12a
0187
(K12a
0187
)
A knot diagram
1
Linearized knot diagam
3 5 9 7 2 10 1 12 11 6 4 8
Solving Sequence
2,6
5 3
1,11
10 7 8 4 9 12
c
5
c
2
c
1
c
10
c
6
c
7
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.70828 × 10
211
u
102
− 4.30580 × 10
211
u
101
+ ··· + 2.02673 × 10
212
b − 2.48946 × 10
212
,
4.27526 × 10
212
u
102
+ 1.62447 × 10
213
u
101
+ ··· + 1.82405 × 10
213
a − 3.78144 × 10
212
,
u
103
+ 2u
102
+ ··· − 50u − 9i
I
u
2
= hb + 1, 3a − 3u + 4, u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 105 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−4.71 × 10
211
u
102
− 4.31 × 10
211
u
101
+ · · · + 2.03 × 10
212
b − 2.49 ×
10
212
, 4.28 × 10
212
u
102
+ 1.62 × 10
213
u
101
+ · · · + 1.82 × 10
213
a − 3.78 ×
10
212
, u
103
+ 2u
102
+ · · · − 50u − 9i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
−0.234382u
102
− 0.890582u
101
+ ··· + 27.2644u + 0.207310
0.232309u
102
+ 0.212451u
101
+ ··· + 5.06954u + 1.22831
a
10
=
−0.466692u
102
− 1.10303u
101
+ ··· + 22.1949u − 1.02100
0.232309u
102
+ 0.212451u
101
+ ··· + 5.06954u + 1.22831
a
7
=
−0.267327u
102
− 0.877958u
101
+ ··· + 39.1849u + 7.35328
0.374555u
102
+ 0.677940u
101
+ ··· − 9.16517u − 0.221474
a
8
=
0.237025u
102
+ 0.234288u
101
+ ··· + 15.8996u + 3.19729
0.115727u
102
+ 0.335221u
101
+ ··· − 7.46104u − 0.621629
a
4
=
0.150719u
102
− 0.268946u
101
+ ··· + 12.7692u + 8.10850
0.538052u
102
+ 0.982186u
101
+ ··· − 20.4638u − 3.33616
a
9
=
−0.243327u
102
− 0.831816u
101
+ ··· + 38.7154u + 9.33905
0.344667u
102
+ 0.390802u
101
+ ··· + 1.82827u + 2.29816
a
12
=
−0.238737u
102
− 1.06579u
101
+ ··· + 25.5129u − 2.83305
0.272415u
102
+ 0.179279u
101
+ ··· + 8.93923u + 1.31134
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.09329u
102
+ 1.70936u
101
+ ··· − 12.5511u − 1.22773
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
103
+ 44u
102
+ ··· + 1510u − 81
c
2
, c
5
u
103
+ 2u
102
+ ··· − 50u − 9
c
3
9(9u
103
− 132u
102
+ ··· + 8034u − 2563)
c
4
9(9u
103
+ 87u
102
+ ··· − 19058u − 1196)
c
6
, c
10
u
103
− 3u
102
+ ··· + 3u − 1
c
7
, c
8
, c
12
u
103
+ 3u
102
+ ··· − 3u − 1
c
9
u
103
+ 37u
102
+ ··· + 13u − 1
c
11
u
103
− 5u
102
+ ··· + 648u − 108
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
103
+ 32y
102
+ ··· + 1346818y −6561
c
2
, c
5
y
103
+ 44y
102
+ ··· + 1510y −81
c
3
81(81y
103
+ 11916y
102
+ ··· + 1.84130 × 10
8
y −6568969)
c
4
81(81y
103
+ 11295y
102
+ ··· + 1.43926 × 10
8
y −1430416)
c
6
, c
10
y
103
+ 37y
102
+ ··· + 13y −1
c
7
, c
8
, c
12
y
103
+ 97y
102
+ ··· + 13y −1
c
9
y
103
+ 45y
102
+ ··· − 379y −1
c
11
y
103
+ 15y
102
+ ··· − 153576y −11664
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.871098 + 0.491257I
a = −1.30022 − 0.63958I
b = −0.694924 − 1.068860I
2.78356 + 8.56668I 0
u = −0.871098 − 0.491257I
a = −1.30022 + 0.63958I
b = −0.694924 + 1.068860I
2.78356 − 8.56668I 0
u = 0.481345 + 0.878527I
a = −8.55020 − 1.64997I
b = −0.531227 + 0.886277I
−5.02226 + 0.00767I 0
u = 0.481345 − 0.878527I
a = −8.55020 + 1.64997I
b = −0.531227 − 0.886277I
−5.02226 − 0.00767I 0
u = 0.915500 + 0.391024I
a = −1.287160 + 0.339540I
b = −0.626849 + 0.812428I
3.16321 − 0.76735I 0
u = 0.915500 − 0.391024I
a = −1.287160 − 0.339540I
b = −0.626849 − 0.812428I
3.16321 + 0.76735I 0
u = 0.111367 + 0.987800I
a = −0.314049 − 0.426026I
b = −0.557089 + 0.278730I
−1.61354 + 2.06379I 0
u = 0.111367 − 0.987800I
a = −0.314049 + 0.426026I
b = −0.557089 − 0.278730I
−1.61354 − 2.06379I 0
u = 0.590356 + 0.821048I
a = 1.35154 − 2.18344I
b = 0.555019 − 0.805027I
0.597431 + 0.086793I 0
u = 0.590356 − 0.821048I
a = 1.35154 + 2.18344I
b = 0.555019 + 0.805027I
0.597431 − 0.086793I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.453314 + 0.866625I
a = 1.014640 + 0.981164I
b = 1.155570 − 0.097756I
1.47294 − 1.87526I 0
u = −0.453314 − 0.866625I
a = 1.014640 − 0.981164I
b = 1.155570 + 0.097756I
1.47294 + 1.87526I 0
u = 0.569820 + 0.848750I
a = −0.214973 + 0.102311I
b = 0.197507 + 0.130121I
0.45171 + 2.26396I 0
u = 0.569820 − 0.848750I
a = −0.214973 − 0.102311I
b = 0.197507 − 0.130121I
0.45171 − 2.26396I 0
u = 0.359432 + 0.905150I
a = −0.75669 + 1.89295I
b = 0.352860 − 0.854813I
−0.888701 + 0.166715I 0
u = 0.359432 − 0.905150I
a = −0.75669 − 1.89295I
b = 0.352860 + 0.854813I
−0.888701 − 0.166715I 0
u = −0.921960 + 0.458261I
a = 1.47257 − 0.41314I
b = 0.852313 − 0.561544I
−1.90097 + 6.60861I 0
u = −0.921960 − 0.458261I
a = 1.47257 + 0.41314I
b = 0.852313 + 0.561544I
−1.90097 − 6.60861I 0
u = −0.793954 + 0.554908I
a = −1.60966 + 0.27728I
b = −0.864736 + 0.590779I
4.25085 + 2.77419I 0
u = −0.793954 − 0.554908I
a = −1.60966 − 0.27728I
b = −0.864736 − 0.590779I
4.25085 − 2.77419I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.495018 + 0.831311I
a = 2.68722 + 5.91244I
b = −0.462208 − 0.898317I
−4.88019 + 3.96585I 0
u = 0.495018 − 0.831311I
a = 2.68722 − 5.91244I
b = −0.462208 + 0.898317I
−4.88019 − 3.96585I 0
u = −0.293989 + 0.900677I
a = −0.340712 − 1.361400I
b = −0.846553 − 0.778278I
−6.38836 + 1.72239I 0
u = −0.293989 − 0.900677I
a = −0.340712 + 1.361400I
b = −0.846553 + 0.778278I
−6.38836 − 1.72239I 0
u = −0.277077 + 1.032330I
a = −1.19938 − 1.04039I
b = −0.201061 + 1.183910I
−5.76408 − 0.70494I 0
u = −0.277077 − 1.032330I
a = −1.19938 + 1.04039I
b = −0.201061 − 1.183910I
−5.76408 + 0.70494I 0
u = −0.986142 + 0.425293I
a = 1.39902 + 0.48943I
b = 0.684015 + 1.076400I
−3.46407 + 12.32820I 0
u = −0.986142 − 0.425293I
a = 1.39902 − 0.48943I
b = 0.684015 − 1.076400I
−3.46407 − 12.32820I 0
u = −0.610418 + 0.687254I
a = 1.81549 + 0.03994I
b = 0.914625 − 0.659767I
3.31217 − 2.28195I 0
u = −0.610418 − 0.687254I
a = 1.81549 − 0.03994I
b = 0.914625 + 0.659767I
3.31217 + 2.28195I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.429365 + 0.993415I
a = −2.23623 − 0.66942I
b = −0.793940 + 1.063610I
−7.22938 − 4.55942I 0
u = −0.429365 − 0.993415I
a = −2.23623 + 0.66942I
b = −0.793940 − 1.063610I
−7.22938 + 4.55942I 0
u = 0.575604 + 0.917006I
a = 3.51154 − 0.47561I
b = 0.558359 + 0.901843I
0.28262 + 4.54488I 0
u = 0.575604 − 0.917006I
a = 3.51154 + 0.47561I
b = 0.558359 − 0.901843I
0.28262 − 4.54488I 0
u = −0.145915 + 0.904009I
a = −0.387490 − 0.748969I
b = 0.477410 + 1.112370I
−2.20452 + 2.91537I 0
u = −0.145915 − 0.904009I
a = −0.387490 + 0.748969I
b = 0.477410 − 1.112370I
−2.20452 − 2.91537I 0
u = 0.928998 + 0.565337I
a = −1.39788 − 0.40407I
b = −0.624297 − 0.867993I
2.99328 + 4.14157I 0
u = 0.928998 − 0.565337I
a = −1.39788 + 0.40407I
b = −0.624297 + 0.867993I
2.99328 − 4.14157I 0
u = −0.439732 + 1.011410I
a = −0.0132110 − 0.0165854I
b = −0.604253 − 1.208440I
−7.11927 − 1.53062I 0
u = −0.439732 − 1.011410I
a = −0.0132110 + 0.0165854I
b = −0.604253 + 1.208440I
−7.11927 + 1.53062I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.572592 + 0.946939I
a = 0.565216 + 1.182330I
b = 1.032180 + 0.543713I
2.52591 − 2.40214I 0
u = −0.572592 − 0.946939I
a = 0.565216 − 1.182330I
b = 1.032180 − 0.543713I
2.52591 + 2.40214I 0
u = 1.118500 + 0.085441I
a = 1.174310 + 0.253168I
b = 0.642035 + 0.840314I
−0.12842 + 2.50437I 0
u = 1.118500 − 0.085441I
a = 1.174310 − 0.253168I
b = 0.642035 − 0.840314I
−0.12842 − 2.50437I 0
u = −0.682041 + 0.552389I
a = 1.12174 + 0.93636I
b = 0.720355 + 1.047180I
2.07846 + 3.71952I 0
u = −0.682041 − 0.552389I
a = 1.12174 − 0.93636I
b = 0.720355 − 1.047180I
2.07846 − 3.71952I 0
u = 0.383137 + 1.058970I
a = −0.133273 − 0.806743I
b = −0.182506 + 0.719748I
−1.47585 + 2.37544I 0
u = 0.383137 − 1.058970I
a = −0.133273 + 0.806743I
b = −0.182506 − 0.719748I
−1.47585 − 2.37544I 0
u = −0.817133 + 0.283548I
a = 0.370079 − 0.207901I
b = −0.057314 − 1.154100I
−8.29042 + 5.22148I 0
u = −0.817133 − 0.283548I
a = 0.370079 + 0.207901I
b = −0.057314 + 1.154100I
−8.29042 − 5.22148I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.550261 + 1.022500I
a = −1.149200 − 0.427257I
b = −0.982102 + 0.426405I
−4.54476 − 7.45140I 0
u = −0.550261 − 1.022500I
a = −1.149200 + 0.427257I
b = −0.982102 − 0.426405I
−4.54476 + 7.45140I 0
u = −0.497337 + 1.051020I
a = 1.096070 + 0.639427I
b = 0.103323 − 1.286110I
−4.45937 − 5.98055I 0
u = −0.497337 − 1.051020I
a = 1.096070 − 0.639427I
b = 0.103323 + 1.286110I
−4.45937 + 5.98055I 0
u = 0.655056 + 0.510094I
a = 0.360724 − 0.250421I
b = −0.384916 − 0.056331I
−3.00355 + 1.46606I 0
u = 0.655056 − 0.510094I
a = 0.360724 + 0.250421I
b = −0.384916 + 0.056331I
−3.00355 − 1.46606I 0
u = 0.632107 + 0.988265I
a = 0.418130 − 0.086811I
b = −0.264416 − 0.326151I
−4.33420 + 3.53568I 0
u = 0.632107 − 0.988265I
a = 0.418130 + 0.086811I
b = −0.264416 + 0.326151I
−4.33420 − 3.53568I 0
u = −0.602669 + 1.030500I
a = 2.12057 + 0.66881I
b = 0.727061 − 1.134850I
0.65689 − 8.70948I 0
u = −0.602669 − 1.030500I
a = 2.12057 − 0.66881I
b = 0.727061 + 1.134850I
0.65689 + 8.70948I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.031145 + 1.207760I
a = −0.462840 + 0.926806I
b = −0.559631 − 1.051590I
−3.52032 + 6.53771I 0
u = 0.031145 − 1.207760I
a = −0.462840 − 0.926806I
b = −0.559631 + 1.051590I
−3.52032 − 6.53771I 0
u = −0.648711 + 1.052320I
a = −0.522042 − 1.067520I
b = −0.946139 − 0.528511I
2.75148 − 8.20254I 0
u = −0.648711 − 1.052320I
a = −0.522042 + 1.067520I
b = −0.946139 + 0.528511I
2.75148 + 8.20254I 0
u = 0.384723 + 1.181550I
a = 0.535525 + 0.949353I
b = 0.040165 − 0.822281I
−7.32781 + 3.96721I 0
u = 0.384723 − 1.181550I
a = 0.535525 − 0.949353I
b = 0.040165 + 0.822281I
−7.32781 − 3.96721I 0
u = −0.580143 + 0.480187I
a = −0.84467 − 1.20839I
b = −0.809110 − 0.334106I
−3.00791 + 2.92106I 6.00000 − 4.14158I
u = −0.580143 − 0.480187I
a = −0.84467 + 1.20839I
b = −0.809110 + 0.334106I
−3.00791 − 2.92106I 6.00000 + 4.14158I
u = −0.216993 + 1.245200I
a = 0.894698 + 1.036440I
b = 0.111870 − 1.129660I
−13.24120 + 1.89785I 0
u = −0.216993 − 1.245200I
a = 0.894698 − 1.036440I
b = 0.111870 + 1.129660I
−13.24120 − 1.89785I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.742441 + 1.029240I
a = −0.484188 + 0.759047I
b = −0.579742 + 0.726146I
1.60775 + 1.95719I 0
u = 0.742441 − 1.029240I
a = −0.484188 − 0.759047I
b = −0.579742 − 0.726146I
1.60775 − 1.95719I 0
u = −0.000731 + 1.276870I
a = 0.546798 + 0.248636I
b = 0.688415 − 0.412207I
−8.39396 + 3.98589I 0
u = −0.000731 − 1.276870I
a = 0.546798 − 0.248636I
b = 0.688415 + 0.412207I
−8.39396 − 3.98589I 0
u = −0.573087 + 1.142630I
a = −0.921485 − 0.642704I
b = −0.056200 + 1.252430I
−10.8112 − 10.3483I 0
u = −0.573087 − 1.142630I
a = −0.921485 + 0.642704I
b = −0.056200 − 1.252430I
−10.8112 + 10.3483I 0
u = −0.660173 + 1.105650I
a = −2.07363 − 0.69473I
b = −0.703524 + 1.121920I
0.9191 − 14.2325I 0
u = −0.660173 − 1.105650I
a = −2.07363 + 0.69473I
b = −0.703524 − 1.121920I
0.9191 + 14.2325I 0
u = 1.056470 + 0.736775I
a = 1.048320 − 0.512228I
b = 0.633156 − 0.779153I
−0.82056 + 1.15724I 0
u = 1.056470 − 0.736775I
a = 1.048320 + 0.512228I
b = 0.633156 + 0.779153I
−0.82056 − 1.15724I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.665628 + 1.136790I
a = 0.483282 + 1.020280I
b = 0.916919 + 0.529397I
−3.97588 − 12.42400I 0
u = −0.665628 − 1.136790I
a = 0.483282 − 1.020280I
b = 0.916919 − 0.529397I
−3.97588 + 12.42400I 0
u = 0.690235 + 1.138730I
a = −1.81858 + 0.59872I
b = −0.596895 − 0.937188I
0.95043 + 6.66404I 0
u = 0.690235 − 1.138730I
a = −1.81858 − 0.59872I
b = −0.596895 + 0.937188I
0.95043 − 6.66404I 0
u = 0.142734 + 0.640869I
a = −1.26726 − 2.96524I
b = −0.385243 + 0.991777I
−5.12697 − 1.48065I −1.36691 + 1.15477I
u = 0.142734 − 0.640869I
a = −1.26726 + 2.96524I
b = −0.385243 − 0.991777I
−5.12697 + 1.48065I −1.36691 − 1.15477I
u = −0.676032 + 1.172660I
a = 2.04749 + 0.72412I
b = 0.694637 − 1.112980I
−5.7675 − 18.3493I 0
u = −0.676032 − 1.172660I
a = 2.04749 − 0.72412I
b = 0.694637 + 1.112980I
−5.7675 + 18.3493I 0
u = 1.046010 + 0.871725I
a = 1.55072 + 0.08520I
b = 0.630633 + 0.895668I
−1.17577 + 6.10865I 0
u = 1.046010 − 0.871725I
a = 1.55072 − 0.08520I
b = 0.630633 − 0.895668I
−1.17577 − 6.10865I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.046045 + 1.397350I
a = 0.620332 − 0.655665I
b = 0.595969 + 1.058400I
−10.18760 + 8.91972I 0
u = −0.046045 − 1.397350I
a = 0.620332 + 0.655665I
b = 0.595969 − 1.058400I
−10.18760 − 8.91972I 0
u = −0.553712 + 0.202731I
a = −0.528223 + 0.679720I
b = 0.082580 + 1.072770I
−2.30024 + 1.90304I 2.77161 − 4.23290I
u = −0.553712 − 0.202731I
a = −0.528223 − 0.679720I
b = 0.082580 − 1.072770I
−2.30024 − 1.90304I 2.77161 + 4.23290I
u = 0.71297 + 1.23459I
a = 0.441416 − 0.393776I
b = 0.601821 − 0.671597I
−3.40579 + 3.89060I 0
u = 0.71297 − 1.23459I
a = 0.441416 + 0.393776I
b = 0.601821 + 0.671597I
−3.40579 − 3.89060I 0
u = 0.65165 + 1.33860I
a = 1.43997 − 0.64498I
b = 0.610272 + 0.961830I
−4.27418 + 8.71872I 0
u = 0.65165 − 1.33860I
a = 1.43997 + 0.64498I
b = 0.610272 − 0.961830I
−4.27418 − 8.71872I 0
u = 0.429540 + 0.149646I
a = 0.296500 + 0.074645I
b = 0.610223 + 0.842011I
0.92491 + 2.40324I 3.00262 − 3.56693I
u = 0.429540 − 0.149646I
a = 0.296500 − 0.074645I
b = 0.610223 − 0.842011I
0.92491 − 2.40324I 3.00262 + 3.56693I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.262708 + 0.122966I
a = −4.95031 + 0.65441I
b = −0.547714 + 1.002260I
−5.18066 − 1.75072I 0.73959 + 1.99347I
u = −0.262708 − 0.122966I
a = −4.95031 − 0.65441I
b = −0.547714 − 1.002260I
−5.18066 + 1.75072I 0.73959 − 1.99347I
u = 0.249622
a = −1.35178
b = 0.346594
0.758713 13.4350
15
II. I
u
2
= hb + 1, 3a − 3u + 4, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u − 1
a
3
=
u
u − 1
a
1
=
−1
0
a
11
=
u −
4
3
−1
a
10
=
u −
1
3
−1
a
7
=
u +
2
3
−1
a
8
=
u −
1
3
−1
a
4
=
4
9
u −
1
9
1
3
u −
1
3
a
9
=
2u −
5
3
−2
a
12
=
u −
4
3
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
116
9
u + 19
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
9(9u
2
− 3u + 1)
c
4
9(9u
2
− 6u + 4)
c
6
, c
7
, c
8
c
9
(u + 1)
2
c
10
, c
12
(u − 1)
2
c
11
u
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
2
+ y + 1
c
3
81(81y
2
+ 9y + 1)
c
4
81(81y
2
+ 36y + 16)
c
6
, c
7
, c
8
c
9
, c
10
, c
12
(y −1)
2
c
11
y
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.833333 + 0.866025I
b = −1.00000
1.64493 + 2.02988I 12.5556 − 11.1621I
u = 0.500000 − 0.866025I
a = −0.833333 − 0.866025I
b = −1.00000
1.64493 − 2.02988I 12.5556 + 11.1621I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
103
+ 44u
102
+ ··· + 1510u − 81)
c
2
(u
2
+ u + 1)(u
103
+ 2u
102
+ ··· − 50u − 9)
c
3
81(9u
2
− 3u + 1)(9u
103
− 132u
102
+ ··· + 8034u − 2563)
c
4
81(9u
2
− 6u + 4)(9u
103
+ 87u
102
+ ··· − 19058u − 1196)
c
5
(u
2
− u + 1)(u
103
+ 2u
102
+ ··· − 50u − 9)
c
6
((u + 1)
2
)(u
103
− 3u
102
+ ··· + 3u − 1)
c
7
, c
8
((u + 1)
2
)(u
103
+ 3u
102
+ ··· − 3u − 1)
c
9
((u + 1)
2
)(u
103
+ 37u
102
+ ··· + 13u − 1)
c
10
((u − 1)
2
)(u
103
− 3u
102
+ ··· + 3u − 1)
c
11
u
2
(u
103
− 5u
102
+ ··· + 648u − 108)
c
12
((u − 1)
2
)(u
103
+ 3u
102
+ ··· − 3u − 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
103
+ 32y
102
+ ··· + 1346818y −6561)
c
2
, c
5
(y
2
+ y + 1)(y
103
+ 44y
102
+ ··· + 1510y −81)
c
3
6561(81y
2
+ 9y + 1)
· (81y
103
+ 11916y
102
+ ··· + 184129610y −6568969)
c
4
6561(81y
2
+ 36y + 16)
· (81y
103
+ 11295y
102
+ ··· + 143925548y −1430416)
c
6
, c
10
((y −1)
2
)(y
103
+ 37y
102
+ ··· + 13y −1)
c
7
, c
8
, c
12
((y −1)
2
)(y
103
+ 97y
102
+ ··· + 13y −1)
c
9
((y −1)
2
)(y
103
+ 45y
102
+ ··· − 379y −1)
c
11
y
2
(y
103
+ 15y
102
+ ··· − 153576y −11664)
21
