Properties

Label 720.6.f
Level $720$
Weight $6$
Character orbit 720.f
Rep. character $\chi_{720}(289,\cdot)$
Character field $\Q$
Dimension $74$
Newform subspaces $16$
Sturm bound $864$
Trace bound $19$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 720.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(864\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(720, [\chi])\).

Total New Old
Modular forms 744 76 668
Cusp forms 696 74 622
Eisenstein series 48 2 46

Trace form

\( 74q + 20q^{5} + O(q^{10}) \) \( 74q + 20q^{5} - 728q^{11} - 3344q^{19} + 2142q^{25} + 304q^{29} - 2184q^{31} - 6464q^{35} + 3584q^{41} - 138498q^{49} - 16688q^{55} + 55416q^{59} + 33196q^{61} + 21752q^{65} - 24128q^{71} + 41912q^{79} + 18972q^{85} + 113352q^{89} - 138880q^{91} + 204040q^{95} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
720.6.f.a \(2\) \(115.476\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-110\) \(0\) \(q+(-55-5i)q^{5}+79iq^{7}-148q^{11}+\cdots\)
720.6.f.b \(2\) \(115.476\) \(\Q(\sqrt{-61}) \) None \(0\) \(0\) \(-80\) \(0\) \(q+(-40-5\beta )q^{5}+2^{4}\beta q^{7}+80q^{11}+\cdots\)
720.6.f.c \(2\) \(115.476\) \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q+5\beta q^{5}+58\beta q^{17}+2164q^{19}-124\beta q^{23}+\cdots\)
720.6.f.d \(2\) \(115.476\) \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(10\) \(0\) \(q+(5-5\beta )q^{5}-11\beta q^{7}-10^{2}q^{11}+\cdots\)
720.6.f.e \(2\) \(115.476\) \(\Q(\sqrt{-61}) \) None \(0\) \(0\) \(80\) \(0\) \(q+(40+5\beta )q^{5}+2^{4}\beta q^{7}-80q^{11}+\cdots\)
720.6.f.f \(2\) \(115.476\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(90\) \(0\) \(q+(45+5\beta )q^{5}-9\beta q^{7}+252q^{11}+\cdots\)
720.6.f.g \(2\) \(115.476\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(110\) \(0\) \(q+(55-5i)q^{5}+2iq^{7}-500q^{11}+\cdots\)
720.6.f.h \(4\) \(115.476\) \(\Q(i, \sqrt{89})\) None \(0\) \(0\) \(-120\) \(0\) \(q+(-30+5\beta _{1})q^{5}+(-12\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
720.6.f.i \(4\) \(115.476\) \(\Q(i, \sqrt{1249})\) None \(0\) \(0\) \(-6\) \(0\) \(q+(-1-\beta _{2})q^{5}+(1-15\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
720.6.f.j \(4\) \(115.476\) \(\Q(i, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) \(q+(5\beta _{1}+20\beta _{2})q^{5}-\beta _{3}q^{7}+(74\beta _{1}+\cdots)q^{11}+\cdots\)
720.6.f.k \(4\) \(115.476\) \(\Q(\sqrt{-5}, \sqrt{-14})\) None \(0\) \(0\) \(0\) \(0\) \(q+(6\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(-5\beta _{1}-10\beta _{2}+\cdots)q^{11}+\cdots\)
720.6.f.l \(6\) \(115.476\) 6.0.\(\cdots\).1 None \(0\) \(0\) \(-50\) \(0\) \(q+(-9-3\beta _{1}-\beta _{2}-\beta _{4}-\beta _{5})q^{5}+\cdots\)
720.6.f.m \(6\) \(115.476\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(38\) \(0\) \(q+(6+\beta _{2})q^{5}+(\beta _{1}-\beta _{2}+\beta _{5})q^{7}+(7^{2}+\cdots)q^{11}+\cdots\)
720.6.f.n \(8\) \(115.476\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-1+\beta _{1})q^{5}+(-\beta _{1}+\beta _{6})q^{7}+(-92+\cdots)q^{11}+\cdots\)
720.6.f.o \(8\) \(115.476\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(66\) \(0\) \(q+(8-3\beta _{1}-\beta _{2})q^{5}+(1-\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots\)
720.6.f.p \(16\) \(115.476\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{5}-\beta _{9}q^{7}+\beta _{1}q^{11}-\beta _{6}q^{13}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(720, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( 1 + 110 T + 3125 T^{2} \))(\( 1 + 80 T + 3125 T^{2} \))(\( 1 + 3125 T^{2} \))(\( 1 - 10 T + 3125 T^{2} \))(\( 1 - 80 T + 3125 T^{2} \))(\( 1 - 90 T + 3125 T^{2} \))(\( 1 - 110 T + 3125 T^{2} \))(\( ( 1 + 60 T + 3125 T^{2} )^{2} \))(\( 1 + 6 T + 5010 T^{2} + 18750 T^{3} + 9765625 T^{4} \))(\( 1 - 1350 T^{2} + 9765625 T^{4} \))(\( 1 - 3830 T^{2} + 9765625 T^{4} \))(\( 1 + 50 T - 625 T^{2} - 283500 T^{3} - 1953125 T^{4} + 488281250 T^{5} + 30517578125 T^{6} \))(\( 1 - 38 T - 2305 T^{2} + 233700 T^{3} - 7203125 T^{4} - 371093750 T^{5} + 30517578125 T^{6} \))(\( 1 + 8 T + 1100 T^{2} - 113000 T^{3} - 438250 T^{4} - 353125000 T^{5} + 10742187500 T^{6} + 244140625000 T^{7} + 95367431640625 T^{8} \))(\( 1 - 66 T + 2460 T^{2} + 290850 T^{3} - 22572250 T^{4} + 908906250 T^{5} + 24023437500 T^{6} - 2014160156250 T^{7} + 95367431640625 T^{8} \))(\( 1 + 744 T^{2} - 15109700 T^{4} + 4853295000 T^{6} + 205682850843750 T^{8} + 47395458984375000 T^{10} - \)\(14\!\cdots\!00\)\( T^{12} + \)\(69\!\cdots\!00\)\( T^{14} + \)\(90\!\cdots\!25\)\( T^{16} \))
$7$ (\( 1 - 8650 T^{2} + 282475249 T^{4} \))(\( 1 - 17998 T^{2} + 282475249 T^{4} \))(\( ( 1 - 16807 T^{2} )^{2} \))(\( 1 - 18610 T^{2} + 282475249 T^{4} \))(\( 1 - 17998 T^{2} + 282475249 T^{4} \))(\( 1 - 30050 T^{2} + 282475249 T^{4} \))(\( 1 - 33598 T^{2} + 282475249 T^{4} \))(\( 1 - 35764 T^{2} + 735230598 T^{4} - 10102444805236 T^{6} + 79792266297612001 T^{8} \))(\( 1 + 1720 T^{2} + 159889998 T^{4} + 485857428280 T^{6} + 79792266297612001 T^{8} \))(\( ( 1 - 33310 T^{2} + 282475249 T^{4} )^{2} \))(\( ( 1 + 16786 T^{2} + 282475249 T^{4} )^{2} \))(\( 1 - 64626 T^{2} + 2028003087 T^{4} - 41058323262556 T^{6} + 572860676973093663 T^{8} - \)\(51\!\cdots\!26\)\( T^{10} + \)\(22\!\cdots\!49\)\( T^{12} \))(\( 1 - 36594 T^{2} + 656281359 T^{4} - 10766281402204 T^{6} + 185383240297583391 T^{8} - \)\(29\!\cdots\!94\)\( T^{10} + \)\(22\!\cdots\!49\)\( T^{12} \))(\( 1 - 44728 T^{2} + 1493128636 T^{4} - 37445733732616 T^{6} + 682894235558230726 T^{8} - \)\(10\!\cdots\!84\)\( T^{10} + \)\(11\!\cdots\!36\)\( T^{12} - \)\(10\!\cdots\!72\)\( T^{14} + \)\(63\!\cdots\!01\)\( T^{16} \))(\( 1 - 50044 T^{2} + 1063808116 T^{4} - 10453791123268 T^{6} + 72544565734839766 T^{8} - \)\(29\!\cdots\!32\)\( T^{10} + \)\(84\!\cdots\!16\)\( T^{12} - \)\(11\!\cdots\!56\)\( T^{14} + \)\(63\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 64504 T^{2} + 2303344348 T^{4} - 55653835395400 T^{6} + 1050929443294374022 T^{8} - \)\(15\!\cdots\!00\)\( T^{10} + \)\(18\!\cdots\!48\)\( T^{12} - \)\(14\!\cdots\!96\)\( T^{14} + \)\(63\!\cdots\!01\)\( T^{16} )^{2} \))
$11$ (\( ( 1 + 148 T + 161051 T^{2} )^{2} \))(\( ( 1 - 80 T + 161051 T^{2} )^{2} \))(\( ( 1 + 161051 T^{2} )^{2} \))(\( ( 1 + 100 T + 161051 T^{2} )^{2} \))(\( ( 1 + 80 T + 161051 T^{2} )^{2} \))(\( ( 1 - 252 T + 161051 T^{2} )^{2} \))(\( ( 1 + 500 T + 161051 T^{2} )^{2} \))(\( ( 1 - 168 T + 69634 T^{2} - 27056568 T^{3} + 25937424601 T^{4} )^{2} \))(\( ( 1 - 174 T + 298446 T^{2} - 28022874 T^{3} + 25937424601 T^{4} )^{2} \))(\( ( 1 - 94074 T^{2} + 25937424601 T^{4} )^{2} \))(\( ( 1 + 70102 T^{2} + 25937424601 T^{4} )^{2} \))(\( ( 1 + 332 T + 408509 T^{2} + 107689464 T^{3} + 65790782959 T^{4} + 8611224967532 T^{5} + 4177248169415651 T^{6} )^{2} \))(\( ( 1 - 148 T + 2621 T^{2} + 31025208 T^{3} + 422114671 T^{4} - 3838738840948 T^{5} + 4177248169415651 T^{6} )^{2} \))(\( ( 1 + 368 T + 176204 T^{2} + 51158896 T^{3} + 42277949270 T^{4} + 8239191359696 T^{5} + 4570277964394604 T^{6} + 1537227326344959568 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 342 T + 443712 T^{2} - 76803486 T^{3} + 83091304430 T^{4} - 12369278223786 T^{5} + 11508746544558912 T^{6} - 1428618873940152642 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 644376 T^{2} + 191792302396 T^{4} + 37148595807242088 T^{6} + \)\(60\!\cdots\!58\)\( T^{8} + \)\(96\!\cdots\!88\)\( T^{10} + \)\(12\!\cdots\!96\)\( T^{12} + \)\(11\!\cdots\!76\)\( T^{14} + \)\(45\!\cdots\!01\)\( T^{16} )^{2} \))
$13$ (\( 1 - 274730 T^{2} + 137858491849 T^{4} \))(\( 1 - 602042 T^{2} + 137858491849 T^{4} \))(\( ( 1 - 371293 T^{2} )^{2} \))(\( 1 - 202442 T^{2} + 137858491849 T^{4} \))(\( 1 - 602042 T^{2} + 137858491849 T^{4} \))(\( 1 - 728330 T^{2} + 137858491849 T^{4} \))(\( 1 - 659642 T^{2} + 137858491849 T^{4} \))(\( 1 - 331372 T^{2} + 39475840758 T^{4} - 45682444160986828 T^{6} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( 1 - 717040 T^{2} + 288425185998 T^{4} - 98850052995406960 T^{6} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 463990 T^{2} + 137858491849 T^{4} )^{2} \))(\( ( 1 - 692186 T^{2} + 137858491849 T^{4} )^{2} \))(\( 1 - 2165574 T^{2} + 1976112655671 T^{4} - 972719104225889812 T^{6} + \)\(27\!\cdots\!79\)\( T^{8} - \)\(41\!\cdots\!74\)\( T^{10} + \)\(26\!\cdots\!49\)\( T^{12} \))(\( 1 - 1145958 T^{2} + 753791118135 T^{4} - 322779460890985940 T^{6} + \)\(10\!\cdots\!15\)\( T^{8} - \)\(21\!\cdots\!58\)\( T^{10} + \)\(26\!\cdots\!49\)\( T^{12} \))(\( 1 - 1578472 T^{2} + 1074189263356 T^{4} - 437549632721743384 T^{6} + \)\(15\!\cdots\!86\)\( T^{8} - \)\(60\!\cdots\!16\)\( T^{10} + \)\(20\!\cdots\!56\)\( T^{12} - \)\(41\!\cdots\!28\)\( T^{14} + \)\(36\!\cdots\!01\)\( T^{16} \))(\( 1 + 78884 T^{2} + 436289293828 T^{4} + 45956706983246780 T^{6} + \)\(82\!\cdots\!62\)\( T^{8} + \)\(63\!\cdots\!20\)\( T^{10} + \)\(82\!\cdots\!28\)\( T^{12} + \)\(20\!\cdots\!16\)\( T^{14} + \)\(36\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 1315240 T^{2} + 1109046819196 T^{4} - 629758658597256280 T^{6} + \)\(27\!\cdots\!06\)\( T^{8} - \)\(86\!\cdots\!20\)\( T^{10} + \)\(21\!\cdots\!96\)\( T^{12} - \)\(34\!\cdots\!60\)\( T^{14} + \)\(36\!\cdots\!01\)\( T^{16} )^{2} \))
$17$ (\( 1 + 1354590 T^{2} + 2015993900449 T^{4} \))(\( 1 - 2540814 T^{2} + 2015993900449 T^{4} \))(\( 1 - 2419214 T^{2} + 2015993900449 T^{4} \))(\( 1 - 1879458 T^{2} + 2015993900449 T^{4} \))(\( 1 - 2540814 T^{2} + 2015993900449 T^{4} \))(\( 1 - 2363810 T^{2} + 2015993900449 T^{4} \))(\( 1 - 541458 T^{2} + 2015993900449 T^{4} \))(\( 1 - 4641340 T^{2} + 9272809536198 T^{4} - 9356913129909961660 T^{6} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( 1 - 3971280 T^{2} + 7330589629598 T^{4} - 8006076256975104720 T^{6} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 1480158 T^{2} + 2015993900449 T^{4} )^{2} \))(\( ( 1 - 57134 T^{2} + 2015993900449 T^{4} )^{2} \))(\( 1 - 6393390 T^{2} + 19617942041247 T^{4} - 35338776492878157220 T^{6} + \)\(39\!\cdots\!03\)\( T^{8} - \)\(25\!\cdots\!90\)\( T^{10} + \)\(81\!\cdots\!49\)\( T^{12} \))(\( 1 - 2590734 T^{2} + 7157717514399 T^{4} - 10576927881230106084 T^{6} + \)\(14\!\cdots\!51\)\( T^{8} - \)\(10\!\cdots\!34\)\( T^{10} + \)\(81\!\cdots\!49\)\( T^{12} \))(\( 1 - 6260872 T^{2} + 17547242668444 T^{4} - 31297293718759478968 T^{6} + \)\(45\!\cdots\!30\)\( T^{8} - \)\(63\!\cdots\!32\)\( T^{10} + \)\(71\!\cdots\!44\)\( T^{12} - \)\(51\!\cdots\!28\)\( T^{14} + \)\(16\!\cdots\!01\)\( T^{16} \))(\( 1 - 3560332 T^{2} + 5896843750180 T^{4} - 4412996604518385652 T^{6} + \)\(28\!\cdots\!34\)\( T^{8} - \)\(88\!\cdots\!48\)\( T^{10} + \)\(23\!\cdots\!80\)\( T^{12} - \)\(29\!\cdots\!68\)\( T^{14} + \)\(16\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 4000504 T^{2} + 8522048810908 T^{4} - 14167372887863087560 T^{6} + \)\(21\!\cdots\!42\)\( T^{8} - \)\(28\!\cdots\!40\)\( T^{10} + \)\(34\!\cdots\!08\)\( T^{12} - \)\(32\!\cdots\!96\)\( T^{14} + \)\(16\!\cdots\!01\)\( T^{16} )^{2} \))
$19$ (\( ( 1 - 2220 T + 2476099 T^{2} )^{2} \))(\( ( 1 + 12 T + 2476099 T^{2} )^{2} \))(\( ( 1 - 2164 T + 2476099 T^{2} )^{2} \))(\( ( 1 + 2244 T + 2476099 T^{2} )^{2} \))(\( ( 1 + 12 T + 2476099 T^{2} )^{2} \))(\( ( 1 - 220 T + 2476099 T^{2} )^{2} \))(\( ( 1 + 1344 T + 2476099 T^{2} )^{2} \))(\( ( 1 + 1336 T + 5283078 T^{2} + 3308068264 T^{3} + 6131066257801 T^{4} )^{2} \))(\( ( 1 + 120 T + 459398 T^{2} + 297131880 T^{3} + 6131066257801 T^{4} )^{2} \))(\( ( 1 + 2244 T + 2476099 T^{2} )^{4} \))(\( ( 1 - 484 T + 2476099 T^{2} )^{4} \))(\( ( 1 + 144 T + 1911561 T^{2} - 1871015072 T^{3} + 4733214280539 T^{4} + 882873541123344 T^{5} + 15181127029874798299 T^{6} )^{2} \))(\( ( 1 - 3000 T + 7745097 T^{2} - 14027154000 T^{3} + 19177626936603 T^{4} - 18393198773403000 T^{5} + 15181127029874798299 T^{6} )^{2} \))(\( ( 1 + 688 T + 5308396 T^{2} + 6058136368 T^{3} + 15069081422710 T^{4} + 15000545402668432 T^{5} + 32546127598645797196 T^{6} + \)\(10\!\cdots\!12\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 1520 T + 8017612 T^{2} - 7503400304 T^{3} + 25990277114806 T^{4} - 18579161989334096 T^{5} + 49156510401340391212 T^{6} - \)\(23\!\cdots\!80\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 688 T + 4775596 T^{2} + 1378597168 T^{3} + 11860428984310 T^{4} + 3413543069087632 T^{5} + 29279495496489424396 T^{6} + \)\(10\!\cdots\!12\)\( T^{7} + \)\(37\!\cdots\!01\)\( T^{8} )^{4} \))
$23$ (\( 1 - 11320170 T^{2} + 41426511213649 T^{4} \))(\( 1 - 8749086 T^{2} + 41426511213649 T^{4} \))(\( 1 - 10950686 T^{2} + 41426511213649 T^{4} \))(\( 1 - 1185810 T^{2} + 41426511213649 T^{4} \))(\( 1 - 8749086 T^{2} + 41426511213649 T^{4} \))(\( 1 - 6946370 T^{2} + 41426511213649 T^{4} \))(\( 1 + 3937314 T^{2} + 41426511213649 T^{4} \))(\( 1 - 7972156 T^{2} + 92735802503718 T^{4} - \)\(33\!\cdots\!44\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 7282620 T^{2} + 10950776597798 T^{4} - \)\(30\!\cdots\!80\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 12622686 T^{2} + 41426511213649 T^{4} )^{2} \))(\( ( 1 - 7751966 T^{2} + 41426511213649 T^{4} )^{2} \))(\( 1 - 12847386 T^{2} + 119828345726079 T^{4} - \)\(79\!\cdots\!56\)\( T^{6} + \)\(49\!\cdots\!71\)\( T^{8} - \)\(22\!\cdots\!86\)\( T^{10} + \)\(71\!\cdots\!49\)\( T^{12} \))(\( 1 - 24763290 T^{2} + 297081932741247 T^{4} - \)\(22\!\cdots\!20\)\( T^{6} + \)\(12\!\cdots\!03\)\( T^{8} - \)\(42\!\cdots\!90\)\( T^{10} + \)\(71\!\cdots\!49\)\( T^{12} \))(\( 1 - 34675896 T^{2} + 569897415616828 T^{4} - \)\(59\!\cdots\!20\)\( T^{6} + \)\(44\!\cdots\!82\)\( T^{8} - \)\(24\!\cdots\!80\)\( T^{10} + \)\(97\!\cdots\!28\)\( T^{12} - \)\(24\!\cdots\!04\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} \))(\( 1 - 37462776 T^{2} + 688226025523036 T^{4} - \)\(78\!\cdots\!72\)\( T^{6} + \)\(60\!\cdots\!26\)\( T^{8} - \)\(32\!\cdots\!28\)\( T^{10} + \)\(11\!\cdots\!36\)\( T^{12} - \)\(26\!\cdots\!24\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 14927352 T^{2} + 114641830602076 T^{4} - \)\(53\!\cdots\!44\)\( T^{6} + \)\(24\!\cdots\!46\)\( T^{8} - \)\(22\!\cdots\!56\)\( T^{10} + \)\(19\!\cdots\!76\)\( T^{12} - \)\(10\!\cdots\!48\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} )^{2} \))
$29$ (\( ( 1 + 270 T + 20511149 T^{2} )^{2} \))(\( ( 1 + 4560 T + 20511149 T^{2} )^{2} \))(\( ( 1 + 20511149 T^{2} )^{2} \))(\( ( 1 + 7854 T + 20511149 T^{2} )^{2} \))(\( ( 1 - 4560 T + 20511149 T^{2} )^{2} \))(\( ( 1 - 6930 T + 20511149 T^{2} )^{2} \))(\( ( 1 + 2646 T + 20511149 T^{2} )^{2} \))(\( ( 1 + 3552 T + 27566938 T^{2} + 72855601248 T^{3} + 420707233300201 T^{4} )^{2} \))(\( ( 1 + 2430 T + 19735498 T^{2} + 49842092070 T^{3} + 420707233300201 T^{4} )^{2} \))(\( ( 1 + 40800682 T^{2} + 420707233300201 T^{4} )^{2} \))(\( ( 1 + 10530298 T^{2} + 420707233300201 T^{4} )^{2} \))(\( ( 1 - 946 T + 36417431 T^{2} - 76110228372 T^{3} + 746963353438219 T^{4} - 397989042701990146 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 - 7962 T + 79928295 T^{2} - 339128680740 T^{3} + 1639421168060955 T^{4} - 3349670991536200362 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 + 2936 T + 58625996 T^{2} + 77951973928 T^{3} + 1466411094282230 T^{4} + 1598884552081323272 T^{5} + \)\(24\!\cdots\!96\)\( T^{6} + \)\(25\!\cdots\!64\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 4002 T + 41245860 T^{2} - 2052028782 T^{3} + 531865053741014 T^{4} - 42089468099890518 T^{5} + \)\(17\!\cdots\!60\)\( T^{6} - \)\(34\!\cdots\!98\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 50036904 T^{2} + 1677424685662204 T^{4} + \)\(36\!\cdots\!96\)\( T^{6} + \)\(78\!\cdots\!90\)\( T^{8} + \)\(15\!\cdots\!96\)\( T^{10} + \)\(29\!\cdots\!04\)\( T^{12} + \)\(37\!\cdots\!04\)\( T^{14} + \)\(31\!\cdots\!01\)\( T^{16} )^{2} \))
$31$ (\( ( 1 - 2048 T + 28629151 T^{2} )^{2} \))(\( ( 1 - 344 T + 28629151 T^{2} )^{2} \))(\( ( 1 - 8152 T + 28629151 T^{2} )^{2} \))(\( ( 1 - 2144 T + 28629151 T^{2} )^{2} \))(\( ( 1 - 344 T + 28629151 T^{2} )^{2} \))(\( ( 1 + 6752 T + 28629151 T^{2} )^{2} \))(\( ( 1 - 5612 T + 28629151 T^{2} )^{2} \))(\( ( 1 - 11648 T + 90715902 T^{2} - 333472350848 T^{3} + 819628286980801 T^{4} )^{2} \))(\( ( 1 + 11684 T + 90263166 T^{2} + 334503000284 T^{3} + 819628286980801 T^{4} )^{2} \))(\( ( 1 + 3856 T + 28629151 T^{2} )^{4} \))(\( ( 1 + 3608 T + 28629151 T^{2} )^{4} \))(\( ( 1 - 5124 T + 61295997 T^{2} - 221905216248 T^{3} + 1754852353808547 T^{4} - 4199775342489624324 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 + 132 T + 14583261 T^{2} - 226177330952 T^{3} + 417506381241411 T^{4} + 108190933881465732 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 + 2112 T + 80187004 T^{2} + 163080265536 T^{3} + 3196344720873606 T^{4} + 4668849547150239936 T^{5} + \)\(65\!\cdots\!04\)\( T^{6} + \)\(49\!\cdots\!12\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 3012 T + 64375804 T^{2} + 104976522036 T^{3} + 1995658050211206 T^{4} + 3005388700823471436 T^{5} + \)\(52\!\cdots\!04\)\( T^{6} + \)\(70\!\cdots\!12\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 1056 T + 33747004 T^{2} - 123082635168 T^{3} + 293348622009606 T^{4} - 3523751347702582368 T^{5} + \)\(27\!\cdots\!04\)\( T^{6} - \)\(24\!\cdots\!56\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} )^{4} \))
$37$ (\( 1 - 119573530 T^{2} + 4808584372417849 T^{4} \))(\( 1 - 119558314 T^{2} + 4808584372417849 T^{4} \))(\( ( 1 - 69343957 T^{2} )^{2} \))(\( 1 - 30515770 T^{2} + 4808584372417849 T^{4} \))(\( 1 - 119558314 T^{2} + 4808584372417849 T^{4} \))(\( 1 + 56462470 T^{2} + 4808584372417849 T^{4} \))(\( 1 - 85572970 T^{2} + 4808584372417849 T^{4} \))(\( 1 - 162528844 T^{2} + 15468333779588118 T^{4} - \)\(78\!\cdots\!56\)\( T^{6} + \)\(23\!\cdots\!01\)\( T^{8} \))(\( 1 - 100197680 T^{2} + 8640930841305198 T^{4} - \)\(48\!\cdots\!20\)\( T^{6} + \)\(23\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 89804410 T^{2} + 4808584372417849 T^{4} )^{2} \))(\( ( 1 - 83802314 T^{2} + 4808584372417849 T^{4} )^{2} \))(\( 1 - 290752854 T^{2} + 38769784471186119 T^{4} - \)\(32\!\cdots\!24\)\( T^{6} + \)\(18\!\cdots\!31\)\( T^{8} - \)\(67\!\cdots\!54\)\( T^{10} + \)\(11\!\cdots\!49\)\( T^{12} \))(\( 1 - 244387830 T^{2} + 33585500520578247 T^{4} - \)\(28\!\cdots\!40\)\( T^{6} + \)\(16\!\cdots\!03\)\( T^{8} - \)\(56\!\cdots\!30\)\( T^{10} + \)\(11\!\cdots\!49\)\( T^{12} \))(\( 1 - 251774632 T^{2} + 38631208311838780 T^{4} - \)\(41\!\cdots\!52\)\( T^{6} + \)\(32\!\cdots\!34\)\( T^{8} - \)\(19\!\cdots\!48\)\( T^{10} + \)\(89\!\cdots\!80\)\( T^{12} - \)\(27\!\cdots\!68\)\( T^{14} + \)\(53\!\cdots\!01\)\( T^{16} \))(\( 1 - 335599612 T^{2} + 58713287095888324 T^{4} - \)\(67\!\cdots\!68\)\( T^{6} + \)\(54\!\cdots\!30\)\( T^{8} - \)\(32\!\cdots\!32\)\( T^{10} + \)\(13\!\cdots\!24\)\( T^{12} - \)\(37\!\cdots\!88\)\( T^{14} + \)\(53\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 156602728 T^{2} + 10376850454113724 T^{4} - \)\(10\!\cdots\!36\)\( T^{6} + \)\(10\!\cdots\!58\)\( T^{8} - \)\(52\!\cdots\!64\)\( T^{10} + \)\(23\!\cdots\!24\)\( T^{12} - \)\(17\!\cdots\!72\)\( T^{14} + \)\(53\!\cdots\!01\)\( T^{16} )^{2} \))
$41$ (\( ( 1 - 2398 T + 115856201 T^{2} )^{2} \))(\( ( 1 + 14240 T + 115856201 T^{2} )^{2} \))(\( ( 1 + 115856201 T^{2} )^{2} \))(\( ( 1 - 7414 T + 115856201 T^{2} )^{2} \))(\( ( 1 - 14240 T + 115856201 T^{2} )^{2} \))(\( ( 1 - 198 T + 115856201 T^{2} )^{2} \))(\( ( 1 - 18986 T + 115856201 T^{2} )^{2} \))(\( ( 1 + 1812 T + 29066422 T^{2} + 209931436212 T^{3} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 + 24984 T + 351666366 T^{2} + 2894551325784 T^{3} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 + 139752402 T^{2} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 + 109744402 T^{2} + 13422659310152401 T^{4} )^{2} \))(\( ( 1 - 662 T + 143511479 T^{2} - 442940770164 T^{3} + 16626694756831279 T^{4} - 8885800463320889462 T^{5} + \)\(15\!\cdots\!01\)\( T^{6} )^{2} \))(\( ( 1 + 8170 T + 309202103 T^{2} + 1569581651340 T^{3} + 35822980994790703 T^{4} + \)\(10\!\cdots\!70\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} )^{2} \))(\( ( 1 + 11800 T + 337909340 T^{2} + 2943020124776 T^{3} + 51155654972384870 T^{4} + \)\(34\!\cdots\!76\)\( T^{5} + \)\(45\!\cdots\!40\)\( T^{6} + \)\(18\!\cdots\!00\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 18900 T + 417574740 T^{2} - 5341513264524 T^{3} + 73890473527486070 T^{4} - \)\(61\!\cdots\!24\)\( T^{5} + \)\(56\!\cdots\!40\)\( T^{6} - \)\(29\!\cdots\!00\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 458567496 T^{2} + 120108387972394204 T^{4} + \)\(21\!\cdots\!04\)\( T^{6} + \)\(28\!\cdots\!90\)\( T^{8} + \)\(28\!\cdots\!04\)\( T^{10} + \)\(21\!\cdots\!04\)\( T^{12} + \)\(11\!\cdots\!96\)\( T^{14} + \)\(32\!\cdots\!01\)\( T^{16} )^{2} \))
$43$ (\( 1 - 288754450 T^{2} + 21611482313284249 T^{4} \))(\( 1 + 66775178 T^{2} + 21611482313284249 T^{4} \))(\( ( 1 - 147008443 T^{2} )^{2} \))(\( 1 + 21442214 T^{2} + 21611482313284249 T^{4} \))(\( 1 + 66775178 T^{2} + 21611482313284249 T^{4} \))(\( 1 - 293842250 T^{2} + 21611482313284249 T^{4} \))(\( 1 - 288237670 T^{2} + 21611482313284249 T^{4} \))(\( 1 - 479075020 T^{2} + 98304124357654998 T^{4} - \)\(10\!\cdots\!80\)\( T^{6} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( 1 - 100144460 T^{2} - 11465052277897002 T^{4} - \)\(21\!\cdots\!40\)\( T^{6} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 265922422 T^{2} + 21611482313284249 T^{4} )^{2} \))(\( ( 1 - 135962486 T^{2} + 21611482313284249 T^{4} )^{2} \))(\( 1 - 502572210 T^{2} + 127464803683947447 T^{4} - \)\(22\!\cdots\!80\)\( T^{6} + \)\(27\!\cdots\!03\)\( T^{8} - \)\(23\!\cdots\!10\)\( T^{10} + \)\(10\!\cdots\!49\)\( T^{12} \))(\( 1 - 45276210 T^{2} + 44529111123627447 T^{4} - \)\(19\!\cdots\!80\)\( T^{6} + \)\(96\!\cdots\!03\)\( T^{8} - \)\(21\!\cdots\!10\)\( T^{10} + \)\(10\!\cdots\!49\)\( T^{12} \))(\( 1 - 283211672 T^{2} + 48021567531024796 T^{4} - \)\(54\!\cdots\!84\)\( T^{6} + \)\(43\!\cdots\!06\)\( T^{8} - \)\(11\!\cdots\!16\)\( T^{10} + \)\(22\!\cdots\!96\)\( T^{12} - \)\(28\!\cdots\!28\)\( T^{14} + \)\(21\!\cdots\!01\)\( T^{16} \))(\( 1 - 780729368 T^{2} + 303614042895665980 T^{4} - \)\(75\!\cdots\!48\)\( T^{6} + \)\(13\!\cdots\!34\)\( T^{8} - \)\(16\!\cdots\!52\)\( T^{10} + \)\(14\!\cdots\!80\)\( T^{12} - \)\(78\!\cdots\!32\)\( T^{14} + \)\(21\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 624453080 T^{2} + 189664879587817660 T^{4} - \)\(38\!\cdots\!52\)\( T^{6} + \)\(61\!\cdots\!10\)\( T^{8} - \)\(83\!\cdots\!48\)\( T^{10} + \)\(88\!\cdots\!60\)\( T^{12} - \)\(63\!\cdots\!20\)\( T^{14} + \)\(21\!\cdots\!01\)\( T^{16} )^{2} \))
$47$ (\( 1 - 344584890 T^{2} + 52599132235830049 T^{4} \))(\( 1 + 142745586 T^{2} + 52599132235830049 T^{4} \))(\( 1 - 311808014 T^{2} + 52599132235830049 T^{4} \))(\( 1 - 369731298 T^{2} + 52599132235830049 T^{4} \))(\( 1 + 142745586 T^{2} + 52599132235830049 T^{4} \))(\( 1 - 347593490 T^{2} + 52599132235830049 T^{4} \))(\( 1 - 379480014 T^{2} + 52599132235830049 T^{4} \))(\( 1 - 838308220 T^{2} + 280500950197161798 T^{4} - \)\(44\!\cdots\!80\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 - 826473900 T^{2} + 275763720563232998 T^{4} - \)\(43\!\cdots\!00\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 62680014 T^{2} + 52599132235830049 T^{4} )^{2} \))(\( ( 1 - 367610894 T^{2} + 52599132235830049 T^{4} )^{2} \))(\( 1 - 288722058 T^{2} + 116437215277524783 T^{4} - \)\(17\!\cdots\!64\)\( T^{6} + \)\(61\!\cdots\!67\)\( T^{8} - \)\(79\!\cdots\!58\)\( T^{10} + \)\(14\!\cdots\!49\)\( T^{12} \))(\( 1 + 124421046 T^{2} + 29946698142211119 T^{4} + \)\(15\!\cdots\!76\)\( T^{6} + \)\(15\!\cdots\!31\)\( T^{8} + \)\(34\!\cdots\!46\)\( T^{10} + \)\(14\!\cdots\!49\)\( T^{12} \))(\( 1 - 963352312 T^{2} + 473832864723586300 T^{4} - \)\(15\!\cdots\!72\)\( T^{6} + \)\(40\!\cdots\!54\)\( T^{8} - \)\(83\!\cdots\!28\)\( T^{10} + \)\(13\!\cdots\!00\)\( T^{12} - \)\(14\!\cdots\!88\)\( T^{14} + \)\(76\!\cdots\!01\)\( T^{16} \))(\( 1 - 948364072 T^{2} + 448732834702283644 T^{4} - \)\(14\!\cdots\!68\)\( T^{6} + \)\(38\!\cdots\!30\)\( T^{8} - \)\(78\!\cdots\!32\)\( T^{10} + \)\(12\!\cdots\!44\)\( T^{12} - \)\(13\!\cdots\!28\)\( T^{14} + \)\(76\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 1310013880 T^{2} + 842382244428730396 T^{4} - \)\(33\!\cdots\!60\)\( T^{6} + \)\(93\!\cdots\!06\)\( T^{8} - \)\(17\!\cdots\!40\)\( T^{10} + \)\(23\!\cdots\!96\)\( T^{12} - \)\(19\!\cdots\!20\)\( T^{14} + \)\(76\!\cdots\!01\)\( T^{16} )^{2} \))
$53$ (\( 1 - 827605690 T^{2} + 174887470365513049 T^{4} \))(\( 1 - 84864886 T^{2} + 174887470365513049 T^{4} \))(\( 1 + 836229514 T^{2} + 174887470365513049 T^{4} \))(\( 1 - 248174170 T^{2} + 174887470365513049 T^{4} \))(\( 1 - 84864886 T^{2} + 174887470365513049 T^{4} \))(\( 1 - 802472090 T^{2} + 174887470365513049 T^{4} \))(\( 1 + 747967430 T^{2} + 174887470365513049 T^{4} \))(\( 1 - 1246752076 T^{2} + 694077861298212438 T^{4} - \)\(21\!\cdots\!24\)\( T^{6} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( 1 - 809517920 T^{2} + 441417135624894798 T^{4} - \)\(14\!\cdots\!80\)\( T^{6} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 835077670 T^{2} + 174887470365513049 T^{4} )^{2} \))(\( ( 1 - 813621206 T^{2} + 174887470365513049 T^{4} )^{2} \))(\( 1 - 1963456710 T^{2} + 1786491383741543655 T^{4} - \)\(95\!\cdots\!64\)\( T^{6} + \)\(31\!\cdots\!95\)\( T^{8} - \)\(60\!\cdots\!10\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} \))(\( 1 - 2370975366 T^{2} + 2397301328123693799 T^{4} - \)\(13\!\cdots\!16\)\( T^{6} + \)\(41\!\cdots\!51\)\( T^{8} - \)\(72\!\cdots\!66\)\( T^{10} + \)\(53\!\cdots\!49\)\( T^{12} \))(\( 1 - 1183385640 T^{2} + 874785099161623996 T^{4} - \)\(49\!\cdots\!80\)\( T^{6} + \)\(23\!\cdots\!06\)\( T^{8} - \)\(86\!\cdots\!20\)\( T^{10} + \)\(26\!\cdots\!96\)\( T^{12} - \)\(63\!\cdots\!60\)\( T^{14} + \)\(93\!\cdots\!01\)\( T^{16} \))(\( 1 - 383978028 T^{2} + 680329857618443044 T^{4} - \)\(19\!\cdots\!32\)\( T^{6} + \)\(17\!\cdots\!30\)\( T^{8} - \)\(34\!\cdots\!68\)\( T^{10} + \)\(20\!\cdots\!44\)\( T^{12} - \)\(20\!\cdots\!72\)\( T^{14} + \)\(93\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 2574268056 T^{2} + 3122678417422540348 T^{4} - \)\(23\!\cdots\!00\)\( T^{6} + \)\(11\!\cdots\!62\)\( T^{8} - \)\(40\!\cdots\!00\)\( T^{10} + \)\(95\!\cdots\!48\)\( T^{12} - \)\(13\!\cdots\!44\)\( T^{14} + \)\(93\!\cdots\!01\)\( T^{16} )^{2} \))
$59$ (\( ( 1 - 39740 T + 714924299 T^{2} )^{2} \))(\( ( 1 - 38000 T + 714924299 T^{2} )^{2} \))(\( ( 1 + 714924299 T^{2} )^{2} \))(\( ( 1 + 25972 T + 714924299 T^{2} )^{2} \))(\( ( 1 + 38000 T + 714924299 T^{2} )^{2} \))(\( ( 1 + 24660 T + 714924299 T^{2} )^{2} \))(\( ( 1 - 28300 T + 714924299 T^{2} )^{2} \))(\( ( 1 + 57336 T + 2002300258 T^{2} + 40990899607464 T^{3} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 - 23730 T + 501951198 T^{2} - 16965153615270 T^{3} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 + 33744102 T^{2} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 + 1399356598 T^{2} + 511116753300641401 T^{4} )^{2} \))(\( ( 1 + 5148 T + 597505773 T^{2} + 370643378904 T^{3} + 427171395910478127 T^{4} + \)\(26\!\cdots\!48\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} )^{2} \))(\( ( 1 - 46228 T + 2374731725 T^{2} - 58250866741320 T^{3} + 1697753413808685775 T^{4} - \)\(23\!\cdots\!28\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} )^{2} \))(\( ( 1 - 45840 T + 3064286732 T^{2} - 94721285480976 T^{3} + 3348109683185502486 T^{4} - \)\(67\!\cdots\!24\)\( T^{5} + \)\(15\!\cdots\!32\)\( T^{6} - \)\(16\!\cdots\!60\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 43014 T + 3138923408 T^{2} + 85511244344238 T^{3} + 3396429745251891150 T^{4} + \)\(61\!\cdots\!62\)\( T^{5} + \)\(16\!\cdots\!08\)\( T^{6} + \)\(15\!\cdots\!86\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 3407992984 T^{2} + 4568722822719661756 T^{4} + \)\(32\!\cdots\!92\)\( T^{6} + \)\(19\!\cdots\!58\)\( T^{8} + \)\(16\!\cdots\!92\)\( T^{10} + \)\(11\!\cdots\!56\)\( T^{12} + \)\(45\!\cdots\!84\)\( T^{14} + \)\(68\!\cdots\!01\)\( T^{16} )^{2} \))
$61$ (\( ( 1 + 42298 T + 844596301 T^{2} )^{2} \))(\( ( 1 + 8206 T + 844596301 T^{2} )^{2} \))(\( ( 1 - 34802 T + 844596301 T^{2} )^{2} \))(\( ( 1 + 3058 T + 844596301 T^{2} )^{2} \))(\( ( 1 + 8206 T + 844596301 T^{2} )^{2} \))(\( ( 1 + 5698 T + 844596301 T^{2} )^{2} \))(\( ( 1 - 18290 T + 844596301 T^{2} )^{2} \))(\( ( 1 + 30140 T + 1692991518 T^{2} + 25456132512140 T^{3} + 713342911662882601 T^{4} )^{2} \))(\( ( 1 - 57124 T + 2217210846 T^{2} - 48246719098324 T^{3} + 713342911662882601 T^{4} )^{2} \))(\( ( 1 + 38158 T + 844596301 T^{2} )^{4} \))(\( ( 1 - 21362 T + 844596301 T^{2} )^{4} \))(\( ( 1 + 26058 T + 886088883 T^{2} + 13089282520252 T^{3} + 748387392939021783 T^{4} + \)\(18\!\cdots\!58\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} )^{2} \))(\( ( 1 - 3126 T + 433417395 T^{2} + 15652173289660 T^{3} + 366062728606055895 T^{4} - \)\(22\!\cdots\!26\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} )^{2} \))(\( ( 1 - 61928 T + 3903014764 T^{2} - 145287706763384 T^{3} + 5198153942066716726 T^{4} - \)\(12\!\cdots\!84\)\( T^{5} + \)\(27\!\cdots\!64\)\( T^{6} - \)\(37\!\cdots\!28\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 19480 T + 1818982540 T^{2} + 11177939991304 T^{3} + 1488458395242824950 T^{4} + \)\(94\!\cdots\!04\)\( T^{5} + \)\(12\!\cdots\!40\)\( T^{6} + \)\(11\!\cdots\!80\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 9032 T + 1492239052 T^{2} - 26562418349336 T^{3} + 1618346221688627830 T^{4} - \)\(22\!\cdots\!36\)\( T^{5} + \)\(10\!\cdots\!52\)\( T^{6} - \)\(54\!\cdots\!32\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} )^{4} \))
$67$ (\( 1 - 1669968610 T^{2} + 1822837804551761449 T^{4} \))(\( 1 - 2524788838 T^{2} + 1822837804551761449 T^{4} \))(\( ( 1 - 1350125107 T^{2} )^{2} \))(\( 1 + 755362070 T^{2} + 1822837804551761449 T^{4} \))(\( 1 - 2524788838 T^{2} + 1822837804551761449 T^{4} \))(\( 1 - 795787610 T^{2} + 1822837804551761449 T^{4} \))(\( 1 + 1649943722 T^{2} + 1822837804551761449 T^{4} \))(\( 1 - 4461748300 T^{2} + 8610041688522039798 T^{4} - \)\(81\!\cdots\!00\)\( T^{6} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( 1 - 4204562300 T^{2} + 7726214820152619798 T^{4} - \)\(76\!\cdots\!00\)\( T^{6} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 1387552678 T^{2} + 1822837804551761449 T^{4} )^{2} \))(\( ( 1 - 1504963814 T^{2} + 1822837804551761449 T^{4} )^{2} \))(\( 1 - 7507145634 T^{2} + 24155236685124504999 T^{4} - \)\(42\!\cdots\!84\)\( T^{6} + \)\(44\!\cdots\!51\)\( T^{8} - \)\(24\!\cdots\!34\)\( T^{10} + \)\(60\!\cdots\!49\)\( T^{12} \))(\( 1 - 1213193634 T^{2} + 1488268869535589799 T^{4} - \)\(31\!\cdots\!84\)\( T^{6} + \)\(27\!\cdots\!51\)\( T^{8} - \)\(40\!\cdots\!34\)\( T^{10} + \)\(60\!\cdots\!49\)\( T^{12} \))(\( 1 - 9281919064 T^{2} + 39492482666681482588 T^{4} - \)\(10\!\cdots\!40\)\( T^{6} + \)\(16\!\cdots\!62\)\( T^{8} - \)\(18\!\cdots\!60\)\( T^{10} + \)\(13\!\cdots\!88\)\( T^{12} - \)\(56\!\cdots\!36\)\( T^{14} + \)\(11\!\cdots\!01\)\( T^{16} \))(\( 1 - 689670088 T^{2} + 6395411832810982876 T^{4} - \)\(31\!\cdots\!36\)\( T^{6} + \)\(16\!\cdots\!46\)\( T^{8} - \)\(56\!\cdots\!64\)\( T^{10} + \)\(21\!\cdots\!76\)\( T^{12} - \)\(41\!\cdots\!12\)\( T^{14} + \)\(11\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 4302504088 T^{2} + 12320798508402903676 T^{4} - \)\(23\!\cdots\!36\)\( T^{6} + \)\(36\!\cdots\!46\)\( T^{8} - \)\(43\!\cdots\!64\)\( T^{10} + \)\(40\!\cdots\!76\)\( T^{12} - \)\(26\!\cdots\!12\)\( T^{14} + \)\(11\!\cdots\!01\)\( T^{16} )^{2} \))
$71$ (\( ( 1 + 4248 T + 1804229351 T^{2} )^{2} \))(\( ( 1 - 48480 T + 1804229351 T^{2} )^{2} \))(\( ( 1 + 1804229351 T^{2} )^{2} \))(\( ( 1 - 37608 T + 1804229351 T^{2} )^{2} \))(\( ( 1 + 48480 T + 1804229351 T^{2} )^{2} \))(\( ( 1 - 53352 T + 1804229351 T^{2} )^{2} \))(\( ( 1 + 28800 T + 1804229351 T^{2} )^{2} \))(\( ( 1 - 17424 T + 3450786046 T^{2} - 31436892211824 T^{3} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 11076 T + 940164046 T^{2} + 19983644291676 T^{3} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 3331783438 T^{2} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 2510746702 T^{2} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 14144 T + 2246377637 T^{2} + 13852014127488 T^{3} + 4052980466105423587 T^{4} + \)\(46\!\cdots\!44\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 + 80400 T + 7314161253 T^{2} + 303984832792800 T^{3} + 13196424410609536803 T^{4} + \)\(26\!\cdots\!00\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 + 62816 T + 3398787356 T^{2} + 184024084124896 T^{3} + 8353296562609817510 T^{4} + \)\(33\!\cdots\!96\)\( T^{5} + \)\(11\!\cdots\!56\)\( T^{6} + \)\(36\!\cdots\!16\)\( T^{7} + \)\(10\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 81036 T + 8128543116 T^{2} - 379257248199228 T^{3} + 21602305876831289798 T^{4} - \)\(68\!\cdots\!28\)\( T^{5} + \)\(26\!\cdots\!16\)\( T^{6} - \)\(47\!\cdots\!36\)\( T^{7} + \)\(10\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 2871156792 T^{2} + 5431095844251854428 T^{4} + \)\(74\!\cdots\!44\)\( T^{6} + \)\(66\!\cdots\!70\)\( T^{8} + \)\(24\!\cdots\!44\)\( T^{10} + \)\(57\!\cdots\!28\)\( T^{12} + \)\(99\!\cdots\!92\)\( T^{14} + \)\(11\!\cdots\!01\)\( T^{16} )^{2} \))
$73$ (\( 1 - 3239892370 T^{2} + 4297625829703557649 T^{4} \))(\( 1 - 2340933586 T^{2} + 4297625829703557649 T^{4} \))(\( ( 1 - 2073071593 T^{2} )^{2} \))(\( 1 - 3569749522 T^{2} + 4297625829703557649 T^{4} \))(\( 1 - 2340933586 T^{2} + 4297625829703557649 T^{4} \))(\( 1 + 883886830 T^{2} + 4297625829703557649 T^{4} \))(\( 1 - 3197010322 T^{2} + 4297625829703557649 T^{4} \))(\( 1 - 8258401156 T^{2} + 25645382375738817318 T^{4} - \)\(35\!\cdots\!44\)\( T^{6} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 - 3772142420 T^{2} + 9801194247527769798 T^{4} - \)\(16\!\cdots\!80\)\( T^{6} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 669338414 T^{2} + 4297625829703557649 T^{4} )^{2} \))(\( ( 1 - 4138885586 T^{2} + 4297625829703557649 T^{4} )^{2} \))(\( 1 - 2138297622 T^{2} + 9645229369668502143 T^{4} - \)\(18\!\cdots\!56\)\( T^{6} + \)\(41\!\cdots\!07\)\( T^{8} - \)\(39\!\cdots\!22\)\( T^{10} + \)\(79\!\cdots\!49\)\( T^{12} \))(\( 1 - 5305758486 T^{2} + 18815441454973655679 T^{4} - \)\(44\!\cdots\!56\)\( T^{6} + \)\(80\!\cdots\!71\)\( T^{8} - \)\(97\!\cdots\!86\)\( T^{10} + \)\(79\!\cdots\!49\)\( T^{12} \))(\( 1 - 9140679496 T^{2} + 46078306824990298588 T^{4} - \)\(15\!\cdots\!60\)\( T^{6} + \)\(37\!\cdots\!02\)\( T^{8} - \)\(66\!\cdots\!40\)\( T^{10} + \)\(85\!\cdots\!88\)\( T^{12} - \)\(72\!\cdots\!04\)\( T^{14} + \)\(34\!\cdots\!01\)\( T^{16} \))(\( 1 - 11933853400 T^{2} + 67221911930035246396 T^{4} - \)\(23\!\cdots\!00\)\( T^{6} + \)\(58\!\cdots\!06\)\( T^{8} - \)\(10\!\cdots\!00\)\( T^{10} + \)\(12\!\cdots\!96\)\( T^{12} - \)\(94\!\cdots\!00\)\( T^{14} + \)\(34\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 4559473480 T^{2} + 20323547981168722396 T^{4} - \)\(57\!\cdots\!60\)\( T^{6} + \)\(13\!\cdots\!06\)\( T^{8} - \)\(24\!\cdots\!40\)\( T^{10} + \)\(37\!\cdots\!96\)\( T^{12} - \)\(36\!\cdots\!20\)\( T^{14} + \)\(34\!\cdots\!01\)\( T^{16} )^{2} \))
$79$ (\( ( 1 - 35280 T + 3077056399 T^{2} )^{2} \))(\( ( 1 + 9264 T + 3077056399 T^{2} )^{2} \))(\( ( 1 + 70064 T + 3077056399 T^{2} )^{2} \))(\( ( 1 - 79728 T + 3077056399 T^{2} )^{2} \))(\( ( 1 + 9264 T + 3077056399 T^{2} )^{2} \))(\( ( 1 + 51920 T + 3077056399 T^{2} )^{2} \))(\( ( 1 - 60228 T + 3077056399 T^{2} )^{2} \))(\( ( 1 + 57520 T + 5031936798 T^{2} + 176992284070480 T^{3} + 9468276082626847201 T^{4} )^{2} \))(\( ( 1 - 14220 T + 4980519998 T^{2} - 43755741993780 T^{3} + 9468276082626847201 T^{4} )^{2} \))(\( ( 1 + 20664 T + 3077056399 T^{2} )^{4} \))(\( ( 1 - 99616 T + 3077056399 T^{2} )^{4} \))(\( ( 1 + 110100 T + 12028730445 T^{2} + 673264081259096 T^{3} + 37013081987633367555 T^{4} + \)\(10\!\cdots\!00\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} )^{2} \))(\( ( 1 + 64476 T + 8552089389 T^{2} + 363282494523336 T^{3} + 26315261379242450211 T^{4} + \)\(61\!\cdots\!76\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} )^{2} \))(\( ( 1 + 21632 T + 7152876604 T^{2} + 332616618908288 T^{3} + 24121899620797566790 T^{4} + \)\(10\!\cdots\!12\)\( T^{5} + \)\(67\!\cdots\!04\)\( T^{6} + \)\(63\!\cdots\!68\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 84988 T + 5906431900 T^{2} - 410334793182028 T^{3} + 30047763404998661254 T^{4} - \)\(12\!\cdots\!72\)\( T^{5} + \)\(55\!\cdots\!00\)\( T^{6} - \)\(24\!\cdots\!12\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 8576 T + 5537482876 T^{2} + 173910727899008 T^{3} + 17190185901357317830 T^{4} + \)\(53\!\cdots\!92\)\( T^{5} + \)\(52\!\cdots\!76\)\( T^{6} + \)\(24\!\cdots\!24\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} )^{4} \))
$83$ (\( 1 - 7103795010 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 6760658886 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 2642233286 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 7612675530 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 6760658886 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 4053674810 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 7871990262 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 4702142572 T^{2} + 17913713453684153718 T^{4} - \)\(72\!\cdots\!28\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 - 2811580140 T^{2} + 17974811933757230198 T^{4} - \)\(43\!\cdots\!60\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( ( 1 + 1524711738 T^{2} + 15516041187205853449 T^{4} )^{2} \))(\( ( 1 - 4615601606 T^{2} + 15516041187205853449 T^{4} )^{2} \))(\( 1 - 5878219362 T^{2} + 30391064056477835847 T^{4} - \)\(17\!\cdots\!76\)\( T^{6} + \)\(47\!\cdots\!03\)\( T^{8} - \)\(14\!\cdots\!62\)\( T^{10} + \)\(37\!\cdots\!49\)\( T^{12} \))(\( 1 - 12098110050 T^{2} + 79589532006740517447 T^{4} - \)\(36\!\cdots\!00\)\( T^{6} + \)\(12\!\cdots\!03\)\( T^{8} - \)\(29\!\cdots\!50\)\( T^{10} + \)\(37\!\cdots\!49\)\( T^{12} \))(\( 1 - 6759897816 T^{2} + 40943120759345365468 T^{4} - \)\(86\!\cdots\!80\)\( T^{6} + \)\(39\!\cdots\!42\)\( T^{8} - \)\(13\!\cdots\!20\)\( T^{10} + \)\(98\!\cdots\!68\)\( T^{12} - \)\(25\!\cdots\!84\)\( T^{14} + \)\(57\!\cdots\!01\)\( T^{16} \))(\( 1 - 21233018712 T^{2} + \)\(22\!\cdots\!96\)\( T^{4} - \)\(15\!\cdots\!64\)\( T^{6} + \)\(70\!\cdots\!06\)\( T^{8} - \)\(23\!\cdots\!36\)\( T^{10} + \)\(53\!\cdots\!96\)\( T^{12} - \)\(79\!\cdots\!88\)\( T^{14} + \)\(57\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 26022519576 T^{2} + \)\(31\!\cdots\!88\)\( T^{4} - \)\(22\!\cdots\!60\)\( T^{6} + \)\(10\!\cdots\!22\)\( T^{8} - \)\(34\!\cdots\!40\)\( T^{10} + \)\(74\!\cdots\!88\)\( T^{12} - \)\(97\!\cdots\!24\)\( T^{14} + \)\(57\!\cdots\!01\)\( T^{16} )^{2} \))
$89$ (\( ( 1 + 85210 T + 5584059449 T^{2} )^{2} \))(\( ( 1 - 24320 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 5584059449 T^{2} )^{2} \))(\( ( 1 + 826 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 24320 T + 5584059449 T^{2} )^{2} \))(\( ( 1 - 9990 T + 5584059449 T^{2} )^{2} \))(\( ( 1 - 22678 T + 5584059449 T^{2} )^{2} \))(\( ( 1 - 136764 T + 15341778358 T^{2} - 763698306483036 T^{3} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 + 60420 T + 10831762998 T^{2} + 337388871908580 T^{3} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 + 7604090994 T^{2} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 - 3347081102 T^{2} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 + 175710 T + 24190100439 T^{2} + 1951044010529988 T^{3} + \)\(13\!\cdots\!11\)\( T^{4} + \)\(54\!\cdots\!10\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 + 38030 T + 13498833047 T^{2} + 295589573171940 T^{3} + 75378286226573811103 T^{4} + \)\(11\!\cdots\!30\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 - 20952 T + 16118164796 T^{2} - 497915996461992 T^{3} + \)\(11\!\cdots\!30\)\( T^{4} - \)\(27\!\cdots\!08\)\( T^{5} + \)\(50\!\cdots\!96\)\( T^{6} - \)\(36\!\cdots\!48\)\( T^{7} + \)\(97\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 - 226488 T + 18828868604 T^{2} - 357850805109192 T^{3} - 29854343234341882650 T^{4} - \)\(19\!\cdots\!08\)\( T^{5} + \)\(58\!\cdots\!04\)\( T^{6} - \)\(39\!\cdots\!12\)\( T^{7} + \)\(97\!\cdots\!01\)\( T^{8} )^{2} \))(\( ( 1 + 10511122888 T^{2} + 32812007833496994652 T^{4} - \)\(11\!\cdots\!16\)\( T^{6} - \)\(28\!\cdots\!50\)\( T^{8} - \)\(34\!\cdots\!16\)\( T^{10} + \)\(31\!\cdots\!52\)\( T^{12} + \)\(31\!\cdots\!88\)\( T^{14} + \)\(94\!\cdots\!01\)\( T^{16} )^{2} \))
$97$ (\( 1 - 7720618690 T^{2} + 73742412689492826049 T^{4} \))(\( 1 + 1515110462 T^{2} + 73742412689492826049 T^{4} \))(\( ( 1 - 8587340257 T^{2} )^{2} \))(\( 1 - 15761405890 T^{2} + 73742412689492826049 T^{4} \))(\( 1 + 1515110462 T^{2} + 73742412689492826049 T^{4} \))(\( 1 - 6923133890 T^{2} + 73742412689492826049 T^{4} \))(\( 1 - 15808047490 T^{2} + 73742412689492826049 T^{4} \))(\( 1 - 19861637380 T^{2} + \)\(20\!\cdots\!98\)\( T^{4} - \)\(14\!\cdots\!20\)\( T^{6} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( 1 - 19675914500 T^{2} + \)\(24\!\cdots\!98\)\( T^{4} - \)\(14\!\cdots\!00\)\( T^{6} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( ( 1 - 17140767490 T^{2} + 73742412689492826049 T^{4} )^{2} \))(\( ( 1 - 13052162114 T^{2} + 73742412689492826049 T^{4} )^{2} \))(\( 1 - 18122177670 T^{2} + \)\(22\!\cdots\!47\)\( T^{4} - \)\(21\!\cdots\!60\)\( T^{6} + \)\(16\!\cdots\!03\)\( T^{8} - \)\(98\!\cdots\!70\)\( T^{10} + \)\(40\!\cdots\!49\)\( T^{12} \))(\( 1 - 7960147590 T^{2} + 45176095155574055247 T^{4} + \)\(10\!\cdots\!80\)\( T^{6} + \)\(33\!\cdots\!03\)\( T^{8} - \)\(43\!\cdots\!90\)\( T^{10} + \)\(40\!\cdots\!49\)\( T^{12} \))(\( 1 - 45263915272 T^{2} + \)\(10\!\cdots\!40\)\( T^{4} - \)\(14\!\cdots\!12\)\( T^{6} + \)\(15\!\cdots\!94\)\( T^{8} - \)\(11\!\cdots\!88\)\( T^{10} + \)\(55\!\cdots\!40\)\( T^{12} - \)\(18\!\cdots\!28\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} \))(\( 1 - 58225283080 T^{2} + \)\(15\!\cdots\!96\)\( T^{4} - \)\(24\!\cdots\!60\)\( T^{6} + \)\(25\!\cdots\!06\)\( T^{8} - \)\(18\!\cdots\!40\)\( T^{10} + \)\(84\!\cdots\!96\)\( T^{12} - \)\(23\!\cdots\!20\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} \))(\( ( 1 + 2457095672 T^{2} + \)\(27\!\cdots\!16\)\( T^{4} + \)\(49\!\cdots\!84\)\( T^{6} + \)\(29\!\cdots\!66\)\( T^{8} + \)\(36\!\cdots\!16\)\( T^{10} + \)\(14\!\cdots\!16\)\( T^{12} + \)\(98\!\cdots\!28\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} )^{2} \))
show more
show less