12n
0481
(K12n
0481
)
A knot diagram
1
Linearized knot diagam
3 6 1 10 8 2 11 1 3 5 7 10
Solving Sequence
3,6
2 7 1
4,10
9 8 5 12 11
c
2
c
6
c
1
c
3
c
9
c
8
c
5
c
12
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
23
+ 2u
22
+ ··· + 2b + 2, u
23
+ 4u
22
+ ··· + 4a + 12, u
24
+ 6u
23
+ ··· + 14u + 4i
I
u
2
= hu
14
− u
13
+ 2u
12
− 2u
11
+ 6u
10
− 5u
9
+ 7u
8
− 7u
7
+ 9u
6
− 8u
5
+ 7u
4
− 7u
3
+ 4u
2
+ b − 3u + 2,
− 2u
15
+ 2u
14
+ ··· + a − 1,
u
16
− u
15
+ 3u
14
− 2u
13
+ 8u
12
− 5u
11
+ 13u
10
− 6u
9
+ 17u
8
− 7u
7
+ 17u
6
− 6u
5
+ 12u
4
− 3u
3
+ 6u
2
− u + 1i
I
u
3
= h−59u
5
a
3
+ 81u
5
a
2
+ ··· − 15a + 343, u
5
a
3
+ 4u
5
a
2
+ ··· − 4a + 8, u
6
− u
5
+ u
4
+ 2u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 64 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
= hu
23
+2u
22
+· · ·+2b+2, u
23
+4u
22
+· · ·+4a+12, u
24
+6u
23
+· · ·+14u+4i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
−
1
4
u
23
− u
22
+ ··· −
31
4
u − 3
−
1
2
u
23
− u
22
+ ··· −
1
2
u − 1
a
9
=
−
3
4
u
23
− 2u
22
+ ··· −
33
4
u − 4
−
1
2
u
23
− u
22
+ ··· −
1
2
u − 1
a
8
=
3
4
u
23
− u
22
+ ··· −
87
4
u − 9
5
2
u
23
+ 8u
22
+ ··· −
17
2
u − 5
a
5
=
−
1
2
u
23
−
5
2
u
22
+ ··· −
7
2
u −
1
2
−
1
2
u
23
− 3u
22
+ ··· −
11
2
u − 2
a
12
=
u
23
−
3
2
u
22
+ ··· − 34u −
29
2
15
2
u
23
+ 34u
22
+ ··· +
59
2
u + 4
a
11
=
−
1
2
u
22
− 2u
21
+ ··· − 3u −
1
2
−
7
2
u
23
− 19u
22
+ ··· −
67
2
u − 10
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
23
+ 16u
22
+ 53u
21
+ 118u
20
+ 215u
19
+ 322u
18
+ 436u
17
+
502u
16
+ 531u
15
+ 480u
14
+ 441u
13
+ 369u
12
+ 374u
11
+ 355u
10
+ 392u
9
+ 344u
8
+
324u
7
+ 245u
6
+ 196u
5
+ 117u
4
+ 92u
3
+ 68u
2
+ 48u + 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
24
+ 6u
23
+ ··· + 52u + 16
c
2
, c
6
u
24
− 6u
23
+ ··· − 14u + 4
c
4
, c
5
, c
10
u
24
− u
23
+ ··· + 2u + 1
c
7
, c
11
u
24
− 15u
23
+ ··· − 544u + 64
c
8
u
24
− 2u
23
+ ··· − 99u + 41
c
9
u
24
+ 29u
22
+ ··· + 4u + 1
c
12
u
24
+ 3u
23
+ ··· + 16u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
24
+ 26y
23
+ ··· + 5520y + 256
c
2
, c
6
y
24
+ 6y
23
+ ··· + 52y + 16
c
4
, c
5
, c
10
y
24
− 11y
23
+ ··· − 6y + 1
c
7
, c
11
y
24
+ 7y
23
+ ··· + 48128y + 4096
c
8
y
24
− 54y
23
+ ··· + 14635y + 1681
c
9
y
24
+ 58y
23
+ ··· + 8y + 1
c
12
y
24
− 45y
23
+ ··· − 10y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.386803 + 0.939568I
a = 0.546906 + 0.473576I
b = 0.233412 − 0.697036I
1.14776 + 2.44837I −4.92674 − 7.51322I
u = 0.386803 − 0.939568I
a = 0.546906 − 0.473576I
b = 0.233412 + 0.697036I
1.14776 − 2.44837I −4.92674 + 7.51322I
u = 0.848616 + 0.384852I
a = 0.386852 − 0.278466I
b = −0.435457 + 0.087430I
−0.11794 − 4.13281I 1.46214 + 3.63821I
u = 0.848616 − 0.384852I
a = 0.386852 + 0.278466I
b = −0.435457 − 0.087430I
−0.11794 + 4.13281I 1.46214 − 3.63821I
u = 0.040508 + 1.108090I
a = −0.488177 + 0.024616I
b = 0.047052 + 0.539945I
−5.52346 − 2.09827I −4.00959 + 3.29797I
u = 0.040508 − 1.108090I
a = −0.488177 − 0.024616I
b = 0.047052 − 0.539945I
−5.52346 + 2.09827I −4.00959 − 3.29797I
u = −0.655613 + 0.578423I
a = 0.092968 − 0.792314I
b = −0.397342 − 0.573226I
−0.030667 − 0.985462I 0.04895 + 2.32635I
u = −0.655613 − 0.578423I
a = 0.092968 + 0.792314I
b = −0.397342 + 0.573226I
−0.030667 + 0.985462I 0.04895 − 2.32635I
u = 0.520277 + 1.085810I
a = −0.285416 − 0.342185I
b = −0.223052 + 0.487939I
−2.45634 + 9.15615I −2.49184 − 8.31719I
u = 0.520277 − 1.085810I
a = −0.285416 + 0.342185I
b = −0.223052 − 0.487939I
−2.45634 − 9.15615I −2.49184 + 8.31719I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.658406 + 1.013050I
a = 0.733469 − 0.062319I
b = 0.419788 − 0.784073I
−1.23495 − 4.21264I −0.00163 + 4.38379I
u = −0.658406 − 1.013050I
a = 0.733469 + 0.062319I
b = 0.419788 + 0.784073I
−1.23495 + 4.21264I −0.00163 − 4.38379I
u = 0.581550 + 0.531676I
a = −0.473776 + 0.623048I
b = 0.606784 − 0.110438I
2.58155 + 1.28427I 4.89493 + 0.75788I
u = 0.581550 − 0.531676I
a = −0.473776 − 0.623048I
b = 0.606784 + 0.110438I
2.58155 − 1.28427I 4.89493 − 0.75788I
u = −0.932185 + 0.856145I
a = −0.97723 + 1.89200I
b = 0.70887 + 2.60034I
10.05900 − 0.11341I 1.099246 + 0.004662I
u = −0.932185 − 0.856145I
a = −0.97723 − 1.89200I
b = 0.70887 − 2.60034I
10.05900 + 0.11341I 1.099246 − 0.004662I
u = −0.973395 + 0.865459I
a = 1.26433 − 1.54946I
b = −0.11030 − 2.60246I
8.07660 + 7.22190I 0.55503 − 3.04448I
u = −0.973395 − 0.865459I
a = 1.26433 + 1.54946I
b = −0.11030 + 2.60246I
8.07660 − 7.22190I 0.55503 + 3.04448I
u = −0.858450 + 1.000080I
a = −1.68242 + 1.24146I
b = −0.20271 + 2.74829I
9.58925 − 6.48997I 0.12796 + 4.63982I
u = −0.858450 − 1.000080I
a = −1.68242 − 1.24146I
b = −0.20271 − 2.74829I
9.58925 + 6.48997I 0.12796 − 4.63982I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.886343 + 1.020850I
a = 1.33428 − 1.55406I
b = −0.40384 − 2.73953I
7.5650 − 14.0430I −0.21532 + 7.35996I
u = −0.886343 − 1.020850I
a = 1.33428 + 1.55406I
b = −0.40384 + 2.73953I
7.5650 + 14.0430I −0.21532 − 7.35996I
u = −0.413363 + 0.497922I
a = 0.298212 − 0.736016I
b = −0.243208 − 0.452728I
−0.046922 − 1.057330I −0.54314 + 5.53414I
u = −0.413363 − 0.497922I
a = 0.298212 + 0.736016I
b = −0.243208 + 0.452728I
−0.046922 + 1.057330I −0.54314 − 5.53414I
7
II.
I
u
2
= hu
14
−u
13
+· · · +b + 2, −2u
15
+2u
14
+· · · +a − 1, u
16
−u
15
+· · · −u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
2u
15
− 2u
14
+ ··· + 8u + 1
−u
14
+ u
13
+ ··· + 3u − 2
a
9
=
2u
15
− 3u
14
+ ··· + 11u − 1
−u
14
+ u
13
+ ··· + 3u − 2
a
8
=
2u
15
− 2u
14
+ ··· − u
2
+ 8u
u
15
− 2u
14
+ ··· + 5u − 3
a
5
=
−2u
15
+ u
14
+ ··· − 9u − 2
−u
15
+ u
14
+ ··· − 5u + 2
a
12
=
−u
14
+ u
13
+ ··· − u − 4
−u
15
+ u
14
+ ··· − 11u
3
− 5u
a
11
=
−u
15
− 2u
13
+ ··· − 3u − 3
−2u
15
+ 2u
14
+ ··· − 6u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −2u
14
+u
13
−7u
12
+2u
11
−15u
10
+3u
9
−28u
8
+3u
7
−29u
6
+2u
5
−32u
4
+3u
3
−18u
2
+u−10
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 5u
15
+ ··· − 11u + 1
c
2
u
16
− u
15
+ ··· − u + 1
c
3
u
16
+ 5u
15
+ ··· + 11u + 1
c
4
u
16
+ u
15
+ ··· + 4u + 1
c
5
, c
10
u
16
− u
15
+ ··· − 4u + 1
c
6
u
16
+ u
15
+ ··· + u + 1
c
7
u
16
− 2u
15
+ ··· + 3u + 1
c
8
u
16
− 2u
15
+ ··· + 63u + 47
c
9
u
16
− 2u
14
+ ··· + 2u + 1
c
11
u
16
+ 2u
15
+ ··· − 3u + 1
c
12
u
16
− 3u
15
+ ··· + 2u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
16
+ 17y
15
+ ··· − 13y + 1
c
2
, c
6
y
16
+ 5y
15
+ ··· + 11y + 1
c
4
, c
5
, c
10
y
16
− 13y
15
+ ··· + 2y + 1
c
7
, c
11
y
16
+ 6y
15
+ ··· − 3y + 1
c
8
y
16
− 14y
14
+ ··· + 10319y + 2209
c
9
y
16
− 4y
15
+ ··· − 8y + 1
c
12
y
16
− 3y
15
+ ··· + 6y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.711929 + 0.760358I
a = −1.02576 + 1.48549I
b = −1.85977 + 0.27762I
−2.76244 − 0.95558I −1.206885 + 0.230523I
u = 0.711929 − 0.760358I
a = −1.02576 − 1.48549I
b = −1.85977 − 0.27762I
−2.76244 + 0.95558I −1.206885 − 0.230523I
u = 0.053541 + 0.950247I
a = −0.292929 − 0.930103I
b = 0.868144 − 0.328154I
−7.15170 − 1.53675I −10.75515 + 0.98813I
u = 0.053541 − 0.950247I
a = −0.292929 + 0.930103I
b = 0.868144 + 0.328154I
−7.15170 + 1.53675I −10.75515 − 0.98813I
u = −0.435996 + 0.803743I
a = 0.254017 − 0.569932I
b = 0.347329 + 0.452652I
1.53953 − 1.76071I 0.705761 + 0.775767I
u = −0.435996 − 0.803743I
a = 0.254017 + 0.569932I
b = 0.347329 − 0.452652I
1.53953 + 1.76071I 0.705761 − 0.775767I
u = −0.825406 + 0.738696I
a = −0.382034 − 0.004020I
b = 0.318303 − 0.278889I
−1.33661 − 2.36299I −2.87352 + 3.64592I
u = −0.825406 − 0.738696I
a = −0.382034 + 0.004020I
b = 0.318303 + 0.278889I
−1.33661 + 2.36299I −2.87352 − 3.64592I
u = 0.682235 + 0.952556I
a = 1.22003 − 0.92717I
b = 1.71553 + 0.52960I
−3.35855 + 6.31371I −2.68318 − 5.80907I
u = 0.682235 − 0.952556I
a = 1.22003 + 0.92717I
b = 1.71553 − 0.52960I
−3.35855 − 6.31371I −2.68318 + 5.80907I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.724914 + 1.000500I
a = 0.270608 + 0.089531I
b = −0.285742 + 0.205840I
−2.17699 − 3.46039I −4.93993 + 0.90325I
u = −0.724914 − 1.000500I
a = 0.270608 − 0.089531I
b = −0.285742 − 0.205840I
−2.17699 + 3.46039I −4.93993 − 0.90325I
u = 0.922397 + 0.947682I
a = −1.20870 − 1.44097I
b = 0.25067 − 2.47461I
10.66490 + 3.39525I 0.77812 − 2.38843I
u = 0.922397 − 0.947682I
a = −1.20870 + 1.44097I
b = 0.25067 + 2.47461I
10.66490 − 3.39525I 0.77812 + 2.38843I
u = 0.116214 + 0.507066I
a = 0.66477 + 2.82354I
b = −1.35447 + 0.66522I
−5.28775 + 2.24439I −7.02522 − 0.50668I
u = 0.116214 − 0.507066I
a = 0.66477 − 2.82354I
b = −1.35447 − 0.66522I
−5.28775 − 2.24439I −7.02522 + 0.50668I
12
III. I
u
3
= h−59u
5
a
3
+ 81u
5
a
2
+ · · · − 15a + 343, u
5
a
3
+ 4u
5
a
2
+ · · · − 4a +
8, u
6
− u
5
+ u
4
+ 2u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
4
=
u
4
+ u
2
+ 1
u
4
a
10
=
a
0.337143a
3
u
5
− 0.462857a
2
u
5
+ ··· + 0.0857143a − 1.96000
a
9
=
0.337143a
3
u
5
− 0.462857a
2
u
5
+ ··· + 1.08571a − 1.96000
0.337143a
3
u
5
− 0.462857a
2
u
5
+ ··· + 0.0857143a − 1.96000
a
8
=
−0.177143a
3
u
5
+ 0.0228571a
2
u
5
+ ··· + 0.514286a − 1.36000
0.160000a
3
u
5
− 0.440000a
2
u
5
+ ··· − 0.400000a − 3.32000
a
5
=
0.0971429a
3
u
5
+ 0.697143a
2
u
5
+ ··· + 0.685714a + 1.52000
3
35
u
5
a
3
+
3
35
u
5
a
2
+ ··· +
3
7
a +
12
5
a
12
=
−0.0285714a
3
u
5
− 0.0285714a
2
u
5
+ ··· + 0.857143a + 3.20000
0.0685714a
3
u
5
+ 0.668571a
2
u
5
+ ··· + 1.54286a + 2.72000
a
11
=
−0.0742857a
3
u
5
− 0.474286a
2
u
5
+ ··· + 0.828571a + 2.72000
−0.102857a
3
u
5
− 0.502857a
2
u
5
+ ··· + 1.68571a + 1.92000
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
144
175
u
5
a
3
−
4
175
u
5
a
2
+ ··· +
52
35
a −
66
25
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
6
+ u
5
+ 5u
4
+ 4u
3
+ 6u
2
+ 3u + 1)
4
c
2
, c
6
(u
6
+ u
5
+ u
4
+ 2u
2
+ u + 1)
4
c
4
, c
5
, c
10
u
24
+ u
23
+ ··· − 60u + 49
c
7
, c
11
(u
2
+ u + 1)
12
c
8
u
24
− u
23
+ ··· − 13006u + 1333
c
9
u
24
+ u
23
+ ··· − 31002u + 7693
c
12
u
24
+ 3u
23
+ ··· + 1484u + 193
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y
6
+ 9y
5
+ 29y
4
+ 40y
3
+ 22y
2
+ 3y + 1)
4
c
2
, c
6
(y
6
+ y
5
+ 5y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
4
c
4
, c
5
, c
10
y
24
− 9y
23
+ ··· + 6984y + 2401
c
7
, c
11
(y
2
+ y + 1)
12
c
8
y
24
− 29y
23
+ ··· − 9462636y + 1776889
c
9
y
24
+ 31y
23
+ ··· − 496651436y + 59182249
c
12
y
24
− 21y
23
+ ··· + 485848y + 37249
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.716019 + 0.809696I
a = 0.176965 − 0.992700I
b = −0.974499 − 0.266636I
−0.291980 − 0.626084I −0.418854 − 0.066014I
u = −0.716019 + 0.809696I
a = −0.412453 − 0.838801I
b = −0.677074 − 0.854080I
−0.291980 − 0.626084I −0.418854 − 0.066014I
u = −0.716019 + 0.809696I
a = 1.168780 + 0.614777I
b = 0.461703 − 0.363781I
−0.29198 − 4.68585I −0.41885 + 6.86219I
u = −0.716019 + 0.809696I
a = 0.535089 + 0.097035I
b = 1.33465 − 0.50617I
−0.29198 − 4.68585I −0.41885 + 6.86219I
u = −0.716019 − 0.809696I
a = 0.176965 + 0.992700I
b = −0.974499 + 0.266636I
−0.291980 + 0.626084I −0.418854 + 0.066014I
u = −0.716019 − 0.809696I
a = −0.412453 + 0.838801I
b = −0.677074 + 0.854080I
−0.291980 + 0.626084I −0.418854 + 0.066014I
u = −0.716019 − 0.809696I
a = 1.168780 − 0.614777I
b = 0.461703 + 0.363781I
−0.29198 + 4.68585I −0.41885 − 6.86219I
u = −0.716019 − 0.809696I
a = 0.535089 − 0.097035I
b = 1.33465 + 0.50617I
−0.29198 + 4.68585I −0.41885 − 6.86219I
u = 0.283231 + 0.633899I
a = −0.168030 + 0.836853I
b = −2.00423 − 0.05495I
−5.19289 − 0.92118I −5.53615 − 2.71707I
u = 0.283231 + 0.633899I
a = −0.78124 + 1.88064I
b = −0.86094 + 1.36524I
−5.19289 + 3.13859I −5.53615 − 9.64527I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.283231 + 0.633899I
a = −1.28946 − 1.93430I
b = 1.413410 − 0.037425I
−5.19289 + 3.13859I −5.53615 − 9.64527I
u = 0.283231 + 0.633899I
a = 1.24986 − 2.60330I
b = 0.578072 − 0.130508I
−5.19289 − 0.92118I −5.53615 − 2.71707I
u = 0.283231 − 0.633899I
a = −0.168030 − 0.836853I
b = −2.00423 + 0.05495I
−5.19289 + 0.92118I −5.53615 + 2.71707I
u = 0.283231 − 0.633899I
a = −0.78124 − 1.88064I
b = −0.86094 − 1.36524I
−5.19289 − 3.13859I −5.53615 + 9.64527I
u = 0.283231 − 0.633899I
a = −1.28946 + 1.93430I
b = 1.413410 + 0.037425I
−5.19289 − 3.13859I −5.53615 + 9.64527I
u = 0.283231 − 0.633899I
a = 1.24986 + 2.60330I
b = 0.578072 + 0.130508I
−5.19289 + 0.92118I −5.53615 + 2.71707I
u = 0.932789 + 0.951611I
a = −0.96648 − 1.44906I
b = 0.36444 − 2.60092I
10.41970 + 5.45709I −0.04500 − 5.71634I
u = 0.932789 + 0.951611I
a = 1.13707 + 1.36590I
b = 0.10273 + 2.42307I
10.41970 + 1.39732I −0.044996 + 1.211865I
u = 0.932789 + 0.951611I
a = −1.35254 − 1.21783I
b = 0.23916 − 2.35614I
10.41970 + 1.39732I −0.044996 + 1.211865I
u = 0.932789 + 0.951611I
a = 1.20244 + 1.56163I
b = −0.47742 + 2.27137I
10.41970 + 5.45709I −0.04500 − 5.71634I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.932789 − 0.951611I
a = −0.96648 + 1.44906I
b = 0.36444 + 2.60092I
10.41970 − 5.45709I −0.04500 + 5.71634I
u = 0.932789 − 0.951611I
a = 1.13707 − 1.36590I
b = 0.10273 − 2.42307I
10.41970 − 1.39732I −0.044996 − 1.211865I
u = 0.932789 − 0.951611I
a = −1.35254 + 1.21783I
b = 0.23916 + 2.35614I
10.41970 − 1.39732I −0.044996 − 1.211865I
u = 0.932789 − 0.951611I
a = 1.20244 − 1.56163I
b = −0.47742 − 2.27137I
10.41970 − 5.45709I −0.04500 + 5.71634I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
+ u
5
+ 5u
4
+ 4u
3
+ 6u
2
+ 3u + 1)
4
)(u
16
− 5u
15
+ ··· − 11u + 1)
· (u
24
+ 6u
23
+ ··· + 52u + 16)
c
2
((u
6
+ u
5
+ u
4
+ 2u
2
+ u + 1)
4
)(u
16
− u
15
+ ··· − u + 1)
· (u
24
− 6u
23
+ ··· − 14u + 4)
c
3
((u
6
+ u
5
+ 5u
4
+ 4u
3
+ 6u
2
+ 3u + 1)
4
)(u
16
+ 5u
15
+ ··· + 11u + 1)
· (u
24
+ 6u
23
+ ··· + 52u + 16)
c
4
(u
16
+ u
15
+ ··· + 4u + 1)(u
24
− u
23
+ ··· + 2u + 1)
· (u
24
+ u
23
+ ··· − 60u + 49)
c
5
, c
10
(u
16
− u
15
+ ··· − 4u + 1)(u
24
− u
23
+ ··· + 2u + 1)
· (u
24
+ u
23
+ ··· − 60u + 49)
c
6
((u
6
+ u
5
+ u
4
+ 2u
2
+ u + 1)
4
)(u
16
+ u
15
+ ··· + u + 1)
· (u
24
− 6u
23
+ ··· − 14u + 4)
c
7
((u
2
+ u + 1)
12
)(u
16
− 2u
15
+ ··· + 3u + 1)
· (u
24
− 15u
23
+ ··· − 544u + 64)
c
8
(u
16
− 2u
15
+ ··· + 63u + 47)(u
24
− 2u
23
+ ··· − 99u + 41)
· (u
24
− u
23
+ ··· − 13006u + 1333)
c
9
(u
16
− 2u
14
+ ··· + 2u + 1)(u
24
+ 29u
22
+ ··· + 4u + 1)
· (u
24
+ u
23
+ ··· − 31002u + 7693)
c
11
((u
2
+ u + 1)
12
)(u
16
+ 2u
15
+ ··· − 3u + 1)
· (u
24
− 15u
23
+ ··· − 544u + 64)
c
12
(u
16
− 3u
15
+ ··· + 2u + 1)(u
24
+ 3u
23
+ ··· + 16u + 1)
· (u
24
+ 3u
23
+ ··· + 1484u + 193)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y
6
+ 9y
5
+ 29y
4
+ 40y
3
+ 22y
2
+ 3y + 1)
4
· (y
16
+ 17y
15
+ ··· − 13y + 1)(y
24
+ 26y
23
+ ··· + 5520y + 256)
c
2
, c
6
((y
6
+ y
5
+ 5y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
4
)(y
16
+ 5y
15
+ ··· + 11y + 1)
· (y
24
+ 6y
23
+ ··· + 52y + 16)
c
4
, c
5
, c
10
(y
16
− 13y
15
+ ··· + 2y + 1)(y
24
− 11y
23
+ ··· − 6y + 1)
· (y
24
− 9y
23
+ ··· + 6984y + 2401)
c
7
, c
11
((y
2
+ y + 1)
12
)(y
16
+ 6y
15
+ ··· − 3y + 1)
· (y
24
+ 7y
23
+ ··· + 48128y + 4096)
c
8
(y
16
− 14y
14
+ ··· + 10319y + 2209)
· (y
24
− 54y
23
+ ··· + 14635y + 1681)
· (y
24
− 29y
23
+ ··· − 9462636y + 1776889)
c
9
(y
16
− 4y
15
+ ··· − 8y + 1)
· (y
24
+ 31y
23
+ ··· − 496651436y + 59182249)
· (y
24
+ 58y
23
+ ··· + 8y + 1)
c
12
(y
16
− 3y
15
+ ··· + 6y + 1)(y
24
− 45y
23
+ ··· − 10y + 1)
· (y
24
− 21y
23
+ ··· + 485848y + 37249)
20
