12a
1073
(K12a
1073
)
A knot diagram
1
Linearized knot diagam
4 7 10 9 12 2 11 5 1 3 6 8
Solving Sequence
5,8 1,9
10 4 2 3 12 6 11 7
c
8
c
9
c
4
c
1
c
3
c
12
c
5
c
11
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.54817 × 10
592
u
140
+ 1.63249 × 10
593
u
139
+ ··· + 1.25499 × 10
594
b + 3.83199 × 10
594
,
− 4.59910 × 10
593
u
140
− 3.23099 × 10
594
u
139
+ ··· + 1.50598 × 10
595
a − 1.02194 × 10
597
,
u
141
+ 4u
140
+ ··· + 2832u + 168i
I
u
2
= h6.58267 × 10
20
u
31
+ 6.86615 × 10
21
u
30
+ ··· + 2.03894 × 10
21
b + 2.89056 × 10
23
,
− 9.29799 × 10
22
u
31
− 4.19012 × 10
23
u
30
+ ··· + 1.20297 × 10
23
a − 2.06819 × 10
25
,
u
32
− u
31
+ ··· − 104u + 59i
I
v
1
= ha, b − 1, v
3
+ 2v + 1i
* 3 irreducible components of dim
C
= 0, with total 176 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
= h2.55 × 10
592
u
140
+ 1.63 × 10
593
u
139
+ · · · + 1.25 × 10
594
b + 3.83 ×
10
594
, −4.60 × 10
593
u
140
− 3.23 × 10
594
u
139
+ · · · + 1.51 × 10
595
a − 1.02 ×
10
597
, u
141
+ 4u
140
+ · · · + 2832u + 168i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
1
=
0.0305389u
140
+ 0.214544u
139
+ ··· + 476.782u + 67.8590
−0.0203043u
140
− 0.130081u
139
+ ··· − 86.0127u − 3.05341
a
9
=
1
u
2
a
10
=
−0.0126430u
140
+ 0.0241027u
139
+ ··· + 167.192u − 2.57404
0.0411553u
140
+ 0.137220u
139
+ ··· − 52.7399u − 4.70944
a
4
=
u
u
3
+ u
a
2
=
0.00790478u
140
+ 0.100131u
139
+ ··· + 430.040u + 65.5289
−0.0187936u
140
− 0.115024u
139
+ ··· − 61.3348u − 1.37233
a
3
=
−0.0198734u
140
+ 0.0433603u
139
+ ··· + 208.509u + 20.4485
−0.0123183u
140
− 0.108437u
139
+ ··· − 107.608u − 5.43547
a
12
=
0.0102345u
140
+ 0.0844631u
139
+ ··· + 390.769u + 64.8056
−0.0203043u
140
− 0.130081u
139
+ ··· − 86.0127u − 3.05341
a
6
=
−0.0488240u
140
− 0.150140u
139
+ ··· + 351.967u + 29.9572
−0.0878505u
140
− 0.280169u
139
+ ··· + 157.323u + 9.17097
a
11
=
−0.116715u
140
− 0.443627u
139
+ ··· + 54.4349u − 12.8563
0.00779702u
140
+ 0.0699302u
139
+ ··· + 64.1007u + 1.77825
a
7
=
−0.0774632u
140
− 0.271390u
139
+ ··· − 30.5227u − 33.3656
0.00340777u
140
+ 0.0631506u
139
+ ··· + 85.7404u + 2.52528
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.143156u
140
− 0.698212u
139
+ ··· − 254.819u − 13.1150
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
141
− 12u
140
+ ··· + 763u − 49
c
2
, c
6
u
141
− 2u
140
+ ··· + 45051u + 32979
c
3
, c
10
u
141
+ u
140
+ ··· + 386164u + 65629
c
4
, c
8
u
141
+ 4u
140
+ ··· + 2832u + 168
c
5
, c
11
u
141
− u
140
+ ··· + 533427u + 47167
c
7
u
141
+ 8u
140
+ ··· + 47275162u + 6401042
c
9
u
141
+ 8u
140
+ ··· + 26u + 1
c
12
u
141
− 2u
140
+ ··· + 14863691u + 980999
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
141
− 2y
140
+ ··· − 122941y −2401
c
2
, c
6
y
141
− 84y
140
+ ··· + 18315150465y −1087614441
c
3
, c
10
y
141
+ 119y
140
+ ··· + 200837368090y −4307165641
c
4
, c
8
y
141
+ 110y
140
+ ··· + 8842080y −28224
c
5
, c
11
y
141
+ 107y
140
+ ··· − 15637743751y −2224725889
c
7
y
141
− 40y
140
+ ··· − 12502874859103792y −40973338685764
c
9
y
141
− 6y
140
+ ··· + 136y −1
c
12
y
141
+ 58y
140
+ ··· − 23268885446441y −962359038001
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.763169 + 0.633004I
a = −1.339640 + 0.080630I
b = 0.715686 + 1.075370I
−3.45255 − 4.17755I 0
u = −0.763169 − 0.633004I
a = −1.339640 − 0.080630I
b = 0.715686 − 1.075370I
−3.45255 + 4.17755I 0
u = 0.155407 + 1.012010I
a = 0.49435 + 1.78486I
b = −0.497754 − 0.766992I
−1.79602 − 1.77015I 0
u = 0.155407 − 1.012010I
a = 0.49435 − 1.78486I
b = −0.497754 + 0.766992I
−1.79602 + 1.77015I 0
u = −0.340769 + 0.969240I
a = −0.50551 − 2.16701I
b = −0.80000 + 2.24860I
−2.47493 + 8.56476I 0
u = −0.340769 − 0.969240I
a = −0.50551 + 2.16701I
b = −0.80000 − 2.24860I
−2.47493 − 8.56476I 0
u = 0.986469 + 0.297194I
a = −0.143405 + 0.208271I
b = 0.837739 + 0.774239I
−1.60144 − 7.36841I 0
u = 0.986469 − 0.297194I
a = −0.143405 − 0.208271I
b = 0.837739 − 0.774239I
−1.60144 + 7.36841I 0
u = 0.939371 + 0.072087I
a = −0.063001 − 0.319054I
b = −1.046510 + 0.355654I
−9.05838 + 7.91895I 0
u = 0.939371 − 0.072087I
a = −0.063001 + 0.319054I
b = −1.046510 − 0.355654I
−9.05838 − 7.91895I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.843079 + 0.393632I
a = 0.564951 + 0.190127I
b = 0.664303 − 0.159681I
−1.86166 + 1.83381I 0
u = 0.843079 − 0.393632I
a = 0.564951 − 0.190127I
b = 0.664303 + 0.159681I
−1.86166 − 1.83381I 0
u = 0.996431 + 0.423590I
a = −0.100176 − 0.242191I
b = −0.546016 − 0.686876I
2.74069 − 3.01528I 0
u = 0.996431 − 0.423590I
a = −0.100176 + 0.242191I
b = −0.546016 + 0.686876I
2.74069 + 3.01528I 0
u = −0.164481 + 1.074710I
a = 0.84942 − 1.93739I
b = 0.129569 + 0.279132I
−2.95677 + 4.09152I 0
u = −0.164481 − 1.074710I
a = 0.84942 + 1.93739I
b = 0.129569 − 0.279132I
−2.95677 − 4.09152I 0
u = 0.277431 + 0.863792I
a = −0.70330 − 1.83929I
b = 0.993033 + 0.994671I
−6.56670 − 4.32297I 0
u = 0.277431 − 0.863792I
a = −0.70330 + 1.83929I
b = 0.993033 − 0.994671I
−6.56670 + 4.32297I 0
u = −0.822181 + 0.321499I
a = 0.721318 − 0.332401I
b = −0.519997 − 0.944704I
−1.21432 − 2.33038I 0
u = −0.822181 − 0.321499I
a = 0.721318 + 0.332401I
b = −0.519997 + 0.944704I
−1.21432 + 2.33038I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.041884 + 1.119270I
a = −0.180792 + 0.017170I
b = 1.68313 + 0.04851I
−0.992191 + 0.266056I 0
u = −0.041884 − 1.119270I
a = −0.180792 − 0.017170I
b = 1.68313 − 0.04851I
−0.992191 − 0.266056I 0
u = −0.410529 + 1.070460I
a = −0.408143 + 0.787586I
b = 0.803532 − 0.455460I
−1.83641 + 1.10256I 0
u = −0.410529 − 1.070460I
a = −0.408143 − 0.787586I
b = 0.803532 + 0.455460I
−1.83641 − 1.10256I 0
u = −0.039398 + 1.150010I
a = 0.46753 + 2.07817I
b = −0.142788 − 0.773798I
−2.16440 − 2.33593I 0
u = −0.039398 − 1.150010I
a = 0.46753 − 2.07817I
b = −0.142788 + 0.773798I
−2.16440 + 2.33593I 0
u = 1.144550 + 0.149559I
a = 0.430020 + 0.204811I
b = −0.256705 + 0.964339I
0.13672 + 2.12290I 0
u = 1.144550 − 0.149559I
a = 0.430020 − 0.204811I
b = −0.256705 − 0.964339I
0.13672 − 2.12290I 0
u = −0.834257 + 0.002736I
a = −0.262575 + 0.153090I
b = 0.874699 + 0.856528I
−7.10130 − 2.33210I 0
u = −0.834257 − 0.002736I
a = −0.262575 − 0.153090I
b = 0.874699 − 0.856528I
−7.10130 + 2.33210I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.002645 + 1.178370I
a = 0.78053 − 2.25107I
b = −1.76800 + 2.30851I
−0.26531 − 7.50044I 0
u = 0.002645 − 1.178370I
a = 0.78053 + 2.25107I
b = −1.76800 − 2.30851I
−0.26531 + 7.50044I 0
u = −1.171170 + 0.248839I
a = −0.128236 − 0.164334I
b = 0.761366 − 0.817171I
−5.1060 + 13.3388I 0
u = −1.171170 − 0.248839I
a = −0.128236 + 0.164334I
b = 0.761366 + 0.817171I
−5.1060 − 13.3388I 0
u = −0.790003 + 0.110290I
a = 0.167515 − 0.456463I
b = −1.057430 + 0.177318I
−4.77992 + 3.20333I 0
u = −0.790003 − 0.110290I
a = 0.167515 + 0.456463I
b = −1.057430 − 0.177318I
−4.77992 − 3.20333I 0
u = −1.198270 + 0.099250I
a = 0.248775 + 0.144482I
b = −0.231409 + 0.617685I
−0.667207 + 0.969556I 0
u = −1.198270 − 0.099250I
a = 0.248775 − 0.144482I
b = −0.231409 − 0.617685I
−0.667207 − 0.969556I 0
u = 0.165118 + 1.197910I
a = 0.193142 − 1.214250I
b = −0.303338 + 0.861689I
3.55356 + 0.06503I 0
u = 0.165118 − 1.197910I
a = 0.193142 + 1.214250I
b = −0.303338 − 0.861689I
3.55356 − 0.06503I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.280111 + 1.177070I
a = 0.01971 + 1.50168I
b = 0.101289 − 0.900632I
1.85029 − 4.46678I 0
u = 0.280111 − 1.177070I
a = 0.01971 − 1.50168I
b = 0.101289 + 0.900632I
1.85029 + 4.46678I 0
u = 0.115170 + 1.209580I
a = −0.00940 + 2.86333I
b = −0.85445 − 2.86153I
4.26570 − 0.47439I 0
u = 0.115170 − 1.209580I
a = −0.00940 − 2.86333I
b = −0.85445 + 2.86153I
4.26570 + 0.47439I 0
u = −0.776246 + 0.081534I
a = 0.444633 + 0.094869I
b = 0.352412 − 0.113169I
−1.104670 − 0.011032I 0
u = −0.776246 − 0.081534I
a = 0.444633 − 0.094869I
b = 0.352412 + 0.113169I
−1.104670 + 0.011032I 0
u = 0.437847 + 1.139360I
a = −0.20526 + 1.49045I
b = −0.530547 − 0.515869I
0.57932 − 6.57678I 0
u = 0.437847 − 1.139360I
a = −0.20526 − 1.49045I
b = −0.530547 + 0.515869I
0.57932 + 6.57678I 0
u = 0.048975 + 1.220130I
a = −0.60346 + 1.50138I
b = −0.623416 − 1.161700I
7.21232 − 0.33115I 0
u = 0.048975 − 1.220130I
a = −0.60346 − 1.50138I
b = −0.623416 + 1.161700I
7.21232 + 0.33115I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.767288 + 0.096580I
a = −0.632730 − 1.129660I
b = 0.664099 − 0.529863I
−0.443046 − 0.013493I 0
u = 0.767288 − 0.096580I
a = −0.632730 + 1.129660I
b = 0.664099 + 0.529863I
−0.443046 + 0.013493I 0
u = 0.223800 + 1.207940I
a = −0.84723 − 1.80670I
b = 0.532875 + 0.811679I
−4.58833 − 0.55821I 0
u = 0.223800 − 1.207940I
a = −0.84723 + 1.80670I
b = 0.532875 − 0.811679I
−4.58833 + 0.55821I 0
u = −0.391296 + 1.171130I
a = 0.23242 + 1.77284I
b = 0.81059 − 1.75306I
1.52382 + 6.81151I 0
u = −0.391296 − 1.171130I
a = 0.23242 − 1.77284I
b = 0.81059 + 1.75306I
1.52382 − 6.81151I 0
u = −0.345880 + 1.188710I
a = −0.53837 − 1.73904I
b = 0.14774 + 1.82262I
−2.44838 + 7.03398I 0
u = −0.345880 − 1.188710I
a = −0.53837 + 1.73904I
b = 0.14774 − 1.82262I
−2.44838 − 7.03398I 0
u = −0.092057 + 1.234850I
a = −0.495450 − 1.295560I
b = −0.852071 + 0.905712I
5.26983 + 5.03199I 0
u = −0.092057 − 1.234850I
a = −0.495450 + 1.295560I
b = −0.852071 − 0.905712I
5.26983 − 5.03199I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455722 + 0.609100I
a = 1.60614 − 0.30820I
b = 0.731630 − 0.135976I
−4.22921 − 1.70726I 0
u = −0.455722 − 0.609100I
a = 1.60614 + 0.30820I
b = 0.731630 + 0.135976I
−4.22921 + 1.70726I 0
u = 0.118808 + 1.242040I
a = −0.42103 − 1.77039I
b = 1.43043 + 1.74539I
7.72459 − 2.11932I 0
u = 0.118808 − 1.242040I
a = −0.42103 + 1.77039I
b = 1.43043 − 1.74539I
7.72459 + 2.11932I 0
u = 0.025646 + 1.248200I
a = −0.486567 + 1.155090I
b = 1.45279 − 1.13691I
5.40281 − 4.22150I 0
u = 0.025646 − 1.248200I
a = −0.486567 − 1.155090I
b = 1.45279 + 1.13691I
5.40281 + 4.22150I 0
u = 1.046810 + 0.723879I
a = 0.220629 + 0.378190I
b = 0.219008 + 0.326159I
−0.137864 + 1.223120I 0
u = 1.046810 − 0.723879I
a = 0.220629 − 0.378190I
b = 0.219008 − 0.326159I
−0.137864 − 1.223120I 0
u = 0.295324 + 0.663831I
a = 1.278920 + 0.064324I
b = −1.61600 + 0.35543I
−7.37847 + 1.50707I 0
u = 0.295324 − 0.663831I
a = 1.278920 − 0.064324I
b = −1.61600 − 0.35543I
−7.37847 − 1.50707I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.421778 + 1.209890I
a = 0.284060 + 0.880545I
b = −0.178646 − 0.822422I
2.06068 + 4.36652I 0
u = −0.421778 − 1.209890I
a = 0.284060 − 0.880545I
b = −0.178646 + 0.822422I
2.06068 − 4.36652I 0
u = 0.194052 + 1.266530I
a = 1.05189 + 1.10759I
b = −2.11133 − 1.16779I
3.44490 − 3.28202I 0
u = 0.194052 − 1.266530I
a = 1.05189 − 1.10759I
b = −2.11133 + 1.16779I
3.44490 + 3.28202I 0
u = −0.311207 + 1.254570I
a = 0.142586 − 1.392110I
b = −0.548700 + 0.808248I
3.01593 + 3.59185I 0
u = −0.311207 − 1.254570I
a = 0.142586 + 1.392110I
b = −0.548700 − 0.808248I
3.01593 − 3.59185I 0
u = 0.109630 + 1.294300I
a = 0.63687 − 1.97796I
b = 0.25579 + 1.54253I
5.52856 − 2.71154I 0
u = 0.109630 − 1.294300I
a = 0.63687 + 1.97796I
b = 0.25579 − 1.54253I
5.52856 + 2.71154I 0
u = 0.310577 + 1.273320I
a = −0.423221 + 0.708684I
b = −0.711935 − 0.835918I
4.88401 − 2.86815I 0
u = 0.310577 − 1.273320I
a = −0.423221 − 0.708684I
b = −0.711935 + 0.835918I
4.88401 + 2.86815I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.176842 + 1.303800I
a = 0.50785 + 1.67290I
b = 0.68002 − 1.31047I
1.91942 + 10.08570I 0
u = −0.176842 − 1.303800I
a = 0.50785 − 1.67290I
b = 0.68002 + 1.31047I
1.91942 − 10.08570I 0
u = −1.263450 + 0.401116I
a = −0.0425548 + 0.0814273I
b = −0.576331 + 0.622987I
0.38888 + 7.14226I 0
u = −1.263450 − 0.401116I
a = −0.0425548 − 0.0814273I
b = −0.576331 − 0.622987I
0.38888 − 7.14226I 0
u = 0.446109 + 1.260540I
a = −0.25071 − 1.58158I
b = 0.784655 + 0.745996I
−5.34892 − 12.83940I 0
u = 0.446109 − 1.260540I
a = −0.25071 + 1.58158I
b = 0.784655 − 0.745996I
−5.34892 + 12.83940I 0
u = −0.391668 + 1.278850I
a = 0.03320 − 1.86506I
b = −0.85717 + 1.62715I
−3.12917 + 6.74906I 0
u = −0.391668 − 1.278850I
a = 0.03320 + 1.86506I
b = −0.85717 − 1.62715I
−3.12917 − 6.74906I 0
u = −0.046529 + 0.649090I
a = 2.50772 − 0.81100I
b = −0.491749 + 0.120286I
−2.51394 + 0.17757I −6.05618 − 1.39616I
u = −0.046529 − 0.649090I
a = 2.50772 + 0.81100I
b = −0.491749 − 0.120286I
−2.51394 − 0.17757I −6.05618 + 1.39616I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.068820 + 1.347760I
a = −0.246233 − 1.056400I
b = −0.564848 + 0.954488I
4.88843 + 0.22573I 0
u = −0.068820 − 1.347760I
a = −0.246233 + 1.056400I
b = −0.564848 − 0.954488I
4.88843 − 0.22573I 0
u = −0.344255 + 1.308110I
a = −0.53489 + 1.47515I
b = 0.697664 − 0.782221I
−0.37425 + 7.27295I 0
u = −0.344255 − 1.308110I
a = −0.53489 − 1.47515I
b = 0.697664 + 0.782221I
−0.37425 − 7.27295I 0
u = −0.645526
a = 0.250346
b = 0.606855
−0.947565 −9.72750
u = −0.313729 + 1.327440I
a = 0.680019 + 0.142631I
b = −0.252065 − 0.409041I
−3.01059 + 1.85656I 0
u = −0.313729 − 1.327440I
a = 0.680019 − 0.142631I
b = −0.252065 + 0.409041I
−3.01059 − 1.85656I 0
u = 0.127866 + 1.386550I
a = 0.474492 + 0.203800I
b = 0.584920 − 0.039831I
4.92879 − 3.19640I 0
u = 0.127866 − 1.386550I
a = 0.474492 − 0.203800I
b = 0.584920 + 0.039831I
4.92879 + 3.19640I 0
u = 0.328285 + 0.461484I
a = −0.0630078 + 0.0210827I
b = 1.128840 − 0.272090I
−3.45580 − 0.57066I −10.8263 + 10.0452I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328285 − 0.461484I
a = −0.0630078 − 0.0210827I
b = 1.128840 + 0.272090I
−3.45580 + 0.57066I −10.8263 − 10.0452I
u = 0.414445 + 0.380512I
a = 0.278638 + 0.993930I
b = 0.197822 − 0.321827I
−0.69284 + 1.33224I −6.64121 − 5.72298I
u = 0.414445 − 0.380512I
a = 0.278638 − 0.993930I
b = 0.197822 + 0.321827I
−0.69284 − 1.33224I −6.64121 + 5.72298I
u = 0.42566 + 1.44158I
a = 0.29544 + 1.59931I
b = −1.24345 − 1.55299I
3.84618 − 12.42980I 0
u = 0.42566 − 1.44158I
a = 0.29544 − 1.59931I
b = −1.24345 + 1.55299I
3.84618 + 12.42980I 0
u = 0.60268 + 1.38693I
a = 0.213078 − 1.243000I
b = 0.70769 + 1.53619I
4.07731 − 8.44790I 0
u = 0.60268 − 1.38693I
a = 0.213078 + 1.243000I
b = 0.70769 − 1.53619I
4.07731 + 8.44790I 0
u = 0.43190 + 1.45404I
a = −0.128219 − 1.354830I
b = 1.09897 + 1.37509I
8.48189 − 8.17323I 0
u = 0.43190 − 1.45404I
a = −0.128219 + 1.354830I
b = 1.09897 − 1.37509I
8.48189 + 8.17323I 0
u = −0.460733 + 0.117371I
a = −1.60906 − 0.55964I
b = 0.098712 + 0.949838I
−5.51191 − 3.66698I −14.0947 + 2.5005I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.460733 − 0.117371I
a = −1.60906 + 0.55964I
b = 0.098712 − 0.949838I
−5.51191 + 3.66698I −14.0947 − 2.5005I
u = −0.53461 + 1.43473I
a = 0.066876 + 1.198560I
b = 0.66261 − 1.35591I
4.11168 + 7.07883I 0
u = −0.53461 − 1.43473I
a = 0.066876 − 1.198560I
b = 0.66261 + 1.35591I
4.11168 − 7.07883I 0
u = −0.51944 + 1.44253I
a = −0.092587 − 0.962490I
b = −0.919807 + 0.848743I
4.12488 + 5.52323I 0
u = −0.51944 − 1.44253I
a = −0.092587 + 0.962490I
b = −0.919807 − 0.848743I
4.12488 − 5.52323I 0
u = 0.47563 + 1.45904I
a = −0.033883 + 0.843184I
b = −0.974844 − 0.950420I
4.99392 − 3.57481I 0
u = 0.47563 − 1.45904I
a = −0.033883 − 0.843184I
b = −0.974844 + 0.950420I
4.99392 + 3.57481I 0
u = −0.49677 + 1.45946I
a = 0.18087 − 1.47841I
b = −1.21370 + 1.46423I
0.2288 + 19.1896I 0
u = −0.49677 − 1.45946I
a = 0.18087 + 1.47841I
b = −1.21370 − 1.46423I
0.2288 − 19.1896I 0
u = 0.427090 + 0.104035I
a = −0.352732 − 1.248570I
b = −1.329230 + 0.275193I
−7.97418 − 2.09016I −17.1983 + 4.1287I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.427090 − 0.104035I
a = −0.352732 + 1.248570I
b = −1.329230 − 0.275193I
−7.97418 + 2.09016I −17.1983 − 4.1287I
u = −0.49606 + 1.48019I
a = −0.080573 + 1.269130I
b = 1.08654 − 1.23612I
6.0966 + 13.1880I 0
u = −0.49606 − 1.48019I
a = −0.080573 − 1.269130I
b = 1.08654 + 1.23612I
6.0966 − 13.1880I 0
u = −0.308733 + 0.265925I
a = −2.81762 + 0.08446I
b = 0.05872 + 1.43909I
−2.84210 + 8.07603I −9.89030 − 5.80751I
u = −0.308733 − 0.265925I
a = −2.81762 − 0.08446I
b = 0.05872 − 1.43909I
−2.84210 − 8.07603I −9.89030 + 5.80751I
u = 0.337030 + 0.134594I
a = −1.89464 − 0.70426I
b = 0.24122 − 1.53038I
1.07758 − 1.14467I −12.8080 + 6.3883I
u = 0.337030 − 0.134594I
a = −1.89464 + 0.70426I
b = 0.24122 + 1.53038I
1.07758 + 1.14467I −12.8080 − 6.3883I
u = −0.45026 + 1.58914I
a = 0.131315 − 0.889361I
b = −0.793852 + 1.046450I
5.79316 + 1.25135I 0
u = −0.45026 − 1.58914I
a = 0.131315 + 0.889361I
b = −0.793852 − 1.046450I
5.79316 − 1.25135I 0
u = 0.57108 + 1.55828I
a = 0.056731 + 0.818240I
b = −0.831959 − 1.014710I
6.56944 − 5.57697I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.57108 − 1.55828I
a = 0.056731 − 0.818240I
b = −0.831959 + 1.014710I
6.56944 + 5.57697I 0
u = −0.01393 + 1.69028I
a = −0.805814 + 0.194122I
b = 1.44212 − 0.26395I
−1.77623 − 3.16930I 0
u = −0.01393 − 1.69028I
a = −0.805814 − 0.194122I
b = 1.44212 + 0.26395I
−1.77623 + 3.16930I 0
u = 0.55784 + 1.62456I
a = −0.304422 − 0.156703I
b = 0.721886 − 0.025192I
−4.09530 + 2.65625I 0
u = 0.55784 − 1.62456I
a = −0.304422 + 0.156703I
b = 0.721886 + 0.025192I
−4.09530 − 2.65625I 0
u = 0.266007 + 0.065605I
a = −0.24391 − 3.42980I
b = −0.370617 − 0.954028I
3.82317 − 0.61322I −0.60379 + 2.61723I
u = 0.266007 − 0.065605I
a = −0.24391 + 3.42980I
b = −0.370617 + 0.954028I
3.82317 + 0.61322I −0.60379 − 2.61723I
u = −1.23690 + 1.22733I
a = 0.199304 − 0.140853I
b = 0.129031 − 0.412552I
−2.48998 − 5.77455I 0
u = −1.23690 − 1.22733I
a = 0.199304 + 0.140853I
b = 0.129031 + 0.412552I
−2.48998 + 5.77455I 0
u = −0.0803798 + 0.0128570I
a = 3.2337 + 14.4075I
b = −0.169883 + 0.813698I
1.59518 − 4.15000I −4.24825 + 2.12593I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0803798 − 0.0128570I
a = 3.2337 − 14.4075I
b = −0.169883 − 0.813698I
1.59518 + 4.15000I −4.24825 − 2.12593I
19
II. I
u
2
= h6.58 × 10
20
u
31
+ 6.87 × 10
21
u
30
+ · · · + 2.04 × 10
21
b + 2.89 ×
10
23
, −9.30 × 10
22
u
31
− 4.19 × 10
23
u
30
+ · · · + 1.20 × 10
23
a − 2.07 ×
10
25
, u
32
− u
31
+ · · · − 104u + 59i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
1
=
0.772916u
31
+ 3.48314u
30
+ ··· − 246.523u + 171.923
−0.322848u
31
− 3.36751u
30
+ ··· + 213.078u − 141.768
a
9
=
1
u
2
a
10
=
−1.09040u
31
+ 4.92530u
30
+ ··· − 351.382u + 192.672
1.44406u
31
− 2.11542u
30
+ ··· + 137.621u − 40.6517
a
4
=
u
u
3
+ u
a
2
=
0.332545u
31
+ 1.26573u
30
+ ··· − 107.425u + 70.6271
−0.738226u
31
− 1.62655u
30
+ ··· + 101.748u − 86.2548
a
3
=
5.82207u
31
− 5.85860u
30
+ ··· + 354.324u − 65.0117
−1.52733u
31
− 0.673710u
30
+ ··· + 79.7183u − 83.1063
a
12
=
0.450069u
31
+ 0.115624u
30
+ ··· − 33.4443u + 30.1556
−0.322848u
31
− 3.36751u
30
+ ··· + 213.078u − 141.768
a
6
=
−2.02011u
31
+ 2.94767u
30
+ ··· − 210.385u + 65.8944
1.85323u
31
− 0.889914u
30
+ ··· + 38.0087u + 22.9748
a
11
=
−3.88876u
31
+ 1.81980u
30
+ ··· − 110.509u − 48.7052
−0.0435544u
31
+ 0.449278u
30
+ ··· − 24.6724u + 10.2843
a
7
=
−2.64728u
31
+ 3.61718u
30
+ ··· − 263.239u + 81.5249
−0.460531u
31
+ 0.444958u
30
+ ··· − 30.1986u + 2.92724
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4360617952060846080885
2038939424063291368097
u
31
+
1071442814931548057311
2038939424063291368097
u
30
+ ··· −
75226765869100235822635
2038939424063291368097
u −
96233838636533270012364
2038939424063291368097
20
(iv) u-Polynomials at the component
21
Crossings u-Polynomials at each crossing
c
1
u
32
− 3u
31
+ ··· + 10u + 1
c
2
u
32
+ 2u
31
+ ··· + 3u + 1
c
3
u
32
+ 15u
30
+ ··· − 15u + 1
c
4
u
32
+ u
31
+ ··· + 104u + 59
c
5
u
32
+ 13u
30
+ ··· + 24u + 11
c
6
u
32
− 2u
31
+ ··· − 3u + 1
c
7
u
32
− 2u
31
+ ··· − 2u + 1
c
8
u
32
− u
31
+ ··· − 104u + 59
c
9
u
32
+ 2u
31
+ ··· + 6u + 1
c
10
u
32
+ 15u
30
+ ··· + 15u + 1
c
11
u
32
+ 13u
30
+ ··· − 24u + 11
c
12
u
32
− 2u
31
+ ··· + 91u + 11
22
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
− 11y
31
+ ··· − 36y + 1
c
2
, c
6
y
32
− 14y
31
+ ··· − 23y + 1
c
3
, c
10
y
32
+ 30y
31
+ ··· − 63y + 1
c
4
, c
8
y
32
+ 29y
31
+ ··· + 55854y + 3481
c
5
, c
11
y
32
+ 26y
31
+ ··· + 854y + 121
c
7
y
32
+ 2y
31
+ ··· + 34y + 1
c
9
y
32
+ 4y
31
+ ··· + 2y + 1
c
12
y
32
+ 32y
31
+ ··· − 2297y + 121
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.362577 + 0.964026I
a = 0.748470 − 0.603980I
b = 0.346090 + 0.007985I
−3.45564 + 2.24438I −10.21333 − 4.38896I
u = 0.362577 − 0.964026I
a = 0.748470 + 0.603980I
b = 0.346090 − 0.007985I
−3.45564 − 2.24438I −10.21333 + 4.38896I
u = −1.001140 + 0.326605I
a = 0.089441 − 0.312551I
b = 0.441919 − 0.010123I
−1.64932 − 0.57277I −15.8069 + 2.6042I
u = −1.001140 − 0.326605I
a = 0.089441 + 0.312551I
b = 0.441919 + 0.010123I
−1.64932 + 0.57277I −15.8069 − 2.6042I
u = 0.112316 + 1.103330I
a = 0.65062 + 2.11417I
b = 0.215633 − 0.782136I
−2.60539 − 3.77746I −4.44880 + 0.99726I
u = 0.112316 − 1.103330I
a = 0.65062 − 2.11417I
b = 0.215633 + 0.782136I
−2.60539 + 3.77746I −4.44880 − 0.99726I
u = −0.285330 + 1.078980I
a = 0.98045 + 2.58949I
b = 0.10799 − 2.53725I
−1.60249 + 9.07145I −6.02655 − 10.36968I
u = −0.285330 − 1.078980I
a = 0.98045 − 2.58949I
b = 0.10799 + 2.53725I
−1.60249 − 9.07145I −6.02655 + 10.36968I
u = 1.182150 + 0.145591I
a = 0.362758 + 0.211827I
b = −0.273043 + 0.840491I
1.19666 + 1.71799I −3.40196 − 3.14843I
u = 1.182150 − 0.145591I
a = 0.362758 − 0.211827I
b = −0.273043 − 0.840491I
1.19666 − 1.71799I −3.40196 + 3.14843I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.074667 + 1.191350I
a = 0.02224 − 2.67498I
b = 0.95555 + 2.46929I
4.15095 − 1.45690I −6.06391 + 3.90496I
u = 0.074667 − 1.191350I
a = 0.02224 + 2.67498I
b = 0.95555 − 2.46929I
4.15095 + 1.45690I −6.06391 − 3.90496I
u = −0.461743 + 1.100780I
a = −0.65437 − 1.25612I
b = −0.391036 + 1.157380I
2.12590 + 5.90675I −4.41809 − 5.95745I
u = −0.461743 − 1.100780I
a = −0.65437 + 1.25612I
b = −0.391036 − 1.157380I
2.12590 − 5.90675I −4.41809 + 5.95745I
u = −0.381182 + 1.202170I
a = 0.007178 − 1.285940I
b = −0.151030 + 0.745397I
1.22735 + 5.15944I −10.65142 − 6.32446I
u = −0.381182 − 1.202170I
a = 0.007178 + 1.285940I
b = −0.151030 − 0.745397I
1.22735 − 5.15944I −10.65142 + 6.32446I
u = 0.142714 + 1.275780I
a = −0.38126 + 1.60828I
b = −0.57553 − 1.42891I
6.62274 − 1.71689I −2.06271 + 1.18758I
u = 0.142714 − 1.275780I
a = −0.38126 − 1.60828I
b = −0.57553 + 1.42891I
6.62274 + 1.71689I −2.06271 − 1.18758I
u = 0.154332 + 1.329780I
a = −0.135624 + 0.304101I
b = −0.940652 − 0.367938I
6.39432 − 2.82994I −0.17514 + 2.86968I
u = 0.154332 − 1.329780I
a = −0.135624 − 0.304101I
b = −0.940652 + 0.367938I
6.39432 + 2.82994I −0.17514 − 2.86968I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.875864 + 1.016080I
a = 0.354410 + 0.314481I
b = 0.181318 − 0.990508I
−2.05254 − 5.40722I −6.25580 + 2.37204I
u = −0.875864 − 1.016080I
a = 0.354410 − 0.314481I
b = 0.181318 + 0.990508I
−2.05254 + 5.40722I −6.25580 − 2.37204I
u = −0.089933 + 0.626357I
a = 0.948435 + 0.750652I
b = −1.57516 − 0.10493I
−7.01308 − 2.03138I −7.61477 + 5.15095I
u = −0.089933 − 0.626357I
a = 0.948435 − 0.750652I
b = −1.57516 + 0.10493I
−7.01308 + 2.03138I −7.61477 − 5.15095I
u = 0.10860 + 1.49383I
a = −0.544144 − 0.265243I
b = 0.776324 − 0.008574I
−3.90622 + 2.22707I −14.6705 + 2.6483I
u = 0.10860 − 1.49383I
a = −0.544144 + 0.265243I
b = 0.776324 + 0.008574I
−3.90622 − 2.22707I −14.6705 − 2.6483I
u = 0.306065 + 0.379215I
a = 1.63844 + 0.22036I
b = −0.005413 + 1.288400I
1.62896 + 0.35162I −5.47099 + 0.61470I
u = 0.306065 − 0.379215I
a = 1.63844 − 0.22036I
b = −0.005413 − 1.288400I
1.62896 − 0.35162I −5.47099 − 0.61470I
u = 0.57465 + 1.42710I
a = 0.086948 − 1.193340I
b = 0.77214 + 1.39851I
5.39835 − 8.08405I −3.41656 + 6.42031I
u = 0.57465 − 1.42710I
a = 0.086948 + 1.193340I
b = 0.77214 − 1.39851I
5.39835 + 8.08405I −3.41656 − 6.42031I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.57712 + 1.52641I
a = −0.012970 + 0.740923I
b = −0.885111 − 0.845760I
5.05400 − 4.18301I −8.00000 + 8.98369I
u = 0.57712 − 1.52641I
a = −0.012970 − 0.740923I
b = −0.885111 + 0.845760I
5.05400 + 4.18301I −8.00000 − 8.98369I
28
III. I
v
1
= ha, b − 1, v
3
+ 2v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
1
=
0
1
a
9
=
1
0
a
10
=
1
1
a
4
=
v
0
a
2
=
−v
2
1
a
3
=
2v
v
a
12
=
1
1
a
6
=
2v
v
a
11
=
2v
2
+ 1
v
2
+ 1
a
7
=
v
2
+ 2v
v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3v
2
− v − 10
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
11
u
3
+ 2u − 1
c
2
, c
9
(u − 1)
3
c
3
, c
5
u
3
+ 2u + 1
c
4
, c
8
u
3
c
6
, c
12
(u + 1)
3
c
7
u
3
+ u
2
− u − 2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
10
, c
11
y
3
+ 4y
2
+ 4y − 1
c
2
, c
6
, c
9
c
12
(y − 1)
3
c
4
, c
8
y
3
c
7
y
3
− 3y
2
+ 5y − 4
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.22670 + 1.46771I
a = 0
b = 1.00000
−3.28987 −16.5351 + 0.5287I
v = 0.22670 − 1.46771I
a = 0
b = 1.00000
−3.28987 −16.5351 − 0.5287I
v = −0.453398
a = 0
b = 1.00000
−3.28987 −8.92990
32
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ 2u − 1)(u
32
− 3u
31
+ ··· + 10u + 1)
· (u
141
− 12u
140
+ ··· + 763u − 49)
c
2
((u − 1)
3
)(u
32
+ 2u
31
+ ··· + 3u + 1)
· (u
141
− 2u
140
+ ··· + 45051u + 32979)
c
3
(u
3
+ 2u + 1)(u
32
+ 15u
30
+ ··· − 15u + 1)
· (u
141
+ u
140
+ ··· + 386164u + 65629)
c
4
u
3
(u
32
+ u
31
+ ··· + 104u + 59)(u
141
+ 4u
140
+ ··· + 2832u + 168)
c
5
(u
3
+ 2u + 1)(u
32
+ 13u
30
+ ··· + 24u + 11)
· (u
141
− u
140
+ ··· + 533427u + 47167)
c
6
((u + 1)
3
)(u
32
− 2u
31
+ ··· − 3u + 1)
· (u
141
− 2u
140
+ ··· + 45051u + 32979)
c
7
(u
3
+ u
2
− u − 2)(u
32
− 2u
31
+ ··· − 2u + 1)
· (u
141
+ 8u
140
+ ··· + 47275162u + 6401042)
c
8
u
3
(u
32
− u
31
+ ··· − 104u + 59)(u
141
+ 4u
140
+ ··· + 2832u + 168)
c
9
((u − 1)
3
)(u
32
+ 2u
31
+ ··· + 6u + 1)(u
141
+ 8u
140
+ ··· + 26u + 1)
c
10
(u
3
+ 2u − 1)(u
32
+ 15u
30
+ ··· + 15u + 1)
· (u
141
+ u
140
+ ··· + 386164u + 65629)
c
11
(u
3
+ 2u − 1)(u
32
+ 13u
30
+ ··· − 24u + 11)
· (u
141
− u
140
+ ··· + 533427u + 47167)
c
12
((u + 1)
3
)(u
32
− 2u
31
+ ··· + 91u + 11)
· (u
141
− 2u
140
+ ··· + 14863691u + 980999)
33
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 4y
2
+ 4y − 1)(y
32
− 11y
31
+ ··· − 36y + 1)
· (y
141
− 2y
140
+ ··· − 122941y − 2401)
c
2
, c
6
((y − 1)
3
)(y
32
− 14y
31
+ ··· − 23y + 1)
· (y
141
− 84y
140
+ ··· + 18315150465y − 1087614441)
c
3
, c
10
(y
3
+ 4y
2
+ 4y − 1)(y
32
+ 30y
31
+ ··· − 63y + 1)
· (y
141
+ 119y
140
+ ··· + 200837368090y − 4307165641)
c
4
, c
8
y
3
(y
32
+ 29y
31
+ ··· + 55854y + 3481)
· (y
141
+ 110y
140
+ ··· + 8842080y − 28224)
c
5
, c
11
(y
3
+ 4y
2
+ 4y − 1)(y
32
+ 26y
31
+ ··· + 854y + 121)
· (y
141
+ 107y
140
+ ··· − 15637743751y − 2224725889)
c
7
(y
3
− 3y
2
+ 5y − 4)(y
32
+ 2y
31
+ ··· + 34y + 1)
· (y
141
− 40y
140
+ ··· − 12502874859103792y − 40973338685764)
c
9
((y − 1)
3
)(y
32
+ 4y
31
+ ··· + 2y + 1)(y
141
− 6y
140
+ ··· + 136y − 1)
c
12
((y − 1)
3
)(y
32
+ 32y
31
+ ··· − 2297y + 121)
· (y
141
+ 58y
140
+ ··· − 23268885446441y − 962359038001)
34
