12a
1267
(K12a
1267
)
A knot diagram
1
Linearized knot diagam
5 7 10 9 12 11 3 1 4 2 6 8
Solving Sequence
4,9 1,5
2 10 11 3 8 7 6 12
c
4
c
1
c
9
c
10
c
3
c
8
c
7
c
6
c
12
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.25299 × 10
186
u
85
− 5.27253 × 10
186
u
84
+ ··· + 1.79012 × 10
186
b + 8.66584 × 10
186
,
− 1.26969 × 10
188
u
85
+ 1.78691 × 10
188
u
84
+ ··· + 1.25308 × 10
187
a − 1.51944 × 10
188
,
3u
86
− 3u
85
+ ··· + 4u + 1i
I
u
2
= h18u
13
− 174u
12
+ ··· + 89b − 27, 75u
13
− 102u
12
+ ··· + 89a − 157,
3u
14
+ 26u
12
+ 88u
10
− u
9
+ 145u
8
− 5u
7
+ 117u
6
− 8u
5
+ 40u
4
− 4u
3
+ 5u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 100 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
= h8.25 × 10
186
u
85
− 5.27 × 10
186
u
84
+ · · · + 1.79 × 10
186
b + 8.67 ×
10
186
, −1.27 × 10
188
u
85
+ 1.79 × 10
188
u
84
+ · · · + 1.25 × 10
187
a − 1.52 ×
10
188
, 3u
86
− 3u
85
+ · · · + 4u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
1
=
10.1325u
85
− 14.2601u
84
+ ··· + 33.2708u + 12.1256
−4.61031u
85
+ 2.94535u
84
+ ··· − 0.310845u − 4.84093
a
5
=
1
−u
2
a
2
=
12.8237u
85
− 16.0117u
84
+ ··· + 31.4557u + 15.5907
−3.45859u
85
+ 4.30170u
84
+ ··· + 1.83913u − 4.52771
a
10
=
u
u
a
11
=
−1.12037u
85
+ 0.720337u
84
+ ··· + 17.0454u + 0.878741
−2.47836u
85
+ 1.02170u
84
+ ··· + 4.70916u − 6.99628
a
3
=
u
2
+ 1
u
2
a
8
=
−17.5488u
85
+ 22.2190u
84
+ ··· + 16.4041u − 18.0315
−4.97010u
85
+ 7.09366u
84
+ ··· − 1.24274u − 5.11704
a
7
=
−14.4489u
85
+ 18.7957u
84
+ ··· + 18.7718u − 13.3281
−6.11026u
85
+ 9.21618u
84
+ ··· − 0.915132u − 4.68180
a
6
=
−14.2020u
85
+ 17.7124u
84
+ ··· − 7.96939u − 10.9258
0.953032u
85
− 2.63390u
84
+ ··· + 7.75357u + 2.84298
a
12
=
−0.365418u
85
+ 0.299031u
84
+ ··· − 12.0524u − 1.61229
−3.84456u
85
+ 3.13245u
84
+ ··· − 0.840605u − 6.14246
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8.37795u
85
− 7.06948u
84
+ ··· − 60.2641u + 24.3494
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
86
+ 7u
85
+ ··· + 486114u + 316869
c
2
, c
7
u
86
+ 3u
85
+ ··· + 148u + 799
c
3
, c
4
, c
9
3(3u
86
+ 3u
85
+ ··· − 4u + 1)
c
5
, c
6
, c
11
3(3u
86
− 3u
85
+ ··· + 4u + 1)
c
8
, c
12
u
86
− 3u
85
+ ··· − 148u + 799
c
10
u
86
− 7u
85
+ ··· − 486114u + 316869
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
86
− 21y
85
+ ··· − 1166956777638y + 100405963161
c
2
, c
7
, c
8
c
12
y
86
− 57y
85
+ ··· − 19180326y + 638401
c
3
, c
4
, c
5
c
6
, c
9
, c
11
9(9y
86
+ 873y
85
+ ··· − 66y + 1)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.487671 + 0.911543I
a = −0.520086 − 0.799977I
b = −0.439016 − 1.321780I
−1.064110 + 0.470205I 0
u = −0.487671 − 0.911543I
a = −0.520086 + 0.799977I
b = −0.439016 + 1.321780I
−1.064110 − 0.470205I 0
u = 0.856002 + 0.610688I
a = 0.628665 − 1.135580I
b = −0.261332 − 1.147530I
7.12197 + 12.14790I 0
u = 0.856002 − 0.610688I
a = 0.628665 + 1.135580I
b = −0.261332 + 1.147530I
7.12197 − 12.14790I 0
u = 0.963439 + 0.540998I
a = −1.023910 + 0.143235I
b = 0.096072 + 0.494800I
7.39198 − 6.24203I 0
u = 0.963439 − 0.540998I
a = −1.023910 − 0.143235I
b = 0.096072 − 0.494800I
7.39198 + 6.24203I 0
u = −0.921313 + 0.623699I
a = 0.669038 + 0.884005I
b = −0.402135 + 1.000600I
− 7.67590I 0
u = −0.921313 − 0.623699I
a = 0.669038 − 0.884005I
b = −0.402135 − 1.000600I
7.67590I 0
u = 0.321220 + 0.803749I
a = 0.37667 + 1.46824I
b = −0.341366 + 0.788072I
4.70459 + 3.23509I 0
u = 0.321220 − 0.803749I
a = 0.37667 − 1.46824I
b = −0.341366 − 0.788072I
4.70459 − 3.23509I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.505194 + 0.690435I
a = −0.215663 + 0.821217I
b = −0.83631 + 1.34916I
9.33013 + 2.31543I 0
u = −0.505194 − 0.690435I
a = −0.215663 − 0.821217I
b = −0.83631 − 1.34916I
9.33013 − 2.31543I 0
u = 0.431731 + 1.091580I
a = −0.014101 − 0.384619I
b = −0.607306 − 0.957724I
1.064110 + 0.470205I 0
u = 0.431731 − 1.091580I
a = −0.014101 + 0.384619I
b = −0.607306 + 0.957724I
1.064110 − 0.470205I 0
u = 0.560237 + 0.564254I
a = −0.77532 + 1.23875I
b = −0.291815 + 1.153590I
−3.23212 + 3.41317I 0
u = 0.560237 − 0.564254I
a = −0.77532 − 1.23875I
b = −0.291815 − 1.153590I
−3.23212 − 3.41317I 0
u = −0.000759 + 1.241220I
a = 0.557676 + 0.663407I
b = −0.981779 + 0.464477I
4.73562 + 2.64695I 0
u = −0.000759 − 1.241220I
a = 0.557676 − 0.663407I
b = −0.981779 − 0.464477I
4.73562 − 2.64695I 0
u = −0.627267 + 0.407754I
a = −1.11760 + 0.99125I
b = 0.262891 + 0.167185I
10.13040 − 6.27484I 6.40999 + 5.74696I
u = −0.627267 − 0.407754I
a = −1.11760 − 0.99125I
b = 0.262891 − 0.167185I
10.13040 + 6.27484I 6.40999 − 5.74696I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.726981 + 0.084860I
a = 1.41693 + 0.38257I
b = 0.767837 + 0.216395I
7.23134 + 0.42251I 5.49191 + 0.I
u = 0.726981 − 0.084860I
a = 1.41693 − 0.38257I
b = 0.767837 − 0.216395I
7.23134 − 0.42251I 5.49191 + 0.I
u = −0.596524 + 0.422138I
a = −1.02316 − 1.47258I
b = −0.315235 − 1.281800I
2.30383 − 6.26437I 1.63409 + 7.43655I
u = −0.596524 − 0.422138I
a = −1.02316 + 1.47258I
b = −0.315235 + 1.281800I
2.30383 + 6.26437I 1.63409 − 7.43655I
u = 0.287124 + 1.241250I
a = −0.244566 + 0.741804I
b = −0.909415 + 0.192812I
3.16071 + 4.12903I 0
u = 0.287124 − 1.241250I
a = −0.244566 − 0.741804I
b = −0.909415 − 0.192812I
3.16071 − 4.12903I 0
u = −0.235693 + 1.263220I
a = 0.032254 − 0.400412I
b = −0.555856 − 0.007715I
−1.86105 − 3.25299I 0
u = −0.235693 − 1.263220I
a = 0.032254 + 0.400412I
b = −0.555856 + 0.007715I
−1.86105 + 3.25299I 0
u = 0.631478 + 0.271047I
a = −0.591175 − 1.013090I
b = 0.344397 − 0.092151I
3.23212 + 3.41317I 5.46052 − 6.79522I
u = 0.631478 − 0.271047I
a = −0.591175 + 1.013090I
b = 0.344397 + 0.092151I
3.23212 − 3.41317I 5.46052 + 6.79522I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.193356 + 0.653858I
a = 0.39714 − 1.66348I
b = −0.120691 − 0.722866I
−0.89196 − 2.61916I −5.06104 + 7.35063I
u = −0.193356 − 0.653858I
a = 0.39714 + 1.66348I
b = −0.120691 + 0.722866I
−0.89196 + 2.61916I −5.06104 − 7.35063I
u = −0.676515
a = 0.391689
b = 0.480875
2.05833 4.89630
u = −0.673175
a = 0.969085
b = 0.605912
1.99887 7.65390
u = −0.144636 + 1.328270I
a = 0.505549 − 0.495815I
b = −0.112467 − 0.581830I
−1.95971 − 2.93883I 0
u = −0.144636 − 1.328270I
a = 0.505549 + 0.495815I
b = −0.112467 + 0.581830I
−1.95971 + 2.93883I 0
u = 0.479835 + 0.420836I
a = 0.892610 + 1.003410I
b = 0.124839 + 0.664543I
6.00993 + 1.65203I 4.77572 − 3.95144I
u = 0.479835 − 0.420836I
a = 0.892610 − 1.003410I
b = 0.124839 − 0.664543I
6.00993 − 1.65203I 4.77572 + 3.95144I
u = −0.06042 + 1.41537I
a = −0.002140 + 0.690224I
b = −0.99592 + 4.19318I
3.28875 − 4.65753I 0
u = −0.06042 − 1.41537I
a = −0.002140 − 0.690224I
b = −0.99592 − 4.19318I
3.28875 + 4.65753I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04706 + 1.42242I
a = 0.613070 − 1.016210I
b = 0.17258 − 2.46335I
−3.16071 − 4.12903I 0
u = −0.04706 − 1.42242I
a = 0.613070 + 1.016210I
b = 0.17258 + 2.46335I
−3.16071 + 4.12903I 0
u = 0.01657 + 1.43758I
a = 0.299100 + 1.063970I
b = −0.34288 + 2.97475I
−7.23134 + 0.42251I 0
u = 0.01657 − 1.43758I
a = 0.299100 − 1.063970I
b = −0.34288 − 2.97475I
−7.23134 − 0.42251I 0
u = 0.03499 + 1.44768I
a = 0.028434 − 0.897624I
b = −0.59814 − 3.42379I
−4.70459 + 3.23509I 0
u = 0.03499 − 1.44768I
a = 0.028434 + 0.897624I
b = −0.59814 + 3.42379I
−4.70459 − 3.23509I 0
u = 0.18665 + 1.43635I
a = 0.825892 + 0.184922I
b = 0.850357 + 0.231410I
−2.30383 + 6.26437I 0
u = 0.18665 − 1.43635I
a = 0.825892 − 0.184922I
b = 0.850357 − 0.231410I
−2.30383 − 6.26437I 0
u = 0.11480 + 1.44688I
a = −0.694209 − 0.053203I
b = −0.679675 − 0.653122I
3.69188I 0
u = 0.11480 − 1.44688I
a = −0.694209 + 0.053203I
b = −0.679675 + 0.653122I
− 3.69188I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.283866 + 0.467353I
a = 1.79360 + 1.70928I
b = 0.239555 + 0.361758I
1.95971 + 2.93883I −0.481864 − 0.328566I
u = −0.283866 − 0.467353I
a = 1.79360 − 1.70928I
b = 0.239555 − 0.361758I
1.95971 − 2.93883I −0.481864 + 0.328566I
u = −0.03514 + 1.45912I
a = −0.566579 + 0.046761I
b = −0.219530 + 0.313848I
−6.00993 − 1.65203I 0
u = −0.03514 − 1.45912I
a = −0.566579 − 0.046761I
b = −0.219530 − 0.313848I
−6.00993 + 1.65203I 0
u = −0.20070 + 1.48548I
a = 0.971535 + 0.007856I
b = 1.236640 + 0.079684I
3.93602 − 9.24074I 0
u = −0.20070 − 1.48548I
a = 0.971535 − 0.007856I
b = 1.236640 − 0.079684I
3.93602 + 9.24074I 0
u = −0.21298 + 1.48636I
a = −0.237402 + 0.916328I
b = 0.86614 + 3.02599I
−3.93602 − 9.24074I 0
u = −0.21298 − 1.48636I
a = −0.237402 − 0.916328I
b = 0.86614 − 3.02599I
−3.93602 + 9.24074I 0
u = 0.02339 + 1.52036I
a = −0.211488 − 1.106500I
b = −0.43560 − 3.21969I
−4.73562 + 2.64695I 0
u = 0.02339 − 1.52036I
a = −0.211488 + 1.106500I
b = −0.43560 + 3.21969I
−4.73562 − 2.64695I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.19979 + 1.53163I
a = −0.172954 − 0.869817I
b = 0.68014 − 2.86249I
−10.13040 + 6.27484I 0
u = 0.19979 − 1.53163I
a = −0.172954 + 0.869817I
b = 0.68014 + 2.86249I
−10.13040 − 6.27484I 0
u = −0.223952 + 0.387967I
a = 0.618142 − 0.502973I
b = −0.169088 − 0.351297I
− 0.900974I 0. + 7.50554I
u = −0.223952 − 0.387967I
a = 0.618142 + 0.502973I
b = −0.169088 + 0.351297I
0.900974I 0. − 7.50554I
u = 0.434522
a = 2.58762
b = 0.222757
−2.05833 −4.89630
u = −0.07485 + 1.56466I
a = −0.441297 + 0.905738I
b = −0.35616 + 2.76608I
−8.34474 − 3.71137I 0
u = −0.07485 − 1.56466I
a = −0.441297 − 0.905738I
b = −0.35616 − 2.76608I
−8.34474 + 3.71137I 0
u = 0.08170 + 1.59085I
a = −0.648395 − 0.893946I
b = −0.65822 − 2.54758I
−3.28875 + 4.65753I 0
u = 0.08170 − 1.59085I
a = −0.648395 + 0.893946I
b = −0.65822 + 2.54758I
−3.28875 − 4.65753I 0
u = 0.29800 + 1.57396I
a = 0.246710 + 0.935520I
b = −0.15569 + 3.07448I
16.4101I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29800 − 1.57396I
a = 0.246710 − 0.935520I
b = −0.15569 − 3.07448I
− 16.4101I 0
u = −0.30827 + 1.57408I
a = 0.140960 − 0.917038I
b = −0.17590 − 3.00993I
−7.12197 − 12.14790I 0
u = −0.30827 − 1.57408I
a = 0.140960 + 0.917038I
b = −0.17590 + 3.00993I
−7.12197 + 12.14790I 0
u = −0.17904 + 1.60291I
a = −0.112096 + 0.747783I
b = 0.52909 + 2.60371I
−9.33013 − 2.31543I 0
u = −0.17904 − 1.60291I
a = −0.112096 − 0.747783I
b = 0.52909 − 2.60371I
−9.33013 + 2.31543I 0
u = 0.34500 + 1.57965I
a = 0.006689 + 0.841214I
b = −0.15345 + 2.86415I
−7.39198 + 6.24203I 0
u = 0.34500 − 1.57965I
a = 0.006689 − 0.841214I
b = −0.15345 − 2.86415I
−7.39198 − 6.24203I 0
u = −0.282381 + 0.029712I
a = 4.00451 + 2.52429I
b = 0.421921 + 0.008830I
1.86105 − 3.25299I 5.47082 − 3.29014I
u = −0.282381 − 0.029712I
a = 4.00451 − 2.52429I
b = 0.421921 − 0.008830I
1.86105 + 3.25299I 5.47082 + 3.29014I
u = 0.150688 + 0.214643I
a = −0.98298 + 3.63099I
b = 0.681811 + 0.988825I
0.89196 + 2.61916I 5.06104 − 7.35063I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.150688 − 0.214643I
a = −0.98298 − 3.63099I
b = 0.681811 − 0.988825I
0.89196 − 2.61916I 5.06104 + 7.35063I
u = −0.229003 + 0.075392I
a = −2.35269 − 2.28645I
b = 1.19133 − 1.76013I
8.34474 − 3.71137I 7.0250 + 12.9569I
u = −0.229003 − 0.075392I
a = −2.35269 + 2.28645I
b = 1.19133 + 1.76013I
8.34474 + 3.71137I 7.0250 − 12.9569I
u = 0.161155
a = 7.85670
b = 0.573794
−1.99887 −7.65390
u = 0.01745 + 2.15189I
a = 0.020095 − 0.458120I
b = 0.20772 − 2.77676I
− 0.140881I 0
u = 0.01745 − 2.15189I
a = 0.020095 + 0.458120I
b = 0.20772 + 2.77676I
0.140881I 0
13
II. I
u
2
= h18u
13
− 174u
12
+ · · · + 89b − 27, 75u
13
− 102u
12
+ · · · + 89a −
157, 3u
14
+ 26u
12
+ · · · + 5u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
1
=
−0.842697u
13
+ 1.14607u
12
+ ··· − 5.56180u + 1.76404
−0.202247u
13
+ 1.95506u
12
+ ··· − 2.13483u + 0.303371
a
5
=
1
−u
2
a
2
=
0.438202u
13
− 0.235955u
12
+ ··· − 3.70787u + 1.84270
0.438202u
13
− 0.235955u
12
+ ··· − 1.70787u − 0.157303
a
10
=
u
u
a
11
=
3.84270u
13
+ 1.85393u
12
+ ··· − 2.43820u + 2.23596
0.842697u
13
+ 1.85393u
12
+ ··· + 2.56180u + 1.23596
a
3
=
u
2
+ 1
u
2
a
8
=
−0.471910u
13
− 0.438202u
12
+ ··· − 7.31461u + 2.70787
−0.235955u
13
− 1.71910u
12
+ ··· − 1.15730u − 0.146067
a
7
=
−1.04494u
13
+ 0.101124u
12
+ ··· − 6.69663u + 2.06742
−2.66292u
13
− 2.25843u
12
+ ··· − 1.77528u − 0.505618
a
6
=
−1.75281u
13
+ 0.943820u
12
+ ··· − 13.1685u + 1.62921
1.55056u
13
− 1.98876u
12
+ ··· + 0.0337079u − 1.32584
a
12
=
−4.41573u
13
− 1.31461u
12
+ ··· + 1.05618u − 3.87640
0.370787u
13
− 1.58427u
12
+ ··· − 0.752809u − 1.05618
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
375
89
u
13
+
777
89
u
12
−
2929
89
u
11
+
4610
89
u
10
−
8245
89
u
9
+
8241
89
u
8
−
9589
89
u
7
+
1708
89
u
6
−
2626
89
u
5
−
7109
89
u
4
+
2607
89
u
3
−
4498
89
u
2
+
1263
89
u −
461
89
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
+ 3u
12
+ ··· − 6u + 3
c
2
, c
12
u
14
− 2u
13
+ ··· − 2u + 1
c
3
, c
4
, c
11
3(3u
14
+ 26u
12
+ ··· + 5u
2
+ 1)
c
5
, c
6
, c
9
3(3u
14
+ 26u
12
+ ··· + 5u
2
+ 1)
c
7
, c
8
u
14
+ 2u
13
+ ··· + 2u + 1
c
10
u
14
+ 3u
12
+ ··· + 6u + 3
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
14
+ 6y
13
+ ··· + 138y + 9
c
2
, c
7
, c
8
c
12
y
14
− 10y
13
+ ··· − 10y + 1
c
3
, c
4
, c
5
c
6
, c
9
, c
11
9(9y
14
+ 156y
13
+ ··· + 10y + 1)
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.049553 + 0.816998I
a = 0.622815 + 1.051080I
b = 0.255119 + 1.055430I
1.85654I 0. − 2.13171I
u = −0.049553 − 0.816998I
a = 0.622815 − 1.051080I
b = 0.255119 − 1.055430I
− 1.85654I 0. + 2.13171I
u = −0.166900 + 1.243020I
a = 0.200539 − 0.505880I
b = −0.307932 + 0.212975I
−1.67379 − 3.65413I 2.66692 + 12.62316I
u = −0.166900 − 1.243020I
a = 0.200539 + 0.505880I
b = −0.307932 − 0.212975I
−1.67379 + 3.65413I 2.66692 − 12.62316I
u = 0.119392 + 1.297390I
a = 0.206627 + 0.369905I
b = −0.61057 − 1.43823I
4.75184 + 4.77157I 5.13799 − 5.06722I
u = 0.119392 − 1.297390I
a = 0.206627 − 0.369905I
b = −0.61057 + 1.43823I
4.75184 − 4.77157I 5.13799 + 5.06722I
u = −0.07305 + 1.52385I
a = −0.623956 + 1.010240I
b = −0.56152 + 2.77414I
−4.75184 − 4.77157I −5.13799 + 5.06722I
u = −0.07305 − 1.52385I
a = −0.623956 − 1.010240I
b = −0.56152 − 2.77414I
−4.75184 + 4.77157I −5.13799 − 5.06722I
u = 0.313574 + 0.311781I
a = 1.44019 − 0.55383I
b = 0.64911 − 1.78138I
8.19608 − 3.29147I 0.69516 − 3.25780I
u = 0.313574 − 0.311781I
a = 1.44019 + 0.55383I
b = 0.64911 + 1.78138I
8.19608 + 3.29147I 0.69516 + 3.25780I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10498 + 1.57135I
a = −0.317975 − 0.874627I
b = −0.18321 − 2.77269I
−8.19608 + 3.29147I −0.69516 + 3.25780I
u = 0.10498 − 1.57135I
a = −0.317975 + 0.874627I
b = −0.18321 + 2.77269I
−8.19608 − 3.29147I −0.69516 − 3.25780I
u = −0.248446 + 0.321511I
a = −0.52824 − 3.56716I
b = −0.240997 − 0.492814I
1.67379 − 3.65413I −2.66692 + 12.62316I
u = −0.248446 − 0.321511I
a = −0.52824 + 3.56716I
b = −0.240997 + 0.492814I
1.67379 + 3.65413I −2.66692 − 12.62316I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
14
+ 3u
12
+ ··· − 6u + 3)(u
86
+ 7u
85
+ ··· + 486114u + 316869)
c
2
(u
14
− 2u
13
+ ··· − 2u + 1)(u
86
+ 3u
85
+ ··· + 148u + 799)
c
3
, c
4
9(3u
14
+ 26u
12
+ ··· + 5u
2
+ 1)(3u
86
+ 3u
85
+ ··· − 4u + 1)
c
5
, c
6
9(3u
14
+ 26u
12
+ ··· + 5u
2
+ 1)(3u
86
− 3u
85
+ ··· + 4u + 1)
c
7
(u
14
+ 2u
13
+ ··· + 2u + 1)(u
86
+ 3u
85
+ ··· + 148u + 799)
c
8
(u
14
+ 2u
13
+ ··· + 2u + 1)(u
86
− 3u
85
+ ··· − 148u + 799)
c
9
9(3u
14
+ 26u
12
+ ··· + 5u
2
+ 1)(3u
86
+ 3u
85
+ ··· − 4u + 1)
c
10
(u
14
+ 3u
12
+ ··· + 6u + 3)(u
86
− 7u
85
+ ··· − 486114u + 316869)
c
11
9(3u
14
+ 26u
12
+ ··· + 5u
2
+ 1)(3u
86
− 3u
85
+ ··· + 4u + 1)
c
12
(u
14
− 2u
13
+ ··· − 2u + 1)(u
86
− 3u
85
+ ··· − 148u + 799)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
14
+ 6y
13
+ ··· + 138y + 9)
· (y
86
− 21y
85
+ ··· − 1166956777638y + 100405963161)
c
2
, c
7
, c
8
c
12
(y
14
− 10y
13
+ ··· − 10y + 1)
· (y
86
− 57y
85
+ ··· − 19180326y + 638401)
c
3
, c
4
, c
5
c
6
, c
9
, c
11
81(9y
14
+ 156y
13
+ ··· + 10y + 1)(9y
86
+ 873y
85
+ ··· − 66y + 1)
20
