12n
0818
(K12n
0818
)
A knot diagram
1
Linearized knot diagam
4 6 11 7 10 2 12 11 5 3 8 7
Solving Sequence
8,11 4,12
3 7 5 1 2 6 10 9
c
11
c
3
c
7
c
4
c
12
c
1
c
6
c
10
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−9u
23
− 69u
22
+ ··· + 4b − 60, −u
23
− 23u
22
+ ··· + 8a − 92, u
24
+ 9u
23
+ ··· + 60u + 8i
I
u
2
= h−23435100677a
5
u
5
+ 10963667366u
5
a
4
+ ··· + 71553959584a + 30822539955,
2u
5
a
4
− 5u
5
a
3
+ ··· + 114a − 114, u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1i
I
u
3
= h−u
13
+ 2u
12
− 9u
11
+ 14u
10
− 29u
9
+ 34u
8
− 38u
7
+ 32u
6
− 14u
5
+ 6u
4
+ 5u
3
− 4u
2
+ b − 1,
u
14
− 2u
13
+ ··· + a + 3, u
15
− 2u
14
+ ··· + 3u + 1i
* 3 irreducible components of dim
C
= 0, with total 75 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−9u
23
− 69u
22
+ · · · + 4b − 60, −u
23
− 23u
22
+ · · · + 8a − 92, u
24
+
9u
23
+ · · · + 60u + 8i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
4
=
1
8
u
23
+
23
8
u
22
+ ··· +
283
4
u +
23
2
9
4
u
23
+
69
4
u
22
+ ··· + 96u + 15
a
12
=
1
−u
2
a
3
=
2.37500u
23
+ 20.1250u
22
+ ··· + 166.750u + 26.5000
9
4
u
23
+
69
4
u
22
+ ··· + 96u + 15
a
7
=
−u
u
3
+ u
a
5
=
1
8
u
23
+
15
8
u
22
+ ··· +
443
4
u +
35
2
−
7
4
u
23
−
51
4
u
22
+ ··· − 4u + 1
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−
13
8
u
23
−
111
8
u
22
+ ··· −
625
4
u − 26
−
1
4
u
23
−
7
4
u
22
+ ··· −
37
2
u − 3
a
6
=
15
8
u
23
+
123
8
u
22
+ ··· +
279
2
u + 22
3
2
u
23
+ 11u
22
+ ··· +
157
2
u + 13
a
10
=
−
1
8
u
23
−
11
8
u
22
+ ··· −
41
4
u − 1
−
3
4
u
23
−
25
4
u
22
+ ··· −
67
2
u − 5
a
9
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 10u
23
+ 83u
22
+ 460u
21
+ 1851u
20
+ 6019u
19
+ 16308u
18
+ 37879u
17
+ 76523u
16
+
135925u
15
+ 213724u
14
+ 298650u
13
+ 371570u
12
+ 411446u
11
+ 404553u
10
+ 351654u
9
+
268406u
8
+ 178327u
7
+ 101993u
6
+ 49649u
5
+ 20388u
4
+ 7050u
3
+ 2063u
2
+ 490u + 66
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
24
+ 11u
22
+ ··· + 2u + 1
c
2
, c
6
u
24
− 13u
23
+ ··· − 736u + 64
c
3
, c
5
, c
9
c
10
u
24
− u
23
+ ··· + 2u + 1
c
7
, c
8
, c
11
c
12
u
24
+ 9u
23
+ ··· + 60u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
24
+ 22y
23
+ ··· + 28y + 1
c
2
, c
6
y
24
+ 21y
23
+ ··· + 19456y + 4096
c
3
, c
5
, c
9
c
10
y
24
− 17y
23
+ ··· − 6y + 1
c
7
, c
8
, c
11
c
12
y
24
+ 23y
23
+ ··· + 624y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.971536 + 0.221960I
a = 0.61723 + 1.27443I
b = −1.38087 − 0.69103I
−3.82723 − 9.97673I −3.43940 + 6.32468I
u = −0.971536 − 0.221960I
a = 0.61723 − 1.27443I
b = −1.38087 + 0.69103I
−3.82723 + 9.97673I −3.43940 − 6.32468I
u = −0.325915 + 0.983831I
a = −0.033935 − 0.418334I
b = −0.624731 + 0.626850I
0.283464 + 0.443199I −0.97811 − 2.48365I
u = −0.325915 − 0.983831I
a = −0.033935 + 0.418334I
b = −0.624731 − 0.626850I
0.283464 − 0.443199I −0.97811 + 2.48365I
u = −0.854577 + 0.270304I
a = −0.133719 − 1.288200I
b = 1.021730 + 0.517114I
2.37599 − 4.87646I −0.51553 + 6.02315I
u = −0.854577 − 0.270304I
a = −0.133719 + 1.288200I
b = 1.021730 − 0.517114I
2.37599 + 4.87646I −0.51553 − 6.02315I
u = −0.238805 + 1.148550I
a = 0.129829 + 1.005970I
b = 0.363709 − 0.617449I
−1.74481 − 4.18781I −4.37804 + 0.87834I
u = −0.238805 − 1.148550I
a = 0.129829 − 1.005970I
b = 0.363709 + 0.617449I
−1.74481 + 4.18781I −4.37804 − 0.87834I
u = 0.193901 + 1.206350I
a = 0.606162 + 0.345461I
b = 0.569981 − 0.522089I
−4.59216 + 2.01653I −7.18080 − 3.39780I
u = 0.193901 − 1.206350I
a = 0.606162 − 0.345461I
b = 0.569981 + 0.522089I
−4.59216 − 2.01653I −7.18080 + 3.39780I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.661561 + 1.033500I
a = −0.328591 − 0.193748I
b = 1.202730 − 0.647830I
−6.30317 + 4.38086I −4.52921 − 3.44715I
u = −0.661561 − 1.033500I
a = −0.328591 + 0.193748I
b = 1.202730 + 0.647830I
−6.30317 − 4.38086I −4.52921 + 3.44715I
u = −0.618272 + 0.317395I
a = −0.638426 + 0.970996I
b = −0.676953 − 0.157022I
0.809068 + 1.101490I −5.35892 + 1.01281I
u = −0.618272 − 0.317395I
a = −0.638426 − 0.970996I
b = −0.676953 + 0.157022I
0.809068 − 1.101490I −5.35892 − 1.01281I
u = −0.42667 + 1.42118I
a = 0.69104 − 1.34370I
b = 1.50579 + 0.65933I
−9.0022 − 14.9856I −7.09597 + 7.57547I
u = −0.42667 − 1.42118I
a = 0.69104 + 1.34370I
b = 1.50579 − 0.65933I
−9.0022 + 14.9856I −7.09597 − 7.57547I
u = −0.37787 + 1.44359I
a = −0.810469 + 1.141880I
b = −1.219090 − 0.464171I
−3.08328 − 9.37984I −4.94083 + 6.69996I
u = −0.37787 − 1.44359I
a = −0.810469 − 1.141880I
b = −1.219090 + 0.464171I
−3.08328 + 9.37984I −4.94083 − 6.69996I
u = −0.30052 + 1.50793I
a = 0.873070 − 0.786162I
b = 1.056120 + 0.111001I
−5.27850 − 2.45819I −6.52768 + 0.I
u = −0.30052 − 1.50793I
a = 0.873070 + 0.786162I
b = 1.056120 − 0.111001I
−5.27850 + 2.45819I −6.52768 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.152565 + 0.389462I
a = −0.640664 − 0.680814I
b = −0.289140 + 0.385262I
−0.049661 + 0.901122I −1.07060 − 7.46829I
u = 0.152565 − 0.389462I
a = −0.640664 + 0.680814I
b = −0.289140 − 0.385262I
−0.049661 − 0.901122I −1.07060 + 7.46829I
u = −0.07074 + 1.75374I
a = −0.581532 + 0.242567I
b = −1.029280 + 0.409939I
−16.4681 + 1.7281I 0
u = −0.07074 − 1.75374I
a = −0.581532 − 0.242567I
b = −1.029280 − 0.409939I
−16.4681 − 1.7281I 0
7
II. I
u
2
= h−2.34 × 10
10
a
5
u
5
+ 1.10 × 10
10
a
4
u
5
+ · · · + 7.16 × 10
10
a + 3.08 ×
10
10
, 2u
5
a
4
− 5u
5
a
3
+ · · · + 114a − 114, u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
4
=
a
0.347931a
5
u
5
− 0.162773a
4
u
5
+ ··· − 1.06233a − 0.457609
a
12
=
1
−u
2
a
3
=
0.347931a
5
u
5
− 0.162773a
4
u
5
+ ··· − 0.0623316a − 0.457609
0.347931a
5
u
5
− 0.162773a
4
u
5
+ ··· − 1.06233a − 0.457609
a
7
=
−u
u
3
+ u
a
5
=
0.180852a
5
u
5
− 0.416166a
4
u
5
+ ··· + 0.491548a − 0.144406
−0.346810a
5
u
5
− 0.643062a
4
u
5
+ ··· + 0.451764a − 1.01177
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−0.204126a
5
u
5
+ 0.255973a
4
u
5
+ ··· + 0.0646899a + 0.294428
0.438515a
5
u
5
− 0.212894a
4
u
5
+ ··· − 0.142744a + 0.592655
a
6
=
0.213990a
5
u
5
− 0.398539a
4
u
5
+ ··· − 0.880353a + 1.01839
−0.329334a
5
u
5
− 0.804316a
4
u
5
+ ··· + 1.33815a − 0.0581934
a
10
=
−0.0846058a
5
u
5
+ 0.661136a
4
u
5
+ ··· + 0.296011a − 0.487725
0.149782a
5
u
5
+ 0.704215a
4
u
5
+ ··· + 0.217957a − 1.60064
a
9
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
5658079336
22451859377
a
5
u
5
+
18778081872
22451859377
u
5
a
4
+ ··· −
16584590624
22451859377
a −
56541555310
22451859377
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
36
− 5u
35
+ ··· − 36u + 1
c
2
, c
6
(u
3
+ u
2
+ 2u + 1)
12
c
3
, c
5
, c
9
c
10
u
36
− u
35
+ ··· + 4988u − 2207
c
7
, c
8
, c
11
c
12
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
36
+ 7y
35
+ ··· − 912y + 1
c
2
, c
6
(y
3
+ 3y
2
+ 2y − 1)
12
c
3
, c
5
, c
9
c
10
y
36
− 25y
35
+ ··· − 47603416y + 4870849
c
7
, c
8
, c
11
c
12
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
6
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.873214
a = −0.419995 + 1.215150I
b = 0.580895 − 0.775278I
3.83874 3.28901 + 0.I
u = 0.873214
a = −0.419995 − 1.215150I
b = 0.580895 + 0.775278I
3.83874 3.28901 + 0.I
u = 0.873214
a = 1.037200 + 0.778295I
b = −1.025490 − 0.187777I
−0.29884 − 2.82812I −3.24026 + 2.97945I
u = 0.873214
a = 1.037200 − 0.778295I
b = −1.025490 + 0.187777I
−0.29884 + 2.82812I −3.24026 − 2.97945I
u = 0.873214
a = −0.06083 + 1.60714I
b = −0.324929 − 1.334150I
−0.29884 + 2.82812I −3.24026 − 2.97945I
u = 0.873214
a = −0.06083 − 1.60714I
b = −0.324929 + 1.334150I
−0.29884 − 2.82812I −3.24026 + 2.97945I
u = −0.138835 + 1.234450I
a = 0.012228 − 1.187000I
b = 1.44703 + 1.08222I
−10.91920 − 4.80053I −10.93403 + 6.66423I
u = −0.138835 + 1.234450I
a = 1.137440 − 0.567294I
b = 1.42862 − 0.02132I
−6.78159 − 1.97241I −4.40477 + 3.68478I
u = −0.138835 + 1.234450I
a = −0.364631 + 0.343650I
b = −1.88950 + 0.34251I
−10.91920 + 0.85571I −10.93403 + 0.70533I
u = −0.138835 + 1.234450I
a = −0.10816 + 1.58237I
b = −1.056330 − 0.412957I
−6.78159 − 1.97241I −4.40477 + 3.68478I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.138835 + 1.234450I
a = −2.21023 + 1.02274I
b = −1.45126 − 0.21009I
−10.91920 − 4.80053I −10.93403 + 6.66423I
u = −0.138835 + 1.234450I
a = 0.16985 − 2.53916I
b = 1.028260 − 0.205085I
−10.91920 + 0.85571I −10.93403 + 0.70533I
u = −0.138835 − 1.234450I
a = 0.012228 + 1.187000I
b = 1.44703 − 1.08222I
−10.91920 + 4.80053I −10.93403 − 6.66423I
u = −0.138835 − 1.234450I
a = 1.137440 + 0.567294I
b = 1.42862 + 0.02132I
−6.78159 + 1.97241I −4.40477 − 3.68478I
u = −0.138835 − 1.234450I
a = −0.364631 − 0.343650I
b = −1.88950 − 0.34251I
−10.91920 − 0.85571I −10.93403 − 0.70533I
u = −0.138835 − 1.234450I
a = −0.10816 − 1.58237I
b = −1.056330 + 0.412957I
−6.78159 + 1.97241I −4.40477 − 3.68478I
u = −0.138835 − 1.234450I
a = −2.21023 − 1.02274I
b = −1.45126 + 0.21009I
−10.91920 + 4.80053I −10.93403 − 6.66423I
u = −0.138835 − 1.234450I
a = 0.16985 + 2.53916I
b = 1.028260 + 0.205085I
−10.91920 − 0.85571I −10.93403 − 0.70533I
u = 0.408802 + 1.276380I
a = 0.887209 + 0.587298I
b = 0.632640 − 0.969780I
−4.26335 + 1.76400I −6.92862 − 0.22537I
u = 0.408802 + 1.276380I
a = −0.659750 − 0.545076I
b = 0.04879 + 1.56085I
−4.26335 + 7.42025I −6.92862 − 6.18427I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.408802 + 1.276380I
a = −0.517890 − 1.088660I
b = −0.847436 + 0.716450I
−0.12577 + 4.59213I −0.39935 − 3.20482I
u = 0.408802 + 1.276380I
a = 0.375953 + 0.353514I
b = −0.300632 − 0.839566I
−0.12577 + 4.59213I −0.39935 − 3.20482I
u = 0.408802 + 1.276380I
a = 0.09934 + 1.53963I
b = 1.164190 − 0.284914I
−4.26335 + 7.42025I −6.92862 − 6.18427I
u = 0.408802 + 1.276380I
a = 0.0031648 + 0.1271530I
b = 0.823310 − 0.019949I
−4.26335 + 1.76400I −6.92862 − 0.22537I
u = 0.408802 − 1.276380I
a = 0.887209 − 0.587298I
b = 0.632640 + 0.969780I
−4.26335 − 1.76400I −6.92862 + 0.22537I
u = 0.408802 − 1.276380I
a = −0.659750 + 0.545076I
b = 0.04879 − 1.56085I
−4.26335 − 7.42025I −6.92862 + 6.18427I
u = 0.408802 − 1.276380I
a = −0.517890 + 1.088660I
b = −0.847436 − 0.716450I
−0.12577 − 4.59213I −0.39935 + 3.20482I
u = 0.408802 − 1.276380I
a = 0.375953 − 0.353514I
b = −0.300632 + 0.839566I
−0.12577 − 4.59213I −0.39935 + 3.20482I
u = 0.408802 − 1.276380I
a = 0.09934 − 1.53963I
b = 1.164190 + 0.284914I
−4.26335 − 7.42025I −6.92862 + 6.18427I
u = 0.408802 − 1.276380I
a = 0.0031648 − 0.1271530I
b = 0.823310 + 0.019949I
−4.26335 − 1.76400I −6.92862 + 0.22537I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.413150
a = 0.833798
b = −1.29141
−3.08250 4.43630
u = −0.413150
a = −1.05083 + 2.06200I
b = 1.54512 − 0.28152I
−7.22008 + 2.82812I −2.09298 − 2.97945I
u = −0.413150
a = −1.05083 − 2.06200I
b = 1.54512 + 0.28152I
−7.22008 − 2.82812I −2.09298 + 2.97945I
u = −0.413150
a = −3.27825
b = 0.926293
−3.08250 4.43630
u = −0.413150
a = 3.89216 + 0.35002I
b = −1.120730 + 0.641787I
−7.22008 + 2.82812I −2.09298 − 2.97945I
u = −0.413150
a = 3.89216 − 0.35002I
b = −1.120730 − 0.641787I
−7.22008 − 2.82812I −2.09298 + 2.97945I
14
III.
I
u
3
= h−u
13
+2u
12
+· · ·+b−1, u
14
−2u
13
+· · ·+a+3, u
15
−2u
14
+· · ·+3u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
4
=
−u
14
+ 2u
13
+ ··· + 6u − 3
u
13
− 2u
12
+ ··· + 4u
2
+ 1
a
12
=
1
−u
2
a
3
=
−u
14
+ 3u
13
+ ··· + 6u − 2
u
13
− 2u
12
+ ··· + 4u
2
+ 1
a
7
=
−u
u
3
+ u
a
5
=
−u
14
+ 3u
13
+ ··· + 9u − 2
u
13
− 2u
12
+ ··· + u
2
+ 1
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
u
13
− 3u
12
+ ··· + 5u − 1
u
14
− 2u
13
+ ··· + u + 1
a
6
=
−2u
13
+ 4u
12
+ ··· − 8u − 1
−u
14
+ u
13
+ ··· − 3u − 1
a
10
=
2u
14
− 5u
13
+ ··· − 5u + 3
−u
13
+ 2u
12
+ ··· − u − 2
a
9
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= u
13
−3u
12
+11u
11
−24u
10
+45u
9
−72u
8
+86u
7
−97u
6
+81u
5
−52u
4
+36u
3
−4u
2
+7u−9
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
15
+ u
13
+ u
12
+ 5u
11
− 3u
10
+ 4u
9
− u
7
− 2u
6
+ 3u
5
+ 4u
3
− 3u − 1
c
2
u
15
+ 9u
13
+ ··· + 7u − 3
c
3
, c
9
u
15
+ u
14
+ ··· + u + 1
c
5
, c
10
u
15
− u
14
+ ··· + u − 1
c
6
u
15
+ 9u
13
+ ··· + 7u + 3
c
7
, c
8
u
15
+ 2u
14
+ ··· + 3u − 1
c
11
, c
12
u
15
− 2u
14
+ ··· + 3u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
15
+ 2y
14
+ ··· + 9y − 1
c
2
, c
6
y
15
+ 18y
14
+ ··· − 29y − 9
c
3
, c
5
, c
9
c
10
y
15
− 13y
14
+ ··· − 5y − 1
c
7
, c
8
, c
11
c
12
y
15
+ 18y
14
+ ··· + 19y − 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.067274 + 1.170430I
a = 0.95387 − 1.52946I
b = 1.53238 + 0.52140I
−10.56770 − 3.31418I −9.17040 + 1.09581I
u = −0.067274 − 1.170430I
a = 0.95387 + 1.52946I
b = 1.53238 − 0.52140I
−10.56770 + 3.31418I −9.17040 − 1.09581I
u = 0.762991 + 0.100003I
a = 0.471363 + 1.179970I
b = 0.113487 − 0.512613I
1.70400 − 1.60852I 1.70832 + 2.29891I
u = 0.762991 − 0.100003I
a = 0.471363 − 1.179970I
b = 0.113487 + 0.512613I
1.70400 + 1.60852I 1.70832 − 2.29891I
u = 0.345661 + 1.264130I
a = 0.235836 + 1.006840I
b = 0.286552 − 0.611540I
−1.97026 + 5.58462I −5.72570 − 5.91133I
u = 0.345661 − 1.264130I
a = 0.235836 − 1.006840I
b = 0.286552 + 0.611540I
−1.97026 − 5.58462I −5.72570 + 5.91133I
u = −0.116103 + 1.321650I
a = −0.771507 + 1.030610I
b = −1.278400 − 0.105005I
−8.11583 − 1.16999I −10.61528 + 0.29534I
u = −0.116103 − 1.321650I
a = −0.771507 − 1.030610I
b = −1.278400 + 0.105005I
−8.11583 + 1.16999I −10.61528 − 0.29534I
u = −0.163781 + 0.551604I
a = 0.74742 + 1.75607I
b = −1.329030 + 0.457754I
−8.48637 + 2.50657I −9.80004 − 1.02375I
u = −0.163781 − 0.551604I
a = 0.74742 − 1.75607I
b = −1.329030 − 0.457754I
−8.48637 − 2.50657I −9.80004 + 1.02375I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.39099 + 1.41773I
a = −0.649469 − 0.501014I
b = −0.528118 + 0.547402I
−3.19548 + 2.58951I −1.00193 − 4.07302I
u = 0.39099 − 1.41773I
a = −0.649469 + 0.501014I
b = −0.528118 − 0.547402I
−3.19548 − 2.58951I −1.00193 + 4.07302I
u = −0.05414 + 1.69785I
a = 0.580701 − 0.387083I
b = 1.114480 − 0.359089I
−16.8509 + 1.5277I −15.4381 + 2.1822I
u = −0.05414 − 1.69785I
a = 0.580701 + 0.387083I
b = 1.114480 + 0.359089I
−16.8509 − 1.5277I −15.4381 − 2.1822I
u = −0.196681
a = −5.13644
b = 1.17730
−3.73109 −10.9140
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
15
+ u
13
+ u
12
+ 5u
11
− 3u
10
+ 4u
9
− u
7
− 2u
6
+ 3u
5
+ 4u
3
− 3u − 1)
· (u
24
+ 11u
22
+ ··· + 2u + 1)(u
36
− 5u
35
+ ··· − 36u + 1)
c
2
((u
3
+ u
2
+ 2u + 1)
12
)(u
15
+ 9u
13
+ ··· + 7u − 3)
· (u
24
− 13u
23
+ ··· − 736u + 64)
c
3
, c
9
(u
15
+ u
14
+ ··· + u + 1)(u
24
− u
23
+ ··· + 2u + 1)
· (u
36
− u
35
+ ··· + 4988u − 2207)
c
5
, c
10
(u
15
− u
14
+ ··· + u − 1)(u
24
− u
23
+ ··· + 2u + 1)
· (u
36
− u
35
+ ··· + 4988u − 2207)
c
6
((u
3
+ u
2
+ 2u + 1)
12
)(u
15
+ 9u
13
+ ··· + 7u + 3)
· (u
24
− 13u
23
+ ··· − 736u + 64)
c
7
, c
8
((u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
)(u
15
+ 2u
14
+ ··· + 3u − 1)
· (u
24
+ 9u
23
+ ··· + 60u + 8)
c
11
, c
12
((u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
)(u
15
− 2u
14
+ ··· + 3u + 1)
· (u
24
+ 9u
23
+ ··· + 60u + 8)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
15
+ 2y
14
+ ··· + 9y − 1)(y
24
+ 22y
23
+ ··· + 28y + 1)
· (y
36
+ 7y
35
+ ··· − 912y + 1)
c
2
, c
6
((y
3
+ 3y
2
+ 2y − 1)
12
)(y
15
+ 18y
14
+ ··· − 29y − 9)
· (y
24
+ 21y
23
+ ··· + 19456y + 4096)
c
3
, c
5
, c
9
c
10
(y
15
− 13y
14
+ ··· − 5y − 1)(y
24
− 17y
23
+ ··· − 6y + 1)
· (y
36
− 25y
35
+ ··· − 47603416y + 4870849)
c
7
, c
8
, c
11
c
12
((y
6
+ 5y
5
+ ··· − 5y + 1)
6
)(y
15
+ 18y
14
+ ··· + 19y − 1)
· (y
24
+ 23y
23
+ ··· + 624y + 64)
21
