12n
0801
(K12n
0801
)
A knot diagram
1
Linearized knot diagam
4 6 9 12 2 10 12 6 4 8 5 7
Solving Sequence
7,12
8
1,5
4 2 11 10 6 3 9
c
7
c
12
c
4
c
1
c
11
c
10
c
6
c
2
c
9
c
3
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h139726521u
15
− 216650645u
14
+ ··· + 864519475b − 245546684, a − 1, u
16
− u
15
+ ··· − 3u
2
− 1i
I
u
2
= h−u
6
+ u
5
− u
4
+ 10u
3
+ 13u
2
+ 5b + u + 1, a + 1, u
7
+ 5u
5
− 4u
4
+ 7u
3
− 4u
2
+ 3u − 1i
I
u
3
= h−51u
11
− 95u
10
+ ··· + 185b + 342, −224u
11
− 188u
10
+ ··· + 185a − 115,
u
12
+ u
11
+ 5u
10
+ 5u
9
+ 9u
8
+ 6u
7
+ u
6
− 5u
5
− 11u
4
− 15u
3
− 11u
2
− 4u − 1i
I
u
4
= h−964489278415u
11
+ 117148284431u
10
+ ··· + 301017906283623b + 191146639374112,
199776571521368u
11
− 160244377858182u
10
+ ··· + 8729519282225067a − 77902584840567367,
u
12
− u
11
+ 15u
10
− 3u
9
+ 83u
8
+ 74u
7
+ 245u
6
+ 355u
5
+ 477u
4
+ 227u
3
− 109u
2
− 372u + 29i
* 4 irreducible components of dim
C
= 0, with total 47 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
= h1.40 × 10
8
u
15
− 2.17 × 10
8
u
14
+ · · · + 8.65 × 10
8
b − 2.46 × 10
8
, a −
1, u
16
− u
15
+ · · · − 3u
2
− 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
5
=
1
−0.161623u
15
+ 0.250602u
14
+ ··· − 0.962108u + 0.284027
a
4
=
1
−0.161623u
15
+ 0.250602u
14
+ ··· − 0.962108u + 0.284027
a
2
=
−0.0889791u
15
+ 0.0677199u
14
+ ··· − 2.28403u + 0.161623
−0.457683u
15
+ 0.568849u
14
+ ··· + 0.832397u + 0.604244
a
11
=
u
0.0889791u
15
− 0.0677199u
14
+ ··· + 1.28403u − 0.161623
a
10
=
0.0889791u
15
− 0.0677199u
14
+ ··· + 2.28403u − 0.161623
0.158988u
15
− 0.177074u
14
+ ··· + 1.37301u − 0.140364
a
6
=
0.127953u
15
+ 0.0697779u
14
+ ··· + 0.974879u + 0.182022
−0.145027u
15
+ 0.362922u
14
+ ··· + 0.962468u − 0.461260
a
3
=
−0.831219u
15
+ 0.864475u
14
+ ··· − 2.13140u + 0.842638
−0.913992u
15
+ 1.16510u
14
+ ··· + 1.31352u + 1.03630
a
9
=
0.476653u
15
− 0.527214u
14
+ ··· + 1.36265u − 0.787127
0.687117u
15
− 0.912956u
14
+ ··· + 0.517385u − 0.960091
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
447574308
864519475
u
15
−
223753298
172903895
u
14
+ ··· +
6627598422
864519475
u −
4377348818
864519475
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
16
− 2u
15
+ ··· − 63u − 27
c
2
, c
5
, c
6
u
16
+ 2u
15
+ ··· + 14u + 1
c
3
, c
9
u
16
+ 7u
15
+ ··· + 39u + 19
c
4
, c
7
, c
11
c
12
u
16
+ u
15
+ ··· − 3u
2
− 1
c
8
u
16
+ 2u
15
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
16
+ 36y
15
+ ··· − 4131y + 729
c
2
, c
5
, c
6
y
16
+ 4y
15
+ ··· − 104y + 1
c
3
, c
9
y
16
− 17y
15
+ ··· − 1977y + 361
c
4
, c
7
, c
11
c
12
y
16
+ 21y
15
+ ··· + 6y + 1
c
8
y
16
+ 16y
15
+ ··· + 8y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.315992 + 0.923692I
a = 1.00000
b = −1.072170 + 0.739909I
0.73896 − 4.05435I −4.39569 + 8.69732I
u = 0.315992 − 0.923692I
a = 1.00000
b = −1.072170 − 0.739909I
0.73896 + 4.05435I −4.39569 − 8.69732I
u = −0.946702
a = 1.00000
b = −0.982882
−3.88612 −24.3560
u = −0.012719 + 1.092980I
a = 1.00000
b = −1.42699 + 0.92099I
10.45990 + 3.54053I 0.82342 − 2.71051I
u = −0.012719 − 1.092980I
a = 1.00000
b = −1.42699 − 0.92099I
10.45990 − 3.54053I 0.82342 + 2.71051I
u = −0.212701 + 0.840300I
a = 1.00000
b = −1.02555 − 1.53512I
−0.301618 + 0.879889I −7.11415 − 1.14520I
u = −0.212701 − 0.840300I
a = 1.00000
b = −1.02555 + 1.53512I
−0.301618 − 0.879889I −7.11415 + 1.14520I
u = 1.24735
a = 1.00000
b = −0.0213320
−2.33062 −0.734580
u = −0.361980 + 0.330445I
a = 1.00000
b = 1.42983 + 0.27839I
5.02983 + 5.57711I −7.96481 − 3.29725I
u = −0.361980 − 0.330445I
a = 1.00000
b = 1.42983 − 0.27839I
5.02983 − 5.57711I −7.96481 + 3.29725I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.264024 + 0.315325I
a = 1.00000
b = 0.055251 − 0.498554I
−0.654553 − 0.896356I −9.07271 + 7.71736I
u = 0.264024 − 0.315325I
a = 1.00000
b = 0.055251 + 0.498554I
−0.654553 + 0.896356I −9.07271 − 7.71736I
u = −0.28076 + 1.98483I
a = 1.00000
b = −6.38980 − 0.96015I
15.0967 + 4.8816I −2.19849 − 4.64135I
u = −0.28076 − 1.98483I
a = 1.00000
b = −6.38980 + 0.96015I
15.0967 − 4.8816I −2.19849 + 4.64135I
u = 0.63782 + 2.37815I
a = 1.00000
b = −7.56846 + 2.89468I
−14.9238 − 11.4240I −3.53223 + 3.90898I
u = 0.63782 − 2.37815I
a = 1.00000
b = −7.56846 − 2.89468I
−14.9238 + 11.4240I −3.53223 − 3.90898I
6
II. I
u
2
=
h−u
6
+u
5
−u
4
+10u
3
+13u
2
+5b+u+1, a+1, u
7
+5u
5
−4u
4
+7u
3
−4u
2
+3u−1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
5
=
−1
1
5
u
6
−
1
5
u
5
+ ··· −
1
5
u −
1
5
a
4
=
−1
1
5
u
6
−
1
5
u
5
+ ··· −
1
5
u −
1
5
a
2
=
−
1
5
u
6
−
4
5
u
5
+ ··· −
14
5
u +
1
5
u
5
+ 5u
3
− 3u
2
+ 5u − 2
a
11
=
u
1
5
u
6
+
4
5
u
5
+ ··· +
9
5
u −
1
5
a
10
=
1
5
u
6
+
4
5
u
5
+ ··· +
14
5
u −
1
5
2
5
u
6
+
3
5
u
5
+ ··· −
2
5
u +
3
5
a
6
=
0
3
5
u
6
+
2
5
u
5
+ ··· −
3
5
u −
3
5
a
3
=
−
1
5
u
6
−
4
5
u
5
+ ··· −
14
5
u +
1
5
−
6
5
u
6
+
6
5
u
5
+ ··· +
46
5
u −
19
5
a
9
=
1
u
5
+ u
4
+ 5u
3
+ u
2
+ 3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
43
5
u
6
−
12
5
u
5
−
208
5
u
4
+ 24u
3
−
216
5
u
2
+
93
5
u −
82
5
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
7
− u
6
+ 7u
5
− 3u
4
− 13u
3
+ 7u
2
+ 8u − 5
c
2
, c
6
u
7
+ u
6
+ u
5
− u
4
− u
2
+ u − 1
c
3
u
7
− 6u
6
+ 16u
5
− 25u
4
+ 26u
3
− 18u
2
+ 6u + 1
c
4
, c
12
u
7
+ 5u
5
+ 4u
4
+ 7u
3
+ 4u
2
+ 3u + 1
c
5
u
7
− u
6
+ u
5
+ u
4
+ u
2
+ u + 1
c
7
, c
11
u
7
+ 5u
5
− 4u
4
+ 7u
3
− 4u
2
+ 3u − 1
c
8
u
7
− u
6
+ 3u
5
− 3u
4
+ 2u
3
+ 3u
2
− u + 1
c
9
u
7
+ 6u
6
+ 16u
5
+ 25u
4
+ 26u
3
+ 18u
2
+ 6u − 1
c
10
u
7
+ u
6
+ 7u
5
+ 3u
4
− 13u
3
− 7u
2
+ 8u + 5
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
7
+ 13y
6
+ 17y
5
− 161y
4
+ 313y
3
− 287y
2
+ 134y −25
c
2
, c
5
, c
6
y
7
+ y
6
+ 3y
5
+ 3y
4
+ 2y
3
− 3y
2
− y −1
c
3
, c
9
y
7
− 4y
6
+ 8y
5
+ 3y
4
− 20y
3
+ 38y
2
+ 72y −1
c
4
, c
7
, c
11
c
12
y
7
+ 10y
6
+ 39y
5
+ 60y
4
+ 47y
3
+ 18y
2
+ y −1
c
8
y
7
+ 5y
6
+ 7y
5
+ 7y
4
+ 18y
3
− 7y
2
− 5y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.381257 + 0.787604I
a = −1.00000
b = 2.24160 − 1.44010I
5.73082 − 6.35876I −3.32185 + 8.09951I
u = 0.381257 − 0.787604I
a = −1.00000
b = 2.24160 + 1.44010I
5.73082 + 6.35876I −3.32185 − 8.09951I
u = −0.060693 + 0.837302I
a = −1.00000
b = 1.43171 + 1.17322I
0.771836 + 0.196666I −1.060679 + 0.531434I
u = −0.060693 − 0.837302I
a = −1.00000
b = 1.43171 − 1.17322I
0.771836 − 0.196666I −1.060679 − 0.531434I
u = 0.414510
a = −1.00000
b = −0.867599
−2.57196 −15.7040
u = −0.52782 + 2.04747I
a = −1.00000
b = 6.26049 + 1.92207I
14.5225 + 3.4415I −3.76523 − 0.87607I
u = −0.52782 − 2.04747I
a = −1.00000
b = 6.26049 − 1.92207I
14.5225 − 3.4415I −3.76523 + 0.87607I
10
III. I
u
3
= h−51u
11
− 95u
10
+ · · · + 185b + 342, −224u
11
− 188u
10
+ · · · +
185a − 115, u
12
+ u
11
+ · · · − 4u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
5
=
1.21081u
11
+ 1.01622u
10
+ ··· − 6.87027u + 0.621622
0.275676u
11
+ 0.513514u
10
+ ··· − 4.89189u − 1.84865
a
4
=
1.21081u
11
+ 1.01622u
10
+ ··· − 6.87027u + 0.621622
0.772973u
11
+ 0.459459u
10
+ ··· − 5.32432u − 1.65405
a
2
=
1.88108u
11
+ 2.02162u
10
+ ··· − 20.8270u − 6.03784
−0.832432u
11
− 0.448649u
10
+ ··· + 4.41081u + 0.135135
a
11
=
−2.07027u
11
− 2.20541u
10
+ ··· + 20.3568u + 5.25946
0.821622u
11
+ 0.232432u
10
+ ··· − 2.14054u + 0.643243
a
10
=
−1.88108u
11
− 2.02162u
10
+ ··· + 20.8270u + 6.03784
0.518919u
11
+ 0.378378u
10
+ ··· − 1.97297u + 0.637838
a
6
=
1.46486u
11
+ 2.49730u
10
+ ··· − 24.0216u − 6.27027
−0.637838u
11
− 0.356757u
10
+ ··· + 3.14595u − 0.675676
a
3
=
0.627027u
11
− 1.05946u
10
+ ··· + 7.52432u + 4.25405
0.432432u
11
+ 0.448649u
10
+ ··· − 3.41081u − 0.335135
a
9
=
−2.70811u
11
− 2.16216u
10
+ ··· + 23.7027u + 4.98378
0.329730u
11
− 0.00540541u
10
+ ··· + 0.956757u + 1.65946
(ii) Obstruction class = 1
(iii) Cusp Shapes =
117
185
u
11
+
24
37
u
10
+
608
185
u
9
+
593
185
u
8
+
1109
185
u
7
+
683
185
u
6
+
14
37
u
5
−
661
185
u
4
−
1488
185
u
3
−
337
37
u
2
−
252
37
u−
1024
185
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 4u
11
+ ··· − 20u − 5
c
2
, c
6
u
12
+ 2u
11
+ ··· − 5u + 1
c
3
(u
2
+ u − 1)
6
c
4
, c
12
u
12
− u
11
+ ··· + 4u − 1
c
5
u
12
− 2u
11
+ ··· + 5u + 1
c
7
, c
11
u
12
+ u
11
+ ··· − 4u − 1
c
8
u
12
+ 2u
11
+ ··· + 25u + 25
c
9
(u
2
− u − 1)
6
c
10
u
12
− 4u
11
+ ··· + 20u − 5
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
12
− 2y
11
+ ··· − 550y + 25
c
2
, c
5
, c
6
y
12
− 4y
11
+ ··· − 49y + 1
c
3
, c
9
(y
2
− 3y + 1)
6
c
4
, c
7
, c
11
c
12
y
12
+ 9y
11
+ ··· + 6y + 1
c
8
y
12
+ 8y
11
+ ··· − 125y + 625
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.09790
a = 0.679223
b = −0.936157
−3.41636 −3.43020
u = −0.686696 + 0.529141I
a = −0.80710 + 1.68749I
b = 0.949158 + 0.164926I
8.61690 + 2.82812I −3.78492 − 1.30714I
u = −0.686696 − 0.529141I
a = −0.80710 − 1.68749I
b = 0.949158 − 0.164926I
8.61690 − 2.82812I −3.78492 + 1.30714I
u = 0.318837 + 1.198780I
a = 0.343080 − 0.063834I
b = −0.531922 + 1.092370I
0.72122 − 2.82812I −3.78492 + 1.30714I
u = 0.318837 − 1.198780I
a = 0.343080 + 0.063834I
b = −0.531922 − 1.092370I
0.72122 + 2.82812I −3.78492 − 1.30714I
u = −0.745717
a = 1.47227
b = −0.936157
−3.41636 −3.43020
u = −0.46101 + 1.38957I
a = 0.801692 − 0.597738I
b = −3.89832
4.47932 −3.43016 + 0.I
u = −0.46101 − 1.38957I
a = 0.801692 + 0.597738I
b = −3.89832
4.47932 −3.43016 + 0.I
u = −0.185910 + 0.390926I
a = 2.81724 − 0.52418I
b = −0.531922 − 1.092370I
0.72122 + 2.82812I −3.78492 − 1.30714I
u = −0.185910 − 0.390926I
a = 2.81724 + 0.52418I
b = −0.531922 + 1.092370I
0.72122 − 2.82812I −3.78492 + 1.30714I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.33869 + 1.58586I
a = −0.230664 − 0.482275I
b = 0.949158 + 0.164926I
8.61690 + 2.82812I −3.78492 − 1.30714I
u = 0.33869 − 1.58586I
a = −0.230664 + 0.482275I
b = 0.949158 − 0.164926I
8.61690 − 2.82812I −3.78492 + 1.30714I
15
IV. I
u
4
= h−9.64 × 10
11
u
11
+ 1.17 × 10
11
u
10
+ · · · + 3.01 × 10
14
b + 1.91 ×
10
14
, 2.00 × 10
14
u
11
− 1.60 × 10
14
u
10
+ · · · + 8.73 × 10
15
a − 7.79 ×
10
16
, u
12
− u
11
+ · · · − 372u + 29i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
u
2
a
1
=
−u
u
a
5
=
−0.0228852u
11
+ 0.0183566u
10
+ ··· + 2.42642u + 8.92404
0.00320409u
11
− 0.000389174u
10
+ ··· − 1.48022u − 0.635001
a
4
=
−0.0228852u
11
+ 0.0183566u
10
+ ··· + 2.42642u + 8.92404
0.000832894u
11
+ 0.000856200u
10
+ ··· − 0.459261u − 0.766329
a
2
=
0.0142037u
11
− 0.0130176u
10
+ ··· − 1.64789u − 5.71216
−0.00197737u
11
+ 0.000849745u
10
+ ··· + 0.812663u + 0.524750
a
11
=
−0.0148371u
11
+ 0.0143087u
10
+ ··· + 0.974746u + 6.24715
−0.00552270u
11
+ 0.00817319u
10
+ ··· + 0.906846u − 0.519668
a
10
=
−0.0142037u
11
+ 0.0130176u
10
+ ··· + 1.64789u + 5.71216
0.000288279u
11
+ 0.00217888u
10
+ ··· + 0.643829u − 0.500596
a
6
=
−0.00769425u
11
+ 0.00607718u
10
+ ··· + 0.854249u + 3.54318
0.000610414u
11
− 0.00374271u
10
+ ··· − 0.565834u − 0.151468
a
3
=
0.0231155u
11
− 0.0220108u
10
+ ··· − 2.29090u − 9.06157
−0.00495739u
11
+ 0.00815269u
10
+ ··· + 1.27226u + 0.682710
a
9
=
0.00121749u
11
− 0.00291598u
10
+ ··· + 0.211235u + 0.193772
−0.00262321u
11
+ 0.00771675u
10
+ ··· + 1.37367u − 0.0600595
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
202582417527
100339302094541
u
11
+
1528171064
100339302094541
u
10
+ ··· −
89065053079638
100339302094541
u −
519580686866412
100339302094541
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
12
+ 4u
11
+ ··· + 306u − 181
c
2
, c
5
, c
6
u
12
+ 2u
11
+ ··· + 51u − 29
c
3
, c
9
(u
2
− u − 1)
6
c
4
, c
7
, c
11
c
12
u
12
+ u
11
+ ··· + 372u + 29
c
8
u
12
− 2u
11
+ ··· + 225u + 71
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
12
+ 26y
11
+ ··· − 185946y + 32761
c
2
, c
5
, c
6
y
12
+ 8y
11
+ ··· − 2253y + 841
c
3
, c
9
(y
2
− 3y + 1)
6
c
4
, c
7
, c
11
c
12
y
12
+ 29y
11
+ ··· − 144706y + 841
c
8
y
12
+ 24y
11
+ ··· − 99473y + 5041
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.008830 + 0.525673I
a = 0.572924 + 0.819609I
b = 0.492128
6.29775 −5.24698 + 0.I
u = −1.008830 − 0.525673I
a = 0.572924 − 0.819609I
b = 0.492128
6.29775 −5.24698 + 0.I
u = 0.694116
a = 0.110299
b = −0.748796
−1.59794 −5.24700
u = −0.556829 + 1.187920I
a = −0.639719 + 0.768609I
b = 2.27616
4.04184 −2.19806 + 0.I
u = −0.556829 − 1.187920I
a = −0.639719 − 0.768609I
b = 2.27616
4.04184 −2.19806 + 0.I
u = 0.0765601
a = 9.06629
b = −0.748796
−1.59794 −5.24700
u = 0.36005 + 2.25095I
a = −0.950106 − 0.311926I
b = 7.44338
−16.2613 −3.55496 + 0.I
u = 0.36005 − 2.25095I
a = −0.950106 + 0.311926I
b = 7.44338
−16.2613 −3.55496 + 0.I
u = 1.45780 + 2.14952I
a = −0.369908 − 0.929068I
b = 7.30056
11.9375 −2.19806 + 0.I
u = 1.45780 − 2.14952I
a = −0.369908 + 0.929068I
b = 7.30056
11.9375 −2.19806 + 0.I
19
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13753 + 2.64020I
a = −0.994588 + 0.103896I
b = 9.23656
15.3214 −3.55496 + 0.I
u = −0.13753 − 2.64020I
a = −0.994588 − 0.103896I
b = 9.23656
15.3214 −3.55496 + 0.I
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
7
− u
6
+ ··· + 8u − 5)(u
12
+ 4u
11
+ ··· − 20u − 5)
· (u
12
+ 4u
11
+ ··· + 306u − 181)(u
16
− 2u
15
+ ··· − 63u − 27)
c
2
, c
6
(u
7
+ u
6
+ u
5
− u
4
− u
2
+ u − 1)(u
12
+ 2u
11
+ ··· − 5u + 1)
· (u
12
+ 2u
11
+ ··· + 51u − 29)(u
16
+ 2u
15
+ ··· + 14u + 1)
c
3
(u
2
− u − 1)
6
(u
2
+ u − 1)
6
· (u
7
− 6u
6
+ 16u
5
− 25u
4
+ 26u
3
− 18u
2
+ 6u + 1)
· (u
16
+ 7u
15
+ ··· + 39u + 19)
c
4
, c
12
(u
7
+ 5u
5
+ ··· + 3u + 1)(u
12
− u
11
+ ··· + 4u − 1)
· (u
12
+ u
11
+ ··· + 372u + 29)(u
16
+ u
15
+ ··· − 3u
2
− 1)
c
5
(u
7
− u
6
+ u
5
+ u
4
+ u
2
+ u + 1)(u
12
− 2u
11
+ ··· + 5u + 1)
· (u
12
+ 2u
11
+ ··· + 51u − 29)(u
16
+ 2u
15
+ ··· + 14u + 1)
c
7
, c
11
(u
7
+ 5u
5
+ ··· + 3u − 1)(u
12
+ u
11
+ ··· − 4u − 1)
· (u
12
+ u
11
+ ··· + 372u + 29)(u
16
+ u
15
+ ··· − 3u
2
− 1)
c
8
(u
7
− u
6
+ ··· − u + 1)(u
12
− 2u
11
+ ··· + 225u + 71)
· (u
12
+ 2u
11
+ ··· + 25u + 25)(u
16
+ 2u
15
+ ··· + 4u + 1)
c
9
(u
2
− u − 1)
12
(u
7
+ 6u
6
+ 16u
5
+ 25u
4
+ 26u
3
+ 18u
2
+ 6u − 1)
· (u
16
+ 7u
15
+ ··· + 39u + 19)
c
10
(u
7
+ u
6
+ ··· + 8u + 5)(u
12
− 4u
11
+ ··· + 20u − 5)
· (u
12
+ 4u
11
+ ··· + 306u − 181)(u
16
− 2u
15
+ ··· − 63u − 27)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
7
+ 13y
6
+ 17y
5
− 161y
4
+ 313y
3
− 287y
2
+ 134y −25)
· (y
12
− 2y
11
+ ··· − 550y + 25)(y
12
+ 26y
11
+ ··· − 185946y + 32761)
· (y
16
+ 36y
15
+ ··· − 4131y + 729)
c
2
, c
5
, c
6
(y
7
+ y
6
+ ··· − y −1)(y
12
− 4y
11
+ ··· − 49y + 1)
· (y
12
+ 8y
11
+ ··· − 2253y + 841)(y
16
+ 4y
15
+ ··· − 104y + 1)
c
3
, c
9
(y
2
− 3y + 1)
12
(y
7
− 4y
6
+ 8y
5
+ 3y
4
− 20y
3
+ 38y
2
+ 72y −1)
· (y
16
− 17y
15
+ ··· − 1977y + 361)
c
4
, c
7
, c
11
c
12
(y
7
+ 10y
6
+ 39y
5
+ 60y
4
+ 47y
3
+ 18y
2
+ y −1)
· (y
12
+ 9y
11
+ ··· + 6y + 1)(y
12
+ 29y
11
+ ··· − 144706y + 841)
· (y
16
+ 21y
15
+ ··· + 6y + 1)
c
8
(y
7
+ 5y
6
+ 7y
5
+ 7y
4
+ 18y
3
− 7y
2
− 5y −1)
· (y
12
+ 8y
11
+ ··· − 125y + 625)(y
12
+ 24y
11
+ ··· − 99473y + 5041)
· (y
16
+ 16y
15
+ ··· + 8y + 1)
22
