10
111
(K10a
98
)
A knot diagram
1
Linearized knot diagam
5 10 6 8 2 9 1 4 3 7
Solving Sequence
3,6 4,10
2 5 1 9 7 8
c
3
c
2
c
5
c
1
c
9
c
6
c
8
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h39480u
13
− 1274u
12
+ ··· + 154933b − 318297, −39480u
13
+ 1274u
12
+ ··· + 154933a + 163364,
u
14
+ u
13
+ u
12
+ u
11
+ 9u
10
+ 5u
9
+ 5u
8
+ 5u
7
+ 17u
6
+ 5u
5
+ 7u
4
− 4u
3
+ 8u
2
− u + 1i
I
u
2
= h−8.27934 × 10
37
u
29
− 3.87934 × 10
38
u
28
+ ··· + 1.76638 × 10
35
b + 2.60429 × 10
38
,
− 2.70329 × 10
43
u
29
− 1.27006 × 10
44
u
28
+ ··· + 1.82589 × 10
40
a + 8.84680 × 10
43
,
u
30
+ 5u
29
+ ··· − 14u − 1i
I
u
3
= h4u
5
− 2u
4
− u
3
+ b + 16u − 8, −4u
5
+ 2u
4
+ u
3
+ a − 16u + 9, u
6
− u
5
+ 4u
2
− 4u + 1i
* 3 irreducible components of dim
C
= 0, with total 50 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
= h39480u
13
− 1274u
12
+ · · · + 154933b − 318297, −3.95 × 10
4
u
13
+
1274u
12
+ · · · + 1.55 × 10
5
a + 1.63 × 10
5
, u
14
+ u
13
+ · · · − u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u
2
a
10
=
0.254820u
13
− 0.00822291u
12
+ ··· + 3.57261u − 1.05442
−0.254820u
13
+ 0.00822291u
12
+ ··· − 3.57261u + 2.05442
a
2
=
−1.23639u
13
− 1.16081u
12
+ ··· − 8.80020u + 1.50958
1.49121u
13
+ 1.15259u
12
+ ··· + 12.3728u − 2.56399
a
5
=
−1.23092u
13
− 1.01347u
12
+ ··· − 9.83592u + 2.03566
1.69744u
13
+ 1.28920u
12
+ ··· + 14.8569u − 3.30753
a
1
=
0.116528u
13
− 0.0612071u
12
+ ··· + 2.26064u − 0.978836
−0.445618u
13
− 0.321436u
12
+ ··· − 4.37795u + 1.58789
a
9
=
1
−0.254820u
13
+ 0.00822291u
12
+ ··· − 3.57261u + 2.05442
a
7
=
−u
−0.263043u
13
− 0.260306u
12
+ ··· − 0.799597u − 0.254820
a
8
=
0.254820u
13
− 0.00822291u
12
+ ··· + 3.57261u − 1.05442
−0.252083u
13
+ 0.0818935u
12
+ ··· − 4.09047u + 2.31746
(ii) Obstruction class = −1
(iii) Cusp Shapes =
319153
154933
u
13
+
874852
154933
u
12
+ ··· +
171234
154933
u +
3427848
154933
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
10
u
14
− 6u
12
+ 15u
10
− u
9
− 15u
8
+ 2u
7
+ 3u
6
− u
3
+ 4u
2
+ 2u + 1
c
2
, c
9
u
14
− 10u
13
+ ··· − 60u + 8
c
3
, c
6
u
14
− u
13
+ ··· + u + 1
c
4
, c
8
u
14
− 11u
13
+ ··· − 224u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
10
y
14
− 12y
13
+ ··· + 4y + 1
c
2
, c
9
y
14
+ 4y
13
+ ··· + 240y + 64
c
3
, c
6
y
14
+ y
13
+ ··· + 15y + 1
c
4
, c
8
y
14
+ 5y
13
+ ··· + 512y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.480433 + 0.861641I
a = 0.839666 + 1.114140I
b = 0.160334 − 1.114140I
3.38735 − 0.25005I −0.72285 + 2.46287I
u = −0.480433 − 0.861641I
a = 0.839666 − 1.114140I
b = 0.160334 + 1.114140I
3.38735 + 0.25005I −0.72285 − 2.46287I
u = −1.048940 + 0.652179I
a = −0.187430 − 0.232557I
b = 1.187430 + 0.232557I
−10.88730 + 7.87015I −12.80126 − 5.10311I
u = −1.048940 − 0.652179I
a = −0.187430 + 0.232557I
b = 1.187430 − 0.232557I
−10.88730 − 7.87015I −12.80126 + 5.10311I
u = 0.486006 + 0.497659I
a = 0.703941 + 0.328567I
b = 0.296059 − 0.328567I
−0.46723 − 1.34385I −4.53324 + 5.44435I
u = 0.486006 − 0.497659I
a = 0.703941 − 0.328567I
b = 0.296059 + 0.328567I
−0.46723 + 1.34385I −4.53324 − 5.44435I
u = 0.775295 + 1.049040I
a = 0.248822 − 1.259320I
b = 0.75118 + 1.25932I
−1.57595 − 8.21733I −8.00559 + 6.90533I
u = 0.775295 − 1.049040I
a = 0.248822 + 1.259320I
b = 0.75118 − 1.25932I
−1.57595 + 8.21733I −8.00559 − 6.90533I
u = 0.96587 + 1.05626I
a = 0.706527 − 1.007890I
b = 0.293473 + 1.007890I
1.24241 − 4.01184I −4.00908 + 1.51637I
u = 0.96587 − 1.05626I
a = 0.706527 + 1.007890I
b = 0.293473 − 1.007890I
1.24241 + 4.01184I −4.00908 − 1.51637I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.025861 + 0.375115I
a = −0.66482 + 1.30083I
b = 1.66482 − 1.30083I
−3.88016 − 0.30866I 21.1851 − 1.2071I
u = 0.025861 − 0.375115I
a = −0.66482 − 1.30083I
b = 1.66482 + 1.30083I
−3.88016 + 0.30866I 21.1851 + 1.2071I
u = −1.22366 + 1.15195I
a = 0.353292 + 1.290880I
b = 0.64671 − 1.29088I
−7.5584 + 14.2650I −9.61306 − 7.45903I
u = −1.22366 − 1.15195I
a = 0.353292 − 1.290880I
b = 0.64671 + 1.29088I
−7.5584 − 14.2650I −9.61306 + 7.45903I
6
II. I
u
2
= h−8.28 × 10
37
u
29
− 3.88 × 10
38
u
28
+ · · · + 1.77 × 10
35
b + 2.60 ×
10
38
, −2.70 × 10
43
u
29
− 1.27 × 10
44
u
28
+ · · · + 1.83 × 10
40
a + 8.85 ×
10
43
, u
30
+ 5u
29
+ · · · − 14u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u
2
a
10
=
1480.53u
29
+ 6955.82u
28
+ ··· − 52108.0u − 4845.20
468.718u
29
+ 2196.21u
28
+ ··· − 16062.1u − 1474.36
a
2
=
−1085.37u
29
− 5070.52u
28
+ ··· + 36285.0u + 3322.75
350.689u
29
+ 1665.42u
28
+ ··· − 13806.5u − 1340.83
a
5
=
−991.168u
29
− 4565.91u
28
+ ··· + 28334.6u + 2429.77
398.530u
29
+ 1884.97u
28
+ ··· − 15091.1u − 1445.96
a
1
=
−1780.35u
29
− 8495.89u
28
+ ··· + 72515.7u + 7062.23
−181.114u
29
− 833.946u
28
+ ··· + 5098.47u + 429.698
a
9
=
1949.25u
29
+ 9152.03u
28
+ ··· − 68170.1u − 6319.56
468.718u
29
+ 2196.21u
28
+ ··· − 16062.1u − 1474.36
a
7
=
1388.04u
29
+ 6649.23u
28
+ ··· − 58366.7u − 5729.66
268.310u
29
+ 1245.03u
28
+ ··· − 8303.63u − 734.682
a
8
=
1659.04u
29
+ 7795.68u
28
+ ··· − 58477.9u − 5439.43
437.990u
29
+ 2052.51u
28
+ ··· − 15026.1u − 1379.63
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1720.55u
29
− 8153.31u
28
+ ··· + 66031.6u + 6330.33
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
10
u
30
+ u
29
+ ··· + 212u + 11
c
2
, c
9
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
6
c
3
, c
6
u
30
− 5u
29
+ ··· + 14u − 1
c
4
, c
8
(u
3
+ u
2
+ 2u + 1)
10
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
10
y
30
− 25y
29
+ ··· − 32360y + 121
c
2
, c
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
6
c
3
, c
6
y
30
− 5y
29
+ ··· − 56y + 1
c
4
, c
8
(y
3
+ 3y
2
+ 2y −1)
10
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.711013 + 0.598106I
a = −0.891374 − 0.831846I
b = −0.455697 + 1.200150I
2.05122 + 4.40083I −2.23618 − 3.49859I
u = −0.711013 − 0.598106I
a = −0.891374 + 0.831846I
b = −0.455697 − 1.200150I
2.05122 − 4.40083I −2.23618 + 3.49859I
u = −1.108120 + 0.043065I
a = 0.244564 − 0.869058I
b = 0.339110 − 0.822375I
−7.62983 − 1.29754I −12.99464 − 1.45120I
u = −1.108120 − 0.043065I
a = 0.244564 + 0.869058I
b = 0.339110 + 0.822375I
−7.62983 + 1.29754I −12.99464 + 1.45120I
u = 0.750590 + 0.816532I
a = −0.254359 + 0.536218I
b = −0.766826
−5.55785 − 2.82812I −12.02861 + 2.97945I
u = 0.750590 − 0.816532I
a = −0.254359 − 0.536218I
b = −0.766826
−5.55785 + 2.82812I −12.02861 − 2.97945I
u = 0.723473 + 0.513234I
a = 0.226305 − 0.956455I
b = −0.455697 + 1.200150I
−2.08637 + 1.57271I −8.76544 − 0.51914I
u = 0.723473 − 0.513234I
a = 0.226305 + 0.956455I
b = −0.455697 − 1.200150I
−2.08637 − 1.57271I −8.76544 + 0.51914I
u = 0.375132 + 0.793055I
a = −0.26221 − 2.41312I
b = 0.339110 + 0.822375I
−3.49225 − 1.53058I −6.46537 + 4.43065I
u = 0.375132 − 0.793055I
a = −0.26221 + 2.41312I
b = 0.339110 − 0.822375I
−3.49225 + 1.53058I −6.46537 − 4.43065I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.953025 + 0.838377I
a = −1.10687 + 1.14990I
b = −0.455697 − 1.200150I
−2.08637 − 7.22895I 0
u = 0.953025 − 0.838377I
a = −1.10687 − 1.14990I
b = −0.455697 + 1.200150I
−2.08637 + 7.22895I 0
u = −1.204330 + 0.431350I
a = −0.000782 + 0.403066I
b = −0.766826
−5.55785 + 2.82812I 0
u = −1.204330 − 0.431350I
a = −0.000782 − 0.403066I
b = −0.766826
−5.55785 − 2.82812I 0
u = 0.737499 + 1.067560I
a = −0.235020 + 1.389000I
b = −0.455697 − 1.200150I
2.05122 − 4.40083I 0
u = 0.737499 − 1.067560I
a = −0.235020 − 1.389000I
b = −0.455697 + 1.200150I
2.05122 + 4.40083I 0
u = 0.680032
a = 0.340860
b = −0.766826
−1.42027 −5.49930
u = 1.290400 + 0.535753I
a = −0.308791 + 0.195205I
b = 0.339110 − 0.822375I
−3.49225 + 1.53058I 0
u = 1.290400 − 0.535753I
a = −0.308791 − 0.195205I
b = 0.339110 + 0.822375I
−3.49225 − 1.53058I 0
u = −0.320748 + 0.034597I
a = 5.85652 − 4.23753I
b = 0.339110 + 0.822375I
−7.62983 − 4.35870I −12.9946 + 7.4101I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.320748 − 0.034597I
a = 5.85652 + 4.23753I
b = 0.339110 − 0.822375I
−7.62983 + 4.35870I −12.9946 − 7.4101I
u = −0.291032 + 0.058576I
a = −1.59228 − 3.37585I
b = −0.455697 + 1.200150I
−2.08637 + 1.57271I −8.76544 − 0.51914I
u = −0.291032 − 0.058576I
a = −1.59228 + 3.37585I
b = −0.455697 − 1.200150I
−2.08637 − 1.57271I −8.76544 + 0.51914I
u = −0.289671
a = −1.58078
b = −0.766826
−1.42027 −5.49930
u = −0.57394 + 1.89944I
a = −0.156804 + 1.350680I
b = 0.339110 − 0.822375I
−7.62983 − 1.29754I 0
u = −0.57394 − 1.89944I
a = −0.156804 − 1.350680I
b = 0.339110 + 0.822375I
−7.62983 + 1.29754I 0
u = −1.44704 + 1.35792I
a = −0.183612 − 1.220710I
b = −0.455697 + 1.200150I
−2.08637 + 7.22895I 0
u = −1.44704 − 1.35792I
a = −0.183612 + 1.220710I
b = −0.455697 − 1.200150I
−2.08637 − 7.22895I 0
u = −1.86908 + 1.30976I
a = −0.215319 − 0.754139I
b = 0.339110 + 0.822375I
−7.62983 − 4.35870I 0
u = −1.86908 − 1.30976I
a = −0.215319 + 0.754139I
b = 0.339110 − 0.822375I
−7.62983 + 4.35870I 0
12
III. I
u
3
=
h4u
5
−2u
4
−u
3
+b+16u−8, −4u
5
+2u
4
+u
3
+a−16u+9, u
6
−u
5
+4u
2
−4u+1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u
2
a
10
=
4u
5
− 2u
4
− u
3
+ 16u − 9
−4u
5
+ 2u
4
+ u
3
− 16u + 8
a
2
=
−3u
5
+ 2u
4
+ u
3
− 12u + 8
−u
5
− 4u + 1
a
5
=
−5u
5
+ 3u
4
+ u
3
+ u
2
− 20u + 12
u − 1
a
1
=
4u
5
− 2u
4
− u
3
+ 15u − 8
−2u
5
+ u
4
− 7u + 3
a
9
=
−1
−4u
5
+ 2u
4
+ u
3
− 16u + 8
a
7
=
−u
−2u
5
+ u
4
− 7u + 4
a
8
=
4u
5
− 2u
4
− u
3
− u
2
+ 16u − 9
−3u
5
+ u
4
+ u
3
− 12u + 6
(ii) Obstruction class = 1
(iii) Cusp Shapes = −25u
5
+ 10u
4
+ 7u
3
+ 5u
2
− 96u + 32
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
6
+ 2u
5
− u
4
− 4u
3
− u
2
+ u + 1
c
2
u
6
+ u
5
+ u
4
− u
2
− 1
c
3
, c
6
u
6
− u
5
+ 4u
2
− 4u + 1
c
4
u
6
+ u
4
− u
2
− u − 1
c
5
, c
10
u
6
− 2u
5
− u
4
+ 4u
3
− u
2
− u + 1
c
8
u
6
+ u
4
− u
2
+ u − 1
c
9
u
6
− u
5
+ u
4
− u
2
− 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
10
y
6
− 6y
5
+ 15y
4
− 16y
3
+ 7y
2
− 3y + 1
c
2
, c
9
y
6
+ y
5
− y
4
− 4y
3
− y
2
+ 2y + 1
c
3
, c
6
y
6
− y
5
+ 8y
4
− 6y
3
+ 16y
2
− 8y + 1
c
4
, c
8
y
6
+ 2y
5
− y
4
− 4y
3
− y
2
+ y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.008100 + 0.927438I
a = −0.516513 + 1.114980I
b = −0.483487 − 1.114980I
0.45357 − 5.18068I −8.71093 + 6.15331I
u = 1.008100 − 0.927438I
a = −0.516513 − 1.114980I
b = −0.483487 + 1.114980I
0.45357 + 5.18068I −8.71093 − 6.15331I
u = 0.584070
a = 0.185012
b = −1.18501
−2.13209 −21.5060
u = −1.02499 + 0.98915I
a = −1.124000 − 0.785288I
b = 0.124001 + 0.785288I
−7.16447 − 3.17324I −9.24905 + 1.07022I
u = −1.02499 − 0.98915I
a = −1.124000 + 0.785288I
b = 0.124001 − 0.785288I
−7.16447 + 3.17324I −9.24905 − 1.07022I
u = 0.449699
a = −1.90398
b = 0.903984
−4.18532 −9.57420
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
6
+ 2u
5
− u
4
− 4u
3
− u
2
+ u + 1)
· (u
14
− 6u
12
+ 15u
10
− u
9
− 15u
8
+ 2u
7
+ 3u
6
− u
3
+ 4u
2
+ 2u + 1)
· (u
30
+ u
29
+ ··· + 212u + 11)
c
2
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
6
(u
6
+ u
5
+ u
4
− u
2
− 1)
· (u
14
− 10u
13
+ ··· − 60u + 8)
c
3
, c
6
(u
6
− u
5
+ 4u
2
− 4u + 1)(u
14
− u
13
+ ··· + u + 1)
· (u
30
− 5u
29
+ ··· + 14u − 1)
c
4
(u
3
+ u
2
+ 2u + 1)
10
(u
6
+ u
4
− u
2
− u − 1)
· (u
14
− 11u
13
+ ··· − 224u + 32)
c
5
, c
10
(u
6
− 2u
5
− u
4
+ 4u
3
− u
2
− u + 1)
· (u
14
− 6u
12
+ 15u
10
− u
9
− 15u
8
+ 2u
7
+ 3u
6
− u
3
+ 4u
2
+ 2u + 1)
· (u
30
+ u
29
+ ··· + 212u + 11)
c
8
(u
3
+ u
2
+ 2u + 1)
10
(u
6
+ u
4
− u
2
+ u − 1)
· (u
14
− 11u
13
+ ··· − 224u + 32)
c
9
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
6
(u
6
− u
5
+ u
4
− u
2
− 1)
· (u
14
− 10u
13
+ ··· − 60u + 8)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
10
(y
6
− 6y
5
+ ··· − 3y + 1)(y
14
− 12y
13
+ ··· + 4y + 1)
· (y
30
− 25y
29
+ ··· − 32360y + 121)
c
2
, c
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
6
(y
6
+ y
5
− y
4
− 4y
3
− y
2
+ 2y + 1)
· (y
14
+ 4y
13
+ ··· + 240y + 64)
c
3
, c
6
(y
6
− y
5
+ ··· − 8y + 1)(y
14
+ y
13
+ ··· + 15y + 1)
· (y
30
− 5y
29
+ ··· − 56y + 1)
c
4
, c
8
(y
3
+ 3y
2
+ 2y −1)
10
(y
6
+ 2y
5
− y
4
− 4y
3
− y
2
+ y + 1)
· (y
14
+ 5y
13
+ ··· + 512y + 1024)
18
