Properties

Label 320.6.a
Level 320
Weight 6
Character orbit a
Rep. character \(\chi_{320}(1,\cdot)\)
Character field \(\Q\)
Dimension 40
Newform subspaces 26
Sturm bound 288
Trace bound 9

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Defining parameters

Level: \( N \) = \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 320.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(288\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(320))\).

Total New Old
Modular forms 252 40 212
Cusp forms 228 40 188
Eisenstein series 24 0 24

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(11\)
\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(18\)
Minus space\(-\)\(22\)

Trace form

\( 40q + 3240q^{9} + O(q^{10}) \) \( 40q + 3240q^{9} + 464q^{13} - 8496q^{21} + 25000q^{25} - 8144q^{29} - 11344q^{33} + 25600q^{37} + 23216q^{41} + 96040q^{49} + 49456q^{53} + 61616q^{57} + 52224q^{61} + 22320q^{69} + 14896q^{77} + 215176q^{81} + 132400q^{85} + 6320q^{89} + 9312q^{93} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(320))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
320.6.a.a \(1\) \(51.323\) \(\Q\) None \(0\) \(-26\) \(25\) \(22\) \(-\) \(-\) \(q-26q^{3}+5^{2}q^{5}+22q^{7}+433q^{9}+\cdots\)
320.6.a.b \(1\) \(51.323\) \(\Q\) None \(0\) \(-24\) \(-25\) \(-172\) \(+\) \(+\) \(q-24q^{3}-5^{2}q^{5}-172q^{7}+333q^{9}+\cdots\)
320.6.a.c \(1\) \(51.323\) \(\Q\) None \(0\) \(-22\) \(25\) \(218\) \(+\) \(-\) \(q-22q^{3}+5^{2}q^{5}+218q^{7}+241q^{9}+\cdots\)
320.6.a.d \(1\) \(51.323\) \(\Q\) None \(0\) \(-18\) \(25\) \(-242\) \(-\) \(-\) \(q-18q^{3}+5^{2}q^{5}-242q^{7}+3^{4}q^{9}+\cdots\)
320.6.a.e \(1\) \(51.323\) \(\Q\) None \(0\) \(-8\) \(-25\) \(108\) \(-\) \(+\) \(q-8q^{3}-5^{2}q^{5}+108q^{7}-179q^{9}+\cdots\)
320.6.a.f \(1\) \(51.323\) \(\Q\) None \(0\) \(-6\) \(25\) \(-118\) \(+\) \(-\) \(q-6q^{3}+5^{2}q^{5}-118q^{7}-207q^{9}+\cdots\)
320.6.a.g \(1\) \(51.323\) \(\Q\) None \(0\) \(-4\) \(-25\) \(-192\) \(-\) \(+\) \(q-4q^{3}-5^{2}q^{5}-192q^{7}-227q^{9}+\cdots\)
320.6.a.h \(1\) \(51.323\) \(\Q\) None \(0\) \(-2\) \(25\) \(62\) \(-\) \(-\) \(q-2q^{3}+5^{2}q^{5}+62q^{7}-239q^{9}+\cdots\)
320.6.a.i \(1\) \(51.323\) \(\Q\) None \(0\) \(2\) \(25\) \(-62\) \(+\) \(-\) \(q+2q^{3}+5^{2}q^{5}-62q^{7}-239q^{9}+\cdots\)
320.6.a.j \(1\) \(51.323\) \(\Q\) None \(0\) \(4\) \(-25\) \(192\) \(+\) \(+\) \(q+4q^{3}-5^{2}q^{5}+192q^{7}-227q^{9}+\cdots\)
320.6.a.k \(1\) \(51.323\) \(\Q\) None \(0\) \(6\) \(25\) \(118\) \(-\) \(-\) \(q+6q^{3}+5^{2}q^{5}+118q^{7}-207q^{9}+\cdots\)
320.6.a.l \(1\) \(51.323\) \(\Q\) None \(0\) \(8\) \(-25\) \(-108\) \(+\) \(+\) \(q+8q^{3}-5^{2}q^{5}-108q^{7}-179q^{9}+\cdots\)
320.6.a.m \(1\) \(51.323\) \(\Q\) None \(0\) \(18\) \(25\) \(242\) \(+\) \(-\) \(q+18q^{3}+5^{2}q^{5}+242q^{7}+3^{4}q^{9}+\cdots\)
320.6.a.n \(1\) \(51.323\) \(\Q\) None \(0\) \(22\) \(25\) \(-218\) \(-\) \(-\) \(q+22q^{3}+5^{2}q^{5}-218q^{7}+241q^{9}+\cdots\)
320.6.a.o \(1\) \(51.323\) \(\Q\) None \(0\) \(24\) \(-25\) \(172\) \(-\) \(+\) \(q+24q^{3}-5^{2}q^{5}+172q^{7}+333q^{9}+\cdots\)
320.6.a.p \(1\) \(51.323\) \(\Q\) None \(0\) \(26\) \(25\) \(-22\) \(+\) \(-\) \(q+26q^{3}+5^{2}q^{5}-22q^{7}+433q^{9}+\cdots\)
320.6.a.q \(2\) \(51.323\) \(\Q(\sqrt{129}) \) None \(0\) \(-12\) \(-50\) \(-52\) \(-\) \(+\) \(q+(-6-\beta )q^{3}-5^{2}q^{5}+(-26+3\beta )q^{7}+\cdots\)
320.6.a.r \(2\) \(51.323\) \(\Q(\sqrt{70}) \) None \(0\) \(-8\) \(-50\) \(104\) \(+\) \(+\) \(q+(-4+\beta )q^{3}-5^{2}q^{5}+(52+\beta )q^{7}+\cdots\)
320.6.a.s \(2\) \(51.323\) \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(-50\) \(0\) \(-\) \(+\) \(q+\beta q^{3}-5^{2}q^{5}-7\beta q^{7}-203q^{9}+\cdots\)
320.6.a.t \(2\) \(51.323\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(50\) \(0\) \(-\) \(-\) \(q-3\beta q^{3}+5^{2}q^{5}+31\beta q^{7}-63q^{9}+\cdots\)
320.6.a.u \(2\) \(51.323\) \(\Q(\sqrt{85}) \) None \(0\) \(0\) \(50\) \(0\) \(-\) \(-\) \(q-\beta q^{3}+5^{2}q^{5}-3\beta q^{7}+97q^{9}+26\beta q^{11}+\cdots\)
320.6.a.v \(2\) \(51.323\) \(\Q(\sqrt{70}) \) None \(0\) \(8\) \(-50\) \(-104\) \(+\) \(+\) \(q+(4+\beta )q^{3}-5^{2}q^{5}+(-52+\beta )q^{7}+\cdots\)
320.6.a.w \(2\) \(51.323\) \(\Q(\sqrt{129}) \) None \(0\) \(12\) \(-50\) \(52\) \(+\) \(+\) \(q+(6+\beta )q^{3}-5^{2}q^{5}+(26-3\beta )q^{7}+\cdots\)
320.6.a.x \(3\) \(51.323\) 3.3.39180.1 None \(0\) \(-10\) \(75\) \(-6\) \(+\) \(-\) \(q+(-3-\beta _{1})q^{3}+5^{2}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
320.6.a.y \(3\) \(51.323\) 3.3.39180.1 None \(0\) \(10\) \(75\) \(6\) \(+\) \(-\) \(q+(3+\beta _{1})q^{3}+5^{2}q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
320.6.a.z \(4\) \(51.323\) 4.4.81998080.1 None \(0\) \(0\) \(-100\) \(0\) \(-\) \(+\) \(q-\beta _{1}q^{3}-5^{2}q^{5}+(6\beta _{1}-\beta _{2})q^{7}+(181+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(320))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(320)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 26 T + 243 T^{2} \))(\( 1 + 24 T + 243 T^{2} \))(\( 1 + 22 T + 243 T^{2} \))(\( 1 + 18 T + 243 T^{2} \))(\( 1 + 8 T + 243 T^{2} \))(\( 1 + 6 T + 243 T^{2} \))(\( 1 + 4 T + 243 T^{2} \))(\( 1 + 2 T + 243 T^{2} \))(\( 1 - 2 T + 243 T^{2} \))(\( 1 - 4 T + 243 T^{2} \))(\( 1 - 6 T + 243 T^{2} \))(\( 1 - 8 T + 243 T^{2} \))(\( 1 - 18 T + 243 T^{2} \))(\( 1 - 22 T + 243 T^{2} \))(\( 1 - 24 T + 243 T^{2} \))(\( 1 - 26 T + 243 T^{2} \))(\( 1 + 12 T + 6 T^{2} + 2916 T^{3} + 59049 T^{4} \))(\( 1 + 8 T + 222 T^{2} + 1944 T^{3} + 59049 T^{4} \))(\( 1 + 446 T^{2} + 59049 T^{4} \))(\( 1 + 306 T^{2} + 59049 T^{4} \))(\( 1 + 146 T^{2} + 59049 T^{4} \))(\( 1 - 8 T + 222 T^{2} - 1944 T^{3} + 59049 T^{4} \))(\( 1 - 12 T + 6 T^{2} - 2916 T^{3} + 59049 T^{4} \))(\( 1 + 10 T + 181 T^{2} + 5268 T^{3} + 43983 T^{4} + 590490 T^{5} + 14348907 T^{6} \))(\( 1 - 10 T + 181 T^{2} - 5268 T^{3} + 43983 T^{4} - 590490 T^{5} + 14348907 T^{6} \))(\( 1 + 124 T^{2} + 25686 T^{4} + 7322076 T^{6} + 3486784401 T^{8} \))
$5$ (\( 1 - 25 T \))(\( 1 + 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 + 25 T \))(\( 1 - 25 T \))(\( 1 + 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 + 25 T \))(\( 1 - 25 T \))(\( 1 + 25 T \))(\( 1 - 25 T \))(\( 1 - 25 T \))(\( 1 + 25 T \))(\( 1 - 25 T \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 - 25 T )^{2} \))(\( ( 1 - 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 + 25 T )^{2} \))(\( ( 1 - 25 T )^{3} \))(\( ( 1 - 25 T )^{3} \))(\( ( 1 + 25 T )^{4} \))
$7$ (\( 1 - 22 T + 16807 T^{2} \))(\( 1 + 172 T + 16807 T^{2} \))(\( 1 - 218 T + 16807 T^{2} \))(\( 1 + 242 T + 16807 T^{2} \))(\( 1 - 108 T + 16807 T^{2} \))(\( 1 + 118 T + 16807 T^{2} \))(\( 1 + 192 T + 16807 T^{2} \))(\( 1 - 62 T + 16807 T^{2} \))(\( 1 + 62 T + 16807 T^{2} \))(\( 1 - 192 T + 16807 T^{2} \))(\( 1 - 118 T + 16807 T^{2} \))(\( 1 + 108 T + 16807 T^{2} \))(\( 1 - 242 T + 16807 T^{2} \))(\( 1 + 218 T + 16807 T^{2} \))(\( 1 - 172 T + 16807 T^{2} \))(\( 1 + 22 T + 16807 T^{2} \))(\( 1 + 52 T + 29646 T^{2} + 873964 T^{3} + 282475249 T^{4} \))(\( 1 - 104 T + 36038 T^{2} - 1747928 T^{3} + 282475249 T^{4} \))(\( 1 + 31654 T^{2} + 282475249 T^{4} \))(\( 1 + 14394 T^{2} + 282475249 T^{4} \))(\( 1 + 30554 T^{2} + 282475249 T^{4} \))(\( 1 + 104 T + 36038 T^{2} + 1747928 T^{3} + 282475249 T^{4} \))(\( 1 - 52 T + 29646 T^{2} - 873964 T^{3} + 282475249 T^{4} \))(\( 1 + 6 T + 27153 T^{2} + 1137532 T^{3} + 456360471 T^{4} + 1694851494 T^{5} + 4747561509943 T^{6} \))(\( 1 - 6 T + 27153 T^{2} - 1137532 T^{3} + 456360471 T^{4} - 1694851494 T^{5} + 4747561509943 T^{6} \))(\( 1 - 27060 T^{2} + 497649542 T^{4} - 7643780237940 T^{6} + 79792266297612001 T^{8} \))
$11$ (\( 1 + 768 T + 161051 T^{2} \))(\( 1 + 132 T + 161051 T^{2} \))(\( 1 - 480 T + 161051 T^{2} \))(\( 1 - 656 T + 161051 T^{2} \))(\( 1 + 604 T + 161051 T^{2} \))(\( 1 + 192 T + 161051 T^{2} \))(\( 1 + 148 T + 161051 T^{2} \))(\( 1 + 144 T + 161051 T^{2} \))(\( 1 - 144 T + 161051 T^{2} \))(\( 1 - 148 T + 161051 T^{2} \))(\( 1 - 192 T + 161051 T^{2} \))(\( 1 - 604 T + 161051 T^{2} \))(\( 1 + 656 T + 161051 T^{2} \))(\( 1 + 480 T + 161051 T^{2} \))(\( 1 - 132 T + 161051 T^{2} \))(\( 1 - 768 T + 161051 T^{2} \))(\( 1 - 560 T + 381926 T^{2} - 90188560 T^{3} + 25937424601 T^{4} \))(\( 1 + 320 T + 319702 T^{2} + 51536320 T^{3} + 25937424601 T^{4} \))(\( 1 - 197738 T^{2} + 25937424601 T^{4} \))(\( 1 + 254822 T^{2} + 25937424601 T^{4} \))(\( 1 + 92262 T^{2} + 25937424601 T^{4} \))(\( 1 - 320 T + 319702 T^{2} - 51536320 T^{3} + 25937424601 T^{4} \))(\( 1 + 560 T + 381926 T^{2} + 90188560 T^{3} + 25937424601 T^{4} \))(\( 1 - 396 T + 327873 T^{2} - 67617992 T^{3} + 52804274523 T^{4} - 10271220141996 T^{5} + 4177248169415651 T^{6} \))(\( 1 + 396 T + 327873 T^{2} + 67617992 T^{3} + 52804274523 T^{4} + 10271220141996 T^{5} + 4177248169415651 T^{6} \))(\( 1 + 382252 T^{2} + 87516901782 T^{4} + 9914632428581452 T^{6} + \)\(67\!\cdots\!01\)\( T^{8} \))
$13$ (\( 1 - 46 T + 371293 T^{2} \))(\( 1 - 946 T + 371293 T^{2} \))(\( 1 - 622 T + 371293 T^{2} \))(\( 1 - 206 T + 371293 T^{2} \))(\( 1 - 306 T + 371293 T^{2} \))(\( 1 + 1106 T + 371293 T^{2} \))(\( 1 + 286 T + 371293 T^{2} \))(\( 1 - 654 T + 371293 T^{2} \))(\( 1 - 654 T + 371293 T^{2} \))(\( 1 + 286 T + 371293 T^{2} \))(\( 1 + 1106 T + 371293 T^{2} \))(\( 1 - 306 T + 371293 T^{2} \))(\( 1 - 206 T + 371293 T^{2} \))(\( 1 - 622 T + 371293 T^{2} \))(\( 1 - 946 T + 371293 T^{2} \))(\( 1 - 46 T + 371293 T^{2} \))(\( 1 + 1388 T + 1149918 T^{2} + 515354684 T^{3} + 137858491849 T^{4} \))(\( 1 - 100 T + 297086 T^{2} - 37129300 T^{3} + 137858491849 T^{4} \))(\( ( 1 - 146 T + 371293 T^{2} )^{2} \))(\( ( 1 + 154 T + 371293 T^{2} )^{2} \))(\( ( 1 + 506 T + 371293 T^{2} )^{2} \))(\( 1 - 100 T + 297086 T^{2} - 37129300 T^{3} + 137858491849 T^{4} \))(\( 1 + 1388 T + 1149918 T^{2} + 515354684 T^{3} + 137858491849 T^{4} \))(\( 1 - 354 T + 845379 T^{2} - 291738444 T^{3} + 313883305047 T^{4} - 48801906114546 T^{5} + 51185893014090757 T^{6} \))(\( 1 - 354 T + 845379 T^{2} - 291738444 T^{3} + 313883305047 T^{4} - 48801906114546 T^{5} + 51185893014090757 T^{6} \))(\( ( 1 - 292 T - 102402 T^{2} - 108417556 T^{3} + 137858491849 T^{4} )^{2} \))
$17$ (\( 1 - 378 T + 1419857 T^{2} \))(\( 1 + 222 T + 1419857 T^{2} \))(\( 1 - 186 T + 1419857 T^{2} \))(\( 1 - 1690 T + 1419857 T^{2} \))(\( 1 - 930 T + 1419857 T^{2} \))(\( 1 - 762 T + 1419857 T^{2} \))(\( 1 + 1678 T + 1419857 T^{2} \))(\( 1 + 1190 T + 1419857 T^{2} \))(\( 1 + 1190 T + 1419857 T^{2} \))(\( 1 + 1678 T + 1419857 T^{2} \))(\( 1 - 762 T + 1419857 T^{2} \))(\( 1 - 930 T + 1419857 T^{2} \))(\( 1 - 1690 T + 1419857 T^{2} \))(\( 1 - 186 T + 1419857 T^{2} \))(\( 1 + 222 T + 1419857 T^{2} \))(\( 1 - 378 T + 1419857 T^{2} \))(\( 1 - 148 T - 795706 T^{2} - 210138836 T^{3} + 2015993900449 T^{4} \))(\( 1 - 580 T + 2475814 T^{2} - 823517060 T^{3} + 2015993900449 T^{4} \))(\( ( 1 + 702 T + 1419857 T^{2} )^{2} \))(\( ( 1 - 178 T + 1419857 T^{2} )^{2} \))(\( ( 1 + 1838 T + 1419857 T^{2} )^{2} \))(\( 1 - 580 T + 2475814 T^{2} - 823517060 T^{3} + 2015993900449 T^{4} \))(\( 1 - 148 T - 795706 T^{2} - 210138836 T^{3} + 2015993900449 T^{4} \))(\( 1 - 1158 T + 1914111 T^{2} - 544550612 T^{3} + 2717763902127 T^{4} - 2334520936719942 T^{5} + 2862423051509815793 T^{6} \))(\( 1 - 1158 T + 1914111 T^{2} - 544550612 T^{3} + 2717763902127 T^{4} - 2334520936719942 T^{5} + 2862423051509815793 T^{6} \))(\( ( 1 + 380 T + 2009510 T^{2} + 539545660 T^{3} + 2015993900449 T^{4} )^{2} \))
$19$ (\( 1 - 1100 T + 2476099 T^{2} \))(\( 1 + 500 T + 2476099 T^{2} \))(\( 1 - 1204 T + 2476099 T^{2} \))(\( 1 + 1364 T + 2476099 T^{2} \))(\( 1 + 1324 T + 2476099 T^{2} \))(\( 1 - 2740 T + 2476099 T^{2} \))(\( 1 - 1060 T + 2476099 T^{2} \))(\( 1 - 556 T + 2476099 T^{2} \))(\( 1 + 556 T + 2476099 T^{2} \))(\( 1 + 1060 T + 2476099 T^{2} \))(\( 1 + 2740 T + 2476099 T^{2} \))(\( 1 - 1324 T + 2476099 T^{2} \))(\( 1 - 1364 T + 2476099 T^{2} \))(\( 1 + 1204 T + 2476099 T^{2} \))(\( 1 - 500 T + 2476099 T^{2} \))(\( 1 + 1100 T + 2476099 T^{2} \))(\( 1 + 1000 T + 4533462 T^{2} + 2476099000 T^{3} + 6131066257801 T^{4} \))(\( 1 + 720 T + 4633798 T^{2} + 1782791280 T^{3} + 6131066257801 T^{4} \))(\( 1 - 2512762 T^{2} + 6131066257801 T^{4} \))(\( 1 + 4019078 T^{2} + 6131066257801 T^{4} \))(\( 1 + 687238 T^{2} + 6131066257801 T^{4} \))(\( 1 - 720 T + 4633798 T^{2} - 1782791280 T^{3} + 6131066257801 T^{4} \))(\( 1 - 1000 T + 4533462 T^{2} - 2476099000 T^{3} + 6131066257801 T^{4} \))(\( 1 + 3192 T + 9330057 T^{2} + 15933739216 T^{3} + 23102144807643 T^{4} + 19570363494900792 T^{5} + 15181127029874798299 T^{6} \))(\( 1 - 3192 T + 9330057 T^{2} - 15933739216 T^{3} + 23102144807643 T^{4} - 19570363494900792 T^{5} + 15181127029874798299 T^{6} \))(\( 1 + 1633036 T^{2} + 154661897526 T^{4} + 10012251917374313836 T^{6} + \)\(37\!\cdots\!01\)\( T^{8} \))
$23$ (\( 1 - 1986 T + 6436343 T^{2} \))(\( 1 - 3564 T + 6436343 T^{2} \))(\( 1 + 3186 T + 6436343 T^{2} \))(\( 1 + 2198 T + 6436343 T^{2} \))(\( 1 - 852 T + 6436343 T^{2} \))(\( 1 - 1566 T + 6436343 T^{2} \))(\( 1 + 2976 T + 6436343 T^{2} \))(\( 1 + 2182 T + 6436343 T^{2} \))(\( 1 - 2182 T + 6436343 T^{2} \))(\( 1 - 2976 T + 6436343 T^{2} \))(\( 1 + 1566 T + 6436343 T^{2} \))(\( 1 + 852 T + 6436343 T^{2} \))(\( 1 - 2198 T + 6436343 T^{2} \))(\( 1 - 3186 T + 6436343 T^{2} \))(\( 1 + 3564 T + 6436343 T^{2} \))(\( 1 + 1986 T + 6436343 T^{2} \))(\( 1 - 2452 T + 6569198 T^{2} - 15781913036 T^{3} + 41426511213649 T^{4} \))(\( 1 - 1688 T + 10950502 T^{2} - 10864546984 T^{3} + 41426511213649 T^{4} \))(\( 1 - 3871674 T^{2} + 41426511213649 T^{4} \))(\( 1 + 5934266 T^{2} + 41426511213649 T^{4} \))(\( 1 + 9265626 T^{2} + 41426511213649 T^{4} \))(\( 1 + 1688 T + 10950502 T^{2} + 10864546984 T^{3} + 41426511213649 T^{4} \))(\( 1 + 2452 T + 6569198 T^{2} + 15781913036 T^{3} + 41426511213649 T^{4} \))(\( 1 - 6126 T + 29722593 T^{2} - 84141222540 T^{3} + 191304803397399 T^{4} - 253778807694813774 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 + 6126 T + 29722593 T^{2} + 84141222540 T^{3} + 191304803397399 T^{4} + 253778807694813774 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 + 25651084 T^{2} + 247347299659206 T^{4} + \)\(10\!\cdots\!16\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} \))
$29$ (\( 1 - 5610 T + 20511149 T^{2} \))(\( 1 + 2190 T + 20511149 T^{2} \))(\( 1 + 5526 T + 20511149 T^{2} \))(\( 1 - 2218 T + 20511149 T^{2} \))(\( 1 + 5902 T + 20511149 T^{2} \))(\( 1 + 5910 T + 20511149 T^{2} \))(\( 1 - 3410 T + 20511149 T^{2} \))(\( 1 - 1578 T + 20511149 T^{2} \))(\( 1 - 1578 T + 20511149 T^{2} \))(\( 1 - 3410 T + 20511149 T^{2} \))(\( 1 + 5910 T + 20511149 T^{2} \))(\( 1 + 5902 T + 20511149 T^{2} \))(\( 1 - 2218 T + 20511149 T^{2} \))(\( 1 + 5526 T + 20511149 T^{2} \))(\( 1 + 2190 T + 20511149 T^{2} \))(\( 1 - 5610 T + 20511149 T^{2} \))(\( 1 + 1340 T - 8758306 T^{2} + 27484939660 T^{3} + 420707233300201 T^{4} \))(\( 1 + 108 T + 39233214 T^{2} + 2215204092 T^{3} + 420707233300201 T^{4} \))(\( ( 1 - 4010 T + 20511149 T^{2} )^{2} \))(\( ( 1 + 4110 T + 20511149 T^{2} )^{2} \))(\( ( 1 - 4530 T + 20511149 T^{2} )^{2} \))(\( 1 + 108 T + 39233214 T^{2} + 2215204092 T^{3} + 420707233300201 T^{4} \))(\( 1 + 1340 T - 8758306 T^{2} + 27484939660 T^{3} + 420707233300201 T^{4} \))(\( 1 + 426 T - 939693 T^{2} - 141773503364 T^{3} - 19274183137257 T^{4} + 179221281385885626 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( 1 + 426 T - 939693 T^{2} - 141773503364 T^{3} - 19274183137257 T^{4} + 179221281385885626 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( ( 1 - 84 T + 9837118 T^{2} - 1722936516 T^{3} + 420707233300201 T^{4} )^{2} \))
$31$ (\( 1 - 3988 T + 28629151 T^{2} \))(\( 1 - 2312 T + 28629151 T^{2} \))(\( 1 - 9356 T + 28629151 T^{2} \))(\( 1 - 1700 T + 28629151 T^{2} \))(\( 1 - 3320 T + 28629151 T^{2} \))(\( 1 + 6868 T + 28629151 T^{2} \))(\( 1 - 2448 T + 28629151 T^{2} \))(\( 1 + 9660 T + 28629151 T^{2} \))(\( 1 - 9660 T + 28629151 T^{2} \))(\( 1 + 2448 T + 28629151 T^{2} \))(\( 1 - 6868 T + 28629151 T^{2} \))(\( 1 + 3320 T + 28629151 T^{2} \))(\( 1 + 1700 T + 28629151 T^{2} \))(\( 1 + 9356 T + 28629151 T^{2} \))(\( 1 + 2312 T + 28629151 T^{2} \))(\( 1 + 3988 T + 28629151 T^{2} \))(\( 1 - 2248 T + 57017022 T^{2} - 64358331448 T^{3} + 819628286980801 T^{4} \))(\( 1 - 9840 T + 76732702 T^{2} - 281710845840 T^{3} + 819628286980801 T^{4} \))(\( 1 + 36406942 T^{2} + 819628286980801 T^{4} \))(\( 1 + 47289582 T^{2} + 819628286980801 T^{4} \))(\( 1 + 43928942 T^{2} + 819628286980801 T^{4} \))(\( 1 + 9840 T + 76732702 T^{2} + 281710845840 T^{3} + 819628286980801 T^{4} \))(\( 1 + 2248 T + 57017022 T^{2} + 64358331448 T^{3} + 819628286980801 T^{4} \))(\( 1 - 3276 T + 2292813 T^{2} + 41639420248 T^{3} + 65641289591763 T^{4} - 2685102268149104076 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( 1 + 3276 T + 2292813 T^{2} - 41639420248 T^{3} + 65641289591763 T^{4} + 2685102268149104076 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( 1 + 24283452 T^{2} + 1637830022018822 T^{4} + \)\(19\!\cdots\!52\)\( T^{6} + \)\(67\!\cdots\!01\)\( T^{8} \))
$37$ (\( 1 - 142 T + 69343957 T^{2} \))(\( 1 - 11242 T + 69343957 T^{2} \))(\( 1 + 5618 T + 69343957 T^{2} \))(\( 1 - 846 T + 69343957 T^{2} \))(\( 1 + 10774 T + 69343957 T^{2} \))(\( 1 - 5518 T + 69343957 T^{2} \))(\( 1 + 182 T + 69343957 T^{2} \))(\( 1 - 3534 T + 69343957 T^{2} \))(\( 1 - 3534 T + 69343957 T^{2} \))(\( 1 + 182 T + 69343957 T^{2} \))(\( 1 - 5518 T + 69343957 T^{2} \))(\( 1 + 10774 T + 69343957 T^{2} \))(\( 1 - 846 T + 69343957 T^{2} \))(\( 1 + 5618 T + 69343957 T^{2} \))(\( 1 - 11242 T + 69343957 T^{2} \))(\( 1 - 142 T + 69343957 T^{2} \))(\( 1 - 5940 T + 123434318 T^{2} - 411903104580 T^{3} + 4808584372417849 T^{4} \))(\( 1 + 6540 T + 61572814 T^{2} + 453509478780 T^{3} + 4808584372417849 T^{4} \))(\( ( 1 - 14778 T + 69343957 T^{2} )^{2} \))(\( ( 1 + 7442 T + 69343957 T^{2} )^{2} \))(\( ( 1 + 338 T + 69343957 T^{2} )^{2} \))(\( 1 + 6540 T + 61572814 T^{2} + 453509478780 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 5940 T + 123434318 T^{2} - 411903104580 T^{3} + 4808584372417849 T^{4} \))(\( 1 - 11562 T + 90623691 T^{2} - 525372493468 T^{3} + 6284205331885287 T^{4} - 55596852513895170138 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( 1 - 11562 T + 90623691 T^{2} - 525372493468 T^{3} + 6284205331885287 T^{4} - 55596852513895170138 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( ( 1 + 9868 T + 159567054 T^{2} + 684286167676 T^{3} + 4808584372417849 T^{4} )^{2} \))
$41$ (\( 1 - 1542 T + 115856201 T^{2} \))(\( 1 - 1242 T + 115856201 T^{2} \))(\( 1 + 14394 T + 115856201 T^{2} \))(\( 1 + 1818 T + 115856201 T^{2} \))(\( 1 + 17958 T + 115856201 T^{2} \))(\( 1 + 378 T + 115856201 T^{2} \))(\( 1 + 9398 T + 115856201 T^{2} \))(\( 1 - 7462 T + 115856201 T^{2} \))(\( 1 - 7462 T + 115856201 T^{2} \))(\( 1 + 9398 T + 115856201 T^{2} \))(\( 1 + 378 T + 115856201 T^{2} \))(\( 1 + 17958 T + 115856201 T^{2} \))(\( 1 + 1818 T + 115856201 T^{2} \))(\( 1 + 14394 T + 115856201 T^{2} \))(\( 1 - 1242 T + 115856201 T^{2} \))(\( 1 - 1542 T + 115856201 T^{2} \))(\( 1 - 23076 T + 352280470 T^{2} - 2673497694276 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 10620 T + 77106582 T^{2} + 1230392854620 T^{3} + 13422659310152401 T^{4} \))(\( ( 1 + 4350 T + 115856201 T^{2} )^{2} \))(\( ( 1 - 7270 T + 115856201 T^{2} )^{2} \))(\( ( 1 + 6330 T + 115856201 T^{2} )^{2} \))(\( 1 + 10620 T + 77106582 T^{2} + 1230392854620 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 23076 T + 352280470 T^{2} - 2673497694276 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 12450 T + 384843783 T^{2} - 2886023186300 T^{3} + 44586538676848383 T^{4} - \)\(16\!\cdots\!50\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( 1 - 12450 T + 384843783 T^{2} - 2886023186300 T^{3} + 44586538676848383 T^{4} - \)\(16\!\cdots\!50\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( ( 1 - 23812 T + 331016342 T^{2} - 2758767858212 T^{3} + 13422659310152401 T^{4} )^{2} \))
$43$ (\( 1 + 5026 T + 147008443 T^{2} \))(\( 1 + 20624 T + 147008443 T^{2} \))(\( 1 - 370 T + 147008443 T^{2} \))(\( 1 - 10534 T + 147008443 T^{2} \))(\( 1 - 9264 T + 147008443 T^{2} \))(\( 1 - 2434 T + 147008443 T^{2} \))(\( 1 + 1244 T + 147008443 T^{2} \))(\( 1 + 7114 T + 147008443 T^{2} \))(\( 1 - 7114 T + 147008443 T^{2} \))(\( 1 - 1244 T + 147008443 T^{2} \))(\( 1 + 2434 T + 147008443 T^{2} \))(\( 1 + 9264 T + 147008443 T^{2} \))(\( 1 + 10534 T + 147008443 T^{2} \))(\( 1 + 370 T + 147008443 T^{2} \))(\( 1 - 20624 T + 147008443 T^{2} \))(\( 1 - 5026 T + 147008443 T^{2} \))(\( 1 - 17684 T + 312898614 T^{2} - 2599697306012 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 25672 T + 364912302 T^{2} + 3774000748696 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 139567886 T^{2} + 21611482313284249 T^{4} \))(\( 1 - 26783614 T^{2} + 21611482313284249 T^{4} \))(\( 1 - 35859614 T^{2} + 21611482313284249 T^{4} \))(\( 1 - 25672 T + 364912302 T^{2} - 3774000748696 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 17684 T + 312898614 T^{2} + 2599697306012 T^{3} + 21611482313284249 T^{4} \))(\( 1 + 26346 T + 640605069 T^{2} + 8098987233524 T^{3} + 94174353771597567 T^{4} + \)\(56\!\cdots\!54\)\( T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( 1 - 26346 T + 640605069 T^{2} - 8098987233524 T^{3} + 94174353771597567 T^{4} - \)\(56\!\cdots\!54\)\( T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( 1 + 385757980 T^{2} + 71059469286049782 T^{4} + \)\(83\!\cdots\!20\)\( T^{6} + \)\(46\!\cdots\!01\)\( T^{8} \))
$47$ (\( 1 + 24738 T + 229345007 T^{2} \))(\( 1 - 6588 T + 229345007 T^{2} \))(\( 1 - 16146 T + 229345007 T^{2} \))(\( 1 + 12074 T + 229345007 T^{2} \))(\( 1 - 9796 T + 229345007 T^{2} \))(\( 1 - 13122 T + 229345007 T^{2} \))(\( 1 - 12088 T + 229345007 T^{2} \))(\( 1 - 28294 T + 229345007 T^{2} \))(\( 1 + 28294 T + 229345007 T^{2} \))(\( 1 + 12088 T + 229345007 T^{2} \))(\( 1 + 13122 T + 229345007 T^{2} \))(\( 1 + 9796 T + 229345007 T^{2} \))(\( 1 - 12074 T + 229345007 T^{2} \))(\( 1 + 16146 T + 229345007 T^{2} \))(\( 1 + 6588 T + 229345007 T^{2} \))(\( 1 - 24738 T + 229345007 T^{2} \))(\( 1 - 2908 T + 56660030 T^{2} - 666935280356 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 28296 T + 617782998 T^{2} - 6489546318072 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 422513974 T^{2} + 52599132235830049 T^{4} \))(\( 1 + 403777034 T^{2} + 52599132235830049 T^{4} \))(\( 1 + 442383274 T^{2} + 52599132235830049 T^{4} \))(\( 1 + 28296 T + 617782998 T^{2} + 6489546318072 T^{3} + 52599132235830049 T^{4} \))(\( 1 + 2908 T + 56660030 T^{2} + 666935280356 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 36762 T + 1119958377 T^{2} - 18490559326820 T^{3} + 256856861812773639 T^{4} - \)\(19\!\cdots\!38\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 + 36762 T + 1119958377 T^{2} + 18490559326820 T^{3} + 256856861812773639 T^{4} + \)\(19\!\cdots\!38\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 + 353765740 T^{2} + 66158288717340582 T^{4} + \)\(18\!\cdots\!60\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} \))
$53$ (\( 1 - 14166 T + 418195493 T^{2} \))(\( 1 - 21066 T + 418195493 T^{2} \))(\( 1 - 4374 T + 418195493 T^{2} \))(\( 1 + 32586 T + 418195493 T^{2} \))(\( 1 - 31434 T + 418195493 T^{2} \))(\( 1 - 9174 T + 418195493 T^{2} \))(\( 1 + 23846 T + 418195493 T^{2} \))(\( 1 - 13046 T + 418195493 T^{2} \))(\( 1 - 13046 T + 418195493 T^{2} \))(\( 1 + 23846 T + 418195493 T^{2} \))(\( 1 - 9174 T + 418195493 T^{2} \))(\( 1 - 31434 T + 418195493 T^{2} \))(\( 1 + 32586 T + 418195493 T^{2} \))(\( 1 - 4374 T + 418195493 T^{2} \))(\( 1 - 21066 T + 418195493 T^{2} \))(\( 1 - 14166 T + 418195493 T^{2} \))(\( 1 - 5412 T + 693247822 T^{2} - 2263274008116 T^{3} + 174887470365513049 T^{4} \))(\( 1 + 31340 T + 755347886 T^{2} + 13106246750620 T^{3} + 174887470365513049 T^{4} \))(\( ( 1 - 18154 T + 418195493 T^{2} )^{2} \))(\( ( 1 + 32226 T + 418195493 T^{2} )^{2} \))(\( ( 1 - 15486 T + 418195493 T^{2} )^{2} \))(\( 1 + 31340 T + 755347886 T^{2} + 13106246750620 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 5412 T + 693247822 T^{2} - 2263274008116 T^{3} + 174887470365513049 T^{4} \))(\( 1 - 21162 T + 395789499 T^{2} + 881498066468 T^{3} + 165517384658528007 T^{4} - \)\(37\!\cdots\!38\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( 1 - 21162 T + 395789499 T^{2} + 881498066468 T^{3} + 165517384658528007 T^{4} - \)\(37\!\cdots\!38\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( ( 1 + 8748 T + 833865262 T^{2} + 3658374172764 T^{3} + 174887470365513049 T^{4} )^{2} \))
$59$ (\( 1 - 28380 T + 714924299 T^{2} \))(\( 1 + 7980 T + 714924299 T^{2} \))(\( 1 - 11748 T + 714924299 T^{2} \))(\( 1 - 8668 T + 714924299 T^{2} \))(\( 1 - 33228 T + 714924299 T^{2} \))(\( 1 - 34980 T + 714924299 T^{2} \))(\( 1 + 20020 T + 714924299 T^{2} \))(\( 1 + 37092 T + 714924299 T^{2} \))(\( 1 - 37092 T + 714924299 T^{2} \))(\( 1 - 20020 T + 714924299 T^{2} \))(\( 1 + 34980 T + 714924299 T^{2} \))(\( 1 + 33228 T + 714924299 T^{2} \))(\( 1 + 8668 T + 714924299 T^{2} \))(\( 1 + 11748 T + 714924299 T^{2} \))(\( 1 - 7980 T + 714924299 T^{2} \))(\( 1 + 28380 T + 714924299 T^{2} \))(\( 1 - 62584 T + 2277965606 T^{2} - 44742822328616 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 30800 T + 1666896598 T^{2} + 22019668409200 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 1041470358 T^{2} + 511116753300641401 T^{4} \))(\( 1 + 270997718 T^{2} + 511116753300641401 T^{4} \))(\( 1 + 1376531158 T^{2} + 511116753300641401 T^{4} \))(\( 1 - 30800 T + 1666896598 T^{2} - 22019668409200 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 62584 T + 2277965606 T^{2} + 44742822328616 T^{3} + 511116753300641401 T^{4} \))(\( 1 + 35040 T + 1757220897 T^{2} + 50989349593920 T^{3} + 1256279917975876203 T^{4} + \)\(17\!\cdots\!40\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( 1 - 35040 T + 1757220897 T^{2} - 50989349593920 T^{3} + 1256279917975876203 T^{4} - \)\(17\!\cdots\!40\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( 1 + 488747308 T^{2} + 896846029819225302 T^{4} + \)\(24\!\cdots\!08\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} \))
$61$ (\( 1 + 5522 T + 844596301 T^{2} \))(\( 1 + 16622 T + 844596301 T^{2} \))(\( 1 + 13202 T + 844596301 T^{2} \))(\( 1 - 34670 T + 844596301 T^{2} \))(\( 1 - 40210 T + 844596301 T^{2} \))(\( 1 - 9838 T + 844596301 T^{2} \))(\( 1 + 32302 T + 844596301 T^{2} \))(\( 1 + 39570 T + 844596301 T^{2} \))(\( 1 + 39570 T + 844596301 T^{2} \))(\( 1 + 32302 T + 844596301 T^{2} \))(\( 1 - 9838 T + 844596301 T^{2} \))(\( 1 - 40210 T + 844596301 T^{2} \))(\( 1 - 34670 T + 844596301 T^{2} \))(\( 1 + 13202 T + 844596301 T^{2} \))(\( 1 + 16622 T + 844596301 T^{2} \))(\( 1 + 5522 T + 844596301 T^{2} \))(\( 1 + 14108 T + 1110042462 T^{2} + 11915564614508 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 24540 T + 1447225822 T^{2} + 20726393226540 T^{3} + 713342911662882601 T^{4} \))(\( ( 1 - 42130 T + 844596301 T^{2} )^{2} \))(\( ( 1 + 26770 T + 844596301 T^{2} )^{2} \))(\( ( 1 - 16750 T + 844596301 T^{2} )^{2} \))(\( 1 + 24540 T + 1447225822 T^{2} + 20726393226540 T^{3} + 713342911662882601 T^{4} \))(\( 1 + 14108 T + 1110042462 T^{2} + 11915564614508 T^{3} + 713342911662882601 T^{4} \))(\( 1 - 24138 T + 393086643 T^{2} + 6904061162564 T^{3} + 331999524650307543 T^{4} - \)\(17\!\cdots\!38\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( 1 - 24138 T + 393086643 T^{2} + 6904061162564 T^{3} + 331999524650307543 T^{4} - \)\(17\!\cdots\!38\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( ( 1 - 31012 T + 1250446302 T^{2} - 26192620486612 T^{3} + 713342911662882601 T^{4} )^{2} \))
$67$ (\( 1 + 24742 T + 1350125107 T^{2} \))(\( 1 + 1808 T + 1350125107 T^{2} \))(\( 1 - 11542 T + 1350125107 T^{2} \))(\( 1 + 47566 T + 1350125107 T^{2} \))(\( 1 - 58864 T + 1350125107 T^{2} \))(\( 1 + 33722 T + 1350125107 T^{2} \))(\( 1 - 60972 T + 1350125107 T^{2} \))(\( 1 + 56734 T + 1350125107 T^{2} \))(\( 1 - 56734 T + 1350125107 T^{2} \))(\( 1 + 60972 T + 1350125107 T^{2} \))(\( 1 - 33722 T + 1350125107 T^{2} \))(\( 1 + 58864 T + 1350125107 T^{2} \))(\( 1 - 47566 T + 1350125107 T^{2} \))(\( 1 + 11542 T + 1350125107 T^{2} \))(\( 1 - 1808 T + 1350125107 T^{2} \))(\( 1 - 24742 T + 1350125107 T^{2} \))(\( 1 + 85412 T + 4371910566 T^{2} + 115316885639084 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 34584 T + 2930656478 T^{2} + 46692726700488 T^{3} + 1822837804551761449 T^{4} \))(\( 1 + 2438310974 T^{2} + 1822837804551761449 T^{4} \))(\( 1 + 219594834 T^{2} + 1822837804551761449 T^{4} \))(\( 1 + 2513562674 T^{2} + 1822837804551761449 T^{4} \))(\( 1 - 34584 T + 2930656478 T^{2} - 46692726700488 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 85412 T + 4371910566 T^{2} - 115316885639084 T^{3} + 1822837804551761449 T^{4} \))(\( 1 - 9570 T + 659335509 T^{2} - 83080838420484 T^{3} + 890185424637524463 T^{4} - \)\(17\!\cdots\!30\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( 1 + 9570 T + 659335509 T^{2} + 83080838420484 T^{3} + 890185424637524463 T^{4} + \)\(17\!\cdots\!30\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( 1 + 3336863100 T^{2} + 6361754088145172822 T^{4} + \)\(60\!\cdots\!00\)\( T^{6} + \)\(33\!\cdots\!01\)\( T^{8} \))
$71$ (\( 1 + 42372 T + 1804229351 T^{2} \))(\( 1 + 24528 T + 1804229351 T^{2} \))(\( 1 + 29532 T + 1804229351 T^{2} \))(\( 1 + 948 T + 1804229351 T^{2} \))(\( 1 - 55312 T + 1804229351 T^{2} \))(\( 1 - 70212 T + 1804229351 T^{2} \))(\( 1 - 32648 T + 1804229351 T^{2} \))(\( 1 + 45588 T + 1804229351 T^{2} \))(\( 1 - 45588 T + 1804229351 T^{2} \))(\( 1 + 32648 T + 1804229351 T^{2} \))(\( 1 + 70212 T + 1804229351 T^{2} \))(\( 1 + 55312 T + 1804229351 T^{2} \))(\( 1 - 948 T + 1804229351 T^{2} \))(\( 1 - 29532 T + 1804229351 T^{2} \))(\( 1 - 24528 T + 1804229351 T^{2} \))(\( 1 - 42372 T + 1804229351 T^{2} \))(\( 1 + 47208 T + 4011779662 T^{2} + 85174059202008 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 12400 T + 1143670702 T^{2} + 22372443952400 T^{3} + 3255243551009881201 T^{4} \))(\( 1 + 1542914862 T^{2} + 3255243551009881201 T^{4} \))(\( 1 + 681226622 T^{2} + 3255243551009881201 T^{4} \))(\( 1 + 1737195262 T^{2} + 3255243551009881201 T^{4} \))(\( 1 - 12400 T + 1143670702 T^{2} - 22372443952400 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 47208 T + 4011779662 T^{2} - 85174059202008 T^{3} + 3255243551009881201 T^{4} \))(\( 1 - 88092 T + 7289446053 T^{2} - 329541325840584 T^{3} + 13151832521353701603 T^{4} - \)\(28\!\cdots\!92\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( 1 + 88092 T + 7289446053 T^{2} + 329541325840584 T^{3} + 13151832521353701603 T^{4} + \)\(28\!\cdots\!92\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( 1 + 6374750812 T^{2} + 16622748841310481702 T^{4} + \)\(20\!\cdots\!12\)\( T^{6} + \)\(10\!\cdots\!01\)\( T^{8} \))
$73$ (\( 1 + 52126 T + 2073071593 T^{2} \))(\( 1 - 20474 T + 2073071593 T^{2} \))(\( 1 - 33698 T + 2073071593 T^{2} \))(\( 1 + 63102 T + 2073071593 T^{2} \))(\( 1 - 27258 T + 2073071593 T^{2} \))(\( 1 - 21986 T + 2073071593 T^{2} \))(\( 1 + 38774 T + 2073071593 T^{2} \))(\( 1 - 11842 T + 2073071593 T^{2} \))(\( 1 - 11842 T + 2073071593 T^{2} \))(\( 1 + 38774 T + 2073071593 T^{2} \))(\( 1 - 21986 T + 2073071593 T^{2} \))(\( 1 - 27258 T + 2073071593 T^{2} \))(\( 1 + 63102 T + 2073071593 T^{2} \))(\( 1 - 33698 T + 2073071593 T^{2} \))(\( 1 - 20474 T + 2073071593 T^{2} \))(\( 1 + 52126 T + 2073071593 T^{2} \))(\( 1 + 67452 T + 4400780438 T^{2} + 139832825091036 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 7180 T + 284279286 T^{2} + 14884654037740 T^{3} + 4297625829703557649 T^{4} \))(\( ( 1 - 26266 T + 2073071593 T^{2} )^{2} \))(\( ( 1 + 18534 T + 2073071593 T^{2} )^{2} \))(\( ( 1 + 20806 T + 2073071593 T^{2} )^{2} \))(\( 1 + 7180 T + 284279286 T^{2} + 14884654037740 T^{3} + 4297625829703557649 T^{4} \))(\( 1 + 67452 T + 4400780438 T^{2} + 139832825091036 T^{3} + 4297625829703557649 T^{4} \))(\( 1 - 66750 T + 3875077479 T^{2} - 111360074258500 T^{3} + 8033313042388954047 T^{4} - \)\(28\!\cdots\!50\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( 1 - 66750 T + 3875077479 T^{2} - 111360074258500 T^{3} + 8033313042388954047 T^{4} - \)\(28\!\cdots\!50\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( ( 1 - 59700 T + 5029368950 T^{2} - 123762374102100 T^{3} + 4297625829703557649 T^{4} )^{2} \))
$79$ (\( 1 - 39640 T + 3077056399 T^{2} \))(\( 1 + 46240 T + 3077056399 T^{2} \))(\( 1 - 31208 T + 3077056399 T^{2} \))(\( 1 + 46536 T + 3077056399 T^{2} \))(\( 1 + 31456 T + 3077056399 T^{2} \))(\( 1 - 4520 T + 3077056399 T^{2} \))(\( 1 - 33360 T + 3077056399 T^{2} \))(\( 1 + 94216 T + 3077056399 T^{2} \))(\( 1 - 94216 T + 3077056399 T^{2} \))(\( 1 + 33360 T + 3077056399 T^{2} \))(\( 1 + 4520 T + 3077056399 T^{2} \))(\( 1 - 31456 T + 3077056399 T^{2} \))(\( 1 - 46536 T + 3077056399 T^{2} \))(\( 1 + 31208 T + 3077056399 T^{2} \))(\( 1 - 46240 T + 3077056399 T^{2} \))(\( 1 + 39640 T + 3077056399 T^{2} \))(\( 1 - 65904 T + 3994274078 T^{2} - 202790324919696 T^{3} + 9468276082626847201 T^{4} \))(\( 1 - 71840 T + 7430807198 T^{2} - 221055731704160 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 6078817438 T^{2} + 9468276082626847201 T^{4} \))(\( 1 - 1369983522 T^{2} + 9468276082626847201 T^{4} \))(\( 1 + 1275471838 T^{2} + 9468276082626847201 T^{4} \))(\( 1 + 71840 T + 7430807198 T^{2} + 221055731704160 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 65904 T + 3994274078 T^{2} + 202790324919696 T^{3} + 9468276082626847201 T^{4} \))(\( 1 + 92952 T + 11164448877 T^{2} + 573846024396496 T^{3} + 34353638858281213923 T^{4} + \)\(88\!\cdots\!52\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( 1 - 92952 T + 11164448877 T^{2} - 573846024396496 T^{3} + 34353638858281213923 T^{4} - \)\(88\!\cdots\!52\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( 1 + 10884258108 T^{2} + 48452581383610561862 T^{4} + \)\(10\!\cdots\!08\)\( T^{6} + \)\(89\!\cdots\!01\)\( T^{8} \))
$83$ (\( 1 + 59826 T + 3939040643 T^{2} \))(\( 1 - 51576 T + 3939040643 T^{2} \))(\( 1 - 38466 T + 3939040643 T^{2} \))(\( 1 + 88778 T + 3939040643 T^{2} \))(\( 1 - 24552 T + 3939040643 T^{2} \))(\( 1 - 109074 T + 3939040643 T^{2} \))(\( 1 - 16716 T + 3939040643 T^{2} \))(\( 1 + 31482 T + 3939040643 T^{2} \))(\( 1 - 31482 T + 3939040643 T^{2} \))(\( 1 + 16716 T + 3939040643 T^{2} \))(\( 1 + 109074 T + 3939040643 T^{2} \))(\( 1 + 24552 T + 3939040643 T^{2} \))(\( 1 - 88778 T + 3939040643 T^{2} \))(\( 1 + 38466 T + 3939040643 T^{2} \))(\( 1 + 51576 T + 3939040643 T^{2} \))(\( 1 - 59826 T + 3939040643 T^{2} \))(\( 1 - 108724 T + 10572459494 T^{2} - 428268254869532 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 31928 T + 5910993662 T^{2} - 125765689649704 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 1875047714 T^{2} + 15516041187205853449 T^{4} \))(\( 1 + 1693436786 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 3421895214 T^{2} + 15516041187205853449 T^{4} \))(\( 1 + 31928 T + 5910993662 T^{2} + 125765689649704 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 108724 T + 10572459494 T^{2} + 428268254869532 T^{3} + 15516041187205853449 T^{4} \))(\( 1 + 30258 T + 4293702405 T^{2} + 426012342532708 T^{3} + 16913068282241846415 T^{4} + \)\(46\!\cdots\!42\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 - 30258 T + 4293702405 T^{2} - 426012342532708 T^{3} + 16913068282241846415 T^{4} - \)\(46\!\cdots\!42\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 + 7906443964 T^{2} + 42876570344126662806 T^{4} + \)\(12\!\cdots\!36\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} \))
$89$ (\( 1 - 57690 T + 5584059449 T^{2} \))(\( 1 + 110310 T + 5584059449 T^{2} \))(\( 1 - 119514 T + 5584059449 T^{2} \))(\( 1 + 104934 T + 5584059449 T^{2} \))(\( 1 + 90854 T + 5584059449 T^{2} \))(\( 1 - 38490 T + 5584059449 T^{2} \))(\( 1 - 101370 T + 5584059449 T^{2} \))(\( 1 + 94054 T + 5584059449 T^{2} \))(\( 1 + 94054 T + 5584059449 T^{2} \))(\( 1 - 101370 T + 5584059449 T^{2} \))(\( 1 - 38490 T + 5584059449 T^{2} \))(\( 1 + 90854 T + 5584059449 T^{2} \))(\( 1 + 104934 T + 5584059449 T^{2} \))(\( 1 - 119514 T + 5584059449 T^{2} \))(\( 1 + 110310 T + 5584059449 T^{2} \))(\( 1 - 57690 T + 5584059449 T^{2} \))(\( 1 + 55020 T + 10818978262 T^{2} + 307234950883980 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 40748 T + 8570866774 T^{2} + 227539254427852 T^{3} + 31181719929966183601 T^{4} \))(\( ( 1 - 30570 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 107590 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 18310 T + 5584059449 T^{2} )^{2} \))(\( 1 + 40748 T + 8570866774 T^{2} + 227539254427852 T^{3} + 31181719929966183601 T^{4} \))(\( 1 + 55020 T + 10818978262 T^{2} + 307234950883980 T^{3} + 31181719929966183601 T^{4} \))(\( 1 - 172686 T + 26445328791 T^{2} - 2103593815517412 T^{3} + \)\(14\!\cdots\!59\)\( T^{4} - \)\(53\!\cdots\!86\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( 1 - 172686 T + 26445328791 T^{2} - 2103593815517412 T^{3} + \)\(14\!\cdots\!59\)\( T^{4} - \)\(53\!\cdots\!86\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( ( 1 - 104660 T + 13126874198 T^{2} - 584427661932340 T^{3} + 31181719929966183601 T^{4} )^{2} \))
$97$ (\( 1 + 144382 T + 8587340257 T^{2} \))(\( 1 + 78382 T + 8587340257 T^{2} \))(\( 1 - 94658 T + 8587340257 T^{2} \))(\( 1 + 36254 T + 8587340257 T^{2} \))(\( 1 - 154706 T + 8587340257 T^{2} \))(\( 1 + 1918 T + 8587340257 T^{2} \))(\( 1 + 119038 T + 8587340257 T^{2} \))(\( 1 - 23714 T + 8587340257 T^{2} \))(\( 1 - 23714 T + 8587340257 T^{2} \))(\( 1 + 119038 T + 8587340257 T^{2} \))(\( 1 + 1918 T + 8587340257 T^{2} \))(\( 1 - 154706 T + 8587340257 T^{2} \))(\( 1 + 36254 T + 8587340257 T^{2} \))(\( 1 - 94658 T + 8587340257 T^{2} \))(\( 1 + 78382 T + 8587340257 T^{2} \))(\( 1 + 144382 T + 8587340257 T^{2} \))(\( 1 - 147668 T + 11612429670 T^{2} - 1268075361070676 T^{3} + 73742412689492826049 T^{4} \))(\( 1 + 190140 T + 19653817414 T^{2} + 1632796876465980 T^{3} + 73742412689492826049 T^{4} \))(\( ( 1 - 66882 T + 8587340257 T^{2} )^{2} \))(\( ( 1 + 108838 T + 8587340257 T^{2} )^{2} \))(\( ( 1 - 49978 T + 8587340257 T^{2} )^{2} \))(\( 1 + 190140 T + 19653817414 T^{2} + 1632796876465980 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 147668 T + 11612429670 T^{2} - 1268075361070676 T^{3} + 73742412689492826049 T^{4} \))(\( 1 - 170910 T + 30283966671 T^{2} - 2852314667192740 T^{3} + \)\(26\!\cdots\!47\)\( T^{4} - \)\(12\!\cdots\!90\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( 1 - 170910 T + 30283966671 T^{2} - 2852314667192740 T^{3} + \)\(26\!\cdots\!47\)\( T^{4} - \)\(12\!\cdots\!90\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( ( 1 + 29564 T + 14772618438 T^{2} + 253876127357948 T^{3} + 73742412689492826049 T^{4} )^{2} \))
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