12a
0322
(K12a
0322
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 10 5 1 12 7 4 9
Solving Sequence
2,6 3,10
7 11 1 5 8 9 4 12
c
2
c
6
c
10
c
1
c
5
c
7
c
8
c
4
c
12
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.21898 × 10
219
u
119
+ 4.76957 × 10
220
u
118
+ ··· + 4.63553 × 10
219
b + 9.71727 × 10
220
,
− 6.19206 × 10
220
u
119
+ 3.81909 × 10
221
u
118
+ ··· + 3.24487 × 10
220
a + 1.01535 × 10
222
,
u
120
− 7u
119
+ ··· − 322u + 28i
I
u
2
= h11u
27
− 7u
26
+ ··· + b + 9, 21u
27
− 14u
26
+ ··· + a + 26, u
28
− 7u
26
+ ··· − 7u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 148 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−8.22 × 10
219
u
119
+ 4.77 × 10
220
u
118
+ · · · + 4.64 × 10
219
b + 9.72 ×
10
220
, −6.19 × 10
220
u
119
+ 3.82 × 10
221
u
118
+ · · · + 3.24 × 10
220
a + 1.02 ×
10
222
, u
120
− 7u
119
+ · · · − 322u + 28i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
1.90826u
119
− 11.7696u
118
+ ··· + 411.586u − 31.2907
1.77304u
119
− 10.2892u
118
+ ··· + 249.202u − 20.9626
a
7
=
1.44392u
119
− 9.00588u
118
+ ··· + 407.842u − 43.3368
1.81874u
119
− 11.5795u
118
+ ··· + 548.122u − 51.0257
a
11
=
0.378475u
119
− 1.79691u
118
+ ··· − 126.882u + 17.7038
0.145425u
119
− 0.0262595u
118
+ ··· − 227.960u + 23.7574
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
8
=
1.88512u
119
− 11.3227u
118
+ ··· + 402.195u − 41.9332
2.25994u
119
− 13.8963u
118
+ ··· + 542.476u − 49.6221
a
9
=
1.46394u
119
− 9.13960u
118
+ ··· + 425.876u − 45.4088
1.86261u
119
− 11.8211u
118
+ ··· + 537.652u − 50.5064
a
4
=
−0.741655u
119
+ 4.42736u
118
+ ··· − 216.390u + 18.8365
−0.0128759u
119
− 0.437223u
118
+ ··· + 131.410u − 13.0382
a
12
=
0.550241u
119
− 3.00283u
118
+ ··· + 75.1762u − 3.88524
−0.0827609u
119
+ 1.69612u
118
+ ··· − 314.707u + 31.3255
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.89337u
119
+ 12.9136u
118
+ ··· − 1169.14u + 100.982
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
120
+ 49u
119
+ ··· + 44492u + 784
c
2
, c
5
u
120
+ 7u
119
+ ··· + 322u + 28
c
3
u
120
+ u
119
+ ··· + 3289256u − 546677
c
4
, c
11
u
120
− 3u
119
+ ··· − 47904u + 17881
c
6
, c
10
u
120
− 3u
119
+ ··· − 110801u − 32041
c
7
u
120
− 3u
119
+ ··· + 8809070u − 639127
c
8
, c
9
, c
12
u
120
− 4u
119
+ ··· − 116u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
120
+ 59y
119
+ ··· − 985957616y + 614656
c
2
, c
5
y
120
− 49y
119
+ ··· − 44492y + 784
c
3
y
120
+ 21y
119
+ ··· + 9174574703856y + 298855742329
c
4
, c
11
y
120
+ 89y
119
+ ··· − 4994108976y + 319730161
c
6
, c
10
y
120
− 81y
119
+ ··· + 2923581045y + 1026625681
c
7
y
120
− 33y
119
+ ··· − 17599469821274y + 408483322129
c
8
, c
9
, c
12
y
120
+ 118y
119
+ ··· + 1566y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.794130 + 0.592091I
a = −1.036180 + 0.139905I
b = −2.73059 + 1.18931I
5.76528 − 4.26197I 0
u = 0.794130 − 0.592091I
a = −1.036180 − 0.139905I
b = −2.73059 − 1.18931I
5.76528 + 4.26197I 0
u = −0.811711 + 0.559362I
a = 0.43814 + 1.54982I
b = −0.135332 + 0.657514I
−1.05368 − 2.08033I 0
u = −0.811711 − 0.559362I
a = 0.43814 − 1.54982I
b = −0.135332 − 0.657514I
−1.05368 + 2.08033I 0
u = 0.795910 + 0.567712I
a = 0.636281 + 0.221317I
b = 0.451032 − 0.933379I
−0.64341 − 1.79431I 0
u = 0.795910 − 0.567712I
a = 0.636281 − 0.221317I
b = 0.451032 + 0.933379I
−0.64341 + 1.79431I 0
u = 0.500076 + 0.838852I
a = −0.21069 + 1.40177I
b = 0.066259 − 0.537185I
−3.58790 + 7.84949I 0
u = 0.500076 − 0.838852I
a = −0.21069 − 1.40177I
b = 0.066259 + 0.537185I
−3.58790 − 7.84949I 0
u = −0.704119 + 0.669771I
a = 0.687117 − 0.261579I
b = 0.614214 − 0.164025I
2.81216 + 1.01478I 0
u = −0.704119 − 0.669771I
a = 0.687117 + 0.261579I
b = 0.614214 + 0.164025I
2.81216 − 1.01478I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.022580 + 0.152770I
a = −1.090080 − 0.430824I
b = −3.13345 − 0.41355I
−7.07823 − 1.36704I 0
u = −1.022580 − 0.152770I
a = −1.090080 + 0.430824I
b = −3.13345 + 0.41355I
−7.07823 + 1.36704I 0
u = 0.876865 + 0.373837I
a = −1.10967 + 1.33609I
b = −1.79299 + 1.08629I
−2.47601 + 2.18680I 0
u = 0.876865 − 0.373837I
a = −1.10967 − 1.33609I
b = −1.79299 − 1.08629I
−2.47601 − 2.18680I 0
u = 0.522358 + 0.796481I
a = 1.166810 + 0.561303I
b = 1.068930 + 0.135249I
6.72132 + 5.58019I 0
u = 0.522358 − 0.796481I
a = 1.166810 − 0.561303I
b = 1.068930 − 0.135249I
6.72132 − 5.58019I 0
u = −0.941729 + 0.027426I
a = −0.341445 − 0.791610I
b = 0.100180 − 1.011340I
−4.48747 − 1.81759I 0
u = −0.941729 − 0.027426I
a = −0.341445 + 0.791610I
b = 0.100180 + 1.011340I
−4.48747 + 1.81759I 0
u = −0.901163 + 0.562425I
a = 1.59113 − 0.13593I
b = 2.59861 + 0.39022I
−1.34992 + 6.56399I 0
u = −0.901163 − 0.562425I
a = 1.59113 + 0.13593I
b = 2.59861 − 0.39022I
−1.34992 − 6.56399I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.755449 + 0.535537I
a = 0.802382 + 0.494497I
b = 3.33001 + 0.42016I
5.39303 − 1.61910I 0
u = −0.755449 − 0.535537I
a = 0.802382 − 0.494497I
b = 3.33001 − 0.42016I
5.39303 + 1.61910I 0
u = −0.773230 + 0.493848I
a = −0.691757 − 0.832970I
b = −0.91976 + 1.11074I
−1.07276 + 1.31581I 0
u = −0.773230 − 0.493848I
a = −0.691757 + 0.832970I
b = −0.91976 − 1.11074I
−1.07276 − 1.31581I 0
u = 1.008900 + 0.403302I
a = 1.24638 − 0.80340I
b = 2.06463 − 0.73656I
−6.67226 − 1.10006I 0
u = 1.008900 − 0.403302I
a = 1.24638 + 0.80340I
b = 2.06463 + 0.73656I
−6.67226 + 1.10006I 0
u = −0.614899 + 0.899173I
a = −0.812781 + 0.037535I
b = −0.927483 + 0.068797I
9.37495 − 0.63348I 0
u = −0.614899 − 0.899173I
a = −0.812781 − 0.037535I
b = −0.927483 − 0.068797I
9.37495 + 0.63348I 0
u = 0.801649 + 0.737933I
a = −0.132730 + 1.004280I
b = 0.791265 + 0.400595I
5.97079 + 0.59954I 0
u = 0.801649 − 0.737933I
a = −0.132730 − 1.004280I
b = 0.791265 − 0.400595I
5.97079 − 0.59954I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.086340 + 0.086609I
a = 0.308477 + 1.178510I
b = 0.032988 + 0.864068I
1.33369 − 4.02049I 0
u = −1.086340 − 0.086609I
a = 0.308477 − 1.178510I
b = 0.032988 − 0.864068I
1.33369 + 4.02049I 0
u = 0.898897 + 0.621029I
a = −0.300747 + 0.963948I
b = 0.481448 − 0.329020I
5.41777 − 0.53995I 0
u = 0.898897 − 0.621029I
a = −0.300747 − 0.963948I
b = 0.481448 + 0.329020I
5.41777 + 0.53995I 0
u = −0.956773 + 0.537580I
a = −0.961289 − 0.377593I
b = −2.89827 + 0.02050I
−1.73966 + 2.88185I 0
u = −0.956773 − 0.537580I
a = −0.961289 + 0.377593I
b = −2.89827 − 0.02050I
−1.73966 − 2.88185I 0
u = 1.034960 + 0.368403I
a = 1.008420 − 0.115464I
b = 2.61007 − 0.63339I
−2.79017 − 2.83849I 0
u = 1.034960 − 0.368403I
a = 1.008420 + 0.115464I
b = 2.61007 + 0.63339I
−2.79017 + 2.83849I 0
u = 0.919120 + 0.621003I
a = −0.137088 − 0.539200I
b = −0.936045 − 0.724378I
−1.08242 − 2.93367I 0
u = 0.919120 − 0.621003I
a = −0.137088 + 0.539200I
b = −0.936045 + 0.724378I
−1.08242 + 2.93367I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.622283 + 0.636232I
a = 0.522471 − 1.276800I
b = −0.266368 + 0.869075I
−3.01210 + 2.31388I 0
u = 0.622283 − 0.636232I
a = 0.522471 + 1.276800I
b = −0.266368 − 0.869075I
−3.01210 − 2.31388I 0
u = −0.952840 + 0.579752I
a = 0.449554 + 0.608808I
b = 0.28964 − 1.39826I
4.71169 + 6.11608I 0
u = −0.952840 − 0.579752I
a = 0.449554 − 0.608808I
b = 0.28964 + 1.39826I
4.71169 − 6.11608I 0
u = 1.107490 + 0.133676I
a = −0.110679 − 0.528564I
b = 0.349142 + 0.391332I
2.29239 + 0.22974I 0
u = 1.107490 − 0.133676I
a = −0.110679 + 0.528564I
b = 0.349142 − 0.391332I
2.29239 − 0.22974I 0
u = −0.764512 + 0.816894I
a = 0.530413 + 0.721861I
b = −0.466501 + 0.530723I
4.85027 − 2.59051I 0
u = −0.764512 − 0.816894I
a = 0.530413 − 0.721861I
b = −0.466501 − 0.530723I
4.85027 + 2.59051I 0
u = 0.622798 + 0.935690I
a = −0.679220 + 0.683589I
b = −0.596800 − 0.335157I
−3.02138 − 3.95990I 0
u = 0.622798 − 0.935690I
a = −0.679220 − 0.683589I
b = −0.596800 + 0.335157I
−3.02138 + 3.95990I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.860655 + 0.725454I
a = −0.652310 − 0.482964I
b = 0.139036 − 1.231600I
−0.29667 + 2.76262I 0
u = −0.860655 − 0.725454I
a = −0.652310 + 0.482964I
b = 0.139036 + 1.231600I
−0.29667 − 2.76262I 0
u = −0.379745 + 0.786895I
a = 0.144930 + 1.215850I
b = 0.204977 − 0.548207I
0.75442 − 2.79835I 0
u = −0.379745 − 0.786895I
a = 0.144930 − 1.215850I
b = 0.204977 + 0.548207I
0.75442 + 2.79835I 0
u = 0.544571 + 0.988118I
a = 0.109348 − 1.307700I
b = −0.107162 + 0.411685I
2.87853 + 11.94920I 0
u = 0.544571 − 0.988118I
a = 0.109348 + 1.307700I
b = −0.107162 − 0.411685I
2.87853 − 11.94920I 0
u = 0.572654 + 0.657256I
a = −0.918894 − 0.645090I
b = −0.672223 − 0.010990I
0.06888 + 2.49159I 0
u = 0.572654 − 0.657256I
a = −0.918894 + 0.645090I
b = −0.672223 + 0.010990I
0.06888 − 2.49159I 0
u = −1.037000 + 0.451230I
a = −1.47342 + 0.12448I
b = −2.64551 − 0.23711I
−6.42153 + 5.29428I 0
u = −1.037000 − 0.451230I
a = −1.47342 − 0.12448I
b = −2.64551 + 0.23711I
−6.42153 − 5.29428I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950352 + 0.641394I
a = −0.272614 + 0.563073I
b = −0.309383 + 0.312781I
2.07781 + 4.07753I 0
u = −0.950352 − 0.641394I
a = −0.272614 − 0.563073I
b = −0.309383 − 0.312781I
2.07781 − 4.07753I 0
u = 0.918739 + 0.696205I
a = −0.980866 − 0.088202I
b = −1.50296 + 0.86093I
5.60147 − 6.06685I 0
u = 0.918739 − 0.696205I
a = −0.980866 + 0.088202I
b = −1.50296 − 0.86093I
5.60147 + 6.06685I 0
u = 1.003780 + 0.616583I
a = 1.091870 − 0.197147I
b = 3.15550 − 0.68952I
−4.15865 − 7.26170I 0
u = 1.003780 − 0.616583I
a = 1.091870 + 0.197147I
b = 3.15550 + 0.68952I
−4.15865 + 7.26170I 0
u = −0.527331 + 1.056560I
a = −0.052343 − 0.958618I
b = −0.009228 + 0.755850I
7.57521 − 5.16330I 0
u = −0.527331 − 1.056560I
a = −0.052343 + 0.958618I
b = −0.009228 − 0.755850I
7.57521 + 5.16330I 0
u = 1.010590 + 0.613047I
a = 0.498677 + 0.841419I
b = 0.931083 + 0.758716I
−1.20483 − 7.46238I 0
u = 1.010590 − 0.613047I
a = 0.498677 − 0.841419I
b = 0.931083 − 0.758716I
−1.20483 + 7.46238I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.077489 + 0.796750I
a = −0.24472 + 1.81974I
b = −0.108308 + 0.309518I
0.842040 + 0.218659I 0
u = −0.077489 − 0.796750I
a = −0.24472 − 1.81974I
b = −0.108308 − 0.309518I
0.842040 − 0.218659I 0
u = 1.146540 + 0.376005I
a = −1.337790 + 0.388782I
b = −2.22294 + 0.56183I
−2.93736 − 4.08892I 0
u = 1.146540 − 0.376005I
a = −1.337790 − 0.388782I
b = −2.22294 − 0.56183I
−2.93736 + 4.08892I 0
u = −1.208590 + 0.007327I
a = 1.117550 + 0.297675I
b = 2.78666 + 0.25946I
−9.67452 − 5.84411I 0
u = −1.208590 − 0.007327I
a = 1.117550 − 0.297675I
b = 2.78666 − 0.25946I
−9.67452 + 5.84411I 0
u = 0.716398 + 0.321337I
a = −1.71073 − 0.13704I
b = −1.209250 − 0.019460I
−2.05269 − 5.09445I 0
u = 0.716398 − 0.321337I
a = −1.71073 + 0.13704I
b = −1.209250 + 0.019460I
−2.05269 + 5.09445I 0
u = −0.966448 + 0.750480I
a = 0.735650 + 0.336987I
b = 0.83498 + 1.25832I
4.22919 + 8.45993I 0
u = −0.966448 − 0.750480I
a = 0.735650 − 0.336987I
b = 0.83498 − 1.25832I
4.22919 − 8.45993I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.175750 + 0.450060I
a = 1.44318 − 0.00301I
b = 2.56049 + 0.14637I
−2.47631 + 4.23288I 0
u = −1.175750 − 0.450060I
a = 1.44318 + 0.00301I
b = 2.56049 − 0.14637I
−2.47631 − 4.23288I 0
u = 1.080030 + 0.647397I
a = −0.471017 − 1.051610I
b = −0.868852 − 0.834680I
5.04528 − 11.02900I 0
u = 1.080030 − 0.647397I
a = −0.471017 + 1.051610I
b = −0.868852 + 0.834680I
5.04528 + 11.02900I 0
u = −1.095400 + 0.623315I
a = 0.965172 + 0.211241I
b = 2.67918 + 0.12256I
−1.26703 + 8.06534I 0
u = −1.095400 − 0.623315I
a = 0.965172 − 0.211241I
b = 2.67918 − 0.12256I
−1.26703 − 8.06534I 0
u = 1.27157
a = −0.897925
b = −2.60589
−5.07839 0
u = 1.090890 + 0.662481I
a = −1.133620 + 0.170602I
b = −2.92856 + 0.42650I
−5.3505 − 13.4421I 0
u = 1.090890 − 0.662481I
a = −1.133620 − 0.170602I
b = −2.92856 − 0.42650I
−5.3505 + 13.4421I 0
u = 0.440478 + 1.209800I
a = 0.483244 − 0.827372I
b = 0.485341 + 0.413522I
2.09189 − 5.37526I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.440478 − 1.209800I
a = 0.483244 + 0.827372I
b = 0.485341 − 0.413522I
2.09189 + 5.37526I 0
u = 0.694130 + 0.155166I
a = 0.629469 − 0.483057I
b = −0.325515 + 0.095039I
−1.130740 − 0.057247I −6.19583 − 1.04594I
u = 0.694130 − 0.155166I
a = 0.629469 + 0.483057I
b = −0.325515 − 0.095039I
−1.130740 + 0.057247I −6.19583 + 1.04594I
u = −1.073550 + 0.721250I
a = 0.099374 − 0.729669I
b = 0.228563 − 0.382128I
7.95621 + 6.61583I 0
u = −1.073550 − 0.721250I
a = 0.099374 + 0.729669I
b = 0.228563 + 0.382128I
7.95621 − 6.61583I 0
u = −0.703529 + 0.055166I
a = 1.17165 + 1.11505I
b = 1.064580 + 0.239864I
2.00066 − 2.73260I 2.52280 + 4.22916I
u = −0.703529 − 0.055166I
a = 1.17165 − 1.11505I
b = 1.064580 − 0.239864I
2.00066 + 2.73260I 2.52280 − 4.22916I
u = −0.660045 + 0.172832I
a = −1.07697 − 1.29046I
b = 0.308962 − 0.774356I
−4.71647 − 2.02134I −14.9131 + 5.4596I
u = −0.660045 − 0.172832I
a = −1.07697 + 1.29046I
b = 0.308962 + 0.774356I
−4.71647 + 2.02134I −14.9131 − 5.4596I
u = 1.136770 + 0.725645I
a = 1.143050 − 0.143379I
b = 2.76538 − 0.38775I
1.0308 − 18.1820I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.136770 − 0.725645I
a = 1.143050 + 0.143379I
b = 2.76538 + 0.38775I
1.0308 + 18.1820I 0
u = 0.967628 + 0.945915I
a = 0.460685 − 0.501451I
b = 0.630580 + 0.435757I
0.71880 − 3.29093I 0
u = 0.967628 − 0.945915I
a = 0.460685 + 0.501451I
b = 0.630580 − 0.435757I
0.71880 + 3.29093I 0
u = −1.350430 + 0.109621I
a = −1.096880 + 0.210583I
b = −2.62257 + 0.16937I
−4.72155 + 9.45612I 0
u = −1.350430 − 0.109621I
a = −1.096880 − 0.210583I
b = −2.62257 − 0.16937I
−4.72155 − 9.45612I 0
u = 0.195074 + 0.613711I
a = −0.513090 − 0.129913I
b = 0.254576 + 1.365830I
5.78993 − 3.08770I 0.92553 + 1.70472I
u = 0.195074 − 0.613711I
a = −0.513090 + 0.129913I
b = 0.254576 − 1.365830I
5.78993 + 3.08770I 0.92553 − 1.70472I
u = −1.152100 + 0.741685I
a = −0.898263 − 0.140497I
b = −2.60841 − 0.20294I
5.62024 + 11.59990I 0
u = −1.152100 − 0.741685I
a = −0.898263 + 0.140497I
b = −2.60841 + 0.20294I
5.62024 − 11.59990I 0
u = 1.205030 + 0.669031I
a = −0.754265 + 0.388060I
b = −2.05625 + 0.20526I
−4.97040 − 2.42339I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.205030 − 0.669031I
a = −0.754265 − 0.388060I
b = −2.05625 − 0.20526I
−4.97040 + 2.42339I 0
u = 1.11740 + 0.90714I
a = 0.580724 − 0.395613I
b = 1.92278 − 0.01409I
0.33213 − 3.94288I 0
u = 1.11740 − 0.90714I
a = 0.580724 + 0.395613I
b = 1.92278 + 0.01409I
0.33213 + 3.94288I 0
u = 0.382040 + 0.407746I
a = 0.485352 + 0.660044I
b = −0.106165 − 0.505429I
−0.554187 − 1.270860I −5.62089 + 5.07499I
u = 0.382040 − 0.407746I
a = 0.485352 − 0.660044I
b = −0.106165 + 0.505429I
−0.554187 + 1.270860I −5.62089 − 5.07499I
u = 1.51444 + 0.46755I
a = 0.760992 − 0.166869I
b = 2.31142 − 0.10041I
−1.71995 − 1.83130I 0
u = 1.51444 − 0.46755I
a = 0.760992 + 0.166869I
b = 2.31142 + 0.10041I
−1.71995 + 1.83130I 0
u = 0.045642 + 0.379691I
a = 1.51813 − 3.01413I
b = 0.492405 − 0.351687I
−4.27910 − 1.96842I −12.93862 + 1.10790I
u = 0.045642 − 0.379691I
a = 1.51813 + 3.01413I
b = 0.492405 + 0.351687I
−4.27910 + 1.96842I −12.93862 − 1.10790I
u = 0.159452
a = 4.64892
b = −0.390195
−0.986368 −9.85060
16
II. I
u
2
=
h11u
27
−7u
26
+· · ·+b+9, 21u
27
−14u
26
+· · ·+a+26, u
28
−7u
26
+· · ·−7u
2
+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
−21u
27
+ 14u
26
+ ··· + 27u − 26
−11u
27
+ 7u
26
+ ··· + 8u − 9
a
7
=
7u
27
− 6u
26
+ ··· − 7u + 6
7u
27
− 5u
26
+ ··· − 4u + 9
a
11
=
−8u
27
− 6u
26
+ ··· + 53u − 25
−20u
27
+ 7u
26
+ ··· + 48u − 31
a
1
=
−u
2
+ 1
−u
4
a
5
=
u
u
a
8
=
10u
27
− 10u
26
+ ··· − 7u + 7
10u
27
− 9u
26
+ ··· − 4u + 10
a
9
=
7u
27
− 5u
26
+ ··· − 12u + 6
11u
27
− 8u
26
+ ··· − 10u + 13
a
4
=
−32u
27
+ 27u
26
+ ··· + 39u − 38
−31u
27
+ 26u
26
+ ··· + 30u − 32
a
12
=
5u
27
+ 2u
26
+ ··· − 36u + 22
8u
27
− 4u
26
+ ··· − 24u + 18
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 44u
27
−36u
26
−279u
25
+ 230u
24
+ 1045u
23
−866u
22
−2680u
21
+ 2324u
20
+ 5347u
19
−
4756u
18
− 8553u
17
+ 7595u
16
+ 11289u
15
− 9642u
14
− 12168u
13
+ 9845u
12
+ 10726u
11
−
8146u
10
−7608u
9
+5266u
8
+4146u
7
−2623u
6
−1545u
5
+981u
4
+347u
3
−263u
2
−32u+24
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
− 14u
27
+ ··· − 14u + 1
c
2
u
28
− 7u
26
+ ··· − 7u
2
+ 1
c
3
u
28
− 4u
26
+ ··· − 6u + 1
c
4
u
28
+ 14u
26
+ ··· − 2u + 1
c
5
u
28
− 7u
26
+ ··· − 7u
2
+ 1
c
6
u
28
+ 4u
27
+ ··· + u + 1
c
7
u
28
+ 6u
27
+ ··· + 4u + 1
c
8
, c
9
u
28
− 3u
27
+ ··· + 10u
2
+ 1
c
10
u
28
− 4u
27
+ ··· − u + 1
c
11
u
28
+ 14u
26
+ ··· + 2u + 1
c
12
u
28
+ 3u
27
+ ··· + 10u
2
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 14y
27
+ ··· + 22y + 1
c
2
, c
5
y
28
− 14y
27
+ ··· − 14y + 1
c
3
y
28
− 8y
27
+ ··· − 10y + 1
c
4
, c
11
y
28
+ 28y
27
+ ··· + 38y + 1
c
6
, c
10
y
28
− 22y
27
+ ··· − 25y + 1
c
7
y
28
− 2y
27
+ ··· + 88y
2
+ 1
c
8
, c
9
, c
12
y
28
+ 29y
27
+ ··· + 20y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.706701 + 0.716899I
a = −0.102563 − 0.600190I
b = 1.44237 − 0.26513I
6.43940 − 2.37940I −2.37700 + 2.25279I
u = −0.706701 − 0.716899I
a = −0.102563 + 0.600190I
b = 1.44237 + 0.26513I
6.43940 + 2.37940I −2.37700 − 2.25279I
u = 0.718124 + 0.740337I
a = −0.788492 + 0.528954I
b = −0.387215 − 0.255973I
−2.98909 − 3.38234I −12.05254 + 0.45693I
u = 0.718124 − 0.740337I
a = −0.788492 − 0.528954I
b = −0.387215 + 0.255973I
−2.98909 + 3.38234I −12.05254 − 0.45693I
u = 0.915118 + 0.103319I
a = 0.779774 − 0.990552I
b = 0.994399 − 0.282028I
1.54534 + 2.57825I −13.53771 + 1.02492I
u = 0.915118 − 0.103319I
a = 0.779774 + 0.990552I
b = 0.994399 + 0.282028I
1.54534 − 2.57825I −13.53771 − 1.02492I
u = −0.864125 + 0.667301I
a = 0.367005 + 0.243795I
b = −0.551476 + 1.276770I
0.63860 + 2.58484I −1.35673 − 2.83169I
u = −0.864125 − 0.667301I
a = 0.367005 − 0.243795I
b = −0.551476 − 1.276770I
0.63860 − 2.58484I −1.35673 + 2.83169I
u = −1.026350 + 0.428145I
a = 1.336690 − 0.045888I
b = 2.79611 + 0.37219I
−5.70170 + 4.73286I −10.95152 − 3.12854I
u = −1.026350 − 0.428145I
a = 1.336690 + 0.045888I
b = 2.79611 − 0.37219I
−5.70170 − 4.73286I −10.95152 + 3.12854I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.057150 + 0.361718I
a = −1.65675 + 0.23711I
b = −2.66296 + 0.02914I
−3.53913 + 5.88320I −13.8678 − 7.1785I
u = −1.057150 − 0.361718I
a = −1.65675 − 0.23711I
b = −2.66296 − 0.02914I
−3.53913 − 5.88320I −13.8678 + 7.1785I
u = −0.988495 + 0.684689I
a = −0.524180 + 0.106244I
b = −0.87095 − 1.13264I
5.57997 + 7.77976I −4.95934 − 6.93937I
u = −0.988495 − 0.684689I
a = −0.524180 − 0.106244I
b = −0.87095 + 1.13264I
5.57997 − 7.77976I −4.95934 + 6.93937I
u = −0.704088 + 0.370257I
a = 0.76108 + 1.29251I
b = −0.489361 + 0.183527I
−4.49557 − 1.33302I −11.01547 − 4.40294I
u = −0.704088 − 0.370257I
a = 0.76108 − 1.29251I
b = −0.489361 − 0.183527I
−4.49557 + 1.33302I −11.01547 + 4.40294I
u = −0.737988 + 0.257469I
a = −1.07122 − 1.74542I
b = −0.502952 − 1.115910I
−2.22679 − 3.19640I −11.28614 + 5.21476I
u = −0.737988 − 0.257469I
a = −1.07122 + 1.74542I
b = −0.502952 + 1.115910I
−2.22679 + 3.19640I −11.28614 − 5.21476I
u = 0.737780 + 0.222485I
a = −0.795526 + 0.493914I
b = −0.311528 − 1.023530I
−1.94292 − 0.62697I −14.8683 + 1.0163I
u = 0.737780 − 0.222485I
a = −0.795526 − 0.493914I
b = −0.311528 + 1.023530I
−1.94292 + 0.62697I −14.8683 − 1.0163I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.137430 + 0.537627I
a = −0.886224 + 0.394814I
b = −2.22498 + 0.42430I
−4.66089 − 1.99657I −12.16305 − 1.57416I
u = 1.137430 − 0.537627I
a = −0.886224 − 0.394814I
b = −2.22498 − 0.42430I
−4.66089 + 1.99657I −12.16305 + 1.57416I
u = 0.816729 + 0.991195I
a = 0.715758 − 0.481142I
b = 1.173860 + 0.196254I
0.98244 − 4.82413I −8.48994 + 7.47474I
u = 0.816729 − 0.991195I
a = 0.715758 + 0.481142I
b = 1.173860 − 0.196254I
0.98244 + 4.82413I −8.48994 − 7.47474I
u = 0.400681 + 0.395040I
a = 1.003930 − 0.632238I
b = 0.04899 + 2.22748I
5.05540 − 3.21461I −10.56109 + 2.81442I
u = 0.400681 − 0.395040I
a = 1.003930 + 0.632238I
b = 0.04899 − 2.22748I
5.05540 + 3.21461I −10.56109 − 2.81442I
u = 1.35904 + 0.56479I
a = 0.860726 − 0.298307I
b = 2.04569 − 0.14889I
−1.26479 − 2.16877I −7.01334 + 4.60309I
u = 1.35904 − 0.56479I
a = 0.860726 + 0.298307I
b = 2.04569 + 0.14889I
−1.26479 + 2.16877I −7.01334 − 4.60309I
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 14u
27
+ ··· − 14u + 1)(u
120
+ 49u
119
+ ··· + 44492u + 784)
c
2
(u
28
− 7u
26
+ ··· − 7u
2
+ 1)(u
120
+ 7u
119
+ ··· + 322u + 28)
c
3
(u
28
− 4u
26
+ ··· − 6u + 1)(u
120
+ u
119
+ ··· + 3289256u − 546677)
c
4
(u
28
+ 14u
26
+ ··· − 2u + 1)(u
120
− 3u
119
+ ··· − 47904u + 17881)
c
5
(u
28
− 7u
26
+ ··· − 7u
2
+ 1)(u
120
+ 7u
119
+ ··· + 322u + 28)
c
6
(u
28
+ 4u
27
+ ··· + u + 1)(u
120
− 3u
119
+ ··· − 110801u − 32041)
c
7
(u
28
+ 6u
27
+ ··· + 4u + 1)(u
120
− 3u
119
+ ··· + 8809070u − 639127)
c
8
, c
9
(u
28
− 3u
27
+ ··· + 10u
2
+ 1)(u
120
− 4u
119
+ ··· − 116u + 7)
c
10
(u
28
− 4u
27
+ ··· − u + 1)(u
120
− 3u
119
+ ··· − 110801u − 32041)
c
11
(u
28
+ 14u
26
+ ··· + 2u + 1)(u
120
− 3u
119
+ ··· − 47904u + 17881)
c
12
(u
28
+ 3u
27
+ ··· + 10u
2
+ 1)(u
120
− 4u
119
+ ··· − 116u + 7)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 14y
27
+ ··· + 22y + 1)
· (y
120
+ 59y
119
+ ··· − 985957616y + 614656)
c
2
, c
5
(y
28
− 14y
27
+ ··· − 14y + 1)(y
120
− 49y
119
+ ··· − 44492y + 784)
c
3
(y
28
− 8y
27
+ ··· − 10y + 1)
· (y
120
+ 21y
119
+ ··· + 9174574703856y + 298855742329)
c
4
, c
11
(y
28
+ 28y
27
+ ··· + 38y + 1)
· (y
120
+ 89y
119
+ ··· − 4994108976y + 319730161)
c
6
, c
10
(y
28
− 22y
27
+ ··· − 25y + 1)
· (y
120
− 81y
119
+ ··· + 2923581045y + 1026625681)
c
7
(y
28
− 2y
27
+ ··· + 88y
2
+ 1)
· (y
120
− 33y
119
+ ··· − 17599469821274y + 408483322129)
c
8
, c
9
, c
12
(y
28
+ 29y
27
+ ··· + 20y + 1)(y
120
+ 118y
119
+ ··· + 1566y + 49)
24
