12a
0127
(K12a
0127
)
A knot diagram
1
Linearized knot diagam
3 5 8 6 2 11 4 12 1 7 10 9
Solving Sequence
6,11 2,7
5 3 1 4 8 10 12 9
c
6
c
5
c
2
c
1
c
4
c
7
c
10
c
11
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.45704 × 10
149
u
92
− 7.46621 × 10
149
u
91
+ ··· + 1.59160 × 10
150
b + 5.16311 × 10
150
,
6.45956 × 10
149
u
92
+ 4.93708 × 10
149
u
91
+ ··· + 3.18320 × 10
150
a + 3.19913 × 10
151
,
u
93
+ 3u
92
+ ··· − 120u − 16i
I
u
2
= hu
2
a + u
2
+ b, u
4
a + 2u
4
+ u
2
a − u
3
+ a
2
+ au + 4u
2
+ 2a + 3, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
v
1
= ha, −3v
3
+ 5v
2
+ b − 19v + 8, v
4
− 2v
3
+ 7v
2
− 5v + 1i
* 3 irreducible components of dim
C
= 0, with total 107 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−2.46 × 10
149
u
92
− 7.47 × 10
149
u
91
+ · · · + 1.59 × 10
150
b + 5.16 ×
10
150
, 6.46 × 10
149
u
92
+ 4.94 × 10
149
u
91
+ · · · + 3.18 × 10
150
a + 3.20 ×
10
151
, u
93
+ 3u
92
+ · · · − 120u − 16i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−0.202927u
92
− 0.155098u
91
+ ··· − 57.5365u − 10.0500
0.154376u
92
+ 0.469101u
91
+ ··· − 27.1347u − 3.24397
a
7
=
1
−u
2
a
5
=
−0.211735u
92
− 0.781695u
91
+ ··· + 27.7607u + 2.37556
−0.0923884u
92
− 0.0171328u
91
+ ··· − 23.5232u − 4.33754
a
3
=
0.0729802u
92
+ 0.383157u
91
+ ··· − 57.9079u − 10.7686
−0.147554u
92
− 0.509873u
91
+ ··· + 32.0130u + 5.00554
a
1
=
−0.0344604u
92
+ 0.130739u
91
+ ··· − 34.8900u − 5.65271
−0.111791u
92
− 0.240569u
91
+ ··· + 5.98147u + 0.720096
a
4
=
−0.304123u
92
− 0.798828u
91
+ ··· + 4.23750u − 1.96198
−0.0923884u
92
− 0.0171328u
91
+ ··· − 23.5232u − 4.33754
a
8
=
−0.146252u
92
− 0.109830u
91
+ ··· − 28.9086u − 4.93261
0.265261u
92
+ 0.829749u
91
+ ··· − 43.1125u − 5.98290
a
10
=
−u
u
3
+ u
a
12
=
−u
3
u
5
+ u
3
+ u
a
9
=
−0.366766u
92
− 0.697201u
91
+ ··· − 4.07313u − 1.66182
0.390430u
92
+ 1.04707u
91
+ ··· − 44.5678u − 5.99304
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.42999u
92
− 4.05788u
91
+ ··· + 297.788u + 41.2511
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
93
+ 29u
92
+ ··· + 33u − 1
c
2
, c
5
u
93
+ 7u
92
+ ··· + 11u + 1
c
3
, c
7
u
93
− 2u
92
+ ··· + 2048u − 1024
c
6
, c
10
u
93
− 3u
92
+ ··· − 120u + 16
c
8
, c
9
, c
12
u
93
− 7u
92
+ ··· + 14u + 1
c
11
u
93
+ 33u
92
+ ··· − 5056u − 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
93
+ 77y
92
+ ··· + 5105y −1
c
2
, c
5
y
93
+ 29y
92
+ ··· + 33y −1
c
3
, c
7
y
93
+ 60y
92
+ ··· − 16777216y −1048576
c
6
, c
10
y
93
+ 33y
92
+ ··· − 5056y −256
c
8
, c
9
, c
12
y
93
− 79y
92
+ ··· − 38y −1
c
11
y
93
+ 49y
92
+ ··· − 2600960y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.665891 + 0.747136I
a = 0.021714 − 0.322214I
b = 0.348160 − 1.076720I
1.13674 − 1.06346I 0
u = 0.665891 − 0.747136I
a = 0.021714 + 0.322214I
b = 0.348160 + 1.076720I
1.13674 + 1.06346I 0
u = 0.028090 + 0.992187I
a = −0.594572 − 0.572329I
b = 0.751152 + 0.516508I
−4.48491 + 1.53376I 0
u = 0.028090 − 0.992187I
a = −0.594572 + 0.572329I
b = 0.751152 − 0.516508I
−4.48491 − 1.53376I 0
u = 0.703650 + 0.696275I
a = −2.89955 − 0.09078I
b = 0.724841 + 0.851661I
0.30953 + 1.50694I 0
u = 0.703650 − 0.696275I
a = −2.89955 + 0.09078I
b = 0.724841 − 0.851661I
0.30953 − 1.50694I 0
u = 0.939231 + 0.294821I
a = 0.605886 − 0.156692I
b = −0.030920 + 0.823464I
−4.04154 − 0.52773I 0
u = 0.939231 − 0.294821I
a = 0.605886 + 0.156692I
b = −0.030920 − 0.823464I
−4.04154 + 0.52773I 0
u = 0.813358 + 0.645627I
a = −1.33911 + 1.56809I
b = 0.723387 − 0.895856I
0.17268 − 4.02210I 0
u = 0.813358 − 0.645627I
a = −1.33911 − 1.56809I
b = 0.723387 + 0.895856I
0.17268 + 4.02210I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772462 + 0.697912I
a = −0.693293 − 0.763022I
b = 0.716539 + 0.040558I
1.00580 + 1.29005I 0
u = −0.772462 − 0.697912I
a = −0.693293 + 0.763022I
b = 0.716539 − 0.040558I
1.00580 − 1.29005I 0
u = −0.641295 + 0.709236I
a = 1.50510 − 0.41623I
b = −0.898015 + 0.834146I
6.07300 − 4.04164I 0
u = −0.641295 − 0.709236I
a = 1.50510 + 0.41623I
b = −0.898015 − 0.834146I
6.07300 + 4.04164I 0
u = −0.902049 + 0.545981I
a = 0.232902 + 0.051229I
b = 0.236858 + 1.071850I
−2.65287 + 4.43575I 0
u = −0.902049 − 0.545981I
a = 0.232902 − 0.051229I
b = 0.236858 − 1.071850I
−2.65287 − 4.43575I 0
u = −0.457956 + 0.959120I
a = 1.59736 + 0.85309I
b = −0.104767 + 0.782745I
−1.41753 − 2.39208I 0
u = −0.457956 − 0.959120I
a = 1.59736 − 0.85309I
b = −0.104767 − 0.782745I
−1.41753 + 2.39208I 0
u = −0.092701 + 1.070930I
a = −1.44126 − 0.68874I
b = 0.607350 − 1.043700I
−6.08658 − 3.61353I 0
u = −0.092701 − 1.070930I
a = −1.44126 + 0.68874I
b = 0.607350 + 1.043700I
−6.08658 + 3.61353I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.723885 + 0.827218I
a = −1.16046 − 1.38117I
b = 0.768196 + 0.844019I
3.73031 + 0.14019I 0
u = −0.723885 − 0.827218I
a = −1.16046 + 1.38117I
b = 0.768196 − 0.844019I
3.73031 − 0.14019I 0
u = 0.893807 + 0.644806I
a = 1.32495 − 0.50673I
b = −0.794613 + 0.999171I
8.57279 − 6.14801I 0
u = 0.893807 − 0.644806I
a = 1.32495 + 0.50673I
b = −0.794613 − 0.999171I
8.57279 + 6.14801I 0
u = 0.887790 + 0.698478I
a = 1.52211 + 0.36437I
b = −0.880968 − 0.777147I
9.26540 + 0.06367I 0
u = 0.887790 − 0.698478I
a = 1.52211 − 0.36437I
b = −0.880968 + 0.777147I
9.26540 − 0.06367I 0
u = 0.734298 + 0.864283I
a = −0.778513 + 0.466600I
b = 0.784078 + 0.062250I
4.44653 + 2.78922I 0
u = 0.734298 − 0.864283I
a = −0.778513 − 0.466600I
b = 0.784078 − 0.062250I
4.44653 − 2.78922I 0
u = −0.563900 + 0.655196I
a = 1.38303 + 0.50824I
b = −0.841777 − 0.975061I
5.63543 + 2.37306I −4.00000 + 2.97537I
u = −0.563900 − 0.655196I
a = 1.38303 − 0.50824I
b = −0.841777 + 0.975061I
5.63543 − 2.37306I −4.00000 − 2.97537I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.709989 + 0.895029I
a = −2.47972 + 0.00567I
b = 0.753350 − 0.911791I
3.52116 − 5.61309I 0
u = −0.709989 − 0.895029I
a = −2.47972 − 0.00567I
b = 0.753350 + 0.911791I
3.52116 + 5.61309I 0
u = −0.462321 + 0.718150I
a = −1.82763 − 2.01499I
b = 0.271223 − 1.003410I
−2.13554 − 2.02980I −7.22138 + 5.99064I
u = −0.462321 − 0.718150I
a = −1.82763 + 2.01499I
b = 0.271223 + 1.003410I
−2.13554 + 2.02980I −7.22138 − 5.99064I
u = −0.091279 + 1.144600I
a = 0.444100 + 1.156810I
b = −0.727814 + 0.904983I
1.61423 − 5.28181I 0
u = −0.091279 − 1.144600I
a = 0.444100 − 1.156810I
b = −0.727814 − 0.904983I
1.61423 + 5.28181I 0
u = −0.596281 + 0.984323I
a = −0.310483 + 0.304748I
b = 0.412190 + 1.128220I
−3.14185 − 2.46938I 0
u = −0.596281 − 0.984323I
a = −0.310483 − 0.304748I
b = 0.412190 − 1.128220I
−3.14185 + 2.46938I 0
u = 0.100508 + 0.842737I
a = 1.33505 − 2.13922I
b = 0.072762 − 0.853196I
−2.84370 − 1.61247I −12.17526 + 3.63901I
u = 0.100508 − 0.842737I
a = 1.33505 + 2.13922I
b = 0.072762 + 0.853196I
−2.84370 + 1.61247I −12.17526 − 3.63901I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373537 + 1.089370I
a = 0.783771 − 0.106400I
b = −0.466204 + 0.310229I
−5.25369 + 3.52820I 0
u = 0.373537 − 1.089370I
a = 0.783771 + 0.106400I
b = −0.466204 − 0.310229I
−5.25369 − 3.52820I 0
u = 0.654147 + 0.948564I
a = −1.29797 + 0.96685I
b = 0.249813 + 1.112570I
0.51216 + 6.20139I 0
u = 0.654147 − 0.948564I
a = −1.29797 − 0.96685I
b = 0.249813 − 1.112570I
0.51216 − 6.20139I 0
u = −0.180203 + 1.141930I
a = −0.066782 − 0.541344I
b = −0.733362 − 0.843879I
1.80341 + 0.28751I 0
u = −0.180203 − 1.141930I
a = −0.066782 + 0.541344I
b = −0.733362 + 0.843879I
1.80341 − 0.28751I 0
u = 1.178410 + 0.045776I
a = 1.332440 + 0.340605I
b = −0.721449 − 0.874875I
−0.31299 + 2.75548I 0
u = 1.178410 − 0.045776I
a = 1.332440 − 0.340605I
b = −0.721449 + 0.874875I
−0.31299 − 2.75548I 0
u = −0.657396 + 0.984250I
a = 0.057650 + 1.054980I
b = −0.858227 − 0.752581I
5.21003 − 1.06475I 0
u = −0.657396 − 0.984250I
a = 0.057650 − 1.054980I
b = −0.858227 + 0.752581I
5.21003 + 1.06475I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.669257 + 0.979936I
a = −1.11762 + 1.21431I
b = 0.812545 − 0.808383I
−0.54672 + 3.79018I 0
u = 0.669257 − 0.979936I
a = −1.11762 − 1.21431I
b = 0.812545 + 0.808383I
−0.54672 − 3.79018I 0
u = −0.606403 + 1.021380I
a = 2.02312 + 1.14152I
b = −0.769467 + 1.002140I
4.43609 − 7.12677I 0
u = −0.606403 − 1.021380I
a = 2.02312 − 1.14152I
b = −0.769467 − 1.002140I
4.43609 + 7.12677I 0
u = −0.698456 + 0.995590I
a = −0.859834 − 0.289365I
b = 0.839179 − 0.129360I
0.09738 − 6.86530I 0
u = −0.698456 − 0.995590I
a = −0.859834 + 0.289365I
b = 0.839179 + 0.129360I
0.09738 + 6.86530I 0
u = 0.110109 + 1.230620I
a = 0.238797 + 1.135160I
b = 0.024424 + 1.043260I
−9.67176 + 2.69506I 0
u = 0.110109 − 1.230620I
a = 0.238797 − 1.135160I
b = 0.024424 − 1.043260I
−9.67176 − 2.69506I 0
u = −1.031690 + 0.700693I
a = 1.53765 − 0.32483I
b = −0.867434 + 0.730543I
4.73954 + 4.00870I 0
u = −1.031690 − 0.700693I
a = 1.53765 + 0.32483I
b = −0.867434 − 0.730543I
4.73954 − 4.00870I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.703437 + 1.030230I
a = −2.26417 − 0.00813I
b = 0.767953 + 0.952069I
−0.99244 + 9.71949I 0
u = 0.703437 − 1.030230I
a = −2.26417 + 0.00813I
b = 0.767953 − 0.952069I
−0.99244 − 9.71949I 0
u = −0.332717 + 0.673554I
a = 0.702724 − 0.002191I
b = −0.098932 − 0.255156I
−0.235055 − 1.159930I −3.79400 + 5.65355I
u = −0.332717 − 0.673554I
a = 0.702724 + 0.002191I
b = −0.098932 + 0.255156I
−0.235055 + 1.159930I −3.79400 − 5.65355I
u = −1.070920 + 0.666799I
a = 1.285280 + 0.509328I
b = −0.764932 − 1.017430I
3.85170 + 10.08040I 0
u = −1.070920 − 0.666799I
a = 1.285280 − 0.509328I
b = −0.764932 + 1.017430I
3.85170 − 10.08040I 0
u = 0.757426 + 1.037860I
a = 0.392734 − 1.088930I
b = −0.888505 + 0.723229I
8.20993 + 6.03208I 0
u = 0.757426 − 1.037860I
a = 0.392734 + 1.088930I
b = −0.888505 − 0.723229I
8.20993 − 6.03208I 0
u = −0.699174 + 1.090670I
a = −1.040200 − 0.722000I
b = 0.223631 − 1.157930I
−4.30881 − 10.31650I 0
u = −0.699174 − 1.090670I
a = −1.040200 + 0.722000I
b = 0.223631 + 1.157930I
−4.30881 + 10.31650I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.734781 + 1.069170I
a = 2.09957 − 0.76870I
b = −0.771412 − 1.030210I
7.2560 + 12.1847I 0
u = 0.734781 − 1.069170I
a = 2.09957 + 0.76870I
b = −0.771412 + 1.030210I
7.2560 − 12.1847I 0
u = 0.559108 + 1.183530I
a = 1.28446 − 0.60827I
b = −0.201625 − 0.849532I
−6.85158 + 5.93082I 0
u = 0.559108 − 1.183530I
a = 1.28446 + 0.60827I
b = −0.201625 + 0.849532I
−6.85158 − 5.93082I 0
u = 0.104371 + 0.637225I
a = −1.78509 + 2.38765I
b = 0.550116 + 0.929746I
−0.65265 + 2.81004I −7.41547 + 0.47034I
u = 0.104371 − 0.637225I
a = −1.78509 − 2.38765I
b = 0.550116 − 0.929746I
−0.65265 − 2.81004I −7.41547 − 0.47034I
u = −0.804628 + 1.104560I
a = 0.575641 + 1.015300I
b = −0.905266 − 0.694338I
3.41954 − 10.67570I 0
u = −0.804628 − 1.104560I
a = 0.575641 − 1.015300I
b = −0.905266 + 0.694338I
3.41954 + 10.67570I 0
u = 0.625980
a = 1.39606
b = −0.118436
−2.21094 −3.96060
u = −0.623742 + 0.005581I
a = 1.40205 − 0.42581I
b = −0.817120 + 0.899544I
5.79457 − 3.05660I 5.70755 + 2.23879I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.623742 − 0.005581I
a = 1.40205 + 0.42581I
b = −0.817120 − 0.899544I
5.79457 + 3.05660I 5.70755 − 2.23879I
u = −0.802626 + 1.138200I
a = 2.02368 + 0.56314I
b = −0.765073 + 1.050410I
2.3123 − 16.8507I 0
u = −0.802626 − 1.138200I
a = 2.02368 − 0.56314I
b = −0.765073 − 1.050410I
2.3123 + 16.8507I 0
u = 0.393753 + 1.338270I
a = 0.360318 + 0.076774I
b = −0.673290 + 0.777836I
−4.96828 + 2.80408I 0
u = 0.393753 − 1.338270I
a = 0.360318 − 0.076774I
b = −0.673290 − 0.777836I
−4.96828 − 2.80408I 0
u = 0.304631 + 1.373780I
a = 1.017700 − 0.772413I
b = −0.679839 − 0.954465I
−5.53600 + 8.05814I 0
u = 0.304631 − 1.373780I
a = 1.017700 + 0.772413I
b = −0.679839 + 0.954465I
−5.53600 − 8.05814I 0
u = −0.342841 + 0.373977I
a = 0.538435 + 0.205024I
b = 0.253462 − 0.569255I
−0.064937 − 1.209350I −0.44197 + 4.81444I
u = −0.342841 − 0.373977I
a = 0.538435 − 0.205024I
b = 0.253462 + 0.569255I
−0.064937 + 1.209350I −0.44197 − 4.81444I
u = −0.427681 + 0.212695I
a = −7.06270 + 0.05989I
b = 0.446144 − 0.898095I
−1.97161 − 1.83092I 13.2051 + 13.6976I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.427681 − 0.212695I
a = −7.06270 − 0.05989I
b = 0.446144 + 0.898095I
−1.97161 + 1.83092I 13.2051 − 13.6976I
u = 0.170011 + 0.377963I
a = 0.94269 + 1.18580I
b = 0.482876 − 0.744659I
0.00175 − 1.44857I −2.22081 + 5.39809I
u = 0.170011 − 0.377963I
a = 0.94269 − 1.18580I
b = 0.482876 + 0.744659I
0.00175 + 1.44857I −2.22081 − 5.39809I
14
II. I
u
2
= hu
2
a + u
2
+ b, u
4
a + 2u
4
+ u
2
a − u
3
+ a
2
+ au + 4u
2
+ 2a + 3, u
5
−
u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
a
−u
2
a − u
2
a
7
=
1
−u
2
a
5
=
u
4
+ u
2
a + 2u
2
+ a + u + 2
−u
2
a − u
2
− 1
a
3
=
u
4
+ u
2
+ a + u + 1
−u
2
a − u
2
− 1
a
1
=
−1
0
a
4
=
u
4
+ u
2
+ a + u + 1
−u
2
a − u
2
− 1
a
8
=
1
−u
2
a
10
=
−u
u
3
+ u
a
12
=
−u
3
u
4
− u
3
+ u
2
+ 1
a
9
=
u
3
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
4
a + u
3
a + u
4
+ 5u
2
a + 5u
3
+ au + u
2
− a + 5u − 7
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
3
, c
7
u
10
c
6
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
8
, c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
10
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
11
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
12
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
5
c
3
, c
7
y
10
c
6
, c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
c
8
, c
9
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 0.219642 + 0.330957I
b = 0.500000 + 0.866025I
−0.329100 + 0.499304I −6.44749 + 1.44665I
u = −0.339110 + 0.822375I
a = −1.32320 − 1.22172I
b = 0.500000 − 0.866025I
−0.32910 − 3.56046I −2.59686 + 8.38554I
u = −0.339110 − 0.822375I
a = 0.219642 − 0.330957I
b = 0.500000 − 0.866025I
−0.329100 − 0.499304I −6.44749 − 1.44665I
u = −0.339110 − 0.822375I
a = −1.32320 + 1.22172I
b = 0.500000 + 0.866025I
−0.32910 + 3.56046I −2.59686 − 8.38554I
u = 0.766826
a = −1.85031 + 1.47278I
b = 0.500000 − 0.866025I
−2.40108 − 2.02988I −7.10008 + 5.66929I
u = 0.766826
a = −1.85031 − 1.47278I
b = 0.500000 + 0.866025I
−2.40108 + 2.02988I −7.10008 − 5.66929I
u = 0.455697 + 1.200150I
a = −1.121840 + 0.594429I
b = 0.500000 + 0.866025I
−5.87256 + 6.43072I −6.27578 − 5.55522I
u = 0.455697 + 1.200150I
a = −0.424290 − 0.191698I
b = 0.500000 − 0.866025I
−5.87256 + 2.37095I −11.57979 + 0.88917I
u = 0.455697 − 1.200150I
a = −1.121840 − 0.594429I
b = 0.500000 − 0.866025I
−5.87256 − 6.43072I −6.27578 + 5.55522I
u = 0.455697 − 1.200150I
a = −0.424290 + 0.191698I
b = 0.500000 + 0.866025I
−5.87256 − 2.37095I −11.57979 − 0.88917I
18
III. I
v
1
= ha, −3v
3
+ 5v
2
+ b − 19v + 8, v
4
− 2v
3
+ 7v
2
− 5v + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
v
0
a
2
=
0
3v
3
− 5v
2
+ 19v − 8
a
7
=
1
0
a
5
=
1
−5v
3
+ 8v
2
− 32v + 12
a
3
=
3v
3
− 5v
2
+ 19v − 8
7v
3
− 11v
2
+ 44v − 16
a
1
=
4v
3
− 6v
2
+ 25v − 8
−v
3
+ 2v
2
− 7v + 5
a
4
=
−5v
3
+ 8v
2
− 32v + 13
−5v
3
+ 8v
2
− 32v + 12
a
8
=
−4v
3
+ 6v
2
− 25v + 8
v
3
− 2v
2
+ 7v − 5
a
10
=
v
0
a
12
=
v
0
a
9
=
−4v
3
+ 6v
2
− 24v + 8
v
3
− 2v
2
+ 7v − 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 13v
3
− 22v
2
+ 85v − 40
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
5
u
4
+ u
3
+ u
2
+ 1
c
6
, c
10
, c
11
u
4
c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
, c
9
(u − 1)
4
c
12
(u + 1)
4
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
5
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
6
, c
10
, c
11
y
4
c
8
, c
9
, c
12
(y − 1)
4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.409261 + 0.055548I
a = 0
b = −0.851808 + 0.911292I
5.14581 − 3.16396I −7.98794 + 4.08190I
v = 0.409261 − 0.055548I
a = 0
b = −0.851808 − 0.911292I
5.14581 + 3.16396I −7.98794 − 4.08190I
v = 0.59074 + 2.34806I
a = 0
b = 0.351808 − 0.720342I
−1.85594 − 1.41510I −0.51206 + 2.21528I
v = 0.59074 − 2.34806I
a = 0
b = 0.351808 + 0.720342I
−1.85594 + 1.41510I −0.51206 − 2.21528I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
5
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
93
+ 29u
92
+ ··· + 33u − 1)
c
2
((u
2
+ u + 1)
5
)(u
4
− u
3
+ u
2
+ 1)(u
93
+ 7u
92
+ ··· + 11u + 1)
c
3
u
10
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
93
− 2u
92
+ ··· + 2048u − 1024)
c
5
((u
2
− u + 1)
5
)(u
4
+ u
3
+ u
2
+ 1)(u
93
+ 7u
92
+ ··· + 11u + 1)
c
6
u
4
(u
5
− u
4
+ ··· + u − 1)
2
(u
93
− 3u
92
+ ··· − 120u + 16)
c
7
u
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
93
− 2u
92
+ ··· + 2048u − 1024)
c
8
, c
9
((u − 1)
4
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
93
− 7u
92
+ ··· + 14u + 1)
c
10
u
4
(u
5
+ u
4
+ ··· + u + 1)
2
(u
93
− 3u
92
+ ··· − 120u + 16)
c
11
u
4
(u
5
+ 3u
4
+ ··· − u − 1)
2
(u
93
+ 33u
92
+ ··· − 5056u − 256)
c
12
((u + 1)
4
)(u
5
− u
4
+ ··· + u + 1)
2
(u
93
− 7u
92
+ ··· + 14u + 1)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
5
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
93
+ 77y
92
+ ··· + 5105y − 1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
93
+ 29y
92
+ ··· + 33y − 1)
c
3
, c
7
y
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
93
+ 60y
92
+ ··· − 16777216y − 1048576)
c
6
, c
10
y
4
(y
5
+ 3y
4
+ ··· − y − 1)
2
(y
93
+ 33y
92
+ ··· − 5056y − 256)
c
8
, c
9
, c
12
((y − 1)
4
)(y
5
− 5y
4
+ ··· − y − 1)
2
(y
93
− 79y
92
+ ··· − 38y − 1)
c
11
y
4
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
· (y
93
+ 49y
92
+ ··· − 2600960y − 65536)
24
