12n
0326
(K12n
0326
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 4 3 12 7 6 8 11
Solving Sequence
3,9 4,12
8 7 10 5 6 2 1 11
c
3
c
8
c
7
c
9
c
4
c
6
c
2
c
1
c
11
c
5
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h8.90151 × 10
60
u
43
+ 2.21948 × 10
61
u
42
+ ··· + 6.59116 × 10
59
b + 1.58663 × 10
62
,
− 1.69548 × 10
62
u
43
− 4.09643 × 10
62
u
42
+ ··· + 5.93204 × 10
60
a − 2.58270 × 10
63
, u
44
+ 3u
43
+ ··· + 9u + 9i
I
u
2
= h−u
11
+ 2u
10
+ u
9
− 2u
8
− 3u
7
+ 2u
6
+ 6u
4
− 8u
2
+ b − u + 5,
− 3u
11
+ 4u
9
+ 3u
8
− 3u
7
− 4u
6
− 8u
5
+ 3u
4
+ 10u
3
− u
2
+ a − 5u − 1,
u
12
− 2u
10
− u
9
+ 2u
8
+ 2u
7
+ 2u
6
− 2u
5
− 5u
4
+ u
3
+ 4u
2
− 1i
I
u
3
= hu
4
+ u
3
− 3u
2
+ b − u + 2, u
5
+ 3u
4
− 5u
2
+ a − u + 3, u
6
+ 2u
5
− 2u
4
− 3u
3
+ 2u
2
+ 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 62 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
= h8.90×10
60
u
43
+2.22×10
61
u
42
+· · ·+6.59×10
59
b+1.59×10
62
, −1.70×
10
62
u
43
−4.10×10
62
u
42
+· · ·+5.93×10
60
a−2.58×10
63
, u
44
+3u
43
+· · ·+9u+9i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
12
=
28.5817u
43
+ 69.0560u
42
+ ··· − 332.125u + 435.381
−13.5052u
43
− 33.6736u
42
+ ··· + 226.276u − 240.720
a
8
=
0.201641u
43
+ 0.460656u
42
+ ··· + 15.3420u + 12.7889
33.2391u
43
+ 81.0853u
42
+ ··· − 419.984u + 535.178
a
7
=
−33.0375u
43
− 80.6247u
42
+ ··· + 435.326u − 522.389
33.2391u
43
+ 81.0853u
42
+ ··· − 419.984u + 535.178
a
10
=
−29.6276u
43
− 73.3721u
42
+ ··· + 433.170u − 489.585
15.3508u
43
+ 38.1625u
42
+ ··· − 238.731u + 261.946
a
5
=
−43.7966u
43
− 107.794u
42
+ ··· + 594.943u − 730.873
28.9508u
43
+ 70.9233u
42
+ ··· − 380.679u + 468.275
a
6
=
−10.3769u
43
− 25.2409u
42
+ ··· + 146.290u − 153.601
26.2888u
43
+ 64.0967u
42
+ ··· − 329.420u + 421.797
a
2
=
27.7669u
43
+ 67.8632u
42
+ ··· − 348.922u + 460.619
−6.20167u
43
− 15.7725u
42
+ ··· + 127.833u − 117.848
a
1
=
21.5652u
43
+ 52.0907u
42
+ ··· − 221.089u + 342.771
−6.20167u
43
− 15.7725u
42
+ ··· + 127.833u − 117.848
a
11
=
16.2299u
43
+ 39.1273u
42
+ ··· − 179.657u + 250.432
−17.7450u
43
− 43.3750u
42
+ ··· + 235.483u − 290.417
(ii) Obstruction class = −1
(iii) Cusp Shapes = −272.965u
43
− 664.404u
42
+ ··· + 3337.83u − 4341.43
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 73u
43
+ ··· + 218241u + 3025
c
2
, c
5
u
44
+ u
43
+ ··· + 969u + 55
c
3
u
44
+ 3u
43
+ ··· + 9u + 9
c
4
u
44
+ u
43
+ ··· + 279u − 9
c
6
u
44
− 6u
43
+ ··· − 13u + 1
c
7
u
44
+ 9u
42
+ ··· + 186673u + 22591
c
8
, c
11
u
44
+ u
43
+ ··· + 15u + 1
c
9
u
44
+ 8u
43
+ ··· + 32u − 320
c
10
u
44
+ 6u
43
+ ··· − 2615847u − 617167
c
12
u
44
+ 33u
43
+ ··· − 19u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
− 241y
43
+ ··· − 12809738481y + 9150625
c
2
, c
5
y
44
− 73y
43
+ ··· − 218241y + 3025
c
3
y
44
− 15y
43
+ ··· − 3087y + 81
c
4
y
44
− 67y
43
+ ··· − 87759y + 81
c
6
y
44
+ 2y
43
+ ··· − 53y + 1
c
7
y
44
+ 18y
43
+ ··· + 780779441y + 510353281
c
8
, c
11
y
44
− 33y
43
+ ··· + 19y + 1
c
9
y
44
+ 10y
43
+ ··· − 226304y + 102400
c
10
y
44
− 126y
43
+ ··· − 7475456601853y + 380895105889
c
12
y
44
− 33y
43
+ ··· + 1919y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.983764 + 0.010812I
a = 0.776164 + 0.657660I
b = 0.179807 + 0.453187I
3.13780 − 0.62989I − 60.10 − 0.363791I
u = 0.983764 − 0.010812I
a = 0.776164 − 0.657660I
b = 0.179807 − 0.453187I
3.13780 + 0.62989I − 60.10 + 0.363791I
u = −0.995926 + 0.212137I
a = −0.684047 − 0.862199I
b = 0.385428 − 1.153220I
2.87592 − 4.66795I 0. + 6.21159I
u = −0.995926 − 0.212137I
a = −0.684047 + 0.862199I
b = 0.385428 + 1.153220I
2.87592 + 4.66795I 0. − 6.21159I
u = 0.649512 + 0.810142I
a = 0.688692 − 1.067530I
b = −0.58720 − 2.06561I
−5.69369 + 0.31371I −11.24262 + 0.I
u = 0.649512 − 0.810142I
a = 0.688692 + 1.067530I
b = −0.58720 + 2.06561I
−5.69369 − 0.31371I −11.24262 + 0.I
u = 1.06624
a = −1.15866
b = −2.12618
−8.79014 −10.1780
u = 0.972073 + 0.504899I
a = 0.496608 + 0.409312I
b = 0.304186 + 0.282887I
1.39378 + 1.89935I 0
u = 0.972073 − 0.504899I
a = 0.496608 − 0.409312I
b = 0.304186 − 0.282887I
1.39378 − 1.89935I 0
u = −1.010890 + 0.500581I
a = 0.0078406 + 0.1363720I
b = −0.020428 − 0.546085I
0.33573 − 4.72377I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.010890 − 0.500581I
a = 0.0078406 − 0.1363720I
b = −0.020428 + 0.546085I
0.33573 + 4.72377I 0
u = −0.660411 + 0.938330I
a = 0.703141 + 0.601609I
b = −0.80986 + 1.28827I
−2.22612 + 0.56711I 0
u = −0.660411 − 0.938330I
a = 0.703141 − 0.601609I
b = −0.80986 − 1.28827I
−2.22612 − 0.56711I 0
u = 1.057930 + 0.650598I
a = −0.899709 + 0.653233I
b = 0.83419 + 2.06344I
−4.35874 + 5.22725I 0
u = 1.057930 − 0.650598I
a = −0.899709 − 0.653233I
b = 0.83419 − 2.06344I
−4.35874 − 5.22725I 0
u = −0.820834 + 0.933777I
a = −1.161680 − 0.646565I
b = 0.541938 − 1.130020I
−15.6870 − 0.6720I 0
u = −0.820834 − 0.933777I
a = −1.161680 + 0.646565I
b = 0.541938 + 1.130020I
−15.6870 + 0.6720I 0
u = −1.050360 + 0.680819I
a = −0.518016 − 0.831087I
b = 0.75737 − 2.31620I
−0.97641 − 6.41642I 0
u = −1.050360 − 0.680819I
a = −0.518016 + 0.831087I
b = 0.75737 + 2.31620I
−0.97641 + 6.41642I 0
u = −0.484046 + 0.563326I
a = 0.363504 + 0.096522I
b = −0.396795 + 0.188011I
−1.234310 + 0.383646I −8.59433 − 2.13005I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.484046 − 0.563326I
a = 0.363504 − 0.096522I
b = −0.396795 − 0.188011I
−1.234310 − 0.383646I −8.59433 + 2.13005I
u = 0.804579 + 0.967738I
a = −0.798757 − 0.489353I
b = −0.453409 − 0.664044I
−11.28860 − 0.64983I 0
u = 0.804579 − 0.967738I
a = −0.798757 + 0.489353I
b = −0.453409 + 0.664044I
−11.28860 + 0.64983I 0
u = −0.652932 + 0.251845I
a = 0.54350 + 1.32899I
b = 0.639215 + 0.232761I
1.23289 − 4.62902I −5.84465 + 4.14155I
u = −0.652932 − 0.251845I
a = 0.54350 − 1.32899I
b = 0.639215 − 0.232761I
1.23289 + 4.62902I −5.84465 − 4.14155I
u = 0.670851
a = 2.40416
b = −2.11628
−10.5877 8.90790
u = −1.048190 + 0.837144I
a = 0.484292 + 1.026390I
b = −0.06811 + 2.25749I
−14.9574 − 5.9017I 0
u = −1.048190 − 0.837144I
a = 0.484292 − 1.026390I
b = −0.06811 − 2.25749I
−14.9574 + 5.9017I 0
u = −0.651141
a = 1.08862
b = −0.346698
−1.21790 −7.98940
u = 1.060320 + 0.850355I
a = −0.636937 − 0.700265I
b = −0.449291 − 0.476529I
−10.46950 + 7.35029I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.060320 − 0.850355I
a = −0.636937 + 0.700265I
b = −0.449291 + 0.476529I
−10.46950 − 7.35029I 0
u = 0.919976 + 1.023950I
a = 0.546144 − 0.830602I
b = −0.86441 − 1.77933I
−4.52279 + 6.69405I 0
u = 0.919976 − 1.023950I
a = 0.546144 + 0.830602I
b = −0.86441 + 1.77933I
−4.52279 − 6.69405I 0
u = −0.582341
a = −1.15614
b = −1.48403
−2.44265 5.79850
u = −0.545744
a = 1.19923
b = −3.94886
−6.50431 −21.3880
u = −0.70181 + 1.29455I
a = −0.760731 − 0.722556I
b = 0.44712 − 1.62807I
−16.5470 + 6.4689I 0
u = −0.70181 − 1.29455I
a = −0.760731 + 0.722556I
b = 0.44712 + 1.62807I
−16.5470 − 6.4689I 0
u = −1.23575 + 0.88133I
a = 0.521632 + 0.894334I
b = −0.61086 + 2.31759I
−14.7157 − 14.1505I 0
u = −1.23575 − 0.88133I
a = 0.521632 − 0.894334I
b = −0.61086 − 2.31759I
−14.7157 + 14.1505I 0
u = 0.298088 + 0.083893I
a = −2.74531 + 3.08989I
b = 0.155988 + 0.909226I
0.144274 + 0.902896I −6.75614 − 2.40130I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.298088 − 0.083893I
a = −2.74531 − 3.08989I
b = 0.155988 − 0.909226I
0.144274 − 0.902896I −6.75614 + 2.40130I
u = 1.34675 + 1.16951I
a = −0.459956 + 0.487071I
b = 0.60751 + 1.79387I
−3.83190 + 1.09484I 0
u = 1.34675 − 1.16951I
a = −0.459956 − 0.487071I
b = 0.60751 − 1.79387I
−3.83190 − 1.09484I 0
u = −1.82155
a = 0.356733
b = −2.16268
−2.68064 0
9
II.
I
u
2
= h−u
11
+2u
10
+· · ·+b+5, −3u
11
+4u
9
+· · ·+a−1, u
12
−2u
10
+· · ·+4u
2
−1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
12
=
3u
11
− 4u
9
− 3u
8
+ 3u
7
+ 4u
6
+ 8u
5
− 3u
4
− 10u
3
+ u
2
+ 5u + 1
u
11
− 2u
10
− u
9
+ 2u
8
+ 3u
7
− 2u
6
− 6u
4
+ 8u
2
+ u − 5
a
8
=
u
11
+ 2u
10
− 2u
9
− 5u
8
+ 5u
6
+ 6u
5
+ 3u
4
− 8u
3
− 9u
2
+ 5u + 5
−2u
10
+ 3u
8
+ 2u
7
− 3u
6
− 3u
5
− 5u
4
+ 3u
3
+ 8u
2
− u − 5
a
7
=
u
11
+ 4u
10
+ ··· + 6u + 10
−2u
10
+ 3u
8
+ 2u
7
− 3u
6
− 3u
5
− 5u
4
+ 3u
3
+ 8u
2
− u − 5
a
10
=
19u
11
+ 6u
10
+ ··· + 46u + 22
−10u
11
− u
10
+ ··· − 23u − 6
a
5
=
−22u
11
− 19u
10
+ ··· − 68u − 45
6u
11
+ 10u
10
+ ··· + 23u + 23
a
6
=
u
11
+ 3u
10
− 2u
9
− 7u
8
− u
7
+ 7u
6
+ 8u
5
+ 5u
4
− 10u
3
− 15u
2
+ 6u + 9
−u
10
+ 2u
8
+ u
7
− 2u
6
− 2u
5
− 2u
4
+ 2u
3
+ 5u
2
− u − 4
a
2
=
6u
11
+ 9u
10
+ ··· + 23u + 22
−u
11
− 4u
10
+ ··· − 6u − 11
a
1
=
5u
11
+ 5u
10
+ ··· + 17u + 11
−u
11
− 4u
10
+ ··· − 6u − 11
a
11
=
−u
11
− u
10
+ 3u
9
+ 2u
8
− 2u
7
− 4u
6
− 3u
5
+ 9u
3
+ u
2
− 6u − 2
2u
11
− 3u
9
− 2u
8
+ 3u
7
+ 3u
6
+ 5u
5
− 3u
4
− 8u
3
+ u
2
+ 6u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −16u
11
− 7u
10
+ 23u
9
+ 24u
8
− 14u
7
− 27u
6
− 48u
5
− u
4
+ 62u
3
+ 12u
2
− 37u − 17
10
(iv) u-Polynomials at the component
11
Crossings u-Polynomials at each crossing
c
1
u
12
− 12u
11
+ ··· + 4u
2
+ 1
c
2
u
12
+ 8u
11
+ ··· + 4u + 1
c
3
u
12
− 2u
10
− u
9
+ 2u
8
+ 2u
7
+ 2u
6
− 2u
5
− 5u
4
+ u
3
+ 4u
2
− 1
c
4
u
12
− 4u
10
+ u
9
+ 5u
8
− 2u
7
− 2u
6
+ 2u
5
− 2u
4
− u
3
+ 2u
2
− 1
c
5
u
12
− 8u
11
+ ··· − 4u + 1
c
6
u
12
+ 4u
11
+ ··· + 4u + 1
c
7
u
12
− 9u
10
+ ··· + 2u + 1
c
8
u
12
− 4u
10
+ 2u
9
+ 8u
8
− 5u
7
− 9u
6
+ 7u
5
+ 6u
4
− 5u
3
− 3u
2
+ 2u + 1
c
9
u
12
+ 3u
11
+ ··· − 65u − 85
c
10
u
12
+ u
11
+ ··· + 9u
2
− 1
c
11
u
12
− 4u
10
− 2u
9
+ 8u
8
+ 5u
7
− 9u
6
− 7u
5
+ 6u
4
+ 5u
3
− 3u
2
− 2u + 1
c
12
u
12
+ 8u
11
+ ··· + 10u + 1
12
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 68y
11
+ ··· + 8y + 1
c
2
, c
5
y
12
− 12y
11
+ ··· + 4y
2
+ 1
c
3
y
12
− 4y
11
+ ··· − 8y + 1
c
4
y
12
− 8y
11
+ ··· − 4y + 1
c
6
y
12
+ 2y
11
+ ··· − 8y + 1
c
7
y
12
− 18y
11
+ ··· + 2y + 1
c
8
, c
11
y
12
− 8y
11
+ ··· − 10y + 1
c
9
y
12
− 11y
11
+ ··· + 21275y + 7225
c
10
y
12
− 45y
11
+ ··· − 18y + 1
c
12
y
12
− 16y
10
+ ··· − 18y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.939264 + 0.357334I
a = −0.418150 + 0.917072I
b = 0.047162 + 0.521207I
1.64330 + 5.76877I −4.39799 − 10.10477I
u = 0.939264 − 0.357334I
a = −0.418150 − 0.917072I
b = 0.047162 − 0.521207I
1.64330 − 5.76877I −4.39799 + 10.10477I
u = −0.802928 + 0.320018I
a = 1.45891 − 0.33944I
b = −0.553518 + 0.244868I
0.590771 − 0.195986I −4.01333 + 2.47510I
u = −0.802928 − 0.320018I
a = 1.45891 + 0.33944I
b = −0.553518 − 0.244868I
0.590771 + 0.195986I −4.01333 − 2.47510I
u = −0.138543 + 1.147500I
a = 0.313010 + 0.802430I
b = −0.53359 + 1.50616I
−2.74984 + 0.99574I −16.1761 − 0.4700I
u = −0.138543 − 1.147500I
a = 0.313010 − 0.802430I
b = −0.53359 − 1.50616I
−2.74984 − 0.99574I −16.1761 + 0.4700I
u = 1.104550 + 0.506014I
a = 0.646485 + 0.051170I
b = 0.573229 + 0.016403I
0.23184 + 3.78473I −8.37575 − 0.92241I
u = 1.104550 − 0.506014I
a = 0.646485 − 0.051170I
b = 0.573229 − 0.016403I
0.23184 − 3.78473I −8.37575 + 0.92241I
u = −1.024920 + 0.684264I
a = −0.502733 − 0.780812I
b = 1.01990 − 2.38727I
−1.11487 − 7.34151I −7.49483 + 10.36656I
u = −1.024920 − 0.684264I
a = −0.502733 + 0.780812I
b = 1.01990 + 2.38727I
−1.11487 + 7.34151I −7.49483 − 10.36656I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.747167
a = −0.620955
b = −3.77110
−6.12374 0.401760
u = 0.592318
a = 2.62591
b = −2.33528
−10.8179 −26.4860
16
III. I
u
3
= hu
4
+ u
3
− 3u
2
+ b − u + 2, u
5
+ 3u
4
− 5u
2
+ a − u + 3, u
6
+ 2u
5
−
2u
4
− 3u
3
+ 2u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
12
=
−u
5
− 3u
4
+ 5u
2
+ u − 3
−u
4
− u
3
+ 3u
2
+ u − 2
a
8
=
u
5
+ 2u
4
− u
3
− u
2
+ u + 1
u
5
+ 2u
4
− u
3
− u
2
+ u + 1
a
7
=
0
u
5
+ 2u
4
− u
3
− u
2
+ u + 1
a
10
=
0
u
a
5
=
1
0
a
6
=
u
5
+ 2u
4
− u
3
− u
2
+ u + 1
1
a
2
=
−u
5
− 2u
4
+ u
3
+ u
2
− u
−1
a
1
=
−u
5
− 2u
4
+ u
3
+ u
2
− u − 1
−1
a
11
=
−u
5
− 3u
4
− u
3
+ 3u
2
+ 2u − 2
−u
4
− 2u
3
+ u
2
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
5
− 20u
4
+ 9u
3
+ 27u
2
− 5u − 24
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
4
u
6
+ 2u
5
− 2u
4
− 3u
3
+ 2u
2
+ 2u − 1
c
5
(u + 1)
6
c
6
, c
7
u
6
+ 3u
5
+ 6u
4
+ 7u
3
+ 5u
2
+ 2u − 1
c
8
(u
3
+ u
2
− 1)
2
c
9
u
6
c
10
, c
12
(u
3
+ u
2
+ 2u + 1)
2
c
11
(u
3
− u
2
+ 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
6
c
3
, c
4
y
6
− 8y
5
+ 20y
4
− 27y
3
+ 20y
2
− 8y + 1
c
6
, c
7
y
6
+ 3y
5
+ 4y
4
− 3y
3
− 15y
2
− 14y + 1
c
8
, c
11
(y
3
− y
2
+ 2y − 1)
2
c
9
y
6
c
10
, c
12
(y
3
+ 3y
2
+ 2y − 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.869124 + 0.347901I
a = 1.165820 + 0.390359I
b = 0.394534 + 0.648615I
1.37919 − 2.82812I −7.23838 + 1.20354I
u = 0.869124 − 0.347901I
a = 1.165820 − 0.390359I
b = 0.394534 − 0.648615I
1.37919 + 2.82812I −7.23838 − 1.20354I
u = −0.991685 + 0.396961I
a = −0.503465 − 0.952639I
b = −0.06982 − 1.77317I
1.37919 − 2.82812I −5.72688 + 3.54360I
u = −0.991685 − 0.396961I
a = −0.503465 + 0.952639I
b = −0.06982 + 1.77317I
1.37919 + 2.82812I −5.72688 − 3.54360I
u = 0.452937
a = −1.66663
b = −1.06662
−2.75839 −20.8640
u = −2.20781
a = 0.341912
b = −2.58282
−2.75839 −86.2050
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
12
− 12u
11
+ ··· + 4u
2
+ 1)
· (u
44
+ 73u
43
+ ··· + 218241u + 3025)
c
2
((u − 1)
6
)(u
12
+ 8u
11
+ ··· + 4u + 1)(u
44
+ u
43
+ ··· + 969u + 55)
c
3
(u
6
+ 2u
5
− 2u
4
− 3u
3
+ 2u
2
+ 2u − 1)
· (u
12
− 2u
10
− u
9
+ 2u
8
+ 2u
7
+ 2u
6
− 2u
5
− 5u
4
+ u
3
+ 4u
2
− 1)
· (u
44
+ 3u
43
+ ··· + 9u + 9)
c
4
(u
6
+ 2u
5
− 2u
4
− 3u
3
+ 2u
2
+ 2u − 1)
· (u
12
− 4u
10
+ u
9
+ 5u
8
− 2u
7
− 2u
6
+ 2u
5
− 2u
4
− u
3
+ 2u
2
− 1)
· (u
44
+ u
43
+ ··· + 279u − 9)
c
5
((u + 1)
6
)(u
12
− 8u
11
+ ··· − 4u + 1)(u
44
+ u
43
+ ··· + 969u + 55)
c
6
(u
6
+ 3u
5
+ ··· + 2u − 1)(u
12
+ 4u
11
+ ··· + 4u + 1)
· (u
44
− 6u
43
+ ··· − 13u + 1)
c
7
(u
6
+ 3u
5
+ ··· + 2u − 1)(u
12
− 9u
10
+ ··· + 2u + 1)
· (u
44
+ 9u
42
+ ··· + 186673u + 22591)
c
8
(u
3
+ u
2
− 1)
2
· (u
12
− 4u
10
+ 2u
9
+ 8u
8
− 5u
7
− 9u
6
+ 7u
5
+ 6u
4
− 5u
3
− 3u
2
+ 2u + 1)
· (u
44
+ u
43
+ ··· + 15u + 1)
c
9
u
6
(u
12
+ 3u
11
+ ··· − 65u − 85)(u
44
+ 8u
43
+ ··· + 32u − 320)
c
10
((u
3
+ u
2
+ 2u + 1)
2
)(u
12
+ u
11
+ ··· + 9u
2
− 1)
· (u
44
+ 6u
43
+ ··· − 2615847u − 617167)
c
11
(u
3
− u
2
+ 1)
2
· (u
12
− 4u
10
− 2u
9
+ 8u
8
+ 5u
7
− 9u
6
− 7u
5
+ 6u
4
+ 5u
3
− 3u
2
− 2u + 1)
· (u
44
+ u
43
+ ··· + 15u + 1)
c
12
((u
3
+ u
2
+ 2u + 1)
2
)(u
12
+ 8u
11
+ ··· + 10u + 1)
· (u
44
+ 33u
43
+ ··· − 19u + 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
12
− 68y
11
+ ··· + 8y + 1)
· (y
44
− 241y
43
+ ··· − 12809738481y + 9150625)
c
2
, c
5
((y − 1)
6
)(y
12
− 12y
11
+ ··· + 4y
2
+ 1)
· (y
44
− 73y
43
+ ··· − 218241y + 3025)
c
3
(y
6
− 8y
5
+ ··· − 8y + 1)(y
12
− 4y
11
+ ··· − 8y + 1)
· (y
44
− 15y
43
+ ··· − 3087y + 81)
c
4
(y
6
− 8y
5
+ ··· − 8y + 1)(y
12
− 8y
11
+ ··· − 4y + 1)
· (y
44
− 67y
43
+ ··· − 87759y + 81)
c
6
(y
6
+ 3y
5
+ ··· − 14y + 1)(y
12
+ 2y
11
+ ··· − 8y + 1)
· (y
44
+ 2y
43
+ ··· − 53y + 1)
c
7
(y
6
+ 3y
5
+ ··· − 14y + 1)(y
12
− 18y
11
+ ··· + 2y + 1)
· (y
44
+ 18y
43
+ ··· + 780779441y + 510353281)
c
8
, c
11
((y
3
− y
2
+ 2y − 1)
2
)(y
12
− 8y
11
+ ··· − 10y + 1)
· (y
44
− 33y
43
+ ··· + 19y + 1)
c
9
y
6
(y
12
− 11y
11
+ ··· + 21275y + 7225)
· (y
44
+ 10y
43
+ ··· − 226304y + 102400)
c
10
((y
3
+ 3y
2
+ 2y − 1)
2
)(y
12
− 45y
11
+ ··· − 18y + 1)
· (y
44
− 126y
43
+ ··· − 7475456601853y + 380895105889)
c
12
((y
3
+ 3y
2
+ 2y − 1)
2
)(y
12
− 16y
10
+ ··· − 18y + 1)
· (y
44
− 33y
43
+ ··· + 1919y + 1)
22
