12n
0603
(K12n
0603
)
A knot diagram
1
Linearized knot diagam
3 7 12 8 10 2 11 4 3 7 5 9
Solving Sequence
4,8
5
9,12
1 3 11 7 2 6 10
c
4
c
8
c
12
c
3
c
11
c
7
c
2
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h478u
12
+ 178u
11
+ ··· + 122b − 1078, a − 1,
u
13
+ 8u
11
+ 3u
10
+ 25u
9
+ 18u
8
+ 32u
7
+ 33u
6
+ 10u
5
+ 14u
4
− u
3
− 10u
2
+ 1i
I
u
2
= h2u
9
+ 7u
7
+ 4u
6
+ 7u
5
+ 10u
4
− 6u
3
+ 7u
2
+ 2b − 8u + 2, a + 1,
u
10
+ 4u
8
+ 2u
7
+ 5u
6
+ 6u
5
− 2u
4
+ 6u
3
− 6u
2
+ 2u − 1i
I
u
3
= hu
5
− 3u
4
+ 7u
3
− 16u
2
+ 9b + 8u − 10, −19u
5
+ 39u
4
− 79u
3
+ 178u
2
+ 9a − 35u + 226,
u
6
− 2u
5
+ 4u
4
− 9u
3
+ u
2
− 11u − 1i
I
u
4
= hb, a − u, u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 31 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
= h478u
12
+ 178u
11
+ · · · + 122b − 1078, a − 1, u
13
+ 8u
11
+ · · · − 10u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
u
a
12
=
1
−3.91803u
12
− 1.45902u
11
+ ··· + 23.6721u + 8.83607
a
1
=
0.729508u
12
+ 0.114754u
11
+ ··· − 3.91803u − 0.459016
−3.18852u
12
− 1.34426u
11
+ ··· + 19.7541u + 7.37705
a
3
=
3.91803u
12
+ 1.45902u
11
+ ··· − 23.6721u − 7.83607
−2.60656u
12
− 0.803279u
11
+ ··· + 16.9262u + 6.21311
a
11
=
−3.91803u
12
− 1.45902u
11
+ ··· + 23.6721u + 9.83607
−3.18852u
12
− 1.34426u
11
+ ··· + 19.7541u + 7.37705
a
7
=
−2.34426u
12
− 1.17213u
11
+ ··· + 15.3770u + 6.68852
−0.549180u
12
− 0.0245902u
11
+ ··· + 4.19672u + 1.59836
a
2
=
6.62295u
12
+ 2.81148u
11
+ ··· − 40.4918u − 14.7459
−1.68852u
12
+ 0.155738u
11
+ ··· + 12.2541u + 4.37705
a
6
=
5.24590u
12
+ 1.12295u
11
+ ··· − 29.9836u − 12.9918
−0.655738u
12
− 2.32787u
11
+ ··· + 3.62295u + 0.311475
a
10
=
−3.07377u
12
− 1.28689u
11
+ ··· + 20.2951u + 9.14754
−3.12295u
12
− 0.811475u
11
+ ··· + 19.9918u + 7.74590
(ii) Obstruction class = −1
(iii) Cusp Shapes =
125
122
u
12
+
215
122
u
11
+
1077
122
u
10
+
1082
61
u
9
+
4329
122
u
8
+
4205
61
u
7
+
4804
61
u
6
+
6996
61
u
5
+
11113
122
u
4
+
8069
122
u
3
+
2702
61
u
2
−
6
61
u −
979
61
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
+ 32u
12
+ ··· + 33u + 1
c
2
, c
6
u
13
− 2u
12
+ ··· − 5u + 1
c
3
u
13
− 8u
12
+ ··· − 9u + 2
c
4
, c
8
u
13
+ 8u
11
+ ··· − 10u
2
+ 1
c
5
u
13
− 25u
12
+ ··· + 9173u + 2591
c
7
, c
10
u
13
+ 8u
12
+ ··· + 27u + 4
c
9
u
13
− 18u
11
+ ··· + 738u + 244
c
11
u
13
+ 8u
12
+ ··· + 20u + 4
c
12
u
13
+ u
12
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 308y
12
+ ··· + 249y −1
c
2
, c
6
y
13
− 32y
12
+ ··· + 33y −1
c
3
y
13
+ 24y
11
+ ··· + 25y −4
c
4
, c
8
y
13
+ 16y
12
+ ··· + 20y −1
c
5
y
13
− 137y
12
+ ··· + 11823937y −6713281
c
7
, c
10
y
13
− 28y
12
+ ··· + 345y −16
c
9
y
13
− 36y
12
+ ··· − 302036y −59536
c
11
y
13
+ 2y
12
+ ··· + 120y −16
c
12
y
13
− 25y
12
+ ··· − 7y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.231299 + 1.092720I
a = 1.00000
b = 0.502972 − 0.016598I
−0.96921 + 1.60705I −6.76099 − 3.52286I
u = 0.231299 − 1.092720I
a = 1.00000
b = 0.502972 + 0.016598I
−0.96921 − 1.60705I −6.76099 + 3.52286I
u = −0.755051 + 0.130841I
a = 1.00000
b = 0.012282 + 0.611071I
−1.91994 − 0.62113I −7.84819 + 2.13633I
u = −0.755051 − 0.130841I
a = 1.00000
b = 0.012282 − 0.611071I
−1.91994 + 0.62113I −7.84819 − 2.13633I
u = −0.06382 + 1.54550I
a = 1.00000
b = 1.25006 + 1.58656I
15.3034 − 0.5963I −12.36984 + 0.02697I
u = −0.06382 − 1.54550I
a = 1.00000
b = 1.25006 − 1.58656I
15.3034 + 0.5963I −12.36984 − 0.02697I
u = 0.404295 + 0.009197I
a = 1.00000
b = −0.308660 − 1.174280I
2.44055 − 2.02483I −0.337255 + 1.060894I
u = 0.404295 − 0.009197I
a = 1.00000
b = −0.308660 + 1.174280I
2.44055 + 2.02483I −0.337255 − 1.060894I
u = −0.31241 + 1.60855I
a = 1.00000
b = 1.354220 − 0.086669I
−8.31754 − 4.12811I −12.63192 + 2.04182I
u = −0.31241 − 1.60855I
a = 1.00000
b = 1.354220 + 0.086669I
−8.31754 + 4.12811I −12.63192 − 2.04182I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.354088
a = 1.00000
b = −0.507588
−0.805953 −12.4890
u = 0.67274 + 1.79353I
a = 1.00000
b = 1.44292 − 1.29558I
14.4274 + 9.8229I −12.30738 − 3.83207I
u = 0.67274 − 1.79353I
a = 1.00000
b = 1.44292 + 1.29558I
14.4274 − 9.8229I −12.30738 + 3.83207I
6
II. I
u
2
= h2u
9
+ 7u
7
+ · · · + 2b + 2, a + 1, u
10
+ 4u
8
+ · · · + 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
u
a
12
=
−1
−u
9
−
7
2
u
7
+ ··· + 4u − 1
a
1
=
−
1
2
u
9
−
3
2
u
7
+ ··· + u − 1
−
3
2
u
9
− 5u
7
+ ··· + 5u − 1
a
3
=
−u
9
−
7
2
u
7
+ ··· −
7
2
u
2
+ 4u
−u
9
−
7
2
u
7
+ ··· +
5
2
u + 1
a
11
=
−u
9
−
7
2
u
7
+ ··· + 4u − 2
−
3
2
u
9
− 5u
7
+ ··· + 5u − 1
a
7
=
−
1
2
u
8
+
1
2
u
7
+ ··· − 2u + 2
−
1
2
u
9
−
1
2
u
8
+ ··· − 2u +
3
2
a
2
=
−u
9
−
1
2
u
8
+ ··· −
3
2
u
2
+
3
2
−u
9
−
1
2
u
8
+ ··· −
1
2
u + 2
a
6
=
1
2
u
8
−
1
2
u
7
+ ··· + u −
1
2
u
5
− u
4
+ 4u
3
− 3u
2
+ 4u − 2
a
10
=
−
1
2
u
9
+
1
2
u
8
+ ··· + 4u − 1
−
1
2
u
9
+
1
2
u
8
+ ··· +
9
2
u −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
5
2
u
9
−
1
2
u
8
+
19
2
u
7
+
7
2
u
6
+ 9u
5
+
27
2
u
4
−
21
2
u
3
+ 12u
2
− 16u − 10
7
(iv) u-Polynomials at the component
8
Crossings u-Polynomials at each crossing
c
1
u
10
− 12u
9
+ 38u
8
− 81u
7
+ 109u
6
− 102u
5
+ 62u
4
− 18u
3
− u + 1
c
2
u
10
− 2u
9
− 4u
8
+ 3u
7
+ 5u
6
− 6u
5
− 4u
4
+ 4u
3
− u + 1
c
3
u
10
+ 5u
9
+ ··· − 15u − 3
c
4
u
10
+ 4u
8
+ 2u
7
+ 5u
6
+ 6u
5
− 2u
4
+ 6u
3
− 6u
2
+ 2u − 1
c
5
u
10
− 3u
9
− 10u
8
− 6u
7
− 8u
6
− 18u
5
+ 7u
3
+ 8u
2
+ 3u + 1
c
6
u
10
+ 2u
9
− 4u
8
− 3u
7
+ 5u
6
+ 6u
5
− 4u
4
− 4u
3
+ u + 1
c
7
u
10
+ 5u
9
+ 6u
8
− 5u
7
− 10u
6
+ 2u
5
− 6u
3
+ 6u
2
+ 3u − 5
c
8
u
10
+ 4u
8
− 2u
7
+ 5u
6
− 6u
5
− 2u
4
− 6u
3
− 6u
2
− 2u − 1
c
9
u
10
− 5u
9
+ 5u
8
+ u
7
− 9u
6
+ 6u
5
− 3u
4
− 7u
3
+ 3u
2
− 1
c
10
u
10
− 5u
9
+ 6u
8
+ 5u
7
− 10u
6
− 2u
5
+ 6u
3
+ 6u
2
− 3u − 5
c
11
u
10
+ 3u
9
+ 6u
8
+ 6u
7
+ 4u
6
− 2u
5
− 5u
4
− 7u
3
+ 2u + 1
c
12
u
10
− u
9
− 6u
8
+ 3u
7
+ 11u
6
− 9u
5
− 11u
4
+ 5u
3
+ 2u
2
− 3u − 1
9
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
10
− 68y
9
+ ··· − y + 1
c
2
, c
6
y
10
− 12y
9
+ 38y
8
− 81y
7
+ 109y
6
− 102y
5
+ 62y
4
− 18y
3
− y + 1
c
3
y
10
+ 3y
9
+ 4y
8
+ 3y
7
+ 9y
6
+ 15y
5
+ 9y
4
− y
3
+ 16y
2
− 57y + 9
c
4
, c
8
y
10
+ 8y
9
+ ··· + 8y + 1
c
5
y
10
− 29y
9
+ ··· + 7y + 1
c
7
, c
10
y
10
− 13y
9
+ ··· − 69y + 25
c
9
y
10
− 15y
9
+ ··· − 6y + 1
c
11
y
10
+ 3y
9
+ 8y
8
+ 14y
7
+ 22y
6
+ 30y
5
− 15y
4
− 33y
3
+ 18y
2
− 4y + 1
c
12
y
10
− 13y
9
+ ··· − 13y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.009496 + 1.155230I
a = −1.00000
b = −0.572116 − 1.276800I
−5.38125 + 0.86206I −11.68799 − 0.71640I
u = 0.009496 − 1.155230I
a = −1.00000
b = −0.572116 + 1.276800I
−5.38125 − 0.86206I −11.68799 + 0.71640I
u = −1.28347
a = −1.00000
b = 0.970806
−17.3343 −8.37670
u = −0.335045 + 1.275960I
a = −1.00000
b = −1.122050 − 0.534600I
−2.32585 − 2.89091I −9.34725 + 3.73381I
u = −0.335045 − 1.275960I
a = −1.00000
b = −1.122050 + 0.534600I
−2.32585 + 2.89091I −9.34725 − 3.73381I
u = 0.612033
a = −1.00000
b = −0.407032
−3.00050 −14.5280
u = 0.116511 + 0.447058I
a = −1.00000
b = −0.261046 + 1.360630I
1.90106 + 2.27397I −12.92039 − 5.58214I
u = 0.116511 − 0.447058I
a = −1.00000
b = −0.261046 − 1.360630I
1.90106 − 2.27397I −12.92039 + 5.58214I
u = 0.54476 + 1.50703I
a = −1.00000
b = −0.826677 + 0.790310I
−7.05562 + 6.53270I −11.09214 − 5.33385I
u = 0.54476 − 1.50703I
a = −1.00000
b = −0.826677 − 0.790310I
−7.05562 − 6.53270I −11.09214 + 5.33385I
12
III. I
u
3
= hu
5
− 3u
4
+ 7u
3
− 16u
2
+ 9b + 8u − 10, −19u
5
+ 39u
4
+ · · · + 9a +
226, u
6
− 2u
5
+ 4u
4
− 9u
3
+ u
2
− 11u − 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
u
a
12
=
19
9
u
5
−
13
3
u
4
+ ··· +
35
9
u −
226
9
−
1
9
u
5
+
1
3
u
4
+ ··· −
8
9
u +
10
9
a
1
=
7
3
u
5
− 5u
4
+ ··· +
11
3
u −
76
3
1
9
u
5
−
1
3
u
4
+ ··· −
10
9
u +
8
9
a
3
=
−
25
9
u
5
+ 6u
4
+ ··· −
56
9
u +
280
9
2
9
u
5
−
1
3
u
4
+ ··· −
11
9
u −
14
9
a
11
=
19
9
u
5
−
13
3
u
4
+ ··· +
35
9
u −
217
9
−
1
9
u
5
+
1
3
u
4
+ ··· −
8
9
u +
10
9
a
7
=
43
9
u
5
− 10u
4
+ ··· +
83
9
u −
478
9
−
2
9
u
5
+
1
3
u
4
+ ··· +
2
9
u +
23
9
a
2
=
−
43
3
u
5
+
91
3
u
4
+ ··· −
83
3
u + 161
8
9
u
5
−
5
3
u
4
+ ··· −
26
9
u −
71
9
a
6
=
−30.7778u
5
+ 63.6667u
4
+ ··· − 57.2222u + 340.444
2u
5
−
11
3
u
4
+ ··· + 9u −
46
3
a
10
=
−8.44444u
5
+ 17.6667u
4
+ ··· − 15.5556u + 93.1111
4
9
u
5
−
1
3
u
4
+ ··· −
4
9
u −
40
9
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1
9
u
5
+
5
9
u
3
−
8
9
u
2
+
19
9
u −
149
9
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 23u
5
+ 149u
4
+ 597u
3
+ 2195u
2
+ 1982u + 529
c
2
, c
6
u
6
+ 3u
5
− 7u
4
− 19u
3
− 7u
2
+ 48u − 23
c
3
(u
3
+ u
2
− u − 2)
2
c
4
, c
8
u
6
− 2u
5
+ 4u
4
− 9u
3
+ u
2
− 11u − 1
c
5
u
6
+ 6u
5
− 36u
4
− 47u
3
+ 329u
2
− 331u + 101
c
7
, c
10
(u
3
− 2u
2
− 1)
2
c
9
u
6
− 5u
5
− 9u
4
+ 42u
3
− 53u
2
− 165u − 83
c
11
(u − 1)
6
c
12
u
6
− 8u
4
+ 3u
3
+ 9u
2
− u − 17
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 231y
5
+ ··· − 1606014y + 279841
c
2
, c
6
y
6
− 23y
5
+ 149y
4
− 597y
3
+ 2195y
2
− 1982y + 529
c
3
(y
3
− 3y
2
+ 5y − 4)
2
c
4
, c
8
y
6
+ 4y
5
− 18y
4
− 119y
3
− 205y
2
− 123y + 1
c
5
y
6
− 108y
5
+ 2518y
4
− 21723y
3
+ 69855y
2
− 43103y + 10201
c
7
, c
10
(y
3
− 4y
2
− 4y − 1)
2
c
9
y
6
− 43y
5
+ 395y
4
− 2626y
3
+ 18163y
2
− 18427y + 6889
c
11
(y − 1)
6
c
12
y
6
− 16y
5
+ 82y
4
− 187y
3
+ 359y
2
− 307y + 289
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.261577 + 1.168950I
a = −1.52339 + 0.20505I
b = −1.102790 − 0.665457I
−3.89790 − 2.56897I −15.1239 + 2.1332I
u = −0.261577 − 1.168950I
a = −1.52339 − 0.20505I
b = −1.102790 + 0.665457I
−3.89790 + 2.56897I −15.1239 − 2.1332I
u = 0.15879 + 1.83440I
a = −0.644748 + 0.086783I
b = −1.102790 + 0.665457I
−3.89790 + 2.56897I −15.1239 − 2.1332I
u = 0.15879 − 1.83440I
a = −0.644748 − 0.086783I
b = −1.102790 − 0.665457I
−3.89790 − 2.56897I −15.1239 + 2.1332I
u = −0.0895674
a = −25.6247
b = 1.20557
−18.5231 −16.7520
u = 2.29514
a = −0.0390249
b = 1.20557
−18.5231 −16.7520
16
IV. I
u
4
= hb, a − u, u
2
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u + 1
a
9
=
u
u
a
12
=
u
0
a
1
=
u − 1
−1
a
3
=
1
0
a
11
=
u − 1
u − 1
a
7
=
−u + 1
1
a
2
=
u
−1
a
6
=
1
0
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −15
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
11
(u − 1)
2
c
3
u
2
c
4
, c
5
u
2
− u + 1
c
6
, c
10
(u + 1)
2
c
8
, c
9
, c
12
u
2
+ u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
10
, c
11
(y − 1)
2
c
3
y
2
c
4
, c
5
, c
8
c
9
, c
12
y
2
+ y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = 0
−3.28987 −15.0000
u = 0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 0
−3.28987 −15.0000
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
(u
6
+ 23u
5
+ 149u
4
+ 597u
3
+ 2195u
2
+ 1982u + 529)
· (u
10
− 12u
9
+ 38u
8
− 81u
7
+ 109u
6
− 102u
5
+ 62u
4
− 18u
3
− u + 1)
· (u
13
+ 32u
12
+ ··· + 33u + 1)
c
2
(u − 1)
2
(u
6
+ 3u
5
− 7u
4
− 19u
3
− 7u
2
+ 48u − 23)
· (u
10
− 2u
9
− 4u
8
+ 3u
7
+ 5u
6
− 6u
5
− 4u
4
+ 4u
3
− u + 1)
· (u
13
− 2u
12
+ ··· − 5u + 1)
c
3
u
2
(u
3
+ u
2
− u − 2)
2
(u
10
+ 5u
9
+ ··· − 15u − 3)
· (u
13
− 8u
12
+ ··· − 9u + 2)
c
4
(u
2
− u + 1)(u
6
− 2u
5
+ 4u
4
− 9u
3
+ u
2
− 11u − 1)
· (u
10
+ 4u
8
+ 2u
7
+ 5u
6
+ 6u
5
− 2u
4
+ 6u
3
− 6u
2
+ 2u − 1)
· (u
13
+ 8u
11
+ ··· − 10u
2
+ 1)
c
5
(u
2
− u + 1)(u
6
+ 6u
5
− 36u
4
− 47u
3
+ 329u
2
− 331u + 101)
· (u
10
− 3u
9
− 10u
8
− 6u
7
− 8u
6
− 18u
5
+ 7u
3
+ 8u
2
+ 3u + 1)
· (u
13
− 25u
12
+ ··· + 9173u + 2591)
c
6
(u + 1)
2
(u
6
+ 3u
5
− 7u
4
− 19u
3
− 7u
2
+ 48u − 23)
· (u
10
+ 2u
9
− 4u
8
− 3u
7
+ 5u
6
+ 6u
5
− 4u
4
− 4u
3
+ u + 1)
· (u
13
− 2u
12
+ ··· − 5u + 1)
c
7
(u − 1)
2
(u
3
− 2u
2
− 1)
2
· (u
10
+ 5u
9
+ 6u
8
− 5u
7
− 10u
6
+ 2u
5
− 6u
3
+ 6u
2
+ 3u − 5)
· (u
13
+ 8u
12
+ ··· + 27u + 4)
c
8
(u
2
+ u + 1)(u
6
− 2u
5
+ 4u
4
− 9u
3
+ u
2
− 11u − 1)
· (u
10
+ 4u
8
− 2u
7
+ 5u
6
− 6u
5
− 2u
4
− 6u
3
− 6u
2
− 2u − 1)
· (u
13
+ 8u
11
+ ··· − 10u
2
+ 1)
c
9
(u
2
+ u + 1)(u
6
− 5u
5
− 9u
4
+ 42u
3
− 53u
2
− 165u − 83)
· (u
10
− 5u
9
+ 5u
8
+ u
7
− 9u
6
+ 6u
5
− 3u
4
− 7u
3
+ 3u
2
− 1)
· (u
13
− 18u
11
+ ··· + 738u + 244)
c
10
(u + 1)
2
(u
3
− 2u
2
− 1)
2
· (u
10
− 5u
9
+ 6u
8
+ 5u
7
− 10u
6
− 2u
5
+ 6u
3
+ 6u
2
− 3u − 5)
· (u
13
+ 8u
12
+ ··· + 27u + 4)
c
11
(u − 1)
8
(u
10
+ 3u
9
+ 6u
8
+ 6u
7
+ 4u
6
− 2u
5
− 5u
4
− 7u
3
+ 2u + 1)
· (u
13
+ 8u
12
+ ··· + 20u + 4)
c
12
(u
2
+ u + 1)(u
6
− 8u
4
+ 3u
3
+ 9u
2
− u − 17)
· (u
10
− u
9
− 6u
8
+ 3u
7
+ 11u
6
− 9u
5
− 11u
4
+ 5u
3
+ 2u
2
− 3u − 1)
· (u
13
+ u
12
+ ··· + u + 1)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
2
)(y
6
− 231y
5
+ ··· − 1606014y + 279841)
· (y
10
− 68y
9
+ ··· − y + 1)(y
13
− 308y
12
+ ··· + 249y − 1)
c
2
, c
6
(y − 1)
2
(y
6
− 23y
5
+ 149y
4
− 597y
3
+ 2195y
2
− 1982y + 529)
· (y
10
− 12y
9
+ 38y
8
− 81y
7
+ 109y
6
− 102y
5
+ 62y
4
− 18y
3
− y + 1)
· (y
13
− 32y
12
+ ··· + 33y − 1)
c
3
y
2
(y
3
− 3y
2
+ 5y − 4)
2
· (y
10
+ 3y
9
+ 4y
8
+ 3y
7
+ 9y
6
+ 15y
5
+ 9y
4
− y
3
+ 16y
2
− 57y + 9)
· (y
13
+ 24y
11
+ ··· + 25y − 4)
c
4
, c
8
(y
2
+ y + 1)(y
6
+ 4y
5
− 18y
4
− 119y
3
− 205y
2
− 123y + 1)
· (y
10
+ 8y
9
+ ··· + 8y + 1)(y
13
+ 16y
12
+ ··· + 20y − 1)
c
5
(y
2
+ y + 1)
· (y
6
− 108y
5
+ 2518y
4
− 21723y
3
+ 69855y
2
− 43103y + 10201)
· (y
10
− 29y
9
+ ··· + 7y + 1)
· (y
13
− 137y
12
+ ··· + 11823937y − 6713281)
c
7
, c
10
((y − 1)
2
)(y
3
− 4y
2
− 4y − 1)
2
(y
10
− 13y
9
+ ··· − 69y + 25)
· (y
13
− 28y
12
+ ··· + 345y − 16)
c
9
(y
2
+ y + 1)(y
6
− 43y
5
+ ··· − 18427y + 6889)
· (y
10
− 15y
9
+ ··· − 6y + 1)(y
13
− 36y
12
+ ··· − 302036y − 59536)
c
11
(y − 1)
8
· (y
10
+ 3y
9
+ 8y
8
+ 14y
7
+ 22y
6
+ 30y
5
− 15y
4
− 33y
3
+ 18y
2
− 4y + 1)
· (y
13
+ 2y
12
+ ··· + 120y − 16)
c
12
(y
2
+ y + 1)(y
6
− 16y
5
+ 82y
4
− 187y
3
+ 359y
2
− 307y + 289)
· (y
10
− 13y
9
+ ··· − 13y + 1)(y
13
− 25y
12
+ ··· − 7y − 1)
22
