LMFDB - Space of modular forms of level 9408, weight 2, and Trivial character

Defining parameters

Level:	$ N $	$=$	$ 9408 = 2^{6} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9408.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 118 $
Sturm bound:			$3584$
Trace bound:			$19$
Distinguishing $T_p$:			$5$, $11$, $13$, $17$, $19$, $31$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(9408))$.

	Total	New	Old
Modular forms	1888	164	1724
Cusp forms	1697	164	1533
Eisenstein series	191	0	191

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

$2$	$3$	$7$	Fricke	Dim.
$+$	$+$	$+$	$+$	$21$
$+$	$+$	$-$	$-$	$21$
$+$	$-$	$+$	$-$	$23$
$+$	$-$	$-$	$+$	$18$
$-$	$+$	$+$	$-$	$19$
$-$	$+$	$-$	$+$	$21$
$-$	$-$	$+$	$+$	$17$
$-$	$-$	$-$	$-$	$24$
Plus space			$+$	$77$
Minus space			$-$	$87$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(9408))$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	2	3	7	$q$-expansion
9408.2.a.a	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-4$	$0$	$-$	$+$	$-$	$q-q^{3}-4q^{5}+q^{9}-6q^{11}+5q^{13}+\cdots$
9408.2.a.b	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-4$	$0$	$-$	$+$	$-$	$q-q^{3}-4q^{5}+q^{9}-4q^{11}-4q^{13}+\cdots$
9408.2.a.c	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-4$	$0$	$+$	$+$	$-$	$q-q^{3}-4q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots$
9408.2.a.d	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-3$	$0$	$+$	$+$	$+$	$q-q^{3}-3q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots$
9408.2.a.e	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-3$	$0$	$-$	$+$	$+$	$q-q^{3}-3q^{5}+q^{9}+q^{11}+4q^{13}+\cdots$
9408.2.a.f	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$-$	$+$	$+$	$q-q^{3}-2q^{5}+q^{9}-6q^{11}+3q^{13}+\cdots$
9408.2.a.g	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots$
9408.2.a.h	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$+$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
9408.2.a.i	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$+$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-2q^{11}-3q^{13}+\cdots$
9408.2.a.j	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$+$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots$
9408.2.a.k	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-2q^{11}+q^{13}+\cdots$
9408.2.a.l	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$+$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots$
9408.2.a.m	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
9408.2.a.n	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$+$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots$
9408.2.a.o	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$q-q^{3}-q^{5}+q^{9}+q^{11}+q^{15}-8q^{17}+\cdots$
9408.2.a.p	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-1$	$0$	$-$	$+$	$-$	$q-q^{3}-q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots$
9408.2.a.q	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$q-q^{3}-q^{5}+q^{9}+5q^{11}+q^{15}-4q^{17}+\cdots$
9408.2.a.r	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}-6q^{11}+2q^{13}+4q^{19}+\cdots$
9408.2.a.s	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$+$	$q-q^{3}+q^{9}-2q^{11}-5q^{13}-2q^{17}+\cdots$
9408.2.a.t	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$q-q^{3}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots$
9408.2.a.u	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$q-q^{3}+q^{9}-4q^{13}+4q^{17}+4q^{19}+\cdots$
9408.2.a.v	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}+4q^{13}-4q^{17}+4q^{19}+\cdots$
9408.2.a.w	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$q-q^{3}+q^{9}+2q^{11}-2q^{13}-4q^{17}+\cdots$
9408.2.a.x	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$q-q^{3}+q^{9}+2q^{11}+q^{13}+2q^{17}+\cdots$
9408.2.a.y	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}+2q^{11}+5q^{13}+2q^{17}+\cdots$
9408.2.a.z	$1$	$75.123$	$\Q$	None	$0$	$-1$	$1$	$0$	$+$	$+$	$-$	$q-q^{3}+q^{5}+q^{9}-5q^{11}-q^{15}+4q^{17}+\cdots$
9408.2.a.ba	$1$	$75.123$	$\Q$	None	$0$	$-1$	$1$	$0$	$+$	$+$	$+$	$q-q^{3}+q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots$
9408.2.a.bb	$1$	$75.123$	$\Q$	None	$0$	$-1$	$1$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{5}+q^{9}-q^{11}-q^{15}+8q^{17}+\cdots$
9408.2.a.bc	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$-$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots$
9408.2.a.bd	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$-$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots$
9408.2.a.be	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$+$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+6q^{13}-2q^{15}+\cdots$
9408.2.a.bf	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$-$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots$
9408.2.a.bg	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$+$	$+$	$+$	$q-q^{3}+2q^{5}+q^{9}+2q^{11}-q^{13}+\cdots$
9408.2.a.bh	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$+$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots$
9408.2.a.bi	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$-$	$+$	$+$	$q-q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots$
9408.2.a.bj	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$+$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
9408.2.a.bk	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$+$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+6q^{11}-3q^{13}+\cdots$
9408.2.a.bl	$1$	$75.123$	$\Q$	None	$0$	$-1$	$3$	$0$	$-$	$+$	$-$	$q-q^{3}+3q^{5}+q^{9}-q^{11}-4q^{13}+\cdots$
9408.2.a.bm	$1$	$75.123$	$\Q$	None	$0$	$-1$	$3$	$0$	$-$	$+$	$-$	$q-q^{3}+3q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots$
9408.2.a.bn	$1$	$75.123$	$\Q$	None	$0$	$-1$	$4$	$0$	$+$	$+$	$-$	$q-q^{3}+4q^{5}+q^{9}-2q^{11}-6q^{13}+\cdots$
9408.2.a.bo	$1$	$75.123$	$\Q$	None	$0$	$-1$	$4$	$0$	$+$	$+$	$-$	$q-q^{3}+4q^{5}+q^{9}+4q^{11}+4q^{13}+\cdots$
9408.2.a.bp	$1$	$75.123$	$\Q$	None	$0$	$-1$	$4$	$0$	$-$	$+$	$+$	$q-q^{3}+4q^{5}+q^{9}+6q^{11}-5q^{13}+\cdots$
9408.2.a.bq	$1$	$75.123$	$\Q$	None	$0$	$1$	$-4$	$0$	$+$	$-$	$-$	$q+q^{3}-4q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots$
9408.2.a.br	$1$	$75.123$	$\Q$	None	$0$	$1$	$-4$	$0$	$+$	$-$	$-$	$q+q^{3}-4q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots$
9408.2.a.bs	$1$	$75.123$	$\Q$	None	$0$	$1$	$-4$	$0$	$-$	$-$	$-$	$q+q^{3}-4q^{5}+q^{9}+6q^{11}+5q^{13}+\cdots$
9408.2.a.bt	$1$	$75.123$	$\Q$	None	$0$	$1$	$-3$	$0$	$-$	$-$	$+$	$q+q^{3}-3q^{5}+q^{9}-q^{11}+4q^{13}+\cdots$
9408.2.a.bu	$1$	$75.123$	$\Q$	None	$0$	$1$	$-3$	$0$	$-$	$-$	$+$	$q+q^{3}-3q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots$
9408.2.a.bv	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$+$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
9408.2.a.bw	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots$
9408.2.a.bx	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots$
9408.2.a.by	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$+$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots$
9408.2.a.bz	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$+$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}+q^{13}+\cdots$
9408.2.a.ca	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots$
9408.2.a.cb	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots$
9408.2.a.cc	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
9408.2.a.cd	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$+$	$-$	$+$	$q+q^{3}-2q^{5}+q^{9}+6q^{11}+3q^{13}+\cdots$
9408.2.a.ce	$1$	$75.123$	$\Q$	None	$0$	$1$	$-1$	$0$	$+$	$-$	$+$	$q+q^{3}-q^{5}+q^{9}-5q^{11}-q^{15}-4q^{17}+\cdots$
9408.2.a.cf	$1$	$75.123$	$\Q$	None	$0$	$1$	$-1$	$0$	$+$	$-$	$-$	$q+q^{3}-q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots$
9408.2.a.cg	$1$	$75.123$	$\Q$	None	$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$q+q^{3}-q^{5}+q^{9}-q^{11}-q^{15}-8q^{17}+\cdots$
9408.2.a.ch	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}-2q^{11}-2q^{13}-4q^{17}+\cdots$
9408.2.a.ci	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}-2q^{11}+q^{13}+2q^{17}+\cdots$
9408.2.a.cj	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{9}-2q^{11}+5q^{13}+2q^{17}+\cdots$
9408.2.a.ck	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{9}-4q^{13}+4q^{17}-4q^{19}+\cdots$
9408.2.a.cl	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}+4q^{13}-4q^{17}-4q^{19}+\cdots$
9408.2.a.cm	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$-$	$+$	$q+q^{3}+q^{9}+2q^{11}-5q^{13}-2q^{17}+\cdots$
9408.2.a.cn	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$+$	$q+q^{3}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots$
9408.2.a.co	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}+6q^{11}+2q^{13}-4q^{19}+\cdots$
9408.2.a.cp	$1$	$75.123$	$\Q$	None	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{9}+q^{11}+q^{15}+8q^{17}+\cdots$
9408.2.a.cq	$1$	$75.123$	$\Q$	None	$0$	$1$	$1$	$0$	$-$	$-$	$+$	$q+q^{3}+q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots$
9408.2.a.cr	$1$	$75.123$	$\Q$	None	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{9}+5q^{11}+q^{15}+4q^{17}+\cdots$
9408.2.a.cs	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}-6q^{11}-3q^{13}+\cdots$
9408.2.a.ct	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
9408.2.a.cu	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots$
9408.2.a.cv	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$-$	$-$	$+$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}-q^{13}+\cdots$
9408.2.a.cw	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots$
9408.2.a.cx	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$+$	$-$	$+$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}+3q^{13}+\cdots$
9408.2.a.cy	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots$
9408.2.a.cz	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots$
9408.2.a.da	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}+6q^{13}+2q^{15}+\cdots$
9408.2.a.db	$1$	$75.123$	$\Q$	None	$0$	$1$	$3$	$0$	$+$	$-$	$-$	$q+q^{3}+3q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots$
9408.2.a.dc	$1$	$75.123$	$\Q$	None	$0$	$1$	$3$	$0$	$-$	$-$	$-$	$q+q^{3}+3q^{5}+q^{9}+q^{11}-4q^{13}+\cdots$
9408.2.a.dd	$1$	$75.123$	$\Q$	None	$0$	$1$	$4$	$0$	$-$	$-$	$+$	$q+q^{3}+4q^{5}+q^{9}-6q^{11}-5q^{13}+\cdots$
9408.2.a.de	$1$	$75.123$	$\Q$	None	$0$	$1$	$4$	$0$	$-$	$-$	$-$	$q+q^{3}+4q^{5}+q^{9}-4q^{11}+4q^{13}+\cdots$
9408.2.a.df	$1$	$75.123$	$\Q$	None	$0$	$1$	$4$	$0$	$-$	$-$	$-$	$q+q^{3}+4q^{5}+q^{9}+2q^{11}-6q^{13}+\cdots$
9408.2.a.dg	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-4$	$0$	$+$	$+$	$+$	$q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots$
9408.2.a.dh	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-4$	$0$	$-$	$+$	$+$	$q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots$
9408.2.a.di	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-4$	$0$	$+$	$+$	$+$	$q-q^{3}+(-2+\beta )q^{5}+q^{9}+2q^{11}+\cdots$
9408.2.a.dj	$2$	$75.123$	$\Q(\sqrt{57}) $	None	$0$	$-2$	$-1$	$0$	$+$	$+$	$-$	$q-q^{3}-\beta q^{5}+q^{9}+\beta q^{11}+(3-\beta )q^{13}+\cdots$
9408.2.a.dk	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}-\beta q^{15}+\cdots$
9408.2.a.dl	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$0$	$-$	$+$	$+$	$q-q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}+\beta q^{13}+\cdots$
9408.2.a.dm	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}+\beta q^{11}-\beta q^{13}+\beta q^{17}+\cdots$
9408.2.a.dn	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$0$	$-$	$+$	$+$	$q-q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}-3\beta q^{13}+\cdots$
9408.2.a.do	$2$	$75.123$	$\Q(\sqrt{3}) $	None	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+\beta q^{5}+q^{9}+(2-\beta )q^{11}+2q^{13}+\cdots$
9408.2.a.dp	$2$	$75.123$	$\Q(\sqrt{57}) $	None	$0$	$-2$	$1$	$0$	$-$	$+$	$+$	$q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+(-3+\beta )q^{13}+\cdots$
9408.2.a.dq	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$4$	$0$	$-$	$+$	$+$	$q-q^{3}+(2+\beta )q^{5}+q^{9}-2q^{11}+(4+\cdots)q^{13}+\cdots$
9408.2.a.dr	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$4$	$0$	$+$	$+$	$+$	$q-q^{3}+(2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots$
9408.2.a.ds	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$4$	$0$	$-$	$+$	$+$	$q-q^{3}+(2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots$
9408.2.a.dt	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$-4$	$0$	$-$	$-$	$+$	$q+q^{3}+(-2+\beta )q^{5}+q^{9}-2q^{11}+\cdots$
9408.2.a.du	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$-4$	$0$	$-$	$-$	$+$	$q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots$
9408.2.a.dv	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$-4$	$0$	$+$	$-$	$+$	$q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots$
9408.2.a.dw	$2$	$75.123$	$\Q(\sqrt{57}) $	None	$0$	$2$	$-1$	$0$	$-$	$-$	$-$	$q+q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(3-\beta )q^{13}+\cdots$
9408.2.a.dx	$2$	$75.123$	$\Q(\sqrt{3}) $	None	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+\beta q^{5}+q^{9}+(-2+\beta )q^{11}+\cdots$
9408.2.a.dy	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$q+q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}-3\beta q^{13}+\cdots$
9408.2.a.dz	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{9}+\beta q^{11}+\beta q^{13}-\beta q^{17}+\cdots$
9408.2.a.ea	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$q+q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+\beta q^{13}+\cdots$
9408.2.a.eb	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots$
9408.2.a.ec	$2$	$75.123$	$\Q(\sqrt{57}) $	None	$0$	$2$	$1$	$0$	$+$	$-$	$+$	$q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+(-3+\beta )q^{13}+\cdots$
9408.2.a.ed	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$4$	$0$	$-$	$-$	$+$	$q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots$
9408.2.a.ee	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$4$	$0$	$+$	$-$	$+$	$q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots$
9408.2.a.ef	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$4$	$0$	$+$	$-$	$+$	$q+q^{3}+(2+\beta )q^{5}+q^{9}+2q^{11}+(4+\cdots)q^{13}+\cdots$
9408.2.a.eg	$3$	$75.123$	3.3.621.1	None	$0$	$-3$	$0$	$0$	$+$	$+$	$-$	$q-q^{3}+\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots$
9408.2.a.eh	$3$	$75.123$	3.3.621.1	None	$0$	$-3$	$0$	$0$	$+$	$+$	$+$	$q-q^{3}-\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots$
9408.2.a.ei	$3$	$75.123$	3.3.621.1	None	$0$	$3$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots$
9408.2.a.ej	$3$	$75.123$	3.3.621.1	None	$0$	$3$	$0$	$0$	$+$	$-$	$+$	$q+q^{3}-\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots$
9408.2.a.ek	$4$	$75.123$	4.4.2624.1	None	$0$	$-4$	$-4$	$0$	$+$	$+$	$+$	$q-q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots$
9408.2.a.el	$4$	$75.123$	4.4.2624.1	None	$0$	$-4$	$4$	$0$	$+$	$+$	$+$	$q-q^{3}+(1+\beta _{3})q^{5}+q^{9}+(1+\beta _{2})q^{11}+\cdots$
9408.2.a.em	$4$	$75.123$	4.4.2624.1	None	$0$	$4$	$-4$	$0$	$+$	$-$	$+$	$q+q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots$
9408.2.a.en	$4$	$75.123$	4.4.2624.1	None	$0$	$4$	$4$	$0$	$+$	$-$	$+$	$q+q^{3}+(1+\beta _{3})q^{5}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(9408))$ into lower level spaces

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	1
$3$	($ 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 $)($ 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 $)($ 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 $)($ 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 $)($ 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 $)($ 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 $)($ 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 )^{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} $)
$5$	($ 1 + 4 T + 5 T^{2} $)($ 1 + 4 T + 5 T^{2} $)($ 1 + 4 T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + T + 5 T^{2} $)($ 1 + T + 5 T^{2} $)($ 1 + T + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 3 T + 5 T^{2} $)($ 1 - 3 T + 5 T^{2} $)($ 1 - 4 T + 5 T^{2} $)($ 1 - 4 T + 5 T^{2} $)($ 1 - 4 T + 5 T^{2} $)($ 1 + 4 T + 5 T^{2} $)($ 1 + 4 T + 5 T^{2} $)($ 1 + 4 T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + T + 5 T^{2} $)($ 1 + T + 5 T^{2} $)($ 1 + T + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 3 T + 5 T^{2} $)($ 1 - 3 T + 5 T^{2} $)($ 1 - 4 T + 5 T^{2} $)($ 1 - 4 T + 5 T^{2} $)($ 1 - 4 T + 5 T^{2} $)($ 1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4} $)($ 1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4} $)($ 1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4} $)($ 1 + T - 4 T^{2} + 5 T^{3} + 25 T^{4} $)($ 1 + 2 T^{2} + 25 T^{4} $)($ 1 + 8 T^{2} + 25 T^{4} $)($ ( 1 + 5 T^{2} )^{2} $)($ 1 + 8 T^{2} + 25 T^{4} $)($ 1 - 2 T^{2} + 25 T^{4} $)($ 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} $)($ 1 - 4 T + 12 T^{2} - 20 T^{3} + 25 T^{4} $)($ 1 - 4 T + 12 T^{2} - 20 T^{3} + 25 T^{4} $)($ 1 - 4 T + 12 T^{2} - 20 T^{3} + 25 T^{4} $)($ 1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4} $)($ 1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4} $)($ 1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4} $)($ 1 + T - 4 T^{2} + 5 T^{3} + 25 T^{4} $)($ 1 - 2 T^{2} + 25 T^{4} $)($ 1 + 8 T^{2} + 25 T^{4} $)($ ( 1 + 5 T^{2} )^{2} $)($ 1 + 8 T^{2} + 25 T^{4} $)($ 1 + 2 T^{2} + 25 T^{4} $)($ 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} $)($ 1 - 4 T + 12 T^{2} - 20 T^{3} + 25 T^{4} $)($ 1 - 4 T + 12 T^{2} - 20 T^{3} + 25 T^{4} $)($ 1 - 4 T + 12 T^{2} - 20 T^{3} + 25 T^{4} $)($ 1 + 6 T^{2} + 4 T^{3} + 30 T^{4} + 125 T^{6} $)($ 1 + 6 T^{2} - 4 T^{3} + 30 T^{4} + 125 T^{6} $)($ 1 + 6 T^{2} + 4 T^{3} + 30 T^{4} + 125 T^{6} $)($ 1 + 6 T^{2} - 4 T^{3} + 30 T^{4} + 125 T^{6} $)($ 1 + 4 T + 12 T^{2} + 36 T^{3} + 98 T^{4} + 180 T^{5} + 300 T^{6} + 500 T^{7} + 625 T^{8} $)($ 1 - 4 T + 12 T^{2} - 36 T^{3} + 98 T^{4} - 180 T^{5} + 300 T^{6} - 500 T^{7} + 625 T^{8} $)($ 1 + 4 T + 12 T^{2} + 36 T^{3} + 98 T^{4} + 180 T^{5} + 300 T^{6} + 500 T^{7} + 625 T^{8} $)($ 1 - 4 T + 12 T^{2} - 36 T^{3} + 98 T^{4} - 180 T^{5} + 300 T^{6} - 500 T^{7} + 625 T^{8} $)
$7$	1
$11$	($ 1 + 6 T + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 - T + 11 T^{2} $)($ 1 + 6 T + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 5 T + 11 T^{2} $)($ 1 + 6 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 + T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 + T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 - T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 5 T + 11 T^{2} $)($ 1 + 6 T + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 - T + 11 T^{2} $)($ 1 + 6 T + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 + 4 T + 18 T^{2} + 44 T^{3} + 121 T^{4} $)($ 1 + 4 T + 18 T^{2} + 44 T^{3} + 121 T^{4} $)($ ( 1 - 2 T + 11 T^{2} )^{2} $)($ 1 - T + 8 T^{2} - 11 T^{3} + 121 T^{4} $)($ 1 + 14 T^{2} + 121 T^{4} $)($ 1 + 14 T^{2} + 121 T^{4} $)($ 1 - 10 T^{2} + 121 T^{4} $)($ 1 + 14 T^{2} + 121 T^{4} $)($ 1 - 4 T + 14 T^{2} - 44 T^{3} + 121 T^{4} $)($ 1 + T + 8 T^{2} + 11 T^{3} + 121 T^{4} $)($ ( 1 + 2 T + 11 T^{2} )^{2} $)($ 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} $)($ 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} $)($ ( 1 + 2 T + 11 T^{2} )^{2} $)($ 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} $)($ 1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4} $)($ 1 + T + 8 T^{2} + 11 T^{3} + 121 T^{4} $)($ 1 + 4 T + 14 T^{2} + 44 T^{3} + 121 T^{4} $)($ 1 + 14 T^{2} + 121 T^{4} $)($ 1 - 10 T^{2} + 121 T^{4} $)($ 1 + 14 T^{2} + 121 T^{4} $)($ 1 + 14 T^{2} + 121 T^{4} $)($ 1 - T + 8 T^{2} - 11 T^{3} + 121 T^{4} $)($ 1 + 4 T + 18 T^{2} + 44 T^{3} + 121 T^{4} $)($ 1 + 4 T + 18 T^{2} + 44 T^{3} + 121 T^{4} $)($ ( 1 - 2 T + 11 T^{2} )^{2} $)($ 1 + 6 T^{2} + 38 T^{3} + 66 T^{4} + 1331 T^{6} $)($ 1 + 6 T^{2} - 38 T^{3} + 66 T^{4} + 1331 T^{6} $)($ 1 + 6 T^{2} - 38 T^{3} + 66 T^{4} + 1331 T^{6} $)($ 1 + 6 T^{2} + 38 T^{3} + 66 T^{4} + 1331 T^{6} $)($ 1 + 4 T + 24 T^{2} + 84 T^{3} + 302 T^{4} + 924 T^{5} + 2904 T^{6} + 5324 T^{7} + 14641 T^{8} $)($ 1 - 4 T + 24 T^{2} - 84 T^{3} + 302 T^{4} - 924 T^{5} + 2904 T^{6} - 5324 T^{7} + 14641 T^{8} $)($ 1 - 4 T + 24 T^{2} - 84 T^{3} + 302 T^{4} - 924 T^{5} + 2904 T^{6} - 5324 T^{7} + 14641 T^{8} $)($ 1 + 4 T + 24 T^{2} + 84 T^{3} + 302 T^{4} + 924 T^{5} + 2904 T^{6} + 5324 T^{7} + 14641 T^{8} $)
$13$	($ 1 - 5 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 - 3 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 + 3 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - 6 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 - 6 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - 3 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 + 3 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - 6 T + 13 T^{2} $)($ 1 + 3 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - 3 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 + 3 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - 3 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 - 6 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 + 24 T^{2} + 169 T^{4} $)($ 1 + 8 T^{2} + 169 T^{4} $)($ 1 + 8 T + 40 T^{2} + 104 T^{3} + 169 T^{4} $)($ 1 - 5 T + 18 T^{2} - 65 T^{3} + 169 T^{4} $)($ ( 1 + 13 T^{2} )^{2} $)($ 1 + 24 T^{2} + 169 T^{4} $)($ 1 - 6 T^{2} + 169 T^{4} $)($ 1 + 8 T^{2} + 169 T^{4} $)($ ( 1 - 2 T + 13 T^{2} )^{2} $)($ 1 + 5 T + 18 T^{2} + 65 T^{3} + 169 T^{4} $)($ 1 - 8 T + 40 T^{2} - 104 T^{3} + 169 T^{4} $)($ 1 + 8 T^{2} + 169 T^{4} $)($ 1 + 24 T^{2} + 169 T^{4} $)($ 1 + 8 T + 40 T^{2} + 104 T^{3} + 169 T^{4} $)($ 1 + 24 T^{2} + 169 T^{4} $)($ 1 + 8 T^{2} + 169 T^{4} $)($ 1 - 5 T + 18 T^{2} - 65 T^{3} + 169 T^{4} $)($ ( 1 - 2 T + 13 T^{2} )^{2} $)($ 1 + 8 T^{2} + 169 T^{4} $)($ 1 - 6 T^{2} + 169 T^{4} $)($ 1 + 24 T^{2} + 169 T^{4} $)($ ( 1 + 13 T^{2} )^{2} $)($ 1 + 5 T + 18 T^{2} + 65 T^{3} + 169 T^{4} $)($ 1 + 8 T^{2} + 169 T^{4} $)($ 1 + 24 T^{2} + 169 T^{4} $)($ 1 - 8 T + 40 T^{2} - 104 T^{3} + 169 T^{4} $)($ 1 + 3 T + 3 T^{2} - 34 T^{3} + 39 T^{4} + 507 T^{5} + 2197 T^{6} $)($ 1 - 3 T + 3 T^{2} + 34 T^{3} + 39 T^{4} - 507 T^{5} + 2197 T^{6} $)($ 1 + 3 T + 3 T^{2} - 34 T^{3} + 39 T^{4} + 507 T^{5} + 2197 T^{6} $)($ 1 - 3 T + 3 T^{2} + 34 T^{3} + 39 T^{4} - 507 T^{5} + 2197 T^{6} $)($ 1 + 8 T + 48 T^{2} + 232 T^{3} + 978 T^{4} + 3016 T^{5} + 8112 T^{6} + 17576 T^{7} + 28561 T^{8} $)($ 1 - 8 T + 48 T^{2} - 232 T^{3} + 978 T^{4} - 3016 T^{5} + 8112 T^{6} - 17576 T^{7} + 28561 T^{8} $)($ 1 + 8 T + 48 T^{2} + 232 T^{3} + 978 T^{4} + 3016 T^{5} + 8112 T^{6} + 17576 T^{7} + 28561 T^{8} $)($ 1 - 8 T + 48 T^{2} - 232 T^{3} + 978 T^{4} - 3016 T^{5} + 8112 T^{6} - 17576 T^{7} + 28561 T^{8} $)
$17$	($ 1 + 2 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 + 8 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 + 8 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 8 T + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 - 8 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 + 8 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 8 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 8 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 - 8 T + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 4 T + 20 T^{2} + 68 T^{3} + 289 T^{4} $)($ 1 - 12 T + 68 T^{2} - 204 T^{3} + 289 T^{4} $)($ 1 - 4 T + 20 T^{2} - 68 T^{3} + 289 T^{4} $)($ ( 1 - 4 T + 17 T^{2} )^{2} $)($ 1 + 26 T^{2} + 289 T^{4} $)($ 1 + 32 T^{2} + 289 T^{4} $)($ 1 + 2 T^{2} + 289 T^{4} $)($ 1 + 16 T^{2} + 289 T^{4} $)($ 1 + 8 T + 38 T^{2} + 136 T^{3} + 289 T^{4} $)($ ( 1 + 4 T + 17 T^{2} )^{2} $)($ 1 + 4 T + 20 T^{2} + 68 T^{3} + 289 T^{4} $)($ 1 + 12 T + 68 T^{2} + 204 T^{3} + 289 T^{4} $)($ 1 - 4 T + 20 T^{2} - 68 T^{3} + 289 T^{4} $)($ 1 - 4 T + 20 T^{2} - 68 T^{3} + 289 T^{4} $)($ 1 + 4 T + 20 T^{2} + 68 T^{3} + 289 T^{4} $)($ 1 - 12 T + 68 T^{2} - 204 T^{3} + 289 T^{4} $)($ ( 1 - 4 T + 17 T^{2} )^{2} $)($ 1 + 8 T + 38 T^{2} + 136 T^{3} + 289 T^{4} $)($ 1 + 16 T^{2} + 289 T^{4} $)($ 1 + 2 T^{2} + 289 T^{4} $)($ 1 + 32 T^{2} + 289 T^{4} $)($ 1 + 26 T^{2} + 289 T^{4} $)($ ( 1 + 4 T + 17 T^{2} )^{2} $)($ 1 + 12 T + 68 T^{2} + 204 T^{3} + 289 T^{4} $)($ 1 - 4 T + 20 T^{2} - 68 T^{3} + 289 T^{4} $)($ 1 + 4 T + 20 T^{2} + 68 T^{3} + 289 T^{4} $)($ 1 + 6 T + 27 T^{2} + 108 T^{3} + 459 T^{4} + 1734 T^{5} + 4913 T^{6} $)($ 1 - 6 T + 27 T^{2} - 108 T^{3} + 459 T^{4} - 1734 T^{5} + 4913 T^{6} $)($ 1 + 6 T + 27 T^{2} + 108 T^{3} + 459 T^{4} + 1734 T^{5} + 4913 T^{6} $)($ 1 - 6 T + 27 T^{2} - 108 T^{3} + 459 T^{4} - 1734 T^{5} + 4913 T^{6} $)($ 1 - 4 T + 44 T^{2} - 84 T^{3} + 818 T^{4} - 1428 T^{5} + 12716 T^{6} - 19652 T^{7} + 83521 T^{8} $)($ 1 + 4 T + 44 T^{2} + 84 T^{3} + 818 T^{4} + 1428 T^{5} + 12716 T^{6} + 19652 T^{7} + 83521 T^{8} $)($ 1 - 4 T + 44 T^{2} - 84 T^{3} + 818 T^{4} - 1428 T^{5} + 12716 T^{6} - 19652 T^{7} + 83521 T^{8} $)($ 1 + 4 T + 44 T^{2} + 84 T^{3} + 818 T^{4} + 1428 T^{5} + 12716 T^{6} + 19652 T^{7} + 83521 T^{8} $)
$19$	($ 1 - T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 + 5 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 8 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 4 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} $)($ 1 + 3 T + 19 T^{2} $)($ 1 - 5 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 5 T + 19 T^{2} $)($ 1 + 3 T + 19 T^{2} $)($ 1 - 8 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 8 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 5 T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 - T + 19 T^{2} $)($ 1 - 8 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - 5 T + 19 T^{2} $)($ 1 + 8 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 5 T + 19 T^{2} $)($ 1 - 3 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 3 T + 19 T^{2} $)($ 1 + 5 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 8 T + 19 T^{2} $)($ 1 - 5 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 8 T + 19 T^{2} $)($ 1 - T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 - T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 8 T + 46 T^{2} + 152 T^{3} + 361 T^{4} $)($ 1 - 8 T + 46 T^{2} - 152 T^{3} + 361 T^{4} $)($ 1 + 30 T^{2} + 361 T^{4} $)($ 1 + 5 T + 30 T^{2} + 95 T^{3} + 361 T^{4} $)($ ( 1 + 4 T + 19 T^{2} )^{2} $)($ ( 1 + 19 T^{2} )^{2} $)($ ( 1 - 4 T + 19 T^{2} )^{2} $)($ ( 1 - 8 T + 19 T^{2} )^{2} $)($ 1 - 10 T^{2} + 361 T^{4} $)($ 1 + 5 T + 30 T^{2} + 95 T^{3} + 361 T^{4} $)($ 1 + 30 T^{2} + 361 T^{4} $)($ 1 - 8 T + 46 T^{2} - 152 T^{3} + 361 T^{4} $)($ 1 + 8 T + 46 T^{2} + 152 T^{3} + 361 T^{4} $)($ 1 + 30 T^{2} + 361 T^{4} $)($ 1 - 8 T + 46 T^{2} - 152 T^{3} + 361 T^{4} $)($ 1 + 8 T + 46 T^{2} + 152 T^{3} + 361 T^{4} $)($ 1 - 5 T + 30 T^{2} - 95 T^{3} + 361 T^{4} $)($ 1 - 10 T^{2} + 361 T^{4} $)($ ( 1 + 8 T + 19 T^{2} )^{2} $)($ ( 1 + 4 T + 19 T^{2} )^{2} $)($ ( 1 + 19 T^{2} )^{2} $)($ ( 1 - 4 T + 19 T^{2} )^{2} $)($ 1 - 5 T + 30 T^{2} - 95 T^{3} + 361 T^{4} $)($ 1 + 8 T + 46 T^{2} + 152 T^{3} + 361 T^{4} $)($ 1 - 8 T + 46 T^{2} - 152 T^{3} + 361 T^{4} $)($ 1 + 30 T^{2} + 361 T^{4} $)($ 1 + 3 T + 21 T^{2} + 2 T^{3} + 399 T^{4} + 1083 T^{5} + 6859 T^{6} $)($ 1 + 3 T + 21 T^{2} + 2 T^{3} + 399 T^{4} + 1083 T^{5} + 6859 T^{6} $)($ 1 - 3 T + 21 T^{2} - 2 T^{3} + 399 T^{4} - 1083 T^{5} + 6859 T^{6} $)($ 1 - 3 T + 21 T^{2} - 2 T^{3} + 399 T^{4} - 1083 T^{5} + 6859 T^{6} $)($ 1 + 8 T + 68 T^{2} + 392 T^{3} + 1926 T^{4} + 7448 T^{5} + 24548 T^{6} + 54872 T^{7} + 130321 T^{8} $)($ 1 + 8 T + 68 T^{2} + 392 T^{3} + 1926 T^{4} + 7448 T^{5} + 24548 T^{6} + 54872 T^{7} + 130321 T^{8} $)($ 1 - 8 T + 68 T^{2} - 392 T^{3} + 1926 T^{4} - 7448 T^{5} + 24548 T^{6} - 54872 T^{7} + 130321 T^{8} $)($ 1 - 8 T + 68 T^{2} - 392 T^{3} + 1926 T^{4} - 7448 T^{5} + 24548 T^{6} - 54872 T^{7} + 130321 T^{8} $)
$23$	($ 1 + 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 8 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 - 8 T + 23 T^{2} $)($ 1 + 2 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 8 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 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 + 6 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 2 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 - 8 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 2 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 2 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 - 2 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 - 8 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 - 8 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 - 2 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 + 2 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 2 T + 23 T^{2} $)($ 1 - 8 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 8 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 2 T + 23 T^{2} $)($ 1 - 4 T + 42 T^{2} - 92 T^{3} + 529 T^{4} $)($ 1 - 4 T + 42 T^{2} - 92 T^{3} + 529 T^{4} $)($ 1 + 4 T + 18 T^{2} + 92 T^{3} + 529 T^{4} $)($ ( 1 - 4 T + 23 T^{2} )^{2} $)($ 1 - 26 T^{2} + 529 T^{4} $)($ 1 + 38 T^{2} + 529 T^{4} $)($ 1 + 14 T^{2} + 529 T^{4} $)($ 1 + 38 T^{2} + 529 T^{4} $)($ 1 + 4 T + 38 T^{2} + 92 T^{3} + 529 T^{4} $)($ ( 1 + 4 T + 23 T^{2} )^{2} $)($ 1 - 4 T + 18 T^{2} - 92 T^{3} + 529 T^{4} $)($ 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} $)($ 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} $)($ 1 - 4 T + 18 T^{2} - 92 T^{3} + 529 T^{4} $)($ 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} $)($ 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} $)($ ( 1 + 4 T + 23 T^{2} )^{2} $)($ 1 - 4 T + 38 T^{2} - 92 T^{3} + 529 T^{4} $)($ 1 + 38 T^{2} + 529 T^{4} $)($ 1 + 14 T^{2} + 529 T^{4} $)($ 1 + 38 T^{2} + 529 T^{4} $)($ 1 - 26 T^{2} + 529 T^{4} $)($ ( 1 - 4 T + 23 T^{2} )^{2} $)($ 1 - 4 T + 42 T^{2} - 92 T^{3} + 529 T^{4} $)($ 1 - 4 T + 42 T^{2} - 92 T^{3} + 529 T^{4} $)($ 1 + 4 T + 18 T^{2} + 92 T^{3} + 529 T^{4} $)($ 1 - 6 T + 45 T^{2} - 180 T^{3} + 1035 T^{4} - 3174 T^{5} + 12167 T^{6} $)($ 1 + 6 T + 45 T^{2} + 180 T^{3} + 1035 T^{4} + 3174 T^{5} + 12167 T^{6} $)($ 1 + 6 T + 45 T^{2} + 180 T^{3} + 1035 T^{4} + 3174 T^{5} + 12167 T^{6} $)($ 1 - 6 T + 45 T^{2} - 180 T^{3} + 1035 T^{4} - 3174 T^{5} + 12167 T^{6} $)($ 1 - 12 T + 120 T^{2} - 780 T^{3} + 4350 T^{4} - 17940 T^{5} + 63480 T^{6} - 146004 T^{7} + 279841 T^{8} $)($ 1 + 12 T + 120 T^{2} + 780 T^{3} + 4350 T^{4} + 17940 T^{5} + 63480 T^{6} + 146004 T^{7} + 279841 T^{8} $)($ 1 + 12 T + 120 T^{2} + 780 T^{3} + 4350 T^{4} + 17940 T^{5} + 63480 T^{6} + 146004 T^{7} + 279841 T^{8} $)($ 1 - 12 T + 120 T^{2} - 780 T^{3} + 4350 T^{4} - 17940 T^{5} + 63480 T^{6} - 146004 T^{7} + 279841 T^{8} $)
$29$	($ 1 + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 - 7 T + 29 T^{2} $)($ 1 - 4 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 8 T + 29 T^{2} $)($ 1 - 8 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 - 8 T + 29 T^{2} $)($ 1 + 8 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 - 4 T + 29 T^{2} $)($ 1 - 7 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 + 29 T^{2} $)($ 1 - 7 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 4 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 - 8 T + 29 T^{2} $)($ 1 + 8 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 + 8 T + 29 T^{2} $)($ 1 - 8 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 - 4 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 - 7 T + 29 T^{2} $)($ 1 + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 - 14 T^{2} + 841 T^{4} $)($ 1 + 50 T^{2} + 841 T^{4} $)($ 1 - 8 T + 66 T^{2} - 232 T^{3} + 841 T^{4} $)($ 1 + 3 T + 46 T^{2} + 87 T^{3} + 841 T^{4} $)($ ( 1 + 2 T + 29 T^{2} )^{2} $)($ ( 1 + 29 T^{2} )^{2} $)($ ( 1 - 6 T + 29 T^{2} )^{2} $)($ ( 1 + 29 T^{2} )^{2} $)($ 1 + 4 T + 14 T^{2} + 116 T^{3} + 841 T^{4} $)($ 1 + 3 T + 46 T^{2} + 87 T^{3} + 841 T^{4} $)($ 1 - 8 T + 66 T^{2} - 232 T^{3} + 841 T^{4} $)($ 1 + 50 T^{2} + 841 T^{4} $)($ 1 - 14 T^{2} + 841 T^{4} $)($ 1 - 8 T + 66 T^{2} - 232 T^{3} + 841 T^{4} $)($ 1 - 14 T^{2} + 841 T^{4} $)($ 1 + 50 T^{2} + 841 T^{4} $)($ 1 + 3 T + 46 T^{2} + 87 T^{3} + 841 T^{4} $)($ 1 + 4 T + 14 T^{2} + 116 T^{3} + 841 T^{4} $)($ ( 1 + 29 T^{2} )^{2} $)($ ( 1 - 6 T + 29 T^{2} )^{2} $)($ ( 1 + 29 T^{2} )^{2} $)($ ( 1 + 2 T + 29 T^{2} )^{2} $)($ 1 + 3 T + 46 T^{2} + 87 T^{3} + 841 T^{4} $)($ 1 + 50 T^{2} + 841 T^{4} $)($ 1 - 14 T^{2} + 841 T^{4} $)($ 1 - 8 T + 66 T^{2} - 232 T^{3} + 841 T^{4} $)($ 1 + 12 T + 126 T^{2} + 728 T^{3} + 3654 T^{4} + 10092 T^{5} + 24389 T^{6} $)($ 1 + 12 T + 126 T^{2} + 728 T^{3} + 3654 T^{4} + 10092 T^{5} + 24389 T^{6} $)($ 1 + 12 T + 126 T^{2} + 728 T^{3} + 3654 T^{4} + 10092 T^{5} + 24389 T^{6} $)($ 1 + 12 T + 126 T^{2} + 728 T^{3} + 3654 T^{4} + 10092 T^{5} + 24389 T^{6} $)($ 1 + 60 T^{2} - 128 T^{3} + 1862 T^{4} - 3712 T^{5} + 50460 T^{6} + 707281 T^{8} $)($ 1 + 60 T^{2} - 128 T^{3} + 1862 T^{4} - 3712 T^{5} + 50460 T^{6} + 707281 T^{8} $)($ 1 + 60 T^{2} - 128 T^{3} + 1862 T^{4} - 3712 T^{5} + 50460 T^{6} + 707281 T^{8} $)($ 1 + 60 T^{2} - 128 T^{3} + 1862 T^{4} - 3712 T^{5} + 50460 T^{6} + 707281 T^{8} $)
$31$	($ 1 - 3 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 + T + 31 T^{2} $)($ 1 - 11 T + 31 T^{2} $)($ 1 + 7 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 + 3 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ 1 - 9 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 + 7 T + 31 T^{2} $)($ 1 + 5 T + 31 T^{2} $)($ 1 + 3 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 + T + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 + T + 31 T^{2} $)($ 1 + 3 T + 31 T^{2} $)($ 1 + 5 T + 31 T^{2} $)($ 1 + 7 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ 1 - 9 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ 1 + 3 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ 1 + 7 T + 31 T^{2} $)($ 1 - 11 T + 31 T^{2} $)($ 1 + T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 + 3 T + 31 T^{2} $)($ 1 + 11 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 9 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 + 3 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 + 3 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 9 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 + 11 T + 31 T^{2} $)($ 1 + 3 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 - 16 T + 118 T^{2} - 496 T^{3} + 961 T^{4} $)($ 1 + 54 T^{2} + 961 T^{4} $)($ 1 + 8 T + 70 T^{2} + 248 T^{3} + 961 T^{4} $)($ ( 1 - T + 31 T^{2} )^{2} $)($ ( 1 + 31 T^{2} )^{2} $)($ ( 1 - 4 T + 31 T^{2} )^{2} $)($ ( 1 + 8 T + 31 T^{2} )^{2} $)($ ( 1 + 4 T + 31 T^{2} )^{2} $)($ 1 + 8 T + 30 T^{2} + 248 T^{3} + 961 T^{4} $)($ ( 1 - T + 31 T^{2} )^{2} $)($ 1 + 8 T + 70 T^{2} + 248 T^{3} + 961 T^{4} $)($ 1 + 54 T^{2} + 961 T^{4} $)($ 1 - 16 T + 118 T^{2} - 496 T^{3} + 961 T^{4} $)($ 1 - 8 T + 70 T^{2} - 248 T^{3} + 961 T^{4} $)($ 1 + 16 T + 118 T^{2} + 496 T^{3} + 961 T^{4} $)($ 1 + 54 T^{2} + 961 T^{4} $)($ ( 1 + T + 31 T^{2} )^{2} $)($ 1 - 8 T + 30 T^{2} - 248 T^{3} + 961 T^{4} $)($ ( 1 - 4 T + 31 T^{2} )^{2} $)($ ( 1 - 8 T + 31 T^{2} )^{2} $)($ ( 1 + 4 T + 31 T^{2} )^{2} $)($ ( 1 + 31 T^{2} )^{2} $)($ ( 1 + T + 31 T^{2} )^{2} $)($ 1 + 54 T^{2} + 961 T^{4} $)($ 1 + 16 T + 118 T^{2} + 496 T^{3} + 961 T^{4} $)($ 1 - 8 T + 70 T^{2} - 248 T^{3} + 961 T^{4} $)($ 1 - 3 T + 72 T^{2} - 139 T^{3} + 2232 T^{4} - 2883 T^{5} + 29791 T^{6} $)($ 1 - 3 T + 72 T^{2} - 139 T^{3} + 2232 T^{4} - 2883 T^{5} + 29791 T^{6} $)($ 1 + 3 T + 72 T^{2} + 139 T^{3} + 2232 T^{4} + 2883 T^{5} + 29791 T^{6} $)($ 1 + 3 T + 72 T^{2} + 139 T^{3} + 2232 T^{4} + 2883 T^{5} + 29791 T^{6} $)($ 1 + 8 T + 84 T^{2} + 616 T^{3} + 3222 T^{4} + 19096 T^{5} + 80724 T^{6} + 238328 T^{7} + 923521 T^{8} $)($ 1 + 8 T + 84 T^{2} + 616 T^{3} + 3222 T^{4} + 19096 T^{5} + 80724 T^{6} + 238328 T^{7} + 923521 T^{8} $)($ 1 - 8 T + 84 T^{2} - 616 T^{3} + 3222 T^{4} - 19096 T^{5} + 80724 T^{6} - 238328 T^{7} + 923521 T^{8} $)($ 1 - 8 T + 84 T^{2} - 616 T^{3} + 3222 T^{4} - 19096 T^{5} + 80724 T^{6} - 238328 T^{7} + 923521 T^{8} $)
$37$	($ 1 + 3 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 + 10 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 - 9 T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + 3 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 5 T + 37 T^{2} $)($ 1 - 9 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 - 9 T + 37 T^{2} $)($ 1 - 5 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + 3 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 - 9 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 + 3 T + 37 T^{2} $)($ 1 + 10 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 + 3 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + 3 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 - 9 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 - 9 T + 37 T^{2} $)($ 1 - 5 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 - 5 T + 37 T^{2} $)($ 1 - 9 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 - 9 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + 3 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 + 3 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 8 T + 58 T^{2} - 296 T^{3} + 1369 T^{4} $)($ 1 + 8 T + 58 T^{2} + 296 T^{3} + 1369 T^{4} $)($ ( 1 - 4 T + 37 T^{2} )^{2} $)($ 1 + 3 T + 62 T^{2} + 111 T^{3} + 1369 T^{4} $)($ ( 1 - 6 T + 37 T^{2} )^{2} $)($ ( 1 + 4 T + 37 T^{2} )^{2} $)($ ( 1 + 2 T + 37 T^{2} )^{2} $)($ ( 1 - 4 T + 37 T^{2} )^{2} $)($ ( 1 - 2 T + 37 T^{2} )^{2} $)($ 1 + 3 T + 62 T^{2} + 111 T^{3} + 1369 T^{4} $)($ ( 1 - 4 T + 37 T^{2} )^{2} $)($ 1 + 8 T + 58 T^{2} + 296 T^{3} + 1369 T^{4} $)($ 1 - 8 T + 58 T^{2} - 296 T^{3} + 1369 T^{4} $)($ ( 1 - 4 T + 37 T^{2} )^{2} $)($ 1 - 8 T + 58 T^{2} - 296 T^{3} + 1369 T^{4} $)($ 1 + 8 T + 58 T^{2} + 296 T^{3} + 1369 T^{4} $)($ 1 + 3 T + 62 T^{2} + 111 T^{3} + 1369 T^{4} $)($ ( 1 - 2 T + 37 T^{2} )^{2} $)($ ( 1 - 4 T + 37 T^{2} )^{2} $)($ ( 1 + 2 T + 37 T^{2} )^{2} $)($ ( 1 + 4 T + 37 T^{2} )^{2} $)($ ( 1 - 6 T + 37 T^{2} )^{2} $)($ 1 + 3 T + 62 T^{2} + 111 T^{3} + 1369 T^{4} $)($ 1 + 8 T + 58 T^{2} + 296 T^{3} + 1369 T^{4} $)($ 1 - 8 T + 58 T^{2} - 296 T^{3} + 1369 T^{4} $)($ ( 1 - 4 T + 37 T^{2} )^{2} $)($ 1 + 3 T + 27 T^{2} - 146 T^{3} + 999 T^{4} + 4107 T^{5} + 50653 T^{6} $)($ 1 + 3 T + 27 T^{2} - 146 T^{3} + 999 T^{4} + 4107 T^{5} + 50653 T^{6} $)($ 1 + 3 T + 27 T^{2} - 146 T^{3} + 999 T^{4} + 4107 T^{5} + 50653 T^{6} $)($ 1 + 3 T + 27 T^{2} - 146 T^{3} + 999 T^{4} + 4107 T^{5} + 50653 T^{6} $)($ ( 1 + 42 T^{2} + 1369 T^{4} )^{2} $)($ ( 1 + 42 T^{2} + 1369 T^{4} )^{2} $)($ ( 1 + 42 T^{2} + 1369 T^{4} )^{2} $)($ ( 1 + 42 T^{2} + 1369 T^{4} )^{2} $)
$41$	($ 1 - 6 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 - 4 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 4 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 10 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 - 4 T + 41 T^{2} $)($ 1 + 8 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 12 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 12 T + 41 T^{2} $)($ 1 + 12 T + 41 T^{2} $)($ 1 + 8 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 - 8 T + 41 T^{2} $)($ 1 + 4 T + 41 T^{2} $)($ 1 - 10 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 10 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 4 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 - 4 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 4 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 10 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 8 T + 41 T^{2} $)($ 1 - 4 T + 41 T^{2} $)($ 1 + 8 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 12 T + 41 T^{2} $)($ 1 + 12 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 + 12 T + 41 T^{2} $)($ 1 + 4 T + 41 T^{2} $)($ 1 - 8 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 10 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 - 10 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 - 4 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 4 T + 84 T^{2} + 164 T^{3} + 1681 T^{4} $)($ 1 - 12 T + 100 T^{2} - 492 T^{3} + 1681 T^{4} $)($ 1 - 4 T + 68 T^{2} - 164 T^{3} + 1681 T^{4} $)($ 1 + 6 T + 34 T^{2} + 246 T^{3} + 1681 T^{4} $)($ 1 + 10 T^{2} + 1681 T^{4} $)($ 1 + 80 T^{2} + 1681 T^{4} $)($ 1 + 50 T^{2} + 1681 T^{4} $)($ 1 + 32 T^{2} + 1681 T^{4} $)($ 1 + 16 T + 134 T^{2} + 656 T^{3} + 1681 T^{4} $)($ 1 - 6 T + 34 T^{2} - 246 T^{3} + 1681 T^{4} $)($ 1 + 4 T + 68 T^{2} + 164 T^{3} + 1681 T^{4} $)($ 1 + 12 T + 100 T^{2} + 492 T^{3} + 1681 T^{4} $)($ 1 - 4 T + 84 T^{2} - 164 T^{3} + 1681 T^{4} $)($ 1 - 4 T + 68 T^{2} - 164 T^{3} + 1681 T^{4} $)($ 1 + 4 T + 84 T^{2} + 164 T^{3} + 1681 T^{4} $)($ 1 - 12 T + 100 T^{2} - 492 T^{3} + 1681 T^{4} $)($ 1 + 6 T + 34 T^{2} + 246 T^{3} + 1681 T^{4} $)($ 1 + 16 T + 134 T^{2} + 656 T^{3} + 1681 T^{4} $)($ 1 + 32 T^{2} + 1681 T^{4} $)($ 1 + 50 T^{2} + 1681 T^{4} $)($ 1 + 80 T^{2} + 1681 T^{4} $)($ 1 + 10 T^{2} + 1681 T^{4} $)($ 1 - 6 T + 34 T^{2} - 246 T^{3} + 1681 T^{4} $)($ 1 + 12 T + 100 T^{2} + 492 T^{3} + 1681 T^{4} $)($ 1 - 4 T + 84 T^{2} - 164 T^{3} + 1681 T^{4} $)($ 1 + 4 T + 68 T^{2} + 164 T^{3} + 1681 T^{4} $)($ 1 - 6 T + 27 T^{2} + 20 T^{3} + 1107 T^{4} - 10086 T^{5} + 68921 T^{6} $)($ 1 + 6 T + 27 T^{2} - 20 T^{3} + 1107 T^{4} + 10086 T^{5} + 68921 T^{6} $)($ 1 - 6 T + 27 T^{2} + 20 T^{3} + 1107 T^{4} - 10086 T^{5} + 68921 T^{6} $)($ 1 + 6 T + 27 T^{2} - 20 T^{3} + 1107 T^{4} + 10086 T^{5} + 68921 T^{6} $)($ 1 - 20 T + 220 T^{2} - 1540 T^{3} + 9874 T^{4} - 63140 T^{5} + 369820 T^{6} - 1378420 T^{7} + 2825761 T^{8} $)($ 1 + 20 T + 220 T^{2} + 1540 T^{3} + 9874 T^{4} + 63140 T^{5} + 369820 T^{6} + 1378420 T^{7} + 2825761 T^{8} $)($ 1 - 20 T + 220 T^{2} - 1540 T^{3} + 9874 T^{4} - 63140 T^{5} + 369820 T^{6} - 1378420 T^{7} + 2825761 T^{8} $)($ 1 + 20 T + 220 T^{2} + 1540 T^{3} + 9874 T^{4} + 63140 T^{5} + 369820 T^{6} + 1378420 T^{7} + 2825761 T^{8} $)
$43$	($ 1 + 5 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 - 8 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + 11 T + 43 T^{2} $)($ 1 + 43 T^{2} $)($ 1 - 5 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 - 6 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + 7 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 - 8 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 - 7 T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 + 6 T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 - 12 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 5 T + 43 T^{2} $)($ 1 + 43 T^{2} $)($ 1 - 11 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 5 T + 43 T^{2} $)($ 1 - 8 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 5 T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 11 T + 43 T^{2} $)($ 1 + 43 T^{2} $)($ 1 + 5 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 + 6 T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 + 7 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 7 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 - 6 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 5 T + 43 T^{2} $)($ 1 + 43 T^{2} $)($ 1 + 11 T + 43 T^{2} $)($ 1 + 12 T + 43 T^{2} $)($ 1 - 8 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 + 5 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ ( 1 - 8 T + 43 T^{2} )^{2} $)($ 1 - 42 T^{2} + 1849 T^{4} $)($ 1 + 54 T^{2} + 1849 T^{4} $)($ 1 - 7 T + 84 T^{2} - 301 T^{3} + 1849 T^{4} $)($ 1 - 42 T^{2} + 1849 T^{4} $)($ 1 + 54 T^{2} + 1849 T^{4} $)($ ( 1 + 43 T^{2} )^{2} $)($ 1 + 54 T^{2} + 1849 T^{4} $)($ ( 1 + 8 T + 43 T^{2} )^{2} $)($ 1 + 7 T + 84 T^{2} + 301 T^{3} + 1849 T^{4} $)($ 1 + 54 T^{2} + 1849 T^{4} $)($ 1 - 42 T^{2} + 1849 T^{4} $)($ ( 1 + 8 T + 43 T^{2} )^{2} $)($ 1 + 54 T^{2} + 1849 T^{4} $)($ ( 1 + 8 T + 43 T^{2} )^{2} $)($ 1 - 42 T^{2} + 1849 T^{4} $)($ 1 + 7 T + 84 T^{2} + 301 T^{3} + 1849 T^{4} $)($ ( 1 - 8 T + 43 T^{2} )^{2} $)($ 1 + 54 T^{2} + 1849 T^{4} $)($ ( 1 + 43 T^{2} )^{2} $)($ 1 + 54 T^{2} + 1849 T^{4} $)($ 1 - 42 T^{2} + 1849 T^{4} $)($ 1 - 7 T + 84 T^{2} - 301 T^{3} + 1849 T^{4} $)($ 1 - 42 T^{2} + 1849 T^{4} $)($ ( 1 - 8 T + 43 T^{2} )^{2} $)($ 1 + 54 T^{2} + 1849 T^{4} $)($ 1 - 15 T + 177 T^{2} - 1318 T^{3} + 7611 T^{4} - 27735 T^{5} + 79507 T^{6} $)($ 1 + 15 T + 177 T^{2} + 1318 T^{3} + 7611 T^{4} + 27735 T^{5} + 79507 T^{6} $)($ 1 + 15 T + 177 T^{2} + 1318 T^{3} + 7611 T^{4} + 27735 T^{5} + 79507 T^{6} $)($ 1 - 15 T + 177 T^{2} - 1318 T^{3} + 7611 T^{4} - 27735 T^{5} + 79507 T^{6} $)($ 1 - 8 T + 124 T^{2} - 648 T^{3} + 6710 T^{4} - 27864 T^{5} + 229276 T^{6} - 636056 T^{7} + 3418801 T^{8} $)($ 1 + 8 T + 124 T^{2} + 648 T^{3} + 6710 T^{4} + 27864 T^{5} + 229276 T^{6} + 636056 T^{7} + 3418801 T^{8} $)($ 1 + 8 T + 124 T^{2} + 648 T^{3} + 6710 T^{4} + 27864 T^{5} + 229276 T^{6} + 636056 T^{7} + 3418801 T^{8} $)($ 1 - 8 T + 124 T^{2} - 648 T^{3} + 6710 T^{4} - 27864 T^{5} + 229276 T^{6} - 636056 T^{7} + 3418801 T^{8} $)
$47$	($ 1 - 4 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 + 4 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 2 T + 47 T^{2} $)($ 1 + 2 T + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 10 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 - 12 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 - 4 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 - 10 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 + 2 T + 47 T^{2} $)($ 1 + 2 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 12 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 4 T + 47 T^{2} $)($ 1 - 4 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 + 4 T + 47 T^{2} $)($ 1 - 2 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 + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 - 2 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 10 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 4 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 + 12 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 10 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 2 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 - 2 T + 47 T^{2} $)($ 1 + 4 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 - 12 T + 47 T^{2} $)($ 1 - 8 T + 102 T^{2} - 376 T^{3} + 2209 T^{4} $)($ 1 + 8 T + 38 T^{2} + 376 T^{3} + 2209 T^{4} $)($ 1 + 86 T^{2} + 2209 T^{4} $)($ ( 1 - 6 T + 47 T^{2} )^{2} $)($ ( 1 - 8 T + 47 T^{2} )^{2} $)($ ( 1 - 12 T + 47 T^{2} )^{2} $)($ ( 1 + 8 T + 47 T^{2} )^{2} $)($ ( 1 - 4 T + 47 T^{2} )^{2} $)($ 1 - 8 T + 62 T^{2} - 376 T^{3} + 2209 T^{4} $)($ ( 1 - 6 T + 47 T^{2} )^{2} $)($ 1 + 86 T^{2} + 2209 T^{4} $)($ 1 + 8 T + 38 T^{2} + 376 T^{3} + 2209 T^{4} $)($ 1 - 8 T + 102 T^{2} - 376 T^{3} + 2209 T^{4} $)($ 1 + 86 T^{2} + 2209 T^{4} $)($ 1 + 8 T + 102 T^{2} + 376 T^{3} + 2209 T^{4} $)($ 1 - 8 T + 38 T^{2} - 376 T^{3} + 2209 T^{4} $)($ ( 1 + 6 T + 47 T^{2} )^{2} $)($ 1 + 8 T + 62 T^{2} + 376 T^{3} + 2209 T^{4} $)($ ( 1 + 4 T + 47 T^{2} )^{2} $)($ ( 1 - 8 T + 47 T^{2} )^{2} $)($ ( 1 + 12 T + 47 T^{2} )^{2} $)($ ( 1 + 8 T + 47 T^{2} )^{2} $)($ ( 1 + 6 T + 47 T^{2} )^{2} $)($ 1 - 8 T + 38 T^{2} - 376 T^{3} + 2209 T^{4} $)($ 1 + 8 T + 102 T^{2} + 376 T^{3} + 2209 T^{4} $)($ 1 + 86 T^{2} + 2209 T^{4} $)($ 1 - 12 T + 153 T^{2} - 1016 T^{3} + 7191 T^{4} - 26508 T^{5} + 103823 T^{6} $)($ 1 - 12 T + 153 T^{2} - 1016 T^{3} + 7191 T^{4} - 26508 T^{5} + 103823 T^{6} $)($ 1 + 12 T + 153 T^{2} + 1016 T^{3} + 7191 T^{4} + 26508 T^{5} + 103823 T^{6} $)($ 1 + 12 T + 153 T^{2} + 1016 T^{3} + 7191 T^{4} + 26508 T^{5} + 103823 T^{6} $)($ 1 + 16 T + 164 T^{2} + 1232 T^{3} + 7990 T^{4} + 57904 T^{5} + 362276 T^{6} + 1661168 T^{7} + 4879681 T^{8} $)($ 1 + 16 T + 164 T^{2} + 1232 T^{3} + 7990 T^{4} + 57904 T^{5} + 362276 T^{6} + 1661168 T^{7} + 4879681 T^{8} $)($ 1 - 16 T + 164 T^{2} - 1232 T^{3} + 7990 T^{4} - 57904 T^{5} + 362276 T^{6} - 1661168 T^{7} + 4879681 T^{8} $)($ 1 - 16 T + 164 T^{2} - 1232 T^{3} + 7990 T^{4} - 57904 T^{5} + 362276 T^{6} - 1661168 T^{7} + 4879681 T^{8} $)
$53$	($ 1 - 6 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)($ 1 + 10 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 - 11 T + 53 T^{2} $)($ 1 + 8 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)($ 1 - 2 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 + 2 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - 2 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 2 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)($ 1 + 2 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 + 10 T + 53 T^{2} $)($ 1 + 8 T + 53 T^{2} $)($ 1 - 11 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 10 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - 11 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 + 2 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)($ 1 - 2 T + 53 T^{2} $)($ 1 + 8 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 2 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 2 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 + 8 T + 53 T^{2} $)($ 1 + 10 T + 53 T^{2} $)($ 1 + 2 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 - 11 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - 4 T - 18 T^{2} - 212 T^{3} + 2809 T^{4} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ 1 + 11 T + 122 T^{2} + 583 T^{3} + 2809 T^{4} $)($ ( 1 + 6 T + 53 T^{2} )^{2} $)($ ( 1 + 10 T + 53 T^{2} )^{2} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ ( 1 - 6 T + 53 T^{2} )^{2} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ 1 + 11 T + 122 T^{2} + 583 T^{3} + 2809 T^{4} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ 1 - 4 T - 18 T^{2} - 212 T^{3} + 2809 T^{4} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ 1 - 4 T - 18 T^{2} - 212 T^{3} + 2809 T^{4} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ 1 + 11 T + 122 T^{2} + 583 T^{3} + 2809 T^{4} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ ( 1 - 6 T + 53 T^{2} )^{2} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ ( 1 + 10 T + 53 T^{2} )^{2} $)($ ( 1 + 6 T + 53 T^{2} )^{2} $)($ 1 + 11 T + 122 T^{2} + 583 T^{3} + 2809 T^{4} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ 1 - 4 T - 18 T^{2} - 212 T^{3} + 2809 T^{4} $)($ ( 1 - 2 T + 53 T^{2} )^{2} $)($ 1 + 6 T + 78 T^{2} + 802 T^{3} + 4134 T^{4} + 16854 T^{5} + 148877 T^{6} $)($ 1 + 6 T + 78 T^{2} + 802 T^{3} + 4134 T^{4} + 16854 T^{5} + 148877 T^{6} $)($ 1 + 6 T + 78 T^{2} + 802 T^{3} + 4134 T^{4} + 16854 T^{5} + 148877 T^{6} $)($ 1 + 6 T + 78 T^{2} + 802 T^{3} + 4134 T^{4} + 16854 T^{5} + 148877 T^{6} $)($ 1 + 140 T^{2} + 128 T^{3} + 9494 T^{4} + 6784 T^{5} + 393260 T^{6} + 7890481 T^{8} $)($ 1 + 140 T^{2} + 128 T^{3} + 9494 T^{4} + 6784 T^{5} + 393260 T^{6} + 7890481 T^{8} $)($ 1 + 140 T^{2} + 128 T^{3} + 9494 T^{4} + 6784 T^{5} + 393260 T^{6} + 7890481 T^{8} $)($ 1 + 140 T^{2} + 128 T^{3} + 9494 T^{4} + 6784 T^{5} + 393260 T^{6} + 7890481 T^{8} $)
$59$	($ 1 + 6 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 8 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 + 7 T + 59 T^{2} $)($ 1 + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 - 9 T + 59 T^{2} $)($ 1 - 5 T + 59 T^{2} $)($ 1 + 11 T + 59 T^{2} $)($ 1 + 59 T^{2} $)($ 1 + 10 T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 + 10 T + 59 T^{2} $)($ 1 + 11 T + 59 T^{2} $)($ 1 - 5 T + 59 T^{2} $)($ 1 - 9 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 59 T^{2} $)($ 1 + 7 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 + 8 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 - 8 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 - 7 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 + 12 T + 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} $)($ 1 - 11 T + 59 T^{2} $)($ 1 + 5 T + 59 T^{2} $)($ 1 + 9 T + 59 T^{2} $)($ 1 + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 - 10 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 - 10 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 + 59 T^{2} $)($ 1 + 9 T + 59 T^{2} $)($ 1 + 5 T + 59 T^{2} $)($ 1 - 11 T + 59 T^{2} $)($ 1 + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 - 7 T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 - 8 T + 59 T^{2} $)($ 1 + 16 T + 174 T^{2} + 944 T^{3} + 3481 T^{4} $)($ 1 + 46 T^{2} + 3481 T^{4} $)($ 1 - 8 T + 126 T^{2} - 472 T^{3} + 3481 T^{4} $)($ 1 - 5 T + 110 T^{2} - 295 T^{3} + 3481 T^{4} $)($ ( 1 + 12 T + 59 T^{2} )^{2} $)($ ( 1 + 59 T^{2} )^{2} $)($ ( 1 - 4 T + 59 T^{2} )^{2} $)($ ( 1 - 8 T + 59 T^{2} )^{2} $)($ 1 - 16 T + 134 T^{2} - 944 T^{3} + 3481 T^{4} $)($ 1 - 5 T + 110 T^{2} - 295 T^{3} + 3481 T^{4} $)($ 1 - 8 T + 126 T^{2} - 472 T^{3} + 3481 T^{4} $)($ 1 + 46 T^{2} + 3481 T^{4} $)($ 1 + 16 T + 174 T^{2} + 944 T^{3} + 3481 T^{4} $)($ 1 + 8 T + 126 T^{2} + 472 T^{3} + 3481 T^{4} $)($ 1 - 16 T + 174 T^{2} - 944 T^{3} + 3481 T^{4} $)($ 1 + 46 T^{2} + 3481 T^{4} $)($ 1 + 5 T + 110 T^{2} + 295 T^{3} + 3481 T^{4} $)($ 1 + 16 T + 134 T^{2} + 944 T^{3} + 3481 T^{4} $)($ ( 1 + 8 T + 59 T^{2} )^{2} $)($ ( 1 + 4 T + 59 T^{2} )^{2} $)($ ( 1 + 59 T^{2} )^{2} $)($ ( 1 - 12 T + 59 T^{2} )^{2} $)($ 1 + 5 T + 110 T^{2} + 295 T^{3} + 3481 T^{4} $)($ 1 + 46 T^{2} + 3481 T^{4} $)($ 1 - 16 T + 174 T^{2} - 944 T^{3} + 3481 T^{4} $)($ 1 + 8 T + 126 T^{2} + 472 T^{3} + 3481 T^{4} $)($ 1 + 12 T + 198 T^{2} + 1334 T^{3} + 11682 T^{4} + 41772 T^{5} + 205379 T^{6} $)($ 1 + 12 T + 198 T^{2} + 1334 T^{3} + 11682 T^{4} + 41772 T^{5} + 205379 T^{6} $)($ 1 - 12 T + 198 T^{2} - 1334 T^{3} + 11682 T^{4} - 41772 T^{5} + 205379 T^{6} $)($ 1 - 12 T + 198 T^{2} - 1334 T^{3} + 11682 T^{4} - 41772 T^{5} + 205379 T^{6} $)($ 1 + 84 T^{2} - 960 T^{3} + 1350 T^{4} - 56640 T^{5} + 292404 T^{6} + 12117361 T^{8} $)($ 1 + 84 T^{2} - 960 T^{3} + 1350 T^{4} - 56640 T^{5} + 292404 T^{6} + 12117361 T^{8} $)($ 1 + 84 T^{2} + 960 T^{3} + 1350 T^{4} + 56640 T^{5} + 292404 T^{6} + 12117361 T^{8} $)($ 1 + 84 T^{2} + 960 T^{3} + 1350 T^{4} + 56640 T^{5} + 292404 T^{6} + 12117361 T^{8} $)
$61$	($ 1 + 2 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 + 12 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 - 2 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 2 T + 61 T^{2} $)($ 1 - 2 T + 61 T^{2} $)($ 1 + 4 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 + 14 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 8 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 12 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 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 + 4 T + 61 T^{2} $)($ 1 - 2 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 + 12 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 2 T + 61 T^{2} $)($ 1 + 14 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 4 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 - 2 T + 61 T^{2} $)($ 1 - 2 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 8 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 12 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 - 2 T + 61 T^{2} $)($ 1 + 4 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 8 T + 40 T^{2} + 488 T^{3} + 3721 T^{4} $)($ 1 + 8 T + 88 T^{2} + 488 T^{3} + 3721 T^{4} $)($ 1 + 16 T + 168 T^{2} + 976 T^{3} + 3721 T^{4} $)($ ( 1 - 10 T + 61 T^{2} )^{2} $)($ 1 + 90 T^{2} + 3721 T^{4} $)($ 1 + 120 T^{2} + 3721 T^{4} $)($ 1 + 90 T^{2} + 3721 T^{4} $)($ 1 + 104 T^{2} + 3721 T^{4} $)($ 1 + 4 T + 78 T^{2} + 244 T^{3} + 3721 T^{4} $)($ ( 1 + 10 T + 61 T^{2} )^{2} $)($ 1 - 16 T + 168 T^{2} - 976 T^{3} + 3721 T^{4} $)($ 1 - 8 T + 88 T^{2} - 488 T^{3} + 3721 T^{4} $)($ 1 - 8 T + 40 T^{2} - 488 T^{3} + 3721 T^{4} $)($ 1 + 16 T + 168 T^{2} + 976 T^{3} + 3721 T^{4} $)($ 1 + 8 T + 40 T^{2} + 488 T^{3} + 3721 T^{4} $)($ 1 + 8 T + 88 T^{2} + 488 T^{3} + 3721 T^{4} $)($ ( 1 - 10 T + 61 T^{2} )^{2} $)($ 1 + 4 T + 78 T^{2} + 244 T^{3} + 3721 T^{4} $)($ 1 + 104 T^{2} + 3721 T^{4} $)($ 1 + 90 T^{2} + 3721 T^{4} $)($ 1 + 120 T^{2} + 3721 T^{4} $)($ 1 + 90 T^{2} + 3721 T^{4} $)($ ( 1 + 10 T + 61 T^{2} )^{2} $)($ 1 - 8 T + 88 T^{2} - 488 T^{3} + 3721 T^{4} $)($ 1 - 8 T + 40 T^{2} - 488 T^{3} + 3721 T^{4} $)($ 1 - 16 T + 168 T^{2} - 976 T^{3} + 3721 T^{4} $)($ 1 + 18 T + 195 T^{2} + 1644 T^{3} + 11895 T^{4} + 66978 T^{5} + 226981 T^{6} $)($ 1 - 18 T + 195 T^{2} - 1644 T^{3} + 11895 T^{4} - 66978 T^{5} + 226981 T^{6} $)($ 1 + 18 T + 195 T^{2} + 1644 T^{3} + 11895 T^{4} + 66978 T^{5} + 226981 T^{6} $)($ 1 - 18 T + 195 T^{2} - 1644 T^{3} + 11895 T^{4} - 66978 T^{5} + 226981 T^{6} $)($ 1 + 16 T + 288 T^{2} + 2768 T^{3} + 27282 T^{4} + 168848 T^{5} + 1071648 T^{6} + 3631696 T^{7} + 13845841 T^{8} $)($ 1 - 16 T + 288 T^{2} - 2768 T^{3} + 27282 T^{4} - 168848 T^{5} + 1071648 T^{6} - 3631696 T^{7} + 13845841 T^{8} $)($ 1 + 16 T + 288 T^{2} + 2768 T^{3} + 27282 T^{4} + 168848 T^{5} + 1071648 T^{6} + 3631696 T^{7} + 13845841 T^{8} $)($ 1 - 16 T + 288 T^{2} - 2768 T^{3} + 27282 T^{4} - 168848 T^{5} + 1071648 T^{6} - 3631696 T^{7} + 13845841 T^{8} $)
$67$	($ 1 + 7 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 10 T + 67 T^{2} $)($ 1 + 10 T + 67 T^{2} $)($ 1 + 15 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 13 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)($ 1 + 5 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 2 T + 67 T^{2} $)($ 1 - 6 T + 67 T^{2} $)($ 1 + 2 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 - 11 T + 67 T^{2} $)($ 1 + 5 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 5 T + 67 T^{2} $)($ 1 + 11 T + 67 T^{2} $)($ 1 - 2 T + 67 T^{2} $)($ 1 + 6 T + 67 T^{2} $)($ 1 + 2 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 + 16 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 - 5 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 - 13 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 15 T + 67 T^{2} $)($ 1 - 10 T + 67 T^{2} $)($ 1 + 10 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 7 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 7 T + 67 T^{2} $)($ 1 - 10 T + 67 T^{2} $)($ 1 + 10 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 13 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 - 5 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 15 T + 67 T^{2} $)($ 1 - 2 T + 67 T^{2} $)($ 1 + 6 T + 67 T^{2} $)($ 1 + 2 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 5 T + 67 T^{2} $)($ 1 - 11 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 11 T + 67 T^{2} $)($ 1 - 5 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 - 2 T + 67 T^{2} $)($ 1 - 6 T + 67 T^{2} $)($ 1 + 2 T + 67 T^{2} $)($ 1 + 15 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 + 5 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)($ 1 + 13 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)($ 1 - 16 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 - 10 T + 67 T^{2} $)($ 1 + 10 T + 67 T^{2} $)($ 1 + 7 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ ( 1 - 8 T + 67 T^{2} )^{2} $)($ 1 + 6 T^{2} + 4489 T^{4} $)($ 1 + 102 T^{2} + 4489 T^{4} $)($ 1 + 7 T + 132 T^{2} + 469 T^{3} + 4489 T^{4} $)($ 1 + 102 T^{2} + 4489 T^{4} $)($ 1 + 6 T^{2} + 4489 T^{4} $)($ 1 + 6 T^{2} + 4489 T^{4} $)($ ( 1 + 67 T^{2} )^{2} $)($ 1 - 8 T + 102 T^{2} - 536 T^{3} + 4489 T^{4} $)($ 1 - 7 T + 132 T^{2} - 469 T^{3} + 4489 T^{4} $)($ 1 + 102 T^{2} + 4489 T^{4} $)($ 1 + 6 T^{2} + 4489 T^{4} $)($ ( 1 + 8 T + 67 T^{2} )^{2} $)($ 1 + 102 T^{2} + 4489 T^{4} $)($ ( 1 + 8 T + 67 T^{2} )^{2} $)($ 1 + 6 T^{2} + 4489 T^{4} $)($ 1 - 7 T + 132 T^{2} - 469 T^{3} + 4489 T^{4} $)($ 1 + 8 T + 102 T^{2} + 536 T^{3} + 4489 T^{4} $)($ ( 1 + 67 T^{2} )^{2} $)($ 1 + 6 T^{2} + 4489 T^{4} $)($ 1 + 6 T^{2} + 4489 T^{4} $)($ 1 + 102 T^{2} + 4489 T^{4} $)($ 1 + 7 T + 132 T^{2} + 469 T^{3} + 4489 T^{4} $)($ 1 + 6 T^{2} + 4489 T^{4} $)($ ( 1 - 8 T + 67 T^{2} )^{2} $)($ 1 + 102 T^{2} + 4489 T^{4} $)($ 1 - 9 T + 189 T^{2} - 1042 T^{3} + 12663 T^{4} - 40401 T^{5} + 300763 T^{6} $)($ 1 + 9 T + 189 T^{2} + 1042 T^{3} + 12663 T^{4} + 40401 T^{5} + 300763 T^{6} $)($ 1 + 9 T + 189 T^{2} + 1042 T^{3} + 12663 T^{4} + 40401 T^{5} + 300763 T^{6} $)($ 1 - 9 T + 189 T^{2} - 1042 T^{3} + 12663 T^{4} - 40401 T^{5} + 300763 T^{6} $)($ 1 - 8 T + 124 T^{2} + 56 T^{3} + 3286 T^{4} + 3752 T^{5} + 556636 T^{6} - 2406104 T^{7} + 20151121 T^{8} $)($ 1 + 8 T + 124 T^{2} - 56 T^{3} + 3286 T^{4} - 3752 T^{5} + 556636 T^{6} + 2406104 T^{7} + 20151121 T^{8} $)($ 1 + 8 T + 124 T^{2} - 56 T^{3} + 3286 T^{4} - 3752 T^{5} + 556636 T^{6} + 2406104 T^{7} + 20151121 T^{8} $)($ 1 - 8 T + 124 T^{2} + 56 T^{3} + 3286 T^{4} + 3752 T^{5} + 556636 T^{6} - 2406104 T^{7} + 20151121 T^{8} $)
$71$	($ 1 - 16 T + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 + 14 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 - 8 T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 - 10 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 8 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 + 2 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 + 4 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 + 2 T + 71 T^{2} $)($ 1 - 4 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 - 2 T + 71 T^{2} $)($ 1 - 10 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 4 T + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 - 10 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 - 10 T + 71 T^{2} $)($ 1 - 16 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 - 14 T + 71 T^{2} $)($ 1 - 8 T + 71 T^{2} $)($ 1 + 16 T + 71 T^{2} $)($ 1 - 14 T + 71 T^{2} $)($ 1 - 8 T + 71 T^{2} $)($ 1 + 16 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 - 10 T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 - 10 T + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 - 2 T + 71 T^{2} $)($ 1 - 10 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 - 2 T + 71 T^{2} $)($ 1 + 4 T + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 - 4 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 + 2 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 16 T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 - 10 T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 - 4 T + 71 T^{2} $)($ 1 - 8 T + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 - 16 T + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 + 14 T + 71 T^{2} $)($ 1 - 4 T + 138 T^{2} - 284 T^{3} + 5041 T^{4} $)($ 1 - 4 T + 74 T^{2} - 284 T^{3} + 5041 T^{4} $)($ 1 + 4 T + 18 T^{2} + 284 T^{3} + 5041 T^{4} $)($ ( 1 - 2 T + 71 T^{2} )^{2} $)($ 1 + 134 T^{2} + 5041 T^{4} $)($ 1 + 134 T^{2} + 5041 T^{4} $)($ 1 + 110 T^{2} + 5041 T^{4} $)($ 1 - 58 T^{2} + 5041 T^{4} $)($ 1 + 12 T + 166 T^{2} + 852 T^{3} + 5041 T^{4} $)($ ( 1 + 2 T + 71 T^{2} )^{2} $)($ 1 - 4 T + 18 T^{2} - 284 T^{3} + 5041 T^{4} $)($ 1 + 4 T + 74 T^{2} + 284 T^{3} + 5041 T^{4} $)($ 1 + 4 T + 138 T^{2} + 284 T^{3} + 5041 T^{4} $)($ 1 - 4 T + 18 T^{2} - 284 T^{3} + 5041 T^{4} $)($ 1 + 4 T + 138 T^{2} + 284 T^{3} + 5041 T^{4} $)($ 1 + 4 T + 74 T^{2} + 284 T^{3} + 5041 T^{4} $)($ ( 1 + 2 T + 71 T^{2} )^{2} $)($ 1 - 12 T + 166 T^{2} - 852 T^{3} + 5041 T^{4} $)($ 1 - 58 T^{2} + 5041 T^{4} $)($ 1 + 110 T^{2} + 5041 T^{4} $)($ 1 + 134 T^{2} + 5041 T^{4} $)($ 1 + 134 T^{2} + 5041 T^{4} $)($ ( 1 - 2 T + 71 T^{2} )^{2} $)($ 1 - 4 T + 74 T^{2} - 284 T^{3} + 5041 T^{4} $)($ 1 - 4 T + 138 T^{2} - 284 T^{3} + 5041 T^{4} $)($ 1 + 4 T + 18 T^{2} + 284 T^{3} + 5041 T^{4} $)($ 1 + 177 T^{2} + 32 T^{3} + 12567 T^{4} + 357911 T^{6} $)($ 1 + 177 T^{2} - 32 T^{3} + 12567 T^{4} + 357911 T^{6} $)($ 1 + 177 T^{2} - 32 T^{3} + 12567 T^{4} + 357911 T^{6} $)($ 1 + 177 T^{2} + 32 T^{3} + 12567 T^{4} + 357911 T^{6} $)($ 1 - 12 T + 248 T^{2} - 2380 T^{3} + 25406 T^{4} - 168980 T^{5} + 1250168 T^{6} - 4294932 T^{7} + 25411681 T^{8} $)($ 1 + 12 T + 248 T^{2} + 2380 T^{3} + 25406 T^{4} + 168980 T^{5} + 1250168 T^{6} + 4294932 T^{7} + 25411681 T^{8} $)($ 1 + 12 T + 248 T^{2} + 2380 T^{3} + 25406 T^{4} + 168980 T^{5} + 1250168 T^{6} + 4294932 T^{7} + 25411681 T^{8} $)($ 1 - 12 T + 248 T^{2} - 2380 T^{3} + 25406 T^{4} - 168980 T^{5} + 1250168 T^{6} - 4294932 T^{7} + 25411681 T^{8} $)
$73$	($ 1 - 3 T + 73 T^{2} $)($ 1 + 16 T + 73 T^{2} $)($ 1 + 6 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 6 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 - 11 T + 73 T^{2} $)($ 1 - 12 T + 73 T^{2} $)($ 1 - 3 T + 73 T^{2} $)($ 1 - 4 T + 73 T^{2} $)($ 1 - 6 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 + 3 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 - 8 T + 73 T^{2} $)($ 1 + 8 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 11 T + 73 T^{2} $)($ 1 - 3 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 6 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 + 4 T + 73 T^{2} $)($ 1 + 3 T + 73 T^{2} $)($ 1 + 12 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 - 6 T + 73 T^{2} $)($ 1 - 11 T + 73 T^{2} $)($ 1 - 6 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 16 T + 73 T^{2} $)($ 1 + 3 T + 73 T^{2} $)($ 1 + 6 T + 73 T^{2} $)($ 1 + 16 T + 73 T^{2} $)($ 1 - 3 T + 73 T^{2} $)($ 1 + 6 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 6 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 - 11 T + 73 T^{2} $)($ 1 - 12 T + 73 T^{2} $)($ 1 - 3 T + 73 T^{2} $)($ 1 - 4 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 11 T + 73 T^{2} $)($ 1 - 3 T + 73 T^{2} $)($ 1 - 8 T + 73 T^{2} $)($ 1 + 8 T + 73 T^{2} $)($ 1 + 3 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 - 11 T + 73 T^{2} $)($ 1 - 6 T + 73 T^{2} $)($ 1 + 4 T + 73 T^{2} $)($ 1 + 3 T + 73 T^{2} $)($ 1 + 12 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 6 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 6 T + 73 T^{2} $)($ 1 + 3 T + 73 T^{2} $)($ 1 - 16 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 8 T + 112 T^{2} + 584 T^{3} + 5329 T^{4} $)($ 1 - 24 T + 272 T^{2} - 1752 T^{3} + 5329 T^{4} $)($ 1 - 8 T + 64 T^{2} - 584 T^{3} + 5329 T^{4} $)($ 1 - T + 132 T^{2} - 73 T^{3} + 5329 T^{4} $)($ 1 + 114 T^{2} + 5329 T^{4} $)($ 1 - 16 T^{2} + 5329 T^{4} $)($ 1 + 18 T^{2} + 5329 T^{4} $)($ 1 + 144 T^{2} + 5329 T^{4} $)($ 1 + 12 T + 134 T^{2} + 876 T^{3} + 5329 T^{4} $)($ 1 + T + 132 T^{2} + 73 T^{3} + 5329 T^{4} $)($ 1 + 8 T + 64 T^{2} + 584 T^{3} + 5329 T^{4} $)($ 1 + 24 T + 272 T^{2} + 1752 T^{3} + 5329 T^{4} $)($ 1 - 8 T + 112 T^{2} - 584 T^{3} + 5329 T^{4} $)($ 1 - 8 T + 64 T^{2} - 584 T^{3} + 5329 T^{4} $)($ 1 + 8 T + 112 T^{2} + 584 T^{3} + 5329 T^{4} $)($ 1 - 24 T + 272 T^{2} - 1752 T^{3} + 5329 T^{4} $)($ 1 - T + 132 T^{2} - 73 T^{3} + 5329 T^{4} $)($ 1 + 12 T + 134 T^{2} + 876 T^{3} + 5329 T^{4} $)($ 1 + 144 T^{2} + 5329 T^{4} $)($ 1 + 18 T^{2} + 5329 T^{4} $)($ 1 - 16 T^{2} + 5329 T^{4} $)($ 1 + 114 T^{2} + 5329 T^{4} $)($ 1 + T + 132 T^{2} + 73 T^{3} + 5329 T^{4} $)($ 1 + 24 T + 272 T^{2} + 1752 T^{3} + 5329 T^{4} $)($ 1 - 8 T + 112 T^{2} - 584 T^{3} + 5329 T^{4} $)($ 1 + 8 T + 64 T^{2} + 584 T^{3} + 5329 T^{4} $)($ 1 + 33 T + 555 T^{2} + 5814 T^{3} + 40515 T^{4} + 175857 T^{5} + 389017 T^{6} $)($ 1 - 33 T + 555 T^{2} - 5814 T^{3} + 40515 T^{4} - 175857 T^{5} + 389017 T^{6} $)($ 1 + 33 T + 555 T^{2} + 5814 T^{3} + 40515 T^{4} + 175857 T^{5} + 389017 T^{6} $)($ 1 - 33 T + 555 T^{2} - 5814 T^{3} + 40515 T^{4} - 175857 T^{5} + 389017 T^{6} $)($ 1 - 8 T + 256 T^{2} - 1608 T^{3} + 27170 T^{4} - 117384 T^{5} + 1364224 T^{6} - 3112136 T^{7} + 28398241 T^{8} $)($ 1 + 8 T + 256 T^{2} + 1608 T^{3} + 27170 T^{4} + 117384 T^{5} + 1364224 T^{6} + 3112136 T^{7} + 28398241 T^{8} $)($ 1 - 8 T + 256 T^{2} - 1608 T^{3} + 27170 T^{4} - 117384 T^{5} + 1364224 T^{6} - 3112136 T^{7} + 28398241 T^{8} $)($ 1 + 8 T + 256 T^{2} + 1608 T^{3} + 27170 T^{4} + 117384 T^{5} + 1364224 T^{6} + 3112136 T^{7} + 28398241 T^{8} $)
$79$	($ 1 - 11 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 + 4 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 - 11 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + 3 T + 79 T^{2} $)($ 1 + 12 T + 79 T^{2} $)($ 1 - T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 - 16 T + 79 T^{2} $)($ 1 + 79 T^{2} $)($ 1 - 9 T + 79 T^{2} $)($ 1 + 11 T + 79 T^{2} $)($ 1 + 3 T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 - 17 T + 79 T^{2} $)($ 1 - 5 T + 79 T^{2} $)($ 1 + 16 T + 79 T^{2} $)($ 1 - 16 T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 + 5 T + 79 T^{2} $)($ 1 + 17 T + 79 T^{2} $)($ 1 - 3 T + 79 T^{2} $)($ 1 - 11 T + 79 T^{2} $)($ 1 + 9 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + 4 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 - 12 T + 79 T^{2} $)($ 1 - 3 T + 79 T^{2} $)($ 1 + 4 T + 79 T^{2} $)($ 1 - T + 79 T^{2} $)($ 1 + 11 T + 79 T^{2} $)($ 1 - T + 79 T^{2} $)($ 1 - 12 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + 11 T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + 11 T + 79 T^{2} $)($ 1 + 11 T + 79 T^{2} $)($ 1 - T + 79 T^{2} $)($ 1 + 16 T + 79 T^{2} $)($ 1 + 79 T^{2} $)($ 1 - 3 T + 79 T^{2} $)($ 1 - 12 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 + 4 T + 79 T^{2} $)($ 1 + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 - T + 79 T^{2} $)($ 1 - 3 T + 79 T^{2} $)($ 1 - 11 T + 79 T^{2} $)($ 1 + 9 T + 79 T^{2} $)($ 1 + 4 T + 79 T^{2} $)($ 1 - 5 T + 79 T^{2} $)($ 1 - 17 T + 79 T^{2} $)($ 1 - 16 T + 79 T^{2} $)($ 1 + 16 T + 79 T^{2} $)($ 1 + 17 T + 79 T^{2} $)($ 1 + 5 T + 79 T^{2} $)($ 1 + 4 T + 79 T^{2} $)($ 1 - 9 T + 79 T^{2} $)($ 1 + 11 T + 79 T^{2} $)($ 1 + 3 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 - T + 79 T^{2} $)($ 1 + 12 T + 79 T^{2} $)($ 1 + 3 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 - 11 T + 79 T^{2} $)($ 1 - 11 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 + 12 T + 79 T^{2} $)($ 1 + 16 T + 190 T^{2} + 1264 T^{3} + 6241 T^{4} $)($ 1 + 16 T + 190 T^{2} + 1264 T^{3} + 6241 T^{4} $)($ 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} $)($ 1 - 8 T + 117 T^{2} - 632 T^{3} + 6241 T^{4} $)($ 1 + 126 T^{2} + 6241 T^{4} $)($ 1 + 30 T^{2} + 6241 T^{4} $)($ 1 + 30 T^{2} + 6241 T^{4} $)($ 1 + 30 T^{2} + 6241 T^{4} $)($ 1 - 8 T + 126 T^{2} - 632 T^{3} + 6241 T^{4} $)($ 1 + 8 T + 117 T^{2} + 632 T^{3} + 6241 T^{4} $)($ 1 + 16 T + 190 T^{2} + 1264 T^{3} + 6241 T^{4} $)($ 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} $)($ 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} $)($ 1 + 16 T + 190 T^{2} + 1264 T^{3} + 6241 T^{4} $)($ 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} $)($ 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} $)($ 1 + 8 T + 117 T^{2} + 632 T^{3} + 6241 T^{4} $)($ 1 + 8 T + 126 T^{2} + 632 T^{3} + 6241 T^{4} $)($ 1 + 30 T^{2} + 6241 T^{4} $)($ 1 + 30 T^{2} + 6241 T^{4} $)($ 1 + 30 T^{2} + 6241 T^{4} $)($ 1 + 126 T^{2} + 6241 T^{4} $)($ 1 - 8 T + 117 T^{2} - 632 T^{3} + 6241 T^{4} $)($ 1 + 16 T + 190 T^{2} + 1264 T^{3} + 6241 T^{4} $)($ 1 + 16 T + 190 T^{2} + 1264 T^{3} + 6241 T^{4} $)($ 1 - 16 T + 190 T^{2} - 1264 T^{3} + 6241 T^{4} $)($ 1 - 27 T + 432 T^{2} - 4619 T^{3} + 34128 T^{4} - 168507 T^{5} + 493039 T^{6} $)($ 1 + 27 T + 432 T^{2} + 4619 T^{3} + 34128 T^{4} + 168507 T^{5} + 493039 T^{6} $)($ 1 + 27 T + 432 T^{2} + 4619 T^{3} + 34128 T^{4} + 168507 T^{5} + 493039 T^{6} $)($ 1 - 27 T + 432 T^{2} - 4619 T^{3} + 34128 T^{4} - 168507 T^{5} + 493039 T^{6} $)($ 1 - 16 T + 284 T^{2} - 2768 T^{3} + 31366 T^{4} - 218672 T^{5} + 1772444 T^{6} - 7888624 T^{7} + 38950081 T^{8} $)($ 1 + 16 T + 284 T^{2} + 2768 T^{3} + 31366 T^{4} + 218672 T^{5} + 1772444 T^{6} + 7888624 T^{7} + 38950081 T^{8} $)($ 1 + 16 T + 284 T^{2} + 2768 T^{3} + 31366 T^{4} + 218672 T^{5} + 1772444 T^{6} + 7888624 T^{7} + 38950081 T^{8} $)($ 1 - 16 T + 284 T^{2} - 2768 T^{3} + 31366 T^{4} - 218672 T^{5} + 1772444 T^{6} - 7888624 T^{7} + 38950081 T^{8} $)
$83$	($ 1 - 12 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 9 T + 83 T^{2} $)($ 1 + 11 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 - 2 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 3 T + 83 T^{2} $)($ 1 + 7 T + 83 T^{2} $)($ 1 + 7 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 16 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 - 16 T + 83 T^{2} $)($ 1 + 7 T + 83 T^{2} $)($ 1 + 7 T + 83 T^{2} $)($ 1 + 3 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 2 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 + 11 T + 83 T^{2} $)($ 1 - 9 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 11 T + 83 T^{2} $)($ 1 + 9 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 + 2 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 - 7 T + 83 T^{2} $)($ 1 - 7 T + 83 T^{2} $)($ 1 - 3 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 16 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 16 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 3 T + 83 T^{2} $)($ 1 - 7 T + 83 T^{2} $)($ 1 - 7 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 2 T + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 9 T + 83 T^{2} $)($ 1 - 11 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 + 8 T + 54 T^{2} + 664 T^{3} + 6889 T^{4} $)($ ( 1 + 4 T + 83 T^{2} )^{2} $)($ 1 - 8 T + 54 T^{2} - 664 T^{3} + 6889 T^{4} $)($ 1 - 7 T + 164 T^{2} - 581 T^{3} + 6889 T^{4} $)($ ( 1 - 4 T + 83 T^{2} )^{2} $)($ ( 1 + 4 T + 83 T^{2} )^{2} $)($ ( 1 + 12 T + 83 T^{2} )^{2} $)($ ( 1 - 12 T + 83 T^{2} )^{2} $)($ ( 1 - 4 T + 83 T^{2} )^{2} $)($ 1 - 7 T + 164 T^{2} - 581 T^{3} + 6889 T^{4} $)($ 1 - 8 T + 54 T^{2} - 664 T^{3} + 6889 T^{4} $)($ ( 1 + 4 T + 83 T^{2} )^{2} $)($ 1 + 8 T + 54 T^{2} + 664 T^{3} + 6889 T^{4} $)($ 1 + 8 T + 54 T^{2} + 664 T^{3} + 6889 T^{4} $)($ 1 - 8 T + 54 T^{2} - 664 T^{3} + 6889 T^{4} $)($ ( 1 - 4 T + 83 T^{2} )^{2} $)($ 1 + 7 T + 164 T^{2} + 581 T^{3} + 6889 T^{4} $)($ ( 1 + 4 T + 83 T^{2} )^{2} $)($ ( 1 + 12 T + 83 T^{2} )^{2} $)($ ( 1 - 12 T + 83 T^{2} )^{2} $)($ ( 1 - 4 T + 83 T^{2} )^{2} $)($ ( 1 + 4 T + 83 T^{2} )^{2} $)($ 1 + 7 T + 164 T^{2} + 581 T^{3} + 6889 T^{4} $)($ ( 1 - 4 T + 83 T^{2} )^{2} $)($ 1 - 8 T + 54 T^{2} - 664 T^{3} + 6889 T^{4} $)($ 1 + 8 T + 54 T^{2} + 664 T^{3} + 6889 T^{4} $)($ 1 + 18 T + 234 T^{2} + 2040 T^{3} + 19422 T^{4} + 124002 T^{5} + 571787 T^{6} $)($ 1 + 18 T + 234 T^{2} + 2040 T^{3} + 19422 T^{4} + 124002 T^{5} + 571787 T^{6} $)($ 1 - 18 T + 234 T^{2} - 2040 T^{3} + 19422 T^{4} - 124002 T^{5} + 571787 T^{6} $)($ 1 - 18 T + 234 T^{2} - 2040 T^{3} + 19422 T^{4} - 124002 T^{5} + 571787 T^{6} $)($ 1 + 204 T^{2} - 256 T^{3} + 21878 T^{4} - 21248 T^{5} + 1405356 T^{6} + 47458321 T^{8} $)($ 1 + 204 T^{2} - 256 T^{3} + 21878 T^{4} - 21248 T^{5} + 1405356 T^{6} + 47458321 T^{8} $)($ 1 + 204 T^{2} + 256 T^{3} + 21878 T^{4} + 21248 T^{5} + 1405356 T^{6} + 47458321 T^{8} $)($ 1 + 204 T^{2} + 256 T^{3} + 21878 T^{4} + 21248 T^{5} + 1405356 T^{6} + 47458321 T^{8} $)
$89$	($ 1 + 4 T + 89 T^{2} $)($ 1 - 8 T + 89 T^{2} $)($ 1 + 4 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 8 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 89 T^{2} $)($ 1 - 14 T + 89 T^{2} $)($ 1 + 16 T + 89 T^{2} $)($ 1 + 14 T + 89 T^{2} $)($ 1 - 14 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 18 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 + 12 T + 89 T^{2} $)($ 1 - 12 T + 89 T^{2} $)($ 1 - 12 T + 89 T^{2} $)($ 1 - 4 T + 89 T^{2} $)($ 1 + 4 T + 89 T^{2} $)($ 1 + 89 T^{2} $)($ 1 + 12 T + 89 T^{2} $)($ 1 + 12 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 18 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 14 T + 89 T^{2} $)($ 1 - 2 T + 89 T^{2} $)($ 1 - 14 T + 89 T^{2} $)($ 1 - 16 T + 89 T^{2} $)($ 1 + 14 T + 89 T^{2} $)($ 1 + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 - 8 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 + 89 T^{2} $)($ 1 + 8 T + 89 T^{2} $)($ 1 - 4 T + 89 T^{2} $)($ 1 + 4 T + 89 T^{2} $)($ 1 - 8 T + 89 T^{2} $)($ 1 + 4 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 - 14 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 89 T^{2} $)($ 1 - 14 T + 89 T^{2} $)($ 1 + 16 T + 89 T^{2} $)($ 1 + 14 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 8 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 18 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 + 89 T^{2} $)($ 1 + 12 T + 89 T^{2} $)($ 1 + 12 T + 89 T^{2} $)($ 1 - 4 T + 89 T^{2} $)($ 1 + 4 T + 89 T^{2} $)($ 1 - 12 T + 89 T^{2} $)($ 1 - 12 T + 89 T^{2} $)($ 1 + 12 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 18 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 - 8 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 - 14 T + 89 T^{2} $)($ 1 - 16 T + 89 T^{2} $)($ 1 + 14 T + 89 T^{2} $)($ 1 + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 14 T + 89 T^{2} $)($ 1 - 2 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 4 T + 89 T^{2} $)($ 1 + 8 T + 89 T^{2} $)($ 1 + 89 T^{2} $)($ 1 - 4 T + 20 T^{2} - 356 T^{3} + 7921 T^{4} $)($ 1 - 20 T + 260 T^{2} - 1780 T^{3} + 7921 T^{4} $)($ 1 + 20 T + 260 T^{2} + 1780 T^{3} + 7921 T^{4} $)($ 1 - 6 T + 130 T^{2} - 534 T^{3} + 7921 T^{4} $)($ 1 + 170 T^{2} + 7921 T^{4} $)($ 1 + 128 T^{2} + 7921 T^{4} $)($ 1 + 146 T^{2} + 7921 T^{4} $)($ 1 + 176 T^{2} + 7921 T^{4} $)($ 1 + 166 T^{2} + 7921 T^{4} $)($ 1 + 6 T + 130 T^{2} + 534 T^{3} + 7921 T^{4} $)($ 1 - 20 T + 260 T^{2} - 1780 T^{3} + 7921 T^{4} $)($ 1 + 20 T + 260 T^{2} + 1780 T^{3} + 7921 T^{4} $)($ 1 + 4 T + 20 T^{2} + 356 T^{3} + 7921 T^{4} $)($ 1 + 20 T + 260 T^{2} + 1780 T^{3} + 7921 T^{4} $)($ 1 - 4 T + 20 T^{2} - 356 T^{3} + 7921 T^{4} $)($ 1 - 20 T + 260 T^{2} - 1780 T^{3} + 7921 T^{4} $)($ 1 - 6 T + 130 T^{2} - 534 T^{3} + 7921 T^{4} $)($ 1 + 166 T^{2} + 7921 T^{4} $)($ 1 + 176 T^{2} + 7921 T^{4} $)($ 1 + 146 T^{2} + 7921 T^{4} $)($ 1 + 128 T^{2} + 7921 T^{4} $)($ 1 + 170 T^{2} + 7921 T^{4} $)($ 1 + 6 T + 130 T^{2} + 534 T^{3} + 7921 T^{4} $)($ 1 + 20 T + 260 T^{2} + 1780 T^{3} + 7921 T^{4} $)($ 1 + 4 T + 20 T^{2} + 356 T^{3} + 7921 T^{4} $)($ 1 - 20 T + 260 T^{2} - 1780 T^{3} + 7921 T^{4} $)($ 1 - 12 T + 279 T^{2} - 2024 T^{3} + 24831 T^{4} - 95052 T^{5} + 704969 T^{6} $)($ 1 + 12 T + 279 T^{2} + 2024 T^{3} + 24831 T^{4} + 95052 T^{5} + 704969 T^{6} $)($ 1 - 12 T + 279 T^{2} - 2024 T^{3} + 24831 T^{4} - 95052 T^{5} + 704969 T^{6} $)($ 1 + 12 T + 279 T^{2} + 2024 T^{3} + 24831 T^{4} + 95052 T^{5} + 704969 T^{6} $)($ 1 - 28 T + 524 T^{2} - 6764 T^{3} + 72658 T^{4} - 601996 T^{5} + 4150604 T^{6} - 19739132 T^{7} + 62742241 T^{8} $)($ 1 + 28 T + 524 T^{2} + 6764 T^{3} + 72658 T^{4} + 601996 T^{5} + 4150604 T^{6} + 19739132 T^{7} + 62742241 T^{8} $)($ 1 - 28 T + 524 T^{2} - 6764 T^{3} + 72658 T^{4} - 601996 T^{5} + 4150604 T^{6} - 19739132 T^{7} + 62742241 T^{8} $)($ 1 + 28 T + 524 T^{2} + 6764 T^{3} + 72658 T^{4} + 601996 T^{5} + 4150604 T^{6} + 19739132 T^{7} + 62742241 T^{8} $)
$97$	($ 1 - 6 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 2 T + 97 T^{2} $)($ 1 + T + 97 T^{2} $)($ 1 - 7 T + 97 T^{2} $)($ 1 + 14 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 + 12 T + 97 T^{2} $)($ 1 - 6 T + 97 T^{2} $)($ 1 - 4 T + 97 T^{2} $)($ 1 + 18 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 + T + 97 T^{2} $)($ 1 - 17 T + 97 T^{2} $)($ 1 - 7 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 + 14 T + 97 T^{2} $)($ 1 - 18 T + 97 T^{2} $)($ 1 - 16 T + 97 T^{2} $)($ 1 + 16 T + 97 T^{2} $)($ 1 + 6 T + 97 T^{2} $)($ 1 + 18 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 + 7 T + 97 T^{2} $)($ 1 + 17 T + 97 T^{2} $)($ 1 - T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 - 6 T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 + 4 T + 97 T^{2} $)($ 1 + 6 T + 97 T^{2} $)($ 1 - 12 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 + 7 T + 97 T^{2} $)($ 1 - T + 97 T^{2} $)($ 1 - 2 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 + 6 T + 97 T^{2} $)($ 1 - 2 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 6 T + 97 T^{2} $)($ 1 - 7 T + 97 T^{2} $)($ 1 + T + 97 T^{2} $)($ 1 + 18 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 + 12 T + 97 T^{2} $)($ 1 - 6 T + 97 T^{2} $)($ 1 - 4 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 14 T + 97 T^{2} $)($ 1 - 7 T + 97 T^{2} $)($ 1 - 17 T + 97 T^{2} $)($ 1 + T + 97 T^{2} $)($ 1 + 6 T + 97 T^{2} $)($ 1 + 18 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 - 16 T + 97 T^{2} $)($ 1 + 16 T + 97 T^{2} $)($ 1 + 14 T + 97 T^{2} $)($ 1 - 18 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 - T + 97 T^{2} $)($ 1 + 17 T + 97 T^{2} $)($ 1 + 7 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 + 4 T + 97 T^{2} $)($ 1 + 6 T + 97 T^{2} $)($ 1 - 12 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 - 6 T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 - T + 97 T^{2} $)($ 1 + 7 T + 97 T^{2} $)($ 1 + 6 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 - 2 T + 97 T^{2} $)($ 1 + 24 T + 320 T^{2} + 2328 T^{3} + 9409 T^{4} $)($ 1 - 8 T + 192 T^{2} - 776 T^{3} + 9409 T^{4} $)($ 1 - 8 T + 208 T^{2} - 776 T^{3} + 9409 T^{4} $)($ 1 + 25 T + 336 T^{2} + 2425 T^{3} + 9409 T^{4} $)($ 1 - 94 T^{2} + 9409 T^{4} $)($ 1 + 96 T^{2} + 9409 T^{4} $)($ ( 1 + 97 T^{2} )^{2} $)($ 1 + 32 T^{2} + 9409 T^{4} $)($ 1 - 4 T + 150 T^{2} - 388 T^{3} + 9409 T^{4} $)($ 1 - 25 T + 336 T^{2} - 2425 T^{3} + 9409 T^{4} $)($ 1 + 8 T + 208 T^{2} + 776 T^{3} + 9409 T^{4} $)($ 1 + 8 T + 192 T^{2} + 776 T^{3} + 9409 T^{4} $)($ 1 - 24 T + 320 T^{2} - 2328 T^{3} + 9409 T^{4} $)($ 1 - 8 T + 208 T^{2} - 776 T^{3} + 9409 T^{4} $)($ 1 + 24 T + 320 T^{2} + 2328 T^{3} + 9409 T^{4} $)($ 1 - 8 T + 192 T^{2} - 776 T^{3} + 9409 T^{4} $)($ 1 + 25 T + 336 T^{2} + 2425 T^{3} + 9409 T^{4} $)($ 1 - 4 T + 150 T^{2} - 388 T^{3} + 9409 T^{4} $)($ 1 + 32 T^{2} + 9409 T^{4} $)($ ( 1 + 97 T^{2} )^{2} $)($ 1 + 96 T^{2} + 9409 T^{4} $)($ 1 - 94 T^{2} + 9409 T^{4} $)($ 1 - 25 T + 336 T^{2} - 2425 T^{3} + 9409 T^{4} $)($ 1 + 8 T + 192 T^{2} + 776 T^{3} + 9409 T^{4} $)($ 1 - 24 T + 320 T^{2} - 2328 T^{3} + 9409 T^{4} $)($ 1 + 8 T + 208 T^{2} + 776 T^{3} + 9409 T^{4} $)($ 1 + 264 T^{2} - 38 T^{3} + 25608 T^{4} + 912673 T^{6} $)($ 1 + 264 T^{2} + 38 T^{3} + 25608 T^{4} + 912673 T^{6} $)($ 1 + 264 T^{2} - 38 T^{3} + 25608 T^{4} + 912673 T^{6} $)($ 1 + 264 T^{2} + 38 T^{3} + 25608 T^{4} + 912673 T^{6} $)($ 1 - 40 T + 896 T^{2} - 13608 T^{3} + 153858 T^{4} - 1319976 T^{5} + 8430464 T^{6} - 36506920 T^{7} + 88529281 T^{8} $)($ 1 + 40 T + 896 T^{2} + 13608 T^{3} + 153858 T^{4} + 1319976 T^{5} + 8430464 T^{6} + 36506920 T^{7} + 88529281 T^{8} $)($ 1 - 40 T + 896 T^{2} - 13608 T^{3} + 153858 T^{4} - 1319976 T^{5} + 8430464 T^{6} - 36506920 T^{7} + 88529281 T^{8} $)($ 1 + 40 T + 896 T^{2} + 13608 T^{3} + 153858 T^{4} + 1319976 T^{5} + 8430464 T^{6} + 36506920 T^{7} + 88529281 T^{8} $)
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Introduction	Features
Universe	News

Level:	\( N \)	\(=\)	\( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9408.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 118 \)
Sturm bound:			\(3584\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(19\), \(31\)

\(2\)	\(3\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(21\)
\(+\)	\(+\)	\(-\)	\(-\)	\(21\)
\(+\)	\(-\)	\(+\)	\(-\)	\(23\)
\(+\)	\(-\)	\(-\)	\(+\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)	\(19\)
\(-\)	\(+\)	\(-\)	\(+\)	\(21\)
\(-\)	\(-\)	\(+\)	\(+\)	\(17\)
\(-\)	\(-\)	\(-\)	\(-\)	\(24\)
Plus space			\(+\)	\(77\)
Minus space			\(-\)	\(87\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	2	3	7	$q$-expansion
9408.2.a.a	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-4\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}-4q^{5}+q^{9}-6q^{11}+5q^{13}+\cdots\)
9408.2.a.b	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-4\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}-4q^{5}+q^{9}-4q^{11}-4q^{13}+\cdots\)
9408.2.a.c	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-4\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-4q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\)
9408.2.a.d	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-3\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-3q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
9408.2.a.e	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-3\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-3q^{5}+q^{9}+q^{11}+4q^{13}+\cdots\)
9408.2.a.f	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-2q^{5}+q^{9}-6q^{11}+3q^{13}+\cdots\)
9408.2.a.g	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\)
9408.2.a.h	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.i	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}-3q^{13}+\cdots\)
9408.2.a.j	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots\)
9408.2.a.k	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}+q^{13}+\cdots\)
9408.2.a.l	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\)
9408.2.a.m	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.n	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
9408.2.a.o	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}+q^{9}+q^{11}+q^{15}-8q^{17}+\cdots\)
9408.2.a.p	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}-q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots\)
9408.2.a.q	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}-q^{5}+q^{9}+5q^{11}+q^{15}-4q^{17}+\cdots\)
9408.2.a.r	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}-6q^{11}+2q^{13}+4q^{19}+\cdots\)
9408.2.a.s	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+q^{9}-2q^{11}-5q^{13}-2q^{17}+\cdots\)
9408.2.a.t	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots\)
9408.2.a.u	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}-4q^{13}+4q^{17}+4q^{19}+\cdots\)
9408.2.a.v	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}+4q^{13}-4q^{17}+4q^{19}+\cdots\)
9408.2.a.w	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}+2q^{11}-2q^{13}-4q^{17}+\cdots\)
9408.2.a.x	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}+2q^{11}+q^{13}+2q^{17}+\cdots\)
9408.2.a.y	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}+2q^{11}+5q^{13}+2q^{17}+\cdots\)
9408.2.a.z	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+q^{5}+q^{9}-5q^{11}-q^{15}+4q^{17}+\cdots\)
9408.2.a.ba	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
9408.2.a.bb	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+q^{5}+q^{9}-q^{11}-q^{15}+8q^{17}+\cdots\)
9408.2.a.bc	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
9408.2.a.bd	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots\)
9408.2.a.be	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+2q^{5}+q^{9}+6q^{13}-2q^{15}+\cdots\)
9408.2.a.bf	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
9408.2.a.bg	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}-q^{13}+\cdots\)
9408.2.a.bh	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots\)
9408.2.a.bi	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots\)
9408.2.a.bj	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.bk	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+2q^{5}+q^{9}+6q^{11}-3q^{13}+\cdots\)
9408.2.a.bl	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(3\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+3q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
9408.2.a.bm	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(3\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+3q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots\)
9408.2.a.bn	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(4\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+4q^{5}+q^{9}-2q^{11}-6q^{13}+\cdots\)
9408.2.a.bo	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(4\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+4q^{5}+q^{9}+4q^{11}+4q^{13}+\cdots\)
9408.2.a.bp	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(-1\)	\(4\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+4q^{5}+q^{9}+6q^{11}-5q^{13}+\cdots\)
9408.2.a.bq	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-4\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}-4q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
9408.2.a.br	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-4\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}-4q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots\)
9408.2.a.bs	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-4\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-4q^{5}+q^{9}+6q^{11}+5q^{13}+\cdots\)
9408.2.a.bt	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-3\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-3q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
9408.2.a.bu	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-3\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-3q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots\)
9408.2.a.bv	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.bw	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
9408.2.a.bx	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots\)
9408.2.a.by	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots\)
9408.2.a.bz	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}+q^{13}+\cdots\)
9408.2.a.ca	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
9408.2.a.cb	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
9408.2.a.cc	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.cd	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}-2q^{5}+q^{9}+6q^{11}+3q^{13}+\cdots\)
9408.2.a.ce	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}-q^{5}+q^{9}-5q^{11}-q^{15}-4q^{17}+\cdots\)
9408.2.a.cf	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}-q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
9408.2.a.cg	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}-q^{5}+q^{9}-q^{11}-q^{15}-8q^{17}+\cdots\)
9408.2.a.ch	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}-2q^{11}-2q^{13}-4q^{17}+\cdots\)
9408.2.a.ci	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}-2q^{11}+q^{13}+2q^{17}+\cdots\)
9408.2.a.cj	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}-2q^{11}+5q^{13}+2q^{17}+\cdots\)
9408.2.a.ck	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}-4q^{13}+4q^{17}-4q^{19}+\cdots\)
9408.2.a.cl	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}+4q^{13}-4q^{17}-4q^{19}+\cdots\)
9408.2.a.cm	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{9}+2q^{11}-5q^{13}-2q^{17}+\cdots\)
9408.2.a.cn	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots\)
9408.2.a.co	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}+6q^{11}+2q^{13}-4q^{19}+\cdots\)
9408.2.a.cp	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+q^{9}+q^{11}+q^{15}+8q^{17}+\cdots\)
9408.2.a.cq	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots\)
9408.2.a.cr	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{5}+q^{9}+5q^{11}+q^{15}+4q^{17}+\cdots\)
9408.2.a.cs	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+2q^{5}+q^{9}-6q^{11}-3q^{13}+\cdots\)
9408.2.a.ct	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.cu	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\)
9408.2.a.cv	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}-q^{13}+\cdots\)
9408.2.a.cw	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots\)
9408.2.a.cx	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}+3q^{13}+\cdots\)
9408.2.a.cy	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
9408.2.a.cz	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
9408.2.a.da	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+2q^{5}+q^{9}+6q^{13}+2q^{15}+\cdots\)
9408.2.a.db	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(3\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+3q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
9408.2.a.dc	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(3\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+3q^{5}+q^{9}+q^{11}-4q^{13}+\cdots\)
9408.2.a.dd	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(4\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+4q^{5}+q^{9}-6q^{11}-5q^{13}+\cdots\)
9408.2.a.de	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(4\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+4q^{5}+q^{9}-4q^{11}+4q^{13}+\cdots\)
9408.2.a.df	\(1\)	\(75.123\)	\(\Q\)	None	\(0\)	\(1\)	\(4\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+4q^{5}+q^{9}+2q^{11}-6q^{13}+\cdots\)
9408.2.a.dg	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-4\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
9408.2.a.dh	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-4\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
9408.2.a.di	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-4\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(-2+\beta )q^{5}+q^{9}+2q^{11}+\cdots\)
9408.2.a.dj	\(2\)	\(75.123\)	\(\Q(\sqrt{57}) \)	None	\(0\)	\(-2\)	\(-1\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}-\beta q^{5}+q^{9}+\beta q^{11}+(3-\beta )q^{13}+\cdots\)
9408.2.a.dk	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}-\beta q^{15}+\cdots\)
9408.2.a.dl	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}+\beta q^{13}+\cdots\)
9408.2.a.dm	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+q^{9}+\beta q^{11}-\beta q^{13}+\beta q^{17}+\cdots\)
9408.2.a.dn	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}-3\beta q^{13}+\cdots\)
9408.2.a.do	\(2\)	\(75.123\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{3}+\beta q^{5}+q^{9}+(2-\beta )q^{11}+2q^{13}+\cdots\)
9408.2.a.dp	\(2\)	\(75.123\)	\(\Q(\sqrt{57}) \)	None	\(0\)	\(-2\)	\(1\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
9408.2.a.dq	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(4\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+(2+\beta )q^{5}+q^{9}-2q^{11}+(4+\cdots)q^{13}+\cdots\)
9408.2.a.dr	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(4\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)
9408.2.a.ds	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(4\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-q^{3}+(2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
9408.2.a.dt	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(-4\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-2+\beta )q^{5}+q^{9}-2q^{11}+\cdots\)
9408.2.a.du	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(-4\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)
9408.2.a.dv	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(-4\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
9408.2.a.dw	\(2\)	\(75.123\)	\(\Q(\sqrt{57}) \)	None	\(0\)	\(2\)	\(-1\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(3-\beta )q^{13}+\cdots\)
9408.2.a.dx	\(2\)	\(75.123\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+\beta q^{5}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9408.2.a.dy	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}-3\beta q^{13}+\cdots\)
9408.2.a.dz	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+q^{9}+\beta q^{11}+\beta q^{13}-\beta q^{17}+\cdots\)
9408.2.a.ea	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+\beta q^{13}+\cdots\)
9408.2.a.eb	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots\)
9408.2.a.ec	\(2\)	\(75.123\)	\(\Q(\sqrt{57}) \)	None	\(0\)	\(2\)	\(1\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
9408.2.a.ed	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(4\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
9408.2.a.ee	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(4\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
9408.2.a.ef	\(2\)	\(75.123\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(4\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+(2+\beta )q^{5}+q^{9}+2q^{11}+(4+\cdots)q^{13}+\cdots\)
9408.2.a.eg	\(3\)	\(75.123\)	3.3.621.1	None	\(0\)	\(-3\)	\(0\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q-q^{3}+\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9408.2.a.eh	\(3\)	\(75.123\)	3.3.621.1	None	\(0\)	\(-3\)	\(0\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}-\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
9408.2.a.ei	\(3\)	\(75.123\)	3.3.621.1	None	\(0\)	\(3\)	\(0\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q+q^{3}+\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
9408.2.a.ej	\(3\)	\(75.123\)	3.3.621.1	None	\(0\)	\(3\)	\(0\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}-\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9408.2.a.ek	\(4\)	\(75.123\)	4.4.2624.1	None	\(0\)	\(-4\)	\(-4\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots\)
9408.2.a.el	\(4\)	\(75.123\)	4.4.2624.1	None	\(0\)	\(-4\)	\(4\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q-q^{3}+(1+\beta _{3})q^{5}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
9408.2.a.em	\(4\)	\(75.123\)	4.4.2624.1	None	\(0\)	\(4\)	\(-4\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)
9408.2.a.en	\(4\)	\(75.123\)	4.4.2624.1	None	\(0\)	\(4\)	\(4\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+q^{3}+(1+\beta _{3})q^{5}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)

Introduction and more

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Knowledge

Properties

Related objects

Downloads

Learn more about

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9408))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9408))\) 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	9408.2.a

Level	9408
Weight	2
Character orbit	a
Rep. character	\(\chi_{9408}(1,\cdot)\)
Character field	\(\Q\)
Dimension	164
Newform subspaces	118
Sturm bound	3584
Trace bound	19