10
107
(K10a
66
)
A knot diagram
1
Linearized knot diagam
6 9 1 8 7 2 10 3 5 4
Solving Sequence
4,8 5,10
1 3 7 6 9 2
c
4
c
10
c
3
c
7
c
5
c
9
c
2
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h3.47436 × 10
121
u
53
+ 1.72858 × 10
122
u
52
+ ··· + 9.59630 × 10
122
b + 1.78292 × 10
122
,
− 1.53764 × 10
122
u
53
− 8.54360 × 10
122
u
52
+ ··· + 9.59630 × 10
122
a − 1.60436 × 10
123
, u
54
+ 5u
53
+ ··· + u + 2i
I
u
2
= hu
7
− u
6
− u
4
+ b + 1, u
4
+ a − u, u
8
− u
5
− u
4
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 62 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
= h3.47 × 10
121
u
53
+ 1.73 × 10
122
u
52
+ · · · + 9.60 × 10
122
b + 1.78 ×
10
122
, −1.54 × 10
122
u
53
− 8.54 × 10
122
u
52
+ · · · + 9.60 × 10
122
a − 1.60 ×
10
123
, u
54
+ 5u
53
+ · · · + u + 2i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
10
=
0.160232u
53
+ 0.890301u
52
+ ··· + 13.7576u + 1.67185
−0.0362051u
53
− 0.180130u
52
+ ··· − 2.75155u − 0.185792
a
1
=
0.196437u
53
+ 1.07043u
52
+ ··· + 16.5092u + 1.85764
−0.0362051u
53
− 0.180130u
52
+ ··· − 2.75155u − 0.185792
a
3
=
0.0961420u
53
+ 0.569261u
52
+ ··· − 3.23497u − 4.09449
0.100644u
53
+ 0.590672u
52
+ ··· + 0.552368u + 1.22006
a
7
=
−0.643905u
53
− 3.03045u
52
+ ··· + 15.9005u + 4.34106
0.176005u
53
+ 0.787005u
52
+ ··· − 3.07121u − 0.393571
a
6
=
−0.101496u
53
− 0.690858u
52
+ ··· − 23.6713u − 4.01578
−0.0385911u
53
− 0.220008u
52
+ ··· + 3.07522u + 0.327925
a
9
=
0.128037u
53
+ 0.744252u
52
+ ··· + 16.9188u + 2.03592
−0.0983217u
53
− 0.460344u
52
+ ··· − 2.80102u − 0.155940
a
2
=
−0.491512u
53
− 2.79234u
52
+ ··· − 8.87717u − 1.13816
0.0534818u
53
+ 0.417725u
52
+ ··· + 0.472700u − 0.0509315
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.461877u
53
+ 2.14757u
52
+ ··· − 1.68088u − 2.26465
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
54
− u
53
+ ··· − 14u + 7
c
2
, c
8
u
54
− u
53
+ ··· + 9u
2
+ 1
c
3
, c
10
u
54
− 2u
53
+ ··· − 75u + 19
c
4
u
54
+ 5u
53
+ ··· + u + 2
c
5
u
54
+ 23u
53
+ ··· + 406u + 49
c
7
u
54
+ 7u
53
+ ··· + 123u + 49
c
9
u
54
− 3u
51
+ ··· + 19u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
54
− 23y
53
+ ··· − 406y + 49
c
2
, c
8
y
54
+ 33y
53
+ ··· + 18y + 1
c
3
, c
10
y
54
+ 36y
53
+ ··· + 911y + 361
c
4
y
54
− 3y
53
+ ··· + 43y + 4
c
5
y
54
+ 21y
53
+ ··· + 31458y + 2401
c
7
y
54
− 15y
53
+ ··· − 60601y + 2401
c
9
y
54
+ 42y
52
+ ··· − 17y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.961364 + 0.112432I
a = −0.572959 − 0.054695I
b = −0.66278 − 1.34570I
2.22290 − 1.39898I 4.85913 − 0.38785I
u = −0.961364 − 0.112432I
a = −0.572959 + 0.054695I
b = −0.66278 + 1.34570I
2.22290 + 1.39898I 4.85913 + 0.38785I
u = 0.558405 + 0.788615I
a = −1.055990 + 0.295330I
b = −1.156370 + 0.001294I
−1.38784 + 3.43862I −1.22590 − 4.16430I
u = 0.558405 − 0.788615I
a = −1.055990 − 0.295330I
b = −1.156370 − 0.001294I
−1.38784 − 3.43862I −1.22590 + 4.16430I
u = −0.679141 + 0.788921I
a = 1.121720 + 0.119877I
b = 1.268940 − 0.162988I
−3.08313 − 8.79179I −2.77233 + 8.25769I
u = −0.679141 − 0.788921I
a = 1.121720 − 0.119877I
b = 1.268940 + 0.162988I
−3.08313 + 8.79179I −2.77233 − 8.25769I
u = 0.149591 + 1.036280I
a = 0.578889 + 1.147670I
b = 0.516207 + 0.654055I
−2.54046 + 2.78962I −3.14255 − 2.96255I
u = 0.149591 − 1.036280I
a = 0.578889 − 1.147670I
b = 0.516207 − 0.654055I
−2.54046 − 2.78962I −3.14255 + 2.96255I
u = −0.830583 + 0.437641I
a = −1.154350 + 0.444935I
b = −0.722840 − 0.321202I
−0.20915 − 4.60279I −0.54557 + 5.84363I
u = −0.830583 − 0.437641I
a = −1.154350 − 0.444935I
b = −0.722840 + 0.321202I
−0.20915 + 4.60279I −0.54557 − 5.84363I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.043990 + 0.201174I
a = 0.829255 − 0.100464I
b = 0.82599 − 1.28687I
1.65482 + 5.78575I 2.51560 − 7.01331I
u = 1.043990 − 0.201174I
a = 0.829255 + 0.100464I
b = 0.82599 + 1.28687I
1.65482 − 5.78575I 2.51560 + 7.01331I
u = 0.992623 + 0.381167I
a = 1.089900 + 0.189030I
b = 0.831671 − 0.901756I
0.562845 + 1.252740I −1.233700 + 0.528973I
u = 0.992623 − 0.381167I
a = 1.089900 − 0.189030I
b = 0.831671 + 0.901756I
0.562845 − 1.252740I −1.233700 − 0.528973I
u = −0.703334 + 0.548552I
a = −1.35884 + 0.54589I
b = −0.486359 − 1.054920I
0.47962 − 3.24903I −2.21240 + 6.16822I
u = −0.703334 − 0.548552I
a = −1.35884 − 0.54589I
b = −0.486359 + 1.054920I
0.47962 + 3.24903I −2.21240 − 6.16822I
u = 0.090692 + 0.846569I
a = −0.681551 + 0.813861I
b = −0.628328 + 0.416871I
−1.44225 + 1.32993I −2.25893 − 3.81749I
u = 0.090692 − 0.846569I
a = −0.681551 − 0.813861I
b = −0.628328 − 0.416871I
−1.44225 − 1.32993I −2.25893 + 3.81749I
u = 0.039167 + 1.215900I
a = 0.12642 + 1.42966I
b = 0.116430 + 0.911737I
−3.14719 − 1.85744I 0. + 4.53165I
u = 0.039167 − 1.215900I
a = 0.12642 − 1.42966I
b = 0.116430 − 0.911737I
−3.14719 + 1.85744I 0. − 4.53165I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.599196 + 1.091280I
a = 0.674349 + 0.091168I
b = 0.815766 − 0.311304I
−6.71595 − 1.65367I −8.08588 + 0.I
u = −0.599196 − 1.091280I
a = 0.674349 − 0.091168I
b = 0.815766 + 0.311304I
−6.71595 + 1.65367I −8.08588 + 0.I
u = 0.741079 + 0.137552I
a = 1.194820 + 0.322038I
b = 0.296885 − 0.144859I
1.46648 + 0.54178I 5.93628 − 0.17488I
u = 0.741079 − 0.137552I
a = 1.194820 − 0.322038I
b = 0.296885 + 0.144859I
1.46648 − 0.54178I 5.93628 + 0.17488I
u = −0.452082 + 0.566184I
a = 0.536326 + 0.764262I
b = 0.02633 + 1.48047I
4.02222 + 2.85318I 6.13116 − 2.92462I
u = −0.452082 − 0.566184I
a = 0.536326 − 0.764262I
b = 0.02633 − 1.48047I
4.02222 − 2.85318I 6.13116 + 2.92462I
u = −0.886321 + 0.919707I
a = −1.361200 − 0.310668I
b = −0.382977 − 1.263990I
4.21764 − 8.45863I 0
u = −0.886321 − 0.919707I
a = −1.361200 + 0.310668I
b = −0.382977 + 1.263990I
4.21764 + 8.45863I 0
u = −1.315250 + 0.034832I
a = −0.573199 + 0.672183I
b = 0.050400 − 0.679787I
−0.77663 − 4.41165I 0
u = −1.315250 − 0.034832I
a = −0.573199 − 0.672183I
b = 0.050400 + 0.679787I
−0.77663 + 4.41165I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.988588 + 0.893719I
a = 1.155390 − 0.272660I
b = 0.293080 − 1.228390I
5.49306 + 3.12677I 0
u = 0.988588 − 0.893719I
a = 1.155390 + 0.272660I
b = 0.293080 + 1.228390I
5.49306 − 3.12677I 0
u = −0.329231 + 0.560992I
a = −0.796917 + 0.754395I
b = −0.573088 + 0.315618I
−1.49546 + 0.86217I −4.23255 − 0.90919I
u = −0.329231 − 0.560992I
a = −0.796917 − 0.754395I
b = −0.573088 − 0.315618I
−1.49546 − 0.86217I −4.23255 + 0.90919I
u = 0.292792 + 0.451123I
a = 2.31599 + 2.42777I
b = 0.430531 − 0.886169I
−1.89398 + 6.72384I −4.13785 − 10.41753I
u = 0.292792 − 0.451123I
a = 2.31599 − 2.42777I
b = 0.430531 + 0.886169I
−1.89398 − 6.72384I −4.13785 + 10.41753I
u = 0.163858 + 0.499123I
a = −0.55065 + 1.32387I
b = −0.25259 + 1.55284I
4.11998 + 2.94109I 7.18387 + 1.28923I
u = 0.163858 − 0.499123I
a = −0.55065 − 1.32387I
b = −0.25259 − 1.55284I
4.11998 − 2.94109I 7.18387 − 1.28923I
u = −0.434000 + 0.294766I
a = −0.68751 + 1.92613I
b = −0.370703 − 1.020660I
0.35569 − 2.65328I 0.15342 + 4.21264I
u = −0.434000 − 0.294766I
a = −0.68751 − 1.92613I
b = −0.370703 + 1.020660I
0.35569 + 2.65328I 0.15342 − 4.21264I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.19805 + 1.12252I
a = 0.970792 + 0.128427I
b = 0.63032 + 1.34945I
0.7043 − 15.3529I 0
u = −1.19805 − 1.12252I
a = 0.970792 − 0.128427I
b = 0.63032 − 1.34945I
0.7043 + 15.3529I 0
u = 1.19648 + 1.14726I
a = −0.856808 + 0.150553I
b = −0.55381 + 1.35250I
2.82560 + 9.37445I 0
u = 1.19648 − 1.14726I
a = −0.856808 − 0.150553I
b = −0.55381 − 1.35250I
2.82560 − 9.37445I 0
u = 0.181881 + 0.235745I
a = 0.11509 + 5.12406I
b = 0.209141 − 0.890213I
−2.94679 − 0.31182I −2.63431 − 1.82332I
u = 0.181881 − 0.235745I
a = 0.11509 − 5.12406I
b = 0.209141 + 0.890213I
−2.94679 + 0.31182I −2.63431 + 1.82332I
u = −1.32732 + 1.15930I
a = 0.674629 − 0.096385I
b = 0.474031 + 1.178630I
−3.96372 − 6.42189I 0
u = −1.32732 − 1.15930I
a = 0.674629 + 0.096385I
b = 0.474031 − 1.178630I
−3.96372 + 6.42189I 0
u = 0.75878 + 1.62635I
a = −0.265244 + 0.312071I
b = −0.154106 + 1.343330I
4.15647 + 3.52492I 0
u = 0.75878 − 1.62635I
a = −0.265244 − 0.312071I
b = −0.154106 − 1.343330I
4.15647 − 3.52492I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.56778 + 0.88249I
a = 0.466526 − 0.069214I
b = −0.029531 − 1.030030I
3.39532 + 0.06056I 0
u = 1.56778 − 0.88249I
a = 0.466526 + 0.069214I
b = −0.029531 + 1.030030I
3.39532 − 0.06056I 0
u = −1.54983 + 1.40253I
a = −0.184901 − 0.232246I
b = 0.187756 − 1.030500I
0.50528 + 5.97519I 0
u = −1.54983 − 1.40253I
a = −0.184901 + 0.232246I
b = 0.187756 + 1.030500I
0.50528 − 5.97519I 0
10
II. I
u
2
= hu
7
− u
6
− u
4
+ b + 1, u
4
+ a − u, u
8
− u
5
− u
4
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
10
=
−u
4
+ u
−u
7
+ u
6
+ u
4
− 1
a
1
=
u
7
− u
6
− 2u
4
+ u + 1
−u
7
+ u
6
+ u
4
− 1
a
3
=
u
5
− u
2
−u
7
+ u
6
− u
5
+ u
4
a
7
=
u
6
− u
5
− u
3
+ u
2
+ u
u
7
− u
4
− u
3
+ u + 1
a
6
=
u
6
− u
3
+ u + 1
u
5
− u
3
− u
2
a
9
=
u
7
− 2u
4
− u
3
+ u + 1
−u
7
+ u
6
+ u
4
+ u − 1
a
2
=
u
7
− u
6
− u
4
+ u
3
+ u
2
u
6
− u
5
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
7
− 3u
6
+ 2u
5
− 5u
4
− u
3
+ 3u
2
− u + 1
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 2u
6
− u
5
+ 3u
4
+ 2u
3
− 2u
2
− u + 1
c
2
u
8
+ 4u
6
− u
5
+ 5u
4
− 2u
3
+ 4u
2
− u + 1
c
3
u
8
+ u
7
+ 4u
6
+ 2u
5
+ 5u
4
+ u
3
+ 4u
2
+ 1
c
4
u
8
− u
5
− u
4
+ u + 1
c
5
u
8
− 4u
7
+ 10u
6
− 17u
5
+ 23u
4
− 22u
3
+ 14u
2
− 5u + 1
c
6
u
8
− 2u
6
+ u
5
+ 3u
4
− 2u
3
− 2u
2
+ u + 1
c
7
u
8
− 2u
6
− 3u
5
+ 4u
3
+ 6u
2
+ 4u + 1
c
8
u
8
+ 4u
6
+ u
5
+ 5u
4
+ 2u
3
+ 4u
2
+ u + 1
c
9
u
8
− u
7
− u
4
+ u
3
+ 1
c
10
u
8
− u
7
+ 4u
6
− 2u
5
+ 5u
4
− u
3
+ 4u
2
+ 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
8
− 4y
7
+ 10y
6
− 17y
5
+ 23y
4
− 22y
3
+ 14y
2
− 5y + 1
c
2
, c
8
y
8
+ 8y
7
+ 26y
6
+ 47y
5
+ 55y
4
+ 42y
3
+ 22y
2
+ 7y + 1
c
3
, c
10
y
8
+ 7y
7
+ 22y
6
+ 42y
5
+ 55y
4
+ 47y
3
+ 26y
2
+ 8y + 1
c
4
y
8
− 2y
6
− y
5
+ 3y
4
+ 2y
3
− 2y
2
− y + 1
c
5
y
8
+ 4y
7
+ 10y
6
+ 23y
5
+ 23y
4
+ 10y
3
+ 22y
2
+ 3y + 1
c
7
y
8
− 4y
7
+ 4y
6
+ 3y
5
+ 2y
4
+ 4y
3
+ 4y
2
− 4y + 1
c
9
y
8
− y
7
− 2y
6
+ 2y
5
+ 3y
4
− y
3
− 2y
2
+ 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.154104 + 0.976543I
a = −0.62000 + 1.53629I
b = 0.043533 + 0.616047I
−3.90365 + 1.24143I −8.13667 − 0.29040I
u = 0.154104 − 0.976543I
a = −0.62000 − 1.53629I
b = 0.043533 − 0.616047I
−3.90365 − 1.24143I −8.13667 + 0.29040I
u = −0.437725 + 1.005550I
a = −0.334414 − 0.437341I
b = −0.25301 − 1.48886I
3.61840 − 3.26075I −5.09230 + 4.26286I
u = −0.437725 − 1.005550I
a = −0.334414 + 0.437341I
b = −0.25301 + 1.48886I
3.61840 + 3.26075I −5.09230 − 4.26286I
u = 1.089750 + 0.225697I
a = 0.039837 − 0.892510I
b = 0.395593 + 0.812604I
−0.91267 − 5.73534I −1.12017 + 7.06636I
u = 1.089750 − 0.225697I
a = 0.039837 + 0.892510I
b = 0.395593 − 0.812604I
−0.91267 + 5.73534I −1.12017 − 7.06636I
u = −0.806126 + 0.192419I
a = −1.085430 + 0.572644I
b = −0.686120 − 0.967795I
1.19791 − 2.24783I 2.34914 + 3.96490I
u = −0.806126 − 0.192419I
a = −1.085430 − 0.572644I
b = −0.686120 + 0.967795I
1.19791 + 2.24783I 2.34914 − 3.96490I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
− 2u
6
+ ··· − u + 1)(u
54
− u
53
+ ··· − 14u + 7)
c
2
(u
8
+ 4u
6
+ ··· − u + 1)(u
54
− u
53
+ ··· + 9u
2
+ 1)
c
3
(u
8
+ u
7
+ ··· + 4u
2
+ 1)(u
54
− 2u
53
+ ··· − 75u + 19)
c
4
(u
8
− u
5
− u
4
+ u + 1)(u
54
+ 5u
53
+ ··· + u + 2)
c
5
(u
8
− 4u
7
+ 10u
6
− 17u
5
+ 23u
4
− 22u
3
+ 14u
2
− 5u + 1)
· (u
54
+ 23u
53
+ ··· + 406u + 49)
c
6
(u
8
− 2u
6
+ ··· + u + 1)(u
54
− u
53
+ ··· − 14u + 7)
c
7
(u
8
− 2u
6
+ ··· + 4u + 1)(u
54
+ 7u
53
+ ··· + 123u + 49)
c
8
(u
8
+ 4u
6
+ ··· + u + 1)(u
54
− u
53
+ ··· + 9u
2
+ 1)
c
9
(u
8
− u
7
− u
4
+ u
3
+ 1)(u
54
− 3u
51
+ ··· + 19u + 1)
c
10
(u
8
− u
7
+ ··· + 4u
2
+ 1)(u
54
− 2u
53
+ ··· − 75u + 19)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
8
− 4y
7
+ 10y
6
− 17y
5
+ 23y
4
− 22y
3
+ 14y
2
− 5y + 1)
· (y
54
− 23y
53
+ ··· − 406y + 49)
c
2
, c
8
(y
8
+ 8y
7
+ 26y
6
+ 47y
5
+ 55y
4
+ 42y
3
+ 22y
2
+ 7y + 1)
· (y
54
+ 33y
53
+ ··· + 18y + 1)
c
3
, c
10
(y
8
+ 7y
7
+ 22y
6
+ 42y
5
+ 55y
4
+ 47y
3
+ 26y
2
+ 8y + 1)
· (y
54
+ 36y
53
+ ··· + 911y + 361)
c
4
(y
8
− 2y
6
+ ··· − y + 1)(y
54
− 3y
53
+ ··· + 43y + 4)
c
5
(y
8
+ 4y
7
+ 10y
6
+ 23y
5
+ 23y
4
+ 10y
3
+ 22y
2
+ 3y + 1)
· (y
54
+ 21y
53
+ ··· + 31458y + 2401)
c
7
(y
8
− 4y
7
+ 4y
6
+ 3y
5
+ 2y
4
+ 4y
3
+ 4y
2
− 4y + 1)
· (y
54
− 15y
53
+ ··· − 60601y + 2401)
c
9
(y
8
− y
7
+ ··· − 2y
2
+ 1)(y
54
+ 42y
52
+ ··· − 17y + 1)
16
