12n
0369
(K12n
0369
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 11 4 12 7 5 8 11
Solving Sequence
5,10 8,11
12 4 3 7 6 2 1 9
c
10
c
11
c
4
c
3
c
7
c
6
c
2
c
1
c
9
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.75957 × 10
30
u
47
+ 3.57679 × 10
30
u
46
+ ··· + 6.32723 × 10
30
b − 3.65231 × 10
30
,
− 2.09830 × 10
31
u
47
− 2.86459 × 10
31
u
46
+ ··· + 6.32723 × 10
30
a + 1.84790 × 10
32
, u
48
+ u
47
+ ··· − 10u + 1i
I
u
2
= hu
14
− 7u
12
+ u
11
+ 17u
10
− 6u
9
− 12u
8
+ 12u
7
− 13u
6
− 8u
5
+ 17u
4
− u
3
+ u
2
+ b + u,
− u
15
− 2u
14
+ ··· + a + 1,
u
16
− 8u
14
+ u
13
+ 25u
12
− 7u
11
− 34u
10
+ 19u
9
+ 7u
8
− 24u
7
+ 30u
6
+ 12u
5
− 25u
4
+ u
3
+ 2u
2
− 2u + 1i
I
u
3
= hb, a − 1, u
4
− u
3
− 1i
I
u
4
= hb, a − 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 69 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−2.76×10
30
u
47
+3.58×10
30
u
46
+· · ·+6.33×10
30
b−3.65×10
30
, −2.10×
10
31
u
47
−2.86×10
31
u
46
+· · ·+6.33×10
30
a+1.85×10
32
, u
48
+u
47
+· · ·−10u+1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
8
=
3.31630u
47
+ 4.52741u
46
+ ··· + 38.4903u − 29.2055
0.436142u
47
− 0.565302u
46
+ ··· + 1.59289u + 0.577237
a
11
=
1
−u
2
a
12
=
0.242854u
47
+ 2.03129u
46
+ ··· + 69.3445u − 20.8066
1.64294u
47
+ 0.0993437u
46
+ ··· − 21.2574u + 1.65185
a
4
=
−u
u
a
3
=
−1.28265u
47
− 0.830559u
46
+ ··· − 36.6527u − 1.12768
0.892123u
47
+ 0.107793u
46
+ ··· − 6.10035u − 1.43370
a
7
=
3.37390u
47
+ 4.39684u
46
+ ··· + 36.8345u − 29.4151
0.378539u
47
− 0.434740u
46
+ ··· + 3.24866u + 0.786904
a
6
=
3.76580u
47
+ 4.48846u
46
+ ··· + 26.7303u − 29.1791
−0.222098u
47
− 0.473962u
46
+ ··· + 6.64344u + 0.486616
a
2
=
2.90620u
47
+ 2.89459u
46
+ ··· − 5.12037u − 23.2385
0.210719u
47
+ 0.258112u
46
+ ··· + 7.62863u − 0.669658
a
1
=
−0.607997u
47
− 1.69785u
46
+ ··· − 72.9604u + 20.6700
−0.837878u
47
− 0.317904u
46
+ ··· + 13.9065u − 0.953269
a
9
=
3.59091u
47
+ 1.91005u
46
+ ··· + 69.2709u − 21.1928
−1.82497u
47
+ 0.418307u
46
+ ··· − 0.762950u + 0.364889
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.37527u
47
− 1.29990u
46
+ ··· + 83.9395u + 0.965224
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
+ 30u
47
+ ··· + 204u + 16
c
2
, c
5
u
48
− 4u
47
+ ··· − 34u + 4
c
3
, c
7
u
48
+ 2u
47
+ ··· − 16u + 1
c
4
, c
10
u
48
+ u
47
+ ··· − 10u + 1
c
6
u
48
+ 3u
47
+ ··· − 18570u + 68953
c
8
, c
11
u
48
+ 5u
47
+ ··· + 120u + 271
c
9
u
48
+ 11u
47
+ ··· + 46158u + 10853
c
12
u
48
+ 59u
47
+ ··· + 2718438u + 73441
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
− 18y
47
+ ··· − 209520y + 256
c
2
, c
5
y
48
− 30y
47
+ ··· − 204y + 16
c
3
, c
7
y
48
+ 10y
47
+ ··· − 162y + 1
c
4
, c
10
y
48
− 43y
47
+ ··· − 166y + 1
c
6
y
48
+ 25y
47
+ ··· − 20064851276y + 4754516209
c
8
, c
11
y
48
− 59y
47
+ ··· − 2718438y + 73441
c
9
y
48
+ 5y
47
+ ··· − 97685534y + 117787609
c
12
y
48
− 143y
47
+ ··· − 163732164302y + 5393580481
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.188816 + 0.986534I
a = −1.187120 − 0.629861I
b = 0.344371 − 0.579813I
−11.1663 + 9.4251I −7.81565 − 5.65269I
u = 0.188816 − 0.986534I
a = −1.187120 + 0.629861I
b = 0.344371 + 0.579813I
−11.1663 − 9.4251I −7.81565 + 5.65269I
u = −0.923856
a = 0.987425
b = −0.00645573
−1.64390 −6.03810
u = −0.118797 + 0.851176I
a = −1.42725 + 0.86776I
b = 0.414622 + 0.529642I
−7.00819 − 3.87744I −6.00183 + 2.83114I
u = −0.118797 − 0.851176I
a = −1.42725 − 0.86776I
b = 0.414622 − 0.529642I
−7.00819 + 3.87744I −6.00183 − 2.83114I
u = −0.237043 + 0.810777I
a = 0.266448 − 0.209284I
b = −0.484219 − 0.035427I
−1.59052 + 1.65508I −10.14529 − 5.18915I
u = −0.237043 − 0.810777I
a = 0.266448 + 0.209284I
b = −0.484219 + 0.035427I
−1.59052 − 1.65508I −10.14529 + 5.18915I
u = −0.058232 + 0.837894I
a = −1.82697 − 0.63370I
b = 0.516515 − 0.576658I
−11.32710 − 1.67337I −8.90827 + 0.94865I
u = −0.058232 − 0.837894I
a = −1.82697 + 0.63370I
b = 0.516515 + 0.576658I
−11.32710 + 1.67337I −8.90827 − 0.94865I
u = −1.147810 + 0.393065I
a = 0.063356 − 0.460733I
b = −1.191290 + 0.713713I
−3.86248 − 0.61447I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.147810 − 0.393065I
a = 0.063356 + 0.460733I
b = −1.191290 − 0.713713I
−3.86248 + 0.61447I 0
u = 1.224880 + 0.039706I
a = −0.84589 + 2.01472I
b = 0.75845 − 3.13225I
5.47066 + 2.81993I 0
u = 1.224880 − 0.039706I
a = −0.84589 − 2.01472I
b = 0.75845 + 3.13225I
5.47066 − 2.81993I 0
u = −1.23724
a = 3.88112
b = −3.94762
−3.66178 3.85220
u = −0.228880 + 0.722151I
a = 0.583716 − 0.181097I
b = −0.334046 − 0.976538I
−3.67584 − 3.60264I −9.48140 + 6.24040I
u = −0.228880 − 0.722151I
a = 0.583716 + 0.181097I
b = −0.334046 + 0.976538I
−3.67584 + 3.60264I −9.48140 − 6.24040I
u = 1.178910 + 0.418615I
a = −0.475538 − 0.859997I
b = 0.42509 + 1.83991I
1.37240 + 4.77913I 0
u = 1.178910 − 0.418615I
a = −0.475538 + 0.859997I
b = 0.42509 − 1.83991I
1.37240 − 4.77913I 0
u = −1.211720 + 0.403316I
a = 0.412396 + 0.097054I
b = −0.007786 + 0.341023I
1.52928 − 6.15730I 0
u = −1.211720 − 0.403316I
a = 0.412396 − 0.097054I
b = −0.007786 − 0.341023I
1.52928 + 6.15730I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.260750 + 0.217181I
a = 0.580734 + 0.080863I
b = −0.153480 − 0.378533I
3.26609 + 1.25196I 0
u = 1.260750 − 0.217181I
a = 0.580734 − 0.080863I
b = −0.153480 + 0.378533I
3.26609 − 1.25196I 0
u = −1.228180 + 0.379942I
a = 0.05711 − 2.29319I
b = 0.30107 + 3.26878I
−7.72334 − 2.70340I 0
u = −1.228180 − 0.379942I
a = 0.05711 + 2.29319I
b = 0.30107 − 3.26878I
−7.72334 + 2.70340I 0
u = −1.289200 + 0.073390I
a = −0.63077 + 1.65237I
b = 0.35618 − 2.71369I
6.48354 − 3.11664I 0
u = −1.289200 − 0.073390I
a = −0.63077 − 1.65237I
b = 0.35618 + 2.71369I
6.48354 + 3.11664I 0
u = 1.154930 + 0.634373I
a = −0.078971 + 0.444060I
b = −0.849057 − 0.707892I
−8.27166 − 3.77639I 0
u = 1.154930 − 0.634373I
a = −0.078971 − 0.444060I
b = −0.849057 + 0.707892I
−8.27166 + 3.77639I 0
u = 1.319420 + 0.377715I
a = 0.051061 + 0.623648I
b = −1.16317 − 1.04567I
−7.01248 + 6.04669I 0
u = 1.319420 − 0.377715I
a = 0.051061 − 0.623648I
b = −1.16317 + 1.04567I
−7.01248 − 6.04669I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.612128
a = −0.328856
b = −1.19564
−2.95942 2.44780
u = 1.353320 + 0.378263I
a = −0.08340 + 1.97303I
b = 0.49945 − 2.98749I
−2.37757 + 8.30419I 0
u = 1.353320 − 0.378263I
a = −0.08340 − 1.97303I
b = 0.49945 + 2.98749I
−2.37757 − 8.30419I 0
u = −1.394650 + 0.226156I
a = −0.28775 + 1.52139I
b = 0.01735 − 2.20388I
4.97003 − 4.04918I 0
u = −1.394650 − 0.226156I
a = −0.28775 − 1.52139I
b = 0.01735 + 2.20388I
4.97003 + 4.04918I 0
u = 0.204671 + 0.542777I
a = 0.606882 + 0.463380I
b = −0.097702 + 0.457637I
−0.184718 + 1.155860I −2.61813 − 5.93351I
u = 0.204671 − 0.542777I
a = 0.606882 − 0.463380I
b = −0.097702 − 0.457637I
−0.184718 − 1.155860I −2.61813 + 5.93351I
u = 1.39354 + 0.29007I
a = −0.54475 − 1.82044I
b = 0.09576 + 2.31209I
1.48745 + 7.27926I 0
u = 1.39354 − 0.29007I
a = −0.54475 + 1.82044I
b = 0.09576 − 2.31209I
1.48745 − 7.27926I 0
u = 1.43184 + 0.09274I
a = 0.510399 − 1.211730I
b = −0.44308 + 1.62054I
4.22730 + 0.98369I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43184 − 0.09274I
a = 0.510399 + 1.211730I
b = −0.44308 − 1.62054I
4.22730 − 0.98369I 0
u = −1.41425 + 0.42968I
a = −0.01233 − 1.80833I
b = 0.45419 + 2.79557I
−6.1055 − 14.4818I 0
u = −1.41425 − 0.42968I
a = −0.01233 + 1.80833I
b = 0.45419 − 2.79557I
−6.1055 + 14.4818I 0
u = −1.50303 + 0.27534I
a = −0.016901 + 1.163320I
b = 0.04802 − 1.86187I
4.18133 − 4.41038I 0
u = −1.50303 − 0.27534I
a = −0.016901 − 1.163320I
b = 0.04802 + 1.86187I
4.18133 + 4.41038I 0
u = −0.212607
a = 5.78141
b = −2.13725
−6.86165 −17.4210
u = 0.1136290 + 0.0195248I
a = −0.87499 + 10.27460I
b = 0.636242 + 0.063087I
2.11273 + 2.53080I 5.85801 − 0.41014I
u = 0.1136290 − 0.0195248I
a = −0.87499 − 10.27460I
b = 0.636242 − 0.063087I
2.11273 − 2.53080I 5.85801 + 0.41014I
9
II.
I
u
2
= hu
14
−7u
12
+· · ·+b+u, −u
15
−2u
14
+· · ·+a+1, u
16
−8u
14
+· · ·−2u+1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
8
=
u
15
+ 2u
14
+ ··· + 4u − 1
−u
14
+ 7u
12
+ ··· − u
2
− u
a
11
=
1
−u
2
a
12
=
−2u
15
+ 4u
14
+ ··· + 6u − 2
u
15
− 4u
14
+ ··· − 8u + 4
a
4
=
−u
u
a
3
=
−u
14
− u
13
+ ··· + 3u − 1
u
15
+ u
14
+ ··· − u
2
+ 2u
a
7
=
u
15
+ 3u
14
+ ··· + 5u − 2
−2u
14
+ 13u
12
+ ··· − 2u + 1
a
6
=
u
15
+ u
14
+ ··· − 6u
2
+ 2u
u
14
− 6u
12
+ ··· + 2u − 1
a
2
=
−u
15
+ 6u
13
+ ··· − 4u
2
+ 6u
2u
15
+ 2u
14
+ ··· + 2u
2
+ u
a
1
=
−2u
15
+ 2u
14
+ ··· + 4u − 2
u
15
− u
14
+ ··· − 4u + 2
a
9
=
2u
15
− 7u
14
+ ··· − 9u + 6
−2u
15
+ 6u
14
+ ··· + 7u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
15
− 3u
14
− 39u
13
+ 23u
12
+ 89u
11
− 65u
10
− 52u
9
+ 74u
8
−
90u
7
− 14u
6
+ 120u
5
− 24u
4
− 7u
3
+ 8u
2
− 21u − 8
10
(iv) u-Polynomials at the component
11
Crossings u-Polynomials at each crossing
c
1
u
16
− 10u
15
+ ··· − 13u + 1
c
2
u
16
− 5u
14
+ ··· + u + 1
c
3
u
16
+ u
15
+ ··· + 2u
2
+ 1
c
4
u
16
− 8u
14
+ ··· + 2u + 1
c
5
u
16
− 5u
14
+ ··· − u + 1
c
6
u
16
− 10u
14
+ ··· − 8u + 1
c
7
u
16
− u
15
+ ··· + 2u
2
+ 1
c
8
u
16
+ 4u
15
+ ··· − 6u
2
+ 1
c
9
u
16
− 10u
14
+ ··· − 10u + 1
c
10
u
16
− 8u
14
+ ··· − 2u + 1
c
11
u
16
− 4u
15
+ ··· − 6u
2
+ 1
c
12
u
16
+ 16u
15
+ ··· + 12u + 1
12
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 2y
15
+ ··· − 17y + 1
c
2
, c
5
y
16
− 10y
15
+ ··· − 13y + 1
c
3
, c
7
y
16
+ 9y
15
+ ··· + 4y + 1
c
4
, c
10
y
16
− 16y
15
+ ··· − 42y
2
+ 1
c
6
y
16
− 20y
15
+ ··· − 26y + 1
c
8
, c
11
y
16
− 16y
15
+ ··· − 12y + 1
c
9
y
16
− 20y
15
+ ··· − 28y + 1
c
12
y
16
− 36y
15
+ ··· − 16y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.157905 + 0.943251I
a = 0.610640 + 0.247441I
b = 0.0788746 − 0.0514506I
−0.93275 − 1.38263I 0.67419 + 2.70676I
u = 0.157905 − 0.943251I
a = 0.610640 − 0.247441I
b = 0.0788746 + 0.0514506I
−0.93275 + 1.38263I 0.67419 − 2.70676I
u = −1.21024
a = 3.35576
b = −2.76311
−4.18180 −12.5660
u = 1.28233
a = 0.698365
b = 0.403528
−0.346283 2.00910
u = 1.316900 + 0.141214I
a = −0.04386 − 2.04828I
b = 0.41477 + 2.95412I
5.70540 − 0.78730I −0.442956 + 0.061759I
u = 1.316900 − 0.141214I
a = −0.04386 + 2.04828I
b = 0.41477 − 2.95412I
5.70540 + 0.78730I −0.442956 − 0.061759I
u = −0.650998
a = 1.51494
b = −2.37753
−6.31388 −1.89280
u = −1.367740 + 0.173395I
a = −0.01802 + 1.80035I
b = 0.08155 − 2.81320I
6.41284 − 4.92457I 1.71154 + 6.19664I
u = −1.367740 − 0.173395I
a = −0.01802 − 1.80035I
b = 0.08155 + 2.81320I
6.41284 + 4.92457I 1.71154 − 6.19664I
u = 1.328650 + 0.387601I
a = −0.708818 − 0.897346I
b = 0.64793 + 1.46365I
2.92923 + 6.21758I 0.04433 − 6.40785I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.328650 − 0.387601I
a = −0.708818 + 0.897346I
b = 0.64793 − 1.46365I
2.92923 − 6.21758I 0.04433 + 6.40785I
u = −1.44285 + 0.29245I
a = −0.118615 + 1.081200I
b = −0.09128 − 1.76349I
4.51337 − 2.97289I −0.738347 + 0.405278I
u = −1.44285 − 0.29245I
a = −0.118615 − 1.081200I
b = −0.09128 + 1.76349I
4.51337 + 2.97289I −0.738347 − 0.405278I
u = 0.441784
a = −1.29505
b = −0.989743
−3.43070 −15.5470
u = 0.075703 + 0.413793I
a = 3.14167 + 1.07241I
b = −0.268420 − 0.065341I
1.66771 + 2.72901I −9.75037 − 6.35303I
u = 0.075703 − 0.413793I
a = 3.14167 − 1.07241I
b = −0.268420 + 0.065341I
1.66771 − 2.72901I −9.75037 + 6.35303I
16
III. I
u
3
= hb, a − 1, u
4
− u
3
− 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
8
=
1
0
a
11
=
1
−u
2
a
12
=
u
2
+ 1
−u
2
a
4
=
−u
u
a
3
=
0
u
a
7
=
u
2
+ 1
−u
2
a
6
=
−u
3
+ u
2
u
3
+ u + 1
a
2
=
u
3
− u
2
−u
3
− 1
a
1
=
u
3
− u
2
−u
3
− u − 1
a
9
=
−u
3
− u
2
u
3
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u + 1)
4
c
3
, c
4
, c
7
c
10
u
4
− u
3
− 1
c
6
u
4
− 5u
3
+ 6u
2
− 4u + 1
c
8
, c
11
u
4
− u
3
− 2u
2
+ 1
c
9
u
4
+ u
3
− 2u
2
+ 1
c
12
u
4
+ 5u
3
+ 6u
2
+ 4u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
7
c
10
y
4
− y
3
− 2y
2
+ 1
c
6
, c
12
y
4
− 13y
3
− 2y
2
− 4y + 1
c
8
, c
9
, c
11
y
4
− 5y
3
+ 6y
2
− 4y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.219447 + 0.914474I
a = 1.00000
b = 0
−1.64493 −6.00000
u = 0.219447 − 0.914474I
a = 1.00000
b = 0
−1.64493 −6.00000
u = −0.819173
a = 1.00000
b = 0
−1.64493 −6.00000
u = 1.38028
a = 1.00000
b = 0
−1.64493 −6.00000
20
IV. I
u
4
= hb, a − 1, u + 1i
(i) Arc colorings
a
5
=
0
−1
a
10
=
1
0
a
8
=
1
0
a
11
=
1
−1
a
12
=
2
−1
a
4
=
1
−1
a
3
=
0
−1
a
7
=
2
−1
a
6
=
1
0
a
2
=
−1
−1
a
1
=
−1
0
a
9
=
−1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
9
, c
10
, c
12
u + 1
c
6
, c
8
, c
11
u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 0
−1.64493 −6.00000
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u + 1)
5
)(u
16
− 10u
15
+ ··· − 13u + 1)(u
48
+ 30u
47
+ ··· + 204u + 16)
c
2
((u + 1)
5
)(u
16
− 5u
14
+ ··· + u + 1)(u
48
− 4u
47
+ ··· − 34u + 4)
c
3
(u + 1)(u
4
− u
3
− 1)(u
16
+ u
15
+ ··· + 2u
2
+ 1)(u
48
+ 2u
47
+ ··· − 16u + 1)
c
4
(u + 1)(u
4
− u
3
− 1)(u
16
− 8u
14
+ ··· + 2u + 1)(u
48
+ u
47
+ ··· − 10u + 1)
c
5
((u + 1)
5
)(u
16
− 5u
14
+ ··· − u + 1)(u
48
− 4u
47
+ ··· − 34u + 4)
c
6
(u − 1)(u
4
− 5u
3
+ ··· − 4u + 1)(u
16
− 10u
14
+ ··· − 8u + 1)
· (u
48
+ 3u
47
+ ··· − 18570u + 68953)
c
7
(u + 1)(u
4
− u
3
− 1)(u
16
− u
15
+ ··· + 2u
2
+ 1)(u
48
+ 2u
47
+ ··· − 16u + 1)
c
8
(u − 1)(u
4
− u
3
− 2u
2
+ 1)(u
16
+ 4u
15
+ ··· − 6u
2
+ 1)
· (u
48
+ 5u
47
+ ··· + 120u + 271)
c
9
(u + 1)(u
4
+ u
3
− 2u
2
+ 1)(u
16
− 10u
14
+ ··· − 10u + 1)
· (u
48
+ 11u
47
+ ··· + 46158u + 10853)
c
10
(u + 1)(u
4
− u
3
− 1)(u
16
− 8u
14
+ ··· − 2u + 1)(u
48
+ u
47
+ ··· − 10u + 1)
c
11
(u − 1)(u
4
− u
3
− 2u
2
+ 1)(u
16
− 4u
15
+ ··· − 6u
2
+ 1)
· (u
48
+ 5u
47
+ ··· + 120u + 271)
c
12
(u + 1)(u
4
+ 5u
3
+ ··· + 4u + 1)(u
16
+ 16u
15
+ ··· + 12u + 1)
· (u
48
+ 59u
47
+ ··· + 2718438u + 73441)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
16
+ 2y
15
+ ··· − 17y + 1)
· (y
48
− 18y
47
+ ··· − 209520y + 256)
c
2
, c
5
((y −1)
5
)(y
16
− 10y
15
+ ··· − 13y + 1)(y
48
− 30y
47
+ ··· − 204y + 16)
c
3
, c
7
(y −1)(y
4
− y
3
− 2y
2
+ 1)(y
16
+ 9y
15
+ ··· + 4y + 1)
· (y
48
+ 10y
47
+ ··· − 162y + 1)
c
4
, c
10
(y −1)(y
4
− y
3
− 2y
2
+ 1)(y
16
− 16y
15
+ ··· − 42y
2
+ 1)
· (y
48
− 43y
47
+ ··· − 166y + 1)
c
6
(y −1)(y
4
− 13y
3
+ ··· − 4y + 1)(y
16
− 20y
15
+ ··· − 26y + 1)
· (y
48
+ 25y
47
+ ··· − 20064851276y + 4754516209)
c
8
, c
11
(y −1)(y
4
− 5y
3
+ ··· − 4y + 1)(y
16
− 16y
15
+ ··· − 12y + 1)
· (y
48
− 59y
47
+ ··· − 2718438y + 73441)
c
9
(y −1)(y
4
− 5y
3
+ ··· − 4y + 1)(y
16
− 20y
15
+ ··· − 28y + 1)
· (y
48
+ 5y
47
+ ··· − 97685534y + 117787609)
c
12
(y −1)(y
4
− 13y
3
+ ··· − 4y + 1)(y
16
− 36y
15
+ ··· − 16y + 1)
· (y
48
− 143y
47
+ ··· − 163732164302y + 5393580481)
26
