12a
0344
(K12a
0344
)
A knot diagram
1
Linearized knot diagam
3 6 9 7 2 5 11 4 12 1 8 10
Solving Sequence
2,5
6 3
7,11
8 1 4 9 10 12
c
5
c
2
c
6
c
7
c
1
c
4
c
8
c
10
c
12
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.85235 × 10
24
u
79
− 2.72115 × 10
25
u
78
+ ··· + 9.93119 × 10
23
b − 7.91401 × 10
24
,
− 6.33480 × 10
24
u
79
− 2.53760 × 10
25
u
78
+ ··· + 1.98624 × 10
24
a − 1.64622 × 10
25
, u
80
+ 4u
79
+ ··· + 6u + 1i
I
u
2
= hu
4
− u
2
+ b − u + 2, 2u
4
+ u
3
+ a − 2u + 2, u
5
+ u
4
− u
2
+ u + 1i
I
u
3
= hu
2
+ b, −2u
2
a + a
2
+ au − 2u
2
+ a + 2u − 1, u
3
− u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 91 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−9.85×10
24
u
79
−2.72×10
25
u
78
+· · ·+9.93×10
23
b−7.91×10
24
, −6.33×
10
24
u
79
−2.54×10
25
u
78
+· · ·+1.99×10
24
a−1.65×10
25
, u
80
+4u
79
+· · ·+6u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
u
2
a
11
=
3.18934u
79
+ 12.7759u
78
+ ··· + 47.5761u + 8.28813
9.92061u
79
+ 27.4001u
78
+ ··· + 40.9951u + 7.96884
a
8
=
7.35876u
79
+ 21.6854u
78
+ ··· + 23.9027u + 7.03413
−0.876176u
79
+ 2.07029u
78
+ ··· + 16.0513u + 4.25701
a
1
=
u
3
u
5
− u
3
+ u
a
4
=
u
4
− u
2
+ 1
−u
4
a
9
=
−1.44610u
79
− 3.25664u
78
+ ··· − 0.0887997u + 2.46775
3.89301u
79
+ 9.15127u
78
+ ··· + 9.76680u + 2.44691
a
10
=
3.89399u
79
+ 14.3516u
78
+ ··· + 46.8184u + 7.87170
8.12729u
79
+ 22.9501u
78
+ ··· + 35.1348u + 6.87334
a
12
=
7.21937u
79
+ 24.5178u
78
+ ··· + 58.4840u + 11.4296
7.78413u
79
+ 24.6495u
78
+ ··· + 45.8212u + 9.60214
(ii) Obstruction class = −1
(iii) Cusp Shapes =
225344555042881471562867245
993119401398295715683309
u
79
+
1486568910759558927791433433
1986238802796591431366618
u
78
+
··· +
2947932581577874658457472291
1986238802796591431366618
u +
619487791938232455082216191
1986238802796591431366618
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
u
80
+ 20u
79
+ ··· + 42u + 1
c
2
, c
5
u
80
+ 4u
79
+ ··· + 6u + 1
c
3
, c
8
u
80
− 2u
79
+ ··· + 160u − 64
c
7
, c
11
u
80
+ 4u
79
+ ··· − 128u − 32
c
9
, c
10
, c
12
u
80
− 9u
79
+ ··· + 27u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
y
80
+ 84y
79
+ ··· − 682y + 1
c
2
, c
5
y
80
− 20y
79
+ ··· − 42y + 1
c
3
, c
8
y
80
+ 42y
79
+ ··· − 5120y + 4096
c
7
, c
11
y
80
− 42y
79
+ ··· − 66048y + 1024
c
9
, c
10
, c
12
y
80
− 75y
79
+ ··· − 213y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.937313 + 0.347751I
a = 0.174266 − 0.787568I
b = −0.727576 + 0.727455I
−3.33822 − 4.82117I 0
u = 0.937313 − 0.347751I
a = 0.174266 + 0.787568I
b = −0.727576 − 0.727455I
−3.33822 + 4.82117I 0
u = 0.582846 + 0.818388I
a = −0.672268 + 0.203176I
b = −0.086980 − 0.893421I
−1.26973 − 4.01147I 0
u = 0.582846 − 0.818388I
a = −0.672268 − 0.203176I
b = −0.086980 + 0.893421I
−1.26973 + 4.01147I 0
u = 0.845099 + 0.506123I
a = −0.017809 + 0.337413I
b = 0.369387 − 0.227156I
1.73618 − 2.77244I 0
u = 0.845099 − 0.506123I
a = −0.017809 − 0.337413I
b = 0.369387 + 0.227156I
1.73618 + 2.77244I 0
u = −0.950543 + 0.403879I
a = 0.090000 − 0.577227I
b = −0.64347 − 1.42153I
−8.56535 + 4.83425I 0
u = −0.950543 − 0.403879I
a = 0.090000 + 0.577227I
b = −0.64347 + 1.42153I
−8.56535 − 4.83425I 0
u = −0.959530 + 0.120935I
a = −0.838995 − 0.755294I
b = −0.656494 + 0.002059I
−2.04664 − 1.46066I 0
u = −0.959530 − 0.120935I
a = −0.838995 + 0.755294I
b = −0.656494 − 0.002059I
−2.04664 + 1.46066I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.975562 + 0.382659I
a = −0.471936 + 0.931640I
b = −1.112520 + 0.332535I
−0.55792 − 7.07014I 0
u = 0.975562 − 0.382659I
a = −0.471936 − 0.931640I
b = −1.112520 − 0.332535I
−0.55792 + 7.07014I 0
u = 0.870682 + 0.332652I
a = 1.25916 − 1.20100I
b = 0.603918 + 0.379611I
−2.02857 − 2.17557I 0
u = 0.870682 − 0.332652I
a = 1.25916 + 1.20100I
b = 0.603918 − 0.379611I
−2.02857 + 2.17557I 0
u = −0.904570 + 0.199072I
a = 0.152725 − 0.178138I
b = 1.40879 + 0.86692I
−4.19881 + 0.29220I 0
u = −0.904570 − 0.199072I
a = 0.152725 + 0.178138I
b = 1.40879 − 0.86692I
−4.19881 − 0.29220I 0
u = −1.069250 + 0.146998I
a = 0.899094 + 0.683161I
b = −0.0510110 − 0.0498696I
−7.63820 − 4.53013I 0
u = −1.069250 − 0.146998I
a = 0.899094 − 0.683161I
b = −0.0510110 + 0.0498696I
−7.63820 + 4.53013I 0
u = −0.853249 + 0.283826I
a = 0.382918 + 1.152640I
b = 0.939067 + 0.906091I
−2.31119 + 2.17762I 0
u = −0.853249 − 0.283826I
a = 0.382918 − 1.152640I
b = 0.939067 − 0.906091I
−2.31119 − 2.17762I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.047550 + 0.374433I
a = 0.269786 − 0.393377I
b = 1.006870 − 0.937317I
−6.26460 − 11.20980I 0
u = 1.047550 − 0.374433I
a = 0.269786 + 0.393377I
b = 1.006870 + 0.937317I
−6.26460 + 11.20980I 0
u = 0.882220 + 0.717129I
a = −0.443888 + 1.246120I
b = −0.226602 − 0.774802I
2.32601 − 2.74241I 0
u = 0.882220 − 0.717129I
a = −0.443888 − 1.246120I
b = −0.226602 + 0.774802I
2.32601 + 2.74241I 0
u = 0.848871 + 0.109256I
a = −1.96581 + 0.51451I
b = 0.377107 − 0.195551I
−10.28610 − 0.13892I −24.9438 + 9.7256I
u = 0.848871 − 0.109256I
a = −1.96581 − 0.51451I
b = 0.377107 + 0.195551I
−10.28610 + 0.13892I −24.9438 − 9.7256I
u = 0.859887 + 0.789823I
a = 2.69951 + 2.32641I
b = −3.15862 + 0.26803I
1.64882 − 2.07054I 0
u = 0.859887 − 0.789823I
a = 2.69951 − 2.32641I
b = −3.15862 − 0.26803I
1.64882 + 2.07054I 0
u = −0.892015 + 0.791150I
a = 0.598424 + 0.150430I
b = 0.240714 − 1.363070I
−5.15784 + 2.97447I 0
u = −0.892015 − 0.791150I
a = 0.598424 − 0.150430I
b = 0.240714 + 1.363070I
−5.15784 − 2.97447I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.836397 + 0.864338I
a = −2.07623 + 0.93166I
b = 2.19378 + 1.00704I
4.36446 − 2.41660I 0
u = −0.836397 − 0.864338I
a = −2.07623 − 0.93166I
b = 2.19378 − 1.00704I
4.36446 + 2.41660I 0
u = 0.865180 + 0.835627I
a = 1.50909 + 1.74688I
b = −2.39004 − 0.66512I
4.48911 − 0.87143I 0
u = 0.865180 − 0.835627I
a = 1.50909 − 1.74688I
b = −2.39004 + 0.66512I
4.48911 + 0.87143I 0
u = 0.917805 + 0.779835I
a = −2.54765 − 1.79888I
b = 3.28237 − 0.10616I
1.47178 − 3.83910I 0
u = 0.917805 − 0.779835I
a = −2.54765 + 1.79888I
b = 3.28237 + 0.10616I
1.47178 + 3.83910I 0
u = 0.494296 + 0.619420I
a = −0.118161 + 0.445938I
b = 0.050487 + 0.469304I
2.81647 − 1.39098I −4.65333 + 3.39574I
u = 0.494296 − 0.619420I
a = −0.118161 − 0.445938I
b = 0.050487 − 0.469304I
2.81647 + 1.39098I −4.65333 − 3.39574I
u = −0.800901 + 0.904702I
a = 1.55800 − 1.78263I
b = −2.53254 + 0.77113I
2.23380 − 9.78191I 0
u = −0.800901 − 0.904702I
a = 1.55800 + 1.78263I
b = −2.53254 − 0.77113I
2.23380 + 9.78191I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856330 + 0.854982I
a = 1.166280 − 0.386013I
b = −1.60157 + 0.16248I
5.34443 + 0.79481I 0
u = −0.856330 − 0.854982I
a = 1.166280 + 0.386013I
b = −1.60157 − 0.16248I
5.34443 − 0.79481I 0
u = −0.828964 + 0.884459I
a = −1.60651 + 1.16176I
b = 2.28569 − 0.38260I
7.64873 − 4.89072I 0
u = −0.828964 − 0.884459I
a = −1.60651 − 1.16176I
b = 2.28569 + 0.38260I
7.64873 + 4.89072I 0
u = 1.017270 + 0.661319I
a = −0.318473 + 0.115749I
b = −0.238056 − 0.984477I
−2.61888 − 1.46312I 0
u = 1.017270 − 0.661319I
a = −0.318473 − 0.115749I
b = −0.238056 + 0.984477I
−2.61888 + 1.46312I 0
u = 0.169440 + 0.760477I
a = 0.000302 + 0.920026I
b = −0.886187 − 0.066321I
−3.38617 + 7.21522I −11.57739 − 4.93181I
u = 0.169440 − 0.760477I
a = 0.000302 − 0.920026I
b = −0.886187 + 0.066321I
−3.38617 − 7.21522I −11.57739 + 4.93181I
u = 0.838303 + 0.889934I
a = −0.82802 − 2.20009I
b = 2.09293 + 1.43375I
−0.22327 + 2.37163I 0
u = 0.838303 − 0.889934I
a = −0.82802 + 2.20009I
b = 2.09293 − 1.43375I
−0.22327 − 2.37163I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.933131 + 0.813064I
a = −2.36608 − 1.04014I
b = 2.31780 − 1.05442I
4.27708 − 5.28117I 0
u = 0.933131 − 0.813064I
a = −2.36608 + 1.04014I
b = 2.31780 + 1.05442I
4.27708 + 5.28117I 0
u = −0.887481 + 0.879573I
a = 1.58106 − 0.65269I
b = −1.76830 − 0.70972I
10.21390 + 1.20204I 0
u = −0.887481 − 0.879573I
a = 1.58106 + 0.65269I
b = −1.76830 + 0.70972I
10.21390 − 1.20204I 0
u = −0.948192 + 0.820603I
a = −1.13552 + 1.28892I
b = 1.38937 + 0.40661I
5.05593 + 5.43924I 0
u = −0.948192 − 0.820603I
a = −1.13552 − 1.28892I
b = 1.38937 − 0.40661I
5.05593 − 5.43924I 0
u = −0.965009 + 0.816000I
a = 1.18309 − 1.63202I
b = −2.56538 + 0.59228I
3.96142 + 8.66250I 0
u = −0.965009 − 0.816000I
a = 1.18309 + 1.63202I
b = −2.56538 − 0.59228I
3.96142 − 8.66250I 0
u = −0.942925 + 0.856435I
a = −0.96892 + 1.24837I
b = 1.88035 − 0.35749I
10.03880 + 5.22302I 0
u = −0.942925 − 0.856435I
a = −0.96892 − 1.24837I
b = 1.88035 + 0.35749I
10.03880 − 5.22302I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.979592 + 0.822863I
a = 1.89112 − 1.38953I
b = −2.23000 − 0.70512I
7.17373 + 11.21830I 0
u = −0.979592 − 0.822863I
a = 1.89112 + 1.38953I
b = −2.23000 + 0.70512I
7.17373 − 11.21830I 0
u = 0.977444 + 0.830015I
a = 2.51218 + 0.28028I
b = −2.10646 + 1.76637I
−0.66511 − 8.73988I 0
u = 0.977444 − 0.830015I
a = 2.51218 − 0.28028I
b = −2.10646 − 1.76637I
−0.66511 + 8.73988I 0
u = −0.321779 + 0.632139I
a = 0.756357 + 0.960282I
b = 0.871646 − 0.585910I
−6.55850 − 1.01923I −15.1391 + 0.I
u = −0.321779 − 0.632139I
a = 0.756357 − 0.960282I
b = 0.871646 + 0.585910I
−6.55850 + 1.01923I −15.1391 + 0.I
u = −1.004210 + 0.817409I
a = −2.33088 + 1.12360I
b = 2.59048 + 1.17800I
1.5910 + 16.1481I 0
u = −1.004210 − 0.817409I
a = −2.33088 − 1.12360I
b = 2.59048 − 1.17800I
1.5910 − 16.1481I 0
u = −0.700562
a = −4.30574
b = −3.73829
−2.59838 −119.010
u = 0.237042 + 0.644569I
a = −0.711917 − 0.474272I
b = 1.050580 − 0.217495I
1.76492 + 3.34953I −6.94493 − 4.05394I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.237042 − 0.644569I
a = −0.711917 + 0.474272I
b = 1.050580 + 0.217495I
1.76492 − 3.34953I −6.94493 + 4.05394I
u = −0.941907 + 0.920353I
a = −0.680992 − 0.844842I
b = 0.006272 + 1.215720I
8.88798 + 3.38254I 0
u = −0.941907 − 0.920353I
a = −0.680992 + 0.844842I
b = 0.006272 − 1.215720I
8.88798 − 3.38254I 0
u = −0.578820
a = −0.441740
b = −0.634881
−0.838544 −11.3510
u = 0.406147 + 0.408093I
a = 1.80938 − 0.53475I
b = −0.854606 + 0.774894I
−0.571047 − 0.765230I −10.03702 + 1.06541I
u = 0.406147 − 0.408093I
a = 1.80938 + 0.53475I
b = −0.854606 − 0.774894I
−0.571047 + 0.765230I −10.03702 − 1.06541I
u = 0.215457 + 0.521353I
a = 0.91607 − 1.54710I
b = −0.199480 − 0.311181I
−1.18117 + 1.56184I −9.13121 − 0.95837I
u = 0.215457 − 0.521353I
a = 0.91607 + 1.54710I
b = −0.199480 + 0.311181I
−1.18117 − 1.56184I −9.13121 + 0.95837I
u = −0.482222
a = −0.713720
b = −0.780848
−0.843561 −10.4350
u = −0.195815
a = −2.15633
b = −0.689441
−0.820251 −11.7060
12
II. I
u
2
= hu
4
− u
2
+ b − u + 2, 2u
4
+ u
3
+ a − 2u + 2, u
5
+ u
4
− u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
u
2
a
11
=
−2u
4
− u
3
+ 2u − 2
−u
4
+ u
2
+ u − 2
a
8
=
−u
2
+ 1
u
2
a
1
=
u
3
−u
4
− u
3
+ u
2
− 1
a
4
=
u
4
− u
2
+ 1
−u
4
a
9
=
−u
3
u
4
+ u
3
− u
2
+ 1
a
10
=
−2u
4
− 2u
3
+ 2u − 2
u
3
+ u − 1
a
12
=
−2u
4
− u
3
+ 2u − 2
−u
4
+ u
2
+ u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10u
4
+ 7u
3
+ u
2
− 10u + 7
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
2
u
5
− u
4
+ u
2
+ u − 1
c
5
u
5
+ u
4
− u
2
+ u + 1
c
6
, c
8
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
7
, c
11
u
5
c
9
, c
10
(u − 1)
5
c
12
(u + 1)
5
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
8
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
2
, c
5
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
c
7
, c
11
y
5
c
9
, c
10
, c
12
(y −1)
5
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758138 + 0.584034I
a = 1.315520 − 0.467517I
b = −0.278580 + 1.055720I
0.17487 − 2.21397I −10.02401 + 4.83884I
u = 0.758138 − 0.584034I
a = 1.315520 + 0.467517I
b = −0.278580 − 1.055720I
0.17487 + 2.21397I −10.02401 − 4.83884I
u = −0.935538 + 0.903908I
a = 0.368676 + 0.566573I
b = −0.020316 − 0.590570I
9.31336 + 3.33174I −1.83654 − 1.25445I
u = −0.935538 − 0.903908I
a = 0.368676 − 0.566573I
b = −0.020316 + 0.590570I
9.31336 − 3.33174I −1.83654 + 1.25445I
u = −0.645200
a = −3.36840
b = −2.40221
−2.52712 13.7210
16
III. I
u
3
= hu
2
+ b, −2u
2
a + a
2
+ au − 2u
2
+ a + 2u − 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
2
+ u + 1
a
7
=
−u
2
+ 1
u
2
a
11
=
a
−u
2
a
8
=
au − 2u
2
+ 2u + 1
u
2
a − au + 3u
2
− a − 1
a
1
=
u
2
− 1
−u
2
a
4
=
−u
−u
2
+ u + 1
a
9
=
au − 2u
2
+ 2u + 1
u
2
a − au + 3u
2
− a − 1
a
10
=
−au + 2u
2
− u − 2
−u
2
a + au − 3u
2
+ a + 1
a
12
=
2au − 3u
2
+ a + 3u + 2
2u
2
a − 2au + 4u
2
− 2a − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
2
a + 4u
2
+ 3a − 2u − 15
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
, c
8
u
6
c
5
(u
3
− u
2
+ 1)
2
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
9
, c
10
(u
2
+ u − 1)
3
c
11
, c
12
(u
2
− u − 1)
3
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
5
(y
3
− y
2
+ 2y −1)
2
c
3
, c
8
y
6
c
7
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
3
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.586612 + 0.101930I
b = −0.215080 − 1.307140I
−5.85852 − 2.82812I −18.4326 + 1.8100I
u = 0.877439 + 0.744862I
a = −0.86067 + 1.76749I
b = −0.215080 − 1.307140I
2.03717 − 2.82812I −25.9630 + 6.8067I
u = 0.877439 − 0.744862I
a = −0.586612 − 0.101930I
b = −0.215080 + 1.307140I
−5.85852 + 2.82812I −18.4326 − 1.8100I
u = 0.877439 − 0.744862I
a = −0.86067 − 1.76749I
b = −0.215080 + 1.307140I
2.03717 + 2.82812I −25.9630 − 6.8067I
u = −0.754878
a = −1.51473
b = −0.569840
−2.10041 −18.3450
u = −0.754878
a = 2.40929
b = −0.569840
−9.99610 0.135730
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
3
− u
2
+ 2u − 1)
2
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)
· (u
80
+ 20u
79
+ ··· + 42u + 1)
c
2
((u
3
+ u
2
− 1)
2
)(u
5
− u
4
+ u
2
+ u − 1)(u
80
+ 4u
79
+ ··· + 6u + 1)
c
3
u
6
(u
5
− u
4
+ ··· + 3u − 1)(u
80
− 2u
79
+ ··· + 160u − 64)
c
5
((u
3
− u
2
+ 1)
2
)(u
5
+ u
4
− u
2
+ u + 1)(u
80
+ 4u
79
+ ··· + 6u + 1)
c
6
(u
3
+ u
2
+ 2u + 1)
2
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
· (u
80
+ 20u
79
+ ··· + 42u + 1)
c
7
u
5
(u
2
+ u − 1)
3
(u
80
+ 4u
79
+ ··· − 128u − 32)
c
8
u
6
(u
5
+ u
4
+ ··· + 3u + 1)(u
80
− 2u
79
+ ··· + 160u − 64)
c
9
, c
10
((u − 1)
5
)(u
2
+ u − 1)
3
(u
80
− 9u
79
+ ··· + 27u + 1)
c
11
u
5
(u
2
− u − 1)
3
(u
80
+ 4u
79
+ ··· − 128u − 32)
c
12
((u + 1)
5
)(u
2
− u − 1)
3
(u
80
− 9u
79
+ ··· + 27u + 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
· (y
80
+ 84y
79
+ ··· − 682y + 1)
c
2
, c
5
(y
3
− y
2
+ 2y −1)
2
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
· (y
80
− 20y
79
+ ··· − 42y + 1)
c
3
, c
8
y
6
(y
5
+ 7y
4
+ ··· + 3y −1)(y
80
+ 42y
79
+ ··· − 5120y + 4096)
c
7
, c
11
y
5
(y
2
− 3y + 1)
3
(y
80
− 42y
79
+ ··· − 66048y + 1024)
c
9
, c
10
, c
12
((y −1)
5
)(y
2
− 3y + 1)
3
(y
80
− 75y
79
+ ··· − 213y + 1)
22
