10
117
(K10a
99
)
A knot diagram
1
Linearized knot diagam
8 5 10 9 1 3 4 2 7 6
Solving Sequence
3,10 4,6
7 8 1 5 2 9
c
3
c
6
c
7
c
10
c
5
c
2
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.20848 × 10
161
u
59
+ 1.04355 × 10
162
u
58
+ ··· + 3.99664 × 10
162
b 4.01482 × 10
162
,
5.43983 × 10
162
u
59
1.65350 × 10
163
u
58
+ ··· + 3.75684 × 10
163
a + 6.18508 × 10
163
,
u
60
3u
59
+ ··· 100u 47i
I
u
2
= h2u
8
+ u
7
2u
6
9u
5
u
4
+ u
3
10u
2
+ 9b + 18u 5,
8u
8
3u
7
9u
6
+ 28u
5
21u
4
+ 40u
3
29u
2
+ 3a + u 11,
u
9
+ u
7
4u
6
+ 4u
5
6u
4
+ 6u
3
2u
2
+ 2u 1i
* 2 irreducible components of dim
C
= 0, with total 69 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
= h−3.21 × 10
161
u
59
+ 1.04 × 10
162
u
58
+ · · · + 4.00 × 10
162
b 4.01 ×
10
162
, 5.44 × 10
162
u
59
1.65 × 10
163
u
58
+ · · · + 3.76 × 10
163
a + 6.19 ×
10
163
, u
60
3u
59
+ · · · 100u 47i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
0.144798u
59
+ 0.440130u
58
+ ··· + 27.2425u 1.64635
0.0802795u
59
0.261107u
58
+ ··· 9.37588u + 1.00455
a
7
=
0.0645187u
59
+ 0.179024u
58
+ ··· + 17.8666u 0.641805
0.0802795u
59
0.261107u
58
+ ··· 9.37588u + 1.00455
a
8
=
0.149789u
59
+ 0.442542u
58
+ ··· + 31.7281u 0.963328
0.0559636u
59
0.178921u
58
+ ··· 6.13906u + 0.642242
a
1
=
0.0151173u
59
0.0879877u
58
+ ··· + 42.0887u + 12.0597
0.0276044u
59
+ 0.0511785u
58
+ ··· + 7.28332u + 2.39479
a
5
=
0.200110u
59
0.575603u
58
+ ··· 63.4707u + 3.83922
0.0114669u
59
+ 0.0348903u
58
+ ··· + 2.13595u 0.466474
a
2
=
0.118992u
59
+ 0.283347u
58
+ ··· + 73.3930u + 13.4060
0.0307095u
59
0.111236u
58
+ ··· 2.62950u + 1.31233
a
9
=
0.0144334u
59
0.0276837u
58
+ ··· + 46.6833u + 14.8115
0.00194635u
59
+ 0.00912555u
58
+ ··· 0.688771u + 0.357009
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.0308620u
59
+ 0.236254u
58
+ ··· 40.3438u + 23.2477
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
60
16u
58
+ ··· 24u + 19
c
2
u
60
u
59
+ ··· 252u + 29
c
3
u
60
3u
59
+ ··· 100u 47
c
4
u
60
+ u
59
+ ··· 295u 37
c
5
, c
10
u
60
+ u
59
+ ··· 328u 49
c
6
u
60
+ 5u
58
+ ··· + 9u + 1
c
7
u
60
+ 2u
59
+ ··· + 74u 19
c
9
u
60
3u
59
+ ··· + 16u 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
60
32y
59
+ ··· 1602y + 361
c
2
y
60
5y
59
+ ··· 61300y + 841
c
3
y
60
+ 13y
59
+ ··· + 47810y + 2209
c
4
y
60
+ 9y
59
+ ··· 29527y + 1369
c
5
, c
10
y
60
+ 37y
59
+ ··· + 42258y + 2401
c
6
y
60
+ 10y
59
+ ··· 45y + 1
c
7
y
60
+ 42y
58
+ ··· 7604y + 361
c
9
y
60
+ y
59
+ ··· 10y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.112870 + 0.986911I
a = 1.159810 + 0.114908I
b = 0.540790 + 0.509640I
3.10319 2.00739I 0.07017 + 3.73576I
u = 0.112870 0.986911I
a = 1.159810 0.114908I
b = 0.540790 0.509640I
3.10319 + 2.00739I 0.07017 3.73576I
u = 0.758675 + 0.611167I
a = 0.595748 0.212189I
b = 0.847394 0.210567I
1.45806 + 0.40357I 7.54100 1.19625I
u = 0.758675 0.611167I
a = 0.595748 + 0.212189I
b = 0.847394 + 0.210567I
1.45806 0.40357I 7.54100 + 1.19625I
u = 0.791211 + 0.664753I
a = 0.043324 + 0.264154I
b = 0.005931 1.204400I
1.99327 + 4.92703I 6.26354 5.97246I
u = 0.791211 0.664753I
a = 0.043324 0.264154I
b = 0.005931 + 1.204400I
1.99327 4.92703I 6.26354 + 5.97246I
u = 0.373335 + 0.846791I
a = 1.34189 + 0.46586I
b = 1.36952 0.80230I
3.50470 2.65606I 0.26583 + 6.15253I
u = 0.373335 0.846791I
a = 1.34189 0.46586I
b = 1.36952 + 0.80230I
3.50470 + 2.65606I 0.26583 6.15253I
u = 0.419068 + 0.994844I
a = 1.154120 + 0.418871I
b = 0.479030 0.178046I
3.24917 2.13718I 0.66405 + 3.46334I
u = 0.419068 0.994844I
a = 1.154120 0.418871I
b = 0.479030 + 0.178046I
3.24917 + 2.13718I 0.66405 3.46334I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.993764 + 0.432758I
a = 0.745249 0.914388I
b = 0.92399 + 1.46999I
1.75235 + 6.26871I 10.64174 5.67281I
u = 0.993764 0.432758I
a = 0.745249 + 0.914388I
b = 0.92399 1.46999I
1.75235 6.26871I 10.64174 + 5.67281I
u = 0.906827
a = 0.722755
b = 0.514151
1.17963 9.59750
u = 0.286214 + 0.854751I
a = 1.69970 0.17441I
b = 0.441193 1.061620I
1.94749 + 7.99248I 0.63462 7.50100I
u = 0.286214 0.854751I
a = 1.69970 + 0.17441I
b = 0.441193 + 1.061620I
1.94749 7.99248I 0.63462 + 7.50100I
u = 0.693182 + 0.924086I
a = 0.459390 + 0.604795I
b = 0.843186 + 0.654005I
0.60848 + 4.96181I 4.00000 6.29782I
u = 0.693182 0.924086I
a = 0.459390 0.604795I
b = 0.843186 0.654005I
0.60848 4.96181I 4.00000 + 6.29782I
u = 0.538025 + 0.635820I
a = 0.059477 + 0.601315I
b = 0.031984 + 0.666688I
1.41050 1.53960I 1.08247 + 1.71398I
u = 0.538025 0.635820I
a = 0.059477 0.601315I
b = 0.031984 0.666688I
1.41050 + 1.53960I 1.08247 1.71398I
u = 0.208530 + 0.777299I
a = 1.54929 + 0.19094I
b = 0.173386 + 1.263770I
4.80506 1.60983I 3.59396 + 7.39228I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.208530 0.777299I
a = 1.54929 0.19094I
b = 0.173386 1.263770I
4.80506 + 1.60983I 3.59396 7.39228I
u = 0.824128 + 0.877490I
a = 0.878482 + 0.225172I
b = 0.96089 1.31598I
3.14073 + 5.21448I 0
u = 0.824128 0.877490I
a = 0.878482 0.225172I
b = 0.96089 + 1.31598I
3.14073 5.21448I 0
u = 0.521047 + 0.599991I
a = 0.246524 1.324130I
b = 0.819658 0.613048I
4.56427 + 0.06184I 9.79376 + 2.89093I
u = 0.521047 0.599991I
a = 0.246524 + 1.324130I
b = 0.819658 + 0.613048I
4.56427 0.06184I 9.79376 2.89093I
u = 0.911068 + 0.857587I
a = 0.800663 0.622002I
b = 0.887791 0.659627I
4.45627 9.81230I 0
u = 0.911068 0.857587I
a = 0.800663 + 0.622002I
b = 0.887791 + 0.659627I
4.45627 + 9.81230I 0
u = 0.520353 + 0.534999I
a = 1.60615 0.69113I
b = 0.244986 0.494041I
1.62697 0.89360I 2.00328 3.90798I
u = 0.520353 0.534999I
a = 1.60615 + 0.69113I
b = 0.244986 + 0.494041I
1.62697 + 0.89360I 2.00328 + 3.90798I
u = 1.242100 + 0.227160I
a = 0.033020 0.829489I
b = 0.352953 + 0.262356I
0.86533 + 2.68701I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.242100 0.227160I
a = 0.033020 + 0.829489I
b = 0.352953 0.262356I
0.86533 2.68701I 0
u = 0.282250 + 0.670079I
a = 1.37086 0.50401I
b = 0.81149 + 1.93630I
4.32803 0.39404I 0.42763 3.09033I
u = 0.282250 0.670079I
a = 1.37086 + 0.50401I
b = 0.81149 1.93630I
4.32803 + 0.39404I 0.42763 + 3.09033I
u = 0.775420 + 1.016880I
a = 0.283940 + 0.475986I
b = 0.385422 0.306091I
2.81417 + 0.85474I 0
u = 0.775420 1.016880I
a = 0.283940 0.475986I
b = 0.385422 + 0.306091I
2.81417 0.85474I 0
u = 0.654495 + 0.222235I
a = 0.913613 + 0.492134I
b = 1.171170 + 0.662981I
5.22239 2.37989I 14.0342 + 3.0404I
u = 0.654495 0.222235I
a = 0.913613 0.492134I
b = 1.171170 0.662981I
5.22239 + 2.37989I 14.0342 3.0404I
u = 0.008423 + 0.554656I
a = 2.05543 + 0.36150I
b = 1.23945 1.72511I
0.66314 6.63784I 0.93799 + 7.96550I
u = 0.008423 0.554656I
a = 2.05543 0.36150I
b = 1.23945 + 1.72511I
0.66314 + 6.63784I 0.93799 7.96550I
u = 0.82689 + 1.22977I
a = 0.911137 0.237809I
b = 1.19326 + 1.23882I
3.51043 9.84939I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.82689 1.22977I
a = 0.911137 + 0.237809I
b = 1.19326 1.23882I
3.51043 + 9.84939I 0
u = 0.81360 + 1.26582I
a = 0.915368 + 0.302763I
b = 0.929673 0.916332I
4.28857 3.85212I 0
u = 0.81360 1.26582I
a = 0.915368 0.302763I
b = 0.929673 + 0.916332I
4.28857 + 3.85212I 0
u = 0.469315
a = 5.77453
b = 0.184074
0.389771 203.390
u = 0.07505 + 1.52982I
a = 0.651890 + 0.069835I
b = 1.327120 0.173804I
2.01747 2.78040I 0
u = 0.07505 1.52982I
a = 0.651890 0.069835I
b = 1.327120 + 0.173804I
2.01747 + 2.78040I 0
u = 0.93774 + 1.26399I
a = 0.536599 + 0.151412I
b = 0.870982 0.095094I
3.61034 + 3.01624I 0
u = 0.93774 1.26399I
a = 0.536599 0.151412I
b = 0.870982 + 0.095094I
3.61034 3.01624I 0
u = 0.047283 + 0.408643I
a = 4.41257 0.03304I
b = 0.656591 0.103431I
0.647397 + 0.825379I 13.47557 + 3.84496I
u = 0.047283 0.408643I
a = 4.41257 + 0.03304I
b = 0.656591 + 0.103431I
0.647397 0.825379I 13.47557 3.84496I
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.96616 + 1.29625I
a = 0.917595 + 0.250498I
b = 1.16052 1.17459I
0.3709 + 16.1254I 0
u = 0.96616 1.29625I
a = 0.917595 0.250498I
b = 1.16052 + 1.17459I
0.3709 16.1254I 0
u = 0.92727 + 1.34544I
a = 0.868668 0.126514I
b = 0.891724 + 0.853255I
3.18307 + 7.41862I 0
u = 0.92727 1.34544I
a = 0.868668 + 0.126514I
b = 0.891724 0.853255I
3.18307 7.41862I 0
u = 1.23044 + 1.25774I
a = 0.588762 + 0.477885I
b = 0.728116 1.050760I
2.92948 5.60961I 0
u = 1.23044 1.25774I
a = 0.588762 0.477885I
b = 0.728116 + 1.050760I
2.92948 + 5.60961I 0
u = 1.02141 + 1.47167I
a = 0.494856 0.297340I
b = 0.694021 + 0.906910I
2.63315 + 3.07819I 0
u = 1.02141 1.47167I
a = 0.494856 + 0.297340I
b = 0.694021 0.906910I
2.63315 3.07819I 0
u = 1.81425 + 0.48435I
a = 0.069087 + 0.592288I
b = 0.314536 0.264463I
2.02262 7.30145I 0
u = 1.81425 0.48435I
a = 0.069087 0.592288I
b = 0.314536 + 0.264463I
2.02262 + 7.30145I 0
10
II.
I
u
2
= h2u
8
+u
7
+· · ·+ 9b 5, 8u
8
3u
7
+· · ·+ 3a 11, u
9
+u
7
+· · ·+ 2u 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
8
3
u
8
+ u
7
+ ···
1
3
u +
11
3
2
9
u
8
1
9
u
7
+ ··· 2u +
5
9
a
7
=
22
9
u
8
+
8
9
u
7
+ ···
7
3
u +
38
9
2
9
u
8
1
9
u
7
+ ··· 2u +
5
9
a
8
=
17
9
u
8
+
4
9
u
7
+ ··· u +
25
9
1
3
u
8
+
1
3
u
7
+ ···
7
3
u + 1
a
1
=
46
9
u
8
+
29
9
u
7
+ ··· +
5
3
u +
77
9
1
9
u
8
7
9
u
7
+ ···
1
3
u
4
9
a
5
=
119
9
u
8
+
64
9
u
7
+ ··· u +
229
9
1
3
u
8
+
1
3
u
7
+ ··· +
1
3
u
2
+
2
3
u
a
2
=
32
9
u
8
+
16
9
u
7
+ ··· u +
64
9
2
9
u
8
+
1
9
u
7
+ ··· u +
4
9
a
9
=
46
9
u
8
+
17
9
u
7
+ ···
8
3
u +
80
9
1
9
u
8
5
9
u
7
+ ··· 2u +
7
9
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
454
9
u
8
245
9
u
7
599
9
u
6
+ 166u
5
1024
9
u
4
+
2203
9
u
3
1618
9
u
2
+ 13u
845
9
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ u
8
u
7
u
6
u
5
u
4
+ 4u
3
+ 2u
2
2u 1
c
2
u
9
+ 4u
8
+ 10u
7
+ 20u
6
+ 34u
5
+ 42u
4
+ 30u
3
+ 9u
2
1
c
3
u
9
+ u
7
4u
6
+ 4u
5
6u
4
+ 6u
3
2u
2
+ 2u 1
c
4
u
9
2u
8
u
7
3u
6
3u
5
5u
3
4u
2
u 1
c
5
u
9
2u
8
+ 3u
7
7u
6
+ u
5
10u
4
4u
3
6u
2
4u 1
c
6
u
9
+ u
8
+ 4u
7
u
6
+ u
5
8u
4
3u
2
+ 7u 1
c
7
u
9
u
8
+ 3u
7
+ u
6
+ u
5
+ 3u
4
+ 3u
3
+ 5u
2
+ 1
c
8
u
9
u
8
u
7
+ u
6
u
5
+ u
4
+ 4u
3
2u
2
2u + 1
c
9
u
9
+ 4u
8
+ 5u
7
+ 3u
6
+ 2u
5
+ 2u
4
+ u
3
+ 1
c
10
u
9
+ 2u
8
+ 3u
7
+ 7u
6
+ u
5
+ 10u
4
4u
3
+ 6u
2
4u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
9
3y
8
+ y
7
+ 11y
6
17y
5
+ y
4
+ 22y
3
22y
2
+ 8y 1
c
2
y
9
+ 4y
8
+ 8y
7
+ 4y
6
+ 4y
5
76y
4
+ 184y
3
+ 3y
2
+ 18y 1
c
3
y
9
+ 2y
8
+ 9y
7
+ 4y
6
16y
5
+ 20y
3
+ 8y
2
1
c
4
y
9
6y
8
17y
7
13y
6
+ y
5
+ 4y
4
+ 25y
3
6y
2
7y 1
c
5
, c
10
y
9
+ 2y
8
17y
7
91y
6
195y
5
220y
4
126y
3
24y
2
+ 4y 1
c
6
y
9
+ 7y
8
+ 20y
7
+ 23y
6
+ 5y
5
12y
4
36y
3
25y
2
+ 43y 1
c
7
y
9
+ 5y
8
+ 13y
7
+ 17y
6
+ 23y
5
11y
4
23y
3
31y
2
10y 1
c
9
y
9
6y
8
+ 5y
7
3y
6
+ 2y
5
8y
4
5y
3
4y
2
1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.055585 + 1.071070I
a = 0.151372 + 0.325268I
b = 0.911604 0.103130I
3.57395 + 1.78451I 10.19091 0.99326I
u = 0.055585 1.071070I
a = 0.151372 0.325268I
b = 0.911604 + 0.103130I
3.57395 1.78451I 10.19091 + 0.99326I
u = 1.040640 + 0.285855I
a = 0.561905 0.895180I
b = 0.161935 + 1.373030I
0.72688 + 6.70635I 3.06894 7.87674I
u = 1.040640 0.285855I
a = 0.561905 + 0.895180I
b = 0.161935 1.373030I
0.72688 6.70635I 3.06894 + 7.87674I
u = 0.244831 + 0.626842I
a = 1.67953 + 0.25795I
b = 0.53282 1.62052I
4.15988 1.15529I 3.41918 + 3.86401I
u = 0.244831 0.626842I
a = 1.67953 0.25795I
b = 0.53282 + 1.62052I
4.15988 + 1.15529I 3.41918 3.86401I
u = 0.524555
a = 4.47522
b = 0.153592
0.416370 105.200
u = 1.11367 + 1.37911I
a = 0.647547 + 0.344854I
b = 0.793645 0.872272I
3.22264 4.71392I 2.42181 + 4.00779I
u = 1.11367 1.37911I
a = 0.647547 0.344854I
b = 0.793645 + 0.872272I
3.22264 + 4.71392I 2.42181 4.00779I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
+ u
8
u
7
u
6
u
5
u
4
+ 4u
3
+ 2u
2
2u 1)
· (u
60
16u
58
+ ··· 24u + 19)
c
2
(u
9
+ 4u
8
+ 10u
7
+ 20u
6
+ 34u
5
+ 42u
4
+ 30u
3
+ 9u
2
1)
· (u
60
u
59
+ ··· 252u + 29)
c
3
(u
9
+ u
7
4u
6
+ 4u
5
6u
4
+ 6u
3
2u
2
+ 2u 1)
· (u
60
3u
59
+ ··· 100u 47)
c
4
(u
9
2u
8
u
7
3u
6
3u
5
5u
3
4u
2
u 1)
· (u
60
+ u
59
+ ··· 295u 37)
c
5
(u
9
2u
8
+ 3u
7
7u
6
+ u
5
10u
4
4u
3
6u
2
4u 1)
· (u
60
+ u
59
+ ··· 328u 49)
c
6
(u
9
+ u
8
+ ··· + 7u 1)(u
60
+ 5u
58
+ ··· + 9u + 1)
c
7
(u
9
u
8
+ 3u
7
+ u
6
+ u
5
+ 3u
4
+ 3u
3
+ 5u
2
+ 1)
· (u
60
+ 2u
59
+ ··· + 74u 19)
c
8
(u
9
u
8
u
7
+ u
6
u
5
+ u
4
+ 4u
3
2u
2
2u + 1)
· (u
60
16u
58
+ ··· 24u + 19)
c
9
(u
9
+ 4u
8
+ ··· + u
3
+ 1)(u
60
3u
59
+ ··· + 16u 1)
c
10
(u
9
+ 2u
8
+ 3u
7
+ 7u
6
+ u
5
+ 10u
4
4u
3
+ 6u
2
4u + 1)
· (u
60
+ u
59
+ ··· 328u 49)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
9
3y
8
+ y
7
+ 11y
6
17y
5
+ y
4
+ 22y
3
22y
2
+ 8y 1)
· (y
60
32y
59
+ ··· 1602y + 361)
c
2
(y
9
+ 4y
8
+ 8y
7
+ 4y
6
+ 4y
5
76y
4
+ 184y
3
+ 3y
2
+ 18y 1)
· (y
60
5y
59
+ ··· 61300y + 841)
c
3
(y
9
+ 2y
8
+ 9y
7
+ 4y
6
16y
5
+ 20y
3
+ 8y
2
1)
· (y
60
+ 13y
59
+ ··· + 47810y + 2209)
c
4
(y
9
6y
8
17y
7
13y
6
+ y
5
+ 4y
4
+ 25y
3
6y
2
7y 1)
· (y
60
+ 9y
59
+ ··· 29527y + 1369)
c
5
, c
10
(y
9
+ 2y
8
17y
7
91y
6
195y
5
220y
4
126y
3
24y
2
+ 4y 1)
· (y
60
+ 37y
59
+ ··· + 42258y + 2401)
c
6
(y
9
+ 7y
8
+ 20y
7
+ 23y
6
+ 5y
5
12y
4
36y
3
25y
2
+ 43y 1)
· (y
60
+ 10y
59
+ ··· 45y + 1)
c
7
(y
9
+ 5y
8
+ 13y
7
+ 17y
6
+ 23y
5
11y
4
23y
3
31y
2
10y 1)
· (y
60
+ 42y
58
+ ··· 7604y + 361)
c
9
(y
9
6y
8
+ 5y
7
3y
6
+ 2y
5
8y
4
5y
3
4y
2
1)
· (y
60
+ y
59
+ ··· 10y + 1)
16