LMFDB - Space of Modular Forms of Level 9450, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	9450.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 128 $
Sturm bound:			$4320$
Trace bound:			$17$
Distinguishing $T_p$:			$11$, $13$, $17$, $19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(9450))$.

	Total	New	Old
Modular forms	2232	152	2080
Cusp forms	2089	152	1937
Eisenstein series	143	0	143

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

$2$	$3$	$5$	$7$	Fricke	Dim.
$+$	$+$	$+$	$+$	$+$	$8$
$+$	$+$	$+$	$-$	$-$	$10$
$+$	$+$	$-$	$+$	$-$	$10$
$+$	$+$	$-$	$-$	$+$	$10$
$+$	$-$	$+$	$+$	$-$	$10$
$+$	$-$	$+$	$-$	$+$	$8$
$+$	$-$	$-$	$+$	$+$	$10$
$+$	$-$	$-$	$-$	$-$	$10$
$-$	$+$	$+$	$+$	$-$	$11$
$-$	$+$	$+$	$-$	$+$	$7$
$-$	$+$	$-$	$+$	$+$	$8$
$-$	$+$	$-$	$-$	$-$	$12$
$-$	$-$	$+$	$+$	$+$	$7$
$-$	$-$	$+$	$-$	$-$	$11$
$-$	$-$	$-$	$+$	$-$	$12$
$-$	$-$	$-$	$-$	$+$	$8$
Plus space				$+$	$66$
Minus space				$-$	$86$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(9450))$ 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	5	7	$q$-expansion
9450.2.a.a	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}-2q^{13}+\cdots$
9450.2.a.b	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}+q^{13}+\cdots$
9450.2.a.c	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{11}-5q^{13}+\cdots$
9450.2.a.d	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{11}+q^{13}+\cdots$
9450.2.a.e	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-5q^{13}+\cdots$
9450.2.a.f	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-q^{13}+\cdots$
9450.2.a.g	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+q^{13}+\cdots$
9450.2.a.h	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+4q^{13}+\cdots$
9450.2.a.i	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+5q^{13}+\cdots$
9450.2.a.j	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}+5q^{13}+\cdots$
9450.2.a.k	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{11}+3q^{13}+\cdots$
9450.2.a.l	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{13}+q^{14}+\cdots$
9450.2.a.m	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{13}+q^{14}+\cdots$
9450.2.a.n	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots$
9450.2.a.o	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{13}+q^{14}+\cdots$
9450.2.a.p	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+7q^{13}+q^{14}+\cdots$
9450.2.a.q	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}-5q^{13}+\cdots$
9450.2.a.r	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}+5q^{13}+\cdots$
9450.2.a.s	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}-5q^{13}+\cdots$
9450.2.a.t	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}+6q^{13}+\cdots$
9450.2.a.u	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}-5q^{13}+\cdots$
9450.2.a.v	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}+q^{13}+\cdots$
9450.2.a.w	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}-6q^{13}+\cdots$
9450.2.a.x	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}-q^{13}+\cdots$
9450.2.a.y	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}-5q^{13}+\cdots$
9450.2.a.z	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}+4q^{13}+\cdots$
9450.2.a.ba	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}+5q^{13}+\cdots$
9450.2.a.bb	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-5q^{11}+5q^{13}+\cdots$
9450.2.a.bc	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}-3q^{13}+\cdots$
9450.2.a.bd	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}+q^{13}+\cdots$
9450.2.a.be	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}+6q^{13}+\cdots$
9450.2.a.bf	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-6q^{13}+\cdots$
9450.2.a.bg	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-q^{14}+\cdots$
9450.2.a.bh	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+3q^{13}+\cdots$
9450.2.a.bi	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+5q^{13}+\cdots$
9450.2.a.bj	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-q^{11}-5q^{13}+\cdots$
9450.2.a.bk	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-q^{11}+5q^{13}+\cdots$
9450.2.a.bl	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-7q^{13}-q^{14}+\cdots$
9450.2.a.bm	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{13}-q^{14}+\cdots$
9450.2.a.bn	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots$
9450.2.a.bo	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{13}-q^{14}+\cdots$
9450.2.a.bp	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}-3q^{13}+\cdots$
9450.2.a.bq	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}-3q^{13}+\cdots$
9450.2.a.br	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}+3q^{13}+\cdots$
9450.2.a.bs	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{11}-4q^{13}+\cdots$
9450.2.a.bt	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-5q^{13}+\cdots$
9450.2.a.bu	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-q^{13}+\cdots$
9450.2.a.bv	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}+q^{13}+\cdots$
9450.2.a.bw	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}-q^{13}+\cdots$
9450.2.a.bx	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}-q^{14}+\cdots$
9450.2.a.by	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}+5q^{13}+\cdots$
9450.2.a.bz	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+6q^{11}+2q^{13}+\cdots$
9450.2.a.ca	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}-5q^{13}+\cdots$
9450.2.a.cb	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}+4q^{13}+\cdots$
9450.2.a.cc	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}-6q^{13}+\cdots$
9450.2.a.cd	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}-q^{13}+\cdots$
9450.2.a.ce	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}-5q^{13}+\cdots$
9450.2.a.cf	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}+q^{13}+\cdots$
9450.2.a.cg	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}-5q^{13}+\cdots$
9450.2.a.ch	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+6q^{13}+\cdots$
9450.2.a.ci	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{11}-5q^{13}+\cdots$
9450.2.a.cj	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{11}+5q^{13}+\cdots$
9450.2.a.ck	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{13}-q^{14}+\cdots$
9450.2.a.cl	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{13}-q^{14}+\cdots$
9450.2.a.cm	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots$
9450.2.a.cn	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{13}-q^{14}+\cdots$
9450.2.a.co	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+7q^{13}-q^{14}+\cdots$
9450.2.a.cp	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}+3q^{13}+\cdots$
9450.2.a.cq	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}+5q^{13}+\cdots$
9450.2.a.cr	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}-5q^{13}+\cdots$
9450.2.a.cs	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}-q^{13}+\cdots$
9450.2.a.ct	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+q^{13}+\cdots$
9450.2.a.cu	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+4q^{13}+\cdots$
9450.2.a.cv	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+5q^{13}+\cdots$
9450.2.a.cw	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}-5q^{13}+\cdots$
9450.2.a.cx	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}+q^{13}+\cdots$
9450.2.a.cy	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}-2q^{13}+\cdots$
9450.2.a.cz	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}+q^{13}+\cdots$
9450.2.a.da	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}+2q^{13}+\cdots$
9450.2.a.db	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}-q^{13}+\cdots$
9450.2.a.dc	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}+q^{14}+\cdots$
9450.2.a.dd	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}+5q^{13}+\cdots$
9450.2.a.de	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}-5q^{13}+\cdots$
9450.2.a.df	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}-q^{13}+\cdots$
9450.2.a.dg	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}+q^{13}+\cdots$
9450.2.a.dh	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{11}-4q^{13}+\cdots$
9450.2.a.di	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}-3q^{13}+\cdots$
9450.2.a.dj	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}-3q^{13}+\cdots$
9450.2.a.dk	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}+3q^{13}+\cdots$
9450.2.a.dl	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-7q^{13}+q^{14}+\cdots$
9450.2.a.dm	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{13}+q^{14}+\cdots$
9450.2.a.dn	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots$
9450.2.a.do	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{13}+q^{14}+\cdots$
9450.2.a.dp	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}-5q^{13}+\cdots$
9450.2.a.dq	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}+5q^{13}+\cdots$
9450.2.a.dr	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}-6q^{13}+\cdots$
9450.2.a.ds	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+q^{14}+\cdots$
9450.2.a.dt	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+3q^{13}+\cdots$
9450.2.a.du	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+5q^{13}+\cdots$
9450.2.a.dv	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}-3q^{13}+\cdots$
9450.2.a.dw	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+q^{13}+\cdots$
9450.2.a.dx	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+6q^{13}+\cdots$
9450.2.a.dy	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}+5q^{13}+\cdots$
9450.2.a.dz	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+6q^{11}+5q^{13}+\cdots$
9450.2.a.ea	$2$	$75.459$	$\Q(\sqrt{6}) $	None	$-2$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots$
9450.2.a.eb	$2$	$75.459$	$\Q(\sqrt{3}) $	None	$-2$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(2+\cdots)q^{13}+\cdots$
9450.2.a.ec	$2$	$75.459$	$\Q(\sqrt{7}) $	None	$-2$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots$
9450.2.a.ed	$2$	$75.459$	$\Q(\sqrt{73}) $	None	$-2$	$0$	$0$	$-2$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.ee	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$-2$	$0$	$0$	$-2$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}+(-1+\cdots)q^{13}+\cdots$
9450.2.a.ef	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$-2$	$0$	$0$	$-2$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+(2+\beta )q^{11}+\cdots$
9450.2.a.eg	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$-2$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+(-2+\beta )q^{11}+\cdots$
9450.2.a.eh	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$-2$	$0$	$0$	$2$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+(1+\cdots)q^{13}+\cdots$
9450.2.a.ei	$2$	$75.459$	$\Q(\sqrt{3}) $	None	$-2$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.ej	$2$	$75.459$	$\Q(\sqrt{7}) $	None	$-2$	$0$	$0$	$2$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.ek	$2$	$75.459$	$\Q(\sqrt{6}) $	None	$-2$	$0$	$0$	$2$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+\beta q^{11}+(1+\cdots)q^{13}+\cdots$
9450.2.a.el	$2$	$75.459$	$\Q(\sqrt{97}) $	None	$-2$	$0$	$0$	$2$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+(1+\beta )q^{11}+\cdots$
9450.2.a.em	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$2$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+(-1+\cdots)q^{13}+\cdots$
9450.2.a.en	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$2$	$0$	$0$	$-2$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+(-2+\beta )q^{11}+\cdots$
9450.2.a.eo	$2$	$75.459$	$\Q(\sqrt{73}) $	None	$2$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.ep	$2$	$75.459$	$\Q(\sqrt{6}) $	None	$2$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots$
9450.2.a.eq	$2$	$75.459$	$\Q(\sqrt{7}) $	None	$2$	$0$	$0$	$-2$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots$
9450.2.a.er	$2$	$75.459$	$\Q(\sqrt{3}) $	None	$2$	$0$	$0$	$-2$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+\beta q^{11}+(2+\cdots)q^{13}+\cdots$
9450.2.a.es	$2$	$75.459$	$\Q(\sqrt{97}) $	None	$2$	$0$	$0$	$2$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+(-1-\beta )q^{11}+\cdots$
9450.2.a.et	$2$	$75.459$	$\Q(\sqrt{7}) $	None	$2$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.eu	$2$	$75.459$	$\Q(\sqrt{3}) $	None	$2$	$0$	$0$	$2$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.ev	$2$	$75.459$	$\Q(\sqrt{6}) $	None	$2$	$0$	$0$	$2$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+\beta q^{11}+(1+\cdots)q^{13}+\cdots$
9450.2.a.ew	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$2$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+(2+\beta )q^{11}+\cdots$
9450.2.a.ex	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$2$	$0$	$0$	$2$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+(1+\cdots)q^{13}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(9450))$ into lower level spaces

Hecke Characteristic Polynomials

$p$	$F_p(T)$
$2$	($ 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 $)($ 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} $)
$3$	1
$5$	1
$7$	($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 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 $)($ 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} $)
$11$	($ 1 + 6 T + 11 T^{2} $)($ 1 + 6 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 - T + 11 T^{2} $)($ 1 - T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 + 6 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 + 4 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 + T + 11 T^{2} $)($ 1 + T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 - T + 11 T^{2} $)($ 1 - T + 11 T^{2} $)($ 1 - T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 5 T + 11 T^{2} $)($ 1 - 5 T + 11 T^{2} $)($ 1 - 5 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 + 6 T + 11 T^{2} $)($ 1 + 6 T + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + T + 11 T^{2} $)($ 1 + T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 - T + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 - 5 T + 11 T^{2} $)($ 1 - 5 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 + 6 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 2 T + 11 T^{2} $)($ 1 + T + 11 T^{2} $)($ 1 + T + 11 T^{2} $)($ 1 + T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 - 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 - 2 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 - 5 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 + 16 T^{2} + 121 T^{4} $)($ 1 + 19 T^{2} + 121 T^{4} $)($ 1 - 6 T^{2} + 121 T^{4} $)($ 1 - T + 4 T^{2} - 11 T^{3} + 121 T^{4} $)($ ( 1 - 2 T + 11 T^{2} )^{2} $)($ 1 - 4 T + 16 T^{2} - 44 T^{3} + 121 T^{4} $)($ 1 + 4 T + 16 T^{2} + 44 T^{3} + 121 T^{4} $)($ ( 1 + 2 T + 11 T^{2} )^{2} $)($ 1 + 19 T^{2} + 121 T^{4} $)($ 1 - 6 T^{2} + 121 T^{4} $)($ 1 + 16 T^{2} + 121 T^{4} $)($ 1 - 3 T - 33 T^{3} + 121 T^{4} $)($ ( 1 + 2 T + 11 T^{2} )^{2} $)($ 1 + 4 T + 16 T^{2} + 44 T^{3} + 121 T^{4} $)($ 1 + T + 4 T^{2} + 11 T^{3} + 121 T^{4} $)($ 1 + 16 T^{2} + 121 T^{4} $)($ 1 - 6 T^{2} + 121 T^{4} $)($ 1 + 19 T^{2} + 121 T^{4} $)($ 1 + 3 T + 33 T^{3} + 121 T^{4} $)($ 1 - 6 T^{2} + 121 T^{4} $)($ 1 + 19 T^{2} + 121 T^{4} $)($ 1 + 16 T^{2} + 121 T^{4} $)($ 1 - 4 T + 16 T^{2} - 44 T^{3} + 121 T^{4} $)($ ( 1 - 2 T + 11 T^{2} )^{2} $)
$13$	($ 1 + 2 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 - 3 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 - 7 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - 6 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 3 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 - 6 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - 3 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 7 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 3 T + 13 T^{2} $)($ 1 + 3 T + 13 T^{2} $)($ 1 - 3 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - 6 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 - 7 T + 13 T^{2} $)($ 1 - 3 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 - 4 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 3 T + 13 T^{2} $)($ 1 + 3 T + 13 T^{2} $)($ 1 - 3 T + 13 T^{2} $)($ 1 + 7 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 + T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 5 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - 3 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 3 T + 13 T^{2} $)($ 1 - T + 13 T^{2} $)($ 1 - 6 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 2 T + 21 T^{2} + 26 T^{3} + 169 T^{4} $)($ 1 - 4 T + 18 T^{2} - 52 T^{3} + 169 T^{4} $)($ 1 - 4 T + 23 T^{2} - 52 T^{3} + 169 T^{4} $)($ 1 + 3 T + 10 T^{2} + 39 T^{3} + 169 T^{4} $)($ 1 + 2 T + 17 T^{2} + 26 T^{3} + 169 T^{4} $)($ 1 - 2 T + 17 T^{2} - 26 T^{3} + 169 T^{4} $)($ 1 + 2 T + 17 T^{2} + 26 T^{3} + 169 T^{4} $)($ 1 - 2 T + 17 T^{2} - 26 T^{3} + 169 T^{4} $)($ 1 + 4 T + 18 T^{2} + 52 T^{3} + 169 T^{4} $)($ 1 + 4 T + 23 T^{2} + 52 T^{3} + 169 T^{4} $)($ 1 - 2 T + 21 T^{2} - 26 T^{3} + 169 T^{4} $)($ ( 1 + T + 13 T^{2} )^{2} $)($ 1 + 2 T + 17 T^{2} + 26 T^{3} + 169 T^{4} $)($ 1 - 2 T + 17 T^{2} - 26 T^{3} + 169 T^{4} $)($ 1 + 3 T + 10 T^{2} + 39 T^{3} + 169 T^{4} $)($ 1 + 2 T + 21 T^{2} + 26 T^{3} + 169 T^{4} $)($ 1 - 4 T + 23 T^{2} - 52 T^{3} + 169 T^{4} $)($ 1 - 4 T + 18 T^{2} - 52 T^{3} + 169 T^{4} $)($ ( 1 + T + 13 T^{2} )^{2} $)($ 1 + 4 T + 23 T^{2} + 52 T^{3} + 169 T^{4} $)($ 1 + 4 T + 18 T^{2} + 52 T^{3} + 169 T^{4} $)($ 1 - 2 T + 21 T^{2} - 26 T^{3} + 169 T^{4} $)($ 1 + 2 T + 17 T^{2} + 26 T^{3} + 169 T^{4} $)($ 1 - 2 T + 17 T^{2} - 26 T^{3} + 169 T^{4} $)
$17$	($ 1 + 3 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 + 8 T + 17 T^{2} $)($ 1 - 7 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 + T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 5 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 - 8 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 + 5 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 - T + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 - 7 T + 17 T^{2} $)($ 1 - T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 5 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 - T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 - 8 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 + 8 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 - 7 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + T + 17 T^{2} $)($ 1 - 7 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 + 8 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 - 5 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 + 8 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 - 5 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 - T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 - 8 T + 17 T^{2} $)($ 1 + 7 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 + 7 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 - 8 T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 17 T^{2} $)($ 1 - T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 - 8 T + 17 T^{2} $)($ 1 + 7 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 + 8 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 + 4 T + 17 T^{2} $)($ 1 - 5 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 + T + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 + 7 T + 17 T^{2} $)($ 1 + T + 17 T^{2} $)($ 1 - 4 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ ( 1 + T + 17 T^{2} )^{2} $)($ ( 1 + 4 T + 17 T^{2} )^{2} $)($ ( 1 - T + 17 T^{2} )^{2} $)($ 1 - T + 16 T^{2} - 17 T^{3} + 289 T^{4} $)($ 1 + 2 T - 5 T^{2} + 34 T^{3} + 289 T^{4} $)($ ( 1 - 5 T + 17 T^{2} )^{2} $)($ ( 1 - 5 T + 17 T^{2} )^{2} $)($ 1 + 2 T - 5 T^{2} + 34 T^{3} + 289 T^{4} $)($ ( 1 + 4 T + 17 T^{2} )^{2} $)($ ( 1 - T + 17 T^{2} )^{2} $)($ ( 1 + T + 17 T^{2} )^{2} $)($ 1 - T + 10 T^{2} - 17 T^{3} + 289 T^{4} $)($ 1 - 2 T - 5 T^{2} - 34 T^{3} + 289 T^{4} $)($ ( 1 + 5 T + 17 T^{2} )^{2} $)($ 1 + T + 16 T^{2} + 17 T^{3} + 289 T^{4} $)($ ( 1 - T + 17 T^{2} )^{2} $)($ ( 1 + T + 17 T^{2} )^{2} $)($ ( 1 - 4 T + 17 T^{2} )^{2} $)($ 1 + T + 10 T^{2} + 17 T^{3} + 289 T^{4} $)($ ( 1 + T + 17 T^{2} )^{2} $)($ ( 1 - 4 T + 17 T^{2} )^{2} $)($ ( 1 - T + 17 T^{2} )^{2} $)($ ( 1 + 5 T + 17 T^{2} )^{2} $)($ 1 - 2 T - 5 T^{2} - 34 T^{3} + 289 T^{4} $)
$19$	($ 1 - 2 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 8 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 7 T + 19 T^{2} $)($ 1 - T + 19 T^{2} $)($ 1 - 8 T + 19 T^{2} $)($ 1 + 6 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 7 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 - 7 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 - 6 T + 19 T^{2} $)($ 1 - 6 T + 19 T^{2} $)($ 1 + 7 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 - 5 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + 6 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 - 5 T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 - 6 T + 19 T^{2} $)($ 1 - 6 T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 - 6 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 - 7 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 7 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 3 T + 19 T^{2} $)($ 1 + 6 T + 19 T^{2} $)($ 1 + 6 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 - T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 8 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 - 5 T + 19 T^{2} $)($ 1 + 7 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 - 6 T + 19 T^{2} $)($ 1 - 6 T + 19 T^{2} $)($ 1 - 7 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + 7 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 6 T + 19 T^{2} $)($ 1 - 8 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 7 T + 19 T^{2} $)($ 1 - T + 19 T^{2} $)($ 1 + 8 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 8 T + 19 T^{2} $)($ 1 - T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)($ 1 + 6 T + 19 T^{2} $)($ 1 + 3 T + 19 T^{2} $)($ 1 + 6 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 7 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 - 7 T + 19 T^{2} $)($ 1 - 6 T + 19 T^{2} $)($ 1 - 6 T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 - 6 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 - 5 T + 19 T^{2} $)($ 1 + 19 T^{2} $)($ 1 + 6 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + 4 T + 36 T^{2} + 76 T^{3} + 361 T^{4} $)($ 1 - 8 T + 51 T^{2} - 152 T^{3} + 361 T^{4} $)($ 1 + 2 T + 11 T^{2} + 38 T^{3} + 361 T^{4} $)($ ( 1 - 2 T + 19 T^{2} )^{2} $)($ ( 1 - 3 T + 19 T^{2} )^{2} $)($ 1 + 8 T + 44 T^{2} + 152 T^{3} + 361 T^{4} $)($ 1 + 8 T + 44 T^{2} + 152 T^{3} + 361 T^{4} $)($ ( 1 - 3 T + 19 T^{2} )^{2} $)($ 1 - 8 T + 51 T^{2} - 152 T^{3} + 361 T^{4} $)($ 1 + 2 T + 11 T^{2} + 38 T^{3} + 361 T^{4} $)($ 1 + 4 T + 36 T^{2} + 76 T^{3} + 361 T^{4} $)($ 1 - 7 T + 26 T^{2} - 133 T^{3} + 361 T^{4} $)($ ( 1 - 3 T + 19 T^{2} )^{2} $)($ 1 + 8 T + 44 T^{2} + 152 T^{3} + 361 T^{4} $)($ ( 1 - 2 T + 19 T^{2} )^{2} $)($ 1 + 4 T + 36 T^{2} + 76 T^{3} + 361 T^{4} $)($ 1 + 2 T + 11 T^{2} + 38 T^{3} + 361 T^{4} $)($ 1 - 8 T + 51 T^{2} - 152 T^{3} + 361 T^{4} $)($ 1 - 7 T + 26 T^{2} - 133 T^{3} + 361 T^{4} $)($ 1 + 2 T + 11 T^{2} + 38 T^{3} + 361 T^{4} $)($ 1 - 8 T + 51 T^{2} - 152 T^{3} + 361 T^{4} $)($ 1 + 4 T + 36 T^{2} + 76 T^{3} + 361 T^{4} $)($ 1 + 8 T + 44 T^{2} + 152 T^{3} + 361 T^{4} $)($ ( 1 - 3 T + 19 T^{2} )^{2} $)
$23$	($ 1 + 9 T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 + T + 23 T^{2} $)($ 1 + 9 T + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 - 7 T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 + T + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 - 9 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 5 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - T + 23 T^{2} $)($ 1 - T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 - 5 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 - 2 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 - 7 T + 23 T^{2} $)($ 1 + 9 T + 23 T^{2} $)($ 1 - T + 23 T^{2} $)($ 1 + T + 23 T^{2} $)($ 1 + 9 T + 23 T^{2} $)($ 1 + 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 - 8 T + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 5 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 9 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 - T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 + 7 T + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 - 8 T + 23 T^{2} $)($ 1 - T + 23 T^{2} $)($ 1 - 9 T + 23 T^{2} $)($ 1 - 9 T + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 - 9 T + 23 T^{2} $)($ 1 - 9 T + 23 T^{2} $)($ 1 + T + 23 T^{2} $)($ 1 - T + 23 T^{2} $)($ 1 - 8 T + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 + 7 T + 23 T^{2} $)($ 1 + 2 T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 4 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 6 T + 23 T^{2} $)($ 1 + 5 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 - 8 T + 23 T^{2} $)($ 1 + T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 + T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 - 2 T + 41 T^{2} - 46 T^{3} + 529 T^{4} $)($ 1 - 2 T + 35 T^{2} - 46 T^{3} + 529 T^{4} $)($ 1 - 2 T + 40 T^{2} - 46 T^{3} + 529 T^{4} $)($ 1 + T + 28 T^{2} + 23 T^{3} + 529 T^{4} $)($ 1 - 4 T + 40 T^{2} - 92 T^{3} + 529 T^{4} $)($ 1 - 6 T + 45 T^{2} - 138 T^{3} + 529 T^{4} $)($ 1 - 6 T + 45 T^{2} - 138 T^{3} + 529 T^{4} $)($ 1 - 4 T + 40 T^{2} - 92 T^{3} + 529 T^{4} $)($ 1 - 2 T + 35 T^{2} - 46 T^{3} + 529 T^{4} $)($ 1 - 2 T + 40 T^{2} - 46 T^{3} + 529 T^{4} $)($ 1 - 2 T + 41 T^{2} - 46 T^{3} + 529 T^{4} $)($ 1 + 3 T + 24 T^{2} + 69 T^{3} + 529 T^{4} $)($ 1 + 4 T + 40 T^{2} + 92 T^{3} + 529 T^{4} $)($ 1 + 6 T + 45 T^{2} + 138 T^{3} + 529 T^{4} $)($ 1 - T + 28 T^{2} - 23 T^{3} + 529 T^{4} $)($ 1 + 2 T + 41 T^{2} + 46 T^{3} + 529 T^{4} $)($ 1 + 2 T + 40 T^{2} + 46 T^{3} + 529 T^{4} $)($ 1 + 2 T + 35 T^{2} + 46 T^{3} + 529 T^{4} $)($ 1 - 3 T + 24 T^{2} - 69 T^{3} + 529 T^{4} $)($ 1 + 2 T + 40 T^{2} + 46 T^{3} + 529 T^{4} $)($ 1 + 2 T + 35 T^{2} + 46 T^{3} + 529 T^{4} $)($ 1 + 2 T + 41 T^{2} + 46 T^{3} + 529 T^{4} $)($ 1 + 6 T + 45 T^{2} + 138 T^{3} + 529 T^{4} $)($ 1 + 4 T + 40 T^{2} + 92 T^{3} + 529 T^{4} $)
$29$	($ 1 + 6 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 - 9 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 + 29 T^{2} $)($ 1 + 10 T + 29 T^{2} $)($ 1 - 9 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 + 7 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 5 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 - 9 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 + T + 29 T^{2} $)($ 1 - T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 3 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 + 3 T + 29 T^{2} $)($ 1 - 7 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 - 9 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 - T + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 5 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 - 4 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 - 9 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 - 9 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 - 7 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 + 5 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ 1 - 2 T + 29 T^{2} $)($ 1 + 10 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 - 5 T + 29 T^{2} $)($ 1 + T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 + 7 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 + 9 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 - 6 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 + 5 T + 29 T^{2} $)($ 1 + T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 - T + 29 T^{2} $)($ 1 - 9 T + 29 T^{2} $)($ 1 - 10 T + 77 T^{2} - 290 T^{3} + 841 T^{4} $)($ 1 - 4 T + 50 T^{2} - 116 T^{3} + 841 T^{4} $)($ 1 + 16 T + 115 T^{2} + 464 T^{3} + 841 T^{4} $)($ ( 1 - 3 T + 29 T^{2} )^{2} $)($ 1 - 10 T + 73 T^{2} - 290 T^{3} + 841 T^{4} $)($ 1 - 2 T + 49 T^{2} - 58 T^{3} + 841 T^{4} $)($ 1 + 2 T + 49 T^{2} + 58 T^{3} + 841 T^{4} $)($ 1 + 10 T + 73 T^{2} + 290 T^{3} + 841 T^{4} $)($ 1 + 4 T + 50 T^{2} + 116 T^{3} + 841 T^{4} $)($ 1 - 16 T + 115 T^{2} - 464 T^{3} + 841 T^{4} $)($ 1 + 10 T + 77 T^{2} + 290 T^{3} + 841 T^{4} $)($ 1 - 3 T + 36 T^{2} - 87 T^{3} + 841 T^{4} $)($ 1 + 10 T + 73 T^{2} + 290 T^{3} + 841 T^{4} $)($ 1 + 2 T + 49 T^{2} + 58 T^{3} + 841 T^{4} $)($ ( 1 + 3 T + 29 T^{2} )^{2} $)($ 1 + 10 T + 77 T^{2} + 290 T^{3} + 841 T^{4} $)($ 1 - 16 T + 115 T^{2} - 464 T^{3} + 841 T^{4} $)($ 1 + 4 T + 50 T^{2} + 116 T^{3} + 841 T^{4} $)($ 1 + 3 T + 36 T^{2} + 87 T^{3} + 841 T^{4} $)($ 1 + 16 T + 115 T^{2} + 464 T^{3} + 841 T^{4} $)($ 1 - 4 T + 50 T^{2} - 116 T^{3} + 841 T^{4} $)($ 1 - 10 T + 77 T^{2} - 290 T^{3} + 841 T^{4} $)($ 1 - 2 T + 49 T^{2} - 58 T^{3} + 841 T^{4} $)($ 1 - 10 T + 73 T^{2} - 290 T^{3} + 841 T^{4} $)
$31$	($ 1 + 4 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + 5 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 - 2 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 - 10 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 + 9 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 - 10 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 2 T + 31 T^{2} $)($ 1 + 7 T + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 5 T + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 + 9 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 - 10 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 2 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + 5 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 + 9 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 5 T + 31 T^{2} $)($ 1 - 3 T + 31 T^{2} $)($ 1 - 2 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 + 7 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 10 T + 31 T^{2} $)($ 1 + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 + 9 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 - 7 T + 31 T^{2} $)($ 1 - T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 - 2 T + 57 T^{2} - 62 T^{3} + 961 T^{4} $)($ 1 + 4 T + 63 T^{2} + 124 T^{3} + 961 T^{4} $)($ 1 + 4 T + 38 T^{2} + 124 T^{3} + 961 T^{4} $)($ 1 - 11 T^{2} + 961 T^{4} $)($ 1 + 22 T^{2} + 961 T^{4} $)($ 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} $)($ 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} $)($ 1 + 22 T^{2} + 961 T^{4} $)($ 1 + 4 T + 63 T^{2} + 124 T^{3} + 961 T^{4} $)($ 1 + 4 T + 38 T^{2} + 124 T^{3} + 961 T^{4} $)($ 1 - 2 T + 57 T^{2} - 62 T^{3} + 961 T^{4} $)($ 1 - 7 T + 50 T^{2} - 217 T^{3} + 961 T^{4} $)($ 1 + 22 T^{2} + 961 T^{4} $)($ 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} $)($ 1 - 11 T^{2} + 961 T^{4} $)($ 1 - 2 T + 57 T^{2} - 62 T^{3} + 961 T^{4} $)($ 1 + 4 T + 38 T^{2} + 124 T^{3} + 961 T^{4} $)($ 1 + 4 T + 63 T^{2} + 124 T^{3} + 961 T^{4} $)($ 1 - 7 T + 50 T^{2} - 217 T^{3} + 961 T^{4} $)($ 1 + 4 T + 38 T^{2} + 124 T^{3} + 961 T^{4} $)($ 1 + 4 T + 63 T^{2} + 124 T^{3} + 961 T^{4} $)($ 1 - 2 T + 57 T^{2} - 62 T^{3} + 961 T^{4} $)($ 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} $)($ 1 + 22 T^{2} + 961 T^{4} $)
$37$	($ 1 + 8 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 - 3 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 - 7 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 - 8 T + 37 T^{2} $)($ 1 + 7 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 7 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + 11 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + 5 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 - 7 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 + 10 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 7 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 3 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 + 5 T + 37 T^{2} $)($ 1 + 3 T + 37 T^{2} $)($ 1 - 8 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + 11 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 7 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 7 T + 37 T^{2} $)($ 1 - 8 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 - 7 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 - 3 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 8 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 - 8 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 + 5 T + 37 T^{2} $)($ 1 + 3 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 3 T + 37 T^{2} $)($ 1 - 7 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 - 7 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 + 10 T + 37 T^{2} $)($ 1 - T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + 5 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 - 4 T + 37 T^{2} $)($ 1 + T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 + 4 T + 37 T^{2} $)($ 1 + 8 T + 36 T^{2} + 296 T^{3} + 1369 T^{4} $)($ 1 - 4 T + 51 T^{2} - 148 T^{3} + 1369 T^{4} $)($ 1 - 14 T + 116 T^{2} - 518 T^{3} + 1369 T^{4} $)($ 1 + 9 T + 76 T^{2} + 333 T^{3} + 1369 T^{4} $)($ 1 - 4 T - 12 T^{2} - 148 T^{3} + 1369 T^{4} $)($ 1 - 12 T + 100 T^{2} - 444 T^{3} + 1369 T^{4} $)($ 1 + 12 T + 100 T^{2} + 444 T^{3} + 1369 T^{4} $)($ 1 + 4 T - 12 T^{2} + 148 T^{3} + 1369 T^{4} $)($ 1 + 4 T + 51 T^{2} + 148 T^{3} + 1369 T^{4} $)($ 1 + 14 T + 116 T^{2} + 518 T^{3} + 1369 T^{4} $)($ 1 - 8 T + 36 T^{2} - 296 T^{3} + 1369 T^{4} $)($ 1 + 2 T - 22 T^{2} + 74 T^{3} + 1369 T^{4} $)($ 1 - 4 T - 12 T^{2} - 148 T^{3} + 1369 T^{4} $)($ 1 - 12 T + 100 T^{2} - 444 T^{3} + 1369 T^{4} $)($ 1 + 9 T + 76 T^{2} + 333 T^{3} + 1369 T^{4} $)($ 1 + 8 T + 36 T^{2} + 296 T^{3} + 1369 T^{4} $)($ 1 - 14 T + 116 T^{2} - 518 T^{3} + 1369 T^{4} $)($ 1 - 4 T + 51 T^{2} - 148 T^{3} + 1369 T^{4} $)($ 1 + 2 T - 22 T^{2} + 74 T^{3} + 1369 T^{4} $)($ 1 + 14 T + 116 T^{2} + 518 T^{3} + 1369 T^{4} $)($ 1 + 4 T + 51 T^{2} + 148 T^{3} + 1369 T^{4} $)($ 1 - 8 T + 36 T^{2} - 296 T^{3} + 1369 T^{4} $)($ 1 + 12 T + 100 T^{2} + 444 T^{3} + 1369 T^{4} $)($ 1 + 4 T - 12 T^{2} + 148 T^{3} + 1369 T^{4} $)
$41$	($ 1 - 9 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 - 9 T + 41 T^{2} $)($ 1 + 9 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 - 6 T + 41 T^{2} $)($ 1 - 9 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 3 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - T + 41 T^{2} $)($ 1 - T + 41 T^{2} $)($ 1 + 3 T + 41 T^{2} $)($ 1 - 3 T + 41 T^{2} $)($ 1 - 7 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 + 3 T + 41 T^{2} $)($ 1 + 9 T + 41 T^{2} $)($ 1 - 3 T + 41 T^{2} $)($ 1 + 4 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 + 7 T + 41 T^{2} $)($ 1 + T + 41 T^{2} $)($ 1 - 5 T + 41 T^{2} $)($ 1 + 10 T + 41 T^{2} $)($ 1 + T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 3 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 9 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 - 11 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 8 T + 41 T^{2} $)($ 1 - 3 T + 41 T^{2} $)($ 1 - 9 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 9 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 9 T + 41 T^{2} $)($ 1 - 3 T + 41 T^{2} $)($ 1 - 9 T + 41 T^{2} $)($ 1 + 7 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 3 T + 41 T^{2} $)($ 1 + 3 T + 41 T^{2} $)($ 1 + T + 41 T^{2} $)($ 1 + T + 41 T^{2} $)($ 1 - 3 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 9 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 9 T + 41 T^{2} $)($ 1 - 9 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 9 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 - 9 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 - 9 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 9 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 + 3 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 + 11 T + 41 T^{2} $)($ 1 + 8 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 - 9 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 + 3 T + 41 T^{2} $)($ 1 - T + 41 T^{2} $)($ 1 + 5 T + 41 T^{2} $)($ 1 - 10 T + 41 T^{2} $)($ 1 - T + 41 T^{2} $)($ 1 + 6 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 7 T + 41 T^{2} $)($ 1 - 4 T + 41 T^{2} $)($ 1 + 3 T + 41 T^{2} $)($ 1 + 58 T^{2} + 1681 T^{4} $)($ 1 + 6 T + 43 T^{2} + 246 T^{3} + 1681 T^{4} $)($ 1 - 4 T + 58 T^{2} - 164 T^{3} + 1681 T^{4} $)($ 1 - 5 T + 70 T^{2} - 205 T^{3} + 1681 T^{4} $)($ ( 1 - 4 T + 41 T^{2} )^{2} $)($ 1 + 8 T + 58 T^{2} + 328 T^{3} + 1681 T^{4} $)($ 1 - 8 T + 58 T^{2} - 328 T^{3} + 1681 T^{4} $)($ ( 1 + 4 T + 41 T^{2} )^{2} $)($ 1 - 6 T + 43 T^{2} - 246 T^{3} + 1681 T^{4} $)($ 1 + 4 T + 58 T^{2} + 164 T^{3} + 1681 T^{4} $)($ 1 + 58 T^{2} + 1681 T^{4} $)($ 1 - 11 T + 88 T^{2} - 451 T^{3} + 1681 T^{4} $)($ ( 1 + 4 T + 41 T^{2} )^{2} $)($ 1 - 8 T + 58 T^{2} - 328 T^{3} + 1681 T^{4} $)($ 1 + 5 T + 70 T^{2} + 205 T^{3} + 1681 T^{4} $)($ 1 + 58 T^{2} + 1681 T^{4} $)($ 1 + 4 T + 58 T^{2} + 164 T^{3} + 1681 T^{4} $)($ 1 - 6 T + 43 T^{2} - 246 T^{3} + 1681 T^{4} $)($ 1 + 11 T + 88 T^{2} + 451 T^{3} + 1681 T^{4} $)($ 1 - 4 T + 58 T^{2} - 164 T^{3} + 1681 T^{4} $)($ 1 + 6 T + 43 T^{2} + 246 T^{3} + 1681 T^{4} $)($ 1 + 58 T^{2} + 1681 T^{4} $)($ 1 + 8 T + 58 T^{2} + 328 T^{3} + 1681 T^{4} $)($ ( 1 - 4 T + 41 T^{2} )^{2} $)
$43$	($ 1 - T + 43 T^{2} $)($ 1 - 7 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 13 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 + 5 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 + 9 T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 + 11 T + 43 T^{2} $)($ 1 + 6 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 7 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + 5 T + 43 T^{2} $)($ 1 + 11 T + 43 T^{2} $)($ 1 + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 + 7 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 - 6 T + 43 T^{2} $)($ 1 - 11 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 - 5 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 - 8 T + 43 T^{2} $)($ 1 - 5 T + 43 T^{2} $)($ 1 + 13 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 7 T + 43 T^{2} $)($ 1 + 11 T + 43 T^{2} $)($ 1 + 6 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 + 2 T + 43 T^{2} $)($ 1 + 9 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 + 5 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 13 T + 43 T^{2} $)($ 1 - T + 43 T^{2} $)($ 1 - 7 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 + 13 T + 43 T^{2} $)($ 1 - 10 T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 - 8 T + 43 T^{2} $)($ 1 - 5 T + 43 T^{2} $)($ 1 + 8 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 - 5 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 - 2 T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 - 6 T + 43 T^{2} $)($ 1 - 11 T + 43 T^{2} $)($ 1 + 7 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 - 4 T + 43 T^{2} $)($ 1 + 11 T + 43 T^{2} $)($ 1 + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 + 5 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 2 T + 63 T^{2} - 86 T^{3} + 1849 T^{4} $)($ 1 + 16 T + 138 T^{2} + 688 T^{3} + 1849 T^{4} $)($ 1 + 6 T + 88 T^{2} + 258 T^{3} + 1849 T^{4} $)($ 1 + 5 T + 74 T^{2} + 215 T^{3} + 1849 T^{4} $)($ 1 + 76 T^{2} + 1849 T^{4} $)($ ( 1 - 7 T + 43 T^{2} )^{2} $)($ ( 1 + 7 T + 43 T^{2} )^{2} $)($ 1 + 76 T^{2} + 1849 T^{4} $)($ 1 - 16 T + 138 T^{2} - 688 T^{3} + 1849 T^{4} $)($ 1 - 6 T + 88 T^{2} - 258 T^{3} + 1849 T^{4} $)($ 1 + 2 T + 63 T^{2} + 86 T^{3} + 1849 T^{4} $)($ ( 1 - 7 T + 43 T^{2} )^{2} $)($ 1 + 76 T^{2} + 1849 T^{4} $)($ ( 1 - 7 T + 43 T^{2} )^{2} $)($ 1 + 5 T + 74 T^{2} + 215 T^{3} + 1849 T^{4} $)($ 1 - 2 T + 63 T^{2} - 86 T^{3} + 1849 T^{4} $)($ 1 + 6 T + 88 T^{2} + 258 T^{3} + 1849 T^{4} $)($ 1 + 16 T + 138 T^{2} + 688 T^{3} + 1849 T^{4} $)($ ( 1 - 7 T + 43 T^{2} )^{2} $)($ 1 - 6 T + 88 T^{2} - 258 T^{3} + 1849 T^{4} $)($ 1 - 16 T + 138 T^{2} - 688 T^{3} + 1849 T^{4} $)($ 1 + 2 T + 63 T^{2} + 86 T^{3} + 1849 T^{4} $)($ ( 1 + 7 T + 43 T^{2} )^{2} $)($ 1 + 76 T^{2} + 1849 T^{4} $)
$47$	($ 1 - 6 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 9 T + 47 T^{2} $)($ 1 + 7 T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 - T + 47 T^{2} $)($ 1 - 3 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 - 13 T + 47 T^{2} $)($ 1 - 2 T + 47 T^{2} $)($ 1 - 7 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 - 9 T + 47 T^{2} $)($ 1 - 3 T + 47 T^{2} $)($ 1 - 7 T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 + T + 47 T^{2} $)($ 1 + T + 47 T^{2} $)($ 1 + 2 T + 47 T^{2} $)($ 1 + 2 T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 + 9 T + 47 T^{2} $)($ 1 - 13 T + 47 T^{2} $)($ 1 + 7 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 11 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 7 T + 47 T^{2} $)($ 1 - 13 T + 47 T^{2} $)($ 1 + 2 T + 47 T^{2} $)($ 1 - T + 47 T^{2} $)($ 1 - 10 T + 47 T^{2} $)($ 1 + 2 T + 47 T^{2} $)($ 1 + T + 47 T^{2} $)($ 1 + T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 - 7 T + 47 T^{2} $)($ 1 - 3 T + 47 T^{2} $)($ 1 - 9 T + 47 T^{2} $)($ 1 - T + 47 T^{2} $)($ 1 - 7 T + 47 T^{2} $)($ 1 - T + 47 T^{2} $)($ 1 - 3 T + 47 T^{2} $)($ 1 - 13 T + 47 T^{2} $)($ 1 - 3 T + 47 T^{2} $)($ 1 - T + 47 T^{2} $)($ 1 + 7 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 9 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 - 3 T + 47 T^{2} $)($ 1 + 13 T + 47 T^{2} $)($ 1 - 7 T + 47 T^{2} $)($ 1 - 3 T + 47 T^{2} $)($ 1 - 9 T + 47 T^{2} $)($ 1 - 2 T + 47 T^{2} $)($ 1 - 2 T + 47 T^{2} $)($ 1 - T + 47 T^{2} $)($ 1 - T + 47 T^{2} $)($ 1 + 9 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 + 7 T + 47 T^{2} $)($ 1 - 3 T + 47 T^{2} $)($ 1 + 7 T + 47 T^{2} $)($ 1 + 2 T + 47 T^{2} $)($ 1 - 3 T + 47 T^{2} $)($ 1 + T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 13 T + 47 T^{2} $)($ 1 - 9 T + 47 T^{2} $)($ 1 - 7 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 7 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 - 9 T + 47 T^{2} $)($ 1 + 13 T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 + T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 + 7 T + 47 T^{2} $)($ 1 + T + 47 T^{2} $)($ 1 + T + 47 T^{2} $)($ 1 - 3 T + 47 T^{2} $)($ 1 + 7 T + 47 T^{2} $)($ 1 + 3 T + 47 T^{2} $)($ 1 + 9 T + 47 T^{2} $)($ 1 - T + 47 T^{2} $)($ 1 - T + 47 T^{2} $)($ 1 - 2 T + 47 T^{2} $)($ 1 + T + 47 T^{2} $)($ 1 + 10 T + 47 T^{2} $)($ 1 - 2 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 7 T + 47 T^{2} $)($ 1 + 13 T + 47 T^{2} $)($ 1 - 11 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 4 T + 2 T^{2} + 188 T^{3} + 2209 T^{4} $)($ 1 + 16 T + 146 T^{2} + 752 T^{3} + 2209 T^{4} $)($ 1 - 4 T + 91 T^{2} - 188 T^{3} + 2209 T^{4} $)($ 1 - 8 T + 37 T^{2} - 376 T^{3} + 2209 T^{4} $)($ 1 - 2 T + 5 T^{2} - 94 T^{3} + 2209 T^{4} $)($ ( 1 + 2 T + 47 T^{2} )^{2} $)($ ( 1 + 2 T + 47 T^{2} )^{2} $)($ 1 - 2 T + 5 T^{2} - 94 T^{3} + 2209 T^{4} $)($ 1 + 16 T + 146 T^{2} + 752 T^{3} + 2209 T^{4} $)($ 1 - 4 T + 91 T^{2} - 188 T^{3} + 2209 T^{4} $)($ 1 + 4 T + 2 T^{2} + 188 T^{3} + 2209 T^{4} $)($ 1 + 11 T + 100 T^{2} + 517 T^{3} + 2209 T^{4} $)($ 1 + 2 T + 5 T^{2} + 94 T^{3} + 2209 T^{4} $)($ ( 1 - 2 T + 47 T^{2} )^{2} $)($ 1 + 8 T + 37 T^{2} + 376 T^{3} + 2209 T^{4} $)($ 1 - 4 T + 2 T^{2} - 188 T^{3} + 2209 T^{4} $)($ 1 + 4 T + 91 T^{2} + 188 T^{3} + 2209 T^{4} $)($ 1 - 16 T + 146 T^{2} - 752 T^{3} + 2209 T^{4} $)($ 1 - 11 T + 100 T^{2} - 517 T^{3} + 2209 T^{4} $)($ 1 + 4 T + 91 T^{2} + 188 T^{3} + 2209 T^{4} $)($ 1 - 16 T + 146 T^{2} - 752 T^{3} + 2209 T^{4} $)($ 1 - 4 T + 2 T^{2} - 188 T^{3} + 2209 T^{4} $)($ ( 1 - 2 T + 47 T^{2} )^{2} $)($ 1 + 2 T + 5 T^{2} + 94 T^{3} + 2209 T^{4} $)
$53$	($ 1 + 6 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 + 8 T + 53 T^{2} $)($ 1 + 4 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - 2 T + 53 T^{2} $)($ 1 + 3 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 + T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 13 T + 53 T^{2} $)($ 1 - 2 T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 + 2 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 - 2 T + 53 T^{2} $)($ 1 + T + 53 T^{2} $)($ 1 - 13 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 + T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 + T + 53 T^{2} $)($ 1 - 2 T + 53 T^{2} $)($ 1 - 2 T + 53 T^{2} $)($ 1 + 2 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 + 4 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 + 8 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 + 3 T + 53 T^{2} $)($ 1 + 13 T + 53 T^{2} $)($ 1 + 2 T + 53 T^{2} $)($ 1 - T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 3 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 + 2 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 + 3 T + 53 T^{2} $)($ 1 - 8 T + 53 T^{2} $)($ 1 - 4 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 + 3 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - 4 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 - 8 T + 53 T^{2} $)($ 1 + 3 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 - 2 T + 53 T^{2} $)($ 1 + 2 T + 53 T^{2} $)($ 1 - T + 53 T^{2} $)($ 1 + 2 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 9 T + 53 T^{2} $)($ 1 + 3 T + 53 T^{2} $)($ 1 - 6 T + 53 T^{2} $)($ 1 - T + 53 T^{2} $)($ 1 + 2 T + 53 T^{2} $)($ 1 + 2 T + 53 T^{2} $)($ 1 - T + 53 T^{2} $)($ 1 + 13 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 + 9 T + 53 T^{2} $)($ 1 - 6 T + 109 T^{2} - 318 T^{3} + 2809 T^{4} $)($ 1 - 86 T^{2} + 2809 T^{4} $)($ 1 + 99 T^{2} + 2809 T^{4} $)($ ( 1 - 6 T + 53 T^{2} )^{2} $)($ 1 + 6 T + 105 T^{2} + 318 T^{3} + 2809 T^{4} $)($ 1 + 6 T + 25 T^{2} + 318 T^{3} + 2809 T^{4} $)($ 1 + 6 T + 25 T^{2} + 318 T^{3} + 2809 T^{4} $)($ 1 + 6 T + 105 T^{2} + 318 T^{3} + 2809 T^{4} $)($ 1 - 86 T^{2} + 2809 T^{4} $)($ 1 + 99 T^{2} + 2809 T^{4} $)($ 1 - 6 T + 109 T^{2} - 318 T^{3} + 2809 T^{4} $)($ ( 1 + 5 T + 53 T^{2} )^{2} $)($ 1 - 6 T + 105 T^{2} - 318 T^{3} + 2809 T^{4} $)($ 1 - 6 T + 25 T^{2} - 318 T^{3} + 2809 T^{4} $)($ ( 1 + 6 T + 53 T^{2} )^{2} $)($ 1 + 6 T + 109 T^{2} + 318 T^{3} + 2809 T^{4} $)($ 1 + 99 T^{2} + 2809 T^{4} $)($ 1 - 86 T^{2} + 2809 T^{4} $)($ ( 1 - 5 T + 53 T^{2} )^{2} $)($ 1 + 99 T^{2} + 2809 T^{4} $)($ 1 - 86 T^{2} + 2809 T^{4} $)($ 1 + 6 T + 109 T^{2} + 318 T^{3} + 2809 T^{4} $)($ 1 - 6 T + 25 T^{2} - 318 T^{3} + 2809 T^{4} $)($ 1 - 6 T + 105 T^{2} - 318 T^{3} + 2809 T^{4} $)
$59$	($ 1 + 15 T + 59 T^{2} $)($ 1 - 9 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 - 14 T + 59 T^{2} $)($ 1 - T + 59 T^{2} $)($ 1 + 13 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 + T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 + 2 T + 59 T^{2} $)($ 1 - 13 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 7 T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 - 5 T + 59 T^{2} $)($ 1 - 10 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 5 T + 59 T^{2} $)($ 1 + 10 T + 59 T^{2} $)($ 1 + 5 T + 59 T^{2} $)($ 1 - 7 T + 59 T^{2} $)($ 1 - 7 T + 59 T^{2} $)($ 1 + 5 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 13 T + 59 T^{2} $)($ 1 - 2 T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 - T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 - 10 T + 59 T^{2} $)($ 1 - 13 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 + 14 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 14 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 - 15 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 + 5 T + 59 T^{2} $)($ 1 + 10 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 - 7 T + 59 T^{2} $)($ 1 - 2 T + 59 T^{2} $)($ 1 + 13 T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 - T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 - 13 T + 59 T^{2} $)($ 1 + T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 + 14 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 - 15 T + 59 T^{2} $)($ 1 + 9 T + 59 T^{2} $)($ 1 + 15 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 - 14 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 - 14 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 + 13 T + 59 T^{2} $)($ 1 + 10 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 + T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 - 13 T + 59 T^{2} $)($ 1 + 2 T + 59 T^{2} $)($ 1 + 7 T + 59 T^{2} $)($ 1 + 7 T + 59 T^{2} $)($ 1 - 5 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 - 5 T + 59 T^{2} $)($ 1 - 10 T + 59 T^{2} $)($ 1 - 5 T + 59 T^{2} $)($ 1 - 4 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 - 10 T + 119 T^{2} - 590 T^{3} + 3481 T^{4} $)($ 1 - 4 T + 74 T^{2} - 236 T^{3} + 3481 T^{4} $)($ 1 + 16 T + 154 T^{2} + 944 T^{3} + 3481 T^{4} $)($ 1 + 5 T + 106 T^{2} + 295 T^{3} + 3481 T^{4} $)($ 1 - 12 T + 114 T^{2} - 708 T^{3} + 3481 T^{4} $)($ ( 1 + 7 T + 59 T^{2} )^{2} $)($ ( 1 - 7 T + 59 T^{2} )^{2} $)($ 1 + 12 T + 114 T^{2} + 708 T^{3} + 3481 T^{4} $)($ 1 + 4 T + 74 T^{2} + 236 T^{3} + 3481 T^{4} $)($ 1 - 16 T + 154 T^{2} - 944 T^{3} + 3481 T^{4} $)($ 1 + 10 T + 119 T^{2} + 590 T^{3} + 3481 T^{4} $)($ 1 - 5 T + 100 T^{2} - 295 T^{3} + 3481 T^{4} $)($ 1 + 12 T + 114 T^{2} + 708 T^{3} + 3481 T^{4} $)($ ( 1 - 7 T + 59 T^{2} )^{2} $)($ 1 - 5 T + 106 T^{2} - 295 T^{3} + 3481 T^{4} $)($ 1 + 10 T + 119 T^{2} + 590 T^{3} + 3481 T^{4} $)($ 1 - 16 T + 154 T^{2} - 944 T^{3} + 3481 T^{4} $)($ 1 + 4 T + 74 T^{2} + 236 T^{3} + 3481 T^{4} $)($ 1 + 5 T + 100 T^{2} + 295 T^{3} + 3481 T^{4} $)($ 1 + 16 T + 154 T^{2} + 944 T^{3} + 3481 T^{4} $)($ 1 - 4 T + 74 T^{2} - 236 T^{3} + 3481 T^{4} $)($ 1 - 10 T + 119 T^{2} - 590 T^{3} + 3481 T^{4} $)($ ( 1 + 7 T + 59 T^{2} )^{2} $)($ 1 - 12 T + 114 T^{2} - 708 T^{3} + 3481 T^{4} $)
$61$	($ 1 + T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 5 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 + 12 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 11 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 - 5 T + 61 T^{2} $)($ 1 + T + 61 T^{2} $)($ 1 - 3 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 + 9 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 + 4 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 + T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 - 7 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 9 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 - 3 T + 61 T^{2} $)($ 1 + T + 61 T^{2} $)($ 1 - 5 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 + 11 T + 61 T^{2} $)($ 1 + 8 T + 61 T^{2} $)($ 1 - 5 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 + 12 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 + 61 T^{2} $)($ 1 - 5 T + 61 T^{2} $)($ 1 + T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 + T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 + 4 T + 61 T^{2} $)($ 1 + 9 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 - 5 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 + T + 61 T^{2} $)($ 1 - 3 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 + 11 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 + 12 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 - 5 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 + T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 + T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 + 61 T^{2} $)($ 1 - 5 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 + 12 T + 61 T^{2} $)($ 1 - 5 T + 61 T^{2} $)($ 1 + 11 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)($ 1 + 8 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 - 3 T + 61 T^{2} $)($ 1 + T + 61 T^{2} $)($ 1 - 5 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 - 7 T + 61 T^{2} $)($ 1 - 10 T + 61 T^{2} $)($ 1 + 9 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 - 13 T + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 + 61 T^{2} $)($ 1 + 7 T + 61 T^{2} $)($ 1 - 12 T + 134 T^{2} - 732 T^{3} + 3721 T^{4} $)($ 1 - 70 T^{2} + 3721 T^{4} $)($ 1 + 115 T^{2} + 3721 T^{4} $)($ 1 + 3 T + 106 T^{2} + 183 T^{3} + 3721 T^{4} $)($ 1 + 14 T + 161 T^{2} + 854 T^{3} + 3721 T^{4} $)($ 1 + 4 T + 86 T^{2} + 244 T^{3} + 3721 T^{4} $)($ 1 + 4 T + 86 T^{2} + 244 T^{3} + 3721 T^{4} $)($ 1 + 14 T + 161 T^{2} + 854 T^{3} + 3721 T^{4} $)($ 1 - 70 T^{2} + 3721 T^{4} $)($ 1 + 115 T^{2} + 3721 T^{4} $)($ 1 - 12 T + 134 T^{2} - 732 T^{3} + 3721 T^{4} $)($ 1 - 2 T + 26 T^{2} - 122 T^{3} + 3721 T^{4} $)($ 1 + 14 T + 161 T^{2} + 854 T^{3} + 3721 T^{4} $)($ 1 + 4 T + 86 T^{2} + 244 T^{3} + 3721 T^{4} $)($ 1 + 3 T + 106 T^{2} + 183 T^{3} + 3721 T^{4} $)($ 1 - 12 T + 134 T^{2} - 732 T^{3} + 3721 T^{4} $)($ 1 + 115 T^{2} + 3721 T^{4} $)($ 1 - 70 T^{2} + 3721 T^{4} $)($ 1 - 2 T + 26 T^{2} - 122 T^{3} + 3721 T^{4} $)($ 1 + 115 T^{2} + 3721 T^{4} $)($ 1 - 70 T^{2} + 3721 T^{4} $)($ 1 - 12 T + 134 T^{2} - 732 T^{3} + 3721 T^{4} $)($ 1 + 4 T + 86 T^{2} + 244 T^{3} + 3721 T^{4} $)($ 1 + 14 T + 161 T^{2} + 854 T^{3} + 3721 T^{4} $)
$67$	($ 1 - 7 T + 67 T^{2} $)($ 1 + 5 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 11 T + 67 T^{2} $)($ 1 - 3 T + 67 T^{2} $)($ 1 + 67 T^{2} $)($ 1 - 13 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 15 T + 67 T^{2} $)($ 1 + 67 T^{2} $)($ 1 - 9 T + 67 T^{2} $)($ 1 - 9 T + 67 T^{2} $)($ 1 - 13 T + 67 T^{2} $)($ 1 + 11 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 6 T + 67 T^{2} $)($ 1 + 5 T + 67 T^{2} $)($ 1 + 14 T + 67 T^{2} $)($ 1 - 5 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)($ 1 + 7 T + 67 T^{2} $)($ 1 + 6 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 9 T + 67 T^{2} $)($ 1 + 6 T + 67 T^{2} $)($ 1 - 3 T + 67 T^{2} $)($ 1 + 9 T + 67 T^{2} $)($ 1 + 67 T^{2} $)($ 1 - 15 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 - 3 T + 67 T^{2} $)($ 1 + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 + 6 T + 67 T^{2} $)($ 1 - 11 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 + 7 T + 67 T^{2} $)($ 1 + 5 T + 67 T^{2} $)($ 1 + 14 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 6 T + 67 T^{2} $)($ 1 - 13 T + 67 T^{2} $)($ 1 + 11 T + 67 T^{2} $)($ 1 - 9 T + 67 T^{2} $)($ 1 - 9 T + 67 T^{2} $)($ 1 + 15 T + 67 T^{2} $)($ 1 + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 - 13 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 67 T^{2} $)($ 1 - 3 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 11 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 - 7 T + 67 T^{2} $)($ 1 + 5 T + 67 T^{2} $)($ 1 + 7 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 - 11 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 + 6 T + 67 T^{2} $)($ 1 + 67 T^{2} $)($ 1 - 3 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 - 8 T + 67 T^{2} $)($ 1 + 67 T^{2} $)($ 1 - 15 T + 67 T^{2} $)($ 1 + 9 T + 67 T^{2} $)($ 1 + 6 T + 67 T^{2} $)($ 1 - 3 T + 67 T^{2} $)($ 1 + 9 T + 67 T^{2} $)($ 1 + 7 T + 67 T^{2} $)($ 1 + 6 T + 67 T^{2} $)($ 1 - 4 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)($ 1 - 5 T + 67 T^{2} $)($ ( 1 + 5 T + 67 T^{2} )^{2} $)($ 1 + 4 T + 30 T^{2} + 268 T^{3} + 4489 T^{4} $)($ 1 - 6 T + 80 T^{2} - 402 T^{3} + 4489 T^{4} $)($ 1 + 2 T + 62 T^{2} + 134 T^{3} + 4489 T^{4} $)($ 1 + 12 T + 80 T^{2} + 804 T^{3} + 4489 T^{4} $)($ 1 - 18 T + 175 T^{2} - 1206 T^{3} + 4489 T^{4} $)($ 1 + 18 T + 175 T^{2} + 1206 T^{3} + 4489 T^{4} $)($ 1 - 12 T + 80 T^{2} - 804 T^{3} + 4489 T^{4} $)($ 1 - 4 T + 30 T^{2} - 268 T^{3} + 4489 T^{4} $)($ 1 + 6 T + 80 T^{2} + 402 T^{3} + 4489 T^{4} $)($ ( 1 - 5 T + 67 T^{2} )^{2} $)($ ( 1 - 3 T + 67 T^{2} )^{2} $)($ 1 + 12 T + 80 T^{2} + 804 T^{3} + 4489 T^{4} $)($ 1 - 18 T + 175 T^{2} - 1206 T^{3} + 4489 T^{4} $)($ 1 + 2 T + 62 T^{2} + 134 T^{3} + 4489 T^{4} $)($ ( 1 + 5 T + 67 T^{2} )^{2} $)($ 1 - 6 T + 80 T^{2} - 402 T^{3} + 4489 T^{4} $)($ 1 + 4 T + 30 T^{2} + 268 T^{3} + 4489 T^{4} $)($ ( 1 - 3 T + 67 T^{2} )^{2} $)($ 1 + 6 T + 80 T^{2} + 402 T^{3} + 4489 T^{4} $)($ 1 - 4 T + 30 T^{2} - 268 T^{3} + 4489 T^{4} $)($ ( 1 - 5 T + 67 T^{2} )^{2} $)($ 1 + 18 T + 175 T^{2} + 1206 T^{3} + 4489 T^{4} $)($ 1 - 12 T + 80 T^{2} - 804 T^{3} + 4489 T^{4} $)
$71$	($ 1 + 3 T + 71 T^{2} $)($ 1 + 15 T + 71 T^{2} $)($ 1 + T + 71 T^{2} $)($ 1 - 10 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 3 T + 71 T^{2} $)($ 1 + 9 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 5 T + 71 T^{2} $)($ 1 - 13 T + 71 T^{2} $)($ 1 - 9 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 3 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 - 16 T + 71 T^{2} $)($ 1 - 11 T + 71 T^{2} $)($ 1 + 15 T + 71 T^{2} $)($ 1 - 7 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 3 T + 71 T^{2} $)($ 1 - 8 T + 71 T^{2} $)($ 1 + 9 T + 71 T^{2} $)($ 1 - 9 T + 71 T^{2} $)($ 1 - 9 T + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 + 7 T + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 + 3 T + 71 T^{2} $)($ 1 + 7 T + 71 T^{2} $)($ 1 + 13 T + 71 T^{2} $)($ 1 - 5 T + 71 T^{2} $)($ 1 - 15 T + 71 T^{2} $)($ 1 + 11 T + 71 T^{2} $)($ 1 + 16 T + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 + 3 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 - 8 T + 71 T^{2} $)($ 1 + 13 T + 71 T^{2} $)($ 1 - 8 T + 71 T^{2} $)($ 1 + 5 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 3 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 + 13 T + 71 T^{2} $)($ 1 - T + 71 T^{2} $)($ 1 - 3 T + 71 T^{2} $)($ 1 - 9 T + 71 T^{2} $)($ 1 + 9 T + 71 T^{2} $)($ 1 + 3 T + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - 15 T + 71 T^{2} $)($ 1 + 7 T + 71 T^{2} $)($ 1 + 16 T + 71 T^{2} $)($ 1 + 11 T + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 + 9 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 3 T + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 + 13 T + 71 T^{2} $)($ 1 + 5 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 - 3 T + 71 T^{2} $)($ 1 - 9 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 - T + 71 T^{2} $)($ 1 + 10 T + 71 T^{2} $)($ 1 - 3 T + 71 T^{2} $)($ 1 - 15 T + 71 T^{2} $)($ 1 + 3 T + 71 T^{2} $)($ 1 - 10 T + 71 T^{2} $)($ 1 - 13 T + 71 T^{2} $)($ 1 + T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 3 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 - 5 T + 71 T^{2} $)($ 1 - 13 T + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 + 8 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 - 3 T + 71 T^{2} $)($ 1 + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 - 11 T + 71 T^{2} $)($ 1 - 16 T + 71 T^{2} $)($ 1 - 7 T + 71 T^{2} $)($ 1 - 13 T + 71 T^{2} $)($ 1 + 5 T + 71 T^{2} $)($ 1 + 15 T + 71 T^{2} $)($ 1 - 7 T + 71 T^{2} $)($ 1 - 8 T + 71 T^{2} $)($ 1 - 3 T + 71 T^{2} $)($ 1 + 12 T + 71 T^{2} $)($ 1 + 9 T + 71 T^{2} $)($ 1 + 6 T + 145 T^{2} + 426 T^{3} + 5041 T^{4} $)($ 1 + 12 T + 175 T^{2} + 852 T^{3} + 5041 T^{4} $)($ 1 + 12 T + 150 T^{2} + 852 T^{3} + 5041 T^{4} $)($ 1 - 5 T + 130 T^{2} - 355 T^{3} + 5041 T^{4} $)($ 1 + 8 T + 118 T^{2} + 568 T^{3} + 5041 T^{4} $)($ 1 + 6 T + 61 T^{2} + 426 T^{3} + 5041 T^{4} $)($ 1 - 6 T + 61 T^{2} - 426 T^{3} + 5041 T^{4} $)($ 1 - 8 T + 118 T^{2} - 568 T^{3} + 5041 T^{4} $)($ 1 - 12 T + 175 T^{2} - 852 T^{3} + 5041 T^{4} $)($ 1 - 12 T + 150 T^{2} - 852 T^{3} + 5041 T^{4} $)($ 1 - 6 T + 145 T^{2} - 426 T^{3} + 5041 T^{4} $)($ 1 - T + 118 T^{2} - 71 T^{3} + 5041 T^{4} $)($ 1 - 8 T + 118 T^{2} - 568 T^{3} + 5041 T^{4} $)($ 1 - 6 T + 61 T^{2} - 426 T^{3} + 5041 T^{4} $)($ 1 + 5 T + 130 T^{2} + 355 T^{3} + 5041 T^{4} $)($ 1 - 6 T + 145 T^{2} - 426 T^{3} + 5041 T^{4} $)($ 1 - 12 T + 150 T^{2} - 852 T^{3} + 5041 T^{4} $)($ 1 - 12 T + 175 T^{2} - 852 T^{3} + 5041 T^{4} $)($ 1 + T + 118 T^{2} + 71 T^{3} + 5041 T^{4} $)($ 1 + 12 T + 150 T^{2} + 852 T^{3} + 5041 T^{4} $)($ 1 + 12 T + 175 T^{2} + 852 T^{3} + 5041 T^{4} $)($ 1 + 6 T + 145 T^{2} + 426 T^{3} + 5041 T^{4} $)($ 1 + 6 T + 61 T^{2} + 426 T^{3} + 5041 T^{4} $)($ 1 + 8 T + 118 T^{2} + 568 T^{3} + 5041 T^{4} $)
$73$	($ 1 + 14 T + 73 T^{2} $)($ 1 + 14 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 14 T + 73 T^{2} $)($ 1 - 16 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 7 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 14 T + 73 T^{2} $)($ 1 - 13 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 - 12 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 - 7 T + 73 T^{2} $)($ 1 - T + 73 T^{2} $)($ 1 - 7 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 4 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 + 4 T + 73 T^{2} $)($ 1 - 12 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 7 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 + 5 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 + 12 T + 73 T^{2} $)($ 1 + 14 T + 73 T^{2} $)($ 1 - 11 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 13 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 8 T + 73 T^{2} $)($ 1 + 7 T + 73 T^{2} $)($ 1 + 7 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 - 4 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 - 7 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 7 T + 73 T^{2} $)($ 1 - T + 73 T^{2} $)($ 1 - 12 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 14 T + 73 T^{2} $)($ 1 - 13 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 16 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 - 7 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 14 T + 73 T^{2} $)($ 1 + 14 T + 73 T^{2} $)($ 1 + 14 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 7 T + 73 T^{2} $)($ 1 + 10 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 7 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 11 T + 73 T^{2} $)($ 1 + 8 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 13 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 14 T + 73 T^{2} $)($ 1 - 11 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 + 5 T + 73 T^{2} $)($ 1 - 10 T + 73 T^{2} $)($ 1 + 12 T + 73 T^{2} $)($ 1 - 14 T + 73 T^{2} $)($ 1 + 2 T + 73 T^{2} $)($ 1 + 7 T + 73 T^{2} $)($ 1 - 12 T + 73 T^{2} $)($ 1 + 4 T + 73 T^{2} $)($ 1 + 4 T + 54 T^{2} + 292 T^{3} + 5329 T^{4} $)($ 1 - 20 T + 198 T^{2} - 1460 T^{3} + 5329 T^{4} $)($ 1 + 118 T^{2} + 5329 T^{4} $)($ 1 + 21 T + 238 T^{2} + 1533 T^{3} + 5329 T^{4} $)($ 1 + 4 T + 110 T^{2} + 292 T^{3} + 5329 T^{4} $)($ ( 1 - 10 T + 73 T^{2} )^{2} $)($ ( 1 + 10 T + 73 T^{2} )^{2} $)($ 1 - 4 T + 110 T^{2} - 292 T^{3} + 5329 T^{4} $)($ 1 + 20 T + 198 T^{2} + 1460 T^{3} + 5329 T^{4} $)($ 1 + 118 T^{2} + 5329 T^{4} $)($ 1 - 4 T + 54 T^{2} - 292 T^{3} + 5329 T^{4} $)($ 1 - 5 T + 128 T^{2} - 365 T^{3} + 5329 T^{4} $)($ 1 + 4 T + 110 T^{2} + 292 T^{3} + 5329 T^{4} $)($ ( 1 - 10 T + 73 T^{2} )^{2} $)($ 1 + 21 T + 238 T^{2} + 1533 T^{3} + 5329 T^{4} $)($ 1 + 4 T + 54 T^{2} + 292 T^{3} + 5329 T^{4} $)($ 1 + 118 T^{2} + 5329 T^{4} $)($ 1 - 20 T + 198 T^{2} - 1460 T^{3} + 5329 T^{4} $)($ 1 - 5 T + 128 T^{2} - 365 T^{3} + 5329 T^{4} $)($ 1 + 118 T^{2} + 5329 T^{4} $)($ 1 + 20 T + 198 T^{2} + 1460 T^{3} + 5329 T^{4} $)($ 1 - 4 T + 54 T^{2} - 292 T^{3} + 5329 T^{4} $)($ ( 1 + 10 T + 73 T^{2} )^{2} $)($ 1 - 4 T + 110 T^{2} - 292 T^{3} + 5329 T^{4} $)
$79$	($ 1 - 14 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 + 11 T + 79 T^{2} $)($ 1 - 17 T + 79 T^{2} $)($ 1 - 5 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 + 12 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 - 11 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 + 16 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 + 4 T + 79 T^{2} $)($ 1 - 12 T + 79 T^{2} $)($ 1 + 3 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 - T + 79 T^{2} $)($ 1 + 6 T + 79 T^{2} $)($ 1 + 3 T + 79 T^{2} $)($ 1 - 12 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 + 16 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 - 11 T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 - T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 - 5 T + 79 T^{2} $)($ 1 + 11 T + 79 T^{2} $)($ 1 - 6 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 - 14 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 - 12 T + 79 T^{2} $)($ 1 + 3 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 + 4 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 + 79 T^{2} $)($ 1 - 11 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 + 16 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + 12 T + 79 T^{2} $)($ 1 - 17 T + 79 T^{2} $)($ 1 - 5 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 + 11 T + 79 T^{2} $)($ 1 - 14 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 - 14 T + 79 T^{2} $)($ 1 + 11 T + 79 T^{2} $)($ 1 - 6 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 - 5 T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 - T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 + 16 T + 79 T^{2} $)($ 1 + T + 79 T^{2} $)($ 1 - 11 T + 79 T^{2} $)($ 1 + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 - 4 T + 79 T^{2} $)($ 1 - 10 T + 79 T^{2} $)($ 1 + 6 T + 79 T^{2} $)($ 1 + 3 T + 79 T^{2} $)($ 1 - 12 T + 79 T^{2} $)($ 1 - T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 + 8 T + 168 T^{2} + 632 T^{3} + 6241 T^{4} $)($ 1 - 4 T + 114 T^{2} - 316 T^{3} + 6241 T^{4} $)($ 1 + 16 T + 159 T^{2} + 1264 T^{3} + 6241 T^{4} $)($ 1 - 5 T + 146 T^{2} - 395 T^{3} + 6241 T^{4} $)($ 1 + 10 T + 93 T^{2} + 790 T^{3} + 6241 T^{4} $)($ 1 - 20 T + 248 T^{2} - 1580 T^{3} + 6241 T^{4} $)($ 1 - 20 T + 248 T^{2} - 1580 T^{3} + 6241 T^{4} $)($ 1 + 10 T + 93 T^{2} + 790 T^{3} + 6241 T^{4} $)($ 1 - 4 T + 114 T^{2} - 316 T^{3} + 6241 T^{4} $)($ 1 + 16 T + 159 T^{2} + 1264 T^{3} + 6241 T^{4} $)($ 1 + 8 T + 168 T^{2} + 632 T^{3} + 6241 T^{4} $)($ ( 1 + 8 T + 79 T^{2} )^{2} $)($ 1 + 10 T + 93 T^{2} + 790 T^{3} + 6241 T^{4} $)($ 1 - 20 T + 248 T^{2} - 1580 T^{3} + 6241 T^{4} $)($ 1 - 5 T + 146 T^{2} - 395 T^{3} + 6241 T^{4} $)($ 1 + 8 T + 168 T^{2} + 632 T^{3} + 6241 T^{4} $)($ 1 + 16 T + 159 T^{2} + 1264 T^{3} + 6241 T^{4} $)($ 1 - 4 T + 114 T^{2} - 316 T^{3} + 6241 T^{4} $)($ ( 1 + 8 T + 79 T^{2} )^{2} $)($ 1 + 16 T + 159 T^{2} + 1264 T^{3} + 6241 T^{4} $)($ 1 - 4 T + 114 T^{2} - 316 T^{3} + 6241 T^{4} $)($ 1 + 8 T + 168 T^{2} + 632 T^{3} + 6241 T^{4} $)($ 1 - 20 T + 248 T^{2} - 1580 T^{3} + 6241 T^{4} $)($ 1 + 10 T + 93 T^{2} + 790 T^{3} + 6241 T^{4} $)
$83$	($ 1 - 9 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 16 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 - 15 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 + 7 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 5 T + 83 T^{2} $)($ 1 + 17 T + 83 T^{2} $)($ 1 + 3 T + 83 T^{2} $)($ 1 - 3 T + 83 T^{2} $)($ 1 - 2 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 3 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 - 3 T + 83 T^{2} $)($ 1 + 16 T + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 2 T + 83 T^{2} $)($ 1 + 17 T + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 - 5 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 7 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 + 11 T + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 - 16 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 15 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 - 12 T + 83 T^{2} $)($ 1 - 9 T + 83 T^{2} $)($ 1 + 3 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 2 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 3 T + 83 T^{2} $)($ 1 + 3 T + 83 T^{2} $)($ 1 + 5 T + 83 T^{2} $)($ 1 - 17 T + 83 T^{2} $)($ 1 - 7 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 15 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 - 16 T + 83 T^{2} $)($ 1 + 9 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 9 T + 83 T^{2} $)($ 1 - 16 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 15 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 - 11 T + 83 T^{2} $)($ 1 + 16 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 - 6 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 - 7 T + 83 T^{2} $)($ 1 - 17 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 5 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 2 T + 83 T^{2} $)($ 1 - 16 T + 83 T^{2} $)($ 1 + 3 T + 83 T^{2} $)($ 1 - 12 T + 178 T^{2} - 996 T^{3} + 6889 T^{4} $)($ 1 + 12 T + 190 T^{2} + 996 T^{3} + 6889 T^{4} $)($ 1 + 2 T + 160 T^{2} + 166 T^{3} + 6889 T^{4} $)($ ( 1 + 83 T^{2} )^{2} $)($ 1 + 156 T^{2} + 6889 T^{4} $)($ 1 + 4 T + 130 T^{2} + 332 T^{3} + 6889 T^{4} $)($ 1 + 4 T + 130 T^{2} + 332 T^{3} + 6889 T^{4} $)($ 1 + 156 T^{2} + 6889 T^{4} $)($ 1 + 12 T + 190 T^{2} + 996 T^{3} + 6889 T^{4} $)($ 1 + 2 T + 160 T^{2} + 166 T^{3} + 6889 T^{4} $)($ 1 - 12 T + 178 T^{2} - 996 T^{3} + 6889 T^{4} $)($ 1 + 25 T + 298 T^{2} + 2075 T^{3} + 6889 T^{4} $)($ 1 + 156 T^{2} + 6889 T^{4} $)($ 1 - 4 T + 130 T^{2} - 332 T^{3} + 6889 T^{4} $)($ ( 1 + 83 T^{2} )^{2} $)($ 1 + 12 T + 178 T^{2} + 996 T^{3} + 6889 T^{4} $)($ 1 - 2 T + 160 T^{2} - 166 T^{3} + 6889 T^{4} $)($ 1 - 12 T + 190 T^{2} - 996 T^{3} + 6889 T^{4} $)($ 1 - 25 T + 298 T^{2} - 2075 T^{3} + 6889 T^{4} $)($ 1 - 2 T + 160 T^{2} - 166 T^{3} + 6889 T^{4} $)($ 1 - 12 T + 190 T^{2} - 996 T^{3} + 6889 T^{4} $)($ 1 + 12 T + 178 T^{2} + 996 T^{3} + 6889 T^{4} $)($ 1 - 4 T + 130 T^{2} - 332 T^{3} + 6889 T^{4} $)($ 1 + 156 T^{2} + 6889 T^{4} $)
$89$	($ 1 - 3 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 - 10 T + 89 T^{2} $)($ 1 - 12 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 15 T + 89 T^{2} $)($ 1 - 11 T + 89 T^{2} $)($ 1 + T + 89 T^{2} $)($ 1 + 4 T + 89 T^{2} $)($ 1 - 15 T + 89 T^{2} $)($ 1 - 9 T + 89 T^{2} $)($ 1 - 15 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 + 15 T + 89 T^{2} $)($ 1 - T + 89 T^{2} $)($ 1 + 4 T + 89 T^{2} $)($ 1 - 11 T + 89 T^{2} $)($ 1 - 11 T + 89 T^{2} $)($ 1 - 9 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ 1 + 14 T + 89 T^{2} $)($ 1 - 11 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 9 T + 89 T^{2} $)($ 1 - 16 T + 89 T^{2} $)($ 1 + 3 T + 89 T^{2} $)($ 1 + 11 T + 89 T^{2} $)($ 1 - 14 T + 89 T^{2} $)($ 1 + 11 T + 89 T^{2} $)($ 1 + 2 T + 89 T^{2} $)($ 1 - T + 89 T^{2} $)($ 1 + 11 T + 89 T^{2} $)($ 1 - 4 T + 89 T^{2} $)($ 1 + T + 89 T^{2} $)($ 1 - 15 T + 89 T^{2} $)($ 1 - 10 T + 89 T^{2} $)($ 1 + 15 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ 1 - 7 T + 89 T^{2} $)($ 1 - 4 T + 89 T^{2} $)($ 1 - 4 T + 89 T^{2} $)($ 1 - 10 T + 89 T^{2} $)($ 1 + 11 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 10 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ 1 - 10 T + 89 T^{2} $)($ 1 + 3 T + 89 T^{2} $)($ 1 - 9 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 - 14 T + 89 T^{2} $)($ 1 + 11 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ 1 - 9 T + 89 T^{2} $)($ 1 + 11 T + 89 T^{2} $)($ 1 + 11 T + 89 T^{2} $)($ 1 + T + 89 T^{2} $)($ 1 - 4 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ 1 + 15 T + 89 T^{2} $)($ 1 + 15 T + 89 T^{2} $)($ 1 - 10 T + 89 T^{2} $)($ 1 - 15 T + 89 T^{2} $)($ 1 - 4 T + 89 T^{2} $)($ 1 - T + 89 T^{2} $)($ 1 + 12 T + 89 T^{2} $)($ 1 - 10 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 15 T + 89 T^{2} $)($ 1 + 11 T + 89 T^{2} $)($ 1 - 10 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 + 3 T + 89 T^{2} $)($ 1 - 9 T + 89 T^{2} $)($ 1 - 3 T + 89 T^{2} $)($ 1 - 10 T + 89 T^{2} $)($ 1 - 9 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 - 11 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 + 4 T + 89 T^{2} $)($ 1 + 7 T + 89 T^{2} $)($ 1 + 4 T + 89 T^{2} $)($ 1 + 15 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)($ 1 - 15 T + 89 T^{2} $)($ 1 - 9 T + 89 T^{2} $)($ 1 + 4 T + 89 T^{2} $)($ 1 - T + 89 T^{2} $)($ 1 - 11 T + 89 T^{2} $)($ 1 - 2 T + 89 T^{2} $)($ 1 + T + 89 T^{2} $)($ 1 - 11 T + 89 T^{2} $)($ 1 - 3 T + 89 T^{2} $)($ 1 - 11 T + 89 T^{2} $)($ 1 + 14 T + 89 T^{2} $)($ 1 + 16 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ ( 1 - 11 T + 89 T^{2} )^{2} $)($ ( 1 + T + 89 T^{2} )^{2} $)($ ( 1 + T + 89 T^{2} )^{2} $)($ 1 + 10 T + 130 T^{2} + 890 T^{3} + 7921 T^{4} $)($ ( 1 - 5 T + 89 T^{2} )^{2} $)($ 1 + 18 T + 219 T^{2} + 1602 T^{3} + 7921 T^{4} $)($ 1 - 18 T + 219 T^{2} - 1602 T^{3} + 7921 T^{4} $)($ ( 1 + 5 T + 89 T^{2} )^{2} $)($ ( 1 - T + 89 T^{2} )^{2} $)($ ( 1 - T + 89 T^{2} )^{2} $)($ ( 1 + 11 T + 89 T^{2} )^{2} $)($ ( 1 - T + 89 T^{2} )^{2} $)($ ( 1 + 5 T + 89 T^{2} )^{2} $)($ 1 - 18 T + 219 T^{2} - 1602 T^{3} + 7921 T^{4} $)($ 1 - 10 T + 130 T^{2} - 890 T^{3} + 7921 T^{4} $)($ ( 1 + 11 T + 89 T^{2} )^{2} $)($ ( 1 - T + 89 T^{2} )^{2} $)($ ( 1 - T + 89 T^{2} )^{2} $)($ ( 1 + T + 89 T^{2} )^{2} $)($ ( 1 + T + 89 T^{2} )^{2} $)($ ( 1 + T + 89 T^{2} )^{2} $)($ ( 1 - 11 T + 89 T^{2} )^{2} $)($ 1 + 18 T + 219 T^{2} + 1602 T^{3} + 7921 T^{4} $)($ ( 1 - 5 T + 89 T^{2} )^{2} $)
$97$	($ 1 + 8 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 + 13 T + 97 T^{2} $)($ 1 - 2 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 + 18 T + 97 T^{2} $)($ 1 - 13 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 - 18 T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 - 17 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 - 16 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 + 6 T + 97 T^{2} $)($ 1 - 4 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 + T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 - 4 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 + 4 T + 97 T^{2} $)($ 1 - 4 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 - T + 97 T^{2} $)($ 1 + 14 T + 97 T^{2} $)($ 1 + 4 T + 97 T^{2} $)($ 1 - 6 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 + 16 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 17 T + 97 T^{2} $)($ 1 - 16 T + 97 T^{2} $)($ 1 + 14 T + 97 T^{2} $)($ 1 + 18 T + 97 T^{2} $)($ 1 + 13 T + 97 T^{2} $)($ 1 - 18 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 16 T + 97 T^{2} $)($ 1 - 13 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 4 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 14 T + 97 T^{2} $)($ 1 + T + 97 T^{2} $)($ 1 - 16 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 + 6 T + 97 T^{2} $)($ 1 - 4 T + 97 T^{2} $)($ 1 - 17 T + 97 T^{2} $)($ 1 + 10 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 + 18 T + 97 T^{2} $)($ 1 - 13 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 - 18 T + 97 T^{2} $)($ 1 + 13 T + 97 T^{2} $)($ 1 - 2 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 16 T + 97 T^{2} $)($ 1 - 13 T + 97 T^{2} $)($ 1 + 18 T + 97 T^{2} $)($ 1 + 13 T + 97 T^{2} $)($ 1 - 18 T + 97 T^{2} $)($ 1 + 14 T + 97 T^{2} $)($ 1 + 17 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 - 16 T + 97 T^{2} $)($ 1 + 4 T + 97 T^{2} $)($ 1 - 6 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 + 16 T + 97 T^{2} $)($ 1 - T + 97 T^{2} $)($ 1 + 14 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 - 4 T + 97 T^{2} $)($ 1 + 4 T + 97 T^{2} $)($ 1 + 24 T + 332 T^{2} + 2328 T^{3} + 9409 T^{4} $)($ 1 + 146 T^{2} + 9409 T^{4} $)($ 1 - 10 T + 156 T^{2} - 970 T^{3} + 9409 T^{4} $)($ 1 - 18 T + 202 T^{2} - 1746 T^{3} + 9409 T^{4} $)($ 1 - 4 T + 108 T^{2} - 388 T^{3} + 9409 T^{4} $)($ 1 + 4 T + 188 T^{2} + 388 T^{3} + 9409 T^{4} $)($ 1 - 4 T + 188 T^{2} - 388 T^{3} + 9409 T^{4} $)($ 1 + 4 T + 108 T^{2} + 388 T^{3} + 9409 T^{4} $)($ 1 + 146 T^{2} + 9409 T^{4} $)($ 1 + 10 T + 156 T^{2} + 970 T^{3} + 9409 T^{4} $)($ 1 - 24 T + 332 T^{2} - 2328 T^{3} + 9409 T^{4} $)($ ( 1 - 10 T + 97 T^{2} )^{2} $)($ 1 - 4 T + 108 T^{2} - 388 T^{3} + 9409 T^{4} $)($ 1 + 4 T + 188 T^{2} + 388 T^{3} + 9409 T^{4} $)($ 1 - 18 T + 202 T^{2} - 1746 T^{3} + 9409 T^{4} $)($ 1 + 24 T + 332 T^{2} + 2328 T^{3} + 9409 T^{4} $)($ 1 - 10 T + 156 T^{2} - 970 T^{3} + 9409 T^{4} $)($ 1 + 146 T^{2} + 9409 T^{4} $)($ ( 1 - 10 T + 97 T^{2} )^{2} $)($ 1 + 10 T + 156 T^{2} + 970 T^{3} + 9409 T^{4} $)($ 1 + 146 T^{2} + 9409 T^{4} $)($ 1 - 24 T + 332 T^{2} - 2328 T^{3} + 9409 T^{4} $)($ 1 - 4 T + 188 T^{2} - 388 T^{3} + 9409 T^{4} $)($ 1 + 4 T + 108 T^{2} + 388 T^{3} + 9409 T^{4} $)
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Introduction	Features
Universe	News

Level:	\( N \)	=	\( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	9450.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 128 \)
Sturm bound:			\(4320\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\)

\(2\)	\(3\)	\(5\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(8\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(10\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(10\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(10\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(10\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(10\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(10\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(11\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(7\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(8\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(7\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(11\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(8\)
Plus space				\(+\)	\(66\)
Minus space				\(-\)	\(86\)

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	5	7	$q$-expansion
9450.2.a.a	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}-2q^{13}+\cdots\)
9450.2.a.b	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}+q^{13}+\cdots\)
9450.2.a.c	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{11}-5q^{13}+\cdots\)
9450.2.a.d	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{11}+q^{13}+\cdots\)
9450.2.a.e	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-5q^{13}+\cdots\)
9450.2.a.f	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-q^{13}+\cdots\)
9450.2.a.g	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+q^{13}+\cdots\)
9450.2.a.h	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+4q^{13}+\cdots\)
9450.2.a.i	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+5q^{13}+\cdots\)
9450.2.a.j	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}+5q^{13}+\cdots\)
9450.2.a.k	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{11}+3q^{13}+\cdots\)
9450.2.a.l	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{13}+q^{14}+\cdots\)
9450.2.a.m	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{13}+q^{14}+\cdots\)
9450.2.a.n	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots\)
9450.2.a.o	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{13}+q^{14}+\cdots\)
9450.2.a.p	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+7q^{13}+q^{14}+\cdots\)
9450.2.a.q	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}-5q^{13}+\cdots\)
9450.2.a.r	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}+5q^{13}+\cdots\)
9450.2.a.s	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}-5q^{13}+\cdots\)
9450.2.a.t	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}+6q^{13}+\cdots\)
9450.2.a.u	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}-5q^{13}+\cdots\)
9450.2.a.v	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
9450.2.a.w	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}-6q^{13}+\cdots\)
9450.2.a.x	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}-q^{13}+\cdots\)
9450.2.a.y	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}-5q^{13}+\cdots\)
9450.2.a.z	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}+4q^{13}+\cdots\)
9450.2.a.ba	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}+5q^{13}+\cdots\)
9450.2.a.bb	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-5q^{11}+5q^{13}+\cdots\)
9450.2.a.bc	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}-3q^{13}+\cdots\)
9450.2.a.bd	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}+q^{13}+\cdots\)
9450.2.a.be	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}+6q^{13}+\cdots\)
9450.2.a.bf	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-6q^{13}+\cdots\)
9450.2.a.bg	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-q^{14}+\cdots\)
9450.2.a.bh	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+3q^{13}+\cdots\)
9450.2.a.bi	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+5q^{13}+\cdots\)
9450.2.a.bj	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{11}-5q^{13}+\cdots\)
9450.2.a.bk	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{11}+5q^{13}+\cdots\)
9450.2.a.bl	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-7q^{13}-q^{14}+\cdots\)
9450.2.a.bm	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{13}-q^{14}+\cdots\)
9450.2.a.bn	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots\)
9450.2.a.bo	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{13}-q^{14}+\cdots\)
9450.2.a.bp	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}-3q^{13}+\cdots\)
9450.2.a.bq	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}-3q^{13}+\cdots\)
9450.2.a.br	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}+3q^{13}+\cdots\)
9450.2.a.bs	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{11}-4q^{13}+\cdots\)
9450.2.a.bt	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-5q^{13}+\cdots\)
9450.2.a.bu	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-q^{13}+\cdots\)
9450.2.a.bv	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
9450.2.a.bw	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}-q^{13}+\cdots\)
9450.2.a.bx	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}-q^{14}+\cdots\)
9450.2.a.by	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}+5q^{13}+\cdots\)
9450.2.a.bz	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+6q^{11}+2q^{13}+\cdots\)
9450.2.a.ca	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}-5q^{13}+\cdots\)
9450.2.a.cb	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}+4q^{13}+\cdots\)
9450.2.a.cc	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}-6q^{13}+\cdots\)
9450.2.a.cd	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}-q^{13}+\cdots\)
9450.2.a.ce	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}-5q^{13}+\cdots\)
9450.2.a.cf	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}+q^{13}+\cdots\)
9450.2.a.cg	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}-5q^{13}+\cdots\)
9450.2.a.ch	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+6q^{13}+\cdots\)
9450.2.a.ci	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{11}-5q^{13}+\cdots\)
9450.2.a.cj	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{11}+5q^{13}+\cdots\)
9450.2.a.ck	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{13}-q^{14}+\cdots\)
9450.2.a.cl	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{13}-q^{14}+\cdots\)
9450.2.a.cm	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots\)
9450.2.a.cn	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{13}-q^{14}+\cdots\)
9450.2.a.co	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+7q^{13}-q^{14}+\cdots\)
9450.2.a.cp	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}+3q^{13}+\cdots\)
9450.2.a.cq	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}+5q^{13}+\cdots\)
9450.2.a.cr	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}-5q^{13}+\cdots\)
9450.2.a.cs	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}-q^{13}+\cdots\)
9450.2.a.ct	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+q^{13}+\cdots\)
9450.2.a.cu	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+4q^{13}+\cdots\)
9450.2.a.cv	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+5q^{13}+\cdots\)
9450.2.a.cw	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}-5q^{13}+\cdots\)
9450.2.a.cx	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}+q^{13}+\cdots\)
9450.2.a.cy	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}-2q^{13}+\cdots\)
9450.2.a.cz	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}+q^{13}+\cdots\)
9450.2.a.da	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}+2q^{13}+\cdots\)
9450.2.a.db	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}-q^{13}+\cdots\)
9450.2.a.dc	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}+q^{14}+\cdots\)
9450.2.a.dd	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}+5q^{13}+\cdots\)
9450.2.a.de	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}-5q^{13}+\cdots\)
9450.2.a.df	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}-q^{13}+\cdots\)
9450.2.a.dg	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}+q^{13}+\cdots\)
9450.2.a.dh	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{11}-4q^{13}+\cdots\)
9450.2.a.di	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}-3q^{13}+\cdots\)
9450.2.a.dj	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}-3q^{13}+\cdots\)
9450.2.a.dk	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}+3q^{13}+\cdots\)
9450.2.a.dl	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-7q^{13}+q^{14}+\cdots\)
9450.2.a.dm	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{13}+q^{14}+\cdots\)
9450.2.a.dn	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots\)
9450.2.a.do	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{13}+q^{14}+\cdots\)
9450.2.a.dp	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}-5q^{13}+\cdots\)
9450.2.a.dq	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}+5q^{13}+\cdots\)
9450.2.a.dr	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}-6q^{13}+\cdots\)
9450.2.a.ds	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+q^{14}+\cdots\)
9450.2.a.dt	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+3q^{13}+\cdots\)
9450.2.a.du	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+5q^{13}+\cdots\)
9450.2.a.dv	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}-3q^{13}+\cdots\)
9450.2.a.dw	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+q^{13}+\cdots\)
9450.2.a.dx	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+6q^{13}+\cdots\)
9450.2.a.dy	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}+5q^{13}+\cdots\)
9450.2.a.dz	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+6q^{11}+5q^{13}+\cdots\)
9450.2.a.ea	\(2\)	\(75.459\)	\(\Q(\sqrt{6}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.eb	\(2\)	\(75.459\)	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.ec	\(2\)	\(75.459\)	\(\Q(\sqrt{7}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.ed	\(2\)	\(75.459\)	\(\Q(\sqrt{73}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ee	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.ef	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+(2+\beta )q^{11}+\cdots\)
9450.2.a.eg	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+(-2+\beta )q^{11}+\cdots\)
9450.2.a.eh	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+(1+\cdots)q^{13}+\cdots\)
9450.2.a.ei	\(2\)	\(75.459\)	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ej	\(2\)	\(75.459\)	\(\Q(\sqrt{7}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ek	\(2\)	\(75.459\)	\(\Q(\sqrt{6}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9450.2.a.el	\(2\)	\(75.459\)	\(\Q(\sqrt{97}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+(1+\beta )q^{11}+\cdots\)
9450.2.a.em	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.en	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+(-2+\beta )q^{11}+\cdots\)
9450.2.a.eo	\(2\)	\(75.459\)	\(\Q(\sqrt{73}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ep	\(2\)	\(75.459\)	\(\Q(\sqrt{6}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.eq	\(2\)	\(75.459\)	\(\Q(\sqrt{7}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.er	\(2\)	\(75.459\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.es	\(2\)	\(75.459\)	\(\Q(\sqrt{97}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+(-1-\beta )q^{11}+\cdots\)
9450.2.a.et	\(2\)	\(75.459\)	\(\Q(\sqrt{7}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.eu	\(2\)	\(75.459\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ev	\(2\)	\(75.459\)	\(\Q(\sqrt{6}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9450.2.a.ew	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+(2+\beta )q^{11}+\cdots\)
9450.2.a.ex	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+(1+\cdots)q^{13}+\cdots\)

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(9450))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9450))\) 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	9450.2.a

Level	9450
Weight	2
Character orbit	a
Rep. character	\(\chi_{9450}(1,\cdot)\)
Character field	\(\Q\)
Dimension	152
Newform subspaces	128
Sturm bound	4320
Trace bound	17