12n
0406
(K12n
0406
)
A knot diagram
1
Linearized knot diagam
3 6 11 8 2 10 3 6 12 4 7 9
Solving Sequence
4,10 7,11
12 3 8 6 2 1 5 9
c
10
c
11
c
3
c
7
c
6
c
2
c
1
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.87440 × 10
71
u
62
− 1.29008 × 10
72
u
61
+ ··· + 1.81459 × 10
71
b − 1.38281 × 10
71
,
− 2.97873 × 10
71
u
62
+ 5.61189 × 10
71
u
61
+ ··· + 1.81459 × 10
71
a + 2.70646 × 10
72
, u
63
+ 2u
62
+ ··· + 6u + 1i
I
u
2
= h−10479u
21
− 2016u
20
+ ··· + 5129b − 19746, 37379u
21
+ 17665u
20
+ ··· + 5129a + 15443,
u
22
+ u
21
+ ··· − u − 1i
* 2 irreducible components of dim
C
= 0, with total 85 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−5.87×10
71
u
62
−1.29×10
72
u
61
+· · ·+1.81×10
71
b−1.38×10
71
, −2.98×
10
71
u
62
+5.61×10
71
u
61
+· · ·+1.81×10
71
a+2.71×10
72
, u
63
+2u
62
+· · ·+6u+1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
7
=
1.64155u
62
− 3.09266u
61
+ ··· − 78.0276u − 14.9150
3.23732u
62
+ 7.10951u
61
+ ··· + 9.94343u + 0.762053
a
11
=
1
u
2
a
12
=
−4.56195u
62
− 4.68616u
61
+ ··· + 86.2185u + 15.8520
−3.41127u
62
− 5.48261u
61
+ ··· + 26.0173u + 4.13758
a
3
=
u
u
3
+ u
a
8
=
3.21507u
62
+ 3.09966u
61
+ ··· − 48.7262u − 10.7328
5.23718u
62
+ 12.3432u
61
+ ··· + 19.3996u + 1.89905
a
6
=
4.87888u
62
+ 4.01685u
61
+ ··· − 68.0842u − 14.1530
3.23732u
62
+ 7.10951u
61
+ ··· + 9.94343u + 0.762053
a
2
=
10.1884u
62
+ 21.3682u
61
+ ··· − 36.8563u − 13.2634
4.69842u
62
+ 7.98433u
61
+ ··· − 13.0129u − 2.93288
a
1
=
9.84597u
62
+ 20.6041u
61
+ ··· − 38.4795u − 13.7100
5.22967u
62
+ 9.33504u
61
+ ··· − 13.8182u − 3.30023
a
5
=
−5.48003u
62
− 12.9936u
61
+ ··· + 17.9312u + 10.1134
0.614387u
62
+ 2.61208u
61
+ ··· − 6.75173u − 1.33074
a
9
=
−6.73921u
62
− 6.56138u
61
+ ··· + 85.1609u + 19.5180
0.137452u
62
+ 2.12280u
61
+ ··· + 9.76922u + 1.53689
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.92172u
62
− 2.79562u
61
+ ··· − 66.9143u − 26.6390
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
63
+ 82u
62
+ ··· + 19u + 1
c
2
, c
5
u
63
+ 4u
62
+ ··· − u + 1
c
3
, c
10
u
63
+ 2u
62
+ ··· + 6u + 1
c
4
u
63
− 45u
61
+ ··· + 113780u + 6263
c
6
u
63
+ 6u
62
+ ··· + 103u + 43
c
7
u
63
− u
62
+ ··· + 83083u + 12017
c
8
u
63
+ 11u
62
+ ··· + 1626730u + 769055
c
9
, c
12
u
63
− 3u
62
+ ··· + 4u + 1
c
11
u
63
− 2u
62
+ ··· + 197u + 23
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
63
− 190y
62
+ ··· − 761y −1
c
2
, c
5
y
63
− 82y
62
+ ··· + 19y −1
c
3
, c
10
y
63
+ 34y
62
+ ··· − 8y −1
c
4
y
63
− 90y
62
+ ··· + 1565666672y −39225169
c
6
y
63
+ 10y
62
+ ··· + 1579y −1849
c
7
y
63
− 19y
62
+ ··· + 1438703057y −144408289
c
8
y
63
− 105y
62
+ ··· + 44795152652180y −591445593025
c
9
, c
12
y
63
+ 27y
62
+ ··· − 16y −1
c
11
y
63
+ 12y
62
+ ··· − 15287y −529
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.990747 + 0.105264I
a = 0.227845 − 0.215922I
b = 0.595296 + 0.556231I
−1.43917 − 1.61508I −12.00000 + 4.60707I
u = −0.990747 − 0.105264I
a = 0.227845 + 0.215922I
b = 0.595296 − 0.556231I
−1.43917 + 1.61508I −12.00000 − 4.60707I
u = −0.362778 + 0.887366I
a = 0.602460 − 0.037525I
b = 0.740076 − 0.367736I
1.42285 + 4.05328I −10.60708 − 8.49104I
u = −0.362778 − 0.887366I
a = 0.602460 + 0.037525I
b = 0.740076 + 0.367736I
1.42285 − 4.05328I −10.60708 + 8.49104I
u = 0.946133 + 0.149538I
a = 0.157340 + 0.179031I
b = −0.703205 + 0.947694I
−0.51505 + 4.80413I −13.8646 − 5.8524I
u = 0.946133 − 0.149538I
a = 0.157340 − 0.179031I
b = −0.703205 − 0.947694I
−0.51505 − 4.80413I −13.8646 + 5.8524I
u = −0.302806 + 1.009340I
a = −0.06447 + 2.59329I
b = 0.79301 − 1.46212I
3.40020 + 4.23251I 0
u = −0.302806 − 1.009340I
a = −0.06447 − 2.59329I
b = 0.79301 + 1.46212I
3.40020 − 4.23251I 0
u = 0.366638 + 1.026710I
a = 1.75134 − 0.08856I
b = 0.551334 + 0.324588I
−7.10790 − 4.96709I 0
u = 0.366638 − 1.026710I
a = 1.75134 + 0.08856I
b = 0.551334 − 0.324588I
−7.10790 + 4.96709I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.432485 + 1.010080I
a = −0.63914 + 1.30892I
b = 0.80072 − 1.37567I
−7.61563 − 1.01111I 0
u = 0.432485 − 1.010080I
a = −0.63914 − 1.30892I
b = 0.80072 + 1.37567I
−7.61563 + 1.01111I 0
u = −1.085820 + 0.228198I
a = 0.0071519 + 0.0592893I
b = −0.908974 − 1.015940I
−9.06594 − 9.39819I 0
u = −1.085820 − 0.228198I
a = 0.0071519 − 0.0592893I
b = −0.908974 + 1.015940I
−9.06594 + 9.39819I 0
u = 0.239732 + 0.837215I
a = 0.16007 + 1.91347I
b = −0.875933 − 0.420278I
−1.11761 − 1.26731I −15.1175 + 4.6617I
u = 0.239732 − 0.837215I
a = 0.16007 − 1.91347I
b = −0.875933 + 0.420278I
−1.11761 + 1.26731I −15.1175 − 4.6617I
u = 0.264496 + 0.829236I
a = 0.10067 + 1.46934I
b = −1.175250 − 0.245574I
−1.14587 − 1.30347I −17.5152 + 4.9826I
u = 0.264496 − 0.829236I
a = 0.10067 − 1.46934I
b = −1.175250 + 0.245574I
−1.14587 + 1.30347I −17.5152 − 4.9826I
u = −0.376805 + 1.065330I
a = −0.80125 − 1.37166I
b = −1.200310 + 0.294963I
−6.60608 + 0.34953I 0
u = −0.376805 − 1.065330I
a = −0.80125 + 1.37166I
b = −1.200310 − 0.294963I
−6.60608 − 0.34953I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.444883 + 1.040440I
a = 1.288050 + 0.198665I
b = −1.64815 − 0.93772I
−7.15825 + 6.18151I 0
u = −0.444883 − 1.040440I
a = 1.288050 − 0.198665I
b = −1.64815 + 0.93772I
−7.15825 − 6.18151I 0
u = 0.266646 + 0.813283I
a = 0.505244 + 0.982367I
b = −1.379120 − 0.085398I
−1.17639 − 1.29143I −15.3554 + 5.4557I
u = 0.266646 − 0.813283I
a = 0.505244 − 0.982367I
b = −1.379120 + 0.085398I
−1.17639 + 1.29143I −15.3554 − 5.4557I
u = −0.896656 + 0.823164I
a = −0.512264 + 0.204586I
b = 0.135578 + 0.584282I
0.351157 + 0.534295I 0
u = −0.896656 − 0.823164I
a = −0.512264 − 0.204586I
b = 0.135578 − 0.584282I
0.351157 − 0.534295I 0
u = −0.401918 + 1.182270I
a = −0.24327 − 1.63490I
b = −0.48135 + 1.46123I
3.27235 + 3.48208I 0
u = −0.401918 − 1.182270I
a = −0.24327 + 1.63490I
b = −0.48135 − 1.46123I
3.27235 − 3.48208I 0
u = 0.394861 + 1.192190I
a = 0.12689 − 1.95895I
b = 0.784716 + 1.058410I
6.38319 − 6.23226I 0
u = 0.394861 − 1.192190I
a = 0.12689 + 1.95895I
b = 0.784716 − 1.058410I
6.38319 + 6.23226I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.154944 + 0.706018I
a = −0.650670 − 0.500412I
b = 1.19705 + 0.87628I
2.19848 − 1.89748I −9.51830 − 4.60789I
u = −0.154944 − 0.706018I
a = −0.650670 + 0.500412I
b = 1.19705 − 0.87628I
2.19848 + 1.89748I −9.51830 + 4.60789I
u = −0.367705 + 1.239600I
a = −0.285293 − 1.181370I
b = −0.007485 + 0.931592I
3.24616 + 2.75157I 0
u = −0.367705 − 1.239600I
a = −0.285293 + 1.181370I
b = −0.007485 − 0.931592I
3.24616 − 2.75157I 0
u = 0.313182 + 1.259970I
a = 0.543704 − 0.954155I
b = 0.172815 + 1.016880I
4.29462 + 0.53295I 0
u = 0.313182 − 1.259970I
a = 0.543704 + 0.954155I
b = 0.172815 − 1.016880I
4.29462 − 0.53295I 0
u = −0.558772 + 1.190380I
a = 0.410167 + 0.900060I
b = 0.693773 − 0.904421I
2.19335 + 4.97234I 0
u = −0.558772 − 1.190380I
a = 0.410167 − 0.900060I
b = 0.693773 + 0.904421I
2.19335 − 4.97234I 0
u = 0.604819 + 1.173120I
a = −0.686547 + 0.580713I
b = 0.107053 − 0.612042I
5.07461 − 2.21684I 0
u = 0.604819 − 1.173120I
a = −0.686547 − 0.580713I
b = 0.107053 + 0.612042I
5.07461 + 2.21684I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.536211 + 1.239640I
a = −0.26898 + 1.68491I
b = −0.95890 − 1.43950I
2.83710 − 10.11180I 0
u = 0.536211 − 1.239640I
a = −0.26898 − 1.68491I
b = −0.95890 + 1.43950I
2.83710 + 10.11180I 0
u = −0.515239 + 1.259240I
a = 0.30480 + 1.49648I
b = 0.806111 − 0.864148I
2.16604 + 6.91375I 0
u = −0.515239 − 1.259240I
a = 0.30480 − 1.49648I
b = 0.806111 + 0.864148I
2.16604 − 6.91375I 0
u = 0.608595 + 0.144028I
a = 0.067285 − 0.477371I
b = 0.757994 + 0.677519I
2.72700 − 2.52576I −6.98143 + 1.65333I
u = 0.608595 − 0.144028I
a = 0.067285 + 0.477371I
b = 0.757994 − 0.677519I
2.72700 + 2.52576I −6.98143 − 1.65333I
u = 0.054830 + 0.620583I
a = −0.55470 − 4.38288I
b = −0.332756 − 0.253543I
−8.90568 + 2.29149I −19.8574 − 3.6503I
u = 0.054830 − 0.620583I
a = −0.55470 + 4.38288I
b = −0.332756 + 0.253543I
−8.90568 − 2.29149I −19.8574 + 3.6503I
u = −0.606194 + 0.122041I
a = 0.612063 + 0.621270I
b = −0.262217 + 0.621399I
−0.290214 − 0.243550I −13.68198 + 0.43894I
u = −0.606194 − 0.122041I
a = 0.612063 − 0.621270I
b = −0.262217 − 0.621399I
−0.290214 + 0.243550I −13.68198 − 0.43894I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.614828 + 1.271960I
a = −0.31937 − 1.70637I
b = −1.08251 + 1.27663I
−5.7998 + 15.4283I 0
u = −0.614828 − 1.271960I
a = −0.31937 + 1.70637I
b = −1.08251 − 1.27663I
−5.7998 − 15.4283I 0
u = 1.40889 + 0.36230I
a = −0.0311359 + 0.0161896I
b = 0.478420 − 0.426890I
−12.34440 + 0.36923I 0
u = 1.40889 − 0.36230I
a = −0.0311359 − 0.0161896I
b = 0.478420 + 0.426890I
−12.34440 − 0.36923I 0
u = 0.69263 + 1.31248I
a = 0.097753 − 1.087490I
b = 0.882208 + 0.799377I
−9.07833 − 7.42766I 0
u = 0.69263 − 1.31248I
a = 0.097753 + 1.087490I
b = 0.882208 − 0.799377I
−9.07833 + 7.42766I 0
u = −0.20493 + 1.49295I
a = 0.516419 + 0.852002I
b = −0.329934 − 1.026900I
−3.00927 − 4.46302I 0
u = −0.20493 − 1.49295I
a = 0.516419 − 0.852002I
b = −0.329934 + 1.026900I
−3.00927 + 4.46302I 0
u = 0.257688 + 0.407987I
a = 1.88508 − 3.61639I
b = −0.199922 + 1.300740I
−9.34370 − 2.46865I −15.4465 + 3.3962I
u = 0.257688 − 0.407987I
a = 1.88508 + 3.61639I
b = −0.199922 − 1.300740I
−9.34370 + 2.46865I −15.4465 − 3.3962I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.322413 + 0.231256I
a = −2.69396 − 3.36716I
b = −0.793788 + 1.024690I
−9.22509 − 2.54978I −16.0238 + 1.2523I
u = −0.322413 − 0.231256I
a = −2.69396 + 3.36716I
b = −0.793788 − 1.024690I
−9.22509 + 2.54978I −16.0238 − 1.2523I
u = −0.360773
a = 0.773414
b = −0.312684
−0.615548 −16.1410
11
II. I
u
2
= h−10479u
21
− 2016u
20
+ · · · + 5129b − 19746, 37379u
21
+
17665u
20
+ · · · + 5129a + 15443, u
22
+ u
21
+ · · · − u − 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
7
=
−7.28778u
21
− 3.44414u
20
+ ··· + 10.7421u − 3.01092
2.04309u
21
+ 0.393059u
20
+ ··· − 3.29674u + 3.84987
a
11
=
1
u
2
a
12
=
−9.38760u
21
− 13.6036u
20
+ ··· + 23.3843u + 11.7306
3.05108u
21
+ 2.68317u
20
+ ··· − 7.03958u + 0.405732
a
3
=
u
u
3
+ u
a
8
=
−4.17235u
21
− 2.57224u
20
+ ··· + 7.18698u − 0.399493
3.95438u
21
+ 1.46617u
20
+ ··· − 5.97992u + 4.21778
a
6
=
−5.24469u
21
− 3.05108u
20
+ ··· + 7.44531u + 0.838955
2.04309u
21
+ 0.393059u
20
+ ··· − 3.29674u + 3.84987
a
2
=
−5.16650u
21
− 1.55508u
20
+ ··· + 6.59466u − 5.01716
1.12127u
21
− 0.110938u
20
+ ··· + 0.852603u − 0.00623903
a
1
=
−7.12673u
21
− 2.03841u
20
+ ··· + 8.16689u − 6.61727
0.0163775u
21
− 0.551959u
20
+ ··· + 1.94151u − 0.129460
a
5
=
4.62800u
21
+ 0.108793u
20
+ ··· − 3.52856u + 6.08345
−0.955937u
21
+ 0.0625853u
20
+ ··· + 0.271203u − 1.25307
a
9
=
6.06200u
21
+ 2.98187u
20
+ ··· − 5.07857u + 0.652759
−2.21213u
21
− 2.08891u
20
+ ··· + 4.61474u + 2.20062
(ii) Obstruction class = 1
(iii) Cusp Shapes =
27167
5129
u
21
+
37974
5129
u
20
+ ··· −
138057
5129
u −
95072
5129
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
22
− 25u
21
+ ··· − 94u + 9
c
2
u
22
+ 3u
21
+ ··· + 4u − 3
c
3
u
22
− u
21
+ ··· + u − 1
c
4
u
22
+ 3u
21
+ ··· + 9u − 1
c
5
u
22
− 3u
21
+ ··· − 4u − 3
c
6
u
22
+ u
21
+ ··· − 6u + 1
c
7
u
22
− 3u
20
+ ··· − 42u − 7
c
8
u
22
+ 16u
21
+ ··· − 21u + 1
c
9
u
22
− 2u
21
+ ··· − 7u + 7
c
10
u
22
+ u
21
+ ··· − u − 1
c
11
u
22
+ u
21
+ ··· + 10u − 3
c
12
u
22
+ 2u
21
+ ··· + 7u + 7
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 45y
21
+ ··· − 970y + 81
c
2
, c
5
y
22
− 25y
21
+ ··· − 94y + 9
c
3
, c
10
y
22
+ 11y
21
+ ··· + 5y + 1
c
4
y
22
− 17y
21
+ ··· + y + 1
c
6
y
22
+ 3y
21
+ ··· − 18y + 1
c
7
y
22
− 6y
21
+ ··· − 504y + 49
c
8
y
22
− 20y
21
+ ··· − 315y + 1
c
9
, c
12
y
22
+ 16y
21
+ ··· + 525y + 49
c
11
y
22
+ 9y
21
+ ··· − 52y + 9
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215981 + 0.880776I
a = 0.42291 + 1.74778I
b = −1.40489 − 0.32594I
−0.729664 − 1.055600I −2.65388 − 3.37536I
u = 0.215981 − 0.880776I
a = 0.42291 − 1.74778I
b = −1.40489 + 0.32594I
−0.729664 + 1.055600I −2.65388 + 3.37536I
u = −0.311175 + 1.080890I
a = −0.488004 + 0.062463I
b = −0.745155 − 0.531362I
−6.87085 + 3.84054I −10.78288 − 1.99979I
u = −0.311175 − 1.080890I
a = −0.488004 − 0.062463I
b = −0.745155 + 0.531362I
−6.87085 − 3.84054I −10.78288 + 1.99979I
u = 1.031220 + 0.501169I
a = −0.131657 + 0.134690I
b = 0.195174 + 0.546308I
0.292897 − 1.232480I −9.81223 + 6.77489I
u = 1.031220 − 0.501169I
a = −0.131657 − 0.134690I
b = 0.195174 − 0.546308I
0.292897 + 1.232480I −9.81223 − 6.77489I
u = −0.110176 + 0.792347I
a = 0.50663 − 4.05553I
b = −0.336422 + 0.901790I
−8.34331 − 2.04079I −6.73669 − 1.53590I
u = −0.110176 − 0.792347I
a = 0.50663 + 4.05553I
b = −0.336422 − 0.901790I
−8.34331 + 2.04079I −6.73669 + 1.53590I
u = 0.342652 + 1.196430I
a = 0.00858 − 1.86730I
b = 0.43597 + 1.36736I
5.26394 − 4.40995I −6.55309 + 3.89134I
u = 0.342652 − 1.196430I
a = 0.00858 + 1.86730I
b = 0.43597 − 1.36736I
5.26394 + 4.40995I −6.55309 − 3.89134I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.476115 + 1.200480I
a = 0.33709 + 1.86499I
b = 1.06414 − 1.14093I
5.11201 + 7.58757I −9.27554 − 6.67902I
u = −0.476115 − 1.200480I
a = 0.33709 − 1.86499I
b = 1.06414 + 1.14093I
5.11201 − 7.58757I −9.27554 + 6.67902I
u = −0.682738 + 0.059063I
a = 0.528403 + 0.030745I
b = 0.879737 + 0.878115I
1.84449 − 3.13922I −13.7549 + 4.3871I
u = −0.682738 − 0.059063I
a = 0.528403 − 0.030745I
b = 0.879737 − 0.878115I
1.84449 + 3.13922I −13.7549 − 4.3871I
u = −0.492309 + 1.236030I
a = −0.723571 − 0.734040I
b = 0.310470 + 1.012790I
5.07188 + 1.32197I −7.08101 + 1.81161I
u = −0.492309 − 1.236030I
a = −0.723571 + 0.734040I
b = 0.310470 − 1.012790I
5.07188 − 1.32197I −7.08101 − 1.81161I
u = −0.113901 + 0.608983I
a = 0.16460 + 1.46569I
b = 1.005810 − 0.896390I
2.12223 + 2.58152I −10.96980 − 5.73632I
u = −0.113901 − 0.608983I
a = 0.16460 − 1.46569I
b = 1.005810 + 0.896390I
2.12223 − 2.58152I −10.96980 + 5.73632I
u = 0.569626 + 1.287640I
a = −0.492631 + 0.851572I
b = −0.436703 − 0.769932I
3.33386 − 4.94613I −6.20084 + 4.11530I
u = 0.569626 − 1.287640I
a = −0.492631 − 0.851572I
b = −0.436703 + 0.769932I
3.33386 + 4.94613I −6.20084 − 4.11530I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43376
a = −0.278601
b = −0.203139
−12.0426 −4.69420
u = 0.487622
a = −0.986099
b = −0.733122
−2.15240 −18.6640
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 25u
21
+ ··· − 94u + 9)(u
63
+ 82u
62
+ ··· + 19u + 1)
c
2
(u
22
+ 3u
21
+ ··· + 4u − 3)(u
63
+ 4u
62
+ ··· − u + 1)
c
3
(u
22
− u
21
+ ··· + u − 1)(u
63
+ 2u
62
+ ··· + 6u + 1)
c
4
(u
22
+ 3u
21
+ ··· + 9u − 1)(u
63
− 45u
61
+ ··· + 113780u + 6263)
c
5
(u
22
− 3u
21
+ ··· − 4u − 3)(u
63
+ 4u
62
+ ··· − u + 1)
c
6
(u
22
+ u
21
+ ··· − 6u + 1)(u
63
+ 6u
62
+ ··· + 103u + 43)
c
7
(u
22
− 3u
20
+ ··· − 42u − 7)(u
63
− u
62
+ ··· + 83083u + 12017)
c
8
(u
22
+ 16u
21
+ ··· − 21u + 1)
· (u
63
+ 11u
62
+ ··· + 1626730u + 769055)
c
9
(u
22
− 2u
21
+ ··· − 7u + 7)(u
63
− 3u
62
+ ··· + 4u + 1)
c
10
(u
22
+ u
21
+ ··· − u − 1)(u
63
+ 2u
62
+ ··· + 6u + 1)
c
11
(u
22
+ u
21
+ ··· + 10u − 3)(u
63
− 2u
62
+ ··· + 197u + 23)
c
12
(u
22
+ 2u
21
+ ··· + 7u + 7)(u
63
− 3u
62
+ ··· + 4u + 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
− 45y
21
+ ··· − 970y + 81)(y
63
− 190y
62
+ ··· − 761y −1)
c
2
, c
5
(y
22
− 25y
21
+ ··· − 94y + 9)(y
63
− 82y
62
+ ··· + 19y −1)
c
3
, c
10
(y
22
+ 11y
21
+ ··· + 5y + 1)(y
63
+ 34y
62
+ ··· − 8y −1)
c
4
(y
22
− 17y
21
+ ··· + y + 1)
· (y
63
− 90y
62
+ ··· + 1565666672y −39225169)
c
6
(y
22
+ 3y
21
+ ··· − 18y + 1)(y
63
+ 10y
62
+ ··· + 1579y −1849)
c
7
(y
22
− 6y
21
+ ··· − 504y + 49)
· (y
63
− 19y
62
+ ··· + 1438703057y −144408289)
c
8
(y
22
− 20y
21
+ ··· − 315y + 1)
· (y
63
− 105y
62
+ ··· + 44795152652180y −591445593025)
c
9
, c
12
(y
22
+ 16y
21
+ ··· + 525y + 49)(y
63
+ 27y
62
+ ··· − 16y −1)
c
11
(y
22
+ 9y
21
+ ··· − 52y + 9)(y
63
+ 12y
62
+ ··· − 15287y −529)
21
