10
118
(K10a
88
)
A knot diagram
1
Linearized knot diagam
8 6 1 2 9 10 4 5 3 7
Solving Sequence
4,7 1,8
2 5 3 10 6 9
c
7
c
1
c
4
c
3
c
10
c
6
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2.17049 × 10
128
u
55
+ 7.04965 × 10
128
u
54
+ ··· + 1.13515 × 10
129
b + 3.31225 × 10
128
,
− 6.03461 × 10
129
u
55
− 1.05486 × 10
130
u
54
+ ··· + 3.29192 × 10
130
a + 8.03066 × 10
131
,
u
56
+ 3u
55
+ ··· − 86u − 29i
I
u
2
= hu
7
− u
5
+ 2u
4
+ 2u
3
+ 3u
2
+ 2b − 1, 2u
7
− u
6
− u
5
+ 5u
4
+ 3u
3
+ 3u
2
+ 2a + 2,
u
8
− u
6
+ 2u
5
+ 3u
4
+ 2u
3
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 64 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
= h2.17 × 10
128
u
55
+ 7.05 × 10
128
u
54
+ · · · + 1.14 × 10
129
b + 3.31 ×
10
128
, −6.03 × 10
129
u
55
− 1.05 × 10
130
u
54
+ · · · + 3.29 × 10
130
a + 8.03 ×
10
131
, u
56
+ 3u
55
+ · · · − 86u − 29i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
1
=
0.183316u
55
+ 0.320439u
54
+ ··· − 36.3951u − 24.3951
−0.191208u
55
− 0.621035u
54
+ ··· − 24.1471u − 0.291791
a
8
=
1
−u
2
a
2
=
0.329942u
55
+ 0.877435u
54
+ ··· + 2.17359u − 17.4475
−0.228740u
55
− 0.774692u
54
+ ··· − 38.4713u − 3.68817
a
5
=
0.00194160u
55
+ 0.125899u
54
+ ··· + 24.9331u − 7.18816
−0.0511468u
55
− 0.283014u
54
+ ··· − 27.4710u − 5.28083
a
3
=
−0.143680u
55
− 0.426284u
54
+ ··· − 13.1771u − 13.3885
0.0842120u
55
+ 0.155045u
54
+ ··· − 15.2642u − 4.53960
a
10
=
0.374524u
55
+ 0.941474u
54
+ ··· − 12.2480u − 24.1033
−0.191208u
55
− 0.621035u
54
+ ··· − 24.1471u − 0.291791
a
6
=
−0.225711u
55
− 0.655623u
54
+ ··· + 8.05046u − 6.26808
0.0691731u
55
+ 0.270220u
54
+ ··· + 4.64014u + 4.46620
a
9
=
−0.120671u
55
− 0.252131u
54
+ ··· + 25.1490u − 10.2596
−0.0170410u
55
− 0.154222u
54
+ ··· − 24.0061u − 3.26683
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0612869u
55
− 0.0909872u
54
+ ··· − 11.4095u − 14.5506
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
56
+ 3u
55
+ ··· − 86u − 29
c
2
u
56
− u
54
+ ··· − 12u + 1
c
3
u
56
+ 3u
55
+ ··· − 23u + 1
c
4
u
56
− 3u
55
+ ··· + 23u + 1
c
5
, c
8
u
56
+ u
55
+ ··· − 21u − 1
c
6
, c
10
u
56
− u
55
+ ··· + 21u − 1
c
7
u
56
− 3u
55
+ ··· + 86u − 29
c
9
u
56
− u
54
+ ··· + 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
56
− 13y
55
+ ··· − 26246y + 841
c
2
, c
9
y
56
− 2y
55
+ ··· − 526y + 1
c
3
, c
4
y
56
+ 5y
55
+ ··· − 155y + 1
c
5
, c
6
, c
8
c
10
y
56
− 41y
55
+ ··· − 91y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.783480 + 0.627461I
a = 0.378022 − 0.391050I
b = −0.230315 + 0.038880I
1.26494 − 1.26950I 4.50876 + 0.89106I
u = −0.783480 − 0.627461I
a = 0.378022 + 0.391050I
b = −0.230315 − 0.038880I
1.26494 + 1.26950I 4.50876 − 0.89106I
u = −0.867481 + 0.465833I
a = −0.535992 − 1.067720I
b = −0.486169 − 0.719576I
−3.60092 − 1.79783I −4.19052 + 2.40869I
u = −0.867481 − 0.465833I
a = −0.535992 + 1.067720I
b = −0.486169 + 0.719576I
−3.60092 + 1.79783I −4.19052 − 2.40869I
u = 0.671481 + 0.714028I
a = −0.790076 − 0.970719I
b = −0.1029550 − 0.0679357I
−1.91385 + 4.83850I −2.53419 − 6.95729I
u = 0.671481 − 0.714028I
a = −0.790076 + 0.970719I
b = −0.1029550 + 0.0679357I
−1.91385 − 4.83850I −2.53419 + 6.95729I
u = −0.907848 + 0.325017I
a = −0.02327 − 1.45567I
b = 1.32128 − 0.52561I
2.56248 − 7.32114I 3.13433 + 7.29187I
u = −0.907848 − 0.325017I
a = −0.02327 + 1.45567I
b = 1.32128 + 0.52561I
2.56248 + 7.32114I 3.13433 − 7.29187I
u = 0.614585 + 0.660088I
a = 0.771966 − 0.367815I
b = 0.794571 − 0.247178I
−3.06725 − 0.91106I −2.78612 + 2.04256I
u = 0.614585 − 0.660088I
a = 0.771966 + 0.367815I
b = 0.794571 + 0.247178I
−3.06725 + 0.91106I −2.78612 − 2.04256I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.495818 + 0.985480I
a = −0.66594 − 1.42520I
b = −1.291500 − 0.294118I
−1.18098 + 5.45507I −4.29936 − 4.75401I
u = 0.495818 − 0.985480I
a = −0.66594 + 1.42520I
b = −1.291500 + 0.294118I
−1.18098 − 5.45507I −4.29936 + 4.75401I
u = −1.048230 + 0.400499I
a = 0.072661 + 0.652197I
b = −1.230370 + 0.109087I
3.06725 − 0.91106I 2.78612 + 2.04256I
u = −1.048230 − 0.400499I
a = 0.072661 − 0.652197I
b = −1.230370 − 0.109087I
3.06725 + 0.91106I 2.78612 − 2.04256I
u = −1.13343
a = 1.35973
b = −1.44691
1.54290 6.38460
u = −0.874453 + 0.768327I
a = 0.122940 − 1.406550I
b = 1.197120 − 0.303609I
1.91385 − 4.83850I 2.53419 + 6.95729I
u = −0.874453 − 0.768327I
a = 0.122940 + 1.406550I
b = 1.197120 + 0.303609I
1.91385 + 4.83850I 2.53419 − 6.95729I
u = 0.987700 + 0.648175I
a = 0.09787 − 1.65319I
b = −1.007190 − 0.370280I
−2.03150 + 6.02280I −3.73094 − 6.75893I
u = 0.987700 − 0.648175I
a = 0.09787 + 1.65319I
b = −1.007190 + 0.370280I
−2.03150 − 6.02280I −3.73094 + 6.75893I
u = −0.330263 + 0.747920I
a = 0.02506 − 1.66118I
b = 0.063233 − 0.654816I
−5.38278 − 1.94709I −9.07863 + 3.78322I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.330263 − 0.747920I
a = 0.02506 + 1.66118I
b = 0.063233 + 0.654816I
−5.38278 + 1.94709I −9.07863 − 3.78322I
u = −0.768372 + 0.912758I
a = 0.078803 + 0.713454I
b = −0.213245 + 1.196470I
− 3.96282I 0. + 12.03346I
u = −0.768372 − 0.912758I
a = 0.078803 − 0.713454I
b = −0.213245 − 1.196470I
3.96282I 0. − 12.03346I
u = 0.768710 + 0.080853I
a = −1.18088 + 1.64494I
b = 1.224820 − 0.066557I
5.38278 − 1.94709I 9.07863 + 3.78322I
u = 0.768710 − 0.080853I
a = −1.18088 − 1.64494I
b = 1.224820 + 0.066557I
5.38278 + 1.94709I 9.07863 − 3.78322I
u = −0.417667 + 0.587372I
a = −0.020230 + 0.413680I
b = 1.13926 + 1.00938I
−2.12732 − 2.99186I −13.6584 + 6.9170I
u = −0.417667 − 0.587372I
a = −0.020230 − 0.413680I
b = 1.13926 − 1.00938I
−2.12732 + 2.99186I −13.6584 − 6.9170I
u = −1.28361
a = −1.43131
b = 0.991270
−3.28334 −1.95800
u = 0.695004 + 0.172107I
a = 0.37195 − 1.39210I
b = −1.46649 − 0.46691I
5.06898 + 2.94565I 6.46008 − 3.65784I
u = 0.695004 − 0.172107I
a = 0.37195 + 1.39210I
b = −1.46649 + 0.46691I
5.06898 − 2.94565I 6.46008 + 3.65784I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.951068 + 0.899353I
a = −0.187043 + 0.873695I
b = 0.179049 + 1.120190I
−5.00346 + 9.83371I 0
u = 0.951068 − 0.899353I
a = −0.187043 − 0.873695I
b = 0.179049 − 1.120190I
−5.00346 − 9.83371I 0
u = 0.531582 + 0.418877I
a = 0.345342 − 1.304770I
b = 0.165425 − 0.641483I
−1.26494 + 1.26950I −4.50876 − 0.89106I
u = 0.531582 − 0.418877I
a = 0.345342 + 1.304770I
b = 0.165425 + 0.641483I
−1.26494 − 1.26950I −4.50876 + 0.89106I
u = −0.246039 + 1.330330I
a = −0.109393 + 0.201685I
b = −0.925946 + 0.365281I
1.17763 − 1.90833I 0
u = −0.246039 − 1.330330I
a = −0.109393 − 0.201685I
b = −0.925946 − 0.365281I
1.17763 + 1.90833I 0
u = 1.36704
a = −0.0603515
b = 1.39639
3.28334 0
u = 0.606940 + 0.092167I
a = 0.587067 + 0.957007I
b = 0.141834 + 0.920236I
−1.17763 − 1.90833I 2.60907 + 2.19068I
u = 0.606940 − 0.092167I
a = 0.587067 − 0.957007I
b = 0.141834 − 0.920236I
−1.17763 + 1.90833I 2.60907 − 2.19068I
u = 0.964815 + 1.009120I
a = −0.473801 + 0.532980I
b = 0.301392 + 0.797095I
−5.06898 − 2.94565I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.964815 − 1.009120I
a = −0.473801 − 0.532980I
b = 0.301392 − 0.797095I
−5.06898 + 2.94565I 0
u = −0.584292 + 0.088844I
a = 0.95463 + 3.53861I
b = −1.181570 − 0.095549I
1.18098 + 5.45507I 4.29936 − 4.75401I
u = −0.584292 − 0.088844I
a = 0.95463 − 3.53861I
b = −1.181570 + 0.095549I
1.18098 − 5.45507I 4.29936 + 4.75401I
u = −1.29911 + 0.91025I
a = 0.216573 + 1.073080I
b = −1.42481 + 0.50052I
− 15.5452I 0
u = −1.29911 − 0.91025I
a = 0.216573 − 1.073080I
b = −1.42481 − 0.50052I
15.5452I 0
u = 1.33347 + 0.88382I
a = −0.220110 + 0.911869I
b = 1.41775 + 0.50903I
5.00346 + 9.83371I 0
u = 1.33347 − 0.88382I
a = −0.220110 − 0.911869I
b = 1.41775 − 0.50903I
5.00346 − 9.83371I 0
u = −0.44552 + 1.55785I
a = 0.212043 + 0.191232I
b = 1.114910 + 0.395467I
−2.56248 + 7.32114I 0
u = −0.44552 − 1.55785I
a = 0.212043 − 0.191232I
b = 1.114910 − 0.395467I
−2.56248 − 7.32114I 0
u = −1.16393 + 1.16318I
a = 0.188659 − 0.820953I
b = 1.234890 − 0.135915I
2.03150 − 6.02280I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.16393 − 1.16318I
a = 0.188659 + 0.820953I
b = 1.234890 + 0.135915I
2.03150 + 6.02280I 0
u = −1.34569 + 0.94875I
a = 0.236623 + 0.596957I
b = −1.32213 + 0.64789I
2.12732 − 2.99186I 0
u = −1.34569 − 0.94875I
a = 0.236623 − 0.596957I
b = −1.32213 − 0.64789I
2.12732 + 2.99186I 0
u = −0.299877
a = −4.00586
b = 1.49366
−1.54290 −6.38460
u = 1.63614 + 0.85817I
a = 0.236114 − 0.548173I
b = −1.130060 − 0.065159I
3.60092 + 1.79783I 0
u = 1.63614 − 0.85817I
a = 0.236114 + 0.548173I
b = −1.130060 + 0.065159I
3.60092 − 1.79783I 0
10
II. I
u
2
= hu
7
− u
5
+ 2u
4
+ 2u
3
+ 3u
2
+ 2b − 1, 2u
7
− u
6
− u
5
+ 5u
4
+ 3u
3
+
3u
2
+ 2a + 2, u
8
− u
6
+ 2u
5
+ 3u
4
+ 2u
3
− u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
1
=
−u
7
+
1
2
u
6
+ ··· −
3
2
u
2
− 1
−
1
2
u
7
+
1
2
u
5
+ ··· −
3
2
u
2
+
1
2
a
8
=
1
−u
2
a
2
=
1
2
u
6
−
1
2
u
5
+ ··· − u − 1
−
1
2
u
7
+
1
2
u
5
+ ··· + u +
1
2
a
5
=
1
2
u
7
−
1
2
u
5
+ ··· +
3
2
u + 1
−
1
2
u
5
+
1
2
u
4
+ ··· +
1
2
u − 1
a
3
=
−
1
2
u
7
+ u
6
+ ··· +
1
2
u − 1
−
1
2
u
5
+
1
2
u
4
+ ··· −
3
2
u
2
+
1
2
u
a
10
=
−
1
2
u
7
+
1
2
u
6
+ ··· −
1
2
u
3
−
3
2
−
1
2
u
7
+
1
2
u
5
+ ··· −
3
2
u
2
+
1
2
a
6
=
1
2
u
7
+
1
2
u
4
+ ··· −
1
2
u +
1
2
−
1
2
u
7
− u
4
− u
3
−
3
2
u
2
− u
a
9
=
u
7
−
1
2
u
6
+ ··· −
3
2
u +
1
2
1
2
u
7
− u
6
+ 2u
4
− u
3
−
3
2
u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
7
+ u
6
+ u
5
− 5u
4
− 10u
3
− 14u
2
+ 4u − 1
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− u
6
− 2u
5
+ 3u
4
− 2u
3
− u
2
+ 1
c
2
u
8
− u
7
+ u
6
+ u
5
− 2u
4
− u
3
− 3u
2
− 2u − 1
c
3
u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 15u
4
+ 8u
3
+ u
2
− u − 1
c
4
u
8
− 4u
7
+ 10u
6
− 16u
5
+ 15u
4
− 8u
3
+ u
2
+ u − 1
c
5
, c
10
u
8
− 3u
6
− u
5
+ 4u
4
+ 3u
3
− 3u
2
− 3u + 1
c
6
, c
8
u
8
− 3u
6
+ u
5
+ 4u
4
− 3u
3
− 3u
2
+ 3u + 1
c
7
u
8
− u
6
+ 2u
5
+ 3u
4
+ 2u
3
− u
2
+ 1
c
9
u
8
+ u
7
+ u
6
− u
5
− 2u
4
+ u
3
− 3u
2
+ 2u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
8
− 2y
7
+ 7y
6
− 12y
5
+ 5y
4
− 12y
3
+ 7y
2
− 2y + 1
c
2
, c
9
y
8
+ y
7
− y
6
− 13y
5
− 6y
4
+ 13y
3
+ 9y
2
+ 2y + 1
c
3
, c
4
y
8
+ 4y
7
+ 2y
6
− 18y
5
− 5y
4
− 22y
3
− 13y
2
− 3y + 1
c
5
, c
6
, c
8
c
10
y
8
− 6y
7
+ 17y
6
− 31y
5
+ 42y
4
− 45y
3
+ 35y
2
− 15y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.564069 + 0.825728I
a = 1.16899 − 1.40408I
b = 1.168990 − 0.247374I
− 6.39156I 0. + 8.17644I
u = −0.564069 − 0.825728I
a = 1.16899 + 1.40408I
b = 1.168990 + 0.247374I
6.39156I 0. − 8.17644I
u = −0.747139
a = −1.89022
b = −0.283291
−4.69721 −8.73000
u = −1.33844
a = 0.308010
b = −1.29891
4.69721 8.73000
u = 0.468348 + 0.438200I
a = −0.445605 − 1.005710I
b = 0.737885 − 0.854835I
−1.62267 + 2.99663I 2.80411 − 6.12718I
u = 0.468348 − 0.438200I
a = −0.445605 + 1.005710I
b = 0.737885 + 0.854835I
−1.62267 − 2.99663I 2.80411 + 6.12718I
u = 1.13851 + 1.06522I
a = 0.067722 − 0.648589I
b = −1.115770 − 0.497712I
1.62267 + 2.99663I −2.80411 − 6.12718I
u = 1.13851 − 1.06522I
a = 0.067722 + 0.648589I
b = −1.115770 + 0.497712I
1.62267 − 2.99663I −2.80411 + 6.12718I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
− u
6
− 2u
5
+ 3u
4
− 2u
3
− u
2
+ 1)(u
56
+ 3u
55
+ ··· − 86u − 29)
c
2
(u
8
− u
7
+ ··· − 2u − 1)(u
56
− u
54
+ ··· − 12u + 1)
c
3
(u
8
+ 4u
7
+ 10u
6
+ 16u
5
+ 15u
4
+ 8u
3
+ u
2
− u − 1)
· (u
56
+ 3u
55
+ ··· − 23u + 1)
c
4
(u
8
− 4u
7
+ 10u
6
− 16u
5
+ 15u
4
− 8u
3
+ u
2
+ u − 1)
· (u
56
− 3u
55
+ ··· + 23u + 1)
c
5
(u
8
− 3u
6
+ ··· − 3u + 1)(u
56
+ u
55
+ ··· − 21u − 1)
c
6
(u
8
− 3u
6
+ ··· + 3u + 1)(u
56
− u
55
+ ··· + 21u − 1)
c
7
(u
8
− u
6
+ 2u
5
+ 3u
4
+ 2u
3
− u
2
+ 1)(u
56
− 3u
55
+ ··· + 86u − 29)
c
8
(u
8
− 3u
6
+ ··· + 3u + 1)(u
56
+ u
55
+ ··· − 21u − 1)
c
9
(u
8
+ u
7
+ ··· + 2u − 1)(u
56
− u
54
+ ··· + 12u + 1)
c
10
(u
8
− 3u
6
+ ··· − 3u + 1)(u
56
− u
55
+ ··· + 21u − 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
8
− 2y
7
+ 7y
6
− 12y
5
+ 5y
4
− 12y
3
+ 7y
2
− 2y + 1)
· (y
56
− 13y
55
+ ··· − 26246y + 841)
c
2
, c
9
(y
8
+ y
7
− y
6
− 13y
5
− 6y
4
+ 13y
3
+ 9y
2
+ 2y + 1)
· (y
56
− 2y
55
+ ··· − 526y + 1)
c
3
, c
4
(y
8
+ 4y
7
+ 2y
6
− 18y
5
− 5y
4
− 22y
3
− 13y
2
− 3y + 1)
· (y
56
+ 5y
55
+ ··· − 155y + 1)
c
5
, c
6
, c
8
c
10
(y
8
− 6y
7
+ 17y
6
− 31y
5
+ 42y
4
− 45y
3
+ 35y
2
− 15y + 1)
· (y
56
− 41y
55
+ ··· − 91y + 1)
16
