12n
0720
(K12n
0720
)
A knot diagram
1
Linearized knot diagam
4 12 11 10 12 3 4 11 5 1 7 9
Solving Sequence
4,10 1,5
11 3 9 8 7 12 6 2
c
4
c
10
c
3
c
9
c
8
c
7
c
12
c
5
c
2
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.07560 × 10
132
u
71
+ 1.26113 × 10
133
u
70
+ ··· + 2.19169 × 10
132
b + 3.53314 × 10
134
,
− 5.04578 × 10
133
u
71
+ 1.39574 × 10
133
u
70
+ ··· + 3.72587 × 10
133
a + 1.11463 × 10
135
,
u
72
+ 24u
70
+ ··· + u + 17i
I
u
2
= h−6463690u
21
− 7551941u
20
+ ··· + 5470469b − 13759554,
− 16456196u
21
+ 170258u
20
+ ··· + 5470469a − 12909429, u
22
− u
21
+ ··· − 4u + 1i
* 2 irreducible components of dim
C
= 0, with total 94 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−3.08 × 10
132
u
71
+ 1.26 × 10
133
u
70
+ · · · + 2.19 × 10
132
b + 3.53 ×
10
134
, −5.05 × 10
133
u
71
+ 1.40 × 10
133
u
70
+ · · · + 3.73 × 10
133
a + 1.11 ×
10
135
, u
72
+ 24u
70
+ · · · + u + 17i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
1
=
1.35425u
71
− 0.374609u
70
+ ··· − 0.0210176u − 29.9160
1.40330u
71
− 5.75416u
70
+ ··· − 30.8710u − 161.206
a
5
=
1
u
2
a
11
=
1.25553u
71
− 0.745166u
70
+ ··· + 19.7594u − 26.2435
−1.91303u
71
− 0.436232u
70
+ ··· − 47.9897u + 4.43250
a
3
=
−0.701200u
71
+ 0.0578726u
70
+ ··· + 47.0698u + 38.4140
1.03169u
71
+ 4.22675u
70
+ ··· + 111.003u + 105.693
a
9
=
u
u
3
+ u
a
8
=
−0.136773u
71
+ 0.391862u
70
+ ··· − 1.59510u + 12.1738
−3.37201u
71
− 0.539374u
70
+ ··· − 67.2143u + 17.8222
a
7
=
3.23524u
71
+ 0.931236u
70
+ ··· + 65.6192u − 5.64844
−3.37201u
71
− 0.539374u
70
+ ··· − 67.2143u + 17.8222
a
12
=
−0.364800u
71
+ 2.58232u
70
+ ··· − 18.9166u + 51.2212
1.51001u
71
− 4.55294u
70
+ ··· − 23.4995u − 130.337
a
6
=
−2.19576u
71
+ 1.19016u
70
+ ··· − 52.7840u + 45.5645
1.33590u
71
− 2.38359u
70
+ ··· + 7.26507u − 84.1876
a
2
=
−0.0490483u
71
+ 5.37955u
70
+ ··· + 30.8499u + 131.290
1.40330u
71
− 5.75416u
70
+ ··· − 30.8710u − 161.206
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10.1241u
71
+ 9.90473u
70
+ ··· − 214.226u + 268.653
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
72
− 9u
71
+ ··· + 1961u − 77
c
2
u
72
+ 10u
71
+ ··· − 907019u − 119125
c
3
u
72
+ 2u
71
+ ··· + 60020u + 6341
c
4
, c
9
u
72
+ 24u
70
+ ··· + u + 17
c
5
u
72
− 21u
70
+ ··· + 35839731u − 10044233
c
6
u
72
+ 4u
71
+ ··· + 28820u + 2887
c
7
u
72
− 4u
71
+ ··· + 157706u + 75839
c
8
u
72
− 17u
71
+ ··· − 149942054u + 20559187
c
10
u
72
− u
71
+ ··· + 7u − 1
c
11
u
72
+ 3u
71
+ ··· − 12u + 1
c
12
u
72
+ u
71
+ ··· + 865u − 575
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
72
− 29y
71
+ ··· − 1058891y + 5929
c
2
y
72
− 78y
71
+ ··· + 24427750639y + 14190765625
c
3
y
72
+ 78y
71
+ ··· − 240503656y + 40208281
c
4
, c
9
y
72
+ 48y
71
+ ··· + 6051y + 289
c
5
y
72
− 42y
71
+ ··· − 2956824736496503y + 100886616558289
c
6
y
72
− 74y
71
+ ··· − 527457400y + 8334769
c
7
y
72
+ 90y
71
+ ··· − 90986257534y + 5751553921
c
8
y
72
− 71y
71
+ ··· − 12442914146716706y + 422680170100969
c
10
y
72
− y
71
+ ··· − 7y + 1
c
11
y
72
+ 5y
71
+ ··· − 44y + 1
c
12
y
72
− 5y
71
+ ··· − 2688275y + 330625
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.477362 + 0.897642I
a = −0.067877 − 0.313856I
b = −1.151550 − 0.136492I
−1.61428 + 1.42833I 0
u = −0.477362 − 0.897642I
a = −0.067877 + 0.313856I
b = −1.151550 + 0.136492I
−1.61428 − 1.42833I 0
u = 0.315889 + 0.926424I
a = 0.432112 − 0.805014I
b = 1.14826 + 2.39805I
−6.56364 + 2.44744I 0
u = 0.315889 − 0.926424I
a = 0.432112 + 0.805014I
b = 1.14826 − 2.39805I
−6.56364 − 2.44744I 0
u = 0.133880 + 0.943058I
a = −0.707754 + 1.162790I
b = −0.66351 − 1.47027I
−0.37726 − 3.40325I −4.42658 + 3.83460I
u = 0.133880 − 0.943058I
a = −0.707754 − 1.162790I
b = −0.66351 + 1.47027I
−0.37726 + 3.40325I −4.42658 − 3.83460I
u = 0.301550 + 0.900946I
a = −0.147062 + 1.390830I
b = −0.742542 − 0.916719I
−2.08548 − 1.83389I −10.93305 + 0.I
u = 0.301550 − 0.900946I
a = −0.147062 − 1.390830I
b = −0.742542 + 0.916719I
−2.08548 + 1.83389I −10.93305 + 0.I
u = −0.215828 + 1.034000I
a = −1.77643 − 0.46095I
b = −0.933208 + 0.211167I
3.17186 + 2.86604I 0
u = −0.215828 − 1.034000I
a = −1.77643 + 0.46095I
b = −0.933208 − 0.211167I
3.17186 − 2.86604I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.377147 + 1.000300I
a = −0.60630 − 1.79537I
b = 0.491494 + 0.082853I
−6.71932 − 7.41916I 0
u = 0.377147 − 1.000300I
a = −0.60630 + 1.79537I
b = 0.491494 − 0.082853I
−6.71932 + 7.41916I 0
u = −0.433501 + 0.982102I
a = −0.464224 − 0.505661I
b = −0.40071 + 1.38684I
0.19065 + 4.37559I 0
u = −0.433501 − 0.982102I
a = −0.464224 + 0.505661I
b = −0.40071 − 1.38684I
0.19065 − 4.37559I 0
u = −0.502019 + 0.960993I
a = −0.38438 + 1.51469I
b = 0.472013 + 0.149646I
−6.73385 − 0.03465I 0
u = −0.502019 − 0.960993I
a = −0.38438 − 1.51469I
b = 0.472013 − 0.149646I
−6.73385 + 0.03465I 0
u = −0.871305 + 0.250604I
a = −1.134100 + 0.159082I
b = −0.910776 + 1.001180I
−3.47313 + 3.50227I −18.3256 − 7.5930I
u = −0.871305 − 0.250604I
a = −1.134100 − 0.159082I
b = −0.910776 − 1.001180I
−3.47313 − 3.50227I −18.3256 + 7.5930I
u = −1.101040 + 0.158588I
a = 0.860403 + 0.773355I
b = 1.230070 + 0.481564I
−10.34360 − 2.43121I 0
u = −1.101040 − 0.158588I
a = 0.860403 − 0.773355I
b = 1.230070 − 0.481564I
−10.34360 + 2.43121I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.027610 + 0.439052I
a = −0.144621 + 0.779286I
b = −0.540452 + 0.832986I
−1.51227 + 2.95975I 0
u = 1.027610 − 0.439052I
a = −0.144621 − 0.779286I
b = −0.540452 − 0.832986I
−1.51227 − 2.95975I 0
u = −0.298638 + 1.108140I
a = 0.589128 + 0.524624I
b = 1.68842 − 2.24180I
−4.91427 + 6.35505I 0
u = −0.298638 − 1.108140I
a = 0.589128 − 0.524624I
b = 1.68842 + 2.24180I
−4.91427 − 6.35505I 0
u = 0.461914 + 1.060090I
a = −1.41949 + 0.47743I
b = −1.32124 − 0.96303I
−1.40577 − 6.31505I 0
u = 0.461914 − 1.060090I
a = −1.41949 − 0.47743I
b = −1.32124 + 0.96303I
−1.40577 + 6.31505I 0
u = 1.158870 + 0.142308I
a = 0.786009 − 0.769271I
b = 1.173780 − 0.714165I
−10.2439 + 10.5771I 0
u = 1.158870 − 0.142308I
a = 0.786009 + 0.769271I
b = 1.173780 + 0.714165I
−10.2439 − 10.5771I 0
u = −0.091289 + 0.794865I
a = 1.00922 − 1.97778I
b = −0.130734 + 0.316777I
2.12580 − 1.30198I −4.55096 − 6.52596I
u = −0.091289 − 0.794865I
a = 1.00922 + 1.97778I
b = −0.130734 − 0.316777I
2.12580 + 1.30198I −4.55096 + 6.52596I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.249808 + 1.185040I
a = 0.975289 − 0.228857I
b = 0.368779 + 0.841330I
3.99365 + 0.15429I 0
u = 0.249808 − 1.185040I
a = 0.975289 + 0.228857I
b = 0.368779 − 0.841330I
3.99365 − 0.15429I 0
u = 0.120517 + 0.770120I
a = −0.162776 − 0.214456I
b = 3.44943 − 0.72600I
−7.47162 − 4.79394I −20.2086 + 8.5185I
u = 0.120517 − 0.770120I
a = −0.162776 + 0.214456I
b = 3.44943 + 0.72600I
−7.47162 + 4.79394I −20.2086 − 8.5185I
u = 0.620042 + 0.447810I
a = −0.64813 + 1.64366I
b = −0.950767 + 0.538188I
−3.27579 + 2.08206I −17.7678 − 0.3325I
u = 0.620042 − 0.447810I
a = −0.64813 − 1.64366I
b = −0.950767 − 0.538188I
−3.27579 − 2.08206I −17.7678 + 0.3325I
u = 0.233988 + 0.718232I
a = −0.897689 + 0.560342I
b = −1.67915 + 0.25556I
−2.73046 − 0.85081I −9.21790 + 8.47139I
u = 0.233988 − 0.718232I
a = −0.897689 − 0.560342I
b = −1.67915 − 0.25556I
−2.73046 + 0.85081I −9.21790 − 8.47139I
u = −0.285520 + 1.237420I
a = 0.909356 + 0.100600I
b = 0.419131 − 0.190885I
2.91597 + 2.97580I 0
u = −0.285520 − 1.237420I
a = 0.909356 − 0.100600I
b = 0.419131 + 0.190885I
2.91597 − 2.97580I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.674386 + 0.248008I
a = 0.258287 − 0.326727I
b = −0.732396 − 0.442297I
−1.74066 − 0.28469I −7.78828 − 0.51945I
u = −0.674386 − 0.248008I
a = 0.258287 + 0.326727I
b = −0.732396 + 0.442297I
−1.74066 + 0.28469I −7.78828 + 0.51945I
u = −0.335449 + 1.244040I
a = 0.946840 + 0.168434I
b = 0.381827 − 0.463105I
2.87885 + 3.03592I 0
u = −0.335449 − 1.244040I
a = 0.946840 − 0.168434I
b = 0.381827 + 0.463105I
2.87885 − 3.03592I 0
u = 0.667924 + 0.216904I
a = 1.260200 + 0.408081I
b = 0.523105 + 0.107419I
2.59475 − 2.25621I −0.944475 + 0.319958I
u = 0.667924 − 0.216904I
a = 1.260200 − 0.408081I
b = 0.523105 − 0.107419I
2.59475 + 2.25621I −0.944475 − 0.319958I
u = −1.31641
a = −0.552186
b = −1.00106
−4.19770 0
u = 0.396288 + 1.256520I
a = 0.850383 − 0.277855I
b = 1.30590 + 0.64512I
6.79619 − 6.17817I 0
u = 0.396288 − 1.256520I
a = 0.850383 + 0.277855I
b = 1.30590 − 0.64512I
6.79619 + 6.17817I 0
u = 0.638512 + 1.215610I
a = −1.076520 + 0.088288I
b = −0.76164 − 1.34841I
1.05057 − 8.98234I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.638512 − 1.215610I
a = −1.076520 − 0.088288I
b = −0.76164 + 1.34841I
1.05057 + 8.98234I 0
u = 0.211859 + 0.584522I
a = 0.413735 + 0.785763I
b = −0.755167 + 0.763418I
−1.03163 + 1.71552I −5.97336 − 2.93223I
u = 0.211859 − 0.584522I
a = 0.413735 − 0.785763I
b = −0.755167 − 0.763418I
−1.03163 − 1.71552I −5.97336 + 2.93223I
u = −0.449186 + 1.330600I
a = −0.990007 − 0.648279I
b = −0.80809 + 1.20012I
1.29689 + 8.20198I 0
u = −0.449186 − 1.330600I
a = −0.990007 + 0.648279I
b = −0.80809 − 1.20012I
1.29689 − 8.20198I 0
u = −0.59562 + 1.28747I
a = 1.008800 + 0.407018I
b = 1.47932 − 1.12490I
−6.83234 + 8.40177I 0
u = −0.59562 − 1.28747I
a = 1.008800 − 0.407018I
b = 1.47932 + 1.12490I
−6.83234 − 8.40177I 0
u = −0.411073 + 0.374057I
a = 2.18791 − 1.24049I
b = 1.376760 − 0.314484I
−8.24212 + 4.00105I −12.46070 − 3.51515I
u = −0.411073 − 0.374057I
a = 2.18791 + 1.24049I
b = 1.376760 + 0.314484I
−8.24212 − 4.00105I −12.46070 + 3.51515I
u = 0.61038 + 1.31809I
a = 1.060960 − 0.401433I
b = 1.32898 + 1.29138I
−6.5694 − 16.7734I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.61038 − 1.31809I
a = 1.060960 + 0.401433I
b = 1.32898 − 1.29138I
−6.5694 + 16.7734I 0
u = −0.63936 + 1.31443I
a = −0.671719 − 0.351431I
b = −1.05068 + 1.00047I
−0.37191 + 6.68129I 0
u = −0.63936 − 1.31443I
a = −0.671719 + 0.351431I
b = −1.05068 − 1.00047I
−0.37191 − 6.68129I 0
u = 0.261621 + 0.430282I
a = 2.82143 + 0.82812I
b = 1.402730 − 0.052584I
−8.34849 + 4.22802I −12.83906 − 0.71232I
u = 0.261621 − 0.430282I
a = 2.82143 − 0.82812I
b = 1.402730 + 0.052584I
−8.34849 − 4.22802I −12.83906 + 0.71232I
u = −0.484388
a = 1.12010
b = 0.0840423
−0.873780 −11.6300
u = 0.59538 + 1.39839I
a = −0.375797 + 0.018450I
b = −0.603812 − 0.400265I
4.97601 − 3.89570I 0
u = 0.59538 − 1.39839I
a = −0.375797 − 0.018450I
b = −0.603812 + 0.400265I
4.97601 + 3.89570I 0
u = −0.56370 + 1.70638I
a = 0.012157 + 0.317984I
b = 0.448416 − 0.201438I
−4.68702 + 3.51849I 0
u = −0.56370 − 1.70638I
a = 0.012157 − 0.317984I
b = 0.448416 + 0.201438I
−4.68702 − 3.51849I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.46249 + 1.84938I
a = −0.138376 − 0.192728I
b = 0.406510 − 0.107185I
−4.41396 + 4.27518I 0
u = 0.46249 − 1.84938I
a = −0.138376 + 0.192728I
b = 0.406510 + 0.107185I
−4.41396 − 4.27518I 0
12
II.
I
u
2
= h−6.46 × 10
6
u
21
− 7.55 × 10
6
u
20
+ · · · + 5.47 × 10
6
b − 1.38 × 10
7
, −1.65 ×
10
7
u
21
+ 1.70× 10
5
u
20
+ · · · + 5.47 × 10
6
a −1.29 × 10
7
, u
22
− u
21
+ · · · − 4u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
1
=
3.00819u
21
− 0.0311231u
20
+ ··· − 11.3724u + 2.35984
1.18156u
21
+ 1.38049u
20
+ ··· − 14.0123u + 2.51524
a
5
=
1
u
2
a
11
=
−0.537044u
21
− 3.70196u
20
+ ··· + 35.3077u − 9.76644
−0.953189u
21
+ 0.862066u
20
+ ··· + 1.08333u − 1.13292
a
3
=
2.10844u
21
− 4.02584u
20
+ ··· + 11.2325u − 0.0780423
0.373706u
21
− 2.38305u
20
+ ··· + 10.5890u − 2.03858
a
9
=
u
u
3
+ u
a
8
=
−5.99193u
21
+ 8.34635u
20
+ ··· − 22.3824u + 3.42673
1.49872u
21
− 1.97473u
20
+ ··· + 5.98233u − 0.526097
a
7
=
−7.49065u
21
+ 10.3211u
20
+ ··· − 28.3647u + 3.95283
1.49872u
21
− 1.97473u
20
+ ··· + 5.98233u − 0.526097
a
12
=
2.42473u
21
− 0.488635u
20
+ ··· − 5.92228u + 1.09391
1.23736u
21
+ 0.981295u
20
+ ··· − 12.1427u + 2.29028
a
6
=
−10.0766u
21
+ 9.72932u
20
+ ··· − 12.2092u + 0.870113
0.0167594u
21
+ 2.37374u
20
+ ··· − 15.6411u + 4.64844
a
2
=
1.82663u
21
− 1.41162u
20
+ ··· + 2.63998u − 0.155403
1.18156u
21
+ 1.38049u
20
+ ··· − 14.0123u + 2.51524
(ii) Obstruction class = 1
(iii) Cusp Shapes =
75092121
5470469
u
21
−
34821641
5470469
u
20
+ ··· −
92994051
5470469
u −
28848469
5470469
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
22
− 6u
21
+ ··· + 2u + 1
c
2
u
22
+ 11u
21
+ ··· + 6u + 1
c
3
u
22
+ u
21
+ ··· + u + 1
c
4
u
22
− u
21
+ ··· − 4u + 1
c
5
u
22
+ u
21
+ ··· + 114u + 13
c
6
u
22
− 3u
21
+ ··· − 13u + 5
c
7
u
22
− u
21
+ ··· + 3u + 1
c
8
u
22
+ 6u
21
+ ··· − 105u + 13
c
9
u
22
+ u
21
+ ··· + 4u + 1
c
10
u
22
+ u
20
+ ··· + 2u + 1
c
11
u
22
+ 6u
20
+ ··· + u + 1
c
12
u
22
+ 5u
20
+ ··· + 4u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 18y
21
+ ··· − 12y + 1
c
2
y
22
− 11y
21
+ ··· + 10y + 1
c
3
y
22
+ 21y
21
+ ··· + 15y + 1
c
4
, c
9
y
22
+ 19y
21
+ ··· + 2y + 1
c
5
y
22
− 7y
21
+ ··· − 2596y + 169
c
6
y
22
− 19y
21
+ ··· − 389y + 25
c
7
y
22
+ 17y
21
+ ··· + y + 1
c
8
y
22
− 20y
21
+ ··· − 2887y + 169
c
10
y
22
+ 2y
21
+ ··· + 12y + 1
c
11
y
22
+ 12y
21
+ ··· + 3y + 1
c
12
y
22
+ 10y
21
+ ··· − 8y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.388555 + 0.923513I
a = −0.853623 + 0.736114I
b = −1.20745 − 1.34705I
−1.50369 − 3.99443I −12.16830 + 6.90515I
u = 0.388555 − 0.923513I
a = −0.853623 − 0.736114I
b = −1.20745 + 1.34705I
−1.50369 + 3.99443I −12.16830 − 6.90515I
u = −0.055836 + 0.829858I
a = 0.943490 − 0.363773I
b = 2.63731 + 0.49911I
−7.05318 + 4.57510I −3.48568 − 0.67518I
u = −0.055836 − 0.829858I
a = 0.943490 + 0.363773I
b = 2.63731 − 0.49911I
−7.05318 − 4.57510I −3.48568 + 0.67518I
u = 0.217691 + 1.176020I
a = 1.43864 − 0.21091I
b = 0.308754 + 0.219854I
4.16265 − 2.72117I 2.10086 + 2.56105I
u = 0.217691 − 1.176020I
a = 1.43864 + 0.21091I
b = 0.308754 − 0.219854I
4.16265 + 2.72117I 2.10086 − 2.56105I
u = 0.751016 + 0.273791I
a = −0.83572 + 1.15453I
b = −0.790163 + 0.824931I
−2.63678 + 2.66212I −11.56563 − 5.13370I
u = 0.751016 − 0.273791I
a = −0.83572 − 1.15453I
b = −0.790163 − 0.824931I
−2.63678 − 2.66212I −11.56563 + 5.13370I
u = −0.763538 + 0.171279I
a = −1.196400 + 0.620756I
b = −0.832121 + 0.312002I
2.06710 + 2.62365I −11.48407 − 6.35850I
u = −0.763538 − 0.171279I
a = −1.196400 − 0.620756I
b = −0.832121 − 0.312002I
2.06710 − 2.62365I −11.48407 + 6.35850I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.064699 + 0.744144I
a = −1.58203 − 1.69510I
b = −0.500021 + 0.426948I
1.98210 + 1.78424I −9.34784 − 7.39339I
u = −0.064699 − 0.744144I
a = −1.58203 + 1.69510I
b = −0.500021 − 0.426948I
1.98210 − 1.78424I −9.34784 + 7.39339I
u = −0.434982 + 1.274440I
a = −0.885624 − 0.332093I
b = −1.37133 + 1.02552I
6.25032 + 7.01593I −5.78583 − 8.24156I
u = −0.434982 − 1.274440I
a = −0.885624 + 0.332093I
b = −1.37133 − 1.02552I
6.25032 − 7.01593I −5.78583 + 8.24156I
u = 0.561065 + 1.277390I
a = −0.985213 + 0.422579I
b = −0.87768 − 1.25355I
0.64404 − 7.81110I −11.10365 + 6.57562I
u = 0.561065 − 1.277390I
a = −0.985213 − 0.422579I
b = −0.87768 + 1.25355I
0.64404 + 7.81110I −11.10365 − 6.57562I
u = −0.48975 + 1.40212I
a = 0.520962 − 0.101567I
b = 0.260442 − 0.282393I
5.35239 + 3.50447I 0.732534 + 0.879738I
u = −0.48975 − 1.40212I
a = 0.520962 + 0.101567I
b = 0.260442 + 0.282393I
5.35239 − 3.50447I 0.732534 − 0.879738I
u = 0.389749 + 0.230136I
a = −1.44318 + 0.91022I
b = −1.261020 + 0.016789I
−3.02242 − 0.02950I −15.3029 − 0.2723I
u = 0.389749 − 0.230136I
a = −1.44318 − 0.91022I
b = −1.261020 − 0.016789I
−3.02242 + 0.02950I −15.3029 + 0.2723I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00073 + 1.70029I
a = −0.121295 − 0.083969I
b = 0.633280 + 0.100713I
−4.59759 − 3.98208I −16.0895 + 3.9194I
u = 0.00073 − 1.70029I
a = −0.121295 + 0.083969I
b = 0.633280 − 0.100713I
−4.59759 + 3.98208I −16.0895 − 3.9194I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 6u
21
+ ··· + 2u + 1)(u
72
− 9u
71
+ ··· + 1961u − 77)
c
2
(u
22
+ 11u
21
+ ··· + 6u + 1)(u
72
+ 10u
71
+ ··· − 907019u − 119125)
c
3
(u
22
+ u
21
+ ··· + u + 1)(u
72
+ 2u
71
+ ··· + 60020u + 6341)
c
4
(u
22
− u
21
+ ··· − 4u + 1)(u
72
+ 24u
70
+ ··· + u + 17)
c
5
(u
22
+ u
21
+ ··· + 114u + 13)
· (u
72
− 21u
70
+ ··· + 35839731u − 10044233)
c
6
(u
22
− 3u
21
+ ··· − 13u + 5)(u
72
+ 4u
71
+ ··· + 28820u + 2887)
c
7
(u
22
− u
21
+ ··· + 3u + 1)(u
72
− 4u
71
+ ··· + 157706u + 75839)
c
8
(u
22
+ 6u
21
+ ··· − 105u + 13)
· (u
72
− 17u
71
+ ··· − 149942054u + 20559187)
c
9
(u
22
+ u
21
+ ··· + 4u + 1)(u
72
+ 24u
70
+ ··· + u + 17)
c
10
(u
22
+ u
20
+ ··· + 2u + 1)(u
72
− u
71
+ ··· + 7u − 1)
c
11
(u
22
+ 6u
20
+ ··· + u + 1)(u
72
+ 3u
71
+ ··· − 12u + 1)
c
12
(u
22
+ 5u
20
+ ··· + 4u + 1)(u
72
+ u
71
+ ··· + 865u − 575)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
− 18y
21
+ ··· − 12y + 1)(y
72
− 29y
71
+ ··· − 1058891y + 5929)
c
2
(y
22
− 11y
21
+ ··· + 10y + 1)
· (y
72
− 78y
71
+ ··· + 24427750639y + 14190765625)
c
3
(y
22
+ 21y
21
+ ··· + 15y + 1)
· (y
72
+ 78y
71
+ ··· − 240503656y + 40208281)
c
4
, c
9
(y
22
+ 19y
21
+ ··· + 2y + 1)(y
72
+ 48y
71
+ ··· + 6051y + 289)
c
5
(y
22
− 7y
21
+ ··· − 2596y + 169)
· (y
72
− 42y
71
+ ··· − 2956824736496503y + 100886616558289)
c
6
(y
22
− 19y
21
+ ··· − 389y + 25)
· (y
72
− 74y
71
+ ··· − 527457400y + 8334769)
c
7
(y
22
+ 17y
21
+ ··· + y + 1)
· (y
72
+ 90y
71
+ ··· − 90986257534y + 5751553921)
c
8
(y
22
− 20y
21
+ ··· − 2887y + 169)
· (y
72
− 71y
71
+ ··· − 12442914146716706y + 422680170100969)
c
10
(y
22
+ 2y
21
+ ··· + 12y + 1)(y
72
− y
71
+ ··· − 7y + 1)
c
11
(y
22
+ 12y
21
+ ··· + 3y + 1)(y
72
+ 5y
71
+ ··· − 44y + 1)
c
12
(y
22
+ 10y
21
+ ··· − 8y + 1)(y
72
− 5y
71
+ ··· − 2688275y + 330625)
22
