12n
0615
(K12n
0615
)
A knot diagram
1
Linearized knot diagam
3 8 6 10 9 10 1 2 12 6 4 5
Solving Sequence
5,9 6,12
10 7 1 4 3 2 8 11
c
5
c
9
c
6
c
12
c
4
c
3
c
1
c
8
c
11
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 9.22136 × 10
39
u
35
+ 9.61638 × 10
39
u
34
+ ··· + 3.09061 × 10
39
a + 1.18258 × 10
40
, u
36
+ u
35
+ ··· + u + 1i
I
u
2
= hb + u, −1.38841 × 10
20
u
26
+ 1.60384 × 10
20
u
25
+ ··· + 4.99386 × 10
19
a − 6.68150 × 10
19
,
u
27
− u
26
+ ··· − 10u
2
− 1i
I
u
3
= h3.16250 × 10
115
u
39
+ 8.23787 × 10
115
u
38
+ ··· + 1.00780 × 10
119
b + 9.36325 × 10
117
,
− 3.47990 × 10
101
u
39
− 7.64552 × 10
101
u
38
+ ··· + 4.09554 × 10
104
a + 7.59932 × 10
103
,
u
40
+ 3u
39
+ ··· + 2382u + 643i
* 3 irreducible components of dim
C
= 0, with total 103 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, 9.22 × 10
39
u
35
+ 9.62 × 10
39
u
34
+ · · · + 3.09 × 10
39
a + 1.18 ×
10
40
, u
36
+ u
35
+ · · · + u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u
2
a
12
=
−2.98367u
35
− 3.11149u
34
+ ··· − 115.302u − 3.82636
u
a
10
=
−6.16242u
35
− 6.04552u
34
+ ··· − 243.525u − 13.8436
0.211237u
35
+ 0.365136u
34
+ ··· + 4.11149u + 0.127813
a
7
=
−2.38369u
35
− 0.856037u
34
+ ··· − 126.270u + 47.5732
0.148878u
35
+ 0.123183u
34
+ ··· − 0.00667650u − 0.728008
a
1
=
−2.98367u
35
− 3.11149u
34
+ ··· − 114.302u − 3.82636
u
a
4
=
0.582610u
35
+ 0.220715u
34
+ ··· + 37.1948u − 18.3213
−0.0943851u
35
− 0.0352064u
34
+ ··· + 0.227391u + 0.366113
a
3
=
0.433732u
35
+ 0.0975317u
34
+ ··· + 37.2014u − 17.5933
−0.254215u
35
− 0.141930u
34
+ ··· + 0.104208u + 0.391808
a
2
=
1.66616u
35
+ 1.85078u
34
+ ··· + 46.2547u + 8.96445
0.0535815u
35
+ 0.110395u
34
+ ··· − 2.21514u + 0.107894
a
8
=
0.209879u
35
+ 0.404528u
34
+ ··· − 9.69810u + 12.3718
0.254215u
35
+ 0.141930u
34
+ ··· − 0.104208u − 0.391808
a
11
=
−6.31730u
35
− 6.14088u
34
+ ··· − 253.682u − 13.8545
0.228158u
35
+ 0.419587u
34
+ ··· + 4.01612u + 0.187326
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.18996u
35
− 0.638271u
34
+ ··· − 106.713u + 50.2757
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
36
+ 17u
35
+ ··· + 896u + 256
c
2
, c
8
u
36
+ 9u
35
+ ··· + 128u + 16
c
3
u
36
− 19u
35
+ ··· − 6400u + 1024
c
4
u
36
− 16u
34
+ ··· + 115u + 42
c
5
, c
12
u
36
− u
35
+ ··· − u + 1
c
6
, c
10
, c
11
u
36
+ u
35
+ ··· + 2u + 1
c
7
u
36
− 9u
35
+ ··· − 273856u + 43216
c
9
u
36
+ 19u
35
+ ··· + 464u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
+ 5y
35
+ ··· + 303104y + 65536
c
2
, c
8
y
36
+ 17y
35
+ ··· + 896y + 256
c
3
y
36
− 43y
35
+ ··· + 39911424y + 1048576
c
4
y
36
− 32y
35
+ ··· − 6169y + 1764
c
5
, c
12
y
36
+ 21y
35
+ ··· + 103y + 1
c
6
, c
10
, c
11
y
36
− 59y
35
+ ··· − 18y + 1
c
7
y
36
− 7y
35
+ ··· + 320081792y + 1867622656
c
9
y
36
− 3y
35
+ ··· + 15616y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.118220 + 0.978327I
a = 0.739900 + 0.147699I
b = −0.118220 + 0.978327I
−4.88832 − 1.24309I −8.27685 + 1.44633I
u = −0.118220 − 0.978327I
a = 0.739900 − 0.147699I
b = −0.118220 − 0.978327I
−4.88832 + 1.24309I −8.27685 − 1.44633I
u = 0.891670 + 0.405032I
a = −0.663932 − 0.116326I
b = 0.891670 + 0.405032I
0.41304 − 2.17632I −2.21227 + 4.08709I
u = 0.891670 − 0.405032I
a = −0.663932 + 0.116326I
b = 0.891670 − 0.405032I
0.41304 + 2.17632I −2.21227 − 4.08709I
u = −0.265738 + 0.876405I
a = 1.84073 + 0.78645I
b = −0.265738 + 0.876405I
−4.60827 − 1.82178I −6.48879 + 2.84582I
u = −0.265738 − 0.876405I
a = 1.84073 − 0.78645I
b = −0.265738 − 0.876405I
−4.60827 + 1.82178I −6.48879 − 2.84582I
u = 0.531923 + 0.956773I
a = −1.54750 + 0.22966I
b = 0.531923 + 0.956773I
−5.00027 + 7.84421I −4.73170 − 7.47375I
u = 0.531923 − 0.956773I
a = −1.54750 − 0.22966I
b = 0.531923 − 0.956773I
−5.00027 − 7.84421I −4.73170 + 7.47375I
u = 0.507758 + 0.970271I
a = 0.25842 + 1.54816I
b = 0.507758 + 0.970271I
−8.28613 + 2.69300I −5.21869 − 2.66219I
u = 0.507758 − 0.970271I
a = 0.25842 − 1.54816I
b = 0.507758 − 0.970271I
−8.28613 − 2.69300I −5.21869 + 2.66219I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.862089 + 0.681772I
a = 0.623323 − 0.090341I
b = −0.862089 + 0.681772I
1.34149 − 2.31581I −1.56931 + 2.47888I
u = −0.862089 − 0.681772I
a = 0.623323 + 0.090341I
b = −0.862089 − 0.681772I
1.34149 + 2.31581I −1.56931 − 2.47888I
u = 0.149552 + 0.886635I
a = 0.853564 + 0.323444I
b = 0.149552 + 0.886635I
−3.37517 + 6.25769I −4.77547 − 7.56558I
u = 0.149552 − 0.886635I
a = 0.853564 − 0.323444I
b = 0.149552 − 0.886635I
−3.37517 − 6.25769I −4.77547 + 7.56558I
u = −0.037592 + 0.765146I
a = −0.949161 + 0.180834I
b = −0.037592 + 0.765146I
−1.05608 − 1.63487I −2.47499 + 3.77648I
u = −0.037592 − 0.765146I
a = −0.949161 − 0.180834I
b = −0.037592 − 0.765146I
−1.05608 + 1.63487I −2.47499 − 3.77648I
u = −0.714501 + 1.020090I
a = −0.024002 + 1.309480I
b = −0.714501 + 1.020090I
−11.31080 − 8.41184I −6.53000 + 5.72334I
u = −0.714501 − 1.020090I
a = −0.024002 − 1.309480I
b = −0.714501 − 1.020090I
−11.31080 + 8.41184I −6.53000 − 5.72334I
u = 0.642524 + 1.081940I
a = −0.594301 + 0.008681I
b = 0.642524 + 1.081940I
−4.41629 + 1.23501I −10.98929 − 1.86840I
u = 0.642524 − 1.081940I
a = −0.594301 − 0.008681I
b = 0.642524 − 1.081940I
−4.41629 − 1.23501I −10.98929 + 1.86840I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.304510 + 1.244830I
a = −0.611400 + 1.161230I
b = −0.304510 + 1.244830I
−13.70880 + 1.48629I −9.47906 − 0.90947I
u = −0.304510 − 1.244830I
a = −0.611400 − 1.161230I
b = −0.304510 − 1.244830I
−13.70880 − 1.48629I −9.47906 + 0.90947I
u = −0.838328 + 1.021100I
a = 0.574776 − 0.036631I
b = −0.838328 + 1.021100I
−0.10678 − 4.05131I −5.35718 + 2.78187I
u = −0.838328 − 1.021100I
a = 0.574776 + 0.036631I
b = −0.838328 − 1.021100I
−0.10678 + 4.05131I −5.35718 − 2.78187I
u = 0.86929 + 1.12336I
a = −0.552780 − 0.027142I
b = 0.86929 + 1.12336I
−2.47606 + 8.95314I −9.63843 − 6.69810I
u = 0.86929 − 1.12336I
a = −0.552780 + 0.027142I
b = 0.86929 − 1.12336I
−2.47606 − 8.95314I −9.63843 + 6.69810I
u = 0.009985 + 0.390472I
a = −1.158280 − 0.683611I
b = 0.009985 + 0.390472I
−0.143687 − 1.154050I −1.70239 + 6.30124I
u = 0.009985 − 0.390472I
a = −1.158280 + 0.683611I
b = 0.009985 − 0.390472I
−0.143687 + 1.154050I −1.70239 − 6.30124I
u = 0.99600 + 1.37401I
a = −0.905942 + 0.047100I
b = 0.99600 + 1.37401I
−9.4005 + 11.0269I 0
u = 0.99600 − 1.37401I
a = −0.905942 − 0.047100I
b = 0.99600 − 1.37401I
−9.4005 − 11.0269I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.81790 + 1.51742I
a = 0.883941 + 0.187003I
b = −0.81790 + 1.51742I
−14.4218 − 6.9271I 0
u = −0.81790 − 1.51742I
a = 0.883941 − 0.187003I
b = −0.81790 − 1.51742I
−14.4218 + 6.9271I 0
u = −1.12027 + 1.43623I
a = 0.832072 + 0.016628I
b = −1.12027 + 1.43623I
−12.4101 − 16.4883I 0
u = −1.12027 − 1.43623I
a = 0.832072 − 0.016628I
b = −1.12027 − 1.43623I
−12.4101 + 16.4883I 0
u = −0.019556 + 0.157716I
a = −3.59942 − 13.15270I
b = −0.019556 + 0.157716I
5.85065 − 3.09111I 34.3315 − 14.8344I
u = −0.019556 − 0.157716I
a = −3.59942 + 13.15270I
b = −0.019556 − 0.157716I
5.85065 + 3.09111I 34.3315 + 14.8344I
8
II. I
u
2
= hb + u, −1.39 × 10
20
u
26
+ 1.60 × 10
20
u
25
+ · · · + 4.99 × 10
19
a −
6.68 × 10
19
, u
27
− u
26
+ · · · − 10u
2
− 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u
2
a
12
=
2.78024u
26
− 3.21163u
25
+ ··· − 21.1050u + 1.33794
−u
a
10
=
5.30922u
26
− 6.52376u
25
+ ··· − 42.9670u + 0.261911
0.295368u
26
− 0.301221u
25
+ ··· − 1.78024u + 0.431384
a
7
=
−1.33794u
26
− 1.44230u
25
+ ··· − 15.2069u + 22.1050
0.341753u
26
− 0.265611u
25
+ ··· − 0.783163u + 0.688731
a
1
=
2.78024u
26
− 3.21163u
25
+ ··· − 22.1050u + 1.33794
−u
a
4
=
0.431384u
26
− 1.13602u
25
+ ··· − 7.33794u + 8.21976
−0.335900u
26
+ 0.248427u
25
+ ··· + 0.351779u + 0.0159013
a
3
=
0.0896309u
26
− 0.870405u
25
+ ··· − 6.55478u + 7.53103
−0.418450u
26
+ 0.307498u
25
+ ··· + 0.693532u + 0.0920432
a
2
=
−1.05574u
26
+ 1.20442u
25
+ ··· + 7.08036u + 1.76225
−0.0188017u
26
− 0.271955u
25
+ ··· − 0.0680159u + 0.737192
a
8
=
−1.14370u
26
+ 0.583208u
25
+ ··· + 0.782926u + 4.82381
0.418450u
26
− 0.307498u
25
+ ··· − 0.693532u − 0.0920432
a
11
=
5.62049u
26
− 7.17679u
25
+ ··· − 46.4959u + 1.04507
0.371510u
26
− 0.459914u
25
+ ··· − 2.09151u + 0.773138
(ii) Obstruction class = 1
(iii) Cusp Shapes =
62283098744443613578
49938603651971298581
u
26
+
232496535338997910625
49938603651971298581
u
25
+ ··· +
2030283186351200219352
49938603651971298581
u −
2398399780063016104203
49938603651971298581
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
− 14u
26
+ ··· − 8u + 1
c
2
u
27
+ 7u
25
+ ··· + 4u
2
+ 1
c
3
u
27
− 20u
26
+ ··· + 413u − 181
c
4
u
27
− 6u
25
+ ··· + 14u − 5
c
5
, c
12
u
27
− u
26
+ ··· − 10u
2
− 1
c
6
, c
11
u
27
+ u
26
+ ··· − u − 1
c
7
u
27
− u
25
+ ··· + 12u − 5
c
8
u
27
+ 7u
25
+ ··· − 4u
2
− 1
c
9
u
27
+ 12u
26
+ ··· + 5u
2
− 1
c
10
u
27
− u
26
+ ··· − u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
+ 6y
26
+ ··· − 8y − 1
c
2
, c
8
y
27
+ 14y
26
+ ··· − 8y − 1
c
3
y
27
− 36y
26
+ ··· + 599539y − 32761
c
4
y
27
− 12y
26
+ ··· − 34y − 25
c
5
, c
12
y
27
− 7y
26
+ ··· − 20y − 1
c
6
, c
10
, c
11
y
27
− 15y
26
+ ··· − 19y − 1
c
7
y
27
− 2y
26
+ ··· − 236y − 25
c
9
y
27
− 4y
26
+ ··· + 10y − 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.336357 + 0.966243I
a = −0.686667 + 0.398689I
b = 0.336357 − 0.966243I
−6.68205 − 0.58234I −13.57427 + 1.26764I
u = −0.336357 − 0.966243I
a = −0.686667 − 0.398689I
b = 0.336357 + 0.966243I
−6.68205 + 0.58234I −13.57427 − 1.26764I
u = −1.005400 + 0.275951I
a = −1.037330 + 0.705161I
b = 1.005400 − 0.275951I
1.83930 − 2.45917I 1.80526 + 7.62829I
u = −1.005400 − 0.275951I
a = −1.037330 − 0.705161I
b = 1.005400 + 0.275951I
1.83930 + 2.45917I 1.80526 − 7.62829I
u = 0.606745 + 0.882798I
a = 0.331286 + 0.517855I
b = −0.606745 − 0.882798I
−5.64281 − 2.15614I −9.19261 − 1.44075I
u = 0.606745 − 0.882798I
a = 0.331286 − 0.517855I
b = −0.606745 + 0.882798I
−5.64281 + 2.15614I −9.19261 + 1.44075I
u = 1.07541
a = −0.461440
b = −1.07541
−7.12921 −4.03220
u = 0.537424 + 1.012470I
a = 0.721465 − 0.486432I
b = −0.537424 − 1.012470I
−3.11876 + 0.97105I −4.34103 − 1.79332I
u = 0.537424 − 1.012470I
a = 0.721465 + 0.486432I
b = −0.537424 + 1.012470I
−3.11876 − 0.97105I −4.34103 + 1.79332I
u = −0.816309 + 0.907921I
a = −0.862083 − 0.153746I
b = 0.816309 − 0.907921I
1.00458 − 4.33611I 2.54294 + 5.25647I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.816309 − 0.907921I
a = −0.862083 + 0.153746I
b = 0.816309 + 0.907921I
1.00458 + 4.33611I 2.54294 − 5.25647I
u = 1.216070 + 0.287083I
a = 0.772680 + 0.609470I
b = −1.216070 − 0.287083I
0.51517 + 5.99705I −4.48976 − 8.64665I
u = 1.216070 − 0.287083I
a = 0.772680 − 0.609470I
b = −1.216070 + 0.287083I
0.51517 − 5.99705I −4.48976 + 8.64665I
u = −1.127710 + 0.614247I
a = −0.861605 + 0.280734I
b = 1.127710 − 0.614247I
2.32898 − 3.69540I 1.96062 + 2.95334I
u = −1.127710 − 0.614247I
a = −0.861605 − 0.280734I
b = 1.127710 + 0.614247I
2.32898 + 3.69540I 1.96062 − 2.95334I
u = −0.079298 + 0.699557I
a = −1.57234 + 0.54120I
b = 0.079298 − 0.699557I
−5.11145 + 5.51494I −8.41780 − 5.72397I
u = −0.079298 − 0.699557I
a = −1.57234 − 0.54120I
b = 0.079298 + 0.699557I
−5.11145 − 5.51494I −8.41780 + 5.72397I
u = −1.326360 + 0.260463I
a = 0.244005 + 0.122908I
b = 1.326360 − 0.260463I
−10.69710 + 4.45935I −7.92473 − 3.01900I
u = −1.326360 − 0.260463I
a = 0.244005 − 0.122908I
b = 1.326360 + 0.260463I
−10.69710 − 4.45935I −7.92473 + 3.01900I
u = 0.859553 + 1.069800I
a = 0.705680 − 0.146031I
b = −0.859553 − 1.069800I
−1.59462 + 9.09497I −0.27825 − 8.37177I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.859553 − 1.069800I
a = 0.705680 + 0.146031I
b = −0.859553 + 1.069800I
−1.59462 − 9.09497I −0.27825 + 8.37177I
u = 1.286270 + 0.526184I
a = 0.741479 + 0.383886I
b = −1.286270 − 0.526184I
0.771357 − 0.260360I −4.29150 + 1.30501I
u = 1.286270 − 0.526184I
a = 0.741479 − 0.383886I
b = −1.286270 + 0.526184I
0.771357 + 0.260360I −4.29150 − 1.30501I
u = 0.221536 + 0.540952I
a = 1.34818 + 1.58969I
b = −0.221536 − 0.540952I
−3.77045 − 0.62259I −2.79230 − 0.12381I
u = 0.221536 − 0.540952I
a = 1.34818 − 1.58969I
b = −0.221536 + 0.540952I
−3.77045 + 0.62259I −2.79230 + 0.12381I
u = −0.073870 + 0.346449I
a = −2.11404 − 5.83905I
b = 0.073870 − 0.346449I
5.75856 − 3.13863I −34.4905 + 20.3622I
u = −0.073870 − 0.346449I
a = −2.11404 + 5.83905I
b = 0.073870 + 0.346449I
5.75856 + 3.13863I −34.4905 − 20.3622I
14
III. I
u
3
= h3.16 × 10
115
u
39
+ 8.24 × 10
115
u
38
+ · · · + 1.01 × 10
119
b + 9.36 ×
10
117
, −3.48 × 10
101
u
39
− 7.65 × 10
101
u
38
+ · · · + 4.10 × 10
104
a + 7.60 ×
10
103
, u
40
+ 3u
39
+ · · · + 2382u + 643i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u
2
a
12
=
0.000849679u
39
+ 0.00186679u
38
+ ··· + 6.51068u − 0.185551
−0.000313802u
39
− 0.000817408u
38
+ ··· − 4.43952u − 0.0929075
a
10
=
0.000285297u
39
+ 0.000692402u
38
+ ··· − 1.15794u + 2.02510
−0.000188165u
39
− 0.000867240u
38
+ ··· − 0.373964u − 1.49124
a
7
=
0.0000666790u
39
+ 0.000133987u
38
+ ··· + 1.52511u − 1.95131
0.000373461u
39
+ 0.00130423u
38
+ ··· − 0.762077u + 1.71070
a
1
=
0.000535877u
39
+ 0.00104938u
38
+ ··· + 2.07116u − 0.278459
−0.000313802u
39
− 0.000817408u
38
+ ··· − 4.43952u − 0.0929075
a
4
=
0.000306782u
39
+ 0.00117024u
38
+ ··· − 2.28718u + 3.66201
−0.000336059u
39
− 0.00126654u
38
+ ··· + 1.55459u − 1.55002
a
3
=
−0.0000666790u
39
− 0.000133987u
38
+ ··· − 1.52511u + 1.95131
−0.000531243u
39
− 0.00193316u
38
+ ··· + 0.876534u − 1.66823
a
2
=
0.000887834u
39
+ 0.00224028u
38
+ ··· + 8.02399u − 0.145440
−0.000846462u
39
− 0.00202870u
38
+ ··· − 6.96651u + 0.487391
a
8
=
−0.000654257u
39
− 0.00227174u
38
+ ··· − 0.869104u − 2.95403
0.000283061u
39
+ 0.000673324u
38
+ ··· + 1.04746u + 2.51922
a
11
=
0.000643096u
39
+ 0.00183202u
38
+ ··· − 0.989966u + 3.41122
−0.000105609u
39
− 0.000634796u
38
+ ··· + 0.0138282u − 1.44866
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00357512u
39
− 0.0100039u
38
+ ··· − 28.2430u − 9.94034
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
8
c
2
, c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
8
c
3
(u
4
+ 3u
3
+ u
2
− 2u + 1)
10
c
4
u
40
− u
39
+ ··· − 525220u + 436829
c
5
, c
12
u
40
− 3u
39
+ ··· − 2382u + 643
c
6
, c
10
, c
11
u
40
− u
39
+ ··· + 60966u + 88157
c
7
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
8
c
9
(u
4
− u
3
+ u
2
+ 1)
10
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
8
c
2
, c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
8
c
3
(y
4
− 7y
3
+ 15y
2
− 2y + 1)
10
c
4
y
40
− 25y
39
+ ··· − 458444454794y + 190819575241
c
5
, c
12
y
40
− 5y
39
+ ··· + 1465948y + 413449
c
6
, c
10
, c
11
y
40
− 45y
39
+ ··· − 9888901040y + 7771656649
c
7
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
8
c
9
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
10
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.915348 + 0.214144I
a = −0.189845 + 0.831374I
b = −0.106490 − 1.134420I
−5.47491 + 0.11547I −6.34185 + 0.47809I
u = 0.915348 − 0.214144I
a = −0.189845 − 0.831374I
b = −0.106490 + 1.134420I
−5.47491 − 0.11547I −6.34185 − 0.47809I
u = −0.683982 + 0.623025I
a = 0.805406 − 0.319531I
b = −1.92283 − 1.60754I
−11.01840 − 5.81594I −10.57105 + 8.40733I
u = −0.683982 − 0.623025I
a = 0.805406 + 0.319531I
b = −1.92283 + 1.60754I
−11.01840 + 5.81594I −10.57105 − 8.40733I
u = 1.078690 + 0.106927I
a = 0.864918 + 0.759081I
b = −1.023340 − 0.427389I
1.52684 + 1.63338I −2.68838 + 1.86585I
u = 1.078690 − 0.106927I
a = 0.864918 − 0.759081I
b = −1.023340 + 0.427389I
1.52684 − 1.63338I −2.68838 − 1.86585I
u = −0.355495 + 1.038010I
a = −1.037300 − 0.465364I
b = 0.99329 − 1.41252I
−4.01662 − 7.56480I −6.91758 + 6.06338I
u = −0.355495 − 1.038010I
a = −1.037300 + 0.465364I
b = 0.99329 + 1.41252I
−4.01662 + 7.56480I −6.91758 − 6.06338I
u = 0.507163 + 0.745285I
a = −0.880172 − 0.126908I
b = 1.80560 − 1.23303I
−7.54689 + 1.41510I −7.30788 − 4.90874I
u = 0.507163 − 0.745285I
a = −0.880172 + 0.126908I
b = 1.80560 + 1.23303I
−7.54689 − 1.41510I −7.30788 + 4.90874I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.612045 + 0.921062I
a = 0.718589 − 0.095543I
b = −2.17034 − 1.07308I
−11.01840 + 2.98573I −10.57105 + 1.41016I
u = −0.612045 − 0.921062I
a = 0.718589 + 0.095543I
b = −2.17034 + 1.07308I
−11.01840 − 2.98573I −10.57105 − 1.41016I
u = −1.023340 + 0.427389I
a = −1.025430 + 0.462244I
b = 1.078690 − 0.106927I
1.52684 − 1.63338I −2.68838 − 1.86585I
u = −1.023340 − 0.427389I
a = −1.025430 − 0.462244I
b = 1.078690 + 0.106927I
1.52684 + 1.63338I −2.68838 + 1.86585I
u = −0.106490 + 1.134420I
a = −0.600583 + 0.366499I
b = 0.915348 − 0.214144I
−5.47491 − 0.11547I −6.34185 − 0.47809I
u = −0.106490 − 1.134420I
a = −0.600583 − 0.366499I
b = 0.915348 + 0.214144I
−5.47491 + 0.11547I −6.34185 + 0.47809I
u = 1.013930 + 0.588855I
a = 1.018540 + 0.307239I
b = −1.316730 − 0.470234I
1.52684 + 4.69454I −2.68838 − 6.99545I
u = 1.013930 − 0.588855I
a = 1.018540 − 0.307239I
b = −1.316730 + 0.470234I
1.52684 − 4.69454I −2.68838 + 6.99545I
u = 0.050553 + 0.805117I
a = −1.06126 − 1.12463I
b = 0.44450 − 1.35463I
−4.01662 + 1.23687I −6.91758 − 0.93379I
u = 0.050553 − 0.805117I
a = −1.06126 + 1.12463I
b = 0.44450 + 1.35463I
−4.01662 − 1.23687I −6.91758 + 0.93379I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.289512 + 0.747747I
a = 1.44340 − 0.58031I
b = −0.775671 − 1.144290I
−0.54514 + 3.16396I −3.65440 − 2.56480I
u = 0.289512 − 0.747747I
a = 1.44340 + 0.58031I
b = −0.775671 + 1.144290I
−0.54514 − 3.16396I −3.65440 + 2.56480I
u = −0.775671 + 1.144290I
a = −0.891390 − 0.140159I
b = 0.289512 − 0.747747I
−0.54514 − 3.16396I −3.65440 + 2.56480I
u = −0.775671 − 1.144290I
a = −0.891390 + 0.140159I
b = 0.289512 + 0.747747I
−0.54514 + 3.16396I −3.65440 − 2.56480I
u = −1.316730 + 0.470234I
a = −0.792945 + 0.408910I
b = 1.013930 − 0.588855I
1.52684 − 4.69454I −2.68838 + 6.99545I
u = −1.316730 − 0.470234I
a = −0.792945 − 0.408910I
b = 1.013930 + 0.588855I
1.52684 + 4.69454I −2.68838 − 6.99545I
u = 0.44450 + 1.35463I
a = 0.793611 − 0.368401I
b = 0.050553 − 0.805117I
−4.01662 − 1.23687I −6.91758 + 0.93379I
u = 0.44450 − 1.35463I
a = 0.793611 + 0.368401I
b = 0.050553 + 0.805117I
−4.01662 + 1.23687I −6.91758 − 0.93379I
u = 0.56798 + 1.35900I
a = 0.359128 + 0.408966I
b = −0.199638 − 0.190466I
−5.47491 − 2.94568I −6.34185 + 9.33939I
u = 0.56798 − 1.35900I
a = 0.359128 − 0.408966I
b = −0.199638 + 0.190466I
−5.47491 + 2.94568I −6.34185 − 9.33939I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.199638 + 0.190466I
a = −0.87961 + 2.76905I
b = 0.56798 − 1.35900I
−5.47491 + 2.94568I −6.34185 − 9.33939I
u = −0.199638 − 0.190466I
a = −0.87961 − 2.76905I
b = 0.56798 + 1.35900I
−5.47491 − 2.94568I −6.34185 + 9.33939I
u = 0.99329 + 1.41252I
a = 0.715433 − 0.099946I
b = −0.355495 − 1.038010I
−4.01662 + 7.56480I 0
u = 0.99329 − 1.41252I
a = 0.715433 + 0.099946I
b = −0.355495 + 1.038010I
−4.01662 − 7.56480I 0
u = 1.80560 + 1.23303I
a = 0.052918 + 0.362812I
b = 0.507163 − 0.745285I
−7.54689 − 1.41510I 0
u = 1.80560 − 1.23303I
a = 0.052918 − 0.362812I
b = 0.507163 + 0.745285I
−7.54689 + 1.41510I 0
u = −2.17034 + 1.07308I
a = −0.001611 + 0.331107I
b = −0.612045 − 0.921062I
−11.01840 − 2.98573I 0
u = −2.17034 − 1.07308I
a = −0.001611 − 0.331107I
b = −0.612045 + 0.921062I
−11.01840 + 2.98573I 0
u = −1.92283 + 1.60754I
a = −0.076655 + 0.310539I
b = −0.683982 − 0.623025I
−11.01840 + 5.81594I 0
u = −1.92283 − 1.60754I
a = −0.076655 − 0.310539I
b = −0.683982 + 0.623025I
−11.01840 − 5.81594I 0
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
8
)(u
27
− 14u
26
+ ··· − 8u + 1)
· (u
36
+ 17u
35
+ ··· + 896u + 256)
c
2
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
8
)(u
27
+ 7u
25
+ ··· + 4u
2
+ 1)
· (u
36
+ 9u
35
+ ··· + 128u + 16)
c
3
((u
4
+ 3u
3
+ u
2
− 2u + 1)
10
)(u
27
− 20u
26
+ ··· + 413u − 181)
· (u
36
− 19u
35
+ ··· − 6400u + 1024)
c
4
(u
27
− 6u
25
+ ··· + 14u − 5)(u
36
− 16u
34
+ ··· + 115u + 42)
· (u
40
− u
39
+ ··· − 525220u + 436829)
c
5
, c
12
(u
27
− u
26
+ ··· − 10u
2
− 1)(u
36
− u
35
+ ··· − u + 1)
· (u
40
− 3u
39
+ ··· − 2382u + 643)
c
6
, c
11
(u
27
+ u
26
+ ··· − u − 1)(u
36
+ u
35
+ ··· + 2u + 1)
· (u
40
− u
39
+ ··· + 60966u + 88157)
c
7
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
8
)(u
27
− u
25
+ ··· + 12u − 5)
· (u
36
− 9u
35
+ ··· − 273856u + 43216)
c
8
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
8
)(u
27
+ 7u
25
+ ··· − 4u
2
− 1)
· (u
36
+ 9u
35
+ ··· + 128u + 16)
c
9
((u
4
− u
3
+ u
2
+ 1)
10
)(u
27
+ 12u
26
+ ··· + 5u
2
− 1)
· (u
36
+ 19u
35
+ ··· + 464u + 32)
c
10
(u
27
− u
26
+ ··· − u + 1)(u
36
+ u
35
+ ··· + 2u + 1)
· (u
40
− u
39
+ ··· + 60966u + 88157)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
8
)(y
27
+ 6y
26
+ ··· − 8y − 1)
· (y
36
+ 5y
35
+ ··· + 303104y + 65536)
c
2
, c
8
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
8
)(y
27
+ 14y
26
+ ··· − 8y − 1)
· (y
36
+ 17y
35
+ ··· + 896y + 256)
c
3
((y
4
− 7y
3
+ 15y
2
− 2y + 1)
10
)(y
27
− 36y
26
+ ··· + 599539y − 32761)
· (y
36
− 43y
35
+ ··· + 39911424y + 1048576)
c
4
(y
27
− 12y
26
+ ··· − 34y − 25)(y
36
− 32y
35
+ ··· − 6169y + 1764)
· (y
40
− 25y
39
+ ··· − 458444454794y + 190819575241)
c
5
, c
12
(y
27
− 7y
26
+ ··· − 20y − 1)(y
36
+ 21y
35
+ ··· + 103y + 1)
· (y
40
− 5y
39
+ ··· + 1465948y + 413449)
c
6
, c
10
, c
11
(y
27
− 15y
26
+ ··· − 19y − 1)(y
36
− 59y
35
+ ··· − 18y + 1)
· (y
40
− 45y
39
+ ··· − 9888901040y + 7771656649)
c
7
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
8
)(y
27
− 2y
26
+ ··· − 236y − 25)
· (y
36
− 7y
35
+ ··· + 320081792y + 1867622656)
c
9
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
10
)(y
27
− 4y
26
+ ··· + 10y − 1)
· (y
36
− 3y
35
+ ··· + 15616y + 1024)
23
