# Properties

 Label 2112.2.a Level 2112 Weight 2 Character orbit a Rep. character $$\chi_{2112}(1,\cdot)$$ Character field $$\Q$$ Dimension 40 Newform subspaces 34 Sturm bound 768 Trace bound 13

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2112 = 2^{6} \cdot 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2112.a (trivial) Character field: $$\Q$$ Newform subspaces: $$34$$ Sturm bound: $$768$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$5$$, $$7$$, $$13$$, $$17$$, $$19$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(2112))$$.

Total New Old
Modular forms 408 40 368
Cusp forms 361 40 321
Eisenstein series 47 0 47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$2$$$$3$$$$11$$FrickeDim.
$$+$$$$+$$$$+$$$$+$$$$4$$
$$+$$$$+$$$$-$$$$-$$$$6$$
$$+$$$$-$$$$+$$$$-$$$$5$$
$$+$$$$-$$$$-$$$$+$$$$3$$
$$-$$$$+$$$$+$$$$-$$$$6$$
$$-$$$$+$$$$-$$$$+$$$$4$$
$$-$$$$-$$$$+$$$$+$$$$5$$
$$-$$$$-$$$$-$$$$-$$$$7$$
Plus space$$+$$$$16$$
Minus space$$-$$$$24$$

## Trace form

 $$40q + 40q^{9} + O(q^{10})$$ $$40q + 40q^{9} - 16q^{13} + 16q^{17} - 16q^{21} + 56q^{25} - 16q^{37} + 16q^{41} + 40q^{49} + 16q^{61} + 32q^{69} - 16q^{73} + 40q^{81} + 32q^{85} - 16q^{89} - 16q^{93} + 16q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(2112))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 2 3 11
2112.2.a.a $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$-4$$ $$-2$$ $$+$$ $$+$$ $$-$$ $$q-q^{3}-4q^{5}-2q^{7}+q^{9}+q^{11}+4q^{15}+\cdots$$
2112.2.a.b $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$-2$$ $$-2$$ $$-$$ $$+$$ $$+$$ $$q-q^{3}-2q^{5}-2q^{7}+q^{9}-q^{11}-6q^{13}+\cdots$$
2112.2.a.c $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$-2$$ $$-2$$ $$+$$ $$+$$ $$+$$ $$q-q^{3}-2q^{5}-2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$$
2112.2.a.d $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$-2$$ $$0$$ $$-$$ $$+$$ $$-$$ $$q-q^{3}-2q^{5}+q^{9}+q^{11}-2q^{13}+\cdots$$
2112.2.a.e $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$-2$$ $$4$$ $$-$$ $$+$$ $$+$$ $$q-q^{3}-2q^{5}+4q^{7}+q^{9}-q^{11}+6q^{13}+\cdots$$
2112.2.a.f $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$-2$$ $$4$$ $$+$$ $$+$$ $$-$$ $$q-q^{3}-2q^{5}+4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$$
2112.2.a.g $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$0$$ $$2$$ $$+$$ $$+$$ $$+$$ $$q-q^{3}+2q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$$
2112.2.a.h $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$0$$ $$2$$ $$+$$ $$+$$ $$+$$ $$q-q^{3}+2q^{7}+q^{9}-q^{11}-2q^{17}+\cdots$$
2112.2.a.i $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$0$$ $$2$$ $$+$$ $$+$$ $$-$$ $$q-q^{3}+2q^{7}+q^{9}+q^{11}+4q^{13}+\cdots$$
2112.2.a.j $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$2$$ $$-4$$ $$-$$ $$+$$ $$-$$ $$q-q^{3}+2q^{5}-4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$$
2112.2.a.k $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$2$$ $$-2$$ $$-$$ $$+$$ $$+$$ $$q-q^{3}+2q^{5}-2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$$
2112.2.a.l $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$2$$ $$0$$ $$+$$ $$+$$ $$-$$ $$q-q^{3}+2q^{5}+q^{9}+q^{11}+6q^{13}+\cdots$$
2112.2.a.m $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$2$$ $$4$$ $$+$$ $$+$$ $$-$$ $$q-q^{3}+2q^{5}+4q^{7}+q^{9}+q^{11}-6q^{13}+\cdots$$
2112.2.a.n $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$4$$ $$-2$$ $$+$$ $$+$$ $$+$$ $$q-q^{3}+4q^{5}-2q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$$
2112.2.a.o $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$-1$$ $$4$$ $$-2$$ $$+$$ $$+$$ $$-$$ $$q-q^{3}+4q^{5}-2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$$
2112.2.a.p $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$-4$$ $$2$$ $$-$$ $$-$$ $$+$$ $$q+q^{3}-4q^{5}+2q^{7}+q^{9}-q^{11}-4q^{15}+\cdots$$
2112.2.a.q $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$-2$$ $$-4$$ $$+$$ $$-$$ $$+$$ $$q+q^{3}-2q^{5}-4q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$$
2112.2.a.r $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$-2$$ $$-4$$ $$+$$ $$-$$ $$-$$ $$q+q^{3}-2q^{5}-4q^{7}+q^{9}+q^{11}+6q^{13}+\cdots$$
2112.2.a.s $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$-2$$ $$0$$ $$+$$ $$-$$ $$+$$ $$q+q^{3}-2q^{5}+q^{9}-q^{11}-2q^{13}+\cdots$$
2112.2.a.t $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$-2$$ $$2$$ $$+$$ $$-$$ $$-$$ $$q+q^{3}-2q^{5}+2q^{7}+q^{9}+q^{11}-6q^{13}+\cdots$$
2112.2.a.u $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$-2$$ $$2$$ $$-$$ $$-$$ $$-$$ $$q+q^{3}-2q^{5}+2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$$
2112.2.a.v $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$0$$ $$-2$$ $$-$$ $$-$$ $$+$$ $$q+q^{3}-2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots$$
2112.2.a.w $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$0$$ $$-2$$ $$+$$ $$-$$ $$-$$ $$q+q^{3}-2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$$
2112.2.a.x $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$0$$ $$-2$$ $$-$$ $$-$$ $$-$$ $$q+q^{3}-2q^{7}+q^{9}+q^{11}-2q^{17}+\cdots$$
2112.2.a.y $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$2$$ $$-4$$ $$-$$ $$-$$ $$+$$ $$q+q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}-6q^{13}+\cdots$$
2112.2.a.z $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$2$$ $$0$$ $$+$$ $$-$$ $$+$$ $$q+q^{3}+2q^{5}+q^{9}-q^{11}+6q^{13}+\cdots$$
2112.2.a.ba $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$2$$ $$2$$ $$-$$ $$-$$ $$-$$ $$q+q^{3}+2q^{5}+2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$$
2112.2.a.bb $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$2$$ $$4$$ $$+$$ $$-$$ $$+$$ $$q+q^{3}+2q^{5}+4q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$$
2112.2.a.bc $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$4$$ $$2$$ $$+$$ $$-$$ $$+$$ $$q+q^{3}+4q^{5}+2q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$$
2112.2.a.bd $$1$$ $$16.864$$ $$\Q$$ None $$0$$ $$1$$ $$4$$ $$2$$ $$-$$ $$-$$ $$-$$ $$q+q^{3}+4q^{5}+2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$$
2112.2.a.be $$2$$ $$16.864$$ $$\Q(\sqrt{5})$$ None $$0$$ $$-2$$ $$-2$$ $$2$$ $$-$$ $$+$$ $$-$$ $$q-q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots$$
2112.2.a.bf $$2$$ $$16.864$$ $$\Q(\sqrt{5})$$ None $$0$$ $$2$$ $$-2$$ $$-2$$ $$-$$ $$-$$ $$+$$ $$q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots$$
2112.2.a.bg $$3$$ $$16.864$$ 3.3.229.1 None $$0$$ $$-3$$ $$0$$ $$4$$ $$-$$ $$+$$ $$+$$ $$q-q^{3}+\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{9}-q^{11}+\cdots$$
2112.2.a.bh $$3$$ $$16.864$$ 3.3.229.1 None $$0$$ $$3$$ $$0$$ $$-4$$ $$-$$ $$-$$ $$-$$ $$q+q^{3}+\beta _{1}q^{5}+(-1-\beta _{2})q^{7}+q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(2112))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(2112)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(11))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(33))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(44))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(66))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(88))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(96))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(132))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(176))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(192))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(264))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(352))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(528))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(704))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(1056))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ ($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$( 1 + T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 + T )^{3}$$)($$( 1 - T )^{3}$$)
$5$ ($$1 + 4 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$1 + 5 T^{2}$$)($$1 + 5 T^{2}$$)($$1 + 5 T^{2}$$)($$1 - 2 T + 5 T^{2}$$)($$1 - 2 T + 5 T^{2}$$)($$1 - 2 T + 5 T^{2}$$)($$1 - 2 T + 5 T^{2}$$)($$1 - 4 T + 5 T^{2}$$)($$1 - 4 T + 5 T^{2}$$)($$1 + 4 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$1 + 5 T^{2}$$)($$1 + 5 T^{2}$$)($$1 + 5 T^{2}$$)($$1 - 2 T + 5 T^{2}$$)($$1 - 2 T + 5 T^{2}$$)($$1 - 2 T + 5 T^{2}$$)($$1 - 2 T + 5 T^{2}$$)($$1 - 4 T + 5 T^{2}$$)($$1 - 4 T + 5 T^{2}$$)($$1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4}$$)($$1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4}$$)($$1 - T^{2} - 8 T^{3} - 5 T^{4} + 125 T^{6}$$)($$1 - T^{2} - 8 T^{3} - 5 T^{4} + 125 T^{6}$$)
$7$ ($$1 + 2 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 - 4 T + 7 T^{2}$$)($$1 - 4 T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 + 4 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 - 4 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 + 4 T + 7 T^{2}$$)($$1 + 4 T + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 + 4 T + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 - 4 T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 - 2 T + 10 T^{2} - 14 T^{3} + 49 T^{4}$$)($$1 + 2 T + 10 T^{2} + 14 T^{3} + 49 T^{4}$$)($$1 - 4 T + 5 T^{2} + 35 T^{4} - 196 T^{5} + 343 T^{6}$$)($$1 + 4 T + 5 T^{2} + 35 T^{4} + 196 T^{5} + 343 T^{6}$$)
$11$ ($$1 - T$$)($$1 + T$$)($$1 + T$$)($$1 - T$$)($$1 + T$$)($$1 - T$$)($$1 + T$$)($$1 + T$$)($$1 - T$$)($$1 - T$$)($$1 + T$$)($$1 - T$$)($$1 - T$$)($$1 + T$$)($$1 - T$$)($$1 + T$$)($$1 + T$$)($$1 - T$$)($$1 + T$$)($$1 - T$$)($$1 - T$$)($$1 + T$$)($$1 - T$$)($$1 - T$$)($$1 + T$$)($$1 + T$$)($$1 - T$$)($$1 + T$$)($$1 + T$$)($$1 - T$$)($$( 1 - T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{3}$$)($$( 1 - T )^{3}$$)
$13$ ($$1 + 13 T^{2}$$)($$1 + 6 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 + 2 T + 13 T^{2}$$)($$1 - 6 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 + 4 T + 13 T^{2}$$)($$1 + 13 T^{2}$$)($$1 - 4 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 - 6 T + 13 T^{2}$$)($$1 + 6 T + 13 T^{2}$$)($$1 + 4 T + 13 T^{2}$$)($$1 + 4 T + 13 T^{2}$$)($$1 + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 - 6 T + 13 T^{2}$$)($$1 + 2 T + 13 T^{2}$$)($$1 + 6 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 - 4 T + 13 T^{2}$$)($$1 + 4 T + 13 T^{2}$$)($$1 + 13 T^{2}$$)($$1 + 6 T + 13 T^{2}$$)($$1 - 6 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 + 4 T + 13 T^{2}$$)($$1 + 4 T + 13 T^{2}$$)($$1 + 6 T + 30 T^{2} + 78 T^{3} + 169 T^{4}$$)($$1 + 6 T + 30 T^{2} + 78 T^{3} + 169 T^{4}$$)($$1 + 23 T^{2} - 8 T^{3} + 299 T^{4} + 2197 T^{6}$$)($$1 + 23 T^{2} - 8 T^{3} + 299 T^{4} + 2197 T^{6}$$)
$17$ ($$1 + 6 T + 17 T^{2}$$)($$1 + 4 T + 17 T^{2}$$)($$1 - 4 T + 17 T^{2}$$)($$1 - 6 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 + 6 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 - 6 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 + 6 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 - 6 T + 17 T^{2}$$)($$1 + 4 T + 17 T^{2}$$)($$1 - 4 T + 17 T^{2}$$)($$1 + 6 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 - 6 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 + 14 T^{2} + 289 T^{4}$$)($$1 + 14 T^{2} + 289 T^{4}$$)($$1 - 8 T + 47 T^{2} - 208 T^{3} + 799 T^{4} - 2312 T^{5} + 4913 T^{6}$$)($$1 - 8 T + 47 T^{2} - 208 T^{3} + 799 T^{4} - 2312 T^{5} + 4913 T^{6}$$)
$19$ ($$1 + 4 T + 19 T^{2}$$)($$1 + 2 T + 19 T^{2}$$)($$1 - 6 T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$1 - 4 T + 19 T^{2}$$)($$1 + 4 T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$1 + 8 T + 19 T^{2}$$)($$1 - 4 T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$1 - 2 T + 19 T^{2}$$)($$1 - 4 T + 19 T^{2}$$)($$1 - 8 T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$1 + 4 T + 19 T^{2}$$)($$1 - 4 T + 19 T^{2}$$)($$1 - 4 T + 19 T^{2}$$)($$1 + 4 T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$1 - 2 T + 19 T^{2}$$)($$1 + 6 T + 19 T^{2}$$)($$1 + 4 T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$1 - 8 T + 19 T^{2}$$)($$1 + 8 T + 19 T^{2}$$)($$1 + 4 T + 19 T^{2}$$)($$1 + 2 T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$1 - 4 T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$1 + 4 T + 22 T^{2} + 76 T^{3} + 361 T^{4}$$)($$1 - 4 T + 22 T^{2} - 76 T^{3} + 361 T^{4}$$)($$1 + 2 T + 33 T^{2} + 44 T^{3} + 627 T^{4} + 722 T^{5} + 6859 T^{6}$$)($$1 - 2 T + 33 T^{2} - 44 T^{3} + 627 T^{4} - 722 T^{5} + 6859 T^{6}$$)
$23$ ($$1 + 6 T + 23 T^{2}$$)($$1 - 8 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 + 4 T + 23 T^{2}$$)($$1 + 4 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 - 2 T + 23 T^{2}$$)($$1 + 2 T + 23 T^{2}$$)($$1 - 6 T + 23 T^{2}$$)($$1 + 8 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 + 4 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 + 6 T + 23 T^{2}$$)($$1 - 6 T + 23 T^{2}$$)($$1 - 6 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 - 4 T + 23 T^{2}$$)($$1 - 4 T + 23 T^{2}$$)($$1 + 8 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 + 6 T + 23 T^{2}$$)($$1 + 2 T + 23 T^{2}$$)($$1 - 2 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 - 4 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 - 8 T + 23 T^{2}$$)($$1 + 6 T + 23 T^{2}$$)($$1 - 6 T + 23 T^{2}$$)($$1 - 2 T + 2 T^{2} - 46 T^{3} + 529 T^{4}$$)($$1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4}$$)($$1 + 6 T + 65 T^{2} + 244 T^{3} + 1495 T^{4} + 3174 T^{5} + 12167 T^{6}$$)($$1 - 6 T + 65 T^{2} - 244 T^{3} + 1495 T^{4} - 3174 T^{5} + 12167 T^{6}$$)
$29$ ($$1 + 6 T + 29 T^{2}$$)($$1 + 29 T^{2}$$)($$1 - 8 T + 29 T^{2}$$)($$1 + 2 T + 29 T^{2}$$)($$1 + 6 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 - 2 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 + 6 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 - 8 T + 29 T^{2}$$)($$1 + 2 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 + 10 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 + 6 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 + 6 T + 29 T^{2}$$)($$1 + 2 T + 29 T^{2}$$)($$1 + 29 T^{2}$$)($$1 - 8 T + 29 T^{2}$$)($$1 + 6 T + 29 T^{2}$$)($$1 - 2 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 + 2 T + 29 T^{2}$$)($$1 - 8 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 + 10 T + 29 T^{2}$$)($$1 + 8 T + 54 T^{2} + 232 T^{3} + 841 T^{4}$$)($$1 + 8 T + 54 T^{2} + 232 T^{3} + 841 T^{4}$$)($$1 + 8 T + 83 T^{2} + 400 T^{3} + 2407 T^{4} + 6728 T^{5} + 24389 T^{6}$$)($$1 + 8 T + 83 T^{2} + 400 T^{3} + 2407 T^{4} + 6728 T^{5} + 24389 T^{6}$$)
$31$ ($$1 + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 + 8 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 - 4 T + 31 T^{2}$$)($$1 - 4 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 - 8 T + 31 T^{2}$$)($$1 - 8 T + 31 T^{2}$$)($$1 + 4 T + 31 T^{2}$$)($$1 + 4 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 + 8 T + 31 T^{2}$$)($$1 - 4 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 + 4 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 - 8 T + 31 T^{2}$$)($$1 + 8 T + 31 T^{2}$$)($$1 + 4 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 - 4 T + 31 T^{2}$$)($$1 - 4 T + 31 T^{2}$$)($$1 + 8 T + 31 T^{2}$$)($$1 + 4 T + 31 T^{2}$$)($$1 - 8 T + 31 T^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$1 - 4 T - 3 T^{2} + 8 T^{3} - 93 T^{4} - 3844 T^{5} + 29791 T^{6}$$)($$1 + 4 T - 3 T^{2} - 8 T^{3} - 93 T^{4} + 3844 T^{5} + 29791 T^{6}$$)
$37$ ($$1 + 6 T + 37 T^{2}$$)($$1 - 6 T + 37 T^{2}$$)($$1 + 10 T + 37 T^{2}$$)($$1 - 10 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 - 10 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 - 6 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 - 10 T + 37 T^{2}$$)($$1 - 6 T + 37 T^{2}$$)($$1 + 10 T + 37 T^{2}$$)($$1 - 10 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 - 6 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$( 1 + 6 T + 37 T^{2} )^{2}$$)($$( 1 + 6 T + 37 T^{2} )^{2}$$)($$1 - 2 T + 11 T^{2} - 204 T^{3} + 407 T^{4} - 2738 T^{5} + 50653 T^{6}$$)($$1 - 2 T + 11 T^{2} - 204 T^{3} + 407 T^{4} - 2738 T^{5} + 50653 T^{6}$$)
$41$ ($$1 + 10 T + 41 T^{2}$$)($$1 + 41 T^{2}$$)($$1 - 8 T + 41 T^{2}$$)($$1 - 6 T + 41 T^{2}$$)($$1 + 6 T + 41 T^{2}$$)($$1 + 6 T + 41 T^{2}$$)($$1 + 6 T + 41 T^{2}$$)($$1 - 2 T + 41 T^{2}$$)($$1 - 6 T + 41 T^{2}$$)($$1 + 2 T + 41 T^{2}$$)($$1 + 4 T + 41 T^{2}$$)($$1 - 10 T + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$1 - 2 T + 41 T^{2}$$)($$1 - 6 T + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$1 + 6 T + 41 T^{2}$$)($$1 + 6 T + 41 T^{2}$$)($$1 - 6 T + 41 T^{2}$$)($$1 + 41 T^{2}$$)($$1 - 8 T + 41 T^{2}$$)($$1 - 6 T + 41 T^{2}$$)($$1 + 6 T + 41 T^{2}$$)($$1 - 2 T + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$1 - 10 T + 41 T^{2}$$)($$1 + 4 T + 41 T^{2}$$)($$1 + 2 T + 41 T^{2}$$)($$1 - 6 T + 41 T^{2}$$)($$1 - 2 T + 41 T^{2}$$)($$1 - 4 T + 6 T^{2} - 164 T^{3} + 1681 T^{4}$$)($$1 - 4 T + 6 T^{2} - 164 T^{3} + 1681 T^{4}$$)($$1 - 8 T + 95 T^{2} - 448 T^{3} + 3895 T^{4} - 13448 T^{5} + 68921 T^{6}$$)($$1 - 8 T + 95 T^{2} - 448 T^{3} + 3895 T^{4} - 13448 T^{5} + 68921 T^{6}$$)
$43$ ($$1 - 8 T + 43 T^{2}$$)($$1 - 10 T + 43 T^{2}$$)($$1 - 2 T + 43 T^{2}$$)($$1 + 8 T + 43 T^{2}$$)($$1 - 4 T + 43 T^{2}$$)($$1 - 4 T + 43 T^{2}$$)($$1 + 12 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 + 8 T + 43 T^{2}$$)($$1 + 43 T^{2}$$)($$1 - 6 T + 43 T^{2}$$)($$1 - 4 T + 43 T^{2}$$)($$1 - 8 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 + 8 T + 43 T^{2}$$)($$1 + 8 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 - 8 T + 43 T^{2}$$)($$1 + 10 T + 43 T^{2}$$)($$1 + 2 T + 43 T^{2}$$)($$1 - 8 T + 43 T^{2}$$)($$1 - 12 T + 43 T^{2}$$)($$1 - 4 T + 43 T^{2}$$)($$1 + 8 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 + 6 T + 43 T^{2}$$)($$1 + 43 T^{2}$$)($$1 - 8 T + 43 T^{2}$$)($$1 - 4 T + 43 T^{2}$$)($$1 - 8 T + 22 T^{2} - 344 T^{3} + 1849 T^{4}$$)($$1 + 8 T + 22 T^{2} + 344 T^{3} + 1849 T^{4}$$)($$1 + 10 T + 113 T^{2} + 828 T^{3} + 4859 T^{4} + 18490 T^{5} + 79507 T^{6}$$)($$1 - 10 T + 113 T^{2} - 828 T^{3} + 4859 T^{4} - 18490 T^{5} + 79507 T^{6}$$)
$47$ ($$1 - 6 T + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 + 8 T + 47 T^{2}$$)($$1 - 4 T + 47 T^{2}$$)($$1 - 12 T + 47 T^{2}$$)($$1 + 8 T + 47 T^{2}$$)($$1 - 6 T + 47 T^{2}$$)($$1 + 6 T + 47 T^{2}$$)($$1 + 6 T + 47 T^{2}$$)($$1 + 8 T + 47 T^{2}$$)($$1 - 8 T + 47 T^{2}$$)($$1 + 4 T + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 + 2 T + 47 T^{2}$$)($$1 - 10 T + 47 T^{2}$$)($$1 + 6 T + 47 T^{2}$$)($$1 - 8 T + 47 T^{2}$$)($$1 + 12 T + 47 T^{2}$$)($$1 + 4 T + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 - 8 T + 47 T^{2}$$)($$1 - 6 T + 47 T^{2}$$)($$1 + 6 T + 47 T^{2}$$)($$1 - 6 T + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 - 4 T + 47 T^{2}$$)($$1 + 8 T + 47 T^{2}$$)($$1 - 8 T + 47 T^{2}$$)($$1 + 10 T + 47 T^{2}$$)($$1 - 2 T + 47 T^{2}$$)($$1 + 2 T + 50 T^{2} + 94 T^{3} + 2209 T^{4}$$)($$1 - 2 T + 50 T^{2} - 94 T^{3} + 2209 T^{4}$$)($$1 + 18 T + 233 T^{2} + 1820 T^{3} + 10951 T^{4} + 39762 T^{5} + 103823 T^{6}$$)($$1 - 18 T + 233 T^{2} - 1820 T^{3} + 10951 T^{4} - 39762 T^{5} + 103823 T^{6}$$)
$53$ ($$1 - 12 T + 53 T^{2}$$)($$1 + 14 T + 53 T^{2}$$)($$1 - 2 T + 53 T^{2}$$)($$1 - 6 T + 53 T^{2}$$)($$1 + 2 T + 53 T^{2}$$)($$1 - 6 T + 53 T^{2}$$)($$1 + 53 T^{2}$$)($$1 - 8 T + 53 T^{2}$$)($$1 + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 - 6 T + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 + 4 T + 53 T^{2}$$)($$1 - 12 T + 53 T^{2}$$)($$1 - 12 T + 53 T^{2}$$)($$1 - 6 T + 53 T^{2}$$)($$1 + 2 T + 53 T^{2}$$)($$1 - 6 T + 53 T^{2}$$)($$1 + 14 T + 53 T^{2}$$)($$1 - 2 T + 53 T^{2}$$)($$1 + 53 T^{2}$$)($$1 + 53 T^{2}$$)($$1 - 8 T + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 - 6 T + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 - 12 T + 53 T^{2}$$)($$1 + 4 T + 53 T^{2}$$)($$1 + 18 T + 182 T^{2} + 954 T^{3} + 2809 T^{4}$$)($$1 + 18 T + 182 T^{2} + 954 T^{3} + 2809 T^{4}$$)($$1 - 4 T + 39 T^{2} - 192 T^{3} + 2067 T^{4} - 11236 T^{5} + 148877 T^{6}$$)($$1 - 4 T + 39 T^{2} - 192 T^{3} + 2067 T^{4} - 11236 T^{5} + 148877 T^{6}$$)
$59$ ($$1 - 8 T + 59 T^{2}$$)($$1 + 12 T + 59 T^{2}$$)($$1 + 12 T + 59 T^{2}$$)($$1 + 12 T + 59 T^{2}$$)($$1 - 12 T + 59 T^{2}$$)($$1 + 12 T + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 - 8 T + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 + 4 T + 59 T^{2}$$)($$1 + 4 T + 59 T^{2}$$)($$1 - 12 T + 59 T^{2}$$)($$1 + 4 T + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 + 8 T + 59 T^{2}$$)($$1 - 12 T + 59 T^{2}$$)($$1 + 12 T + 59 T^{2}$$)($$1 - 12 T + 59 T^{2}$$)($$1 - 12 T + 59 T^{2}$$)($$1 - 12 T + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 + 8 T + 59 T^{2}$$)($$1 - 4 T + 59 T^{2}$$)($$1 + 12 T + 59 T^{2}$$)($$1 - 4 T + 59 T^{2}$$)($$1 - 4 T + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 - 20 T + 198 T^{2} - 1180 T^{3} + 3481 T^{4}$$)($$1 + 20 T + 198 T^{2} + 1180 T^{3} + 3481 T^{4}$$)($$1 + 113 T^{2} + 64 T^{3} + 6667 T^{4} + 205379 T^{6}$$)($$1 + 113 T^{2} - 64 T^{3} + 6667 T^{4} + 205379 T^{6}$$)
$61$ ($$1 + 4 T + 61 T^{2}$$)($$1 - 14 T + 61 T^{2}$$)($$1 + 10 T + 61 T^{2}$$)($$1 + 2 T + 61 T^{2}$$)($$1 - 14 T + 61 T^{2}$$)($$1 - 10 T + 61 T^{2}$$)($$1 + 61 T^{2}$$)($$1 - 4 T + 61 T^{2}$$)($$1 + 8 T + 61 T^{2}$$)($$1 + 6 T + 61 T^{2}$$)($$1 - 6 T + 61 T^{2}$$)($$1 - 6 T + 61 T^{2}$$)($$1 - 2 T + 61 T^{2}$$)($$1 - 8 T + 61 T^{2}$$)($$1 + 8 T + 61 T^{2}$$)($$1 + 4 T + 61 T^{2}$$)($$1 - 10 T + 61 T^{2}$$)($$1 - 14 T + 61 T^{2}$$)($$1 + 2 T + 61 T^{2}$$)($$1 - 14 T + 61 T^{2}$$)($$1 + 10 T + 61 T^{2}$$)($$1 + 8 T + 61 T^{2}$$)($$1 + 61 T^{2}$$)($$1 - 4 T + 61 T^{2}$$)($$1 - 2 T + 61 T^{2}$$)($$1 - 6 T + 61 T^{2}$$)($$1 - 6 T + 61 T^{2}$$)($$1 + 6 T + 61 T^{2}$$)($$1 + 8 T + 61 T^{2}$$)($$1 - 8 T + 61 T^{2}$$)($$1 + 10 T + 102 T^{2} + 610 T^{3} + 3721 T^{4}$$)($$1 + 10 T + 102 T^{2} + 610 T^{3} + 3721 T^{4}$$)($$1 + 8 T + 127 T^{2} + 584 T^{3} + 7747 T^{4} + 29768 T^{5} + 226981 T^{6}$$)($$1 + 8 T + 127 T^{2} + 584 T^{3} + 7747 T^{4} + 29768 T^{5} + 226981 T^{6}$$)
$67$ ($$1 - 12 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 + 12 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 + 12 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 - 12 T + 67 T^{2}$$)($$1 - 12 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 + 12 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 - 12 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 - 12 T + 67 T^{2}$$)($$1 + 12 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 + 12 T + 67 T^{2}$$)($$( 1 + 8 T + 67 T^{2} )^{2}$$)($$( 1 - 8 T + 67 T^{2} )^{2}$$)($$1 - 4 T + 9 T^{2} + 488 T^{3} + 603 T^{4} - 17956 T^{5} + 300763 T^{6}$$)($$1 + 4 T + 9 T^{2} - 488 T^{3} + 603 T^{4} + 17956 T^{5} + 300763 T^{6}$$)
$71$ ($$1 - 10 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 - 8 T + 71 T^{2}$$)($$1 + 12 T + 71 T^{2}$$)($$1 - 12 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 - 10 T + 71 T^{2}$$)($$1 + 10 T + 71 T^{2}$$)($$1 - 6 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 - 8 T + 71 T^{2}$$)($$1 + 4 T + 71 T^{2}$$)($$1 + 8 T + 71 T^{2}$$)($$1 - 2 T + 71 T^{2}$$)($$1 - 6 T + 71 T^{2}$$)($$1 + 10 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 12 T + 71 T^{2}$$)($$1 - 12 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 8 T + 71 T^{2}$$)($$1 + 6 T + 71 T^{2}$$)($$1 + 10 T + 71 T^{2}$$)($$1 - 10 T + 71 T^{2}$$)($$1 - 8 T + 71 T^{2}$$)($$1 - 4 T + 71 T^{2}$$)($$1 + 8 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 6 T + 71 T^{2}$$)($$1 + 2 T + 71 T^{2}$$)($$1 - 2 T + 98 T^{2} - 142 T^{3} + 5041 T^{4}$$)($$1 + 2 T + 98 T^{2} + 142 T^{3} + 5041 T^{4}$$)($$1 + 30 T + 497 T^{2} + 5092 T^{3} + 35287 T^{4} + 151230 T^{5} + 357911 T^{6}$$)($$1 - 30 T + 497 T^{2} - 5092 T^{3} + 35287 T^{4} - 151230 T^{5} + 357911 T^{6}$$)
$73$ ($$1 - 2 T + 73 T^{2}$$)($$1 - 6 T + 73 T^{2}$$)($$1 - 6 T + 73 T^{2}$$)($$1 + 14 T + 73 T^{2}$$)($$1 + 6 T + 73 T^{2}$$)($$1 - 10 T + 73 T^{2}$$)($$1 - 2 T + 73 T^{2}$$)($$1 + 6 T + 73 T^{2}$$)($$1 - 2 T + 73 T^{2}$$)($$1 + 14 T + 73 T^{2}$$)($$1 + 10 T + 73 T^{2}$$)($$1 - 10 T + 73 T^{2}$$)($$1 - 2 T + 73 T^{2}$$)($$1 + 6 T + 73 T^{2}$$)($$1 - 10 T + 73 T^{2}$$)($$1 - 2 T + 73 T^{2}$$)($$1 - 10 T + 73 T^{2}$$)($$1 + 6 T + 73 T^{2}$$)($$1 + 14 T + 73 T^{2}$$)($$1 - 6 T + 73 T^{2}$$)($$1 - 6 T + 73 T^{2}$$)($$1 - 2 T + 73 T^{2}$$)($$1 - 2 T + 73 T^{2}$$)($$1 + 6 T + 73 T^{2}$$)($$1 - 2 T + 73 T^{2}$$)($$1 - 10 T + 73 T^{2}$$)($$1 + 10 T + 73 T^{2}$$)($$1 + 14 T + 73 T^{2}$$)($$1 - 10 T + 73 T^{2}$$)($$1 + 6 T + 73 T^{2}$$)($$( 1 + 6 T + 73 T^{2} )^{2}$$)($$( 1 + 6 T + 73 T^{2} )^{2}$$)($$1 - 10 T + 55 T^{2} - 76 T^{3} + 4015 T^{4} - 53290 T^{5} + 389017 T^{6}$$)($$1 - 10 T + 55 T^{2} - 76 T^{3} + 4015 T^{4} - 53290 T^{5} + 389017 T^{6}$$)
$79$ ($$1 - 2 T + 79 T^{2}$$)($$1 + 2 T + 79 T^{2}$$)($$1 + 2 T + 79 T^{2}$$)($$1 + 16 T + 79 T^{2}$$)($$1 - 4 T + 79 T^{2}$$)($$1 - 12 T + 79 T^{2}$$)($$1 + 2 T + 79 T^{2}$$)($$1 + 10 T + 79 T^{2}$$)($$1 - 14 T + 79 T^{2}$$)($$1 - 4 T + 79 T^{2}$$)($$1 - 14 T + 79 T^{2}$$)($$1 + 16 T + 79 T^{2}$$)($$1 + 4 T + 79 T^{2}$$)($$1 - 10 T + 79 T^{2}$$)($$1 + 6 T + 79 T^{2}$$)($$1 + 2 T + 79 T^{2}$$)($$1 + 12 T + 79 T^{2}$$)($$1 + 4 T + 79 T^{2}$$)($$1 - 16 T + 79 T^{2}$$)($$1 - 2 T + 79 T^{2}$$)($$1 - 2 T + 79 T^{2}$$)($$1 + 14 T + 79 T^{2}$$)($$1 - 2 T + 79 T^{2}$$)($$1 - 10 T + 79 T^{2}$$)($$1 - 4 T + 79 T^{2}$$)($$1 - 16 T + 79 T^{2}$$)($$1 + 14 T + 79 T^{2}$$)($$1 + 4 T + 79 T^{2}$$)($$1 - 6 T + 79 T^{2}$$)($$1 + 10 T + 79 T^{2}$$)($$1 + 10 T + 138 T^{2} + 790 T^{3} + 6241 T^{4}$$)($$1 - 10 T + 138 T^{2} - 790 T^{3} + 6241 T^{4}$$)($$1 - 16 T + 261 T^{2} - 2536 T^{3} + 20619 T^{4} - 99856 T^{5} + 493039 T^{6}$$)($$1 + 16 T + 261 T^{2} + 2536 T^{3} + 20619 T^{4} + 99856 T^{5} + 493039 T^{6}$$)
$83$ ($$1 + 12 T + 83 T^{2}$$)($$1 - 16 T + 83 T^{2}$$)($$1 + 16 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$1 - 4 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$1 + 4 T + 83 T^{2}$$)($$1 - 4 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 + 8 T + 83 T^{2}$$)($$1 + 4 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 + 4 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 + 4 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 + 16 T + 83 T^{2}$$)($$1 - 16 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$1 - 4 T + 83 T^{2}$$)($$1 + 4 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$1 - 4 T + 83 T^{2}$$)($$1 - 8 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$1 - 4 T + 83 T^{2}$$)($$1 - 8 T + 102 T^{2} - 664 T^{3} + 6889 T^{4}$$)($$1 + 8 T + 102 T^{2} + 664 T^{3} + 6889 T^{4}$$)($$( 1 - 8 T + 83 T^{2} )^{3}$$)($$( 1 + 8 T + 83 T^{2} )^{3}$$)
$89$ ($$1 + 6 T + 89 T^{2}$$)($$1 + 14 T + 89 T^{2}$$)($$1 + 14 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 + 14 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)($$1 - 2 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 + 14 T + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 + 14 T + 89 T^{2}$$)($$1 + 14 T + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)($$1 + 14 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 - 2 T + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)($$1 + 14 T + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$( 1 - 2 T + 89 T^{2} )^{2}$$)($$( 1 - 2 T + 89 T^{2} )^{2}$$)($$( 1 - 2 T + 89 T^{2} )^{3}$$)($$( 1 - 2 T + 89 T^{2} )^{3}$$)
$97$ ($$1 - 14 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 + 14 T + 97 T^{2}$$)($$1 + 14 T + 97 T^{2}$$)($$1 - 18 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 - 14 T + 97 T^{2}$$)($$1 - 2 T + 97 T^{2}$$)($$1 - 14 T + 97 T^{2}$$)($$1 - 2 T + 97 T^{2}$$)($$1 - 2 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 + 18 T + 97 T^{2}$$)($$1 - 14 T + 97 T^{2}$$)($$1 - 18 T + 97 T^{2}$$)($$1 + 14 T + 97 T^{2}$$)($$1 + 14 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 - 14 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 - 2 T + 97 T^{2}$$)($$1 - 2 T + 97 T^{2}$$)($$1 - 14 T + 97 T^{2}$$)($$1 - 2 T + 97 T^{2}$$)($$1 + 18 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 + 8 T + 190 T^{2} + 776 T^{3} + 9409 T^{4}$$)($$1 + 8 T + 190 T^{2} + 776 T^{3} + 9409 T^{4}$$)($$1 - 6 T + 239 T^{2} - 980 T^{3} + 23183 T^{4} - 56454 T^{5} + 912673 T^{6}$$)($$1 - 6 T + 239 T^{2} - 980 T^{3} + 23183 T^{4} - 56454 T^{5} + 912673 T^{6}$$)