12n
0085
(K12n
0085
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 8 3 10 5 12 7 9 11
Solving Sequence
8,10
7
3,11
6 5 9 12 2 1 4
c
7
c
10
c
6
c
5
c
8
c
11
c
2
c
1
c
4
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.01204 × 10
90
u
45
+ 1.50405 × 10
91
u
44
+ ··· + 3.33019 × 10
91
b − 2.86123 × 10
92
,
− 5.16653 × 10
90
u
45
+ 9.63398 × 10
90
u
44
+ ··· + 3.33019 × 10
91
a − 3.97217 × 10
92
,
u
46
− 2u
45
+ ··· + 32u + 32i
I
u
2
= hu
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
+ b − 2u + 1,
3u
8
− 4u
7
+ 8u
6
− 7u
5
+ 13u
4
− 9u
3
+ 11u
2
+ a − 6u + 6, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
v
1
= ha, −16v
4
+ 47v
3
− 36v
2
+ 29b + 104v + 5, v
5
− 3v
4
+ 3v
3
− 8v
2
+ v −1i
* 3 irreducible components of dim
C
= 0, with total 60 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−8.01 × 10
90
u
45
+ 1.50 × 10
91
u
44
+ · · · + 3.33 × 10
91
b − 2.86 ×
10
92
, −5.17 × 10
90
u
45
+ 9.63 × 10
90
u
44
+ · · · + 3.33 × 10
91
a − 3.97 ×
10
92
, u
46
− 2u
45
+ · · · + 32u + 32i
(i) Arc colorings
a
8
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
0.155142u
45
− 0.289292u
44
+ ··· + 3.45866u + 11.9278
0.240588u
45
− 0.451642u
44
+ ··· + 31.6377u + 8.59181
a
11
=
u
u
3
+ u
a
6
=
0.180370u
45
− 0.347609u
44
+ ··· + 22.1880u + 3.90329
0.00906533u
45
− 0.0528530u
44
+ ··· − 1.97758u − 5.86471
a
5
=
0.189435u
45
− 0.400462u
44
+ ··· + 20.2104u − 1.96143
0.00906533u
45
− 0.0528530u
44
+ ··· − 1.97758u − 5.86471
a
9
=
0.0972359u
45
− 0.101045u
44
+ ··· + 18.1876u + 12.7399
0.0831514u
45
− 0.0596108u
44
+ ··· + 23.5834u + 14.7786
a
12
=
0.0216467u
45
− 0.00784512u
44
+ ··· + 11.4970u + 5.02842
0.118455u
45
− 0.115438u
44
+ ··· + 27.8576u + 16.6339
a
2
=
−0.0465827u
45
+ 0.0735841u
44
+ ··· − 26.1646u + 6.17270
0.203398u
45
− 0.521213u
44
+ ··· + 12.7874u − 10.4351
a
1
=
0.0140845u
45
− 0.0414345u
44
+ ··· − 5.39582u − 2.03877
−0.0959655u
45
+ 0.0891363u
44
+ ··· − 23.6096u − 14.3541
a
4
=
0.422424u
45
− 0.812824u
44
+ ··· + 41.9060u + 18.8214
−0.0860042u
45
+ 0.279668u
44
+ ··· − 6.21471u + 14.2803
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.27338u
45
− 5.41938u
44
+ ··· + 115.558u − 6.90034
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
46
+ 61u
45
+ ··· + 62504u + 1
c
2
, c
4
u
46
− 11u
45
+ ··· + 260u − 1
c
3
, c
6
u
46
+ 8u
45
+ ··· + 9216u + 512
c
5
, c
8
u
46
− 3u
45
+ ··· + 2u − 1
c
7
, c
10
u
46
+ 2u
45
+ ··· − 32u + 32
c
9
, c
11
u
46
+ 7u
45
+ ··· + 4u + 1
c
12
u
46
− 17u
45
+ ··· − 22u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
− 141y
45
+ ··· − 3903085204y + 1
c
2
, c
4
y
46
− 61y
45
+ ··· − 62504y + 1
c
3
, c
6
y
46
+ 60y
45
+ ··· − 71827456y + 262144
c
5
, c
8
y
46
− y
45
+ ··· − 32y + 1
c
7
, c
10
y
46
+ 36y
45
+ ··· + 8704y + 1024
c
9
, c
11
y
46
− 17y
45
+ ··· − 22y + 1
c
12
y
46
+ 31y
45
+ ··· + 246y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.378169 + 0.944081I
a = 0.311249 − 0.267542I
b = 0.391023 − 0.209753I
0.00959 − 1.79095I 3.07595 + 1.44696I
u = −0.378169 − 0.944081I
a = 0.311249 + 0.267542I
b = 0.391023 + 0.209753I
0.00959 + 1.79095I 3.07595 − 1.44696I
u = 0.733270 + 0.623347I
a = 0.092842 + 0.753829I
b = −0.073700 + 0.162456I
3.69426 − 1.19679I 10.96091 + 0.32680I
u = 0.733270 − 0.623347I
a = 0.092842 − 0.753829I
b = −0.073700 − 0.162456I
3.69426 + 1.19679I 10.96091 − 0.32680I
u = −0.172617 + 1.096660I
a = 0.353108 − 0.099187I
b = −0.924288 − 0.155002I
−2.08149 − 2.37209I 2.00000 + 4.29323I
u = −0.172617 − 1.096660I
a = 0.353108 + 0.099187I
b = −0.924288 + 0.155002I
−2.08149 + 2.37209I 2.00000 − 4.29323I
u = 0.863631 + 0.008081I
a = 0.668878 − 0.492509I
b = 0.385328 + 1.024490I
−1.00247 + 2.85719I −1.18117 − 7.51903I
u = 0.863631 − 0.008081I
a = 0.668878 + 0.492509I
b = 0.385328 − 1.024490I
−1.00247 − 2.85719I −1.18117 + 7.51903I
u = 0.681454 + 1.055760I
a = 0.120812 + 0.262349I
b = 0.266053 − 0.121547I
2.40464 + 6.60583I 0
u = 0.681454 − 1.055760I
a = 0.120812 − 0.262349I
b = 0.266053 + 0.121547I
2.40464 − 6.60583I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.668016 + 0.132668I
a = 2.07679 − 1.43704I
b = 0.55122 − 1.51352I
−0.282269 + 0.067141I −3.72609 − 3.28540I
u = −0.668016 − 0.132668I
a = 2.07679 + 1.43704I
b = 0.55122 + 1.51352I
−0.282269 − 0.067141I −3.72609 + 3.28540I
u = −0.023048 + 1.365510I
a = −0.38400 − 1.87511I
b = 0.22263 + 1.67589I
−8.03047 + 4.15846I 0
u = −0.023048 − 1.365510I
a = −0.38400 + 1.87511I
b = 0.22263 − 1.67589I
−8.03047 − 4.15846I 0
u = −0.114821 + 0.599864I
a = 2.68162 + 4.45685I
b = −0.366474 − 1.006750I
0.67146 + 1.37994I −4.76488 − 1.12257I
u = −0.114821 − 0.599864I
a = 2.68162 − 4.45685I
b = −0.366474 + 1.006750I
0.67146 − 1.37994I −4.76488 + 1.12257I
u = −0.112394 + 1.389540I
a = −0.32079 − 1.75033I
b = 0.52928 + 2.75631I
−5.00017 − 2.00257I 0
u = −0.112394 − 1.389540I
a = −0.32079 + 1.75033I
b = 0.52928 − 2.75631I
−5.00017 + 2.00257I 0
u = −0.33097 + 1.38999I
a = 0.40326 + 1.52193I
b = 0.86712 − 2.24790I
−4.56947 − 3.99633I 0
u = −0.33097 − 1.38999I
a = 0.40326 − 1.52193I
b = 0.86712 + 2.24790I
−4.56947 + 3.99633I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43559 + 0.20920I
a = 0.0826736 − 0.0873667I
b = −0.35430 + 1.77050I
−9.88679 − 7.22887I 0
u = 1.43559 − 0.20920I
a = 0.0826736 + 0.0873667I
b = −0.35430 − 1.77050I
−9.88679 + 7.22887I 0
u = −1.44123 + 0.24926I
a = 0.0867294 − 0.0859579I
b = −0.05866 + 1.66324I
−9.81126 − 1.05399I 0
u = −1.44123 − 0.24926I
a = 0.0867294 + 0.0859579I
b = −0.05866 − 1.66324I
−9.81126 + 1.05399I 0
u = −0.059330 + 0.523960I
a = 0.581860 − 0.155990I
b = 0.354786 − 0.661801I
−0.00303 − 1.48232I −0.37531 + 3.95565I
u = −0.059330 − 0.523960I
a = 0.581860 + 0.155990I
b = 0.354786 + 0.661801I
−0.00303 + 1.48232I −0.37531 − 3.95565I
u = −0.518539
a = 1.22775
b = 0.266871
1.19409 8.46120
u = 0.468629 + 0.218617I
a = 2.90732 − 0.59799I
b = −0.422461 + 0.238430I
−2.59187 − 0.05584I −4.82458 − 1.57408I
u = 0.468629 − 0.218617I
a = 2.90732 + 0.59799I
b = −0.422461 − 0.238430I
−2.59187 + 0.05584I −4.82458 + 1.57408I
u = −0.036031 + 0.497495I
a = 0.0857590 − 0.0907207I
b = −0.486106 + 1.121140I
−4.57386 − 4.46577I −14.2933 + 6.3376I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.036031 − 0.497495I
a = 0.0857590 + 0.0907207I
b = −0.486106 − 1.121140I
−4.57386 + 4.46577I −14.2933 − 6.3376I
u = −0.01432 + 1.50322I
a = 0.01812 − 1.61025I
b = −0.329831 + 1.321610I
−6.74889 − 1.48702I 0
u = −0.01432 − 1.50322I
a = 0.01812 + 1.61025I
b = −0.329831 − 1.321610I
−6.74889 + 1.48702I 0
u = 0.42976 + 1.47936I
a = −0.49516 + 1.50593I
b = −0.55785 − 1.32892I
−5.92831 + 7.90364I 0
u = 0.42976 − 1.47936I
a = −0.49516 − 1.50593I
b = −0.55785 + 1.32892I
−5.92831 − 7.90364I 0
u = −0.454217
a = 13.1649
b = 2.50456
−0.417366 104.440
u = 0.22265 + 1.54878I
a = −0.805531 − 0.171147I
b = −0.575158 + 0.178603I
−8.83417 + 3.29298I 0
u = 0.22265 − 1.54878I
a = −0.805531 + 0.171147I
b = −0.575158 − 0.178603I
−8.83417 − 3.29298I 0
u = 0.75835 + 1.48548I
a = 0.71873 − 1.30334I
b = 0.71630 + 1.88752I
−13.8837 + 14.9590I 0
u = 0.75835 − 1.48548I
a = 0.71873 + 1.30334I
b = 0.71630 − 1.88752I
−13.8837 − 14.9590I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.78780 + 1.48222I
a = −0.848946 − 0.878958I
b = −0.33270 + 1.50685I
−13.6512 − 6.7959I 0
u = −0.78780 − 1.48222I
a = −0.848946 + 0.878958I
b = −0.33270 − 1.50685I
−13.6512 + 6.7959I 0
u = −0.49918 + 1.64813I
a = 0.36892 + 1.38078I
b = 0.51136 − 1.96440I
−16.0716 − 8.0734I 0
u = −0.49918 − 1.64813I
a = 0.36892 − 1.38078I
b = 0.51136 + 1.96440I
−16.0716 + 8.0734I 0
u = 0.53098 + 1.64910I
a = −0.650566 + 1.090820I
b = −0.19927 − 1.71975I
−15.9425 − 0.1123I 0
u = 0.53098 − 1.64910I
a = −0.650566 − 1.090820I
b = −0.19927 + 1.71975I
−15.9425 + 0.1123I 0
9
II. I
u
2
= hu
8
− 2u
7
+ · · · + b + 1, 3u
8
− 4u
7
+ · · · + a + 6, u
9
− u
8
+ 2u
7
−
u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
8
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
−3u
8
+ 4u
7
− 8u
6
+ 7u
5
− 13u
4
+ 9u
3
− 11u
2
+ 6u − 6
−u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 3u
2
+ 2u − 1
a
11
=
u
u
3
+ u
a
6
=
1
u
2
a
5
=
u
2
+ 1
u
2
a
9
=
u
4
+ u
2
+ 1
u
4
a
12
=
−u
6
− u
4
− 2u
2
− 1
−u
8
− 2u
6
− 2u
4
− 2u
2
a
2
=
−3u
8
+ 4u
7
− 8u
6
+ 7u
5
− 13u
4
+ 9u
3
− 12u
2
+ 6u − 7
−u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 4u
2
+ 2u − 1
a
1
=
−u
2
− 1
−u
2
a
4
=
−3u
8
+ 4u
7
− 8u
6
+ 7u
5
− 13u
4
+ 9u
3
− 11u
2
+ 6u − 6
−u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 3u
2
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −45u
8
+ 63u
7
− 119u
6
+ 104u
5
− 184u
4
+ 133u
3
− 157u
2
+ 83u − 85
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
u
9
c
4
(u + 1)
9
c
5
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
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
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
11
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
12
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ 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
6
y
9
c
5
, c
8
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
9
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
12
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 = −0.140343 + 0.966856I
a = −0.920144 + 0.598375I
b = 1.004430 − 0.297869I
−3.42837 − 2.09337I −5.34027 + 4.50528I
u = −0.140343 − 0.966856I
a = −0.920144 − 0.598375I
b = 1.004430 + 0.297869I
−3.42837 + 2.09337I −5.34027 − 4.50528I
u = −0.628449 + 0.875112I
a = 0.590648 + 0.449402I
b = 0.275254 − 0.816341I
−1.02799 − 2.45442I −2.30315 + 4.13179I
u = −0.628449 − 0.875112I
a = 0.590648 − 0.449402I
b = 0.275254 + 0.816341I
−1.02799 + 2.45442I −2.30315 − 4.13179I
u = 0.796005 + 0.733148I
a = 0.719281 + 0.119276I
b = −0.070080 + 0.850995I
2.72642 − 1.33617I 1.00050 + 1.13735I
u = 0.796005 − 0.733148I
a = 0.719281 − 0.119276I
b = −0.070080 − 0.850995I
2.72642 + 1.33617I 1.00050 − 1.13735I
u = 0.728966 + 0.986295I
a = 0.365868 − 0.247975I
b = 0.195086 + 0.635552I
1.95319 + 7.08493I −0.39190 − 10.48669I
u = 0.728966 − 0.986295I
a = 0.365868 + 0.247975I
b = 0.195086 − 0.635552I
1.95319 − 7.08493I −0.39190 + 10.48669I
u = −0.512358
a = −14.5113
b = −3.80937
−0.446489 −205.930
13
III.
I
v
1
= ha, −16v
4
+ 47v
3
− 36v
2
+ 29b + 104v + 5, v
5
− 3v
4
+ 3v
3
− 8v
2
+ v − 1i
(i) Arc colorings
a
8
=
1
0
a
10
=
v
0
a
7
=
1
0
a
3
=
0
0.551724v
4
− 1.62069v
3
+ ··· − 3.58621v − 0.172414
a
11
=
v
0
a
6
=
1
−0.344828v
4
+ 1.13793v
3
+ ··· + 3.24138v − 1.51724
a
5
=
−0.344828v
4
+ 1.13793v
3
+ ··· + 3.24138v − 0.517241
−0.344828v
4
+ 1.13793v
3
+ ··· + 3.24138v − 1.51724
a
9
=
0.655172v
4
− 1.86207v
3
+ ··· − 4.75862v + 0.482759
v
4
− 3v
3
+ 3v
2
− 8v + 1
a
12
=
−0.655172v
4
+ 1.86207v
3
+ ··· + 5.75862v − 0.482759
−v
4
+ 3v
3
− 3v
2
+ 8v − 1
a
2
=
−0.655172v
4
+ 1.86207v
3
+ ··· + 4.75862v − 0.482759
−0.137931v
4
+ 0.655172v
3
+ ··· + 1.89655v − 2.20690
a
1
=
−0.655172v
4
+ 1.86207v
3
+ ··· + 4.75862v − 0.482759
−v
4
+ 3v
3
− 3v
2
+ 8v − 1
a
4
=
0.551724v
4
− 1.62069v
3
+ ··· − 3.58621v − 0.172414
0.0344828v
4
− 0.413793v
3
+ ··· − 0.724138v + 1.55172
(ii) Obstruction class = 1
(iii) Cusp Shapes =
7
29
v
4
−
26
29
v
3
+
23
29
v
2
−
147
29
v +
257
29
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1
c
2
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
3
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
4
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
5
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
6
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
, c
10
u
5
c
8
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
9
(u + 1)
5
c
11
, c
12
(u − 1)
5
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y − 1
c
2
, c
4
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
c
3
, c
6
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
5
, c
8
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1
c
7
, c
10
y
5
c
9
, c
11
, c
12
(y − 1)
5
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.01014 + 1.59703I
a = 0
b = 0.339110 + 0.822375I
1.31583 + 1.53058I 8.42731 − 4.45807I
v = 0.01014 − 1.59703I
a = 0
b = 0.339110 − 0.822375I
1.31583 − 1.53058I 8.42731 + 4.45807I
v = 0.043806 + 0.365575I
a = 0
b = −0.455697 − 1.200150I
−4.22763 + 4.40083I 8.55516 − 1.78781I
v = 0.043806 − 0.365575I
a = 0
b = −0.455697 + 1.200150I
−4.22763 − 4.40083I 8.55516 + 1.78781I
v = 2.89210
a = 0
b = −0.766826
−0.756147 −3.96490
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
5
− 5u
4
+ ··· − u − 1)(u
46
+ 61u
45
+ ··· + 62504u + 1)
c
2
((u − 1)
9
)(u
5
+ u
4
+ ··· + u − 1)(u
46
− 11u
45
+ ··· + 260u − 1)
c
3
u
9
(u
5
− u
4
+ ··· + u − 1)(u
46
+ 8u
45
+ ··· + 9216u + 512)
c
4
((u + 1)
9
)(u
5
− u
4
+ ··· + u + 1)(u
46
− 11u
45
+ ··· + 260u − 1)
c
5
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
46
− 3u
45
+ ··· + 2u − 1)
c
6
u
9
(u
5
+ u
4
+ ··· + u + 1)(u
46
+ 8u
45
+ ··· + 9216u + 512)
c
7
u
5
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
46
+ 2u
45
+ ··· − 32u + 32)
c
8
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
46
− 3u
45
+ ··· + 2u − 1)
c
9
(u + 1)
5
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
46
+ 7u
45
+ ··· + 4u + 1)
c
10
u
5
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
46
+ 2u
45
+ ··· − 32u + 32)
c
11
(u − 1)
5
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
46
+ 7u
45
+ ··· + 4u + 1)
c
12
(u − 1)
5
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
46
− 17u
45
+ ··· − 22u + 1)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
9
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y − 1)
· (y
46
− 141y
45
+ ··· − 3903085204y + 1)
c
2
, c
4
((y − 1)
9
)(y
5
− 5y
4
+ ··· − y − 1)(y
46
− 61y
45
+ ··· − 62504y + 1)
c
3
, c
6
y
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
· (y
46
+ 60y
45
+ ··· − 71827456y + 262144)
c
5
, c
8
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
46
− y
45
+ ··· − 32y + 1)
c
7
, c
10
y
5
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
46
+ 36y
45
+ ··· + 8704y + 1024)
c
9
, c
11
(y − 1)
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
46
− 17y
45
+ ··· − 22y + 1)
c
12
(y − 1)
5
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
46
+ 31y
45
+ ··· + 246y + 1)
19
