12a
0101
(K12a
0101
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 12 4 11 7 1 9 6
Solving Sequence
8,11
9
4,12
3 7 10 6 1 5 2
c
8
c
11
c
3
c
7
c
9
c
6
c
12
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.17649 × 10
609
u
124
− 3.36190 × 10
609
u
123
+ ··· + 1.03048 × 10
610
b + 8.64846 × 10
610
,
− 1.13257 × 10
610
u
124
+ 3.05226 × 10
610
u
123
+ ··· + 9.27430 × 10
610
a − 4.30072 × 10
612
,
u
125
− 4u
124
+ ··· − 2358u − 81i
I
u
2
= hb, −u
8
+ 2u
7
+ u
6
− 4u
5
+ u
4
+ 2u
3
− 2u
2
+ a + 2u − 1, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
u
3
= hb + 3a + 2, 9a
2
+ 15a + 5, u + 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
= h1.18 × 10
609
u
124
− 3.36 × 10
609
u
123
+ · · · + 1.03 × 10
610
b + 8.65 ×
10
610
, −1.13 × 10
610
u
124
+ 3.05 × 10
610
u
123
+ · · · + 9.27 × 10
610
a − 4.30 ×
10
612
, u
125
− 4u
124
+ · · · − 2358u − 81i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
4
=
0.122120u
124
− 0.329110u
123
+ ··· + 830.926u + 46.3724
−0.114169u
124
+ 0.326247u
123
+ ··· − 267.251u − 8.39267
a
12
=
u
−u
3
+ u
a
3
=
0.00795030u
124
− 0.00286248u
123
+ ··· + 563.675u + 37.9797
−0.114169u
124
+ 0.326247u
123
+ ··· − 267.251u − 8.39267
a
7
=
−0.0897427u
124
+ 0.263504u
123
+ ··· − 662.051u − 35.8488
0.165533u
124
− 0.472119u
123
+ ··· + 397.821u + 12.7393
a
10
=
0.0447494u
124
− 0.159277u
123
+ ··· − 891.931u − 40.9827
−0.0497440u
124
+ 0.142055u
123
+ ··· − 80.7797u − 3.74242
a
6
=
0.114516u
124
− 0.320981u
123
+ ··· − 240.354u − 21.7764
0.107402u
124
− 0.302520u
123
+ ··· + 254.621u + 7.97521
a
1
=
−0.0581366u
124
+ 0.249551u
123
+ ··· + 1107.65u + 46.5213
−0.0948218u
124
+ 0.265936u
123
+ ··· − 149.169u − 3.89415
a
5
=
0.106209u
124
− 0.294233u
123
+ ··· + 57.8710u − 7.77602
0.0561392u
124
− 0.160305u
123
+ ··· + 133.289u + 4.09848
a
2
=
0.115742u
124
− 0.290456u
123
+ ··· + 744.384u + 37.5680
−0.0561392u
124
+ 0.160305u
123
+ ··· − 133.289u − 4.09848
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.594099u
124
− 1.86176u
123
+ ··· + 270.776u − 11.5444
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
u
125
− 2u
124
+ ··· − 756u + 324
c
6
, c
12
u
125
− 3u
124
+ ··· + 3u − 1
c
8
, c
11
u
125
+ 4u
124
+ ··· − 2358u + 81
c
9
9(9u
125
− 12u
124
+ ··· + 2.83664 × 10
9
u + 2.59859 × 10
8
)
c
10
9(9u
125
− 21u
124
+ ··· + 1.22889 × 10
8
u + 5290529)
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
y
125
− 12y
124
+ ··· + 16685352y −104976
c
6
, c
12
y
125
+ 85y
124
+ ··· + 31y −1
c
8
, c
11
y
125
− 90y
124
+ ··· + 665982y −6561
c
9
81(81y
125
− 3294y
124
+ ··· + 2.87254 × 10
18
y −6.75265 × 10
16
)
c
10
81
· (81y
125
− 4023y
124
+ ··· + 7567318376329835y −27989697099841)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00462
a = 1.20830
b = −1.62729
−7.22833 0
u = −1.019800 + 0.033143I
a = −7.66625 + 0.65119I
b = −0.634089 + 0.498710I
1.42901 − 1.00847I 0
u = −1.019800 − 0.033143I
a = −7.66625 − 0.65119I
b = −0.634089 − 0.498710I
1.42901 + 1.00847I 0
u = 0.553570 + 0.776320I
a = −0.580852 − 0.370960I
b = −0.495636 + 0.814877I
−4.15405 + 3.73457I 0
u = 0.553570 − 0.776320I
a = −0.580852 + 0.370960I
b = −0.495636 − 0.814877I
−4.15405 − 3.73457I 0
u = −0.942125 + 0.068730I
a = 4.37119 + 1.11654I
b = −0.523784 + 1.069500I
3.20788 + 5.56394I 0
u = −0.942125 − 0.068730I
a = 4.37119 − 1.11654I
b = −0.523784 − 1.069500I
3.20788 − 5.56394I 0
u = −1.007240 + 0.321358I
a = −0.005539 − 0.814282I
b = 0.828223 − 0.376343I
0.06073 − 2.33875I 0
u = −1.007240 − 0.321358I
a = −0.005539 + 0.814282I
b = 0.828223 + 0.376343I
0.06073 + 2.33875I 0
u = −0.185640 + 0.922819I
a = −0.853594 − 0.485251I
b = −0.750828 + 0.154017I
1.33029 − 2.74208I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.185640 − 0.922819I
a = −0.853594 + 0.485251I
b = −0.750828 − 0.154017I
1.33029 + 2.74208I 0
u = 0.116638 + 0.927275I
a = −0.451443 + 0.206067I
b = −0.675422 − 1.130710I
−1.80399 − 8.86816I 0
u = 0.116638 − 0.927275I
a = −0.451443 − 0.206067I
b = −0.675422 + 1.130710I
−1.80399 + 8.86816I 0
u = −0.897003 + 0.223487I
a = 2.41978 − 2.54927I
b = 0.327090 + 0.526695I
−0.596246 − 0.416978I 0
u = −0.897003 − 0.223487I
a = 2.41978 + 2.54927I
b = 0.327090 − 0.526695I
−0.596246 + 0.416978I 0
u = 0.882115 + 0.621544I
a = 0.394622 + 0.050709I
b = −0.277864 − 0.645271I
−3.17582 + 1.37189I 0
u = 0.882115 − 0.621544I
a = 0.394622 − 0.050709I
b = −0.277864 + 0.645271I
−3.17582 − 1.37189I 0
u = −0.679856 + 0.613009I
a = −0.028106 − 0.438962I
b = 0.442173 − 1.054840I
1.15542 + 3.12032I 0
u = −0.679856 − 0.613009I
a = −0.028106 + 0.438962I
b = 0.442173 + 1.054840I
1.15542 − 3.12032I 0
u = 1.015900 + 0.407589I
a = 0.100594 + 0.423342I
b = 0.599973 − 0.683518I
1.14990 + 7.95106I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.015900 − 0.407589I
a = 0.100594 − 0.423342I
b = 0.599973 + 0.683518I
1.14990 − 7.95106I 0
u = −1.106370 + 0.091912I
a = −0.07489 + 1.53113I
b = −0.699810 − 0.253258I
0.621061 + 0.585081I 0
u = −1.106370 − 0.091912I
a = −0.07489 − 1.53113I
b = −0.699810 + 0.253258I
0.621061 − 0.585081I 0
u = −0.068597 + 1.117030I
a = 0.747329 − 1.138740I
b = 0.422750 + 0.821064I
−1.03348 − 4.20848I 0
u = −0.068597 − 1.117030I
a = 0.747329 + 1.138740I
b = 0.422750 − 0.821064I
−1.03348 + 4.20848I 0
u = 0.492983 + 0.726321I
a = −0.733517 − 0.012243I
b = 0.235520 + 0.777319I
−0.40273 − 3.66473I 0
u = 0.492983 − 0.726321I
a = −0.733517 + 0.012243I
b = 0.235520 − 0.777319I
−0.40273 + 3.66473I 0
u = −0.877189
a = −0.512937
b = −0.239647
1.26613 0
u = 0.301986 + 1.083050I
a = 0.658017 + 0.117846I
b = 0.413672 − 0.836934I
−0.983702 − 0.642828I 0
u = 0.301986 − 1.083050I
a = 0.658017 − 0.117846I
b = 0.413672 + 0.836934I
−0.983702 + 0.642828I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.120200 + 0.229947I
a = −0.611354 + 0.118039I
b = 1.185770 + 0.210987I
0.98816 + 1.89695I 0
u = 1.120200 − 0.229947I
a = −0.611354 − 0.118039I
b = 1.185770 − 0.210987I
0.98816 − 1.89695I 0
u = 1.169660 + 0.122507I
a = 0.21593 − 1.74311I
b = 0.585773 + 1.136850I
2.57218 + 2.94748I 0
u = 1.169660 − 0.122507I
a = 0.21593 + 1.74311I
b = 0.585773 − 1.136850I
2.57218 − 2.94748I 0
u = 1.177470 + 0.040674I
a = −0.451479 + 0.498059I
b = 1.212360 − 0.646222I
3.33646 − 0.19030I 0
u = 1.177470 − 0.040674I
a = −0.451479 − 0.498059I
b = 1.212360 + 0.646222I
3.33646 + 0.19030I 0
u = 1.129450 + 0.338053I
a = −0.66428 − 2.18288I
b = −0.380832 + 1.099280I
−1.50629 + 4.23005I 0
u = 1.129450 − 0.338053I
a = −0.66428 + 2.18288I
b = −0.380832 − 1.099280I
−1.50629 − 4.23005I 0
u = −1.122780 + 0.361086I
a = −1.36902 + 1.80748I
b = −0.349086 − 1.109990I
4.36419 − 2.43164I 0
u = −1.122780 − 0.361086I
a = −1.36902 − 1.80748I
b = −0.349086 + 1.109990I
4.36419 + 2.43164I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.148820 + 0.276283I
a = 0.363713 + 0.676943I
b = 0.234925 + 0.344834I
4.30327 − 1.14568I 0
u = −1.148820 − 0.276283I
a = 0.363713 − 0.676943I
b = 0.234925 − 0.344834I
4.30327 + 1.14568I 0
u = 0.041879 + 0.816044I
a = 0.269286 − 0.269487I
b = 0.505552 + 1.083710I
0.63717 − 3.65490I 0
u = 0.041879 − 0.816044I
a = 0.269286 + 0.269487I
b = 0.505552 − 1.083710I
0.63717 + 3.65490I 0
u = −1.103650 + 0.458723I
a = 1.44919 − 1.57677I
b = 0.581083 + 1.144450I
2.41939 − 7.59298I 0
u = −1.103650 − 0.458723I
a = 1.44919 + 1.57677I
b = 0.581083 − 1.144450I
2.41939 + 7.59298I 0
u = −0.790545 + 0.019933I
a = −2.56910 + 1.61319I
b = 0.189225 + 0.989929I
4.85915 − 0.90928I 0
u = −0.790545 − 0.019933I
a = −2.56910 − 1.61319I
b = 0.189225 − 0.989929I
4.85915 + 0.90928I 0
u = 1.202640 + 0.156735I
a = 0.32002 + 1.71886I
b = 0.79848 − 1.26772I
5.49346 + 7.52898I 0
u = 1.202640 − 0.156735I
a = 0.32002 − 1.71886I
b = 0.79848 + 1.26772I
5.49346 − 7.52898I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.210680 + 0.161896I
a = −0.85895 + 2.04089I
b = 0.248400 − 1.101470I
4.76652 + 0.18641I 0
u = −1.210680 − 0.161896I
a = −0.85895 − 2.04089I
b = 0.248400 + 1.101470I
4.76652 − 0.18641I 0
u = −0.093015 + 1.226720I
a = 0.818202 + 0.177043I
b = 0.962365 − 0.485559I
−0.31912 − 6.67340I 0
u = −0.093015 − 1.226720I
a = 0.818202 − 0.177043I
b = 0.962365 + 0.485559I
−0.31912 + 6.67340I 0
u = 1.244620 + 0.045072I
a = −0.21770 − 1.70656I
b = −0.69181 + 1.30600I
8.30974 + 1.49559I 0
u = 1.244620 − 0.045072I
a = −0.21770 + 1.70656I
b = −0.69181 − 1.30600I
8.30974 − 1.49559I 0
u = 1.187700 + 0.381857I
a = 0.554894 − 0.073688I
b = −1.156140 − 0.507162I
−0.51148 + 7.10641I 0
u = 1.187700 − 0.381857I
a = 0.554894 + 0.073688I
b = −1.156140 + 0.507162I
−0.51148 − 7.10641I 0
u = 0.160915 + 0.733050I
a = −1.081860 − 0.619622I
b = −0.918385 + 0.543413I
−3.67094 − 2.96823I 0
u = 0.160915 − 0.733050I
a = −1.081860 + 0.619622I
b = −0.918385 − 0.543413I
−3.67094 + 2.96823I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.232930 + 0.206914I
a = 0.297530 − 0.400461I
b = −1.112620 + 0.422938I
5.54144 + 5.18578I 0
u = 1.232930 − 0.206914I
a = 0.297530 + 0.400461I
b = −1.112620 − 0.422938I
5.54144 − 5.18578I 0
u = −1.250040 + 0.092802I
a = 0.72374 − 1.97517I
b = −0.521373 + 1.124290I
3.12453 + 5.20896I 0
u = −1.250040 − 0.092802I
a = 0.72374 + 1.97517I
b = −0.521373 − 1.124290I
3.12453 − 5.20896I 0
u = −0.412931 + 0.603388I
a = −0.095407 + 0.251832I
b = −0.080750 + 1.051060I
2.33153 − 1.50993I 0
u = −0.412931 − 0.603388I
a = −0.095407 − 0.251832I
b = −0.080750 − 1.051060I
2.33153 + 1.50993I 0
u = 1.290240 + 0.072671I
a = 0.10997 + 1.96088I
b = 0.09910 − 1.49843I
7.75260 + 3.19534I 0
u = 1.290240 − 0.072671I
a = 0.10997 − 1.96088I
b = 0.09910 + 1.49843I
7.75260 − 3.19534I 0
u = 0.244690 + 0.651544I
a = −0.393078 + 0.825816I
b = −0.532227 − 0.797562I
−4.18791 − 0.46329I 0
u = 0.244690 − 0.651544I
a = −0.393078 − 0.825816I
b = −0.532227 + 0.797562I
−4.18791 + 0.46329I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.581513 + 1.178610I
a = 0.126337 + 0.538620I
b = 0.064934 − 1.160180I
5.99018 − 4.39123I 0
u = −0.581513 − 1.178610I
a = 0.126337 − 0.538620I
b = 0.064934 + 1.160180I
5.99018 + 4.39123I 0
u = 1.267760 + 0.400092I
a = 0.65528 + 1.83753I
b = 0.60524 − 1.28225I
4.45793 + 8.07080I 0
u = 1.267760 − 0.400092I
a = 0.65528 − 1.83753I
b = 0.60524 + 1.28225I
4.45793 − 8.07080I 0
u = 1.204790 + 0.577085I
a = −0.241931 − 0.008506I
b = 0.349910 + 0.596945I
1.92234 + 6.42207I 0
u = 1.204790 − 0.577085I
a = −0.241931 + 0.008506I
b = 0.349910 − 0.596945I
1.92234 − 6.42207I 0
u = −0.157172 + 1.342160I
a = −0.519932 + 0.623225I
b = −0.492797 − 1.146900I
4.19431 − 7.27901I 0
u = −0.157172 − 1.342160I
a = −0.519932 − 0.623225I
b = −0.492797 + 1.146900I
4.19431 + 7.27901I 0
u = 1.274590 + 0.475627I
a = −0.76131 − 1.73414I
b = −0.75063 + 1.23502I
1.84566 + 13.92260I 0
u = 1.274590 − 0.475627I
a = −0.76131 + 1.73414I
b = −0.75063 − 1.23502I
1.84566 − 13.92260I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.212427 + 0.597178I
a = −0.79710 − 1.31566I
b = −0.675342 − 0.102623I
1.33240 − 2.49877I 0. + 4.74869I
u = −0.212427 − 0.597178I
a = −0.79710 + 1.31566I
b = −0.675342 + 0.102623I
1.33240 + 2.49877I 0. − 4.74869I
u = −0.865830 + 1.116940I
a = −0.279168 − 0.263603I
b = −0.375408 + 1.108420I
5.08150 + 0.59588I 0
u = −0.865830 − 1.116940I
a = −0.279168 + 0.263603I
b = −0.375408 − 1.108420I
5.08150 − 0.59588I 0
u = −0.057273 + 1.412250I
a = 0.651883 − 0.489377I
b = 0.670642 + 1.165170I
1.83437 − 12.66320I 0
u = −0.057273 − 1.412250I
a = 0.651883 + 0.489377I
b = 0.670642 − 1.165170I
1.83437 + 12.66320I 0
u = 0.333290 + 0.446397I
a = 0.481540 + 1.142050I
b = 0.666834 − 0.423916I
−1.37803 + 0.83267I −5.49260 − 3.40594I
u = 0.333290 − 0.446397I
a = 0.481540 − 1.142050I
b = 0.666834 + 0.423916I
−1.37803 − 0.83267I −5.49260 + 3.40594I
u = 1.37538 + 0.44635I
a = 0.302307 − 0.183909I
b = −1.090330 − 0.256832I
6.12909 + 7.71732I 0
u = 1.37538 − 0.44635I
a = 0.302307 + 0.183909I
b = −1.090330 + 0.256832I
6.12909 − 7.71732I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44585 + 0.24233I
a = 0.12542 + 1.74268I
b = −0.15570 − 1.44249I
12.41370 + 3.14260I 0
u = 1.44585 − 0.24233I
a = 0.12542 − 1.74268I
b = −0.15570 + 1.44249I
12.41370 − 3.14260I 0
u = 1.38238 + 0.50485I
a = 0.81540 + 1.93506I
b = 0.433618 − 1.055720I
3.54058 + 9.87816I 0
u = 1.38238 − 0.50485I
a = 0.81540 − 1.93506I
b = 0.433618 + 1.055720I
3.54058 − 9.87816I 0
u = −1.38774 + 0.55875I
a = −0.77889 + 2.27384I
b = −0.164951 − 0.699060I
3.23791 − 1.80187I 0
u = −1.38774 − 0.55875I
a = −0.77889 − 2.27384I
b = −0.164951 + 0.699060I
3.23791 + 1.80187I 0
u = 1.41215 + 0.53166I
a = −0.334971 + 0.142327I
b = 1.124900 + 0.535801I
4.42812 + 12.73300I 0
u = 1.41215 − 0.53166I
a = −0.334971 − 0.142327I
b = 1.124900 − 0.535801I
4.42812 − 12.73300I 0
u = 1.47473 + 0.34073I
a = −0.30661 − 1.75055I
b = −0.07864 + 1.43412I
12.5560 + 9.3062I 0
u = 1.47473 − 0.34073I
a = −0.30661 + 1.75055I
b = −0.07864 − 1.43412I
12.5560 − 9.3062I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45909 + 0.54825I
a = −0.77553 − 1.64678I
b = −0.612331 + 1.251960I
9.2901 + 13.7168I 0
u = 1.45909 − 0.54825I
a = −0.77553 + 1.64678I
b = −0.612331 − 1.251960I
9.2901 − 13.7168I 0
u = 1.45536 + 0.59783I
a = 0.86347 + 1.55441I
b = 0.75455 − 1.21679I
6.6329 + 19.4885I 0
u = 1.45536 − 0.59783I
a = 0.86347 − 1.55441I
b = 0.75455 + 1.21679I
6.6329 − 19.4885I 0
u = −1.55646 + 0.40868I
a = 0.518712 − 0.265693I
b = 0.840842 + 0.156626I
4.74563 − 0.17252I 0
u = −1.55646 − 0.40868I
a = 0.518712 + 0.265693I
b = 0.840842 − 0.156626I
4.74563 + 0.17252I 0
u = −1.46287 + 0.71096I
a = −0.371021 + 0.154004I
b = −0.913335 + 0.327879I
4.24550 − 3.85404I 0
u = −1.46287 − 0.71096I
a = −0.371021 − 0.154004I
b = −0.913335 − 0.327879I
4.24550 + 3.85404I 0
u = −0.030715 + 0.308294I
a = 3.97429 + 3.34727I
b = 0.329817 − 0.655522I
−0.74776 − 1.32568I −1.37223 − 2.12566I
u = −0.030715 − 0.308294I
a = 3.97429 − 3.34727I
b = 0.329817 + 0.655522I
−0.74776 + 1.32568I −1.37223 + 2.12566I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.260858 + 0.061690I
a = −3.63799 − 2.80332I
b = −0.402370 − 1.037470I
3.98203 − 1.01780I 4.25072 + 0.21693I
u = −0.260858 − 0.061690I
a = −3.63799 + 2.80332I
b = −0.402370 + 1.037470I
3.98203 + 1.01780I 4.25072 − 0.21693I
u = −0.115813 + 0.180186I
a = 0.86751 + 4.37451I
b = 0.615779 + 1.088750I
1.80618 − 5.96754I −0.06922 + 4.13588I
u = −0.115813 − 0.180186I
a = 0.86751 − 4.37451I
b = 0.615779 − 1.088750I
1.80618 + 5.96754I −0.06922 − 4.13588I
u = −1.60735 + 0.80298I
a = 0.661431 − 1.241730I
b = 0.360615 + 1.181320I
8.85777 − 3.95009I 0
u = −1.60735 − 0.80298I
a = 0.661431 + 1.241730I
b = 0.360615 − 1.181320I
8.85777 + 3.95009I 0
u = −1.55437 + 0.93343I
a = −0.809344 + 1.082050I
b = −0.585027 − 1.188980I
6.93778 − 9.34093I 0
u = −1.55437 − 0.93343I
a = −0.809344 − 1.082050I
b = −0.585027 + 1.188980I
6.93778 + 9.34093I 0
u = −1.78470 + 0.47323I
a = 0.045779 − 1.243050I
b = −0.234448 + 1.189590I
9.39087 − 0.67963I 0
u = −1.78470 − 0.47323I
a = 0.045779 + 1.243050I
b = −0.234448 − 1.189590I
9.39087 + 0.67963I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.114414 + 0.096397I
a = 1.63704 + 7.33370I
b = 0.807203 + 0.430889I
−0.121971 + 0.719876I −2.41456 − 1.33477I
u = −0.114414 − 0.096397I
a = 1.63704 − 7.33370I
b = 0.807203 − 0.430889I
−0.121971 − 0.719876I −2.41456 + 1.33477I
u = −0.108848
a = 7.05890
b = 0.546681
−1.13268 −9.63470
u = −1.87167 + 0.32925I
a = 0.124876 + 1.068020I
b = 0.494783 − 1.183550I
7.89707 + 4.62521I 0
u = −1.87167 − 0.32925I
a = 0.124876 − 1.068020I
b = 0.494783 + 1.183550I
7.89707 − 4.62521I 0
17
II.
I
u
2
= hb, −u
8
+ 2u
7
+ · · · + a − 1, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−u
2
a
4
=
u
8
− 2u
7
− u
6
+ 4u
5
− u
4
− 2u
3
+ 2u
2
− 2u + 1
0
a
12
=
u
−u
3
+ u
a
3
=
u
8
− 2u
7
− u
6
+ 4u
5
− u
4
− 2u
3
+ 2u
2
− 2u + 1
0
a
7
=
1
0
a
10
=
−u
2
+ 1
−u
2
a
6
=
u
4
− u
2
+ 1
−u
6
+ 2u
4
− u
2
a
1
=
u
7
− 2u
5
+ 2u
3
−u
8
+ u
7
+ 3u
6
− 2u
5
− 3u
4
+ 2u
3
+ 1
a
5
=
−u
7
+ 2u
5
− 2u
3
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u
3
− 1
a
2
=
u
8
− u
7
− u
6
+ 2u
5
− u
4
+ 2u
2
− 2u + 1
−u
8
+ u
7
+ 3u
6
− 2u
5
− 3u
4
+ 2u
3
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
8
− 9u
7
+ 2u
6
+ 15u
5
− 11u
4
− 11u
3
+ 10u
2
− 11u − 1
18
(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
, c
10
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ 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
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
9
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
11
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
19
(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
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
6
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
8
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
9
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = −0.483566 − 0.305056I
b = 0
−3.42837 + 2.09337I −7.05683 − 6.62869I
u = 0.772920 − 0.510351I
a = −0.483566 + 0.305056I
b = 0
−3.42837 − 2.09337I −7.05683 + 6.62869I
u = −0.825933
a = 3.56378
b = 0
−0.446489 13.4320
u = −1.173910 + 0.391555I
a = −1.23246 + 1.62704I
b = 0
2.72642 − 1.33617I −1.90921 − 3.07774I
u = −1.173910 − 0.391555I
a = −1.23246 − 1.62704I
b = 0
2.72642 + 1.33617I −1.90921 + 3.07774I
u = 0.141484 + 0.739668I
a = 1.022450 + 0.246780I
b = 0
−1.02799 − 2.45442I −3.88318 + 3.00529I
u = 0.141484 − 0.739668I
a = 1.022450 − 0.246780I
b = 0
−1.02799 + 2.45442I −3.88318 − 3.00529I
u = 1.172470 + 0.500383I
a = 0.411691 + 0.129409I
b = 0
1.95319 + 7.08493I 2.13339 − 8.87891I
u = 1.172470 − 0.500383I
a = 0.411691 − 0.129409I
b = 0
1.95319 − 7.08493I 2.13339 + 8.87891I
21
III. I
u
3
= hb + 3a + 2, 9a
2
+ 15a + 5, u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
−1
a
9
=
1
−1
a
4
=
a
−3a − 2
a
12
=
−1
0
a
3
=
−2a − 2
−3a − 2
a
7
=
−3a −
2
3
3a + 1
a
10
=
a +
11
9
−a −
4
3
a
6
=
0.333333
3a + 1
a
1
=
−a −
4
3
9a + 4
a
5
=
0.333333
3a + 1
a
2
=
−3a −
8
3
3a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 560a +
2255
9
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
7
u
2
− u − 1
c
5
u
2
c
6
u
2
+ 3u + 1
c
8
(u + 1)
2
c
9
9(3u − 1)
2
c
10
9(9u
2
+ 9u + 1)
c
11
(u − 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
12
y
2
− 7y + 1
c
2
, c
3
, c
4
c
7
y
2
− 3y + 1
c
5
y
2
c
8
, c
11
(y −1)
2
c
9
81(9y −1)
2
c
10
81(81y
2
− 63y + 1)
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.20601
b = 1.61803
−7.23771 −424.810
u = −1.00000
a = −0.460655
b = −0.618034
0.657974 −7.41140
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
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
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
(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
9
81(3u − 1)
2
(u
9
− 5u
8
+ ··· + u − 1)
· (9u
125
− 12u
124
+ ··· + 2836642102u + 259858639)
c
10
81(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
11
(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
12
(u
2
− 3u + 1)(u
9
+ 3u
8
+ ··· + u − 1)
· (u
125
− 3u
124
+ ··· + 3u − 1)
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
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)
c
6
, c
12
(y
2
− 7y + 1)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
125
+ 85y
124
+ ··· + 31y −1)
c
8
, c
11
(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
9
6561(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
10
6561(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)
27
