LMFDB - Space of Modular Forms of Level 378, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	378.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 8 $
Sturm bound:			$144$
Trace bound:			$5$
Distinguishing $T_p$:			$5$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(378))$.

	Total	New	Old
Modular forms	84	8	76
Cusp forms	61	8	53
Eisenstein series	23	0	23

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.
$+$	$+$	$+$	$+$	$1$
$+$	$+$	$-$	$-$	$1$
$+$	$-$	$+$	$-$	$1$
$+$	$-$	$-$	$+$	$1$
$-$	$+$	$+$	$-$	$2$
$-$	$-$	$-$	$-$	$2$
Plus space			$+$	$2$
Minus space			$-$	$6$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(378))$ 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
378.2.a.a	$1$	$3.018$	$\Q$	None	$-1$	$0$	$-4$	$-1$	$+$	$-$	$+$	$q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}+4q^{10}+\cdots$
378.2.a.b	$1$	$3.018$	$\Q$	None	$-1$	$0$	$-3$	$1$	$+$	$-$	$-$	$q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots$
378.2.a.c	$1$	$3.018$	$\Q$	None	$-1$	$0$	$-1$	$-1$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
378.2.a.d	$1$	$3.018$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{13}-q^{14}+\cdots$
378.2.a.e	$1$	$3.018$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{13}+q^{14}+\cdots$
378.2.a.f	$1$	$3.018$	$\Q$	None	$1$	$0$	$1$	$-1$	$-$	$+$	$+$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
378.2.a.g	$1$	$3.018$	$\Q$	None	$1$	$0$	$3$	$1$	$-$	$-$	$-$	$q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots$
378.2.a.h	$1$	$3.018$	$\Q$	None	$1$	$0$	$4$	$-1$	$-$	$+$	$+$	$q+q^{2}+q^{4}+4q^{5}-q^{7}+q^{8}+4q^{10}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(378))$ into lower level spaces

$ S_{2}^{\mathrm{old}}(\Gamma_0(378)) \cong $ $S_{2}^{\mathrm{new}}(\Gamma_0(14))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(21))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(27))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(42))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(54))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(63))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(126))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(189))$$^{\oplus 2}$

Hecke Characteristic Polynomials

$p$	$F_p(T)$
$2$	($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 + T $)($ 1 - T $)($ 1 - T $)($ 1 - T $)($ 1 - T $)
$3$	()()()()()()()()
$5$	($ 1 + 4 T + 5 T^{2} $)($ 1 + 3 T + 5 T^{2} $)($ 1 + T + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 + 5 T^{2} $)($ 1 - T + 5 T^{2} $)($ 1 - 3 T + 5 T^{2} $)($ 1 - 4 T + 5 T^{2} $)
$7$	($ 1 + T $)($ 1 - T $)($ 1 + T $)($ 1 - T $)($ 1 - T $)($ 1 + T $)($ 1 - T $)($ 1 + T $)
$11$	($ 1 - 4 T + 11 T^{2} $)($ 1 - 3 T + 11 T^{2} $)($ 1 + 5 T + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 + 11 T^{2} $)($ 1 - 5 T + 11 T^{2} $)($ 1 + 3 T + 11 T^{2} $)($ 1 + 4 T + 11 T^{2} $)
$13$	($ 1 - 3 T + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 - 5 T + 13 T^{2} $)($ 1 + 13 T^{2} $)($ 1 + 4 T + 13 T^{2} $)($ 1 - 3 T + 13 T^{2} $)
$17$	($ 1 - 7 T + 17 T^{2} $)($ 1 + 6 T + 17 T^{2} $)($ 1 + 2 T + 17 T^{2} $)($ 1 + 3 T + 17 T^{2} $)($ 1 - 3 T + 17 T^{2} $)($ 1 - 2 T + 17 T^{2} $)($ 1 - 6 T + 17 T^{2} $)($ 1 + 7 T + 17 T^{2} $)
$19$	($ 1 - 2 T + 19 T^{2} $)($ 1 + 7 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)($ 1 + T + 19 T^{2} $)($ 1 + 7 T + 19 T^{2} $)($ 1 - 2 T + 19 T^{2} $)
$23$	($ 1 - T + 23 T^{2} $)($ 1 + 3 T + 23 T^{2} $)($ 1 - T + 23 T^{2} $)($ 1 - 9 T + 23 T^{2} $)($ 1 + 9 T + 23 T^{2} $)($ 1 + T + 23 T^{2} $)($ 1 - 3 T + 23 T^{2} $)($ 1 + T + 23 T^{2} $)
$29$	($ 1 + T + 29 T^{2} $)($ 1 + 29 T^{2} $)($ 1 + 4 T + 29 T^{2} $)($ 1 - 3 T + 29 T^{2} $)($ 1 + 3 T + 29 T^{2} $)($ 1 - 4 T + 29 T^{2} $)($ 1 + 29 T^{2} $)($ 1 - T + 29 T^{2} $)
$31$	($ 1 + 9 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + 9 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + 9 T + 31 T^{2} $)($ 1 - 5 T + 31 T^{2} $)($ 1 + 9 T + 31 T^{2} $)
$37$	($ 1 - 2 T + 37 T^{2} $)($ 1 + 7 T + 37 T^{2} $)($ 1 - 5 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)($ 1 - 5 T + 37 T^{2} $)($ 1 + 7 T + 37 T^{2} $)($ 1 - 2 T + 37 T^{2} $)
$41$	($ 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 - 9 T + 41 T^{2} $)($ 1 - 6 T + 41 T^{2} $)
$43$	($ 1 - 11 T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 + T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 + 10 T + 43 T^{2} $)($ 1 - 11 T + 43 T^{2} $)
$47$	($ 1 - 6 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 - 6 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)($ 1 + 6 T + 47 T^{2} $)
$53$	($ 1 - 9 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 + 3 T + 53 T^{2} $)($ 1 - 3 T + 53 T^{2} $)($ 1 - 12 T + 53 T^{2} $)($ 1 + 12 T + 53 T^{2} $)($ 1 + 9 T + 53 T^{2} $)
$59$	($ 1 - 5 T + 59 T^{2} $)($ 1 + 6 T + 59 T^{2} $)($ 1 - 14 T + 59 T^{2} $)($ 1 - 3 T + 59 T^{2} $)($ 1 + 3 T + 59 T^{2} $)($ 1 + 14 T + 59 T^{2} $)($ 1 - 6 T + 59 T^{2} $)($ 1 + 5 T + 59 T^{2} $)
$61$	($ 1 + 6 T + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 + 10 T + 61 T^{2} $)($ 1 + 61 T^{2} $)($ 1 - 8 T + 61 T^{2} $)($ 1 + 6 T + 61 T^{2} $)
$67$	($ 1 - 7 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 + 13 T + 67 T^{2} $)($ 1 + 13 T + 67 T^{2} $)($ 1 + 8 T + 67 T^{2} $)($ 1 + 4 T + 67 T^{2} $)($ 1 - 7 T + 67 T^{2} $)
$71$	($ 1 - 7 T + 71 T^{2} $)($ 1 - 9 T + 71 T^{2} $)($ 1 - 13 T + 71 T^{2} $)($ 1 + 9 T + 71 T^{2} $)($ 1 - 9 T + 71 T^{2} $)($ 1 + 13 T + 71 T^{2} $)($ 1 + 9 T + 71 T^{2} $)($ 1 + 7 T + 71 T^{2} $)
$73$	($ 1 + 14 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 + 2 T + 73 T^{2} $)($ 1 - 2 T + 73 T^{2} $)($ 1 + 14 T + 73 T^{2} $)
$79$	($ 1 + 6 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 - 6 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 - 6 T + 79 T^{2} $)($ 1 + 10 T + 79 T^{2} $)($ 1 + 6 T + 79 T^{2} $)
$83$	($ 1 - 4 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 - 4 T + 83 T^{2} $)($ 1 - 12 T + 83 T^{2} $)($ 1 + 12 T + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)($ 1 + 83 T^{2} $)($ 1 + 4 T + 83 T^{2} $)
$89$	($ 1 - 3 T + 89 T^{2} $)($ 1 - 15 T + 89 T^{2} $)($ 1 - 9 T + 89 T^{2} $)($ 1 + 15 T + 89 T^{2} $)($ 1 - 15 T + 89 T^{2} $)($ 1 + 9 T + 89 T^{2} $)($ 1 + 15 T + 89 T^{2} $)($ 1 + 3 T + 89 T^{2} $)
$97$	($ 1 + 8 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 16 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 - 16 T + 97 T^{2} $)($ 1 - 8 T + 97 T^{2} $)($ 1 + 8 T + 97 T^{2} $)
show more
show less

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	378.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(17\)

\(2\)	\(3\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(2\)
Plus space			\(+\)	\(2\)
Minus space			\(-\)	\(6\)

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
378.2.a.a	\(1\)	\(3.018\)	\(\Q\)	None	\(-1\)	\(0\)	\(-4\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}+4q^{10}+\cdots\)
378.2.a.b	\(1\)	\(3.018\)	\(\Q\)	None	\(-1\)	\(0\)	\(-3\)	\(1\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
378.2.a.c	\(1\)	\(3.018\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
378.2.a.d	\(1\)	\(3.018\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{13}-q^{14}+\cdots\)
378.2.a.e	\(1\)	\(3.018\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{13}+q^{14}+\cdots\)
378.2.a.f	\(1\)	\(3.018\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
378.2.a.g	\(1\)	\(3.018\)	\(\Q\)	None	\(1\)	\(0\)	\(3\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
378.2.a.h	\(1\)	\(3.018\)	\(\Q\)	None	\(1\)	\(0\)	\(4\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}+4q^{5}-q^{7}+q^{8}+4q^{10}+\cdots\)

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(378))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(378))\) 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	378.2.a

Level	378
Weight	2
Character orbit	a
Rep. character	\(\chi_{378}(1,\cdot)\)
Character field	\(\Q\)
Dimension	8
Newform subspaces	8
Sturm bound	144
Trace bound	5

$p$	$F_p(T)$
$2$	(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))
$3$	(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))
$5$	(\( 1 + 4 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))
$7$	(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))
$11$	(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))
$13$	(\( 1 - 3 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))
$17$	(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))
$19$	(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))
$23$	(\( 1 - T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))
$29$	(\( 1 + T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))
$31$	(\( 1 + 9 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 9 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 9 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 9 T + 31 T^{2} \))
$37$	(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))
$41$	(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 9 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))
$43$	(\( 1 - 11 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 11 T + 43 T^{2} \))
$47$	(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))
$53$	(\( 1 - 9 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))
$59$	(\( 1 - 5 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 5 T + 59 T^{2} \))
$61$	(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))
$67$	(\( 1 - 7 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))
$71$	(\( 1 - 7 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 - 13 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 + 13 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 7 T + 71 T^{2} \))
$73$	(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))
$79$	(\( 1 + 6 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 6 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 6 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 6 T + 79 T^{2} \))
$83$	(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))
$89$	(\( 1 - 3 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 - 9 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 9 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 + 3 T + 89 T^{2} \))
$97$	(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 16 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 16 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))
show more
show less