# Properties

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

# Related objects

## Defining parameters

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

## Dimensions

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

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

## Trace form

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

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

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

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

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

## Hecke characteristic polynomials

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