12a
1284
(K12a
1284
)
A knot diagram
1
Linearized knot diagam
5 10 8 9 11 12 1 4 2 3 7 6
Solving Sequence
2,9
10 3
5,11
6 1 4 8 7 12
c
9
c
2
c
10
c
5
c
1
c
4
c
8
c
7
c
12
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, u
28
− u
27
+ ··· + 16a − 1, u
30
− u
29
+ ··· + 2u + 1i
I
u
2
= h6.24110 × 10
20
u
39
+ 5.89445 × 10
20
u
38
+ ··· + 1.64141 × 10
21
b + 4.89782 × 10
20
,
− 1.01730 × 10
21
u
39
+ 2.23086 × 10
21
u
38
+ ··· + 1.64141 × 10
21
a − 2.79305 × 10
21
, u
40
− u
39
+ ··· + 2u − 1i
I
u
3
= hb − 1, a
4
− 3a
2
+ 3, u + 1i
I
u
4
= hb + 1, a
4
− a
2
− 1, u − 1i
I
u
5
= hb − 1, a, u + 1i
* 5 irreducible components of dim
C
= 0, with total 79 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
= hb − u, u
28
− u
27
+ · · · + 16a − 1, u
30
− u
29
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
3
=
u
−u
3
+ u
a
5
=
−0.0625000u
28
+ 0.0625000u
27
+ ··· + 3.12500u + 0.0625000
u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
−0.0625000u
28
+ 0.0625000u
27
+ ··· + 2.12500u + 0.0625000
−
1
16
u
28
+
1
16
u
27
+ ··· +
9
8
u +
1
16
a
1
=
1
16
u
29
−
1
16
u
28
+ ··· +
3
16
u +
1
8
−
1
16
u
28
+
1
16
u
27
+ ··· +
9
8
u +
1
16
a
4
=
−0.0625000u
28
+ 0.0625000u
27
+ ··· + 2.12500u + 0.0625000
u
a
8
=
−
1
16
u
29
+
1
16
u
28
+ ··· +
1
16
u + 1
u
2
a
7
=
11
16
u
29
−
13
16
u
28
+ ··· −
9
16
u +
5
4
1
16
u
29
−
1
8
u
28
+ ··· −
1
16
u +
1
16
a
12
=
−
3
16
u
29
+
7
2
u
27
+ ··· −
5
16
u −
7
16
−0.375000u
29
+ 0.937500u
28
+ ··· − 0.250000u − 1.18750
(ii) Obstruction class = −1
(iii) Cusp Shapes =
5
4
u
29
−
13
8
u
28
+ ··· +
43
4
u +
33
8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 21u
29
+ ··· − 31648u − 3214
c
2
, c
3
, c
4
c
8
, c
9
, c
10
u
30
+ u
29
+ ··· − 2u + 1
c
5
, c
7
u
30
+ 3u
29
+ ··· − 180u − 34
c
6
, c
11
, c
12
u
30
− 3u
29
+ ··· − 7u
2
− 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 5y
29
+ ··· + 33781340y + 10329796
c
2
, c
3
, c
4
c
8
, c
9
, c
10
y
30
− 37y
29
+ ··· − 4y + 1
c
5
, c
7
y
30
− 19y
29
+ ··· + 9692y + 1156
c
6
, c
11
, c
12
y
30
+ 25y
29
+ ··· + 28y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.352980 + 0.621053I
a = −0.54691 + 1.67340I
b = −0.352980 + 0.621053I
0.67916 − 7.00854I 0.01450 + 8.24477I
u = −0.352980 − 0.621053I
a = −0.54691 − 1.67340I
b = −0.352980 − 0.621053I
0.67916 + 7.00854I 0.01450 − 8.24477I
u = 0.294160 + 0.620614I
a = 0.46496 + 1.62443I
b = 0.294160 + 0.620614I
−3.74541 + 3.07076I −5.43052 − 5.87151I
u = 0.294160 − 0.620614I
a = 0.46496 − 1.62443I
b = 0.294160 − 0.620614I
−3.74541 − 3.07076I −5.43052 + 5.87151I
u = −0.209229 + 0.628257I
a = −0.33328 + 1.58251I
b = −0.209229 + 0.628257I
−0.424922 + 0.787716I −2.53323 + 1.27592I
u = −0.209229 − 0.628257I
a = −0.33328 − 1.58251I
b = −0.209229 − 0.628257I
−0.424922 − 0.787716I −2.53323 − 1.27592I
u = 1.38964
a = −1.59527
b = 1.38964
2.23351 3.74940
u = −1.391950 + 0.032239I
a = 1.56027 + 0.24632I
b = −1.391950 + 0.032239I
6.15309 − 4.53590I 7.37130 + 3.41569I
u = −1.391950 − 0.032239I
a = 1.56027 − 0.24632I
b = −1.391950 − 0.032239I
6.15309 + 4.53590I 7.37130 − 3.41569I
u = 0.416588 + 0.365315I
a = 0.98597 + 1.30700I
b = 0.416588 + 0.365315I
5.06214 + 1.29762I 5.37578 − 5.33556I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.416588 − 0.365315I
a = 0.98597 − 1.30700I
b = 0.416588 − 0.365315I
5.06214 − 1.29762I 5.37578 + 5.33556I
u = −0.517665 + 0.077298I
a = −1.88180 + 0.43471I
b = −0.517665 + 0.077298I
1.63781 + 3.82634I 1.68492 − 2.14247I
u = −0.517665 − 0.077298I
a = −1.88180 − 0.43471I
b = −0.517665 − 0.077298I
1.63781 − 3.82634I 1.68492 + 2.14247I
u = 0.496783
a = 1.81590
b = 0.496783
−2.35493 −2.87800
u = 1.49927 + 0.29227I
a = −0.387167 + 1.211670I
b = 1.49927 + 0.29227I
10.74230 + 6.05762I 6.37484 − 2.22999I
u = 1.49927 − 0.29227I
a = −0.387167 − 1.211670I
b = 1.49927 − 0.29227I
10.74230 − 6.05762I 6.37484 + 2.22999I
u = −1.51089 + 0.32477I
a = 0.274857 + 1.261600I
b = −1.51089 + 0.32477I
8.04859 − 10.42510I 3.37060 + 6.14879I
u = −1.51089 − 0.32477I
a = 0.274857 − 1.261600I
b = −1.51089 − 0.32477I
8.04859 + 10.42510I 3.37060 − 6.14879I
u = 1.53112 + 0.22334I
a = −0.460811 + 0.930719I
b = 1.53112 + 0.22334I
11.80090 + 5.69316I 7.29124 − 4.91871I
u = 1.53112 − 0.22334I
a = −0.460811 − 0.930719I
b = 1.53112 − 0.22334I
11.80090 − 5.69316I 7.29124 + 4.91871I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.54555 + 0.16201I
a = 0.530144 + 0.687150I
b = −1.54555 + 0.16201I
10.58750 − 1.81546I 5.41289 + 0.I
u = −1.54555 − 0.16201I
a = 0.530144 − 0.687150I
b = −1.54555 − 0.16201I
10.58750 + 1.81546I 5.41289 + 0.I
u = 1.52517 + 0.34179I
a = −0.201317 + 1.264960I
b = 1.52517 + 0.34179I
12.9098 + 14.6347I 7.58491 − 7.68189I
u = 1.52517 − 0.34179I
a = −0.201317 − 1.264960I
b = 1.52517 − 0.34179I
12.9098 − 14.6347I 7.58491 + 7.68189I
u = −0.195804 + 0.351319I
a = −0.470190 + 1.033650I
b = −0.195804 + 0.351319I
−0.006279 − 0.796564I −0.20542 + 8.65055I
u = −0.195804 − 0.351319I
a = −0.470190 − 1.033650I
b = −0.195804 − 0.351319I
−0.006279 + 0.796564I −0.20542 − 8.65055I
u = 1.59665 + 0.14347I
a = −0.371698 + 0.545654I
b = 1.59665 + 0.14347I
15.9724 − 1.4645I 10.01323 + 0.I
u = 1.59665 − 0.14347I
a = −0.371698 − 0.545654I
b = 1.59665 − 0.14347I
15.9724 + 1.4645I 10.01323 + 0.I
u = −1.58211 + 0.26365I
a = 0.226662 + 0.948412I
b = −1.58211 + 0.26365I
18.5173 − 6.9140I 11.23927 + 3.74532I
u = −1.58211 − 0.26365I
a = 0.226662 − 0.948412I
b = −1.58211 − 0.26365I
18.5173 + 6.9140I 11.23927 − 3.74532I
7
II.
I
u
2
= h6.24×10
20
u
39
+5.89×10
20
u
38
+· · ·+1.64×10
21
b+4.90×10
20
, −1.02×
10
21
u
39
+2.23×10
21
u
38
+· · ·+1.64×10
21
a−2.79×10
21
, u
40
−u
39
+· · ·+2u−1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
3
=
u
−u
3
+ u
a
5
=
0.619773u
39
− 1.35911u
38
+ ··· + 22.9232u + 1.70161
−0.380227u
39
− 0.359108u
38
+ ··· + 4.92321u − 0.298390
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
0.543102u
39
− 1.19599u
38
+ ··· + 16.4379u + 1.69783
−0.0232908u
39
− 0.365372u
38
+ ··· + 4.85714u + 0.0127958
a
1
=
1.26580u
39
− 1.30533u
38
+ ··· + 27.7480u + 2.14255
0.646027u
39
+ 0.0537756u
38
+ ··· + 5.82476u + 0.440945
a
4
=
u
39
− u
38
+ ··· + 18u + 2
−0.380227u
39
− 0.359108u
38
+ ··· + 4.92321u − 0.298390
a
8
=
−0.298390u
39
− 0.0818367u
38
+ ··· + 15.7873u + 5.32643
0.739335u
39
+ 0.286919u
38
+ ··· − 0.462064u + 1.38023
a
7
=
−0.525272u
39
− 0.0557406u
38
+ ··· + 1.36459u − 3.86438
0.0790643u
39
+ 0.253718u
38
+ ··· + 0.778092u − 0.531600
a
12
=
0.268227u
39
− 0.849361u
38
+ ··· + 0.608273u + 1.83922
0.302594u
39
+ 0.273543u
38
+ ··· + 1.54337u + 0.135768
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
6400585822088433349960
1641414549632366281823
u
39
−
1917396265968610128824
1641414549632366281823
u
38
+ ··· −
21817392701530411229944
1641414549632366281823
u −
8303876159610635920642
1641414549632366281823
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
20
− 7u
19
+ ··· − 6u + 1)
2
c
2
, c
3
, c
4
c
8
, c
9
, c
10
u
40
+ u
39
+ ··· − 2u − 1
c
5
, c
7
(u
20
− u
19
+ ··· + 4u − 1)
2
c
6
, c
11
, c
12
(u
20
+ u
19
+ ··· + 2u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 13y
19
+ ··· − 6y + 1)
2
c
2
, c
3
, c
4
c
8
, c
9
, c
10
y
40
− 33y
39
+ ··· − 40y + 1
c
5
, c
7
(y
20
− 11y
19
+ ··· − 6y + 1)
2
c
6
, c
11
, c
12
(y
20
+ 17y
19
+ ··· − 6y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.775780 + 0.647591I
a = −0.630465 − 0.581990I
b = −1.390130 + 0.052152I
2.96536 − 0.81573I 2.32828 + 1.07888I
u = 0.775780 − 0.647591I
a = −0.630465 + 0.581990I
b = −1.390130 − 0.052152I
2.96536 + 0.81573I 2.32828 − 1.07888I
u = −0.434102 + 0.914548I
a = 1.03581 − 1.10998I
b = 1.45939 − 0.21760I
6.57229 − 10.05770I 5.29166 + 7.26612I
u = −0.434102 − 0.914548I
a = 1.03581 + 1.10998I
b = 1.45939 + 0.21760I
6.57229 + 10.05770I 5.29166 − 7.26612I
u = −0.939888 + 0.425646I
a = 0.373710 − 0.231234I
b = 1.256600 + 0.168597I
6.05405 − 2.16136I 7.26252 + 3.31855I
u = −0.939888 − 0.425646I
a = 0.373710 + 0.231234I
b = 1.256600 − 0.168597I
6.05405 + 2.16136I 7.26252 − 3.31855I
u = 0.416544 + 0.869986I
a = −0.98007 − 1.14721I
b = −1.42778 − 0.21212I
1.80703 + 6.07240I 0.54715 − 5.87540I
u = 0.416544 − 0.869986I
a = −0.98007 + 1.14721I
b = −1.42778 + 0.21212I
1.80703 − 6.07240I 0.54715 + 5.87540I
u = 0.608596 + 0.846537I
a = −0.914359 − 0.871769I
b = −1.47424 − 0.09300I
11.26460 + 2.84648I 9.60998 − 2.97861I
u = 0.608596 − 0.846537I
a = −0.914359 + 0.871769I
b = −1.47424 + 0.09300I
11.26460 − 2.84648I 9.60998 + 2.97861I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.946129 + 0.119622I
a = −1.166750 − 0.332930I
b = −0.126443 − 0.201400I
1.63329 − 3.96853I 0.10651 + 3.79787I
u = −0.946129 − 0.119622I
a = −1.166750 + 0.332930I
b = −0.126443 + 0.201400I
1.63329 + 3.96853I 0.10651 − 3.79787I
u = 0.916645
a = 1.24074
b = 0.149808
−2.26801 −4.44030
u = −0.807999 + 0.735436I
a = 0.774534 − 0.558298I
b = 1.45140 + 0.05778I
7.72048 + 4.43308I 7.31630 − 2.52728I
u = −0.807999 − 0.735436I
a = 0.774534 + 0.558298I
b = 1.45140 − 0.05778I
7.72048 − 4.43308I 7.31630 + 2.52728I
u = −0.549205 + 0.695984I
a = 0.673732 − 0.972316I
b = 1.372450 − 0.086864I
4.95641 − 2.35832I 5.64775 + 4.49783I
u = −0.549205 − 0.695984I
a = 0.673732 + 0.972316I
b = 1.372450 + 0.086864I
4.95641 + 2.35832I 5.64775 − 4.49783I
u = −0.398694 + 0.774094I
a = 0.84367 − 1.21023I
b = 1.369530 − 0.189240I
4.55875 − 2.13456I 3.49102 + 2.16962I
u = −0.398694 − 0.774094I
a = 0.84367 + 1.21023I
b = 1.369530 + 0.189240I
4.55875 + 2.13456I 3.49102 − 2.16962I
u = −1.15120
a = −0.215264
b = 0.653394
2.60969 −2.76210
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.256600 + 0.168597I
a = −0.158159 + 0.320761I
b = −0.939888 + 0.425646I
6.05405 − 2.16136I 7.26252 + 3.31855I
u = 1.256600 − 0.168597I
a = −0.158159 − 0.320761I
b = −0.939888 − 0.425646I
6.05405 + 2.16136I 7.26252 − 3.31855I
u = 0.653394
a = 0.379269
b = −1.15120
2.60969 −2.76210
u = 1.372450 + 0.086864I
a = 0.176513 − 0.741916I
b = −0.549205 − 0.695984I
4.95641 + 2.35832I 0
u = 1.372450 − 0.086864I
a = 0.176513 + 0.741916I
b = −0.549205 + 0.695984I
4.95641 − 2.35832I 0
u = 1.369530 + 0.189240I
a = 0.317804 − 0.873099I
b = −0.398694 − 0.774094I
4.55875 + 2.13456I 0
u = 1.369530 − 0.189240I
a = 0.317804 + 0.873099I
b = −0.398694 + 0.774094I
4.55875 − 2.13456I 0
u = −1.390130 + 0.052152I
a = 0.057435 + 0.620642I
b = 0.775780 + 0.647591I
2.96536 − 0.81573I 0
u = −1.390130 − 0.052152I
a = 0.057435 − 0.620642I
b = 0.775780 − 0.647591I
2.96536 + 0.81573I 0
u = −1.42778 + 0.21212I
a = −0.268719 − 0.971795I
b = 0.416544 − 0.869986I
1.80703 − 6.07240I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42778 − 0.21212I
a = −0.268719 + 0.971795I
b = 0.416544 + 0.869986I
1.80703 + 6.07240I 0
u = 1.45140 + 0.05778I
a = −0.120101 + 0.708049I
b = −0.807999 + 0.735436I
7.72048 + 4.43308I 0
u = 1.45140 − 0.05778I
a = −0.120101 − 0.708049I
b = −0.807999 − 0.735436I
7.72048 − 4.43308I 0
u = 1.45939 + 0.21760I
a = 0.236213 − 1.014500I
b = −0.434102 − 0.914548I
6.57229 + 10.05770I 0
u = 1.45939 − 0.21760I
a = 0.236213 + 1.014500I
b = −0.434102 + 0.914548I
6.57229 − 10.05770I 0
u = −1.47424 + 0.09300I
a = −0.067033 − 0.889156I
b = 0.608596 − 0.846537I
11.26460 − 2.84648I 0
u = −1.47424 − 0.09300I
a = −0.067033 + 0.889156I
b = 0.608596 + 0.846537I
11.26460 + 2.84648I 0
u = −0.126443 + 0.201400I
a = −3.18208 − 3.68109I
b = −0.946129 − 0.119622I
1.63329 + 3.96853I 0.10651 − 3.79787I
u = −0.126443 − 0.201400I
a = −3.18208 + 3.68109I
b = −0.946129 + 0.119622I
1.63329 − 3.96853I 0.10651 + 3.79787I
u = 0.149808
a = 7.59187
b = 0.916645
−2.26801 −4.44030
14
III. I
u
3
= hb − 1, a
4
− 3a
2
+ 3, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
9
=
1
0
a
10
=
1
−1
a
3
=
−1
0
a
5
=
a
1
a
11
=
0
−1
a
6
=
a
a + 1
a
1
=
−a
2
−a − 1
a
4
=
a − 1
1
a
8
=
a
1
a
7
=
−a
3
+ a
−a
2
− a + 1
a
12
=
a
2
− 3
a
3
+ 2a
2
− 2a − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a
2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
4
− 3u
2
+ 3
c
2
, c
8
(u − 1)
4
c
3
, c
4
, c
9
c
10
(u + 1)
4
c
6
, c
11
, c
12
u
4
+ 3u
2
+ 3
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y
2
− 3y + 3)
2
c
2
, c
3
, c
4
c
8
, c
9
, c
10
(y −1)
4
c
6
, c
11
, c
12
(y
2
+ 3y + 3)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.271230 + 0.340625I
b = 1.00000
3.28987 − 4.05977I 6.00000 + 3.46410I
u = −1.00000
a = 1.271230 − 0.340625I
b = 1.00000
3.28987 + 4.05977I 6.00000 − 3.46410I
u = −1.00000
a = −1.271230 + 0.340625I
b = 1.00000
3.28987 + 4.05977I 6.00000 − 3.46410I
u = −1.00000
a = −1.271230 − 0.340625I
b = 1.00000
3.28987 − 4.05977I 6.00000 + 3.46410I
18
IV. I
u
4
= hb + 1, a
4
− a
2
− 1, u − 1i
(i) Arc colorings
a
2
=
0
1
a
9
=
1
0
a
10
=
1
−1
a
3
=
1
0
a
5
=
a
−1
a
11
=
0
−1
a
6
=
a
a − 1
a
1
=
a
2
−a + 1
a
4
=
a + 1
−1
a
8
=
−a
1
a
7
=
a
3
− a
−a
2
+ a + 1
a
12
=
a
2
− 1
a
3
− 2a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
2
+ 8
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
4
− u
2
− 1
c
2
, c
8
(u + 1)
4
c
3
, c
4
, c
9
c
10
(u − 1)
4
c
6
, c
11
, c
12
u
4
+ u
2
− 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y
2
− y −1)
2
c
2
, c
3
, c
4
c
8
, c
9
, c
10
(y −1)
4
c
6
, c
11
, c
12
(y
2
+ y −1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.786151I
b = −1.00000
7.23771 10.4720
u = 1.00000
a = − 0.786151I
b = −1.00000
7.23771 10.4720
u = 1.00000
a = 1.27202
b = −1.00000
−0.657974 1.52790
u = 1.00000
a = −1.27202
b = −1.00000
−0.657974 1.52790
22
V. I
u
5
= hb − 1, a, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
9
=
1
0
a
10
=
1
−1
a
3
=
−1
0
a
5
=
0
1
a
11
=
0
−1
a
6
=
0
1
a
1
=
0
−1
a
4
=
−1
1
a
8
=
0
1
a
7
=
0
1
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
u
c
2
, c
8
u − 1
c
3
, c
4
, c
9
c
10
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
y
c
2
, c
3
, c
4
c
8
, c
9
, c
10
y −1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = 1.00000
3.28987 12.0000
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
4
− 3u
2
+ 3)(u
4
− u
2
− 1)(u
20
− 7u
19
+ ··· − 6u + 1)
2
· (u
30
+ 21u
29
+ ··· − 31648u − 3214)
c
2
, c
8
((u − 1)
5
)(u + 1)
4
(u
30
+ u
29
+ ··· − 2u + 1)(u
40
+ u
39
+ ··· − 2u − 1)
c
3
, c
4
, c
9
c
10
((u − 1)
4
)(u + 1)
5
(u
30
+ u
29
+ ··· − 2u + 1)(u
40
+ u
39
+ ··· − 2u − 1)
c
5
, c
7
u(u
4
− 3u
2
+ 3)(u
4
− u
2
− 1)(u
20
− u
19
+ ··· + 4u − 1)
2
· (u
30
+ 3u
29
+ ··· − 180u − 34)
c
6
, c
11
, c
12
u(u
4
+ u
2
− 1)(u
4
+ 3u
2
+ 3)(u
20
+ u
19
+ ··· + 2u − 1)
2
· (u
30
− 3u
29
+ ··· − 7u
2
− 2)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
− 3y + 3)
2
(y
2
− y −1)
2
(y
20
+ 13y
19
+ ··· − 6y + 1)
2
· (y
30
+ 5y
29
+ ··· + 33781340y + 10329796)
c
2
, c
3
, c
4
c
8
, c
9
, c
10
((y −1)
9
)(y
30
− 37y
29
+ ··· − 4y + 1)(y
40
− 33y
39
+ ··· − 40y + 1)
c
5
, c
7
y(y
2
− 3y + 3)
2
(y
2
− y −1)
2
(y
20
− 11y
19
+ ··· − 6y + 1)
2
· (y
30
− 19y
29
+ ··· + 9692y + 1156)
c
6
, c
11
, c
12
y(y
2
+ y −1)
2
(y
2
+ 3y + 3)
2
(y
20
+ 17y
19
+ ··· − 6y + 1)
2
· (y
30
+ 25y
29
+ ··· + 28y + 4)
28
