12n
0129
(K12n
0129
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 8 4 10 12 6 5 9 11
Solving Sequence
7,10 4,8
6 3 5 11 2 1 9 12
c
7
c
6
c
3
c
5
c
10
c
2
c
1
c
9
c
11
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h7.80956 × 10
63
u
23
− 1.02547 × 10
64
u
22
+ ··· + 2.29425 × 10
67
b − 5.89286 × 10
67
,
1.97576 × 10
64
u
23
− 3.89917 × 10
64
u
22
+ ··· + 4.58851 × 10
67
a − 3.71378 × 10
68
,
u
24
− 2u
23
+ ··· − 28672u + 4096i
I
u
2
= hb, −u
8
+ 2u
7
+ 2u
6
− 5u
5
− u
4
+ 5u
3
− u
2
+ a, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
v
1
= ha, −164522v
11
− 355934v
10
+ ··· + 707733b + 176501,
v
12
+ 3v
11
+ 3v
10
+ 18v
9
+ 31v
8
− 29v
7
− 31v
6
− 9v
5
+ 19v
4
+ 5v
3
− 4v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 45 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
=
h7.81×10
63
u
23
−1.03×10
64
u
22
+· · ·+2.29×10
67
b−5.89×10
67
, 1.98×10
64
u
23
−
3.90×10
64
u
22
+· · ·+4.59×10
67
a−3.71×10
68
, u
24
−2u
23
+· · ·−28672u+4096 i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
4
=
−0.000430588u
23
+ 0.000849769u
22
+ ··· − 30.4322u + 8.09365
−0.000340396u
23
+ 0.000446971u
22
+ ··· − 15.0993u + 2.56853
a
8
=
1
−u
2
a
6
=
−0.000770690u
23
+ 0.000886997u
22
+ ··· − 28.3683u + 4.83639
0.0000627821u
23
− 2.14799 × 10
−6
u
22
+ ··· + 0.966055u − 0.729487
a
3
=
−0.000177123u
23
+ 0.000316023u
22
+ ··· − 20.9747u + 7.59248
−0.000440550u
23
+ 0.000737374u
22
+ ··· − 27.4672u + 4.56426
a
5
=
−0.000247524u
23
+ 0.000151248u
22
+ ··· − 13.7287u + 2.88552
−0.0000743622u
23
+ 0.000208018u
22
+ ··· − 5.79607u + 0.542658
a
11
=
0.00108442u
23
− 0.00207040u
22
+ ··· + 62.2122u − 10.2669
0.000158575u
23
+ 0.0000350829u
22
+ ··· − 7.95177u + 2.38129
a
2
=
−0.000349715u
23
+ 0.000929736u
22
+ ··· − 27.5141u + 7.63549
−0.000471953u
23
+ 0.000545981u
22
+ ··· − 19.0997u + 3.40520
a
1
=
−0.000974598u
23
+ 0.00198880u
22
+ ··· − 59.8532u + 10.2543
−0.000406712u
23
+ 0.000387216u
22
+ ··· − 5.12759u + 0.162234
a
9
=
0.00105057u
23
− 0.00167229u
22
+ ··· + 45.4181u − 7.13094
−0.000133803u
23
+ 0.000328867u
22
+ ··· − 13.2158u + 2.91448
a
12
=
0.00207530u
23
− 0.00334512u
22
+ ··· + 88.7435u − 14.5857
0.000298832u
23
− 0.0000705567u
22
+ ··· − 4.27903u + 1.62940
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.000912531u
23
+ 0.00194308u
22
+ ··· − 44.5011u + 4.80932
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 24u
23
+ ··· − 179u + 1
c
2
, c
4
u
24
− 12u
23
+ ··· + 17u − 1
c
3
, c
6
u
24
+ u
23
+ ··· − 2560u + 512
c
5
u
24
+ 4u
23
+ ··· − 3u − 1
c
7
u
24
+ 2u
23
+ ··· + 28672u + 4096
c
8
, c
11
u
24
+ 8u
23
+ ··· + 7u + 1
c
9
u
24
+ u
23
+ ··· − 74162u − 19441
c
10
u
24
− 5u
23
+ ··· − 389242u + 249139
c
12
u
24
+ 20u
22
+ ··· + 19u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 204y
23
+ ··· − 2901y + 1
c
2
, c
4
y
24
− 24y
23
+ ··· + 179y + 1
c
3
, c
6
y
24
− 63y
23
+ ··· − 3932160y + 262144
c
5
y
24
+ 26y
22
+ ··· − y + 1
c
7
y
24
− 90y
23
+ ··· + 67108864y + 16777216
c
8
, c
11
y
24
+ 20y
22
+ ··· + 19y + 1
c
9
y
24
− 61y
23
+ ··· − 296113128y + 377952481
c
10
y
24
+ 111y
23
+ ··· − 469614992544y + 62070241321
c
12
y
24
+ 40y
23
+ ··· + 2151y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.632443 + 0.726844I
a = 0.114777 + 0.151496I
b = 1.063560 + 0.162285I
2.67249 − 0.06243I 6.49122 − 0.13400I
u = −0.632443 − 0.726844I
a = 0.114777 − 0.151496I
b = 1.063560 − 0.162285I
2.67249 + 0.06243I 6.49122 + 0.13400I
u = 1.201550 + 0.153048I
a = 0.0923620 + 0.0946298I
b = −0.828567 + 0.942729I
1.03909 − 7.66938I 3.58752 + 6.84907I
u = 1.201550 − 0.153048I
a = 0.0923620 − 0.0946298I
b = −0.828567 − 0.942729I
1.03909 + 7.66938I 3.58752 − 6.84907I
u = 0.690057 + 0.202830I
a = 2.59655 − 0.30553I
b = −0.024221 − 0.599362I
−1.38798 − 2.82419I 0.59813 + 2.55909I
u = 0.690057 − 0.202830I
a = 2.59655 + 0.30553I
b = −0.024221 + 0.599362I
−1.38798 + 2.82419I 0.59813 − 2.55909I
u = 0.505730 + 0.448375I
a = 2.58887 − 1.75795I
b = −0.950717 + 0.074911I
−2.60567 + 1.37963I −1.96914 − 4.05392I
u = 0.505730 − 0.448375I
a = 2.58887 + 1.75795I
b = −0.950717 − 0.074911I
−2.60567 − 1.37963I −1.96914 + 4.05392I
u = −0.661121
a = 0.510618
b = 0.373534
1.02845 10.2860
u = 0.049304 + 0.644470I
a = 1.84071 − 0.43802I
b = 0.232697 − 0.155126I
0.59509 − 2.36713I 1.40991 + 3.67925I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.049304 − 0.644470I
a = 1.84071 + 0.43802I
b = 0.232697 + 0.155126I
0.59509 + 2.36713I 1.40991 − 3.67925I
u = 1.17039 + 0.90470I
a = 0.319512 − 0.046660I
b = −0.893023 + 0.472118I
−1.87950 + 2.72151I 1.13774 − 4.25269I
u = 1.17039 − 0.90470I
a = 0.319512 + 0.046660I
b = −0.893023 − 0.472118I
−1.87950 − 2.72151I 1.13774 + 4.25269I
u = 0.188201 + 0.357668I
a = 2.01717 − 1.17792I
b = −0.349958 − 0.812535I
−1.83062 − 1.07717I −2.53581 + 1.58170I
u = 0.188201 − 0.357668I
a = 2.01717 + 1.17792I
b = −0.349958 + 0.812535I
−1.83062 + 1.07717I −2.53581 − 1.58170I
u = −2.38858 + 1.57335I
a = −0.524904 − 0.425161I
b = 2.09180 − 1.57981I
18.8685 − 6.6483I 0
u = −2.38858 − 1.57335I
a = −0.524904 + 0.425161I
b = 2.09180 + 1.57981I
18.8685 + 6.6483I 0
u = 2.25638 + 1.80466I
a = 0.568423 − 0.488334I
b = −2.24002 − 1.53390I
18.7357 + 14.2573I 0
u = 2.25638 − 1.80466I
a = 0.568423 + 0.488334I
b = −2.24002 + 1.53390I
18.7357 − 14.2573I 0
u = −3.61633
a = −0.660672
b = 2.14769
0.756608 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 4.44102 + 1.22807I
a = −0.408012 + 0.133656I
b = 3.93681 + 1.85539I
−18.9745 − 1.9748I 0
u = 4.44102 − 1.22807I
a = −0.408012 − 0.133656I
b = 3.93681 − 1.85539I
−18.9745 + 1.9748I 0
u = −4.34288 + 2.39260I
a = 0.369569 + 0.203301I
b = −3.79897 + 1.84880I
−18.5925 − 5.6388I 0
u = −4.34288 − 2.39260I
a = 0.369569 − 0.203301I
b = −3.79897 − 1.84880I
−18.5925 + 5.6388I 0
7
II. I
u
2
= hb, −u
8
+ 2u
7
+ 2u
6
− 5u
5
− u
4
+ 5u
3
− u
2
+ a, u
9
− u
8
− 2u
7
+
3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
4
=
u
8
− 2u
7
− 2u
6
+ 5u
5
+ u
4
− 5u
3
+ u
2
0
a
8
=
1
−u
2
a
6
=
1
0
a
3
=
u
8
− 2u
7
− 2u
6
+ 5u
5
+ u
4
− 5u
3
+ u
2
0
a
5
=
−u
2
+ 1
u
4
a
11
=
−u
5
+ 2u
3
− u
u
7
− u
5
+ u
a
2
=
u
8
− 2u
7
− 2u
6
+ 5u
5
+ u
4
− 5u
3
+ 2u
2
− 1
−u
4
a
1
=
u
2
− 1
−u
4
a
9
=
−u
u
a
12
=
u
8
− 3u
6
+ 3u
4
− 1
−u
8
+ u
7
+ 3u
6
− 2u
5
− 3u
4
+ 2u
3
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
8
+ u
7
+ 7u
6
− 6u
5
− 6u
4
+ 7u
3
− 5u
2
− 7u + 1
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
u
9
c
4
(u + 1)
9
c
5
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
7
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
8
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
, c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
6
y
9
c
5
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
7
, c
9
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
8
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
10
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = −0.939568 − 0.981640I
b = 0
−3.42837 + 2.09337I −4.41045 − 5.46639I
u = 0.772920 − 0.510351I
a = −0.939568 + 0.981640I
b = 0
−3.42837 − 2.09337I −4.41045 + 5.46639I
u = −0.825933
a = 2.14893
b = 0
−0.446489 −0.182090
u = −1.173910 + 0.391555I
a = 0.119081 + 0.409451I
b = 0
2.72642 − 1.33617I 8.07941 + 3.55369I
u = −1.173910 − 0.391555I
a = 0.119081 − 0.409451I
b = 0
2.72642 + 1.33617I 8.07941 − 3.55369I
u = 0.141484 + 0.739668I
a = 2.26219 + 2.13290I
b = 0
−1.02799 − 2.45442I −2.24638 − 6.63381I
u = 0.141484 − 0.739668I
a = 2.26219 − 2.13290I
b = 0
−1.02799 + 2.45442I −2.24638 + 6.63381I
u = 1.172470 + 0.500383I
a = −0.016164 − 0.378317I
b = 0
1.95319 + 7.08493I 8.66846 − 5.33071I
u = 1.172470 − 0.500383I
a = −0.016164 + 0.378317I
b = 0
1.95319 − 7.08493I 8.66846 + 5.33071I
11
III. I
v
1
= ha, −1.65 × 10
5
v
11
− 3.56 × 10
5
v
10
+ · · · + 7.08 × 10
5
b + 1.77 ×
10
5
, v
12
+ 3v
11
+ · · · + v + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
v
0
a
4
=
0
0.232463v
11
+ 0.502921v
10
+ ··· − 0.152902v − 0.249389
a
8
=
1
0
a
6
=
1
−1.04198v
11
− 2.90360v
10
+ ··· + 1.23849v − 0.574544
a
3
=
−0.232463v
11
− 0.502921v
10
+ ··· + 0.152902v + 0.249389
−1.00827v
11
− 2.68986v
10
+ ··· + 1.09637v − 2.28028
a
5
=
1.04198v
11
+ 2.90360v
10
+ ··· − 1.23849v + 1.57454
−1.04198v
11
− 2.90360v
10
+ ··· + 1.23849v − 0.574544
a
11
=
−0.126775v
11
− 0.205966v
10
+ ··· + 2.64946v − 0.819476
0.349127v
11
+ 0.655942v
10
+ ··· − 1.18202v + 1.86146
a
2
=
0.819476v
11
+ 2.33165v
10
+ ··· − 1.01499v + 1.46894
−1.62222v
11
− 4.40786v
10
+ ··· + 1.83221v − 1.73501
a
1
=
−1
0
a
9
=
0.222352v
11
+ 0.449976v
10
+ ··· + 1.46744v + 1.04198
0.349127v
11
+ 0.655942v
10
+ ··· − 1.18202v + 1.86146
a
12
=
−0.989917v
11
− 2.68233v
10
+ ··· + 3.73598v − 2.22768
0.349127v
11
+ 0.655942v
10
+ ··· − 1.18202v + 0.861460
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1086197
235911
v
11
+
2821982
235911
v
10
+ ··· −
94285
235911
v +
2199643
235911
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
, c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
3
, c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
c
7
u
12
c
8
, c
12
(u
2
+ u + 1)
6
c
9
, c
10
u
12
− u
11
+ ··· − 3u + 1
c
11
(u
2
− u + 1)
6
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
3
, c
4
c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
7
y
12
c
8
, c
11
, c
12
(y
2
+ y + 1)
6
c
9
, c
10
y
12
− 3y
11
+ ··· − y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.834826 + 0.083652I
a = 0
b = 1.002190 − 0.295542I
1.89061 + 1.10558I 3.63443 − 2.52768I
v = 0.834826 − 0.083652I
a = 0
b = 1.002190 + 0.295542I
1.89061 − 1.10558I 3.63443 + 2.52768I
v = −0.489858 + 0.681154I
a = 0
b = 1.002190 − 0.295542I
1.89061 − 2.95419I 6.39280 + 3.57892I
v = −0.489858 − 0.681154I
a = 0
b = 1.002190 + 0.295542I
1.89061 + 2.95419I 6.39280 − 3.57892I
v = −0.458424 + 0.081263I
a = 0
b = −1.073950 + 0.558752I
− 7.72290I −2.53591 + 7.46338I
v = −0.458424 − 0.081263I
a = 0
b = −1.073950 − 0.558752I
7.72290I −2.53591 − 7.46338I
v = 0.299588 + 0.356375I
a = 0
b = −1.073950 + 0.558752I
− 3.66314I 2.83009 + 6.37777I
v = 0.299588 − 0.356375I
a = 0
b = −1.073950 − 0.558752I
3.66314I 2.83009 − 6.37777I
v = −2.51133 + 0.49706I
a = 0
b = −0.428243 + 0.664531I
−1.89061 + 2.95419I −7.91752 − 1.81989I
v = −2.51133 − 0.49706I
a = 0
b = −0.428243 − 0.664531I
−1.89061 − 2.95419I −7.91752 + 1.81989I
15
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.82520 + 2.42341I
a = 0
b = −0.428243 − 0.664531I
−1.89061 + 1.10558I 3.59610 − 6.57635I
v = 0.82520 − 2.42341I
a = 0
b = −0.428243 + 0.664531I
−1.89061 − 1.10558I 3.59610 + 6.57635I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
24
+ 24u
23
+ ··· − 179u + 1)
c
2
((u − 1)
9
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
24
− 12u
23
+ ··· + 17u − 1)
c
3
u
9
(u
6
− u
5
+ ··· − u + 1)
2
(u
24
+ u
23
+ ··· − 2560u + 512)
c
4
((u + 1)
9
)(u
6
− u
5
+ ··· − u + 1)
2
(u
24
− 12u
23
+ ··· + 17u − 1)
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
24
+ 4u
23
+ ··· − 3u − 1)
c
6
u
9
(u
6
+ u
5
+ ··· + u + 1)
2
(u
24
+ u
23
+ ··· − 2560u + 512)
c
7
u
12
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
24
+ 2u
23
+ ··· + 28672u + 4096)
c
8
(u
2
+ u + 1)
6
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
24
+ 8u
23
+ ··· + 7u + 1)
c
9
(u
9
+ u
8
+ ··· − u − 1)(u
12
− u
11
+ ··· − 3u + 1)
· (u
24
+ u
23
+ ··· − 74162u − 19441)
c
10
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
12
− u
11
+ ··· − 3u + 1)(u
24
− 5u
23
+ ··· − 389242u + 249139)
c
11
(u
2
− u + 1)
6
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
24
+ 8u
23
+ ··· + 7u + 1)
c
12
(u
2
+ u + 1)
6
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
24
+ 20u
22
+ ··· + 19u + 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
24
+ 204y
23
+ ··· − 2901y + 1)
c
2
, c
4
(y − 1)
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
24
− 24y
23
+ ··· + 179y + 1)
c
3
, c
6
y
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
24
− 63y
23
+ ··· − 3932160y + 262144)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
24
+ 26y
22
+ ··· − y + 1)
c
7
y
12
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
24
− 90y
23
+ ··· + 67108864y + 16777216)
c
8
, c
11
(y
2
+ y + 1)
6
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
24
+ 20y
22
+ ··· + 19y + 1)
c
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
12
− 3y
11
+ ··· − y + 1)
· (y
24
− 61y
23
+ ··· − 296113128y + 377952481)
c
10
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
12
− 3y
11
+ ··· − y + 1)
· (y
24
+ 111y
23
+ ··· − 469614992544y + 62070241321)
c
12
((y
2
+ y + 1)
6
)(y
9
+ 7y
8
+ ··· + 13y − 1)
· (y
24
+ 40y
23
+ ··· + 2151y + 1)
18
