12a
1116
(K12a
1116
)
A knot diagram
1
Linearized knot diagam
4 7 12 10 11 9 3 1 6 5 2 8
Solving Sequence
1,8 3,9
7 2 6 10 12 4 11 5
c
8
c
7
c
2
c
6
c
9
c
12
c
3
c
11
c
5
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 1.05217 × 10
27
u
39
+ 1.39337 × 10
27
u
38
+ ··· + 7.10616 × 10
26
a − 1.70682 × 10
27
,
u
40
+ u
39
+ ··· − 2u + 1i
I
u
2
= h−2.26032 × 10
209
u
71
+ 5.90990 × 10
209
u
70
+ ··· + 4.11003 × 10
210
b − 1.25850 × 10
213
,
− 1.04624 × 10
212
u
71
+ 2.60608 × 10
212
u
70
+ ··· + 1.55912 × 10
213
a − 4.97927 × 10
215
,
u
72
− u
71
+ ··· − 10866u + 3667i
I
u
3
= hb + u, 2u
19
+ 2u
18
+ ··· + a − 4, u
20
+ u
19
+ ··· − 4u − 1i
* 3 irreducible components of dim
C
= 0, with total 132 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, 1.05 × 10
27
u
39
+ 1.39 × 10
27
u
38
+ · · · + 7.11 × 10
26
a − 1.71 ×
10
27
, u
40
+ u
39
+ · · · − 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
3
=
−1.48065u
39
− 1.96079u
38
+ ··· + 1.35762u + 2.40188
u
a
9
=
1
−u
2
a
7
=
−0.480143u
39
− 1.10267u
38
+ ··· − 0.559408u + 2.48065
u
2
a
2
=
−0.858121u
39
− 1.37178u
38
+ ··· − 0.162740u + 1.92174
−u
3
+ u
a
6
=
−0.513657u
39
− 0.937281u
38
+ ··· + 0.205499u + 1.85812
0.0881220u
39
− 0.00106714u
38
+ ··· − 0.431317u + 0.198901
a
10
=
0.170926u
39
+ 0.314539u
38
+ ··· + 0.337548u + 0.372176
−0.269415u
39
− 0.112280u
38
+ ··· + 1.12121u − 0.412140
a
12
=
−u
u
a
4
=
−0.858121u
39
− 1.37178u
38
+ ··· + 0.837260u + 1.92174
−0.622525u
39
− 0.589010u
38
+ ··· + 1.52036u + 0.480143
a
11
=
1.17203u
39
+ 1.77115u
38
+ ··· − 0.353657u − 2.38079
−0.313912u
39
− 0.399375u
38
+ ··· + 0.516397u + 0.459050
a
5
=
−1.61039u
39
− 2.45419u
38
+ ··· + 0.621411u + 3.20931
0.249610u
39
− 0.0431241u
38
+ ··· − 1.08313u + 0.723404
(ii) Obstruction class = −1
(iii) Cusp Shapes =
151015313886743544528267445
710615561412313479871799093
u
39
−
543514532737677763668736672
710615561412313479871799093
u
38
+
··· −
196468822280070142794468717
710615561412313479871799093
u +
7938621198965187441158388505
710615561412313479871799093
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
40
+ u
39
+ ··· − 14u + 1
c
2
, c
7
, c
8
c
12
u
40
+ u
39
+ ··· − 2u + 1
c
3
u
40
+ 35u
39
+ ··· + 4063232u + 262144
c
4
, c
5
, c
10
u
40
− 6u
39
+ ··· + 14u + 4
c
6
, c
9
u
40
+ 18u
39
+ ··· − 286u − 52
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
40
− 17y
39
+ ··· − 104y + 1
c
2
, c
7
, c
8
c
12
y
40
− 27y
39
+ ··· − 6y + 1
c
3
y
40
− 5y
39
+ ··· − 738734374912y + 68719476736
c
4
, c
5
, c
10
y
40
− 34y
39
+ ··· − 76y + 16
c
6
, c
9
y
40
+ 22y
39
+ ··· − 227084y + 2704
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.829708 + 0.582758I
a = −0.335057 + 0.593668I
b = 0.829708 + 0.582758I
0.31185 + 6.62575I 5.80735 − 6.70847I
u = 0.829708 − 0.582758I
a = −0.335057 − 0.593668I
b = 0.829708 − 0.582758I
0.31185 − 6.62575I 5.80735 + 6.70847I
u = 0.950467 + 0.117799I
a = −2.79305 − 0.18733I
b = 0.950467 + 0.117799I
0.479393 + 0.290586I 9.02412 − 0.47721I
u = 0.950467 − 0.117799I
a = −2.79305 + 0.18733I
b = 0.950467 − 0.117799I
0.479393 − 0.290586I 9.02412 + 0.47721I
u = −1.045880 + 0.174408I
a = 2.78432 − 0.39606I
b = −1.045880 + 0.174408I
−1.95597 − 4.61343I 6.17888 + 5.30120I
u = −1.045880 − 0.174408I
a = 2.78432 + 0.39606I
b = −1.045880 − 0.174408I
−1.95597 + 4.61343I 6.17888 − 5.30120I
u = −1.06992
a = 3.35821
b = −1.06992
8.23937 8.13250
u = −0.709739 + 0.591170I
a = 0.136387 + 0.470227I
b = −0.709739 + 0.591170I
−3.66425 − 2.23553I 2.10476 + 3.41235I
u = −0.709739 − 0.591170I
a = 0.136387 − 0.470227I
b = −0.709739 − 0.591170I
−3.66425 + 2.23553I 2.10476 − 3.41235I
u = 1.099650 + 0.175182I
a = −2.79566 − 0.50433I
b = 1.099650 + 0.175182I
3.02582 + 8.81935I 10.62324 − 6.97053I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.099650 − 0.175182I
a = −2.79566 + 0.50433I
b = 1.099650 − 0.175182I
3.02582 − 8.81935I 10.62324 + 6.97053I
u = −0.301242 + 0.810427I
a = 1.231820 − 0.046364I
b = −0.301242 + 0.810427I
−1.68748 + 6.67297I 4.33952 − 4.30566I
u = −0.301242 − 0.810427I
a = 1.231820 + 0.046364I
b = −0.301242 − 0.810427I
−1.68748 − 6.67297I 4.33952 + 4.30566I
u = 0.575167 + 0.621713I
a = 0.009634 + 0.324370I
b = 0.575167 + 0.621713I
0.17012 − 2.02828I 6.28682 − 0.18788I
u = 0.575167 − 0.621713I
a = 0.009634 − 0.324370I
b = 0.575167 − 0.621713I
0.17012 + 2.02828I 6.28682 + 0.18788I
u = 0.347115 + 0.764028I
a = −1.348860 + 0.000533I
b = 0.347115 + 0.764028I
−5.94604 − 2.55676I −0.337170 + 1.059387I
u = 0.347115 − 0.764028I
a = −1.348860 − 0.000533I
b = 0.347115 − 0.764028I
−5.94604 + 2.55676I −0.337170 − 1.059387I
u = −0.408843 + 0.706524I
a = 1.51264 + 0.04027I
b = −0.408843 + 0.706524I
−2.38796 − 1.54380I 3.59940 + 3.55875I
u = −0.408843 − 0.706524I
a = 1.51264 − 0.04027I
b = −0.408843 − 0.706524I
−2.38796 + 1.54380I 3.59940 − 3.55875I
u = −0.744235
a = −1.54163
b = −0.744235
7.13720 26.0990
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.233550 + 0.336291I
a = 1.58613 + 1.22068I
b = −1.233550 + 0.336291I
10.81870 − 1.65128I 14.7327 + 4.5795I
u = −1.233550 − 0.336291I
a = 1.58613 − 1.22068I
b = −1.233550 − 0.336291I
10.81870 + 1.65128I 14.7327 − 4.5795I
u = 1.230890 + 0.434304I
a = −1.40654 + 0.97624I
b = 1.230890 + 0.434304I
4.92417 + 4.68998I 8.58815 − 3.67892I
u = 1.230890 − 0.434304I
a = −1.40654 − 0.97624I
b = 1.230890 − 0.434304I
4.92417 − 4.68998I 8.58815 + 3.67892I
u = −0.008320 + 0.688792I
a = −0.644264 + 0.267316I
b = −0.008320 + 0.688792I
3.24536 − 1.80566I 7.66277 + 3.84341I
u = −0.008320 − 0.688792I
a = −0.644264 − 0.267316I
b = −0.008320 − 0.688792I
3.24536 + 1.80566I 7.66277 − 3.84341I
u = 0.619486
a = −2.75105
b = 0.619486
0.329159 14.0190
u = −1.306240 + 0.490977I
a = 1.50397 + 0.75841I
b = −1.306240 + 0.490977I
5.64753 − 8.73681I 9.75964 + 8.45348I
u = −1.306240 − 0.490977I
a = 1.50397 − 0.75841I
b = −1.306240 − 0.490977I
5.64753 + 8.73681I 9.75964 − 8.45348I
u = 1.39043 + 0.46049I
a = −1.69234 + 0.71463I
b = 1.39043 + 0.46049I
12.1702 + 10.4927I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39043 − 0.46049I
a = −1.69234 − 0.71463I
b = 1.39043 − 0.46049I
12.1702 − 10.4927I 0
u = −1.37616 + 0.58894I
a = 1.53982 + 0.51187I
b = −1.37616 + 0.58894I
3.95118 − 8.98770I 0
u = −1.37616 − 0.58894I
a = 1.53982 − 0.51187I
b = −1.37616 − 0.58894I
3.95118 + 8.98770I 0
u = −0.114437 + 0.486204I
a = 0.910358 + 0.962474I
b = −0.114437 + 0.486204I
−1.35206 + 0.83491I −2.58594 − 2.82924I
u = −0.114437 − 0.486204I
a = 0.910358 − 0.962474I
b = −0.114437 − 0.486204I
−1.35206 − 0.83491I −2.58594 + 2.82924I
u = 1.41567 + 0.59218I
a = −1.60292 + 0.47452I
b = 1.41567 + 0.59218I
1.03205 + 13.48300I 0
u = 1.41567 − 0.59218I
a = −1.60292 − 0.47452I
b = 1.41567 − 0.59218I
1.03205 − 13.48300I 0
u = −1.44142 + 0.58645I
a = 1.64842 + 0.46268I
b = −1.44142 + 0.58645I
5.7710 − 17.8215I 0
u = −1.44142 − 0.58645I
a = 1.64842 − 0.46268I
b = −1.44142 − 0.58645I
5.7710 + 17.8215I 0
u = 0.408146
a = 0.444839
b = 0.408146
0.723836 14.2940
8
II. I
u
2
= h−2.26 × 10
209
u
71
+ 5.91 × 10
209
u
70
+ · · · + 4.11 × 10
210
b − 1.26 ×
10
213
, −1.05 × 10
212
u
71
+ 2.61 × 10
212
u
70
+ · · · + 1.56 × 10
213
a − 4.98 ×
10
215
, u
72
− u
71
+ · · · − 10866u + 3667i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
3
=
0.0671046u
71
− 0.167151u
70
+ ··· − 1109.95u + 319.364
0.0549952u
71
− 0.143792u
70
+ ··· − 1113.13u + 306.203
a
9
=
1
−u
2
a
7
=
−0.0301419u
71
+ 0.0293224u
70
+ ··· + 395.244u − 87.4100
0.328648u
71
− 0.521975u
70
+ ··· − 3059.47u + 668.529
a
2
=
0.278968u
71
− 0.729274u
70
+ ··· − 5396.58u + 1506.02
−0.454216u
71
+ 1.22463u
70
+ ··· + 8943.08u − 2530.76
a
6
=
−0.339538u
71
+ 0.567129u
70
+ ··· + 3353.09u − 758.945
0.688383u
71
− 1.16484u
70
+ ··· − 6675.94u + 1506.11
a
10
=
0.541344u
71
− 0.890028u
70
+ ··· − 4490.24u + 952.255
−0.342960u
71
+ 0.537379u
70
+ ··· + 2175.57u − 399.573
a
12
=
−u
u
a
4
=
−0.0741667u
71
+ 0.182756u
70
+ ··· + 1389.76u − 373.122
0.196267u
71
− 0.493699u
70
+ ··· − 3612.84u + 998.690
a
11
=
0.447909u
71
− 1.21674u
70
+ ··· − 8536.05u + 2445.31
−0.367683u
71
+ 1.02998u
70
+ ··· + 7199.69u − 2091.60
a
5
=
0.621670u
71
− 1.32742u
70
+ ··· − 8696.78u + 2258.81
−0.208971u
71
+ 0.514036u
70
+ ··· + 3370.06u − 922.984
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.552929u
71
− 1.11719u
70
+ ··· − 7329.04u + 1860.11
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
72
− 19u
71
+ ··· + 178u + 13
c
2
, c
7
, c
8
c
12
u
72
− u
71
+ ··· − 10866u + 3667
c
3
(u
2
− u + 1)
36
c
4
, c
5
, c
10
(u
18
+ u
17
+ ··· − u − 1)
4
c
6
, c
9
(u
18
− 3u
17
+ ··· − 3u + 3)
4
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
72
+ 11y
71
+ ··· − 11560y + 169
c
2
, c
7
, c
8
c
12
y
72
− 57y
71
+ ··· − 103020588y + 13446889
c
3
(y
2
+ y + 1)
36
c
4
, c
5
, c
10
(y
18
− 15y
17
+ ··· − 7y + 1)
4
c
6
, c
9
(y
18
+ 13y
17
+ ··· − 75y + 9)
4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.017220 + 0.027464I
a = 2.13206 − 0.52858I
b = −1.66385 − 0.33543I
2.50861 + 0.14420I 0
u = 1.017220 − 0.027464I
a = 2.13206 + 0.52858I
b = −1.66385 + 0.33543I
2.50861 − 0.14420I 0
u = 0.693662 + 0.751370I
a = 0.303778 + 0.388548I
b = 0.650141 − 0.173344I
−0.21034 − 1.47092I 0
u = 0.693662 − 0.751370I
a = 0.303778 − 0.388548I
b = 0.650141 + 0.173344I
−0.21034 + 1.47092I 0
u = 1.033500 + 0.072324I
a = 0.293773 − 0.211699I
b = 0.129307 − 0.655859I
1.58118 + 0.45801I 0
u = 1.033500 − 0.072324I
a = 0.293773 + 0.211699I
b = 0.129307 + 0.655859I
1.58118 − 0.45801I 0
u = 0.031660 + 0.944468I
a = 0.220232 − 0.330295I
b = −1.118420 − 0.229212I
1.58118 + 3.60176I 0. − 7.68480I
u = 0.031660 − 0.944468I
a = 0.220232 + 0.330295I
b = −1.118420 + 0.229212I
1.58118 − 3.60176I 0. + 7.68480I
u = −1.066340 + 0.019440I
a = −2.19706 + 0.41240I
b = 1.71352 + 0.39093I
6.82360 − 3.68439I 0
u = −1.066340 − 0.019440I
a = −2.19706 − 0.41240I
b = 1.71352 − 0.39093I
6.82360 + 3.68439I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.913482 + 0.085334I
a = −2.06764 − 0.75190I
b = 1.61282 − 0.23864I
6.06357 − 3.81683I 11.23943 + 0.I
u = −0.913482 − 0.085334I
a = −2.06764 + 0.75190I
b = 1.61282 + 0.23864I
6.06357 + 3.81683I 11.23943 + 0.I
u = −0.846987 + 0.697488I
a = −0.333673 + 0.483654I
b = −0.519849 − 0.164047I
−3.45249 − 2.84406I 0
u = −0.846987 − 0.697488I
a = −0.333673 − 0.483654I
b = −0.519849 + 0.164047I
−3.45249 + 2.84406I 0
u = −0.289505 + 1.062300I
a = −0.594187 − 0.376086I
b = 1.233660 − 0.268864I
7.08808 − 5.25662I 0
u = −0.289505 − 1.062300I
a = −0.594187 + 0.376086I
b = 1.233660 + 0.268864I
7.08808 + 5.25662I 0
u = −1.118420 + 0.229212I
a = −0.308403 + 0.113424I
b = 0.031660 − 0.944468I
1.58118 − 3.60176I 0
u = −1.118420 − 0.229212I
a = −0.308403 − 0.113424I
b = 0.031660 + 0.944468I
1.58118 + 3.60176I 0
u = 0.955436 + 0.668372I
a = 0.353081 + 0.532513I
b = 0.424031 − 0.169720I
1.04456 + 7.10521I 0
u = 0.955436 − 0.668372I
a = 0.353081 − 0.532513I
b = 0.424031 + 0.169720I
1.04456 − 7.10521I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.098140 + 0.393816I
a = −0.078496 + 0.425133I
b = −0.074344 − 1.268570I
−0.21034 − 2.58885I 0
u = −1.098140 − 0.393816I
a = −0.078496 − 0.425133I
b = −0.074344 + 1.268570I
−0.21034 + 2.58885I 0
u = −1.187800 + 0.128492I
a = −0.522626 + 0.383206I
b = 0.028590 + 0.292450I
7.08808 − 1.19685I 0
u = −1.187800 − 0.128492I
a = −0.522626 − 0.383206I
b = 0.028590 − 0.292450I
7.08808 + 1.19685I 0
u = 1.137940 + 0.411255I
a = 0.137911 + 0.514671I
b = 0.007450 − 1.328250I
−3.45249 + 6.90382I 0
u = 1.137940 − 0.411255I
a = 0.137911 − 0.514671I
b = 0.007450 + 1.328250I
−3.45249 − 6.90382I 0
u = −1.224820 + 0.174181I
a = −1.71777 − 0.24428I
b = 1.41620 − 0.50567I
5.55672 − 2.02988I 0
u = −1.224820 − 0.174181I
a = −1.71777 + 0.24428I
b = 1.41620 + 0.50567I
5.55672 + 2.02988I 0
u = −1.166860 + 0.418865I
a = −0.188865 + 0.570472I
b = 0.045286 − 1.364190I
1.04456 − 11.16500I 0
u = −1.166860 − 0.418865I
a = −0.188865 − 0.570472I
b = 0.045286 + 1.364190I
1.04456 + 11.16500I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.248510 + 0.052716I
a = 1.95056 − 0.08236I
b = −1.58003 − 0.62693I
10.76740 + 2.02988I 0
u = 1.248510 − 0.052716I
a = 1.95056 + 0.08236I
b = −1.58003 + 0.62693I
10.76740 − 2.02988I 0
u = 1.233660 + 0.268864I
a = 0.530370 + 0.307807I
b = −0.289505 − 1.062300I
7.08808 + 5.25662I 0
u = 1.233660 − 0.268864I
a = 0.530370 − 0.307807I
b = −0.289505 + 1.062300I
7.08808 − 5.25662I 0
u = −0.074344 + 1.268570I
a = 0.394783 + 0.040892I
b = −1.098140 − 0.393816I
−0.21034 + 2.58885I 0
u = −0.074344 − 1.268570I
a = 0.394783 − 0.040892I
b = −1.098140 + 0.393816I
−0.21034 − 2.58885I 0
u = 0.650141 + 0.173344I
a = −0.307229 − 0.683719I
b = 0.693662 − 0.751370I
−0.21034 + 1.47092I 7.51114 − 3.72400I
u = 0.650141 − 0.173344I
a = −0.307229 + 0.683719I
b = 0.693662 + 0.751370I
−0.21034 − 1.47092I 7.51114 + 3.72400I
u = 0.007450 + 1.328250I
a = −0.483846 + 0.038488I
b = 1.137940 − 0.411255I
−3.45249 − 6.90382I 0
u = 0.007450 − 1.328250I
a = −0.483846 − 0.038488I
b = 1.137940 + 0.411255I
−3.45249 + 6.90382I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.129307 + 0.655859I
a = 0.382215 − 0.410916I
b = 1.033500 − 0.072324I
1.58118 − 0.45801I 7.80878 − 0.75660I
u = 0.129307 − 0.655859I
a = 0.382215 + 0.410916I
b = 1.033500 + 0.072324I
1.58118 + 0.45801I 7.80878 + 0.75660I
u = 0.045286 + 1.364190I
a = 0.544891 + 0.031701I
b = −1.166860 − 0.418865I
1.04456 + 11.16500I 0
u = 0.045286 − 1.364190I
a = 0.544891 − 0.031701I
b = −1.166860 + 0.418865I
1.04456 − 11.16500I 0
u = 1.370090 + 0.136727I
a = 1.61237 + 0.18879I
b = −1.31349 − 0.85071I
2.50861 + 3.91557I 0
u = 1.370090 − 0.136727I
a = 1.61237 − 0.18879I
b = −1.31349 + 0.85071I
2.50861 − 3.91557I 0
u = −1.372800 + 0.107076I
a = −1.71771 + 0.21747I
b = 1.40460 − 0.87274I
6.82360 − 7.74416I 0
u = −1.372800 − 0.107076I
a = −1.71771 − 0.21747I
b = 1.40460 + 0.87274I
6.82360 + 7.74416I 0
u = −1.377880 + 0.171851I
a = −1.44111 + 0.19069I
b = 1.16098 − 0.85415I
6.06357 − 0.24294I 0
u = −1.377880 − 0.171851I
a = −1.44111 − 0.19069I
b = 1.16098 + 0.85415I
6.06357 + 0.24294I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16098 + 0.85415I
a = 1.301240 − 0.517704I
b = −1.377880 − 0.171851I
6.06357 + 0.24294I 0
u = 1.16098 − 0.85415I
a = 1.301240 + 0.517704I
b = −1.377880 + 0.171851I
6.06357 − 0.24294I 0
u = −0.519849 + 0.164047I
a = 0.450371 − 1.093590I
b = −0.846987 − 0.697488I
−3.45249 + 2.84406I 4.47320 − 0.13726I
u = −0.519849 − 0.164047I
a = 0.450371 + 1.093590I
b = −0.846987 + 0.697488I
−3.45249 − 2.84406I 4.47320 + 0.13726I
u = 1.41620 + 0.50567I
a = 1.34430 − 0.47999I
b = −1.224820 − 0.174181I
5.55672 + 2.02988I 0
u = 1.41620 − 0.50567I
a = 1.34430 + 0.47999I
b = −1.224820 + 0.174181I
5.55672 − 2.02988I 0
u = 0.424031 + 0.169720I
a = −0.64369 − 1.49877I
b = 0.955436 − 0.668372I
1.04456 − 7.10521I 8.98695 + 2.40068I
u = 0.424031 − 0.169720I
a = −0.64369 + 1.49877I
b = 0.955436 + 0.668372I
1.04456 + 7.10521I 8.98695 − 2.40068I
u = −1.31349 + 0.85071I
a = −1.33743 − 0.50145I
b = 1.370090 − 0.136727I
2.50861 − 3.91557I 0
u = −1.31349 − 0.85071I
a = −1.33743 + 0.50145I
b = 1.370090 + 0.136727I
2.50861 + 3.91557I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61282 + 0.23864I
a = 1.139110 − 0.485015I
b = −0.913482 − 0.085334I
6.06357 + 3.81683I 0
u = 1.61282 − 0.23864I
a = 1.139110 + 0.485015I
b = −0.913482 + 0.085334I
6.06357 − 3.81683I 0
u = 1.40460 + 0.87274I
a = 1.35323 − 0.49733I
b = −1.372800 − 0.107076I
6.82360 + 7.74416I 0
u = 1.40460 − 0.87274I
a = 1.35323 + 0.49733I
b = −1.372800 + 0.107076I
6.82360 − 7.74416I 0
u = −1.66385 + 0.33543I
a = −1.205150 − 0.530920I
b = 1.017220 − 0.027464I
2.50861 − 0.14420I 0
u = −1.66385 − 0.33543I
a = −1.205150 + 0.530920I
b = 1.017220 + 0.027464I
2.50861 + 0.14420I 0
u = −1.58003 + 0.62693I
a = −1.33401 − 0.52932I
b = 1.248510 − 0.052716I
10.76740 − 2.02988I 0
u = −1.58003 − 0.62693I
a = −1.33401 + 0.52932I
b = 1.248510 + 0.052716I
10.76740 + 2.02988I 0
u = 0.028590 + 0.292450I
a = −1.57989 − 2.10875I
b = −1.187800 + 0.128492I
7.08808 − 1.19685I 13.05526 + 0.16546I
u = 0.028590 − 0.292450I
a = −1.57989 + 2.10875I
b = −1.187800 − 0.128492I
7.08808 + 1.19685I 13.05526 − 0.16546I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.71352 + 0.39093I
a = 1.234100 − 0.563121I
b = −1.066340 + 0.019440I
6.82360 − 3.68439I 0
u = 1.71352 − 0.39093I
a = 1.234100 + 0.563121I
b = −1.066340 − 0.019440I
6.82360 + 3.68439I 0
19
III. I
u
3
= hb + u, 2u
19
+ 2u
18
+ · · · + a − 4, u
20
+ u
19
+ · · · − 4u − 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
3
=
−2u
19
− 2u
18
+ ··· − 3u + 4
−u
a
9
=
1
−u
2
a
7
=
u
18
+ u
17
+ ··· + 4u + 3
u
2
a
2
=
−u
19
− u
18
+ ··· − 23u
2
+ 4
u
3
− u
a
6
=
u
4
− 3u
2
+ 2
u
18
+ u
17
+ ··· + 4u + 1
a
10
=
u
8
− 5u
6
+ 9u
4
− 6u
2
+ 1
−u
18
− u
17
+ ··· − 8u − 2
a
12
=
−u
u
a
4
=
−u
19
− u
18
+ ··· − u + 4
−u
19
− u
18
+ ··· − 4u
2
− 3u
a
11
=
u
19
+ u
18
+ ··· − 2u − 4
u
5
− 2u
3
+ 2u
a
5
=
−u
18
− u
17
+ ··· − 4u + 4
2u
18
+ 2u
17
+ ··· + 8u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
19
−7u
18
+ 3u
17
+ 65u
16
+ 20u
15
−268u
14
−151u
13
+ 623u
12
+
438u
11
− 868u
10
− 705u
9
+ 708u
8
+ 674u
7
− 305u
6
− 385u
5
+ 57u
4
+ 140u
3
− 34u − 7
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
20
+ u
19
+ ··· − 2u + 1
c
2
, c
8
u
20
+ u
19
+ ··· − 4u − 1
c
3
u
20
+ 2u
19
+ ··· − u + 1
c
4
, c
5
u
20
− u
19
+ ··· + u − 1
c
6
u
20
+ 3u
19
+ ··· + 3u + 1
c
7
, c
12
u
20
− u
19
+ ··· + 4u − 1
c
9
u
20
− 3u
19
+ ··· − 3u + 1
c
10
u
20
+ u
19
+ ··· − u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
20
+ y
19
+ ··· − 6y + 1
c
2
, c
7
, c
8
c
12
y
20
− 21y
19
+ ··· − 20y + 1
c
3
y
20
− 6y
19
+ ··· + y + 1
c
4
, c
5
, c
10
y
20
− 19y
19
+ ··· + 13y + 1
c
6
, c
9
y
20
+ 9y
19
+ ··· + 7y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.668831 + 0.463717I
a = 0.572743 + 0.372465I
b = 0.668831 − 0.463717I
0.99019 − 8.34686I 8.11381 + 8.96345I
u = −0.668831 − 0.463717I
a = 0.572743 − 0.372465I
b = 0.668831 + 0.463717I
0.99019 + 8.34686I 8.11381 − 8.96345I
u = 1.258910 + 0.181820I
a = 1.99407 − 0.63175I
b = −1.258910 − 0.181820I
9.55967 + 0.46214I 14.09005 − 0.25844I
u = 1.258910 − 0.181820I
a = 1.99407 + 0.63175I
b = −1.258910 + 0.181820I
9.55967 − 0.46214I 14.09005 + 0.25844I
u = 0.725943
a = −2.18632
b = −0.725943
6.91929 −11.6540
u = −1.236350 + 0.313248I
a = −1.46303 − 0.54202I
b = 1.236350 − 0.313248I
4.72409 − 1.84698I 6.40432 + 0.80024I
u = −1.236350 − 0.313248I
a = −1.46303 + 0.54202I
b = 1.236350 + 0.313248I
4.72409 + 1.84698I 6.40432 − 0.80024I
u = 1.204020 + 0.427966I
a = 1.139070 − 0.304352I
b = −1.204020 − 0.427966I
8.43027 + 3.23489I 15.8353 − 3.8708I
u = 1.204020 − 0.427966I
a = 1.139070 + 0.304352I
b = −1.204020 + 0.427966I
8.43027 − 3.23489I 15.8353 + 3.8708I
u = 0.578178 + 0.423999I
a = −0.840664 + 0.576748I
b = −0.578178 − 0.423999I
−3.69104 + 4.05229I 2.53314 − 6.60174I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.578178 − 0.423999I
a = −0.840664 − 0.576748I
b = −0.578178 + 0.423999I
−3.69104 − 4.05229I 2.53314 + 6.60174I
u = −1.38058 + 0.41854I
a = −1.51557 − 0.07010I
b = 1.38058 − 0.41854I
6.22565 + 1.09815I 12.16495 − 2.52978I
u = −1.38058 − 0.41854I
a = −1.51557 + 0.07010I
b = 1.38058 + 0.41854I
6.22565 − 1.09815I 12.16495 + 2.52978I
u = 1.39961 + 0.36809I
a = 1.61183 − 0.11089I
b = −1.39961 − 0.36809I
2.44488 + 2.56909I 7.07712 − 1.16744I
u = 1.39961 − 0.36809I
a = 1.61183 + 0.11089I
b = −1.39961 + 0.36809I
2.44488 − 2.56909I 7.07712 + 1.16744I
u = −0.421666 + 0.351150I
a = 1.27891 + 1.05193I
b = 0.421666 − 0.351150I
−0.757748 + 0.237341I 4.04858 + 0.92208I
u = −0.421666 − 0.351150I
a = 1.27891 − 1.05193I
b = 0.421666 + 0.351150I
−0.757748 − 0.237341I 4.04858 − 0.92208I
u = −1.42948 + 0.32689I
a = −1.70399 − 0.10936I
b = 1.42948 − 0.32689I
6.63079 − 6.29581I 12.13979 + 4.17305I
u = −1.42948 − 0.32689I
a = −1.70399 + 0.10936I
b = 1.42948 + 0.32689I
6.63079 + 6.29581I 12.13979 − 4.17305I
u = −0.333578
a = 3.03956
b = 0.333578
−0.365832 0.839520
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
20
+ u
19
+ ··· − 2u + 1)(u
40
+ u
39
+ ··· − 14u + 1)
· (u
72
− 19u
71
+ ··· + 178u + 13)
c
2
, c
8
(u
20
+ u
19
+ ··· − 4u − 1)(u
40
+ u
39
+ ··· − 2u + 1)
· (u
72
− u
71
+ ··· − 10866u + 3667)
c
3
((u
2
− u + 1)
36
)(u
20
+ 2u
19
+ ··· − u + 1)
· (u
40
+ 35u
39
+ ··· + 4063232u + 262144)
c
4
, c
5
((u
18
+ u
17
+ ··· − u − 1)
4
)(u
20
− u
19
+ ··· + u − 1)
· (u
40
− 6u
39
+ ··· + 14u + 4)
c
6
((u
18
− 3u
17
+ ··· − 3u + 3)
4
)(u
20
+ 3u
19
+ ··· + 3u + 1)
· (u
40
+ 18u
39
+ ··· − 286u − 52)
c
7
, c
12
(u
20
− u
19
+ ··· + 4u − 1)(u
40
+ u
39
+ ··· − 2u + 1)
· (u
72
− u
71
+ ··· − 10866u + 3667)
c
9
((u
18
− 3u
17
+ ··· − 3u + 3)
4
)(u
20
− 3u
19
+ ··· − 3u + 1)
· (u
40
+ 18u
39
+ ··· − 286u − 52)
c
10
((u
18
+ u
17
+ ··· − u − 1)
4
)(u
20
+ u
19
+ ··· − u − 1)
· (u
40
− 6u
39
+ ··· + 14u + 4)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
20
+ y
19
+ ··· − 6y + 1)(y
40
− 17y
39
+ ··· − 104y + 1)
· (y
72
+ 11y
71
+ ··· − 11560y + 169)
c
2
, c
7
, c
8
c
12
(y
20
− 21y
19
+ ··· − 20y + 1)(y
40
− 27y
39
+ ··· − 6y + 1)
· (y
72
− 57y
71
+ ··· − 103020588y + 13446889)
c
3
((y
2
+ y + 1)
36
)(y
20
− 6y
19
+ ··· + y + 1)
· (y
40
− 5y
39
+ ··· − 738734374912y + 68719476736)
c
4
, c
5
, c
10
((y
18
− 15y
17
+ ··· − 7y + 1)
4
)(y
20
− 19y
19
+ ··· + 13y + 1)
· (y
40
− 34y
39
+ ··· − 76y + 16)
c
6
, c
9
((y
18
+ 13y
17
+ ··· − 75y + 9)
4
)(y
20
+ 9y
19
+ ··· + 7y + 1)
· (y
40
+ 22y
39
+ ··· − 227084y + 2704)
26
