# Properties

 Label 2016.2.s Level 2016 Weight 2 Character orbit s Rep. character $$\chi_{2016}(289,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 80 Newform subspaces 24 Sturm bound 768 Trace bound 11

# Related objects

## Defining parameters

 Level: $$N$$ = $$2016 = 2^{5} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 2016.s (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$24$$ Sturm bound: $$768$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2016, [\chi])$$.

Total New Old
Modular forms 832 80 752
Cusp forms 704 80 624
Eisenstein series 128 0 128

## Trace form

 $$80q + O(q^{10})$$ $$80q + 16q^{13} - 32q^{25} - 16q^{29} - 8q^{37} + 16q^{41} - 16q^{49} - 8q^{53} + 8q^{61} - 24q^{65} - 24q^{73} + 16q^{77} - 16q^{85} - 8q^{89} + 16q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2016, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
2016.2.s.a $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-4$$ $$-5$$ $$q-4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots$$
2016.2.s.b $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-4$$ $$5$$ $$q-4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots$$
2016.2.s.c $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$-1$$ $$q-3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots$$
2016.2.s.d $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$1$$ $$q-3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots$$
2016.2.s.e $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-5$$ $$q+(-2-\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$$
2016.2.s.f $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q+(-2+3\zeta_{6})q^{7}+(-2+2\zeta_{6})q^{11}+\cdots$$
2016.2.s.g $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$1$$ $$q+(2-3\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+5q^{13}+\cdots$$
2016.2.s.h $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$5$$ $$q+(2+\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+q^{13}+\cdots$$
2016.2.s.i $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$-5$$ $$q+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots$$
2016.2.s.j $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$1$$ $$5$$ $$q+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots$$
2016.2.s.k $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$-1$$ $$q+3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots$$
2016.2.s.l $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$-1$$ $$q+3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots$$
2016.2.s.m $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$1$$ $$q+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots$$
2016.2.s.n $$2$$ $$16.098$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$1$$ $$q+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots$$
2016.2.s.o $$4$$ $$16.098$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q+3\beta _{2}q^{5}+\beta _{3}q^{7}-\beta _{1}q^{11}-4q^{13}+\cdots$$
2016.2.s.p $$4$$ $$16.098$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-2\beta _{2}q^{5}+\beta _{3}q^{7}-3q^{13}+(2-2\beta _{2}+\cdots)q^{17}+\cdots$$
2016.2.s.q $$4$$ $$16.098$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$-4$$ $$q+(1+2\beta _{1}+\beta _{2})q^{5}+(-1-2\beta _{1}-\beta _{3})q^{7}+\cdots$$
2016.2.s.r $$4$$ $$16.098$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1-\zeta_{12}^{2})q^{5}+(2\zeta_{12}-3\zeta_{12}^{3})q^{7}+\cdots$$
2016.2.s.s $$4$$ $$16.098$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$2$$ $$4$$ $$q+(1+2\beta _{1}+\beta _{2})q^{5}+(1+2\beta _{1}+\beta _{3})q^{7}+\cdots$$
2016.2.s.t $$4$$ $$16.098$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+2\beta _{2}q^{5}+\beta _{3}q^{7}-3q^{13}+(-2+2\beta _{2}+\cdots)q^{17}+\cdots$$
2016.2.s.u $$6$$ $$16.098$$ 6.0.1156923.1 None $$0$$ $$0$$ $$0$$ $$-3$$ $$q+\beta _{4}q^{5}+(-1+\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots$$
2016.2.s.v $$6$$ $$16.098$$ 6.0.1156923.1 None $$0$$ $$0$$ $$0$$ $$3$$ $$q+\beta _{4}q^{5}+(1-\beta _{3}+\beta _{4})q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$$
2016.2.s.w $$8$$ $$16.098$$ 8.0.1445900625.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{5}+(\beta _{1}-\beta _{4}+\beta _{5})q^{7}+\beta _{6}q^{11}+\cdots$$
2016.2.s.x $$8$$ $$16.098$$ 8.0.1445900625.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{7}q^{5}+(-\beta _{1}+\beta _{4}-\beta _{5})q^{7}-\beta _{6}q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2016, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2016, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(336, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(504, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(672, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1008, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ ($$1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4}$$)($$1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4}$$)($$1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$$)($$1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$$)($$1 - 5 T^{2} + 25 T^{4}$$)($$1 - 5 T^{2} + 25 T^{4}$$)($$1 - 5 T^{2} + 25 T^{4}$$)($$1 - 5 T^{2} + 25 T^{4}$$)($$1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4}$$)($$1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4}$$)($$1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4}$$)($$1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4}$$)($$1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4}$$)($$1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4}$$)($$( 1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4} )^{2}$$)($$( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} )^{2}$$)($$1 - 2 T + T^{2} + 14 T^{3} - 36 T^{4} + 70 T^{5} + 25 T^{6} - 250 T^{7} + 625 T^{8}$$)($$( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} )^{2}$$)($$1 - 2 T + T^{2} + 14 T^{3} - 36 T^{4} + 70 T^{5} + 25 T^{6} - 250 T^{7} + 625 T^{8}$$)($$( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} )^{2}$$)($$1 - 6 T^{2} - 8 T^{3} + 6 T^{4} + 24 T^{5} + 86 T^{6} + 120 T^{7} + 150 T^{8} - 1000 T^{9} - 3750 T^{10} + 15625 T^{12}$$)($$1 - 6 T^{2} - 8 T^{3} + 6 T^{4} + 24 T^{5} + 86 T^{6} + 120 T^{7} + 150 T^{8} - 1000 T^{9} - 3750 T^{10} + 15625 T^{12}$$)($$1 - 11 T^{2} + 57 T^{4} - 154 T^{6} + 446 T^{8} - 3850 T^{10} + 35625 T^{12} - 171875 T^{14} + 390625 T^{16}$$)($$1 - 11 T^{2} + 57 T^{4} - 154 T^{6} + 446 T^{8} - 3850 T^{10} + 35625 T^{12} - 171875 T^{14} + 390625 T^{16}$$)
$7$ ($$1 + 5 T + 7 T^{2}$$)($$1 - 5 T + 7 T^{2}$$)($$1 + T + 7 T^{2}$$)($$1 - T + 7 T^{2}$$)($$1 + 5 T + 7 T^{2}$$)($$1 + T + 7 T^{2}$$)($$1 - T + 7 T^{2}$$)($$1 - 5 T + 7 T^{2}$$)($$1 + 5 T + 7 T^{2}$$)($$1 - 5 T + 7 T^{2}$$)($$1 + T + 7 T^{2}$$)($$1 + T + 7 T^{2}$$)($$1 - T + 7 T^{2}$$)($$1 - T + 7 T^{2}$$)($$( 1 - 7 T^{2} )^{2}$$)($$1 - 7 T^{2} + 49 T^{4}$$)($$( 1 + 2 T + 7 T^{2} )^{2}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$( 1 - 2 T + 7 T^{2} )^{2}$$)($$1 - 7 T^{2} + 49 T^{4}$$)($$1 + 3 T - 5 T^{3} + 147 T^{5} + 343 T^{6}$$)($$1 - 3 T + 5 T^{3} - 147 T^{5} + 343 T^{6}$$)($$( 1 + T^{2} + 49 T^{4} )^{2}$$)($$( 1 + T^{2} + 49 T^{4} )^{2}$$)
$11$ ($$1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4}$$)($$1 + 6 T + 25 T^{2} + 66 T^{3} + 121 T^{4}$$)($$1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4}$$)($$1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4}$$)($$1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4}$$)($$1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4}$$)($$1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4}$$)($$1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4}$$)($$1 + T - 10 T^{2} + 11 T^{3} + 121 T^{4}$$)($$1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4}$$)($$1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4}$$)($$1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4}$$)($$1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4}$$)($$1 + T - 10 T^{2} + 11 T^{3} + 121 T^{4}$$)($$1 - 15 T^{2} + 104 T^{4} - 1815 T^{6} + 14641 T^{8}$$)($$( 1 - 11 T^{2} + 121 T^{4} )^{2}$$)($$1 + 2 T - 17 T^{2} - 2 T^{3} + 276 T^{4} - 22 T^{5} - 2057 T^{6} + 2662 T^{7} + 14641 T^{8}$$)($$1 + 5 T^{2} - 96 T^{4} + 605 T^{6} + 14641 T^{8}$$)($$1 - 2 T - 17 T^{2} + 2 T^{3} + 276 T^{4} + 22 T^{5} - 2057 T^{6} - 2662 T^{7} + 14641 T^{8}$$)($$( 1 - 11 T^{2} + 121 T^{4} )^{2}$$)($$1 - 6 T^{2} - 76 T^{3} - 30 T^{4} + 228 T^{5} + 3710 T^{6} + 2508 T^{7} - 3630 T^{8} - 101156 T^{9} - 87846 T^{10} + 1771561 T^{12}$$)($$1 - 6 T^{2} + 76 T^{3} - 30 T^{4} - 228 T^{5} + 3710 T^{6} - 2508 T^{7} - 3630 T^{8} + 101156 T^{9} - 87846 T^{10} + 1771561 T^{12}$$)($$( 1 + T - 5 T^{2} - 16 T^{3} - 96 T^{4} - 176 T^{5} - 605 T^{6} + 1331 T^{7} + 14641 T^{8} )^{2}$$)($$( 1 - T - 5 T^{2} + 16 T^{3} - 96 T^{4} + 176 T^{5} - 605 T^{6} - 1331 T^{7} + 14641 T^{8} )^{2}$$)
$13$ ($$( 1 - 5 T + 13 T^{2} )^{2}$$)($$( 1 - 5 T + 13 T^{2} )^{2}$$)($$( 1 - 2 T + 13 T^{2} )^{2}$$)($$( 1 - 2 T + 13 T^{2} )^{2}$$)($$( 1 - T + 13 T^{2} )^{2}$$)($$( 1 - 5 T + 13 T^{2} )^{2}$$)($$( 1 - 5 T + 13 T^{2} )^{2}$$)($$( 1 - T + 13 T^{2} )^{2}$$)($$( 1 + 13 T^{2} )^{2}$$)($$( 1 + 13 T^{2} )^{2}$$)($$( 1 + 4 T + 13 T^{2} )^{2}$$)($$( 1 - 2 T + 13 T^{2} )^{2}$$)($$( 1 - 2 T + 13 T^{2} )^{2}$$)($$( 1 + 4 T + 13 T^{2} )^{2}$$)($$( 1 + 4 T + 13 T^{2} )^{4}$$)($$( 1 + 3 T + 13 T^{2} )^{4}$$)($$( 1 + 18 T^{2} + 169 T^{4} )^{2}$$)($$( 1 + 13 T^{2} )^{4}$$)($$( 1 + 18 T^{2} + 169 T^{4} )^{2}$$)($$( 1 + 3 T + 13 T^{2} )^{4}$$)($$( 1 + 3 T + 3 T^{2} - 34 T^{3} + 39 T^{4} + 507 T^{5} + 2197 T^{6} )^{2}$$)($$( 1 + 3 T + 3 T^{2} - 34 T^{3} + 39 T^{4} + 507 T^{5} + 2197 T^{6} )^{2}$$)($$( 1 - 3 T + 12 T^{2} - 39 T^{3} + 169 T^{4} )^{4}$$)($$( 1 - 3 T + 12 T^{2} - 39 T^{3} + 169 T^{4} )^{4}$$)
$17$ ($$1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4}$$)($$1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4}$$)($$1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4}$$)($$1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4}$$)($$1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4}$$)($$1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4}$$)($$1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4}$$)($$1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4}$$)($$1 + 8 T + 47 T^{2} + 136 T^{3} + 289 T^{4}$$)($$1 + 8 T + 47 T^{2} + 136 T^{3} + 289 T^{4}$$)($$1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4}$$)($$1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4}$$)($$1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4}$$)($$1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4}$$)($$( 1 - T - 16 T^{2} - 17 T^{3} + 289 T^{4} )^{2}$$)($$( 1 - 2 T - 13 T^{2} - 34 T^{3} + 289 T^{4} )^{2}$$)($$1 + 6 T + T^{2} + 6 T^{3} + 324 T^{4} + 102 T^{5} + 289 T^{6} + 29478 T^{7} + 83521 T^{8}$$)($$( 1 - 5 T + 8 T^{2} - 85 T^{3} + 289 T^{4} )^{2}$$)($$1 + 6 T + T^{2} + 6 T^{3} + 324 T^{4} + 102 T^{5} + 289 T^{6} + 29478 T^{7} + 83521 T^{8}$$)($$( 1 + 2 T - 13 T^{2} + 34 T^{3} + 289 T^{4} )^{2}$$)($$1 - 6 T + 9 T^{2} + 54 T^{3} - 378 T^{4} + 858 T^{5} - 1307 T^{6} + 14586 T^{7} - 109242 T^{8} + 265302 T^{9} + 751689 T^{10} - 8519142 T^{11} + 24137569 T^{12}$$)($$1 - 6 T + 9 T^{2} + 54 T^{3} - 378 T^{4} + 858 T^{5} - 1307 T^{6} + 14586 T^{7} - 109242 T^{8} + 265302 T^{9} + 751689 T^{10} - 8519142 T^{11} + 24137569 T^{12}$$)($$( 1 - 12 T + 65 T^{2} - 204 T^{3} + 289 T^{4} )^{2}( 1 + 12 T + 65 T^{2} + 204 T^{3} + 289 T^{4} )^{2}$$)($$( 1 - 12 T + 65 T^{2} - 204 T^{3} + 289 T^{4} )^{2}( 1 + 12 T + 65 T^{2} + 204 T^{3} + 289 T^{4} )^{2}$$)
$19$ ($$( 1 - 7 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} )$$)($$( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} )$$)($$1 + 6 T + 17 T^{2} + 114 T^{3} + 361 T^{4}$$)($$1 - 6 T + 17 T^{2} - 114 T^{3} + 361 T^{4}$$)($$1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4}$$)($$1 - 3 T - 10 T^{2} - 57 T^{3} + 361 T^{4}$$)($$1 + 3 T - 10 T^{2} + 57 T^{3} + 361 T^{4}$$)($$1 - 5 T + 6 T^{2} - 95 T^{3} + 361 T^{4}$$)($$1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4}$$)($$1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4}$$)($$1 - 19 T^{2} + 361 T^{4}$$)($$1 + 6 T + 17 T^{2} + 114 T^{3} + 361 T^{4}$$)($$1 - 6 T + 17 T^{2} - 114 T^{3} + 361 T^{4}$$)($$1 - 19 T^{2} + 361 T^{4}$$)($$1 + 25 T^{2} + 264 T^{4} + 9025 T^{6} + 130321 T^{8}$$)($$1 - 17 T^{2} - 72 T^{4} - 6137 T^{6} + 130321 T^{8}$$)($$1 + 10 T + 39 T^{2} + 230 T^{3} + 1460 T^{4} + 4370 T^{5} + 14079 T^{6} + 68590 T^{7} + 130321 T^{8}$$)($$1 - 35 T^{2} + 864 T^{4} - 12635 T^{6} + 130321 T^{8}$$)($$1 - 10 T + 39 T^{2} - 230 T^{3} + 1460 T^{4} - 4370 T^{5} + 14079 T^{6} - 68590 T^{7} + 130321 T^{8}$$)($$1 - 17 T^{2} - 72 T^{4} - 6137 T^{6} + 130321 T^{8}$$)($$1 + 3 T - 12 T^{2} + 59 T^{3} + 36 T^{4} - 1269 T^{5} + 2094 T^{6} - 24111 T^{7} + 12996 T^{8} + 404681 T^{9} - 1563852 T^{10} + 7428297 T^{11} + 47045881 T^{12}$$)($$1 - 3 T - 12 T^{2} - 59 T^{3} + 36 T^{4} + 1269 T^{5} + 2094 T^{6} + 24111 T^{7} + 12996 T^{8} - 404681 T^{9} - 1563852 T^{10} - 7428297 T^{11} + 47045881 T^{12}$$)($$1 - 67 T^{2} + 2661 T^{4} - 74102 T^{6} + 1590734 T^{8} - 26750822 T^{10} + 346784181 T^{12} - 3152074027 T^{14} + 16983563041 T^{16}$$)($$1 - 67 T^{2} + 2661 T^{4} - 74102 T^{6} + 1590734 T^{8} - 26750822 T^{10} + 346784181 T^{12} - 3152074027 T^{14} + 16983563041 T^{16}$$)
$23$ ($$1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4}$$)($$1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4}$$)($$1 + 2 T - 19 T^{2} + 46 T^{3} + 529 T^{4}$$)($$1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4}$$)($$1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4}$$)($$1 + 2 T - 19 T^{2} + 46 T^{3} + 529 T^{4}$$)($$1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4}$$)($$1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4}$$)($$1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4}$$)($$1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4}$$)($$1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4}$$)($$1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4}$$)($$1 + 2 T - 19 T^{2} + 46 T^{3} + 529 T^{4}$$)($$1 - 8 T + 41 T^{2} - 184 T^{3} + 529 T^{4}$$)($$1 - 39 T^{2} + 992 T^{4} - 20631 T^{6} + 279841 T^{8}$$)($$1 + 38 T^{2} + 915 T^{4} + 20102 T^{6} + 279841 T^{8}$$)($$1 + 2 T - 25 T^{2} - 34 T^{3} + 220 T^{4} - 782 T^{5} - 13225 T^{6} + 24334 T^{7} + 279841 T^{8}$$)($$1 - 43 T^{2} + 1320 T^{4} - 22747 T^{6} + 279841 T^{8}$$)($$1 - 2 T - 25 T^{2} + 34 T^{3} + 220 T^{4} + 782 T^{5} - 13225 T^{6} - 24334 T^{7} + 279841 T^{8}$$)($$1 + 38 T^{2} + 915 T^{4} + 20102 T^{6} + 279841 T^{8}$$)($$1 + 6 T - 9 T^{2} - 90 T^{3} - 90 T^{4} - 1146 T^{5} - 8885 T^{6} - 26358 T^{7} - 47610 T^{8} - 1095030 T^{9} - 2518569 T^{10} + 38618058 T^{11} + 148035889 T^{12}$$)($$1 - 6 T - 9 T^{2} + 90 T^{3} - 90 T^{4} + 1146 T^{5} - 8885 T^{6} + 26358 T^{7} - 47610 T^{8} + 1095030 T^{9} - 2518569 T^{10} - 38618058 T^{11} + 148035889 T^{12}$$)($$( 1 + 2 T - 19 T^{2} + 46 T^{3} + 529 T^{4} )^{4}$$)($$( 1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4} )^{4}$$)
$29$ ($$( 1 + 29 T^{2} )^{2}$$)($$( 1 + 29 T^{2} )^{2}$$)($$( 1 - T + 29 T^{2} )^{2}$$)($$( 1 - T + 29 T^{2} )^{2}$$)($$( 1 - 8 T + 29 T^{2} )^{2}$$)($$( 1 + 8 T + 29 T^{2} )^{2}$$)($$( 1 + 8 T + 29 T^{2} )^{2}$$)($$( 1 - 8 T + 29 T^{2} )^{2}$$)($$( 1 - 5 T + 29 T^{2} )^{2}$$)($$( 1 - 5 T + 29 T^{2} )^{2}$$)($$( 1 - 7 T + 29 T^{2} )^{2}$$)($$( 1 + T + 29 T^{2} )^{2}$$)($$( 1 + T + 29 T^{2} )^{2}$$)($$( 1 - 7 T + 29 T^{2} )^{2}$$)($$( 1 - 4 T + 29 T^{2} )^{4}$$)($$( 1 - 4 T + 29 T^{2} )^{4}$$)($$( 1 + 50 T^{2} + 841 T^{4} )^{2}$$)($$( 1 + 8 T + 29 T^{2} )^{4}$$)($$( 1 + 50 T^{2} + 841 T^{4} )^{2}$$)($$( 1 + 4 T + 29 T^{2} )^{4}$$)($$( 1 + 12 T + 126 T^{2} + 728 T^{3} + 3654 T^{4} + 10092 T^{5} + 24389 T^{6} )^{2}$$)($$( 1 + 12 T + 126 T^{2} + 728 T^{3} + 3654 T^{4} + 10092 T^{5} + 24389 T^{6} )^{2}$$)($$( 1 + 55 T^{2} + 2292 T^{4} + 46255 T^{6} + 707281 T^{8} )^{2}$$)($$( 1 + 55 T^{2} + 2292 T^{4} + 46255 T^{6} + 707281 T^{8} )^{2}$$)
$31$ ($$1 - 3 T - 22 T^{2} - 93 T^{3} + 961 T^{4}$$)($$1 + 3 T - 22 T^{2} + 93 T^{3} + 961 T^{4}$$)($$1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4}$$)($$1 - T - 30 T^{2} - 31 T^{3} + 961 T^{4}$$)($$1 - 3 T - 22 T^{2} - 93 T^{3} + 961 T^{4}$$)($$1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4}$$)($$1 - T - 30 T^{2} - 31 T^{3} + 961 T^{4}$$)($$1 + 3 T - 22 T^{2} + 93 T^{3} + 961 T^{4}$$)($$( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} )$$)($$( 1 - 4 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} )$$)($$( 1 - 7 T + 31 T^{2} )( 1 - 4 T + 31 T^{2} )$$)($$1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4}$$)($$1 - T - 30 T^{2} - 31 T^{3} + 961 T^{4}$$)($$( 1 + 4 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} )$$)($$1 - 55 T^{2} + 2064 T^{4} - 52855 T^{6} + 923521 T^{8}$$)($$1 - 41 T^{2} + 720 T^{4} - 39401 T^{6} + 923521 T^{8}$$)($$1 + 14 T + 87 T^{2} + 658 T^{3} + 4844 T^{4} + 20398 T^{5} + 83607 T^{6} + 417074 T^{7} + 923521 T^{8}$$)($$( 1 - 46 T^{2} + 961 T^{4} )( 1 + 59 T^{2} + 961 T^{4} )$$)($$1 - 14 T + 87 T^{2} - 658 T^{3} + 4844 T^{4} - 20398 T^{5} + 83607 T^{6} - 417074 T^{7} + 923521 T^{8}$$)($$1 - 41 T^{2} + 720 T^{4} - 39401 T^{6} + 923521 T^{8}$$)($$1 + 3 T - 63 T^{2} - 62 T^{3} + 2535 T^{4} - 501 T^{5} - 90450 T^{6} - 15531 T^{7} + 2436135 T^{8} - 1847042 T^{9} - 58181823 T^{10} + 85887453 T^{11} + 887503681 T^{12}$$)($$1 - 3 T - 63 T^{2} + 62 T^{3} + 2535 T^{4} + 501 T^{5} - 90450 T^{6} + 15531 T^{7} + 2436135 T^{8} + 1847042 T^{9} - 58181823 T^{10} - 85887453 T^{11} + 887503681 T^{12}$$)($$1 - 58 T^{2} + 1641 T^{4} + 11542 T^{6} - 1187596 T^{8} + 11091862 T^{10} + 1515497961 T^{12} - 51475213498 T^{14} + 852891037441 T^{16}$$)($$1 - 58 T^{2} + 1641 T^{4} + 11542 T^{6} - 1187596 T^{8} + 11091862 T^{10} + 1515497961 T^{12} - 51475213498 T^{14} + 852891037441 T^{16}$$)
$37$ ($$1 + 3 T - 28 T^{2} + 111 T^{3} + 1369 T^{4}$$)($$1 + 3 T - 28 T^{2} + 111 T^{3} + 1369 T^{4}$$)($$( 1 - T + 37 T^{2} )( 1 + 11 T + 37 T^{2} )$$)($$( 1 - T + 37 T^{2} )( 1 + 11 T + 37 T^{2} )$$)($$1 - 9 T + 44 T^{2} - 333 T^{3} + 1369 T^{4}$$)($$1 - 5 T - 12 T^{2} - 185 T^{3} + 1369 T^{4}$$)($$1 - 5 T - 12 T^{2} - 185 T^{3} + 1369 T^{4}$$)($$1 - 9 T + 44 T^{2} - 333 T^{3} + 1369 T^{4}$$)($$1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4}$$)($$1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4}$$)($$1 + 4 T - 21 T^{2} + 148 T^{3} + 1369 T^{4}$$)($$( 1 - T + 37 T^{2} )( 1 + 11 T + 37 T^{2} )$$)($$( 1 - T + 37 T^{2} )( 1 + 11 T + 37 T^{2} )$$)($$1 + 4 T - 21 T^{2} + 148 T^{3} + 1369 T^{4}$$)($$( 1 - 5 T - 12 T^{2} - 185 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 - 5 T - 12 T^{2} - 185 T^{3} + 1369 T^{4} )^{2}$$)($$1 + 6 T - 15 T^{2} - 138 T^{3} - 100 T^{4} - 5106 T^{5} - 20535 T^{6} + 303918 T^{7} + 1874161 T^{8}$$)($$( 1 - 5 T - 12 T^{2} - 185 T^{3} + 1369 T^{4} )^{2}$$)($$1 + 6 T - 15 T^{2} - 138 T^{3} - 100 T^{4} - 5106 T^{5} - 20535 T^{6} + 303918 T^{7} + 1874161 T^{8}$$)($$( 1 - 5 T - 12 T^{2} - 185 T^{3} + 1369 T^{4} )^{2}$$)($$1 + 3 T - 18 T^{2} + 373 T^{3} + 168 T^{4} - 5829 T^{5} + 83328 T^{6} - 215673 T^{7} + 229992 T^{8} + 18893569 T^{9} - 33734898 T^{10} + 208031871 T^{11} + 2565726409 T^{12}$$)($$1 + 3 T - 18 T^{2} + 373 T^{3} + 168 T^{4} - 5829 T^{5} + 83328 T^{6} - 215673 T^{7} + 229992 T^{8} + 18893569 T^{9} - 33734898 T^{10} + 208031871 T^{11} + 2565726409 T^{12}$$)($$( 1 - 3 T - 51 T^{2} + 42 T^{3} + 1898 T^{4} + 1554 T^{5} - 69819 T^{6} - 151959 T^{7} + 1874161 T^{8} )^{2}$$)($$( 1 - 3 T - 51 T^{2} + 42 T^{3} + 1898 T^{4} + 1554 T^{5} - 69819 T^{6} - 151959 T^{7} + 1874161 T^{8} )^{2}$$)
$41$ ($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 - 4 T + 41 T^{2} )^{2}$$)($$( 1 - 4 T + 41 T^{2} )^{2}$$)($$( 1 + 2 T + 41 T^{2} )^{2}$$)($$( 1 + 2 T + 41 T^{2} )^{2}$$)($$( 1 + 2 T + 41 T^{2} )^{2}$$)($$( 1 + 2 T + 41 T^{2} )^{2}$$)($$( 1 + 4 T + 41 T^{2} )^{2}$$)($$( 1 + 4 T + 41 T^{2} )^{2}$$)($$( 1 - 4 T + 41 T^{2} )^{2}$$)($$( 1 + 4 T + 41 T^{2} )^{2}$$)($$( 1 + 4 T + 41 T^{2} )^{2}$$)($$( 1 - 4 T + 41 T^{2} )^{2}$$)($$( 1 + 8 T + 41 T^{2} )^{4}$$)($$( 1 + 4 T + 41 T^{2} )^{4}$$)($$( 1 - 8 T + 90 T^{2} - 328 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 4 T + 41 T^{2} )^{4}$$)($$( 1 - 8 T + 90 T^{2} - 328 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 - 4 T + 41 T^{2} )^{4}$$)($$( 1 - 6 T + 27 T^{2} + 20 T^{3} + 1107 T^{4} - 10086 T^{5} + 68921 T^{6} )^{2}$$)($$( 1 - 6 T + 27 T^{2} + 20 T^{3} + 1107 T^{4} - 10086 T^{5} + 68921 T^{6} )^{2}$$)($$( 1 + 20 T^{2} - 698 T^{4} + 33620 T^{6} + 2825761 T^{8} )^{2}$$)($$( 1 + 20 T^{2} - 698 T^{4} + 33620 T^{6} + 2825761 T^{8} )^{2}$$)
$43$ ($$( 1 - 5 T + 43 T^{2} )^{2}$$)($$( 1 + 5 T + 43 T^{2} )^{2}$$)($$( 1 + 4 T + 43 T^{2} )^{2}$$)($$( 1 - 4 T + 43 T^{2} )^{2}$$)($$( 1 - T + 43 T^{2} )^{2}$$)($$( 1 + 7 T + 43 T^{2} )^{2}$$)($$( 1 - 7 T + 43 T^{2} )^{2}$$)($$( 1 + T + 43 T^{2} )^{2}$$)($$( 1 + 10 T + 43 T^{2} )^{2}$$)($$( 1 - 10 T + 43 T^{2} )^{2}$$)($$( 1 - 2 T + 43 T^{2} )^{2}$$)($$( 1 + 4 T + 43 T^{2} )^{2}$$)($$( 1 - 4 T + 43 T^{2} )^{2}$$)($$( 1 + 2 T + 43 T^{2} )^{2}$$)($$( 1 - 26 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 + 65 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 8 T + 70 T^{2} - 344 T^{3} + 1849 T^{4} )^{2}$$)($$( 1 + 38 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 + 8 T + 70 T^{2} + 344 T^{3} + 1849 T^{4} )^{2}$$)($$( 1 + 65 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 15 T + 177 T^{2} - 1318 T^{3} + 7611 T^{4} - 27735 T^{5} + 79507 T^{6} )^{2}$$)($$( 1 + 15 T + 177 T^{2} + 1318 T^{3} + 7611 T^{4} + 27735 T^{5} + 79507 T^{6} )^{2}$$)($$( 1 + 103 T^{2} + 5944 T^{4} + 190447 T^{6} + 3418801 T^{8} )^{2}$$)($$( 1 + 103 T^{2} + 5944 T^{4} + 190447 T^{6} + 3418801 T^{8} )^{2}$$)
$47$ ($$1 + 4 T - 31 T^{2} + 188 T^{3} + 2209 T^{4}$$)($$1 - 4 T - 31 T^{2} - 188 T^{3} + 2209 T^{4}$$)($$1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4}$$)($$1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4}$$)($$1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4}$$)($$1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4}$$)($$1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4}$$)($$1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4}$$)($$1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4}$$)($$1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4}$$)($$1 - 2 T - 43 T^{2} - 94 T^{3} + 2209 T^{4}$$)($$1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4}$$)($$1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4}$$)($$1 + 2 T - 43 T^{2} + 94 T^{3} + 2209 T^{4}$$)($$1 - 87 T^{2} + 5360 T^{4} - 192183 T^{6} + 4879681 T^{8}$$)($$1 - 10 T^{2} - 2109 T^{4} - 22090 T^{6} + 4879681 T^{8}$$)($$1 - 18 T + 151 T^{2} - 1422 T^{3} + 12492 T^{4} - 66834 T^{5} + 333559 T^{6} - 1868814 T^{7} + 4879681 T^{8}$$)($$1 - 19 T^{2} - 1848 T^{4} - 41971 T^{6} + 4879681 T^{8}$$)($$1 + 18 T + 151 T^{2} + 1422 T^{3} + 12492 T^{4} + 66834 T^{5} + 333559 T^{6} + 1868814 T^{7} + 4879681 T^{8}$$)($$1 - 10 T^{2} - 2109 T^{4} - 22090 T^{6} + 4879681 T^{8}$$)($$1 - 12 T - 9 T^{2} + 196 T^{3} + 4026 T^{4} - 9372 T^{5} - 178417 T^{6} - 440484 T^{7} + 8893434 T^{8} + 20349308 T^{9} - 43917129 T^{10} - 2752140084 T^{11} + 10779215329 T^{12}$$)($$1 + 12 T - 9 T^{2} - 196 T^{3} + 4026 T^{4} + 9372 T^{5} - 178417 T^{6} + 440484 T^{7} + 8893434 T^{8} - 20349308 T^{9} - 43917129 T^{10} + 2752140084 T^{11} + 10779215329 T^{12}$$)($$( 1 + 6 T - 2 T^{2} - 336 T^{3} - 2457 T^{4} - 15792 T^{5} - 4418 T^{6} + 622938 T^{7} + 4879681 T^{8} )^{2}$$)($$( 1 - 6 T - 2 T^{2} + 336 T^{3} - 2457 T^{4} + 15792 T^{5} - 4418 T^{6} - 622938 T^{7} + 4879681 T^{8} )^{2}$$)
$53$ ($$1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4}$$)($$1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4}$$)($$1 + 5 T - 28 T^{2} + 265 T^{3} + 2809 T^{4}$$)($$1 + 5 T - 28 T^{2} + 265 T^{3} + 2809 T^{4}$$)($$1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4}$$)($$1 + 2 T - 49 T^{2} + 106 T^{3} + 2809 T^{4}$$)($$1 + 2 T - 49 T^{2} + 106 T^{3} + 2809 T^{4}$$)($$1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4}$$)($$1 + T - 52 T^{2} + 53 T^{3} + 2809 T^{4}$$)($$1 + T - 52 T^{2} + 53 T^{3} + 2809 T^{4}$$)($$1 + 11 T + 68 T^{2} + 583 T^{3} + 2809 T^{4}$$)($$1 - 5 T - 28 T^{2} - 265 T^{3} + 2809 T^{4}$$)($$1 - 5 T - 28 T^{2} - 265 T^{3} + 2809 T^{4}$$)($$1 + 11 T + 68 T^{2} + 583 T^{3} + 2809 T^{4}$$)($$( 1 - 7 T - 4 T^{2} - 371 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 + 10 T + 47 T^{2} + 530 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 + T - 52 T^{2} + 53 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 + T - 52 T^{2} + 53 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 + T - 52 T^{2} + 53 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4} )^{2}$$)($$1 - 6 T - 42 T^{2} + 1136 T^{3} - 2862 T^{4} - 29802 T^{5} + 517382 T^{6} - 1579506 T^{7} - 8039358 T^{8} + 169124272 T^{9} - 331400202 T^{10} - 2509172958 T^{11} + 22164361129 T^{12}$$)($$1 - 6 T - 42 T^{2} + 1136 T^{3} - 2862 T^{4} - 29802 T^{5} + 517382 T^{6} - 1579506 T^{7} - 8039358 T^{8} + 169124272 T^{9} - 331400202 T^{10} - 2509172958 T^{11} + 22164361129 T^{12}$$)($$1 - 3 T^{2} - 4295 T^{4} + 3942 T^{6} + 10608654 T^{8} + 11073078 T^{10} - 33889615895 T^{12} - 66493083387 T^{14} + 62259690411361 T^{16}$$)($$1 - 3 T^{2} - 4295 T^{4} + 3942 T^{6} + 10608654 T^{8} + 11073078 T^{10} - 33889615895 T^{12} - 66493083387 T^{14} + 62259690411361 T^{16}$$)
$59$ ($$1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4}$$)($$1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4}$$)($$1 + 13 T + 110 T^{2} + 767 T^{3} + 3481 T^{4}$$)($$1 - 13 T + 110 T^{2} - 767 T^{3} + 3481 T^{4}$$)($$1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4}$$)($$1 + 10 T + 41 T^{2} + 590 T^{3} + 3481 T^{4}$$)($$1 - 10 T + 41 T^{2} - 590 T^{3} + 3481 T^{4}$$)($$1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4}$$)($$1 + 9 T + 22 T^{2} + 531 T^{3} + 3481 T^{4}$$)($$1 - 9 T + 22 T^{2} - 531 T^{3} + 3481 T^{4}$$)($$1 + 7 T - 10 T^{2} + 413 T^{3} + 3481 T^{4}$$)($$1 - 13 T + 110 T^{2} - 767 T^{3} + 3481 T^{4}$$)($$1 + 13 T + 110 T^{2} + 767 T^{3} + 3481 T^{4}$$)($$1 - 7 T - 10 T^{2} - 413 T^{3} + 3481 T^{4}$$)($$1 - 111 T^{2} + 8840 T^{4} - 386391 T^{6} + 12117361 T^{8}$$)($$1 - 34 T^{2} - 2325 T^{4} - 118354 T^{6} + 12117361 T^{8}$$)($$1 - 2 T - 17 T^{2} + 194 T^{3} - 3276 T^{4} + 11446 T^{5} - 59177 T^{6} - 410758 T^{7} + 12117361 T^{8}$$)($$1 - 115 T^{2} + 9744 T^{4} - 400315 T^{6} + 12117361 T^{8}$$)($$1 + 2 T - 17 T^{2} - 194 T^{3} - 3276 T^{4} - 11446 T^{5} - 59177 T^{6} + 410758 T^{7} + 12117361 T^{8}$$)($$1 - 34 T^{2} - 2325 T^{4} - 118354 T^{6} + 12117361 T^{8}$$)($$1 - 12 T - 54 T^{2} + 292 T^{3} + 11514 T^{4} - 25536 T^{5} - 623986 T^{6} - 1506624 T^{7} + 40080234 T^{8} + 59970668 T^{9} - 654337494 T^{10} - 8579091588 T^{11} + 42180533641 T^{12}$$)($$1 + 12 T - 54 T^{2} - 292 T^{3} + 11514 T^{4} + 25536 T^{5} - 623986 T^{6} + 1506624 T^{7} + 40080234 T^{8} - 59970668 T^{9} - 654337494 T^{10} + 8579091588 T^{11} + 42180533641 T^{12}$$)($$( 1 + 11 T - 11 T^{2} + 154 T^{3} + 6804 T^{4} + 9086 T^{5} - 38291 T^{6} + 2259169 T^{7} + 12117361 T^{8} )^{2}$$)($$( 1 - 11 T - 11 T^{2} - 154 T^{3} + 6804 T^{4} - 9086 T^{5} - 38291 T^{6} - 2259169 T^{7} + 12117361 T^{8} )^{2}$$)
$61$ ($$1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4}$$)($$1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4}$$)($$1 - 8 T + 3 T^{2} - 488 T^{3} + 3721 T^{4}$$)($$1 - 8 T + 3 T^{2} - 488 T^{3} + 3721 T^{4}$$)($$1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4}$$)($$1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4}$$)($$1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4}$$)($$1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4}$$)($$1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4}$$)($$1 - 2 T - 57 T^{2} - 122 T^{3} + 3721 T^{4}$$)($$1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4}$$)($$1 - 8 T + 3 T^{2} - 488 T^{3} + 3721 T^{4}$$)($$1 - 8 T + 3 T^{2} - 488 T^{3} + 3721 T^{4}$$)($$1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4}$$)($$( 1 - 5 T - 36 T^{2} - 305 T^{3} + 3721 T^{4} )^{2}$$)($$( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} )^{2}$$)($$1 + 6 T - 63 T^{2} - 138 T^{3} + 3884 T^{4} - 8418 T^{5} - 234423 T^{6} + 1361886 T^{7} + 13845841 T^{8}$$)($$( 1 + 11 T + 60 T^{2} + 671 T^{3} + 3721 T^{4} )^{2}$$)($$1 + 6 T - 63 T^{2} - 138 T^{3} + 3884 T^{4} - 8418 T^{5} - 234423 T^{6} + 1361886 T^{7} + 13845841 T^{8}$$)($$( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} )^{2}$$)($$1 - 18 T + 129 T^{2} - 222 T^{3} - 3462 T^{4} + 40662 T^{5} - 368431 T^{6} + 2480382 T^{7} - 12882102 T^{8} - 50389782 T^{9} + 1786113489 T^{10} - 15202733418 T^{11} + 51520374361 T^{12}$$)($$1 - 18 T + 129 T^{2} - 222 T^{3} - 3462 T^{4} + 40662 T^{5} - 368431 T^{6} + 2480382 T^{7} - 12882102 T^{8} - 50389782 T^{9} + 1786113489 T^{10} - 15202733418 T^{11} + 51520374361 T^{12}$$)($$( 1 + 6 T - 30 T^{2} - 336 T^{3} - 1561 T^{4} - 20496 T^{5} - 111630 T^{6} + 1361886 T^{7} + 13845841 T^{8} )^{2}$$)($$( 1 + 6 T - 30 T^{2} - 336 T^{3} - 1561 T^{4} - 20496 T^{5} - 111630 T^{6} + 1361886 T^{7} + 13845841 T^{8} )^{2}$$)
$67$ ($$1 + 7 T - 18 T^{2} + 469 T^{3} + 4489 T^{4}$$)($$1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4}$$)($$1 + 14 T + 129 T^{2} + 938 T^{3} + 4489 T^{4}$$)($$1 - 14 T + 129 T^{2} - 938 T^{3} + 4489 T^{4}$$)($$( 1 - 16 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} )$$)($$( 1 - 5 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} )$$)($$( 1 - 16 T + 67 T^{2} )( 1 + 5 T + 67 T^{2} )$$)($$( 1 - 11 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} )$$)($$1 - 2 T - 63 T^{2} - 134 T^{3} + 4489 T^{4}$$)($$1 + 2 T - 63 T^{2} + 134 T^{3} + 4489 T^{4}$$)($$1 - 10 T + 33 T^{2} - 670 T^{3} + 4489 T^{4}$$)($$1 + 14 T + 129 T^{2} + 938 T^{3} + 4489 T^{4}$$)($$1 - 14 T + 129 T^{2} - 938 T^{3} + 4489 T^{4}$$)($$1 + 10 T + 33 T^{2} + 670 T^{3} + 4489 T^{4}$$)($$1 - 127 T^{2} + 11640 T^{4} - 570103 T^{6} + 20151121 T^{8}$$)($$1 - 113 T^{2} + 8280 T^{4} - 507257 T^{6} + 20151121 T^{8}$$)($$1 - 14 T + 31 T^{2} - 434 T^{3} + 9604 T^{4} - 29078 T^{5} + 139159 T^{6} - 4210682 T^{7} + 20151121 T^{8}$$)($$( 1 - 109 T^{2} + 4489 T^{4} )( 1 + 122 T^{2} + 4489 T^{4} )$$)($$1 + 14 T + 31 T^{2} + 434 T^{3} + 9604 T^{4} + 29078 T^{5} + 139159 T^{6} + 4210682 T^{7} + 20151121 T^{8}$$)($$1 - 113 T^{2} + 8280 T^{4} - 507257 T^{6} + 20151121 T^{8}$$)($$1 + 9 T - 108 T^{2} - 383 T^{3} + 13680 T^{4} + 9405 T^{5} - 1069626 T^{6} + 630135 T^{7} + 61409520 T^{8} - 115192229 T^{9} - 2176321068 T^{10} + 12151125963 T^{11} + 90458382169 T^{12}$$)($$1 - 9 T - 108 T^{2} + 383 T^{3} + 13680 T^{4} - 9405 T^{5} - 1069626 T^{6} - 630135 T^{7} + 61409520 T^{8} + 115192229 T^{9} - 2176321068 T^{10} - 12151125963 T^{11} + 90458382169 T^{12}$$)($$1 - 83 T^{2} - 155 T^{4} + 160522 T^{6} - 1457906 T^{8} + 720583258 T^{10} - 3123423755 T^{12} - 7508045720027 T^{14} + 406067677556641 T^{16}$$)($$1 - 83 T^{2} - 155 T^{4} + 160522 T^{6} - 1457906 T^{8} + 720583258 T^{10} - 3123423755 T^{12} - 7508045720027 T^{14} + 406067677556641 T^{16}$$)
$71$ ($$( 1 + 16 T + 71 T^{2} )^{2}$$)($$( 1 - 16 T + 71 T^{2} )^{2}$$)($$( 1 + 12 T + 71 T^{2} )^{2}$$)($$( 1 - 12 T + 71 T^{2} )^{2}$$)($$( 1 + 4 T + 71 T^{2} )^{2}$$)($$( 1 - 12 T + 71 T^{2} )^{2}$$)($$( 1 + 12 T + 71 T^{2} )^{2}$$)($$( 1 - 4 T + 71 T^{2} )^{2}$$)($$( 1 - 6 T + 71 T^{2} )^{2}$$)($$( 1 + 6 T + 71 T^{2} )^{2}$$)($$( 1 - 6 T + 71 T^{2} )^{2}$$)($$( 1 - 12 T + 71 T^{2} )^{2}$$)($$( 1 + 12 T + 71 T^{2} )^{2}$$)($$( 1 + 6 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{4}$$)($$( 1 + 58 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 16 T + 174 T^{2} + 1136 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 16 T + 174 T^{2} - 1136 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 + 58 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 177 T^{2} + 32 T^{3} + 12567 T^{4} + 357911 T^{6} )^{2}$$)($$( 1 + 177 T^{2} - 32 T^{3} + 12567 T^{4} + 357911 T^{6} )^{2}$$)($$( 1 + 2 T + 78 T^{2} + 142 T^{3} + 5041 T^{4} )^{4}$$)($$( 1 - 2 T + 78 T^{2} - 142 T^{3} + 5041 T^{4} )^{4}$$)
$73$ ($$1 - 3 T - 64 T^{2} - 219 T^{3} + 5329 T^{4}$$)($$1 - 3 T - 64 T^{2} - 219 T^{3} + 5329 T^{4}$$)($$1 - 6 T - 37 T^{2} - 438 T^{3} + 5329 T^{4}$$)($$1 - 6 T - 37 T^{2} - 438 T^{3} + 5329 T^{4}$$)($$1 - 11 T + 48 T^{2} - 803 T^{3} + 5329 T^{4}$$)($$1 - 3 T - 64 T^{2} - 219 T^{3} + 5329 T^{4}$$)($$1 - 3 T - 64 T^{2} - 219 T^{3} + 5329 T^{4}$$)($$1 - 11 T + 48 T^{2} - 803 T^{3} + 5329 T^{4}$$)($$1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4}$$)($$1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4}$$)($$1 - 6 T - 37 T^{2} - 438 T^{3} + 5329 T^{4}$$)($$1 - 6 T - 37 T^{2} - 438 T^{3} + 5329 T^{4}$$)($$1 - 6 T - 37 T^{2} - 438 T^{3} + 5329 T^{4}$$)($$1 - 6 T - 37 T^{2} - 438 T^{3} + 5329 T^{4}$$)($$( 1 - 9 T + 8 T^{2} - 657 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 + 9 T + 8 T^{2} + 657 T^{3} + 5329 T^{4} )^{2}$$)($$1 - 18 T + 129 T^{2} - 882 T^{3} + 9044 T^{4} - 64386 T^{5} + 687441 T^{6} - 7002306 T^{7} + 28398241 T^{8}$$)($$( 1 + 15 T + 152 T^{2} + 1095 T^{3} + 5329 T^{4} )^{2}$$)($$1 - 18 T + 129 T^{2} - 882 T^{3} + 9044 T^{4} - 64386 T^{5} + 687441 T^{6} - 7002306 T^{7} + 28398241 T^{8}$$)($$( 1 + 9 T + 8 T^{2} + 657 T^{3} + 5329 T^{4} )^{2}$$)($$1 + 33 T + 534 T^{2} + 6687 T^{3} + 75648 T^{4} + 728637 T^{5} + 6291524 T^{6} + 53190501 T^{7} + 403128192 T^{8} + 2601356679 T^{9} + 15164660694 T^{10} + 68411362569 T^{11} + 151334226289 T^{12}$$)($$1 + 33 T + 534 T^{2} + 6687 T^{3} + 75648 T^{4} + 728637 T^{5} + 6291524 T^{6} + 53190501 T^{7} + 403128192 T^{8} + 2601356679 T^{9} + 15164660694 T^{10} + 68411362569 T^{11} + 151334226289 T^{12}$$)($$( 1 + 3 T - 123 T^{2} - 42 T^{3} + 11438 T^{4} - 3066 T^{5} - 655467 T^{6} + 1167051 T^{7} + 28398241 T^{8} )^{2}$$)($$( 1 + 3 T - 123 T^{2} - 42 T^{3} + 11438 T^{4} - 3066 T^{5} - 655467 T^{6} + 1167051 T^{7} + 28398241 T^{8} )^{2}$$)
$79$ ($$1 + 11 T + 42 T^{2} + 869 T^{3} + 6241 T^{4}$$)($$1 - 11 T + 42 T^{2} - 869 T^{3} + 6241 T^{4}$$)($$1 - 11 T + 42 T^{2} - 869 T^{3} + 6241 T^{4}$$)($$1 + 11 T + 42 T^{2} + 869 T^{3} + 6241 T^{4}$$)($$1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4}$$)($$( 1 - 13 T + 79 T^{2} )( 1 - 4 T + 79 T^{2} )$$)($$( 1 + 4 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} )$$)($$1 + 5 T - 54 T^{2} + 395 T^{3} + 6241 T^{4}$$)($$1 + 9 T + 2 T^{2} + 711 T^{3} + 6241 T^{4}$$)($$1 - 9 T + 2 T^{2} - 711 T^{3} + 6241 T^{4}$$)($$1 - 11 T + 42 T^{2} - 869 T^{3} + 6241 T^{4}$$)($$1 - 11 T + 42 T^{2} - 869 T^{3} + 6241 T^{4}$$)($$1 + 11 T + 42 T^{2} + 869 T^{3} + 6241 T^{4}$$)($$1 + 11 T + 42 T^{2} + 869 T^{3} + 6241 T^{4}$$)($$1 - 151 T^{2} + 16560 T^{4} - 942391 T^{6} + 38950081 T^{8}$$)($$1 - 137 T^{2} + 12528 T^{4} - 855017 T^{6} + 38950081 T^{8}$$)($$1 - 2 T - 105 T^{2} + 98 T^{3} + 5324 T^{4} + 7742 T^{5} - 655305 T^{6} - 986078 T^{7} + 38950081 T^{8}$$)($$1 - 155 T^{2} + 17784 T^{4} - 967355 T^{6} + 38950081 T^{8}$$)($$1 + 2 T - 105 T^{2} - 98 T^{3} + 5324 T^{4} - 7742 T^{5} - 655305 T^{6} + 986078 T^{7} + 38950081 T^{8}$$)($$1 - 137 T^{2} + 12528 T^{4} - 855017 T^{6} + 38950081 T^{8}$$)($$1 - 27 T + 297 T^{2} - 2426 T^{3} + 27783 T^{4} - 321003 T^{5} + 3028254 T^{6} - 25359237 T^{7} + 173393703 T^{8} - 1196112614 T^{9} + 11568174057 T^{10} - 83080522773 T^{11} + 243087455521 T^{12}$$)($$1 + 27 T + 297 T^{2} + 2426 T^{3} + 27783 T^{4} + 321003 T^{5} + 3028254 T^{6} + 25359237 T^{7} + 173393703 T^{8} + 1196112614 T^{9} + 11568174057 T^{10} + 83080522773 T^{11} + 243087455521 T^{12}$$)($$1 + 110 T^{2} + 753 T^{4} - 124850 T^{6} + 14288228 T^{8} - 779188850 T^{10} + 29329410993 T^{12} + 26739620107310 T^{14} + 1517108809906561 T^{16}$$)($$1 + 110 T^{2} + 753 T^{4} - 124850 T^{6} + 14288228 T^{8} - 779188850 T^{10} + 29329410993 T^{12} + 26739620107310 T^{14} + 1517108809906561 T^{16}$$)
$83$ ($$( 1 + 12 T + 83 T^{2} )^{2}$$)($$( 1 - 12 T + 83 T^{2} )^{2}$$)($$( 1 + 7 T + 83 T^{2} )^{2}$$)($$( 1 - 7 T + 83 T^{2} )^{2}$$)($$( 1 + 83 T^{2} )^{2}$$)($$( 1 + 16 T + 83 T^{2} )^{2}$$)($$( 1 - 16 T + 83 T^{2} )^{2}$$)($$( 1 + 83 T^{2} )^{2}$$)($$( 1 + 3 T + 83 T^{2} )^{2}$$)($$( 1 - 3 T + 83 T^{2} )^{2}$$)($$( 1 - 11 T + 83 T^{2} )^{2}$$)($$( 1 - 7 T + 83 T^{2} )^{2}$$)($$( 1 + 7 T + 83 T^{2} )^{2}$$)($$( 1 + 11 T + 83 T^{2} )^{2}$$)($$( 1 + 54 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 + 82 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 + 8 T + 54 T^{2} + 664 T^{3} + 6889 T^{4} )^{2}$$)($$( 1 + 118 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 8 T + 54 T^{2} - 664 T^{3} + 6889 T^{4} )^{2}$$)($$( 1 + 82 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 + 18 T + 234 T^{2} + 2040 T^{3} + 19422 T^{4} + 124002 T^{5} + 571787 T^{6} )^{2}$$)($$( 1 - 18 T + 234 T^{2} - 2040 T^{3} + 19422 T^{4} - 124002 T^{5} + 571787 T^{6} )^{2}$$)($$( 1 - 11 T + 180 T^{2} - 913 T^{3} + 6889 T^{4} )^{4}$$)($$( 1 + 11 T + 180 T^{2} + 913 T^{3} + 6889 T^{4} )^{4}$$)
$89$ ($$1 - 4 T - 73 T^{2} - 356 T^{3} + 7921 T^{4}$$)($$1 - 4 T - 73 T^{2} - 356 T^{3} + 7921 T^{4}$$)($$1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4}$$)($$1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4}$$)($$1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4}$$)($$1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4}$$)($$1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4}$$)($$1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4}$$)($$1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4}$$)($$1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4}$$)($$1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4}$$)($$1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4}$$)($$1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4}$$)($$1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4}$$)($$( 1 + 9 T - 8 T^{2} + 801 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 - 4 T - 73 T^{2} - 356 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 9 T - 8 T^{2} + 801 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 - 7 T - 40 T^{2} - 623 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 9 T - 8 T^{2} + 801 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 4 T - 73 T^{2} + 356 T^{3} + 7921 T^{4} )^{2}$$)($$1 + 12 T - 135 T^{2} - 700 T^{3} + 28722 T^{4} + 63804 T^{5} - 2561959 T^{6} + 5678556 T^{7} + 227506962 T^{8} - 493478300 T^{9} - 8470202535 T^{10} + 67008713388 T^{11} + 496981290961 T^{12}$$)($$1 + 12 T - 135 T^{2} - 700 T^{3} + 28722 T^{4} + 63804 T^{5} - 2561959 T^{6} + 5678556 T^{7} + 227506962 T^{8} - 493478300 T^{9} - 8470202535 T^{10} + 67008713388 T^{11} + 496981290961 T^{12}$$)($$1 - 32 T^{2} + 5986 T^{4} + 665728 T^{6} - 46231901 T^{8} + 5273231488 T^{10} + 375575054626 T^{12} - 15903401310752 T^{14} + 3936588805702081 T^{16}$$)($$1 - 32 T^{2} + 5986 T^{4} + 665728 T^{6} - 46231901 T^{8} + 5273231488 T^{10} + 375575054626 T^{12} - 15903401310752 T^{14} + 3936588805702081 T^{16}$$)
$97$ ($$( 1 + 6 T + 97 T^{2} )^{2}$$)($$( 1 + 6 T + 97 T^{2} )^{2}$$)($$( 1 - 19 T + 97 T^{2} )^{2}$$)($$( 1 - 19 T + 97 T^{2} )^{2}$$)($$( 1 - 18 T + 97 T^{2} )^{2}$$)($$( 1 + 14 T + 97 T^{2} )^{2}$$)($$( 1 + 14 T + 97 T^{2} )^{2}$$)($$( 1 - 18 T + 97 T^{2} )^{2}$$)($$( 1 + T + 97 T^{2} )^{2}$$)($$( 1 + T + 97 T^{2} )^{2}$$)($$( 1 - 7 T + 97 T^{2} )^{2}$$)($$( 1 - 19 T + 97 T^{2} )^{2}$$)($$( 1 - 19 T + 97 T^{2} )^{2}$$)($$( 1 - 7 T + 97 T^{2} )^{2}$$)($$( 1 + 8 T + 97 T^{2} )^{4}$$)($$( 1 + 6 T + 97 T^{2} )^{4}$$)($$( 1 + 8 T + 202 T^{2} + 776 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 - 12 T + 97 T^{2} )^{4}$$)($$( 1 + 8 T + 202 T^{2} + 776 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 6 T + 97 T^{2} )^{4}$$)($$( 1 + 264 T^{2} + 38 T^{3} + 25608 T^{4} + 912673 T^{6} )^{2}$$)($$( 1 + 264 T^{2} + 38 T^{3} + 25608 T^{4} + 912673 T^{6} )^{2}$$)($$( 1 + 11 T + 208 T^{2} + 1067 T^{3} + 9409 T^{4} )^{4}$$)($$( 1 + 11 T + 208 T^{2} + 1067 T^{3} + 9409 T^{4} )^{4}$$)