Properties

Label 800.6.c
Level 800
Weight 6
Character orbit c
Rep. character \(\chi_{800}(449,\cdot)\)
Character field \(\Q\)
Dimension 90
Newform subspaces 16
Sturm bound 720
Trace bound 11

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 800.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(720\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(800, [\chi])\).

Total New Old
Modular forms 624 90 534
Cusp forms 576 90 486
Eisenstein series 48 0 48

Trace form

\( 90q - 7290q^{9} + O(q^{10}) \) \( 90q - 7290q^{9} + 3280q^{21} + 24484q^{29} + 11852q^{41} - 227354q^{49} + 91580q^{61} + 243392q^{69} + 569098q^{81} + 182308q^{89} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
800.6.c.a \(2\) \(128.307\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4iq^{3}-104iq^{7}+179q^{9}-536q^{11}+\cdots\)
800.6.c.b \(2\) \(128.307\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+4iq^{3}-104iq^{7}+179q^{9}+536q^{11}+\cdots\)
800.6.c.c \(2\) \(128.307\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+3^{5}q^{9}+597iq^{13}+1121iq^{17}+\cdots\)
800.6.c.d \(4\) \(128.307\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{3}-6\zeta_{12}^{3}q^{7}-525q^{9}+\cdots\)
800.6.c.e \(4\) \(128.307\) \(\Q(i, \sqrt{85})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+3\beta _{2}q^{7}-97q^{9}+13\beta _{3}q^{11}+\cdots\)
800.6.c.f \(4\) \(128.307\) \(\Q(i, \sqrt{70})\) None \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}-\beta _{2})q^{3}+(-26\beta _{1}-\beta _{2})q^{7}+\cdots\)
800.6.c.g \(4\) \(128.307\) \(\Q(i, \sqrt{70})\) None \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}-\beta _{2})q^{3}+(-26\beta _{1}-\beta _{2})q^{7}+\cdots\)
800.6.c.h \(4\) \(128.307\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-3\beta _{2}q^{3}+31\beta _{2}q^{7}+63q^{9}-29\beta _{3}q^{11}+\cdots\)
800.6.c.i \(4\) \(128.307\) \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+7\beta _{2}q^{7}+203q^{9}-57\beta _{3}q^{11}+\cdots\)
800.6.c.j \(6\) \(128.307\) 6.0.6140289600.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-2\beta _{1}+\beta _{3})q^{3}+(-\beta _{1}+\beta _{3}+\beta _{5})q^{7}+\cdots\)
800.6.c.k \(6\) \(128.307\) 6.0.6140289600.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-2\beta _{1}+\beta _{3})q^{3}+(-\beta _{1}+\beta _{3}+\beta _{5})q^{7}+\cdots\)
800.6.c.l \(8\) \(128.307\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(6\beta _{1}-\beta _{4})q^{7}+(-181+\beta _{3}+\cdots)q^{9}+\cdots\)
800.6.c.m \(8\) \(128.307\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{3}+(2\beta _{5}+\beta _{6})q^{7}+(-56-\beta _{3}+\cdots)q^{9}+\cdots\)
800.6.c.n \(10\) \(128.307\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}+(-22\beta _{5}+\beta _{7})q^{7}+(-11^{2}+\cdots)q^{9}+\cdots\)
800.6.c.o \(10\) \(128.307\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}+(-22\beta _{5}+\beta _{7})q^{7}+(-11^{2}+\cdots)q^{9}+\cdots\)
800.6.c.p \(12\) \(128.307\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{3}+(-\beta _{7}-\beta _{8})q^{7}+(-38+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(800, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(800, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 - 422 T^{2} + 59049 T^{4} \))(\( 1 - 422 T^{2} + 59049 T^{4} \))(\( ( 1 - 243 T^{2} )^{2} \))(\( ( 1 + 282 T^{2} + 59049 T^{4} )^{2} \))(\( ( 1 - 146 T^{2} + 59049 T^{4} )^{2} \))(\( 1 - 380 T^{2} + 136278 T^{4} - 22438620 T^{6} + 3486784401 T^{8} \))(\( 1 - 380 T^{2} + 136278 T^{4} - 22438620 T^{6} + 3486784401 T^{8} \))(\( ( 1 - 306 T^{2} + 59049 T^{4} )^{2} \))(\( ( 1 - 446 T^{2} + 59049 T^{4} )^{2} \))(\( 1 - 262 T^{2} + 15367 T^{4} - 5058036 T^{6} + 907405983 T^{8} - 913537513062 T^{10} + 205891132094649 T^{12} \))(\( 1 - 262 T^{2} + 15367 T^{4} - 5058036 T^{6} + 907405983 T^{8} - 913537513062 T^{10} + 205891132094649 T^{12} \))(\( ( 1 - 124 T^{2} + 25686 T^{4} - 7322076 T^{6} + 3486784401 T^{8} )^{2} \))(\( ( 1 - 374 T^{2} + 118791 T^{4} - 22084326 T^{6} + 3486784401 T^{8} )^{2} \))(\( 1 - 609 T^{2} + 266679 T^{4} - 91457894 T^{6} + 25373368413 T^{8} - 6535895135319 T^{10} + 1498272031419237 T^{12} - 318893958147511494 T^{14} + 54906841215868900671 T^{16} - \)\(74\!\cdots\!09\)\( T^{18} + \)\(71\!\cdots\!49\)\( T^{20} \))(\( 1 - 609 T^{2} + 266679 T^{4} - 91457894 T^{6} + 25373368413 T^{8} - 6535895135319 T^{10} + 1498272031419237 T^{12} - 318893958147511494 T^{14} + 54906841215868900671 T^{16} - \)\(74\!\cdots\!09\)\( T^{18} + \)\(71\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 615 T^{2} + 166214 T^{4} - 36215523 T^{6} + 9814770486 T^{8} - 2144372406615 T^{10} + 205891132094649 T^{12} )^{2} \))
$5$ 1
$7$ (\( 1 + 9650 T^{2} + 282475249 T^{4} \))(\( 1 + 9650 T^{2} + 282475249 T^{4} \))(\( ( 1 - 16807 T^{2} )^{2} \))(\( ( 1 - 5966 T^{2} + 282475249 T^{4} )^{2} \))(\( ( 1 - 30554 T^{2} + 282475249 T^{4} )^{2} \))(\( 1 - 61260 T^{2} + 1500118918 T^{4} - 17304433753740 T^{6} + 79792266297612001 T^{8} \))(\( 1 - 61260 T^{2} + 1500118918 T^{4} - 17304433753740 T^{6} + 79792266297612001 T^{8} \))(\( ( 1 - 14394 T^{2} + 282475249 T^{4} )^{2} \))(\( ( 1 - 31654 T^{2} + 282475249 T^{4} )^{2} \))(\( 1 - 54270 T^{2} + 1636355967 T^{4} - 32963917489060 T^{6} + 462230059230960783 T^{8} - \)\(43\!\cdots\!70\)\( T^{10} + \)\(22\!\cdots\!49\)\( T^{12} \))(\( 1 - 54270 T^{2} + 1636355967 T^{4} - 32963917489060 T^{6} + 462230059230960783 T^{8} - \)\(43\!\cdots\!70\)\( T^{10} + \)\(22\!\cdots\!49\)\( T^{12} \))(\( ( 1 + 27060 T^{2} + 497649542 T^{4} + 7643780237940 T^{6} + 79792266297612001 T^{8} )^{2} \))(\( ( 1 - 35620 T^{2} + 881598182 T^{4} - 10061768369380 T^{6} + 79792266297612001 T^{8} )^{2} \))(\( 1 - 57810 T^{2} + 1918138525 T^{4} - 42709020665560 T^{6} + 768467956211993170 T^{8} - \)\(12\!\cdots\!60\)\( T^{10} + \)\(21\!\cdots\!30\)\( T^{12} - \)\(34\!\cdots\!60\)\( T^{14} + \)\(43\!\cdots\!25\)\( T^{16} - \)\(36\!\cdots\!10\)\( T^{18} + \)\(17\!\cdots\!49\)\( T^{20} \))(\( 1 - 57810 T^{2} + 1918138525 T^{4} - 42709020665560 T^{6} + 768467956211993170 T^{8} - \)\(12\!\cdots\!60\)\( T^{10} + \)\(21\!\cdots\!30\)\( T^{12} - \)\(34\!\cdots\!60\)\( T^{14} + \)\(43\!\cdots\!25\)\( T^{16} - \)\(36\!\cdots\!10\)\( T^{18} + \)\(17\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 49694 T^{2} + 1199156991 T^{4} - 21295076725348 T^{6} + 338732169622815759 T^{8} - \)\(39\!\cdots\!94\)\( T^{10} + \)\(22\!\cdots\!49\)\( T^{12} )^{2} \))
$11$ (\( ( 1 + 536 T + 161051 T^{2} )^{2} \))(\( ( 1 - 536 T + 161051 T^{2} )^{2} \))(\( ( 1 + 161051 T^{2} )^{2} \))(\( ( 1 + 315190 T^{2} + 25937424601 T^{4} )^{2} \))(\( ( 1 + 92262 T^{2} + 25937424601 T^{4} )^{2} \))(\( ( 1 + 320 T + 319702 T^{2} + 51536320 T^{3} + 25937424601 T^{4} )^{2} \))(\( ( 1 - 320 T + 319702 T^{2} - 51536320 T^{3} + 25937424601 T^{4} )^{2} \))(\( ( 1 + 254822 T^{2} + 25937424601 T^{4} )^{2} \))(\( ( 1 - 197738 T^{2} + 25937424601 T^{4} )^{2} \))(\( ( 1 + 396 T + 327873 T^{2} + 67617992 T^{3} + 52804274523 T^{4} + 10271220141996 T^{5} + 4177248169415651 T^{6} )^{2} \))(\( ( 1 - 396 T + 327873 T^{2} - 67617992 T^{3} + 52804274523 T^{4} - 10271220141996 T^{5} + 4177248169415651 T^{6} )^{2} \))(\( ( 1 + 382252 T^{2} + 87516901782 T^{4} + 9914632428581452 T^{6} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 609342 T^{2} + 144686893807 T^{4} + 15804762181222542 T^{6} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 5 T + 223729 T^{2} - 31546290 T^{3} + 60901707257 T^{4} + 855449808035 T^{5} + 9808280855447107 T^{6} - 818229518316280290 T^{7} + \)\(93\!\cdots\!79\)\( T^{8} + \)\(33\!\cdots\!05\)\( T^{9} + \)\(10\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 - 5 T + 223729 T^{2} + 31546290 T^{3} + 60901707257 T^{4} - 855449808035 T^{5} + 9808280855447107 T^{6} + 818229518316280290 T^{7} + \)\(93\!\cdots\!79\)\( T^{8} - \)\(33\!\cdots\!05\)\( T^{9} + \)\(10\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 + 185119 T^{2} + 36552934342 T^{4} + 3245101100106923 T^{6} + \)\(94\!\cdots\!42\)\( T^{8} + \)\(12\!\cdots\!19\)\( T^{10} + \)\(17\!\cdots\!01\)\( T^{12} )^{2} \))
$13$ (\( 1 - 260950 T^{2} + 137858491849 T^{4} \))(\( 1 - 260950 T^{2} + 137858491849 T^{4} \))(\( ( 1 - 244 T + 371293 T^{2} )( 1 + 244 T + 371293 T^{2} ) \))(\( ( 1 - 740822 T^{2} + 137858491849 T^{4} )^{2} \))(\( ( 1 - 486550 T^{2} + 137858491849 T^{4} )^{2} \))(\( 1 - 584172 T^{2} + 356551215094 T^{4} - 80533070900414028 T^{6} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( 1 - 584172 T^{2} + 356551215094 T^{4} - 80533070900414028 T^{6} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 718870 T^{2} + 137858491849 T^{4} )^{2} \))(\( ( 1 - 721270 T^{2} + 137858491849 T^{4} )^{2} \))(\( 1 - 1565442 T^{2} + 1135881445383 T^{4} - 513409425866197436 T^{6} + \)\(15\!\cdots\!67\)\( T^{8} - \)\(29\!\cdots\!42\)\( T^{10} + \)\(26\!\cdots\!49\)\( T^{12} \))(\( 1 - 1565442 T^{2} + 1135881445383 T^{4} - 513409425866197436 T^{6} + \)\(15\!\cdots\!67\)\( T^{8} - \)\(29\!\cdots\!42\)\( T^{10} + \)\(26\!\cdots\!49\)\( T^{12} \))(\( ( 1 + 290068 T^{2} + 222887300598 T^{4} + 39988337013655732 T^{6} + \)\(19\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 813092 T^{2} + 406994293398 T^{4} - 112091636854487108 T^{6} + \)\(19\!\cdots\!01\)\( T^{8} )^{2} \))(\( 1 - 2471298 T^{2} + 2972266887253 T^{4} - 2305045840595130584 T^{6} + \)\(12\!\cdots\!26\)\( T^{8} - \)\(54\!\cdots\!36\)\( T^{10} + \)\(17\!\cdots\!74\)\( T^{12} - \)\(43\!\cdots\!84\)\( T^{14} + \)\(77\!\cdots\!97\)\( T^{16} - \)\(89\!\cdots\!98\)\( T^{18} + \)\(49\!\cdots\!49\)\( T^{20} \))(\( 1 - 2471298 T^{2} + 2972266887253 T^{4} - 2305045840595130584 T^{6} + \)\(12\!\cdots\!26\)\( T^{8} - \)\(54\!\cdots\!36\)\( T^{10} + \)\(17\!\cdots\!74\)\( T^{12} - \)\(43\!\cdots\!84\)\( T^{14} + \)\(77\!\cdots\!97\)\( T^{16} - \)\(89\!\cdots\!98\)\( T^{18} + \)\(49\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 561102 T^{2} + 281897614407 T^{4} - 156815847547855396 T^{6} + \)\(38\!\cdots\!43\)\( T^{8} - \)\(10\!\cdots\!02\)\( T^{10} + \)\(26\!\cdots\!49\)\( T^{12} )^{2} \))
$17$ (\( 1 - 1206430 T^{2} + 2015993900449 T^{4} \))(\( 1 - 1206430 T^{2} + 2015993900449 T^{4} \))(\( ( 1 - 808 T + 1419857 T^{2} )( 1 + 808 T + 1419857 T^{2} ) \))(\( ( 1 - 1914270 T^{2} + 2015993900449 T^{4} )^{2} \))(\( ( 1 + 538530 T^{2} + 2015993900449 T^{4} )^{2} \))(\( 1 - 4615228 T^{2} + 9206362973894 T^{4} - 9304271497181437372 T^{6} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( 1 - 4615228 T^{2} + 9206362973894 T^{4} - 9304271497181437372 T^{6} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 2808030 T^{2} + 2015993900449 T^{4} )^{2} \))(\( ( 1 - 2346910 T^{2} + 2015993900449 T^{4} )^{2} \))(\( 1 - 2487258 T^{2} + 7838169507183 T^{4} - 10425763805475099564 T^{6} + \)\(15\!\cdots\!67\)\( T^{8} - \)\(10\!\cdots\!58\)\( T^{10} + \)\(81\!\cdots\!49\)\( T^{12} \))(\( 1 - 2487258 T^{2} + 7838169507183 T^{4} - 10425763805475099564 T^{6} + \)\(15\!\cdots\!67\)\( T^{8} - \)\(10\!\cdots\!58\)\( T^{10} + \)\(81\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 3874620 T^{2} + 7660063539398 T^{4} - 7811210286557704380 T^{6} + \)\(40\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 2023930 T^{2} + 4060271182523 T^{4} - 4080230534935744570 T^{6} + \)\(40\!\cdots\!01\)\( T^{8} )^{2} \))(\( 1 - 9110077 T^{2} + 41366402295503 T^{4} - \)\(12\!\cdots\!66\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} - \)\(43\!\cdots\!39\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} - \)\(50\!\cdots\!66\)\( T^{14} + \)\(33\!\cdots\!47\)\( T^{16} - \)\(15\!\cdots\!77\)\( T^{18} + \)\(33\!\cdots\!49\)\( T^{20} \))(\( 1 - 9110077 T^{2} + 41366402295503 T^{4} - \)\(12\!\cdots\!66\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} - \)\(43\!\cdots\!39\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} - \)\(50\!\cdots\!66\)\( T^{14} + \)\(33\!\cdots\!47\)\( T^{16} - \)\(15\!\cdots\!77\)\( T^{18} + \)\(33\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 1018155 T^{2} + 3734942516022 T^{4} - 1670881124593450815 T^{6} + \)\(75\!\cdots\!78\)\( T^{8} - \)\(41\!\cdots\!55\)\( T^{10} + \)\(81\!\cdots\!49\)\( T^{12} )^{2} \))
$19$ (\( ( 1 + 1112 T + 2476099 T^{2} )^{2} \))(\( ( 1 - 1112 T + 2476099 T^{2} )^{2} \))(\( ( 1 + 2476099 T^{2} )^{2} \))(\( ( 1 + 632198 T^{2} + 6131066257801 T^{4} )^{2} \))(\( ( 1 + 687238 T^{2} + 6131066257801 T^{4} )^{2} \))(\( ( 1 - 720 T + 4633798 T^{2} - 1782791280 T^{3} + 6131066257801 T^{4} )^{2} \))(\( ( 1 + 720 T + 4633798 T^{2} + 1782791280 T^{3} + 6131066257801 T^{4} )^{2} \))(\( ( 1 + 4019078 T^{2} + 6131066257801 T^{4} )^{2} \))(\( ( 1 - 2512762 T^{2} + 6131066257801 T^{4} )^{2} \))(\( ( 1 + 3192 T + 9330057 T^{2} + 15933739216 T^{3} + 23102144807643 T^{4} + 19570363494900792 T^{5} + 15181127029874798299 T^{6} )^{2} \))(\( ( 1 - 3192 T + 9330057 T^{2} - 15933739216 T^{3} + 23102144807643 T^{4} - 19570363494900792 T^{5} + 15181127029874798299 T^{6} )^{2} \))(\( ( 1 + 1633036 T^{2} + 154661897526 T^{4} + 10012251917374313836 T^{6} + \)\(37\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 8574646 T^{2} + 30599890459431 T^{4} + 52571722763188313446 T^{6} + \)\(37\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 4485 T + 12501601 T^{2} - 21607836470 T^{3} + 29093337227017 T^{4} - 38411986388536715 T^{5} + 72037983214479566683 T^{6} - \)\(13\!\cdots\!70\)\( T^{7} + \)\(18\!\cdots\!99\)\( T^{8} - \)\(16\!\cdots\!85\)\( T^{9} + \)\(93\!\cdots\!99\)\( T^{10} )^{2} \))(\( ( 1 + 4485 T + 12501601 T^{2} + 21607836470 T^{3} + 29093337227017 T^{4} + 38411986388536715 T^{5} + 72037983214479566683 T^{6} + \)\(13\!\cdots\!70\)\( T^{7} + \)\(18\!\cdots\!99\)\( T^{8} + \)\(16\!\cdots\!85\)\( T^{9} + \)\(93\!\cdots\!99\)\( T^{10} )^{2} \))(\( ( 1 + 8807519 T^{2} + 39268629467990 T^{4} + \)\(11\!\cdots\!55\)\( T^{6} + \)\(24\!\cdots\!90\)\( T^{8} + \)\(33\!\cdots\!19\)\( T^{10} + \)\(23\!\cdots\!01\)\( T^{12} )^{2} \))
$23$ (\( 1 - 2530030 T^{2} + 41426511213649 T^{4} \))(\( 1 - 2530030 T^{2} + 41426511213649 T^{4} \))(\( ( 1 - 6436343 T^{2} )^{2} \))(\( ( 1 - 2891758 T^{2} + 41426511213649 T^{4} )^{2} \))(\( ( 1 - 9265626 T^{2} + 41426511213649 T^{4} )^{2} \))(\( 1 - 19051660 T^{2} + 166087805861318 T^{4} - \)\(78\!\cdots\!40\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 19051660 T^{2} + 166087805861318 T^{4} - \)\(78\!\cdots\!40\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 5934266 T^{2} + 41426511213649 T^{4} )^{2} \))(\( ( 1 + 3871674 T^{2} + 41426511213649 T^{4} )^{2} \))(\( 1 - 21917310 T^{2} + 235143882878367 T^{4} - \)\(17\!\cdots\!80\)\( T^{6} + \)\(97\!\cdots\!83\)\( T^{8} - \)\(37\!\cdots\!10\)\( T^{10} + \)\(71\!\cdots\!49\)\( T^{12} \))(\( 1 - 21917310 T^{2} + 235143882878367 T^{4} - \)\(17\!\cdots\!80\)\( T^{6} + \)\(97\!\cdots\!83\)\( T^{8} - \)\(37\!\cdots\!10\)\( T^{10} + \)\(71\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 25651084 T^{2} + 247347299659206 T^{4} - \)\(10\!\cdots\!16\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 5911844 T^{2} + 79263706443686 T^{4} - \)\(24\!\cdots\!56\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} )^{2} \))(\( 1 - 42038290 T^{2} + 863811546681725 T^{4} - \)\(11\!\cdots\!40\)\( T^{6} + \)\(11\!\cdots\!70\)\( T^{8} - \)\(81\!\cdots\!40\)\( T^{10} + \)\(46\!\cdots\!30\)\( T^{12} - \)\(19\!\cdots\!40\)\( T^{14} + \)\(61\!\cdots\!25\)\( T^{16} - \)\(12\!\cdots\!90\)\( T^{18} + \)\(12\!\cdots\!49\)\( T^{20} \))(\( 1 - 42038290 T^{2} + 863811546681725 T^{4} - \)\(11\!\cdots\!40\)\( T^{6} + \)\(11\!\cdots\!70\)\( T^{8} - \)\(81\!\cdots\!40\)\( T^{10} + \)\(46\!\cdots\!30\)\( T^{12} - \)\(19\!\cdots\!40\)\( T^{14} + \)\(61\!\cdots\!25\)\( T^{16} - \)\(12\!\cdots\!90\)\( T^{18} + \)\(12\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 13074430 T^{2} + 26099998735519 T^{4} + \)\(24\!\cdots\!92\)\( T^{6} + \)\(10\!\cdots\!31\)\( T^{8} - \)\(22\!\cdots\!30\)\( T^{10} + \)\(71\!\cdots\!49\)\( T^{12} )^{2} \))
$29$ (\( ( 1 + 2918 T + 20511149 T^{2} )^{2} \))(\( ( 1 + 2918 T + 20511149 T^{2} )^{2} \))(\( ( 1 + 2950 T + 20511149 T^{2} )^{2} \))(\( ( 1 - 2554 T + 20511149 T^{2} )^{4} \))(\( ( 1 - 4530 T + 20511149 T^{2} )^{4} \))(\( ( 1 + 108 T + 39233214 T^{2} + 2215204092 T^{3} + 420707233300201 T^{4} )^{2} \))(\( ( 1 + 108 T + 39233214 T^{2} + 2215204092 T^{3} + 420707233300201 T^{4} )^{2} \))(\( ( 1 + 4110 T + 20511149 T^{2} )^{4} \))(\( ( 1 - 4010 T + 20511149 T^{2} )^{4} \))(\( ( 1 + 426 T - 939693 T^{2} - 141773503364 T^{3} - 19274183137257 T^{4} + 179221281385885626 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 + 426 T - 939693 T^{2} - 141773503364 T^{3} - 19274183137257 T^{4} + 179221281385885626 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 - 84 T + 9837118 T^{2} - 1722936516 T^{3} + 420707233300201 T^{4} )^{4} \))(\( ( 1 - 2804 T + 24855898 T^{2} - 57513261796 T^{3} + 420707233300201 T^{4} )^{4} \))(\( ( 1 - 3252 T + 58920849 T^{2} - 180794629712 T^{3} + 1901306884501354 T^{4} - 5432007039260706936 T^{5} + \)\(38\!\cdots\!46\)\( T^{6} - \)\(76\!\cdots\!12\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} - \)\(57\!\cdots\!52\)\( T^{9} + \)\(36\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 - 3252 T + 58920849 T^{2} - 180794629712 T^{3} + 1901306884501354 T^{4} - 5432007039260706936 T^{5} + \)\(38\!\cdots\!46\)\( T^{6} - \)\(76\!\cdots\!12\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} - \)\(57\!\cdots\!52\)\( T^{9} + \)\(36\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 + 2076 T + 3518727 T^{2} + 42075647448 T^{3} + 72173133787323 T^{4} + 873388216331217276 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} )^{4} \))
$31$ (\( ( 1 + 2624 T + 28629151 T^{2} )^{2} \))(\( ( 1 - 2624 T + 28629151 T^{2} )^{2} \))(\( ( 1 + 28629151 T^{2} )^{2} \))(\( ( 1 + 53276990 T^{2} + 819628286980801 T^{4} )^{2} \))(\( ( 1 + 43928942 T^{2} + 819628286980801 T^{4} )^{2} \))(\( ( 1 + 9840 T + 76732702 T^{2} + 281710845840 T^{3} + 819628286980801 T^{4} )^{2} \))(\( ( 1 - 9840 T + 76732702 T^{2} - 281710845840 T^{3} + 819628286980801 T^{4} )^{2} \))(\( ( 1 + 47289582 T^{2} + 819628286980801 T^{4} )^{2} \))(\( ( 1 + 36406942 T^{2} + 819628286980801 T^{4} )^{2} \))(\( ( 1 - 3276 T + 2292813 T^{2} + 41639420248 T^{3} + 65641289591763 T^{4} - 2685102268149104076 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 + 3276 T + 2292813 T^{2} - 41639420248 T^{3} + 65641289591763 T^{4} + 2685102268149104076 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 + 24283452 T^{2} + 1637830022018822 T^{4} + \)\(19\!\cdots\!52\)\( T^{6} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 103009732 T^{2} + 4259568177035462 T^{4} + \)\(84\!\cdots\!32\)\( T^{6} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 8250 T + 120556099 T^{2} + 854323338280 T^{3} + 6336384967622242 T^{4} + 35548315279501204060 T^{5} + \)\(18\!\cdots\!42\)\( T^{6} + \)\(70\!\cdots\!80\)\( T^{7} + \)\(28\!\cdots\!49\)\( T^{8} + \)\(55\!\cdots\!50\)\( T^{9} + \)\(19\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 - 8250 T + 120556099 T^{2} - 854323338280 T^{3} + 6336384967622242 T^{4} - 35548315279501204060 T^{5} + \)\(18\!\cdots\!42\)\( T^{6} - \)\(70\!\cdots\!80\)\( T^{7} + \)\(28\!\cdots\!49\)\( T^{8} - \)\(55\!\cdots\!50\)\( T^{9} + \)\(19\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 + 26131694 T^{2} + 414413614760367 T^{4} + \)\(25\!\cdots\!48\)\( T^{6} + \)\(33\!\cdots\!67\)\( T^{8} + \)\(17\!\cdots\!94\)\( T^{10} + \)\(55\!\cdots\!01\)\( T^{12} )^{2} \))
$37$ (\( 1 - 49234150 T^{2} + 4808584372417849 T^{4} \))(\( 1 - 49234150 T^{2} + 4808584372417849 T^{4} \))(\( ( 1 - 11292 T + 69343957 T^{2} )( 1 + 11292 T + 69343957 T^{2} ) \))(\( ( 1 + 4114586 T^{2} + 4808584372417849 T^{4} )^{2} \))(\( ( 1 - 138573670 T^{2} + 4808584372417849 T^{4} )^{2} \))(\( 1 - 80374028 T^{2} + 7476476186271894 T^{4} - \)\(38\!\cdots\!72\)\( T^{6} + \)\(23\!\cdots\!01\)\( T^{8} \))(\( 1 - 80374028 T^{2} + 7476476186271894 T^{4} - \)\(38\!\cdots\!72\)\( T^{6} + \)\(23\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 83304550 T^{2} + 4808584372417849 T^{4} )^{2} \))(\( ( 1 + 79701370 T^{2} + 4808584372417849 T^{4} )^{2} \))(\( 1 - 47567538 T^{2} + 8632350495280023 T^{4} - \)\(24\!\cdots\!84\)\( T^{6} + \)\(41\!\cdots\!27\)\( T^{8} - \)\(10\!\cdots\!38\)\( T^{10} + \)\(11\!\cdots\!49\)\( T^{12} \))(\( 1 - 47567538 T^{2} + 8632350495280023 T^{4} - \)\(24\!\cdots\!84\)\( T^{6} + \)\(41\!\cdots\!27\)\( T^{8} - \)\(10\!\cdots\!38\)\( T^{10} + \)\(11\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 221756684 T^{2} + 21573741661821078 T^{4} - \)\(10\!\cdots\!16\)\( T^{6} + \)\(23\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 276548364 T^{2} + 28736866127669398 T^{4} - \)\(13\!\cdots\!36\)\( T^{6} + \)\(23\!\cdots\!01\)\( T^{8} )^{2} \))(\( 1 - 374023262 T^{2} + 69966140684637573 T^{4} - \)\(87\!\cdots\!56\)\( T^{6} + \)\(84\!\cdots\!06\)\( T^{8} - \)\(64\!\cdots\!64\)\( T^{10} + \)\(40\!\cdots\!94\)\( T^{12} - \)\(20\!\cdots\!56\)\( T^{14} + \)\(77\!\cdots\!77\)\( T^{16} - \)\(19\!\cdots\!62\)\( T^{18} + \)\(25\!\cdots\!49\)\( T^{20} \))(\( 1 - 374023262 T^{2} + 69966140684637573 T^{4} - \)\(87\!\cdots\!56\)\( T^{6} + \)\(84\!\cdots\!06\)\( T^{8} - \)\(64\!\cdots\!64\)\( T^{10} + \)\(40\!\cdots\!94\)\( T^{12} - \)\(20\!\cdots\!56\)\( T^{14} + \)\(77\!\cdots\!77\)\( T^{16} - \)\(19\!\cdots\!62\)\( T^{18} + \)\(25\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 211439154 T^{2} + 25700211767834007 T^{4} - \)\(20\!\cdots\!92\)\( T^{6} + \)\(12\!\cdots\!43\)\( T^{8} - \)\(48\!\cdots\!54\)\( T^{10} + \)\(11\!\cdots\!49\)\( T^{12} )^{2} \))
$41$ (\( ( 1 - 170 T + 115856201 T^{2} )^{2} \))(\( ( 1 - 170 T + 115856201 T^{2} )^{2} \))(\( ( 1 + 20950 T + 115856201 T^{2} )^{2} \))(\( ( 1 + 5078 T + 115856201 T^{2} )^{4} \))(\( ( 1 + 6330 T + 115856201 T^{2} )^{4} \))(\( ( 1 + 10620 T + 77106582 T^{2} + 1230392854620 T^{3} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 + 10620 T + 77106582 T^{2} + 1230392854620 T^{3} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 - 7270 T + 115856201 T^{2} )^{4} \))(\( ( 1 + 4350 T + 115856201 T^{2} )^{4} \))(\( ( 1 - 12450 T + 384843783 T^{2} - 2886023186300 T^{3} + 44586538676848383 T^{4} - \)\(16\!\cdots\!50\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} )^{2} \))(\( ( 1 - 12450 T + 384843783 T^{2} - 2886023186300 T^{3} + 44586538676848383 T^{4} - \)\(16\!\cdots\!50\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} )^{2} \))(\( ( 1 - 23812 T + 331016342 T^{2} - 2758767858212 T^{3} + 13422659310152401 T^{4} )^{4} \))(\( ( 1 - 2362 T + 166748827 T^{2} - 273652346762 T^{3} + 13422659310152401 T^{4} )^{4} \))(\( ( 1 + 11415 T + 343211175 T^{2} + 1948003513210 T^{3} + 41961472497955645 T^{4} + \)\(14\!\cdots\!65\)\( T^{5} + \)\(48\!\cdots\!45\)\( T^{6} + \)\(26\!\cdots\!10\)\( T^{7} + \)\(53\!\cdots\!75\)\( T^{8} + \)\(20\!\cdots\!15\)\( T^{9} + \)\(20\!\cdots\!01\)\( T^{10} )^{2} \))(\( ( 1 + 11415 T + 343211175 T^{2} + 1948003513210 T^{3} + 41961472497955645 T^{4} + \)\(14\!\cdots\!65\)\( T^{5} + \)\(48\!\cdots\!45\)\( T^{6} + \)\(26\!\cdots\!10\)\( T^{7} + \)\(53\!\cdots\!75\)\( T^{8} + \)\(20\!\cdots\!15\)\( T^{9} + \)\(20\!\cdots\!01\)\( T^{10} )^{2} \))(\( ( 1 - 5167 T + 303702118 T^{2} - 1155964650859 T^{3} + 35185773627133718 T^{4} - 69354880655557455967 T^{5} + \)\(15\!\cdots\!01\)\( T^{6} )^{4} \))
$43$ (\( 1 + 103108298 T^{2} + 21611482313284249 T^{4} \))(\( 1 + 103108298 T^{2} + 21611482313284249 T^{4} \))(\( ( 1 - 147008443 T^{2} )^{2} \))(\( ( 1 - 136416374 T^{2} + 21611482313284249 T^{4} )^{2} \))(\( ( 1 + 35859614 T^{2} + 21611482313284249 T^{4} )^{2} \))(\( 1 - 70773020 T^{2} - 17388341663539722 T^{4} - \)\(15\!\cdots\!80\)\( T^{6} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( 1 - 70773020 T^{2} - 17388341663539722 T^{4} - \)\(15\!\cdots\!80\)\( T^{6} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 26783614 T^{2} + 21611482313284249 T^{4} )^{2} \))(\( ( 1 - 139567886 T^{2} + 21611482313284249 T^{4} )^{2} \))(\( 1 - 587098422 T^{2} + 171971726662843287 T^{4} - \)\(31\!\cdots\!16\)\( T^{6} + \)\(37\!\cdots\!63\)\( T^{8} - \)\(27\!\cdots\!22\)\( T^{10} + \)\(10\!\cdots\!49\)\( T^{12} \))(\( 1 - 587098422 T^{2} + 171971726662843287 T^{4} - \)\(31\!\cdots\!16\)\( T^{6} + \)\(37\!\cdots\!63\)\( T^{8} - \)\(27\!\cdots\!22\)\( T^{10} + \)\(10\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 385757980 T^{2} + 71059469286049782 T^{4} - \)\(83\!\cdots\!20\)\( T^{6} + \)\(46\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 541044700 T^{2} + 115921260979035702 T^{4} - \)\(11\!\cdots\!00\)\( T^{6} + \)\(46\!\cdots\!01\)\( T^{8} )^{2} \))(\( 1 - 1207416734 T^{2} + 682735937965865829 T^{4} - \)\(23\!\cdots\!44\)\( T^{6} + \)\(57\!\cdots\!38\)\( T^{8} - \)\(98\!\cdots\!44\)\( T^{10} + \)\(12\!\cdots\!62\)\( T^{12} - \)\(11\!\cdots\!44\)\( T^{14} + \)\(68\!\cdots\!21\)\( T^{16} - \)\(26\!\cdots\!34\)\( T^{18} + \)\(47\!\cdots\!49\)\( T^{20} \))(\( 1 - 1207416734 T^{2} + 682735937965865829 T^{4} - \)\(23\!\cdots\!44\)\( T^{6} + \)\(57\!\cdots\!38\)\( T^{8} - \)\(98\!\cdots\!44\)\( T^{10} + \)\(12\!\cdots\!62\)\( T^{12} - \)\(11\!\cdots\!44\)\( T^{14} + \)\(68\!\cdots\!21\)\( T^{16} - \)\(26\!\cdots\!34\)\( T^{18} + \)\(47\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 76382546 T^{2} + 58843802853385271 T^{4} - \)\(33\!\cdots\!12\)\( T^{6} + \)\(12\!\cdots\!79\)\( T^{8} - \)\(35\!\cdots\!46\)\( T^{10} + \)\(10\!\cdots\!49\)\( T^{12} )^{2} \))
$47$ (\( 1 - 458688990 T^{2} + 52599132235830049 T^{4} \))(\( 1 - 458688990 T^{2} + 52599132235830049 T^{4} \))(\( ( 1 - 229345007 T^{2} )^{2} \))(\( ( 1 - 307289566 T^{2} + 52599132235830049 T^{4} )^{2} \))(\( ( 1 - 442383274 T^{2} + 52599132235830049 T^{4} )^{2} \))(\( 1 - 434902380 T^{2} + 119597691857197478 T^{4} - \)\(22\!\cdots\!20\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 - 434902380 T^{2} + 119597691857197478 T^{4} - \)\(22\!\cdots\!20\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 403777034 T^{2} + 52599132235830049 T^{4} )^{2} \))(\( ( 1 - 422513974 T^{2} + 52599132235830049 T^{4} )^{2} \))(\( 1 - 888472110 T^{2} + 408520605892907727 T^{4} - \)\(11\!\cdots\!80\)\( T^{6} + \)\(21\!\cdots\!23\)\( T^{8} - \)\(24\!\cdots\!10\)\( T^{10} + \)\(14\!\cdots\!49\)\( T^{12} \))(\( 1 - 888472110 T^{2} + 408520605892907727 T^{4} - \)\(11\!\cdots\!80\)\( T^{6} + \)\(21\!\cdots\!23\)\( T^{8} - \)\(24\!\cdots\!10\)\( T^{10} + \)\(14\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 353765740 T^{2} + 66158288717340582 T^{4} - \)\(18\!\cdots\!60\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 464873580 T^{2} + 117215868278322022 T^{4} - \)\(24\!\cdots\!20\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} )^{2} \))(\( 1 - 998947830 T^{2} + 484280818092021965 T^{4} - \)\(16\!\cdots\!80\)\( T^{6} + \)\(49\!\cdots\!50\)\( T^{8} - \)\(12\!\cdots\!80\)\( T^{10} + \)\(25\!\cdots\!50\)\( T^{12} - \)\(46\!\cdots\!80\)\( T^{14} + \)\(70\!\cdots\!85\)\( T^{16} - \)\(76\!\cdots\!30\)\( T^{18} + \)\(40\!\cdots\!49\)\( T^{20} \))(\( 1 - 998947830 T^{2} + 484280818092021965 T^{4} - \)\(16\!\cdots\!80\)\( T^{6} + \)\(49\!\cdots\!50\)\( T^{8} - \)\(12\!\cdots\!80\)\( T^{10} + \)\(25\!\cdots\!50\)\( T^{12} - \)\(46\!\cdots\!80\)\( T^{14} + \)\(70\!\cdots\!85\)\( T^{16} - \)\(76\!\cdots\!30\)\( T^{18} + \)\(40\!\cdots\!49\)\( T^{20} \))(\( ( 1 + 303942406 T^{2} + 125400301199290991 T^{4} + \)\(20\!\cdots\!52\)\( T^{6} + \)\(65\!\cdots\!59\)\( T^{8} + \)\(84\!\cdots\!06\)\( T^{10} + \)\(14\!\cdots\!49\)\( T^{12} )^{2} \))
$53$ (\( 1 - 344527302 T^{2} + 174887470365513049 T^{4} \))(\( 1 - 344527302 T^{2} + 174887470365513049 T^{4} \))(\( ( 1 - 40244 T + 418195493 T^{2} )( 1 + 40244 T + 418195493 T^{2} ) \))(\( ( 1 - 447749190 T^{2} + 174887470365513049 T^{4} )^{2} \))(\( ( 1 - 596574790 T^{2} + 174887470365513049 T^{4} )^{2} \))(\( 1 - 528500172 T^{2} + 98825823286833494 T^{4} - \)\(92\!\cdots\!28\)\( T^{6} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( 1 - 528500172 T^{2} + 98825823286833494 T^{4} - \)\(92\!\cdots\!28\)\( T^{6} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 202124090 T^{2} + 174887470365513049 T^{4} )^{2} \))(\( ( 1 - 506823270 T^{2} + 174887470365513049 T^{4} )^{2} \))(\( 1 - 343748754 T^{2} + 524992621000918647 T^{4} - \)\(11\!\cdots\!64\)\( T^{6} + \)\(91\!\cdots\!03\)\( T^{8} - \)\(10\!\cdots\!54\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} \))(\( 1 - 343748754 T^{2} + 524992621000918647 T^{4} - \)\(11\!\cdots\!64\)\( T^{6} + \)\(91\!\cdots\!03\)\( T^{8} - \)\(10\!\cdots\!54\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 1591203020 T^{2} + 981099301374675798 T^{4} - \)\(27\!\cdots\!80\)\( T^{6} + \)\(30\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 1223228620 T^{2} + 719099673851296598 T^{4} - \)\(21\!\cdots\!80\)\( T^{6} + \)\(30\!\cdots\!01\)\( T^{8} )^{2} \))(\( 1 - 1929957822 T^{2} + 1979021800259468069 T^{4} - \)\(14\!\cdots\!92\)\( T^{6} + \)\(78\!\cdots\!34\)\( T^{8} - \)\(35\!\cdots\!16\)\( T^{10} + \)\(13\!\cdots\!66\)\( T^{12} - \)\(43\!\cdots\!92\)\( T^{14} + \)\(10\!\cdots\!81\)\( T^{16} - \)\(18\!\cdots\!22\)\( T^{18} + \)\(16\!\cdots\!49\)\( T^{20} \))(\( 1 - 1929957822 T^{2} + 1979021800259468069 T^{4} - \)\(14\!\cdots\!92\)\( T^{6} + \)\(78\!\cdots\!34\)\( T^{8} - \)\(35\!\cdots\!16\)\( T^{10} + \)\(13\!\cdots\!66\)\( T^{12} - \)\(43\!\cdots\!92\)\( T^{14} + \)\(10\!\cdots\!81\)\( T^{16} - \)\(18\!\cdots\!22\)\( T^{18} + \)\(16\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 817365810 T^{2} + 139168553420345847 T^{4} + \)\(41\!\cdots\!20\)\( T^{6} + \)\(24\!\cdots\!03\)\( T^{8} - \)\(24\!\cdots\!10\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} )^{2} \))
$59$ (\( ( 1 + 41480 T + 714924299 T^{2} )^{2} \))(\( ( 1 - 41480 T + 714924299 T^{2} )^{2} \))(\( ( 1 + 714924299 T^{2} )^{2} \))(\( ( 1 + 1350713110 T^{2} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 + 1376531158 T^{2} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 - 30800 T + 1666896598 T^{2} - 22019668409200 T^{3} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 + 30800 T + 1666896598 T^{2} + 22019668409200 T^{3} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 + 270997718 T^{2} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 + 1041470358 T^{2} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 + 35040 T + 1757220897 T^{2} + 50989349593920 T^{3} + 1256279917975876203 T^{4} + \)\(17\!\cdots\!40\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} )^{2} \))(\( ( 1 - 35040 T + 1757220897 T^{2} - 50989349593920 T^{3} + 1256279917975876203 T^{4} - \)\(17\!\cdots\!40\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} )^{2} \))(\( ( 1 + 488747308 T^{2} + 896846029819225302 T^{4} + \)\(24\!\cdots\!08\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 2385664988 T^{2} + 2388942263952556022 T^{4} + \)\(12\!\cdots\!88\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 39280 T + 2477107495 T^{2} + 66121066498880 T^{3} + 2998757238928356010 T^{4} + \)\(66\!\cdots\!80\)\( T^{5} + \)\(21\!\cdots\!90\)\( T^{6} + \)\(33\!\cdots\!80\)\( T^{7} + \)\(90\!\cdots\!05\)\( T^{8} + \)\(10\!\cdots\!80\)\( T^{9} + \)\(18\!\cdots\!99\)\( T^{10} )^{2} \))(\( ( 1 - 39280 T + 2477107495 T^{2} - 66121066498880 T^{3} + 2998757238928356010 T^{4} - \)\(66\!\cdots\!80\)\( T^{5} + \)\(21\!\cdots\!90\)\( T^{6} - \)\(33\!\cdots\!80\)\( T^{7} + \)\(90\!\cdots\!05\)\( T^{8} - \)\(10\!\cdots\!80\)\( T^{9} + \)\(18\!\cdots\!99\)\( T^{10} )^{2} \))(\( ( 1 + 1182931106 T^{2} + 405497478006370967 T^{4} - \)\(86\!\cdots\!48\)\( T^{6} + \)\(20\!\cdots\!67\)\( T^{8} + \)\(30\!\cdots\!06\)\( T^{10} + \)\(13\!\cdots\!01\)\( T^{12} )^{2} \))
$61$ (\( ( 1 - 15462 T + 844596301 T^{2} )^{2} \))(\( ( 1 - 15462 T + 844596301 T^{2} )^{2} \))(\( ( 1 - 18950 T + 844596301 T^{2} )^{2} \))(\( ( 1 - 29318 T + 844596301 T^{2} )^{4} \))(\( ( 1 + 16750 T + 844596301 T^{2} )^{4} \))(\( ( 1 - 24540 T + 1447225822 T^{2} - 20726393226540 T^{3} + 713342911662882601 T^{4} )^{2} \))(\( ( 1 - 24540 T + 1447225822 T^{2} - 20726393226540 T^{3} + 713342911662882601 T^{4} )^{2} \))(\( ( 1 - 26770 T + 844596301 T^{2} )^{4} \))(\( ( 1 + 42130 T + 844596301 T^{2} )^{4} \))(\( ( 1 + 24138 T + 393086643 T^{2} - 6904061162564 T^{3} + 331999524650307543 T^{4} + \)\(17\!\cdots\!38\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} )^{2} \))(\( ( 1 + 24138 T + 393086643 T^{2} - 6904061162564 T^{3} + 331999524650307543 T^{4} + \)\(17\!\cdots\!38\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} )^{2} \))(\( ( 1 + 31012 T + 1250446302 T^{2} + 26192620486612 T^{3} + 713342911662882601 T^{4} )^{4} \))(\( ( 1 + 16392 T + 1727540902 T^{2} + 13844622565992 T^{3} + 713342911662882601 T^{4} )^{4} \))(\( ( 1 - 34854 T + 2057496889 T^{2} - 44185370435336 T^{3} + 2177762976578344882 T^{4} - \)\(41\!\cdots\!64\)\( T^{5} + \)\(18\!\cdots\!82\)\( T^{6} - \)\(31\!\cdots\!36\)\( T^{7} + \)\(12\!\cdots\!89\)\( T^{8} - \)\(17\!\cdots\!54\)\( T^{9} + \)\(42\!\cdots\!01\)\( T^{10} )^{2} \))(\( ( 1 - 34854 T + 2057496889 T^{2} - 44185370435336 T^{3} + 2177762976578344882 T^{4} - \)\(41\!\cdots\!64\)\( T^{5} + \)\(18\!\cdots\!82\)\( T^{6} - \)\(31\!\cdots\!36\)\( T^{7} + \)\(12\!\cdots\!89\)\( T^{8} - \)\(17\!\cdots\!54\)\( T^{9} + \)\(42\!\cdots\!01\)\( T^{10} )^{2} \))(\( ( 1 - 12898 T + 1453238243 T^{2} - 7609599436396 T^{3} + 1227399644509539143 T^{4} - \)\(92\!\cdots\!98\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} )^{4} \))
$67$ (\( 1 - 2269936678 T^{2} + 1822837804551761449 T^{4} \))(\( 1 - 2269936678 T^{2} + 1822837804551761449 T^{4} \))(\( ( 1 - 1350125107 T^{2} )^{2} \))(\( ( 1 - 2415413606 T^{2} + 1822837804551761449 T^{4} )^{2} \))(\( ( 1 - 2513562674 T^{2} + 1822837804551761449 T^{4} )^{2} \))(\( 1 - 4665259900 T^{2} + 9004780480727533398 T^{4} - \)\(85\!\cdots\!00\)\( T^{6} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( 1 - 4665259900 T^{2} + 9004780480727533398 T^{4} - \)\(85\!\cdots\!00\)\( T^{6} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 219594834 T^{2} + 1822837804551761449 T^{4} )^{2} \))(\( ( 1 - 2438310974 T^{2} + 1822837804551761449 T^{4} )^{2} \))(\( 1 - 1227086118 T^{2} + 624926915335274247 T^{4} + \)\(11\!\cdots\!36\)\( T^{6} + \)\(11\!\cdots\!03\)\( T^{8} - \)\(40\!\cdots\!18\)\( T^{10} + \)\(60\!\cdots\!49\)\( T^{12} \))(\( 1 - 1227086118 T^{2} + 624926915335274247 T^{4} + \)\(11\!\cdots\!36\)\( T^{6} + \)\(11\!\cdots\!03\)\( T^{8} - \)\(40\!\cdots\!18\)\( T^{10} + \)\(60\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 3336863100 T^{2} + 6361754088145172822 T^{4} - \)\(60\!\cdots\!00\)\( T^{6} + \)\(33\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 1059995890 T^{2} + 3926502810495156767 T^{4} + \)\(19\!\cdots\!10\)\( T^{6} + \)\(33\!\cdots\!01\)\( T^{8} )^{2} \))(\( 1 - 9201103561 T^{2} + 41955211928457148119 T^{4} - \)\(12\!\cdots\!06\)\( T^{6} + \)\(25\!\cdots\!13\)\( T^{8} - \)\(40\!\cdots\!91\)\( T^{10} + \)\(47\!\cdots\!37\)\( T^{12} - \)\(41\!\cdots\!06\)\( T^{14} + \)\(25\!\cdots\!31\)\( T^{16} - \)\(10\!\cdots\!61\)\( T^{18} + \)\(20\!\cdots\!49\)\( T^{20} \))(\( 1 - 9201103561 T^{2} + 41955211928457148119 T^{4} - \)\(12\!\cdots\!06\)\( T^{6} + \)\(25\!\cdots\!13\)\( T^{8} - \)\(40\!\cdots\!91\)\( T^{10} + \)\(47\!\cdots\!37\)\( T^{12} - \)\(41\!\cdots\!06\)\( T^{14} + \)\(25\!\cdots\!31\)\( T^{16} - \)\(10\!\cdots\!61\)\( T^{18} + \)\(20\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 2147578559 T^{2} + 5794049304914432886 T^{4} - \)\(68\!\cdots\!83\)\( T^{6} + \)\(10\!\cdots\!14\)\( T^{8} - \)\(71\!\cdots\!59\)\( T^{10} + \)\(60\!\cdots\!49\)\( T^{12} )^{2} \))
$71$ (\( ( 1 - 28592 T + 1804229351 T^{2} )^{2} \))(\( ( 1 + 28592 T + 1804229351 T^{2} )^{2} \))(\( ( 1 + 1804229351 T^{2} )^{2} \))(\( ( 1 - 2948789810 T^{2} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 1737195262 T^{2} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 - 12400 T + 1143670702 T^{2} - 22372443952400 T^{3} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 12400 T + 1143670702 T^{2} + 22372443952400 T^{3} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 681226622 T^{2} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 1542914862 T^{2} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 - 88092 T + 7289446053 T^{2} - 329541325840584 T^{3} + 13151832521353701603 T^{4} - \)\(28\!\cdots\!92\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 + 88092 T + 7289446053 T^{2} + 329541325840584 T^{3} + 13151832521353701603 T^{4} + \)\(28\!\cdots\!92\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 + 6374750812 T^{2} + 16622748841310481702 T^{4} + \)\(20\!\cdots\!12\)\( T^{6} + \)\(10\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 2309254412 T^{2} + 2458167894389978822 T^{4} + \)\(75\!\cdots\!12\)\( T^{6} + \)\(10\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 51200 T + 4847837491 T^{2} + 294113026009600 T^{3} + 15407476450683661018 T^{4} + \)\(67\!\cdots\!00\)\( T^{5} + \)\(27\!\cdots\!18\)\( T^{6} + \)\(95\!\cdots\!00\)\( T^{7} + \)\(28\!\cdots\!41\)\( T^{8} + \)\(54\!\cdots\!00\)\( T^{9} + \)\(19\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 - 51200 T + 4847837491 T^{2} - 294113026009600 T^{3} + 15407476450683661018 T^{4} - \)\(67\!\cdots\!00\)\( T^{5} + \)\(27\!\cdots\!18\)\( T^{6} - \)\(95\!\cdots\!00\)\( T^{7} + \)\(28\!\cdots\!41\)\( T^{8} - \)\(54\!\cdots\!00\)\( T^{9} + \)\(19\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 + 5042886794 T^{2} + 14326830934494036767 T^{4} + \)\(28\!\cdots\!48\)\( T^{6} + \)\(46\!\cdots\!67\)\( T^{8} + \)\(53\!\cdots\!94\)\( T^{10} + \)\(34\!\cdots\!01\)\( T^{12} )^{2} \))
$73$ (\( 1 - 1265674286 T^{2} + 4297625829703557649 T^{4} \))(\( 1 - 1265674286 T^{2} + 4297625829703557649 T^{4} \))(\( ( 1 - 20144 T + 2073071593 T^{2} )( 1 + 20144 T + 2073071593 T^{2} ) \))(\( ( 1 - 2708671790 T^{2} + 4297625829703557649 T^{4} )^{2} \))(\( ( 1 - 3713253550 T^{2} + 4297625829703557649 T^{4} )^{2} \))(\( 1 - 517006172 T^{2} + 8462322739873838694 T^{4} - \)\(22\!\cdots\!28\)\( T^{6} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 - 517006172 T^{2} + 8462322739873838694 T^{4} - \)\(22\!\cdots\!28\)\( T^{6} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 3802634030 T^{2} + 4297625829703557649 T^{4} )^{2} \))(\( ( 1 - 3456240430 T^{2} + 4297625829703557649 T^{4} )^{2} \))(\( 1 - 3294592458 T^{2} + 16216281639521153535 T^{4} - \)\(29\!\cdots\!40\)\( T^{6} + \)\(69\!\cdots\!15\)\( T^{8} - \)\(60\!\cdots\!58\)\( T^{10} + \)\(79\!\cdots\!49\)\( T^{12} \))(\( 1 - 3294592458 T^{2} + 16216281639521153535 T^{4} - \)\(29\!\cdots\!40\)\( T^{6} + \)\(69\!\cdots\!15\)\( T^{8} - \)\(60\!\cdots\!58\)\( T^{10} + \)\(79\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 6494647900 T^{2} + 19112576226840477798 T^{4} - \)\(27\!\cdots\!00\)\( T^{6} + \)\(18\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 4264106010 T^{2} + 10045388799818564923 T^{4} - \)\(18\!\cdots\!90\)\( T^{6} + \)\(18\!\cdots\!01\)\( T^{8} )^{2} \))(\( 1 - 6688101005 T^{2} + 33627409971935496255 T^{4} - \)\(11\!\cdots\!90\)\( T^{6} + \)\(32\!\cdots\!85\)\( T^{8} - \)\(73\!\cdots\!11\)\( T^{10} + \)\(14\!\cdots\!65\)\( T^{12} - \)\(20\!\cdots\!90\)\( T^{14} + \)\(26\!\cdots\!95\)\( T^{16} - \)\(22\!\cdots\!05\)\( T^{18} + \)\(14\!\cdots\!49\)\( T^{20} \))(\( 1 - 6688101005 T^{2} + 33627409971935496255 T^{4} - \)\(11\!\cdots\!90\)\( T^{6} + \)\(32\!\cdots\!85\)\( T^{8} - \)\(73\!\cdots\!11\)\( T^{10} + \)\(14\!\cdots\!65\)\( T^{12} - \)\(20\!\cdots\!90\)\( T^{14} + \)\(26\!\cdots\!95\)\( T^{16} - \)\(22\!\cdots\!05\)\( T^{18} + \)\(14\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 10513810235 T^{2} + 49438605550895597222 T^{4} - \)\(13\!\cdots\!55\)\( T^{6} + \)\(21\!\cdots\!78\)\( T^{8} - \)\(19\!\cdots\!35\)\( T^{10} + \)\(79\!\cdots\!49\)\( T^{12} )^{2} \))
$79$ (\( ( 1 - 69152 T + 3077056399 T^{2} )^{2} \))(\( ( 1 + 69152 T + 3077056399 T^{2} )^{2} \))(\( ( 1 + 3077056399 T^{2} )^{2} \))(\( ( 1 - 1729880290 T^{2} + 9468276082626847201 T^{4} )^{2} \))(\( ( 1 + 1275471838 T^{2} + 9468276082626847201 T^{4} )^{2} \))(\( ( 1 - 71840 T + 7430807198 T^{2} - 221055731704160 T^{3} + 9468276082626847201 T^{4} )^{2} \))(\( ( 1 + 71840 T + 7430807198 T^{2} + 221055731704160 T^{3} + 9468276082626847201 T^{4} )^{2} \))(\( ( 1 - 1369983522 T^{2} + 9468276082626847201 T^{4} )^{2} \))(\( ( 1 + 6078817438 T^{2} + 9468276082626847201 T^{4} )^{2} \))(\( ( 1 - 92952 T + 11164448877 T^{2} - 573846024396496 T^{3} + 34353638858281213923 T^{4} - \)\(88\!\cdots\!52\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} )^{2} \))(\( ( 1 + 92952 T + 11164448877 T^{2} + 573846024396496 T^{3} + 34353638858281213923 T^{4} + \)\(88\!\cdots\!52\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} )^{2} \))(\( ( 1 + 10884258108 T^{2} + 48452581383610561862 T^{4} + \)\(10\!\cdots\!08\)\( T^{6} + \)\(89\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 776704228 T^{2} + 16002995794169193542 T^{4} + \)\(73\!\cdots\!28\)\( T^{6} + \)\(89\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 550 T + 7503320051 T^{2} + 274548109457880 T^{3} + 19206677484654564642 T^{4} + \)\(16\!\cdots\!40\)\( T^{5} + \)\(59\!\cdots\!58\)\( T^{6} + \)\(25\!\cdots\!80\)\( T^{7} + \)\(21\!\cdots\!49\)\( T^{8} + \)\(49\!\cdots\!50\)\( T^{9} + \)\(27\!\cdots\!99\)\( T^{10} )^{2} \))(\( ( 1 - 550 T + 7503320051 T^{2} - 274548109457880 T^{3} + 19206677484654564642 T^{4} - \)\(16\!\cdots\!40\)\( T^{5} + \)\(59\!\cdots\!58\)\( T^{6} - \)\(25\!\cdots\!80\)\( T^{7} + \)\(21\!\cdots\!49\)\( T^{8} - \)\(49\!\cdots\!50\)\( T^{9} + \)\(27\!\cdots\!99\)\( T^{10} )^{2} \))(\( ( 1 + 9344137006 T^{2} + 37793088345036567567 T^{4} + \)\(11\!\cdots\!52\)\( T^{6} + \)\(35\!\cdots\!67\)\( T^{8} + \)\(83\!\cdots\!06\)\( T^{10} + \)\(84\!\cdots\!01\)\( T^{12} )^{2} \))
$83$ (\( 1 - 6449241286 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 6449241286 T^{2} + 15516041187205853449 T^{4} \))(\( ( 1 - 3939040643 T^{2} )^{2} \))(\( ( 1 - 6331666438 T^{2} + 15516041187205853449 T^{4} )^{2} \))(\( ( 1 + 3421895214 T^{2} + 15516041187205853449 T^{4} )^{2} \))(\( 1 - 10802590140 T^{2} + 57941034568344378518 T^{4} - \)\(16\!\cdots\!60\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 - 10802590140 T^{2} + 57941034568344378518 T^{4} - \)\(16\!\cdots\!60\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 1693436786 T^{2} + 15516041187205853449 T^{4} )^{2} \))(\( ( 1 + 1875047714 T^{2} + 15516041187205853449 T^{4} )^{2} \))(\( 1 - 7671858246 T^{2} + 26481453986477119527 T^{4} - \)\(57\!\cdots\!28\)\( T^{6} + \)\(41\!\cdots\!23\)\( T^{8} - \)\(18\!\cdots\!46\)\( T^{10} + \)\(37\!\cdots\!49\)\( T^{12} \))(\( 1 - 7671858246 T^{2} + 26481453986477119527 T^{4} - \)\(57\!\cdots\!28\)\( T^{6} + \)\(41\!\cdots\!23\)\( T^{8} - \)\(18\!\cdots\!46\)\( T^{10} + \)\(37\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 7906443964 T^{2} + 42876570344126662806 T^{4} - \)\(12\!\cdots\!36\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 1156437054 T^{2} + 31359576788930042671 T^{4} - \)\(17\!\cdots\!46\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} )^{2} \))(\( 1 - 32607062097 T^{2} + \)\(49\!\cdots\!71\)\( T^{4} - \)\(45\!\cdots\!22\)\( T^{6} + \)\(28\!\cdots\!37\)\( T^{8} - \)\(13\!\cdots\!87\)\( T^{10} + \)\(44\!\cdots\!13\)\( T^{12} - \)\(10\!\cdots\!22\)\( T^{14} + \)\(18\!\cdots\!79\)\( T^{16} - \)\(18\!\cdots\!97\)\( T^{18} + \)\(89\!\cdots\!49\)\( T^{20} \))(\( 1 - 32607062097 T^{2} + \)\(49\!\cdots\!71\)\( T^{4} - \)\(45\!\cdots\!22\)\( T^{6} + \)\(28\!\cdots\!37\)\( T^{8} - \)\(13\!\cdots\!87\)\( T^{10} + \)\(44\!\cdots\!13\)\( T^{12} - \)\(10\!\cdots\!22\)\( T^{14} + \)\(18\!\cdots\!79\)\( T^{16} - \)\(18\!\cdots\!97\)\( T^{18} + \)\(89\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 13262102935 T^{2} + 90316800668278051654 T^{4} - \)\(41\!\cdots\!03\)\( T^{6} + \)\(14\!\cdots\!46\)\( T^{8} - \)\(31\!\cdots\!35\)\( T^{10} + \)\(37\!\cdots\!49\)\( T^{12} )^{2} \))
$89$ (\( ( 1 - 126806 T + 5584059449 T^{2} )^{2} \))(\( ( 1 - 126806 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 51050 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 13930 T + 5584059449 T^{2} )^{4} \))(\( ( 1 - 18310 T + 5584059449 T^{2} )^{4} \))(\( ( 1 - 40748 T + 8570866774 T^{2} - 227539254427852 T^{3} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 - 40748 T + 8570866774 T^{2} - 227539254427852 T^{3} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 - 107590 T + 5584059449 T^{2} )^{4} \))(\( ( 1 + 30570 T + 5584059449 T^{2} )^{4} \))(\( ( 1 + 172686 T + 26445328791 T^{2} + 2103593815517412 T^{3} + \)\(14\!\cdots\!59\)\( T^{4} + \)\(53\!\cdots\!86\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 + 172686 T + 26445328791 T^{2} + 2103593815517412 T^{3} + \)\(14\!\cdots\!59\)\( T^{4} + \)\(53\!\cdots\!86\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 + 104660 T + 13126874198 T^{2} + 584427661932340 T^{3} + 31181719929966183601 T^{4} )^{4} \))(\( ( 1 - 37390 T + 10694141023 T^{2} - 208787982798110 T^{3} + 31181719929966183601 T^{4} )^{4} \))(\( ( 1 - 103829 T + 15106086583 T^{2} - 610465478713486 T^{3} + 75789271213040104957 T^{4} - \)\(20\!\cdots\!39\)\( T^{5} + \)\(42\!\cdots\!93\)\( T^{6} - \)\(19\!\cdots\!86\)\( T^{7} + \)\(26\!\cdots\!67\)\( T^{8} - \)\(10\!\cdots\!29\)\( T^{9} + \)\(54\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 - 103829 T + 15106086583 T^{2} - 610465478713486 T^{3} + 75789271213040104957 T^{4} - \)\(20\!\cdots\!39\)\( T^{5} + \)\(42\!\cdots\!93\)\( T^{6} - \)\(19\!\cdots\!86\)\( T^{7} + \)\(26\!\cdots\!67\)\( T^{8} - \)\(10\!\cdots\!29\)\( T^{9} + \)\(54\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 + 41725 T + 9631028222 T^{2} + 540555874270425 T^{3} + 53780234146644769678 T^{4} + \)\(13\!\cdots\!25\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{4} \))
$97$ (\( 1 - 13294636414 T^{2} + 73742412689492826049 T^{4} \))(\( 1 - 13294636414 T^{2} + 73742412689492826049 T^{4} \))(\( ( 1 - 160808 T + 8587340257 T^{2} )( 1 + 160808 T + 8587340257 T^{2} ) \))(\( ( 1 + 9590933890 T^{2} + 73742412689492826049 T^{4} )^{2} \))(\( ( 1 - 14676880030 T^{2} + 73742412689492826049 T^{4} )^{2} \))(\( 1 - 3154415228 T^{2} - 87162631860647574906 T^{4} - \)\(23\!\cdots\!72\)\( T^{6} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( 1 - 3154415228 T^{2} - 87162631860647574906 T^{4} - \)\(23\!\cdots\!72\)\( T^{6} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 5328970270 T^{2} + 73742412689492826049 T^{4} )^{2} \))(\( ( 1 - 12701478590 T^{2} + 73742412689492826049 T^{4} )^{2} \))(\( 1 - 31357705242 T^{2} + \)\(46\!\cdots\!35\)\( T^{4} - \)\(45\!\cdots\!60\)\( T^{6} + \)\(34\!\cdots\!15\)\( T^{8} - \)\(17\!\cdots\!42\)\( T^{10} + \)\(40\!\cdots\!49\)\( T^{12} \))(\( 1 - 31357705242 T^{2} + \)\(46\!\cdots\!35\)\( T^{4} - \)\(45\!\cdots\!60\)\( T^{6} + \)\(34\!\cdots\!15\)\( T^{8} - \)\(17\!\cdots\!42\)\( T^{10} + \)\(40\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 28671206780 T^{2} + \)\(35\!\cdots\!98\)\( T^{4} - \)\(21\!\cdots\!20\)\( T^{6} + \)\(54\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 19175208540 T^{2} + \)\(23\!\cdots\!98\)\( T^{4} - \)\(14\!\cdots\!60\)\( T^{6} + \)\(54\!\cdots\!01\)\( T^{8} )^{2} \))(\( 1 - 36494827670 T^{2} + \)\(67\!\cdots\!05\)\( T^{4} - \)\(89\!\cdots\!60\)\( T^{6} + \)\(98\!\cdots\!10\)\( T^{8} - \)\(92\!\cdots\!64\)\( T^{10} + \)\(72\!\cdots\!90\)\( T^{12} - \)\(48\!\cdots\!60\)\( T^{14} + \)\(27\!\cdots\!45\)\( T^{16} - \)\(10\!\cdots\!70\)\( T^{18} + \)\(21\!\cdots\!49\)\( T^{20} \))(\( 1 - 36494827670 T^{2} + \)\(67\!\cdots\!05\)\( T^{4} - \)\(89\!\cdots\!60\)\( T^{6} + \)\(98\!\cdots\!10\)\( T^{8} - \)\(92\!\cdots\!64\)\( T^{10} + \)\(72\!\cdots\!90\)\( T^{12} - \)\(48\!\cdots\!60\)\( T^{14} + \)\(27\!\cdots\!45\)\( T^{16} - \)\(10\!\cdots\!70\)\( T^{18} + \)\(21\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 43299754650 T^{2} + \)\(82\!\cdots\!47\)\( T^{4} - \)\(91\!\cdots\!00\)\( T^{6} + \)\(61\!\cdots\!03\)\( T^{8} - \)\(23\!\cdots\!50\)\( T^{10} + \)\(40\!\cdots\!49\)\( T^{12} )^{2} \))
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