LMFDB - Space of Modular Forms of Level 2541, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	2541.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 44 $
Sturm bound:			$704$
Trace bound:			$7$
Distinguishing $T_p$:			$2$, $5$, $13$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(2541))$.

	Total	New	Old
Modular forms	376	108	268
Cusp forms	329	108	221
Eisenstein series	47	0	47

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

$3$	$7$	$11$	Fricke	Dim.
$+$	$+$	$+$	$+$	$12$
$+$	$+$	$-$	$-$	$15$
$+$	$-$	$+$	$-$	$12$
$+$	$-$	$-$	$+$	$15$
$-$	$+$	$+$	$-$	$16$
$-$	$+$	$-$	$+$	$10$
$-$	$-$	$+$	$+$	$8$
$-$	$-$	$-$	$-$	$20$
Plus space			$+$	$45$
Minus space			$-$	$63$

Trace form

$ 108q + 104q^{4} - 8q^{5} - 4q^{6} + 2q^{7} + 108q^{9} + O(q^{10}) $

$ 108q + 104q^{4} - 8q^{5} - 4q^{6} + 2q^{7} + 108q^{9} + 8q^{12} + 2q^{14} + 104q^{16} - 16q^{17} - 8q^{19} + 2q^{21} + 8q^{23} - 12q^{24} + 92q^{25} + 16q^{26} + 6q^{28} - 16q^{29} + 16q^{30} + 16q^{31} + 40q^{32} + 8q^{34} - 4q^{35} + 104q^{36} + 48q^{38} + 16q^{39} + 48q^{40} - 32q^{41} - 2q^{42} + 24q^{43} - 8q^{45} + 32q^{46} + 32q^{47} + 32q^{48} + 108q^{49} + 64q^{50} + 56q^{52} - 4q^{54} + 18q^{56} + 16q^{57} + 64q^{58} + 8q^{59} + 16q^{60} - 24q^{61} + 16q^{62} + 2q^{63} + 96q^{64} - 40q^{65} + 16q^{67} - 32q^{68} - 16q^{69} + 12q^{70} - 32q^{73} - 48q^{74} + 16q^{75} + 24q^{78} + 32q^{80} + 108q^{81} + 56q^{82} + 16q^{83} + 6q^{84} - 8q^{85} + 32q^{86} + 8q^{87} - 24q^{89} - 12q^{91} + 56q^{92} + 8q^{93} - 24q^{94} + 24q^{95} - 28q^{96} - 8q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(2541))$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	3	7	11	$q$-expansion
2541.2.a.a	$1$	$20.290$	$\Q$	None	$-2$	$-1$	$-3$	$1$	$+$	$-$	$-$	$q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots$
2541.2.a.b	$1$	$20.290$	$\Q$	None	$-2$	$-1$	$1$	$-1$	$+$	$+$	$-$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots$
2541.2.a.c	$1$	$20.290$	$\Q$	None	$-1$	$-1$	$-3$	$-1$	$+$	$+$	$-$	$q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\cdots$
2541.2.a.d	$1$	$20.290$	$\Q$	None	$-1$	$-1$	$1$	$1$	$+$	$-$	$-$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
2541.2.a.e	$1$	$20.290$	$\Q$	None	$0$	$1$	$-3$	$-1$	$-$	$+$	$-$	$q+q^{3}-2q^{4}-3q^{5}-q^{7}+q^{9}-2q^{12}+\cdots$
2541.2.a.f	$1$	$20.290$	$\Q$	None	$0$	$1$	$-3$	$1$	$-$	$-$	$-$	$q+q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}-2q^{12}+\cdots$
2541.2.a.g	$1$	$20.290$	$\Q$	None	$1$	$-1$	$-3$	$1$	$+$	$-$	$-$	$q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots$
2541.2.a.h	$1$	$20.290$	$\Q$	None	$1$	$-1$	$-2$	$-1$	$+$	$+$	$-$	$q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
2541.2.a.i	$1$	$20.290$	$\Q$	None	$1$	$-1$	$1$	$-1$	$+$	$+$	$-$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
2541.2.a.j	$1$	$20.290$	$\Q$	None	$1$	$1$	$-2$	$1$	$-$	$-$	$-$	$q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
2541.2.a.k	$1$	$20.290$	$\Q$	None	$2$	$-1$	$-3$	$-1$	$+$	$+$	$-$	$q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots$
2541.2.a.l	$1$	$20.290$	$\Q$	None	$2$	$-1$	$1$	$1$	$+$	$-$	$-$	$q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots$
2541.2.a.m	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-3$	$-2$	$1$	$-2$	$+$	$+$	$-$	$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+\cdots$
2541.2.a.n	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-2$	$-2$	$1$	$2$	$+$	$-$	$+$	$q-q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}+q^{6}+\cdots$
2541.2.a.o	$2$	$20.290$	$\Q(\sqrt{3}) $	None	$-2$	$-2$	$-4$	$2$	$+$	$-$	$-$	$q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots$
2541.2.a.p	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-1$	$-2$	$-1$	$-2$	$+$	$+$	$+$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
2541.2.a.q	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-1$	$-2$	$0$	$-2$	$+$	$+$	$+$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots$
2541.2.a.r	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-1$	$2$	$-4$	$2$	$-$	$-$	$+$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots$
2541.2.a.s	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-1$	$2$	$-3$	$-2$	$-$	$+$	$-$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
2541.2.a.t	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$-1$	$2$	$2$	$-2$	$-$	$+$	$-$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots$
2541.2.a.u	$2$	$20.290$	$\Q(\sqrt{17}) $	None	$-1$	$2$	$2$	$-2$	$-$	$+$	$-$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots$
2541.2.a.v	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$0$	$-2$	$1$	$-2$	$+$	$+$	$-$	$q+(1-2\beta )q^{2}-q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots$
2541.2.a.w	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$0$	$-2$	$1$	$2$	$+$	$-$	$+$	$q+(1-2\beta )q^{2}-q^{3}+3q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
2541.2.a.x	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$1$	$-2$	$-1$	$2$	$+$	$-$	$-$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
2541.2.a.y	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$1$	$-2$	$0$	$2$	$+$	$-$	$+$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots$
2541.2.a.z	$2$	$20.290$	$\Q(\sqrt{21}) $	None	$1$	$-2$	$6$	$-2$	$+$	$+$	$-$	$q+\beta q^{2}-q^{3}+(3+\beta )q^{4}+3q^{5}-\beta q^{6}+\cdots$
2541.2.a.ba	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$1$	$2$	$-4$	$-2$	$-$	$+$	$+$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots$
2541.2.a.bb	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$1$	$2$	$-3$	$2$	$-$	$-$	$+$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
2541.2.a.bc	$2$	$20.290$	$\Q(\sqrt{17}) $	None	$1$	$2$	$2$	$2$	$-$	$-$	$-$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots$
2541.2.a.bd	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$2$	$-2$	$1$	$-2$	$+$	$+$	$-$	$q+q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}-q^{6}+\cdots$
2541.2.a.be	$2$	$20.290$	$\Q(\sqrt{3}) $	None	$2$	$-2$	$-4$	$-2$	$+$	$+$	$-$	$q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots$
2541.2.a.bf	$2$	$20.290$	$\Q(\sqrt{5}) $	None	$3$	$-2$	$1$	$2$	$+$	$-$	$+$	$q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
2541.2.a.bg	$3$	$20.290$	3.3.229.1	None	$-2$	$3$	$4$	$3$	$-$	$-$	$-$	$q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+\cdots$
2541.2.a.bh	$3$	$20.290$	3.3.316.1	None	$-1$	$3$	$1$	$-3$	$-$	$+$	$-$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
2541.2.a.bi	$3$	$20.290$	3.3.837.1	None	$0$	$-3$	$0$	$3$	$+$	$-$	$-$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
2541.2.a.bj	$3$	$20.290$	3.3.316.1	None	$1$	$3$	$1$	$3$	$-$	$-$	$-$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
2541.2.a.bk	$4$	$20.290$	4.4.7488.1	None	$-2$	$-4$	$6$	$-4$	$+$	$+$	$+$	$q+\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots$
2541.2.a.bl	$4$	$20.290$	4.4.7488.1	None	$-2$	$4$	$-2$	$4$	$-$	$-$	$+$	$q+\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots$
2541.2.a.bm	$4$	$20.290$	4.4.725.1	None	$-1$	$-4$	$-4$	$4$	$+$	$-$	$-$	$q+(-1+\beta _{1}+\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots$
2541.2.a.bn	$4$	$20.290$	4.4.725.1	None	$1$	$-4$	$-4$	$-4$	$+$	$+$	$+$	$q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots$
2541.2.a.bo	$4$	$20.290$	4.4.7488.1	None	$2$	$-4$	$6$	$4$	$+$	$-$	$+$	$q-\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots$
2541.2.a.bp	$4$	$20.290$	4.4.7488.1	None	$2$	$4$	$-2$	$-4$	$-$	$+$	$+$	$q-\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots$
2541.2.a.bq	$10$	$20.290$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$10$	$5$	$-10$	$-$	$+$	$+$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$
2541.2.a.br	$10$	$20.290$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$0$	$10$	$5$	$10$	$-$	$-$	$-$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(2541))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(2541)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(11))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(21))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(33))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(77))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(121))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(231))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(363))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(847))$$^{\oplus 2}$

Hecke Characteristic Polynomials

$p$	$F_p(T)$
$2$	($ 1 + 2 T + 2 T^{2} $)($ 1 + 2 T + 2 T^{2} $)($ 1 + T + 2 T^{2} $)($ 1 + T + 2 T^{2} $)($ 1 + 2 T^{2} $)($ 1 + 2 T^{2} $)($ 1 - T + 2 T^{2} $)($ 1 - T + 2 T^{2} $)($ 1 - T + 2 T^{2} $)($ 1 - T + 2 T^{2} $)($ 1 - 2 T + 2 T^{2} $)($ 1 - 2 T + 2 T^{2} $)($ 1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4} $)($ ( 1 + T + 2 T^{2} )^{2} $)($ 1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4} $)($ 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} $)($ 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} $)($ 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} $)($ 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} $)($ 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} $)($ 1 + T + 2 T^{3} + 4 T^{4} $)($ 1 - T^{2} + 4 T^{4} $)($ 1 - T^{2} + 4 T^{4} $)($ 1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4} $)($ 1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4} $)($ 1 - T - T^{2} - 2 T^{3} + 4 T^{4} $)($ 1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4} $)($ 1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4} $)($ 1 - T - 2 T^{3} + 4 T^{4} $)($ ( 1 - T + 2 T^{2} )^{2} $)($ 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} $)($ 1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4} $)($ 1 + 2 T + 2 T^{2} + T^{3} + 4 T^{4} + 8 T^{5} + 8 T^{6} $)($ 1 + T + 2 T^{2} + 2 T^{3} + 4 T^{4} + 4 T^{5} + 8 T^{6} $)($ 1 + T^{3} + 8 T^{6} $)($ 1 - T + 2 T^{2} - 2 T^{3} + 4 T^{4} - 4 T^{5} + 8 T^{6} $)($ 1 + 2 T + 4 T^{2} + 4 T^{3} + 6 T^{4} + 8 T^{5} + 16 T^{6} + 16 T^{7} + 16 T^{8} $)($ 1 + 2 T + 4 T^{2} + 4 T^{3} + 6 T^{4} + 8 T^{5} + 16 T^{6} + 16 T^{7} + 16 T^{8} $)($ 1 + T + 3 T^{2} - T^{3} + 3 T^{4} - 2 T^{5} + 12 T^{6} + 8 T^{7} + 16 T^{8} $)($ 1 - T + 3 T^{2} + T^{3} + 3 T^{4} + 2 T^{5} + 12 T^{6} - 8 T^{7} + 16 T^{8} $)($ 1 - 2 T + 4 T^{2} - 4 T^{3} + 6 T^{4} - 8 T^{5} + 16 T^{6} - 16 T^{7} + 16 T^{8} $)($ 1 - 2 T + 4 T^{2} - 4 T^{3} + 6 T^{4} - 8 T^{5} + 16 T^{6} - 16 T^{7} + 16 T^{8} $)($ 1 + T^{2} - T^{3} - 8 T^{5} + 4 T^{6} - 7 T^{7} + 13 T^{8} - 8 T^{9} + 41 T^{10} - 16 T^{11} + 52 T^{12} - 56 T^{13} + 64 T^{14} - 256 T^{15} - 128 T^{17} + 256 T^{18} + 1024 T^{20} $)($ 1 + T^{2} + T^{3} + 8 T^{5} + 4 T^{6} + 7 T^{7} + 13 T^{8} + 8 T^{9} + 41 T^{10} + 16 T^{11} + 52 T^{12} + 56 T^{13} + 64 T^{14} + 256 T^{15} + 128 T^{17} + 256 T^{18} + 1024 T^{20} $)
$3$	($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 - T $)($ 1 - T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 - T $)($ 1 + T $)($ 1 + T $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 - T )^{3} $)($ ( 1 - T )^{3} $)($ ( 1 + T )^{3} $)($ ( 1 - T )^{3} $)($ ( 1 + T )^{4} $)($ ( 1 - T )^{4} $)($ ( 1 + T )^{4} $)($ ( 1 + T )^{4} $)($ ( 1 + T )^{4} $)($ ( 1 - T )^{4} $)($ ( 1 - T )^{10} $)($ ( 1 - T )^{10} $)
$5$	($ 1 + 3 T + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4} $)($ 1 - T - T^{2} - 5 T^{3} + 25 T^{4} $)($ 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} $)($ 1 + T + 9 T^{2} + 5 T^{3} + 25 T^{4} $)($ 1 + 5 T^{2} + 25 T^{4} $)($ 1 + 4 T + 9 T^{2} + 20 T^{3} + 25 T^{4} $)($ 1 + 3 T + 11 T^{2} + 15 T^{3} + 25 T^{4} $)($ ( 1 - T + 5 T^{2} )^{2} $)($ ( 1 - T + 5 T^{2} )^{2} $)($ 1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4} $)($ 1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4} $)($ 1 + T + 9 T^{2} + 5 T^{3} + 25 T^{4} $)($ 1 + 5 T^{2} + 25 T^{4} $)($ ( 1 - 3 T + 5 T^{2} )^{2} $)($ 1 + 4 T + 9 T^{2} + 20 T^{3} + 25 T^{4} $)($ 1 + 3 T + 11 T^{2} + 15 T^{3} + 25 T^{4} $)($ ( 1 - T + 5 T^{2} )^{2} $)($ 1 - T - T^{2} - 5 T^{3} + 25 T^{4} $)($ 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} $)($ 1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4} $)($ 1 - 4 T + 8 T^{2} - 14 T^{3} + 40 T^{4} - 100 T^{5} + 125 T^{6} $)($ 1 - T + 8 T^{2} - 11 T^{3} + 40 T^{4} - 25 T^{5} + 125 T^{6} $)($ 1 + 2 T^{3} + 125 T^{6} $)($ 1 - T + 8 T^{2} - 11 T^{3} + 40 T^{4} - 25 T^{5} + 125 T^{6} $)($ 1 - 6 T + 28 T^{2} - 84 T^{3} + 219 T^{4} - 420 T^{5} + 700 T^{6} - 750 T^{7} + 625 T^{8} $)($ 1 + 2 T + 16 T^{2} + 28 T^{3} + 111 T^{4} + 140 T^{5} + 400 T^{6} + 250 T^{7} + 625 T^{8} $)($ 1 + 4 T + 12 T^{2} + 36 T^{3} + 86 T^{4} + 180 T^{5} + 300 T^{6} + 500 T^{7} + 625 T^{8} $)($ 1 + 4 T + 12 T^{2} + 36 T^{3} + 86 T^{4} + 180 T^{5} + 300 T^{6} + 500 T^{7} + 625 T^{8} $)($ 1 - 6 T + 28 T^{2} - 84 T^{3} + 219 T^{4} - 420 T^{5} + 700 T^{6} - 750 T^{7} + 625 T^{8} $)($ 1 + 2 T + 16 T^{2} + 28 T^{3} + 111 T^{4} + 140 T^{5} + 400 T^{6} + 250 T^{7} + 625 T^{8} $)($ 1 - 5 T + 22 T^{2} - 46 T^{3} + 113 T^{4} - 108 T^{5} + 391 T^{6} - 538 T^{7} + 4002 T^{8} - 9087 T^{9} + 31806 T^{10} - 45435 T^{11} + 100050 T^{12} - 67250 T^{13} + 244375 T^{14} - 337500 T^{15} + 1765625 T^{16} - 3593750 T^{17} + 8593750 T^{18} - 9765625 T^{19} + 9765625 T^{20} $)($ 1 - 5 T + 22 T^{2} - 46 T^{3} + 113 T^{4} - 108 T^{5} + 391 T^{6} - 538 T^{7} + 4002 T^{8} - 9087 T^{9} + 31806 T^{10} - 45435 T^{11} + 100050 T^{12} - 67250 T^{13} + 244375 T^{14} - 337500 T^{15} + 1765625 T^{16} - 3593750 T^{17} + 8593750 T^{18} - 9765625 T^{19} + 9765625 T^{20} $)
$7$	($ 1 - T $)($ 1 + T $)($ 1 + T $)($ 1 - T $)($ 1 + T $)($ 1 - T $)($ 1 - T $)($ 1 + T $)($ 1 + T $)($ 1 - T $)($ 1 + T $)($ 1 - T $)($ ( 1 + T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 - T )^{3} $)($ ( 1 + T )^{3} $)($ ( 1 - T )^{3} $)($ ( 1 - T )^{3} $)($ ( 1 + T )^{4} $)($ ( 1 - T )^{4} $)($ ( 1 - T )^{4} $)($ ( 1 + T )^{4} $)($ ( 1 - T )^{4} $)($ ( 1 + T )^{4} $)($ ( 1 + T )^{10} $)($ ( 1 - T )^{10} $)
$11$	1
$13$	($ 1 + 2 T + 13 T^{2} $)($ 1 - 6 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 - 7 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 + 2 T + 7 T^{2} + 26 T^{3} + 169 T^{4} $)($ 1 - 2 T + 22 T^{2} - 26 T^{3} + 169 T^{4} $)($ 1 + 2 T + 24 T^{2} + 26 T^{3} + 169 T^{4} $)($ 1 - 4 T + 25 T^{2} - 52 T^{3} + 169 T^{4} $)($ 1 - 4 T + 25 T^{2} - 52 T^{3} + 169 T^{4} $)($ 1 + 8 T + 37 T^{2} + 104 T^{3} + 169 T^{4} $)($ ( 1 - T + 13 T^{2} )^{2} $)($ 1 - 2 T + 7 T^{2} - 26 T^{3} + 169 T^{4} $)($ 1 + 7 T + 34 T^{2} + 91 T^{3} + 169 T^{4} $)($ 1 + 2 T + 22 T^{2} + 26 T^{3} + 169 T^{4} $)($ 1 - 2 T + 22 T^{2} - 26 T^{3} + 169 T^{4} $)($ 1 + 4 T + 25 T^{2} + 52 T^{3} + 169 T^{4} $)($ 1 + 4 T + 25 T^{2} + 52 T^{3} + 169 T^{4} $)($ ( 1 + T + 13 T^{2} )^{2} $)($ 1 - 8 T + 37 T^{2} - 104 T^{3} + 169 T^{4} $)($ ( 1 + T + 13 T^{2} )^{2} $)($ 1 - 7 T + 34 T^{2} - 91 T^{3} + 169 T^{4} $)($ 1 + 2 T + 22 T^{2} + 26 T^{3} + 169 T^{4} $)($ 1 - 2 T + 24 T^{2} - 26 T^{3} + 169 T^{4} $)($ 1 - 2 T + 7 T^{2} - 26 T^{3} + 169 T^{4} $)($ 1 - 4 T + 12 T^{2} - 10 T^{3} + 156 T^{4} - 676 T^{5} + 2197 T^{6} $)($ 1 + 7 T + 51 T^{2} + 184 T^{3} + 663 T^{4} + 1183 T^{5} + 2197 T^{6} $)($ 1 + 24 T^{2} - 2 T^{3} + 312 T^{4} + 2197 T^{6} $)($ 1 - 7 T + 51 T^{2} - 184 T^{3} + 663 T^{4} - 1183 T^{5} + 2197 T^{6} $)($ 1 - 2 T + 12 T^{2} - 46 T^{3} + 332 T^{4} - 598 T^{5} + 2028 T^{6} - 4394 T^{7} + 28561 T^{8} $)($ 1 + 10 T + 84 T^{2} + 422 T^{3} + 1844 T^{4} + 5486 T^{5} + 14196 T^{6} + 21970 T^{7} + 28561 T^{8} $)($ 1 + 6 T + 44 T^{2} + 218 T^{3} + 822 T^{4} + 2834 T^{5} + 7436 T^{6} + 13182 T^{7} + 28561 T^{8} $)($ 1 - 6 T + 44 T^{2} - 218 T^{3} + 822 T^{4} - 2834 T^{5} + 7436 T^{6} - 13182 T^{7} + 28561 T^{8} $)($ 1 + 2 T + 12 T^{2} + 46 T^{3} + 332 T^{4} + 598 T^{5} + 2028 T^{6} + 4394 T^{7} + 28561 T^{8} $)($ 1 - 10 T + 84 T^{2} - 422 T^{3} + 1844 T^{4} - 5486 T^{5} + 14196 T^{6} - 21970 T^{7} + 28561 T^{8} $)($ 1 + 6 T + 65 T^{2} + 368 T^{3} + 2385 T^{4} + 10918 T^{5} + 56756 T^{6} + 221994 T^{7} + 984630 T^{8} + 3474482 T^{9} + 13929014 T^{10} + 45168266 T^{11} + 166402470 T^{12} + 487720818 T^{13} + 1621008116 T^{14} + 4053776974 T^{15} + 11511939465 T^{16} + 23091454256 T^{17} + 53022496865 T^{18} + 63626996238 T^{19} + 137858491849 T^{20} $)($ 1 - 6 T + 65 T^{2} - 368 T^{3} + 2385 T^{4} - 10918 T^{5} + 56756 T^{6} - 221994 T^{7} + 984630 T^{8} - 3474482 T^{9} + 13929014 T^{10} - 45168266 T^{11} + 166402470 T^{12} - 487720818 T^{13} + 1621008116 T^{14} - 4053776974 T^{15} + 11511939465 T^{16} - 23091454256 T^{17} + 53022496865 T^{18} - 63626996238 T^{19} + 137858491849 T^{20} $)
$17$	($ 1 + 3 T + 17 T^{2} $)($ 1 - 7 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 + 7 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 - 7 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 + 7 T + 17 T^{2} $)($ ( 1 - 3 T + 17 T^{2} )^{2} $)($ 1 - 9 T + 43 T^{2} - 153 T^{3} + 289 T^{4} $)($ 1 - 4 T + 35 T^{2} - 68 T^{3} + 289 T^{4} $)($ 1 - 2 T + 15 T^{2} - 34 T^{3} + 289 T^{4} $)($ ( 1 + 2 T + 17 T^{2} )^{2} $)($ 1 + 14 T^{2} + 289 T^{4} $)($ 1 - 4 T + 33 T^{2} - 68 T^{3} + 289 T^{4} $)($ 1 + 6 T + 38 T^{2} + 102 T^{3} + 289 T^{4} $)($ 1 + 17 T^{2} + 289 T^{4} $)($ 1 + 3 T + 25 T^{2} + 51 T^{3} + 289 T^{4} $)($ 1 - 3 T + 25 T^{2} - 51 T^{3} + 289 T^{4} $)($ 1 + 2 T + 15 T^{2} + 34 T^{3} + 289 T^{4} $)($ ( 1 - 2 T + 17 T^{2} )^{2} $)($ 1 + 6 T + 22 T^{2} + 102 T^{3} + 289 T^{4} $)($ 1 + 14 T^{2} + 289 T^{4} $)($ 1 + 4 T + 33 T^{2} + 68 T^{3} + 289 T^{4} $)($ 1 + 17 T^{2} + 289 T^{4} $)($ 1 + 9 T + 43 T^{2} + 153 T^{3} + 289 T^{4} $)($ 1 + 4 T + 35 T^{2} + 68 T^{3} + 289 T^{4} $)($ ( 1 + 3 T + 17 T^{2} )^{2} $)($ 1 + 8 T + 11 T^{2} - 56 T^{3} + 187 T^{4} + 2312 T^{5} + 4913 T^{6} $)($ 1 + T + 44 T^{2} + 35 T^{3} + 748 T^{4} + 289 T^{5} + 4913 T^{6} $)($ 1 + 27 T^{2} - 8 T^{3} + 459 T^{4} + 4913 T^{6} $)($ 1 - T + 44 T^{2} - 35 T^{3} + 748 T^{4} - 289 T^{5} + 4913 T^{6} $)($ 1 + 2 T + 56 T^{2} + 80 T^{3} + 1339 T^{4} + 1360 T^{5} + 16184 T^{6} + 9826 T^{7} + 83521 T^{8} $)($ 1 + 6 T + 28 T^{2} + 24 T^{3} + 111 T^{4} + 408 T^{5} + 8092 T^{6} + 29478 T^{7} + 83521 T^{8} $)($ 1 + 8 T + 48 T^{2} + 264 T^{3} + 1358 T^{4} + 4488 T^{5} + 13872 T^{6} + 39304 T^{7} + 83521 T^{8} $)($ 1 - 8 T + 48 T^{2} - 264 T^{3} + 1358 T^{4} - 4488 T^{5} + 13872 T^{6} - 39304 T^{7} + 83521 T^{8} $)($ 1 - 2 T + 56 T^{2} - 80 T^{3} + 1339 T^{4} - 1360 T^{5} + 16184 T^{6} - 9826 T^{7} + 83521 T^{8} $)($ 1 - 6 T + 28 T^{2} - 24 T^{3} + 111 T^{4} - 408 T^{5} + 8092 T^{6} - 29478 T^{7} + 83521 T^{8} $)($ 1 + 8 T + 136 T^{2} + 954 T^{3} + 9093 T^{4} + 54096 T^{5} + 378365 T^{6} + 1910556 T^{7} + 10713786 T^{8} + 46048194 T^{9} + 215035238 T^{10} + 782819298 T^{11} + 3096284154 T^{12} + 9386561628 T^{13} + 31601423165 T^{14} + 76808584272 T^{15} + 219482914917 T^{16} + 391463094042 T^{17} + 948703011976 T^{18} + 948703011976 T^{19} + 2015993900449 T^{20} $)($ 1 - 8 T + 136 T^{2} - 954 T^{3} + 9093 T^{4} - 54096 T^{5} + 378365 T^{6} - 1910556 T^{7} + 10713786 T^{8} - 46048194 T^{9} + 215035238 T^{10} - 782819298 T^{11} + 3096284154 T^{12} - 9386561628 T^{13} + 31601423165 T^{14} - 76808584272 T^{15} + 219482914917 T^{16} - 391463094042 T^{17} + 948703011976 T^{18} - 948703011976 T^{19} + 2015993900449 T^{20} $)
$19$	($ 1 - 4 T + 19 T^{2} $)($ 1 - 8 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + 6 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 6 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 8 T + 19 T^{2} $)($ ( 1 + 4 T + 19 T^{2} )^{2} $)($ 1 - 3 T + 39 T^{2} - 57 T^{3} + 361 T^{4} $)($ 1 + 6 T + 20 T^{2} + 114 T^{3} + 361 T^{4} $)($ 1 - 4 T + 22 T^{2} - 76 T^{3} + 361 T^{4} $)($ 1 + 6 T + 27 T^{2} + 114 T^{3} + 361 T^{4} $)($ ( 1 + 3 T + 19 T^{2} )^{2} $)($ ( 1 + 19 T^{2} )^{2} $)($ 1 - 7 T^{2} + 361 T^{4} $)($ ( 1 + 6 T + 19 T^{2} )^{2} $)($ 1 - T + 27 T^{2} - 19 T^{3} + 361 T^{4} $)($ 1 + T + 27 T^{2} + 19 T^{3} + 361 T^{4} $)($ 1 + 4 T + 22 T^{2} + 76 T^{3} + 361 T^{4} $)($ 1 - 6 T + 27 T^{2} - 114 T^{3} + 361 T^{4} $)($ 1 - 4 T + 21 T^{2} - 76 T^{3} + 361 T^{4} $)($ ( 1 - 3 T + 19 T^{2} )^{2} $)($ ( 1 + 19 T^{2} )^{2} $)($ ( 1 - 6 T + 19 T^{2} )^{2} $)($ 1 + 3 T + 39 T^{2} + 57 T^{3} + 361 T^{4} $)($ 1 - 6 T + 20 T^{2} - 114 T^{3} + 361 T^{4} $)($ ( 1 - 4 T + 19 T^{2} )^{2} $)($ 1 - 8 T + 72 T^{2} - 308 T^{3} + 1368 T^{4} - 2888 T^{5} + 6859 T^{6} $)($ 1 + 8 T + 63 T^{2} + 260 T^{3} + 1197 T^{4} + 2888 T^{5} + 6859 T^{6} $)($ 1 + 12 T + 84 T^{2} + 420 T^{3} + 1596 T^{4} + 4332 T^{5} + 6859 T^{6} $)($ 1 - 8 T + 63 T^{2} - 260 T^{3} + 1197 T^{4} - 2888 T^{5} + 6859 T^{6} $)($ 1 + 6 T + 72 T^{2} + 330 T^{3} + 2012 T^{4} + 6270 T^{5} + 25992 T^{6} + 41154 T^{7} + 130321 T^{8} $)($ 1 + 18 T + 184 T^{2} + 1278 T^{3} + 6468 T^{4} + 24282 T^{5} + 66424 T^{6} + 123462 T^{7} + 130321 T^{8} $)($ 1 - 10 T + 100 T^{2} - 570 T^{3} + 3062 T^{4} - 10830 T^{5} + 36100 T^{6} - 68590 T^{7} + 130321 T^{8} $)($ 1 + 10 T + 100 T^{2} + 570 T^{3} + 3062 T^{4} + 10830 T^{5} + 36100 T^{6} + 68590 T^{7} + 130321 T^{8} $)($ 1 - 6 T + 72 T^{2} - 330 T^{3} + 2012 T^{4} - 6270 T^{5} + 25992 T^{6} - 41154 T^{7} + 130321 T^{8} $)($ 1 - 18 T + 184 T^{2} - 1278 T^{3} + 6468 T^{4} - 24282 T^{5} + 66424 T^{6} - 123462 T^{7} + 130321 T^{8} $)($ 1 + 69 T^{2} - 136 T^{3} + 2758 T^{4} - 8362 T^{5} + 89118 T^{6} - 289638 T^{7} + 2274617 T^{8} - 7545660 T^{9} + 46843450 T^{10} - 143367540 T^{11} + 821136737 T^{12} - 1986627042 T^{13} + 11613946878 T^{14} - 20705139838 T^{15} + 129752539798 T^{16} - 121566556504 T^{17} + 1171865849829 T^{18} + 6131066257801 T^{20} $)($ 1 + 69 T^{2} + 136 T^{3} + 2758 T^{4} + 8362 T^{5} + 89118 T^{6} + 289638 T^{7} + 2274617 T^{8} + 7545660 T^{9} + 46843450 T^{10} + 143367540 T^{11} + 821136737 T^{12} + 1986627042 T^{13} + 11613946878 T^{14} + 20705139838 T^{15} + 129752539798 T^{16} + 121566556504 T^{17} + 1171865849829 T^{18} + 6131066257801 T^{20} $)
$23$	($ 1 - 2 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 2 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 10 T + 66 T^{2} + 230 T^{3} + 529 T^{4} $)($ 1 - 5 T + 21 T^{2} - 115 T^{3} + 529 T^{4} $)($ 1 - 10 T + 68 T^{2} - 230 T^{3} + 529 T^{4} $)($ 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} $)($ ( 1 + 2 T + 23 T^{2} )^{2} $)($ 1 - 8 T + 42 T^{2} - 184 T^{3} + 529 T^{4} $)($ 1 + 2 T + 42 T^{2} + 46 T^{3} + 529 T^{4} $)($ 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} $)($ ( 1 + 4 T + 23 T^{2} )^{2} $)($ 1 - 11 T + 75 T^{2} - 253 T^{3} + 529 T^{4} $)($ 1 - 11 T + 75 T^{2} - 253 T^{3} + 529 T^{4} $)($ 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} $)($ ( 1 + 2 T + 23 T^{2} )^{2} $)($ 1 + 2 T + 26 T^{2} + 46 T^{3} + 529 T^{4} $)($ 1 - 8 T + 42 T^{2} - 184 T^{3} + 529 T^{4} $)($ 1 + 2 T + 42 T^{2} + 46 T^{3} + 529 T^{4} $)($ ( 1 + 4 T + 23 T^{2} )^{2} $)($ 1 - 5 T + 21 T^{2} - 115 T^{3} + 529 T^{4} $)($ 1 - 10 T + 68 T^{2} - 230 T^{3} + 529 T^{4} $)($ 1 + 10 T + 66 T^{2} + 230 T^{3} + 529 T^{4} $)($ 1 - 10 T + 81 T^{2} - 396 T^{3} + 1863 T^{4} - 5290 T^{5} + 12167 T^{6} $)($ 1 + 2 T - 9 T^{2} - 60 T^{3} - 207 T^{4} + 1058 T^{5} + 12167 T^{6} $)($ 1 + 6 T + 57 T^{2} + 244 T^{3} + 1311 T^{4} + 3174 T^{5} + 12167 T^{6} $)($ 1 + 2 T - 9 T^{2} - 60 T^{3} - 207 T^{4} + 1058 T^{5} + 12167 T^{6} $)($ 1 - 10 T + 116 T^{2} - 694 T^{3} + 4276 T^{4} - 15962 T^{5} + 61364 T^{6} - 121670 T^{7} + 279841 T^{8} $)($ 1 + 2 T + 28 T^{2} + 190 T^{3} + 516 T^{4} + 4370 T^{5} + 14812 T^{6} + 24334 T^{7} + 279841 T^{8} $)($ 1 + 10 T + 83 T^{2} + 500 T^{3} + 2869 T^{4} + 11500 T^{5} + 43907 T^{6} + 121670 T^{7} + 279841 T^{8} $)($ 1 + 10 T + 83 T^{2} + 500 T^{3} + 2869 T^{4} + 11500 T^{5} + 43907 T^{6} + 121670 T^{7} + 279841 T^{8} $)($ 1 - 10 T + 116 T^{2} - 694 T^{3} + 4276 T^{4} - 15962 T^{5} + 61364 T^{6} - 121670 T^{7} + 279841 T^{8} $)($ 1 + 2 T + 28 T^{2} + 190 T^{3} + 516 T^{4} + 4370 T^{5} + 14812 T^{6} + 24334 T^{7} + 279841 T^{8} $)($ 1 + 124 T^{2} + 38 T^{3} + 8330 T^{4} + 3634 T^{5} + 381506 T^{6} + 180342 T^{7} + 12965000 T^{8} + 5936040 T^{9} + 338330610 T^{10} + 136528920 T^{11} + 6858485000 T^{12} + 2194221114 T^{13} + 106761020546 T^{14} + 23389670462 T^{15} + 1233138955370 T^{16} + 129383366986 T^{17} + 9710562174844 T^{18} + 41426511213649 T^{20} $)($ 1 + 124 T^{2} + 38 T^{3} + 8330 T^{4} + 3634 T^{5} + 381506 T^{6} + 180342 T^{7} + 12965000 T^{8} + 5936040 T^{9} + 338330610 T^{10} + 136528920 T^{11} + 6858485000 T^{12} + 2194221114 T^{13} + 106761020546 T^{14} + 23389670462 T^{15} + 1233138955370 T^{16} + 129383366986 T^{17} + 9710562174844 T^{18} + 41426511213649 T^{20} $)
$29$	($ 1 + 8 T + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ 1 + 7 T + 29 T^{2} $)($ 1 - 9 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 7 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 - 8 T + 29 T^{2} $)($ 1 - 4 T + 29 T^{2} $)($ ( 1 + 3 T + 29 T^{2} )^{2} $)($ ( 1 + 2 T + 29 T^{2} )^{2} $)($ 1 + 6 T + 64 T^{2} + 174 T^{3} + 841 T^{4} $)($ 1 - 4 T + 57 T^{2} - 116 T^{3} + 841 T^{4} $)($ ( 1 + 5 T + 29 T^{2} )^{2} $)($ ( 1 - 3 T + 29 T^{2} )^{2} $)($ 1 + 13 T^{2} + 841 T^{4} $)($ ( 1 + 5 T + 29 T^{2} )^{2} $)($ 1 + T + 20 T^{2} + 29 T^{3} + 841 T^{4} $)($ ( 1 - 6 T + 29 T^{2} )^{2} $)($ ( 1 + 6 T + 29 T^{2} )^{2} $)($ 1 + 4 T + 57 T^{2} + 116 T^{3} + 841 T^{4} $)($ ( 1 - 5 T + 29 T^{2} )^{2} $)($ 1 + 2 T - 25 T^{2} + 58 T^{3} + 841 T^{4} $)($ ( 1 + 3 T + 29 T^{2} )^{2} $)($ 1 + 13 T^{2} + 841 T^{4} $)($ 1 - T + 20 T^{2} - 29 T^{3} + 841 T^{4} $)($ ( 1 - 2 T + 29 T^{2} )^{2} $)($ 1 - 6 T + 64 T^{2} - 174 T^{3} + 841 T^{4} $)($ ( 1 - 3 T + 29 T^{2} )^{2} $)($ 1 - 4 T + 60 T^{2} - 138 T^{3} + 1740 T^{4} - 3364 T^{5} + 24389 T^{6} $)($ 1 + 7 T + 99 T^{2} + 408 T^{3} + 2871 T^{4} + 5887 T^{5} + 24389 T^{6} $)($ 1 + 12 T + 120 T^{2} + 702 T^{3} + 3480 T^{4} + 10092 T^{5} + 24389 T^{6} $)($ 1 - 7 T + 99 T^{2} - 408 T^{3} + 2871 T^{4} - 5887 T^{5} + 24389 T^{6} $)($ 1 + 14 T + 164 T^{2} + 1238 T^{3} + 7756 T^{4} + 35902 T^{5} + 137924 T^{6} + 341446 T^{7} + 707281 T^{8} $)($ 1 + 6 T + 20 T^{2} + 126 T^{3} + 1404 T^{4} + 3654 T^{5} + 16820 T^{6} + 146334 T^{7} + 707281 T^{8} $)($ 1 + 37 T^{2} + 493 T^{4} + 31117 T^{6} + 707281 T^{8} $)($ 1 + 37 T^{2} + 493 T^{4} + 31117 T^{6} + 707281 T^{8} $)($ 1 - 14 T + 164 T^{2} - 1238 T^{3} + 7756 T^{4} - 35902 T^{5} + 137924 T^{6} - 341446 T^{7} + 707281 T^{8} $)($ 1 - 6 T + 20 T^{2} - 126 T^{3} + 1404 T^{4} - 3654 T^{5} + 16820 T^{6} - 146334 T^{7} + 707281 T^{8} $)($ 1 - 14 T + 200 T^{2} - 1928 T^{3} + 18575 T^{4} - 144068 T^{5} + 1110481 T^{6} - 7337936 T^{7} + 48191364 T^{8} - 277661302 T^{9} + 1587859174 T^{10} - 8052177758 T^{11} + 40528937124 T^{12} - 178964921104 T^{13} + 785422112161 T^{14} - 2955000214132 T^{15} + 11048843187575 T^{16} - 33257761523752 T^{17} + 100049282592200 T^{18} - 203100043662166 T^{19} + 420707233300201 T^{20} $)($ 1 + 14 T + 200 T^{2} + 1928 T^{3} + 18575 T^{4} + 144068 T^{5} + 1110481 T^{6} + 7337936 T^{7} + 48191364 T^{8} + 277661302 T^{9} + 1587859174 T^{10} + 8052177758 T^{11} + 40528937124 T^{12} + 178964921104 T^{13} + 785422112161 T^{14} + 2955000214132 T^{15} + 11048843187575 T^{16} + 33257761523752 T^{17} + 100049282592200 T^{18} + 203100043662166 T^{19} + 420707233300201 T^{20} $)
$31$	($ 1 - 2 T + 31 T^{2} $)($ 1 - 2 T + 31 T^{2} $)($ 1 + 10 T + 31 T^{2} $)($ 1 + 2 T + 31 T^{2} $)($ 1 - 2 T + 31 T^{2} $)($ 1 - 2 T + 31 T^{2} $)($ 1 + 10 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 + 2 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 - 2 T + 31 T^{2} $)($ 1 - 2 T + 31 T^{2} $)($ 1 + 4 T + 61 T^{2} + 124 T^{3} + 961 T^{4} $)($ 1 - T + T^{2} - 31 T^{3} + 961 T^{4} $)($ 1 - 8 T + 66 T^{2} - 248 T^{3} + 961 T^{4} $)($ ( 1 - 3 T + 31 T^{2} )^{2} $)($ 1 - 12 T + 78 T^{2} - 372 T^{3} + 961 T^{4} $)($ ( 1 + 31 T^{2} )^{2} $)($ 1 + 16 T + 121 T^{2} + 496 T^{3} + 961 T^{4} $)($ 1 + 6 T + 66 T^{2} + 186 T^{3} + 961 T^{4} $)($ 1 - 6 T^{2} + 961 T^{4} $)($ 1 - 5 T + 37 T^{2} - 155 T^{3} + 961 T^{4} $)($ 1 - 5 T + 37 T^{2} - 155 T^{3} + 961 T^{4} $)($ ( 1 - 3 T + 31 T^{2} )^{2} $)($ 1 - 12 T + 78 T^{2} - 372 T^{3} + 961 T^{4} $)($ 1 + 2 T + 42 T^{2} + 62 T^{3} + 961 T^{4} $)($ ( 1 + 31 T^{2} )^{2} $)($ 1 + 16 T + 121 T^{2} + 496 T^{3} + 961 T^{4} $)($ 1 - 6 T^{2} + 961 T^{4} $)($ 1 - T + T^{2} - 31 T^{3} + 961 T^{4} $)($ 1 - 8 T + 66 T^{2} - 248 T^{3} + 961 T^{4} $)($ 1 + 4 T + 61 T^{2} + 124 T^{3} + 961 T^{4} $)($ 1 + 2 T + 17 T^{2} - 132 T^{3} + 527 T^{4} + 1922 T^{5} + 29791 T^{6} $)($ 1 + 2 T + 65 T^{2} + 132 T^{3} + 2015 T^{4} + 1922 T^{5} + 29791 T^{6} $)($ 1 + 6 T + 57 T^{2} + 404 T^{3} + 1767 T^{4} + 5766 T^{5} + 29791 T^{6} $)($ 1 + 2 T + 65 T^{2} + 132 T^{3} + 2015 T^{4} + 1922 T^{5} + 29791 T^{6} $)($ 1 + 108 T^{2} - 24 T^{3} + 4766 T^{4} - 744 T^{5} + 103788 T^{6} + 923521 T^{8} $)($ 1 + 28 T^{2} - 216 T^{3} + 606 T^{4} - 6696 T^{5} + 26908 T^{6} + 923521 T^{8} $)($ 1 + 18 T + 192 T^{2} + 1362 T^{3} + 8238 T^{4} + 42222 T^{5} + 184512 T^{6} + 536238 T^{7} + 923521 T^{8} $)($ 1 + 18 T + 192 T^{2} + 1362 T^{3} + 8238 T^{4} + 42222 T^{5} + 184512 T^{6} + 536238 T^{7} + 923521 T^{8} $)($ 1 + 108 T^{2} - 24 T^{3} + 4766 T^{4} - 744 T^{5} + 103788 T^{6} + 923521 T^{8} $)($ 1 + 28 T^{2} - 216 T^{3} + 606 T^{4} - 6696 T^{5} + 26908 T^{6} + 923521 T^{8} $)($ 1 - 26 T + 482 T^{2} - 6400 T^{3} + 71453 T^{4} - 670846 T^{5} + 5624329 T^{6} - 41976980 T^{7} + 287918626 T^{8} - 1800633596 T^{9} + 10465823578 T^{10} - 55819641476 T^{11} + 276689799586 T^{12} - 1250536211180 T^{13} + 5194185942409 T^{14} - 19205751431746 T^{15} + 63414800518493 T^{16} - 176080730310400 T^{17} + 411093480046562 T^{18} - 687430176177446 T^{19} + 819628286980801 T^{20} $)($ 1 - 26 T + 482 T^{2} - 6400 T^{3} + 71453 T^{4} - 670846 T^{5} + 5624329 T^{6} - 41976980 T^{7} + 287918626 T^{8} - 1800633596 T^{9} + 10465823578 T^{10} - 55819641476 T^{11} + 276689799586 T^{12} - 1250536211180 T^{13} + 5194185942409 T^{14} - 19205751431746 T^{15} + 63414800518493 T^{16} - 176080730310400 T^{17} + 411093480046562 T^{18} - 687430176177446 T^{19} + 819628286980801 T^{20} $)
$37$	($ 1 - 10 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 - 9 T + 37 T^{2} $)($ 1 + 10 T + 37 T^{2} $)($ 1 + 10 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 - 9 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + 8 T + 70 T^{2} + 296 T^{3} + 1369 T^{4} $)($ 1 + 13 T + 85 T^{2} + 481 T^{3} + 1369 T^{4} $)($ 1 + 12 T + 98 T^{2} + 444 T^{3} + 1369 T^{4} $)($ ( 1 - 6 T + 37 T^{2} )^{2} $)($ 1 - 6 T + 63 T^{2} - 222 T^{3} + 1369 T^{4} $)($ 1 + 2 T + 55 T^{2} + 74 T^{3} + 1369 T^{4} $)($ 1 + 4 T - 2 T^{2} + 148 T^{3} + 1369 T^{4} $)($ ( 1 + 7 T + 37 T^{2} )^{2} $)($ 1 - 7 T + 48 T^{2} - 259 T^{3} + 1369 T^{4} $)($ 1 - 7 T + 85 T^{2} - 259 T^{3} + 1369 T^{4} $)($ 1 - 7 T + 85 T^{2} - 259 T^{3} + 1369 T^{4} $)($ ( 1 - 6 T + 37 T^{2} )^{2} $)($ 1 - 6 T + 63 T^{2} - 222 T^{3} + 1369 T^{4} $)($ ( 1 - T + 37 T^{2} )^{2} $)($ 1 + 2 T + 55 T^{2} + 74 T^{3} + 1369 T^{4} $)($ 1 + 4 T - 2 T^{2} + 148 T^{3} + 1369 T^{4} $)($ 1 - 7 T + 48 T^{2} - 259 T^{3} + 1369 T^{4} $)($ 1 + 13 T + 85 T^{2} + 481 T^{3} + 1369 T^{4} $)($ 1 + 12 T + 98 T^{2} + 444 T^{3} + 1369 T^{4} $)($ 1 + 8 T + 70 T^{2} + 296 T^{3} + 1369 T^{4} $)($ 1 + 68 T^{2} + 106 T^{3} + 2516 T^{4} + 50653 T^{6} $)($ 1 + 3 T + 107 T^{2} + 214 T^{3} + 3959 T^{4} + 4107 T^{5} + 50653 T^{6} $)($ 1 + 36 T^{2} - 246 T^{3} + 1332 T^{4} + 50653 T^{6} $)($ 1 + 3 T + 107 T^{2} + 214 T^{3} + 3959 T^{4} + 4107 T^{5} + 50653 T^{6} $)($ 1 + 12 T + 168 T^{2} + 1284 T^{3} + 9650 T^{4} + 47508 T^{5} + 229992 T^{6} + 607836 T^{7} + 1874161 T^{8} $)($ 1 + 4 T + 72 T^{2} + 284 T^{3} + 4082 T^{4} + 10508 T^{5} + 98568 T^{6} + 202612 T^{7} + 1874161 T^{8} $)($ 1 + 2 T + 71 T^{2} + 4 T^{3} + 2797 T^{4} + 148 T^{5} + 97199 T^{6} + 101306 T^{7} + 1874161 T^{8} $)($ 1 + 2 T + 71 T^{2} + 4 T^{3} + 2797 T^{4} + 148 T^{5} + 97199 T^{6} + 101306 T^{7} + 1874161 T^{8} $)($ 1 + 12 T + 168 T^{2} + 1284 T^{3} + 9650 T^{4} + 47508 T^{5} + 229992 T^{6} + 607836 T^{7} + 1874161 T^{8} $)($ 1 + 4 T + 72 T^{2} + 284 T^{3} + 4082 T^{4} + 10508 T^{5} + 98568 T^{6} + 202612 T^{7} + 1874161 T^{8} $)($ 1 - 24 T + 440 T^{2} - 5840 T^{3} + 65456 T^{4} - 634664 T^{5} + 5522032 T^{6} - 43933344 T^{7} + 323265704 T^{8} - 2198445368 T^{9} + 13921174566 T^{10} - 81342478616 T^{11} + 442550748776 T^{12} - 2225355673632 T^{13} + 10349177015152 T^{14} - 44010113125448 T^{15} + 167942187827504 T^{16} - 554402162456720 T^{17} + 1545490959725240 T^{18} - 3119081755081848 T^{19} + 4808584372417849 T^{20} $)($ 1 - 24 T + 440 T^{2} - 5840 T^{3} + 65456 T^{4} - 634664 T^{5} + 5522032 T^{6} - 43933344 T^{7} + 323265704 T^{8} - 2198445368 T^{9} + 13921174566 T^{10} - 81342478616 T^{11} + 442550748776 T^{12} - 2225355673632 T^{13} + 10349177015152 T^{14} - 44010113125448 T^{15} + 167942187827504 T^{16} - 554402162456720 T^{17} + 1545490959725240 T^{18} - 3119081755081848 T^{19} + 4808584372417849 T^{20} $)
$41$	($ 1 + 2 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 5 T + 41 T^{2} $)($ 1 + 7 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 5 T + 41 T^{2} $)($ 1 + 10 T + 41 T^{2} $)($ 1 - 7 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 + 5 T + 57 T^{2} + 205 T^{3} + 1681 T^{4} $)($ 1 + 15 T + 127 T^{2} + 615 T^{3} + 1681 T^{4} $)($ ( 1 + 4 T + 41 T^{2} )^{2} $)($ 1 + 13 T + 113 T^{2} + 533 T^{3} + 1681 T^{4} $)($ 1 - 4 T + 66 T^{2} - 164 T^{3} + 1681 T^{4} $)($ 1 + 12 T + 98 T^{2} + 492 T^{3} + 1681 T^{4} $)($ 1 - T + 51 T^{2} - 41 T^{3} + 1681 T^{4} $)($ 1 + 4 T + 66 T^{2} + 164 T^{3} + 1681 T^{4} $)($ 1 - 11 T + 108 T^{2} - 451 T^{3} + 1681 T^{4} $)($ 1 + 17 T + 153 T^{2} + 697 T^{3} + 1681 T^{4} $)($ 1 - 17 T + 153 T^{2} - 697 T^{3} + 1681 T^{4} $)($ 1 - 13 T + 113 T^{2} - 533 T^{3} + 1681 T^{4} $)($ 1 + 4 T + 66 T^{2} + 164 T^{3} + 1681 T^{4} $)($ 1 - 4 T + 2 T^{2} - 164 T^{3} + 1681 T^{4} $)($ 1 - 12 T + 98 T^{2} - 492 T^{3} + 1681 T^{4} $)($ 1 + T + 51 T^{2} + 41 T^{3} + 1681 T^{4} $)($ 1 + 11 T + 108 T^{2} + 451 T^{3} + 1681 T^{4} $)($ 1 - 15 T + 127 T^{2} - 615 T^{3} + 1681 T^{4} $)($ ( 1 - 4 T + 41 T^{2} )^{2} $)($ 1 - 5 T + 57 T^{2} - 205 T^{3} + 1681 T^{4} $)($ 1 + 14 T + 163 T^{2} + 1116 T^{3} + 6683 T^{4} + 23534 T^{5} + 68921 T^{6} $)($ 1 + 13 T + 163 T^{2} + 1098 T^{3} + 6683 T^{4} + 21853 T^{5} + 68921 T^{6} $)($ 1 + 6 T + 51 T^{2} + 460 T^{3} + 2091 T^{4} + 10086 T^{5} + 68921 T^{6} $)($ 1 - 13 T + 163 T^{2} - 1098 T^{3} + 6683 T^{4} - 21853 T^{5} + 68921 T^{6} $)($ 1 + 16 T + 196 T^{2} + 1712 T^{3} + 11994 T^{4} + 70192 T^{5} + 329476 T^{6} + 1102736 T^{7} + 2825761 T^{8} $)($ 1 + 124 T^{2} - 48 T^{3} + 6810 T^{4} - 1968 T^{5} + 208444 T^{6} + 2825761 T^{8} $)($ 1 + 10 T + 60 T^{2} - 290 T^{3} - 2938 T^{4} - 11890 T^{5} + 100860 T^{6} + 689210 T^{7} + 2825761 T^{8} $)($ 1 - 10 T + 60 T^{2} + 290 T^{3} - 2938 T^{4} + 11890 T^{5} + 100860 T^{6} - 689210 T^{7} + 2825761 T^{8} $)($ 1 - 16 T + 196 T^{2} - 1712 T^{3} + 11994 T^{4} - 70192 T^{5} + 329476 T^{6} - 1102736 T^{7} + 2825761 T^{8} $)($ 1 + 124 T^{2} + 48 T^{3} + 6810 T^{4} + 1968 T^{5} + 208444 T^{6} + 2825761 T^{8} $)($ 1 + 19 T + 484 T^{2} + 6388 T^{3} + 94475 T^{4} + 963532 T^{5} + 10457893 T^{6} + 86623352 T^{7} + 748989936 T^{8} + 5154844493 T^{9} + 36776727094 T^{10} + 211348624213 T^{11} + 1259052082416 T^{12} + 5970168043192 T^{13} + 29551506181573 T^{14} + 111631157061932 T^{15} + 448766098168475 T^{16} + 1244090301551828 T^{17} + 3864703810894564 T^{18} + 6220256753485259 T^{19} + 13422659310152401 T^{20} $)($ 1 - 19 T + 484 T^{2} - 6388 T^{3} + 94475 T^{4} - 963532 T^{5} + 10457893 T^{6} - 86623352 T^{7} + 748989936 T^{8} - 5154844493 T^{9} + 36776727094 T^{10} - 211348624213 T^{11} + 1259052082416 T^{12} - 5970168043192 T^{13} + 29551506181573 T^{14} - 111631157061932 T^{15} + 448766098168475 T^{16} - 1244090301551828 T^{17} + 3864703810894564 T^{18} - 6220256753485259 T^{19} + 13422659310152401 T^{20} $)
$43$	($ 1 + 9 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 + 6 T + 43 T^{2} $)($ 1 + 6 T + 43 T^{2} $)($ 1 + 11 T + 43 T^{2} $)($ 1 - 11 T + 43 T^{2} $)($ 1 - 6 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 - 6 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 - 9 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ ( 1 - 9 T + 43 T^{2} )^{2} $)($ 1 - 2 T + 82 T^{2} - 86 T^{3} + 1849 T^{4} $)($ 1 - 6 T + 83 T^{2} - 258 T^{3} + 1849 T^{4} $)($ 1 + 14 T + 115 T^{2} + 602 T^{3} + 1849 T^{4} $)($ 1 - 8 T + 82 T^{2} - 344 T^{3} + 1849 T^{4} $)($ 1 + 4 T + 10 T^{2} + 172 T^{3} + 1849 T^{4} $)($ ( 1 - T + 43 T^{2} )^{2} $)($ 1 - 2 T + 42 T^{2} - 86 T^{3} + 1849 T^{4} $)($ 1 + T + 48 T^{2} + 43 T^{3} + 1849 T^{4} $)($ 1 + 6 T + 50 T^{2} + 258 T^{3} + 1849 T^{4} $)($ 1 - 6 T + 50 T^{2} - 258 T^{3} + 1849 T^{4} $)($ 1 - 14 T + 115 T^{2} - 602 T^{3} + 1849 T^{4} $)($ 1 + 8 T + 82 T^{2} + 344 T^{3} + 1849 T^{4} $)($ 1 - 6 T + 74 T^{2} - 258 T^{3} + 1849 T^{4} $)($ 1 - 4 T + 10 T^{2} - 172 T^{3} + 1849 T^{4} $)($ ( 1 + T + 43 T^{2} )^{2} $)($ 1 - T + 48 T^{2} - 43 T^{3} + 1849 T^{4} $)($ 1 + 2 T + 82 T^{2} + 86 T^{3} + 1849 T^{4} $)($ 1 + 6 T + 83 T^{2} + 258 T^{3} + 1849 T^{4} $)($ ( 1 + 9 T + 43 T^{2} )^{2} $)($ 1 - 14 T + 85 T^{2} - 356 T^{3} + 3655 T^{4} - 25886 T^{5} + 79507 T^{6} $)($ 1 + 8 T + 58 T^{2} + 266 T^{3} + 2494 T^{4} + 14792 T^{5} + 79507 T^{6} $)($ 1 + 6 T + 117 T^{2} + 468 T^{3} + 5031 T^{4} + 11094 T^{5} + 79507 T^{6} $)($ 1 - 8 T + 58 T^{2} - 266 T^{3} + 2494 T^{4} - 14792 T^{5} + 79507 T^{6} $)($ 1 + 20 T + 306 T^{2} + 2920 T^{3} + 22895 T^{4} + 125560 T^{5} + 565794 T^{6} + 1590140 T^{7} + 3418801 T^{8} $)($ 1 + 20 T + 282 T^{2} + 2632 T^{3} + 19943 T^{4} + 113176 T^{5} + 521418 T^{6} + 1590140 T^{7} + 3418801 T^{8} $)($ 1 - 4 T + 69 T^{2} - 392 T^{3} + 4097 T^{4} - 16856 T^{5} + 127581 T^{6} - 318028 T^{7} + 3418801 T^{8} $)($ 1 + 4 T + 69 T^{2} + 392 T^{3} + 4097 T^{4} + 16856 T^{5} + 127581 T^{6} + 318028 T^{7} + 3418801 T^{8} $)($ 1 - 20 T + 306 T^{2} - 2920 T^{3} + 22895 T^{4} - 125560 T^{5} + 565794 T^{6} - 1590140 T^{7} + 3418801 T^{8} $)($ 1 - 20 T + 282 T^{2} - 2632 T^{3} + 19943 T^{4} - 113176 T^{5} + 521418 T^{6} - 1590140 T^{7} + 3418801 T^{8} $)($ 1 - 6 T + 312 T^{2} - 1828 T^{3} + 47319 T^{4} - 259736 T^{5} + 4576717 T^{6} - 22838020 T^{7} + 311402464 T^{8} - 1377461130 T^{9} + 15540959670 T^{10} - 59230828590 T^{11} + 575783155936 T^{12} - 1815782456140 T^{13} + 15646884656317 T^{14} - 38183384951048 T^{15} + 299120578115631 T^{16} - 496884421103596 T^{17} + 3646718486611512 T^{18} - 3015555671621058 T^{19} + 21611482313284249 T^{20} $)($ 1 + 6 T + 312 T^{2} + 1828 T^{3} + 47319 T^{4} + 259736 T^{5} + 4576717 T^{6} + 22838020 T^{7} + 311402464 T^{8} + 1377461130 T^{9} + 15540959670 T^{10} + 59230828590 T^{11} + 575783155936 T^{12} + 1815782456140 T^{13} + 15646884656317 T^{14} + 38183384951048 T^{15} + 299120578115631 T^{16} + 496884421103596 T^{17} + 3646718486611512 T^{18} + 3015555671621058 T^{19} + 21611482313284249 T^{20} $)
$47$	($ 1 - 9 T + 47 T^{2} $)($ 1 - 13 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 2 T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 - 2 T + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 - 9 T + 47 T^{2} $)($ 1 - 13 T + 47 T^{2} $)($ 1 - 9 T + 83 T^{2} - 423 T^{3} + 2209 T^{4} $)($ ( 1 - 2 T + 47 T^{2} )^{2} $)($ 1 + 8 T + 83 T^{2} + 376 T^{3} + 2209 T^{4} $)($ 1 + 17 T + 155 T^{2} + 799 T^{3} + 2209 T^{4} $)($ 1 - 10 T + 99 T^{2} - 470 T^{3} + 2209 T^{4} $)($ ( 1 + 3 T + 47 T^{2} )^{2} $)($ 1 - T + 33 T^{2} - 47 T^{3} + 2209 T^{4} $)($ 1 + 4 T + 93 T^{2} + 188 T^{3} + 2209 T^{4} $)($ 1 - 11 T + 120 T^{2} - 517 T^{3} + 2209 T^{4} $)($ 1 + 74 T^{2} + 2209 T^{4} $)($ 1 + 74 T^{2} + 2209 T^{4} $)($ 1 + 17 T + 155 T^{2} + 799 T^{3} + 2209 T^{4} $)($ 1 - 10 T + 99 T^{2} - 470 T^{3} + 2209 T^{4} $)($ 1 - 12 T + 109 T^{2} - 564 T^{3} + 2209 T^{4} $)($ ( 1 + 3 T + 47 T^{2} )^{2} $)($ 1 - T + 33 T^{2} - 47 T^{3} + 2209 T^{4} $)($ 1 - 11 T + 120 T^{2} - 517 T^{3} + 2209 T^{4} $)($ ( 1 - 2 T + 47 T^{2} )^{2} $)($ 1 + 8 T + 83 T^{2} + 376 T^{3} + 2209 T^{4} $)($ 1 - 9 T + 83 T^{2} - 423 T^{3} + 2209 T^{4} $)($ 1 + 80 T^{2} + 32 T^{3} + 3760 T^{4} + 103823 T^{6} $)($ 1 + 6 T + 110 T^{2} + 530 T^{3} + 5170 T^{4} + 13254 T^{5} + 103823 T^{6} $)($ 1 + 24 T + 312 T^{2} + 2584 T^{3} + 14664 T^{4} + 53016 T^{5} + 103823 T^{6} $)($ 1 + 6 T + 110 T^{2} + 530 T^{3} + 5170 T^{4} + 13254 T^{5} + 103823 T^{6} $)($ 1 - 2 T + 88 T^{2} - 568 T^{3} + 4023 T^{4} - 26696 T^{5} + 194392 T^{6} - 207646 T^{7} + 4879681 T^{8} $)($ 1 + 6 T + 44 T^{2} + 504 T^{3} + 4371 T^{4} + 23688 T^{5} + 97196 T^{6} + 622938 T^{7} + 4879681 T^{8} $)($ 1 - 4 T + 108 T^{2} + 4 T^{3} + 4758 T^{4} + 188 T^{5} + 238572 T^{6} - 415292 T^{7} + 4879681 T^{8} $)($ 1 - 4 T + 108 T^{2} + 4 T^{3} + 4758 T^{4} + 188 T^{5} + 238572 T^{6} - 415292 T^{7} + 4879681 T^{8} $)($ 1 - 2 T + 88 T^{2} - 568 T^{3} + 4023 T^{4} - 26696 T^{5} + 194392 T^{6} - 207646 T^{7} + 4879681 T^{8} $)($ 1 + 6 T + 44 T^{2} + 504 T^{3} + 4371 T^{4} + 23688 T^{5} + 97196 T^{6} + 622938 T^{7} + 4879681 T^{8} $)($ 1 - 15 T + 333 T^{2} - 4161 T^{3} + 56109 T^{4} - 576028 T^{5} + 5980092 T^{6} - 51937604 T^{7} + 445599026 T^{8} - 3323250890 T^{9} + 24323199470 T^{10} - 156192791830 T^{11} + 984328248434 T^{12} - 5392317860092 T^{13} + 29180941310652 T^{14} - 132109145692196 T^{15} + 604810992894861 T^{16} - 2108058804246543 T^{17} + 7929158458366413 T^{18} - 16786957096541505 T^{19} + 52599132235830049 T^{20} $)($ 1 - 15 T + 333 T^{2} - 4161 T^{3} + 56109 T^{4} - 576028 T^{5} + 5980092 T^{6} - 51937604 T^{7} + 445599026 T^{8} - 3323250890 T^{9} + 24323199470 T^{10} - 156192791830 T^{11} + 984328248434 T^{12} - 5392317860092 T^{13} + 29180941310652 T^{14} - 132109145692196 T^{15} + 604810992894861 T^{16} - 2108058804246543 T^{17} + 7929158458366413 T^{18} - 16786957096541505 T^{19} + 52599132235830049 T^{20} $)
$53$	($ 1 + 8 T + 53 T^{2} $)($ 1 + 53 T^{2} $)($ 1 + 5 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 + 5 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 8 T + 53 T^{2} $)($ 1 + 53 T^{2} $)($ 1 + 3 T + 77 T^{2} + 159 T^{3} + 2809 T^{4} $)($ 1 - 2 T - 18 T^{2} - 106 T^{3} + 2809 T^{4} $)($ 1 - 12 T + 130 T^{2} - 636 T^{3} + 2809 T^{4} $)($ 1 + 5 T + 11 T^{2} + 265 T^{3} + 2809 T^{4} $)($ 1 - 4 T + 90 T^{2} - 212 T^{3} + 2809 T^{4} $)($ 1 + 26 T^{2} + 2809 T^{4} $)($ 1 - 13 T + 147 T^{2} - 689 T^{3} + 2809 T^{4} $)($ 1 + 2 T - 18 T^{2} + 106 T^{3} + 2809 T^{4} $)($ 1 + 5 T + 6 T^{2} + 265 T^{3} + 2809 T^{4} $)($ 1 - 18 T + 182 T^{2} - 954 T^{3} + 2809 T^{4} $)($ 1 - 18 T + 182 T^{2} - 954 T^{3} + 2809 T^{4} $)($ 1 + 5 T + 11 T^{2} + 265 T^{3} + 2809 T^{4} $)($ 1 - 4 T + 90 T^{2} - 212 T^{3} + 2809 T^{4} $)($ 1 + 10 T + 110 T^{2} + 530 T^{3} + 2809 T^{4} $)($ 1 + 26 T^{2} + 2809 T^{4} $)($ 1 - 13 T + 147 T^{2} - 689 T^{3} + 2809 T^{4} $)($ 1 + 5 T + 6 T^{2} + 265 T^{3} + 2809 T^{4} $)($ 1 - 2 T - 18 T^{2} - 106 T^{3} + 2809 T^{4} $)($ 1 - 12 T + 130 T^{2} - 636 T^{3} + 2809 T^{4} $)($ 1 + 3 T + 77 T^{2} + 159 T^{3} + 2809 T^{4} $)($ 1 + 143 T^{2} + 8 T^{3} + 7579 T^{4} + 148877 T^{6} $)($ 1 + 21 T + 299 T^{2} + 2522 T^{3} + 15847 T^{4} + 58989 T^{5} + 148877 T^{6} $)($ 1 + 111 T^{2} - 120 T^{3} + 5883 T^{4} + 148877 T^{6} $)($ 1 + 21 T + 299 T^{2} + 2522 T^{3} + 15847 T^{4} + 58989 T^{5} + 148877 T^{6} $)($ 1 + 16 T + 244 T^{2} + 2096 T^{3} + 18582 T^{4} + 111088 T^{5} + 685396 T^{6} + 2382032 T^{7} + 7890481 T^{8} $)($ 1 + 148 T^{2} - 192 T^{3} + 9942 T^{4} - 10176 T^{5} + 415732 T^{6} + 7890481 T^{8} $)($ 1 + 161 T^{2} - 20 T^{3} + 11657 T^{4} - 1060 T^{5} + 452249 T^{6} + 7890481 T^{8} $)($ 1 + 161 T^{2} - 20 T^{3} + 11657 T^{4} - 1060 T^{5} + 452249 T^{6} + 7890481 T^{8} $)($ 1 + 16 T + 244 T^{2} + 2096 T^{3} + 18582 T^{4} + 111088 T^{5} + 685396 T^{6} + 2382032 T^{7} + 7890481 T^{8} $)($ 1 + 148 T^{2} - 192 T^{3} + 9942 T^{4} - 10176 T^{5} + 415732 T^{6} + 7890481 T^{8} $)($ 1 + T + 254 T^{2} - 378 T^{3} + 28817 T^{4} - 120372 T^{5} + 2050339 T^{6} - 14991722 T^{7} + 109654718 T^{8} - 1160429241 T^{9} + 5512758766 T^{10} - 61502749773 T^{11} + 308020102862 T^{12} - 2231922596194 T^{13} + 16178160923059 T^{14} - 50339027883396 T^{15} + 638710394654393 T^{16} - 444040810858386 T^{17} + 15813961364485694 T^{18} + 3299763591802133 T^{19} + 174887470365513049 T^{20} $)($ 1 + T + 254 T^{2} - 378 T^{3} + 28817 T^{4} - 120372 T^{5} + 2050339 T^{6} - 14991722 T^{7} + 109654718 T^{8} - 1160429241 T^{9} + 5512758766 T^{10} - 61502749773 T^{11} + 308020102862 T^{12} - 2231922596194 T^{13} + 16178160923059 T^{14} - 50339027883396 T^{15} + 638710394654393 T^{16} - 444040810858386 T^{17} + 15813961364485694 T^{18} + 3299763591802133 T^{19} + 174887470365513049 T^{20} $)
$59$	($ 1 + 3 T + 59 T^{2} $)($ 1 - T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 - 2 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 - 2 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 - T + 59 T^{2} $)($ 1 - 23 T + 249 T^{2} - 1357 T^{3} + 3481 T^{4} $)($ 1 - 18 T + 194 T^{2} - 1062 T^{3} + 3481 T^{4} $)($ 1 - 4 T - 25 T^{2} - 236 T^{3} + 3481 T^{4} $)($ 1 + 7 T + 129 T^{2} + 413 T^{3} + 3481 T^{4} $)($ 1 + 2 T + 39 T^{2} + 118 T^{3} + 3481 T^{4} $)($ 1 - 6 T + 107 T^{2} - 354 T^{3} + 3481 T^{4} $)($ 1 + 15 T + 163 T^{2} + 885 T^{3} + 3481 T^{4} $)($ 1 - 7 T^{2} + 3481 T^{4} $)($ 1 + 21 T + 224 T^{2} + 1239 T^{3} + 3481 T^{4} $)($ 1 - 2 T + 114 T^{2} - 118 T^{3} + 3481 T^{4} $)($ 1 - 2 T + 114 T^{2} - 118 T^{3} + 3481 T^{4} $)($ 1 + 7 T + 129 T^{2} + 413 T^{3} + 3481 T^{4} $)($ 1 + 2 T + 39 T^{2} + 118 T^{3} + 3481 T^{4} $)($ 1 + 97 T^{2} + 3481 T^{4} $)($ 1 - 6 T + 107 T^{2} - 354 T^{3} + 3481 T^{4} $)($ 1 + 15 T + 163 T^{2} + 885 T^{3} + 3481 T^{4} $)($ 1 + 21 T + 224 T^{2} + 1239 T^{3} + 3481 T^{4} $)($ 1 - 18 T + 194 T^{2} - 1062 T^{3} + 3481 T^{4} $)($ 1 - 4 T - 25 T^{2} - 236 T^{3} + 3481 T^{4} $)($ 1 - 23 T + 249 T^{2} - 1357 T^{3} + 3481 T^{4} $)($ 1 + 120 T^{2} - 52 T^{3} + 7080 T^{4} + 205379 T^{6} $)($ 1 - 6 T + 150 T^{2} - 622 T^{3} + 8850 T^{4} - 20886 T^{5} + 205379 T^{6} $)($ 1 + 24 T + 264 T^{2} + 2116 T^{3} + 15576 T^{4} + 83544 T^{5} + 205379 T^{6} $)($ 1 - 6 T + 150 T^{2} - 622 T^{3} + 8850 T^{4} - 20886 T^{5} + 205379 T^{6} $)($ 1 - 2 T - 20 T^{2} - 136 T^{3} + 6195 T^{4} - 8024 T^{5} - 69620 T^{6} - 410758 T^{7} + 12117361 T^{8} $)($ 1 + 6 T + 208 T^{2} + 936 T^{3} + 17751 T^{4} + 55224 T^{5} + 724048 T^{6} + 1232274 T^{7} + 12117361 T^{8} $)($ 1 + 16 T + 308 T^{2} + 2936 T^{3} + 29398 T^{4} + 173224 T^{5} + 1072148 T^{6} + 3286064 T^{7} + 12117361 T^{8} $)($ 1 + 16 T + 308 T^{2} + 2936 T^{3} + 29398 T^{4} + 173224 T^{5} + 1072148 T^{6} + 3286064 T^{7} + 12117361 T^{8} $)($ 1 - 2 T - 20 T^{2} - 136 T^{3} + 6195 T^{4} - 8024 T^{5} - 69620 T^{6} - 410758 T^{7} + 12117361 T^{8} $)($ 1 + 6 T + 208 T^{2} + 936 T^{3} + 17751 T^{4} + 55224 T^{5} + 724048 T^{6} + 1232274 T^{7} + 12117361 T^{8} $)($ 1 - 23 T + 495 T^{2} - 6037 T^{3} + 71081 T^{4} - 556772 T^{5} + 4700924 T^{6} - 26168124 T^{7} + 209482574 T^{8} - 1016636482 T^{9} + 10462754634 T^{10} - 59981552438 T^{11} + 729208840094 T^{12} - 5374383138996 T^{13} + 56962793141564 T^{14} - 398049831802828 T^{15} + 2998234511735921 T^{16} - 15023989013852303 T^{17} + 72681066614138895 T^{18} - 199248903829063597 T^{19} + 511116753300641401 T^{20} $)($ 1 - 23 T + 495 T^{2} - 6037 T^{3} + 71081 T^{4} - 556772 T^{5} + 4700924 T^{6} - 26168124 T^{7} + 209482574 T^{8} - 1016636482 T^{9} + 10462754634 T^{10} - 59981552438 T^{11} + 729208840094 T^{12} - 5374383138996 T^{13} + 56962793141564 T^{14} - 398049831802828 T^{15} + 2998234511735921 T^{16} - 15023989013852303 T^{17} + 72681066614138895 T^{18} - 199248903829063597 T^{19} + 511116753300641401 T^{20} $)
$61$	($ 1 - 10 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 8 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 - 2 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 + 77 T^{2} + 3721 T^{4} $)($ 1 + 42 T^{2} + 3721 T^{4} $)($ 1 + 6 T + 104 T^{2} + 366 T^{3} + 3721 T^{4} $)($ 1 - 2 T + 43 T^{2} - 122 T^{3} + 3721 T^{4} $)($ 1 + 16 T + 166 T^{2} + 976 T^{3} + 3721 T^{4} $)($ 1 + 16 T + 166 T^{2} + 976 T^{3} + 3721 T^{4} $)($ 1 - 16 T + 181 T^{2} - 976 T^{3} + 3721 T^{4} $)($ ( 1 + 2 T + 61 T^{2} )^{2} $)($ 1 - 2 T - 30 T^{2} - 122 T^{3} + 3721 T^{4} $)($ ( 1 + 61 T^{2} )^{2} $)($ ( 1 + 61 T^{2} )^{2} $)($ 1 + 2 T + 43 T^{2} + 122 T^{3} + 3721 T^{4} $)($ 1 - 16 T + 166 T^{2} - 976 T^{3} + 3721 T^{4} $)($ ( 1 + 10 T + 61 T^{2} )^{2} $)($ 1 - 16 T + 166 T^{2} - 976 T^{3} + 3721 T^{4} $)($ 1 + 16 T + 181 T^{2} + 976 T^{3} + 3721 T^{4} $)($ 1 + 2 T - 30 T^{2} + 122 T^{3} + 3721 T^{4} $)($ 1 + 42 T^{2} + 3721 T^{4} $)($ 1 - 6 T + 104 T^{2} - 366 T^{3} + 3721 T^{4} $)($ 1 + 77 T^{2} + 3721 T^{4} $)($ ( 1 - 2 T + 61 T^{2} )^{3} $)($ 1 + 12 T + 165 T^{2} + 1172 T^{3} + 10065 T^{4} + 44652 T^{5} + 226981 T^{6} $)($ ( 1 + 6 T + 61 T^{2} )^{3} $)($ 1 - 12 T + 165 T^{2} - 1172 T^{3} + 10065 T^{4} - 44652 T^{5} + 226981 T^{6} $)($ 1 + 2 T + 180 T^{2} + 418 T^{3} + 14804 T^{4} + 25498 T^{5} + 669780 T^{6} + 453962 T^{7} + 13845841 T^{8} $)($ 1 - 10 T + 108 T^{2} - 314 T^{3} + 3596 T^{4} - 19154 T^{5} + 401868 T^{6} - 2269810 T^{7} + 13845841 T^{8} $)($ 1 + 14 T + 260 T^{2} + 2306 T^{3} + 24294 T^{4} + 140666 T^{5} + 967460 T^{6} + 3177734 T^{7} + 13845841 T^{8} $)($ 1 - 14 T + 260 T^{2} - 2306 T^{3} + 24294 T^{4} - 140666 T^{5} + 967460 T^{6} - 3177734 T^{7} + 13845841 T^{8} $)($ 1 - 2 T + 180 T^{2} - 418 T^{3} + 14804 T^{4} - 25498 T^{5} + 669780 T^{6} - 453962 T^{7} + 13845841 T^{8} $)($ 1 + 10 T + 108 T^{2} + 314 T^{3} + 3596 T^{4} + 19154 T^{5} + 401868 T^{6} + 2269810 T^{7} + 13845841 T^{8} $)($ 1 + 215 T^{2} + 490 T^{3} + 23725 T^{4} + 88654 T^{5} + 1906100 T^{6} + 8267970 T^{7} + 125871770 T^{8} + 598496950 T^{9} + 7588984906 T^{10} + 36508313950 T^{11} + 468368856170 T^{12} + 1876672098570 T^{13} + 26391557530100 T^{14} + 74876840468854 T^{15} + 1222320881714725 T^{16} + 1539943989650290 T^{17} + 41217072294415415 T^{18} + 713342911662882601 T^{20} $)($ 1 + 215 T^{2} - 490 T^{3} + 23725 T^{4} - 88654 T^{5} + 1906100 T^{6} - 8267970 T^{7} + 125871770 T^{8} - 598496950 T^{9} + 7588984906 T^{10} - 36508313950 T^{11} + 468368856170 T^{12} - 1876672098570 T^{13} + 26391557530100 T^{14} - 74876840468854 T^{15} + 1222320881714725 T^{16} - 1539943989650290 T^{17} + 41217072294415415 T^{18} + 713342911662882601 T^{20} $)
$67$	($ 1 - 13 T + 67 T^{2} $)($ 1 + 3 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 - 5 T + 67 T^{2} $)($ 1 - 5 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 13 T + 67 T^{2} $)($ 1 + 3 T + 67 T^{2} $)($ 1 - 6 T + 98 T^{2} - 402 T^{3} + 4489 T^{4} $)($ ( 1 - 8 T + 67 T^{2} )^{2} $)($ ( 1 + 7 T + 67 T^{2} )^{2} $)($ 1 - 22 T + 250 T^{2} - 1474 T^{3} + 4489 T^{4} $)($ 1 + 4 T + 13 T^{2} + 268 T^{3} + 4489 T^{4} $)($ 1 + 4 T + 93 T^{2} + 268 T^{3} + 4489 T^{4} $)($ 1 + 14 T + 178 T^{2} + 938 T^{3} + 4489 T^{4} $)($ 1 + 24 T + 273 T^{2} + 1608 T^{3} + 4489 T^{4} $)($ 1 + 3 T + 30 T^{2} + 201 T^{3} + 4489 T^{4} $)($ ( 1 + 67 T^{2} )^{2} $)($ ( 1 + 67 T^{2} )^{2} $)($ 1 - 22 T + 250 T^{2} - 1474 T^{3} + 4489 T^{4} $)($ 1 + 4 T + 13 T^{2} + 268 T^{3} + 4489 T^{4} $)($ 1 - 8 T + 129 T^{2} - 536 T^{3} + 4489 T^{4} $)($ 1 + 4 T + 93 T^{2} + 268 T^{3} + 4489 T^{4} $)($ 1 + 14 T + 178 T^{2} + 938 T^{3} + 4489 T^{4} $)($ 1 + 3 T + 30 T^{2} + 201 T^{3} + 4489 T^{4} $)($ ( 1 - 8 T + 67 T^{2} )^{2} $)($ ( 1 + 7 T + 67 T^{2} )^{2} $)($ 1 - 6 T + 98 T^{2} - 402 T^{3} + 4489 T^{4} $)($ 1 + 4 T + 116 T^{2} + 300 T^{3} + 7772 T^{4} + 17956 T^{5} + 300763 T^{6} $)($ 1 - 2 T + 50 T^{2} - 852 T^{3} + 3350 T^{4} - 8978 T^{5} + 300763 T^{6} $)($ 1 - 12 T + 228 T^{2} - 1604 T^{3} + 15276 T^{4} - 53868 T^{5} + 300763 T^{6} $)($ 1 - 2 T + 50 T^{2} - 852 T^{3} + 3350 T^{4} - 8978 T^{5} + 300763 T^{6} $)($ 1 + 20 T + 282 T^{2} + 2776 T^{3} + 24707 T^{4} + 185992 T^{5} + 1265898 T^{6} + 6015260 T^{7} + 20151121 T^{8} $)($ 1 - 4 T + 130 T^{2} + 56 T^{3} + 8299 T^{4} + 3752 T^{5} + 583570 T^{6} - 1203052 T^{7} + 20151121 T^{8} $)($ 1 + 28 T + 541 T^{2} + 6696 T^{3} + 64817 T^{4} + 448632 T^{5} + 2428549 T^{6} + 8421364 T^{7} + 20151121 T^{8} $)($ 1 + 28 T + 541 T^{2} + 6696 T^{3} + 64817 T^{4} + 448632 T^{5} + 2428549 T^{6} + 8421364 T^{7} + 20151121 T^{8} $)($ 1 + 20 T + 282 T^{2} + 2776 T^{3} + 24707 T^{4} + 185992 T^{5} + 1265898 T^{6} + 6015260 T^{7} + 20151121 T^{8} $)($ 1 - 4 T + 130 T^{2} + 56 T^{3} + 8299 T^{4} + 3752 T^{5} + 583570 T^{6} - 1203052 T^{7} + 20151121 T^{8} $)($ 1 - 38 T + 939 T^{2} - 16920 T^{3} + 253022 T^{4} - 3231648 T^{5} + 37034650 T^{6} - 384823180 T^{7} + 3720320353 T^{8} - 33446868814 T^{9} + 283134556406 T^{10} - 2240940210538 T^{11} + 16700518064617 T^{12} - 115740574086340 T^{13} + 746289713342650 T^{14} - 4363129101786336 T^{15} + 22887960773164718 T^{16} - 102547240362065160 T^{17} + 381297549225685899 T^{18} - 1033848307059207986 T^{19} + 1822837804551761449 T^{20} $)($ 1 - 38 T + 939 T^{2} - 16920 T^{3} + 253022 T^{4} - 3231648 T^{5} + 37034650 T^{6} - 384823180 T^{7} + 3720320353 T^{8} - 33446868814 T^{9} + 283134556406 T^{10} - 2240940210538 T^{11} + 16700518064617 T^{12} - 115740574086340 T^{13} + 746289713342650 T^{14} - 4363129101786336 T^{15} + 22887960773164718 T^{16} - 102547240362065160 T^{17} + 381297549225685899 T^{18} - 1033848307059207986 T^{19} + 1822837804551761449 T^{20} $)
$71$	($ 1 - 14 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 14 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 - 20 T + 237 T^{2} - 1420 T^{3} + 5041 T^{4} $)($ 1 + 62 T^{2} + 5041 T^{4} $)($ 1 + 6 T + 4 T^{2} + 426 T^{3} + 5041 T^{4} $)($ 1 + 18 T + 203 T^{2} + 1278 T^{3} + 5041 T^{4} $)($ 1 - 4 T + 126 T^{2} - 284 T^{3} + 5041 T^{4} $)($ 1 - 12 T + 158 T^{2} - 852 T^{3} + 5041 T^{4} $)($ 1 + 6 T + 131 T^{2} + 426 T^{3} + 5041 T^{4} $)($ 1 - 4 T + 126 T^{2} - 284 T^{3} + 5041 T^{4} $)($ 1 + 2 T + 126 T^{2} + 142 T^{3} + 5041 T^{4} $)($ 1 - 8 T + 78 T^{2} - 568 T^{3} + 5041 T^{4} $)($ 1 - 8 T + 78 T^{2} - 568 T^{3} + 5041 T^{4} $)($ 1 + 18 T + 203 T^{2} + 1278 T^{3} + 5041 T^{4} $)($ 1 - 4 T + 126 T^{2} - 284 T^{3} + 5041 T^{4} $)($ 1 - 4 T + 62 T^{2} - 284 T^{3} + 5041 T^{4} $)($ 1 - 12 T + 158 T^{2} - 852 T^{3} + 5041 T^{4} $)($ 1 + 6 T + 131 T^{2} + 426 T^{3} + 5041 T^{4} $)($ 1 + 2 T + 126 T^{2} + 142 T^{3} + 5041 T^{4} $)($ 1 + 62 T^{2} + 5041 T^{4} $)($ 1 + 6 T + 4 T^{2} + 426 T^{3} + 5041 T^{4} $)($ 1 - 20 T + 237 T^{2} - 1420 T^{3} + 5041 T^{4} $)($ 1 + 12 T + 197 T^{2} + 1448 T^{3} + 13987 T^{4} + 60492 T^{5} + 357911 T^{6} $)($ 1 + 179 T^{2} - 76 T^{3} + 12709 T^{4} + 357911 T^{6} $)($ 1 - 12 T + 165 T^{2} - 1320 T^{3} + 11715 T^{4} - 60492 T^{5} + 357911 T^{6} $)($ 1 + 179 T^{2} - 76 T^{3} + 12709 T^{4} + 357911 T^{6} $)($ 1 + 10 T + 76 T^{2} - 790 T^{3} - 8172 T^{4} - 56090 T^{5} + 383116 T^{6} + 3579110 T^{7} + 25411681 T^{8} $)($ 1 + 6 T + 220 T^{2} + 1014 T^{3} + 20916 T^{4} + 71994 T^{5} + 1109020 T^{6} + 2147466 T^{7} + 25411681 T^{8} $)($ 1 + 18 T + 327 T^{2} + 3632 T^{3} + 36173 T^{4} + 257872 T^{5} + 1648407 T^{6} + 6442398 T^{7} + 25411681 T^{8} $)($ 1 + 18 T + 327 T^{2} + 3632 T^{3} + 36173 T^{4} + 257872 T^{5} + 1648407 T^{6} + 6442398 T^{7} + 25411681 T^{8} $)($ 1 + 10 T + 76 T^{2} - 790 T^{3} - 8172 T^{4} - 56090 T^{5} + 383116 T^{6} + 3579110 T^{7} + 25411681 T^{8} $)($ 1 + 6 T + 220 T^{2} + 1014 T^{3} + 20916 T^{4} + 71994 T^{5} + 1109020 T^{6} + 2147466 T^{7} + 25411681 T^{8} $)($ 1 - 26 T + 632 T^{2} - 9130 T^{3} + 126663 T^{4} - 1295526 T^{5} + 13933979 T^{6} - 123894450 T^{7} + 1257395276 T^{8} - 10721089596 T^{9} + 100241082738 T^{10} - 761197361316 T^{11} + 6338529586316 T^{12} - 44343186493950 T^{13} + 354085829408699 T^{14} - 2337426034183626 T^{15} + 16225566262285623 T^{16} - 83038447046109830 T^{17} + 408116231747320952 T^{18} - 1192061018679674806 T^{19} + 3255243551009881201 T^{20} $)($ 1 - 26 T + 632 T^{2} - 9130 T^{3} + 126663 T^{4} - 1295526 T^{5} + 13933979 T^{6} - 123894450 T^{7} + 1257395276 T^{8} - 10721089596 T^{9} + 100241082738 T^{10} - 761197361316 T^{11} + 6338529586316 T^{12} - 44343186493950 T^{13} + 354085829408699 T^{14} - 2337426034183626 T^{15} + 16225566262285623 T^{16} - 83038447046109830 T^{17} + 408116231747320952 T^{18} - 1192061018679674806 T^{19} + 3255243551009881201 T^{20} $)
$73$	($ 1 - 10 T + 73 T^{2} $)($ 1 + 14 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 + 8 T + 73 T^{2} $)($ 1 - 8 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 - 6 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 - T + 135 T^{2} - 73 T^{3} + 5329 T^{4} $)($ 1 + 6 T + 150 T^{2} + 438 T^{3} + 5329 T^{4} $)($ 1 - 10 T + 168 T^{2} - 730 T^{3} + 5329 T^{4} $)($ 1 - 17 T + 217 T^{2} - 1241 T^{3} + 5329 T^{4} $)($ 1 - 8 T + 117 T^{2} - 584 T^{3} + 5329 T^{4} $)($ 1 + 20 T + 241 T^{2} + 1460 T^{3} + 5329 T^{4} $)($ 1 + 3 T + 47 T^{2} + 219 T^{3} + 5329 T^{4} $)($ 1 + 18 T + 207 T^{2} + 1314 T^{3} + 5329 T^{4} $)($ 1 + 6 T + 138 T^{2} + 438 T^{3} + 5329 T^{4} $)($ 1 + 14 T + 150 T^{2} + 1022 T^{3} + 5329 T^{4} $)($ 1 - 14 T + 150 T^{2} - 1022 T^{3} + 5329 T^{4} $)($ 1 + 17 T + 217 T^{2} + 1241 T^{3} + 5329 T^{4} $)($ 1 + 8 T + 117 T^{2} + 584 T^{3} + 5329 T^{4} $)($ ( 1 + 7 T + 73 T^{2} )^{2} $)($ 1 - 20 T + 241 T^{2} - 1460 T^{3} + 5329 T^{4} $)($ 1 - 3 T + 47 T^{2} - 219 T^{3} + 5329 T^{4} $)($ 1 - 6 T + 138 T^{2} - 438 T^{3} + 5329 T^{4} $)($ 1 - 6 T + 150 T^{2} - 438 T^{3} + 5329 T^{4} $)($ 1 + 10 T + 168 T^{2} + 730 T^{3} + 5329 T^{4} $)($ 1 + T + 135 T^{2} + 73 T^{3} + 5329 T^{4} $)($ 1 - 20 T + 320 T^{2} - 3054 T^{3} + 23360 T^{4} - 106580 T^{5} + 389017 T^{6} $)($ 1 - 4 T - 7 T^{2} + 1044 T^{3} - 511 T^{4} - 21316 T^{5} + 389017 T^{6} $)($ 1 + 24 T + 396 T^{2} + 3898 T^{3} + 28908 T^{4} + 127896 T^{5} + 389017 T^{6} $)($ 1 + 4 T - 7 T^{2} - 1044 T^{3} - 511 T^{4} + 21316 T^{5} + 389017 T^{6} $)($ 1 - 10 T + 52 T^{2} - 406 T^{3} + 7828 T^{4} - 29638 T^{5} + 277108 T^{6} - 3890170 T^{7} + 28398241 T^{8} $)($ 1 + 34 T + 708 T^{2} + 9614 T^{3} + 96764 T^{4} + 701822 T^{5} + 3772932 T^{6} + 13226578 T^{7} + 28398241 T^{8} $)($ 1 - 4 T + 284 T^{2} - 852 T^{3} + 30822 T^{4} - 62196 T^{5} + 1513436 T^{6} - 1556068 T^{7} + 28398241 T^{8} $)($ 1 + 4 T + 284 T^{2} + 852 T^{3} + 30822 T^{4} + 62196 T^{5} + 1513436 T^{6} + 1556068 T^{7} + 28398241 T^{8} $)($ 1 + 10 T + 52 T^{2} + 406 T^{3} + 7828 T^{4} + 29638 T^{5} + 277108 T^{6} + 3890170 T^{7} + 28398241 T^{8} $)($ 1 - 34 T + 708 T^{2} - 9614 T^{3} + 96764 T^{4} - 701822 T^{5} + 3772932 T^{6} - 13226578 T^{7} + 28398241 T^{8} $)($ 1 - T + 393 T^{2} - 817 T^{3} + 74513 T^{4} - 250396 T^{5} + 9185572 T^{6} - 43089004 T^{7} + 854063166 T^{8} - 4726643438 T^{9} + 66584553318 T^{10} - 345044970974 T^{11} + 4551302611614 T^{12} - 16762355069068 T^{13} + 260854087378852 T^{14} - 519088834600828 T^{15} + 11276367203472257 T^{16} - 9025724590102249 T^{17} + 316938816114373833 T^{18} - 58871586708267913 T^{19} + 4297625829703557649 T^{20} $)($ 1 + T + 393 T^{2} + 817 T^{3} + 74513 T^{4} + 250396 T^{5} + 9185572 T^{6} + 43089004 T^{7} + 854063166 T^{8} + 4726643438 T^{9} + 66584553318 T^{10} + 345044970974 T^{11} + 4551302611614 T^{12} + 16762355069068 T^{13} + 260854087378852 T^{14} + 519088834600828 T^{15} + 11276367203472257 T^{16} + 9025724590102249 T^{17} + 316938816114373833 T^{18} + 58871586708267913 T^{19} + 4297625829703557649 T^{20} $)
$79$	($ 1 - 4 T + 79 T^{2} $)($ 1 + 4 T + 79 T^{2} $)($ 1 - 2 T + 79 T^{2} $)($ 1 + 14 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 + 2 T + 79 T^{2} $)($ 1 + 16 T + 79 T^{2} $)($ 1 - 14 T + 79 T^{2} $)($ 1 - 16 T + 79 T^{2} $)($ 1 + 4 T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 + 7 T + 159 T^{2} + 553 T^{3} + 6241 T^{4} $)($ ( 1 + 14 T + 79 T^{2} )^{2} $)($ 1 - 8 T + 162 T^{2} - 632 T^{3} + 6241 T^{4} $)($ 1 + T + 127 T^{2} + 79 T^{3} + 6241 T^{4} $)($ 1 + 8 T + 154 T^{2} + 632 T^{3} + 6241 T^{4} $)($ 1 - 22 T^{2} + 6241 T^{4} $)($ 1 + 15 T + 203 T^{2} + 1185 T^{3} + 6241 T^{4} $)($ 1 - 20 T + 238 T^{2} - 1580 T^{3} + 6241 T^{4} $)($ 1 - 2 T + 142 T^{2} - 158 T^{3} + 6241 T^{4} $)($ ( 1 - 10 T + 79 T^{2} )^{2} $)($ ( 1 + 10 T + 79 T^{2} )^{2} $)($ 1 - T + 127 T^{2} - 79 T^{3} + 6241 T^{4} $)($ 1 - 8 T + 154 T^{2} - 632 T^{3} + 6241 T^{4} $)($ 1 - 4 T + 78 T^{2} - 316 T^{3} + 6241 T^{4} $)($ 1 - 22 T^{2} + 6241 T^{4} $)($ 1 - 15 T + 203 T^{2} - 1185 T^{3} + 6241 T^{4} $)($ 1 + 2 T + 142 T^{2} + 158 T^{3} + 6241 T^{4} $)($ ( 1 - 14 T + 79 T^{2} )^{2} $)($ 1 + 8 T + 162 T^{2} + 632 T^{3} + 6241 T^{4} $)($ 1 - 7 T + 159 T^{2} - 553 T^{3} + 6241 T^{4} $)($ 1 + 12 T + 221 T^{2} + 1640 T^{3} + 17459 T^{4} + 74892 T^{5} + 493039 T^{6} $)($ 1 + 18 T + 209 T^{2} + 1636 T^{3} + 16511 T^{4} + 112338 T^{5} + 493039 T^{6} $)($ 1 + 12 T + 189 T^{2} + 1640 T^{3} + 14931 T^{4} + 74892 T^{5} + 493039 T^{6} $)($ 1 - 18 T + 209 T^{2} - 1636 T^{3} + 16511 T^{4} - 112338 T^{5} + 493039 T^{6} $)($ 1 + 16 T + 312 T^{2} + 3272 T^{3} + 37490 T^{4} + 258488 T^{5} + 1947192 T^{6} + 7888624 T^{7} + 38950081 T^{8} $)($ 1 + 24 T + 280 T^{2} + 1584 T^{3} + 8754 T^{4} + 125136 T^{5} + 1747480 T^{6} + 11832936 T^{7} + 38950081 T^{8} $)($ 1 - 20 T + 445 T^{2} - 5040 T^{3} + 57977 T^{4} - 398160 T^{5} + 2777245 T^{6} - 9860780 T^{7} + 38950081 T^{8} $)($ 1 + 20 T + 445 T^{2} + 5040 T^{3} + 57977 T^{4} + 398160 T^{5} + 2777245 T^{6} + 9860780 T^{7} + 38950081 T^{8} $)($ 1 - 16 T + 312 T^{2} - 3272 T^{3} + 37490 T^{4} - 258488 T^{5} + 1947192 T^{6} - 7888624 T^{7} + 38950081 T^{8} $)($ 1 - 24 T + 280 T^{2} - 1584 T^{3} + 8754 T^{4} - 125136 T^{5} + 1747480 T^{6} - 11832936 T^{7} + 38950081 T^{8} $)($ 1 + 5 T + 552 T^{2} + 2604 T^{3} + 151027 T^{4} + 658718 T^{5} + 26569829 T^{6} + 105054020 T^{7} + 3304178864 T^{8} + 11590016269 T^{9} + 302495065710 T^{10} + 915611285251 T^{11} + 20621380290224 T^{12} + 51795728966780 T^{13} + 1034896991706149 T^{14} + 2026912437036482 T^{15} + 36712769144970067 T^{16} + 50006978999958036 T^{17} + 837444063068421672 T^{18} + 599257979913091595 T^{19} + 9468276082626847201 T^{20} $)($ 1 - 5 T + 552 T^{2} - 2604 T^{3} + 151027 T^{4} - 658718 T^{5} + 26569829 T^{6} - 105054020 T^{7} + 3304178864 T^{8} - 11590016269 T^{9} + 302495065710 T^{10} - 915611285251 T^{11} + 20621380290224 T^{12} - 51795728966780 T^{13} + 1034896991706149 T^{14} - 2026912437036482 T^{15} + 36712769144970067 T^{16} - 50006978999958036 T^{17} + 837444063068421672 T^{18} - 599257979913091595 T^{19} + 9468276082626847201 T^{20} $)
$83$	($ 1 + T + 83 T^{2} $)($ 1 - 5 T + 83 T^{2} $)($ 1 - 16 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 15 T + 83 T^{2} $)($ 1 - 15 T + 83 T^{2} $)($ 1 + 16 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - T + 83 T^{2} $)($ 1 + 5 T + 83 T^{2} $)($ 1 - 12 T + 122 T^{2} - 996 T^{3} + 6889 T^{4} $)($ 1 + 12 T + 122 T^{2} + 996 T^{3} + 6889 T^{4} $)($ 1 + 12 T + 199 T^{2} + 996 T^{3} + 6889 T^{4} $)($ 1 - 8 T + 162 T^{2} - 664 T^{3} + 6889 T^{4} $)($ 1 + 24 T + 290 T^{2} + 1992 T^{3} + 6889 T^{4} $)($ ( 1 + 6 T + 83 T^{2} )^{2} $)($ ( 1 - 6 T + 83 T^{2} )^{2} $)($ 1 + 18 T + 242 T^{2} + 1494 T^{3} + 6889 T^{4} $)($ 1 + 3 T + 62 T^{2} + 249 T^{3} + 6889 T^{4} $)($ 1 + 24 T + 290 T^{2} + 1992 T^{3} + 6889 T^{4} $)($ 1 - 24 T + 290 T^{2} - 1992 T^{3} + 6889 T^{4} $)($ 1 + 8 T + 162 T^{2} + 664 T^{3} + 6889 T^{4} $)($ 1 - 24 T + 290 T^{2} - 1992 T^{3} + 6889 T^{4} $)($ 1 - 14 T + 194 T^{2} - 1162 T^{3} + 6889 T^{4} $)($ ( 1 - 6 T + 83 T^{2} )^{2} $)($ ( 1 + 6 T + 83 T^{2} )^{2} $)($ 1 - 3 T + 62 T^{2} - 249 T^{3} + 6889 T^{4} $)($ 1 - 12 T + 122 T^{2} - 996 T^{3} + 6889 T^{4} $)($ 1 - 12 T + 199 T^{2} - 996 T^{3} + 6889 T^{4} $)($ 1 + 12 T + 122 T^{2} + 996 T^{3} + 6889 T^{4} $)($ 1 + 6 T + 117 T^{2} + 500 T^{3} + 9711 T^{4} + 41334 T^{5} + 571787 T^{6} $)($ 1 - 12 T + 78 T^{2} + 64 T^{3} + 6474 T^{4} - 82668 T^{5} + 571787 T^{6} $)($ 1 - 18 T + 309 T^{2} - 3036 T^{3} + 25647 T^{4} - 124002 T^{5} + 571787 T^{6} $)($ 1 + 12 T + 78 T^{2} - 64 T^{3} + 6474 T^{4} + 82668 T^{5} + 571787 T^{6} $)($ 1 + 18 T + 400 T^{2} + 4404 T^{3} + 52635 T^{4} + 365532 T^{5} + 2755600 T^{6} + 10292166 T^{7} + 47458321 T^{8} $)($ 1 + 6 T + 260 T^{2} + 1188 T^{3} + 30039 T^{4} + 98604 T^{5} + 1791140 T^{6} + 3430722 T^{7} + 47458321 T^{8} $)($ 1 + 6 T + 212 T^{2} + 982 T^{3} + 24278 T^{4} + 81506 T^{5} + 1460468 T^{6} + 3430722 T^{7} + 47458321 T^{8} $)($ 1 - 6 T + 212 T^{2} - 982 T^{3} + 24278 T^{4} - 81506 T^{5} + 1460468 T^{6} - 3430722 T^{7} + 47458321 T^{8} $)($ 1 - 18 T + 400 T^{2} - 4404 T^{3} + 52635 T^{4} - 365532 T^{5} + 2755600 T^{6} - 10292166 T^{7} + 47458321 T^{8} $)($ 1 - 6 T + 260 T^{2} - 1188 T^{3} + 30039 T^{4} - 98604 T^{5} + 1791140 T^{6} - 3430722 T^{7} + 47458321 T^{8} $)($ 1 + 6 T + 490 T^{2} + 3578 T^{3} + 118805 T^{4} + 976848 T^{5} + 19084536 T^{6} + 164833504 T^{7} + 2271305170 T^{8} + 19148739052 T^{9} + 211320377724 T^{10} + 1589345341316 T^{11} + 15647021316130 T^{12} + 94249654751648 T^{13} + 905720035624056 T^{14} + 3847843974033264 T^{15} + 38842151058104045 T^{16} + 97092790440885406 T^{17} + 1103623193748130090 T^{18} + 1121641531605242418 T^{19} + 15516041187205853449 T^{20} $)($ 1 - 6 T + 490 T^{2} - 3578 T^{3} + 118805 T^{4} - 976848 T^{5} + 19084536 T^{6} - 164833504 T^{7} + 2271305170 T^{8} - 19148739052 T^{9} + 211320377724 T^{10} - 1589345341316 T^{11} + 15647021316130 T^{12} - 94249654751648 T^{13} + 905720035624056 T^{14} - 3847843974033264 T^{15} + 38842151058104045 T^{16} - 97092790440885406 T^{17} + 1103623193748130090 T^{18} - 1121641531605242418 T^{19} + 15516041187205853449 T^{20} $)
$89$	($ 1 + 9 T + 89 T^{2} $)($ 1 - 3 T + 89 T^{2} $)($ 1 - 3 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ 1 - 15 T + 89 T^{2} $)($ 1 - 15 T + 89 T^{2} $)($ 1 - 3 T + 89 T^{2} $)($ 1 - 18 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ 1 + 14 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ 1 - 3 T + 89 T^{2} $)($ 1 - 21 T + 227 T^{2} - 1869 T^{3} + 7921 T^{4} $)($ 1 + 9 T + 167 T^{2} + 801 T^{3} + 7921 T^{4} $)($ 1 + 12 T + 139 T^{2} + 1068 T^{3} + 7921 T^{4} $)($ 1 + 13 T + 159 T^{2} + 1157 T^{3} + 7921 T^{4} $)($ 1 - 8 T + 174 T^{2} - 712 T^{3} + 7921 T^{4} $)($ 1 + 158 T^{2} + 7921 T^{4} $)($ 1 + 15 T + 233 T^{2} + 1335 T^{3} + 7921 T^{4} $)($ 1 + 158 T^{2} + 7921 T^{4} $)($ 1 + 6 T + 119 T^{2} + 534 T^{3} + 7921 T^{4} $)($ 1 - 9 T + 197 T^{2} - 801 T^{3} + 7921 T^{4} $)($ 1 - 9 T + 197 T^{2} - 801 T^{3} + 7921 T^{4} $)($ 1 + 13 T + 159 T^{2} + 1157 T^{3} + 7921 T^{4} $)($ 1 - 8 T + 174 T^{2} - 712 T^{3} + 7921 T^{4} $)($ 1 + 94 T^{2} + 7921 T^{4} $)($ 1 + 158 T^{2} + 7921 T^{4} $)($ 1 + 15 T + 233 T^{2} + 1335 T^{3} + 7921 T^{4} $)($ 1 + 6 T + 119 T^{2} + 534 T^{3} + 7921 T^{4} $)($ 1 + 9 T + 167 T^{2} + 801 T^{3} + 7921 T^{4} $)($ 1 + 12 T + 139 T^{2} + 1068 T^{3} + 7921 T^{4} $)($ 1 - 21 T + 227 T^{2} - 1869 T^{3} + 7921 T^{4} $)($ 1 - 26 T + 407 T^{2} - 4300 T^{3} + 36223 T^{4} - 205946 T^{5} + 704969 T^{6} $)($ 1 + T + 188 T^{2} + 251 T^{3} + 16732 T^{4} + 7921 T^{5} + 704969 T^{6} $)($ 1 - 18 T + 183 T^{2} - 1308 T^{3} + 16287 T^{4} - 142578 T^{5} + 704969 T^{6} $)($ 1 + T + 188 T^{2} + 251 T^{3} + 16732 T^{4} + 7921 T^{5} + 704969 T^{6} $)($ 1 + 14 T + 244 T^{2} + 2764 T^{3} + 32067 T^{4} + 245996 T^{5} + 1932724 T^{6} + 9869566 T^{7} + 62742241 T^{8} $)($ 1 - 18 T + 352 T^{2} - 4068 T^{3} + 48255 T^{4} - 362052 T^{5} + 2788192 T^{6} - 12689442 T^{7} + 62742241 T^{8} $)($ 1 + 16 T + 308 T^{2} + 3096 T^{3} + 38678 T^{4} + 275544 T^{5} + 2439668 T^{6} + 11279504 T^{7} + 62742241 T^{8} $)($ 1 + 16 T + 308 T^{2} + 3096 T^{3} + 38678 T^{4} + 275544 T^{5} + 2439668 T^{6} + 11279504 T^{7} + 62742241 T^{8} $)($ 1 + 14 T + 244 T^{2} + 2764 T^{3} + 32067 T^{4} + 245996 T^{5} + 1932724 T^{6} + 9869566 T^{7} + 62742241 T^{8} $)($ 1 - 18 T + 352 T^{2} - 4068 T^{3} + 48255 T^{4} - 362052 T^{5} + 2788192 T^{6} - 12689442 T^{7} + 62742241 T^{8} $)($ 1 + 9 T + 640 T^{2} + 4050 T^{3} + 178355 T^{4} + 698876 T^{5} + 29313265 T^{6} + 51732294 T^{7} + 3369419368 T^{8} + 1036172651 T^{9} + 317703552166 T^{10} + 92219365939 T^{11} + 26689170813928 T^{12} + 36469663568886 T^{13} + 1839179937126865 T^{14} + 3902565131479324 T^{15} + 88639098149349155 T^{16} + 179136906326892450 T^{17} + 2519416835649331840 T^{18} + 3153207633367366881 T^{19} + 31181719929966183601 T^{20} $)($ 1 + 9 T + 640 T^{2} + 4050 T^{3} + 178355 T^{4} + 698876 T^{5} + 29313265 T^{6} + 51732294 T^{7} + 3369419368 T^{8} + 1036172651 T^{9} + 317703552166 T^{10} + 92219365939 T^{11} + 26689170813928 T^{12} + 36469663568886 T^{13} + 1839179937126865 T^{14} + 3902565131479324 T^{15} + 88639098149349155 T^{16} + 179136906326892450 T^{17} + 2519416835649331840 T^{18} + 3153207633367366881 T^{19} + 31181719929966183601 T^{20} $)
$97$	($ 1 + 16 T + 97 T^{2} $)($ 1 + 4 T + 97 T^{2} $)($ 1 + 19 T + 97 T^{2} $)($ 1 - 17 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 + 19 T + 97 T^{2} $)($ 1 - 2 T + 97 T^{2} $)($ 1 - 17 T + 97 T^{2} $)($ 1 - 18 T + 97 T^{2} $)($ 1 + 16 T + 97 T^{2} $)($ 1 + 4 T + 97 T^{2} $)($ 1 + 6 T + 23 T^{2} + 582 T^{3} + 9409 T^{4} $)($ 1 + 16 T + 238 T^{2} + 1552 T^{3} + 9409 T^{4} $)($ 1 - 10 T + 216 T^{2} - 970 T^{3} + 9409 T^{4} $)($ 1 + 24 T + 293 T^{2} + 2328 T^{3} + 9409 T^{4} $)($ 1 + 8 T + 30 T^{2} + 776 T^{3} + 9409 T^{4} $)($ ( 1 - 2 T + 97 T^{2} )^{2} $)($ ( 1 + 17 T + 97 T^{2} )^{2} $)($ 1 - 6 T + 158 T^{2} - 582 T^{3} + 9409 T^{4} $)($ 1 - 15 T + 212 T^{2} - 1455 T^{3} + 9409 T^{4} $)($ ( 1 + 6 T + 97 T^{2} )^{2} $)($ ( 1 + 6 T + 97 T^{2} )^{2} $)($ 1 + 24 T + 293 T^{2} + 2328 T^{3} + 9409 T^{4} $)($ 1 + 8 T + 30 T^{2} + 776 T^{3} + 9409 T^{4} $)($ 1 + 14 T + 222 T^{2} + 1358 T^{3} + 9409 T^{4} $)($ ( 1 - 2 T + 97 T^{2} )^{2} $)($ ( 1 + 17 T + 97 T^{2} )^{2} $)($ 1 - 15 T + 212 T^{2} - 1455 T^{3} + 9409 T^{4} $)($ 1 + 16 T + 238 T^{2} + 1552 T^{3} + 9409 T^{4} $)($ 1 - 10 T + 216 T^{2} - 970 T^{3} + 9409 T^{4} $)($ 1 + 6 T + 23 T^{2} + 582 T^{3} + 9409 T^{4} $)($ 1 + 4 T + 171 T^{2} + 544 T^{3} + 16587 T^{4} + 37636 T^{5} + 912673 T^{6} $)($ 1 + 25 T + 315 T^{2} + 2968 T^{3} + 30555 T^{4} + 235225 T^{5} + 912673 T^{6} $)($ 1 - 24 T + 435 T^{2} - 4664 T^{3} + 42195 T^{4} - 225816 T^{5} + 912673 T^{6} $)($ 1 + 25 T + 315 T^{2} + 2968 T^{3} + 30555 T^{4} + 235225 T^{5} + 912673 T^{6} $)($ 1 - 38 T + 844 T^{2} - 12458 T^{3} + 140980 T^{4} - 1208426 T^{5} + 7941196 T^{6} - 34681574 T^{7} + 88529281 T^{8} $)($ 1 + 10 T + 388 T^{2} + 2758 T^{3} + 56428 T^{4} + 267526 T^{5} + 3650692 T^{6} + 9126730 T^{7} + 88529281 T^{8} $)($ 1 - 32 T + 656 T^{2} - 8944 T^{3} + 99982 T^{4} - 867568 T^{5} + 6172304 T^{6} - 29205536 T^{7} + 88529281 T^{8} $)($ 1 - 32 T + 656 T^{2} - 8944 T^{3} + 99982 T^{4} - 867568 T^{5} + 6172304 T^{6} - 29205536 T^{7} + 88529281 T^{8} $)($ 1 - 38 T + 844 T^{2} - 12458 T^{3} + 140980 T^{4} - 1208426 T^{5} + 7941196 T^{6} - 34681574 T^{7} + 88529281 T^{8} $)($ 1 + 10 T + 388 T^{2} + 2758 T^{3} + 56428 T^{4} + 267526 T^{5} + 3650692 T^{6} + 9126730 T^{7} + 88529281 T^{8} $)($ 1 - 24 T + 1069 T^{2} - 19604 T^{3} + 490777 T^{4} - 7233428 T^{5} + 130302052 T^{6} - 1582958620 T^{7} + 22393814246 T^{8} - 226465922980 T^{9} + 2616113341790 T^{10} - 21967194529060 T^{11} + 210703398240614 T^{12} - 1444723592591260 T^{13} + 11535546976384612 T^{14} - 62115907460510996 T^{15} + 408803501663039833 T^{16} - 1583969568908927252 T^{17} + 8378216512388971309 T^{18} - 18245545407709565208 T^{19} + 73742412689492826049 T^{20} $)($ 1 - 24 T + 1069 T^{2} - 19604 T^{3} + 490777 T^{4} - 7233428 T^{5} + 130302052 T^{6} - 1582958620 T^{7} + 22393814246 T^{8} - 226465922980 T^{9} + 2616113341790 T^{10} - 21967194529060 T^{11} + 210703398240614 T^{12} - 1444723592591260 T^{13} + 11535546976384612 T^{14} - 62115907460510996 T^{15} + 408803501663039833 T^{16} - 1583969568908927252 T^{17} + 8378216512388971309 T^{18} - 18245545407709565208 T^{19} + 73742412689492826049 T^{20} $)
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Introduction	Features
Universe	News

Level:	\( N \)	=	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	2541.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 44 \)
Sturm bound:			\(704\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\), \(13\)

\(3\)	\(7\)	\(11\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(12\)
\(+\)	\(+\)	\(-\)	\(-\)	\(15\)
\(+\)	\(-\)	\(+\)	\(-\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)	\(15\)
\(-\)	\(+\)	\(+\)	\(-\)	\(16\)
\(-\)	\(+\)	\(-\)	\(+\)	\(10\)
\(-\)	\(-\)	\(+\)	\(+\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)	\(20\)
Plus space			\(+\)	\(45\)
Minus space			\(-\)	\(63\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	3	7	11	$q$-expansion
2541.2.a.a	\(1\)	\(20.290\)	\(\Q\)	None	\(-2\)	\(-1\)	\(-3\)	\(1\)	\(+\)	\(-\)	\(-\)	\(q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
2541.2.a.b	\(1\)	\(20.290\)	\(\Q\)	None	\(-2\)	\(-1\)	\(1\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
2541.2.a.c	\(1\)	\(20.290\)	\(\Q\)	None	\(-1\)	\(-1\)	\(-3\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
2541.2.a.d	\(1\)	\(20.290\)	\(\Q\)	None	\(-1\)	\(-1\)	\(1\)	\(1\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
2541.2.a.e	\(1\)	\(20.290\)	\(\Q\)	None	\(0\)	\(1\)	\(-3\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(q+q^{3}-2q^{4}-3q^{5}-q^{7}+q^{9}-2q^{12}+\cdots\)
2541.2.a.f	\(1\)	\(20.290\)	\(\Q\)	None	\(0\)	\(1\)	\(-3\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}-2q^{12}+\cdots\)
2541.2.a.g	\(1\)	\(20.290\)	\(\Q\)	None	\(1\)	\(-1\)	\(-3\)	\(1\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
2541.2.a.h	\(1\)	\(20.290\)	\(\Q\)	None	\(1\)	\(-1\)	\(-2\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
2541.2.a.i	\(1\)	\(20.290\)	\(\Q\)	None	\(1\)	\(-1\)	\(1\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
2541.2.a.j	\(1\)	\(20.290\)	\(\Q\)	None	\(1\)	\(1\)	\(-2\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
2541.2.a.k	\(1\)	\(20.290\)	\(\Q\)	None	\(2\)	\(-1\)	\(-3\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots\)
2541.2.a.l	\(1\)	\(20.290\)	\(\Q\)	None	\(2\)	\(-1\)	\(1\)	\(1\)	\(+\)	\(-\)	\(-\)	\(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
2541.2.a.m	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(-3\)	\(-2\)	\(1\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+\cdots\)
2541.2.a.n	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(-2\)	\(-2\)	\(1\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}+q^{6}+\cdots\)
2541.2.a.o	\(2\)	\(20.290\)	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(-2\)	\(-4\)	\(2\)	\(+\)	\(-\)	\(-\)	\(q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
2541.2.a.p	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(-2\)	\(-1\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
2541.2.a.q	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(-2\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
2541.2.a.r	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(2\)	\(-4\)	\(2\)	\(-\)	\(-\)	\(+\)	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
2541.2.a.s	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(2\)	\(-3\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
2541.2.a.t	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(2\)	\(2\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2541.2.a.u	\(2\)	\(20.290\)	\(\Q(\sqrt{17}) \)	None	\(-1\)	\(2\)	\(2\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2541.2.a.v	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(1\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(q+(1-2\beta )q^{2}-q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots\)
2541.2.a.w	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(1\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q+(1-2\beta )q^{2}-q^{3}+3q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
2541.2.a.x	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(1\)	\(-2\)	\(-1\)	\(2\)	\(+\)	\(-\)	\(-\)	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
2541.2.a.y	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(1\)	\(-2\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots\)
2541.2.a.z	\(2\)	\(20.290\)	\(\Q(\sqrt{21}) \)	None	\(1\)	\(-2\)	\(6\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(q+\beta q^{2}-q^{3}+(3+\beta )q^{4}+3q^{5}-\beta q^{6}+\cdots\)
2541.2.a.ba	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(1\)	\(2\)	\(-4\)	\(-2\)	\(-\)	\(+\)	\(+\)	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-2\beta )q^{5}+\cdots\)
2541.2.a.bb	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(1\)	\(2\)	\(-3\)	\(2\)	\(-\)	\(-\)	\(+\)	\(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
2541.2.a.bc	\(2\)	\(20.290\)	\(\Q(\sqrt{17}) \)	None	\(1\)	\(2\)	\(2\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
2541.2.a.bd	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(2\)	\(-2\)	\(1\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}-q^{3}-q^{4}+(2-3\beta )q^{5}-q^{6}+\cdots\)
2541.2.a.be	\(2\)	\(20.290\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(-2\)	\(-4\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
2541.2.a.bf	\(2\)	\(20.290\)	\(\Q(\sqrt{5}) \)	None	\(3\)	\(-2\)	\(1\)	\(2\)	\(+\)	\(-\)	\(+\)	\(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
2541.2.a.bg	\(3\)	\(20.290\)	3.3.229.1	None	\(-2\)	\(3\)	\(4\)	\(3\)	\(-\)	\(-\)	\(-\)	\(q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+\cdots\)
2541.2.a.bh	\(3\)	\(20.290\)	3.3.316.1	None	\(-1\)	\(3\)	\(1\)	\(-3\)	\(-\)	\(+\)	\(-\)	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bi	\(3\)	\(20.290\)	3.3.837.1	None	\(0\)	\(-3\)	\(0\)	\(3\)	\(+\)	\(-\)	\(-\)	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bj	\(3\)	\(20.290\)	3.3.316.1	None	\(1\)	\(3\)	\(1\)	\(3\)	\(-\)	\(-\)	\(-\)	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2541.2.a.bk	\(4\)	\(20.290\)	4.4.7488.1	None	\(-2\)	\(-4\)	\(6\)	\(-4\)	\(+\)	\(+\)	\(+\)	\(q+\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bl	\(4\)	\(20.290\)	4.4.7488.1	None	\(-2\)	\(4\)	\(-2\)	\(4\)	\(-\)	\(-\)	\(+\)	\(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bm	\(4\)	\(20.290\)	4.4.725.1	None	\(-1\)	\(-4\)	\(-4\)	\(4\)	\(+\)	\(-\)	\(-\)	\(q+(-1+\beta _{1}+\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
2541.2.a.bn	\(4\)	\(20.290\)	4.4.725.1	None	\(1\)	\(-4\)	\(-4\)	\(-4\)	\(+\)	\(+\)	\(+\)	\(q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
2541.2.a.bo	\(4\)	\(20.290\)	4.4.7488.1	None	\(2\)	\(-4\)	\(6\)	\(4\)	\(+\)	\(-\)	\(+\)	\(q-\beta _{3}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bp	\(4\)	\(20.290\)	4.4.7488.1	None	\(2\)	\(4\)	\(-2\)	\(-4\)	\(-\)	\(+\)	\(+\)	\(q-\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2541.2.a.bq	\(10\)	\(20.290\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(10\)	\(5\)	\(-10\)	\(-\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
2541.2.a.br	\(10\)	\(20.290\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(0\)	\(10\)	\(5\)	\(10\)	\(-\)	\(-\)	\(-\)	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Properties

Related objects

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Learn more about

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2541))\) 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	2541.2.a

Level	2541
Weight	2
Character orbit	a
Rep. character	\(\chi_{2541}(1,\cdot)\)
Character field	\(\Q\)
Dimension	108
Newform subspaces	44
Sturm bound	704
Trace bound	7