12n
0626
(K12n
0626
)
A knot diagram
1
Linearized knot diagam
3 8 6 11 1 12 11 2 7 4 9 4
Solving Sequence
4,11 1,5
6 3 10 12 7 8 2 9
c
4
c
5
c
3
c
10
c
12
c
6
c
7
c
2
c
9
c
1
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.45261 × 10
107
u
44
− 2.43067 × 10
108
u
43
+ ··· + 5.67762 × 10
109
b + 1.45136 × 10
110
,
− 1.02261 × 10
111
u
44
+ 3.49755 × 10
111
u
43
+ ··· + 3.12269 × 10
112
a − 1.77035 × 10
113
,
u
45
− 3u
44
+ ··· − 216u − 50i
I
u
2
= h−1.57405 × 10
49
au
34
− 7.29045 × 10
49
u
34
+ ··· − 1.01763 × 10
50
a − 5.06550 × 10
50
,
4.89851 × 10
51
au
34
− 1.12145 × 10
52
u
34
+ ··· + 3.20904 × 10
52
a − 7.96667 × 10
52
, u
35
+ u
34
+ ··· + 9u − 1i
I
u
3
= h24290268766301u
37
− 28827427845386u
36
+ ··· + 64246238253402b + 686511198649974,
− 193561107143803u
37
+ 110734887539683u
36
+ ··· + 64246238253402a − 901423536620652,
u
38
+ 5u
36
+ ··· − 71u
2
+ 6i
I
v
1
= ha, b − 1, v + 1i
* 4 irreducible components of dim
C
= 0, with total 154 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
= h6.45 × 10
107
u
44
− 2.43 × 10
108
u
43
+ · · · + 5.68 × 10
109
b + 1.45 ×
10
110
, −1.02 × 10
111
u
44
+ 3.50 × 10
111
u
43
+ · · · + 3.12 × 10
112
a − 1.77 ×
10
113
, u
45
− 3u
44
+ · · · − 216u − 50i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
1
=
0.0327477u
44
− 0.112004u
43
+ ··· + 14.6356u + 5.66930
−0.0113650u
44
+ 0.0428114u
43
+ ··· − 7.23755u − 2.55629
a
5
=
1
−u
2
a
6
=
0.000138274u
44
− 0.0215805u
43
+ ··· + 48.5815u + 14.2524
−0.00976057u
44
+ 0.0369257u
43
+ ··· − 11.2636u − 3.57324
a
3
=
0.0549640u
44
− 0.133609u
43
+ ··· − 78.7955u − 12.0431
−0.0224776u
44
+ 0.0618353u
43
+ ··· + 17.7539u + 2.20564
a
10
=
−u
u
a
12
=
0.0441127u
44
− 0.154816u
43
+ ··· + 21.8732u + 8.22559
−0.0113650u
44
+ 0.0428114u
43
+ ··· − 7.23755u − 2.55629
a
7
=
−0.0648870u
44
+ 0.178186u
43
+ ··· + 48.2969u + 5.44301
0.0137612u
44
− 0.0361735u
43
+ ··· − 12.7428u − 1.63739
a
8
=
−0.0648870u
44
+ 0.178186u
43
+ ··· + 48.2969u + 5.44301
0.00125770u
44
+ 0.00211282u
43
+ ··· − 5.93985u − 0.813634
a
2
=
−0.0253004u
44
+ 0.110341u
43
+ ··· − 46.4915u − 11.6489
−0.00636661u
44
+ 0.0145163u
43
+ ··· + 13.8908u + 2.19911
a
9
=
−0.0714648u
44
+ 0.204634u
43
+ ··· + 46.2269u + 4.17282
0.0149532u
44
− 0.0451343u
43
+ ··· − 8.51402u + 0.0701677
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0618399u
44
− 0.112199u
43
+ ··· − 99.5480u − 9.36086
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ 19u
44
+ ··· + 296u − 100
c
2
, c
8
u
45
+ 3u
44
+ ··· − 44u − 10
c
3
, c
11
u
45
+ u
44
+ ··· + 5u − 1
c
4
, c
10
u
45
− 3u
44
+ ··· − 216u − 50
c
5
, c
7
u
45
− u
44
+ ··· + 11u − 143
c
6
u
45
− 3u
44
+ ··· + 8824u − 1928
c
9
, c
12
u
45
+ 3u
44
+ ··· + 33u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
+ 15y
44
+ ··· + 417216y −10000
c
2
, c
8
y
45
+ 19y
44
+ ··· + 296y −100
c
3
, c
11
y
45
− 7y
44
+ ··· + 25y −1
c
4
, c
10
y
45
+ 29y
44
+ ··· − 66944y −2500
c
5
, c
7
y
45
+ 27y
44
+ ··· − 283019y −20449
c
6
y
45
− 5y
44
+ ··· + 32639808y −3717184
c
9
, c
12
y
45
+ 35y
44
+ ··· − 6847y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.982052 + 0.344463I
a = 0.897344 + 0.387946I
b = −0.088808 − 0.284640I
3.90111 + 0.24103I 11.14977 − 0.22983I
u = 0.982052 − 0.344463I
a = 0.897344 − 0.387946I
b = −0.088808 + 0.284640I
3.90111 − 0.24103I 11.14977 + 0.22983I
u = −0.972469 + 0.418664I
a = −0.875723 + 0.572022I
b = 0.215420 − 0.332153I
3.69660 − 5.52791I 11.56773 + 6.24960I
u = −0.972469 − 0.418664I
a = −0.875723 − 0.572022I
b = 0.215420 + 0.332153I
3.69660 + 5.52791I 11.56773 − 6.24960I
u = −0.268181 + 1.172890I
a = −1.099600 − 0.836869I
b = −1.32797 − 1.27587I
−4.61487 − 1.65819I −5.41137 + 0.80754I
u = −0.268181 − 1.172890I
a = −1.099600 + 0.836869I
b = −1.32797 + 1.27587I
−4.61487 + 1.65819I −5.41137 − 0.80754I
u = −0.133716 + 1.210450I
a = 0.46886 − 1.72677I
b = 1.06503 − 1.77331I
−1.11353 − 5.69606I 6.4348 + 13.2641I
u = −0.133716 − 1.210450I
a = 0.46886 + 1.72677I
b = 1.06503 + 1.77331I
−1.11353 + 5.69606I 6.4348 − 13.2641I
u = 0.133959 + 1.289230I
a = −0.30874 + 1.56623I
b = −0.35217 + 1.59122I
−3.03297 + 3.57228I 2.57196 − 5.14807I
u = 0.133959 − 1.289230I
a = −0.30874 − 1.56623I
b = −0.35217 − 1.59122I
−3.03297 − 3.57228I 2.57196 + 5.14807I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.381503 + 1.269590I
a = 0.440182 + 0.942074I
b = −0.322936 + 1.028520I
−3.88171 + 0.13510I 6.67770 − 1.97779I
u = −0.381503 − 1.269590I
a = 0.440182 − 0.942074I
b = −0.322936 − 1.028520I
−3.88171 − 0.13510I 6.67770 + 1.97779I
u = 0.018489 + 1.337230I
a = 0.584739 + 1.185070I
b = −0.133197 + 0.864237I
−2.93966 + 2.29015I 3.98465 − 3.47136I
u = 0.018489 − 1.337230I
a = 0.584739 − 1.185070I
b = −0.133197 − 0.864237I
−2.93966 − 2.29015I 3.98465 + 3.47136I
u = −0.537745 + 0.270263I
a = 1.193340 − 0.691780I
b = 0.823079 + 0.760072I
1.78194 + 3.46593I 14.6287 − 5.6907I
u = −0.537745 − 0.270263I
a = 1.193340 + 0.691780I
b = 0.823079 − 0.760072I
1.78194 − 3.46593I 14.6287 + 5.6907I
u = −0.06352 + 1.41822I
a = −0.577294 + 1.275210I
b = 0.084859 + 0.840729I
−4.25393 − 7.67261I 0. + 9.08596I
u = −0.06352 − 1.41822I
a = −0.577294 − 1.275210I
b = 0.084859 − 0.840729I
−4.25393 + 7.67261I 0. − 9.08596I
u = −0.481194 + 0.313751I
a = −0.59895 + 1.71117I
b = 0.662716 − 0.478922I
1.48372 − 3.19466I 14.2637 + 3.1183I
u = −0.481194 − 0.313751I
a = −0.59895 − 1.71117I
b = 0.662716 + 0.478922I
1.48372 + 3.19466I 14.2637 − 3.1183I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45205 + 0.30573I
a = 0.189061 + 0.075403I
b = −0.202622 − 1.155420I
−1.85503 + 3.23232I 0
u = 1.45205 − 0.30573I
a = 0.189061 − 0.075403I
b = −0.202622 + 1.155420I
−1.85503 − 3.23232I 0
u = 0.11068 + 1.49218I
a = −0.362471 + 1.218380I
b = 0.021640 + 1.003810I
−8.41188 − 1.42060I 0
u = 0.11068 − 1.49218I
a = −0.362471 − 1.218380I
b = 0.021640 − 1.003810I
−8.41188 + 1.42060I 0
u = −0.352040 + 0.357974I
a = 0.018861 + 1.267180I
b = −0.675952 + 0.468271I
−2.55936 − 1.04400I 3.67071 + 4.11672I
u = −0.352040 − 0.357974I
a = 0.018861 − 1.267180I
b = −0.675952 − 0.468271I
−2.55936 + 1.04400I 3.67071 − 4.11672I
u = −1.46794 + 0.33452I
a = 0.1160420 + 0.0084688I
b = 0.584119 + 1.190960I
2.62425 + 5.00892I 0
u = −1.46794 − 0.33452I
a = 0.1160420 − 0.0084688I
b = 0.584119 − 1.190960I
2.62425 − 5.00892I 0
u = 0.457354
a = 0.515813
b = 0.287710
0.695378 13.8950
u = 0.71712 + 1.42041I
a = −0.377061 + 0.827181I
b = 0.458019 + 1.197090I
−5.71574 + 4.33440I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.71712 − 1.42041I
a = −0.377061 − 0.827181I
b = 0.458019 − 1.197090I
−5.71574 − 4.33440I 0
u = 0.045115 + 0.375785I
a = 0.502574 − 0.452745I
b = −0.076285 + 0.710609I
1.59089 + 2.72032I 6.64779 − 2.49427I
u = 0.045115 − 0.375785I
a = 0.502574 + 0.452745I
b = −0.076285 − 0.710609I
1.59089 − 2.72032I 6.64779 + 2.49427I
u = 0.37049 + 1.59283I
a = −0.049575 − 1.215240I
b = −1.06311 − 1.54495I
−8.64456 + 9.60665I 0
u = 0.37049 − 1.59283I
a = −0.049575 + 1.215240I
b = −1.06311 + 1.54495I
−8.64456 − 9.60665I 0
u = −0.68867 + 1.49281I
a = −0.230013 − 1.255740I
b = 1.03402 − 1.44601I
−1.39112 − 12.65970I 0
u = −0.68867 − 1.49281I
a = −0.230013 + 1.255740I
b = 1.03402 + 1.44601I
−1.39112 + 12.65970I 0
u = 0.008729 + 0.329890I
a = 2.99643 + 1.73672I
b = −0.844063 − 0.436623I
0.04511 + 7.55751I 10.37988 − 8.84114I
u = 0.008729 − 0.329890I
a = 2.99643 − 1.73672I
b = −0.844063 + 0.436623I
0.04511 − 7.55751I 10.37988 + 8.84114I
u = 0.78407 + 1.59419I
a = 0.265720 − 1.158860I
b = −1.07883 − 1.42333I
−3.5107 + 18.8570I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.78407 − 1.59419I
a = 0.265720 + 1.158860I
b = −1.07883 + 1.42333I
−3.5107 − 18.8570I 0
u = 1.76555 + 0.27957I
a = −0.0198463 + 0.0768389I
b = −0.54488 + 1.32858I
0.87619 − 10.06840I 0
u = 1.76555 − 0.27957I
a = −0.0198463 − 0.0768389I
b = −0.54488 − 1.32858I
0.87619 + 10.06840I 0
u = 0.23000 + 2.00315I
a = −0.091790 + 0.847105I
b = 0.11807 + 1.45362I
−7.19068 − 1.47568I 0
u = 0.23000 − 2.00315I
a = −0.091790 − 0.847105I
b = 0.11807 − 1.45362I
−7.19068 + 1.47568I 0
9
II.
I
u
2
= h−1.57×10
49
au
34
−7.29×10
49
u
34
+· · ·−1.02×10
50
a−5.07×10
50
, 4.90×
10
51
au
34
−1.12×10
52
u
34
+· · ·+3.21×10
52
a−7.97×10
52
, u
35
+u
34
+· · ·+9u−1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
1
=
a
0.0958186au
34
+ 0.443798u
34
+ ··· + 0.619469a + 3.08357
a
5
=
1
−u
2
a
6
=
1.41657au
34
− 6.79284u
34
+ ··· + 9.76303a − 47.0037
0.132146au
34
+ 1.39494u
34
+ ··· + 0.980193a + 8.18591
a
3
=
1.32752au
34
+ 6.79284u
34
+ ··· + 9.36987a + 47.0037
0.0201917au
34
− 4.25432u
34
+ ··· + 0.0958186a − 28.9986
a
10
=
−u
u
a
12
=
−0.0958186au
34
− 0.443798u
34
+ ··· + 0.380531a − 3.08357
0.0958186au
34
+ 0.443798u
34
+ ··· + 0.619469a + 3.08357
a
7
=
−0.619469au
34
− 9.76303u
34
+ ··· − 4.12036a − 68.6369
4.36514u
34
+ 4.96123u
33
+ ··· − 73.0252u + 29.8191
a
8
=
−0.619469au
34
− 9.76303u
34
+ ··· − 4.12036a − 68.6369
0.0201917au
34
+ 4.57371u
34
+ ··· + 0.0958186a + 31.2357
a
2
=
1.55451au
34
− 2.98159u
34
+ ··· + 10.6192a − 22.8488
−0.180352au
34
+ 0.0676458u
34
+ ··· − 1.24871a + 0.423180
a
9
=
−0.980193au
34
+ u
34
+ ··· − 7.39826a + 9
0.110817au
34
− 0.212265u
34
+ ··· + 0.820472a − 1.03387
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.08049u
34
+ 3.61372u
33
+ ··· − 30.9682u + 20.7546
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
35
+ 17u
34
+ ··· − 405u − 49)
2
c
2
, c
8
(u
35
− u
34
+ ··· + 13u − 7)
2
c
3
, c
11
u
70
+ 5u
69
+ ··· − 787u + 338
c
4
, c
10
(u
35
+ u
34
+ ··· + 9u − 1)
2
c
5
, c
7
u
70
+ 2u
69
+ ··· + 625113u + 75346
c
6
(u
35
− 4u
33
+ ··· + 10u − 1)
2
c
9
, c
12
u
70
+ 8u
69
+ ··· + 10573u + 7727
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
35
+ 9y
34
+ ··· − 10317y −2401)
2
c
2
, c
8
(y
35
+ 17y
34
+ ··· − 405y −49)
2
c
3
, c
11
y
70
− 33y
69
+ ··· − 4966725y + 114244
c
4
, c
10
(y
35
+ 25y
34
+ ··· + 53y −1)
2
c
5
, c
7
y
70
− 34y
69
+ ··· + 95484723835y + 5677019716
c
6
(y
35
− 8y
34
+ ··· − 34y −1)
2
c
9
, c
12
y
70
− 16y
69
+ ··· + 1891683685y + 59706529
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.122175 + 0.986614I
a = 0.582179 − 0.688338I
b = −0.900472 − 0.553302I
−1.55635 + 4.47504I 1.34280 − 7.96658I
u = 0.122175 + 0.986614I
a = 0.76307 + 1.63237I
b = 0.314080 + 1.149240I
−1.55635 + 4.47504I 1.34280 − 7.96658I
u = 0.122175 − 0.986614I
a = 0.582179 + 0.688338I
b = −0.900472 + 0.553302I
−1.55635 − 4.47504I 1.34280 + 7.96658I
u = 0.122175 − 0.986614I
a = 0.76307 − 1.63237I
b = 0.314080 − 1.149240I
−1.55635 − 4.47504I 1.34280 + 7.96658I
u = −0.986091 + 0.308478I
a = 0.323626 − 0.149701I
b = −0.312187 + 1.052900I
−2.68277 + 3.53319I 3.87375 − 3.61929I
u = −0.986091 + 0.308478I
a = −0.009681 − 0.269791I
b = −0.756261 − 0.798331I
−2.68277 + 3.53319I 3.87375 − 3.61929I
u = −0.986091 − 0.308478I
a = 0.323626 + 0.149701I
b = −0.312187 − 1.052900I
−2.68277 − 3.53319I 3.87375 + 3.61929I
u = −0.986091 − 0.308478I
a = −0.009681 + 0.269791I
b = −0.756261 + 0.798331I
−2.68277 − 3.53319I 3.87375 + 3.61929I
u = 0.828222
a = 0.300662 + 0.115629I
b = 0.375408 − 0.648173I
0.343351 9.69750
u = 0.828222
a = 0.300662 − 0.115629I
b = 0.375408 + 0.648173I
0.343351 9.69750
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.396765 + 1.108360I
a = −0.887638 − 0.628092I
b = −0.751428 − 0.613802I
−4.24240 − 1.50990I 8.8808 + 16.4628I
u = −0.396765 + 1.108360I
a = −1.131370 + 0.343875I
b = −2.18711 − 0.71208I
−4.24240 − 1.50990I 8.8808 + 16.4628I
u = −0.396765 − 1.108360I
a = −0.887638 + 0.628092I
b = −0.751428 + 0.613802I
−4.24240 + 1.50990I 8.8808 − 16.4628I
u = −0.396765 − 1.108360I
a = −1.131370 − 0.343875I
b = −2.18711 + 0.71208I
−4.24240 + 1.50990I 8.8808 − 16.4628I
u = −0.139847 + 1.201950I
a = 0.574461 + 0.251080I
b = 1.90213 + 0.43070I
1.53141 − 2.94190I 13.20720 + 3.19373I
u = −0.139847 + 1.201950I
a = 0.53860 − 1.38331I
b = 0.693129 − 0.806116I
1.53141 − 2.94190I 13.20720 + 3.19373I
u = −0.139847 − 1.201950I
a = 0.574461 − 0.251080I
b = 1.90213 − 0.43070I
1.53141 + 2.94190I 13.20720 − 3.19373I
u = −0.139847 − 1.201950I
a = 0.53860 + 1.38331I
b = 0.693129 + 0.806116I
1.53141 + 2.94190I 13.20720 − 3.19373I
u = 0.078064 + 1.285270I
a = 0.029464 + 1.200230I
b = 0.10096 + 1.70807I
0.13057 + 2.97268I 14.4575 − 1.7124I
u = 0.078064 + 1.285270I
a = 0.25391 − 1.49964I
b = −0.093566 − 0.382690I
0.13057 + 2.97268I 14.4575 − 1.7124I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.078064 − 1.285270I
a = 0.029464 − 1.200230I
b = 0.10096 − 1.70807I
0.13057 − 2.97268I 14.4575 + 1.7124I
u = 0.078064 − 1.285270I
a = 0.25391 + 1.49964I
b = −0.093566 + 0.382690I
0.13057 − 2.97268I 14.4575 + 1.7124I
u = 0.362335 + 1.321800I
a = −0.641012 + 0.802633I
b = −0.167993 + 1.339300I
−2.66413 − 1.60535I 5.78287 + 1.84520I
u = 0.362335 + 1.321800I
a = −0.438948 − 0.459649I
b = 1.135110 − 0.524610I
−2.66413 − 1.60535I 5.78287 + 1.84520I
u = 0.362335 − 1.321800I
a = −0.641012 − 0.802633I
b = −0.167993 − 1.339300I
−2.66413 + 1.60535I 5.78287 − 1.84520I
u = 0.362335 − 1.321800I
a = −0.438948 + 0.459649I
b = 1.135110 + 0.524610I
−2.66413 + 1.60535I 5.78287 − 1.84520I
u = 0.23174 + 1.41839I
a = 0.758833 − 0.408790I
b = −0.976834 − 0.169918I
−0.81863 + 2.60111I 13.7993 + 4.7460I
u = 0.23174 + 1.41839I
a = 0.313108 + 1.168680I
b = 0.335578 + 1.268760I
−0.81863 + 2.60111I 13.7993 + 4.7460I
u = 0.23174 − 1.41839I
a = 0.758833 + 0.408790I
b = −0.976834 + 0.169918I
−0.81863 − 2.60111I 13.7993 − 4.7460I
u = 0.23174 − 1.41839I
a = 0.313108 − 1.168680I
b = 0.335578 − 1.268760I
−0.81863 − 2.60111I 13.7993 − 4.7460I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.66653 + 1.30929I
a = 0.444844 − 0.721904I
b = −0.534035 − 0.891882I
−2.98334 + 5.43570I 8.00000 + 0.I
u = 0.66653 + 1.30929I
a = −0.31156 + 1.41548I
b = 0.90010 + 1.29402I
−2.98334 + 5.43570I 8.00000 + 0.I
u = 0.66653 − 1.30929I
a = 0.444844 + 0.721904I
b = −0.534035 + 0.891882I
−2.98334 − 5.43570I 8.00000 + 0.I
u = 0.66653 − 1.30929I
a = −0.31156 − 1.41548I
b = 0.90010 − 1.29402I
−2.98334 − 5.43570I 8.00000 + 0.I
u = −1.47037 + 0.12982I
a = −1.58687 − 0.24850I
b = 1.49658 − 0.23084I
6.52279 − 1.14319I 8.0000 − 12.7886I
u = −1.47037 + 0.12982I
a = −0.0710353 + 0.0682410I
b = 0.428181 + 0.300914I
6.52279 − 1.14319I 8.0000 − 12.7886I
u = −1.47037 − 0.12982I
a = −1.58687 + 0.24850I
b = 1.49658 + 0.23084I
6.52279 + 1.14319I 8.0000 + 12.7886I
u = −1.47037 − 0.12982I
a = −0.0710353 − 0.0682410I
b = 0.428181 − 0.300914I
6.52279 + 1.14319I 8.0000 + 12.7886I
u = 0.245407 + 0.458419I
a = 0.54395 − 1.75933I
b = 1.002270 − 0.148814I
3.19287 − 1.90206I 11.14226 + 4.07695I
u = 0.245407 + 0.458419I
a = 1.22736 − 1.77188I
b = −1.116590 − 0.014897I
3.19287 − 1.90206I 11.14226 + 4.07695I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.245407 − 0.458419I
a = 0.54395 + 1.75933I
b = 1.002270 + 0.148814I
3.19287 + 1.90206I 11.14226 − 4.07695I
u = 0.245407 − 0.458419I
a = 1.22736 + 1.77188I
b = −1.116590 + 0.014897I
3.19287 + 1.90206I 11.14226 − 4.07695I
u = 0.23477 + 1.48829I
a = −0.236746 − 1.162590I
b = −0.668132 − 0.889707I
−1.25551 + 8.87249I 0. − 8.86121I
u = 0.23477 + 1.48829I
a = −0.434625 + 0.395783I
b = −1.99829 + 0.79541I
−1.25551 + 8.87249I 0. − 8.86121I
u = 0.23477 − 1.48829I
a = −0.236746 + 1.162590I
b = −0.668132 + 0.889707I
−1.25551 − 8.87249I 0. + 8.86121I
u = 0.23477 − 1.48829I
a = −0.434625 − 0.395783I
b = −1.99829 − 0.79541I
−1.25551 − 8.87249I 0. + 8.86121I
u = 1.56254 + 0.00406I
a = 1.41351 − 0.06592I
b = −1.73935 − 0.27949I
5.52620 − 2.95010I 0. + 8.72441I
u = 1.56254 + 0.00406I
a = 0.159345 + 0.107098I
b = −0.068679 + 0.333255I
5.52620 − 2.95010I 0. + 8.72441I
u = 1.56254 − 0.00406I
a = 1.41351 + 0.06592I
b = −1.73935 + 0.27949I
5.52620 + 2.95010I 0. − 8.72441I
u = 1.56254 − 0.00406I
a = 0.159345 − 0.107098I
b = −0.068679 − 0.333255I
5.52620 + 2.95010I 0. − 8.72441I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11131 + 1.60139I
a = −0.307301 + 1.022180I
b = −0.356340 + 1.331780I
−1.65142 − 6.94317I 0
u = −0.11131 + 1.60139I
a = −0.633853 − 0.338866I
b = 1.156250 − 0.216455I
−1.65142 − 6.94317I 0
u = −0.11131 − 1.60139I
a = −0.307301 − 1.022180I
b = −0.356340 − 1.331780I
−1.65142 + 6.94317I 0
u = −0.11131 − 1.60139I
a = −0.633853 + 0.338866I
b = 1.156250 + 0.216455I
−1.65142 + 6.94317I 0
u = −0.87193 + 1.38649I
a = −0.402673 − 0.661450I
b = 0.540404 − 1.042830I
−5.21900 − 10.67790I 0
u = −0.87193 + 1.38649I
a = 0.478540 + 1.263030I
b = −1.10306 + 1.20383I
−5.21900 − 10.67790I 0
u = −0.87193 − 1.38649I
a = −0.402673 + 0.661450I
b = 0.540404 + 1.042830I
−5.21900 + 10.67790I 0
u = −0.87193 − 1.38649I
a = 0.478540 − 1.263030I
b = −1.10306 − 1.20383I
−5.21900 + 10.67790I 0
u = −0.49788 + 1.61012I
a = −0.311048 − 0.789120I
b = 0.253542 − 0.891638I
−8.09778 − 2.45577I 0
u = −0.49788 + 1.61012I
a = 0.129952 + 1.184880I
b = −1.06396 + 1.72980I
−8.09778 − 2.45577I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.49788 − 1.61012I
a = −0.311048 + 0.789120I
b = 0.253542 + 0.891638I
−8.09778 + 2.45577I 0
u = −0.49788 − 1.61012I
a = 0.129952 − 1.184880I
b = −1.06396 − 1.72980I
−8.09778 + 2.45577I 0
u = −0.088118 + 0.149852I
a = 0.33309 − 2.06906I
b = 1.243760 + 0.402683I
5.31617 + 1.46739I 2.24063 + 6.21713I
u = −0.088118 + 0.149852I
a = 10.6816 − 11.5410I
b = 0.235948 − 0.724246I
5.31617 + 1.46739I 2.24063 + 6.21713I
u = −0.088118 − 0.149852I
a = 0.33309 + 2.06906I
b = 1.243760 − 0.402683I
5.31617 − 1.46739I 2.24063 − 6.21713I
u = −0.088118 − 0.149852I
a = 10.6816 + 11.5410I
b = 0.235948 + 0.724246I
5.31617 − 1.46739I 2.24063 − 6.21713I
u = 0.144643 + 0.006325I
a = 2.37387 + 1.10720I
b = −1.226470 − 0.510677I
4.66730 + 7.46710I −2.03060 − 2.52158I
u = 0.144643 + 0.006325I
a = 1.1804 + 20.8132I
b = −0.092665 + 0.683797I
4.66730 + 7.46710I −2.03060 − 2.52158I
u = 0.144643 − 0.006325I
a = 2.37387 − 1.10720I
b = −1.226470 + 0.510677I
4.66730 − 7.46710I −2.03060 + 2.52158I
u = 0.144643 − 0.006325I
a = 1.1804 − 20.8132I
b = −0.092665 − 0.683797I
4.66730 − 7.46710I −2.03060 + 2.52158I
19
III. I
u
3
= h2.43 × 10
13
u
37
− 2.88 × 10
13
u
36
+ · · · + 6.42 × 10
13
b + 6.87 ×
10
14
, −1.94 × 10
14
u
37
+ 1.11 × 10
14
u
36
+ · · · + 6.42 × 10
13
a − 9.01 ×
10
14
, u
38
+ 5u
36
+ · · · − 71u
2
+ 6i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
1
=
3.01280u
37
− 1.72360u
36
+ ··· − 58.9003u + 14.0308
−0.378081u
37
+ 0.448702u
36
+ ··· + 6.74398u − 10.6856
a
5
=
1
−u
2
a
6
=
3.32307u
37
− 0.184882u
36
+ ··· − 63.9677u + 20.0354
−0.479845u
37
− 0.378081u
36
+ ··· − 0.344018u + 6.74398
a
3
=
−2.78639u
37
− 0.796764u
36
+ ··· + 50.3434u + 2.24838
2.17230u
37
+ 1.06709u
36
+ ··· − 24.7164u − 20.3453
a
10
=
−u
u
a
12
=
3.39088u
37
− 2.17230u
36
+ ··· − 65.6443u + 24.7164
−0.378081u
37
+ 0.448702u
36
+ ··· + 6.74398u − 10.6856
a
7
=
−0.0573364u
37
+ 0.534502u
36
+ ··· + 24.9253u − 11.3328
−1.72360u
37
− 0.912583u
36
+ ··· + 14.0308u + 18.0768
a
8
=
−0.0573364u
37
+ 0.534502u
36
+ ··· + 24.9253u − 11.3328
−2.20345u
37
− 0.981646u
36
+ ··· + 13.6867u + 21.2838
a
2
=
−2.19500u
37
+ 1.44104u
36
+ ··· + 35.4543u − 40.0548
0.626832u
37
− 0.891527u
36
+ ··· + 0.626809u + 27.6898
a
9
=
−1.12400u
37
+ 0.479845u
36
+ ··· + 12.9875u + 0.344018
0.139363u
37
− 0.376224u
36
+ ··· + 1.55622u + 13.3778
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
60222003814599
10707706375567
u
36
−
927366664244716
32123119126701
u
34
+ ··· −
31107186917052254
32123119126701
u
2
+
1491502287952988
10707706375567
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
19
− 10u
18
+ ··· + 43u − 6)
2
c
2
, c
8
u
38
+ 10u
36
+ ··· + 43u
2
+ 6
c
3
u
38
+ 12u
37
+ ··· + 14u + 1
c
4
, c
10
u
38
+ 5u
36
+ ··· − 71u
2
+ 6
c
5
u
38
− u
37
+ ··· + 172u + 47
c
6
u
38
− 3u
36
+ ··· + 547u
2
+ 96
c
7
u
38
+ u
37
+ ··· − 172u + 47
c
9
u
38
+ 5u
37
+ ··· − u + 1
c
11
u
38
− 12u
37
+ ··· − 14u + 1
c
12
u
38
− 5u
37
+ ··· + u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
19
+ 6y
18
+ ··· − 215y −36)
2
c
2
, c
8
(y
19
+ 10y
18
+ ··· + 43y + 6)
2
c
3
, c
11
y
38
− 24y
37
+ ··· − 26y + 1
c
4
, c
10
(y
19
+ 5y
18
+ ··· − 71y + 6)
2
c
5
, c
7
y
38
− 27y
37
+ ··· + 12622y + 2209
c
6
(y
19
− 3y
18
+ ··· + 547y + 96)
2
c
9
, c
12
y
38
− 13y
37
+ ··· − 21y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.368536 + 1.093010I
a = −0.986741 + 0.631954I
b = −0.940577 + 0.679042I
−4.21942 + 1.26411I 12.1206 + 15.2461I
u = 0.368536 − 1.093010I
a = −0.986741 − 0.631954I
b = −0.940577 − 0.679042I
−4.21942 − 1.26411I 12.1206 − 15.2461I
u = −0.368536 + 1.093010I
a = −1.394300 + 0.011872I
b = −2.13686 − 1.19210I
−4.21942 − 1.26411I 12.1206 − 15.2461I
u = −0.368536 − 1.093010I
a = −1.394300 − 0.011872I
b = −2.13686 + 1.19210I
−4.21942 + 1.26411I 12.1206 + 15.2461I
u = −0.013881 + 1.164430I
a = −0.230677 − 1.137970I
b = 0.942976 − 0.768703I
−0.60660 − 4.23103I 10.84352 + 5.49488I
u = −0.013881 − 1.164430I
a = −0.230677 + 1.137970I
b = 0.942976 + 0.768703I
−0.60660 + 4.23103I 10.84352 − 5.49488I
u = 0.013881 + 1.164430I
a = 0.56219 + 1.35923I
b = 0.40374 + 1.44459I
−0.60660 + 4.23103I 10.84352 − 5.49488I
u = 0.013881 − 1.164430I
a = 0.56219 − 1.35923I
b = 0.40374 − 1.44459I
−0.60660 − 4.23103I 10.84352 + 5.49488I
u = −0.759283 + 0.094992I
a = 0.730936 + 1.201440I
b = 0.431216 − 0.484111I
0.16259 − 3.72611I 6.99269 + 5.17162I
u = −0.759283 − 0.094992I
a = 0.730936 − 1.201440I
b = 0.431216 + 0.484111I
0.16259 + 3.72611I 6.99269 − 5.17162I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.759283 + 0.094992I
a = 0.436068 + 0.675604I
b = −0.738626 − 0.833855I
0.16259 + 3.72611I 6.99269 − 5.17162I
u = 0.759283 − 0.094992I
a = 0.436068 − 0.675604I
b = −0.738626 + 0.833855I
0.16259 − 3.72611I 6.99269 + 5.17162I
u = 0.119211 + 1.305140I
a = 0.510570 + 1.206620I
b = 0.242071 + 1.162830I
−1.09905 + 3.04243I 5.98833 − 7.64000I
u = 0.119211 − 1.305140I
a = 0.510570 − 1.206620I
b = 0.242071 − 1.162830I
−1.09905 − 3.04243I 5.98833 + 7.64000I
u = −0.119211 + 1.305140I
a = −0.791102 − 0.160934I
b = 0.921216 − 0.192699I
−1.09905 − 3.04243I 5.98833 + 7.64000I
u = −0.119211 − 1.305140I
a = −0.791102 + 0.160934I
b = 0.921216 + 0.192699I
−1.09905 + 3.04243I 5.98833 − 7.64000I
u = −1.397230 + 0.042898I
a = 0.050699 + 0.243992I
b = 0.379606 + 0.024239I
5.81015 − 2.87084I 23.5562 + 1.4672I
u = −1.397230 − 0.042898I
a = 0.050699 − 0.243992I
b = 0.379606 − 0.024239I
5.81015 + 2.87084I 23.5562 − 1.4672I
u = 1.397230 + 0.042898I
a = 1.61376 − 0.00003I
b = −1.62179 + 0.34327I
5.81015 + 2.87084I 23.5562 − 1.4672I
u = 1.397230 − 0.042898I
a = 1.61376 + 0.00003I
b = −1.62179 − 0.34327I
5.81015 − 2.87084I 23.5562 + 1.4672I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.562133 + 0.095497I
a = 0.177386 − 0.049756I
b = −1.134900 − 0.504327I
4.96687 + 7.56367I 22.5743 − 10.6396I
u = 0.562133 − 0.095497I
a = 0.177386 + 0.049756I
b = −1.134900 + 0.504327I
4.96687 − 7.56367I 22.5743 + 10.6396I
u = −0.562133 + 0.095497I
a = −1.22829 + 4.81684I
b = −0.071224 − 0.508369I
4.96687 − 7.56367I 22.5743 + 10.6396I
u = −0.562133 − 0.095497I
a = −1.22829 − 4.81684I
b = −0.071224 + 0.508369I
4.96687 + 7.56367I 22.5743 − 10.6396I
u = 0.07040 + 1.43087I
a = 0.448064 + 0.297197I
b = −1.095240 + 0.082567I
−2.58584 + 7.60431I 5.46655 − 8.14788I
u = 0.07040 − 1.43087I
a = 0.448064 − 0.297197I
b = −1.095240 − 0.082567I
−2.58584 − 7.60431I 5.46655 + 8.14788I
u = −0.07040 + 1.43087I
a = −0.472121 + 1.169250I
b = −0.294525 + 1.029090I
−2.58584 − 7.60431I 5.46655 + 8.14788I
u = −0.07040 − 1.43087I
a = −0.472121 − 1.169250I
b = −0.294525 − 1.029090I
−2.58584 + 7.60431I 5.46655 − 8.14788I
u = −1.45503 + 0.04243I
a = −1.64584 + 0.02145I
b = 1.43982 + 0.16028I
6.54210 + 1.44717I 14.2109 − 13.0887I
u = −1.45503 − 0.04243I
a = −1.64584 − 0.02145I
b = 1.43982 − 0.16028I
6.54210 − 1.44717I 14.2109 + 13.0887I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45503 + 0.04243I
a = 0.168020 + 0.166232I
b = −0.362779 + 0.013140I
6.54210 − 1.44717I 14.2109 + 13.0887I
u = 1.45503 − 0.04243I
a = 0.168020 − 0.166232I
b = −0.362779 − 0.013140I
6.54210 + 1.44717I 14.2109 − 13.0887I
u = 0.504819 + 0.158284I
a = 3.15850 + 3.82239I
b = 0.256978 − 0.566965I
5.57840 + 1.68245I 21.0505 − 8.6684I
u = 0.504819 − 0.158284I
a = 3.15850 − 3.82239I
b = 0.256978 + 0.566965I
5.57840 − 1.68245I 21.0505 + 8.6684I
u = −0.504819 + 0.158284I
a = −0.072394 − 0.241315I
b = 1.143790 − 0.355417I
5.57840 − 1.68245I 21.0505 + 8.6684I
u = −0.504819 − 0.158284I
a = −0.072394 + 0.241315I
b = 1.143790 + 0.355417I
5.57840 + 1.68245I 21.0505 − 8.6684I
u = 1.74570I
a = −0.034725 + 1.007300I
b = −0.264899 + 1.262950I
−7.71427 0
u = − 1.74570I
a = −0.034725 − 1.007300I
b = −0.264899 − 1.262950I
−7.71427 0
26
IV. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
−1
0
a
1
=
0
1
a
5
=
1
0
a
6
=
1
−1
a
3
=
0
1
a
10
=
−1
0
a
12
=
−1
1
a
7
=
1
−1
a
8
=
0
−1
a
2
=
0
1
a
9
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
10
u
c
3
, c
7
, c
12
u + 1
c
5
, c
9
, c
11
u − 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
10
y
c
3
, c
5
, c
7
c
9
, c
11
, c
12
y −1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
3.28987 12.0000
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
19
− 10u
18
+ ··· + 43u − 6)
2
(u
35
+ 17u
34
+ ··· − 405u − 49)
2
· (u
45
+ 19u
44
+ ··· + 296u − 100)
c
2
, c
8
u(u
35
− u
34
+ ··· + 13u − 7)
2
(u
38
+ 10u
36
+ ··· + 43u
2
+ 6)
· (u
45
+ 3u
44
+ ··· − 44u − 10)
c
3
(u + 1)(u
38
+ 12u
37
+ ··· + 14u + 1)(u
45
+ u
44
+ ··· + 5u − 1)
· (u
70
+ 5u
69
+ ··· − 787u + 338)
c
4
, c
10
u(u
35
+ u
34
+ ··· + 9u − 1)
2
(u
38
+ 5u
36
+ ··· − 71u
2
+ 6)
· (u
45
− 3u
44
+ ··· − 216u − 50)
c
5
(u − 1)(u
38
− u
37
+ ··· + 172u + 47)(u
45
− u
44
+ ··· + 11u − 143)
· (u
70
+ 2u
69
+ ··· + 625113u + 75346)
c
6
u(u
35
− 4u
33
+ ··· + 10u − 1)
2
(u
38
− 3u
36
+ ··· + 547u
2
+ 96)
· (u
45
− 3u
44
+ ··· + 8824u − 1928)
c
7
(u + 1)(u
38
+ u
37
+ ··· − 172u + 47)(u
45
− u
44
+ ··· + 11u − 143)
· (u
70
+ 2u
69
+ ··· + 625113u + 75346)
c
9
(u − 1)(u
38
+ 5u
37
+ ··· − u + 1)(u
45
+ 3u
44
+ ··· + 33u − 16)
· (u
70
+ 8u
69
+ ··· + 10573u + 7727)
c
11
(u − 1)(u
38
− 12u
37
+ ··· − 14u + 1)(u
45
+ u
44
+ ··· + 5u − 1)
· (u
70
+ 5u
69
+ ··· − 787u + 338)
c
12
(u + 1)(u
38
− 5u
37
+ ··· + u + 1)(u
45
+ 3u
44
+ ··· + 33u − 16)
· (u
70
+ 8u
69
+ ··· + 10573u + 7727)
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
19
+ 6y
18
+ ··· − 215y −36)
2
· (y
35
+ 9y
34
+ ··· − 10317y −2401)
2
· (y
45
+ 15y
44
+ ··· + 417216y −10000)
c
2
, c
8
y(y
19
+ 10y
18
+ ··· + 43y + 6)
2
(y
35
+ 17y
34
+ ··· − 405y −49)
2
· (y
45
+ 19y
44
+ ··· + 296y −100)
c
3
, c
11
(y −1)(y
38
− 24y
37
+ ··· − 26y + 1)(y
45
− 7y
44
+ ··· + 25y −1)
· (y
70
− 33y
69
+ ··· − 4966725y + 114244)
c
4
, c
10
y(y
19
+ 5y
18
+ ··· − 71y + 6)
2
(y
35
+ 25y
34
+ ··· + 53y −1)
2
· (y
45
+ 29y
44
+ ··· − 66944y −2500)
c
5
, c
7
(y −1)(y
38
− 27y
37
+ ··· + 12622y + 2209)
· (y
45
+ 27y
44
+ ··· − 283019y −20449)
· (y
70
− 34y
69
+ ··· + 95484723835y + 5677019716)
c
6
y(y
19
− 3y
18
+ ··· + 547y + 96)
2
(y
35
− 8y
34
+ ··· − 34y −1)
2
· (y
45
− 5y
44
+ ··· + 32639808y −3717184)
c
9
, c
12
(y −1)(y
38
− 13y
37
+ ··· − 21y + 1)(y
45
+ 35y
44
+ ··· − 6847y −256)
· (y
70
− 16y
69
+ ··· + 1891683685y + 59706529)
32
