# Properties

 Label 5376.2.c Level 5376 Weight 2 Character orbit c Rep. character $$\chi_{5376}(2689,\cdot)$$ Character field $$\Q$$ Dimension 96 Newform subspaces 40 Sturm bound 2048 Trace bound 17

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$5376 = 2^{8} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5376.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$40$$ Sturm bound: $$2048$$ Trace bound: $$17$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$13$$, $$17$$, $$23$$, $$31$$, $$47$$, $$71$$, $$79$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(5376, [\chi])$$.

Total New Old
Modular forms 1072 96 976
Cusp forms 976 96 880
Eisenstein series 96 0 96

## Trace form

 $$96q - 96q^{9} + O(q^{10})$$ $$96q - 96q^{9} - 96q^{25} + 96q^{49} + 64q^{65} - 64q^{73} + 96q^{81} - 64q^{89} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(5376, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
5376.2.c.a $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+4iq^{5}-q^{7}-q^{9}-6iq^{11}+\cdots$$
5376.2.c.b $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+4iq^{5}-q^{7}-q^{9}+2iq^{11}+\cdots$$
5376.2.c.c $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+2iq^{5}-q^{7}-q^{9}+4iq^{11}+\cdots$$
5376.2.c.d $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+2iq^{5}-q^{7}-q^{9}-6iq^{13}+\cdots$$
5376.2.c.e $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+2iq^{5}-q^{7}-q^{9}-4iq^{11}+\cdots$$
5376.2.c.f $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}+2iq^{5}-q^{7}-q^{9}+2iq^{13}+\cdots$$
5376.2.c.g $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}-q^{7}-q^{9}-2iq^{11}-6q^{17}+\cdots$$
5376.2.c.h $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}-q^{7}-q^{9}-2iq^{11}+4iq^{13}+\cdots$$
5376.2.c.i $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}-q^{7}-q^{9}+6iq^{11}+2iq^{13}+\cdots$$
5376.2.c.j $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}-q^{7}-q^{9}-2iq^{11}-2iq^{13}+\cdots$$
5376.2.c.k $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q+iq^{3}-q^{7}-q^{9}+6iq^{11}-4iq^{13}+\cdots$$
5376.2.c.l $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}+2iq^{5}-q^{7}-q^{9}+4iq^{11}+\cdots$$
5376.2.c.m $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}+2iq^{5}-q^{7}-q^{9}-4iq^{11}+\cdots$$
5376.2.c.n $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}+2iq^{5}-q^{7}-q^{9}+2q^{15}+\cdots$$
5376.2.c.o $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{13}+\cdots$$
5376.2.c.p $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-iq^{3}+4iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots$$
5376.2.c.q $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+4iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots$$
5376.2.c.r $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+2iq^{5}+q^{7}-q^{9}-4iq^{11}+\cdots$$
5376.2.c.s $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+2iq^{5}+q^{7}-q^{9}+4iq^{11}+\cdots$$
5376.2.c.t $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+2iq^{5}+q^{7}-q^{9}-2q^{15}+\cdots$$
5376.2.c.u $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+2iq^{5}+q^{7}-q^{9}-2iq^{13}+\cdots$$
5376.2.c.v $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+q^{7}-q^{9}-2iq^{11}-6q^{17}+\cdots$$
5376.2.c.w $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+q^{7}-q^{9}-2iq^{11}-4iq^{13}+\cdots$$
5376.2.c.x $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+q^{7}-q^{9}+6iq^{11}-2iq^{13}+\cdots$$
5376.2.c.y $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+iq^{3}+q^{7}-q^{9}-2iq^{11}+2iq^{13}+\cdots$$
5376.2.c.z $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+q^{7}-q^{9}-6iq^{11}-4iq^{13}+\cdots$$
5376.2.c.ba $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+2iq^{5}+q^{7}-q^{9}-4iq^{11}+\cdots$$
5376.2.c.bb $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+2iq^{5}+q^{7}-q^{9}-6iq^{13}+\cdots$$
5376.2.c.bc $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+2iq^{5}+q^{7}-q^{9}+4iq^{11}+\cdots$$
5376.2.c.bd $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{13}+\cdots$$
5376.2.c.be $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+4iq^{5}+q^{7}-q^{9}+6iq^{11}+\cdots$$
5376.2.c.bf $$2$$ $$42.928$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q-iq^{3}+4iq^{5}+q^{7}-q^{9}-2iq^{11}+\cdots$$
5376.2.c.bg $$4$$ $$42.928$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}-q^{7}-q^{9}+(2\zeta_{8}+\cdots)q^{11}+\cdots$$
5376.2.c.bh $$4$$ $$42.928$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots$$
5376.2.c.bi $$4$$ $$42.928$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots$$
5376.2.c.bj $$4$$ $$42.928$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-q^{7}-q^{9}+\cdots$$
5376.2.c.bk $$4$$ $$42.928$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots$$
5376.2.c.bl $$4$$ $$42.928$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-q^{9}+\cdots$$
5376.2.c.bm $$4$$ $$42.928$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+q^{7}-q^{9}+(-2\zeta_{8}+\cdots)q^{11}+\cdots$$
5376.2.c.bn $$4$$ $$42.928$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(5376, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(5376, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(224, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(256, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(384, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(448, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(672, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(768, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(896, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1344, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1792, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2688, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ ($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)($$( 1 + T^{2} )^{2}$$)
$5$ ($$( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$$)($$( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 5 T^{2} )^{2}$$)($$( 1 - 5 T^{2} )^{2}$$)($$( 1 - 5 T^{2} )^{2}$$)($$( 1 - 5 T^{2} )^{2}$$)($$( 1 - 5 T^{2} )^{2}$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$$)($$( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 5 T^{2} )^{2}$$)($$( 1 - 5 T^{2} )^{2}$$)($$( 1 - 5 T^{2} )^{2}$$)($$( 1 - 5 T^{2} )^{2}$$)($$( 1 - 5 T^{2} )^{2}$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$$)($$( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$$)($$( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$$)($$( 1 - 2 T^{2} + 25 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 25 T^{4} )^{2}$$)($$1 - 8 T^{2} + 46 T^{4} - 200 T^{6} + 625 T^{8}$$)($$1 - 8 T^{2} + 46 T^{4} - 200 T^{6} + 625 T^{8}$$)($$1 - 8 T^{2} + 46 T^{4} - 200 T^{6} + 625 T^{8}$$)($$1 - 8 T^{2} + 46 T^{4} - 200 T^{6} + 625 T^{8}$$)($$( 1 - 2 T^{2} + 25 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 25 T^{4} )^{2}$$)
$7$ ($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 + T )^{4}$$)($$( 1 + T )^{4}$$)($$( 1 + T )^{4}$$)($$( 1 + T )^{4}$$)($$( 1 - T )^{4}$$)($$( 1 - T )^{4}$$)($$( 1 - T )^{4}$$)($$( 1 - T )^{4}$$)
$11$ ($$1 + 14 T^{2} + 121 T^{4}$$)($$1 - 18 T^{2} + 121 T^{4}$$)($$1 - 6 T^{2} + 121 T^{4}$$)($$( 1 - 11 T^{2} )^{2}$$)($$1 - 6 T^{2} + 121 T^{4}$$)($$( 1 - 11 T^{2} )^{2}$$)($$1 - 18 T^{2} + 121 T^{4}$$)($$1 - 18 T^{2} + 121 T^{4}$$)($$1 + 14 T^{2} + 121 T^{4}$$)($$1 - 18 T^{2} + 121 T^{4}$$)($$1 + 14 T^{2} + 121 T^{4}$$)($$1 - 6 T^{2} + 121 T^{4}$$)($$1 - 6 T^{2} + 121 T^{4}$$)($$( 1 - 11 T^{2} )^{2}$$)($$( 1 - 11 T^{2} )^{2}$$)($$1 - 18 T^{2} + 121 T^{4}$$)($$1 - 18 T^{2} + 121 T^{4}$$)($$1 - 6 T^{2} + 121 T^{4}$$)($$1 - 6 T^{2} + 121 T^{4}$$)($$( 1 - 11 T^{2} )^{2}$$)($$( 1 - 11 T^{2} )^{2}$$)($$1 - 18 T^{2} + 121 T^{4}$$)($$1 - 18 T^{2} + 121 T^{4}$$)($$1 + 14 T^{2} + 121 T^{4}$$)($$1 - 18 T^{2} + 121 T^{4}$$)($$1 + 14 T^{2} + 121 T^{4}$$)($$1 - 6 T^{2} + 121 T^{4}$$)($$( 1 - 11 T^{2} )^{2}$$)($$1 - 6 T^{2} + 121 T^{4}$$)($$( 1 - 11 T^{2} )^{2}$$)($$1 + 14 T^{2} + 121 T^{4}$$)($$1 - 18 T^{2} + 121 T^{4}$$)($$1 - 20 T^{2} + 214 T^{4} - 2420 T^{6} + 14641 T^{8}$$)($$1 - 12 T^{2} + 86 T^{4} - 1452 T^{6} + 14641 T^{8}$$)($$1 - 32 T^{2} + 478 T^{4} - 3872 T^{6} + 14641 T^{8}$$)($$1 - 32 T^{2} + 478 T^{4} - 3872 T^{6} + 14641 T^{8}$$)($$1 - 32 T^{2} + 478 T^{4} - 3872 T^{6} + 14641 T^{8}$$)($$1 - 32 T^{2} + 478 T^{4} - 3872 T^{6} + 14641 T^{8}$$)($$1 - 20 T^{2} + 214 T^{4} - 2420 T^{6} + 14641 T^{8}$$)($$1 - 12 T^{2} + 86 T^{4} - 1452 T^{6} + 14641 T^{8}$$)
$13$ ($$( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 13 T^{2} )^{2}$$)($$( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$( 1 - 13 T^{2} )^{2}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$( 1 - 13 T^{2} )^{2}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 13 T^{2} )^{2}$$)($$( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$)($$( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 13 T^{2} )^{4}$$)($$( 1 - 22 T^{2} + 169 T^{4} )^{2}$$)($$1 - 4 T^{2} + 22 T^{4} - 676 T^{6} + 28561 T^{8}$$)($$1 - 4 T^{2} + 22 T^{4} - 676 T^{6} + 28561 T^{8}$$)($$1 - 4 T^{2} + 22 T^{4} - 676 T^{6} + 28561 T^{8}$$)($$1 - 4 T^{2} + 22 T^{4} - 676 T^{6} + 28561 T^{8}$$)($$( 1 - 13 T^{2} )^{4}$$)($$( 1 - 22 T^{2} + 169 T^{4} )^{2}$$)
$17$ ($$( 1 + 6 T + 17 T^{2} )^{2}$$)($$( 1 + 17 T^{2} )^{2}$$)($$( 1 + 8 T + 17 T^{2} )^{2}$$)($$( 1 + 2 T + 17 T^{2} )^{2}$$)($$( 1 - 2 T + 17 T^{2} )^{2}$$)($$( 1 - 6 T + 17 T^{2} )^{2}$$)($$( 1 + 6 T + 17 T^{2} )^{2}$$)($$( 1 + 2 T + 17 T^{2} )^{2}$$)($$( 1 + 17 T^{2} )^{2}$$)($$( 1 - 4 T + 17 T^{2} )^{2}$$)($$( 1 - 6 T + 17 T^{2} )^{2}$$)($$( 1 + 6 T + 17 T^{2} )^{2}$$)($$( 1 + 2 T + 17 T^{2} )^{2}$$)($$( 1 + 17 T^{2} )^{2}$$)($$( 1 - 2 T + 17 T^{2} )^{2}$$)($$( 1 + 4 T + 17 T^{2} )^{2}$$)($$( 1 + 4 T + 17 T^{2} )^{2}$$)($$( 1 + 6 T + 17 T^{2} )^{2}$$)($$( 1 + 2 T + 17 T^{2} )^{2}$$)($$( 1 + 17 T^{2} )^{2}$$)($$( 1 - 2 T + 17 T^{2} )^{2}$$)($$( 1 + 6 T + 17 T^{2} )^{2}$$)($$( 1 + 2 T + 17 T^{2} )^{2}$$)($$( 1 + 17 T^{2} )^{2}$$)($$( 1 - 4 T + 17 T^{2} )^{2}$$)($$( 1 - 6 T + 17 T^{2} )^{2}$$)($$( 1 + 8 T + 17 T^{2} )^{2}$$)($$( 1 + 2 T + 17 T^{2} )^{2}$$)($$( 1 - 2 T + 17 T^{2} )^{2}$$)($$( 1 - 6 T + 17 T^{2} )^{2}$$)($$( 1 + 6 T + 17 T^{2} )^{2}$$)($$( 1 + 17 T^{2} )^{2}$$)($$( 1 - 4 T + 30 T^{2} - 68 T^{3} + 289 T^{4} )^{2}$$)($$( 1 - 8 T + 38 T^{2} - 136 T^{3} + 289 T^{4} )^{2}$$)($$( 1 + 2 T + 30 T^{2} + 34 T^{3} + 289 T^{4} )^{2}$$)($$( 1 - 6 T + 38 T^{2} - 102 T^{3} + 289 T^{4} )^{2}$$)($$( 1 + 2 T + 30 T^{2} + 34 T^{3} + 289 T^{4} )^{2}$$)($$( 1 - 6 T + 38 T^{2} - 102 T^{3} + 289 T^{4} )^{2}$$)($$( 1 - 4 T + 30 T^{2} - 68 T^{3} + 289 T^{4} )^{2}$$)($$( 1 - 8 T + 38 T^{2} - 136 T^{3} + 289 T^{4} )^{2}$$)
$19$ ($$( 1 - 19 T^{2} )^{2}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$( 1 - 19 T^{2} )^{2}$$)($$1 + 26 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$( 1 - 19 T^{2} )^{2}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$( 1 - 19 T^{2} )^{2}$$)($$1 + 26 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$( 1 - 19 T^{2} )^{2}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$( 1 - 19 T^{2} )^{2}$$)($$1 - 22 T^{2} + 361 T^{4}$$)($$( 1 - 19 T^{2} )^{4}$$)($$( 1 + 10 T^{2} + 361 T^{4} )^{2}$$)($$1 - 28 T^{2} + 598 T^{4} - 10108 T^{6} + 130321 T^{8}$$)($$1 - 28 T^{2} + 598 T^{4} - 10108 T^{6} + 130321 T^{8}$$)($$1 - 28 T^{2} + 598 T^{4} - 10108 T^{6} + 130321 T^{8}$$)($$1 - 28 T^{2} + 598 T^{4} - 10108 T^{6} + 130321 T^{8}$$)($$( 1 - 19 T^{2} )^{4}$$)($$( 1 + 10 T^{2} + 361 T^{4} )^{2}$$)
$23$ ($$( 1 + 23 T^{2} )^{2}$$)($$( 1 - 6 T + 23 T^{2} )^{2}$$)($$( 1 - 2 T + 23 T^{2} )^{2}$$)($$( 1 - 4 T + 23 T^{2} )^{2}$$)($$( 1 - 8 T + 23 T^{2} )^{2}$$)($$( 1 + 4 T + 23 T^{2} )^{2}$$)($$( 1 - 8 T + 23 T^{2} )^{2}$$)($$( 1 + 4 T + 23 T^{2} )^{2}$$)($$( 1 - 6 T + 23 T^{2} )^{2}$$)($$( 1 + 6 T + 23 T^{2} )^{2}$$)($$( 1 - 4 T + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 + 4 T + 23 T^{2} )^{2}$$)($$( 1 + 6 T + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 - 2 T + 23 T^{2} )^{2}$$)($$( 1 + 2 T + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 - 4 T + 23 T^{2} )^{2}$$)($$( 1 - 6 T + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 + 8 T + 23 T^{2} )^{2}$$)($$( 1 - 4 T + 23 T^{2} )^{2}$$)($$( 1 + 6 T + 23 T^{2} )^{2}$$)($$( 1 - 6 T + 23 T^{2} )^{2}$$)($$( 1 + 4 T + 23 T^{2} )^{2}$$)($$( 1 + 2 T + 23 T^{2} )^{2}$$)($$( 1 + 4 T + 23 T^{2} )^{2}$$)($$( 1 + 8 T + 23 T^{2} )^{2}$$)($$( 1 - 4 T + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 + 6 T + 23 T^{2} )^{2}$$)($$( 1 + 38 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 4 T + 38 T^{2} - 92 T^{3} + 529 T^{4} )^{2}$$)($$( 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} )^{2}$$)($$( 1 + 2 T + 42 T^{2} + 46 T^{3} + 529 T^{4} )^{2}$$)($$( 1 - 2 T + 2 T^{2} - 46 T^{3} + 529 T^{4} )^{2}$$)($$( 1 - 2 T + 42 T^{2} - 46 T^{3} + 529 T^{4} )^{2}$$)($$( 1 + 38 T^{2} + 529 T^{4} )^{2}$$)($$( 1 + 4 T + 38 T^{2} + 92 T^{3} + 529 T^{4} )^{2}$$)
$29$ ($$1 - 22 T^{2} + 841 T^{4}$$)($$( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} )$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} )$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} )$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} )$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} )$$)($$1 - 54 T^{2} + 841 T^{4}$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$1 - 22 T^{2} + 841 T^{4}$$)($$( 1 - 4 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} )$$)($$( 1 - 54 T^{2} + 841 T^{4} )^{2}$$)($$1 - 12 T^{2} + 950 T^{4} - 10092 T^{6} + 707281 T^{8}$$)($$1 - 44 T^{2} + 886 T^{4} - 37004 T^{6} + 707281 T^{8}$$)($$( 1 - 38 T^{2} + 841 T^{4} )^{2}$$)($$1 - 44 T^{2} + 886 T^{4} - 37004 T^{6} + 707281 T^{8}$$)($$( 1 - 38 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 54 T^{2} + 841 T^{4} )^{2}$$)($$1 - 12 T^{2} + 950 T^{4} - 10092 T^{6} + 707281 T^{8}$$)
$31$ ($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 + 30 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 8 T + 30 T^{2} - 248 T^{3} + 961 T^{4} )^{2}$$)($$( 1 - 4 T + 31 T^{2} )^{4}$$)($$( 1 + 4 T + 31 T^{2} )^{4}$$)($$( 1 + 4 T + 31 T^{2} )^{4}$$)($$( 1 - 4 T + 31 T^{2} )^{4}$$)($$( 1 + 30 T^{2} + 961 T^{4} )^{2}$$)($$( 1 + 8 T + 30 T^{2} + 248 T^{3} + 961 T^{4} )^{2}$$)
$37$ ($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$1 - 12 T^{2} - 1834 T^{4} - 16428 T^{6} + 1874161 T^{8}$$)($$( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2}$$)($$( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2}$$)($$1 + 20 T^{2} + 1558 T^{4} + 27380 T^{6} + 1874161 T^{8}$$)($$( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2}$$)($$1 + 20 T^{2} + 1558 T^{4} + 27380 T^{6} + 1874161 T^{8}$$)($$1 - 12 T^{2} - 1834 T^{4} - 16428 T^{6} + 1874161 T^{8}$$)($$( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2}$$)
$41$ ($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 - 4 T + 41 T^{2} )^{2}$$)($$( 1 - 12 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 + 10 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 + 12 T + 41 T^{2} )^{2}$$)($$( 1 + 8 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 + 2 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 - 4 T + 41 T^{2} )^{2}$$)($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 + 41 T^{2} )^{2}$$)($$( 1 + 41 T^{2} )^{2}$$)($$( 1 + 2 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 - 4 T + 41 T^{2} )^{2}$$)($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 + 10 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 + 12 T + 41 T^{2} )^{2}$$)($$( 1 + 8 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 - 12 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 - 4 T + 41 T^{2} )^{2}$$)($$( 1 + 4 T + 14 T^{2} + 164 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 16 T + 134 T^{2} + 656 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 10 T + 102 T^{2} + 410 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 2 T + 78 T^{2} + 82 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 10 T + 102 T^{2} + 410 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 2 T + 78 T^{2} + 82 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 4 T + 14 T^{2} + 164 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 16 T + 134 T^{2} + 656 T^{3} + 1681 T^{4} )^{2}$$)
$43$ ($$1 - 50 T^{2} + 1849 T^{4}$$)($$1 - 22 T^{2} + 1849 T^{4}$$)($$1 - 50 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 + 58 T^{2} + 1849 T^{4}$$)($$1 + 14 T^{2} + 1849 T^{4}$$)($$1 - 82 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 22 T^{2} + 1849 T^{4}$$)($$1 - 82 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 22 T^{2} + 1849 T^{4}$$)($$1 - 82 T^{2} + 1849 T^{4}$$)($$1 - 22 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 22 T^{2} + 1849 T^{4}$$)($$1 - 82 T^{2} + 1849 T^{4}$$)($$1 - 22 T^{2} + 1849 T^{4}$$)($$1 + 14 T^{2} + 1849 T^{4}$$)($$1 - 82 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 22 T^{2} + 1849 T^{4}$$)($$1 - 82 T^{2} + 1849 T^{4}$$)($$1 - 50 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 + 58 T^{2} + 1849 T^{4}$$)($$1 - 50 T^{2} + 1849 T^{4}$$)($$1 - 22 T^{2} + 1849 T^{4}$$)($$1 - 36 T^{2} - 586 T^{4} - 66564 T^{6} + 3418801 T^{8}$$)($$( 1 - 22 T^{2} + 1849 T^{4} )^{2}$$)($$1 - 100 T^{2} + 4918 T^{4} - 184900 T^{6} + 3418801 T^{8}$$)($$( 1 - 66 T^{2} + 1849 T^{4} )^{2}$$)($$1 - 100 T^{2} + 4918 T^{4} - 184900 T^{6} + 3418801 T^{8}$$)($$( 1 - 66 T^{2} + 1849 T^{4} )^{2}$$)($$1 - 36 T^{2} - 586 T^{4} - 66564 T^{6} + 3418801 T^{8}$$)($$( 1 - 22 T^{2} + 1849 T^{4} )^{2}$$)
$47$ ($$( 1 - 8 T + 47 T^{2} )^{2}$$)($$( 1 + 4 T + 47 T^{2} )^{2}$$)($$( 1 + 8 T + 47 T^{2} )^{2}$$)($$( 1 - 8 T + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 - 8 T + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 8 T + 47 T^{2} )^{2}$$)($$( 1 - 12 T + 47 T^{2} )^{2}$$)($$( 1 - 4 T + 47 T^{2} )^{2}$$)($$( 1 + 8 T + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 - 8 T + 47 T^{2} )^{2}$$)($$( 1 + 8 T + 47 T^{2} )^{2}$$)($$( 1 + 12 T + 47 T^{2} )^{2}$$)($$( 1 - 12 T + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 8 T + 47 T^{2} )^{2}$$)($$( 1 - 8 T + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 - 8 T + 47 T^{2} )^{2}$$)($$( 1 + 12 T + 47 T^{2} )^{2}$$)($$( 1 + 4 T + 47 T^{2} )^{2}$$)($$( 1 - 8 T + 47 T^{2} )^{2}$$)($$( 1 - 8 T + 47 T^{2} )^{2}$$)($$( 1 + 8 T + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 8 T + 47 T^{2} )^{2}$$)($$( 1 + 8 T + 47 T^{2} )^{2}$$)($$( 1 - 4 T + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{4}$$)($$( 1 + 8 T + 62 T^{2} + 376 T^{3} + 2209 T^{4} )^{2}$$)($$( 1 - 8 T + 47 T^{2} )^{4}$$)($$( 1 + 8 T + 30 T^{2} + 376 T^{3} + 2209 T^{4} )^{2}$$)($$( 1 + 8 T + 47 T^{2} )^{4}$$)($$( 1 - 8 T + 30 T^{2} - 376 T^{3} + 2209 T^{4} )^{2}$$)($$( 1 + 47 T^{2} )^{4}$$)($$( 1 - 8 T + 62 T^{2} - 376 T^{3} + 2209 T^{4} )^{2}$$)
$53$ ($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$( 1 - 4 T + 53 T^{2} )( 1 + 4 T + 53 T^{2} )$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$( 1 - 4 T + 53 T^{2} )( 1 + 4 T + 53 T^{2} )$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 + 52 T^{2} + 4246 T^{4} + 146068 T^{6} + 7890481 T^{8}$$)($$( 1 - 102 T^{2} + 2809 T^{4} )^{2}$$)($$1 - 44 T^{2} + 982 T^{4} - 123596 T^{6} + 7890481 T^{8}$$)($$( 1 - 86 T^{2} + 2809 T^{4} )^{2}$$)($$1 - 44 T^{2} + 982 T^{4} - 123596 T^{6} + 7890481 T^{8}$$)($$( 1 - 86 T^{2} + 2809 T^{4} )^{2}$$)($$1 + 52 T^{2} + 4246 T^{4} + 146068 T^{6} + 7890481 T^{8}$$)($$( 1 - 102 T^{2} + 2809 T^{4} )^{2}$$)
$59$ ($$1 + 26 T^{2} + 3481 T^{4}$$)($$1 - 54 T^{2} + 3481 T^{4}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 + 26 T^{2} + 3481 T^{4}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 + 26 T^{2} + 3481 T^{4}$$)($$( 1 - 59 T^{2} )^{2}$$)($$( 1 - 59 T^{2} )^{2}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 + 26 T^{2} + 3481 T^{4}$$)($$1 + 26 T^{2} + 3481 T^{4}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 + 26 T^{2} + 3481 T^{4}$$)($$1 - 54 T^{2} + 3481 T^{4}$$)($$1 - 54 T^{2} + 3481 T^{4}$$)($$1 + 26 T^{2} + 3481 T^{4}$$)($$1 + 26 T^{2} + 3481 T^{4}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 + 26 T^{2} + 3481 T^{4}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 + 26 T^{2} + 3481 T^{4}$$)($$( 1 - 59 T^{2} )^{2}$$)($$( 1 - 59 T^{2} )^{2}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 + 26 T^{2} + 3481 T^{4}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 - 102 T^{2} + 3481 T^{4}$$)($$1 + 26 T^{2} + 3481 T^{4}$$)($$1 - 54 T^{2} + 3481 T^{4}$$)($$( 1 - 102 T^{2} + 3481 T^{4} )^{2}$$)($$1 - 12 T^{2} - 5290 T^{4} - 41772 T^{6} + 12117361 T^{8}$$)($$( 1 - 38 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 - 102 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 - 38 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 - 102 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 - 102 T^{2} + 3481 T^{4} )^{2}$$)($$1 - 12 T^{2} - 5290 T^{4} - 41772 T^{6} + 12117361 T^{8}$$)
$61$ ($$( 1 - 61 T^{2} )^{2}$$)($$1 - 86 T^{2} + 3721 T^{4}$$)($$1 - 106 T^{2} + 3721 T^{4}$$)($$1 - 118 T^{2} + 3721 T^{4}$$)($$1 - 86 T^{2} + 3721 T^{4}$$)($$( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} )$$)($$1 - 106 T^{2} + 3721 T^{4}$$)($$( 1 - 61 T^{2} )^{2}$$)($$( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} )$$)($$1 + 74 T^{2} + 3721 T^{4}$$)($$1 - 58 T^{2} + 3721 T^{4}$$)($$1 - 118 T^{2} + 3721 T^{4}$$)($$( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} )$$)($$1 - 58 T^{2} + 3721 T^{4}$$)($$( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} )$$)($$1 - 86 T^{2} + 3721 T^{4}$$)($$1 - 86 T^{2} + 3721 T^{4}$$)($$1 - 118 T^{2} + 3721 T^{4}$$)($$( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} )$$)($$1 - 58 T^{2} + 3721 T^{4}$$)($$( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} )$$)($$1 - 106 T^{2} + 3721 T^{4}$$)($$( 1 - 61 T^{2} )^{2}$$)($$( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} )$$)($$1 + 74 T^{2} + 3721 T^{4}$$)($$1 - 58 T^{2} + 3721 T^{4}$$)($$1 - 106 T^{2} + 3721 T^{4}$$)($$1 - 118 T^{2} + 3721 T^{4}$$)($$1 - 86 T^{2} + 3721 T^{4}$$)($$( 1 - 12 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} )$$)($$( 1 - 61 T^{2} )^{2}$$)($$1 - 86 T^{2} + 3721 T^{4}$$)($$1 - 148 T^{2} + 10870 T^{4} - 550708 T^{6} + 13845841 T^{8}$$)($$1 - 140 T^{2} + 11574 T^{4} - 520940 T^{6} + 13845841 T^{8}$$)($$1 - 52 T^{2} + 2998 T^{4} - 193492 T^{6} + 13845841 T^{8}$$)($$( 1 - 106 T^{2} + 3721 T^{4} )^{2}$$)($$1 - 52 T^{2} + 2998 T^{4} - 193492 T^{6} + 13845841 T^{8}$$)($$( 1 - 106 T^{2} + 3721 T^{4} )^{2}$$)($$1 - 148 T^{2} + 10870 T^{4} - 550708 T^{6} + 13845841 T^{8}$$)($$1 - 140 T^{2} + 11574 T^{4} - 520940 T^{6} + 13845841 T^{8}$$)
$67$ ($$1 - 130 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 34 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 130 T^{2} + 4489 T^{4}$$)($$1 + 62 T^{2} + 4489 T^{4}$$)($$1 - 70 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 + 62 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 70 T^{2} + 4489 T^{4}$$)($$1 - 34 T^{2} + 4489 T^{4}$$)($$1 + 122 T^{2} + 4489 T^{4}$$)($$1 - 70 T^{2} + 4489 T^{4}$$)($$1 - 70 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 70 T^{2} + 4489 T^{4}$$)($$1 - 34 T^{2} + 4489 T^{4}$$)($$1 + 122 T^{2} + 4489 T^{4}$$)($$1 - 130 T^{2} + 4489 T^{4}$$)($$1 + 62 T^{2} + 4489 T^{4}$$)($$1 - 70 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 + 62 T^{2} + 4489 T^{4}$$)($$1 - 34 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 130 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 4 T^{2} + 6934 T^{4} - 17956 T^{6} + 20151121 T^{8}$$)($$1 - 140 T^{2} + 10806 T^{4} - 628460 T^{6} + 20151121 T^{8}$$)($$( 1 - 98 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 98 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 98 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 98 T^{2} + 4489 T^{4} )^{2}$$)($$1 - 4 T^{2} + 6934 T^{4} - 17956 T^{6} + 20151121 T^{8}$$)($$1 - 140 T^{2} + 10806 T^{4} - 628460 T^{6} + 20151121 T^{8}$$)
$71$ ($$( 1 - 4 T + 71 T^{2} )^{2}$$)($$( 1 + 14 T + 71 T^{2} )^{2}$$)($$( 1 + 6 T + 71 T^{2} )^{2}$$)($$( 1 - 12 T + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 - 4 T + 71 T^{2} )^{2}$$)($$( 1 - 4 T + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 + 6 T + 71 T^{2} )^{2}$$)($$( 1 + 2 T + 71 T^{2} )^{2}$$)($$( 1 - 16 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 - 12 T + 71 T^{2} )^{2}$$)($$( 1 + 6 T + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 - 14 T + 71 T^{2} )^{2}$$)($$( 1 + 14 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 12 T + 71 T^{2} )^{2}$$)($$( 1 - 6 T + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 + 4 T + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 - 6 T + 71 T^{2} )^{2}$$)($$( 1 - 2 T + 71 T^{2} )^{2}$$)($$( 1 + 16 T + 71 T^{2} )^{2}$$)($$( 1 - 6 T + 71 T^{2} )^{2}$$)($$( 1 + 12 T + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 + 4 T + 71 T^{2} )^{2}$$)($$( 1 + 4 T + 71 T^{2} )^{2}$$)($$( 1 - 14 T + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 12 T + 166 T^{2} - 852 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 10 T + 122 T^{2} - 710 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 + 6 T + 146 T^{2} + 426 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 + 10 T + 122 T^{2} + 710 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 6 T + 146 T^{2} - 426 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 + 12 T + 166 T^{2} + 852 T^{3} + 5041 T^{4} )^{2}$$)
$73$ ($$( 1 + 2 T + 73 T^{2} )^{2}$$)($$( 1 + 6 T + 73 T^{2} )^{2}$$)($$( 1 - 10 T + 73 T^{2} )^{2}$$)($$( 1 - 14 T + 73 T^{2} )^{2}$$)($$( 1 + 10 T + 73 T^{2} )^{2}$$)($$( 1 + 2 T + 73 T^{2} )^{2}$$)($$( 1 + 2 T + 73 T^{2} )^{2}$$)($$( 1 + 10 T + 73 T^{2} )^{2}$$)($$( 1 - 10 T + 73 T^{2} )^{2}$$)($$( 1 - 2 T + 73 T^{2} )^{2}$$)($$( 1 + 10 T + 73 T^{2} )^{2}$$)($$( 1 - 6 T + 73 T^{2} )^{2}$$)($$( 1 + 2 T + 73 T^{2} )^{2}$$)($$( 1 - 10 T + 73 T^{2} )^{2}$$)($$( 1 - 6 T + 73 T^{2} )^{2}$$)($$( 1 - 2 T + 73 T^{2} )^{2}$$)($$( 1 - 2 T + 73 T^{2} )^{2}$$)($$( 1 - 6 T + 73 T^{2} )^{2}$$)($$( 1 + 2 T + 73 T^{2} )^{2}$$)($$( 1 - 10 T + 73 T^{2} )^{2}$$)($$( 1 - 6 T + 73 T^{2} )^{2}$$)($$( 1 + 2 T + 73 T^{2} )^{2}$$)($$( 1 + 10 T + 73 T^{2} )^{2}$$)($$( 1 - 10 T + 73 T^{2} )^{2}$$)($$( 1 - 2 T + 73 T^{2} )^{2}$$)($$( 1 + 10 T + 73 T^{2} )^{2}$$)($$( 1 - 10 T + 73 T^{2} )^{2}$$)($$( 1 - 14 T + 73 T^{2} )^{2}$$)($$( 1 + 10 T + 73 T^{2} )^{2}$$)($$( 1 + 2 T + 73 T^{2} )^{2}$$)($$( 1 + 2 T + 73 T^{2} )^{2}$$)($$( 1 + 6 T + 73 T^{2} )^{2}$$)($$( 1 + 4 T + 118 T^{2} + 292 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 + 12 T + 134 T^{2} + 876 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 + 16 T + 190 T^{2} + 1168 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 + 126 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 + 16 T + 190 T^{2} + 1168 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 + 126 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 + 4 T + 118 T^{2} + 292 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 + 12 T + 134 T^{2} + 876 T^{3} + 5329 T^{4} )^{2}$$)
$79$ ($$( 1 - 4 T + 79 T^{2} )^{2}$$)($$( 1 - 4 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 - 12 T + 79 T^{2} )^{2}$$)($$( 1 - 12 T + 79 T^{2} )^{2}$$)($$( 1 + 4 T + 79 T^{2} )^{2}$$)($$( 1 + 4 T + 79 T^{2} )^{2}$$)($$( 1 + 4 T + 79 T^{2} )^{2}$$)($$( 1 - 16 T + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 12 T + 79 T^{2} )^{2}$$)($$( 1 - 12 T + 79 T^{2} )^{2}$$)($$( 1 + 16 T + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 + 12 T + 79 T^{2} )^{2}$$)($$( 1 + 12 T + 79 T^{2} )^{2}$$)($$( 1 - 4 T + 79 T^{2} )^{2}$$)($$( 1 - 4 T + 79 T^{2} )^{2}$$)($$( 1 - 4 T + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 + 4 T + 79 T^{2} )^{2}$$)($$( 1 + 4 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 142 T^{2} + 632 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 - 8 T + 126 T^{2} - 632 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 - 12 T + 174 T^{2} - 948 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + 20 T + 238 T^{2} + 1580 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + 12 T + 174 T^{2} + 948 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 - 20 T + 238 T^{2} - 1580 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 - 8 T + 142 T^{2} - 632 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + 8 T + 126 T^{2} + 632 T^{3} + 6241 T^{4} )^{2}$$)
$83$ ($$( 1 - 83 T^{2} )^{2}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$( 1 - 83 T^{2} )^{2}$$)($$( 1 - 83 T^{2} )^{2}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 102 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$( 1 - 83 T^{2} )^{2}$$)($$( 1 - 83 T^{2} )^{2}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 102 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$( 1 - 83 T^{2} )^{2}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 140 T^{2} + 10486 T^{4} - 964460 T^{6} + 47458321 T^{8}$$)($$( 1 - 150 T^{2} + 6889 T^{4} )^{2}$$)($$1 - 92 T^{2} + 7894 T^{4} - 633788 T^{6} + 47458321 T^{8}$$)($$1 + 36 T^{2} + 11222 T^{4} + 248004 T^{6} + 47458321 T^{8}$$)($$1 - 92 T^{2} + 7894 T^{4} - 633788 T^{6} + 47458321 T^{8}$$)($$1 + 36 T^{2} + 11222 T^{4} + 248004 T^{6} + 47458321 T^{8}$$)($$1 - 140 T^{2} + 10486 T^{4} - 964460 T^{6} + 47458321 T^{8}$$)($$( 1 - 150 T^{2} + 6889 T^{4} )^{2}$$)
$89$ ($$( 1 - 18 T + 89 T^{2} )^{2}$$)($$( 1 + 4 T + 89 T^{2} )^{2}$$)($$( 1 + 16 T + 89 T^{2} )^{2}$$)($$( 1 - 2 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 6 T + 89 T^{2} )^{2}$$)($$( 1 - 10 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 12 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 2 T + 89 T^{2} )^{2}$$)($$( 1 - 14 T + 89 T^{2} )^{2}$$)($$( 1 + 6 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 14 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 14 T + 89 T^{2} )^{2}$$)($$( 1 + 6 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 14 T + 89 T^{2} )^{2}$$)($$( 1 - 10 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 12 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 2 T + 89 T^{2} )^{2}$$)($$( 1 + 16 T + 89 T^{2} )^{2}$$)($$( 1 - 2 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 6 T + 89 T^{2} )^{2}$$)($$( 1 - 18 T + 89 T^{2} )^{2}$$)($$( 1 + 4 T + 89 T^{2} )^{2}$$)($$( 1 + 28 T + 366 T^{2} + 2492 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 166 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 + 10 T + 78 T^{2} + 890 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 2 T + 134 T^{2} + 178 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 10 T + 78 T^{2} + 890 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 2 T + 134 T^{2} + 178 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 28 T + 366 T^{2} + 2492 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 166 T^{2} + 7921 T^{4} )^{2}$$)
$97$ ($$( 1 + 10 T + 97 T^{2} )^{2}$$)($$( 1 + 2 T + 97 T^{2} )^{2}$$)($$( 1 - 10 T + 97 T^{2} )^{2}$$)($$( 1 - 10 T + 97 T^{2} )^{2}$$)($$( 1 + 14 T + 97 T^{2} )^{2}$$)($$( 1 - 10 T + 97 T^{2} )^{2}$$)($$( 1 + 18 T + 97 T^{2} )^{2}$$)($$( 1 + 2 T + 97 T^{2} )^{2}$$)($$( 1 + 10 T + 97 T^{2} )^{2}$$)($$( 1 - 6 T + 97 T^{2} )^{2}$$)($$( 1 - 14 T + 97 T^{2} )^{2}$$)($$( 1 - 18 T + 97 T^{2} )^{2}$$)($$( 1 - 2 T + 97 T^{2} )^{2}$$)($$( 1 + 14 T + 97 T^{2} )^{2}$$)($$( 1 + 6 T + 97 T^{2} )^{2}$$)($$( 1 + 2 T + 97 T^{2} )^{2}$$)($$( 1 + 2 T + 97 T^{2} )^{2}$$)($$( 1 - 18 T + 97 T^{2} )^{2}$$)($$( 1 - 2 T + 97 T^{2} )^{2}$$)($$( 1 + 14 T + 97 T^{2} )^{2}$$)($$( 1 + 6 T + 97 T^{2} )^{2}$$)($$( 1 + 18 T + 97 T^{2} )^{2}$$)($$( 1 + 2 T + 97 T^{2} )^{2}$$)($$( 1 + 10 T + 97 T^{2} )^{2}$$)($$( 1 - 6 T + 97 T^{2} )^{2}$$)($$( 1 - 14 T + 97 T^{2} )^{2}$$)($$( 1 - 10 T + 97 T^{2} )^{2}$$)($$( 1 - 10 T + 97 T^{2} )^{2}$$)($$( 1 + 14 T + 97 T^{2} )^{2}$$)($$( 1 - 10 T + 97 T^{2} )^{2}$$)($$( 1 + 10 T + 97 T^{2} )^{2}$$)($$( 1 + 2 T + 97 T^{2} )^{2}$$)($$( 1 + 4 T + 166 T^{2} + 388 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 4 T + 150 T^{2} + 388 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 - 16 T + 238 T^{2} - 1552 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 14 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 16 T + 238 T^{2} - 1552 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 14 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 + 4 T + 166 T^{2} + 388 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 4 T + 150 T^{2} + 388 T^{3} + 9409 T^{4} )^{2}$$)