12n
0873
(K12n
0873
)
A knot diagram
1
Linearized knot diagam
4 8 6 11 1 2 11 3 1 8 5 10
Solving Sequence
8,10 5,11
12 1 4 2 3 7 6 9
c
10
c
11
c
12
c
4
c
1
c
2
c
7
c
6
c
9
c
3
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−14522454433989u
21
− 25681776487073u
20
+ ··· + 3586941656707b − 31211211235135,
− 36929494073687u
21
− 51455949517906u
20
+ ··· + 7173883313414a − 58527943826811,
u
22
+ u
21
+ ··· + 11u
2
− 1i
I
u
2
= h4.95406 × 10
129
u
47
− 1.26151 × 10
130
u
46
+ ··· + 1.96857 × 10
131
b − 1.02263 × 10
133
,
4.32742 × 10
130
u
47
− 2.32616 × 10
130
u
46
+ ··· + 1.83077 × 10
133
a + 1.08093 × 10
134
,
u
48
− 3u
47
+ ··· − 5967u + 837i
I
u
3
= h4.59095 × 10
33
u
27
+ 3.06795 × 10
34
u
26
+ ··· + 1.27873 × 10
34
b − 2.02070 × 10
34
,
5.39233 × 10
33
u
27
+ 3.74664 × 10
34
u
26
+ ··· + 1.27873 × 10
34
a + 1.86540 × 10
33
, u
28
+ 6u
27
+ ··· − 3u + 1i
I
u
4
= hb − u − 1, a + 1, u
2
+ u + 1i
I
u
5
= hb, a
2
− a − 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 102 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−1.45 × 10
13
u
21
− 2.57 × 10
13
u
20
+ · · · + 3.59 × 10
12
b − 3.12 ×
10
13
, −3.69 × 10
13
u
21
− 5.15 × 10
13
u
20
+ · · · + 7.17 × 10
12
a − 5.85 ×
10
13
, u
22
+ u
21
+ · · · + 11u
2
− 1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
5
=
5.14777u
21
+ 7.17268u
20
+ ··· + 31.1983u + 8.15847
4.04870u
21
+ 7.15980u
20
+ ··· + 19.2083u + 8.70134
a
11
=
1
u
2
a
12
=
−1.60242u
21
− 2.95306u
20
+ ··· − 16.8212u − 10.3165
−1.34149u
21
− 3.53682u
20
+ ··· + 5.21457u + 1.60180
a
1
=
−2.94390u
21
− 6.48988u
20
+ ··· − 11.6066u − 8.71475
−1.34149u
21
− 3.53682u
20
+ ··· + 5.21457u + 1.60180
a
4
=
7.46458u
21
+ 11.2167u
20
+ ··· + 45.2589u + 14.8349
5.25346u
21
+ 9.78267u
20
+ ··· + 21.5251u + 10.4285
a
2
=
0.808188u
21
+ 0.198874u
20
+ ··· + 3.22832u − 1.25017
3.18771u
21
+ 5.17826u
20
+ ··· + 15.6431u + 6.85526
a
3
=
0.808188u
21
+ 0.198874u
20
+ ··· + 3.22832u − 1.25017
3.75209u
21
+ 6.68875u
20
+ ··· + 14.8349u + 7.46458
a
7
=
u
u
3
+ u
a
6
=
−5.04727u
21
− 8.95412u
20
+ ··· − 17.3452u − 2.58840
0.141857u
21
− 1.92509u
20
+ ··· + 17.6199u + 3.65407
a
9
=
−0.597562u
21
− 0.425433u
20
+ ··· − 9.43715u − 7.53117
−5.64484u
21
− 9.37955u
20
+ ··· − 26.7823u − 10.1196
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
10307681188458
3586941656707
u
21
−
33226595290622
3586941656707
u
20
+ ··· +
96107874232352
3586941656707
u +
30375267725218
3586941656707
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
22
+ u
21
+ ··· + 11u
2
− 1
c
2
, c
8
u
22
+ 6u
21
+ ··· + 228u + 52
c
3
, c
9
, c
12
u
22
− u
21
+ ··· + 11u
2
− 1
c
4
, c
11
u
22
− 6u
21
+ ··· − 228u + 52
c
5
u
22
− 8u
20
+ ··· − 7u + 1
c
6
u
22
− 8u
20
+ ··· + 7u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
9
, c
10
, c
12
y
22
− 17y
21
+ ··· − 22y + 1
c
2
, c
4
, c
8
c
11
y
22
− 10y
21
+ ··· − 5184y + 2704
c
5
, c
6
y
22
− 16y
21
+ ··· − 23y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.273252 + 1.034170I
a = −0.328090 + 1.002630I
b = 0.35769 − 1.45925I
5.13893 + 2.17267I 4.11172 − 1.64759I
u = 0.273252 − 1.034170I
a = −0.328090 − 1.002630I
b = 0.35769 + 1.45925I
5.13893 − 2.17267I 4.11172 + 1.64759I
u = −1.091870 + 0.170196I
a = 0.341986 − 0.237190I
b = 0.10871 − 1.70943I
1.44857I 0. − 4.63298I
u = −1.091870 − 0.170196I
a = 0.341986 + 0.237190I
b = 0.10871 + 1.70943I
− 1.44857I 0. + 4.63298I
u = 1.16697
a = 1.93759
b = 1.31755
−1.38914 −6.49920
u = 1.17007
a = 1.37304
b = 0.0438181
−3.90973 −1.47180
u = −1.184230 + 0.406235I
a = −0.892904 − 0.595909I
b = −0.677358 − 0.477546I
−5.13893 + 2.17267I −4.11172 − 1.64759I
u = −1.184230 − 0.406235I
a = −0.892904 + 0.595909I
b = −0.677358 + 0.477546I
−5.13893 − 2.17267I −4.11172 + 1.64759I
u = 1.28862
a = −0.871497
b = −0.541661
3.90973 1.47180
u = 1.190010 + 0.539033I
a = −0.019482 + 0.174480I
b = 0.02634 − 1.57051I
4.41609 − 8.09582I −0.16704 + 6.20921I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.190010 − 0.539033I
a = −0.019482 − 0.174480I
b = 0.02634 + 1.57051I
4.41609 + 8.09582I −0.16704 − 6.20921I
u = −1.21834 + 0.77453I
a = −1.046370 − 0.586364I
b = −0.586487 + 1.182500I
−6.16492 + 3.65327I −2.07624 − 2.63478I
u = −1.21834 − 0.77453I
a = −1.046370 + 0.586364I
b = −0.586487 − 1.182500I
−6.16492 − 3.65327I −2.07624 + 2.63478I
u = −0.216738 + 0.333613I
a = −0.485538 + 0.537232I
b = −0.157505 + 0.459074I
0.962560I 0. − 6.99490I
u = −0.216738 − 0.333613I
a = −0.485538 − 0.537232I
b = −0.157505 − 0.459074I
− 0.962560I 0. + 6.99490I
u = −0.378784
a = −4.90098
b = 0.719440
1.38914 6.49920
u = 0.360251 + 0.017332I
a = −2.22248 − 2.14516I
b = 0.179710 − 1.357060I
6.16492 + 3.65327I 2.07624 − 2.63478I
u = 0.360251 − 0.017332I
a = −2.22248 + 2.14516I
b = 0.179710 + 1.357060I
6.16492 − 3.65327I 2.07624 + 2.63478I
u = 1.36719 + 1.01562I
a = −1.161550 + 0.457478I
b = −0.66619 − 2.08430I
− 16.7035I 0. + 8.00505I
u = 1.36719 − 1.01562I
a = −1.161550 − 0.457478I
b = −0.66619 + 2.08430I
16.7035I 0. − 8.00505I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60296 + 0.80967I
a = 1.045340 + 0.230207I
b = 1.14552 − 1.72907I
−4.41609 + 8.09582I 0.16704 − 6.20921I
u = −1.60296 − 0.80967I
a = 1.045340 − 0.230207I
b = 1.14552 + 1.72907I
−4.41609 − 8.09582I 0.16704 + 6.20921I
7
II. I
u
2
= h4.95 × 10
129
u
47
− 1.26 × 10
130
u
46
+ · · · + 1.97 × 10
131
b − 1.02 ×
10
133
, 4.33 × 10
130
u
47
− 2.33 × 10
130
u
46
+ · · · + 1.83 × 10
133
a + 1.08 ×
10
134
, u
48
− 3u
47
+ · · · − 5967u + 837i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
5
=
−0.00236372u
47
+ 0.00127060u
46
+ ··· + 10.6580u − 5.90425
−0.0251658u
47
+ 0.0640825u
46
+ ··· − 235.966u + 51.9482
a
11
=
1
u
2
a
12
=
0.00497228u
47
− 0.0142819u
46
+ ··· + 74.3726u − 16.8118
−0.00444746u
47
+ 0.0103317u
46
+ ··· − 25.1012u − 0.497195
a
1
=
0.000524815u
47
− 0.00395021u
46
+ ··· + 49.2714u − 17.3090
−0.00444746u
47
+ 0.0103317u
46
+ ··· − 25.1012u − 0.497195
a
4
=
−0.0219581u
47
+ 0.0536482u
46
+ ··· − 192.555u + 41.1721
−0.0271058u
47
+ 0.0694191u
46
+ ··· − 257.787u + 57.3096
a
2
=
0.0195013u
47
− 0.0514279u
46
+ ··· + 199.464u − 49.3221
−0.0119878u
47
+ 0.0295546u
46
+ ··· − 95.9203u + 11.6620
a
3
=
0.0195013u
47
− 0.0514279u
46
+ ··· + 199.464u − 49.3221
−0.0145623u
47
+ 0.0363578u
46
+ ··· − 121.820u + 17.5845
a
7
=
u
u
3
+ u
a
6
=
0.0346889u
47
− 0.0882496u
46
+ ··· + 311.521u − 61.0827
0.0537102u
47
− 0.141102u
46
+ ··· + 536.795u − 116.450
a
9
=
−0.0446323u
47
+ 0.118128u
46
+ ··· − 444.439u + 104.355
−0.00994333u
47
+ 0.0298788u
46
+ ··· − 132.918u + 43.2723
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.114747u
47
− 0.304395u
46
+ ··· + 1165.62u − 288.012
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
48
− 3u
47
+ ··· − 5967u + 837
c
2
, c
8
(u
24
− 2u
23
+ ··· − 26u + 5)
2
c
3
, c
9
, c
12
u
48
+ 3u
47
+ ··· + 5967u + 837
c
4
, c
11
(u
24
+ 2u
23
+ ··· + 26u + 5)
2
c
5
u
48
+ 2u
47
+ ··· − 8589u + 13231
c
6
u
48
− 2u
47
+ ··· + 8589u + 13231
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
9
, c
10
, c
12
y
48
− 9y
47
+ ··· − 17495757y + 700569
c
2
, c
4
, c
8
c
11
(y
24
− 18y
23
+ ··· + 334y + 25)
2
c
5
, c
6
y
48
+ 26y
47
+ ··· − 324498371y + 175059361
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.958660 + 0.298797I
a = 0.376872 + 0.274158I
b = −0.155597 + 1.008680I
−0.341972 + 0.186667I 0.771855 − 1.155242I
u = −0.958660 − 0.298797I
a = 0.376872 − 0.274158I
b = −0.155597 − 1.008680I
−0.341972 − 0.186667I 0.771855 + 1.155242I
u = −0.927474 + 0.188250I
a = 1.23408 − 0.85486I
b = −0.141625 − 1.292960I
0.341972 − 0.186667I −0.771855 + 1.155242I
u = −0.927474 − 0.188250I
a = 1.23408 + 0.85486I
b = −0.141625 + 1.292960I
0.341972 + 0.186667I −0.771855 − 1.155242I
u = 0.248762 + 1.032370I
a = −0.885685 − 1.056230I
b = −0.112244 + 0.467226I
1.06211 − 4.31695I 5.31417 + 5.03356I
u = 0.248762 − 1.032370I
a = −0.885685 + 1.056230I
b = −0.112244 − 0.467226I
1.06211 + 4.31695I 5.31417 − 5.03356I
u = −0.517584 + 0.767984I
a = −1.211360 + 0.673550I
b = 0.446787 + 0.626280I
1.74551 + 3.59835I 5.29658 − 4.26820I
u = −0.517584 − 0.767984I
a = −1.211360 − 0.673550I
b = 0.446787 − 0.626280I
1.74551 − 3.59835I 5.29658 + 4.26820I
u = 0.893934 + 0.235448I
a = −1.94028 + 0.49910I
b = −0.079495 − 0.156983I
−7.28426 − 4.94903I 5.86283 − 2.23169I
u = 0.893934 − 0.235448I
a = −1.94028 − 0.49910I
b = −0.079495 + 0.156983I
−7.28426 + 4.94903I 5.86283 + 2.23169I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.743755 + 0.786205I
a = 0.042242 − 0.266110I
b = −0.316899 + 1.063790I
−0.341972 + 0.186667I 0.771855 − 1.155242I
u = 0.743755 − 0.786205I
a = 0.042242 + 0.266110I
b = −0.316899 − 1.063790I
−0.341972 − 0.186667I 0.771855 + 1.155242I
u = 0.970625 + 0.493744I
a = −0.625929 + 0.915628I
b = −0.149584 + 0.499982I
−8.26951 − 2.06542I 13.8209 + 10.2120I
u = 0.970625 − 0.493744I
a = −0.625929 − 0.915628I
b = −0.149584 − 0.499982I
−8.26951 + 2.06542I 13.8209 − 10.2120I
u = −0.780031 + 0.456023I
a = −1.86496 + 0.15206I
b = 0.44953 + 1.58443I
−1.74551 + 3.59835I −5.29658 − 4.26820I
u = −0.780031 − 0.456023I
a = −1.86496 − 0.15206I
b = 0.44953 − 1.58443I
−1.74551 − 3.59835I −5.29658 + 4.26820I
u = 0.856030 + 0.700750I
a = 1.40609 − 0.41827I
b = −0.70218 + 1.44760I
1.06211 − 4.31695I 5.31417 + 5.03356I
u = 0.856030 − 0.700750I
a = 1.40609 + 0.41827I
b = −0.70218 − 1.44760I
1.06211 + 4.31695I 5.31417 − 5.03356I
u = −1.005980 + 0.512244I
a = 0.923914 + 0.398084I
b = −0.255731 + 0.295435I
−2.04801 + 7.52457I −0.48629 − 6.47027I
u = −1.005980 − 0.512244I
a = 0.923914 − 0.398084I
b = −0.255731 − 0.295435I
−2.04801 − 7.52457I −0.48629 + 6.47027I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.766030 + 0.192205I
a = 1.67093 + 2.06429I
b = 0.271992 + 0.572930I
−1.06211 − 4.31695I −5.31417 + 5.03356I
u = −0.766030 − 0.192205I
a = 1.67093 − 2.06429I
b = 0.271992 − 0.572930I
−1.06211 + 4.31695I −5.31417 − 5.03356I
u = −0.460646 + 1.148330I
a = 0.259504 − 0.217863I
b = 0.570637 + 0.163273I
−1.74551 + 3.59835I −5.29658 − 4.26820I
u = −0.460646 − 1.148330I
a = 0.259504 + 0.217863I
b = 0.570637 − 0.163273I
−1.74551 − 3.59835I −5.29658 + 4.26820I
u = 0.577948 + 1.101290I
a = 0.808072 − 0.465185I
b = −0.59660 + 1.55739I
1.74551 − 3.59835I 5.29658 + 4.26820I
u = 0.577948 − 1.101290I
a = 0.808072 + 0.465185I
b = −0.59660 − 1.55739I
1.74551 + 3.59835I 5.29658 − 4.26820I
u = 0.446675 + 1.196060I
a = 0.095623 + 0.368138I
b = −0.513294 − 0.617816I
7.28426 − 4.94903I −5.86283 − 2.23169I
u = 0.446675 − 1.196060I
a = 0.095623 − 0.368138I
b = −0.513294 + 0.617816I
7.28426 + 4.94903I −5.86283 + 2.23169I
u = 1.189580 + 0.533084I
a = −1.46844 − 0.02027I
b = −0.25289 − 1.57803I
2.04801 − 7.52457I 0. + 6.47027I
u = 1.189580 − 0.533084I
a = −1.46844 + 0.02027I
b = −0.25289 + 1.57803I
2.04801 + 7.52457I 0. − 6.47027I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.663899 + 0.150986I
a = −1.68387 − 4.10135I
b = 0.11621 − 1.78501I
7.28426 + 4.94903I −5.86283 + 2.23169I
u = 0.663899 − 0.150986I
a = −1.68387 + 4.10135I
b = 0.11621 + 1.78501I
7.28426 − 4.94903I −5.86283 − 2.23169I
u = −0.078702 + 1.358830I
a = 0.094159 + 0.120663I
b = −1.008410 − 0.085223I
0.341972 + 0.186667I 0
u = −0.078702 − 1.358830I
a = 0.094159 − 0.120663I
b = −1.008410 + 0.085223I
0.341972 − 0.186667I 0
u = 0.29380 + 1.47214I
a = −0.49515 + 1.46933I
b = −0.32541 − 1.86032I
8.26951 + 2.06542I 0
u = 0.29380 − 1.47214I
a = −0.49515 − 1.46933I
b = −0.32541 + 1.86032I
8.26951 − 2.06542I 0
u = 1.26636 + 0.99041I
a = 1.193410 − 0.552573I
b = 0.77074 + 1.70024I
−2.04801 − 7.52457I 0
u = 1.26636 − 0.99041I
a = 1.193410 + 0.552573I
b = 0.77074 − 1.70024I
−2.04801 + 7.52457I 0
u = 0.359351 + 0.042465I
a = −0.487925 + 0.301808I
b = −0.15610 − 1.60194I
8.26951 − 2.06542I −13.8209 + 10.2120I
u = 0.359351 − 0.042465I
a = −0.487925 − 0.301808I
b = −0.15610 + 1.60194I
8.26951 + 2.06542I −13.8209 − 10.2120I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52589 + 0.93816I
a = 1.064660 − 0.119286I
b = 0.62872 + 2.80534I
−1.06211 − 4.31695I 0
u = 1.52589 − 0.93816I
a = 1.064660 + 0.119286I
b = 0.62872 − 2.80534I
−1.06211 + 4.31695I 0
u = −1.39474 + 1.20682I
a = −0.987942 − 0.484496I
b = −0.54043 + 2.80033I
−7.28426 + 4.94903I 0
u = −1.39474 − 1.20682I
a = −0.987942 + 0.484496I
b = −0.54043 − 2.80033I
−7.28426 − 4.94903I 0
u = 0.81660 + 1.67474I
a = −0.380578 + 0.335441I
b = 1.27825 − 2.06541I
2.04801 + 7.52457I 0
u = 0.81660 − 1.67474I
a = −0.380578 − 0.335441I
b = 1.27825 + 2.06541I
2.04801 − 7.52457I 0
u = −2.46337 + 0.42003I
a = −0.911634 − 0.251459I
b = −4.72637 − 0.05555I
−8.26951 + 2.06542I 0
u = −2.46337 − 0.42003I
a = −0.911634 + 0.251459I
b = −4.72637 + 0.05555I
−8.26951 − 2.06542I 0
15
III.
I
u
3
= h4.59 × 10
33
u
27
+ 3.07 × 10
34
u
26
+ · · · + 1.28 × 10
34
b − 2.02 × 10
34
, 5.39 ×
10
33
u
27
+3.75×10
34
u
26
+· · ·+1.28×10
34
a+1.87×10
33
, u
28
+6u
27
+· · ·−3u+1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
5
=
−0.421693u
27
− 2.92996u
26
+ ··· − 2.09762u − 0.145879
−0.359023u
27
− 2.39921u
26
+ ··· − 5.77272u + 1.58023
a
11
=
1
u
2
a
12
=
0.954342u
27
+ 5.86514u
26
+ ··· + 6.04496u − 1.51386
0.134097u
27
+ 0.515511u
26
+ ··· − 4.49632u − 1.02598
a
1
=
1.08844u
27
+ 6.38065u
26
+ ··· + 1.54864u − 2.53984
0.134097u
27
+ 0.515511u
26
+ ··· − 4.49632u − 1.02598
a
4
=
−0.689779u
27
− 4.66131u
26
+ ··· − 7.09262u + 1.03455
−0.335035u
27
− 2.26908u
26
+ ··· − 5.87314u + 1.70307
a
2
=
0.0597787u
27
+ 0.142366u
26
+ ··· + 7.32896u − 2.61415
−0.0666295u
27
− 0.814578u
26
+ ··· − 5.10096u − 2.05238
a
3
=
0.0597787u
27
+ 0.142366u
26
+ ··· + 7.32896u − 2.61415
0.0481419u
27
− 0.114863u
26
+ ··· − 4.39226u − 2.26869
a
7
=
u
u
3
+ u
a
6
=
1.78475u
27
+ 10.6659u
26
+ ··· + 10.3844u − 2.81942
0.367722u
27
+ 2.14716u
26
+ ··· + 5.94205u − 3.52131
a
9
=
−0.808930u
27
− 4.70663u
26
+ ··· − 2.90576u + 5.60831
0.975824u
27
+ 5.95926u
26
+ ··· + 7.47861u + 2.78889
(ii) Obstruction class = 1
(iii) Cusp Shapes = −0.542938u
27
− 2.92005u
26
+ ··· + 27.3198u + 13.5933
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
12
u
28
− 6u
27
+ ··· + 3u + 1
c
2
, c
4
, c
8
c
11
u
28
− 7u
26
+ ··· + 238u
2
+ 49
c
3
, c
9
, c
10
u
28
+ 6u
27
+ ··· − 3u + 1
c
5
u
28
− 3u
27
+ ··· + 621u + 411
c
6
u
28
+ 3u
27
+ ··· − 621u + 411
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
9
, c
10
, c
12
y
28
− 10y
27
+ ··· + 5y + 1
c
2
, c
4
, c
8
c
11
(y
14
− 7y
13
+ ··· + 238y + 49)
2
c
5
, c
6
y
28
+ 5y
27
+ ··· − 761295y + 168921
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.014730 + 0.343268I
a = 1.66043 + 0.58864I
b = 0.383484 − 0.329857I
−7.59311 + 5.18447I −11.1956 − 10.4086I
u = −1.014730 − 0.343268I
a = 1.66043 − 0.58864I
b = 0.383484 + 0.329857I
−7.59311 − 5.18447I −11.1956 + 10.4086I
u = 0.979232 + 0.467680I
a = 0.749738 − 0.970349I
b = 0.237326 − 0.450547I
−8.46326 − 1.96093I −18.7110 − 7.0175I
u = 0.979232 − 0.467680I
a = 0.749738 + 0.970349I
b = 0.237326 + 0.450547I
−8.46326 + 1.96093I −18.7110 + 7.0175I
u = −0.496673 + 0.768001I
a = 1.005340 − 0.286801I
b = −0.563773 − 1.206430I
1.93477 5.92241 + 0.I
u = −0.496673 − 0.768001I
a = 1.005340 + 0.286801I
b = −0.563773 + 1.206430I
1.93477 5.92241 + 0.I
u = −0.992052 + 0.459650I
a = 0.003979 + 0.143588I
b = 0.134027 + 1.181700I
−1.93477 −5.92241 + 0.I
u = −0.992052 − 0.459650I
a = 0.003979 − 0.143588I
b = 0.134027 − 1.181700I
−1.93477 −5.92241 + 0.I
u = 0.387299 + 1.069450I
a = 0.036211 + 0.233151I
b = −0.423206 − 0.850595I
7.59311 − 5.18447I 11.1956 + 10.4086I
u = 0.387299 − 1.069450I
a = 0.036211 − 0.233151I
b = −0.423206 + 0.850595I
7.59311 + 5.18447I 11.1956 − 10.4086I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.047247 + 0.733479I
a = 1.61892 + 0.33925I
b = 0.440102 − 0.460280I
4.89300I 0. − 7.60186I
u = −0.047247 − 0.733479I
a = 1.61892 − 0.33925I
b = 0.440102 + 0.460280I
− 4.89300I 0. + 7.60186I
u = −0.679081 + 0.083690I
a = −2.12459 + 1.06002I
b = 0.454670 + 0.928650I
2.46314I 0. − 2.00039I
u = −0.679081 − 0.083690I
a = −2.12459 − 1.06002I
b = 0.454670 − 0.928650I
− 2.46314I 0. + 2.00039I
u = 1.051370 + 0.863549I
a = 1.319180 − 0.300420I
b = −0.26399 + 2.12102I
− 4.89300I 0. + 7.60186I
u = 1.051370 − 0.863549I
a = 1.319180 + 0.300420I
b = −0.26399 − 2.12102I
4.89300I 0. − 7.60186I
u = 0.265070 + 1.360020I
a = −0.55094 + 1.63469I
b = −0.34283 − 1.80566I
8.46326 + 1.96093I 18.7110 + 7.0175I
u = 0.265070 − 1.360020I
a = −0.55094 − 1.63469I
b = −0.34283 + 1.80566I
8.46326 − 1.96093I 18.7110 − 7.0175I
u = 0.85372 + 1.18626I
a = 0.397120 − 0.660605I
b = −0.23043 + 1.45825I
− 2.46314I 0. + 2.00039I
u = 0.85372 − 1.18626I
a = 0.397120 + 0.660605I
b = −0.23043 − 1.45825I
2.46314I 0. − 2.00039I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.416735 + 0.077196I
a = −2.99728 − 5.98223I
b = 0.07631 − 1.84503I
7.59311 + 5.18447I 11.1956 − 10.4086I
u = 0.416735 − 0.077196I
a = −2.99728 + 5.98223I
b = 0.07631 + 1.84503I
7.59311 − 5.18447I 11.1956 + 10.4086I
u = 0.119064 + 0.246970I
a = −1.248920 + 0.006958I
b = 0.20262 − 1.57409I
8.46326 + 1.96093I 18.7110 + 7.0175I
u = 0.119064 − 0.246970I
a = −1.248920 − 0.006958I
b = 0.20262 + 1.57409I
8.46326 − 1.96093I 18.7110 − 7.0175I
u = −1.46353 + 1.26810I
a = −0.946510 − 0.455742I
b = −0.65629 + 2.97983I
−7.59311 + 5.18447I −11.1956 − 10.4086I
u = −1.46353 − 1.26810I
a = −0.946510 + 0.455742I
b = −0.65629 − 2.97983I
−7.59311 − 5.18447I −11.1956 + 10.4086I
u = −2.37916 + 0.47274I
a = −0.922686 − 0.283543I
b = −4.44802 + 0.11490I
−8.46326 + 1.96093I 0
u = −2.37916 − 0.47274I
a = −0.922686 + 0.283543I
b = −4.44802 − 0.11490I
−8.46326 − 1.96093I 0
21
IV. I
u
4
= hb − u − 1, a + 1, u
2
+ u + 1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
5
=
−1
u + 1
a
11
=
1
−u − 1
a
12
=
1
−u − 1
a
1
=
−u
−u − 1
a
4
=
−1
u + 1
a
2
=
0
−u
a
3
=
0
−u
a
7
=
u
u + 1
a
6
=
u
u + 2
a
9
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u − 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
12
u
2
− u + 1
c
2
, c
4
, c
8
c
11
u
2
c
3
, c
5
, c
9
c
10
u
2
+ u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
, c
9
c
10
, c
12
y
2
+ y + 1
c
2
, c
4
, c
8
c
11
y
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.00000
b = 0.500000 + 0.866025I
4.05977I 0. − 6.92820I
u = −0.500000 − 0.866025I
a = −1.00000
b = 0.500000 − 0.866025I
− 4.05977I 0. + 6.92820I
25
V. I
u
5
= hb, a
2
− a − 1, u − 1i
(i) Arc colorings
a
8
=
0
1
a
10
=
1
0
a
5
=
a
0
a
11
=
1
1
a
12
=
−a
1
a
1
=
−a + 1
1
a
4
=
0
−a
a
2
=
−a + 1
−a + 1
a
3
=
−a + 1
0
a
7
=
1
2
a
6
=
a − 1
a
a
9
=
−a + 2
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
(u − 1)
2
c
2
, c
6
, c
8
u
2
− u − 1
c
3
, c
9
, c
12
(u + 1)
2
c
4
, c
5
, c
11
u
2
+ u − 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
9
, c
10
, c
12
(y −1)
2
c
2
, c
4
, c
5
c
6
, c
8
, c
11
y
2
− 3y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.618034
b = 0
3.94784 0
u = 1.00000
a = 1.61803
b = 0
−3.94784 0
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
((u − 1)
2
)(u
2
− u + 1)(u
22
+ u
21
+ ··· + 11u
2
− 1)
· (u
28
− 6u
27
+ ··· + 3u + 1)(u
48
− 3u
47
+ ··· − 5967u + 837)
c
2
, c
8
u
2
(u
2
− u − 1)(u
22
+ 6u
21
+ ··· + 228u + 52)
· ((u
24
− 2u
23
+ ··· − 26u + 5)
2
)(u
28
− 7u
26
+ ··· + 238u
2
+ 49)
c
3
, c
9
((u + 1)
2
)(u
2
+ u + 1)(u
22
− u
21
+ ··· + 11u
2
− 1)
· (u
28
+ 6u
27
+ ··· − 3u + 1)(u
48
+ 3u
47
+ ··· + 5967u + 837)
c
4
, c
11
u
2
(u
2
+ u − 1)(u
22
− 6u
21
+ ··· − 228u + 52)
· ((u
24
+ 2u
23
+ ··· + 26u + 5)
2
)(u
28
− 7u
26
+ ··· + 238u
2
+ 49)
c
5
(u
2
+ u − 1)(u
2
+ u + 1)(u
22
− 8u
20
+ ··· − 7u + 1)
· (u
28
− 3u
27
+ ··· + 621u + 411)(u
48
+ 2u
47
+ ··· − 8589u + 13231)
c
6
(u
2
− u − 1)(u
2
− u + 1)(u
22
− 8u
20
+ ··· + 7u + 1)
· (u
28
+ 3u
27
+ ··· − 621u + 411)(u
48
− 2u
47
+ ··· + 8589u + 13231)
c
10
((u − 1)
2
)(u
2
+ u + 1)(u
22
+ u
21
+ ··· + 11u
2
− 1)
· (u
28
+ 6u
27
+ ··· − 3u + 1)(u
48
− 3u
47
+ ··· − 5967u + 837)
c
12
((u + 1)
2
)(u
2
− u + 1)(u
22
− u
21
+ ··· + 11u
2
− 1)
· (u
28
− 6u
27
+ ··· + 3u + 1)(u
48
+ 3u
47
+ ··· + 5967u + 837)
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
9
, c
10
, c
12
((y −1)
2
)(y
2
+ y + 1)(y
22
− 17y
21
+ ··· − 22y + 1)
· (y
28
− 10y
27
+ ··· + 5y + 1)(y
48
− 9y
47
+ ··· − 1.74958 × 10
7
y + 700569)
c
2
, c
4
, c
8
c
11
y
2
(y
2
− 3y + 1)(y
14
− 7y
13
+ ··· + 238y + 49)
2
· (y
22
− 10y
21
+ ··· − 5184y + 2704)(y
24
− 18y
23
+ ··· + 334y + 25)
2
c
5
, c
6
(y
2
− 3y + 1)(y
2
+ y + 1)(y
22
− 16y
21
+ ··· − 23y + 1)
· (y
28
+ 5y
27
+ ··· − 761295y + 168921)
· (y
48
+ 26y
47
+ ··· − 324498371y + 175059361)
31
