12n
0392
(K12n
0392
)
A knot diagram
1
Linearized knot diagam
3 5 7 9 2 11 1 5 4 12 6 4
Solving Sequence
3,5
2 6
1,9
4 10 8 7 12 11
c
2
c
5
c
1
c
4
c
9
c
8
c
7
c
12
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−18u
26
+ 125u
25
+ ··· + 4b − 220, −9u
26
+ 43u
25
+ ··· + 16a + 312, u
27
− 7u
26
+ ··· + 128u − 16i
I
u
2
= h22944250a
7
u
4
− 33783291a
6
u
4
+ ··· + 121889135a + 78299476, 2a
6
u
4
− a
5
u
4
+ ··· − 13a + 5,
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
I
u
3
= h2u
17
+ 4u
16
+ ··· + b + 3, u
17
+ 4u
16
+ ··· + 2a − 1, u
18
+ 2u
17
+ ··· + u + 2i
* 3 irreducible components of dim
C
= 0, with total 85 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−18u
26
+ 125u
25
+ · · · + 4b − 220, −9u
26
+ 43u
25
+ · · · + 16a +
312, u
27
− 7u
26
+ · · · + 128u − 16i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
9
=
0.562500u
26
− 2.68750u
25
+ ··· + 128.250u − 19.5000
9
2
u
26
−
125
4
u
25
+ ··· −
903
2
u + 55
a
4
=
9
16
u
26
−
57
16
u
25
+ ··· −
135
2
u + 10
3
8
u
26
−
19
8
u
25
+ ··· − 62u + 9
a
10
=
75
16
u
26
−
349
16
u
25
+ ··· −
1055
4
u + 42
57
4
u
26
−
333
4
u
25
+ ··· − 918u + 121
a
8
=
0.562500u
26
− 2.68750u
25
+ ··· + 128.250u − 19.5000
21
4
u
26
− 33u
25
+ ··· −
601
2
u + 35
a
7
=
−3.43750u
26
+ 19.5625u
25
+ ··· − 25.2500u + 11.5000
−
5
4
u
26
+
19
2
u
25
+ ··· +
183
2
u − 9
a
12
=
2.12500u
26
− 11.7500u
25
+ ··· − 299.750u + 46.5000
25
8
u
26
−
135
8
u
25
+ ··· −
453
2
u + 34
a
11
=
13
8
u
26
−
35
4
u
25
+ ··· −
111
4
u +
9
2
−
11
8
u
26
+
57
8
u
25
+ ··· +
203
2
u − 16
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5
2
u
26
+
27
2
u
25
+ ··· + 66u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
+ 13u
26
+ ··· + 640u − 256
c
2
, c
5
u
27
+ 7u
26
+ ··· + 128u + 16
c
3
, c
4
, c
8
c
9
u
27
− u
24
+ ··· + u + 1
c
6
, c
11
u
27
− 9u
26
+ ··· − 176u + 32
c
7
u
27
− 2u
26
+ ··· + 3u + 1
c
10
u
27
− 9u
26
+ ··· + 768u + 1024
c
12
u
27
+ 2u
26
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
+ y
26
+ ··· + 1384448y −65536
c
2
, c
5
y
27
+ 13y
26
+ ··· + 640y −256
c
3
, c
4
, c
8
c
9
y
27
+ 26y
25
+ ··· − 5y −1
c
6
, c
11
y
27
+ 9y
26
+ ··· + 768y −1024
c
7
y
27
− 28y
26
+ ··· − 33y −1
c
10
y
27
+ 17y
26
+ ··· + 196608y −1048576
c
12
y
27
+ 44y
26
+ ··· + 43y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.105020 + 1.000790I
a = 0.488571 − 0.501972I
b = −0.442028 − 0.586779I
−1.48211 − 1.37107I −5.86313 + 4.22011I
u = 0.105020 − 1.000790I
a = 0.488571 + 0.501972I
b = −0.442028 + 0.586779I
−1.48211 + 1.37107I −5.86313 − 4.22011I
u = 0.960149 + 0.220645I
a = −1.19030 − 0.88560I
b = −0.40669 − 1.51529I
−3.42062 − 10.51250I −2.02610 + 6.29525I
u = 0.960149 − 0.220645I
a = −1.19030 + 0.88560I
b = −0.40669 + 1.51529I
−3.42062 + 10.51250I −2.02610 − 6.29525I
u = −0.914332 + 0.494714I
a = −0.185333 + 0.579265I
b = 0.383928 + 0.944693I
3.55128 + 0.44727I 1.70598 + 5.83861I
u = −0.914332 − 0.494714I
a = −0.185333 − 0.579265I
b = 0.383928 − 0.944693I
3.55128 − 0.44727I 1.70598 − 5.83861I
u = −0.567653 + 0.888742I
a = 0.362550 − 0.525693I
b = −0.627644 − 0.668484I
−0.19746 − 2.14437I −2.39759 + 4.10548I
u = −0.567653 − 0.888742I
a = 0.362550 + 0.525693I
b = −0.627644 + 0.668484I
−0.19746 + 2.14437I −2.39759 − 4.10548I
u = 0.907665 + 0.211669I
a = 1.28828 + 0.73242I
b = 0.427679 + 1.271000I
−4.63592 − 4.02746I −3.88519 + 2.04862I
u = 0.907665 − 0.211669I
a = 1.28828 − 0.73242I
b = 0.427679 − 1.271000I
−4.63592 + 4.02746I −3.88519 − 2.04862I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.782200 + 0.463303I
a = −0.855769 − 0.381199I
b = 0.482293 − 1.128990I
3.60283 − 2.96457I 0.31391 + 6.24123I
u = 0.782200 − 0.463303I
a = −0.855769 + 0.381199I
b = 0.482293 + 1.128990I
3.60283 + 2.96457I 0.31391 − 6.24123I
u = 0.430772 + 1.068380I
a = −0.168300 + 0.664974I
b = −0.42525 + 1.51993I
−3.69679 + 3.48476I −13.31039 − 2.89782I
u = 0.430772 − 1.068380I
a = −0.168300 − 0.664974I
b = −0.42525 − 1.51993I
−3.69679 − 3.48476I −13.31039 + 2.89782I
u = 0.610468 + 1.088930I
a = −0.267324 − 0.684625I
b = 1.07720 − 1.97646I
1.72849 + 8.21568I −1.80289 − 11.79925I
u = 0.610468 − 1.088930I
a = −0.267324 + 0.684625I
b = 1.07720 + 1.97646I
1.72849 − 8.21568I −1.80289 + 11.79925I
u = −0.812166 + 1.037250I
a = −0.307751 + 0.460402I
b = 0.775885 + 0.808103I
2.00054 − 6.71137I 5.59443 + 7.11847I
u = −0.812166 − 1.037250I
a = −0.307751 − 0.460402I
b = 0.775885 − 0.808103I
2.00054 + 6.71137I 5.59443 − 7.11847I
u = 0.314258 + 1.294970I
a = −0.734896 + 0.716407I
b = −0.460968 − 0.046381I
−9.49935 + 0.08820I −8.66011 − 0.47394I
u = 0.314258 − 1.294970I
a = −0.734896 − 0.716407I
b = −0.460968 + 0.046381I
−9.49935 − 0.08820I −8.66011 + 0.47394I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.568799 + 1.214060I
a = 0.374995 + 1.080590I
b = −1.38523 + 1.89586I
−7.66112 + 9.39517I −6.37444 − 5.16259I
u = 0.568799 − 1.214060I
a = 0.374995 − 1.080590I
b = −1.38523 − 1.89586I
−7.66112 − 9.39517I −6.37444 + 5.16259I
u = 0.583706 + 1.232160I
a = −0.495185 − 1.079000I
b = 1.39179 − 2.00551I
−6.5130 + 16.0862I −4.70147 − 9.04652I
u = 0.583706 − 1.232160I
a = −0.495185 + 1.079000I
b = 1.39179 + 2.00551I
−6.5130 − 16.0862I −4.70147 + 9.04652I
u = 0.295074 + 1.337790I
a = 0.784593 − 0.621842I
b = 0.280592 + 0.245697I
−8.59495 − 6.20996I −7.14590 + 4.78100I
u = 0.295074 − 1.337790I
a = 0.784593 + 0.621842I
b = 0.280592 − 0.245697I
−8.59495 + 6.20996I −7.14590 − 4.78100I
u = 0.472076
a = 1.31174
b = −0.143102
−1.09573 −8.89420
7
II. I
u
2
= h2.29 × 10
7
a
7
u
4
− 3.38 × 10
7
a
6
u
4
+ · · · + 1.22 × 10
8
a + 7.83 ×
10
7
, 2a
6
u
4
− a
5
u
4
+ · · · − 13a + 5, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
9
=
a
−0.152525a
7
u
4
+ 0.224579a
6
u
4
+ ··· − 0.810275a − 0.520506
a
4
=
a
2
u
−0.0581439a
7
u
4
+ 0.207419a
6
u
4
+ ··· + 0.849709a + 0.0905920
a
10
=
a
3
u
2
+ a
−0.0582063a
7
u
4
+ 0.399323a
6
u
4
+ ··· + 0.137201a − 0.457433
a
8
=
a
−0.152525a
7
u
4
+ 0.224579a
6
u
4
+ ··· − 0.810275a − 0.520506
a
7
=
0.00165024a
7
u
4
− 0.254221a
6
u
4
+ ··· − 1.89342a + 0.571381
0.173042a
7
u
4
− 0.0836413a
6
u
4
+ ··· − 1.43436a + 0.112553
a
12
=
−0.0109763a
7
u
4
− 0.288743a
6
u
4
+ ··· − 0.102938a + 0.823334
0.581663a
7
u
4
+ 0.775628a
6
u
4
+ ··· + 0.143633a + 0.940342
a
11
=
−0.823892a
7
u
4
− 0.601307a
6
u
4
+ ··· − 1.11580a + 0.598288
1.04050a
7
u
4
+ 0.372132a
6
u
4
+ ··· − 0.973792a + 1.25647
(ii) Obstruction class = −1
(iii) Cusp Shapes =
431301936
150429427
a
7
u
4
−
176114536
150429427
a
6
u
4
+ ··· +
1120165784
150429427
a −
579968226
150429427
8
(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
5
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
8
c
3
, c
4
, c
8
c
9
u
40
+ u
39
+ ··· − 18u + 1
c
6
, c
11
(u
4
+ u
3
+ u
2
+ 1)
10
c
7
u
40
− 5u
39
+ ··· + 6786u + 4091
c
10
(u
4
− u
3
+ 3u
2
− 2u + 1)
10
c
12
u
40
+ 3u
39
+ ··· + 51794u + 10331
9
(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
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
8
c
3
, c
4
, c
8
c
9
y
40
+ 15y
39
+ ··· − 60y + 1
c
6
, c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
10
c
7
y
40
+ 3y
39
+ ··· − 154444932y + 16736281
c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
10
c
12
y
40
+ 15y
39
+ ··· − 1122430816y + 106729561
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = 0.887800 − 0.823092I
b = −0.602228 − 0.591346I
−2.18504 − 1.63338I −2.34185 − 1.86585I
u = 0.339110 + 0.822375I
a = −0.338775 + 1.230210I
b = 0.404723 + 1.019570I
−2.18504 + 4.69454I −2.34185 − 6.99545I
u = 0.339110 + 0.822375I
a = −0.481121 − 0.490646I
b = 2.29252 + 0.64029I
−2.18504 + 4.69454I −2.34185 − 6.99545I
u = 0.339110 + 0.822375I
a = −1.30373 − 0.59561I
b = 0.27467 − 2.40003I
4.81671 + 0.11547I 1.311623 + 0.478094I
u = 0.339110 + 0.822375I
a = −1.46190 − 0.67259I
b = 1.46239 − 1.70199I
4.81671 + 2.94568I 1.31162 − 9.33939I
u = 0.339110 + 0.822375I
a = 1.35254 + 1.11532I
b = −0.15556 + 1.64570I
4.81671 + 2.94568I 1.31162 − 9.33939I
u = 0.339110 + 0.822375I
a = 0.024114 + 0.200518I
b = −1.84727 − 1.41620I
−2.18504 − 1.63338I −2.34185 − 1.86585I
u = 0.339110 + 0.822375I
a = 1.75976 + 0.59364I
b = −0.648103 + 1.146440I
4.81671 + 0.11547I 1.311623 + 0.478094I
u = 0.339110 − 0.822375I
a = 0.887800 + 0.823092I
b = −0.602228 + 0.591346I
−2.18504 + 1.63338I −2.34185 + 1.86585I
u = 0.339110 − 0.822375I
a = −0.338775 − 1.230210I
b = 0.404723 − 1.019570I
−2.18504 − 4.69454I −2.34185 + 6.99545I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 − 0.822375I
a = −0.481121 + 0.490646I
b = 2.29252 − 0.64029I
−2.18504 − 4.69454I −2.34185 + 6.99545I
u = 0.339110 − 0.822375I
a = −1.30373 + 0.59561I
b = 0.27467 + 2.40003I
4.81671 − 0.11547I 1.311623 − 0.478094I
u = 0.339110 − 0.822375I
a = −1.46190 + 0.67259I
b = 1.46239 + 1.70199I
4.81671 − 2.94568I 1.31162 + 9.33939I
u = 0.339110 − 0.822375I
a = 1.35254 − 1.11532I
b = −0.15556 − 1.64570I
4.81671 − 2.94568I 1.31162 + 9.33939I
u = 0.339110 − 0.822375I
a = 0.024114 − 0.200518I
b = −1.84727 + 1.41620I
−2.18504 + 1.63338I −2.34185 + 1.86585I
u = 0.339110 − 0.822375I
a = 1.75976 − 0.59364I
b = −0.648103 − 1.146440I
4.81671 − 0.11547I 1.311623 − 0.478094I
u = −0.766826
a = 0.549386 + 0.507019I
b = 0.452245 − 0.131425I
2.74473 − 1.41510I 0.34560 + 4.90874I
u = −0.766826
a = 0.549386 − 0.507019I
b = 0.452245 + 0.131425I
2.74473 + 1.41510I 0.34560 − 4.90874I
u = −0.766826
a = 0.078079 + 1.311900I
b = 0.277726 + 0.804944I
2.74473 + 1.41510I 0.34560 − 4.90874I
u = −0.766826
a = 0.078079 − 1.311900I
b = 0.277726 − 0.804944I
2.74473 − 1.41510I 0.34560 + 4.90874I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.766826
a = 1.38939 + 1.09929I
b = 0.58051 + 1.38468I
−4.25702 + 3.16396I −3.30788 − 2.56480I
u = −0.766826
a = 1.38939 − 1.09929I
b = 0.58051 − 1.38468I
−4.25702 − 3.16396I −3.30788 + 2.56480I
u = −0.766826
a = −1.22285 + 1.36610I
b = −0.38676 + 1.48347I
−4.25702 + 3.16396I −3.30788 − 2.56480I
u = −0.766826
a = −1.22285 − 1.36610I
b = −0.38676 − 1.48347I
−4.25702 − 3.16396I −3.30788 + 2.56480I
u = −0.455697 + 1.200150I
a = 0.459956 − 0.714930I
b = −0.596601 − 0.998981I
−0.72676 − 2.98573I −2.91758 − 1.41016I
u = −0.455697 + 1.200150I
a = 0.570507 − 1.025120I
b = −1.59735 − 1.91202I
−7.72850 − 1.23687I −6.57105 + 0.93379I
u = −0.455697 + 1.200150I
a = −0.066285 − 0.811197I
b = −0.418344 − 0.464261I
−0.72676 − 5.81594I −2.91758 + 8.40733I
u = −0.455697 + 1.200150I
a = −0.683595 + 0.994828I
b = 1.39769 + 2.15846I
−7.72850 − 7.56480I −6.57105 + 6.06338I
u = −0.455697 + 1.200150I
a = 1.103220 + 0.549135I
b = 0.411410 − 0.510767I
−7.72850 − 1.23687I −6.57105 + 0.93379I
u = −0.455697 + 1.200150I
a = −0.580054 + 0.496951I
b = 0.11645 + 1.53667I
−0.72676 − 5.81594I −2.91758 + 8.40733I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455697 + 1.200150I
a = −1.038940 − 0.748270I
b = −0.548374 + 0.401816I
−7.72850 − 7.56480I −6.57105 + 6.06338I
u = −0.455697 + 1.200150I
a = 0.002489 + 0.164794I
b = −0.369744 + 0.444563I
−0.72676 − 2.98573I −2.91758 − 1.41016I
u = −0.455697 − 1.200150I
a = 0.459956 + 0.714930I
b = −0.596601 + 0.998981I
−0.72676 + 2.98573I −2.91758 + 1.41016I
u = −0.455697 − 1.200150I
a = 0.570507 + 1.025120I
b = −1.59735 + 1.91202I
−7.72850 + 1.23687I −6.57105 − 0.93379I
u = −0.455697 − 1.200150I
a = −0.066285 + 0.811197I
b = −0.418344 + 0.464261I
−0.72676 + 5.81594I −2.91758 − 8.40733I
u = −0.455697 − 1.200150I
a = −0.683595 − 0.994828I
b = 1.39769 − 2.15846I
−7.72850 + 7.56480I −6.57105 − 6.06338I
u = −0.455697 − 1.200150I
a = 1.103220 − 0.549135I
b = 0.411410 + 0.510767I
−7.72850 + 1.23687I −6.57105 − 0.93379I
u = −0.455697 − 1.200150I
a = −0.580054 − 0.496951I
b = 0.11645 − 1.53667I
−0.72676 + 5.81594I −2.91758 − 8.40733I
u = −0.455697 − 1.200150I
a = −1.038940 + 0.748270I
b = −0.548374 − 0.401816I
−7.72850 + 7.56480I −6.57105 − 6.06338I
u = −0.455697 − 1.200150I
a = 0.002489 − 0.164794I
b = −0.369744 − 0.444563I
−0.72676 + 2.98573I −2.91758 + 1.41016I
14
III.
I
u
3
= h2u
17
+4u
16
+· · ·+b+3, u
17
+4u
16
+· · ·+2a−1, u
18
+2u
17
+· · ·+u+2i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
9
=
−
1
2
u
17
− 2u
16
+ ··· + 2u +
1
2
−2u
17
− 4u
16
+ ··· − 4u
2
− 3
a
4
=
1
2
u
17
+ 2u
16
+ ··· + 5u +
3
2
u
17
+ 2u
16
+ ··· + u − 1
a
10
=
u
17
− u
16
+ ··· − 2u − 7
−4u
17
− 9u
16
+ ··· − 9u − 6
a
8
=
−
1
2
u
17
− 2u
16
+ ··· + 2u +
1
2
−3u
17
− 7u
16
+ ··· − 2u − 5
a
7
=
3
2
u
17
+ u
16
+ ··· + 8u +
3
2
−u
17
− u
16
+ ··· + u + 1
a
12
=
−
1
2
u
17
− 4u
16
+ ··· − 8u −
13
2
−3u
17
− 6u
16
+ ··· − 7u + 1
a
11
=
3
2
u
17
− u
16
+ ··· − 4u −
17
2
−2u
17
− 4u
16
+ ··· − 6u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
17
+ 6u
16
− u
15
+ 42u
14
+ 28u
13
+ 114u
12
+ 103u
11
+
179u
10
+ 184u
9
+ 171u
8
+ 200u
7
+ 124u
6
+ 116u
5
+ 104u
4
+ 17u
3
+ 82u
2
− 12u + 24
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 10u
17
+ ··· − 31u + 4
c
2
u
18
+ 2u
17
+ ··· + u + 2
c
3
, c
8
, c
9
u
18
+ 8u
16
+ ··· + 3u
2
+ 1
c
4
u
18
+ 8u
16
+ ··· + 3u
2
+ 1
c
5
u
18
− 2u
17
+ ··· − u + 2
c
6
u
18
− 2u
17
+ ··· + 5u
2
+ 1
c
7
u
18
+ 2u
17
+ ··· − u
2
+ 1
c
10
u
18
+ 8u
17
+ ··· + 10u + 1
c
11
u
18
+ 2u
17
+ ··· + 5u
2
+ 1
c
12
u
18
− 2u
17
+ ··· − 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 2y
17
+ ··· + 15y + 16
c
2
, c
5
y
18
+ 10y
17
+ ··· + 31y + 4
c
3
, c
4
, c
8
c
9
y
18
+ 16y
17
+ ··· + 6y + 1
c
6
, c
11
y
18
+ 8y
17
+ ··· + 10y + 1
c
7
y
18
+ 12y
17
+ ··· − 2y + 1
c
10
y
18
+ 12y
17
+ ··· + 10y + 1
c
12
y
18
− 8y
17
+ ··· − 6y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.981310 + 0.253960I
a = −0.170640 + 0.664485I
b = 0.361254 + 0.716420I
3.92201 + 1.01481I 9.79163 − 3.00403I
u = −0.981310 − 0.253960I
a = −0.170640 − 0.664485I
b = 0.361254 − 0.716420I
3.92201 − 1.01481I 9.79163 + 3.00403I
u = −0.328225 + 1.000660I
a = −0.082288 − 0.739992I
b = 0.91593 − 1.17432I
−3.31131 − 4.67882I −11.61723 + 7.16331I
u = −0.328225 − 1.000660I
a = −0.082288 + 0.739992I
b = 0.91593 + 1.17432I
−3.31131 + 4.67882I −11.61723 − 7.16331I
u = 0.380092 + 0.983829I
a = 1.38047 + 0.47143I
b = −0.58784 + 1.75887I
3.70424 + 0.63886I −6.05292 − 1.95753I
u = 0.380092 − 0.983829I
a = 1.38047 − 0.47143I
b = −0.58784 − 1.75887I
3.70424 − 0.63886I −6.05292 + 1.95753I
u = −0.283854 + 0.855152I
a = 0.579753 + 0.661116I
b = −1.47974 + 1.16317I
−2.71569 + 2.14208I −12.8091 − 7.3341I
u = −0.283854 − 0.855152I
a = 0.579753 − 0.661116I
b = −1.47974 − 1.16317I
−2.71569 − 2.14208I −12.8091 + 7.3341I
u = 0.544716 + 1.021100I
a = −1.113210 − 0.501413I
b = 0.65241 − 1.74620I
4.89940 + 5.26946I −0.57060 − 6.44056I
u = 0.544716 − 1.021100I
a = −1.113210 + 0.501413I
b = 0.65241 + 1.74620I
4.89940 − 5.26946I −0.57060 + 6.44056I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.582727 + 0.579138I
a = −1.06558 − 1.15811I
b = 0.48001 − 1.75959I
6.26078 − 0.75053I 5.05157 + 1.48269I
u = 0.582727 − 0.579138I
a = −1.06558 + 1.15811I
b = 0.48001 + 1.75959I
6.26078 + 0.75053I 5.05157 − 1.48269I
u = 0.242753 + 0.766873I
a = 1.65221 + 0.85517I
b = −0.73209 + 1.72171I
4.64682 + 2.16850I −1.86140 + 1.62519I
u = 0.242753 − 0.766873I
a = 1.65221 − 0.85517I
b = −0.73209 − 1.72171I
4.64682 − 2.16850I −1.86140 − 1.62519I
u = −0.687587 + 1.152070I
a = −0.252159 + 0.422500I
b = 0.728223 + 1.164210I
1.34269 − 7.01585I −4.35793 + 9.22386I
u = −0.687587 − 1.152070I
a = −0.252159 − 0.422500I
b = 0.728223 − 1.164210I
1.34269 + 7.01585I −4.35793 − 9.22386I
u = −0.469311 + 1.274980I
a = 0.321439 − 0.522684I
b = −0.338152 − 0.733061I
−0.65466 − 3.82739I −1.57397 + 9.48512I
u = −0.469311 − 1.274980I
a = 0.321439 + 0.522684I
b = −0.338152 + 0.733061I
−0.65466 + 3.82739I −1.57397 − 9.48512I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
8
)(u
18
− 10u
17
+ ··· − 31u + 4)
· (u
27
+ 13u
26
+ ··· + 640u − 256)
c
2
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
8
)(u
18
+ 2u
17
+ ··· + u + 2)
· (u
27
+ 7u
26
+ ··· + 128u + 16)
c
3
, c
8
, c
9
(u
18
+ 8u
16
+ ··· + 3u
2
+ 1)(u
27
− u
24
+ ··· + u + 1)
· (u
40
+ u
39
+ ··· − 18u + 1)
c
4
(u
18
+ 8u
16
+ ··· + 3u
2
+ 1)(u
27
− u
24
+ ··· + u + 1)
· (u
40
+ u
39
+ ··· − 18u + 1)
c
5
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
8
)(u
18
− 2u
17
+ ··· − u + 2)
· (u
27
+ 7u
26
+ ··· + 128u + 16)
c
6
((u
4
+ u
3
+ u
2
+ 1)
10
)(u
18
− 2u
17
+ ··· + 5u
2
+ 1)
· (u
27
− 9u
26
+ ··· − 176u + 32)
c
7
(u
18
+ 2u
17
+ ··· − u
2
+ 1)(u
27
− 2u
26
+ ··· + 3u + 1)
· (u
40
− 5u
39
+ ··· + 6786u + 4091)
c
10
((u
4
− u
3
+ 3u
2
− 2u + 1)
10
)(u
18
+ 8u
17
+ ··· + 10u + 1)
· (u
27
− 9u
26
+ ··· + 768u + 1024)
c
11
((u
4
+ u
3
+ u
2
+ 1)
10
)(u
18
+ 2u
17
+ ··· + 5u
2
+ 1)
· (u
27
− 9u
26
+ ··· − 176u + 32)
c
12
(u
18
− 2u
17
+ ··· − 2u + 1)(u
27
+ 2u
26
+ ··· + u + 1)
· (u
40
+ 3u
39
+ ··· + 51794u + 10331)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
8
)(y
18
+ 2y
17
+ ··· + 15y + 16)
· (y
27
+ y
26
+ ··· + 1384448y −65536)
c
2
, c
5
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
8
)(y
18
+ 10y
17
+ ··· + 31y + 4)
· (y
27
+ 13y
26
+ ··· + 640y −256)
c
3
, c
4
, c
8
c
9
(y
18
+ 16y
17
+ ··· + 6y + 1)(y
27
+ 26y
25
+ ··· − 5y −1)
· (y
40
+ 15y
39
+ ··· − 60y + 1)
c
6
, c
11
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
10
)(y
18
+ 8y
17
+ ··· + 10y + 1)
· (y
27
+ 9y
26
+ ··· + 768y −1024)
c
7
(y
18
+ 12y
17
+ ··· − 2y + 1)(y
27
− 28y
26
+ ··· − 33y −1)
· (y
40
+ 3y
39
+ ··· − 154444932y + 16736281)
c
10
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
10
)(y
18
+ 12y
17
+ ··· + 10y + 1)
· (y
27
+ 17y
26
+ ··· + 196608y −1048576)
c
12
(y
18
− 8y
17
+ ··· − 6y + 1)(y
27
+ 44y
26
+ ··· + 43y −1)
· (y
40
+ 15y
39
+ ··· − 1122430816y + 106729561)
21
