12n
0072
(K12n
0072
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 8 10 3 12 11 6 1 9
Solving Sequence
9,12 1,3
2 8 4 5 7 11 10 6
c
12
c
1
c
8
c
3
c
4
c
7
c
11
c
9
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.81279 × 10
18
u
59
− 1.05287 × 10
19
u
58
+ ··· + 6.77112 × 10
17
b − 1.27731 × 10
18
,
9.49759 × 10
17
u
59
− 1.92602 × 10
18
u
58
+ ··· + 6.77112 × 10
17
a − 3.84134 × 10
17
, u
60
− 5u
59
+ ··· + 2u + 1i
I
u
2
= h−u
8
+ u
7
+ u
6
− 2u
5
+ u
3
− 2u
2
+ b + u − 1, −u
8
+ u
7
+ u
6
− 2u
5
+ u
3
− 2u
2
+ a + u − 1,
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
I
u
3
= h−a
2
+ b + a − 1, a
3
− 2a
2
+ a − 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 72 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
= h2.81 × 10
18
u
59
− 1.05 × 10
19
u
58
+ · · · + 6.77 × 10
17
b − 1.28 × 10
18
, 9.50 ×
10
17
u
59
−1.93×10
18
u
58
+· · ·+6.77×10
17
a−3.84×10
17
, u
60
−5u
59
+· · ·+2u+1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
3
=
−1.40266u
59
+ 2.84446u
58
+ ··· − 20.1139u + 0.567312
−4.15409u
59
+ 15.5494u
58
+ ··· + 1.51219u + 1.88640
a
2
=
−4.29143u
59
+ 12.8571u
58
+ ··· − 15.7514u + 0.224484
−5.29000u
59
+ 18.1522u
58
+ ··· − 3.12746u + 0.655392
a
8
=
u
u
a
4
=
−1.47255u
59
+ 1.96750u
58
+ ··· − 24.9698u − 0.484933
−4.22398u
59
+ 14.6724u
58
+ ··· − 3.34373u + 0.834159
a
5
=
1.93062u
59
− 6.99368u
58
+ ··· − 6.44373u + 1.45359
0.932046u
59
− 1.69858u
58
+ ··· + 6.18018u + 1.88449
a
7
=
−1.88449u
59
+ 10.3545u
58
+ ··· + 20.5308u + 2.41119
2.65941u
59
− 9.86960u
58
+ ··· − 2.40765u − 1.93062
a
11
=
−u
2
+ 1
−u
4
a
10
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
6
=
−3.11073u
59
+ 10.8706u
58
+ ··· + 6.04965u − 1.15134
−2.11216u
59
+ 5.57554u
58
+ ··· − 6.57426u − 1.58225
(ii) Obstruction class = −1
(iii) Cusp Shapes =
254104713520312101
338556134519489602
u
59
−
287234417535105935
338556134519489602
u
58
+···+
9811882428269304349
338556134519489602
u−
403682827173379753
169278067259744801
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
60
+ 17u
59
+ ··· + 51u + 1
c
2
, c
4
u
60
− 11u
59
+ ··· + u + 1
c
3
, c
7
u
60
− 2u
59
+ ··· − 512u − 512
c
5
u
60
+ 3u
59
+ ··· − u − 1
c
6
, c
10
u
60
+ 2u
59
+ ··· − 28u − 8
c
8
, c
12
u
60
− 5u
59
+ ··· + 2u + 1
c
9
u
60
− 24u
59
+ ··· + 336u + 64
c
11
u
60
+ 31u
59
+ ··· + 52u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
60
+ 63y
59
+ ··· − 259y + 1
c
2
, c
4
y
60
− 17y
59
+ ··· − 51y + 1
c
3
, c
7
y
60
+ 60y
59
+ ··· + 262144y + 262144
c
5
y
60
− 69y
59
+ ··· − 55y + 1
c
6
, c
10
y
60
+ 24y
59
+ ··· − 336y + 64
c
8
, c
12
y
60
− 31y
59
+ ··· − 52y + 1
c
9
y
60
+ 20y
59
+ ··· − 486656y + 4096
c
11
y
60
+ y
59
+ ··· − 1872y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.337858 + 0.894600I
a = 0.13383 + 1.43636I
b = −1.48207 + 0.70345I
7.94883 + 2.76650I −3.24347 − 1.05730I
u = 0.337858 − 0.894600I
a = 0.13383 − 1.43636I
b = −1.48207 − 0.70345I
7.94883 − 2.76650I −3.24347 + 1.05730I
u = 0.275210 + 0.913906I
a = −0.05027 − 1.70048I
b = 1.38687 − 0.67504I
6.81572 + 9.76098I −4.86985 − 5.65372I
u = 0.275210 − 0.913906I
a = −0.05027 + 1.70048I
b = 1.38687 + 0.67504I
6.81572 − 9.76098I −4.86985 + 5.65372I
u = −0.933032
a = 4.22833
b = 4.57203
−3.01686 −67.5230
u = 0.888711 + 0.272847I
a = −0.078190 − 0.558523I
b = 0.405126 + 0.581562I
1.58683 − 3.66181I −4.28823 + 9.48383I
u = 0.888711 − 0.272847I
a = −0.078190 + 0.558523I
b = 0.405126 − 0.581562I
1.58683 + 3.66181I −4.28823 − 9.48383I
u = 0.925197 + 0.542464I
a = 0.489920 − 0.539197I
b = 0.407019 + 0.364942I
1.95619 − 3.10505I 0. + 4.26282I
u = 0.925197 − 0.542464I
a = 0.489920 + 0.539197I
b = 0.407019 − 0.364942I
1.95619 + 3.10505I 0. − 4.26282I
u = 0.775160 + 0.782039I
a = 1.08347 − 1.85556I
b = 2.09668 − 0.60592I
10.65710 + 0.79828I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.775160 − 0.782039I
a = 1.08347 + 1.85556I
b = 2.09668 + 0.60592I
10.65710 − 0.79828I 0
u = 0.639144 + 0.625775I
a = 0.407955 + 0.337968I
b = −0.642419 + 0.534726I
2.79847 − 1.51236I −1.81428 + 3.54798I
u = 0.639144 − 0.625775I
a = 0.407955 − 0.337968I
b = −0.642419 − 0.534726I
2.79847 + 1.51236I −1.81428 − 3.54798I
u = 1.053880 + 0.334060I
a = 0.281699 + 0.729493I
b = 0.305612 − 0.503382I
0.75501 + 1.63619I 0
u = 1.053880 − 0.334060I
a = 0.281699 − 0.729493I
b = 0.305612 + 0.503382I
0.75501 − 1.63619I 0
u = −1.042430 + 0.414082I
a = −0.353731 − 1.109550I
b = −1.17215 − 1.41693I
−2.88310 + 2.96934I 0
u = −1.042430 − 0.414082I
a = −0.353731 + 1.109550I
b = −1.17215 + 1.41693I
−2.88310 − 2.96934I 0
u = −1.085610 + 0.332010I
a = −1.27018 − 2.13218I
b = −1.40022 − 1.45408I
−4.66678 + 1.12394I 0
u = −1.085610 − 0.332010I
a = −1.27018 + 2.13218I
b = −1.40022 + 1.45408I
−4.66678 − 1.12394I 0
u = 0.844243 + 0.760095I
a = −1.12133 + 1.75611I
b = −2.35320 + 0.80071I
10.45220 − 6.50197I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.844243 − 0.760095I
a = −1.12133 − 1.75611I
b = −2.35320 − 0.80071I
10.45220 + 6.50197I 0
u = −1.141290 + 0.233441I
a = 1.112610 + 0.300698I
b = 1.85544 + 0.38885I
−3.30337 − 0.69653I 0
u = −1.141290 − 0.233441I
a = 1.112610 − 0.300698I
b = 1.85544 − 0.38885I
−3.30337 + 0.69653I 0
u = −1.035450 + 0.539611I
a = 2.13511 + 1.38666I
b = 2.82243 + 0.20160I
3.27029 + 1.99564I 0
u = −1.035450 − 0.539611I
a = 2.13511 − 1.38666I
b = 2.82243 − 0.20160I
3.27029 − 1.99564I 0
u = 0.325660 + 0.762789I
a = 0.550531 − 1.183860I
b = 0.204288 + 0.081198I
1.25130 + 3.50817I −4.71158 − 4.55526I
u = 0.325660 − 0.762789I
a = 0.550531 + 1.183860I
b = 0.204288 − 0.081198I
1.25130 − 3.50817I −4.71158 + 4.55526I
u = 1.058140 + 0.503774I
a = 0.862782 − 0.336531I
b = 1.78762 − 0.38804I
−2.23222 − 3.63610I 0
u = 1.058140 − 0.503774I
a = 0.862782 + 0.336531I
b = 1.78762 + 0.38804I
−2.23222 + 3.63610I 0
u = −1.096800 + 0.538710I
a = −2.26195 − 1.34848I
b = −3.18815 − 0.39611I
2.24129 + 8.72496I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.096800 − 0.538710I
a = −2.26195 + 1.34848I
b = −3.18815 + 0.39611I
2.24129 − 8.72496I 0
u = 1.103150 + 0.529889I
a = −0.90009 + 1.69435I
b = −1.069960 + 0.856532I
−3.28631 − 6.19021I 0
u = 1.103150 − 0.529889I
a = −0.90009 − 1.69435I
b = −1.069960 − 0.856532I
−3.28631 + 6.19021I 0
u = 0.096441 + 0.769173I
a = 0.709332 + 0.054966I
b = −0.1034940 − 0.0442376I
−1.35021 + 2.66631I −2.81466 − 3.68602I
u = 0.096441 − 0.769173I
a = 0.709332 − 0.054966I
b = −0.1034940 + 0.0442376I
−1.35021 − 2.66631I −2.81466 + 3.68602I
u = −0.484975 + 0.602832I
a = 0.07018 − 2.49429I
b = −1.59748 − 1.32332I
4.88218 + 2.55090I −5.75322 − 3.65479I
u = −0.484975 − 0.602832I
a = 0.07018 + 2.49429I
b = −1.59748 + 1.32332I
4.88218 − 2.55090I −5.75322 + 3.65479I
u = −0.355933 + 0.652328I
a = −0.10224 + 2.47624I
b = 1.46844 + 1.04544I
4.38705 − 4.06822I −6.35132 + 1.53091I
u = −0.355933 − 0.652328I
a = −0.10224 − 2.47624I
b = 1.46844 − 1.04544I
4.38705 + 4.06822I −6.35132 − 1.53091I
u = 1.127800 + 0.566306I
a = −0.440646 + 0.632335I
b = −1.31378 + 1.01990I
−1.10174 − 8.51688I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.127800 − 0.566306I
a = −0.440646 − 0.632335I
b = −1.31378 − 1.01990I
−1.10174 + 8.51688I 0
u = −1.197690 + 0.405791I
a = 0.367973 − 0.288662I
b = 0.525918 − 0.753873I
−5.12612 + 1.38879I 0
u = −1.197690 − 0.405791I
a = 0.367973 + 0.288662I
b = 0.525918 + 0.753873I
−5.12612 − 1.38879I 0
u = 1.186970 + 0.490457I
a = 0.232541 + 0.230233I
b = 0.436907 + 0.672759I
−4.52134 − 7.29315I 0
u = 1.186970 − 0.490457I
a = 0.232541 − 0.230233I
b = 0.436907 − 0.672759I
−4.52134 + 7.29315I 0
u = 0.312115 + 0.635855I
a = 0.281014 − 0.263517I
b = 1.50466 − 0.17613I
−1.03251 + 1.61115I −5.03240 − 0.45414I
u = 0.312115 − 0.635855I
a = 0.281014 + 0.263517I
b = 1.50466 + 0.17613I
−1.03251 − 1.61115I −5.03240 + 0.45414I
u = −0.692437 + 0.039676I
a = 1.343570 + 0.174908I
b = 0.691006 + 0.039688I
−1.092530 + 0.001807I −8.18169 + 0.37203I
u = −0.692437 − 0.039676I
a = 1.343570 − 0.174908I
b = 0.691006 − 0.039688I
−1.092530 − 0.001807I −8.18169 − 0.37203I
u = −1.293890 + 0.191302I
a = 0.184711 + 0.635831I
b = 0.353270 − 0.535335I
2.43582 + 0.64946I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.293890 − 0.191302I
a = 0.184711 − 0.635831I
b = 0.353270 + 0.535335I
2.43582 − 0.64946I 0
u = 0.459124 + 0.506719I
a = −0.06558 + 1.82861I
b = 0.108857 + 0.574464I
−0.435329 − 0.564285I −6.58756 + 0.11639I
u = 0.459124 − 0.506719I
a = −0.06558 − 1.82861I
b = 0.108857 − 0.574464I
−0.435329 + 0.564285I −6.58756 − 0.11639I
u = 1.165420 + 0.613877I
a = 1.78237 − 1.00307I
b = 2.52278 + 0.05328I
5.45561 − 8.29310I 0
u = 1.165420 − 0.613877I
a = 1.78237 + 1.00307I
b = 2.52278 − 0.05328I
5.45561 + 8.29310I 0
u = −1.301730 + 0.255705I
a = 0.233918 − 0.675467I
b = 0.351604 + 0.513151I
1.58747 − 5.92424I 0
u = −1.301730 − 0.255705I
a = 0.233918 + 0.675467I
b = 0.351604 − 0.513151I
1.58747 + 5.92424I 0
u = 1.196470 + 0.595496I
a = −2.01101 + 0.96883I
b = −2.93963 + 0.12005I
4.0303 − 15.2628I 0
u = 1.196470 − 0.595496I
a = −2.01101 − 0.96883I
b = −2.93963 − 0.12005I
4.0303 + 15.2628I 0
u = −0.151881
a = 4.55507
b = 0.484061
−0.986470 −9.89900
10
II. I
u
2
= h−u
8
+ u
7
+ u
6
− 2u
5
+ u
3
− 2u
2
+ b + u − 1, −u
8
+ u
7
+ u
6
− 2u
5
+
u
3
− 2u
2
+ a + u − 1, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
3
=
u
8
− u
7
− u
6
+ 2u
5
− u
3
+ 2u
2
− u + 1
u
8
− u
7
− u
6
+ 2u
5
− u
3
+ 2u
2
− u + 1
a
2
=
u
8
− u
7
− u
6
+ 2u
5
− u
3
+ 2u
2
− u + 2
u
8
− u
7
− u
6
+ 2u
5
− u
3
+ 3u
2
− u + 1
a
8
=
u
u
a
4
=
u
8
− u
7
− u
6
+ 2u
5
− u
3
+ 2u
2
− u + 1
u
8
− u
7
− u
6
+ 2u
5
− u
3
+ 2u
2
− u + 1
a
5
=
−1
−u
2
a
7
=
u
u
a
11
=
−u
2
+ 1
−u
4
a
10
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
6
=
−u
4
+ u
2
− 1
−u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
8
− u
7
+ u
5
− 4u
4
+ 5u
3
+ 7u
2
− 4u − 6
11
(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
, c
9
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
8
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
11
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
12
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
12
(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
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
6
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
8
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
11
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = 0.624323 + 0.742839I
b = 0.624323 + 0.742839I
0.13850 − 2.09337I −5.80108 + 4.26451I
u = 0.772920 − 0.510351I
a = 0.624323 − 0.742839I
b = 0.624323 − 0.742839I
0.13850 + 2.09337I −5.80108 − 4.26451I
u = −0.825933
a = 3.14628
b = 3.14628
−2.84338 −2.07210
u = −1.173910 + 0.391555I
a = −0.250943 − 1.026430I
b = −0.250943 − 1.026430I
−6.01628 + 1.33617I −17.3564 − 0.5967I
u = −1.173910 − 0.391555I
a = −0.250943 + 1.026430I
b = −0.250943 + 1.026430I
−6.01628 − 1.33617I −17.3564 + 0.5967I
u = 0.141484 + 0.739668I
a = 0.642765 + 0.088097I
b = 0.642765 + 0.088097I
−2.26187 + 2.45442I −11.99086 − 2.54651I
u = 0.141484 − 0.739668I
a = 0.642765 − 0.088097I
b = 0.642765 − 0.088097I
−2.26187 − 2.45442I −11.99086 + 2.54651I
u = 1.172470 + 0.500383I
a = −0.089286 + 0.842785I
b = −0.089286 + 0.842785I
−5.24306 − 7.08493I −15.8155 + 4.8919I
u = 1.172470 − 0.500383I
a = −0.089286 − 0.842785I
b = −0.089286 − 0.842785I
−5.24306 + 7.08493I −15.8155 − 4.8919I
14
III. I
u
3
= h−a
2
+ b + a − 1, a
3
− 2a
2
+ a − 1, u + 1i
(i) Arc colorings
a
9
=
0
−1
a
12
=
1
0
a
1
=
1
1
a
3
=
a
a
2
− a + 1
a
2
=
2
a
2
− a + 1
a
8
=
−1
−1
a
4
=
−a
2
+ 3a − 1
a
a
5
=
−a
2
+ a + 1
0
a
7
=
0
a
2
− a − 1
a
11
=
0
−1
a
10
=
0
−1
a
6
=
0
a
2
− a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = a
2
− 2a − 7
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
u
3
+ 3u
2
+ 2u − 1
c
6
, c
9
, c
10
u
3
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
11
(u − 1)
3
c
12
(u + 1)
3
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
y
3
− y
2
+ 2y −1
c
5
y
3
− 5y
2
+ 10y −1
c
6
, c
9
, c
10
y
3
c
8
, c
11
, c
12
(y −1)
3
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.122561 + 0.744862I
b = 0.337641 − 0.562280I
1.37919 + 2.82812I −7.78492 − 1.30714I
u = −1.00000
a = 0.122561 − 0.744862I
b = 0.337641 + 0.562280I
1.37919 − 2.82812I −7.78492 + 1.30714I
u = −1.00000
a = 1.75488
b = 2.32472
−2.75839 −7.43020
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
3
− u
2
+ 2u − 1)(u
60
+ 17u
59
+ ··· + 51u + 1)
c
2
((u − 1)
9
)(u
3
+ u
2
− 1)(u
60
− 11u
59
+ ··· + u + 1)
c
3
u
9
(u
3
− u
2
+ 2u − 1)(u
60
− 2u
59
+ ··· − 512u − 512)
c
4
((u + 1)
9
)(u
3
− u
2
+ 1)(u
60
− 11u
59
+ ··· + u + 1)
c
5
(u
3
+ 3u
2
+ 2u − 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
60
+ 3u
59
+ ··· − u − 1)
c
6
u
3
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
60
+ 2u
59
+ ··· − 28u − 8)
c
7
u
9
(u
3
+ u
2
+ 2u + 1)(u
60
− 2u
59
+ ··· − 512u − 512)
c
8
(u − 1)
3
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
60
− 5u
59
+ ··· + 2u + 1)
c
9
u
3
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
60
− 24u
59
+ ··· + 336u + 64)
c
10
u
3
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
60
+ 2u
59
+ ··· − 28u − 8)
c
11
(u − 1)
3
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
60
+ 31u
59
+ ··· + 52u + 1)
c
12
(u + 1)
3
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
60
− 5u
59
+ ··· + 2u + 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
3
+ 3y
2
+ 2y −1)(y
60
+ 63y
59
+ ··· − 259y + 1)
c
2
, c
4
((y −1)
9
)(y
3
− y
2
+ 2y −1)(y
60
− 17y
59
+ ··· − 51y + 1)
c
3
, c
7
y
9
(y
3
+ 3y
2
+ 2y −1)(y
60
+ 60y
59
+ ··· + 262144y + 262144)
c
5
(y
3
− 5y
2
+ 10y −1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
60
− 69y
59
+ ··· − 55y + 1)
c
6
, c
10
y
3
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
60
+ 24y
59
+ ··· − 336y + 64)
c
8
, c
12
(y −1)
3
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
60
− 31y
59
+ ··· − 52y + 1)
c
9
y
3
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
60
+ 20y
59
+ ··· − 486656y + 4096)
c
11
(y −1)
3
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
60
+ y
59
+ ··· − 1872y + 1)
20
