11a
250
(K11a
250
)
A knot diagram
1
Linearized knot diagam
4 7 1 2 10 3 5 11 6 8 9
Solving Sequence
2,7
3
6,10
5 8 4 1 9 11
c
2
c
6
c
5
c
7
c
4
c
1
c
9
c
11
c
3
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h15u
9
− 5u
8
+ 43u
7
− 48u
6
+ 65u
5
− 93u
4
+ 16u
3
− 58u
2
+ 11b − 11u − 34,
− 8u
9
− u
8
− 31u
7
+ 19u
6
− 42u
5
+ 65u
4
− 10u
3
+ 61u
2
+ 11a + 22u + 24,
u
10
+ 3u
8
− 2u
7
+ 4u
6
− 5u
5
− u
4
− 4u
3
− 3u
2
− 3u − 1i
I
u
2
= h−3.80757 × 10
52
u
41
− 8.35941 × 10
52
u
40
+ ··· + 3.13757 × 10
53
b − 1.31429 × 10
54
,
4.68086 × 10
52
u
41
+ 1.61851 × 10
53
u
40
+ ··· + 6.27515 × 10
53
a + 2.05544 × 10
54
,
u
42
+ 2u
41
+ ··· + 160u − 32i
I
u
3
= h−u
4
+ u
3
− 2u
2
+ b − 1, u
4
− u
3
+ 2u
2
+ a − u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
v
1
= ha, v
4
+ 2v
3
+ v
2
+ b − 2v −1, v
5
+ 3v
4
+ 4v
3
+ v
2
− v −1i
* 4 irreducible components of dim
C
= 0, with total 62 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
=
h15u
9
−5u
8
+· · ·+11b−34, −8u
9
−u
8
+· · ·+11a+24, u
10
+3u
8
+· · ·−3u−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
6
=
−u
u
3
+ u
a
10
=
8
11
u
9
+
1
11
u
8
+ ··· − 2u −
24
11
−
15
11
u
9
+
5
11
u
8
+ ··· + u +
34
11
a
5
=
−
1
11
u
9
−
7
11
u
8
+ ··· − u −
8
11
−
5
11
u
9
−
2
11
u
8
+ ··· + 2u +
15
11
a
8
=
3
11
u
9
+
10
11
u
8
+ ··· − 3u −
9
11
−
1
11
u
9
+
4
11
u
8
+ ··· − u −
8
11
a
4
=
−
6
11
u
9
−
9
11
u
8
+ ··· + u +
7
11
−
5
11
u
9
−
2
11
u
8
+ ··· + 2u +
15
11
a
1
=
−
6
11
u
9
−
9
11
u
8
+ ··· + u +
7
11
2
11
u
9
−
8
11
u
8
+ ··· + u −
6
11
a
9
=
8
11
u
9
+
1
11
u
8
+ ··· − 2u −
24
11
−
15
11
u
9
+
5
11
u
8
+ ··· + u +
34
11
a
11
=
4
11
u
9
−
16
11
u
8
+ ··· + 2u −
12
11
−
8
11
u
9
−
1
11
u
8
+ ··· + 3u +
35
11
a
11
=
4
11
u
9
−
16
11
u
8
+ ··· + 2u −
12
11
−
8
11
u
9
−
1
11
u
8
+ ··· + 3u +
35
11
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
148
11
u
9
+
20
11
u
8
−
436
11
u
7
+
368
11
u
6
−
612
11
u
5
+
856
11
u
4
+
24
11
u
3
+
584
11
u
2
+ 20u +
290
11
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
10
, c
11
u
10
− 2u
9
− 3u
8
+ 6u
7
+ 4u
6
− 3u
5
− 7u
4
− 2u
3
+ 5u
2
+ u + 1
c
2
, c
5
, c
6
c
9
u
10
+ 3u
8
+ 2u
7
+ 4u
6
+ 5u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
7
u
10
− 5u
9
+ 9u
8
− 14u
7
+ 43u
6
− 86u
5
+ 82u
4
− 44u
3
+ 25u
2
− 8u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
10
, c
11
y
10
− 10y
9
+ ··· + 9y + 1
c
2
, c
5
, c
6
c
9
y
10
+ 6y
9
+ ··· − 3y + 1
c
7
y
10
− 7y
9
+ ··· − 264y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.374996 + 0.969123I
a = 0.826766 − 0.465071I
b = 0.495440 − 0.507246I
−8.15821 + 5.73058I −13.3587 − 7.2455I
u = 0.374996 − 0.969123I
a = 0.826766 + 0.465071I
b = 0.495440 + 0.507246I
−8.15821 − 5.73058I −13.3587 + 7.2455I
u = 0.303403 + 1.209990I
a = −1.85109 − 0.20327I
b = 0.162109 + 1.283500I
−3.86974 + 5.20060I −7.96519 − 6.38440I
u = 0.303403 − 1.209990I
a = −1.85109 + 0.20327I
b = 0.162109 − 1.283500I
−3.86974 − 5.20060I −7.96519 + 6.38440I
u = 1.26706
a = −0.176572
b = 1.46005
−8.35920 −10.3000
u = −0.414534 + 0.541688I
a = 0.458424 + 0.234315I
b = 0.492085 + 0.000051I
0.503273 − 1.263700I 1.66471 + 5.41761I
u = −0.414534 − 0.541688I
a = 0.458424 − 0.234315I
b = 0.492085 − 0.000051I
0.503273 + 1.263700I 1.66471 − 5.41761I
u = −0.70104 + 1.44191I
a = −1.59910 + 0.43476I
b = −0.81865 − 2.97735I
−17.0313 − 13.8030I −11.75052 + 6.72032I
u = −0.70104 − 1.44191I
a = −1.59910 − 0.43476I
b = −0.81865 + 2.97735I
−17.0313 + 13.8030I −11.75052 − 6.72032I
u = −0.392717
a = −2.49343
b = 3.87798
−3.61603 29.1200
5
II. I
u
2
= h−3.81 × 10
52
u
41
− 8.36 × 10
52
u
40
+ · · · + 3.14 × 10
53
b − 1.31 ×
10
54
, 4.68 × 10
52
u
41
+ 1.62 × 10
53
u
40
+ · · · + 6.28 × 10
53
a + 2.06 ×
10
54
, u
42
+ 2u
41
+ · · · + 160u − 32i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
6
=
−u
u
3
+ u
a
10
=
−0.0745936u
41
− 0.257923u
40
+ ··· + 10.8293u − 3.27552
0.121354u
41
+ 0.266429u
40
+ ··· − 19.1733u + 4.18888
a
5
=
−0.0112067u
41
− 0.0509172u
40
+ ··· − 4.57717u + 1.68714
0.00951074u
41
− 0.0118752u
40
+ ··· − 2.00158u + 0.586771
a
8
=
−0.0211940u
41
− 0.0128576u
40
+ ··· + 0.540899u + 0.0730818
−0.0173614u
41
− 0.0459107u
40
+ ··· + 3.62331u − 0.532689
a
4
=
−0.00169594u
41
− 0.0627924u
40
+ ··· − 6.57875u + 2.27391
0.00951074u
41
− 0.0118752u
40
+ ··· − 2.00158u + 0.586771
a
1
=
−0.00169594u
41
− 0.0627924u
40
+ ··· − 6.57875u + 2.27391
0.0149506u
41
− 0.0121379u
40
+ ··· − 7.44824u + 1.31405
a
9
=
−0.0427439u
41
− 0.190593u
40
+ ··· + 5.62950u − 1.94845
0.104819u
41
+ 0.228367u
40
+ ··· − 14.4116u + 2.74560
a
11
=
−0.0436568u
41
− 0.175667u
40
+ ··· − 0.119113u + 0.363250
0.0599628u
41
+ 0.102136u
40
+ ··· − 11.3816u + 1.97870
a
11
=
−0.0436568u
41
− 0.175667u
40
+ ··· − 0.119113u + 0.363250
0.0599628u
41
+ 0.102136u
40
+ ··· − 11.3816u + 1.97870
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.134327u
41
− 0.260180u
40
+ ··· + 20.1282u − 10.6371
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
10
, c
11
u
42
− 5u
41
+ ··· + 4u − 1
c
2
, c
5
, c
6
c
9
u
42
− 2u
41
+ ··· − 160u − 32
c
7
(u
21
+ u
20
+ ··· + 15u − 7)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
10
, c
11
y
42
− 43y
41
+ ··· − 36y + 1
c
2
, c
5
, c
6
c
9
y
42
+ 30y
41
+ ··· + 512y + 1024
c
7
(y
21
− 15y
20
+ ··· − 377y −49)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.301475 + 0.932312I
a = 0.142420 − 0.134100I
b = 0.006905 − 0.449760I
−0.61084 − 1.86636I −1.02291 + 4.31006I
u = −0.301475 − 0.932312I
a = 0.142420 + 0.134100I
b = 0.006905 + 0.449760I
−0.61084 + 1.86636I −1.02291 − 4.31006I
u = −0.718495 + 0.746583I
a = −0.362067 + 0.111337I
b = −0.659494 + 0.166997I
−4.18012 − 2.65523I −7.15894 + 3.42593I
u = −0.718495 − 0.746583I
a = −0.362067 − 0.111337I
b = −0.659494 − 0.166997I
−4.18012 + 2.65523I −7.15894 − 3.42593I
u = 0.908340
a = 0.133290
b = −0.776221
−2.69284 −1.88820
u = 0.757860 + 0.809559I
a = −0.258757 + 0.022774I
b = 1.06122 + 1.11890I
−7.75684 − 1.37799I −11.45551 + 0.55128I
u = 0.757860 − 0.809559I
a = −0.258757 − 0.022774I
b = 1.06122 − 1.11890I
−7.75684 + 1.37799I −11.45551 − 0.55128I
u = 0.143080 + 1.138160I
a = −0.198727 + 1.091130I
b = −0.423136 + 0.904996I
−4.18012 + 2.65523I −7.15894 − 3.42593I
u = 0.143080 − 1.138160I
a = −0.198727 − 1.091130I
b = −0.423136 − 0.904996I
−4.18012 − 2.65523I −7.15894 + 3.42593I
u = 0.124893 + 1.179730I
a = 1.79724 − 0.20938I
b = −0.363469 − 0.817762I
−4.26486 −9.59286 + 0.I
9
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.124893 − 1.179730I
a = 1.79724 + 0.20938I
b = −0.363469 + 0.817762I
−4.26486 −9.59286 + 0.I
u = −0.217762 + 1.215900I
a = −0.204545 + 0.152670I
b = −0.067025 + 0.964677I
−6.20610 − 2.63643I −9.50660 + 3.19431I
u = −0.217762 − 1.215900I
a = −0.204545 − 0.152670I
b = −0.067025 − 0.964677I
−6.20610 + 2.63643I −9.50660 − 3.19431I
u = −1.246850 + 0.095334I
a = −0.20702 + 1.83731I
b = 0.18969 − 3.74340I
−6.20610 + 2.63643I −9.50660 − 3.19431I
u = −1.246850 − 0.095334I
a = −0.20702 − 1.83731I
b = 0.18969 + 3.74340I
−6.20610 − 2.63643I −9.50660 + 3.19431I
u = −0.062851 + 1.267190I
a = −0.44654 − 1.42775I
b = 0.56639 − 1.55859I
−7.75684 − 1.37799I −11.45551 + 0.55128I
u = −0.062851 − 1.267190I
a = −0.44654 + 1.42775I
b = 0.56639 + 1.55859I
−7.75684 + 1.37799I −11.45551 − 0.55128I
u = 0.689788 + 0.085244I
a = 0.10873 − 2.08386I
b = 0.036159 + 1.125850I
−6.62038 − 4.96325I −4.39047 + 4.44885I
u = 0.689788 − 0.085244I
a = 0.10873 + 2.08386I
b = 0.036159 − 1.125850I
−6.62038 + 4.96325I −4.39047 − 4.44885I
u = −0.032710 + 1.316850I
a = −1.48074 + 0.27407I
b = 0.018660 + 0.415709I
−11.38730 − 3.50676I −11.48794 + 0.92420I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.032710 − 1.316850I
a = −1.48074 − 0.27407I
b = 0.018660 − 0.415709I
−11.38730 + 3.50676I −11.48794 − 0.92420I
u = 0.406565 + 1.308170I
a = 1.60327 + 0.37435I
b = 0.143307 − 1.393340I
−10.51330 + 9.23526I −9.80018 − 6.18592I
u = 0.406565 − 1.308170I
a = 1.60327 − 0.37435I
b = 0.143307 + 1.393340I
−10.51330 − 9.23526I −9.80018 + 6.18592I
u = 0.467929 + 1.287910I
a = −0.218735 − 0.332109I
b = −0.383046 − 0.376778I
−6.62038 + 4.96325I −3.00000 − 4.44885I
u = 0.467929 − 1.287910I
a = −0.218735 + 0.332109I
b = −0.383046 + 0.376778I
−6.62038 − 4.96325I −3.00000 + 4.44885I
u = −1.366190 + 0.229409I
a = 0.34075 − 1.54880I
b = −0.20630 + 3.45897I
−13.1353 + 6.4924I −11.37675 − 3.43184I
u = −1.366190 − 0.229409I
a = 0.34075 + 1.54880I
b = −0.20630 − 3.45897I
−13.1353 − 6.4924I −11.37675 + 3.43184I
u = 0.138201 + 0.576503I
a = 0.45895 − 1.80328I
b = −1.144560 + 0.354358I
−2.01761 + 0.71796I −7.31049 + 2.90991I
u = 0.138201 − 0.576503I
a = 0.45895 + 1.80328I
b = −1.144560 − 0.354358I
−2.01761 − 0.71796I −7.31049 − 2.90991I
u = 0.392577 + 0.424549I
a = 0.431238 + 0.140015I
b = −0.94305 − 1.13247I
−2.01761 − 0.71796I −7.31049 − 2.90991I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.392577 − 0.424549I
a = 0.431238 − 0.140015I
b = −0.94305 + 1.13247I
−2.01761 + 0.71796I −7.31049 + 2.90991I
u = 0.532799 + 0.134282I
a = 0.06196 + 2.20487I
b = 0.119696 − 1.020460I
−0.61084 − 1.86636I −1.02291 + 4.31006I
u = 0.532799 − 0.134282I
a = 0.06196 − 2.20487I
b = 0.119696 + 1.020460I
−0.61084 + 1.86636I −1.02291 − 4.31006I
u = −0.484104
a = −1.21008
b = −0.382654
−2.69284 −1.88820
u = −0.48774 + 1.47380I
a = −1.79650 − 0.31481I
b = −0.41376 − 3.12338I
−11.38730 − 3.50676I 0
u = −0.48774 − 1.47380I
a = −1.79650 + 0.31481I
b = −0.41376 + 3.12338I
−11.38730 + 3.50676I 0
u = −0.60041 + 1.43488I
a = 1.85685 − 0.18315I
b = 0.73561 + 3.15502I
−10.51330 − 9.23526I 0
u = −0.60041 − 1.43488I
a = 1.85685 + 0.18315I
b = 0.73561 − 3.15502I
−10.51330 + 9.23526I 0
u = 0.55352 + 1.47008I
a = 0.389275 + 0.429297I
b = 0.861596 + 0.598814I
−13.1353 + 6.4924I 0
u = 0.55352 − 1.47008I
a = 0.389275 − 0.429297I
b = 0.861596 − 0.598814I
−13.1353 − 6.4924I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.38484 + 1.62533I
a = 1.271330 + 0.448418I
b = 0.44405 + 2.70859I
−19.5206 0
u = −0.38484 − 1.62533I
a = 1.271330 − 0.448418I
b = 0.44405 − 2.70859I
−19.5206 0
13
III.
I
u
3
= h−u
4
+u
3
−2u
2
+b−1, u
4
−u
3
+2u
2
+a−u+1, u
5
−u
4
+2u
3
−u
2
+u−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
6
=
−u
u
3
+ u
a
10
=
−u
4
+ u
3
− 2u
2
+ u − 1
u
4
− u
3
+ 2u
2
+ 1
a
5
=
−u
u
3
+ u
a
8
=
−u
3
u
4
− u
3
+ u
2
+ 1
a
4
=
u
3
u
3
+ u
a
1
=
u
3
−u
4
+ u
3
− u
2
− 1
a
9
=
−u
4
+ u
3
− 2u
2
+ u − 1
u
4
− u
3
+ 2u
2
+ 1
a
11
=
−u
4
+ 2u
3
− 2u
2
+ u − 1
u
2
a
11
=
−u
4
+ 2u
3
− 2u
2
+ u − 1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
+ 5u
3
− 7u
2
+ 5u − 12
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
, c
4
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
5
, c
9
u
5
c
6
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
8
(u − 1)
5
c
10
, c
11
(u + 1)
5
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
2
, c
6
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
5
, c
9
y
5
c
7
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
8
, c
10
, c
11
(y −1)
5
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 0.428550 + 1.039280I
b = −0.767660 − 0.216900I
−1.97403 − 1.53058I −6.52924 + 5.40154I
u = −0.339110 − 0.822375I
a = 0.428550 − 1.039280I
b = −0.767660 + 0.216900I
−1.97403 + 1.53058I −6.52924 − 5.40154I
u = 0.766826
a = −1.30408
b = 2.07090
−4.04602 −10.7190
u = 0.455697 + 1.200150I
a = −0.276511 + 0.728237I
b = 0.732208 + 0.471915I
−7.51750 + 4.40083I −11.11126 − 1.16747I
u = 0.455697 − 1.200150I
a = −0.276511 − 0.728237I
b = 0.732208 − 0.471915I
−7.51750 − 4.40083I −11.11126 + 1.16747I
17
IV. I
v
1
= ha, v
4
+ 2v
3
+ v
2
+ b − 2v − 1, v
5
+ 3v
4
+ 4v
3
+ v
2
− v − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
v
0
a
3
=
1
0
a
6
=
v
0
a
10
=
0
−v
4
− 2v
3
− v
2
+ 2v + 1
a
5
=
v
1
a
8
=
v
2
+ v
v
a
4
=
v + 1
1
a
1
=
−v
−1
a
9
=
v
3
+ v
2
− 1
−v
4
− 2v
3
− v
2
+ 2v + 1
a
11
=
−v
3
− v
2
− v
v
a
11
=
−v
3
− v
2
− v
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5v
4
+ 10v
3
+ 8v
2
− 7v − 12
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
6
u
5
c
3
, c
4
(u + 1)
5
c
5
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
7
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
8
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
9
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
10
, c
11
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
(y − 1)
5
c
2
, c
6
y
5
c
5
, c
9
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
7
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1
c
8
, c
10
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.561306 + 0.557752I
a = 0
b = −0.428550 + 1.039280I
−1.97403 + 1.53058I −6.52924 − 5.40154I
v = −0.561306 − 0.557752I
a = 0
b = −0.428550 − 1.039280I
−1.97403 − 1.53058I −6.52924 + 5.40154I
v = 0.588022
a = 0
b = 1.30408
−4.04602 −10.7190
v = −1.23271 + 1.09381I
a = 0
b = 0.276511 − 0.728237I
−7.51750 + 4.40083I −11.11126 − 1.16747I
v = −1.23271 − 1.09381I
a = 0
b = 0.276511 + 0.728237I
−7.51750 − 4.40083I −11.11126 + 1.16747I
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u − 1)
5
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
10
− 2u
9
− 3u
8
+ 6u
7
+ 4u
6
− 3u
5
− 7u
4
− 2u
3
+ 5u
2
+ u + 1)
· (u
42
− 5u
41
+ ··· + 4u − 1)
c
2
, c
5
u
5
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
· (u
10
+ 3u
8
+ 2u
7
+ 4u
6
+ 5u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)
· (u
42
− 2u
41
+ ··· − 160u − 32)
c
3
, c
4
, c
10
c
11
(u + 1)
5
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
· (u
10
− 2u
9
− 3u
8
+ 6u
7
+ 4u
6
− 3u
5
− 7u
4
− 2u
3
+ 5u
2
+ u + 1)
· (u
42
− 5u
41
+ ··· + 4u − 1)
c
6
, c
9
u
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
· (u
10
+ 3u
8
+ 2u
7
+ 4u
6
+ 5u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)
· (u
42
− 2u
41
+ ··· − 160u − 32)
c
7
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
· (u
10
− 5u
9
+ 9u
8
− 14u
7
+ 43u
6
− 86u
5
+ 82u
4
− 44u
3
+ 25u
2
− 8u − 4)
· (u
21
+ u
20
+ ··· + 15u − 7)
2
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
10
, c
11
((y − 1)
5
)(y
5
− 5y
4
+ ··· − y − 1)(y
10
− 10y
9
+ ··· + 9y + 1)
· (y
42
− 43y
41
+ ··· − 36y + 1)
c
2
, c
5
, c
6
c
9
y
5
(y
5
+ 3y
4
+ ··· − y − 1)(y
10
+ 6y
9
+ ··· − 3y + 1)
· (y
42
+ 30y
41
+ ··· + 512y + 1024)
c
7
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
)(y
10
− 7y
9
+ ··· − 264y + 16)
· (y
21
− 15y
20
+ ··· − 377y − 49)
2
23
