12n
0606
(K12n
0606
)
A knot diagram
1
Linearized knot diagam
3 7 8 11 9 2 12 5 3 7 4 10
Solving Sequence
4,8 3,12
7 2 1 6 11 5 9 10
c
3
c
7
c
2
c
1
c
6
c
11
c
4
c
8
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.60434 × 10
191
u
60
+ 3.06370 × 10
190
u
59
+ ··· + 9.90808 × 10
192
b − 1.81924 × 10
193
,
1.45667 × 10
192
u
60
− 2.33309 × 10
192
u
59
+ ··· + 1.98162 × 10
193
a + 2.73135 × 10
192
, u
61
− u
60
+ ··· + 58u + 25i
I
u
2
= h6183716894369u
21
+ 1374457475661u
20
+ ··· + 20376431428799b − 1818725790068,
23344139331015u
21
+ 15115284063805u
20
+ ··· + 40752862857598a + 81671293633640,
u
22
+ u
20
+ ··· + 7u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 83 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−1.60 × 10
191
u
60
+ 3.06 × 10
190
u
59
+ · · · + 9.91 × 10
192
b − 1.82 ×
10
193
, 1.46 × 10
192
u
60
− 2.33 × 10
192
u
59
+ · · · + 1.98 × 10
193
a + 2.73 ×
10
192
, u
61
− u
60
+ · · · + 58u + 25i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
12
=
−0.0735091u
60
+ 0.117737u
59
+ ··· − 2.04132u − 0.137835
0.0161923u
60
− 0.00309212u
59
+ ··· + 4.89491u + 1.83612
a
7
=
0.139781u
60
− 0.129132u
59
+ ··· + 15.7191u + 4.33924
−0.00116829u
60
+ 0.0144033u
59
+ ··· + 1.86244u + 0.197937
a
2
=
0.0704268u
60
− 0.0732087u
59
+ ··· + 2.42540u + 0.360156
0.0813783u
60
− 0.0764120u
59
+ ··· + 12.8465u + 2.33043
a
1
=
0.178777u
60
− 0.179760u
59
+ ··· + 16.8712u + 2.62104
0.0511130u
60
− 0.0380784u
59
+ ··· + 10.0334u + 2.28547
a
6
=
0.103262u
60
− 0.0386507u
59
+ ··· + 17.0502u + 9.16938
−0.172371u
60
+ 0.154684u
59
+ ··· − 24.1023u − 5.29676
a
11
=
−0.0897013u
60
+ 0.120829u
59
+ ··· − 6.93623u − 1.97395
0.0161923u
60
− 0.00309212u
59
+ ··· + 4.89491u + 1.83612
a
5
=
0.0660658u
60
− 0.0890977u
59
+ ··· + 6.16157u − 0.139445
−0.0739833u
60
+ 0.0958469u
59
+ ··· − 5.82769u + 1.54267
a
9
=
−0.0689463u
60
+ 0.140243u
59
+ ··· − 1.52496u + 4.30676
0.0119356u
60
− 0.0639002u
59
+ ··· − 6.32232u − 5.61607
a
10
=
−0.0431325u
60
+ 0.0739412u
59
+ ··· − 5.43574u + 0.473106
0.0113729u
60
− 0.0535091u
59
+ ··· − 4.61936u − 4.60387
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.625154u
60
− 0.710423u
59
+ ··· + 55.0401u + 12.7589
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
61
+ 80u
60
+ ··· + 86779u + 2401
c
2
, c
6
u
61
− 2u
60
+ ··· + 441u − 49
c
3
u
61
+ u
60
+ ··· + 58u − 25
c
4
, c
11
u
61
− 2u
60
+ ··· − 33u − 19
c
5
, c
8
u
61
− 2u
60
+ ··· + 261u − 29
c
7
u
61
+ 2u
60
+ ··· − 276u − 333
c
9
u
61
− 2u
60
+ ··· + 96105u − 40873
c
10
u
61
+ 2u
60
+ ··· − 3730060u − 1063025
c
12
u
61
+ u
60
+ ··· + 24262u − 3637
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
61
− 188y
60
+ ··· − 978957329y −5764801
c
2
, c
6
y
61
− 80y
60
+ ··· + 86779y −2401
c
3
y
61
+ 9y
60
+ ··· − 4186y −625
c
4
, c
11
y
61
+ 42y
60
+ ··· + 367y −361
c
5
, c
8
y
61
− 24y
60
+ ··· + 17197y −841
c
7
y
61
+ 24y
60
+ ··· − 3453624y −110889
c
9
y
61
+ 106y
60
+ ··· − 28850843549y −1670602129
c
10
y
61
+ 50y
60
+ ··· + 4847404798650y −1130022150625
c
12
y
61
+ 83y
60
+ ··· − 463357606y −13227769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.910345 + 0.431030I
a = 0.083295 − 0.454008I
b = 0.591145 + 0.176936I
2.26261 − 0.47311I 6.00000 + 0.82328I
u = −0.910345 − 0.431030I
a = 0.083295 + 0.454008I
b = 0.591145 − 0.176936I
2.26261 + 0.47311I 6.00000 − 0.82328I
u = −0.905896 + 0.155656I
a = −0.855256 + 0.495486I
b = −0.471322 + 0.022876I
1.384080 − 0.049647I 8.60374 + 0.34198I
u = −0.905896 − 0.155656I
a = −0.855256 − 0.495486I
b = −0.471322 − 0.022876I
1.384080 + 0.049647I 8.60374 − 0.34198I
u = 0.873224 + 0.669571I
a = 0.981899 + 0.270500I
b = 0.849049 − 0.003724I
0.68598 + 5.02449I 6.00000 − 6.97083I
u = 0.873224 − 0.669571I
a = 0.981899 − 0.270500I
b = 0.849049 + 0.003724I
0.68598 − 5.02449I 6.00000 + 6.97083I
u = 0.796281 + 0.378338I
a = −1.116940 − 0.754299I
b = −0.339467 − 1.155790I
−2.21988 + 2.71821I 2.79760 − 2.35403I
u = 0.796281 − 0.378338I
a = −1.116940 + 0.754299I
b = −0.339467 + 1.155790I
−2.21988 − 2.71821I 2.79760 + 2.35403I
u = −0.783728 + 0.810034I
a = −1.086800 + 0.185128I
b = −1.269080 − 0.034183I
−8.29039 − 8.79817I 0. + 5.94350I
u = −0.783728 − 0.810034I
a = −1.086800 − 0.185128I
b = −1.269080 + 0.034183I
−8.29039 + 8.79817I 0. − 5.94350I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.100430 + 0.405618I
a = 0.564804 − 0.867691I
b = 0.668724 − 0.343543I
−7.18810 + 2.78232I 0
u = 1.100430 − 0.405618I
a = 0.564804 + 0.867691I
b = 0.668724 + 0.343543I
−7.18810 − 2.78232I 0
u = 0.902535 + 0.787150I
a = 1.38806 + 0.58993I
b = 0.077875 + 1.023620I
−2.49063 + 3.37367I 0
u = 0.902535 − 0.787150I
a = 1.38806 − 0.58993I
b = 0.077875 − 1.023620I
−2.49063 − 3.37367I 0
u = −0.143701 + 1.197970I
a = −0.758684 − 0.050261I
b = −0.81574 − 1.26237I
−12.04860 + 3.96320I 0
u = −0.143701 − 1.197970I
a = −0.758684 + 0.050261I
b = −0.81574 + 1.26237I
−12.04860 − 3.96320I 0
u = −0.737649 + 0.288030I
a = −1.22841 + 1.53957I
b = 0.141796 + 0.826845I
1.16799 + 0.97942I 11.64968 − 5.59628I
u = −0.737649 − 0.288030I
a = −1.22841 − 1.53957I
b = 0.141796 − 0.826845I
1.16799 − 0.97942I 11.64968 + 5.59628I
u = 0.409288 + 1.166070I
a = −0.968903 + 0.296598I
b = −0.873837 − 0.531957I
−10.15910 + 2.60373I 0
u = 0.409288 − 1.166070I
a = −0.968903 − 0.296598I
b = −0.873837 + 0.531957I
−10.15910 − 2.60373I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.178219 + 1.234730I
a = 0.704583 + 0.086186I
b = 0.489122 − 1.159650I
−4.94617 − 1.68496I 0
u = −0.178219 − 1.234730I
a = 0.704583 − 0.086186I
b = 0.489122 + 1.159650I
−4.94617 + 1.68496I 0
u = 0.548172 + 0.498732I
a = −0.827761 − 0.239428I
b = −1.175910 + 0.324455I
3.56437 + 0.65529I 6.54598 − 9.43946I
u = 0.548172 − 0.498732I
a = −0.827761 + 0.239428I
b = −1.175910 − 0.324455I
3.56437 − 0.65529I 6.54598 + 9.43946I
u = −0.783796 + 0.998521I
a = −1.48491 + 0.19075I
b = −0.301845 + 1.321410I
−15.6806 − 6.1080I 0
u = −0.783796 − 0.998521I
a = −1.48491 − 0.19075I
b = −0.301845 − 1.321410I
−15.6806 + 6.1080I 0
u = −0.514875 + 0.492130I
a = 1.59948 + 2.11483I
b = 0.398091 − 1.052590I
−9.26345 − 6.82861I 3.46166 + 7.84368I
u = −0.514875 − 0.492130I
a = 1.59948 − 2.11483I
b = 0.398091 + 1.052590I
−9.26345 + 6.82861I 3.46166 − 7.84368I
u = 0.264074 + 0.645372I
a = 1.328340 + 0.443782I
b = −0.016093 + 1.164140I
−3.08605 − 2.29569I 1.42347 + 3.66981I
u = 0.264074 − 0.645372I
a = 1.328340 − 0.443782I
b = −0.016093 − 1.164140I
−3.08605 + 2.29569I 1.42347 − 3.66981I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.773573 + 1.049630I
a = 1.183780 + 0.080595I
b = 0.573481 + 1.240910I
−4.00356 + 7.17574I 0
u = 0.773573 − 1.049630I
a = 1.183780 − 0.080595I
b = 0.573481 − 1.240910I
−4.00356 − 7.17574I 0
u = −0.338814 + 1.265940I
a = −0.521179 + 0.796599I
b = 0.139314 − 0.503690I
−9.74367 + 3.57994I 0
u = −0.338814 − 1.265940I
a = −0.521179 − 0.796599I
b = 0.139314 + 0.503690I
−9.74367 − 3.57994I 0
u = −0.308314 + 0.613085I
a = 1.345220 + 0.160561I
b = 0.935401 + 0.570302I
−1.34263 − 1.55470I 1.10269 + 5.91362I
u = −0.308314 − 0.613085I
a = 1.345220 − 0.160561I
b = 0.935401 − 0.570302I
−1.34263 + 1.55470I 1.10269 − 5.91362I
u = −0.122393 + 0.642085I
a = 1.260040 + 0.577361I
b = 0.488074 + 0.349651I
−1.49067 − 1.69118I 1.10870 + 3.00446I
u = −0.122393 − 0.642085I
a = 1.260040 − 0.577361I
b = 0.488074 − 0.349651I
−1.49067 + 1.69118I 1.10870 − 3.00446I
u = −0.846285 + 1.110770I
a = −0.848090 + 0.034436I
b = −0.62079 + 1.29122I
0.31756 − 6.96705I 0
u = −0.846285 − 1.110770I
a = −0.848090 − 0.034436I
b = −0.62079 − 1.29122I
0.31756 + 6.96705I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.203948 + 0.521772I
a = −2.18101 − 1.13787I
b = 0.195182 + 0.839910I
1.01441 + 1.12155I 11.43554 + 3.06720I
u = −0.203948 − 0.521772I
a = −2.18101 + 1.13787I
b = 0.195182 − 0.839910I
1.01441 − 1.12155I 11.43554 − 3.06720I
u = −0.075463 + 0.501572I
a = −1.70075 + 0.64346I
b = −0.47776 + 1.67863I
−13.75710 + 1.91932I −2.60893 − 4.18261I
u = −0.075463 − 0.501572I
a = −1.70075 − 0.64346I
b = −0.47776 − 1.67863I
−13.75710 − 1.91932I −2.60893 + 4.18261I
u = 1.20031 + 0.90858I
a = −0.708252 − 0.230947I
b = −0.317542 − 1.245240I
−2.34363 + 3.20308I 0
u = 1.20031 − 0.90858I
a = −0.708252 + 0.230947I
b = −0.317542 + 1.245240I
−2.34363 − 3.20308I 0
u = −0.441996
a = −1.57855
b = −0.366410
0.849580 12.6400
u = 0.360834 + 0.209871I
a = −2.67749 + 1.83256I
b = −0.229649 − 0.967482I
−0.79546 + 2.56100I 5.10158 − 6.10959I
u = 0.360834 − 0.209871I
a = −2.67749 − 1.83256I
b = −0.229649 + 0.967482I
−0.79546 − 2.56100I 5.10158 + 6.10959I
u = −1.62571 + 0.49135I
a = −0.031980 + 0.495894I
b = 0.09176 + 1.50621I
−13.41560 − 0.23117I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62571 − 0.49135I
a = −0.031980 − 0.495894I
b = 0.09176 − 1.50621I
−13.41560 + 0.23117I 0
u = 1.10477 + 1.32184I
a = −0.921810 − 0.135912I
b = −0.59623 − 1.40084I
−12.6177 + 15.2705I 0
u = 1.10477 − 1.32184I
a = −0.921810 + 0.135912I
b = −0.59623 + 1.40084I
−12.6177 − 15.2705I 0
u = −1.21132 + 1.26115I
a = 0.809022 − 0.138932I
b = 0.447860 − 1.318690I
−3.42883 − 9.78730I 0
u = −1.21132 − 1.26115I
a = 0.809022 + 0.138932I
b = 0.447860 + 1.318690I
−3.42883 + 9.78730I 0
u = 1.23693 + 1.30689I
a = 0.413103 + 0.160610I
b = 0.357957 + 1.350540I
−1.82315 + 4.26546I 0
u = 1.23693 − 1.30689I
a = 0.413103 − 0.160610I
b = 0.357957 − 1.350540I
−1.82315 − 4.26546I 0
u = −0.77616 + 1.81286I
a = 0.418912 − 0.019439I
b = 0.057249 − 1.068760I
−4.52908 − 0.45066I 0
u = −0.77616 − 1.81286I
a = 0.418912 + 0.019439I
b = 0.057249 + 1.068760I
−4.52908 + 0.45066I 0
u = 1.61718 + 1.51372I
a = −0.213047 − 0.314323I
b = 0.186383 − 1.117350I
−11.73450 − 5.28579I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61718 − 1.51372I
a = −0.213047 + 0.314323I
b = 0.186383 + 1.117350I
−11.73450 + 5.28579I 0
11
II.
I
u
2
= h6.18 × 10
12
u
21
+ 1.37 × 10
12
u
20
+ · · · + 2.04 × 10
13
b − 1.82 × 10
12
, 2.33 ×
10
13
u
21
+1.51×10
13
u
20
+· · ·+4.08×10
13
a+8.17×10
13
, u
22
+u
20
+· · ·+7u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
12
=
−0.572822u
21
− 0.370901u
20
+ ··· − 6.42292u − 2.00406
−0.303474u
21
− 0.0674533u
20
+ ··· − 2.11438u + 0.0892563
a
7
=
−0.490404u
21
+ 0.544286u
20
+ ··· + 1.63604u + 3.54751
0.450223u
21
+ 0.166556u
20
+ ··· + 1.84761u + 0.395045
a
2
=
0.127478u
21
− 0.0969833u
20
+ ··· − 2.82648u − 1.83138
−0.272013u
21
− 0.162826u
20
+ ··· − 3.02486u − 0.530692
a
1
=
−0.160976u
21
− 0.342532u
20
+ ··· − 5.72386u − 2.45906
−0.0738264u
21
− 0.215757u
20
+ ··· − 2.73641u − 0.285144
a
6
=
−0.902443u
21
+ 0.369937u
20
+ ··· − 3.12076u + 1.80659
−0.508034u
21
+ 0.236676u
20
+ ··· − 2.08651u − 0.447991
a
11
=
−0.269348u
21
− 0.303448u
20
+ ··· − 4.30854u − 2.09332
−0.303474u
21
− 0.0674533u
20
+ ··· − 2.11438u + 0.0892563
a
5
=
0.224994u
21
+ 0.335014u
20
+ ··· − 1.53934u + 1.95806
−0.620039u
21
+ 0.115209u
20
+ ··· − 2.49559u − 0.110441
a
9
=
−0.843674u
21
+ 0.135737u
20
+ ··· − 1.44434u + 0.954289
0.0771103u
21
+ 0.230053u
20
+ ··· + 0.290077u + 0.454193
a
10
=
−0.798104u
21
+ 0.208278u
20
+ ··· − 1.99794u + 1.54422
−0.0334405u
21
+ 0.446821u
20
+ ··· + 0.244507u + 0.381653
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
40525880426923
40752862857598
u
21
+
9112819862999
40752862857598
u
20
+ ··· −
281490623171531
40752862857598
u +
94744620113174
20376431428799
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
22
− 23u
21
+ ··· − 11u + 1
c
2
u
22
− u
21
+ ··· + u + 1
c
3
u
22
+ u
20
+ ··· + 7u
2
+ 1
c
4
u
22
+ u
21
+ ··· + u + 7
c
5
u
22
− u
21
+ ··· − 3u + 5
c
6
u
22
+ u
21
+ ··· − u + 1
c
7
u
22
+ u
21
+ ··· − 4u + 1
c
8
u
22
+ u
21
+ ··· + 3u + 5
c
9
u
22
− u
21
+ ··· + u + 1
c
10
u
22
+ u
21
+ ··· − 10u + 1
c
11
u
22
− u
21
+ ··· − u + 7
c
12
u
22
+ 6u
20
+ ··· − 5u
2
+ 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 39y
21
+ ··· − 3y + 1
c
2
, c
6
y
22
− 23y
21
+ ··· − 11y + 1
c
3
y
22
+ 2y
21
+ ··· + 14y + 1
c
4
, c
11
y
22
+ 15y
21
+ ··· + 377y + 49
c
5
, c
8
y
22
− 19y
21
+ ··· − 289y + 25
c
7
y
22
+ 9y
21
+ ··· − 4y + 1
c
9
y
22
+ 15y
21
+ ··· + 21y + 1
c
10
y
22
+ 15y
21
+ ··· + 38y + 1
c
12
y
22
+ 12y
21
+ ··· − 10y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.749223 + 0.536697I
a = −1.93401 − 0.91661I
b = −0.274538 − 0.968002I
−1.82723 + 4.27576I 7.30430 − 9.72989I
u = 0.749223 − 0.536697I
a = −1.93401 + 0.91661I
b = −0.274538 + 0.968002I
−1.82723 − 4.27576I 7.30430 + 9.72989I
u = −1.044190 + 0.356102I
a = −0.001977 − 0.673618I
b = 0.26050 − 1.56100I
−12.82310 + 1.58068I 4.83519 − 2.88611I
u = −1.044190 − 0.356102I
a = −0.001977 + 0.673618I
b = 0.26050 + 1.56100I
−12.82310 − 1.58068I 4.83519 + 2.88611I
u = 0.724340 + 0.845777I
a = −0.821898 − 0.205533I
b = −0.988487 + 0.528451I
1.66671 + 2.20771I 4.34569 − 3.65314I
u = 0.724340 − 0.845777I
a = −0.821898 + 0.205533I
b = −0.988487 − 0.528451I
1.66671 − 2.20771I 4.34569 + 3.65314I
u = −1.046380 + 0.423272I
a = −0.356014 + 1.178150I
b = 0.173677 + 0.903500I
0.651107 + 0.405045I 1.85611 + 1.13547I
u = −1.046380 − 0.423272I
a = −0.356014 − 1.178150I
b = 0.173677 − 0.903500I
0.651107 − 0.405045I 1.85611 − 1.13547I
u = 0.558979 + 1.026050I
a = −0.045467 + 0.826842I
b = 0.431345 − 0.856577I
−9.94231 − 5.09085I 2.90449 + 4.36039I
u = 0.558979 − 1.026050I
a = −0.045467 − 0.826842I
b = 0.431345 + 0.856577I
−9.94231 + 5.09085I 2.90449 − 4.36039I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.791899 + 0.115857I
a = 0.458376 − 0.091009I
b = 0.915727 + 0.059496I
3.54705 − 0.01004I 10.61413 − 1.28755I
u = −0.791899 − 0.115857I
a = 0.458376 + 0.091009I
b = 0.915727 − 0.059496I
3.54705 + 0.01004I 10.61413 + 1.28755I
u = 0.231354 + 0.517578I
a = −0.34516 − 2.70664I
b = 0.205725 + 0.843817I
0.70306 + 1.50488I 1.38672 − 8.70491I
u = 0.231354 − 0.517578I
a = −0.34516 + 2.70664I
b = 0.205725 − 0.843817I
0.70306 − 1.50488I 1.38672 + 8.70491I
u = 1.20809 + 0.84251I
a = 0.628241 + 0.196989I
b = 0.41864 + 1.39129I
−0.85413 + 4.66448I 7.24755 − 5.70143I
u = 1.20809 − 0.84251I
a = 0.628241 − 0.196989I
b = 0.41864 − 1.39129I
−0.85413 − 4.66448I 7.24755 + 5.70143I
u = −0.001953 + 0.372411I
a = −1.81291 − 1.77055I
b = −0.710684 − 0.658976I
−0.954258 − 0.910761I 7.17839 − 3.05875I
u = −0.001953 − 0.372411I
a = −1.81291 + 1.77055I
b = −0.710684 + 0.658976I
−0.954258 + 0.910761I 7.17839 + 3.05875I
u = −0.96547 + 1.31719I
a = −0.814621 + 0.048696I
b = −0.615052 + 1.219520I
−0.76029 − 8.11167I 3.91676 + 7.17455I
u = −0.96547 − 1.31719I
a = −0.814621 − 0.048696I
b = −0.615052 − 1.219520I
−0.76029 + 8.11167I 3.91676 − 7.17455I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.37791 + 1.60370I
a = −0.454559 + 0.086376I
b = −0.316854 − 1.049130I
−4.08064 + 1.37556I 5.91066 − 3.80739I
u = 0.37791 − 1.60370I
a = −0.454559 − 0.086376I
b = −0.316854 + 1.049130I
−4.08064 − 1.37556I 5.91066 + 3.80739I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 23u
21
+ ··· − 11u + 1)(u
61
+ 80u
60
+ ··· + 86779u + 2401)
c
2
(u
22
− u
21
+ ··· + u + 1)(u
61
− 2u
60
+ ··· + 441u − 49)
c
3
(u
22
+ u
20
+ ··· + 7u
2
+ 1)(u
61
+ u
60
+ ··· + 58u − 25)
c
4
(u
22
+ u
21
+ ··· + u + 7)(u
61
− 2u
60
+ ··· − 33u − 19)
c
5
(u
22
− u
21
+ ··· − 3u + 5)(u
61
− 2u
60
+ ··· + 261u − 29)
c
6
(u
22
+ u
21
+ ··· − u + 1)(u
61
− 2u
60
+ ··· + 441u − 49)
c
7
(u
22
+ u
21
+ ··· − 4u + 1)(u
61
+ 2u
60
+ ··· − 276u − 333)
c
8
(u
22
+ u
21
+ ··· + 3u + 5)(u
61
− 2u
60
+ ··· + 261u − 29)
c
9
(u
22
− u
21
+ ··· + u + 1)(u
61
− 2u
60
+ ··· + 96105u − 40873)
c
10
(u
22
+ u
21
+ ··· − 10u + 1)(u
61
+ 2u
60
+ ··· − 3730060u − 1063025)
c
11
(u
22
− u
21
+ ··· − u + 7)(u
61
− 2u
60
+ ··· − 33u − 19)
c
12
(u
22
+ 6u
20
+ ··· − 5u
2
+ 1)(u
61
+ u
60
+ ··· + 24262u − 3637)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
− 39y
21
+ ··· − 3y + 1)
· (y
61
− 188y
60
+ ··· − 978957329y −5764801)
c
2
, c
6
(y
22
− 23y
21
+ ··· − 11y + 1)(y
61
− 80y
60
+ ··· + 86779y −2401)
c
3
(y
22
+ 2y
21
+ ··· + 14y + 1)(y
61
+ 9y
60
+ ··· − 4186y −625)
c
4
, c
11
(y
22
+ 15y
21
+ ··· + 377y + 49)(y
61
+ 42y
60
+ ··· + 367y −361)
c
5
, c
8
(y
22
− 19y
21
+ ··· − 289y + 25)(y
61
− 24y
60
+ ··· + 17197y −841)
c
7
(y
22
+ 9y
21
+ ··· − 4y + 1)(y
61
+ 24y
60
+ ··· − 3453624y −110889)
c
9
(y
22
+ 15y
21
+ ··· + 21y + 1)
· (y
61
+ 106y
60
+ ··· − 28850843549y −1670602129)
c
10
(y
22
+ 15y
21
+ ··· + 38y + 1)
· (y
61
+ 50y
60
+ ··· + 4847404798650y −1130022150625)
c
12
(y
22
+ 12y
21
+ ··· − 10y + 1)
· (y
61
+ 83y
60
+ ··· − 463357606y −13227769)
21
