12a
0067
(K12a
0067
)
A knot diagram
1
Linearized knot diagam
3 5 7 8 2 10 1 11 12 6 9 4
Solving Sequence
2,6
5 3
1,11
10 7 4 8 12 9
c
5
c
2
c
1
c
10
c
6
c
3
c
7
c
12
c
9
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.38800 × 10
265
u
118
+ 3.02980 × 10
267
u
117
+ ··· + 1.78088 × 10
268
b − 1.33871 × 10
268
,
− 3.99262 × 10
266
u
118
− 9.19047 × 10
266
u
117
+ ··· + 4.68652 × 10
266
a − 9.37332 × 10
266
,
u
119
+ 2u
118
+ ··· + 10u − 1i
I
u
2
= hb, −u
3
+ a + 2, u
4
+ u
2
− u + 1i
I
u
3
= hb, −u
3
− u
2
+ a − 2u − 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 129 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−4.39 × 10
265
u
118
+ 3.03 × 10
267
u
117
+ · · · + 1.78 × 10
268
b − 1.34 ×
10
268
, −3.99 × 10
266
u
118
− 9.19 × 10
266
u
117
+ · · · + 4.69 × 10
266
a − 9.37 ×
10
266
, u
119
+ 2u
118
+ · · · + 10u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
0.851939u
118
+ 1.96105u
117
+ ··· + 5.50935u + 2.00006
0.00246395u
118
− 0.170130u
117
+ ··· − 6.39561u + 0.751713
a
10
=
0.854403u
118
+ 1.79092u
117
+ ··· − 0.886258u + 2.75177
0.00246395u
118
− 0.170130u
117
+ ··· − 6.39561u + 0.751713
a
7
=
−1.38396u
118
− 2.75797u
117
+ ··· + 1.94382u + 0.347631
0.656679u
118
+ 1.41118u
117
+ ··· − 19.9698u + 2.06499
a
4
=
0.330028u
118
+ 1.31635u
117
+ ··· + 19.6110u − 6.37259
−0.517151u
118
− 0.974647u
117
+ ··· + 15.4648u − 0.903539
a
8
=
−1.41875u
118
− 2.80068u
117
+ ··· + 1.91552u + 0.343327
0.587614u
118
+ 1.30438u
117
+ ··· − 17.5478u + 1.69309
a
12
=
−0.151740u
118
− 0.172258u
117
+ ··· + 0.396525u − 1.04773
−0.132957u
118
− 0.203298u
117
+ ··· + 7.68780u − 0.734713
a
9
=
0.448776u
118
+ 1.21621u
117
+ ··· − 5.54442u + 2.77419
0.132957u
118
+ 0.203298u
117
+ ··· − 7.68780u + 0.734713
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.699441u
118
− 1.36103u
117
+ ··· − 108.370u + 12.9128
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
119
+ 48u
118
+ ··· + 10u − 1
c
2
, c
5
u
119
+ 2u
118
+ ··· + 10u − 1
c
3
u
119
+ 2u
118
+ ··· − 140120u + 18392
c
4
u
119
− 2u
118
+ ··· + 83530u + 30653
c
6
, c
10
u
119
+ u
118
+ ··· + 8192u − 1024
c
7
u
119
− 10u
118
+ ··· − 2u + 1
c
8
, c
9
, c
11
u
119
+ 11u
118
+ ··· − 5u − 1
c
12
u
119
+ 12u
118
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
119
+ 48y
118
+ ··· + 2322y −1
c
2
, c
5
y
119
+ 48y
118
+ ··· + 10y −1
c
3
y
119
+ 132y
118
+ ··· − 23236923728y −338265664
c
4
y
119
+ 108y
118
+ ··· − 59171729182y −939606409
c
6
, c
10
y
119
+ 63y
118
+ ··· − 16252928y −1048576
c
7
y
119
+ 12y
118
+ ··· − 10y −1
c
8
, c
9
, c
11
y
119
− 111y
118
+ ··· + 61y −1
c
12
y
119
+ 120y
117
+ ··· + 10y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.838953 + 0.544196I
a = 0.109175 − 0.804084I
b = 0.227389 − 1.188850I
4.58267 + 3.41945I 0
u = −0.838953 − 0.544196I
a = 0.109175 + 0.804084I
b = 0.227389 + 1.188850I
4.58267 − 3.41945I 0
u = −0.566709 + 0.823835I
a = 1.41781 − 0.98974I
b = −1.49166 − 0.40339I
4.10120 − 1.40763I 0
u = −0.566709 − 0.823835I
a = 1.41781 + 0.98974I
b = −1.49166 + 0.40339I
4.10120 + 1.40763I 0
u = 0.929890 + 0.372568I
a = 0.494702 − 0.637233I
b = −0.186613 − 0.978134I
3.57632 − 0.41841I 0
u = 0.929890 − 0.372568I
a = 0.494702 + 0.637233I
b = −0.186613 + 0.978134I
3.57632 + 0.41841I 0
u = 0.528551 + 0.860721I
a = −1.65774 + 2.41316I
b = −0.856075 − 0.055946I
2.60459 + 2.12994I 0
u = 0.528551 − 0.860721I
a = −1.65774 − 2.41316I
b = −0.856075 + 0.055946I
2.60459 − 2.12994I 0
u = 0.429351 + 0.877830I
a = −0.87746 − 3.07903I
b = 0.391668 + 0.704858I
−0.147900 + 0.561296I 0
u = 0.429351 − 0.877830I
a = −0.87746 + 3.07903I
b = 0.391668 − 0.704858I
−0.147900 − 0.561296I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.595363 + 0.770782I
a = −0.47331 − 1.67093I
b = −0.426559 − 1.254360I
6.60297 − 2.40686I 0
u = 0.595363 − 0.770782I
a = −0.47331 + 1.67093I
b = −0.426559 + 1.254360I
6.60297 + 2.40686I 0
u = −0.886727 + 0.528667I
a = −0.901289 + 0.300957I
b = 1.234610 + 0.383617I
5.90606 + 6.30718I 0
u = −0.886727 − 0.528667I
a = −0.901289 − 0.300957I
b = 1.234610 − 0.383617I
5.90606 − 6.30718I 0
u = 0.518493 + 0.815351I
a = 0.25894 + 3.45551I
b = 0.260712 + 0.872493I
0.677780 + 0.375001I 0
u = 0.518493 − 0.815351I
a = 0.25894 − 3.45551I
b = 0.260712 − 0.872493I
0.677780 − 0.375001I 0
u = 0.356864 + 0.974923I
a = 0.19087 + 3.03439I
b = −0.382865 − 1.138070I
4.96842 − 1.91691I 0
u = 0.356864 − 0.974923I
a = 0.19087 − 3.03439I
b = −0.382865 + 1.138070I
4.96842 + 1.91691I 0
u = −0.575407 + 0.865942I
a = 0.67706 − 1.41907I
b = −1.38391 + 0.66586I
3.96253 − 3.15795I 0
u = −0.575407 − 0.865942I
a = 0.67706 + 1.41907I
b = −1.38391 − 0.66586I
3.96253 + 3.15795I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.526299 + 0.896866I
a = −4.03635 − 2.50678I
b = 0.356301 − 0.893080I
0.40789 + 3.85492I 0
u = 0.526299 − 0.896866I
a = −4.03635 + 2.50678I
b = 0.356301 + 0.893080I
0.40789 − 3.85492I 0
u = −0.913451 + 0.496996I
a = 0.431272 + 0.500496I
b = −0.520481 + 1.196970I
3.03897 + 8.76012I 0
u = −0.913451 − 0.496996I
a = 0.431272 − 0.500496I
b = −0.520481 − 1.196970I
3.03897 − 8.76012I 0
u = −0.555202 + 0.776269I
a = 1.94351 − 0.74037I
b = −0.651991 − 1.218550I
3.14030 + 0.25233I 0
u = −0.555202 − 0.776269I
a = 1.94351 + 0.74037I
b = −0.651991 + 1.218550I
3.14030 − 0.25233I 0
u = −0.311297 + 1.010080I
a = −0.730790 + 0.796137I
b = 0.720782 − 0.097822I
−3.66803 − 0.76142I 0
u = −0.311297 − 1.010080I
a = −0.730790 − 0.796137I
b = 0.720782 + 0.097822I
−3.66803 + 0.76142I 0
u = 0.494555 + 0.800584I
a = 4.89193 − 0.43239I
b = −0.486675 + 0.231669I
2.15098 + 1.56600I 0
u = 0.494555 − 0.800584I
a = 4.89193 + 0.43239I
b = −0.486675 − 0.231669I
2.15098 − 1.56600I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.442347 + 0.967147I
a = 0.187163 + 0.721442I
b = 0.203483 − 0.360440I
−0.42288 + 2.75298I 0
u = 0.442347 − 0.967147I
a = 0.187163 − 0.721442I
b = 0.203483 + 0.360440I
−0.42288 − 2.75298I 0
u = −0.098695 + 0.931045I
a = 0.77161 − 1.97635I
b = −0.628406 + 1.083000I
3.41353 + 5.41155I 0
u = −0.098695 − 0.931045I
a = 0.77161 + 1.97635I
b = −0.628406 − 1.083000I
3.41353 − 5.41155I 0
u = 0.951835 + 0.487655I
a = −1.263630 + 0.008890I
b = 1.025210 + 0.046098I
5.49536 + 1.71804I 0
u = 0.951835 − 0.487655I
a = −1.263630 − 0.008890I
b = 1.025210 − 0.046098I
5.49536 − 1.71804I 0
u = −0.578907 + 0.899689I
a = −0.491377 − 0.195288I
b = −0.40200 + 1.40800I
2.74244 − 4.81471I 0
u = −0.578907 − 0.899689I
a = −0.491377 + 0.195288I
b = −0.40200 − 1.40800I
2.74244 + 4.81471I 0
u = 0.557211 + 0.926119I
a = 2.25509 − 2.77223I
b = −0.148264 − 0.425639I
1.67285 + 2.69563I 0
u = 0.557211 − 0.926119I
a = 2.25509 + 2.77223I
b = −0.148264 + 0.425639I
1.67285 − 2.69563I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.561845 + 0.934937I
a = −2.05105 + 0.47513I
b = 0.64960 + 1.35081I
0.66033 − 5.93367I 0
u = −0.561845 − 0.934937I
a = −2.05105 − 0.47513I
b = 0.64960 − 1.35081I
0.66033 + 5.93367I 0
u = 0.567410 + 0.933478I
a = 3.34553 + 1.33510I
b = −0.498602 + 1.231420I
6.08874 + 7.00877I 0
u = 0.567410 − 0.933478I
a = 3.34553 − 1.33510I
b = −0.498602 − 1.231420I
6.08874 − 7.00877I 0
u = −0.976182 + 0.493516I
a = −0.586235 − 0.134004I
b = 0.71252 − 1.31592I
8.9345 + 13.2205I 0
u = −0.976182 − 0.493516I
a = −0.586235 + 0.134004I
b = 0.71252 + 1.31592I
8.9345 − 13.2205I 0
u = −0.837165 + 0.713055I
a = −0.907014 + 0.200119I
b = 0.10091 + 1.56443I
13.31560 + 1.26216I 0
u = −0.837165 − 0.713055I
a = −0.907014 − 0.200119I
b = 0.10091 − 1.56443I
13.31560 − 1.26216I 0
u = −0.511882 + 0.735751I
a = 0.633141 − 0.149979I
b = 0.39152 − 1.36600I
1.31767 + 1.52824I 0
u = −0.511882 − 0.735751I
a = 0.633141 + 0.149979I
b = 0.39152 + 1.36600I
1.31767 − 1.52824I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.783521 + 0.422905I
a = 0.486131 − 0.247012I
b = −0.755611 − 0.251969I
0.15512 + 3.88915I 0
u = −0.783521 − 0.422905I
a = 0.486131 + 0.247012I
b = −0.755611 + 0.251969I
0.15512 − 3.88915I 0
u = −0.652570 + 0.596164I
a = −0.0981409 + 0.0613103I
b = −0.68690 + 1.37885I
7.74142 + 6.02428I 0
u = −0.652570 − 0.596164I
a = −0.0981409 − 0.0613103I
b = −0.68690 − 1.37885I
7.74142 − 6.02428I 0
u = 0.952391 + 0.588335I
a = 0.591023 + 0.694941I
b = −0.270109 + 1.002650I
3.36143 + 3.82787I 0
u = 0.952391 − 0.588335I
a = 0.591023 − 0.694941I
b = −0.270109 − 1.002650I
3.36143 − 3.82787I 0
u = 0.017038 + 1.121140I
a = −0.763804 + 0.103402I
b = 0.392618 − 0.845484I
−1.51868 + 2.01224I 0
u = 0.017038 − 1.121140I
a = −0.763804 − 0.103402I
b = 0.392618 + 0.845484I
−1.51868 − 2.01224I 0
u = −0.522097 + 1.002300I
a = −1.43550 + 0.42911I
b = 1.002750 + 0.439220I
−2.32372 − 5.35556I 0
u = −0.522097 − 1.002300I
a = −1.43550 − 0.42911I
b = 1.002750 − 0.439220I
−2.32372 + 5.35556I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.109750 + 0.291509I
a = −0.578286 − 0.115750I
b = 0.431413 + 1.312020I
9.92813 − 3.32978I 0
u = 1.109750 − 0.291509I
a = −0.578286 + 0.115750I
b = 0.431413 − 1.312020I
9.92813 + 3.32978I 0
u = 0.618376 + 0.563906I
a = 0.730085 − 0.169336I
b = −0.337347 − 0.043445I
1.11265 + 1.43327I 0
u = 0.618376 − 0.563906I
a = 0.730085 + 0.169336I
b = −0.337347 + 0.043445I
1.11265 − 1.43327I 0
u = −0.615027 + 1.005040I
a = 2.23322 − 0.35155I
b = −0.81135 − 1.33905I
6.53771 − 10.99580I 0
u = −0.615027 − 1.005040I
a = 2.23322 + 0.35155I
b = −0.81135 + 1.33905I
6.53771 + 10.99580I 0
u = −0.106450 + 1.175170I
a = 1.60470 + 0.24304I
b = −0.708952 − 0.522934I
−5.13196 + 1.58072I 0
u = −0.106450 − 1.175170I
a = 1.60470 − 0.24304I
b = −0.708952 + 0.522934I
−5.13196 − 1.58072I 0
u = −0.322092 + 0.754108I
a = −0.39118 + 1.39798I
b = 0.803778 − 0.818065I
−1.06689 + 1.52634I 0
u = −0.322092 − 0.754108I
a = −0.39118 − 1.39798I
b = 0.803778 + 0.818065I
−1.06689 − 1.52634I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.803859 + 0.148657I
a = −0.225213 − 0.234367I
b = −0.064271 + 0.891155I
2.46591 + 3.13553I 0
u = −0.803859 − 0.148657I
a = −0.225213 + 0.234367I
b = −0.064271 − 0.891155I
2.46591 − 3.13553I 0
u = 0.520708 + 1.090110I
a = 0.693612 + 0.589861I
b = −0.366092 − 0.404737I
−0.47565 + 2.99344I 0
u = 0.520708 − 1.090110I
a = 0.693612 − 0.589861I
b = −0.366092 + 0.404737I
−0.47565 − 2.99344I 0
u = 0.058363 + 1.216070I
a = −2.32308 − 0.15998I
b = 0.971579 + 0.429480I
−0.70650 + 4.43937I 0
u = 0.058363 − 1.216070I
a = −2.32308 + 0.15998I
b = 0.971579 − 0.429480I
−0.70650 − 4.43937I 0
u = −0.727403 + 0.981872I
a = 1.071830 + 0.200891I
b = −0.01760 − 1.62299I
12.4827 − 7.0839I 0
u = −0.727403 − 0.981872I
a = 1.071830 − 0.200891I
b = −0.01760 + 1.62299I
12.4827 + 7.0839I 0
u = −0.612589 + 1.094200I
a = 0.767693 − 0.894702I
b = −0.892482 + 0.262426I
−1.81583 − 9.13295I 0
u = −0.612589 − 1.094200I
a = 0.767693 + 0.894702I
b = −0.892482 − 0.262426I
−1.81583 + 9.13295I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.735041 + 1.019170I
a = −0.316372 − 0.656191I
b = −0.077697 − 0.865759I
2.05334 + 2.32542I 0
u = 0.735041 − 1.019170I
a = −0.316372 + 0.656191I
b = −0.077697 + 0.865759I
2.05334 − 2.32542I 0
u = −0.518341 + 1.151770I
a = 0.645899 + 0.752822I
b = −0.126191 − 0.699313I
−0.44007 − 7.88693I 0
u = −0.518341 − 1.151770I
a = 0.645899 − 0.752822I
b = −0.126191 + 0.699313I
−0.44007 + 7.88693I 0
u = 1.082210 + 0.653636I
a = −0.837140 − 0.100407I
b = 0.485630 − 1.303600I
9.53931 + 7.04970I 0
u = 1.082210 − 0.653636I
a = −0.837140 + 0.100407I
b = 0.485630 + 1.303600I
9.53931 − 7.04970I 0
u = −0.285135 + 1.235900I
a = −0.837715 − 1.017010I
b = 0.191982 + 0.843692I
−1.96720 − 0.65100I 0
u = −0.285135 − 1.235900I
a = −0.837715 + 1.017010I
b = 0.191982 − 0.843692I
−1.96720 + 0.65100I 0
u = −0.670191 + 1.077940I
a = −1.54529 + 0.46264I
b = 0.332562 + 1.244600I
2.96632 − 9.05048I 0
u = −0.670191 − 1.077940I
a = −1.54529 − 0.46264I
b = 0.332562 − 1.244600I
2.96632 + 9.05048I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.022366 + 1.275070I
a = 1.23684 − 0.76817I
b = −0.545853 + 1.021420I
−3.60584 + 6.39853I 0
u = 0.022366 − 1.275070I
a = 1.23684 + 0.76817I
b = −0.545853 − 1.021420I
−3.60584 − 6.39853I 0
u = −0.683411 + 1.099690I
a = −1.00098 + 1.27401I
b = 1.272770 − 0.469310I
4.16552 − 12.10780I 0
u = −0.683411 − 1.099690I
a = −1.00098 − 1.27401I
b = 1.272770 + 0.469310I
4.16552 + 12.10780I 0
u = −0.681332 + 1.121330I
a = 1.99277 − 0.41746I
b = −0.585302 − 1.226580I
1.1322 − 14.6195I 0
u = −0.681332 − 1.121330I
a = 1.99277 + 0.41746I
b = −0.585302 + 1.226580I
1.1322 + 14.6195I 0
u = 0.720492 + 1.113940I
a = −1.51475 − 0.74596I
b = 0.982362 + 0.178327I
3.61125 + 4.38522I 0
u = 0.720492 − 1.113940I
a = −1.51475 + 0.74596I
b = 0.982362 − 0.178327I
3.61125 − 4.38522I 0
u = −0.701138 + 1.147870I
a = −2.22521 + 0.22453I
b = 0.76422 + 1.30680I
6.9107 − 19.3213I 0
u = −0.701138 − 1.147870I
a = −2.22521 − 0.22453I
b = 0.76422 − 1.30680I
6.9107 + 19.3213I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.693659 + 1.171160I
a = 1.59038 + 0.32423I
b = −0.382587 + 1.003640I
1.19440 + 6.39011I 0
u = 0.693659 − 1.171160I
a = 1.59038 − 0.32423I
b = −0.382587 − 1.003640I
1.19440 − 6.39011I 0
u = 0.035679 + 1.363720I
a = −1.36652 + 1.22183I
b = 0.638039 − 1.211900I
1.81121 + 10.37090I 0
u = 0.035679 − 1.363720I
a = −1.36652 − 1.22183I
b = 0.638039 + 1.211900I
1.81121 − 10.37090I 0
u = 0.388544 + 1.308910I
a = −0.21975 − 1.45578I
b = 0.271184 + 1.181390I
4.63253 + 1.58055I 0
u = 0.388544 − 1.308910I
a = −0.21975 + 1.45578I
b = 0.271184 − 1.181390I
4.63253 − 1.58055I 0
u = 0.906319 + 1.043070I
a = 0.150159 − 0.428837I
b = 0.364395 + 1.282450I
8.37474 − 0.01682I 0
u = 0.906319 − 1.043070I
a = 0.150159 + 0.428837I
b = 0.364395 − 1.282450I
8.37474 + 0.01682I 0
u = 0.73537 + 1.25030I
a = −1.76430 + 0.25295I
b = 0.545981 − 1.269200I
7.05259 + 9.90887I 0
u = 0.73537 − 1.25030I
a = −1.76430 − 0.25295I
b = 0.545981 + 1.269200I
7.05259 − 9.90887I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.412631 + 0.283829I
a = −0.447411 − 0.881091I
b = −0.455410 + 1.286190I
6.81704 + 5.01481I 2.95424 − 4.27680I
u = 0.412631 − 0.283829I
a = −0.447411 + 0.881091I
b = −0.455410 − 1.286190I
6.81704 − 5.01481I 2.95424 + 4.27680I
u = −0.332585 + 0.209939I
a = 1.001600 + 0.735256I
b = 0.599999 − 0.527709I
−0.78514 + 1.51036I −1.09782 − 4.16173I
u = −0.332585 − 0.209939I
a = 1.001600 − 0.735256I
b = 0.599999 + 0.527709I
−0.78514 − 1.51036I −1.09782 + 4.16173I
u = 0.144570 + 0.213517I
a = 5.52126 − 0.96142I
b = −0.480746 − 0.462220I
2.12966 + 0.82300I 5.18127 + 1.42411I
u = 0.144570 − 0.213517I
a = 5.52126 + 0.96142I
b = −0.480746 + 0.462220I
2.12966 − 0.82300I 5.18127 − 1.42411I
u = 0.111732 + 0.194107I
a = 2.24806 + 1.10571I
b = 0.275565 − 0.965943I
0.69537 + 1.96234I 0.92100 − 4.57588I
u = 0.111732 − 0.194107I
a = 2.24806 − 1.10571I
b = 0.275565 + 0.965943I
0.69537 − 1.96234I 0.92100 + 4.57588I
u = 0.133516
a = 6.38767
b = −0.945861
2.76788 1.73080
16
II. I
u
2
= hb, −u
3
+ a + 2, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
2
a
11
=
u
3
− 2
0
a
10
=
u
3
− 2
0
a
7
=
1
0
a
4
=
−u
3
u
3
+ u
a
8
=
−u
3
+ u
2
− u + 1
−u
2
+ u − 1
a
12
=
u
3
− u
2
+ u − 1
u
2
− u + 1
a
9
=
u
2
− u − 1
−u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9u
3
− 2u
2
− 2u + 11
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
4
, c
12
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
u
4
+ u
2
− u + 1
c
6
, c
10
u
4
c
7
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
8
, c
9
(u + 1)
4
c
11
(u − 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
4
, c
5
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
6
, c
10
y
4
c
8
, c
9
, c
11
(y −1)
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −2.39923 + 0.32564I
b = 0
2.62503 + 1.39709I 13.5849 − 5.3845I
u = 0.547424 − 0.585652I
a = −2.39923 − 0.32564I
b = 0
2.62503 − 1.39709I 13.5849 + 5.3845I
u = −0.547424 + 1.120870I
a = −0.100768 − 0.400532I
b = 0
−0.98010 − 7.64338I −3.08487 + 3.81741I
u = −0.547424 − 1.120870I
a = −0.100768 + 0.400532I
b = 0
−0.98010 + 7.64338I −3.08487 − 3.81741I
20
III. I
u
3
= hb, −u
3
− u
2
+ a − 2u − 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
u
3
+ u
2
+ 2u + 1
0
a
10
=
u
3
+ u
2
+ 2u + 1
0
a
7
=
1
0
a
4
=
−u
3
u
3
+ u
a
8
=
u
4
+ u
2
+ u + 1
−2u
5
− u
4
− 3u
3
− 2u
2
− 3u − 2
a
12
=
−u
4
− u
2
− u − 1
2u
5
+ u
4
+ 3u
3
+ 2u
2
+ 3u + 2
a
9
=
u
4
+ u
3
+ 2u
2
+ 3u + 2
−2u
5
− u
4
− 3u
3
− 2u
2
− 3u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
5
+ u
4
+ 2u
2
− 3u
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
4
, c
12
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
5
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
6
, c
10
u
6
c
7
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
8
, c
9
(u + 1)
6
c
11
(u − 1)
6
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
4
, c
5
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y −1)
2
c
6
, c
10
y
6
c
8
, c
9
, c
11
(y −1)
6
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = −0.13238 + 2.74513I
b = 0
1.37919 + 2.82812I −2.14022 − 3.69351I
u = 0.498832 − 1.001300I
a = −0.13238 − 2.74513I
b = 0
1.37919 − 2.82812I −2.14022 + 3.69351I
u = −0.284920 + 1.115140I
a = 0.307599 + 0.479689I
b = 0
−2.75839 −2.43992 − 2.50363I
u = −0.284920 − 1.115140I
a = 0.307599 − 0.479689I
b = 0
−2.75839 −2.43992 + 2.50363I
u = −0.713912 + 0.305839I
a = −0.175218 + 0.614017I
b = 0
1.37919 + 2.82812I 3.08014 − 1.90022I
u = −0.713912 − 0.305839I
a = −0.175218 − 0.614017I
b = 0
1.37919 − 2.82812I 3.08014 + 1.90022I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
119
+ 48u
118
+ ··· + 10u − 1)
c
2
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
119
+ 2u
118
+ ··· + 10u − 1)
c
3
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
119
+ 2u
118
+ ··· − 140120u + 18392)
c
4
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
119
− 2u
118
+ ··· + 83530u + 30653)
c
5
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
119
+ 2u
118
+ ··· + 10u − 1)
c
6
, c
10
u
10
(u
119
+ u
118
+ ··· + 8192u − 1024)
c
7
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
119
− 10u
118
+ ··· − 2u + 1)
c
8
, c
9
((u + 1)
10
)(u
119
+ 11u
118
+ ··· − 5u − 1)
c
11
((u − 1)
10
)(u
119
+ 11u
118
+ ··· − 5u − 1)
c
12
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
119
+ 12u
118
+ ··· + 2u + 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
119
+ 48y
118
+ ··· + 2322y −1)
c
2
, c
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
119
+ 48y
118
+ ··· + 10y −1)
c
3
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
119
+ 132y
118
+ ··· − 23236923728y −338265664)
c
4
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
119
+ 108y
118
+ ··· − 59171729182y −939606409)
c
6
, c
10
y
10
(y
119
+ 63y
118
+ ··· − 1.62529 × 10
7
y −1048576)
c
7
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
119
+ 12y
118
+ ··· − 10y −1)
c
8
, c
9
, c
11
((y −1)
10
)(y
119
− 111y
118
+ ··· + 61y −1)
c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
119
+ 120y
117
+ ··· + 10y −1)
26
