Properties

Label 8400.2.a
Level $8400$
Weight $2$
Character orbit 8400.a
Rep. character $\chi_{8400}(1,\cdot)$
Character field $\Q$
Dimension $114$
Newform subspaces $90$
Sturm bound $3840$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8400.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 90 \)
Sturm bound: \(3840\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8400))\).

Total New Old
Modular forms 1992 114 1878
Cusp forms 1849 114 1735
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.

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(7\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(51\)
Minus space\(-\)\(63\)

Trace form

\( 114q + 2q^{7} + 114q^{9} + O(q^{10}) \) \( 114q + 2q^{7} + 114q^{9} + 4q^{11} - 4q^{13} + 4q^{17} - 8q^{19} + 4q^{23} - 12q^{29} - 8q^{31} - 12q^{37} - 8q^{39} + 4q^{41} - 24q^{43} - 24q^{47} + 114q^{49} + 4q^{51} - 12q^{53} - 24q^{59} + 12q^{61} + 2q^{63} + 16q^{67} + 16q^{69} - 20q^{71} + 20q^{73} - 8q^{77} - 48q^{79} + 114q^{81} - 64q^{83} + 24q^{87} + 36q^{89} + 12q^{91} - 8q^{93} + 20q^{97} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8400))\) 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
8400.2.a.a \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}-q^{7}+q^{9}-6q^{11}-q^{13}+3q^{17}+\cdots\)
8400.2.a.b \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8400.2.a.c \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
8400.2.a.d \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}-2q^{11}-q^{13}+3q^{17}+\cdots\)
8400.2.a.e \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
8400.2.a.f \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}-2q^{13}-2q^{17}+\cdots\)
8400.2.a.g \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}+q^{11}-4q^{13}-2q^{17}+\cdots\)
8400.2.a.h \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}+q^{11}+2q^{13}-6q^{19}+\cdots\)
8400.2.a.i \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}-q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots\)
8400.2.a.j \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}-q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
8400.2.a.k \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
8400.2.a.l \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
8400.2.a.m \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
8400.2.a.n \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}-5q^{11}-2q^{13}+\cdots\)
8400.2.a.o \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
8400.2.a.p \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8400.2.a.q \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8400.2.a.r \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}-3q^{11}-2q^{17}+\cdots\)
8400.2.a.s \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}-2q^{11}-3q^{13}+\cdots\)
8400.2.a.t \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}-2q^{11}+q^{13}-q^{17}+\cdots\)
8400.2.a.u \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
8400.2.a.v \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
8400.2.a.w \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
8400.2.a.x \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}-q^{11}-4q^{13}-2q^{17}+\cdots\)
8400.2.a.y \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
8400.2.a.z \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots\)
8400.2.a.ba \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}+q^{11}-2q^{13}+8q^{17}+\cdots\)
8400.2.a.bb \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}+2q^{11}-7q^{13}+\cdots\)
8400.2.a.bc \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
8400.2.a.bd \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
8400.2.a.be \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}+2q^{11}+5q^{13}+\cdots\)
8400.2.a.bf \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
8400.2.a.bg \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
8400.2.a.bh \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
8400.2.a.bi \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots\)
8400.2.a.bj \(1\) \(67.074\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
8400.2.a.bk \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots\)
8400.2.a.bl \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8400.2.a.bm \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8400.2.a.bn \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8400.2.a.bo \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}-3q^{11}+2q^{17}+\cdots\)
8400.2.a.bp \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
8400.2.a.bq \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
8400.2.a.br \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
8400.2.a.bs \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
8400.2.a.bt \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}-2q^{11}-q^{13}+q^{17}+\cdots\)
8400.2.a.bu \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}-2q^{11}+3q^{13}+\cdots\)
8400.2.a.bv \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}-q^{11}+4q^{13}+2q^{17}+\cdots\)
8400.2.a.bw \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
8400.2.a.bx \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots\)
8400.2.a.by \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}+q^{11}+2q^{13}-8q^{17}+\cdots\)
8400.2.a.bz \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}+2q^{11}-5q^{13}+\cdots\)
8400.2.a.ca \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
8400.2.a.cb \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}+2q^{11}+7q^{13}+\cdots\)
8400.2.a.cc \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}+3q^{11}-2q^{13}+\cdots\)
8400.2.a.cd \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
8400.2.a.ce \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
8400.2.a.cf \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
8400.2.a.cg \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}+5q^{11}-4q^{13}+\cdots\)
8400.2.a.ch \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
8400.2.a.ci \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}-6q^{11}+q^{13}-3q^{17}+\cdots\)
8400.2.a.cj \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
8400.2.a.ck \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}-2q^{11}+q^{13}-3q^{17}+\cdots\)
8400.2.a.cl \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}-2q^{13}-2q^{17}+\cdots\)
8400.2.a.cm \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)
8400.2.a.cn \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)
8400.2.a.co \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots\)
8400.2.a.cp \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}+q^{11}-2q^{13}-6q^{19}+\cdots\)
8400.2.a.cq \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}+q^{11}+4q^{13}+2q^{17}+\cdots\)
8400.2.a.cr \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}+3q^{11}-2q^{13}+\cdots\)
8400.2.a.cs \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots\)
8400.2.a.ct \(1\) \(67.074\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
8400.2.a.cu \(2\) \(67.074\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}-q^{7}+q^{9}+(-1-\beta )q^{11}+(2+\cdots)q^{13}+\cdots\)
8400.2.a.cv \(2\) \(67.074\) \(\Q(\sqrt{73}) \) None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}-\beta q^{11}+(1+\beta )q^{13}+\cdots\)
8400.2.a.cw \(2\) \(67.074\) \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}-q^{7}+q^{9}+3q^{11}+(1+\beta )q^{13}+\cdots\)
8400.2.a.cx \(2\) \(67.074\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}+(-2-\beta )q^{11}-\beta q^{13}+\cdots\)
8400.2.a.cy \(2\) \(67.074\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{7}+q^{9}+(1+2\beta )q^{11}+(3+\cdots)q^{13}+\cdots\)
8400.2.a.cz \(2\) \(67.074\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{7}+q^{9}+2q^{11}-\beta q^{13}+\cdots\)
8400.2.a.da \(2\) \(67.074\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}+(1+2\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
8400.2.a.db \(2\) \(67.074\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{7}+q^{9}+2q^{11}-\beta q^{13}+\cdots\)
8400.2.a.dc \(2\) \(67.074\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(0\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}+(-1-\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
8400.2.a.dd \(2\) \(67.074\) \(\Q(\sqrt{73}) \) None \(0\) \(2\) \(0\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}-\beta q^{11}+(-1-\beta )q^{13}+\cdots\)
8400.2.a.de \(2\) \(67.074\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(2\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots\)
8400.2.a.df \(2\) \(67.074\) \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{7}+q^{9}+3q^{11}+(-1+\beta )q^{13}+\cdots\)
8400.2.a.dg \(3\) \(67.074\) 3.3.148.1 None \(0\) \(-3\) \(0\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}-q^{7}+q^{9}-2q^{11}+(2-\beta _{2})q^{13}+\cdots\)
8400.2.a.dh \(3\) \(67.074\) 3.3.148.1 None \(0\) \(-3\) \(0\) \(-3\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}-q^{7}+q^{9}+(-1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
8400.2.a.di \(3\) \(67.074\) 3.3.148.1 None \(0\) \(-3\) \(0\) \(-3\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}-q^{7}+q^{9}+(1+\beta _{1}-\beta _{2})q^{11}+\cdots\)
8400.2.a.dj \(3\) \(67.074\) 3.3.148.1 None \(0\) \(3\) \(0\) \(3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}-2q^{11}+(-2+\beta _{2})q^{13}+\cdots\)
8400.2.a.dk \(3\) \(67.074\) 3.3.148.1 None \(0\) \(3\) \(0\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}+(-1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
8400.2.a.dl \(3\) \(67.074\) 3.3.148.1 None \(0\) \(3\) \(0\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}+(1+\beta _{1}-\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8400))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8400)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(700))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1050))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4200))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))
$5$ 1
$7$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))
$11$ (\( 1 + 6 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 3 T + 20 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + T + 4 T^{2} + 11 T^{3} + 121 T^{4} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( 1 + 4 T + 6 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 - 2 T + 3 T^{2} - 22 T^{3} + 121 T^{4} \))(\( ( 1 - 2 T + 11 T^{2} )^{2} \))(\( 1 - 2 T + 3 T^{2} - 22 T^{3} + 121 T^{4} \))(\( ( 1 - 2 T + 11 T^{2} )^{2} \))(\( 1 + 3 T + 20 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + T + 4 T^{2} + 11 T^{3} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{3} \))(\( 1 + 2 T + 13 T^{2} + 36 T^{3} + 143 T^{4} + 242 T^{5} + 1331 T^{6} \))(\( 1 - 2 T - 3 T^{2} + 60 T^{3} - 33 T^{4} - 242 T^{5} + 1331 T^{6} \))(\( ( 1 + 2 T + 11 T^{2} )^{3} \))(\( 1 + 2 T + 13 T^{2} + 36 T^{3} + 143 T^{4} + 242 T^{5} + 1331 T^{6} \))(\( 1 - 2 T - 3 T^{2} + 60 T^{3} - 33 T^{4} - 242 T^{5} + 1331 T^{6} \))
$13$ (\( 1 + T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 3 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 7 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 7 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} \))(\( 1 - 3 T + 10 T^{2} - 39 T^{3} + 169 T^{4} \))(\( 1 - 2 T + 14 T^{2} - 26 T^{3} + 169 T^{4} \))(\( 1 + 6 T^{2} + 169 T^{4} \))(\( 1 - 6 T + 30 T^{2} - 78 T^{3} + 169 T^{4} \))(\( 1 + 6 T^{2} + 169 T^{4} \))(\( 1 + 6 T + 30 T^{2} + 78 T^{3} + 169 T^{4} \))(\( 1 + 6 T^{2} + 169 T^{4} \))(\( 1 + T - 12 T^{2} + 13 T^{3} + 169 T^{4} \))(\( 1 + 3 T + 10 T^{2} + 39 T^{3} + 169 T^{4} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( 1 + 2 T + 14 T^{2} + 26 T^{3} + 169 T^{4} \))(\( 1 - 6 T + 35 T^{2} - 148 T^{3} + 455 T^{4} - 1014 T^{5} + 2197 T^{6} \))(\( 1 - 2 T + 27 T^{2} - 44 T^{3} + 351 T^{4} - 338 T^{5} + 2197 T^{6} \))(\( 1 + 10 T + 59 T^{2} + 252 T^{3} + 767 T^{4} + 1690 T^{5} + 2197 T^{6} \))(\( 1 + 6 T + 35 T^{2} + 148 T^{3} + 455 T^{4} + 1014 T^{5} + 2197 T^{6} \))(\( 1 + 2 T + 27 T^{2} + 44 T^{3} + 351 T^{4} + 338 T^{5} + 2197 T^{6} \))(\( 1 - 10 T + 59 T^{2} - 252 T^{3} + 767 T^{4} - 1690 T^{5} + 2197 T^{6} \))
$17$ (\( 1 - 3 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 5 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - 5 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 7 T + 42 T^{2} - 119 T^{3} + 289 T^{4} \))(\( 1 - T + 16 T^{2} - 17 T^{3} + 289 T^{4} \))(\( 1 - 2 T + 22 T^{2} - 34 T^{3} + 289 T^{4} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( 1 + 2 T - 10 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 2 T - 10 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 7 T + 42 T^{2} + 119 T^{3} + 289 T^{4} \))(\( 1 + T + 16 T^{2} + 17 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 6 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 + 2 T + 22 T^{2} + 34 T^{3} + 289 T^{4} \))(\( 1 + 35 T^{2} + 16 T^{3} + 595 T^{4} + 4913 T^{6} \))(\( 1 + 35 T^{2} + 16 T^{3} + 595 T^{4} + 4913 T^{6} \))(\( 1 + 8 T + 19 T^{2} + 323 T^{4} + 2312 T^{5} + 4913 T^{6} \))(\( 1 + 35 T^{2} - 16 T^{3} + 595 T^{4} + 4913 T^{6} \))(\( 1 + 35 T^{2} - 16 T^{3} + 595 T^{4} + 4913 T^{6} \))(\( 1 - 8 T + 19 T^{2} + 323 T^{4} - 2312 T^{5} + 4913 T^{6} \))
$19$ (\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 6 T + 30 T^{2} + 114 T^{3} + 361 T^{4} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( 1 + 6 T + 34 T^{2} + 114 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 22 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 2 T + 34 T^{2} - 38 T^{3} + 361 T^{4} \))(\( ( 1 + 2 T + 19 T^{2} )^{2} \))(\( 1 - 2 T + 34 T^{2} - 38 T^{3} + 361 T^{4} \))(\( ( 1 + 2 T + 19 T^{2} )^{2} \))(\( 1 + 6 T + 30 T^{2} + 114 T^{3} + 361 T^{4} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( 1 + 6 T^{2} + 361 T^{4} \))(\( 1 + 6 T + 34 T^{2} + 114 T^{3} + 361 T^{4} \))(\( 1 + 6 T + 53 T^{2} + 188 T^{3} + 1007 T^{4} + 2166 T^{5} + 6859 T^{6} \))(\( 1 + 2 T + 45 T^{2} + 68 T^{3} + 855 T^{4} + 722 T^{5} + 6859 T^{6} \))(\( 1 - 2 T - 3 T^{2} + 124 T^{3} - 57 T^{4} - 722 T^{5} + 6859 T^{6} \))(\( 1 + 6 T + 53 T^{2} + 188 T^{3} + 1007 T^{4} + 2166 T^{5} + 6859 T^{6} \))(\( 1 + 2 T + 45 T^{2} + 68 T^{3} + 855 T^{4} + 722 T^{5} + 6859 T^{6} \))(\( 1 - 2 T - 3 T^{2} + 124 T^{3} - 57 T^{4} - 722 T^{5} + 6859 T^{6} \))
$23$ (\( 1 - 3 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 7 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 5 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 7 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 7 T + 23 T^{2} \))(\( 1 + 5 T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 9 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 29 T^{2} + 529 T^{4} \))(\( ( 1 + 3 T + 23 T^{2} )^{2} \))(\( 1 + 2 T - 5 T^{2} + 46 T^{3} + 529 T^{4} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 5 T + 23 T^{2} )^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 - 5 T + 23 T^{2} )^{2} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( 1 + 29 T^{2} + 529 T^{4} \))(\( ( 1 - 3 T + 23 T^{2} )^{2} \))(\( 1 + 14 T^{2} + 529 T^{4} \))(\( 1 - 2 T - 5 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 61 T^{2} - 168 T^{3} + 1403 T^{4} - 2116 T^{5} + 12167 T^{6} \))(\( 1 + 8 T + 77 T^{2} + 352 T^{3} + 1771 T^{4} + 4232 T^{5} + 12167 T^{6} \))(\( 1 - 8 T + 29 T^{2} - 64 T^{3} + 667 T^{4} - 4232 T^{5} + 12167 T^{6} \))(\( 1 + 4 T + 61 T^{2} + 168 T^{3} + 1403 T^{4} + 2116 T^{5} + 12167 T^{6} \))(\( 1 - 8 T + 77 T^{2} - 352 T^{3} + 1771 T^{4} - 4232 T^{5} + 12167 T^{6} \))(\( 1 + 8 T + 29 T^{2} + 64 T^{3} + 667 T^{4} + 4232 T^{5} + 12167 T^{6} \))
$29$ (\( 1 - 3 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 7 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 - 10 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + 7 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 8 T + 57 T^{2} - 232 T^{3} + 841 T^{4} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( 1 + 8 T + 61 T^{2} + 232 T^{3} + 841 T^{4} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( 1 + 4 T + 17 T^{2} + 116 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 + 4 T + 17 T^{2} + 116 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 57 T^{2} - 232 T^{3} + 841 T^{4} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( 1 + 4 T + 30 T^{2} + 116 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 61 T^{2} + 232 T^{3} + 841 T^{4} \))(\( 1 - 2 T + 35 T^{2} - 76 T^{3} + 1015 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( 1 - 2 T + 3 T^{2} - 12 T^{3} + 87 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( ( 1 + 2 T + 29 T^{2} )^{3} \))(\( 1 - 2 T + 35 T^{2} - 76 T^{3} + 1015 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( 1 - 2 T + 3 T^{2} - 12 T^{3} + 87 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( ( 1 + 2 T + 29 T^{2} )^{3} \))
$31$ (\( 1 + 5 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 9 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 9 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - T + 24 T^{2} - 31 T^{3} + 961 T^{4} \))(\( 1 + T + 44 T^{2} + 31 T^{3} + 961 T^{4} \))(\( 1 + 10 T^{2} + 961 T^{4} \))(\( 1 + 12 T + 78 T^{2} + 372 T^{3} + 961 T^{4} \))(\( 1 + 42 T^{2} + 961 T^{4} \))(\( 1 + 8 T + 58 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + 42 T^{2} + 961 T^{4} \))(\( 1 + 8 T + 58 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - T + 24 T^{2} - 31 T^{3} + 961 T^{4} \))(\( 1 + T + 44 T^{2} + 31 T^{3} + 961 T^{4} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( 1 + 10 T^{2} + 961 T^{4} \))(\( 1 + 2 T + 41 T^{2} - 60 T^{3} + 1271 T^{4} + 1922 T^{5} + 29791 T^{6} \))(\( 1 - 2 T + 81 T^{2} - 116 T^{3} + 2511 T^{4} - 1922 T^{5} + 29791 T^{6} \))(\( 1 - 14 T + 145 T^{2} - 908 T^{3} + 4495 T^{4} - 13454 T^{5} + 29791 T^{6} \))(\( 1 + 2 T + 41 T^{2} - 60 T^{3} + 1271 T^{4} + 1922 T^{5} + 29791 T^{6} \))(\( 1 - 2 T + 81 T^{2} - 116 T^{3} + 2511 T^{4} - 1922 T^{5} + 29791 T^{6} \))(\( 1 - 14 T + 145 T^{2} - 908 T^{3} + 4495 T^{4} - 13454 T^{5} + 29791 T^{6} \))
$37$ (\( 1 + 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 9 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + 11 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 9 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 11 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 3 T + 72 T^{2} - 111 T^{3} + 1369 T^{4} \))(\( 1 + 7 T + 68 T^{2} + 259 T^{3} + 1369 T^{4} \))(\( 1 - 6 T + 31 T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 + 4 T - 2 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 2 T + 55 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 58 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 + 2 T + 55 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 58 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 3 T + 72 T^{2} + 111 T^{3} + 1369 T^{4} \))(\( 1 - 7 T + 68 T^{2} - 259 T^{3} + 1369 T^{4} \))(\( 1 + 12 T + 78 T^{2} + 444 T^{3} + 1369 T^{4} \))(\( 1 + 6 T + 31 T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 31 T^{2} - 232 T^{3} + 1147 T^{4} - 5476 T^{5} + 50653 T^{6} \))(\( 1 + 4 T + 63 T^{2} + 232 T^{3} + 2331 T^{4} + 5476 T^{5} + 50653 T^{6} \))(\( 1 + 12 T + 95 T^{2} + 568 T^{3} + 3515 T^{4} + 16428 T^{5} + 50653 T^{6} \))(\( 1 + 4 T + 31 T^{2} + 232 T^{3} + 1147 T^{4} + 5476 T^{5} + 50653 T^{6} \))(\( 1 - 4 T + 63 T^{2} - 232 T^{3} + 2331 T^{4} - 5476 T^{5} + 50653 T^{6} \))(\( 1 - 12 T + 95 T^{2} - 568 T^{3} + 3515 T^{4} - 16428 T^{5} + 50653 T^{6} \))
$41$ (\( 1 - 9 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 - T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 11 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 - T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 11 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 + 11 T + 74 T^{2} + 451 T^{3} + 1681 T^{4} \))(\( 1 - 3 T + 66 T^{2} - 123 T^{3} + 1681 T^{4} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( 1 + 16 T + 126 T^{2} + 656 T^{3} + 1681 T^{4} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( 1 + 16 T + 126 T^{2} + 656 T^{3} + 1681 T^{4} \))(\( 1 + 11 T + 74 T^{2} + 451 T^{3} + 1681 T^{4} \))(\( 1 - 3 T + 66 T^{2} - 123 T^{3} + 1681 T^{4} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( 1 - 2 T + 63 T^{2} + 36 T^{3} + 2583 T^{4} - 3362 T^{5} + 68921 T^{6} \))(\( 1 - 14 T + 175 T^{2} - 1188 T^{3} + 7175 T^{4} - 23534 T^{5} + 68921 T^{6} \))(\( 1 + 10 T + 143 T^{2} + 812 T^{3} + 5863 T^{4} + 16810 T^{5} + 68921 T^{6} \))(\( 1 - 2 T + 63 T^{2} + 36 T^{3} + 2583 T^{4} - 3362 T^{5} + 68921 T^{6} \))(\( 1 - 14 T + 175 T^{2} - 1188 T^{3} + 7175 T^{4} - 23534 T^{5} + 68921 T^{6} \))(\( 1 + 10 T + 143 T^{2} + 812 T^{3} + 5863 T^{4} + 16810 T^{5} + 68921 T^{6} \))
$43$ (\( 1 - T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 11 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 + 3 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 9 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 - 3 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 - 5 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 11 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 7 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 - 3 T + 43 T^{2} \))(\( 1 - 9 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 3 T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 + 11 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 11 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))(\( 1 + 7 T + 43 T^{2} \))(\( 1 + T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 85 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 + 8 T + 29 T^{2} + 344 T^{3} + 1849 T^{4} \))(\( 1 + 12 T + 109 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 + 6 T^{2} + 1849 T^{4} \))(\( 1 + 12 T + 117 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 - 4 T + 70 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 - 12 T + 117 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 + 4 T + 70 T^{2} + 172 T^{3} + 1849 T^{4} \))(\( 1 + 8 T + 85 T^{2} + 344 T^{3} + 1849 T^{4} \))(\( 1 - 8 T + 29 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 + 8 T + 70 T^{2} + 344 T^{3} + 1849 T^{4} \))(\( 1 - 12 T + 109 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 - 4 T - 15 T^{2} + 488 T^{3} - 645 T^{4} - 7396 T^{5} + 79507 T^{6} \))(\( 1 + 12 T + 113 T^{2} + 712 T^{3} + 4859 T^{4} + 22188 T^{5} + 79507 T^{6} \))(\( 1 - 4 T + 81 T^{2} - 280 T^{3} + 3483 T^{4} - 7396 T^{5} + 79507 T^{6} \))(\( 1 + 4 T - 15 T^{2} - 488 T^{3} - 645 T^{4} + 7396 T^{5} + 79507 T^{6} \))(\( 1 - 12 T + 113 T^{2} - 712 T^{3} + 4859 T^{4} - 22188 T^{5} + 79507 T^{6} \))(\( 1 + 4 T + 81 T^{2} + 280 T^{3} + 3483 T^{4} + 7396 T^{5} + 79507 T^{6} \))
$47$ (\( 1 + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 2 T + 78 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( 1 + 14 T + 130 T^{2} + 658 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 30 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 10 T + 114 T^{2} + 470 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 78 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 - 10 T + 114 T^{2} - 470 T^{3} + 2209 T^{4} \))(\( 1 + 4 T + 78 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 - 2 T + 78 T^{2} - 94 T^{3} + 2209 T^{4} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( 1 + 16 T + 126 T^{2} + 752 T^{3} + 2209 T^{4} \))(\( 1 - 14 T + 130 T^{2} - 658 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 109 T^{2} - 624 T^{3} + 5123 T^{4} - 17672 T^{5} + 103823 T^{6} \))(\( 1 + 8 T + 77 T^{2} + 496 T^{3} + 3619 T^{4} + 17672 T^{5} + 103823 T^{6} \))(\( ( 1 + 47 T^{2} )^{3} \))(\( 1 + 8 T + 109 T^{2} + 624 T^{3} + 5123 T^{4} + 17672 T^{5} + 103823 T^{6} \))(\( 1 - 8 T + 77 T^{2} - 496 T^{3} + 3619 T^{4} - 17672 T^{5} + 103823 T^{6} \))(\( ( 1 + 47 T^{2} )^{3} \))
$53$ (\( 1 - 9 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 11 T + 53 T^{2} \))(\( 1 - 11 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 3 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 13 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 8 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 13 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 3 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 - T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 5 T + 108 T^{2} + 265 T^{3} + 2809 T^{4} \))(\( 1 - T + 88 T^{2} - 53 T^{3} + 2809 T^{4} \))(\( 1 + 8 T + 70 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( 1 - 16 T + 150 T^{2} - 848 T^{3} + 2809 T^{4} \))(\( 1 + 8 T + 102 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( ( 1 + 2 T + 53 T^{2} )^{2} \))(\( 1 - 8 T + 102 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( ( 1 - 2 T + 53 T^{2} )^{2} \))(\( 1 - 5 T + 108 T^{2} - 265 T^{3} + 2809 T^{4} \))(\( 1 + T + 88 T^{2} + 53 T^{3} + 2809 T^{4} \))(\( 1 + 4 T + 78 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 - 8 T + 70 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( 1 + 14 T + 171 T^{2} + 1188 T^{3} + 9063 T^{4} + 39326 T^{5} + 148877 T^{6} \))(\( 1 - 14 T + 131 T^{2} - 1012 T^{3} + 6943 T^{4} - 39326 T^{5} + 148877 T^{6} \))(\( 1 + 14 T + 211 T^{2} + 1524 T^{3} + 11183 T^{4} + 39326 T^{5} + 148877 T^{6} \))(\( 1 - 14 T + 171 T^{2} - 1188 T^{3} + 9063 T^{4} - 39326 T^{5} + 148877 T^{6} \))(\( 1 + 14 T + 131 T^{2} + 1012 T^{3} + 6943 T^{4} + 39326 T^{5} + 148877 T^{6} \))(\( 1 - 14 T + 211 T^{2} - 1524 T^{3} + 11183 T^{4} - 39326 T^{5} + 148877 T^{6} \))
$59$ (\( 1 + 9 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 5 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 5 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 7 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 15 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + 5 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 15 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 7 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 9 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 5 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 7 T + 92 T^{2} + 413 T^{3} + 3481 T^{4} \))(\( 1 + 3 T + 102 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 - 14 T + 154 T^{2} - 826 T^{3} + 3481 T^{4} \))(\( 1 + 38 T^{2} + 3481 T^{4} \))(\( 1 - 6 T + 122 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( 1 - 6 T + 122 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( 1 + 7 T + 92 T^{2} + 413 T^{3} + 3481 T^{4} \))(\( 1 + 3 T + 102 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( 1 - 14 T + 154 T^{2} - 826 T^{3} + 3481 T^{4} \))(\( 1 + 16 T + 113 T^{2} + 608 T^{3} + 6667 T^{4} + 55696 T^{5} + 205379 T^{6} \))(\( 1 + 8 T + 113 T^{2} + 688 T^{3} + 6667 T^{4} + 27848 T^{5} + 205379 T^{6} \))(\( 1 - 8 T + 113 T^{2} - 688 T^{3} + 6667 T^{4} - 27848 T^{5} + 205379 T^{6} \))(\( 1 + 16 T + 113 T^{2} + 608 T^{3} + 6667 T^{4} + 55696 T^{5} + 205379 T^{6} \))(\( 1 + 8 T + 113 T^{2} + 688 T^{3} + 6667 T^{4} + 27848 T^{5} + 205379 T^{6} \))(\( 1 - 8 T + 113 T^{2} - 688 T^{3} + 6667 T^{4} - 27848 T^{5} + 205379 T^{6} \))
$61$ (\( 1 - 11 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 3 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 12 T + 61 T^{2} \))(\( 1 - 9 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 12 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 12 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - 9 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 7 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 12 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 11 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 3 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 9 T + 138 T^{2} + 549 T^{3} + 3721 T^{4} \))(\( 1 - 5 T + 110 T^{2} - 305 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 106 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( 1 + 4 T - 54 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 16 T + 166 T^{2} + 976 T^{3} + 3721 T^{4} \))(\( 1 + 4 T - 54 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 16 T + 166 T^{2} + 976 T^{3} + 3721 T^{4} \))(\( 1 + 9 T + 138 T^{2} + 549 T^{3} + 3721 T^{4} \))(\( 1 - 5 T + 110 T^{2} - 305 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 126 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 106 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 + 6 T + 131 T^{2} + 484 T^{3} + 7991 T^{4} + 22326 T^{5} + 226981 T^{6} \))(\( 1 - 2 T + 35 T^{2} - 780 T^{3} + 2135 T^{4} - 7442 T^{5} + 226981 T^{6} \))(\( 1 - 2 T - 29 T^{2} - 140 T^{3} - 1769 T^{4} - 7442 T^{5} + 226981 T^{6} \))(\( 1 + 6 T + 131 T^{2} + 484 T^{3} + 7991 T^{4} + 22326 T^{5} + 226981 T^{6} \))(\( 1 - 2 T + 35 T^{2} - 780 T^{3} + 2135 T^{4} - 7442 T^{5} + 226981 T^{6} \))(\( 1 - 2 T - 29 T^{2} - 140 T^{3} - 1769 T^{4} - 7442 T^{5} + 226981 T^{6} \))
$67$ (\( 1 - 4 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 - 13 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 9 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 - 16 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 9 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 9 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 + 16 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 13 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 5 T + 34 T^{2} - 335 T^{3} + 4489 T^{4} \))(\( 1 - 11 T + 146 T^{2} - 737 T^{3} + 4489 T^{4} \))(\( 1 + 24 T + 265 T^{2} + 1608 T^{3} + 4489 T^{4} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( 1 + 8 T + 105 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 150 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 - 8 T + 105 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 150 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 + 5 T + 34 T^{2} + 335 T^{3} + 4489 T^{4} \))(\( 1 + 11 T + 146 T^{2} + 737 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 118 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 24 T + 265 T^{2} - 1608 T^{3} + 4489 T^{4} \))(\( 1 - 8 T + 169 T^{2} - 944 T^{3} + 11323 T^{4} - 35912 T^{5} + 300763 T^{6} \))(\( ( 1 + 67 T^{2} )^{3} \))(\( 1 + 16 T + 201 T^{2} + 1888 T^{3} + 13467 T^{4} + 71824 T^{5} + 300763 T^{6} \))(\( 1 + 8 T + 169 T^{2} + 944 T^{3} + 11323 T^{4} + 35912 T^{5} + 300763 T^{6} \))(\( ( 1 + 67 T^{2} )^{3} \))(\( 1 - 16 T + 201 T^{2} - 1888 T^{3} + 13467 T^{4} - 71824 T^{5} + 300763 T^{6} \))
$71$ (\( 1 - 12 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 14 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 + 14 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 5 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 7 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 - 10 T + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 + 14 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 + 5 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 + 7 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 - T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 5 T + 42 T^{2} + 355 T^{3} + 5041 T^{4} \))(\( 1 + 11 T + 154 T^{2} + 781 T^{3} + 5041 T^{4} \))(\( ( 1 - 3 T + 71 T^{2} )^{2} \))(\( 1 + 20 T + 222 T^{2} + 1420 T^{3} + 5041 T^{4} \))(\( 1 - 10 T + 147 T^{2} - 710 T^{3} + 5041 T^{4} \))(\( 1 + 16 T + 186 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 - 10 T + 147 T^{2} - 710 T^{3} + 5041 T^{4} \))(\( 1 + 16 T + 186 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 + 5 T + 42 T^{2} + 355 T^{3} + 5041 T^{4} \))(\( 1 + 11 T + 154 T^{2} + 781 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 30 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( ( 1 - 3 T + 71 T^{2} )^{2} \))(\( ( 1 + 2 T + 71 T^{2} )^{3} \))(\( 1 - 6 T + 113 T^{2} - 1052 T^{3} + 8023 T^{4} - 30246 T^{5} + 357911 T^{6} \))(\( 1 - 18 T + 161 T^{2} - 1204 T^{3} + 11431 T^{4} - 90738 T^{5} + 357911 T^{6} \))(\( ( 1 + 2 T + 71 T^{2} )^{3} \))(\( 1 - 6 T + 113 T^{2} - 1052 T^{3} + 8023 T^{4} - 30246 T^{5} + 357911 T^{6} \))(\( 1 - 18 T + 161 T^{2} - 1204 T^{3} + 11431 T^{4} - 90738 T^{5} + 357911 T^{6} \))
$73$ (\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 8 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 8 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 6 T + 2 T^{2} - 438 T^{3} + 5329 T^{4} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( 1 + 6 T + 142 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( 1 - 16 T + 190 T^{2} - 1168 T^{3} + 5329 T^{4} \))(\( 1 + 2 T + 142 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 24 T + 270 T^{2} + 1752 T^{3} + 5329 T^{4} \))(\( 1 - 2 T + 142 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 - 24 T + 270 T^{2} - 1752 T^{3} + 5329 T^{4} \))(\( 1 + 6 T + 2 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 6 T + 73 T^{2} )^{2} \))(\( 1 - 6 T + 142 T^{2} - 438 T^{3} + 5329 T^{4} \))(\( 1 - 18 T + 311 T^{2} - 2732 T^{3} + 22703 T^{4} - 95922 T^{5} + 389017 T^{6} \))(\( 1 - 6 T + 95 T^{2} - 116 T^{3} + 6935 T^{4} - 31974 T^{5} + 389017 T^{6} \))(\( 1 + 22 T + 319 T^{2} + 3316 T^{3} + 23287 T^{4} + 117238 T^{5} + 389017 T^{6} \))(\( 1 + 18 T + 311 T^{2} + 2732 T^{3} + 22703 T^{4} + 95922 T^{5} + 389017 T^{6} \))(\( 1 + 6 T + 95 T^{2} + 116 T^{3} + 6935 T^{4} + 31974 T^{5} + 389017 T^{6} \))(\( 1 - 22 T + 319 T^{2} - 3316 T^{3} + 23287 T^{4} - 117238 T^{5} + 389017 T^{6} \))
$79$ (\( 1 - 10 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 + 17 T + 79 T^{2} \))(\( 1 - 13 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 3 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 15 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 - 6 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 7 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 3 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 - 5 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 - 15 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 6 T + 79 T^{2} \))(\( 1 - T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 7 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 - T + 79 T^{2} \))(\( 1 - 13 T + 79 T^{2} \))(\( 1 + 17 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 21 T + 264 T^{2} + 1659 T^{3} + 6241 T^{4} \))(\( 1 - 3 T - 4 T^{2} - 237 T^{3} + 6241 T^{4} \))(\( 1 - 8 T + 57 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 94 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 169 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 78 T^{2} + 6241 T^{4} \))(\( 1 + 8 T + 169 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 78 T^{2} + 6241 T^{4} \))(\( 1 + 21 T + 264 T^{2} + 1659 T^{3} + 6241 T^{4} \))(\( 1 - 3 T - 4 T^{2} - 237 T^{3} + 6241 T^{4} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( 1 - 8 T + 57 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 + 12 T + 221 T^{2} + 1576 T^{3} + 17459 T^{4} + 74892 T^{5} + 493039 T^{6} \))(\( 1 - 20 T + 317 T^{2} - 3096 T^{3} + 25043 T^{4} - 124820 T^{5} + 493039 T^{6} \))(\( 1 + 4 T + 189 T^{2} + 568 T^{3} + 14931 T^{4} + 24964 T^{5} + 493039 T^{6} \))(\( 1 + 12 T + 221 T^{2} + 1576 T^{3} + 17459 T^{4} + 74892 T^{5} + 493039 T^{6} \))(\( 1 - 20 T + 317 T^{2} - 3096 T^{3} + 25043 T^{4} - 124820 T^{5} + 493039 T^{6} \))(\( 1 + 4 T + 189 T^{2} + 568 T^{3} + 14931 T^{4} + 24964 T^{5} + 493039 T^{6} \))
$83$ (\( 1 + 9 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 11 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 5 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 - 5 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 11 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 7 T + 140 T^{2} + 581 T^{3} + 6889 T^{4} \))(\( 1 + 23 T + 280 T^{2} + 1909 T^{3} + 6889 T^{4} \))(\( 1 + 8 T + 130 T^{2} + 664 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 150 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 210 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 - 8 T + 102 T^{2} - 664 T^{3} + 6889 T^{4} \))(\( 1 - 16 T + 210 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 + 8 T + 102 T^{2} + 664 T^{3} + 6889 T^{4} \))(\( 1 - 7 T + 140 T^{2} - 581 T^{3} + 6889 T^{4} \))(\( 1 - 23 T + 280 T^{2} - 1909 T^{3} + 6889 T^{4} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( 1 - 8 T + 130 T^{2} - 664 T^{3} + 6889 T^{4} \))(\( 1 - 8 T + 185 T^{2} - 1072 T^{3} + 15355 T^{4} - 55112 T^{5} + 571787 T^{6} \))(\( 1 + 8 T + 185 T^{2} + 1072 T^{3} + 15355 T^{4} + 55112 T^{5} + 571787 T^{6} \))(\( 1 - 8 T + 185 T^{2} - 1072 T^{3} + 15355 T^{4} - 55112 T^{5} + 571787 T^{6} \))(\( 1 + 8 T + 185 T^{2} + 1072 T^{3} + 15355 T^{4} + 55112 T^{5} + 571787 T^{6} \))(\( 1 - 8 T + 185 T^{2} - 1072 T^{3} + 15355 T^{4} - 55112 T^{5} + 571787 T^{6} \))(\( 1 + 8 T + 185 T^{2} + 1072 T^{3} + 15355 T^{4} + 55112 T^{5} + 571787 T^{6} \))
$89$ (\( 1 + 6 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 16 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 - 16 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 4 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 2 T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( 1 - 18 T + 186 T^{2} - 1602 T^{3} + 7921 T^{4} \))(\( 1 + 6 T + 70 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( ( 1 + 2 T + 89 T^{2} )^{2} \))(\( 1 - 2 T + 134 T^{2} - 178 T^{3} + 7921 T^{4} \))(\( 1 + 8 T + 14 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 - 2 T + 134 T^{2} - 178 T^{3} + 7921 T^{4} \))(\( 1 + 8 T + 14 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( 1 - 18 T + 186 T^{2} - 1602 T^{3} + 7921 T^{4} \))(\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( 1 + 6 T + 70 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 14 T + 319 T^{2} - 2532 T^{3} + 28391 T^{4} - 110894 T^{5} + 704969 T^{6} \))(\( 1 - 2 T + 207 T^{2} - 156 T^{3} + 18423 T^{4} - 15842 T^{5} + 704969 T^{6} \))(\( 1 + 6 T + 143 T^{2} + 1300 T^{3} + 12727 T^{4} + 47526 T^{5} + 704969 T^{6} \))(\( 1 - 14 T + 319 T^{2} - 2532 T^{3} + 28391 T^{4} - 110894 T^{5} + 704969 T^{6} \))(\( 1 - 2 T + 207 T^{2} - 156 T^{3} + 18423 T^{4} - 15842 T^{5} + 704969 T^{6} \))(\( 1 + 6 T + 143 T^{2} + 1300 T^{3} + 12727 T^{4} + 47526 T^{5} + 704969 T^{6} \))
$97$ (\( 1 - 14 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 6 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 16 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( ( 1 - 6 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( 1 + 16 T + 206 T^{2} + 1552 T^{3} + 9409 T^{4} \))(\( 1 + 8 T + 190 T^{2} + 776 T^{3} + 9409 T^{4} \))(\( 1 - 16 T + 238 T^{2} - 1552 T^{3} + 9409 T^{4} \))(\( 1 + 16 T + 238 T^{2} + 1552 T^{3} + 9409 T^{4} \))(\( 1 + 16 T + 238 T^{2} + 1552 T^{3} + 9409 T^{4} \))(\( 1 - 16 T + 238 T^{2} - 1552 T^{3} + 9409 T^{4} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( 1 - 16 T + 206 T^{2} - 1552 T^{3} + 9409 T^{4} \))(\( 1 - 22 T + 255 T^{2} - 2404 T^{3} + 24735 T^{4} - 206998 T^{5} + 912673 T^{6} \))(\( 1 + 14 T + 295 T^{2} + 2372 T^{3} + 28615 T^{4} + 131726 T^{5} + 912673 T^{6} \))(\( 1 + 2 T + 231 T^{2} + 188 T^{3} + 22407 T^{4} + 18818 T^{5} + 912673 T^{6} \))(\( 1 + 22 T + 255 T^{2} + 2404 T^{3} + 24735 T^{4} + 206998 T^{5} + 912673 T^{6} \))(\( 1 - 14 T + 295 T^{2} - 2372 T^{3} + 28615 T^{4} - 131726 T^{5} + 912673 T^{6} \))(\( 1 - 2 T + 231 T^{2} - 188 T^{3} + 22407 T^{4} - 18818 T^{5} + 912673 T^{6} \))
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