12n
0034
(K12n
0034
)
A knot diagram
1
Linearized knot diagam
3 5 6 7 2 9 4 11 12 7 6 10
Solving Sequence
5,7
4
8,11
9 6 12 3 2 1 10
c
4
c
7
c
8
c
6
c
11
c
3
c
2
c
1
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.80347 × 10
133
u
37
− 4.04668 × 10
133
u
36
+ ··· + 1.44050 × 10
137
b + 7.58135 × 10
136
,
2.78701 × 10
134
u
37
− 5.34254 × 10
134
u
36
+ ··· + 2.01671 × 10
138
a + 5.65465 × 10
138
,
u
38
− 2u
37
+ ··· + 12288u + 4096i
I
u
2
= hu
3
− u
2
+ b + 2u, −u
2
+ a + u − 1, u
4
+ u
2
+ u + 1i
I
u
3
= h3u
5
− u
4
+ 5u
3
− 3u
2
+ b + 4u − 4, 2u
5
+ 3u
3
− u
2
+ a + 2u − 2, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
I
v
1
= ha, −963772v
11
+ 658631v
10
+ ··· + 707733b + 3141326,
v
12
− v
11
− 4v
10
− 5v
9
+ 19v
8
+ 9v
7
− 31v
6
+ 29v
5
+ 31v
4
− 18v
3
+ 3v
2
− 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 60 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
= h1.80 × 10
133
u
37
− 4.05 × 10
133
u
36
+ · · · + 1.44 × 10
137
b + 7.58 ×
10
136
, 2.79 × 10
134
u
37
− 5.34 × 10
134
u
36
+ · · · + 2.02 × 10
138
a + 5.65 ×
10
138
, u
38
− 2u
37
+ · · · + 12288u + 4096i
(i) Arc colorings
a
5
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
u
u
3
+ u
a
11
=
−0.000138196u
37
+ 0.000264914u
36
+ ··· + 2.22627u − 2.80391
−0.000125197u
37
+ 0.000280921u
36
+ ··· + 3.09647u − 0.526298
a
9
=
−0.0000643751u
37
+ 0.000175800u
36
+ ··· − 4.14636u + 0.169342
0.0000210320u
37
− 0.0000415391u
36
+ ··· − 0.351856u − 0.288364
a
6
=
0.0000103293u
37
+ 5.50817 × 10
−6
u
36
+ ··· + 0.765170u + 1.22937
−0.0000463037u
37
+ 0.0000938416u
36
+ ··· + 0.102969u − 0.0432937
a
12
=
−0.000154935u
37
+ 0.000266148u
36
+ ··· + 3.91415u − 3.54515
−0.000183169u
37
+ 0.000395135u
36
+ ··· + 2.91568u − 0.405958
a
3
=
0.0000125731u
37
− 0.0000323095u
36
+ ··· − 0.598837u + 0.850308
0.0000180956u
37
− 0.0000598188u
36
+ ··· − 0.780260u − 0.190793
a
2
=
−5.52255 × 10
−6
u
37
+ 0.0000275093u
36
+ ··· + 0.181423u + 1.04110
0.0000180956u
37
− 0.0000598188u
36
+ ··· − 0.780260u − 0.190793
a
1
=
0.0000555017u
37
− 0.0000873032u
36
+ ··· + 0.298354u + 1.16548
0.0000451724u
37
− 0.0000928114u
36
+ ··· − 0.466816u − 0.0638856
a
10
=
−0.000138196u
37
+ 0.000264914u
36
+ ··· + 2.22627u − 2.80391
−0.000147500u
37
+ 0.000324572u
36
+ ··· + 2.38937u − 0.573314
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.000218010u
37
+ 0.000603676u
36
+ ··· − 22.4576u − 0.864966
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
+ 28u
37
+ ··· + 159u + 1
c
2
, c
5
u
38
+ 8u
37
+ ··· + 11u + 1
c
3
u
38
− 8u
37
+ ··· + 17360u + 1732
c
4
, c
7
u
38
+ 2u
37
+ ··· − 12288u + 4096
c
6
u
38
− 4u
37
+ ··· − 3u + 1
c
8
u
38
− 3u
37
+ ··· − 11264u + 1024
c
9
, c
12
u
38
+ 13u
37
+ ··· + 8u + 1
c
10
u
38
+ 2u
37
+ ··· + 575973u + 248449
c
11
u
38
+ 8u
37
+ ··· − 149993u + 47809
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
− 28y
37
+ ··· − 10893y + 1
c
2
, c
5
y
38
+ 28y
37
+ ··· + 159y + 1
c
3
y
38
− 84y
37
+ ··· + 436784552y + 2999824
c
4
, c
7
y
38
+ 70y
37
+ ··· + 134217728y + 16777216
c
6
y
38
+ 4y
37
+ ··· + 19y + 1
c
8
y
38
− 69y
37
+ ··· − 7864320y + 1048576
c
9
, c
12
y
38
+ y
37
+ ··· − 84y + 1
c
10
y
38
− 84y
37
+ ··· + 1086486467931y + 61726905601
c
11
y
38
+ 48y
37
+ ··· + 51838210455y + 2285700481
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.269512 + 0.935520I
a = −0.458289 − 0.782512I
b = 0.677405 + 0.518877I
−0.61516 + 8.47206I −1.23185 − 12.18265I
u = 0.269512 − 0.935520I
a = −0.458289 + 0.782512I
b = 0.677405 − 0.518877I
−0.61516 − 8.47206I −1.23185 + 12.18265I
u = −0.615656 + 0.694581I
a = −0.427914 + 0.398057I
b = 0.267942 + 0.980799I
1.12636 − 1.44186I 2.40380 + 3.54555I
u = −0.615656 − 0.694581I
a = −0.427914 − 0.398057I
b = 0.267942 − 0.980799I
1.12636 + 1.44186I 2.40380 − 3.54555I
u = −0.690714 + 0.617908I
a = −0.599875 − 0.724392I
b = −0.695539 + 0.625151I
0.91553 − 4.18220I 3.10264 + 7.31279I
u = −0.690714 − 0.617908I
a = −0.599875 + 0.724392I
b = −0.695539 − 0.625151I
0.91553 + 4.18220I 3.10264 − 7.31279I
u = −0.962152 + 0.487944I
a = 0.020845 + 0.197190I
b = −0.32060 + 1.60868I
0.067821 + 0.704860I 1.59983 − 2.96425I
u = −0.962152 − 0.487944I
a = 0.020845 − 0.197190I
b = −0.32060 − 1.60868I
0.067821 − 0.704860I 1.59983 + 2.96425I
u = 0.334991 + 0.821597I
a = −0.428276 + 0.927379I
b = −0.299801 − 0.583140I
−3.35491 − 0.78621I −8.48784 + 2.29609I
u = 0.334991 − 0.821597I
a = −0.428276 − 0.927379I
b = −0.299801 + 0.583140I
−3.35491 + 0.78621I −8.48784 − 2.29609I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.730737 + 0.068723I
a = 0.810489 + 0.363992I
b = 1.45774 + 1.16856I
−0.42860 − 2.78462I 1.78865 + 4.97070I
u = 0.730737 − 0.068723I
a = 0.810489 − 0.363992I
b = 1.45774 − 1.16856I
−0.42860 + 2.78462I 1.78865 − 4.97070I
u = 0.154768 + 0.641440I
a = −0.858708 + 0.997854I
b = 0.415361 − 0.487054I
−1.32113 − 1.32492I −1.95750 + 1.98412I
u = 0.154768 − 0.641440I
a = −0.858708 − 0.997854I
b = 0.415361 + 0.487054I
−1.32113 + 1.32492I −1.95750 − 1.98412I
u = 1.336190 + 0.226899I
a = 0.552450 + 0.930807I
b = 0.80282 + 3.46642I
−0.61371 − 2.86891I −0.25435 + 4.83204I
u = 1.336190 − 0.226899I
a = 0.552450 − 0.930807I
b = 0.80282 − 3.46642I
−0.61371 + 2.86891I −0.25435 − 4.83204I
u = 0.300084 + 0.412662I
a = 0.10831 + 2.92562I
b = −0.16429 + 3.48640I
1.67684 − 2.65330I 7.7232 − 16.8130I
u = 0.300084 − 0.412662I
a = 0.10831 − 2.92562I
b = −0.16429 − 3.48640I
1.67684 + 2.65330I 7.7232 + 16.8130I
u = −0.392217 + 0.325280I
a = −1.29311 + 2.21775I
b = −0.16047 + 3.66337I
2.15015 − 1.46241I −0.02794 + 14.08993I
u = −0.392217 − 0.325280I
a = −1.29311 − 2.21775I
b = −0.16047 − 3.66337I
2.15015 + 1.46241I −0.02794 − 14.08993I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.209980 + 0.250980I
a = −3.00779 + 0.52768I
b = −0.802018 + 0.832176I
1.91078 − 0.79833I 4.44525 − 0.45789I
u = −0.209980 − 0.250980I
a = −3.00779 − 0.52768I
b = −0.802018 − 0.832176I
1.91078 + 0.79833I 4.44525 + 0.45789I
u = −1.10703 + 1.69579I
a = 0.928872 − 0.073456I
b = −2.06666 − 3.80312I
−6.26733 + 3.08288I 0
u = −1.10703 − 1.69579I
a = 0.928872 + 0.073456I
b = −2.06666 + 3.80312I
−6.26733 − 3.08288I 0
u = 0.41366 + 2.27352I
a = 0.273778 − 1.053910I
b = 0.83748 + 3.68747I
−12.39510 + 1.09723I 0
u = 0.41366 − 2.27352I
a = 0.273778 + 1.053910I
b = 0.83748 − 3.68747I
−12.39510 − 1.09723I 0
u = −0.98102 + 2.10542I
a = −0.285160 − 1.017430I
b = −3.48637 + 2.72417I
−16.2164 − 7.5794I 0
u = −0.98102 − 2.10542I
a = −0.285160 + 1.017430I
b = −3.48637 − 2.72417I
−16.2164 + 7.5794I 0
u = 1.14222 + 2.13195I
a = −0.006500 + 1.260510I
b = −6.15185 − 1.87143I
−15.9377 + 14.9717I 0
u = 1.14222 − 2.13195I
a = −0.006500 − 1.260510I
b = −6.15185 + 1.87143I
−15.9377 − 14.9717I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.58138 + 2.41986I
a = −0.021457 + 1.260750I
b = 3.60201 − 4.67413I
−12.2225 − 8.2203I 0
u = −0.58138 − 2.41986I
a = −0.021457 − 1.260750I
b = 3.60201 + 4.67413I
−12.2225 + 8.2203I 0
u = 1.75400 + 1.85534I
a = 1.163960 + 0.099561I
b = −0.64784 + 7.80385I
−6.74677 + 2.59569I 0
u = 1.75400 − 1.85534I
a = 1.163960 − 0.099561I
b = −0.64784 − 7.80385I
−6.74677 − 2.59569I 0
u = 0.32782 + 2.75595I
a = −0.238367 − 1.046580I
b = 3.58759 + 5.29844I
−17.5824 + 5.0951I 0
u = 0.32782 − 2.75595I
a = −0.238367 + 1.046580I
b = 3.58759 − 5.29844I
−17.5824 − 5.0951I 0
u = −0.22384 + 3.07549I
a = 0.016754 + 1.242340I
b = 1.64709 − 9.59445I
−17.7767 + 1.7959I 0
u = −0.22384 − 3.07549I
a = 0.016754 − 1.242340I
b = 1.64709 + 9.59445I
−17.7767 − 1.7959I 0
8
II. I
u
2
= hu
3
− u
2
+ b + 2u, −u
2
+ a + u − 1, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
u
u
3
+ u
a
11
=
u
2
− u + 1
−u
3
+ u
2
− 2u
a
9
=
u
u
3
+ u
a
6
=
u
3
−u
2
a
12
=
u
2
− 2u + 1
−u
3
+ u
2
− 2u + 1
a
3
=
u
3
+ u
2
+ 1
−u
a
2
=
u
3
+ u
2
+ u + 1
−u
a
1
=
−u
−u
3
− u
a
10
=
u
2
− u + 1
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9u
3
− 2u
2
+ 2u + 11
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
4
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
, c
7
u
4
+ u
2
− u + 1
c
8
u
4
c
9
(u + 1)
4
c
10
, c
11
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
12
(u − 1)
4
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
4
, c
5
c
7
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
8
y
4
c
9
, c
12
(y −1)
4
c
10
, c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = 1.50411 − 1.22685I
b = 0.65230 − 2.13814I
2.62503 − 1.39709I 13.5849 + 5.3845I
u = −0.547424 − 0.585652I
a = 1.50411 + 1.22685I
b = 0.65230 + 2.13814I
2.62503 + 1.39709I 13.5849 − 5.3845I
u = 0.547424 + 1.120870I
a = −0.504108 + 0.106312I
b = −0.152300 − 0.614030I
−0.98010 + 7.64338I −3.08487 − 3.81741I
u = 0.547424 − 1.120870I
a = −0.504108 − 0.106312I
b = −0.152300 + 0.614030I
−0.98010 − 7.64338I −3.08487 + 3.81741I
12
III. I
u
3
= h3u
5
− u
4
+ 5u
3
− 3u
2
+ b + 4u − 4, 2u
5
+ 3u
3
− u
2
+ a + 2u −
2, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
u
u
3
+ u
a
11
=
−2u
5
− 3u
3
+ u
2
− 2u + 2
−3u
5
+ u
4
− 5u
3
+ 3u
2
− 4u + 4
a
9
=
u
u
3
+ u
a
6
=
u
3
u
5
+ u
3
+ u
a
12
=
−2u
5
− 3u
3
+ u
2
− 3u + 2
−2u
5
− 4u
3
+ u
2
− 3u + 2
a
3
=
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 2
−u
5
− 2u
3
+ u
2
− u + 1
a
2
=
u
4
+ u
2
− u + 1
−u
5
− 2u
3
+ u
2
− u + 1
a
1
=
−u
−u
3
− u
a
10
=
−2u
5
− 3u
3
+ u
2
− 2u + 2
−2u
5
− 3u
3
+ u
2
− 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
5
− u
4
+ 8u
3
− 4u
2
+ 5u − 5
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
4
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
5
, c
7
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
8
u
6
c
9
(u + 1)
6
c
10
, c
11
u
6
+ 2u
3
+ 4u
2
+ 3u + 1
c
12
(u − 1)
6
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
4
, c
5
c
7
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y −1)
2
c
8
y
6
c
9
, c
12
(y −1)
6
c
10
, c
11
y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = 0.702221 + 0.130845I
b = 0.303615 − 0.669275I
1.37919 − 2.82812I 3.08014 + 1.90022I
u = −0.498832 − 1.001300I
a = 0.702221 − 0.130845I
b = 0.303615 + 0.669275I
1.37919 + 2.82812I 3.08014 − 1.90022I
u = 0.284920 + 1.115140I
a = −0.447279 + 0.479689I
b = −0.232199 − 0.362106I
−2.75839 −2.43992 − 2.50363I
u = 0.284920 − 1.115140I
a = −0.447279 − 0.479689I
b = −0.232199 + 0.362106I
−2.75839 −2.43992 + 2.50363I
u = 0.713912 + 0.305839I
a = 0.74506 − 2.00027I
b = 1.92858 − 2.50729I
1.37919 − 2.82812I −2.14022 + 3.69351I
u = 0.713912 − 0.305839I
a = 0.74506 + 2.00027I
b = 1.92858 + 2.50729I
1.37919 + 2.82812I −2.14022 − 3.69351I
16
IV. I
v
1
= ha, −9.64 × 10
5
v
11
+ 6.59 × 10
5
v
10
+ · · · + 7.08 × 10
5
b + 3.14 ×
10
6
, v
12
− v
11
+ · · · − 3v + 1i
(i) Arc colorings
a
5
=
1
0
a
7
=
v
0
a
4
=
1
0
a
8
=
v
0
a
11
=
0
1.36177v
11
− 0.930621v
10
+ ··· + 5.08294v − 4.43857
a
9
=
v
−0.546453v
11
+ 0.201388v
10
+ ··· − 2.43405v + 1.91940
a
6
=
0.181358v
11
− 0.113940v
10
+ ··· + 1.48874v − 0.345065
−0.678951v
11
+ 0.501804v
10
+ ··· − 2.40704v + 2.15346
a
12
=
0.0595846v
11
− 0.0327468v
10
+ ··· − 1.31733v − 0.160053
2.02290v
11
− 1.34063v
10
+ ··· + 7.63126v − 6.61613
a
3
=
0.160053v
11
− 0.100469v
10
+ ··· − 0.150791v + 0.202506
0.678951v
11
− 0.501804v
10
+ ··· + 2.40704v − 1.15346
a
2
=
−0.518898v
11
+ 0.401335v
10
+ ··· − 2.55783v + 1.35596
0.678951v
11
− 0.501804v
10
+ ··· + 2.40704v − 1.15346
a
1
=
−0.181358v
11
+ 0.113940v
10
+ ··· − 1.48874v + 0.345065
0.678951v
11
− 0.501804v
10
+ ··· + 2.40704v − 2.15346
a
10
=
0.222666v
11
− 0.152658v
10
+ ··· − 0.0683153v − 0.431153
1.36177v
11
− 0.930621v
10
+ ··· + 5.08294v − 4.43857
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2217
3419
v
11
−
1754
78637
v
10
−
289681
78637
v
9
−
404567
78637
v
8
+
848176
78637
v
7
+
1557570
78637
v
6
−
1880820
78637
v
5
−
7308
3419
v
4
+
308622
6049
v
3
−
471268
78637
v
2
−
64283
3419
v +
405712
78637
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
7
u
12
c
6
, c
11
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
8
, c
12
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
9
, c
10
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
6
c
4
, c
7
y
12
c
6
, c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
8
, c
9
, c
10
c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.695888 + 0.967642I
a = 0
b = 0.289622 − 0.827421I
−1.89061 − 1.10558I −1.04064 + 1.99047I
v = 0.695888 − 0.967642I
a = 0
b = 0.289622 + 0.827421I
−1.89061 + 1.10558I −1.04064 − 1.99047I
v = −1.185950 + 0.118836I
a = 0
b = −0.861379 + 0.162890I
−1.89061 + 2.95419I −3.79900 − 4.11613I
v = −1.185950 − 0.118836I
a = 0
b = −0.861379 − 0.162890I
−1.89061 − 2.95419I −3.79900 + 4.11613I
v = −0.125911 + 0.369768I
a = 0
b = −1.25704 + 1.58618I
1.89061 + 2.95419I 11.02954 − 8.16480I
v = −0.125911 − 0.369768I
a = 0
b = −1.25704 − 1.58618I
1.89061 − 2.95419I 11.02954 + 8.16480I
v = 0.383184 + 0.075842I
a = 0
b = −0.74515 + 1.88172I
1.89061 + 1.10558I −0.484082 − 0.231437I
v = 0.383184 − 0.075842I
a = 0
b = −0.74515 − 1.88172I
1.89061 − 1.10558I −0.484082 + 0.231437I
v = −1.38214 + 1.64413I
a = 0
b = 0.520868 + 0.215334I
7.72290I 2.83009 − 4.64337I
v = −1.38214 − 1.64413I
a = 0
b = 0.520868 − 0.215334I
− 7.72290I 2.83009 + 4.64337I
20
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 2.11493 + 0.37491I
a = 0
b = −0.446919 + 0.343418I
3.66314I −2.53591 − 3.55776I
v = 2.11493 − 0.37491I
a = 0
b = −0.446919 − 0.343418I
− 3.66314I −2.53591 + 3.55776I
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
38
+ 28u
37
+ ··· + 159u + 1)
c
2
(u
2
+ u + 1)
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
38
+ 8u
37
+ ··· + 11u + 1)
c
3
(u
2
− u + 1)
6
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
38
− 8u
37
+ ··· + 17360u + 1732)
c
4
u
12
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
38
+ 2u
37
+ ··· − 12288u + 4096)
c
5
(u
2
− u + 1)
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
38
+ 8u
37
+ ··· + 11u + 1)
c
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· ((u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
)(u
38
− 4u
37
+ ··· − 3u + 1)
c
7
u
12
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
38
+ 2u
37
+ ··· − 12288u + 4096)
c
8
u
10
(u
6
+ u
5
+ ··· + u + 1)
2
(u
38
− 3u
37
+ ··· − 11264u + 1024)
c
9
((u + 1)
10
)(u
6
− u
5
+ ··· − u + 1)
2
(u
38
+ 13u
37
+ ··· + 8u + 1)
c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
6
+ 2u
3
+ 4u
2
+ 3u + 1)
· ((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
38
+ 2u
37
+ ··· + 575973u + 248449)
c
11
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
6
+ 2u
3
+ 4u
2
+ 3u + 1)
· (u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
38
+ 8u
37
+ ··· − 149993u + 47809)
c
12
((u − 1)
10
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
38
+ 13u
37
+ ··· + 8u + 1)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
38
− 28y
37
+ ··· − 10893y + 1)
c
2
, c
5
(y
2
+ y + 1)
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
38
+ 28y
37
+ ··· + 159y + 1)
c
3
(y
2
+ y + 1)
6
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
38
− 84y
37
+ ··· + 436784552y + 2999824)
c
4
, c
7
y
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
38
+ 70y
37
+ ··· + 134217728y + 16777216)
c
6
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· ((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
38
+ 4y
37
+ ··· + 19y + 1)
c
8
y
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
38
− 69y
37
+ ··· − 7864320y + 1048576)
c
9
, c
12
(y − 1)
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
38
+ y
37
+ ··· − 84y + 1)
c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1)
· (y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
38
− 84y
37
+ ··· + 1086486467931y + 61726905601)
c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
6
+ 8y
4
− 2y
3
+ 4y
2
− y + 1)
· (y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
38
+ 48y
37
+ ··· + 51838210455y + 2285700481)
23
