LMFDB - Space of modular forms of level 504, weight 2, and Trivial character

Defining parameters

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 8 $
Sturm bound:			$192$
Trace bound:			$11$
Distinguishing $T_p$:			$5$, $11$, $13$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(504))$.

	Total	New	Old
Modular forms	112	8	104
Cusp forms	81	8	73
Eisenstein series	31	0	31

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

$2$	$3$	$7$	Fricke	Dim.
$+$	$+$	$+$	$+$	$1$
$+$	$+$	$-$	$-$	$1$
$+$	$-$	$+$	$-$	$1$
$-$	$+$	$+$	$-$	$1$
$-$	$+$	$-$	$+$	$1$
$-$	$-$	$+$	$+$	$1$
$-$	$-$	$-$	$-$	$2$
Plus space			$+$	$3$
Minus space			$-$	$5$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(504))$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	2	3	7	$q$-expansion
504.2.a.a	$1$	$4.024$	$\Q$	None	$0$	$0$	$-2$	$-1$	$+$	$+$	$+$	$q-2q^{5}-q^{7}-2q^{11}+2q^{13}-6q^{17}+\cdots$
504.2.a.b	$1$	$4.024$	$\Q$	None	$0$	$0$	$-2$	$-1$	$-$	$-$	$+$	$q-2q^{5}-q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots$
504.2.a.c	$1$	$4.024$	$\Q$	None	$0$	$0$	$-2$	$-1$	$+$	$-$	$+$	$q-2q^{5}-q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots$
504.2.a.d	$1$	$4.024$	$\Q$	None	$0$	$0$	$-2$	$1$	$-$	$+$	$-$	$q-2q^{5}+q^{7}-6q^{11}-6q^{13}+2q^{17}+\cdots$
504.2.a.e	$1$	$4.024$	$\Q$	None	$0$	$0$	$-2$	$1$	$-$	$-$	$-$	$q-2q^{5}+q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots$
504.2.a.f	$1$	$4.024$	$\Q$	None	$0$	$0$	$2$	$-1$	$-$	$+$	$+$	$q+2q^{5}-q^{7}+2q^{11}+2q^{13}+6q^{17}+\cdots$
504.2.a.g	$1$	$4.024$	$\Q$	None	$0$	$0$	$2$	$1$	$+$	$+$	$-$	$q+2q^{5}+q^{7}+6q^{11}-6q^{13}-2q^{17}+\cdots$
504.2.a.h	$1$	$4.024$	$\Q$	None	$0$	$0$	$4$	$1$	$-$	$-$	$-$	$q+4q^{5}+q^{7}+2q^{17}-2q^{19}-8q^{23}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(504))$ into lower level spaces

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	1
$3$	1
$5$	($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 + 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 2 T + 5 T^{2} $)($ 1 - 4 T + 5 T^{2} $)
$7$	($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 - T $)($ 1 - T $)($ 1 + T $)($ 1 - T $)($ 1 - T $)
$11$	($ 1 + 2 T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 - 4 T + 11 T^{2} $)($ 1 + 6 T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 - 2 T + 11 T^{2} $)($ 1 - 6 T + 11 T^{2} $)($ 1 + 11 T^{2} $)
$13$	($ 1 - 2 T + 13 T^{2} $)($ 1 + 2 T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 - 6 T + 13 T^{2} $)($ 1 - 2 T + 13 T^{2} $)($ 1 + 6 T + 13 T^{2} $)($ 1 + 13 T^{2} $)
$17$	($ 1 + 6 T + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)
$19$	($ 1 + 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 8 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 4 T + 19 T^{2} $)($ 1 - 4 T + 19 T^{2} $)($ 1 + 2 T + 19 T^{2} $)
$23$	($ 1 + 6 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 + 23 T^{2} $)($ 1 + 2 T + 23 T^{2} $)($ 1 - 4 T + 23 T^{2} $)($ 1 - 6 T + 23 T^{2} $)($ 1 - 2 T + 23 T^{2} $)($ 1 + 8 T + 23 T^{2} $)
$29$	($ 1 + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 6 T + 29 T^{2} $)($ 1 + 8 T + 29 T^{2} $)($ 1 - 10 T + 29 T^{2} $)($ 1 + 29 T^{2} $)($ 1 - 8 T + 29 T^{2} $)($ 1 + 2 T + 29 T^{2} $)
$31$	($ 1 + 4 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 - 8 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ 1 + 8 T + 31 T^{2} $)($ 1 + 4 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)($ 1 - 4 T + 31 T^{2} $)
$37$	($ 1 - 10 T + 37 T^{2} $)($ 1 + 10 T + 37 T^{2} $)($ 1 + 2 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 - 6 T + 37 T^{2} $)($ 1 - 10 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)($ 1 + 6 T + 37 T^{2} $)
$41$	($ 1 + 2 T + 41 T^{2} $)($ 1 - 10 T + 41 T^{2} $)($ 1 + 2 T + 41 T^{2} $)($ 1 + 10 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)($ 1 - 10 T + 41 T^{2} $)($ 1 - 2 T + 41 T^{2} $)
$43$	($ 1 + 4 T + 43 T^{2} $)($ 1 - 12 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 + 4 T + 43 T^{2} $)($ 1 - 8 T + 43 T^{2} $)
$47$	($ 1 + 4 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 8 T + 47 T^{2} $)($ 1 - 4 T + 47 T^{2} $)($ 1 + 8 T + 47 T^{2} $)($ 1 - 4 T + 47 T^{2} $)($ 1 + 4 T + 47 T^{2} $)($ 1 - 4 T + 47 T^{2} $)
$53$	($ 1 - 12 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 + 6 T + 53 T^{2} $)($ 1 - 4 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 + 4 T + 53 T^{2} $)($ 1 - 10 T + 53 T^{2} $)
$59$	($ 1 + 12 T + 59 T^{2} $)($ 1 + 4 T + 59 T^{2} $)($ 1 + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 - 12 T + 59 T^{2} $)($ 1 + 12 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)
$61$	($ 1 - 6 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 - 6 T + 61 T^{2} $)($ 1 + 2 T + 61 T^{2} $)($ 1 - 4 T + 61 T^{2} $)
$67$	($ 1 + 4 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 12 T + 67 T^{2} $)($ 1 + 12 T + 67 T^{2} $)
$71$	($ 1 - 14 T + 71 T^{2} $)($ 1 + 4 T + 71 T^{2} $)($ 1 - 8 T + 71 T^{2} $)($ 1 + 6 T + 71 T^{2} $)($ 1 - 12 T + 71 T^{2} $)($ 1 + 14 T + 71 T^{2} $)($ 1 - 6 T + 71 T^{2} $)($ 1 + 71 T^{2} $)
$73$	($ 1 + 2 T + 73 T^{2} $)($ 1 - 2 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} $)
$79$	($ 1 + 8 T + 79 T^{2} $)($ 1 - 8 T + 79 T^{2} $)($ 1 - 16 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)($ 1 + 8 T + 79 T^{2} $)
$83$	($ 1 - 16 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 8 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 16 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 6 T + 83 T^{2} $)
$89$	($ 1 - 6 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 - 6 T + 89 T^{2} $)($ 1 - 14 T + 89 T^{2} $)($ 1 - 2 T + 89 T^{2} $)($ 1 + 6 T + 89 T^{2} $)($ 1 + 14 T + 89 T^{2} $)($ 1 + 10 T + 89 T^{2} $)
$97$	($ 1 + 18 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 + 6 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 - 10 T + 97 T^{2} $)($ 1 + 18 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)($ 1 + 2 T + 97 T^{2} $)
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Overview	Features
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(192\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(504))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(504))\) 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	504.2.a

Level	504
Weight	2
Character orbit	a
Rep. character	\(\chi_{504}(1,\cdot)\)
Character field	\(\Q\)
Dimension	8
Newform subspaces	8
Sturm bound	192
Trace bound	11

\(2\)	\(3\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(2\)
Plus space			\(+\)	\(3\)
Minus space			\(-\)	\(5\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	2	3	7	$q$-expansion
504.2.a.a	\(1\)	\(4.024\)	\(\Q\)	None	\(0\)	\(0\)	\(-2\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(q-2q^{5}-q^{7}-2q^{11}+2q^{13}-6q^{17}+\cdots\)
504.2.a.b	\(1\)	\(4.024\)	\(\Q\)	None	\(0\)	\(0\)	\(-2\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(q-2q^{5}-q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
504.2.a.c	\(1\)	\(4.024\)	\(\Q\)	None	\(0\)	\(0\)	\(-2\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(q-2q^{5}-q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
504.2.a.d	\(1\)	\(4.024\)	\(\Q\)	None	\(0\)	\(0\)	\(-2\)	\(1\)	\(-\)	\(+\)	\(-\)	\(q-2q^{5}+q^{7}-6q^{11}-6q^{13}+2q^{17}+\cdots\)
504.2.a.e	\(1\)	\(4.024\)	\(\Q\)	None	\(0\)	\(0\)	\(-2\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q-2q^{5}+q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots\)
504.2.a.f	\(1\)	\(4.024\)	\(\Q\)	None	\(0\)	\(0\)	\(2\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(q+2q^{5}-q^{7}+2q^{11}+2q^{13}+6q^{17}+\cdots\)
504.2.a.g	\(1\)	\(4.024\)	\(\Q\)	None	\(0\)	\(0\)	\(2\)	\(1\)	\(+\)	\(+\)	\(-\)	\(q+2q^{5}+q^{7}+6q^{11}-6q^{13}-2q^{17}+\cdots\)
504.2.a.h	\(1\)	\(4.024\)	\(\Q\)	None	\(0\)	\(0\)	\(4\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q+4q^{5}+q^{7}+2q^{17}-2q^{19}-8q^{23}+\cdots\)

$p$	$F_p(T)$
$2$	1
$3$	1
$5$	(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))
$7$	(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))
$11$	(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))
$13$	(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))
$17$	(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))
$19$	(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))
$23$	(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))
$29$	(\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 - 10 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))
$31$	(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))
$37$	(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))
$41$	(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))
$43$	(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))
$47$	(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))
$53$	(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))
$59$	(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))
$61$	(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))
$67$	(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))
$71$	(\( 1 - 14 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 14 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))
$73$	(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))
$79$	(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))
$83$	(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))
$89$	(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))
$97$	(\( 1 + 18 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))
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