# Properties

 Label 1134.2.f Level 1134 Weight 2 Character orbit f Rep. character $$\chi_{1134}(379,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 48 Newform subspaces 20 Sturm bound 432 Trace bound 13

# Related objects

## Defining parameters

 Level: $$N$$ = $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1134.f (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$20$$ Sturm bound: $$432$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1134, [\chi])$$.

Total New Old
Modular forms 480 48 432
Cusp forms 384 48 336
Eisenstein series 96 0 96

## Trace form

 $$48q - 24q^{4} + O(q^{10})$$ $$48q - 24q^{4} - 24q^{16} - 24q^{19} + 12q^{22} + 24q^{31} + 12q^{34} - 48q^{37} + 12q^{43} - 24q^{49} - 48q^{55} + 48q^{64} + 36q^{67} - 24q^{73} + 12q^{76} + 24q^{79} + 12q^{85} + 12q^{88} - 48q^{91} + 24q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1134, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1134.2.f.a $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-4$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots$$
1134.2.f.b $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-3$$ $$-1$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$$
1134.2.f.c $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-1$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$$
1134.2.f.d $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-1$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$$
1134.2.f.e $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$0$$ $$-1$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots$$
1134.2.f.f $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$0$$ $$-1$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots$$
1134.2.f.g $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$2$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots$$
1134.2.f.h $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$3$$ $$-1$$ $$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots$$
1134.2.f.i $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-3$$ $$-1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$$
1134.2.f.j $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$-2$$ $$1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$$
1134.2.f.k $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$0$$ $$-1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots$$
1134.2.f.l $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$0$$ $$-1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots$$
1134.2.f.m $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$1$$ $$1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$$
1134.2.f.n $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$1$$ $$1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$$
1134.2.f.o $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$3$$ $$-1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$$
1134.2.f.p $$2$$ $$9.055$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$4$$ $$1$$ $$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$$
1134.2.f.q $$4$$ $$9.055$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$0$$ $$-2$$ $$q+(-1+\zeta_{12})q^{2}-\zeta_{12}q^{4}-\zeta_{12}^{2}q^{5}+\cdots$$
1134.2.f.r $$4$$ $$9.055$$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$4$$ $$2$$ $$q-\zeta_{12}q^{2}+(-1+\zeta_{12})q^{4}+(2-2\zeta_{12}+\cdots)q^{5}+\cdots$$
1134.2.f.s $$4$$ $$9.055$$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$-4$$ $$2$$ $$q+(1-\zeta_{12})q^{2}-\zeta_{12}q^{4}+(-2\zeta_{12}+\cdots)q^{5}+\cdots$$
1134.2.f.t $$4$$ $$9.055$$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$-2$$ $$q+(1-\zeta_{12})q^{2}-\zeta_{12}q^{4}-\zeta_{12}^{2}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1134, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1134, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(162, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(189, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(378, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(567, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 + T + T^{2}$$)($$1 + T + T^{2}$$)($$1 + T + T^{2}$$)($$1 + T + T^{2}$$)($$1 + T + T^{2}$$)($$1 + T + T^{2}$$)($$1 + T + T^{2}$$)($$1 + T + T^{2}$$)($$1 - T + T^{2}$$)($$1 - T + T^{2}$$)($$1 - T + T^{2}$$)($$1 - T + T^{2}$$)($$1 - T + T^{2}$$)($$1 - T + T^{2}$$)($$1 - T + T^{2}$$)($$1 - T + T^{2}$$)($$( 1 + T + T^{2} )^{2}$$)($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)
$3$ 1
$5$ ($$1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4}$$)($$1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$$)($$1 + T - 4 T^{2} + 5 T^{3} + 25 T^{4}$$)($$1 + T - 4 T^{2} + 5 T^{3} + 25 T^{4}$$)($$1 - 5 T^{2} + 25 T^{4}$$)($$1 - 5 T^{2} + 25 T^{4}$$)($$1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4}$$)($$1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4}$$)($$1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$$)($$1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4}$$)($$1 - 5 T^{2} + 25 T^{4}$$)($$1 - 5 T^{2} + 25 T^{4}$$)($$1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4}$$)($$1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4}$$)($$1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4}$$)($$1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4}$$)($$1 - 7 T^{2} + 24 T^{4} - 175 T^{6} + 625 T^{8}$$)($$( 1 - 4 T + 5 T^{2} )^{2}( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} )$$)($$( 1 + 4 T + 5 T^{2} )^{2}( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} )$$)($$1 - 7 T^{2} + 24 T^{4} - 175 T^{6} + 625 T^{8}$$)
$7$ ($$1 - T + T^{2}$$)($$1 + T + T^{2}$$)($$1 - T + T^{2}$$)($$1 - T + T^{2}$$)($$1 + T + T^{2}$$)($$1 + T + T^{2}$$)($$1 - T + T^{2}$$)($$1 + T + T^{2}$$)($$1 + T + T^{2}$$)($$1 - T + T^{2}$$)($$1 + T + T^{2}$$)($$1 + T + T^{2}$$)($$1 - T + T^{2}$$)($$1 - T + T^{2}$$)($$1 + T + T^{2}$$)($$1 - T + T^{2}$$)($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 + T + T^{2} )^{2}$$)
$11$ ($$1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4}$$)($$1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4}$$)($$1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4}$$)($$1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4}$$)($$1 - 11 T^{2} + 121 T^{4}$$)($$1 - 11 T^{2} + 121 T^{4}$$)($$1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4}$$)($$1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4}$$)($$1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4}$$)($$1 + 4 T + 5 T^{2} + 44 T^{3} + 121 T^{4}$$)($$1 - 11 T^{2} + 121 T^{4}$$)($$1 - 11 T^{2} + 121 T^{4}$$)($$1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4}$$)($$1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4}$$)($$1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4}$$)($$1 + 4 T + 5 T^{2} + 44 T^{3} + 121 T^{4}$$)($$1 + 6 T + 8 T^{2} + 36 T^{3} + 267 T^{4} + 396 T^{5} + 968 T^{6} + 7986 T^{7} + 14641 T^{8}$$)($$1 - 2 T + 8 T^{2} + 52 T^{3} - 149 T^{4} + 572 T^{5} + 968 T^{6} - 2662 T^{7} + 14641 T^{8}$$)($$1 + 2 T + 8 T^{2} - 52 T^{3} - 149 T^{4} - 572 T^{5} + 968 T^{6} + 2662 T^{7} + 14641 T^{8}$$)($$1 - 6 T + 8 T^{2} - 36 T^{3} + 267 T^{4} - 396 T^{5} + 968 T^{6} - 7986 T^{7} + 14641 T^{8}$$)
$13$ ($$1 + 3 T - 4 T^{2} + 39 T^{3} + 169 T^{4}$$)($$1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4}$$)($$1 - 13 T^{2} + 169 T^{4}$$)($$1 + 3 T - 4 T^{2} + 39 T^{3} + 169 T^{4}$$)($$( 1 - 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} )$$)($$1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4}$$)($$1 + 6 T + 23 T^{2} + 78 T^{3} + 169 T^{4}$$)($$1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4}$$)($$1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4}$$)($$1 + 6 T + 23 T^{2} + 78 T^{3} + 169 T^{4}$$)($$( 1 - 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} )$$)($$1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4}$$)($$1 + 3 T - 4 T^{2} + 39 T^{3} + 169 T^{4}$$)($$1 - 13 T^{2} + 169 T^{4}$$)($$1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4}$$)($$1 + 3 T - 4 T^{2} + 39 T^{3} + 169 T^{4}$$)($$( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} )^{2}$$)($$( 1 - 6 T + 13 T^{2} )^{2}( 1 + 6 T + 23 T^{2} + 78 T^{3} + 169 T^{4} )$$)($$( 1 - 6 T + 13 T^{2} )^{2}( 1 + 6 T + 23 T^{2} + 78 T^{3} + 169 T^{4} )$$)($$( 1 - T - 12 T^{2} - 13 T^{3} + 169 T^{4} )^{2}$$)
$17$ ($$( 1 + 7 T + 17 T^{2} )^{2}$$)($$( 1 - 6 T + 17 T^{2} )^{2}$$)($$( 1 - 2 T + 17 T^{2} )^{2}$$)($$( 1 + T + 17 T^{2} )^{2}$$)($$( 1 - 3 T + 17 T^{2} )^{2}$$)($$( 1 + 6 T + 17 T^{2} )^{2}$$)($$( 1 - 2 T + 17 T^{2} )^{2}$$)($$( 1 - 3 T + 17 T^{2} )^{2}$$)($$( 1 + 3 T + 17 T^{2} )^{2}$$)($$( 1 + 2 T + 17 T^{2} )^{2}$$)($$( 1 + 3 T + 17 T^{2} )^{2}$$)($$( 1 - 6 T + 17 T^{2} )^{2}$$)($$( 1 - T + 17 T^{2} )^{2}$$)($$( 1 + 2 T + 17 T^{2} )^{2}$$)($$( 1 + 6 T + 17 T^{2} )^{2}$$)($$( 1 - 7 T + 17 T^{2} )^{2}$$)($$( 1 - 6 T + 31 T^{2} - 102 T^{3} + 289 T^{4} )^{2}$$)($$( 1 + 7 T + 17 T^{2} )^{4}$$)($$( 1 - 7 T + 17 T^{2} )^{4}$$)($$( 1 + 6 T + 31 T^{2} + 102 T^{3} + 289 T^{4} )^{2}$$)
$19$ ($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 + 7 T + 19 T^{2} )^{2}$$)($$( 1 + T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 + T + 19 T^{2} )^{2}$$)($$( 1 + 7 T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 + 2 T + 12 T^{2} + 38 T^{3} + 361 T^{4} )^{2}$$)($$( 1 + 2 T + 36 T^{2} + 38 T^{3} + 361 T^{4} )^{2}$$)($$( 1 + 2 T + 36 T^{2} + 38 T^{3} + 361 T^{4} )^{2}$$)($$( 1 + 2 T + 12 T^{2} + 38 T^{3} + 361 T^{4} )^{2}$$)
$23$ ($$1 - T - 22 T^{2} - 23 T^{3} + 529 T^{4}$$)($$1 + 3 T - 14 T^{2} + 69 T^{3} + 529 T^{4}$$)($$1 - T - 22 T^{2} - 23 T^{3} + 529 T^{4}$$)($$1 + 2 T - 19 T^{2} + 46 T^{3} + 529 T^{4}$$)($$1 - 9 T + 58 T^{2} - 207 T^{3} + 529 T^{4}$$)($$1 - 23 T^{2} + 529 T^{4}$$)($$1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4}$$)($$1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4}$$)($$1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4}$$)($$1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4}$$)($$1 + 9 T + 58 T^{2} + 207 T^{3} + 529 T^{4}$$)($$1 - 23 T^{2} + 529 T^{4}$$)($$1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4}$$)($$1 + T - 22 T^{2} + 23 T^{3} + 529 T^{4}$$)($$1 - 3 T - 14 T^{2} - 69 T^{3} + 529 T^{4}$$)($$1 + T - 22 T^{2} + 23 T^{3} + 529 T^{4}$$)($$1 + 6 T - 16 T^{2} + 36 T^{3} + 1347 T^{4} + 828 T^{5} - 8464 T^{6} + 73002 T^{7} + 279841 T^{8}$$)($$1 - 2 T - 16 T^{2} + 52 T^{3} - 221 T^{4} + 1196 T^{5} - 8464 T^{6} - 24334 T^{7} + 279841 T^{8}$$)($$1 + 2 T - 16 T^{2} - 52 T^{3} - 221 T^{4} - 1196 T^{5} - 8464 T^{6} + 24334 T^{7} + 279841 T^{8}$$)($$1 - 6 T - 16 T^{2} - 36 T^{3} + 1347 T^{4} - 828 T^{5} - 8464 T^{6} - 73002 T^{7} + 279841 T^{8}$$)
$29$ ($$1 + T - 28 T^{2} + 29 T^{3} + 841 T^{4}$$)($$1 - 29 T^{2} + 841 T^{4}$$)($$1 + 4 T - 13 T^{2} + 116 T^{3} + 841 T^{4}$$)($$1 + 7 T + 20 T^{2} + 203 T^{3} + 841 T^{4}$$)($$1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4}$$)($$1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4}$$)($$1 - 2 T - 25 T^{2} - 58 T^{3} + 841 T^{4}$$)($$1 - 9 T + 52 T^{2} - 261 T^{3} + 841 T^{4}$$)($$1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4}$$)($$1 + 2 T - 25 T^{2} + 58 T^{3} + 841 T^{4}$$)($$1 + 3 T - 20 T^{2} + 87 T^{3} + 841 T^{4}$$)($$1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4}$$)($$1 - 7 T + 20 T^{2} - 203 T^{3} + 841 T^{4}$$)($$1 - 4 T - 13 T^{2} - 116 T^{3} + 841 T^{4}$$)($$1 - 29 T^{2} + 841 T^{4}$$)($$1 - T - 28 T^{2} - 29 T^{3} + 841 T^{4}$$)($$1 + 6 T - 19 T^{2} - 18 T^{3} + 1140 T^{4} - 522 T^{5} - 15979 T^{6} + 146334 T^{7} + 707281 T^{8}$$)($$( 1 - 10 T + 29 T^{2} )^{2}( 1 + 10 T + 71 T^{2} + 290 T^{3} + 841 T^{4} )$$)($$( 1 + 10 T + 29 T^{2} )^{2}( 1 - 10 T + 71 T^{2} - 290 T^{3} + 841 T^{4} )$$)($$1 - 6 T - 19 T^{2} + 18 T^{3} + 1140 T^{4} + 522 T^{5} - 15979 T^{6} - 146334 T^{7} + 707281 T^{8}$$)
$31$ ($$1 - 9 T + 50 T^{2} - 279 T^{3} + 961 T^{4}$$)($$1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4}$$)($$1 - 9 T + 50 T^{2} - 279 T^{3} + 961 T^{4}$$)($$1 + 6 T + 5 T^{2} + 186 T^{3} + 961 T^{4}$$)($$1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4}$$)($$( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} )$$)($$1 - 31 T^{2} + 961 T^{4}$$)($$1 - 10 T + 69 T^{2} - 310 T^{3} + 961 T^{4}$$)($$1 - 10 T + 69 T^{2} - 310 T^{3} + 961 T^{4}$$)($$1 - 31 T^{2} + 961 T^{4}$$)($$1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4}$$)($$( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} )$$)($$1 + 6 T + 5 T^{2} + 186 T^{3} + 961 T^{4}$$)($$1 - 9 T + 50 T^{2} - 279 T^{3} + 961 T^{4}$$)($$1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4}$$)($$1 - 9 T + 50 T^{2} - 279 T^{3} + 961 T^{4}$$)($$1 - 2 T - 32 T^{2} + 52 T^{3} + 211 T^{4} + 1612 T^{5} - 30752 T^{6} - 59582 T^{7} + 923521 T^{8}$$)($$1 + 6 T - 8 T^{2} - 108 T^{3} - 141 T^{4} - 3348 T^{5} - 7688 T^{6} + 178746 T^{7} + 923521 T^{8}$$)($$1 + 6 T - 8 T^{2} - 108 T^{3} - 141 T^{4} - 3348 T^{5} - 7688 T^{6} + 178746 T^{7} + 923521 T^{8}$$)($$1 - 2 T - 32 T^{2} + 52 T^{3} + 211 T^{4} + 1612 T^{5} - 30752 T^{6} - 59582 T^{7} + 923521 T^{8}$$)
$37$ ($$( 1 - 2 T + 37 T^{2} )^{2}$$)($$( 1 + 7 T + 37 T^{2} )^{2}$$)($$( 1 - 5 T + 37 T^{2} )^{2}$$)($$( 1 + 7 T + 37 T^{2} )^{2}$$)($$( 1 - 2 T + 37 T^{2} )^{2}$$)($$( 1 - 2 T + 37 T^{2} )^{2}$$)($$( 1 + 10 T + 37 T^{2} )^{2}$$)($$( 1 + 7 T + 37 T^{2} )^{2}$$)($$( 1 + 7 T + 37 T^{2} )^{2}$$)($$( 1 + 10 T + 37 T^{2} )^{2}$$)($$( 1 - 2 T + 37 T^{2} )^{2}$$)($$( 1 - 2 T + 37 T^{2} )^{2}$$)($$( 1 + 7 T + 37 T^{2} )^{2}$$)($$( 1 - 5 T + 37 T^{2} )^{2}$$)($$( 1 + 7 T + 37 T^{2} )^{2}$$)($$( 1 - 2 T + 37 T^{2} )^{2}$$)($$( 1 - 4 T + 51 T^{2} - 148 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 - 4 T + 3 T^{2} - 148 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 - 4 T + 3 T^{2} - 148 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 - 4 T + 51 T^{2} - 148 T^{3} + 1369 T^{4} )^{2}$$)
$41$ ($$1 + 6 T - 5 T^{2} + 246 T^{3} + 1681 T^{4}$$)($$1 + 9 T + 40 T^{2} + 369 T^{3} + 1681 T^{4}$$)($$1 - 9 T + 40 T^{2} - 369 T^{3} + 1681 T^{4}$$)($$1 + 6 T - 5 T^{2} + 246 T^{3} + 1681 T^{4}$$)($$1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4}$$)($$1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4}$$)($$1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4}$$)($$1 + 6 T - 5 T^{2} + 246 T^{3} + 1681 T^{4}$$)($$1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4}$$)($$1 + 6 T - 5 T^{2} + 246 T^{3} + 1681 T^{4}$$)($$1 + 6 T - 5 T^{2} + 246 T^{3} + 1681 T^{4}$$)($$1 + 6 T - 5 T^{2} + 246 T^{3} + 1681 T^{4}$$)($$1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4}$$)($$1 + 9 T + 40 T^{2} + 369 T^{3} + 1681 T^{4}$$)($$1 - 9 T + 40 T^{2} - 369 T^{3} + 1681 T^{4}$$)($$1 - 6 T - 5 T^{2} - 246 T^{3} + 1681 T^{4}$$)($$1 + 12 T + 38 T^{2} + 288 T^{3} + 3651 T^{4} + 11808 T^{5} + 63878 T^{6} + 827052 T^{7} + 2825761 T^{8}$$)($$1 - 12 T + 38 T^{2} - 288 T^{3} + 3651 T^{4} - 11808 T^{5} + 63878 T^{6} - 827052 T^{7} + 2825761 T^{8}$$)($$1 + 12 T + 38 T^{2} + 288 T^{3} + 3651 T^{4} + 11808 T^{5} + 63878 T^{6} + 827052 T^{7} + 2825761 T^{8}$$)($$1 - 12 T + 38 T^{2} - 288 T^{3} + 3651 T^{4} - 11808 T^{5} + 63878 T^{6} - 827052 T^{7} + 2825761 T^{8}$$)
$43$ ($$1 + 11 T + 78 T^{2} + 473 T^{3} + 1849 T^{4}$$)($$1 - 10 T + 57 T^{2} - 430 T^{3} + 1849 T^{4}$$)($$1 - 10 T + 57 T^{2} - 430 T^{3} + 1849 T^{4}$$)($$1 - 4 T - 27 T^{2} - 172 T^{3} + 1849 T^{4}$$)($$1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4}$$)($$( 1 - 5 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} )$$)($$1 - 4 T - 27 T^{2} - 172 T^{3} + 1849 T^{4}$$)($$1 - 4 T - 27 T^{2} - 172 T^{3} + 1849 T^{4}$$)($$1 - 4 T - 27 T^{2} - 172 T^{3} + 1849 T^{4}$$)($$1 - 4 T - 27 T^{2} - 172 T^{3} + 1849 T^{4}$$)($$1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4}$$)($$( 1 - 5 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} )$$)($$1 - 4 T - 27 T^{2} - 172 T^{3} + 1849 T^{4}$$)($$1 - 10 T + 57 T^{2} - 430 T^{3} + 1849 T^{4}$$)($$1 - 10 T + 57 T^{2} - 430 T^{3} + 1849 T^{4}$$)($$1 + 11 T + 78 T^{2} + 473 T^{3} + 1849 T^{4}$$)($$1 + 4 T + 34 T^{2} - 416 T^{3} - 2213 T^{4} - 17888 T^{5} + 62866 T^{6} + 318028 T^{7} + 3418801 T^{8}$$)($$1 + 4 T - 62 T^{2} - 32 T^{3} + 3547 T^{4} - 1376 T^{5} - 114638 T^{6} + 318028 T^{7} + 3418801 T^{8}$$)($$1 + 4 T - 62 T^{2} - 32 T^{3} + 3547 T^{4} - 1376 T^{5} - 114638 T^{6} + 318028 T^{7} + 3418801 T^{8}$$)($$1 + 4 T + 34 T^{2} - 416 T^{3} - 2213 T^{4} - 17888 T^{5} + 62866 T^{6} + 318028 T^{7} + 3418801 T^{8}$$)
$47$ ($$1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4}$$)($$1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4}$$)($$1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4}$$)($$1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4}$$)($$1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4}$$)($$1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4}$$)($$1 - 47 T^{2} + 2209 T^{4}$$)($$1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4}$$)($$1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4}$$)($$1 - 47 T^{2} + 2209 T^{4}$$)($$1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4}$$)($$1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4}$$)($$1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4}$$)($$1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4}$$)($$1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4}$$)($$1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4}$$)($$1 - 6 T - 40 T^{2} + 108 T^{3} + 1875 T^{4} + 5076 T^{5} - 88360 T^{6} - 622938 T^{7} + 4879681 T^{8}$$)($$1 - 6 T - 64 T^{2} - 36 T^{3} + 6099 T^{4} - 1692 T^{5} - 141376 T^{6} - 622938 T^{7} + 4879681 T^{8}$$)($$1 + 6 T - 64 T^{2} + 36 T^{3} + 6099 T^{4} + 1692 T^{5} - 141376 T^{6} + 622938 T^{7} + 4879681 T^{8}$$)($$1 + 6 T - 40 T^{2} - 108 T^{3} + 1875 T^{4} - 5076 T^{5} - 88360 T^{6} + 622938 T^{7} + 4879681 T^{8}$$)
$53$ ($$( 1 + 9 T + 53 T^{2} )^{2}$$)($$( 1 + 12 T + 53 T^{2} )^{2}$$)($$( 1 - 12 T + 53 T^{2} )^{2}$$)($$( 1 + 6 T + 53 T^{2} )^{2}$$)($$( 1 - 3 T + 53 T^{2} )^{2}$$)($$( 1 + 6 T + 53 T^{2} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{2}$$)($$( 1 + 6 T + 53 T^{2} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{2}$$)($$( 1 + 6 T + 53 T^{2} )^{2}$$)($$( 1 + 3 T + 53 T^{2} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{2}$$)($$( 1 + 12 T + 53 T^{2} )^{2}$$)($$( 1 - 12 T + 53 T^{2} )^{2}$$)($$( 1 - 9 T + 53 T^{2} )^{2}$$)($$( 1 - 12 T + 130 T^{2} - 636 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 - 12 T + 130 T^{2} - 636 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 + 12 T + 130 T^{2} + 636 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 + 12 T + 130 T^{2} + 636 T^{3} + 2809 T^{4} )^{2}$$)
$59$ ($$1 - 5 T - 34 T^{2} - 295 T^{3} + 3481 T^{4}$$)($$1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4}$$)($$1 - 14 T + 137 T^{2} - 826 T^{3} + 3481 T^{4}$$)($$1 + 10 T + 41 T^{2} + 590 T^{3} + 3481 T^{4}$$)($$1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4}$$)($$1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4}$$)($$1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4}$$)($$1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4}$$)($$1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4}$$)($$1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4}$$)($$1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4}$$)($$1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4}$$)($$1 - 10 T + 41 T^{2} - 590 T^{3} + 3481 T^{4}$$)($$1 + 14 T + 137 T^{2} + 826 T^{3} + 3481 T^{4}$$)($$1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4}$$)($$1 + 5 T - 34 T^{2} + 295 T^{3} + 3481 T^{4}$$)($$1 - 6 T - 64 T^{2} + 108 T^{3} + 4395 T^{4} + 6372 T^{5} - 222784 T^{6} - 1232274 T^{7} + 12117361 T^{8}$$)($$1 + 2 T - 88 T^{2} - 52 T^{3} + 4747 T^{4} - 3068 T^{5} - 306328 T^{6} + 410758 T^{7} + 12117361 T^{8}$$)($$1 - 2 T - 88 T^{2} + 52 T^{3} + 4747 T^{4} + 3068 T^{5} - 306328 T^{6} - 410758 T^{7} + 12117361 T^{8}$$)($$1 + 6 T - 64 T^{2} - 108 T^{3} + 4395 T^{4} - 6372 T^{5} - 222784 T^{6} + 1232274 T^{7} + 12117361 T^{8}$$)
$61$ ($$1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4}$$)($$1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4}$$)($$1 - 61 T^{2} + 3721 T^{4}$$)($$1 - 9 T + 20 T^{2} - 549 T^{3} + 3721 T^{4}$$)($$1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4}$$)($$1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4}$$)($$1 + 6 T - 25 T^{2} + 366 T^{3} + 3721 T^{4}$$)($$1 + 11 T + 60 T^{2} + 671 T^{3} + 3721 T^{4}$$)($$1 + 11 T + 60 T^{2} + 671 T^{3} + 3721 T^{4}$$)($$1 + 6 T - 25 T^{2} + 366 T^{3} + 3721 T^{4}$$)($$1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4}$$)($$1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4}$$)($$1 - 9 T + 20 T^{2} - 549 T^{3} + 3721 T^{4}$$)($$1 - 61 T^{2} + 3721 T^{4}$$)($$1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4}$$)($$1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4}$$)($$1 - 2 T - 11 T^{2} + 214 T^{3} - 3740 T^{4} + 13054 T^{5} - 40931 T^{6} - 453962 T^{7} + 13845841 T^{8}$$)($$1 - 6 T - 47 T^{2} + 234 T^{3} + 972 T^{4} + 14274 T^{5} - 174887 T^{6} - 1361886 T^{7} + 13845841 T^{8}$$)($$1 - 6 T - 47 T^{2} + 234 T^{3} + 972 T^{4} + 14274 T^{5} - 174887 T^{6} - 1361886 T^{7} + 13845841 T^{8}$$)($$1 - 2 T - 11 T^{2} + 214 T^{3} - 3740 T^{4} + 13054 T^{5} - 40931 T^{6} - 453962 T^{7} + 13845841 T^{8}$$)
$67$ ($$1 + 7 T - 18 T^{2} + 469 T^{3} + 4489 T^{4}$$)($$1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4}$$)($$1 - 8 T - 3 T^{2} - 536 T^{3} + 4489 T^{4}$$)($$1 + 10 T + 33 T^{2} + 670 T^{3} + 4489 T^{4}$$)($$1 - 13 T + 102 T^{2} - 871 T^{3} + 4489 T^{4}$$)($$1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4}$$)($$1 + 4 T - 51 T^{2} + 268 T^{3} + 4489 T^{4}$$)($$1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4}$$)($$1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4}$$)($$1 + 4 T - 51 T^{2} + 268 T^{3} + 4489 T^{4}$$)($$1 - 13 T + 102 T^{2} - 871 T^{3} + 4489 T^{4}$$)($$1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4}$$)($$1 + 10 T + 33 T^{2} + 670 T^{3} + 4489 T^{4}$$)($$1 - 8 T - 3 T^{2} - 536 T^{3} + 4489 T^{4}$$)($$1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4}$$)($$1 + 7 T - 18 T^{2} + 469 T^{3} + 4489 T^{4}$$)($$1 - 2 T - 104 T^{2} + 52 T^{3} + 6907 T^{4} + 3484 T^{5} - 466856 T^{6} - 601526 T^{7} + 20151121 T^{8}$$)($$1 - 10 T - 56 T^{2} - 220 T^{3} + 13147 T^{4} - 14740 T^{5} - 251384 T^{6} - 3007630 T^{7} + 20151121 T^{8}$$)($$1 - 10 T - 56 T^{2} - 220 T^{3} + 13147 T^{4} - 14740 T^{5} - 251384 T^{6} - 3007630 T^{7} + 20151121 T^{8}$$)($$1 - 2 T - 104 T^{2} + 52 T^{3} + 6907 T^{4} + 3484 T^{5} - 466856 T^{6} - 601526 T^{7} + 20151121 T^{8}$$)
$71$ ($$( 1 + 7 T + 71 T^{2} )^{2}$$)($$( 1 + 9 T + 71 T^{2} )^{2}$$)($$( 1 + 13 T + 71 T^{2} )^{2}$$)($$( 1 + 4 T + 71 T^{2} )^{2}$$)($$( 1 - 9 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 - 12 T + 71 T^{2} )^{2}$$)($$( 1 + 12 T + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 + 9 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 - 4 T + 71 T^{2} )^{2}$$)($$( 1 - 13 T + 71 T^{2} )^{2}$$)($$( 1 - 9 T + 71 T^{2} )^{2}$$)($$( 1 - 7 T + 71 T^{2} )^{2}$$)($$( 1 - 12 T + 70 T^{2} - 852 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 + 20 T + 230 T^{2} + 1420 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 20 T + 230 T^{2} - 1420 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 + 12 T + 70 T^{2} + 852 T^{3} + 5041 T^{4} )^{2}$$)
$73$ ($$( 1 + 14 T + 73 T^{2} )^{2}$$)($$( 1 - 2 T + 73 T^{2} )^{2}$$)($$( 1 + 2 T + 73 T^{2} )^{2}$$)($$( 1 + 11 T + 73 T^{2} )^{2}$$)($$( 1 - 2 T + 73 T^{2} )^{2}$$)($$( 1 - 2 T + 73 T^{2} )^{2}$$)($$( 1 - 10 T + 73 T^{2} )^{2}$$)($$( 1 + 7 T + 73 T^{2} )^{2}$$)($$( 1 + 7 T + 73 T^{2} )^{2}$$)($$( 1 - 10 T + 73 T^{2} )^{2}$$)($$( 1 - 2 T + 73 T^{2} )^{2}$$)($$( 1 - 2 T + 73 T^{2} )^{2}$$)($$( 1 + 11 T + 73 T^{2} )^{2}$$)($$( 1 + 2 T + 73 T^{2} )^{2}$$)($$( 1 - 2 T + 73 T^{2} )^{2}$$)($$( 1 + 14 T + 73 T^{2} )^{2}$$)($$( 1 + 8 T + 135 T^{2} + 584 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 - 20 T + 243 T^{2} - 1460 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 - 20 T + 243 T^{2} - 1460 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 + 8 T + 135 T^{2} + 584 T^{3} + 5329 T^{4} )^{2}$$)
$79$ ($$1 - 6 T - 43 T^{2} - 474 T^{3} + 6241 T^{4}$$)($$1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4}$$)($$1 + 6 T - 43 T^{2} + 474 T^{3} + 6241 T^{4}$$)($$1 - 6 T - 43 T^{2} - 474 T^{3} + 6241 T^{4}$$)($$1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4}$$)($$1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4}$$)($$1 - 79 T^{2} + 6241 T^{4}$$)($$1 + 2 T - 75 T^{2} + 158 T^{3} + 6241 T^{4}$$)($$1 + 2 T - 75 T^{2} + 158 T^{3} + 6241 T^{4}$$)($$1 - 79 T^{2} + 6241 T^{4}$$)($$1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4}$$)($$1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4}$$)($$1 - 6 T - 43 T^{2} - 474 T^{3} + 6241 T^{4}$$)($$1 + 6 T - 43 T^{2} + 474 T^{3} + 6241 T^{4}$$)($$1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4}$$)($$1 - 6 T - 43 T^{2} - 474 T^{3} + 6241 T^{4}$$)($$1 - 2 T - 128 T^{2} + 52 T^{3} + 10867 T^{4} + 4108 T^{5} - 798848 T^{6} - 986078 T^{7} + 38950081 T^{8}$$)($$1 + 6 T + 16 T^{2} - 828 T^{3} - 8685 T^{4} - 65412 T^{5} + 99856 T^{6} + 2958234 T^{7} + 38950081 T^{8}$$)($$1 + 6 T + 16 T^{2} - 828 T^{3} - 8685 T^{4} - 65412 T^{5} + 99856 T^{6} + 2958234 T^{7} + 38950081 T^{8}$$)($$1 - 2 T - 128 T^{2} + 52 T^{3} + 10867 T^{4} + 4108 T^{5} - 798848 T^{6} - 986078 T^{7} + 38950081 T^{8}$$)
$83$ ($$1 - 4 T - 67 T^{2} - 332 T^{3} + 6889 T^{4}$$)($$1 - 83 T^{2} + 6889 T^{4}$$)($$1 - 4 T - 67 T^{2} - 332 T^{3} + 6889 T^{4}$$)($$1 - 10 T + 17 T^{2} - 830 T^{3} + 6889 T^{4}$$)($$1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4}$$)($$1 + 6 T - 47 T^{2} + 498 T^{3} + 6889 T^{4}$$)($$1 - 4 T - 67 T^{2} - 332 T^{3} + 6889 T^{4}$$)($$1 + 6 T - 47 T^{2} + 498 T^{3} + 6889 T^{4}$$)($$1 - 6 T - 47 T^{2} - 498 T^{3} + 6889 T^{4}$$)($$1 + 4 T - 67 T^{2} + 332 T^{3} + 6889 T^{4}$$)($$1 + 12 T + 61 T^{2} + 996 T^{3} + 6889 T^{4}$$)($$1 - 6 T - 47 T^{2} - 498 T^{3} + 6889 T^{4}$$)($$1 + 10 T + 17 T^{2} + 830 T^{3} + 6889 T^{4}$$)($$1 + 4 T - 67 T^{2} + 332 T^{3} + 6889 T^{4}$$)($$1 - 83 T^{2} + 6889 T^{4}$$)($$1 + 4 T - 67 T^{2} + 332 T^{3} + 6889 T^{4}$$)($$1 + 6 T - 136 T^{2} + 36 T^{3} + 19707 T^{4} + 2988 T^{5} - 936904 T^{6} + 3430722 T^{7} + 47458321 T^{8}$$)($$1 - 2 T + 80 T^{2} + 484 T^{3} - 1445 T^{4} + 40172 T^{5} + 551120 T^{6} - 1143574 T^{7} + 47458321 T^{8}$$)($$1 + 2 T + 80 T^{2} - 484 T^{3} - 1445 T^{4} - 40172 T^{5} + 551120 T^{6} + 1143574 T^{7} + 47458321 T^{8}$$)($$1 - 6 T - 136 T^{2} - 36 T^{3} + 19707 T^{4} - 2988 T^{5} - 936904 T^{6} - 3430722 T^{7} + 47458321 T^{8}$$)
$89$ ($$( 1 + 3 T + 89 T^{2} )^{2}$$)($$( 1 + 15 T + 89 T^{2} )^{2}$$)($$( 1 + 9 T + 89 T^{2} )^{2}$$)($$( 1 - 15 T + 89 T^{2} )^{2}$$)($$( 1 - 15 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 6 T + 89 T^{2} )^{2}$$)($$( 1 - 3 T + 89 T^{2} )^{2}$$)($$( 1 + 3 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 15 T + 89 T^{2} )^{2}$$)($$( 1 + 6 T + 89 T^{2} )^{2}$$)($$( 1 + 15 T + 89 T^{2} )^{2}$$)($$( 1 - 9 T + 89 T^{2} )^{2}$$)($$( 1 - 15 T + 89 T^{2} )^{2}$$)($$( 1 - 3 T + 89 T^{2} )^{2}$$)($$( 1 + 18 T + 247 T^{2} + 1602 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 6 T + 139 T^{2} + 534 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 - 6 T + 139 T^{2} - 534 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 - 18 T + 247 T^{2} - 1602 T^{3} + 7921 T^{4} )^{2}$$)
$97$ ($$1 - 8 T - 33 T^{2} - 776 T^{3} + 9409 T^{4}$$)($$1 + 8 T - 33 T^{2} + 776 T^{3} + 9409 T^{4}$$)($$1 + 16 T + 159 T^{2} + 1552 T^{3} + 9409 T^{4}$$)($$1 - 2 T - 93 T^{2} - 194 T^{3} + 9409 T^{4}$$)($$1 + 8 T - 33 T^{2} + 776 T^{3} + 9409 T^{4}$$)($$1 - 10 T + 3 T^{2} - 970 T^{3} + 9409 T^{4}$$)($$( 1 - 19 T + 97 T^{2} )( 1 + 5 T + 97 T^{2} )$$)($$( 1 - 5 T + 97 T^{2} )( 1 + 19 T + 97 T^{2} )$$)($$( 1 - 5 T + 97 T^{2} )( 1 + 19 T + 97 T^{2} )$$)($$( 1 - 19 T + 97 T^{2} )( 1 + 5 T + 97 T^{2} )$$)($$1 + 8 T - 33 T^{2} + 776 T^{3} + 9409 T^{4}$$)($$1 - 10 T + 3 T^{2} - 970 T^{3} + 9409 T^{4}$$)($$1 - 2 T - 93 T^{2} - 194 T^{3} + 9409 T^{4}$$)($$1 + 16 T + 159 T^{2} + 1552 T^{3} + 9409 T^{4}$$)($$1 + 8 T - 33 T^{2} + 776 T^{3} + 9409 T^{4}$$)($$1 - 8 T - 33 T^{2} - 776 T^{3} + 9409 T^{4}$$)($$( 1 - 16 T + 159 T^{2} - 1552 T^{3} + 9409 T^{4} )^{2}$$)($$1 + 8 T - 98 T^{2} - 256 T^{3} + 10627 T^{4} - 24832 T^{5} - 922082 T^{6} + 7301384 T^{7} + 88529281 T^{8}$$)($$1 + 8 T - 98 T^{2} - 256 T^{3} + 10627 T^{4} - 24832 T^{5} - 922082 T^{6} + 7301384 T^{7} + 88529281 T^{8}$$)($$( 1 - 16 T + 159 T^{2} - 1552 T^{3} + 9409 T^{4} )^{2}$$)