12a
0363
(K12a
0363
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 11 2 12 10 4 1 7 5
Solving Sequence
3,9
4
6,10
2 1 11 8 5 12 7
c
3
c
9
c
2
c
1
c
10
c
8
c
4
c
12
c
7
c
5
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.13651 × 10
190
u
139
− 2.21719 × 10
190
u
138
+ ··· + 1.74140 × 10
190
b + 8.78867 × 10
191
,
− 2.57843 × 10
192
u
139
+ 1.13373 × 10
192
u
138
+ ··· + 1.91554 × 10
191
a − 2.84745 × 10
193
,
u
140
− u
139
+ ··· + 3u − 11i
I
u
2
= h−5u
25
+ 33u
23
+ ··· + b + 1, 10u
25
+ 8u
24
+ ··· + a − 17, u
26
− 7u
24
+ ··· − 5u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 166 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
= h6.14 × 10
190
u
139
− 2.22 × 10
190
u
138
+ · · · + 1.74 × 10
190
b + 8.79 ×
10
191
, −2.58 × 10
192
u
139
+ 1.13 × 10
192
u
138
+ · · · + 1.92 × 10
191
a − 2.85 ×
10
193
, u
140
− u
139
+ · · · + 3u − 11i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
6
=
13.4606u
139
− 5.91858u
138
+ ··· + 177.633u + 148.650
−3.52390u
139
+ 1.27322u
138
+ ··· − 71.2813u − 50.4690
a
10
=
u
−u
3
+ u
a
2
=
2.65083u
139
− 3.89431u
138
+ ··· + 111.399u + 82.2790
3.04276u
139
+ 1.43378u
138
+ ··· + 1.82150u + 47.9135
a
1
=
5.69359u
139
− 2.46052u
138
+ ··· + 113.221u + 130.193
3.04276u
139
+ 1.43378u
138
+ ··· + 1.82150u + 47.9135
a
11
=
4.08136u
139
− 4.79781u
138
+ ··· + 109.917u + 54.4416
−0.606961u
139
+ 0.806119u
138
+ ··· − 37.3582u − 6.65478
a
8
=
−u
3
u
5
− u
3
+ u
a
5
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
12
=
3.82378u
139
− 2.26440u
138
+ ··· + 91.3649u + 97.7676
3.89747u
139
+ 1.15101u
138
+ ··· + 15.4401u + 61.6666
a
7
=
4.67478u
139
− 4.01428u
138
+ ··· + 108.440u + 70.0227
0.589215u
139
− 0.565928u
138
+ ··· + 33.8266u + 15.2231
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8.36211u
139
− 4.62818u
138
+ ··· + 41.7553u − 36.0403
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
140
+ 52u
139
+ ··· + 337740u + 6241
c
2
, c
6
u
140
+ 26u
138
+ ··· − 482u + 79
c
3
, c
9
u
140
+ u
139
+ ··· − 3u − 11
c
4
u
140
+ 3u
139
+ ··· − 25984085u − 6280527
c
5
u
140
+ u
139
+ ··· + 404117u − 144771
c
7
, c
11
u
140
+ u
139
+ ··· + 45u − 1
c
8
u
140
− 73u
139
+ ··· − 1461u + 121
c
10
u
140
− 23u
139
+ ··· − 258635u + 11863
c
12
u
140
− 3u
139
+ ··· − 3347197u + 538957
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
140
+ 84y
139
+ ··· − 2917146088y + 38950081
c
2
, c
6
y
140
+ 52y
139
+ ··· + 337740y + 6241
c
3
, c
9
y
140
− 73y
139
+ ··· − 1461y + 121
c
4
y
140
+ 91y
139
+ ··· − 1096216389691129y + 39445019397729
c
5
y
140
− 39y
139
+ ··· − 438067087459y + 20958642441
c
7
, c
11
y
140
− 117y
139
+ ··· + 107y + 1
c
8
y
140
− 9y
139
+ ··· − 804005y + 14641
c
10
y
140
+ 29y
139
+ ··· − 922560827y + 140730769
c
12
y
140
− 43y
139
+ ··· − 16999596958743y + 290474647849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.819465 + 0.601104I
a = −0.273785 − 0.601175I
b = −0.526903 − 0.936919I
−1.91446 + 1.71102I 0
u = −0.819465 − 0.601104I
a = −0.273785 + 0.601175I
b = −0.526903 + 0.936919I
−1.91446 − 1.71102I 0
u = 0.208895 + 0.998000I
a = 0.738442 − 0.049131I
b = −0.629531 − 0.861460I
3.98141 + 1.29056I 0
u = 0.208895 − 0.998000I
a = 0.738442 + 0.049131I
b = −0.629531 + 0.861460I
3.98141 − 1.29056I 0
u = 0.725777 + 0.641046I
a = 0.361709 − 0.866119I
b = 0.012192 − 1.196540I
−2.90283 + 4.25393I 0
u = 0.725777 − 0.641046I
a = 0.361709 + 0.866119I
b = 0.012192 + 1.196540I
−2.90283 − 4.25393I 0
u = −0.280451 + 0.996079I
a = 0.991224 − 0.455528I
b = −0.627884 − 0.845310I
4.03314 + 3.63347I 0
u = −0.280451 − 0.996079I
a = 0.991224 + 0.455528I
b = −0.627884 + 0.845310I
4.03314 − 3.63347I 0
u = 0.904664 + 0.324825I
a = 0.84139 − 1.90792I
b = −0.161953 + 0.649634I
−1.85564 + 1.33643I 0
u = 0.904664 − 0.324825I
a = 0.84139 + 1.90792I
b = −0.161953 − 0.649634I
−1.85564 − 1.33643I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.741408 + 0.605549I
a = −1.23895 − 1.65423I
b = 0.567177 − 0.983427I
−2.13460 − 6.43998I 0
u = −0.741408 − 0.605549I
a = −1.23895 + 1.65423I
b = 0.567177 + 0.983427I
−2.13460 + 6.43998I 0
u = −0.588581 + 0.752891I
a = 0.932767 + 0.669322I
b = −0.581080 + 0.505008I
2.01572 + 1.08008I 0
u = −0.588581 − 0.752891I
a = 0.932767 − 0.669322I
b = −0.581080 − 0.505008I
2.01572 − 1.08008I 0
u = 0.840582 + 0.637624I
a = 1.35916 − 0.66753I
b = −0.106758 − 1.116930I
−2.58040 + 0.68173I 0
u = 0.840582 − 0.637624I
a = 1.35916 + 0.66753I
b = −0.106758 + 1.116930I
−2.58040 − 0.68173I 0
u = 0.791527 + 0.515926I
a = 0.485552 + 0.133390I
b = 0.436044 − 0.572285I
−0.96654 + 2.06636I 0
u = 0.791527 − 0.515926I
a = 0.485552 − 0.133390I
b = 0.436044 + 0.572285I
−0.96654 − 2.06636I 0
u = −0.903401 + 0.251863I
a = 1.11305 − 1.68568I
b = 0.483060 + 1.013160I
3.28601 + 2.69223I 0
u = −0.903401 − 0.251863I
a = 1.11305 + 1.68568I
b = 0.483060 − 1.013160I
3.28601 − 2.69223I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.959593 + 0.510875I
a = 2.44943 + 0.92553I
b = −0.293618 + 0.965605I
−3.27126 − 3.56568I 0
u = −0.959593 − 0.510875I
a = 2.44943 − 0.92553I
b = −0.293618 − 0.965605I
−3.27126 + 3.56568I 0
u = 0.713368 + 0.820999I
a = 0.220508 + 0.255280I
b = −0.611825 + 1.026880I
0.58642 − 5.94419I 0
u = 0.713368 − 0.820999I
a = 0.220508 − 0.255280I
b = −0.611825 − 1.026880I
0.58642 + 5.94419I 0
u = 0.781067 + 0.463227I
a = 0.546918 − 0.488424I
b = −0.122889 − 0.449806I
−1.08917 + 1.93792I 0
u = 0.781067 − 0.463227I
a = 0.546918 + 0.488424I
b = −0.122889 + 0.449806I
−1.08917 − 1.93792I 0
u = 0.220674 + 0.880594I
a = −1.185880 − 0.572351I
b = 0.727382 − 1.104240I
5.2183 − 13.9708I 0
u = 0.220674 − 0.880594I
a = −1.185880 + 0.572351I
b = 0.727382 + 1.104240I
5.2183 + 13.9708I 0
u = −0.900493 + 0.639852I
a = −0.382863 − 0.499656I
b = 0.785510 + 0.473472I
2.88856 − 6.23663I 0
u = −0.900493 − 0.639852I
a = −0.382863 + 0.499656I
b = 0.785510 − 0.473472I
2.88856 + 6.23663I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.197932 + 0.854508I
a = −0.578891 + 0.278552I
b = 0.945512 − 0.580759I
6.84078 + 7.84586I 0
u = −0.197932 − 0.854508I
a = −0.578891 − 0.278552I
b = 0.945512 + 0.580759I
6.84078 − 7.84586I 0
u = 1.065320 + 0.362248I
a = −1.23718 + 1.47542I
b = −0.239406 + 0.696587I
5.72554 + 1.31498I 0
u = 1.065320 − 0.362248I
a = −1.23718 − 1.47542I
b = −0.239406 − 0.696587I
5.72554 − 1.31498I 0
u = 1.058820 + 0.408764I
a = 0.447932 − 0.024635I
b = 0.089918 − 1.060490I
−0.35657 + 1.41502I 0
u = 1.058820 − 0.408764I
a = 0.447932 + 0.024635I
b = 0.089918 + 1.060490I
−0.35657 − 1.41502I 0
u = 0.894142 + 0.715299I
a = −1.55420 + 0.89153I
b = 0.643659 + 1.070540I
1.16619 + 11.59850I 0
u = 0.894142 − 0.715299I
a = −1.55420 − 0.89153I
b = 0.643659 − 1.070540I
1.16619 − 11.59850I 0
u = −1.112620 + 0.299776I
a = 0.445941 − 1.027240I
b = 0.308610 + 1.222730I
3.41072 + 2.93577I 0
u = −1.112620 − 0.299776I
a = 0.445941 + 1.027240I
b = 0.308610 − 1.222730I
3.41072 − 2.93577I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805266 + 0.256270I
a = −3.13134 − 0.38971I
b = 0.696447 + 0.964734I
3.20266 + 5.85000I 10.8328 − 11.3116I
u = 0.805266 − 0.256270I
a = −3.13134 + 0.38971I
b = 0.696447 − 0.964734I
3.20266 − 5.85000I 10.8328 + 11.3116I
u = 0.645976 + 0.544508I
a = 0.749819 − 0.949600I
b = −0.386740 − 0.877417I
−1.34695 + 2.10493I 6.00000 + 0.I
u = 0.645976 − 0.544508I
a = 0.749819 + 0.949600I
b = −0.386740 + 0.877417I
−1.34695 − 2.10493I 6.00000 + 0.I
u = −0.766449 + 0.341769I
a = 1.204510 − 0.117120I
b = −0.897138 + 0.663381I
3.97663 − 2.55791I 11.57076 + 6.03390I
u = −0.766449 − 0.341769I
a = 1.204510 + 0.117120I
b = −0.897138 − 0.663381I
3.97663 + 2.55791I 11.57076 − 6.03390I
u = −0.428607 + 0.720357I
a = 1.18236 + 0.83855I
b = −0.240114 + 0.474540I
2.03051 + 0.98271I 6.00000 − 2.59458I
u = −0.428607 − 0.720357I
a = 1.18236 − 0.83855I
b = −0.240114 − 0.474540I
2.03051 − 0.98271I 6.00000 + 2.59458I
u = 0.836775
a = −0.207422
b = −0.879420
5.63574 19.3000
u = −1.123800 + 0.305845I
a = −1.09854 − 1.18868I
b = 0.716453 + 0.948727I
4.40051 + 0.60498I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.123800 − 0.305845I
a = −1.09854 + 1.18868I
b = 0.716453 − 0.948727I
4.40051 − 0.60498I 0
u = 1.149630 + 0.330362I
a = 1.60976 − 0.69797I
b = −0.673469 + 1.009790I
4.26218 − 4.49247I 0
u = 1.149630 − 0.330362I
a = 1.60976 + 0.69797I
b = −0.673469 − 1.009790I
4.26218 + 4.49247I 0
u = 0.112882 + 0.792728I
a = 0.557215 + 0.068936I
b = −0.067761 + 0.609858I
1.52861 − 1.68586I 4.68797 + 3.45114I
u = 0.112882 − 0.792728I
a = 0.557215 − 0.068936I
b = −0.067761 − 0.609858I
1.52861 + 1.68586I 4.68797 − 3.45114I
u = 0.263276 + 0.754577I
a = 0.176137 + 0.788252I
b = −0.167287 + 1.295340I
−0.76781 − 5.99748I 3.63087 + 7.05574I
u = 0.263276 − 0.754577I
a = 0.176137 − 0.788252I
b = −0.167287 − 1.295340I
−0.76781 + 5.99748I 3.63087 − 7.05574I
u = 0.280187 + 0.746806I
a = 0.788485 + 0.671446I
b = −0.594752 + 1.020860I
0.24157 − 3.64223I 4.72165 + 0.97424I
u = 0.280187 − 0.746806I
a = 0.788485 − 0.671446I
b = −0.594752 − 1.020860I
0.24157 + 3.64223I 4.72165 − 0.97424I
u = −0.750280 + 0.268239I
a = −1.14819 − 2.22811I
b = 0.746169 + 0.729878I
3.91151 − 0.35414I 10.25180 + 4.64821I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.750280 − 0.268239I
a = −1.14819 + 2.22811I
b = 0.746169 − 0.729878I
3.91151 + 0.35414I 10.25180 − 4.64821I
u = −0.229412 + 0.756603I
a = −1.35042 + 1.16217I
b = 0.637868 + 1.026790I
0.17383 + 7.83476I 5.17246 − 7.94900I
u = −0.229412 − 0.756603I
a = −1.35042 − 1.16217I
b = 0.637868 − 1.026790I
0.17383 − 7.83476I 5.17246 + 7.94900I
u = −1.160530 + 0.363731I
a = 1.53233 − 0.71195I
b = −0.739607 + 0.623924I
5.39201 − 0.90370I 0
u = −1.160530 − 0.363731I
a = 1.53233 + 0.71195I
b = −0.739607 − 0.623924I
5.39201 + 0.90370I 0
u = −1.111320 + 0.495860I
a = −1.258030 − 0.397388I
b = −0.031319 − 1.141470I
−1.06553 − 5.82110I 0
u = −1.111320 − 0.495860I
a = −1.258030 + 0.397388I
b = −0.031319 + 1.141470I
−1.06553 + 5.82110I 0
u = 1.164220 + 0.393081I
a = −1.81411 − 0.11891I
b = 0.768058 + 0.682952I
5.17383 + 5.00452I 0
u = 1.164220 − 0.393081I
a = −1.81411 + 0.11891I
b = 0.768058 − 0.682952I
5.17383 − 5.00452I 0
u = 0.748592 + 0.181734I
a = 0.878651 − 0.642024I
b = −0.779626 + 1.003540I
2.97274 − 3.60491I 10.36671 + 1.22859I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.748592 − 0.181734I
a = 0.878651 + 0.642024I
b = −0.779626 − 1.003540I
2.97274 + 3.60491I 10.36671 − 1.22859I
u = 1.157840 + 0.417927I
a = −1.32716 + 1.59285I
b = 1.185410 − 0.389801I
9.09011 + 1.84231I 0
u = 1.157840 − 0.417927I
a = −1.32716 − 1.59285I
b = 1.185410 + 0.389801I
9.09011 − 1.84231I 0
u = 1.150750 + 0.437661I
a = −0.85517 + 1.59029I
b = 0.86610 − 1.15636I
6.79845 − 0.84188I 0
u = 1.150750 − 0.437661I
a = −0.85517 − 1.59029I
b = 0.86610 + 1.15636I
6.79845 + 0.84188I 0
u = −0.572554 + 0.509279I
a = −0.61241 + 1.78069I
b = 0.190353 + 1.009410I
−4.40135 − 0.63333I −1.24969 − 1.21453I
u = −0.572554 − 0.509279I
a = −0.61241 − 1.78069I
b = 0.190353 − 1.009410I
−4.40135 + 0.63333I −1.24969 + 1.21453I
u = 1.149570 + 0.451749I
a = 3.62115 − 0.51783I
b = −0.636854 − 0.872531I
7.99476 + 4.59039I 0
u = 1.149570 − 0.451749I
a = 3.62115 + 0.51783I
b = −0.636854 + 0.872531I
7.99476 − 4.59039I 0
u = −1.151660 + 0.448221I
a = 2.03999 + 1.35586I
b = −0.697290 − 0.849589I
8.01842 − 3.49746I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.151660 − 0.448221I
a = 2.03999 − 1.35586I
b = −0.697290 + 0.849589I
8.01842 + 3.49746I 0
u = 0.177381 + 0.742334I
a = −0.071572 − 0.448830I
b = 0.690228 + 0.563342I
1.51325 − 2.67968I 7.37592 + 3.47726I
u = 0.177381 − 0.742334I
a = −0.071572 + 0.448830I
b = 0.690228 − 0.563342I
1.51325 + 2.67968I 7.37592 − 3.47726I
u = −1.151040 + 0.461160I
a = −2.84467 − 0.14834I
b = 0.82302 − 1.21891I
6.62997 − 8.93464I 0
u = −1.151040 − 0.461160I
a = −2.84467 + 0.14834I
b = 0.82302 + 1.21891I
6.62997 + 8.93464I 0
u = −1.121350 + 0.557992I
a = −0.201215 + 0.594207I
b = 0.111316 + 0.716162I
4.18372 − 5.94348I 0
u = −1.121350 − 0.557992I
a = −0.201215 − 0.594207I
b = 0.111316 − 0.716162I
4.18372 + 5.94348I 0
u = −1.159140 + 0.475194I
a = −2.12166 − 0.42257I
b = 1.181410 − 0.526785I
8.68313 − 6.36401I 0
u = −1.159140 − 0.475194I
a = −2.12166 + 0.42257I
b = 1.181410 + 0.526785I
8.68313 + 6.36401I 0
u = −0.689219 + 0.285983I
a = 0.82099 + 1.64476I
b = −0.646260 + 1.169410I
2.53323 − 5.41442I 5.96568 + 11.95972I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.689219 − 0.285983I
a = 0.82099 − 1.64476I
b = −0.646260 − 1.169410I
2.53323 + 5.41442I 5.96568 − 11.95972I
u = −1.175170 + 0.439114I
a = 0.66966 + 2.43954I
b = −0.642836 − 0.837836I
8.10380 + 0.40309I 0
u = −1.175170 − 0.439114I
a = 0.66966 − 2.43954I
b = −0.642836 + 0.837836I
8.10380 − 0.40309I 0
u = −1.158520 + 0.481809I
a = −0.768217 − 1.063910I
b = 0.744387 + 0.464103I
4.56933 − 3.26362I 0
u = −1.158520 − 0.481809I
a = −0.768217 + 1.063910I
b = 0.744387 − 0.464103I
4.56933 + 3.26362I 0
u = 1.172110 + 0.458685I
a = 2.49739 + 1.15826I
b = −0.688342 − 0.866363I
7.96453 + 8.82066I 0
u = 1.172110 − 0.458685I
a = 2.49739 − 1.15826I
b = −0.688342 + 0.866363I
7.96453 − 8.82066I 0
u = −1.206400 + 0.381025I
a = −0.055606 − 0.766674I
b = −0.044579 + 0.675540I
5.49976 − 2.33349I 0
u = −1.206400 − 0.381025I
a = −0.055606 + 0.766674I
b = −0.044579 − 0.675540I
5.49976 + 2.33349I 0
u = −0.087509 + 0.729576I
a = 0.481488 + 0.083455I
b = −0.609447 + 0.579754I
1.53007 − 1.15987I 7.43225 + 3.70763I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.087509 − 0.729576I
a = 0.481488 − 0.083455I
b = −0.609447 − 0.579754I
1.53007 + 1.15987I 7.43225 − 3.70763I
u = 1.146500 + 0.537372I
a = −1.61922 − 0.09495I
b = 0.194322 + 1.356190I
1.82460 + 10.85730I 0
u = 1.146500 − 0.537372I
a = −1.61922 + 0.09495I
b = 0.194322 − 1.356190I
1.82460 − 10.85730I 0
u = 1.143940 + 0.543522I
a = −2.29631 + 0.37953I
b = 0.634804 + 1.084940I
2.77562 + 8.52497I 0
u = 1.143940 − 0.543522I
a = −2.29631 − 0.37953I
b = 0.634804 − 1.084940I
2.77562 − 8.52497I 0
u = 1.163270 + 0.510441I
a = 0.29398 − 1.49105I
b = −0.734529 + 0.532186I
4.37382 + 7.36822I 0
u = 1.163270 − 0.510441I
a = 0.29398 + 1.49105I
b = −0.734529 − 0.532186I
4.37382 − 7.36822I 0
u = −1.156860 + 0.529818I
a = 2.77811 + 0.81836I
b = −0.647927 + 1.047350I
2.88783 − 12.66090I 0
u = −1.156860 − 0.529818I
a = 2.77811 − 0.81836I
b = −0.647927 − 1.047350I
2.88783 + 12.66090I 0
u = 1.244700 + 0.323559I
a = 2.00246 + 0.40466I
b = −0.927208 − 0.629923I
11.38690 − 3.94355I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.244700 − 0.323559I
a = 2.00246 − 0.40466I
b = −0.927208 + 0.629923I
11.38690 + 3.94355I 0
u = 0.023047 + 0.710804I
a = −1.05257 + 1.27195I
b = 0.654278 − 0.878099I
4.72416 − 4.54539I 11.00938 + 6.82756I
u = 0.023047 − 0.710804I
a = −1.05257 − 1.27195I
b = 0.654278 + 0.878099I
4.72416 + 4.54539I 11.00938 − 6.82756I
u = 1.188310 + 0.501202I
a = −0.936338 − 0.411125I
b = 0.010051 + 0.549485I
4.67098 + 6.41520I 0
u = 1.188310 − 0.501202I
a = −0.936338 + 0.411125I
b = 0.010051 − 0.549485I
4.67098 − 6.41520I 0
u = −1.263960 + 0.301245I
a = 1.44206 + 1.06783I
b = −0.739648 − 1.076720I
9.9965 + 10.0671I 0
u = −1.263960 − 0.301245I
a = 1.44206 − 1.06783I
b = −0.739648 + 1.076720I
9.9965 − 10.0671I 0
u = 0.658838 + 0.215652I
a = −2.41715 + 4.42010I
b = 0.499698 + 0.742419I
4.17541 + 1.35875I 8.54380 − 7.13093I
u = 0.658838 − 0.215652I
a = −2.41715 − 4.42010I
b = 0.499698 − 0.742419I
4.17541 − 1.35875I 8.54380 + 7.13093I
u = −0.085778 + 0.683615I
a = 0.570129 + 0.264834I
b = −1.105130 − 0.475850I
5.66691 + 2.02008I 15.5707 − 2.4843I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.085778 − 0.683615I
a = 0.570129 − 0.264834I
b = −1.105130 + 0.475850I
5.66691 − 2.02008I 15.5707 + 2.4843I
u = −1.196310 + 0.545973I
a = 0.80595 + 1.53573I
b = −0.978656 − 0.585263I
9.8239 − 12.9726I 0
u = −1.196310 − 0.545973I
a = 0.80595 − 1.53573I
b = −0.978656 + 0.585263I
9.8239 + 12.9726I 0
u = 1.304550 + 0.214866I
a = −1.51929 + 0.62867I
b = 0.701903 − 0.787117I
9.65087 + 0.28641I 0
u = 1.304550 − 0.214866I
a = −1.51929 − 0.62867I
b = 0.701903 + 0.787117I
9.65087 − 0.28641I 0
u = 1.200350 + 0.561477I
a = 2.63905 − 0.38998I
b = −0.741029 − 1.116420I
8.1649 + 19.2372I 0
u = 1.200350 − 0.561477I
a = 2.63905 + 0.38998I
b = −0.741029 + 1.116420I
8.1649 − 19.2372I 0
u = −0.258586 + 0.598774I
a = 0.12063 − 1.72443I
b = 0.058980 − 1.075560I
−3.48227 + 1.48199I −0.50148 − 1.95380I
u = −0.258586 − 0.598774I
a = 0.12063 + 1.72443I
b = 0.058980 + 1.075560I
−3.48227 − 1.48199I −0.50148 + 1.95380I
u = −1.322690 + 0.273102I
a = −1.71019 + 0.64607I
b = 0.679577 − 0.912322I
9.26823 − 5.59425I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.322690 − 0.273102I
a = −1.71019 − 0.64607I
b = 0.679577 + 0.912322I
9.26823 + 5.59425I 0
u = −0.040169 + 0.639825I
a = 1.211900 − 0.489008I
b = −0.80372 − 1.16410I
3.59821 + 4.78398I 9.75116 − 7.27352I
u = −0.040169 − 0.639825I
a = 1.211900 + 0.489008I
b = −0.80372 + 1.16410I
3.59821 − 4.78398I 9.75116 + 7.27352I
u = −0.639327
a = 0.726186
b = −0.366444
0.799879 13.3670
u = −0.000275 + 0.633985I
a = −2.82175 − 0.28828I
b = 0.654959 − 0.820280I
4.90145 − 0.54303I 11.38278 + 0.21652I
u = −0.000275 − 0.633985I
a = −2.82175 + 0.28828I
b = 0.654959 + 0.820280I
4.90145 + 0.54303I 11.38278 − 0.21652I
u = −1.228690 + 0.597989I
a = −2.18358 − 0.41182I
b = 0.647702 − 0.888812I
7.00616 − 9.37399I 0
u = −1.228690 − 0.597989I
a = −2.18358 + 0.41182I
b = 0.647702 + 0.888812I
7.00616 + 9.37399I 0
u = 1.245460 + 0.567445I
a = −0.564762 + 1.129130I
b = 0.653490 − 0.817424I
7.22938 + 4.31143I 0
u = 1.245460 − 0.567445I
a = −0.564762 − 1.129130I
b = 0.653490 + 0.817424I
7.22938 − 4.31143I 0
18
II. I
u
2
=
h−5u
25
+33u
23
+· · ·+b+1, 10u
25
+8u
24
+· · ·+a−17, u
26
−7u
24
+· · ·−5u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
6
=
−10u
25
− 8u
24
+ ··· + 15u + 17
5u
25
− 33u
23
+ ··· − 9u − 1
a
10
=
u
−u
3
+ u
a
2
=
8u
25
− 50u
23
+ ··· + 39u
3
− 8u
−6u
25
+ 39u
23
+ ··· − 38u
3
+ 12u
a
1
=
2u
25
− 11u
23
+ ··· + u
3
+ 4u
−6u
25
+ 39u
23
+ ··· − 38u
3
+ 12u
a
11
=
−12u
25
− 5u
24
+ ··· + 22u + 6
2u
25
+ 4u
24
+ ··· − 7u − 5
a
8
=
−u
3
u
5
− u
3
+ u
a
5
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
12
=
4u
25
− 25u
23
+ ··· + 19u
3
− 3u
−6u
25
+ 39u
23
+ ··· − 39u
3
+ 13u
a
7
=
−10u
25
− u
24
+ ··· + 12u + 1
8u
25
+ u
24
+ ··· − 17u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 7u
24
−2u
23
−42u
22
+14u
21
+119u
20
−45u
19
−182u
18
+75u
17
+140u
16
−50u
15
−17u
14
−
38u
13
−22u
12
+91u
11
−44u
10
−42u
9
+57u
8
−17u
7
+18u
6
+3u
5
−40u
4
+22u
3
+7u
2
−8u+15
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
26
− 11u
25
+ ··· − 11u + 1
c
2
u
26
− u
25
+ ··· − u + 1
c
3
u
26
− 7u
24
+ ··· − 5u
2
+ 1
c
4
u
26
+ 9u
24
+ ··· − 11u
2
+ 1
c
5
u
26
− 2u
24
+ ··· − 2u
2
+ 1
c
6
u
26
+ u
25
+ ··· + u + 1
c
7
u
26
− 2u
25
+ ··· + 14u + 1
c
8
u
26
+ 14u
25
+ ··· + 10u + 1
c
9
u
26
− 7u
24
+ ··· − 5u
2
+ 1
c
10
u
26
+ 4u
25
+ ··· + 4u + 1
c
11
u
26
+ 2u
25
+ ··· − 14u + 1
c
12
u
26
− 2u
24
+ ··· − 2u
2
+ 1
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 19y
25
+ ··· + 15y + 1
c
2
, c
6
y
26
+ 11y
25
+ ··· + 11y + 1
c
3
, c
9
y
26
− 14y
25
+ ··· − 10y + 1
c
4
y
26
+ 18y
25
+ ··· − 22y + 1
c
5
y
26
− 4y
25
+ ··· − 4y + 1
c
7
, c
11
y
26
− 30y
25
+ ··· − 102y + 1
c
8
y
26
− 2y
25
+ ··· − 14y + 1
c
10
y
26
− 4y
24
+ ··· + 4y + 1
c
12
y
26
− 4y
25
+ ··· − 4y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825135 + 0.508225I
a = 1.36943 − 1.52226I
b = −0.066172 − 0.982940I
−3.35311 + 2.06301I 1.39065 − 3.71553I
u = 0.825135 − 0.508225I
a = 1.36943 + 1.52226I
b = −0.066172 + 0.982940I
−3.35311 − 2.06301I 1.39065 + 3.71553I
u = −0.855624 + 0.353050I
a = 0.238376 + 1.300270I
b = −0.054290 − 0.756100I
−2.36698 − 1.52858I −2.86650 + 4.86955I
u = −0.855624 − 0.353050I
a = 0.238376 − 1.300270I
b = −0.054290 + 0.756100I
−2.36698 + 1.52858I −2.86650 − 4.86955I
u = −0.315764 + 0.828222I
a = 0.352002 + 0.799429I
b = −0.462284 + 0.673643I
2.60995 + 0.45997I 11.74182 + 2.43605I
u = −0.315764 − 0.828222I
a = 0.352002 − 0.799429I
b = −0.462284 − 0.673643I
2.60995 − 0.45997I 11.74182 − 2.43605I
u = −1.076730 + 0.364608I
a = −0.359851 − 0.867622I
b = 0.680612 + 1.135030I
4.75806 + 2.35961I 13.53237 − 1.98828I
u = −1.076730 − 0.364608I
a = −0.359851 + 0.867622I
b = 0.680612 − 1.135030I
4.75806 − 2.35961I 13.53237 + 1.98828I
u = 0.428688 + 0.729292I
a = 0.225847 + 0.591542I
b = −0.570493 + 1.069890I
1.14653 − 4.70780I 8.27206 + 4.54145I
u = 0.428688 − 0.729292I
a = 0.225847 − 0.591542I
b = −0.570493 − 1.069890I
1.14653 + 4.70780I 8.27206 − 4.54145I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.084031 + 0.840686I
a = 1.134640 − 0.009916I
b = −0.680697 − 0.815439I
3.83702 + 2.66410I 9.60930 − 2.37084I
u = −0.084031 − 0.840686I
a = 1.134640 + 0.009916I
b = −0.680697 + 0.815439I
3.83702 − 2.66410I 9.60930 + 2.37084I
u = 1.133610 + 0.353115I
a = −0.431201 + 0.314762I
b = 0.516870 + 0.563465I
6.77557 + 2.59635I 15.0550 − 3.8504I
u = 1.133610 − 0.353115I
a = −0.431201 − 0.314762I
b = 0.516870 − 0.563465I
6.77557 − 2.59635I 15.0550 + 3.8504I
u = 1.175950 + 0.404171I
a = −1.35687 + 1.72419I
b = 0.750394 − 0.713643I
7.67013 + 1.36274I 13.27996 − 0.65875I
u = 1.175950 − 0.404171I
a = −1.35687 − 1.72419I
b = 0.750394 + 0.713643I
7.67013 − 1.36274I 13.27996 + 0.65875I
u = 1.119170 + 0.556109I
a = −1.97264 + 0.46255I
b = 0.561985 + 1.146370I
3.28974 + 9.64848I 11.0008 − 9.5958I
u = 1.119170 − 0.556109I
a = −1.97264 − 0.46255I
b = 0.561985 − 1.146370I
3.28974 − 9.64848I 11.0008 + 9.5958I
u = −1.188490 + 0.462679I
a = −2.46262 + 0.22759I
b = 0.777932 − 0.858774I
7.23113 − 7.24661I 12.56748 + 6.12049I
u = −1.188490 − 0.462679I
a = −2.46262 − 0.22759I
b = 0.777932 + 0.858774I
7.23113 + 7.24661I 12.56748 − 6.12049I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.711494 + 0.046646I
a = −1.06824 − 2.79983I
b = −0.632044 + 0.590527I
4.50647 − 0.59346I 13.48668 + 0.11205I
u = 0.711494 − 0.046646I
a = −1.06824 + 2.79983I
b = −0.632044 − 0.590527I
4.50647 + 0.59346I 13.48668 − 0.11205I
u = −0.695999 + 0.145042I
a = 2.23149 + 0.76210I
b = −0.726435 + 1.055240I
3.00744 − 4.83361I 11.88974 + 3.52567I
u = −0.695999 − 0.145042I
a = 2.23149 − 0.76210I
b = −0.726435 − 1.055240I
3.00744 + 4.83361I 11.88974 − 3.52567I
u = −1.177410 + 0.545635I
a = 0.099635 − 0.360617I
b = 0.404622 + 0.620501I
5.30128 − 5.58909I 13.04059 + 2.30306I
u = −1.177410 − 0.545635I
a = 0.099635 + 0.360617I
b = 0.404622 − 0.620501I
5.30128 + 5.58909I 13.04059 − 2.30306I
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
− 11u
25
+ ··· − 11u + 1)(u
140
+ 52u
139
+ ··· + 337740u + 6241)
c
2
(u
26
− u
25
+ ··· − u + 1)(u
140
+ 26u
138
+ ··· − 482u + 79)
c
3
(u
26
− 7u
24
+ ··· − 5u
2
+ 1)(u
140
+ u
139
+ ··· − 3u − 11)
c
4
(u
26
+ 9u
24
+ ··· − 11u
2
+ 1)
· (u
140
+ 3u
139
+ ··· − 25984085u − 6280527)
c
5
(u
26
− 2u
24
+ ··· − 2u
2
+ 1)(u
140
+ u
139
+ ··· + 404117u − 144771)
c
6
(u
26
+ u
25
+ ··· + u + 1)(u
140
+ 26u
138
+ ··· − 482u + 79)
c
7
(u
26
− 2u
25
+ ··· + 14u + 1)(u
140
+ u
139
+ ··· + 45u − 1)
c
8
(u
26
+ 14u
25
+ ··· + 10u + 1)(u
140
− 73u
139
+ ··· − 1461u + 121)
c
9
(u
26
− 7u
24
+ ··· − 5u
2
+ 1)(u
140
+ u
139
+ ··· − 3u − 11)
c
10
(u
26
+ 4u
25
+ ··· + 4u + 1)(u
140
− 23u
139
+ ··· − 258635u + 11863)
c
11
(u
26
+ 2u
25
+ ··· − 14u + 1)(u
140
+ u
139
+ ··· + 45u − 1)
c
12
(u
26
− 2u
24
+ ··· − 2u
2
+ 1)(u
140
− 3u
139
+ ··· − 3347197u + 538957)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
26
+ 19y
25
+ ··· + 15y + 1)
· (y
140
+ 84y
139
+ ··· − 2917146088y + 38950081)
c
2
, c
6
(y
26
+ 11y
25
+ ··· + 11y + 1)(y
140
+ 52y
139
+ ··· + 337740y + 6241)
c
3
, c
9
(y
26
− 14y
25
+ ··· − 10y + 1)(y
140
− 73y
139
+ ··· − 1461y + 121)
c
4
(y
26
+ 18y
25
+ ··· − 22y + 1)
· (y
140
+ 91y
139
+ ··· − 1096216389691129y + 39445019397729)
c
5
(y
26
− 4y
25
+ ··· − 4y + 1)
· (y
140
− 39y
139
+ ··· − 438067087459y + 20958642441)
c
7
, c
11
(y
26
− 30y
25
+ ··· − 102y + 1)(y
140
− 117y
139
+ ··· + 107y + 1)
c
8
(y
26
− 2y
25
+ ··· − 14y + 1)(y
140
− 9y
139
+ ··· − 804005y + 14641)
c
10
(y
26
− 4y
24
+ ··· + 4y + 1)
· (y
140
+ 29y
139
+ ··· − 922560827y + 140730769)
c
12
(y
26
− 4y
25
+ ··· − 4y + 1)
· (y
140
− 43y
139
+ ··· − 16999596958743y + 290474647849)
28
