12a
0663
(K12a
0663
)
A knot diagram
1
Linearized knot diagam
3 7 10 12 11 2 1 5 4 6 9 8
Solving Sequence
4,12 5,9
10 3 8 1 7 2 11 6
c
4
c
9
c
3
c
8
c
12
c
7
c
2
c
11
c
5
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.53926 × 10
31
u
38
− 4.08337 × 10
30
u
37
+ ··· + 6.57846 × 10
31
b + 8.43133 × 10
30
,
− 1.38800 × 10
31
u
38
− 2.23113 × 10
31
u
37
+ ··· + 6.57846 × 10
31
a − 3.08771 × 10
32
, u
39
+ u
38
+ ··· + 7u
2
+ 1i
I
u
2
= h−6.98995 × 10
294
u
71
− 1.49499 × 10
295
u
70
+ ··· + 1.56256 × 10
295
b − 1.00003 × 10
298
,
− 4.22283 × 10
228
u
71
− 9.43208 × 10
228
u
70
+ ··· + 1.97531 × 10
229
a − 7.72233 × 10
231
,
u
72
+ 3u
71
+ ··· − 300u + 1393i
I
u
3
= h−227849189u
23
− 908034262u
22
+ ··· + 2211913739b − 16196133,
18343895u
23
− 2147762u
22
+ ··· + 2211913739a + 1387418052, u
24
− u
23
+ ··· − 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 135 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−6.54×10
31
u
38
−4.08×10
30
u
37
+· · ·+6.58×10
31
b+8.43×10
30
, −1.39×
10
31
u
38
−2.23×10
31
u
37
+· · ·+6.58 ×10
31
a−3.09×10
32
, u
39
+u
38
+· · ·+7u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
0.210991u
38
+ 0.339157u
37
+ ··· − 4.36758u + 4.69367
0.994042u
38
+ 0.0620718u
37
+ ··· + 0.789009u − 0.128166
a
10
=
1.20503u
38
+ 0.401229u
37
+ ··· − 3.57857u + 4.56550
0.994042u
38
+ 0.0620718u
37
+ ··· + 0.789009u − 0.128166
a
3
=
5.20733u
38
+ 1.32756u
37
+ ··· − 1.16737u + 6.24635
1.20174u
38
− 0.260291u
37
+ ··· − 4.13375u + 1.42369
a
8
=
0.210991u
38
+ 0.339157u
37
+ ··· − 3.36758u + 4.69367
0.994042u
38
+ 0.0620718u
37
+ ··· + 0.789009u − 0.128166
a
1
=
−2.04556u
38
− 0.0320806u
37
+ ··· + 6.93865u − 1.98362
−0.970929u
38
− 0.311046u
37
+ ··· + 2.83457u − 2.14165
a
7
=
1.03526u
38
+ 0.698475u
37
+ ··· + 0.632919u + 5.82032
−0.0773108u
38
− 0.183940u
37
+ ··· + 1.79931u − 1.80486
a
2
=
0.410708u
38
+ 0.579404u
37
+ ··· + 4.25907u + 3.42658
−1.55656u
38
− 0.282778u
37
+ ··· + 2.55983u − 2.67790
a
11
=
−4.03365u
38
− 0.156224u
37
+ ··· + 7.36063u − 1.72729
−2.41774u
38
− 0.284021u
37
+ ··· + 4.82266u − 4.00559
a
6
=
3.57384u
38
+ 0.937443u
37
+ ··· − 8.23572u + 5.85575
1.32991u
38
+ 0.861916u
37
+ ··· + 0.559915u + 1.21270
(ii) Obstruction class = −1
(iii) Cusp Shapes = 9.50767u
38
+ 2.94061u
37
+ ··· − 7.93931u − 0.143921
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
+ 21u
38
+ ··· + 16u + 64
c
2
, c
6
u
39
− 7u
38
+ ··· − 68u + 8
c
3
, c
5
, c
9
c
10
u
39
+ 20u
37
+ ··· − u + 1
c
4
, c
8
u
39
+ u
38
+ ··· + 7u
2
+ 1
c
7
, c
12
u
39
− 21u
38
+ ··· − 10052u + 1192
c
11
u
39
− 36u
38
+ ··· + 90112u − 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
− 5y
38
+ ··· − 2816y −4096
c
2
, c
6
y
39
− 21y
38
+ ··· + 16y −64
c
3
, c
5
, c
9
c
10
y
39
+ 40y
38
+ ··· + 19y −1
c
4
, c
8
y
39
− 15y
38
+ ··· − 14y −1
c
7
, c
12
y
39
+ 31y
38
+ ··· + 64653328y −1420864
c
11
y
39
− 10y
38
+ ··· + 125829120y −16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.567111 + 0.787760I
a = 0.697115 + 0.159087I
b = −0.633371 + 0.117333I
1.32490 + 3.31400I 4.45912 − 5.74087I
u = −0.567111 − 0.787760I
a = 0.697115 − 0.159087I
b = −0.633371 − 0.117333I
1.32490 − 3.31400I 4.45912 + 5.74087I
u = −0.765136 + 0.571280I
a = 2.16539 + 0.12213I
b = −0.097378 − 1.290100I
−4.07768 + 4.05588I −5.30316 − 7.20111I
u = −0.765136 − 0.571280I
a = 2.16539 − 0.12213I
b = −0.097378 + 1.290100I
−4.07768 − 4.05588I −5.30316 + 7.20111I
u = −0.943048 + 0.012408I
a = 1.34635 − 1.58586I
b = 0.21700 − 1.42922I
−15.0496 + 1.0975I −12.20549 − 0.94590I
u = −0.943048 − 0.012408I
a = 1.34635 + 1.58586I
b = 0.21700 + 1.42922I
−15.0496 − 1.0975I −12.20549 + 0.94590I
u = −0.852570 + 0.138373I
a = 0.96600 + 2.04699I
b = 0.314074 + 1.359160I
−13.8330 + 8.7861I −10.86252 − 6.43696I
u = −0.852570 − 0.138373I
a = 0.96600 − 2.04699I
b = 0.314074 − 1.359160I
−13.8330 − 8.7861I −10.86252 + 6.43696I
u = 0.837375 + 0.048442I
a = −1.32421 + 2.02490I
b = −0.252328 + 1.356110I
−10.43840 − 3.43951I −9.01036 + 2.72933I
u = 0.837375 − 0.048442I
a = −1.32421 − 2.02490I
b = −0.252328 − 1.356110I
−10.43840 + 3.43951I −9.01036 − 2.72933I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.695786 + 0.401836I
a = −2.78898 − 0.37450I
b = 0.005349 − 1.278550I
−4.95357 + 1.37371I −9.10851 + 2.59492I
u = 0.695786 − 0.401836I
a = −2.78898 + 0.37450I
b = 0.005349 + 1.278550I
−4.95357 − 1.37371I −9.10851 − 2.59492I
u = 0.351727 + 0.722046I
a = −0.822254 + 0.137329I
b = 0.608935 + 0.249794I
1.85851 + 0.64123I 6.33062 − 2.65229I
u = 0.351727 − 0.722046I
a = −0.822254 − 0.137329I
b = 0.608935 − 0.249794I
1.85851 − 0.64123I 6.33062 + 2.65229I
u = −0.967742 + 0.763288I
a = 0.568572 + 0.141085I
b = −0.558086 − 0.026749I
−1.51812 + 3.17788I 2.76285 − 2.10152I
u = −0.967742 − 0.763288I
a = 0.568572 − 0.141085I
b = −0.558086 + 0.026749I
−1.51812 − 3.17788I 2.76285 + 2.10152I
u = 1.082180 + 0.592049I
a = −1.46368 − 0.22780I
b = 0.17300 − 1.47046I
−10.66960 − 5.07856I −10.53992 + 4.00671I
u = 1.082180 − 0.592049I
a = −1.46368 + 0.22780I
b = 0.17300 + 1.47046I
−10.66960 + 5.07856I −10.53992 − 4.00671I
u = −0.764518
a = 0.569386
b = −0.431719
−1.66339 −4.64910
u = 1.093730 + 0.671358I
a = −0.540699 + 0.117342I
b = 0.518302 − 0.035214I
−5.30148 + 0.79401I −2.08945 − 2.40704I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.093730 − 0.671358I
a = −0.540699 − 0.117342I
b = 0.518302 + 0.035214I
−5.30148 − 0.79401I −2.08945 + 2.40704I
u = −0.993018 + 0.816568I
a = 1.369400 + 0.161395I
b = −0.294026 − 1.352700I
−4.89712 + 7.00444I −3.44470 − 5.09853I
u = −0.993018 − 0.816568I
a = 1.369400 − 0.161395I
b = −0.294026 + 1.352700I
−4.89712 − 7.00444I −3.44470 + 5.09853I
u = 1.027790 + 0.860017I
a = −0.550444 + 0.162872I
b = 0.565522 − 0.061491I
−4.63847 − 7.81620I 0. + 5.15619I
u = 1.027790 − 0.860017I
a = −0.550444 − 0.162872I
b = 0.565522 + 0.061491I
−4.63847 + 7.81620I 0. − 5.15619I
u = 0.075508 + 0.610308I
a = 1.53525 + 0.35499I
b = −0.520301 + 0.621604I
−1.47213 − 5.06690I −0.37269 + 8.17616I
u = 0.075508 − 0.610308I
a = 1.53525 − 0.35499I
b = −0.520301 − 0.621604I
−1.47213 + 5.06690I −0.37269 − 8.17616I
u = 1.082800 + 0.904573I
a = −1.192250 + 0.140890I
b = 0.38451 − 1.38106I
−6.47260 − 12.07610I 0
u = 1.082800 − 0.904573I
a = −1.192250 − 0.140890I
b = 0.38451 + 1.38106I
−6.47260 + 12.07610I 0
u = 0.093806 + 0.574754I
a = −1.190660 − 0.013225I
b = 0.478079 + 0.450617I
0.88043 + 1.10691I 4.57256 − 4.10450I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.093806 − 0.574754I
a = −1.190660 + 0.013225I
b = 0.478079 − 0.450617I
0.88043 − 1.10691I 4.57256 + 4.10450I
u = 0.032561 + 0.358979I
a = 1.98747 − 1.70278I
b = −0.181643 + 0.623066I
−1.79359 + 1.44290I −3.00301 − 2.32178I
u = 0.032561 − 0.358979I
a = 1.98747 + 1.70278I
b = −0.181643 − 0.623066I
−1.79359 − 1.44290I −3.00301 + 2.32178I
u = −1.37493 + 0.89777I
a = 0.985563 − 0.068694I
b = −0.47573 − 1.60982I
−16.4040 + 8.0432I 0
u = −1.37493 − 0.89777I
a = 0.985563 + 0.068694I
b = −0.47573 + 1.60982I
−16.4040 − 8.0432I 0
u = 1.34788 + 0.94806I
a = −0.977771 − 0.023278I
b = 0.50981 − 1.57225I
−12.0675 − 12.5408I 0
u = 1.34788 − 0.94806I
a = −0.977771 + 0.023278I
b = 0.50981 + 1.57225I
−12.0675 + 12.5408I 0
u = −1.37533 + 0.98042I
a = 0.945129 − 0.018463I
b = −0.54586 − 1.58560I
−15.4829 + 17.6772I 0
u = −1.37533 − 0.98042I
a = 0.945129 + 0.018463I
b = −0.54586 + 1.58560I
−15.4829 − 17.6772I 0
8
II. I
u
2
= h−6.99 × 10
294
u
71
− 1.49 × 10
295
u
70
+ · · · + 1.56 × 10
295
b − 1.00 ×
10
298
, −4.22 × 10
228
u
71
− 9.43 × 10
228
u
70
+ · · · + 1.98 × 10
229
a − 7.72 ×
10
231
, u
72
+ 3u
71
+ · · · − 300u + 1393i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
0.213781u
71
+ 0.477499u
70
+ ··· − 559.380u + 390.943
0.447340u
71
+ 0.956757u
70
+ ··· − 863.774u + 639.995
a
10
=
0.661121u
71
+ 1.43426u
70
+ ··· − 1423.15u + 1030.94
0.447340u
71
+ 0.956757u
70
+ ··· − 863.774u + 639.995
a
3
=
−0.326580u
71
− 0.679236u
70
+ ··· + 636.636u − 521.167
−0.652852u
71
− 1.39754u
70
+ ··· + 1534.59u − 1128.73
a
8
=
0.547431u
71
+ 1.17282u
70
+ ··· − 1076.20u + 802.706
0.756568u
71
+ 1.61079u
70
+ ··· − 1420.24u + 1065.74
a
1
=
0.321622u
71
+ 0.694407u
70
+ ··· − 667.373u + 482.233
0.838420u
71
+ 1.84757u
70
+ ··· − 2017.81u + 1381.44
a
7
=
−0.712040u
71
− 1.48815u
70
+ ··· + 1236.05u − 996.432
−0.302736u
71
− 0.544396u
70
+ ··· − 34.3875u − 183.143
a
2
=
−1.12512u
71
− 2.32951u
70
+ ··· + 1885.56u − 1615.02
−0.379009u
71
− 0.633666u
70
+ ··· − 279.657u − 203.153
a
11
=
0.0534466u
71
+ 0.0989686u
70
+ ··· + 24.9761u + 17.5353
−0.260512u
71
− 0.587739u
70
+ ··· + 705.445u − 454.496
a
6
=
−0.269362u
71
− 0.561548u
70
+ ··· + 542.389u − 431.908
0.102472u
71
+ 0.265357u
70
+ ··· − 421.508u + 224.345
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.32211u
71
+ 2.68881u
70
+ ··· − 2261.71u + 1971.25
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
12
+ 7u
11
+ ··· + 2u + 1)
6
c
2
, c
6
(u
12
+ u
11
+ ··· + 2u + 1)
6
c
3
, c
5
, c
9
c
10
u
72
+ u
71
+ ··· + 83070u + 21519
c
4
, c
8
u
72
+ 3u
71
+ ··· − 300u + 1393
c
7
, c
12
(u
12
+ 3u
11
+ ··· + 2u + 1)
6
c
11
(u
3
+ u
2
− 1)
24
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
12
− 3y
11
+ ··· + 6y + 1)
6
c
2
, c
6
(y
12
− 7y
11
+ ··· − 2y + 1)
6
c
3
, c
5
, c
9
c
10
y
72
+ 63y
71
+ ··· + 7005211128y + 463067361
c
4
, c
8
y
72
− 21y
71
+ ··· − 73762984y + 1940449
c
7
, c
12
(y
12
+ 13y
11
+ ··· + 6y + 1)
6
c
11
(y
3
− y
2
+ 2y −1)
24
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.938864 + 0.351889I
a = 1.080190 + 0.388507I
b = −0.577650 + 1.026610I
−3.65041 − 3.54405I 0
u = 0.938864 − 0.351889I
a = 1.080190 − 0.388507I
b = −0.577650 − 1.026610I
−3.65041 + 3.54405I 0
u = −0.695969 + 0.703547I
a = −1.158640 − 0.101005I
b = 0.419002 + 0.949358I
−0.47337 + 2.47502I 0
u = −0.695969 − 0.703547I
a = −1.158640 + 0.101005I
b = 0.419002 − 0.949358I
−0.47337 − 2.47502I 0
u = −0.896798 + 0.544160I
a = 0.615230 + 0.373310I
b = −0.345138 − 1.320250I
−4.61095 + 0.35310I 0
u = −0.896798 − 0.544160I
a = 0.615230 − 0.373310I
b = −0.345138 + 1.320250I
−4.61095 − 0.35310I 0
u = 0.895151 + 0.285594I
a = −0.765387 + 0.244193I
b = 0.55798 − 1.40222I
−5.97151 − 4.24921I 0
u = 0.895151 − 0.285594I
a = −0.765387 − 0.244193I
b = 0.55798 + 1.40222I
−5.97151 + 4.24921I 0
u = −0.950167 + 0.477676I
a = −1.051750 + 0.255184I
b = 0.893429 + 0.652076I
−3.65041 + 2.11219I 0
u = −0.950167 − 0.477676I
a = −1.051750 − 0.255184I
b = 0.893429 − 0.652076I
−3.65041 − 2.11219I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.683356 + 0.629564I
a = −1.237700 − 0.050269I
b = 1.079820 + 0.047803I
−1.83393 + 7.07733I 0
u = −0.683356 − 0.629564I
a = −1.237700 + 0.050269I
b = 1.079820 − 0.047803I
−1.83393 − 7.07733I 0
u = −0.875823 + 0.032748I
a = −0.968691 − 0.886691I
b = 0.28771 − 1.42938I
−9.82586 − 4.31046I 0
u = −0.875823 − 0.032748I
a = −0.968691 + 0.886691I
b = 0.28771 + 1.42938I
−9.82586 + 4.31046I 0
u = −1.139340 + 0.018524I
a = −0.759301 − 0.666112I
b = −0.074632 − 0.480507I
−3.65041 − 3.54405I 0
u = −1.139340 − 0.018524I
a = −0.759301 + 0.666112I
b = −0.074632 + 0.480507I
−3.65041 + 3.54405I 0
u = −0.902629 + 0.771402I
a = −0.969350 − 0.003209I
b = 1.43937 + 0.34561I
−5.95086 + 5.84119I 0
u = −0.902629 − 0.771402I
a = −0.969350 + 0.003209I
b = 1.43937 − 0.34561I
−5.95086 − 5.84119I 0
u = −0.800373 + 0.084657I
a = 0.932723 + 0.098656I
b = −0.83388 + 1.77828I
−13.6064 − 7.8013I 0
u = −0.800373 − 0.084657I
a = 0.932723 − 0.098656I
b = −0.83388 − 1.77828I
−13.6064 + 7.8013I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.795207 + 0.114501I
a = −0.94886 − 1.07332I
b = 0.15311 − 1.42762I
−9.46883 + 4.97322I 0
u = −0.795207 − 0.114501I
a = −0.94886 + 1.07332I
b = 0.15311 + 1.42762I
−9.46883 − 4.97322I 0
u = 0.798362 + 0.043303I
a = 1.04537 − 0.98969I
b = −0.215067 − 1.374770I
−5.95086 − 0.18495I 0
u = 0.798362 − 0.043303I
a = 1.04537 + 0.98969I
b = −0.215067 + 1.374770I
−5.95086 + 0.18495I 0
u = 0.897012 + 0.814806I
a = 0.949236 − 0.031863I
b = −1.50801 + 0.30673I
−9.4688 − 10.6295I 0
u = 0.897012 − 0.814806I
a = 0.949236 + 0.031863I
b = −1.50801 − 0.30673I
−9.4688 + 10.6295I 0
u = 0.626598 + 0.460862I
a = 1.47612 + 0.10306I
b = −0.787136 − 0.000822I
−0.47337 − 3.18123I 0
u = 0.626598 − 0.460862I
a = 1.47612 − 0.10306I
b = −0.787136 + 0.000822I
−0.47337 + 3.18123I 0
u = 0.952137 + 0.766731I
a = 0.941188 + 0.024391I
b = −1.46635 + 0.43270I
−9.82586 − 1.34579I 0
u = 0.952137 − 0.766731I
a = 0.941188 − 0.024391I
b = −1.46635 − 0.43270I
−9.82586 + 1.34579I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.755114 + 0.049866I
a = −0.995346 + 0.065731I
b = 0.75652 + 1.78049I
−10.08840 + 3.01307I −10.38776 − 2.63251I
u = 0.755114 − 0.049866I
a = −0.995346 − 0.065731I
b = 0.75652 − 1.78049I
−10.08840 − 3.01307I −10.38776 + 2.63251I
u = −0.947835 + 0.818100I
a = −0.141799 − 0.908246I
b = −0.642677 − 0.031476I
−5.95086 + 0.18495I 0
u = −0.947835 − 0.818100I
a = −0.141799 + 0.908246I
b = −0.642677 + 0.031476I
−5.95086 − 0.18495I 0
u = −0.704713 + 0.094468I
a = 1.052280 + 0.141059I
b = −0.73862 + 1.86694I
−13.96340 + 1.48234I −14.1721 + 0.I
u = −0.704713 − 0.094468I
a = 1.052280 − 0.141059I
b = −0.73862 − 1.86694I
−13.96340 − 1.48234I −14.1721 + 0.I
u = −0.993660 + 0.871930I
a = −0.870522 − 0.014263I
b = 0.404190 + 1.044340I
−0.47337 + 3.18123I 0
u = −0.993660 − 0.871930I
a = −0.870522 + 0.014263I
b = 0.404190 − 1.044340I
−0.47337 − 3.18123I 0
u = 0.936142 + 0.935766I
a = 0.070999 − 0.866642I
b = 0.723217 + 0.009280I
−9.46883 − 4.97322I 0
u = 0.936142 − 0.935766I
a = 0.070999 + 0.866642I
b = 0.723217 − 0.009280I
−9.46883 + 4.97322I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.080580 + 0.805746I
a = 0.191523 − 0.832126I
b = 0.672492 − 0.130639I
−9.82586 + 4.31046I 0
u = 1.080580 − 0.805746I
a = 0.191523 + 0.832126I
b = 0.672492 + 0.130639I
−9.82586 − 4.31046I 0
u = −1.022110 + 0.909480I
a = 0.412193 + 0.366771I
b = −0.125230 − 1.230710I
−4.61095 − 0.35310I 0
u = −1.022110 − 0.909480I
a = 0.412193 − 0.366771I
b = −0.125230 + 1.230710I
−4.61095 + 0.35310I 0
u = 0.357941 + 0.426085I
a = 2.03909 − 0.34633I
b = −0.269982 + 0.860169I
−1.83393 + 1.42109I −2.31375 − 4.00366I
u = 0.357941 − 0.426085I
a = 2.03909 + 0.34633I
b = −0.269982 − 0.860169I
−1.83393 − 1.42109I −2.31375 + 4.00366I
u = 1.37134 + 0.47480I
a = 0.739279 + 0.287203I
b = −0.100560 + 0.960389I
−3.65041 − 2.11219I 0
u = 1.37134 − 0.47480I
a = 0.739279 − 0.287203I
b = −0.100560 − 0.960389I
−3.65041 + 2.11219I 0
u = 0.505627 + 0.186361I
a = 2.00583 + 0.73385I
b = −0.391125 − 0.163404I
−0.47337 − 2.47502I 2.17667 + 2.34964I
u = 0.505627 − 0.186361I
a = 2.00583 − 0.73385I
b = −0.391125 + 0.163404I
−0.47337 + 2.47502I 2.17667 − 2.34964I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21048 + 1.01361I
a = 0.728986 + 0.004921I
b = −0.376227 + 1.161460I
−1.83393 − 7.07733I 0
u = 1.21048 − 1.01361I
a = 0.728986 − 0.004921I
b = −0.376227 − 1.161460I
−1.83393 + 7.07733I 0
u = 0.310247 + 0.268232I
a = −1.39237 + 1.20381I
b = 0.21533 − 1.75580I
−7.78799 + 0.71593I −14.9760 − 0.6487I
u = 0.310247 − 0.268232I
a = −1.39237 − 1.20381I
b = 0.21533 + 1.75580I
−7.78799 − 0.71593I −14.9760 + 0.6487I
u = 0.44953 + 1.55332I
a = −0.129774 + 0.448422I
b = −0.02909 − 1.44080I
−7.78799 − 0.71593I 0
u = 0.44953 − 1.55332I
a = −0.129774 − 0.448422I
b = −0.02909 + 1.44080I
−7.78799 + 0.71593I 0
u = −0.266678 + 0.219690I
a = −0.58934 − 3.27861I
b = −0.039691 + 0.420211I
−1.83393 + 1.42109I −2.31375 − 4.00366I
u = −0.266678 − 0.219690I
a = −0.58934 + 3.27861I
b = −0.039691 − 0.420211I
−1.83393 − 1.42109I −2.31375 + 4.00366I
u = 1.23371 + 1.18663I
a = −0.317836 + 0.305705I
b = −0.036152 − 1.181350I
−5.97151 + 4.24921I 0
u = 1.23371 − 1.18663I
a = −0.317836 − 0.305705I
b = −0.036152 + 1.181350I
−5.97151 − 4.24921I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65678 + 1.00359I
a = 0.586672 + 0.094210I
b = −0.196438 + 1.343260I
−5.95086 − 5.84119I 0
u = 1.65678 − 1.00359I
a = 0.586672 − 0.094210I
b = −0.196438 − 1.343260I
−5.95086 + 5.84119I 0
u = −1.73068 + 0.94927I
a = −0.571209 + 0.117082I
b = 0.140642 + 1.355310I
−9.82586 + 1.34579I 0
u = −1.73068 − 0.94927I
a = −0.571209 − 0.117082I
b = 0.140642 − 1.355310I
−9.82586 − 1.34579I 0
u = −1.68817 + 1.07636I
a = −0.569546 + 0.078087I
b = 0.217490 + 1.387090I
−9.4688 + 10.6295I 0
u = −1.68817 − 1.07636I
a = −0.569546 − 0.078087I
b = 0.217490 − 1.387090I
−9.4688 − 10.6295I 0
u = 1.32654 + 1.81813I
a = −0.197693 + 0.270954I
b = −0.246263 − 1.322600I
−10.08840 + 3.01307I 0
u = 1.32654 − 1.81813I
a = −0.197693 − 0.270954I
b = −0.246263 + 1.322600I
−10.08840 − 3.01307I 0
u = −1.27060 + 1.93825I
a = 0.178571 + 0.272404I
b = 0.254431 − 1.368670I
−13.96340 + 1.48234I 0
u = −1.27060 − 1.93825I
a = 0.178571 − 0.272404I
b = 0.254431 + 1.368670I
−13.96340 − 1.48234I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43807 + 1.84219I
a = 0.198760 + 0.254615I
b = 0.285192 − 1.305970I
−13.6064 − 7.8013I 0
u = −1.43807 − 1.84219I
a = 0.198760 − 0.254615I
b = 0.285192 + 1.305970I
−13.6064 + 7.8013I 0
19
III.
I
u
3
= h−2.28 × 10
8
u
23
− 9.08 × 10
8
u
22
+ · · · + 2.21 × 10
9
b − 1.62 × 10
7
, 1.83 ×
10
7
u
23
− 2.15 × 10
6
u
22
+ · · · + 2.21 × 10
9
a + 1.39 × 10
9
, u
24
− u
23
+ · · · − 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
−0.00829322u
23
+ 0.000970997u
22
+ ··· + 3.13796u − 0.627248
0.103010u
23
+ 0.410520u
22
+ ··· − 1.00635u + 0.00732223
a
10
=
0.0947168u
23
+ 0.411491u
22
+ ··· + 2.13161u − 0.619926
0.103010u
23
+ 0.410520u
22
+ ··· − 1.00635u + 0.00732223
a
3
=
1.48647u
23
− 0.847060u
22
+ ··· + 3.78666u − 0.896990
−0.513530u
23
+ 0.152940u
22
+ ··· − 0.213342u − 0.896990
a
8
=
−0.00829322u
23
+ 0.000970997u
22
+ ··· + 2.13796u − 0.627248
0.103010u
23
+ 0.410520u
22
+ ··· − 1.00635u + 0.00732223
a
1
=
0.785687u
23
+ 0.179932u
22
+ ··· − 0.849337u + 1.35811
0.278821u
23
− 0.517601u
22
+ ··· + 2.15190u − 0.972941
a
7
=
0.639618u
23
− 0.463929u
22
+ ··· + 4.65504u − 3.70638
0.412506u
23
+ 0.450938u
22
+ ··· − 2.44014u + 0.797252
a
2
=
1.22661u
23
+ 0.892452u
22
+ ··· − 2.34404u + 2.86926
0.699270u
23
− 0.972534u
22
+ ··· + 4.68130u − 2.44294
a
11
=
0.991707u
23
+ 1.00097u
22
+ ··· − 0.862039u + 1.37275
u
23
− u
22
+ ··· + 4u − 2
a
6
=
−0.627248u
23
+ 0.635541u
22
+ ··· − 5.12240u − 0.883465
0.520852u
23
− 0.263272u
22
+ ··· + 0.857176u + 0.888697
(ii) Obstruction class = 1
(iii) Cusp Shapes =
5968239010
2211913739
u
23
−
1305237733
2211913739
u
22
+ ··· −
9063563809
2211913739
u −
14136299053
2211913739
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 14u
23
+ ··· − 6u + 1
c
2
u
24
− 7u
22
+ ··· − 3u
2
+ 1
c
3
, c
10
u
24
+ 12u
22
+ ··· + u + 1
c
4
, c
8
u
24
− u
23
+ ··· − 2u + 1
c
5
, c
9
u
24
+ 12u
22
+ ··· − u + 1
c
6
u
24
− 7u
22
+ ··· − 3u
2
+ 1
c
7
u
24
+ 9u
22
+ ··· − 3u
2
+ 1
c
11
u
24
+ 7u
23
+ ··· − 2u
2
+ 1
c
12
u
24
+ 9u
22
+ ··· − 3u
2
+ 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 2y
23
+ ··· − 10y + 1
c
2
, c
6
y
24
− 14y
23
+ ··· − 6y + 1
c
3
, c
5
, c
9
c
10
y
24
+ 24y
23
+ ··· + 17y + 1
c
4
, c
8
y
24
− 7y
23
+ ··· + 2y + 1
c
7
, c
12
y
24
+ 18y
23
+ ··· − 6y + 1
c
11
y
24
− 9y
23
+ ··· − 4y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.997020 + 0.104625I
a = 0.704736 + 0.787573I
b = −0.468500 + 0.816667I
−3.55627 − 4.90016I −6.21271 + 9.68873I
u = 0.997020 − 0.104625I
a = 0.704736 − 0.787573I
b = −0.468500 − 0.816667I
−3.55627 + 4.90016I −6.21271 − 9.68873I
u = −0.703505 + 0.735651I
a = 0.632532 − 0.188269I
b = 0.47937 − 1.38166I
−12.2595 − 7.5343I −6.02935 + 3.97375I
u = −0.703505 − 0.735651I
a = 0.632532 + 0.188269I
b = 0.47937 + 1.38166I
−12.2595 + 7.5343I −6.02935 − 3.97375I
u = 0.103114 + 0.971310I
a = −0.167285 + 0.634171I
b = −0.07410 − 1.59638I
−7.17860 − 0.99670I −0.90029 + 7.28189I
u = 0.103114 − 0.971310I
a = −0.167285 − 0.634171I
b = −0.07410 + 1.59638I
−7.17860 + 0.99670I −0.90029 − 7.28189I
u = −0.576512 + 0.863171I
a = 0.596740 + 0.076087I
b = 0.40597 − 1.48848I
−12.74230 + 1.79763I −6.41469 − 2.68582I
u = −0.576512 − 0.863171I
a = 0.596740 − 0.076087I
b = 0.40597 + 1.48848I
−12.74230 − 1.79763I −6.41469 + 2.68582I
u = 0.592444 + 0.738728I
a = −0.764665 − 0.046892I
b = −0.40249 − 1.39892I
−8.77245 + 2.65917I −3.02353 − 0.59148I
u = 0.592444 − 0.738728I
a = −0.764665 + 0.046892I
b = −0.40249 + 1.39892I
−8.77245 − 2.65917I −3.02353 + 0.59148I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.776941 + 0.496560I
a = −1.53086 + 0.07470I
b = 0.287961 + 0.711322I
−1.18860 + 3.44984I −3.33019 − 8.27194I
u = −0.776941 − 0.496560I
a = −1.53086 − 0.07470I
b = 0.287961 − 0.711322I
−1.18860 − 3.44984I −3.33019 + 8.27194I
u = −1.144190 + 0.324015I
a = −0.783368 + 0.352427I
b = 0.462181 + 0.681220I
−2.31746 + 2.30300I −0.67195 − 2.29633I
u = −1.144190 − 0.324015I
a = −0.783368 − 0.352427I
b = 0.462181 − 0.681220I
−2.31746 − 2.30300I −0.67195 + 2.29633I
u = −1.096320 + 0.676877I
a = −0.882148 − 0.062508I
b = 0.347449 + 0.585870I
−2.59301 + 3.66859I −4.93513 − 4.53769I
u = −1.096320 − 0.676877I
a = −0.882148 + 0.062508I
b = 0.347449 − 0.585870I
−2.59301 − 3.66859I −4.93513 + 4.53769I
u = 0.628567 + 0.303903I
a = 2.25583 + 0.83507I
b = −0.264677 + 0.810740I
−2.29425 + 0.73380I −8.11311 + 4.27669I
u = 0.628567 − 0.303903I
a = 2.25583 − 0.83507I
b = −0.264677 − 0.810740I
−2.29425 − 0.73380I −8.11311 − 4.27669I
u = 1.126770 + 0.807829I
a = 0.801307 − 0.169418I
b = −0.323926 + 0.546394I
−5.53609 − 8.08592I −8.83517 + 7.64981I
u = 1.126770 − 0.807829I
a = 0.801307 + 0.169418I
b = −0.323926 − 0.546394I
−5.53609 + 8.08592I −8.83517 − 7.64981I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.25611 + 0.66382I
a = 0.737015 − 0.016313I
b = −0.390803 + 0.546724I
−6.03991 + 0.15086I −8.95024 + 1.76304I
u = 1.25611 − 0.66382I
a = 0.737015 + 0.016313I
b = −0.390803 − 0.546724I
−6.03991 − 0.15086I −8.95024 − 1.76304I
u = 0.093446 + 0.516975I
a = −1.09983 + 2.58045I
b = −0.058427 − 1.290360I
−4.60878 + 2.39167I −5.58364 − 4.20201I
u = 0.093446 − 0.516975I
a = −1.09983 − 2.58045I
b = −0.058427 + 1.290360I
−4.60878 − 2.39167I −5.58364 + 4.20201I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
12
+ 7u
11
+ ··· + 2u + 1)
6
)(u
24
− 14u
23
+ ··· − 6u + 1)
· (u
39
+ 21u
38
+ ··· + 16u + 64)
c
2
((u
12
+ u
11
+ ··· + 2u + 1)
6
)(u
24
− 7u
22
+ ··· − 3u
2
+ 1)
· (u
39
− 7u
38
+ ··· − 68u + 8)
c
3
, c
10
(u
24
+ 12u
22
+ ··· + u + 1)(u
39
+ 20u
37
+ ··· − u + 1)
· (u
72
+ u
71
+ ··· + 83070u + 21519)
c
4
, c
8
(u
24
− u
23
+ ··· − 2u + 1)(u
39
+ u
38
+ ··· + 7u
2
+ 1)
· (u
72
+ 3u
71
+ ··· − 300u + 1393)
c
5
, c
9
(u
24
+ 12u
22
+ ··· − u + 1)(u
39
+ 20u
37
+ ··· − u + 1)
· (u
72
+ u
71
+ ··· + 83070u + 21519)
c
6
((u
12
+ u
11
+ ··· + 2u + 1)
6
)(u
24
− 7u
22
+ ··· − 3u
2
+ 1)
· (u
39
− 7u
38
+ ··· − 68u + 8)
c
7
((u
12
+ 3u
11
+ ··· + 2u + 1)
6
)(u
24
+ 9u
22
+ ··· − 3u
2
+ 1)
· (u
39
− 21u
38
+ ··· − 10052u + 1192)
c
11
((u
3
+ u
2
− 1)
24
)(u
24
+ 7u
23
+ ··· − 2u
2
+ 1)
· (u
39
− 36u
38
+ ··· + 90112u − 4096)
c
12
((u
12
+ 3u
11
+ ··· + 2u + 1)
6
)(u
24
+ 9u
22
+ ··· − 3u
2
+ 1)
· (u
39
− 21u
38
+ ··· − 10052u + 1192)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
12
− 3y
11
+ ··· + 6y + 1)
6
)(y
24
− 2y
23
+ ··· − 10y + 1)
· (y
39
− 5y
38
+ ··· − 2816y −4096)
c
2
, c
6
((y
12
− 7y
11
+ ··· − 2y + 1)
6
)(y
24
− 14y
23
+ ··· − 6y + 1)
· (y
39
− 21y
38
+ ··· + 16y −64)
c
3
, c
5
, c
9
c
10
(y
24
+ 24y
23
+ ··· + 17y + 1)(y
39
+ 40y
38
+ ··· + 19y −1)
· (y
72
+ 63y
71
+ ··· + 7005211128y + 463067361)
c
4
, c
8
(y
24
− 7y
23
+ ··· + 2y + 1)(y
39
− 15y
38
+ ··· − 14y −1)
· (y
72
− 21y
71
+ ··· − 73762984y + 1940449)
c
7
, c
12
((y
12
+ 13y
11
+ ··· + 6y + 1)
6
)(y
24
+ 18y
23
+ ··· − 6y + 1)
· (y
39
+ 31y
38
+ ··· + 64653328y −1420864)
c
11
((y
3
− y
2
+ 2y −1)
24
)(y
24
− 9y
23
+ ··· − 4y + 1)
· (y
39
− 10y
38
+ ··· + 125829120y −16777216)
27
