11a
280
(K11a
280
)
A knot diagram
1
Linearized knot diagam
6 9 1 10 2 4 11 3 5 8 7
Solving Sequence
2,9 3,5
6 10 1 4 8 11 7
c
2
c
5
c
9
c
1
c
4
c
8
c
10
c
7
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h37345311u
21
+ 18480167u
20
+ ··· + 14331796b − 87054847, a − 1, u
22
+ 9u
20
+ ··· − 3u
2
+ 1i
I
u
2
= h−2105832678u
17
+ 16757581u
16
+ ··· + 17708562289b − 38848951730,
721895222078u
17
− 1381269075020u
16
+ ··· + 12944959033259a − 17573961275067,
u
18
+ 5u
16
+ ··· + 50u + 17i
I
u
3
= h6u
11
+ 12u
10
+ 38u
9
+ 71u
8
+ 111u
7
+ 169u
6
+ 154u
5
+ 168u
4
+ 93u
3
+ 67u
2
+ 11b + 26u + 19, a + 1,
u
12
+ 6u
10
+ u
9
+ 15u
8
+ 4u
7
+ 17u
6
+ 6u
5
+ 9u
4
+ 4u
3
+ 4u
2
+ 1i
I
u
4
= h−1.19860 × 10
15
u
23
+ 6.59553 × 10
15
u
22
+ ··· + 1.10953 × 10
17
b + 2.38445 × 10
17
,
6.76587 × 10
19
u
23
− 7.15855 × 10
18
u
22
+ ··· + 7.49046 × 10
20
a + 4.99902 × 10
21
, u
24
− u
23
+ ··· − 188u + 43i
* 4 irreducible components of dim
C
= 0, with total 76 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
= h3.73 × 10
7
u
21
+ 1.85 × 10
7
u
20
+ · · · + 1.43 × 10
7
b − 8.71 × 10
7
, a −
1, u
22
+ 9u
20
+ · · · − 3u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
5
=
1
−2.60577u
21
− 1.28945u
20
+ ··· + 13.4587u + 6.07425
a
6
=
−2.60577u
21
− 1.28945u
20
+ ··· + 13.4587u + 7.07425
−2.60577u
21
− 1.28945u
20
+ ··· + 13.4587u + 6.07425
a
10
=
u
−1.28945u
21
− 0.754726u
20
+ ··· + 7.07425u + 2.60577
a
1
=
−0.192382u
21
− 0.424472u
20
+ ··· + 1.45999u + 1.31709
2.41338u
21
+ 0.864980u
20
+ ··· − 11.9987u − 5.75715
a
4
=
u
2
+ 1
−3.36049u
21
− 1.72488u
20
+ ··· + 16.0645u + 7.36370
a
8
=
−u
u
3
+ u
a
11
=
0.435428u
21
+ 0.0330632u
20
+ ··· − 0.289452u − 0.754726
−1.66963u
21
− 0.847225u
20
+ ··· + 8.79913u + 3.39356
a
7
=
0.125776u
21
+ 0.298531u
20
+ ··· − 0.550624u + 0.520875
−0.660480u
21
− 0.405082u
20
+ ··· + 5.84008u + 2.31835
a
7
=
0.125776u
21
+ 0.298531u
20
+ ··· − 0.550624u + 0.520875
−0.660480u
21
− 0.405082u
20
+ ··· + 5.84008u + 2.31835
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
30437693
3582949
u
21
−
22461818
3582949
u
20
+ ··· +
186266132
3582949
u +
101532156
3582949
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
22
− 14u
21
+ ··· − 1344u + 128
c
2
, c
4
, c
8
c
9
u
22
+ 9u
20
+ ··· − 3u
2
+ 1
c
3
, c
6
u
22
− u
21
+ ··· + 3u + 1
c
7
, c
10
, c
11
u
22
− 9u
21
+ ··· − 88u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
22
+ 14y
21
+ ··· + 20480y + 16384
c
2
, c
4
, c
8
c
9
y
22
+ 18y
21
+ ··· − 6y + 1
c
3
, c
6
y
22
+ 5y
21
+ ··· + 11y + 1
c
7
, c
10
, c
11
y
22
+ 21y
21
+ ··· + 224y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.767600 + 0.519015I
a = 1.00000
b = −0.721664 − 0.260594I
6.82374 − 0.02012I 7.10708 − 2.25648I
u = 0.767600 − 0.519015I
a = 1.00000
b = −0.721664 + 0.260594I
6.82374 + 0.02012I 7.10708 + 2.25648I
u = −0.020372 + 1.119260I
a = 1.00000
b = −1.15684 + 1.18640I
−0.15255 + 1.75803I 3.02278 − 3.33932I
u = −0.020372 − 1.119260I
a = 1.00000
b = −1.15684 − 1.18640I
−0.15255 − 1.75803I 3.02278 + 3.33932I
u = −0.440574 + 0.756721I
a = 1.00000
b = 0.232862 + 1.365440I
1.47923 − 2.31516I 0.190328 − 0.743726I
u = −0.440574 − 0.756721I
a = 1.00000
b = 0.232862 − 1.365440I
1.47923 + 2.31516I 0.190328 + 0.743726I
u = 0.202451 + 1.186340I
a = 1.00000
b = −1.37277 − 0.52957I
−3.56765 + 4.49595I −1.80270 − 7.56758I
u = 0.202451 − 1.186340I
a = 1.00000
b = −1.37277 + 0.52957I
−3.56765 − 4.49595I −1.80270 + 7.56758I
u = −0.699025 + 0.302848I
a = 1.00000
b = −0.492780 − 1.057530I
4.51267 + 4.47073I 3.53570 − 1.33986I
u = −0.699025 − 0.302848I
a = 1.00000
b = −0.492780 + 1.057530I
4.51267 − 4.47073I 3.53570 + 1.33986I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.375582 + 1.259580I
a = 1.00000
b = −1.201050 + 0.354294I
2.08640 − 9.42284I 1.11756 + 6.83027I
u = −0.375582 − 1.259580I
a = 1.00000
b = −1.201050 − 0.354294I
2.08640 + 9.42284I 1.11756 − 6.83027I
u = 0.408516 + 1.337620I
a = 1.00000
b = −0.49290 − 1.67050I
−8.96137 + 5.23240I −4.36005 − 4.78438I
u = 0.408516 − 1.337620I
a = 1.00000
b = −0.49290 + 1.67050I
−8.96137 − 5.23240I −4.36005 + 4.78438I
u = −0.408610 + 0.359797I
a = 1.00000
b = −0.421704 + 0.476349I
0.735294 − 0.892872I 5.94617 + 4.93873I
u = −0.408610 − 0.359797I
a = 1.00000
b = −0.421704 − 0.476349I
0.735294 + 0.892872I 5.94617 − 4.93873I
u = 0.468145 + 0.007430I
a = 1.00000
b = −0.420259 − 0.946349I
−0.61105 + 2.59129I 5.45931 − 3.44339I
u = 0.468145 − 0.007430I
a = 1.00000
b = −0.420259 + 0.946349I
−0.61105 − 2.59129I 5.45931 + 3.44339I
u = −0.50268 + 1.47148I
a = 1.00000
b = −0.48500 + 1.56416I
−10.0188 − 10.9083I −4.45406 + 7.18292I
u = −0.50268 − 1.47148I
a = 1.00000
b = −0.48500 − 1.56416I
−10.0188 + 10.9083I −4.45406 − 7.18292I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.60013 + 1.53489I
a = 1.00000
b = −0.46789 − 1.52014I
−3.8405 + 15.3110I −0.76212 − 7.48531I
u = 0.60013 − 1.53489I
a = 1.00000
b = −0.46789 + 1.52014I
−3.8405 − 15.3110I −0.76212 + 7.48531I
7
II. I
u
2
=
h−2.11×10
9
u
17
+1.68×10
7
u
16
+· · ·+1.77×10
10
b−3.88×10
10
, 7.22×10
11
u
17
−
1.38 × 10
12
u
16
+ · · · + 1.29 × 10
13
a − 1.76 × 10
13
, u
18
+ 5u
16
+ · · · + 50u + 17i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
5
=
−0.0557665u
17
+ 0.106703u
16
+ ··· + 0.722131u + 1.35759
0.118916u
17
− 0.000946298u
16
+ ··· + 6.12291u + 2.19379
a
6
=
0.0631496u
17
+ 0.105757u
16
+ ··· + 6.84504u + 3.55139
0.118916u
17
− 0.000946298u
16
+ ··· + 6.12291u + 2.19379
a
10
=
0.130783u
17
− 0.0146315u
16
+ ··· + 6.70179u + 1.56799
0.0513201u
17
− 0.0379460u
16
+ ··· + 0.584746u − 1.26324
a
1
=
0.188268u
17
− 0.0221695u
16
+ ··· + 11.5572u + 3.70897
0.113960u
17
− 0.0734896u
16
+ ··· + 2.32962u − 0.591198
a
4
=
−0.107317u
17
+ 0.0530305u
16
+ ··· − 3.48734u − 0.130270
−0.0319178u
17
+ 0.00397222u
16
+ ··· − 1.09097u + 0.444642
a
8
=
−u
u
3
+ u
a
11
=
0.177385u
17
− 0.0241995u
16
+ ··· + 7.23582u + 1.00022
0.0170138u
17
+ 0.0119503u
16
+ ··· + 0.364535u − 0.858135
a
7
=
0.0390174u
17
+ 0.163125u
16
+ ··· + 11.0037u + 5.75564
0.0837045u
17
+ 0.0724798u
16
+ ··· + 9.54514u + 3.51844
a
7
=
0.0390174u
17
+ 0.163125u
16
+ ··· + 11.0037u + 5.75564
0.0837045u
17
+ 0.0724798u
16
+ ··· + 9.54514u + 3.51844
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
51417446992
761468178427
u
17
−
67393412288
761468178427
u
16
+ ··· +
1217139205928
761468178427
u +
1642023548414
761468178427
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
3
+ u
2
+ 2u + 1)
6
c
2
, c
4
, c
8
c
9
u
18
+ 5u
16
+ ··· − 50u + 17
c
3
, c
6
u
18
− 2u
17
+ ··· + 4u + 1
c
7
, c
10
, c
11
(u
3
+ 2u − 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
+ 3y
2
+ 2y −1)
6
c
2
, c
4
, c
8
c
9
y
18
+ 10y
17
+ ··· + 968y + 289
c
3
, c
6
y
18
+ 2y
17
+ ··· + 8y + 1
c
7
, c
10
, c
11
(y
3
+ 4y
2
+ 4y −1)
6
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.487685 + 0.847949I
a = 0.746708 + 0.050102I
b = 0.215080 + 1.307140I
1.48181 − 2.30982I −0.191821 + 0.229571I
u = −0.487685 − 0.847949I
a = 0.746708 − 0.050102I
b = 0.215080 − 1.307140I
1.48181 + 2.30982I −0.191821 − 0.229571I
u = 0.640673 + 0.946857I
a = −0.281235 + 0.667073I
b = 0.569840
5.61939 + 5.13794I 6.33744 − 3.20902I
u = 0.640673 − 0.946857I
a = −0.281235 − 0.667073I
b = 0.569840
5.61939 − 5.13794I 6.33744 + 3.20902I
u = −0.811802 + 0.161086I
a = −0.536626 − 1.272850I
b = 0.569840
5.61939 + 5.13794I 6.33744 − 3.20902I
u = −0.811802 − 0.161086I
a = −0.536626 + 1.272850I
b = 0.569840
5.61939 − 5.13794I 6.33744 + 3.20902I
u = −0.287016 + 1.229120I
a = −0.369488 − 1.198520I
b = 0.215080 − 1.307140I
1.48181 − 7.96606I −0.19182 + 6.18847I
u = −0.287016 − 1.229120I
a = −0.369488 + 1.198520I
b = 0.215080 + 1.307140I
1.48181 + 7.96606I −0.19182 − 6.18847I
u = −0.406642 + 0.608737I
a = 1.333210 − 0.089454I
b = 0.215080 + 1.307140I
1.48181 − 2.30982I −0.191821 + 0.229571I
u = −0.406642 − 0.608737I
a = 1.333210 + 0.089454I
b = 0.215080 − 1.307140I
1.48181 + 2.30982I −0.191821 − 0.229571I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.171130 + 1.267460I
a = −0.964193 − 0.265202I
b = 0.569840
−4.60855 −5.61636 + 0.I
u = 0.171130 − 1.267460I
a = −0.964193 + 0.265202I
b = 0.569840
−4.60855 −5.61636 + 0.I
u = 0.264938 + 1.312560I
a = −1.306010 + 0.241327I
b = 0.215080 + 1.307140I
−8.74613 + 2.82812I −12.14562 − 2.97945I
u = 0.264938 − 1.312560I
a = −1.306010 − 0.241327I
b = 0.215080 − 1.307140I
−8.74613 − 2.82812I −12.14562 + 2.97945I
u = 1.57917 + 0.11015I
a = −0.234896 − 0.761944I
b = 0.215080 + 1.307140I
1.48181 + 7.96606I −0.19182 − 6.18847I
u = 1.57917 − 0.11015I
a = −0.234896 + 0.761944I
b = 0.215080 − 1.307140I
1.48181 − 7.96606I −0.19182 + 6.18847I
u = −0.66277 + 1.65028I
a = −0.740410 + 0.136814I
b = 0.215080 − 1.307140I
−8.74613 − 2.82812I −12.14562 + 2.97945I
u = −0.66277 − 1.65028I
a = −0.740410 − 0.136814I
b = 0.215080 + 1.307140I
−8.74613 + 2.82812I −12.14562 − 2.97945I
12
III. I
u
3
= h6u
11
+ 12u
10
+ · · · + 11b + 19, a + 1, u
12
+ 6u
10
+ · · · + 4u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
5
=
−1
−0.545455u
11
− 1.09091u
10
+ ··· − 2.36364u − 1.72727
a
6
=
−0.545455u
11
− 1.09091u
10
+ ··· − 2.36364u − 2.72727
−0.545455u
11
− 1.09091u
10
+ ··· − 2.36364u − 1.72727
a
10
=
u
1.09091u
11
+ 0.181818u
10
+ ··· + 2.72727u − 0.545455
a
1
=
0.454545u
11
+ 1.90909u
10
+ ··· + 4.63636u + 4.27273
−0.0909091u
11
+ 0.818182u
10
+ ··· + 2.27273u + 1.54545
a
4
=
−u
2
− 1
−0.727273u
11
− 0.454545u
10
+ ··· − 1.81818u − 0.636364
a
8
=
−u
u
3
+ u
a
11
=
0.636364u
11
+ 0.272727u
10
+ ··· + 2.09091u + 0.181818
0.909091u
11
− 0.181818u
10
+ ··· + 2.27273u − 0.454545
a
7
=
−1.18182u
11
− 1.36364u
10
+ ··· − 3.45455u − 1.90909
−0.454545u
11
− 0.909091u
10
+ ··· − 1.63636u − 0.272727
a
7
=
−1.18182u
11
− 1.36364u
10
+ ··· − 3.45455u − 1.90909
−0.454545u
11
− 0.909091u
10
+ ··· − 1.63636u − 0.272727
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
68
11
u
11
+
26
11
u
10
+
394
11
u
9
+
174
11
u
8
+
939
11
u
7
+
368
11
u
6
+81u
5
+
144
11
u
4
+
163
11
u
3
−
183
11
u
2
−
17
11
u−
111
11
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ u
11
+ ··· + u + 2
c
2
, c
9
u
12
+ 6u
10
+ u
9
+ 15u
8
+ 4u
7
+ 17u
6
+ 6u
5
+ 9u
4
+ 4u
3
+ 4u
2
+ 1
c
3
, c
6
u
12
+ u
11
+ 7u
8
+ 8u
7
+ 2u
6
+ 7u
4
+ 7u
3
+ 3u
2
+ u + 1
c
4
, c
8
u
12
+ 6u
10
− u
9
+ 15u
8
− 4u
7
+ 17u
6
− 6u
5
+ 9u
4
− 4u
3
+ 4u
2
+ 1
c
5
u
12
− u
11
+ ··· − u + 2
c
7
u
12
− 2u
11
+ ··· + 5u
2
+ 1
c
10
, c
11
u
12
+ 2u
11
+ ··· + 5u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
12
+ 11y
11
+ ··· + 23y + 4
c
2
, c
4
, c
8
c
9
y
12
+ 12y
11
+ ··· + 8y + 1
c
3
, c
6
y
12
− y
11
+ ··· + 5y + 1
c
7
, c
10
, c
11
y
12
+ 14y
11
+ ··· + 10y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.353153 + 0.740023I
a = −1.00000
b = −0.68102 + 1.43177I
1.75746 + 2.66133I 12.8054 − 12.9695I
u = 0.353153 − 0.740023I
a = −1.00000
b = −0.68102 − 1.43177I
1.75746 − 2.66133I 12.8054 + 12.9695I
u = −0.584665 + 0.421028I
a = −1.00000
b = −0.304944 + 0.791823I
3.88659 − 5.94873I 0.46248 + 5.63778I
u = −0.584665 − 0.421028I
a = −1.00000
b = −0.304944 − 0.791823I
3.88659 + 5.94873I 0.46248 − 5.63778I
u = −0.064712 + 1.283160I
a = −1.00000
b = 0.542055 + 0.545095I
−1.86805 − 1.05670I −2.71042 + 0.18734I
u = −0.064712 − 1.283160I
a = −1.00000
b = 0.542055 − 0.545095I
−1.86805 + 1.05670I −2.71042 − 0.18734I
u = 0.201550 + 0.519773I
a = −1.00000
b = −0.483540 − 0.658126I
−1.60251 + 2.75174I −4.88343 − 6.08146I
u = 0.201550 − 0.519773I
a = −1.00000
b = −0.483540 + 0.658126I
−1.60251 − 2.75174I −4.88343 + 6.08146I
u = −0.42250 + 1.38326I
a = −1.00000
b = 0.250152 − 1.336200I
−7.83316 − 2.65596I −1.52426 + 0.93584I
u = −0.42250 − 1.38326I
a = −1.00000
b = 0.250152 + 1.336200I
−7.83316 + 2.65596I −1.52426 − 0.93584I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.51717 + 1.54995I
a = −1.00000
b = 0.177296 + 1.218930I
−4.20993 + 3.36477I −1.14978 − 1.06937I
u = 0.51717 − 1.54995I
a = −1.00000
b = 0.177296 − 1.218930I
−4.20993 − 3.36477I −1.14978 + 1.06937I
17
IV. I
u
4
= h−1.20 × 10
15
u
23
+ 6.60 × 10
15
u
22
+ · · · + 1.11 × 10
17
b + 2.38 ×
10
17
, 6.77 × 10
19
u
23
− 7.16 × 10
18
u
22
+ · · · + 7.49 × 10
20
a + 5.00 ×
10
21
, u
24
− u
23
+ · · · − 188u + 43i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
5
=
−0.0903265u
23
+ 0.00955690u
22
+ ··· + 16.8092u − 6.67385
0.0108028u
23
− 0.0594442u
22
+ ··· + 8.04468u − 2.14906
a
6
=
−0.0795237u
23
− 0.0498873u
22
+ ··· + 24.8539u − 8.82291
0.0108028u
23
− 0.0594442u
22
+ ··· + 8.04468u − 2.14906
a
10
=
−0.0548672u
23
− 0.158796u
22
+ ··· + 35.2329u − 8.35726
−0.162059u
23
+ 0.221193u
22
+ ··· − 5.49296u − 0.358870
a
1
=
−0.0246027u
23
− 0.123036u
22
+ ··· + 37.7004u − 9.02318
−0.0329485u
23
+ 0.0473687u
22
+ ··· + 5.64183u − 1.96121
a
4
=
0.249442u
23
− 0.673491u
22
+ ··· + 65.4921u − 13.1533
−0.127630u
23
− 0.280631u
22
+ ··· + 50.5898u − 11.2434
a
8
=
−u
u
3
+ u
a
11
=
−0.151470u
23
− 0.000506225u
22
+ ··· + 28.6722u − 7.97711
−0.193270u
23
+ 0.267635u
22
+ ··· − 14.6835u + 1.91355
a
7
=
0.274885u
23
− 0.492041u
22
+ ··· + 41.2304u − 8.05206
0.0166130u
23
− 0.260145u
22
+ ··· + 41.2683u − 8.45437
a
7
=
0.274885u
23
− 0.492041u
22
+ ··· + 41.2304u − 8.05206
0.0166130u
23
− 0.260145u
22
+ ··· + 41.2683u − 8.45437
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
901134440831258928
17419664957510598109
u
23
+
9229142131207094064
17419664957510598109
u
22
+ ··· −
158274106809001817232
17419664957510598109
u −
28047718789326057950
17419664957510598109
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
3
+ u
2
+ 2u + 1)
8
c
2
, c
4
, c
8
c
9
u
24
+ u
23
+ ··· + 188u + 43
c
3
, c
6
u
24
− 5u
23
+ ··· − 16u + 1
c
7
, c
10
, c
11
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
6
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
+ 3y
2
+ 2y −1)
8
c
2
, c
4
, c
8
c
9
y
24
+ 25y
23
+ ··· − 5588y + 1849
c
3
, c
6
y
24
− 7y
23
+ ··· − 64y + 1
c
7
, c
10
, c
11
(y
4
+ 3y
3
+ 2y
2
+ 1)
6
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.176624 + 1.067610I
a = −1.80748 − 0.07001I
b = 0.215080 − 1.307140I
−4.66906 − 0.79824I −3.50976 − 0.48465I
u = −0.176624 − 1.067610I
a = −1.80748 + 0.07001I
b = 0.215080 + 1.307140I
−4.66906 + 0.79824I −3.50976 + 0.48465I
u = −0.337989 + 0.848465I
a = −0.033948 − 0.493146I
b = 0.569840
−0.53148 − 2.02988I 3.01951 + 3.46410I
u = −0.337989 − 0.848465I
a = −0.033948 + 0.493146I
b = 0.569840
−0.53148 + 2.02988I 3.01951 − 3.46410I
u = −0.418722 + 1.110050I
a = −1.122680 + 0.469087I
b = 0.569840
−0.53148 − 2.02988I 3.01951 + 3.46410I
u = −0.418722 − 1.110050I
a = −1.122680 − 0.469087I
b = 0.569840
−0.53148 + 2.02988I 3.01951 − 3.46410I
u = 0.786120 + 0.023283I
a = 0.05462 − 1.60499I
b = 0.215080 + 1.307140I
−4.66906 + 0.79824I −3.50976 + 0.48465I
u = 0.786120 − 0.023283I
a = 0.05462 + 1.60499I
b = 0.215080 − 1.307140I
−4.66906 − 0.79824I −3.50976 − 0.48465I
u = −1.239540 + 0.226298I
a = −0.307239 + 0.978244I
b = 0.215080 − 1.307140I
−4.66906 − 4.85801I −3.50976 + 6.44355I
u = −1.239540 − 0.226298I
a = −0.307239 − 0.978244I
b = 0.215080 + 1.307140I
−4.66906 + 4.85801I −3.50976 − 6.44355I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.080309 + 1.260450I
a = 0.021180 − 0.622334I
b = 0.215080 − 1.307140I
−4.66906 − 0.79824I −3.50976 − 0.48465I
u = 0.080309 − 1.260450I
a = 0.021180 + 0.622334I
b = 0.215080 + 1.307140I
−4.66906 + 0.79824I −3.50976 + 0.48465I
u = 0.159459 + 1.282100I
a = −0.292231 + 0.930458I
b = 0.215080 + 1.307140I
−4.66906 + 4.85801I −3.50976 − 6.44355I
u = 0.159459 − 1.282100I
a = −0.292231 − 0.930458I
b = 0.215080 − 1.307140I
−4.66906 − 4.85801I −3.50976 + 6.44355I
u = −0.05062 + 1.44264I
a = −0.758336 + 0.316854I
b = 0.569840
−0.53148 + 2.02988I 3.01951 − 3.46410I
u = −0.05062 − 1.44264I
a = −0.758336 − 0.316854I
b = 0.569840
−0.53148 − 2.02988I 3.01951 + 3.46410I
u = −0.20056 + 1.44305I
a = −1.134580 − 0.586767I
b = 0.215080 − 1.307140I
−4.66906 − 4.85801I −3.50976 + 6.44355I
u = −0.20056 − 1.44305I
a = −1.134580 + 0.586767I
b = 0.215080 + 1.307140I
−4.66906 + 4.85801I −3.50976 − 6.44355I
u = 0.429892 + 0.137875I
a = −0.13893 + 2.01823I
b = 0.569840
−0.53148 − 2.02988I 3.01951 + 3.46410I
u = 0.429892 − 0.137875I
a = −0.13893 − 2.01823I
b = 0.569840
−0.53148 + 2.02988I 3.01951 − 3.46410I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.07429 + 1.51957I
a = −0.695394 − 0.359636I
b = 0.215080 + 1.307140I
−4.66906 + 4.85801I −3.50976 − 6.44355I
u = 1.07429 − 1.51957I
a = −0.695394 + 0.359636I
b = 0.215080 − 1.307140I
−4.66906 − 4.85801I −3.50976 + 6.44355I
u = 0.39398 + 1.91732I
a = −0.552427 − 0.021396I
b = 0.215080 + 1.307140I
−4.66906 + 0.79824I −3.50976 + 0.48465I
u = 0.39398 − 1.91732I
a = −0.552427 + 0.021396I
b = 0.215080 − 1.307140I
−4.66906 − 0.79824I −3.50976 − 0.48465I
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
+ 2u + 1)
14
)(u
12
+ u
11
+ ··· + u + 2)
· (u
22
− 14u
21
+ ··· − 1344u + 128)
c
2
, c
9
(u
12
+ 6u
10
+ u
9
+ 15u
8
+ 4u
7
+ 17u
6
+ 6u
5
+ 9u
4
+ 4u
3
+ 4u
2
+ 1)
· (u
18
+ 5u
16
+ ··· − 50u + 17)(u
22
+ 9u
20
+ ··· − 3u
2
+ 1)
· (u
24
+ u
23
+ ··· + 188u + 43)
c
3
, c
6
(u
12
+ u
11
+ 7u
8
+ 8u
7
+ 2u
6
+ 7u
4
+ 7u
3
+ 3u
2
+ u + 1)
· (u
18
− 2u
17
+ ··· + 4u + 1)(u
22
− u
21
+ ··· + 3u + 1)
· (u
24
− 5u
23
+ ··· − 16u + 1)
c
4
, c
8
(u
12
+ 6u
10
− u
9
+ 15u
8
− 4u
7
+ 17u
6
− 6u
5
+ 9u
4
− 4u
3
+ 4u
2
+ 1)
· (u
18
+ 5u
16
+ ··· − 50u + 17)(u
22
+ 9u
20
+ ··· − 3u
2
+ 1)
· (u
24
+ u
23
+ ··· + 188u + 43)
c
5
((u
3
+ u
2
+ 2u + 1)
14
)(u
12
− u
11
+ ··· − u + 2)
· (u
22
− 14u
21
+ ··· − 1344u + 128)
c
7
((u
3
+ 2u − 1)
6
)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
6
(u
12
− 2u
11
+ ··· + 5u
2
+ 1)
· (u
22
− 9u
21
+ ··· − 88u + 8)
c
10
, c
11
((u
3
+ 2u − 1)
6
)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
6
(u
12
+ 2u
11
+ ··· + 5u
2
+ 1)
· (u
22
− 9u
21
+ ··· − 88u + 8)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
3
+ 3y
2
+ 2y −1)
14
)(y
12
+ 11y
11
+ ··· + 23y + 4)
· (y
22
+ 14y
21
+ ··· + 20480y + 16384)
c
2
, c
4
, c
8
c
9
(y
12
+ 12y
11
+ ··· + 8y + 1)(y
18
+ 10y
17
+ ··· + 968y + 289)
· (y
22
+ 18y
21
+ ··· − 6y + 1)(y
24
+ 25y
23
+ ··· − 5588y + 1849)
c
3
, c
6
(y
12
− y
11
+ ··· + 5y + 1)(y
18
+ 2y
17
+ ··· + 8y + 1)
· (y
22
+ 5y
21
+ ··· + 11y + 1)(y
24
− 7y
23
+ ··· − 64y + 1)
c
7
, c
10
, c
11
(y
3
+ 4y
2
+ 4y −1)
6
(y
4
+ 3y
3
+ 2y
2
+ 1)
6
· (y
12
+ 14y
11
+ ··· + 10y + 1)(y
22
+ 21y
21
+ ··· + 224y + 64)
25
