12a
0351
(K12a
0351
)
A knot diagram
1
Linearized knot diagam
3 6 9 7 11 2 12 10 4 1 5 8
Solving Sequence
3,9
4
6,10
2 7 5 1 8 12 11
c
3
c
9
c
2
c
6
c
4
c
1
c
8
c
12
c
11
c
5
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h8.22708 × 10
260
u
115
+ 5.90473 × 10
259
u
114
+ ··· + 7.11945 × 10
261
b + 7.95379 × 10
261
,
5.48204 × 10
262
u
115
+ 3.62166 × 10
262
u
114
+ ··· + 9.25529 × 10
262
a − 1.21893 × 10
263
, u
116
+ u
115
+ ··· − 12u + 4i
I
u
2
= h−3au + 7b + 12a − 5u + 13, 18a
2
− 3au + 48a − u + 39, u
2
− 2i
I
v
1
= ha, b − v, v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 122 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
= h8.23 × 10
260
u
115
+ 5.90 × 10
259
u
114
+ · · · + 7.12 × 10
261
b + 7.95 ×
10
261
, 5.48 × 10
262
u
115
+ 3.62 × 10
262
u
114
+ · · · + 9.26 × 10
262
a − 1.22 ×
10
263
, u
116
+ u
115
+ · · · − 12u + 4i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
6
=
−0.592314u
115
− 0.391307u
114
+ ··· + 4.00136u + 1.31701
−0.115558u
115
− 0.00829380u
114
+ ··· + 6.41816u − 1.11719
a
10
=
u
−u
3
+ u
a
2
=
−0.0576376u
115
− 0.341529u
114
+ ··· + 2.70043u + 6.41023
−0.109926u
115
− 0.000292556u
114
+ ··· + 5.86706u − 2.13299
a
7
=
−0.624496u
115
− 0.335359u
114
+ ··· + 13.6484u + 4.37568
0.130256u
115
+ 0.108791u
114
+ ··· + 2.77584u − 1.42974
a
5
=
0.918893u
115
+ 0.826941u
114
+ ··· + 5.11609u − 0.840015
0.278228u
115
+ 0.0809501u
114
+ ··· − 9.46479u + 0.173513
a
1
=
−0.167564u
115
− 0.341822u
114
+ ··· + 8.56749u + 4.27725
−0.109926u
115
− 0.000292556u
114
+ ··· + 5.86706u − 2.13299
a
8
=
−u
3
u
5
− u
3
+ u
a
12
=
−0.105593u
115
− 0.334986u
114
+ ··· + 6.85446u + 4.76672
−0.132149u
115
+ 0.0239453u
114
+ ··· + 5.21273u − 2.20714
a
11
=
0.453168u
115
+ 0.309762u
114
+ ··· − 5.33012u − 6.99372
−0.199402u
115
− 0.129061u
114
+ ··· + 1.83081u + 0.396491
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.30353u
115
+ 0.380419u
114
+ ··· − 48.9228u + 9.39672
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
116
+ 52u
115
+ ··· − 5438u + 289
c
2
, c
6
u
116
− 2u
115
+ ··· + 44u + 17
c
3
, c
9
u
116
+ u
115
+ ··· − 12u + 4
c
4
28561(28561u
116
− 153790u
115
+ ··· − 8.25675 × 10
8
u + 3.49024 × 10
7
)
c
5
, c
11
u
116
+ u
115
+ ··· + 44u + 4
c
7
, c
12
u
116
+ 3u
115
+ ··· − 989u + 343
c
8
u
116
− 51u
115
+ ··· − 304u + 16
c
10
28561(28561u
116
+ 173563u
115
+ ··· − 6624257u + 463351)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
116
+ 28y
115
+ ··· − 20164894y + 83521
c
2
, c
6
y
116
+ 52y
115
+ ··· − 5438y + 289
c
3
, c
9
y
116
− 51y
115
+ ··· − 304y + 16
c
4
815730721
· (8.16 × 10
8
y
116
− 2.56 × 10
10
y
115
+ ··· + 3.19 × 10
16
y + 1.22 × 10
15
)
c
5
, c
11
y
116
+ 69y
115
+ ··· + 80y + 16
c
7
, c
12
y
116
− 93y
115
+ ··· − 1659319y + 117649
c
8
y
116
+ 33y
115
+ ··· − 4864y + 256
c
10
815730721
· (8.16 × 10
8
y
116
− 5.43 × 10
10
y
115
+ ··· − 1.02 × 10
13
y + 2.15 × 10
11
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.466716 + 0.884426I
a = −0.783595 − 0.126337I
b = 0.653585 − 0.363267I
−2.67219 + 1.89988I 0
u = −0.466716 − 0.884426I
a = −0.783595 + 0.126337I
b = 0.653585 + 0.363267I
−2.67219 − 1.89988I 0
u = 0.833896 + 0.554451I
a = −0.727306 − 0.756093I
b = 0.541090 − 1.019580I
−2.32060 + 0.05845I 0
u = 0.833896 − 0.554451I
a = −0.727306 + 0.756093I
b = 0.541090 + 1.019580I
−2.32060 − 0.05845I 0
u = 0.515699 + 0.858960I
a = 0.768671 + 0.054540I
b = −0.664056 + 0.147665I
−6.86951 + 3.26307I 0
u = 0.515699 − 0.858960I
a = 0.768671 − 0.054540I
b = −0.664056 − 0.147665I
−6.86951 − 3.26307I 0
u = −0.796622 + 0.599234I
a = −0.234219 + 0.406414I
b = −0.68922 − 1.38197I
−5.98756 + 0.45829I 0
u = −0.796622 − 0.599234I
a = −0.234219 − 0.406414I
b = −0.68922 + 1.38197I
−5.98756 − 0.45829I 0
u = 0.496277 + 0.882378I
a = 0.683895 − 0.105274I
b = −0.921430 − 0.377905I
−6.72237 − 7.44661I 0
u = 0.496277 − 0.882378I
a = 0.683895 + 0.105274I
b = −0.921430 + 0.377905I
−6.72237 + 7.44661I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.821230 + 0.618768I
a = −0.794720 − 1.140120I
b = 0.261743 − 0.895424I
−2.04215 − 2.50988I 0
u = −0.821230 − 0.618768I
a = −0.794720 + 1.140120I
b = 0.261743 + 0.895424I
−2.04215 + 2.50988I 0
u = 0.872725 + 0.555380I
a = 2.93230 − 0.92577I
b = −0.622964 − 0.983728I
−2.19443 + 4.38805I 0
u = 0.872725 − 0.555380I
a = 2.93230 + 0.92577I
b = −0.622964 + 0.983728I
−2.19443 − 4.38805I 0
u = −0.314014 + 0.987232I
a = 0.779419 − 0.361334I
b = −0.337968 − 1.111900I
−10.48240 + 0.02403I 0
u = −0.314014 − 0.987232I
a = 0.779419 + 0.361334I
b = −0.337968 + 1.111900I
−10.48240 − 0.02403I 0
u = −0.835930 + 0.617038I
a = −0.597118 − 0.860842I
b = −0.061420 − 0.822216I
−2.00858 − 2.35815I 0
u = −0.835930 − 0.617038I
a = −0.597118 + 0.860842I
b = −0.061420 + 0.822216I
−2.00858 + 2.35815I 0
u = 0.838690 + 0.617546I
a = 1.269560 − 0.256708I
b = −0.09071 − 1.52895I
−6.41289 + 2.42988I 0
u = 0.838690 − 0.617546I
a = 1.269560 + 0.256708I
b = −0.09071 + 1.52895I
−6.41289 − 2.42988I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.041140 + 0.185992I
a = −1.83112 − 0.13921I
b = 0.815154 + 0.555869I
3.19024 − 0.63993I 0
u = 1.041140 − 0.185992I
a = −1.83112 + 0.13921I
b = 0.815154 − 0.555869I
3.19024 + 0.63993I 0
u = −0.640644 + 0.848844I
a = 0.735683 + 0.692782I
b = −0.112380 + 1.305980I
−12.68570 + 4.21380I 0
u = −0.640644 − 0.848844I
a = 0.735683 − 0.692782I
b = −0.112380 − 1.305980I
−12.68570 − 4.21380I 0
u = −0.883251 + 0.602570I
a = −2.08121 − 0.54168I
b = 0.83111 − 1.31723I
−5.71767 − 5.21650I 0
u = −0.883251 − 0.602570I
a = −2.08121 + 0.54168I
b = 0.83111 + 1.31723I
−5.71767 + 5.21650I 0
u = −0.995874 + 0.401809I
a = −0.71960 − 2.00101I
b = 0.329550 + 0.745071I
−1.73973 − 1.33290I 0
u = −0.995874 − 0.401809I
a = −0.71960 + 2.00101I
b = 0.329550 − 0.745071I
−1.73973 + 1.33290I 0
u = −0.495701 + 0.956635I
a = 0.742573 − 0.406437I
b = −0.634931 − 1.162860I
−9.1087 + 13.1311I 0
u = −0.495701 − 0.956635I
a = 0.742573 + 0.406437I
b = −0.634931 + 1.162860I
−9.1087 − 13.1311I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.775905 + 0.497045I
a = −0.165278 − 0.775090I
b = −0.238451 − 0.070476I
−1.78328 − 2.08266I 0
u = −0.775905 − 0.497045I
a = −0.165278 + 0.775090I
b = −0.238451 + 0.070476I
−1.78328 + 2.08266I 0
u = 0.494221 + 0.759596I
a = 0.307685 + 0.600397I
b = −0.590578 + 1.186130I
−3.60510 − 7.79415I 0
u = 0.494221 − 0.759596I
a = 0.307685 − 0.600397I
b = −0.590578 − 1.186130I
−3.60510 + 7.79415I 0
u = −0.779427 + 0.450974I
a = 0.39113 + 1.97543I
b = −0.670300 − 0.709245I
−1.32894 + 0.70219I 0
u = −0.779427 − 0.450974I
a = 0.39113 − 1.97543I
b = −0.670300 + 0.709245I
−1.32894 − 0.70219I 0
u = −0.957835 + 0.541099I
a = −0.955456 + 0.073183I
b = 0.723527 − 0.452906I
−0.57651 − 4.79475I 0
u = −0.957835 − 0.541099I
a = −0.955456 − 0.073183I
b = 0.723527 + 0.452906I
−0.57651 + 4.79475I 0
u = 0.713321 + 0.547036I
a = −0.287533 + 1.169400I
b = 1.054150 − 0.828225I
−4.19877 − 2.44712I 0
u = 0.713321 − 0.547036I
a = −0.287533 − 1.169400I
b = 1.054150 + 0.828225I
−4.19877 + 2.44712I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.943567 + 0.584400I
a = 1.68583 − 0.51157I
b = −1.159030 − 0.663749I
−3.47234 + 7.03624I 0
u = 0.943567 − 0.584400I
a = 1.68583 + 0.51157I
b = −1.159030 + 0.663749I
−3.47234 − 7.03624I 0
u = 0.942127 + 0.604306I
a = 1.162640 − 0.293149I
b = 0.439750 − 0.953612I
−2.77882 − 0.58975I 0
u = 0.942127 − 0.604306I
a = 1.162640 + 0.293149I
b = 0.439750 + 0.953612I
−2.77882 + 0.58975I 0
u = −1.117360 + 0.069621I
a = −1.28817 − 1.08342I
b = 0.642708 + 1.046490I
1.70184 + 6.08053I 0
u = −1.117360 − 0.069621I
a = −1.28817 + 1.08342I
b = 0.642708 − 1.046490I
1.70184 − 6.08053I 0
u = 0.832789 + 0.225789I
a = −0.601053 + 0.233524I
b = 0.550015 + 0.084883I
1.292750 + 0.325346I 0
u = 0.832789 − 0.225789I
a = −0.601053 − 0.233524I
b = 0.550015 − 0.084883I
1.292750 − 0.325346I 0
u = 0.670876 + 0.535881I
a = 0.90736 + 2.57743I
b = −0.366397 + 0.954160I
−3.79397 − 0.49844I 0
u = 0.670876 − 0.535881I
a = 0.90736 − 2.57743I
b = −0.366397 − 0.954160I
−3.79397 + 0.49844I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.484795 + 1.034740I
a = −0.722748 − 0.354639I
b = 0.551009 − 1.081070I
−4.70990 − 6.59407I 0
u = 0.484795 − 1.034740I
a = −0.722748 + 0.354639I
b = 0.551009 + 1.081070I
−4.70990 + 6.59407I 0
u = 0.555186 + 0.644462I
a = 0.004936 − 0.922208I
b = −0.449425 − 1.037710I
−3.82491 + 5.40390I 0
u = 0.555186 − 0.644462I
a = 0.004936 + 0.922208I
b = −0.449425 + 1.037710I
−3.82491 − 5.40390I 0
u = 1.016380 + 0.540681I
a = −3.12129 + 0.64540I
b = 0.461647 + 0.967079I
−2.64987 + 4.84972I 0
u = 1.016380 − 0.540681I
a = −3.12129 − 0.64540I
b = 0.461647 − 0.967079I
−2.64987 − 4.84972I 0
u = −1.024480 + 0.567357I
a = −0.768018 − 1.100840I
b = 1.056100 + 0.312277I
0.82781 − 7.00319I 0
u = −1.024480 − 0.567357I
a = −0.768018 + 1.100840I
b = 1.056100 − 0.312277I
0.82781 + 7.00319I 0
u = −0.592343 + 1.011110I
a = 0.918671 + 0.496773I
b = −0.481119 + 1.110180I
−9.55063 − 7.53106I 0
u = −0.592343 − 1.011110I
a = 0.918671 − 0.496773I
b = −0.481119 − 1.110180I
−9.55063 + 7.53106I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.054510 + 0.527628I
a = 0.612085 − 1.147380I
b = −0.787200 + 0.516832I
3.25793 + 3.13597I 0
u = 1.054510 − 0.527628I
a = 0.612085 + 1.147380I
b = −0.787200 − 0.516832I
3.25793 − 3.13597I 0
u = −1.151090 + 0.257276I
a = 1.87268 − 0.39708I
b = −0.691766 + 0.756944I
4.99239 − 4.08939I 0
u = −1.151090 − 0.257276I
a = 1.87268 + 0.39708I
b = −0.691766 − 0.756944I
4.99239 + 4.08939I 0
u = 0.736999 + 0.921312I
a = −1.021070 + 0.667460I
b = 0.245911 + 1.047670I
−6.68894 + 0.36281I 0
u = 0.736999 − 0.921312I
a = −1.021070 − 0.667460I
b = 0.245911 − 1.047670I
−6.68894 − 0.36281I 0
u = −0.416152 + 0.702982I
a = −0.657214 + 0.652284I
b = 0.550081 + 1.020460I
−0.25960 + 3.42242I 0
u = −0.416152 − 0.702982I
a = −0.657214 − 0.652284I
b = 0.550081 − 1.020460I
−0.25960 − 3.42242I 0
u = 1.190070 + 0.157741I
a = 1.33756 − 0.93877I
b = −0.634540 + 0.887405I
4.59187 − 1.01993I 0
u = 1.190070 − 0.157741I
a = 1.33756 + 0.93877I
b = −0.634540 − 0.887405I
4.59187 + 1.01993I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.075010 + 0.604590I
a = 2.23506 + 0.54337I
b = −0.625953 + 1.067030I
1.59755 − 8.45756I 0
u = −1.075010 − 0.604590I
a = 2.23506 − 0.54337I
b = −0.625953 − 1.067030I
1.59755 + 8.45756I 0
u = −0.755200 + 0.125730I
a = 0.54008 + 1.48819I
b = −0.787063 − 0.237062I
−1.07137 + 2.52393I 3.16937 − 4.49551I
u = −0.755200 − 0.125730I
a = 0.54008 − 1.48819I
b = −0.787063 + 0.237062I
−1.07137 − 2.52393I 3.16937 + 4.49551I
u = 1.203200 + 0.280770I
a = −0.617584 + 0.816387I
b = 0.118500 − 0.988627I
−5.27584 + 3.81255I 0
u = 1.203200 − 0.280770I
a = −0.617584 − 0.816387I
b = 0.118500 + 0.988627I
−5.27584 − 3.81255I 0
u = −1.239360 + 0.011306I
a = −1.72127 + 0.47650I
b = 0.754990 − 0.485834I
−0.39657 + 5.22699I 0
u = −1.239360 − 0.011306I
a = −1.72127 − 0.47650I
b = 0.754990 + 0.485834I
−0.39657 − 5.22699I 0
u = 1.067530 + 0.631606I
a = −2.14334 + 0.54583I
b = 0.656745 + 1.212430I
−1.92381 + 13.07300I 0
u = 1.067530 − 0.631606I
a = −2.14334 − 0.54583I
b = 0.656745 − 1.212430I
−1.92381 − 13.07300I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.985981 + 0.756728I
a = −0.260236 + 0.487469I
b = −0.096176 + 1.081310I
−5.88877 + 5.77264I 0
u = 0.985981 − 0.756728I
a = −0.260236 − 0.487469I
b = −0.096176 − 1.081310I
−5.88877 − 5.77264I 0
u = −1.031980 + 0.710550I
a = 0.884175 + 0.148388I
b = 0.038755 + 1.349030I
−11.4894 − 10.0129I 0
u = −1.031980 − 0.710550I
a = 0.884175 − 0.148388I
b = 0.038755 − 1.349030I
−11.4894 + 10.0129I 0
u = 1.092310 + 0.648197I
a = −1.064780 + 0.605997I
b = 0.519866 − 0.069837I
−5.11265 + 2.34089I 0
u = 1.092310 − 0.648197I
a = −1.064780 − 0.605997I
b = 0.519866 + 0.069837I
−5.11265 − 2.34089I 0
u = 1.110740 + 0.671729I
a = −0.748880 + 1.141040I
b = 0.972089 − 0.432265I
−4.85981 + 13.19030I 0
u = 1.110740 − 0.671729I
a = −0.748880 − 1.141040I
b = 0.972089 + 0.432265I
−4.85981 − 13.19030I 0
u = −1.121050 + 0.670941I
a = 0.699124 + 0.904242I
b = −0.783809 − 0.455402I
−0.70851 − 7.64661I 0
u = −1.121050 − 0.670941I
a = 0.699124 − 0.904242I
b = −0.783809 + 0.455402I
−0.70851 + 7.64661I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.422603 + 0.538929I
a = 0.225851 + 0.641616I
b = −0.854397 + 0.188053I
−0.74861 + 2.47173I 0.57968 − 3.86930I
u = −0.422603 − 0.538929I
a = 0.225851 − 0.641616I
b = −0.854397 − 0.188053I
−0.74861 − 2.47173I 0.57968 + 3.86930I
u = −1.139660 + 0.696578I
a = −2.22336 − 0.45953I
b = 0.671975 − 1.167110I
−7.1260 − 19.1636I 0
u = −1.139660 − 0.696578I
a = −2.22336 + 0.45953I
b = 0.671975 + 1.167110I
−7.1260 + 19.1636I 0
u = 1.339520 + 0.019185I
a = −1.53348 − 0.82587I
b = 0.609430 + 1.074170I
−2.15349 + 10.41260I 0
u = 1.339520 − 0.019185I
a = −1.53348 + 0.82587I
b = 0.609430 − 1.074170I
−2.15349 − 10.41260I 0
u = 1.163830 + 0.723777I
a = 1.99794 − 0.40565I
b = −0.614263 − 1.092660I
−2.60839 + 12.91820I 0
u = 1.163830 − 0.723777I
a = 1.99794 + 0.40565I
b = −0.614263 + 1.092660I
−2.60839 − 12.91820I 0
u = −0.616361 + 0.117547I
a = −0.631662 − 0.993118I
b = 0.385313 − 0.950143I
−0.95525 − 2.77494I 4.16705 + 7.27073I
u = −0.616361 − 0.117547I
a = −0.631662 + 0.993118I
b = 0.385313 + 0.950143I
−0.95525 + 2.77494I 4.16705 − 7.27073I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.108530 + 0.821412I
a = −0.122967 − 0.159962I
b = 0.396192 + 1.068680I
−7.99961 + 0.94403I 0
u = −1.108530 − 0.821412I
a = −0.122967 + 0.159962I
b = 0.396192 − 1.068680I
−7.99961 − 0.94403I 0
u = 0.181878 + 0.591925I
a = −0.490273 + 0.249127I
b = 0.581289 + 0.577000I
1.10147 + 1.10758I 4.88695 − 3.86624I
u = 0.181878 − 0.591925I
a = −0.490273 − 0.249127I
b = 0.581289 − 0.577000I
1.10147 − 1.10758I 4.88695 + 3.86624I
u = −1.24962 + 0.66959I
a = −1.86159 − 0.03426I
b = 0.450242 − 1.071500I
−7.64422 − 6.06435I 0
u = −1.24962 − 0.66959I
a = −1.86159 + 0.03426I
b = 0.450242 + 1.071500I
−7.64422 + 6.06435I 0
u = 1.41551 + 0.14998I
a = 1.42035 + 0.40663I
b = −0.451135 − 0.719052I
3.52152 + 1.19712I 0
u = 1.41551 − 0.14998I
a = 1.42035 − 0.40663I
b = −0.451135 + 0.719052I
3.52152 − 1.19712I 0
u = −0.173548 + 0.435678I
a = −1.77580 − 0.00885I
b = −0.281662 − 0.593654I
−1.84260 + 1.06316I −2.87257 + 1.74785I
u = −0.173548 − 0.435678I
a = −1.77580 + 0.00885I
b = −0.281662 + 0.593654I
−1.84260 − 1.06316I −2.87257 − 1.74785I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.54440 + 0.09700I
a = 1.188900 + 0.578674I
b = −0.480566 − 0.964286I
2.68981 + 2.67919I 0
u = −1.54440 − 0.09700I
a = 1.188900 − 0.578674I
b = −0.480566 + 0.964286I
2.68981 − 2.67919I 0
u = 0.026779 + 0.320029I
a = 1.91460 − 1.84893I
b = −0.389926 + 1.065330I
−4.03516 − 1.34228I −3.61078 + 0.66174I
u = 0.026779 − 0.320029I
a = 1.91460 + 1.84893I
b = −0.389926 − 1.065330I
−4.03516 + 1.34228I −3.61078 − 0.66174I
u = 0.221346 + 0.109152I
a = 0.17931 − 5.05439I
b = 0.706323 + 0.848981I
−3.45719 + 2.69856I −2.19132 − 3.25247I
u = 0.221346 − 0.109152I
a = 0.17931 + 5.05439I
b = 0.706323 − 0.848981I
−3.45719 − 2.69856I −2.19132 + 3.25247I
16
II. I
u
2
= h−3au + 7b + 12a − 5u + 13, 18a
2
− 3au + 48a − u + 39, u
2
− 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−2
a
6
=
a
3
7
au −
12
7
a +
5
7
u −
13
7
a
10
=
u
−u
a
2
=
−0.714286au + 2.85714a − 1.02381u + 4.76190
3
7
au −
12
7
a +
5
7
u −
20
7
a
7
=
−0.285714au + 1.14286a − 0.309524u + 1.90476
3
7
au −
12
7
a +
5
7
u −
20
7
a
5
=
8
21
au +
1
7
a +
40
63
u +
71
63
−
3
7
au −
2
7
a −
5
7
u −
15
7
a
1
=
−0.285714au + 1.14286a − 0.309524u + 1.90476
3
7
au −
12
7
a +
5
7
u −
20
7
a
8
=
−2u
3u
a
12
=
−0.285714au + 1.14286a + 1.69048u + 1.90476
3
7
au −
12
7
a −
16
7
u −
20
7
a
11
=
−0.428571au + 0.380952a + 0.563492u + 0.634921
5
7
au −
6
7
a −
1
7
u −
10
7
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
12
7
au +
48
7
a −
20
7
u +
80
7
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
− u + 1)
2
c
3
, c
5
, c
9
c
11
(u
2
− 2)
2
c
4
81(81u
4
− 54u
3
− 9u
2
+ 6u + 7)
c
6
(u
2
+ u + 1)
2
c
7
(u + 1)
4
c
8
(u + 2)
4
c
10
81(81u
4
− 108u
3
+ 72u
2
− 24u + 7)
c
12
(u − 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
2
c
3
, c
5
, c
9
c
11
(y −2)
4
c
4
6561(6561y
4
− 4374y
3
+ 1863y
2
− 162y + 49)
c
7
, c
12
(y −1)
4
c
8
(y −4)
4
c
10
6561(6561y
4
+ 1134y
2
+ 432y + 49)
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −1.21548 + 0.78147I
b = 0.500000 − 0.866025I
3.28987 − 2.02988I 2.00000 + 3.46410I
u = 1.41421
a = −1.21548 − 0.78147I
b = 0.500000 + 0.866025I
3.28987 + 2.02988I 2.00000 − 3.46410I
u = −1.41421
a = −1.45118 + 0.37323I
b = 0.500000 − 0.866025I
3.28987 − 2.02988I 2.00000 + 3.46410I
u = −1.41421
a = −1.45118 − 0.37323I
b = 0.500000 + 0.866025I
3.28987 + 2.02988I 2.00000 − 3.46410I
20
III. I
v
1
= ha, b − v, v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
6
=
0
v
a
10
=
v
0
a
2
=
1
−v − 1
a
7
=
v
v + 1
a
5
=
0
v
a
1
=
−v
−v − 1
a
8
=
v
0
a
12
=
0
−v − 1
a
11
=
0
−v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 2
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
5
, c
8
c
9
, c
11
u
2
c
7
, c
10
(u − 1)
2
c
12
(u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
y
2
+ y + 1
c
3
, c
5
, c
8
c
9
, c
11
y
2
c
7
, c
10
, c
12
(y − 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −0.500000 + 0.866025I
−1.64493 − 2.02988I 0. + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −0.500000 − 0.866025I
−1.64493 + 2.02988I 0. − 3.46410I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
3
)(u
116
+ 52u
115
+ ··· − 5438u + 289)
c
2
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
116
− 2u
115
+ ··· + 44u + 17)
c
3
, c
9
u
2
(u
2
− 2)
2
(u
116
+ u
115
+ ··· − 12u + 4)
c
4
2313441(u
2
− u + 1)(81u
4
− 54u
3
− 9u
2
+ 6u + 7)
· (28561u
116
− 153790u
115
+ ··· − 825674530u + 34902367)
c
5
, c
11
u
2
(u
2
− 2)
2
(u
116
+ u
115
+ ··· + 44u + 4)
c
6
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
116
− 2u
115
+ ··· + 44u + 17)
c
7
((u − 1)
2
)(u + 1)
4
(u
116
+ 3u
115
+ ··· − 989u + 343)
c
8
u
2
(u + 2)
4
(u
116
− 51u
115
+ ··· − 304u + 16)
c
10
2313441(u − 1)
2
(81u
4
− 108u
3
+ 72u
2
− 24u + 7)
· (28561u
116
+ 173563u
115
+ ··· − 6624257u + 463351)
c
12
((u − 1)
4
)(u + 1)
2
(u
116
+ 3u
115
+ ··· − 989u + 343)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
116
+ 28y
115
+ ··· − 2.01649 × 10
7
y + 83521)
c
2
, c
6
((y
2
+ y + 1)
3
)(y
116
+ 52y
115
+ ··· − 5438y + 289)
c
3
, c
9
y
2
(y − 2)
4
(y
116
− 51y
115
+ ··· − 304y + 16)
c
4
5352009260481(y
2
+ y + 1)
· (6561y
4
− 4374y
3
+ 1863y
2
− 162y + 49)
· (8.16 × 10
8
y
116
− 2.56 × 10
10
y
115
+ ··· + 3.19 × 10
16
y + 1.22 × 10
15
)
c
5
, c
11
y
2
(y − 2)
4
(y
116
+ 69y
115
+ ··· + 80y + 16)
c
7
, c
12
((y − 1)
6
)(y
116
− 93y
115
+ ··· − 1659319y + 117649)
c
8
y
2
(y − 4)
4
(y
116
+ 33y
115
+ ··· − 4864y + 256)
c
10
5352009260481(y − 1)
2
(6561y
4
+ 1134y
2
+ 432y + 49)
· (8.16 × 10
8
y
116
− 5.43 × 10
10
y
115
+ ··· − 1.02 × 10
13
y + 2.15 × 10
11
)
26
