12a
0142
(K12a
0142
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 11 12 4 8 1 7 6
Solving Sequence
6,11
7 12 8
1,3
2 10 5 4 9
c
6
c
11
c
7
c
12
c
1
c
10
c
5
c
4
c
9
c
2
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
96
− u
95
+ ··· − u
2
+ b, −2u
96
− 2u
95
+ ··· + a − 3, u
97
+ 2u
96
+ ··· + u + 1i
I
u
2
= hb + 1, u
3
+ a − 2u, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 102 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−u
96
−u
95
+· · ·−u
2
+b, −2u
96
−2u
95
+· · ·+a−3, u
97
+2u
96
+· · ·+u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
3
− 2u
−u
3
+ u
a
3
=
2u
96
+ 2u
95
+ ··· − 2u
2
+ 3
u
96
+ u
95
+ ··· + 6u
3
+ u
2
a
2
=
u
96
+ u
95
+ ··· − u
2
+ 2
u
96
+ u
95
+ ··· + 2u
2
+ u
a
10
=
−u
7
+ 4u
5
− 4u
3
u
7
− 3u
5
+ 2u
3
+ u
a
5
=
−u
14
+ 7u
12
− 18u
10
+ 19u
8
− 4u
6
− 4u
4
+ 1
u
14
− 6u
12
+ 13u
10
− 10u
8
− 2u
6
+ 4u
4
+ u
2
a
4
=
u
83
− 38u
81
+ ··· − 9u
3
+ 2
u
96
+ u
95
+ ··· + 3u
2
+ u
a
9
=
−u
13
+ 6u
11
− 13u
9
+ 10u
7
+ 2u
5
− 4u
3
− u
−u
15
+ 7u
13
− 18u
11
+ 19u
9
− 4u
7
− 4u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6u
96
+ 4u
95
+ ··· + 5u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
97
+ 52u
96
+ ··· + 7u + 1
c
2
, c
4
u
97
− 6u
96
+ ··· − 5u + 1
c
3
, c
8
u
97
− u
96
+ ··· + 32u + 32
c
5
u
97
− 2u
96
+ ··· − 939u + 137
c
6
, c
7
, c
11
u
97
+ 2u
96
+ ··· + u + 1
c
9
u
97
− 33u
96
+ ··· − 22016u + 1024
c
10
u
97
+ 20u
96
+ ··· + 152213u + 6497
c
12
u
97
− 6u
96
+ ··· − 63u + 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
97
− 8y
96
+ ··· + 23y −1
c
2
, c
4
y
97
− 52y
96
+ ··· + 7y −1
c
3
, c
8
y
97
+ 33y
96
+ ··· − 22016y −1024
c
5
y
97
+ 86y
95
+ ··· + 940357y −18769
c
6
, c
7
, c
11
y
97
− 88y
96
+ ··· + 5y −1
c
9
y
97
+ 53y
96
+ ··· + 30015488y −1048576
c
10
y
97
+ 36y
96
+ ··· + 514538009y −42211009
c
12
y
97
− 8y
96
+ ··· + 569y −25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.943941 + 0.121484I
a = −0.496423 − 0.405418I
b = 0.061982 − 0.953000I
2.92060 − 2.48348I 0
u = 0.943941 − 0.121484I
a = −0.496423 + 0.405418I
b = 0.061982 + 0.953000I
2.92060 + 2.48348I 0
u = 1.111500 + 0.195710I
a = −0.991198 + 0.480915I
b = 0.157594 + 0.050205I
0.42510 − 4.54620I 0
u = 1.111500 − 0.195710I
a = −0.991198 − 0.480915I
b = 0.157594 − 0.050205I
0.42510 + 4.54620I 0
u = −1.132700 + 0.052850I
a = 0.910466 + 0.414617I
b = 0.450519 + 0.261516I
−1.77925 + 0.16252I 0
u = −1.132700 − 0.052850I
a = 0.910466 − 0.414617I
b = 0.450519 − 0.261516I
−1.77925 − 0.16252I 0
u = 1.134230 + 0.229902I
a = 0.951922 − 0.710835I
b = −0.076764 − 0.808674I
−2.13303 − 9.58468I 0
u = 1.134230 − 0.229902I
a = 0.951922 + 0.710835I
b = −0.076764 + 0.808674I
−2.13303 + 9.58468I 0
u = −1.145920 + 0.167609I
a = −0.559216 − 1.229480I
b = −0.169401 − 1.056630I
−3.77103 + 3.82064I 0
u = −1.145920 − 0.167609I
a = −0.559216 + 1.229480I
b = −0.169401 + 1.056630I
−3.77103 − 3.82064I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.168790 + 0.130280I
a = 0.892219 − 0.513776I
b = −1.193000 + 0.490171I
−4.25351 − 1.40778I 0
u = 1.168790 − 0.130280I
a = 0.892219 + 0.513776I
b = −1.193000 − 0.490171I
−4.25351 + 1.40778I 0
u = 0.312759 + 0.712439I
a = 2.39656 + 3.11419I
b = −2.56647 − 1.59551I
−1.81149 − 13.02420I −6.49881 + 10.34514I
u = 0.312759 − 0.712439I
a = 2.39656 − 3.11419I
b = −2.56647 + 1.59551I
−1.81149 + 13.02420I −6.49881 − 10.34514I
u = 0.300843 + 0.702322I
a = −1.91199 − 2.03390I
b = 1.65378 + 0.88080I
1.08712 − 7.85100I −3.11991 + 7.31455I
u = 0.300843 − 0.702322I
a = −1.91199 + 2.03390I
b = 1.65378 − 0.88080I
1.08712 + 7.85100I −3.11991 − 7.31455I
u = −0.308505 + 0.689688I
a = −3.08907 + 2.22676I
b = 2.80515 − 0.95593I
−3.16701 + 6.77469I −8.01279 − 6.91414I
u = −0.308505 − 0.689688I
a = −3.08907 − 2.22676I
b = 2.80515 + 0.95593I
−3.16701 − 6.77469I −8.01279 + 6.91414I
u = 0.623987 + 0.420887I
a = 2.44137 + 1.67780I
b = −1.90511 + 0.66513I
−3.01492 + 9.05165I −8.99353 − 5.05015I
u = 0.623987 − 0.420887I
a = 2.44137 − 1.67780I
b = −1.90511 − 0.66513I
−3.01492 − 9.05165I −8.99353 + 5.05015I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.353257 + 0.664610I
a = −2.80675 − 0.31529I
b = 1.59380 + 1.22211I
−3.61011 − 0.93729I −8.61161 + 0.95257I
u = −0.353257 − 0.664610I
a = −2.80675 + 0.31529I
b = 1.59380 − 1.22211I
−3.61011 + 0.93729I −8.61161 − 0.95257I
u = 0.729778 + 0.164872I
a = −0.173384 + 0.743443I
b = −0.170411 + 0.615315I
2.85417 + 2.45539I −3.14691 − 2.99420I
u = 0.729778 − 0.164872I
a = −0.173384 − 0.743443I
b = −0.170411 − 0.615315I
2.85417 − 2.45539I −3.14691 + 2.99420I
u = 0.311458 + 0.677389I
a = 3.11096 + 0.73852I
b = −2.00323 + 0.70708I
−3.56160 − 4.04042I −8.16281 + 6.14210I
u = 0.311458 − 0.677389I
a = 3.11096 − 0.73852I
b = −2.00323 − 0.70708I
−3.56160 + 4.04042I −8.16281 − 6.14210I
u = 0.234210 + 0.696927I
a = 0.505572 + 0.362097I
b = −0.947702 − 0.309326I
4.69343 − 5.97822I −0.22935 + 7.86187I
u = 0.234210 − 0.696927I
a = 0.505572 − 0.362097I
b = −0.947702 + 0.309326I
4.69343 + 5.97822I −0.22935 − 7.86187I
u = −0.302548 + 0.652337I
a = 1.69438 − 1.39167I
b = −1.276750 + 0.594963I
−0.47477 + 2.56834I −4.93539 − 3.16377I
u = −0.302548 − 0.652337I
a = 1.69438 + 1.39167I
b = −1.276750 − 0.594963I
−0.47477 − 2.56834I −4.93539 + 3.16377I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.607220 + 0.381444I
a = −1.51037 − 1.12452I
b = 1.240080 − 0.073557I
−0.15886 + 4.01632I −5.76175 − 1.99933I
u = 0.607220 − 0.381444I
a = −1.51037 + 1.12452I
b = 1.240080 + 0.073557I
−0.15886 − 4.01632I −5.76175 + 1.99933I
u = −0.520379 + 0.490382I
a = 0.35702 + 2.38031I
b = 1.09071 − 1.54215I
−4.31532 + 4.81391I −10.30909 − 7.09591I
u = −0.520379 − 0.490382I
a = 0.35702 − 2.38031I
b = 1.09071 + 1.54215I
−4.31532 − 4.81391I −10.30909 + 7.09591I
u = 0.198968 + 0.686527I
a = −0.629727 − 1.247650I
b = 0.923922 + 0.937313I
5.13223 − 0.90715I 1.37210 + 1.29920I
u = 0.198968 − 0.686527I
a = −0.629727 + 1.247650I
b = 0.923922 − 0.937313I
5.13223 + 0.90715I 1.37210 − 1.29920I
u = −1.278380 + 0.233147I
a = −0.144124 − 0.663246I
b = 0.813649 + 0.516215I
−3.08467 − 2.82936I 0
u = −1.278380 − 0.233147I
a = −0.144124 + 0.663246I
b = 0.813649 − 0.516215I
−3.08467 + 2.82936I 0
u = −0.567881 + 0.398456I
a = −1.90800 + 2.59584I
b = 1.73968 − 0.00180I
−4.28231 − 2.99360I −10.93115 + 1.06271I
u = −0.567881 − 0.398456I
a = −1.90800 − 2.59584I
b = 1.73968 + 0.00180I
−4.28231 + 2.99360I −10.93115 − 1.06271I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.068167 + 0.685266I
a = 0.172272 + 1.080270I
b = 0.519079 + 0.016412I
1.06783 + 6.16150I −2.45385 − 4.75788I
u = 0.068167 − 0.685266I
a = 0.172272 − 1.080270I
b = 0.519079 − 0.016412I
1.06783 − 6.16150I −2.45385 + 4.75788I
u = −0.375160 + 0.561170I
a = 0.268255 + 0.166885I
b = 0.1081490 + 0.0316957I
−1.03389 + 1.75402I −2.33100 − 5.04441I
u = −0.375160 − 0.561170I
a = 0.268255 − 0.166885I
b = 0.1081490 − 0.0316957I
−1.03389 − 1.75402I −2.33100 + 5.04441I
u = 0.535382 + 0.408739I
a = 0.20878 + 2.11033I
b = −1.56265 − 1.13569I
−4.57857 + 0.32685I −11.21882 + 0.05170I
u = 0.535382 − 0.408739I
a = 0.20878 − 2.11033I
b = −1.56265 + 1.13569I
−4.57857 − 0.32685I −11.21882 − 0.05170I
u = 0.105616 + 0.661702I
a = −0.41822 − 1.42393I
b = 0.045797 + 0.498373I
3.40166 + 1.28266I 1.322307 − 0.278436I
u = 0.105616 − 0.661702I
a = −0.41822 + 1.42393I
b = 0.045797 − 0.498373I
3.40166 − 1.28266I 1.322307 + 0.278436I
u = −0.217493 + 0.618562I
a = −0.39149 − 1.70038I
b = 0.474158 + 1.007980I
0.49581 + 2.43913I −3.27691 − 6.47368I
u = −0.217493 − 0.618562I
a = −0.39149 + 1.70038I
b = 0.474158 − 1.007980I
0.49581 − 2.43913I −3.27691 + 6.47368I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.326350 + 0.232749I
a = 0.341783 + 0.812780I
b = 0.219491 − 0.801362I
−1.07006 + 1.93167I 0
u = −1.326350 − 0.232749I
a = 0.341783 − 0.812780I
b = 0.219491 + 0.801362I
−1.07006 − 1.93167I 0
u = −1.365960 + 0.054249I
a = −0.218600 − 0.681410I
b = 0.273700 + 0.033467I
−3.12013 − 1.90937I 0
u = −1.365960 − 0.054249I
a = −0.218600 + 0.681410I
b = 0.273700 − 0.033467I
−3.12013 + 1.90937I 0
u = −0.467096 + 0.419960I
a = 0.90569 − 1.35055I
b = −0.820519 + 0.455130I
−1.34526 + 0.92967I −7.49316 − 3.69890I
u = −0.467096 − 0.419960I
a = 0.90569 + 1.35055I
b = −0.820519 − 0.455130I
−1.34526 − 0.92967I −7.49316 + 3.69890I
u = 1.361400 + 0.206058I
a = 0.723724 + 0.180323I
b = −1.75482 + 0.80199I
−5.27906 − 1.90423I 0
u = 1.361400 − 0.206058I
a = 0.723724 − 0.180323I
b = −1.75482 − 0.80199I
−5.27906 + 1.90423I 0
u = −0.089375 + 0.596895I
a = 1.24278 + 1.08334I
b = −1.095750 + 0.055567I
−0.654118 − 0.881098I −4.24003 + 0.39048I
u = −0.089375 − 0.596895I
a = 1.24278 − 1.08334I
b = −1.095750 − 0.055567I
−0.654118 + 0.881098I −4.24003 − 0.39048I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.373470 + 0.266918I
a = 0.479744 + 0.763399I
b = 1.43196 − 0.71930I
0.14596 + 4.36125I 0
u = −1.373470 − 0.266918I
a = 0.479744 − 0.763399I
b = 1.43196 + 0.71930I
0.14596 − 4.36125I 0
u = −1.383370 + 0.219886I
a = −0.61670 − 1.52897I
b = −1.54081 + 0.33905I
−6.34678 + 3.87671I 0
u = −1.383370 − 0.219886I
a = −0.61670 + 1.52897I
b = −1.54081 − 0.33905I
−6.34678 − 3.87671I 0
u = 1.385740 + 0.240581I
a = −0.777813 + 0.354416I
b = 0.50379 − 1.82800I
−4.61803 − 5.57776I 0
u = 1.385740 − 0.240581I
a = −0.777813 − 0.354416I
b = 0.50379 + 1.82800I
−4.61803 + 5.57776I 0
u = −1.39052 + 0.27429I
a = −0.183283 − 0.415905I
b = −1.247440 − 0.130862I
−0.47363 + 9.50479I 0
u = −1.39052 − 0.27429I
a = −0.183283 + 0.415905I
b = −1.247440 + 0.130862I
−0.47363 − 9.50479I 0
u = 0.187132 + 0.543748I
a = 1.14094 + 2.10115I
b = −1.284210 − 0.281999I
−1.29274 − 1.03812I −1.55594 − 0.13944I
u = 0.187132 − 0.543748I
a = 1.14094 − 2.10115I
b = −1.284210 + 0.281999I
−1.29274 + 1.03812I −1.55594 + 0.13944I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43202 + 0.16090I
a = −0.448090 + 0.955833I
b = −1.47938 − 1.33154I
−7.33738 − 3.08646I 0
u = 1.43202 − 0.16090I
a = −0.448090 − 0.955833I
b = −1.47938 + 1.33154I
−7.33738 + 3.08646I 0
u = 1.41933 + 0.25558I
a = −0.012553 + 1.400220I
b = −2.01561 − 0.87988I
−5.98214 − 5.89543I 0
u = 1.41933 − 0.25558I
a = −0.012553 − 1.400220I
b = −2.01561 + 0.87988I
−5.98214 + 5.89543I 0
u = −1.43824 + 0.12743I
a = 0.263451 + 1.016370I
b = 1.92173 − 0.86852I
−6.50701 − 2.29026I 0
u = −1.43824 − 0.12743I
a = 0.263451 − 1.016370I
b = 1.92173 + 0.86852I
−6.50701 + 2.29026I 0
u = −1.43864 + 0.14807I
a = −1.32009 − 0.89318I
b = −1.84164 + 1.95956I
−10.76520 + 1.67811I 0
u = −1.43864 − 0.14807I
a = −1.32009 + 0.89318I
b = −1.84164 − 1.95956I
−10.76520 − 1.67811I 0
u = 1.43979 + 0.13950I
a = 0.44600 − 1.88435I
b = 2.30164 + 1.55417I
−10.55100 + 1.09910I 0
u = 1.43979 − 0.13950I
a = 0.44600 + 1.88435I
b = 2.30164 − 1.55417I
−10.55100 − 1.09910I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42444 + 0.26341I
a = 0.92067 − 1.92713I
b = −2.38606 − 0.59877I
−9.11571 + 7.47577I 0
u = −1.42444 − 0.26341I
a = 0.92067 + 1.92713I
b = −2.38606 + 0.59877I
−9.11571 − 7.47577I 0
u = −1.42255 + 0.27432I
a = 0.21487 + 1.75795I
b = 2.20011 − 1.19121I
−4.42341 + 11.40850I 0
u = −1.42255 − 0.27432I
a = 0.21487 − 1.75795I
b = 2.20011 + 1.19121I
−4.42341 − 11.40850I 0
u = 1.42451 + 0.26845I
a = 0.02143 − 2.31717I
b = 3.74912 + 1.01151I
−8.71124 − 10.26900I 0
u = 1.42451 − 0.26845I
a = 0.02143 + 2.31717I
b = 3.74912 − 1.01151I
−8.71124 + 10.26900I 0
u = 1.43397 + 0.21556I
a = 0.232723 − 0.151810I
b = 0.0590316 − 0.0776960I
−6.82096 − 4.62626I 0
u = 1.43397 − 0.21556I
a = 0.232723 + 0.151810I
b = 0.0590316 + 0.0776960I
−6.82096 + 4.62626I 0
u = −1.42861 + 0.27754I
a = −0.65259 − 2.39504I
b = −3.29315 + 1.85894I
−7.3834 + 16.6288I 0
u = −1.42861 − 0.27754I
a = −0.65259 + 2.39504I
b = −3.29315 − 1.85894I
−7.3834 − 16.6288I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45265 + 0.12554I
a = −0.02515 − 1.78570I
b = −2.63824 + 0.60627I
−9.55042 − 7.23704I 0
u = −1.45265 − 0.12554I
a = −0.02515 + 1.78570I
b = −2.63824 − 0.60627I
−9.55042 + 7.23704I 0
u = 1.43834 + 0.25272I
a = −1.21346 − 1.31458I
b = 2.01713 − 1.23238I
−9.35467 − 2.41231I 0
u = 1.43834 − 0.25272I
a = −1.21346 + 1.31458I
b = 2.01713 + 1.23238I
−9.35467 + 2.41231I 0
u = 1.45325 + 0.16584I
a = 1.40656 − 0.73172I
b = 1.09821 + 2.30833I
−10.60000 − 7.15506I 0
u = 1.45325 − 0.16584I
a = 1.40656 + 0.73172I
b = 1.09821 − 2.30833I
−10.60000 + 7.15506I 0
u = −0.317685
a = 2.49633
b = −0.369663
−1.03010 −10.3530
14
II. I
u
2
= hb + 1, u
3
+ a − 2u, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
3
− 2u
−u
3
+ u
a
3
=
−u
3
+ 2u
−1
a
2
=
0
−u
3
+ u − 1
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
5
=
−u
3
+ 2u
u
3
− u
a
4
=
−u
3
+ 2u
−1
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
3
+ u
2
+ 8u − 15
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
8
, c
9
u
5
c
4
(u + 1)
5
c
5
, c
10
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
6
, c
7
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
11
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
12
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
8
, c
9
y
5
c
5
, c
10
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
6
, c
7
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
12
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = 0.629714
b = −1.00000
−4.04602 −9.19250
u = 0.309916 + 0.549911I
a = 0.871221 + 1.107660I
b = −1.00000
−1.97403 − 1.53058I −11.97286 + 4.76366I
u = 0.309916 − 0.549911I
a = 0.871221 − 1.107660I
b = −1.00000
−1.97403 + 1.53058I −11.97286 − 4.76366I
u = −1.41878 + 0.21917I
a = −0.186078 − 0.874646I
b = −1.00000
−7.51750 + 4.40083I −16.4309 − 2.8075I
u = −1.41878 − 0.21917I
a = −0.186078 + 0.874646I
b = −1.00000
−7.51750 − 4.40083I −16.4309 + 2.8075I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
97
+ 52u
96
+ ··· + 7u + 1)
c
2
((u − 1)
5
)(u
97
− 6u
96
+ ··· − 5u + 1)
c
3
, c
8
u
5
(u
97
− u
96
+ ··· + 32u + 32)
c
4
((u + 1)
5
)(u
97
− 6u
96
+ ··· − 5u + 1)
c
5
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
97
− 2u
96
+ ··· − 939u + 137)
c
6
, c
7
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
97
+ 2u
96
+ ··· + u + 1)
c
9
u
5
(u
97
− 33u
96
+ ··· − 22016u + 1024)
c
10
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
97
+ 20u
96
+ ··· + 152213u + 6497)
c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
97
+ 2u
96
+ ··· + u + 1)
c
12
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)(u
97
− 6u
96
+ ··· − 63u + 5)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
97
− 8y
96
+ ··· + 23y −1)
c
2
, c
4
((y −1)
5
)(y
97
− 52y
96
+ ··· + 7y −1)
c
3
, c
8
y
5
(y
97
+ 33y
96
+ ··· − 22016y −1024)
c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
97
+ 86y
95
+ ··· + 940357y −18769)
c
6
, c
7
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
97
− 88y
96
+ ··· + 5y −1)
c
9
y
5
(y
97
+ 53y
96
+ ··· + 3.00155 × 10
7
y −1048576)
c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
97
+ 36y
96
+ ··· + 514538009y −42211009)
c
12
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
97
− 8y
96
+ ··· + 569y −25)
20
