12a
1182
(K12a
1182
)
A knot diagram
1
Linearized knot diagam
4 10 8 1 11 12 3 5 2 7 6 9
Solving Sequence
1,5
4
2,9
10 8 3 7 11 12 6
c
4
c
1
c
9
c
8
c
3
c
7
c
10
c
12
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1393u
37
+ 27813u
36
+ ··· + 128b + 48128, 188u
37
− 2555u
36
+ ··· + 128a + 149824,
u
38
− 21u
37
+ ··· − 4864u + 256i
I
u
2
= h−3.88208 × 10
52
a
15
u
4
+ 1.90625 × 10
52
a
14
u
4
+ ··· + 3.57811 × 10
52
a + 3.35225 × 10
51
,
− a
15
u
4
− 6a
14
u
4
+ ··· − 102a − 31, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
I
u
3
= h−9u
24
− 37u
23
+ ··· + b + 37, −37u
24
− 231u
23
+ ··· + a − 6, u
25
+ 6u
24
+ ··· + 5u + 1i
* 3 irreducible components of dim
C
= 0, with total 143 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−1393u
37
+ 27813u
36
+ · · · + 128b + 48128, 188u
37
− 2555u
36
+
· · · + 128a + 149824, u
38
− 21u
37
+ · · · − 4864u + 256i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
−1.46875u
37
+ 19.9609u
36
+ ··· + 21583.3u − 1170.50
10.8828u
37
− 217.289u
36
+ ··· + 8314.50u − 376
a
10
=
−15.7188u
37
+ 312.086u
36
+ ··· − 11376.8u + 539.500
6.07031u
37
− 147.727u
36
+ ··· + 72282.5u − 3910
a
8
=
9.41406u
37
− 197.328u
36
+ ··· + 29897.8u − 1546.50
10.8828u
37
− 217.289u
36
+ ··· + 8314.50u − 376
a
3
=
−
3
256
u
37
+
77
256
u
36
+ ··· − 159u + 9
59
128
u
37
−
1173
128
u
36
+ ··· + 2170u − 121
a
7
=
−13.9961u
37
+ 294.926u
36
+ ··· − 43159.8u + 2266
−8.22656u
37
+ 153.602u
36
+ ··· + 27840u − 1591
a
11
=
5.77734u
37
− 105.535u
36
+ ··· − 21165.3u + 1168.50
−6.44531u
37
+ 137.477u
36
+ ··· − 21511.5u + 1137
a
12
=
−1.52734u
37
+ 31.5352u
36
+ ··· − 7145u + 382
69
128
u
37
−
1515
128
u
36
+ ··· + 7048u − 391
a
6
=
−4.78906u
37
+ 89.7813u
36
+ ··· + 14346.5u − 796
185
128
u
37
−
4709
128
u
36
+ ··· + 16332u − 884
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
129
32
u
37
+
3399
32
u
36
+ ··· − 67794u + 3762
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
38
− 21u
37
+ ··· − 4864u + 256
c
2
, c
3
, c
7
c
9
u
38
− u
37
+ ··· − u + 1
c
5
, c
6
, c
11
u
38
+ 11u
37
+ ··· − 64u + 32
c
8
, c
12
u
38
+ u
37
+ ··· + 4u + 1
c
10
u
38
− 30u
37
+ ··· − 1495744u + 104800
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
38
+ 21y
37
+ ··· + 262144y + 65536
c
2
, c
3
, c
7
c
9
y
38
− 29y
37
+ ··· + 5y + 1
c
5
, c
6
, c
11
y
38
− 31y
37
+ ··· + 2560y + 1024
c
8
, c
12
y
38
+ 9y
37
+ ··· + 40y + 1
c
10
y
38
+ 10y
37
+ ··· − 49765582336y + 10983040000
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.276578 + 1.023820I
a = −1.159910 + 0.544755I
b = 0.878533 + 1.036860I
1.78144 − 3.49513I 0
u = 0.276578 − 1.023820I
a = −1.159910 − 0.544755I
b = 0.878533 − 1.036860I
1.78144 + 3.49513I 0
u = 0.176776 + 1.066540I
a = 0.864750 − 0.422278I
b = −0.603241 − 0.847638I
3.09560 − 0.11489I 0
u = 0.176776 − 1.066540I
a = 0.864750 + 0.422278I
b = −0.603241 + 0.847638I
3.09560 + 0.11489I 0
u = 0.325919 + 1.043810I
a = 1.331630 − 0.450348I
b = −0.90408 − 1.24319I
7.05489 − 6.79305I 0
u = 0.325919 − 1.043810I
a = 1.331630 + 0.450348I
b = −0.90408 + 1.24319I
7.05489 + 6.79305I 0
u = 1.140690 + 0.256725I
a = −0.708610 + 0.838720I
b = 1.023630 − 0.774803I
−4.62360 + 11.93760I 0
u = 1.140690 − 0.256725I
a = −0.708610 − 0.838720I
b = 1.023630 + 0.774803I
−4.62360 − 11.93760I 0
u = 0.112836 + 0.804337I
a = 0.478801 − 0.929435I
b = −0.801605 − 0.280244I
2.99988 − 0.94819I 0
u = 0.112836 − 0.804337I
a = 0.478801 + 0.929435I
b = −0.801605 + 0.280244I
2.99988 + 0.94819I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.229363 + 1.183590I
a = −0.935452 + 0.110373I
b = 0.345193 + 1.081870I
9.08075 + 1.15702I 0
u = 0.229363 − 1.183590I
a = −0.935452 − 0.110373I
b = 0.345193 − 1.081870I
9.08075 − 1.15702I 0
u = 1.193720 + 0.264532I
a = 0.662558 − 0.703782I
b = −0.977082 + 0.664851I
−9.66231 + 7.26737I 0
u = 1.193720 − 0.264532I
a = 0.662558 + 0.703782I
b = −0.977082 − 0.664851I
−9.66231 − 7.26737I 0
u = 1.287920 + 0.305018I
a = −0.520579 + 0.543865I
b = 0.836351 − 0.541667I
−7.01204 + 2.08978I 0
u = 1.287920 − 0.305018I
a = −0.520579 − 0.543865I
b = 0.836351 + 0.541667I
−7.01204 − 2.08978I 0
u = 1.055980 + 0.854615I
a = −0.315540 − 0.650906I
b = −0.223072 + 0.957006I
3.89637 + 2.48033I 0
u = 1.055980 − 0.854615I
a = −0.315540 + 0.650906I
b = −0.223072 − 0.957006I
3.89637 − 2.48033I 0
u = 0.722105 + 1.185770I
a = 1.056810 + 0.054104I
b = −0.69897 − 1.29220I
5.48491 − 9.18131I 0
u = 0.722105 − 1.185770I
a = 1.056810 − 0.054104I
b = −0.69897 + 1.29220I
5.48491 + 9.18131I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.63913 + 1.27635I
a = −1.162370 + 0.368591I
b = 1.21336 + 1.24802I
−1.4096 − 18.1977I 0
u = 0.63913 − 1.27635I
a = −1.162370 − 0.368591I
b = 1.21336 − 1.24802I
−1.4096 + 18.1977I 0
u = 0.65333 + 1.28434I
a = 1.089340 − 0.358794I
b = −1.17251 − 1.16467I
−6.4291 − 13.7041I 0
u = 0.65333 − 1.28434I
a = 1.089340 + 0.358794I
b = −1.17251 + 1.16467I
−6.4291 + 13.7041I 0
u = 0.502236 + 0.232158I
a = 0.00110 − 1.66945I
b = −0.388127 + 0.838203I
4.87896 + 3.61554I 2.09736 − 5.51387I
u = 0.502236 − 0.232158I
a = 0.00110 + 1.66945I
b = −0.388127 − 0.838203I
4.87896 − 3.61554I 2.09736 + 5.51387I
u = 0.68009 + 1.29011I
a = −0.993287 + 0.304581I
b = 1.06847 + 1.07431I
−3.83257 − 8.83430I 0
u = 0.68009 − 1.29011I
a = −0.993287 − 0.304581I
b = 1.06847 − 1.07431I
−3.83257 + 8.83430I 0
u = 0.83997 + 1.26540I
a = −0.711539 − 0.018103I
b = 0.574764 + 0.915591I
−2.21139 − 6.84601I 0
u = 0.83997 − 1.26540I
a = −0.711539 + 0.018103I
b = 0.574764 − 0.915591I
−2.21139 + 6.84601I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.62513 + 1.45533I
a = −0.118959 + 0.108907I
b = 0.084131 + 0.241205I
−1.33149 + 1.81451I 0
u = −0.62513 − 1.45533I
a = −0.118959 − 0.108907I
b = 0.084131 − 0.241205I
−1.33149 − 1.81451I 0
u = 1.06314 + 1.22972I
a = 0.438610 + 0.194376I
b = −0.227277 − 0.746019I
−3.13120 − 1.44216I 0
u = 1.06314 − 1.22972I
a = 0.438610 − 0.194376I
b = −0.227277 + 0.746019I
−3.13120 + 1.44216I 0
u = −0.02275 + 1.63264I
a = 0.260992 + 0.073977I
b = 0.126715 − 0.424424I
2.33032 + 6.70905I 0
u = −0.02275 − 1.63264I
a = 0.260992 − 0.073977I
b = 0.126715 + 0.424424I
2.33032 − 6.70905I 0
u = 0.248102 + 0.239177I
a = 0.19166 + 1.64054I
b = 0.344830 − 0.452862I
−0.137370 + 1.058430I −2.37760 − 6.58966I
u = 0.248102 − 0.239177I
a = 0.19166 − 1.64054I
b = 0.344830 + 0.452862I
−0.137370 − 1.058430I −2.37760 + 6.58966I
8
II. I
u
2
= h−3.88 × 10
52
a
15
u
4
+ 1.91 × 10
52
a
14
u
4
+ · · · + 3.58 × 10
52
a + 3.35 ×
10
51
, −a
15
u
4
− 6a
14
u
4
+ · · · − 102a − 31, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
a
5.32421a
15
u
4
− 2.61440a
14
u
4
+ ··· − 4.90733a − 0.459757
a
10
=
0.490922a
15
u
4
+ 0.697262a
14
u
4
+ ··· − 1.84896a − 1.19139
−8.42480a
15
u
4
+ 5.50719a
14
u
4
+ ··· − 1.01737a − 0.0149474
a
8
=
5.32421a
15
u
4
− 2.61440a
14
u
4
+ ··· − 3.90733a − 0.459757
5.32421a
15
u
4
− 2.61440a
14
u
4
+ ··· − 4.90733a − 0.459757
a
3
=
1.60664a
15
u
4
− 4.72751a
14
u
4
+ ··· + 0.297334a + 0.986032
−0.511136a
15
u
4
− 3.50909a
14
u
4
+ ··· + 0.264202a − 0.293605
a
7
=
4.36323a
15
u
4
− 4.09965a
14
u
4
+ ··· − 0.228422a + 0.634601
10.9156a
15
u
4
− 9.67127a
14
u
4
+ ··· − 0.843113a − 0.611571
a
11
=
4.21926a
15
u
4
− 5.16470a
14
u
4
+ ··· + 1.00869a − 0.253935
3.09316a
15
u
4
− 4.46543a
14
u
4
+ ··· + 2.87103a + 0.821975
a
12
=
a
2
u
1.84334a
15
u
4
− 2.28395a
14
u
4
+ ··· + 0.634977a + 0.138061
a
6
=
3.14774a
15
u
4
− 3.78321a
14
u
4
+ ··· − 0.0774317a + 0.793497
8.97044a
15
u
4
− 4.81864a
14
u
4
+ ··· + 1.38621a − 0.694416
(ii) Obstruction class = −1
(iii) Cusp Shapes = −13.7656a
15
u
4
+ 38.1880a
14
u
4
+ ··· − 3.46066a − 3.15724
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
16
c
2
, c
3
, c
7
c
9
u
80
− u
79
+ ··· + 99094u − 20507
c
5
, c
6
, c
11
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
10
c
8
, c
12
u
80
+ 5u
79
+ ··· − 22u − 1
c
10
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
10
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
16
c
2
, c
3
, c
7
c
9
y
80
− 65y
79
+ ··· − 11196460816y + 420537049
c
5
, c
6
, c
11
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
10
c
8
, c
12
y
80
− 13y
79
+ ··· − 92y + 1
c
10
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
10
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = −0.367485 + 0.952224I
b = 0.10278 + 1.82740I
−3.56505 − 2.66181I −8.06966 + 4.94144I
u = 0.339110 + 0.822375I
a = −0.922856 − 0.158406I
b = 1.148420 − 0.607014I
−3.76067 − 1.53058I −3.59042 + 4.43065I
u = 0.339110 + 0.822375I
a = 1.073940 − 0.580876I
b = −1.58109 + 0.31189I
1.89703 − 1.53058I −1.62085 + 4.43065I
u = 0.339110 + 0.822375I
a = 0.466007 − 1.158660I
b = −0.54911 − 1.77038I
−6.76512 + 1.04791I −11.20781 + 0.86269I
u = 0.339110 + 0.822375I
a = −0.546602 + 1.252020I
b = 0.83813 + 1.77295I
−2.22602 + 4.91296I −6.05644 − 0.86352I
u = 0.339110 + 0.822375I
a = −0.206431 + 0.502758I
b = 2.01649 − 1.09378I
−2.22602 − 7.97412I −6.05644 + 9.72482I
u = 0.339110 + 0.822375I
a = 0.13870 + 1.45366I
b = 0.182681 + 0.812651I
−3.76067 − 1.53058I −3.59042 + 4.43065I
u = 0.339110 + 0.822375I
a = 0.181301 − 0.315913I
b = −1.79265 + 1.21965I
−6.76512 − 4.10907I −11.20781 + 7.99861I
u = 0.339110 + 0.822375I
a = 0.35344 − 1.77685I
b = −0.841882 − 0.686202I
1.89703 − 1.53058I −1.62085 + 4.43065I
u = 0.339110 + 0.822375I
a = −0.0634617 + 0.0334338I
b = 1.45957 − 1.45839I
−3.56505 − 0.39935I −8.06966 + 3.91986I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = −1.94322 − 0.67631I
b = 0.907703 − 0.020698I
−3.56505 − 2.66181I −8.06966 + 4.94144I
u = 0.339110 + 0.822375I
a = 2.07524 + 0.18802I
b = −1.110880 + 0.009680I
−6.76512 + 1.04791I −11.20781 + 0.86269I
u = 0.339110 + 0.822375I
a = −2.20176 + 0.11125I
b = 1.214990 + 0.024941I
−2.22602 + 4.91296I −6.05644 − 0.86352I
u = 0.339110 + 0.822375I
a = 0.89017 + 2.14189I
b = 0.0490156 + 0.0408516I
−3.56505 − 0.39935I −8.06966 + 3.91986I
u = 0.339110 + 0.822375I
a = −0.49932 − 2.38574I
b = −0.321280 − 0.041968I
−6.76512 − 4.10907I −11.20781 + 7.99861I
u = 0.339110 + 0.822375I
a = 0.27257 + 2.56443I
b = 0.483459 − 0.000726I
−2.22602 − 7.97412I −6.05644 + 9.72482I
u = 0.339110 − 0.822375I
a = −0.367485 − 0.952224I
b = 0.10278 − 1.82740I
−3.56505 + 2.66181I −8.06966 − 4.94144I
u = 0.339110 − 0.822375I
a = −0.922856 + 0.158406I
b = 1.148420 + 0.607014I
−3.76067 + 1.53058I −3.59042 − 4.43065I
u = 0.339110 − 0.822375I
a = 1.073940 + 0.580876I
b = −1.58109 − 0.31189I
1.89703 + 1.53058I −1.62085 − 4.43065I
u = 0.339110 − 0.822375I
a = 0.466007 + 1.158660I
b = −0.54911 + 1.77038I
−6.76512 − 1.04791I −11.20781 − 0.86269I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 − 0.822375I
a = −0.546602 − 1.252020I
b = 0.83813 − 1.77295I
−2.22602 − 4.91296I −6.05644 + 0.86352I
u = 0.339110 − 0.822375I
a = −0.206431 − 0.502758I
b = 2.01649 + 1.09378I
−2.22602 + 7.97412I −6.05644 − 9.72482I
u = 0.339110 − 0.822375I
a = 0.13870 − 1.45366I
b = 0.182681 − 0.812651I
−3.76067 + 1.53058I −3.59042 − 4.43065I
u = 0.339110 − 0.822375I
a = 0.181301 + 0.315913I
b = −1.79265 − 1.21965I
−6.76512 + 4.10907I −11.20781 − 7.99861I
u = 0.339110 − 0.822375I
a = 0.35344 + 1.77685I
b = −0.841882 + 0.686202I
1.89703 + 1.53058I −1.62085 − 4.43065I
u = 0.339110 − 0.822375I
a = −0.0634617 − 0.0334338I
b = 1.45957 + 1.45839I
−3.56505 + 0.39935I −8.06966 − 3.91986I
u = 0.339110 − 0.822375I
a = −1.94322 + 0.67631I
b = 0.907703 + 0.020698I
−3.56505 + 2.66181I −8.06966 − 4.94144I
u = 0.339110 − 0.822375I
a = 2.07524 − 0.18802I
b = −1.110880 − 0.009680I
−6.76512 − 1.04791I −11.20781 − 0.86269I
u = 0.339110 − 0.822375I
a = −2.20176 − 0.11125I
b = 1.214990 − 0.024941I
−2.22602 − 4.91296I −6.05644 + 0.86352I
u = 0.339110 − 0.822375I
a = 0.89017 − 2.14189I
b = 0.0490156 − 0.0408516I
−3.56505 + 0.39935I −8.06966 − 3.91986I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 − 0.822375I
a = −0.49932 + 2.38574I
b = −0.321280 + 0.041968I
−6.76512 + 4.10907I −11.20781 − 7.99861I
u = 0.339110 − 0.822375I
a = 0.27257 − 2.56443I
b = 0.483459 + 0.000726I
−2.22602 + 7.97412I −6.05644 − 9.72482I
u = −0.766826
a = 1.05576
b = −0.497603
−1.68869 −2.62440
u = −0.766826
a = −0.370286 + 0.780866I
b = −0.283945 − 0.598788I
3.96901 −6 − 0.654819 + 0.10I
u = −0.766826
a = −0.370286 − 0.780866I
b = −0.283945 + 0.598788I
3.96901 −6 − 0.654819 + 0.10I
u = −0.766826
a = 0.903923 + 0.982518I
b = −1.135410 − 0.409074I
−4.69313 − 2.57849I −10.24178 + 3.56796I
u = −0.766826
a = 0.903923 − 0.982518I
b = −1.135410 + 0.409074I
−4.69313 + 2.57849I −10.24178 − 3.56796I
u = −0.766826
a = −0.648913
b = 0.809583
−1.68869 −2.62440
u = −0.766826
a = −1.174490 + 0.730601I
b = 1.195840 − 0.182400I
−1.49307 − 1.13123I −7.10363 + 0.51079I
u = −0.766826
a = −1.174490 − 0.730601I
b = 1.195840 + 0.182400I
−1.49307 + 1.13123I −7.10363 − 0.51079I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.766826
a = −0.761892 + 1.188100I
b = 1.117810 − 0.572107I
−0.15404 + 6.44354I −5.09041 − 5.29417I
u = −0.766826
a = −0.761892 − 1.188100I
b = 1.117810 + 0.572107I
−0.15404 − 6.44354I −5.09041 + 5.29417I
u = −0.766826
a = −1.48066 + 0.53346I
b = 0.693152 − 0.753420I
−4.69313 + 2.57849I −10.24178 − 3.56796I
u = −0.766826
a = −1.48066 − 0.53346I
b = 0.693152 + 0.753420I
−4.69313 − 2.57849I −10.24178 + 3.56796I
u = −0.766826
a = 1.55946 + 0.23786I
b = −0.900629 − 0.560243I
−1.49307 + 1.13123I −7.10363 − 0.51079I
u = −0.766826
a = 1.55946 − 0.23786I
b = −0.900629 + 0.560243I
−1.49307 − 1.13123I −7.10363 + 0.51079I
u = −0.766826
a = 1.45770 + 0.74607I
b = −0.584238 − 0.911062I
−0.15404 − 6.44354I −5.09041 + 5.29417I
u = −0.766826
a = 1.45770 − 0.74607I
b = −0.584238 + 0.911062I
−0.15404 + 6.44354I −5.09041 − 5.29417I
u = −0.455697 + 1.200150I
a = −0.901615 − 0.399433I
b = 1.33408 − 1.51873I
3.31744 + 10.84440I −1.82724 − 8.79276I
u = −0.455697 + 1.200150I
a = 0.911125 + 0.324769I
b = −0.783801 + 0.570300I
1.78280 + 4.40083I 0.63878 − 3.49859I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455697 + 1.200150I
a = 0.850967 + 0.443554I
b = −1.36424 + 1.32767I
−1.22165 + 6.97933I −6.97861 − 7.06654I
u = −0.455697 + 1.200150I
a = −0.785387 − 0.510249I
b = 1.44471 − 1.03945I
1.97842 + 3.26960I −3.84046 − 2.98779I
u = −0.455697 + 1.200150I
a = −0.276309 − 0.774749I
b = 0.621358 − 0.359220I
1.97842 + 5.53207I −3.84046 − 4.00938I
u = −0.455697 + 1.200150I
a = −1.199160 − 0.026312I
b = 0.539500 − 0.744228I
7.44049 + 4.40083I 2.60835 − 3.49859I
u = −0.455697 + 1.200150I
a = 0.531846 − 0.561321I
b = 0.059879 + 0.229413I
3.31744 − 2.04270I −1.82724 + 1.79559I
u = −0.455697 + 1.200150I
a = −0.632043 − 0.413099I
b = 0.804969 − 0.945492I
1.78280 + 4.40083I 0.63878 − 3.49859I
u = −0.455697 + 1.200150I
a = 0.691152 + 0.187097I
b = −0.57803 + 1.42718I
7.44049 + 4.40083I 2.60835 − 3.49859I
u = −0.455697 + 1.200150I
a = 1.156440 + 0.764669I
b = −0.970275 + 0.710064I
1.97842 + 3.26960I −3.84046 − 2.98779I
u = −0.455697 + 1.200150I
a = 0.433409 + 0.353168I
b = −1.055730 − 0.021438I
1.97842 + 5.53207I −3.84046 − 4.00938I
u = −0.455697 + 1.200150I
a = −1.34408 − 0.62637I
b = 0.920116 − 0.819164I
−1.22165 + 6.97933I −6.97861 − 7.06654I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455697 + 1.200150I
a = −0.094497 + 0.497973I
b = −0.170473 + 0.214897I
−1.22165 + 1.82234I −6.97861 + 0.06937I
u = −0.455697 + 1.200150I
a = 1.47489 + 0.55158I
b = −0.890243 + 0.900055I
3.31744 + 10.84440I −1.82724 − 8.79276I
u = −0.455697 + 1.200150I
a = −0.203634 − 0.064723I
b = 0.554582 + 0.340336I
−1.22165 + 1.82234I −6.97861 + 0.06937I
u = −0.455697 + 1.200150I
a = −0.150510 + 0.107041I
b = −0.431310 − 0.894088I
3.31744 − 2.04270I −1.82724 + 1.79559I
u = −0.455697 − 1.200150I
a = −0.901615 + 0.399433I
b = 1.33408 + 1.51873I
3.31744 − 10.84440I −1.82724 + 8.79276I
u = −0.455697 − 1.200150I
a = 0.911125 − 0.324769I
b = −0.783801 − 0.570300I
1.78280 − 4.40083I 0.63878 + 3.49859I
u = −0.455697 − 1.200150I
a = 0.850967 − 0.443554I
b = −1.36424 − 1.32767I
−1.22165 − 6.97933I −6.97861 + 7.06654I
u = −0.455697 − 1.200150I
a = −0.785387 + 0.510249I
b = 1.44471 + 1.03945I
1.97842 − 3.26960I −3.84046 + 2.98779I
u = −0.455697 − 1.200150I
a = −0.276309 + 0.774749I
b = 0.621358 + 0.359220I
1.97842 − 5.53207I −3.84046 + 4.00938I
u = −0.455697 − 1.200150I
a = −1.199160 + 0.026312I
b = 0.539500 + 0.744228I
7.44049 − 4.40083I 2.60835 + 3.49859I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455697 − 1.200150I
a = 0.531846 + 0.561321I
b = 0.059879 − 0.229413I
3.31744 + 2.04270I −1.82724 − 1.79559I
u = −0.455697 − 1.200150I
a = −0.632043 + 0.413099I
b = 0.804969 + 0.945492I
1.78280 − 4.40083I 0.63878 + 3.49859I
u = −0.455697 − 1.200150I
a = 0.691152 − 0.187097I
b = −0.57803 − 1.42718I
7.44049 − 4.40083I 2.60835 + 3.49859I
u = −0.455697 − 1.200150I
a = 1.156440 − 0.764669I
b = −0.970275 − 0.710064I
1.97842 − 3.26960I −3.84046 + 2.98779I
u = −0.455697 − 1.200150I
a = 0.433409 − 0.353168I
b = −1.055730 + 0.021438I
1.97842 − 5.53207I −3.84046 + 4.00938I
u = −0.455697 − 1.200150I
a = −1.34408 + 0.62637I
b = 0.920116 + 0.819164I
−1.22165 − 6.97933I −6.97861 + 7.06654I
u = −0.455697 − 1.200150I
a = −0.094497 − 0.497973I
b = −0.170473 − 0.214897I
−1.22165 − 1.82234I −6.97861 − 0.06937I
u = −0.455697 − 1.200150I
a = 1.47489 − 0.55158I
b = −0.890243 − 0.900055I
3.31744 − 10.84440I −1.82724 + 8.79276I
u = −0.455697 − 1.200150I
a = −0.203634 + 0.064723I
b = 0.554582 − 0.340336I
−1.22165 − 1.82234I −6.97861 − 0.06937I
u = −0.455697 − 1.200150I
a = −0.150510 − 0.107041I
b = −0.431310 + 0.894088I
3.31744 + 2.04270I −1.82724 − 1.79559I
19
III. I
u
3
= h−9u
24
− 37u
23
+ · · · + b + 37, −37u
24
− 231u
23
+ · · · + a −
6, u
25
+ 6u
24
+ · · · + 5u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
37u
24
+ 231u
23
+ ··· + 89u + 6
9u
24
+ 37u
23
+ ··· − 179u − 37
a
10
=
59u
24
+ 357u
23
+ ··· + 23u − 13
2u
24
− 22u
22
+ ··· − 121u − 24
a
8
=
46u
24
+ 268u
23
+ ··· − 90u − 31
9u
24
+ 37u
23
+ ··· − 179u − 37
a
3
=
2u
24
+ 13u
23
+ ··· + 28u + 6
u
24
+ 6u
23
+ ··· + u − 1
a
7
=
−33u
24
− 167u
23
+ ··· + 327u + 70
18u
24
+ 122u
23
+ ··· + 122u + 16
a
11
=
4u
24
+ 14u
23
+ ··· − 63u − 10
−2u
24
− 7u
23
+ ··· + 62u + 11
a
12
=
u
24
+ 5u
23
+ ··· − 20u − 6
−u
24
− 7u
23
+ ··· − 10u − 1
a
6
=
−41u
24
− 232u
23
+ ··· + 170u + 45
6u
24
+ 56u
23
+ ··· + 158u + 26
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −25u
24
− 177u
23
− 829u
22
− 2723u
21
− 7226u
20
− 15772u
19
− 29737u
18
− 48930u
17
−
72023u
16
− 95436u
15
− 115378u
14
− 127790u
13
− 130502u
12
− 123370u
11
− 107948u
10
−
87762u
9
−65715u
8
−45408u
7
−28463u
6
−16040u
5
−7996u
4
−3326u
3
−1187u
2
−278u −47
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 6u
24
+ ··· + 5u − 1
c
2
, c
7
u
25
+ u
24
+ ··· − 8u
2
+ 1
c
3
, c
9
u
25
− u
24
+ ··· + 8u
2
− 1
c
4
u
25
+ 6u
24
+ ··· + 5u + 1
c
5
, c
6
u
25
− 12u
23
+ ··· + 3u + 1
c
8
, c
12
u
25
− u
24
+ ··· + u + 1
c
10
u
25
− 3u
24
+ ··· + 3u − 1
c
11
u
25
− 12u
23
+ ··· + 3u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
25
+ 18y
24
+ ··· − 17y − 1
c
2
, c
3
, c
7
c
9
y
25
− 25y
24
+ ··· + 16y − 1
c
5
, c
6
, c
11
y
25
− 24y
24
+ ··· + 9y − 1
c
8
, c
12
y
25
− 3y
24
+ ··· − 3y − 1
c
10
y
25
+ 5y
24
+ ··· + 11y − 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.340280 + 0.970760I
a = 0.733035 + 0.521131I
b = −0.256456 + 0.888932I
−2.20822 − 2.79065I −0.19722 + 5.18724I
u = 0.340280 − 0.970760I
a = 0.733035 − 0.521131I
b = −0.256456 − 0.888932I
−2.20822 + 2.79065I −0.19722 − 5.18724I
u = −0.891094
a = −0.881711
b = 0.785688
−2.38230 −17.1210
u = 0.554051 + 0.677642I
a = −0.056453 − 0.756727I
b = 0.481512 − 0.457520I
−4.53381 − 0.67178I −10.16652 − 1.08812I
u = 0.554051 − 0.677642I
a = −0.056453 + 0.756727I
b = 0.481512 + 0.457520I
−4.53381 + 0.67178I −10.16652 + 1.08812I
u = 0.181522 + 0.834696I
a = −1.03147 − 1.16547I
b = 0.785575 − 1.072520I
−3.03532 + 0.50472I −2.24331 − 3.79308I
u = 0.181522 − 0.834696I
a = −1.03147 + 1.16547I
b = 0.785575 + 1.072520I
−3.03532 − 0.50472I −2.24331 + 3.79308I
u = −0.538681 + 1.071460I
a = 1.200210 + 0.187835I
b = −0.84779 + 1.18479I
6.00109 + 7.29942I −2.15509 − 5.87834I
u = −0.538681 − 1.071460I
a = 1.200210 − 0.187835I
b = −0.84779 − 1.18479I
6.00109 − 7.29942I −2.15509 + 5.87834I
u = −0.386902 + 1.136400I
a = 0.831743 + 0.795993I
b = −1.226370 + 0.637222I
4.07499 + 3.15086I 1.69913 − 3.52727I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.386902 − 1.136400I
a = 0.831743 − 0.795993I
b = −1.226370 − 0.637222I
4.07499 − 3.15086I 1.69913 + 3.52727I
u = 0.141401 + 0.765915I
a = 0.93288 + 1.45565I
b = −0.982993 + 0.920335I
−6.37841 − 2.94813I −8.04865 + 1.32415I
u = 0.141401 − 0.765915I
a = 0.93288 − 1.45565I
b = −0.982993 − 0.920335I
−6.37841 + 2.94813I −8.04865 − 1.32415I
u = −0.487588 + 1.143510I
a = −0.921982 − 0.433012I
b = 0.944703 − 0.843167I
0.70838 + 4.90768I −7.77575 − 6.66550I
u = −0.487588 − 1.143510I
a = −0.921982 + 0.433012I
b = 0.944703 + 0.843167I
0.70838 − 4.90768I −7.77575 + 6.66550I
u = 0.079572 + 0.746253I
a = −0.98768 − 1.67072I
b = 1.16819 − 0.87000I
−1.83007 − 6.62683I −2.82890 + 4.28250I
u = 0.079572 − 0.746253I
a = −0.98768 + 1.67072I
b = 1.16819 + 0.87000I
−1.83007 + 6.62683I −2.82890 − 4.28250I
u = −0.911745 + 0.923852I
a = −0.294927 + 0.558621I
b = −0.247185 − 0.781789I
4.88033 − 1.87857I 5.35915 + 0.90270I
u = −0.911745 − 0.923852I
a = −0.294927 − 0.558621I
b = −0.247185 + 0.781789I
4.88033 + 1.87857I 5.35915 − 0.90270I
u = −0.36759 + 1.47078I
a = −0.220626 − 0.390624I
b = 0.655619 − 0.180904I
1.63072 + 6.74212I −7.67319 − 10.61500I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.36759 − 1.47078I
a = −0.220626 + 0.390624I
b = 0.655619 + 0.180904I
1.63072 − 6.74212I −7.67319 + 10.61500I
u = −0.231611 + 0.293375I
a = 2.01917 + 2.37829I
b = −1.165390 + 0.041539I
1.50367 + 0.07763I −4.28149 + 0.94334I
u = −0.231611 − 0.293375I
a = 2.01917 − 2.37829I
b = −1.165390 − 0.041539I
1.50367 − 0.07763I −4.28149 − 0.94334I
u = −0.92717 + 1.53126I
a = 0.236952 − 0.011389I
b = −0.202255 + 0.373394I
−1.26713 + 2.06104I 0
u = −0.92717 − 1.53126I
a = 0.236952 + 0.011389I
b = −0.202255 − 0.373394I
−1.26713 − 2.06104I 0
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
16
)(u
25
− 6u
24
+ ··· + 5u − 1)
· (u
38
− 21u
37
+ ··· − 4864u + 256)
c
2
, c
7
(u
25
+ u
24
+ ··· − 8u
2
+ 1)(u
38
− u
37
+ ··· − u + 1)
· (u
80
− u
79
+ ··· + 99094u − 20507)
c
3
, c
9
(u
25
− u
24
+ ··· + 8u
2
− 1)(u
38
− u
37
+ ··· − u + 1)
· (u
80
− u
79
+ ··· + 99094u − 20507)
c
4
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
16
)(u
25
+ 6u
24
+ ··· + 5u + 1)
· (u
38
− 21u
37
+ ··· − 4864u + 256)
c
5
, c
6
((u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
10
)(u
25
− 12u
23
+ ··· + 3u + 1)
· (u
38
+ 11u
37
+ ··· − 64u + 32)
c
8
, c
12
(u
25
− u
24
+ ··· + u + 1)(u
38
+ u
37
+ ··· + 4u + 1)
· (u
80
+ 5u
79
+ ··· − 22u − 1)
c
10
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
10
· (u
25
− 3u
24
+ ··· + 3u − 1)(u
38
− 30u
37
+ ··· − 1495744u + 104800)
c
11
((u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
10
)(u
25
− 12u
23
+ ··· + 3u − 1)
· (u
38
+ 11u
37
+ ··· − 64u + 32)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
16
)(y
25
+ 18y
24
+ ··· − 17y − 1)
· (y
38
+ 21y
37
+ ··· + 262144y + 65536)
c
2
, c
3
, c
7
c
9
(y
25
− 25y
24
+ ··· + 16y − 1)(y
38
− 29y
37
+ ··· + 5y + 1)
· (y
80
− 65y
79
+ ··· − 11196460816y + 420537049)
c
5
, c
6
, c
11
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
10
· (y
25
− 24y
24
+ ··· + 9y − 1)(y
38
− 31y
37
+ ··· + 2560y + 1024)
c
8
, c
12
(y
25
− 3y
24
+ ··· − 3y − 1)(y
38
+ 9y
37
+ ··· + 40y + 1)
· (y
80
− 13y
79
+ ··· − 92y + 1)
c
10
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
10
· (y
25
+ 5y
24
+ ··· + 11y − 1)
· (y
38
+ 10y
37
+ ··· − 49765582336y + 10983040000)
27
