12a
0136
(K12a
0136
)
A knot diagram
1
Linearized knot diagam
3 5 8 9 2 4 11 6 12 1 7 10
Solving Sequence
4,8 3,11
7 12 6 9 5 2 1 10
c
3
c
7
c
11
c
6
c
8
c
4
c
2
c
1
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.92138 × 10
1091
u
118
+ 4.64324 × 10
1091
u
117
+ ··· + 1.00650 × 10
1094
b + 1.39253 × 10
1096
,
− 1.61183 × 10
1095
u
118
− 4.22365 × 10
1095
u
117
+ ··· + 3.08521 × 10
1098
a − 6.78233 × 10
1099
,
u
119
+ 2u
118
+ ··· + 83530u − 30653i
I
u
2
= h−u
2
+ b + u − 1, a, u
4
+ u
2
+ u + 1i
I
u
3
= h2u
5
+ 3u
3
− u
2
+ b + 2u − 2, a, 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
= h1.92 × 10
1091
u
118
+ 4.64 × 10
1091
u
117
+ · · · + 1.01 × 10
1094
b + 1.39 ×
10
1096
, −1.61 × 10
1095
u
118
− 4.22 × 10
1095
u
117
+ · · · + 3.09 × 10
1098
a −
6.78 × 10
1099
, u
119
+ 2u
118
+ · · · + 83530u − 30653i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
11
=
0.000522436u
118
+ 0.00136900u
117
+ ··· + 6.20057u + 21.9834
−0.00190898u
118
− 0.00461328u
117
+ ··· + 48.5697u − 138.354
a
7
=
−0.00200655u
118
− 0.00486829u
117
+ ··· + 55.9628u − 133.379
−0.00152654u
118
− 0.00376370u
117
+ ··· + 65.0969u − 99.4643
a
12
=
−0.00285140u
118
− 0.00709019u
117
+ ··· + 151.015u − 185.338
−0.00192121u
118
− 0.00470284u
117
+ ··· + 64.2476u − 130.571
a
6
=
−0.000480013u
118
− 0.00110460u
117
+ ··· − 9.13415u − 33.9147
−0.00152654u
118
− 0.00376370u
117
+ ··· + 65.0969u − 99.4643
a
9
=
0.00245573u
118
+ 0.00629867u
117
+ ··· − 225.013u + 121.139
−0.00168112u
118
− 0.00408093u
117
+ ··· + 55.9312u − 118.865
a
5
=
−0.00412868u
118
− 0.0102821u
117
+ ··· + 131.372u − 247.767
−0.00103999u
118
− 0.00252566u
117
+ ··· + 35.1546u − 74.9025
a
2
=
−0.00467142u
118
− 0.0112071u
117
+ ··· + 116.802u − 339.632
0.00104931u
118
+ 0.00255345u
117
+ ··· − 31.3528u + 73.5724
a
1
=
−0.00289772u
118
− 0.00693478u
117
+ ··· + 72.9161u − 208.913
0.00133844u
118
+ 0.00324465u
117
+ ··· − 37.5398u + 95.7947
a
10
=
−0.00225121u
118
− 0.00540515u
117
+ ··· + 56.8808u − 167.552
−0.00193168u
118
− 0.00471512u
117
+ ··· + 65.4873u − 133.140
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00773579u
118
+ 0.0192693u
117
+ ··· − 357.195u + 464.026
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
+ ··· + 83530u + 30653
c
4
u
119
+ 2u
118
+ ··· − 140120u + 18392
c
6
u
119
+ 12u
118
+ ··· + 2u + 1
c
7
, c
11
u
119
+ u
118
+ ··· + 8192u − 1024
c
8
u
119
− 10u
118
+ ··· − 2u + 1
c
9
, c
10
, c
12
u
119
+ 11u
118
+ ··· − 5u − 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
+ 108y
118
+ ··· − 59171729182y −939606409
c
4
y
119
+ 132y
118
+ ··· − 23236923728y −338265664
c
6
y
119
+ 120y
117
+ ··· + 10y −1
c
7
, c
11
y
119
+ 63y
118
+ ··· − 16252928y −1048576
c
8
y
119
+ 12y
118
+ ··· − 10y −1
c
9
, c
10
, c
12
y
119
− 111y
118
+ ··· + 61y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.227226 + 0.970712I
a = −0.069245 + 0.726320I
b = −0.003345 + 0.144442I
−3.66803 − 0.76142I 0
u = 0.227226 − 0.970712I
a = −0.069245 − 0.726320I
b = −0.003345 − 0.144442I
−3.66803 + 0.76142I 0
u = −0.458534 + 0.875185I
a = −0.573576 + 0.749123I
b = 1.05671 + 2.08096I
−1.51868 − 2.01224I 0
u = −0.458534 − 0.875185I
a = −0.573576 − 0.749123I
b = 1.05671 − 2.08096I
−1.51868 + 2.01224I 0
u = −0.871485 + 0.537431I
a = −0.266119 + 0.944276I
b = 0.39942 + 1.42963I
0.69537 − 1.96234I 0
u = −0.871485 − 0.537431I
a = −0.266119 − 0.944276I
b = 0.39942 − 1.42963I
0.69537 + 1.96234I 0
u = 0.570079 + 0.787703I
a = −0.943640 + 0.550499I
b = −0.518404 + 0.107984I
−0.70650 + 4.43937I 0
u = 0.570079 − 0.787703I
a = −0.943640 − 0.550499I
b = −0.518404 − 0.107984I
−0.70650 − 4.43937I 0
u = −0.843856 + 0.434969I
a = −0.490567 + 0.773091I
b = −0.74992 + 1.76092I
2.05334 − 2.32542I 0
u = −0.843856 − 0.434969I
a = −0.490567 − 0.773091I
b = −0.74992 − 1.76092I
2.05334 + 2.32542I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.578503 + 0.878040I
a = −0.63889 − 1.34499I
b = 0.393897 − 1.228490I
6.53771 + 10.99580I 0
u = 0.578503 − 0.878040I
a = −0.63889 + 1.34499I
b = 0.393897 + 1.228490I
6.53771 − 10.99580I 0
u = 0.647414 + 0.685423I
a = −0.426111 − 0.105610I
b = 1.25322 + 0.74492I
−0.42288 − 2.75298I 0
u = 0.647414 − 0.685423I
a = −0.426111 + 0.105610I
b = 1.25322 − 0.74492I
−0.42288 + 2.75298I 0
u = −0.682886 + 0.836097I
a = 0.412953 − 0.990140I
b = −0.70679 − 2.20076I
−3.60584 − 6.39853I 0
u = −0.682886 − 0.836097I
a = 0.412953 + 0.990140I
b = −0.70679 + 2.20076I
−3.60584 + 6.39853I 0
u = 0.905424 + 0.062884I
a = 0.220350 − 1.122690I
b = 0.82535 − 2.10816I
3.36143 + 3.82787I 0
u = 0.905424 − 0.062884I
a = 0.220350 + 1.122690I
b = 0.82535 + 2.10816I
3.36143 − 3.82787I 0
u = 0.891680
a = 1.06076
b = −0.552916
2.76788 0
u = −0.412585 + 0.786762I
a = −0.97982 + 1.20779I
b = −0.96051 + 1.16770I
7.05259 − 9.90887I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.412585 − 0.786762I
a = −0.97982 − 1.20779I
b = −0.96051 − 1.16770I
7.05259 + 9.90887I 0
u = 0.506568 + 1.016050I
a = 0.690828 − 0.353328I
b = 0.279387 − 0.079858I
−5.13196 + 1.58072I 0
u = 0.506568 − 1.016050I
a = 0.690828 + 0.353328I
b = 0.279387 + 0.079858I
−5.13196 − 1.58072I 0
u = 1.143980 + 0.022473I
a = −0.446724 − 1.130760I
b = −0.62739 − 1.96638I
9.53931 − 7.04970I 0
u = 1.143980 − 0.022473I
a = −0.446724 + 1.130760I
b = −0.62739 + 1.96638I
9.53931 + 7.04970I 0
u = −0.628999 + 0.563193I
a = −0.73378 + 1.51469I
b = 0.395937 + 0.936020I
1.31767 − 1.52824I 0
u = −0.628999 − 0.563193I
a = −0.73378 − 1.51469I
b = 0.395937 − 0.936020I
1.31767 + 1.52824I 0
u = 0.661309 + 0.513777I
a = −1.056990 + 0.551531I
b = −0.03459 + 1.78175I
3.61125 + 4.38522I 0
u = 0.661309 − 0.513777I
a = −1.056990 − 0.551531I
b = −0.03459 − 1.78175I
3.61125 − 4.38522I 0
u = −0.871425 + 0.799162I
a = −0.295055 + 1.120120I
b = 0.54242 + 2.17142I
1.81121 − 10.37090I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.871425 − 0.799162I
a = −0.295055 − 1.120120I
b = 0.54242 − 2.17142I
1.81121 + 10.37090I 0
u = −0.795944 + 0.896828I
a = −0.575449 − 0.331820I
b = 0.0216863 + 0.1208320I
0.15512 − 3.88915I 0
u = −0.795944 − 0.896828I
a = −0.575449 + 0.331820I
b = 0.0216863 − 0.1208320I
0.15512 + 3.88915I 0
u = −1.201230 + 0.003094I
a = −0.122513 − 0.354651I
b = 0.15746 − 3.63081I
1.67285 + 2.69563I 0
u = −1.201230 − 0.003094I
a = −0.122513 + 0.354651I
b = 0.15746 + 3.63081I
1.67285 − 2.69563I 0
u = −1.035290 + 0.645706I
a = 0.809624 − 0.733776I
b = 0.60332 − 1.40085I
8.37474 + 0.01682I 0
u = −1.035290 − 0.645706I
a = 0.809624 + 0.733776I
b = 0.60332 + 1.40085I
8.37474 − 0.01682I 0
u = −0.770287 + 0.033210I
a = 1.325900 + 0.117010I
b = 0.455580 + 1.112010I
5.49536 + 1.71804I 0
u = −0.770287 − 0.033210I
a = 1.325900 − 0.117010I
b = 0.455580 − 1.112010I
5.49536 − 1.71804I 0
u = −0.595551 + 0.465148I
a = −0.387214 − 0.229479I
b = −0.109374 + 0.599273I
1.11265 − 1.43327I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.595551 − 0.465148I
a = −0.387214 + 0.229479I
b = −0.109374 − 0.599273I
1.11265 + 1.43327I 0
u = −0.915922 + 0.849986I
a = 0.347678 − 1.182770I
b = −0.34821 − 1.37810I
7.74142 − 6.02428I 0
u = −0.915922 − 0.849986I
a = 0.347678 + 1.182770I
b = −0.34821 + 1.37810I
7.74142 + 6.02428I 0
u = −0.501801 + 0.547946I
a = 0.64841 − 1.29203I
b = 1.11076 − 1.33870I
1.19440 − 6.39011I 0
u = −0.501801 − 0.547946I
a = 0.64841 + 1.29203I
b = 1.11076 + 1.33870I
1.19440 + 6.39011I 0
u = 0.480917 + 0.563864I
a = −0.42711 + 1.41408I
b = 0.124535 − 0.079324I
−2.32372 + 5.35556I 0
u = 0.480917 − 0.563864I
a = −0.42711 − 1.41408I
b = 0.124535 + 0.079324I
−2.32372 − 5.35556I 0
u = 0.576442 + 0.455993I
a = 0.64713 + 1.76416I
b = 0.83734 + 1.59170I
9.92813 + 3.32978I 0
u = 0.576442 − 0.455993I
a = 0.64713 − 1.76416I
b = 0.83734 − 1.59170I
9.92813 − 3.32978I 0
u = 0.690310 + 0.238601I
a = 2.11068 − 0.14518I
b = −0.129854 − 0.082411I
4.10120 − 1.40763I 18.7311 + 0.I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.690310 − 0.238601I
a = 2.11068 + 0.14518I
b = −0.129854 + 0.082411I
4.10120 + 1.40763I 18.7311 + 0.I
u = 0.384533 + 0.620392I
a = 1.10415 + 1.73146I
b = −0.360742 + 0.823418I
0.66033 + 5.93367I 0. − 14.7806I
u = 0.384533 − 0.620392I
a = 1.10415 − 1.73146I
b = −0.360742 − 0.823418I
0.66033 − 5.93367I 0. + 14.7806I
u = −0.717868 + 0.102867I
a = −0.82413 + 1.84327I
b = 0.466437 + 0.767007I
2.74244 − 4.81471I 12.3271 + 12.8956I
u = −0.717868 − 0.102867I
a = −0.82413 − 1.84327I
b = 0.466437 − 0.767007I
2.74244 + 4.81471I 12.3271 − 12.8956I
u = 1.097930 + 0.692029I
a = 0.340225 + 0.868364I
b = −0.94296 + 1.96509I
4.58267 + 3.41945I 0
u = 1.097930 − 0.692029I
a = 0.340225 − 0.868364I
b = −0.94296 − 1.96509I
4.58267 − 3.41945I 0
u = 1.284090 + 0.193684I
a = −0.256513 − 1.179630I
b = 0.54214 − 1.59105I
13.31560 + 1.26216I 0
u = 1.284090 − 0.193684I
a = −0.256513 + 1.179630I
b = 0.54214 + 1.59105I
13.31560 − 1.26216I 0
u = 0.376935 + 1.251730I
a = −0.484394 − 0.246679I
b = 0.0295176 + 0.0943329I
−0.44007 + 7.88693I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.376935 − 1.251730I
a = −0.484394 + 0.246679I
b = 0.0295176 − 0.0943329I
−0.44007 − 7.88693I 0
u = −0.008429 + 0.688830I
a = −0.755322 + 0.880283I
b = 0.272395 − 0.101671I
−0.78514 − 1.51036I −1.09782 + 4.16173I
u = −0.008429 − 0.688830I
a = −0.755322 − 0.880283I
b = 0.272395 + 0.101671I
−0.78514 + 1.51036I −1.09782 − 4.16173I
u = 0.887268 + 1.013340I
a = 0.583096 − 0.370180I
b = −0.1102590 + 0.0091720I
−1.81583 + 9.13295I 0
u = 0.887268 − 1.013340I
a = 0.583096 + 0.370180I
b = −0.1102590 − 0.0091720I
−1.81583 − 9.13295I 0
u = 0.397514 + 1.298860I
a = −0.635295 − 0.046623I
b = −0.160822 − 0.083225I
−1.96720 − 0.65100I 0
u = 0.397514 − 1.298860I
a = −0.635295 + 0.046623I
b = −0.160822 + 0.083225I
−1.96720 + 0.65100I 0
u = 0.592037 + 0.189421I
a = 1.49379 + 1.35134I
b = −0.096927 + 0.993633I
3.41353 − 5.41155I 3.18534 + 4.54525I
u = 0.592037 − 0.189421I
a = 1.49379 − 1.35134I
b = −0.096927 − 0.993633I
3.41353 + 5.41155I 3.18534 − 4.54525I
u = 0.584711 + 0.094811I
a = 0.04667 − 1.68042I
b = −1.10281 − 1.73501I
3.57632 + 0.41841I 13.20113 − 1.07744I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.584711 − 0.094811I
a = 0.04667 + 1.68042I
b = −1.10281 + 1.73501I
3.57632 − 0.41841I 13.20113 + 1.07744I
u = −0.338083 + 1.368750I
a = 0.602705 − 0.195825I
b = −0.1226270 − 0.0651669I
2.46591 − 3.13553I 0
u = −0.338083 − 1.368750I
a = 0.602705 + 0.195825I
b = −0.1226270 + 0.0651669I
2.46591 + 3.13553I 0
u = −0.456225 + 0.354720I
a = −2.59775 − 0.56029I
b = 0.024019 − 0.169501I
3.96253 − 3.15795I 17.5033 + 8.3260I
u = −0.456225 − 0.354720I
a = −2.59775 + 0.56029I
b = 0.024019 + 0.169501I
3.96253 + 3.15795I 17.5033 − 8.3260I
u = −1.20227 + 0.80391I
a = 0.857055 + 0.254004I
b = −0.043208 − 0.159734I
5.90606 − 6.30718I 0
u = −1.20227 − 0.80391I
a = 0.857055 − 0.254004I
b = −0.043208 + 0.159734I
5.90606 + 6.30718I 0
u = −1.42725 + 0.42121I
a = 0.297357 − 1.049380I
b = −0.54083 − 1.60196I
12.4827 − 7.0839I 0
u = −1.42725 − 0.42121I
a = 0.297357 + 1.049380I
b = −0.54083 + 1.60196I
12.4827 + 7.0839I 0
u = −1.18458 + 0.92935I
a = −0.336460 + 0.786705I
b = 0.93173 + 2.00817I
2.96632 − 9.05048I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.18458 − 0.92935I
a = −0.336460 − 0.786705I
b = 0.93173 − 2.00817I
2.96632 + 9.05048I 0
u = 0.017922 + 0.468594I
a = 1.02414 − 0.98676I
b = −1.234810 − 0.303579I
2.12966 + 0.82300I 5.18127 + 1.42411I
u = 0.017922 − 0.468594I
a = 1.02414 + 0.98676I
b = −1.234810 + 0.303579I
2.12966 − 0.82300I 5.18127 − 1.42411I
u = 0.459841 + 0.060954I
a = 1.04819 − 2.78887I
b = −0.441558 − 0.586635I
3.14030 − 0.25233I 14.2606 + 5.7419I
u = 0.459841 − 0.060954I
a = 1.04819 + 2.78887I
b = −0.441558 + 0.586635I
3.14030 + 0.25233I 14.2606 − 5.7419I
u = 1.22053 + 0.93339I
a = −0.204150 − 0.824578I
b = 0.72089 − 2.23369I
3.03897 + 8.76012I 0
u = 1.22053 − 0.93339I
a = −0.204150 + 0.824578I
b = 0.72089 + 2.23369I
3.03897 − 8.76012I 0
u = 0.433059 + 0.036880I
a = 0.760255 − 0.999346I
b = 0.172856 + 1.286630I
−0.47565 − 2.99344I −0.91688 + 4.95906I
u = 0.433059 − 0.036880I
a = 0.760255 + 0.999346I
b = 0.172856 − 1.286630I
−0.47565 + 2.99344I −0.91688 − 4.95906I
u = −0.400882 + 0.024145I
a = 0.49717 + 2.97691I
b = −0.44269 + 1.74289I
4.63253 + 1.58055I 6.19334 − 4.35640I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.400882 − 0.024145I
a = 0.49717 − 2.97691I
b = −0.44269 − 1.74289I
4.63253 − 1.58055I 6.19334 + 4.35640I
u = 1.05514 + 1.24476I
a = 0.084551 − 0.319307I
b = −0.91842 − 3.74214I
2.15098 + 1.56600I 0
u = 1.05514 − 1.24476I
a = 0.084551 + 0.319307I
b = −0.91842 + 3.74214I
2.15098 − 1.56600I 0
u = 1.25865 + 1.04197I
a = −0.783169 + 0.275475I
b = 0.146558 − 0.003419I
4.16552 + 12.10780I 0
u = 1.25865 − 1.04197I
a = −0.783169 − 0.275475I
b = 0.146558 + 0.003419I
4.16552 − 12.10780I 0
u = −1.25071 + 1.15986I
a = 0.237364 − 0.760587I
b = −0.74169 − 2.24934I
1.1322 − 14.6195I 0
u = −1.25071 − 1.15986I
a = 0.237364 + 0.760587I
b = −0.74169 + 2.24934I
1.1322 + 14.6195I 0
u = 1.38453 + 1.06187I
a = 0.134943 + 0.846950I
b = −0.52790 + 2.23828I
8.9345 + 13.2205I 0
u = 1.38453 − 1.06187I
a = 0.134943 − 0.846950I
b = −0.52790 − 2.23828I
8.9345 − 13.2205I 0
u = −0.0246772 + 0.1316340I
a = −4.89784 + 7.02433I
b = −0.033463 − 0.462669I
−1.06689 − 1.52634I −1.89715 + 6.60245I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0246772 − 0.1316340I
a = −4.89784 − 7.02433I
b = −0.033463 + 0.462669I
−1.06689 + 1.52634I −1.89715 − 6.60245I
u = −1.59527 + 0.97067I
a = 0.149683 − 0.715174I
b = −0.32902 − 1.87611I
6.81704 − 5.01481I 0
u = −1.59527 − 0.97067I
a = 0.149683 + 0.715174I
b = −0.32902 + 1.87611I
6.81704 + 5.01481I 0
u = −1.36534 + 1.30604I
a = −0.185809 + 0.779388I
b = 0.56365 + 2.26985I
6.9107 − 19.3213I 0
u = −1.36534 − 1.30604I
a = −0.185809 − 0.779388I
b = 0.56365 − 2.26985I
6.9107 + 19.3213I 0
u = 0.70604 + 1.99947I
a = −0.445963 − 0.348961I
b = 1.08401 − 1.65863I
4.96842 + 1.91691I 0
u = 0.70604 − 1.99947I
a = −0.445963 + 0.348961I
b = 1.08401 + 1.65863I
4.96842 − 1.91691I 0
u = −0.26533 + 2.14842I
a = 0.345330 + 0.139656I
b = −2.08231 + 1.43058I
−0.147900 − 0.561296I 0
u = −0.26533 − 2.14842I
a = 0.345330 − 0.139656I
b = −2.08231 − 1.43058I
−0.147900 + 0.561296I 0
u = −0.19121 + 2.90584I
a = −0.293083 + 0.109006I
b = 2.54042 + 1.17016I
0.677780 + 0.375001I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19121 − 2.90584I
a = −0.293083 − 0.109006I
b = 2.54042 − 1.17016I
0.677780 − 0.375001I 0
u = 0.50055 + 3.13901I
a = 0.410827 − 0.070379I
b = −1.84960 − 0.39242I
6.60297 − 2.40686I 0
u = 0.50055 − 3.13901I
a = 0.410827 + 0.070379I
b = −1.84960 + 0.39242I
6.60297 + 2.40686I 0
u = −0.03777 + 3.43353I
a = 0.261216 + 0.100898I
b = −2.94136 + 1.41454I
0.40789 + 3.85492I 0
u = −0.03777 − 3.43353I
a = 0.261216 − 0.100898I
b = −2.94136 − 1.41454I
0.40789 − 3.85492I 0
u = 0.22635 + 3.47214I
a = −0.000040 − 0.246558I
b = −0.02704 − 4.43203I
2.60459 − 2.12994I 0
u = 0.22635 − 3.47214I
a = −0.000040 + 0.246558I
b = −0.02704 + 4.43203I
2.60459 + 2.12994I 0
u = −0.24994 + 3.53203I
a = −0.356846 − 0.115914I
b = 2.06428 − 0.95141I
6.08874 + 7.00877I 0
u = −0.24994 − 3.53203I
a = −0.356846 + 0.115914I
b = 2.06428 + 0.95141I
6.08874 − 7.00877I 0
16
II. I
u
2
= h−u
2
+ b + u − 1, a, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
11
=
0
u
2
− u + 1
a
7
=
0
u
a
12
=
0
u
2
− u + 1
a
6
=
−u
u
a
9
=
−u
3
u
3
+ u
a
5
=
u
3
+ u
2
+ 1
−u
3
− u
2
− u − 1
a
2
=
u
3
− u
2
−u
3
+ u
2
+ 1
a
1
=
u
3
−u
3
− u
a
10
=
−u
3
u
3
+ u
2
+ 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
3
u
4
+ u
2
+ u + 1
c
4
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
, c
6
u
4
+ u
2
− u + 1
c
7
, c
11
u
4
c
8
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
9
, c
10
(u + 1)
4
c
12
(u − 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
3
, c
5
c
6
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
4
y
4
− y
3
+ 2y
2
+ 7y + 4
c
7
, c
11
y
4
c
9
, c
10
, c
12
(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 = 0
b = 1.50411 − 1.22685I
2.62503 − 1.39709I 13.5849 + 5.3845I
u = −0.547424 − 0.585652I
a = 0
b = 1.50411 + 1.22685I
2.62503 + 1.39709I 13.5849 − 5.3845I
u = 0.547424 + 1.120870I
a = 0
b = −0.504108 + 0.106312I
−0.98010 + 7.64338I −3.08487 − 3.81741I
u = 0.547424 − 1.120870I
a = 0
b = −0.504108 − 0.106312I
−0.98010 − 7.64338I −3.08487 + 3.81741I
20
III. I
u
3
= h2u
5
+ 3u
3
− u
2
+ b + 2u − 2, a, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
11
=
0
−2u
5
− 3u
3
+ u
2
− 2u + 2
a
7
=
0
u
a
12
=
0
−2u
5
− 3u
3
+ u
2
− 2u + 2
a
6
=
−u
u
a
9
=
−u
3
u
3
+ u
a
5
=
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 2
u
5
+ 2u
3
− u
2
+ 2u − 1
a
2
=
u
5
+ 2u
3
+ u
−1
a
1
=
u
3
−u
3
− u
a
10
=
−u
3
−2u
5
− 2u
3
+ u
2
− u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
5
− u
4
+ 8u
3
− 4u
2
+ 5u − 5
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
3
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
7
, c
11
u
6
c
8
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
9
, c
10
(u + 1)
6
c
12
(u − 1)
6
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
3
, c
5
c
6
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
4
(y
3
− y
2
+ 2y −1)
2
c
7
, c
11
y
6
c
9
, c
10
, c
12
(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
b = 0.702221 + 0.130845I
1.37919 − 2.82812I 3.08014 + 1.90022I
u = −0.498832 − 1.001300I
a = 0
b = 0.702221 − 0.130845I
1.37919 + 2.82812I 3.08014 − 1.90022I
u = 0.284920 + 1.115140I
a = 0
b = −0.447279 + 0.479689I
−2.75839 −2.43992 − 2.50363I
u = 0.284920 − 1.115140I
a = 0
b = −0.447279 − 0.479689I
−2.75839 −2.43992 + 2.50363I
u = 0.713912 + 0.305839I
a = 0
b = 0.74506 − 2.00027I
1.37919 − 2.82812I −2.14022 + 3.69351I
u = 0.713912 − 0.305839I
a = 0
b = 0.74506 + 2.00027I
1.37919 + 2.82812I −2.14022 − 3.69351I
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
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
119
− 2u
118
+ ··· + 83530u + 30653)
c
4
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
119
+ 2u
118
+ ··· − 140120u + 18392)
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
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
119
+ 12u
118
+ ··· + 2u + 1)
c
7
, c
11
u
10
(u
119
+ u
118
+ ··· + 8192u − 1024)
c
8
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
119
− 10u
118
+ ··· − 2u + 1)
c
9
, c
10
((u + 1)
10
)(u
119
+ 11u
118
+ ··· − 5u − 1)
c
12
((u − 1)
10
)(u
119
+ 11u
118
+ ··· − 5u − 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
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
119
+ 108y
118
+ ··· − 59171729182y −939606409)
c
4
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
119
+ 132y
118
+ ··· − 23236923728y −338265664)
c
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
119
+ 120y
117
+ ··· + 10y −1)
c
7
, c
11
y
10
(y
119
+ 63y
118
+ ··· − 1.62529 × 10
7
y −1048576)
c
8
(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
9
, c
10
, c
12
((y −1)
10
)(y
119
− 111y
118
+ ··· + 61y −1)
26
