Properties

Label 2010.2.e
Level 2010
Weight 2
Character orbit e
Rep. character \(\chi_{2010}(1609,\cdot)\)
Character field \(\Q\)
Dimension 64
Newform subspaces 10
Sturm bound 816
Trace bound 6

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Defining parameters

Level: \( N \) = \( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2010.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(816\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2010, [\chi])\).

Total New Old
Modular forms 416 64 352
Cusp forms 400 64 336
Eisenstein series 16 0 16

Trace form

\( 64q - 64q^{4} + 8q^{5} - 4q^{6} - 64q^{9} + O(q^{10}) \) \( 64q - 64q^{4} + 8q^{5} - 4q^{6} - 64q^{9} + 4q^{10} - 8q^{11} - 8q^{14} + 4q^{15} + 64q^{16} - 8q^{20} - 8q^{21} + 4q^{24} - 4q^{25} + 24q^{26} + 16q^{29} + 8q^{30} - 8q^{31} - 16q^{34} - 16q^{35} + 64q^{36} - 4q^{40} + 24q^{41} + 8q^{44} - 8q^{45} - 8q^{46} - 32q^{49} - 16q^{50} + 4q^{54} - 40q^{55} + 8q^{56} + 40q^{59} - 4q^{60} - 64q^{64} - 56q^{65} + 8q^{70} + 8q^{74} - 16q^{75} + 72q^{79} + 8q^{80} + 64q^{81} + 8q^{84} - 8q^{85} - 24q^{89} - 4q^{90} - 48q^{91} - 8q^{94} - 16q^{95} - 4q^{96} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2010, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2010.2.e.a \(2\) \(16.050\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}+(-2-i)q^{5}+\cdots\)
2010.2.e.b \(2\) \(16.050\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
2010.2.e.c \(2\) \(16.050\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}+(1+2i)q^{5}-q^{6}+\cdots\)
2010.2.e.d \(2\) \(16.050\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+(1-2i)q^{5}+q^{6}+\cdots\)
2010.2.e.e \(2\) \(16.050\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}-q^{6}+\cdots\)
2010.2.e.f \(2\) \(16.050\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+(2+i)q^{5}+q^{6}+\cdots\)
2010.2.e.g \(8\) \(16.050\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{4}q^{2}+\beta _{4}q^{3}-q^{4}+(\beta _{1}-\beta _{5})q^{5}+\cdots\)
2010.2.e.h \(10\) \(16.050\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
2010.2.e.i \(16\) \(16.050\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{10}q^{2}-\beta _{10}q^{3}-q^{4}+\beta _{2}q^{5}+\cdots\)
2010.2.e.j \(18\) \(16.050\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{7}q^{2}+\beta _{7}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2010, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2010, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(670, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{5} \))(\( ( 1 + T^{2} )^{8} \))(\( ( 1 + T^{2} )^{9} \))
$3$ (\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{5} \))(\( ( 1 + T^{2} )^{8} \))(\( ( 1 + T^{2} )^{9} \))
$5$ (\( 1 + 4 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 2 T + 4 T^{2} - 10 T^{3} - 18 T^{4} - 50 T^{5} + 100 T^{6} + 250 T^{7} + 625 T^{8} \))(\( 1 + 2 T + T^{2} - 22 T^{4} - 68 T^{5} - 110 T^{6} + 125 T^{8} + 1250 T^{9} + 3125 T^{10} \))(\( 1 - 2 T + T^{2} + 20 T^{3} - 14 T^{4} - 8 T^{5} + 143 T^{6} + 174 T^{7} - 278 T^{8} + 870 T^{9} + 3575 T^{10} - 1000 T^{11} - 8750 T^{12} + 62500 T^{13} + 15625 T^{14} - 156250 T^{15} + 390625 T^{16} \))(\( 1 - 4 T + 10 T^{2} - 16 T^{3} - T^{4} + 104 T^{5} - 279 T^{6} + 160 T^{7} + 857 T^{8} - 2344 T^{9} + 4285 T^{10} + 4000 T^{11} - 34875 T^{12} + 65000 T^{13} - 3125 T^{14} - 250000 T^{15} + 781250 T^{16} - 1562500 T^{17} + 1953125 T^{18} \))
$7$ (\( 1 + 2 T^{2} + 49 T^{4} \))(\( 1 - 5 T^{2} + 49 T^{4} \))(\( 1 - 13 T^{2} + 49 T^{4} \))(\( 1 - 5 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 24 T^{2} + 324 T^{4} - 3260 T^{6} + 25650 T^{8} - 159740 T^{10} + 777924 T^{12} - 2823576 T^{14} + 5764801 T^{16} \))(\( 1 - 42 T^{2} + 909 T^{4} - 13068 T^{6} + 137366 T^{8} - 1096940 T^{10} + 6730934 T^{12} - 31376268 T^{14} + 106942941 T^{16} - 242121642 T^{18} + 282475249 T^{20} \))(\( 1 - 50 T^{2} + 1285 T^{4} - 22642 T^{6} + 308562 T^{8} - 3474922 T^{10} + 33583223 T^{12} - 283895650 T^{14} + 2115024066 T^{16} - 13910886850 T^{18} + 80633318423 T^{20} - 408821098378 T^{22} + 1778798526162 T^{24} - 6395804587858 T^{26} + 17786054053285 T^{28} - 33911153642450 T^{30} + 33232930569601 T^{32} \))(\( 1 - 43 T^{2} + 916 T^{4} - 13001 T^{6} + 142361 T^{8} - 1324078 T^{10} + 11013787 T^{12} - 83450323 T^{14} + 590600407 T^{16} - 4106747830 T^{18} + 28939419943 T^{20} - 200364225523 T^{22} + 1295761026763 T^{24} - 7633046178478 T^{26} + 40213458922889 T^{28} - 179950574900201 T^{30} + 621252334729684 T^{32} - 1429016014492843 T^{34} + 1628413597910449 T^{36} \))
$11$ (\( ( 1 - 6 T + 11 T^{2} )^{2} \))(\( ( 1 - T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 + 10 T + 48 T^{2} + 138 T^{3} + 378 T^{4} + 1518 T^{5} + 5808 T^{6} + 13310 T^{7} + 14641 T^{8} )^{2} \))(\( ( 1 + 2 T + 43 T^{2} + 72 T^{3} + 842 T^{4} + 1132 T^{5} + 9262 T^{6} + 8712 T^{7} + 57233 T^{8} + 29282 T^{9} + 161051 T^{10} )^{2} \))(\( ( 1 + 10 T + 70 T^{2} + 358 T^{3} + 1564 T^{4} + 5870 T^{5} + 20274 T^{6} + 66034 T^{7} + 215190 T^{8} + 726374 T^{9} + 2453154 T^{10} + 7812970 T^{11} + 22898524 T^{12} + 57656258 T^{13} + 124009270 T^{14} + 194871710 T^{15} + 214358881 T^{16} )^{2} \))(\( ( 1 - 7 T + 75 T^{2} - 366 T^{3} + 2372 T^{4} - 9316 T^{5} + 47556 T^{6} - 161658 T^{7} + 700238 T^{8} - 2071002 T^{9} + 7702618 T^{10} - 19560618 T^{11} + 63297036 T^{12} - 136395556 T^{13} + 382012972 T^{14} - 648391326 T^{15} + 1461537825 T^{16} - 1500512167 T^{17} + 2357947691 T^{18} )^{2} \))
$13$ (\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 - 56 T^{2} + 1352 T^{4} - 20052 T^{6} + 253354 T^{8} - 3388788 T^{10} + 38614472 T^{12} - 270301304 T^{14} + 815730721 T^{16} \))(\( 1 - 26 T^{2} - 7 T^{4} + 4772 T^{6} + 24146 T^{8} - 1466604 T^{10} + 4080674 T^{12} + 136293092 T^{14} - 33787663 T^{16} - 21208998746 T^{18} + 137858491849 T^{20} \))(\( 1 - 100 T^{2} + 5380 T^{4} - 199960 T^{6} + 5690896 T^{8} - 130832864 T^{10} + 2508397644 T^{12} - 40884638788 T^{14} + 572475059582 T^{16} - 6909503955172 T^{18} + 71642345110284 T^{20} - 631505245450976 T^{22} + 4642238697216016 T^{24} - 27566184030126040 T^{26} + 125343697958947780 T^{28} - 393737638569928900 T^{30} + 665416609183179841 T^{32} \))(\( 1 - 146 T^{2} + 10797 T^{4} - 532916 T^{6} + 19581388 T^{8} - 567125352 T^{10} + 13392331476 T^{12} - 263335393964 T^{14} + 4367630768346 T^{16} - 61535894392140 T^{18} + 738129599850474 T^{20} - 7521122187005804 T^{22} + 64642226099340084 T^{24} - 462621572284338792 T^{26} + 2699460617990106412 T^{28} - 12415922331132084596 T^{30} + 42511852836395223333 T^{32} - 97150824940744256786 T^{34} + \)\(11\!\cdots\!29\)\( T^{36} \))
$17$ (\( ( 1 - 2 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} ) \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( 1 - 80 T^{2} + 3380 T^{4} - 94752 T^{6} + 1888262 T^{8} - 27383328 T^{10} + 282300980 T^{12} - 1931005520 T^{14} + 6975757441 T^{16} \))(\( 1 - 86 T^{2} + 4197 T^{4} - 139176 T^{6} + 3467594 T^{8} - 66566116 T^{10} + 1002134666 T^{12} - 11624118696 T^{14} + 101305377093 T^{16} - 599915139926 T^{18} + 2015993900449 T^{20} \))(\( 1 - 148 T^{2} + 11100 T^{4} - 555612 T^{6} + 20769268 T^{8} - 617254004 T^{10} + 15196067364 T^{12} - 318819072668 T^{14} + 5801845963286 T^{16} - 92138712001052 T^{18} + 1269190742308644 T^{20} - 14899011112076276 T^{22} + 144881375795123188 T^{24} - 1120110403016269788 T^{26} + 6467106833250347100 T^{28} - 24919918330791337492 T^{30} + 48661191875666868481 T^{32} \))(\( 1 - 198 T^{2} + 19125 T^{4} - 1204680 T^{6} + 55784824 T^{8} - 2027706680 T^{10} + 60240841040 T^{12} - 1501363640376 T^{14} + 31912056070946 T^{16} - 583863129580036 T^{18} + 9222584204503394 T^{20} - 125395392607843896 T^{22} + 1454067457221031760 T^{24} - 14144789961175405880 T^{26} + \)\(11\!\cdots\!76\)\( T^{28} - \)\(70\!\cdots\!80\)\( T^{30} + \)\(32\!\cdots\!25\)\( T^{32} - \)\(96\!\cdots\!38\)\( T^{34} + \)\(14\!\cdots\!09\)\( T^{36} \))
$19$ (\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 10 T + 92 T^{2} - 522 T^{3} + 2714 T^{4} - 9918 T^{5} + 33212 T^{6} - 68590 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 - 6 T + 63 T^{2} - 248 T^{3} + 1486 T^{4} - 4964 T^{5} + 28234 T^{6} - 89528 T^{7} + 432117 T^{8} - 781926 T^{9} + 2476099 T^{10} )^{2} \))(\( ( 1 + 2 T + 56 T^{2} + 154 T^{3} + 2032 T^{4} + 6762 T^{5} + 55192 T^{6} + 185698 T^{7} + 1135774 T^{8} + 3528262 T^{9} + 19924312 T^{10} + 46380558 T^{11} + 264812272 T^{12} + 381319246 T^{13} + 2634569336 T^{14} + 1787743478 T^{15} + 16983563041 T^{16} )^{2} \))(\( ( 1 + 2 T + 99 T^{2} + 80 T^{3} + 4768 T^{4} + 104 T^{5} + 153616 T^{6} - 65296 T^{7} + 3716254 T^{8} - 1955860 T^{9} + 70608826 T^{10} - 23571856 T^{11} + 1053652144 T^{12} + 13553384 T^{13} + 11806040032 T^{14} + 3763670480 T^{15} + 88493302161 T^{16} + 33967126082 T^{17} + 322687697779 T^{18} )^{2} \))
$23$ (\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 42 T^{2} + 529 T^{4} \))(\( 1 - 42 T^{2} + 529 T^{4} \))(\( 1 - 10 T^{2} + 529 T^{4} \))(\( 1 - 56 T^{2} + 2988 T^{4} - 93420 T^{6} + 2608162 T^{8} - 49419180 T^{10} + 836164908 T^{12} - 8290009784 T^{14} + 78310985281 T^{16} \))(\( 1 - 166 T^{2} + 13285 T^{4} - 678364 T^{6} + 24480334 T^{8} - 651628900 T^{10} + 12950096686 T^{12} - 189834060124 T^{14} + 1966656785365 T^{16} - 12999623556646 T^{18} + 41426511213649 T^{20} \))(\( 1 - 206 T^{2} + 20837 T^{4} - 1377710 T^{6} + 66974970 T^{8} - 2562676334 T^{10} + 81118626103 T^{12} - 2213389701926 T^{14} + 53679647812530 T^{16} - 1170883152318854 T^{18} + 22700317447289623 T^{20} - 379368069322950926 T^{22} + 5244875889865416570 T^{24} - 57073718764156363790 T^{26} + \)\(45\!\cdots\!77\)\( T^{28} - \)\(23\!\cdots\!54\)\( T^{30} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 - 244 T^{2} + 29602 T^{4} - 2373914 T^{6} + 141223987 T^{8} - 6637597656 T^{10} + 256572656629 T^{12} - 8386327178446 T^{14} + 236304385214117 T^{16} - 5807811590866584 T^{18} + 125005019778267893 T^{20} - 2346838183943507086 T^{22} + 37981961317165758181 T^{24} - \)\(51\!\cdots\!36\)\( T^{26} + \)\(58\!\cdots\!63\)\( T^{28} - \)\(52\!\cdots\!94\)\( T^{30} + \)\(34\!\cdots\!18\)\( T^{32} - \)\(14\!\cdots\!84\)\( T^{34} + \)\(32\!\cdots\!69\)\( T^{36} \))
$29$ (\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 8 T + 29 T^{2} )^{2} \))(\( ( 1 - 8 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 26 T + 358 T^{2} - 3216 T^{3} + 20432 T^{4} - 93264 T^{5} + 301078 T^{6} - 634114 T^{7} + 707281 T^{8} )^{2} \))(\( ( 1 - 2 T + 87 T^{2} - 274 T^{3} + 3942 T^{4} - 11620 T^{5} + 114318 T^{6} - 230434 T^{7} + 2121843 T^{8} - 1414562 T^{9} + 20511149 T^{10} )^{2} \))(\( ( 1 + 12 T + 118 T^{2} + 422 T^{3} + 1246 T^{4} - 7114 T^{5} + 24338 T^{6} + 291472 T^{7} + 3992050 T^{8} + 8452688 T^{9} + 20468258 T^{10} - 173503346 T^{11} + 881272126 T^{12} + 8655704878 T^{13} + 70189151878 T^{14} + 206998515708 T^{15} + 500246412961 T^{16} )^{2} \))(\( ( 1 + 14 T + 255 T^{2} + 2558 T^{3} + 27944 T^{4} + 221300 T^{5} + 1802684 T^{6} + 11692498 T^{7} + 76394528 T^{8} + 411103100 T^{9} + 2215441312 T^{10} + 9833390818 T^{11} + 43965660076 T^{12} + 156521285300 T^{13} + 573163547656 T^{14} + 1521558055118 T^{15} + 4398718458795 T^{16} + 7003449781454 T^{17} + 14507145975869 T^{18} )^{2} \))
$31$ (\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 10 T + 31 T^{2} )^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( ( 1 + 2 T + 80 T^{2} + 132 T^{3} + 3088 T^{4} + 4092 T^{5} + 76880 T^{6} + 59582 T^{7} + 923521 T^{8} )^{2} \))(\( ( 1 + 6 T + 87 T^{2} + 582 T^{3} + 4964 T^{4} + 22204 T^{5} + 153884 T^{6} + 559302 T^{7} + 2591817 T^{8} + 5541126 T^{9} + 28629151 T^{10} )^{2} \))(\( ( 1 + 4 T + 55 T^{2} + 130 T^{3} + 2118 T^{4} + 7148 T^{5} + 91239 T^{6} + 129178 T^{7} + 2361586 T^{8} + 4004518 T^{9} + 87680679 T^{10} + 212946068 T^{11} + 1956017478 T^{12} + 3721789630 T^{13} + 48812702455 T^{14} + 110050456444 T^{15} + 852891037441 T^{16} )^{2} \))(\( ( 1 - 4 T + 222 T^{2} - 742 T^{3} + 23091 T^{4} - 65822 T^{5} + 1484585 T^{6} - 3624682 T^{7} + 65072679 T^{8} - 135045636 T^{9} + 2017253049 T^{10} - 3483319402 T^{11} + 44227271735 T^{12} - 60787999262 T^{13} + 661075725741 T^{14} - 658527731302 T^{15} + 6107800332642 T^{16} - 3411564149764 T^{17} + 26439622160671 T^{18} )^{2} \))
$37$ (\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 65 T^{2} + 1369 T^{4} \))(\( 1 - 49 T^{2} + 1369 T^{4} \))(\( 1 - 65 T^{2} + 1369 T^{4} \))(\( ( 1 - 2 T + 37 T^{2} )( 1 + 2 T + 37 T^{2} ) \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 + 24 T^{2} + 1436 T^{4} + 6120 T^{6} + 2395686 T^{8} + 8378280 T^{10} + 2691295196 T^{12} + 61577433816 T^{14} + 3512479453921 T^{16} \))(\( 1 - 66 T^{2} + 4229 T^{4} - 223896 T^{6} + 9527250 T^{8} - 363046412 T^{10} + 13042805250 T^{12} - 419617151256 T^{14} + 10850456983661 T^{16} - 231823643958786 T^{18} + 4808584372417849 T^{20} \))(\( 1 - 382 T^{2} + 71553 T^{4} - 8802498 T^{6} + 800438874 T^{8} - 57183111894 T^{10} + 3321446813647 T^{12} - 159976647909898 T^{14} + 6455972500236874 T^{16} - 219008030988650362 T^{18} + 6224926081711475167 T^{20} - \)\(14\!\cdots\!46\)\( T^{22} + \)\(28\!\cdots\!54\)\( T^{24} - \)\(42\!\cdots\!02\)\( T^{26} + \)\(47\!\cdots\!93\)\( T^{28} - \)\(34\!\cdots\!98\)\( T^{30} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 - 423 T^{2} + 87840 T^{4} - 11984985 T^{6} + 1210272069 T^{8} - 96373040866 T^{10} + 6284271909455 T^{12} - 343593187879095 T^{14} + 15983792361468819 T^{16} - 637755468715846638 T^{18} + 21881811742850813211 T^{20} - \)\(64\!\cdots\!95\)\( T^{22} + \)\(16\!\cdots\!95\)\( T^{24} - \)\(33\!\cdots\!86\)\( T^{26} + \)\(58\!\cdots\!81\)\( T^{28} - \)\(78\!\cdots\!85\)\( T^{30} + \)\(79\!\cdots\!60\)\( T^{32} - \)\(52\!\cdots\!43\)\( T^{34} + \)\(16\!\cdots\!29\)\( T^{36} \))
$41$ (\( ( 1 - 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 12 T + 136 T^{2} + 992 T^{3} + 7810 T^{4} + 40672 T^{5} + 228616 T^{6} + 827052 T^{7} + 2825761 T^{8} )^{2} \))(\( ( 1 + 81 T^{2} + 148 T^{3} + 5370 T^{4} + 2952 T^{5} + 220170 T^{6} + 248788 T^{7} + 5582601 T^{8} + 115856201 T^{10} )^{2} \))(\( ( 1 - 4 T + 183 T^{2} - 776 T^{3} + 15976 T^{4} - 74748 T^{5} + 915173 T^{6} - 4530320 T^{7} + 40905422 T^{8} - 185743120 T^{9} + 1538405813 T^{10} - 5151706908 T^{11} + 45144357736 T^{12} - 89904411976 T^{13} + 869269076103 T^{14} - 779017095524 T^{15} + 7984925229121 T^{16} )^{2} \))(\( ( 1 - 24 T + 460 T^{2} - 6264 T^{3} + 73967 T^{4} - 732396 T^{5} + 6562701 T^{6} - 52021696 T^{7} + 381638183 T^{8} - 2530664360 T^{9} + 15647165503 T^{10} - 87448470976 T^{11} + 452307915621 T^{12} - 2069576053356 T^{13} + 8569535619367 T^{14} - 29754652965624 T^{15} + 89586965985260 T^{16} - 191638205498904 T^{17} + 327381934393961 T^{18} )^{2} \))
$43$ (\( 1 + 58 T^{2} + 1849 T^{4} \))(\( 1 - 50 T^{2} + 1849 T^{4} \))(\( 1 - 50 T^{2} + 1849 T^{4} \))(\( 1 - 82 T^{2} + 1849 T^{4} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 + 58 T^{2} + 1849 T^{4} \))(\( ( 1 - 82 T^{2} + 1849 T^{4} )^{4} \))(\( 1 - 174 T^{2} + 17637 T^{4} - 1260456 T^{6} + 70461266 T^{8} - 3298258580 T^{10} + 130282880834 T^{12} - 4309248233256 T^{14} + 111489880095213 T^{16} - 2033746848302574 T^{18} + 21611482313284249 T^{20} \))(\( 1 - 454 T^{2} + 99957 T^{4} - 14263694 T^{6} + 1487061606 T^{8} - 120964552130 T^{10} + 7996140132747 T^{12} - 440729527009386 T^{14} + 20553607939812434 T^{16} - 814908895440354714 T^{18} + 27337211881975576347 T^{20} - \)\(76\!\cdots\!70\)\( T^{22} + \)\(17\!\cdots\!06\)\( T^{24} - \)\(30\!\cdots\!06\)\( T^{26} + \)\(39\!\cdots\!57\)\( T^{28} - \)\(33\!\cdots\!46\)\( T^{30} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 216 T^{2} + 30362 T^{4} - 3113950 T^{6} + 262668143 T^{8} - 18761020300 T^{10} + 1176271752165 T^{12} - 65395435220834 T^{14} + 3273035905356217 T^{16} - 147772351824503544 T^{18} + 6051843389003645233 T^{20} - \)\(22\!\cdots\!34\)\( T^{22} + \)\(74\!\cdots\!85\)\( T^{24} - \)\(21\!\cdots\!00\)\( T^{26} + \)\(56\!\cdots\!07\)\( T^{28} - \)\(12\!\cdots\!50\)\( T^{30} + \)\(22\!\cdots\!38\)\( T^{32} - \)\(29\!\cdots\!16\)\( T^{34} + \)\(25\!\cdots\!49\)\( T^{36} \))
$47$ (\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 78 T^{2} + 2209 T^{4} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 356 T^{2} + 56268 T^{4} - 5161872 T^{6} + 300786562 T^{8} - 11402575248 T^{10} + 274569890508 T^{12} - 3837400657124 T^{14} + 23811286661761 T^{16} \))(\( 1 - 258 T^{2} + 36605 T^{4} - 3492636 T^{6} + 245576806 T^{8} - 13145000364 T^{10} + 542479164454 T^{12} - 17042949529116 T^{14} + 394573177118045 T^{16} - 6143311958734338 T^{18} + 52599132235830049 T^{20} \))(\( 1 - 416 T^{2} + 90168 T^{4} - 13269572 T^{6} + 1471818456 T^{8} - 129856701140 T^{10} + 9401934509720 T^{12} - 568967544587464 T^{14} + 29062119402188206 T^{16} - 1256849305993707976 T^{18} + 45878441190324999320 T^{20} - \)\(13\!\cdots\!60\)\( T^{22} + \)\(35\!\cdots\!16\)\( T^{24} - \)\(69\!\cdots\!28\)\( T^{26} + \)\(10\!\cdots\!88\)\( T^{28} - \)\(10\!\cdots\!04\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 - 458 T^{2} + 107297 T^{4} - 17037236 T^{6} + 2049508032 T^{8} - 197926594296 T^{10} + 15874172589808 T^{12} - 1079560747994540 T^{14} + 63045159469043918 T^{16} - 3183254712981007292 T^{18} + \)\(13\!\cdots\!62\)\( T^{20} - \)\(52\!\cdots\!40\)\( T^{22} + \)\(17\!\cdots\!32\)\( T^{24} - \)\(47\!\cdots\!56\)\( T^{26} + \)\(10\!\cdots\!68\)\( T^{28} - \)\(19\!\cdots\!76\)\( T^{30} + \)\(27\!\cdots\!93\)\( T^{32} - \)\(25\!\cdots\!18\)\( T^{34} + \)\(12\!\cdots\!89\)\( T^{36} \))
$53$ (\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( 1 - 6 T^{2} + 2809 T^{4} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 360 T^{2} + 59420 T^{4} - 5872536 T^{6} + 380080038 T^{8} - 16495953624 T^{10} + 468852381020 T^{12} - 7979170006440 T^{14} + 62259690411361 T^{16} \))(\( 1 - 398 T^{2} + 75269 T^{4} - 8987368 T^{6} + 753291762 T^{8} - 46325081684 T^{10} + 2115996559458 T^{12} - 70914656444008 T^{14} + 1668289297818701 T^{16} - 24779356783721678 T^{18} + 174887470365513049 T^{20} \))(\( 1 - 166 T^{2} + 17221 T^{4} - 1350190 T^{6} + 102882406 T^{8} - 7409291810 T^{10} + 485050814139 T^{12} - 27754283842186 T^{14} + 1495940955431762 T^{16} - 77961783312700474 T^{18} + 3827284232998310859 T^{20} - \)\(16\!\cdots\!90\)\( T^{22} + \)\(64\!\cdots\!66\)\( T^{24} - \)\(23\!\cdots\!10\)\( T^{26} + \)\(84\!\cdots\!61\)\( T^{28} - \)\(22\!\cdots\!54\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 - 588 T^{2} + 172066 T^{4} - 33304994 T^{6} + 4783963415 T^{8} - 542449786756 T^{10} + 50410958206013 T^{12} - 3932472651430814 T^{14} + 261382350928734577 T^{16} - 14926116533200172192 T^{18} + \)\(73\!\cdots\!93\)\( T^{20} - \)\(31\!\cdots\!34\)\( T^{22} + \)\(11\!\cdots\!77\)\( T^{24} - \)\(33\!\cdots\!16\)\( T^{26} + \)\(83\!\cdots\!35\)\( T^{28} - \)\(16\!\cdots\!54\)\( T^{30} + \)\(23\!\cdots\!54\)\( T^{32} - \)\(22\!\cdots\!48\)\( T^{34} + \)\(10\!\cdots\!89\)\( T^{36} \))
$59$ (\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 28 T + 448 T^{2} - 5080 T^{3} + 44562 T^{4} - 299720 T^{5} + 1559488 T^{6} - 5750612 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 + 167 T^{2} + 116 T^{3} + 15774 T^{4} + 4680 T^{5} + 930666 T^{6} + 403796 T^{7} + 34298293 T^{8} + 714924299 T^{10} )^{2} \))(\( ( 1 - 22 T + 397 T^{2} - 4630 T^{3} + 49394 T^{4} - 424570 T^{5} + 3748687 T^{6} - 29070666 T^{7} + 239362098 T^{8} - 1715169294 T^{9} + 13049179447 T^{10} - 87197762030 T^{11} + 598524929234 T^{12} - 3310099504370 T^{13} + 16745671855477 T^{14} - 54750332666018 T^{15} + 146830437604321 T^{16} )^{2} \))(\( ( 1 + 10 T + 220 T^{2} + 1524 T^{3} + 18553 T^{4} + 78636 T^{5} + 736245 T^{6} - 1138612 T^{7} + 3454723 T^{8} - 305704492 T^{9} + 203828657 T^{10} - 3963508372 T^{11} + 151209261855 T^{12} + 952860799596 T^{13} + 13263990519347 T^{14} + 64283133268884 T^{15} + 547503326660180 T^{16} + 1468304376043210 T^{17} + 8662995818654939 T^{18} )^{2} \))
$61$ (\( ( 1 + 4 T + 61 T^{2} )^{2} \))(\( ( 1 + 7 T + 61 T^{2} )^{2} \))(\( ( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 - 11 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 8 T + 61 T^{2} )^{2} \))(\( ( 1 + 12 T + 230 T^{2} + 1806 T^{3} + 19884 T^{4} + 110166 T^{5} + 855830 T^{6} + 2723772 T^{7} + 13845841 T^{8} )^{2} \))(\( ( 1 + 20 T + 263 T^{2} + 2858 T^{3} + 28594 T^{4} + 252280 T^{5} + 1744234 T^{6} + 10634618 T^{7} + 59696003 T^{8} + 276916820 T^{9} + 844596301 T^{10} )^{2} \))(\( ( 1 - 18 T + 396 T^{2} - 5496 T^{3} + 74634 T^{4} - 814632 T^{5} + 8482112 T^{6} - 74654966 T^{7} + 632551762 T^{8} - 4553952926 T^{9} + 31561938752 T^{10} - 184905985992 T^{11} + 1033370497194 T^{12} - 4641901270296 T^{13} + 20402068246956 T^{14} - 56569371048378 T^{15} + 191707312997281 T^{16} )^{2} \))(\( ( 1 - 5 T + 237 T^{2} - 1122 T^{3} + 33652 T^{4} - 146514 T^{5} + 3449596 T^{6} - 13705298 T^{7} + 267029022 T^{8} - 947042378 T^{9} + 16288770342 T^{10} - 50997413858 T^{11} + 782992749676 T^{12} - 2028609548274 T^{13} + 28422354721252 T^{14} - 57805860033042 T^{15} + 744830052136977 T^{16} - 958536564986405 T^{17} + 11694146092834141 T^{18} )^{2} \))
$67$ (\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{5} \))(\( ( 1 + T^{2} )^{8} \))(\( ( 1 + T^{2} )^{9} \))
$71$ (\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 9 T + 71 T^{2} )^{2} \))(\( ( 1 + 13 T + 71 T^{2} )^{2} \))(\( ( 1 + T + 71 T^{2} )^{2} \))(\( ( 1 - 16 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 120 T^{2} - 198 T^{3} + 6988 T^{4} - 14058 T^{5} + 604920 T^{6} + 25411681 T^{8} )^{2} \))(\( ( 1 + 6 T + 299 T^{2} + 1558 T^{3} + 39616 T^{4} + 159528 T^{5} + 2812736 T^{6} + 7853878 T^{7} + 107015389 T^{8} + 152470086 T^{9} + 1804229351 T^{10} )^{2} \))(\( ( 1 - 10 T + 564 T^{2} - 4644 T^{3} + 138554 T^{4} - 944560 T^{5} + 19498492 T^{6} - 109208390 T^{7} + 1724790954 T^{8} - 7753795690 T^{9} + 98291898172 T^{10} - 338068414160 T^{11} + 3520890049274 T^{12} - 8378841106044 T^{13} + 72248560131444 T^{14} - 90951201583910 T^{15} + 645753531245761 T^{16} )^{2} \))(\( ( 1 + 5 T + 375 T^{2} + 2274 T^{3} + 69092 T^{4} + 499150 T^{5} + 8362724 T^{6} + 66240494 T^{7} + 752399470 T^{8} + 5750647930 T^{9} + 53420362370 T^{10} + 333918330254 T^{11} + 2993110909564 T^{12} + 12684240571150 T^{13} + 124657814319292 T^{14} + 291300045636354 T^{15} + 3410670059396625 T^{16} + 3228767656228805 T^{17} + 45848500718449031 T^{18} )^{2} \))
$73$ (\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 82 T^{2} + 5329 T^{4} \))(\( 1 - 82 T^{2} + 5329 T^{4} \))(\( ( 1 - 6 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))(\( 1 - 130 T^{2} + 5329 T^{4} \))(\( 1 - 312 T^{2} + 53724 T^{4} - 6304520 T^{6} + 534065670 T^{8} - 33596787080 T^{10} + 1525667099484 T^{12} - 47216278602168 T^{14} + 806460091894081 T^{16} \))(\( 1 - 586 T^{2} + 161949 T^{4} - 27828024 T^{6} + 3296522546 T^{8} - 281566182780 T^{10} + 17567168647634 T^{12} - 790266932105784 T^{14} + 24508426613277261 T^{16} - 472585613849931466 T^{18} + 4297625829703557649 T^{20} \))(\( 1 - 650 T^{2} + 190573 T^{4} - 33436154 T^{6} + 3976261926 T^{8} - 355043063542 T^{10} + 27088167799779 T^{12} - 2002272797253126 T^{14} + 147723366933244114 T^{16} - 10670111736561908454 T^{18} + \)\(76\!\cdots\!39\)\( T^{20} - \)\(53\!\cdots\!38\)\( T^{22} + \)\(32\!\cdots\!06\)\( T^{24} - \)\(14\!\cdots\!46\)\( T^{26} + \)\(43\!\cdots\!33\)\( T^{28} - \)\(79\!\cdots\!50\)\( T^{30} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 - 236 T^{2} + 63186 T^{4} - 10232478 T^{6} + 1581014295 T^{8} - 192946442524 T^{10} + 21545177357781 T^{12} - 2069042672470402 T^{14} + 179629967367125425 T^{16} - 13809576787114260784 T^{18} + \)\(95\!\cdots\!25\)\( T^{20} - \)\(58\!\cdots\!82\)\( T^{22} + \)\(32\!\cdots\!09\)\( T^{24} - \)\(15\!\cdots\!44\)\( T^{26} + \)\(67\!\cdots\!55\)\( T^{28} - \)\(23\!\cdots\!38\)\( T^{30} + \)\(77\!\cdots\!74\)\( T^{32} - \)\(15\!\cdots\!96\)\( T^{34} + \)\(34\!\cdots\!69\)\( T^{36} \))
$79$ (\( ( 1 - 12 T + 79 T^{2} )^{2} \))(\( ( 1 - 2 T + 79 T^{2} )^{2} \))(\( ( 1 - 6 T + 79 T^{2} )^{2} \))(\( ( 1 - 14 T + 79 T^{2} )^{2} \))(\( ( 1 - 14 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 14 T + 236 T^{2} + 2604 T^{3} + 27920 T^{4} + 205716 T^{5} + 1472876 T^{6} + 6902546 T^{7} + 38950081 T^{8} )^{2} \))(\( ( 1 + 6 T + 155 T^{2} + 210 T^{3} + 8856 T^{4} - 40108 T^{5} + 699624 T^{6} + 1310610 T^{7} + 76421045 T^{8} + 233700486 T^{9} + 3077056399 T^{10} )^{2} \))(\( ( 1 - 4 T + 450 T^{2} - 2438 T^{3} + 94514 T^{4} - 603190 T^{5} + 12411194 T^{6} - 80766068 T^{7} + 1147323538 T^{8} - 6380519372 T^{9} + 77458261754 T^{10} - 297396194410 T^{11} + 3681327955634 T^{12} - 7501863500762 T^{13} + 109389354984450 T^{14} - 76815635944636 T^{15} + 1517108809906561 T^{16} )^{2} \))(\( ( 1 - 8 T + 353 T^{2} - 3142 T^{3} + 68260 T^{4} - 599324 T^{5} + 8984260 T^{6} - 76209218 T^{7} + 895892560 T^{8} - 6982074056 T^{9} + 70775512240 T^{10} - 475621729538 T^{11} + 4429590566140 T^{12} - 23343718345244 T^{13} + 210039869795740 T^{14} - 763780785246982 T^{15} + 6778979872114127 T^{16} - 12136870479252488 T^{17} + 119851595982618319 T^{18} )^{2} \))
$83$ (\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 157 T^{2} + 6889 T^{4} \))(\( 1 - 85 T^{2} + 6889 T^{4} \))(\( 1 - 157 T^{2} + 6889 T^{4} \))(\( 1 - 130 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 472 T^{2} + 106364 T^{4} - 15114024 T^{6} + 1488397478 T^{8} - 104120511336 T^{10} + 5047856854844 T^{12} - 154315856230168 T^{14} + 2252292232139041 T^{16} \))(\( 1 - 314 T^{2} + 62485 T^{4} - 8745016 T^{6} + 998552786 T^{8} - 90915632220 T^{10} + 6879030142754 T^{12} - 415023776478136 T^{14} + 20428869229961965 T^{16} - 707219760891658874 T^{18} + 15516041187205853449 T^{20} \))(\( 1 - 718 T^{2} + 262721 T^{4} - 64979026 T^{6} + 12152583098 T^{8} - 1822430832422 T^{10} + 226619630442863 T^{12} - 23818376848314010 T^{14} + 2136672210169558410 T^{16} - \)\(16\!\cdots\!90\)\( T^{18} + \)\(10\!\cdots\!23\)\( T^{20} - \)\(59\!\cdots\!18\)\( T^{22} + \)\(27\!\cdots\!18\)\( T^{24} - \)\(10\!\cdots\!74\)\( T^{26} + \)\(28\!\cdots\!81\)\( T^{28} - \)\(52\!\cdots\!22\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 811 T^{2} + 324856 T^{4} - 86091469 T^{6} + 17077086701 T^{8} - 2718386816970 T^{10} + 362690256013431 T^{12} - 41660865131508835 T^{14} + 4182491101843352475 T^{16} - \)\(36\!\cdots\!90\)\( T^{18} + \)\(28\!\cdots\!75\)\( T^{20} - \)\(19\!\cdots\!35\)\( T^{22} + \)\(11\!\cdots\!39\)\( T^{24} - \)\(61\!\cdots\!70\)\( T^{26} + \)\(26\!\cdots\!49\)\( T^{28} - \)\(92\!\cdots\!09\)\( T^{30} + \)\(23\!\cdots\!24\)\( T^{32} - \)\(41\!\cdots\!91\)\( T^{34} + \)\(34\!\cdots\!09\)\( T^{36} \))
$89$ (\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 - T + 89 T^{2} )^{2} \))(\( ( 1 - T + 89 T^{2} )^{2} \))(\( ( 1 - 5 T + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 4 T + 52 T^{2} + 748 T^{3} + 9414 T^{4} + 66572 T^{5} + 411892 T^{6} + 2819876 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 2 T + 341 T^{2} + 72 T^{3} + 50226 T^{4} - 19508 T^{5} + 4470114 T^{6} + 570312 T^{7} + 240394429 T^{8} + 125484482 T^{9} + 5584059449 T^{10} )^{2} \))(\( ( 1 - 20 T + 628 T^{2} - 8012 T^{3} + 143748 T^{4} - 1287428 T^{5} + 17822284 T^{6} - 125397084 T^{7} + 1655130806 T^{8} - 11160340476 T^{9} + 141170311564 T^{10} - 907596829732 T^{11} + 9019071659268 T^{12} - 44739484305388 T^{13} + 312104250723508 T^{14} - 884626697910580 T^{15} + 3936588805702081 T^{16} )^{2} \))(\( ( 1 + 39 T + 1089 T^{2} + 22348 T^{3} + 390020 T^{4} + 5783260 T^{5} + 76803028 T^{6} + 908632308 T^{7} + 9842500638 T^{8} + 96689288250 T^{9} + 875982556782 T^{10} + 7197276511668 T^{11} + 54143753846132 T^{12} + 362854692685660 T^{13} + 2177894866298980 T^{14} + 11106537890396428 T^{15} + 48167923701231081 T^{16} + 153526963422381159 T^{17} + 350356403707485209 T^{18} )^{2} \))
$97$ (\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 145 T^{2} + 9409 T^{4} \))(\( 1 - 193 T^{2} + 9409 T^{4} \))(\( 1 - 73 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 384 T^{2} + 87396 T^{4} - 13398704 T^{6} + 1509920166 T^{8} - 126068405936 T^{10} + 7737105042276 T^{12} - 319861249892736 T^{14} + 7837433594376961 T^{16} \))(\( 1 - 438 T^{2} + 91349 T^{4} - 12529608 T^{6} + 1361625978 T^{8} - 134519612900 T^{10} + 12811538827002 T^{12} - 1109237187451848 T^{14} + 76091159678259221 T^{16} - 3432795914337108918 T^{18} + 73742412689492826049 T^{20} \))(\( 1 - 392 T^{2} + 94080 T^{4} - 14786792 T^{6} + 1704310300 T^{8} - 129112558616 T^{10} + 4406068331520 T^{12} + 451588562247304 T^{14} - 77304220777639226 T^{16} + 4248996782184883336 T^{18} + \)\(39\!\cdots\!20\)\( T^{20} - \)\(10\!\cdots\!64\)\( T^{22} + \)\(13\!\cdots\!00\)\( T^{24} - \)\(10\!\cdots\!08\)\( T^{26} + \)\(65\!\cdots\!80\)\( T^{28} - \)\(25\!\cdots\!48\)\( T^{30} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 - 1001 T^{2} + 511665 T^{4} - 176341264 T^{6} + 45723262492 T^{8} - 9443482475548 T^{10} + 1606766584089852 T^{12} - 229960593489573744 T^{14} + 28039953050858521078 T^{16} - \)\(29\!\cdots\!34\)\( T^{18} + \)\(26\!\cdots\!02\)\( T^{20} - \)\(20\!\cdots\!64\)\( T^{22} + \)\(13\!\cdots\!08\)\( T^{24} - \)\(74\!\cdots\!28\)\( T^{26} + \)\(33\!\cdots\!08\)\( T^{28} - \)\(12\!\cdots\!24\)\( T^{30} + \)\(33\!\cdots\!85\)\( T^{32} - \)\(61\!\cdots\!21\)\( T^{34} + \)\(57\!\cdots\!89\)\( T^{36} \))
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