12a
1268
(K12a
1268
)
A knot diagram
1
Linearized knot diagam
5 7 10 11 9 12 3 1 2 4 8 6
Solving Sequence
3,10 4,7
8 11 5 12 2 1 6 9
c
3
c
7
c
10
c
4
c
11
c
2
c
1
c
6
c
9
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h9.11346 × 10
461
u
147
+ 3.95273 × 10
461
u
146
+ ··· + 3.62863 × 10
462
b − 1.72199 × 10
463
,
4.51564 × 10
464
u
147
+ 9.26536 × 10
463
u
146
+ ··· + 1.34259 × 10
464
a − 2.14693 × 10
466
,
u
148
− u
147
+ ··· − 565u + 37i
I
u
2
= h−21787693u
37
− 17833328u
36
+ ··· + 4484003b + 11235058,
4256822446u
37
+ 1213250697u
36
+ ··· + 587404393a − 4089312198, u
38
− 20u
36
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 186 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
= h9.11 × 10
461
u
147
+ 3.95 × 10
461
u
146
+ · · · + 3.63 × 10
462
b − 1.72 ×
10
463
, 4.52 × 10
464
u
147
+ 9.27 × 10
463
u
146
+ · · · + 1.34 × 10
464
a − 2.15 ×
10
466
, u
148
− u
147
+ · · · − 565u + 37i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
7
=
−3.36337u
147
− 0.690109u
146
+ ··· − 1732.60u + 159.909
−0.251154u
147
− 0.108932u
146
+ ··· − 88.7224u + 4.74555
a
8
=
−3.61452u
147
− 0.799040u
146
+ ··· − 1821.32u + 164.655
−0.251154u
147
− 0.108932u
146
+ ··· − 88.7224u + 4.74555
a
11
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
12
=
−0.585914u
147
+ 0.232383u
146
+ ··· − 797.840u + 110.149
1.37060u
147
+ 0.380173u
146
+ ··· + 566.237u − 37.5510
a
2
=
−1.84258u
147
− 0.465549u
146
+ ··· − 904.057u + 86.1561
−0.299998u
147
− 0.0844511u
146
+ ··· − 89.1876u + 3.14636
a
1
=
−2.61434u
147
− 0.697404u
146
+ ··· − 1189.37u + 102.524
0.372888u
147
+ 0.126054u
146
+ ··· + 198.348u − 16.7759
a
6
=
4.65490u
147
+ 1.63243u
146
+ ··· + 1539.37u − 78.1800
−0.150348u
147
− 0.0242958u
146
+ ··· − 118.307u + 13.7502
a
9
=
−1.51255u
147
− 0.235174u
146
+ ··· − 911.852u + 102.320
−0.818133u
147
− 0.239079u
146
+ ··· − 290.745u + 17.0314
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.568977u
147
+ 0.0557856u
146
+ ··· − 394.985u + 37.7750
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
148
+ 5u
147
+ ··· − 47u + 1
c
2
, c
7
u
148
+ u
147
+ ··· + 28032u + 9472
c
3
, c
4
, c
10
u
148
+ u
147
+ ··· + 565u + 37
c
5
u
148
− 5u
147
+ ··· + 207817u + 10777
c
6
, c
12
u
148
+ u
147
+ ··· − 4721u + 6513
c
8
u
148
+ 15u
146
+ ··· + 608u + 64
c
9
u
148
− 3u
147
+ ··· + 733241455u + 110567423
c
11
u
148
+ u
147
+ ··· − 13110u + 65501
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
148
+ 7y
147
+ ··· − 253y + 1
c
2
, c
7
y
148
− 71y
147
+ ··· − 3723476992y + 89718784
c
3
, c
4
, c
10
y
148
− 143y
147
+ ··· − 187357y + 1369
c
5
y
148
+ 35y
147
+ ··· − 9055314399y + 116143729
c
6
, c
12
y
148
+ 111y
147
+ ··· + 1135280675y + 42419169
c
8
y
148
+ 30y
147
+ ··· + 113664y + 4096
c
9
y
148
− 27y
147
+ ··· − 884023777418158187y + 12225155028860929
c
11
y
148
+ 21y
147
+ ··· + 171350880528y + 4290381001
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.231974 + 0.965550I
a = 1.61605 + 0.24726I
b = −0.942533 + 0.407635I
2.28070 − 2.18616I 0
u = 0.231974 − 0.965550I
a = 1.61605 − 0.24726I
b = −0.942533 − 0.407635I
2.28070 + 2.18616I 0
u = 0.357273 + 0.925002I
a = −1.82625 − 0.10771I
b = 1.147880 − 0.497498I
3.40517 − 8.71558I 0
u = 0.357273 − 0.925002I
a = −1.82625 + 0.10771I
b = 1.147880 + 0.497498I
3.40517 + 8.71558I 0
u = 0.498173 + 0.850756I
a = 0.924558 + 0.879436I
b = −0.899190 − 0.367524I
−1.79766 + 2.02965I 0
u = 0.498173 − 0.850756I
a = 0.924558 − 0.879436I
b = −0.899190 + 0.367524I
−1.79766 − 2.02965I 0
u = −0.403377 + 0.895392I
a = 1.87705 − 0.26722I
b = −1.203460 − 0.645179I
−1.2856 + 14.9681I 0
u = −0.403377 − 0.895392I
a = 1.87705 + 0.26722I
b = −1.203460 + 0.645179I
−1.2856 − 14.9681I 0
u = −0.581403 + 0.840266I
a = −1.58415 + 0.76045I
b = 1.077340 + 0.458818I
1.49467 + 5.83890I 0
u = −0.581403 − 0.840266I
a = −1.58415 − 0.76045I
b = 1.077340 − 0.458818I
1.49467 − 5.83890I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.919473 + 0.484488I
a = 0.0697847 − 0.0236496I
b = −0.961453 + 0.453445I
−1.63528 + 2.03359I 0
u = −0.919473 − 0.484488I
a = 0.0697847 + 0.0236496I
b = −0.961453 − 0.453445I
−1.63528 − 2.03359I 0
u = −0.439196 + 0.782732I
a = 1.55816 − 0.07528I
b = −0.865042 − 0.251362I
1.171650 − 0.269264I 0
u = −0.439196 − 0.782732I
a = 1.55816 + 0.07528I
b = −0.865042 + 0.251362I
1.171650 + 0.269264I 0
u = −0.826059 + 0.740595I
a = −0.814168 + 0.620310I
b = 1.072910 − 0.550619I
−2.53181 − 9.42226I 0
u = −0.826059 − 0.740595I
a = −0.814168 − 0.620310I
b = 1.072910 + 0.550619I
−2.53181 + 9.42226I 0
u = −0.034444 + 0.878485I
a = 1.89031 + 0.70285I
b = −0.860373 − 0.345168I
−1.96259 + 1.02583I 0
u = −0.034444 − 0.878485I
a = 1.89031 − 0.70285I
b = −0.860373 + 0.345168I
−1.96259 − 1.02583I 0
u = 0.534463 + 0.676615I
a = −1.50415 − 0.26281I
b = 1.141460 − 0.585695I
−2.15552 − 6.96261I 0
u = 0.534463 − 0.676615I
a = −1.50415 + 0.26281I
b = 1.141460 + 0.585695I
−2.15552 + 6.96261I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.134210 + 0.178307I
a = 0.377680 − 1.136420I
b = −1.174710 − 0.194516I
−0.73408 − 2.34311I 0
u = −1.134210 − 0.178307I
a = 0.377680 + 1.136420I
b = −1.174710 + 0.194516I
−0.73408 + 2.34311I 0
u = −0.085848 + 0.829903I
a = −1.269460 + 0.287223I
b = 0.925969 + 0.640871I
1.02925 + 2.54980I 0
u = −0.085848 − 0.829903I
a = −1.269460 − 0.287223I
b = 0.925969 − 0.640871I
1.02925 − 2.54980I 0
u = −0.559642 + 0.607958I
a = 1.235330 − 0.392564I
b = −0.883726 + 0.285594I
1.61185 − 0.79071I 0
u = −0.559642 − 0.607958I
a = 1.235330 + 0.392564I
b = −0.883726 − 0.285594I
1.61185 + 0.79071I 0
u = −1.18648
a = 1.47562
b = −1.37704
2.50742 0
u = 0.406779 + 0.689175I
a = 0.313889 + 0.646488I
b = −0.341716 − 1.020640I
−3.95306 − 9.00700I 0
u = 0.406779 − 0.689175I
a = 0.313889 − 0.646488I
b = −0.341716 + 1.020640I
−3.95306 + 9.00700I 0
u = 1.170200 + 0.268964I
a = −0.669958 − 0.078471I
b = 1.139010 + 0.011760I
−1.83354 − 2.63838I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.170200 − 0.268964I
a = −0.669958 + 0.078471I
b = 1.139010 − 0.011760I
−1.83354 + 2.63838I 0
u = −1.202940 + 0.056948I
a = 0.49506 − 1.40003I
b = −0.916918 − 0.221604I
−0.57689 − 2.41463I 0
u = −1.202940 − 0.056948I
a = 0.49506 + 1.40003I
b = −0.916918 + 0.221604I
−0.57689 + 2.41463I 0
u = 0.518061 + 0.599429I
a = −1.84450 − 0.23958I
b = 0.447686 − 0.624149I
−4.39188 + 4.76426I 0
u = 0.518061 − 0.599429I
a = −1.84450 + 0.23958I
b = 0.447686 + 0.624149I
−4.39188 − 4.76426I 0
u = 0.969698 + 0.723097I
a = 0.840280 + 0.610020I
b = −0.939321 − 0.364404I
1.65398 + 3.04001I 0
u = 0.969698 − 0.723097I
a = 0.840280 − 0.610020I
b = −0.939321 + 0.364404I
1.65398 − 3.04001I 0
u = −1.027600 + 0.643845I
a = −0.936026 + 0.521892I
b = 0.770178 + 0.128613I
−0.53222 + 5.38699I 0
u = −1.027600 − 0.643845I
a = −0.936026 − 0.521892I
b = 0.770178 − 0.128613I
−0.53222 − 5.38699I 0
u = 1.217800 + 0.064206I
a = −1.45530 − 0.44097I
b = 1.40696 + 0.26755I
−1.48726 + 4.40757I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.217800 − 0.064206I
a = −1.45530 + 0.44097I
b = 1.40696 − 0.26755I
−1.48726 − 4.40757I 0
u = −1.235750 + 0.091204I
a = −0.43938 + 1.34729I
b = 0.920254 + 0.739833I
−0.73290 + 3.63524I 0
u = −1.235750 − 0.091204I
a = −0.43938 − 1.34729I
b = 0.920254 − 0.739833I
−0.73290 − 3.63524I 0
u = 1.219060 + 0.291929I
a = 0.50325 + 1.35547I
b = −0.725811 + 0.783881I
−2.92076 − 6.62114I 0
u = 1.219060 − 0.291929I
a = 0.50325 − 1.35547I
b = −0.725811 − 0.783881I
−2.92076 + 6.62114I 0
u = 0.287982 + 0.688219I
a = 2.31177 + 0.21530I
b = −1.28082 + 0.69341I
−1.24927 − 6.03078I 0
u = 0.287982 − 0.688219I
a = 2.31177 − 0.21530I
b = −1.28082 − 0.69341I
−1.24927 + 6.03078I 0
u = 0.458218 + 0.576877I
a = 0.170233 + 0.210030I
b = 0.140250 + 0.589316I
−1.03752 − 1.89033I 0
u = 0.458218 − 0.576877I
a = 0.170233 − 0.210030I
b = 0.140250 − 0.589316I
−1.03752 + 1.89033I 0
u = −0.140642 + 0.720016I
a = 1.70726 − 0.00510I
b = −1.034190 + 0.373297I
2.10224 − 1.09113I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140642 − 0.720016I
a = 1.70726 + 0.00510I
b = −1.034190 − 0.373297I
2.10224 + 1.09113I 0
u = −0.730255
a = 1.11996
b = −1.32462
3.06001 −8.56100
u = 0.649683 + 0.314154I
a = −0.244478 − 1.052680I
b = 1.025140 + 0.506575I
−2.61593 + 2.34139I 0
u = 0.649683 − 0.314154I
a = −0.244478 + 1.052680I
b = 1.025140 − 0.506575I
−2.61593 − 2.34139I 0
u = 1.112220 + 0.642467I
a = −1.019790 − 0.109869I
b = 0.845030 + 0.254151I
−0.35240 − 3.50987I 0
u = 1.112220 − 0.642467I
a = −1.019790 + 0.109869I
b = 0.845030 − 0.254151I
−0.35240 + 3.50987I 0
u = 1.290390 + 0.000987I
a = −0.19706 − 2.58477I
b = 0.603591 − 0.237569I
−6.04126 + 4.91083I 0
u = 1.290390 − 0.000987I
a = −0.19706 + 2.58477I
b = 0.603591 + 0.237569I
−6.04126 − 4.91083I 0
u = −0.436057 + 0.546770I
a = −0.428162 + 0.469987I
b = 0.059678 − 0.716117I
0.42984 + 4.27755I 0. − 7.44048I
u = −0.436057 − 0.546770I
a = −0.428162 − 0.469987I
b = 0.059678 + 0.716117I
0.42984 − 4.27755I 0. + 7.44048I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.312390 + 0.075260I
a = −0.879452 − 0.081211I
b = 1.63590 − 0.28141I
0.59044 + 1.54011I 0
u = −1.312390 − 0.075260I
a = −0.879452 + 0.081211I
b = 1.63590 + 0.28141I
0.59044 − 1.54011I 0
u = 1.306620 + 0.153364I
a = 0.929239 + 0.431892I
b = −1.62061 + 0.09033I
−1.46158 − 7.64296I 0
u = 1.306620 − 0.153364I
a = 0.929239 − 0.431892I
b = −1.62061 − 0.09033I
−1.46158 + 7.64296I 0
u = −1.311090 + 0.267331I
a = −0.69685 + 1.26432I
b = 0.524955 − 0.035818I
−6.00022 + 2.90444I 0
u = −1.311090 − 0.267331I
a = −0.69685 − 1.26432I
b = 0.524955 + 0.035818I
−6.00022 − 2.90444I 0
u = −0.310054 + 0.579111I
a = −2.67185 + 0.52775I
b = 1.132180 + 0.385562I
1.60699 + 4.39494I 3.80477 − 6.29138I
u = −0.310054 − 0.579111I
a = −2.67185 − 0.52775I
b = 1.132180 − 0.385562I
1.60699 − 4.39494I 3.80477 + 6.29138I
u = 0.574132 + 0.313958I
a = 0.391302 − 0.115976I
b = 0.159559 + 0.454310I
−1.01872 − 1.03669I −3.23722 + 2.14537I
u = 0.574132 − 0.313958I
a = 0.391302 + 0.115976I
b = 0.159559 − 0.454310I
−1.01872 + 1.03669I −3.23722 − 2.14537I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.347740 + 0.050519I
a = −0.319306 + 0.481732I
b = −0.108122 + 1.409470I
−8.17730 + 1.59186I 0
u = −1.347740 − 0.050519I
a = −0.319306 − 0.481732I
b = −0.108122 − 1.409470I
−8.17730 − 1.59186I 0
u = 1.325700 + 0.259766I
a = 1.46677 + 0.82776I
b = −0.770450 + 0.838843I
−8.34614 − 5.53646I 0
u = 1.325700 − 0.259766I
a = 1.46677 − 0.82776I
b = −0.770450 − 0.838843I
−8.34614 + 5.53646I 0
u = 1.342900 + 0.151224I
a = −0.095382 − 1.008510I
b = 1.007090 − 0.685964I
−0.38120 − 2.04979I 0
u = 1.342900 − 0.151224I
a = −0.095382 + 1.008510I
b = 1.007090 + 0.685964I
−0.38120 + 2.04979I 0
u = 1.359610 + 0.005401I
a = 1.18867 − 1.17358I
b = −1.091510 − 0.559910I
−7.51476 + 2.09734I 0
u = 1.359610 − 0.005401I
a = 1.18867 + 1.17358I
b = −1.091510 + 0.559910I
−7.51476 − 2.09734I 0
u = 1.380180 + 0.167017I
a = 0.579275 + 0.342435I
b = 0.50037 + 1.43440I
−9.61734 − 1.54022I 0
u = 1.380180 − 0.167017I
a = 0.579275 − 0.342435I
b = 0.50037 − 1.43440I
−9.61734 + 1.54022I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.230279 + 0.545245I
a = 0.950294 + 0.175173I
b = −0.271315 + 0.208505I
1.132270 − 0.814488I 5.26248 + 1.58736I
u = −0.230279 − 0.545245I
a = 0.950294 − 0.175173I
b = −0.271315 − 0.208505I
1.132270 + 0.814488I 5.26248 − 1.58736I
u = −1.399940 + 0.152619I
a = −0.265555 − 0.235941I
b = −0.731550 + 0.950615I
−8.44367 − 0.90685I 0
u = −1.399940 − 0.152619I
a = −0.265555 + 0.235941I
b = −0.731550 − 0.950615I
−8.44367 + 0.90685I 0
u = 1.393500 + 0.203394I
a = 0.22592 + 1.40527I
b = −0.947788 + 0.304142I
−0.34472 − 4.74783I 0
u = 1.393500 − 0.203394I
a = 0.22592 − 1.40527I
b = −0.947788 − 0.304142I
−0.34472 + 4.74783I 0
u = −0.223272 + 0.544621I
a = −1.77385 + 1.82010I
b = 1.135460 + 0.115630I
4.83779 + 2.01072I 12.25456 − 3.74989I
u = −0.223272 − 0.544621I
a = −1.77385 − 1.82010I
b = 1.135460 − 0.115630I
4.83779 − 2.01072I 12.25456 + 3.74989I
u = −1.42046 + 0.14849I
a = −0.15829 + 1.69585I
b = 1.149430 + 0.449259I
−3.78499 + 8.03533I 0
u = −1.42046 − 0.14849I
a = −0.15829 − 1.69585I
b = 1.149430 − 0.449259I
−3.78499 − 8.03533I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.029302 + 0.562569I
a = −2.46302 − 0.66526I
b = 1.389300 − 0.041819I
2.65855 + 5.14896I 6.64503 − 6.03362I
u = −0.029302 − 0.562569I
a = −2.46302 + 0.66526I
b = 1.389300 + 0.041819I
2.65855 − 5.14896I 6.64503 + 6.03362I
u = 1.43464 + 0.12245I
a = 0.042930 − 0.354425I
b = −0.70296 − 1.28233I
−10.52140 − 2.89327I 0
u = 1.43464 − 0.12245I
a = 0.042930 + 0.354425I
b = −0.70296 + 1.28233I
−10.52140 + 2.89327I 0
u = −1.41589 + 0.26694I
a = −1.11354 + 1.18359I
b = 1.36123 + 0.84739I
−6.69510 + 9.50656I 0
u = −1.41589 − 0.26694I
a = −1.11354 − 1.18359I
b = 1.36123 − 0.84739I
−6.69510 − 9.50656I 0
u = 1.42467 + 0.23536I
a = 1.16887 + 1.06243I
b = −1.280100 + 0.566385I
−3.96712 − 7.44185I 0
u = 1.42467 − 0.23536I
a = 1.16887 − 1.06243I
b = −1.280100 − 0.566385I
−3.96712 + 7.44185I 0
u = 1.43341 + 0.20250I
a = −0.017891 + 0.161314I
b = 0.558005 + 0.771819I
−4.43305 − 1.75009I 0
u = 1.43341 − 0.20250I
a = −0.017891 − 0.161314I
b = 0.558005 − 0.771819I
−4.43305 + 1.75009I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47020 + 0.15176I
a = −1.59839 + 1.30186I
b = 1.022140 + 0.369358I
−8.99633 + 7.05209I 0
u = −1.47020 − 0.15176I
a = −1.59839 − 1.30186I
b = 1.022140 − 0.369358I
−8.99633 − 7.05209I 0
u = 1.46270 + 0.21310I
a = −0.142736 − 0.173221I
b = −0.227870 − 1.122090I
−5.68487 − 7.13165I 0
u = 1.46270 − 0.21310I
a = −0.142736 + 0.173221I
b = −0.227870 + 1.122090I
−5.68487 + 7.13165I 0
u = 1.42546 + 0.39274I
a = −1.36128 − 0.55307I
b = 1.142140 − 0.479132I
−6.72741 − 5.79831I 0
u = 1.42546 − 0.39274I
a = −1.36128 + 0.55307I
b = 1.142140 + 0.479132I
−6.72741 + 5.79831I 0
u = −0.101290 + 0.511238I
a = −2.14533 − 1.04906I
b = 0.509521 + 0.806501I
−3.90419 + 2.55982I −2.62906 − 7.29419I
u = −0.101290 − 0.511238I
a = −2.14533 + 1.04906I
b = 0.509521 − 0.806501I
−3.90419 − 2.55982I −2.62906 + 7.29419I
u = −1.43430 + 0.37339I
a = −1.058510 + 0.905972I
b = 1.023020 + 0.604829I
−3.03968 + 6.93540I 0
u = −1.43430 − 0.37339I
a = −1.058510 − 0.905972I
b = 1.023020 − 0.604829I
−3.03968 − 6.93540I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46650 + 0.25755I
a = 0.296956 − 0.125687I
b = 0.464819 − 1.231230I
−9.9905 + 12.4697I 0
u = −1.46650 − 0.25755I
a = 0.296956 + 0.125687I
b = 0.464819 + 1.231230I
−9.9905 − 12.4697I 0
u = −1.49351 + 0.01902I
a = −0.215924 + 0.277483I
b = 0.136381 + 0.909194I
−7.96267 + 2.08453I 0
u = −1.49351 − 0.01902I
a = −0.215924 − 0.277483I
b = 0.136381 − 0.909194I
−7.96267 − 2.08453I 0
u = −1.49385 + 0.19179I
a = 1.144530 − 0.769768I
b = −0.882187 − 0.601831I
−10.96370 − 1.88768I 0
u = −1.49385 − 0.19179I
a = 1.144530 + 0.769768I
b = −0.882187 + 0.601831I
−10.96370 + 1.88768I 0
u = 1.48782 + 0.23942I
a = −0.907046 − 0.656945I
b = 1.149940 − 0.604968I
−5.17711 − 3.29052I 0
u = 1.48782 − 0.23942I
a = −0.907046 + 0.656945I
b = 1.149940 + 0.604968I
−5.17711 + 3.29052I 0
u = −1.49627 + 0.22205I
a = −0.166815 + 0.452830I
b = −0.423367 + 0.821156I
−7.45351 + 4.85219I 0
u = −1.49627 − 0.22205I
a = −0.166815 − 0.452830I
b = −0.423367 − 0.821156I
−7.45351 − 4.85219I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50052 + 0.24103I
a = 0.738671 − 0.816667I
b = −1.19425 − 0.83194I
−8.72033 + 10.31820I 0
u = −1.50052 − 0.24103I
a = 0.738671 + 0.816667I
b = −1.19425 + 0.83194I
−8.72033 − 10.31820I 0
u = −1.47983 + 0.35404I
a = 1.12539 − 0.87052I
b = −1.26217 − 0.64271I
−2.48744 + 13.31390I 0
u = −1.47983 − 0.35404I
a = 1.12539 + 0.87052I
b = −1.26217 + 0.64271I
−2.48744 − 13.31390I 0
u = −1.52104 + 0.08000I
a = −0.380554 − 0.125846I
b = −0.443776 − 0.501170I
−9.49093 + 2.40825I 0
u = −1.52104 − 0.08000I
a = −0.380554 + 0.125846I
b = −0.443776 + 0.501170I
−9.49093 − 2.40825I 0
u = 1.49631 + 0.34247I
a = −1.10832 − 1.03411I
b = 1.26318 − 0.75191I
−7.3907 − 19.4532I 0
u = 1.49631 − 0.34247I
a = −1.10832 + 1.03411I
b = 1.26318 + 0.75191I
−7.3907 + 19.4532I 0
u = 0.198827 + 0.400882I
a = 2.71094 + 2.85249I
b = −1.287750 + 0.321247I
1.55006 − 6.01113I 10.85844 + 7.29417I
u = 0.198827 − 0.400882I
a = 2.71094 − 2.85249I
b = −1.287750 − 0.321247I
1.55006 + 6.01113I 10.85844 − 7.29417I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.211986 + 0.388735I
a = −0.241725 − 1.269730I
b = −0.254453 + 1.253030I
−4.51951 − 0.62712I −3.68881 − 5.60669I
u = −0.211986 − 0.388735I
a = −0.241725 + 1.269730I
b = −0.254453 − 1.253030I
−4.51951 + 0.62712I −3.68881 + 5.60669I
u = −0.131845 + 0.409309I
a = 1.56478 − 1.40321I
b = −1.267540 − 0.366593I
4.31325 − 0.09049I 10.59814 + 2.57116I
u = −0.131845 − 0.409309I
a = 1.56478 + 1.40321I
b = −1.267540 + 0.366593I
4.31325 + 0.09049I 10.59814 − 2.57116I
u = 1.55242 + 0.32483I
a = 0.882185 + 1.092690I
b = −1.109860 + 0.615948I
−5.40215 − 10.20940I 0
u = 1.55242 − 0.32483I
a = 0.882185 − 1.092690I
b = −1.109860 − 0.615948I
−5.40215 + 10.20940I 0
u = 0.345174 + 0.219410I
a = 4.97865 + 3.99088I
b = −0.729915 + 0.244689I
−2.85893 − 5.32704I 1.7544 + 14.6717I
u = 0.345174 − 0.219410I
a = 4.97865 − 3.99088I
b = −0.729915 − 0.244689I
−2.85893 + 5.32704I 1.7544 − 14.6717I
u = −0.329448 + 0.225873I
a = −0.918001 + 0.200629I
b = 0.349362 − 1.064470I
−4.75595 + 1.37248I −8.78992 − 8.55346I
u = −0.329448 − 0.225873I
a = −0.918001 − 0.200629I
b = 0.349362 + 1.064470I
−4.75595 − 1.37248I −8.78992 + 8.55346I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60484 + 0.10691I
a = 0.468225 + 0.210671I
b = 0.721145 + 0.333609I
−10.09430 − 4.00612I 0
u = 1.60484 − 0.10691I
a = 0.468225 − 0.210671I
b = 0.721145 − 0.333609I
−10.09430 + 4.00612I 0
u = −1.61017 + 0.19252I
a = −0.170100 + 0.160853I
b = 0.405342 − 0.296802I
−9.18901 + 2.02315I 0
u = −1.61017 − 0.19252I
a = −0.170100 − 0.160853I
b = 0.405342 + 0.296802I
−9.18901 − 2.02315I 0
u = 1.64023 + 0.08816I
a = 0.107633 − 0.118889I
b = −0.775130 − 0.567616I
−11.30980 + 6.51473I 0
u = 1.64023 − 0.08816I
a = 0.107633 + 0.118889I
b = −0.775130 + 0.567616I
−11.30980 − 6.51473I 0
u = 0.1150890 + 0.0113492I
a = 6.46636 − 8.23535I
b = 0.798969 + 0.513988I
−3.22422 + 2.14561I −5.03973 − 3.74291I
u = 0.1150890 − 0.0113492I
a = 6.46636 + 8.23535I
b = 0.798969 − 0.513988I
−3.22422 − 2.14561I −5.03973 + 3.74291I
19
II.
I
u
2
= h−2.18 × 10
7
u
37
− 1.78 × 10
7
u
36
+ · · · + 4.48 × 10
6
b + 1.12 × 10
7
, 4.26 ×
10
9
u
37
+1.21×10
9
u
36
+· · ·+5.87×10
8
a−4.09×10
9
, u
38
−20u
36
+· · ·−2u+1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
7
=
−7.24683u
37
− 2.06544u
36
+ ··· + 0.0910287u + 6.96166
4.85898u
37
+ 3.97710u
36
+ ··· + 4.12861u − 2.50559
a
8
=
−2.38785u
37
+ 1.91166u
36
+ ··· + 4.21963u + 4.45608
4.85898u
37
+ 3.97710u
36
+ ··· + 4.12861u − 2.50559
a
11
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
12
=
−6.38265u
37
− 5.01518u
36
+ ··· − 8.26376u + 0.998020
3.14211u
37
+ 0.0643919u
36
+ ··· − 1.37747u + 1.42376
a
2
=
4.01381u
37
− 0.618644u
36
+ ··· + 1.81924u + 4.06511
3.54241u
37
+ 7.35746u
36
+ ··· + 7.06166u − 4.66694
a
1
=
7.29480u
37
+ 2.27644u
36
+ ··· + 4.43642u + 0.855798
−1.43554u
37
+ 2.73952u
36
+ ··· + 3.24977u − 1.30639
a
6
=
2.66041u
37
+ 1.15232u
36
+ ··· − 4.76282u − 8.07943
−4.83578u
37
+ 0.462250u
36
+ ··· + 2.98577u + 0.864912
a
9
=
2.29440u
37
− 0.754655u
36
+ ··· − 2.61969u + 2.26480
−2.50399u
37
+ 10.6731u
36
+ ··· + 14.5809u − 6.45742
(ii) Obstruction class = 1
(iii) Cusp Shapes =
8002109886
587404393
u
37
−
7511164177
587404393
u
36
+ ··· −
15820511680
587404393
u +
8864632311
587404393
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
+ 2u
37
+ ··· + 2u
2
+ 1
c
2
u
38
− 10u
36
+ ··· + u + 1
c
3
, c
4
u
38
− 20u
36
+ ··· − 2u + 1
c
5
u
38
+ 5u
36
+ ··· − 4u + 1
c
6
u
38
+ 17u
36
+ ··· + 76u
2
+ 1
c
7
u
38
− 10u
36
+ ··· − u + 1
c
8
u
38
+ u
37
+ ··· − 6u
2
+ 1
c
9
u
38
+ 4u
36
+ ··· − 98u + 43
c
10
u
38
− 20u
36
+ ··· + 2u + 1
c
11
u
38
+ 4u
37
+ ··· − 5u + 1
c
12
u
38
+ 17u
36
+ ··· + 76u
2
+ 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
+ 6y
37
+ ··· + 4y + 1
c
2
, c
7
y
38
− 20y
37
+ ··· − 35y + 1
c
3
, c
4
, c
10
y
38
− 40y
37
+ ··· + 8y + 1
c
5
y
38
+ 10y
37
+ ··· + 14y + 1
c
6
, c
12
y
38
+ 34y
37
+ ··· + 152y + 1
c
8
y
38
+ 17y
37
+ ··· − 12y + 1
c
9
y
38
+ 8y
37
+ ··· + 24366y + 1849
c
11
y
38
+ 12y
37
+ ··· + 101y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.724754 + 0.466721I
a = 1.28706 − 1.06845I
b = −0.808877 + 0.208230I
1.43893 − 1.80066I 5.39717 + 3.18059I
u = −0.724754 − 0.466721I
a = 1.28706 + 1.06845I
b = −0.808877 − 0.208230I
1.43893 + 1.80066I 5.39717 − 3.18059I
u = 0.038624 + 0.856037I
a = 1.54407 + 0.33359I
b = −0.940689 + 0.374426I
2.61089 − 1.54488I 12.92325 + 1.16108I
u = 0.038624 − 0.856037I
a = 1.54407 − 0.33359I
b = −0.940689 − 0.374426I
2.61089 + 1.54488I 12.92325 − 1.16108I
u = −0.221875 + 0.790952I
a = 1.47435 − 1.19835I
b = −0.860378 + 0.342829I
−2.06383 − 1.55637I −5.18101 + 2.32111I
u = −0.221875 − 0.790952I
a = 1.47435 + 1.19835I
b = −0.860378 − 0.342829I
−2.06383 + 1.55637I −5.18101 − 2.32111I
u = −0.664256 + 0.459387I
a = −1.43109 + 1.22763I
b = 1.175520 + 0.313920I
0.69682 + 5.95632I 0.91457 − 8.64129I
u = −0.664256 − 0.459387I
a = −1.43109 − 1.22763I
b = 1.175520 − 0.313920I
0.69682 − 5.95632I 0.91457 + 8.64129I
u = −0.693540 + 0.397168I
a = −1.29504 + 1.27098I
b = 1.187210 + 0.286839I
0.69724 + 5.95571I 1.26355 − 8.07193I
u = −0.693540 − 0.397168I
a = −1.29504 − 1.27098I
b = 1.187210 − 0.286839I
0.69724 − 5.95571I 1.26355 + 8.07193I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.227810 + 0.039060I
a = 1.098400 − 0.856168I
b = −1.45751 + 0.19388I
−1.65265 − 5.06370I 0. + 9.62078I
u = −1.227810 − 0.039060I
a = 1.098400 + 0.856168I
b = −1.45751 − 0.19388I
−1.65265 + 5.06370I 0. − 9.62078I
u = 1.230970 + 0.049626I
a = −0.748202 + 0.487136I
b = 1.44390 + 0.24716I
1.18377 − 0.94005I 4.33430 + 0.I
u = 1.230970 − 0.049626I
a = −0.748202 − 0.487136I
b = 1.44390 − 0.24716I
1.18377 + 0.94005I 4.33430 + 0.I
u = 1.274220 + 0.096196I
a = 0.86870 + 2.57943I
b = −0.620577 + 0.272731I
−5.94975 − 5.80302I 0. + 8.64052I
u = 1.274220 − 0.096196I
a = 0.86870 − 2.57943I
b = −0.620577 − 0.272731I
−5.94975 + 5.80302I 0. − 8.64052I
u = 1.124380 + 0.648756I
a = −0.823612 − 0.002003I
b = 0.833040 + 0.229721I
−0.45359 − 3.86378I 0. + 13.77418I
u = 1.124380 − 0.648756I
a = −0.823612 + 0.002003I
b = 0.833040 − 0.229721I
−0.45359 + 3.86378I 0. − 13.77418I
u = 0.681966 + 0.108872I
a = 0.915571 − 0.315211I
b = −1.277390 + 0.105664I
3.37958 + 0.31409I 5.07982 − 8.68577I
u = 0.681966 − 0.108872I
a = 0.915571 + 0.315211I
b = −1.277390 − 0.105664I
3.37958 − 0.31409I 5.07982 + 8.68577I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.330470 + 0.194404I
a = −0.346350 + 1.364350I
b = 0.815625 + 0.569407I
−1.41232 + 4.80713I 0
u = −1.330470 − 0.194404I
a = −0.346350 − 1.364350I
b = 0.815625 − 0.569407I
−1.41232 − 4.80713I 0
u = −1.377820 + 0.116121I
a = −0.363180 + 0.687232I
b = −0.379983 + 1.273240I
−8.97301 + 2.54427I 0
u = −1.377820 − 0.116121I
a = −0.363180 − 0.687232I
b = −0.379983 − 1.273240I
−8.97301 − 2.54427I 0
u = 1.381520 + 0.115723I
a = 0.309327 + 0.082842I
b = 0.271911 + 1.294690I
−9.00458 − 0.22425I 0
u = 1.381520 − 0.115723I
a = 0.309327 − 0.082842I
b = 0.271911 − 1.294690I
−9.00458 + 0.22425I 0
u = −1.38108 + 0.32679I
a = −1.43795 + 0.68681I
b = 1.103380 + 0.505490I
−6.15200 + 5.66713I 0
u = −1.38108 − 0.32679I
a = −1.43795 − 0.68681I
b = 1.103380 − 0.505490I
−6.15200 − 5.66713I 0
u = 1.46827 + 0.25645I
a = 0.91817 + 1.20189I
b = −1.240190 + 0.663386I
−5.72684 − 9.08504I 0
u = 1.46827 − 0.25645I
a = 0.91817 − 1.20189I
b = −1.240190 − 0.663386I
−5.72684 + 9.08504I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.57831 + 0.04794I
a = −0.310175 + 0.692536I
b = −0.435749 + 0.068585I
−10.17910 + 4.89622I 0
u = −1.57831 − 0.04794I
a = −0.310175 − 0.692536I
b = −0.435749 − 0.068585I
−10.17910 − 4.89622I 0
u = 0.397426 + 0.124415I
a = −1.32013 − 5.43287I
b = 0.593080 + 0.105928I
−2.87625 + 4.88335I 1.85351 + 2.68366I
u = 0.397426 − 0.124415I
a = −1.32013 + 5.43287I
b = 0.593080 − 0.105928I
−2.87625 − 4.88335I 1.85351 − 2.68366I
u = 1.60462 + 0.16501I
a = 0.066932 − 0.251467I
b = 0.542537 + 0.167224I
−8.85350 − 1.99548I 0
u = 1.60462 − 0.16501I
a = 0.066932 + 0.251467I
b = 0.542537 − 0.167224I
−8.85350 + 1.99548I 0
u = −0.002074 + 0.254628I
a = 1.59315 − 1.32913I
b = 0.055133 + 1.178490I
−4.28248 − 1.15744I 5.04389 + 4.34187I
u = −0.002074 − 0.254628I
a = 1.59315 + 1.32913I
b = 0.055133 − 1.178490I
−4.28248 + 1.15744I 5.04389 − 4.34187I
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
38
+ 2u
37
+ ··· + 2u
2
+ 1)(u
148
+ 5u
147
+ ··· − 47u + 1)
c
2
(u
38
− 10u
36
+ ··· + u + 1)(u
148
+ u
147
+ ··· + 28032u + 9472)
c
3
, c
4
(u
38
− 20u
36
+ ··· − 2u + 1)(u
148
+ u
147
+ ··· + 565u + 37)
c
5
(u
38
+ 5u
36
+ ··· − 4u + 1)(u
148
− 5u
147
+ ··· + 207817u + 10777)
c
6
(u
38
+ 17u
36
+ ··· + 76u
2
+ 1)(u
148
+ u
147
+ ··· − 4721u + 6513)
c
7
(u
38
− 10u
36
+ ··· − u + 1)(u
148
+ u
147
+ ··· + 28032u + 9472)
c
8
(u
38
+ u
37
+ ··· − 6u
2
+ 1)(u
148
+ 15u
146
+ ··· + 608u + 64)
c
9
(u
38
+ 4u
36
+ ··· − 98u + 43)
· (u
148
− 3u
147
+ ··· + 733241455u + 110567423)
c
10
(u
38
− 20u
36
+ ··· + 2u + 1)(u
148
+ u
147
+ ··· + 565u + 37)
c
11
(u
38
+ 4u
37
+ ··· − 5u + 1)(u
148
+ u
147
+ ··· − 13110u + 65501)
c
12
(u
38
+ 17u
36
+ ··· + 76u
2
+ 1)(u
148
+ u
147
+ ··· − 4721u + 6513)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
38
+ 6y
37
+ ··· + 4y + 1)(y
148
+ 7y
147
+ ··· − 253y + 1)
c
2
, c
7
(y
38
− 20y
37
+ ··· − 35y + 1)
· (y
148
− 71y
147
+ ··· − 3723476992y + 89718784)
c
3
, c
4
, c
10
(y
38
− 40y
37
+ ··· + 8y + 1)(y
148
− 143y
147
+ ··· − 187357y + 1369)
c
5
(y
38
+ 10y
37
+ ··· + 14y + 1)
· (y
148
+ 35y
147
+ ··· − 9055314399y + 116143729)
c
6
, c
12
(y
38
+ 34y
37
+ ··· + 152y + 1)
· (y
148
+ 111y
147
+ ··· + 1135280675y + 42419169)
c
8
(y
38
+ 17y
37
+ ··· − 12y + 1)(y
148
+ 30y
147
+ ··· + 113664y + 4096)
c
9
(y
38
+ 8y
37
+ ··· + 24366y + 1849)
· (y
148
− 27y
147
+ ··· − 884023777418158187y + 12225155028860929)
c
11
(y
38
+ 12y
37
+ ··· + 101y + 1)
· (y
148
+ 21y
147
+ ··· + 171350880528y + 4290381001)
28
