12a
0788
(K12a
0788
)
A knot diagram
1
Linearized knot diagam
3 8 11 10 1 4 2 5 12 7 6 9
Solving Sequence
2,8 3,11
4 1 7 6 10 5 9 12
c
2
c
3
c
1
c
7
c
6
c
10
c
4
c
8
c
12
c
5
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.48372 × 10
14
u
59
− 1.40888 × 10
16
u
58
+ ··· + 1.09132 × 10
11
b + 1.02559 × 10
18
,
− 1.00155 × 10
15
u
59
− 1.85343 × 10
16
u
58
+ ··· + 2.18264 × 10
11
a + 9.84042 × 10
17
,
u
60
+ 20u
59
+ ··· − 27648u − 2048i
I
u
2
= h1.40209 × 10
270
a
21
u
5
+ 1.35540 × 10
271
a
20
u
5
+ ··· − 1.14418 × 10
274
a − 7.36836 × 10
272
,
− 3a
21
u
5
+ 2a
20
u
5
+ ··· + 91a + 98, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
u
3
= h−2121378380u
44
+ 1708716794u
43
+ ··· + 57230447b − 2318247446,
− 2318247446u
44
+ 2515116512u
43
+ ··· + 57230447a − 1658167052, u
45
− 2u
44
+ ··· + 2u − 1i
I
u
4
= hb − 1, a − u − 1, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 239 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−7.48 × 10
14
u
59
− 1.41 × 10
16
u
58
+ · · · + 1.09 × 10
11
b + 1.03 ×
10
18
, −1.00 × 10
15
u
59
− 1.85 × 10
16
u
58
+ · · · + 2.18 × 10
11
a + 9.84 ×
10
17
, u
60
+ 20u
59
+ · · · − 27648u − 2048i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
11
=
4588.72u
59
+ 84916.9u
58
+ ··· − 6.02606 × 10
7
u − 4.50849 × 10
6
6857.49u
59
+ 129098.u
58
+ ··· − 1.22360 × 10
8
u − 9.39770 × 10
6
a
4
=
250.351u
59
+ 5495.68u
58
+ ··· − 1.44691 × 10
7
u − 1.15895 × 10
6
−488.667u
59
− 8145.45u
58
+ ··· − 5.76275 × 10
6
u − 512719.
a
1
=
−u
2
+ 1
−u
4
a
7
=
u
u
a
6
=
1325.73u
59
+ 24882.4u
58
+ ··· − 2.45048 × 10
7
u − 1.89309 × 10
6
1986.08u
59
+ 36969.0u
58
+ ··· − 3.14103 × 10
7
u − 2.40620 × 10
6
a
10
=
3514.76u
59
+ 67929.5u
58
+ ··· − 8.86252 × 10
7
u − 6.95375 × 10
6
5783.53u
59
+ 112111.u
58
+ ··· − 1.50725 × 10
8
u − 1.18430 × 10
7
a
5
=
238.438u
59
+ 3950.12u
58
+ ··· + 5.58629 × 10
6
u + 496872.
−218.983u
59
− 5479.84u
58
+ ··· + 2.60400 × 10
7
u + 2.13851 × 10
6
a
9
=
−129.456u
59
− 2345.21u
58
+ ··· + 2.05852 × 10
6
u + 170613.
−1118.08u
59
− 21011.6u
58
+ ··· + 2.28800 × 10
7
u + 1.79800 × 10
6
a
12
=
−1645.01u
59
− 30594.3u
58
+ ··· + 2.26877 × 10
7
u + 1.70023 × 10
6
−3467.72u
59
− 64602.7u
58
+ ··· + 5.02340 × 10
7
u + 3.79319 × 10
6
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
36746774069337
13641503552
u
59
+
1434372875041167
27283007104
u
58
+ ··· −
15915677814015894
213148493
u −
1254542070951070
213148493
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
60
+ 34u
59
+ ··· + 13631488u + 4194304
c
2
, c
7
u
60
− 20u
59
+ ··· + 27648u − 2048
c
3
, c
10
u
60
+ 2u
59
+ ··· + 4u − 1
c
4
, c
11
u
60
+ 7u
58
+ ··· − 2u − 21
c
5
, c
8
u
60
+ 4u
59
+ ··· + 23u − 1
c
6
u
60
− 41u
59
+ ··· − 416u + 64
c
9
, c
12
u
60
− 21u
59
+ ··· − 66560u + 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
60
− 14y
59
+ ··· + 355142255771648y + 17592186044416
c
2
, c
7
y
60
− 34y
59
+ ··· − 13631488y + 4194304
c
3
, c
10
y
60
+ 10y
59
+ ··· + 18y + 1
c
4
, c
11
y
60
+ 14y
59
+ ··· + 2768y + 441
c
5
, c
8
y
60
− 30y
59
+ ··· − 629y + 1
c
6
y
60
− 7y
59
+ ··· − 119808y + 4096
c
9
, c
12
y
60
+ 29y
59
+ ··· + 103809024y + 16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.333620 + 0.934820I
a = 0.674936 + 1.218260I
b = 1.364030 − 0.224508I
2.2681 − 15.8299I 0
u = −0.333620 − 0.934820I
a = 0.674936 − 1.218260I
b = 1.364030 + 0.224508I
2.2681 + 15.8299I 0
u = −0.313471 + 0.961263I
a = −0.601185 − 1.165240I
b = −1.308550 + 0.212628I
−1.49873 − 9.71181I 0
u = −0.313471 − 0.961263I
a = −0.601185 + 1.165240I
b = −1.308550 − 0.212628I
−1.49873 + 9.71181I 0
u = 0.944174 + 0.249030I
a = −0.081713 + 0.383364I
b = 0.172621 − 0.341613I
−0.507559 − 0.907664I 0
u = 0.944174 − 0.249030I
a = −0.081713 − 0.383364I
b = 0.172621 + 0.341613I
−0.507559 + 0.907664I 0
u = −0.697333 + 0.759169I
a = 0.809520 + 0.902124I
b = 1.249370 + 0.014518I
3.10973 + 0.23218I 0
u = −0.697333 − 0.759169I
a = 0.809520 − 0.902124I
b = 1.249370 − 0.014518I
3.10973 − 0.23218I 0
u = −0.145685 + 0.934102I
a = −0.001093 − 0.424826I
b = −0.396990 − 0.060870I
0.27991 − 2.30790I 0
u = −0.145685 − 0.934102I
a = −0.001093 + 0.424826I
b = −0.396990 + 0.060870I
0.27991 + 2.30790I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.780293 + 0.715158I
a = −0.08445 − 1.54692I
b = −1.17219 − 1.14665I
7.75560 + 1.60562I 0
u = −0.780293 − 0.715158I
a = −0.08445 + 1.54692I
b = −1.17219 + 1.14665I
7.75560 − 1.60562I 0
u = −0.187677 + 0.905842I
a = 0.367951 + 1.279140I
b = 1.227760 − 0.093240I
4.33323 − 3.97038I 0
u = −0.187677 − 0.905842I
a = 0.367951 − 1.279140I
b = 1.227760 + 0.093240I
4.33323 + 3.97038I 0
u = −0.303550 + 1.037960I
a = 0.270953 + 0.350153I
b = 0.445694 − 0.174951I
2.68007 − 6.88503I 0
u = −0.303550 − 1.037960I
a = 0.270953 − 0.350153I
b = 0.445694 + 0.174951I
2.68007 + 6.88503I 0
u = −0.848038 + 0.707790I
a = −1.104920 − 0.731601I
b = −1.45484 + 0.16163I
7.56196 + 3.77097I 0
u = −0.848038 − 0.707790I
a = −1.104920 + 0.731601I
b = −1.45484 − 0.16163I
7.56196 − 3.77097I 0
u = −1.070680 + 0.508372I
a = 1.26524 + 0.88222I
b = 1.80317 + 0.30136I
1.92878 + 5.49302I 0
u = −1.070680 − 0.508372I
a = 1.26524 − 0.88222I
b = 1.80317 − 0.30136I
1.92878 − 5.49302I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.824091 + 0.858404I
a = −0.070507 − 1.171040I
b = −1.063330 − 0.904520I
5.37941 + 11.52000I 0
u = −0.824091 − 0.858404I
a = −0.070507 + 1.171040I
b = −1.063330 + 0.904520I
5.37941 − 11.52000I 0
u = −0.905721 + 0.787538I
a = 0.293055 + 1.287800I
b = 1.27962 + 0.93560I
2.52360 + 5.52538I 0
u = −0.905721 − 0.787538I
a = 0.293055 − 1.287800I
b = 1.27962 − 0.93560I
2.52360 − 5.52538I 0
u = −0.420754 + 0.679305I
a = −0.26528 − 1.64093I
b = −1.226310 − 0.510218I
3.52442 − 0.82636I 0
u = −0.420754 − 0.679305I
a = −0.26528 + 1.64093I
b = −1.226310 + 0.510218I
3.52442 + 0.82636I 0
u = −1.075920 + 0.562568I
a = −1.32077 − 1.35476I
b = −2.18319 − 0.71459I
1.61159 + 5.63980I 0
u = −1.075920 − 0.562568I
a = −1.32077 + 1.35476I
b = −2.18319 + 0.71459I
1.61159 − 5.63980I 0
u = −0.838313 + 0.884571I
a = −0.727740 − 0.574385I
b = −1.118160 + 0.162223I
5.35357 − 5.24503I 0
u = −0.838313 − 0.884571I
a = −0.727740 + 0.574385I
b = −1.118160 − 0.162223I
5.35357 + 5.24503I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.159010 + 0.393572I
a = 0.221908 − 0.440917I
b = −0.430725 + 0.423688I
0.101185 − 0.165210I 0
u = 1.159010 − 0.393572I
a = 0.221908 + 0.440917I
b = −0.430725 − 0.423688I
0.101185 + 0.165210I 0
u = −0.456971 + 0.622877I
a = −0.07193 + 1.60525I
b = 0.967003 + 0.778358I
3.74351 − 1.00486I 0
u = −0.456971 − 0.622877I
a = −0.07193 − 1.60525I
b = 0.967003 − 0.778358I
3.74351 + 1.00486I 0
u = −1.079430 + 0.603300I
a = 0.80779 + 1.26432I
b = 1.63471 + 0.87741I
1.49576 + 5.38757I 0
u = −1.079430 − 0.603300I
a = 0.80779 − 1.26432I
b = 1.63471 − 0.87741I
1.49576 − 5.38757I 0
u = 0.733772
a = 0.687778
b = −0.504672
−1.46322 0
u = 1.324830 + 0.182582I
a = 0.269732 − 0.353967I
b = −0.421977 + 0.419697I
−3.44520 + 12.20910I 0
u = 1.324830 − 0.182582I
a = 0.269732 + 0.353967I
b = −0.421977 − 0.419697I
−3.44520 − 12.20910I 0
u = −1.184740 + 0.623579I
a = 1.01088 + 1.65429I
b = 2.22921 + 1.32954I
−0.3203 + 21.5045I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.184740 − 0.623579I
a = 1.01088 − 1.65429I
b = 2.22921 − 1.32954I
−0.3203 − 21.5045I 0
u = −1.198680 + 0.625931I
a = −1.00532 − 1.57397I
b = −2.19026 − 1.25744I
−4.1959 + 15.4585I 0
u = −1.198680 − 0.625931I
a = −1.00532 + 1.57397I
b = −2.19026 + 1.25744I
−4.1959 − 15.4585I 0
u = −1.232080 + 0.594174I
a = −0.480166 − 0.705714I
b = −1.010920 − 0.584195I
−2.90188 + 7.84313I 0
u = −1.232080 − 0.594174I
a = −0.480166 + 0.705714I
b = −1.010920 + 0.584195I
−2.90188 − 7.84313I 0
u = −1.357810 + 0.168665I
a = −0.502833 + 0.534844I
b = −0.592539 + 0.811023I
−5.60267 + 3.59176I 0
u = −1.357810 − 0.168665I
a = −0.502833 − 0.534844I
b = −0.592539 − 0.811023I
−5.60267 − 3.59176I 0
u = −1.238410 + 0.587165I
a = 1.17216 + 1.44428I
b = 2.29964 + 1.10036I
1.18187 + 9.43402I 0
u = −1.238410 − 0.587165I
a = 1.17216 − 1.44428I
b = 2.29964 − 1.10036I
1.18187 − 9.43402I 0
u = −1.214920 + 0.640884I
a = 0.325458 + 0.864460I
b = 0.949425 + 0.841673I
−0.12077 + 12.85670I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.214920 − 0.640884I
a = 0.325458 − 0.864460I
b = 0.949425 − 0.841673I
−0.12077 − 12.85670I 0
u = 1.376690 + 0.208793I
a = −0.227645 + 0.340466I
b = 0.384484 − 0.421186I
−7.27211 + 5.75378I 0
u = 1.376690 − 0.208793I
a = −0.227645 − 0.340466I
b = 0.384484 + 0.421186I
−7.27211 − 5.75378I 0
u = 1.41503 + 0.05159I
a = 0.189430 + 0.088042I
b = −0.263507 − 0.134354I
−4.01041 + 2.67707I 0
u = 1.41503 − 0.05159I
a = 0.189430 − 0.088042I
b = −0.263507 + 0.134354I
−4.01041 − 2.67707I 0
u = 0.362341 + 0.451988I
a = 0.473557 + 0.229618I
b = −0.067805 − 0.297242I
−0.34589 − 1.42851I 0
u = 0.362341 − 0.451988I
a = 0.473557 − 0.229618I
b = −0.067805 + 0.297242I
−0.34589 + 1.42851I 0
u = 1.58428 + 0.31201I
a = −0.0680742 − 0.0136247I
b = 0.1035970 + 0.0428251I
−4.90655 − 3.22898I 0
u = 1.58428 − 0.31201I
a = −0.0680742 + 0.0136247I
b = 0.1035970 − 0.0428251I
−4.90655 + 3.22898I 0
u = −1.65006
a = −1.76564
b = −2.91341
−9.98161 0
10
II. I
u
2
= h1.40 × 10
270
a
21
u
5
+ 1.36 × 10
271
a
20
u
5
+ · · · − 1.14 × 10
274
a −
7.37 × 10
272
, −3a
21
u
5
+ 2a
20
u
5
+ · · · + 91a + 98, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
11
=
a
−0.000363549a
21
u
5
− 0.00351444a
20
u
5
+ ··· + 2.96676a + 0.191055
a
4
=
0.000759916a
21
u
5
− 0.000594802a
20
u
5
+ ··· − 1.22098a + 1.04533
−0.00153762a
21
u
5
− 0.00216772a
20
u
5
+ ··· − 2.50590a + 1.50725
a
1
=
−u
2
+ 1
−u
4
a
7
=
u
u
a
6
=
−0.00106816a
21
u
5
+ 0.00333324a
20
u
5
+ ··· + 1.71747a − 0.564711
−0.00254284a
21
u
5
+ 0.00301452a
20
u
5
+ ··· + 3.28250a − 2.04730
a
10
=
0.0000888451a
21
u
5
− 0.0000384555a
20
u
5
+ ··· + 5.04034a − 2.00457
−0.000274704a
21
u
5
− 0.00355290a
20
u
5
+ ··· + 7.00710a − 1.81352
a
5
=
−0.00102679a
21
u
5
+ 0.00234859a
20
u
5
+ ··· + 0.564123a + 0.490125
−0.00183032a
21
u
5
+ 0.00341665a
20
u
5
+ ··· + 1.51139a − 1.71646
a
9
=
−0.00165500a
21
u
5
+ 0.00153794a
20
u
5
+ ··· − 3.86117a + 1.10515
−0.000225977a
21
u
5
− 0.00143759a
20
u
5
+ ··· − 9.27202a + 1.99918
a
12
=
0.00102916a
21
u
5
− 0.00283999a
20
u
5
+ ··· − 6.13904a + 1.54232
0.00177077a
21
u
5
− 0.00397137a
20
u
5
+ ··· − 3.96200a + 2.57725
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −8.89321 × 10
−7
a
21
u
5
+ 0.0105424a
20
u
5
+ ··· − 6.69822a − 15.5822
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
22
c
2
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
22
c
3
, c
10
u
132
+ 3u
131
+ ··· + 1266u + 83
c
4
, c
11
u
132
+ u
131
+ ··· + 14455610u + 3138347
c
5
, c
8
u
132
− u
131
+ ··· − 758u + 67
c
6
(u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
12
c
9
, c
12
(u
11
+ 3u
10
+ ··· + 2u + 1)
12
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
22
c
2
, c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
22
c
3
, c
10
y
132
− 45y
131
+ ··· − 1080188y + 6889
c
4
, c
11
y
132
+ 39y
131
+ ··· − 615346853465156y + 9849221892409
c
5
, c
8
y
132
+ 27y
131
+ ··· + 10768000y + 4489
c
6
(y
11
− y
10
+ ··· + 6y −1)
12
c
9
, c
12
(y
11
+ 7y
10
+ ··· − 6y −1)
12
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = −0.639750 − 0.756577I
b = 0.336258 − 0.656288I
−3.39789 + 6.14059I −10.15275 − 9.80700I
u = −1.002190 + 0.295542I
a = 0.158001 + 0.975492I
b = 1.36089 + 1.68840I
1.09519 − 4.07643I −1.87613 + 5.43329I
u = −1.002190 + 0.295542I
a = −1.002450 + 0.210092I
b = 0.227642 + 0.569565I
−4.33844 + 3.62871I −13.18434 − 0.71090I
u = −1.002190 + 0.295542I
a = −0.674793 + 0.781681I
b = −1.46049 + 0.69130I
−3.95954 + 3.17209I −13.3525 − 5.8578I
u = −1.002190 + 0.295542I
a = 0.008409 − 0.917004I
b = 0.931121 − 0.184282I
−4.33844 − 1.78010I −13.18434 − 0.87755I
u = −1.002190 + 0.295542I
a = 0.904638 + 0.082895I
b = −0.262585 − 0.921500I
−4.33844 − 1.78010I −13.18434 − 0.87755I
u = −1.002190 + 0.295542I
a = 1.015710 + 0.658026I
b = 1.92772 + 0.15809I
1.09519 + 5.92504I −1.87613 − 7.02174I
u = −1.002190 + 0.295542I
a = 1.078360 − 0.597521I
b = −0.20300 − 1.52029I
−3.95954 − 1.32348I −13.35253 + 4.26937I
u = −1.002190 + 0.295542I
a = −1.049240 − 0.705437I
b = −0.073777 + 0.441684I
−3.39789 − 4.29198I −10.15275 + 8.21855I
u = −1.002190 + 0.295542I
a = 0.486341 − 0.511433I
b = −0.864753 − 0.569164I
−3.39789 + 6.14059I −10.15275 − 9.80700I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 0.054785 + 0.584474I
b = −0.942552 + 0.506817I
−4.33844 + 3.62871I −13.18434 − 0.71090I
u = −1.002190 + 0.295542I
a = 0.22520 − 1.45055I
b = 0.904135 − 0.917533I
−3.95954 − 1.32348I −13.35253 + 4.26937I
u = −1.002190 + 0.295542I
a = −1.52785 + 0.23923I
b = −0.445254 + 0.982825I
−3.95954 + 3.17209I −13.3525 − 5.8578I
u = −1.002190 + 0.295542I
a = −0.187294 + 0.385486I
b = −1.260030 − 0.396890I
−3.39789 − 4.29198I −10.15275 + 8.21855I
u = −1.002190 + 0.295542I
a = 1.72681 + 0.66697I
b = 1.212410 + 0.359284I
1.09519 + 5.92504I −1.87613 − 7.02174I
u = −1.002190 + 0.295542I
a = 0.79220 + 1.91832I
b = 0.446646 + 0.930935I
1.09519 − 4.07643I −1.87613 + 5.43329I
u = −1.002190 + 0.295542I
a = 1.87501 + 2.12992I
b = 2.41815 + 2.28154I
−1.77531 + 6.84873I −12.8872 − 10.8178I
u = −1.002190 + 0.295542I
a = 2.46678 + 1.68983I
b = 2.62310 + 1.84390I
−1.77531 − 5.00012I 0
u = −1.002190 + 0.295542I
a = 1.90880 + 2.40276I
b = 2.97160 + 0.96450I
−1.77531 − 5.00012I 0
u = −1.002190 + 0.295542I
a = −2.32648 − 2.04569I
b = −2.64223 − 2.17398I
−5.91430 + 0.92430I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 1.60219 + 2.74903I
b = 2.50860 + 1.58044I
−1.77531 + 6.84873I 0
u = −1.002190 + 0.295542I
a = −1.83700 − 2.71095I
b = −2.93617 − 1.36260I
−5.91430 + 0.92430I 0
u = −1.002190 − 0.295542I
a = −0.639750 + 0.756577I
b = 0.336258 + 0.656288I
−3.39789 − 6.14059I −10.15275 + 9.80700I
u = −1.002190 − 0.295542I
a = 0.158001 − 0.975492I
b = 1.36089 − 1.68840I
1.09519 + 4.07643I −1.87613 − 5.43329I
u = −1.002190 − 0.295542I
a = −1.002450 − 0.210092I
b = 0.227642 − 0.569565I
−4.33844 − 3.62871I −13.18434 + 0.71090I
u = −1.002190 − 0.295542I
a = −0.674793 − 0.781681I
b = −1.46049 − 0.69130I
−3.95954 − 3.17209I −13.3525 + 5.8578I
u = −1.002190 − 0.295542I
a = 0.008409 + 0.917004I
b = 0.931121 + 0.184282I
−4.33844 + 1.78010I −13.18434 + 0.87755I
u = −1.002190 − 0.295542I
a = 0.904638 − 0.082895I
b = −0.262585 + 0.921500I
−4.33844 + 1.78010I −13.18434 + 0.87755I
u = −1.002190 − 0.295542I
a = 1.015710 − 0.658026I
b = 1.92772 − 0.15809I
1.09519 − 5.92504I −1.87613 + 7.02174I
u = −1.002190 − 0.295542I
a = 1.078360 + 0.597521I
b = −0.20300 + 1.52029I
−3.95954 + 1.32348I −13.35253 − 4.26937I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 − 0.295542I
a = −1.049240 + 0.705437I
b = −0.073777 − 0.441684I
−3.39789 + 4.29198I −10.15275 − 8.21855I
u = −1.002190 − 0.295542I
a = 0.486341 + 0.511433I
b = −0.864753 + 0.569164I
−3.39789 − 6.14059I −10.15275 + 9.80700I
u = −1.002190 − 0.295542I
a = 0.054785 − 0.584474I
b = −0.942552 − 0.506817I
−4.33844 − 3.62871I −13.18434 + 0.71090I
u = −1.002190 − 0.295542I
a = 0.22520 + 1.45055I
b = 0.904135 + 0.917533I
−3.95954 + 1.32348I −13.35253 − 4.26937I
u = −1.002190 − 0.295542I
a = −1.52785 − 0.23923I
b = −0.445254 − 0.982825I
−3.95954 − 3.17209I −13.3525 + 5.8578I
u = −1.002190 − 0.295542I
a = −0.187294 − 0.385486I
b = −1.260030 + 0.396890I
−3.39789 + 4.29198I −10.15275 − 8.21855I
u = −1.002190 − 0.295542I
a = 1.72681 − 0.66697I
b = 1.212410 − 0.359284I
1.09519 − 5.92504I −1.87613 + 7.02174I
u = −1.002190 − 0.295542I
a = 0.79220 − 1.91832I
b = 0.446646 − 0.930935I
1.09519 + 4.07643I −1.87613 − 5.43329I
u = −1.002190 − 0.295542I
a = 1.87501 − 2.12992I
b = 2.41815 − 2.28154I
−1.77531 − 6.84873I −12.8872 + 10.8178I
u = −1.002190 − 0.295542I
a = 2.46678 − 1.68983I
b = 2.62310 − 1.84390I
−1.77531 + 5.00012I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 − 0.295542I
a = 1.90880 − 2.40276I
b = 2.97160 − 0.96450I
−1.77531 + 5.00012I 0
u = −1.002190 − 0.295542I
a = −2.32648 + 2.04569I
b = −2.64223 + 2.17398I
−5.91430 − 0.92430I 0
u = −1.002190 − 0.295542I
a = 1.60219 − 2.74903I
b = 2.50860 − 1.58044I
−1.77531 − 6.84873I 0
u = −1.002190 − 0.295542I
a = −1.83700 + 2.71095I
b = −2.93617 + 1.36260I
−5.91430 − 0.92430I 0
u = 0.428243 + 0.664531I
a = 0.937359 + 0.290616I
b = −0.034445 + 0.972282I
0.38333 − 4.29198I −2.71931 + 8.21855I
u = 0.428243 + 0.664531I
a = 0.888537 + 0.363534I
b = 0.084731 + 0.430342I
−0.55723 − 1.78010I −5.75090 − 0.87755I
u = 0.428243 + 0.664531I
a = 0.513515 − 0.791746I
b = 0.481721 − 0.568584I
−0.178329 − 1.323480I −5.91910 + 4.26937I
u = 0.428243 + 0.664531I
a = 0.274480 + 0.901786I
b = −0.746049 − 0.002187I
−0.178329 − 1.323480I −5.91910 + 4.26937I
u = 0.428243 + 0.664531I
a = 1.007060 − 0.367162I
b = −0.944493 + 0.754666I
−2.13309 + 0.92430I −14.5446 − 0.7942I
u = 0.428243 + 0.664531I
a = −1.010190 − 0.702828I
b = −0.208294 − 0.747359I
0.38333 − 4.29198I −2.71931 + 8.21855I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428243 + 0.664531I
a = −1.307470 − 0.198828I
b = 1.12264 − 1.02990I
2.00590 + 6.84873I −5.45374 − 10.81777I
u = 0.428243 + 0.664531I
a = −1.135580 − 0.768212I
b = 0.788220 − 0.886069I
4.87640 − 4.07643I 5.55731 + 5.43329I
u = 0.428243 + 0.664531I
a = 0.99399 − 1.03232I
b = 1.78426 − 0.19433I
4.87640 + 5.92504I 5.55731 − 7.02174I
u = 0.428243 + 0.664531I
a = −0.515623 − 0.204777I
b = −0.138930 − 0.746141I
−0.55723 − 1.78010I −5.75090 − 0.87755I
u = 0.428243 + 0.664531I
a = 0.40204 + 1.44521I
b = −0.024195 + 1.083610I
4.87640 − 4.07643I 5.55731 + 5.43329I
u = 0.428243 + 0.664531I
a = −0.15524 − 1.52134I
b = −0.675255 − 0.511985I
−2.13309 + 0.92430I −14.5446 − 0.7942I
u = 0.428243 + 0.664531I
a = −1.18622 + 1.07737I
b = −1.309380 + 0.296275I
−0.17833 + 3.17209I −5.91910 − 5.85782I
u = 0.428243 + 0.664531I
a = −1.01261 + 1.34820I
b = −1.62757 − 0.23946I
0.38333 + 6.14059I −2.71931 − 9.80700I
u = 0.428243 + 0.664531I
a = 0.58216 − 1.59522I
b = 1.223930 + 0.326901I
−0.17833 + 3.17209I −5.91910 − 5.85782I
u = 0.428243 + 0.664531I
a = 0.94767 − 1.44455I
b = 1.40651 + 0.32895I
−0.55723 + 3.62871I −5.75090 − 0.71090I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428243 + 0.664531I
a = 0.091076 + 0.184671I
b = 1.42088 − 0.24221I
2.00590 − 5.00012I −5.45374 + 9.22932I
u = 0.428243 + 0.664531I
a = −0.71604 + 1.67673I
b = 0.083717 − 0.139607I
2.00590 − 5.00012I −5.45374 + 9.22932I
u = 0.428243 + 0.664531I
a = −1.31350 + 1.27009I
b = −1.365780 − 0.011137I
−0.55723 + 3.62871I −5.75090 − 0.71090I
u = 0.428243 + 0.664531I
a = 0.32582 + 1.89934I
b = 0.427787 + 0.953999I
2.00590 + 6.84873I −5.45374 − 10.81777I
u = 0.428243 + 0.664531I
a = 1.36981 − 1.56645I
b = 1.329570 + 0.095549I
0.38333 + 6.14059I −2.71931 − 9.80700I
u = 0.428243 + 0.664531I
a = −1.01595 + 2.03029I
b = −1.111680 − 0.218457I
4.87640 + 5.92504I 5.55731 − 7.02174I
u = 0.428243 − 0.664531I
a = 0.937359 − 0.290616I
b = −0.034445 − 0.972282I
0.38333 + 4.29198I −2.71931 − 8.21855I
u = 0.428243 − 0.664531I
a = 0.888537 − 0.363534I
b = 0.084731 − 0.430342I
−0.55723 + 1.78010I −5.75090 + 0.87755I
u = 0.428243 − 0.664531I
a = 0.513515 + 0.791746I
b = 0.481721 + 0.568584I
−0.178329 + 1.323480I −5.91910 − 4.26937I
u = 0.428243 − 0.664531I
a = 0.274480 − 0.901786I
b = −0.746049 + 0.002187I
−0.178329 + 1.323480I −5.91910 − 4.26937I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428243 − 0.664531I
a = 1.007060 + 0.367162I
b = −0.944493 − 0.754666I
−2.13309 − 0.92430I −14.5446 + 0.7942I
u = 0.428243 − 0.664531I
a = −1.010190 + 0.702828I
b = −0.208294 + 0.747359I
0.38333 + 4.29198I −2.71931 − 8.21855I
u = 0.428243 − 0.664531I
a = −1.307470 + 0.198828I
b = 1.12264 + 1.02990I
2.00590 − 6.84873I −5.45374 + 10.81777I
u = 0.428243 − 0.664531I
a = −1.135580 + 0.768212I
b = 0.788220 + 0.886069I
4.87640 + 4.07643I 5.55731 − 5.43329I
u = 0.428243 − 0.664531I
a = 0.99399 + 1.03232I
b = 1.78426 + 0.19433I
4.87640 − 5.92504I 5.55731 + 7.02174I
u = 0.428243 − 0.664531I
a = −0.515623 + 0.204777I
b = −0.138930 + 0.746141I
−0.55723 + 1.78010I −5.75090 + 0.87755I
u = 0.428243 − 0.664531I
a = 0.40204 − 1.44521I
b = −0.024195 − 1.083610I
4.87640 + 4.07643I 5.55731 − 5.43329I
u = 0.428243 − 0.664531I
a = −0.15524 + 1.52134I
b = −0.675255 + 0.511985I
−2.13309 − 0.92430I −14.5446 + 0.7942I
u = 0.428243 − 0.664531I
a = −1.18622 − 1.07737I
b = −1.309380 − 0.296275I
−0.17833 − 3.17209I −5.91910 + 5.85782I
u = 0.428243 − 0.664531I
a = −1.01261 − 1.34820I
b = −1.62757 + 0.23946I
0.38333 − 6.14059I −2.71931 + 9.80700I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428243 − 0.664531I
a = 0.58216 + 1.59522I
b = 1.223930 − 0.326901I
−0.17833 − 3.17209I −5.91910 + 5.85782I
u = 0.428243 − 0.664531I
a = 0.94767 + 1.44455I
b = 1.40651 − 0.32895I
−0.55723 − 3.62871I −5.75090 + 0.71090I
u = 0.428243 − 0.664531I
a = 0.091076 − 0.184671I
b = 1.42088 + 0.24221I
2.00590 + 5.00012I −5.45374 − 9.22932I
u = 0.428243 − 0.664531I
a = −0.71604 − 1.67673I
b = 0.083717 + 0.139607I
2.00590 + 5.00012I −5.45374 − 9.22932I
u = 0.428243 − 0.664531I
a = −1.31350 − 1.27009I
b = −1.365780 + 0.011137I
−0.55723 − 3.62871I −5.75090 + 0.71090I
u = 0.428243 − 0.664531I
a = 0.32582 − 1.89934I
b = 0.427787 − 0.953999I
2.00590 − 6.84873I −5.45374 + 10.81777I
u = 0.428243 − 0.664531I
a = 1.36981 + 1.56645I
b = 1.329570 − 0.095549I
0.38333 − 6.14059I −2.71931 + 9.80700I
u = 0.428243 − 0.664531I
a = −1.01595 − 2.03029I
b = −1.111680 + 0.218457I
4.87640 − 5.92504I 5.55731 + 7.02174I
u = 1.073950 + 0.558752I
a = −0.084014 + 1.015950I
b = −0.837758 + 0.839734I
−2.44783 − 2.98861I −9.46762 + 5.59390I
u = 1.073950 + 0.558752I
a = 0.293747 − 0.934741I
b = 0.657888 − 1.044130I
−2.44783 − 2.98861I −9.46762 + 5.59390I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 + 0.558752I
a = 0.362631 − 0.954585I
b = −0.1327270 − 0.0315553I
0.115297 + 0.231405I −9.17045 − 4.51298I
u = 1.073950 + 0.558752I
a = 0.120889 + 0.856405I
b = −0.070409 + 0.946845I
−1.50728 − 0.47673I −6.43603 − 3.50221I
u = 1.073950 + 0.558752I
a = −1.182070 − 0.073943I
b = −1.50537 − 0.12930I
2.98579 − 0.69228I 1.84059 − 0.71694I
u = 1.073950 + 0.558752I
a = −0.309392 − 0.720678I
b = 0.348689 − 0.987283I
−1.50728 − 0.47673I −6.43603 − 3.50221I
u = 1.073950 + 0.558752I
a = 1.152410 − 0.479176I
b = 1.22817 + 0.73990I
2.98579 − 0.69228I 1.84059 − 0.71694I
u = 1.073950 + 0.558752I
a = 0.911073 + 0.930551I
b = 1.48352 + 0.56702I
−4.02369 − 5.69302I −18.2613 + 5.5106I
u = 1.073950 + 0.558752I
a = −1.303280 + 0.150088I
b = −0.45850 − 1.50843I
−4.02369 − 5.69302I −18.2613 + 5.5106I
u = 1.073950 + 0.558752I
a = 0.97227 − 1.06551I
b = 1.40323 − 1.08047I
−2.06894 − 3.44524I −9.63582 + 0.44697I
u = 1.073950 + 0.558752I
a = −0.61633 + 1.32674I
b = −1.63952 + 0.60105I
−2.06894 − 3.44524I −9.63582 + 0.44697I
u = 1.073950 + 0.558752I
a = −1.39370 − 0.74791I
b = −1.95662 − 0.59736I
0.11530 − 11.61740I −9.1705 + 15.5341I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 + 0.558752I
a = 1.66153 − 0.30823I
b = 1.07887 + 1.58195I
0.11530 − 11.61740I −9.1705 + 15.5341I
u = 1.073950 + 0.558752I
a = −0.69767 + 1.69151I
b = −2.32631 + 1.65114I
2.98579 − 10.69380I 1.84059 + 11.73808I
u = 1.073950 + 0.558752I
a = 0.1092910 − 0.0274790I
b = −0.922823 + 0.822556I
0.115297 + 0.231405I −9.17045 − 4.51298I
u = 1.073950 + 0.558752I
a = 0.63890 − 1.86392I
b = 2.18525 − 1.36863I
−2.06894 − 7.94081I −9.6358 + 10.5742I
u = 1.073950 + 0.558752I
a = −1.07953 + 1.83604I
b = −1.72761 + 1.64477I
−2.06894 − 7.94081I −9.6358 + 10.5742I
u = 1.073950 + 0.558752I
a = 0.89609 − 1.93458I
b = 2.10722 − 1.85079I
−1.50728 − 10.90930I −6.4360 + 14.5233I
u = 1.073950 + 0.558752I
a = 0.70039 − 2.02609I
b = 2.07265 − 1.58800I
−2.44783 − 8.39743I −9.46762 + 5.42724I
u = 1.073950 + 0.558752I
a = −0.91338 + 1.95387I
b = −1.88426 + 1.78457I
−2.44783 − 8.39743I −9.46762 + 5.42724I
u = 1.073950 + 0.558752I
a = −0.83852 + 2.15961I
b = −2.04330 + 1.57695I
−1.50728 − 10.90930I −6.4360 + 14.5233I
u = 1.073950 + 0.558752I
a = 1.07519 − 2.09684I
b = 1.69439 − 1.42677I
2.98579 − 10.69380I 1.84059 + 11.73808I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = −0.084014 − 1.015950I
b = −0.837758 − 0.839734I
−2.44783 + 2.98861I −9.46762 − 5.59390I
u = 1.073950 − 0.558752I
a = 0.293747 + 0.934741I
b = 0.657888 + 1.044130I
−2.44783 + 2.98861I −9.46762 − 5.59390I
u = 1.073950 − 0.558752I
a = 0.362631 + 0.954585I
b = −0.1327270 + 0.0315553I
0.115297 − 0.231405I −9.17045 + 4.51298I
u = 1.073950 − 0.558752I
a = 0.120889 − 0.856405I
b = −0.070409 − 0.946845I
−1.50728 + 0.47673I −6.43603 + 3.50221I
u = 1.073950 − 0.558752I
a = −1.182070 + 0.073943I
b = −1.50537 + 0.12930I
2.98579 + 0.69228I 1.84059 + 0.71694I
u = 1.073950 − 0.558752I
a = −0.309392 + 0.720678I
b = 0.348689 + 0.987283I
−1.50728 + 0.47673I −6.43603 + 3.50221I
u = 1.073950 − 0.558752I
a = 1.152410 + 0.479176I
b = 1.22817 − 0.73990I
2.98579 + 0.69228I 1.84059 + 0.71694I
u = 1.073950 − 0.558752I
a = 0.911073 − 0.930551I
b = 1.48352 − 0.56702I
−4.02369 + 5.69302I −18.2613 − 5.5106I
u = 1.073950 − 0.558752I
a = −1.303280 − 0.150088I
b = −0.45850 + 1.50843I
−4.02369 + 5.69302I −18.2613 − 5.5106I
u = 1.073950 − 0.558752I
a = 0.97227 + 1.06551I
b = 1.40323 + 1.08047I
−2.06894 + 3.44524I −9.63582 − 0.44697I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = −0.61633 − 1.32674I
b = −1.63952 − 0.60105I
−2.06894 + 3.44524I −9.63582 − 0.44697I
u = 1.073950 − 0.558752I
a = −1.39370 + 0.74791I
b = −1.95662 + 0.59736I
0.11530 + 11.61740I −9.1705 − 15.5341I
u = 1.073950 − 0.558752I
a = 1.66153 + 0.30823I
b = 1.07887 − 1.58195I
0.11530 + 11.61740I −9.1705 − 15.5341I
u = 1.073950 − 0.558752I
a = −0.69767 − 1.69151I
b = −2.32631 − 1.65114I
2.98579 + 10.69380I 1.84059 − 11.73808I
u = 1.073950 − 0.558752I
a = 0.1092910 + 0.0274790I
b = −0.922823 − 0.822556I
0.115297 − 0.231405I −9.17045 + 4.51298I
u = 1.073950 − 0.558752I
a = 0.63890 + 1.86392I
b = 2.18525 + 1.36863I
−2.06894 + 7.94081I −9.6358 − 10.5742I
u = 1.073950 − 0.558752I
a = −1.07953 − 1.83604I
b = −1.72761 − 1.64477I
−2.06894 + 7.94081I −9.6358 − 10.5742I
u = 1.073950 − 0.558752I
a = 0.89609 + 1.93458I
b = 2.10722 + 1.85079I
−1.50728 + 10.90930I −6.4360 − 14.5233I
u = 1.073950 − 0.558752I
a = 0.70039 + 2.02609I
b = 2.07265 + 1.58800I
−2.44783 + 8.39743I −9.46762 − 5.42724I
u = 1.073950 − 0.558752I
a = −0.91338 − 1.95387I
b = −1.88426 − 1.78457I
−2.44783 + 8.39743I −9.46762 − 5.42724I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = −0.83852 − 2.15961I
b = −2.04330 − 1.57695I
−1.50728 + 10.90930I −6.4360 − 14.5233I
u = 1.073950 − 0.558752I
a = 1.07519 + 2.09684I
b = 1.69439 + 1.42677I
2.98579 + 10.69380I 1.84059 − 11.73808I
27
III.
I
u
3
= h−2.12 × 10
9
u
44
+ 1.71 × 10
9
u
43
+ · · · + 5.72 × 10
7
b − 2.32 × 10
9
, −2.32 ×
10
9
u
44
+2.52×10
9
u
43
+· · · +5.72×10
7
a−1.66×10
9
, u
45
−2u
44
+· · · +2u −1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
11
=
40.5072u
44
− 43.9472u
43
+ ··· − 23.0765u + 28.9735
37.0673u
44
− 29.8568u
43
+ ··· − 52.0410u + 40.5072
a
4
=
−4.90785u
44
+ 23.9865u
43
+ ··· − 24.0880u + 17.4586
14.1708u
44
− 37.1237u
43
+ ··· + 26.2743u − 4.90785
a
1
=
−u
2
+ 1
−u
4
a
7
=
u
u
a
6
=
−7.44768u
44
+ 22.4355u
43
+ ··· + 9.09415u − 3.38213
42.1786u
44
− 124.862u
43
+ ··· + 137.203u − 48.7766
a
10
=
35.5786u
44
− 36.8812u
43
+ ··· − 40.9375u + 36.1840
32.1387u
44
− 22.7908u
43
+ ··· − 69.9020u + 47.7178
a
5
=
7.10030u
44
− 15.4634u
43
+ ··· + 52.4706u − 17.1345
63.4171u
44
− 184.881u
43
+ ··· + 181.398u − 64.2316
a
9
=
7.54710u
44
− 8.57726u
43
+ ··· − 8.43501u + 1.14124
15.0041u
44
− 22.4267u
43
+ ··· − 14.1267u + 10.1107
a
12
=
27.6269u
44
− 30.3038u
43
+ ··· − 2.18605u + 15.3122
37.8156u
44
− 51.7656u
43
+ ··· − 20.3289u + 24.3846
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3996664524
57230447
u
44
−
10950155072
57230447
u
43
+ ··· +
10553998747
57230447
u −
2768249785
57230447
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
− 30u
44
+ ··· + 16u − 1
c
2
u
45
− 2u
44
+ ··· + 2u − 1
c
3
, c
10
u
45
− u
44
+ ··· + 6u − 1
c
4
, c
11
u
45
+ 9u
43
+ ··· + 16u − 4
c
5
, c
8
u
45
+ 2u
44
+ ··· + 14u + 1
c
6
u
45
+ 22u
44
+ ··· + 5u + 1
c
7
u
45
+ 2u
44
+ ··· + 2u + 1
c
9
u
45
− 15u
44
+ ··· + 292u − 29
c
12
u
45
+ 15u
44
+ ··· + 292u + 29
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 14y
44
+ ··· − 44y −1
c
2
, c
7
y
45
− 30y
44
+ ··· + 16y −1
c
3
, c
10
y
45
− 25y
44
+ ··· − 14y −1
c
4
, c
11
y
45
+ 18y
44
+ ··· + 216y −16
c
5
, c
8
y
45
+ 12y
44
+ ··· + 156y −1
c
6
y
45
− 8y
44
+ ··· + 19y −1
c
9
, c
12
y
45
+ 23y
44
+ ··· − 18614y −841
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.953181 + 0.282182I
a = −2.48300 + 1.93285I
b = −2.91216 + 1.14170I
−5.31781 − 1.12767I −6.32235 + 5.99209I
u = 0.953181 − 0.282182I
a = −2.48300 − 1.93285I
b = −2.91216 − 1.14170I
−5.31781 + 1.12767I −6.32235 − 5.99209I
u = −0.950979 + 0.351708I
a = −0.572715 − 0.262540I
b = 0.636978 + 0.048242I
−3.72251 + 4.31570I −5.05810 − 7.71164I
u = −0.950979 − 0.351708I
a = −0.572715 + 0.262540I
b = 0.636978 − 0.048242I
−3.72251 − 4.31570I −5.05810 + 7.71164I
u = 0.969732 + 0.319689I
a = 2.22637 − 2.18286I
b = 2.85682 − 1.40504I
−1.30775 + 4.51511I −2.36632 + 1.74372I
u = 0.969732 − 0.319689I
a = 2.22637 + 2.18286I
b = 2.85682 + 1.40504I
−1.30775 − 4.51511I −2.36632 − 1.74372I
u = −0.982303 + 0.350110I
a = −0.411329 − 0.586289I
b = 0.609316 + 0.431903I
−3.01185 − 3.53079I −4.00000 − 2.37834I
u = −0.982303 − 0.350110I
a = −0.411329 + 0.586289I
b = 0.609316 − 0.431903I
−3.01185 + 3.53079I −4.00000 + 2.37834I
u = 0.883888 + 0.578691I
a = −0.247609 − 1.234170I
b = 0.495346 − 1.234160I
−1.53567 − 3.97017I −6.72669 + 9.84978I
u = 0.883888 − 0.578691I
a = −0.247609 + 1.234170I
b = 0.495346 + 1.234160I
−1.53567 + 3.97017I −6.72669 − 9.84978I
31
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.901426 + 0.246511I
a = 2.92569 − 2.03463I
b = 3.13885 − 1.11285I
−0.92509 − 6.86041I −1.09352 + 11.39986I
u = 0.901426 − 0.246511I
a = 2.92569 + 2.03463I
b = 3.13885 + 1.11285I
−0.92509 + 6.86041I −1.09352 − 11.39986I
u = −0.882476 + 0.284343I
a = 0.546817 + 0.566293I
b = −0.643574 − 0.344256I
−3.34359 − 1.65680I −2.43487 − 2.50445I
u = −0.882476 − 0.284343I
a = 0.546817 − 0.566293I
b = −0.643574 + 0.344256I
−3.34359 + 1.65680I −2.43487 + 2.50445I
u = 0.320812 + 0.829837I
a = −0.535247 − 0.173656I
b = −0.027608 − 0.499879I
−0.51214 − 2.42117I −6.7641 + 14.3760I
u = 0.320812 − 0.829837I
a = −0.535247 + 0.173656I
b = −0.027608 + 0.499879I
−0.51214 + 2.42117I −6.7641 − 14.3760I
u = −0.853109 + 0.239315I
a = 0.775539 + 0.087226I
b = −0.682494 + 0.111185I
−2.34208 + 6.04810I −0.84715 − 8.85910I
u = −0.853109 − 0.239315I
a = 0.775539 − 0.087226I
b = −0.682494 − 0.111185I
−2.34208 − 6.04810I −0.84715 + 8.85910I
u = 0.503965 + 0.668700I
a = −1.30449 + 1.23303I
b = −1.48195 − 0.25091I
0.27709 + 4.89364I −1.57571 − 2.92107I
u = 0.503965 − 0.668700I
a = −1.30449 − 1.23303I
b = −1.48195 + 0.25091I
0.27709 − 4.89364I −1.57571 + 2.92107I
32
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.374875 + 0.744478I
a = −0.124461 − 0.557366I
b = 0.461604 + 0.116284I
2.79366 − 5.92565I −0.22534 + 3.53136I
u = −0.374875 − 0.744478I
a = −0.124461 + 0.557366I
b = 0.461604 − 0.116284I
2.79366 + 5.92565I −0.22534 − 3.53136I
u = 1.052430 + 0.563594I
a = −0.74140 + 2.08043I
b = −1.95280 + 1.77166I
−1.36854 − 9.68680I 0
u = 1.052430 − 0.563594I
a = −0.74140 − 2.08043I
b = −1.95280 − 1.77166I
−1.36854 + 9.68680I 0
u = 1.003330 + 0.650345I
a = 0.298580 + 0.722828I
b = −0.170514 + 0.919412I
−1.84991 − 1.11758I 0
u = 1.003330 − 0.650345I
a = 0.298580 − 0.722828I
b = −0.170514 − 0.919412I
−1.84991 + 1.11758I 0
u = −0.548617 + 0.587502I
a = 0.337767 + 0.841668I
b = −0.679786 − 0.263315I
−1.42913 − 1.34791I −3.76096 + 6.63178I
u = −0.548617 − 0.587502I
a = 0.337767 − 0.841668I
b = −0.679786 + 0.263315I
−1.42913 + 1.34791I −3.76096 − 6.63178I
u = −1.074590 + 0.536692I
a = −0.212698 − 0.371950I
b = 0.428186 + 0.285542I
−3.15166 + 5.80304I 0
u = −1.074590 − 0.536692I
a = −0.212698 + 0.371950I
b = 0.428186 − 0.285542I
−3.15166 − 5.80304I 0
33
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.081080 + 0.570431I
a = 0.108294 + 0.386648I
b = −0.337630 − 0.356222I
0.78478 + 10.87500I 0
u = −1.081080 − 0.570431I
a = 0.108294 − 0.386648I
b = −0.337630 + 0.356222I
0.78478 − 10.87500I 0
u = 1.137610 + 0.512505I
a = 1.20595 − 1.84848I
b = 2.31925 − 1.48479I
0.35457 − 8.85047I 0
u = 1.137610 − 0.512505I
a = 1.20595 + 1.84848I
b = 2.31925 + 1.48479I
0.35457 + 8.85047I 0
u = −1.148970 + 0.579575I
a = 0.187415 + 0.493262I
b = −0.501217 − 0.458123I
0.633057 − 0.173557I 0
u = −1.148970 − 0.579575I
a = 0.187415 − 0.493262I
b = −0.501217 + 0.458123I
0.633057 + 0.173557I 0
u = −1.326280 + 0.098070I
a = −0.257662 + 0.124130I
b = 0.329558 − 0.189899I
−5.90926 + 4.60306I 0
u = −1.326280 − 0.098070I
a = −0.257662 − 0.124130I
b = 0.329558 + 0.189899I
−5.90926 − 4.60306I 0
u = −0.240188 + 0.543925I
a = −0.73101 − 1.33621I
b = 0.902376 − 0.076675I
3.20060 + 4.86291I 2.02471 − 7.80621I
u = −0.240188 − 0.543925I
a = −0.73101 + 1.33621I
b = 0.902376 + 0.076675I
3.20060 − 4.86291I 2.02471 + 7.80621I
34
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54844 + 0.26943I
a = −0.189437 − 0.102924I
b = −0.265601 − 0.210410I
−4.84265 − 3.15872I 0
u = 1.54844 − 0.26943I
a = −0.189437 + 0.102924I
b = −0.265601 + 0.210410I
−4.84265 + 3.15872I 0
u = 0.362650 + 0.227595I
a = 2.07931 − 2.97836I
b = 1.43192 − 0.60686I
2.97085 + 4.86862I 1.96874 − 5.64966I
u = 0.362650 − 0.227595I
a = 2.07931 + 2.97836I
b = 1.43192 + 0.60686I
2.97085 − 4.86862I 1.96874 + 5.64966I
u = 1.65201
a = −1.76135
b = −2.90977
−9.97717 0
35
IV. I
u
4
= hb − 1, a − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u − 1
a
11
=
u + 1
1
a
4
=
u + 1
0
a
1
=
u + 2
−u
a
7
=
u
u
a
6
=
−1
u
a
10
=
u
0
a
5
=
u + 1
0
a
9
=
−u − 1
u
a
12
=
u + 1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
9
, c
10
c
12
u
2
− u + 1
c
4
, c
11
u
2
c
5
, c
6
, c
8
(u − 1)
2
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
9
, c
10
c
12
y
2
+ y + 1
c
4
, c
11
y
2
c
5
, c
6
, c
8
(y −1)
2
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = 1.00000
3.28987 3.00000
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 1.00000
3.28987 3.00000
39
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
22
· (u
45
− 30u
44
+ ··· + 16u − 1)
· (u
60
+ 34u
59
+ ··· + 13631488u + 4194304)
c
2
(u
2
− u + 1)(u
6
+ u
5
+ ··· + u + 1)
22
(u
45
− 2u
44
+ ··· + 2u − 1)
· (u
60
− 20u
59
+ ··· + 27648u − 2048)
c
3
, c
10
(u
2
− u + 1)(u
45
− u
44
+ ··· + 6u − 1)(u
60
+ 2u
59
+ ··· + 4u − 1)
· (u
132
+ 3u
131
+ ··· + 1266u + 83)
c
4
, c
11
u
2
(u
45
+ 9u
43
+ ··· + 16u − 4)(u
60
+ 7u
58
+ ··· − 2u − 21)
· (u
132
+ u
131
+ ··· + 14455610u + 3138347)
c
5
, c
8
((u − 1)
2
)(u
45
+ 2u
44
+ ··· + 14u + 1)(u
60
+ 4u
59
+ ··· + 23u − 1)
· (u
132
− u
131
+ ··· − 758u + 67)
c
6
(u − 1)
2
· (u
11
+ 5u
10
+ 12u
9
+ 15u
8
+ 8u
7
− 4u
6
− 8u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
12
· (u
45
+ 22u
44
+ ··· + 5u + 1)(u
60
− 41u
59
+ ··· − 416u + 64)
c
7
(u
2
− u + 1)(u
6
+ u
5
+ ··· + u + 1)
22
(u
45
+ 2u
44
+ ··· + 2u + 1)
· (u
60
− 20u
59
+ ··· + 27648u − 2048)
c
9
(u
2
− u + 1)(u
11
+ 3u
10
+ ··· + 2u + 1)
12
· (u
45
− 15u
44
+ ··· + 292u − 29)(u
60
− 21u
59
+ ··· − 66560u + 4096)
c
12
(u
2
− u + 1)(u
11
+ 3u
10
+ ··· + 2u + 1)
12
· (u
45
+ 15u
44
+ ··· + 292u + 29)(u
60
− 21u
59
+ ··· − 66560u + 4096)
40
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
22
· (y
45
− 14y
44
+ ··· − 44y −1)
· (y
60
− 14y
59
+ ··· + 355142255771648y + 17592186044416)
c
2
, c
7
(y
2
+ y + 1)(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
22
· (y
45
− 30y
44
+ ··· + 16y −1)
· (y
60
− 34y
59
+ ··· − 13631488y + 4194304)
c
3
, c
10
(y
2
+ y + 1)(y
45
− 25y
44
+ ··· − 14y −1)(y
60
+ 10y
59
+ ··· + 18y + 1)
· (y
132
− 45y
131
+ ··· − 1080188y + 6889)
c
4
, c
11
y
2
(y
45
+ 18y
44
+ ··· + 216y −16)(y
60
+ 14y
59
+ ··· + 2768y + 441)
· (y
132
+ 39y
131
+ ··· − 615346853465156y + 9849221892409)
c
5
, c
8
((y −1)
2
)(y
45
+ 12y
44
+ ··· + 156y −1)(y
60
− 30y
59
+ ··· − 629y + 1)
· (y
132
+ 27y
131
+ ··· + 10768000y + 4489)
c
6
((y −1)
2
)(y
11
− y
10
+ ··· + 6y −1)
12
(y
45
− 8y
44
+ ··· + 19y −1)
· (y
60
− 7y
59
+ ··· − 119808y + 4096)
c
9
, c
12
(y
2
+ y + 1)(y
11
+ 7y
10
+ ··· − 6y −1)
12
· (y
45
+ 23y
44
+ ··· − 18614y −841)
· (y
60
+ 29y
59
+ ··· + 103809024y + 16777216)
41
