62$$ T^{23} - $$10\!\cdots\!67$$ T^{24} + $$68\!\cdots\!91$$ T^{25} - $$31\!\cdots\!96$$ T^{26} + $$87\!\cdots\!41$$ T^{27} + $$95\!\cdots\!58$$ T^{28} - $$31\!\cdots\!81$$ T^{29} + $$30\!\cdots\!47$$ T^{30} - $$20\!\cdots\!14$$ T^{31} + $$10\!\cdots\!89$$ T^{32} - $$44\!\cdots\!44$$ T^{33} + $$17\!\cdots\!70$$ T^{34} - $$54\!\cdots\!01$$ T^{35} + $$10\!\cdots\!21$$ T^{36} $)($ 1 + 18 T + 181 T^{2} + 1314 T^{3} + 8076 T^{4} + 53874 T^{5} + 304261 T^{6} + 1240578 T^{7} + 2825761 T^{8} $)($ 1 + 73 T^{2} + 3648 T^{4} + 122713 T^{6} + 2825761 T^{8} $)($ 1 + 73 T^{2} + 3648 T^{4} + 122713 T^{6} + 2825761 T^{8} $)($ 1 - 18 T + 181 T^{2} - 1314 T^{3} + 8076 T^{4} - 53874 T^{5} + 304261 T^{6} - 1240578 T^{7} + 2825761 T^{8} $)
$43$	($ 1 - 8 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 - 8 T + 43 T^{2} $)($ ( 1 - 8 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} ) $)($ ( 1 - 8 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} ) $)($ ( 1 - 8 T + 43 T^{2} )^{2}( 1 + 8 T + 43 T^{2} )^{2} $)($ 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} $)($ 1 + T - 42 T^{2} + 43 T^{3} + 1849 T^{4} $)($ 1 + T - 42 T^{2} + 43 T^{3} + 1849 T^{4} $)($ 1 - 8 T - 5 T^{2} + 136 T^{3} + 160 T^{4} + 5848 T^{5} - 9245 T^{6} - 636056 T^{7} + 3418801 T^{8} $)($ ( 1 - 2 T + 2 T^{2} - 86 T^{3} + 1849 T^{4} )^{2} $)($ ( 1 - 14 T + 98 T^{2} - 602 T^{3} + 1849 T^{4} )^{2} $)($ 1 - 9 T + 70 T^{2} - 387 T^{3} + 1849 T^{4} $)($ 1 + 9 T + 70 T^{2} + 387 T^{3} + 1849 T^{4} $)($ 1 - 9 T + 70 T^{2} - 387 T^{3} + 1849 T^{4} $)($ 1 + 9 T + 70 T^{2} + 387 T^{3} + 1849 T^{4} $)($ 1 + 77 T^{2} + 4080 T^{4} + 142373 T^{6} + 3418801 T^{8} $)($ 1 - 18 T + 144 T^{2} - 740 T^{3} + 432 T^{4} + 23706 T^{5} - 185739 T^{6} + 1019358 T^{7} + 798768 T^{8} - 58835180 T^{9} + 492307344 T^{10} - 2646151974 T^{11} + 6321363049 T^{12} $)($ 1 + 9 T + 36 T^{2} + 248 T^{3} + 1629 T^{4} + 13671 T^{5} + 99658 T^{6} + 1291248 T^{7} + 7996347 T^{8} + 44034284 T^{9} + 342067257 T^{10} + 2064609882 T^{11} + 16750938331 T^{12} + 88778224926 T^{13} + 632482358193 T^{14} + 3501033817988 T^{15} + 27337919119947 T^{16} + 189824358006864 T^{17} + 629974398737242 T^{18} + 3716032232443797 T^{19} + 19040078252212029 T^{20} + 124642967760337064 T^{21} + 778013363278232964 T^{22} + 8363643655241004363 T^{23} + 39959630797262576401 T^{24} $)($ 1 + 3 T - 60 T^{2} - 16 T^{3} + 606 T^{4} - 5874 T^{5} + 128269 T^{6} + 73818 T^{7} - 5307417 T^{8} + 22910987 T^{9} - 79924800 T^{10} - 580797228 T^{11} + 14492410483 T^{12} - 24974280804 T^{13} - 147780955200 T^{14} + 1821583843409 T^{15} - 18145002547017 T^{16} + 10851869245374 T^{17} + 810834916932181 T^{18} - 1596662521642518 T^{19} + 7083049368226206 T^{20} - 8041481790989488 T^{21} - 1296688938797054940 T^{22} + 2787881218413668121 T^{23} + 39959630797262576401 T^{24} $)($ 1 - 9 T + 99 T^{2} - 816 T^{3} + 7380 T^{4} - 44028 T^{5} + 425784 T^{6} - 2654973 T^{7} + 17329428 T^{8} - 77745686 T^{9} + 612406224 T^{10} - 1498691268 T^{11} + 14593371894 T^{12} - 17177157162 T^{13} + 121626443133 T^{14} + 4355914982778 T^{15} - 8046633177891 T^{16} + 188327320360398 T^{17} - 573554182033272 T^{18} + 8098074775497114 T^{19} - 14878224745920459 T^{20} + 346325732535730446 T^{21} + 415816605409543533 T^{22} - 2525187129551918766 T^{23} + 92250001851046744806 T^{24} - $$40\!\cdots\!76$$ T^{25} + $$71\!\cdots\!24$$ T^{26} - $$39\!\cdots\!98$$ T^{27} + $$37\!\cdots\!72$$ T^{28} - $$24\!\cdots\!11$$ T^{29} + $$17\!\cdots\!84$$ T^{30} - $$75\!\cdots\!04$$ T^{31} + $$54\!\cdots\!20$$ T^{32} - $$25\!\cdots\!12$$ T^{33} + $$13\!\cdots\!99$$ T^{34} - $$52\!\cdots\!87$$ T^{35} + $$25\!\cdots\!49$$ T^{36} $)($ 1 - 8 T + 65 T^{2} + 120 T^{3} - 604 T^{4} + 5160 T^{5} + 120185 T^{6} - 636056 T^{7} + 3418801 T^{8} $)($ 1 - 2 T + 65 T^{2} - 426 T^{3} + 2744 T^{4} - 18318 T^{5} + 120185 T^{6} - 159014 T^{7} + 3418801 T^{8} $)($ 1 + 16 T + 65 T^{2} - 624 T^{3} - 8092 T^{4} - 26832 T^{5} + 120185 T^{6} + 1272112 T^{7} + 3418801 T^{8} $)($ 1 - 14 T + 65 T^{2} + 474 T^{3} - 6280 T^{4} + 20382 T^{5} + 120185 T^{6} - 1113098 T^{7} + 3418801 T^{8} $)
$47$	($ 1 + 12 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 12 T + 47 T^{2} $)($ ( 1 + 47 T^{2} )^{2} $)($ ( 1 + 47 T^{2} )^{2} $)($ ( 1 - 14 T^{2} + 2209 T^{4} )^{2} $)($ 1 - 3 T - 38 T^{2} - 141 T^{3} + 2209 T^{4} $)($ 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} $)($ 1 - 9 T + 34 T^{2} - 423 T^{3} + 2209 T^{4} $)($ 1 + 3 T - 79 T^{2} - 18 T^{3} + 5112 T^{4} - 846 T^{5} - 174511 T^{6} + 311469 T^{7} + 4879681 T^{8} $)($ ( 1 + 76 T^{2} + 2209 T^{4} )^{2} $)($ ( 1 + 76 T^{2} + 2209 T^{4} )^{2} $)($ 1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4} $)($ 1 - 3 T - 38 T^{2} - 141 T^{3} + 2209 T^{4} $)($ 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} $)($ 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} $)($ 1 - 67 T^{2} + 2280 T^{4} - 148003 T^{6} + 4879681 T^{8} $)($ 1 + 9 T + 9 T^{2} - 495 T^{3} - 3222 T^{4} + 3726 T^{5} + 123409 T^{6} + 175122 T^{7} - 7117398 T^{8} - 51392385 T^{9} + 43917129 T^{10} + 2064105063 T^{11} + 10779215329 T^{12} $)($ 1 - 9 T + 99 T^{2} - 981 T^{3} + 6354 T^{4} - 60768 T^{5} + 331868 T^{6} - 2211183 T^{7} + 13193361 T^{8} - 82909494 T^{9} + 638454717 T^{10} - 3119341005 T^{11} + 27438934035 T^{12} - 146609027235 T^{13} + 1410346469853 T^{14} - 8607912395562 T^{15} + 64379392997841 T^{16} - 507123780613281 T^{17} + 3577276632804572 T^{18} - 30786473784295584 T^{19} + 151296915448829394 T^{20} - 1097866994113814427 T^{21} + 5207314091347174851 T^{22} - 22249432935756110727 T^{23} + $$11\!\cdots\!41$$ T^{24} $)($ 1 - 15 T + 111 T^{2} - 873 T^{3} + 6828 T^{4} - 69612 T^{5} + 654227 T^{6} - 4732173 T^{7} + 31522707 T^{8} - 170376048 T^{9} + 1258782219 T^{10} - 11485670769 T^{11} + 82734051465 T^{12} - 539826526143 T^{13} + 2780649921771 T^{14} - 17688952431504 T^{15} + 153820754416467 T^{16} - 1085300249810211 T^{17} + 7052053707045683 T^{18} - 35267048661670356 T^{19} + 162583465326504108 T^{20} - 977000903018715591 T^{21} + 5838503678177135439 T^{22} - 37082388226260184545 T^{23} + $$11\!\cdots\!41$$ T^{24} $)($ 1 + 45 T + 1026 T^{2} + 15507 T^{3} + 173529 T^{4} + 1550934 T^{5} + 12137826 T^{6} + 94180626 T^{7} + 777562713 T^{8} + 6408653373 T^{9} + 47766713094 T^{10} + 314746073955 T^{11} + 2010959274003 T^{12} + 14589090065835 T^{13} + 120231976929849 T^{14} + 958518905650704 T^{15} + 6721325237600946 T^{16} + 42688545402868929 T^{17} + 277542048358340170 T^{18} + 2006361633934839663 T^{19} + 14847407449860489714 T^{20} + 99516308341373041392 T^{21} + $$58\!\cdots\!69$$ T^{22} + $$33\!\cdots\!45$$ T^{23} + $$21\!\cdots\!87$$ T^{24} + $$15\!\cdots\!65$$ T^{25} + $$11\!\cdots\!34$$ T^{26} + $$71\!\cdots\!91$$ T^{27} + $$40\!\cdots\!37$$ T^{28} + $$23\!\cdots\!78$$ T^{29} + $$14\!\cdots\!66$$ T^{30} + $$84\!\cdots\!18$$ T^{31} + $$44\!\cdots\!01$$ T^{32} + $$18\!\cdots\!01$$ T^{33} + $$58\!\cdots\!46$$ T^{34} + $$11\!\cdots\!15$$ T^{35} + $$12\!\cdots\!89$$ T^{36} $)($ 1 + 8 T - 19 T^{2} - 88 T^{3} + 1672 T^{4} - 4136 T^{5} - 41971 T^{6} + 830584 T^{7} + 4879681 T^{8} $)($ 1 - 2 T - 16 T^{2} + 148 T^{3} - 1997 T^{4} + 6956 T^{5} - 35344 T^{6} - 207646 T^{7} + 4879681 T^{8} $)($ 1 - 2 T - 16 T^{2} + 148 T^{3} - 1997 T^{4} + 6956 T^{5} - 35344 T^{6} - 207646 T^{7} + 4879681 T^{8} $)($ 1 + 8 T - 19 T^{2} - 88 T^{3} + 1672 T^{4} - 4136 T^{5} - 41971 T^{6} + 830584 T^{7} + 4879681 T^{8} $)
$53$	($ 1 - 8 T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - 5 T + 53 T^{2} $)($ 1 + 53 T^{2} $)($ 1 + 53 T^{2} $)($ 1 + 5 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 + 8 T + 53 T^{2} $)($ ( 1 - 53 T^{2} )^{2} $)($ ( 1 - 53 T^{2} )^{2} $)($ ( 1 - 25 T^{2} + 2809 T^{4} )^{2} $)($ ( 1 + 2 T + 53 T^{2} )^{2} $)($ ( 1 + 12 T + 53 T^{2} )^{2} $)($ ( 1 - 6 T + 53 T^{2} )^{2} $)($ ( 1 - 10 T + 98 T^{2} - 530 T^{3} + 2809 T^{4} )^{2} $)($ 1 - 5393 T^{4} + 7890481 T^{8} $)($ 1 + 5407 T^{4} + 7890481 T^{8} $)($ ( 1 - 53 T^{2} )^{2} $)($ ( 1 - 53 T^{2} )^{2} $)($ ( 1 - 53 T^{2} )^{2} $)($ ( 1 - 53 T^{2} )^{2} $)($ ( 1 + 2 T^{2} + 2809 T^{4} )^{2} $)($ ( 1 + 6 T + 150 T^{2} + 639 T^{3} + 7950 T^{4} + 16854 T^{5} + 148877 T^{6} )^{2} $)($ ( 1 + 6 T + 255 T^{2} + 1593 T^{3} + 29193 T^{4} + 168801 T^{5} + 1959550 T^{6} + 8946453 T^{7} + 82003137 T^{8} + 237161061 T^{9} + 2012072655 T^{10} + 2509172958 T^{11} + 22164361129 T^{12} )^{2} $)($ ( 1 + 9 T + 210 T^{2} + 1872 T^{3} + 23856 T^{4} + 168327 T^{5} + 1634317 T^{6} + 8921331 T^{7} + 67011504 T^{8} + 278697744 T^{9} + 1657001010 T^{10} + 3763759437 T^{11} + 22164361129 T^{12} )^{2} $)($ ( 1 - 33 T + 711 T^{2} - 11529 T^{3} + 156285 T^{4} - 1818492 T^{5} + 18782340 T^{6} - 173567805 T^{7} + 1455502203 T^{8} - 11084684058 T^{9} + 77141616759 T^{10} - 487551964245 T^{11} + 2796258432180 T^{12} - 14348776574652 T^{13} + 65357682623505 T^{14} - 255532919456241 T^{15} + 835219620424107 T^{16} - 2054569783574913 T^{17} + 3299763591802133 T^{18} )^{2} $)($ 1 + 16 T + 128 T^{2} + 1264 T^{3} + 11806 T^{4} + 66992 T^{5} + 359552 T^{6} + 2382032 T^{7} + 7890481 T^{8} $)($ 1 - 16 T + 128 T^{2} - 976 T^{3} + 7378 T^{4} - 51728 T^{5} + 359552 T^{6} - 2382032 T^{7} + 7890481 T^{8} $)($ 1 - 16 T + 128 T^{2} - 976 T^{3} + 7378 T^{4} - 51728 T^{5} + 359552 T^{6} - 2382032 T^{7} + 7890481 T^{8} $)($ 1 + 16 T + 128 T^{2} + 1264 T^{3} + 11806 T^{4} + 66992 T^{5} + 359552 T^{6} + 2382032 T^{7} + 7890481 T^{8} $)
$59$	($ 1 - 4 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 59 T^{2} $)($ 1 + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ ( 1 + 59 T^{2} )^{2} $)($ ( 1 + 59 T^{2} )^{2} $)($ ( 1 + 10 T^{2} + 3481 T^{4} )^{2} $)($ 1 + 11 T + 62 T^{2} + 649 T^{3} + 3481 T^{4} $)($ 1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4} $)($ 1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4} $)($ ( 1 + 7 T - 10 T^{2} + 413 T^{3} + 3481 T^{4} )^{2} $)($ 1 - 6638 T^{4} + 12117361 T^{8} $)($ 1 - 6638 T^{4} + 12117361 T^{8} $)($ 1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4} $)($ 1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4} $)($ 1 - 15 T + 166 T^{2} - 885 T^{3} + 3481 T^{4} $)($ 1 + 15 T + 166 T^{2} + 885 T^{3} + 3481 T^{4} $)($ 1 - 91 T^{2} + 4800 T^{4} - 316771 T^{6} + 12117361 T^{8} $)($ 1 - 6 T + 36 T^{2} - 261 T^{3} - 639 T^{4} + 33681 T^{5} - 161243 T^{6} + 1987179 T^{7} - 2224359 T^{8} - 53603919 T^{9} + 436224996 T^{10} - 4289545794 T^{11} + 42180533641 T^{12} $)($ 1 + 12 T + 9 T^{2} - 288 T^{3} - 7416 T^{4} - 73437 T^{5} + 128189 T^{6} + 3672837 T^{7} + 36794322 T^{8} + 361771704 T^{9} - 137989746 T^{10} - 18392855166 T^{11} - 121796603070 T^{12} - 1085178454794 T^{13} - 480342305826 T^{14} + 74300310795816 T^{15} + 445850082424242 T^{16} + 2625800417566263 T^{17} + 5407080426906149 T^{18} - 182759099090652903 T^{19} - 1088894525273644536 T^{20} - 2494942795772622432 T^{21} + 4600050779705772609 T^{22} + $$36\!\cdots\!08$$ T^{23} + $$17\!\cdots\!81$$ T^{24} $)($ 1 - 12 T + 192 T^{2} - 2349 T^{3} + 25089 T^{4} - 223824 T^{5} + 1972808 T^{6} - 12709350 T^{7} + 71501877 T^{8} - 339681357 T^{9} - 107943444 T^{10} + 13247965206 T^{11} - 122980417173 T^{12} + 781629947154 T^{13} - 375751128564 T^{14} - 69763417419303 T^{15} + 866414055786597 T^{16} - 9086223139495650 T^{17} + 83214094211233928 T^{18} - 557019929938127856 T^{19} + 3683828849054809569 T^{20} - 20349377178020451711 T^{21} + 98134416633723148992 T^{22} - $$36\!\cdots\!08$$ T^{23} + $$17\!\cdots\!81$$ T^{24} $)($ 1 + 60 T + 1593 T^{2} + 24660 T^{3} + 247662 T^{4} + 1708872 T^{5} + 8490216 T^{6} + 33550125 T^{7} + 148813002 T^{8} + 1136539629 T^{9} + 11730436263 T^{10} + 113179328610 T^{11} + 651096766104 T^{12} - 3048081644244 T^{13} - 120313325069001 T^{14} - 1538872617278898 T^{15} - 13453209049931613 T^{16} - 98005926759519540 T^{17} - 714266619705703766 T^{18} - 5782349678811652860 T^{19} - 46830620702811944853 T^{20} - $$31\!\cdots\!42$$ T^{21} - $$14\!\cdots\!61$$ T^{22} - $$21\!\cdots\!56$$ T^{23} + $$27\!\cdots\!64$$ T^{24} + $$28\!\cdots\!90$$ T^{25} + $$17\!\cdots\!23$$ T^{26} + $$98\!\cdots\!31$$ T^{27} + $$76\!\cdots\!02$$ T^{28} + $$10\!\cdots\!75$$ T^{29} + $$15\!\cdots\!96$$ T^{30} + $$17\!\cdots\!88$$ T^{31} + $$15\!\cdots\!82$$ T^{32} + $$90\!\cdots\!40$$ T^{33} + $$34\!\cdots\!13$$ T^{34} + $$76\!\cdots\!40$$ T^{35} + $$75\!\cdots\!21$$ T^{36} $)($ 1 + 12 T + 45 T^{2} - 300 T^{3} - 5524 T^{4} - 17700 T^{5} + 156645 T^{6} + 2464548 T^{7} + 12117361 T^{8} $)($ 1 + 12 T + 45 T^{2} - 828 T^{3} - 9748 T^{4} - 48852 T^{5} + 156645 T^{6} + 2464548 T^{7} + 12117361 T^{8} $)($ 1 + 6 T + 45 T^{2} - 594 T^{3} - 3376 T^{4} - 35046 T^{5} + 156645 T^{6} + 1232274 T^{7} + 12117361 T^{8} $)($ 1 - 6 T + 45 T^{2} - 462 T^{3} + 848 T^{4} - 27258 T^{5} + 156645 T^{6} - 1232274 T^{7} + 12117361 T^{8} $)
$61$	($ 1 + 5 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 + 8 T + 61 T^{2} $)($ 1 + 13 T + 61 T^{2} $)($ 1 + T + 61 T^{2} $)($ 1 + 8 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 + 5 T + 61 T^{2} $)($ ( 1 + T + 61 T^{2} )^{2} $)($ ( 1 + 13 T + 61 T^{2} )^{2} $)($ ( 1 + 4 T + 61 T^{2} )^{4} $)($ 1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4} $)($ 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} $)($ ( 1 - 14 T + 61 T^{2} )( 1 + T + 61 T^{2} ) $)($ 1 - T - 113 T^{2} + 8 T^{3} + 9214 T^{4} + 488 T^{5} - 420473 T^{6} - 226981 T^{7} + 13845841 T^{8} $)($ ( 1 + 4 T + 8 T^{2} + 244 T^{3} + 3721 T^{4} )^{2} $)($ ( 1 - 20 T + 200 T^{2} - 1220 T^{3} + 3721 T^{4} )^{2} $)($ ( 1 - 14 T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) $)($ ( 1 - 14 T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) $)($ 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} $)($ 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} $)($ ( 1 - 7 T - 12 T^{2} - 427 T^{3} + 3721 T^{4} )^{2} $)($ 1 - 18 T + 153 T^{2} - 745 T^{3} - 3915 T^{4} + 107703 T^{5} - 1034862 T^{6} + 6569883 T^{7} - 14567715 T^{8} - 169100845 T^{9} + 2118413673 T^{10} - 15202733418 T^{11} + 51520374361 T^{12} $)($ 1 + 36 T + 531 T^{2} + 3559 T^{3} + 3123 T^{4} - 91953 T^{5} - 447281 T^{6} - 4553469 T^{7} - 84400488 T^{8} - 593953490 T^{9} - 1210754052 T^{10} - 5462757351 T^{11} - 104608387268 T^{12} - 333228198411 T^{13} - 4505215827492 T^{14} - 134816157113690 T^{15} - 1168595737170408 T^{16} - 3845843074118169 T^{17} - 23044084564562441 T^{18} - 288984632000639013 T^{19} + 598701938490508563 T^{20} + 41619465944396707819 T^{21} + $$37\!\cdots\!31$$ T^{22} + $$15\!\cdots\!96$$ T^{23} + $$26\!\cdots\!21$$ T^{24} $)($ 1 - 12 T - 51 T^{2} + 583 T^{3} + 2127 T^{4} + 45474 T^{5} - 455363 T^{6} - 2399139 T^{7} + 11507670 T^{8} + 53383966 T^{9} + 844033821 T^{10} - 2578276122 T^{11} - 56950876769 T^{12} - 157274843442 T^{13} + 3140649847941 T^{14} + 12117145986646 T^{15} + 159333369100470 T^{16} - 2026303924984839 T^{17} - 23460472230148043 T^{18} + 142913087725218954 T^{19} + 407761454745216687 T^{20} + 6817687172122304203 T^{21} - 36380488494807012651 T^{22} - $$52\!\cdots\!32$$ T^{23} + $$26\!\cdots\!21$$ T^{24} $)($ 1 + 18 T + 144 T^{2} + 870 T^{3} + 693 T^{4} + 46719 T^{5} + 1363548 T^{6} + 13321629 T^{7} + 112641282 T^{8} + 631876487 T^{9} + 4072259232 T^{10} + 57229816275 T^{11} + 499398580341 T^{12} + 4512706586946 T^{13} + 40501364633055 T^{14} + 302618732115951 T^{15} + 2515574747971161 T^{16} + 17759529627029685 T^{17} + 116077839022099230 T^{18} + 1083331307248810785 T^{19} + 9360453637200690081 T^{20} + 68688702434410673931 T^{21} + $$56\!\cdots\!55$$ T^{22} + $$38\!\cdots\!46$$ T^{23} + $$25\!\cdots\!01$$ T^{24} + $$17\!\cdots\!75$$ T^{25} + $$78\!\cdots\!92$$ T^{26} + $$73\!\cdots\!67$$ T^{27} + $$80\!\cdots\!82$$ T^{28} + $$57\!\cdots\!69$$ T^{29} + $$36\!\cdots\!08$$ T^{30} + $$75\!\cdots\!39$$ T^{31} + $$68\!\cdots\!13$$ T^{32} + $$52\!\cdots\!70$$ T^{33} + $$52\!\cdots\!84$$ T^{34} + $$40\!\cdots\!78$$ T^{35} + $$13\!\cdots\!81$$ T^{36} $)($ 1 - 30 T + 261 T^{2} + 702 T^{3} - 21664 T^{4} + 42822 T^{5} + 971181 T^{6} - 6809430 T^{7} + 13845841 T^{8} $)($ 1 - 24 T + 180 T^{2} + 300 T^{3} - 11209 T^{4} + 18300 T^{5} + 669780 T^{6} - 5447544 T^{7} + 13845841 T^{8} $)($ 1 + 12 T + 180 T^{2} + 1596 T^{3} + 15143 T^{4} + 97356 T^{5} + 669780 T^{6} + 2723772 T^{7} + 13845841 T^{8} $)($ 1 + 12 T + 261 T^{2} + 2088 T^{3} + 24452 T^{4} + 127368 T^{5} + 971181 T^{6} + 2723772 T^{7} + 13845841 T^{8} $)
$67$	($ 1 + 11 T + 67 T^{2} $)($ 1 + 14 T + 67 T^{2} $)($ 1 - 10 T + 67 T^{2} $)($ 1 + 11 T + 67 T^{2} $)($ 1 + 5 T + 67 T^{2} $)($ 1 - 10 T + 67 T^{2} $)($ 1 + 14 T + 67 T^{2} $)($ 1 + 11 T + 67 T^{2} $)($ ( 1 - 5 T + 67 T^{2} )( 1 + 5 T + 67 T^{2} ) $)($ ( 1 - 11 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} ) $)($ ( 1 - 16 T + 67 T^{2} )^{2}( 1 + 16 T + 67 T^{2} )^{2} $)($ 1 + T - 66 T^{2} + 67 T^{3} + 4489 T^{4} $)($ ( 1 - 16 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} ) $)($ 1 + 7 T - 18 T^{2} + 469 T^{3} + 4489 T^{4} $)($ 1 - 4 T - 89 T^{2} + 116 T^{3} + 5464 T^{4} + 7772 T^{5} - 399521 T^{6} - 1203052 T^{7} + 20151121 T^{8} $)($ ( 1 + 10 T + 50 T^{2} + 670 T^{3} + 4489 T^{4} )^{2} $)($ ( 1 - 2 T + 2 T^{2} - 134 T^{3} + 4489 T^{4} )^{2} $)($ 1 - 15 T + 142 T^{2} - 1005 T^{3} + 4489 T^{4} $)($ 1 + 15 T + 142 T^{2} + 1005 T^{3} + 4489 T^{4} $)($ 1 + 15 T + 142 T^{2} + 1005 T^{3} + 4489 T^{4} $)($ 1 - 15 T + 142 T^{2} - 1005 T^{3} + 4489 T^{4} $)($ 1 + 53 T^{2} - 1680 T^{4} + 237917 T^{6} + 20151121 T^{8} $)($ 1 - 9 T + 45 T^{2} - 281 T^{3} - 1836 T^{4} + 68094 T^{5} - 564675 T^{6} + 4562298 T^{7} - 8241804 T^{8} - 84514403 T^{9} + 906800445 T^{10} - 12151125963 T^{11} + 90458382169 T^{12} $)($ 1 + 36 T + 630 T^{2} + 7592 T^{3} + 71910 T^{4} + 581724 T^{5} + 4963294 T^{6} + 52102143 T^{7} + 557562474 T^{8} + 5169740204 T^{9} + 40448438361 T^{10} + 276054423399 T^{11} + 1991438619445 T^{12} + 18495646367733 T^{13} + 181573039802529 T^{14} + 1554866572975652 T^{15} + 11235508878633354 T^{16} + 70344411392804301 T^{17} + 448971545469104686 T^{18} + 3525661397894916852 T^{19} + 29200326693098054310 T^{20} + $$20\!\cdots\!24$$ T^{21} + $$11\!\cdots\!70$$ T^{22} + $$43\!\cdots\!88$$ T^{23} + $$81\!\cdots\!61$$ T^{24} $)($ 1 - 15 T + 255 T^{2} - 2968 T^{3} + 36174 T^{4} - 397221 T^{5} + 4107115 T^{6} - 41367024 T^{7} + 386429292 T^{8} - 3556146616 T^{9} + 31289775603 T^{10} - 264760435272 T^{11} + 2216964278029 T^{12} - 17738949163224 T^{13} + 140459802681867 T^{14} - 1069557324668008 T^{15} + 7786983421036332 T^{16} - 55850657704271568 T^{17} + 371522978282032435 T^{18} - 2407441924578007383 T^{19} + 14689092167933931534 T^{20} - 80748994088203402696 T^{21} + $$46\!\cdots\!95$$ T^{22} - $$18\!\cdots\!45$$ T^{23} + $$81\!\cdots\!61$$ T^{24} $)($ 1 - 27 T + 378 T^{2} - 4110 T^{3} + 42309 T^{4} - 359532 T^{5} + 1903683 T^{6} + 2087343 T^{7} - 177145164 T^{8} + 2600725729 T^{9} - 29272869126 T^{10} + 274304636919 T^{11} - 1972009698093 T^{12} + 9826793958816 T^{13} - 14621223469968 T^{14} - 409049170442514 T^{15} + 7291627922092167 T^{16} - 85616450880794064 T^{17} + 791533857384890682 T^{18} - 5736302209013202288 T^{19} + 32732117742271737663 T^{20} - $$12\!\cdots\!82$$ T^{21} - $$29\!\cdots\!28$$ T^{22} + $$13\!\cdots\!12$$ T^{23} - $$17\!\cdots\!17$$ T^{24} + $$16\!\cdots\!37$$ T^{25} - $$11\!\cdots\!66$$ T^{26} + $$70\!\cdots\!63$$ T^{27} - $$32\!\cdots\!36$$ T^{28} + $$25\!\cdots\!69$$ T^{29} + $$15\!\cdots\!63$$ T^{30} - $$19\!\cdots\!84$$ T^{31} + $$15\!\cdots\!61$$ T^{32} - $$10\!\cdots\!30$$ T^{33} + $$62\!\cdots\!18$$ T^{34} - $$29\!\cdots\!29$$ T^{35} + $$74\!\cdots\!09$$ T^{36} $)($ 1 - 16 T + 65 T^{2} + 960 T^{3} - 14284 T^{4} + 64320 T^{5} + 291785 T^{6} - 4812208 T^{7} + 20151121 T^{8} $)($ 1 + 14 T + 113 T^{2} + 726 T^{3} + 3848 T^{4} + 48642 T^{5} + 507257 T^{6} + 4210682 T^{7} + 20151121 T^{8} $)($ 1 - 16 T + 113 T^{2} - 384 T^{3} - 172 T^{4} - 25728 T^{5} + 507257 T^{6} - 4812208 T^{7} + 20151121 T^{8} $)($ 1 + 2 T + 65 T^{2} + 762 T^{3} + 2600 T^{4} + 51054 T^{5} + 291785 T^{6} + 601526 T^{7} + 20151121 T^{8} $)
$71$	($ 1 - 8 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 8 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ ( 1 + 71 T^{2} )^{2} $)($ ( 1 + 71 T^{2} )^{2} $)($ ( 1 + 34 T^{2} + 5041 T^{4} )^{2} $)($ ( 1 - 4 T + 71 T^{2} )^{2} $)($ ( 1 + 12 T + 71 T^{2} )^{2} $)($ ( 1 + 12 T + 71 T^{2} )^{2} $)($ ( 1 + 4 T + 71 T^{2} )^{4} $)($ ( 1 - 140 T^{2} + 5041 T^{4} )^{2} $)($ ( 1 + 100 T^{2} + 5041 T^{4} )^{2} $)($ ( 1 - 12 T + 71 T^{2} )^{2} $)($ ( 1 + 12 T + 71 T^{2} )^{2} $)($ ( 1 - 6 T + 71 T^{2} )^{2} $)($ ( 1 + 6 T + 71 T^{2} )^{2} $)($ ( 1 + 34 T^{2} + 5041 T^{4} )^{2} $)($ 1 + 12 T - 24 T^{2} - 738 T^{3} - 228 T^{4} + 5556 T^{5} - 117857 T^{6} + 394476 T^{7} - 1149348 T^{8} - 264138318 T^{9} - 609880344 T^{10} + 21650752212 T^{11} + 128100283921 T^{12} $)($ 1 + 12 T - 201 T^{2} - 2430 T^{3} + 25608 T^{4} + 247278 T^{5} - 2990308 T^{6} - 17740170 T^{7} + 310819581 T^{8} + 1005967566 T^{9} - 26322276303 T^{10} - 30298327380 T^{11} + 1913975417427 T^{12} - 2151181243980 T^{13} - 132690594843423 T^{14} + 360046857514626 T^{15} + 7898448040925661 T^{16} - 32007335405729670 T^{17} - 383059303811237668 T^{18} + 2249023122526609698 T^{19} + 16536456428141447688 T^{20} - $$11\!\cdots\!30$$ T^{21} - $$65\!\cdots\!01$$ T^{22} + $$27\!\cdots\!52$$ T^{23} + $$16\!\cdots\!41$$ T^{24} $)($ 1 + 27 T + 78 T^{2} - 2565 T^{3} + 13071 T^{4} + 524664 T^{5} - 751711 T^{6} - 30297321 T^{7} + 410765508 T^{8} + 3391054713 T^{9} - 30034133541 T^{10} - 13624108308 T^{11} + 3600759258249 T^{12} - 967311689868 T^{13} - 151402067180181 T^{14} + 1213695783384543 T^{15} + 10438242055098948 T^{16} - 54663315804868671 T^{17} - 96294392526538831 T^{18} + 4771882122782055624 T^{19} + 8440644406913342031 T^{20} - $$11\!\cdots\!15$$ T^{21} + $$25\!\cdots\!78$$ T^{22} + $$62\!\cdots\!17$$ T^{23} + $$16\!\cdots\!41$$ T^{24} $)($ 1 - 12 T - 216 T^{2} + 3978 T^{3} + 8901 T^{4} - 529392 T^{5} + 1798959 T^{6} + 37173408 T^{7} - 298164978 T^{8} - 1281013128 T^{9} + 23327409465 T^{10} - 43122203202 T^{11} - 995587443048 T^{12} + 12405448357179 T^{13} - 32462907484212 T^{14} - 1158165262802520 T^{15} + 11716337115395100 T^{16} + 40103807685557901 T^{17} - 1167130398411512264 T^{18} + 2847370345674610971 T^{19} + 59062055398706699100 T^{20} - $$41\!\cdots\!20$$ T^{21} - $$82\!\cdots\!72$$ T^{22} + $$22\!\cdots\!29$$ T^{23} - $$12\!\cdots\!08$$ T^{24} - $$39\!\cdots\!82$$ T^{25} + $$15\!\cdots\!65$$ T^{26} - $$58\!\cdots\!68$$ T^{27} - $$97\!\cdots\!78$$ T^{28} + $$85\!\cdots\!68$$ T^{29} + $$29\!\cdots\!19$$ T^{30} - $$61\!\cdots\!12$$ T^{31} + $$73\!\cdots\!81$$ T^{32} + $$23\!\cdots\!78$$ T^{33} - $$90\!\cdots\!36$$ T^{34} - $$35\!\cdots\!92$$ T^{35} + $$21\!\cdots\!61$$ T^{36} $)($ 1 - 156 T^{2} + 13094 T^{4} - 786396 T^{6} + 25411681 T^{8} $)($ 1 - 156 T^{2} + 13094 T^{4} - 786396 T^{6} + 25411681 T^{8} $)($ 1 - 156 T^{2} + 13094 T^{4} - 786396 T^{6} + 25411681 T^{8} $)($ 1 - 156 T^{2} + 13094 T^{4} - 786396 T^{6} + 25411681 T^{8} $)
$73$	($ 1 - T + 73 T^{2} $)($ 1 + 7 T + 73 T^{2} $)($ 1 - T + 73 T^{2} $)($ 1 - 17 T + 73 T^{2} $)($ 1 + 7 T + 73 T^{2} $)($ 1 - T + 73 T^{2} $)($ 1 + 7 T + 73 T^{2} $)($ 1 - T + 73 T^{2} $)($ ( 1 - 7 T + 73 T^{2} )^{2} $)($ ( 1 + 17 T + 73 T^{2} )^{2} $)($ ( 1 - T + 73 T^{2} )^{4} $)($ ( 1 + 2 T + 73 T^{2} )^{2} $)($ ( 1 - 11 T + 73 T^{2} )^{2} $)($ ( 1 + 10 T + 73 T^{2} )^{2} $)($ ( 1 + 7 T + 84 T^{2} + 511 T^{3} + 5329 T^{4} )^{2} $)($ ( 1 - 137 T^{2} + 5329 T^{4} )^{2} $)($ ( 1 + 79 T^{2} + 5329 T^{4} )^{2} $)($ ( 1 + 2 T + 73 T^{2} )^{2} $)($ ( 1 + 2 T + 73 T^{2} )^{2} $)($ ( 1 + 11 T + 73 T^{2} )^{2} $)($ ( 1 + 11 T + 73 T^{2} )^{2} $)($ ( 1 - 4 T + 73 T^{2} )^{4} $)($ 1 - 3 T - 96 T^{2} + 23 T^{3} + 2853 T^{4} + 12258 T^{5} - 46191 T^{6} + 894834 T^{7} + 15203637 T^{8} + 8947391 T^{9} - 2726231136 T^{10} - 6219214779 T^{11} + 151334226289 T^{12} $)($ 1 + 21 T - 48 T^{2} - 3887 T^{3} - 4845 T^{4} + 448266 T^{5} + 1641574 T^{6} - 22871205 T^{7} - 33688827 T^{8} + 739848004 T^{9} - 9072236607 T^{10} + 8731491045 T^{11} + 1415682555505 T^{12} + 637398846285 T^{13} - 48345948878703 T^{14} + 287813450972068 T^{15} - 956703428153307 T^{16} - 47413645383179565 T^{17} + 248426331186138886 T^{18} + 4952173144561535802 T^{19} - 3907299145226822445 T^{20} - $$22\!\cdots\!31$$ T^{21} - $$20\!\cdots\!52$$ T^{22} + $$65\!\cdots\!17$$ T^{23} + $$22\!\cdots\!21$$ T^{24} $)($ 1 - 6 T - 228 T^{2} + 2296 T^{3} + 24945 T^{4} - 381255 T^{5} - 980072 T^{6} + 40200363 T^{7} - 102286134 T^{8} - 2648934335 T^{9} + 21743689350 T^{10} + 78452536893 T^{11} - 2017821540323 T^{12} + 5727035193189 T^{13} + 115872120546150 T^{14} - 1030480488198695 T^{15} - 2904746284290294 T^{16} + 83338230563588259 T^{17} - 148318437827512808 T^{18} - 4211875922398326735 T^{19} + 20117146992297850545 T^{20} + $$13\!\cdots\!48$$ T^{21} - $$97\!\cdots\!72$$ T^{22} - $$18\!\cdots\!62$$ T^{23} + $$22\!\cdots\!21$$ T^{24} $)($ 1 - 9 T - 423 T^{2} + 3174 T^{3} + 104238 T^{4} - 633897 T^{5} - 17768040 T^{6} + 86261373 T^{7} + 2286597285 T^{8} - 8821811794 T^{9} - 229412589363 T^{10} + 696472394517 T^{11} + 18405723457890 T^{12} - 43263862214751 T^{13} - 1209322407919761 T^{14} + 2007285699967488 T^{15} + 70978846328739252 T^{16} - 49678641613188693 T^{17} - 4558841577782266638 T^{18} - 3626540837762774589 T^{19} + $$37\!\cdots\!08$$ T^{20} + $$78\!\cdots\!96$$ T^{21} - $$34\!\cdots\!01$$ T^{22} - $$89\!\cdots\!43$$ T^{23} + $$27\!\cdots\!10$$ T^{24} + $$76\!\cdots\!49$$ T^{25} - $$18\!\cdots\!03$$ T^{26} - $$51\!\cdots\!22$$ T^{27} + $$98\!\cdots\!65$$ T^{28} + $$27\!\cdots\!21$$ T^{29} - $$40\!\cdots\!40$$ T^{30} - $$10\!\cdots\!01$$ T^{31} + $$12\!\cdots\!42$$ T^{32} + $$28\!\cdots\!18$$ T^{33} - $$27\!\cdots\!03$$ T^{34} - $$42\!\cdots\!77$$ T^{35} + $$34\!\cdots\!69$$ T^{36} $)($ 1 - 236 T^{2} + 23814 T^{4} - 1257644 T^{6} + 28398241 T^{8} $)($ 1 - 158 T^{2} + 16131 T^{4} - 841982 T^{6} + 28398241 T^{8} $)($ 1 - 158 T^{2} + 16131 T^{4} - 841982 T^{6} + 28398241 T^{8} $)($ 1 - 236 T^{2} + 23814 T^{4} - 1257644 T^{6} + 28398241 T^{8} $)
$79$	($ 1 - 5 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + 16 T + 79 T^{2} $)($ 1 - 13 T + 79 T^{2} $)($ 1 + 17 T + 79 T^{2} $)($ 1 + 16 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 - 5 T + 79 T^{2} $)($ ( 1 - 17 T + 79 T^{2} )( 1 + 17 T + 79 T^{2} ) $)($ ( 1 - 13 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) $)($ ( 1 - 146 T^{2} + 6241 T^{4} )^{2} $)($ 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} $)($ ( 1 - 13 T + 79 T^{2} )( 1 + 17 T + 79 T^{2} ) $)($ 1 - 11 T + 42 T^{2} - 869 T^{3} + 6241 T^{4} $)($ 1 + 7 T - 113 T^{2} + 28 T^{3} + 16132 T^{4} + 2212 T^{5} - 705233 T^{6} + 3451273 T^{7} + 38950081 T^{8} $)($ ( 1 - 14 T + 79 T^{2} )^{4} $)($ ( 1 - 2 T + 79 T^{2} )^{4} $)($ 1 + 15 T + 154 T^{2} + 1185 T^{3} + 6241 T^{4} $)($ 1 - 15 T + 154 T^{2} - 1185 T^{3} + 6241 T^{4} $)($ 1 - 6 T + 91 T^{2} - 474 T^{3} + 6241 T^{4} $)($ 1 + 6 T + 91 T^{2} + 474 T^{3} + 6241 T^{4} $)($ 1 - 67 T^{2} - 1752 T^{4} - 418147 T^{6} + 38950081 T^{8} $)($ 1 + 33 T + 510 T^{2} + 4168 T^{3} + 3429 T^{4} - 380187 T^{5} - 5136507 T^{6} - 30034773 T^{7} + 21400389 T^{8} + 2054986552 T^{9} + 19864541310 T^{10} + 101542861167 T^{11} + 243087455521 T^{12} $)($ 1 + 39 T + 822 T^{2} + 11936 T^{3} + 137379 T^{4} + 1304607 T^{5} + 9780148 T^{6} + 42815682 T^{7} - 154130391 T^{8} - 6081344458 T^{9} - 88425769017 T^{10} - 1013814962454 T^{11} - 9774915393497 T^{12} - 80091382033866 T^{13} - 551865224435097 T^{14} - 2998339990227862 T^{15} - 6003391214011671 T^{16} + 131746268275649118 T^{17} + 2377431291938797108 T^{18} + 25053554090705934513 T^{19} + $$20\!\cdots\!19$$ T^{20} + $$14\!\cdots\!84$$ T^{21} + $$77\!\cdots\!22$$ T^{22} + $$29\!\cdots\!81$$ T^{23} + $$59\!\cdots\!41$$ T^{24} $)($ 1 - 42 T + 813 T^{2} - 9520 T^{3} + 72840 T^{4} - 356811 T^{5} + 973207 T^{6} + 893781 T^{7} - 62793603 T^{8} + 1355379536 T^{9} - 23955645108 T^{10} + 329298299862 T^{11} - 3388931313773 T^{12} + 26014565689098 T^{13} - 149507181119028 T^{14} + 668254971049904 T^{15} - 2445815923131843 T^{16} + 2750214545354619 T^{17} + 236574413325225847 T^{18} - 6852165969260378949 T^{19} + $$11\!\cdots\!40$$ T^{20} - $$11\!\cdots\!80$$ T^{21} + $$76\!\cdots\!13$$ T^{22} - $$31\!\cdots\!18$$ T^{23} + $$59\!\cdots\!41$$ T^{24} $)($ 1 - 36 T + 702 T^{2} - 9861 T^{3} + 119196 T^{4} - 1409409 T^{5} + 16913820 T^{6} - 201585240 T^{7} + 2283030162 T^{8} - 24444793301 T^{9} + 255412728198 T^{10} - 2659995762120 T^{11} + 27368820023094 T^{12} - 271885146597855 T^{13} + 2605507077760911 T^{14} - 24385423616176365 T^{15} + 226920837770375571 T^{16} - 2103229216817817381 T^{17} + 19027927100722312626 T^{18} - $$16\!\cdots\!99$$ T^{19} + $$14\!\cdots\!11$$ T^{20} - $$12\!\cdots\!35$$ T^{21} + $$10\!\cdots\!91$$ T^{22} - $$83\!\cdots\!45$$ T^{23} + $$66\!\cdots\!74$$ T^{24} - $$51\!\cdots\!80$$ T^{25} + $$38\!\cdots\!78$$ T^{26} - $$29\!\cdots\!19$$ T^{27} + $$21\!\cdots\!62$$ T^{28} - $$15\!\cdots\!60$$ T^{29} + $$99\!\cdots\!20$$ T^{30} - $$65\!\cdots\!51$$ T^{31} + $$43\!\cdots\!76$$ T^{32} - $$28\!\cdots\!39$$ T^{33} + $$16\!\cdots\!42$$ T^{34} - $$65\!\cdots\!24$$ T^{35} + $$14\!\cdots\!61$$ T^{36} $)($ 1 - 155 T^{2} + 17784 T^{4} - 967355 T^{6} + 38950081 T^{8} $)($ ( 1 + 12 T + 65 T^{2} + 948 T^{3} + 6241 T^{4} )^{2} $)($ ( 1 + 12 T + 65 T^{2} + 948 T^{3} + 6241 T^{4} )^{2} $)($ 1 - 155 T^{2} + 17784 T^{4} - 967355 T^{6} + 38950081 T^{8} $)
$83$	($ 1 - 8 T + 83 T^{2} $)($ 1 + 3 T + 83 T^{2} $)($ 1 - 11 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 11 T + 83 T^{2} $)($ 1 - 3 T + 83 T^{2} $)($ 1 + 8 T + 83 T^{2} $)($ ( 1 + 83 T^{2} )^{2} $)($ ( 1 + 83 T^{2} )^{2} $)($ ( 1 + 139 T^{2} + 6889 T^{4} )^{2} $)($ 1 + T - 82 T^{2} + 83 T^{3} + 6889 T^{4} $)($ 1 + 12 T + 61 T^{2} + 996 T^{3} + 6889 T^{4} $)($ 1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4} $)($ 1 + 25 T + 311 T^{2} + 3700 T^{3} + 39832 T^{4} + 307100 T^{5} + 2142479 T^{6} + 14294675 T^{7} + 47458321 T^{8} $)($ 1 - 89 T^{4} + 47458321 T^{8} $)($ 1 - 11753 T^{4} + 47458321 T^{8} $)($ 1 + 15 T + 142 T^{2} + 1245 T^{3} + 6889 T^{4} $)($ 1 - 15 T + 142 T^{2} - 1245 T^{3} + 6889 T^{4} $)($ 1 + 12 T + 61 T^{2} + 996 T^{3} + 6889 T^{4} $)($ 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} $)($ 1 - 139 T^{2} + 12432 T^{4} - 957571 T^{6} + 47458321 T^{8} $)($ 1 - 18 T + 144 T^{2} - 720 T^{3} + 5580 T^{4} - 58968 T^{5} + 392545 T^{6} - 4894344 T^{7} + 38440620 T^{8} - 411686640 T^{9} + 6833998224 T^{10} - 70902731574 T^{11} + 326940373369 T^{12} $)($ 1 + 18 T + 126 T^{2} - 1260 T^{3} - 41166 T^{4} - 525114 T^{5} - 2039866 T^{6} + 36031104 T^{7} + 749106684 T^{8} + 6189995052 T^{9} + 9354005928 T^{10} - 495774705924 T^{11} - 6862378086069 T^{12} - 41149300591692 T^{13} + 64439746837992 T^{14} + 3539358700797924 T^{15} + 35551345472517564 T^{16} + 141927983068159872 T^{17} - 666914551662728554 T^{18} - 14249520279366992478 T^{19} - 92717862028235761806 T^{20} - $$23\!\cdots\!80$$ T^{21} + $$19\!\cdots\!74$$ T^{22} + $$23\!\cdots\!06$$ T^{23} + $$10\!\cdots\!61$$ T^{24} $)($ 1 + 39 T + 912 T^{2} + 16200 T^{3} + 251079 T^{4} + 3515997 T^{5} + 45358019 T^{6} + 541131408 T^{7} + 6100532325 T^{8} + 65514800025 T^{9} + 671478204717 T^{10} + 6541571603403 T^{11} + 60933732837525 T^{12} + 542950443082449 T^{13} + 4625813352295413 T^{14} + 37460510961894675 T^{15} + 289521021350726325 T^{16} + 2131538609315815344 T^{17} + 14829367667138196011 T^{18} + 95410273871375563119 T^{19} + $$56\!\cdots\!39$$ T^{20} + $$30\!\cdots\!00$$ T^{21} + $$14\!\cdots\!88$$ T^{22} + $$50\!\cdots\!13$$ T^{23} + $$10\!\cdots\!61$$ T^{24} $)($ 1 - 45 T + 945 T^{2} - 10116 T^{3} + 12339 T^{4} + 1380339 T^{5} - 22826715 T^{6} + 161300349 T^{7} + 246197610 T^{8} - 18368963478 T^{9} + 201770388396 T^{10} - 948024221238 T^{11} - 3270167174595 T^{12} + 95828229532791 T^{13} - 847092215711700 T^{14} + 3777334618062672 T^{15} + 7299207689386761 T^{16} - 335349191198370492 T^{17} + 3919398090577201708 T^{18} - 27833982869464750836 T^{19} + 50284241772185396529 T^{20} + $$21\!\cdots\!64$$ T^{21} - $$40\!\cdots\!00$$ T^{22} + $$37\!\cdots\!13$$ T^{23} - $$10\!\cdots\!55$$ T^{24} - $$25\!\cdots\!26$$ T^{25} + $$45\!\cdots\!36$$ T^{26} - $$34\!\cdots\!34$$ T^{27} + $$38\!\cdots\!90$$ T^{28} + $$20\!\cdots\!83$$ T^{29} - $$24\!\cdots\!15$$ T^{30} + $$12\!\cdots\!57$$ T^{31} + $$90\!\cdots\!31$$ T^{32} - $$61\!\cdots\!12$$ T^{33} + $$47\!\cdots\!45$$ T^{34} - $$18\!\cdots\!35$$ T^{35} + $$34\!\cdots\!09$$ T^{36} $)($ 1 - 16 T + 185 T^{2} - 784 T^{3} + 4900 T^{4} - 65072 T^{5} + 1274465 T^{6} - 9148592 T^{7} + 47458321 T^{8} $)($ 1 - 2 T + 2 T^{2} + 328 T^{3} - 7217 T^{4} + 27224 T^{5} + 13778 T^{6} - 1143574 T^{7} + 47458321 T^{8} $)($ 1 - 2 T + 2 T^{2} + 328 T^{3} - 7217 T^{4} + 27224 T^{5} + 13778 T^{6} - 1143574 T^{7} + 47458321 T^{8} $)($ 1 - 22 T + 185 T^{2} + 290 T^{3} - 14024 T^{4} + 24070 T^{5} + 1274465 T^{6} - 12579314 T^{7} + 47458321 T^{8} $)
$89$	($ 1 + 12 T + 89 T^{2} $)($ 1 - 18 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 89 T^{2} $)($ 1 + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 + 18 T + 89 T^{2} $)($ 1 - 12 T + 89 T^{2} $)($ ( 1 - 89 T^{2} )^{2} $)($ ( 1 - 89 T^{2} )^{2} $)($ ( 1 - 142 T^{2} + 7921 T^{4} )^{2} $)($ ( 1 - 18 T + 89 T^{2} )^{2} $)($ ( 1 + 6 T + 89 T^{2} )^{2} $)($ ( 1 + 6 T + 89 T^{2} )^{2} $)($ ( 1 + 6 T + 89 T^{2} )^{4} $)($ ( 1 + 64 T^{2} + 7921 T^{4} )^{2} $)($ ( 1 - 176 T^{2} + 7921 T^{4} )^{2} $)($ 1 - 130 T^{2} + 7921 T^{4} $)($ 1 - 130 T^{2} + 7921 T^{4} $)($ 1 + 14 T^{2} + 7921 T^{4} $)($ 1 + 14 T^{2} + 7921 T^{4} $)($ ( 1 - 166 T^{2} + 7921 T^{4} )^{2} $)($ 1 + 15 T - 78 T^{2} - 477 T^{3} + 27177 T^{4} + 70638 T^{5} - 2238167 T^{6} + 6286782 T^{7} + 215269017 T^{8} - 336270213 T^{9} - 4893894798 T^{10} + 83760891735 T^{11} + 496981290961 T^{12} $)($ 1 - 12 T - 120 T^{2} + 3294 T^{3} - 12273 T^{4} - 248142 T^{5} + 2973695 T^{6} - 4697397 T^{7} - 153066366 T^{8} + 1115642430 T^{9} + 2098738827 T^{10} - 25141746861 T^{11} - 47336761416 T^{12} - 2237615470629 T^{13} + 16624110248667 T^{14} + 786493328234670 T^{15} - 9603726824566206 T^{16} - 26230544103554253 T^{17} + 1477870780024270895 T^{18} - 10975651903646357118 T^{19} - 48313754412381640113 T^{20} + $$11\!\cdots\!46$$ T^{21} - $$37\!\cdots\!20$$ T^{22} - $$33\!\cdots\!68$$ T^{23} + $$24\!\cdots\!21$$ T^{24} $)($ 1 - 9 T - 273 T^{2} + 2772 T^{3} + 38802 T^{4} - 449316 T^{5} - 3561871 T^{6} + 54551502 T^{7} + 157767516 T^{8} - 4371660207 T^{9} + 3816883044 T^{10} + 152630961444 T^{11} - 900621732009 T^{12} + 13584155568516 T^{13} + 30233530591524 T^{14} - 3081884924468583 T^{15} + 9898687510843356 T^{16} + 304618830200242398 T^{17} - 1770183247816548031 T^{18} - 19873846469919508164 T^{19} + $$15\!\cdots\!62$$ T^{20} + $$97\!\cdots\!48$$ T^{21} - $$85\!\cdots\!73$$ T^{22} - $$24\!\cdots\!01$$ T^{23} + $$24\!\cdots\!21$$ T^{24} $)($ 1 + 48 T + 729 T^{2} + 540 T^{3} - 60516 T^{4} + 309648 T^{5} + 9164505 T^{6} - 43924695 T^{7} - 296290449 T^{8} + 17649268605 T^{9} + 60514001892 T^{10} - 1616101715796 T^{11} + 6831214397718 T^{12} + 217593105310137 T^{13} - 956051155825812 T^{14} - 10434643262054325 T^{15} + 213339340235303568 T^{16} + 707450617777750446 T^{17} - 16906270535571748808 T^{18} + 62963104982219789694 T^{19} + $$16\!\cdots\!28$$ T^{20} - $$73\!\cdots\!25$$ T^{21} - $$59\!\cdots\!92$$ T^{22} + $$12\!\cdots\!13$$ T^{23} + $$33\!\cdots\!98$$ T^{24} - $$71\!\cdots\!84$$ T^{25} + $$23\!\cdots\!52$$ T^{26} + $$61\!\cdots\!45$$ T^{27} - $$92\!\cdots\!49$$ T^{28} - $$12\!\cdots\!55$$ T^{29} + $$22\!\cdots\!05$$ T^{30} + $$68\!\cdots\!12$$ T^{31} - $$11\!\cdots\!56$$ T^{32} + $$94\!\cdots\!60$$ T^{33} + $$11\!\cdots\!69$$ T^{34} + $$66\!\cdots\!92$$ T^{35} + $$12\!\cdots\!81$$ T^{36} $)($ 1 + 36 T^{2} + 13094 T^{4} + 285156 T^{6} + 62742241 T^{8} $)($ ( 1 - 174 T^{2} + 7921 T^{4} )^{2} $)($ ( 1 - 174 T^{2} + 7921 T^{4} )^{2} $)($ 1 + 36 T^{2} + 13094 T^{4} + 285156 T^{6} + 62742241 T^{8} $)
$97$	($ 1 - 5 T + 97 T^{2} $)($ 1 + T + 97 T^{2} $)($ 1 + T + 97 T^{2} $)($ 1 - 5 T + 97 T^{2} $)($ 1 + 19 T + 97 T^{2} $)($ 1 + T + 97 T^{2} $)($ 1 + T + 97 T^{2} $)($ 1 - 5 T + 97 T^{2} $)($ ( 1 - 19 T + 97 T^{2} )^{2} $)($ ( 1 + 5 T + 97 T^{2} )^{2} $)($ ( 1 + 5 T + 97 T^{2} )^{4} $)($ 1 - 13 T + 72 T^{2} - 1261 T^{3} + 9409 T^{4} $)($ ( 1 - 14 T + 97 T^{2} )( 1 + 19 T + 97 T^{2} ) $)($ 1 + 11 T + 24 T^{2} + 1067 T^{3} + 9409 T^{4} $)($ 1 - 8 T - 113 T^{2} + 136 T^{3} + 15712 T^{4} + 13192 T^{5} - 1063217 T^{6} - 7301384 T^{7} + 88529281 T^{8} $)($ ( 1 - 5 T + 97 T^{2} )^{4} $)($ ( 1 + 7 T + 97 T^{2} )^{4} $)($ ( 1 - 19 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) $)($ ( 1 - 19 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) $)($ 1 + 13 T + 72 T^{2} + 1261 T^{3} + 9409 T^{4} $)($ 1 + 13 T + 72 T^{2} + 1261 T^{3} + 9409 T^{4} $)($ ( 1 + T - 96 T^{2} + 97 T^{3} + 9409 T^{4} )^{2} $)($ 1 + 12 T + 51 T^{2} + 1277 T^{3} + 801 T^{4} - 56169 T^{5} + 617238 T^{6} - 5448393 T^{7} + 7536609 T^{8} + 1165483421 T^{9} + 4514993331 T^{10} + 103048083084 T^{11} + 832972004929 T^{12} $)($ 1 - 39 T + 993 T^{2} - 19028 T^{3} + 304221 T^{4} - 4077399 T^{5} + 47593567 T^{6} - 476249436 T^{7} + 4125278700 T^{8} - 29493453512 T^{9} + 169040152338 T^{10} - 681702895626 T^{11} + 3451348757128 T^{12} - 66125180875722 T^{13} + 1590498793348242 T^{14} - 26917878697157576 T^{15} + 365207957235614700 T^{16} - 4089715954136345052 T^{17} + 39644108925712691743 T^{18} - $$32\!\cdots\!87$$ T^{19} + $$23\!\cdots\!81$$ T^{20} - $$14\!\cdots\!76$$ T^{21} + $$73\!\cdots\!57$$ T^{22} - $$27\!\cdots\!67$$ T^{23} + $$69\!\cdots\!41$$ T^{24} $)($ 1 - 3 T + 102 T^{2} - 1010 T^{3} + 15132 T^{4} - 13512 T^{5} + 1127323 T^{6} - 7762230 T^{7} + 23311719 T^{8} + 575063737 T^{9} + 1596748254 T^{10} + 54554445012 T^{11} - 1453572795209 T^{12} + 5291781166164 T^{13} + 15023804321886 T^{14} + 524845146039001 T^{15} + 2063769721944039 T^{16} - 66656910163093110 T^{17} + 939028499512575067 T^{18} - 1091746419868262856 T^{19} + $$11\!\cdots\!52$$ T^{20} - $$76\!\cdots\!70$$ T^{21} + $$75\!\cdots\!98$$ T^{22} - $$21\!\cdots\!59$$ T^{23} + $$69\!\cdots\!41$$ T^{24} $)($ 1 + 27 T + 171 T^{2} - 1506 T^{3} - 5796 T^{4} + 238266 T^{5} - 1047822 T^{6} - 47407473 T^{7} + 141058260 T^{8} + 5136199520 T^{9} - 34758298530 T^{10} - 613734906312 T^{11} + 4119485195664 T^{12} + 37279586300094 T^{13} - 763210465522713 T^{14} - 3540249166293810 T^{15} + 84441145547637873 T^{16} + 225577194346293930 T^{17} - 6812284288441068552 T^{18} + 21880987851590511210 T^{19} + $$79\!\cdots\!57$$ T^{20} - $$32\!\cdots\!30$$ T^{21} - $$67\!\cdots\!53$$ T^{22} + $$32\!\cdots\!58$$ T^{23} + $$34\!\cdots\!56$$ T^{24} - $$49\!\cdots\!56$$ T^{25} - $$27\!\cdots\!30$$ T^{26} + $$39\!\cdots\!40$$ T^{27} + $$10\!\cdots\!40$$ T^{28} - $$33\!\cdots\!69$$ T^{29} - $$72\!\cdots\!02$$ T^{30} + $$16\!\cdots\!82$$ T^{31} - $$37\!\cdots\!24$$ T^{32} - $$95\!\cdots\!58$$ T^{33} + $$10\!\cdots\!91$$ T^{34} + $$16\!\cdots\!99$$ T^{35} + $$57\!\cdots\!89$$ T^{36} $)($ ( 1 + T - 96 T^{2} + 97 T^{3} + 9409 T^{4} )^{2} $)($ 1 + 20 T + 109 T^{2} + 1940 T^{3} + 36472 T^{4} + 188180 T^{5} + 1025581 T^{6} + 18253460 T^{7} + 88529281 T^{8} $)($ 1 + 20 T + 109 T^{2} + 1940 T^{3} + 36472 T^{4} + 188180 T^{5} + 1025581 T^{6} + 18253460 T^{7} + 88529281 T^{8} $)($ ( 1 + T - 96 T^{2} + 97 T^{3} + 9409 T^{4} )^{2} $)
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Introduction	Features
Universe	News

Level:	\( N \)	=	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 43 \)
Sturm bound:			\(20736\)
Trace bound:			\(10\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(432))\) 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	432.2

Level	432
Weight	2
Dimension	2232
Nonzero newspaces	12
Newform subspaces	43
Sturm bound	20736
Trace bound	10

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
432.2.a	\(\chi_{432}(1, \cdot)\)	432.2.a.a	1	1
		432.2.a.b	1
		432.2.a.c	1
		432.2.a.d	1
		432.2.a.e	1
		432.2.a.f	1
		432.2.a.g	1
		432.2.a.h	1
432.2.c	\(\chi_{432}(431, \cdot)\)	432.2.c.a	2	1
		432.2.c.b	2
		432.2.c.c	4
432.2.d	\(\chi_{432}(217, \cdot)\)	None	0	1
432.2.f	\(\chi_{432}(215, \cdot)\)	None	0	1
432.2.i	\(\chi_{432}(145, \cdot)\)	432.2.i.a	2	2
		432.2.i.b	2
		432.2.i.c	2
		432.2.i.d	4
432.2.k	\(\chi_{432}(109, \cdot)\)	432.2.k.a	4	2
		432.2.k.b	4
		432.2.k.c	24
		432.2.k.d	32
432.2.l	\(\chi_{432}(107, \cdot)\)	432.2.l.a	32	2
432.2.l	\(\chi_{432}(107, \cdot)\)	432.2.l.b	32	2
432.2.p	\(\chi_{432}(71, \cdot)\)	None	0	2
432.2.r	\(\chi_{432}(73, \cdot)\)	None	0	2
432.2.s	\(\chi_{432}(143, \cdot)\)	432.2.s.a	2	2
		432.2.s.b	2
		432.2.s.c	2
		432.2.s.d	2
		432.2.s.e	4
432.2.u	\(\chi_{432}(49, \cdot)\)	432.2.u.a	6	6
		432.2.u.b	12
		432.2.u.c	12
		432.2.u.d	18
		432.2.u.e	24
		432.2.u.f	30
432.2.v	\(\chi_{432}(35, \cdot)\)	432.2.v.a	88	4
432.2.y	\(\chi_{432}(37, \cdot)\)	432.2.y.a	4	4
		432.2.y.b	4
		432.2.y.c	4
		432.2.y.d	4
		432.2.y.e	72
432.2.bb	\(\chi_{432}(25, \cdot)\)	None	0	6
432.2.bd	\(\chi_{432}(23, \cdot)\)	None	0	6
432.2.be	\(\chi_{432}(47, \cdot)\)	432.2.be.a	36	6
		432.2.be.b	36
		432.2.be.c	36
432.2.bg	\(\chi_{432}(13, \cdot)\)	432.2.bg.a	840	12
432.2.bj	\(\chi_{432}(11, \cdot)\)	432.2.bj.a	840	12