12a
0615
(K12a
0615
)
A knot diagram
1
Linearized knot diagam
3 7 9 1 11 2 5 10 4 12 6 8
Solving Sequence
2,6
7
3,11
12 1 5 8 4 10 9
c
6
c
2
c
11
c
1
c
5
c
7
c
4
c
10
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, u
5
+ u
4
− 2u
2
+ a − u, u
7
+ u
6
− u
5
− 3u
4
+ 2u
2
+ 2u − 1i
I
u
2
= hb − u, 3u
21
+ 2u
20
+ ··· + 2a + 6, u
22
− 3u
21
+ ··· − 2u + 1i
I
u
3
= h−u
21
+ 4u
20
+ ··· + 2b + 3, −5u
21
+ 14u
20
+ ··· + 2a + 7, u
22
− 3u
21
+ ··· − 2u + 1i
I
u
4
= h−2489u
21
− 8939u
20
+ ··· + 2212b − 39100, 8695u
21
+ 75565u
20
+ ··· + 4424a − 81736,
u
22
+ 9u
21
+ ··· − 8u − 8i
I
u
5
= hb + u, −u
5
+ u
4
+ a − u + 2, u
7
− u
6
− u
5
+ u
4
+ 2u
3
− 2u
2
+ 1i
I
u
6
= h−708u
35
a + 2695u
35
+ ··· + 9336a + 5225, 708u
35
a + 584u
35
+ ··· − 348a − 950,
u
36
− 3u
35
+ ··· − 4u + 3i
I
u
7
= hb + u, −u
6
+ 2u
4
− u
3
− 3u
2
+ a + 2u + 1, u
7
+ u
6
− u
5
− u
4
+ 2u
3
+ u
2
− u − 1i
I
u
8
= h−u
6
− u
5
+ u
4
+ u
3
− 2u
2
+ b − u + 1, −u
6
− u
5
− 2u
2
+ a − u, u
7
+ u
6
− u
5
− u
4
+ 2u
3
+ u
2
− u − 1i
I
u
9
= hu
6
− u
5
− u
4
+ 2u
3
+ u
2
+ b − u − 1, u
6
− u
5
− u
4
+ u
3
+ 2u
2
+ a − u − 2, u
7
− u
6
− u
5
+ 2u
4
+ u
3
− u
2
− u + 1i
I
u
10
= hb, a + 1, 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
I
u
11
= hb + 1, a + 2, u + 1i
I
u
12
= hb + 1, a + 3, u + 1i
I
v
1
= ha, b + 1, v −1i
* 13 irreducible components of dim
C
= 0, with total 177 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
= hb − u, u
5
+ u
4
− 2u
2
+ a − u, u
7
+ u
6
− u
5
− 3u
4
+ 2u
2
+ 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−u
5
− u
4
+ 2u
2
+ u
u
a
12
=
−u
5
− u
4
+ 2u
2
u
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
u
6
+ u
5
− 2u
3
− u
2
+ 1
−u
2
a
8
=
u
6
+ u
5
− u
3
− u
2
+ 1
u
5
− u
3
− u
2
+ u
a
4
=
u
5
+ u
4
− 2u
2
+ 1
u
2
− u
a
10
=
−u + 1
−u
3
+ u
a
9
=
u
6
+ u
5
− 2u
3
+ 1
−u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6u
4
+ 3u
3
− 3u
2
− 12u − 12
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
u
7
+ 3u
6
+ 7u
5
+ 9u
4
+ 10u
3
+ 10u
2
+ 8u + 1
c
2
, c
3
, c
5
c
6
, c
9
, c
11
u
7
− u
6
− u
5
+ 3u
4
− 2u
2
+ 2u + 1
c
4
, c
7
, c
12
u
7
− 6u
6
+ 18u
5
− 32u
4
+ 35u
3
− 21u
2
+ 3u + 3
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
y
7
+ 5y
6
+ 15y
5
+ 15y
4
+ 26y
3
+ 42y
2
+ 44y −1
c
2
, c
3
, c
5
c
6
, c
9
, c
11
y
7
− 3y
6
+ 7y
5
− 9y
4
+ 10y
3
− 10y
2
+ 8y −1
c
4
, c
7
, c
12
y
7
+ 10y
5
− 10y
4
+ 25y
3
− 39y
2
+ 135y −9
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.627087 + 0.878886I
a = −0.251298 − 0.695933I
b = −0.627087 + 0.878886I
7.19181 − 1.70769I −6.14495 − 1.15014I
u = −0.627087 − 0.878886I
a = −0.251298 + 0.695933I
b = −0.627087 − 0.878886I
7.19181 + 1.70769I −6.14495 + 1.15014I
u = 1.066700 + 0.299026I
a = 2.13291 − 1.39668I
b = 1.066700 + 0.299026I
−7.70407 − 2.73497I −21.0094 + 5.5060I
u = 1.066700 − 0.299026I
a = 2.13291 + 1.39668I
b = 1.066700 − 0.299026I
−7.70407 + 2.73497I −21.0094 − 5.5060I
u = −1.132720 + 0.725853I
a = −1.70846 − 1.34533I
b = −1.132720 + 0.725853I
2.4536 + 19.8535I −12.4578 − 11.4641I
u = −1.132720 − 0.725853I
a = −1.70846 + 1.34533I
b = −1.132720 − 0.725853I
2.4536 − 19.8535I −12.4578 + 11.4641I
u = 0.386210
a = 0.653686
b = 0.386210
−0.592790 −16.7760
6
II. I
u
2
= hb − u, 3u
21
+ 2u
20
+ · · · + 2a + 6, u
22
− 3u
21
+ · · · − 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−
3
2
u
21
− u
20
+ ··· +
9
2
u − 3
u
a
12
=
−
3
2
u
21
− u
20
+ ··· +
7
2
u − 3
u
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
11
2
u
21
− 8u
20
+ ··· + 6u −
1
2
−u
2
a
8
=
41
2
u
21
−
65
2
u
20
+ ··· +
43
2
u −
13
2
−
1
2
u
21
−
11
2
u
20
+ ··· + 2u − 5
a
4
=
3u
21
− 6u
20
+ ··· + 4u − 1
−
3
2
u
21
+
9
2
u
20
+ ··· −
5
2
u +
5
2
a
10
=
7u
21
−
37
2
u
20
+ ··· + 14u −
17
2
−u
3
+ u
a
9
=
1
2
u
21
− u
20
+ ··· +
5
2
u − 1
3
2
u
21
−
9
2
u
20
+ ··· +
5
2
u −
5
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 6u
21
−22u
20
−3u
19
+ 83u
18
−38u
17
−188u
16
+ 170u
15
+ 255u
14
−367u
13
−200u
12
+
523u
11
+ 42u
10
− 531u
9
+ 145u
8
+ 346u
7
− 200u
6
− 136u
5
+ 138u
4
− 53u
2
+ 20u − 23
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
22
+ 9u
21
+ ··· − 6u + 1
c
2
, c
5
, c
6
c
11
u
22
+ 3u
21
+ ··· + 2u + 1
c
3
, c
9
u
22
− 9u
21
+ ··· + 8u − 8
c
4
, c
12
u
22
+ 4u
21
+ ··· + 4u + 1
c
7
u
22
− 24u
21
+ ··· − 53248u + 4096
c
8
u
22
+ 7u
21
+ ··· + 2528u + 64
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
22
+ 11y
21
+ ··· − 54y + 1
c
2
, c
5
, c
6
c
11
y
22
− 9y
21
+ ··· + 6y + 1
c
3
, c
9
y
22
− 7y
21
+ ··· − 2528y + 64
c
4
, c
12
y
22
+ 6y
21
+ ··· + 2y + 1
c
7
y
22
+ 70y
20
+ ··· − 159383552y + 16777216
c
8
y
22
+ 13y
21
+ ··· − 5071360y + 4096
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.836840 + 0.581799I
a = −1.72055 − 3.05333I
b = −0.836840 + 0.581799I
2.49482 − 0.03580I −9.19656 − 1.18782I
u = −0.836840 − 0.581799I
a = −1.72055 + 3.05333I
b = −0.836840 − 0.581799I
2.49482 + 0.03580I −9.19656 + 1.18782I
u = −0.958571
a = −3.30128
b = −0.958571
−4.93723 −17.9860
u = −0.795188 + 0.673491I
a = 0.482964 − 1.043980I
b = −0.795188 + 0.673491I
4.79008 + 3.04512I −1.46454 − 3.95630I
u = −0.795188 − 0.673491I
a = 0.482964 + 1.043980I
b = −0.795188 − 0.673491I
4.79008 − 3.04512I −1.46454 + 3.95630I
u = −1.08445
a = −2.31049
b = −1.08445
−5.01957 −16.9370
u = 0.580710 + 0.919219I
a = 0.325305 − 0.694106I
b = 0.580710 + 0.919219I
5.86563 + 7.62274I −8.03926 − 3.67301I
u = 0.580710 − 0.919219I
a = 0.325305 + 0.694106I
b = 0.580710 − 0.919219I
5.86563 − 7.62274I −8.03926 + 3.67301I
u = 0.919954 + 0.624468I
a = 2.09163 − 2.53678I
b = 0.919954 + 0.624468I
4.00179 − 7.08200I −5.03530 + 8.12849I
u = 0.919954 − 0.624468I
a = 2.09163 + 2.53678I
b = 0.919954 − 0.624468I
4.00179 + 7.08200I −5.03530 − 8.12849I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.906778 + 0.649704I
a = −0.03604 − 1.82735I
b = 0.906778 + 0.649704I
2.00908 − 9.79924I −10.3132 + 13.5800I
u = 0.906778 − 0.649704I
a = −0.03604 + 1.82735I
b = 0.906778 − 0.649704I
2.00908 + 9.79924I −10.3132 − 13.5800I
u = 0.514242 + 0.653281I
a = 0.268297 − 0.175648I
b = 0.514242 + 0.653281I
−0.046256 + 1.148600I −11.80195 − 1.32419I
u = 0.514242 − 0.653281I
a = 0.268297 + 0.175648I
b = 0.514242 − 0.653281I
−0.046256 − 1.148600I −11.80195 + 1.32419I
u = 1.201870 + 0.120067I
a = 2.05957 − 0.60124I
b = 1.201870 + 0.120067I
−6.50144 + 3.58049I −19.3843 − 4.8932I
u = 1.201870 − 0.120067I
a = 2.05957 + 0.60124I
b = 1.201870 − 0.120067I
−6.50144 − 3.58049I −19.3843 + 4.8932I
u = −1.073910 + 0.601774I
a = −2.29187 − 1.39130I
b = −1.073910 + 0.601774I
−3.37508 + 11.10700I −16.0470 − 11.0853I
u = −1.073910 − 0.601774I
a = −2.29187 + 1.39130I
b = −1.073910 − 0.601774I
−3.37508 − 11.10700I −16.0470 + 11.0853I
u = 1.093640 + 0.715729I
a = 1.76706 − 1.47100I
b = 1.093640 + 0.715729I
4.2815 − 13.6348I −10.24905 + 7.91781I
u = 1.093640 − 0.715729I
a = 1.76706 + 1.47100I
b = 1.093640 − 0.715729I
4.2815 + 13.6348I −10.24905 − 7.91781I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.010269 + 0.423690I
a = 0.85952 + 2.24965I
b = 0.010269 + 0.423690I
2.15030 − 2.68120I −8.00708 + 4.43159I
u = 0.010269 − 0.423690I
a = 0.85952 − 2.24965I
b = 0.010269 − 0.423690I
2.15030 + 2.68120I −8.00708 − 4.43159I
12
III. I
u
3
=
h−u
21
+4u
20
+· · ·+2b+3, −5u
21
+14u
20
+· · ·+2a+7, u
22
−3u
21
+· · ·−2u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
5
2
u
21
− 7u
20
+ ··· + 6u −
7
2
1
2
u
21
− 2u
20
+ ··· − 3u
2
−
3
2
a
12
=
2u
21
− 5u
20
+ ··· + 6u − 2
1
2
u
21
− 2u
20
+ ··· − 3u
2
−
3
2
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
3
2
u
21
− 8u
20
+ ··· +
11
2
u − 5
−4u
21
+ 6u
20
+ ··· −
11
2
u +
1
2
a
8
=
−3u
21
+
11
2
u
20
+ ··· −
7
2
u + 3
3u
20
−
7
2
u
19
+ ··· −
1
2
u +
3
2
a
4
=
17
2
u
21
−
35
2
u
20
+ ··· +
23
2
u −
11
2
−
7
2
u
21
+ 2u
20
+ ··· − 3u −
5
2
a
10
=
−
5
2
u
21
+ 11u
20
+ ··· −
11
2
u + 8
11u
21
−
49
2
u
20
+ ··· + 15u −
21
2
a
9
=
11
2
u
21
− 8u
20
+ ··· + 6u −
1
2
5
2
u
21
− 11u
20
+ ··· +
11
2
u − 7
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 6u
21
−22u
20
−3u
19
+ 83u
18
−38u
17
−188u
16
+ 170u
15
+ 255u
14
−367u
13
−200u
12
+
523u
11
+ 42u
10
− 531u
9
+ 145u
8
+ 346u
7
− 200u
6
− 136u
5
+ 138u
4
− 53u
2
+ 20u − 23
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
22
+ 9u
21
+ ··· − 6u + 1
c
2
, c
3
, c
6
c
9
u
22
+ 3u
21
+ ··· + 2u + 1
c
4
u
22
− 24u
21
+ ··· − 53248u + 4096
c
5
, c
11
u
22
− 9u
21
+ ··· + 8u − 8
c
7
, c
12
u
22
+ 4u
21
+ ··· + 4u + 1
c
10
u
22
+ 7u
21
+ ··· + 2528u + 64
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
22
+ 11y
21
+ ··· − 54y + 1
c
2
, c
3
, c
6
c
9
y
22
− 9y
21
+ ··· + 6y + 1
c
4
y
22
+ 70y
20
+ ··· − 159383552y + 16777216
c
5
, c
11
y
22
− 7y
21
+ ··· − 2528y + 64
c
7
, c
12
y
22
+ 6y
21
+ ··· + 2y + 1
c
10
y
22
+ 13y
21
+ ··· − 5071360y + 4096
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.836840 + 0.581799I
a = −0.079524 − 0.136665I
b = −1.101550 − 0.880614I
2.49482 − 0.03580I −9.19656 − 1.18782I
u = −0.836840 − 0.581799I
a = −0.079524 + 0.136665I
b = −1.101550 + 0.880614I
2.49482 + 0.03580I −9.19656 + 1.18782I
u = −0.958571
a = −1.05475
b = 0.168704
−4.93723 −17.9860
u = −0.795188 + 0.673491I
a = 0.892746 − 0.143126I
b = −0.302170 − 1.111950I
4.79008 + 3.04512I −1.46454 − 3.95630I
u = −0.795188 − 0.673491I
a = 0.892746 + 0.143126I
b = −0.302170 + 1.111950I
4.79008 − 3.04512I −1.46454 + 3.95630I
u = −1.08445
a = −1.47024
b = −0.658865
−5.01957 −16.9370
u = 0.580710 + 0.919219I
a = −0.476892 − 0.652029I
b = −1.057640 + 0.718065I
5.86563 + 7.62274I −8.03926 − 3.67301I
u = 0.580710 − 0.919219I
a = −0.476892 + 0.652029I
b = −1.057640 − 0.718065I
5.86563 − 7.62274I −8.03926 + 3.67301I
u = 0.919954 + 0.624468I
a = −0.930867 + 0.453984I
b = −0.599409 − 1.137210I
4.00179 − 7.08200I −5.03530 + 8.12849I
u = 0.919954 − 0.624468I
a = −0.930867 − 0.453984I
b = −0.599409 + 1.137210I
4.00179 + 7.08200I −5.03530 − 8.12849I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.906778 + 0.649704I
a = −1.70529 + 1.50502I
b = −1.24193 − 0.77433I
2.00908 − 9.79924I −10.3132 + 13.5800I
u = 0.906778 − 0.649704I
a = −1.70529 − 1.50502I
b = −1.24193 + 0.77433I
2.00908 + 9.79924I −10.3132 − 13.5800I
u = 0.514242 + 0.653281I
a = 0.769810 − 0.437698I
b = 1.090770 − 0.240404I
−0.046256 + 1.148600I −11.80195 − 1.32419I
u = 0.514242 − 0.653281I
a = 0.769810 + 0.437698I
b = 1.090770 + 0.240404I
−0.046256 − 1.148600I −11.80195 + 1.32419I
u = 1.201870 + 0.120067I
a = −2.05250 + 0.39422I
b = −0.998510 + 0.502784I
−6.50144 + 3.58049I −19.3843 − 4.8932I
u = 1.201870 − 0.120067I
a = −2.05250 − 0.39422I
b = −0.998510 − 0.502784I
−6.50144 − 3.58049I −19.3843 + 4.8932I
u = −1.073910 + 0.601774I
a = 1.72007 + 0.95190I
b = 1.375940 − 0.121987I
−3.37508 + 11.10700I −16.0470 − 11.0853I
u = −1.073910 − 0.601774I
a = 1.72007 − 0.95190I
b = 1.375940 + 0.121987I
−3.37508 − 11.10700I −16.0470 + 11.0853I
u = 1.093640 + 0.715729I
a = 0.513238 + 0.359274I
b = −0.545268 + 0.984025I
4.2815 − 13.6348I −10.24905 + 7.91781I
u = 1.093640 − 0.715729I
a = 0.513238 − 0.359274I
b = −0.545268 − 0.984025I
4.2815 + 13.6348I −10.24905 − 7.91781I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.010269 + 0.423690I
a = 0.111698 + 1.290160I
b = −0.875150 − 0.696689I
2.15030 − 2.68120I −8.00708 + 4.43159I
u = 0.010269 − 0.423690I
a = 0.111698 − 1.290160I
b = −0.875150 + 0.696689I
2.15030 + 2.68120I −8.00708 − 4.43159I
18
IV. I
u
4
= h−2489u
21
− 8939u
20
+ · · · + 2212b − 39100, 8695u
21
+ 75565u
20
+
· · · + 4424a − 81736, u
22
+ 9u
21
+ · · · − 8u − 8i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−1.96542u
21
− 17.0807u
20
+ ··· + 21.8454u + 18.4756
1.12523u
21
+ 4.04114u
20
+ ··· − 10.3834u + 17.6763
a
12
=
−3.09064u
21
− 21.1218u
20
+ ··· + 32.2288u + 0.799277
1.12523u
21
+ 4.04114u
20
+ ··· − 10.3834u + 17.6763
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
6.31736u
21
+ 53.0095u
20
+ ··· + 15.0077u − 55.9593
2.25723u
21
+ 22.5665u
20
+ ··· + 5.23237u − 40.3580
a
8
=
−4.21090u
21
− 33.7579u
20
+ ··· − 3.57188u + 20.5018
−0.244123u
21
− 3.93038u
20
+ ··· + 1.53255u + 10.5841
a
4
=
−1.05335u
21
− 4.45886u
20
+ ··· + 27.7238u − 13.1094
−1.97604u
21
− 16.8892u
20
+ ··· + 14.8635u + 7.68897
a
10
=
−4.06533u
21
− 34.7642u
20
+ ··· + 14.0420u + 27.5461
5.82188u
21
+ 44.0823u
20
+ ··· − 22.9096u − 17.9331
a
9
=
−4.48440u
21
− 31.0364u
20
+ ··· + 2.54792u − 3.33454
−4.63608u
21
− 42.5158u
20
+ ··· + 14.7848u + 49.8608
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
223
553
u
21
+
601
79
u
20
+ ··· +
44196
553
u −
62234
553
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
+ 7u
21
+ ··· + 2528u + 64
c
2
, c
6
u
22
− 9u
21
+ ··· + 8u − 8
c
3
, c
5
, c
9
c
11
u
22
+ 3u
21
+ ··· + 2u + 1
c
4
, c
7
u
22
+ 4u
21
+ ··· + 4u + 1
c
8
, c
10
u
22
+ 9u
21
+ ··· − 6u + 1
c
12
u
22
− 24u
21
+ ··· − 53248u + 4096
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 13y
21
+ ··· − 5071360y + 4096
c
2
, c
6
y
22
− 7y
21
+ ··· − 2528y + 64
c
3
, c
5
, c
9
c
11
y
22
− 9y
21
+ ··· + 6y + 1
c
4
, c
7
y
22
+ 6y
21
+ ··· + 2y + 1
c
8
, c
10
y
22
+ 11y
21
+ ··· − 54y + 1
c
12
y
22
+ 70y
20
+ ··· − 159383552y + 16777216
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.090770 + 0.240404I
a = 0.542580 − 0.374285I
b = 0.514242 − 0.653281I
−0.046256 − 1.148600I −11.80195 + 1.32419I
u = 1.090770 − 0.240404I
a = 0.542580 + 0.374285I
b = 0.514242 + 0.653281I
−0.046256 + 1.148600I −11.80195 − 1.32419I
u = −0.998510 + 0.502784I
a = 2.10010 + 0.82977I
b = 1.201870 + 0.120067I
−6.50144 + 3.58049I −19.3843 − 4.8932I
u = −0.998510 − 0.502784I
a = 2.10010 − 0.82977I
b = 1.201870 − 0.120067I
−6.50144 − 3.58049I −19.3843 + 4.8932I
u = −0.875150 + 0.696689I
a = 0.347791 + 0.346084I
b = 0.010269 − 0.423690I
2.15030 + 2.68120I −8.00708 − 4.43159I
u = −0.875150 − 0.696689I
a = 0.347791 − 0.346084I
b = 0.010269 + 0.423690I
2.15030 − 2.68120I −8.00708 + 4.43159I
u = −0.545268 + 0.984025I
a = 0.460061 − 0.564019I
b = 1.093640 + 0.715729I
4.2815 − 13.6348I −10.24905 + 7.91781I
u = −0.545268 − 0.984025I
a = 0.460061 + 0.564019I
b = 1.093640 − 0.715729I
4.2815 + 13.6348I −10.24905 − 7.91781I
u = −0.302170 + 1.111950I
a = −0.459228 + 0.676532I
b = −0.795188 − 0.673491I
4.79008 − 3.04512I −1.46454 + 3.95630I
u = −0.302170 − 1.111950I
a = −0.459228 − 0.676532I
b = −0.795188 + 0.673491I
4.79008 + 3.04512I −1.46454 − 3.95630I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.057640 + 0.718065I
a = −0.567651 + 0.387084I
b = 0.580710 + 0.919219I
5.86563 + 7.62274I −8.03926 − 3.67301I
u = −1.057640 − 0.718065I
a = −0.567651 − 0.387084I
b = 0.580710 − 0.919219I
5.86563 − 7.62274I −8.03926 + 3.67301I
u = −0.599409 + 1.137210I
a = 0.526068 + 0.725042I
b = 0.919954 − 0.624468I
4.00179 + 7.08200I −5.03530 − 8.12849I
u = −0.599409 − 1.137210I
a = 0.526068 − 0.725042I
b = 0.919954 + 0.624468I
4.00179 − 7.08200I −5.03530 + 8.12849I
u = −0.658865
a = −2.41993
b = −1.08445
−5.01957 −16.9370
u = 1.375940 + 0.121987I
a = −1.74592 + 0.14546I
b = −1.073910 − 0.601774I
−3.37508 − 11.10700I −16.0470 + 11.0853I
u = 1.375940 − 0.121987I
a = −1.74592 − 0.14546I
b = −1.073910 + 0.601774I
−3.37508 + 11.10700I −16.0470 − 11.0853I
u = −1.101550 + 0.880614I
a = −0.1110480 − 0.0269532I
b = −0.836840 − 0.581799I
2.49482 + 0.03580I −9.19656 + 1.18782I
u = −1.101550 − 0.880614I
a = −0.1110480 + 0.0269532I
b = −0.836840 + 0.581799I
2.49482 − 0.03580I −9.19656 − 1.18782I
u = −1.24193 + 0.77433I
a = 1.37068 + 1.06137I
b = 0.906778 − 0.649704I
2.00908 + 9.79924I −10.3132 − 13.5800I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24193 − 0.77433I
a = 1.37068 − 1.06137I
b = 0.906778 + 0.649704I
2.00908 − 9.79924I −10.3132 + 13.5800I
u = 0.168704
a = 5.99308
b = −0.958571
−4.93723 −17.9860
24
V. I
u
5
= hb + u, −u
5
+ u
4
+ a − u + 2, u
7
− u
6
− u
5
+ u
4
+ 2u
3
− 2u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
u
5
− u
4
+ u − 2
−u
a
12
=
u
5
− u
4
+ 2u − 2
−u
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
u
6
− u
5
+ u
2
− 2u + 1
−u
2
a
8
=
−u
6
+ u
5
− u
3
− u
2
+ 2u − 1
−u
5
+ u
3
+ u
2
− u
a
4
=
−u
5
+ u
4
− 2u + 1
−u
2
+ u
a
10
=
u − 1
u
3
− u
a
9
=
−u
6
+ u
5
− 2u
2
+ 2u − 1
u
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
6
− 6u
4
− 3u
3
+ 15u
2
− 12
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
u
7
− 3u
6
+ 7u
5
− 9u
4
+ 10u
3
− 6u
2
+ 4u − 1
c
2
, c
5
, c
9
u
7
+ u
6
− u
5
− u
4
+ 2u
3
+ 2u
2
− 1
c
3
, c
6
, c
11
u
7
− u
6
− u
5
+ u
4
+ 2u
3
− 2u
2
+ 1
c
4
, c
7
, c
12
u
7
− u
3
+ u
2
− u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
y
7
+ 5y
6
+ 15y
5
+ 31y
4
+ 42y
3
+ 26y
2
+ 4y − 1
c
2
, c
3
, c
5
c
6
, c
9
, c
11
y
7
− 3y
6
+ 7y
5
− 9y
4
+ 10y
3
− 6y
2
+ 4y − 1
c
4
, c
7
, c
12
y
7
− 2y
5
− 2y
4
+ y
3
+ y
2
− y − 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.624311 + 0.652659I
a = −1.088180 + 0.242247I
b = −0.624311 − 0.652659I
3.14416 − 4.35714I −6.47040 + 7.89451I
u = 0.624311 − 0.652659I
a = −1.088180 − 0.242247I
b = −0.624311 + 0.652659I
3.14416 + 4.35714I −6.47040 − 7.89451I
u = −0.938309 + 0.714070I
a = 0.98531 + 1.45468I
b = 0.938309 − 0.714070I
2.23584 + 8.24520I −9.99047 − 7.58188I
u = −0.938309 − 0.714070I
a = 0.98531 − 1.45468I
b = 0.938309 + 0.714070I
2.23584 − 8.24520I −9.99047 + 7.58188I
u = 1.111470 + 0.496667I
a = −1.99974 + 0.62011I
b = −1.111470 − 0.496667I
−1.76596 − 9.37850I −13.2669 + 9.6588I
u = 1.111470 − 0.496667I
a = −1.99974 − 0.62011I
b = −1.111470 + 0.496667I
−1.76596 + 9.37850I −13.2669 − 9.6588I
u = −0.594946
a = −2.79477
b = 0.594946
−3.93822 −6.54450
28
VI. I
u
6
= h−708u
35
a + 2695u
35
+ · · · + 9336a + 5225, 708u
35
a + 584u
35
+
· · · − 348a − 950, u
36
− 3u
35
+ · · · − 4u + 3i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
a
0.404110au
35
− 1.53824u
35
+ ··· − 5.32877a − 2.98231
a
12
=
−0.404110au
35
+ 1.53824u
35
+ ··· + 6.32877a + 2.98231
0.404110au
35
− 1.53824u
35
+ ··· − 5.32877a − 2.98231
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
1.71176au
35
− 19.1083u
35
+ ··· − 18.2323a + 42.1745
2.54966au
35
− 6.68779u
35
+ ··· − 18.3476a + 31.5645
a
8
=
17.4024au
35
+ 15.4395u
35
+ ··· − 6.81678a − 34.0765
−7.90240au
35
− 16.1895u
35
+ ··· + 3.56678a + 48.3265
a
4
=
9.90354au
35
− 12.8651u
35
+ ··· − 23.5748a − 7.02759
−1.64212au
35
− 11.1809u
35
+ ··· − 16.7551a + 58.0166
a
10
=
4.29737au
35
+ 40.7131u
35
+ ··· + 0.168379a − 110.825
−0.205479au
35
− 34.0879u
35
+ ··· − 11.0616a + 58.8653
a
9
=
−0.235160au
35
+ 21.5818u
35
+ ··· + 7.64612a − 21.6560
2.10959au
35
− 2.70034u
35
+ ··· − 7.76712a − 31.8476
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −20u
35
+ 59u
34
+ 68u
33
− 401u
32
+ 23u
31
+ 1440u
30
− 896u
29
− 3434u
28
+ 3778u
27
+
5817u
26
− 9944u
25
− 6644u
24
+ 19472u
23
+ 3275u
22
− 29861u
21
+ 5436u
20
+ 36810u
19
−
16946u
18
−36863u
17
+26081u
16
+30326u
15
−28140u
14
−21370u
13
+23633u
12
+13830u
11
−
16213u
10
−8829u
9
+9789u
8
+5308u
7
−5435u
6
−2437u
5
+2520u
4
+690u
3
−790u
2
−83u+105
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
(u
36
+ 13u
35
+ ··· + 124u + 9)
2
c
2
, c
3
, c
5
c
6
, c
9
, c
11
(u
36
+ 3u
35
+ ··· + 4u + 3)
2
c
4
, c
7
, c
12
(u
36
+ 9u
35
+ ··· + 10u + 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
(y
36
+ 23y
35
+ ··· + 248y + 81)
2
c
2
, c
3
, c
5
c
6
, c
9
, c
11
(y
36
− 13y
35
+ ··· − 124y + 9)
2
c
4
, c
7
, c
12
(y
36
+ 9y
35
+ ··· − 2y + 1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.765456 + 0.633383I
a = −0.940028 − 0.378523I
b = 0.449327 − 1.113840I
4.48033 + 2.14866I −2.67250 − 1.35700I
u = 0.765456 + 0.633383I
a = −0.25382 − 1.52848I
b = −0.897412 + 0.669456I
4.48033 + 2.14866I −2.67250 − 1.35700I
u = 0.765456 − 0.633383I
a = −0.940028 + 0.378523I
b = 0.449327 + 1.113840I
4.48033 − 2.14866I −2.67250 + 1.35700I
u = 0.765456 − 0.633383I
a = −0.25382 + 1.52848I
b = −0.897412 − 0.669456I
4.48033 − 2.14866I −2.67250 + 1.35700I
u = 0.791040 + 0.669232I
a = 1.43100 − 0.12353I
b = −0.874503 + 0.590035I
2.36818 + 4.68398I −9.65950 − 6.77168I
u = 0.791040 + 0.669232I
a = 0.126481 − 0.130137I
b = 1.161280 − 0.806628I
2.36818 + 4.68398I −9.65950 − 6.77168I
u = 0.791040 − 0.669232I
a = 1.43100 + 0.12353I
b = −0.874503 − 0.590035I
2.36818 − 4.68398I −9.65950 + 6.77168I
u = 0.791040 − 0.669232I
a = 0.126481 + 0.130137I
b = 1.161280 + 0.806628I
2.36818 − 4.68398I −9.65950 + 6.77168I
u = 0.586231 + 0.743195I
a = 0.410954 + 0.075568I
b = 1.006090 − 0.548032I
0.472211 + 0.976866I −14.3955 − 0.4630I
u = 0.586231 + 0.743195I
a = 0.249828 + 0.293949I
b = 0.736568 + 0.185891I
0.472211 + 0.976866I −14.3955 − 0.4630I
32
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.586231 − 0.743195I
a = 0.410954 − 0.075568I
b = 1.006090 + 0.548032I
0.472211 − 0.976866I −14.3955 + 0.4630I
u = 0.586231 − 0.743195I
a = 0.249828 − 0.293949I
b = 0.736568 − 0.185891I
0.472211 − 0.976866I −14.3955 + 0.4630I
u = −0.874503 + 0.590035I
a = −0.498526 − 1.319730I
b = 0.791040 + 0.669232I
2.36818 + 4.68398I −9.65950 − 6.77168I
u = −0.874503 + 0.590035I
a = 1.88013 + 1.56326I
b = 1.161280 − 0.806628I
2.36818 + 4.68398I −9.65950 − 6.77168I
u = −0.874503 − 0.590035I
a = −0.498526 + 1.319730I
b = 0.791040 − 0.669232I
2.36818 − 4.68398I −9.65950 + 6.77168I
u = −0.874503 − 0.590035I
a = 1.88013 − 1.56326I
b = 1.161280 + 0.806628I
2.36818 − 4.68398I −9.65950 + 6.77168I
u = −0.897412 + 0.669456I
a = 0.880393 + 0.409454I
b = 0.449327 − 1.113840I
4.48033 + 2.14866I −2.67250 − 1.35700I
u = −0.897412 + 0.669456I
a = −1.264700 + 0.539429I
b = 0.765456 + 0.633383I
4.48033 + 2.14866I −2.67250 − 1.35700I
u = −0.897412 − 0.669456I
a = 0.880393 − 0.409454I
b = 0.449327 + 1.113840I
4.48033 − 2.14866I −2.67250 + 1.35700I
u = −0.897412 − 0.669456I
a = −1.264700 − 0.539429I
b = 0.765456 − 0.633383I
4.48033 − 2.14866I −2.67250 + 1.35700I
33
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.733727 + 0.454500I
a = −1.013730 + 0.749389I
b = −0.843469 − 0.867742I
1.53502 − 3.16618I −13.8126 + 4.1206I
u = 0.733727 + 0.454500I
a = −2.96583 + 1.78018I
b = −0.738825 + 0.237774I
1.53502 − 3.16618I −13.8126 + 4.1206I
u = 0.733727 − 0.454500I
a = −1.013730 − 0.749389I
b = −0.843469 + 0.867742I
1.53502 + 3.16618I −13.8126 − 4.1206I
u = 0.733727 − 0.454500I
a = −2.96583 − 1.78018I
b = −0.738825 − 0.237774I
1.53502 + 3.16618I −13.8126 − 4.1206I
u = 1.006090 + 0.548032I
a = 1.350300 + 0.212798I
b = 0.736568 − 0.185891I
0.472211 − 0.976866I −14.3955 + 0.4630I
u = 1.006090 + 0.548032I
a = −0.004403 − 0.345202I
b = 0.586231 − 0.743195I
0.472211 − 0.976866I −14.3955 + 0.4630I
u = 1.006090 − 0.548032I
a = 1.350300 − 0.212798I
b = 0.736568 + 0.185891I
0.472211 + 0.976866I −14.3955 − 0.4630I
u = 1.006090 − 0.548032I
a = −0.004403 + 0.345202I
b = 0.586231 + 0.743195I
0.472211 + 0.976866I −14.3955 − 0.4630I
u = 1.019320 + 0.615916I
a = 0.397656 + 0.603735I
b = −0.366959 + 0.715720I
−1.44376 − 6.11028I −13.9015 + 6.5551I
u = 1.019320 + 0.615916I
a = −1.81070 + 1.09398I
b = −1.213430 − 0.161296I
−1.44376 − 6.11028I −13.9015 + 6.5551I
34
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.019320 − 0.615916I
a = 0.397656 − 0.603735I
b = −0.366959 − 0.715720I
−1.44376 + 6.11028I −13.9015 − 6.5551I
u = 1.019320 − 0.615916I
a = −1.81070 − 1.09398I
b = −1.213430 + 0.161296I
−1.44376 + 6.11028I −13.9015 − 6.5551I
u = −0.366959 + 0.715720I
a = 0.932830 − 0.525065I
b = 1.019320 + 0.615916I
−1.44376 − 6.11028I −13.9015 + 6.5551I
u = −0.366959 + 0.715720I
a = −0.510617 − 0.708686I
b = −1.213430 − 0.161296I
−1.44376 − 6.11028I −13.9015 + 6.5551I
u = −0.366959 − 0.715720I
a = 0.932830 + 0.525065I
b = 1.019320 − 0.615916I
−1.44376 + 6.11028I −13.9015 − 6.5551I
u = −0.366959 − 0.715720I
a = −0.510617 + 0.708686I
b = −1.213430 + 0.161296I
−1.44376 + 6.11028I −13.9015 − 6.5551I
u = 0.449327 + 1.113840I
a = −0.502843 + 0.752573I
b = −0.897412 − 0.669456I
4.48033 − 2.14866I −2.67250 + 1.35700I
u = 0.449327 + 1.113840I
a = 0.534004 + 0.646181I
b = 0.765456 − 0.633383I
4.48033 − 2.14866I −2.67250 + 1.35700I
u = 0.449327 − 1.113840I
a = −0.502843 − 0.752573I
b = −0.897412 + 0.669456I
4.48033 + 2.14866I −2.67250 − 1.35700I
u = 0.449327 − 1.113840I
a = 0.534004 − 0.646181I
b = 0.765456 + 0.633383I
4.48033 + 2.14866I −2.67250 − 1.35700I
35
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.843469 + 0.867742I
a = 0.571786 + 0.693885I
b = 0.733727 − 0.454500I
1.53502 + 3.16618I −13.8126 − 4.1206I
u = −0.843469 + 0.867742I
a = −0.098320 + 0.115418I
b = −0.738825 − 0.237774I
1.53502 + 3.16618I −13.8126 − 4.1206I
u = −0.843469 − 0.867742I
a = 0.571786 − 0.693885I
b = 0.733727 + 0.454500I
1.53502 − 3.16618I −13.8126 + 4.1206I
u = −0.843469 − 0.867742I
a = −0.098320 − 0.115418I
b = −0.738825 + 0.237774I
1.53502 − 3.16618I −13.8126 + 4.1206I
u = −0.738825 + 0.237774I
a = 0.093225 − 0.217239I
b = −0.843469 − 0.867742I
1.53502 − 3.16618I −13.8126 + 4.1206I
u = −0.738825 + 0.237774I
a = 3.64477 + 1.22956I
b = 0.733727 + 0.454500I
1.53502 − 3.16618I −13.8126 + 4.1206I
u = −0.738825 − 0.237774I
a = 0.093225 + 0.217239I
b = −0.843469 + 0.867742I
1.53502 + 3.16618I −13.8126 − 4.1206I
u = −0.738825 − 0.237774I
a = 3.64477 − 1.22956I
b = 0.733727 − 0.454500I
1.53502 + 3.16618I −13.8126 − 4.1206I
u = 1.030420 + 0.660763I
a = −0.390502 + 1.097780I
b = −0.667141 + 0.151533I
−0.83225 − 6.33849I −17.5584 + 8.2556I
u = 1.030420 + 0.660763I
a = −1.66395 + 1.22058I
b = −1.177730 − 0.499138I
−0.83225 − 6.33849I −17.5584 + 8.2556I
36
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.030420 − 0.660763I
a = −0.390502 − 1.097780I
b = −0.667141 − 0.151533I
−0.83225 + 6.33849I −17.5584 − 8.2556I
u = 1.030420 − 0.660763I
a = −1.66395 − 1.22058I
b = −1.177730 + 0.499138I
−0.83225 + 6.33849I −17.5584 − 8.2556I
u = −1.213430 + 0.161296I
a = −0.551140 − 0.160122I
b = −0.366959 − 0.715720I
−1.44376 + 6.11028I −13.9015 − 6.5551I
u = −1.213430 + 0.161296I
a = 2.04030 + 0.27111I
b = 1.019320 − 0.615916I
−1.44376 + 6.11028I −13.9015 − 6.5551I
u = −1.213430 − 0.161296I
a = −0.551140 + 0.160122I
b = −0.366959 + 0.715720I
−1.44376 − 6.11028I −13.9015 + 6.5551I
u = −1.213430 − 0.161296I
a = 2.04030 − 0.27111I
b = 1.019320 + 0.615916I
−1.44376 − 6.11028I −13.9015 + 6.5551I
u = 0.736568 + 0.185891I
a = 0.023413 + 0.480119I
b = 0.586231 + 0.743195I
0.472211 + 0.976866I −14.3955 − 0.4630I
u = 0.736568 + 0.185891I
a = 1.27778 − 1.61781I
b = 1.006090 − 0.548032I
0.472211 + 0.976866I −14.3955 − 0.4630I
u = 0.736568 − 0.185891I
a = 0.023413 − 0.480119I
b = 0.586231 − 0.743195I
0.472211 − 0.976866I −14.3955 + 0.4630I
u = 0.736568 − 0.185891I
a = 1.27778 + 1.61781I
b = 1.006090 + 0.548032I
0.472211 − 0.976866I −14.3955 + 0.4630I
37
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.177730 + 0.499138I
a = −1.47958 + 0.27092I
b = −0.667141 − 0.151533I
−0.83225 + 6.33849I −17.5584 − 8.2556I
u = −1.177730 + 0.499138I
a = 1.76641 + 0.88298I
b = 1.030420 − 0.660763I
−0.83225 + 6.33849I −17.5584 − 8.2556I
u = −1.177730 − 0.499138I
a = −1.47958 − 0.27092I
b = −0.667141 + 0.151533I
−0.83225 − 6.33849I −17.5584 + 8.2556I
u = −1.177730 − 0.499138I
a = 1.76641 − 0.88298I
b = 1.030420 + 0.660763I
−0.83225 − 6.33849I −17.5584 + 8.2556I
u = −0.667141 + 0.151533I
a = 1.89018 − 0.87945I
b = 1.030420 + 0.660763I
−0.83225 − 6.33849I −17.5584 + 8.2556I
u = −0.667141 + 0.151533I
a = −1.94866 − 2.02787I
b = −1.177730 − 0.499138I
−0.83225 − 6.33849I −17.5584 + 8.2556I
u = −0.667141 − 0.151533I
a = 1.89018 + 0.87945I
b = 1.030420 − 0.660763I
−0.83225 + 6.33849I −17.5584 − 8.2556I
u = −0.667141 − 0.151533I
a = −1.94866 + 2.02787I
b = −1.177730 + 0.499138I
−0.83225 + 6.33849I −17.5584 − 8.2556I
u = 1.161280 + 0.806628I
a = −1.38684 + 1.18524I
b = −0.874503 − 0.590035I
2.36818 − 4.68398I 0
u = 1.161280 + 0.806628I
a = 0.1160880 − 0.0648776I
b = 0.791040 − 0.669232I
2.36818 − 4.68398I 0
38
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.161280 − 0.806628I
a = −1.38684 − 1.18524I
b = −0.874503 + 0.590035I
2.36818 + 4.68398I 0
u = 1.161280 − 0.806628I
a = 0.1160880 + 0.0648776I
b = 0.791040 + 0.669232I
2.36818 + 4.68398I 0
39
VII.
I
u
7
= hb+u, −u
6
+2u
4
−u
3
−3u
2
+a+2u+1, u
7
+u
6
−u
5
−u
4
+2u
3
+u
2
−u−1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
u
6
− 2u
4
+ u
3
+ 3u
2
− 2u − 1
−u
a
12
=
u
6
− 2u
4
+ u
3
+ 3u
2
− u − 1
−u
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−u
6
− u
5
+ 2u
4
+ u
3
− 3u
2
+ 2
−u
2
a
8
=
u
6
+ u
5
− 2u
4
− u
3
+ 3u
2
+ u − 2
u
6
+ u
5
− u
4
+ 3u
2
− 1
a
4
=
−2u
6
− u
5
+ 3u
4
+ u
3
− 4u
2
+ 2
−u
3
− u
2
a
10
=
u
6
− u
5
− 2u
4
+ u
3
+ 2u
2
− 2u
u
3
− u
a
9
=
−u
6
− u
5
+ u
4
− 3u
2
+ 2
u
3
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
6
− 7u
5
+ u
4
+ 2u
3
− 8u
2
− 6u − 10
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
7
− 3u
6
+ 7u
5
− 9u
4
+ 10u
3
− 7u
2
+ 3u − 1
c
2
, c
5
u
7
− u
6
− u
5
+ u
4
+ 2u
3
− u
2
− u + 1
c
3
u
7
− u
6
− u
5
+ 2u
4
+ u
3
− u
2
− u + 1
c
4
, c
12
u
7
+ u
6
+ u
5
+ u
4
− u
2
− u − 1
c
6
, c
11
u
7
+ u
6
− u
5
− u
4
+ 2u
3
+ u
2
− u − 1
c
7
u
7
+ 2u
6
+ u
5
+ 2u
3
+ u
2
− u + 1
c
8
u
7
− 3u
6
+ 7u
5
− 10u
4
+ 9u
3
− 7u
2
+ 3u − 1
c
9
u
7
+ u
6
− u
5
− 2u
4
+ u
3
+ u
2
− u − 1
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
7
+ 5y
6
+ 15y
5
+ 23y
4
+ 10y
3
− 7y
2
− 5y − 1
c
2
, c
5
, c
6
c
11
y
7
− 3y
6
+ 7y
5
− 9y
4
+ 10y
3
− 7y
2
+ 3y − 1
c
3
, c
9
y
7
− 3y
6
+ 7y
5
− 10y
4
+ 9y
3
− 7y
2
+ 3y − 1
c
4
, c
12
y
7
+ y
6
− y
5
− y
4
+ 2y
3
+ y
2
− y − 1
c
7
y
7
− 2y
6
+ 5y
5
− 2y
4
− 2y
3
− 5y
2
− y − 1
c
8
y
7
+ 5y
6
+ 7y
5
− 10y
4
− 23y
3
− 15y
2
− 5y − 1
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.793128 + 0.750889I
a = −0.681620 + 1.079830I
b = −0.793128 − 0.750889I
3.14237 − 2.89342I −8.32420 + 3.05402I
u = 0.793128 − 0.750889I
a = −0.681620 − 1.079830I
b = −0.793128 + 0.750889I
3.14237 + 2.89342I −8.32420 − 3.05402I
u = 0.879508
a = −0.491945
b = −0.879508
−6.32616 −25.5040
u = −0.610619 + 0.459179I
a = 1.29367 − 1.68827I
b = 0.610619 − 0.459179I
1.77813 − 1.30245I −8.67647 + 1.87180I
u = −0.610619 − 0.459179I
a = 1.29367 + 1.68827I
b = 0.610619 + 0.459179I
1.77813 + 1.30245I −8.67647 − 1.87180I
u = −1.122260 + 0.611121I
a = 1.63392 + 0.95531I
b = 1.122260 − 0.611121I
−0.11249 + 5.75449I −9.24715 − 2.11869I
u = −1.122260 − 0.611121I
a = 1.63392 − 0.95531I
b = 1.122260 + 0.611121I
−0.11249 − 5.75449I −9.24715 + 2.11869I
43
VIII. I
u
8
= h−u
6
− u
5
+ u
4
+ u
3
− 2u
2
+ b − u + 1, −u
6
− u
5
− 2u
2
+ a −
u, u
7
+ u
6
− u
5
− u
4
+ 2u
3
+ u
2
− u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
u
6
+ u
5
+ 2u
2
+ u
u
6
+ u
5
− u
4
− u
3
+ 2u
2
+ u − 1
a
12
=
u
4
+ u
3
+ 1
u
6
+ u
5
− u
4
− u
3
+ 2u
2
+ u − 1
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−u
5
− u
4
− 2u
u
6
− 2u
4
+ 3u
2
− u − 2
a
8
=
−u
4
+ u
2
− u − 1
−u
6
+ u
4
− u
3
− u
2
+ u
a
4
=
−u
5
− u
2
− 2u + 1
u
6
− 2u
4
+ 3u
2
− 2
a
10
=
2u
6
+ u
5
− 2u
4
+ 4u
2
− u − 2
−u
6
+ u
4
− u
3
− 2u
2
+ 2u
a
9
=
u
6
+ u
5
− 2u
4
− u
3
+ 2u
2
− 2
−2u
6
− u
5
+ 2u
4
− 3u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
6
− 7u
5
+ u
4
+ 2u
3
− 8u
2
− 6u − 10
44
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
7
− 3u
6
+ 7u
5
− 9u
4
+ 10u
3
− 7u
2
+ 3u − 1
c
2
, c
9
u
7
− u
6
− u
5
+ u
4
+ 2u
3
− u
2
− u + 1
c
3
, c
6
u
7
+ u
6
− u
5
− u
4
+ 2u
3
+ u
2
− u − 1
c
4
u
7
+ 2u
6
+ u
5
+ 2u
3
+ u
2
− u + 1
c
5
u
7
+ u
6
− u
5
− 2u
4
+ u
3
+ u
2
− u − 1
c
7
, c
12
u
7
+ u
6
+ u
5
+ u
4
− u
2
− u − 1
c
10
u
7
− 3u
6
+ 7u
5
− 10u
4
+ 9u
3
− 7u
2
+ 3u − 1
c
11
u
7
− u
6
− u
5
+ 2u
4
+ u
3
− u
2
− u + 1
45
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
7
+ 5y
6
+ 15y
5
+ 23y
4
+ 10y
3
− 7y
2
− 5y − 1
c
2
, c
3
, c
6
c
9
y
7
− 3y
6
+ 7y
5
− 9y
4
+ 10y
3
− 7y
2
+ 3y − 1
c
4
y
7
− 2y
6
+ 5y
5
− 2y
4
− 2y
3
− 5y
2
− y − 1
c
5
, c
11
y
7
− 3y
6
+ 7y
5
− 10y
4
+ 9y
3
− 7y
2
+ 3y − 1
c
7
, c
12
y
7
+ y
6
− y
5
− y
4
+ 2y
3
+ y
2
− y − 1
c
10
y
7
+ 5y
6
+ 7y
5
− 10y
4
− 23y
3
− 15y
2
− 5y − 1
46
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.793128 + 0.750889I
a = −0.592251 + 0.519555I
b = 0.664881 − 0.629473I
3.14237 − 2.89342I −8.32420 + 3.05402I
u = 0.793128 − 0.750889I
a = −0.592251 − 0.519555I
b = 0.664881 + 0.629473I
3.14237 + 2.89342I −8.32420 − 3.05402I
u = 0.879508
a = 3.41568
b = 1.13700
−6.32616 −25.5040
u = −0.610619 + 0.459179I
a = −0.175763 − 0.551563I
b = −1.046120 − 0.786669I
1.77813 − 1.30245I −8.67647 + 1.87180I
u = −0.610619 − 0.459179I
a = −0.175763 + 0.551563I
b = −1.046120 + 0.786669I
1.77813 + 1.30245I −8.67647 − 1.87180I
u = −1.122260 + 0.611121I
a = −0.939829 − 0.724033I
b = −0.687264 − 0.374245I
−0.11249 + 5.75449I −9.24715 − 2.11869I
u = −1.122260 − 0.611121I
a = −0.939829 + 0.724033I
b = −0.687264 + 0.374245I
−0.11249 − 5.75449I −9.24715 + 2.11869I
47
IX. I
u
9
= hu
6
− u
5
− u
4
+ 2u
3
+ u
2
+ b − u − 1, u
6
− u
5
− u
4
+ u
3
+ 2u
2
+ a −
u − 2, u
7
− u
6
− u
5
+ 2u
4
+ u
3
− u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−u
6
+ u
5
+ u
4
− u
3
− 2u
2
+ u + 2
−u
6
+ u
5
+ u
4
− 2u
3
− u
2
+ u + 1
a
12
=
u
3
− u
2
+ 1
−u
6
+ u
5
+ u
4
− 2u
3
− u
2
+ u + 1
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
2u
6
− u
5
− 3u
4
+ 3u
3
+ 3u
2
− 2
u
6
− 2u
4
+ u
3
+ 3u
2
− 2
a
8
=
−u
4
+ u
2
− u − 1
−u
5
+ u
3
− u − 1
a
4
=
2u
6
− u
5
− 2u
4
+ 3u
3
+ 2u
2
− 1
u
6
− 2u
4
+ 3u
2
− 2
a
10
=
u
5
− u
4
+ u
2
+ 1
u
6
− u
4
+ 2u
2
+ 2u − 1
a
9
=
−u
6
+ u
4
− 3u
2
− u + 2
−u
6
+ u
5
+ u
4
− 2u
3
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
6
+ 2u
5
+ u
4
− 6u
2
+ u − 8
48
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
7
− 3u
6
+ 7u
5
− 10u
4
+ 9u
3
− 7u
2
+ 3u − 1
c
2
u
7
+ u
6
− u
5
− 2u
4
+ u
3
+ u
2
− u − 1
c
3
, c
11
u
7
+ u
6
− u
5
− u
4
+ 2u
3
+ u
2
− u − 1
c
4
, c
7
u
7
+ u
6
+ u
5
+ u
4
− u
2
− u − 1
c
5
, c
9
u
7
− u
6
− u
5
+ u
4
+ 2u
3
− u
2
− u + 1
c
6
u
7
− u
6
− u
5
+ 2u
4
+ u
3
− u
2
− u + 1
c
8
, c
10
u
7
− 3u
6
+ 7u
5
− 9u
4
+ 10u
3
− 7u
2
+ 3u − 1
c
12
u
7
+ 2u
6
+ u
5
+ 2u
3
+ u
2
− u + 1
49
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
7
+ 5y
6
+ 7y
5
− 10y
4
− 23y
3
− 15y
2
− 5y − 1
c
2
, c
6
y
7
− 3y
6
+ 7y
5
− 10y
4
+ 9y
3
− 7y
2
+ 3y − 1
c
3
, c
5
, c
9
c
11
y
7
− 3y
6
+ 7y
5
− 9y
4
+ 10y
3
− 7y
2
+ 3y − 1
c
4
, c
7
y
7
+ y
6
− y
5
− y
4
+ 2y
3
+ y
2
− y − 1
c
8
, c
10
y
7
+ 5y
6
+ 15y
5
+ 23y
4
+ 10y
3
− 7y
2
− 5y − 1
c
12
y
7
− 2y
6
+ 5y
5
− 2y
4
− 2y
3
− 5y
2
− y − 1
50
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.664881 + 0.629473I
a = 0.657468 + 0.671547I
b = −0.793128 − 0.750889I
3.14237 − 2.89342I −8.32420 + 3.05402I
u = −0.664881 − 0.629473I
a = 0.657468 − 0.671547I
b = −0.793128 + 0.750889I
3.14237 + 2.89342I −8.32420 − 3.05402I
u = −1.13700
a = −2.64215
b = −0.879508
−6.32616 −25.5040
u = 0.687264 + 0.374245I
a = 1.82583 − 0.64764I
b = 1.122260 − 0.611121I
−0.11249 + 5.75449I −9.24715 − 2.11869I
u = 0.687264 − 0.374245I
a = 1.82583 + 0.64764I
b = 1.122260 + 0.611121I
−0.11249 − 5.75449I −9.24715 + 2.11869I
u = 1.046120 + 0.786669I
a = 0.337773 − 0.009203I
b = 0.610619 − 0.459179I
1.77813 − 1.30245I −8.67647 + 1.87180I
u = 1.046120 − 0.786669I
a = 0.337773 + 0.009203I
b = 0.610619 + 0.459179I
1.77813 + 1.30245I −8.67647 − 1.87180I
51
X. I
u
10
= hb, a + 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
11
=
−1
0
a
12
=
−1
0
a
1
=
−1
−1
a
5
=
1
0
a
8
=
0
1
a
4
=
0
−1
a
10
=
−1
0
a
9
=
−1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
52
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
8
c
12
u + 1
c
2
, c
3
, c
4
c
6
, c
9
u − 1
c
5
, c
10
, c
11
u
53
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
9
, c
12
y − 1
c
5
, c
10
, c
11
y
54
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−4.93480 −18.0000
55
XI. I
u
11
= hb + 1, a + 2, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
11
=
−2
−1
a
12
=
−1
−1
a
1
=
−1
−1
a
5
=
−1
−1
a
8
=
1
1
a
4
=
−1
−1
a
10
=
−1
0
a
9
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
56
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
u + 1
c
2
, c
3
, c
5
c
6
, c
9
, c
11
u − 1
c
4
, c
7
, c
12
u
57
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y − 1
c
4
, c
7
, c
12
y
58
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −2.00000
b = −1.00000
−4.93480 −18.0000
59
XII. I
u
12
= hb + 1, a + 3, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
11
=
−3
−1
a
12
=
−2
−1
a
1
=
−1
−1
a
5
=
−2
−1
a
8
=
−1
0
a
4
=
−1
0
a
10
=
−1
0
a
9
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
60
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
10
c
12
u + 1
c
2
, c
5
, c
6
c
7
, c
11
u − 1
c
3
, c
8
, c
9
u
61
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y − 1
c
3
, c
8
, c
9
y
62
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −3.00000
b = −1.00000
−4.93480 −18.0000
63
XIII. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
1
0
a
7
=
1
0
a
3
=
1
0
a
11
=
0
−1
a
12
=
1
−1
a
1
=
1
0
a
5
=
1
−1
a
8
=
0
1
a
4
=
0
−1
a
10
=
−1
0
a
9
=
−1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
64
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
c
3
, c
5
, c
9
c
11
, c
12
u − 1
c
4
, c
7
, c
8
c
10
u + 1
65
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
c
3
, c
4
, c
5
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y − 1
66
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
−4.93480 −18.0000
67
XIV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
u(u + 1)
3
(u
7
− 3u
6
+ 7u
5
− 10u
4
+ 9u
3
− 7u
2
+ 3u − 1)
· (u
7
− 3u
6
+ 7u
5
− 9u
4
+ 10u
3
− 7u
2
+ 3u − 1)
2
· (u
7
− 3u
6
+ 7u
5
− 9u
4
+ 10u
3
− 6u
2
+ 4u − 1)
· (u
7
+ 3u
6
+ 7u
5
+ 9u
4
+ 10u
3
+ 10u
2
+ 8u + 1)
· (u
22
+ 7u
21
+ ··· + 2528u + 64)(u
22
+ 9u
21
+ ··· − 6u + 1)
2
· (u
36
+ 13u
35
+ ··· + 124u + 9)
2
c
2
, c
5
, c
9
u(u − 1)
3
(u
7
− u
6
− u
5
+ u
4
+ 2u
3
− u
2
− u + 1)
2
· (u
7
− u
6
− u
5
+ 3u
4
− 2u
2
+ 2u + 1)(u
7
+ u
6
+ ··· − u − 1)
· (u
7
+ u
6
− u
5
− u
4
+ 2u
3
+ 2u
2
− 1)(u
22
− 9u
21
+ ··· + 8u − 8)
· ((u
22
+ 3u
21
+ ··· + 2u + 1)
2
)(u
36
+ 3u
35
+ ··· + 4u + 3)
2
c
3
, c
6
, c
11
u(u − 1)
3
(u
7
− u
6
− u
5
+ u
4
+ 2u
3
− 2u
2
+ 1)
· (u
7
− u
6
+ ··· − u + 1)(u
7
− u
6
− u
5
+ 3u
4
− 2u
2
+ 2u + 1)
· ((u
7
+ u
6
+ ··· − u − 1)
2
)(u
22
− 9u
21
+ ··· + 8u − 8)
· ((u
22
+ 3u
21
+ ··· + 2u + 1)
2
)(u
36
+ 3u
35
+ ··· + 4u + 3)
2
c
4
, c
7
, c
12
u(u − 1)(u + 1)
2
(u
7
− u
3
+ u
2
− u + 1)
· (u
7
− 6u
6
+ 18u
5
− 32u
4
+ 35u
3
− 21u
2
+ 3u + 3)
· (u
7
+ u
6
+ u
5
+ u
4
− u
2
− u − 1)
2
(u
7
+ 2u
6
+ u
5
+ 2u
3
+ u
2
− u + 1)
· (u
22
− 24u
21
+ ··· − 53248u + 4096)(u
22
+ 4u
21
+ ··· + 4u + 1)
2
· (u
36
+ 9u
35
+ ··· + 10u + 1)
2
68
XV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
y(y − 1)
3
(y
7
+ 5y
6
+ 7y
5
− 10y
4
− 23y
3
− 15y
2
− 5y − 1)
· (y
7
+ 5y
6
+ 15y
5
+ 15y
4
+ 26y
3
+ 42y
2
+ 44y − 1)
· (y
7
+ 5y
6
+ 15y
5
+ 23y
4
+ 10y
3
− 7y
2
− 5y − 1)
2
· (y
7
+ 5y
6
+ 15y
5
+ 31y
4
+ 42y
3
+ 26y
2
+ 4y − 1)
· (y
22
+ 11y
21
+ ··· − 54y + 1)
2
· (y
22
+ 13y
21
+ ··· − 5071360y + 4096)
· (y
36
+ 23y
35
+ ··· + 248y + 81)
2
c
2
, c
3
, c
5
c
6
, c
9
, c
11
y(y − 1)
3
(y
7
− 3y
6
+ 7y
5
− 10y
4
+ 9y
3
− 7y
2
+ 3y − 1)
· (y
7
− 3y
6
+ 7y
5
− 9y
4
+ 10y
3
− 10y
2
+ 8y − 1)
· (y
7
− 3y
6
+ 7y
5
− 9y
4
+ 10y
3
− 7y
2
+ 3y − 1)
2
· (y
7
− 3y
6
+ 7y
5
− 9y
4
+ 10y
3
− 6y
2
+ 4y − 1)
· ((y
22
− 9y
21
+ ··· + 6y + 1)
2
)(y
22
− 7y
21
+ ··· − 2528y + 64)
· (y
36
− 13y
35
+ ··· − 124y + 9)
2
c
4
, c
7
, c
12
y(y − 1)
3
(y
7
− 2y
5
− 2y
4
+ y
3
+ y
2
− y − 1)
· (y
7
+ 10y
5
− 10y
4
+ 25y
3
− 39y
2
+ 135y − 9)
· (y
7
− 2y
6
+ 5y
5
− 2y
4
− 2y
3
− 5y
2
− y − 1)
· (y
7
+ y
6
− y
5
− y
4
+ 2y
3
+ y
2
− y − 1)
2
· (y
22
+ 70y
20
+ ··· − 159383552y + 16777216)
· ((y
22
+ 6y
21
+ ··· + 2y + 1)
2
)(y
36
+ 9y
35
+ ··· − 2y + 1)
2
69
