11n
39
(K11n
39
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 10 9 3 11 1 8 6
Solving Sequence
9,11 3,8
4 7 6 1 2 5 10
c
8
c
3
c
7
c
6
c
11
c
2
c
4
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
9
+ 4u
8
+ 5u
7
− 2u
6
− 9u
5
− 4u
4
+ 2u
3
+ b − u, −u
9
− 4u
8
− 6u
7
+ 9u
5
+ 8u
4
− 2u
3
− 4u
2
+ a + u + 2,
u
12
+ 5u
11
+ 9u
10
− 21u
8
− 22u
7
+ 10u
6
+ 26u
5
+ 4u
4
− 11u
3
− 3u
2
+ 2u + 1i
I
u
2
= hu
4
+ u
3
− u
2
+ b − 2u − 1, −u
5
− 2u
4
+ 2u
2
+ a + u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
3
= h10a
5
− 46a
4
+ 69a
3
+ 18a
2
+ 13b − 18a − 12, a
6
− 5a
5
+ 9a
4
− 2a
3
− 2a
2
− a + 1, u − 1i
I
u
4
= hu
11
+ 3u
10
+ 11u
9
+ 10u
8
+ 19u
7
− 16u
6
+ 8u
5
− 48u
4
+ 50u
3
− 15u
2
+ 16b + 63u − 6,
− 7u
11
− 22u
10
− 58u
9
− 55u
8
− 65u
7
+ 41u
6
+ 6u
5
+ 108u
4
− 134u
3
− 73u
2
+ 32a − 174u − 79,
u
12
+ 3u
11
+ 8u
10
+ 7u
9
+ 8u
8
− 8u
7
− u
6
− 14u
5
+ 22u
4
+ 9u
3
+ 25u
2
+ 3u + 1i
* 4 irreducible components of dim
C
= 0, with total 36 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
= hu
9
+ 4u
8
+ · · · +b − u, −u
9
− 4u
8
+ · · · +a + 2, u
12
+ 5u
11
+ · · · +2u + 1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
u
a
3
=
u
9
+ 4u
8
+ 6u
7
− 9u
5
− 8u
4
+ 2u
3
+ 4u
2
− u − 2
−u
9
− 4u
8
− 5u
7
+ 2u
6
+ 9u
5
+ 4u
4
− 2u
3
+ u
a
8
=
1
−u
2
a
4
=
u
11
+ 4u
10
+ 6u
9
− 8u
7
− 6u
6
+ 2u
5
− u
3
+ 2u
2
− 2
−u
11
− 5u
10
− 8u
9
+ u
8
+ 16u
7
+ 10u
6
− 10u
5
− 9u
4
+ 5u
3
+ 5u
2
− 1
a
7
=
−u
3
− 2u
2
+ 2
u
5
+ 2u
4
+ u
3
− 2u
2
− u
a
6
=
u
5
+ 2u
4
− 4u
2
− u + 2
u
5
+ 2u
4
+ u
3
− 2u
2
− u
a
1
=
u
11
+ 4u
10
+ 4u
9
− 8u
8
− 18u
7
+ 24u
5
+ 8u
4
− 15u
3
− 4u
2
+ 4u
u
11
+ 4u
10
+ 5u
9
− 4u
8
− 14u
7
− 6u
6
+ 11u
5
+ 8u
4
− 3u
3
− 2u
2
+ u
a
2
=
u
10
+ 4u
9
+ 5u
8
− 2u
7
− 8u
6
− 2u
5
+ 3u
4
− 2u
3
− u
2
− 1
u
11
+ 5u
10
+ ··· + 2u + 1
a
5
=
u
9
+ 2u
8
− 4u
6
− u
5
+ 2u
4
+ 2u
2
+ u − 2
−u
11
− 2u
10
+ u
9
+ 6u
8
− 8u
6
− u
5
+ 4u
4
− u
3
+ u
a
10
=
u
−u
3
+ u
a
10
=
u
−u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
11
− 16u
10
− 24u
9
+ 24u
7
− 32u
5
+ 16u
4
+ 36u
3
− 16u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
c
10
u
12
− 5u
11
+ ··· − 2u + 1
c
2
u
12
+ 7u
11
+ ··· + 10u + 1
c
3
, c
7
, c
9
u
12
+ u
11
+ ··· + 2u + 1
c
5
u
12
− u
11
+ ··· + 44u + 23
c
6
u
12
− 3u
11
+ ··· − 14u + 4
c
11
u
12
+ u
11
+ u
10
+ 5u
8
− 4u
6
− 8u
5
+ 6u
4
+ 3u
3
+ 3u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
10
y
12
− 7y
11
+ ··· − 10y + 1
c
2
y
12
+ 29y
11
+ ··· + 22y + 1
c
3
, c
7
, c
9
y
12
− 15y
11
+ ··· − 2y + 1
c
5
y
12
− 23y
11
+ ··· − 4098y + 529
c
6
y
12
+ 5y
11
+ ··· + 68y + 16
c
11
y
12
+ y
11
+ ··· + 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.017000 + 0.101771I
a = −4.30103 + 2.01922I
b = 5.15079 − 0.85342I
−3.52730 − 0.57280I −2.7091 − 26.6989I
u = 1.017000 − 0.101771I
a = −4.30103 − 2.01922I
b = 5.15079 + 0.85342I
−3.52730 + 0.57280I −2.7091 + 26.6989I
u = −0.997809 + 0.382742I
a = 0.095986 + 0.498664I
b = 0.336025 + 0.091002I
−1.70690 + 6.65526I −0.69156 − 12.28500I
u = −0.997809 − 0.382742I
a = 0.095986 − 0.498664I
b = 0.336025 − 0.091002I
−1.70690 − 6.65526I −0.69156 + 12.28500I
u = 0.568808 + 0.252332I
a = −1.155830 − 0.548735I
b = 0.126143 + 1.177030I
−1.61529 − 1.35793I −3.64822 + 4.51645I
u = 0.568808 − 0.252332I
a = −1.155830 + 0.548735I
b = 0.126143 − 1.177030I
−1.61529 + 1.35793I −3.64822 − 4.51645I
u = −0.417930 + 0.278210I
a = −1.043110 − 0.681779I
b = −0.414535 − 0.062132I
1.46216 − 0.16286I 7.96188 − 1.03516I
u = −0.417930 − 0.278210I
a = −1.043110 + 0.681779I
b = −0.414535 + 0.062132I
1.46216 + 0.16286I 7.96188 + 1.03516I
u = −1.29679 + 1.06566I
a = 0.784134 − 0.966249I
b = 0.21322 + 1.93092I
12.72390 + 5.46645I −0.22295 − 2.11548I
u = −1.29679 − 1.06566I
a = 0.784134 + 0.966249I
b = 0.21322 − 1.93092I
12.72390 − 5.46645I −0.22295 + 2.11548I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37328 + 1.07803I
a = −0.880154 + 0.892257I
b = 0.08836 − 2.35166I
12.4026 + 12.7511I −0.69002 − 5.94531I
u = −1.37328 − 1.07803I
a = −0.880154 − 0.892257I
b = 0.08836 + 2.35166I
12.4026 − 12.7511I −0.69002 + 5.94531I
6
II.
I
u
2
= hu
4
+u
3
−u
2
+b−2u−1, −u
5
−2u
4
+2u
2
+a+u, u
6
+u
5
−u
4
−2u
3
+u+1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
u
a
3
=
u
5
+ 2u
4
− 2u
2
− u
−u
4
− u
3
+ u
2
+ 2u + 1
a
8
=
1
−u
2
a
4
=
u
5
+ 2u
4
− 2u
2
− u
−u
4
− u
3
+ u
2
+ 2u + 1
a
7
=
1
−u
2
a
6
=
−u
2
+ 1
−u
2
a
1
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
2
=
2u
5
+ 2u
4
− 2u
3
− 2u
2
u
5
− u
4
− 2u
3
+ u
2
+ 3u + 1
a
5
=
−u
5
+ 2u
3
− u
−u
5
+ u
3
− u
a
10
=
u
−u
3
+ u
a
10
=
u
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
5
+ 7u
4
+ u
3
− 6u
2
− 5u − 1
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
4
(u + 1)
6
c
3
, c
7
u
6
c
5
, c
9
, c
10
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
6
, c
11
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
8
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
8
, c
9
c
10
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
6
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −1.68613 + 1.92635I
b = 2.68739 − 0.76772I
−3.53554 − 0.92430I −6.82874 + 7.13914I
u = 1.002190 − 0.295542I
a = −1.68613 − 1.92635I
b = 2.68739 + 0.76772I
−3.53554 + 0.92430I −6.82874 − 7.13914I
u = −0.428243 + 0.664531I
a = 0.344968 + 0.764807I
b = −0.346225 + 0.393823I
0.245672 − 0.924305I 1.12292 + 1.33143I
u = −0.428243 − 0.664531I
a = 0.344968 − 0.764807I
b = −0.346225 − 0.393823I
0.245672 + 0.924305I 1.12292 − 1.33143I
u = −1.073950 + 0.558752I
a = −0.158836 − 0.437639I
b = 0.658836 + 0.177500I
−1.64493 + 5.69302I −0.29418 − 2.69056I
u = −1.073950 − 0.558752I
a = −0.158836 + 0.437639I
b = 0.658836 − 0.177500I
−1.64493 − 5.69302I −0.29418 + 2.69056I
10
III.
I
u
3
= h10a
5
+ 13b + · · · − 18a − 12, a
6
− 5a
5
+ 9a
4
− 2a
3
− 2a
2
− a + 1, u − 1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
1
a
3
=
a
−0.769231a
5
+ 3.53846a
4
+ ··· + 1.38462a + 0.923077
a
8
=
1
−1
a
4
=
−0.769231a
5
+ 3.53846a
4
+ ··· + 3.38462a + 0.923077
−a
a
7
=
−0.307692a
5
+ 1.61538a
4
+ ··· + 0.153846a + 1.76923
−0.846154a
5
+ 3.69231a
4
+ ··· − 0.0769231a + 0.615385
a
6
=
−1.15385a
5
+ 5.30769a
4
+ ··· + 0.0769231a + 2.38462
−0.846154a
5
+ 3.69231a
4
+ ··· − 0.0769231a + 0.615385
a
1
=
−2.30769a
5
+ 10.6154a
4
+ ··· + 1.15385a + 2.76923
0
a
2
=
0.0769231a
5
− 0.153846a
4
+ ··· − 2.53846a + 0.307692
−0.769231a
5
+ 3.53846a
4
+ ··· + 1.38462a + 0.923077
a
5
=
−0.307692a
5
+ 1.61538a
4
+ ··· + 0.153846a + 1.76923
−0.846154a
5
+ 3.69231a
4
+ ··· − 0.0769231a + 0.615385
a
10
=
1
0
a
10
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes =
33
13
a
5
−
144
13
a
4
+
216
13
a
3
+
10
13
a
2
+
16
13
a −
37
13
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
2
, c
11
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
, c
6
u
6
− u
5
+ 2u
4
− 4u
3
+ 5u
2
− 3u + 1
c
8
(u − 1)
6
c
9
u
6
c
10
(u + 1)
6
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
2
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
5
, c
6
y
6
+ 3y
5
+ 6y
4
+ 5y
2
+ y + 1
c
8
, c
10
(y −1)
6
c
9
y
6
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.655968 + 0.098281I
b = 0.346225 − 0.393823I
0.245672 − 0.924305I 1.12292 + 1.33143I
u = 1.00000
a = 0.655968 − 0.098281I
b = 0.346225 + 0.393823I
0.245672 + 0.924305I 1.12292 − 1.33143I
u = 1.00000
a = −0.415113 + 0.381252I
b = −0.658836 + 0.177500I
−1.64493 − 5.69302I −0.29418 + 2.69056I
u = 1.00000
a = −0.415113 − 0.381252I
b = −0.658836 − 0.177500I
−1.64493 + 5.69302I −0.29418 − 2.69056I
u = 1.00000
a = 2.25915 + 1.43225I
b = −2.68739 − 0.76772I
−3.53554 + 0.92430I −6.82874 − 7.13914I
u = 1.00000
a = 2.25915 − 1.43225I
b = −2.68739 + 0.76772I
−3.53554 − 0.92430I −6.82874 + 7.13914I
14
IV. I
u
4
=
hu
11
+3u
10
+· · ·+16b−6, −7u
11
−22u
10
+· · ·+32a−79, u
12
+3u
11
+· · ·+3u+1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
u
a
3
=
0.218750u
11
+ 0.687500u
10
+ ··· + 5.43750u + 2.46875
−0.0625000u
11
− 0.187500u
10
+ ··· − 3.93750u + 0.375000
a
8
=
1
−u
2
a
4
=
1
8
u
11
+
7
16
u
10
+ ··· +
19
16
u +
45
16
−0.0937500u
11
− 0.187500u
10
+ ··· − 3.93750u + 0.406250
a
7
=
−0.250000u
11
− 0.562500u
10
+ ··· − 6.56250u + 2.68750
−
11
32
u
11
− u
10
+ ··· − 5u −
25
32
a
6
=
−0.593750u
11
− 1.56250u
10
+ ··· − 11.5625u + 1.90625
−
11
32
u
11
− u
10
+ ··· − 5u −
25
32
a
1
=
0.218750u
11
+ 0.687500u
10
+ ··· + 5.43750u + 2.46875
−
1
4
u
9
−
1
2
u
8
+ ··· −
3
2
u +
1
4
a
2
=
−0.0312500u
11
+ 0.250000u
10
+ ··· + 0.750000u + 5.15625
−0.125000u
11
− 0.437500u
10
+ ··· − 6.68750u + 0.437500
a
5
=
0.875000u
11
+ 2.31250u
10
+ ··· + 12.3125u − 1.56250
27
32
u
11
+
7
4
u
10
+ ··· +
23
4
u +
33
32
a
10
=
u
−u
3
+ u
a
10
=
u
−u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
3
16
u
11
−
11
16
u
10
−
33
16
u
9
−3u
8
−
55
16
u
7
+
1
2
u
6
+
11
4
u
5
+
21
4
u
4
−
21
8
u
3
−
83
16
u
2
−
183
16
u −
23
8
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
c
10
u
12
− 3u
11
+ ··· − 3u + 1
c
2
u
12
− 7u
11
+ ··· − 41u + 1
c
3
, c
7
, c
9
u
12
+ u
11
+ ··· + 320u + 64
c
5
u
12
− 14u
10
+ ··· + 120u + 77
c
6
u
12
− 2u
11
+ ··· + 144u + 121
c
11
(u
6
+ u
5
+ u
4
+ 2u
2
+ u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
10
y
12
+ 7y
11
+ ··· + 41y + 1
c
2
y
12
+ 27y
11
+ ··· − 451y + 1
c
3
, c
7
, c
9
y
12
− 27y
11
+ ··· − 12288y + 4096
c
5
y
12
− 28y
11
+ ··· + 53360y + 5929
c
6
y
12
+ 24y
11
+ ··· + 28148y + 14641
c
11
(y
6
+ y
5
+ 5y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.282006 + 0.991713I
a = 1.119650 − 0.174269I
b = −0.287706 − 0.831147I
2.99789 + 2.65597I 1.54637 − 3.55162I
u = −0.282006 − 0.991713I
a = 1.119650 + 0.174269I
b = −0.287706 + 0.831147I
2.99789 − 2.65597I 1.54637 + 3.55162I
u = 1.032840 + 0.430283I
a = −0.388751 − 0.185708I
b = 0.552079 + 0.783280I
−1.90302 − 1.10871I −2.03402 + 2.13465I
u = 1.032840 − 0.430283I
a = −0.388751 + 0.185708I
b = 0.552079 − 0.783280I
−1.90302 + 1.10871I −2.03402 − 2.13465I
u = −0.042043 + 1.323160I
a = −0.872012 + 0.135725I
b = −0.287706 + 0.831147I
2.99789 − 2.65597I 1.54637 + 3.55162I
u = −0.042043 − 1.323160I
a = −0.872012 − 0.135725I
b = −0.287706 − 0.831147I
2.99789 + 2.65597I 1.54637 − 3.55162I
u = −1.07187 + 1.35065I
a = 0.819272 − 0.623911I
b = −0.26437 + 2.03792I
13.70950 + 3.42721I 0.48765 − 2.36550I
u = −1.07187 − 1.35065I
a = 0.819272 + 0.623911I
b = −0.26437 − 2.03792I
13.70950 − 3.42721I 0.48765 + 2.36550I
u = −0.058341 + 0.199318I
a = 2.09440 + 1.00050I
b = 0.552079 − 0.783280I
−1.90302 + 1.10871I −2.03402 − 2.13465I
u = −0.058341 − 0.199318I
a = 2.09440 − 1.00050I
b = 0.552079 + 0.783280I
−1.90302 − 1.10871I −2.03402 + 2.13465I
18
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.07857 + 1.47659I
a = −0.772555 + 0.588334I
b = −0.26437 − 2.03792I
13.70950 − 3.42721I 0.48765 + 2.36550I
u = −1.07857 − 1.47659I
a = −0.772555 − 0.588334I
b = −0.26437 + 2.03792I
13.70950 + 3.42721I 0.48765 − 2.36550I
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
((u − 1)
6
)(u
6
+ u
5
+ ··· + u + 1)(u
12
− 5u
11
+ ··· − 2u + 1)
· (u
12
− 3u
11
+ ··· − 3u + 1)
c
2
(u + 1)
6
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
12
− 7u
11
+ ··· − 41u + 1)(u
12
+ 7u
11
+ ··· + 10u + 1)
c
3
, c
9
u
6
(u
6
− u
5
+ ··· − u + 1)(u
12
+ u
11
+ ··· + 320u + 64)
· (u
12
+ u
11
+ ··· + 2u + 1)
c
4
, c
10
((u + 1)
6
)(u
6
− u
5
+ ··· − u + 1)(u
12
− 5u
11
+ ··· − 2u + 1)
· (u
12
− 3u
11
+ ··· − 3u + 1)
c
5
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
6
− u
5
+ 2u
4
− 4u
3
+ 5u
2
− 3u + 1)
· (u
12
− 14u
10
+ ··· + 120u + 77)(u
12
− u
11
+ ··· + 44u + 23)
c
6
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
6
− u
5
+ 2u
4
− 4u
3
+ 5u
2
− 3u + 1)
· (u
12
− 3u
11
+ ··· − 14u + 4)(u
12
− 2u
11
+ ··· + 144u + 121)
c
7
u
6
(u
6
+ u
5
+ ··· + u + 1)(u
12
+ u
11
+ ··· + 320u + 64)
· (u
12
+ u
11
+ ··· + 2u + 1)
c
11
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
6
+ u
5
+ u
4
+ 2u
2
+ u + 1)
2
· (u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
12
+ u
11
+ u
10
+ 5u
8
− 4u
6
− 8u
5
+ 6u
4
+ 3u
3
+ 3u
2
+ 1)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
10
(y −1)
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
12
− 7y
11
+ ··· − 10y + 1)(y
12
+ 7y
11
+ ··· + 41y + 1)
c
2
((y −1)
6
)(y
6
+ y
5
+ ··· + 3y + 1)(y
12
+ 27y
11
+ ··· − 451y + 1)
· (y
12
+ 29y
11
+ ··· + 22y + 1)
c
3
, c
7
, c
9
y
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
12
− 27y
11
+ ··· − 12288y + 4096)(y
12
− 15y
11
+ ··· − 2y + 1)
c
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
6
+ 3y
5
+ 6y
4
+ 5y
2
+ y + 1)
· (y
12
− 28y
11
+ ··· + 53360y + 5929)
· (y
12
− 23y
11
+ ··· − 4098y + 529)
c
6
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
6
+ 3y
5
+ 6y
4
+ 5y
2
+ y + 1)
· (y
12
+ 5y
11
+ ··· + 68y + 16)(y
12
+ 24y
11
+ ··· + 28148y + 14641)
c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
(y
6
+ y
5
+ 5y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
2
· (y
12
+ y
11
+ ··· + 6y + 1)
21
