12n
0184
(K12n
0184
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 12 4 6 5 9 7 11
Solving Sequence
5,10 3,6
2 1 4 9 11 8 7 12
c
5
c
2
c
1
c
4
c
9
c
10
c
8
c
7
c
12
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.91771 × 10
36
u
41
− 1.79820 × 10
38
u
40
+ ··· + 2.88772 × 10
39
b + 4.22720 × 10
39
,
9.16076 × 10
39
u
41
− 6.73128 × 10
39
u
40
+ ··· + 4.90913 × 10
40
a + 8.21058 × 10
40
, u
42
− 2u
41
+ ··· + 16u − 17i
I
u
2
= hb + 1, −2u
8
+ u
7
+ 5u
6
− 3u
5
− 4u
4
+ 3u
3
− 2u
2
+ a + 2, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
u
3
= h33u
3
a
2
− 5a
2
u
2
− 4u
3
a − 30a
2
u + 106u
2
a + 89u
3
− 19a
2
+ 7au + 28u
2
+ 185b − 19a − 54u − 160,
− a
2
u
2
− 5u
3
a + a
3
+ 3a
2
u + 4u
2
a − a
2
+ 4au + 6u
2
− a − u + 1, u
4
− u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 63 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
= h−4.92 × 10
36
u
41
− 1.80 × 10
38
u
40
+ · · · + 2.89 × 10
39
b + 4.23 ×
10
39
, 9.16 × 10
39
u
41
− 6.73 × 10
39
u
40
+ · · · + 4.91 × 10
40
a + 8.21 ×
10
40
, u
42
− 2u
41
+ · · · + 16u − 17i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
−0.186607u
41
+ 0.137118u
40
+ ··· + 5.29366u − 1.67251
0.00170297u
41
+ 0.0622705u
40
+ ··· − 0.201147u − 1.46385
a
6
=
1
−u
2
a
2
=
−0.184904u
41
+ 0.199388u
40
+ ··· + 5.09252u − 3.13636
0.00170297u
41
+ 0.0622705u
40
+ ··· − 0.201147u − 1.46385
a
1
=
0.0588482u
41
− 0.261568u
40
+ ··· + 3.71273u + 4.22681
0.266107u
41
− 0.115441u
40
+ ··· − 1.21463u + 2.00517
a
4
=
0.0875371u
41
− 0.115951u
40
+ ··· + 5.83351u + 3.00873
0.0353514u
41
− 0.0574630u
40
+ ··· − 0.374380u − 0.0632026
a
9
=
−u
u
a
11
=
u
3
−u
3
+ u
a
8
=
−u
3
u
5
− u
3
+ u
a
7
=
−0.596514u
41
+ 0.435647u
40
+ ··· + 2.54867u − 8.20884
0.687055u
41
− 0.666732u
40
+ ··· − 0.496210u + 10.8635
a
12
=
0.589024u
41
− 0.658891u
40
+ ··· + 2.42549u + 11.2674
0.0500035u
41
+ 0.0678910u
40
+ ··· − 1.20598u − 1.53919
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.57605u
41
− 2.80061u
40
+ ··· + 23.4107u + 46.2988
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
42
+ 2u
41
+ ··· + 24u + 1
c
2
, c
4
u
42
− 14u
41
+ ··· + 12u − 1
c
3
, c
7
u
42
− u
41
+ ··· + 5632u + 512
c
5
, c
9
u
42
− 2u
41
+ ··· + 16u − 17
c
6
, c
11
u
42
− 2u
41
+ ··· − 70u − 49
c
8
u
42
− 6u
41
+ ··· − 2688u + 2567
c
10
u
42
− 28u
41
+ ··· + 1206u + 289
c
12
u
42
+ 6u
41
+ ··· + 26460u + 2401
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
+ 90y
41
+ ··· + 1420y + 1
c
2
, c
4
y
42
− 2y
41
+ ··· − 24y + 1
c
3
, c
7
y
42
− 69y
41
+ ··· − 17301504y + 262144
c
5
, c
9
y
42
− 28y
41
+ ··· + 1206y + 289
c
6
, c
11
y
42
+ 6y
41
+ ··· + 26460y + 2401
c
8
y
42
+ 68y
41
+ ··· + 1240622y + 6589489
c
10
y
42
− 20y
41
+ ··· − 5069826y + 83521
c
12
y
42
+ 74y
41
+ ··· − 29647548y + 5764801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.961799 + 0.311389I
a = 2.02690 − 2.18124I
b = −0.464784 + 0.408421I
−1.72797 − 1.37637I 4.55612 − 0.38965I
u = −0.961799 − 0.311389I
a = 2.02690 + 2.18124I
b = −0.464784 − 0.408421I
−1.72797 + 1.37637I 4.55612 + 0.38965I
u = −0.829534 + 0.589200I
a = 0.947623 + 0.399065I
b = −0.343165 − 0.102736I
−1.74074 − 2.33828I 4.84594 + 5.31700I
u = −0.829534 − 0.589200I
a = 0.947623 − 0.399065I
b = −0.343165 + 0.102736I
−1.74074 + 2.33828I 4.84594 − 5.31700I
u = 0.944203 + 0.228207I
a = −0.16949 + 2.29855I
b = 0.993256 − 0.666835I
2.48881 + 3.70265I 6.29949 − 2.05838I
u = 0.944203 − 0.228207I
a = −0.16949 − 2.29855I
b = 0.993256 + 0.666835I
2.48881 − 3.70265I 6.29949 + 2.05838I
u = 0.835994 + 0.489683I
a = −3.35442 + 8.86991I
b = −1.016890 + 0.004699I
−3.34089 + 2.03680I 95.8127 + 26.5459I
u = 0.835994 − 0.489683I
a = −3.35442 − 8.86991I
b = −1.016890 − 0.004699I
−3.34089 − 2.03680I 95.8127 − 26.5459I
u = 0.965269 + 0.439008I
a = −0.983823 − 0.359781I
b = 0.899894 + 0.651256I
2.81421 − 1.00795I 8.57321 + 1.27913I
u = 0.965269 − 0.439008I
a = −0.983823 + 0.359781I
b = 0.899894 − 0.651256I
2.81421 + 1.00795I 8.57321 − 1.27913I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.726987 + 0.560951I
a = 0.802280 + 0.067898I
b = 0.101623 + 0.134205I
−1.85016 − 2.19168I 2.73443 + 3.94919I
u = −0.726987 − 0.560951I
a = 0.802280 − 0.067898I
b = 0.101623 − 0.134205I
−1.85016 + 2.19168I 2.73443 − 3.94919I
u = 0.205294 + 1.093670I
a = −0.50667 − 1.38304I
b = 1.23869 + 1.08212I
11.4259 − 8.4418I 2.24860 + 3.75985I
u = 0.205294 − 1.093670I
a = −0.50667 + 1.38304I
b = 1.23869 − 1.08212I
11.4259 + 8.4418I 2.24860 − 3.75985I
u = 0.053594 + 1.137510I
a = −0.59511 + 1.46169I
b = 1.05760 − 1.28040I
12.15940 + 0.20639I 3.10494 − 0.07106I
u = 0.053594 − 1.137510I
a = −0.59511 − 1.46169I
b = 1.05760 + 1.28040I
12.15940 − 0.20639I 3.10494 + 0.07106I
u = 0.232942 + 0.816588I
a = 0.184697 − 0.861641I
b = 0.151638 + 0.884654I
1.95152 + 0.96411I 4.49813 − 1.84965I
u = 0.232942 − 0.816588I
a = 0.184697 + 0.861641I
b = 0.151638 − 0.884654I
1.95152 − 0.96411I 4.49813 + 1.84965I
u = −1.18461
a = 1.51253
b = −1.40973
0.934538 7.24150
u = −1.126130 + 0.490429I
a = −0.039913 − 1.285050I
b = 0.828323 + 0.354167I
2.33209 − 7.91667I 6.88839 + 11.06602I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.126130 − 0.490429I
a = −0.039913 + 1.285050I
b = 0.828323 − 0.354167I
2.33209 + 7.91667I 6.88839 − 11.06602I
u = 1.259460 + 0.006196I
a = −0.97423 − 2.37844I
b = 0.506833 + 1.138780I
4.47907 − 1.92884I 6.47929 + 1.71581I
u = 1.259460 − 0.006196I
a = −0.97423 + 2.37844I
b = 0.506833 − 1.138780I
4.47907 + 1.92884I 6.47929 − 1.71581I
u = 1.072950 + 0.670917I
a = 0.45051 + 1.91983I
b = 0.590513 − 1.035150I
4.15910 + 4.29767I 6.40450 − 3.97494I
u = 1.072950 − 0.670917I
a = 0.45051 − 1.91983I
b = 0.590513 + 1.035150I
4.15910 − 4.29767I 6.40450 + 3.97494I
u = 1.254550 + 0.204489I
a = 1.39168 − 2.27514I
b = −1.145780 + 0.655072I
2.23820 + 2.99548I 5.68648 − 2.96480I
u = 1.254550 − 0.204489I
a = 1.39168 + 2.27514I
b = −1.145780 − 0.655072I
2.23820 − 2.99548I 5.68648 + 2.96480I
u = −0.274846 + 0.651125I
a = 0.435590 + 0.051488I
b = 0.661252 − 0.443712I
−0.15519 + 3.49196I 2.75035 − 5.76254I
u = −0.274846 − 0.651125I
a = 0.435590 − 0.051488I
b = 0.661252 + 0.443712I
−0.15519 − 3.49196I 2.75035 + 5.76254I
u = 0.698771
a = 0.544644
b = 0.196513
0.929263 11.4390
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.360000 + 0.378690I
a = −0.10332 + 2.56500I
b = −0.202310 − 1.252300I
6.81382 − 5.26231I 0
u = −1.360000 − 0.378690I
a = −0.10332 − 2.56500I
b = −0.202310 + 1.252300I
6.81382 + 5.26231I 0
u = 1.29496 + 0.63382I
a = −0.59935 + 2.83045I
b = 1.31294 − 0.99932I
14.7912 + 14.5915I 0
u = 1.29496 − 0.63382I
a = −0.59935 − 2.83045I
b = 1.31294 + 0.99932I
14.7912 − 14.5915I 0
u = 1.38494 + 0.58465I
a = −1.93831 − 1.93197I
b = 0.92670 + 1.41166I
16.3124 + 5.9260I 0
u = 1.38494 − 0.58465I
a = −1.93831 + 1.93197I
b = 0.92670 − 1.41166I
16.3124 − 5.9260I 0
u = −1.42037 + 0.52003I
a = −0.95320 − 2.91761I
b = 1.24919 + 1.24050I
16.8335 − 6.1018I 0
u = −1.42037 − 0.52003I
a = −0.95320 + 2.91761I
b = 1.24919 − 1.24050I
16.8335 + 6.1018I 0
u = −1.46489 + 0.38079I
a = −2.05057 + 2.08335I
b = 1.22965 − 1.27108I
16.9282 + 3.1689I 0
u = −1.46489 − 0.38079I
a = −2.05057 − 2.08335I
b = 1.22965 + 1.27108I
16.9282 − 3.1689I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.096688 + 0.349533I
a = −0.82299 + 1.83040I
b = −0.968549 − 0.219170I
−1.74611 − 0.73385I −3.54446 + 0.56735I
u = −0.096688 − 0.349533I
a = −0.82299 − 1.83040I
b = −0.968549 + 0.219170I
−1.74611 + 0.73385I −3.54446 − 0.56735I
9
II.
I
u
2
= hb+1, −2u
8
+u
7
+· · ·+a+2, u
9
−u
8
−2u
7
+3u
6
+u
5
−3u
4
+2u
3
−u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
2u
8
− u
7
− 5u
6
+ 3u
5
+ 4u
4
− 3u
3
+ 2u
2
− 2
−1
a
6
=
1
−u
2
a
2
=
2u
8
− u
7
− 5u
6
+ 3u
5
+ 4u
4
− 3u
3
+ 2u
2
− 3
−1
a
1
=
−1
0
a
4
=
2u
8
− u
7
− 5u
6
+ 3u
5
+ 4u
4
− 3u
3
+ 2u
2
− 2
−1
a
9
=
−u
u
a
11
=
u
3
−u
3
+ u
a
8
=
−u
3
u
5
− u
3
+ u
a
7
=
−u
3
u
5
− u
3
+ u
a
12
=
−u
6
+ u
4
− 1
u
6
− 2u
4
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
8
− 5u
7
+ 10u
6
+ 8u
5
− 10u
4
− 8u
3
− 4u
2
− 8u − 2
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
6
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
, c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
, c
9
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
8
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
10
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = −1.67861 + 2.31573I
b = −1.00000
−3.42837 + 2.09337I −12.6725 − 14.2088I
u = 0.772920 − 0.510351I
a = −1.67861 − 2.31573I
b = −1.00000
−3.42837 − 2.09337I −12.6725 + 14.2088I
u = −0.825933
a = 0.871015
b = −1.00000
−0.446489 1.84400
u = −1.173910 + 0.391555I
a = 0.893484 + 0.630694I
b = −1.00000
2.72642 − 1.33617I 6.61905 + 0.64999I
u = −1.173910 − 0.391555I
a = 0.893484 − 0.630694I
b = −1.00000
2.72642 + 1.33617I 6.61905 − 0.64999I
u = 0.141484 + 0.739668I
a = −0.309843 + 0.043204I
b = −1.00000
−1.02799 − 2.45442I −0.10038 + 1.90984I
u = 0.141484 − 0.739668I
a = −0.309843 − 0.043204I
b = −1.00000
−1.02799 + 2.45442I −0.10038 − 1.90984I
u = 1.172470 + 0.500383I
a = 0.659464 − 0.874093I
b = −1.00000
1.95319 + 7.08493I 3.23178 − 2.93209I
u = 1.172470 − 0.500383I
a = 0.659464 + 0.874093I
b = −1.00000
1.95319 − 7.08493I 3.23178 + 2.93209I
13
III.
I
u
3
= h33u
3
a
2
−4u
3
a + · · · − 19a − 160, −a
2
u
2
−5u
3
a + · · · − a + 1, u
4
−u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
a
−0.178378a
2
u
3
+ 0.0216216au
3
+ ··· + 0.102703a + 0.864865
a
6
=
1
−u
2
a
2
=
−0.178378a
2
u
3
+ 0.0216216au
3
+ ··· + 1.10270a + 0.864865
−0.178378a
2
u
3
+ 0.0216216au
3
+ ··· + 0.102703a + 0.864865
a
1
=
0.156757a
2
u
3
− 0.0432432au
3
+ ··· − 0.00540541a − 1.32973
−0.232432a
2
u
3
− 0.632432au
3
+ ··· − 0.0540541a + 2.10270
a
4
=
1
5
u
3
a
2
−
3
5
u
3
a + ··· −
3
5
a + 1
−0.0540541a
2
u
3
− 0.654054au
3
+ ··· − 0.156757a + 0.237838
a
9
=
−u
u
a
11
=
u
3
−u
3
+ u
a
8
=
−u
3
0
a
7
=
0.340541a
2
u
3
− 0.0594595au
3
+ ··· − 0.632432a + 0.421622
−0.194595a
2
u
3
+ 0.00540541au
3
+ ··· + 0.675676a + 1.01622
a
12
=
0.156757a
2
u
3
− 0.0432432au
3
+ ··· − 0.00540541a − 1.32973
−0.232432a
2
u
3
− 0.632432au
3
+ ··· − 0.0540541a + 2.10270
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
132
185
u
3
a
2
+
4
37
a
2
u
2
+
16
185
u
3
a +
24
37
a
2
u −
424
185
u
2
a −
356
185
u
3
+
76
185
a
2
−
28
185
au −
852
185
u
2
+
76
185
a +
216
185
u +
128
37
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
4
c
2
(u
3
+ u
2
− 1)
4
c
3
, c
7
(u
6
− 3u
4
+ 2u
2
+ 1)
2
c
4
(u
3
− u
2
+ 1)
4
c
5
, c
8
, c
9
(u
4
− u
2
+ 1)
3
c
6
, c
11
(u
2
+ 1)
6
c
10
(u
2
− u + 1)
6
c
12
(u + 1)
12
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y −1)
4
c
2
, c
4
(y
3
− y
2
+ 2y −1)
4
c
3
, c
7
(y
3
− 3y
2
+ 2y + 1)
4
c
5
, c
8
, c
9
(y
2
− y + 1)
6
c
6
, c
11
(y + 1)
12
c
10
(y
2
+ y + 1)
6
c
12
(y −1)
12
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.972493 − 1.013180I
b = 0.877439 + 0.744862I
1.37919 − 0.79824I 1.50976 − 0.48465I
u = 0.866025 + 0.500000I
a = 0.11905 − 1.81610I
b = −0.754878
−2.75839 + 2.02988I −5.01951 − 3.46410I
u = 0.866025 + 0.500000I
a = −0.24463 + 2.19530I
b = 0.877439 − 0.744862I
1.37919 + 4.85801I 1.50976 − 6.44355I
u = 0.866025 − 0.500000I
a = −0.972493 + 1.013180I
b = 0.877439 − 0.744862I
1.37919 + 0.79824I 1.50976 + 0.48465I
u = 0.866025 − 0.500000I
a = 0.11905 + 1.81610I
b = −0.754878
−2.75839 − 2.02988I −5.01951 + 3.46410I
u = 0.866025 − 0.500000I
a = −0.24463 − 2.19530I
b = 0.877439 + 0.744862I
1.37919 − 4.85801I 1.50976 + 6.44355I
u = −0.866025 + 0.500000I
a = −0.949962 − 0.298361I
b = 0.877439 − 0.744862I
1.37919 + 0.79824I 1.50976 + 0.48465I
u = −0.866025 + 0.500000I
a = 0.90246 − 1.55905I
b = 0.877439 + 0.744862I
1.37919 − 4.85801I 1.50976 + 6.44355I
u = −0.866025 + 0.500000I
a = 4.14558 − 0.50862I
b = −0.754878
−2.75839 − 2.02988I −5.01951 + 3.46410I
u = −0.866025 − 0.500000I
a = −0.949962 + 0.298361I
b = 0.877439 + 0.744862I
1.37919 − 0.79824I 1.50976 − 0.48465I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866025 − 0.500000I
a = 0.90246 + 1.55905I
b = 0.877439 − 0.744862I
1.37919 + 4.85801I 1.50976 − 6.44355I
u = −0.866025 − 0.500000I
a = 4.14558 + 0.50862I
b = −0.754878
−2.75839 + 2.02988I −5.01951 − 3.46410I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
3
− u
2
+ 2u − 1)
4
(u
42
+ 2u
41
+ ··· + 24u + 1)
c
2
((u − 1)
9
)(u
3
+ u
2
− 1)
4
(u
42
− 14u
41
+ ··· + 12u − 1)
c
3
, c
7
u
9
(u
6
− 3u
4
+ 2u
2
+ 1)
2
(u
42
− u
41
+ ··· + 5632u + 512)
c
4
((u + 1)
9
)(u
3
− u
2
+ 1)
4
(u
42
− 14u
41
+ ··· + 12u − 1)
c
5
(u
4
− u
2
+ 1)
3
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
42
− 2u
41
+ ··· + 16u − 17)
c
6
(u
2
+ 1)
6
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
42
− 2u
41
+ ··· − 70u − 49)
c
8
(u
4
− u
2
+ 1)
3
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
42
− 6u
41
+ ··· − 2688u + 2567)
c
9
(u
4
− u
2
+ 1)
3
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
42
− 2u
41
+ ··· + 16u − 17)
c
10
((u
2
− u + 1)
6
)(u
9
− 5u
8
+ ··· + u − 1)
· (u
42
− 28u
41
+ ··· + 1206u + 289)
c
11
(u
2
+ 1)
6
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
42
− 2u
41
+ ··· − 70u − 49)
c
12
((u + 1)
12
)(u
9
+ 3u
8
+ ··· + u − 1)
· (u
42
+ 6u
41
+ ··· + 26460u + 2401)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
3
+ 3y
2
+ 2y −1)
4
(y
42
+ 90y
41
+ ··· + 1420y + 1)
c
2
, c
4
((y −1)
9
)(y
3
− y
2
+ 2y −1)
4
(y
42
− 2y
41
+ ··· − 24y + 1)
c
3
, c
7
y
9
(y
3
− 3y
2
+ 2y + 1)
4
(y
42
− 69y
41
+ ··· − 1.73015 × 10
7
y + 262144)
c
5
, c
9
((y
2
− y + 1)
6
)(y
9
− 5y
8
+ ··· + y −1)
· (y
42
− 28y
41
+ ··· + 1206y + 289)
c
6
, c
11
((y + 1)
12
)(y
9
+ 3y
8
+ ··· + y −1)
· (y
42
+ 6y
41
+ ··· + 26460y + 2401)
c
8
((y
2
− y + 1)
6
)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
42
+ 68y
41
+ ··· + 1240622y + 6589489)
c
10
(y
2
+ y + 1)
6
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
42
− 20y
41
+ ··· − 5069826y + 83521)
c
12
(y −1)
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
42
+ 74y
41
+ ··· − 29647548y + 5764801)
20
