11n
123
(K11n
123
)
A knot diagram
1
Linearized knot diagam
6 1 9 8 2 5 10 11 1 5 4
Solving Sequence
5,8 4,11
1 10 7 6 2 3 9
c
4
c
11
c
10
c
7
c
6
c
1
c
2
c
9
c
3
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−2418u
15
− 2313u
14
+ ··· + 1243b − 778, −8755u
15
− 9533u
14
+ ··· + 1243a − 8595,
u
16
+ u
15
+ 5u
14
+ 3u
13
+ 16u
12
+ 7u
11
+ 34u
10
+ 8u
9
+ 46u
8
− 3u
7
+ 40u
6
− 10u
5
+ 24u
4
− 3u
3
+ 8u
2
+ 1i
I
u
2
= h613651112649u
21
+ 1301363271193u
20
+ ··· + 2238186198787b + 596588806112,
− 1570251208513u
21
− 3146564850505u
20
+ ··· + 2238186198787a − 6111907356770,
u
22
+ 2u
21
+ ··· + 3u + 1i
I
u
3
= h−u
5
+ u
4
− 2u
3
+ u
2
+ b − u, −2u
5
+ 2u
4
− 3u
3
+ u
2
+ a − 1, u
6
− u
5
+ 2u
4
− u
3
+ u
2
+ 1i
I
u
4
= h−u
3
+ u
2
+ b − 3u + 1, a, u
4
− u
3
+ 3u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 48 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−2418u
15
− 2313u
14
+ · · · + 1243b − 778, −8755u
15
− 9533u
14
+
· · · + 1243a − 8595, u
16
+ u
15
+ · · · + 8u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
11
=
7.04344u
15
+ 7.66935u
14
+ ··· + 21.9067u + 6.91472
1.94529u
15
+ 1.86082u
14
+ ··· + 8.04344u + 0.625905
a
1
=
7.04344u
15
+ 7.66935u
14
+ ··· + 20.9067u + 6.91472
1.94529u
15
+ 1.86082u
14
+ ··· + 8.04344u + 0.625905
a
10
=
5.09815u
15
+ 5.80853u
14
+ ··· + 13.8632u + 6.28882
1.94529u
15
+ 1.86082u
14
+ ··· + 8.04344u + 0.625905
a
7
=
−3.95414u
15
− 0.515688u
14
+ ··· − 25.6541u + 11.7989
2.08367u
15
+ 2.91874u
14
+ ··· + 4.22767u + 4.98391
a
6
=
−1.87047u
15
+ 2.40306u
14
+ ··· − 21.4264u + 16.7828
2.08367u
15
+ 2.91874u
14
+ ··· + 4.22767u + 4.98391
a
2
=
−4.35800u
15
− 4.21963u
14
+ ··· − 16.1569u − 4.81577
−0.679002u
15
+ 0.390185u
14
+ ··· − 5.57844u + 3.59212
a
3
=
−12.5093u
15
− 14.9574u
14
+ ··· − 35.6838u − 21.5559
−4.06436u
15
− 2.39903u
14
+ ··· − 18.7136u + 3.08930
a
9
=
1.72164u
15
+ 6.67418u
14
+ ··· − 13.6613u + 22.3612
3.59212u
15
+ 4.27112u
14
+ ··· + 9.76508u + 5.57844
a
9
=
1.72164u
15
+ 6.67418u
14
+ ··· − 13.6613u + 22.3612
3.59212u
15
+ 4.27112u
14
+ ··· + 9.76508u + 5.57844
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
7257
1243
u
15
−
4223
1243
u
14
+ ··· −
16867
1243
u +
8997
1243
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
16
− 5u
15
+ ··· − 25u + 4
c
2
, c
6
u
16
+ 11u
15
+ ··· + 15u + 16
c
3
, c
10
u
16
+ 8u
14
+ ··· − u + 1
c
4
, c
11
u
16
− u
15
+ ··· + 8u
2
+ 1
c
7
, c
9
u
16
− 2u
15
+ ··· − 5u + 1
c
8
u
16
− 11u
15
+ ··· − 9u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
16
+ 11y
15
+ ··· + 15y + 16
c
2
, c
6
y
16
− 9y
15
+ ··· + 3679y + 256
c
3
, c
10
y
16
+ 16y
15
+ ··· + 13y + 1
c
4
, c
11
y
16
+ 9y
15
+ ··· + 16y + 1
c
7
, c
9
y
16
+ 20y
15
+ ··· + 89y + 1
c
8
y
16
− 9y
15
+ ··· + 67y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.182868 + 1.082360I
a = −0.245163 + 0.184305I
b = −0.534837 + 1.195060I
0.087550 − 0.115204I 2.02768 − 0.43913I
u = −0.182868 − 1.082360I
a = −0.245163 − 0.184305I
b = −0.534837 − 1.195060I
0.087550 + 0.115204I 2.02768 + 0.43913I
u = 0.153974 + 1.184900I
a = 0.067583 − 1.055900I
b = −0.138027 − 0.297204I
4.72589 − 3.00353I 9.61260 + 1.22526I
u = 0.153974 − 1.184900I
a = 0.067583 + 1.055900I
b = −0.138027 + 0.297204I
4.72589 + 3.00353I 9.61260 − 1.22526I
u = 0.571189 + 0.516899I
a = 0.465400 + 0.095953I
b = 0.600357 + 0.236415I
−0.30256 − 1.83448I 0.83977 + 3.70409I
u = 0.571189 − 0.516899I
a = 0.465400 − 0.095953I
b = 0.600357 − 0.236415I
−0.30256 + 1.83448I 0.83977 − 3.70409I
u = −0.025357 + 0.613269I
a = −1.140780 + 0.093929I
b = −0.456590 + 0.613056I
0.807041 − 1.112270I 4.93277 + 4.22512I
u = −0.025357 − 0.613269I
a = −1.140780 − 0.093929I
b = −0.456590 − 0.613056I
0.807041 + 1.112270I 4.93277 − 4.22512I
u = −0.87363 + 1.12508I
a = −1.102560 − 0.750912I
b = 0.04840 − 1.41972I
−9.63409 + 1.32861I −2.22452 − 1.49647I
u = −0.87363 − 1.12508I
a = −1.102560 + 0.750912I
b = 0.04840 + 1.41972I
−9.63409 − 1.32861I −2.22452 + 1.49647I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.93365 + 1.17761I
a = 1.064180 − 0.515654I
b = 0.34787 − 1.42806I
−5.07602 − 7.48555I 0.37702 + 4.74920I
u = 0.93365 − 1.17761I
a = 1.064180 + 0.515654I
b = 0.34787 + 1.42806I
−5.07602 + 7.48555I 0.37702 − 4.74920I
u = −0.101130 + 0.483106I
a = 4.05859 + 0.78880I
b = 0.727529 + 1.055710I
−4.12337 + 3.39887I 1.84182 + 0.78536I
u = −0.101130 − 0.483106I
a = 4.05859 − 0.78880I
b = 0.727529 − 1.055710I
−4.12337 − 3.39887I 1.84182 − 0.78536I
u = −0.97583 + 1.17333I
a = −1.167260 − 0.382800I
b = −0.59470 − 1.66211I
−9.5135 + 13.5240I −1.40716 − 7.09485I
u = −0.97583 − 1.17333I
a = −1.167260 + 0.382800I
b = −0.59470 + 1.66211I
−9.5135 − 13.5240I −1.40716 + 7.09485I
6
II.
I
u
2
= h6.14×10
11
u
21
+1.30×10
12
u
20
+· · ·+2.24×10
12
b+5.97×10
11
, −1.57×
10
12
u
21
−3.15×10
12
u
20
+· · ·+2.24×10
12
a−6.11×10
12
, u
22
+2u
21
+· · ·+3u+1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
11
=
0.701573u
21
+ 1.40585u
20
+ ··· + 9.05835u + 2.73074
−0.274173u
21
− 0.581437u
20
+ ··· − 5.23195u − 0.266550
a
1
=
u
21
+ 2u
20
+ ··· + 15u + 3
−0.298427u
21
− 0.594145u
20
+ ··· − 4.94165u − 0.269259
a
10
=
0.975746u
21
+ 1.98729u
20
+ ··· + 14.2903u + 2.99729
−0.274173u
21
− 0.581437u
20
+ ··· − 5.23195u − 0.266550
a
7
=
0.959986u
21
+ 1.89743u
20
+ ··· + 13.7253u + 3.00284
−0.378333u
21
− 0.739672u
20
+ ··· − 4.23796u − 0.332002
a
6
=
0.581652u
21
+ 1.15776u
20
+ ··· + 9.48733u + 2.67084
−0.378333u
21
− 0.739672u
20
+ ··· − 4.23796u − 0.332002
a
2
=
0.119474u
21
+ 0.251847u
20
+ ··· + 4.26741u + 2.58228
−0.0953666u
21
− 0.241791u
20
+ ··· − 3.21559u − 0.997831
a
3
=
0.451476u
21
+ 0.537517u
20
+ ··· + 7.60383u − 0.659673
0.0178553u
21
+ 0.0471570u
20
+ ··· − 1.48034u + 0.254377
a
9
=
0.391301u
21
+ 0.842507u
20
+ ··· + 4.87766u + 2.29577
−0.190351u
21
− 0.315251u
20
+ ··· − 2.60967u − 0.375067
a
9
=
0.391301u
21
+ 0.842507u
20
+ ··· + 4.87766u + 2.29577
−0.190351u
21
− 0.315251u
20
+ ··· − 2.60967u − 0.375067
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
2340479983939
2238186198787
u
21
−
5426028325222
2238186198787
u
20
+ ··· −
64839493010449
2238186198787
u −
12900652043582
2238186198787
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
11
+ 2u
10
+ ··· + 4u + 1)
2
c
2
, c
6
(u
11
+ 8u
10
+ ··· − 18u
2
− 1)
2
c
3
, c
10
u
22
+ 10u
20
+ ··· + 265u + 47
c
4
, c
11
u
22
− 2u
21
+ ··· − 3u + 1
c
7
, c
9
u
22
+ 5u
21
+ ··· − 94u + 53
c
8
(u
11
+ 5u
10
+ ··· − 10u − 4)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
11
+ 8y
10
+ ··· − 18y
2
− 1)
2
c
2
, c
6
(y
11
− 8y
10
+ ··· − 36y −1)
2
c
3
, c
10
y
22
+ 20y
21
+ ··· − 5647y + 2209
c
4
, c
11
y
22
+ 12y
20
+ ··· + 21y + 1
c
7
, c
9
y
22
+ 23y
21
+ ··· − 34700y + 2809
c
8
(y
11
− 5y
10
+ ··· + 108y −16)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.459600 + 0.859618I
a = −1.56146 + 0.19719I
b = −1.74595 + 0.63036I
−2.74251 − 5.63735I −0.48609 + 8.17754I
u = 0.459600 − 0.859618I
a = −1.56146 − 0.19719I
b = −1.74595 − 0.63036I
−2.74251 + 5.63735I −0.48609 − 8.17754I
u = −0.670381 + 0.843079I
a = 1.36153 + 0.63867I
b = 0.41764 + 1.61796I
−5.00595 + 2.60776I −5.49826 − 2.04245I
u = −0.670381 − 0.843079I
a = 1.36153 − 0.63867I
b = 0.41764 − 1.61796I
−5.00595 − 2.60776I −5.49826 + 2.04245I
u = 0.783710 + 0.088000I
a = −1.93047 − 0.70159I
b = 0.403600 − 0.151320I
−5.00595 − 2.60776I −5.49826 + 2.04245I
u = 0.783710 − 0.088000I
a = −1.93047 + 0.70159I
b = 0.403600 + 0.151320I
−5.00595 + 2.60776I −5.49826 − 2.04245I
u = 0.816160 + 0.913545I
a = −1.019150 + 0.057227I
b = −0.561626 + 0.977866I
−0.25878 − 3.13682I 5.62912 + 1.87495I
u = 0.816160 − 0.913545I
a = −1.019150 − 0.057227I
b = −0.561626 − 0.977866I
−0.25878 + 3.13682I 5.62912 − 1.87495I
u = −0.475290 + 0.551526I
a = 1.71279 + 0.12691I
b = 0.883704 − 0.005644I
−0.25878 + 3.13682I 5.62912 − 1.87495I
u = −0.475290 − 0.551526I
a = 1.71279 − 0.12691I
b = 0.883704 + 0.005644I
−0.25878 − 3.13682I 5.62912 + 1.87495I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.077760 + 0.707508I
a = 1.108020 − 0.433957I
b = 0.389001 + 1.117020I
−2.74251 + 5.63735I −0.48609 − 8.17754I
u = −1.077760 − 0.707508I
a = 1.108020 + 0.433957I
b = 0.389001 − 1.117020I
−2.74251 − 5.63735I −0.48609 + 8.17754I
u = −1.011520 + 0.825413I
a = −0.633146 − 0.377582I
b = −0.37963 − 1.79002I
−10.59450 + 5.64581I −3.10897 − 3.66343I
u = −1.011520 − 0.825413I
a = −0.633146 + 0.377582I
b = −0.37963 + 1.79002I
−10.59450 − 5.64581I −3.10897 + 3.66343I
u = 1.133190 + 0.778692I
a = 0.533769 − 0.366790I
b = 0.12411 − 1.47210I
−6.33840 −6 − 1.167441 + 0.10I
u = 1.133190 − 0.778692I
a = 0.533769 + 0.366790I
b = 0.12411 + 1.47210I
−6.33840 −6 − 1.167441 + 0.10I
u = 0.35734 + 1.44486I
a = −0.249751 + 0.405356I
b = −0.159367 + 0.805498I
1.20928 − 2.43685I −2.45208 + 7.14380I
u = 0.35734 − 1.44486I
a = −0.249751 − 0.405356I
b = −0.159367 − 0.805498I
1.20928 + 2.43685I −2.45208 − 7.14380I
u = −1.22659 + 0.86184I
a = −0.465716 − 0.441913I
b = 0.27756 − 1.47343I
−10.59450 − 5.64581I −3.10897 + 3.66343I
u = −1.22659 − 0.86184I
a = −0.465716 + 0.441913I
b = 0.27756 + 1.47343I
−10.59450 + 5.64581I −3.10897 − 3.66343I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.088447 + 0.246861I
a = 1.64359 + 2.14516I
b = 0.350965 − 1.259140I
1.20928 + 2.43685I −2.45208 − 7.14380I
u = −0.088447 − 0.246861I
a = 1.64359 − 2.14516I
b = 0.350965 + 1.259140I
1.20928 − 2.43685I −2.45208 + 7.14380I
12
III. I
u
3
= h−u
5
+ u
4
− 2u
3
+ u
2
+ b − u, −2u
5
+ 2u
4
− 3u
3
+ u
2
+ a − 1, u
6
−
u
5
+ 2u
4
− u
3
+ u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
11
=
2u
5
− 2u
4
+ 3u
3
− u
2
+ 1
u
5
− u
4
+ 2u
3
− u
2
+ u
a
1
=
2u
5
− 2u
4
+ 3u
3
− u
2
+ u + 1
u
5
− u
4
+ u
3
− u
2
+ u
a
10
=
u
5
− u
4
+ u
3
− u + 1
u
5
− u
4
+ 2u
3
− u
2
+ u
a
7
=
−u
5
+ 2u
4
− 4u
3
+ 4u
2
− 3u + 1
u
5
− u
4
+ u
3
+ 1
a
6
=
u
4
− 3u
3
+ 4u
2
− 3u + 2
u
5
− u
4
+ u
3
+ 1
a
2
=
−u
5
+ u
4
− 2u
3
+ u
2
− 2
−u
3
+ u
2
− u
a
3
=
−3u
5
+ 5u
4
− 7u
3
+ 3u
2
− 3
−u
5
+ 3u
4
− 4u
3
+ 3u
2
− 2u + 1
a
9
=
2u
5
− u
4
+ 3u
2
− 4u + 3
2u
5
− 2u
4
+ 3u
3
− u
2
+ u + 1
a
9
=
2u
5
− u
4
+ 3u
2
− 4u + 3
2u
5
− 2u
4
+ 3u
3
− u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
4
− 7u
3
+ 12u
2
− 4u + 2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 2u
5
+ 4u
4
− 4u
3
+ 4u
2
− u + 1
c
2
, c
6
u
6
+ 4u
5
+ 8u
4
+ 14u
3
+ 16u
2
+ 7u + 1
c
3
, c
10
u
6
+ u
4
− u
3
+ 2u
2
− u + 1
c
4
, c
11
u
6
− u
5
+ 2u
4
− u
3
+ u
2
+ 1
c
5
u
6
+ 2u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ u + 1
c
7
, c
9
u
6
− 2u
5
+ 5u
4
− 5u
3
+ 4u
2
− 3u + 1
c
8
u
6
− 8u
5
+ 30u
4
− 65u
3
+ 84u
2
− 62u + 21
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
6
+ 4y
5
+ 8y
4
+ 14y
3
+ 16y
2
+ 7y + 1
c
2
, c
6
y
6
− 16y
4
+ 6y
3
+ 76y
2
− 17y + 1
c
3
, c
10
y
6
+ 2y
5
+ 5y
4
+ 5y
3
+ 4y
2
+ 3y + 1
c
4
, c
11
y
6
+ 3y
5
+ 4y
4
+ 5y
3
+ 5y
2
+ 2y + 1
c
7
, c
9
y
6
+ 6y
5
+ 13y
4
+ 5y
3
− 4y
2
− y + 1
c
8
y
6
− 4y
5
+ 28y
4
− 135y
3
+ 256y
2
− 316y + 441
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.800501 + 0.710292I
a = −1.163950 − 0.050182I
b = −0.698934 + 0.620170I
−1.27956 − 3.69612I −2.32375 + 5.61497I
u = 0.800501 − 0.710292I
a = −1.163950 + 0.050182I
b = −0.698934 − 0.620170I
−1.27956 + 3.69612I −2.32375 − 5.61497I
u = 0.155981 + 1.227730I
a = −0.297083 + 1.291660I
b = −0.101839 + 0.801573I
3.99825 − 3.41127I 0.80640 + 5.19600I
u = 0.155981 − 1.227730I
a = −0.297083 − 1.291660I
b = −0.101839 − 0.801573I
3.99825 + 3.41127I 0.80640 − 5.19600I
u = −0.456483 + 0.601395I
a = 2.96104 + 0.19968I
b = 0.800773 + 1.054980I
−4.36362 + 4.05299I −2.48265 − 9.09326I
u = −0.456483 − 0.601395I
a = 2.96104 − 0.19968I
b = 0.800773 − 1.054980I
−4.36362 − 4.05299I −2.48265 + 9.09326I
16
IV. I
u
4
= h−u
3
+ u
2
+ b − 3u + 1, a, u
4
− u
3
+ 3u
2
− u + 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
11
=
0
u
3
− u
2
+ 3u − 1
a
1
=
−u
3
+ u
2
− 3u + 1
u
3
− u
2
+ 2u − 1
a
10
=
−u
3
+ u
2
− 3u + 1
u
3
− u
2
+ 3u − 1
a
7
=
u
3
− u
2
+ 3u − 1
−u
3
+ u
2
− 2u + 1
a
6
=
u
−u
3
+ u
2
− 2u + 1
a
2
=
−u
3
− 2u
u
3
− u
2
+ 2u
a
3
=
1
0
a
9
=
0
u
a
9
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
3
− u
2
+ 2u + 7
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
(u
2
+ u + 1)
2
c
3
, c
4
, c
10
c
11
u
4
− u
3
+ 3u
2
− u + 1
c
5
(u
2
− u + 1)
2
c
7
, c
9
(u + 1)
4
c
8
u
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
10
c
11
y
4
+ 5y
3
+ 9y
2
+ 5y + 1
c
7
, c
9
(y −1)
4
c
8
y
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.148403 + 0.632502I
a = 0
b = −0.35160 + 1.49853I
1.64493 + 2.02988I 7.50000 + 0.86603I
u = 0.148403 − 0.632502I
a = 0
b = −0.35160 − 1.49853I
1.64493 − 2.02988I 7.50000 − 0.86603I
u = 0.35160 + 1.49853I
a = 0
b = −0.148403 + 0.632502I
1.64493 − 2.02988I 7.50000 − 0.86603I
u = 0.35160 − 1.49853I
a = 0
b = −0.148403 − 0.632502I
1.64493 + 2.02988I 7.50000 + 0.86603I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)
2
(u
6
− 2u
5
+ 4u
4
− 4u
3
+ 4u
2
− u + 1)
· ((u
11
+ 2u
10
+ ··· + 4u + 1)
2
)(u
16
− 5u
15
+ ··· − 25u + 4)
c
2
, c
6
(u
2
+ u + 1)
2
(u
6
+ 4u
5
+ 8u
4
+ 14u
3
+ 16u
2
+ 7u + 1)
· ((u
11
+ 8u
10
+ ··· − 18u
2
− 1)
2
)(u
16
+ 11u
15
+ ··· + 15u + 16)
c
3
, c
10
(u
4
− u
3
+ 3u
2
− u + 1)(u
6
+ u
4
− u
3
+ 2u
2
− u + 1)
· (u
16
+ 8u
14
+ ··· − u + 1)(u
22
+ 10u
20
+ ··· + 265u + 47)
c
4
, c
11
(u
4
− u
3
+ 3u
2
− u + 1)(u
6
− u
5
+ 2u
4
− u
3
+ u
2
+ 1)
· (u
16
− u
15
+ ··· + 8u
2
+ 1)(u
22
− 2u
21
+ ··· − 3u + 1)
c
5
(u
2
− u + 1)
2
(u
6
+ 2u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ u + 1)
· ((u
11
+ 2u
10
+ ··· + 4u + 1)
2
)(u
16
− 5u
15
+ ··· − 25u + 4)
c
7
, c
9
(u + 1)
4
(u
6
− 2u
5
+ 5u
4
− 5u
3
+ 4u
2
− 3u + 1)
· (u
16
− 2u
15
+ ··· − 5u + 1)(u
22
+ 5u
21
+ ··· − 94u + 53)
c
8
u
4
(u
6
− 8u
5
+ 30u
4
− 65u
3
+ 84u
2
− 62u + 21)
· ((u
11
+ 5u
10
+ ··· − 10u − 4)
2
)(u
16
− 11u
15
+ ··· − 9u + 2)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
2
+ y + 1)
2
(y
6
+ 4y
5
+ 8y
4
+ 14y
3
+ 16y
2
+ 7y + 1)
· ((y
11
+ 8y
10
+ ··· − 18y
2
− 1)
2
)(y
16
+ 11y
15
+ ··· + 15y + 16)
c
2
, c
6
(y
2
+ y + 1)
2
(y
6
− 16y
4
+ 6y
3
+ 76y
2
− 17y + 1)
· ((y
11
− 8y
10
+ ··· − 36y −1)
2
)(y
16
− 9y
15
+ ··· + 3679y + 256)
c
3
, c
10
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
6
+ 2y
5
+ 5y
4
+ 5y
3
+ 4y
2
+ 3y + 1)
· (y
16
+ 16y
15
+ ··· + 13y + 1)(y
22
+ 20y
21
+ ··· − 5647y + 2209)
c
4
, c
11
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
6
+ 3y
5
+ 4y
4
+ 5y
3
+ 5y
2
+ 2y + 1)
· (y
16
+ 9y
15
+ ··· + 16y + 1)(y
22
+ 12y
20
+ ··· + 21y + 1)
c
7
, c
9
(y −1)
4
(y
6
+ 6y
5
+ 13y
4
+ 5y
3
− 4y
2
− y + 1)
· (y
16
+ 20y
15
+ ··· + 89y + 1)(y
22
+ 23y
21
+ ··· − 34700y + 2809)
c
8
y
4
(y
6
− 4y
5
+ 28y
4
− 135y
3
+ 256y
2
− 316y + 441)
· ((y
11
− 5y
10
+ ··· + 108y −16)
2
)(y
16
− 9y
15
+ ··· + 67y + 4)
22
