12a
0529
(K12a
0529
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 9 11 2 1 5 12 6 4
Solving Sequence
4,10
5 9
1,6
8 3 12 11 7 2
c
4
c
9
c
5
c
8
c
3
c
12
c
10
c
6
c
2
c
1
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.53233 × 10
65
u
75
+ 2.53432 × 10
65
u
74
+ ··· + 3.87343 × 10
66
b + 4.07069 × 10
67
,
− 6.56457 × 10
66
u
75
+ 6.09413 × 10
66
u
74
+ ··· + 6.58484 × 10
67
a + 8.05766 × 10
68
,
u
76
− u
75
+ ··· − 158u + 17i
I
u
2
= h−u
3
+ b − u, −u
3
+ a, u
12
+ 4u
10
+ 6u
8
+ 5u
6
+ 3u
4
− u
3
+ u
2
− u + 1i
I
u
3
= hb − a − u, a
6
+ 6a
5
u + a
5
+ 5a
4
u − 16a
4
− 24a
3
u − 12a
3
− 16a
2
u + 21a
2
+ 10au + 12a + 4u − 1, u
2
+ 1i
I
u
4
= h−u
3
+ b − u, −u
3
+ a, u
18
+ 6u
16
+ ··· + 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 118 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−3.53 × 10
65
u
75
+ 2.53 × 10
65
u
74
+ · · · + 3.87 × 10
66
b + 4.07 ×
10
67
, −6.56 × 10
66
u
75
+ 6.09 × 10
66
u
74
+ · · · + 6.58 × 10
67
a + 8.06 ×
10
68
, u
76
− u
75
+ · · · − 158u + 17i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
9
=
−u
u
3
+ u
a
1
=
0.0996921u
75
− 0.0925479u
74
+ ··· + 85.8969u − 12.2367
0.0911937u
75
− 0.0654283u
74
+ ··· + 51.1583u − 10.5093
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
0.600810u
75
− 0.591223u
74
+ ··· + 251.305u − 43.7031
0.257472u
75
− 0.267396u
74
+ ··· + 57.0402u − 9.17170
a
3
=
0.723306u
75
− 0.563802u
74
+ ··· + 284.437u − 45.2027
0.217757u
75
− 0.0902812u
74
+ ··· + 78.2752u − 11.1735
a
12
=
0.00849846u
75
− 0.0271196u
74
+ ··· + 34.7387u − 1.72742
0.0911937u
75
− 0.0654283u
74
+ ··· + 51.1583u − 10.5093
a
11
=
0.0993703u
75
− 0.0950018u
74
+ ··· + 84.3319u − 12.4324
0.124410u
75
− 0.0564865u
74
+ ··· + 53.1573u − 10.4350
a
7
=
0.625336u
75
− 0.501248u
74
+ ··· + 242.513u − 48.2108
−0.0722923u
75
+ 0.0771458u
74
+ ··· − 12.4899u + 3.80427
a
2
=
1.62071u
75
− 1.09263u
74
+ ··· + 534.442u − 76.5897
0.191754u
75
− 0.0384194u
74
+ ··· + 32.9728u − 7.14572
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.569931u
75
+ 0.359505u
74
+ ··· − 304.744u + 50.6300
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ 36u
75
+ ··· + 19u + 4
c
2
, c
7
u
76
− 2u
75
+ ··· − 5u + 2
c
3
u
76
+ 2u
75
+ ··· − 1177u + 202
c
4
, c
5
, c
9
u
76
− u
75
+ ··· − 158u + 17
c
6
, c
11
u
76
− u
75
+ ··· − 100u + 17
c
8
u
76
− 10u
75
+ ··· − 18835u + 1862
c
10
u
76
− 29u
75
+ ··· − 3906u + 289
c
12
u
76
+ 8u
75
+ ··· + 1172713u + 156832
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
+ 8y
75
+ ··· + 191y + 16
c
2
, c
7
y
76
+ 36y
75
+ ··· + 19y + 4
c
3
y
76
− 20y
75
+ ··· − 1880229y + 40804
c
4
, c
5
, c
9
y
76
+ 81y
75
+ ··· − 13438y + 289
c
6
, c
11
y
76
+ 29y
75
+ ··· + 3906y + 289
c
8
y
76
+ 12y
75
+ ··· + 54812019y + 3467044
c
10
y
76
+ 49y
75
+ ··· + 20899954y + 83521
c
12
y
76
+ 24y
75
+ ··· + 1500857096879y + 24596276224
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.871703 + 0.337657I
a = 0.531191 − 0.397620I
b = −0.72291 − 1.41153I
−0.96411 + 12.75580I 0
u = 0.871703 − 0.337657I
a = 0.531191 + 0.397620I
b = −0.72291 + 1.41153I
−0.96411 − 12.75580I 0
u = −0.341605 + 0.864408I
a = −0.850996 + 0.602062I
b = −0.568836 + 0.390828I
−2.34126 − 6.14169I 0
u = −0.341605 − 0.864408I
a = −0.850996 − 0.602062I
b = −0.568836 − 0.390828I
−2.34126 + 6.14169I 0
u = −0.154405 + 0.907290I
a = −0.406956 + 0.726577I
b = −0.308364 + 0.691108I
−3.62597 + 0.74459I 0
u = −0.154405 − 0.907290I
a = −0.406956 − 0.726577I
b = −0.308364 − 0.691108I
−3.62597 − 0.74459I 0
u = 0.835900 + 0.374263I
a = 0.683754 − 0.340500I
b = −0.536338 − 1.288420I
−3.08946 + 4.96821I 0
u = 0.835900 − 0.374263I
a = 0.683754 + 0.340500I
b = −0.536338 + 1.288420I
−3.08946 − 4.96821I 0
u = −0.850183 + 0.331328I
a = −0.543534 − 0.324415I
b = 0.72960 − 1.31268I
1.39164 − 7.76709I 0
u = −0.850183 − 0.331328I
a = −0.543534 + 0.324415I
b = 0.72960 + 1.31268I
1.39164 + 7.76709I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.742033 + 0.489974I
a = −1.023820 − 0.198435I
b = 0.045626 − 0.959753I
−4.05338 − 4.76438I 0. + 6.53613I
u = −0.742033 − 0.489974I
a = −1.023820 + 0.198435I
b = 0.045626 + 0.959753I
−4.05338 + 4.76438I 0. − 6.53613I
u = −0.682242 + 0.569438I
a = −1.158730 − 0.084714I
b = −0.222157 − 0.733705I
−2.82768 + 2.89502I 0
u = −0.682242 − 0.569438I
a = −1.158730 + 0.084714I
b = −0.222157 + 0.733705I
−2.82768 − 2.89502I 0
u = −0.789625 + 0.287686I
a = −0.527894 − 0.089515I
b = 0.842261 − 1.020140I
2.89325 − 5.78254I 6.56857 + 7.64192I
u = −0.789625 − 0.287686I
a = −0.527894 + 0.089515I
b = 0.842261 + 1.020140I
2.89325 + 5.78254I 6.56857 − 7.64192I
u = 0.648168 + 0.502376I
a = 1.058750 − 0.048900I
b = −0.003990 − 0.637730I
−0.33883 + 1.60186I 1.60546 − 3.53406I
u = 0.648168 − 0.502376I
a = 1.058750 + 0.048900I
b = −0.003990 + 0.637730I
−0.33883 − 1.60186I 1.60546 + 3.53406I
u = 0.296301 + 0.763935I
a = 0.741212 + 0.381539I
b = 0.358971 + 0.318208I
−0.23116 + 1.74291I −0.33130 − 4.94390I
u = 0.296301 − 0.763935I
a = 0.741212 − 0.381539I
b = 0.358971 − 0.318208I
−0.23116 − 1.74291I −0.33130 + 4.94390I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.737315 + 0.251878I
a = 0.553553 + 0.102566I
b = −0.910825 − 0.780758I
2.01584 + 1.14854I 5.44751 − 1.47076I
u = 0.737315 − 0.251878I
a = 0.553553 − 0.102566I
b = −0.910825 + 0.780758I
2.01584 − 1.14854I 5.44751 + 1.47076I
u = 0.075673 + 1.290750I
a = −0.992398 + 0.464694I
b = −1.59071 + 0.73360I
−1.73230 − 4.32456I 0
u = 0.075673 − 1.290750I
a = −0.992398 − 0.464694I
b = −1.59071 − 0.73360I
−1.73230 + 4.32456I 0
u = −0.096475 + 1.302650I
a = 0.965712 + 0.242844I
b = 1.61430 + 0.52832I
0.119164 − 0.754172I 0
u = −0.096475 − 1.302650I
a = 0.965712 − 0.242844I
b = 1.61430 − 0.52832I
0.119164 + 0.754172I 0
u = −0.147580 + 1.317830I
a = 0.943837 − 0.268717I
b = 1.69097 + 0.06926I
0.41502 − 3.35037I 0
u = −0.147580 − 1.317830I
a = 0.943837 + 0.268717I
b = 1.69097 − 0.06926I
0.41502 + 3.35037I 0
u = 0.172897 + 1.322130I
a = −0.933142 − 0.519121I
b = −1.72379 − 0.15408I
−1.15919 + 8.40041I 0
u = 0.172897 − 1.322130I
a = −0.933142 + 0.519121I
b = −1.72379 + 0.15408I
−1.15919 − 8.40041I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.096112 + 1.369190I
a = −0.414099 + 0.096497I
b = −1.162900 + 0.290588I
−4.86388 + 2.38505I 0
u = 0.096112 − 1.369190I
a = −0.414099 − 0.096497I
b = −1.162900 − 0.290588I
−4.86388 − 2.38505I 0
u = 0.574787 + 0.059330I
a = 0.755800 + 1.027700I
b = −1.230110 + 0.059628I
3.16394 + 5.76384I 7.59245 − 6.65665I
u = 0.574787 − 0.059330I
a = 0.755800 − 1.027700I
b = −1.230110 − 0.059628I
3.16394 − 5.76384I 7.59245 + 6.65665I
u = −0.15045 + 1.41553I
a = −0.03804 + 1.43925I
b = −0.619065 + 1.211410I
−5.22619 + 0.59013I 0
u = −0.15045 − 1.41553I
a = −0.03804 − 1.43925I
b = −0.619065 − 1.211410I
−5.22619 − 0.59013I 0
u = 0.19788 + 1.43555I
a = 0.03726 + 1.65451I
b = 0.61403 + 1.34363I
−4.71578 + 4.11924I 0
u = 0.19788 − 1.43555I
a = 0.03726 − 1.65451I
b = 0.61403 − 1.34363I
−4.71578 − 4.11924I 0
u = 0.28500 + 1.42398I
a = −0.01702 − 1.54807I
b = −1.07658 − 1.19558I
−3.37812 + 4.85193I 0
u = 0.28500 − 1.42398I
a = −0.01702 + 1.54807I
b = −1.07658 + 1.19558I
−3.37812 − 4.85193I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.278329 + 0.467042I
a = 0.924246 − 0.203547I
b = −0.054022 + 0.191619I
0.259106 + 1.284090I 2.32882 − 5.74974I
u = 0.278329 − 0.467042I
a = 0.924246 + 0.203547I
b = −0.054022 − 0.191619I
0.259106 − 1.284090I 2.32882 + 5.74974I
u = −0.30726 + 1.43756I
a = −0.10602 − 1.73731I
b = 0.99502 − 1.37945I
−2.64476 − 9.75402I 0
u = −0.30726 − 1.43756I
a = −0.10602 + 1.73731I
b = 0.99502 + 1.37945I
−2.64476 + 9.75402I 0
u = −0.512415 + 0.037742I
a = −1.03347 + 1.23529I
b = 1.150490 + 0.265747I
4.65569 − 1.02094I 10.89176 + 0.78170I
u = −0.512415 − 0.037742I
a = −1.03347 − 1.23529I
b = 1.150490 − 0.265747I
4.65569 + 1.02094I 10.89176 − 0.78170I
u = −0.33234 + 1.46432I
a = −0.34154 − 1.94756I
b = 0.81603 − 1.59781I
−4.37511 − 12.05130I 0
u = −0.33234 − 1.46432I
a = −0.34154 + 1.94756I
b = 0.81603 + 1.59781I
−4.37511 + 12.05130I 0
u = 0.23373 + 1.48440I
a = −0.06822 + 1.91050I
b = 0.55244 + 1.51628I
−6.60995 + 6.08840I 0
u = 0.23373 − 1.48440I
a = −0.06822 − 1.91050I
b = 0.55244 − 1.51628I
−6.60995 − 6.08840I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22302 + 1.48750I
a = 0.518649 − 1.000800I
b = −0.533732 − 0.791660I
−6.77024 + 4.75215I 0
u = 0.22302 − 1.48750I
a = 0.518649 + 1.000800I
b = −0.533732 + 0.791660I
−6.77024 − 4.75215I 0
u = 0.34151 + 1.47055I
a = 0.39657 − 2.02539I
b = −0.77786 − 1.67431I
−6.7695 + 17.1494I 0
u = 0.34151 − 1.47055I
a = 0.39657 + 2.02539I
b = −0.77786 + 1.67431I
−6.7695 − 17.1494I 0
u = −0.09089 + 1.50978I
a = 0.495455 + 1.282740I
b = −0.266796 + 1.066350I
−8.01141 + 1.22205I 0
u = −0.09089 − 1.50978I
a = 0.495455 − 1.282740I
b = −0.266796 − 1.066350I
−8.01141 − 1.22205I 0
u = 0.31811 + 1.48037I
a = 0.47750 − 1.82213I
b = −0.67878 − 1.50521I
−9.06725 + 9.15754I 0
u = 0.31811 − 1.48037I
a = 0.47750 + 1.82213I
b = −0.67878 + 1.50521I
−9.06725 − 9.15754I 0
u = −0.24631 + 1.49576I
a = 0.07793 + 1.99376I
b = −0.54974 + 1.57474I
−9.0697 − 11.1049I 0
u = −0.24631 − 1.49576I
a = 0.07793 − 1.99376I
b = −0.54974 − 1.57474I
−9.0697 + 11.1049I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.21177 + 1.50566I
a = 0.21791 + 1.87599I
b = −0.44690 + 1.49711I
−11.13890 − 3.08586I 0
u = −0.21177 − 1.50566I
a = 0.21791 − 1.87599I
b = −0.44690 − 1.49711I
−11.13890 + 3.08586I 0
u = −0.20729 + 1.51082I
a = −0.712545 − 0.860726I
b = 0.347976 − 0.695792I
−9.63663 − 0.24582I 0
u = −0.20729 − 1.51082I
a = −0.712545 + 0.860726I
b = 0.347976 + 0.695792I
−9.63663 + 0.24582I 0
u = −0.24937 + 1.50646I
a = −0.687883 − 1.221840I
b = 0.415475 − 1.005740I
−10.56700 − 8.34790I 0
u = −0.24937 − 1.50646I
a = −0.687883 + 1.221840I
b = 0.415475 + 1.005740I
−10.56700 + 8.34790I 0
u = 0.12347 + 1.52923I
a = −0.54368 + 1.49764I
b = 0.218811 + 1.221180I
−12.01490 + 2.19277I 0
u = 0.12347 − 1.52923I
a = −0.54368 − 1.49764I
b = 0.218811 − 1.221180I
−12.01490 − 2.19277I 0
u = 0.07739 + 1.53445I
a = −0.659918 + 1.245080I
b = 0.147057 + 1.026510I
−10.74150 − 5.90257I 0
u = 0.07739 − 1.53445I
a = −0.659918 − 1.245080I
b = 0.147057 − 1.026510I
−10.74150 + 5.90257I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.405149 + 0.030083I
a = −1.61760 − 1.88667I
b = 1.048300 − 0.659964I
4.09237 − 1.00331I 10.38328 + 0.46979I
u = −0.405149 − 0.030083I
a = −1.61760 + 1.88667I
b = 1.048300 + 0.659964I
4.09237 + 1.00331I 10.38328 − 0.46979I
u = 0.373698 + 0.075865I
a = 1.72252 − 2.37204I
b = −1.054630 − 0.839020I
2.05319 + 5.88077I 6.97041 − 5.00849I
u = 0.373698 − 0.075865I
a = 1.72252 + 2.37204I
b = −1.054630 + 0.839020I
2.05319 − 5.88077I 6.97041 + 5.00849I
u = 0.256387 + 0.066382I
a = 3.22271 + 0.78997I
b = −0.548321 + 0.680367I
−0.110048 + 1.027080I 3.94313 − 1.31174I
u = 0.256387 − 0.066382I
a = 3.22271 − 0.78997I
b = −0.548321 − 0.680367I
−0.110048 − 1.027080I 3.94313 + 1.31174I
12
II.
I
u
2
= h−u
3
+ b − u, −u
3
+ a, u
12
+ 4u
10
+ 6u
8
+ 5u
6
+ 3u
4
− u
3
+ u
2
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
9
=
−u
u
3
+ u
a
1
=
u
3
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
u
9
+ 2u
7
+ u
5
− u
u
9
+ 3u
7
+ 3u
5
+ 2u
3
+ u
a
3
=
u
10
− u
9
+ 3u
8
− 2u
7
+ 4u
6
− u
5
+ 3u
4
+ u
2
+ 1
−u
9
− 3u
7
+ u
6
− 3u
5
+ 2u
4
− 2u
3
+ u
2
− u + 1
a
12
=
−u
u
3
+ u
a
11
=
u
3
−u
5
− u
3
+ u
a
7
=
u
4
+ u
2
+ 1
−u
6
− 2u
4
− u
2
a
2
=
u
10
− u
9
+ 3u
8
− 3u
7
+ 4u
6
− 3u
5
+ 3u
4
− 2u
3
+ u
2
− u + 1
u
6
+ 2u
4
− u
3
+ u
2
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
9
− 12u
7
− 4u
6
− 12u
5
− 8u
4
− 4u
3
− 4u
2
+ 2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
c
2
, c
7
, c
12
(u
4
+ u
2
− u + 1)
3
c
3
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
3
c
4
, c
5
, c
6
c
9
, c
11
u
12
+ 4u
10
+ 6u
8
+ 5u
6
+ 3u
4
− u
3
+ u
2
− u + 1
c
10
u
12
− 8u
11
+ ··· − u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
c
2
, c
7
, c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
c
3
(y
4
− y
3
+ 2y
2
+ 7y + 4)
3
c
4
, c
5
, c
6
c
9
, c
11
y
12
+ 8y
11
+ ··· + y + 1
c
10
y
12
− 8y
11
+ ··· + 9y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.400261 + 0.917946I
a = 0.947685 − 0.332294I
b = 0.547424 + 0.585652I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = −0.400261 − 0.917946I
a = 0.947685 + 0.332294I
b = 0.547424 − 0.585652I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = 0.590343 + 0.870977I
a = −1.137770 + 0.249897I
b = −0.547424 + 1.120870I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = 0.590343 − 0.870977I
a = −1.137770 − 0.249897I
b = −0.547424 − 1.120870I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = −0.709936 + 0.494274I
a = 0.162512 + 0.626600I
b = −0.547424 + 1.120870I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = −0.709936 − 0.494274I
a = 0.162512 − 0.626600I
b = −0.547424 − 1.120870I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = −0.152052 + 1.241420I
a = 0.69948 − 1.82707I
b = 0.547424 − 0.585652I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = −0.152052 − 1.241420I
a = 0.69948 + 1.82707I
b = 0.547424 + 0.585652I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.552313 + 0.323472I
a = −0.004890 + 0.262180I
b = 0.547424 + 0.585652I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.552313 − 0.323472I
a = −0.004890 − 0.262180I
b = 0.547424 − 0.585652I
0.98010 − 1.39709I 3.77019 + 3.86736I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.119592 + 1.365250I
a = −0.66702 − 2.48612I
b = −0.547424 − 1.120870I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = 0.119592 − 1.365250I
a = −0.66702 + 2.48612I
b = −0.547424 + 1.120870I
−2.62503 − 7.64338I −1.77019 + 6.51087I
17
III. I
u
3
= hb − a − u, 6a
5
u + 5a
4
u + · · · + 12a − 1, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
1
a
9
=
−u
0
a
1
=
a
a + u
a
6
=
0
1
a
8
=
a
2
u − a − u
a
2
u − 2a − u
a
3
=
a
4
+ 3a
3
u − 4a
2
− 3au + 2
a
4
+ 4a
3
u − 6a
2
− 4au + 1
a
12
=
−u
a + u
a
11
=
−u
a + 2u
a
7
=
1
au − 1
a
2
=
a
5
u − 4a
4
− 8a
3
u + 9a
2
+ 6au − 1
a
5
+ 5a
4
u + a
4
+ 4a
3
u − 12a
3
− 16a
2
u − 7a
2
− 6au + 12a + 4u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
4
− 16a
3
u + 28a
2
+ 24au + 4a + 4u − 8
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
, c
7
, c
8
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
3
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
4
, c
5
, c
6
c
9
, c
11
(u
2
+ 1)
6
c
10
(u + 1)
12
c
12
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
7
, c
8
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
3
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
4
, c
5
, c
6
c
9
, c
11
(y + 1)
12
c
10
(y − 1)
12
c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.073950 − 0.441248I
b = −1.073950 + 0.558752I
− 5.69302I 2.00000 + 5.51057I
u = 1.000000I
a = 1.002190 − 0.704458I
b = 1.002190 + 0.295542I
1.89061 + 0.92430I 5.71672 − 0.79423I
u = 1.000000I
a = −0.428243 − 0.335469I
b = −0.428243 + 0.664531I
−1.89061 + 0.92430I −1.71672 − 0.79423I
u = 1.000000I
a = 1.00219 − 1.29554I
b = 1.002190 − 0.295542I
1.89061 − 0.92430I 5.71672 + 0.79423I
u = 1.000000I
a = −0.42824 − 1.66453I
b = −0.428243 − 0.664531I
−1.89061 − 0.92430I −1.71672 + 0.79423I
u = 1.000000I
a = −1.07395 − 1.55875I
b = −1.073950 − 0.558752I
5.69302I 2.00000 − 5.51057I
u = − 1.000000I
a = −1.073950 + 0.441248I
b = −1.073950 − 0.558752I
5.69302I 2.00000 − 5.51057I
u = − 1.000000I
a = 1.002190 + 0.704458I
b = 1.002190 − 0.295542I
1.89061 − 0.92430I 5.71672 + 0.79423I
u = − 1.000000I
a = −0.428243 + 0.335469I
b = −0.428243 − 0.664531I
−1.89061 − 0.92430I −1.71672 + 0.79423I
u = − 1.000000I
a = 1.00219 + 1.29554I
b = 1.002190 + 0.295542I
1.89061 + 0.92430I 5.71672 − 0.79423I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = −0.42824 + 1.66453I
b = −0.428243 + 0.664531I
−1.89061 + 0.92430I −1.71672 − 0.79423I
u = − 1.000000I
a = −1.07395 + 1.55875I
b = −1.073950 + 0.558752I
− 5.69302I 2.00000 + 5.51057I
22
IV. I
u
4
= h−u
3
+ b − u, −u
3
+ a, u
18
+ 6u
16
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
9
=
−u
u
3
+ u
a
1
=
u
3
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
u
9
+ 2u
7
+ u
5
− u
u
9
+ 3u
7
+ 3u
5
+ 2u
3
+ u
a
3
=
u
16
+ u
15
+ ··· + 2u + 2
u
15
+ 5u
13
+ 10u
11
+ 12u
9
+ 11u
7
+ u
6
+ 7u
5
+ 2u
4
+ 4u
3
+ u
2
+ 2u + 1
a
12
=
−u
u
3
+ u
a
11
=
u
3
−u
5
− u
3
+ u
a
7
=
u
4
+ u
2
+ 1
−u
6
− 2u
4
− u
2
a
2
=
2u
16
+ 10u
14
+ ··· + 2u + 1
2u
15
+ 10u
13
+ ··· + 3u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
9
− 12u
7
− 12u
5
− 8u
3
− 4u − 2
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
c
2
, c
7
, c
12
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
c
3
(u
3
+ u
2
− 1)
6
c
4
, c
5
, c
6
c
9
, c
11
u
18
+ 6u
16
+ ··· + 2u + 1
c
10
u
18
− 12u
17
+ ··· − 2u
3
+ 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
c
2
, c
7
, c
12
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
c
3
(y
3
− y
2
+ 2y − 1)
6
c
4
, c
5
, c
6
c
9
, c
11
y
18
+ 12y
17
+ ··· + 2y
3
+ 1
c
10
y
18
− 12y
17
+ ··· + 32y
2
+ 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.548726 + 0.858326I
a = 1.047560 + 0.142976I
b = 0.498832 + 1.001300I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.548726 − 0.858326I
a = 1.047560 − 0.142976I
b = 0.498832 − 1.001300I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.588153 + 0.781101I
a = −0.873073 + 0.334040I
b = −0.284920 + 1.115140I
−4.40332 −5.01951 + 0.I
u = 0.588153 − 0.781101I
a = −0.873073 − 0.334040I
b = −0.284920 − 1.115140I
−4.40332 −5.01951 + 0.I
u = 0.345660 + 1.030350I
a = −1.059570 − 0.724507I
b = −0.713912 + 0.305839I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.345660 − 1.030350I
a = −1.059570 + 0.724507I
b = −0.713912 − 0.305839I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.651446 + 0.573590I
a = 0.366526 + 0.541550I
b = −0.284920 + 1.115140I
−4.40332 −5.01951 + 0.I
u = −0.651446 − 0.573590I
a = 0.366526 − 0.541550I
b = −0.284920 − 1.115140I
−4.40332 −5.01951 + 0.I
u = 0.663361 + 0.478912I
a = −0.164529 + 0.522390I
b = 0.498832 + 1.001300I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.663361 − 0.478912I
a = −0.164529 − 0.522390I
b = 0.498832 − 1.001300I
−0.26574 − 2.82812I 1.50976 + 2.97945I
26
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.224719 + 1.187070I
a = −0.93863 − 1.49291I
b = −0.713912 − 0.305839I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.224719 − 1.187070I
a = −0.93863 + 1.49291I
b = −0.713912 + 0.305839I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.114635 + 1.337240I
a = 0.61347 − 2.33854I
b = 0.498832 − 1.001300I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.114635 − 1.337240I
a = 0.61347 + 2.33854I
b = 0.498832 + 1.001300I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.063294 + 1.354690I
a = −0.34821 − 2.46983I
b = −0.284920 − 1.115140I
−4.40332 −5.01951 + 0.I
u = 0.063294 − 1.354690I
a = −0.34821 + 2.46983I
b = −0.284920 + 1.115140I
−4.40332 −5.01951 + 0.I
u = −0.570379 + 0.156725I
a = −0.143533 + 0.149114I
b = −0.713912 + 0.305839I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.570379 − 0.156725I
a = −0.143533 − 0.149114I
b = −0.713912 − 0.305839I
−0.26574 − 2.82812I 1.50976 + 2.97945I
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· ((u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
)(u
76
+ 36u
75
+ ··· + 19u + 4)
c
2
, c
7
(u
4
+ u
2
− u + 1)
3
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
· (u
12
+ 3u
10
+ ··· + u
2
+ 1)(u
76
− 2u
75
+ ··· − 5u + 2)
c
3
(u
3
+ u
2
− 1)
6
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
3
· (u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1)(u
76
+ 2u
75
+ ··· − 1177u + 202)
c
4
, c
5
, c
9
(u
2
+ 1)
6
(u
12
+ 4u
10
+ 6u
8
+ 5u
6
+ 3u
4
− u
3
+ u
2
− u + 1)
· (u
18
+ 6u
16
+ ··· + 2u + 1)(u
76
− u
75
+ ··· − 158u + 17)
c
6
, c
11
(u
2
+ 1)
6
(u
12
+ 4u
10
+ 6u
8
+ 5u
6
+ 3u
4
− u
3
+ u
2
− u + 1)
· (u
18
+ 6u
16
+ ··· + 2u + 1)(u
76
− u
75
+ ··· − 100u + 17)
c
8
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
· (u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1)
· (u
76
− 10u
75
+ ··· − 18835u + 1862)
c
10
((u + 1)
12
)(u
12
− 8u
11
+ ··· − u + 1)(u
18
− 12u
17
+ ··· − 2u
3
+ 1)
· (u
76
− 29u
75
+ ··· − 3906u + 289)
c
12
(u
4
+ u
2
− u + 1)
3
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
· (u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
· (u
76
+ 8u
75
+ ··· + 1172713u + 156832)
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
· ((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
76
+ 8y
75
+ ··· + 191y + 16)
c
2
, c
7
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
· ((y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
)(y
76
+ 36y
75
+ ··· + 19y + 4)
c
3
(y
3
− y
2
+ 2y − 1)
6
(y
4
− y
3
+ 2y
2
+ 7y + 4)
3
· (y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
· (y
76
− 20y
75
+ ··· − 1880229y + 40804)
c
4
, c
5
, c
9
((y + 1)
12
)(y
12
+ 8y
11
+ ··· + y + 1)(y
18
+ 12y
17
+ ··· + 2y
3
+ 1)
· (y
76
+ 81y
75
+ ··· − 13438y + 289)
c
6
, c
11
((y + 1)
12
)(y
12
+ 8y
11
+ ··· + y + 1)(y
18
+ 12y
17
+ ··· + 2y
3
+ 1)
· (y
76
+ 29y
75
+ ··· + 3906y + 289)
c
8
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
· (y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
· (y
76
+ 12y
75
+ ··· + 54812019y + 3467044)
c
10
((y − 1)
12
)(y
12
− 8y
11
+ ··· + 9y + 1)(y
18
− 12y
17
+ ··· + 32y
2
+ 1)
· (y
76
+ 49y
75
+ ··· + 20899954y + 83521)
c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
· (y
76
+ 24y
75
+ ··· + 1500857096879y + 24596276224)
29
