12n
0839
(K12n
0839
)
A knot diagram
1
Linearized knot diagam
4 10 6 9 8 2 10 1 12 6 2 5
Solving Sequence
5,9 1,4
2 8 6 3 12 10 7 11
c
4
c
1
c
8
c
5
c
3
c
12
c
9
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, a − 1, u
9
− 5u
8
+ 12u
7
− 16u
6
+ 13u
5
− 6u
4
+ 2u
3
− u
2
+ 2u − 1i
I
u
2
= hb + u, a + 1, u
9
− 3u
8
+ 4u
7
− 2u
6
+ u
5
− 2u
4
+ 2u
3
− u
2
− 1i
I
u
3
= hb − u, 4u
17
+ 8u
16
+ ··· + 2a − 5, u
18
+ 5u
17
+ ··· + 5u + 1i
I
u
4
= h−12u
17
− 44u
16
+ ··· + 2b − 4, a − 1, u
18
+ 5u
17
+ ··· + 5u + 1i
I
u
5
= h−582u
17
+ 8001u
16
+ ··· + 6236b + 10944, −342u
17
+ 5232u
16
+ ··· + 6236a − 30,
u
18
− 17u
17
+ ··· − 176u + 32i
I
u
6
= hb + u, −2u
7
− 5u
6
− 8u
5
− 9u
4
− 10u
3
− 7u
2
+ a − 7u − 3,
u
8
+ 3u
7
+ 5u
6
+ 6u
5
+ 7u
4
+ 6u
3
+ 5u
2
+ 3u + 1i
I
u
7
= hu
7
+ 2u
6
+ 3u
5
+ 4u
4
+ 5u
3
+ 3u
2
+ b + 3u + 2, a + 1, u
8
+ 3u
7
+ 5u
6
+ 6u
5
+ 7u
4
+ 6u
3
+ 5u
2
+ 3u + 1i
I
u
8
= h−au + b, −u
3
+ a
2
+ au + 4u
2
− 2a − 6u + 4, u
4
− 3u
3
+ 3u
2
− u − 1i
I
u
9
= h−14u
14
− 57u
13
+ ··· + 4b − 4, 4u
14
a − 24u
14
+ ··· + 5a − 25,
u
15
+ 5u
14
+ 11u
13
+ 10u
12
− 9u
11
− 36u
10
− 42u
9
− 10u
8
+ 31u
7
+ 50u
6
+ 38u
5
+ 7u
4
− 11u
3
− 6u
2
+ u + 1i
* 9 irreducible components of dim
C
= 0, with total 126 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
= hb − u, a − 1, u
9
− 5u
8
+ · · · + 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
1
u
a
4
=
1
u
2
a
2
=
u
2
− u + 1
u
4
− u
3
+ u
a
8
=
−u
−u
2
+ u
a
6
=
u
3
− u
2
+ 1
u
4
− 2u
3
+ u
2
a
3
=
−u
8
+ 3u
7
− 4u
6
+ u
5
+ 2u
4
− 2u
3
+ 1
−u
8
+ 5u
7
− 10u
6
+ 11u
5
− 6u
4
+ 2u
3
+ 2u − 1
a
12
=
−u + 1
u
a
10
=
−u
3
+ 2u
2
− u
u
3
− u
2
+ u
a
7
=
u
8
− 4u
7
+ 7u
6
− 6u
5
+ 2u
4
− u
−u
8
+ 3u
7
− 5u
6
+ 4u
5
− 2u
4
− u
2
+ u
a
11
=
−u
7
+ 3u
6
− 5u
5
+ 4u
4
− 2u
3
− u + 1
−2u
8
+ 8u
7
− 15u
6
+ 15u
5
− 8u
4
+ 2u
3
− u
2
+ 3u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
8
− 15u
7
+ 36u
6
− 45u
5
+ 33u
4
− 15u
3
+ 9u
2
− 3u + 12
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
u
9
− 4u
8
+ 10u
7
− 15u
6
+ 16u
5
− 14u
4
+ 12u
3
− 10u
2
+ 6u − 1
c
2
, c
6
, c
10
u
9
− 7u
8
+ 18u
7
− 19u
6
+ 4u
5
+ 5u
4
− 2u
3
− u
2
+ 3u − 1
c
3
, c
7
, c
11
u
9
+ 6u
8
+ 15u
7
+ 16u
6
+ 2u
5
− 9u
4
− 2u
3
+ 6u
2
+ 3u − 1
c
4
, c
8
, c
12
u
9
− 5u
8
+ 12u
7
− 16u
6
+ 13u
5
− 6u
4
+ 2u
3
− u
2
+ 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
y
9
+ 4y
8
+ 12y
7
+ 7y
6
+ 8y
5
+ 26y
3
+ 16y
2
+ 16y −1
c
2
, c
6
, c
10
y
9
− 13y
8
+ 66y
7
− 151y
6
+ 126y
5
+ 15y
4
− 3y
2
+ 7y −1
c
3
, c
7
, c
11
y
9
− 6y
8
+ 37y
7
− 92y
6
+ 166y
5
− 179y
4
+ 156y
3
− 66y
2
+ 21y −1
c
4
, c
8
, c
12
y
9
− y
8
+ 10y
7
+ 19y
5
+ 22y
4
+ 12y
3
− 5y
2
+ 2y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.286198 + 0.902700I
a = 1.00000
b = 0.286198 + 0.902700I
3.22071 − 2.28420I 3.39173 + 1.61517I
u = 0.286198 − 0.902700I
a = 1.00000
b = 0.286198 − 0.902700I
3.22071 + 2.28420I 3.39173 − 1.61517I
u = −0.447949 + 0.409095I
a = 1.00000
b = −0.447949 + 0.409095I
0.58147 + 2.13776I 3.86167 − 3.88522I
u = −0.447949 − 0.409095I
a = 1.00000
b = −0.447949 − 0.409095I
0.58147 − 2.13776I 3.86167 + 3.88522I
u = 1.128820 + 0.825655I
a = 1.00000
b = 1.128820 + 0.825655I
4.45533 + 4.10271I 9.59034 − 1.40424I
u = 1.128820 − 0.825655I
a = 1.00000
b = 1.128820 − 0.825655I
4.45533 − 4.10271I 9.59034 + 1.40424I
u = 0.587597
a = 1.00000
b = 0.587597
0.838784 12.2450
u = 1.23914 + 1.04927I
a = 1.00000
b = 1.23914 + 1.04927I
12.7072 + 17.7651I 10.03383 − 8.20740I
u = 1.23914 − 1.04927I
a = 1.00000
b = 1.23914 − 1.04927I
12.7072 − 17.7651I 10.03383 + 8.20740I
5
II. I
u
2
= hb + u, a + 1, u
9
− 3u
8
+ 4u
7
− 2u
6
+ u
5
− 2u
4
+ 2u
3
− u
2
− 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−1
−u
a
4
=
1
u
2
a
2
=
−u
2
+ u − 1
−u
4
+ u
3
− u
a
8
=
−u
−u
2
+ u
a
6
=
u
3
− u
2
+ 1
u
4
− 2u
3
+ u
2
a
3
=
−u
8
+ 3u
7
− 4u
6
+ u
5
+ 2u
4
− 2u
3
+ 1
u
8
− 3u
7
+ 4u
6
− u
5
− 2u
4
+ 2u
3
− 1
a
12
=
u − 1
−u
a
10
=
−u
3
+ 2u
2
− u
u
3
− u
2
+ u
a
7
=
u
8
− 4u
7
+ 7u
6
− 6u
5
+ 2u
4
− u
−u
8
+ 3u
7
− 5u
6
+ 4u
5
− 2u
4
− u
2
+ u
a
11
=
u
7
− 3u
6
+ 5u
5
− 4u
4
+ 2u
3
+ u − 1
u
6
− 3u
5
+ 4u
4
− 2u
3
+ u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
8
+ 15u
7
− 24u
6
+ 15u
5
+ 3u
4
+ 3u
3
− 9u
2
+ 3u + 6
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
u
9
− 2u
8
+ 4u
7
− 5u
6
+ 8u
5
− 10u
4
+ 8u
3
− 6u
2
+ 2u + 1
c
2
, c
6
, c
10
u
9
+ 5u
8
+ 8u
7
+ 5u
6
+ 4u
5
+ 3u
4
+ 3u
2
− u + 1
c
3
, c
7
, c
11
u
9
+ 4u
8
+ 5u
7
− 2u
5
+ u
4
+ 4u
2
+ u + 5
c
4
, c
8
, c
12
u
9
− 3u
8
+ 4u
7
− 2u
6
+ u
5
− 2u
4
+ 2u
3
− u
2
− 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
y
9
+ 4y
8
+ 12y
7
+ 15y
6
+ 8y
5
− 12y
4
− 14y
3
+ 16y
2
+ 16y −1
c
2
, c
6
, c
10
y
9
− 9y
8
+ 22y
7
+ 9y
6
− 46y
5
− 65y
4
− 36y
3
− 15y
2
− 5y −1
c
3
, c
7
, c
11
y
9
− 6y
8
+ 21y
7
− 28y
6
− 26y
5
− 31y
4
− 12y
3
− 26y
2
− 39y −25
c
4
, c
8
, c
12
y
9
− y
8
+ 6y
7
− 4y
6
+ 3y
5
− 10y
4
− 4y
3
− 5y
2
− 2y −1
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.640457 + 0.839014I
a = −1.00000
b = −0.640457 − 0.839014I
−3.41503 + 2.80054I −2.62634 − 4.93597I
u = 0.640457 − 0.839014I
a = −1.00000
b = −0.640457 + 0.839014I
−3.41503 − 2.80054I −2.62634 + 4.93597I
u = −0.611257 + 0.526811I
a = −1.00000
b = 0.611257 − 0.526811I
10.77880 + 7.66911I 9.14267 − 3.23917I
u = −0.611257 − 0.526811I
a = −1.00000
b = 0.611257 + 0.526811I
10.77880 − 7.66911I 9.14267 + 3.23917I
u = 1.20234
a = −1.00000
b = −1.20234
11.2685 14.6480
u = −0.274779 + 0.650965I
a = −1.00000
b = 0.274779 − 0.650965I
1.42494 − 3.44509I 5.30781 + 7.71847I
u = −0.274779 − 0.650965I
a = −1.00000
b = 0.274779 + 0.650965I
1.42494 + 3.44509I 5.30781 − 7.71847I
u = 1.14441 + 0.99327I
a = −1.00000
b = −1.14441 − 0.99327I
2.02642 + 11.00000I 4.85190 − 8.60523I
u = 1.14441 − 0.99327I
a = −1.00000
b = −1.14441 + 0.99327I
2.02642 − 11.00000I 4.85190 + 8.60523I
9
III. I
u
3
= hb − u, 4u
17
+ 8u
16
+ · · · + 2a − 5, u
18
+ 5u
17
+ · · · + 5u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−2u
17
− 4u
16
+ ··· + 8u +
5
2
u
a
4
=
1
u
2
a
2
=
−10u
17
− 36u
16
+ ··· − 21u −
7
2
−
13
2
u
17
− 28u
16
+ ··· − 31u − 8
a
8
=
−3u
17
− 31u
16
+ ··· − 98u − 36
8u
17
+ 32u
16
+ ··· + 29u + 6
a
6
=
−
3
2
u
17
−
21
2
u
16
+ ··· −
75
2
u −
37
2
11
2
u
17
+ 24u
16
+ ··· +
57
2
u +
13
2
a
3
=
−10.5000u
17
− 46.5000u
16
+ ··· − 59.5000u − 21.5000
6u
17
+ 25u
16
+ ··· +
57
2
u +
15
2
a
12
=
−2u
17
− 4u
16
+ ··· + 7u +
5
2
u
a
10
=
−19u
17
− 95u
16
+ ··· − 154u − 48
8u
17
+ 32u
16
+ ··· + 29u + 6
a
7
=
−
77
2
u
17
−
327
2
u
16
+ ··· − 181u −
85
2
−
27
2
u
17
−
121
2
u
16
+ ··· − 78u −
43
2
a
11
=
48u
17
+
413
2
u
16
+ ··· + 234u + 60
7u
17
+
65
2
u
16
+ ··· +
91
2
u + 13
(ii) Obstruction class = −1
(iii) Cusp Shapes = 37u
17
+ 174u
16
+ 393u
15
+ 512u
14
+ 582u
13
+ 849u
12
+ 1180u
11
+
897u
10
+ 226u
9
− 106u
8
− 125u
7
− 507u
6
− 919u
5
− 725u
4
− 89u
3
+ 317u
2
+ 285u + 100
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
18
+ 2u
17
+ ··· + 11u + 7
c
2
, c
10
u
18
+ 6u
17
+ ··· + 2u + 1
c
3
u
18
+ 18u
17
+ ··· + 5632u + 1024
c
4
, c
12
u
18
+ 5u
17
+ ··· + 5u + 1
c
6
u
18
− 12u
17
+ ··· − 1552u + 352
c
7
, c
11
u
18
− 7u
17
+ ··· − 40u + 7
c
8
u
18
− 17u
17
+ ··· − 176u + 32
c
9
u
18
− 16u
17
+ ··· − 240u + 32
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
18
+ 10y
17
+ ··· + 313y + 49
c
2
, c
10
y
18
− 30y
17
+ ··· − 8y + 1
c
3
y
18
− 10y
17
+ ··· + 1572864y + 1048576
c
4
, c
12
y
18
− y
17
+ ··· − 5y + 1
c
6
y
18
− 12y
17
+ ··· + 401664y + 123904
c
7
, c
11
y
18
− 15y
17
+ ··· − 634y + 49
c
8
y
18
− 7y
17
+ ··· − 1792y + 1024
c
9
y
18
+ 2y
17
+ ··· + 15616y + 1024
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768042 + 0.719269I
a = −0.875237 + 0.270339I
b = −0.768042 + 0.719269I
−2.27200 − 2.57043I 6.54941 + 3.50069I
u = −0.768042 − 0.719269I
a = −0.875237 − 0.270339I
b = −0.768042 − 0.719269I
−2.27200 + 2.57043I 6.54941 − 3.50069I
u = 0.535137 + 0.962955I
a = 1.40580 − 0.92249I
b = 0.535137 + 0.962955I
7.73898 + 8.44090I 7.63933 − 9.24995I
u = 0.535137 − 0.962955I
a = 1.40580 + 0.92249I
b = 0.535137 − 0.962955I
7.73898 − 8.44090I 7.63933 + 9.24995I
u = 0.782103 + 0.053724I
a = 1.91617 + 1.26164I
b = 0.782103 + 0.053724I
3.58305 − 1.24938I 17.0632 + 1.0174I
u = 0.782103 − 0.053724I
a = 1.91617 − 1.26164I
b = 0.782103 − 0.053724I
3.58305 + 1.24938I 17.0632 − 1.0174I
u = −0.262844 + 0.715699I
a = 0.165375 + 0.643986I
b = −0.262844 + 0.715699I
0.72242 + 2.18469I 2.93233 − 4.07670I
u = −0.262844 − 0.715699I
a = 0.165375 − 0.643986I
b = −0.262844 − 0.715699I
0.72242 − 2.18469I 2.93233 + 4.07670I
u = 0.777809 + 0.987076I
a = 0.288479 + 0.024311I
b = 0.777809 + 0.987076I
5.99338 + 3.58170I 6.02957 − 2.59118I
u = 0.777809 − 0.987076I
a = 0.288479 − 0.024311I
b = 0.777809 − 0.987076I
5.99338 − 3.58170I 6.02957 + 2.59118I
13
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.695734 + 0.191789I
a = −1.21725 − 2.62700I
b = −0.695734 + 0.191789I
11.7749 − 8.5337I 15.3206 + 8.5140I
u = −0.695734 − 0.191789I
a = −1.21725 + 2.62700I
b = −0.695734 − 0.191789I
11.7749 + 8.5337I 15.3206 − 8.5140I
u = −0.594298 + 0.360810I
a = −2.76005 + 0.70415I
b = −0.594298 + 0.360810I
2.40603 − 4.20864I 12.3347 + 11.0008I
u = −0.594298 − 0.360810I
a = −2.76005 − 0.70415I
b = −0.594298 − 0.360810I
2.40603 + 4.20864I 12.3347 − 11.0008I
u = −1.18514 + 0.90997I
a = −1.051240 + 0.105286I
b = −1.18514 + 0.90997I
3.54942 − 10.06710I 10.59088 + 5.55087I
u = −1.18514 − 0.90997I
a = −1.051240 − 0.105286I
b = −1.18514 − 0.90997I
3.54942 + 10.06710I 10.59088 − 5.55087I
u = −1.08899 + 1.07733I
a = −0.872048 − 0.388084I
b = −1.08899 + 1.07733I
10.91700 − 4.65632I 14.5399 + 2.8811I
u = −1.08899 − 1.07733I
a = −0.872048 + 0.388084I
b = −1.08899 − 1.07733I
10.91700 + 4.65632I 14.5399 − 2.8811I
14
IV. I
u
4
= h−12u
17
− 44u
16
+ · · · + 2b − 4, a − 1, u
18
+ 5u
17
+ · · · + 5u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
1
6u
17
+ 22u
16
+ ··· +
25
2
u + 2
a
4
=
1
u
2
a
2
=
−6u
17
− 22u
16
+ ··· −
25
2
u − 1
−2u
17
−
23
2
u
16
+ ··· −
43
2
u − 6
a
8
=
−u
8u
17
+ 32u
16
+ ··· + 29u + 6
a
6
=
8u
17
+
67
2
u
16
+ ··· + 34u + 9
11
2
u
17
+ 24u
16
+ ··· +
57
2
u +
13
2
a
3
=
−13u
17
− 58u
16
+ ··· − 72u −
39
2
−
25
2
u
17
− 54u
16
+ ··· − 65u − 17
a
12
=
−6u
17
− 22u
16
+ ··· −
25
2
u − 1
6u
17
+ 22u
16
+ ··· +
25
2
u + 2
a
10
=
13
2
u
17
+ 27u
16
+ ··· + 26u + 4
−
29
2
u
17
− 59u
16
+ ··· − 54u − 10
a
7
=
15
2
u
17
+
63
2
u
16
+ ··· + 38u + 9
−24u
17
− 105u
16
+ ··· −
255
2
u −
65
2
a
11
=
43
2
u
17
+ 94u
16
+ ··· + 112u +
59
2
−
11
2
u
17
− 24u
16
+ ··· − 28u − 7
(ii) Obstruction class = −1
(iii) Cusp Shapes = 37u
17
+ 174u
16
+ 393u
15
+ 512u
14
+ 582u
13
+ 849u
12
+ 1180u
11
+
897u
10
+ 226u
9
− 106u
8
− 125u
7
− 507u
6
− 919u
5
− 725u
4
− 89u
3
+ 317u
2
+ 285u + 100
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 16u
17
+ ··· − 240u + 32
c
2
, c
6
u
18
+ 6u
17
+ ··· + 2u + 1
c
3
, c
11
u
18
− 7u
17
+ ··· − 40u + 7
c
4
, c
8
u
18
+ 5u
17
+ ··· + 5u + 1
c
5
, c
9
u
18
+ 2u
17
+ ··· + 11u + 7
c
7
u
18
+ 18u
17
+ ··· + 5632u + 1024
c
10
u
18
− 12u
17
+ ··· − 1552u + 352
c
12
u
18
− 17u
17
+ ··· − 176u + 32
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 2y
17
+ ··· + 15616y + 1024
c
2
, c
6
y
18
− 30y
17
+ ··· − 8y + 1
c
3
, c
11
y
18
− 15y
17
+ ··· − 634y + 49
c
4
, c
8
y
18
− y
17
+ ··· − 5y + 1
c
5
, c
9
y
18
+ 10y
17
+ ··· + 313y + 49
c
7
y
18
− 10y
17
+ ··· + 1572864y + 1048576
c
10
y
18
− 12y
17
+ ··· + 401664y + 123904
c
12
y
18
− 7y
17
+ ··· − 1792y + 1024
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768042 + 0.719269I
a = 1.00000
b = 0.477772 − 0.837163I
−2.27200 − 2.57043I 6.54941 + 3.50069I
u = −0.768042 − 0.719269I
a = 1.00000
b = 0.477772 + 0.837163I
−2.27200 + 2.57043I 6.54941 − 3.50069I
u = 0.535137 + 0.962955I
a = 1.00000
b = 1.64061 + 0.86007I
7.73898 + 8.44090I 7.63933 − 9.24995I
u = 0.535137 − 0.962955I
a = 1.00000
b = 1.64061 − 0.86007I
7.73898 − 8.44090I 7.63933 + 9.24995I
u = 0.782103 + 0.053724I
a = 1.00000
b = 1.43086 + 1.08968I
3.58305 − 1.24938I 17.0632 + 1.0174I
u = 0.782103 − 0.053724I
a = 1.00000
b = 1.43086 − 1.08968I
3.58305 + 1.24938I 17.0632 − 1.0174I
u = −0.262844 + 0.715699I
a = 1.00000
b = −0.504368 − 0.050909I
0.72242 + 2.18469I 2.93233 − 4.07670I
u = −0.262844 − 0.715699I
a = 1.00000
b = −0.504368 + 0.050909I
0.72242 − 2.18469I 2.93233 + 4.07670I
u = 0.777809 + 0.987076I
a = 1.00000
b = 0.200384 + 0.303660I
5.99338 + 3.58170I 6.02957 − 2.59118I
u = 0.777809 − 0.987076I
a = 1.00000
b = 0.200384 − 0.303660I
5.99338 − 3.58170I 6.02957 + 2.59118I
18
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.695734 + 0.191789I
a = 1.00000
b = 1.35071 + 1.59423I
11.7749 − 8.5337I 15.3206 + 8.5140I
u = −0.695734 − 0.191789I
a = 1.00000
b = 1.35071 − 1.59423I
11.7749 + 8.5337I 15.3206 − 8.5140I
u = −0.594298 + 0.360810I
a = 1.00000
b = 1.38623 − 1.41433I
2.40603 − 4.20864I 12.3347 + 11.0008I
u = −0.594298 − 0.360810I
a = 1.00000
b = 1.38623 + 1.41433I
2.40603 + 4.20864I 12.3347 − 11.0008I
u = −1.18514 + 0.90997I
a = 1.00000
b = 1.15005 − 1.08137I
3.54942 − 10.06710I 10.59088 + 5.55087I
u = −1.18514 − 0.90997I
a = 1.00000
b = 1.15005 + 1.08137I
3.54942 + 10.06710I 10.59088 − 5.55087I
u = −1.08899 + 1.07733I
a = 1.00000
b = 1.36775 − 0.51686I
10.91700 − 4.65632I 14.5399 + 2.8811I
u = −1.08899 − 1.07733I
a = 1.00000
b = 1.36775 + 0.51686I
10.91700 + 4.65632I 14.5399 − 2.8811I
19
V. I
u
5
= h−582u
17
+ 8001u
16
+ · · · + 6236b + 10944, −342u
17
+ 5232u
16
+
· · · + 6236a − 30, u
18
− 17u
17
+ · · · − 176u + 32i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
0.0548428u
17
− 0.838999u
16
+ ··· + 14.0253u + 0.00481078
0.0933291u
17
− 1.28303u
16
+ ··· + 9.65715u − 1.75497
a
4
=
1
u
2
a
2
=
0.265074u
17
− 4.05516u
16
+ ··· + 19.0391u − 1.22675
0.381976u
17
− 6.48829u
16
+ ··· + 65.8958u − 13.2033
a
8
=
−0.0831462u
17
+ 1.44524u
16
+ ··· − 38.8754u + 6.77999
0.0317511u
17
− 0.472579u
16
+ ··· − 6.85375u + 2.66068
a
6
=
0.0383659u
17
− 0.560616u
16
+ ··· + 2.67672u − 5.61835
0.158796u
17
− 2.55320u
16
+ ··· + 8.38294u − 2.24375
a
3
=
0.377205u
17
− 6.21685u
16
+ ··· + 81.8435u − 10.5930
0.0953335u
17
− 1.67335u
16
+ ··· + 37.2421u − 9.11225
a
12
=
−0.0384862u
17
+ 0.444035u
16
+ ··· + 4.36818u + 1.75978
0.0933291u
17
− 1.28303u
16
+ ··· + 9.65715u − 1.75497
a
10
=
−0.0794580u
17
+ 1.18706u
16
+ ··· − 14.9190u + 0.442591
−0.0354394u
17
+ 0.730757u
16
+ ··· − 15.1026u + 3.67672
a
7
=
0.121572u
17
− 2.10381u
16
+ ··· + 19.2797u − 3.21905
−0.435014u
17
+ 6.63851u
16
+ ··· − 28.5946u + 5.07697
a
11
=
0.690186u
17
− 10.8130u
16
+ ··· + 61.6639u − 7.15876
0.967768u
17
− 15.7437u
16
+ ··· + 140.533u − 28.0949
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
741
3118
u
17
+
7227
1559
u
16
+ ··· −
161008
1559
u +
45958
1559
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
18
+ 2u
17
+ ··· + 11u + 7
c
2
u
18
− 12u
17
+ ··· − 1552u + 352
c
3
, c
7
u
18
− 7u
17
+ ··· − 40u + 7
c
4
u
18
− 17u
17
+ ··· − 176u + 32
c
5
u
18
− 16u
17
+ ··· − 240u + 32
c
6
, c
10
u
18
+ 6u
17
+ ··· + 2u + 1
c
8
, c
12
u
18
+ 5u
17
+ ··· + 5u + 1
c
11
u
18
+ 18u
17
+ ··· + 5632u + 1024
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
18
+ 10y
17
+ ··· + 313y + 49
c
2
y
18
− 12y
17
+ ··· + 401664y + 123904
c
3
, c
7
y
18
− 15y
17
+ ··· − 634y + 49
c
4
y
18
− 7y
17
+ ··· − 1792y + 1024
c
5
y
18
+ 2y
17
+ ··· + 15616y + 1024
c
6
, c
10
y
18
− 30y
17
+ ··· − 8y + 1
c
8
, c
12
y
18
− y
17
+ ··· − 5y + 1
c
11
y
18
− 10y
17
+ ··· + 1572864y + 1048576
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.477772 + 0.837163I
a = −1.043040 + 0.322168I
b = −0.768042 − 0.719269I
−2.27200 + 2.57043I 6.54941 − 3.50069I
u = 0.477772 − 0.837163I
a = −1.043040 − 0.322168I
b = −0.768042 + 0.719269I
−2.27200 − 2.57043I 6.54941 + 3.50069I
u = 1.36775 + 0.51686I
a = −0.957162 − 0.425962I
b = −1.08899 − 1.07733I
10.91700 + 4.65632I 14.5399 − 2.8811I
u = 1.36775 − 0.51686I
a = −0.957162 + 0.425962I
b = −1.08899 + 1.07733I
10.91700 − 4.65632I 14.5399 + 2.8811I
u = −0.504368 + 0.050909I
a = 0.37410 + 1.45676I
b = −0.262844 − 0.715699I
0.72242 − 2.18469I 2.93233 + 4.07670I
u = −0.504368 − 0.050909I
a = 0.37410 − 1.45676I
b = −0.262844 + 0.715699I
0.72242 + 2.18469I 2.93233 − 4.07670I
u = 1.15005 + 1.08137I
a = −0.941815 + 0.094327I
b = −1.18514 − 0.90997I
3.54942 + 10.06710I 10.59088 − 5.55087I
u = 1.15005 − 1.08137I
a = −0.941815 − 0.094327I
b = −1.18514 + 0.90997I
3.54942 − 10.06710I 10.59088 + 5.55087I
u = 0.200384 + 0.303660I
a = 3.44201 − 0.29007I
b = 0.777809 + 0.987076I
5.99338 + 3.58170I 6.02957 − 2.59118I
u = 0.200384 − 0.303660I
a = 3.44201 + 0.29007I
b = 0.777809 − 0.987076I
5.99338 − 3.58170I 6.02957 + 2.59118I
23
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43086 + 1.08968I
a = 0.364052 − 0.239699I
b = 0.782103 + 0.053724I
3.58305 − 1.24938I 17.0632 + 1.0174I
u = 1.43086 − 1.08968I
a = 0.364052 + 0.239699I
b = 0.782103 − 0.053724I
3.58305 + 1.24938I 17.0632 − 1.0174I
u = 1.64061 + 0.86007I
a = 0.497231 + 0.326283I
b = 0.535137 + 0.962955I
7.73898 + 8.44090I 7.63933 − 9.24995I
u = 1.64061 − 0.86007I
a = 0.497231 − 0.326283I
b = 0.535137 − 0.962955I
7.73898 − 8.44090I 7.63933 + 9.24995I
u = 1.38623 + 1.41433I
a = −0.340171 + 0.086786I
b = −0.594298 − 0.360810I
2.40603 + 4.20864I 12.3347 − 11.0008I
u = 1.38623 − 1.41433I
a = −0.340171 − 0.086786I
b = −0.594298 + 0.360810I
2.40603 − 4.20864I 12.3347 + 11.0008I
u = 1.35071 + 1.59423I
a = −0.145208 + 0.313379I
b = −0.695734 + 0.191789I
11.7749 − 8.5337I 15.3206 + 8.5140I
u = 1.35071 − 1.59423I
a = −0.145208 − 0.313379I
b = −0.695734 − 0.191789I
11.7749 + 8.5337I 15.3206 − 8.5140I
24
VI. I
u
6
= hb + u, −2u
7
− 5u
6
+ · · · + a − 3, u
8
+ 3u
7
+ · · · + 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
2u
7
+ 5u
6
+ 8u
5
+ 9u
4
+ 10u
3
+ 7u
2
+ 7u + 3
−u
a
4
=
1
u
2
a
2
=
3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 13u
3
+ 9u
2
+ 9u + 4
u
6
+ 2u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ u + 1
a
8
=
u
7
+ 2u
6
+ 4u
5
+ 5u
4
+ 5u
3
+ 3u
2
+ 5u + 1
u
7
+ 2u
6
+ 2u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ 2u + 1
a
6
=
−2u
7
− 6u
6
− 9u
5
− 9u
4
− 10u
3
− 9u
2
− 6u − 2
u
3
+ u
2
+ u
a
3
=
−4u
7
− 12u
6
− 16u
5
− 13u
4
− 15u
3
− 14u
2
− 7u
u
7
+ 3u
6
+ 4u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ u
a
12
=
2u
7
+ 5u
6
+ 8u
5
+ 9u
4
+ 10u
3
+ 7u
2
+ 8u + 3
−u
a
10
=
−u
7
− 2u
6
+ u
4
− 2u
3
− u
2
+ 3u − 1
u
7
+ 2u
6
+ 2u
5
+ 2u
4
+ 4u
3
+ 2u
2
+ 2u + 1
a
7
=
−3u
7
− 8u
6
− 11u
5
− 10u
4
− 12u
3
− 9u
2
− 7u − 2
−u
5
− 2u
4
− 2u
3
− 2u
2
− u − 1
a
11
=
−u
6
− u
5
− u
4
− 2u
3
− 3u
2
− 2
u
7
+ 2u
6
+ 2u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 15u
7
+ 35u
6
+ 47u
5
+ 47u
4
+ 60u
3
+ 37u
2
+ 32u + 19
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
8
+ 2u
6
+ u
5
+ 4u
4
− u
3
+ 4u
2
− u + 1
c
2
, c
10
u
8
− 4u
7
+ 8u
6
− 14u
5
+ 19u
4
− 17u
3
+ 11u
2
− 4u + 1
c
3
u
8
− 3u
7
− 2u
6
+ 3u
5
+ 22u
4
+ 24u
3
+ 18u
2
+ 3u + 1
c
4
, c
12
u
8
+ 3u
7
+ 5u
6
+ 6u
5
+ 7u
4
+ 6u
3
+ 5u
2
+ 3u + 1
c
6
u
8
+ 3u
7
+ u
6
+ 8u
4
+ 6u
3
− 2u
2
− u + 1
c
7
, c
11
u
8
+ u
7
− 2u
6
− 5u
5
− u
4
+ 6u
3
+ 8u
2
+ 4u + 1
c
8
(u
4
− 3u
3
+ 3u
2
− u − 1)
2
c
9
u
8
− 7u
7
+ 20u
6
− 37u
5
+ 52u
4
− 48u
3
+ 44u
2
− 19u + 11
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
8
+ 4y
7
+ 12y
6
+ 23y
5
+ 36y
4
+ 37y
3
+ 22y
2
+ 7y + 1
c
2
, c
10
y
8
− 10y
6
− 6y
5
+ 31y
4
+ 33y
3
+ 23y
2
+ 6y + 1
c
3
y
8
− 13y
7
+ 66y
6
+ 83y
5
+ 288y
4
+ 194y
3
+ 224y
2
+ 27y + 1
c
4
, c
12
y
8
+ y
7
+ 3y
6
+ 8y
5
+ 11y
4
+ 8y
3
+ 3y
2
+ y + 1
c
6
y
8
− 7y
7
+ 17y
6
− 24y
5
+ 68y
4
− 66y
3
+ 32y
2
− 5y + 1
c
7
, c
11
y
8
− 5y
7
+ 12y
6
− 17y
5
+ 23y
4
− 16y
3
+ 14y
2
+ 1
c
8
(y
4
− 3y
3
+ y
2
− 7y + 1)
2
c
9
y
8
− 9y
7
− 14y
6
+ 127y
5
+ 668y
4
+ 1306y
3
+ 1256y
2
+ 607y + 121
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.164478 + 0.986381I
a = 0.29921 + 1.79440I
b = 0.164478 − 0.986381I
−0.891430 + 0.808282I 4.38747 − 7.84089I
u = −0.164478 − 0.986381I
a = 0.29921 − 1.79440I
b = 0.164478 + 0.986381I
−0.891430 − 0.808282I 4.38747 + 7.84089I
u = 0.452583 + 0.891722I
a = 0.172107 − 0.339102I
b = −0.452583 − 0.891722I
1.13995 − 1.35977I 7.04382 − 3.05706I
u = 0.452583 − 0.891722I
a = 0.172107 + 0.339102I
b = −0.452583 + 0.891722I
1.13995 + 1.35977I 7.04382 + 3.05706I
u = −0.584796 + 0.379478I
a = 0.22519 + 1.70988I
b = 0.584796 − 0.379478I
1.15941 − 3.26530I 7.76010 + 9.86097I
u = −0.584796 − 0.379478I
a = 0.22519 − 1.70988I
b = 0.584796 + 0.379478I
1.15941 + 3.26530I 7.76010 − 9.86097I
u = −1.20331 + 0.78084I
a = 0.803486 − 0.238578I
b = 1.20331 − 0.78084I
8.46167 − 5.22804I 9.80861 + 4.92233I
u = −1.20331 − 0.78084I
a = 0.803486 + 0.238578I
b = 1.20331 + 0.78084I
8.46167 + 5.22804I 9.80861 − 4.92233I
28
VII.
I
u
7
= hu
7
+2u
6
+3u
5
+4u
4
+5u
3
+3u
2
+b+3u+2, a+1, u
8
+3u
7
+· · ·+3u+1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
−1
−u
7
− 2u
6
− 3u
5
− 4u
4
− 5u
3
− 3u
2
− 3u − 2
a
4
=
1
u
2
a
2
=
u
7
+ 2u
6
+ 3u
5
+ 4u
4
+ 5u
3
+ 2u
2
+ 3u + 1
u
6
+ u
5
− u
4
− u
3
+ u
2
− u − 1
a
8
=
−u
u
7
+ 2u
6
+ 2u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ 2u + 1
a
6
=
u
7
+ 3u
6
+ 4u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 2u + 2
u
3
+ u
2
+ u
a
3
=
u
7
+ 2u
6
+ 3u
5
+ 4u
4
+ 5u
3
+ 3u
2
+ 3u + 1
−u
7
− 2u
6
− 3u
5
− 4u
4
− 5u
3
− 3u
2
− 3u − 1
a
12
=
u
7
+ 2u
6
+ 3u
5
+ 4u
4
+ 5u
3
+ 3u
2
+ 3u + 1
−u
7
− 2u
6
− 3u
5
− 4u
4
− 5u
3
− 3u
2
− 3u − 2
a
10
=
−u
2
− u − 1
−u
7
− 2u
6
− 2u
5
− 2u
4
− 3u
3
− u
2
a
7
=
−u
6
− 3u
5
− 4u
4
− 4u
3
− 4u
2
− 4u − 1
u
7
+ 5u
6
+ 10u
5
+ 12u
4
+ 11u
3
+ 12u
2
+ 10u + 4
a
11
=
−u
7
− 3u
6
− 5u
5
− 5u
4
− 5u
3
− 4u
2
− 3u − 2
−u
7
− u
6
− u
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 15u
7
+ 35u
6
+ 47u
5
+ 47u
4
+ 60u
3
+ 37u
2
+ 32u + 19
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 7u
7
+ 20u
6
− 37u
5
+ 52u
4
− 48u
3
+ 44u
2
− 19u + 11
c
2
, c
6
u
8
− 4u
7
+ 8u
6
− 14u
5
+ 19u
4
− 17u
3
+ 11u
2
− 4u + 1
c
3
, c
11
u
8
+ u
7
− 2u
6
− 5u
5
− u
4
+ 6u
3
+ 8u
2
+ 4u + 1
c
4
, c
8
u
8
+ 3u
7
+ 5u
6
+ 6u
5
+ 7u
4
+ 6u
3
+ 5u
2
+ 3u + 1
c
5
, c
9
u
8
+ 2u
6
+ u
5
+ 4u
4
− u
3
+ 4u
2
− u + 1
c
7
u
8
− 3u
7
− 2u
6
+ 3u
5
+ 22u
4
+ 24u
3
+ 18u
2
+ 3u + 1
c
10
u
8
+ 3u
7
+ u
6
+ 8u
4
+ 6u
3
− 2u
2
− u + 1
c
12
(u
4
− 3u
3
+ 3u
2
− u − 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 9y
7
− 14y
6
+ 127y
5
+ 668y
4
+ 1306y
3
+ 1256y
2
+ 607y + 121
c
2
, c
6
y
8
− 10y
6
− 6y
5
+ 31y
4
+ 33y
3
+ 23y
2
+ 6y + 1
c
3
, c
11
y
8
− 5y
7
+ 12y
6
− 17y
5
+ 23y
4
− 16y
3
+ 14y
2
+ 1
c
4
, c
8
y
8
+ y
7
+ 3y
6
+ 8y
5
+ 11y
4
+ 8y
3
+ 3y
2
+ y + 1
c
5
, c
9
y
8
+ 4y
7
+ 12y
6
+ 23y
5
+ 36y
4
+ 37y
3
+ 22y
2
+ 7y + 1
c
7
y
8
− 13y
7
+ 66y
6
+ 83y
5
+ 288y
4
+ 194y
3
+ 224y
2
+ 27y + 1
c
10
y
8
− 7y
7
+ 17y
6
− 24y
5
+ 68y
4
− 66y
3
+ 32y
2
− 5y + 1
c
12
(y
4
− 3y
3
+ y
2
− 7y + 1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.164478 + 0.986381I
a = −1.00000
b = −1.81917
−0.891430 + 0.808282I 4.38747 − 7.84089I
u = −0.164478 − 0.986381I
a = −1.00000
b = −1.81917
−0.891430 − 0.808282I 4.38747 + 7.84089I
u = 0.452583 + 0.891722I
a = −1.00000
b = 0.380278
1.13995 − 1.35977I 7.04382 − 3.05706I
u = 0.452583 − 0.891722I
a = −1.00000
b = 0.380278
1.13995 + 1.35977I 7.04382 + 3.05706I
u = −0.584796 + 0.379478I
a = −1.00000
b = −0.780553 − 0.914474I
1.15941 − 3.26530I 7.76010 + 9.86097I
u = −0.584796 − 0.379478I
a = −1.00000
b = −0.780553 + 0.914474I
1.15941 + 3.26530I 7.76010 − 9.86097I
u = −1.20331 + 0.78084I
a = −1.00000
b = −0.780553 + 0.914474I
8.46167 − 5.22804I 9.80861 + 4.92233I
u = −1.20331 − 0.78084I
a = −1.00000
b = −0.780553 − 0.914474I
8.46167 + 5.22804I 9.80861 − 4.92233I
32
VIII.
I
u
8
= h−au + b, −u
3
+ a
2
+ au + 4u
2
− 2a − 6u + 4, u
4
− 3u
3
+ 3u
2
− u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
a
au
a
4
=
1
u
2
a
2
=
u
2
a − au + a
2u
3
a − 3u
2
a + 2au + a
a
8
=
u
2
a + u
3
− 2au − 3u
2
+ 3u − 1
u
3
a − 2u
2
a + u + 1
a
6
=
−u
3
a + 2u
2
a − au + u
2
− u + 1
−u
2
a + u
3
+ u
a
3
=
−u
2
a − u
3
+ 3au + 3u
2
− 2u
2u
2
a + u
3
− u
2
− u
a
12
=
−au + a
au
a
10
=
−u
3
a + 2u
2
a + u
3
− au − 3u
2
+ a + 4u − 3
u
2
a − au − a + 1
a
7
=
−u
3
+ 3u
2
− 3u + 2
u
2
− 1
a
11
=
2u
3
a − 3u
2
a + u
3
+ au − 3u
2
+ 2a + 4u − 2
4u
3
a − 4u
2
a + u
3
+ 4au − u
2
+ 2a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 11u
3
a − 21u
2
a − 7u
3
+ 7au + 11u
2
+ 5a + u + 7
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
8
+ 2u
6
+ u
5
+ 4u
4
− u
3
+ 4u
2
− u + 1
c
2
u
8
+ 3u
7
+ u
6
+ 8u
4
+ 6u
3
− 2u
2
− u + 1
c
3
, c
7
u
8
+ u
7
− 2u
6
− 5u
5
− u
4
+ 6u
3
+ 8u
2
+ 4u + 1
c
4
(u
4
− 3u
3
+ 3u
2
− u − 1)
2
c
5
u
8
− 7u
7
+ 20u
6
− 37u
5
+ 52u
4
− 48u
3
+ 44u
2
− 19u + 11
c
6
, c
10
u
8
− 4u
7
+ 8u
6
− 14u
5
+ 19u
4
− 17u
3
+ 11u
2
− 4u + 1
c
8
, c
12
u
8
+ 3u
7
+ 5u
6
+ 6u
5
+ 7u
4
+ 6u
3
+ 5u
2
+ 3u + 1
c
11
u
8
− 3u
7
− 2u
6
+ 3u
5
+ 22u
4
+ 24u
3
+ 18u
2
+ 3u + 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
8
+ 4y
7
+ 12y
6
+ 23y
5
+ 36y
4
+ 37y
3
+ 22y
2
+ 7y + 1
c
2
y
8
− 7y
7
+ 17y
6
− 24y
5
+ 68y
4
− 66y
3
+ 32y
2
− 5y + 1
c
3
, c
7
y
8
− 5y
7
+ 12y
6
− 17y
5
+ 23y
4
− 16y
3
+ 14y
2
+ 1
c
4
(y
4
− 3y
3
+ y
2
− 7y + 1)
2
c
5
y
8
− 9y
7
− 14y
6
+ 127y
5
+ 668y
4
+ 1306y
3
+ 1256y
2
+ 607y + 121
c
6
, c
10
y
8
− 10y
6
− 6y
5
+ 31y
4
+ 33y
3
+ 23y
2
+ 6y + 1
c
8
, c
12
y
8
+ y
7
+ 3y
6
+ 8y
5
+ 11y
4
+ 8y
3
+ 3y
2
+ y + 1
c
11
y
8
− 13y
7
+ 66y
6
+ 83y
5
+ 288y
4
+ 194y
3
+ 224y
2
+ 27y + 1
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.780553 + 0.914474I
a = 1.143740 − 0.339608I
b = 1.20331 + 0.78084I
8.46167 + 5.22804I 9.80861 − 4.92233I
u = 0.780553 + 0.914474I
a = 0.075710 − 0.574866I
b = 0.584796 − 0.379478I
1.15941 − 3.26530I 7.76010 + 9.86097I
u = 0.780553 − 0.914474I
a = 1.143740 + 0.339608I
b = 1.20331 − 0.78084I
8.46167 − 5.22804I 9.80861 + 4.92233I
u = 0.780553 − 0.914474I
a = 0.075710 + 0.574866I
b = 0.584796 + 0.379478I
1.15941 + 3.26530I 7.76010 − 9.86097I
u = −0.380278
a = 1.19014 + 2.34492I
b = −0.452583 − 0.891722I
1.13995 − 1.35977I 7.04382 − 3.05706I
u = −0.380278
a = 1.19014 − 2.34492I
b = −0.452583 + 0.891722I
1.13995 + 1.35977I 7.04382 + 3.05706I
u = 1.81917
a = 0.090414 + 0.542214I
b = 0.164478 + 0.986381I
−0.891430 − 0.808282I 4.38747 + 7.84089I
u = 1.81917
a = 0.090414 − 0.542214I
b = 0.164478 − 0.986381I
−0.891430 + 0.808282I 4.38747 − 7.84089I
36
IX. I
u
9
= h−14u
14
− 57u
13
+ · · · + 4b − 4, 4u
14
a − 24u
14
+ · · · + 5a −
25, u
15
+ 5u
14
+ · · · + u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
1
=
a
7
2
u
14
+
57
4
u
13
+ ··· −
1
4
u + 1
a
4
=
1
u
2
a
2
=
−
7
2
u
14
−
57
4
u
13
+ ··· + a − 1
1
2
u
14
+
3
2
u
13
+ ··· − au −
9
4
a
8
=
−
7
2
u
14
a + u
14
+ ··· − a + 6
5
4
u
13
+
19
4
u
12
+ ··· − 4u + 1
a
6
=
−u
14
a −
3
2
u
14
+ ··· −
5
2
a −
7
2
u
−
7
4
u
14
−
29
4
u
13
+ ··· +
1
2
u −
3
2
a
3
=
3
4
u
14
a −
13
4
u
14
+ ··· +
5
4
a −
19
4
−
3
2
u
14
a +
7
4
u
14
+ ··· − a +
7
4
a
12
=
−
7
2
u
14
−
57
4
u
13
+ ··· + a − 1
7
2
u
14
+
57
4
u
13
+ ··· −
1
4
u + 1
a
10
=
−
1
2
u
14
a +
3
4
u
14
+ ··· +
9
4
a +
19
4
−3u
14
a +
1
4
u
14
+ ··· −
13
4
a +
1
4
a
7
=
−
7
4
u
14
a +
13
2
u
14
+ ··· −
3
2
a +
19
2
1
4
u
14
a + 2u
14
+ ··· +
1
2
a +
13
4
a
11
=
u
14
a + 7u
14
+ ··· + a +
41
4
u
14
a −
9
4
u
14
+ ··· + a − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
14
+ 18u
13
+ 34u
12
+ 18u
11
− 56u
10
− 126u
9
− 96u
8
+ 44u
7
+
144u
6
+ 138u
5
+ 52u
4
− 46u
3
− 56u
2
− 2u + 24
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
(u
15
+ 3u
14
+ ··· + 13u + 11)
2
c
2
, c
6
, c
10
(u
15
+ 3u
14
+ ··· + 23u + 1)
2
c
3
, c
7
, c
11
(u
15
− 5u
14
+ ··· − 205u + 61)
2
c
4
, c
8
, c
12
(u
15
+ 5u
14
+ ··· + u + 1)
2
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
(y
15
+ 5y
14
+ ··· − 1107y − 121)
2
c
2
, c
6
, c
10
(y
15
− 15y
14
+ ··· + 201y − 1)
2
c
3
, c
7
, c
11
(y
15
− 19y
14
+ ··· + 9085y − 3721)
2
c
4
, c
8
, c
12
(y
15
− 3y
14
+ ··· + 13y − 1)
2
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.046733 + 1.000910I
a = −0.995650 + 0.093177I
b = −1.81124
−0.882183 4.39116 + 0.I
u = −0.046733 + 1.000910I
a = 0.08431 + 1.80566I
b = −0.046733 − 1.000910I
−0.882183 4.39116 + 0.I
u = −0.046733 − 1.000910I
a = −0.995650 − 0.093177I
b = −1.81124
−0.882183 4.39116 + 0.I
u = −0.046733 − 1.000910I
a = 0.08431 − 1.80566I
b = −0.046733 + 1.000910I
−0.882183 4.39116 + 0.I
u = 1.217660 + 0.183120I
a = −0.751696 + 0.987223I
b = −0.738859 + 0.190472I
10.95830 − 3.33174I 13.91874 + 2.36228I
u = 1.217660 + 0.183120I
a = −0.570362 + 0.242199I
b = −1.09609 + 1.06445I
10.95830 − 3.33174I 13.91874 + 2.36228I
u = 1.217660 − 0.183120I
a = −0.751696 − 0.987223I
b = −0.738859 − 0.190472I
10.95830 + 3.33174I 13.91874 − 2.36228I
u = 1.217660 − 0.183120I
a = −0.570362 − 0.242199I
b = −1.09609 − 1.06445I
10.95830 + 3.33174I 13.91874 − 2.36228I
u = −0.738859 + 0.190472I
a = −1.48542 − 0.63077I
b = −1.09609 + 1.06445I
10.95830 − 3.33174I 13.91874 + 2.36228I
u = −0.738859 + 0.190472I
a = 1.73930 − 0.99229I
b = 1.217660 + 0.183120I
10.95830 − 3.33174I 13.91874 + 2.36228I
40
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.738859 − 0.190472I
a = −1.48542 + 0.63077I
b = −1.09609 − 1.06445I
10.95830 + 3.33174I 13.91874 − 2.36228I
u = −0.738859 − 0.190472I
a = 1.73930 + 0.99229I
b = 1.217660 − 0.183120I
10.95830 + 3.33174I 13.91874 − 2.36228I
u = −0.652116 + 0.353801I
a = −0.571565 − 0.118668I
b = −0.69295 − 1.45068I
1.81981 − 2.21397I 12.88568 + 4.22289I
u = −0.652116 + 0.353801I
a = −0.11149 + 2.16409I
b = 0.414711 − 0.124835I
1.81981 − 2.21397I 12.88568 + 4.22289I
u = −0.652116 − 0.353801I
a = −0.571565 + 0.118668I
b = −0.69295 + 1.45068I
1.81981 + 2.21397I 12.88568 − 4.22289I
u = −0.652116 − 0.353801I
a = −0.11149 − 2.16409I
b = 0.414711 + 0.124835I
1.81981 + 2.21397I 12.88568 − 4.22289I
u = −1.09609 + 1.06445I
a = −0.488224 − 0.641197I
b = −0.738859 + 0.190472I
10.95830 − 3.33174I 13.91874 + 2.36228I
u = −1.09609 + 1.06445I
a = 0.433762 + 0.247467I
b = 1.217660 + 0.183120I
10.95830 − 3.33174I 13.91874 + 2.36228I
u = −1.09609 − 1.06445I
a = −0.488224 + 0.641197I
b = −0.738859 − 0.190472I
10.95830 + 3.33174I 13.91874 − 2.36228I
u = −1.09609 − 1.06445I
a = 0.433762 − 0.247467I
b = 1.217660 − 0.183120I
10.95830 + 3.33174I 13.91874 − 2.36228I
41
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.414711 + 0.124835I
a = −1.67728 − 0.34824I
b = −0.69295 + 1.45068I
1.81981 + 2.21397I 12.88568 − 4.22289I
u = 0.414711 + 0.124835I
a = −0.56662 + 3.66862I
b = −0.652116 − 0.353801I
1.81981 + 2.21397I 12.88568 − 4.22289I
u = 0.414711 − 0.124835I
a = −1.67728 + 0.34824I
b = −0.69295 − 1.45068I
1.81981 − 2.21397I 12.88568 + 4.22289I
u = 0.414711 − 0.124835I
a = −0.56662 − 3.66862I
b = −0.652116 + 0.353801I
1.81981 − 2.21397I 12.88568 + 4.22289I
u = −0.69295 + 1.45068I
a = −0.023743 + 0.460864I
b = 0.414711 + 0.124835I
1.81981 + 2.21397I 12.88568 − 4.22289I
u = −0.69295 + 1.45068I
a = −0.041119 − 0.266231I
b = −0.652116 − 0.353801I
1.81981 + 2.21397I 12.88568 − 4.22289I
u = −0.69295 − 1.45068I
a = −0.023743 − 0.460864I
b = 0.414711 − 0.124835I
1.81981 − 2.21397I 12.88568 + 4.22289I
u = −0.69295 − 1.45068I
a = −0.041119 + 0.266231I
b = −0.652116 + 0.353801I
1.81981 − 2.21397I 12.88568 + 4.22289I
u = −1.81124
a = 0.025801 + 0.552610I
b = −0.046733 + 1.000910I
−0.882183 4.39120
u = −1.81124
a = 0.025801 − 0.552610I
b = −0.046733 − 1.000910I
−0.882183 4.39120
42
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
(u
8
+ 2u
6
+ u
5
+ 4u
4
− u
3
+ 4u
2
− u + 1)
2
· (u
8
− 7u
7
+ 20u
6
− 37u
5
+ 52u
4
− 48u
3
+ 44u
2
− 19u + 11)
· (u
9
− 4u
8
+ 10u
7
− 15u
6
+ 16u
5
− 14u
4
+ 12u
3
− 10u
2
+ 6u − 1)
· (u
9
− 2u
8
+ 4u
7
− 5u
6
+ 8u
5
− 10u
4
+ 8u
3
− 6u
2
+ 2u + 1)
· ((u
15
+ 3u
14
+ ··· + 13u + 11)
2
)(u
18
− 16u
17
+ ··· − 240u + 32)
· (u
18
+ 2u
17
+ ··· + 11u + 7)
2
c
2
, c
6
, c
10
(u
8
− 4u
7
+ 8u
6
− 14u
5
+ 19u
4
− 17u
3
+ 11u
2
− 4u + 1)
2
· (u
8
+ 3u
7
+ u
6
+ 8u
4
+ 6u
3
− 2u
2
− u + 1)
· (u
9
− 7u
8
+ 18u
7
− 19u
6
+ 4u
5
+ 5u
4
− 2u
3
− u
2
+ 3u − 1)
· (u
9
+ 5u
8
+ 8u
7
+ 5u
6
+ 4u
5
+ 3u
4
+ 3u
2
− u + 1)
· ((u
15
+ 3u
14
+ ··· + 23u + 1)
2
)(u
18
− 12u
17
+ ··· − 1552u + 352)
· (u
18
+ 6u
17
+ ··· + 2u + 1)
2
c
3
, c
7
, c
11
(u
8
− 3u
7
− 2u
6
+ 3u
5
+ 22u
4
+ 24u
3
+ 18u
2
+ 3u + 1)
· (u
8
+ u
7
− 2u
6
− 5u
5
− u
4
+ 6u
3
+ 8u
2
+ 4u + 1)
2
· (u
9
+ 4u
8
+ 5u
7
− 2u
5
+ u
4
+ 4u
2
+ u + 5)
· (u
9
+ 6u
8
+ 15u
7
+ 16u
6
+ 2u
5
− 9u
4
− 2u
3
+ 6u
2
+ 3u − 1)
· ((u
15
− 5u
14
+ ··· − 205u + 61)
2
)(u
18
− 7u
17
+ ··· − 40u + 7)
2
· (u
18
+ 18u
17
+ ··· + 5632u + 1024)
c
4
, c
8
, c
12
(u
4
− 3u
3
+ 3u
2
− u − 1)
2
· (u
8
+ 3u
7
+ 5u
6
+ 6u
5
+ 7u
4
+ 6u
3
+ 5u
2
+ 3u + 1)
2
· (u
9
− 5u
8
+ 12u
7
− 16u
6
+ 13u
5
− 6u
4
+ 2u
3
− u
2
+ 2u − 1)
· (u
9
− 3u
8
+ 4u
7
− 2u
6
+ u
5
− 2u
4
+ 2u
3
− u
2
− 1)
· ((u
15
+ 5u
14
+ ··· + u + 1)
2
)(u
18
− 17u
17
+ ··· − 176u + 32)
· (u
18
+ 5u
17
+ ··· + 5u + 1)
2
43
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
9
(y
8
− 9y
7
− 14y
6
+ 127y
5
+ 668y
4
+ 1306y
3
+ 1256y
2
+ 607y + 121)
· (y
8
+ 4y
7
+ 12y
6
+ 23y
5
+ 36y
4
+ 37y
3
+ 22y
2
+ 7y + 1)
2
· (y
9
+ 4y
8
+ 12y
7
+ 7y
6
+ 8y
5
+ 26y
3
+ 16y
2
+ 16y − 1)
· (y
9
+ 4y
8
+ 12y
7
+ 15y
6
+ 8y
5
− 12y
4
− 14y
3
+ 16y
2
+ 16y − 1)
· (y
15
+ 5y
14
+ ··· − 1107y − 121)
2
· (y
18
+ 2y
17
+ ··· + 15616y + 1024)(y
18
+ 10y
17
+ ··· + 313y + 49)
2
c
2
, c
6
, c
10
(y
8
− 10y
6
− 6y
5
+ 31y
4
+ 33y
3
+ 23y
2
+ 6y + 1)
2
· (y
8
− 7y
7
+ 17y
6
− 24y
5
+ 68y
4
− 66y
3
+ 32y
2
− 5y + 1)
· (y
9
− 13y
8
+ 66y
7
− 151y
6
+ 126y
5
+ 15y
4
− 3y
2
+ 7y − 1)
· (y
9
− 9y
8
+ 22y
7
+ 9y
6
− 46y
5
− 65y
4
− 36y
3
− 15y
2
− 5y − 1)
· ((y
15
− 15y
14
+ ··· + 201y − 1)
2
)(y
18
− 30y
17
+ ··· − 8y + 1)
2
· (y
18
− 12y
17
+ ··· + 401664y + 123904)
c
3
, c
7
, c
11
(y
8
− 13y
7
+ 66y
6
+ 83y
5
+ 288y
4
+ 194y
3
+ 224y
2
+ 27y + 1)
· (y
8
− 5y
7
+ 12y
6
− 17y
5
+ 23y
4
− 16y
3
+ 14y
2
+ 1)
2
· (y
9
− 6y
8
+ 21y
7
− 28y
6
− 26y
5
− 31y
4
− 12y
3
− 26y
2
− 39y − 25)
· (y
9
− 6y
8
+ 37y
7
− 92y
6
+ 166y
5
− 179y
4
+ 156y
3
− 66y
2
+ 21y − 1)
· (y
15
− 19y
14
+ ··· + 9085y − 3721)
2
· (y
18
− 15y
17
+ ··· − 634y + 49)
2
· (y
18
− 10y
17
+ ··· + 1572864y + 1048576)
c
4
, c
8
, c
12
(y
4
− 3y
3
+ y
2
− 7y + 1)
2
· (y
8
+ y
7
+ 3y
6
+ 8y
5
+ 11y
4
+ 8y
3
+ 3y
2
+ y + 1)
2
· (y
9
− y
8
+ 6y
7
− 4y
6
+ 3y
5
− 10y
4
− 4y
3
− 5y
2
− 2y − 1)
· (y
9
− y
8
+ 10y
7
+ 19y
5
+ 22y
4
+ 12y
3
− 5y
2
+ 2y − 1)
· ((y
15
− 3y
14
+ ··· + 13y − 1)
2
)(y
18
− 7y
17
+ ··· − 1792y + 1024)
· (y
18
− y
17
+ ··· − 5y + 1)
2
44
