# Properties

 Label 4800.2.f Level 4800 Weight 2 Character orbit f Rep. character $$\chi_{4800}(3649,\cdot)$$ Character field $$\Q$$ Dimension 72 Newform subspaces 36 Sturm bound 1920 Trace bound 31

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$4800 = 2^{6} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4800.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$36$$ Sturm bound: $$1920$$ Trace bound: $$31$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$13$$, $$19$$, $$23$$, $$31$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(4800, [\chi])$$.

Total New Old
Modular forms 1032 72 960
Cusp forms 888 72 816
Eisenstein series 144 0 144

## Trace form

 $$72q - 72q^{9} + O(q^{10})$$ $$72q - 72q^{9} - 16q^{41} - 72q^{49} + 32q^{61} - 32q^{69} + 72q^{81} - 16q^{89} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(4800, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
4800.2.f.a $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+5iq^{7}-q^{9}-6q^{11}-3iq^{13}+\cdots$$
4800.2.f.b $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{7}-q^{9}-6q^{11}-5iq^{13}+\cdots$$
4800.2.f.c $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}-4q^{11}+2iq^{13}-2iq^{17}+\cdots$$
4800.2.f.d $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}-4q^{11}+2iq^{13}-2iq^{17}+\cdots$$
4800.2.f.e $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}-4q^{11}+2iq^{13}+\cdots$$
4800.2.f.f $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{7}-q^{9}-4q^{11}+7iq^{13}+\cdots$$
4800.2.f.g $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}-4q^{11}+3iq^{13}+\cdots$$
4800.2.f.h $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}-4q^{11}-6iq^{13}+\cdots$$
4800.2.f.i $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}-4q^{11}+6iq^{13}-6iq^{17}+\cdots$$
4800.2.f.j $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}-4q^{11}-2iq^{13}+2iq^{17}+\cdots$$
4800.2.f.k $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}-2q^{11}-3iq^{13}+\cdots$$
4800.2.f.l $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}-2q^{11}-iq^{13}+\cdots$$
4800.2.f.m $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{7}-q^{9}-5iq^{13}-5q^{19}+\cdots$$
4800.2.f.n $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}+6iq^{13}+2iq^{17}+\cdots$$
4800.2.f.o $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}-2iq^{13}-6iq^{17}-4q^{19}+\cdots$$
4800.2.f.p $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}-2iq^{13}-6iq^{17}+\cdots$$
4800.2.f.q $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}-iq^{13}-3q^{19}+\cdots$$
4800.2.f.r $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}+2iq^{13}+6iq^{17}+\cdots$$
4800.2.f.s $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}-2iq^{13}-6iq^{17}+\cdots$$
4800.2.f.t $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}+iq^{13}+3q^{19}+\cdots$$
4800.2.f.u $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}-6iq^{13}-2iq^{17}+\cdots$$
4800.2.f.v $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}+2iq^{13}+6iq^{17}+4q^{19}+\cdots$$
4800.2.f.w $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}+2iq^{13}+6iq^{17}+\cdots$$
4800.2.f.x $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{7}-q^{9}+5iq^{13}+5q^{19}+\cdots$$
4800.2.f.y $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}+2q^{11}+iq^{13}+\cdots$$
4800.2.f.z $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+3iq^{7}-q^{9}+2q^{11}+3iq^{13}+\cdots$$
4800.2.f.ba $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}+4q^{11}+2iq^{13}-2iq^{17}+\cdots$$
4800.2.f.bb $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}-q^{9}+4q^{11}+6iq^{13}+\cdots$$
4800.2.f.bc $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}+4q^{11}-6iq^{13}+6iq^{17}+\cdots$$
4800.2.f.bd $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+iq^{7}-q^{9}+4q^{11}-3iq^{13}+\cdots$$
4800.2.f.be $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+3iq^{7}-q^{9}+4q^{11}-7iq^{13}+\cdots$$
4800.2.f.bf $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-q^{9}+4q^{11}+2iq^{13}-2iq^{17}+\cdots$$
4800.2.f.bg $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}-q^{9}+4q^{11}+2iq^{13}-2iq^{17}+\cdots$$
4800.2.f.bh $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+4iq^{7}-q^{9}+4q^{11}-2iq^{13}+\cdots$$
4800.2.f.bi $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{7}-q^{9}+6q^{11}+5iq^{13}+\cdots$$
4800.2.f.bj $$2$$ $$38.328$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+5iq^{7}-q^{9}+6q^{11}+3iq^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(4800, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(4800, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(75, [\chi])$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(150, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(200, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(300, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(400, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(600, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(800, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(960, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1200, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1600, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(2400, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ ($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)
$5$ 1
$7$ ($$1 + 11 T^{2} + 49 T^{4}$$)($$1 - 13 T^{2} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{2}$$)($$( 1 - 7 T^{2} )^{2}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$1 - 13 T^{2} + 49 T^{4}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{2}$$)($$( 1 - 7 T^{2} )^{2}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{2}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$1 - 13 T^{2} + 49 T^{4}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$1 - 13 T^{2} + 49 T^{4}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{2}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{2}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{2}$$)($$1 - 13 T^{2} + 49 T^{4}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{2}$$)($$( 1 - 7 T^{2} )^{2}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$1 - 13 T^{2} + 49 T^{4}$$)($$1 + 11 T^{2} + 49 T^{4}$$)
$11$ ($$( 1 + 6 T + 11 T^{2} )^{2}$$)($$( 1 + 6 T + 11 T^{2} )^{2}$$)($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 + 2 T + 11 T^{2} )^{2}$$)($$( 1 + 2 T + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 - 2 T + 11 T^{2} )^{2}$$)($$( 1 - 2 T + 11 T^{2} )^{2}$$)($$( 1 - 4 T + 11 T^{2} )^{2}$$)($$( 1 - 4 T + 11 T^{2} )^{2}$$)($$( 1 - 4 T + 11 T^{2} )^{2}$$)($$( 1 - 4 T + 11 T^{2} )^{2}$$)($$( 1 - 4 T + 11 T^{2} )^{2}$$)($$( 1 - 4 T + 11 T^{2} )^{2}$$)($$( 1 - 4 T + 11 T^{2} )^{2}$$)($$( 1 - 4 T + 11 T^{2} )^{2}$$)($$( 1 - 6 T + 11 T^{2} )^{2}$$)($$( 1 - 6 T + 11 T^{2} )^{2}$$)
$13$ ($$1 - 17 T^{2} + 169 T^{4}$$)($$1 - T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 + 23 T^{2} + 169 T^{4}$$)($$1 - 17 T^{2} + 169 T^{4}$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 17 T^{2} + 169 T^{4}$$)($$1 - 25 T^{2} + 169 T^{4}$$)($$1 - T^{2} + 169 T^{4}$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 25 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 25 T^{2} + 169 T^{4}$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - T^{2} + 169 T^{4}$$)($$1 - 25 T^{2} + 169 T^{4}$$)($$1 - 17 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$1 - 17 T^{2} + 169 T^{4}$$)($$1 + 23 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - T^{2} + 169 T^{4}$$)($$1 - 17 T^{2} + 169 T^{4}$$)
$17$ ($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$1 - 18 T^{2} + 289 T^{4}$$)($$1 - 18 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$( 1 - 17 T^{2} )^{2}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 17 T^{2} )^{2}$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 17 T^{2} )^{2}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 17 T^{2} )^{2}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$1 - 18 T^{2} + 289 T^{4}$$)($$1 - 18 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)
$19$ ($$( 1 + T + 19 T^{2} )^{2}$$)($$( 1 - 5 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 + T + 19 T^{2} )^{2}$$)($$( 1 - T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$( 1 - 8 T + 19 T^{2} )^{2}$$)($$( 1 + 7 T + 19 T^{2} )^{2}$$)($$( 1 + 5 T + 19 T^{2} )^{2}$$)($$( 1 + 5 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 + 3 T + 19 T^{2} )^{2}$$)($$( 1 + 19 T^{2} )^{2}$$)($$( 1 + 19 T^{2} )^{2}$$)($$( 1 - 3 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$( 1 - 5 T + 19 T^{2} )^{2}$$)($$( 1 - 5 T + 19 T^{2} )^{2}$$)($$( 1 - 7 T + 19 T^{2} )^{2}$$)($$( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 + T + 19 T^{2} )^{2}$$)($$( 1 - T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$( 1 + 5 T + 19 T^{2} )^{2}$$)($$( 1 - T + 19 T^{2} )^{2}$$)
$23$ ($$1 - 42 T^{2} + 529 T^{4}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$1 + 18 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$1 + 18 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$( 1 - 23 T^{2} )^{2}$$)($$( 1 - 23 T^{2} )^{2}$$)($$1 - 30 T^{2} + 529 T^{4}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$1 - 30 T^{2} + 529 T^{4}$$)($$1 + 18 T^{2} + 529 T^{4}$$)($$1 + 18 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$1 - 30 T^{2} + 529 T^{4}$$)($$1 - 30 T^{2} + 529 T^{4}$$)($$1 - 30 T^{2} + 529 T^{4}$$)($$1 - 30 T^{2} + 529 T^{4}$$)($$1 + 18 T^{2} + 529 T^{4}$$)($$1 + 18 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$1 - 30 T^{2} + 529 T^{4}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$1 - 30 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$( 1 - 23 T^{2} )^{2}$$)($$( 1 - 23 T^{2} )^{2}$$)($$1 + 18 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$1 + 18 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$1 - 42 T^{2} + 529 T^{4}$$)
$29$ ($$( 1 - 6 T + 29 T^{2} )^{2}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 - 6 T + 29 T^{2} )^{2}$$)($$( 1 - 2 T + 29 T^{2} )^{2}$$)($$( 1 + 29 T^{2} )^{2}$$)($$( 1 + 8 T + 29 T^{2} )^{2}$$)($$( 1 - 10 T + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 - 10 T + 29 T^{2} )^{2}$$)($$( 1 - 4 T + 29 T^{2} )^{2}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 - 4 T + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 - 4 T + 29 T^{2} )^{2}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 - 4 T + 29 T^{2} )^{2}$$)($$( 1 - 10 T + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 - 10 T + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 + 8 T + 29 T^{2} )^{2}$$)($$( 1 + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 - 6 T + 29 T^{2} )^{2}$$)($$( 1 - 2 T + 29 T^{2} )^{2}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 - 6 T + 29 T^{2} )^{2}$$)
$31$ ($$( 1 + 3 T + 31 T^{2} )^{2}$$)($$( 1 + T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 - 4 T + 31 T^{2} )^{2}$$)($$( 1 + 3 T + 31 T^{2} )^{2}$$)($$( 1 + T + 31 T^{2} )^{2}$$)($$( 1 + 4 T + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 5 T + 31 T^{2} )^{2}$$)($$( 1 + 3 T + 31 T^{2} )^{2}$$)($$( 1 - 5 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 - 4 T + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 - 7 T + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 + 7 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 4 T + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 + 5 T + 31 T^{2} )^{2}$$)($$( 1 - 3 T + 31 T^{2} )^{2}$$)($$( 1 - 5 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 - 4 T + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 - T + 31 T^{2} )^{2}$$)($$( 1 - 3 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 + 4 T + 31 T^{2} )^{2}$$)($$( 1 - T + 31 T^{2} )^{2}$$)($$( 1 - 3 T + 31 T^{2} )^{2}$$)
$37$ ($$1 - 38 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)
$41$ ($$( 1 - 4 T + 41 T^{2} )^{2}$$)($$( 1 + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 12 T + 41 T^{2} )^{2}$$)($$( 1 + 8 T + 41 T^{2} )^{2}$$)($$( 1 + 10 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 + 10 T + 41 T^{2} )^{2}$$)($$( 1 + 8 T + 41 T^{2} )^{2}$$)($$( 1 - 12 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 + 41 T^{2} )^{2}$$)($$( 1 - 4 T + 41 T^{2} )^{2}$$)
$43$ ($$1 + 35 T^{2} + 1849 T^{4}$$)($$1 - 85 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 + 35 T^{2} + 1849 T^{4}$$)($$1 + 35 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 + 58 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 77 T^{2} + 1849 T^{4}$$)($$1 - 85 T^{2} + 1849 T^{4}$$)($$1 - 85 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 5 T^{2} + 1849 T^{4}$$)($$1 + 58 T^{2} + 1849 T^{4}$$)($$1 + 58 T^{2} + 1849 T^{4}$$)($$1 - 5 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 85 T^{2} + 1849 T^{4}$$)($$1 - 85 T^{2} + 1849 T^{4}$$)($$1 - 77 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 + 58 T^{2} + 1849 T^{4}$$)($$1 + 35 T^{2} + 1849 T^{4}$$)($$1 + 35 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 85 T^{2} + 1849 T^{4}$$)($$1 + 35 T^{2} + 1849 T^{4}$$)
$47$ ($$1 + 6 T^{2} + 2209 T^{4}$$)($$1 - 58 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$( 1 - 47 T^{2} )^{2}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$1 - 58 T^{2} + 2209 T^{4}$$)($$1 - 90 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$1 + 50 T^{2} + 2209 T^{4}$$)($$1 + 6 T^{2} + 2209 T^{4}$$)($$1 - 90 T^{2} + 2209 T^{4}$$)($$1 - 90 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$( 1 - 47 T^{2} )^{2}$$)($$1 - 58 T^{2} + 2209 T^{4}$$)($$1 + 50 T^{2} + 2209 T^{4}$$)($$1 + 50 T^{2} + 2209 T^{4}$$)($$1 - 58 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$( 1 - 47 T^{2} )^{2}$$)($$1 - 90 T^{2} + 2209 T^{4}$$)($$1 - 90 T^{2} + 2209 T^{4}$$)($$1 + 6 T^{2} + 2209 T^{4}$$)($$1 + 50 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$1 - 90 T^{2} + 2209 T^{4}$$)($$1 - 58 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$( 1 - 47 T^{2} )^{2}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$1 - 58 T^{2} + 2209 T^{4}$$)($$1 + 6 T^{2} + 2209 T^{4}$$)
$53$ ($$1 - 42 T^{2} + 2809 T^{4}$$)($$1 + 38 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} )$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} )$$)($$( 1 - 53 T^{2} )^{2}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 + 38 T^{2} + 2809 T^{4}$$)($$1 - 42 T^{2} + 2809 T^{4}$$)
$59$ ($$( 1 - 6 T + 59 T^{2} )^{2}$$)($$( 1 + 6 T + 59 T^{2} )^{2}$$)($$( 1 - 4 T + 59 T^{2} )^{2}$$)($$( 1 - 4 T + 59 T^{2} )^{2}$$)($$( 1 + 4 T + 59 T^{2} )^{2}$$)($$( 1 + 6 T + 59 T^{2} )^{2}$$)($$( 1 - 6 T + 59 T^{2} )^{2}$$)($$( 1 - 12 T + 59 T^{2} )^{2}$$)($$( 1 + 12 T + 59 T^{2} )^{2}$$)($$( 1 - 12 T + 59 T^{2} )^{2}$$)($$( 1 + 6 T + 59 T^{2} )^{2}$$)($$( 1 + 10 T + 59 T^{2} )^{2}$$)($$( 1 - 10 T + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 - 8 T + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 10 T + 59 T^{2} )^{2}$$)($$( 1 - 8 T + 59 T^{2} )^{2}$$)($$( 1 + 8 T + 59 T^{2} )^{2}$$)($$( 1 - 10 T + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 8 T + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 10 T + 59 T^{2} )^{2}$$)($$( 1 - 10 T + 59 T^{2} )^{2}$$)($$( 1 - 6 T + 59 T^{2} )^{2}$$)($$( 1 + 12 T + 59 T^{2} )^{2}$$)($$( 1 + 12 T + 59 T^{2} )^{2}$$)($$( 1 - 12 T + 59 T^{2} )^{2}$$)($$( 1 + 6 T + 59 T^{2} )^{2}$$)($$( 1 - 6 T + 59 T^{2} )^{2}$$)($$( 1 + 4 T + 59 T^{2} )^{2}$$)($$( 1 + 4 T + 59 T^{2} )^{2}$$)($$( 1 - 4 T + 59 T^{2} )^{2}$$)($$( 1 - 6 T + 59 T^{2} )^{2}$$)($$( 1 + 6 T + 59 T^{2} )^{2}$$)
$61$ ($$( 1 + 3 T + 61 T^{2} )^{2}$$)($$( 1 - 13 T + 61 T^{2} )^{2}$$)($$( 1 - 2 T + 61 T^{2} )^{2}$$)($$( 1 - 2 T + 61 T^{2} )^{2}$$)($$( 1 + 6 T + 61 T^{2} )^{2}$$)($$( 1 - T + 61 T^{2} )^{2}$$)($$( 1 + 11 T + 61 T^{2} )^{2}$$)($$( 1 - 10 T + 61 T^{2} )^{2}$$)($$( 1 + 14 T + 61 T^{2} )^{2}$$)($$( 1 + 14 T + 61 T^{2} )^{2}$$)($$( 1 - 13 T + 61 T^{2} )^{2}$$)($$( 1 + 7 T + 61 T^{2} )^{2}$$)($$( 1 - 5 T + 61 T^{2} )^{2}$$)($$( 1 + 6 T + 61 T^{2} )^{2}$$)($$( 1 - 2 T + 61 T^{2} )^{2}$$)($$( 1 - 10 T + 61 T^{2} )^{2}$$)($$( 1 - T + 61 T^{2} )^{2}$$)($$( 1 - 10 T + 61 T^{2} )^{2}$$)($$( 1 - 10 T + 61 T^{2} )^{2}$$)($$( 1 - T + 61 T^{2} )^{2}$$)($$( 1 + 6 T + 61 T^{2} )^{2}$$)($$( 1 - 2 T + 61 T^{2} )^{2}$$)($$( 1 - 10 T + 61 T^{2} )^{2}$$)($$( 1 - 5 T + 61 T^{2} )^{2}$$)($$( 1 + 7 T + 61 T^{2} )^{2}$$)($$( 1 - 13 T + 61 T^{2} )^{2}$$)($$( 1 + 14 T + 61 T^{2} )^{2}$$)($$( 1 - 10 T + 61 T^{2} )^{2}$$)($$( 1 + 14 T + 61 T^{2} )^{2}$$)($$( 1 + 11 T + 61 T^{2} )^{2}$$)($$( 1 - T + 61 T^{2} )^{2}$$)($$( 1 - 2 T + 61 T^{2} )^{2}$$)($$( 1 - 2 T + 61 T^{2} )^{2}$$)($$( 1 + 6 T + 61 T^{2} )^{2}$$)($$( 1 - 13 T + 61 T^{2} )^{2}$$)($$( 1 + 3 T + 61 T^{2} )^{2}$$)
$67$ ($$1 - 133 T^{2} + 4489 T^{4}$$)($$1 - 13 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 + 91 T^{2} + 4489 T^{4}$$)($$1 - 53 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 85 T^{2} + 4489 T^{4}$$)($$1 - 125 T^{2} + 4489 T^{4}$$)($$1 - 125 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 125 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 125 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 125 T^{2} + 4489 T^{4}$$)($$1 - 125 T^{2} + 4489 T^{4}$$)($$1 - 85 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 53 T^{2} + 4489 T^{4}$$)($$1 + 91 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 13 T^{2} + 4489 T^{4}$$)($$1 - 133 T^{2} + 4489 T^{4}$$)
$71$ ($$( 1 - 12 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 + 16 T + 71 T^{2} )^{2}$$)($$( 1 - 6 T + 71 T^{2} )^{2}$$)($$( 1 + 6 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 4 T + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 - 10 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 - 14 T + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 + 14 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 10 T + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 - 4 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 - 6 T + 71 T^{2} )^{2}$$)($$( 1 + 6 T + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 - 16 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 12 T + 71 T^{2} )^{2}$$)
$73$ ($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 - 142 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} )$$)($$1 - 142 T^{2} + 5329 T^{4}$$)($$1 + 50 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} )$$)($$1 - 142 T^{2} + 5329 T^{4}$$)($$( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} )$$)($$1 + 50 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 + 50 T^{2} + 5329 T^{4}$$)($$1 + 50 T^{2} + 5329 T^{4}$$)($$1 - 142 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 + 50 T^{2} + 5329 T^{4}$$)($$1 + 50 T^{2} + 5329 T^{4}$$)($$1 - 142 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 + 50 T^{2} + 5329 T^{4}$$)($$( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} )$$)($$1 - 142 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} )$$)($$1 + 50 T^{2} + 5329 T^{4}$$)($$1 - 142 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} )$$)($$1 - 142 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)
$79$ ($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 + 4 T + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 - 16 T + 79 T^{2} )^{2}$$)($$( 1 - 4 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 - 16 T + 79 T^{2} )^{2}$$)($$( 1 - 12 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 + 16 T + 79 T^{2} )^{2}$$)($$( 1 - 16 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 16 T + 79 T^{2} )^{2}$$)($$( 1 + 12 T + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 4 T + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 + 16 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 - 4 T + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)
$83$ ($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 162 T^{2} + 6889 T^{4}$$)($$1 - 162 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 + 30 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 + 158 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 + 158 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 + 30 T^{2} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 162 T^{2} + 6889 T^{4}$$)($$1 - 162 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)
$89$ ($$( 1 - 16 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 10 T + 89 T^{2} )^{2}$$)($$( 1 - 16 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 10 T + 89 T^{2} )^{2}$$)($$( 1 + 2 T + 89 T^{2} )^{2}$$)($$( 1 + 16 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 16 T + 89 T^{2} )^{2}$$)($$( 1 + 2 T + 89 T^{2} )^{2}$$)($$( 1 - 14 T + 89 T^{2} )^{2}$$)($$( 1 + 18 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 2 T + 89 T^{2} )^{2}$$)($$( 1 - 14 T + 89 T^{2} )^{2}$$)($$( 1 + 18 T + 89 T^{2} )^{2}$$)($$( 1 + 16 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 16 T + 89 T^{2} )^{2}$$)($$( 1 + 2 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 10 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 16 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 10 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 16 T + 89 T^{2} )^{2}$$)
$97$ ($$1 - 145 T^{2} + 9409 T^{4}$$)($$1 - 145 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 + 2 T^{2} + 9409 T^{4}$$)($$1 - 25 T^{2} + 9409 T^{4}$$)($$1 - 73 T^{2} + 9409 T^{4}$$)($$1 + 2 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 + 2 T^{2} + 9409 T^{4}$$)($$1 - 145 T^{2} + 9409 T^{4}$$)($$1 + 95 T^{2} + 9409 T^{4}$$)($$1 - 169 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 185 T^{2} + 9409 T^{4}$$)($$( 1 - 8 T + 97 T^{2} )( 1 + 8 T + 97 T^{2} )$$)($$( 1 - 8 T + 97 T^{2} )( 1 + 8 T + 97 T^{2} )$$)($$1 - 185 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 169 T^{2} + 9409 T^{4}$$)($$1 + 95 T^{2} + 9409 T^{4}$$)($$1 - 145 T^{2} + 9409 T^{4}$$)($$1 + 2 T^{2} + 9409 T^{4}$$)($$1 + 2 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 73 T^{2} + 9409 T^{4}$$)($$1 - 25 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 + 2 T^{2} + 9409 T^{4}$$)($$1 - 145 T^{2} + 9409 T^{4}$$)($$1 - 145 T^{2} + 9409 T^{4}$$)