12n
0424
(K12n
0424
)
A knot diagram
1
Linearized knot diagam
3 6 11 7 2 9 3 12 6 8 4 10
Solving Sequence
3,6
2 1
5,10
9 7 8 11 4 12
c
2
c
1
c
5
c
9
c
6
c
7
c
10
c
4
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.60349 × 10
202
u
67
− 1.26475 × 10
203
u
66
+ ··· + 3.63435 × 10
205
b + 1.56735 × 10
205
,
2.69439 × 10
205
u
67
− 1.16805 × 10
206
u
66
+ ··· + 1.15209 × 10
208
a + 8.44586 × 10
207
,
u
68
− 5u
67
+ ··· + 86u − 317i
I
u
2
= h56939u
20
+ 161982u
19
+ ··· + 59123b + 87648, 299698u
20
+ 645903u
19
+ ··· + 59123a + 588498,
u
21
+ 2u
20
+ ··· + 4u − 1i
* 2 irreducible components of dim
C
= 0, with total 89 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
= h2.60 × 10
202
u
67
− 1.26 × 10
203
u
66
+ · · · + 3.63 × 10
205
b + 1.57 ×
10
205
, 2.69 × 10
205
u
67
− 1.17 × 10
206
u
66
+ · · · + 1.15 × 10
208
a + 8.45 ×
10
207
, u
68
− 5u
67
+ · · · + 86u − 317i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
10
=
−0.00233870u
67
+ 0.0101386u
66
+ ··· − 11.2417u − 0.733090
−0.000716356u
67
+ 0.00347999u
66
+ ··· − 5.24442u − 0.431259
a
9
=
−0.00233870u
67
+ 0.0101386u
66
+ ··· − 11.2417u − 0.733090
−0.00117955u
67
+ 0.00620829u
66
+ ··· − 4.63678u + 0.0616603
a
7
=
0.00491528u
67
− 0.0262227u
66
+ ··· + 25.2225u + 6.20953
−0.000952899u
67
+ 0.00487972u
66
+ ··· + 0.0569866u + 0.671964
a
8
=
0.00396238u
67
− 0.0213429u
66
+ ··· + 25.2795u + 6.88149
−0.000952899u
67
+ 0.00487972u
66
+ ··· + 0.0569866u + 0.671964
a
11
=
0.00373541u
67
− 0.0186514u
66
+ ··· + 30.2287u + 11.1920
−0.000136580u
67
+ 0.000781749u
66
+ ··· + 3.37713u + 0.340186
a
4
=
−0.00276461u
67
+ 0.0125786u
66
+ ··· − 47.0972u − 12.3994
−0.0000159099u
67
+ 0.000183427u
66
+ ··· − 4.26921u + 0.0576805
a
12
=
−0.000531157u
67
+ 0.00366050u
66
+ ··· + 31.7108u + 3.30930
−0.00101402u
67
+ 0.00536595u
66
+ ··· + 0.703120u − 0.416678
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00431587u
67
+ 0.0232128u
66
+ ··· + 33.1103u + 8.26277
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 81u
67
+ ··· + 7054940u + 100489
c
2
, c
5
u
68
+ 5u
67
+ ··· − 86u − 317
c
3
, c
11
u
68
− 23u
66
+ ··· + 2u + 1
c
4
u
68
+ 12u
67
+ ··· − 352006u + 2124268
c
6
, c
9
u
68
+ 6u
67
+ ··· − 23u + 1
c
7
u
68
− 3u
67
+ ··· + 4608u − 512
c
8
u
68
+ u
67
+ ··· + 30u − 4
c
10
u
68
+ 4u
65
+ ··· + 101u + 41
c
12
u
68
− 15u
67
+ ··· + 4125551u − 99557
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
− 173y
67
+ ··· + 1338138438004y + 10098039121
c
2
, c
5
y
68
− 81y
67
+ ··· − 7054940y + 100489
c
3
, c
11
y
68
− 46y
67
+ ··· + 10y + 1
c
4
y
68
+ 72y
67
+ ··· + 70533073386900y + 4512514535824
c
6
, c
9
y
68
+ 12y
67
+ ··· − 193y + 1
c
7
y
68
+ 21y
67
+ ··· + 15597568y + 262144
c
8
y
68
− 3y
67
+ ··· + 100y + 16
c
10
y
68
+ 60y
66
+ ··· − 19877y + 1681
c
12
y
68
− 59y
67
+ ··· − 745245389293y + 9911596249
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.871128 + 0.509881I
a = −0.251428 − 0.802924I
b = 0.018453 + 0.953747I
−1.05916 − 0.94846I 0
u = 0.871128 − 0.509881I
a = −0.251428 + 0.802924I
b = 0.018453 − 0.953747I
−1.05916 + 0.94846I 0
u = −0.544948 + 0.820477I
a = −0.774935 + 0.270468I
b = −1.058330 + 0.233379I
4.15929 − 0.82146I 0
u = −0.544948 − 0.820477I
a = −0.774935 − 0.270468I
b = −1.058330 − 0.233379I
4.15929 + 0.82146I 0
u = 1.046280 + 0.158379I
a = −0.05036 + 1.45147I
b = 0.389019 + 0.679852I
4.06606 + 4.41418I 0
u = 1.046280 − 0.158379I
a = −0.05036 − 1.45147I
b = 0.389019 − 0.679852I
4.06606 − 4.41418I 0
u = −0.885188 + 0.133345I
a = −0.609940 + 0.064726I
b = −0.36252 + 1.60437I
2.00126 + 7.10030I −5.49116 − 6.13012I
u = −0.885188 − 0.133345I
a = −0.609940 − 0.064726I
b = −0.36252 − 1.60437I
2.00126 − 7.10030I −5.49116 + 6.13012I
u = 0.440543 + 0.709904I
a = −0.925199 + 0.715716I
b = −0.563366 + 0.659728I
−0.315752 − 0.651012I −5.42332 − 3.40225I
u = 0.440543 − 0.709904I
a = −0.925199 − 0.715716I
b = −0.563366 − 0.659728I
−0.315752 + 0.651012I −5.42332 + 3.40225I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.800978 + 0.142572I
a = 0.366163 − 0.014633I
b = 0.69817 + 1.28569I
−1.37004 − 1.79460I −8.18525 + 5.97883I
u = 0.800978 − 0.142572I
a = 0.366163 + 0.014633I
b = 0.69817 − 1.28569I
−1.37004 + 1.79460I −8.18525 − 5.97883I
u = −0.188648 + 0.784530I
a = 1.113550 + 0.741221I
b = 0.823409 + 0.516607I
0.44809 + 2.22556I −2.79693 − 5.37400I
u = −0.188648 − 0.784530I
a = 1.113550 − 0.741221I
b = 0.823409 − 0.516607I
0.44809 − 2.22556I −2.79693 + 5.37400I
u = −1.042970 + 0.640059I
a = 0.252793 − 0.689948I
b = 0.583572 + 0.375949I
2.60331 + 6.17342I 0
u = −1.042970 − 0.640059I
a = 0.252793 + 0.689948I
b = 0.583572 − 0.375949I
2.60331 − 6.17342I 0
u = −0.588960 + 0.496925I
a = −0.393461 + 1.028770I
b = 0.135056 + 0.879028I
1.71068 − 2.22744I −2.20317 + 3.51892I
u = −0.588960 − 0.496925I
a = −0.393461 − 1.028770I
b = 0.135056 − 0.879028I
1.71068 + 2.22744I −2.20317 − 3.51892I
u = 0.558593 + 0.526304I
a = −0.860916 − 0.104097I
b = −0.292526 + 0.378622I
−0.41361 − 1.51672I −4.11702 + 3.50590I
u = 0.558593 − 0.526304I
a = −0.860916 + 0.104097I
b = −0.292526 − 0.378622I
−0.41361 + 1.51672I −4.11702 − 3.50590I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.698428 + 0.225559I
a = −0.06120 + 1.66744I
b = 0.059794 + 0.692238I
1.94783 − 2.44722I 0.47230 − 2.86417I
u = −0.698428 − 0.225559I
a = −0.06120 − 1.66744I
b = 0.059794 − 0.692238I
1.94783 + 2.44722I 0.47230 + 2.86417I
u = −1.149490 + 0.645257I
a = −0.244780 + 0.273572I
b = 0.201289 + 0.916767I
2.21731 − 2.65488I 0
u = −1.149490 − 0.645257I
a = −0.244780 − 0.273572I
b = 0.201289 − 0.916767I
2.21731 + 2.65488I 0
u = −0.734034 + 1.108720I
a = −0.095793 − 0.323746I
b = −0.023606 + 0.235560I
1.83474 − 2.80065I 0
u = −0.734034 − 1.108720I
a = −0.095793 + 0.323746I
b = −0.023606 − 0.235560I
1.83474 + 2.80065I 0
u = −0.537572 + 0.292817I
a = 1.59768 − 1.26454I
b = 0.424708 − 0.016900I
1.85960 + 4.70737I −2.52304 − 10.70995I
u = −0.537572 − 0.292817I
a = 1.59768 + 1.26454I
b = 0.424708 + 0.016900I
1.85960 − 4.70737I −2.52304 + 10.70995I
u = −0.753527 + 1.166220I
a = −0.762293 − 0.164274I
b = −0.822320 + 0.177075I
1.79765 + 10.38310I 0
u = −0.753527 − 1.166220I
a = −0.762293 + 0.164274I
b = −0.822320 − 0.177075I
1.79765 − 10.38310I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.474569 + 0.362132I
a = −1.72365 + 0.23562I
b = −0.443265 + 0.309260I
−0.87147 − 2.49560I −8.19061 + 9.19024I
u = 0.474569 − 0.362132I
a = −1.72365 − 0.23562I
b = −0.443265 − 0.309260I
−0.87147 + 2.49560I −8.19061 − 9.19024I
u = 0.830722 + 1.137770I
a = 0.613745 − 0.111412I
b = 0.732990 + 0.363720I
−2.05341 − 4.26526I 0
u = 0.830722 − 1.137770I
a = 0.613745 + 0.111412I
b = 0.732990 − 0.363720I
−2.05341 + 4.26526I 0
u = −0.429455 + 0.392611I
a = 0.56873 − 1.67827I
b = −0.460162 + 1.313910I
3.56883 − 5.49597I −0.35708 + 7.00581I
u = −0.429455 − 0.392611I
a = 0.56873 + 1.67827I
b = −0.460162 − 1.313910I
3.56883 + 5.49597I −0.35708 − 7.00581I
u = −1.43036
a = −0.0534743
b = −1.45724
−3.29592 0
u = 1.45239 + 0.17220I
a = −0.751230 − 0.429370I
b = −2.36893 − 0.07099I
−6.96130 − 1.46154I 0
u = 1.45239 − 0.17220I
a = −0.751230 + 0.429370I
b = −2.36893 + 0.07099I
−6.96130 + 1.46154I 0
u = 1.46944
a = 0.392688
b = 1.69276
−3.78770 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55873 + 0.13384I
a = 0.852639 − 0.619616I
b = 2.29095 − 0.57702I
−7.71397 + 4.42312I 0
u = −1.55873 − 0.13384I
a = 0.852639 + 0.619616I
b = 2.29095 + 0.57702I
−7.71397 − 4.42312I 0
u = 1.58955 + 0.06373I
a = −0.636720 − 0.744311I
b = −1.89607 − 0.94307I
−5.50713 − 5.89389I 0
u = 1.58955 − 0.06373I
a = −0.636720 + 0.744311I
b = −1.89607 + 0.94307I
−5.50713 + 5.89389I 0
u = −1.63011 + 0.19482I
a = 0.777479 − 0.591084I
b = 1.98605 − 0.45195I
−8.12749 + 4.22844I 0
u = −1.63011 − 0.19482I
a = 0.777479 + 0.591084I
b = 1.98605 + 0.45195I
−8.12749 − 4.22844I 0
u = 1.60712 + 0.36324I
a = −0.745239 − 0.676686I
b = −1.82570 − 0.29640I
−5.64912 − 6.82670I 0
u = 1.60712 − 0.36324I
a = −0.745239 + 0.676686I
b = −1.82570 + 0.29640I
−5.64912 + 6.82670I 0
u = −0.297585 + 0.072176I
a = 2.48257 + 0.33875I
b = 0.492290 + 0.055394I
−1.42607 + 0.01276I −9.44279 + 0.81659I
u = −0.297585 − 0.072176I
a = 2.48257 − 0.33875I
b = 0.492290 − 0.055394I
−1.42607 − 0.01276I −9.44279 − 0.81659I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.70975 + 0.05552I
a = −0.624502 − 0.582986I
b = −1.88329 − 0.29548I
−10.76850 + 2.56396I 0
u = −1.70975 − 0.05552I
a = −0.624502 + 0.582986I
b = −1.88329 + 0.29548I
−10.76850 − 2.56396I 0
u = 1.71065 + 0.07105I
a = 0.732714 − 0.538117I
b = 1.95223 − 0.29659I
−7.52248 − 8.09991I 0
u = 1.71065 − 0.07105I
a = 0.732714 + 0.538117I
b = 1.95223 + 0.29659I
−7.52248 + 8.09991I 0
u = −1.74721 + 0.17347I
a = 0.813534 − 0.514883I
b = 1.85421 − 0.43442I
−8.31422 + 4.53840I 0
u = −1.74721 − 0.17347I
a = 0.813534 + 0.514883I
b = 1.85421 + 0.43442I
−8.31422 − 4.53840I 0
u = 1.72573 + 0.38376I
a = 0.702168 + 0.550948I
b = 2.08835 + 0.55587I
−6.2957 − 16.2757I 0
u = 1.72573 − 0.38376I
a = 0.702168 − 0.550948I
b = 2.08835 − 0.55587I
−6.2957 + 16.2757I 0
u = −1.73754 + 0.38845I
a = −0.676834 + 0.471111I
b = −2.07579 + 0.51144I
−10.3272 + 10.1790I 0
u = −1.73754 − 0.38845I
a = −0.676834 − 0.471111I
b = −2.07579 − 0.51144I
−10.3272 − 10.1790I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.186071 + 0.088469I
a = 2.84558 + 5.76663I
b = −0.584481 + 0.792155I
6.79008 + 4.75733I 3.79704 − 5.76566I
u = 0.186071 − 0.088469I
a = 2.84558 − 5.76663I
b = −0.584481 − 0.792155I
6.79008 − 4.75733I 3.79704 + 5.76566I
u = 1.79378 + 0.03621I
a = −0.667026 − 0.311610I
b = −1.61634 − 0.35448I
−8.03735 − 1.00540I 0
u = 1.79378 − 0.03621I
a = −0.667026 + 0.311610I
b = −1.61634 + 0.35448I
−8.03735 + 1.00540I 0
u = 1.80621 + 0.03283I
a = 0.404169 − 0.562395I
b = 1.88508 − 0.20648I
−4.91628 + 2.38789I 0
u = 1.80621 − 0.03283I
a = 0.404169 + 0.562395I
b = 1.88508 + 0.20648I
−4.91628 − 2.38789I 0
u = 1.82029 + 0.48597I
a = 0.530834 + 0.328063I
b = 2.04333 + 0.51887I
−5.36733 − 3.53838I 0
u = 1.82029 − 0.48597I
a = 0.530834 − 0.328063I
b = 2.04333 − 0.51887I
−5.36733 + 3.53838I 0
11
II. I
u
2
= h56939u
20
+ 161982u
19
+ · · · + 59123b + 87648, 3.00 × 10
5
u
20
+
6.46 × 10
5
u
19
+ · · · + 5.91 × 10
4
a + 5.88 × 10
5
, u
21
+ 2u
20
+ · · · + 4u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
5
=
u
−u
3
+ u
a
10
=
−5.06906u
20
− 10.9247u
19
+ ··· + 10.8398u − 9.95379
−0.963060u
20
− 2.73975u
19
+ ··· − 0.169291u − 1.48247
a
9
=
−5.06906u
20
− 10.9247u
19
+ ··· + 10.8398u − 9.95379
−0.775925u
20
− 2.17956u
19
+ ··· + 1.75331u − 0.695854
a
7
=
−4.90401u
20
− 9.43501u
19
+ ··· + 9.38474u − 3.34662
0.681072u
20
+ 1.87392u
19
+ ··· + 4.01839u + 1.44754
a
8
=
−4.22294u
20
− 7.56108u
19
+ ··· + 13.4031u − 1.89907
0.681072u
20
+ 1.87392u
19
+ ··· + 4.01839u + 1.44754
a
11
=
−3.58847u
20
− 10.1130u
19
+ ··· + 43.2427u − 15.5705
3.67141u
20
+ 2.70835u
19
+ ··· + 18.6702u − 4.15388
a
4
=
9.71688u
20
+ 17.8748u
19
+ ··· − 12.3073u + 12.5600
0.519409u
20
+ 1.18825u
19
+ ··· − 18.4028u + 4.61670
a
12
=
1.21986u
20
+ 0.289397u
19
+ ··· + 10.6943u + 1.02261
0.313381u
20
+ 2.64743u
19
+ ··· + 0.618761u + 1.59928
(ii) Obstruction class = 1
(iii) Cusp Shapes =
13845
59123
u
20
−
277255
59123
u
19
+ ··· −
4783788
59123
u +
1378541
59123
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
21
− 20u
20
+ ··· + 16u − 1
c
2
u
21
+ 2u
20
+ ··· + 4u − 1
c
3
u
21
+ u
20
+ ··· + 4u − 1
c
4
u
21
+ u
20
+ ··· − 94u − 29
c
5
u
21
− 2u
20
+ ··· + 4u + 1
c
6
u
21
− 7u
20
+ ··· − u + 1
c
7
u
21
+ u
19
+ ··· + 6u + 1
c
8
u
21
+ u
19
+ ··· + 2u − 1
c
9
u
21
+ 7u
20
+ ··· − u − 1
c
10
u
21
+ u
20
+ ··· + u + 1
c
11
u
21
− u
20
+ ··· + 4u + 1
c
12
u
21
− 4u
20
+ ··· + 117u + 29
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 24y
20
+ ··· + 36y −1
c
2
, c
5
y
21
− 20y
20
+ ··· + 16y −1
c
3
, c
11
y
21
− 17y
20
+ ··· + 10y −1
c
4
y
21
+ 17y
20
+ ··· − 14364y −841
c
6
, c
9
y
21
+ 13y
20
+ ··· − 7y −1
c
7
y
21
+ 2y
20
+ ··· + 28y −1
c
8
y
21
+ 2y
20
+ ··· − 16y −1
c
10
y
21
+ 9y
20
+ ··· + y −1
c
12
y
21
− 10y
20
+ ··· + 5685y −841
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.894035 + 0.426850I
a = −0.519136 + 0.655370I
b = −0.26891 − 1.39537I
3.24028 + 7.57467I 0.82215 − 8.81507I
u = −0.894035 − 0.426850I
a = −0.519136 − 0.655370I
b = −0.26891 + 1.39537I
3.24028 − 7.57467I 0.82215 + 8.81507I
u = −0.858392 + 0.405679I
a = −0.462130 + 1.325320I
b = −0.144594 − 0.205272I
6.04821 − 3.54076I 0.72244 + 2.01321I
u = −0.858392 − 0.405679I
a = −0.462130 − 1.325320I
b = −0.144594 + 0.205272I
6.04821 + 3.54076I 0.72244 − 2.01321I
u = 0.899032 + 0.074143I
a = −0.325588 − 1.368960I
b = −0.179975 − 0.662985I
1.60454 − 2.95721I −6.36375 + 7.33949I
u = 0.899032 − 0.074143I
a = −0.325588 + 1.368960I
b = −0.179975 + 0.662985I
1.60454 + 2.95721I −6.36375 − 7.33949I
u = −1.072430 + 0.326023I
a = 0.271074 − 1.129650I
b = 0.251948 − 1.072700I
5.27529 + 6.34734I 0.57668 − 6.47209I
u = −1.072430 − 0.326023I
a = 0.271074 + 1.129650I
b = 0.251948 + 1.072700I
5.27529 − 6.34734I 0.57668 + 6.47209I
u = 0.685692 + 0.369999I
a = 0.279617 + 0.898848I
b = −0.38782 − 1.43241I
−0.58771 − 1.41759I 1.42036 + 5.33647I
u = 0.685692 − 0.369999I
a = 0.279617 − 0.898848I
b = −0.38782 + 1.43241I
−0.58771 + 1.41759I 1.42036 − 5.33647I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.141080 + 0.631558I
a = −1.00212 + 1.21363I
b = −0.429943 + 0.543747I
−0.39852 − 1.44153I −7.16101 + 3.82962I
u = 0.141080 − 0.631558I
a = −1.00212 − 1.21363I
b = −0.429943 − 0.543747I
−0.39852 + 1.44153I −7.16101 − 3.82962I
u = 1.42200
a = 0.221842
b = 1.73232
−4.94331 −8.42450
u = −1.14688 + 0.98533I
a = 0.183692 − 0.275325I
b = −0.147350 − 0.800918I
2.40941 − 2.93010I 12.0576 + 13.5784I
u = −1.14688 − 0.98533I
a = 0.183692 + 0.275325I
b = −0.147350 + 0.800918I
2.40941 + 2.93010I 12.0576 − 13.5784I
u = 0.388530 + 0.117903I
a = −0.32404 + 3.02809I
b = 0.367355 + 0.666272I
2.06332 + 3.63257I −2.19231 − 4.68251I
u = 0.388530 − 0.117903I
a = −0.32404 − 3.02809I
b = 0.367355 − 0.666272I
2.06332 − 3.63257I −2.19231 + 4.68251I
u = −1.60153 + 0.15283I
a = 0.846635 − 0.626675I
b = 2.07762 − 0.56851I
−7.02711 + 4.47993I −0.55876 − 3.70470I
u = −1.60153 − 0.15283I
a = 0.846635 + 0.626675I
b = 2.07762 + 0.56851I
−7.02711 − 4.47993I −0.55876 + 3.70470I
u = 1.74793 + 0.28216I
a = −0.558930 − 0.427389I
b = −2.00449 − 0.42484I
−5.22125 − 3.17687I −5.61119 − 1.61845I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.74793 − 0.28216I
a = −0.558930 + 0.427389I
b = −2.00449 + 0.42484I
−5.22125 + 3.17687I −5.61119 + 1.61845I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 20u
20
+ ··· + 16u − 1)
· (u
68
+ 81u
67
+ ··· + 7054940u + 100489)
c
2
(u
21
+ 2u
20
+ ··· + 4u − 1)(u
68
+ 5u
67
+ ··· − 86u − 317)
c
3
(u
21
+ u
20
+ ··· + 4u − 1)(u
68
− 23u
66
+ ··· + 2u + 1)
c
4
(u
21
+ u
20
+ ··· − 94u − 29)(u
68
+ 12u
67
+ ··· − 352006u + 2124268)
c
5
(u
21
− 2u
20
+ ··· + 4u + 1)(u
68
+ 5u
67
+ ··· − 86u − 317)
c
6
(u
21
− 7u
20
+ ··· − u + 1)(u
68
+ 6u
67
+ ··· − 23u + 1)
c
7
(u
21
+ u
19
+ ··· + 6u + 1)(u
68
− 3u
67
+ ··· + 4608u − 512)
c
8
(u
21
+ u
19
+ ··· + 2u − 1)(u
68
+ u
67
+ ··· + 30u − 4)
c
9
(u
21
+ 7u
20
+ ··· − u − 1)(u
68
+ 6u
67
+ ··· − 23u + 1)
c
10
(u
21
+ u
20
+ ··· + u + 1)(u
68
+ 4u
65
+ ··· + 101u + 41)
c
11
(u
21
− u
20
+ ··· + 4u + 1)(u
68
− 23u
66
+ ··· + 2u + 1)
c
12
(u
21
− 4u
20
+ ··· + 117u + 29)
· (u
68
− 15u
67
+ ··· + 4125551u − 99557)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
− 24y
20
+ ··· + 36y −1)
· (y
68
− 173y
67
+ ··· + 1338138438004y + 10098039121)
c
2
, c
5
(y
21
− 20y
20
+ ··· + 16y −1)
· (y
68
− 81y
67
+ ··· − 7054940y + 100489)
c
3
, c
11
(y
21
− 17y
20
+ ··· + 10y −1)(y
68
− 46y
67
+ ··· + 10y + 1)
c
4
(y
21
+ 17y
20
+ ··· − 14364y −841)
· (y
68
+ 72y
67
+ ··· + 70533073386900y + 4512514535824)
c
6
, c
9
(y
21
+ 13y
20
+ ··· − 7y −1)(y
68
+ 12y
67
+ ··· − 193y + 1)
c
7
(y
21
+ 2y
20
+ ··· + 28y −1)
· (y
68
+ 21y
67
+ ··· + 15597568y + 262144)
c
8
(y
21
+ 2y
20
+ ··· − 16y −1)(y
68
− 3y
67
+ ··· + 100y + 16)
c
10
(y
21
+ 9y
20
+ ··· + y −1)(y
68
+ 60y
66
+ ··· − 19877y + 1681)
c
12
(y
21
− 10y
20
+ ··· + 5685y −841)
· (y
68
− 59y
67
+ ··· − 745245389293y + 9911596249)
21
