12a
0079
(K12a
0079
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 10 12 4 11 6 1 7
Solving Sequence
7,12 3,8
4 9 1 2 5 11 10 6
c
7
c
3
c
8
c
12
c
1
c
4
c
11
c
9
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−37u
43
− 23u
42
+ ··· + 64b + 15, −81u
43
− 51u
42
+ ··· + 64a − 37, u
44
+ 11u
42
+ ··· − u + 1i
I
u
2
= h7.20931 × 10
43
u
71
+ 8.12549 × 10
43
u
70
+ ··· + 4.80383 × 10
43
b + 1.14427 × 10
45
,
3.81637 × 10
44
u
71
+ 4.59955 × 10
44
u
70
+ ··· + 8.16652 × 10
44
a + 1.32091 × 10
46
, u
72
+ 2u
71
+ ··· + 36u + 17i
I
u
3
= h−u
3
+ u
2
+ 2b + 1, −u
3
− u
2
+ 2a − 2u + 1, u
4
+ u
2
− u + 1i
I
u
4
= h−a
2
− 2au + 2b − 2u, a
3
+ 2a
2
u + 2a
2
+ 2au + 2u − 2, u
2
+ 1i
I
u
5
= h−u
4
− u
3
− u
2
+ b − u − 1, −u
5
− u
3
− u
2
+ a − u − 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
* 5 irreducible components of dim
C
= 0, with total 132 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−37u
43
− 23u
42
+ · · · + 64b + 15, −81u
43
− 51u
42
+ · · · + 64a −
37, u
44
+ 11u
42
+ · · · − u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
1.26563u
43
+ 0.796875u
42
+ ··· − 0.218750u + 0.578125
0.578125u
43
+ 0.359375u
42
+ ··· + 1.28125u − 0.234375
a
8
=
1
u
2
a
4
=
2.45313u
43
+ 1.48438u
42
+ ··· + 1.53125u + 1.14063
0.765625u
43
− 0.203125u
42
+ ··· + 0.781250u − 0.921875
a
9
=
−
1
8
u
42
−
5
4
u
40
+ ··· −
7
8
u −
1
8
−u
5
− u
3
− u
a
1
=
−u
u
a
2
=
−0.140625u
43
− 0.0468750u
42
+ ··· − 2.15625u − 0.578125
−0.140625u
43
+ 0.328125u
42
+ ··· − 0.0312500u + 0.0468750
a
5
=
−
1
8
u
43
−
5
4
u
41
+ ··· −
1
8
u + 1
u
8
+ 2u
6
+ 2u
4
a
11
=
−u
3
u
3
+ u
a
10
=
−
1
8
u
42
−
5
4
u
40
+ ··· −
7
8
u −
1
8
−u
a
6
=
−
1
8
u
43
−
5
4
u
41
+ ··· −
1
8
u + 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
237
128
u
43
+
161
128
u
42
+ ··· −
897
64
u +
503
128
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 19u
43
+ ··· + 97u + 16
c
2
, c
4
u
44
− 5u
43
+ ··· − 5u + 4
c
3
, c
8
u
44
+ 3u
43
+ ··· + 368u + 64
c
5
u
44
− 6u
43
+ ··· + 256u + 256
c
6
, c
7
, c
10
c
12
u
44
+ 11u
42
+ ··· − u + 1
c
9
, c
11
u
44
− 22u
43
+ ··· − 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
+ 17y
43
+ ··· + 16607y + 256
c
2
, c
4
y
44
− 19y
43
+ ··· − 97y + 16
c
3
, c
8
y
44
− 27y
43
+ ··· − 41216y + 4096
c
5
y
44
− 26y
43
+ ··· + 950272y + 65536
c
6
, c
7
, c
10
c
12
y
44
+ 22y
43
+ ··· + 5y + 1
c
9
, c
11
y
44
+ 10y
43
+ ··· + 13y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.702421 + 0.710564I
a = −1.287360 + 0.247682I
b = 1.17050 + 0.88517I
−2.39002 − 0.58411I −3.85735 + 0.95240I
u = −0.702421 − 0.710564I
a = −1.287360 − 0.247682I
b = 1.17050 − 0.88517I
−2.39002 + 0.58411I −3.85735 − 0.95240I
u = 0.541516 + 0.820982I
a = 0.98705 + 1.86895I
b = −1.263540 − 0.356717I
−2.85868 − 3.18935I −4.19435 + 7.32491I
u = 0.541516 − 0.820982I
a = 0.98705 − 1.86895I
b = −1.263540 + 0.356717I
−2.85868 + 3.18935I −4.19435 − 7.32491I
u = −0.557234 + 0.884832I
a = −0.648682 + 1.028180I
b = 1.88818 − 0.70589I
−2.41767 + 5.64663I −4.29082 − 7.41369I
u = −0.557234 − 0.884832I
a = −0.648682 − 1.028180I
b = 1.88818 + 0.70589I
−2.41767 − 5.64663I −4.29082 + 7.41369I
u = −0.721004 + 0.533121I
a = 1.084590 + 0.670648I
b = −0.088037 − 0.937684I
−1.95150 + 2.85445I −3.41509 − 7.01559I
u = −0.721004 − 0.533121I
a = 1.084590 − 0.670648I
b = −0.088037 + 0.937684I
−1.95150 − 2.85445I −3.41509 + 7.01559I
u = 0.244276 + 0.862218I
a = −0.915850 − 0.492227I
b = −0.586924 + 0.069748I
5.65660 − 4.11751I 1.23792 + 9.55977I
u = 0.244276 − 0.862218I
a = −0.915850 + 0.492227I
b = −0.586924 − 0.069748I
5.65660 + 4.11751I 1.23792 − 9.55977I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.544223 + 0.973766I
a = −0.278642 − 1.322870I
b = 0.697971 + 1.101770I
1.52721 − 6.41039I 1.82640 + 7.81068I
u = 0.544223 − 0.973766I
a = −0.278642 + 1.322870I
b = 0.697971 − 1.101770I
1.52721 + 6.41039I 1.82640 − 7.81068I
u = −0.442356 + 0.755964I
a = 0.482101 − 0.625125I
b = −0.874574 + 0.696057I
−0.20950 + 1.79654I −1.30424 − 3.42560I
u = −0.442356 − 0.755964I
a = 0.482101 + 0.625125I
b = −0.874574 − 0.696057I
−0.20950 − 1.79654I −1.30424 + 3.42560I
u = 0.832803 + 0.215660I
a = 0.75668 + 1.33967I
b = −1.233260 + 0.537697I
1.44514 + 7.55819I −3.62079 − 4.72412I
u = 0.832803 − 0.215660I
a = 0.75668 − 1.33967I
b = −1.233260 − 0.537697I
1.44514 − 7.55819I −3.62079 + 4.72412I
u = 0.649723 + 0.968222I
a = −0.18195 + 1.78717I
b = −1.09227 − 1.73252I
−0.80144 − 11.01560I −2.00000 + 10.95786I
u = 0.649723 − 0.968222I
a = −0.18195 − 1.78717I
b = −1.09227 + 1.73252I
−0.80144 + 11.01560I −2.00000 − 10.95786I
u = 0.176389 + 0.813834I
a = 0.934275 + 0.229215I
b = 0.760943 + 0.376418I
5.40728 + 1.98799I −0.95684 + 3.34899I
u = 0.176389 − 0.813834I
a = 0.934275 − 0.229215I
b = 0.760943 − 0.376418I
5.40728 − 1.98799I −0.95684 − 3.34899I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.797934 + 0.136440I
a = −0.612709 − 0.824826I
b = 1.050600 − 0.288526I
3.34091 + 1.92831I −0.894274 − 0.474213I
u = 0.797934 − 0.136440I
a = −0.612709 + 0.824826I
b = 1.050600 + 0.288526I
3.34091 − 1.92831I −0.894274 + 0.474213I
u = −0.417301 + 1.171170I
a = −0.422635 + 0.232582I
b = −0.687150 + 0.658493I
9.45367 + 0.05362I 4.61954 − 1.87073I
u = −0.417301 − 1.171170I
a = −0.422635 − 0.232582I
b = −0.687150 − 0.658493I
9.45367 − 0.05362I 4.61954 + 1.87073I
u = 0.578501 + 1.115170I
a = 0.465998 − 0.498361I
b = −0.439910 + 0.963467I
1.63069 − 7.23684I 5.33785 + 2.87723I
u = 0.578501 − 1.115170I
a = 0.465998 + 0.498361I
b = −0.439910 − 0.963467I
1.63069 + 7.23684I 5.33785 − 2.87723I
u = 0.487023 + 1.174590I
a = −0.758113 − 0.569228I
b = 1.45662 + 0.94452I
5.00692 − 6.15874I 2.59172 + 3.93805I
u = 0.487023 − 1.174590I
a = −0.758113 + 0.569228I
b = 1.45662 − 0.94452I
5.00692 + 6.15874I 2.59172 − 3.93805I
u = −0.447381 + 1.195090I
a = 0.562721 − 0.572930I
b = 0.165779 − 0.146697I
10.86750 + 6.35684I 6.13401 − 6.10559I
u = −0.447381 − 1.195090I
a = 0.562721 + 0.572930I
b = 0.165779 + 0.146697I
10.86750 − 6.35684I 6.13401 + 6.10559I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.512554 + 1.180140I
a = −1.39016 + 1.09028I
b = 1.81341 + 0.28882I
3.05902 + 8.57495I 0. − 6.88977I
u = −0.512554 − 1.180140I
a = −1.39016 − 1.09028I
b = 1.81341 − 0.28882I
3.05902 − 8.57495I 0. + 6.88977I
u = 0.523499 + 1.198030I
a = 0.956798 + 0.395110I
b = −1.94303 − 0.43216I
4.40755 − 11.25480I 0. + 8.58519I
u = 0.523499 − 1.198030I
a = 0.956798 − 0.395110I
b = −1.94303 + 0.43216I
4.40755 + 11.25480I 0. − 8.58519I
u = −0.665201 + 0.175880I
a = 0.29757 + 1.73222I
b = 0.213621 − 0.295527I
−1.46430 − 1.85279I −5.99718 + 2.24487I
u = −0.665201 − 0.175880I
a = 0.29757 − 1.73222I
b = 0.213621 + 0.295527I
−1.46430 + 1.85279I −5.99718 − 2.24487I
u = −0.527362 + 1.224400I
a = 0.83924 − 1.57599I
b = −1.67956 + 1.31887I
9.7294 + 11.8297I 0
u = −0.527362 − 1.224400I
a = 0.83924 + 1.57599I
b = −1.67956 − 1.31887I
9.7294 − 11.8297I 0
u = −0.550329 + 1.227230I
a = −0.86593 + 1.85592I
b = 2.23259 − 1.75027I
7.5382 + 17.9201I 0
u = −0.550329 − 1.227230I
a = −0.86593 − 1.85592I
b = 2.23259 + 1.75027I
7.5382 − 17.9201I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.327143 + 0.524057I
a = 0.410580 − 0.825478I
b = −0.146771 + 0.642611I
−0.272632 + 1.272590I −2.20676 − 6.23144I
u = −0.327143 − 0.524057I
a = 0.410580 + 0.825478I
b = −0.146771 − 0.642611I
−0.272632 − 1.272590I −2.20676 + 6.23144I
u = 0.494397 + 0.271698I
a = −1.16558 + 1.11171I
b = −1.165190 − 0.400869I
−2.42152 − 0.21458I −4.60274 − 1.73756I
u = 0.494397 − 0.271698I
a = −1.16558 − 1.11171I
b = −1.165190 + 0.400869I
−2.42152 + 0.21458I −4.60274 + 1.73756I
9
II. I
u
2
=
h7.21×10
43
u
71
+8.13×10
43
u
70
+· · ·+4.80×10
43
b+1.14×10
45
, 3.82×10
44
u
71
+
4.60 × 10
44
u
70
+ · · · + 8.17 × 10
44
a + 1.32 × 10
46
, u
72
+ 2u
71
+ · · · + 36u + 17i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
−0.467319u
71
− 0.563220u
70
+ ··· − 14.2494u − 16.1748
−1.50074u
71
− 1.69146u
70
+ ··· − 17.9037u − 23.8200
a
8
=
1
u
2
a
4
=
−1.25930u
71
− 1.57923u
70
+ ··· − 26.7265u − 33.6806
−1.70682u
71
− 1.97705u
70
+ ··· − 24.8865u − 33.4752
a
9
=
−1.00551u
71
− 1.34156u
70
+ ··· − 23.0730u − 26.3589
0.279157u
71
+ 0.474972u
70
+ ··· + 8.92590u + 6.88474
a
1
=
−u
u
a
2
=
0.895599u
71
+ 1.36883u
70
+ ··· + 19.3192u + 14.3574
1.42522u
71
+ 1.78940u
70
+ ··· + 23.2939u + 40.2087
a
5
=
−0.117896u
71
− 0.0392528u
70
+ ··· − 2.09819u − 6.93997
1.19235u
71
+ 1.44737u
70
+ ··· + 18.2425u + 29.6873
a
11
=
−u
3
u
3
+ u
a
10
=
−1.56516u
71
− 2.10935u
70
+ ··· − 32.8257u − 36.3231
1.50634u
71
+ 1.99171u
70
+ ··· + 28.8257u + 34.2054
a
6
=
0.991116u
71
+ 1.14343u
70
+ ··· + 12.9794u + 18.0016
1.02097u
71
+ 1.37440u
70
+ ··· + 20.0227u + 26.6077
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.80981u
71
− 4.48043u
70
+ ··· − 78.5168u − 56.1900
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
36
+ 16u
35
+ ··· + 24u + 1)
2
c
2
, c
4
(u
36
− 4u
35
+ ··· + 8u − 1)
2
c
3
, c
8
(u
36
− u
35
+ ··· − 12u + 8)
2
c
5
(u
36
+ 2u
35
+ ··· − 19u − 17)
2
c
6
, c
7
, c
10
c
12
u
72
+ 2u
71
+ ··· + 36u + 17
c
9
, c
11
u
72
− 42u
71
+ ··· − 1016u + 289
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
36
+ 12y
35
+ ··· − 516y + 1)
2
c
2
, c
4
(y
36
− 16y
35
+ ··· − 24y + 1)
2
c
3
, c
8
(y
36
− 21y
35
+ ··· − 784y + 64)
2
c
5
(y
36
− 26y
35
+ ··· + 2461y + 289)
2
c
6
, c
7
, c
10
c
12
y
72
+ 42y
71
+ ··· + 1016y + 289
c
9
, c
11
y
72
− 26y
71
+ ··· − 1428764y + 83521
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.409149 + 0.888281I
a = 1.70792 − 1.42545I
b = −1.04226 + 2.02155I
4.75623 + 0.53351I 3.64819 + 0.I
u = 0.409149 − 0.888281I
a = 1.70792 + 1.42545I
b = −1.04226 − 2.02155I
4.75623 − 0.53351I 3.64819 + 0.I
u = −0.455168 + 0.847626I
a = 0.212523 − 1.097530I
b = −0.370366 + 0.906924I
0.05729 + 1.97104I −0.62656 − 3.58123I
u = −0.455168 − 0.847626I
a = 0.212523 + 1.097530I
b = −0.370366 − 0.906924I
0.05729 − 1.97104I −0.62656 + 3.58123I
u = 0.755491 + 0.560366I
a = 1.238410 + 0.681717I
b = −1.25454 + 0.72755I
−1.98700 + 5.74916I −4.01965 − 6.40491I
u = 0.755491 − 0.560366I
a = 1.238410 − 0.681717I
b = −1.25454 − 0.72755I
−1.98700 − 5.74916I −4.01965 + 6.40491I
u = −0.659290 + 0.847574I
a = 0.60077 + 1.61013I
b = 0.63373 − 1.62428I
−1.98700 + 5.74916I 0
u = −0.659290 − 0.847574I
a = 0.60077 − 1.61013I
b = 0.63373 + 1.62428I
−1.98700 − 5.74916I 0
u = −0.910210 + 0.166809I
a = −0.590692 + 1.275390I
b = 1.198450 + 0.543963I
4.33227 − 12.63140I −0.57875 + 8.03158I
u = −0.910210 − 0.166809I
a = −0.590692 − 1.275390I
b = 1.198450 − 0.543963I
4.33227 + 12.63140I −0.57875 − 8.03158I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.228178 + 1.075270I
a = −0.104567 − 0.878124I
b = 0.096051 + 0.918252I
4.07897 0
u = 0.228178 − 1.075270I
a = −0.104567 + 0.878124I
b = 0.096051 − 0.918252I
4.07897 0
u = −0.881164 + 0.129616I
a = 0.512396 − 0.784455I
b = −1.113380 − 0.271093I
6.43964 − 6.72875I 2.21840 + 3.94329I
u = −0.881164 − 0.129616I
a = 0.512396 + 0.784455I
b = −1.113380 + 0.271093I
6.43964 + 6.72875I 2.21840 − 3.94329I
u = 0.534292 + 0.706507I
a = 0.243547 + 1.316740I
b = −1.67125 − 0.77862I
−3.18873 − 1.16610I −6.74685 + 0.24767I
u = 0.534292 − 0.706507I
a = 0.243547 − 1.316740I
b = −1.67125 + 0.77862I
−3.18873 + 1.16610I −6.74685 − 0.24767I
u = −0.045170 + 1.119970I
a = 1.55994 − 1.48818I
b = −1.83564 + 2.24406I
1.63239 − 0.63628I 0
u = −0.045170 − 1.119970I
a = 1.55994 + 1.48818I
b = −1.83564 − 2.24406I
1.63239 + 0.63628I 0
u = 0.791769 + 0.369472I
a = −0.900892 + 0.256022I
b = 0.168348 − 0.537368I
−0.58092 + 2.11524I 0.291403 + 1.121671I
u = 0.791769 − 0.369472I
a = −0.900892 − 0.256022I
b = 0.168348 + 0.537368I
−0.58092 − 2.11524I 0.291403 − 1.121671I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.112400 + 0.841063I
a = −1.51856 + 3.83928I
b = 2.04934 − 2.91850I
1.63239 + 0.63628I −7.12504 − 1.61784I
u = −0.112400 − 0.841063I
a = −1.51856 − 3.83928I
b = 2.04934 + 2.91850I
1.63239 − 0.63628I −7.12504 + 1.61784I
u = −0.581173 + 0.999377I
a = −0.773782 − 0.567783I
b = 0.611840 + 1.138310I
−0.58092 + 2.11524I 0
u = −0.581173 − 0.999377I
a = −0.773782 + 0.567783I
b = 0.611840 − 1.138310I
−0.58092 − 2.11524I 0
u = 0.828510 + 0.154792I
a = −0.19112 + 1.52316I
b = −0.180527 − 0.134893I
1.31256 + 6.30262I −1.69943 − 5.66674I
u = 0.828510 − 0.154792I
a = −0.19112 − 1.52316I
b = −0.180527 + 0.134893I
1.31256 − 6.30262I −1.69943 + 5.66674I
u = −0.561309 + 0.609175I
a = −0.51140 + 2.05101I
b = 0.806153 − 0.446308I
−3.18873 − 1.16610I −6.74685 + 0.24767I
u = −0.561309 − 0.609175I
a = −0.51140 − 2.05101I
b = 0.806153 + 0.446308I
−3.18873 + 1.16610I −6.74685 − 0.24767I
u = 0.407068 + 0.708583I
a = −2.07466 + 2.08069I
b = 0.60334 − 2.22141I
4.19715 − 4.09703I 1.30644 + 6.77310I
u = 0.407068 − 0.708583I
a = −2.07466 − 2.08069I
b = 0.60334 + 2.22141I
4.19715 + 4.09703I 1.30644 − 6.77310I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.410573 + 1.128750I
a = 0.771523 − 0.647562I
b = −1.37966 + 1.04264I
1.93253 + 1.63914I 0
u = −0.410573 − 1.128750I
a = 0.771523 + 0.647562I
b = −1.37966 − 1.04264I
1.93253 − 1.63914I 0
u = −0.777062 + 0.158927I
a = 0.704276 + 0.326097I
b = 1.45389 − 0.15969I
0.06849 − 3.79621I −0.47580 + 4.06401I
u = −0.777062 − 0.158927I
a = 0.704276 − 0.326097I
b = 1.45389 + 0.15969I
0.06849 + 3.79621I −0.47580 − 4.06401I
u = 0.465720 + 1.120490I
a = 1.51946 + 1.22973I
b = −1.89566 + 0.13420I
0.06849 − 3.79621I 0
u = 0.465720 − 1.120490I
a = 1.51946 − 1.22973I
b = −1.89566 − 0.13420I
0.06849 + 3.79621I 0
u = −0.763968 + 0.014323I
a = 0.524811 − 1.023410I
b = −1.076360 − 0.366532I
7.37183 + 2.02960I 3.16240 − 2.61607I
u = −0.763968 − 0.014323I
a = 0.524811 + 1.023410I
b = −1.076360 + 0.366532I
7.37183 − 2.02960I 3.16240 + 2.61607I
u = −0.370509 + 1.188210I
a = −1.75509 + 0.96312I
b = 2.15450 + 0.31778I
4.05359 0
u = −0.370509 − 1.188210I
a = −1.75509 − 0.96312I
b = 2.15450 − 0.31778I
4.05359 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.411287 + 1.177490I
a = 1.217730 + 0.365979I
b = −2.06128 − 0.33109I
5.54767 − 2.29689I 0
u = 0.411287 − 1.177490I
a = 1.217730 − 0.365979I
b = −2.06128 + 0.33109I
5.54767 + 2.29689I 0
u = −0.492711 + 1.148580I
a = −1.035490 + 0.488094I
b = 2.00387 − 0.44833I
1.31256 + 6.30262I 0
u = −0.492711 − 1.148580I
a = −1.035490 − 0.488094I
b = 2.00387 + 0.44833I
1.31256 − 6.30262I 0
u = 0.037461 + 1.251950I
a = 0.441175 − 0.103555I
b = 0.424615 + 0.528208I
4.19715 + 4.09703I 0
u = 0.037461 − 1.251950I
a = 0.441175 + 0.103555I
b = 0.424615 − 0.528208I
4.19715 − 4.09703I 0
u = 0.309956 + 1.214780I
a = 0.432531 + 0.143154I
b = 0.611055 + 0.634446I
5.93992 + 3.86936I 0
u = 0.309956 − 1.214780I
a = 0.432531 − 0.143154I
b = 0.611055 − 0.634446I
5.93992 − 3.86936I 0
u = 0.133945 + 1.249350I
a = −0.423831 − 0.310303I
b = −0.258882 + 0.442938I
4.75623 − 0.53351I 0
u = 0.133945 − 1.249350I
a = −0.423831 + 0.310303I
b = −0.258882 − 0.442938I
4.75623 + 0.53351I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.375140 + 1.206170I
a = −0.563016 − 0.541789I
b = −0.1299830 − 0.0395878I
7.37183 − 2.02960I 0
u = 0.375140 − 1.206170I
a = −0.563016 + 0.541789I
b = −0.1299830 + 0.0395878I
7.37183 + 2.02960I 0
u = −0.482731 + 1.167840I
a = −0.86793 + 2.26662I
b = 2.23105 − 2.18148I
8.98461 + 8.30646I 0
u = −0.482731 − 1.167840I
a = −0.86793 − 2.26662I
b = 2.23105 + 2.18148I
8.98461 − 8.30646I 0
u = 0.727286 + 0.101479I
a = −0.46105 − 1.37059I
b = 0.036653 + 0.262952I
1.93253 + 1.63914I −0.522063 − 0.383588I
u = 0.727286 − 0.101479I
a = −0.46105 + 1.37059I
b = 0.036653 − 0.262952I
1.93253 − 1.63914I −0.522063 + 0.383588I
u = 0.362076 + 1.228520I
a = −0.884432 − 0.604137I
b = 1.53193 + 1.11081I
5.54767 + 2.29689I 0
u = 0.362076 − 1.228520I
a = −0.884432 + 0.604137I
b = 1.53193 − 1.11081I
5.54767 − 2.29689I 0
u = −0.456591 + 1.196920I
a = 0.84132 − 1.84000I
b = −1.69455 + 1.68616I
10.80280 + 2.38075I 0
u = −0.456591 − 1.196920I
a = 0.84132 + 1.84000I
b = −1.69455 − 1.68616I
10.80280 − 2.38075I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.566008 + 0.431209I
a = −0.514563 − 0.449521I
b = 0.735432 + 0.198154I
0.05729 + 1.97104I −0.62656 − 3.58123I
u = 0.566008 − 0.431209I
a = −0.514563 + 0.449521I
b = 0.735432 − 0.198154I
0.05729 − 1.97104I −0.62656 + 3.58123I
u = −0.702958 + 0.092048I
a = −0.64196 + 1.78168I
b = 1.234370 + 0.442175I
5.93992 − 3.86936I 1.24553 + 2.32285I
u = −0.702958 − 0.092048I
a = −0.64196 − 1.78168I
b = 1.234370 − 0.442175I
5.93992 + 3.86936I 1.24553 − 2.32285I
u = 0.508850 + 1.189940I
a = −0.75750 − 1.66176I
b = 1.56542 + 1.44723I
6.43964 − 6.72875I 0
u = 0.508850 − 1.189940I
a = −0.75750 + 1.66176I
b = 1.56542 − 1.44723I
6.43964 + 6.72875I 0
u = 0.544890 + 1.184880I
a = 0.74938 + 1.98359I
b = −2.10683 − 1.88484I
4.33227 − 12.63140I 0
u = 0.544890 − 1.184880I
a = 0.74938 − 1.98359I
b = −2.10683 + 1.88484I
4.33227 + 12.63140I 0
u = −0.380779 + 1.271410I
a = 0.541111 − 0.546274I
b = 0.0212990 − 0.0734012I
10.80280 − 2.38075I 0
u = −0.380779 − 1.271410I
a = 0.541111 + 0.546274I
b = 0.0212990 + 0.0734012I
10.80280 + 2.38075I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.353308 + 1.294920I
a = −0.365915 + 0.150791I
b = −0.600175 + 0.697735I
8.98461 − 8.30646I 0
u = −0.353308 − 1.294920I
a = −0.365915 − 0.150791I
b = −0.600175 − 0.697735I
8.98461 + 8.30646I 0
20
III. I
u
3
= h−u
3
+ u
2
+ 2b + 1, −u
3
− u
2
+ 2a − 2u + 1, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
1
2
u
3
+
1
2
u
2
+ u −
1
2
1
2
u
3
−
1
2
u
2
−
1
2
a
8
=
1
u
2
a
4
=
1
2
u
3
+
1
2
u
2
+ u −
1
2
1
2
u
3
−
1
2
u
2
−
1
2
a
9
=
1
u
2
a
1
=
−u
u
a
2
=
1
2
u
3
+
1
2
u
2
−
1
2
1
2
u
3
−
1
2
u
2
+ u −
1
2
a
5
=
u
−u
a
11
=
−u
3
u
3
+ u
a
10
=
−u
3
+ u
2
− u + 1
u
a
6
=
−u
3
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
11
4
u
3
+
21
4
u
2
−
1
2
u −
17
4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
u
4
− 3u
3
+ 4u
2
− 3u + 2
c
6
, c
7
u
4
+ u
2
− u + 1
c
9
, c
11
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
10
, c
12
u
4
+ u
2
+ u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
8
y
4
c
5
y
4
− y
3
+ 2y
2
+ 7y + 4
c
6
, c
7
, c
10
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
9
, c
11
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −0.173850 + 1.069070I
b = −0.677958 − 0.157780I
−2.62503 − 1.39709I −5.84901 + 3.96898I
u = 0.547424 − 0.585652I
a = −0.173850 − 1.069070I
b = −0.677958 + 0.157780I
−2.62503 + 1.39709I −5.84901 − 3.96898I
u = −0.547424 + 1.120870I
a = −0.576150 + 0.307015I
b = 0.927958 + 0.413327I
0.98010 + 7.64338I −3.77599 − 8.10462I
u = −0.547424 − 1.120870I
a = −0.576150 − 0.307015I
b = 0.927958 − 0.413327I
0.98010 − 7.64338I −3.77599 + 8.10462I
24
IV. I
u
4
= h−a
2
− 2au + 2b − 2u, a
3
+ 2a
2
u + 2a
2
+ 2au + 2u − 2, u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
a
1
2
a
2
+ au + u
a
8
=
1
−1
a
4
=
1
2
a
2
+ au + 2a + u
−a
a
9
=
−
1
2
a
2
u −
1
2
au +
1
2
a + u − 1
−u
a
1
=
−u
u
a
2
=
−2u − 1
1
2
a
2
+
1
2
au +
1
2
a + u + 1
a
5
=
1
2
a
2
+
1
2
au +
1
2
a − u − 1
1
a
11
=
u
0
a
10
=
−
1
2
a
2
u −
1
2
au +
1
2
a + 2u − 1
−u
a
6
=
1
2
a
2
+
1
2
au +
1
2
a − u − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2au + 2a + 8
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
, c
8
u
6
− 3u
4
+ 2u
2
+ 1
c
4
(u
3
− u
2
+ 1)
2
c
5
u
6
c
6
, c
7
, c
10
c
12
(u
2
+ 1)
3
c
9
, c
11
(u + 1)
6
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
3
, c
8
(y
3
− 3y
2
+ 2y + 1)
2
c
5
y
6
c
6
, c
7
, c
10
c
12
(y + 1)
6
c
9
, c
11
(y −1)
6
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.867423 + 0.622301I
b = −0.439718 − 0.407221I
6.31400 + 2.82812I 7.50976 − 2.97945I
u = 1.000000I
a = 0.622301 − 0.867423I
b = 0.684841 + 1.082500I
6.31400 − 2.82812I 7.50976 + 2.97945I
u = 1.000000I
a = −1.75488 − 1.75488I
b = 1.75488 + 2.32472I
2.17641 − 60.980489 + 0.10I
u = − 1.000000I
a = −0.867423 − 0.622301I
b = −0.439718 + 0.407221I
6.31400 − 2.82812I 7.50976 + 2.97945I
u = − 1.000000I
a = 0.622301 + 0.867423I
b = 0.684841 − 1.082500I
6.31400 + 2.82812I 7.50976 − 2.97945I
u = − 1.000000I
a = −1.75488 + 1.75488I
b = 1.75488 − 2.32472I
2.17641 − 60.980489 + 0.10I
28
V. I
u
5
= h−u
4
− u
3
− u
2
+ b − u − 1, −u
5
− u
3
− u
2
+ a − u − 1, u
6
+ u
5
+
2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
u
5
+ u
3
+ u
2
+ u + 1
u
4
+ u
3
+ u
2
+ u + 1
a
8
=
1
u
2
a
4
=
u
5
+ u
3
+ u
2
+ u + 1
u
4
+ u
3
+ u
2
+ u + 1
a
9
=
1
u
2
a
1
=
−u
u
a
2
=
u
5
+ u
3
+ u
2
+ 1
u
4
+ u
3
+ u
2
+ 2u + 1
a
5
=
u
−u
a
11
=
−u
3
u
3
+ u
a
10
=
u
4
+ u
2
+ u + 1
u
5
+ 2u
3
+ u
2
+ u + 1
a
6
=
−u
3
−u
5
− u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
5
+ 5u
3
+ u
2
+ 5u − 2
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
u
6
c
4
(u + 1)
6
c
5
(u
3
+ u
2
− 1)
2
c
6
, c
7
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
9
, c
11
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
10
, c
12
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
8
y
6
c
5
(y
3
− y
2
+ 2y −1)
2
c
6
, c
7
, c
10
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
9
, c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = 0.662359 + 0.562280I
b = −1.060970 + 0.237841I
−1.37919 − 2.82812I −5.84740 + 3.54173I
u = 0.498832 − 1.001300I
a = 0.662359 − 0.562280I
b = −1.060970 − 0.237841I
−1.37919 + 2.82812I −5.84740 − 3.54173I
u = −0.284920 + 1.115140I
a = −1.32472
b = 1.53980 + 0.84179I
2.75839 −6 − 1.305207 + 0.10I
u = −0.284920 − 1.115140I
a = −1.32472
b = 1.53980 − 0.84179I
2.75839 −6 − 1.305207 + 0.10I
u = −0.713912 + 0.305839I
a = 0.662359 + 0.562280I
b = 0.521167 − 0.055259I
−1.37919 − 2.82812I −5.84740 + 3.54173I
u = −0.713912 − 0.305839I
a = 0.662359 − 0.562280I
b = 0.521167 + 0.055259I
−1.37919 + 2.82812I −5.84740 − 3.54173I
32
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
3
− u
2
+ 2u − 1)
2
(u
36
+ 16u
35
+ ··· + 24u + 1)
2
· (u
44
+ 19u
43
+ ··· + 97u + 16)
c
2
((u − 1)
10
)(u
3
+ u
2
− 1)
2
(u
36
− 4u
35
+ ··· + 8u − 1)
2
· (u
44
− 5u
43
+ ··· − 5u + 4)
c
3
, c
8
u
10
(u
6
− 3u
4
+ 2u
2
+ 1)(u
36
− u
35
+ ··· − 12u + 8)
2
· (u
44
+ 3u
43
+ ··· + 368u + 64)
c
4
((u + 1)
10
)(u
3
− u
2
+ 1)
2
(u
36
− 4u
35
+ ··· + 8u − 1)
2
· (u
44
− 5u
43
+ ··· − 5u + 4)
c
5
u
6
(u
3
+ u
2
− 1)
2
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
· ((u
36
+ 2u
35
+ ··· − 19u − 17)
2
)(u
44
− 6u
43
+ ··· + 256u + 256)
c
6
, c
7
(u
2
+ 1)
3
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
44
+ 11u
42
+ ··· − u + 1)(u
72
+ 2u
71
+ ··· + 36u + 17)
c
9
, c
11
(u + 1)
6
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
44
− 22u
43
+ ··· − 5u + 1)(u
72
− 42u
71
+ ··· − 1016u + 289)
c
10
, c
12
(u
2
+ 1)
3
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
44
+ 11u
42
+ ··· − u + 1)(u
72
+ 2u
71
+ ··· + 36u + 17)
33
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
3
+ 3y
2
+ 2y −1)
2
(y
36
+ 12y
35
+ ··· − 516y + 1)
2
· (y
44
+ 17y
43
+ ··· + 16607y + 256)
c
2
, c
4
((y −1)
10
)(y
3
− y
2
+ 2y −1)
2
(y
36
− 16y
35
+ ··· − 24y + 1)
2
· (y
44
− 19y
43
+ ··· − 97y + 16)
c
3
, c
8
y
10
(y
3
− 3y
2
+ 2y + 1)
2
(y
36
− 21y
35
+ ··· − 784y + 64)
2
· (y
44
− 27y
43
+ ··· − 41216y + 4096)
c
5
y
6
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
36
− 26y
35
+ ··· + 2461y + 289)
2
· (y
44
− 26y
43
+ ··· + 950272y + 65536)
c
6
, c
7
, c
10
c
12
(y + 1)
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
44
+ 22y
43
+ ··· + 5y + 1)(y
72
+ 42y
71
+ ··· + 1016y + 289)
c
9
, c
11
(y −1)
6
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
44
+ 10y
43
+ ··· + 13y + 1)(y
72
− 26y
71
+ ··· − 1428764y + 83521)
34
