12n
0509
(K12n
0509
)
A knot diagram
1
Linearized knot diagam
3 6 10 7 9 2 11 5 3 12 7 9
Solving Sequence
2,7
6
3,9
10 1 5 4 8 12 11
c
6
c
2
c
9
c
1
c
5
c
4
c
8
c
12
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
6
+ 3u
5
− 6u
4
+ 7u
3
− 6u
2
+ b + 3u − 1, u
6
− 3u
5
+ 6u
4
− 7u
3
+ 5u
2
+ a − 3u,
u
7
− 3u
6
+ 7u
5
− 10u
4
+ 10u
3
− 8u
2
+ 3u − 1i
I
u
2
= h−3u
13
+ 14u
12
+ ··· + 4b + 4, u
13
− 8u
12
+ ··· + 8a − 4, u
14
− 6u
13
+ ··· − 28u + 8i
I
u
3
= h−u
2
+ b + a − 1, a
2
+ au + 2u
2
− a + u, u
3
+ u
2
+ 2u + 1i
I
u
4
= h−u
6
− u
5
− 2u
4
− u
3
− 2u
2
+ b − u − 1, u
6
+ u
5
+ 2u
4
+ u
3
+ 3u
2
+ a + u + 2,
u
7
+ u
6
+ 3u
5
+ 2u
4
+ 4u
3
+ 2u
2
+ 3u + 1i
I
u
5
= h−2u
2
a − au − 2u
2
+ b − 2a − u − 4, 2u
2
a + a
2
+ 2u
2
+ 3a + 2u + 4, u
3
+ u
2
+ 2u + 1i
I
u
6
= h−u
2
a + 2u
2
+ 2b + u + 3, a
2
+ 3u
2
+ 3u + 2, u
3
+ u
2
+ 2u + 1i
I
u
7
= hu
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ b + u + 1, −2u
7
− 2u
6
− 5u
5
− 3u
4
− 3u
3
− 3u
2
+ a − 4u − 1,
u
8
+ u
7
+ 3u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ u + 1i
* 7 irreducible components of dim
C
= 0, with total 54 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−u
6
+ 3u
5
− 6u
4
+ 7u
3
− 6u
2
+ b + 3u − 1, u
6
− 3u
5
+ 6u
4
− 7u
3
+
5u
2
+ a − 3u, u
7
− 3u
6
+ 7u
5
− 10u
4
+ 10u
3
− 8u
2
+ 3u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
9
=
−u
6
+ 3u
5
− 6u
4
+ 7u
3
− 5u
2
+ 3u
u
6
− 3u
5
+ 6u
4
− 7u
3
+ 6u
2
− 3u + 1
a
10
=
−u
6
+ 2u
5
− 4u
4
+ 4u
3
− 3u
2
+ 2u
−u
3
− u
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
−u
5
+ 2u
4
− 3u
3
+ 3u
2
− u + 1
−u
6
+ 3u
5
− 6u
4
+ 7u
3
− 6u
2
+ 3u − 1
a
4
=
−u
6
+ 2u
5
− 4u
4
+ 4u
3
− 3u
2
+ 2u
−u
6
+ 3u
5
− 6u
4
+ 7u
3
− 6u
2
+ 3u − 1
a
8
=
−u
6
+ 2u
5
− 4u
4
+ 4u
3
− u
2
+ u + 1
−u
2
a
12
=
u
5
− 2u
4
+ 4u
3
− 4u
2
+ 2u − 1
u
a
11
=
u
5
− 2u
4
+ 4u
3
− 4u
2
+ u − 1
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
6
− 8u
5
+ 20u
4
− 32u
3
+ 36u
2
− 30u + 5
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
7
+ 5u
6
+ 9u
5
− 2u
4
− 24u
3
− 24u
2
− 7u − 1
c
2
, c
6
, c
7
c
11
u
7
− 3u
6
+ 7u
5
− 10u
4
+ 10u
3
− 8u
2
+ 3u − 1
c
3
, c
5
, c
8
c
9
u
7
+ 5u
6
+ 8u
5
+ 4u
4
+ 2u
3
+ 5u
2
+ 3u + 1
c
4
, c
12
u
7
− u
6
− 8u
5
+ 5u
4
+ 21u
3
+ 14u
2
+ 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
7
− 7y
6
+ 53y
5
− 210y
4
+ 364y
3
− 244y
2
+ y −1
c
2
, c
6
, c
7
c
11
y
7
+ 5y
6
+ 9y
5
− 2y
4
− 24y
3
− 24y
2
− 7y −1
c
3
, c
5
, c
8
c
9
y
7
− 9y
6
+ 28y
5
− 28y
4
+ 2y
3
− 21y
2
− y −1
c
4
, c
12
y
7
− 17y
6
+ 116y
5
− 325y
4
+ 239y
3
− 38y
2
− 12y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.136302 + 1.137730I
a = −1.052660 + 0.165088I
b = 0.776815 + 0.145062I
−4.44698 + 2.33074I −9.82174 − 3.80507I
u = 0.136302 − 1.137730I
a = −1.052660 − 0.165088I
b = 0.776815 − 0.145062I
−4.44698 − 2.33074I −9.82174 + 3.80507I
u = 1.24390
a = 0.333091
b = 2.21419
−11.4456 −6.73760
u = 0.194340 + 0.463986I
a = 0.726250 + 0.493271I
b = 0.096235 − 0.312929I
−0.189704 + 0.962753I −3.67202 − 7.06800I
u = 0.194340 − 0.463986I
a = 0.726250 − 0.493271I
b = 0.096235 + 0.312929I
−0.189704 − 0.962753I −3.67202 + 7.06800I
u = 0.54741 + 1.45600I
a = 1.65987 + 0.82195I
b = −2.48014 + 0.77211I
18.5842 + 12.7630I −10.63743 − 5.46514I
u = 0.54741 − 1.45600I
a = 1.65987 − 0.82195I
b = −2.48014 − 0.77211I
18.5842 − 12.7630I −10.63743 + 5.46514I
5
II. I
u
2
=
h−3u
13
+14u
12
+· · ·+4b+4, u
13
−8u
12
+· · ·+8a−4, u
14
−6u
13
+· · ·−28u+8i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
9
=
−
1
8
u
13
+ u
12
+ ··· −
3
4
u +
1
2
3
4
u
13
−
7
2
u
12
+ ··· + 5u − 1
a
10
=
−
1
8
u
13
+
3
4
u
11
+ ··· +
21
4
u −
3
2
−
5
4
u
13
+
13
2
u
12
+ ··· − 17u + 5
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
1
8
u
13
− u
12
+ ··· +
21
4
u − 1
1
4
u
13
− u
12
+ ··· +
13
2
u − 3
a
4
=
3
8
u
13
− 2u
12
+ ··· +
47
4
u − 4
1
4
u
13
− u
12
+ ··· +
13
2
u − 3
a
8
=
5
8
u
13
−
13
4
u
12
+ ··· + 7u − 1
−
1
2
u
13
+
5
2
u
12
+ ··· −
13
2
u + 3
a
12
=
−
1
8
u
13
+ u
12
+ ··· −
17
4
u + 1
3
4
u
13
− 4u
12
+ ··· +
31
2
u − 5
a
11
=
−
7
8
u
13
+ 5u
12
+ ··· −
79
4
u + 6
3
4
u
13
− 4u
12
+ ··· +
31
2
u − 5
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
13
+ 12u
12
− 43u
11
+ 105u
10
− 196u
9
+ 295u
8
− 375u
7
+
414u
6
− 395u
5
+ 319u
4
− 217u
3
+ 130u
2
− 70u + 18
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
14
+ 8u
13
+ ··· + 240u + 64
c
2
, c
6
, c
7
c
11
u
14
− 6u
13
+ ··· − 28u + 8
c
3
, c
5
, c
8
c
9
(u
7
− 2u
6
− 3u
5
+ 7u
4
− 3u
2
+ 1)
2
c
4
, c
12
u
14
− 2u
13
+ ··· + 15u + 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
14
+ 72y
12
+ ··· + 13056y + 4096
c
2
, c
6
, c
7
c
11
y
14
+ 8y
13
+ ··· + 240y + 64
c
3
, c
5
, c
8
c
9
(y
7
− 10y
6
+ 37y
5
− 61y
4
+ 46y
3
− 23y
2
+ 6y −1)
2
c
4
, c
12
y
14
− 24y
13
+ ··· − 53y + 1
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.625244 + 0.634655I
a = 0.339092 + 0.351980I
b = 0.233020 − 0.022062I
0.091886 + 0.891330I −6.03895 − 5.74662I
u = 0.625244 − 0.634655I
a = 0.339092 − 0.351980I
b = 0.233020 + 0.022062I
0.091886 − 0.891330I −6.03895 + 5.74662I
u = −0.378126 + 1.062500I
a = −1.121480 − 0.077660I
b = 0.404958 + 1.328870I
−1.03722 − 4.17104I −10.56067 + 2.18298I
u = −0.378126 − 1.062500I
a = −1.121480 + 0.077660I
b = 0.404958 − 1.328870I
−1.03722 + 4.17104I −10.56067 − 2.18298I
u = 0.643460 + 1.009790I
a = −0.104502 − 0.643158I
b = 0.260752 − 0.097466I
−1.03722 + 4.17104I −10.56067 − 2.18298I
u = 0.643460 − 1.009790I
a = −0.104502 + 0.643158I
b = 0.260752 + 0.097466I
−1.03722 − 4.17104I −10.56067 + 2.18298I
u = 1.204680 + 0.069237I
a = −0.311651 − 0.047691I
b = −2.19150 + 0.08443I
−16.0632 + 6.5463I −8.56192 − 3.00206I
u = 1.204680 − 0.069237I
a = −0.311651 + 0.047691I
b = −2.19150 − 0.08443I
−16.0632 − 6.5463I −8.56192 + 3.00206I
u = −0.321436 + 0.722211I
a = 1.113680 + 0.162158I
b = 0.125852 − 0.871897I
0.091886 + 0.891330I −6.03895 − 5.74662I
u = −0.321436 − 0.722211I
a = 1.113680 − 0.162158I
b = 0.125852 + 0.871897I
0.091886 − 0.891330I −6.03895 + 5.74662I
9
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.63252 + 1.42544I
a = 1.28836 + 1.02059I
b = −2.20148 + 0.65782I
19.2127 −10.67691 + 0.I
u = 0.63252 − 1.42544I
a = 1.28836 − 1.02059I
b = −2.20148 − 0.65782I
19.2127 −10.67691 + 0.I
u = 0.59366 + 1.46472I
a = −1.45351 − 0.86882I
b = 2.36839 − 0.76461I
−16.0632 + 6.5463I −8.56192 − 3.00206I
u = 0.59366 − 1.46472I
a = −1.45351 + 0.86882I
b = 2.36839 + 0.76461I
−16.0632 − 6.5463I −8.56192 + 3.00206I
10
III. I
u
3
= h−u
2
+ b + a − 1, a
2
+ au + 2u
2
− a + u, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
−u
2
− u − 1
a
9
=
a
u
2
− a + 1
a
10
=
u
2
a + au + 2a − u − 1
u
2
+ u + 1
a
1
=
−u
2
− 2u − 1
u
2
+ 2u
a
5
=
u
2
a + au + u
2
+ a − u
−u
2
+ a − 1
a
4
=
u
2
a + au + 2a − u − 1
−u
2
+ a − 1
a
8
=
−u
2
a − au + 3u
2
− a + 3u + 2
−u
2
a
12
=
−u
2
a + u
2
− a − u − 1
u
a
11
=
−u
2
a + u
2
− a − 2u − 1
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u
2
+ 8u + 2
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
3
+ 3u
2
+ 2u − 1)
2
c
2
, c
6
, c
7
c
11
(u
3
+ u
2
+ 2u + 1)
2
c
3
, c
5
, c
8
c
9
u
6
+ u
5
− 2u
4
+ 5u
3
+ 14u
2
− 8
c
4
, c
12
u
6
− 4u
5
− 3u
4
+ 14u
3
+ 14u
2
+ 2u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
3
− 5y
2
+ 10y −1)
2
c
2
, c
6
, c
7
c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
3
, c
5
, c
8
c
9
y
6
− 5y
5
+ 22y
4
− 97y
3
+ 228y
2
− 224y + 64
c
4
, c
12
y
6
− 22y
5
+ 149y
4
− 266y
3
+ 146y
2
− 32y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −1.276330 − 0.394337I
b = 0.613967 − 0.167943I
−10.98310 − 5.65624I −13.0195 + 5.9589I
u = −0.215080 + 1.307140I
a = 2.49141 − 0.91280I
b = −3.15376 + 0.35052I
−10.98310 − 5.65624I −13.0195 + 5.9589I
u = −0.215080 − 1.307140I
a = −1.276330 + 0.394337I
b = 0.613967 + 0.167943I
−10.98310 + 5.65624I −13.0195 − 5.9589I
u = −0.215080 − 1.307140I
a = 2.49141 + 0.91280I
b = −3.15376 − 0.35052I
−10.98310 + 5.65624I −13.0195 − 5.9589I
u = −0.569840
a = 1.51738
b = −0.192667
−2.70789 0.0390210
u = −0.569840
a = 0.0524558
b = 1.27226
−2.70789 0.0390210
14
IV. I
u
4
= h−u
6
− u
5
− 2u
4
− u
3
− 2u
2
+ b − u − 1, u
6
+ u
5
+ 2u
4
+ u
3
+
3u
2
+ a + u + 2, u
7
+ u
6
+ 3u
5
+ 2u
4
+ 4u
3
+ 2u
2
+ 3u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
9
=
−u
6
− u
5
− 2u
4
− u
3
− 3u
2
− u − 2
u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ u + 1
a
10
=
−u
6
− 2u
4
− 3u
2
− 2
−u
3
− u
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
2u
6
+ u
5
+ 4u
4
+ u
3
+ 5u
2
+ u + 3
−u
6
− u
5
− 2u
4
− u
3
− 2u
2
− u − 1
a
4
=
u
6
+ 2u
4
+ 3u
2
+ 2
−u
6
− u
5
− 2u
4
− u
3
− 2u
2
− u − 1
a
8
=
u
6
+ 2u
4
+ 3u
2
− u + 1
−u
2
a
12
=
u
5
+ 2u
3
+ 2u − 1
−u
a
11
=
u
5
+ 2u
3
+ 3u − 1
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
6
− 4u
3
− 4u
2
− 2u − 11
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
7
− 5u
6
+ 13u
5
− 22u
4
+ 24u
3
− 16u
2
+ 5u + 1
c
2
, c
7
u
7
− u
6
+ 3u
5
− 2u
4
+ 4u
3
− 2u
2
+ 3u − 1
c
3
, c
8
u
7
+ u
6
− 4u
5
− 4u
4
+ 6u
3
+ 3u
2
− 3u + 1
c
4
u
7
+ u
6
− u
4
+ 3u
3
− 4u
2
+ 2u − 1
c
5
, c
9
u
7
− u
6
− 4u
5
+ 4u
4
+ 6u
3
− 3u
2
− 3u − 1
c
6
, c
11
u
7
+ u
6
+ 3u
5
+ 2u
4
+ 4u
3
+ 2u
2
+ 3u + 1
c
12
u
7
− u
6
+ u
4
+ 3u
3
+ 4u
2
+ 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
7
+ y
6
− 3y
5
− 10y
4
+ 12y
3
+ 28y
2
+ 57y −1
c
2
, c
6
, c
7
c
11
y
7
+ 5y
6
+ 13y
5
+ 22y
4
+ 24y
3
+ 16y
2
+ 5y −1
c
3
, c
5
, c
8
c
9
y
7
− 9y
6
+ 36y
5
− 76y
4
+ 82y
3
− 37y
2
+ 3y −1
c
4
, c
12
y
7
− y
6
+ 8y
5
+ 11y
4
+ 3y
3
− 6y
2
− 4y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.537424 + 0.962927I
a = −0.662429 − 0.173919I
b = 0.300834 − 0.861081I
−0.10098 + 4.46523I −0.57946 − 5.51833I
u = 0.537424 − 0.962927I
a = −0.662429 + 0.173919I
b = 0.300834 + 0.861081I
−0.10098 − 4.46523I −0.57946 + 5.51833I
u = −0.132251 + 1.213860I
a = 1.92214 − 0.71131I
b = −1.46616 + 1.03238I
−10.69670 − 3.59676I −12.51315 + 1.73858I
u = −0.132251 − 1.213860I
a = 1.92214 + 0.71131I
b = −1.46616 − 1.03238I
−10.69670 + 3.59676I −12.51315 − 1.73858I
u = −0.723592 + 0.997572I
a = −0.752025 + 0.832832I
b = 0.223589 + 0.610838I
−3.82765 − 5.64420I −9.10487 + 5.57424I
u = −0.723592 − 0.997572I
a = −0.752025 − 0.832832I
b = 0.223589 − 0.610838I
−3.82765 + 5.64420I −9.10487 − 5.57424I
u = −0.363162
a = −2.01537
b = 0.883481
−3.64806 −10.6050
18
V. I
u
5
=
h−2u
2
a−au−2u
2
+b−2a−u−4, 2u
2
a+a
2
+2u
2
+3a+2u+4, u
3
+u
2
+2u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
−u
2
− u − 1
a
9
=
a
2u
2
a + au + 2u
2
+ 2a + u + 4
a
10
=
u
2
a + au − u
2
+ a − 1
u
2
a + au + u
2
+ 2a + 2
a
1
=
−u
2
− 2u − 1
u
2
+ 2u
a
5
=
u
2
a + 4u
2
+ 2a + 2u + 7
−u
2
a − 2u
2
− 2a − 2u − 4
a
4
=
2u
2
+ 3
−u
2
a − 2u
2
− 2a − 2u − 4
a
8
=
4u
2
a + 2au + 8u
2
+ 8a + 3u + 14
u
2
a + 2u
2
+ a + u + 4
a
12
=
u
2
a + u
2
+ 2a + 1
2u
2
a + au + 3u
2
+ 3a + u + 5
a
11
=
−u
2
a − au − 2u
2
− a − u − 4
2u
2
a + au + 3u
2
+ 3a + u + 5
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
a + 4au + 8u
2
+ 8a + 4u + 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
3
+ 3u
2
+ 2u − 1)
2
c
2
, c
6
, c
7
c
11
(u
3
+ u
2
+ 2u + 1)
2
c
3
, c
9
, c
12
(u
3
− u
2
− 4u + 5)
2
c
4
u
6
+ u
5
+ 6u
4
− 3u
3
+ 10u
2
+ 8
c
5
, c
8
(u
3
+ u
2
− 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
3
− 5y
2
+ 10y −1)
2
c
2
, c
6
, c
7
c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
3
, c
9
, c
12
(y
3
− 9y
2
+ 26y −25)
2
c
4
y
6
+ 11y
5
+ 62y
4
+ 127y
3
+ 196y
2
+ 160y + 64
c
5
, c
8
(y
3
− y
2
+ 2y −1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.824718 − 0.424452I
b = −0.732199 + 0.986732I
−6.84548 − 2.82812I −6.49024 + 2.97945I
u = −0.215080 + 1.307140I
a = −0.50000 + 1.54901I
b = 0.94728 − 2.29387I
−10.9831 −13.01951 + 0.I
u = −0.215080 − 1.307140I
a = 0.824718 + 0.424452I
b = −0.732199 − 0.986732I
−6.84548 + 2.82812I −6.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = −0.50000 − 1.54901I
b = 0.94728 + 2.29387I
−10.9831 −13.01951 + 0.I
u = −0.569840
a = −1.82472 + 0.42445I
b = 0.284920 + 0.882689I
−6.84548 − 2.82812I −6.49024 + 2.97945I
u = −0.569840
a = −1.82472 − 0.42445I
b = 0.284920 − 0.882689I
−6.84548 + 2.82812I −6.49024 − 2.97945I
22
VI. I
u
6
= h−u
2
a + 2u
2
+ 2b + u + 3, a
2
+ 3u
2
+ 3u + 2, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
−u
2
− u − 1
a
9
=
a
1
2
u
2
a − u
2
−
1
2
u −
3
2
a
10
=
1
2
u
2
a +
1
2
au +
3
2
a +
1
2
1
2
u
2
a −
1
2
u
2
+
1
2
a −
1
2
u − 1
a
1
=
−u
2
− 2u − 1
u
2
+ 2u
a
5
=
u
2
a +
1
2
au + 2u
2
+
3
2
a +
3
2
u + 1
−2u
2
− u − 2
a
4
=
u
2
a +
1
2
au +
3
2
a +
1
2
u − 1
−2u
2
− u − 2
a
8
=
1
2
u
2
−
3
2
a + u −
1
2
1
2
u
2
+
1
2
a +
3
2
a
12
=
1
2
au +
1
2
u
2
+
3
2
u +
3
2
1
2
u
2
a + a −
1
2
u −
1
2
a
11
=
−
1
2
u
2
a +
1
2
au +
1
2
u
2
− a + 2u + 2
1
2
u
2
a + a −
1
2
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
2
a + 2u
2
+ 2a + 2u − 6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
3
+ 3u
2
+ 2u − 1)
2
c
2
, c
6
, c
7
c
11
(u
3
+ u
2
+ 2u + 1)
2
c
3
, c
9
(u
3
+ u
2
− 1)
2
c
4
, c
5
, c
8
(u
3
− u
2
− 4u + 5)
2
c
12
u
6
+ u
5
+ 6u
4
− 3u
3
+ 10u
2
+ 8
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
3
− 5y
2
+ 10y −1)
2
c
2
, c
6
, c
7
c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
3
, c
9
(y
3
− y
2
+ 2y −1)
2
c
4
, c
5
, c
8
(y
3
− 9y
2
+ 26y −25)
2
c
12
y
6
+ 11y
5
+ 62y
4
+ 127y
3
+ 196y
2
+ 160y + 64
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 1.98708 − 0.56228I
b = −1.53980 − 0.18258I
−10.9831 −13.01951 + 0.I
u = −0.215080 + 1.307140I
a = −1.98708 + 0.56228I
b = 2.07960
−6.84548 − 2.82812I −6.49024 + 2.97945I
u = −0.215080 − 1.307140I
a = 1.98708 + 0.56228I
b = −1.53980 + 0.18258I
−10.9831 −13.01951 + 0.I
u = −0.215080 − 1.307140I
a = −1.98708 − 0.56228I
b = 2.07960
−6.84548 + 2.82812I −6.49024 − 2.97945I
u = −0.569840
a = 1.124560I
b = −1.53980 + 0.18258I
−6.84548 − 2.82812I −6.49024 + 2.97945I
u = −0.569840
a = − 1.124560I
b = −1.53980 − 0.18258I
−6.84548 + 2.82812I −6.49024 − 2.97945I
26
VII. I
u
7
= hu
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ b + u + 1, −2u
7
− 2u
6
+ · · · + a −
1, u
8
+ u
7
+ 3u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
9
=
2u
7
+ 2u
6
+ 5u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ 4u + 1
−u
6
− u
5
− 2u
4
− u
3
− u
2
− u − 1
a
10
=
u
7
+ u
6
+ 2u
5
+ u
4
+ u
3
+ u
2
+ 2u
−u
7
− 2u
6
− 3u
5
− 4u
4
− 2u
3
− 3u
2
− 2u − 2
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
2u
7
+ 3u
6
+ 6u
5
+ 5u
4
+ 5u
3
+ 4u
2
+ 6u + 3
−u
6
− u
5
− 2u
4
− u
3
− u
2
− u − 2
a
4
=
2u
7
+ 2u
6
+ 5u
5
+ 3u
4
+ 4u
3
+ 3u
2
+ 5u + 1
−u
6
− u
5
− 2u
4
− u
3
− u
2
− u − 2
a
8
=
−3u
6
− 2u
5
− 7u
4
− 3u
3
− 5u
2
− 3u − 5
−u
7
− 2u
5
+ u
4
− u
3
+ u
2
− u + 2
a
12
=
−2u
7
− u
6
− 4u
5
− u
4
− 2u
3
− u
2
− 3u + 1
u
7
+ u
6
+ 3u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ 3u + 1
a
11
=
−3u
7
− 2u
6
− 7u
5
− 3u
4
− 5u
3
− 3u
2
− 6u
u
7
+ u
6
+ 3u
5
+ 2u
4
+ 3u
3
+ 2u
2
+ 3u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
7
− 4u
6
− 5u
5
− 10u
4
− 7u
3
− 7u
2
− 5u − 14
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
8
− 5u
7
+ 11u
6
− 16u
5
+ 19u
4
− 16u
3
+ 11u
2
− 5u + 1
c
2
, c
7
u
8
− u
7
+ 3u
6
− 2u
5
+ 3u
4
− 2u
3
+ 3u
2
− u + 1
c
3
, c
8
(u
4
− u
3
− 2u
2
+ 2u + 1)
2
c
4
u
8
− 4u
7
+ 5u
6
− u
5
− u
4
− u
3
+ 4u
2
− 3u + 1
c
5
, c
9
(u
4
+ u
3
− 2u
2
− 2u + 1)
2
c
6
, c
11
u
8
+ u
7
+ 3u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ u + 1
c
12
u
8
+ 4u
7
+ 5u
6
+ u
5
− u
4
+ u
3
+ 4u
2
+ 3u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
8
− 3y
7
− y
6
+ 24y
5
+ 43y
4
+ 24y
3
− y
2
− 3y + 1
c
2
, c
6
, c
7
c
11
y
8
+ 5y
7
+ 11y
6
+ 16y
5
+ 19y
4
+ 16y
3
+ 11y
2
+ 5y + 1
c
3
, c
5
, c
8
c
9
(y
4
− 5y
3
+ 10y
2
− 8y + 1)
2
c
4
, c
12
y
8
− 6y
7
+ 15y
6
− 11y
5
+ 17y
4
− 5y
3
+ 8y
2
− y + 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.589362 + 0.807869I
a = 0.618883 − 0.314577I
b = 0.500000 + 0.685376I
0.398187 −4.14403 + 0.I
u = 0.589362 − 0.807869I
a = 0.618883 + 0.314577I
b = 0.500000 − 0.685376I
0.398187 −4.14403 + 0.I
u = −0.756438 + 0.654065I
a = 0.313901 − 0.842956I
b = 0.500000 − 0.432332I
−2.83064 −8.01125 + 0.I
u = −0.756438 − 0.654065I
a = 0.313901 + 0.842956I
b = 0.500000 + 0.432332I
−2.83064 −8.01125 + 0.I
u = −0.112930 + 0.707515I
a = −0.42892 + 2.19402I
b = −0.779254 − 0.555127I
−8.65338 + 2.52742I −12.42236 − 1.86858I
u = −0.112930 − 0.707515I
a = −0.42892 − 2.19402I
b = −0.779254 + 0.555127I
−8.65338 − 2.52742I −12.42236 + 1.86858I
u = −0.219994 + 1.378280I
a = −1.50387 + 0.55124I
b = 1.77925 − 0.55513I
−8.65338 − 2.52742I −12.42236 + 1.86858I
u = −0.219994 − 1.378280I
a = −1.50387 − 0.55124I
b = 1.77925 + 0.55513I
−8.65338 + 2.52742I −12.42236 − 1.86858I
30
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
((u
3
+ 3u
2
+ 2u − 1)
6
)(u
7
− 5u
6
+ ··· + 5u + 1)
· (u
7
+ 5u
6
+ 9u
5
− 2u
4
− 24u
3
− 24u
2
− 7u − 1)
· (u
8
− 5u
7
+ 11u
6
− 16u
5
+ 19u
4
− 16u
3
+ 11u
2
− 5u + 1)
· (u
14
+ 8u
13
+ ··· + 240u + 64)
c
2
, c
7
(u
3
+ u
2
+ 2u + 1)
6
(u
7
− 3u
6
+ 7u
5
− 10u
4
+ 10u
3
− 8u
2
+ 3u − 1)
· (u
7
− u
6
+ 3u
5
− 2u
4
+ 4u
3
− 2u
2
+ 3u − 1)
· (u
8
− u
7
+ 3u
6
− 2u
5
+ 3u
4
− 2u
3
+ 3u
2
− u + 1)
· (u
14
− 6u
13
+ ··· − 28u + 8)
c
3
, c
8
(u
3
− u
2
− 4u + 5)
2
(u
3
+ u
2
− 1)
2
(u
4
− u
3
− 2u
2
+ 2u + 1)
2
· (u
6
+ u
5
− 2u
4
+ 5u
3
+ 14u
2
− 8)(u
7
− 2u
6
− 3u
5
+ 7u
4
− 3u
2
+ 1)
2
· (u
7
+ u
6
− 4u
5
− 4u
4
+ 6u
3
+ 3u
2
− 3u + 1)
· (u
7
+ 5u
6
+ 8u
5
+ 4u
4
+ 2u
3
+ 5u
2
+ 3u + 1)
c
4
(u
3
− u
2
− 4u + 5)
2
(u
6
− 4u
5
− 3u
4
+ 14u
3
+ 14u
2
+ 2u − 1)
· (u
6
+ u
5
+ 6u
4
− 3u
3
+ 10u
2
+ 8)
· (u
7
− u
6
− 8u
5
+ 5u
4
+ 21u
3
+ 14u
2
+ 4u + 1)
· (u
7
+ u
6
− u
4
+ 3u
3
− 4u
2
+ 2u − 1)
· (u
8
− 4u
7
+ 5u
6
− u
5
− u
4
− u
3
+ 4u
2
− 3u + 1)
· (u
14
− 2u
13
+ ··· + 15u + 1)
c
5
, c
9
(u
3
− u
2
− 4u + 5)
2
(u
3
+ u
2
− 1)
2
(u
4
+ u
3
− 2u
2
− 2u + 1)
2
· (u
6
+ u
5
− 2u
4
+ 5u
3
+ 14u
2
− 8)(u
7
− 2u
6
− 3u
5
+ 7u
4
− 3u
2
+ 1)
2
· (u
7
− u
6
− 4u
5
+ 4u
4
+ 6u
3
− 3u
2
− 3u − 1)
· (u
7
+ 5u
6
+ 8u
5
+ 4u
4
+ 2u
3
+ 5u
2
+ 3u + 1)
c
6
, c
11
(u
3
+ u
2
+ 2u + 1)
6
(u
7
− 3u
6
+ 7u
5
− 10u
4
+ 10u
3
− 8u
2
+ 3u − 1)
· (u
7
+ u
6
+ 3u
5
+ 2u
4
+ 4u
3
+ 2u
2
+ 3u + 1)
· (u
8
+ u
7
+ 3u
6
+ 2u
5
+ 3u
4
+ 2u
3
+ 3u
2
+ u + 1)
· (u
14
− 6u
13
+ ··· − 28u + 8)
c
12
(u
3
− u
2
− 4u + 5)
2
(u
6
− 4u
5
− 3u
4
+ 14u
3
+ 14u
2
+ 2u − 1)
· (u
6
+ u
5
+ 6u
4
− 3u
3
+ 10u
2
+ 8)(u
7
− u
6
+ u
4
+ 3u
3
+ 4u
2
+ 2u + 1)
· (u
7
− u
6
− 8u
5
+ 5u
4
+ 21u
3
+ 14u
2
+ 4u + 1)
· (u
8
+ 4u
7
+ 5u
6
+ u
5
− u
4
+ u
3
+ 4u
2
+ 3u + 1)
· (u
14
− 2u
13
+ ··· + 15u + 1)
31
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
3
− 5y
2
+ 10y −1)
6
· (y
7
− 7y
6
+ 53y
5
− 210y
4
+ 364y
3
− 244y
2
+ y −1)
· (y
7
+ y
6
− 3y
5
− 10y
4
+ 12y
3
+ 28y
2
+ 57y −1)
· (y
8
− 3y
7
− y
6
+ 24y
5
+ 43y
4
+ 24y
3
− y
2
− 3y + 1)
· (y
14
+ 72y
12
+ ··· + 13056y + 4096)
c
2
, c
6
, c
7
c
11
(y
3
+ 3y
2
+ 2y −1)
6
(y
7
+ 5y
6
+ 9y
5
− 2y
4
− 24y
3
− 24y
2
− 7y −1)
· (y
7
+ 5y
6
+ 13y
5
+ 22y
4
+ 24y
3
+ 16y
2
+ 5y −1)
· (y
8
+ 5y
7
+ 11y
6
+ 16y
5
+ 19y
4
+ 16y
3
+ 11y
2
+ 5y + 1)
· (y
14
+ 8y
13
+ ··· + 240y + 64)
c
3
, c
5
, c
8
c
9
(y
3
− 9y
2
+ 26y −25)
2
(y
3
− y
2
+ 2y −1)
2
· (y
4
− 5y
3
+ 10y
2
− 8y + 1)
2
· (y
6
− 5y
5
+ 22y
4
− 97y
3
+ 228y
2
− 224y + 64)
· (y
7
− 10y
6
+ 37y
5
− 61y
4
+ 46y
3
− 23y
2
+ 6y −1)
2
· (y
7
− 9y
6
+ 28y
5
− 28y
4
+ 2y
3
− 21y
2
− y −1)
· (y
7
− 9y
6
+ 36y
5
− 76y
4
+ 82y
3
− 37y
2
+ 3y −1)
c
4
, c
12
(y
3
− 9y
2
+ 26y −25)
2
· (y
6
− 22y
5
+ 149y
4
− 266y
3
+ 146y
2
− 32y + 1)
· (y
6
+ 11y
5
+ 62y
4
+ 127y
3
+ 196y
2
+ 160y + 64)
· (y
7
− 17y
6
+ 116y
5
− 325y
4
+ 239y
3
− 38y
2
− 12y −1)
· (y
7
− y
6
+ 8y
5
+ 11y
4
+ 3y
3
− 6y
2
− 4y −1)
· (y
8
− 6y
7
+ 15y
6
− 11y
5
+ 17y
4
− 5y
3
+ 8y
2
− y + 1)
· (y
14
− 24y
13
+ ··· − 53y + 1)
32
