12a
0871
(K12a
0871
)
A knot diagram
1
Linearized knot diagam
4 6 7 9 11 10 12 1 2 3 5 8
Solving Sequence
6,10 3,7
4 11 2 1 5 12 9 8
c
6
c
3
c
10
c
2
c
1
c
5
c
11
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.80079 × 10
1000
u
138
+ 3.01263 × 10
1000
u
137
+ ··· + 9.21046 × 10
999
b + 1.47252 × 10
1000
,
− 3.52539 × 10
999
u
138
− 7.82925 × 10
998
u
137
+ ··· + 9.21046 × 10
999
a − 2.10793 × 10
1000
,
5u
139
+ 6u
138
+ ··· + 7u − 1i
I
u
2
= h−3.15864 × 10
37
u
27
− 2.23009 × 10
38
u
26
+ ··· + 1.72151 × 10
35
b − 1.40370 × 10
37
,
− 1.15651 × 10
38
u
27
− 8.15998 × 10
38
u
26
+ ··· + 1.72151 × 10
35
a − 5.00345 × 10
37
,
5u
28
+ 33u
27
+ ··· + 3u − 1i
* 2 irreducible components of dim
C
= 0, with total 167 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
= h1.80 × 10
1000
u
138
+ 3.01 × 10
1000
u
137
+ · · · + 9.21 × 10
999
b + 1.47 ×
10
1000
, −3.53 × 10
999
u
138
− 7.83 × 10
998
u
137
+ · · · + 9.21 × 10
999
a − 2.11 ×
10
1000
, 5u
139
+ 6u
138
+ · · · + 7u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
0.382760u
138
+ 0.0850039u
137
+ ··· − 50.6825u + 2.28863
−1.95515u
138
− 3.27088u
137
+ ··· + 5.78117u − 1.59875
a
7
=
1
u
2
a
4
=
2.22730u
138
+ 3.34356u
137
+ ··· − 55.8631u + 3.81252
−1.30760u
138
− 2.14564u
137
+ ··· + 4.68692u − 1.38973
a
11
=
4.67273u
138
+ 7.93391u
137
+ ··· − 23.1138u − 4.60306
1.35292u
138
+ 2.48173u
137
+ ··· + 0.210969u − 0.0658331
a
2
=
2.33791u
138
+ 3.35588u
137
+ ··· − 56.4637u + 3.88738
−1.95515u
138
− 3.27088u
137
+ ··· + 5.78117u − 1.59875
a
1
=
−4.38463u
138
− 8.32463u
137
+ ··· − 32.1407u + 2.35356
−1.10194u
138
− 2.10304u
137
+ ··· + 4.27185u − 1.04163
a
5
=
0.269116u
138
+ 0.793757u
137
+ ··· − 10.8788u + 4.40556
−0.861170u
138
− 1.19922u
137
+ ··· − 1.11359u − 1.62966
a
12
=
−14.5571u
138
− 24.2886u
137
+ ··· + 59.8087u − 4.14929
−1.68970u
138
− 3.29711u
137
+ ··· + 4.79931u − 0.320587
a
9
=
3.20950u
138
+ 5.01416u
137
+ ··· − 23.9423u − 3.84170
0.110306u
138
+ 0.438015u
137
+ ··· + 2.61756u − 0.695526
a
8
=
0.875161u
138
+ 4.27144u
137
+ ··· − 9.78423u − 1.97659
1.90839u
138
+ 3.38088u
137
+ ··· + 3.96701u − 0.143899
(ii) Obstruction class = −1
(iii) Cusp Shapes = −16.2600u
138
− 26.4039u
137
+ ··· + 39.3754u − 2.10248
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
5(5u
139
+ 44u
138
+ ··· − 138u + 207)
c
2
u
139
+ 23u
137
+ ··· + 1342610u + 79075
c
3
u
139
− 4u
138
+ ··· + 9955539065u − 2811030979
c
4
u
139
+ u
138
+ ··· + 132792u − 9535
c
5
, c
11
5(5u
139
− 6u
138
+ ··· + 1.08748 × 10
7
u + 3500629)
c
6
5(5u
139
− 6u
138
+ ··· + 7u + 1)
c
7
, c
8
, c
12
u
139
+ u
138
+ ··· + 3436u + 335
c
9
u
139
− 36u
137
+ ··· + 911022429u − 918419671
c
10
u
139
+ 2u
138
+ ··· − 161606u + 44905
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
139
− 376y
138
+ ··· + 5015196y −42849)
c
2
y
139
+ 46y
138
+ ··· − 50108241400y −6252855625
c
3
y
139
− 52y
138
+ ··· + 2.84 × 10
20
y −7.90 × 10
18
c
4
y
139
− y
138
+ ··· + 15265736154y −90916225
c
5
, c
11
25
· (25y
139
+ 2274y
138
+ ··· + 494385524795298y −12254403395641)
c
6
25(25y
139
− 1076y
138
+ ··· + y −1)
c
7
, c
8
, c
12
y
139
− 133y
138
+ ··· − 2468254y −112225
c
9
y
139
− 72y
138
+ ··· + 4.72 × 10
19
y −8.43 × 10
17
c
10
y
139
+ 26y
138
+ ··· − 67481776374y −2016459025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.454159 + 0.925702I
a = 0.433657 + 1.045870I
b = −0.556673 + 0.354972I
1.56214 − 3.03714I 0
u = 0.454159 − 0.925702I
a = 0.433657 − 1.045870I
b = −0.556673 − 0.354972I
1.56214 + 3.03714I 0
u = −0.545285 + 0.799666I
a = −0.76183 + 1.80296I
b = 0.889411 + 0.684684I
3.70539 + 10.84170I 0
u = −0.545285 − 0.799666I
a = −0.76183 − 1.80296I
b = 0.889411 − 0.684684I
3.70539 − 10.84170I 0
u = 0.579540 + 0.856958I
a = −0.81515 − 1.44704I
b = 0.989461 − 0.709822I
−1.62905 − 6.09919I 0
u = 0.579540 − 0.856958I
a = −0.81515 + 1.44704I
b = 0.989461 + 0.709822I
−1.62905 + 6.09919I 0
u = 0.512414 + 0.802283I
a = −0.134631 − 0.653974I
b = 0.898303 − 0.996558I
1.03847 − 3.81042I 0
u = 0.512414 − 0.802283I
a = −0.134631 + 0.653974I
b = 0.898303 + 0.996558I
1.03847 + 3.81042I 0
u = −1.032020 + 0.194301I
a = −0.92778 − 1.65014I
b = −0.311234 − 0.727864I
−1.07058 + 4.85081I 0
u = −1.032020 − 0.194301I
a = −0.92778 + 1.65014I
b = −0.311234 + 0.727864I
−1.07058 − 4.85081I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.317012 + 1.009220I
a = 0.024118 − 1.114040I
b = −0.57254 − 1.80463I
3.91816 + 8.58212I 0
u = −0.317012 − 1.009220I
a = 0.024118 + 1.114040I
b = −0.57254 + 1.80463I
3.91816 − 8.58212I 0
u = −0.358199 + 0.999813I
a = 0.055652 + 0.541167I
b = 0.90570 + 1.10239I
6.96221 + 5.11889I 0
u = −0.358199 − 0.999813I
a = 0.055652 − 0.541167I
b = 0.90570 − 1.10239I
6.96221 − 5.11889I 0
u = −0.345236 + 1.004870I
a = 0.205548 − 0.698744I
b = −0.622097 − 0.311021I
2.04191 − 1.41526I 0
u = −0.345236 − 1.004870I
a = 0.205548 + 0.698744I
b = −0.622097 + 0.311021I
2.04191 + 1.41526I 0
u = −0.857338 + 0.641083I
a = 0.851243 − 0.478779I
b = −0.307343 − 0.640466I
2.98587 + 0.74386I 0
u = −0.857338 − 0.641083I
a = 0.851243 + 0.478779I
b = −0.307343 + 0.640466I
2.98587 − 0.74386I 0
u = 0.929112 + 0.000626I
a = −1.26622 − 1.56043I
b = −0.283437 − 0.747004I
−6.02192 + 2.58152I 0
u = 0.929112 − 0.000626I
a = −1.26622 + 1.56043I
b = −0.283437 + 0.747004I
−6.02192 − 2.58152I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.275231 + 1.045340I
a = −0.361649 + 0.389825I
b = −0.856942 + 0.145353I
2.01281 + 2.83927I 0
u = −0.275231 − 1.045340I
a = −0.361649 − 0.389825I
b = −0.856942 − 0.145353I
2.01281 − 2.83927I 0
u = 0.487669 + 0.764261I
a = −0.394995 − 0.525292I
b = −0.879480 − 0.189002I
−2.88075 − 1.07465I 0
u = 0.487669 − 0.764261I
a = −0.394995 + 0.525292I
b = −0.879480 + 0.189002I
−2.88075 + 1.07465I 0
u = −0.597979 + 0.663487I
a = −0.132314 + 1.224530I
b = 0.837696 + 0.818188I
1.69040 + 2.58209I 0
u = −0.597979 − 0.663487I
a = −0.132314 − 1.224530I
b = 0.837696 − 0.818188I
1.69040 − 2.58209I 0
u = −1.112970 + 0.017737I
a = 0.359835 − 0.688759I
b = 0.91354 − 1.24565I
0.93563 − 6.68754I 0
u = −1.112970 − 0.017737I
a = 0.359835 + 0.688759I
b = 0.91354 + 1.24565I
0.93563 + 6.68754I 0
u = −0.575742 + 0.953904I
a = 0.168929 − 1.223110I
b = −0.559038 − 0.428056I
7.87824 + 6.61806I 0
u = −0.575742 − 0.953904I
a = 0.168929 + 1.223110I
b = −0.559038 + 0.428056I
7.87824 − 6.61806I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.501428 + 0.720235I
a = −0.07202 − 1.55219I
b = 0.873672 − 0.767181I
7.99970 − 1.36692I 0
u = 0.501428 − 0.720235I
a = −0.07202 + 1.55219I
b = 0.873672 + 0.767181I
7.99970 + 1.36692I 0
u = 0.864462 + 0.036717I
a = 0.415148 − 0.649210I
b = −0.409048 − 0.636701I
−2.05815 − 0.28164I 0
u = 0.864462 − 0.036717I
a = 0.415148 + 0.649210I
b = −0.409048 + 0.636701I
−2.05815 + 0.28164I 0
u = −1.035100 + 0.472436I
a = −1.16379 + 0.84962I
b = −0.232650 + 0.758383I
−3.18324 − 0.97148I 0
u = −1.035100 − 0.472436I
a = −1.16379 − 0.84962I
b = −0.232650 − 0.758383I
−3.18324 + 0.97148I 0
u = −0.774721 + 0.835973I
a = −0.595369 + 1.188130I
b = 1.018810 + 0.900468I
1.75155 + 0.93943I 0
u = −0.774721 − 0.835973I
a = −0.595369 − 1.188130I
b = 1.018810 − 0.900468I
1.75155 − 0.93943I 0
u = 0.817341 + 0.195341I
a = 0.204775 − 0.801112I
b = 1.25221 − 1.87533I
−5.28197 − 1.01152I 0
u = 0.817341 − 0.195341I
a = 0.204775 + 0.801112I
b = 1.25221 + 1.87533I
−5.28197 + 1.01152I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.983298 + 0.633060I
a = −0.059502 + 1.200200I
b = −0.99841 + 1.36559I
−4.02455 − 5.06834I 0
u = 0.983298 − 0.633060I
a = −0.059502 − 1.200200I
b = −0.99841 − 1.36559I
−4.02455 + 5.06834I 0
u = −0.815116 + 0.839011I
a = 0.398743 − 0.348381I
b = 0.42801 − 1.36675I
1.51467 + 4.82372I 0
u = −0.815116 − 0.839011I
a = 0.398743 + 0.348381I
b = 0.42801 + 1.36675I
1.51467 − 4.82372I 0
u = 0.484530 + 0.665994I
a = 0.061350 + 1.180790I
b = −0.98511 + 1.80947I
−3.35447 − 5.91360I 0
u = 0.484530 − 0.665994I
a = 0.061350 − 1.180790I
b = −0.98511 − 1.80947I
−3.35447 + 5.91360I 0
u = 0.355169 + 1.128710I
a = 0.009783 + 0.766365I
b = −0.682362 + 0.341294I
8.55394 + 4.38913I 0
u = 0.355169 − 1.128710I
a = 0.009783 − 0.766365I
b = −0.682362 − 0.341294I
8.55394 − 4.38913I 0
u = 0.731637 + 0.293858I
a = −1.11313 − 1.30768I
b = 0.682606 − 0.819383I
3.43176 − 6.69109I 0
u = 0.731637 − 0.293858I
a = −1.11313 + 1.30768I
b = 0.682606 + 0.819383I
3.43176 + 6.69109I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.733476 + 0.210444I
a = 2.58997 + 1.29698I
b = −0.023515 + 0.661031I
0.09986 − 10.07060I 0
u = 0.733476 − 0.210444I
a = 2.58997 − 1.29698I
b = −0.023515 − 0.661031I
0.09986 + 10.07060I 0
u = 1.231920 + 0.289750I
a = 0.321374 + 0.498605I
b = 0.49412 + 1.60140I
−4.17320 + 1.01953I 0
u = 1.231920 − 0.289750I
a = 0.321374 − 0.498605I
b = 0.49412 − 1.60140I
−4.17320 − 1.01953I 0
u = −0.089882 + 0.725958I
a = −0.97317 − 1.32370I
b = −0.235341 + 0.556648I
−3.74565 − 1.35219I 0
u = −0.089882 − 0.725958I
a = −0.97317 + 1.32370I
b = −0.235341 − 0.556648I
−3.74565 + 1.35219I 0
u = 0.672419 + 0.214980I
a = −1.25963 + 2.53653I
b = −0.104128 + 0.790192I
−1.70245 + 0.96159I 0
u = 0.672419 − 0.214980I
a = −1.25963 − 2.53653I
b = −0.104128 − 0.790192I
−1.70245 − 0.96159I 0
u = −0.615705 + 0.256123I
a = 3.17364 − 0.62542I
b = −0.049646 − 0.595641I
−5.52303 + 6.10934I 0
u = −0.615705 − 0.256123I
a = 3.17364 + 0.62542I
b = −0.049646 + 0.595641I
−5.52303 − 6.10934I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.631994 + 0.161465I
a = −1.55237 − 2.49186I
b = −0.227100 − 0.829357I
−5.99163 + 1.30767I 0
u = −0.631994 − 0.161465I
a = −1.55237 + 2.49186I
b = −0.227100 + 0.829357I
−5.99163 − 1.30767I 0
u = −0.628832 + 0.154188I
a = 0.610632 + 1.142230I
b = −0.655466 + 1.071690I
−1.95329 + 3.36933I 0
u = −0.628832 − 0.154188I
a = 0.610632 − 1.142230I
b = −0.655466 − 1.071690I
−1.95329 − 3.36933I 0
u = 0.635921 + 0.088468I
a = 0.059146 − 1.367840I
b = −1.22700 − 0.95709I
−1.63754 − 2.16969I 0
u = 0.635921 − 0.088468I
a = 0.059146 + 1.367840I
b = −1.22700 + 0.95709I
−1.63754 + 2.16969I 0
u = −0.938174 + 0.984075I
a = −0.202303 + 0.359761I
b = −0.732719 + 0.104372I
0.943475 + 0.180216I 0
u = −0.938174 − 0.984075I
a = −0.202303 − 0.359761I
b = −0.732719 − 0.104372I
0.943475 − 0.180216I 0
u = −1.006700 + 0.934775I
a = −0.013762 + 0.832761I
b = 0.86086 + 1.56528I
3.48061 + 5.90359I 0
u = −1.006700 − 0.934775I
a = −0.013762 − 0.832761I
b = 0.86086 − 1.56528I
3.48061 − 5.90359I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.144940 + 0.773503I
a = −0.081075 − 1.118290I
b = −0.92413 − 1.24542I
−7.14691 + 7.50851I 0
u = −1.144940 − 0.773503I
a = −0.081075 + 1.118290I
b = −0.92413 + 1.24542I
−7.14691 − 7.50851I 0
u = −0.566022 + 0.226737I
a = −1.60142 + 1.04892I
b = 0.680772 + 0.629248I
−1.63260 + 3.62503I 0. − 7.01965I
u = −0.566022 − 0.226737I
a = −1.60142 − 1.04892I
b = 0.680772 − 0.629248I
−1.63260 − 3.62503I 0. + 7.01965I
u = −1.210000 + 0.693149I
a = 0.482400 − 0.217523I
b = −0.183573 − 0.566721I
3.16663 + 1.03587I 0
u = −1.210000 − 0.693149I
a = 0.482400 + 0.217523I
b = −0.183573 + 0.566721I
3.16663 − 1.03587I 0
u = 0.419153 + 0.429170I
a = 2.48762 − 1.61431I
b = −0.144438 + 0.526974I
−3.82277 − 1.67156I 4.00000 + 8.20740I
u = 0.419153 − 0.429170I
a = 2.48762 + 1.61431I
b = −0.144438 − 0.526974I
−3.82277 + 1.67156I 4.00000 − 8.20740I
u = 0.559088 + 0.215093I
a = 0.79671 − 1.40979I
b = −0.725517 − 1.212240I
4.16059 − 6.26171I 4.00000 + 6.52713I
u = 0.559088 − 0.215093I
a = 0.79671 + 1.40979I
b = −0.725517 + 1.212240I
4.16059 + 6.26171I 4.00000 − 6.52713I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578150 + 0.072378I
a = 0.236700 − 0.861457I
b = 1.98816 − 1.67942I
−5.47215 + 5.31432I −12.4517 − 9.3806I
u = −0.578150 − 0.072378I
a = 0.236700 + 0.861457I
b = 1.98816 + 1.67942I
−5.47215 − 5.31432I −12.4517 + 9.3806I
u = −0.94004 + 1.07350I
a = −0.017882 + 0.795941I
b = 0.527630 + 1.221600I
3.91030 + 5.63479I 0
u = −0.94004 − 1.07350I
a = −0.017882 − 0.795941I
b = 0.527630 − 1.221600I
3.91030 − 5.63479I 0
u = 0.502775 + 0.259723I
a = 0.204571 + 0.901891I
b = 2.14262 + 1.10273I
1.15881 − 10.16980I −0.6406 + 16.1383I
u = 0.502775 − 0.259723I
a = 0.204571 − 0.901891I
b = 2.14262 − 1.10273I
1.15881 + 10.16980I −0.6406 − 16.1383I
u = −0.498559 + 0.209737I
a = 0.123636 − 1.345490I
b = −1.62724 − 1.42770I
−5.44288 + 1.47386I −9.42398 − 6.09833I
u = −0.498559 − 0.209737I
a = 0.123636 + 1.345490I
b = −1.62724 + 1.42770I
−5.44288 − 1.47386I −9.42398 + 6.09833I
u = 0.490861 + 0.196741I
a = −1.76872 + 3.08258I
b = −0.314830 + 0.921638I
−2.09911 − 3.09769I 2.52105 + 7.06130I
u = 0.490861 − 0.196741I
a = −1.76872 − 3.08258I
b = −0.314830 − 0.921638I
−2.09911 + 3.09769I 2.52105 − 7.06130I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.25977 + 0.80522I
a = −0.122478 + 1.054350I
b = −0.94227 + 1.15404I
−2.64330 − 10.05980I 0
u = 1.25977 − 0.80522I
a = −0.122478 − 1.054350I
b = −0.94227 − 1.15404I
−2.64330 + 10.05980I 0
u = 1.10994 + 1.02993I
a = 0.034787 + 1.134560I
b = −0.69484 + 1.27072I
−6.11196 − 6.88546I 0
u = 1.10994 − 1.02993I
a = 0.034787 − 1.134560I
b = −0.69484 − 1.27072I
−6.11196 + 6.88546I 0
u = 1.16827 + 0.98211I
a = −0.009802 − 0.671229I
b = 0.466002 − 0.947757I
−2.04557 − 3.54333I 0
u = 1.16827 − 0.98211I
a = −0.009802 + 0.671229I
b = 0.466002 + 0.947757I
−2.04557 + 3.54333I 0
u = 1.04939 + 1.11131I
a = −0.626890 − 0.390471I
b = −0.066671 − 0.719893I
−5.89507 − 1.03350I 0
u = 1.04939 − 1.11131I
a = −0.626890 + 0.390471I
b = −0.066671 + 0.719893I
−5.89507 + 1.03350I 0
u = 1.13153 + 1.04471I
a = −0.121044 − 0.952270I
b = 1.03040 − 1.35187I
−6.17357 − 9.38764I 0
u = 1.13153 − 1.04471I
a = −0.121044 + 0.952270I
b = 1.03040 + 1.35187I
−6.17357 + 9.38764I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.03106 + 1.14561I
a = 0.018688 − 1.169490I
b = −0.64092 − 1.34652I
−1.73219 + 8.36924I 0
u = −1.03106 − 1.14561I
a = 0.018688 + 1.169490I
b = −0.64092 + 1.34652I
−1.73219 − 8.36924I 0
u = −1.15362 + 1.06200I
a = −0.088134 + 1.011790I
b = 1.00054 + 1.31698I
−7.1312 + 15.1507I 0
u = −1.15362 − 1.06200I
a = −0.088134 − 1.011790I
b = 1.00054 − 1.31698I
−7.1312 − 15.1507I 0
u = −1.21185 + 1.01611I
a = 0.102880 − 1.110870I
b = −0.645899 − 1.179020I
−1.90033 + 5.26365I 0
u = −1.21185 − 1.01611I
a = 0.102880 + 1.110870I
b = −0.645899 + 1.179020I
−1.90033 − 5.26365I 0
u = −0.009942 + 0.410551I
a = −0.19377 − 1.95750I
b = 1.051090 − 0.282577I
7.26060 − 0.44792I 12.96344 − 0.73898I
u = −0.009942 − 0.410551I
a = −0.19377 + 1.95750I
b = 1.051090 + 0.282577I
7.26060 + 0.44792I 12.96344 + 0.73898I
u = 1.16831 + 1.08373I
a = −0.053637 − 1.033410I
b = 0.98438 − 1.30778I
−0.8364 − 19.5945I 0
u = 1.16831 − 1.08373I
a = −0.053637 + 1.033410I
b = 0.98438 + 1.30778I
−0.8364 + 19.5945I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.18647 + 1.08891I
a = 0.131418 + 0.649119I
b = −0.745703 + 0.843714I
−1.65423 − 4.97090I 0
u = 1.18647 − 1.08891I
a = 0.131418 − 0.649119I
b = −0.745703 − 0.843714I
−1.65423 + 4.97090I 0
u = 0.333334 + 0.086020I
a = −3.31141 − 0.16769I
b = 0.652072 − 0.186479I
0.347375 − 0.135300I 11.76125 + 3.15246I
u = 0.333334 − 0.086020I
a = −3.31141 + 0.16769I
b = 0.652072 + 0.186479I
0.347375 + 0.135300I 11.76125 − 3.15246I
u = −1.28028 + 1.07012I
a = −0.021607 − 0.709952I
b = −0.830795 − 0.878277I
−1.41370 + 9.46023I 0
u = −1.28028 − 1.07012I
a = −0.021607 + 0.709952I
b = −0.830795 + 0.878277I
−1.41370 − 9.46023I 0
u = 1.64581 + 0.44067I
a = 0.278482 − 0.479146I
b = 0.741249 − 0.651181I
4.05125 + 1.73784I 0
u = 1.64581 − 0.44067I
a = 0.278482 + 0.479146I
b = 0.741249 + 0.651181I
4.05125 − 1.73784I 0
u = −1.17316 + 1.24243I
a = 0.123073 − 0.379581I
b = −0.709722 − 0.761145I
4.83149 + 1.08715I 0
u = −1.17316 − 1.24243I
a = 0.123073 + 0.379581I
b = −0.709722 + 0.761145I
4.83149 − 1.08715I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.26040 + 1.15540I
a = 0.371400 + 0.273144I
b = 0.034679 + 1.022870I
−5.96169 + 0.95106I 0
u = 1.26040 − 1.15540I
a = 0.371400 − 0.273144I
b = 0.034679 − 1.022870I
−5.96169 − 0.95106I 0
u = 1.33557 + 1.09559I
a = −0.111703 + 0.680656I
b = −0.887064 + 0.851809I
5.05232 − 12.72990I 0
u = 1.33557 − 1.09559I
a = −0.111703 − 0.680656I
b = −0.887064 − 0.851809I
5.05232 + 12.72990I 0
u = −1.54200 + 0.79273I
a = 0.114483 + 0.494540I
b = 0.549281 + 0.699482I
−1.81510 + 0.49244I 0
u = −1.54200 − 0.79273I
a = 0.114483 − 0.494540I
b = 0.549281 − 0.699482I
−1.81510 − 0.49244I 0
u = −1.26738 + 1.18985I
a = −0.427396 + 0.574021I
b = 0.020829 + 0.824776I
−1.42422 + 3.51843I 0
u = −1.26738 − 1.18985I
a = −0.427396 − 0.574021I
b = 0.020829 − 0.824776I
−1.42422 − 3.51843I 0
u = −0.236924
a = 2.20153
b = 0.435206
0.794229 12.4310
u = −1.29484 + 1.23940I
a = 0.406008 − 0.268017I
b = 0.141468 − 0.896273I
−6.85359 − 6.49863I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.29484 − 1.23940I
a = 0.406008 + 0.268017I
b = 0.141468 + 0.896273I
−6.85359 + 6.49863I 0
u = −0.094100 + 0.118558I
a = 5.90150 + 3.38437I
b = −0.929370 + 1.060970I
3.68943 − 4.85621I 8.33889 + 2.35560I
u = −0.094100 − 0.118558I
a = 5.90150 − 3.38437I
b = −0.929370 − 1.060970I
3.68943 + 4.85621I 8.33889 − 2.35560I
u = 1.35589 + 1.28224I
a = 0.421769 + 0.260887I
b = 0.172363 + 0.823818I
−0.59569 + 10.72620I 0
u = 1.35589 − 1.28224I
a = 0.421769 − 0.260887I
b = 0.172363 − 0.823818I
−0.59569 − 10.72620I 0
u = 0.0660922 + 0.0936501I
a = −3.07496 − 7.99149I
b = −1.075710 + 0.468338I
−3.02252 − 1.91759I 3.73120 + 4.31493I
u = 0.0660922 − 0.0936501I
a = −3.07496 + 7.99149I
b = −1.075710 − 0.468338I
−3.02252 + 1.91759I 3.73120 − 4.31493I
u = −2.88099
a = 0.120081
b = −0.200030
1.24668 0
u = 2.98199
a = 0.182194
b = 0.508908
1.07227 0
18
II. I
u
2
= h−3.16 × 10
37
u
27
− 2.23 × 10
38
u
26
+ · · · + 1.72 × 10
35
b − 1.40 ×
10
37
, −1.16 × 10
38
u
27
− 8.16 × 10
38
u
26
+ · · · + 1.72 × 10
35
a − 5.00 ×
10
37
, 5u
28
+ 33u
27
+ · · · + 3u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
671.803u
27
+ 4740.02u
26
+ ··· − 240.048u + 290.644
183.481u
27
+ 1295.43u
26
+ ··· − 65.8536u + 81.5388
a
7
=
1
u
2
a
4
=
628.295u
27
+ 4431.73u
26
+ ··· − 223.509u + 270.330
173.624u
27
+ 1225.73u
26
+ ··· − 61.8736u + 77.3116
a
11
=
−2465.95u
27
− 17382.0u
26
+ ··· + 852.690u − 1099.68
−372.411u
27
− 2621.37u
26
+ ··· + 120.759u − 169.093
a
2
=
488.322u
27
+ 3444.59u
26
+ ··· − 174.194u + 209.105
183.481u
27
+ 1295.43u
26
+ ··· − 65.8536u + 81.5388
a
1
=
660.620u
27
+ 4645.16u
26
+ ··· − 205.822u + 307.709
95.0908u
27
+ 670.121u
26
+ ··· − 35.7213u + 42.1151
a
5
=
−2408.59u
27
− 16930.0u
26
+ ··· + 757.766u − 1119.00
−23.4798u
27
− 164.198u
26
+ ··· + 5.03978u − 14.2574
a
12
=
1397.71u
27
+ 9862.96u
26
+ ··· − 495.752u + 614.029
310.534u
27
+ 2184.63u
26
+ ··· − 102.826u + 142.238
a
9
=
−1740.25u
27
− 12272.3u
26
+ ··· + 619.039u − 772.358
−353.296u
27
− 2488.38u
26
+ ··· + 114.893u − 158.228
a
8
=
−1005.12u
27
− 7089.04u
26
+ ··· + 357.983u − 444.544
−292.100u
27
− 2060.87u
26
+ ··· + 102.084u − 127.364
(ii) Obstruction class = 1
(iii) Cusp Shapes = 643.001u
27
+ 4565.08u
26
+ ··· − 263.510u + 263.109
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
5(5u
28
− 23u
27
+ ··· + 8u − 1)
c
2
u
28
− u
27
+ ··· + 8u − 5
c
3
u
28
+ 7u
27
+ ··· − 15u + 1
c
4
u
28
+ 4u
26
+ ··· + 22u − 5
c
5
5(5u
28
+ 23u
27
+ ··· + 16u − 1)
c
6
5(5u
28
+ 33u
27
+ ··· + 3u − 1)
c
7
, c
8
u
28
− 14u
26
+ ··· − 16u − 5
c
9
u
28
− u
27
+ ··· − 3u + 1
c
10
u
28
− u
27
+ ··· + 18u − 5
c
11
5(5u
28
− 23u
27
+ ··· − 16u − 1)
c
12
u
28
− 14u
26
+ ··· + 16u − 5
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
28
− 679y
27
+ ··· − 16y + 1)
c
2
y
28
+ 19y
27
+ ··· − 784y + 25
c
3
y
28
− 7y
27
+ ··· − 125y + 1
c
4
y
28
+ 8y
27
+ ··· − 614y + 25
c
5
, c
11
25(25y
28
+ 171y
27
+ ··· − 30y + 1)
c
6
25(25y
28
− 679y
27
+ ··· − 29y + 1)
c
7
, c
8
, c
12
y
28
− 28y
27
+ ··· − 146y + 25
c
9
y
28
− 15y
27
+ ··· + 61y + 1
c
10
y
28
+ 3y
27
+ ··· − 34y + 25
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.375537 + 0.908959I
a = −0.419864 + 0.941622I
b = 0.375754 + 1.173510I
5.99435 + 6.10849I 7.86640 − 7.03827I
u = −0.375537 − 0.908959I
a = −0.419864 − 0.941622I
b = 0.375754 − 1.173510I
5.99435 − 6.10849I 7.86640 + 7.03827I
u = 0.536304 + 0.812141I
a = −0.437441 − 0.811355I
b = 0.667741 − 0.875405I
0.34667 − 3.66787I 1.90881 + 6.77780I
u = 0.536304 − 0.812141I
a = −0.437441 + 0.811355I
b = 0.667741 + 0.875405I
0.34667 + 3.66787I 1.90881 − 6.77780I
u = −0.878472 + 0.562488I
a = −0.468900 + 0.958110I
b = −0.418888 + 0.809345I
−0.28577 + 2.75438I 3.07087 − 2.91509I
u = −0.878472 − 0.562488I
a = −0.468900 − 0.958110I
b = −0.418888 − 0.809345I
−0.28577 − 2.75438I 3.07087 + 2.91509I
u = −0.904597 + 0.078680I
a = −0.87667 − 1.77475I
b = −0.420914 − 0.861703I
−2.61367 + 2.03309I −0.43249 − 3.01662I
u = −0.904597 − 0.078680I
a = −0.87667 + 1.77475I
b = −0.420914 + 0.861703I
−2.61367 − 2.03309I −0.43249 + 3.01662I
u = 1.097610 + 0.206815I
a = −0.315527 − 0.583039I
b = −0.74081 − 1.53148I
−4.34831 + 0.83141I −4.51787 + 8.76566I
u = 1.097610 − 0.206815I
a = −0.315527 + 0.583039I
b = −0.74081 + 1.53148I
−4.34831 − 0.83141I −4.51787 − 8.76566I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.886387 + 0.743109I
a = −0.131593 − 0.863477I
b = −0.77605 − 1.72910I
2.93039 + 6.50271I 3.62346 − 10.61490I
u = −0.886387 − 0.743109I
a = −0.131593 + 0.863477I
b = −0.77605 + 1.72910I
2.93039 − 6.50271I 3.62346 + 10.61490I
u = 0.629738 + 0.507538I
a = −0.972574 − 0.262845I
b = −0.330778 − 1.097170I
−4.80377 + 0.54369I −1.91796 − 0.05430I
u = 0.629738 − 0.507538I
a = −0.972574 + 0.262845I
b = −0.330778 + 1.097170I
−4.80377 − 0.54369I −1.91796 + 0.05430I
u = 0.685641
a = 1.89909
b = −0.185357
−0.252884 −2.15640
u = −1.090140 + 0.861739I
a = −0.204407 + 0.520785I
b = 0.761784 + 0.601784I
4.52838 + 0.56273I 0
u = −1.090140 − 0.861739I
a = −0.204407 − 0.520785I
b = 0.761784 − 0.601784I
4.52838 − 0.56273I 0
u = 1.06202 + 0.95575I
a = 0.041681 + 1.110010I
b = −0.79533 + 1.28829I
−5.64873 − 6.71284I 0
u = 1.06202 − 0.95575I
a = 0.041681 − 1.110010I
b = −0.79533 − 1.28829I
−5.64873 + 6.71284I 0
u = 0.473673 + 0.165860I
a = −0.20638 + 1.66181I
b = 1.162000 − 0.458164I
1.37627 + 9.52114I 4.52699 − 4.03433I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.473673 − 0.165860I
a = −0.20638 − 1.66181I
b = 1.162000 + 0.458164I
1.37627 − 9.52114I 4.52699 + 4.03433I
u = −1.14419 + 0.97425I
a = −0.047944 − 1.189140I
b = −0.678421 − 1.237390I
−1.97747 + 7.67744I 0
u = −1.14419 − 0.97425I
a = −0.047944 + 1.189140I
b = −0.678421 + 1.237390I
−1.97747 − 7.67744I 0
u = 0.441726 + 0.008989I
a = −4.32415 − 2.17189I
b = −0.131013 − 0.639309I
−4.36155 + 1.32316I −9.31478 − 2.17152I
u = 0.441726 − 0.008989I
a = −4.32415 + 2.17189I
b = −0.131013 + 0.639309I
−4.36155 − 1.32316I −9.31478 + 2.17152I
u = −0.357621 + 0.193316I
a = −1.12045 − 1.61343I
b = 0.777494 + 1.072400I
−4.83906 − 5.20210I 1.75952 + 5.15190I
u = −0.357621 − 0.193316I
a = −1.12045 + 1.61343I
b = 0.777494 − 1.072400I
−4.83906 + 5.20210I 1.75952 − 5.15190I
u = −4.49390
a = 0.0693211
b = 0.280244
1.33846 0
24
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
25(5u
28
− 23u
27
+ ··· + 8u − 1)(5u
139
+ 44u
138
+ ··· − 138u + 207)
c
2
(u
28
− u
27
+ ··· + 8u − 5)(u
139
+ 23u
137
+ ··· + 1342610u + 79075)
c
3
(u
28
+ 7u
27
+ ··· − 15u + 1)
· (u
139
− 4u
138
+ ··· + 9955539065u − 2811030979)
c
4
(u
28
+ 4u
26
+ ··· + 22u − 5)(u
139
+ u
138
+ ··· + 132792u − 9535)
c
5
25(5u
28
+ 23u
27
+ ··· + 16u − 1)
· (5u
139
− 6u
138
+ ··· + 10874800u + 3500629)
c
6
25(5u
28
+ 33u
27
+ ··· + 3u − 1)(5u
139
− 6u
138
+ ··· + 7u + 1)
c
7
, c
8
(u
28
− 14u
26
+ ··· − 16u − 5)(u
139
+ u
138
+ ··· + 3436u + 335)
c
9
(u
28
− u
27
+ ··· − 3u + 1)
· (u
139
− 36u
137
+ ··· + 911022429u − 918419671)
c
10
(u
28
− u
27
+ ··· + 18u − 5)(u
139
+ 2u
138
+ ··· − 161606u + 44905)
c
11
25(5u
28
− 23u
27
+ ··· − 16u − 1)
· (5u
139
− 6u
138
+ ··· + 10874800u + 3500629)
c
12
(u
28
− 14u
26
+ ··· + 16u − 5)(u
139
+ u
138
+ ··· + 3436u + 335)
25
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
625(25y
28
− 679y
27
+ ··· − 16y + 1)
· (25y
139
− 376y
138
+ ··· + 5015196y −42849)
c
2
(y
28
+ 19y
27
+ ··· − 784y + 25)
· (y
139
+ 46y
138
+ ··· − 50108241400y −6252855625)
c
3
(y
28
− 7y
27
+ ··· − 125y + 1)
· (y
139
− 52y
138
+ ··· + 2.84 × 10
20
y −7.90 × 10
18
)
c
4
(y
28
+ 8y
27
+ ··· − 614y + 25)
· (y
139
− y
138
+ ··· + 15265736154y −90916225)
c
5
, c
11
625(25y
28
+ 171y
27
+ ··· − 30y + 1)
· (25y
139
+ 2274y
138
+ ··· + 494385524795298y −12254403395641)
c
6
625(25y
28
− 679y
27
+ ··· − 29y + 1)(25y
139
− 1076y
138
+ ··· + y −1)
c
7
, c
8
, c
12
(y
28
− 28y
27
+ ··· − 146y + 25)
· (y
139
− 133y
138
+ ··· − 2468254y −112225)
c
9
(y
28
− 15y
27
+ ··· + 61y + 1)
· (y
139
− 72y
138
+ ··· + 4.72 × 10
19
y −8.43 × 10
17
)
c
10
(y
28
+ 3y
27
+ ··· − 34y + 25)
· (y
139
+ 26y
138
+ ··· − 67481776374y −2016459025)
26
