12n
0373
(K12n
0373
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 11 5 12 4 12 7 8
Solving Sequence
6,11
7
3,12
2 1 5 8 9 10 4
c
6
c
11
c
2
c
1
c
5
c
7
c
8
c
10
c
4
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−20u
23
+ 115u
22
+ ··· + 8b − 400, 113u
23
− 773u
22
+ ··· + 16a + 440, u
24
− 9u
23
+ ··· − 144u + 32i
I
u
2
= h−6u
15
+ 21u
14
+ ··· + b + 10, u
15
− 6u
14
+ ··· + a + 1, u
16
− 4u
15
+ ··· − 3u + 1i
I
u
3
= h2.19606 × 10
33
a
9
u
2
− 2.28616 × 10
35
a
8
u
2
+ ··· + 1.69568 × 10
37
a − 5.01516 × 10
36
,
− 6a
8
u
2
+ 14a
7
u
2
+ ··· + 668a − 417, u
3
+ u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 70 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−20u
23
+ 115u
22
+ · · · + 8b − 400, 113u
23
− 773u
22
+ · · · + 16a +
440, u
24
− 9u
23
+ · · · − 144u + 32i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
3
=
−7.06250u
23
+ 48.3125u
22
+ ··· − 47.5000u − 27.5000
5
2
u
23
−
115
8
u
22
+ ··· −
255
2
u + 50
a
12
=
−u
−u
3
+ u
a
2
=
−
73
16
u
23
+
543
16
u
22
+ ··· − 175u +
45
2
5
2
u
23
−
115
8
u
22
+ ··· −
255
2
u + 50
a
1
=
−
17
8
u
23
+
141
8
u
22
+ ··· −
783
4
u + 46
5
2
u
23
−
75
4
u
22
+ ··· + 113u − 20
a
5
=
−
45
32
u
23
+
511
32
u
22
+ ··· − 324u +
183
2
169
16
u
23
−
1237
16
u
22
+ ··· + 601u − 133
a
8
=
1
8
u
23
−
7
8
u
22
+ ··· + 2u +
1
2
−
1
4
u
22
+
7
4
u
21
+ ··· +
27
2
u − 4
a
9
=
3
8
u
23
−
21
8
u
22
+ ··· + 6u +
1
2
1
4
u
23
− 3u
22
+ ··· +
147
2
u − 20
a
10
=
u
3
u
5
− u
3
+ u
a
4
=
595
32
u
23
−
4705
32
u
22
+ ··· + 1560u −
761
2
−
47
16
u
23
+
79
16
u
22
+ ··· + 831u − 267
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
17
4
u
23
+
127
4
u
22
+ ··· − 152u + 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 7u
23
+ ··· + 352u + 64
c
2
, c
5
u
24
+ 7u
23
+ ··· − 40u − 8
c
3
u
24
+ u
23
+ ··· + 4u + 1
c
4
, c
7
, c
9
u
24
− u
23
+ ··· + 5u
2
− 1
c
6
, c
11
u
24
− 9u
23
+ ··· − 144u + 32
c
8
, c
12
u
24
+ 5u
23
+ ··· + 21u + 1
c
10
u
24
+ 9u
23
+ ··· + 9984u + 1024
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 21y
23
+ ··· − 45568y + 4096
c
2
, c
5
y
24
− 7y
23
+ ··· − 352y + 64
c
3
y
24
+ 49y
23
+ ··· + 36y
2
+ 1
c
4
, c
7
, c
9
y
24
+ y
23
+ ··· − 10y + 1
c
6
, c
11
y
24
− 9y
23
+ ··· − 9984y + 1024
c
8
, c
12
y
24
− 45y
23
+ ··· − 81y + 1
c
10
y
24
+ 23y
23
+ ··· − 52625408y + 1048576
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.358950 + 0.915726I
a = −0.281055 + 0.691430I
b = 0.969760 − 0.428409I
1.06715 + 3.63668I −7.18463 − 6.28452I
u = 0.358950 − 0.915726I
a = −0.281055 − 0.691430I
b = 0.969760 + 0.428409I
1.06715 − 3.63668I −7.18463 + 6.28452I
u = 0.971229 + 0.342277I
a = −0.827201 + 0.300439I
b = −1.194730 + 0.185573I
−3.31191 − 1.22688I −3.32734 + 6.48080I
u = 0.971229 − 0.342277I
a = −0.827201 − 0.300439I
b = −1.194730 − 0.185573I
−3.31191 + 1.22688I −3.32734 − 6.48080I
u = 0.599488 + 0.713660I
a = 0.192159 − 1.348680I
b = 0.420693 + 0.742906I
2.96075 − 0.65298I −2.76291 + 1.36989I
u = 0.599488 − 0.713660I
a = 0.192159 + 1.348680I
b = 0.420693 − 0.742906I
2.96075 + 0.65298I −2.76291 − 1.36989I
u = −1.013520 + 0.559120I
a = 0.612654 + 0.784722I
b = −0.650003 − 0.671485I
−0.262441 + 0.570709I −9.39335 + 1.17121I
u = −1.013520 − 0.559120I
a = 0.612654 − 0.784722I
b = −0.650003 + 0.671485I
−0.262441 − 0.570709I −9.39335 − 1.17121I
u = 1.015720 + 0.612901I
a = −0.703890 + 0.704696I
b = 0.240215 − 0.895769I
1.70127 − 4.44241I −4.62824 + 5.23976I
u = 1.015720 − 0.612901I
a = −0.703890 − 0.704696I
b = 0.240215 + 0.895769I
1.70127 + 4.44241I −4.62824 − 5.23976I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.677310 + 1.062590I
a = 0.57929 + 1.84135I
b = −0.833778 − 0.933127I
10.12360 + 1.49333I −5.20253 − 0.24126I
u = 0.677310 − 1.062590I
a = 0.57929 − 1.84135I
b = −0.833778 + 0.933127I
10.12360 − 1.49333I −5.20253 + 0.24126I
u = 0.668113 + 1.109120I
a = 0.78027 − 1.56151I
b = −1.008260 + 0.845621I
9.55770 + 8.04939I −6.22396 − 5.15641I
u = 0.668113 − 1.109120I
a = 0.78027 + 1.56151I
b = −1.008260 − 0.845621I
9.55770 − 8.04939I −6.22396 + 5.15641I
u = 1.159060 + 0.639780I
a = 0.61767 − 1.49231I
b = 1.139350 + 0.458160I
−1.32139 − 9.31339I −10.43226 + 9.48781I
u = 1.159060 − 0.639780I
a = 0.61767 + 1.49231I
b = 1.139350 − 0.458160I
−1.32139 + 9.31339I −10.43226 − 9.48781I
u = 1.122650 + 0.803919I
a = 1.28271 − 0.73294I
b = −0.826847 + 0.971617I
8.67010 − 8.22857I −6.89988 + 3.89573I
u = 1.122650 − 0.803919I
a = 1.28271 + 0.73294I
b = −0.826847 − 0.971617I
8.67010 + 8.22857I −6.89988 − 3.89573I
u = −1.39743
a = 0.800635
b = 1.04024
−5.27800 −20.1480
u = 1.144620 + 0.817338I
a = −0.33093 + 2.27568I
b = −1.034060 − 0.861926I
7.9963 − 14.9529I −7.95884 + 8.20619I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.144620 − 0.817338I
a = −0.33093 − 2.27568I
b = −1.034060 + 0.861926I
7.9963 + 14.9529I −7.95884 − 8.20619I
u = −1.32133 + 0.60253I
a = −0.32353 − 1.55196I
b = −0.992690 + 0.658211I
−1.26748 + 5.76484I −12.40197 − 1.93041I
u = −1.32133 − 0.60253I
a = −0.32353 + 1.55196I
b = −0.992690 − 0.658211I
−1.26748 − 5.76484I −12.40197 + 1.93041I
u = −0.367172
a = 1.00307
b = −0.499556
−0.751981 −13.0200
7
II.
I
u
2
= h−6u
15
+21u
14
+· · ·+b+10, u
15
−6u
14
+· · ·+a+1, u
16
−4u
15
+· · ·−3u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
3
=
−u
15
+ 6u
14
+ ··· + 11u − 1
6u
15
− 21u
14
+ ··· + 12u − 10
a
12
=
−u
−u
3
+ u
a
2
=
5u
15
− 15u
14
+ ··· + 23u − 11
6u
15
− 21u
14
+ ··· + 12u − 10
a
1
=
−8u
15
+ 30u
14
+ ··· − 6u + 16
−3u
15
+ 11u
14
+ ··· − 5u + 10
a
5
=
−17u
15
+ 59u
14
+ ··· − 40u + 35
−10u
15
+ 35u
14
+ ··· − 20u + 20
a
8
=
2u
15
− 7u
14
+ ··· + 9u − 9
u
15
− 4u
14
+ ··· − 2u − 3
a
9
=
2u
15
− 7u
14
+ ··· + 9u − 10
u
15
− 4u
14
+ ··· − 2u − 2
a
10
=
u
3
u
5
− u
3
+ u
a
4
=
−16u
15
+ 56u
14
+ ··· − 37u + 33
−8u
15
+ 28u
14
+ ··· − 14u + 15
(ii) Obstruction class = 1
(iii) Cusp Shapes = 24u
15
− 81u
14
+ 50u
13
+ 205u
12
− 308u
11
− 190u
10
+ 653u
9
−
51u
8
− 732u
7
+ 325u
6
+ 487u
5
− 327u
4
− 186u
3
+ 183u
2
+ 37u − 37
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 6u
15
+ ··· − 10u + 1
c
2
u
16
− 3u
14
+ ··· − 5u
2
+ 1
c
3
u
16
+ u
15
+ ··· − u − 1
c
4
, c
7
u
16
+ u
15
+ ··· + u − 1
c
5
u
16
− 3u
14
+ ··· − 5u
2
+ 1
c
6
u
16
− 4u
15
+ ··· − 3u + 1
c
8
u
16
− u
15
+ ··· − 8u − 1
c
9
u
16
− u
15
+ ··· − u − 1
c
10
u
16
− 8u
15
+ ··· − 15u + 1
c
11
u
16
+ 4u
15
+ ··· + 3u + 1
c
12
u
16
+ u
15
+ ··· + 8u − 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 14y
15
+ ··· − 6y + 1
c
2
, c
5
y
16
− 6y
15
+ ··· − 10y + 1
c
3
y
16
− 13y
15
+ ··· + 25y + 1
c
4
, c
7
, c
9
y
16
− 13y
15
+ ··· − 9y + 1
c
6
, c
11
y
16
− 8y
15
+ ··· − 15y + 1
c
8
, c
12
y
16
+ 9y
15
+ ··· − 88y + 1
c
10
y
16
+ 20y
15
+ ··· − 31y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.709766 + 0.705344I
a = −0.887882 + 0.353548I
b = −0.601245 − 0.326299I
−2.08950 − 3.52175I −8.50730 + 9.07031I
u = 0.709766 − 0.705344I
a = −0.887882 − 0.353548I
b = −0.601245 + 0.326299I
−2.08950 + 3.52175I −8.50730 − 9.07031I
u = −1.05256
a = 2.33736
b = 0.930995
−8.18293 −21.4460
u = −0.953259 + 0.474374I
a = −0.62204 − 2.51263I
b = −0.964515 + 0.707349I
−3.82901 + 4.66397I −11.36785 − 5.44923I
u = −0.953259 − 0.474374I
a = −0.62204 + 2.51263I
b = −0.964515 − 0.707349I
−3.82901 − 4.66397I −11.36785 + 5.44923I
u = 1.023350 + 0.406048I
a = −0.813062 + 0.284492I
b = −1.053970 + 0.235975I
−3.87328 − 1.04203I −17.8883 + 0.9825I
u = 1.023350 − 0.406048I
a = −0.813062 − 0.284492I
b = −1.053970 − 0.235975I
−3.87328 + 1.04203I −17.8883 − 0.9825I
u = −0.780571 + 0.429913I
a = 1.97567 + 0.68038I
b = −0.759833 − 0.760705I
−3.18956 − 0.91432I −8.94555 − 0.72822I
u = −0.780571 − 0.429913I
a = 1.97567 − 0.68038I
b = −0.759833 + 0.760705I
−3.18956 + 0.91432I −8.94555 + 0.72822I
u = −0.656018
a = −4.43206
b = 0.525031
−6.47624 −0.995250
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.08165 + 0.99947I
a = −0.608758 + 1.080850I
b = 0.755790 − 0.644213I
−0.62149 − 1.50137I −13.1344 + 5.7705I
u = 1.08165 − 0.99947I
a = −0.608758 − 1.080850I
b = 0.755790 + 0.644213I
−0.62149 + 1.50137I −13.1344 − 5.7705I
u = 0.498658 + 0.050338I
a = 1.333420 − 0.022372I
b = 0.939536 + 0.925652I
5.74280 − 3.39525I −1.03709 + 3.22174I
u = 0.498658 − 0.050338I
a = 1.333420 + 0.022372I
b = 0.939536 − 0.925652I
5.74280 + 3.39525I −1.03709 − 3.22174I
u = 1.27470 + 0.89882I
a = 0.17000 − 1.67912I
b = 0.956222 + 0.637553I
−1.25971 − 6.51826I −12.8990 + 11.7858I
u = 1.27470 − 0.89882I
a = 0.17000 + 1.67912I
b = 0.956222 − 0.637553I
−1.25971 + 6.51826I −12.8990 − 11.7858I
12
III. I
u
3
= h2.20 × 10
33
a
9
u
2
− 2.29 × 10
35
a
8
u
2
+ · · · + 1.70 × 10
37
a − 5.02 ×
10
36
, −6a
8
u
2
+ 14a
7
u
2
+ · · · + 668a − 417, u
3
+ u
2
− 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
3
=
a
−0.0000462419a
9
u
2
+ 0.00481392a
8
u
2
+ ··· − 0.357057a + 0.105603
a
12
=
−u
u
2
+ u − 1
a
2
=
−0.0000462419a
9
u
2
+ 0.00481392a
8
u
2
+ ··· + 0.642943a + 0.105603
−0.0000462419a
9
u
2
+ 0.00481392a
8
u
2
+ ··· − 0.357057a + 0.105603
a
1
=
0.00475440a
9
u
2
+ 0.00480716a
8
u
2
+ ··· + 0.0172392a − 0.130341
−0.00112922a
9
u
2
+ 0.00379948a
8
u
2
+ ··· − 0.0267617a + 0.417054
a
5
=
−0.00191453a
9
u
2
+ 0.00196977a
8
u
2
+ ··· + 0.241462a + 0.176462
−0.00155225a
9
u
2
+ 0.00591527a
8
u
2
+ ··· + 0.265525a − 0.949030
a
8
=
−0.000908415a
9
u
2
− 0.00637770a
8
u
2
+ ··· − 0.765719a + 0.776006
0.00239576a
9
u
2
− 0.000899242a
8
u
2
+ ··· − 1.10079a + 0.879248
a
9
=
−0.00243411a
9
u
2
− 0.0183142a
8
u
2
+ ··· − 1.55079a + 0.788681
−0.00291032a
9
u
2
+ 0.00645185a
8
u
2
+ ··· − 1.78599a + 0.677141
a
10
=
−u
2
+ 1
u
2
a
4
=
−0.00229203a
9
u
2
− 0.0113418a
8
u
2
+ ··· + 1.51032a − 0.111646
−0.00770163a
9
u
2
+ 0.0107723a
8
u
2
+ ··· − 1.51618a − 0.830861
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00101199a
9
u
2
− 0.0550471a
8
u
2
+ ··· − 0.470919a − 12.5272
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
6
c
2
, c
5
(u
5
− u
4
+ u
2
+ u − 1)
6
c
3
u
30
+ u
29
+ ··· + 269958u − 26963
c
4
, c
7
, c
9
u
30
+ u
29
+ ··· − 10u − 11
c
6
, c
11
(u
3
+ u
2
− 1)
10
c
8
, c
12
u
30
+ 3u
29
+ ··· + 4930u − 289
c
10
(u
3
+ u
2
+ 2u + 1)
10
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
6
c
2
, c
5
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
6
c
3
y
30
+ 27y
29
+ ··· − 29765426100y + 727003369
c
4
, c
7
, c
9
y
30
− 9y
29
+ ··· + 516y + 121
c
6
, c
11
(y
3
− y
2
+ 2y −1)
10
c
8
, c
12
y
30
− 21y
29
+ ··· − 50794640y + 83521
c
10
(y
3
+ 3y
2
+ 2y −1)
10
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.283563 + 0.915777I
b = −0.758138 − 0.584034I
−0.090868 + 0.614153I −7.60456 + 1.24344I
u = −0.877439 + 0.744862I
a = 1.019500 + 0.839116I
b = −0.758138 − 0.584034I
−0.090868 + 0.614153I −7.60456 + 1.24344I
u = −0.877439 + 0.744862I
a = 0.038650 − 1.390540I
b = −0.758138 + 0.584034I
−0.09087 + 5.04209I −7.60456 − 7.20234I
u = −0.877439 + 0.744862I
a = 0.073356 − 0.330206I
b = 0.645200
−2.79286 + 2.82812I −16.0991 − 2.9794I
u = −0.877439 + 0.744862I
a = 1.24901 + 1.29138I
b = 0.645200
−2.79286 + 2.82812I −16.0991 − 2.9794I
u = −0.877439 + 0.744862I
a = −1.00422 − 1.60730I
b = 0.935538 + 0.903908I
9.04762 − 0.50362I −6.57151 − 0.61717I
u = −0.877439 + 0.744862I
a = −1.81399 − 0.55743I
b = 0.935538 + 0.903908I
9.04762 − 0.50362I −6.57151 − 0.61717I
u = −0.877439 + 0.744862I
a = −0.58303 + 2.03306I
b = 0.935538 − 0.903908I
9.04762 + 6.15987I −6.57151 − 5.34173I
u = −0.877439 + 0.744862I
a = −0.47568 − 2.62318I
b = −0.758138 + 0.584034I
−0.09087 + 5.04209I −7.60456 − 7.20234I
u = −0.877439 + 0.744862I
a = 0.45796 + 2.91906I
b = 0.935538 − 0.903908I
9.04762 + 6.15987I −6.57151 − 5.34173I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 − 0.744862I
a = 0.283563 − 0.915777I
b = −0.758138 + 0.584034I
−0.090868 − 0.614153I −7.60456 − 1.24344I
u = −0.877439 − 0.744862I
a = 1.019500 − 0.839116I
b = −0.758138 + 0.584034I
−0.090868 − 0.614153I −7.60456 − 1.24344I
u = −0.877439 − 0.744862I
a = 0.038650 + 1.390540I
b = −0.758138 − 0.584034I
−0.09087 − 5.04209I −7.60456 + 7.20234I
u = −0.877439 − 0.744862I
a = 0.073356 + 0.330206I
b = 0.645200
−2.79286 − 2.82812I −16.0991 + 2.9794I
u = −0.877439 − 0.744862I
a = 1.24901 − 1.29138I
b = 0.645200
−2.79286 − 2.82812I −16.0991 + 2.9794I
u = −0.877439 − 0.744862I
a = −1.00422 + 1.60730I
b = 0.935538 − 0.903908I
9.04762 + 0.50362I −6.57151 + 0.61717I
u = −0.877439 − 0.744862I
a = −1.81399 + 0.55743I
b = 0.935538 − 0.903908I
9.04762 + 0.50362I −6.57151 + 0.61717I
u = −0.877439 − 0.744862I
a = −0.58303 − 2.03306I
b = 0.935538 + 0.903908I
9.04762 − 6.15987I −6.57151 + 5.34173I
u = −0.877439 − 0.744862I
a = −0.47568 + 2.62318I
b = −0.758138 − 0.584034I
−0.09087 − 5.04209I −7.60456 + 7.20234I
u = −0.877439 − 0.744862I
a = 0.45796 − 2.91906I
b = 0.935538 + 0.903908I
9.04762 − 6.15987I −6.57151 + 5.34173I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.754878
a = −0.152878 + 1.046890I
b = 0.935538 − 0.903908I
4.91003 + 3.33174I −13.10077 − 2.36228I
u = 0.754878
a = −0.152878 − 1.046890I
b = 0.935538 + 0.903908I
4.91003 − 3.33174I −13.10077 + 2.36228I
u = 0.754878
a = 0.997843 + 0.652805I
b = −0.758138 + 0.584034I
−4.22845 + 2.21397I −14.1338 − 4.2229I
u = 0.754878
a = 0.997843 − 0.652805I
b = −0.758138 − 0.584034I
−4.22845 − 2.21397I −14.1338 + 4.2229I
u = 0.754878
a = 1.73543 + 0.43939I
b = 0.935538 + 0.903908I
4.91003 − 3.33174I −13.10077 + 2.36228I
u = 0.754878
a = 1.73543 − 0.43939I
b = 0.935538 − 0.903908I
4.91003 + 3.33174I −13.10077 − 2.36228I
u = 0.754878
a = −2.59655
b = 0.645200
−6.93044 −22.6280
u = 0.754878
a = −3.03987 + 1.63046I
b = −0.758138 − 0.584034I
−4.22845 − 2.21397I −14.1338 + 4.2229I
u = 0.754878
a = −3.03987 − 1.63046I
b = −0.758138 + 0.584034I
−4.22845 + 2.21397I −14.1338 − 4.2229I
u = 0.754878
a = 6.02526
b = 0.645200
−6.93044 −22.6280
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
6
)(u
16
− 6u
15
+ ··· − 10u + 1)
· (u
24
+ 7u
23
+ ··· + 352u + 64)
c
2
((u
5
− u
4
+ u
2
+ u − 1)
6
)(u
16
− 3u
14
+ ··· − 5u
2
+ 1)
· (u
24
+ 7u
23
+ ··· − 40u − 8)
c
3
(u
16
+ u
15
+ ··· − u − 1)(u
24
+ u
23
+ ··· + 4u + 1)
· (u
30
+ u
29
+ ··· + 269958u − 26963)
c
4
, c
7
(u
16
+ u
15
+ ··· + u − 1)(u
24
− u
23
+ ··· + 5u
2
− 1)
· (u
30
+ u
29
+ ··· − 10u − 11)
c
5
((u
5
− u
4
+ u
2
+ u − 1)
6
)(u
16
− 3u
14
+ ··· − 5u
2
+ 1)
· (u
24
+ 7u
23
+ ··· − 40u − 8)
c
6
((u
3
+ u
2
− 1)
10
)(u
16
− 4u
15
+ ··· − 3u + 1)(u
24
− 9u
23
+ ··· − 144u + 32)
c
8
(u
16
− u
15
+ ··· − 8u − 1)(u
24
+ 5u
23
+ ··· + 21u + 1)
· (u
30
+ 3u
29
+ ··· + 4930u − 289)
c
9
(u
16
− u
15
+ ··· − u − 1)(u
24
− u
23
+ ··· + 5u
2
− 1)
· (u
30
+ u
29
+ ··· − 10u − 11)
c
10
((u
3
+ u
2
+ 2u + 1)
10
)(u
16
− 8u
15
+ ··· − 15u + 1)
· (u
24
+ 9u
23
+ ··· + 9984u + 1024)
c
11
((u
3
+ u
2
− 1)
10
)(u
16
+ 4u
15
+ ··· + 3u + 1)(u
24
− 9u
23
+ ··· − 144u + 32)
c
12
(u
16
+ u
15
+ ··· + 8u − 1)(u
24
+ 5u
23
+ ··· + 21u + 1)
· (u
30
+ 3u
29
+ ··· + 4930u − 289)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
6
)(y
16
+ 14y
15
+ ··· − 6y + 1)
· (y
24
+ 21y
23
+ ··· − 45568y + 4096)
c
2
, c
5
((y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
6
)(y
16
− 6y
15
+ ··· − 10y + 1)
· (y
24
− 7y
23
+ ··· − 352y + 64)
c
3
(y
16
− 13y
15
+ ··· + 25y + 1)(y
24
+ 49y
23
+ ··· + 36y
2
+ 1)
· (y
30
+ 27y
29
+ ··· − 29765426100y + 727003369)
c
4
, c
7
, c
9
(y
16
− 13y
15
+ ··· − 9y + 1)(y
24
+ y
23
+ ··· − 10y + 1)
· (y
30
− 9y
29
+ ··· + 516y + 121)
c
6
, c
11
((y
3
− y
2
+ 2y −1)
10
)(y
16
− 8y
15
+ ··· − 15y + 1)
· (y
24
− 9y
23
+ ··· − 9984y + 1024)
c
8
, c
12
(y
16
+ 9y
15
+ ··· − 88y + 1)(y
24
− 45y
23
+ ··· − 81y + 1)
· (y
30
− 21y
29
+ ··· − 50794640y + 83521)
c
10
((y
3
+ 3y
2
+ 2y −1)
10
)(y
16
+ 20y
15
+ ··· − 31y + 1)
· (y
24
+ 23y
23
+ ··· − 52625408y + 1048576)
20
