Properties

Label 2100.2.a
Level 2100
Weight 2
Character orbit a
Rep. character \(\chi_{2100}(1,\cdot)\)
Character field \(\Q\)
Dimension 18
Newform subspaces 18
Sturm bound 960
Trace bound 13

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Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(960\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2100))\).

Total New Old
Modular forms 516 18 498
Cusp forms 445 18 427
Eisenstein series 71 0 71

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

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(6\)
Minus space\(-\)\(12\)

Trace form

\( 18q + 18q^{9} + O(q^{10}) \) \( 18q + 18q^{9} - 4q^{11} - 4q^{13} - 12q^{17} - 2q^{21} + 4q^{23} + 28q^{29} - 8q^{31} - 12q^{37} - 8q^{39} + 28q^{41} + 8q^{43} - 8q^{47} + 18q^{49} - 4q^{51} + 12q^{53} + 8q^{57} + 32q^{59} + 44q^{61} + 16q^{67} + 4q^{71} + 20q^{73} + 8q^{77} + 16q^{79} + 18q^{81} + 32q^{83} - 8q^{87} + 36q^{89} + 16q^{93} + 20q^{97} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2100))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 7
2100.2.a.a \(1\) \(16.769\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
2100.2.a.b \(1\) \(16.769\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
2100.2.a.c \(1\) \(16.769\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}-q^{7}+q^{9}-q^{11}-2q^{13}+6q^{19}+\cdots\)
2100.2.a.d \(1\) \(16.769\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
2100.2.a.e \(1\) \(16.769\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
2100.2.a.f \(1\) \(16.769\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}-q^{11}+2q^{13}-8q^{17}+\cdots\)
2100.2.a.g \(1\) \(16.769\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}+q^{11}+4q^{13}+2q^{17}+\cdots\)
2100.2.a.h \(1\) \(16.769\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
2100.2.a.i \(1\) \(16.769\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
2100.2.a.j \(1\) \(16.769\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
2100.2.a.k \(1\) \(16.769\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
2100.2.a.l \(1\) \(16.769\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}-q^{11}-2q^{13}+8q^{17}+\cdots\)
2100.2.a.m \(1\) \(16.769\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}+q^{11}-4q^{13}-2q^{17}+\cdots\)
2100.2.a.n \(1\) \(16.769\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
2100.2.a.o \(1\) \(16.769\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots\)
2100.2.a.p \(1\) \(16.769\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}-q^{11}+2q^{13}+6q^{19}+\cdots\)
2100.2.a.q \(1\) \(16.769\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
2100.2.a.r \(1\) \(16.769\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2100)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1050))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

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