12a
0709
(K12a
0709
)
A knot diagram
1
Linearized knot diagam
3 8 6 12 9 1 11 2 4 7 5 10
Solving Sequence
3,8
2 9
1,11
7 6 4 5 10 12
c
2
c
8
c
1
c
7
c
6
c
3
c
5
c
10
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.12238 × 10
643
u
173
− 1.44902 × 10
644
u
172
+ ··· + 5.70533 × 10
643
b + 4.68445 × 10
646
,
− 4.22603 × 10
644
u
173
− 1.65272 × 10
645
u
172
+ ··· + 2.45329 × 10
645
a + 8.91828 × 10
647
,
u
174
+ 4u
173
+ ··· + 860u − 1849i
I
u
2
= h−5.49547 × 10
30
u
44
+ 1.24545 × 10
32
u
43
+ ··· + 1.16778 × 10
31
b − 1.49742 × 10
32
,
8.02764 × 10
31
u
44
− 2.04849 × 10
32
u
43
+ ··· + 1.16778 × 10
31
a − 7.33963 × 10
31
, u
45
− 3u
44
+ ··· + 5u − 1i
* 2 irreducible components of dim
C
= 0, with total 219 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−4.12 × 10
643
u
173
− 1.45 × 10
644
u
172
+ · · · + 5.71 × 10
643
b + 4.68 ×
10
646
, −4.23 × 10
644
u
173
− 1.65 × 10
645
u
172
+ · · · + 2.45 × 10
645
a + 8.92 ×
10
647
, u
174
+ 4u
173
+ · · · + 860u − 1849i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
9
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
0.172259u
173
+ 0.673674u
172
+ ··· + 253.690u − 363.523
0.722548u
173
+ 2.53976u
172
+ ··· − 53.2667u − 821.065
a
7
=
0.422411u
173
+ 1.39381u
172
+ ··· − 302.931u − 346.299
0.615721u
173
+ 2.61270u
172
+ ··· + 1393.76u − 1631.60
a
6
=
−0.0184136u
173
+ 0.0945368u
172
+ ··· + 652.785u − 378.198
0.202712u
173
+ 1.00516u
172
+ ··· + 981.542u − 855.900
a
4
=
0.193671u
173
+ 0.530332u
172
+ ··· − 488.877u − 18.5190
0.111537u
173
+ 0.537748u
172
+ ··· + 289.103u − 383.316
a
5
=
0.307311u
173
+ 1.07846u
172
+ ··· − 26.6558u − 386.220
0.566995u
173
+ 2.38261u
172
+ ··· + 1178.68u − 1453.70
a
10
=
−0.204957u
173
− 0.619119u
172
+ ··· + 448.630u − 11.9952
0.00105037u
173
+ 0.0260070u
172
+ ··· + 66.3987u − 59.8984
a
12
=
0.0524607u
173
+ 0.336201u
172
+ ··· + 567.209u − 430.018
0.303407u
173
+ 1.43438u
172
+ ··· + 1226.11u − 1130.46
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.188361u
173
− 1.56403u
172
+ ··· − 2713.89u + 2013.65
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
174
+ 78u
173
+ ··· + 38633006u + 3418801
c
2
, c
8
u
174
+ 4u
173
+ ··· + 860u − 1849
c
3
81(81u
174
− 2520u
173
+ ··· + 1289568u − 74248)
c
4
, c
11
9(9u
174
+ 30u
173
+ ··· + 188726u − 372821)
c
5
u
174
− 5u
173
+ ··· + 9544707u + 120123
c
6
u
174
+ 2u
173
+ ··· + 4585039248u − 391773717
c
7
, c
10
9(9u
174
+ 12u
173
+ ··· − 2.70063 × 10
7
u − 1.08127 × 10
7
)
c
9
u
174
+ u
173
+ ··· − 62865261u + 31013523
c
12
u
174
+ 13u
173
+ ··· + 3315627075u + 351801391
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
174
+ 50y
173
+ ··· − 1038422793520482y + 11688200277601
c
2
, c
8
y
174
+ 78y
173
+ ··· + 38633006y + 3418801
c
3
6561
· (6561y
174
− 457002y
173
+ ··· + 161502458592y + 5512765504)
c
4
, c
11
81(81y
174
+ 10620y
173
+ ··· + 5.06180 × 10
12
y + 1.38995 × 10
11
)
c
5
y
174
− 21y
173
+ ··· + 1241320767183y + 14429535129
c
6
y
174
+ 52y
173
+ ··· + 2.28 × 10
19
y + 1.53 × 10
17
c
7
, c
10
81
· (81y
174
− 8172y
173
+ ··· + 749524157872730y + 116915411184049)
c
9
y
174
− 25y
173
+ ··· − 29120310824125347y + 961838608871529
c
12
y
174
− 57y
173
+ ··· − 3.54 × 10
18
y + 1.24 × 10
17
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.788449 + 0.612244I
a = 1.01781 + 1.02674I
b = 2.04982 − 0.76639I
10.83900 + 1.99487I 0
u = −0.788449 − 0.612244I
a = 1.01781 − 1.02674I
b = 2.04982 + 0.76639I
10.83900 − 1.99487I 0
u = 0.416392 + 0.912492I
a = −0.709660 + 0.446722I
b = −1.43573 + 0.63145I
−0.96633 + 2.24854I 0
u = 0.416392 − 0.912492I
a = −0.709660 − 0.446722I
b = −1.43573 − 0.63145I
−0.96633 − 2.24854I 0
u = 0.879645 + 0.469234I
a = −0.969777 + 1.013240I
b = −1.66320 − 0.81580I
5.45213 − 8.38927I 0
u = 0.879645 − 0.469234I
a = −0.969777 − 1.013240I
b = −1.66320 + 0.81580I
5.45213 + 8.38927I 0
u = −0.830633 + 0.547297I
a = 1.128490 + 0.494286I
b = 1.75016 − 0.96820I
5.98006 − 4.36530I 0
u = −0.830633 − 0.547297I
a = 1.128490 − 0.494286I
b = 1.75016 + 0.96820I
5.98006 + 4.36530I 0
u = −0.205645 + 0.985061I
a = −0.192720 + 1.021700I
b = −1.37963 + 0.31976I
−0.464505 + 1.123620I 0
u = −0.205645 − 0.985061I
a = −0.192720 − 1.021700I
b = −1.37963 − 0.31976I
−0.464505 − 1.123620I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509642 + 0.868302I
a = −2.52058 − 1.09872I
b = −0.57422 − 2.65776I
1.66281 + 2.05945I 0
u = 0.509642 − 0.868302I
a = −2.52058 + 1.09872I
b = −0.57422 + 2.65776I
1.66281 − 2.05945I 0
u = 0.847140 + 0.550886I
a = −0.715555 − 1.063980I
b = −0.156423 − 0.621752I
5.23383 − 8.16565I 0
u = 0.847140 − 0.550886I
a = −0.715555 + 1.063980I
b = −0.156423 + 0.621752I
5.23383 + 8.16565I 0
u = −0.857862 + 0.488258I
a = −0.793497 − 1.022840I
b = −1.41627 + 0.86799I
4.48914 + 3.16789I 0
u = −0.857862 − 0.488258I
a = −0.793497 + 1.022840I
b = −1.41627 − 0.86799I
4.48914 − 3.16789I 0
u = −0.553950 + 0.811931I
a = 1.036070 + 0.516539I
b = 2.70747 − 0.97654I
4.71428 − 4.00424I 0
u = −0.553950 − 0.811931I
a = 1.036070 − 0.516539I
b = 2.70747 + 0.97654I
4.71428 + 4.00424I 0
u = 0.444757 + 0.876054I
a = 0.055749 − 1.041920I
b = −0.624114 + 0.797198I
−0.91368 + 1.26387I 0
u = 0.444757 − 0.876054I
a = 0.055749 + 1.041920I
b = −0.624114 − 0.797198I
−0.91368 − 1.26387I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.582917 + 0.786807I
a = 0.664644 − 0.051473I
b = 0.695866 + 0.908138I
2.79384 + 2.54567I 0
u = −0.582917 − 0.786807I
a = 0.664644 + 0.051473I
b = 0.695866 − 0.908138I
2.79384 − 2.54567I 0
u = 0.856148 + 0.442793I
a = 0.740460 + 0.113118I
b = 0.769940 + 0.388323I
3.66763 − 1.64101I 0
u = 0.856148 − 0.442793I
a = 0.740460 − 0.113118I
b = 0.769940 − 0.388323I
3.66763 + 1.64101I 0
u = 0.519628 + 0.898339I
a = 0.658729 − 0.895442I
b = 2.42535 + 1.86755I
−0.42494 + 3.13721I 0
u = 0.519628 − 0.898339I
a = 0.658729 + 0.895442I
b = 2.42535 − 1.86755I
−0.42494 − 3.13721I 0
u = 0.502439 + 0.820329I
a = −0.656678 + 0.899785I
b = −2.77196 − 0.97511I
−0.150778 + 1.016630I 0
u = 0.502439 − 0.820329I
a = −0.656678 − 0.899785I
b = −2.77196 + 0.97511I
−0.150778 − 1.016630I 0
u = −0.530533 + 0.801440I
a = −0.373337 + 0.942920I
b = −0.344420 + 1.232770I
4.56110 + 0.83538I 0
u = −0.530533 − 0.801440I
a = −0.373337 − 0.942920I
b = −0.344420 − 1.232770I
4.56110 − 0.83538I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.907540 + 0.309398I
a = −1.199770 + 0.493946I
b = −1.26792 − 0.85092I
8.98527 − 1.41087I 0
u = 0.907540 − 0.309398I
a = −1.199770 − 0.493946I
b = −1.26792 + 0.85092I
8.98527 + 1.41087I 0
u = 0.609436 + 0.738669I
a = 0.37175 − 1.45775I
b = 1.32690 + 0.89870I
7.20384 − 0.46140I 0
u = 0.609436 − 0.738669I
a = 0.37175 + 1.45775I
b = 1.32690 − 0.89870I
7.20384 + 0.46140I 0
u = −0.296938 + 1.003170I
a = 0.565307 − 0.171457I
b = 0.140666 − 1.099500I
−4.39226 − 0.92413I 0
u = −0.296938 − 1.003170I
a = 0.565307 + 0.171457I
b = 0.140666 + 1.099500I
−4.39226 + 0.92413I 0
u = −0.120585 + 0.942140I
a = 0.799507 + 0.275853I
b = 0.69259 − 1.47538I
−4.23234 − 0.72890I 0
u = −0.120585 − 0.942140I
a = 0.799507 − 0.275853I
b = 0.69259 + 1.47538I
−4.23234 + 0.72890I 0
u = −0.210708 + 0.925205I
a = 0.39737 − 1.36081I
b = −0.083189 − 0.618925I
3.48985 + 5.80165I 0
u = −0.210708 − 0.925205I
a = 0.39737 + 1.36081I
b = −0.083189 + 0.618925I
3.48985 − 5.80165I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570101 + 0.884212I
a = 0.015682 − 0.719462I
b = 1.28793 + 0.62148I
2.51288 − 7.14488I 0
u = −0.570101 − 0.884212I
a = 0.015682 + 0.719462I
b = 1.28793 − 0.62148I
2.51288 + 7.14488I 0
u = 0.575061 + 0.886207I
a = 0.430024 + 0.773580I
b = 0.255620 + 0.322750I
0.49719 + 2.39840I 0
u = 0.575061 − 0.886207I
a = 0.430024 − 0.773580I
b = 0.255620 − 0.322750I
0.49719 − 2.39840I 0
u = −0.921707 + 0.196650I
a = −1.016840 − 0.345457I
b = −0.955062 + 0.093842I
3.16769 + 2.04593I 0
u = −0.921707 − 0.196650I
a = −1.016840 + 0.345457I
b = −0.955062 − 0.093842I
3.16769 − 2.04593I 0
u = 0.310030 + 0.888107I
a = 0.208411 + 1.186460I
b = 0.24090 + 1.43456I
4.71271 − 0.49839I 0
u = 0.310030 − 0.888107I
a = 0.208411 − 1.186460I
b = 0.24090 − 1.43456I
4.71271 + 0.49839I 0
u = −0.574024 + 0.902802I
a = −0.801230 + 0.227269I
b = −0.029174 + 0.674347I
4.18267 − 5.28131I 0
u = −0.574024 − 0.902802I
a = −0.801230 − 0.227269I
b = −0.029174 − 0.674347I
4.18267 + 5.28131I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.451909 + 0.804149I
a = −0.439945 − 0.865803I
b = −2.43686 + 2.82591I
1.61089 + 3.44055I 0
u = −0.451909 − 0.804149I
a = −0.439945 + 0.865803I
b = −2.43686 − 2.82591I
1.61089 − 3.44055I 0
u = −0.896887 + 0.195389I
a = −0.994969 + 0.922661I
b = −0.473587 − 0.233835I
3.82562 − 4.47952I 0
u = −0.896887 − 0.195389I
a = −0.994969 − 0.922661I
b = −0.473587 + 0.233835I
3.82562 + 4.47952I 0
u = −0.613954 + 0.893993I
a = −0.307752 − 1.008490I
b = −1.56842 + 1.03840I
4.39810 − 0.61912I 0
u = −0.613954 − 0.893993I
a = −0.307752 + 1.008490I
b = −1.56842 − 1.03840I
4.39810 + 0.61912I 0
u = −0.502718 + 0.961665I
a = 0.646850 + 0.625919I
b = 3.47641 − 0.87747I
1.00657 − 7.31352I 0
u = −0.502718 − 0.961665I
a = 0.646850 − 0.625919I
b = 3.47641 + 0.87747I
1.00657 + 7.31352I 0
u = 0.950587 + 0.523389I
a = 0.901621 − 0.492910I
b = 1.79889 + 0.70489I
3.91175 − 1.20767I 0
u = 0.950587 − 0.523389I
a = 0.901621 + 0.492910I
b = 1.79889 − 0.70489I
3.91175 + 1.20767I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.975202 + 0.476395I
a = 0.932416 + 1.058510I
b = 1.55870 − 0.62570I
9.6819 + 14.6759I 0
u = −0.975202 − 0.476395I
a = 0.932416 − 1.058510I
b = 1.55870 + 0.62570I
9.6819 − 14.6759I 0
u = 0.779983 + 0.764641I
a = 0.584538 − 1.019180I
b = 2.14257 + 0.77812I
9.16649 − 3.94263I 0
u = 0.779983 − 0.764641I
a = 0.584538 + 1.019180I
b = 2.14257 − 0.77812I
9.16649 + 3.94263I 0
u = −0.144961 + 1.101830I
a = −0.658501 − 0.071678I
b = −1.054210 + 0.368660I
−3.69034 + 1.64460I 0
u = −0.144961 − 1.101830I
a = −0.658501 + 0.071678I
b = −1.054210 − 0.368660I
−3.69034 − 1.64460I 0
u = 0.594361 + 0.944090I
a = −1.131300 + 0.591256I
b = −2.76769 − 0.55383I
6.55577 + 5.22032I 0
u = 0.594361 − 0.944090I
a = −1.131300 − 0.591256I
b = −2.76769 + 0.55383I
6.55577 − 5.22032I 0
u = 0.321822 + 1.068880I
a = 0.226669 − 0.933314I
b = 0.18146 − 1.76395I
2.46802 − 3.60078I 0
u = 0.321822 − 1.068880I
a = 0.226669 + 0.933314I
b = 0.18146 + 1.76395I
2.46802 + 3.60078I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.591500 + 0.651600I
a = 0.71368 + 1.72135I
b = 1.75926 − 0.46653I
6.85976 + 6.40056I 0
u = −0.591500 − 0.651600I
a = 0.71368 − 1.72135I
b = 1.75926 + 0.46653I
6.85976 − 6.40056I 0
u = −0.013497 + 1.122500I
a = 0.730961 − 0.147448I
b = 1.44512 + 0.85124I
−0.91118 − 6.76727I 0
u = −0.013497 − 1.122500I
a = 0.730961 + 0.147448I
b = 1.44512 − 0.85124I
−0.91118 + 6.76727I 0
u = −0.428520 + 1.044480I
a = −0.382204 − 0.699174I
b = −0.71749 − 2.17704I
−2.04035 − 3.33168I 0
u = −0.428520 − 1.044480I
a = −0.382204 + 0.699174I
b = −0.71749 + 2.17704I
−2.04035 + 3.33168I 0
u = 0.133638 + 1.122340I
a = −0.706346 + 0.409998I
b = −1.36776 − 0.59980I
−3.24033 + 3.92881I 0
u = 0.133638 − 1.122340I
a = −0.706346 − 0.409998I
b = −1.36776 + 0.59980I
−3.24033 − 3.92881I 0
u = −0.755610 + 0.418520I
a = −0.761460 − 0.961494I
b = −0.876987 + 0.463630I
3.72376 + 2.25698I 0
u = −0.755610 − 0.418520I
a = −0.761460 + 0.961494I
b = −0.876987 − 0.463630I
3.72376 − 2.25698I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.397925 + 0.758164I
a = 1.177970 + 0.654686I
b = 0.383299 + 0.715396I
1.13275 + 2.12141I 0
u = 0.397925 − 0.758164I
a = 1.177970 − 0.654686I
b = 0.383299 − 0.715396I
1.13275 − 2.12141I 0
u = −0.850217 + 0.765655I
a = −1.32988 − 0.68895I
b = −2.03213 + 0.62242I
10.80740 + 1.27452I 0
u = −0.850217 − 0.765655I
a = −1.32988 + 0.68895I
b = −2.03213 − 0.62242I
10.80740 − 1.27452I 0
u = −0.592114 + 0.981639I
a = −1.22265 − 0.80862I
b = −2.60126 + 0.93774I
5.85271 − 11.13600I 0
u = −0.592114 − 0.981639I
a = −1.22265 + 0.80862I
b = −2.60126 − 0.93774I
5.85271 + 11.13600I 0
u = −0.525066 + 1.022420I
a = −0.708241 + 0.034716I
b = −0.776199 + 0.013317I
−2.91050 − 5.36294I 0
u = −0.525066 − 1.022420I
a = −0.708241 − 0.034716I
b = −0.776199 − 0.013317I
−2.91050 + 5.36294I 0
u = 0.666681 + 0.527148I
a = 0.696683 + 0.479398I
b = 0.005850 + 0.189052I
1.75089 + 1.44266I 0
u = 0.666681 − 0.527148I
a = 0.696683 − 0.479398I
b = 0.005850 − 0.189052I
1.75089 − 1.44266I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.736885 + 0.420620I
a = 0.420931 − 0.886731I
b = −0.106217 − 0.358832I
1.13423 + 3.72015I 0
u = −0.736885 − 0.420620I
a = 0.420931 + 0.886731I
b = −0.106217 + 0.358832I
1.13423 − 3.72015I 0
u = 0.516331 + 1.039110I
a = 0.641289 − 0.653561I
b = 1.84017 − 1.48225I
3.66935 + 10.30690I 0
u = 0.516331 − 1.039110I
a = 0.641289 + 0.653561I
b = 1.84017 + 1.48225I
3.66935 − 10.30690I 0
u = −1.000990 + 0.603899I
a = −0.601010 − 0.668841I
b = −1.67708 + 0.85608I
4.81828 + 4.72800I 0
u = −1.000990 − 0.603899I
a = −0.601010 + 0.668841I
b = −1.67708 − 0.85608I
4.81828 − 4.72800I 0
u = 0.696877 + 0.948342I
a = −0.920906 + 0.662677I
b = −2.60161 − 1.41450I
8.57887 + 9.52339I 0
u = 0.696877 − 0.948342I
a = −0.920906 − 0.662677I
b = −2.60161 + 1.41450I
8.57887 − 9.52339I 0
u = −0.618056 + 0.540937I
a = −0.064462 + 0.196398I
b = 0.459494 + 0.978463I
5.11024 + 1.07610I 0
u = −0.618056 − 0.540937I
a = −0.064462 − 0.196398I
b = 0.459494 − 0.978463I
5.11024 − 1.07610I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.553879 + 1.045560I
a = 0.348358 + 0.593036I
b = 0.382471 + 0.881411I
0.20800 + 3.32564I 0
u = 0.553879 − 1.045560I
a = 0.348358 − 0.593036I
b = 0.382471 − 0.881411I
0.20800 − 3.32564I 0
u = −0.517823 + 1.075050I
a = −0.136147 − 0.338123I
b = 0.553162 + 0.638887I
3.47537 − 5.55026I 0
u = −0.517823 − 1.075050I
a = −0.136147 + 0.338123I
b = 0.553162 − 0.638887I
3.47537 + 5.55026I 0
u = 1.094820 + 0.490508I
a = 1.02968 − 0.98754I
b = 1.47764 + 0.39277I
7.20004 − 4.96464I 0
u = 1.094820 − 0.490508I
a = 1.02968 + 0.98754I
b = 1.47764 − 0.39277I
7.20004 + 4.96464I 0
u = −0.583287 + 1.059650I
a = 0.744253 + 0.476700I
b = 2.17689 − 0.19697I
1.87572 − 7.24751I 0
u = −0.583287 − 1.059650I
a = 0.744253 − 0.476700I
b = 2.17689 + 0.19697I
1.87572 + 7.24751I 0
u = −0.747423 + 0.952057I
a = 0.68870 + 1.24621I
b = 1.83589 − 0.27612I
10.20790 − 7.19940I 0
u = −0.747423 − 0.952057I
a = 0.68870 − 1.24621I
b = 1.83589 + 0.27612I
10.20790 + 7.19940I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.053577 + 1.211040I
a = −0.466601 + 0.687550I
b = −0.816297 + 0.034218I
−2.23129 + 0.70905I 0
u = 0.053577 − 1.211040I
a = −0.466601 − 0.687550I
b = −0.816297 − 0.034218I
−2.23129 − 0.70905I 0
u = 1.027180 + 0.644653I
a = −1.140880 + 0.413605I
b = −1.78484 − 0.63991I
10.57080 + 8.80357I 0
u = 1.027180 − 0.644653I
a = −1.140880 − 0.413605I
b = −1.78484 + 0.63991I
10.57080 − 8.80357I 0
u = 0.311904 + 1.178150I
a = 0.289554 − 0.815097I
b = −0.0451810 − 0.0670340I
4.14078 + 2.11359I 0
u = 0.311904 − 1.178150I
a = 0.289554 + 0.815097I
b = −0.0451810 + 0.0670340I
4.14078 − 2.11359I 0
u = −0.665783 + 1.025060I
a = −0.847652 − 0.882125I
b = −2.52750 + 0.97821I
9.58913 − 7.47469I 0
u = −0.665783 − 1.025060I
a = −0.847652 + 0.882125I
b = −2.52750 − 0.97821I
9.58913 + 7.47469I 0
u = −0.592318 + 1.080490I
a = 0.694939 − 0.340214I
b = 0.685767 − 0.869695I
−0.78986 − 8.76955I 0
u = −0.592318 − 1.080490I
a = 0.694939 + 0.340214I
b = 0.685767 + 0.869695I
−0.78986 + 8.76955I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.048736 + 1.241430I
a = −0.311504 − 0.956796I
b = −0.618095 + 0.192942I
−0.67077 − 5.96925I 0
u = 0.048736 − 1.241430I
a = −0.311504 + 0.956796I
b = −0.618095 − 0.192942I
−0.67077 + 5.96925I 0
u = −0.114625 + 0.746785I
a = −0.450192 + 0.952040I
b = −0.641456 + 0.416697I
−1.14640 + 1.46119I 0
u = −0.114625 − 0.746785I
a = −0.450192 − 0.952040I
b = −0.641456 − 0.416697I
−1.14640 − 1.46119I 0
u = 0.047921 + 0.748944I
a = 0.67851 − 1.54364I
b = 0.114790 + 0.475167I
5.09394 + 2.42686I 0
u = 0.047921 − 0.748944I
a = 0.67851 + 1.54364I
b = 0.114790 − 0.475167I
5.09394 − 2.42686I 0
u = −0.635866 + 1.076000I
a = −0.414926 − 0.781734I
b = −2.08830 + 0.71509I
4.37960 − 1.11749I 0
u = −0.635866 − 1.076000I
a = −0.414926 + 0.781734I
b = −2.08830 − 0.71509I
4.37960 + 1.11749I 0
u = 0.675275 + 1.080570I
a = −0.823186 − 0.665682I
b = −0.607956 − 1.054570I
3.6231 + 13.8410I 0
u = 0.675275 − 1.080570I
a = −0.823186 + 0.665682I
b = −0.607956 + 1.054570I
3.6231 − 13.8410I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.638899 + 1.112080I
a = 0.171956 + 0.581692I
b = −0.301501 + 0.341530I
1.65893 + 7.16858I 0
u = 0.638899 − 1.112080I
a = 0.171956 − 0.581692I
b = −0.301501 − 0.341530I
1.65893 − 7.16858I 0
u = −0.667643 + 1.112210I
a = 0.862610 + 0.571711I
b = 2.68054 − 0.69797I
2.60607 − 8.84890I 0
u = −0.667643 − 1.112210I
a = 0.862610 − 0.571711I
b = 2.68054 + 0.69797I
2.60607 + 8.84890I 0
u = 0.660260 + 1.119840I
a = 0.860704 − 0.694694I
b = 2.77747 + 0.75425I
3.4845 + 14.0804I 0
u = 0.660260 − 1.119840I
a = 0.860704 + 0.694694I
b = 2.77747 − 0.75425I
3.4845 − 14.0804I 0
u = −0.530601 + 1.190690I
a = 0.370038 + 0.543490I
b = 0.897562 + 0.057083I
0.06054 − 7.22713I 0
u = −0.530601 − 1.190690I
a = 0.370038 − 0.543490I
b = 0.897562 − 0.057083I
0.06054 + 7.22713I 0
u = 0.308884 + 0.619234I
a = −0.19636 + 1.77403I
b = 1.006330 − 0.541638I
5.29236 − 6.37968I 0
u = 0.308884 − 0.619234I
a = −0.19636 − 1.77403I
b = 1.006330 + 0.541638I
5.29236 + 6.37968I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.673942 + 1.123630I
a = 0.533615 + 0.856778I
b = 0.444715 + 0.790421I
0.15125 + 3.00625I 0
u = 0.673942 − 1.123630I
a = 0.533615 − 0.856778I
b = 0.444715 − 0.790421I
0.15125 − 3.00625I 0
u = 0.708306 + 1.109020I
a = −0.565270 + 0.685659I
b = −2.04538 − 0.90332I
2.12544 + 7.24295I 0
u = 0.708306 − 1.109020I
a = −0.565270 − 0.685659I
b = −2.04538 + 0.90332I
2.12544 − 7.24295I 0
u = −0.242655 + 1.306060I
a = 0.246545 + 0.777376I
b = 0.531308 + 0.281897I
−1.88680 − 1.96129I 0
u = −0.242655 − 1.306060I
a = 0.246545 − 0.777376I
b = 0.531308 − 0.281897I
−1.88680 + 1.96129I 0
u = −0.857647 + 1.028040I
a = −0.838168 + 0.983286I
b = −0.603259 + 0.885731I
0.63437 − 3.41769I 0
u = −0.857647 − 1.028040I
a = −0.838168 − 0.983286I
b = −0.603259 − 0.885731I
0.63437 + 3.41769I 0
u = −0.746821 + 1.116740I
a = 0.686670 + 0.470964I
b = 2.36868 − 1.00580I
3.18957 − 11.07640I 0
u = −0.746821 − 1.116740I
a = 0.686670 − 0.470964I
b = 2.36868 + 1.00580I
3.18957 + 11.07640I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.695007 + 1.153870I
a = −0.950851 − 0.637660I
b = −2.73027 + 0.62676I
7.5919 − 20.7503I 0
u = −0.695007 − 1.153870I
a = −0.950851 + 0.637660I
b = −2.73027 − 0.62676I
7.5919 + 20.7503I 0
u = 0.446765 + 0.467700I
a = 1.15748 + 0.86583I
b = 0.450314 + 0.484270I
1.19301 + 2.15799I 0
u = 0.446765 − 0.467700I
a = 1.15748 − 0.86583I
b = 0.450314 − 0.484270I
1.19301 − 2.15799I 0
u = −0.004668 + 1.367980I
a = 0.349363 − 0.946580I
b = 0.701760 − 0.034141I
2.73865 + 11.67240I 0
u = −0.004668 − 1.367980I
a = 0.349363 + 0.946580I
b = 0.701760 + 0.034141I
2.73865 − 11.67240I 0
u = 0.627012 + 1.216180I
a = 0.528168 − 0.707533I
b = 2.20444 + 0.19957I
6.25035 + 7.07033I 0
u = 0.627012 − 1.216180I
a = 0.528168 + 0.707533I
b = 2.20444 − 0.19957I
6.25035 − 7.07033I 0
u = 0.869067 + 1.077500I
a = 0.550700 − 0.887131I
b = 1.65518 + 0.37623I
9.27706 − 2.03382I 0
u = 0.869067 − 1.077500I
a = 0.550700 + 0.887131I
b = 1.65518 − 0.37623I
9.27706 + 2.03382I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.733883 + 1.180060I
a = −0.974651 + 0.663904I
b = −2.48146 − 0.42011I
5.02765 + 11.47050I 0
u = 0.733883 − 1.180060I
a = −0.974651 − 0.663904I
b = −2.48146 + 0.42011I
5.02765 − 11.47050I 0
u = 0.585270 + 0.067798I
a = 1.39984 + 0.64670I
b = 1.169810 + 0.571543I
3.22912 + 0.25064I 5.80861 + 0.20603I
u = 0.585270 − 0.067798I
a = 1.39984 − 0.64670I
b = 1.169810 − 0.571543I
3.22912 − 0.25064I 5.80861 − 0.20603I
u = −0.415126 + 0.303546I
a = 0.109225 + 1.163050I
b = −0.293527 + 0.363796I
−1.21459 + 1.26814I −2.15978 − 3.69059I
u = −0.415126 − 0.303546I
a = 0.109225 − 1.163050I
b = −0.293527 − 0.363796I
−1.21459 − 1.26814I −2.15978 + 3.69059I
u = 0.04209 + 1.49794I
a = −0.087924 + 0.598148I
b = −0.378400 − 0.993460I
−3.51694 + 1.95817I 0
u = 0.04209 − 1.49794I
a = −0.087924 − 0.598148I
b = −0.378400 + 0.993460I
−3.51694 − 1.95817I 0
u = −0.429146
a = 2.51913
b = −0.484635
0.404418 12.8710
u = 0.410568
a = 1.88993
b = 0.424521
1.02841 11.3140
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.376333 + 0.064902I
a = −3.08692 + 1.33935I
b = 0.269702 + 0.127451I
5.51352 − 6.43959I 7.12907 + 6.64873I
u = 0.376333 − 0.064902I
a = −3.08692 − 1.33935I
b = 0.269702 − 0.127451I
5.51352 + 6.43959I 7.12907 − 6.64873I
u = −0.15135 + 1.64585I
a = −0.085353 + 0.951308I
b = −0.193252 + 0.190615I
−1.50834 − 0.71822I 0
u = −0.15135 − 1.64585I
a = −0.085353 − 0.951308I
b = −0.193252 − 0.190615I
−1.50834 + 0.71822I 0
22
II.
I
u
2
= h−5.50×10
30
u
44
+1.25×10
32
u
43
+· · ·+1.17×10
31
b−1.50×10
32
, 8.03×
10
31
u
44
−2.05×10
32
u
43
+· · ·+1.17×10
31
a−7.34×10
31
, u
45
−3u
44
+· · ·+5u−1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
9
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
11
=
−6.87427u
44
+ 17.5418u
43
+ ··· − 15.9166u + 6.28511
0.470591u
44
− 10.6651u
43
+ ··· − 58.4300u + 12.8227
a
7
=
−0.474709u
44
− 2.36017u
43
+ ··· + 20.6410u − 7.40124
0.115692u
44
+ 5.23944u
43
+ ··· + 35.2367u − 7.84686
a
6
=
0.818060u
44
− 8.37831u
43
+ ··· + 12.9990u − 5.52306
−3.74760u
44
+ 14.3352u
43
+ ··· + 38.6217u − 7.49263
a
4
=
14.1766u
44
− 35.1101u
43
+ ··· − 62.3938u + 3.17226
0.713159u
44
− 0.509756u
43
+ ··· + 6.59948u − 2.20822
a
5
=
−2.72558u
44
+ 5.84663u
43
+ ··· + 42.9764u − 11.5021
−2.42891u
44
+ 14.1740u
43
+ ··· + 47.0853u − 9.87764
a
10
=
4.61964u
44
− 5.66033u
43
+ ··· + 17.3196u − 11.4330
1.77609u
44
− 10.2215u
43
+ ··· − 24.3487u + 4.54119
a
12
=
−0.202893u
44
− 4.79320u
43
+ ··· − 24.9818u + 15.2661
0.537241u
44
− 4.67239u
43
+ ··· − 24.4568u + 4.79949
(ii) Obstruction class = 1
(iii) Cusp Shapes = −18.1755u
44
+ 9.35956u
43
+ ··· − 210.360u + 64.5647
23
(iv) u-Polynomials at the component
24
Crossings u-Polynomials at each crossing
c
1
u
45
− 27u
44
+ ··· − 31u + 1
c
2
u
45
− 3u
44
+ ··· + 5u − 1
c
3
81(81u
45
− 99u
44
+ ··· + 3u − 1)
c
4
9(9u
45
+ 3u
44
+ ··· − 33u + 13)
c
5
u
45
− 2u
43
+ ··· − 1314u + 81
c
6
u
45
− u
44
+ ··· − 1551u + 153
c
7
9(9u
45
− 15u
44
+ ··· − 3u + 1)
c
8
u
45
+ 3u
44
+ ··· + 5u + 1
c
9
u
45
+ 10u
43
+ ··· + 24u − 9
c
10
9(9u
45
+ 15u
44
+ ··· − 3u − 1)
c
11
9(9u
45
− 3u
44
+ ··· − 33u − 13)
c
12
u
45
− 8u
44
+ ··· − 8u − 1
25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 5y
44
+ ··· + 137y −1
c
2
, c
8
y
45
+ 27y
44
+ ··· − 31y −1
c
3
6561(6561y
45
+ 5427y
44
+ ··· − 19y −1)
c
4
, c
11
81(81y
45
+ 2493y
44
+ ··· − 5671y −169)
c
5
y
45
− 4y
44
+ ··· + 987228y −6561
c
6
y
45
− 3y
44
+ ··· − 20367y −23409
c
7
, c
10
81(81y
45
− 2043y
44
+ ··· + 45y −1)
c
9
y
45
+ 20y
44
+ ··· + 2934y −81
c
12
y
45
+ 4y
44
+ ··· + 18y −1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.811967 + 0.587525I
a = −0.485549 − 0.570539I
b = −0.631242 + 1.040740I
4.39701 + 3.42973I 9.31675 − 4.56118I
u = −0.811967 − 0.587525I
a = −0.485549 + 0.570539I
b = −0.631242 − 1.040740I
4.39701 − 3.42973I 9.31675 + 4.56118I
u = −0.309514 + 0.929522I
a = −0.194893 − 0.566006I
b = 2.29640 + 0.34594I
0.72842 − 6.16656I 1.79233 + 4.55157I
u = −0.309514 − 0.929522I
a = −0.194893 + 0.566006I
b = 2.29640 − 0.34594I
0.72842 + 6.16656I 1.79233 − 4.55157I
u = 0.933177 + 0.270134I
a = 0.680687 − 0.191588I
b = 1.135390 + 0.112558I
2.28676 − 1.50243I −1.20527 + 1.63991I
u = 0.933177 − 0.270134I
a = 0.680687 + 0.191588I
b = 1.135390 − 0.112558I
2.28676 + 1.50243I −1.20527 − 1.63991I
u = −0.335868 + 0.907694I
a = 0.127948 + 0.573319I
b = −1.15952 + 2.63117I
0.75847 + 3.48141I −2.81180 − 4.04929I
u = −0.335868 − 0.907694I
a = 0.127948 − 0.573319I
b = −1.15952 − 2.63117I
0.75847 − 3.48141I −2.81180 + 4.04929I
u = 0.258330 + 0.922748I
a = −0.777253 − 0.042499I
b = −0.11745 − 1.51207I
−3.98857 + 1.10625I 7.56890 − 9.75124I
u = 0.258330 − 0.922748I
a = −0.777253 + 0.042499I
b = −0.11745 + 1.51207I
−3.98857 − 1.10625I 7.56890 + 9.75124I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.948027 + 0.477909I
a = −0.751961 − 0.876023I
b = −1.40637 + 0.83259I
5.34823 + 3.64956I 12.00215 − 3.78154I
u = −0.948027 − 0.477909I
a = −0.751961 + 0.876023I
b = −1.40637 − 0.83259I
5.34823 − 3.64956I 12.00215 + 3.78154I
u = −0.506404 + 0.946373I
a = −1.296240 + 0.122527I
b = −0.98189 + 1.31998I
1.57614 − 2.18609I 0. + 3.45049I
u = −0.506404 − 0.946373I
a = −1.296240 − 0.122527I
b = −0.98189 − 1.31998I
1.57614 + 2.18609I 0. − 3.45049I
u = 0.439127 + 1.022880I
a = −0.321190 + 0.593109I
b = −0.57400 + 2.27954I
−2.42797 + 3.18142I −10.08161 + 0.I
u = 0.439127 − 1.022880I
a = −0.321190 − 0.593109I
b = −0.57400 − 2.27954I
−2.42797 − 3.18142I −10.08161 + 0.I
u = 0.383094 + 1.052830I
a = 0.712405 − 0.827628I
b = 1.63665 − 0.50353I
4.03133 + 8.67969I 6.07869 − 7.99133I
u = 0.383094 − 1.052830I
a = 0.712405 + 0.827628I
b = 1.63665 + 0.50353I
4.03133 − 8.67969I 6.07869 + 7.99133I
u = 0.846047 + 0.759410I
a = 0.742044 − 1.012220I
b = 1.85959 + 0.53761I
8.06564 − 3.35955I 8.15723 + 0.I
u = 0.846047 − 0.759410I
a = 0.742044 + 1.012220I
b = 1.85959 − 0.53761I
8.06564 + 3.35955I 8.15723 + 0.I
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.336979 + 0.778549I
a = −0.03075 + 1.58795I
b = 0.201212 − 0.629805I
5.07417 − 5.68346I 4.95145 + 0.17109I
u = 0.336979 − 0.778549I
a = −0.03075 − 1.58795I
b = 0.201212 + 0.629805I
5.07417 + 5.68346I 4.95145 − 0.17109I
u = 0.141847 + 1.150600I
a = −0.350102 + 0.638161I
b = −0.330072 − 0.108030I
−3.32514 + 1.54689I −4.11921 + 0.I
u = 0.141847 − 1.150600I
a = −0.350102 − 0.638161I
b = −0.330072 + 0.108030I
−3.32514 − 1.54689I −4.11921 + 0.I
u = 0.700262 + 0.935864I
a = −0.981391 + 0.775102I
b = −2.25764 − 1.14853I
7.51252 + 9.10440I 0. − 7.33875I
u = 0.700262 − 0.935864I
a = −0.981391 − 0.775102I
b = −2.25764 + 1.14853I
7.51252 − 9.10440I 0. + 7.33875I
u = 0.231393 + 0.763152I
a = 0.090033 − 1.021570I
b = −1.84983 − 0.08678I
−1.063630 − 0.141180I −1.32991 − 1.00606I
u = 0.231393 − 0.763152I
a = 0.090033 + 1.021570I
b = −1.84983 + 0.08678I
−1.063630 + 0.141180I −1.32991 + 1.00606I
u = −0.619286 + 1.032600I
a = 0.414937 + 0.366288I
b = 2.02703 + 0.57044I
3.01255 − 8.75626I 0
u = −0.619286 − 1.032600I
a = 0.414937 − 0.366288I
b = 2.02703 − 0.57044I
3.01255 + 8.75626I 0
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.565674 + 1.166380I
a = −0.177867 + 0.371021I
b = −0.583657 − 0.348014I
−0.48445 + 6.82399I 0
u = 0.565674 − 1.166380I
a = −0.177867 − 0.371021I
b = −0.583657 + 0.348014I
−0.48445 − 6.82399I 0
u = −0.706785 + 1.144000I
a = 0.783773 + 0.554705I
b = 2.50596 − 0.68425I
3.33384 − 9.72057I 0
u = −0.706785 − 1.144000I
a = 0.783773 − 0.554705I
b = 2.50596 + 0.68425I
3.33384 + 9.72057I 0
u = 0.844129 + 1.089590I
a = 0.683518 + 0.924699I
b = 0.563650 + 0.709749I
0.10334 + 3.53220I 0
u = 0.844129 − 1.089590I
a = 0.683518 − 0.924699I
b = 0.563650 − 0.709749I
0.10334 − 3.53220I 0
u = 0.06966 + 1.43448I
a = −0.101552 + 0.556141I
b = −0.391557 − 0.864961I
−3.76821 + 1.91608I 0
u = 0.06966 − 1.43448I
a = −0.101552 − 0.556141I
b = −0.391557 + 0.864961I
−3.76821 − 1.91608I 0
u = −0.144798 + 0.482362I
a = −1.34392 − 0.86515I
b = 0.937807 − 0.856480I
4.04044 − 2.54503I 6.38563 + 2.73143I
u = −0.144798 − 0.482362I
a = −1.34392 + 0.86515I
b = 0.937807 + 0.856480I
4.04044 + 2.54503I 6.38563 − 2.73143I
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.411883
a = 2.23443
b = −0.355358
−0.200837 −1.12310
u = −0.14955 + 1.64984I
a = −0.072646 + 0.923181I
b = −0.169049 + 0.097728I
−1.41455 − 0.67993I 0
u = −0.14955 − 1.64984I
a = −0.072646 − 0.923181I
b = −0.169049 − 0.097728I
−1.41455 + 0.67993I 0
u = 0.076531 + 0.334412I
a = 2.19943 − 2.78346I
b = −0.200412 − 0.502367I
5.78250 + 1.96052I 11.31719 − 0.45408I
u = 0.076531 − 0.334412I
a = 2.19943 + 2.78346I
b = −0.200412 + 0.502367I
5.78250 − 1.96052I 11.31719 + 0.45408I
32
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
45
− 27u
44
+ ··· − 31u + 1)
· (u
174
+ 78u
173
+ ··· + 38633006u + 3418801)
c
2
(u
45
− 3u
44
+ ··· + 5u − 1)(u
174
+ 4u
173
+ ··· + 860u − 1849)
c
3
6561(81u
45
− 99u
44
+ ··· + 3u − 1)
· (81u
174
− 2520u
173
+ ··· + 1289568u − 74248)
c
4
81(9u
45
+ 3u
44
+ ··· − 33u + 13)
· (9u
174
+ 30u
173
+ ··· + 188726u − 372821)
c
5
(u
45
− 2u
43
+ ··· − 1314u + 81)
· (u
174
− 5u
173
+ ··· + 9544707u + 120123)
c
6
(u
45
− u
44
+ ··· − 1551u + 153)
· (u
174
+ 2u
173
+ ··· + 4585039248u − 391773717)
c
7
81(9u
45
− 15u
44
+ ··· − 3u + 1)
· (9u
174
+ 12u
173
+ ··· − 27006326u − 10812743)
c
8
(u
45
+ 3u
44
+ ··· + 5u + 1)(u
174
+ 4u
173
+ ··· + 860u − 1849)
c
9
(u
45
+ 10u
43
+ ··· + 24u − 9)
· (u
174
+ u
173
+ ··· − 62865261u + 31013523)
c
10
81(9u
45
+ 15u
44
+ ··· − 3u − 1)
· (9u
174
+ 12u
173
+ ··· − 27006326u − 10812743)
c
11
81(9u
45
− 3u
44
+ ··· − 33u − 13)
· (9u
174
+ 30u
173
+ ··· + 188726u − 372821)
c
12
(u
45
− 8u
44
+ ··· − 8u − 1)
· (u
174
+ 13u
173
+ ··· + 3315627075u + 351801391)
33
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
45
− 5y
44
+ ··· + 137y −1)
· (y
174
+ 50y
173
+ ··· − 1038422793520482y + 11688200277601)
c
2
, c
8
(y
45
+ 27y
44
+ ··· − 31y −1)
· (y
174
+ 78y
173
+ ··· + 38633006y + 3418801)
c
3
43046721(6561y
45
+ 5427y
44
+ ··· − 19y −1)
· (6561y
174
− 457002y
173
+ ··· + 161502458592y + 5512765504)
c
4
, c
11
6561(81y
45
+ 2493y
44
+ ··· − 5671y −169)
· (81y
174
+ 10620y
173
+ ··· + 5061796260474y + 138995498041)
c
5
(y
45
− 4y
44
+ ··· + 987228y −6561)
· (y
174
− 21y
173
+ ··· + 1241320767183y + 14429535129)
c
6
(y
45
− 3y
44
+ ··· − 20367y −23409)
· (y
174
+ 52y
173
+ ··· + 2.28 × 10
19
y + 1.53 × 10
17
)
c
7
, c
10
6561(81y
45
− 2043y
44
+ ··· + 45y −1)
· (81y
174
− 8172y
173
+ ··· + 749524157872730y + 116915411184049)
c
9
(y
45
+ 20y
44
+ ··· + 2934y −81)
· (y
174
− 25y
173
+ ··· − 29120310824125347y + 961838608871529)
c
12
(y
45
+ 4y
44
+ ··· + 18y −1)
· (y
174
− 57y
173
+ ··· − 3.54 × 10
18
y + 1.24 × 10
17
)
34
