12a
0436
(K12a
0436
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 1 5 11 12 4 9 7
Solving Sequence
2,6 3,10
4 11 1 7 5 8 12 9
c
2
c
3
c
10
c
1
c
6
c
5
c
7
c
12
c
9
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2u
79
+ u
78
+ ··· + b − u, −u
78
− u
77
+ ··· + a + 3, u
80
− 2u
79
+ ··· − u − 1i
I
u
2
= h−u
6
+ 2u
4
+ u
3
− u
2
+ b − u − 1, −u
7
− u
6
+ 2u
5
+ 2u
4
− u
3
− u
2
+ a − u − 1,
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 89 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−2u
79
+u
78
+· · ·+b−u, −u
78
−u
77
+· · ·+a+3, u
80
−2u
79
+· · ·−u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
u
78
+ u
77
+ ··· − u − 3
2u
79
− u
78
+ ··· − 4u
2
+ u
a
4
=
u
17
− 4u
15
+ 7u
13
− 4u
11
− 3u
9
+ 6u
7
− 2u
5
+ u
u
17
− 5u
15
+ 11u
13
− 12u
11
+ 5u
9
+ 2u
7
− 2u
5
+ u
a
11
=
−u
78
+ u
77
+ ··· + u − 2
−u
78
+ u
77
+ ··· − 2u
3
+ 2u
a
1
=
−u
2
+ 1
−u
4
a
7
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
5
=
u
u
a
8
=
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
−u
9
+ 3u
7
− 3u
5
+ u
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
10
+ 2u
8
− u
6
− 2u
4
+ u
2
a
9
=
u
77
− u
76
+ ··· + 2u
2
− 2
u
79
− u
78
+ ··· − u
2
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
79
+ 9u
78
+ ··· − 29u − 1
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
80
+ 42u
79
+ ··· + 9u + 1
c
2
, c
5
u
80
+ 2u
79
+ ··· + u − 1
c
3
, c
10
u
80
+ u
79
+ ··· − 768u
2
+ 512
c
4
, c
7
u
80
− 6u
79
+ ··· + 1829u + 145
c
6
, c
12
u
80
+ 6u
79
+ ··· − 577u + 53
c
8
, c
9
, c
11
u
80
+ 10u
79
+ ··· − 7u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
80
− 6y
79
+ ··· − 41y + 1
c
2
, c
5
y
80
− 42y
79
+ ··· − 9y + 1
c
3
, c
10
y
80
− 57y
79
+ ··· − 786432y + 262144
c
4
, c
7
y
80
+ 66y
79
+ ··· − 1478221y + 21025
c
6
, c
12
y
80
+ 54y
79
+ ··· − 584997y + 2809
c
8
, c
9
, c
11
y
80
− 82y
79
+ ··· − 5y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.788241 + 0.593267I
a = 2.89714 + 1.16358I
b = 0.97355 + 2.78858I
6.24334 − 5.11064I 8.14762 + 6.48257I
u = 0.788241 − 0.593267I
a = 2.89714 − 1.16358I
b = 0.97355 − 2.78858I
6.24334 + 5.11064I 8.14762 − 6.48257I
u = 0.813592 + 0.609570I
a = −2.93002 − 1.26264I
b = −1.10331 − 2.68448I
13.2744 − 9.2224I 0
u = 0.813592 − 0.609570I
a = −2.93002 + 1.26264I
b = −1.10331 + 2.68448I
13.2744 + 9.2224I 0
u = −0.772569 + 0.598380I
a = 1.07413 + 1.28706I
b = 1.42261 + 0.64929I
8.47306 + 2.34861I 9.12486 − 3.37977I
u = −0.772569 − 0.598380I
a = 1.07413 − 1.28706I
b = 1.42261 − 0.64929I
8.47306 − 2.34861I 9.12486 + 3.37977I
u = 1.03436
a = 1.16159
b = 0.0399622
3.30231 0
u = 0.755447 + 0.596084I
a = −2.64657 − 0.97416I
b = −0.97087 − 2.78244I
6.33746 + 0.43474I 8.59846 + 0.I
u = 0.755447 − 0.596084I
a = −2.64657 + 0.97416I
b = −0.97087 + 2.78244I
6.33746 − 0.43474I 8.59846 + 0.I
u = 0.731741 + 0.621831I
a = 2.26610 + 1.17730I
b = 0.78459 + 2.79549I
13.5099 + 4.4268I 10.35839 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.731741 − 0.621831I
a = 2.26610 − 1.17730I
b = 0.78459 − 2.79549I
13.5099 − 4.4268I 10.35839 + 0.I
u = −0.877134 + 0.339225I
a = 1.21807 − 1.37277I
b = 0.81822 − 1.38163I
0.06759 + 3.08443I 2.43309 − 8.76495I
u = −0.877134 − 0.339225I
a = 1.21807 + 1.37277I
b = 0.81822 + 1.38163I
0.06759 − 3.08443I 2.43309 + 8.76495I
u = −0.770687 + 0.535889I
a = −0.521106 − 0.626440I
b = −0.657130 − 0.323997I
2.28869 + 2.16821I 1.72867 − 4.00408I
u = −0.770687 − 0.535889I
a = −0.521106 + 0.626440I
b = −0.657130 + 0.323997I
2.28869 − 2.16821I 1.72867 + 4.00408I
u = −0.967844 + 0.492553I
a = −1.03957 + 1.74058I
b = −0.42685 + 2.01970I
6.45001 + 4.97903I 0
u = −0.967844 − 0.492553I
a = −1.03957 − 1.74058I
b = −0.42685 − 2.01970I
6.45001 − 4.97903I 0
u = 0.850210 + 0.090701I
a = −0.438624 − 0.409673I
b = 0.1052960 + 0.0201192I
−1.39732 − 0.27454I −6.35667 + 0.34095I
u = 0.850210 − 0.090701I
a = −0.438624 + 0.409673I
b = 0.1052960 − 0.0201192I
−1.39732 + 0.27454I −6.35667 − 0.34095I
u = −1.127480 + 0.258399I
a = −0.133039 + 1.121980I
b = −0.965050 + 0.962471I
7.10133 + 5.72796I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.127480 − 0.258399I
a = −0.133039 − 1.121980I
b = −0.965050 − 0.962471I
7.10133 − 5.72796I 0
u = 0.205648 + 0.805086I
a = −2.13997 + 0.84059I
b = −0.44039 − 1.84984I
10.2271 + 10.5873I 8.12464 − 5.54004I
u = 0.205648 − 0.805086I
a = −2.13997 − 0.84059I
b = −0.44039 + 1.84984I
10.2271 − 10.5873I 8.12464 + 5.54004I
u = 0.754822 + 0.340700I
a = 0.270589 + 1.097730I
b = −0.621443 − 0.083376I
2.17846 − 1.57925I 3.82899 + 3.54363I
u = 0.754822 − 0.340700I
a = 0.270589 − 1.097730I
b = −0.621443 + 0.083376I
2.17846 + 1.57925I 3.82899 − 3.54363I
u = −1.139280 + 0.328895I
a = 0.804519 − 0.439781I
b = 1.79318 − 1.05870I
−0.07200 + 2.42458I 0
u = −1.139280 − 0.328895I
a = 0.804519 + 0.439781I
b = 1.79318 + 1.05870I
−0.07200 − 2.42458I 0
u = 0.207211 + 0.779709I
a = 2.31171 − 0.83656I
b = 0.22750 + 1.53793I
3.51520 + 6.34636I 6.24074 − 5.42401I
u = 0.207211 − 0.779709I
a = 2.31171 + 0.83656I
b = 0.22750 − 1.53793I
3.51520 − 6.34636I 6.24074 + 5.42401I
u = −0.219389 + 0.769412I
a = 0.587178 − 0.807351I
b = −0.709890 − 1.068920I
5.91566 − 3.66945I 7.65776 + 2.47936I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.219389 − 0.769412I
a = 0.587178 + 0.807351I
b = −0.709890 + 1.068920I
5.91566 + 3.66945I 7.65776 − 2.47936I
u = 0.272716 + 0.749664I
a = 2.07259 − 0.63049I
b = 0.774645 + 0.671760I
11.39820 − 2.75257I 9.62649 + 1.18045I
u = 0.272716 − 0.749664I
a = 2.07259 + 0.63049I
b = 0.774645 − 0.671760I
11.39820 + 2.75257I 9.62649 − 1.18045I
u = −0.079116 + 0.793763I
a = −0.273217 − 0.675415I
b = −1.057360 + 0.708134I
2.72585 − 4.14449I 6.24638 + 3.84786I
u = −0.079116 − 0.793763I
a = −0.273217 + 0.675415I
b = −1.057360 − 0.708134I
2.72585 + 4.14449I 6.24638 − 3.84786I
u = 1.163210 + 0.326788I
a = 0.185302 + 1.026710I
b = −0.411450 + 0.171697I
1.76495 + 0.23636I 0
u = 1.163210 − 0.326788I
a = 0.185302 − 1.026710I
b = −0.411450 − 0.171697I
1.76495 − 0.23636I 0
u = 0.226952 + 0.751765I
a = −2.32110 + 0.59136I
b = −0.256373 − 1.002050I
3.98475 + 0.88483I 7.59092 + 0.37098I
u = 0.226952 − 0.751765I
a = −2.32110 − 0.59136I
b = −0.256373 + 1.002050I
3.98475 − 0.88483I 7.59092 − 0.37098I
u = −1.177730 + 0.334016I
a = −0.472654 − 0.401659I
b = −2.13844 + 0.19517I
−0.65300 − 2.79770I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.177730 − 0.334016I
a = −0.472654 + 0.401659I
b = −2.13844 − 0.19517I
−0.65300 + 2.79770I 0
u = 1.167430 + 0.376595I
a = −0.002258 − 0.504828I
b = 0.295211 − 0.022642I
−3.96959 − 0.86076I 0
u = 1.167430 − 0.376595I
a = −0.002258 + 0.504828I
b = 0.295211 + 0.022642I
−3.96959 + 0.86076I 0
u = −1.150850 + 0.438169I
a = 1.26868 − 1.79458I
b = 0.29661 − 2.76608I
−2.44030 + 2.93931I 0
u = −1.150850 − 0.438169I
a = 1.26868 + 1.79458I
b = 0.29661 + 2.76608I
−2.44030 − 2.93931I 0
u = −0.166236 + 0.742708I
a = −0.347964 + 0.352578I
b = 0.365823 + 0.491960I
−0.13713 − 2.80838I −0.38510 + 3.25626I
u = −0.166236 − 0.742708I
a = −0.347964 − 0.352578I
b = 0.365823 − 0.491960I
−0.13713 + 2.80838I −0.38510 − 3.25626I
u = 1.154970 + 0.462037I
a = −0.067535 − 0.742060I
b = 1.304340 − 0.231466I
−2.26506 − 5.18346I 0
u = 1.154970 − 0.462037I
a = −0.067535 + 0.742060I
b = 1.304340 + 0.231466I
−2.26506 + 5.18346I 0
u = −1.199980 + 0.328265I
a = −0.111881 + 0.662316I
b = 1.80309 + 0.35042I
5.92061 − 6.93082I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.199980 − 0.328265I
a = −0.111881 − 0.662316I
b = 1.80309 − 0.35042I
5.92061 + 6.93082I 0
u = −0.491306 + 0.571190I
a = 1.91932 − 0.18659I
b = 1.09981 − 1.13296I
7.80506 − 0.69666I 10.81571 + 0.01021I
u = −0.491306 − 0.571190I
a = 1.91932 + 0.18659I
b = 1.09981 + 1.13296I
7.80506 + 0.69666I 10.81571 − 0.01021I
u = 1.175660 + 0.429014I
a = 0.607234 + 0.484749I
b = −0.402768 + 0.642166I
−5.55054 − 2.10141I 0
u = 1.175660 − 0.429014I
a = 0.607234 − 0.484749I
b = −0.402768 − 0.642166I
−5.55054 + 2.10141I 0
u = 1.138020 + 0.537928I
a = −0.45342 − 1.67252I
b = 0.04188 − 2.69443I
8.86470 − 2.09320I 0
u = 1.138020 − 0.537928I
a = −0.45342 + 1.67252I
b = 0.04188 + 2.69443I
8.86470 + 2.09320I 0
u = −1.175440 + 0.467052I
a = −0.49611 + 1.66574I
b = 0.51823 + 1.94433I
−5.28059 + 6.34553I 0
u = −1.175440 − 0.467052I
a = −0.49611 − 1.66574I
b = 0.51823 − 1.94433I
−5.28059 − 6.34553I 0
u = 1.155270 + 0.526476I
a = 1.25110 + 1.63810I
b = 0.59528 + 3.31320I
1.27066 − 5.68261I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.155270 − 0.526476I
a = 1.25110 − 1.63810I
b = 0.59528 − 3.31320I
1.27066 + 5.68261I 0
u = −1.168040 + 0.507921I
a = 0.922596 − 0.067964I
b = 0.845713 − 0.551844I
−3.04347 + 7.48824I 0
u = −1.168040 − 0.507921I
a = 0.922596 + 0.067964I
b = 0.845713 + 0.551844I
−3.04347 − 7.48824I 0
u = −0.052039 + 0.722252I
a = 0.562731 + 0.651978I
b = 0.444609 − 0.874281I
−2.07776 − 1.97235I −0.72819 + 4.37507I
u = −0.052039 − 0.722252I
a = 0.562731 − 0.651978I
b = 0.444609 + 0.874281I
−2.07776 + 1.97235I −0.72819 − 4.37507I
u = 1.207880 + 0.410981I
a = −1.070520 + 0.052109I
b = −0.330465 − 0.774725I
−1.086150 − 0.034868I 0
u = 1.207880 − 0.410981I
a = −1.070520 − 0.052109I
b = −0.330465 + 0.774725I
−1.086150 + 0.034868I 0
u = −1.162360 + 0.529806I
a = −1.79136 + 0.10388I
b = −1.64200 + 0.99199I
3.15047 + 8.52143I 0
u = −1.162360 − 0.529806I
a = −1.79136 − 0.10388I
b = −1.64200 − 0.99199I
3.15047 − 8.52143I 0
u = 1.168930 + 0.529133I
a = −1.57379 − 2.15421I
b = −0.32158 − 3.94599I
0.69066 − 11.21750I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.168930 − 0.529133I
a = −1.57379 + 2.15421I
b = −0.32158 + 3.94599I
0.69066 + 11.21750I 0
u = −1.198680 + 0.484977I
a = −0.36067 − 1.77130I
b = −1.37224 − 1.41960I
−0.56388 + 8.80154I 0
u = −1.198680 − 0.484977I
a = −0.36067 + 1.77130I
b = −1.37224 + 1.41960I
−0.56388 − 8.80154I 0
u = 1.177620 + 0.535604I
a = 1.54399 + 2.51779I
b = −0.02257 + 4.06707I
7.3556 − 15.5480I 0
u = 1.177620 − 0.535604I
a = 1.54399 − 2.51779I
b = −0.02257 − 4.06707I
7.3556 + 15.5480I 0
u = 0.051946 + 0.647928I
a = −1.20181 − 0.95038I
b = 0.032509 + 0.883301I
0.779065 + 0.993473I 4.68420 + 0.71894I
u = 0.051946 − 0.647928I
a = −1.20181 + 0.95038I
b = 0.032509 − 0.883301I
0.779065 − 0.993473I 4.68420 − 0.71894I
u = −0.543478 + 0.231554I
a = −2.18956 + 0.34629I
b = −1.118450 + 0.604202I
1.049580 − 0.014357I 9.39150 − 0.35736I
u = −0.543478 − 0.231554I
a = −2.18956 − 0.34629I
b = −1.118450 − 0.604202I
1.049580 + 0.014357I 9.39150 + 0.35736I
u = −0.490124
a = −2.52204
b = −1.18809
1.02225 10.6740
12
II. I
u
2
= h−u
6
+ 2u
4
+ u
3
− u
2
+ b − u − 1, −u
7
− u
6
+ 2u
5
+ 2u
4
− u
3
− u
2
+
a − u − 1, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
u
7
+ u
6
− 2u
5
− 2u
4
+ u
3
+ u
2
+ u + 1
u
6
− 2u
4
− u
3
+ u
2
+ u + 1
a
4
=
1
u
2
a
11
=
u
7
+ u
6
− 2u
5
− 2u
4
+ u
3
+ u
2
+ u + 1
u
6
− 2u
4
− u
3
+ u
2
+ u + 1
a
1
=
−u
2
+ 1
−u
4
a
7
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
5
=
u
u
a
8
=
u
8
− 3u
6
+ 3u
4
− 1
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u
3
− 1
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
− u
7
+ 3u
6
+ 2u
5
− 3u
4
− 2u
3
+ 1
a
9
=
u
8
+ u
7
− 2u
6
− 2u
5
+ u
4
+ u
3
+ u
2
+ u
u
8
+ u
7
− 2u
6
− 2u
5
+ u
4
+ u
3
+ u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
8
− 6u
7
+ u
6
+ 12u
5
+ 5u
4
− 10u
3
− 7u
2
− 7u + 6
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
2
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
3
, c
10
u
9
c
4
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
5
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
6
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
, c
9
(u + 1)
9
c
11
(u − 1)
9
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
5
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
10
y
9
c
4
, c
7
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
6
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
8
, c
9
, c
11
(y −1)
9
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = 0.147032 + 1.012940I
b = 0.848670 + 0.225310I
3.42837 + 2.09337I 10.43453 − 4.18932I
u = −0.772920 − 0.510351I
a = 0.147032 − 1.012940I
b = 0.848670 − 0.225310I
3.42837 − 2.09337I 10.43453 + 4.18932I
u = 0.825933
a = 1.95176
b = 1.33142
0.446489 −4.72420
u = 1.173910 + 0.391555I
a = −0.679689 − 0.626017I
b = −0.25695 − 1.39155I
−2.72642 − 1.33617I 0.549708 + 1.017936I
u = 1.173910 − 0.391555I
a = −0.679689 + 0.626017I
b = −0.25695 + 1.39155I
−2.72642 + 1.33617I 0.549708 − 1.017936I
u = −0.141484 + 0.739668I
a = 0.541407 − 0.753907I
b = −0.443165 + 0.284059I
1.02799 − 2.45442I 6.31821 + 2.62939I
u = −0.141484 − 0.739668I
a = 0.541407 + 0.753907I
b = −0.443165 − 0.284059I
1.02799 + 2.45442I 6.31821 − 2.62939I
u = −1.172470 + 0.500383I
a = −0.484630 − 0.655708I
b = −1.314260 − 0.168567I
−1.95319 + 7.08493I 3.05967 − 5.11095I
u = −1.172470 − 0.500383I
a = −0.484630 + 0.655708I
b = −1.314260 + 0.168567I
−1.95319 − 7.08493I 3.05967 + 5.11095I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
80
+ 42u
79
+ ··· + 9u + 1)
c
2
(u
9
+ u
8
+ ··· − u − 1)(u
80
+ 2u
79
+ ··· + u − 1)
c
3
, c
10
u
9
(u
80
+ u
79
+ ··· − 768u
2
+ 512)
c
4
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
80
− 6u
79
+ ··· + 1829u + 145)
c
5
(u
9
− u
8
+ ··· − u + 1)(u
80
+ 2u
79
+ ··· + u − 1)
c
6
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
80
+ 6u
79
+ ··· − 577u + 53)
c
7
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
80
− 6u
79
+ ··· + 1829u + 145)
c
8
, c
9
((u + 1)
9
)(u
80
+ 10u
79
+ ··· − 7u − 1)
c
11
((u − 1)
9
)(u
80
+ 10u
79
+ ··· − 7u − 1)
c
12
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
80
+ 6u
79
+ ··· − 577u + 53)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
80
− 6y
79
+ ··· − 41y + 1)
c
2
, c
5
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
80
− 42y
79
+ ··· − 9y + 1)
c
3
, c
10
y
9
(y
80
− 57y
79
+ ··· − 786432y + 262144)
c
4
, c
7
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
80
+ 66y
79
+ ··· − 1478221y + 21025)
c
6
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
80
+ 54y
79
+ ··· − 584997y + 2809)
c
8
, c
9
, c
11
((y −1)
9
)(y
80
− 82y
79
+ ··· − 5y + 1)
18
