12n
0088
(K12n
0088
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 8 4 11 5 12 8 1 10
Solving Sequence
3,7 4,11
8 6 5 2 1 12 10 9
c
3
c
7
c
6
c
5
c
2
c
1
c
11
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1052u
13
+ 1602u
12
+ ··· + 303b + 1332, a − 1,
u
14
+ u
13
+ 2u
12
+ u
11
+ 6u
10
+ 4u
9
+ 4u
8
+ u
7
+ 6u
6
+ 4u
5
− 2u
3
− 4u
2
+ 4u − 1i
I
u
2
= h−9.89889 × 10
121
u
57
− 3.65306 × 10
122
u
56
+ ··· + 1.87725 × 10
122
b + 2.30550 × 10
123
,
− 1.95314 × 10
123
u
57
− 7.22784 × 10
123
u
56
+ ··· + 3.00360 × 10
123
a + 3.04298 × 10
124
,
u
58
+ 4u
57
+ ··· − 32u − 4i
I
u
3
= hu
2
+ b + 2, a + 1, u
3
− u
2
+ 2u − 1i
I
u
4
= h−2au + b + 2u − 1, u
2
a + a
2
− au + 3u
2
+ a − u + 5, u
3
− u
2
+ 2u − 1i
I
u
5
= hb + 2u + 3, a, u
2
+ u − 1i
I
v
1
= ha, 3b + 2v + 13, v
2
+ 7v + 1i
* 6 irreducible components of dim
C
= 0, with total 85 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
= h1052u
13
+ 1602u
12
+ · · · + 303b + 1332, a − 1, u
14
+ u
13
+ · · · + 4u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
1
−3.47195u
13
− 5.28713u
12
+ ··· + 16.2145u − 4.39604
a
8
=
−u
1.81518u
13
+ 2.61716u
12
+ ··· − 8.49175u + 3.47195
a
6
=
u
u
3
+ u
a
5
=
0.264026u
13
+ 0.356436u
12
+ ··· − 0.392739u + 0.801980
−0.276128u
13
− 0.611661u
12
+ ··· + 1.62046u + 0.179318
a
2
=
0.264026u
13
+ 0.356436u
12
+ ··· − 0.392739u + 0.801980
0.375138u
13
+ 0.578658u
12
+ ··· − 1.72607u − 0.0869087
a
1
=
0.639164u
13
+ 0.935094u
12
+ ··· − 2.11881u + 0.715072
0.375138u
13
+ 0.578658u
12
+ ··· − 1.72607u − 0.0869087
a
12
=
0.106711u
13
+ 0.0385039u
12
+ ··· + 0.567657u + 0.558856
−3.35314u
13
− 4.99340u
12
+ ··· + 15.5545u − 4.81848
a
10
=
u
2
+ 1
−4.27393u
13
− 6.35314u
12
+ ··· + 20.0033u − 6.21122
a
9
=
0.573157u
13
+ 0.512651u
12
+ ··· − 0.937294u + 1.09791
−1.34103u
13
− 2.07151u
12
+ ··· + 6.66007u − 2.46645
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1196
303
u
13
+
1124
101
u
12
+ ··· −
3188
303
u −
3026
101
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
14
+ 9u
13
+ ··· + 16u + 1
c
2
, c
4
, c
9
c
12
u
14
− 3u
13
+ ··· − 2u − 1
c
3
, c
6
, c
7
c
10
u
14
− u
13
+ ··· − 4u − 1
c
5
, c
8
u
14
− 7u
13
+ ··· − 24u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
14
− 5y
13
+ ··· − 208y + 1
c
2
, c
4
, c
9
c
12
y
14
− 9y
13
+ ··· − 16y + 1
c
3
, c
6
, c
7
c
10
y
14
+ 3y
13
+ ··· − 8y + 1
c
5
, c
8
y
14
− 7y
13
+ ··· + 384y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.985278
a = 1.00000
b = 0.711293
−10.4546 −24.6220
u = −0.336026 + 0.979953I
a = 1.00000
b = 0.255618 − 1.069010I
3.75566 − 0.17244I −4.31674 + 1.33622I
u = −0.336026 − 0.979953I
a = 1.00000
b = 0.255618 + 1.069010I
3.75566 + 0.17244I −4.31674 − 1.33622I
u = 0.811264 + 0.869909I
a = 1.00000
b = 0.73524 + 1.21182I
−1.53918 − 8.57795I −13.9694 + 8.6920I
u = 0.811264 − 0.869909I
a = 1.00000
b = 0.73524 − 1.21182I
−1.53918 + 8.57795I −13.9694 − 8.6920I
u = −0.920950 + 0.794472I
a = 1.00000
b = 2.22969 − 0.56400I
−7.24910 − 2.92807I −16.0849 + 1.6852I
u = −0.920950 − 0.794472I
a = 1.00000
b = 2.22969 + 0.56400I
−7.24910 + 2.92807I −16.0849 − 1.6852I
u = 0.685146 + 1.154840I
a = 1.00000
b = 1.095700 + 0.836675I
1.33116 − 5.50874I −7.69545 + 3.70076I
u = 0.685146 − 1.154840I
a = 1.00000
b = 1.095700 − 0.836675I
1.33116 + 5.50874I −7.69545 − 3.70076I
u = 0.495258
a = 1.00000
b = −0.192497
−0.942520 −9.45120
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.90906 + 1.21001I
a = 1.00000
b = 1.54300 − 1.48268I
−4.9818 + 17.0516I −13.2441 − 9.4300I
u = −0.90906 − 1.21001I
a = 1.00000
b = 1.54300 + 1.48268I
−4.9818 − 17.0516I −13.2441 + 9.4300I
u = 0.414634 + 0.221302I
a = 1.00000
b = 3.88135 + 1.29131I
−2.88995 + 0.46660I −33.6526 + 15.6404I
u = 0.414634 − 0.221302I
a = 1.00000
b = 3.88135 − 1.29131I
−2.88995 − 0.46660I −33.6526 − 15.6404I
6
II. I
u
2
= h−9.90 × 10
121
u
57
− 3.65 × 10
122
u
56
+ · · · + 1.88 × 10
122
b + 2.31 ×
10
123
, −1.95 × 10
123
u
57
− 7.23 × 10
123
u
56
+ · · · + 3.00 × 10
123
a + 3.04 ×
10
124
, u
58
+ 4u
57
+ · · · − 32u − 4i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
0.650266u
57
+ 2.40639u
56
+ ··· − 29.2651u − 10.1311
0.527307u
57
+ 1.94596u
56
+ ··· − 22.7262u − 12.2812
a
8
=
0.436407u
57
+ 1.53830u
56
+ ··· − 28.9670u − 2.62090
−0.0748277u
57
− 0.332438u
56
+ ··· − 0.473003u + 4.86221
a
6
=
u
u
3
+ u
a
5
=
−1.28188u
57
− 4.65236u
56
+ ··· + 75.0228u + 14.7864
−0.168206u
57
− 0.619830u
56
+ ··· + 8.16456u + 2.60510
a
2
=
−1.28188u
57
− 4.65236u
56
+ ··· + 75.0228u + 14.7864
−0.0117219u
57
− 0.0393795u
56
+ ··· + 1.91334u − 0.704417
a
1
=
−1.29360u
57
− 4.69174u
56
+ ··· + 76.9361u + 14.0819
−0.0117219u
57
− 0.0393795u
56
+ ··· + 1.91334u − 0.704417
a
12
=
−2.62838u
57
− 9.50925u
56
+ ··· + 161.265u + 25.9962
0.376226u
57
+ 1.39349u
56
+ ··· − 13.2103u − 10.9310
a
10
=
1.25102u
57
+ 4.66027u
56
+ ··· − 63.7398u − 18.6633
0.372290u
57
+ 1.46092u
56
+ ··· − 14.4154u − 13.9819
a
9
=
−3.61469u
57
− 13.0974u
56
+ ··· + 213.519u + 37.6085
−0.129312u
57
− 0.407792u
56
+ ··· + 12.1768u − 2.92917
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.07218u
57
+ 30.8062u
56
+ ··· − 296.329u − 286.736
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
58
+ 32u
57
+ ··· + 25u + 1
c
2
, c
4
, c
9
c
12
u
58
− 4u
57
+ ··· + 5u + 1
c
3
, c
6
, c
7
c
10
u
58
− 4u
57
+ ··· + 32u − 4
c
5
, c
8
(u
29
+ 2u
28
+ ··· − 28u − 8)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
58
− 8y
57
+ ··· + 195y + 1
c
2
, c
4
, c
9
c
12
y
58
− 32y
57
+ ··· − 25y + 1
c
3
, c
6
, c
7
c
10
y
58
+ 18y
57
+ ··· − 984y + 16
c
5
, c
8
(y
29
− 28y
28
+ ··· + 2896y − 64)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.721948 + 0.675707I
a = −1.050020 + 0.447654I
b = −0.511195 + 1.317100I
2.03816 + 4.43643I −7.12586 − 5.70665I
u = −0.721948 − 0.675707I
a = −1.050020 − 0.447654I
b = −0.511195 − 1.317100I
2.03816 − 4.43643I −7.12586 + 5.70665I
u = −0.244212 + 0.907147I
a = −1.73124 + 0.12831I
b = −0.254583 + 0.569117I
4.34822 + 5.30129I −10.14110 − 5.91971I
u = −0.244212 − 0.907147I
a = −1.73124 − 0.12831I
b = −0.254583 − 0.569117I
4.34822 − 5.30129I −10.14110 + 5.91971I
u = 0.578373 + 0.893018I
a = −0.516169 − 0.639005I
b = 0.175167 − 1.077130I
−1.15248 + 2.97907I −12.00000 + 0.I
u = 0.578373 − 0.893018I
a = −0.516169 + 0.639005I
b = 0.175167 + 1.077130I
−1.15248 − 2.97907I −12.00000 + 0.I
u = −0.676773 + 0.824397I
a = −0.377087 − 1.293150I
b = −0.982001 + 0.458444I
−4.05295 + 3.42058I −12.00000 + 0.I
u = −0.676773 − 0.824397I
a = −0.377087 + 1.293150I
b = −0.982001 − 0.458444I
−4.05295 − 3.42058I −12.00000 + 0.I
u = 0.978563 + 0.440662I
a = 0.331345 + 0.627843I
b = −0.228672 + 1.138160I
−0.488787 − 0.370462I −12.00000 + 0.I
u = 0.978563 − 0.440662I
a = 0.331345 − 0.627843I
b = −0.228672 − 1.138160I
−0.488787 + 0.370462I −12.00000 + 0.I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.012023 + 0.920805I
a = 1.65342 − 0.02280I
b = 0.209786 − 0.307915I
4.90257 − 1.34329I −7.80264 + 1.36225I
u = −0.012023 − 0.920805I
a = 1.65342 + 0.02280I
b = 0.209786 + 0.307915I
4.90257 + 1.34329I −7.80264 − 1.36225I
u = −0.580576 + 0.921658I
a = −1.003690 − 0.228249I
b = −1.66287 + 0.18113I
−3.74876 + 1.54341I 0
u = −0.580576 − 0.921658I
a = −1.003690 + 0.228249I
b = −1.66287 − 0.18113I
−3.74876 − 1.54341I 0
u = 0.793089 + 0.792547I
a = −0.947329 − 0.215431I
b = −1.66287 − 0.18113I
−3.74876 − 1.54341I 0
u = 0.793089 − 0.792547I
a = −0.947329 + 0.215431I
b = −1.66287 + 0.18113I
−3.74876 + 1.54341I 0
u = 0.272105 + 0.830532I
a = −0.764969 − 0.947014I
b = 0.175167 + 1.077130I
−1.15248 − 2.97907I −9.53425 + 4.84429I
u = 0.272105 − 0.830532I
a = −0.764969 + 0.947014I
b = 0.175167 − 1.077130I
−1.15248 + 2.97907I −9.53425 − 4.84429I
u = 0.455577 + 1.032690I
a = −0.805887 + 0.343573I
b = −0.511195 − 1.317100I
2.03816 − 4.43643I 0
u = 0.455577 − 1.032690I
a = −0.805887 − 0.343573I
b = −0.511195 + 1.317100I
2.03816 + 4.43643I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.802696 + 0.874767I
a = −0.085771 + 0.996315I
b = 0.307471
−7.39364 0
u = −0.802696 − 0.874767I
a = −0.085771 − 0.996315I
b = 0.307471
−7.39364 0
u = −1.031050 + 0.638573I
a = −0.116942 − 1.016090I
b = −0.777038 − 0.585721I
−3.19564 − 4.35308I 0
u = −1.031050 − 0.638573I
a = −0.116942 + 1.016090I
b = −0.777038 + 0.585721I
−3.19564 + 4.35308I 0
u = −0.797235 + 0.914221I
a = 1.140830 − 0.268629I
b = 1.25483 − 0.74117I
−7.27243 + 6.00653I 0
u = −0.797235 − 0.914221I
a = 1.140830 + 0.268629I
b = 1.25483 + 0.74117I
−7.27243 − 6.00653I 0
u = 0.047575 + 0.760395I
a = 0.657460 − 1.245780I
b = −0.228672 + 1.138160I
−0.488787 − 0.370462I −8.36692 + 2.50640I
u = 0.047575 − 0.760395I
a = 0.657460 + 1.245780I
b = −0.228672 − 1.138160I
−0.488787 + 0.370462I −8.36692 − 2.50640I
u = 0.769423 + 0.972965I
a = −0.111786 + 0.971295I
b = −0.777038 − 0.585721I
−3.19564 − 4.35308I 0
u = 0.769423 − 0.972965I
a = −0.111786 − 0.971295I
b = −0.777038 + 0.585721I
−3.19564 + 4.35308I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.824653 + 1.012890I
a = 0.164016 + 1.106820I
b = 1.240200 − 0.434590I
−6.56035 + 9.36152I 0
u = −0.824653 − 1.012890I
a = 0.164016 − 1.106820I
b = 1.240200 + 0.434590I
−6.56035 − 9.36152I 0
u = 0.202324 + 1.331240I
a = −0.027585 + 0.375583I
b = −0.20707 − 3.33341I
1.81502 − 2.87998I 0
u = 0.202324 − 1.331240I
a = −0.027585 − 0.375583I
b = −0.20707 + 3.33341I
1.81502 + 2.87998I 0
u = −0.803948 + 1.131230I
a = −1.108550 + 0.044327I
b = −1.28128 + 1.27353I
−1.66044 + 11.01250I 0
u = −0.803948 − 1.131230I
a = −1.108550 − 0.044327I
b = −1.28128 − 1.27353I
−1.66044 − 11.01250I 0
u = 0.601388
a = −0.244736
b = −7.40752
−2.67255 −211.680
u = 0.557093 + 0.195871I
a = 0.779962 − 0.625827I
b = −0.0910519
−0.942618 −9.31087 + 0.I
u = 0.557093 − 0.195871I
a = 0.779962 + 0.625827I
b = −0.0910519
−0.942618 −9.31087 + 0.I
u = −0.66392 + 1.25713I
a = 0.830507 + 0.195558I
b = 1.25483 − 0.74117I
−7.27243 + 6.00653I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.66392 − 1.25713I
a = 0.830507 − 0.195558I
b = 1.25483 + 0.74117I
−7.27243 − 6.00653I 0
u = 1.32127 + 0.56430I
a = −0.207826 + 0.712702I
b = −0.982001 + 0.458444I
−4.05295 + 3.42058I 0
u = 1.32127 − 0.56430I
a = −0.207826 − 0.712702I
b = −0.982001 − 0.458444I
−4.05295 − 3.42058I 0
u = −1.25634 + 0.74661I
a = 0.131009 + 0.884078I
b = 1.240200 + 0.434590I
−6.56035 − 9.36152I 0
u = −1.25634 − 0.74661I
a = 0.131009 − 0.884078I
b = 1.240200 − 0.434590I
−6.56035 + 9.36152I 0
u = 0.513312 + 0.101132I
a = 0.925268 − 0.379313I
b = −0.165385
−0.942376 −9.38299 + 0.I
u = 0.513312 − 0.101132I
a = 0.925268 + 0.379313I
b = −0.165385
−0.942376 −9.38299 + 0.I
u = −0.505572 + 0.039267I
a = −0.19450 − 2.64824I
b = −0.20707 − 3.33341I
1.81502 − 2.87998I −58.6220 + 17.5185I
u = −0.505572 − 0.039267I
a = −0.19450 + 2.64824I
b = −0.20707 + 3.33341I
1.81502 + 2.87998I −58.6220 − 17.5185I
u = 0.00112 + 1.52275I
a = 0.604691 + 0.008340I
b = 0.209786 − 0.307915I
4.90257 − 1.34329I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00112 − 1.52275I
a = 0.604691 − 0.008340I
b = 0.209786 + 0.307915I
4.90257 + 1.34329I 0
u = −1.52437
a = 0.237820
b = 0.405949
−10.6310 0
u = 0.84107 + 1.28967I
a = −0.900638 + 0.036014I
b = −1.28128 − 1.27353I
−1.66044 − 11.01250I 0
u = 0.84107 − 1.28967I
a = −0.900638 − 0.036014I
b = −1.28128 + 1.27353I
−1.66044 + 11.01250I 0
u = 0.30639 + 1.60183I
a = −0.574465 + 0.042578I
b = −0.254583 − 0.569117I
4.34822 − 5.30129I 0
u = 0.30639 − 1.60183I
a = −0.574465 − 0.042578I
b = −0.254583 + 0.569117I
4.34822 + 5.30129I 0
u = −0.362526
a = 4.20485
b = 0.405949
−10.6310 −48.5360
u = −0.147181
a = −4.08603
b = −7.40752
−2.67255 −211.680
15
III. I
u
3
= hu
2
+ b + 2, a + 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
−1
−u
2
− 2
a
8
=
−u
−u
2
+ u − 1
a
6
=
u
u
2
− u + 1
a
5
=
u
u
2
− u + 1
a
2
=
u
−u
a
1
=
0
−u
a
12
=
−1
−2u
2
− 2
a
10
=
−u
2
− 1
−u
2
+ u − 3
a
9
=
−u
−u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
+ 8u − 20
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
11
u
3
− u
2
+ 2u − 1
c
2
, c
9
u
3
+ u
2
− 1
c
4
, c
12
u
3
− u
2
+ 1
c
5
, c
8
u
3
c
6
, c
10
u
3
+ u
2
+ 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
11
y
3
+ 3y
2
+ 2y − 1
c
2
, c
4
, c
9
c
12
y
3
− y
2
+ 2y − 1
c
5
, c
8
y
3
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −1.00000
b = −0.337641 − 0.562280I
6.04826 − 5.65624I −4.98049 + 5.95889I
u = 0.215080 − 1.307140I
a = −1.00000
b = −0.337641 + 0.562280I
6.04826 + 5.65624I −4.98049 − 5.95889I
u = 0.569840
a = −1.00000
b = −2.32472
−2.22691 −18.0390
19
IV.
I
u
4
= h−2au + b + 2u − 1, u
2
a + a
2
− au + 3u
2
+ a − u + 5, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
11
=
a
2au − 2u + 1
a
8
=
−au + 2u
2
+ a − u + 3
au + 2u
2
− u + 4
a
6
=
u
u
2
− u + 1
a
5
=
u
u
2
− u + 1
a
2
=
u
−u
a
1
=
0
−u
a
12
=
a
u
2
a + 2au − 2u + 1
a
10
=
−au + u
2
+ 1
−2u
2
a + 3au + u
2
− 2a − 3u + 3
a
9
=
−au + 2u
2
+ a − u + 3
au + 2u
2
− u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 11u
2
a + 5au − 5u + 15
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
11
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
9
(u
3
+ u
2
− 1)
2
c
4
, c
12
(u
3
− u
2
+ 1)
2
c
5
, c
8
u
6
c
6
, c
10
(u
3
+ u
2
+ 2u + 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
11
(y
3
+ 3y
2
+ 2y − 1)
2
c
2
, c
4
, c
9
c
12
(y
3
− y
2
+ 2y − 1)
2
c
5
, c
8
y
6
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.947279 + 0.320410I
b = 0.139681
6.04826 −6.45445 + 0.I
u = 0.215080 + 1.307140I
a = −0.069840 + 0.424452I
b = −0.56984 − 2.61428I
1.91067 − 2.82812I 9.7272 − 14.7292I
u = 0.215080 − 1.307140I
a = 0.947279 − 0.320410I
b = 0.139681
6.04826 −6.45445 + 0.I
u = 0.215080 − 1.307140I
a = −0.069840 − 0.424452I
b = −0.56984 + 2.61428I
1.91067 + 2.82812I 9.7272 + 14.7292I
u = 0.569840
a = −0.37744 + 2.29387I
b = −0.56984 + 2.61428I
1.91067 + 2.82812I 9.7272 + 14.7292I
u = 0.569840
a = −0.37744 − 2.29387I
b = −0.56984 − 2.61428I
1.91067 − 2.82812I 9.7272 − 14.7292I
23
V. I
u
5
= hb + 2u + 3, a, u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u + 1
a
11
=
0
−2u − 3
a
8
=
0
u
a
6
=
u
3u − 1
a
5
=
u
u
a
2
=
u
u − 1
a
1
=
2u − 1
u − 1
a
12
=
2u − 1
−u − 4
a
10
=
0
−2u − 3
a
9
=
−2u + 1
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 29
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
6
u
2
− u − 1
c
7
, c
10
u
2
c
8
u
2
+ 3u + 1
c
9
, c
11
(u − 1)
2
c
12
(u + 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
8
y
2
− 7y + 1
c
2
, c
3
, c
4
c
6
y
2
− 3y + 1
c
7
, c
10
y
2
c
9
, c
11
, c
12
(y − 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0
b = −4.23607
−2.63189 29.0000
u = −1.61803
a = 0
b = 0.236068
−10.5276 29.0000
27
VI. I
v
1
= ha, 3b + 2v + 13, v
2
+ 7v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
11
=
0
−
2
3
v −
13
3
a
8
=
v
−
1
3
v −
8
3
a
6
=
v
0
a
5
=
−
5
3
v −
1
3
1
a
2
=
5
3
v +
4
3
−1
a
1
=
5
3
v +
1
3
−1
a
12
=
13
3
v +
2
3
−
1
3
v −
14
3
a
10
=
−
5
3
v −
1
3
−v − 6
a
9
=
16
3
v +
2
3
−3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 29
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
6
u
2
c
4
(u + 1)
2
c
5
, c
11
u
2
− 3u + 1
c
7
, c
9
u
2
+ u − 1
c
8
u
2
+ 3u + 1
c
10
, c
12
u
2
− u − 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
6
y
2
c
5
, c
8
, c
11
y
2
− 7y + 1
c
7
, c
9
, c
10
c
12
y
2
− 3y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.145898
a = 0
b = −4.23607
−2.63189 29.0000
v = −6.85410
a = 0
b = 0.236068
−10.5276 29.0000
31
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u − 1)
2
)(u
2
− 3u + 1)(u
3
− u
2
+ 2u − 1)
3
(u
14
+ 9u
13
+ ··· + 16u + 1)
· (u
58
+ 32u
57
+ ··· + 25u + 1)
c
2
, c
9
((u − 1)
2
)(u
2
+ u − 1)(u
3
+ u
2
− 1)
3
(u
14
− 3u
13
+ ··· − 2u − 1)
· (u
58
− 4u
57
+ ··· + 5u + 1)
c
3
, c
7
u
2
(u
2
+ u − 1)(u
3
− u
2
+ 2u − 1)
3
(u
14
− u
13
+ ··· − 4u − 1)
· (u
58
− 4u
57
+ ··· + 32u − 4)
c
4
, c
12
((u + 1)
2
)(u
2
− u − 1)(u
3
− u
2
+ 1)
3
(u
14
− 3u
13
+ ··· − 2u − 1)
· (u
58
− 4u
57
+ ··· + 5u + 1)
c
5
u
9
(u
2
− 3u + 1)
2
(u
14
− 7u
13
+ ··· − 24u + 8)
· (u
29
+ 2u
28
+ ··· − 28u − 8)
2
c
6
, c
10
u
2
(u
2
− u − 1)(u
3
+ u
2
+ 2u + 1)
3
(u
14
− u
13
+ ··· − 4u − 1)
· (u
58
− 4u
57
+ ··· + 32u − 4)
c
8
u
9
(u
2
+ 3u + 1)
2
(u
14
− 7u
13
+ ··· − 24u + 8)
· (u
29
+ 2u
28
+ ··· − 28u − 8)
2
32
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y − 1)
2
)(y
2
− 7y + 1)(y
3
+ 3y
2
+ 2y − 1)
3
(y
14
− 5y
13
+ ··· − 208y + 1)
· (y
58
− 8y
57
+ ··· + 195y + 1)
c
2
, c
4
, c
9
c
12
((y − 1)
2
)(y
2
− 3y + 1)(y
3
− y
2
+ 2y − 1)
3
(y
14
− 9y
13
+ ··· − 16y + 1)
· (y
58
− 32y
57
+ ··· − 25y + 1)
c
3
, c
6
, c
7
c
10
y
2
(y
2
− 3y + 1)(y
3
+ 3y
2
+ 2y − 1)
3
(y
14
+ 3y
13
+ ··· − 8y + 1)
· (y
58
+ 18y
57
+ ··· − 984y + 16)
c
5
, c
8
y
9
(y
2
− 7y + 1)
2
(y
14
− 7y
13
+ ··· + 384y + 64)
· (y
29
− 28y
28
+ ··· + 2896y − 64)
2
33
