Properties

Label 3150.2.m
Level 3150
Weight 2
Character orbit m
Rep. character \(\chi_{3150}(1457,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 72
Newform subspaces 12
Sturm bound 1440
Trace bound 14

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Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 12 \)
Sturm bound: \(1440\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 1536 72 1464
Cusp forms 1344 72 1272
Eisenstein series 192 0 192

Trace form

\( 72q + O(q^{10}) \) \( 72q - 24q^{13} - 72q^{16} + 16q^{22} - 64q^{31} - 8q^{37} + 32q^{43} + 64q^{46} + 24q^{52} - 8q^{58} - 96q^{67} - 72q^{73} + 8q^{82} + 16q^{88} + 56q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3150.2.m.a \(4\) \(25.153\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{7}+\zeta_{8}q^{8}+\cdots\)
3150.2.m.b \(4\) \(25.153\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)
3150.2.m.c \(4\) \(25.153\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{7}+\zeta_{8}q^{8}+\cdots\)
3150.2.m.d \(4\) \(25.153\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)
3150.2.m.e \(4\) \(25.153\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}-\zeta_{8}q^{8}+\cdots\)
3150.2.m.f \(4\) \(25.153\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
3150.2.m.g \(8\) \(25.153\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}-\zeta_{24}^{3}q^{4}+\zeta_{24}q^{7}+\zeta_{24}q^{8}+\cdots\)
3150.2.m.h \(8\) \(25.153\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{5}q^{2}-\zeta_{24}^{3}q^{4}+\zeta_{24}q^{7}-\zeta_{24}q^{8}+\cdots\)
3150.2.m.i \(8\) \(25.153\) 8.0.1698758656.6 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{4}q^{4}+\beta _{2}q^{7}+\beta _{2}q^{8}+\cdots\)
3150.2.m.j \(8\) \(25.153\) 8.0.1698758656.6 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{4}q^{4}+\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots\)
3150.2.m.k \(8\) \(25.153\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{5}q^{2}-\zeta_{24}^{3}q^{4}-\zeta_{24}q^{7}-\zeta_{24}q^{8}+\cdots\)
3150.2.m.l \(8\) \(25.153\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{5}q^{2}-\zeta_{24}^{3}q^{4}+\zeta_{24}q^{7}-\zeta_{24}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$3$ (\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))
$5$ (\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))
$7$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))
$11$ (\( 1 - 32 T^{2} + 466 T^{4} - 3872 T^{6} + 14641 T^{8} \))(\( 1 - 32 T^{2} + 466 T^{4} - 3872 T^{6} + 14641 T^{8} \))(\( 1 - 20 T^{2} + 214 T^{4} - 2420 T^{6} + 14641 T^{8} \))(\( 1 - 20 T^{2} + 214 T^{4} - 2420 T^{6} + 14641 T^{8} \))(\( 1 - 20 T^{2} + 214 T^{4} - 2420 T^{6} + 14641 T^{8} \))(\( 1 - 20 T^{2} + 214 T^{4} - 2420 T^{6} + 14641 T^{8} \))(\( ( 1 - 32 T^{2} + 466 T^{4} - 3872 T^{6} + 14641 T^{8} )^{2} \))(\( ( 1 - 32 T^{2} + 466 T^{4} - 3872 T^{6} + 14641 T^{8} )^{2} \))(\( 1 - 12 T^{2} + 40 T^{4} - 260 T^{6} + 15086 T^{8} - 31460 T^{10} + 585640 T^{12} - 21258732 T^{14} + 214358881 T^{16} \))(\( 1 - 12 T^{2} + 40 T^{4} - 260 T^{6} + 15086 T^{8} - 31460 T^{10} + 585640 T^{12} - 21258732 T^{14} + 214358881 T^{16} \))(\( ( 1 - 32 T^{2} + 466 T^{4} - 3872 T^{6} + 14641 T^{8} )^{2} \))(\( ( 1 - 32 T^{2} + 466 T^{4} - 3872 T^{6} + 14641 T^{8} )^{2} \))
$13$ (\( ( 1 + 8 T + 32 T^{2} + 104 T^{3} + 169 T^{4} )^{2} \))(\( ( 1 + 8 T + 32 T^{2} + 104 T^{3} + 169 T^{4} )^{2} \))(\( 1 + 8 T + 32 T^{2} + 136 T^{3} + 562 T^{4} + 1768 T^{5} + 5408 T^{6} + 17576 T^{7} + 28561 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 136 T^{3} + 562 T^{4} + 1768 T^{5} + 5408 T^{6} + 17576 T^{7} + 28561 T^{8} \))(\( 1 - 8 T + 32 T^{2} - 136 T^{3} + 562 T^{4} - 1768 T^{5} + 5408 T^{6} - 17576 T^{7} + 28561 T^{8} \))(\( 1 - 8 T + 32 T^{2} - 136 T^{3} + 562 T^{4} - 1768 T^{5} + 5408 T^{6} - 17576 T^{7} + 28561 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 128 T^{3} + 574 T^{4} + 2360 T^{5} + 8704 T^{6} + 35112 T^{7} + 139491 T^{8} + 456456 T^{9} + 1470976 T^{10} + 5184920 T^{11} + 16394014 T^{12} + 47525504 T^{13} + 154457888 T^{14} + 501988136 T^{15} + 815730721 T^{16} \))(\( 1 + 8 T + 32 T^{2} + 128 T^{3} + 574 T^{4} + 2360 T^{5} + 8704 T^{6} + 35112 T^{7} + 139491 T^{8} + 456456 T^{9} + 1470976 T^{10} + 5184920 T^{11} + 16394014 T^{12} + 47525504 T^{13} + 154457888 T^{14} + 501988136 T^{15} + 815730721 T^{16} \))(\( 1 - 4 T + 8 T^{2} - 28 T^{3} + 80 T^{4} - 372 T^{5} + 1240 T^{6} - 6412 T^{7} + 34174 T^{8} - 83356 T^{9} + 209560 T^{10} - 817284 T^{11} + 2284880 T^{12} - 10396204 T^{13} + 38614472 T^{14} - 250994068 T^{15} + 815730721 T^{16} \))(\( 1 - 4 T + 8 T^{2} - 28 T^{3} + 80 T^{4} - 372 T^{5} + 1240 T^{6} - 6412 T^{7} + 34174 T^{8} - 83356 T^{9} + 209560 T^{10} - 817284 T^{11} + 2284880 T^{12} - 10396204 T^{13} + 38614472 T^{14} - 250994068 T^{15} + 815730721 T^{16} \))(\( 1 - 8 T + 32 T^{2} - 128 T^{3} + 574 T^{4} - 2360 T^{5} + 8704 T^{6} - 35112 T^{7} + 139491 T^{8} - 456456 T^{9} + 1470976 T^{10} - 5184920 T^{11} + 16394014 T^{12} - 47525504 T^{13} + 154457888 T^{14} - 501988136 T^{15} + 815730721 T^{16} \))(\( 1 - 8 T + 32 T^{2} - 128 T^{3} + 574 T^{4} - 2360 T^{5} + 8704 T^{6} - 35112 T^{7} + 139491 T^{8} - 456456 T^{9} + 1470976 T^{10} - 5184920 T^{11} + 16394014 T^{12} - 47525504 T^{13} + 154457888 T^{14} - 501988136 T^{15} + 815730721 T^{16} \))
$17$ (\( 1 - 8 T + 32 T^{2} - 168 T^{3} + 866 T^{4} - 2856 T^{5} + 9248 T^{6} - 39304 T^{7} + 83521 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 168 T^{3} + 866 T^{4} + 2856 T^{5} + 9248 T^{6} + 39304 T^{7} + 83521 T^{8} \))(\( 1 + 12 T + 72 T^{2} + 372 T^{3} + 1726 T^{4} + 6324 T^{5} + 20808 T^{6} + 58956 T^{7} + 83521 T^{8} \))(\( 1 - 12 T + 72 T^{2} - 372 T^{3} + 1726 T^{4} - 6324 T^{5} + 20808 T^{6} - 58956 T^{7} + 83521 T^{8} \))(\( 1 - 12 T + 72 T^{2} - 372 T^{3} + 1726 T^{4} - 6324 T^{5} + 20808 T^{6} - 58956 T^{7} + 83521 T^{8} \))(\( 1 + 12 T + 72 T^{2} + 372 T^{3} + 1726 T^{4} + 6324 T^{5} + 20808 T^{6} + 58956 T^{7} + 83521 T^{8} \))(\( 1 + 96 T^{3} + 158 T^{4} - 2400 T^{5} + 4608 T^{6} - 8544 T^{7} - 207741 T^{8} - 145248 T^{9} + 1331712 T^{10} - 11791200 T^{11} + 13196318 T^{12} + 136306272 T^{13} + 6975757441 T^{16} \))(\( 1 - 96 T^{3} + 158 T^{4} + 2400 T^{5} + 4608 T^{6} + 8544 T^{7} - 207741 T^{8} + 145248 T^{9} + 1331712 T^{10} + 11791200 T^{11} + 13196318 T^{12} - 136306272 T^{13} + 6975757441 T^{16} \))(\( 1 - 64 T^{3} - 252 T^{4} + 960 T^{5} + 2048 T^{6} + 6016 T^{7} - 17786 T^{8} + 102272 T^{9} + 591872 T^{10} + 4716480 T^{11} - 21047292 T^{12} - 90870848 T^{13} + 6975757441 T^{16} \))(\( 1 + 64 T^{3} - 252 T^{4} - 960 T^{5} + 2048 T^{6} - 6016 T^{7} - 17786 T^{8} - 102272 T^{9} + 591872 T^{10} - 4716480 T^{11} - 21047292 T^{12} + 90870848 T^{13} + 6975757441 T^{16} \))(\( 1 - 96 T^{3} + 158 T^{4} + 2400 T^{5} + 4608 T^{6} + 8544 T^{7} - 207741 T^{8} + 145248 T^{9} + 1331712 T^{10} + 11791200 T^{11} + 13196318 T^{12} - 136306272 T^{13} + 6975757441 T^{16} \))(\( 1 + 96 T^{3} + 158 T^{4} - 2400 T^{5} + 4608 T^{6} - 8544 T^{7} - 207741 T^{8} - 145248 T^{9} + 1331712 T^{10} - 11791200 T^{11} + 13196318 T^{12} + 136306272 T^{13} + 6975757441 T^{16} \))
$19$ (\( ( 1 - 30 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 30 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 12 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 12 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 12 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 12 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 48 T^{2} + 1202 T^{4} - 17328 T^{6} + 130321 T^{8} )^{2} \))(\( ( 1 - 48 T^{2} + 1202 T^{4} - 17328 T^{6} + 130321 T^{8} )^{2} \))(\( ( 1 - 19 T^{2} )^{8} \))(\( ( 1 - 19 T^{2} )^{8} \))(\( ( 1 - 48 T^{2} + 1202 T^{4} - 17328 T^{6} + 130321 T^{8} )^{2} \))(\( ( 1 - 48 T^{2} + 1202 T^{4} - 17328 T^{6} + 130321 T^{8} )^{2} \))
$23$ (\( 1 - 8 T + 32 T^{2} - 120 T^{3} + 386 T^{4} - 2760 T^{5} + 16928 T^{6} - 97336 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 120 T^{3} + 386 T^{4} + 2760 T^{5} + 16928 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 120 T^{3} + 386 T^{4} + 2760 T^{5} + 16928 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 - 8 T + 32 T^{2} - 120 T^{3} + 386 T^{4} - 2760 T^{5} + 16928 T^{6} - 97336 T^{7} + 279841 T^{8} \))(\( 1 - 8 T + 32 T^{2} - 120 T^{3} + 386 T^{4} - 2760 T^{5} + 16928 T^{6} - 97336 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 120 T^{3} + 386 T^{4} + 2760 T^{5} + 16928 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 - 16 T + 128 T^{2} - 800 T^{3} + 4670 T^{4} - 26576 T^{5} + 147456 T^{6} - 807760 T^{7} + 4140483 T^{8} - 18578480 T^{9} + 78004224 T^{10} - 323350192 T^{11} + 1306857470 T^{12} - 5149074400 T^{13} + 18948593792 T^{14} - 54477207152 T^{15} + 78310985281 T^{16} \))(\( 1 + 16 T + 128 T^{2} + 800 T^{3} + 4670 T^{4} + 26576 T^{5} + 147456 T^{6} + 807760 T^{7} + 4140483 T^{8} + 18578480 T^{9} + 78004224 T^{10} + 323350192 T^{11} + 1306857470 T^{12} + 5149074400 T^{13} + 18948593792 T^{14} + 54477207152 T^{15} + 78310985281 T^{16} \))(\( 1 + 8 T + 32 T^{2} - 8 T^{3} - 924 T^{4} - 5032 T^{5} - 10656 T^{6} + 28456 T^{7} + 420614 T^{8} + 654488 T^{9} - 5637024 T^{10} - 61224344 T^{11} - 258573084 T^{12} - 51490744 T^{13} + 4737148448 T^{14} + 27238603576 T^{15} + 78310985281 T^{16} \))(\( 1 - 8 T + 32 T^{2} + 8 T^{3} - 924 T^{4} + 5032 T^{5} - 10656 T^{6} - 28456 T^{7} + 420614 T^{8} - 654488 T^{9} - 5637024 T^{10} + 61224344 T^{11} - 258573084 T^{12} + 51490744 T^{13} + 4737148448 T^{14} - 27238603576 T^{15} + 78310985281 T^{16} \))(\( 1 + 16 T + 128 T^{2} + 800 T^{3} + 4670 T^{4} + 26576 T^{5} + 147456 T^{6} + 807760 T^{7} + 4140483 T^{8} + 18578480 T^{9} + 78004224 T^{10} + 323350192 T^{11} + 1306857470 T^{12} + 5149074400 T^{13} + 18948593792 T^{14} + 54477207152 T^{15} + 78310985281 T^{16} \))(\( 1 - 16 T + 128 T^{2} - 800 T^{3} + 4670 T^{4} - 26576 T^{5} + 147456 T^{6} - 807760 T^{7} + 4140483 T^{8} - 18578480 T^{9} + 78004224 T^{10} - 323350192 T^{11} + 1306857470 T^{12} - 5149074400 T^{13} + 18948593792 T^{14} - 54477207152 T^{15} + 78310985281 T^{16} \))
$29$ (\( ( 1 - 4 T + 54 T^{2} - 116 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 4 T + 54 T^{2} + 116 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 12 T + 86 T^{2} - 348 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 12 T + 86 T^{2} + 348 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 12 T + 86 T^{2} - 348 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 12 T + 86 T^{2} + 348 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 58 T^{2} + 96 T^{3} + 2019 T^{4} + 2784 T^{5} + 48778 T^{6} + 707281 T^{8} )^{2} \))(\( ( 1 + 58 T^{2} - 96 T^{3} + 2019 T^{4} - 2784 T^{5} + 48778 T^{6} + 707281 T^{8} )^{2} \))(\( ( 1 + 12 T + 78 T^{2} + 252 T^{3} + 738 T^{4} + 7308 T^{5} + 65598 T^{6} + 292668 T^{7} + 707281 T^{8} )^{2} \))(\( ( 1 - 12 T + 78 T^{2} - 252 T^{3} + 738 T^{4} - 7308 T^{5} + 65598 T^{6} - 292668 T^{7} + 707281 T^{8} )^{2} \))(\( ( 1 + 58 T^{2} + 96 T^{3} + 2019 T^{4} + 2784 T^{5} + 48778 T^{6} + 707281 T^{8} )^{2} \))(\( ( 1 + 58 T^{2} - 96 T^{3} + 2019 T^{4} - 2784 T^{5} + 48778 T^{6} + 707281 T^{8} )^{2} \))
$31$ (\( ( 1 - 12 T + 80 T^{2} - 372 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 12 T + 80 T^{2} - 372 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 12 T + 90 T^{2} + 372 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 12 T + 90 T^{2} + 372 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 12 T + 90 T^{2} + 372 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 12 T + 90 T^{2} + 372 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 42 T^{2} - 192 T^{3} + 1139 T^{4} - 5952 T^{5} + 40362 T^{6} + 923521 T^{8} )^{2} \))(\( ( 1 + 42 T^{2} - 192 T^{3} + 1139 T^{4} - 5952 T^{5} + 40362 T^{6} + 923521 T^{8} )^{2} \))(\( ( 1 + 4 T + 110 T^{2} + 356 T^{3} + 4930 T^{4} + 11036 T^{5} + 105710 T^{6} + 119164 T^{7} + 923521 T^{8} )^{2} \))(\( ( 1 + 4 T + 110 T^{2} + 356 T^{3} + 4930 T^{4} + 11036 T^{5} + 105710 T^{6} + 119164 T^{7} + 923521 T^{8} )^{2} \))(\( ( 1 + 42 T^{2} - 192 T^{3} + 1139 T^{4} - 5952 T^{5} + 40362 T^{6} + 923521 T^{8} )^{2} \))(\( ( 1 + 42 T^{2} - 192 T^{3} + 1139 T^{4} - 5952 T^{5} + 40362 T^{6} + 923521 T^{8} )^{2} \))
$37$ (\( 1 + 8 T + 32 T^{2} + 72 T^{3} - 622 T^{4} + 2664 T^{5} + 43808 T^{6} + 405224 T^{7} + 1874161 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 72 T^{3} - 622 T^{4} + 2664 T^{5} + 43808 T^{6} + 405224 T^{7} + 1874161 T^{8} \))(\( 1 - 4 T + 8 T^{2} + 244 T^{3} - 2162 T^{4} + 9028 T^{5} + 10952 T^{6} - 202612 T^{7} + 1874161 T^{8} \))(\( 1 - 4 T + 8 T^{2} + 244 T^{3} - 2162 T^{4} + 9028 T^{5} + 10952 T^{6} - 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 4 T + 8 T^{2} - 244 T^{3} - 2162 T^{4} - 9028 T^{5} + 10952 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 4 T + 8 T^{2} - 244 T^{3} - 2162 T^{4} - 9028 T^{5} + 10952 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( 1 - 16 T + 128 T^{2} - 784 T^{3} + 4324 T^{4} - 27760 T^{5} + 198016 T^{6} - 1322736 T^{7} + 8422566 T^{8} - 48941232 T^{9} + 271083904 T^{10} - 1406127280 T^{11} + 8103872164 T^{12} - 54365662288 T^{13} + 328412980352 T^{14} - 1518910034128 T^{15} + 3512479453921 T^{16} \))(\( 1 - 16 T + 128 T^{2} - 784 T^{3} + 4324 T^{4} - 27760 T^{5} + 198016 T^{6} - 1322736 T^{7} + 8422566 T^{8} - 48941232 T^{9} + 271083904 T^{10} - 1406127280 T^{11} + 8103872164 T^{12} - 54365662288 T^{13} + 328412980352 T^{14} - 1518910034128 T^{15} + 3512479453921 T^{16} \))(\( 1 - 4 T + 8 T^{2} - 220 T^{3} - 48 T^{4} + 8684 T^{5} - 10152 T^{6} + 208404 T^{7} - 3196994 T^{8} + 7710948 T^{9} - 13898088 T^{10} + 439870652 T^{11} - 89959728 T^{12} - 15255670540 T^{13} + 20525811272 T^{14} - 379727508532 T^{15} + 3512479453921 T^{16} \))(\( 1 - 4 T + 8 T^{2} - 220 T^{3} - 48 T^{4} + 8684 T^{5} - 10152 T^{6} + 208404 T^{7} - 3196994 T^{8} + 7710948 T^{9} - 13898088 T^{10} + 439870652 T^{11} - 89959728 T^{12} - 15255670540 T^{13} + 20525811272 T^{14} - 379727508532 T^{15} + 3512479453921 T^{16} \))(\( 1 + 16 T + 128 T^{2} + 784 T^{3} + 4324 T^{4} + 27760 T^{5} + 198016 T^{6} + 1322736 T^{7} + 8422566 T^{8} + 48941232 T^{9} + 271083904 T^{10} + 1406127280 T^{11} + 8103872164 T^{12} + 54365662288 T^{13} + 328412980352 T^{14} + 1518910034128 T^{15} + 3512479453921 T^{16} \))(\( 1 + 16 T + 128 T^{2} + 784 T^{3} + 4324 T^{4} + 27760 T^{5} + 198016 T^{6} + 1322736 T^{7} + 8422566 T^{8} + 48941232 T^{9} + 271083904 T^{10} + 1406127280 T^{11} + 8103872164 T^{12} + 54365662288 T^{13} + 328412980352 T^{14} + 1518910034128 T^{15} + 3512479453921 T^{16} \))
$41$ (\( 1 - 76 T^{2} + 3654 T^{4} - 127756 T^{6} + 2825761 T^{8} \))(\( 1 - 76 T^{2} + 3654 T^{4} - 127756 T^{6} + 2825761 T^{8} \))(\( 1 - 140 T^{2} + 8134 T^{4} - 235340 T^{6} + 2825761 T^{8} \))(\( 1 - 140 T^{2} + 8134 T^{4} - 235340 T^{6} + 2825761 T^{8} \))(\( 1 - 140 T^{2} + 8134 T^{4} - 235340 T^{6} + 2825761 T^{8} \))(\( 1 - 140 T^{2} + 8134 T^{4} - 235340 T^{6} + 2825761 T^{8} \))(\( 1 - 172 T^{2} + 15786 T^{4} - 1010672 T^{6} + 47929043 T^{8} - 1698939632 T^{10} + 44607463146 T^{12} - 817017929452 T^{14} + 7984925229121 T^{16} \))(\( 1 - 172 T^{2} + 15786 T^{4} - 1010672 T^{6} + 47929043 T^{8} - 1698939632 T^{10} + 44607463146 T^{12} - 817017929452 T^{14} + 7984925229121 T^{16} \))(\( 1 - 76 T^{2} + 5480 T^{4} - 315940 T^{6} + 12648846 T^{8} - 531095140 T^{10} + 15485170280 T^{12} - 361007922316 T^{14} + 7984925229121 T^{16} \))(\( 1 - 76 T^{2} + 5480 T^{4} - 315940 T^{6} + 12648846 T^{8} - 531095140 T^{10} + 15485170280 T^{12} - 361007922316 T^{14} + 7984925229121 T^{16} \))(\( 1 - 172 T^{2} + 15786 T^{4} - 1010672 T^{6} + 47929043 T^{8} - 1698939632 T^{10} + 44607463146 T^{12} - 817017929452 T^{14} + 7984925229121 T^{16} \))(\( 1 - 172 T^{2} + 15786 T^{4} - 1010672 T^{6} + 47929043 T^{8} - 1698939632 T^{10} + 44607463146 T^{12} - 817017929452 T^{14} + 7984925229121 T^{16} \))
$43$ (\( 1 - 4 T + 8 T^{2} + 220 T^{3} - 3554 T^{4} + 9460 T^{5} + 14792 T^{6} - 318028 T^{7} + 3418801 T^{8} \))(\( 1 - 4 T + 8 T^{2} + 220 T^{3} - 3554 T^{4} + 9460 T^{5} + 14792 T^{6} - 318028 T^{7} + 3418801 T^{8} \))(\( 1 - 20 T + 200 T^{2} - 1780 T^{3} + 13726 T^{4} - 76540 T^{5} + 369800 T^{6} - 1590140 T^{7} + 3418801 T^{8} \))(\( 1 - 20 T + 200 T^{2} - 1780 T^{3} + 13726 T^{4} - 76540 T^{5} + 369800 T^{6} - 1590140 T^{7} + 3418801 T^{8} \))(\( 1 + 20 T + 200 T^{2} + 1780 T^{3} + 13726 T^{4} + 76540 T^{5} + 369800 T^{6} + 1590140 T^{7} + 3418801 T^{8} \))(\( 1 + 20 T + 200 T^{2} + 1780 T^{3} + 13726 T^{4} + 76540 T^{5} + 369800 T^{6} + 1590140 T^{7} + 3418801 T^{8} \))(\( 1 - 8 T + 32 T^{2} - 368 T^{3} + 1438 T^{4} + 5752 T^{5} - 24320 T^{6} + 270552 T^{7} - 3004701 T^{8} + 11633736 T^{9} - 44967680 T^{10} + 457324264 T^{11} + 4916235838 T^{12} - 54099107024 T^{13} + 202283617568 T^{14} - 2174548888856 T^{15} + 11688200277601 T^{16} \))(\( 1 - 8 T + 32 T^{2} - 368 T^{3} + 1438 T^{4} + 5752 T^{5} - 24320 T^{6} + 270552 T^{7} - 3004701 T^{8} + 11633736 T^{9} - 44967680 T^{10} + 457324264 T^{11} + 4916235838 T^{12} - 54099107024 T^{13} + 202283617568 T^{14} - 2174548888856 T^{15} + 11688200277601 T^{16} \))(\( 1 - 12 T + 72 T^{2} - 300 T^{3} - 1008 T^{4} + 17988 T^{5} - 98280 T^{6} + 509316 T^{7} - 2377282 T^{8} + 21900588 T^{9} - 181719720 T^{10} + 1430171916 T^{11} - 3446151408 T^{12} - 44102532900 T^{13} + 455138139528 T^{14} - 3261823333284 T^{15} + 11688200277601 T^{16} \))(\( 1 - 12 T + 72 T^{2} - 300 T^{3} - 1008 T^{4} + 17988 T^{5} - 98280 T^{6} + 509316 T^{7} - 2377282 T^{8} + 21900588 T^{9} - 181719720 T^{10} + 1430171916 T^{11} - 3446151408 T^{12} - 44102532900 T^{13} + 455138139528 T^{14} - 3261823333284 T^{15} + 11688200277601 T^{16} \))(\( 1 + 8 T + 32 T^{2} + 368 T^{3} + 1438 T^{4} - 5752 T^{5} - 24320 T^{6} - 270552 T^{7} - 3004701 T^{8} - 11633736 T^{9} - 44967680 T^{10} - 457324264 T^{11} + 4916235838 T^{12} + 54099107024 T^{13} + 202283617568 T^{14} + 2174548888856 T^{15} + 11688200277601 T^{16} \))(\( 1 + 8 T + 32 T^{2} + 368 T^{3} + 1438 T^{4} - 5752 T^{5} - 24320 T^{6} - 270552 T^{7} - 3004701 T^{8} - 11633736 T^{9} - 44967680 T^{10} - 457324264 T^{11} + 4916235838 T^{12} + 54099107024 T^{13} + 202283617568 T^{14} + 2174548888856 T^{15} + 11688200277601 T^{16} \))
$47$ (\( 1 - 20 T + 200 T^{2} - 1220 T^{3} + 7246 T^{4} - 57340 T^{5} + 441800 T^{6} - 2076460 T^{7} + 4879681 T^{8} \))(\( 1 + 20 T + 200 T^{2} + 1220 T^{3} + 7246 T^{4} + 57340 T^{5} + 441800 T^{6} + 2076460 T^{7} + 4879681 T^{8} \))(\( 1 + 20 T + 200 T^{2} + 1860 T^{3} + 15182 T^{4} + 87420 T^{5} + 441800 T^{6} + 2076460 T^{7} + 4879681 T^{8} \))(\( 1 - 20 T + 200 T^{2} - 1860 T^{3} + 15182 T^{4} - 87420 T^{5} + 441800 T^{6} - 2076460 T^{7} + 4879681 T^{8} \))(\( 1 - 20 T + 200 T^{2} - 1860 T^{3} + 15182 T^{4} - 87420 T^{5} + 441800 T^{6} - 2076460 T^{7} + 4879681 T^{8} \))(\( 1 + 20 T + 200 T^{2} + 1860 T^{3} + 15182 T^{4} + 87420 T^{5} + 441800 T^{6} + 2076460 T^{7} + 4879681 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 520 T^{3} + 2012 T^{4} - 17432 T^{5} - 68640 T^{6} - 1046296 T^{7} - 15494202 T^{8} - 49175912 T^{9} - 151625760 T^{10} - 1809842536 T^{11} + 9817918172 T^{12} + 119259403640 T^{13} + 344934890528 T^{14} + 4052984963704 T^{15} + 23811286661761 T^{16} \))(\( 1 - 8 T + 32 T^{2} - 520 T^{3} + 2012 T^{4} + 17432 T^{5} - 68640 T^{6} + 1046296 T^{7} - 15494202 T^{8} + 49175912 T^{9} - 151625760 T^{10} + 1809842536 T^{11} + 9817918172 T^{12} - 119259403640 T^{13} + 344934890528 T^{14} - 4052984963704 T^{15} + 23811286661761 T^{16} \))(\( 1 - 12 T + 72 T^{2} - 220 T^{3} - 2352 T^{4} + 10116 T^{5} + 72152 T^{6} - 1599596 T^{7} + 18271774 T^{8} - 75181012 T^{9} + 159383768 T^{10} + 1050273468 T^{11} - 11477009712 T^{12} - 50455901540 T^{13} + 776103503688 T^{14} - 6079477445556 T^{15} + 23811286661761 T^{16} \))(\( 1 + 12 T + 72 T^{2} + 220 T^{3} - 2352 T^{4} - 10116 T^{5} + 72152 T^{6} + 1599596 T^{7} + 18271774 T^{8} + 75181012 T^{9} + 159383768 T^{10} - 1050273468 T^{11} - 11477009712 T^{12} + 50455901540 T^{13} + 776103503688 T^{14} + 6079477445556 T^{15} + 23811286661761 T^{16} \))(\( 1 - 8 T + 32 T^{2} - 520 T^{3} + 2012 T^{4} + 17432 T^{5} - 68640 T^{6} + 1046296 T^{7} - 15494202 T^{8} + 49175912 T^{9} - 151625760 T^{10} + 1809842536 T^{11} + 9817918172 T^{12} - 119259403640 T^{13} + 344934890528 T^{14} - 4052984963704 T^{15} + 23811286661761 T^{16} \))(\( 1 + 8 T + 32 T^{2} + 520 T^{3} + 2012 T^{4} - 17432 T^{5} - 68640 T^{6} - 1046296 T^{7} - 15494202 T^{8} - 49175912 T^{9} - 151625760 T^{10} - 1809842536 T^{11} + 9817918172 T^{12} + 119259403640 T^{13} + 344934890528 T^{14} + 4052984963704 T^{15} + 23811286661761 T^{16} \))
$53$ (\( 1 + 16 T + 128 T^{2} + 1296 T^{3} + 12338 T^{4} + 68688 T^{5} + 359552 T^{6} + 2382032 T^{7} + 7890481 T^{8} \))(\( 1 - 16 T + 128 T^{2} - 1296 T^{3} + 12338 T^{4} - 68688 T^{5} + 359552 T^{6} - 2382032 T^{7} + 7890481 T^{8} \))(\( 1 - 8 T + 32 T^{2} - 360 T^{3} + 3986 T^{4} - 19080 T^{5} + 89888 T^{6} - 1191016 T^{7} + 7890481 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 360 T^{3} + 3986 T^{4} + 19080 T^{5} + 89888 T^{6} + 1191016 T^{7} + 7890481 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 360 T^{3} + 3986 T^{4} + 19080 T^{5} + 89888 T^{6} + 1191016 T^{7} + 7890481 T^{8} \))(\( 1 - 8 T + 32 T^{2} - 360 T^{3} + 3986 T^{4} - 19080 T^{5} + 89888 T^{6} - 1191016 T^{7} + 7890481 T^{8} \))(\( 1 - 32 T + 512 T^{2} - 6592 T^{3} + 79454 T^{4} - 821920 T^{5} + 7348224 T^{6} - 61872608 T^{7} + 480643491 T^{8} - 3279248224 T^{9} + 20641161216 T^{10} - 122364983840 T^{11} + 626930277374 T^{12} - 2756744689856 T^{13} + 11348152898048 T^{14} - 37590756474784 T^{15} + 62259690411361 T^{16} \))(\( 1 + 32 T + 512 T^{2} + 6592 T^{3} + 79454 T^{4} + 821920 T^{5} + 7348224 T^{6} + 61872608 T^{7} + 480643491 T^{8} + 3279248224 T^{9} + 20641161216 T^{10} + 122364983840 T^{11} + 626930277374 T^{12} + 2756744689856 T^{13} + 11348152898048 T^{14} + 37590756474784 T^{15} + 62259690411361 T^{16} \))(\( 1 + 32 T + 512 T^{2} + 5792 T^{3} + 60388 T^{4} + 619872 T^{5} + 5690880 T^{6} + 44817632 T^{7} + 328258854 T^{8} + 2375334496 T^{9} + 15985681920 T^{10} + 92284683744 T^{11} + 476490366628 T^{12} + 2422188295456 T^{13} + 11348152898048 T^{14} + 37590756474784 T^{15} + 62259690411361 T^{16} \))(\( 1 - 32 T + 512 T^{2} - 5792 T^{3} + 60388 T^{4} - 619872 T^{5} + 5690880 T^{6} - 44817632 T^{7} + 328258854 T^{8} - 2375334496 T^{9} + 15985681920 T^{10} - 92284683744 T^{11} + 476490366628 T^{12} - 2422188295456 T^{13} + 11348152898048 T^{14} - 37590756474784 T^{15} + 62259690411361 T^{16} \))(\( 1 + 32 T + 512 T^{2} + 6592 T^{3} + 79454 T^{4} + 821920 T^{5} + 7348224 T^{6} + 61872608 T^{7} + 480643491 T^{8} + 3279248224 T^{9} + 20641161216 T^{10} + 122364983840 T^{11} + 626930277374 T^{12} + 2756744689856 T^{13} + 11348152898048 T^{14} + 37590756474784 T^{15} + 62259690411361 T^{16} \))(\( 1 - 32 T + 512 T^{2} - 6592 T^{3} + 79454 T^{4} - 821920 T^{5} + 7348224 T^{6} - 61872608 T^{7} + 480643491 T^{8} - 3279248224 T^{9} + 20641161216 T^{10} - 122364983840 T^{11} + 626930277374 T^{12} - 2756744689856 T^{13} + 11348152898048 T^{14} - 37590756474784 T^{15} + 62259690411361 T^{16} \))
$59$ (\( ( 1 + 110 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 110 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 8 T + 59 T^{2} )^{4} \))(\( ( 1 + 8 T + 59 T^{2} )^{4} \))(\( ( 1 - 8 T + 59 T^{2} )^{4} \))(\( ( 1 + 8 T + 59 T^{2} )^{4} \))(\( ( 1 + 4 T + 170 T^{2} + 856 T^{3} + 13027 T^{4} + 50504 T^{5} + 591770 T^{6} + 821516 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 4 T + 170 T^{2} - 856 T^{3} + 13027 T^{4} - 50504 T^{5} + 591770 T^{6} - 821516 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 + 8 T + 148 T^{2} + 520 T^{3} + 8710 T^{4} + 30680 T^{5} + 515188 T^{6} + 1643032 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 8 T + 148 T^{2} - 520 T^{3} + 8710 T^{4} - 30680 T^{5} + 515188 T^{6} - 1643032 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 + 4 T + 170 T^{2} + 856 T^{3} + 13027 T^{4} + 50504 T^{5} + 591770 T^{6} + 821516 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 4 T + 170 T^{2} - 856 T^{3} + 13027 T^{4} - 50504 T^{5} + 591770 T^{6} - 821516 T^{7} + 12117361 T^{8} )^{2} \))
$61$ (\( ( 1 + 24 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 + 24 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 16 T + 184 T^{2} - 976 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 16 T + 184 T^{2} - 976 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 16 T + 184 T^{2} - 976 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 16 T + 184 T^{2} - 976 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 16 T + 222 T^{2} + 2480 T^{3} + 20579 T^{4} + 151280 T^{5} + 826062 T^{6} + 3631696 T^{7} + 13845841 T^{8} )^{2} \))(\( ( 1 + 16 T + 222 T^{2} + 2480 T^{3} + 20579 T^{4} + 151280 T^{5} + 826062 T^{6} + 3631696 T^{7} + 13845841 T^{8} )^{2} \))(\( ( 1 + 226 T^{2} + 16 T^{3} + 20162 T^{4} + 976 T^{5} + 840946 T^{6} + 13845841 T^{8} )^{2} \))(\( ( 1 + 226 T^{2} + 16 T^{3} + 20162 T^{4} + 976 T^{5} + 840946 T^{6} + 13845841 T^{8} )^{2} \))(\( ( 1 + 16 T + 222 T^{2} + 2480 T^{3} + 20579 T^{4} + 151280 T^{5} + 826062 T^{6} + 3631696 T^{7} + 13845841 T^{8} )^{2} \))(\( ( 1 + 16 T + 222 T^{2} + 2480 T^{3} + 20579 T^{4} + 151280 T^{5} + 826062 T^{6} + 3631696 T^{7} + 13845841 T^{8} )^{2} \))
$67$ (\( 1 + 28 T + 392 T^{2} + 4508 T^{3} + 43006 T^{4} + 302036 T^{5} + 1759688 T^{6} + 8421364 T^{7} + 20151121 T^{8} \))(\( 1 + 28 T + 392 T^{2} + 4508 T^{3} + 43006 T^{4} + 302036 T^{5} + 1759688 T^{6} + 8421364 T^{7} + 20151121 T^{8} \))(\( 1 + 4 T + 8 T^{2} + 260 T^{3} + 8446 T^{4} + 17420 T^{5} + 35912 T^{6} + 1203052 T^{7} + 20151121 T^{8} \))(\( 1 + 4 T + 8 T^{2} + 260 T^{3} + 8446 T^{4} + 17420 T^{5} + 35912 T^{6} + 1203052 T^{7} + 20151121 T^{8} \))(\( 1 - 4 T + 8 T^{2} - 260 T^{3} + 8446 T^{4} - 17420 T^{5} + 35912 T^{6} - 1203052 T^{7} + 20151121 T^{8} \))(\( 1 - 4 T + 8 T^{2} - 260 T^{3} + 8446 T^{4} - 17420 T^{5} + 35912 T^{6} - 1203052 T^{7} + 20151121 T^{8} \))(\( 1 + 16 T + 128 T^{2} + 1648 T^{3} + 12196 T^{4} - 9104 T^{5} - 348800 T^{6} - 6630000 T^{7} - 95097114 T^{8} - 444210000 T^{9} - 1565763200 T^{10} - 2738146352 T^{11} + 245763071716 T^{12} + 2225006176336 T^{13} + 11578672917632 T^{14} + 96971385685168 T^{15} + 406067677556641 T^{16} \))(\( 1 + 16 T + 128 T^{2} + 1648 T^{3} + 12196 T^{4} - 9104 T^{5} - 348800 T^{6} - 6630000 T^{7} - 95097114 T^{8} - 444210000 T^{9} - 1565763200 T^{10} - 2738146352 T^{11} + 245763071716 T^{12} + 2225006176336 T^{13} + 11578672917632 T^{14} + 96971385685168 T^{15} + 406067677556641 T^{16} \))(\( 1 + 20 T + 200 T^{2} + 1332 T^{3} + 9104 T^{4} + 102596 T^{5} + 1118232 T^{6} + 8938244 T^{7} + 69729150 T^{8} + 598862348 T^{9} + 5019743448 T^{10} + 30857080748 T^{11} + 183455805584 T^{12} + 1798366642524 T^{13} + 18091676433800 T^{14} + 121214232106460 T^{15} + 406067677556641 T^{16} \))(\( 1 + 20 T + 200 T^{2} + 1332 T^{3} + 9104 T^{4} + 102596 T^{5} + 1118232 T^{6} + 8938244 T^{7} + 69729150 T^{8} + 598862348 T^{9} + 5019743448 T^{10} + 30857080748 T^{11} + 183455805584 T^{12} + 1798366642524 T^{13} + 18091676433800 T^{14} + 121214232106460 T^{15} + 406067677556641 T^{16} \))(\( 1 - 16 T + 128 T^{2} - 1648 T^{3} + 12196 T^{4} + 9104 T^{5} - 348800 T^{6} + 6630000 T^{7} - 95097114 T^{8} + 444210000 T^{9} - 1565763200 T^{10} + 2738146352 T^{11} + 245763071716 T^{12} - 2225006176336 T^{13} + 11578672917632 T^{14} - 96971385685168 T^{15} + 406067677556641 T^{16} \))(\( 1 - 16 T + 128 T^{2} - 1648 T^{3} + 12196 T^{4} + 9104 T^{5} - 348800 T^{6} + 6630000 T^{7} - 95097114 T^{8} + 444210000 T^{9} - 1565763200 T^{10} + 2738146352 T^{11} + 245763071716 T^{12} - 2225006176336 T^{13} + 11578672917632 T^{14} - 96971385685168 T^{15} + 406067677556641 T^{16} \))
$71$ (\( 1 - 236 T^{2} + 23494 T^{4} - 1189676 T^{6} + 25411681 T^{8} \))(\( 1 - 236 T^{2} + 23494 T^{4} - 1189676 T^{6} + 25411681 T^{8} \))(\( 1 - 120 T^{2} + 9074 T^{4} - 604920 T^{6} + 25411681 T^{8} \))(\( 1 - 120 T^{2} + 9074 T^{4} - 604920 T^{6} + 25411681 T^{8} \))(\( 1 - 120 T^{2} + 9074 T^{4} - 604920 T^{6} + 25411681 T^{8} \))(\( 1 - 120 T^{2} + 9074 T^{4} - 604920 T^{6} + 25411681 T^{8} \))(\( ( 1 - 156 T^{2} + 13094 T^{4} - 786396 T^{6} + 25411681 T^{8} )^{2} \))(\( ( 1 - 156 T^{2} + 13094 T^{4} - 786396 T^{6} + 25411681 T^{8} )^{2} \))(\( 1 - 216 T^{2} + 31388 T^{4} - 3350120 T^{6} + 263319558 T^{8} - 16887954920 T^{10} + 797621843228 T^{12} - 27669661326936 T^{14} + 645753531245761 T^{16} \))(\( 1 - 216 T^{2} + 31388 T^{4} - 3350120 T^{6} + 263319558 T^{8} - 16887954920 T^{10} + 797621843228 T^{12} - 27669661326936 T^{14} + 645753531245761 T^{16} \))(\( ( 1 - 156 T^{2} + 13094 T^{4} - 786396 T^{6} + 25411681 T^{8} )^{2} \))(\( ( 1 - 156 T^{2} + 13094 T^{4} - 786396 T^{6} + 25411681 T^{8} )^{2} \))
$73$ (\( 1 - 8542 T^{4} + 28398241 T^{8} \))(\( 1 - 8542 T^{4} + 28398241 T^{8} \))(\( ( 1 + 12 T + 72 T^{2} + 876 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 12 T + 72 T^{2} + 876 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 12 T + 72 T^{2} - 876 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 12 T + 72 T^{2} - 876 T^{3} + 5329 T^{4} )^{2} \))(\( 1 + 2044 T^{4} + 20460870 T^{8} + 58046004604 T^{12} + 806460091894081 T^{16} \))(\( 1 + 2044 T^{4} + 20460870 T^{8} + 58046004604 T^{12} + 806460091894081 T^{16} \))(\( 1 + 36 T + 648 T^{2} + 8620 T^{3} + 98192 T^{4} + 980116 T^{5} + 8807960 T^{6} + 73999132 T^{7} + 618591198 T^{8} + 5401936636 T^{9} + 46937618840 T^{10} + 381281785972 T^{11} + 2788480080272 T^{12} + 17869877131660 T^{13} + 98064578635272 T^{14} + 397706346687492 T^{15} + 806460091894081 T^{16} \))(\( 1 + 36 T + 648 T^{2} + 8620 T^{3} + 98192 T^{4} + 980116 T^{5} + 8807960 T^{6} + 73999132 T^{7} + 618591198 T^{8} + 5401936636 T^{9} + 46937618840 T^{10} + 381281785972 T^{11} + 2788480080272 T^{12} + 17869877131660 T^{13} + 98064578635272 T^{14} + 397706346687492 T^{15} + 806460091894081 T^{16} \))(\( 1 + 2044 T^{4} + 20460870 T^{8} + 58046004604 T^{12} + 806460091894081 T^{16} \))(\( 1 + 2044 T^{4} + 20460870 T^{8} + 58046004604 T^{12} + 806460091894081 T^{16} \))
$79$ (\( ( 1 - 126 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 - 126 T^{2} + 6241 T^{4} )^{2} \))(\( 1 - 52 T^{2} + 11110 T^{4} - 324532 T^{6} + 38950081 T^{8} \))(\( 1 - 52 T^{2} + 11110 T^{4} - 324532 T^{6} + 38950081 T^{8} \))(\( 1 - 52 T^{2} + 11110 T^{4} - 324532 T^{6} + 38950081 T^{8} \))(\( 1 - 52 T^{2} + 11110 T^{4} - 324532 T^{6} + 38950081 T^{8} \))(\( 1 - 320 T^{2} + 58500 T^{4} - 7347136 T^{6} + 669209222 T^{8} - 45853475776 T^{10} + 2278579738500 T^{12} - 77787985766720 T^{14} + 1517108809906561 T^{16} \))(\( 1 - 320 T^{2} + 58500 T^{4} - 7347136 T^{6} + 669209222 T^{8} - 45853475776 T^{10} + 2278579738500 T^{12} - 77787985766720 T^{14} + 1517108809906561 T^{16} \))(\( 1 - 280 T^{2} + 32732 T^{4} - 1914792 T^{6} + 96372294 T^{8} - 11950216872 T^{10} + 1274914051292 T^{12} - 68064487545880 T^{14} + 1517108809906561 T^{16} \))(\( 1 - 280 T^{2} + 32732 T^{4} - 1914792 T^{6} + 96372294 T^{8} - 11950216872 T^{10} + 1274914051292 T^{12} - 68064487545880 T^{14} + 1517108809906561 T^{16} \))(\( 1 - 320 T^{2} + 58500 T^{4} - 7347136 T^{6} + 669209222 T^{8} - 45853475776 T^{10} + 2278579738500 T^{12} - 77787985766720 T^{14} + 1517108809906561 T^{16} \))(\( 1 - 320 T^{2} + 58500 T^{4} - 7347136 T^{6} + 669209222 T^{8} - 45853475776 T^{10} + 2278579738500 T^{12} - 77787985766720 T^{14} + 1517108809906561 T^{16} \))
$83$ (\( 1 - 8 T + 32 T^{2} - 600 T^{3} + 11186 T^{4} - 49800 T^{5} + 220448 T^{6} - 4574296 T^{7} + 47458321 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 600 T^{3} + 11186 T^{4} + 49800 T^{5} + 220448 T^{6} + 4574296 T^{7} + 47458321 T^{8} \))(\( 1 - 16 T + 128 T^{2} - 816 T^{3} + 4178 T^{4} - 67728 T^{5} + 881792 T^{6} - 9148592 T^{7} + 47458321 T^{8} \))(\( 1 + 16 T + 128 T^{2} + 816 T^{3} + 4178 T^{4} + 67728 T^{5} + 881792 T^{6} + 9148592 T^{7} + 47458321 T^{8} \))(\( 1 + 16 T + 128 T^{2} + 816 T^{3} + 4178 T^{4} + 67728 T^{5} + 881792 T^{6} + 9148592 T^{7} + 47458321 T^{8} \))(\( 1 - 16 T + 128 T^{2} - 816 T^{3} + 4178 T^{4} - 67728 T^{5} + 881792 T^{6} - 9148592 T^{7} + 47458321 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 160 T^{3} + 10142 T^{4} + 122968 T^{5} + 672000 T^{6} + 7632056 T^{7} + 75142083 T^{8} + 633460648 T^{9} + 4629408000 T^{10} + 70311503816 T^{11} + 481322291582 T^{12} + 630246502880 T^{13} + 10462091947808 T^{14} + 217088407917016 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 8 T + 32 T^{2} - 160 T^{3} + 10142 T^{4} - 122968 T^{5} + 672000 T^{6} - 7632056 T^{7} + 75142083 T^{8} - 633460648 T^{9} + 4629408000 T^{10} - 70311503816 T^{11} + 481322291582 T^{12} - 630246502880 T^{13} + 10462091947808 T^{14} - 217088407917016 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 56 T + 1568 T^{2} + 30056 T^{3} + 449924 T^{4} + 5649064 T^{5} + 62548320 T^{6} + 632947128 T^{7} + 5962291750 T^{8} + 52534611624 T^{9} + 430895376480 T^{10} + 3230061357368 T^{11} + 21352637617604 T^{12} + 118391805566008 T^{13} + 512642505442592 T^{14} + 1519618855419112 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 56 T + 1568 T^{2} - 30056 T^{3} + 449924 T^{4} - 5649064 T^{5} + 62548320 T^{6} - 632947128 T^{7} + 5962291750 T^{8} - 52534611624 T^{9} + 430895376480 T^{10} - 3230061357368 T^{11} + 21352637617604 T^{12} - 118391805566008 T^{13} + 512642505442592 T^{14} - 1519618855419112 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 8 T + 32 T^{2} - 160 T^{3} + 10142 T^{4} - 122968 T^{5} + 672000 T^{6} - 7632056 T^{7} + 75142083 T^{8} - 633460648 T^{9} + 4629408000 T^{10} - 70311503816 T^{11} + 481322291582 T^{12} - 630246502880 T^{13} + 10462091947808 T^{14} - 217088407917016 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 8 T + 32 T^{2} + 160 T^{3} + 10142 T^{4} + 122968 T^{5} + 672000 T^{6} + 7632056 T^{7} + 75142083 T^{8} + 633460648 T^{9} + 4629408000 T^{10} + 70311503816 T^{11} + 481322291582 T^{12} + 630246502880 T^{13} + 10462091947808 T^{14} + 217088407917016 T^{15} + 2252292232139041 T^{16} \))
$89$ (\( ( 1 + 12 T + 206 T^{2} + 1068 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 12 T + 206 T^{2} - 1068 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 4 T + 54 T^{2} - 356 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 4 T + 54 T^{2} + 356 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 4 T + 54 T^{2} - 356 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 4 T + 54 T^{2} + 356 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 8 T + 316 T^{2} - 1912 T^{3} + 40422 T^{4} - 170168 T^{5} + 2503036 T^{6} - 5639752 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 8 T + 316 T^{2} + 1912 T^{3} + 40422 T^{4} + 170168 T^{5} + 2503036 T^{6} + 5639752 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 36 T + 734 T^{2} + 10004 T^{3} + 106562 T^{4} + 890356 T^{5} + 5814014 T^{6} + 25378884 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 - 36 T + 734 T^{2} - 10004 T^{3} + 106562 T^{4} - 890356 T^{5} + 5814014 T^{6} - 25378884 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 - 8 T + 316 T^{2} - 1912 T^{3} + 40422 T^{4} - 170168 T^{5} + 2503036 T^{6} - 5639752 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 8 T + 316 T^{2} + 1912 T^{3} + 40422 T^{4} + 170168 T^{5} + 2503036 T^{6} + 5639752 T^{7} + 62742241 T^{8} )^{2} \))
$97$ (\( 1 - 24 T + 288 T^{2} - 3960 T^{3} + 49826 T^{4} - 384120 T^{5} + 2709792 T^{6} - 21904152 T^{7} + 88529281 T^{8} \))(\( 1 - 24 T + 288 T^{2} - 3960 T^{3} + 49826 T^{4} - 384120 T^{5} + 2709792 T^{6} - 21904152 T^{7} + 88529281 T^{8} \))(\( 1 + 16 T + 128 T^{2} + 1488 T^{3} + 17282 T^{4} + 144336 T^{5} + 1204352 T^{6} + 14602768 T^{7} + 88529281 T^{8} \))(\( 1 + 16 T + 128 T^{2} + 1488 T^{3} + 17282 T^{4} + 144336 T^{5} + 1204352 T^{6} + 14602768 T^{7} + 88529281 T^{8} \))(\( 1 - 16 T + 128 T^{2} - 1488 T^{3} + 17282 T^{4} - 144336 T^{5} + 1204352 T^{6} - 14602768 T^{7} + 88529281 T^{8} \))(\( 1 - 16 T + 128 T^{2} - 1488 T^{3} + 17282 T^{4} - 144336 T^{5} + 1204352 T^{6} - 14602768 T^{7} + 88529281 T^{8} \))(\( 1 + 16 T + 128 T^{2} + 1136 T^{3} + 10556 T^{4} + 116816 T^{5} + 1163136 T^{6} + 11493168 T^{7} + 113239174 T^{8} + 1114837296 T^{9} + 10943946624 T^{10} + 106614809168 T^{11} + 934515090236 T^{12} + 9755218531952 T^{13} + 106620416630912 T^{14} + 1292772551649808 T^{15} + 7837433594376961 T^{16} \))(\( 1 + 16 T + 128 T^{2} + 1136 T^{3} + 10556 T^{4} + 116816 T^{5} + 1163136 T^{6} + 11493168 T^{7} + 113239174 T^{8} + 1114837296 T^{9} + 10943946624 T^{10} + 106614809168 T^{11} + 934515090236 T^{12} + 9755218531952 T^{13} + 106620416630912 T^{14} + 1292772551649808 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 4 T + 8 T^{2} - 1852 T^{3} + 7856 T^{4} + 48156 T^{5} + 1459480 T^{6} - 10407580 T^{7} - 90680354 T^{8} - 1009535260 T^{9} + 13732247320 T^{10} + 43950680988 T^{11} + 695486031536 T^{12} - 15903754155964 T^{13} + 6663776039432 T^{14} - 323193137912452 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 4 T + 8 T^{2} - 1852 T^{3} + 7856 T^{4} + 48156 T^{5} + 1459480 T^{6} - 10407580 T^{7} - 90680354 T^{8} - 1009535260 T^{9} + 13732247320 T^{10} + 43950680988 T^{11} + 695486031536 T^{12} - 15903754155964 T^{13} + 6663776039432 T^{14} - 323193137912452 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 16 T + 128 T^{2} - 1136 T^{3} + 10556 T^{4} - 116816 T^{5} + 1163136 T^{6} - 11493168 T^{7} + 113239174 T^{8} - 1114837296 T^{9} + 10943946624 T^{10} - 106614809168 T^{11} + 934515090236 T^{12} - 9755218531952 T^{13} + 106620416630912 T^{14} - 1292772551649808 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 16 T + 128 T^{2} - 1136 T^{3} + 10556 T^{4} - 116816 T^{5} + 1163136 T^{6} - 11493168 T^{7} + 113239174 T^{8} - 1114837296 T^{9} + 10943946624 T^{10} - 106614809168 T^{11} + 934515090236 T^{12} - 9755218531952 T^{13} + 106620416630912 T^{14} - 1292772551649808 T^{15} + 7837433594376961 T^{16} \))
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