12n
0086
(K12n
0086
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 9 3 11 6 12 8 1 10
Solving Sequence
3,6 7,11
8 9 5 2 1 4 10 12
c
6
c
7
c
8
c
5
c
2
c
1
c
4
c
10
c
12
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.19780 × 10
241
u
65
+ 8.81073 × 10
241
u
64
+ ··· + 3.02569 × 10
240
b + 9.53394 × 10
243
,
8.96655 × 10
240
u
65
+ 6.61765 × 10
241
u
64
+ ··· + 3.02569 × 10
240
a + 6.94724 × 10
243
,
u
66
+ 8u
65
+ ··· − 7168u + 512i
I
u
2
= hu
5
− 2u
3
− u
2
+ b + 2u + 1, u
5
+ 2u
4
− u
3
− 3u
2
+ a + 2, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
v
1
= ha, 1742v
8
− 24207v
7
− 17107v
6
+ 21829v
5
+ 12682v
4
− 26226v
3
− 24997v
2
+ 683b − 5624v + 648,
v
9
− 13v
8
− 22v
7
+ 15v
5
− 5v
4
− 25v
3
− 20v
2
− 7v −1i
* 3 irreducible components of dim
C
= 0, with total 81 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
= h1.20 × 10
241
u
65
+ 8.81 × 10
241
u
64
+ · · · + 3.03 × 10
240
b + 9.53 ×
10
243
, 8.97 × 10
240
u
65
+ 6.62 × 10
241
u
64
+ · · · + 3.03 × 10
240
a + 6.95 ×
10
243
, u
66
+ 8u
65
+ · · · − 7168u + 512i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
11
=
−2.96348u
65
− 21.8716u
64
+ ··· + 37209.0u − 2296.09
−3.95876u
65
− 29.1198u
64
+ ··· + 48993.3u − 3151.00
a
8
=
−0.189192u
65
− 1.42917u
64
+ ··· + 3725.71u − 278.930
−3.64017u
65
− 26.9641u
64
+ ··· + 48969.5u − 3124.72
a
9
=
−3.82936u
65
− 28.3933u
64
+ ··· + 52695.2u − 3403.65
−3.64017u
65
− 26.9641u
64
+ ··· + 48969.5u − 3124.72
a
5
=
−0.597599u
65
− 4.38854u
64
+ ··· + 7145.50u − 452.205
−1.29177u
65
− 9.48251u
64
+ ··· + 15607.1u − 1005.22
a
2
=
−0.694167u
65
− 5.09397u
64
+ ··· + 8461.64u − 553.013
−1.29177u
65
− 9.48251u
64
+ ··· + 15607.1u − 1005.22
a
1
=
−0.694167u
65
− 5.09397u
64
+ ··· + 8461.64u − 553.013
−0.988463u
65
− 7.25680u
64
+ ··· + 11959.0u − 770.026
a
4
=
u
u
a
10
=
−3.85958u
65
− 28.4537u
64
+ ··· + 47856.5u − 2957.77
−7.03239u
65
− 51.8312u
64
+ ··· + 89324.7u − 5730.22
a
12
=
−4.70834u
65
− 34.8004u
64
+ ··· + 60886.6u − 3811.37
−7.53902u
65
− 55.6488u
64
+ ··· + 97468.3u − 6242.36
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12.0986u
65
+ 88.8600u
64
+ ··· − 142679.u + 8879.59
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ 21u
65
+ ··· + 31524u + 1
c
2
, c
4
u
66
− 11u
65
+ ··· + 184u − 1
c
3
, c
6
u
66
+ 8u
65
+ ··· − 7168u + 512
c
5
, c
8
u
66
+ 3u
65
+ ··· − 2u − 1
c
7
, c
10
u
66
− 2u
65
+ ··· + 192u + 64
c
9
, c
12
u
66
− 8u
65
+ ··· − 11u + 1
c
11
u
66
+ 28u
65
+ ··· − 143u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
+ 59y
65
+ ··· − 992297680y + 1
c
2
, c
4
y
66
− 21y
65
+ ··· − 31524y + 1
c
3
, c
6
y
66
− 60y
65
+ ··· − 76021760y + 262144
c
5
, c
8
y
66
+ 15y
65
+ ··· − 20y + 1
c
7
, c
10
y
66
+ 42y
65
+ ··· + 77824y + 4096
c
9
, c
12
y
66
− 28y
65
+ ··· + 143y + 1
c
11
y
66
+ 28y
65
+ ··· − 12229y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.896621 + 0.222919I
a = −0.68390 + 2.68834I
b = −0.03058 − 1.93558I
−4.31795 + 0.78820I 0
u = −0.896621 − 0.222919I
a = −0.68390 − 2.68834I
b = −0.03058 + 1.93558I
−4.31795 − 0.78820I 0
u = −0.161444 + 0.873142I
a = 0.24159 − 2.29188I
b = 0.96672 − 2.19128I
−3.21013 + 1.26950I 0
u = −0.161444 − 0.873142I
a = 0.24159 + 2.29188I
b = 0.96672 + 2.19128I
−3.21013 − 1.26950I 0
u = 0.734614 + 0.498569I
a = −0.296201 + 0.045995I
b = 0.216817 + 0.815085I
1.31523 + 1.27199I 0
u = 0.734614 − 0.498569I
a = −0.296201 − 0.045995I
b = 0.216817 − 0.815085I
1.31523 − 1.27199I 0
u = 0.015880 + 1.156380I
a = −1.200970 + 0.600425I
b = −0.773578 + 1.087150I
−2.23471 + 2.98196I 0
u = 0.015880 − 1.156380I
a = −1.200970 − 0.600425I
b = −0.773578 − 1.087150I
−2.23471 − 2.98196I 0
u = 0.043693 + 0.829853I
a = 1.154180 + 0.810143I
b = 0.493220 − 0.823559I
2.07274 − 4.10478I 0
u = 0.043693 − 0.829853I
a = 1.154180 − 0.810143I
b = 0.493220 + 0.823559I
2.07274 + 4.10478I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.010290 + 0.635704I
a = 0.0712092 − 0.0097906I
b = 0.045899 − 0.458605I
−1.20228 − 5.48361I 0
u = −1.010290 − 0.635704I
a = 0.0712092 + 0.0097906I
b = 0.045899 + 0.458605I
−1.20228 + 5.48361I 0
u = −0.178380 + 0.763029I
a = −1.123200 − 0.224763I
b = −0.584767 + 0.854259I
2.74552 + 1.51786I 0
u = −0.178380 − 0.763029I
a = −1.123200 + 0.224763I
b = −0.584767 − 0.854259I
2.74552 − 1.51786I 0
u = 0.710476 + 0.000507I
a = −0.047677 + 0.256353I
b = −0.191197 − 0.906715I
1.17931 − 1.63015I 0. + 3.30141I
u = 0.710476 − 0.000507I
a = −0.047677 − 0.256353I
b = −0.191197 + 0.906715I
1.17931 + 1.63015I 0. − 3.30141I
u = −0.438003 + 0.525280I
a = −1.44839 − 0.54246I
b = −0.083240 − 0.461268I
−1.91057 + 0.79816I −4.00000 + 0.I
u = −0.438003 − 0.525280I
a = −1.44839 + 0.54246I
b = −0.083240 + 0.461268I
−1.91057 − 0.79816I −4.00000 + 0.I
u = −0.681040 + 0.017244I
a = 0.147299 − 0.561967I
b = −0.847666 − 0.591726I
−1.43375 − 2.91518I 0. + 4.85019I
u = −0.681040 − 0.017244I
a = 0.147299 + 0.561967I
b = −0.847666 + 0.591726I
−1.43375 + 2.91518I 0. − 4.85019I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.006104 + 0.635645I
a = 1.91287 − 1.80281I
b = 0.052848 − 0.610826I
−1.82059 − 0.01526I −7.87182 + 0.48568I
u = −0.006104 − 0.635645I
a = 1.91287 + 1.80281I
b = 0.052848 + 0.610826I
−1.82059 + 0.01526I −7.87182 − 0.48568I
u = −0.619648 + 0.008490I
a = −0.511507 − 0.814092I
b = 1.051820 − 0.516985I
−5.23148 − 1.44469I −2.19147 + 1.36304I
u = −0.619648 − 0.008490I
a = −0.511507 + 0.814092I
b = 1.051820 + 0.516985I
−5.23148 + 1.44469I −2.19147 − 1.36304I
u = −0.598433 + 0.144408I
a = −0.338653 + 0.326080I
b = 0.823727 + 0.764068I
−4.86194 − 7.45999I −0.96246 + 11.41011I
u = −0.598433 − 0.144408I
a = −0.338653 − 0.326080I
b = 0.823727 − 0.764068I
−4.86194 + 7.45999I −0.96246 − 11.41011I
u = 0.557706 + 0.143081I
a = 2.02290 + 5.39960I
b = 0.061106 − 0.673706I
0.81136 + 2.64313I 13.7570 − 9.2546I
u = 0.557706 − 0.143081I
a = 2.02290 − 5.39960I
b = 0.061106 + 0.673706I
0.81136 − 2.64313I 13.7570 + 9.2546I
u = 1.47897 + 0.04915I
a = 0.36193 − 1.79756I
b = −1.17938 + 2.79473I
2.17496 + 0.19887I 0
u = 1.47897 − 0.04915I
a = 0.36193 + 1.79756I
b = −1.17938 − 2.79473I
2.17496 − 0.19887I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49869 + 0.12364I
a = 0.028754 + 0.149012I
b = −1.196520 − 0.662560I
3.57906 + 2.47635I 0
u = 1.49869 − 0.12364I
a = 0.028754 − 0.149012I
b = −1.196520 + 0.662560I
3.57906 − 2.47635I 0
u = −1.51285 + 0.03928I
a = 0.346340 − 1.327240I
b = −1.21560 + 1.60059I
7.72304 − 2.79945I 0
u = −1.51285 − 0.03928I
a = 0.346340 + 1.327240I
b = −1.21560 − 1.60059I
7.72304 + 2.79945I 0
u = −1.47811 + 0.34080I
a = −0.1005600 − 0.0917447I
b = −0.972026 + 0.012478I
3.17239 − 3.89822I 0
u = −1.47811 − 0.34080I
a = −0.1005600 + 0.0917447I
b = −0.972026 − 0.012478I
3.17239 + 3.89822I 0
u = −1.46366 + 0.47734I
a = −0.26778 + 1.74931I
b = −1.79456 − 2.53218I
1.18870 − 6.56344I 0
u = −1.46366 − 0.47734I
a = −0.26778 − 1.74931I
b = −1.79456 + 2.53218I
1.18870 + 6.56344I 0
u = 1.47312 + 0.46657I
a = 0.767438 + 1.139500I
b = −0.63144 − 1.94704I
6.78475 + 9.23321I 0
u = 1.47312 − 0.46657I
a = 0.767438 − 1.139500I
b = −0.63144 + 1.94704I
6.78475 − 9.23321I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.45244 + 1.51129I
a = 0.073063 + 0.503097I
b = 0.72561 + 2.13556I
2.19847 + 2.32521I 0
u = 0.45244 − 1.51129I
a = 0.073063 − 0.503097I
b = 0.72561 − 2.13556I
2.19847 − 2.32521I 0
u = 1.60960 + 0.20036I
a = −0.031037 + 0.149711I
b = 1.349420 − 0.252092I
4.03833 + 2.66127I 0
u = 1.60960 − 0.20036I
a = −0.031037 − 0.149711I
b = 1.349420 + 0.252092I
4.03833 − 2.66127I 0
u = −1.62095 + 0.14520I
a = −0.146836 − 1.371110I
b = 1.32921 + 1.94937I
9.29382 − 3.78649I 0
u = −1.62095 − 0.14520I
a = −0.146836 + 1.371110I
b = 1.32921 − 1.94937I
9.29382 + 3.78649I 0
u = −1.52811 + 0.57582I
a = 0.0964491 + 0.0666214I
b = 0.958300 − 0.287281I
2.66554 − 9.42263I 0
u = −1.52811 − 0.57582I
a = 0.0964491 − 0.0666214I
b = 0.958300 + 0.287281I
2.66554 + 9.42263I 0
u = 1.61436 + 0.32070I
a = −0.579677 − 1.239460I
b = 0.64699 + 2.29322I
8.98485 + 3.05406I 0
u = 1.61436 − 0.32070I
a = −0.579677 + 1.239460I
b = 0.64699 − 2.29322I
8.98485 − 3.05406I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.17931 + 1.15054I
a = −0.565320 + 0.704718I
b = −1.72394 − 0.50610I
−1.42259 − 0.46359I 0
u = −1.17931 − 1.15054I
a = −0.565320 − 0.704718I
b = −1.72394 + 0.50610I
−1.42259 + 0.46359I 0
u = −1.56100 + 0.72853I
a = 0.337392 − 0.874324I
b = 1.67630 + 1.29876I
−1.87995 + 4.31692I 0
u = −1.56100 − 0.72853I
a = 0.337392 + 0.874324I
b = 1.67630 − 1.29876I
−1.87995 − 4.31692I 0
u = 0.11530 + 1.78369I
a = −0.289375 − 0.485587I
b = −0.66341 − 2.67095I
1.02644 + 7.74901I 0
u = 0.11530 − 1.78369I
a = −0.289375 + 0.485587I
b = −0.66341 + 2.67095I
1.02644 − 7.74901I 0
u = −1.65910 + 0.67262I
a = 0.481831 − 1.322710I
b = 1.33635 + 2.65341I
8.24876 − 10.14770I 0
u = −1.65910 − 0.67262I
a = 0.481831 + 1.322710I
b = 1.33635 − 2.65341I
8.24876 + 10.14770I 0
u = −1.60879 + 0.80973I
a = −0.657052 + 1.243910I
b = −1.24884 − 2.74717I
5.9981 − 16.5072I 0
u = −1.60879 − 0.80973I
a = −0.657052 − 1.243910I
b = −1.24884 + 2.74717I
5.9981 + 16.5072I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.104054
a = −86.7705
b = 0.408951
−2.82917 365.350
u = 1.89844 + 0.28442I
a = 0.119565 + 1.273780I
b = 0.64384 − 3.14134I
9.83371 + 2.67210I 0
u = 1.89844 − 0.28442I
a = 0.119565 − 1.273780I
b = 0.64384 + 3.14134I
9.83371 − 2.67210I 0
u = 0.0750607
a = 9.20491
b = −0.556076
−1.20362 −8.91660
u = 1.90900 + 0.52880I
a = −0.341894 − 1.190340I
b = −0.66785 + 3.28864I
8.19227 + 8.99833I 0
u = 1.90900 − 0.52880I
a = −0.341894 + 1.190340I
b = −0.66785 − 3.28864I
8.19227 − 8.99833I 0
11
II. I
u
2
=
hu
5
−2u
3
−u
2
+b+2u+1, u
5
+2u
4
−u
3
−3u
2
+a+2, u
6
+u
5
−u
4
−2u
3
+u+1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
11
=
−u
5
− 2u
4
+ u
3
+ 3u
2
− 2
−u
5
+ 2u
3
+ u
2
− 2u − 1
a
8
=
1
−u
2
a
9
=
−u
2
+ 1
−u
2
a
5
=
u
4
− u
2
+ 1
u
4
a
2
=
u
2
− 1
u
4
a
1
=
u
2
− 1
u
2
a
4
=
u
u
a
10
=
−u
5
− 2u
4
+ u
3
+ 3u
2
− 2
−u
5
+ 2u
3
+ u
2
− 2u − 1
a
12
=
−u
5
− 2u
4
+ u
3
+ 4u
2
− 3
−u
5
+ 2u
3
+ 2u
2
− 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
5
− u
4
− 4u
3
− 3u
2
+ 8u − 8
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
6
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
7
, c
10
u
6
c
9
, c
11
(u − 1)
6
c
12
(u + 1)
6
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
8
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
6
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
7
, c
10
y
6
c
9
, c
11
, c
12
(y −1)
6
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 0.344968 − 0.764807I
b = −0.769407 + 0.497010I
0.245672 + 0.924305I −5.68949 − 0.25702I
u = 1.002190 − 0.295542I
a = 0.344968 + 0.764807I
b = −0.769407 − 0.497010I
0.245672 − 0.924305I −5.68949 + 0.25702I
u = −0.428243 + 0.664531I
a = −1.68613 − 1.92635I
b = 0.66103 − 1.45708I
−3.53554 + 0.92430I −12.60470 + 5.55069I
u = −0.428243 − 0.664531I
a = −1.68613 + 1.92635I
b = 0.66103 + 1.45708I
−3.53554 − 0.92430I −12.60470 − 5.55069I
u = −1.073950 + 0.558752I
a = −0.158836 + 0.437639I
b = −0.391622 − 0.558752I
−1.64493 − 5.69302I −11.7058 + 8.3306I
u = −1.073950 − 0.558752I
a = −0.158836 − 0.437639I
b = −0.391622 + 0.558752I
−1.64493 + 5.69302I −11.7058 − 8.3306I
15
III. I
v
1
= ha, 1742v
8
− 24207v
7
+ · · · + 683b + 648, v
9
− 13v
8
+ · · · − 7v − 1i
(i) Arc colorings
a
3
=
v
0
a
6
=
1
0
a
7
=
1
0
a
11
=
0
−2.55051v
8
+ 35.4422v
7
+ ··· + 8.23426v − 0.948755
a
8
=
1
0.0146413v
8
− 2.49048v
7
+ ··· + 26.1640v + 6.53587
a
9
=
0.0146413v
8
− 2.49048v
7
+ ··· + 26.1640v + 7.53587
0.0146413v
8
− 2.49048v
7
+ ··· + 26.1640v + 6.53587
a
5
=
1.01464v
8
− 15.4905v
7
+ ··· + 6.16398v + 0.535871
v
8
− 13v
7
− 22v
6
+ 15v
4
− 5v
3
− 25v
2
− 20v − 7
a
2
=
−1.01464v
8
+ 15.4905v
7
+ ··· − 5.16398v − 0.535871
−v
8
+ 13v
7
+ 22v
6
− 15v
4
+ 5v
3
+ 25v
2
+ 20v + 7
a
1
=
−1.01464v
8
+ 15.4905v
7
+ ··· − 6.16398v − 0.535871
−v
8
+ 13v
7
+ 22v
6
− 15v
4
+ 5v
3
+ 25v
2
+ 20v + 7
a
4
=
v
0
a
10
=
−2.55051v
8
+ 35.4422v
7
+ ··· + 8.23426v − 0.948755
−3.04539v
8
+ 45.0205v
7
+ ··· − 17.1083v − 5.46120
a
12
=
0.535871v
8
− 5.95168v
7
+ ··· − 7.39824v + 1.41288
−11.9649v
8
+ 161.823v
7
+ ··· + 128.794v + 26.4861
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
1777
683
v
8
−
26404
683
v
7
+
7013
683
v
6
+
29374
683
v
5
−
14769
683
v
4
−
23374
683
v
3
−
329
683
v
2
+
9111
683
v −
4901
683
16
(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
− 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
17
(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
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
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.920144 + 0.598375I
a = 0
b = 0.140343 + 0.966856I
0.13850 − 2.09337I −4.31028 + 3.82038I
v = 0.920144 − 0.598375I
a = 0
b = 0.140343 − 0.966856I
0.13850 + 2.09337I −4.31028 − 3.82038I
v = −0.590648 + 0.449402I
a = 0
b = 0.628449 + 0.875112I
−2.26187 − 2.45442I −6.95900 + 1.69416I
v = −0.590648 − 0.449402I
a = 0
b = 0.628449 − 0.875112I
−2.26187 + 2.45442I −6.95900 − 1.69416I
v = −0.719281 + 0.119276I
a = 0
b = −0.796005 + 0.733148I
−6.01628 − 1.33617I −13.56769 + 0.26615I
v = −0.719281 − 0.119276I
a = 0
b = −0.796005 − 0.733148I
−6.01628 + 1.33617I −13.56769 − 0.26615I
v = −0.365868 + 0.247975I
a = 0
b = −0.728966 − 0.986295I
−5.24306 − 7.08493I −11.54551 + 1.34000I
v = −0.365868 − 0.247975I
a = 0
b = −0.728966 + 0.986295I
−5.24306 + 7.08493I −11.54551 − 1.34000I
v = 14.5113
a = 0
b = 0.512358
−2.84338 −223.240
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
66
+ 21u
65
+ ··· + 31524u + 1)
c
2
((u − 1)
9
)(u
6
+ u
5
+ ··· + u + 1)(u
66
− 11u
65
+ ··· + 184u − 1)
c
3
u
9
(u
6
− u
5
+ ··· − u + 1)(u
66
+ 8u
65
+ ··· − 7168u + 512)
c
4
((u + 1)
9
)(u
6
− u
5
+ ··· − u + 1)(u
66
− 11u
65
+ ··· + 184u − 1)
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
66
+ 3u
65
+ ··· − 2u − 1)
c
6
u
9
(u
6
+ u
5
+ ··· + u + 1)(u
66
+ 8u
65
+ ··· − 7168u + 512)
c
7
u
6
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
66
− 2u
65
+ ··· + 192u + 64)
c
8
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
66
+ 3u
65
+ ··· − 2u − 1)
c
9
(u − 1)
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
66
− 8u
65
+ ··· − 11u + 1)
c
10
u
6
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
66
− 2u
65
+ ··· + 192u + 64)
c
11
(u − 1)
6
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
66
+ 28u
65
+ ··· − 143u + 1)
c
12
(u + 1)
6
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
66
− 8u
65
+ ··· − 11u + 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
66
+ 59y
65
+ ··· − 992297680y + 1)
c
2
, c
4
(y − 1)
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
66
− 21y
65
+ ··· − 31524y + 1)
c
3
, c
6
y
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
66
− 60y
65
+ ··· − 76021760y + 262144)
c
5
, c
8
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
66
+ 15y
65
+ ··· − 20y + 1)
c
7
, c
10
y
6
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
66
+ 42y
65
+ ··· + 77824y + 4096)
c
9
, c
12
(y − 1)
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
66
− 28y
65
+ ··· + 143y + 1)
c
11
(y − 1)
6
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
66
+ 28y
65
+ ··· − 12229y + 1)
21
