12a
1206
(K12a
1206
)
A knot diagram
1
Linearized knot diagam
4 11 8 1 12 3 10 5 2 7 6 9
Solving Sequence
1,5
4
2,9
10 8 3 7 12 6 11
c
4
c
1
c
9
c
8
c
3
c
7
c
12
c
5
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
18
+ 21u
17
+ ··· + 4b + 12, 3u
18
− 15u
17
+ ··· + 8a + 60, u
19
− 7u
18
+ ··· − 36u + 8i
I
u
2
= h−992688u
27
+ 12625506u
26
+ ··· + 34453b + 67406583,
67406583u
27
− 859313682u
26
+ ··· + 2928505a − 5202887920, u
28
− 14u
27
+ ··· − 855u + 85i
I
u
3
= h545822815415u
11
a
5
− 8124336604603u
11
a
4
+ ··· − 7690591677159a + 38068629937764,
− 3u
11
a
4
+ u
11
a
3
+ ··· + 21a + 95,
u
12
+ 3u
11
+ 8u
10
+ 13u
9
+ 18u
8
+ 21u
7
+ 19u
6
+ 17u
5
+ 10u
4
+ 6u
3
+ 4u
2
+ 1i
I
u
4
= h−15385u
25
− 30619u
24
+ ··· + 143017b + 1607536,
− 229648u
25
− 1852569u
24
+ ··· + 143017a − 478848, u
26
+ 8u
25
+ ··· + 62u + 7i
I
u
5
= h−a
3
u
2
+ a
3
u − a
2
u
2
+ a
3
− 2a
2
u − 2u
2
a − a
2
− 6au + 2u
2
+ 2b − 2a + u + 2,
a
3
u
2
+ a
4
+ 2a
3
− 2a
2
u + 3u
2
a − a
2
+ au + 10u
2
+ 5a + 5u + 17, u
3
+ u
2
+ 2u + 1i
I
u
6
= h−9a
5
u − 20a
5
+ 14a
4
u − 31a
4
+ 73a
3
u + 38a
3
− 18a
2
u + 46a
2
− 82au + 43b − 15a − 17u − 33,
a
6
− a
5
u − 2a
4
u − 3a
4
+ 3a
3
u + 2a
3
+ a
2
u − a
2
− 2au + a + u + 1, u
2
+ u + 1i
I
u
7
= h−u
2
+ b − u − 1, u
2
+ a + 1, u
3
+ u
2
+ 2u + 1i
I
u
8
= hb, a − 1, u
3
+ u
2
+ 2u + 1i
I
u
9
= hb + u, a, u
3
+ u
2
+ 2u + 1i
I
u
10
= hb + u, a − 1, u
2
− u + 1i
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).
1
* 10 irreducible components of dim
C
= 0, with total 180 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= h−3u
18
+ 21u
17
+ · · · + 4b + 12, 3u
18
− 15u
17
+ · · · + 8a + 60, u
19
−
7u
18
+ · · · − 36u + 8i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
−0.375000u
18
+ 1.87500u
17
+ ··· + 29.7500u − 7.50000
3
4
u
18
−
21
4
u
17
+ ··· + 21u − 3
a
10
=
−
3
8
u
18
+
7
8
u
17
+ ··· +
239
4
u −
27
2
−
1
4
u
18
−
1
4
u
17
+ ··· + 27u − 5
a
8
=
3
8
u
18
−
27
8
u
17
+ ··· +
203
4
u −
21
2
3
4
u
18
−
21
4
u
17
+ ··· + 21u − 3
a
3
=
5
8
u
18
−
37
8
u
17
+ ··· +
83
4
u − 3
3
4
u
18
−
19
4
u
17
+ ··· +
15
2
u − 1
a
7
=
−1.37500u
18
+ 9.87500u
17
+ ··· + 23.7500u − 7.50000
−
5
4
u
18
+
31
4
u
17
+ ··· + 7u − 1
a
12
=
−
7
8
u
18
+
47
8
u
17
+ ··· −
57
4
u + 2
1
4
u
18
−
9
4
u
17
+ ··· +
61
2
u − 7
a
6
=
7
8
u
18
−
37
8
u
17
+ ··· −
25
2
u + 3
−u
18
+
15
2
u
17
+ ··· −
71
2
u + 9
a
11
=
1
8
u
18
−
17
8
u
17
+ ··· −
11
4
u +
5
2
5
4
u
18
−
35
4
u
17
+ ··· + 19u − 5
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
18
−7u
17
+ 28u
16
−77u
15
+ 159u
14
−256u
13
+ 322u
12
−304u
11
+
174u
10
+ 38u
9
− 247u
8
+ 357u
7
− 324u
6
+ 183u
5
− 32u
4
− 69u
3
+ 81u
2
− 50u + 10
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
19
− 7u
18
+ ··· − 36u + 8
c
2
, c
6
, c
8
c
12
u
19
+ 2u
17
+ ··· + 5u + 1
c
3
, c
9
u
19
− 5u
18
+ ··· + 22u + 12
c
5
, c
11
u
19
− 11u
18
+ ··· − 224u + 32
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
19
+ 11y
18
+ ··· − 304y −64
c
2
, c
6
, c
8
c
12
y
19
+ 4y
18
+ ··· + 5y −1
c
3
, c
9
y
19
− 15y
18
+ ··· − 164y −144
c
5
, c
11
y
19
+ 9y
18
+ ··· + 512y −1024
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.089256 + 1.007980I
a = 1.05363 − 1.09151I
b = −1.00618 − 1.15946I
0.28070 − 2.38140I −5.46513 + 2.98597I
u = −0.089256 − 1.007980I
a = 1.05363 + 1.09151I
b = −1.00618 + 1.15946I
0.28070 + 2.38140I −5.46513 − 2.98597I
u = −0.129693 + 1.056200I
a = −0.901489 + 0.653587I
b = 0.573401 + 1.036920I
4.83655 + 0.75731I 0.29531 + 1.48803I
u = −0.129693 − 1.056200I
a = −0.901489 − 0.653587I
b = 0.573401 − 1.036920I
4.83655 − 0.75731I 0.29531 − 1.48803I
u = 1.070160 + 0.136306I
a = 0.880972 − 0.767951I
b = −1.047450 + 0.701745I
−8.89959 + 8.35587I −14.4938 − 6.1627I
u = 1.070160 − 0.136306I
a = 0.880972 + 0.767951I
b = −1.047450 − 0.701745I
−8.89959 − 8.35587I −14.4938 + 6.1627I
u = −0.283957 + 1.128460I
a = 0.468063 − 0.377219I
b = −0.292767 − 0.635305I
2.62810 + 3.46250I −5.41765 − 4.29370I
u = −0.283957 − 1.128460I
a = 0.468063 + 0.377219I
b = −0.292767 + 0.635305I
2.62810 − 3.46250I −5.41765 + 4.29370I
u = 1.041110 + 0.527820I
a = −0.102160 + 0.634385I
b = 0.441200 − 0.606542I
−1.27781 + 2.04691I −4.21735 − 12.06061I
u = 1.041110 − 0.527820I
a = −0.102160 − 0.634385I
b = 0.441200 + 0.606542I
−1.27781 − 2.04691I −4.21735 + 12.06061I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.726236
a = 0.400633
b = 0.290954
−1.16657 −7.54420
u = 0.311802 + 0.537677I
a = 0.371981 + 1.120770I
b = 0.486627 − 0.549464I
−0.73404 + 1.68177I −4.58767 − 4.23908I
u = 0.311802 − 0.537677I
a = 0.371981 − 1.120770I
b = 0.486627 + 0.549464I
−0.73404 − 1.68177I −4.58767 + 4.23908I
u = 0.56617 + 1.36797I
a = −1.054680 + 0.464599I
b = 1.23269 + 1.17973I
−1.0494 − 20.1774I −7.61137 + 10.06897I
u = 0.56617 − 1.36797I
a = −1.054680 − 0.464599I
b = 1.23269 − 1.17973I
−1.0494 + 20.1774I −7.61137 − 10.06897I
u = 0.61070 + 1.36309I
a = 0.904319 − 0.205921I
b = −0.832955 − 1.106920I
5.3054 − 14.5379I −4.33039 + 10.14035I
u = 0.61070 − 1.36309I
a = 0.904319 + 0.205921I
b = −0.832955 + 1.106920I
5.3054 + 14.5379I −4.33039 − 10.14035I
u = 0.76609 + 1.32486I
a = −0.570950 − 0.103738I
b = 0.299958 + 0.835901I
4.42824 − 6.79161I 0.60019 + 10.60796I
u = 0.76609 − 1.32486I
a = −0.570950 + 0.103738I
b = 0.299958 − 0.835901I
4.42824 + 6.79161I 0.60019 − 10.60796I
7
II. I
u
2
=
h−9.93×10
5
u
27
+1.26×10
7
u
26
+· · · +3.45×10
4
b+6.74×10
7
, 6.74×10
7
u
27
−
8.59 × 10
8
u
26
+ · · · + 2.93 × 10
6
a − 5.20 × 10
9
, u
28
− 14u
27
+ · · · − 855u + 85i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
−23.0174u
27
+ 293.431u
26
+ ··· − 16206.9u + 1776.64
28.8128u
27
− 366.456u
26
+ ··· + 17903.2u − 1956.48
a
10
=
15.6733u
27
− 202.020u
26
+ ··· + 10608.3u − 1152.25
−66.8738u
27
+ 859.315u
26
+ ··· − 45141.3u + 4901.10
a
8
=
5.79541u
27
− 73.0251u
26
+ ··· + 1696.29u − 179.843
28.8128u
27
− 366.456u
26
+ ··· + 17903.2u − 1956.48
a
3
=
−10.2277u
27
+ 130.845u
26
+ ··· − 6911.51u + 756.352
−76.4924u
27
+ 982.058u
26
+ ··· − 51779.1u + 5632.50
a
7
=
45.0001u
27
− 576.476u
26
+ ··· + 28129.0u − 3053.06
−140.536u
27
+ 1807.65u
26
+ ··· − 95332.1u + 10352.0
a
12
=
54.3698u
27
− 696.998u
26
+ ··· + 37058.1u − 4043.28
−64.1800u
27
+ 822.445u
26
+ ··· − 42441.9u + 4621.44
a
6
=
14.5690u
27
− 185.347u
26
+ ··· + 7527.26u − 813.539
57.4557u
27
− 734.448u
26
+ ··· + 38610.4u − 4216.93
a
11
=
−36.9975u
27
+ 469.587u
26
+ ··· − 23688.5u + 2597.06
54.5215u
27
− 700.386u
26
+ ··· + 34381.6u − 3716.35
(ii) Obstruction class = −1
(iii) Cusp Shapes =
12799129
34453
u
27
−
164577489
34453
u
26
+ ··· +
8305113305
34453
u −
900475230
34453
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
u
28
− 14u
27
+ ··· − 855u + 85
c
2
, c
6
, c
8
c
12
u
28
+ 4u
27
+ ··· − 2u + 1
c
3
, c
9
(u
14
+ 2u
13
+ ··· − u + 1)
2
c
5
, c
11
(u
14
− 9u
13
+ ··· − 416u + 64)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
28
+ 22y
27
+ ··· + 79025y + 7225
c
2
, c
6
, c
8
c
12
y
28
+ 4y
27
+ ··· − 10y + 1
c
3
, c
9
(y
14
+ 4y
12
+ ··· − 3y + 1)
2
c
5
, c
11
(y
14
+ 15y
13
+ ··· − 5120y + 4096)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.220870 + 0.964019I
a = 0.976311 − 0.269060I
b = −0.475016 − 0.881755I
3.33157 − 0.04587I 0
u = 0.220870 − 0.964019I
a = 0.976311 + 0.269060I
b = −0.475016 + 0.881755I
3.33157 + 0.04587I 0
u = 0.122015 + 0.951919I
a = −1.22987 + 0.91180I
b = 1.01802 + 1.05948I
−0.07368 − 3.51148I −8.00000 + 0.I
u = 0.122015 − 0.951919I
a = −1.22987 − 0.91180I
b = 1.01802 − 1.05948I
−0.07368 + 3.51148I −8.00000 + 0.I
u = −0.244537 + 0.840894I
a = −0.869115 − 0.048582I
b = −0.253383 + 0.718954I
−0.07368 + 3.51148I −8.00000 − 3.11087I
u = −0.244537 − 0.840894I
a = −0.869115 + 0.048582I
b = −0.253383 − 0.718954I
−0.07368 − 3.51148I −8.00000 + 3.11087I
u = 1.160470 + 0.000299I
a = −0.944468 − 0.613736I
b = 1.095850 + 0.712507I
−5.3108 − 14.1347I 0
u = 1.160470 − 0.000299I
a = −0.944468 + 0.613736I
b = 1.095850 − 0.712507I
−5.3108 + 14.1347I 0
u = 0.725406 + 0.404321I
a = −0.59123 + 1.38586I
b = 0.989219 − 0.766265I
−3.19044 + 2.69182I −19.3369 − 28.0122I
u = 0.725406 − 0.404321I
a = −0.59123 − 1.38586I
b = 0.989219 + 0.766265I
−3.19044 − 2.69182I −19.3369 + 28.0122I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493746 + 1.144530I
a = −1.266750 + 0.472811I
b = 1.16660 + 1.21638I
−0.82954 − 7.36918I 0
u = 0.493746 − 1.144530I
a = −1.266750 − 0.472811I
b = 1.16660 − 1.21638I
−0.82954 + 7.36918I 0
u = 0.288974 + 1.259790I
a = 0.981923 − 0.455892I
b = −0.858078 − 1.105270I
8.09763 − 2.64325I 0
u = 0.288974 − 1.259790I
a = 0.981923 + 0.455892I
b = −0.858078 + 1.105270I
8.09763 + 2.64325I 0
u = 0.601682 + 1.216810I
a = −1.019270 + 0.137827I
b = 0.780986 + 1.157340I
1.26514 − 7.93875I 0
u = 0.601682 − 1.216810I
a = −1.019270 − 0.137827I
b = 0.780986 − 1.157340I
1.26514 + 7.93875I 0
u = 1.366350 + 0.089976I
a = 0.354535 − 0.376999I
b = −0.518338 + 0.483212I
1.26514 + 7.93875I 0
u = 1.366350 − 0.089976I
a = 0.354535 + 0.376999I
b = −0.518338 − 0.483212I
1.26514 − 7.93875I 0
u = 0.567715 + 1.286990I
a = 1.111150 − 0.453605I
b = −1.21460 − 1.17252I
−5.3108 − 14.1347I 0
u = 0.567715 − 1.286990I
a = 1.111150 + 0.453605I
b = −1.21460 + 1.17252I
−5.3108 + 14.1347I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.250099 + 0.518873I
a = 1.58195 + 0.00658I
b = −0.392229 − 0.822475I
3.33157 + 0.04587I −1.17760 + 1.07149I
u = 0.250099 − 0.518873I
a = 1.58195 − 0.00658I
b = −0.392229 + 0.822475I
3.33157 − 0.04587I −1.17760 − 1.07149I
u = 0.24300 + 1.41025I
a = −0.643805 + 0.208891I
b = 0.451032 + 0.857168I
8.09763 + 2.64325I 0
u = 0.24300 − 1.41025I
a = −0.643805 − 0.208891I
b = 0.451032 − 0.857168I
8.09763 − 2.64325I 0
u = 0.82492 + 1.56847I
a = −0.060677 + 0.273569I
b = 0.479139 − 0.130503I
−0.82954 + 7.36918I 0
u = 0.82492 − 1.56847I
a = −0.060677 − 0.273569I
b = 0.479139 + 0.130503I
−0.82954 − 7.36918I 0
u = 0.37929 + 1.83155I
a = −0.057146 − 0.158811I
b = −0.269196 + 0.164900I
−3.19044 + 2.69182I 0
u = 0.37929 − 1.83155I
a = −0.057146 + 0.158811I
b = −0.269196 − 0.164900I
−3.19044 − 2.69182I 0
13
III. I
u
3
= h5.46 × 10
11
a
5
u
11
− 8.12 × 10
12
a
4
u
11
+ · · · − 7.69 × 10
12
a + 3.81 ×
10
13
, −3u
11
a
4
+ u
11
a
3
+ · · · + 21a + 95, u
12
+ 3u
11
+ · · · + 4u
2
+ 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
a
−0.0661105a
5
u
11
+ 0.984027a
4
u
11
+ ··· + 0.931491a − 4.61091
a
10
=
−0.141190a
5
u
11
+ 0.271994a
4
u
11
+ ··· + 1.47180a − 3.20730
−0.292464a
5
u
11
+ 0.0577256a
4
u
11
+ ··· + 0.826930a − 2.94212
a
8
=
−0.0661105a
5
u
11
+ 0.984027a
4
u
11
+ ··· + 1.93149a − 4.61091
−0.0661105a
5
u
11
+ 0.984027a
4
u
11
+ ··· + 0.931491a − 4.61091
a
3
=
−1.03112a
5
u
11
− 0.0958048a
4
u
11
+ ··· − 3.35664a − 3.06813
−0.807877a
5
u
11
+ 0.0734221a
4
u
11
+ ··· − 2.59366a − 0.289458
a
7
=
−0.300034a
5
u
11
+ 0.348634a
4
u
11
+ ··· + 1.91449a − 1.62119
−0.528393a
5
u
11
+ 0.238256a
4
u
11
+ ··· − 0.0490275a + 0.579304
a
12
=
a
2
u
−0.619812a
5
u
11
− 0.0748662a
4
u
11
+ ··· − 0.523197a + 1.74280
a
6
=
−0.418102a
5
u
11
− 0.227140a
4
u
11
+ ··· − 1.99363a − 0.387884
−0.0626009a
5
u
11
+ 0.0471036a
4
u
11
+ ··· − 0.374182a + 2.20004
a
11
=
0.348882a
5
u
11
− 0.0682222a
4
u
11
+ ··· − 0.105524a − 2.43122
0.557211a
5
u
11
+ 0.121970a
4
u
11
+ ··· + 0.149015a − 0.542756
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
18401813591608
8256215143297
u
11
a
5
−
4028033611868
8256215143297
u
11
a
4
+ ··· −
4921195373544
8256215143297
a −
130687438596918
8256215143297
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(u
12
+ 3u
11
+ ··· + 4u
2
+ 1)
6
c
2
, c
6
, c
8
c
12
u
72
+ 3u
71
+ ··· + 354u + 59
c
3
, c
9
(u
36
− 11u
34
+ ··· + 1120u + 320)
2
c
5
, c
11
(u
3
+ u
2
+ 2u + 1)
24
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y
12
+ 7y
11
+ ··· + 8y + 1)
6
c
2
, c
6
, c
8
c
12
y
72
− 23y
71
+ ··· − 406510y + 3481
c
3
, c
9
(y
36
− 22y
35
+ ··· − 97280y + 102400)
2
c
5
, c
11
(y
3
+ 3y
2
+ 2y −1)
24
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.234552 + 1.002020I
a = −0.720810 + 1.054620I
b = 0.95349 + 1.51437I
−0.94621 − 4.13739I −9.48147 + 7.59495I
u = 0.234552 + 1.002020I
a = 0.688527 − 0.072860I
b = −1.69950 + 0.60321I
3.19138 − 6.96551I −2.95220 + 10.57440I
u = 0.234552 + 1.002020I
a = −1.64398 + 0.56675I
b = 1.225820 + 0.474901I
−0.94621 − 4.13739I −9.48147 + 7.59495I
u = 0.234552 + 1.002020I
a = −0.19432 − 1.74157I
b = −0.234503 − 0.672828I
3.19138 − 6.96551I −2.95220 + 10.57440I
u = 0.234552 + 1.002020I
a = −0.064271 + 0.176004I
b = 2.12527 − 1.85054I
−0.94621 − 9.79363I −9.4815 + 13.5538I
u = 0.234552 + 1.002020I
a = 1.28018 + 2.42066I
b = 0.191434 + 0.023119I
−0.94621 − 9.79363I −9.4815 + 13.5538I
u = 0.234552 − 1.002020I
a = −0.720810 − 1.054620I
b = 0.95349 − 1.51437I
−0.94621 + 4.13739I −9.48147 − 7.59495I
u = 0.234552 − 1.002020I
a = 0.688527 + 0.072860I
b = −1.69950 − 0.60321I
3.19138 + 6.96551I −2.95220 − 10.57440I
u = 0.234552 − 1.002020I
a = −1.64398 − 0.56675I
b = 1.225820 − 0.474901I
−0.94621 + 4.13739I −9.48147 − 7.59495I
u = 0.234552 − 1.002020I
a = −0.19432 + 1.74157I
b = −0.234503 + 0.672828I
3.19138 + 6.96551I −2.95220 − 10.57440I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.234552 − 1.002020I
a = −0.064271 − 0.176004I
b = 2.12527 + 1.85054I
−0.94621 + 9.79363I −9.4815 − 13.5538I
u = 0.234552 − 1.002020I
a = 1.28018 − 2.42066I
b = 0.191434 − 0.023119I
−0.94621 + 9.79363I −9.4815 − 13.5538I
u = −1.090290 + 0.140460I
a = −1.014270 + 0.266172I
b = 1.17507 − 0.87900I
−5.72690 + 3.91075I −17.7913 − 8.6071I
u = −1.090290 + 0.140460I
a = 0.748871 + 0.516780I
b = −1.31217 − 0.63591I
−5.72690 − 1.74550I −17.7913 − 2.6482I
u = −1.090290 + 0.140460I
a = 0.702755 + 0.135494I
b = −0.649097 + 0.219395I
−1.58932 + 1.08263I −11.26202 − 5.62762I
u = −1.090290 + 0.140460I
a = −1.109950 − 0.726241I
b = 0.889075 + 0.458254I
−5.72690 − 1.74550I −17.7913 − 2.6482I
u = −1.090290 + 0.140460I
a = 1.162330 − 0.656465I
b = −1.068470 + 0.432670I
−5.72690 + 3.91075I −17.7913 − 8.6071I
u = −1.090290 + 0.140460I
a = −0.611124 + 0.122496I
b = 0.785240 + 0.049019I
−1.58932 + 1.08263I −11.26202 − 5.62762I
u = −1.090290 − 0.140460I
a = −1.014270 − 0.266172I
b = 1.17507 + 0.87900I
−5.72690 − 3.91075I −17.7913 + 8.6071I
u = −1.090290 − 0.140460I
a = 0.748871 − 0.516780I
b = −1.31217 + 0.63591I
−5.72690 + 1.74550I −17.7913 + 2.6482I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.090290 − 0.140460I
a = 0.702755 − 0.135494I
b = −0.649097 − 0.219395I
−1.58932 − 1.08263I −11.26202 + 5.62762I
u = −1.090290 − 0.140460I
a = −1.109950 + 0.726241I
b = 0.889075 − 0.458254I
−5.72690 + 1.74550I −17.7913 + 2.6482I
u = −1.090290 − 0.140460I
a = 1.162330 + 0.656465I
b = −1.068470 − 0.432670I
−5.72690 − 3.91075I −17.7913 + 8.6071I
u = −1.090290 − 0.140460I
a = −0.611124 − 0.122496I
b = 0.785240 − 0.049019I
−1.58932 − 1.08263I −11.26202 + 5.62762I
u = 0.185688 + 0.817666I
a = −0.948598 + 0.343126I
b = 1.295990 − 0.229859I
−1.58932 − 1.08263I −11.26202 + 5.62762I
u = 0.185688 + 0.817666I
a = 0.344955 − 1.070660I
b = −0.62210 − 2.20652I
−5.72690 + 1.74550I −17.7913 + 2.6482I
u = 0.185688 + 0.817666I
a = −0.07496 + 1.56796I
b = 0.456706 + 0.711922I
−1.58932 − 1.08263I −11.26202 + 5.62762I
u = 0.185688 + 0.817666I
a = −0.067503 − 0.291607I
b = −2.28703 + 1.05977I
−5.72690 − 3.91075I −17.7913 + 8.6071I
u = 0.185688 + 0.817666I
a = 2.73052 − 0.14073I
b = −0.939496 − 0.083249I
−5.72690 + 1.74550I −17.7913 + 2.6482I
u = 0.185688 + 0.817666I
a = −0.62849 − 2.93974I
b = −0.225903 + 0.109343I
−5.72690 − 3.91075I −17.7913 + 8.6071I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.185688 − 0.817666I
a = −0.948598 − 0.343126I
b = 1.295990 + 0.229859I
−1.58932 + 1.08263I −11.26202 − 5.62762I
u = 0.185688 − 0.817666I
a = 0.344955 + 1.070660I
b = −0.62210 + 2.20652I
−5.72690 − 1.74550I −17.7913 − 2.6482I
u = 0.185688 − 0.817666I
a = −0.07496 − 1.56796I
b = 0.456706 − 0.711922I
−1.58932 + 1.08263I −11.26202 − 5.62762I
u = 0.185688 − 0.817666I
a = −0.067503 + 0.291607I
b = −2.28703 − 1.05977I
−5.72690 + 3.91075I −17.7913 − 8.6071I
u = 0.185688 − 0.817666I
a = 2.73052 + 0.14073I
b = −0.939496 + 0.083249I
−5.72690 − 1.74550I −17.7913 − 2.6482I
u = 0.185688 − 0.817666I
a = −0.62849 + 2.93974I
b = −0.225903 − 0.109343I
−5.72690 + 3.91075I −17.7913 − 8.6071I
u = −0.529049 + 1.245360I
a = 0.890029 + 0.495100I
b = −1.31752 + 1.32168I
−2.39928 + 7.38625I −13.25651 − 4.74994I
u = −0.529049 + 1.245360I
a = 0.870453 + 0.208440I
b = −0.806758 + 0.638494I
1.73831 + 4.55813I −6.72725 − 1.77049I
u = −0.529049 + 1.245360I
a = −0.667447 − 0.364270I
b = 0.720095 − 0.973752I
1.73831 + 4.55813I −6.72725 − 1.77049I
u = −0.529049 + 1.245360I
a = 0.056263 + 0.623747I
b = −0.375011 + 0.044252I
−2.39928 + 1.73000I −13.25651 + 1.20895I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.529049 + 1.245360I
a = −1.279760 − 0.514283I
b = 1.087450 − 0.846474I
−2.39928 + 7.38625I −13.25651 − 4.74994I
u = −0.529049 + 1.245360I
a = −0.138468 − 0.242303I
b = 0.806554 + 0.259924I
−2.39928 + 1.73000I −13.25651 + 1.20895I
u = −0.529049 − 1.245360I
a = 0.890029 − 0.495100I
b = −1.31752 − 1.32168I
−2.39928 − 7.38625I −13.25651 + 4.74994I
u = −0.529049 − 1.245360I
a = 0.870453 − 0.208440I
b = −0.806758 − 0.638494I
1.73831 − 4.55813I −6.72725 + 1.77049I
u = −0.529049 − 1.245360I
a = −0.667447 + 0.364270I
b = 0.720095 + 0.973752I
1.73831 − 4.55813I −6.72725 + 1.77049I
u = −0.529049 − 1.245360I
a = 0.056263 − 0.623747I
b = −0.375011 − 0.044252I
−2.39928 − 1.73000I −13.25651 − 1.20895I
u = −0.529049 − 1.245360I
a = −1.279760 + 0.514283I
b = 1.087450 + 0.846474I
−2.39928 − 7.38625I −13.25651 + 4.74994I
u = −0.529049 − 1.245360I
a = −0.138468 + 0.242303I
b = 0.806554 − 0.259924I
−2.39928 − 1.73000I −13.25651 − 1.20895I
u = 0.251512 + 0.449740I
a = 0.157220 + 1.333380I
b = 1.273440 − 0.607533I
−2.39928 + 1.73000I −13.25651 + 1.20895I
u = 0.251512 + 0.449740I
a = 1.78243 − 0.04706I
b = −0.877545 + 0.518333I
1.73831 + 4.55813I −6.72725 − 1.77049I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.251512 + 0.449740I
a = −0.04671 − 1.97735I
b = −0.469465 − 0.789793I
1.73831 + 4.55813I −6.72725 − 1.77049I
u = 0.251512 + 0.449740I
a = −0.78901 + 1.82839I
b = 0.27710 + 1.74968I
−2.39928 + 7.38625I −13.25651 − 4.74994I
u = 0.251512 + 0.449740I
a = −0.17720 + 2.73239I
b = 0.560132 − 0.406069I
−2.39928 + 1.73000I −13.25651 + 1.20895I
u = 0.251512 + 0.449740I
a = −3.22606 − 1.18799I
b = 1.020750 − 0.105012I
−2.39928 + 7.38625I −13.25651 − 4.74994I
u = 0.251512 − 0.449740I
a = 0.157220 − 1.333380I
b = 1.273440 + 0.607533I
−2.39928 − 1.73000I −13.25651 − 1.20895I
u = 0.251512 − 0.449740I
a = 1.78243 + 0.04706I
b = −0.877545 − 0.518333I
1.73831 − 4.55813I −6.72725 + 1.77049I
u = 0.251512 − 0.449740I
a = −0.04671 + 1.97735I
b = −0.469465 + 0.789793I
1.73831 − 4.55813I −6.72725 + 1.77049I
u = 0.251512 − 0.449740I
a = −0.78901 − 1.82839I
b = 0.27710 − 1.74968I
−2.39928 − 7.38625I −13.25651 + 4.74994I
u = 0.251512 − 0.449740I
a = −0.17720 − 2.73239I
b = 0.560132 + 0.406069I
−2.39928 − 1.73000I −13.25651 − 1.20895I
u = 0.251512 − 0.449740I
a = −3.22606 + 1.18799I
b = 1.020750 + 0.105012I
−2.39928 − 7.38625I −13.25651 + 4.74994I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.55241 + 1.40748I
a = −0.848748 − 0.631916I
b = 1.07565 − 1.32900I
−0.94621 + 9.79363I −9.4815 − 13.5538I
u = −0.55241 + 1.40748I
a = 1.078110 + 0.341098I
b = −1.35827 + 0.84552I
−0.94621 + 9.79363I −9.4815 − 13.5538I
u = −0.55241 + 1.40748I
a = 0.717143 + 0.435072I
b = −0.661991 + 0.890809I
3.19138 + 6.96551I −2.95220 − 10.57440I
u = −0.55241 + 1.40748I
a = −0.708387 − 0.192308I
b = 1.008510 − 0.769026I
3.19138 + 6.96551I −2.95220 − 10.57440I
u = −0.55241 + 1.40748I
a = −0.352995 − 0.502106I
b = 0.378753 − 0.019095I
−0.94621 + 4.13739I −9.48147 − 7.59495I
u = −0.55241 + 1.40748I
a = 0.103275 + 0.228566I
b = −0.901704 + 0.219465I
−0.94621 + 4.13739I −9.48147 − 7.59495I
u = −0.55241 − 1.40748I
a = −0.848748 + 0.631916I
b = 1.07565 + 1.32900I
−0.94621 − 9.79363I −9.4815 + 13.5538I
u = −0.55241 − 1.40748I
a = 1.078110 − 0.341098I
b = −1.35827 − 0.84552I
−0.94621 − 9.79363I −9.4815 + 13.5538I
u = −0.55241 − 1.40748I
a = 0.717143 − 0.435072I
b = −0.661991 − 0.890809I
3.19138 − 6.96551I −2.95220 + 10.57440I
u = −0.55241 − 1.40748I
a = −0.708387 + 0.192308I
b = 1.008510 + 0.769026I
3.19138 − 6.96551I −2.95220 + 10.57440I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.55241 − 1.40748I
a = −0.352995 + 0.502106I
b = 0.378753 + 0.019095I
−0.94621 − 4.13739I −9.48147 + 7.59495I
u = −0.55241 − 1.40748I
a = 0.103275 − 0.228566I
b = −0.901704 − 0.219465I
−0.94621 − 4.13739I −9.48147 + 7.59495I
24
IV.
I
u
4
= h−1.54 × 10
4
u
25
− 3.06 × 10
4
u
24
+ · · · + 1.43 × 10
5
b + 1.61 × 10
6
, −2.30 ×
10
5
u
25
−1.85×10
6
u
24
+· · ·+1.43×10
5
a−4.79×10
5
, u
26
+8u
25
+· · ·+62u+7i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
u
3
+ u
a
9
=
1.60574u
25
+ 12.9535u
24
+ ··· + 63.1609u + 3.34819
0.107575u
25
+ 0.214093u
24
+ ··· − 96.2076u − 11.2402
a
10
=
2.07086u
25
+ 16.3907u
24
+ ··· + 10.9392u − 3.39093
0.398428u
25
+ 2.68665u
24
+ ··· − 58.3252u − 6.48759
a
8
=
1.71331u
25
+ 13.1676u
24
+ ··· − 33.0468u − 7.89198
0.107575u
25
+ 0.214093u
24
+ ··· − 96.2076u − 11.2402
a
3
=
0.145276u
25
+ 1.23548u
24
+ ··· + 3.71046u + 2.78149
0.555451u
25
+ 3.96142u
24
+ ··· + 24.3411u + 2.87123
a
7
=
1.44082u
25
+ 10.9124u
24
+ ··· + 70.0376u + 8.96126
−1.20267u
25
− 9.48464u
24
+ ··· − 131.319u − 16.8348
a
12
=
0.548480u
25
+ 3.60536u
24
+ ··· + 10.5103u − 0.548263
−0.782480u
25
− 5.61567u
24
+ ··· − 33.5540u − 3.83936
a
6
=
1.07562u
25
+ 8.70837u
24
+ ··· + 161.903u + 22.9308
−0.540768u
25
− 4.59087u
24
+ ··· − 89.4320u − 13.0067
a
11
=
−2.51044u
25
− 18.3829u
24
+ ··· − 187.442u − 25.5075
2.60958u
25
+ 19.0437u
24
+ ··· + 155.294u + 19.2651
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1001674
143017
u
25
+
7560050
143017
u
24
+ ··· +
64577203
143017
u +
731282
20431
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
26
− 8u
25
+ ··· − 62u + 7
c
2
, c
6
, c
8
c
12
u
26
+ 2u
25
+ ··· − 3u + 1
c
3
, c
9
(u
13
− 3u
11
+ ··· + 7u − 2)
2
c
4
, c
10
u
26
+ 8u
25
+ ··· + 62u + 7
c
5
, c
11
u
26
+ 17u
24
+ ··· + 127u
2
+ 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
y
26
+ 20y
25
+ ··· + 160y + 49
c
2
, c
6
, c
8
c
12
y
26
− 8y
25
+ ··· − 21y + 1
c
3
, c
9
(y
13
− 6y
12
+ ··· + 25y −4)
2
c
5
, c
11
(y
13
+ 17y
12
+ ··· + 127y + 1)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.126752 + 0.966195I
a = −0.91926 − 1.23027I
b = 1.07216 − 1.04412I
−0.80008 − 8.71139I −7.24650 + 3.93807I
u = 0.126752 − 0.966195I
a = −0.91926 + 1.23027I
b = 1.07216 + 1.04412I
−0.80008 + 8.71139I −7.24650 − 3.93807I
u = −1.104360 + 0.054100I
a = 1.029820 − 0.483545I
b = −1.111120 + 0.589718I
−5.20764 + 2.92822I −11.13108 − 2.29409I
u = −1.104360 − 0.054100I
a = 1.029820 + 0.483545I
b = −1.111120 − 0.589718I
−5.20764 − 2.92822I −11.13108 + 2.29409I
u = −0.249520 + 0.858731I
a = −1.26530 − 0.94200I
b = 1.124640 − 0.851506I
−1.63936 + 3.42007I −15.9102 − 3.3285I
u = −0.249520 − 0.858731I
a = −1.26530 + 0.94200I
b = 1.124640 + 0.851506I
−1.63936 − 3.42007I −15.9102 + 3.3285I
u = 0.311736 + 0.833354I
a = 0.122888 + 0.916019I
b = −0.725060 + 0.387965I
2.45972 − 6.02995I −7.20901 + 5.92270I
u = 0.311736 − 0.833354I
a = 0.122888 − 0.916019I
b = −0.725060 − 0.387965I
2.45972 + 6.02995I −7.20901 − 5.92270I
u = 0.027785 + 0.872149I
a = 1.09086 + 1.27146I
b = −1.07859 + 0.98672I
−5.20764 − 2.92822I −11.13108 + 2.29409I
u = 0.027785 − 0.872149I
a = 1.09086 − 1.27146I
b = −1.07859 − 0.98672I
−5.20764 + 2.92822I −11.13108 − 2.29409I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.456886 + 1.136290I
a = 0.398294 − 0.124934I
b = 0.323935 + 0.395494I
−0.37057 + 6.99005I −6.13816 − 3.85066I
u = 0.456886 − 1.136290I
a = 0.398294 + 0.124934I
b = 0.323935 − 0.395494I
−0.37057 − 6.99005I −6.13816 + 3.85066I
u = −0.673860 + 0.329753I
a = −0.79797 − 1.42231I
b = 1.006730 + 0.695309I
−3.19822 − 2.47147I −18.8522 − 7.6031I
u = −0.673860 − 0.329753I
a = −0.79797 + 1.42231I
b = 1.006730 − 0.695309I
−3.19822 + 2.47147I −18.8522 + 7.6031I
u = −0.475346 + 1.203380I
a = −1.135870 − 0.510890I
b = 1.15472 − 1.12403I
−0.37057 + 6.99005I −6.13816 − 3.85066I
u = −0.475346 − 1.203380I
a = −1.135870 + 0.510890I
b = 1.15472 + 1.12403I
−0.37057 − 6.99005I −6.13816 + 3.85066I
u = −0.781203 + 1.177850I
a = 0.326732 + 0.382643I
b = −0.705942 + 0.085920I
−1.63936 + 3.42007I −15.9102 − 3.3285I
u = −0.781203 − 1.177850I
a = 0.326732 − 0.382643I
b = −0.705942 − 0.085920I
−1.63936 − 3.42007I −15.9102 + 3.3285I
u = −0.570925 + 0.073702I
a = −1.299550 − 0.186223I
b = 0.755669 + 0.010539I
−2.22694 −18.0258 + 0.I
u = −0.570925 − 0.073702I
a = −1.299550 + 0.186223I
b = 0.755669 − 0.010539I
−2.22694 −18.0258 + 0.I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.53769 + 1.36875I
a = 0.986018 + 0.509889I
b = −1.22809 + 1.07545I
−0.80008 + 8.71139I −8.00000 − 3.93807I
u = −0.53769 − 1.36875I
a = 0.986018 − 0.509889I
b = −1.22809 − 1.07545I
−0.80008 − 8.71139I −8.00000 + 3.93807I
u = −0.59852 + 1.38494I
a = −0.661103 − 0.232284I
b = 0.717382 − 0.776563I
2.45972 + 6.02995I −8.00000 − 5.92270I
u = −0.59852 − 1.38494I
a = −0.661103 + 0.232284I
b = 0.717382 + 0.776563I
2.45972 − 6.02995I −8.00000 + 5.92270I
u = 0.06826 + 1.64669I
a = −0.089846 + 0.182370I
b = −0.306439 − 0.135500I
−3.19822 + 2.47147I −18.8522 + 0.I
u = 0.06826 − 1.64669I
a = −0.089846 − 0.182370I
b = −0.306439 + 0.135500I
−3.19822 − 2.47147I −18.8522 + 0.I
30
V.
I
u
5
= h−a
3
u
2
−a
2
u
2
+· · ·−2a+2, a
3
u
2
+3u
2
a+· · ·+5a+17, u
3
+u
2
+2u +1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
−u
2
− u − 1
a
9
=
a
1
2
a
3
u
2
+
1
2
a
2
u
2
+ ··· + a − 1
a
10
=
1
2
a
3
u
2
+ a
2
u
2
+ ··· + 2a +
1
2
3
2
a
2
u
2
+ 4u
2
a + ··· + a − 1
a
8
=
1
2
a
3
u
2
+
1
2
a
2
u
2
+ ··· + 2a − 1
1
2
a
3
u
2
+
1
2
a
2
u
2
+ ··· + a − 1
a
3
=
1
2
a
3
u
2
− a
2
u
2
+ ··· + a −
3
2
1
2
a
3
u
2
−
3
2
u
2
+ ··· + a
2
− 1
a
7
=
−
3
2
a
3
u
2
+ a
2
u
2
+ ··· − a −
1
2
−2a
3
u
2
+
1
2
a
2
u
2
+ ··· − 3a +
1
2
a
12
=
a
2
u
1
2
a
3
u
2
−
1
2
u
2
+ ··· + a −
3
2
a
6
=
1
2
a
3
u
2
− u
2
a + ··· −
3
2
u − 4
1
2
a
3
u
2
+
1
2
a
2
u
2
+ ··· + a + 1
a
11
=
1
2
a
3
u
2
+
1
2
a
2
u
2
+ ··· +
1
2
a
2
− 1
1
2
a
2
u
2
+ u
2
a + ··· −
1
2
a
3
+
3
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4a
3
u − 2a
2
u
2
+ 2a
3
− 2a
2
u − 4u
2
a − 4au − 10u
2
− 10u − 20
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
7
, c
10
, c
11
(u
3
+ u
2
+ 2u + 1)
4
c
2
, c
6
, c
8
c
12
u
12
− 2u
10
+ ··· + 18u
2
+ 23
c
3
, c
9
u
12
− u
11
+ ··· − 112u + 64
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
7
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)
4
c
2
, c
6
, c
8
c
12
y
12
− 4y
11
+ ··· + 828y + 529
c
3
, c
9
y
12
+ 25y
11
+ ··· + 7936y + 4096
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.854517 − 0.303520I
b = 1.90525 − 1.05169I
3.02413 + 8.48437I −2.49024 − 8.93834I
u = −0.215080 + 1.307140I
a = −1.061910 − 0.672209I
b = 0.444709 − 0.681213I
7.16171 + 5.65624I 4.03902 − 5.95889I
u = −0.215080 + 1.307140I
a = 0.561914 + 0.247756I
b = −1.10707 + 1.24349I
7.16171 + 5.65624I 4.03902 − 5.95889I
u = −0.215080 + 1.307140I
a = 1.01688 + 1.29025I
b = −0.580533 + 1.051690I
3.02413 + 8.48437I −2.49024 − 8.93834I
u = −0.215080 − 1.307140I
a = −0.854517 + 0.303520I
b = 1.90525 + 1.05169I
3.02413 − 8.48437I −2.49024 + 8.93834I
u = −0.215080 − 1.307140I
a = −1.061910 + 0.672209I
b = 0.444709 + 0.681213I
7.16171 − 5.65624I 4.03902 + 5.95889I
u = −0.215080 − 1.307140I
a = 0.561914 − 0.247756I
b = −1.10707 − 1.24349I
7.16171 − 5.65624I 4.03902 + 5.95889I
u = −0.215080 − 1.307140I
a = 1.01688 − 1.29025I
b = −0.580533 − 1.051690I
3.02413 − 8.48437I −2.49024 + 8.93834I
u = −0.569840
a = 0.97401 + 1.60320I
b = −1.217390 − 0.351288I
−5.25104 − 2.82812I −15.5488 + 2.9794I
u = −0.569840
a = 0.97401 − 1.60320I
b = −1.217390 + 0.351288I
−5.25104 + 2.82812I −15.5488 − 2.9794I
34
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.569840
a = −2.13637 + 0.61647I
b = 0.555029 − 0.913568I
−5.25104 + 2.82812I −15.5488 − 2.9794I
u = −0.569840
a = −2.13637 − 0.61647I
b = 0.555029 + 0.913568I
−5.25104 − 2.82812I −15.5488 + 2.9794I
35
VI.
I
u
6
= h−9a
5
u + 14a
4
u + · · · − 15a − 33, −a
5
u − 2a
4
u + · · · + a + 1, u
2
+ u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
u + 1
a
2
=
−u
u + 1
a
9
=
a
0.209302a
5
u − 0.325581a
4
u + ··· + 0.348837a + 0.767442
a
10
=
0.465116a
5
u + 0.720930a
4
u + ··· + 0.441860a + 0.372093
au
a
8
=
0.209302a
5
u − 0.325581a
4
u + ··· + 1.34884a + 0.767442
0.209302a
5
u − 0.325581a
4
u + ··· + 0.348837a + 0.767442
a
3
=
0.139535a
5
u + 1.11628a
4
u + ··· + 0.232558a + 0.511628
−0.441860a
5
u + 0.465116a
4
u + ··· + 0.930233a + 0.0465116
a
7
=
2au + a
0.209302a
5
u − 0.325581a
4
u + ··· − 0.651163a + 0.767442
a
12
=
a
2
u
0.581395a
5
u + 0.651163a
4
u + ··· − 0.697674a + 0.465116
a
6
=
0.279070a
5
u + 0.232558a
4
u + ··· − 0.534884a + 1.02326
0.325581a
5
u − 0.395349a
4
u + ··· + 0.209302a + 1.86047
a
11
=
−0.465116a
5
u − 0.720930a
4
u + ··· + 1.55814a − 0.372093
−0.255814a
5
u − 1.04651a
4
u + ··· + 0.906977a + 0.395349
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
44
43
a
5
u−
36
43
a
5
+
180
43
a
4
u+
56
43
a
4
+
140
43
a
3
u+
292
43
a
3
−
256
43
a
2
u−
72
43
a
2
−
96
43
au−
156
43
a−
280
43
u−
670
43
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(u
2
+ u + 1)
6
c
2
, c
6
, c
8
c
12
u
12
+ u
11
+ 5u
9
+ 12u
8
+ 5u
7
− 5u
6
− 9u
5
+ 8u
3
+ 4u
2
− 4u + 1
c
3
, c
9
(u
3
+ u
2
− 1)
4
c
5
, c
11
(u
3
+ u
2
+ 2u + 1)
4
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
(y
2
+ y + 1)
6
c
2
, c
6
, c
8
c
12
y
12
− y
11
+ ··· − 8y + 1
c
3
, c
9
(y
3
− y
2
+ 2y −1)
4
c
5
, c
11
(y
3
+ 3y
2
+ 2y −1)
4
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.045930 − 0.181543I
b = −0.743183 + 0.342830I
1.11345 + 4.05977I −6.98049 − 6.92820I
u = −0.500000 + 0.866025I
a = 0.921971 + 0.577427I
b = −1.16740 + 1.64205I
−3.02413 + 6.88789I −13.5098 − 9.9077I
u = −0.500000 + 0.866025I
a = −0.668492 − 0.472201I
b = 0.365745 − 0.996574I
1.11345 + 4.05977I −6.98049 − 6.92820I
u = −0.500000 + 0.866025I
a = 0.18118 + 1.48292I
b = −0.291045 − 0.197103I
−3.02413 + 1.23164I −13.50976 − 3.94876I
u = −0.500000 + 0.866025I
a = 0.025174 − 0.350604I
b = 1.37483 + 0.58456I
−3.02413 + 1.23164I −13.50976 − 3.94876I
u = −0.500000 + 0.866025I
a = −2.00576 − 0.18997I
b = 0.961053 − 0.509737I
−3.02413 + 6.88789I −13.5098 − 9.9077I
u = −0.500000 − 0.866025I
a = 1.045930 + 0.181543I
b = −0.743183 − 0.342830I
1.11345 − 4.05977I −6.98049 + 6.92820I
u = −0.500000 − 0.866025I
a = 0.921971 − 0.577427I
b = −1.16740 − 1.64205I
−3.02413 − 6.88789I −13.5098 + 9.9077I
u = −0.500000 − 0.866025I
a = −0.668492 + 0.472201I
b = 0.365745 + 0.996574I
1.11345 − 4.05977I −6.98049 + 6.92820I
u = −0.500000 − 0.866025I
a = 0.18118 − 1.48292I
b = −0.291045 + 0.197103I
−3.02413 − 1.23164I −13.50976 + 3.94876I
39
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 − 0.866025I
a = 0.025174 + 0.350604I
b = 1.37483 − 0.58456I
−3.02413 − 1.23164I −13.50976 + 3.94876I
u = −0.500000 − 0.866025I
a = −2.00576 + 0.18997I
b = 0.961053 + 0.509737I
−3.02413 − 6.88789I −13.5098 + 9.9077I
40
VII. I
u
7
= h−u
2
+ b − u − 1, u
2
+ a + 1, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
−u
2
− u − 1
a
9
=
−u
2
− 1
u
2
+ u + 1
a
10
=
−1
u
2
a
8
=
u
u
2
+ u + 1
a
3
=
u
2
+ 1
−u
2
− u − 1
a
7
=
0
−u
a
12
=
−1
0
a
6
=
1
0
a
11
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
− 8u − 20
41
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
9
u
3
− u
2
+ 2u − 1
c
2
, c
6
, c
8
c
12
u
3
− u
2
+ 1
c
4
, c
10
u
3
+ u
2
+ 2u + 1
c
5
, c
11
u
3
42
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
9
, c
10
y
3
+ 3y
2
+ 2y −1
c
2
, c
6
, c
8
c
12
y
3
− y
2
+ 2y −1
c
5
, c
11
y
3
43
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.662359 + 0.562280I
b = −0.877439 + 0.744862I
6.04826 + 5.65624I −4.98049 − 5.95889I
u = −0.215080 − 1.307140I
a = 0.662359 − 0.562280I
b = −0.877439 − 0.744862I
6.04826 − 5.65624I −4.98049 + 5.95889I
u = −0.569840
a = −1.32472
b = 0.754878
−2.22691 −18.0390
44
VIII. I
u
8
= hb, a − 1, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
−u
2
− u − 1
a
9
=
1
0
a
10
=
−u
−u
a
8
=
1
0
a
3
=
−u
2
+ 1
−u
2
a
7
=
−u
2
+ 1
−u
2
a
12
=
u
u
a
6
=
−u
2
+ 1
−u
2
a
11
=
−u
2
− 2u − 1
−u
2
− u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 10
45
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
10
c
11
, c
12
u
3
+ u
2
+ 2u + 1
c
3
u
3
− 3u
2
+ 2u + 1
c
6
, c
8
u
3
c
9
u
3
− u
2
+ 1
46
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
10
c
11
, c
12
y
3
+ 3y
2
+ 2y −1
c
3
y
3
− 5y
2
+ 10y −1
c
6
, c
8
y
3
c
9
y
3
− y
2
+ 2y −1
47
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 1.00000
b = 0
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = 1.00000
b = 0
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.569840
a = 1.00000
b = 0
−1.11345 −9.01950
48
IX. I
u
9
= hb + u, a, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
2
=
−u
−u
2
− u − 1
a
9
=
0
−u
a
10
=
−u
2
− 2u − 1
−u
2
− 2u
a
8
=
−u
−u
a
3
=
−u
−u
2
− u − 1
a
7
=
−u
2
+ 1
−u
2
+ u + 1
a
12
=
0
u
a
6
=
1
−u
2
a
11
=
−u
−u
2
− u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 10
49
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
7
, c
8
c
10
, c
11
u
3
+ u
2
+ 2u + 1
c
2
, c
12
u
3
c
3
u
3
− u
2
+ 1
c
9
u
3
− 3u
2
+ 2u + 1
50
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
7
, c
8
c
10
, c
11
y
3
+ 3y
2
+ 2y −1
c
2
, c
12
y
3
c
3
y
3
− y
2
+ 2y −1
c
9
y
3
− 5y
2
+ 10y −1
51
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0
b = 0.215080 − 1.307140I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = 0
b = 0.215080 + 1.307140I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.569840
a = 0
b = 0.569840
−1.11345 −9.01950
52
X. I
u
10
= hb + u, a − 1, u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u + 1
a
2
=
−u
u − 1
a
9
=
1
−u
a
10
=
1
−u
a
8
=
−u + 1
−u
a
3
=
1
−u + 1
a
7
=
−2u + 2
−u − 1
a
12
=
u
1
a
6
=
−u + 1
−1
a
11
=
2u − 1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3
53
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
10
, c
12
u
2
− u + 1
c
3
, c
9
u
2
c
5
, c
11
(u − 1)
2
54
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
10
, c
12
y
2
+ y + 1
c
3
, c
9
y
2
c
5
, c
11
(y −1)
2
55
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.00000
b = −0.500000 − 0.866025I
3.28987 −3.00000
u = 0.500000 − 0.866025I
a = 1.00000
b = −0.500000 + 0.866025I
3.28987 −3.00000
56
XI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
− u + 1)(u
2
+ u + 1)
6
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
6
· ((u
12
+ 3u
11
+ ··· + 4u
2
+ 1)
6
)(u
19
− 7u
18
+ ··· − 36u + 8)
· (u
26
− 8u
25
+ ··· − 62u + 7)(u
28
− 14u
27
+ ··· − 855u + 85)
c
2
, c
6
, c
8
c
12
u
3
(u
2
− u + 1)(u
3
− u
2
+ 1)(u
3
+ u
2
+ 2u + 1)(u
12
− 2u
10
+ ··· + 18u
2
+ 23)
· (u
12
+ u
11
+ 5u
9
+ 12u
8
+ 5u
7
− 5u
6
− 9u
5
+ 8u
3
+ 4u
2
− 4u + 1)
· (u
19
+ 2u
17
+ ··· + 5u + 1)(u
26
+ 2u
25
+ ··· − 3u + 1)
· (u
28
+ 4u
27
+ ··· − 2u + 1)(u
72
+ 3u
71
+ ··· + 354u + 59)
c
3
, c
9
u
2
(u
3
− 3u
2
+ 2u + 1)(u
3
− u
2
+ 1)(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
− 1)
4
· (u
12
− u
11
+ ··· − 112u + 64)(u
13
− 3u
11
+ ··· + 7u − 2)
2
· ((u
14
+ 2u
13
+ ··· − u + 1)
2
)(u
19
− 5u
18
+ ··· + 22u + 12)
· (u
36
− 11u
34
+ ··· + 1120u + 320)
2
c
4
, c
10
(u
2
− u + 1)(u
2
+ u + 1)
6
(u
3
+ u
2
+ 2u + 1)
7
· ((u
12
+ 3u
11
+ ··· + 4u
2
+ 1)
6
)(u
19
− 7u
18
+ ··· − 36u + 8)
· (u
26
+ 8u
25
+ ··· + 62u + 7)(u
28
− 14u
27
+ ··· − 855u + 85)
c
5
, c
11
u
3
(u − 1)
2
(u
3
+ u
2
+ 2u + 1)
34
(u
14
− 9u
13
+ ··· − 416u + 64)
2
· (u
19
− 11u
18
+ ··· − 224u + 32)(u
26
+ 17u
24
+ ··· + 127u
2
+ 1)
57
XII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
((y
2
+ y + 1)
7
)(y
3
+ 3y
2
+ 2y −1)
7
(y
12
+ 7y
11
+ ··· + 8y + 1)
6
· (y
19
+ 11y
18
+ ··· − 304y −64)(y
26
+ 20y
25
+ ··· + 160y + 49)
· (y
28
+ 22y
27
+ ··· + 79025y + 7225)
c
2
, c
6
, c
8
c
12
y
3
(y
2
+ y + 1)(y
3
− y
2
+ 2y −1)(y
3
+ 3y
2
+ 2y −1)
· (y
12
− 4y
11
+ ··· + 828y + 529)(y
12
− y
11
+ ··· − 8y + 1)
· (y
19
+ 4y
18
+ ··· + 5y −1)(y
26
− 8y
25
+ ··· − 21y + 1)
· (y
28
+ 4y
27
+ ··· − 10y + 1)(y
72
− 23y
71
+ ··· − 406510y + 3481)
c
3
, c
9
y
2
(y
3
− 5y
2
+ 10y −1)(y
3
− y
2
+ 2y −1)
5
(y
3
+ 3y
2
+ 2y −1)
· (y
12
+ 25y
11
+ ··· + 7936y + 4096)(y
13
− 6y
12
+ ··· + 25y −4)
2
· ((y
14
+ 4y
12
+ ··· − 3y + 1)
2
)(y
19
− 15y
18
+ ··· − 164y −144)
· (y
36
− 22y
35
+ ··· − 97280y + 102400)
2
c
5
, c
11
y
3
(y −1)
2
(y
3
+ 3y
2
+ 2y −1)
34
(y
13
+ 17y
12
+ ··· + 127y + 1)
2
· (y
14
+ 15y
13
+ ··· − 5120y + 4096)
2
· (y
19
+ 9y
18
+ ··· + 512y −1024)
58
