12n
0855
(K12n
0855
)
A knot diagram
1
Linearized knot diagam
4 7 9 11 12 10 3 12 2 6 5 9
Solving Sequence
5,12 6,9
1 8 11 4 2 3 7 10
c
5
c
12
c
8
c
11
c
4
c
1
c
3
c
7
c
10
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5u
24
− 19u
23
+ ··· + 2b + 18, −u
24
− 3u
23
+ ··· + 4a + 4, u
25
+ 5u
24
+ ··· + 10u − 4i
I
u
2
= h20u
7
a
3
− 10u
7
a
2
+ ··· − 62a + 47, −3u
7
a
2
+ 6u
7
a + ··· − 20a − 11, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
I
u
3
= hu
14
− u
13
− 5u
12
+ 5u
11
+ 8u
10
− 8u
9
− u
8
+ u
7
− 8u
6
+ 8u
5
+ 3u
4
− 4u
3
+ 4u
2
+ b − 3u,
u
14
− 6u
12
+ 13u
10
− 9u
8
− 7u
6
+ 11u
4
− u
3
+ a + u − 3,
u
15
− 7u
13
+ 19u
11
− 22u
9
+ 3u
7
+ 14u
5
− u
4
− 6u
3
+ 2u
2
− 3u − 1i
* 3 irreducible components of dim
C
= 0, with total 72 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−5u
24
−19u
23
+· · ·+2b+18, −u
24
−3u
23
+· · ·+4a+4, u
25
+5u
24
+· · ·+10u−4i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
9
=
1
4
u
24
+
3
4
u
23
+ ··· +
25
4
u − 1
5
2
u
24
+
19
2
u
23
+ ··· +
61
2
u − 9
a
1
=
−7u
24
−
51
2
u
23
+ ··· −
131
2
u +
41
2
−
45
2
u
24
−
161
2
u
23
+ ··· −
391
2
u + 62
a
8
=
1
4
u
24
+
3
4
u
23
+ ··· +
25
4
u − 1
7
2
u
24
+
25
2
u
23
+ ··· +
73
2
u − 11
a
11
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
2
=
1
2
u
24
+ 3u
23
+ ··· + 11u −
7
2
−
11
2
u
24
−
35
2
u
23
+ ··· −
55
2
u + 10
a
3
=
−7u
24
−
51
2
u
23
+ ··· −
131
2
u +
43
2
−
45
2
u
24
−
161
2
u
23
+ ··· −
393
2
u + 62
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
u
8
− 2u
6
+ 2u
2
a
10
=
−u
3
+ 2u
−u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11u
24
+ 41u
23
− 32u
22
− 241u
21
+ 37u
20
+ 663u
19
− 146u
18
−
999u
17
+ 733u
16
+ 604u
15
−1604u
14
+ 758u
13
+ 1393u
12
−2013u
11
+ 411u
10
+ 1454u
9
−
1775u
8
+ 369u
7
+ 901u
6
− 1088u
5
+ 350u
4
+ 208u
3
− 373u
2
+ 164u − 46
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 21u
24
+ ··· + 1792u − 256
c
2
, c
7
, c
9
u
25
+ u
24
+ ··· + u + 1
c
3
, c
8
, c
12
u
25
+ 18u
23
+ ··· + 20u
2
+ 1
c
4
, c
5
, c
11
u
25
− 5u
24
+ ··· + 10u + 4
c
6
, c
10
u
25
+ 15u
24
+ ··· − 1986u − 196
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 13y
24
+ ··· − 131072y −65536
c
2
, c
7
, c
9
y
25
− 15y
24
+ ··· + 9y −1
c
3
, c
8
, c
12
y
25
+ 36y
24
+ ··· − 40y −1
c
4
, c
5
, c
11
y
25
− 21y
24
+ ··· − 100y −16
c
6
, c
10
y
25
+ 15y
24
+ ··· − 132996y −38416
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.042442 + 0.868462I
a = −0.716248 + 0.009860I
b = −0.315314 − 0.333618I
6.65854 − 2.22451I 1.85427 + 3.24248I
u = 0.042442 − 0.868462I
a = −0.716248 − 0.009860I
b = −0.315314 + 0.333618I
6.65854 + 2.22451I 1.85427 − 3.24248I
u = 0.170420 + 0.851806I
a = −1.68479 − 1.05733I
b = −0.313941 − 1.151630I
1.36106 − 10.21960I 3.12273 + 6.18876I
u = 0.170420 − 0.851806I
a = −1.68479 + 1.05733I
b = −0.313941 + 1.151630I
1.36106 + 10.21960I 3.12273 − 6.18876I
u = 0.689863 + 0.516195I
a = 0.90028 + 1.54729I
b = 0.157173 + 0.858656I
−2.89781 − 4.73922I 0.64335 + 6.01647I
u = 0.689863 − 0.516195I
a = 0.90028 − 1.54729I
b = 0.157173 − 0.858656I
−2.89781 + 4.73922I 0.64335 − 6.01647I
u = 1.062620 + 0.439244I
a = −0.93017 − 1.06985I
b = −0.393102 − 0.665533I
−1.37637 + 5.59077I 0.49701 − 2.52369I
u = 1.062620 − 0.439244I
a = −0.93017 + 1.06985I
b = −0.393102 + 0.665533I
−1.37637 − 5.59077I 0.49701 + 2.52369I
u = 0.370519 + 0.720063I
a = 1.56474 + 0.89351I
b = 0.401573 + 0.852679I
−1.86125 + 0.38147I 3.19263 − 0.66430I
u = 0.370519 − 0.720063I
a = 1.56474 − 0.89351I
b = 0.401573 − 0.852679I
−1.86125 − 0.38147I 3.19263 + 0.66430I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.27648
a = 0.500312
b = 0.280537
−2.96177 −0.698220
u = −1.296580 + 0.136250I
a = 0.004316 − 0.323358I
b = 0.429924 − 1.218120I
−4.47329 + 2.69307I −5.03326 − 5.98784I
u = −1.296580 − 0.136250I
a = 0.004316 + 0.323358I
b = 0.429924 + 1.218120I
−4.47329 − 2.69307I −5.03326 + 5.98784I
u = 1.235760 + 0.416433I
a = −0.139402 − 0.504528I
b = −0.038519 − 0.297655I
2.97397 − 2.37583I −1.057681 + 0.915229I
u = 1.235760 − 0.416433I
a = −0.139402 + 0.504528I
b = −0.038519 + 0.297655I
2.97397 + 2.37583I −1.057681 − 0.915229I
u = −1.304980 + 0.396966I
a = −0.149198 + 0.398993I
b = −0.962816 + 0.648234I
2.45389 + 6.76060I −2.28268 − 6.77573I
u = −1.304980 − 0.396966I
a = −0.149198 − 0.398993I
b = −0.962816 − 0.648234I
2.45389 − 6.76060I −2.28268 + 6.77573I
u = −1.37760 + 0.36657I
a = 0.142768 + 1.259210I
b = −1.32923 + 3.16497I
−3.5266 + 14.6054I −1.02784 − 7.76061I
u = −1.37760 − 0.36657I
a = 0.142768 − 1.259210I
b = −1.32923 − 3.16497I
−3.5266 − 14.6054I −1.02784 + 7.76061I
u = −1.44314 + 0.25974I
a = 0.006895 − 1.095370I
b = 1.09681 − 2.92836I
−7.68655 + 3.14182I 0.46512 + 1.43904I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44314 − 0.25974I
a = 0.006895 + 1.095370I
b = 1.09681 + 2.92836I
−7.68655 − 3.14182I 0.46512 − 1.43904I
u = −1.46408 + 0.08648I
a = −0.108140 − 1.228800I
b = 0.14349 − 3.82971I
−9.92989 + 6.47027I −4.20740 − 5.48144I
u = −1.46408 − 0.08648I
a = −0.108140 + 1.228800I
b = 0.14349 + 3.82971I
−9.92989 − 6.47027I −4.20740 + 5.48144I
u = 0.176540 + 0.371053I
a = 0.608793 + 0.633615I
b = −0.016319 + 0.292219I
0.045964 − 0.832254I 1.18286 + 8.33998I
u = 0.176540 − 0.371053I
a = 0.608793 − 0.633615I
b = −0.016319 − 0.292219I
0.045964 + 0.832254I 1.18286 − 8.33998I
7
II. I
u
2
= h20u
7
a
3
− 10u
7
a
2
+ · · · − 62a + 47, −3u
7
a
2
+ 6u
7
a + · · · − 20a −
11, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
9
=
a
−0.465116a
3
u
7
+ 0.232558a
2
u
7
+ ··· + 1.44186a − 1.09302
a
1
=
a
2
u
−0.790698a
3
u
7
+ 1.39535a
2
u
7
+ ··· + 0.651163a − 0.558140
a
8
=
a
−0.465116a
3
u
7
+ 0.232558a
2
u
7
+ ··· + 1.44186a − 1.09302
a
11
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
2
=
0.116279a
3
u
7
+ 0.441860a
2
u
7
+ ··· + 0.139535a + 1.02326
−0.302326a
3
u
7
+ 1.65116a
2
u
7
+ ··· + 0.837209a + 0.139535
a
3
=
0.186047a
3
u
7
− 0.0930233a
2
u
7
+ ··· + 0.0232558a + 0.837209
1.90698a
3
u
7
− 1.95349a
2
u
7
+ ··· − 0.511628a − 0.418605
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
u
7
+ u
6
− 2u
5
− 3u
4
+ 2u
2
+ 2u + 1
a
10
=
−u
3
+ 2u
−u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
6
+ 12u
4
+ 4u
3
− 8u
2
− 8u − 6
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u − 1)
16
c
2
, c
7
, c
9
u
32
+ u
31
+ ··· + 318u + 199
c
3
, c
8
, c
12
u
32
− u
31
+ ··· − 1792u − 271
c
4
, c
5
, c
11
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
4
c
6
, c
10
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 3y + 1)
16
c
2
, c
7
, c
9
y
32
− 13y
31
+ ··· − 651956y + 39601
c
3
, c
8
, c
12
y
32
+ 19y
31
+ ··· − 1289332y + 73441
c
4
, c
5
, c
11
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
4
c
6
, c
10
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = −0.573305 + 0.724047I
b = 0.069236 − 0.301245I
−4.98850 + 1.13123I 0.584775 − 0.510791I
u = −1.180120 + 0.268597I
a = 0.977884 + 0.579436I
b = −0.33020 + 2.17451I
2.90719 + 1.13123I 0.584775 − 0.510791I
u = −1.180120 + 0.268597I
a = 0.371867 − 1.152550I
b = 0.48288 − 1.38255I
−4.98850 + 1.13123I 0.584775 − 0.510791I
u = −1.180120 + 0.268597I
a = −0.450513 + 0.542402I
b = −1.11527 + 2.23372I
2.90719 + 1.13123I 0.584775 − 0.510791I
u = −1.180120 − 0.268597I
a = −0.573305 − 0.724047I
b = 0.069236 + 0.301245I
−4.98850 − 1.13123I 0.584775 + 0.510791I
u = −1.180120 − 0.268597I
a = 0.977884 − 0.579436I
b = −0.33020 − 2.17451I
2.90719 − 1.13123I 0.584775 + 0.510791I
u = −1.180120 − 0.268597I
a = 0.371867 + 1.152550I
b = 0.48288 + 1.38255I
−4.98850 − 1.13123I 0.584775 + 0.510791I
u = −1.180120 − 0.268597I
a = −0.450513 − 0.542402I
b = −1.11527 − 2.23372I
2.90719 − 1.13123I 0.584775 + 0.510791I
u = −0.108090 + 0.747508I
a = −1.029300 + 0.246196I
b = 0.524935 − 0.257181I
6.10726 + 2.57849I 3.72292 − 3.56796I
u = −0.108090 + 0.747508I
a = −1.46947 + 1.05203I
b = −0.428409 + 1.312810I
−1.78843 + 2.57849I 3.72292 − 3.56796I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.108090 + 0.747508I
a = −0.64475 − 1.85535I
b = −0.208281 − 1.216220I
6.10726 + 2.57849I 3.72292 − 3.56796I
u = −0.108090 + 0.747508I
a = 2.10891 − 0.43739I
b = 0.307458 − 0.750018I
−1.78843 + 2.57849I 3.72292 − 3.56796I
u = −0.108090 − 0.747508I
a = −1.029300 − 0.246196I
b = 0.524935 + 0.257181I
6.10726 − 2.57849I 3.72292 + 3.56796I
u = −0.108090 − 0.747508I
a = −1.46947 − 1.05203I
b = −0.428409 − 1.312810I
−1.78843 − 2.57849I 3.72292 + 3.56796I
u = −0.108090 − 0.747508I
a = −0.64475 + 1.85535I
b = −0.208281 + 1.216220I
6.10726 − 2.57849I 3.72292 + 3.56796I
u = −0.108090 − 0.747508I
a = 2.10891 + 0.43739I
b = 0.307458 + 0.750018I
−1.78843 − 2.57849I 3.72292 + 3.56796I
u = 1.37100
a = 0.975338
b = 1.58426
−2.55489 −5.86400
u = 1.37100
a = −0.247524 + 1.200480I
b = −0.14313 + 4.43627I
−10.4506 −5.86400
u = 1.37100
a = −0.247524 − 1.200480I
b = −0.14313 − 4.43627I
−10.4506 −5.86400
u = 1.37100
a = 0.320715
b = −0.834836
−2.55489 −5.86400
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.334530 + 0.318930I
a = 0.283327 − 1.065010I
b = −1.51898 − 2.93006I
−6.32752 − 6.44354I −1.42845 + 5.29417I
u = 1.334530 + 0.318930I
a = −1.130370 + 0.118813I
b = −1.00572 + 1.40159I
1.56816 − 6.44354I −1.42845 + 5.29417I
u = 1.334530 + 0.318930I
a = 0.237323 + 1.244130I
b = 1.81040 + 3.06377I
−6.32752 − 6.44354I −1.42845 + 5.29417I
u = 1.334530 + 0.318930I
a = −0.232706 − 0.587777I
b = 0.24276 − 1.75166I
1.56816 − 6.44354I −1.42845 + 5.29417I
u = 1.334530 − 0.318930I
a = 0.283327 + 1.065010I
b = −1.51898 + 2.93006I
−6.32752 + 6.44354I −1.42845 − 5.29417I
u = 1.334530 − 0.318930I
a = −1.130370 − 0.118813I
b = −1.00572 − 1.40159I
1.56816 + 6.44354I −1.42845 − 5.29417I
u = 1.334530 − 0.318930I
a = 0.237323 − 1.244130I
b = 1.81040 − 3.06377I
−6.32752 + 6.44354I −1.42845 − 5.29417I
u = 1.334530 − 0.318930I
a = −0.232706 + 0.587777I
b = 0.24276 + 1.75166I
1.56816 + 6.44354I −1.42845 − 5.29417I
u = −0.463640
a = −0.460586
b = −1.38936
3.10281 −3.89450
u = −0.463640
a = 2.56602
b = −0.430619
3.10281 −3.89450
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.463640
a = −0.40210 + 3.00975I
b = 0.347586 + 0.953404I
−4.79288 −3.89450
u = −0.463640
a = −0.40210 − 3.00975I
b = 0.347586 − 0.953404I
−4.79288 −3.89450
14
III.
I
u
3
= hu
14
−u
13
+· · ·+b −3u, u
14
−6u
12
+· · ·+a −3, u
15
−7u
13
+· · ·−3u −1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
9
=
−u
14
+ 6u
12
− 13u
10
+ 9u
8
+ 7u
6
− 11u
4
+ u
3
− u + 3
−u
14
+ u
13
+ ··· − 4u
2
+ 3u
a
1
=
u
11
− 5u
9
+ 9u
7
− 5u
5
− 3u
3
+ u
2
+ 3u − 2
−u
14
+ u
13
+ ··· + u + 1
a
8
=
−u
14
+ 6u
12
− 13u
10
+ 9u
8
+ 7u
6
− 11u
4
+ u
3
− u + 3
−2u
14
+ u
13
+ ··· − 4u
2
+ 2u
a
11
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
2
=
u
14
− 6u
12
+ ··· + 4u − 2
u
13
+ u
12
+ ··· + u + 1
a
3
=
u
11
− 5u
9
+ 9u
7
− 5u
5
− 3u
3
+ 3u − 1
−u
14
+ u
13
+ ··· + 6u
3
+ 1
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
u
8
− 2u
6
+ 2u
2
a
10
=
−u
3
+ 2u
−u
5
+ u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
14
+ 2u
13
+ 28u
12
− 10u
11
− 72u
10
+ 16u
9
+ 72u
8
− 2u
7
+
5u
6
− 16u
5
− 46u
4
+ 13u
3
+ 3u
2
− 5u + 10
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 6u
14
+ ··· + 7u − 1
c
2
, c
9
u
15
+ u
14
+ ··· + 3u
2
+ 1
c
3
, c
8
u
15
+ 3u
13
+ ··· + u + 1
c
4
, c
5
u
15
− 7u
13
+ 19u
11
− 22u
9
+ 3u
7
+ 14u
5
− u
4
− 6u
3
+ 2u
2
− 3u − 1
c
6
u
15
+ 5u
13
+ ··· − 3u − 1
c
7
u
15
− u
14
+ ··· − 3u
2
− 1
c
10
u
15
+ 5u
13
+ ··· − 3u + 1
c
11
u
15
− 7u
13
+ 19u
11
− 22u
9
+ 3u
7
+ 14u
5
+ u
4
− 6u
3
− 2u
2
− 3u + 1
c
12
u
15
+ 3u
13
+ ··· + u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
− 10y
14
+ ··· + 65y −1
c
2
, c
7
, c
9
y
15
− 9y
14
+ ··· − 6y −1
c
3
, c
8
, c
12
y
15
+ 6y
14
+ ··· + 9y −1
c
4
, c
5
, c
11
y
15
− 14y
14
+ ··· + 13y −1
c
6
, c
10
y
15
+ 10y
14
+ ··· + 15y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.067646 + 0.825365I
a = −0.380175 − 0.868214I
b = 0.310598 − 0.548513I
7.99475 + 1.92226I 9.12294 − 1.22401I
u = −0.067646 − 0.825365I
a = −0.380175 + 0.868214I
b = 0.310598 + 0.548513I
7.99475 − 1.92226I 9.12294 + 1.22401I
u = −1.20404
a = −0.582456
b = −3.43713
0.894455 −3.21180
u = 1.202120 + 0.181369I
a = 0.277876 + 0.914400I
b = 0.118572 + 0.512284I
−6.17070 − 1.65898I −7.52412 + 4.06635I
u = 1.202120 − 0.181369I
a = 0.277876 − 0.914400I
b = 0.118572 − 0.512284I
−6.17070 + 1.65898I −7.52412 − 4.06635I
u = −1.216500 + 0.366926I
a = 0.493698 + 0.310572I
b = 0.45473 + 1.67906I
4.46605 + 2.37005I 5.16588 − 2.66961I
u = −1.216500 − 0.366926I
a = 0.493698 − 0.310572I
b = 0.45473 − 1.67906I
4.46605 − 2.37005I 5.16588 + 2.66961I
u = 1.322630 + 0.369202I
a = −0.597920 − 0.072527I
b = −0.341991 − 0.081983I
3.63687 − 6.22447I 4.70740 + 3.89231I
u = 1.322630 − 0.369202I
a = −0.597920 + 0.072527I
b = −0.341991 + 0.081983I
3.63687 + 6.22447I 4.70740 − 3.89231I
u = 1.38580
a = 0.772897
b = 0.448939
−1.59422 4.26710
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.191847 + 0.580989I
a = 2.04075 + 1.02550I
b = 0.318346 + 1.004690I
−3.17279 − 1.01583I 0.86576 + 1.51873I
u = 0.191847 − 0.580989I
a = 2.04075 − 1.02550I
b = 0.318346 − 1.004690I
−3.17279 + 1.01583I 0.86576 − 1.51873I
u = −1.393270 + 0.230580I
a = −0.026700 − 1.147080I
b = 1.19545 − 3.34732I
−8.28883 + 4.00739I −4.40865 − 4.46883I
u = −1.393270 − 0.230580I
a = −0.026700 + 1.147080I
b = 1.19545 + 3.34732I
−8.28883 − 4.00739I −4.40865 + 4.46883I
u = −0.260139
a = 3.19450
b = −1.12320
3.76907 11.0860
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u − 1)
16
)(u
15
− 6u
14
+ ··· + 7u − 1)
· (u
25
− 21u
24
+ ··· + 1792u − 256)
c
2
, c
9
(u
15
+ u
14
+ ··· + 3u
2
+ 1)(u
25
+ u
24
+ ··· + u + 1)
· (u
32
+ u
31
+ ··· + 318u + 199)
c
3
, c
8
(u
15
+ 3u
13
+ ··· + u + 1)(u
25
+ 18u
23
+ ··· + 20u
2
+ 1)
· (u
32
− u
31
+ ··· − 1792u − 271)
c
4
, c
5
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
4
· (u
15
− 7u
13
+ 19u
11
− 22u
9
+ 3u
7
+ 14u
5
− u
4
− 6u
3
+ 2u
2
− 3u − 1)
· (u
25
− 5u
24
+ ··· + 10u + 4)
c
6
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
4
· (u
15
+ 5u
13
+ ··· − 3u − 1)(u
25
+ 15u
24
+ ··· − 1986u − 196)
c
7
(u
15
− u
14
+ ··· − 3u
2
− 1)(u
25
+ u
24
+ ··· + u + 1)
· (u
32
+ u
31
+ ··· + 318u + 199)
c
10
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
4
· (u
15
+ 5u
13
+ ··· − 3u + 1)(u
25
+ 15u
24
+ ··· − 1986u − 196)
c
11
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
4
· (u
15
− 7u
13
+ 19u
11
− 22u
9
+ 3u
7
+ 14u
5
+ u
4
− 6u
3
− 2u
2
− 3u + 1)
· (u
25
− 5u
24
+ ··· + 10u + 4)
c
12
(u
15
+ 3u
13
+ ··· + u − 1)(u
25
+ 18u
23
+ ··· + 20u
2
+ 1)
· (u
32
− u
31
+ ··· − 1792u − 271)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
− 3y + 1)
16
)(y
15
− 10y
14
+ ··· + 65y −1)
· (y
25
− 13y
24
+ ··· − 131072y −65536)
c
2
, c
7
, c
9
(y
15
− 9y
14
+ ··· − 6y −1)(y
25
− 15y
24
+ ··· + 9y −1)
· (y
32
− 13y
31
+ ··· − 651956y + 39601)
c
3
, c
8
, c
12
(y
15
+ 6y
14
+ ··· + 9y −1)(y
25
+ 36y
24
+ ··· − 40y −1)
· (y
32
+ 19y
31
+ ··· − 1289332y + 73441)
c
4
, c
5
, c
11
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
4
· (y
15
− 14y
14
+ ··· + 13y −1)(y
25
− 21y
24
+ ··· − 100y −16)
c
6
, c
10
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
4
· (y
15
+ 10y
14
+ ··· + 15y −1)(y
25
+ 15y
24
+ ··· − 132996y −38416)
21
