11a
198
(K11a
198
)
A knot diagram
1
Linearized knot diagam
6 1 8 11 10 2 4 3 5 9 7
Solving Sequence
4,7
8 3
1,9
2 6 11 5 10
c
7
c
3
c
8
c
2
c
6
c
11
c
4
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
16
+ 9u
15
+ ··· + 4b − 2, 5u
16
+ 19u
15
+ ··· + 8a − 18, u
17
+ 5u
16
+ ··· − 16u − 4i
I
u
2
= hu
23
a + 101u
23
+ ··· − a − 645, 5u
23
a + 6u
23
+ ··· + a + 15, u
24
− 2u
23
+ ··· − 13u
2
+ 1i
I
u
3
= h−au + 2b − a, a
2
+ au + a + 2u, u
2
+ 1i
I
u
4
= hau + 2b − a + u − 1, a
2
+ au + a − u, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 73 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
16
+9u
15
+· · ·+4b−2, 5u
16
+19u
15
+· · ·+8a−18, u
17
+5u
16
+· · ·−16u−4i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
3
=
−u
u
3
+ u
a
1
=
−
5
8
u
16
−
19
8
u
15
+ ··· +
43
8
u +
9
4
−
3
4
u
16
−
9
4
u
15
+ ··· +
15
4
u +
1
2
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−
1
8
u
16
−
3
8
u
15
+ ··· −
9
8
u −
1
4
−
1
4
u
16
−
3
4
u
15
+ ··· +
9
4
u +
1
2
a
6
=
7
8
u
16
+
29
8
u
15
+ ··· −
49
8
u −
3
4
−
3
4
u
16
−
15
4
u
15
+ ··· +
65
4
u +
11
2
a
11
=
1
8
u
16
−
1
8
u
15
+ ··· +
13
8
u +
7
4
−
3
4
u
16
−
9
4
u
15
+ ··· +
15
4
u +
1
2
a
5
=
−
3
8
u
16
−
13
8
u
15
+ ··· +
37
8
u +
5
4
1
4
u
16
+
5
4
u
15
+ ··· −
15
4
u −
3
2
a
10
=
7
8
u
16
+
25
8
u
15
+ ··· −
93
8
u −
15
4
−
3
4
u
16
−
11
4
u
15
+ ··· +
23
4
u +
5
2
a
10
=
7
8
u
16
+
25
8
u
15
+ ··· −
93
8
u −
15
4
−
3
4
u
16
−
11
4
u
15
+ ··· +
23
4
u +
5
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
16
− 5u
15
− 19u
14
− 54u
13
− 118u
12
− 225u
11
− 344u
10
−
469u
9
− 531u
8
− 526u
7
− 437u
6
− 296u
5
− 150u
4
− 37u
3
+ 20u
2
+ 28u + 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
u
17
− 5u
15
+ ··· + u + 1
c
2
, c
10
u
17
+ 10u
16
+ ··· + 3u + 1
c
3
, c
7
, c
8
u
17
− 5u
16
+ ··· − 16u + 4
c
4
, c
11
u
17
+ 7u
15
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
17
− 10y
16
+ ··· + 3y −1
c
2
, c
10
y
17
− 2y
16
+ ··· − 5y −1
c
3
, c
7
, c
8
y
17
+ 15y
16
+ ··· + 40y −16
c
4
, c
11
y
17
+ 14y
16
+ ··· + 7y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.384204 + 0.955896I
a = −0.642349 − 0.376214I
b = −0.201052 − 0.409172I
−4.00659 + 3.27252I −10.51806 − 4.95844I
u = 0.384204 − 0.955896I
a = −0.642349 + 0.376214I
b = −0.201052 + 0.409172I
−4.00659 − 3.27252I −10.51806 + 4.95844I
u = −0.890867 + 0.377667I
a = −0.539314 − 0.319140I
b = 0.62144 − 1.41173I
−3.61361 − 10.59010I −4.60527 + 8.92878I
u = −0.890867 − 0.377667I
a = −0.539314 + 0.319140I
b = 0.62144 + 1.41173I
−3.61361 + 10.59010I −4.60527 − 8.92878I
u = −0.660302 + 0.842733I
a = −1.022380 − 0.230270I
b = −0.366663 − 1.179130I
−5.05206 + 5.24154I −7.63274 − 4.49417I
u = −0.660302 − 0.842733I
a = −1.022380 + 0.230270I
b = −0.366663 + 1.179130I
−5.05206 − 5.24154I −7.63274 + 4.49417I
u = −0.244707 + 1.043020I
a = 0.676808 − 0.521819I
b = 0.696756 + 0.141517I
−0.92388 − 2.05590I −0.93009 + 3.10857I
u = −0.244707 − 1.043020I
a = 0.676808 + 0.521819I
b = 0.696756 − 0.141517I
−0.92388 + 2.05590I −0.93009 − 3.10857I
u = −0.650467 + 0.269191I
a = 0.586208 + 0.134225I
b = −0.652154 + 0.703929I
1.27984 − 1.28287I 3.35042 + 1.93548I
u = −0.650467 − 0.269191I
a = 0.586208 − 0.134225I
b = −0.652154 − 0.703929I
1.27984 + 1.28287I 3.35042 − 1.93548I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.24757 + 1.43191I
a = −0.14316 − 1.60229I
b = 0.77487 − 1.21986I
−4.23745 − 4.56036I −1.76092 + 2.27650I
u = −0.24757 − 1.43191I
a = −0.14316 + 1.60229I
b = 0.77487 + 1.21986I
−4.23745 + 4.56036I −1.76092 − 2.27650I
u = 0.502705
a = 0.826549
b = 0.276508
−1.52550 −5.61090
u = −0.34289 + 1.49249I
a = 0.42197 + 1.89700I
b = −0.74695 + 1.66508I
−9.6338 − 15.0660I −7.10421 + 9.07102I
u = −0.34289 − 1.49249I
a = 0.42197 − 1.89700I
b = −0.74695 − 1.66508I
−9.6338 + 15.0660I −7.10421 − 9.07102I
u = −0.09876 + 1.57175I
a = 0.498949 + 1.308380I
b = −0.264501 + 1.188070I
−13.35050 + 2.91507I −10.99366 − 2.99630I
u = −0.09876 − 1.57175I
a = 0.498949 − 1.308380I
b = −0.264501 − 1.188070I
−13.35050 − 2.91507I −10.99366 + 2.99630I
6
II. I
u
2
= hu
23
a + 101u
23
+ · · · − a − 645, 5u
23
a + 6u
23
+ · · · + a + 15, u
24
−
2u
23
+ · · · − 13u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
3
=
−u
u
3
+ u
a
1
=
a
−0.00367647au
23
− 0.371324u
23
+ ··· + 0.00367647a + 2.37132
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−0.128676au
23
+ 0.503676u
23
+ ··· + 1.62868a + 3.49632
0.613971au
23
+ 0.0110294u
23
+ ··· − 0.613971a + 0.488971
a
6
=
−0.00367647au
23
− 2.37132u
23
+ ··· − 0.996324a − 0.128676
0.00367647au
23
− 0.128676u
23
+ ··· − 0.00367647a − 0.371324
a
11
=
0.00367647au
23
+ 0.371324u
23
+ ··· + 0.996324a − 2.37132
−0.00367647au
23
− 0.371324u
23
+ ··· + 0.00367647a + 2.37132
a
5
=
−0.371324au
23
+ 0.496324u
23
+ ··· + 2.37132a + 2.00368
−
1
2
u
20
+
1
2
u
19
+ ··· − 2u +
1
2
a
10
=
0.0110294au
23
− 0.386029u
23
+ ··· + 0.988971a − 0.613971
−0.0147059au
23
+ 0.0147059u
23
+ ··· + 0.0147059a + 1.48529
a
10
=
0.0110294au
23
− 0.386029u
23
+ ··· + 0.988971a − 0.613971
−0.0147059au
23
+ 0.0147059u
23
+ ··· + 0.0147059a + 1.48529
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
23
+ 4u
22
− 32u
21
+ 52u
20
− 208u
19
+ 280u
18
− 720u
17
+
808u
16
− 1448u
15
+ 1360u
14
− 1760u
13
+ 1424u
12
− 1440u
11
+ 1116u
10
− 1084u
9
+
820u
8
− 730u
7
+ 352u
6
− 148u
5
− 88u
4
+ 100u
3
− 76u
2
+ 8u + 8
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
u
48
− u
47
+ ··· − 2u + 1
c
2
, c
10
u
48
+ 23u
47
+ ··· + 2u + 1
c
3
, c
7
, c
8
(u
24
+ 2u
23
+ ··· − 13u
2
+ 1)
2
c
4
, c
11
u
48
− 3u
47
+ ··· − 1432u + 517
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
48
− 23y
47
+ ··· − 2y + 1
c
2
, c
10
y
48
+ 5y
47
+ ··· − 30y + 1
c
3
, c
7
, c
8
(y
24
+ 24y
23
+ ··· − 26y + 1)
2
c
4
, c
11
y
48
+ 13y
47
+ ··· − 341422y + 267289
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.761584 + 0.575116I
a = −1.062990 − 0.130786I
b = −0.020543 − 0.903159I
−5.05945 − 2.59591I −7.61304 + 3.04974I
u = −0.761584 + 0.575116I
a = −0.203429 − 0.419558I
b = 0.349703 − 1.187750I
−5.05945 − 2.59591I −7.61304 + 3.04974I
u = −0.761584 − 0.575116I
a = −1.062990 + 0.130786I
b = −0.020543 + 0.903159I
−5.05945 + 2.59591I −7.61304 − 3.04974I
u = −0.761584 − 0.575116I
a = −0.203429 + 0.419558I
b = 0.349703 + 1.187750I
−5.05945 + 2.59591I −7.61304 − 3.04974I
u = 0.186022 + 1.063970I
a = 0.916877 − 0.413619I
b = 0.982102 − 0.768293I
−1.95017 − 2.09169I −5.42289 + 2.15037I
u = 0.186022 + 1.063970I
a = −0.933580 − 1.021610I
b = −0.389494 − 0.003420I
−1.95017 − 2.09169I −5.42289 + 2.15037I
u = 0.186022 − 1.063970I
a = 0.916877 + 0.413619I
b = 0.982102 + 0.768293I
−1.95017 + 2.09169I −5.42289 − 2.15037I
u = 0.186022 − 1.063970I
a = −0.933580 + 1.021610I
b = −0.389494 + 0.003420I
−1.95017 + 2.09169I −5.42289 − 2.15037I
u = 0.772868 + 0.366845I
a = 0.536799 − 0.512090I
b = −0.638086 − 1.241260I
−1.01177 + 5.79366I −1.10840 − 5.84891I
u = 0.772868 + 0.366845I
a = −0.655414 + 0.003636I
b = 0.640538 + 0.994553I
−1.01177 + 5.79366I −1.10840 − 5.84891I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772868 − 0.366845I
a = 0.536799 + 0.512090I
b = −0.638086 + 1.241260I
−1.01177 − 5.79366I −1.10840 + 5.84891I
u = 0.772868 − 0.366845I
a = −0.655414 − 0.003636I
b = 0.640538 − 0.994553I
−1.01177 − 5.79366I −1.10840 + 5.84891I
u = 0.518255 + 0.626071I
a = 1.151290 − 0.224523I
b = 0.354929 − 0.825030I
−2.06743 − 1.34975I −3.70130 + 0.61741I
u = 0.518255 + 0.626071I
a = −0.466736 − 0.173905I
b = 0.036758 + 0.809795I
−2.06743 − 1.34975I −3.70130 + 0.61741I
u = 0.518255 − 0.626071I
a = 1.151290 + 0.224523I
b = 0.354929 + 0.825030I
−2.06743 + 1.34975I −3.70130 − 0.61741I
u = 0.518255 − 0.626071I
a = −0.466736 + 0.173905I
b = 0.036758 − 0.809795I
−2.06743 + 1.34975I −3.70130 − 0.61741I
u = −0.105109 + 1.230930I
a = 0.782932 − 0.414854I
b = 1.289160 − 0.195621I
−1.53555 − 2.45321I −1.73083 + 3.64393I
u = −0.105109 + 1.230930I
a = 0.07652 − 1.62634I
b = 0.323070 − 0.600087I
−1.53555 − 2.45321I −1.73083 + 3.64393I
u = −0.105109 − 1.230930I
a = 0.782932 + 0.414854I
b = 1.289160 + 0.195621I
−1.53555 + 2.45321I −1.73083 − 3.64393I
u = −0.105109 − 1.230930I
a = 0.07652 + 1.62634I
b = 0.323070 + 0.600087I
−1.53555 + 2.45321I −1.73083 − 3.64393I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.059730 + 1.371060I
a = −0.818424 − 0.361459I
b = −1.60423 − 0.59087I
−4.45021 − 0.95435I −6.93920 + 1.02665I
u = −0.059730 + 1.371060I
a = −0.74073 + 2.25028I
b = −0.361469 + 1.063690I
−4.45021 − 0.95435I −6.93920 + 1.02665I
u = −0.059730 − 1.371060I
a = −0.818424 + 0.361459I
b = −1.60423 + 0.59087I
−4.45021 + 0.95435I −6.93920 − 1.02665I
u = −0.059730 − 1.371060I
a = −0.74073 − 2.25028I
b = −0.361469 − 1.063690I
−4.45021 + 0.95435I −6.93920 − 1.02665I
u = 0.139725 + 1.381280I
a = −0.770884 − 0.370544I
b = −1.66412 − 0.10648I
−4.08023 + 6.55700I −5.63713 − 6.78251I
u = 0.139725 + 1.381280I
a = 0.29262 + 2.38176I
b = 0.489560 + 1.196920I
−4.08023 + 6.55700I −5.63713 − 6.78251I
u = 0.139725 − 1.381280I
a = −0.770884 + 0.370544I
b = −1.66412 + 0.10648I
−4.08023 − 6.55700I −5.63713 + 6.78251I
u = 0.139725 − 1.381280I
a = 0.29262 − 2.38176I
b = 0.489560 − 1.196920I
−4.08023 − 6.55700I −5.63713 + 6.78251I
u = −0.554352
a = 0.740835 + 0.680093I
b = −0.921542 + 0.242552I
2.09657 5.17700
u = −0.554352
a = 0.740835 − 0.680093I
b = −0.921542 − 0.242552I
2.09657 5.17700
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29578 + 1.47095I
a = 0.18443 − 1.56957I
b = −0.92779 − 1.33458I
−6.94105 + 9.69379I −4.61840 − 5.69034I
u = 0.29578 + 1.47095I
a = −0.31932 + 1.99740I
b = 0.67461 + 1.56652I
−6.94105 + 9.69379I −4.61840 − 5.69034I
u = 0.29578 − 1.47095I
a = 0.18443 + 1.56957I
b = −0.92779 + 1.33458I
−6.94105 − 9.69379I −4.61840 + 5.69034I
u = 0.29578 − 1.47095I
a = −0.31932 − 1.99740I
b = 0.67461 − 1.56652I
−6.94105 − 9.69379I −4.61840 + 5.69034I
u = 0.16919 + 1.49858I
a = −0.711118 + 1.168250I
b = 0.274092 + 0.921694I
−8.88235 + 1.10950I −6.99514 + 0.17623I
u = 0.16919 + 1.49858I
a = 0.09153 − 1.54673I
b = −0.53616 − 1.43470I
−8.88235 + 1.10950I −6.99514 + 0.17623I
u = 0.16919 − 1.49858I
a = −0.711118 − 1.168250I
b = 0.274092 − 0.921694I
−8.88235 − 1.10950I −6.99514 − 0.17623I
u = 0.16919 − 1.49858I
a = 0.09153 + 1.54673I
b = −0.53616 + 1.43470I
−8.88235 − 1.10950I −6.99514 − 0.17623I
u = 0.466344 + 0.139064I
a = −1.18545 − 1.21183I
b = 1.039580 + 0.010832I
0.81638 + 4.44188I 2.19708 − 6.84090I
u = 0.466344 + 0.139064I
a = 1.18593 − 1.46874I
b = −0.867602 − 0.879604I
0.81638 + 4.44188I 2.19708 − 6.84090I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.466344 − 0.139064I
a = −1.18545 + 1.21183I
b = 1.039580 − 0.010832I
0.81638 − 4.44188I 2.19708 + 6.84090I
u = 0.466344 − 0.139064I
a = 1.18593 + 1.46874I
b = −0.867602 + 0.879604I
0.81638 − 4.44188I 2.19708 + 6.84090I
u = −0.23640 + 1.53629I
a = 0.609636 + 1.013420I
b = −0.471274 + 0.872850I
−12.00220 − 6.17786I −9.83600 + 3.42505I
u = −0.23640 + 1.53629I
a = 0.12964 + 1.84162I
b = −0.47148 + 1.62736I
−12.00220 − 6.17786I −9.83600 + 3.42505I
u = −0.23640 − 1.53629I
a = 0.609636 − 1.013420I
b = −0.471274 − 0.872850I
−12.00220 + 6.17786I −9.83600 − 3.42505I
u = −0.23640 − 1.53629I
a = 0.12964 − 1.84162I
b = −0.47148 − 1.62736I
−12.00220 + 6.17786I −9.83600 − 3.42505I
u = −0.216364
a = −3.33097 + 3.65605I
b = 0.919690 + 0.650330I
0.115142 1.63340
u = −0.216364
a = −3.33097 − 3.65605I
b = 0.919690 − 0.650330I
0.115142 1.63340
14
III. I
u
3
= h−au + 2b − a, a
2
+ au + a + 2u, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
1
a
3
=
−u
0
a
1
=
a
1
2
au +
1
2
a
a
9
=
0
1
a
2
=
a + 1
1
2
au +
1
2
a + u
a
6
=
−
1
2
au −
1
2
a
−
1
2
au +
1
2
a
a
11
=
−
1
2
au +
1
2
a
1
2
au +
1
2
a
a
5
=
−
1
2
au −
1
2
a − u
−
1
2
au +
1
2
a + u + 1
a
10
=
−
1
2
au +
1
2
a
au
a
10
=
−
1
2
au +
1
2
a
au
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4au − 4a − 8
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
, c
11
u
4
− u
2
+ 1
c
2
, c
10
(u
2
+ u + 1)
2
c
3
, c
7
, c
8
(u
2
+ 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
, c
11
(y
2
− y + 1)
2
c
2
, c
10
(y
2
+ y + 1)
2
c
3
, c
7
, c
8
(y + 1)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.36603 − 1.36603I
b = 0.866025 − 0.500000I
−1.64493 − 4.05977I −4.00000 + 6.92820I
u = 1.000000I
a = −1.36603 + 0.36603I
b = −0.866025 − 0.500000I
−1.64493 + 4.05977I −4.00000 − 6.92820I
u = − 1.000000I
a = 0.36603 + 1.36603I
b = 0.866025 + 0.500000I
−1.64493 + 4.05977I −4.00000 − 6.92820I
u = − 1.000000I
a = −1.36603 − 0.36603I
b = −0.866025 + 0.500000I
−1.64493 − 4.05977I −4.00000 + 6.92820I
18
IV. I
u
4
= hau + 2b − a + u − 1, a
2
+ au + a − u, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
1
a
3
=
−u
0
a
1
=
a
−
1
2
au +
1
2
a −
1
2
u +
1
2
a
9
=
0
1
a
2
=
−
1
2
au +
1
2
a −
1
2
u −
1
2
−
1
2
au +
1
2
a +
1
2
u +
1
2
a
6
=
−
1
2
au +
1
2
a +
1
2
u +
1
2
−
1
2
au −
1
2
a −
1
2
u −
1
2
a
11
=
1
2
au +
1
2
a +
1
2
u −
1
2
−
1
2
au +
1
2
a −
1
2
u +
1
2
a
5
=
−
1
2
au +
1
2
a −
1
2
u +
1
2
u − 1
a
10
=
1
2
au +
1
2
a +
1
2
u −
1
2
−au − u + 1
a
10
=
1
2
au +
1
2
a +
1
2
u −
1
2
−au − u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
, c
11
u
4
− u
2
+ 1
c
2
, c
10
(u
2
+ u + 1)
2
c
3
, c
7
, c
8
(u
2
+ 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
, c
11
(y
2
− y + 1)
2
c
2
, c
10
(y
2
+ y + 1)
2
c
3
, c
7
, c
8
(y + 1)
4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.366025 + 0.366025I
b = 0.866025 − 0.500000I
−1.64493 −4.00000
u = 1.000000I
a = −1.36603 − 1.36603I
b = −0.866025 − 0.500000I
−1.64493 −4.00000
u = − 1.000000I
a = 0.366025 − 0.366025I
b = 0.866025 + 0.500000I
−1.64493 −4.00000
u = − 1.000000I
a = −1.36603 + 1.36603I
b = −0.866025 + 0.500000I
−1.64493 −4.00000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
((u
4
− u
2
+ 1)
2
)(u
17
− 5u
15
+ ··· + u + 1)(u
48
− u
47
+ ··· − 2u + 1)
c
2
, c
10
((u
2
+ u + 1)
4
)(u
17
+ 10u
16
+ ··· + 3u + 1)(u
48
+ 23u
47
+ ··· + 2u + 1)
c
3
, c
7
, c
8
((u
2
+ 1)
4
)(u
17
− 5u
16
+ ··· − 16u + 4)(u
24
+ 2u
23
+ ··· − 13u
2
+ 1)
2
c
4
, c
11
((u
4
− u
2
+ 1)
2
)(u
17
+ 7u
15
+ ··· + 3u + 1)
· (u
48
− 3u
47
+ ··· − 1432u + 517)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
((y
2
− y + 1)
4
)(y
17
− 10y
16
+ ··· + 3y −1)(y
48
− 23y
47
+ ··· − 2y + 1)
c
2
, c
10
((y
2
+ y + 1)
4
)(y
17
− 2y
16
+ ··· − 5y −1)(y
48
+ 5y
47
+ ··· − 30y + 1)
c
3
, c
7
, c
8
((y + 1)
8
)(y
17
+ 15y
16
+ ··· + 40y −16)
· (y
24
+ 24y
23
+ ··· − 26y + 1)
2
c
4
, c
11
((y
2
− y + 1)
4
)(y
17
+ 14y
16
+ ··· + 7y −1)
· (y
48
+ 13y
47
+ ··· − 341422y + 267289)
24
