11n
112
(K11n
112
)
A knot diagram
1
Linearized knot diagam
5 1 9 7 2 10 3 1 4 6 9
Solving Sequence
1,5
2 3
6,9
8 7 4 11 10
c
1
c
2
c
5
c
8
c
7
c
4
c
11
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
17
− 18u
16
+ ··· + 2b + 10, 5u
17
− 20u
16
+ ··· + 4a + 12, u
18
− 6u
17
+ ··· + 10u − 4i
I
u
2
= h−27u
4
a
3
− 15u
4
a
2
+ ··· + 53a − 207, −u
4
a
3
− 2u
4
a
2
+ ··· + 14a + 29, u
5
+ u
4
− u
2
+ u + 1i
I
u
3
= h−u
10
− u
9
+ 2u
8
+ 3u
7
− 3u
6
− 5u
5
+ 2u
4
+ 3u
3
− 2u
2
+ b − u + 1,
u
10
+ u
9
− 3u
8
− 3u
7
+ 5u
6
+ 6u
5
− 6u
4
− 5u
3
+ 5u
2
+ a + 2u − 3,
u
11
+ u
10
− 2u
9
− 3u
8
+ 3u
7
+ 5u
6
− 2u
5
− 4u
4
+ 2u
3
+ 2u
2
− u − 1i
* 3 irreducible components of dim
C
= 0, with total 49 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
=
h3u
17
−18u
16
+· · ·+2b+10, 5u
17
−20u
16
+· · ·+4a+12, u
18
−6u
17
+· · ·+10u−4i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
−
5
4
u
17
+ 5u
16
+ ··· +
19
4
u − 3
−
3
2
u
17
+ 9u
16
+ ··· +
21
2
u − 5
a
8
=
1
4
u
17
− 4u
16
+ ··· −
23
4
u + 2
−
3
2
u
17
+ 9u
16
+ ··· +
21
2
u − 5
a
7
=
−
5
4
u
17
+ 9u
16
+ ··· +
59
4
u − 9
5
2
u
17
− 15u
16
+ ··· −
39
2
u + 11
a
4
=
−
1
2
u
17
+
5
2
u
16
+ ··· +
5
2
u −
1
2
1
2
u
17
− 2u
16
+ ··· + 2u
2
−
1
2
u
a
11
=
3u
17
−
35
2
u
16
+ ··· − 26u +
31
2
−
7
2
u
17
+ 18u
16
+ ··· +
45
2
u − 10
a
10
=
−
1
2
u
16
+ 2u
15
+ ··· − u +
3
2
3
2
u
17
− 6u
16
+ ··· + 5u
2
−
9
2
u
a
10
=
−
1
2
u
16
+ 2u
15
+ ··· − u +
3
2
3
2
u
17
− 6u
16
+ ··· + 5u
2
−
9
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3u
17
+ 18u
16
− 43u
15
+ 32u
14
+ 66u
13
− 182u
12
+ 133u
11
+
115u
10
− 314u
9
+ 239u
8
+ 3u
7
− 163u
6
+ 156u
5
− 65u
4
− 7u
3
+ 6u
2
+ 24u − 26
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
18
+ 6u
17
+ ··· − 10u − 4
c
2
u
18
+ 6u
17
+ ··· + 44u + 16
c
3
, c
4
, c
9
u
18
− u
17
+ ··· + 2u + 1
c
6
, c
10
u
18
− 12u
17
+ ··· + 144u − 32
c
7
u
18
+ 17u
16
+ ··· − 4u − 1
c
8
, c
11
u
18
+ 2u
17
+ ··· − 15u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
18
− 6y
17
+ ··· − 44y + 16
c
2
y
18
+ 14y
17
+ ··· + 1680y + 256
c
3
, c
4
, c
9
y
18
− 9y
17
+ ··· − 8y + 1
c
6
, c
10
y
18
+ 6y
17
+ ··· − 9984y + 1024
c
7
y
18
+ 34y
17
+ ··· − 6y + 1
c
8
, c
11
y
18
− 30y
17
+ ··· − 93y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.03064
a = −0.576519
b = −1.20658
−0.344722 −12.6080
u = 0.034225 + 0.854848I
a = −0.575049 + 0.286242I
b = 0.667178 + 0.239294I
−1.28974 − 2.24091I −2.04967 + 3.46388I
u = 0.034225 − 0.854848I
a = −0.575049 − 0.286242I
b = 0.667178 − 0.239294I
−1.28974 + 2.24091I −2.04967 − 3.46388I
u = 0.761337 + 0.893787I
a = 1.58989 + 0.60538I
b = −1.84179 + 0.14912I
6.17929 − 0.49659I −2.59772 − 0.34027I
u = 0.761337 − 0.893787I
a = 1.58989 − 0.60538I
b = −1.84179 − 0.14912I
6.17929 + 0.49659I −2.59772 + 0.34027I
u = 0.745128
a = −0.611661
b = 0.116162
−0.993591 −11.3770
u = 0.783872 + 0.987963I
a = −1.19142 − 0.90650I
b = 1.87322 + 0.37011I
3.90675 + 6.64708I −3.39037 − 3.27550I
u = 0.783872 − 0.987963I
a = −1.19142 + 0.90650I
b = 1.87322 − 0.37011I
3.90675 − 6.64708I −3.39037 + 3.27550I
u = 1.172860 + 0.467576I
a = −0.060409 − 0.687195I
b = 0.433362 − 0.027095I
−4.67695 − 2.28427I −4.21274 + 1.51830I
u = 1.172860 − 0.467576I
a = −0.060409 + 0.687195I
b = 0.433362 + 0.027095I
−4.67695 + 2.28427I −4.21274 − 1.51830I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.232750 + 0.324924I
a = 0.257894 + 0.181216I
b = 0.886664 + 0.189258I
−5.50095 + 6.46042I −6.77713 − 7.07518I
u = −1.232750 − 0.324924I
a = 0.257894 − 0.181216I
b = 0.886664 − 0.189258I
−5.50095 − 6.46042I −6.77713 + 7.07518I
u = 1.038010 + 0.783746I
a = 1.12937 + 1.35055I
b = −1.78812 + 0.17611I
5.30009 − 5.74871I −4.51000 + 4.97294I
u = 1.038010 − 0.783746I
a = 1.12937 − 1.35055I
b = −1.78812 − 0.17611I
5.30009 + 5.74871I −4.51000 − 4.97294I
u = 1.063090 + 0.847970I
a = −1.42765 − 0.98450I
b = 1.87096 − 0.72149I
3.01116 − 13.36860I −4.65398 + 7.41233I
u = 1.063090 − 0.847970I
a = −1.42765 + 0.98450I
b = 1.87096 + 0.72149I
3.01116 + 13.36860I −4.65398 − 7.41233I
u = −0.477881 + 0.414788I
a = 0.121456 − 0.765696I
b = −0.556271 − 0.507565I
1.14170 + 1.25649I 2.18406 − 4.14834I
u = −0.477881 − 0.414788I
a = 0.121456 + 0.765696I
b = −0.556271 + 0.507565I
1.14170 − 1.25649I 2.18406 + 4.14834I
6
II. I
u
2
= h−27u
4
a
3
− 15u
4
a
2
+ · · · + 53a − 207, −u
4
a
3
− 2u
4
a
2
+ · · · + 14a +
29, u
5
+ u
4
− u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
a
0.380282a
3
u
4
+ 0.211268a
2
u
4
+ ··· − 0.746479a + 2.91549
a
8
=
−0.380282a
3
u
4
− 0.211268a
2
u
4
+ ··· + 1.74648a − 2.91549
0.380282a
3
u
4
+ 0.211268a
2
u
4
+ ··· − 0.746479a + 2.91549
a
7
=
−0.0140845a
3
u
4
+ 0.436620a
2
u
4
+ ··· + 0.323944a − 1.77465
0.394366a
3
u
4
− 0.225352a
2
u
4
+ ··· − 0.0704225a + 4.69014
a
4
=
0.140845a
3
u
4
− 0.366197a
2
u
4
+ ··· − 0.239437a − 2.25352
−0.0140845a
3
u
4
− 0.563380a
2
u
4
+ ··· + 0.323944a + 6.22535
a
11
=
−0.0845070a
3
u
4
+ 0.619718a
2
u
4
+ ··· − 0.0563380a − 4.64789
−0.0563380a
3
u
4
− 0.253521a
2
u
4
+ ··· + 0.295775a + 4.90141
a
10
=
−0.309859a
3
u
4
+ 0.605634a
2
u
4
+ ··· + 0.126761a − 5.04225
−0.0985915a
3
u
4
− 0.943662a
2
u
4
+ ··· + 0.267606a + 5.57746
a
10
=
−0.309859a
3
u
4
+ 0.605634a
2
u
4
+ ··· + 0.126761a − 5.04225
−0.0985915a
3
u
4
− 0.943662a
2
u
4
+ ··· + 0.267606a + 5.57746
(ii) Obstruction class = −1
(iii) Cusp Shapes =
20
71
u
4
a
3
−
52
71
u
4
a
2
+ ··· −
176
71
a −
462
71
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
5
− u
4
+ u
2
+ u − 1)
4
c
2
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
4
c
3
, c
4
, c
9
u
20
+ u
19
+ ··· − 78u + 43
c
6
, c
10
(u
2
+ u + 1)
10
c
7
u
20
+ u
19
+ ··· + 860u + 1849
c
8
, c
11
u
20
+ 3u
19
+ ··· + 982u + 169
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y − 1)
4
c
2
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y − 1)
4
c
3
, c
4
, c
9
y
20
− 9y
19
+ ··· − 12276y + 1849
c
6
, c
10
(y
2
+ y + 1)
10
c
7
y
20
+ 15y
19
+ ··· − 22905412y + 3418801
c
8
, c
11
y
20
− 13y
19
+ ··· + 46972y + 28561
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758138 + 0.584034I
a = 0.749890 − 0.621375I
b = −0.08602 + 1.68144I
−3.11500 − 4.24385I −5.11432 + 7.68699I
u = 0.758138 + 0.584034I
a = −0.566965 + 0.314182I
b = 0.882926 + 0.389982I
−3.11500 − 0.18409I −5.11432 + 0.75879I
u = 0.758138 + 0.584034I
a = −0.06960 − 1.47984I
b = 0.362793 − 0.374311I
−3.11500 − 4.24385I −5.11432 + 7.68699I
u = 0.758138 + 0.584034I
a = −1.59288 + 0.14727I
b = 0.110691 − 1.283240I
−3.11500 − 0.18409I −5.11432 + 0.75879I
u = 0.758138 − 0.584034I
a = 0.749890 + 0.621375I
b = −0.08602 − 1.68144I
−3.11500 + 4.24385I −5.11432 − 7.68699I
u = 0.758138 − 0.584034I
a = −0.566965 − 0.314182I
b = 0.882926 − 0.389982I
−3.11500 + 0.18409I −5.11432 − 0.75879I
u = 0.758138 − 0.584034I
a = −0.06960 + 1.47984I
b = 0.362793 + 0.374311I
−3.11500 + 4.24385I −5.11432 − 7.68699I
u = 0.758138 − 0.584034I
a = −1.59288 − 0.14727I
b = 0.110691 + 1.283240I
−3.11500 + 0.18409I −5.11432 − 0.75879I
u = −0.935538 + 0.903908I
a = −0.917729 + 0.847158I
b = 1.52925 − 0.42833I
6.02349 + 1.30186I −4.08126 + 1.10182I
u = −0.935538 + 0.903908I
a = 1.18464 − 0.79636I
b = −2.04795 − 0.07963I
6.02349 + 5.36163I −4.08126 − 5.82638I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.935538 + 0.903908I
a = 1.16701 − 1.04206I
b = −1.78733 − 0.41229I
6.02349 + 1.30186I −4.08126 + 1.10182I
u = −0.935538 + 0.903908I
a = −1.47807 + 0.67792I
b = 1.44900 + 0.72345I
6.02349 + 5.36163I −4.08126 − 5.82638I
u = −0.935538 − 0.903908I
a = −0.917729 − 0.847158I
b = 1.52925 + 0.42833I
6.02349 − 1.30186I −4.08126 − 1.10182I
u = −0.935538 − 0.903908I
a = 1.18464 + 0.79636I
b = −2.04795 + 0.07963I
6.02349 − 5.36163I −4.08126 + 5.82638I
u = −0.935538 − 0.903908I
a = 1.16701 + 1.04206I
b = −1.78733 + 0.41229I
6.02349 − 1.30186I −4.08126 − 1.10182I
u = −0.935538 − 0.903908I
a = −1.47807 − 0.67792I
b = 1.44900 − 0.72345I
6.02349 − 5.36163I −4.08126 + 5.82638I
u = −0.645200
a = −1.90553 + 0.26854I
b = 1.09670 + 1.08254I
−5.81699 − 2.02988I −13.60884 + 3.46410I
u = −0.645200
a = −1.90553 − 0.26854I
b = 1.09670 − 1.08254I
−5.81699 + 2.02988I −13.60884 − 3.46410I
u = −0.645200
a = 2.92924 + 1.50457I
b = −0.010057 + 0.799590I
−5.81699 − 2.02988I −13.60884 + 3.46410I
u = −0.645200
a = 2.92924 − 1.50457I
b = −0.010057 − 0.799590I
−5.81699 + 2.02988I −13.60884 − 3.46410I
11
III.
I
u
3
= h−u
10
− u
9
+ · · · + b + 1, u
10
+ u
9
+ · · · + a − 3, u
11
+ u
10
+ · · · − u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
9
=
−u
10
− u
9
+ 3u
8
+ 3u
7
− 5u
6
− 6u
5
+ 6u
4
+ 5u
3
− 5u
2
− 2u + 3
u
10
+ u
9
− 2u
8
− 3u
7
+ 3u
6
+ 5u
5
− 2u
4
− 3u
3
+ 2u
2
+ u − 1
a
8
=
−2u
10
− 2u
9
+ 5u
8
+ 6u
7
− 8u
6
− 11u
5
+ 8u
4
+ 8u
3
− 7u
2
− 3u + 4
u
10
+ u
9
− 2u
8
− 3u
7
+ 3u
6
+ 5u
5
− 2u
4
− 3u
3
+ 2u
2
+ u − 1
a
7
=
−u
10
− u
9
+ 3u
8
+ 3u
7
− 5u
6
− 6u
5
+ 5u
4
+ 5u
3
− 4u
2
− 2u + 2
u
9
− 2u
7
− u
6
+ 4u
5
+ 2u
4
− 3u
3
− u
2
+ 2u
a
4
=
2u
10
+ u
9
− 5u
8
− 4u
7
+ 9u
6
+ 7u
5
− 9u
4
− 6u
3
+ 7u
2
+ 2u − 3
−u
10
− u
9
+ 2u
8
+ 3u
7
− 3u
6
− 5u
5
+ 2u
4
+ 4u
3
− u
2
− u + 1
a
11
=
2u
10
+ u
9
− 5u
8
− 3u
7
+ 9u
6
+ 5u
5
− 9u
4
− 3u
3
+ 8u
2
− 2
−u
10
+ 3u
8
+ u
7
− 5u
6
− 2u
5
+ 5u
4
+ 2u
3
− 3u
2
+ 1
a
10
=
u
10
− 3u
8
− u
7
+ 6u
6
+ 2u
5
− 6u
4
− 2u
3
+ 5u
2
− 1
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 3u
3
− u
a
10
=
u
10
− 3u
8
− u
7
+ 6u
6
+ 2u
5
− 6u
4
− 2u
3
+ 5u
2
− 1
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 3u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
10
+ u
9
+ u
8
− u
7
+ u
6
+ u
5
+ 2u
4
+ u
3
+ 4u
2
+ u − 6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
+ u
10
− 2u
9
− 3u
8
+ 3u
7
+ 5u
6
− 2u
5
− 4u
4
+ 2u
3
+ 2u
2
− u − 1
c
2
u
11
+ 5u
10
+ ··· + 5u + 1
c
3
u
11
+ u
10
− 4u
9
− 4u
8
+ 6u
7
+ 6u
6
− 2u
5
− 3u
4
− 4u
3
− u
2
+ 4u + 1
c
4
, c
9
u
11
− u
10
− 4u
9
+ 4u
8
+ 6u
7
− 6u
6
− 2u
5
+ 3u
4
− 4u
3
+ u
2
+ 4u − 1
c
5
u
11
− u
10
− 2u
9
+ 3u
8
+ 3u
7
− 5u
6
− 2u
5
+ 4u
4
+ 2u
3
− 2u
2
− u + 1
c
6
u
11
− u
10
+ 3u
9
+ u
8
+ u
7
+ 6u
6
+ 4u
4
+ 4u
3
+ u
2
+ 2u + 1
c
7
u
11
− u
9
− 5u
8
− 9u
7
+ 7u
6
+ 24u
5
− 3u
4
+ 6u
3
+ 6u
2
+ 2u + 1
c
8
u
11
+ 2u
10
+ u
9
+ 4u
8
+ 4u
7
+ 6u
5
+ u
4
+ u
3
+ 3u
2
− u + 1
c
10
u
11
+ u
10
+ 3u
9
− u
8
+ u
7
− 6u
6
− 4u
4
+ 4u
3
− u
2
+ 2u − 1
c
11
u
11
− 2u
10
+ u
9
− 4u
8
+ 4u
7
+ 6u
5
− u
4
+ u
3
− 3u
2
− u − 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
11
− 5y
10
+ ··· + 5y − 1
c
2
y
11
+ 7y
10
+ ··· − 7y − 1
c
3
, c
4
, c
9
y
11
− 9y
10
+ ··· + 18y − 1
c
6
, c
10
y
11
+ 5y
10
+ ··· + 2y − 1
c
7
y
11
− 2y
10
+ ··· − 8y − 1
c
8
, c
11
y
11
− 2y
10
+ ··· − 5y − 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.890464
a = 0.557576
b = 0.938618
0.241342 1.70090
u = −1.050460 + 0.434817I
a = −0.953762 − 0.951226I
b = −0.325584 + 0.585988I
−6.50834 + 4.79164I −9.43330 − 4.58871I
u = −1.050460 − 0.434817I
a = −0.953762 + 0.951226I
b = −0.325584 − 0.585988I
−6.50834 − 4.79164I −9.43330 + 4.58871I
u = 0.568178 + 0.624341I
a = −0.810571 − 0.115740I
b = −0.251884 − 1.139160I
−4.04644 − 2.66477I −7.34246 + 3.51719I
u = 0.568178 − 0.624341I
a = −0.810571 + 0.115740I
b = −0.251884 + 1.139160I
−4.04644 + 2.66477I −7.34246 − 3.51719I
u = 1.087470 + 0.533146I
a = 0.213335 + 0.242827I
b = 0.012610 + 0.843323I
−5.77248 − 1.97523I −11.11734 + 0.94758I
u = 1.087470 − 0.533146I
a = 0.213335 − 0.242827I
b = 0.012610 − 0.843323I
−5.77248 + 1.97523I −11.11734 − 0.94758I
u = −0.931392 + 0.876271I
a = −1.23579 + 0.88821I
b = 1.69939 + 0.19552I
6.35313 + 3.25083I −3.04144 − 2.67262I
u = −0.931392 − 0.876271I
a = −1.23579 − 0.88821I
b = 1.69939 − 0.19552I
6.35313 − 3.25083I −3.04144 + 2.67262I
u = −0.619026 + 0.353653I
a = 2.00800 + 1.43553I
b = −0.603838 − 0.687137I
−4.95095 − 1.33491I −5.91593 − 1.31203I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.619026 − 0.353653I
a = 2.00800 − 1.43553I
b = −0.603838 + 0.687137I
−4.95095 + 1.33491I −5.91593 + 1.31203I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− u
4
+ u
2
+ u − 1)
4
· (u
11
+ u
10
− 2u
9
− 3u
8
+ 3u
7
+ 5u
6
− 2u
5
− 4u
4
+ 2u
3
+ 2u
2
− u − 1)
· (u
18
+ 6u
17
+ ··· − 10u − 4)
c
2
((u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
4
)(u
11
+ 5u
10
+ ··· + 5u + 1)
· (u
18
+ 6u
17
+ ··· + 44u + 16)
c
3
(u
11
+ u
10
− 4u
9
− 4u
8
+ 6u
7
+ 6u
6
− 2u
5
− 3u
4
− 4u
3
− u
2
+ 4u + 1)
· (u
18
− u
17
+ ··· + 2u + 1)(u
20
+ u
19
+ ··· − 78u + 43)
c
4
, c
9
(u
11
− u
10
− 4u
9
+ 4u
8
+ 6u
7
− 6u
6
− 2u
5
+ 3u
4
− 4u
3
+ u
2
+ 4u − 1)
· (u
18
− u
17
+ ··· + 2u + 1)(u
20
+ u
19
+ ··· − 78u + 43)
c
5
(u
5
− u
4
+ u
2
+ u − 1)
4
· (u
11
− u
10
− 2u
9
+ 3u
8
+ 3u
7
− 5u
6
− 2u
5
+ 4u
4
+ 2u
3
− 2u
2
− u + 1)
· (u
18
+ 6u
17
+ ··· − 10u − 4)
c
6
((u
2
+ u + 1)
10
)(u
11
− u
10
+ ··· + 2u + 1)
· (u
18
− 12u
17
+ ··· + 144u − 32)
c
7
(u
11
− u
9
− 5u
8
− 9u
7
+ 7u
6
+ 24u
5
− 3u
4
+ 6u
3
+ 6u
2
+ 2u + 1)
· (u
18
+ 17u
16
+ ··· − 4u − 1)(u
20
+ u
19
+ ··· + 860u + 1849)
c
8
(u
11
+ 2u
10
+ u
9
+ 4u
8
+ 4u
7
+ 6u
5
+ u
4
+ u
3
+ 3u
2
− u + 1)
· (u
18
+ 2u
17
+ ··· − 15u − 1)(u
20
+ 3u
19
+ ··· + 982u + 169)
c
10
((u
2
+ u + 1)
10
)(u
11
+ u
10
+ ··· + 2u − 1)
· (u
18
− 12u
17
+ ··· + 144u − 32)
c
11
(u
11
− 2u
10
+ u
9
− 4u
8
+ 4u
7
+ 6u
5
− u
4
+ u
3
− 3u
2
− u − 1)
· (u
18
+ 2u
17
+ ··· − 15u − 1)(u
20
+ 3u
19
+ ··· + 982u + 169)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
5
− y
4
+ 4y
3
− 3y
2
+ 3y − 1)
4
)(y
11
− 5y
10
+ ··· + 5y − 1)
· (y
18
− 6y
17
+ ··· − 44y + 16)
c
2
((y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y − 1)
4
)(y
11
+ 7y
10
+ ··· − 7y − 1)
· (y
18
+ 14y
17
+ ··· + 1680y + 256)
c
3
, c
4
, c
9
(y
11
− 9y
10
+ ··· + 18y − 1)(y
18
− 9y
17
+ ··· − 8y + 1)
· (y
20
− 9y
19
+ ··· − 12276y + 1849)
c
6
, c
10
((y
2
+ y + 1)
10
)(y
11
+ 5y
10
+ ··· + 2y − 1)
· (y
18
+ 6y
17
+ ··· − 9984y + 1024)
c
7
(y
11
− 2y
10
+ ··· − 8y − 1)(y
18
+ 34y
17
+ ··· − 6y + 1)
· (y
20
+ 15y
19
+ ··· − 22905412y + 3418801)
c
8
, c
11
(y
11
− 2y
10
+ ··· − 5y − 1)(y
18
− 30y
17
+ ··· − 93y + 1)
· (y
20
− 13y
19
+ ··· + 46972y + 28561)
18
