12a
0006
(K12a
0006
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 10 4 12 11 7 1 9
Solving Sequence
6,10
7
2,11
5 3 4 8 1 9 12
c
6
c
10
c
5
c
2
c
3
c
7
c
1
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.65110 × 10
246
u
117
+ 2.10342 × 10
247
u
116
+ ··· + 7.39617 × 10
247
b − 4.75087 × 10
248
,
− 7.08530 × 10
247
u
117
+ 1.80151 × 10
248
u
116
+ ··· + 4.43770 × 10
248
a − 1.26778 × 10
249
,
u
118
− 3u
117
+ ··· − 32u + 32i
I
u
2
= hu
4
a − u
3
a + u
4
− u
3
+ au + b − a + u − 1,
− u
5
a + 2u
5
+ 2u
3
a − 2u
4
− u
2
a − 3u
3
+ a
2
− 2au + 4u
2
+ 2a + 2u − 2, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
v
1
= ha, −3v
4
+ 4v
3
− 10v
2
+ b − 21v −7, v
5
− v
4
+ 3v
3
+ 8v
2
+ 5v + 1i
* 3 irreducible components of dim
C
= 0, with total 135 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−7.65 × 10
246
u
117
+ 2.10 × 10
247
u
116
+ · · · + 7.40 × 10
247
b − 4.75 ×
10
248
, −7.09 × 10
247
u
117
+ 1.80 × 10
248
u
116
+ · · · + 4.44 × 10
248
a − 1.27 ×
10
249
, u
118
− 3u
117
+ · · · − 32u + 32i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
0.159661u
117
− 0.405956u
116
+ ··· − 50.6753u + 2.85683
0.103447u
117
− 0.284393u
116
+ ··· − 22.6938u + 6.42342
a
11
=
u
−u
3
+ u
a
5
=
0.489272u
117
− 1.92202u
116
+ ··· − 100.177u + 40.5651
0.340316u
117
− 1.27077u
116
+ ··· − 47.3105u + 17.7814
a
3
=
−0.758810u
117
+ 2.70567u
116
+ ··· + 104.493u − 38.0247
−0.704038u
117
+ 2.56247u
116
+ ··· + 117.303u − 43.3608
a
4
=
−0.0547723u
117
+ 0.143196u
116
+ ··· − 12.8108u + 5.33612
−0.704038u
117
+ 2.56247u
116
+ ··· + 117.303u − 43.3608
a
8
=
−0.0350744u
117
+ 0.212518u
116
+ ··· − 0.864347u − 4.50525
0.0107154u
117
− 0.0648548u
116
+ ··· − 13.9025u + 5.51561
a
1
=
−0.0588332u
117
+ 0.244742u
116
+ ··· + 8.48235u − 6.58741
−0.0237588u
117
+ 0.0322234u
116
+ ··· + 9.34669u − 2.08216
a
9
=
−u
3
u
5
− u
3
+ u
a
12
=
−0.0347330u
117
+ 0.229528u
116
+ ··· + 10.9263u − 7.78172
0.0194075u
117
− 0.0731735u
116
+ ··· + 7.91588u − 1.10392
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.13497u
117
− 4.19176u
116
+ ··· − 276.130u + 125.354
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
118
+ 60u
117
+ ··· + 8u + 1
c
2
, c
5
u
118
+ 8u
117
+ ··· + 8u + 1
c
3
u
118
− 8u
117
+ ··· − 20012u + 337
c
4
, c
7
u
118
+ 2u
117
+ ··· − 8192u − 4096
c
6
, c
10
u
118
− 3u
117
+ ··· − 32u + 32
c
8
, c
12
u
118
− 8u
117
+ ··· − 2u − 1
c
9
u
118
− 39u
117
+ ··· − 22016u + 1024
c
11
u
118
+ 64u
117
+ ··· + 46u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
118
+ 4y
117
+ ··· − 48y + 1
c
2
, c
5
y
118
+ 60y
117
+ ··· + 8y + 1
c
3
y
118
− 52y
117
+ ··· + 347123352y + 113569
c
4
, c
7
y
118
− 70y
117
+ ··· − 285212672y + 16777216
c
6
, c
10
y
118
− 39y
117
+ ··· − 22016y + 1024
c
8
, c
12
y
118
− 64y
117
+ ··· − 46y + 1
c
9
y
118
+ 73y
117
+ ··· − 33161216y + 1048576
c
11
y
118
− 12y
117
+ ··· + 1158y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.057111 + 0.994719I
a = 0.36450 − 1.63146I
b = −0.479763 − 1.116650I
−3.79426 + 5.91242I 0
u = −0.057111 − 0.994719I
a = 0.36450 + 1.63146I
b = −0.479763 + 1.116650I
−3.79426 − 5.91242I 0
u = −0.914029 + 0.393303I
a = 0.297266 − 1.272970I
b = −0.004632 − 0.992140I
−1.56812 − 4.24852I 0
u = −0.914029 − 0.393303I
a = 0.297266 + 1.272970I
b = −0.004632 + 0.992140I
−1.56812 + 4.24852I 0
u = −0.641087 + 0.760665I
a = 0.779065 − 0.477001I
b = 0.509907 − 0.068037I
−2.44908 + 1.22370I 0
u = −0.641087 − 0.760665I
a = 0.779065 + 0.477001I
b = 0.509907 + 0.068037I
−2.44908 − 1.22370I 0
u = −0.849815 + 0.541103I
a = −0.268387 − 0.139659I
b = 0.674649 + 0.872777I
0.565713 + 0.424578I 0
u = −0.849815 − 0.541103I
a = −0.268387 + 0.139659I
b = 0.674649 − 0.872777I
0.565713 − 0.424578I 0
u = −0.991085 + 0.050636I
a = −1.44835 + 0.47132I
b = 0.610150 + 0.985347I
2.32252 + 1.20341I 0
u = −0.991085 − 0.050636I
a = −1.44835 − 0.47132I
b = 0.610150 − 0.985347I
2.32252 − 1.20341I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.750948 + 0.648450I
a = 0.52003 − 2.23767I
b = 0.403810 − 1.096830I
−1.81430 − 1.19890I 0
u = 0.750948 − 0.648450I
a = 0.52003 + 2.23767I
b = 0.403810 + 1.096830I
−1.81430 + 1.19890I 0
u = 0.704841 + 0.728643I
a = −1.42404 + 1.25197I
b = 0.687054 + 0.817693I
−3.03391 + 1.35788I 0
u = 0.704841 − 0.728643I
a = −1.42404 − 1.25197I
b = 0.687054 − 0.817693I
−3.03391 − 1.35788I 0
u = −0.595125 + 0.821259I
a = −0.192234 + 0.242458I
b = −0.804532 + 0.208505I
−3.00739 + 1.82099I 0
u = −0.595125 − 0.821259I
a = −0.192234 − 0.242458I
b = −0.804532 − 0.208505I
−3.00739 − 1.82099I 0
u = −0.242106 + 0.999487I
a = 0.49124 + 1.66110I
b = −0.423992 + 1.099160I
−4.22546 − 1.56777I 0
u = −0.242106 − 0.999487I
a = 0.49124 − 1.66110I
b = −0.423992 − 1.099160I
−4.22546 + 1.56777I 0
u = 0.761083 + 0.704310I
a = 0.18432 + 1.73897I
b = −0.534333 + 1.210310I
−9.66639 − 3.23714I 0
u = 0.761083 − 0.704310I
a = 0.18432 − 1.73897I
b = −0.534333 − 1.210310I
−9.66639 + 3.23714I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.026530 + 0.206251I
a = −1.70974 + 1.21108I
b = 0.573243 + 1.038280I
1.95085 + 5.61000I 0
u = 1.026530 − 0.206251I
a = −1.70974 − 1.21108I
b = 0.573243 − 1.038280I
1.95085 − 5.61000I 0
u = 0.667456 + 0.812256I
a = 0.291954 + 0.052077I
b = 0.700820 − 0.783953I
−2.93079 − 3.91418I 0
u = 0.667456 − 0.812256I
a = 0.291954 − 0.052077I
b = 0.700820 + 0.783953I
−2.93079 + 3.91418I 0
u = −0.441663 + 0.835178I
a = 0.448495 − 0.613915I
b = −0.185637 − 0.547949I
−2.01865 + 1.48429I 0
u = −0.441663 − 0.835178I
a = 0.448495 + 0.613915I
b = −0.185637 + 0.547949I
−2.01865 − 1.48429I 0
u = 1.054750 + 0.101458I
a = −0.158985 + 0.740344I
b = 0.645223 − 0.470242I
3.58808 + 0.84208I 0
u = 1.054750 − 0.101458I
a = −0.158985 − 0.740344I
b = 0.645223 + 0.470242I
3.58808 − 0.84208I 0
u = −1.056930 + 0.134697I
a = −0.653037 + 0.468905I
b = 0.679183 − 0.575083I
3.51464 − 3.77326I 0
u = −1.056930 − 0.134697I
a = −0.653037 − 0.468905I
b = 0.679183 + 0.575083I
3.51464 + 3.77326I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.574725 + 0.902696I
a = 0.21041 − 1.67524I
b = −0.538247 − 1.172420I
−5.84550 + 6.78193I 0
u = −0.574725 − 0.902696I
a = 0.21041 + 1.67524I
b = −0.538247 + 1.172420I
−5.84550 − 6.78193I 0
u = 0.926136 + 0.543311I
a = 0.583704 + 0.628251I
b = 0.581906 − 0.193380I
1.35120 + 2.05184I 0
u = 0.926136 − 0.543311I
a = 0.583704 − 0.628251I
b = 0.581906 + 0.193380I
1.35120 − 2.05184I 0
u = 0.817393 + 0.699752I
a = −0.274441 − 0.202673I
b = −0.874488 − 0.173434I
−6.53571 + 1.89043I 0
u = 0.817393 − 0.699752I
a = −0.274441 + 0.202673I
b = −0.874488 + 0.173434I
−6.53571 − 1.89043I 0
u = −0.918223 + 0.103095I
a = 0.860492 + 1.120820I
b = −0.448856 − 1.120990I
−5.56593 + 3.83415I 0
u = −0.918223 − 0.103095I
a = 0.860492 − 1.120820I
b = −0.448856 + 1.120990I
−5.56593 − 3.83415I 0
u = −0.790275 + 0.740752I
a = −1.51469 − 2.91008I
b = 0.439874 − 1.114530I
−5.31904 − 2.44166I 0
u = −0.790275 − 0.740752I
a = −1.51469 + 2.91008I
b = 0.439874 + 1.114530I
−5.31904 + 2.44166I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.938249 + 0.587408I
a = −1.164570 − 0.579553I
b = 0.718691 − 0.741494I
0.95583 − 4.87112I 0
u = −0.938249 − 0.587408I
a = −1.164570 + 0.579553I
b = 0.718691 + 0.741494I
0.95583 + 4.87112I 0
u = −0.712579 + 0.849832I
a = 0.51391 + 2.00089I
b = −0.315907 + 1.207150I
−7.37780 − 1.81999I 0
u = −0.712579 − 0.849832I
a = 0.51391 − 2.00089I
b = −0.315907 − 1.207150I
−7.37780 + 1.81999I 0
u = −0.713912 + 0.864317I
a = 0.38520 + 2.30740I
b = 0.460796 + 1.118670I
−5.16425 + 5.15948I 0
u = −0.713912 − 0.864317I
a = 0.38520 − 2.30740I
b = 0.460796 − 1.118670I
−5.16425 − 5.15948I 0
u = 0.903754 + 0.685135I
a = −0.229534 − 1.073390I
b = −0.834503 + 0.236031I
−6.26654 + 3.43511I 0
u = 0.903754 − 0.685135I
a = −0.229534 + 1.073390I
b = −0.834503 − 0.236031I
−6.26654 − 3.43511I 0
u = −0.092158 + 0.857430I
a = 0.093803 + 0.222170I
b = −0.555039 + 0.193650I
−1.24389 + 1.74559I 0
u = −0.092158 − 0.857430I
a = 0.093803 − 0.222170I
b = −0.555039 − 0.193650I
−1.24389 − 1.74559I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.843744 + 0.765170I
a = 0.42452 − 2.02910I
b = −0.333480 − 1.250080I
−11.06080 + 5.93333I 0
u = 0.843744 − 0.765170I
a = 0.42452 + 2.02910I
b = −0.333480 + 1.250080I
−11.06080 − 5.93333I 0
u = 1.072050 + 0.405478I
a = 1.268290 − 0.321054I
b = −0.356382 − 0.560236I
2.19895 + 1.79255I 0
u = 1.072050 − 0.405478I
a = 1.268290 + 0.321054I
b = −0.356382 + 0.560236I
2.19895 − 1.79255I 0
u = 0.949358 + 0.655602I
a = −1.50109 + 2.42720I
b = 0.487936 + 1.117660I
−1.19730 + 6.30191I 0
u = 0.949358 − 0.655602I
a = −1.50109 − 2.42720I
b = 0.487936 − 1.117660I
−1.19730 − 6.30191I 0
u = 1.154880 + 0.081470I
a = 0.850435 − 0.258649I
b = −0.594989 + 0.390000I
3.41320 + 0.71117I 0
u = 1.154880 − 0.081470I
a = 0.850435 + 0.258649I
b = −0.594989 − 0.390000I
3.41320 − 0.71117I 0
u = 0.952170 + 0.675540I
a = 2.08030 − 1.86808I
b = −0.554021 − 1.178320I
−9.07220 + 8.55233I 0
u = 0.952170 − 0.675540I
a = 2.08030 + 1.86808I
b = −0.554021 + 1.178320I
−9.07220 − 8.55233I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.933711 + 0.711611I
a = 0.42213 + 2.16878I
b = 0.395467 + 1.151170I
−4.87773 − 3.09159I 0
u = −0.933711 − 0.711611I
a = 0.42213 − 2.16878I
b = 0.395467 − 1.151170I
−4.87773 + 3.09159I 0
u = 0.906410 + 0.760816I
a = −1.12132 + 1.34343I
b = −0.292550 + 1.220230I
−10.87470 − 0.17205I 0
u = 0.906410 − 0.760816I
a = −1.12132 − 1.34343I
b = −0.292550 − 1.220230I
−10.87470 + 0.17205I 0
u = 0.703346 + 0.968542I
a = −0.234705 − 0.299671I
b = −0.841845 − 0.256862I
−5.90980 − 6.28332I 0
u = 0.703346 − 0.968542I
a = −0.234705 + 0.299671I
b = −0.841845 + 0.256862I
−5.90980 + 6.28332I 0
u = 0.981963 + 0.689993I
a = −0.119645 − 0.167424I
b = 0.727220 − 0.874257I
−2.20059 + 4.08134I 0
u = 0.981963 − 0.689993I
a = −0.119645 + 0.167424I
b = 0.727220 + 0.874257I
−2.20059 − 4.08134I 0
u = −1.174600 + 0.288507I
a = 0.551612 + 0.463296I
b = −0.695913 − 0.362854I
2.63779 − 5.83888I 0
u = −1.174600 − 0.288507I
a = 0.551612 − 0.463296I
b = −0.695913 + 0.362854I
2.63779 + 5.83888I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.766573 + 0.949834I
a = 0.54077 − 2.08818I
b = −0.275600 − 1.221680I
−10.63780 − 2.75551I 0
u = 0.766573 − 0.949834I
a = 0.54077 + 2.08818I
b = −0.275600 + 1.221680I
−10.63780 + 2.75551I 0
u = 0.776994 + 0.041855I
a = 0.66142 − 1.68179I
b = 0.218885 − 1.009740I
−0.490861 − 0.714549I −2.00000 − 0.48683I
u = 0.776994 − 0.041855I
a = 0.66142 + 1.68179I
b = 0.218885 + 1.009740I
−0.490861 + 0.714549I −2.00000 + 0.48683I
u = −1.012390 + 0.692789I
a = 0.584170 − 0.489883I
b = 0.672262 + 0.132528I
−1.36149 − 6.75234I 0
u = −1.012390 − 0.692789I
a = 0.584170 + 0.489883I
b = 0.672262 − 0.132528I
−1.36149 + 6.75234I 0
u = −0.628903 + 0.449098I
a = 2.54132 − 0.00188I
b = 0.020939 + 0.603233I
−2.54168 + 0.64755I −6.08336 + 1.44392I
u = −0.628903 − 0.449098I
a = 2.54132 + 0.00188I
b = 0.020939 − 0.603233I
−2.54168 − 0.64755I −6.08336 − 1.44392I
u = 0.706770 + 1.008380I
a = 0.16558 + 1.66086I
b = −0.563795 + 1.176200I
−8.6542 − 11.4670I 0
u = 0.706770 − 1.008380I
a = 0.16558 − 1.66086I
b = −0.563795 − 1.176200I
−8.6542 + 11.4670I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.199720 + 0.314561I
a = 0.370854 + 0.093116I
b = −0.424562 + 1.045720I
0.62638 − 1.63995I 0
u = 1.199720 − 0.314561I
a = 0.370854 − 0.093116I
b = −0.424562 − 1.045720I
0.62638 + 1.63995I 0
u = 1.019770 + 0.714724I
a = −0.901138 + 0.757961I
b = 0.760109 + 0.761507I
−1.86733 + 9.65076I 0
u = 1.019770 − 0.714724I
a = −0.901138 − 0.757961I
b = 0.760109 − 0.761507I
−1.86733 − 9.65076I 0
u = −1.001870 + 0.750136I
a = −0.82058 − 1.37636I
b = −0.252783 − 1.215880I
−6.49755 − 4.12996I 0
u = −1.001870 − 0.750136I
a = −0.82058 + 1.37636I
b = −0.252783 + 1.215880I
−6.49755 + 4.12996I 0
u = 1.246440 + 0.134432I
a = 1.263590 − 0.327615I
b = −0.513444 − 1.082540I
1.38319 + 5.13395I 0
u = 1.246440 − 0.134432I
a = 1.263590 + 0.327615I
b = −0.513444 + 1.082540I
1.38319 − 5.13395I 0
u = −0.739637
a = 2.08237
b = −0.538572
−2.71088 −0.754640
u = −1.050650 + 0.696469I
a = −0.151310 + 0.784583I
b = −0.842658 − 0.284149I
−1.65144 − 7.50770I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.050650 − 0.696469I
a = −0.151310 − 0.784583I
b = −0.842658 + 0.284149I
−1.65144 + 7.50770I 0
u = −1.021640 + 0.750308I
a = −1.24048 − 2.43396I
b = 0.490690 − 1.148020I
−4.20666 − 11.16730I 0
u = −1.021640 − 0.750308I
a = −1.24048 + 2.43396I
b = 0.490690 + 1.148020I
−4.20666 + 11.16730I 0
u = −1.115320 + 0.606056I
a = 1.230240 + 0.596883I
b = −0.351425 + 0.666628I
0.06726 − 6.85727I 0
u = −1.115320 − 0.606056I
a = 1.230240 − 0.596883I
b = −0.351425 − 0.666628I
0.06726 + 6.85727I 0
u = −1.178770 + 0.503879I
a = 0.134512 − 0.367275I
b = −0.373896 − 1.016460I
−1.02731 − 3.71542I 0
u = −1.178770 − 0.503879I
a = 0.134512 + 0.367275I
b = −0.373896 + 1.016460I
−1.02731 + 3.71542I 0
u = −1.244210 + 0.324599I
a = 1.48321 + 0.70609I
b = −0.542963 + 1.102660I
0.46596 − 10.60320I 0
u = −1.244210 − 0.324599I
a = 1.48321 − 0.70609I
b = −0.542963 − 1.102660I
0.46596 + 10.60320I 0
u = −1.085240 + 0.716483I
a = 1.69229 + 1.72293I
b = −0.574228 + 1.169280I
−4.29675 − 12.74330I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.085240 − 0.716483I
a = 1.69229 − 1.72293I
b = −0.574228 − 1.169280I
−4.29675 + 12.74330I 0
u = 1.038110 + 0.809700I
a = −0.78762 + 1.55153I
b = −0.242507 + 1.244090I
−9.75711 + 9.21690I 0
u = 1.038110 − 0.809700I
a = −0.78762 − 1.55153I
b = −0.242507 − 1.244090I
−9.75711 − 9.21690I 0
u = 1.076560 + 0.786701I
a = −0.280801 − 0.696971I
b = −0.872930 + 0.288064I
−4.71420 + 12.71440I 0
u = 1.076560 − 0.786701I
a = −0.280801 + 0.696971I
b = −0.872930 − 0.288064I
−4.71420 − 12.71440I 0
u = 1.095540 + 0.803347I
a = 1.53896 − 1.87042I
b = −0.584656 − 1.179320I
−7.3958 + 18.0717I 0
u = 1.095540 − 0.803347I
a = 1.53896 + 1.87042I
b = −0.584656 + 1.179320I
−7.3958 − 18.0717I 0
u = 0.000311 + 0.619720I
a = 1.179420 + 0.284191I
b = 0.461261 + 0.641991I
−0.273430 + 1.372910I −0.92246 − 4.39657I
u = 0.000311 − 0.619720I
a = 1.179420 − 0.284191I
b = 0.461261 − 0.641991I
−0.273430 − 1.372910I −0.92246 + 4.39657I
u = 0.107100 + 0.609744I
a = 0.34928 − 3.67096I
b = 0.513118 − 0.944398I
−1.17462 − 2.74263I −1.96021 − 1.22948I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.107100 − 0.609744I
a = 0.34928 + 3.67096I
b = 0.513118 + 0.944398I
−1.17462 + 2.74263I −1.96021 + 1.22948I
u = −0.558444
a = −0.222379
b = −0.828891
−3.44166 4.59440
u = −0.514322 + 0.057744I
a = 0.29748 + 1.83788I
b = −0.452092 + 1.222260I
−7.09844 − 4.55536I 3.30166 + 6.83611I
u = −0.514322 − 0.057744I
a = 0.29748 − 1.83788I
b = −0.452092 − 1.222260I
−7.09844 + 4.55536I 3.30166 − 6.83611I
u = 0.105677 + 0.401308I
a = 1.34221 + 0.72343I
b = 0.349596 + 0.719198I
−0.21143 + 1.41432I −1.77271 − 4.99852I
u = 0.105677 − 0.401308I
a = 1.34221 − 0.72343I
b = 0.349596 − 0.719198I
−0.21143 − 1.41432I −1.77271 + 4.99852I
u = 0.323334 + 0.183829I
a = −11.23030 + 0.98495I
b = 0.437589 + 0.866044I
−1.91740 + 1.80747I 15.1049 − 30.5244I
u = 0.323334 − 0.183829I
a = −11.23030 − 0.98495I
b = 0.437589 − 0.866044I
−1.91740 − 1.80747I 15.1049 + 30.5244I
16
II. I
u
2
= hu
4
a − u
3
a + u
4
− u
3
+ au + b − a + u − 1, −u
5
a + 2u
5
+ · · · + 2a −
2, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
a
−u
4
a + u
3
a − u
4
+ u
3
− au + a − u + 1
a
11
=
u
−u
3
+ u
a
5
=
u
4
a − u
5
− u
3
a + u
4
+ u
3
+ au − u
2
− u + 1
−u
4
a + u
3
a − u
4
+ u
3
− au + a − u
a
3
=
−u
5
+ 2u
3
− u
2
+ a − 2u + 1
−u
4
a + u
3
a − u
4
+ u
3
− au + a − u
a
4
=
u
4
a − u
5
− u
3
a + u
4
+ u
3
+ au − u
2
− u + 1
−u
4
a + u
3
a − u
4
+ u
3
− au + a − u
a
8
=
1
−u
2
a
1
=
−1
0
a
9
=
−u
3
u
5
− u
3
+ u
a
12
=
u
3
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
5
a + 5u
4
a − u
5
− 2u
3
a − 2u
3
+ 2au + 4u
2
− 2a − 2u − 4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
7
u
12
c
6
, c
12
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
8
, c
10
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
9
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
c
11
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
6
c
4
, c
7
y
12
c
6
, c
8
, c
10
c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
9
, c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = −1.315130 − 0.448204I
b = 0.500000 − 0.866025I
1.89061 − 2.95419I −0.30406 + 4.29351I
u = −1.002190 + 0.295542I
a = −0.454280 − 0.048806I
b = 0.500000 + 0.866025I
1.89061 + 1.10558I 2.90246 − 2.38339I
u = −1.002190 − 0.295542I
a = −1.315130 + 0.448204I
b = 0.500000 + 0.866025I
1.89061 + 2.95419I −0.30406 − 4.29351I
u = −1.002190 − 0.295542I
a = −0.454280 + 0.048806I
b = 0.500000 − 0.866025I
1.89061 − 1.10558I 2.90246 + 2.38339I
u = 0.428243 + 0.664531I
a = 1.092390 − 0.709952I
b = 0.500000 − 0.866025I
−1.89061 − 2.95419I −6.66783 + 2.20469I
u = 0.428243 + 0.664531I
a = −1.43136 + 2.16703I
b = 0.500000 + 0.866025I
−1.89061 + 1.10558I −2.82220 − 2.24866I
u = 0.428243 − 0.664531I
a = 1.092390 + 0.709952I
b = 0.500000 + 0.866025I
−1.89061 + 2.95419I −6.66783 − 2.20469I
u = 0.428243 − 0.664531I
a = −1.43136 − 2.16703I
b = 0.500000 − 0.866025I
−1.89061 − 1.10558I −2.82220 + 2.24866I
u = 1.073950 + 0.558752I
a = −1.17970 + 0.80625I
b = 0.500000 + 0.866025I
7.72290I −3.68173 − 10.26242I
u = 1.073950 + 0.558752I
a = −0.211918 − 0.247495I
b = 0.500000 − 0.866025I
3.66314I 0.57335 − 2.34011I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = −1.17970 − 0.80625I
b = 0.500000 − 0.866025I
− 7.72290I −3.68173 + 10.26242I
u = 1.073950 − 0.558752I
a = −0.211918 + 0.247495I
b = 0.500000 + 0.866025I
− 3.66314I 0.57335 + 2.34011I
21
III. I
v
1
= ha, −3v
4
+ 4v
3
− 10v
2
+ b − 21v − 7, v
5
− v
4
+ 3v
3
+ 8v
2
+ 5v + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
v
0
a
7
=
1
0
a
2
=
0
3v
4
− 4v
3
+ 10v
2
+ 21v + 7
a
11
=
v
0
a
5
=
1
−v
3
+ 2v
2
− 5v − 4
a
3
=
3v
4
− 4v
3
+ 10v
2
+ 21v + 7
−4v
4
+ 7v
3
− 17v
2
− 20v − 4
a
4
=
7v
4
− 11v
3
+ 27v
2
+ 41v + 11
−4v
4
+ 7v
3
− 17v
2
− 20v − 4
a
8
=
7v
4
− 11v
3
+ 27v
2
+ 41v + 11
v
4
− v
3
+ 3v
2
+ 8v + 5
a
1
=
−7v
4
+ 11v
3
− 27v
2
− 41v − 11
−v
4
+ v
3
− 3v
2
− 8v − 5
a
9
=
v
0
a
12
=
−7v
4
+ 11v
3
− 27v
2
− 40v − 11
−v
4
+ v
3
− 3v
2
− 8v − 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 11v
4
− 18v
3
+ 43v
2
+ 63v + 5
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
, c
4
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
5
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
6
, c
9
, c
10
u
5
c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
, c
11
(u − 1)
5
c
12
(u + 1)
5
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1
c
2
, c
5
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
3
, c
4
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
c
6
, c
9
, c
10
y
5
c
8
, c
11
, c
12
(y − 1)
5
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.674363
a = 0
b = −0.766826
−4.04602 −10.1350
v = −0.462589 + 0.146410I
a = 0
b = −0.455697 + 1.200150I
−7.51750 − 4.40083I −14.4110 + 1.1901I
v = −0.462589 − 0.146410I
a = 0
b = −0.455697 − 1.200150I
−7.51750 + 4.40083I −14.4110 − 1.1901I
v = 1.29977 + 2.14694I
a = 0
b = 0.339110 − 0.822375I
−1.97403 − 1.53058I −3.52158 − 1.00973I
v = 1.29977 − 2.14694I
a = 0
b = 0.339110 + 0.822375I
−1.97403 + 1.53058I −3.52158 + 1.00973I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
5
− 3u
4
+ ··· − u + 1)(u
118
+ 60u
117
+ ··· + 8u + 1)
c
2
((u
2
+ u + 1)
6
)(u
5
− u
4
+ ··· + u − 1)(u
118
+ 8u
117
+ ··· + 8u + 1)
c
3
(u
2
− u + 1)
6
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
118
− 8u
117
+ ··· − 20012u + 337)
c
4
u
12
(u
5
+ u
4
+ ··· + u − 1)(u
118
+ 2u
117
+ ··· − 8192u − 4096)
c
5
((u
2
− u + 1)
6
)(u
5
+ u
4
+ ··· + u + 1)(u
118
+ 8u
117
+ ··· + 8u + 1)
c
6
u
5
(u
6
− u
5
+ ··· − u + 1)
2
(u
118
− 3u
117
+ ··· − 32u + 32)
c
7
u
12
(u
5
− u
4
+ ··· + u + 1)(u
118
+ 2u
117
+ ··· − 8192u − 4096)
c
8
((u − 1)
5
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
118
− 8u
117
+ ··· − 2u − 1)
c
9
u
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
· (u
118
− 39u
117
+ ··· − 22016u + 1024)
c
10
u
5
(u
6
+ u
5
+ ··· + u + 1)
2
(u
118
− 3u
117
+ ··· − 32u + 32)
c
11
(u − 1)
5
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
118
+ 64u
117
+ ··· + 46u + 1)
c
12
((u + 1)
5
)(u
6
− u
5
+ ··· − u + 1)
2
(u
118
− 8u
117
+ ··· − 2u − 1)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
5
− y
4
+ ··· + 3y − 1)(y
118
+ 4y
117
+ ··· − 48y + 1)
c
2
, c
5
((y
2
+ y + 1)
6
)(y
5
+ 3y
4
+ ··· − y − 1)(y
118
+ 60y
117
+ ··· + 8y + 1)
c
3
(y
2
+ y + 1)
6
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
118
− 52y
117
+ ··· + 347123352y + 113569)
c
4
, c
7
y
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
118
− 70y
117
+ ··· − 285212672y + 16777216)
c
6
, c
10
y
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
118
− 39y
117
+ ··· − 22016y + 1024)
c
8
, c
12
(y − 1)
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
118
− 64y
117
+ ··· − 46y + 1)
c
9
y
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
118
+ 73y
117
+ ··· − 33161216y + 1048576)
c
11
(y − 1)
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
118
− 12y
117
+ ··· + 1158y + 1)
27
