12a
0290
(K12a
0290
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 5 11 12 1 7 4 9
Solving Sequence
9,12
1
4,10
5 8 3 2 11 7 6
c
12
c
9
c
4
c
8
c
3
c
1
c
11
c
7
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.57175 × 10
132
u
87
+ 1.72314 × 10
133
u
86
+ ··· + 9.74392 × 10
132
b + 5.16952 × 10
132
,
6.77338 × 10
132
u
87
+ 6.23699 × 10
133
u
86
+ ··· + 9.74392 × 10
132
a − 1.46464 × 10
132
, u
88
+ 7u
87
+ ··· + 6u − 2i
I
u
2
= hb + 1, 2a − u, u
2
− 2i
I
v
1
= ha, b − 1, v + 1i
* 3 irreducible components of dim
C
= 0, with total 91 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
= h1.57 × 10
132
u
87
+ 1.72 × 10
133
u
86
+ · · · + 9.74 × 10
132
b + 5.17 ×
10
132
, 6.77 × 10
132
u
87
+ 6.24 × 10
133
u
86
+ · · · + 9.74 × 10
132
a − 1.46 ×
10
132
, u
88
+ 7u
87
+ · · · + 6u − 2i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
−0.695139u
87
− 6.40091u
86
+ ··· − 9.75797u + 0.150314
−0.161305u
87
− 1.76843u
86
+ ··· + 3.10463u − 0.530538
a
10
=
−u
−u
3
+ u
a
5
=
0.671807u
87
+ 4.32742u
86
+ ··· − 10.5704u + 1.48658
1.00155u
87
+ 7.58488u
86
+ ··· − 0.307323u + 0.452612
a
8
=
u
u
a
3
=
1.42894u
87
+ 10.3800u
86
+ ··· − 14.0642u + 1.94160
1.96278u
87
+ 15.0125u
86
+ ··· − 1.20156u + 1.26075
a
2
=
1.09670u
87
+ 5.26132u
86
+ ··· + 11.8149u − 1.97450
0.586103u
87
+ 0.737960u
86
+ ··· + 12.2825u − 4.91592
a
11
=
−0.555259u
87
− 2.94764u
86
+ ··· − 12.5540u + 2.00113
−0.932863u
87
− 5.26350u
86
+ ··· − 0.350537u − 0.580112
a
7
=
0.555259u
87
+ 2.94764u
86
+ ··· + 12.5540u − 2.00113
0.445220u
87
+ 2.37310u
86
+ ··· + 6.39498u − 2.45844
a
6
=
−0.986580u
87
− 5.40335u
86
+ ··· + 0.0651781u + 0.914542
−0.613296u
87
− 1.77328u
86
+ ··· − 8.33907u + 2.76232
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.29383u
87
− 32.7289u
86
+ ··· − 26.3353u + 8.92622
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
88
+ 28u
87
+ ··· − 66u + 1
c
2
, c
5
u
88
+ 4u
87
+ ··· + 2u + 1
c
3
u
88
− 26u
87
+ ··· + 4u + 1
c
4
u
88
+ 32u
87
+ ··· − 17646936u − 2939221
c
7
, c
10
u
88
− 2u
87
+ ··· − 34u − 1
c
8
, c
9
, c
12
u
88
+ 7u
87
+ ··· + 6u − 2
c
11
u
88
− 4u
87
+ ··· + 10u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
88
+ 68y
87
+ ··· − 1966y + 1
c
2
, c
5
y
88
− 28y
87
+ ··· + 66y + 1
c
3
y
88
− 512y
87
+ ··· − 758y + 1
c
4
y
88
− 588y
87
+ ··· − 154392187987162y + 8639020086841
c
7
, c
10
y
88
− 68y
87
+ ··· − 630y + 1
c
8
, c
9
, c
12
y
88
− 85y
87
+ ··· + 28y + 4
c
11
y
88
+ 4y
87
+ ··· − 70y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.495208 + 0.877151I
a = 0.411455 + 0.753705I
b = −1.015090 + 0.935019I
7.6509 − 12.9288I 0
u = 0.495208 − 0.877151I
a = 0.411455 − 0.753705I
b = −1.015090 − 0.935019I
7.6509 + 12.9288I 0
u = −0.281152 + 0.967426I
a = −0.291698 + 0.134353I
b = 0.472094 + 0.654902I
2.59156 + 1.21821I 0
u = −0.281152 − 0.967426I
a = −0.291698 − 0.134353I
b = 0.472094 − 0.654902I
2.59156 − 1.21821I 0
u = 0.444403 + 0.862629I
a = −0.409808 − 0.736494I
b = 1.025420 − 0.939996I
8.42853 − 6.77648I 0
u = 0.444403 − 0.862629I
a = −0.409808 + 0.736494I
b = 1.025420 + 0.939996I
8.42853 + 6.77648I 0
u = −0.612876 + 0.708935I
a = 0.346947 − 0.372276I
b = −0.395815 − 0.656615I
−2.85481 + 2.65153I 0
u = −0.612876 − 0.708935I
a = 0.346947 + 0.372276I
b = −0.395815 + 0.656615I
−2.85481 − 2.65153I 0
u = −0.386006 + 1.003120I
a = 0.270380 − 0.196109I
b = −0.456111 − 0.671602I
2.15335 + 6.83792I 0
u = −0.386006 − 1.003120I
a = 0.270380 + 0.196109I
b = −0.456111 + 0.671602I
2.15335 − 6.83792I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.752047 + 0.815149I
a = −0.563170 + 0.131031I
b = −0.816592 − 0.610525I
7.57889 + 1.20760I 0
u = 0.752047 − 0.815149I
a = −0.563170 − 0.131031I
b = −0.816592 + 0.610525I
7.57889 − 1.20760I 0
u = 0.704958 + 0.876898I
a = 0.479501 − 0.130087I
b = 0.785629 + 0.624303I
7.10312 + 7.15665I 0
u = 0.704958 − 0.876898I
a = 0.479501 + 0.130087I
b = 0.785629 − 0.624303I
7.10312 − 7.15665I 0
u = −1.174970 + 0.061073I
a = −0.00514 − 2.91113I
b = −0.18951 − 1.68930I
5.02727 + 3.33290I 0
u = −1.174970 − 0.061073I
a = −0.00514 + 2.91113I
b = −0.18951 + 1.68930I
5.02727 − 3.33290I 0
u = 0.508152 + 0.646507I
a = 0.502496 + 0.724043I
b = −1.051760 + 0.875815I
0.64818 − 7.68033I −4.00000 + 9.27908I
u = 0.508152 − 0.646507I
a = 0.502496 − 0.724043I
b = −1.051760 − 0.875815I
0.64818 + 7.68033I −4.00000 − 9.27908I
u = 0.385530 + 0.718019I
a = 0.210598 − 0.555538I
b = 0.667580 + 0.521758I
1.01440 + 3.28538I −4.00000 − 6.83921I
u = 0.385530 − 0.718019I
a = 0.210598 + 0.555538I
b = 0.667580 − 0.521758I
1.01440 − 3.28538I −4.00000 + 6.83921I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.271860 + 0.189390I
a = −1.57244 − 0.54471I
b = −1.62915 − 0.67700I
3.80798 − 2.18851I 0
u = 1.271860 − 0.189390I
a = −1.57244 + 0.54471I
b = −1.62915 + 0.67700I
3.80798 + 2.18851I 0
u = 1.30786
a = 2.40716
b = 2.44403
−3.20868 0
u = 0.312791 + 0.615361I
a = −0.457552 − 0.634789I
b = 1.12009 − 0.93330I
3.95546 − 4.04673I 2.71866 + 5.71962I
u = 0.312791 − 0.615361I
a = −0.457552 + 0.634789I
b = 1.12009 + 0.93330I
3.95546 + 4.04673I 2.71866 − 5.71962I
u = 0.578857 + 0.359329I
a = −1.23689 + 0.76115I
b = −0.804602 − 0.317174I
2.95975 + 0.61087I 0.98547 + 2.25403I
u = 0.578857 − 0.359329I
a = −1.23689 − 0.76115I
b = −0.804602 + 0.317174I
2.95975 − 0.61087I 0.98547 − 2.25403I
u = 1.328780 + 0.000300I
a = 0.44226 + 2.75769I
b = −0.128258 + 0.645110I
−0.20961 − 2.93911I 0
u = 1.328780 − 0.000300I
a = 0.44226 − 2.75769I
b = −0.128258 − 0.645110I
−0.20961 + 2.93911I 0
u = −1.325330 + 0.124435I
a = −0.037394 + 0.440662I
b = −0.911325 + 0.455131I
−1.304860 + 0.085633I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.325330 − 0.124435I
a = −0.037394 − 0.440662I
b = −0.911325 − 0.455131I
−1.304860 − 0.085633I 0
u = 1.355190 + 0.192450I
a = 1.51658 + 0.83209I
b = 1.63713 + 0.93870I
2.27442 − 8.32858I 0
u = 1.355190 − 0.192450I
a = 1.51658 − 0.83209I
b = 1.63713 − 0.93870I
2.27442 + 8.32858I 0
u = −1.368320 + 0.067286I
a = 0.466668 − 0.523121I
b = −0.324757 − 0.265684I
−3.14744 + 0.11184I 0
u = −1.368320 − 0.067286I
a = 0.466668 + 0.523121I
b = −0.324757 + 0.265684I
−3.14744 − 0.11184I 0
u = 1.383300 + 0.016208I
a = −1.70570 + 5.79045I
b = 0.082745 + 0.273472I
−0.20747 − 2.85455I 0
u = 1.383300 − 0.016208I
a = −1.70570 − 5.79045I
b = 0.082745 − 0.273472I
−0.20747 + 2.85455I 0
u = −0.088016 + 0.606452I
a = −0.304643 − 0.577626I
b = 1.05284 − 1.12404I
7.98061 − 0.72495I 5.07684 + 0.22833I
u = −0.088016 − 0.606452I
a = −0.304643 + 0.577626I
b = 1.05284 + 1.12404I
7.98061 + 0.72495I 5.07684 − 0.22833I
u = −1.386200 + 0.131809I
a = 0.141767 − 0.467812I
b = 1.028830 − 0.460792I
−2.12556 + 5.58667I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.386200 − 0.131809I
a = 0.141767 + 0.467812I
b = 1.028830 + 0.460792I
−2.12556 − 5.58667I 0
u = −0.187730 + 0.577154I
a = 0.271356 + 0.574587I
b = −0.99826 + 1.15457I
7.13319 + 5.55022I 3.18440 − 6.17368I
u = −0.187730 − 0.577154I
a = 0.271356 − 0.574587I
b = −0.99826 − 1.15457I
7.13319 − 5.55022I 3.18440 + 6.17368I
u = −0.603442 + 0.033860I
a = 0.196407 − 0.659993I
b = −0.346103 − 0.850656I
−1.47881 − 1.50127I −9.75731 + 4.59132I
u = −0.603442 − 0.033860I
a = 0.196407 + 0.659993I
b = −0.346103 + 0.850656I
−1.47881 + 1.50127I −9.75731 − 4.59132I
u = −1.40622
a = 0.301859
b = 1.14642
−6.56478 0
u = 1.41892
a = −17.7637
b = 0.0959723
−4.41271 0
u = −1.41358 + 0.13459I
a = 0.70257 + 2.34250I
b = 1.28835 + 1.74535I
−5.42809 + 2.53490I 0
u = −1.41358 − 0.13459I
a = 0.70257 − 2.34250I
b = 1.28835 − 1.74535I
−5.42809 − 2.53490I 0
u = −1.32882 + 0.54023I
a = 0.185595 − 0.497662I
b = −0.302391 − 0.629403I
−0.626564 − 0.632614I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32882 − 0.54023I
a = 0.185595 + 0.497662I
b = −0.302391 + 0.629403I
−0.626564 + 0.632614I 0
u = −1.42235 + 0.21993I
a = −0.32909 − 2.17060I
b = −1.08443 − 1.47205I
−1.60919 + 7.07285I 0
u = −1.42235 − 0.21993I
a = −0.32909 + 2.17060I
b = −1.08443 + 1.47205I
−1.60919 − 7.07285I 0
u = 1.43564 + 0.16847I
a = 0.16509 + 1.64037I
b = −0.549615 + 1.090380I
−5.77675 − 3.38269I 0
u = 1.43564 − 0.16847I
a = 0.16509 − 1.64037I
b = −0.549615 − 1.090380I
−5.77675 + 3.38269I 0
u = −0.289821 + 0.442277I
a = −0.750944 + 0.488100I
b = 0.357107 + 0.565907I
−0.130405 + 1.105450I −2.09917 − 6.01174I
u = −0.289821 − 0.442277I
a = −0.750944 − 0.488100I
b = 0.357107 − 0.565907I
−0.130405 − 1.105450I −2.09917 + 6.01174I
u = −0.511705 + 0.082203I
a = −0.71931 + 4.95483I
b = 0.076717 + 0.762273I
5.46748 − 2.98633I −9.54273 + 0.07763I
u = −0.511705 − 0.082203I
a = −0.71931 − 4.95483I
b = 0.076717 − 0.762273I
5.46748 + 2.98633I −9.54273 − 0.07763I
u = 1.49176 + 0.09347I
a = 0.04638 − 1.73361I
b = 0.526261 − 1.275590I
−8.28685 + 0.58022I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49176 − 0.09347I
a = 0.04638 + 1.73361I
b = 0.526261 + 1.275590I
−8.28685 − 0.58022I 0
u = 1.45601 + 0.33912I
a = 0.213193 + 1.364660I
b = −0.705900 + 1.030080I
−3.01725 − 5.77701I 0
u = 1.45601 − 0.33912I
a = 0.213193 − 1.364660I
b = −0.705900 − 1.030080I
−3.01725 + 5.77701I 0
u = −1.49951 + 0.23063I
a = 0.31462 + 1.91220I
b = 1.16988 + 1.31138I
−5.86501 + 10.90410I 0
u = −1.49951 − 0.23063I
a = 0.31462 − 1.91220I
b = 1.16988 − 1.31138I
−5.86501 − 10.90410I 0
u = −1.50089 + 0.31943I
a = −0.08694 − 1.91626I
b = −1.04827 − 1.23901I
2.16726 + 11.06000I 0
u = −1.50089 − 0.31943I
a = −0.08694 + 1.91626I
b = −1.04827 + 1.23901I
2.16726 − 11.06000I 0
u = 1.52101 + 0.22715I
a = −0.07136 − 1.47097I
b = 0.670679 − 1.121100I
−9.75078 − 5.99442I 0
u = 1.52101 − 0.22715I
a = −0.07136 + 1.47097I
b = 0.670679 + 1.121100I
−9.75078 + 5.99442I 0
u = 1.49977 + 0.35416I
a = −0.169871 − 1.334190I
b = 0.726021 − 1.048360I
−3.92744 − 11.62280I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49977 − 0.35416I
a = −0.169871 + 1.334190I
b = 0.726021 + 1.048360I
−3.92744 + 11.62280I 0
u = −1.44949 + 0.53145I
a = −0.163719 + 0.509241I
b = 0.266614 + 0.630247I
−0.92471 + 4.84296I 0
u = −1.44949 − 0.53145I
a = −0.163719 − 0.509241I
b = 0.266614 − 0.630247I
−0.92471 − 4.84296I 0
u = 0.138985 + 0.421598I
a = −2.15402 + 0.79461I
b = 0.495998 + 0.378459I
3.24864 + 1.94975I 1.19053 − 4.83237I
u = 0.138985 − 0.421598I
a = −2.15402 − 0.79461I
b = 0.495998 − 0.378459I
3.24864 − 1.94975I 1.19053 + 4.83237I
u = 0.214419 + 0.386537I
a = 2.09607 − 0.79831I
b = −0.523520 − 0.343025I
2.99114 − 3.65929I −0.015901 + 1.155769I
u = 0.214419 − 0.386537I
a = 2.09607 + 0.79831I
b = −0.523520 + 0.343025I
2.99114 + 3.65929I −0.015901 − 1.155769I
u = −1.52678 + 0.32069I
a = 0.08431 + 1.86114I
b = 1.06520 + 1.21191I
1.1224 + 17.2916I 0
u = −1.52678 − 0.32069I
a = 0.08431 − 1.86114I
b = 1.06520 − 1.21191I
1.1224 − 17.2916I 0
u = 0.236533 + 0.350847I
a = 0.500224 + 0.460847I
b = −1.36632 + 0.90743I
−0.050934 − 0.701211I −0.63507 + 10.01092I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.236533 − 0.350847I
a = 0.500224 − 0.460847I
b = −1.36632 − 0.90743I
−0.050934 + 0.701211I −0.63507 − 10.01092I
u = −1.59145 + 0.26362I
a = −0.134574 + 0.593608I
b = 0.167504 + 0.553471I
−5.30315 + 0.91565I 0
u = −1.59145 − 0.26362I
a = −0.134574 − 0.593608I
b = 0.167504 − 0.553471I
−5.30315 − 0.91565I 0
u = −0.044960 + 0.270419I
a = −6.63109 − 1.30460I
b = 0.334940 + 0.390113I
0.341234 − 0.326787I 14.7581 − 8.3281I
u = −0.044960 − 0.270419I
a = −6.63109 + 1.30460I
b = 0.334940 − 0.390113I
0.341234 + 0.326787I 14.7581 + 8.3281I
u = −1.78630 + 0.04448I
a = −0.015880 + 0.601472I
b = 0.020823 + 0.591274I
−1.85916 − 2.69456I 0
u = −1.78630 − 0.04448I
a = −0.015880 − 0.601472I
b = 0.020823 − 0.591274I
−1.85916 + 2.69456I 0
u = 0.208416
a = 2.54821
b = −0.467771
−1.37179 −7.17100
13
II. I
u
2
= hb + 1, 2a − u, u
2
− 2i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
2
a
4
=
1
2
u
−1
a
10
=
−u
−u
a
5
=
−
1
2
u − 2
−u − 3
a
8
=
u
u
a
3
=
−
1
2
u − 2
−u − 3
a
2
=
−
1
2
u − 1
−u − 1
a
11
=
−
1
2
u + 1
1
a
7
=
1
2
u + 1
u + 1
a
6
=
−1
−2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
(u − 1)
2
c
3
u
2
− 2u − 1
c
4
u
2
+ 2u − 1
c
5
, c
6
, c
10
c
11
(u + 1)
2
c
8
, c
9
, c
12
u
2
− 2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
10
c
11
(y −1)
2
c
3
, c
4
y
2
− 6y + 1
c
8
, c
9
, c
12
(y −2)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 0.707107
b = −1.00000
−4.93480 −8.00000
u = −1.41421
a = −0.707107
b = −1.00000
−4.93480 −8.00000
17
III. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
9
=
−1
0
a
12
=
1
0
a
1
=
1
0
a
4
=
0
1
a
10
=
−1
0
a
5
=
1
1
a
8
=
−1
0
a
3
=
1
1
a
2
=
2
1
a
11
=
1
1
a
7
=
−2
−1
a
6
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
10
, c
11
u − 1
c
5
, c
6
, c
7
u + 1
c
8
, c
9
, c
12
u
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
10
, c
11
y −1
c
8
, c
9
, c
12
y
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
0 0
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
88
+ 28u
87
+ ··· − 66u + 1)
c
2
((u − 1)
3
)(u
88
+ 4u
87
+ ··· + 2u + 1)
c
3
(u − 1)(u
2
− 2u − 1)(u
88
− 26u
87
+ ··· + 4u + 1)
c
4
(u − 1)(u
2
+ 2u − 1)(u
88
+ 32u
87
+ ··· − 1.76469 × 10
7
u − 2939221)
c
5
((u + 1)
3
)(u
88
+ 4u
87
+ ··· + 2u + 1)
c
6
((u + 1)
3
)(u
88
+ 28u
87
+ ··· − 66u + 1)
c
7
((u − 1)
2
)(u + 1)(u
88
− 2u
87
+ ··· − 34u − 1)
c
8
, c
9
, c
12
u(u
2
− 2)(u
88
+ 7u
87
+ ··· + 6u − 2)
c
10
(u − 1)(u + 1)
2
(u
88
− 2u
87
+ ··· − 34u − 1)
c
11
(u − 1)(u + 1)
2
(u
88
− 4u
87
+ ··· + 10u − 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y −1)
3
)(y
88
+ 68y
87
+ ··· − 1966y + 1)
c
2
, c
5
((y −1)
3
)(y
88
− 28y
87
+ ··· + 66y + 1)
c
3
(y −1)(y
2
− 6y + 1)(y
88
− 512y
87
+ ··· − 758y + 1)
c
4
(y −1)(y
2
− 6y + 1)
· (y
88
− 588y
87
+ ··· − 154392187987162y + 8639020086841)
c
7
, c
10
((y −1)
3
)(y
88
− 68y
87
+ ··· − 630y + 1)
c
8
, c
9
, c
12
y(y −2)
2
(y
88
− 85y
87
+ ··· + 28y + 4)
c
11
((y −1)
3
)(y
88
+ 4y
87
+ ··· − 70y + 1)
23
