11a
304
(K11a
304
)
A knot diagram
1
Linearized knot diagam
5 10 1 7 2 9 4 11 6 3 8
Solving Sequence
2,10
3
6,11
5 1 9 7 4 8
c
2
c
10
c
5
c
1
c
9
c
6
c
4
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hb + u, −3859u
17
+ 8014u
16
+ ··· + 13433a − 31560, u
18
− 9u
16
+ ··· + 2u − 1i
I
u
2
= h−6.09740 × 10
97
u
47
+ 2.58938 × 10
98
u
46
+ ··· + 2.24272 × 10
98
b − 1.38856 × 10
100
,
1.06648 × 10
100
u
47
− 4.25205 × 10
100
u
46
+ ··· + 7.15429 × 10
100
a + 2.73856 × 10
102
,
u
48
− 3u
47
+ ··· + 2258u + 319i
I
u
3
= hb + u, u
7
− u
6
− 4u
5
+ 3u
4
+ 5u
3
− 4u
2
+ a + 1, u
8
− 4u
6
+ 6u
4
− u
3
− 3u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 74 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
= hb+u, −3859u
17
+8014u
16
+· · ·+13433a−31560, u
18
−9u
16
+· · ·+2u−1i
(i) Arc colorings
a
2
=
1
0
a
10
=
0
u
a
3
=
1
u
2
a
6
=
0.287278u
17
− 0.596590u
16
+ ··· + 2.96665u + 2.34944
−u
a
11
=
−u
−u
3
+ u
a
5
=
0.287278u
17
− 0.596590u
16
+ ··· + 1.96665u + 2.34944
−u
a
1
=
−0.596590u
17
+ 0.330157u
16
+ ··· + 1.77488u + 1.28728
−u
2
a
9
=
0.581553u
17
− 0.0745180u
16
+ ··· − 7.40646u + 0.419489
0.330157u
17
− 0.592868u
16
+ ··· + 2.48046u − 0.596590
a
7
=
−1.20948u
17
+ 0.0859823u
16
+ ··· + 3.46899u + 0.746743
−0.0831534u
17
− 0.239857u
16
+ ··· − 1.74987u + 0.522073
a
4
=
−0.722102u
17
+ 0.840095u
16
+ ··· − 0.833246u + 1.68138
−0.833991u
17
+ 1.04913u
16
+ ··· − 2.01772u + 0.712425
a
8
=
0.661877u
17
+ 0.0748158u
16
+ ··· − 7.07243u + 0.584828
0.186407u
17
− 0.456041u
16
+ ··· + 1.92809u − 0.612596
a
8
=
0.661877u
17
+ 0.0748158u
16
+ ··· − 7.07243u + 0.584828
0.186407u
17
− 0.456041u
16
+ ··· + 1.92809u − 0.612596
(ii) Obstruction class = −1
(iii) Cusp Shapes =
37965
13433
u
17
−
30147
13433
u
16
+ ··· −
4675
1919
u −
54291
13433
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
10
u
18
− 9u
16
+ ··· + 2u − 1
c
3
u
18
− 17u
17
+ ··· + 640u − 64
c
4
, c
7
, c
8
c
11
u
18
− u
17
+ ··· + 4u + 1
c
6
, c
9
u
18
+ 11u
17
+ ··· + 208u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
y
18
− 18y
17
+ ··· + 6y + 1
c
3
y
18
− 3y
17
+ ··· − 24576y + 4096
c
4
, c
7
, c
8
c
11
y
18
+ 13y
17
+ ··· − 14y + 1
c
6
, c
9
y
18
+ 11y
17
+ ··· − 12160y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.408078 + 0.786624I
a = 0.191327 + 1.032300I
b = −0.408078 − 0.786624I
6.34892 + 0.61291I −0.81864 + 1.96169I
u = 0.408078 − 0.786624I
a = 0.191327 − 1.032300I
b = −0.408078 + 0.786624I
6.34892 − 0.61291I −0.81864 − 1.96169I
u = −1.181090 + 0.239212I
a = −0.11707 + 1.45553I
b = 1.181090 − 0.239212I
−5.93754 − 0.90931I −12.67105 + 3.59251I
u = −1.181090 − 0.239212I
a = −0.11707 − 1.45553I
b = 1.181090 + 0.239212I
−5.93754 + 0.90931I −12.67105 − 3.59251I
u = 0.108330 + 0.747006I
a = −1.32407 + 0.67886I
b = −0.108330 − 0.747006I
5.38862 + 5.69558I −1.81453 − 3.55021I
u = 0.108330 − 0.747006I
a = −1.32407 − 0.67886I
b = −0.108330 + 0.747006I
5.38862 − 5.69558I −1.81453 + 3.55021I
u = −1.275010 + 0.262336I
a = 1.175550 + 0.241403I
b = 1.275010 − 0.262336I
0.95391 + 8.87623I −7.74572 − 6.85139I
u = −1.275010 − 0.262336I
a = 1.175550 − 0.241403I
b = 1.275010 + 0.262336I
0.95391 − 8.87623I −7.74572 + 6.85139I
u = 1.33028
a = −0.683762
b = −1.33028
−6.40721 −14.9220
u = 1.41995 + 0.20994I
a = −0.613065 + 1.144820I
b = −1.41995 − 0.20994I
−6.13065 − 4.90278I −7.01114 + 4.15155I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41995 − 0.20994I
a = −0.613065 − 1.144820I
b = −1.41995 + 0.20994I
−6.13065 + 4.90278I −7.01114 − 4.15155I
u = −0.542099
a = 0.262417
b = 0.542099
−0.811801 −12.0990
u = 1.49966 + 0.40429I
a = −0.028686 + 0.907225I
b = −1.49966 − 0.40429I
−10.72730 − 4.74355I −14.8235 + 1.3888I
u = 1.49966 − 0.40429I
a = −0.028686 − 0.907225I
b = −1.49966 + 0.40429I
−10.72730 + 4.74355I −14.8235 − 1.3888I
u = −1.53397 + 0.54225I
a = 0.050667 + 1.000190I
b = 1.53397 − 0.54225I
−3.9883 + 16.2483I −8.61000 − 8.11381I
u = −1.53397 − 0.54225I
a = 0.050667 − 1.000190I
b = 1.53397 + 0.54225I
−3.9883 − 16.2483I −8.61000 + 8.11381I
u = 0.159971 + 0.264831I
a = 2.87602 + 0.51667I
b = −0.159971 − 0.264831I
−0.39235 + 1.59654I −2.49522 − 4.52605I
u = 0.159971 − 0.264831I
a = 2.87602 − 0.51667I
b = −0.159971 + 0.264831I
−0.39235 − 1.59654I −2.49522 + 4.52605I
6
II. I
u
2
= h−6.10 × 10
97
u
47
+ 2.59 × 10
98
u
46
+ · · · + 2.24 × 10
98
b − 1.39 ×
10
100
, 1.07 × 10
100
u
47
− 4.25 × 10
100
u
46
+ · · · + 7.15 × 10
100
a + 2.74 ×
10
102
, u
48
− 3u
47
+ · · · + 2258u + 319i
(i) Arc colorings
a
2
=
1
0
a
10
=
0
u
a
3
=
1
u
2
a
6
=
−0.149069u
47
+ 0.594336u
46
+ ··· − 256.237u − 38.2785
0.271875u
47
− 1.15457u
46
+ ··· + 396.158u + 61.9139
a
11
=
−u
−u
3
+ u
a
5
=
0.122806u
47
− 0.560233u
46
+ ··· + 139.921u + 23.6354
0.271875u
47
− 1.15457u
46
+ ··· + 396.158u + 61.9139
a
1
=
1.54072u
47
− 6.38173u
46
+ ··· + 2672.27u + 435.306
1.99109u
47
− 8.19373u
46
+ ··· + 3481.47u + 562.648
a
9
=
−0.0375732u
47
+ 0.143876u
46
+ ··· − 130.196u − 23.4217
0.460900u
47
− 1.84389u
46
+ ··· + 889.590u + 143.667
a
7
=
−0.00542028u
47
+ 0.0383142u
46
+ ··· + 63.9028u + 9.35070
0.0486115u
47
− 0.222442u
46
+ ··· + 91.9873u + 18.1913
a
4
=
0.185270u
47
− 0.834683u
46
+ ··· + 187.771u + 28.3446
0.335022u
47
− 1.41596u
46
+ ··· + 528.630u + 82.1633
a
8
=
0.456200u
47
− 1.83795u
46
+ ··· + 821.370u + 131.984
0.476207u
47
− 1.90758u
46
+ ··· + 910.659u + 147.924
a
8
=
0.456200u
47
− 1.83795u
46
+ ··· + 821.370u + 131.984
0.476207u
47
− 1.90758u
46
+ ··· + 910.659u + 147.924
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.23467u
47
− 25.2293u
46
+ ··· + 11604.2u + 1881.95
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
10
u
48
− 3u
47
+ ··· + 2258u + 319
c
3
(u
24
+ 4u
23
+ ··· + 2u + 1)
2
c
4
, c
7
, c
8
c
11
u
48
− 5u
47
+ ··· + 314u + 61
c
6
, c
9
(u
24
− 4u
23
+ ··· − 2u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
y
48
− 37y
47
+ ··· + 318056y + 101761
c
3
(y
24
+ 6y
23
+ ··· + 8y + 1)
2
c
4
, c
7
, c
8
c
11
y
48
+ 31y
47
+ ··· − 55164y + 3721
c
6
, c
9
(y
24
+ 20y
23
+ ··· + 52y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.507410 + 0.882826I
a = −1.098430 + 0.558103I
b = 1.264200 − 0.100697I
−4.43678 − 0.22592I −13.45627 + 0.I
u = −0.507410 − 0.882826I
a = −1.098430 − 0.558103I
b = 1.264200 + 0.100697I
−4.43678 + 0.22592I −13.45627 + 0.I
u = 0.762695 + 0.579511I
a = 0.392365 − 0.571771I
b = 0.154819 + 0.470368I
1.82625 − 2.21677I −1.73188 + 4.68950I
u = 0.762695 − 0.579511I
a = 0.392365 + 0.571771I
b = 0.154819 − 0.470368I
1.82625 + 2.21677I −1.73188 − 4.68950I
u = −0.737778 + 0.756607I
a = 0.143305 − 0.121548I
b = 0.916292 + 0.212779I
−0.282838 − 0.252163I −7.00000 + 0.I
u = −0.737778 − 0.756607I
a = 0.143305 + 0.121548I
b = 0.916292 − 0.212779I
−0.282838 + 0.252163I −7.00000 + 0.I
u = −0.916292 + 0.212779I
a = −0.033385 + 0.208446I
b = 0.737778 + 0.756607I
−0.282838 + 0.252163I −7.62766 − 0.43499I
u = −0.916292 − 0.212779I
a = −0.033385 − 0.208446I
b = 0.737778 − 0.756607I
−0.282838 − 0.252163I −7.62766 + 0.43499I
u = −1.084950 + 0.073103I
a = −0.008039 − 0.977174I
b = −2.83805 + 2.46715I
−1.83976 + 0.26235I 18.4351 + 36.8531I
u = −1.084950 − 0.073103I
a = −0.008039 + 0.977174I
b = −2.83805 − 2.46715I
−1.83976 − 0.26235I 18.4351 − 36.8531I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.185015 + 0.891964I
a = 1.39762 − 0.46861I
b = −1.241010 + 0.316801I
−3.16425 + 4.93690I −9.72258 − 5.53812I
u = −0.185015 − 0.891964I
a = 1.39762 + 0.46861I
b = −1.241010 − 0.316801I
−3.16425 − 4.93690I −9.72258 + 5.53812I
u = −1.143710 + 0.210666I
a = −0.37949 − 1.52464I
b = −1.389740 + 0.219183I
−6.06530 + 3.64576I 0
u = −1.143710 − 0.210666I
a = −0.37949 + 1.52464I
b = −1.389740 − 0.219183I
−6.06530 − 3.64576I 0
u = 1.013570 + 0.603926I
a = −0.671512 + 0.079817I
b = 0.137025 − 0.636866I
4.61294 − 5.64930I 0
u = 1.013570 − 0.603926I
a = −0.671512 − 0.079817I
b = 0.137025 + 0.636866I
4.61294 + 5.64930I 0
u = 1.076670 + 0.546759I
a = 0.593477 + 0.736101I
b = 0.316671 − 0.434852I
−0.782529 + 1.065850I 0
u = 1.076670 − 0.546759I
a = 0.593477 − 0.736101I
b = 0.316671 + 0.434852I
−0.782529 − 1.065850I 0
u = −1.200180 + 0.290326I
a = −0.837459 − 0.455709I
b = −1.305520 + 0.094166I
−2.69997 + 4.12763I 0
u = −1.200180 − 0.290326I
a = −0.837459 + 0.455709I
b = −1.305520 − 0.094166I
−2.69997 − 4.12763I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.264200 + 0.100697I
a = −0.129257 + 0.980773I
b = 0.507410 − 0.882826I
−4.43678 − 0.22592I 0
u = −1.264200 − 0.100697I
a = −0.129257 − 0.980773I
b = 0.507410 + 0.882826I
−4.43678 + 0.22592I 0
u = 1.241010 + 0.316801I
a = −0.136900 − 1.039440I
b = 0.185015 + 0.891964I
−3.16425 − 4.93690I 0
u = 1.241010 − 0.316801I
a = −0.136900 + 1.039440I
b = 0.185015 − 0.891964I
−3.16425 + 4.93690I 0
u = 1.262020 + 0.321043I
a = −0.023468 + 0.958439I
b = −0.28931 − 1.41057I
1.74071 − 9.53525I 0
u = 1.262020 − 0.321043I
a = −0.023468 − 0.958439I
b = −0.28931 + 1.41057I
1.74071 + 9.53525I 0
u = 1.305520 + 0.094166I
a = 0.850020 − 0.294012I
b = 1.200180 + 0.290326I
−2.69997 − 4.12763I 0
u = 1.305520 − 0.094166I
a = 0.850020 + 0.294012I
b = 1.200180 − 0.290326I
−2.69997 + 4.12763I 0
u = −0.350000 + 0.566175I
a = −0.98088 + 1.39510I
b = 1.49434 + 0.04435I
−0.47769 + 2.08395I −4.74669 − 3.16145I
u = −0.350000 − 0.566175I
a = −0.98088 − 1.39510I
b = 1.49434 − 0.04435I
−0.47769 − 2.08395I −4.74669 + 3.16145I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.137025 + 0.636866I
a = −0.251867 + 1.198590I
b = −1.013570 − 0.603926I
4.61294 − 5.64930I −2.87192 + 2.20392I
u = −0.137025 − 0.636866I
a = −0.251867 − 1.198590I
b = −1.013570 + 0.603926I
4.61294 + 5.64930I −2.87192 − 2.20392I
u = 1.389740 + 0.219183I
a = 0.345996 − 1.251770I
b = 1.143710 + 0.210666I
−6.06530 − 3.64576I 0
u = 1.389740 − 0.219183I
a = 0.345996 + 1.251770I
b = 1.143710 − 0.210666I
−6.06530 + 3.64576I 0
u = 0.28931 + 1.41057I
a = 0.770694 + 0.397207I
b = −1.262020 − 0.321043I
1.74071 − 9.53525I 0
u = 0.28931 − 1.41057I
a = 0.770694 − 0.397207I
b = −1.262020 + 0.321043I
1.74071 + 9.53525I 0
u = −0.316671 + 0.434852I
a = 1.41976 − 1.57779I
b = −1.076670 − 0.546759I
−0.782529 + 1.065850I −2.95105 − 0.35875I
u = −0.316671 − 0.434852I
a = 1.41976 + 1.57779I
b = −1.076670 + 0.546759I
−0.782529 − 1.065850I −2.95105 + 0.35875I
u = 1.40310 + 0.41281I
a = 0.022975 − 1.042370I
b = 1.58930 + 0.62087I
−8.17000 − 9.69978I 0
u = 1.40310 − 0.41281I
a = 0.022975 + 1.042370I
b = 1.58930 − 0.62087I
−8.17000 + 9.69978I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49434 + 0.04435I
a = 0.319282 − 0.688916I
b = 0.350000 + 0.566175I
−0.47769 − 2.08395I 0
u = −1.49434 − 0.04435I
a = 0.319282 + 0.688916I
b = 0.350000 − 0.566175I
−0.47769 + 2.08395I 0
u = −0.154819 + 0.470368I
a = 0.002200 − 1.341380I
b = −0.762695 + 0.579511I
1.82625 + 2.21677I −1.73188 − 4.68950I
u = −0.154819 − 0.470368I
a = 0.002200 + 1.341380I
b = −0.762695 − 0.579511I
1.82625 − 2.21677I −1.73188 + 4.68950I
u = −1.58930 + 0.62087I
a = 0.057376 − 0.891861I
b = −1.40310 + 0.41281I
−8.17000 + 9.69978I 0
u = −1.58930 − 0.62087I
a = 0.057376 + 0.891861I
b = −1.40310 − 0.41281I
−8.17000 − 9.69978I 0
u = 2.83805 + 2.46715I
a = −0.168774 − 0.226636I
b = 1.084950 + 0.073103I
−1.83976 − 0.26235I 0
u = 2.83805 − 2.46715I
a = −0.168774 + 0.226636I
b = 1.084950 − 0.073103I
−1.83976 + 0.26235I 0
14
III. I
u
3
=
hb+u, u
7
−u
6
−4u
5
+3u
4
+5u
3
−4u
2
+a +1, u
8
−4u
6
+6u
4
−u
3
−3u
2
+u +1i
(i) Arc colorings
a
2
=
1
0
a
10
=
0
u
a
3
=
1
u
2
a
6
=
−u
7
+ u
6
+ 4u
5
− 3u
4
− 5u
3
+ 4u
2
− 1
−u
a
11
=
−u
−u
3
+ u
a
5
=
−u
7
+ u
6
+ 4u
5
− 3u
4
− 5u
3
+ 4u
2
− u − 1
−u
a
1
=
u
7
− 3u
5
+ u
4
+ 3u
3
− 4u
2
+ 2
−u
2
a
9
=
−u
7
+ u
6
+ 4u
5
− 3u
4
− 5u
3
+ 5u
2
+ u − 2
u
6
+ u
5
− 3u
4
− 2u
3
+ 3u
2
+ u − 1
a
7
=
−2u
7
+ 7u
5
− 8u
3
+ 3u
2
+ 2u − 1
u
4
+ u
3
− u
2
− u
a
4
=
u
6
+ u
5
− 2u
4
− u
3
+ 2u
2
− 2u − 1
u
7
+ u
6
− 3u
5
− 3u
4
+ 3u
3
+ 3u
2
− 2u − 1
a
8
=
−u
7
+ u
6
+ 4u
5
− 4u
4
− 5u
3
+ 7u
2
+ u − 3
u
5
− 2u
3
+ u
a
8
=
−u
7
+ u
6
+ 4u
5
− 4u
4
− 5u
3
+ 7u
2
+ u − 3
u
5
− 2u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
7
+ u
6
− 22u
5
− 2u
4
+ 23u
3
− 5u
2
− u − 9
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
8
− 4u
6
+ 6u
4
+ u
3
− 3u
2
− u + 1
c
2
, c
5
u
8
− 4u
6
+ 6u
4
− u
3
− 3u
2
+ u + 1
c
3
u
8
− 2u
6
− u
5
+ 16u
4
+ 32u
3
+ 24u
2
+ 8u + 1
c
4
, c
8
u
8
− u
7
+ 4u
6
− 3u
5
+ 6u
4
− 3u
3
+ 3u
2
− u + 1
c
6
u
8
+ 2u
7
+ 5u
6
+ 2u
5
+ 4u
4
− 2u
3
+ u
2
− u + 1
c
7
, c
11
u
8
+ u
7
+ 4u
6
+ 3u
5
+ 6u
4
+ 3u
3
+ 3u
2
+ u + 1
c
9
u
8
− 2u
7
+ 5u
6
− 2u
5
+ 4u
4
+ 2u
3
+ u
2
+ u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
y
8
− 8y
7
+ 28y
6
− 54y
5
+ 62y
4
− 45y
3
+ 23y
2
− 7y + 1
c
3
y
8
− 4y
7
+ 36y
6
− 17y
5
+ 226y
4
− 244y
3
+ 96y
2
− 16y + 1
c
4
, c
7
, c
8
c
11
y
8
+ 7y
7
+ 22y
6
+ 39y
5
+ 42y
4
+ 29y
3
+ 15y
2
+ 5y + 1
c
6
, c
9
y
8
+ 6y
7
+ 25y
6
+ 46y
5
+ 40y
4
+ 18y
3
+ 5y
2
+ y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637594 + 0.491904I
a = 0.269821 − 0.686725I
b = −0.637594 − 0.491904I
3.58036 − 6.89137I −7.40021 + 6.36507I
u = 0.637594 − 0.491904I
a = 0.269821 + 0.686725I
b = −0.637594 + 0.491904I
3.58036 + 6.89137I −7.40021 − 6.36507I
u = 1.350130 + 0.230207I
a = −0.520365 + 1.298460I
b = −1.350130 − 0.230207I
−7.12528 − 4.91384I −15.9725 + 5.8373I
u = 1.350130 − 0.230207I
a = −0.520365 − 1.298460I
b = −1.350130 + 0.230207I
−7.12528 + 4.91384I −15.9725 − 5.8373I
u = −0.603955 + 0.161841I
a = 0.880661 − 0.975730I
b = 0.603955 − 0.161841I
−1.17049 − 1.46276I −13.60538 + 3.21811I
u = −0.603955 − 0.161841I
a = 0.880661 + 0.975730I
b = 0.603955 + 0.161841I
−1.17049 + 1.46276I −13.60538 − 3.21811I
u = −1.38377 + 0.43339I
a = −0.130117 + 0.725566I
b = 1.38377 − 0.43339I
−1.86433 + 0.65741I −7.52191 − 0.35368I
u = −1.38377 − 0.43339I
a = −0.130117 − 0.725566I
b = 1.38377 + 0.43339I
−1.86433 − 0.65741I −7.52191 + 0.35368I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
8
− 4u
6
+ 6u
4
+ u
3
− 3u
2
− u + 1)(u
18
− 9u
16
+ ··· + 2u − 1)
· (u
48
− 3u
47
+ ··· + 2258u + 319)
c
2
, c
5
(u
8
− 4u
6
+ 6u
4
− u
3
− 3u
2
+ u + 1)(u
18
− 9u
16
+ ··· + 2u − 1)
· (u
48
− 3u
47
+ ··· + 2258u + 319)
c
3
(u
8
− 2u
6
− u
5
+ 16u
4
+ 32u
3
+ 24u
2
+ 8u + 1)
· (u
18
− 17u
17
+ ··· + 640u − 64)(u
24
+ 4u
23
+ ··· + 2u + 1)
2
c
4
, c
8
(u
8
− u
7
+ ··· − u + 1)(u
18
− u
17
+ ··· + 4u + 1)
· (u
48
− 5u
47
+ ··· + 314u + 61)
c
6
(u
8
+ 2u
7
+ 5u
6
+ 2u
5
+ 4u
4
− 2u
3
+ u
2
− u + 1)
· (u
18
+ 11u
17
+ ··· + 208u + 16)(u
24
− 4u
23
+ ··· − 2u + 1)
2
c
7
, c
11
(u
8
+ u
7
+ ··· + u + 1)(u
18
− u
17
+ ··· + 4u + 1)
· (u
48
− 5u
47
+ ··· + 314u + 61)
c
9
(u
8
− 2u
7
+ 5u
6
− 2u
5
+ 4u
4
+ 2u
3
+ u
2
+ u + 1)
· (u
18
+ 11u
17
+ ··· + 208u + 16)(u
24
− 4u
23
+ ··· − 2u + 1)
2
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
10
(y
8
− 8y
7
+ 28y
6
− 54y
5
+ 62y
4
− 45y
3
+ 23y
2
− 7y + 1)
· (y
18
− 18y
17
+ ··· + 6y + 1)(y
48
− 37y
47
+ ··· + 318056y + 101761)
c
3
(y
8
− 4y
7
+ 36y
6
− 17y
5
+ 226y
4
− 244y
3
+ 96y
2
− 16y + 1)
· (y
18
− 3y
17
+ ··· − 24576y + 4096)(y
24
+ 6y
23
+ ··· + 8y + 1)
2
c
4
, c
7
, c
8
c
11
(y
8
+ 7y
7
+ 22y
6
+ 39y
5
+ 42y
4
+ 29y
3
+ 15y
2
+ 5y + 1)
· (y
18
+ 13y
17
+ ··· − 14y + 1)(y
48
+ 31y
47
+ ··· − 55164y + 3721)
c
6
, c
9
(y
8
+ 6y
7
+ 25y
6
+ 46y
5
+ 40y
4
+ 18y
3
+ 5y
2
+ y + 1)
· (y
18
+ 11y
17
+ ··· − 12160y + 256)(y
24
+ 20y
23
+ ··· + 52y + 1)
2
20
