11a
317
(K11a
317
)
A knot diagram
1
Linearized knot diagam
7 9 1 11 8 2 10 3 6 4 5
Solving Sequence
2,9 3,6
7 10 1 4 8 5 11
c
2
c
6
c
9
c
1
c
3
c
8
c
5
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 9521222u
24
+ 7310497u
23
+ ··· + 51467938a + 84913603, u
25
+ 9u
23
+ ··· + 2u − 1i
I
u
2
= h−3.79702 × 10
56
u
47
− 2.02674 × 10
55
u
46
+ ··· + 3.40179 × 10
58
b + 1.47690 × 10
59
,
− 2.59043 × 10
36
u
47
− 5.89061 × 10
36
u
46
+ ··· + 8.97537 × 10
37
a − 1.46834 × 10
39
,
u
48
+ u
47
+ ··· − 114u + 76i
I
u
3
= hb + u, −u
8
− 5u
6
− u
5
− 10u
4
− 3u
3
− 9u
2
+ a − 3u − 3,
u
11
+ 6u
9
+ u
8
+ 15u
7
+ 4u
6
+ 19u
5
+ 6u
4
+ 12u
3
+ 3u
2
+ 3u + 1i
* 3 irreducible components of dim
C
= 0, with total 84 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, 9.52 × 10
6
u
24
+ 7.31 × 10
6
u
23
+ · · · + 5.15 × 10
7
a + 8.49 ×
10
7
, u
25
+ 9u
23
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
−0.184993u
24
− 0.142040u
23
+ ··· + 0.533191u − 1.64983
u
a
7
=
−0.184993u
24
− 0.142040u
23
+ ··· + 1.53319u − 1.64983
u
a
10
=
0.249484u
24
+ 0.573176u
23
+ ··· − 1.83450u + 1.36074
−0.208863u
24
− 0.229234u
23
+ ··· + 1.09909u − 0.142040
a
1
=
−0.142040u
24
− 0.208863u
23
+ ··· − 1.27985u + 0.815007
u
2
a
4
=
−0.404984u
24
− 0.142520u
23
+ ··· − 0.371512u + 1.03005
0.127693u
24
− 0.0749250u
23
+ ··· − 0.532638u + 0.151702
a
8
=
−u
u
3
+ u
a
5
=
−0.127833u
24
− 0.0404991u
23
+ ··· + 0.184500u − 1.27856
0.0196164u
24
+ 0.173697u
23
+ ··· + 1.49461u − 0.472814
a
11
=
−0.127434u
24
+ 0.297945u
23
+ ··· − 1.85707u + 1.03254
−0.293850u
24
− 0.0592649u
23
+ ··· + 1.55630u − 0.291252
a
11
=
−0.127434u
24
+ 0.297945u
23
+ ··· − 1.85707u + 1.03254
−0.293850u
24
− 0.0592649u
23
+ ··· + 1.55630u − 0.291252
(ii) Obstruction class = −1
(iii) Cusp Shapes =
82053183
25733969
u
24
+
57865173
25733969
u
23
+ ··· −
4551724
25733969
u +
217825726
25733969
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
25
+ 9u
23
+ ··· + 2u − 1
c
3
u
25
− 18u
24
+ ··· + 1946u − 188
c
4
, c
10
, c
11
u
25
+ 6u
24
+ ··· + 14u − 4
c
5
, c
7
u
25
− u
24
+ ··· − 3u − 1
c
9
u
25
− 23u
24
+ ··· + 49152u − 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
25
+ 18y
24
+ ··· + 4y −1
c
3
y
25
+ 2y
24
+ ··· + 360428y −35344
c
4
, c
10
, c
11
y
25
− 22y
24
+ ··· + 140y −16
c
5
, c
7
y
25
− 5y
24
+ ··· + 19y −1
c
9
y
25
− y
24
+ ··· + 25165824y −16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.062688 + 1.054190I
a = −0.22875 + 2.02308I
b = −0.062688 + 1.054190I
−1.10259 − 2.56061I 2.13530 + 4.85725I
u = −0.062688 − 1.054190I
a = −0.22875 − 2.02308I
b = −0.062688 − 1.054190I
−1.10259 + 2.56061I 2.13530 − 4.85725I
u = −0.431005 + 1.014420I
a = 1.57469 − 0.29419I
b = −0.431005 + 1.014420I
−3.98322 − 6.30520I 2.04460 + 8.85471I
u = −0.431005 − 1.014420I
a = 1.57469 + 0.29419I
b = −0.431005 − 1.014420I
−3.98322 + 6.30520I 2.04460 − 8.85471I
u = 0.111664 + 1.150710I
a = 0.55005 + 1.77135I
b = 0.111664 + 1.150710I
−7.45610 + 6.63321I −3.37442 − 6.60504I
u = 0.111664 − 1.150710I
a = 0.55005 − 1.77135I
b = 0.111664 − 1.150710I
−7.45610 − 6.63321I −3.37442 + 6.60504I
u = 0.817149 + 0.195179I
a = −0.818471 + 0.839836I
b = 0.817149 + 0.195179I
−1.75933 − 5.22873I 2.70405 + 4.29469I
u = 0.817149 − 0.195179I
a = −0.818471 − 0.839836I
b = 0.817149 − 0.195179I
−1.75933 + 5.22873I 2.70405 − 4.29469I
u = 0.329284 + 0.707437I
a = −1.12449 − 1.00862I
b = 0.329284 + 0.707437I
0.24887 + 1.85876I 5.21169 − 1.18731I
u = 0.329284 − 0.707437I
a = −1.12449 + 1.00862I
b = 0.329284 − 0.707437I
0.24887 − 1.85876I 5.21169 + 1.18731I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.682331 + 0.261986I
a = 0.916549 + 0.989308I
b = −0.682331 + 0.261986I
2.97560 + 1.99862I 9.19617 − 1.79116I
u = −0.682331 − 0.261986I
a = 0.916549 − 0.989308I
b = −0.682331 − 0.261986I
2.97560 − 1.99862I 9.19617 + 1.79116I
u = −0.650446 + 0.309358I
a = 0.859033 − 0.557233I
b = −0.650446 + 0.309358I
−2.96955 + 0.98970I 0.58497 + 1.31216I
u = −0.650446 − 0.309358I
a = 0.859033 + 0.557233I
b = −0.650446 − 0.309358I
−2.96955 − 0.98970I 0.58497 − 1.31216I
u = 0.506874 + 0.472329I
a = −0.77448 + 1.43912I
b = 0.506874 + 0.472329I
0.027101 + 0.899324I 2.44779 − 5.98780I
u = 0.506874 − 0.472329I
a = −0.77448 − 1.43912I
b = 0.506874 − 0.472329I
0.027101 − 0.899324I 2.44779 + 5.98780I
u = 0.343162 + 1.368570I
a = −1.274410 + 0.462559I
b = 0.343162 + 1.368570I
−13.7635 + 5.7019I −6.58533 − 4.59320I
u = 0.343162 − 1.368570I
a = −1.274410 − 0.462559I
b = 0.343162 − 1.368570I
−13.7635 − 5.7019I −6.58533 + 4.59320I
u = −0.49075 + 1.33946I
a = 1.212400 + 0.228564I
b = −0.49075 + 1.33946I
−5.95198 − 7.41816I −1.58248 + 3.87242I
u = −0.49075 − 1.33946I
a = 1.212400 − 0.228564I
b = −0.49075 − 1.33946I
−5.95198 + 7.41816I −1.58248 − 3.87242I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.54170 + 1.40648I
a = −1.106250 + 0.225454I
b = 0.54170 + 1.40648I
−4.43838 + 12.03070I 0.63983 − 8.03648I
u = 0.54170 − 1.40648I
a = −1.106250 − 0.225454I
b = 0.54170 − 1.40648I
−4.43838 − 12.03070I 0.63983 + 8.03648I
u = −0.54820 + 1.46070I
a = 1.052770 + 0.249978I
b = −0.54820 + 1.46070I
−10.0254 − 16.0606I −3.24174 + 8.45261I
u = −0.54820 − 1.46070I
a = 1.052770 − 0.249978I
b = −0.54820 − 1.46070I
−10.0254 + 16.0606I −3.24174 − 8.45261I
u = 0.431188
a = −1.67732
b = 0.431188
0.990720 10.6390
7
II. I
u
2
= h−3.80 × 10
56
u
47
− 2.03 × 10
55
u
46
+ · · · + 3.40 × 10
58
b + 1.48 ×
10
59
, −2.59 × 10
36
u
47
− 5.89 × 10
36
u
46
+ · · · + 8.98 × 10
37
a − 1.47 ×
10
39
, u
48
+ u
47
+ · · · − 114u + 76i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
0.0288615u
47
+ 0.0656308u
46
+ ··· − 20.8449u + 16.3597
0.0111618u
47
+ 0.000595787u
46
+ ··· + 9.23632u − 4.34154
a
7
=
0.0400233u
47
+ 0.0662266u
46
+ ··· − 11.6086u + 12.0181
0.0111618u
47
+ 0.000595787u
46
+ ··· + 9.23632u − 4.34154
a
10
=
0.0420194u
47
+ 0.0787887u
46
+ ··· − 0.594941u + 14.8597
0.111068u
47
+ 0.0434318u
46
+ ··· + 17.5888u − 7.60663
a
1
=
0.0168138u
47
+ 0.0776572u
46
+ ··· + 24.0640u + 0.627739
−0.0832734u
47
− 0.133498u
46
+ ··· − 8.45658u − 5.55110
a
4
=
−0.145940u
47
+ 0.0918329u
46
+ ··· − 59.0154u + 24.9472
−0.101135u
47
+ 0.0935008u
46
+ ··· − 8.22727u + 14.4058
a
8
=
−u
u
3
+ u
a
5
=
0.0201071u
47
+ 0.104301u
46
+ ··· − 26.0937u + 18.7558
0.00804912u
47
+ 0.0333014u
46
+ ··· + 8.41343u − 3.13339
a
11
=
0.106068u
47
+ 0.361549u
46
+ ··· + 20.9043u + 2.41440
−0.0231108u
47
+ 0.124603u
46
+ ··· − 30.6445u + 6.90238
a
11
=
0.106068u
47
+ 0.361549u
46
+ ··· + 20.9043u + 2.41440
−0.0231108u
47
+ 0.124603u
46
+ ··· − 30.6445u + 6.90238
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.299258u
47
− 0.246468u
46
+ ··· + 7.59368u − 10.2839
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
48
+ u
47
+ ··· − 114u + 76
c
3
(u
12
+ 3u
11
+ ··· + 4u + 1)
4
c
4
, c
10
, c
11
(u
12
− u
11
− 5u
10
+ 4u
9
+ 9u
8
− 4u
7
− 6u
6
− 2u
5
+ 3u
3
+ u
2
+ 1)
4
c
5
, c
7
u
48
+ 13u
47
+ ··· + 54u + 4
c
9
(u
2
+ u + 1)
24
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
48
+ 39y
47
+ ··· + 220932y + 5776
c
3
(y
12
+ y
11
+ ··· − 2y + 1)
4
c
4
, c
10
, c
11
(y
12
− 11y
11
+ ··· + 2y + 1)
4
c
5
, c
7
y
48
+ 11y
47
+ ··· + 356y + 16
c
9
(y
2
+ y + 1)
24
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.119725 + 0.978589I
a = 0.933512 − 0.396730I
b = −0.735953 + 0.216627I
−1.81971 + 1.93627I −0.00912 − 4.22614I
u = 0.119725 − 0.978589I
a = 0.933512 + 0.396730I
b = −0.735953 − 0.216627I
−1.81971 − 1.93627I −0.00912 + 4.22614I
u = −0.975387 + 0.053637I
a = −0.462394 − 0.913306I
b = 0.248414 + 1.077640I
−1.81971 + 2.12349I −0.00912 − 2.70206I
u = −0.975387 − 0.053637I
a = −0.462394 + 0.913306I
b = 0.248414 − 1.077640I
−1.81971 − 2.12349I −0.00912 + 2.70206I
u = 0.248414 + 1.077640I
a = 0.864641 − 0.264663I
b = −0.975387 + 0.053637I
−1.81971 + 2.12349I 0. − 2.70206I
u = 0.248414 − 1.077640I
a = 0.864641 + 0.264663I
b = −0.975387 − 0.053637I
−1.81971 − 2.12349I 0. + 2.70206I
u = 0.423066 + 0.782946I
a = −0.589046 − 0.956905I
b = 0.087660 + 0.519316I
0.20418 + 1.85492I 2.80561 − 0.70730I
u = 0.423066 − 0.782946I
a = −0.589046 + 0.956905I
b = 0.087660 − 0.519316I
0.20418 − 1.85492I 2.80561 + 0.70730I
u = 0.839580 + 0.740780I
a = 0.846588 + 0.284535I
b = −0.200259 − 1.354980I
−8.04990 + 1.93627I −3.99088 − 4.22614I
u = 0.839580 − 0.740780I
a = 0.846588 − 0.284535I
b = −0.200259 + 1.354980I
−8.04990 − 1.93627I −3.99088 + 4.22614I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.103555 + 1.115340I
a = −0.811099 − 0.372987I
b = 0.42519 − 1.56466I
−4.93480 − 0.82777I −2.00000 − 2.17330I
u = −0.103555 − 1.115340I
a = −0.811099 + 0.372987I
b = 0.42519 + 1.56466I
−4.93480 + 0.82777I −2.00000 + 2.17330I
u = −0.021432 + 1.150630I
a = 0.744302 − 0.448409I
b = −0.49671 − 1.71193I
−10.07380 − 1.85492I −6.80561 + 0.70730I
u = −0.021432 − 1.150630I
a = 0.744302 + 0.448409I
b = −0.49671 + 1.71193I
−10.07380 + 1.85492I −6.80561 − 0.70730I
u = −0.531251 + 1.069240I
a = 0.463250 − 0.697786I
b = 0.089046 + 0.280790I
−4.93480 − 5.55830I −2.00000 + 1.67128I
u = −0.531251 − 1.069240I
a = 0.463250 + 0.697786I
b = 0.089046 − 0.280790I
−4.93480 + 5.55830I −2.00000 − 1.67128I
u = −0.358210 + 1.155170I
a = −0.806376 − 0.182786I
b = 1.230640 − 0.061737I
0.20418 − 5.91469I 3.00000 + 7.63550I
u = −0.358210 − 1.155170I
a = −0.806376 + 0.182786I
b = 1.230640 + 0.061737I
0.20418 + 5.91469I 3.00000 − 7.63550I
u = 1.230640 + 0.061737I
a = 0.440487 + 0.681622I
b = −0.358210 − 1.155170I
0.20418 + 5.91469I 3.00000 − 7.63550I
u = 1.230640 − 0.061737I
a = 0.440487 − 0.681622I
b = −0.358210 + 1.155170I
0.20418 − 5.91469I 3.00000 + 7.63550I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.735953 + 0.216627I
a = −0.306466 − 1.266950I
b = 0.119725 + 0.978589I
−1.81971 + 1.93627I −0.00912 − 4.22614I
u = −0.735953 − 0.216627I
a = −0.306466 + 1.266950I
b = 0.119725 − 0.978589I
−1.81971 − 1.93627I −0.00912 + 4.22614I
u = 0.393376 + 1.207210I
a = 0.770526 − 0.163098I
b = −1.341440 − 0.149230I
−4.93480 + 9.61806I 0. − 8.59949I
u = 0.393376 − 1.207210I
a = 0.770526 + 0.163098I
b = −1.341440 + 0.149230I
−4.93480 − 9.61806I 0. + 8.59949I
u = 0.139190 + 1.313850I
a = 0.691702 − 0.307281I
b = −0.68913 − 1.36774I
−4.93480 + 3.23200I 0
u = 0.139190 − 1.313850I
a = 0.691702 + 0.307281I
b = −0.68913 + 1.36774I
−4.93480 − 3.23200I 0
u = −0.068128 + 1.345270I
a = −0.660883 − 0.338204I
b = 0.81330 − 1.51334I
−10.07380 − 5.91469I 0
u = −0.068128 − 1.345270I
a = −0.660883 + 0.338204I
b = 0.81330 + 1.51334I
−10.07380 + 5.91469I 0
u = 0.280065 + 0.589338I
a = 1.52767 − 0.12243I
b = −0.06781 − 1.45011I
−8.04990 + 2.12349I −3.99088 − 2.70206I
u = 0.280065 − 0.589338I
a = 1.52767 + 0.12243I
b = −0.06781 + 1.45011I
−8.04990 − 2.12349I −3.99088 + 2.70206I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.341440 + 0.149230I
a = −0.439121 + 0.596745I
b = 0.393376 − 1.207210I
−4.93480 − 9.61806I 0
u = −1.341440 − 0.149230I
a = −0.439121 − 0.596745I
b = 0.393376 + 1.207210I
−4.93480 + 9.61806I 0
u = −0.200259 + 1.354980I
a = −0.678850 − 0.268678I
b = 0.839580 − 0.740780I
−8.04990 − 1.93627I 0
u = −0.200259 − 1.354980I
a = −0.678850 + 0.268678I
b = 0.839580 + 0.740780I
−8.04990 + 1.93627I 0
u = −0.06781 + 1.45011I
a = −0.612000 − 0.316184I
b = 0.280065 − 0.589338I
−8.04990 − 2.12349I 0
u = −0.06781 − 1.45011I
a = −0.612000 + 0.316184I
b = 0.280065 + 0.589338I
−8.04990 + 2.12349I 0
u = 0.087660 + 0.519316I
a = −1.46341 − 1.20983I
b = 0.423066 + 0.782946I
0.20418 + 1.85492I 2.80561 − 0.70730I
u = 0.087660 − 0.519316I
a = −1.46341 + 1.20983I
b = 0.423066 − 0.782946I
0.20418 − 1.85492I 2.80561 + 0.70730I
u = −0.68913 + 1.36774I
a = −0.651882 − 0.037119I
b = 0.139190 − 1.313850I
−4.93480 − 3.23200I 0
u = −0.68913 − 1.36774I
a = −0.651882 + 0.037119I
b = 0.139190 + 1.313850I
−4.93480 + 3.23200I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.42519 + 1.56466I
a = 0.596297 − 0.157517I
b = −0.103555 − 1.115340I
−4.93480 + 0.82777I 0
u = 0.42519 − 1.56466I
a = 0.596297 + 0.157517I
b = −0.103555 + 1.115340I
−4.93480 − 0.82777I 0
u = 0.089046 + 0.280790I
a = 3.31552 − 0.72925I
b = −0.531251 + 1.069240I
−4.93480 − 5.55830I −2.00000 + 1.67128I
u = 0.089046 − 0.280790I
a = 3.31552 + 0.72925I
b = −0.531251 − 1.069240I
−4.93480 + 5.55830I −2.00000 − 1.67128I
u = 0.81330 + 1.51334I
a = 0.581788 − 0.017729I
b = −0.068128 − 1.345270I
−10.07380 + 5.91469I 0
u = 0.81330 − 1.51334I
a = 0.581788 + 0.017729I
b = −0.068128 + 1.345270I
−10.07380 − 5.91469I 0
u = −0.49671 + 1.71193I
a = −0.544757 − 0.134009I
b = −0.021432 − 1.150630I
−10.07380 + 1.85492I 0
u = −0.49671 − 1.71193I
a = −0.544757 + 0.134009I
b = −0.021432 + 1.150630I
−10.07380 − 1.85492I 0
15
III. I
u
3
= hb + u, −u
8
− 5u
6
+ · · · + a − 3, u
11
+ 6u
9
+ · · · + 3u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
u
8
+ 5u
6
+ u
5
+ 10u
4
+ 3u
3
+ 9u
2
+ 3u + 3
−u
a
7
=
u
8
+ 5u
6
+ u
5
+ 10u
4
+ 3u
3
+ 9u
2
+ 2u + 3
−u
a
10
=
u
10
+ 5u
8
+ u
7
+ 9u
6
+ 3u
5
+ 5u
4
+ 2u
3
− 3u
2
− 2u − 3
−u
10
− 5u
8
− u
7
− 10u
6
− 3u
5
− 9u
4
− 3u
3
− 3u
2
+ u
a
1
=
−u
9
− 5u
7
− u
6
− 10u
5
− 3u
4
− 9u
3
− 2u
2
− 3u + 1
u
2
a
4
=
u
9
+ 6u
7
+ 2u
6
+ 14u
5
+ 7u
4
+ 15u
3
+ 9u
2
+ 6u + 3
−u
9
− 5u
7
− 10u
5
− u
4
− 9u
3
− 3u
2
− 3u − 1
a
8
=
−u
u
3
+ u
a
5
=
u
8
+ 5u
6
+ u
5
+ 10u
4
+ 4u
3
+ 9u
2
+ 4u + 3
−u
5
− 2u
3
− 2u
a
11
=
u
10
− u
9
+ 5u
8
− 5u
7
+ 9u
6
− 10u
5
+ 5u
4
− 9u
3
− 2u
2
− 3u − 2
u
9
− u
8
+ 4u
7
− 4u
6
+ 6u
5
− 6u
4
+ 3u
3
− 2u
2
+ u
a
11
=
u
10
− u
9
+ 5u
8
− 5u
7
+ 9u
6
− 10u
5
+ 5u
4
− 9u
3
− 2u
2
− 3u − 2
u
9
− u
8
+ 4u
7
− 4u
6
+ 6u
5
− 6u
4
+ 3u
3
− 2u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
10
− 7u
9
− 6u
8
− 40u
7
− 22u
6
− 92u
5
− 44u
4
− 96u
3
− 43u
2
− 37u − 10
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
11
+ 6u
9
− u
8
+ 15u
7
− 4u
6
+ 19u
5
− 6u
4
+ 12u
3
− 3u
2
+ 3u − 1
c
2
, c
6
u
11
+ 6u
9
+ u
8
+ 15u
7
+ 4u
6
+ 19u
5
+ 6u
4
+ 12u
3
+ 3u
2
+ 3u + 1
c
3
u
11
+ 3u
10
+ 5u
9
+ u
8
− 2u
7
+ 6u
6
+ 25u
5
+ 21u
4
+ 4u
3
− 2u
2
+ 3u − 1
c
4
u
11
− u
10
− 5u
9
+ 4u
8
+ 9u
7
− 3u
6
− 7u
5
− 5u
4
+ 3u
3
+ 5u
2
− u + 1
c
5
, c
7
u
11
− u
10
+ u
9
+ 2u
8
− u
7
+ u
6
+ 2u
5
+ 2u
4
+ u
2
+ 2u + 1
c
9
u
11
− 2u
10
+ u
9
+ 2u
7
− 2u
6
+ u
5
+ u
4
+ 2u
3
− u
2
− u − 1
c
10
, c
11
u
11
+ u
10
− 5u
9
− 4u
8
+ 9u
7
+ 3u
6
− 7u
5
+ 5u
4
+ 3u
3
− 5u
2
− u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
11
+ 12y
10
+ ··· + 3y −1
c
3
y
11
+ y
10
+ ··· + 5y −1
c
4
, c
10
, c
11
y
11
− 11y
10
+ ··· − 9y −1
c
5
, c
7
y
11
+ y
10
+ 3y
9
+ 5y
7
− 7y
6
+ 2y
5
− 14y
4
+ 2y
3
− 5y
2
+ 2y −1
c
9
y
11
− 2y
10
+ 5y
9
− 2y
8
+ 14y
7
− 2y
6
+ 7y
5
− 5y
4
− 3y
2
− y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.418339 + 0.831995I
a = −0.606054 + 1.113310I
b = 0.418339 − 0.831995I
−5.21814 − 6.73322I −3.33459 + 9.11200I
u = −0.418339 − 0.831995I
a = −0.606054 − 1.113310I
b = 0.418339 + 0.831995I
−5.21814 + 6.73322I −3.33459 − 9.11200I
u = 0.206293 + 0.670051I
a = 0.29791 + 2.15781I
b = −0.206293 − 0.670051I
0.39973 + 2.50595I 8.65215 − 11.04149I
u = 0.206293 − 0.670051I
a = 0.29791 − 2.15781I
b = −0.206293 + 0.670051I
0.39973 − 2.50595I 8.65215 + 11.04149I
u = −0.336362 + 1.325590I
a = −0.618059 − 0.244698I
b = 0.336362 − 1.325590I
−4.66204 − 2.24789I 1.66012 + 1.37513I
u = −0.336362 − 1.325590I
a = −0.618059 + 0.244698I
b = 0.336362 + 1.325590I
−4.66204 + 2.24789I 1.66012 − 1.37513I
u = 0.462153 + 1.313220I
a = 0.544440 − 0.032729I
b = −0.462153 − 1.313220I
−8.67034 + 0.51327I −6.20283 + 0.66507I
u = 0.462153 − 1.313220I
a = 0.544440 + 0.032729I
b = −0.462153 + 1.313220I
−8.67034 − 0.51327I −6.20283 − 0.66507I
u = 0.24138 + 1.42400I
a = 0.411635 − 0.412221I
b = −0.24138 − 1.42400I
−9.65640 + 4.37744I −5.30226 − 2.74758I
u = 0.24138 − 1.42400I
a = 0.411635 + 0.412221I
b = −0.24138 + 1.42400I
−9.65640 − 4.37744I −5.30226 + 2.74758I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.310244
a = 2.94026
b = 0.310244
−0.313358 0.0548380
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
11
+ 6u
9
− u
8
+ 15u
7
− 4u
6
+ 19u
5
− 6u
4
+ 12u
3
− 3u
2
+ 3u − 1)
· (u
25
+ 9u
23
+ ··· + 2u − 1)(u
48
+ u
47
+ ··· − 114u + 76)
c
2
, c
6
(u
11
+ 6u
9
+ u
8
+ 15u
7
+ 4u
6
+ 19u
5
+ 6u
4
+ 12u
3
+ 3u
2
+ 3u + 1)
· (u
25
+ 9u
23
+ ··· + 2u − 1)(u
48
+ u
47
+ ··· − 114u + 76)
c
3
(u
11
+ 3u
10
+ 5u
9
+ u
8
− 2u
7
+ 6u
6
+ 25u
5
+ 21u
4
+ 4u
3
− 2u
2
+ 3u − 1)
· ((u
12
+ 3u
11
+ ··· + 4u + 1)
4
)(u
25
− 18u
24
+ ··· + 1946u − 188)
c
4
(u
11
− u
10
− 5u
9
+ 4u
8
+ 9u
7
− 3u
6
− 7u
5
− 5u
4
+ 3u
3
+ 5u
2
− u + 1)
· (u
12
− u
11
− 5u
10
+ 4u
9
+ 9u
8
− 4u
7
− 6u
6
− 2u
5
+ 3u
3
+ u
2
+ 1)
4
· (u
25
+ 6u
24
+ ··· + 14u − 4)
c
5
, c
7
(u
11
− u
10
+ u
9
+ 2u
8
− u
7
+ u
6
+ 2u
5
+ 2u
4
+ u
2
+ 2u + 1)
· (u
25
− u
24
+ ··· − 3u − 1)(u
48
+ 13u
47
+ ··· + 54u + 4)
c
9
((u
2
+ u + 1)
24
)(u
11
− 2u
10
+ ··· − u − 1)
· (u
25
− 23u
24
+ ··· + 49152u − 4096)
c
10
, c
11
(u
11
+ u
10
− 5u
9
− 4u
8
+ 9u
7
+ 3u
6
− 7u
5
+ 5u
4
+ 3u
3
− 5u
2
− u − 1)
· (u
12
− u
11
− 5u
10
+ 4u
9
+ 9u
8
− 4u
7
− 6u
6
− 2u
5
+ 3u
3
+ u
2
+ 1)
4
· (u
25
+ 6u
24
+ ··· + 14u − 4)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(y
11
+ 12y
10
+ ··· + 3y −1)(y
25
+ 18y
24
+ ··· + 4y −1)
· (y
48
+ 39y
47
+ ··· + 220932y + 5776)
c
3
(y
11
+ y
10
+ ··· + 5y −1)(y
12
+ y
11
+ ··· − 2y + 1)
4
· (y
25
+ 2y
24
+ ··· + 360428y −35344)
c
4
, c
10
, c
11
(y
11
− 11y
10
+ ··· − 9y −1)(y
12
− 11y
11
+ ··· + 2y + 1)
4
· (y
25
− 22y
24
+ ··· + 140y −16)
c
5
, c
7
(y
11
+ y
10
+ 3y
9
+ 5y
7
− 7y
6
+ 2y
5
− 14y
4
+ 2y
3
− 5y
2
+ 2y −1)
· (y
25
− 5y
24
+ ··· + 19y −1)(y
48
+ 11y
47
+ ··· + 356y + 16)
c
9
(y
2
+ y + 1)
24
· (y
11
− 2y
10
+ 5y
9
− 2y
8
+ 14y
7
− 2y
6
+ 7y
5
− 5y
4
− 3y
2
− y −1)
· (y
25
− y
24
+ ··· + 25165824y −16777216)
22
