12n
0173
(K12n
0173
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 12 11 3 6 5 8 9 10
Solving Sequence
6,11 3,7
8 9 12 5 2 4 10 1
c
6
c
7
c
8
c
11
c
5
c
2
c
4
c
10
c
12
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.58032 × 10
67
u
39
+ 2.06674 × 10
67
u
38
+ ··· + 9.73803 × 10
65
b − 1.02729 × 10
69
,
5.45075 × 10
69
u
39
− 3.75387 × 10
69
u
38
+ ··· + 1.65547 × 10
67
a + 1.34484 × 10
71
, u
40
− 4u
38
+ ··· + 97u + 17i
I
u
2
= h9.27676 × 10
169
u
45
− 2.27749 × 10
170
u
44
+ ··· + 9.75406 × 10
172
b + 4.16059 × 10
173
,
9.42080 × 10
173
u
45
− 2.43360 × 10
174
u
44
+ ··· + 2.48046 × 10
176
a + 3.47623 × 10
177
,
u
46
− 2u
45
+ ··· + 9446u + 2543i
I
u
3
= hu
3
+ 3u
2
+ 4b + 2u + 1, −3u
3
− u
2
+ 4a − 2u + 5, u
4
+ u
2
− u + 1i
I
u
4
= h−4u
14
− 2u
13
+ ··· + b − 5,
− 2u
14
− u
13
+ 5u
12
− 3u
11
− 10u
10
+ 11u
9
+ 10u
8
− 14u
7
− 3u
6
+ 14u
5
+ u
4
− 8u
3
+ u
2
+ a + 3u − 1,
u
15
− 3u
13
+ 3u
12
+ 5u
11
− 9u
10
− 3u
9
+ 12u
8
− 2u
7
− 11u
6
+ 4u
5
+ 7u
4
− 5u
3
− 2u
2
+ 3u − 1i
I
u
5
= h−u
5
− u
4
− 2u
3
− 2u
2
+ b − u − 1, −u
5
− 2u
3
− u
2
+ a − 2u − 2, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
* 5 irreducible components of dim
C
= 0, with total 111 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−3.58 × 10
67
u
39
+ 2.07 × 10
67
u
38
+ · · · + 9.74 × 10
65
b − 1.03 ×
10
69
, 5.45 × 10
69
u
39
− 3.75 × 10
69
u
38
+ · · · + 1.66 × 10
67
a + 1.34 ×
10
71
, u
40
− 4u
38
+ · · · + 97u + 17i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−329.258u
39
+ 226.756u
38
+ ··· − 34572.1u − 8123.67
36.7664u
39
− 21.2234u
38
+ ··· + 4276.56u + 1054.93
a
7
=
1
u
2
a
8
=
−79.7827u
39
+ 49.4021u
38
+ ··· − 8924.80u − 2162.21
−83.0595u
39
+ 59.0553u
38
+ ··· − 8544.73u − 1992.63
a
9
=
−162.842u
39
+ 108.457u
38
+ ··· − 17469.5u − 4154.84
−83.0595u
39
+ 59.0553u
38
+ ··· − 8544.73u − 1992.63
a
12
=
−398.430u
39
+ 268.461u
38
+ ··· − 42420.9u − 10043.8
−83.0595u
39
+ 59.0553u
38
+ ··· − 8544.73u − 1992.63
a
5
=
8.75622u
39
− 10.8797u
38
+ ··· + 451.374u + 56.6766
−120.738u
39
+ 80.3482u
38
+ ··· − 12927.2u − 3059.02
a
2
=
−90.2726u
39
+ 62.6721u
38
+ ··· − 9459.34u − 2231.28
87.9281u
39
− 59.6344u
38
+ ··· + 9289.11u + 2178.55
a
4
=
136.341u
39
− 97.9644u
38
+ ··· + 13897.5u + 3213.89
−122.755u
39
+ 78.6483u
38
+ ··· − 13489.8u − 3244.38
a
10
=
−151.962u
39
+ 97.3994u
38
+ ··· − 16676.8u − 4005.99
−163.408u
39
+ 112.006u
38
+ ··· − 17197.3u − 4045.18
a
1
=
−107.859u
39
+ 79.5764u
38
+ ··· − 10793.0u − 2477.92
152.528u
39
− 100.948u
38
+ ··· + 16405.7u + 3896.33
(ii) Obstruction class = −1
(iii) Cusp Shapes = −185.230u
39
+ 123.975u
38
+ ··· − 19743.3u − 4644.59
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
+ 41u
39
+ ··· + 8641u + 256
c
2
, c
4
u
40
− 7u
39
+ ··· − 81u + 16
c
3
, c
7
u
40
− 5u
39
+ ··· + 1632u + 256
c
5
, c
8
u
40
+ u
39
+ ··· + 2u + 1
c
6
, c
9
u
40
− 4u
38
+ ··· − 97u + 17
c
10
, c
12
u
40
+ 4u
39
+ ··· − 3u + 1
c
11
u
40
+ 25u
39
+ ··· + 36u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
− 77y
39
+ ··· − 6662529y + 65536
c
2
, c
4
y
40
− 41y
39
+ ··· − 8641y + 256
c
3
, c
7
y
40
+ 27y
39
+ ··· − 226304y + 65536
c
5
, c
8
y
40
+ 17y
39
+ ··· + 40y + 1
c
6
, c
9
y
40
− 8y
39
+ ··· − 4275y + 289
c
10
, c
12
y
40
− 40y
39
+ ··· − 15y + 1
c
11
y
40
− y
39
+ ··· + 1144y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.916795 + 0.271284I
a = 0.07185 − 2.25689I
b = −0.886132 − 0.556013I
−4.61460 + 4.21677I −10.36400 − 7.96016I
u = −0.916795 − 0.271284I
a = 0.07185 + 2.25689I
b = −0.886132 + 0.556013I
−4.61460 − 4.21677I −10.36400 + 7.96016I
u = −0.257747 + 1.059350I
a = −1.51427 + 1.70732I
b = 2.53555 − 1.59062I
−2.65950 + 0.01537I −10.44302 + 0.45727I
u = −0.257747 − 1.059350I
a = −1.51427 − 1.70732I
b = 2.53555 + 1.59062I
−2.65950 − 0.01537I −10.44302 − 0.45727I
u = −0.773206 + 0.447559I
a = 0.294992 − 0.155460I
b = 1.237270 + 0.037085I
1.37570 + 6.93076I −8.7508 − 11.5757I
u = −0.773206 − 0.447559I
a = 0.294992 + 0.155460I
b = 1.237270 − 0.037085I
1.37570 − 6.93076I −8.7508 + 11.5757I
u = 0.843869 + 0.116958I
a = 0.699504 + 0.268479I
b = −0.806806 + 0.392167I
−6.65685 − 1.58265I −10.51643 + 4.50982I
u = 0.843869 − 0.116958I
a = 0.699504 − 0.268479I
b = −0.806806 − 0.392167I
−6.65685 + 1.58265I −10.51643 − 4.50982I
u = −0.742457 + 0.416076I
a = −1.13504 + 1.53730I
b = −0.146732 − 0.117931I
−10.74610 + 5.03761I −8.95297 − 0.57470I
u = −0.742457 − 0.416076I
a = −1.13504 − 1.53730I
b = −0.146732 + 0.117931I
−10.74610 − 5.03761I −8.95297 + 0.57470I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.596745 + 1.034040I
a = 0.0958413 − 0.0250611I
b = 0.457567 − 0.044691I
1.35612 + 7.74333I 9.28204 − 10.17690I
u = −0.596745 − 1.034040I
a = 0.0958413 + 0.0250611I
b = 0.457567 + 0.044691I
1.35612 − 7.74333I 9.28204 + 10.17690I
u = 0.515825 + 1.095850I
a = 0.699738 + 0.145025I
b = −0.618119 − 0.598353I
−5.33600 − 3.23521I 0
u = 0.515825 − 1.095850I
a = 0.699738 − 0.145025I
b = −0.618119 + 0.598353I
−5.33600 + 3.23521I 0
u = 0.297740 + 0.729548I
a = −0.726912 − 0.545199I
b = 0.205553 + 0.589406I
0.08293 − 1.53752I 0.71639 + 4.76389I
u = 0.297740 − 0.729548I
a = −0.726912 + 0.545199I
b = 0.205553 − 0.589406I
0.08293 + 1.53752I 0.71639 − 4.76389I
u = 0.594134 + 0.510868I
a = −0.461994 + 0.161353I
b = 0.337579 − 0.191190I
−1.25513 − 1.56952I −2.17390 + 4.23177I
u = 0.594134 − 0.510868I
a = −0.461994 − 0.161353I
b = 0.337579 + 0.191190I
−1.25513 + 1.56952I −2.17390 − 4.23177I
u = −1.178420 + 0.383003I
a = −0.27016 + 1.72025I
b = 0.672757 + 0.873454I
−11.7135 + 8.0385I −13.2209 − 9.1027I
u = −1.178420 − 0.383003I
a = −0.27016 − 1.72025I
b = 0.672757 − 0.873454I
−11.7135 − 8.0385I −13.2209 + 9.1027I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.668836 + 0.264877I
a = 0.282272 + 1.160020I
b = 0.135893 − 0.315911I
−1.90192 + 1.40153I −6.20748 − 1.19828I
u = 0.668836 − 0.264877I
a = 0.282272 − 1.160020I
b = 0.135893 + 0.315911I
−1.90192 − 1.40153I −6.20748 + 1.19828I
u = −0.679465 + 0.012974I
a = 0.90700 − 2.42772I
b = 0.690272 + 0.025224I
−4.35694 + 0.92822I −9.14930 + 0.28573I
u = −0.679465 − 0.012974I
a = 0.90700 + 2.42772I
b = 0.690272 − 0.025224I
−4.35694 − 0.92822I −9.14930 − 0.28573I
u = −0.423175 + 0.521589I
a = 1.35188 + 1.41277I
b = 1.03242 − 1.13997I
−2.35252 + 0.61317I −4.61633 + 3.05486I
u = −0.423175 − 0.521589I
a = 1.35188 − 1.41277I
b = 1.03242 + 1.13997I
−2.35252 − 0.61317I −4.61633 − 3.05486I
u = −0.663180 + 0.080866I
a = −0.505742 + 0.206401I
b = −1.384640 − 0.132216I
2.64301 + 1.48294I −4.81453 + 7.72547I
u = −0.663180 − 0.080866I
a = −0.505742 − 0.206401I
b = −1.384640 + 0.132216I
2.64301 − 1.48294I −4.81453 − 7.72547I
u = 1.31926 + 0.81503I
a = −0.254068 − 1.123980I
b = 2.08311 − 0.15702I
−5.42435 − 5.89974I 0
u = 1.31926 − 0.81503I
a = −0.254068 + 1.123980I
b = 2.08311 + 0.15702I
−5.42435 + 5.89974I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.33509 + 1.00004I
a = −0.103766 + 0.191805I
b = −1.191910 + 0.700889I
−7.28442 + 9.37900I 0
u = −1.33509 − 1.00004I
a = −0.103766 − 0.191805I
b = −1.191910 − 0.700889I
−7.28442 − 9.37900I 0
u = 1.64955 + 0.34859I
a = 0.041797 + 0.918280I
b = −1.41260 + 0.58964I
−14.3131 − 1.3284I 0
u = 1.64955 − 0.34859I
a = 0.041797 − 0.918280I
b = −1.41260 − 0.58964I
−14.3131 + 1.3284I 0
u = 1.25011 + 1.13972I
a = 0.537152 + 1.115220I
b = −2.58218 + 0.30646I
−4.50733 − 12.55940I 0
u = 1.25011 − 1.13972I
a = 0.537152 − 1.115220I
b = −2.58218 − 0.30646I
−4.50733 + 12.55940I 0
u = −0.82513 + 1.61273I
a = 0.619679 − 0.520496I
b = −2.49695 + 0.94026I
−10.55600 + 0.42655I 0
u = −0.82513 − 1.61273I
a = 0.619679 + 0.520496I
b = −2.49695 − 0.94026I
−10.55600 − 0.42655I 0
u = 1.25209 + 1.40579I
a = −0.710628 − 0.936920I
b = 2.76309 − 0.57698I
−11.2981 − 17.8760I 0
u = 1.25209 − 1.40579I
a = −0.710628 + 0.936920I
b = 2.76309 + 0.57698I
−11.2981 + 17.8760I 0
8
II. I
u
2
= h9.28 × 10
169
u
45
− 2.28 × 10
170
u
44
+ · · · + 9.75 × 10
172
b + 4.16 ×
10
173
, 9.42 × 10
173
u
45
− 2.43 × 10
174
u
44
+ · · · + 2.48 × 10
176
a + 3.48 ×
10
177
, u
46
− 2u
45
+ · · · + 9446u + 2543i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−0.00379801u
45
+ 0.00981109u
44
+ ··· − 43.1222u − 14.0145
−0.000951066u
45
+ 0.00233492u
44
+ ··· − 8.80677u − 4.26549
a
7
=
1
u
2
a
8
=
0.000716237u
45
− 0.00105546u
44
+ ··· + 4.58476u + 9.05145
0.00144541u
45
− 0.00363803u
44
+ ··· + 12.3847u + 6.56682
a
9
=
0.00216165u
45
− 0.00469349u
44
+ ··· + 16.9695u + 15.6183
0.00144541u
45
− 0.00363803u
44
+ ··· + 12.3847u + 6.56682
a
12
=
−0.00398318u
45
+ 0.00931129u
44
+ ··· − 34.5587u − 20.7912
−0.000496329u
45
+ 0.000994531u
44
+ ··· − 6.30884u − 5.67547
a
5
=
0.00412015u
45
− 0.0103795u
44
+ ··· + 41.9047u + 14.6677
0.000976621u
45
− 0.00236780u
44
+ ··· + 11.0461u + 5.89430
a
2
=
−0.00289423u
45
+ 0.00709969u
44
+ ··· − 29.5330u − 10.4974
−0.000537120u
45
+ 0.00126553u
44
+ ··· − 6.34240u − 3.78873
a
4
=
0.00382997u
45
− 0.00995571u
44
+ ··· + 40.6638u + 12.6470
0.00116221u
45
− 0.00292917u
44
+ ··· + 9.48770u + 4.47069
a
10
=
−0.00461706u
45
+ 0.0113680u
44
+ ··· − 34.2999u − 16.9762
0.00113021u
45
− 0.00305123u
44
+ ··· + 8.04999u + 1.86051
a
1
=
−0.00527624u
45
+ 0.0130113u
44
+ ··· − 46.7854u − 17.7735
0.000580431u
45
− 0.00159375u
44
+ ··· + 1.15606u − 0.758198
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00495504u
45
− 0.00970261u
44
+ ··· + 38.8323u + 37.7445
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
23
+ 26u
22
+ ··· − 7u + 1)
2
c
2
, c
4
(u
23
− 4u
22
+ ··· − 3u − 1)
2
c
3
, c
7
(u
23
+ 3u
22
+ ··· + 36u − 8)
2
c
5
, c
8
u
46
+ 6u
45
+ ··· + 116u + 17
c
6
, c
9
u
46
+ 2u
45
+ ··· − 9446u + 2543
c
10
, c
12
u
46
− 3u
44
+ ··· − 76140u + 32521
c
11
(u
23
− 10u
22
+ ··· + 4u
2
+ 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
23
− 54y
22
+ ··· − 215y −1)
2
c
2
, c
4
(y
23
− 26y
22
+ ··· − 7y −1)
2
c
3
, c
7
(y
23
+ 21y
22
+ ··· − 48y −64)
2
c
5
, c
8
y
46
− 10y
45
+ ··· + 3136y + 289
c
6
, c
9
y
46
− 10y
45
+ ··· − 111757896y + 6466849
c
10
, c
12
y
46
− 6y
45
+ ··· + 636394872y + 1057615441
c
11
(y
23
+ 20y
21
+ ··· − 8y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.938998 + 0.344976I
a = −2.24368 + 0.34394I
b = −2.40240 − 0.99716I
−1.23158 − 3.46001I −0.93966 + 11.94434I
u = 0.938998 − 0.344976I
a = −2.24368 − 0.34394I
b = −2.40240 + 0.99716I
−1.23158 + 3.46001I −0.93966 − 11.94434I
u = 0.381487 + 0.925362I
a = 0.036904 − 0.397055I
b = −0.308362 + 0.632471I
0.22577 − 2.35596I 1.37102 + 5.00512I
u = 0.381487 − 0.925362I
a = 0.036904 + 0.397055I
b = −0.308362 − 0.632471I
0.22577 + 2.35596I 1.37102 − 5.00512I
u = −0.662967 + 0.741919I
a = −0.882738 + 0.492316I
b = 0.019759 + 1.137980I
0.22577 − 2.35596I 1.37102 + 5.00512I
u = −0.662967 − 0.741919I
a = −0.882738 − 0.492316I
b = 0.019759 − 1.137980I
0.22577 + 2.35596I 1.37102 − 5.00512I
u = −0.776430 + 0.599101I
a = 0.64174 − 1.41107I
b = −0.331275 + 0.637663I
−9.93186 + 9.38993I −5.00822 − 8.89816I
u = −0.776430 − 0.599101I
a = 0.64174 + 1.41107I
b = −0.331275 − 0.637663I
−9.93186 − 9.38993I −5.00822 + 8.89816I
u = −0.347658 + 0.962709I
a = −0.094250 − 0.137661I
b = −0.617430 + 0.174037I
3.29942 11.64034 + 0.I
u = −0.347658 − 0.962709I
a = −0.094250 + 0.137661I
b = −0.617430 − 0.174037I
3.29942 11.64034 + 0.I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.363894 + 0.859272I
a = 0.961328 − 0.913318I
b = 0.081085 + 0.409837I
0.07682 − 4.67687I −2.82043 + 11.56965I
u = 0.363894 − 0.859272I
a = 0.961328 + 0.913318I
b = 0.081085 − 0.409837I
0.07682 + 4.67687I −2.82043 − 11.56965I
u = −0.576444 + 0.916663I
a = −3.57574 + 2.35289I
b = 3.83467 + 2.38953I
−1.23158 + 3.46001I −0.93966 − 11.94434I
u = −0.576444 − 0.916663I
a = −3.57574 − 2.35289I
b = 3.83467 − 2.38953I
−1.23158 − 3.46001I −0.93966 + 11.94434I
u = 0.091395 + 1.210170I
a = −0.143737 + 0.825821I
b = −0.195131 + 0.246758I
−6.90053 − 6.33030I −5.55743 + 6.60020I
u = 0.091395 − 1.210170I
a = −0.143737 − 0.825821I
b = −0.195131 − 0.246758I
−6.90053 + 6.33030I −5.55743 − 6.60020I
u = −0.642034 + 0.452369I
a = −0.21983 + 1.87152I
b = 1.23526 − 0.94866I
−4.25470 + 2.83401I −16.2136 − 5.6542I
u = −0.642034 − 0.452369I
a = −0.21983 − 1.87152I
b = 1.23526 + 0.94866I
−4.25470 − 2.83401I −16.2136 + 5.6542I
u = 0.669574 + 1.086330I
a = −0.208906 − 0.373689I
b = 0.927797 + 0.477174I
0.78715 − 2.82758I 2.28819 − 1.37730I
u = 0.669574 − 1.086330I
a = −0.208906 + 0.373689I
b = 0.927797 − 0.477174I
0.78715 + 2.82758I 2.28819 + 1.37730I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.046560 + 0.783431I
a = 0.59848 − 1.43771I
b = −1.59045 + 0.05140I
−12.8626 + 6.8428I −11.21020 − 4.32033I
u = −1.046560 − 0.783431I
a = 0.59848 + 1.43771I
b = −1.59045 − 0.05140I
−12.8626 − 6.8428I −11.21020 + 4.32033I
u = 0.625428 + 0.116207I
a = −0.714645 + 0.198843I
b = 1.353840 − 0.397532I
−5.87167 + 0.65487I −18.5419 − 8.9539I
u = 0.625428 − 0.116207I
a = −0.714645 − 0.198843I
b = 1.353840 + 0.397532I
−5.87167 − 0.65487I −18.5419 + 8.9539I
u = −0.548542 + 0.193866I
a = −0.45786 + 1.86963I
b = −0.184586 − 1.004710I
−2.99002 + 3.94578I −4.9106 − 15.5031I
u = −0.548542 − 0.193866I
a = −0.45786 − 1.86963I
b = −0.184586 + 1.004710I
−2.99002 − 3.94578I −4.9106 + 15.5031I
u = −1.24048 + 0.78112I
a = −0.03322 − 1.87174I
b = −3.56571 − 0.92903I
0.07682 + 4.67687I 0. − 11.56965I
u = −1.24048 − 0.78112I
a = −0.03322 + 1.87174I
b = −3.56571 + 0.92903I
0.07682 − 4.67687I 0. + 11.56965I
u = 0.467204 + 0.217984I
a = 1.94284 + 2.82388I
b = −0.202604 − 0.456157I
−4.75468 − 2.62879I −2.77736 + 1.99528I
u = 0.467204 − 0.217984I
a = 1.94284 − 2.82388I
b = −0.202604 + 0.456157I
−4.75468 + 2.62879I −2.77736 − 1.99528I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428413 + 0.172818I
a = 3.71471 − 1.22148I
b = 0.621273 − 1.245390I
0.78715 + 2.82758I 2.28819 + 1.37730I
u = −0.428413 − 0.172818I
a = 3.71471 + 1.22148I
b = 0.621273 + 1.245390I
0.78715 − 2.82758I 2.28819 − 1.37730I
u = 0.35071 + 1.65209I
a = 0.0912328 + 0.0808853I
b = −0.29070 − 1.43919I
−4.75468 − 2.62879I 0
u = 0.35071 − 1.65209I
a = 0.0912328 − 0.0808853I
b = −0.29070 + 1.43919I
−4.75468 + 2.62879I 0
u = −1.85979 + 1.16230I
a = −0.246221 + 0.939586I
b = 3.32130 + 1.56395I
−6.90053 + 6.33030I 0
u = −1.85979 − 1.16230I
a = −0.246221 − 0.939586I
b = 3.32130 − 1.56395I
−6.90053 − 6.33030I 0
u = 1.70741 + 1.40554I
a = 0.358502 + 0.842210I
b = −3.51166 + 1.04732I
−4.25470 + 2.83401I 0
u = 1.70741 − 1.40554I
a = 0.358502 − 0.842210I
b = −3.51166 − 1.04732I
−4.25470 − 2.83401I 0
u = 1.43109 + 1.69613I
a = 0.593848 + 0.717598I
b = −3.15094 + 0.70927I
−9.93186 − 9.38993I 0
u = 1.43109 − 1.69613I
a = 0.593848 − 0.717598I
b = −3.15094 − 0.70927I
−9.93186 + 9.38993I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.76806 + 1.35630I
a = −0.392722 − 0.812608I
b = 2.93041 − 1.33454I
−2.99002 − 3.94578I 0
u = 1.76806 − 1.35630I
a = −0.392722 + 0.812608I
b = 2.93041 + 1.33454I
−2.99002 + 3.94578I 0
u = 2.24798 + 0.96891I
a = −0.049286 − 0.718312I
b = 3.40524 − 1.44518I
−12.8626 + 6.8428I 0
u = 2.24798 − 0.96891I
a = −0.049286 + 0.718312I
b = 3.40524 + 1.44518I
−12.8626 − 6.8428I 0
u = −1.91392 + 1.52870I
a = 0.405621 − 0.097399I
b = 1.62062 − 2.87145I
−5.87167 + 0.65487I 0
u = −1.91392 − 1.52870I
a = 0.405621 + 0.097399I
b = 1.62062 + 2.87145I
−5.87167 − 0.65487I 0
16
III. I
u
3
= hu
3
+ 3u
2
+ 4b + 2u + 1, −3u
3
− u
2
+ 4a − 2u + 5, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
3
4
u
3
+
1
4
u
2
+
1
2
u −
5
4
−
1
4
u
3
−
3
4
u
2
−
1
2
u −
1
4
a
7
=
1
u
2
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
u
3
+ u
2
u
2
a
5
=
−u
3
−u
2
+ u − 1
a
2
=
7
4
u
3
+
1
4
u
2
+
1
2
u −
5
4
−
1
4
u
3
+
1
4
u
2
−
3
2
u +
3
4
a
4
=
3
4
u
3
+
1
4
u
2
+
1
2
u −
5
4
−
1
4
u
3
−
3
4
u
2
−
1
2
u −
1
4
a
10
=
u
u
3
+ u
a
1
=
u
3
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
39
16
u
3
+
77
16
u
2
+
19
8
u −
149
16
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
6
u
4
+ u
2
− u + 1
c
8
u
4
− 2u
3
+ 3u
2
− u + 1
c
9
, c
10
, c
12
u
4
+ u
2
+ u + 1
c
11
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
8
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
6
, c
9
, c
10
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
11
y
4
− y
3
+ 2y
2
+ 7y + 4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −1.28654 + 0.69736I
b = −0.391417 − 0.855136I
−2.62503 − 1.39709I −9.19395 + 5.27044I
u = 0.547424 − 0.585652I
a = −1.28654 − 0.69736I
b = −0.391417 + 0.855136I
−2.62503 + 1.39709I −9.19395 − 5.27044I
u = −0.547424 + 1.120870I
a = −0.338459 − 0.046758I
b = 0.266417 + 0.460085I
0.98010 + 7.64338I −10.58730 − 4.22005I
u = −0.547424 − 1.120870I
a = −0.338459 + 0.046758I
b = 0.266417 − 0.460085I
0.98010 − 7.64338I −10.58730 + 4.22005I
20
IV.
I
u
4
= h−4u
14
−2u
13
+· · ·+b−5, −2u
14
−u
13
+· · ·+a−1, u
15
−3u
13
+· · ·+3u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
2u
14
+ u
13
+ ··· − 3u + 1
4u
14
+ 2u
13
+ ··· − 11u + 5
a
7
=
1
u
2
a
8
=
u
−u
14
+ 3u
12
+ ··· + 2u − 3
a
9
=
−u
14
+ 3u
12
+ ··· + 3u − 3
−u
14
+ 3u
12
+ ··· + 2u − 3
a
12
=
u
14
− 3u
12
+ ··· − 4u + 3
u
14
− 3u
12
+ ··· − 2u + 3
a
5
=
3u
14
+ u
13
+ ··· − 11u + 6
3u
14
+ u
13
+ ··· − 11u + 7
a
2
=
2u
14
− 6u
12
+ ··· − 6u + 4
3u
14
+ u
13
+ ··· − 9u + 6
a
4
=
5u
14
+ 3u
13
+ ··· − 13u + 5
4u
14
+ 2u
13
+ ··· − 14u + 7
a
10
=
u
3
0
a
1
=
u
14
− 3u
12
+ ··· − 4u + 3
u
14
− 3u
12
+ ··· − 2u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9u
14
− 12u
13
+ 18u
12
+ 3u
11
− 57u
10
+ 9u
9
+ 81u
8
− 23u
7
−
69u
6
+ 49u
5
+ 71u
4
− 33u
3
− 20u
2
+ 30u − 2
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 14u
14
+ ··· + 27u − 1
c
2
u
15
+ 4u
14
+ ··· + 5u − 1
c
3
u
15
− 2u
14
+ ··· + u − 1
c
4
u
15
− 4u
14
+ ··· + 5u + 1
c
5
, c
8
u
15
− 3u
14
+ ··· + 3u
2
− 1
c
6
, c
9
u
15
− 3u
13
+ ··· + 3u − 1
c
7
u
15
+ 2u
14
+ ··· + u + 1
c
10
, c
12
u
15
+ 6u
14
+ ··· + 5u + 1
c
11
u
15
− 9u
14
+ ··· − 3u
2
+ 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 22y
14
+ ··· + 247y −1
c
2
, c
4
y
15
− 14y
14
+ ··· + 27y −1
c
3
, c
7
y
15
+ 6y
14
+ ··· − 21y −1
c
5
, c
8
y
15
− 5y
14
+ ··· + 6y −1
c
6
, c
9
y
15
− 6y
14
+ ··· + 5y −1
c
10
, c
12
y
15
+ 2y
14
+ ··· − 15y −1
c
11
y
15
− y
14
+ ··· + 6y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.705269 + 0.671023I
a = −1.91716 − 4.45800I
b = −4.32167 + 1.98193I
−0.66574 + 3.66922I −23.4278 − 4.1308I
u = −0.705269 − 0.671023I
a = −1.91716 + 4.45800I
b = −4.32167 − 1.98193I
−0.66574 − 3.66922I −23.4278 + 4.1308I
u = 0.705292 + 0.773370I
a = −1.49935 − 0.52629I
b = 0.711264 − 1.062020I
0.41822 − 3.68052I −1.64123 + 6.14138I
u = 0.705292 − 0.773370I
a = −1.49935 + 0.52629I
b = 0.711264 + 1.062020I
0.41822 + 3.68052I −1.64123 − 6.14138I
u = −1.095560 + 0.159935I
a = 0.03742 − 1.42622I
b = −0.305259 − 0.223093I
−3.30273 + 3.15661I −6.01525 − 3.84939I
u = −1.095560 − 0.159935I
a = 0.03742 + 1.42622I
b = −0.305259 + 0.223093I
−3.30273 − 3.15661I −6.01525 + 3.84939I
u = 1.13479
a = 0.0880681
b = −1.41713
−5.52469 −6.90180
u = 0.655711 + 0.316603I
a = 0.319019 − 0.248033I
b = 1.361690 − 0.044903I
2.79458 − 1.83819I 3.69149 + 10.41016I
u = 0.655711 − 0.316603I
a = 0.319019 + 0.248033I
b = 1.361690 + 0.044903I
2.79458 + 1.83819I 3.69149 − 10.41016I
u = 0.713404 + 1.059640I
a = 0.846522 + 0.167681I
b = −0.686002 − 0.092107I
−5.32622 − 4.02081I −6.72360 + 8.77622I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.713404 − 1.059640I
a = 0.846522 − 0.167681I
b = −0.686002 + 0.092107I
−5.32622 + 4.02081I −6.72360 − 8.77622I
u = 0.461092 + 0.464467I
a = −0.605558 + 0.197442I
b = −1.113150 + 0.171029I
1.69267 − 6.59893I 3.21319 + 0.18543I
u = 0.461092 − 0.464467I
a = −0.605558 − 0.197442I
b = −1.113150 − 0.171029I
1.69267 + 6.59893I 3.21319 − 0.18543I
u = −1.302070 + 0.416047I
a = −0.224921 + 1.360520I
b = 0.561688 + 0.716944I
−10.94270 + 7.51080I −5.14589 − 4.08277I
u = −1.302070 − 0.416047I
a = −0.224921 − 1.360520I
b = 0.561688 − 0.716944I
−10.94270 − 7.51080I −5.14589 + 4.08277I
25
V. I
u
5
= h−u
5
− u
4
− 2u
3
− 2u
2
+ b − u − 1, −u
5
− 2u
3
− u
2
+ a − 2u −
2, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
u
5
+ 2u
3
+ u
2
+ 2u + 2
u
5
+ u
4
+ 2u
3
+ 2u
2
+ u + 1
a
7
=
1
u
2
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
u
5
+ 2u
3
+ u
u
5
+ u
3
+ u
a
5
=
−2u
5
− 3u
3
− u
2
− 2u − 1
−2u
5
− u
4
− 3u
3
− 2u
2
− 3u − 2
a
2
=
3u
5
+ 5u
3
+ 2u
2
+ 4u + 3
3u
5
+ 2u
4
+ 5u
3
+ 4u
2
+ 4u + 3
a
4
=
u
5
+ 2u
3
+ u
2
+ 2u + 2
u
5
+ u
4
+ 2u
3
+ 2u
2
+ u + 1
a
10
=
u
u
3
+ u
a
1
=
2u
5
+ 3u
3
+ u
2
+ 2u + 1
2u
5
+ u
4
+ 3u
3
+ 2u
2
+ 3u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
5
+ 2u
3
+ u
2
+ 2u − 3
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
6
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
8
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
9
, c
10
, c
12
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
11
(u
3
− u
2
+ 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
8
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
6
, c
9
, c
10
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
11
(y
3
− y
2
+ 2y −1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = 0.78492 + 1.30714I
b = −1.89744 − 0.20118I
−1.37919 − 2.82812I −4.21508 + 1.30714I
u = 0.498832 − 1.001300I
a = 0.78492 − 1.30714I
b = −1.89744 + 0.20118I
−1.37919 + 2.82812I −4.21508 − 1.30714I
u = −0.284920 + 1.115140I
a = 0.430160
b = −0.500000 − 0.273346I
2.75839 −4.56984 + 0.I
u = −0.284920 − 1.115140I
a = 0.430160
b = −0.500000 + 0.273346I
2.75839 −4.56984 + 0.I
u = −0.713912 + 0.305839I
a = 0.78492 + 1.30714I
b = 0.897438 + 0.201182I
−1.37919 − 2.82812I −4.21508 + 1.30714I
u = −0.713912 − 0.305839I
a = 0.78492 − 1.30714I
b = 0.897438 − 0.201182I
−1.37919 + 2.82812I −4.21508 − 1.30714I
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
15
− 14u
14
+ ··· + 27u − 1)(u
23
+ 26u
22
+ ··· − 7u + 1)
2
· (u
40
+ 41u
39
+ ··· + 8641u + 256)
c
2
((u − 1)
10
)(u
15
+ 4u
14
+ ··· + 5u − 1)(u
23
− 4u
22
+ ··· − 3u − 1)
2
· (u
40
− 7u
39
+ ··· − 81u + 16)
c
3
u
10
(u
15
− 2u
14
+ ··· + u − 1)(u
23
+ 3u
22
+ ··· + 36u − 8)
2
· (u
40
− 5u
39
+ ··· + 1632u + 256)
c
4
((u + 1)
10
)(u
15
− 4u
14
+ ··· + 5u + 1)(u
23
− 4u
22
+ ··· − 3u − 1)
2
· (u
40
− 7u
39
+ ··· − 81u + 16)
c
5
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
15
− 3u
14
+ ··· + 3u
2
− 1)(u
40
+ u
39
+ ··· + 2u + 1)
· (u
46
+ 6u
45
+ ··· + 116u + 17)
c
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
15
− 3u
13
+ ··· + 3u − 1)(u
40
− 4u
38
+ ··· − 97u + 17)
· (u
46
+ 2u
45
+ ··· − 9446u + 2543)
c
7
u
10
(u
15
+ 2u
14
+ ··· + u + 1)(u
23
+ 3u
22
+ ··· + 36u − 8)
2
· (u
40
− 5u
39
+ ··· + 1632u + 256)
c
8
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
15
− 3u
14
+ ··· + 3u
2
− 1)(u
40
+ u
39
+ ··· + 2u + 1)
· (u
46
+ 6u
45
+ ··· + 116u + 17)
c
9
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
15
− 3u
13
+ ··· + 3u − 1)(u
40
− 4u
38
+ ··· − 97u + 17)
· (u
46
+ 2u
45
+ ··· − 9446u + 2543)
c
10
, c
12
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
15
+ 6u
14
+ ··· + 5u + 1)(u
40
+ 4u
39
+ ··· − 3u + 1)
· (u
46
− 3u
44
+ ··· − 76140u + 32521)
c
11
((u
3
− u
2
+ 1)
2
)(u
4
+ 3u
3
+ ··· + 3u + 2)(u
15
− 9u
14
+ ··· − 3u
2
+ 1)
· ((u
23
− 10u
22
+ ··· + 4u
2
+ 1)
2
)(u
40
+ 25u
39
+ ··· + 36u + 4)
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
15
− 22y
14
+ ··· + 247y −1)
· (y
23
− 54y
22
+ ··· − 215y −1)
2
· (y
40
− 77y
39
+ ··· − 6662529y + 65536)
c
2
, c
4
((y −1)
10
)(y
15
− 14y
14
+ ··· + 27y −1)(y
23
− 26y
22
+ ··· − 7y −1)
2
· (y
40
− 41y
39
+ ··· − 8641y + 256)
c
3
, c
7
y
10
(y
15
+ 6y
14
+ ··· − 21y −1)(y
23
+ 21y
22
+ ··· − 48y −64)
2
· (y
40
+ 27y
39
+ ··· − 226304y + 65536)
c
5
, c
8
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
15
− 5y
14
+ ··· + 6y −1)(y
40
+ 17y
39
+ ··· + 40y + 1)
· (y
46
− 10y
45
+ ··· + 3136y + 289)
c
6
, c
9
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
15
− 6y
14
+ ··· + 5y −1)(y
40
− 8y
39
+ ··· − 4275y + 289)
· (y
46
− 10y
45
+ ··· − 111757896y + 6466849)
c
10
, c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
15
+ 2y
14
+ ··· − 15y −1)(y
40
− 40y
39
+ ··· − 15y + 1)
· (y
46
− 6y
45
+ ··· + 636394872y + 1057615441)
c
11
((y
3
− y
2
+ 2y −1)
2
)(y
4
− y
3
+ 2y
2
+ 7y + 4)(y
15
− y
14
+ ··· + 6y −1)
· ((y
23
+ 20y
21
+ ··· − 8y −1)
2
)(y
40
− y
39
+ ··· + 1144y + 16)
31
