12n
0147
(K12n
0147
)
A knot diagram
1
Linearized knot diagam
3 4 8 2 9 3 12 10 6 4 7 11
Solving Sequence
7,12 4,8
3 2 5 6 11 1 10 9
c
7
c
3
c
2
c
4
c
6
c
11
c
12
c
10
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
15
− 5u
14
+ ··· + 4b − 5, −3u
15
− 3u
14
+ ··· + 2a − 4,
u
16
+ u
15
− 5u
14
− 5u
13
+ 11u
12
+ 12u
11
− 8u
10
− 13u
9
− 8u
8
+ 2u
7
+ 18u
6
+ 11u
5
− 7u
4
− 9u
3
− u
2
+ 2u + 1i
I
u
2
= h1404675088u
27
+ 680434033u
26
+ ··· + 5440114508b + 183536430,
4259487893u
27
+ 5117778300u
26
+ ··· + 10880229016a − 10842072870,
u
28
+ 2u
27
+ ··· + 12u + 4i
I
u
3
= hu
3
+ b + u + 1, −u
2
+ a + 2u + 1, u
4
− u
2
+ 1i
I
u
4
= h−u
3
+ b − u + 1, −u
2
+ a − u + 1, u
4
− u
2
+ 1i
I
u
5
= h−u
3
+ u
2
+ b − u − 1, u
2
+ a − u, u
4
− u
2
+ 1i
I
u
6
= hu
3
− u
2
+ b + u, a + 2u − 1, u
4
− u
2
+ 1i
I
u
7
= h−u
3
+ b − u, a − u, u
4
+ u
3
+ 1i
I
u
8
= ha
3
+ 2a
2
+ b + 3a + 1, a
4
+ 3a
3
+ 6a
2
+ 4a + 1, u − 1i
I
u
9
= hb − 2, a − 1, u − 1i
* 9 irreducible components of dim
C
= 0, with total 69 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−3u
15
−5u
14
+· · ·+4b−5, −3u
15
−3u
14
+· · ·+2a−4, u
16
+u
15
+· · ·+2u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
3
2
u
15
+
3
2
u
14
+ ··· +
5
2
u + 2
3
4
u
15
+
5
4
u
14
+ ··· +
1
2
u +
5
4
a
8
=
1
u
2
a
3
=
1
4
u
15
+
3
4
u
14
+ ··· +
1
2
u +
3
4
1
2
u
15
+
3
4
u
14
+ ··· +
3
4
u +
3
4
a
2
=
−
11
4
u
15
− u
14
+ ··· −
17
4
u −
7
2
−u
15
−
1
2
u
14
+ ··· −
1
2
u −
3
2
a
5
=
5
2
u
15
+ u
14
+ ··· +
9
2
u + 2
u
15
+
1
2
u
14
+ ··· +
3
2
u +
3
2
a
6
=
−2u
15
−
3
4
u
14
+ ··· −
13
4
u −
5
4
−
3
4
u
15
−
1
4
u
14
+ ··· −
3
2
u −
5
4
a
11
=
u
u
a
1
=
−u
3
−u
3
+ u
a
10
=
−2u
15
−
3
4
u
14
+ ··· −
13
4
u −
9
4
−
3
4
u
15
−
1
4
u
14
+ ··· −
1
2
u −
5
4
a
9
=
−
3
4
u
15
−
1
4
u
14
+ ··· −
1
2
u −
1
4
−
1
4
u
15
+
3
2
u
13
+ ··· −
1
4
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
15
−
1
2
u
14
+ 32u
13
+ u
12
−
151
2
u
11
− 4u
10
+
147
2
u
9
+
29
2
u
8
+
21
2
u
7
− 30u
6
−
159
2
u
5
+
41
2
u
4
+
103
2
u
3
+
5
2
u
2
−
35
2
u −
13
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 16u
15
+ ··· + 1760u + 256
c
2
, c
4
u
16
− 4u
15
+ ··· − 56u + 16
c
3
u
16
+ 4u
15
+ ··· + 12u + 4
c
5
, c
7
, c
9
c
11
u
16
− u
15
+ ··· − 2u + 1
c
6
, c
10
u
16
− u
15
+ ··· + 64u + 16
c
8
, c
12
u
16
+ 11u
15
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 24y
15
+ ··· − 508416y + 65536
c
2
, c
4
y
16
+ 16y
15
+ ··· + 1760y + 256
c
3
y
16
− 4y
15
+ ··· − 56y + 16
c
5
, c
7
, c
9
c
11
y
16
− 11y
15
+ ··· − 6y + 1
c
6
, c
10
y
16
+ 25y
15
+ ··· + 256y + 256
c
8
, c
12
y
16
− 7y
15
+ ··· + 10y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.053870 + 0.977866I
a = 1.287840 − 0.220850I
b = −0.321900 − 0.803375I
−5.56822 − 3.25567I −1.25924 + 2.26983I
u = −0.053870 − 0.977866I
a = 1.287840 + 0.220850I
b = −0.321900 + 0.803375I
−5.56822 + 3.25567I −1.25924 − 2.26983I
u = 1.201500 + 0.360870I
a = −1.62412 − 1.03706I
b = −2.42883 − 2.34865I
−3.59239 − 7.60004I −5.70207 + 6.90528I
u = 1.201500 − 0.360870I
a = −1.62412 + 1.03706I
b = −2.42883 + 2.34865I
−3.59239 + 7.60004I −5.70207 − 6.90528I
u = −0.670764 + 0.317932I
a = 2.23583 − 1.40717I
b = 1.14025 − 0.90622I
−0.26009 + 4.34202I −3.06611 − 5.18312I
u = −0.670764 − 0.317932I
a = 2.23583 + 1.40717I
b = 1.14025 + 0.90622I
−0.26009 − 4.34202I −3.06611 + 5.18312I
u = 0.703515 + 0.140913I
a = 0.003040 + 0.299544I
b = 0.501025 + 0.546651I
−1.337230 − 0.185301I −7.62381 + 0.24647I
u = 0.703515 − 0.140913I
a = 0.003040 − 0.299544I
b = 0.501025 − 0.546651I
−1.337230 + 0.185301I −7.62381 − 0.24647I
u = −1.280950 + 0.212067I
a = 0.273114 − 0.087546I
b = 0.130376 + 0.667731I
−6.90379 + 2.57028I −9.79223 − 1.93561I
u = −1.280950 − 0.212067I
a = 0.273114 + 0.087546I
b = 0.130376 − 0.667731I
−6.90379 − 2.57028I −9.79223 + 1.93561I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.29321 + 0.59629I
a = 1.59347 + 1.06533I
b = 1.53873 + 2.99555I
−12.8610 − 14.5081I −5.76542 + 7.91129I
u = 1.29321 − 0.59629I
a = 1.59347 − 1.06533I
b = 1.53873 − 2.99555I
−12.8610 + 14.5081I −5.76542 − 7.91129I
u = −0.358572 + 0.446053I
a = −2.09650 + 0.59301I
b = −0.541243 + 0.861918I
1.55250 − 0.72268I 4.27343 + 0.90071I
u = −0.358572 − 0.446053I
a = −2.09650 − 0.59301I
b = −0.541243 − 0.861918I
1.55250 + 0.72268I 4.27343 − 0.90071I
u = −1.33407 + 0.55318I
a = −0.172674 − 0.381772I
b = −0.018408 − 1.337270I
−13.7981 + 7.5953I −7.06455 − 3.46610I
u = −1.33407 − 0.55318I
a = −0.172674 + 0.381772I
b = −0.018408 + 1.337270I
−13.7981 − 7.5953I −7.06455 + 3.46610I
6
II. I
u
2
= h1.40 × 10
9
u
27
+ 6.80 × 10
8
u
26
+ · · · + 5.44 × 10
9
b + 1.84 × 10
8
, 4.26 ×
10
9
u
27
+5.12×10
9
u
26
+· · ·+1.09×10
10
a−1.08×10
10
, u
28
+2u
27
+· · ·+12u+4i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
−0.391489u
27
− 0.470374u
26
+ ··· − 3.81459u + 0.996493
−0.258207u
27
− 0.125077u
26
+ ··· − 0.732283u − 0.0337376
a
8
=
1
u
2
a
3
=
−0.413924u
27
− 0.597145u
26
+ ··· − 5.26760u − 0.220183
−0.0582121u
27
− 0.0675302u
26
+ ··· + 0.340267u + 0.293866
a
2
=
−0.477856u
27
− 0.996708u
26
+ ··· − 13.3082u − 4.41263
−0.112376u
27
− 0.407794u
26
+ ··· − 2.58251u − 1.23931
a
5
=
0.954572u
27
+ 1.16393u
26
+ ··· + 13.8778u + 5.23994
0.578242u
27
+ 0.838640u
26
+ ··· + 6.12426u + 2.98085
a
6
=
−0.553377u
27
− 0.805395u
26
+ ··· − 4.19380u − 0.220141
−0.289887u
27
− 0.549598u
26
+ ··· − 2.44368u − 1.38590
a
11
=
u
u
a
1
=
−u
3
−u
3
+ u
a
10
=
−0.344773u
27
− 0.559849u
26
+ ··· − 12.5913u − 2.43833
−0.107385u
27
− 0.0325593u
26
+ ··· − 1.42978u − 0.191489
a
9
=
0.122884u
27
+ 0.0337522u
26
+ ··· − 7.99636u − 2.60537
−0.0118276u
27
+ 0.0954702u
26
+ ··· − 1.56095u − 0.292717
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3864981188
1360028627
u
27
−
4406004267
1360028627
u
26
+ ··· −
49326955058
1360028627
u −
19445189018
1360028627
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
14
+ 21u
13
+ ··· − 66u + 1)
2
c
2
, c
4
(u
14
− 3u
13
+ ··· − 14u + 1)
2
c
3
(u
14
− u
13
+ ··· − 2u + 1)
2
c
5
, c
7
, c
9
c
11
u
28
− 2u
27
+ ··· − 12u + 4
c
6
, c
10
u
28
+ 5u
27
+ ··· + 251482u + 48331
c
8
, c
12
u
28
+ 16u
27
+ ··· − 104u + 16
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
14
− 59y
13
+ ··· − 3858y + 1)
2
c
2
, c
4
(y
14
+ 21y
13
+ ··· − 66y + 1)
2
c
3
(y
14
− 3y
13
+ ··· − 14y + 1)
2
c
5
, c
7
, c
9
c
11
y
28
− 16y
27
+ ··· + 104y + 16
c
6
, c
10
y
28
+ 29y
27
+ ··· + 1236737368y + 2335885561
c
8
, c
12
y
28
− 8y
27
+ ··· − 14112y + 256
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.944960 + 0.389379I
a = 1.68750 − 1.23439I
b = 1.31224 − 1.71461I
−0.06814 + 4.27159I −1.66019 − 6.67920I
u = −0.944960 − 0.389379I
a = 1.68750 + 1.23439I
b = 1.31224 + 1.71461I
−0.06814 − 4.27159I −1.66019 + 6.67920I
u = 0.167349 + 1.046550I
a = −1.56673 − 0.27072I
b = 0.750716 − 1.143810I
−9.38462 + 8.62895I −3.88181 − 4.95064I
u = 0.167349 − 1.046550I
a = −1.56673 + 0.27072I
b = 0.750716 + 1.143810I
−9.38462 − 8.62895I −3.88181 + 4.95064I
u = −0.071840 + 1.060620I
a = −1.156110 − 0.491907I
b = 0.349038 − 0.236829I
−9.86399 − 1.83809I −4.68358 + 0.51446I
u = −0.071840 − 1.060620I
a = −1.156110 + 0.491907I
b = 0.349038 + 0.236829I
−9.86399 + 1.83809I −4.68358 − 0.51446I
u = 0.930250 + 0.540185I
a = −0.39656 − 1.39984I
b = 0.82318 − 1.20145I
0.178509 −1.66494 + 0.I
u = 0.930250 − 0.540185I
a = −0.39656 + 1.39984I
b = 0.82318 + 1.20145I
0.178509 −1.66494 + 0.I
u = −0.967293 + 0.545264I
a = 1.19253 − 1.46190I
b = −0.09011 − 2.03761I
0.97692 + 4.37418I 1.48632 − 5.65859I
u = −0.967293 − 0.545264I
a = 1.19253 + 1.46190I
b = −0.09011 + 2.03761I
0.97692 − 4.37418I 1.48632 + 5.65859I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.120270 + 0.185451I
a = 0.336290 + 0.781567I
b = 0.0603554 + 0.0344181I
−2.83422 + 5.28701I −7.29071 − 5.64998I
u = −1.120270 − 0.185451I
a = 0.336290 − 0.781567I
b = 0.0603554 − 0.0344181I
−2.83422 − 5.28701I −7.29071 + 5.64998I
u = 0.661296 + 0.516335I
a = 1.39638 − 1.24212I
b = 1.77737 + 0.58800I
0.97692 − 4.37418I 1.48632 + 5.65859I
u = 0.661296 − 0.516335I
a = 1.39638 + 1.24212I
b = 1.77737 − 0.58800I
0.97692 + 4.37418I 1.48632 − 5.65859I
u = 0.986837 + 0.702176I
a = −1.43243 − 0.29298I
b = −0.95756 − 1.34618I
−2.83422 − 5.28701I −7.29071 + 5.64998I
u = 0.986837 − 0.702176I
a = −1.43243 + 0.29298I
b = −0.95756 + 1.34618I
−2.83422 + 5.28701I −7.29071 − 5.64998I
u = −0.576536 + 0.519983I
a = −1.80604 − 0.49276I
b = −1.20129 + 1.05231I
2.08354 4.91356 + 0.I
u = −0.576536 − 0.519983I
a = −1.80604 + 0.49276I
b = −1.20129 − 1.05231I
2.08354 4.91356 + 0.I
u = −1.296330 + 0.525251I
a = −1.29110 + 1.10158I
b = −1.32954 + 2.42151I
−9.38462 + 8.62895I −3.88181 − 4.95064I
u = −1.296330 − 0.525251I
a = −1.29110 − 1.10158I
b = −1.32954 − 2.42151I
−9.38462 − 8.62895I −3.88181 + 4.95064I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.323650 + 0.464051I
a = 0.131487 − 0.110768I
b = −0.532418 − 0.972507I
−9.86399 − 1.83809I −4.68358 + 0.51446I
u = 1.323650 − 0.464051I
a = 0.131487 + 0.110768I
b = −0.532418 + 0.972507I
−9.86399 + 1.83809I −4.68358 − 0.51446I
u = −1.39944 + 0.38754I
a = 0.184103 − 0.013266I
b = 1.29482 − 1.20212I
−14.5006 − 3.5759I −7.59435 + 2.22005I
u = −1.39944 − 0.38754I
a = 0.184103 + 0.013266I
b = 1.29482 + 1.20212I
−14.5006 + 3.5759I −7.59435 − 2.22005I
u = 1.38126 + 0.46460I
a = 1.074130 + 0.763312I
b = 1.81408 + 1.69170I
−14.5006 − 3.5759I −7.59435 + 2.22005I
u = 1.38126 − 0.46460I
a = 1.074130 − 0.763312I
b = 1.81408 − 1.69170I
−14.5006 + 3.5759I −7.59435 − 2.22005I
u = −0.073973 + 0.383908I
a = 3.89655 + 0.21962I
b = 0.429118 + 0.189827I
−0.06814 + 4.27159I −1.66019 − 6.67920I
u = −0.073973 − 0.383908I
a = 3.89655 − 0.21962I
b = 0.429118 − 0.189827I
−0.06814 − 4.27159I −1.66019 + 6.67920I
12
III. I
u
3
= hu
3
+ b + u + 1, −u
2
+ a + 2u + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
u
2
− 2u − 1
−u
3
− u − 1
a
8
=
1
u
2
a
3
=
−u
3
+ u
2
− u − 1
−u
3
− 1
a
2
=
−3u
3
+ u − 1
−2u
3
− u
2
+ 2u
a
5
=
u
3
u
3
− u
a
6
=
u
3
+ 2u
2u
3
a
11
=
u
u
a
1
=
−u
3
−u
3
+ u
a
10
=
3u
2
− 3
u
2
− 3
a
9
=
−2
−u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12u
2
− 8
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
(u
2
− u + 1)
2
c
2
, c
12
(u
2
+ u + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
u
4
− u
2
+ 1
c
6
(u
2
+ 2u + 2)
2
c
10
(u
2
− 2u + 2)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
12
(y
2
+ y + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
(y
2
− y + 1)
2
c
6
, c
10
(y
2
+ 4)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −2.23205 − 0.13397I
b = −1.86603 − 1.50000I
− 6.08965I −2.00000 + 10.39230I
u = 0.866025 − 0.500000I
a = −2.23205 + 0.13397I
b = −1.86603 + 1.50000I
6.08965I −2.00000 − 10.39230I
u = −0.866025 + 0.500000I
a = 1.23205 − 1.86603I
b = −0.13397 − 1.50000I
6.08965I −2.00000 − 10.39230I
u = −0.866025 − 0.500000I
a = 1.23205 + 1.86603I
b = −0.13397 + 1.50000I
− 6.08965I −2.00000 + 10.39230I
16
IV. I
u
4
= h−u
3
+ b − u + 1, −u
2
+ a − u + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
u
2
+ u − 1
u
3
+ u − 1
a
8
=
1
u
2
a
3
=
u
2
− 1
u − 1
a
2
=
−u
3
+ u
2
−2u
3
+ u
2
+ 2u − 1
a
5
=
u
3
u
3
− u
a
6
=
u
3
− u
2
− u + 2
u
2
− 2u + 1
a
11
=
u
u
a
1
=
−u
3
−u
3
+ u
a
10
=
u
3
− 2u
2
+ u + 1
2u
3
− 2u
2
− u + 3
a
9
=
−u
3
− u
2
+ 2u
u
3
− 2u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
(u
2
− u + 1)
2
c
2
, c
12
(u
2
+ u + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
u
4
− u
2
+ 1
c
6
u
4
+ 4u
3
+ 5u
2
+ 2u + 1
c
10
u
4
+ 2u
3
+ 5u
2
+ 4u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
12
(y
2
+ y + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
(y
2
− y + 1)
2
c
6
y
4
− 6y
3
+ 11y
2
+ 6y + 1
c
10
y
4
+ 6y
3
+ 11y
2
− 6y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 0.36603 + 1.36603I
b = −0.13397 + 1.50000I
2.02988I −2.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = 0.36603 − 1.36603I
b = −0.13397 − 1.50000I
− 2.02988I −2.00000 + 3.46410I
u = −0.866025 + 0.500000I
a = −1.36603 − 0.36603I
b = −1.86603 + 1.50000I
− 2.02988I −2.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = −1.36603 + 0.36603I
b = −1.86603 − 1.50000I
2.02988I −2.00000 − 3.46410I
20
V. I
u
5
= h−u
3
+ u
2
+ b − u − 1, u
2
+ a − u, u
4
− u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
−u
2
+ u
u
3
− u
2
+ u + 1
a
8
=
1
u
2
a
3
=
−u
2
−u
2
+ u + 1
a
2
=
−u
3
− 1
−2u
3
− u
2
+ 2u
a
5
=
u
3
u
3
− u
a
6
=
−u
3
−2u
3
+ 2u
a
11
=
u
u
a
1
=
−u
3
−u
3
+ u
a
10
=
u
2
+ 1
3u
2
− 1
a
9
=
2u
2
3u
2
− 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
(u
2
− u + 1)
2
c
2
, c
12
(u
2
+ u + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
u
4
− u
2
+ 1
c
6
u
4
− 2u
3
+ 2u
2
− 4u + 4
c
10
u
4
+ 2u
3
+ 2u
2
+ 4u + 4
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
12
(y
2
+ y + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
(y
2
− y + 1)
2
c
6
, c
10
y
4
− 4y
2
+ 16
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 0.366025 − 0.366025I
b = 1.36603 + 0.63397I
− 2.02988I −2.00000 + 3.46410I
u = 0.866025 − 0.500000I
a = 0.366025 + 0.366025I
b = 1.36603 − 0.63397I
2.02988I −2.00000 − 3.46410I
u = −0.866025 + 0.500000I
a = −1.36603 + 1.36603I
b = −0.36603 + 2.36603I
2.02988I −2.00000 − 3.46410I
u = −0.866025 − 0.500000I
a = −1.36603 − 1.36603I
b = −0.36603 − 2.36603I
− 2.02988I −2.00000 + 3.46410I
24
VI. I
u
6
= hu
3
− u
2
+ b + u, a + 2u − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
−2u + 1
−u
3
+ u
2
− u
a
8
=
1
u
2
a
3
=
−u
3
− u + 1
−u
3
+ u
2
a
2
=
−3u
3
+ u
2
+ u
−2u
3
+ u
2
+ 2u − 1
a
5
=
u
3
u
3
− u
a
6
=
−3u
3
+ 2u
2
+ u − 1
−2u
3
+ u
2
+ 2u − 2
a
11
=
u
u
a
1
=
−u
3
−u
3
+ u
a
10
=
u
3
− 2u + 3
−u
3
+ 2u
2
− u + 1
a
9
=
2u
3
− 3u
2
− u + 4
u
3
− 2u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 4
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
(u
2
− u + 1)
2
c
2
, c
12
(u
2
+ u + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
u
4
− u
2
+ 1
c
6
u
4
− 2u
3
+ 5u
2
− 4u + 1
c
10
u
4
− 4u
3
+ 5u
2
− 2u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
12
(y
2
+ y + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
(y
2
− y + 1)
2
c
6
y
4
+ 6y
3
+ 11y
2
− 6y + 1
c
10
y
4
− 6y
3
+ 11y
2
+ 6y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.732051 − 1.000000I
b = −0.366025 − 0.633975I
− 2.02988I −2.00000 + 3.46410I
u = 0.866025 − 0.500000I
a = −0.732051 + 1.000000I
b = −0.366025 + 0.633975I
2.02988I −2.00000 − 3.46410I
u = −0.866025 + 0.500000I
a = 2.73205 − 1.00000I
b = 1.36603 − 2.36603I
2.02988I −2.00000 − 3.46410I
u = −0.866025 − 0.500000I
a = 2.73205 + 1.00000I
b = 1.36603 + 2.36603I
− 2.02988I −2.00000 + 3.46410I
28
VII. I
u
7
= h−u
3
+ b − u, a − u, u
4
+ u
3
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
u
u
3
+ u
a
8
=
1
u
2
a
3
=
0
u
a
2
=
−u
3
−2u
3
+ 2u − 1
a
5
=
u
3
+ 1
u
3
+ u
2
− u + 2
a
6
=
1
u
2
a
11
=
u
u
a
1
=
−u
3
−u
3
+ u
a
10
=
u
3
+ 1
u
3
+ u
2
− u + 2
a
9
=
u
3
+ 2
u
3
+ 2u
2
− u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 3u
3
+ 6u
2
+ 4u + 1
c
2
, c
4
u
4
− u
3
+ 2u
2
+ 1
c
3
, c
6
, c
7
c
11
u
4
− u
3
+ 1
c
5
, c
8
, c
9
(u + 1)
4
c
10
u
4
− 3u
3
+ 6u
2
− 4u + 1
c
12
u
4
+ u
3
+ 2u
2
+ 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
4
+ 3y
3
+ 14y
2
− 4y + 1
c
2
, c
4
, c
12
y
4
+ 3y
3
+ 6y
2
+ 4y + 1
c
3
, c
6
, c
7
c
11
y
4
− y
3
+ 2y
2
+ 1
c
5
, c
8
, c
9
(y −1)
4
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.518913 + 0.666610I
a = 0.518913 + 0.666610I
b = −0.033125 + 0.908884I
−1.64493 −6.00000
u = 0.518913 − 0.666610I
a = 0.518913 − 0.666610I
b = −0.033125 − 0.908884I
−1.64493 −6.00000
u = −1.018910 + 0.602565I
a = −1.018910 + 0.602565I
b = −0.96687 + 2.26050I
−1.64493 −6.00000
u = −1.018910 − 0.602565I
a = −1.018910 − 0.602565I
b = −0.96687 − 2.26050I
−1.64493 −6.00000
32
VIII. I
u
8
= ha
3
+ 2a
2
+ b + 3a + 1, a
4
+ 3a
3
+ 6a
2
+ 4a + 1, u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
1
a
4
=
a
−a
3
− 2a
2
− 3a − 1
a
8
=
1
1
a
3
=
a
3
+ 2a
2
+ 5a + 1
a
a
2
=
a
3
+ a
2
+ 3a
−a
2
a
5
=
−2a − 2
−2a − 1
a
6
=
−a
3
− a
2
− 3a
a
2
a
11
=
1
1
a
1
=
−1
0
a
10
=
a
3
+ 2a
2
+ 3a + 2
−a
2
− 2a
a
9
=
−a
3
− 4a
2
− 6a − 1
−a
3
− 4a
2
− 5a − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 3u
3
+ 6u
2
+ 4u + 1
c
2
, c
4
u
4
− u
3
+ 2u
2
+ 1
c
3
, c
5
, c
9
c
10
u
4
− u
3
+ 1
c
6
u
4
− 3u
3
+ 6u
2
− 4u + 1
c
7
, c
11
, c
12
(u + 1)
4
c
8
u
4
+ u
3
+ 2u
2
+ 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
4
+ 3y
3
+ 14y
2
− 4y + 1
c
2
, c
4
, c
8
y
4
+ 3y
3
+ 6y
2
+ 4y + 1
c
3
, c
5
, c
9
c
10
y
4
− y
3
+ 2y
2
+ 1
c
7
, c
11
, c
12
(y −1)
4
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.447962 + 0.242275I
b = 0.070951 − 0.424335I
−1.64493 −6.00000
u = 1.00000
a = −0.447962 − 0.242275I
b = 0.070951 + 0.424335I
−1.64493 −6.00000
u = 1.00000
a = −1.05204 + 1.65794I
b = −2.07095 + 1.05537I
−1.64493 −6.00000
u = 1.00000
a = −1.05204 − 1.65794I
b = −2.07095 − 1.05537I
−1.64493 −6.00000
36
IX. I
u
9
= hb − 2, a − 1, u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
1
a
4
=
1
2
a
8
=
1
1
a
3
=
0
1
a
2
=
−1
−1
a
5
=
2
3
a
6
=
1
1
a
11
=
1
1
a
1
=
−1
0
a
10
=
2
3
a
9
=
3
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u − 1
c
3
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
u + 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y − 1
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 2.00000
−1.64493 −6.00000
40
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
2
− u + 1)
8
(u
4
+ 3u
3
+ 6u
2
+ 4u + 1)
2
· ((u
14
+ 21u
13
+ ··· − 66u + 1)
2
)(u
16
+ 16u
15
+ ··· + 1760u + 256)
c
2
(u − 1)(u
2
+ u + 1)
8
(u
4
− u
3
+ 2u
2
+ 1)
2
(u
14
− 3u
13
+ ··· − 14u + 1)
2
· (u
16
− 4u
15
+ ··· − 56u + 16)
c
3
(u + 1)(u
4
− u
2
+ 1)
4
(u
4
− u
3
+ 1)
2
(u
14
− u
13
+ ··· − 2u + 1)
2
· (u
16
+ 4u
15
+ ··· + 12u + 4)
c
4
(u − 1)(u
2
− u + 1)
8
(u
4
− u
3
+ 2u
2
+ 1)
2
(u
14
− 3u
13
+ ··· − 14u + 1)
2
· (u
16
− 4u
15
+ ··· − 56u + 16)
c
5
, c
7
, c
9
c
11
((u + 1)
5
)(u
4
− u
2
+ 1)
4
(u
4
− u
3
+ 1)(u
16
− u
15
+ ··· − 2u + 1)
· (u
28
− 2u
27
+ ··· − 12u + 4)
c
6
(u + 1)(u
2
+ 2u + 2)
2
(u
4
− 3u
3
+ ··· − 4u + 1)(u
4
− 2u
3
+ ··· − 4u + 4)
· (u
4
− 2u
3
+ 5u
2
− 4u + 1)(u
4
− u
3
+ 1)(u
4
+ 4u
3
+ 5u
2
+ 2u + 1)
· (u
16
− u
15
+ ··· + 64u + 16)(u
28
+ 5u
27
+ ··· + 251482u + 48331)
c
8
((u + 1)
5
)(u
2
− u + 1)
8
(u
4
+ u
3
+ 2u
2
+ 1)(u
16
+ 11u
15
+ ··· + 6u + 1)
· (u
28
+ 16u
27
+ ··· − 104u + 16)
c
10
(u + 1)(u
2
− 2u + 2)
2
(u
4
− 4u
3
+ ··· − 2u + 1)(u
4
− 3u
3
+ ··· − 4u + 1)
· (u
4
− u
3
+ 1)(u
4
+ 2u
3
+ 2u
2
+ 4u + 4)(u
4
+ 2u
3
+ 5u
2
+ 4u + 1)
· (u
16
− u
15
+ ··· + 64u + 16)(u
28
+ 5u
27
+ ··· + 251482u + 48331)
c
12
((u + 1)
5
)(u
2
+ u + 1)
8
(u
4
+ u
3
+ 2u
2
+ 1)(u
16
+ 11u
15
+ ··· + 6u + 1)
· (u
28
+ 16u
27
+ ··· − 104u + 16)
41
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)(y
2
+ y + 1)
8
(y
4
+ 3y
3
+ 14y
2
− 4y + 1)
2
· (y
14
− 59y
13
+ ··· − 3858y + 1)
2
· (y
16
− 24y
15
+ ··· − 508416y + 65536)
c
2
, c
4
(y − 1)(y
2
+ y + 1)
8
(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
2
· ((y
14
+ 21y
13
+ ··· − 66y + 1)
2
)(y
16
+ 16y
15
+ ··· + 1760y + 256)
c
3
(y − 1)(y
2
− y + 1)
8
(y
4
− y
3
+ 2y
2
+ 1)
2
(y
14
− 3y
13
+ ··· − 14y + 1)
2
· (y
16
− 4y
15
+ ··· − 56y + 16)
c
5
, c
7
, c
9
c
11
((y − 1)
5
)(y
2
− y + 1)
8
(y
4
− y
3
+ 2y
2
+ 1)(y
16
− 11y
15
+ ··· − 6y + 1)
· (y
28
− 16y
27
+ ··· + 104y + 16)
c
6
, c
10
(y − 1)(y
2
+ 4)
2
(y
4
− 4y
2
+ 16)(y
4
− 6y
3
+ 11y
2
+ 6y + 1)
· (y
4
− y
3
+ 2y
2
+ 1)(y
4
+ 3y
3
+ ··· − 4y + 1)(y
4
+ 6y
3
+ ··· − 6y + 1)
· (y
16
+ 25y
15
+ ··· + 256y + 256)
· (y
28
+ 29y
27
+ ··· + 1236737368y + 2335885561)
c
8
, c
12
(y − 1)
5
(y
2
+ y + 1)
8
(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
· (y
16
− 7y
15
+ ··· + 10y + 1)(y
28
− 8y
27
+ ··· − 14112y + 256)
42
