12a
0884
(K12a
0884
)
A knot diagram
1
Linearized knot diagam
4 6 7 10 12 9 11 3 2 1 8 5
Solving Sequence
3,8 9,11
12 7 4 6 2 10 1 5
c
8
c
11
c
7
c
3
c
6
c
2
c
9
c
1
c
5
c
4
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.10959 × 10
2657
u
208
− 3.50955 × 10
2658
u
207
+ ··· + 1.60346 × 10
2656
b + 2.47009 × 10
2658
,
− 4.18869 × 10
2656
u
208
− 1.82159 × 10
2657
u
207
+ ··· + 1.60346 × 10
2656
a + 3.34044 × 10
2657
,
u
209
+ 4u
208
+ ··· − 29u + 1i
I
u
2
= h1.17477 × 10
183
u
59
− 5.87917 × 10
183
u
58
+ ··· + 1.06262 × 10
184
b + 6.00821 × 10
183
,
− 1.29179 × 10
183
u
59
+ 6.69835 × 10
183
u
58
+ ··· + 1.06262 × 10
184
a + 2.98562 × 10
184
,
u
60
− 5u
59
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 269 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−8.11 × 10
2657
u
208
− 3.51 × 10
2658
u
207
+ · · · + 1.60 × 10
2656
b +
2.47 × 10
2658
, −4.19 × 10
2656
u
208
− 1.82 × 10
2657
u
207
+ · · · + 1.60 ×
10
2656
a + 3.34 × 10
2657
, u
209
+ 4u
208
+ · · · − 29u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
11
=
2.61228u
208
+ 11.3604u
207
+ ··· + 180.337u − 20.8327
50.5754u
208
+ 218.873u
207
+ ··· + 4014.81u − 154.047
a
12
=
−47.9632u
208
− 207.513u
207
+ ··· − 3834.47u + 133.215
50.5754u
208
+ 218.873u
207
+ ··· + 4014.81u − 154.047
a
7
=
−12.8554u
208
− 54.2835u
207
+ ··· − 705.347u + 32.3403
−35.1135u
208
− 150.396u
207
+ ··· − 3067.90u + 121.566
a
4
=
15.6991u
208
+ 66.6144u
207
+ ··· + 1787.26u − 69.4800
36.5093u
208
+ 157.712u
207
+ ··· + 2975.82u − 113.861
a
6
=
21.9369u
208
+ 94.9669u
207
+ ··· + 2292.42u − 86.3643
−32.2544u
208
− 138.171u
207
+ ··· − 2810.34u + 111.485
a
2
=
−0.0115095u
208
− 1.71675u
207
+ ··· + 539.399u − 23.5712
−21.2435u
208
− 91.7499u
207
+ ··· − 1679.37u + 65.8054
a
10
=
39.6261u
208
+ 171.881u
207
+ ··· + 3100.82u − 107.250
−19.3332u
208
− 83.3766u
207
+ ··· − 1615.68u + 62.4346
a
1
=
29.0576u
208
+ 124.992u
207
+ ··· + 2371.98u − 105.034
25.8012u
208
+ 111.596u
207
+ ··· + 2077.10u − 79.6954
a
5
=
−5.04414u
208
− 22.4581u
207
+ ··· − 299.878u + 11.0691
4.32188u
208
+ 18.7946u
207
+ ··· + 329.949u − 12.6917
(ii) Obstruction class = −1
(iii) Cusp Shapes = −339.908u
208
− 1483.97u
207
+ ··· − 23747.8u + 897.796
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
209
+ 16u
208
+ ··· − 229u + 7
c
2
u
209
+ 20u
207
+ ··· + 1001187u + 56817
c
3
u
209
+ 8u
208
+ ··· + 10140313539u − 1878370717
c
4
u
209
− 5u
208
+ ··· + 4624338u − 184123
c
5
, c
12
u
209
+ u
208
+ ··· + 4331046357u + 113222443
c
6
u
209
+ 16u
208
+ ··· + 12u + 1
c
7
, c
11
u
209
+ 4u
208
+ ··· + 2657560u + 2311849
c
8
u
209
+ 4u
208
+ ··· − 29u + 1
c
9
u
209
+ 45u
207
+ ··· + 739402858830u + 26116631329
c
10
u
209
− 7u
208
+ ··· − 17609u + 341
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
209
− 2y
208
+ ··· − 6625y −49
c
2
y
209
+ 40y
208
+ ··· − 266988642255y −3228171489
c
3
y
209
− 8y
208
+ ··· + 2.14 × 10
20
y −3.53 × 10
18
c
4
y
209
− 47y
208
+ ··· + 8724659978546y −33901279129
c
5
, c
12
y
209
+ 165y
208
+ ··· + 833990559064792201y −12819321598888249
c
6
y
209
+ 30y
208
+ ··· − 56y −1
c
7
, c
11
y
209
− 118y
208
+ ··· + 340566951866202y −5344645798801
c
8
y
209
− 8y
208
+ ··· − 1269y −1
c
9
y
209
+ 90y
208
+ ··· − 4.99 × 10
22
y −6.82 × 10
20
c
10
y
209
− 37y
208
+ ··· + 35347503y −116281
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.322396 + 0.941816I
a = 1.078060 − 0.213369I
b = −0.766823 + 0.134796I
−4.12956 + 5.33084I 0
u = −0.322396 − 0.941816I
a = 1.078060 + 0.213369I
b = −0.766823 − 0.134796I
−4.12956 − 5.33084I 0
u = 0.688925 + 0.735337I
a = −2.12587 + 0.58108I
b = −1.251480 − 0.234975I
−6.95554 − 5.82618I 0
u = 0.688925 − 0.735337I
a = −2.12587 − 0.58108I
b = −1.251480 + 0.234975I
−6.95554 + 5.82618I 0
u = −0.466678 + 0.900813I
a = 0.457825 + 0.401507I
b = 0.605901 − 0.696082I
0.41107 + 1.81059I 0
u = −0.466678 − 0.900813I
a = 0.457825 − 0.401507I
b = 0.605901 + 0.696082I
0.41107 − 1.81059I 0
u = −0.295002 + 0.983333I
a = −0.979898 + 0.538820I
b = 1.062930 + 0.226140I
0.24315 + 2.45125I 0
u = −0.295002 − 0.983333I
a = −0.979898 − 0.538820I
b = 1.062930 − 0.226140I
0.24315 − 2.45125I 0
u = 0.491065 + 0.809479I
a = 0.52229 − 1.70212I
b = 1.166850 + 0.481470I
−3.68167 − 7.05122I 0
u = 0.491065 − 0.809479I
a = 0.52229 + 1.70212I
b = 1.166850 − 0.481470I
−3.68167 + 7.05122I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.035890 + 0.197559I
a = −0.977539 + 0.294685I
b = −1.45275 − 0.37250I
−7.67423 + 1.32305I 0
u = 1.035890 − 0.197559I
a = −0.977539 − 0.294685I
b = −1.45275 + 0.37250I
−7.67423 − 1.32305I 0
u = 0.909494 + 0.536845I
a = 0.592526 − 0.548109I
b = 0.057360 + 0.567159I
−0.36766 + 3.81034I 0
u = 0.909494 − 0.536845I
a = 0.592526 + 0.548109I
b = 0.057360 − 0.567159I
−0.36766 − 3.81034I 0
u = 0.629677 + 0.700527I
a = −1.88696 + 1.75127I
b = −0.917287 − 0.597759I
−1.68445 − 7.10492I 0
u = 0.629677 − 0.700527I
a = −1.88696 − 1.75127I
b = −0.917287 + 0.597759I
−1.68445 + 7.10492I 0
u = 0.669692 + 0.832374I
a = −0.080351 − 1.150370I
b = 0.737976 + 0.128827I
−6.00830 − 5.33123I 0
u = 0.669692 − 0.832374I
a = −0.080351 + 1.150370I
b = 0.737976 − 0.128827I
−6.00830 + 5.33123I 0
u = −1.057120 + 0.161356I
a = −0.326208 + 0.027726I
b = −0.57041 − 1.41267I
−1.82198 − 3.52569I 0
u = −1.057120 − 0.161356I
a = −0.326208 − 0.027726I
b = −0.57041 + 1.41267I
−1.82198 + 3.52569I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.684254 + 0.842297I
a = 1.70966 − 0.98842I
b = 1.001110 + 0.102873I
−5.12674 − 2.17128I 0
u = 0.684254 − 0.842297I
a = 1.70966 + 0.98842I
b = 1.001110 − 0.102873I
−5.12674 + 2.17128I 0
u = −0.778986 + 0.473422I
a = −0.830172 − 0.538918I
b = 0.034639 + 0.766751I
−0.52177 + 2.57685I 0
u = −0.778986 − 0.473422I
a = −0.830172 + 0.538918I
b = 0.034639 − 0.766751I
−0.52177 − 2.57685I 0
u = 0.664235 + 0.602411I
a = −0.085565 + 0.192954I
b = −0.272651 − 1.117750I
1.23843 − 4.89844I 0
u = 0.664235 − 0.602411I
a = −0.085565 − 0.192954I
b = −0.272651 + 1.117750I
1.23843 + 4.89844I 0
u = −0.170528 + 0.868979I
a = −0.346178 − 0.206792I
b = 0.060765 + 0.793071I
−1.02684 + 1.21925I 0
u = −0.170528 − 0.868979I
a = −0.346178 + 0.206792I
b = 0.060765 − 0.793071I
−1.02684 − 1.21925I 0
u = 0.702475 + 0.535536I
a = 2.13084 − 1.02466I
b = 1.214860 + 0.463350I
−4.04158 − 5.84535I 0
u = 0.702475 − 0.535536I
a = 2.13084 + 1.02466I
b = 1.214860 − 0.463350I
−4.04158 + 5.84535I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.645436 + 0.601214I
a = 1.32439 + 0.58808I
b = 1.39035 − 0.75314I
−6.3552 + 13.4802I 0
u = −0.645436 − 0.601214I
a = 1.32439 − 0.58808I
b = 1.39035 + 0.75314I
−6.3552 − 13.4802I 0
u = 0.808900 + 0.349105I
a = −1.40992 + 0.29775I
b = −1.47742 − 0.81750I
−4.62811 − 4.87068I 0
u = 0.808900 − 0.349105I
a = −1.40992 − 0.29775I
b = −1.47742 + 0.81750I
−4.62811 + 4.87068I 0
u = −0.629684 + 0.614199I
a = 0.391089 − 0.612087I
b = −0.556757 − 0.560991I
−0.72140 + 2.54607I 0
u = −0.629684 − 0.614199I
a = 0.391089 + 0.612087I
b = −0.556757 + 0.560991I
−0.72140 − 2.54607I 0
u = −1.13018
a = −1.24879
b = −1.26027
−2.54194 0
u = 0.509588 + 0.696373I
a = 1.65326 − 0.94616I
b = 1.283870 + 0.477392I
−4.83547 − 5.83889I 0
u = 0.509588 − 0.696373I
a = 1.65326 + 0.94616I
b = 1.283870 − 0.477392I
−4.83547 + 5.83889I 0
u = −0.324124 + 1.094780I
a = −0.405834 + 0.280821I
b = 0.864367 + 0.041365I
0.38083 + 2.95440I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.324124 − 1.094780I
a = −0.405834 − 0.280821I
b = 0.864367 − 0.041365I
0.38083 − 2.95440I 0
u = −1.127800 + 0.184799I
a = 1.51057 + 0.77910I
b = 1.118360 + 0.319243I
−8.37201 − 0.61813I 0
u = −1.127800 − 0.184799I
a = 1.51057 − 0.77910I
b = 1.118360 − 0.319243I
−8.37201 + 0.61813I 0
u = −0.523025 + 1.017600I
a = −0.237001 + 0.429116I
b = 0.669239 + 0.319052I
0.27896 + 2.84359I 0
u = −0.523025 − 1.017600I
a = −0.237001 − 0.429116I
b = 0.669239 − 0.319052I
0.27896 − 2.84359I 0
u = 0.170881 + 0.834356I
a = −0.366988 + 0.118463I
b = 0.202472 + 0.688941I
3.46797 + 1.79940I 0
u = 0.170881 − 0.834356I
a = −0.366988 − 0.118463I
b = 0.202472 − 0.688941I
3.46797 − 1.79940I 0
u = 0.058309 + 0.838997I
a = 0.584408 − 0.004947I
b = 0.835937 − 0.827738I
−0.17588 + 3.87813I 0
u = 0.058309 − 0.838997I
a = 0.584408 + 0.004947I
b = 0.835937 + 0.827738I
−0.17588 − 3.87813I 0
u = −1.065600 + 0.484501I
a = 1.79052 − 0.01229I
b = 1.237350 − 0.267508I
−8.93721 + 6.04392I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.065600 − 0.484501I
a = 1.79052 + 0.01229I
b = 1.237350 + 0.267508I
−8.93721 − 6.04392I 0
u = 1.171450 + 0.184950I
a = −1.56947 + 0.52835I
b = −1.108940 + 0.402672I
−7.47840 + 2.37028I 0
u = 1.171450 − 0.184950I
a = −1.56947 − 0.52835I
b = −1.108940 − 0.402672I
−7.47840 − 2.37028I 0
u = −0.541897 + 0.600862I
a = −1.097950 − 0.794729I
b = −1.33090 + 0.60363I
−6.04307 + 4.07584I 0
u = −0.541897 − 0.600862I
a = −1.097950 + 0.794729I
b = −1.33090 − 0.60363I
−6.04307 − 4.07584I 0
u = −0.206432 + 1.175830I
a = −0.045813 + 0.308018I
b = −0.734888 + 0.220198I
−1.02960 + 3.25121I 0
u = −0.206432 − 1.175830I
a = −0.045813 − 0.308018I
b = −0.734888 − 0.220198I
−1.02960 − 3.25121I 0
u = −0.528057 + 0.591427I
a = −0.691390 − 0.251399I
b = −0.464598 + 0.503732I
−0.94301 + 1.39215I 0
u = −0.528057 − 0.591427I
a = −0.691390 + 0.251399I
b = −0.464598 − 0.503732I
−0.94301 − 1.39215I 0
u = −0.781626 + 0.129198I
a = −3.14009 + 0.40454I
b = −1.190240 + 0.476110I
−7.16288 + 11.23080I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.781626 − 0.129198I
a = −3.14009 − 0.40454I
b = −1.190240 − 0.476110I
−7.16288 − 11.23080I 0
u = 0.106093 + 0.780214I
a = 1.90788 + 0.87396I
b = −1.203160 − 0.350716I
−5.28742 − 11.13400I 0
u = 0.106093 − 0.780214I
a = 1.90788 − 0.87396I
b = −1.203160 + 0.350716I
−5.28742 + 11.13400I 0
u = −0.755053 + 0.171762I
a = −0.980882 − 0.379650I
b = 0.029016 − 0.473614I
−4.57808 − 1.05851I 0
u = −0.755053 − 0.171762I
a = −0.980882 + 0.379650I
b = 0.029016 + 0.473614I
−4.57808 + 1.05851I 0
u = −0.763634 + 0.116736I
a = −1.198410 − 0.196738I
b = −1.237830 + 0.539694I
−2.42927 + 1.02706I 0
u = −0.763634 − 0.116736I
a = −1.198410 + 0.196738I
b = −1.237830 − 0.539694I
−2.42927 − 1.02706I 0
u = −0.054084 + 0.764953I
a = −0.660638 + 1.153620I
b = 0.792541 − 0.465137I
1.59684 + 2.06914I 0
u = −0.054084 − 0.764953I
a = −0.660638 − 1.153620I
b = 0.792541 + 0.465137I
1.59684 − 2.06914I 0
u = −0.866749 + 0.877622I
a = 0.150703 − 0.082080I
b = 0.101478 + 0.884405I
−3.29272 + 6.59289I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866749 − 0.877622I
a = 0.150703 + 0.082080I
b = 0.101478 − 0.884405I
−3.29272 − 6.59289I 0
u = −0.726304 + 1.000820I
a = −0.328436 + 0.144576I
b = 0.457951 + 1.017620I
0.49729 + 3.11019I 0
u = −0.726304 − 1.000820I
a = −0.328436 − 0.144576I
b = 0.457951 − 1.017620I
0.49729 − 3.11019I 0
u = −0.000760 + 0.760636I
a = 2.40210 + 0.01528I
b = −0.886866 + 0.198642I
0.67024 + 4.87492I 0
u = −0.000760 − 0.760636I
a = 2.40210 − 0.01528I
b = −0.886866 − 0.198642I
0.67024 − 4.87492I 0
u = 0.779227 + 0.982253I
a = 0.062814 + 0.165899I
b = 0.380044 − 0.921225I
3.78269 − 2.72916I 0
u = 0.779227 − 0.982253I
a = 0.062814 − 0.165899I
b = 0.380044 + 0.921225I
3.78269 + 2.72916I 0
u = −0.965297 + 0.807005I
a = 1.78691 + 0.92455I
b = 0.724314 − 0.740370I
−0.80196 + 8.84500I 0
u = −0.965297 − 0.807005I
a = 1.78691 − 0.92455I
b = 0.724314 + 0.740370I
−0.80196 − 8.84500I 0
u = 0.586580 + 0.439517I
a = 0.87193 − 2.03254I
b = 1.017320 + 0.497045I
−6.81632 − 4.67724I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.586580 − 0.439517I
a = 0.87193 + 2.03254I
b = 1.017320 − 0.497045I
−6.81632 + 4.67724I 0
u = −0.491431 + 0.540049I
a = −0.486115 − 1.192940I
b = −1.106500 + 0.760056I
−5.60199 + 6.65769I 0
u = −0.491431 − 0.540049I
a = −0.486115 + 1.192940I
b = −1.106500 − 0.760056I
−5.60199 − 6.65769I 0
u = 0.749807 + 1.040040I
a = 0.179131 − 0.036316I
b = −0.221447 + 0.877552I
1.12746 − 9.87504I 0
u = 0.749807 − 1.040040I
a = 0.179131 + 0.036316I
b = −0.221447 − 0.877552I
1.12746 + 9.87504I 0
u = −1.211380 + 0.428496I
a = 1.086930 − 0.170859I
b = 1.284470 + 0.371708I
−9.29642 + 2.85337I 0
u = −1.211380 − 0.428496I
a = 1.086930 + 0.170859I
b = 1.284470 − 0.371708I
−9.29642 − 2.85337I 0
u = −1.144490 + 0.596072I
a = −1.394560 − 0.220003I
b = −1.58038 + 0.07420I
−11.74990 − 0.76353I 0
u = −1.144490 − 0.596072I
a = −1.394560 + 0.220003I
b = −1.58038 − 0.07420I
−11.74990 + 0.76353I 0
u = −0.356131 + 0.599507I
a = −0.781460 + 0.167908I
b = −0.033703 + 0.651955I
−0.49466 + 1.57044I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.356131 − 0.599507I
a = −0.781460 − 0.167908I
b = −0.033703 − 0.651955I
−0.49466 − 1.57044I 0
u = 1.300980 + 0.077838I
a = 1.71807 − 0.61544I
b = 0.703123 − 0.066080I
−6.24661 + 1.36052I 0
u = 1.300980 − 0.077838I
a = 1.71807 + 0.61544I
b = 0.703123 + 0.066080I
−6.24661 − 1.36052I 0
u = −0.242624 + 0.642130I
a = 1.233290 + 0.278528I
b = −0.314217 + 0.677082I
2.04033 + 4.97528I 0
u = −0.242624 − 0.642130I
a = 1.233290 − 0.278528I
b = −0.314217 − 0.677082I
2.04033 − 4.97528I 0
u = 1.114240 + 0.721512I
a = −0.777343 + 0.487861I
b = −0.708900 − 1.039380I
−2.69324 − 4.70021I 0
u = 1.114240 − 0.721512I
a = −0.777343 − 0.487861I
b = −0.708900 + 1.039380I
−2.69324 + 4.70021I 0
u = 1.164070 + 0.641233I
a = 1.78988 − 0.01138I
b = 0.833987 + 0.192797I
0.23188 − 5.10410I 0
u = 1.164070 − 0.641233I
a = 1.78988 + 0.01138I
b = 0.833987 − 0.192797I
0.23188 + 5.10410I 0
u = −1.192820 + 0.629157I
a = 0.149440 − 0.304496I
b = 0.213744 + 1.238980I
0.80140 + 5.95799I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.192820 − 0.629157I
a = 0.149440 + 0.304496I
b = 0.213744 − 1.238980I
0.80140 − 5.95799I 0
u = 1.275470 + 0.448096I
a = 1.181370 − 0.075161I
b = 1.68724 − 0.11728I
−11.3203 − 9.1823I 0
u = 1.275470 − 0.448096I
a = 1.181370 + 0.075161I
b = 1.68724 + 0.11728I
−11.3203 + 9.1823I 0
u = 0.350726 + 1.320310I
a = 0.567274 − 1.075350I
b = 0.961762 + 0.116949I
−5.21579 + 1.27171I 0
u = 0.350726 − 1.320310I
a = 0.567274 + 1.075350I
b = 0.961762 − 0.116949I
−5.21579 − 1.27171I 0
u = 0.441729 + 1.300830I
a = −0.376778 − 0.676021I
b = −0.752920 + 0.405467I
−4.50061 + 0.79094I 0
u = 0.441729 − 1.300830I
a = −0.376778 + 0.676021I
b = −0.752920 − 0.405467I
−4.50061 − 0.79094I 0
u = 0.949179 + 0.994624I
a = 0.013031 − 0.198535I
b = −0.225303 + 0.901007I
−4.70725 − 7.00555I 0
u = 0.949179 − 0.994624I
a = 0.013031 + 0.198535I
b = −0.225303 − 0.901007I
−4.70725 + 7.00555I 0
u = 0.924357 + 1.038340I
a = −1.48280 + 0.68496I
b = −1.216760 − 0.294912I
−4.47375 − 4.32105I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.924357 − 1.038340I
a = −1.48280 − 0.68496I
b = −1.216760 + 0.294912I
−4.47375 + 4.32105I 0
u = 0.496521 + 0.344242I
a = 0.18871 + 2.28511I
b = −0.067962 + 0.610939I
−3.99208 − 6.87855I 0
u = 0.496521 − 0.344242I
a = 0.18871 − 2.28511I
b = −0.067962 − 0.610939I
−3.99208 + 6.87855I 0
u = 0.984378 + 0.990283I
a = 1.48490 − 0.76569I
b = 1.241480 + 0.577395I
−2.35966 − 8.78709I 0
u = 0.984378 − 0.990283I
a = 1.48490 + 0.76569I
b = 1.241480 − 0.577395I
−2.35966 + 8.78709I 0
u = 0.900819 + 1.089060I
a = −0.097203 − 0.311197I
b = 0.980159 − 0.955119I
−1.44934 − 2.63226I 0
u = 0.900819 − 1.089060I
a = −0.097203 + 0.311197I
b = 0.980159 + 0.955119I
−1.44934 + 2.63226I 0
u = −1.111000 + 0.874024I
a = −1.64601 − 0.18293I
b = −0.863367 + 0.173694I
0.593140 − 0.837431I 0
u = −1.111000 − 0.874024I
a = −1.64601 + 0.18293I
b = −0.863367 − 0.173694I
0.593140 + 0.837431I 0
u = 0.511783 + 0.276135I
a = −2.54957 + 0.54639I
b = −1.36817 − 0.43861I
−3.85751 − 3.99663I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.511783 − 0.276135I
a = −2.54957 − 0.54639I
b = −1.36817 + 0.43861I
−3.85751 + 3.99663I 0
u = −1.06473 + 0.94908I
a = 0.1021850 + 0.0108808I
b = −0.317108 − 1.293180I
−3.8676 + 15.0450I 0
u = −1.06473 − 0.94908I
a = 0.1021850 − 0.0108808I
b = −0.317108 + 1.293180I
−3.8676 − 15.0450I 0
u = 0.80407 + 1.18759I
a = −1.077920 + 0.296378I
b = −0.945234 + 0.268326I
−2.04693 + 1.79819I 0
u = 0.80407 − 1.18759I
a = −1.077920 − 0.296378I
b = −0.945234 − 0.268326I
−2.04693 − 1.79819I 0
u = 0.41092 + 1.37865I
a = 0.222568 − 0.079705I
b = 0.802679 + 0.173569I
−0.81179 − 8.99703I 0
u = 0.41092 − 1.37865I
a = 0.222568 + 0.079705I
b = 0.802679 − 0.173569I
−0.81179 + 8.99703I 0
u = 0.404967 + 0.373483I
a = 3.58722 − 1.28827I
b = 0.902761 − 0.075341I
−5.00701 − 2.05377I 0
u = 0.404967 − 0.373483I
a = 3.58722 + 1.28827I
b = 0.902761 + 0.075341I
−5.00701 + 2.05377I 0
u = −0.334439 + 0.419804I
a = 1.312330 + 0.022411I
b = 1.27683 + 0.65156I
−2.58242 + 5.66926I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.334439 − 0.419804I
a = 1.312330 − 0.022411I
b = 1.27683 − 0.65156I
−2.58242 − 5.66926I 0
u = −0.79821 + 1.23051I
a = −0.300446 − 0.001747I
b = −0.734406 − 0.513778I
2.44622 + 0.52569I 0
u = −0.79821 − 1.23051I
a = −0.300446 + 0.001747I
b = −0.734406 + 0.513778I
2.44622 − 0.52569I 0
u = −1.28744 + 0.75136I
a = 1.206900 + 0.017155I
b = 1.048350 + 0.384911I
−2.97406 − 7.34824I 0
u = −1.28744 − 0.75136I
a = 1.206900 − 0.017155I
b = 1.048350 − 0.384911I
−2.97406 + 7.34824I 0
u = −0.99750 + 1.11240I
a = −1.38383 − 0.78354I
b = −1.239090 + 0.550472I
−2.0207 + 15.1691I 0
u = −0.99750 − 1.11240I
a = −1.38383 + 0.78354I
b = −1.239090 − 0.550472I
−2.0207 − 15.1691I 0
u = 0.051599 + 0.495913I
a = −0.89820 + 3.02702I
b = 0.696414 − 0.416769I
1.81863 + 1.79255I 0
u = 0.051599 − 0.495913I
a = −0.89820 − 3.02702I
b = 0.696414 + 0.416769I
1.81863 − 1.79255I 0
u = −1.14035 + 0.98072I
a = 1.36170 + 0.41686I
b = 1.286390 − 0.300749I
−4.29860 + 9.17115I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.14035 − 0.98072I
a = 1.36170 − 0.41686I
b = 1.286390 + 0.300749I
−4.29860 − 9.17115I 0
u = −0.411961 + 0.254783I
a = 2.63464 + 3.04877I
b = 1.223210 − 0.485631I
−7.14058 − 2.43999I 0
u = −0.411961 − 0.254783I
a = 2.63464 − 3.04877I
b = 1.223210 + 0.485631I
−7.14058 + 2.43999I 0
u = 0.51517 + 1.43790I
a = −0.268703 − 0.374285I
b = −0.970630 + 0.490035I
−4.52126 + 0.82411I 0
u = 0.51517 − 1.43790I
a = −0.268703 + 0.374285I
b = −0.970630 − 0.490035I
−4.52126 − 0.82411I 0
u = 0.288411 + 0.364185I
a = 1.82013 − 0.27949I
b = 1.48449 + 0.49915I
−0.71442 − 5.80111I 0
u = 0.288411 − 0.364185I
a = 1.82013 + 0.27949I
b = 1.48449 − 0.49915I
−0.71442 + 5.80111I 0
u = 0.018399 + 0.451695I
a = 2.79357 + 3.49623I
b = 0.442975 + 0.370091I
−4.17268 − 6.81527I 0
u = 0.018399 − 0.451695I
a = 2.79357 − 3.49623I
b = 0.442975 − 0.370091I
−4.17268 + 6.81527I 0
u = 0.422986 + 0.064738I
a = −1.75812 + 3.47289I
b = 0.433240 − 0.092790I
1.53288 − 1.93683I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.422986 − 0.064738I
a = −1.75812 − 3.47289I
b = 0.433240 + 0.092790I
1.53288 + 1.93683I 0
u = 0.422642 + 0.017712I
a = −1.81175 + 0.65238I
b = −1.38410 − 0.44025I
−3.43796 − 0.85276I −20.5501 + 7.2770I
u = 0.422642 − 0.017712I
a = −1.81175 − 0.65238I
b = −1.38410 + 0.44025I
−3.43796 + 0.85276I −20.5501 − 7.2770I
u = −1.08328 + 1.14893I
a = 1.206760 + 0.707769I
b = 1.135250 − 0.600805I
1.43118 + 8.24052I 0
u = −1.08328 − 1.14893I
a = 1.206760 − 0.707769I
b = 1.135250 + 0.600805I
1.43118 − 8.24052I 0
u = −0.415206 + 0.027280I
a = 6.31775 − 4.01940I
b = −0.327891 + 0.087046I
−2.12749 − 8.52880I 6.89273 + 0.I
u = −0.415206 − 0.027280I
a = 6.31775 + 4.01940I
b = −0.327891 − 0.087046I
−2.12749 + 8.52880I 6.89273 + 0.I
u = 0.49424 + 1.51764I
a = −0.214632 + 0.065103I
b = −0.934609 + 0.149758I
0.47170 + 2.45044I 0
u = 0.49424 − 1.51764I
a = −0.214632 − 0.065103I
b = −0.934609 − 0.149758I
0.47170 − 2.45044I 0
u = 0.231275 + 0.317769I
a = 5.65283 − 1.31027I
b = 0.827298 + 0.191137I
0.87334 − 4.03318I −2.00000 + 7.97726I
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.231275 − 0.317769I
a = 5.65283 + 1.31027I
b = 0.827298 − 0.191137I
0.87334 + 4.03318I −2.00000 − 7.97726I
u = 0.376469 + 0.068668I
a = 2.65686 + 0.35677I
b = −0.544505 − 0.494974I
−4.67836 + 1.46115I −8.19948 + 0.I
u = 0.376469 − 0.068668I
a = 2.65686 − 0.35677I
b = −0.544505 + 0.494974I
−4.67836 − 1.46115I −8.19948 + 0.I
u = 1.35870 + 0.88608I
a = −0.282403 + 0.077544I
b = 0.13835 − 1.77117I
−0.76584 − 5.06931I 0
u = 1.35870 − 0.88608I
a = −0.282403 − 0.077544I
b = 0.13835 + 1.77117I
−0.76584 + 5.06931I 0
u = 0.334173 + 0.170801I
a = −1.63384 + 1.58675I
b = −0.987842 − 0.763040I
−1.07900 − 3.08318I −6.95602 + 6.86916I
u = 0.334173 − 0.170801I
a = −1.63384 − 1.58675I
b = −0.987842 + 0.763040I
−1.07900 + 3.08318I −6.95602 − 6.86916I
u = −1.19194 + 1.17231I
a = −1.096720 − 0.625218I
b = −1.107580 + 0.239050I
−3.86760 − 0.76443I 0
u = −1.19194 − 1.17231I
a = −1.096720 + 0.625218I
b = −1.107580 − 0.239050I
−3.86760 + 0.76443I 0
u = 1.28506 + 1.07395I
a = −1.38035 + 0.55966I
b = −0.930137 − 0.426988I
1.82933 − 4.43364I 0
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28506 − 1.07395I
a = −1.38035 − 0.55966I
b = −0.930137 + 0.426988I
1.82933 + 4.43364I 0
u = 0.322952 + 0.024184I
a = 0.217338 + 0.478307I
b = 0.70190 + 1.49734I
−3.23727 + 5.52143I −39.6829 − 3.6883I
u = 0.322952 − 0.024184I
a = 0.217338 − 0.478307I
b = 0.70190 − 1.49734I
−3.23727 − 5.52143I −39.6829 + 3.6883I
u = 1.17387 + 1.20470I
a = −1.178410 + 0.710886I
b = −1.33869 − 0.70367I
−7.1744 − 22.0288I 0
u = 1.17387 − 1.20470I
a = −1.178410 − 0.710886I
b = −1.33869 + 0.70367I
−7.1744 + 22.0288I 0
u = −1.16025 + 1.22971I
a = 1.094970 + 0.730357I
b = 1.45024 − 0.73662I
−4.95101 + 13.22520I 0
u = −1.16025 − 1.22971I
a = 1.094970 − 0.730357I
b = 1.45024 + 0.73662I
−4.95101 − 13.22520I 0
u = 0.268103 + 0.138296I
a = 0.739517 − 0.285375I
b = −0.565455 − 1.158540I
−2.86146 − 2.76530I −9.6410 + 15.7974I
u = 0.268103 − 0.138296I
a = 0.739517 + 0.285375I
b = −0.565455 + 1.158540I
−2.86146 + 2.76530I −9.6410 − 15.7974I
u = −0.63748 + 1.57746I
a = 0.227163 + 1.027840I
b = −0.372244 − 1.062920I
−2.71512 − 7.64573I 0
22
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.63748 − 1.57746I
a = 0.227163 − 1.027840I
b = −0.372244 + 1.062920I
−2.71512 + 7.64573I 0
u = 1.29365 + 1.12087I
a = 1.243560 − 0.527756I
b = 1.258520 + 0.545587I
−6.74339 − 11.85900I 0
u = 1.29365 − 1.12087I
a = 1.243560 + 0.527756I
b = 1.258520 − 0.545587I
−6.74339 + 11.85900I 0
u = −1.18403 + 1.24970I
a = −1.178540 − 0.704351I
b = −1.231320 + 0.571900I
−7.7687 + 12.4276I 0
u = −1.18403 − 1.24970I
a = −1.178540 + 0.704351I
b = −1.231320 − 0.571900I
−7.7687 − 12.4276I 0
u = −0.070030 + 0.166933I
a = −11.13840 − 6.88788I
b = −0.803848 + 0.272267I
0.72447 − 2.52624I 1.92830 − 3.31742I
u = −0.070030 − 0.166933I
a = −11.13840 + 6.88788I
b = −0.803848 − 0.272267I
0.72447 + 2.52624I 1.92830 + 3.31742I
u = −0.87127 + 1.61950I
a = 0.746586 + 0.709323I
b = 1.295760 − 0.316558I
−8.71492 + 8.17150I 0
u = −0.87127 − 1.61950I
a = 0.746586 − 0.709323I
b = 1.295760 + 0.316558I
−8.71492 − 8.17150I 0
u = 1.43139 + 1.25692I
a = 1.002340 − 0.497305I
b = 1.32751 + 0.61186I
−2.85815 − 12.36320I 0
23
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43139 − 1.25692I
a = 1.002340 + 0.497305I
b = 1.32751 − 0.61186I
−2.85815 + 12.36320I 0
u = 0.0055951 + 0.0382005I
a = −13.93980 − 0.71648I
b = −0.425463 + 1.149720I
−0.03206 + 2.08683I 1.60477 + 0.55920I
u = 0.0055951 − 0.0382005I
a = −13.93980 + 0.71648I
b = −0.425463 − 1.149720I
−0.03206 − 2.08683I 1.60477 − 0.55920I
u = −1.78555 + 0.81813I
a = 1.042670 − 0.063541I
b = 1.177710 + 0.269970I
−8.99733 − 2.59091I 0
u = −1.78555 − 0.81813I
a = 1.042670 + 0.063541I
b = 1.177710 − 0.269970I
−8.99733 + 2.59091I 0
u = −1.91420 + 0.85379I
a = −0.770193 − 0.033529I
b = −1.52640 − 0.54245I
−6.01707 − 3.44905I 0
u = −1.91420 − 0.85379I
a = −0.770193 + 0.033529I
b = −1.52640 + 0.54245I
−6.01707 + 3.44905I 0
u = 2.09803 + 0.44581I
a = −0.907819 + 0.149845I
b = −1.389030 − 0.143916I
−5.85857 + 0.95537I 0
u = 2.09803 − 0.44581I
a = −0.907819 − 0.149845I
b = −1.389030 + 0.143916I
−5.85857 − 0.95537I 0
u = 1.76826 + 1.30107I
a = 0.791422 − 0.037858I
b = 1.314220 − 0.435181I
−7.6241 + 12.3354I 0
24
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.76826 − 1.30107I
a = 0.791422 + 0.037858I
b = 1.314220 + 0.435181I
−7.6241 − 12.3354I 0
u = −1.36925 + 1.76897I
a = −0.738018 − 0.668899I
b = −1.23103 + 0.82894I
−5.12499 + 5.61769I 0
u = −1.36925 − 1.76897I
a = −0.738018 + 0.668899I
b = −1.23103 − 0.82894I
−5.12499 − 5.61769I 0
u = −0.38813 + 2.23115I
a = −0.765659 − 0.330416I
b = −0.954752 + 0.124007I
−4.58258 + 0.88159I 0
u = −0.38813 − 2.23115I
a = −0.765659 + 0.330416I
b = −0.954752 − 0.124007I
−4.58258 − 0.88159I 0
u = 1.23708 + 2.24326I
a = −0.562477 + 0.441210I
b = −1.55593 − 0.44300I
−6.85720 + 0.60791I 0
u = 1.23708 − 2.24326I
a = −0.562477 − 0.441210I
b = −1.55593 + 0.44300I
−6.85720 − 0.60791I 0
u = −2.83234 + 0.76328I
a = −1.226790 − 0.096261I
b = −0.847037 + 0.017028I
−4.61790 + 0.14975I 0
u = −2.83234 − 0.76328I
a = −1.226790 + 0.096261I
b = −0.847037 − 0.017028I
−4.61790 − 0.14975I 0
25
II. I
u
2
= h1.17 × 10
183
u
59
− 5.88 × 10
183
u
58
+ · · · + 1.06 × 10
184
b + 6.01 ×
10
183
, −1.29 × 10
183
u
59
+ 6.70 × 10
183
u
58
+ · · · + 1.06 × 10
184
a + 2.99 ×
10
184
, u
60
− 5u
59
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
11
=
0.121567u
59
− 0.630365u
58
+ ··· + 0.257863u − 2.80969
−0.110554u
59
+ 0.553273u
58
+ ··· − 5.12053u − 0.565417
a
12
=
0.232121u
59
− 1.18364u
58
+ ··· + 5.37839u − 2.24427
−0.110554u
59
+ 0.553273u
58
+ ··· − 5.12053u − 0.565417
a
7
=
−0.251982u
59
+ 1.26786u
58
+ ··· − 13.0230u − 0.946991
−0.115915u
59
+ 0.613594u
58
+ ··· − 8.33385u + 0.579084
a
4
=
0.0448519u
59
− 0.322238u
58
+ ··· + 3.23579u + 0.337461
0.0183401u
59
− 0.167218u
58
+ ··· + 4.77207u − 0.326633
a
6
=
−0.144689u
59
+ 0.691837u
58
+ ··· − 4.42124u − 1.53402
−0.115082u
59
+ 0.614514u
58
+ ··· − 8.52026u + 0.618642
a
2
=
−0.112394u
59
+ 0.552273u
58
+ ··· − 2.65457u + 0.598674
0.0632461u
59
− 0.351078u
58
+ ··· + 2.97049u + 0.173094
a
10
=
−0.146986u
59
+ 0.741280u
58
+ ··· − 0.913095u + 0.924393
−0.0939558u
59
+ 0.503192u
58
+ ··· − 3.03735u + 0.728603
a
1
=
0.212462u
59
− 0.938768u
58
+ ··· − 2.47338u − 1.69518
0.0834050u
59
− 0.373831u
58
+ ··· − 2.58527u − 0.617122
a
5
=
−0.000386417u
59
− 0.0446264u
58
+ ··· + 1.94209u + 0.962014
−0.100661u
59
+ 0.469098u
58
+ ··· + 0.0231930u − 0.125135
(ii) Obstruction class = 1
(iii) Cusp Shapes = −1.69323u
59
+ 8.90146u
58
+ ··· − 62.4836u + 2.34825
26
(iv) u-Polynomials at the component
27
Crossings u-Polynomials at each crossing
c
1
u
60
− 17u
59
+ ··· + 2u + 1
c
2
u
60
− u
59
+ ··· + 2u + 1
c
3
u
60
− 5u
59
+ ··· − 66u + 13
c
4
u
60
+ 4u
59
+ ··· − u + 1
c
5
u
60
+ 27u
58
+ ··· + 53u
2
+ 1
c
6
u
60
+ 5u
59
+ ··· + 3u + 1
c
7
u
60
− 3u
59
+ ··· + u + 1
c
8
u
60
− 5u
59
+ ··· − 2u + 1
c
9
u
60
− 5u
59
+ ··· − 7u + 1
c
10
u
60
− 14u
59
+ ··· − 2u + 1
c
11
u
60
+ 3u
59
+ ··· − u + 1
c
12
u
60
+ 27u
58
+ ··· + 53u
2
+ 1
28
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
60
+ 3y
59
+ ··· + 12y + 1
c
2
y
60
+ 25y
59
+ ··· + 30y + 1
c
3
y
60
+ 25y
59
+ ··· − 300y + 169
c
4
y
60
− 10y
59
+ ··· − 43y + 1
c
5
, c
12
y
60
+ 54y
59
+ ··· + 106y + 1
c
6
y
60
+ 11y
59
+ ··· + 35y + 1
c
7
, c
11
y
60
− 29y
59
+ ··· − 55y + 1
c
8
y
60
− 3y
59
+ ··· + 40y + 1
c
9
y
60
+ 27y
59
+ ··· + 67y + 1
c
10
y
60
− 16y
59
+ ··· − 16y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.731730 + 0.676367I
a = −2.12054 + 0.41836I
b = −1.244870 − 0.231631I
−6.70946 − 5.84589I 2.90093 + 9.28141I
u = 0.731730 − 0.676367I
a = −2.12054 − 0.41836I
b = −1.244870 + 0.231631I
−6.70946 + 5.84589I 2.90093 − 9.28141I
u = −0.383677 + 0.978825I
a = 0.900205 − 0.281177I
b = −0.726249 + 0.060266I
−4.14811 + 5.12809I −9.0993 + 13.6747I
u = −0.383677 − 0.978825I
a = 0.900205 + 0.281177I
b = −0.726249 − 0.060266I
−4.14811 − 5.12809I −9.0993 − 13.6747I
u = −0.470936 + 0.819275I
a = 0.395337 − 0.100565I
b = 0.205954 − 0.879960I
−0.08198 + 2.97739I −2.93488 − 6.71135I
u = −0.470936 − 0.819275I
a = 0.395337 + 0.100565I
b = 0.205954 + 0.879960I
−0.08198 − 2.97739I −2.93488 + 6.71135I
u = 0.751406 + 0.523993I
a = 1.308320 − 0.405169I
b = 1.191740 − 0.011686I
−2.98008 + 0.25858I −7.59712 − 3.27117I
u = 0.751406 − 0.523993I
a = 1.308320 + 0.405169I
b = 1.191740 + 0.011686I
−2.98008 − 0.25858I −7.59712 + 3.27117I
u = −1.097130 + 0.145531I
a = 0.982430 + 0.295728I
b = 1.39272 − 0.35306I
−7.52112 − 1.33982I 9.97881 + 2.88727I
u = −1.097130 − 0.145531I
a = 0.982430 − 0.295728I
b = 1.39272 + 0.35306I
−7.52112 + 1.33982I 9.97881 − 2.88727I
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.761335 + 0.424930I
a = 1.46387 − 0.51262I
b = 1.35828 + 0.69710I
−4.39791 − 4.66369I −4.03422 + 1.62939I
u = 0.761335 − 0.424930I
a = 1.46387 + 0.51262I
b = 1.35828 − 0.69710I
−4.39791 + 4.66369I −4.03422 − 1.62939I
u = −0.548313 + 0.673892I
a = 0.08852 + 1.74358I
b = 0.612735 − 0.225113I
1.46546 + 2.73490I 2.08992 − 6.61589I
u = −0.548313 − 0.673892I
a = 0.08852 − 1.74358I
b = 0.612735 + 0.225113I
1.46546 − 2.73490I 2.08992 + 6.61589I
u = 0.481780 + 0.676787I
a = −0.054262 − 0.984085I
b = 0.919570 + 0.653607I
−5.14682 − 6.75162I −3.35141 + 13.09581I
u = 0.481780 − 0.676787I
a = −0.054262 + 0.984085I
b = 0.919570 − 0.653607I
−5.14682 + 6.75162I −3.35141 − 13.09581I
u = −0.194909 + 0.776979I
a = 0.381386 − 0.024748I
b = 0.635089 − 0.818653I
0.00958 + 3.02884I 0.71094 − 5.19051I
u = −0.194909 − 0.776979I
a = 0.381386 + 0.024748I
b = 0.635089 + 0.818653I
0.00958 − 3.02884I 0.71094 + 5.19051I
u = 0.790700 + 0.923889I
a = 1.22043 − 0.93308I
b = 1.200080 + 0.597664I
−4.74631 − 4.87413I 0
u = 0.790700 − 0.923889I
a = 1.22043 + 0.93308I
b = 1.200080 − 0.597664I
−4.74631 + 4.87413I 0
32
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.439423 + 0.638563I
a = 0.45197 − 2.19123I
b = −0.782616 − 0.261764I
0.65593 + 3.19145I 1.52659 − 8.49110I
u = −0.439423 − 0.638563I
a = 0.45197 + 2.19123I
b = −0.782616 + 0.261764I
0.65593 − 3.19145I 1.52659 + 8.49110I
u = −0.726330 + 0.253130I
a = −1.40984 − 1.34821I
b = −1.250360 − 0.457362I
−6.47871 − 11.14530I −5.10342 + 8.31313I
u = −0.726330 − 0.253130I
a = −1.40984 + 1.34821I
b = −1.250360 + 0.457362I
−6.47871 + 11.14530I −5.10342 − 8.31313I
u = −0.039775 + 0.765074I
a = −1.78815 − 0.57716I
b = 0.610936 − 0.151606I
1.59348 + 3.45910I 4.47704 − 4.53722I
u = −0.039775 − 0.765074I
a = −1.78815 + 0.57716I
b = 0.610936 + 0.151606I
1.59348 − 3.45910I 4.47704 + 4.53722I
u = 0.549064 + 1.131790I
a = 0.705466 − 0.330527I
b = 0.393731 − 0.153498I
1.61636 + 1.86430I 0
u = 0.549064 − 1.131790I
a = 0.705466 + 0.330527I
b = 0.393731 + 0.153498I
1.61636 − 1.86430I 0
u = −0.590797 + 1.117570I
a = 0.392837 − 0.334861I
b = −0.953319 − 0.689017I
0.71738 + 2.72811I 0
u = −0.590797 − 1.117570I
a = 0.392837 + 0.334861I
b = −0.953319 + 0.689017I
0.71738 − 2.72811I 0
33
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.556616 + 0.440634I
a = −0.827246 + 0.645841I
b = 0.166278 − 0.836782I
1.99883 + 3.87427I 2.63144 − 3.57408I
u = −0.556616 − 0.440634I
a = −0.827246 − 0.645841I
b = 0.166278 + 0.836782I
1.99883 − 3.87427I 2.63144 + 3.57408I
u = 0.998819 + 0.818430I
a = −1.64252 + 0.69495I
b = −0.984772 − 0.611016I
0.22883 − 7.41071I 0
u = 0.998819 − 0.818430I
a = −1.64252 − 0.69495I
b = −0.984772 + 0.611016I
0.22883 + 7.41071I 0
u = −1.281230 + 0.173153I
a = −1.99530 + 0.09834I
b = −0.734861 + 0.253842I
−6.18680 − 0.46889I 0
u = −1.281230 − 0.173153I
a = −1.99530 − 0.09834I
b = −0.734861 − 0.253842I
−6.18680 + 0.46889I 0
u = 1.258120 + 0.363818I
a = −1.126510 + 0.519407I
b = −1.058990 + 0.339218I
−7.49858 + 3.04558I 0
u = 1.258120 − 0.363818I
a = −1.126510 − 0.519407I
b = −1.058990 − 0.339218I
−7.49858 − 3.04558I 0
u = 0.541767 + 1.254590I
a = −0.464971 − 0.145269I
b = −0.370991 − 0.004408I
−0.24058 − 8.51869I 0
u = 0.541767 − 1.254590I
a = −0.464971 + 0.145269I
b = −0.370991 + 0.004408I
−0.24058 + 8.51869I 0
34
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.610541 + 0.151672I
a = −3.77174 + 4.14355I
b = −0.495954 − 0.051383I
−2.33487 − 8.68372I −17.7954 + 16.8659I
u = 0.610541 − 0.151672I
a = −3.77174 − 4.14355I
b = −0.495954 + 0.051383I
−2.33487 + 8.68372I −17.7954 − 16.8659I
u = −0.583074 + 0.142721I
a = 0.779221 − 0.372707I
b = 0.819548 + 0.972596I
−3.00333 − 2.34035I −15.0591 − 0.0627I
u = −0.583074 − 0.142721I
a = 0.779221 + 0.372707I
b = 0.819548 − 0.972596I
−3.00333 + 2.34035I −15.0591 + 0.0627I
u = −0.241335 + 1.383220I
a = 0.29093 + 1.53604I
b = 0.623018 − 0.886555I
−2.98567 + 7.14494I 0
u = −0.241335 − 1.383220I
a = 0.29093 − 1.53604I
b = 0.623018 + 0.886555I
−2.98567 − 7.14494I 0
u = 1.33349 + 0.78917I
a = 0.265036 − 0.146740I
b = −0.01191 + 1.63539I
−0.98366 − 5.04416I 0
u = 1.33349 − 0.78917I
a = 0.265036 + 0.146740I
b = −0.01191 − 1.63539I
−0.98366 + 5.04416I 0
u = 0.59649 + 1.50222I
a = 0.755747 − 0.865035I
b = 1.005560 + 0.290416I
−4.48368 + 0.27359I 0
u = 0.59649 − 1.50222I
a = 0.755747 + 0.865035I
b = 1.005560 − 0.290416I
−4.48368 − 0.27359I 0
35
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.257263 + 0.184039I
a = −3.43725 − 0.18490I
b = −1.236960 − 0.436653I
−0.80077 − 5.45644I −4.67556 + 2.83152I
u = 0.257263 − 0.184039I
a = −3.43725 + 0.18490I
b = −1.236960 + 0.436653I
−0.80077 + 5.45644I −4.67556 − 2.83152I
u = −1.23666 + 1.20361I
a = −1.148980 − 0.600727I
b = −1.33219 + 0.55807I
−5.45783 + 11.79900I 0
u = −1.23666 − 1.20361I
a = −1.148980 + 0.600727I
b = −1.33219 − 0.55807I
−5.45783 − 11.79900I 0
u = −0.014539 + 0.196356I
a = −2.57273 + 0.15207I
b = −0.787454 − 1.134290I
−3.06006 + 5.59875I −1.4848 − 15.3280I
u = −0.014539 − 0.196356I
a = −2.57273 − 0.15207I
b = −0.787454 + 1.134290I
−3.06006 − 5.59875I −1.4848 + 15.3280I
u = −1.56827 + 1.37903I
a = 0.827096 + 0.479442I
b = 1.43230 − 0.35095I
−6.57515 − 0.89106I 0
u = −1.56827 − 1.37903I
a = 0.827096 − 0.479442I
b = 1.43230 + 0.35095I
−6.57515 + 0.89106I 0
u = 2.81051 + 2.15096I
a = 1.151240 − 0.153666I
b = 0.903960 + 0.064250I
−4.71109 − 0.17990I 0
u = 2.81051 − 2.15096I
a = 1.151240 + 0.153666I
b = 0.903960 − 0.064250I
−4.71109 + 0.17990I 0
36
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
60
− 17u
59
+ ··· + 2u + 1)(u
209
+ 16u
208
+ ··· − 229u + 7)
c
2
(u
60
− u
59
+ ··· + 2u + 1)(u
209
+ 20u
207
+ ··· + 1001187u + 56817)
c
3
(u
60
− 5u
59
+ ··· − 66u + 13)
· (u
209
+ 8u
208
+ ··· + 10140313539u − 1878370717)
c
4
(u
60
+ 4u
59
+ ··· − u + 1)(u
209
− 5u
208
+ ··· + 4624338u − 184123)
c
5
(u
60
+ 27u
58
+ ··· + 53u
2
+ 1)
· (u
209
+ u
208
+ ··· + 4331046357u + 113222443)
c
6
(u
60
+ 5u
59
+ ··· + 3u + 1)(u
209
+ 16u
208
+ ··· + 12u + 1)
c
7
(u
60
− 3u
59
+ ··· + u + 1)(u
209
+ 4u
208
+ ··· + 2657560u + 2311849)
c
8
(u
60
− 5u
59
+ ··· − 2u + 1)(u
209
+ 4u
208
+ ··· − 29u + 1)
c
9
(u
60
− 5u
59
+ ··· − 7u + 1)
· (u
209
+ 45u
207
+ ··· + 739402858830u + 26116631329)
c
10
(u
60
− 14u
59
+ ··· − 2u + 1)(u
209
− 7u
208
+ ··· − 17609u + 341)
c
11
(u
60
+ 3u
59
+ ··· − u + 1)(u
209
+ 4u
208
+ ··· + 2657560u + 2311849)
c
12
(u
60
+ 27u
58
+ ··· + 53u
2
+ 1)
· (u
209
+ u
208
+ ··· + 4331046357u + 113222443)
37
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
60
+ 3y
59
+ ··· + 12y + 1)(y
209
− 2y
208
+ ··· − 6625y −49)
c
2
(y
60
+ 25y
59
+ ··· + 30y + 1)
· (y
209
+ 40y
208
+ ··· − 266988642255y −3228171489)
c
3
(y
60
+ 25y
59
+ ··· − 300y + 169)
· (y
209
− 8y
208
+ ··· + 2.14 × 10
20
y −3.53 × 10
18
)
c
4
(y
60
− 10y
59
+ ··· − 43y + 1)
· (y
209
− 47y
208
+ ··· + 8724659978546y −33901279129)
c
5
, c
12
(y
60
+ 54y
59
+ ··· + 106y + 1)
· (y
209
+ 165y
208
+ ··· + 833990559064792201y −12819321598888249)
c
6
(y
60
+ 11y
59
+ ··· + 35y + 1)(y
209
+ 30y
208
+ ··· − 56y −1)
c
7
, c
11
(y
60
− 29y
59
+ ··· − 55y + 1)
· (y
209
− 118y
208
+ ··· + 340566951866202y −5344645798801)
c
8
(y
60
− 3y
59
+ ··· + 40y + 1)(y
209
− 8y
208
+ ··· − 1269y −1)
c
9
(y
60
+ 27y
59
+ ··· + 67y + 1)
· (y
209
+ 90y
208
+ ··· − 4.99 × 10
22
y −6.82 × 10
20
)
c
10
(y
60
− 16y
59
+ ··· − 16y + 1)
· (y
209
− 37y
208
+ ··· + 35347503y −116281)
38
