11a
353
(K11a
353
)
A knot diagram
1
Linearized knot diagam
8 6 9 1 10 2 11 3 4 7 5
Solving Sequence
5,11 1,8
2 4 7 10 6 9 3
c
11
c
1
c
4
c
7
c
10
c
5
c
9
c
3
c
2
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h69111097161u
27
+ 244636080010u
26
+ ··· + 952258493696b + 221044616913,
1298199346297u
27
+ 505498875842u
26
+ ··· + 1904516987392a − 5516498326615,
u
28
+ u
27
+ ··· − 2u − 1i
I
u
2
= h8.06418 × 10
31
u
39
− 4.28071 × 10
32
u
38
+ ··· + 1.02068 × 10
33
b − 2.55200 × 10
33
,
1.25131 × 10
34
u
39
− 4.24308 × 10
34
u
38
+ ··· + 1.32688 × 10
34
a − 8.48739 × 10
34
, u
40
− 3u
39
+ ··· − 16u + 13i
I
u
3
= h3au + 26b + 15a + 6u + 4, 3a
2
+ 3au − 3a − 4u + 6, u
2
+ 1i
I
u
4
= hb − 1, 4a
2
− 4a − 1, u + 1i
I
u
5
= hb + 1, 2a + 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 75 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
= h6.91 × 10
10
u
27
+ 2.45 × 10
11
u
26
+ · · · + 9.52 × 10
11
b + 2.21 × 10
11
, 1.30 ×
10
12
u
27
+5.05×10
11
u
26
+· · ·+1.90×10
12
a−5.52×10
12
, u
28
+u
27
+· · ·−2u−1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
−0.681642u
27
− 0.265421u
26
+ ··· − 8.40509u + 2.89653
−0.0725760u
27
− 0.256901u
26
+ ··· + 1.97317u − 0.232127
a
2
=
1.00409u
27
+ 0.785997u
26
+ ··· + 7.89767u − 2.87424
−0.231896u
27
− 0.203248u
26
+ ··· − 1.15597u + 0.754218
a
4
=
u
u
3
+ u
a
7
=
−0.754218u
27
− 0.522322u
26
+ ··· − 6.43192u + 2.66441
−0.0725760u
27
− 0.256901u
26
+ ··· + 1.97317u − 0.232127
a
10
=
−0.648348u
27
− 0.423262u
26
+ ··· − 4.84322u + 3.11906
0.482066u
27
+ 0.675821u
26
+ ··· + 0.0882181u − 0.722887
a
6
=
−0.972307u
27
− 0.800001u
26
+ ··· − 7.29799u + 3.66849
−0.0439280u
27
− 0.179789u
26
+ ··· + 2.26359u − 0.464023
a
9
=
−0.792144u
27
− 0.721116u
26
+ ··· − 3.87937u + 3.04143
0.393556u
27
+ 0.597667u
26
+ ··· + 0.600150u − 0.954582
a
3
=
1.17639u
27
+ 0.886244u
26
+ ··· + 9.62155u − 3.84654
−0.367757u
27
− 0.177799u
26
+ ··· − 1.70785u + 0.710290
a
3
=
1.17639u
27
+ 0.886244u
26
+ ··· + 9.62155u − 3.84654
−0.367757u
27
− 0.177799u
26
+ ··· − 1.70785u + 0.710290
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
35588886371
59516155856
u
27
−
299228759547
238064623424
u
26
+ ··· −
368522604615
59516155856
u −
3433039175621
238064623424
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
8(8u
28
− 4u
27
+ ··· + 13u − 1)
c
2
, c
4
, c
6
c
11
u
28
− u
27
+ ··· + 2u − 1
c
3
, c
8
, c
9
u
28
+ 3u
27
+ ··· + 18u
2
− 8
c
7
, c
10
u
28
+ 2u
27
+ ··· + 7u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
64(64y
28
− 752y
27
+ ··· − 97y + 1)
c
2
, c
4
, c
6
c
11
y
28
+ 9y
27
+ ··· − 22y + 1
c
3
, c
8
, c
9
y
28
− 25y
27
+ ··· − 288y + 64
c
7
, c
10
y
28
− 12y
27
+ ··· − 2657y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.296911 + 0.949247I
a = −0.96640 + 1.46558I
b = 0.704207 − 1.129850I
2.99004 + 0.45030I −10.69982 + 4.65118I
u = 0.296911 − 0.949247I
a = −0.96640 − 1.46558I
b = 0.704207 + 1.129850I
2.99004 − 0.45030I −10.69982 − 4.65118I
u = −0.565343 + 0.834957I
a = 0.34126 − 2.13613I
b = −0.958692 + 0.629682I
−7.22525 + 3.79352I −14.6297 − 6.8044I
u = −0.565343 − 0.834957I
a = 0.34126 + 2.13613I
b = −0.958692 − 0.629682I
−7.22525 − 3.79352I −14.6297 + 6.8044I
u = 0.569801 + 0.943146I
a = 0.319047 + 0.157096I
b = −1.44195 + 0.24008I
−6.49386 − 5.21032I −14.7449 + 6.2628I
u = 0.569801 − 0.943146I
a = 0.319047 − 0.157096I
b = −1.44195 − 0.24008I
−6.49386 + 5.21032I −14.7449 − 6.2628I
u = 1.084120 + 0.332892I
a = −0.376217 + 0.052666I
b = −1.023200 + 0.176678I
−3.53318 + 0.46316I −13.8889 − 10.1726I
u = 1.084120 − 0.332892I
a = −0.376217 − 0.052666I
b = −1.023200 − 0.176678I
−3.53318 − 0.46316I −13.8889 + 10.1726I
u = −0.413566 + 1.107250I
a = 0.70776 + 1.31080I
b = −0.399769 − 1.157150I
5.21251 + 5.27743I −6.65035 − 6.45030I
u = −0.413566 − 1.107250I
a = 0.70776 − 1.31080I
b = −0.399769 + 1.157150I
5.21251 − 5.27743I −6.65035 + 6.45030I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.487268 + 1.106840I
a = −0.24485 − 1.78265I
b = 1.182220 + 0.759370I
1.23650 − 6.41971I −10.13891 + 5.40596I
u = 0.487268 − 1.106840I
a = −0.24485 + 1.78265I
b = 1.182220 − 0.759370I
1.23650 + 6.41971I −10.13891 − 5.40596I
u = 0.125014 + 0.759051I
a = −0.26909 − 1.95210I
b = 0.364417 + 1.088690I
2.21675 − 2.65344I −14.3737 + 6.7757I
u = 0.125014 − 0.759051I
a = −0.26909 + 1.95210I
b = 0.364417 − 1.088690I
2.21675 + 2.65344I −14.3737 − 6.7757I
u = −0.443360 + 0.614385I
a = −0.110599 + 0.746253I
b = 1.324740 + 0.017239I
−2.17233 + 1.46597I −11.44165 − 4.82002I
u = −0.443360 − 0.614385I
a = −0.110599 − 0.746253I
b = 1.324740 − 0.017239I
−2.17233 − 1.46597I −11.44165 + 4.82002I
u = −0.739750
a = 1.24980
b = −0.228388
−6.49503 −15.0760
u = 0.555730 + 1.199460I
a = −0.619404 + 1.141470I
b = 0.252799 − 1.095220I
−0.48195 − 10.01540I −10.05091 + 6.46543I
u = 0.555730 − 1.199460I
a = −0.619404 − 1.141470I
b = 0.252799 + 1.095220I
−0.48195 + 10.01540I −10.05091 − 6.46543I
u = −1.33082
a = 0.528817
b = 0.666845
−6.93788 −10.0440
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.576628 + 1.229500I
a = 0.07988 − 1.67005I
b = −1.25864 + 0.68359I
2.41139 + 11.80860I −9.11501 − 8.63273I
u = −0.576628 − 1.229500I
a = 0.07988 + 1.67005I
b = −1.25864 − 0.68359I
2.41139 − 11.80860I −9.11501 + 8.63273I
u = −1.27260 + 0.62076I
a = 0.246074 − 0.052570I
b = 1.061760 + 0.348290I
−8.94292 − 2.37104I −16.4575 + 4.6309I
u = −1.27260 − 0.62076I
a = 0.246074 + 0.052570I
b = 1.061760 − 0.348290I
−8.94292 + 2.37104I −16.4575 − 4.6309I
u = 0.67592 + 1.27886I
a = 0.05910 − 1.64694I
b = 1.27791 + 0.62904I
−3.7021 − 16.1510I −12.8937 + 8.8766I
u = 0.67592 − 1.27886I
a = 0.05910 + 1.64694I
b = 1.27791 − 0.62904I
−3.7021 + 16.1510I −12.8937 − 8.8766I
u = 0.274821
a = −0.815209
b = 0.252280
−0.508062 −19.5920
u = −0.250785
a = 5.20342
b = −0.862317
−6.66293 −13.6170
7
II. I
u
2
=
h8.06×10
31
u
39
−4.28×10
32
u
38
+· · ·+1.02×10
33
b−2.55×10
33
, 1.25×10
34
u
39
−
4.24 × 10
34
u
38
+ · · · + 1.33 × 10
34
a − 8.49 × 10
34
, u
40
− 3u
39
+ · · · − 16u + 13i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
−0.943051u
39
+ 3.19779u
38
+ ··· − 19.6208u + 6.39651
−0.0790083u
39
+ 0.419400u
38
+ ··· − 0.209068u + 2.50031
a
2
=
11.7005u
39
− 33.4368u
38
+ ··· + 142.585u + 2.45039
0.555148u
39
− 2.34820u
38
+ ··· + 18.1223u − 8.20329
a
4
=
u
u
3
+ u
a
7
=
−1.02206u
39
+ 3.61719u
38
+ ··· − 19.8299u + 8.89682
−0.0790083u
39
+ 0.419400u
38
+ ··· − 0.209068u + 2.50031
a
10
=
−0.482674u
39
+ 2.13009u
38
+ ··· − 12.5233u + 7.32471
−0.0389140u
39
+ 0.110695u
38
+ ··· − 1.34364u − 0.742144
a
6
=
−0.984515u
39
+ 15.5078u
38
+ ··· − 183.199u + 159.124
0.692717u
39
− 1.33169u
38
+ ··· + 1.41679u + 8.33951
a
9
=
−0.307007u
39
+ 1.68682u
38
+ ··· − 11.7608u + 8.03870
0.00580630u
39
− 0.0556998u
38
+ ··· − 1.52504u − 1.11673
a
3
=
−1.00713u
39
+ 3.70631u
38
+ ··· − 27.7037u + 12.4566
0.0249322u
39
+ 0.0795189u
38
+ ··· − 1.22395u + 1.61735
a
3
=
−1.00713u
39
+ 3.70631u
38
+ ··· − 27.7037u + 12.4566
0.0249322u
39
+ 0.0795189u
38
+ ··· − 1.22395u + 1.61735
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.612855u
39
+ 1.79290u
38
+ ··· − 0.230525u − 14.6778
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
40
− 21u
39
+ ··· + 1158u + 199
c
2
, c
4
, c
6
c
11
u
40
+ 3u
39
+ ··· + 16u + 13
c
3
, c
8
, c
9
(u
20
− u
19
+ ··· + 2u − 1)
2
c
7
, c
10
(u
20
+ u
19
+ ··· − 2u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
40
+ 11y
39
+ ··· + 1102756y + 39601
c
2
, c
4
, c
6
c
11
y
40
+ 23y
39
+ ··· − 724y + 169
c
3
, c
8
, c
9
(y
20
− 19y
19
+ ··· − 2y + 1)
2
c
7
, c
10
(y
20
− 11y
19
+ ··· − 2y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.067663 + 1.006840I
a = −8.85268 + 7.75794I
b = −1.06181
−3.24334 −17.8998 + 0.I
u = 0.067663 − 1.006840I
a = −8.85268 − 7.75794I
b = −1.06181
−3.24334 −17.8998 + 0.I
u = −0.966472 + 0.204987I
a = −0.256846 + 0.129583I
b = −1.174860 − 0.481002I
−0.72067 − 6.27316I −12.10015 + 6.54347I
u = −0.966472 − 0.204987I
a = −0.256846 − 0.129583I
b = −1.174860 + 0.481002I
−0.72067 + 6.27316I −12.10015 − 6.54347I
u = −0.402724 + 0.973230I
a = −0.15139 + 1.58308I
b = 1.170970 − 0.421653I
−1.14846 + 2.14390I −13.45592 − 0.24308I
u = −0.402724 − 0.973230I
a = −0.15139 − 1.58308I
b = 1.170970 + 0.421653I
−1.14846 − 2.14390I −13.45592 + 0.24308I
u = 0.169382 + 1.042150I
a = −1.25981 − 2.02462I
b = 0.733657
2.31303 −14.9388 + 0.I
u = 0.169382 − 1.042150I
a = −1.25981 + 2.02462I
b = 0.733657
2.31303 −14.9388 + 0.I
u = −0.531514 + 0.736461I
a = 0.267570 + 0.697869I
b = −1.224930 − 0.393654I
−7.52808 + 0.63661I −16.9604 + 0.1699I
u = −0.531514 − 0.736461I
a = 0.267570 − 0.697869I
b = −1.224930 + 0.393654I
−7.52808 − 0.63661I −16.9604 − 0.1699I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.880675 + 0.188465I
a = 0.647845 − 0.561612I
b = 0.113113 + 0.821783I
−3.49387 + 4.79919I −12.69810 − 3.09464I
u = 0.880675 − 0.188465I
a = 0.647845 + 0.561612I
b = 0.113113 − 0.821783I
−3.49387 − 4.79919I −12.69810 + 3.09464I
u = 0.222487 + 1.085200I
a = 0.087467 − 1.071580I
b = −0.092790 + 0.716473I
2.37392 − 1.80448I −8.82463 + 3.70058I
u = 0.222487 − 1.085200I
a = 0.087467 + 1.071580I
b = −0.092790 − 0.716473I
2.37392 + 1.80448I −8.82463 − 3.70058I
u = 0.792130 + 0.867615I
a = 0.866838 − 0.759884I
b = 0.912041 + 0.514968I
0.30488 − 4.84109I −11.63163 + 6.37981I
u = 0.792130 − 0.867615I
a = 0.866838 + 0.759884I
b = 0.912041 − 0.514968I
0.30488 + 4.84109I −11.63163 − 6.37981I
u = 0.575083 + 0.580865I
a = −0.24945 + 2.07330I
b = −1.224930 − 0.393654I
−7.52808 + 0.63661I −16.9604 + 0.1699I
u = 0.575083 − 0.580865I
a = −0.24945 − 2.07330I
b = −1.224930 + 0.393654I
−7.52808 − 0.63661I −16.9604 − 0.1699I
u = −0.536847 + 1.066780I
a = −0.700413 − 1.158910I
b = −0.774874 + 0.460321I
4.54605 + 1.94645I −5.05320 − 4.81876I
u = −0.536847 − 1.066780I
a = −0.700413 + 1.158910I
b = −0.774874 − 0.460321I
4.54605 − 1.94645I −5.05320 + 4.81876I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.164960 + 0.329003I
a = 0.277968 + 0.291634I
b = 1.205800 − 0.505812I
−6.73027 + 9.64430I −15.6547 − 6.2054I
u = 1.164960 − 0.329003I
a = 0.277968 − 0.291634I
b = 1.205800 + 0.505812I
−6.73027 − 9.64430I −15.6547 + 6.2054I
u = 0.541181 + 1.104510I
a = −0.212099 − 0.073365I
b = 0.529602 − 0.535861I
1.34713 − 0.58469I −9.20205 + 0.I
u = 0.541181 − 1.104510I
a = −0.212099 + 0.073365I
b = 0.529602 + 0.535861I
1.34713 + 0.58469I −9.20205 + 0.I
u = −0.539846 + 1.156750I
a = −0.162259 − 0.939426I
b = 0.113113 + 0.821783I
−3.49387 + 4.79919I −12.69810 − 3.09464I
u = −0.539846 − 1.156750I
a = −0.162259 + 0.939426I
b = 0.113113 − 0.821783I
−3.49387 − 4.79919I −12.69810 + 3.09464I
u = 0.597799 + 1.194490I
a = −0.009099 + 1.334750I
b = −1.174860 − 0.481002I
−0.72067 − 6.27316I −11.00000 + 6.54347I
u = 0.597799 − 1.194490I
a = −0.009099 − 1.334750I
b = −1.174860 + 0.481002I
−0.72067 + 6.27316I −11.00000 − 6.54347I
u = 0.592656 + 0.264629I
a = −0.246458 − 0.190586I
b = 1.170970 − 0.421653I
−1.14846 + 2.14390I −13.45592 − 0.24308I
u = 0.592656 − 0.264629I
a = −0.246458 + 0.190586I
b = 1.170970 + 0.421653I
−1.14846 − 2.14390I −13.45592 + 0.24308I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.265345 + 1.338090I
a = 0.647027 + 0.331729I
b = −0.774874 − 0.460321I
4.54605 − 1.94645I −5.05320 + 4.81876I
u = −0.265345 − 1.338090I
a = 0.647027 − 0.331729I
b = −0.774874 + 0.460321I
4.54605 + 1.94645I −5.05320 − 4.81876I
u = 0.296099 + 1.343350I
a = 0.248195 − 1.097590I
b = 0.529602 + 0.535861I
1.34713 + 0.58469I −11.00000 + 0.I
u = 0.296099 − 1.343350I
a = 0.248195 + 1.097590I
b = 0.529602 − 0.535861I
1.34713 − 0.58469I −11.00000 + 0.I
u = −0.78685 + 1.24207I
a = 0.148743 + 1.262730I
b = 1.205800 − 0.505812I
−6.73027 + 9.64430I 0
u = −0.78685 − 1.24207I
a = 0.148743 − 1.262730I
b = 1.205800 + 0.505812I
−6.73027 − 9.64430I 0
u = 0.08686 + 1.50116I
a = −0.484527 + 0.706500I
b = 0.912041 − 0.514968I
0.30488 + 4.84109I 0
u = 0.08686 − 1.50116I
a = −0.484527 − 0.706500I
b = 0.912041 + 0.514968I
0.30488 − 4.84109I 0
u = −0.457374 + 0.019438I
a = −1.41432 + 0.28953I
b = −0.092790 − 0.716473I
2.37392 + 1.80448I −8.82463 − 3.70058I
u = −0.457374 − 0.019438I
a = −1.41432 − 0.28953I
b = −0.092790 + 0.716473I
2.37392 − 1.80448I −8.82463 + 3.70058I
14
III. I
u
3
= h3au + 26b + 15a + 6u + 4, 3a
2
+ 3au − 3a − 4u + 6, u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
1
=
1
−1
a
8
=
a
−0.115385au − 0.576923a − 0.230769u − 0.153846
a
2
=
−0.769231au + 0.153846a + 0.794872u + 0.307692
0.346154au − 0.269231a − 0.307692u − 0.538462
a
4
=
u
0
a
7
=
−0.115385au + 0.423077a − 0.230769u − 0.153846
−0.115385au − 0.576923a − 0.230769u − 0.153846
a
10
=
−0.346154au + 0.269231a + 0.307692u + 0.538462
−0.115385au − 0.576923a − 0.230769u + 0.846154
a
6
=
−0.269231au − 0.346154a − 0.538462u + 0.641026
0.153846au − 0.230769a + 0.307692u − 0.461538
a
9
=
−0.230769au + 0.846154a + 0.538462u − 0.307692
−0.115385au − 0.576923a − 0.230769u + 0.846154
a
3
=
−0.423077au − 0.115385a + 0.153846u − 0.230769
0.576923au − 0.115385a + 0.153846u − 0.230769
a
3
=
−0.423077au − 0.115385a + 0.153846u − 0.230769
0.576923au − 0.115385a + 0.153846u − 0.230769
(ii) Obstruction class = 1
(iii) Cusp Shapes =
6
13
au +
30
13
a +
12
13
u −
96
13
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
9(9u
4
+ 9u
2
− 6u + 1)
c
2
, c
4
, c
6
c
11
(u
2
+ 1)
2
c
3
, c
8
, c
9
u
4
− u
2
+ 1
c
5
9(9u
4
+ 9u
2
+ 6u + 1)
c
7
(u
2
− u + 1)
2
c
10
(u
2
+ u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
81(81y
4
+ 162y
3
+ 99y
2
− 18y + 1)
c
2
, c
4
, c
6
c
11
(y + 1)
4
c
3
, c
8
, c
9
(y
2
− y + 1)
2
c
7
, c
10
(y
2
+ y + 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.788675 + 0.943376I
b = −0.500000 − 0.866025I
3.28987 − 2.02988I −6.00000 + 3.46410I
u = 1.000000I
a = 0.21132 − 1.94338I
b = −0.500000 + 0.866025I
3.28987 + 2.02988I −6.00000 − 3.46410I
u = − 1.000000I
a = 0.788675 − 0.943376I
b = −0.500000 + 0.866025I
3.28987 + 2.02988I −6.00000 − 3.46410I
u = − 1.000000I
a = 0.21132 + 1.94338I
b = −0.500000 − 0.866025I
3.28987 − 2.02988I −6.00000 + 3.46410I
18
IV. I
u
4
= hb − 1, 4a
2
− 4a − 1, u + 1i
(i) Arc colorings
a
5
=
0
−1
a
11
=
1
0
a
1
=
1
1
a
8
=
a
1
a
2
=
0.75
−a + 2
a
4
=
−1
−2
a
7
=
a + 1
1
a
10
=
−a
−1
a
6
=
a +
1
4
a − 1
a
9
=
a − 1
4a − 3
a
3
=
−a +
1
2
−2a + 3
a
3
=
−a +
1
2
−2a + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −20
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
2
− 4u − 1)
c
2
, c
7
, c
11
(u + 1)
2
c
3
, c
8
, c
9
u
2
− 2
c
4
, c
6
, c
10
(u − 1)
2
c
5
4(4u
2
+ 4u − 1)
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
16(16y
2
− 24y + 1)
c
2
, c
4
, c
6
c
7
, c
10
, c
11
(y −1)
2
c
3
, c
8
, c
9
(y −2)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.20711
b = 1.00000
−8.22467 −20.0000
u = −1.00000
a = −0.207107
b = 1.00000
−8.22467 −20.0000
22
V. I
u
5
= hb + 1, 2a + 1, u − 1i
(i) Arc colorings
a
5
=
0
1
a
11
=
1
0
a
1
=
1
1
a
8
=
−0.5
−1
a
2
=
1.25
1.5
a
4
=
1
2
a
7
=
−1.5
−1
a
10
=
−0.5
−1
a
6
=
−0.25
0.5
a
9
=
−0.5
−1
a
3
=
1
2
a
3
=
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7.5
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
2(2u + 1)
c
2
, c
7
, c
11
u − 1
c
3
, c
8
, c
9
u
c
4
, c
6
, c
10
u + 1
c
5
2(2u − 1)
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
4(4y −1)
c
2
, c
4
, c
6
c
7
, c
10
, c
11
y −1
c
3
, c
8
, c
9
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.500000
b = −1.00000
−3.28987 −7.50000
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
576(2u + 1)(4u
2
− 4u − 1)(9u
4
+ 9u
2
− 6u + 1)
· (8u
28
− 4u
27
+ ··· + 13u − 1)(u
40
− 21u
39
+ ··· + 1158u + 199)
c
2
, c
11
(u − 1)(u + 1)
2
(u
2
+ 1)
2
(u
28
− u
27
+ ··· + 2u − 1)
· (u
40
+ 3u
39
+ ··· + 16u + 13)
c
3
, c
8
, c
9
u(u
2
− 2)(u
4
− u
2
+ 1)(u
20
− u
19
+ ··· + 2u − 1)
2
· (u
28
+ 3u
27
+ ··· + 18u
2
− 8)
c
4
, c
6
((u − 1)
2
)(u + 1)(u
2
+ 1)
2
(u
28
− u
27
+ ··· + 2u − 1)
· (u
40
+ 3u
39
+ ··· + 16u + 13)
c
5
576(2u − 1)(4u
2
+ 4u − 1)(9u
4
+ 9u
2
+ 6u + 1)
· (8u
28
− 4u
27
+ ··· + 13u − 1)(u
40
− 21u
39
+ ··· + 1158u + 199)
c
7
(u − 1)(u + 1)
2
(u
2
− u + 1)
2
(u
20
+ u
19
+ ··· − 2u − 1)
2
· (u
28
+ 2u
27
+ ··· + 7u + 8)
c
10
((u − 1)
2
)(u + 1)(u
2
+ u + 1)
2
(u
20
+ u
19
+ ··· − 2u − 1)
2
· (u
28
+ 2u
27
+ ··· + 7u + 8)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
331776(4y −1)(16y
2
− 24y + 1)(81y
4
+ 162y
3
+ ··· − 18y + 1)
· (64y
28
− 752y
27
+ ··· − 97y + 1)
· (y
40
+ 11y
39
+ ··· + 1102756y + 39601)
c
2
, c
4
, c
6
c
11
((y −1)
3
)(y + 1)
4
(y
28
+ 9y
27
+ ··· − 22y + 1)
· (y
40
+ 23y
39
+ ··· − 724y + 169)
c
3
, c
8
, c
9
y(y −2)
2
(y
2
− y + 1)
2
(y
20
− 19y
19
+ ··· − 2y + 1)
2
· (y
28
− 25y
27
+ ··· − 288y + 64)
c
7
, c
10
((y −1)
3
)(y
2
+ y + 1)
2
(y
20
− 11y
19
+ ··· − 2y + 1)
2
· (y
28
− 12y
27
+ ··· − 2657y + 64)
28
