12a
0564
(K12a
0564
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 11 12 2 4 1 6 5 10
Solving Sequence
5,12
11 6
3,7
2 8 4 10 1 9
c
11
c
5
c
6
c
2
c
7
c
4
c
10
c
12
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
53
+ 4u
52
+ ··· + 4b + 4, 2u
55
− 4u
54
+ ··· + 4a − 12, u
56
− 2u
55
+ ··· − 5u + 2i
I
u
2
= ha
2
u
2
+ 2u
2
a + 2a
2
− 2u
2
+ b + 4a − 4, 2a
2
u
2
+ a
3
+ 2u
2
a + 4a
2
+ au − 2u
2
+ 2a − u − 4, u
3
+ 2u − 1i
I
u
3
= h−u
8
+ u
7
− 4u
6
+ 3u
5
− 4u
4
+ 2u
3
+ b − u − 1, −u
9
− 5u
7
− 8u
5
− 3u
3
+ a + u,
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1i
I
u
4
= h3a
2
u
2
− 2u
3
a + 4a
2
u − 2u
2
a + 2u
3
+ 2a
2
− 2au + 2u
2
+ b + 2u,
− 2u
3
a
2
− 2a
2
u
2
+ 8u
3
a + a
3
− 4a
2
u + 3u
2
a − 2u
3
− 4a
2
+ 13au − u
2
+ 8a − 3u − 2,
u
4
+ u
3
+ 2u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 87 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
53
+4u
52
+· · ·+4b+4, 2u
55
−4u
54
+· · ·+4a−12, u
56
−2u
55
+· · ·−5u+2i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
11
=
1
−u
2
a
6
=
−u
u
3
+ u
a
3
=
−
1
2
u
55
+ u
54
+ ··· −
7
4
u + 3
1
4
u
53
− u
52
+ ··· +
3
2
u − 1
a
7
=
−u
3
− 2u
u
3
+ u
a
2
=
1
4
u
51
+ 6u
49
+ ··· +
5
4
u + 1
−
1
4
u
53
−
25
4
u
51
+ ··· +
1
2
u
2
+
1
2
u
a
8
=
−
1
4
u
55
−
13
2
u
53
+ ··· −
1
4
u − 1
3
4
u
55
− u
54
+ ··· +
5
2
u − 1
a
4
=
1
4
u
44
+
21
4
u
42
+ ··· +
1
2
u +
1
2
−
1
4
u
44
− 5u
42
+ ··· −
3
4
u
2
+ u
a
10
=
u
2
+ 1
−u
4
− 2u
2
a
1
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
9
=
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
−u
12
− 6u
10
− 12u
8
− 8u
6
− u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
55
− 4u
54
+ ··· + 20u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
56
+ 19u
55
+ ··· − 20u + 1
c
2
, c
7
u
56
+ u
55
+ ··· − 10u
2
+ 1
c
3
, c
4
, c
8
u
56
+ u
55
+ ··· + 2u + 1
c
5
, c
10
, c
11
u
56
+ 2u
55
+ ··· + 5u + 2
c
6
u
56
− 2u
55
+ ··· − 231u + 202
c
9
, c
12
u
56
− 8u
55
+ ··· − 1317u + 136
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
56
+ 47y
55
+ ··· + 1224y + 1
c
2
, c
7
y
56
+ 19y
55
+ ··· − 20y + 1
c
3
, c
4
, c
8
y
56
+ 63y
55
+ ··· − 84y + 1
c
5
, c
10
, c
11
y
56
+ 52y
55
+ ··· + 19y + 4
c
6
y
56
+ 20y
55
+ ··· + 498907y + 40804
c
9
, c
12
y
56
+ 48y
55
+ ··· − 423177y + 18496
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.167031 + 1.023460I
a = 0.581239 + 0.389226I
b = 0.786716 − 0.931788I
4.78319 + 2.48153I −3.50379 − 2.32484I
u = 0.167031 − 1.023460I
a = 0.581239 − 0.389226I
b = 0.786716 + 0.931788I
4.78319 − 2.48153I −3.50379 + 2.32484I
u = 0.692071 + 0.437803I
a = −0.66383 − 2.04682I
b = −0.37969 + 1.48563I
10.54030 − 5.20317I −1.76462 + 3.90235I
u = 0.692071 − 0.437803I
a = −0.66383 + 2.04682I
b = −0.37969 − 1.48563I
10.54030 + 5.20317I −1.76462 − 3.90235I
u = −0.708508 + 0.410403I
a = 1.96906 − 2.08951I
b = −1.10648 + 2.12776I
8.5419 + 11.5420I −4.16165 − 8.13234I
u = −0.708508 − 0.410403I
a = 1.96906 + 2.08951I
b = −1.10648 − 2.12776I
8.5419 − 11.5420I −4.16165 + 8.13234I
u = 0.622613 + 0.525563I
a = 1.77821 + 0.87570I
b = −0.85453 − 1.37150I
10.86790 + 0.81891I −1.02610 + 2.14303I
u = 0.622613 − 0.525563I
a = 1.77821 − 0.87570I
b = −0.85453 + 1.37150I
10.86790 − 0.81891I −1.02610 − 2.14303I
u = −0.592033 + 0.557273I
a = −1.57209 + 2.23463I
b = −0.22451 − 1.53219I
9.08740 − 7.17759I −2.84487 + 2.35339I
u = −0.592033 − 0.557273I
a = −1.57209 − 2.23463I
b = −0.22451 + 1.53219I
9.08740 + 7.17759I −2.84487 − 2.35339I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.103142 + 1.185330I
a = 0.186061 − 0.410343I
b = 1.46690 + 0.65983I
−0.051945 − 0.385761I 0
u = −0.103142 − 1.185330I
a = 0.186061 + 0.410343I
b = 1.46690 − 0.65983I
−0.051945 + 0.385761I 0
u = 0.669252 + 0.412330I
a = 2.47043 + 1.87049I
b = −1.39269 − 1.97696I
2.26755 − 7.24573I −6.66677 + 8.30952I
u = 0.669252 − 0.412330I
a = 2.47043 − 1.87049I
b = −1.39269 + 1.97696I
2.26755 + 7.24573I −6.66677 − 8.30952I
u = −0.206699 + 0.752355I
a = 0.574163 − 0.045388I
b = 0.468649 − 0.514420I
4.95627 + 2.53829I −2.18457 − 3.78654I
u = −0.206699 − 0.752355I
a = 0.574163 + 0.045388I
b = 0.468649 + 0.514420I
4.95627 − 2.53829I −2.18457 + 3.78654I
u = 0.582613 + 0.498044I
a = −1.36009 − 2.66583I
b = −0.26540 + 1.65618I
2.62946 + 3.09884I −5.44089 − 2.20028I
u = 0.582613 − 0.498044I
a = −1.36009 + 2.66583I
b = −0.26540 − 1.65618I
2.62946 − 3.09884I −5.44089 + 2.20028I
u = −0.676046 + 0.203719I
a = 0.329443 + 0.139721I
b = 0.294607 − 0.292968I
3.00074 + 0.91231I −5.60324 − 1.33604I
u = −0.676046 − 0.203719I
a = 0.329443 − 0.139721I
b = 0.294607 + 0.292968I
3.00074 − 0.91231I −5.60324 + 1.33604I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.692318 + 0.121292I
a = −0.85392 − 1.33610I
b = 0.25519 + 1.45796I
2.08625 − 5.88981I −8.03014 + 6.36741I
u = 0.692318 − 0.121292I
a = −0.85392 + 1.33610I
b = 0.25519 − 1.45796I
2.08625 + 5.88981I −8.03014 − 6.36741I
u = −0.201418 + 1.293670I
a = −0.870058 − 0.579976I
b = −0.43169 − 1.56082I
1.14651 + 5.97963I 0
u = −0.201418 − 1.293670I
a = −0.870058 + 0.579976I
b = −0.43169 + 1.56082I
1.14651 − 5.97963I 0
u = 0.261428 + 1.299180I
a = −1.039600 + 0.218945I
b = −0.49696 + 1.44809I
6.50957 − 9.34599I 0
u = 0.261428 − 1.299180I
a = −1.039600 − 0.218945I
b = −0.49696 − 1.44809I
6.50957 + 9.34599I 0
u = 0.580660 + 0.311133I
a = 0.0703685 − 0.0523659I
b = 0.409701 + 0.523982I
−1.38214 − 1.50697I −13.53047 + 3.87884I
u = 0.580660 − 0.311133I
a = 0.0703685 + 0.0523659I
b = 0.409701 − 0.523982I
−1.38214 + 1.50697I −13.53047 − 3.87884I
u = −0.008074 + 1.347070I
a = 0.668271 + 0.576392I
b = 0.353028 + 0.821443I
4.43635 − 1.45929I 0
u = −0.008074 − 1.347070I
a = 0.668271 − 0.576392I
b = 0.353028 − 0.821443I
4.43635 + 1.45929I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.521433 + 0.341179I
a = 1.33055 + 0.94373I
b = −0.774976 − 0.280233I
2.02037 + 1.59760I −0.90500 − 4.85866I
u = −0.521433 − 0.341179I
a = 1.33055 − 0.94373I
b = −0.774976 + 0.280233I
2.02037 − 1.59760I −0.90500 + 4.85866I
u = −0.246474 + 1.358800I
a = 0.252006 + 0.237582I
b = −0.157937 − 0.612956I
7.93137 + 4.24929I 0
u = −0.246474 − 1.358800I
a = 0.252006 − 0.237582I
b = −0.157937 + 0.612956I
7.93137 − 4.24929I 0
u = −0.604464 + 0.090171I
a = −1.22485 + 0.96150I
b = 0.55744 − 1.31425I
−3.13696 + 3.05067I −15.3053 − 6.1769I
u = −0.604464 − 0.090171I
a = −1.22485 − 0.96150I
b = 0.55744 + 1.31425I
−3.13696 − 3.05067I −15.3053 + 6.1769I
u = −0.20414 + 1.41040I
a = 0.154106 + 0.721195I
b = −1.068550 − 0.531298I
7.58921 + 4.29042I 0
u = −0.20414 − 1.41040I
a = 0.154106 − 0.721195I
b = −1.068550 + 0.531298I
7.58921 − 4.29042I 0
u = 0.22437 + 1.42514I
a = 0.0464407 − 0.0037704I
b = −0.198621 + 1.070760I
4.20552 − 4.47801I 0
u = 0.22437 − 1.42514I
a = 0.0464407 + 0.0037704I
b = −0.198621 − 1.070760I
4.20552 + 4.47801I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.02481 + 1.45160I
a = 0.437034 − 0.432649I
b = −0.071252 − 1.121650I
11.67150 + 3.02727I 0
u = −0.02481 − 1.45160I
a = 0.437034 + 0.432649I
b = −0.071252 + 1.121650I
11.67150 − 3.02727I 0
u = 0.24729 + 1.46542I
a = 1.75227 − 0.41488I
b = −1.92961 − 2.80986I
8.32154 − 10.59610I 0
u = 0.24729 − 1.46542I
a = 1.75227 + 0.41488I
b = −1.92961 + 2.80986I
8.32154 + 10.59610I 0
u = 0.20280 + 1.47543I
a = −1.64369 − 0.44402I
b = 0.68333 + 2.27056I
8.98647 + 0.24581I 0
u = 0.20280 − 1.47543I
a = −1.64369 + 0.44402I
b = 0.68333 − 2.27056I
8.98647 − 0.24581I 0
u = −0.26313 + 1.47028I
a = 1.68249 + 0.12616I
b = −1.40694 + 2.97582I
14.6067 + 15.0877I 0
u = −0.26313 − 1.47028I
a = 1.68249 − 0.12616I
b = −1.40694 − 2.97582I
14.6067 − 15.0877I 0
u = 0.25179 + 1.47848I
a = −1.236920 − 0.501404I
b = −0.07447 + 1.78181I
16.7327 − 8.6480I 0
u = 0.25179 − 1.47848I
a = −1.236920 + 0.501404I
b = −0.07447 − 1.78181I
16.7327 + 8.6480I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.18754 + 1.49529I
a = −1.54445 + 0.24504I
b = 0.90159 − 1.78028I
15.7506 − 4.3922I 0
u = −0.18754 − 1.49529I
a = −1.54445 − 0.24504I
b = 0.90159 + 1.78028I
15.7506 + 4.3922I 0
u = 0.20634 + 1.49448I
a = 1.075950 − 0.501942I
b = −1.36447 − 1.63496I
17.4257 − 2.1759I 0
u = 0.20634 − 1.49448I
a = 1.075950 + 0.501942I
b = −1.36447 + 1.63496I
17.4257 + 2.1759I 0
u = 0.147340 + 0.378273I
a = 0.901441 + 0.594340I
b = 0.521618 + 0.321445I
−0.581405 − 1.167200I −7.43245 + 5.35431I
u = 0.147340 − 0.378273I
a = 0.901441 − 0.594340I
b = 0.521618 − 0.321445I
−0.581405 + 1.167200I −7.43245 − 5.35431I
10
II.
I
u
2
= ha
2
u
2
+2u
2
a+2a
2
−2u
2
+b+4a−4, 2a
2
u
2
+2u
2
a+· · ·+2a−4, u
3
+2u−1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
11
=
1
−u
2
a
6
=
−u
−u + 1
a
3
=
a
−a
2
u
2
− 2u
2
a − 2a
2
+ 2u
2
− 4a + 4
a
7
=
−1
−u + 1
a
2
=
a
2
u
2
+ 2u
2
a + 2a
2
+ au − 2u
2
+ 4a − 4
−2a
2
u
2
− 3u
2
a − 3a
2
− 2au + 4u
2
− 5a + 6
a
8
=
2a
2
u
2
+ a
2
u + 3u
2
a + 4a
2
+ 2au − 4u
2
+ 7a − 2u − 8
−a
2
u
2
− a
2
u − a
2
− au + 2u
2
− 2a + 2u + 2
a
4
=
a
2
u
2
+ 2u
2
a + 2a
2
+ au − 2u
2
+ 4a − 4
−2a
2
u
2
− 3u
2
a − 3a
2
− 2au + 4u
2
− 5a + 6
a
10
=
u
2
+ 1
−u
a
1
=
u
u
2
a
9
=
1
u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 10
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 6u
8
+ 15u
7
+ 24u
6
+ 31u
5
+ 30u
4
+ 21u
3
+ 12u
2
+ 4u − 1
c
2
, c
3
, c
4
c
7
, c
8
u
9
+ 3u
7
+ 3u
5
+ 3u
3
+ 2u + 1
c
5
, c
9
, c
10
c
11
, c
12
(u
3
+ 2u + 1)
3
c
6
(u
3
+ 3u
2
+ 5u + 2)
3
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− 6y
8
− y
7
+ 36y
6
+ 15y
5
− 42y
4
+ 17y
3
+ 84y
2
+ 40y −1
c
2
, c
3
, c
4
c
7
, c
8
y
9
+ 6y
8
+ 15y
7
+ 24y
6
+ 31y
5
+ 30y
4
+ 21y
3
+ 12y
2
+ 4y −1
c
5
, c
9
, c
10
c
11
, c
12
(y
3
+ 4y
2
+ 4y −1)
3
c
6
(y
3
+ y
2
+ 13y −4)
3
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = −1.41033 + 0.65322I
b = 0.02182 − 2.22338I
9.44074 + 5.13794I −0.68207 − 3.20902I
u = −0.22670 + 1.46771I
a = 1.44687 + 0.73836I
b = −2.15352 + 1.99644I
9.44074 + 5.13794I −0.68207 − 3.20902I
u = −0.22670 + 1.46771I
a = 0.169027 − 0.060668I
b = −0.073872 − 1.103970I
9.44074 + 5.13794I −0.68207 − 3.20902I
u = −0.22670 − 1.46771I
a = −1.41033 − 0.65322I
b = 0.02182 + 2.22338I
9.44074 − 5.13794I −0.68207 + 3.20902I
u = −0.22670 − 1.46771I
a = 1.44687 − 0.73836I
b = −2.15352 − 1.99644I
9.44074 − 5.13794I −0.68207 + 3.20902I
u = −0.22670 − 1.46771I
a = 0.169027 + 0.060668I
b = −0.073872 + 1.103970I
9.44074 − 5.13794I −0.68207 + 3.20902I
u = 0.453398
a = 0.733086
b = −0.00791217
−0.787199 −12.6360
u = 0.453398
a = −2.57211 + 0.14119I
b = 1.20953 + 0.97910I
−0.787199 −12.6360
u = 0.453398
a = −2.57211 − 0.14119I
b = 1.20953 − 0.97910I
−0.787199 −12.6360
14
III. I
u
3
= h−u
8
+ u
7
− 4u
6
+ 3u
5
− 4u
4
+ 2u
3
+ b − u − 1, −u
9
− 5u
7
− 8u
5
−
3u
3
+ a + u, u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
11
=
1
−u
2
a
6
=
−u
u
3
+ u
a
3
=
u
9
+ 5u
7
+ 8u
5
+ 3u
3
− u
u
8
− u
7
+ 4u
6
− 3u
5
+ 4u
4
− 2u
3
+ u + 1
a
7
=
−u
3
− 2u
u
3
+ u
a
2
=
u
9
+ 5u
7
− u
6
+ 8u
5
− 3u
4
+ 3u
3
− 2u
2
− u + 1
2u
8
− u
7
+ 8u
6
− 3u
5
+ 8u
4
− 2u
3
+ u + 1
a
8
=
−u
8
− 4u
6
− 5u
4
− 2u
2
− 1
u
9
+ 4u
7
+ 5u
5
+ u
4
+ u
3
+ 2u
2
a
4
=
u
9
+ 5u
7
+ 8u
5
+ 3u
3
− u
u
8
− u
7
+ 4u
6
− 3u
5
+ 4u
4
− 2u
3
+ 2u + 1
a
10
=
u
2
+ 1
−u
4
− 2u
2
a
1
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
9
=
0
u
8
+ 3u
6
+ u
4
− 2u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
6
+ 12u
4
+ 8u
2
− 8
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
c
2
, c
3
, c
4
c
7
, c
8
(u
2
+ 1)
5
c
5
, c
10
, c
11
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
6
u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1
c
9
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
12
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
10
c
2
, c
3
, c
4
c
7
, c
8
(y + 1)
10
c
5
, c
10
, c
11
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
6
(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
c
9
, c
12
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.217740I
a = 0.821196I
b = 1.58802 + 0.76683I
2.40108 −6.51890
u = − 1.217740I
a = − 0.821196I
b = 1.58802 − 0.76683I
2.40108 −6.51890
u = 0.549911 + 0.309916I
a = −1.38013 + 0.77780I
b = 1.261070 + 0.218641I
0.32910 − 1.53058I −7.48489 + 4.43065I
u = 0.549911 − 0.309916I
a = −1.38013 − 0.77780I
b = 1.261070 − 0.218641I
0.32910 + 1.53058I −7.48489 − 4.43065I
u = −0.549911 + 0.309916I
a = 1.38013 + 0.77780I
b = −0.383681 − 0.896862I
0.32910 + 1.53058I −7.48489 − 4.43065I
u = −0.549911 − 0.309916I
a = 1.38013 − 0.77780I
b = −0.383681 + 0.896862I
0.32910 − 1.53058I −7.48489 + 4.43065I
u = −0.21917 + 1.41878I
a = 0.106340 + 0.688402I
b = −1.43286 − 1.54951I
5.87256 + 4.40083I −3.25569 − 3.49859I
u = −0.21917 − 1.41878I
a = 0.106340 − 0.688402I
b = −1.43286 + 1.54951I
5.87256 − 4.40083I −3.25569 + 3.49859I
u = 0.21917 + 1.41878I
a = −0.106340 + 0.688402I
b = 0.967447 + 0.638115I
5.87256 − 4.40083I −3.25569 + 3.49859I
u = 0.21917 − 1.41878I
a = −0.106340 − 0.688402I
b = 0.967447 − 0.638115I
5.87256 + 4.40083I −3.25569 − 3.49859I
18
IV. I
u
4
=
h−2u
3
a+2u
3
+· · ·+2a
2
+b, −2u
3
a
2
+8u
3
a+· · ·+8a−2, u
4
+u
3
+2u
2
+2u+1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
11
=
1
−u
2
a
6
=
−u
u
3
+ u
a
3
=
a
−3a
2
u
2
+ 2u
3
a − 4a
2
u + 2u
2
a − 2u
3
− 2a
2
+ 2au − 2u
2
− 2u
a
7
=
−u
3
− 2u
u
3
+ u
a
2
=
−u
3
a
2
− a
2
u
2
− a
2
u − u
2
a + 2u
3
− au + 2u
2
− a + 4u + 4
−5a
2
u
2
+ 3u
3
a − 6a
2
u + 4u
2
a − 4u
3
− 3a
2
+ 3au − 4u
2
+ a − 4u − 2
a
8
=
u
3
a
2
+ 2a
2
u
2
− 2u
3
a + 2a
2
u − u
2
a + 2u
3
+ a
2
− 2au − a + 2u
−2u
3
a
2
− 2a
2
u
2
+ u
3
a − a
2
u − 2u
2
a − 2au + 2u
2
− a + 2u + 2
a
4
=
−u
3
a
2
− a
2
u
2
− a
2
u − u
2
a + 2u
3
− au + 2u
2
− a + 4u + 4
−5a
2
u
2
+ 3u
3
a − 6a
2
u + 4u
2
a − 4u
3
− 3a
2
+ 3au − 4u
2
+ a − 4u − 2
a
10
=
u
2
+ 1
u
3
+ 2u + 1
a
1
=
2u
3
+ u
2
+ 3u + 3
−u
3
− u
2
− u − 2
a
9
=
u
3
+ 2u
−u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u − 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 8u
11
+ ··· + 2u
2
+ 1
c
2
, c
3
, c
4
c
7
, c
8
u
12
+ 4u
10
− u
9
+ 6u
8
− 3u
7
+ 6u
6
− 3u
5
+ 5u
4
− 3u
3
+ 2u
2
− 2u + 1
c
5
, c
9
, c
10
c
11
, c
12
(u
4
− u
3
+ 2u
2
− 2u + 1)
3
c
6
(u
2
− u + 1)
6
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 8y
11
+ ··· + 4y + 1
c
2
, c
3
, c
4
c
7
, c
8
y
12
+ 8y
11
+ ··· + 2y
2
+ 1
c
5
, c
9
, c
10
c
11
, c
12
(y
4
+ 3y
3
+ 2y
2
+ 1)
3
c
6
(y
2
+ y + 1)
6
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = 0.231503 − 0.048586I
b = 0.496332 − 0.463157I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.621744 + 0.440597I
a = −0.64313 + 2.57341I
b = −0.45889 − 1.59209I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.621744 + 0.440597I
a = 2.55302 − 1.00733I
b = −1.42232 + 1.41895I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = 0.231503 + 0.048586I
b = 0.496332 + 0.463157I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = −0.621744 − 0.440597I
a = −0.64313 − 2.57341I
b = −0.45889 + 1.59209I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = −0.621744 − 0.440597I
a = 2.55302 + 1.00733I
b = −1.42232 − 1.41895I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = 0.121744 + 1.306620I
a = −0.305126 + 1.095260I
b = −0.07449 + 1.73534I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = 0.121744 + 1.306620I
a = −0.365118 + 0.741654I
b = 2.37156 − 0.58328I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = 0.121744 + 1.306620I
a = 0.528852 − 0.319426I
b = 0.0878104 − 0.0563109I
3.28987 − 2.02988I −4.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = −0.305126 − 1.095260I
b = −0.07449 − 1.73534I
3.28987 + 2.02988I −4.00000 − 3.46410I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.121744 − 1.306620I
a = −0.365118 − 0.741654I
b = 2.37156 + 0.58328I
3.28987 + 2.02988I −4.00000 − 3.46410I
u = 0.121744 − 1.306620I
a = 0.528852 + 0.319426I
b = 0.0878104 + 0.0563109I
3.28987 + 2.02988I −4.00000 − 3.46410I
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
· (u
9
+ 6u
8
+ 15u
7
+ 24u
6
+ 31u
5
+ 30u
4
+ 21u
3
+ 12u
2
+ 4u − 1)
· (u
12
+ 8u
11
+ ··· + 2u
2
+ 1)(u
56
+ 19u
55
+ ··· − 20u + 1)
c
2
, c
7
(u
2
+ 1)
5
(u
9
+ 3u
7
+ 3u
5
+ 3u
3
+ 2u + 1)
· (u
12
+ 4u
10
− u
9
+ 6u
8
− 3u
7
+ 6u
6
− 3u
5
+ 5u
4
− 3u
3
+ 2u
2
− 2u + 1)
· (u
56
+ u
55
+ ··· − 10u
2
+ 1)
c
3
, c
4
, c
8
(u
2
+ 1)
5
(u
9
+ 3u
7
+ 3u
5
+ 3u
3
+ 2u + 1)
· (u
12
+ 4u
10
− u
9
+ 6u
8
− 3u
7
+ 6u
6
− 3u
5
+ 5u
4
− 3u
3
+ 2u
2
− 2u + 1)
· (u
56
+ u
55
+ ··· + 2u + 1)
c
5
, c
10
, c
11
((u
3
+ 2u + 1)
3
)(u
4
− u
3
+ 2u
2
− 2u + 1)
3
(u
10
+ 5u
8
+ ··· − u
2
+ 1)
· (u
56
+ 2u
55
+ ··· + 5u + 2)
c
6
(u
2
− u + 1)
6
(u
3
+ 3u
2
+ 5u + 2)
3
(u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1)
· (u
56
− 2u
55
+ ··· − 231u + 202)
c
9
(u
3
+ 2u + 1)
3
(u
4
− u
3
+ 2u
2
− 2u + 1)
3
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
· (u
56
− 8u
55
+ ··· − 1317u + 136)
c
12
(u
3
+ 2u + 1)
3
(u
4
− u
3
+ 2u
2
− 2u + 1)
3
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
· (u
56
− 8u
55
+ ··· − 1317u + 136)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
10
· (y
9
− 6y
8
− y
7
+ 36y
6
+ 15y
5
− 42y
4
+ 17y
3
+ 84y
2
+ 40y −1)
· (y
12
− 8y
11
+ ··· + 4y + 1)(y
56
+ 47y
55
+ ··· + 1224y + 1)
c
2
, c
7
(y + 1)
10
· (y
9
+ 6y
8
+ 15y
7
+ 24y
6
+ 31y
5
+ 30y
4
+ 21y
3
+ 12y
2
+ 4y −1)
· (y
12
+ 8y
11
+ ··· + 2y
2
+ 1)(y
56
+ 19y
55
+ ··· − 20y + 1)
c
3
, c
4
, c
8
(y + 1)
10
· (y
9
+ 6y
8
+ 15y
7
+ 24y
6
+ 31y
5
+ 30y
4
+ 21y
3
+ 12y
2
+ 4y −1)
· (y
12
+ 8y
11
+ ··· + 2y
2
+ 1)(y
56
+ 63y
55
+ ··· − 84y + 1)
c
5
, c
10
, c
11
(y
3
+ 4y
2
+ 4y −1)
3
(y
4
+ 3y
3
+ 2y
2
+ 1)
3
· ((y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
)(y
56
+ 52y
55
+ ··· + 19y + 4)
c
6
(y
2
+ y + 1)
6
(y
3
+ y
2
+ 13y −4)
3
(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
· (y
56
+ 20y
55
+ ··· + 498907y + 40804)
c
9
, c
12
(y
3
+ 4y
2
+ 4y −1)
3
(y
4
+ 3y
3
+ 2y
2
+ 1)
3
· ((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
56
+ 48y
55
+ ··· − 423177y + 18496)
25
