Properties

Label 324.3.f
Level 324
Weight 3
Character orbit f
Rep. character \(\chi_{324}(55,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 92
Newform subspaces 19
Sturm bound 162
Trace bound 5

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 19 \)
Sturm bound: \(162\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(324, [\chi])\).

Total New Old
Modular forms 240 100 140
Cusp forms 192 92 100
Eisenstein series 48 8 40

Trace form

\( 92q + 2q^{4} + O(q^{10}) \) \( 92q + 2q^{4} - 20q^{10} + 4q^{13} + 2q^{16} - 6q^{22} - 186q^{25} + 60q^{28} + 40q^{34} - 8q^{37} - 98q^{40} + 432q^{46} + 242q^{49} + 52q^{52} - 80q^{58} + 4q^{61} - 412q^{64} - 54q^{70} - 56q^{73} - 420q^{76} - 416q^{82} + 104q^{85} - 186q^{88} + 60q^{94} + 124q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
324.3.f.a \(2\) \(8.828\) \(\Q(\sqrt{-3}) \) None \(-4\) \(0\) \(-2\) \(12\) \(q-2q^{2}+4q^{4}+(-2+2\zeta_{6})q^{5}+(8+\cdots)q^{7}+\cdots\)
324.3.f.b \(2\) \(8.828\) \(\Q(\sqrt{-3}) \) None \(-4\) \(0\) \(7\) \(-15\) \(q-2q^{2}+4q^{4}+(7-7\zeta_{6})q^{5}+(-10+\cdots)q^{7}+\cdots\)
324.3.f.c \(2\) \(8.828\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-7\) \(15\) \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-7+7\zeta_{6})q^{5}+\cdots\)
324.3.f.d \(2\) \(8.828\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(2\) \(-12\) \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(2-2\zeta_{6})q^{5}+\cdots\)
324.3.f.e \(2\) \(8.828\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(8\) \(0\) \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+(8-8\zeta_{6})q^{5}+\cdots\)
324.3.f.f \(2\) \(8.828\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) \(2\) \(0\) \(-8\) \(0\) \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+(-8+8\zeta_{6})q^{5}+\cdots\)
324.3.f.g \(2\) \(8.828\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-2\) \(-12\) \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)
324.3.f.h \(2\) \(8.828\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(7\) \(15\) \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(7-7\zeta_{6})q^{5}+\cdots\)
324.3.f.i \(2\) \(8.828\) \(\Q(\sqrt{-3}) \) None \(4\) \(0\) \(-7\) \(-15\) \(q+2q^{2}+4q^{4}+(-7+7\zeta_{6})q^{5}+(-10+\cdots)q^{7}+\cdots\)
324.3.f.j \(2\) \(8.828\) \(\Q(\sqrt{-3}) \) None \(4\) \(0\) \(2\) \(12\) \(q+2q^{2}+4q^{4}+(2-2\zeta_{6})q^{5}+(8-4\zeta_{6})q^{7}+\cdots\)
324.3.f.k \(4\) \(8.828\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) \(-4\) \(0\) \(-8\) \(0\) \(q+(-2+2\zeta_{12})q^{2}-4\zeta_{12}q^{4}+(-4\zeta_{12}+\cdots)q^{5}+\cdots\)
324.3.f.l \(4\) \(8.828\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(-3\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+3\beta _{2}+\beta _{3})q^{4}+\cdots\)
324.3.f.m \(4\) \(8.828\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(3\) \(0\) \(0\) \(0\) \(q+(1-\beta _{1})q^{2}+(-\beta _{1}+3\beta _{2}+\beta _{3})q^{4}+\cdots\)
324.3.f.n \(4\) \(8.828\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) \(4\) \(0\) \(8\) \(0\) \(q+(2-2\zeta_{12})q^{2}-4\zeta_{12}q^{4}+(4\zeta_{12}+\cdots)q^{5}+\cdots\)
324.3.f.o \(8\) \(8.828\) 8.0.207360000.1 None \(0\) \(0\) \(0\) \(-12\) \(q+(-\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{7})q^{4}+\cdots\)
324.3.f.p \(8\) \(8.828\) 8.0.207360000.1 None \(0\) \(0\) \(0\) \(12\) \(q-\beta _{2}q^{2}+(1-\beta _{5}-\beta _{7})q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
324.3.f.q \(12\) \(8.828\) 12.0.\(\cdots\).2 None \(-1\) \(0\) \(-2\) \(0\) \(q+(-\beta _{3}+\beta _{6})q^{2}+(1+\beta _{2}+\beta _{4})q^{4}+\cdots\)
324.3.f.r \(12\) \(8.828\) 12.0.\(\cdots\).2 None \(1\) \(0\) \(2\) \(0\) \(q+(\beta _{3}-\beta _{6})q^{2}+(1+\beta _{2}+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
324.3.f.s \(16\) \(8.828\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(1-\beta _{2}-\beta _{3}-\beta _{7})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(324, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + 2 T )^{2} \))(\( ( 1 + 2 T )^{2} \))(\( 1 + 2 T + 4 T^{2} \))(\( 1 + 2 T + 4 T^{2} \))(\( 1 + 2 T + 4 T^{2} \))(\( 1 - 2 T + 4 T^{2} \))(\( 1 - 2 T + 4 T^{2} \))(\( 1 - 2 T + 4 T^{2} \))(\( ( 1 - 2 T )^{2} \))(\( ( 1 - 2 T )^{2} \))(\( ( 1 + 2 T + 4 T^{2} )^{2} \))(\( 1 + 3 T + 7 T^{2} + 12 T^{3} + 16 T^{4} \))(\( 1 - 3 T + 7 T^{2} - 12 T^{3} + 16 T^{4} \))(\( ( 1 - 2 T + 4 T^{2} )^{2} \))(\( 1 + 2 T^{2} - 12 T^{4} + 32 T^{6} + 256 T^{8} \))(\( ( 1 - 2 T^{2} + 16 T^{4} )^{2} \))(\( 1 + T - T^{2} - 6 T^{3} - 8 T^{4} + 8 T^{5} + 112 T^{6} + 32 T^{7} - 128 T^{8} - 384 T^{9} - 256 T^{10} + 1024 T^{11} + 4096 T^{12} \))(\( 1 - T - T^{2} + 6 T^{3} - 8 T^{4} - 8 T^{5} + 112 T^{6} - 32 T^{7} - 128 T^{8} + 384 T^{9} - 256 T^{10} - 1024 T^{11} + 4096 T^{12} \))(\( 1 - 5 T^{2} + T^{4} + 40 T^{6} - 80 T^{8} + 640 T^{10} + 256 T^{12} - 20480 T^{14} + 65536 T^{16} \))
$3$ 1
$5$ (\( 1 + 2 T - 21 T^{2} + 50 T^{3} + 625 T^{4} \))(\( 1 - 7 T + 24 T^{2} - 175 T^{3} + 625 T^{4} \))(\( 1 + 7 T + 24 T^{2} + 175 T^{3} + 625 T^{4} \))(\( 1 - 2 T - 21 T^{2} - 50 T^{3} + 625 T^{4} \))(\( 1 - 8 T + 39 T^{2} - 200 T^{3} + 625 T^{4} \))(\( 1 + 8 T + 39 T^{2} + 200 T^{3} + 625 T^{4} \))(\( 1 + 2 T - 21 T^{2} + 50 T^{3} + 625 T^{4} \))(\( 1 - 7 T + 24 T^{2} - 175 T^{3} + 625 T^{4} \))(\( 1 + 7 T + 24 T^{2} + 175 T^{3} + 625 T^{4} \))(\( 1 - 2 T - 21 T^{2} - 50 T^{3} + 625 T^{4} \))(\( ( 1 + 8 T + 25 T^{2} )^{2}( 1 - 8 T + 39 T^{2} - 200 T^{3} + 625 T^{4} ) \))(\( 1 - 37 T^{2} + 744 T^{4} - 23125 T^{6} + 390625 T^{8} \))(\( 1 - 37 T^{2} + 744 T^{4} - 23125 T^{6} + 390625 T^{8} \))(\( ( 1 - 8 T + 25 T^{2} )^{2}( 1 + 8 T + 39 T^{2} + 200 T^{3} + 625 T^{4} ) \))(\( 1 - 44 T^{2} + 922 T^{4} + 10384 T^{6} - 572429 T^{8} + 6490000 T^{10} + 360156250 T^{12} - 10742187500 T^{14} + 152587890625 T^{16} \))(\( 1 - 44 T^{2} + 922 T^{4} + 10384 T^{6} - 572429 T^{8} + 6490000 T^{10} + 360156250 T^{12} - 10742187500 T^{14} + 152587890625 T^{16} \))(\( ( 1 + T - 37 T^{2} - 180 T^{3} + 385 T^{4} + 2867 T^{5} + 6406 T^{6} + 71675 T^{7} + 240625 T^{8} - 2812500 T^{9} - 14453125 T^{10} + 9765625 T^{11} + 244140625 T^{12} )^{2} \))(\( ( 1 - T - 37 T^{2} + 180 T^{3} + 385 T^{4} - 2867 T^{5} + 6406 T^{6} - 71675 T^{7} + 240625 T^{8} + 2812500 T^{9} - 14453125 T^{10} - 9765625 T^{11} + 244140625 T^{12} )^{2} \))(\( ( 1 - 38 T^{2} + 745 T^{4} + 20938 T^{6} - 804524 T^{8} + 13086250 T^{10} + 291015625 T^{12} - 9277343750 T^{14} + 152587890625 T^{16} )^{2} \))
$7$ (\( 1 - 12 T + 97 T^{2} - 588 T^{3} + 2401 T^{4} \))(\( ( 1 + 2 T + 49 T^{2} )( 1 + 13 T + 49 T^{2} ) \))(\( ( 1 - 13 T + 49 T^{2} )( 1 - 2 T + 49 T^{2} ) \))(\( 1 + 12 T + 97 T^{2} + 588 T^{3} + 2401 T^{4} \))(\( ( 1 - 7 T + 49 T^{2} )( 1 + 7 T + 49 T^{2} ) \))(\( ( 1 - 7 T + 49 T^{2} )( 1 + 7 T + 49 T^{2} ) \))(\( 1 + 12 T + 97 T^{2} + 588 T^{3} + 2401 T^{4} \))(\( ( 1 - 13 T + 49 T^{2} )( 1 - 2 T + 49 T^{2} ) \))(\( ( 1 + 2 T + 49 T^{2} )( 1 + 13 T + 49 T^{2} ) \))(\( 1 - 12 T + 97 T^{2} - 588 T^{3} + 2401 T^{4} \))(\( ( 1 - 7 T + 49 T^{2} )^{2}( 1 + 7 T + 49 T^{2} )^{2} \))(\( 1 + 59 T^{2} + 1080 T^{4} + 141659 T^{6} + 5764801 T^{8} \))(\( 1 + 59 T^{2} + 1080 T^{4} + 141659 T^{6} + 5764801 T^{8} \))(\( ( 1 - 7 T + 49 T^{2} )^{2}( 1 + 7 T + 49 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} + 246 T^{3} - 132 T^{4} + 12054 T^{5} + 127253 T^{6} + 705894 T^{7} + 5764801 T^{8} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} - 246 T^{3} - 132 T^{4} - 12054 T^{5} + 127253 T^{6} - 705894 T^{7} + 5764801 T^{8} )^{2} \))(\( 1 + 114 T^{2} + 5397 T^{4} + 56438 T^{6} - 6661734 T^{8} - 425700582 T^{10} - 21918600819 T^{12} - 1022107097382 T^{14} - 38403570824934 T^{16} + 781174567050038 T^{18} + 179358126284136597 T^{20} + 9096318357927768114 T^{22} + \)\(19\!\cdots\!01\)\( T^{24} \))(\( 1 + 114 T^{2} + 5397 T^{4} + 56438 T^{6} - 6661734 T^{8} - 425700582 T^{10} - 21918600819 T^{12} - 1022107097382 T^{14} - 38403570824934 T^{16} + 781174567050038 T^{18} + 179358126284136597 T^{20} + 9096318357927768114 T^{22} + \)\(19\!\cdots\!01\)\( T^{24} \))(\( ( 1 + 40 T^{2} + 2098 T^{4} - 212000 T^{6} - 9358397 T^{8} - 509012000 T^{10} + 12094552498 T^{12} + 553651488040 T^{14} + 33232930569601 T^{16} )^{2} \))
$11$ (\( 1 - 12 T + 169 T^{2} - 1452 T^{3} + 14641 T^{4} \))(\( 1 + 15 T + 196 T^{2} + 1815 T^{3} + 14641 T^{4} \))(\( 1 + 15 T + 196 T^{2} + 1815 T^{3} + 14641 T^{4} \))(\( 1 - 12 T + 169 T^{2} - 1452 T^{3} + 14641 T^{4} \))(\( ( 1 - 11 T + 121 T^{2} )( 1 + 11 T + 121 T^{2} ) \))(\( ( 1 - 11 T + 121 T^{2} )( 1 + 11 T + 121 T^{2} ) \))(\( 1 + 12 T + 169 T^{2} + 1452 T^{3} + 14641 T^{4} \))(\( 1 - 15 T + 196 T^{2} - 1815 T^{3} + 14641 T^{4} \))(\( 1 - 15 T + 196 T^{2} - 1815 T^{3} + 14641 T^{4} \))(\( 1 + 12 T + 169 T^{2} + 1452 T^{3} + 14641 T^{4} \))(\( ( 1 - 11 T + 121 T^{2} )^{2}( 1 + 11 T + 121 T^{2} )^{2} \))(\( ( 1 + 21 T + 268 T^{2} + 2541 T^{3} + 14641 T^{4} )^{2} \))(\( ( 1 - 21 T + 268 T^{2} - 2541 T^{3} + 14641 T^{4} )^{2} \))(\( ( 1 - 11 T + 121 T^{2} )^{2}( 1 + 11 T + 121 T^{2} )^{2} \))(\( 1 + 124 T^{2} + 250 T^{4} - 1755344 T^{6} - 210683021 T^{8} - 25699991504 T^{10} + 53589720250 T^{12} + 389165118713404 T^{14} + 45949729863572161 T^{16} \))(\( 1 + 124 T^{2} + 250 T^{4} - 1755344 T^{6} - 210683021 T^{8} - 25699991504 T^{10} + 53589720250 T^{12} + 389165118713404 T^{14} + 45949729863572161 T^{16} \))(\( 1 + 210 T^{2} + 6309 T^{4} - 1603594 T^{6} - 126807270 T^{8} - 7112331078 T^{10} - 1334567686275 T^{12} - 104131639312998 T^{14} - 27182264499864870 T^{16} - 5032764914339535274 T^{18} + \)\(28\!\cdots\!49\)\( T^{20} + \)\(14\!\cdots\!10\)\( T^{22} + \)\(98\!\cdots\!41\)\( T^{24} \))(\( 1 + 210 T^{2} + 6309 T^{4} - 1603594 T^{6} - 126807270 T^{8} - 7112331078 T^{10} - 1334567686275 T^{12} - 104131639312998 T^{14} - 27182264499864870 T^{16} - 5032764914339535274 T^{18} + \)\(28\!\cdots\!49\)\( T^{20} + \)\(14\!\cdots\!10\)\( T^{22} + \)\(98\!\cdots\!41\)\( T^{24} \))(\( ( 1 + 208 T^{2} + 3394 T^{4} + 2202304 T^{6} + 741829795 T^{8} + 32243932864 T^{10} + 727534042114 T^{12} + 652793102357968 T^{14} + 45949729863572161 T^{16} )^{2} \))
$13$ (\( 1 + 2 T - 165 T^{2} + 338 T^{3} + 28561 T^{4} \))(\( 1 + 20 T + 231 T^{2} + 3380 T^{3} + 28561 T^{4} \))(\( 1 + 20 T + 231 T^{2} + 3380 T^{3} + 28561 T^{4} \))(\( 1 + 2 T - 165 T^{2} + 338 T^{3} + 28561 T^{4} \))(\( 1 - 10 T - 69 T^{2} - 1690 T^{3} + 28561 T^{4} \))(\( 1 - 10 T - 69 T^{2} - 1690 T^{3} + 28561 T^{4} \))(\( 1 + 2 T - 165 T^{2} + 338 T^{3} + 28561 T^{4} \))(\( 1 + 20 T + 231 T^{2} + 3380 T^{3} + 28561 T^{4} \))(\( 1 + 20 T + 231 T^{2} + 3380 T^{3} + 28561 T^{4} \))(\( 1 + 2 T - 165 T^{2} + 338 T^{3} + 28561 T^{4} \))(\( ( 1 + 10 T + 169 T^{2} )^{2}( 1 - 10 T - 69 T^{2} - 1690 T^{3} + 28561 T^{4} ) \))(\( ( 1 - 16 T + 87 T^{2} - 2704 T^{3} + 28561 T^{4} )^{2} \))(\( ( 1 - 16 T + 87 T^{2} - 2704 T^{3} + 28561 T^{4} )^{2} \))(\( ( 1 + 10 T + 169 T^{2} )^{2}( 1 - 10 T - 69 T^{2} - 1690 T^{3} + 28561 T^{4} ) \))(\( ( 1 - 2 T - 155 T^{2} + 358 T^{3} - 3956 T^{4} + 60502 T^{5} - 4426955 T^{6} - 9653618 T^{7} + 815730721 T^{8} )^{2} \))(\( ( 1 - 2 T - 155 T^{2} + 358 T^{3} - 3956 T^{4} + 60502 T^{5} - 4426955 T^{6} - 9653618 T^{7} + 815730721 T^{8} )^{2} \))(\( ( 1 + 3 T - 333 T^{2} + 980 T^{3} + 59097 T^{4} - 253239 T^{5} - 10369818 T^{6} - 42797391 T^{7} + 1687869417 T^{8} + 4730272820 T^{9} - 271638330093 T^{10} + 413575475547 T^{11} + 23298085122481 T^{12} )^{2} \))(\( ( 1 + 3 T - 333 T^{2} + 980 T^{3} + 59097 T^{4} - 253239 T^{5} - 10369818 T^{6} - 42797391 T^{7} + 1687869417 T^{8} + 4730272820 T^{9} - 271638330093 T^{10} + 413575475547 T^{11} + 23298085122481 T^{12} )^{2} \))(\( ( 1 - 8 T - 233 T^{2} + 328 T^{3} + 48832 T^{4} + 55432 T^{5} - 6654713 T^{6} - 38614472 T^{7} + 815730721 T^{8} )^{4} \))
$17$ (\( ( 1 + 10 T + 289 T^{2} )^{2} \))(\( ( 1 - 8 T + 289 T^{2} )^{2} \))(\( ( 1 + 8 T + 289 T^{2} )^{2} \))(\( ( 1 - 10 T + 289 T^{2} )^{2} \))(\( ( 1 - 16 T + 289 T^{2} )^{2} \))(\( ( 1 + 16 T + 289 T^{2} )^{2} \))(\( ( 1 + 10 T + 289 T^{2} )^{2} \))(\( ( 1 - 8 T + 289 T^{2} )^{2} \))(\( ( 1 + 8 T + 289 T^{2} )^{2} \))(\( ( 1 - 10 T + 289 T^{2} )^{2} \))(\( ( 1 + 16 T - 33 T^{2} + 4624 T^{3} + 83521 T^{4} )^{2} \))(\( ( 1 + 370 T^{2} + 83521 T^{4} )^{2} \))(\( ( 1 + 370 T^{2} + 83521 T^{4} )^{2} \))(\( ( 1 - 16 T - 33 T^{2} - 4624 T^{3} + 83521 T^{4} )^{2} \))(\( ( 1 + 140 T^{2} + 136662 T^{4} + 11692940 T^{6} + 6975757441 T^{8} )^{2} \))(\( ( 1 + 140 T^{2} + 136662 T^{4} + 11692940 T^{6} + 6975757441 T^{8} )^{2} \))(\( ( 1 + 5 T + 710 T^{2} + 2657 T^{3} + 205190 T^{4} + 417605 T^{5} + 24137569 T^{6} )^{4} \))(\( ( 1 - 5 T + 710 T^{2} - 2657 T^{3} + 205190 T^{4} - 417605 T^{5} + 24137569 T^{6} )^{4} \))(\( ( 1 + 398 T^{2} + 115443 T^{4} + 33241358 T^{6} + 6975757441 T^{8} )^{4} \))
$19$ (\( 1 - 290 T^{2} + 130321 T^{4} \))(\( 1 - 614 T^{2} + 130321 T^{4} \))(\( 1 - 614 T^{2} + 130321 T^{4} \))(\( 1 - 290 T^{2} + 130321 T^{4} \))(\( ( 1 - 19 T )^{2}( 1 + 19 T )^{2} \))(\( ( 1 - 19 T )^{2}( 1 + 19 T )^{2} \))(\( 1 - 290 T^{2} + 130321 T^{4} \))(\( 1 - 614 T^{2} + 130321 T^{4} \))(\( 1 - 614 T^{2} + 130321 T^{4} \))(\( 1 - 290 T^{2} + 130321 T^{4} \))(\( ( 1 - 19 T )^{4}( 1 + 19 T )^{4} \))(\( ( 1 + 682 T^{2} + 130321 T^{4} )^{2} \))(\( ( 1 + 682 T^{2} + 130321 T^{4} )^{2} \))(\( ( 1 - 19 T )^{4}( 1 + 19 T )^{4} \))(\( ( 1 - 695 T^{2} + 130321 T^{4} )^{4} \))(\( ( 1 - 695 T^{2} + 130321 T^{4} )^{4} \))(\( ( 1 - 690 T^{2} + 175551 T^{4} - 20841212 T^{6} + 22877981871 T^{8} - 11718658498290 T^{10} + 2213314919066161 T^{12} )^{2} \))(\( ( 1 - 690 T^{2} + 175551 T^{4} - 20841212 T^{6} + 22877981871 T^{8} - 11718658498290 T^{10} + 2213314919066161 T^{12} )^{2} \))(\( ( 1 - 616 T^{2} + 353454 T^{4} - 80277736 T^{6} + 16983563041 T^{8} )^{4} \))
$23$ (\( 1 - 48 T + 1297 T^{2} - 25392 T^{3} + 279841 T^{4} \))(\( 1 + 6 T + 541 T^{2} + 3174 T^{3} + 279841 T^{4} \))(\( 1 + 6 T + 541 T^{2} + 3174 T^{3} + 279841 T^{4} \))(\( 1 - 48 T + 1297 T^{2} - 25392 T^{3} + 279841 T^{4} \))(\( ( 1 - 23 T + 529 T^{2} )( 1 + 23 T + 529 T^{2} ) \))(\( ( 1 - 23 T + 529 T^{2} )( 1 + 23 T + 529 T^{2} ) \))(\( 1 + 48 T + 1297 T^{2} + 25392 T^{3} + 279841 T^{4} \))(\( 1 - 6 T + 541 T^{2} - 3174 T^{3} + 279841 T^{4} \))(\( 1 - 6 T + 541 T^{2} - 3174 T^{3} + 279841 T^{4} \))(\( 1 + 48 T + 1297 T^{2} + 25392 T^{3} + 279841 T^{4} \))(\( ( 1 - 23 T + 529 T^{2} )^{2}( 1 + 23 T + 529 T^{2} )^{2} \))(\( ( 1 + 30 T + 829 T^{2} + 15870 T^{3} + 279841 T^{4} )^{2} \))(\( ( 1 - 30 T + 829 T^{2} - 15870 T^{3} + 279841 T^{4} )^{2} \))(\( ( 1 - 23 T + 529 T^{2} )^{2}( 1 + 23 T + 529 T^{2} )^{2} \))(\( 1 + 604 T^{2} - 268070 T^{4} + 44215216 T^{6} + 220143229459 T^{8} + 12373230260656 T^{10} - 20992825824277670 T^{12} + 13236433156940273884 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( 1 + 604 T^{2} - 268070 T^{4} + 44215216 T^{6} + 220143229459 T^{8} + 12373230260656 T^{10} - 20992825824277670 T^{12} + 13236433156940273884 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( 1 + 306 T^{2} - 294315 T^{4} - 101578186 T^{6} + 8236830234 T^{8} + 252722985690 T^{10} + 6510830262749901 T^{12} + 70722253038475290 T^{14} + \)\(64\!\cdots\!54\)\( T^{16} - \)\(22\!\cdots\!06\)\( T^{18} - \)\(18\!\cdots\!15\)\( T^{20} + \)\(52\!\cdots\!06\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( 1 + 306 T^{2} - 294315 T^{4} - 101578186 T^{6} + 8236830234 T^{8} + 252722985690 T^{10} + 6510830262749901 T^{12} + 70722253038475290 T^{14} + \)\(64\!\cdots\!54\)\( T^{16} - \)\(22\!\cdots\!06\)\( T^{18} - \)\(18\!\cdots\!15\)\( T^{20} + \)\(52\!\cdots\!06\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( ( 1 + 1360 T^{2} + 970018 T^{4} + 435064000 T^{6} + 177759595843 T^{8} + 121748744824000 T^{10} + 75963065320305058 T^{12} + 29803889227547636560 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} )^{2} \))
$29$ (\( 1 + 26 T - 165 T^{2} + 21866 T^{3} + 707281 T^{4} \))(\( 1 - 10 T - 741 T^{2} - 8410 T^{3} + 707281 T^{4} \))(\( 1 + 10 T - 741 T^{2} + 8410 T^{3} + 707281 T^{4} \))(\( 1 - 26 T - 165 T^{2} - 21866 T^{3} + 707281 T^{4} \))(\( 1 + 40 T + 759 T^{2} + 33640 T^{3} + 707281 T^{4} \))(\( 1 - 40 T + 759 T^{2} - 33640 T^{3} + 707281 T^{4} \))(\( 1 + 26 T - 165 T^{2} + 21866 T^{3} + 707281 T^{4} \))(\( 1 - 10 T - 741 T^{2} - 8410 T^{3} + 707281 T^{4} \))(\( 1 + 10 T - 741 T^{2} + 8410 T^{3} + 707281 T^{4} \))(\( 1 - 26 T - 165 T^{2} - 21866 T^{3} + 707281 T^{4} \))(\( ( 1 - 40 T + 841 T^{2} )^{2}( 1 + 40 T + 759 T^{2} + 33640 T^{3} + 707281 T^{4} ) \))(\( 1 + 866 T^{2} + 42675 T^{4} + 612505346 T^{6} + 500246412961 T^{8} \))(\( 1 + 866 T^{2} + 42675 T^{4} + 612505346 T^{6} + 500246412961 T^{8} \))(\( ( 1 + 40 T + 841 T^{2} )^{2}( 1 - 40 T + 759 T^{2} - 33640 T^{3} + 707281 T^{4} ) \))(\( 1 - 2468 T^{2} + 3338026 T^{4} - 3303260048 T^{6} + 2770686029299 T^{8} - 2336333070009488 T^{10} + 1669835532870554986 T^{12} - \)\(87\!\cdots\!88\)\( T^{14} + \)\(25\!\cdots\!21\)\( T^{16} \))(\( 1 - 2468 T^{2} + 3338026 T^{4} - 3303260048 T^{6} + 2770686029299 T^{8} - 2336333070009488 T^{10} + 1669835532870554986 T^{12} - \)\(87\!\cdots\!88\)\( T^{14} + \)\(25\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 11 T - 541 T^{2} - 35316 T^{3} + 35689 T^{4} + 13747487 T^{5} + 931978726 T^{6} + 11561636567 T^{7} + 25242151609 T^{8} - 21006780404436 T^{9} - 270633309411901 T^{10} - 4627779566302211 T^{11} + 353814783205469041 T^{12} )^{2} \))(\( ( 1 + 11 T - 541 T^{2} + 35316 T^{3} + 35689 T^{4} - 13747487 T^{5} + 931978726 T^{6} - 11561636567 T^{7} + 25242151609 T^{8} + 21006780404436 T^{9} - 270633309411901 T^{10} + 4627779566302211 T^{11} + 353814783205469041 T^{12} )^{2} \))(\( ( 1 - 2942 T^{2} + 5091553 T^{4} - 6323090558 T^{6} + 6078727925476 T^{8} - 4472201812952798 T^{10} + 2547031124650818433 T^{12} - \)\(10\!\cdots\!22\)\( T^{14} + \)\(25\!\cdots\!21\)\( T^{16} )^{2} \))
$31$ (\( 1 - 12 T + 1009 T^{2} - 11532 T^{3} + 923521 T^{4} \))(\( ( 1 - 31 T )^{2}( 1 - 31 T + 961 T^{2} ) \))(\( ( 1 + 31 T )^{2}( 1 + 31 T + 961 T^{2} ) \))(\( 1 + 12 T + 1009 T^{2} + 11532 T^{3} + 923521 T^{4} \))(\( ( 1 - 31 T + 961 T^{2} )( 1 + 31 T + 961 T^{2} ) \))(\( ( 1 - 31 T + 961 T^{2} )( 1 + 31 T + 961 T^{2} ) \))(\( 1 + 12 T + 1009 T^{2} + 11532 T^{3} + 923521 T^{4} \))(\( ( 1 + 31 T )^{2}( 1 + 31 T + 961 T^{2} ) \))(\( ( 1 - 31 T )^{2}( 1 - 31 T + 961 T^{2} ) \))(\( 1 - 12 T + 1009 T^{2} - 11532 T^{3} + 923521 T^{4} \))(\( ( 1 - 31 T + 961 T^{2} )^{2}( 1 + 31 T + 961 T^{2} )^{2} \))(\( 1 + 1883 T^{2} + 2622168 T^{4} + 1738990043 T^{6} + 852891037441 T^{8} \))(\( 1 + 1883 T^{2} + 2622168 T^{4} + 1738990043 T^{6} + 852891037441 T^{8} \))(\( ( 1 - 31 T + 961 T^{2} )^{2}( 1 + 31 T + 961 T^{2} )^{2} \))(\( ( 1 - 48 T + 1922 T^{2} - 55392 T^{3} + 1146243 T^{4} - 53231712 T^{5} + 1775007362 T^{6} - 42600176688 T^{7} + 852891037441 T^{8} )^{2} \))(\( ( 1 + 48 T + 1922 T^{2} + 55392 T^{3} + 1146243 T^{4} + 53231712 T^{5} + 1775007362 T^{6} + 42600176688 T^{7} + 852891037441 T^{8} )^{2} \))(\( 1 + 390 T^{2} - 211563 T^{4} - 3351258190 T^{6} - 884751558054 T^{8} + 705817384212990 T^{10} + 4373878248652847373 T^{12} + \)\(65\!\cdots\!90\)\( T^{14} - \)\(75\!\cdots\!14\)\( T^{16} - \)\(26\!\cdots\!90\)\( T^{18} - \)\(15\!\cdots\!03\)\( T^{20} + \)\(26\!\cdots\!90\)\( T^{22} + \)\(62\!\cdots\!21\)\( T^{24} \))(\( 1 + 390 T^{2} - 211563 T^{4} - 3351258190 T^{6} - 884751558054 T^{8} + 705817384212990 T^{10} + 4373878248652847373 T^{12} + \)\(65\!\cdots\!90\)\( T^{14} - \)\(75\!\cdots\!14\)\( T^{16} - \)\(26\!\cdots\!90\)\( T^{18} - \)\(15\!\cdots\!03\)\( T^{20} + \)\(26\!\cdots\!90\)\( T^{22} + \)\(62\!\cdots\!21\)\( T^{24} \))(\( ( 1 + 1300 T^{2} + 737386 T^{4} - 1162756400 T^{6} - 1506168094445 T^{8} - 1073829953284400 T^{10} + 628909910534469226 T^{12} + \)\(10\!\cdots\!00\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} )^{2} \))
$37$ (\( ( 1 - 26 T + 1369 T^{2} )^{2} \))(\( ( 1 + 10 T + 1369 T^{2} )^{2} \))(\( ( 1 + 10 T + 1369 T^{2} )^{2} \))(\( ( 1 - 26 T + 1369 T^{2} )^{2} \))(\( ( 1 + 70 T + 1369 T^{2} )^{2} \))(\( ( 1 + 70 T + 1369 T^{2} )^{2} \))(\( ( 1 - 26 T + 1369 T^{2} )^{2} \))(\( ( 1 + 10 T + 1369 T^{2} )^{2} \))(\( ( 1 + 10 T + 1369 T^{2} )^{2} \))(\( ( 1 - 26 T + 1369 T^{2} )^{2} \))(\( ( 1 - 70 T + 3531 T^{2} - 95830 T^{3} + 1874161 T^{4} )^{2} \))(\( ( 1 - 26 T + 1369 T^{2} )^{4} \))(\( ( 1 - 26 T + 1369 T^{2} )^{4} \))(\( ( 1 - 70 T + 3531 T^{2} - 95830 T^{3} + 1874161 T^{4} )^{2} \))(\( ( 1 + 14 T + 2607 T^{2} + 19166 T^{3} + 1874161 T^{4} )^{4} \))(\( ( 1 + 14 T + 2607 T^{2} + 19166 T^{3} + 1874161 T^{4} )^{4} \))(\( ( 1 - 27 T + 78 T^{2} + 70681 T^{3} + 106782 T^{4} - 50602347 T^{5} + 2565726409 T^{6} )^{4} \))(\( ( 1 - 27 T + 78 T^{2} + 70681 T^{3} + 106782 T^{4} - 50602347 T^{5} + 2565726409 T^{6} )^{4} \))(\( ( 1 + 56 T + 3465 T^{2} + 76664 T^{3} + 1874161 T^{4} )^{8} \))
$41$ (\( 1 - 58 T + 1683 T^{2} - 97498 T^{3} + 2825761 T^{4} \))(\( 1 + 50 T + 819 T^{2} + 84050 T^{3} + 2825761 T^{4} \))(\( 1 - 50 T + 819 T^{2} - 84050 T^{3} + 2825761 T^{4} \))(\( 1 + 58 T + 1683 T^{2} + 97498 T^{3} + 2825761 T^{4} \))(\( 1 - 80 T + 4719 T^{2} - 134480 T^{3} + 2825761 T^{4} \))(\( 1 + 80 T + 4719 T^{2} + 134480 T^{3} + 2825761 T^{4} \))(\( 1 - 58 T + 1683 T^{2} - 97498 T^{3} + 2825761 T^{4} \))(\( 1 + 50 T + 819 T^{2} + 84050 T^{3} + 2825761 T^{4} \))(\( 1 - 50 T + 819 T^{2} - 84050 T^{3} + 2825761 T^{4} \))(\( 1 + 58 T + 1683 T^{2} + 97498 T^{3} + 2825761 T^{4} \))(\( ( 1 - 80 T + 4719 T^{2} - 134480 T^{3} + 2825761 T^{4} )^{2} \))(\( 1 - 3310 T^{2} + 8130339 T^{4} - 9353268910 T^{6} + 7984925229121 T^{8} \))(\( 1 - 3310 T^{2} + 8130339 T^{4} - 9353268910 T^{6} + 7984925229121 T^{8} \))(\( ( 1 + 80 T + 4719 T^{2} + 134480 T^{3} + 2825761 T^{4} )^{2} \))(\( 1 - 3140 T^{2} + 4692298 T^{4} + 1520450800 T^{6} - 9144788425517 T^{8} + 4296430573058800 T^{10} + 37467648682754010058 T^{12} - \)\(70\!\cdots\!40\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} \))(\( 1 - 3140 T^{2} + 4692298 T^{4} + 1520450800 T^{6} - 9144788425517 T^{8} + 4296430573058800 T^{10} + 37467648682754010058 T^{12} - \)\(70\!\cdots\!40\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} \))(\( ( 1 + 46 T - 1915 T^{2} - 79926 T^{3} + 3369754 T^{4} + 41399750 T^{5} - 6190684259 T^{6} + 69592979750 T^{7} + 9522119432794 T^{8} - 379656831566166 T^{9} - 15291131813766715 T^{10} + 617442328267010446 T^{11} + 22563490300366186081 T^{12} )^{2} \))(\( ( 1 - 46 T - 1915 T^{2} + 79926 T^{3} + 3369754 T^{4} - 41399750 T^{5} - 6190684259 T^{6} - 69592979750 T^{7} + 9522119432794 T^{8} + 379656831566166 T^{9} - 15291131813766715 T^{10} - 617442328267010446 T^{11} + 22563490300366186081 T^{12} )^{2} \))(\( ( 1 - 6548 T^{2} + 26509354 T^{4} - 70164622544 T^{6} + 138733939406035 T^{8} - 198268453964555984 T^{10} + \)\(21\!\cdots\!34\)\( T^{12} - \)\(14\!\cdots\!88\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} )^{2} \))
$43$ (\( 1 - 84 T + 4201 T^{2} - 155316 T^{3} + 3418801 T^{4} \))(\( 1 - 30 T + 2149 T^{2} - 55470 T^{3} + 3418801 T^{4} \))(\( 1 + 30 T + 2149 T^{2} + 55470 T^{3} + 3418801 T^{4} \))(\( 1 + 84 T + 4201 T^{2} + 155316 T^{3} + 3418801 T^{4} \))(\( ( 1 - 43 T + 1849 T^{2} )( 1 + 43 T + 1849 T^{2} ) \))(\( ( 1 - 43 T + 1849 T^{2} )( 1 + 43 T + 1849 T^{2} ) \))(\( 1 + 84 T + 4201 T^{2} + 155316 T^{3} + 3418801 T^{4} \))(\( 1 + 30 T + 2149 T^{2} + 55470 T^{3} + 3418801 T^{4} \))(\( 1 - 30 T + 2149 T^{2} - 55470 T^{3} + 3418801 T^{4} \))(\( 1 - 84 T + 4201 T^{2} - 155316 T^{3} + 3418801 T^{4} \))(\( ( 1 - 43 T + 1849 T^{2} )^{2}( 1 + 43 T + 1849 T^{2} )^{2} \))(\( 1 + 3542 T^{2} + 9126963 T^{4} + 12109393142 T^{6} + 11688200277601 T^{8} \))(\( 1 + 3542 T^{2} + 9126963 T^{4} + 12109393142 T^{6} + 11688200277601 T^{8} \))(\( ( 1 - 43 T + 1849 T^{2} )^{2}( 1 + 43 T + 1849 T^{2} )^{2} \))(\( ( 1 - 120 T + 9458 T^{2} - 558960 T^{3} + 27153363 T^{4} - 1033517040 T^{5} + 32335019858 T^{6} - 758563565880 T^{7} + 11688200277601 T^{8} )^{2} \))(\( ( 1 + 120 T + 9458 T^{2} + 558960 T^{3} + 27153363 T^{4} + 1033517040 T^{5} + 32335019858 T^{6} + 758563565880 T^{7} + 11688200277601 T^{8} )^{2} \))(\( 1 + 4722 T^{2} + 9868965 T^{4} + 6464505302 T^{6} - 11323018434534 T^{8} - 21567457514631462 T^{10} - 26989739893391669379 T^{12} - \)\(73\!\cdots\!62\)\( T^{14} - \)\(13\!\cdots\!34\)\( T^{16} + \)\(25\!\cdots\!02\)\( T^{18} + \)\(13\!\cdots\!65\)\( T^{20} + \)\(22\!\cdots\!22\)\( T^{22} + \)\(15\!\cdots\!01\)\( T^{24} \))(\( 1 + 4722 T^{2} + 9868965 T^{4} + 6464505302 T^{6} - 11323018434534 T^{8} - 21567457514631462 T^{10} - 26989739893391669379 T^{12} - \)\(73\!\cdots\!62\)\( T^{14} - \)\(13\!\cdots\!34\)\( T^{16} + \)\(25\!\cdots\!02\)\( T^{18} + \)\(13\!\cdots\!65\)\( T^{20} + \)\(22\!\cdots\!22\)\( T^{22} + \)\(15\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 3416 T^{2} + 2937682 T^{4} - 6469125152 T^{6} + 24654511328419 T^{8} - 22116651538782752 T^{10} + 34336215567903460882 T^{12} - \)\(13\!\cdots\!16\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \))
$47$ (\( 1 - 120 T + 7009 T^{2} - 265080 T^{3} + 4879681 T^{4} \))(\( 1 + 150 T + 9709 T^{2} + 331350 T^{3} + 4879681 T^{4} \))(\( 1 + 150 T + 9709 T^{2} + 331350 T^{3} + 4879681 T^{4} \))(\( 1 - 120 T + 7009 T^{2} - 265080 T^{3} + 4879681 T^{4} \))(\( ( 1 - 47 T + 2209 T^{2} )( 1 + 47 T + 2209 T^{2} ) \))(\( ( 1 - 47 T + 2209 T^{2} )( 1 + 47 T + 2209 T^{2} ) \))(\( 1 + 120 T + 7009 T^{2} + 265080 T^{3} + 4879681 T^{4} \))(\( 1 - 150 T + 9709 T^{2} - 331350 T^{3} + 4879681 T^{4} \))(\( 1 - 150 T + 9709 T^{2} - 331350 T^{3} + 4879681 T^{4} \))(\( 1 + 120 T + 7009 T^{2} + 265080 T^{3} + 4879681 T^{4} \))(\( ( 1 - 47 T + 2209 T^{2} )^{2}( 1 + 47 T + 2209 T^{2} )^{2} \))(\( ( 1 - 6 T + 2221 T^{2} - 13254 T^{3} + 4879681 T^{4} )^{2} \))(\( ( 1 + 6 T + 2221 T^{2} + 13254 T^{3} + 4879681 T^{4} )^{2} \))(\( ( 1 - 47 T + 2209 T^{2} )^{2}( 1 + 47 T + 2209 T^{2} )^{2} \))(\( 1 + 4444 T^{2} + 5312410 T^{4} + 20786205616 T^{6} + 88238287231699 T^{8} + 101430052606488496 T^{10} + \)\(12\!\cdots\!10\)\( T^{12} + \)\(51\!\cdots\!04\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( 1 + 4444 T^{2} + 5312410 T^{4} + 20786205616 T^{6} + 88238287231699 T^{8} + 101430052606488496 T^{10} + \)\(12\!\cdots\!10\)\( T^{12} + \)\(51\!\cdots\!04\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( 1 + 5046 T^{2} + 15715797 T^{4} + 19923312194 T^{6} - 26382629404518 T^{8} - 217240801372523922 T^{10} - \)\(62\!\cdots\!35\)\( T^{12} - \)\(10\!\cdots\!82\)\( T^{14} - \)\(62\!\cdots\!98\)\( T^{16} + \)\(23\!\cdots\!54\)\( T^{18} + \)\(89\!\cdots\!37\)\( T^{20} + \)\(13\!\cdots\!46\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( 1 + 5046 T^{2} + 15715797 T^{4} + 19923312194 T^{6} - 26382629404518 T^{8} - 217240801372523922 T^{10} - \)\(62\!\cdots\!35\)\( T^{12} - \)\(10\!\cdots\!82\)\( T^{14} - \)\(62\!\cdots\!98\)\( T^{16} + \)\(23\!\cdots\!54\)\( T^{18} + \)\(89\!\cdots\!37\)\( T^{20} + \)\(13\!\cdots\!46\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( ( 1 + 3460 T^{2} + 153226 T^{4} + 7124181520 T^{6} + 57445088282515 T^{8} + 34763733203695120 T^{10} + 3648508210034990986 T^{12} + \)\(40\!\cdots\!60\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} )^{2} \))
$53$ (\( ( 1 - 74 T + 2809 T^{2} )^{2} \))(\( ( 1 - 47 T + 2809 T^{2} )^{2} \))(\( ( 1 + 47 T + 2809 T^{2} )^{2} \))(\( ( 1 + 74 T + 2809 T^{2} )^{2} \))(\( ( 1 + 56 T + 2809 T^{2} )^{2} \))(\( ( 1 - 56 T + 2809 T^{2} )^{2} \))(\( ( 1 - 74 T + 2809 T^{2} )^{2} \))(\( ( 1 - 47 T + 2809 T^{2} )^{2} \))(\( ( 1 + 47 T + 2809 T^{2} )^{2} \))(\( ( 1 + 74 T + 2809 T^{2} )^{2} \))(\( ( 1 + 56 T + 2809 T^{2} )^{4} \))(\( ( 1 + 925 T^{2} + 7890481 T^{4} )^{2} \))(\( ( 1 + 925 T^{2} + 7890481 T^{4} )^{2} \))(\( ( 1 - 56 T + 2809 T^{2} )^{4} \))(\( ( 1 - 508 T^{2} + 14912358 T^{4} - 4008364348 T^{6} + 62259690411361 T^{8} )^{2} \))(\( ( 1 - 508 T^{2} + 14912358 T^{4} - 4008364348 T^{6} + 62259690411361 T^{8} )^{2} \))(\( ( 1 - 58 T + 8567 T^{2} - 320716 T^{3} + 24064703 T^{4} - 457647898 T^{5} + 22164361129 T^{6} )^{4} \))(\( ( 1 + 58 T + 8567 T^{2} + 320716 T^{3} + 24064703 T^{4} + 457647898 T^{5} + 22164361129 T^{6} )^{4} \))(\( ( 1 + 5492 T^{2} + 15934278 T^{4} + 43334521652 T^{6} + 62259690411361 T^{8} )^{4} \))
$59$ (\( 1 - 156 T + 11593 T^{2} - 543036 T^{3} + 12117361 T^{4} \))(\( 1 + 60 T + 4681 T^{2} + 208860 T^{3} + 12117361 T^{4} \))(\( 1 + 60 T + 4681 T^{2} + 208860 T^{3} + 12117361 T^{4} \))(\( 1 - 156 T + 11593 T^{2} - 543036 T^{3} + 12117361 T^{4} \))(\( ( 1 - 59 T + 3481 T^{2} )( 1 + 59 T + 3481 T^{2} ) \))(\( ( 1 - 59 T + 3481 T^{2} )( 1 + 59 T + 3481 T^{2} ) \))(\( 1 + 156 T + 11593 T^{2} + 543036 T^{3} + 12117361 T^{4} \))(\( 1 - 60 T + 4681 T^{2} - 208860 T^{3} + 12117361 T^{4} \))(\( 1 - 60 T + 4681 T^{2} - 208860 T^{3} + 12117361 T^{4} \))(\( 1 + 156 T + 11593 T^{2} + 543036 T^{3} + 12117361 T^{4} \))(\( ( 1 - 59 T + 3481 T^{2} )^{2}( 1 + 59 T + 3481 T^{2} )^{2} \))(\( ( 1 - 132 T + 9289 T^{2} - 459492 T^{3} + 12117361 T^{4} )^{2} \))(\( ( 1 + 132 T + 9289 T^{2} + 459492 T^{3} + 12117361 T^{4} )^{2} \))(\( ( 1 - 59 T + 3481 T^{2} )^{2}( 1 + 59 T + 3481 T^{2} )^{2} \))(\( 1 + 6076 T^{2} + 12975610 T^{4} - 1777570256 T^{6} - 20949143941901 T^{8} - 21539460494814416 T^{10} + \)\(19\!\cdots\!10\)\( T^{12} + \)\(10\!\cdots\!56\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} \))(\( 1 + 6076 T^{2} + 12975610 T^{4} - 1777570256 T^{6} - 20949143941901 T^{8} - 21539460494814416 T^{10} + \)\(19\!\cdots\!10\)\( T^{12} + \)\(10\!\cdots\!56\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} \))(\( 1 + 7494 T^{2} + 23269317 T^{4} + 14290664786 T^{6} - 186774179935398 T^{8} - 1054613632918700418 T^{10} - \)\(43\!\cdots\!15\)\( T^{12} - \)\(12\!\cdots\!98\)\( T^{14} - \)\(27\!\cdots\!58\)\( T^{16} + \)\(25\!\cdots\!66\)\( T^{18} + \)\(50\!\cdots\!97\)\( T^{20} + \)\(19\!\cdots\!94\)\( T^{22} + \)\(31\!\cdots\!61\)\( T^{24} \))(\( 1 + 7494 T^{2} + 23269317 T^{4} + 14290664786 T^{6} - 186774179935398 T^{8} - 1054613632918700418 T^{10} - \)\(43\!\cdots\!15\)\( T^{12} - \)\(12\!\cdots\!98\)\( T^{14} - \)\(27\!\cdots\!58\)\( T^{16} + \)\(25\!\cdots\!66\)\( T^{18} + \)\(50\!\cdots\!97\)\( T^{20} + \)\(19\!\cdots\!94\)\( T^{22} + \)\(31\!\cdots\!61\)\( T^{24} \))(\( ( 1 + 12580 T^{2} + 94515946 T^{4} + 496982108560 T^{6} + 1998365109161395 T^{8} + 6022111619962710160 T^{10} + \)\(13\!\cdots\!66\)\( T^{12} + \)\(22\!\cdots\!80\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} )^{2} \))
$61$ (\( 1 + 26 T - 3045 T^{2} + 96746 T^{3} + 13845841 T^{4} \))(\( 1 - 64 T + 375 T^{2} - 238144 T^{3} + 13845841 T^{4} \))(\( 1 - 64 T + 375 T^{2} - 238144 T^{3} + 13845841 T^{4} \))(\( 1 + 26 T - 3045 T^{2} + 96746 T^{3} + 13845841 T^{4} \))(\( 1 - 22 T - 3237 T^{2} - 81862 T^{3} + 13845841 T^{4} \))(\( 1 - 22 T - 3237 T^{2} - 81862 T^{3} + 13845841 T^{4} \))(\( 1 + 26 T - 3045 T^{2} + 96746 T^{3} + 13845841 T^{4} \))(\( 1 - 64 T + 375 T^{2} - 238144 T^{3} + 13845841 T^{4} \))(\( 1 - 64 T + 375 T^{2} - 238144 T^{3} + 13845841 T^{4} \))(\( 1 + 26 T - 3045 T^{2} + 96746 T^{3} + 13845841 T^{4} \))(\( ( 1 + 22 T + 3721 T^{2} )^{2}( 1 - 22 T - 3237 T^{2} - 81862 T^{3} + 13845841 T^{4} ) \))(\( ( 1 + 8 T - 3657 T^{2} + 29768 T^{3} + 13845841 T^{4} )^{2} \))(\( ( 1 + 8 T - 3657 T^{2} + 29768 T^{3} + 13845841 T^{4} )^{2} \))(\( ( 1 + 22 T + 3721 T^{2} )^{2}( 1 - 22 T - 3237 T^{2} - 81862 T^{3} + 13845841 T^{4} ) \))(\( ( 1 + 10 T - 7187 T^{2} - 1550 T^{3} + 38882428 T^{4} - 5767550 T^{5} - 99510059267 T^{6} + 515203743610 T^{7} + 191707312997281 T^{8} )^{2} \))(\( ( 1 + 10 T - 7187 T^{2} - 1550 T^{3} + 38882428 T^{4} - 5767550 T^{5} - 99510059267 T^{6} + 515203743610 T^{7} + 191707312997281 T^{8} )^{2} \))(\( ( 1 + 27 T - 5613 T^{2} - 28252 T^{3} + 13929321 T^{4} - 267915615 T^{5} - 46766410362 T^{6} - 996914003415 T^{7} + 192863163803961 T^{8} - 1455553616446972 T^{9} - 1076053147853738253 T^{10} + 19260258614897830227 T^{11} + \)\(26\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 + 27 T - 5613 T^{2} - 28252 T^{3} + 13929321 T^{4} - 267915615 T^{5} - 46766410362 T^{6} - 996914003415 T^{7} + 192863163803961 T^{8} - 1455553616446972 T^{9} - 1076053147853738253 T^{10} + 19260258614897830227 T^{11} + \)\(26\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 8 T - 4601 T^{2} + 22216 T^{3} + 7678240 T^{4} + 82665736 T^{5} - 63704714441 T^{6} - 412162994888 T^{7} + 191707312997281 T^{8} )^{4} \))
$67$ (\( 1 - 12 T + 4537 T^{2} - 53868 T^{3} + 20151121 T^{4} \))(\( 1 + 150 T + 11989 T^{2} + 673350 T^{3} + 20151121 T^{4} \))(\( 1 - 150 T + 11989 T^{2} - 673350 T^{3} + 20151121 T^{4} \))(\( 1 + 12 T + 4537 T^{2} + 53868 T^{3} + 20151121 T^{4} \))(\( ( 1 - 67 T + 4489 T^{2} )( 1 + 67 T + 4489 T^{2} ) \))(\( ( 1 - 67 T + 4489 T^{2} )( 1 + 67 T + 4489 T^{2} ) \))(\( 1 + 12 T + 4537 T^{2} + 53868 T^{3} + 20151121 T^{4} \))(\( 1 - 150 T + 11989 T^{2} - 673350 T^{3} + 20151121 T^{4} \))(\( 1 + 150 T + 11989 T^{2} + 673350 T^{3} + 20151121 T^{4} \))(\( 1 - 12 T + 4537 T^{2} - 53868 T^{3} + 20151121 T^{4} \))(\( ( 1 - 67 T + 4489 T^{2} )^{2}( 1 + 67 T + 4489 T^{2} )^{2} \))(\( 1 + 5078 T^{2} + 5634963 T^{4} + 102327392438 T^{6} + 406067677556641 T^{8} \))(\( 1 + 5078 T^{2} + 5634963 T^{4} + 102327392438 T^{6} + 406067677556641 T^{8} \))(\( ( 1 - 67 T + 4489 T^{2} )^{2}( 1 + 67 T + 4489 T^{2} )^{2} \))(\( ( 1 + 114 T + 10553 T^{2} + 709194 T^{3} + 37996068 T^{4} + 3183571866 T^{5} + 212654779913 T^{6} + 10312255567266 T^{7} + 406067677556641 T^{8} )^{2} \))(\( ( 1 - 114 T + 10553 T^{2} - 709194 T^{3} + 37996068 T^{4} - 3183571866 T^{5} + 212654779913 T^{6} - 10312255567266 T^{7} + 406067677556641 T^{8} )^{2} \))(\( 1 + 12786 T^{2} + 67742277 T^{4} + 199597066262 T^{6} + 686986653965466 T^{8} + 4900908833643326682 T^{10} + \)\(27\!\cdots\!01\)\( T^{12} + \)\(98\!\cdots\!22\)\( T^{14} + \)\(27\!\cdots\!06\)\( T^{16} + \)\(16\!\cdots\!82\)\( T^{18} + \)\(11\!\cdots\!37\)\( T^{20} + \)\(42\!\cdots\!86\)\( T^{22} + \)\(66\!\cdots\!21\)\( T^{24} \))(\( 1 + 12786 T^{2} + 67742277 T^{4} + 199597066262 T^{6} + 686986653965466 T^{8} + 4900908833643326682 T^{10} + \)\(27\!\cdots\!01\)\( T^{12} + \)\(98\!\cdots\!22\)\( T^{14} + \)\(27\!\cdots\!06\)\( T^{16} + \)\(16\!\cdots\!82\)\( T^{18} + \)\(11\!\cdots\!37\)\( T^{20} + \)\(42\!\cdots\!86\)\( T^{22} + \)\(66\!\cdots\!21\)\( T^{24} \))(\( ( 1 + 12904 T^{2} + 90640402 T^{4} + 459002661088 T^{6} + 1995188263006819 T^{8} + 9249418162906279648 T^{10} + \)\(36\!\cdots\!82\)\( T^{12} + \)\(10\!\cdots\!44\)\( T^{14} + \)\(16\!\cdots\!81\)\( T^{16} )^{2} \))
$71$ (\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 71 T )^{4}( 1 + 71 T )^{4} \))(\( ( 1 - 6194 T^{2} + 25411681 T^{4} )^{2} \))(\( ( 1 - 6194 T^{2} + 25411681 T^{4} )^{2} \))(\( ( 1 - 71 T )^{4}( 1 + 71 T )^{4} \))(\( ( 1 - 292 T^{2} + 42446598 T^{4} - 7420210852 T^{6} + 645753531245761 T^{8} )^{2} \))(\( ( 1 - 292 T^{2} + 42446598 T^{4} - 7420210852 T^{6} + 645753531245761 T^{8} )^{2} \))(\( ( 1 - 21714 T^{2} + 225392559 T^{4} - 1424221410044 T^{6} + 5727603809081679 T^{8} - 14021892177470454354 T^{10} + \)\(16\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 21714 T^{2} + 225392559 T^{4} - 1424221410044 T^{6} + 5727603809081679 T^{8} - 14021892177470454354 T^{10} + \)\(16\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 7312 T^{2} + 62463966 T^{4} - 185810211472 T^{6} + 645753531245761 T^{8} )^{4} \))
$73$ (\( ( 1 + 46 T + 5329 T^{2} )^{2} \))(\( ( 1 + 55 T + 5329 T^{2} )^{2} \))(\( ( 1 + 55 T + 5329 T^{2} )^{2} \))(\( ( 1 + 46 T + 5329 T^{2} )^{2} \))(\( ( 1 - 110 T + 5329 T^{2} )^{2} \))(\( ( 1 - 110 T + 5329 T^{2} )^{2} \))(\( ( 1 + 46 T + 5329 T^{2} )^{2} \))(\( ( 1 + 55 T + 5329 T^{2} )^{2} \))(\( ( 1 + 55 T + 5329 T^{2} )^{2} \))(\( ( 1 + 46 T + 5329 T^{2} )^{2} \))(\( ( 1 + 110 T + 6771 T^{2} + 586190 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 + 19 T + 5329 T^{2} )^{4} \))(\( ( 1 + 19 T + 5329 T^{2} )^{4} \))(\( ( 1 + 110 T + 6771 T^{2} + 586190 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 - 58 T + 10779 T^{2} - 309082 T^{3} + 28398241 T^{4} )^{4} \))(\( ( 1 - 58 T + 10779 T^{2} - 309082 T^{3} + 28398241 T^{4} )^{4} \))(\( ( 1 + 39 T + 7086 T^{2} - 32189 T^{3} + 37761294 T^{4} + 1107531399 T^{5} + 151334226289 T^{6} )^{4} \))(\( ( 1 + 39 T + 7086 T^{2} - 32189 T^{3} + 37761294 T^{4} + 1107531399 T^{5} + 151334226289 T^{6} )^{4} \))(\( ( 1 - 94 T + 12639 T^{2} - 500926 T^{3} + 28398241 T^{4} )^{8} \))
$79$ (\( 1 + 204 T + 20113 T^{2} + 1273164 T^{3} + 38950081 T^{4} \))(\( 1 - 12 T + 6289 T^{2} - 74892 T^{3} + 38950081 T^{4} \))(\( 1 + 12 T + 6289 T^{2} + 74892 T^{3} + 38950081 T^{4} \))(\( 1 - 204 T + 20113 T^{2} - 1273164 T^{3} + 38950081 T^{4} \))(\( ( 1 - 79 T + 6241 T^{2} )( 1 + 79 T + 6241 T^{2} ) \))(\( ( 1 - 79 T + 6241 T^{2} )( 1 + 79 T + 6241 T^{2} ) \))(\( 1 - 204 T + 20113 T^{2} - 1273164 T^{3} + 38950081 T^{4} \))(\( 1 + 12 T + 6289 T^{2} + 74892 T^{3} + 38950081 T^{4} \))(\( 1 - 12 T + 6289 T^{2} - 74892 T^{3} + 38950081 T^{4} \))(\( 1 + 204 T + 20113 T^{2} + 1273164 T^{3} + 38950081 T^{4} \))(\( ( 1 - 79 T + 6241 T^{2} )^{2}( 1 + 79 T + 6241 T^{2} )^{2} \))(\( 1 + 9986 T^{2} + 60770115 T^{4} + 388955508866 T^{6} + 1517108809906561 T^{8} \))(\( 1 + 9986 T^{2} + 60770115 T^{4} + 388955508866 T^{6} + 1517108809906561 T^{8} \))(\( ( 1 - 79 T + 6241 T^{2} )^{2}( 1 + 79 T + 6241 T^{2} )^{2} \))(\( ( 1 + 330 T + 54917 T^{2} + 6143610 T^{3} + 534190908 T^{4} + 38342270010 T^{5} + 2139021598277 T^{6} + 80218860321930 T^{7} + 1517108809906561 T^{8} )^{2} \))(\( ( 1 - 330 T + 54917 T^{2} - 6143610 T^{3} + 534190908 T^{4} - 38342270010 T^{5} + 2139021598277 T^{6} - 80218860321930 T^{7} + 1517108809906561 T^{8} )^{2} \))(\( 1 + 29682 T^{2} + 478317045 T^{4} + 5552299732022 T^{6} + 51491498910113946 T^{8} + \)\(40\!\cdots\!78\)\( T^{10} + \)\(27\!\cdots\!81\)\( T^{12} + \)\(15\!\cdots\!18\)\( T^{14} + \)\(78\!\cdots\!06\)\( T^{16} + \)\(32\!\cdots\!02\)\( T^{18} + \)\(11\!\cdots\!45\)\( T^{20} + \)\(26\!\cdots\!82\)\( T^{22} + \)\(34\!\cdots\!81\)\( T^{24} \))(\( 1 + 29682 T^{2} + 478317045 T^{4} + 5552299732022 T^{6} + 51491498910113946 T^{8} + \)\(40\!\cdots\!78\)\( T^{10} + \)\(27\!\cdots\!81\)\( T^{12} + \)\(15\!\cdots\!18\)\( T^{14} + \)\(78\!\cdots\!06\)\( T^{16} + \)\(32\!\cdots\!02\)\( T^{18} + \)\(11\!\cdots\!45\)\( T^{20} + \)\(26\!\cdots\!82\)\( T^{22} + \)\(34\!\cdots\!81\)\( T^{24} \))(\( ( 1 + 15496 T^{2} + 123683122 T^{4} + 597258175072 T^{6} + 2688910979781379 T^{8} + 23263254296966580832 T^{10} + \)\(18\!\cdots\!42\)\( T^{12} + \)\(91\!\cdots\!36\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} )^{2} \))
$83$ (\( 1 - 84 T + 9241 T^{2} - 578676 T^{3} + 47458321 T^{4} \))(\( 1 + 51 T + 7756 T^{2} + 351339 T^{3} + 47458321 T^{4} \))(\( 1 + 51 T + 7756 T^{2} + 351339 T^{3} + 47458321 T^{4} \))(\( 1 - 84 T + 9241 T^{2} - 578676 T^{3} + 47458321 T^{4} \))(\( ( 1 - 83 T + 6889 T^{2} )( 1 + 83 T + 6889 T^{2} ) \))(\( ( 1 - 83 T + 6889 T^{2} )( 1 + 83 T + 6889 T^{2} ) \))(\( 1 + 84 T + 9241 T^{2} + 578676 T^{3} + 47458321 T^{4} \))(\( 1 - 51 T + 7756 T^{2} - 351339 T^{3} + 47458321 T^{4} \))(\( 1 - 51 T + 7756 T^{2} - 351339 T^{3} + 47458321 T^{4} \))(\( 1 + 84 T + 9241 T^{2} + 578676 T^{3} + 47458321 T^{4} \))(\( ( 1 - 83 T + 6889 T^{2} )^{2}( 1 + 83 T + 6889 T^{2} )^{2} \))(\( ( 1 + 201 T + 20356 T^{2} + 1384689 T^{3} + 47458321 T^{4} )^{2} \))(\( ( 1 - 201 T + 20356 T^{2} - 1384689 T^{3} + 47458321 T^{4} )^{2} \))(\( ( 1 - 83 T + 6889 T^{2} )^{2}( 1 + 83 T + 6889 T^{2} )^{2} \))(\( 1 + 26116 T^{2} + 416905450 T^{4} + 4445553374224 T^{6} + 35678198362101619 T^{8} + \)\(21\!\cdots\!04\)\( T^{10} + \)\(93\!\cdots\!50\)\( T^{12} + \)\(27\!\cdots\!76\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( 1 + 26116 T^{2} + 416905450 T^{4} + 4445553374224 T^{6} + 35678198362101619 T^{8} + \)\(21\!\cdots\!04\)\( T^{10} + \)\(93\!\cdots\!50\)\( T^{12} + \)\(27\!\cdots\!76\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( 1 + 6438 T^{2} - 50128155 T^{4} - 217903183822 T^{6} + 1440876227339226 T^{8} - 4486982814512549538 T^{10} - \)\(11\!\cdots\!39\)\( T^{12} - \)\(21\!\cdots\!98\)\( T^{14} + \)\(32\!\cdots\!66\)\( T^{16} - \)\(23\!\cdots\!42\)\( T^{18} - \)\(25\!\cdots\!55\)\( T^{20} + \)\(15\!\cdots\!38\)\( T^{22} + \)\(11\!\cdots\!21\)\( T^{24} \))(\( 1 + 6438 T^{2} - 50128155 T^{4} - 217903183822 T^{6} + 1440876227339226 T^{8} - 4486982814512549538 T^{10} - \)\(11\!\cdots\!39\)\( T^{12} - \)\(21\!\cdots\!98\)\( T^{14} + \)\(32\!\cdots\!66\)\( T^{16} - \)\(23\!\cdots\!42\)\( T^{18} - \)\(25\!\cdots\!55\)\( T^{20} + \)\(15\!\cdots\!38\)\( T^{22} + \)\(11\!\cdots\!21\)\( T^{24} \))(\( ( 1 + 26452 T^{2} + 429868234 T^{4} + 4627074517456 T^{6} + 37354389847868275 T^{8} + \)\(21\!\cdots\!76\)\( T^{10} + \)\(96\!\cdots\!94\)\( T^{12} + \)\(28\!\cdots\!72\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} )^{2} \))
$89$ (\( ( 1 + 82 T + 7921 T^{2} )^{2} \))(\( ( 1 + 10 T + 7921 T^{2} )^{2} \))(\( ( 1 - 10 T + 7921 T^{2} )^{2} \))(\( ( 1 - 82 T + 7921 T^{2} )^{2} \))(\( ( 1 - 160 T + 7921 T^{2} )^{2} \))(\( ( 1 + 160 T + 7921 T^{2} )^{2} \))(\( ( 1 + 82 T + 7921 T^{2} )^{2} \))(\( ( 1 + 10 T + 7921 T^{2} )^{2} \))(\( ( 1 - 10 T + 7921 T^{2} )^{2} \))(\( ( 1 - 82 T + 7921 T^{2} )^{2} \))(\( ( 1 + 160 T + 17679 T^{2} + 1267360 T^{3} + 62742241 T^{4} )^{2} \))(\( ( 1 + 9550 T^{2} + 62742241 T^{4} )^{2} \))(\( ( 1 + 9550 T^{2} + 62742241 T^{4} )^{2} \))(\( ( 1 - 160 T + 17679 T^{2} - 1267360 T^{3} + 62742241 T^{4} )^{2} \))(\( ( 1 + 30668 T^{2} + 360580758 T^{4} + 1924179046988 T^{6} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 + 30668 T^{2} + 360580758 T^{4} + 1924179046988 T^{6} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 + 125 T + 19286 T^{2} + 1872473 T^{3} + 152764406 T^{4} + 7842780125 T^{5} + 496981290961 T^{6} )^{4} \))(\( ( 1 - 125 T + 19286 T^{2} - 1872473 T^{3} + 152764406 T^{4} - 7842780125 T^{5} + 496981290961 T^{6} )^{4} \))(\( ( 1 + 15758 T^{2} + 176527923 T^{4} + 988692233678 T^{6} + 3936588805702081 T^{8} )^{4} \))
$97$ (\( ( 1 - 167 T + 9409 T^{2} )( 1 + 169 T + 9409 T^{2} ) \))(\( 1 - 25 T - 8784 T^{2} - 235225 T^{3} + 88529281 T^{4} \))(\( 1 - 25 T - 8784 T^{2} - 235225 T^{3} + 88529281 T^{4} \))(\( ( 1 - 167 T + 9409 T^{2} )( 1 + 169 T + 9409 T^{2} ) \))(\( 1 - 130 T + 7491 T^{2} - 1223170 T^{3} + 88529281 T^{4} \))(\( 1 - 130 T + 7491 T^{2} - 1223170 T^{3} + 88529281 T^{4} \))(\( ( 1 - 167 T + 9409 T^{2} )( 1 + 169 T + 9409 T^{2} ) \))(\( 1 - 25 T - 8784 T^{2} - 235225 T^{3} + 88529281 T^{4} \))(\( 1 - 25 T - 8784 T^{2} - 235225 T^{3} + 88529281 T^{4} \))(\( ( 1 - 167 T + 9409 T^{2} )( 1 + 169 T + 9409 T^{2} ) \))(\( ( 1 - 130 T + 7491 T^{2} - 1223170 T^{3} + 88529281 T^{4} )^{2} \))(\( ( 1 + 119 T + 4752 T^{2} + 1119671 T^{3} + 88529281 T^{4} )^{2} \))(\( ( 1 + 119 T + 4752 T^{2} + 1119671 T^{3} + 88529281 T^{4} )^{2} \))(\( ( 1 - 130 T + 7491 T^{2} - 1223170 T^{3} + 88529281 T^{4} )^{2} \))(\( ( 1 - 62 T - 4415 T^{2} + 654658 T^{3} - 56486396 T^{4} + 6159677122 T^{5} - 390856775615 T^{6} - 51644264305598 T^{7} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 - 62 T - 4415 T^{2} + 654658 T^{3} - 56486396 T^{4} + 6159677122 T^{5} - 390856775615 T^{6} - 51644264305598 T^{7} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 - 102 T - 13323 T^{2} + 680174 T^{3} + 181606458 T^{4} - 268269918 T^{5} - 2149095910131 T^{6} - 2524151658462 T^{7} + 16077489151696698 T^{8} + 566565900480577646 T^{9} - \)\(10\!\cdots\!03\)\( T^{10} - \)\(75\!\cdots\!98\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 102 T - 13323 T^{2} + 680174 T^{3} + 181606458 T^{4} - 268269918 T^{5} - 2149095910131 T^{6} - 2524151658462 T^{7} + 16077489151696698 T^{8} + 566565900480577646 T^{9} - \)\(10\!\cdots\!03\)\( T^{10} - \)\(75\!\cdots\!98\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 232 T + 21778 T^{2} + 3068896 T^{3} + 431986819 T^{4} + 28875242464 T^{5} + 1927990681618 T^{6} + 193249505143528 T^{7} + 7837433594376961 T^{8} )^{4} \))
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