12a
0115
(K12a
0115
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 9 4 11 6 1 7 10
Solving Sequence
4,7 8,11
9 12 3 6 5 2 1 10
c
7
c
8
c
11
c
3
c
6
c
5
c
2
c
1
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.03066 × 10
465
u
124
+ 3.82536 × 10
465
u
123
+ ··· + 1.54622 × 10
467
b + 1.91851 × 10
468
,
7.22439 × 10
466
u
124
+ 2.12080 × 10
467
u
123
+ ··· + 2.31933 × 10
468
a + 1.10931 × 10
470
,
u
125
+ 2u
124
+ ··· + 512u + 512i
I
u
2
= hb, 3a + 3u − 5, u
2
− u − 1i
I
v
1
= ha, 16726v
8
− 41423v
7
+ ··· + 11959b + 26601,
v
9
− 3v
8
− 2v
7
− 6v
6
+ 25v
5
− 11v
4
− 9v
3
+ 2v
2
+ 3v −1i
* 3 irreducible components of dim
C
= 0, with total 136 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
= h1.03 × 10
465
u
124
+ 3.83 × 10
465
u
123
+ · · · + 1.55 × 10
467
b + 1.92 ×
10
468
, 7.22 × 10
466
u
124
+ 2.12 × 10
467
u
123
+ · · · + 2.32 × 10
468
a + 1.11 ×
10
470
, u
125
+ 2u
124
+ · · · + 512u + 512i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
−0.0311487u
124
− 0.0914405u
123
+ ··· − 13.8068u − 47.8291
−0.00666572u
124
− 0.0247401u
123
+ ··· − 5.19981u − 12.4077
a
9
=
−0.0129299u
124
− 0.0674498u
123
+ ··· + 31.3986u − 57.3336
0.00112353u
124
+ 0.0331708u
123
+ ··· − 7.29416u + 30.7948
a
12
=
−0.0378144u
124
− 0.116181u
123
+ ··· − 19.0066u − 60.2369
−0.00666572u
124
− 0.0247401u
123
+ ··· − 5.19981u − 12.4077
a
3
=
u
u
3
+ u
a
6
=
−0.0591666u
124
− 0.127059u
123
+ ··· − 50.3219u − 34.3988
−0.0116249u
124
− 0.0371386u
123
+ ··· + 1.86792u − 26.7347
a
5
=
−0.0241892u
124
− 0.0463826u
123
+ ··· − 18.7830u − 12.5336
−0.0277806u
124
− 0.0245777u
123
+ ··· − 33.9805u + 8.02032
a
2
=
−0.0165610u
124
+ 0.00694800u
123
+ ··· − 26.5606u + 21.5758
−0.0651205u
124
− 0.0919181u
123
+ ··· − 57.3802u − 11.4736
a
1
=
−0.00359135u
124
+ 0.0218049u
123
+ ··· − 15.1975u + 20.5539
−0.0514815u
124
− 0.0693144u
123
+ ··· − 46.9834u − 6.82131
a
10
=
−0.0277532u
124
− 0.0756995u
123
+ ··· − 20.2561u − 33.4474
0.0514815u
124
+ 0.0693144u
123
+ ··· + 46.9834u + 6.82131
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0955818u
124
− 0.136137u
123
+ ··· − 86.1084u − 11.1303
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
125
+ 63u
124
+ ··· + 271u + 1
c
2
, c
4
u
125
− 11u
124
+ ··· − 9u − 1
c
3
, c
7
u
125
+ 2u
124
+ ··· + 512u + 512
c
5
9(9u
125
− 12u
124
+ ··· + 2.83664 × 10
9
u + 2.59859 × 10
8
)
c
6
, c
9
u
125
− 3u
124
+ ··· + 3u − 1
c
8
9(9u
125
− 21u
124
+ ··· + 1.22889 × 10
8
u + 5290529)
c
10
, c
12
u
125
+ 4u
124
+ ··· − 2358u + 81
c
11
u
125
− 2u
124
+ ··· − 756u + 324
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
125
+ 9y
124
+ ··· + 91007y −1
c
2
, c
4
y
125
− 63y
124
+ ··· + 271y −1
c
3
, c
7
y
125
+ 54y
124
+ ··· − 1572864y −262144
c
5
81(81y
125
− 3294y
124
+ ··· + 2.87254 × 10
18
y −6.75265 × 10
16
)
c
6
, c
9
y
125
+ 85y
124
+ ··· + 31y −1
c
8
81
· (81y
125
− 4023y
124
+ ··· + 7567318376329835y −27989697099841)
c
10
, c
12
y
125
− 90y
124
+ ··· + 665982y −6561
c
11
y
125
− 12y
124
+ ··· + 16685352y −104976
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.189225 + 0.989929I
a = −2.72604 − 1.67999I
b = 0.545603 − 0.015975I
4.85915 + 0.90928I 0
u = −0.189225 − 0.989929I
a = −2.72604 + 1.67999I
b = 0.545603 + 0.015975I
4.85915 − 0.90928I 0
u = 0.913335 + 0.327879I
a = −0.13404 − 1.61461I
b = 1.42964 − 1.22199I
4.24550 + 3.85404I 0
u = 0.913335 − 0.327879I
a = −0.13404 + 1.61461I
b = 1.42964 + 1.22199I
4.24550 − 3.85404I 0
u = 0.532227 + 0.797562I
a = 1.88338 + 0.31904I
b = −0.465658 + 0.870917I
−4.18791 − 0.46329I 0
u = 0.532227 − 0.797562I
a = 1.88338 − 0.31904I
b = −0.465658 − 0.870917I
−4.18791 + 0.46329I 0
u = 0.495636 + 0.814877I
a = 0.168018 + 0.065540I
b = 0.221515 + 1.197440I
−4.15405 − 3.73457I 0
u = 0.495636 − 0.814877I
a = 0.168018 − 0.065540I
b = 0.221515 − 1.197440I
−4.15405 + 3.73457I 0
u = 0.080750 + 1.051060I
a = 1.320830 + 0.182380I
b = −0.932530 − 0.275816I
2.33153 + 1.50993I 0
u = 0.080750 − 1.051060I
a = 1.320830 − 0.182380I
b = −0.932530 + 0.275816I
2.33153 − 1.50993I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.413672 + 0.836934I
a = −0.275409 − 0.177834I
b = −0.74713 + 1.37671I
−0.983702 − 0.642828I 0
u = −0.413672 − 0.836934I
a = −0.275409 + 0.177834I
b = −0.74713 − 1.37671I
−0.983702 + 0.642828I 0
u = 0.918385 + 0.543413I
a = 0.240683 + 0.155590I
b = 0.604955 + 0.884379I
−3.67094 + 2.96823I 0
u = 0.918385 − 0.543413I
a = 0.240683 − 0.155590I
b = 0.604955 − 0.884379I
−3.67094 − 2.96823I 0
u = −0.422750 + 0.821064I
a = −3.17983 + 0.68595I
b = 1.19189 + 1.04668I
−1.03348 + 4.20848I 0
u = −0.422750 − 0.821064I
a = −3.17983 − 0.68595I
b = 1.19189 − 1.04668I
−1.03348 − 4.20848I 0
u = −0.962365 + 0.485559I
a = −0.437124 − 0.102030I
b = −1.34087 + 1.13393I
−0.31912 − 6.67340I 0
u = −0.962365 − 0.485559I
a = −0.437124 + 0.102030I
b = −1.34087 − 1.13393I
−0.31912 + 6.67340I 0
u = −0.807203 + 0.430889I
a = 0.056330 + 0.856214I
b = −0.364132 − 0.128397I
−0.121971 − 0.719876I 0
u = −0.807203 − 0.430889I
a = 0.056330 − 0.856214I
b = −0.364132 + 0.128397I
−0.121971 + 0.719876I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.828223 + 0.376343I
a = 1.21716 − 1.20280I
b = −0.702944 − 0.443518I
0.06073 − 2.33875I 0
u = −0.828223 − 0.376343I
a = 1.21716 + 1.20280I
b = −0.702944 + 0.443518I
0.06073 + 2.33875I 0
u = −0.599973 + 0.683518I
a = −0.077597 + 0.147796I
b = 0.471466 + 0.834279I
1.14990 + 7.95106I 0
u = −0.599973 − 0.683518I
a = −0.077597 − 0.147796I
b = 0.471466 − 0.834279I
1.14990 − 7.95106I 0
u = 0.402370 + 1.037470I
a = −0.86209 − 1.36616I
b = 0.498531 − 0.049477I
3.98203 − 1.01780I 0
u = 0.402370 − 1.037470I
a = −0.86209 + 1.36616I
b = 0.498531 + 0.049477I
3.98203 + 1.01780I 0
u = 1.090330 + 0.256832I
a = −0.0476149 + 0.1171240I
b = 1.10513 + 0.90387I
6.12909 + 7.71732I 0
u = 1.090330 − 0.256832I
a = −0.0476149 − 0.1171240I
b = 1.10513 − 0.90387I
6.12909 − 7.71732I 0
u = −0.248400 + 1.101470I
a = −1.33263 + 0.83830I
b = 0.354052 + 0.770723I
4.76652 + 0.18641I 0
u = −0.248400 − 1.101470I
a = −1.33263 − 0.83830I
b = 0.354052 − 0.770723I
4.76652 − 0.18641I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.433618 + 1.055720I
a = 2.35530 − 0.20832I
b = −1.11177 − 1.01672I
3.54058 + 9.87816I 0
u = −0.433618 − 1.055720I
a = 2.35530 + 0.20832I
b = −1.11177 + 1.01672I
3.54058 − 9.87816I 0
u = −0.442173 + 1.054840I
a = 1.210110 − 0.399870I
b = −1.063990 − 0.003120I
1.15542 + 3.12032I 0
u = −0.442173 − 1.054840I
a = 1.210110 + 0.399870I
b = −1.063990 + 0.003120I
1.15542 − 3.12032I 0
u = −0.840842 + 0.156626I
a = 0.52324 − 1.86364I
b = 0.84914 − 1.46811I
4.74563 + 0.17252I 5.48395 + 0.I
u = −0.840842 − 0.156626I
a = 0.52324 + 1.86364I
b = 0.84914 + 1.46811I
4.74563 − 0.17252I 5.48395 + 0.I
u = −0.064934 + 1.160180I
a = −1.74953 + 0.85168I
b = 1.73930 − 0.46575I
5.99018 − 4.39123I 0
u = −0.064934 − 1.160180I
a = −1.74953 − 0.85168I
b = 1.73930 + 0.46575I
5.99018 + 4.39123I 0
u = 0.380832 + 1.099280I
a = −1.49403 + 0.23024I
b = 0.649724 − 0.705708I
−1.50629 − 4.23005I 0
u = 0.380832 − 1.099280I
a = −1.49403 − 0.23024I
b = 0.649724 + 0.705708I
−1.50629 + 4.23005I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.349086 + 1.109990I
a = −1.222110 − 0.226288I
b = 0.746699 + 0.641099I
4.36419 − 2.43164I 0
u = 0.349086 − 1.109990I
a = −1.222110 + 0.226288I
b = 0.746699 − 0.641099I
4.36419 + 2.43164I 0
u = 0.375408 + 1.108420I
a = −1.25787 − 1.15535I
b = 1.85937 − 0.00043I
5.08150 − 0.59588I 0
u = 0.375408 − 1.108420I
a = −1.25787 + 1.15535I
b = 1.85937 + 0.00043I
5.08150 + 0.59588I 0
u = −0.235520 + 0.777319I
a = −0.153207 + 0.244390I
b = −0.262287 − 1.105520I
−0.40273 + 3.66473I 0. − 6.36269I
u = −0.235520 − 0.777319I
a = −0.153207 − 0.244390I
b = −0.262287 + 1.105520I
−0.40273 − 3.66473I 0. + 6.36269I
u = 1.112620 + 0.422938I
a = −0.0662946 − 0.1070030I
b = 0.823523 − 0.441900I
5.54144 − 5.18578I 0
u = 1.112620 − 0.422938I
a = −0.0662946 + 0.1070030I
b = 0.823523 + 0.441900I
5.54144 + 5.18578I 0
u = 0.523784 + 1.069500I
a = −4.10601 − 0.42204I
b = 0.376955 − 0.151157I
3.20788 − 5.56394I 0
u = 0.523784 − 1.069500I
a = −4.10601 + 0.42204I
b = 0.376955 + 0.151157I
3.20788 + 5.56394I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.634089 + 0.498710I
a = 3.69497 + 8.88764I
b = −0.145181 + 0.241855I
1.42901 + 1.00847I −31.0649 + 44.2359I
u = 0.634089 − 0.498710I
a = 3.69497 − 8.88764I
b = −0.145181 − 0.241855I
1.42901 − 1.00847I −31.0649 − 44.2359I
u = −0.505552 + 1.083710I
a = 1.41400 − 0.27693I
b = −0.785972 − 0.862103I
0.63717 + 3.65490I 0
u = −0.505552 − 1.083710I
a = 1.41400 + 0.27693I
b = −0.785972 + 0.862103I
0.63717 − 3.65490I 0
u = −1.185770 + 0.210987I
a = 0.0868843 − 0.0106217I
b = −0.608506 + 0.512349I
0.98816 − 1.89695I 0
u = −1.185770 − 0.210987I
a = 0.0868843 + 0.0106217I
b = −0.608506 − 0.512349I
0.98816 + 1.89695I 0
u = −0.666834 + 0.423916I
a = 0.286152 − 0.017589I
b = 0.257842 − 0.749663I
−1.37803 + 0.83267I −5.49260 − 3.40594I
u = −0.666834 − 0.423916I
a = 0.286152 + 0.017589I
b = 0.257842 + 0.749663I
−1.37803 − 0.83267I −5.49260 + 3.40594I
u = 0.234448 + 1.189590I
a = 1.74701 − 0.56723I
b = −1.01937 + 1.93388I
9.39087 + 0.67963I 0
u = 0.234448 − 1.189590I
a = 1.74701 + 0.56723I
b = −1.01937 − 1.93388I
9.39087 − 0.67963I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.750828 + 0.154017I
a = −0.540540 + 0.290736I
b = −1.094100 − 0.737261I
1.33029 + 2.74208I 0.45355 − 2.62957I
u = 0.750828 − 0.154017I
a = −0.540540 − 0.290736I
b = −1.094100 + 0.737261I
1.33029 − 2.74208I 0.45355 + 2.62957I
u = −0.360615 + 1.181320I
a = 0.77945 − 1.47555I
b = −1.65817 + 1.47843I
8.85777 + 3.95009I 0
u = −0.360615 − 1.181320I
a = 0.77945 + 1.47555I
b = −1.65817 − 1.47843I
8.85777 − 3.95009I 0
u = 0.521373 + 1.124290I
a = −0.96167 − 1.14782I
b = 0.202332 − 0.843758I
3.12453 − 5.20896I 0
u = 0.521373 − 1.124290I
a = −0.96167 + 1.14782I
b = 0.202332 + 0.843758I
3.12453 + 5.20896I 0
u = −1.124900 + 0.535801I
a = −0.0411915 − 0.1178360I
b = 1.16484 − 1.07257I
4.42812 − 12.73300I 0
u = −1.124900 − 0.535801I
a = −0.0411915 + 0.1178360I
b = 1.16484 + 1.07257I
4.42812 + 12.73300I 0
u = 0.492797 + 1.146900I
a = −2.03102 − 0.36281I
b = 1.54887 − 1.18166I
4.19431 − 7.27901I 0
u = 0.492797 − 1.146900I
a = −2.03102 + 0.36281I
b = 1.54887 + 1.18166I
4.19431 + 7.27901I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.615779 + 1.088750I
a = −0.650976 + 1.024930I
b = 0.414729 + 0.215546I
1.80618 + 5.96754I 0
u = −0.615779 − 1.088750I
a = −0.650976 − 1.024930I
b = 0.414729 − 0.215546I
1.80618 − 5.96754I 0
u = 0.699810 + 0.253258I
a = 0.45949 − 2.64155I
b = −0.233666 − 0.523885I
0.621061 + 0.585081I −8.38094 − 6.55158I
u = 0.699810 − 0.253258I
a = 0.45949 + 2.64155I
b = −0.233666 + 0.523885I
0.621061 − 0.585081I −8.38094 + 6.55158I
u = 1.156140 + 0.507162I
a = 0.0934185 − 0.0006937I
b = −0.757298 − 0.778048I
−0.51148 + 7.10641I 0
u = 1.156140 − 0.507162I
a = 0.0934185 + 0.0006937I
b = −0.757298 + 0.778048I
−0.51148 − 7.10641I 0
u = −0.329817 + 0.655522I
a = 0.27779 + 2.85032I
b = 0.435012 − 0.387028I
−0.74776 − 1.32568I −1.37223 − 2.12566I
u = −0.329817 − 0.655522I
a = 0.27779 − 2.85032I
b = 0.435012 + 0.387028I
−0.74776 + 1.32568I −1.37223 + 2.12566I
u = −0.585773 + 1.136850I
a = 0.270868 − 0.774974I
b = −0.675543 + 0.280117I
2.57218 − 2.94748I 0
u = −0.585773 − 1.136850I
a = 0.270868 + 0.774974I
b = −0.675543 − 0.280117I
2.57218 + 2.94748I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.164951 + 0.699060I
a = 2.01057 + 3.83403I
b = −1.12027 − 1.11356I
3.23791 − 1.80187I 7.60062 + 5.39442I
u = 0.164951 − 0.699060I
a = 2.01057 − 3.83403I
b = −1.12027 + 1.11356I
3.23791 + 1.80187I 7.60062 − 5.39442I
u = −0.494783 + 1.183550I
a = 1.67549 + 0.02049I
b = −0.72180 − 2.14415I
7.89707 + 4.62521I 0
u = −0.494783 − 1.183550I
a = 1.67549 − 0.02049I
b = −0.72180 + 2.14415I
7.89707 − 4.62521I 0
u = −0.581083 + 1.144450I
a = −0.927414 + 0.371926I
b = 0.912764 − 0.614051I
2.41939 + 7.59298I 0
u = −0.581083 − 1.144450I
a = −0.927414 − 0.371926I
b = 0.912764 + 0.614051I
2.41939 − 7.59298I 0
u = 0.277864 + 0.645271I
a = 0.1293420 − 0.0177373I
b = −0.259855 − 1.133830I
−3.17582 + 1.37189I −2.02901 + 3.10189I
u = 0.277864 − 0.645271I
a = 0.1293420 + 0.0177373I
b = −0.259855 + 1.133830I
−3.17582 − 1.37189I −2.02901 − 3.10189I
u = −0.349910 + 0.596945I
a = −0.044338 − 0.135561I
b = 0.776083 − 1.123390I
1.92234 − 6.42207I 1.61043 − 2.58323I
u = −0.349910 − 0.596945I
a = −0.044338 + 0.135561I
b = 0.776083 + 1.123390I
1.92234 + 6.42207I 1.61043 + 2.58323I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.675342 + 0.102623I
a = −0.475944 − 0.632806I
b = −0.798997 + 0.456385I
1.33240 − 2.49877I 0.06108 + 4.74869I
u = 0.675342 − 0.102623I
a = −0.475944 + 0.632806I
b = −0.798997 − 0.456385I
1.33240 + 2.49877I 0.06108 − 4.74869I
u = 0.675422 + 1.130710I
a = 1.322000 + 0.441156I
b = −0.812816 + 1.037590I
−1.80399 − 8.86816I 0
u = 0.675422 − 1.130710I
a = 1.322000 − 0.441156I
b = −0.812816 − 1.037590I
−1.80399 + 8.86816I 0
u = 0.585027 + 1.188980I
a = 0.35499 + 1.37574I
b = −1.89934 − 1.32123I
6.93778 − 9.34093I 0
u = 0.585027 − 1.188980I
a = 0.35499 − 1.37574I
b = −1.89934 + 1.32123I
6.93778 + 9.34093I 0
u = −0.670642 + 1.165170I
a = −1.78726 + 0.65220I
b = 1.52212 + 1.38459I
1.83437 + 12.66320I 0
u = −0.670642 − 1.165170I
a = −1.78726 − 0.65220I
b = 1.52212 − 1.38459I
1.83437 − 12.66320I 0
u = −1.212360 + 0.646222I
a = −0.0620166 + 0.0911191I
b = 0.676884 + 0.094872I
3.33646 − 0.19030I 0
u = −1.212360 − 0.646222I
a = −0.0620166 − 0.0911191I
b = 0.676884 − 0.094872I
3.33646 + 0.19030I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.327090 + 0.526695I
a = −2.03892 + 2.29943I
b = 0.609994 − 0.249849I
−0.596246 + 0.416978I 0.26642 − 6.11778I
u = −0.327090 − 0.526695I
a = −2.03892 − 2.29943I
b = 0.609994 + 0.249849I
−0.596246 − 0.416978I 0.26642 + 6.11778I
u = 0.612331 + 1.251960I
a = 1.73548 + 0.43034I
b = −1.25293 + 1.11281I
9.2901 − 13.7168I 0
u = 0.612331 − 1.251960I
a = 1.73548 − 0.43034I
b = −1.25293 − 1.11281I
9.2901 + 13.7168I 0
u = −0.60524 + 1.28225I
a = −1.283780 + 0.186550I
b = 0.904103 + 0.810181I
4.45793 + 8.07080I 0
u = −0.60524 − 1.28225I
a = −1.283780 − 0.186550I
b = 0.904103 − 0.810181I
4.45793 − 8.07080I 0
u = −0.75455 + 1.21679I
a = 1.62826 − 0.67265I
b = −1.23586 − 1.20855I
6.6329 + 19.4885I 0
u = −0.75455 − 1.21679I
a = 1.62826 + 0.67265I
b = −1.23586 + 1.20855I
6.6329 − 19.4885I 0
u = 0.07864 + 1.43412I
a = 1.38519 − 0.43108I
b = −1.30927 + 0.70376I
12.5560 − 9.3062I 0
u = 0.07864 − 1.43412I
a = 1.38519 + 0.43108I
b = −1.30927 − 0.70376I
12.5560 + 9.3062I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.75063 + 1.23502I
a = −1.301480 − 0.365678I
b = 0.913051 − 0.950042I
1.84566 − 13.92260I 0
u = 0.75063 − 1.23502I
a = −1.301480 + 0.365678I
b = 0.913051 + 0.950042I
1.84566 + 13.92260I 0
u = 0.15570 + 1.44249I
a = 1.116080 + 0.615912I
b = −1.255060 − 0.503238I
12.41370 + 3.14260I 0
u = 0.15570 − 1.44249I
a = 1.116080 − 0.615912I
b = −1.255060 + 0.503238I
12.41370 − 3.14260I 0
u = −0.546681
a = 0.853690
b = 0.327961
−1.13268 −9.63470
u = 0.69181 + 1.30600I
a = 0.556692 + 0.479724I
b = −0.828035 + 0.099208I
8.30974 − 1.49559I 0
u = 0.69181 − 1.30600I
a = 0.556692 − 0.479724I
b = −0.828035 − 0.099208I
8.30974 + 1.49559I 0
u = −0.79848 + 1.26772I
a = 0.617339 − 0.371174I
b = −0.753084 − 0.344913I
5.49346 + 7.52898I 0
u = −0.79848 − 1.26772I
a = 0.617339 + 0.371174I
b = −0.753084 + 0.344913I
5.49346 − 7.52898I 0
u = −0.09910 + 1.49843I
a = −0.912897 − 0.029897I
b = 0.928225 + 0.156147I
7.75260 + 3.19534I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.09910 − 1.49843I
a = −0.912897 + 0.029897I
b = 0.928225 − 0.156147I
7.75260 − 3.19534I 0
u = −0.234925 + 0.344834I
a = −0.39694 − 3.35327I
b = 0.591198 − 0.673652I
4.30327 + 1.14568I 3.56993 + 0.21405I
u = −0.234925 − 0.344834I
a = −0.39694 + 3.35327I
b = 0.591198 + 0.673652I
4.30327 − 1.14568I 3.56993 − 0.21405I
u = 1.62729
a = 0.0237227
b = −0.0964470
−7.22833 0
u = 0.239647
a = 3.21183
b = −0.449696
1.26613 9.42890
17
II. I
u
2
= hb, 3a + 3u − 5, u
2
− u − 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u + 1
a
11
=
−u +
5
3
0
a
9
=
−
8
9
u +
22
9
u + 1
a
12
=
−u +
5
3
0
a
3
=
u
3u + 1
a
6
=
−
2
3
u −
5
9
−3u − 2
a
5
=
−u
−3u − 2
a
2
=
−1
−2u − 2
a
1
=
−2u − 2
−9u − 6
a
10
=
u +
11
3
9u + 6
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
560
3
u −
1105
9
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
7
u
2
− u − 1
c
5
(3u − 1)
2
c
8
9u
2
+ 9u + 1
c
9
u
2
+ 3u + 1
c
10
(u + 1)
2
c
11
u
2
c
12
(u − 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
y
2
− 7y + 1
c
2
, c
3
, c
4
c
7
y
2
− 3y + 1
c
5
(9y −1)
2
c
8
81y
2
− 63y + 1
c
10
, c
12
(y −1)
2
c
11
y
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 2.28470
b = 0
0.657974 −7.41140
u = 1.61803
a = 0.0486327
b = 0
−7.23771 −424.810
21
III.
I
v
1
= ha, 16726v
8
− 41423v
7
+ · · · + 11959b + 26601, v
9
− 3v
8
+ · · · + 3v − 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
−1.39861v
8
+ 3.46375v
7
+ ··· + 3.94598v −2.22435
a
9
=
1
1.45213v
8
− 3.82515v
7
+ ··· − 3.73944v + 4.14098
a
12
=
−1.39861v
8
+ 3.46375v
7
+ ··· + 3.94598v −2.22435
−1.39861v
8
+ 3.46375v
7
+ ··· + 3.94598v −2.22435
a
3
=
v
0
a
6
=
−1.45213v
8
+ 3.82515v
7
+ ··· + 3.73944v −3.14098
−1.21114v
8
+ 2.94147v
7
+ ··· + 5.63826v −2.00702
a
5
=
0.759010v
8
− 2.11631v
7
+ ··· + 0.101179v + 1.86604
v
8
− 3v
7
− 2v
6
− 6v
5
+ 25v
4
− 11v
3
− 9v
2
+ 2v + 3
a
2
=
−0.759010v
8
+ 2.11631v
7
+ ··· + 0.898821v −1.86604
−v
8
+ 3v
7
+ 2v
6
+ 6v
5
− 25v
4
+ 11v
3
+ 9v
2
− 2v −3
a
1
=
−0.759010v
8
+ 2.11631v
7
+ ··· − 0.101179v −1.86604
−v
8
+ 3v
7
+ 2v
6
+ 6v
5
− 25v
4
+ 11v
3
+ 9v
2
− 2v −3
a
10
=
−0.240990v
8
+ 0.883686v
7
+ ··· − 1.89882v −1.13396
−v
8
+ 3v
7
+ 2v
6
+ 6v
5
− 25v
4
+ 11v
3
+ 9v
2
− 2v −3
(ii) Obstruction class = 1
(iii) Cusp Shapes =
109765
11959
v
8
−
294476
11959
v
7
−
325323
11959
v
6
−
729072
11959
v
5
+
2542695
11959
v
4
−
295872
11959
v
3
−
1329263
11959
v
2
−
115465
11959
v+
259811
11959
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
6
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
8
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
9
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
10
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
12
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
6
, c
9
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
8
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
10
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.022450 + 0.246780I
a = 0
b = −0.628449 + 0.875112I
−1.02799 − 2.45442I −3.88318 + 3.00529I
v = 1.022450 − 0.246780I
a = 0
b = −0.628449 − 0.875112I
−1.02799 + 2.45442I −3.88318 − 3.00529I
v = −0.483566 + 0.305056I
a = 0
b = −0.140343 + 0.966856I
−3.42837 − 2.09337I −7.05683 + 6.62869I
v = −0.483566 − 0.305056I
a = 0
b = −0.140343 − 0.966856I
−3.42837 + 2.09337I −7.05683 − 6.62869I
v = 0.411691 + 0.129409I
a = 0
b = 0.728966 + 0.986295I
1.95319 + 7.08493I 2.13339 − 8.87891I
v = 0.411691 − 0.129409I
a = 0
b = 0.728966 − 0.986295I
1.95319 − 7.08493I 2.13339 + 8.87891I
v = −1.23246 + 1.62704I
a = 0
b = 0.796005 + 0.733148I
2.72642 − 1.33617I −1.90921 − 3.07774I
v = −1.23246 − 1.62704I
a = 0
b = 0.796005 − 0.733148I
2.72642 + 1.33617I −1.90921 + 3.07774I
v = 3.56378
a = 0
b = −0.512358
−0.446489 13.4320
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
2
− 3u + 1)(u
125
+ 63u
124
+ ··· + 271u + 1)
c
2
((u − 1)
9
)(u
2
+ u − 1)(u
125
− 11u
124
+ ··· − 9u − 1)
c
3
u
9
(u
2
+ u − 1)(u
125
+ 2u
124
+ ··· + 512u + 512)
c
4
((u + 1)
9
)(u
2
− u − 1)(u
125
− 11u
124
+ ··· − 9u − 1)
c
5
(3u − 1)
2
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (9u
125
− 12u
124
+ ··· + 2836642102u + 259858639)
c
6
(u
2
− 3u + 1)(u
9
− 3u
8
+ ··· + u + 1)
· (u
125
− 3u
124
+ ··· + 3u − 1)
c
7
u
9
(u
2
− u − 1)(u
125
+ 2u
124
+ ··· + 512u + 512)
c
8
(9u
2
+ 9u + 1)(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (9u
125
− 21u
124
+ ··· + 122889219u + 5290529)
c
9
(u
2
+ 3u + 1)(u
9
+ 3u
8
+ ··· + u − 1)
· (u
125
− 3u
124
+ ··· + 3u − 1)
c
10
(u + 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
125
+ 4u
124
+ ··· − 2358u + 81)
c
11
u
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
125
− 2u
124
+ ··· − 756u + 324)
c
12
(u − 1)
2
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
125
+ 4u
124
+ ··· − 2358u + 81)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
2
− 7y + 1)(y
125
+ 9y
124
+ ··· + 91007y −1)
c
2
, c
4
((y −1)
9
)(y
2
− 3y + 1)(y
125
− 63y
124
+ ··· + 271y −1)
c
3
, c
7
y
9
(y
2
− 3y + 1)(y
125
+ 54y
124
+ ··· − 1572864y −262144)
c
5
(9y −1)
2
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (81y
125
− 3294y
124
+ ··· + 2.87 × 10
18
y −6.75 × 10
16
)
c
6
, c
9
(y
2
− 7y + 1)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
125
+ 85y
124
+ ··· + 31y −1)
c
8
(81y
2
− 63y + 1)
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (81y
125
− 4023y
124
+ ··· + 7567318376329835y −27989697099841)
c
10
, c
12
(y −1)
2
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
125
− 90y
124
+ ··· + 665982y −6561)
c
11
y
2
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
125
− 12y
124
+ ··· + 16685352y −104976)
27
