12n
0658
(K12n
0658
)
A knot diagram
1
Linearized knot diagam
3 8 11 9 8 10 2 12 3 6 4 5
Solving Sequence
4,9 5,12
1 8 6 11 3 2 7 10
c
4
c
12
c
8
c
5
c
11
c
3
c
2
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.74970 × 10
220
u
64
− 1.41335 × 10
221
u
63
+ ··· + 1.94971 × 10
223
b − 7.61654 × 10
223
,
− 4.48176 × 10
225
u
64
− 5.69453 × 10
225
u
63
+ ··· + 3.97935 × 10
226
a − 1.23630 × 10
228
,
u
65
+ 2u
64
+ ··· + 1458u + 157i
I
u
2
= h10854430144646u
20
+ 12300724825690u
19
+ ··· + 24764957468951b + 6039231440791,
− 12861674233129u
20
− 2850243387257u
19
+ ··· + 24764957468951a − 12778119826149,
u
21
+ u
20
+ ··· − 2u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 86 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
= h1.75 × 10
220
u
64
− 1.41 × 10
221
u
63
+ · · · + 1.95 × 10
223
b − 7.62 ×
10
223
, −4.48 × 10
225
u
64
− 5.69 × 10
225
u
63
+ · · · + 3.98 × 10
226
a − 1.24 ×
10
228
, u
65
+ 2u
64
+ · · · + 1458u + 157i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
0.112625u
64
+ 0.143102u
63
+ ··· + 200.060u + 31.0678
−0.000897414u
64
+ 0.00724903u
63
+ ··· + 27.8175u + 3.90651
a
1
=
0.0572491u
64
+ 0.0774845u
63
+ ··· + 125.786u + 22.0769
−0.0345792u
64
− 0.0375444u
63
+ ··· − 29.2953u − 3.17970
a
8
=
0.173334u
64
+ 0.262177u
63
+ ··· + 356.620u + 53.0601
−0.0965680u
64
− 0.124883u
63
+ ··· − 167.497u − 21.7230
a
6
=
−0.387923u
64
− 0.492677u
63
+ ··· − 664.492u − 77.1226
−0.0795910u
64
− 0.138562u
63
+ ··· − 238.004u − 33.3801
a
11
=
0.111728u
64
+ 0.150351u
63
+ ··· + 227.877u + 34.9743
−0.000897414u
64
+ 0.00724903u
63
+ ··· + 27.8175u + 3.90651
a
3
=
0.149474u
64
+ 0.217371u
63
+ ··· + 298.867u + 44.4819
0.0111114u
64
+ 0.0372127u
63
+ ··· + 70.3743u + 10.2454
a
2
=
0.154001u
64
+ 0.263124u
63
+ ··· + 403.453u + 65.6548
−0.165095u
64
− 0.209683u
63
+ ··· − 275.946u − 35.1275
a
7
=
0.366877u
64
+ 0.486483u
63
+ ··· + 650.185u + 78.1246
0.146693u
64
+ 0.235468u
63
+ ··· + 370.754u + 50.5795
a
10
=
0.0507079u
64
+ 0.0927285u
63
+ ··· + 147.777u + 24.8200
−0.123127u
64
− 0.167850u
63
+ ··· − 230.663u − 29.1889
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.737275u
64
− 0.996152u
63
+ ··· − 1391.45u − 188.248
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
+ 80u
64
+ ··· + 26201631u + 703921
c
2
, c
7
u
65
+ 2u
64
+ ··· + 2635u − 839
c
3
, c
11
u
65
− 25u
63
+ ··· − 25u − 1
c
4
u
65
+ 2u
64
+ ··· + 1458u + 157
c
5
u
65
+ 9u
64
+ ··· − 13866064u + 772201
c
6
, c
10
u
65
+ 6u
63
+ ··· − 13u + 1
c
8
u
65
+ 2u
64
+ ··· + 1534u + 169
c
9
u
65
+ u
64
+ ··· + 626468359u − 113770343
c
12
u
65
− 2u
64
+ ··· − 23392u − 2011
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
− 160y
64
+ ··· − 124582077762381y −495504774241
c
2
, c
7
y
65
− 80y
64
+ ··· + 26201631y −703921
c
3
, c
11
y
65
− 50y
64
+ ··· + 31y −1
c
4
y
65
− 14y
64
+ ··· + 1831546y −24649
c
5
y
65
+ 93y
64
+ ··· + 51698127994114y −596294384401
c
6
, c
10
y
65
+ 12y
64
+ ··· + 43y −1
c
8
y
65
+ 16y
64
+ ··· − 184548y −28561
c
9
y
65
− 71y
64
+ ··· + 305883945614896799y −12943690946337649
c
12
y
65
+ 28y
64
+ ··· − 291747228y −4044121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.999373 + 0.102603I
a = 0.183495 + 1.114360I
b = 1.47107 − 0.62237I
−13.3785 + 4.9395I 0
u = 0.999373 − 0.102603I
a = 0.183495 − 1.114360I
b = 1.47107 + 0.62237I
−13.3785 − 4.9395I 0
u = 0.914140 + 0.418551I
a = −0.274231 + 1.015020I
b = −0.037132 − 0.951807I
−0.55815 − 5.01766I 0
u = 0.914140 − 0.418551I
a = −0.274231 − 1.015020I
b = −0.037132 + 0.951807I
−0.55815 + 5.01766I 0
u = 0.544942 + 0.848280I
a = 0.017892 + 0.636408I
b = 0.311547 − 0.836295I
3.81958 − 0.87527I 0
u = 0.544942 − 0.848280I
a = 0.017892 − 0.636408I
b = 0.311547 + 0.836295I
3.81958 + 0.87527I 0
u = −0.943989 + 0.244778I
a = 1.89766 − 0.46660I
b = 1.322510 − 0.167180I
−12.02340 − 0.63123I 0
u = −0.943989 − 0.244778I
a = 1.89766 + 0.46660I
b = 1.322510 + 0.167180I
−12.02340 + 0.63123I 0
u = −0.718967 + 0.646460I
a = −0.19383 + 1.54085I
b = 1.39393 − 0.34126I
−3.94325 + 5.68345I 0
u = −0.718967 − 0.646460I
a = −0.19383 − 1.54085I
b = 1.39393 + 0.34126I
−3.94325 − 5.68345I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.564992 + 0.766638I
a = 0.273439 − 1.139240I
b = −0.098849 + 0.697594I
0.17289 + 2.65260I 0
u = −0.564992 − 0.766638I
a = 0.273439 + 1.139240I
b = −0.098849 − 0.697594I
0.17289 − 2.65260I 0
u = 1.032050 + 0.210054I
a = 0.007300 + 0.663633I
b = −1.346550 − 0.430450I
−4.69587 − 0.11151I 0
u = 1.032050 − 0.210054I
a = 0.007300 − 0.663633I
b = −1.346550 + 0.430450I
−4.69587 + 0.11151I 0
u = −1.008770 + 0.311992I
a = −0.87655 − 2.02191I
b = −1.147410 + 0.096132I
−3.68102 + 0.89750I 0
u = −1.008770 − 0.311992I
a = −0.87655 + 2.02191I
b = −1.147410 − 0.096132I
−3.68102 − 0.89750I 0
u = 0.819844 + 0.666051I
a = −0.04947 + 1.83615I
b = −1.264320 − 0.103822I
−2.80582 − 3.86569I 0
u = 0.819844 − 0.666051I
a = −0.04947 − 1.83615I
b = −1.264320 + 0.103822I
−2.80582 + 3.86569I 0
u = −1.06438
a = 1.18973
b = −0.491702
−2.53871 0
u = −0.861352 + 0.321812I
a = 0.165841 − 0.909305I
b = 1.47564 + 0.76252I
−11.72340 + 3.05933I −13.80482 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.861352 − 0.321812I
a = 0.165841 + 0.909305I
b = 1.47564 − 0.76252I
−11.72340 − 3.05933I −13.80482 + 0.I
u = 0.768490 + 0.184024I
a = 2.38615 + 1.30513I
b = 1.293180 + 0.139730I
−12.35970 − 6.17999I −13.5430 + 5.2560I
u = 0.768490 − 0.184024I
a = 2.38615 − 1.30513I
b = 1.293180 − 0.139730I
−12.35970 + 6.17999I −13.5430 − 5.2560I
u = 0.681468 + 1.023020I
a = −0.584449 − 0.266422I
b = 1.169520 − 0.114705I
−2.82139 + 3.87224I 0
u = 0.681468 − 1.023020I
a = −0.584449 + 0.266422I
b = 1.169520 + 0.114705I
−2.82139 − 3.87224I 0
u = 1.059320 + 0.651414I
a = −0.068250 − 0.898603I
b = 0.142000 + 1.206150I
−9.20705 − 1.83942I 0
u = 1.059320 − 0.651414I
a = −0.068250 + 0.898603I
b = 0.142000 − 1.206150I
−9.20705 + 1.83942I 0
u = −0.699109 + 0.200716I
a = 0.822915 − 0.817830I
b = −0.173433 + 0.242316I
−1.208910 + 0.548314I −8.64501 − 2.55655I
u = −0.699109 − 0.200716I
a = 0.822915 + 0.817830I
b = −0.173433 − 0.242316I
−1.208910 − 0.548314I −8.64501 + 2.55655I
u = 0.862620 + 1.000680I
a = −0.850831 − 0.045360I
b = −0.106228 − 0.377671I
−8.01748 − 4.29475I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.862620 − 1.000680I
a = −0.850831 + 0.045360I
b = −0.106228 + 0.377671I
−8.01748 + 4.29475I 0
u = 1.158140 + 0.659100I
a = 0.117313 − 1.313300I
b = 1.318680 + 0.427978I
−4.81417 − 9.90537I 0
u = 1.158140 − 0.659100I
a = 0.117313 + 1.313300I
b = 1.318680 − 0.427978I
−4.81417 + 9.90537I 0
u = 0.512850 + 0.407512I
a = −0.54396 + 1.92014I
b = −1.227830 − 0.206235I
−1.82076 − 0.96957I −1.84094 − 0.74780I
u = 0.512850 − 0.407512I
a = −0.54396 − 1.92014I
b = −1.227830 + 0.206235I
−1.82076 + 0.96957I −1.84094 + 0.74780I
u = −1.075290 + 0.820321I
a = 0.029326 + 0.907628I
b = 0.210489 − 1.168250I
−8.16440 + 10.11900I 0
u = −1.075290 − 0.820321I
a = 0.029326 − 0.907628I
b = 0.210489 + 1.168250I
−8.16440 − 10.11900I 0
u = −0.633443 + 0.121495I
a = 0.80489 − 1.99874I
b = −1.072970 + 0.269722I
−2.58233 + 0.73416I −9.39358 + 8.45936I
u = −0.633443 − 0.121495I
a = 0.80489 + 1.99874I
b = −1.072970 − 0.269722I
−2.58233 − 0.73416I −9.39358 − 8.45936I
u = −1.144370 + 0.749445I
a = 0.001986 − 0.627491I
b = −1.32660 + 0.55872I
−1.63568 + 5.32861I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.144370 − 0.749445I
a = 0.001986 + 0.627491I
b = −1.32660 − 0.55872I
−1.63568 − 5.32861I 0
u = 0.551203 + 0.205508I
a = 0.96007 − 1.78056I
b = −0.0840652 + 0.0654924I
0.93353 − 2.84266I −8.27444 − 0.53942I
u = 0.551203 − 0.205508I
a = 0.96007 + 1.78056I
b = −0.0840652 − 0.0654924I
0.93353 + 2.84266I −8.27444 + 0.53942I
u = −0.94708 + 1.13082I
a = −0.289084 + 0.976259I
b = 1.321940 − 0.311580I
−4.26583 + 6.35751I 0
u = −0.94708 − 1.13082I
a = −0.289084 − 0.976259I
b = 1.321940 + 0.311580I
−4.26583 − 6.35751I 0
u = −0.96950 + 1.11387I
a = −0.666748 − 0.221312I
b = −0.152577 + 0.535195I
−7.36307 − 3.09669I 0
u = −0.96950 − 1.11387I
a = −0.666748 + 0.221312I
b = −0.152577 − 0.535195I
−7.36307 + 3.09669I 0
u = 0.017003 + 0.520994I
a = 0.52264 − 1.79134I
b = −0.170066 + 0.616830I
1.35247 + 2.01752I −0.32815 − 3.57932I
u = 0.017003 − 0.520994I
a = 0.52264 + 1.79134I
b = −0.170066 − 0.616830I
1.35247 − 2.01752I −0.32815 + 3.57932I
u = −0.487051 + 0.184553I
a = −0.523976 + 0.683896I
b = −0.364029 − 1.277030I
2.05730 − 1.12785I −14.5677 + 6.0985I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.487051 − 0.184553I
a = −0.523976 − 0.683896I
b = −0.364029 + 1.277030I
2.05730 + 1.12785I −14.5677 − 6.0985I
u = 1.34403 + 0.87395I
a = 0.245632 − 0.677061I
b = 1.137180 + 0.382997I
1.20608 − 5.29372I 0
u = 1.34403 − 0.87395I
a = 0.245632 + 0.677061I
b = 1.137180 − 0.382997I
1.20608 + 5.29372I 0
u = −1.62477
a = 0.128143
b = 1.37061
−8.24749 0
u = 1.48370 + 0.87202I
a = −0.057752 + 0.890430I
b = −1.44306 − 0.50190I
−14.2637 − 7.7830I 0
u = 1.48370 − 0.87202I
a = −0.057752 − 0.890430I
b = −1.44306 + 0.50190I
−14.2637 + 7.7830I 0
u = −1.44711 + 0.93929I
a = −0.099582 − 0.974443I
b = −1.45292 + 0.48475I
−13.4195 + 15.8987I 0
u = −1.44711 − 0.93929I
a = −0.099582 + 0.974443I
b = −1.45292 − 0.48475I
−13.4195 − 15.8987I 0
u = −1.37855 + 1.03960I
a = −0.123840 + 0.435880I
b = 1.190040 − 0.087701I
−4.94093 + 1.63213I 0
u = −1.37855 − 1.03960I
a = −0.123840 − 0.435880I
b = 1.190040 + 0.087701I
−4.94093 − 1.63213I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.144278
a = 5.40384
b = −0.674268
−1.17407 −8.98220
u = 1.62504 + 2.08961I
a = 0.195235 + 0.198274I
b = −1.214090 + 0.100227I
−11.29140 − 2.66062I 0
u = 1.62504 − 2.08961I
a = 0.195235 − 0.198274I
b = −1.214090 − 0.100227I
−11.29140 + 2.66062I 0
u = −1.07793 + 2.55737I
a = 0.184452 + 0.002607I
b = −1.177930 − 0.198966I
−10.35930 − 5.79368I 0
u = −1.07793 − 2.55737I
a = 0.184452 − 0.002607I
b = −1.177930 + 0.198966I
−10.35930 + 5.79368I 0
11
II.
I
u
2
= h1.09×10
13
u
20
+1.23×10
13
u
19
+· · ·+2.48×10
13
b+6.04×10
12
, −1.29×
10
13
u
20
−2.85×10
12
u
19
+· · ·+2.48 ×10
13
a−1.28×10
13
, u
21
+u
20
+· · ·−2u
2
−1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
0.519350u
20
+ 0.115092u
19
+ ··· + 4.75906u + 0.515976
−0.438298u
20
− 0.496699u
19
+ ··· − 1.49110u − 0.243862
a
1
=
0.432185u
20
− 0.347015u
19
+ ··· + 2.74861u + 0.676372
0.0360697u
20
− 0.276002u
19
+ ··· − 1.57826u − 0.618804
a
8
=
0.343067u
20
+ 0.800587u
19
+ ··· + 0.543328u + 2.17015
−0.349292u
20
− 0.630439u
19
+ ··· + 2.20499u + 0.0265777
a
6
=
0.561265u
20
+ 1.60373u
19
+ ··· − 5.73182u − 0.208417
0.0890616u
20
− 0.213890u
19
+ ··· + 2.41615u + 1.51061
a
11
=
0.0810518u
20
− 0.381607u
19
+ ··· + 3.26796u + 0.272114
−0.438298u
20
− 0.496699u
19
+ ··· − 1.49110u − 0.243862
a
3
=
−0.713332u
20
− 0.888724u
19
+ ··· + 4.27797u + 1.97434
−0.739910u
20
− 0.566010u
19
+ ··· − 2.10462u − 0.230652
a
2
=
0.0219095u
20
− 0.283308u
19
+ ··· + 2.48653u + 0.812160
−0.519367u
20
− 0.445460u
19
+ ··· − 2.03367u + 0.145816
a
7
=
1.01832u
20
+ 1.08146u
19
+ ··· + 1.09672u + 1.27496
0.272340u
20
− 0.310322u
19
+ ··· + 2.54320u − 0.924913
a
10
=
0.684289u
20
+ 0.403574u
19
+ ··· + 1.29439u + 3.50062
−0.623557u
20
− 1.06224u
19
+ ··· + 1.98393u − 0.232468
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
11118351519795
24764957468951
u
20
−
6479749559907
3537851066993
u
19
+ ··· −
134928284668245
24764957468951
u −
205361301351383
24764957468951
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
21
− 21u
20
+ ··· − 3u − 1
c
2
u
21
− u
20
+ ··· + 3u − 1
c
3
u
21
− u
20
+ ··· + 11u + 7
c
4
u
21
+ u
20
+ ··· − 2u
2
− 1
c
5
u
21
+ 2u
20
+ ··· + 6u − 7
c
6
u
21
+ u
20
+ ··· − u + 1
c
7
u
21
+ u
20
+ ··· + 3u + 1
c
8
u
21
+ u
20
+ ··· − 4u + 1
c
9
u
21
+ 2u
20
+ ··· − 71u + 19
c
10
u
21
− u
20
+ ··· − u − 1
c
11
u
21
+ u
20
+ ··· + 11u − 7
c
12
u
21
− 3u
20
+ ··· + 2u − 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 53y
20
+ ··· + 73y −1
c
2
, c
7
y
21
− 21y
20
+ ··· − 3y −1
c
3
, c
11
y
21
− 15y
20
+ ··· + 93y −49
c
4
y
21
+ 5y
20
+ ··· − 4y −1
c
5
y
21
− 12y
20
+ ··· + 2108y −49
c
6
, c
10
y
21
+ 15y
20
+ ··· + 5y −1
c
8
y
21
+ 3y
20
+ ··· + 6y −1
c
9
y
21
− 8y
20
+ ··· − 6815y −361
c
12
y
21
− y
20
+ ··· + 2y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.995040
a = 1.53732
b = −0.633509
−2.63990 −61.2880
u = 0.887942 + 0.265832I
a = −0.27186 + 1.60857I
b = −1.105880 − 0.231970I
−3.10576 − 1.08145I −11.60473 − 1.20772I
u = 0.887942 − 0.265832I
a = −0.27186 − 1.60857I
b = −1.105880 + 0.231970I
−3.10576 + 1.08145I −11.60473 + 1.20772I
u = 0.335007 + 0.764873I
a = 0.349475 + 0.797361I
b = 0.126425 − 1.048160I
2.99868 − 1.45719I −4.59366 + 6.14585I
u = 0.335007 − 0.764873I
a = 0.349475 − 0.797361I
b = 0.126425 + 1.048160I
2.99868 + 1.45719I −4.59366 − 6.14585I
u = −0.768678 + 0.960873I
a = −0.391291 + 1.331950I
b = 1.355210 − 0.281637I
−3.38645 + 6.55264I −3.36004 − 8.68236I
u = −0.768678 − 0.960873I
a = −0.391291 − 1.331950I
b = 1.355210 + 0.281637I
−3.38645 − 6.55264I −3.36004 + 8.68236I
u = −0.480430 + 0.542921I
a = 0.03174 − 1.74407I
b = −0.102734 + 0.532504I
1.33027 + 3.34421I 0.81047 − 9.50324I
u = −0.480430 − 0.542921I
a = 0.03174 + 1.74407I
b = −0.102734 − 0.532504I
1.33027 − 3.34421I 0.81047 + 9.50324I
u = −0.598889 + 0.406001I
a = 0.173713 + 0.637671I
b = −0.631828 − 1.130440I
2.34945 − 0.74831I −4.02686 − 6.25327I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.598889 − 0.406001I
a = 0.173713 − 0.637671I
b = −0.631828 + 1.130440I
2.34945 + 0.74831I −4.02686 + 6.25327I
u = −1.166620 + 0.527651I
a = −0.579151 − 0.728388I
b = −1.089360 + 0.405520I
0.49818 + 4.56432I −8.19695 − 3.48083I
u = −1.166620 − 0.527651I
a = −0.579151 + 0.728388I
b = −1.089360 − 0.405520I
0.49818 − 4.56432I −8.19695 + 3.48083I
u = −0.725758 + 1.061050I
a = 0.271335 + 0.349520I
b = 1.175310 + 0.315124I
−10.06770 + 2.53564I −8.77876 − 1.65013I
u = −0.725758 − 1.061050I
a = 0.271335 − 0.349520I
b = 1.175310 − 0.315124I
−10.06770 − 2.53564I −8.77876 + 1.65013I
u = 0.216516 + 0.360136I
a = 2.00760 + 2.33089I
b = −1.304550 − 0.087060I
−3.10125 − 2.22500I −10.50218 + 2.63419I
u = 0.216516 − 0.360136I
a = 2.00760 − 2.33089I
b = −1.304550 + 0.087060I
−3.10125 + 2.22500I −10.50218 − 2.63419I
u = 1.06547 + 1.24110I
a = −0.085748 − 0.678299I
b = 1.279400 + 0.468268I
−0.73617 − 6.70838I −6.14219 + 7.52338I
u = 1.06547 − 1.24110I
a = −0.085748 + 0.678299I
b = 1.279400 − 0.468268I
−0.73617 + 6.70838I −6.14219 − 7.52338I
u = 0.23792 + 1.75774I
a = −0.274467 − 0.304190I
b = 1.114760 − 0.227134I
−10.13330 + 5.08046I −10.46087 − 0.93338I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23792 − 1.75774I
a = −0.274467 + 0.304190I
b = 1.114760 + 0.227134I
−10.13330 − 5.08046I −10.46087 + 0.93338I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 21u
20
+ ··· − 3u − 1)
· (u
65
+ 80u
64
+ ··· + 26201631u + 703921)
c
2
(u
21
− u
20
+ ··· + 3u − 1)(u
65
+ 2u
64
+ ··· + 2635u − 839)
c
3
(u
21
− u
20
+ ··· + 11u + 7)(u
65
− 25u
63
+ ··· − 25u − 1)
c
4
(u
21
+ u
20
+ ··· − 2u
2
− 1)(u
65
+ 2u
64
+ ··· + 1458u + 157)
c
5
(u
21
+ 2u
20
+ ··· + 6u − 7)(u
65
+ 9u
64
+ ··· − 1.38661 × 10
7
u + 772201)
c
6
(u
21
+ u
20
+ ··· − u + 1)(u
65
+ 6u
63
+ ··· − 13u + 1)
c
7
(u
21
+ u
20
+ ··· + 3u + 1)(u
65
+ 2u
64
+ ··· + 2635u − 839)
c
8
(u
21
+ u
20
+ ··· − 4u + 1)(u
65
+ 2u
64
+ ··· + 1534u + 169)
c
9
(u
21
+ 2u
20
+ ··· − 71u + 19)
· (u
65
+ u
64
+ ··· + 626468359u − 113770343)
c
10
(u
21
− u
20
+ ··· − u − 1)(u
65
+ 6u
63
+ ··· − 13u + 1)
c
11
(u
21
+ u
20
+ ··· + 11u − 7)(u
65
− 25u
63
+ ··· − 25u − 1)
c
12
(u
21
− 3u
20
+ ··· + 2u − 1)(u
65
− 2u
64
+ ··· − 23392u − 2011)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
− 53y
20
+ ··· + 73y −1)
· (y
65
− 160y
64
+ ··· − 124582077762381y −495504774241)
c
2
, c
7
(y
21
− 21y
20
+ ··· − 3y −1)
· (y
65
− 80y
64
+ ··· + 26201631y −703921)
c
3
, c
11
(y
21
− 15y
20
+ ··· + 93y −49)(y
65
− 50y
64
+ ··· + 31y −1)
c
4
(y
21
+ 5y
20
+ ··· − 4y −1)(y
65
− 14y
64
+ ··· + 1831546y −24649)
c
5
(y
21
− 12y
20
+ ··· + 2108y −49)
· (y
65
+ 93y
64
+ ··· + 51698127994114y −596294384401)
c
6
, c
10
(y
21
+ 15y
20
+ ··· + 5y −1)(y
65
+ 12y
64
+ ··· + 43y −1)
c
8
(y
21
+ 3y
20
+ ··· + 6y −1)(y
65
+ 16y
64
+ ··· − 184548y −28561)
c
9
(y
21
− 8y
20
+ ··· − 6815y −361)
· (y
65
− 71y
64
+ ··· + 305883945614896799y −12943690946337649)
c
12
(y
21
− y
20
+ ··· + 2y −1)
· (y
65
+ 28y
64
+ ··· − 291747228y −4044121)
21
