11a
137
(K11a
137
)
A knot diagram
1
Linearized knot diagam
6 1 8 11 2 10 4 3 5 7 9
Solving Sequence
6,10
7
2,11
1 3 5 4 9 8
c
6
c
10
c
1
c
2
c
5
c
4
c
9
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.62286 × 10
122
u
66
− 5.83233 × 10
122
u
65
+ ··· + 8.34384 × 10
121
b + 3.23422 × 10
123
,
7.89658 × 10
122
u
66
− 1.90489 × 10
123
u
65
+ ··· + 5.84069 × 10
122
a + 4.77578 × 10
123
,
u
67
− u
66
+ ··· + 178u + 14i
I
u
2
= hu
6
− u
5
− 3u
4
+ 3u
3
+ 3u
2
+ b − 2u − 1,
− u
11
+ 2u
10
+ 5u
9
− 12u
8
− 9u
7
+ 31u
6
+ 4u
5
− 43u
4
+ 8u
3
+ 31u
2
+ 2a − 10u − 9,
u
12
− 2u
11
− 5u
10
+ 12u
9
+ 9u
8
− 29u
7
− 6u
6
+ 35u
5
− 21u
3
+ 5u + 2i
* 2 irreducible components of dim
C
= 0, with total 79 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
= h2.62 × 10
122
u
66
− 5.83 × 10
122
u
65
+ · · · + 8.34 × 10
121
b + 3.23 ×
10
123
, 7.90 × 10
122
u
66
− 1.90 × 10
123
u
65
+ · · · + 5.84 × 10
122
a + 4.78 ×
10
123
, u
67
− u
66
+ · · · + 178u + 14i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
−1.35200u
66
+ 3.26141u
65
+ ··· − 118.518u − 8.17674
−3.14346u
66
+ 6.98998u
65
+ ··· − 456.720u − 38.7618
a
11
=
u
−u
3
+ u
a
1
=
1.79147u
66
− 3.72857u
65
+ ··· + 338.203u + 30.5851
−3.14346u
66
+ 6.98998u
65
+ ··· − 456.720u − 38.7618
a
3
=
6.35511u
66
− 14.1634u
65
+ ··· + 956.320u + 88.5224
−5.13936u
66
+ 11.5473u
65
+ ··· − 761.528u − 66.6848
a
5
=
1.65994u
66
− 3.47429u
65
+ ··· + 303.006u + 31.5407
−5.11342u
66
+ 11.2674u
65
+ ··· − 724.107u − 63.0777
a
4
=
8.11928u
66
− 17.8617u
65
+ ··· + 1164.71u + 104.265
−8.57661u
66
+ 18.9928u
65
+ ··· − 1183.18u − 101.347
a
9
=
−1.57345u
66
+ 3.70563u
65
+ ··· − 91.7422u − 2.61257
2.16777u
66
− 4.87111u
65
+ ··· + 235.385u + 18.0302
a
8
=
4.14278u
66
− 9.73696u
65
+ ··· + 392.893u + 31.7183
−6.68802u
66
+ 15.1248u
65
+ ··· − 868.092u − 73.9457
a
8
=
4.14278u
66
− 9.73696u
65
+ ··· + 392.893u + 31.7183
−6.68802u
66
+ 15.1248u
65
+ ··· − 868.092u − 73.9457
(ii) Obstruction class = −1
(iii) Cusp Shapes = 15.0826u
66
− 33.1683u
65
+ ··· + 1975.74u + 173.234
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
67
+ 12u
65
+ ··· + 23u + 1
c
2
u
67
+ 24u
66
+ ··· + 655u − 1
c
3
, c
7
, c
8
u
67
+ u
66
+ ··· + 34u − 11
c
4
u
67
− 3u
66
+ ··· − 56360u + 14843
c
6
, c
10
u
67
+ u
66
+ ··· + 178u − 14
c
9
u
67
+ u
66
+ ··· + 1218u − 523
c
11
u
67
− 11u
66
+ ··· + 19734u − 3697
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
67
+ 24y
66
+ ··· + 655y −1
c
2
y
67
+ 44y
66
+ ··· + 467315y −1
c
3
, c
7
, c
8
y
67
+ 73y
66
+ ··· − 5026y −121
c
4
y
67
− 31y
66
+ ··· + 4845129346y −220314649
c
6
, c
10
y
67
− 59y
66
+ ··· + 2144y −196
c
9
y
67
− 19y
66
+ ··· + 1068262y −273529
c
11
y
67
+ 25y
66
+ ··· − 401527606y −13667809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.142657 + 0.992860I
a = 0.56636 + 1.48377I
b = 0.033263 + 1.144420I
1.70877 + 2.32867I 0
u = −0.142657 − 0.992860I
a = 0.56636 − 1.48377I
b = 0.033263 − 1.144420I
1.70877 − 2.32867I 0
u = −0.099779 + 1.006020I
a = −0.20395 − 1.63071I
b = 0.623398 − 0.982401I
−0.20027 − 6.31062I 0
u = −0.099779 − 1.006020I
a = −0.20395 + 1.63071I
b = 0.623398 + 0.982401I
−0.20027 + 6.31062I 0
u = −0.981096 + 0.054455I
a = −0.76387 − 1.69840I
b = −0.044418 − 0.942425I
0.0186179 + 0.0387429I 0
u = −0.981096 − 0.054455I
a = −0.76387 + 1.69840I
b = −0.044418 + 0.942425I
0.0186179 − 0.0387429I 0
u = −0.270773 + 0.833923I
a = 0.195059 + 0.748297I
b = 0.604424 + 0.639267I
0.80579 − 1.40750I 0. + 4.43919I
u = −0.270773 − 0.833923I
a = 0.195059 − 0.748297I
b = 0.604424 − 0.639267I
0.80579 + 1.40750I 0. − 4.43919I
u = 1.107010 + 0.303823I
a = 0.50610 − 1.37239I
b = −0.121641 − 1.174720I
−0.89603 + 4.38119I 0
u = 1.107010 − 0.303823I
a = 0.50610 + 1.37239I
b = −0.121641 + 1.174720I
−0.89603 − 4.38119I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.136800 + 0.224242I
a = 0.966929 − 0.878075I
b = −0.740988 − 1.111300I
2.93656 + 4.60816I 0
u = 1.136800 − 0.224242I
a = 0.966929 + 0.878075I
b = −0.740988 + 1.111300I
2.93656 − 4.60816I 0
u = 1.224370 + 0.009584I
a = 0.293275 + 0.010079I
b = −0.933790 + 0.466037I
4.82838 − 1.51282I 0
u = 1.224370 − 0.009584I
a = 0.293275 − 0.010079I
b = −0.933790 − 0.466037I
4.82838 + 1.51282I 0
u = 1.104740 + 0.538484I
a = 0.98881 + 1.60795I
b = −0.048348 + 0.578810I
7.98310 + 2.39539I 0
u = 1.104740 − 0.538484I
a = 0.98881 − 1.60795I
b = −0.048348 − 0.578810I
7.98310 − 2.39539I 0
u = −1.246690 + 0.004314I
a = −0.902444 − 0.638257I
b = 0.86616 − 1.20415I
9.42380 − 4.94858I 0
u = −1.246690 − 0.004314I
a = −0.902444 + 0.638257I
b = 0.86616 + 1.20415I
9.42380 + 4.94858I 0
u = 0.424436 + 1.177450I
a = 0.101432 + 0.607388I
b = −0.768711 + 0.568168I
7.58682 + 3.59183I 0
u = 0.424436 − 1.177450I
a = 0.101432 − 0.607388I
b = −0.768711 − 0.568168I
7.58682 − 3.59183I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.244190 + 0.216049I
a = 1.84039 + 1.27405I
b = −0.662475 + 0.965347I
3.73550 − 4.99700I 0
u = −1.244190 − 0.216049I
a = 1.84039 − 1.27405I
b = −0.662475 − 0.965347I
3.73550 + 4.99700I 0
u = −1.267400 + 0.140376I
a = −0.324635 + 0.014077I
b = 1.231450 − 0.468321I
11.62150 − 2.40537I 0
u = −1.267400 − 0.140376I
a = −0.324635 − 0.014077I
b = 1.231450 + 0.468321I
11.62150 + 2.40537I 0
u = 1.275090 + 0.042068I
a = −1.97186 − 0.47485I
b = 0.704366 − 0.840178I
11.39430 + 0.35805I 0
u = 1.275090 − 0.042068I
a = −1.97186 + 0.47485I
b = 0.704366 + 0.840178I
11.39430 − 0.35805I 0
u = 0.275788 + 0.662423I
a = −1.09829 + 1.97732I
b = 0.088329 + 0.994872I
−3.44236 − 0.72466I −6.99887 + 1.47430I
u = 0.275788 − 0.662423I
a = −1.09829 − 1.97732I
b = 0.088329 − 0.994872I
−3.44236 + 0.72466I −6.99887 − 1.47430I
u = −1.28332
a = −0.480905
b = 0.0382466
2.83439 0
u = −1.290700 + 0.141599I
a = 0.109094 + 0.820721I
b = −0.682399 − 0.719924I
4.48457 + 0.21946I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.290700 − 0.141599I
a = 0.109094 − 0.820721I
b = −0.682399 + 0.719924I
4.48457 − 0.21946I 0
u = −1.223810 + 0.441106I
a = −0.440377 − 1.113580I
b = 0.263799 − 1.354580I
5.11820 − 7.37502I 0
u = −1.223810 − 0.441106I
a = −0.440377 + 1.113580I
b = 0.263799 + 1.354580I
5.11820 + 7.37502I 0
u = −0.642398 + 0.199393I
a = 2.73814 + 0.59347I
b = −0.329606 + 0.827830I
−1.07794 − 1.38861I 3.80624 + 5.85827I
u = −0.642398 − 0.199393I
a = 2.73814 − 0.59347I
b = −0.329606 − 0.827830I
−1.07794 + 1.38861I 3.80624 − 5.85827I
u = 1.372630 + 0.064390I
a = −0.790042 − 0.625685I
b = 0.699831 + 0.881652I
11.26670 + 5.74067I 0
u = 1.372630 − 0.064390I
a = −0.790042 + 0.625685I
b = 0.699831 − 0.881652I
11.26670 − 5.74067I 0
u = 1.357220 + 0.338528I
a = −0.054546 + 0.327019I
b = 0.845002 − 0.591998I
5.80090 + 5.54175I 0
u = 1.357220 − 0.338528I
a = −0.054546 − 0.327019I
b = 0.845002 + 0.591998I
5.80090 − 5.54175I 0
u = 1.35728 + 0.42005I
a = −1.27110 + 1.25208I
b = 0.700232 + 1.058400I
4.39822 + 11.29900I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.35728 − 0.42005I
a = −1.27110 − 1.25208I
b = 0.700232 − 1.058400I
4.39822 − 11.29900I 0
u = 0.30910 + 1.39948I
a = 0.307214 − 1.270910I
b = −0.670107 − 1.042710I
6.20108 + 9.04828I 0
u = 0.30910 − 1.39948I
a = 0.307214 + 1.270910I
b = −0.670107 + 1.042710I
6.20108 − 9.04828I 0
u = −1.33379 + 0.59022I
a = −0.882996 − 1.086150I
b = 0.632519 − 0.943685I
3.61989 − 4.42085I 0
u = −1.33379 − 0.59022I
a = −0.882996 + 1.086150I
b = 0.632519 + 0.943685I
3.61989 + 4.42085I 0
u = −0.157526 + 0.467985I
a = −0.59248 − 2.72678I
b = −0.580708 − 0.850266I
0.31179 + 2.36087I 1.49175 − 2.57935I
u = −0.157526 − 0.467985I
a = −0.59248 + 2.72678I
b = −0.580708 + 0.850266I
0.31179 − 2.36087I 1.49175 + 2.57935I
u = −1.46858 + 0.37754I
a = −0.250474 + 0.202698I
b = 0.642292 + 0.738861I
4.25449 + 0.57931I 0
u = −1.46858 − 0.37754I
a = −0.250474 − 0.202698I
b = 0.642292 − 0.738861I
4.25449 − 0.57931I 0
u = 1.50959 + 0.30643I
a = 0.553270 − 0.283027I
b = −0.041798 − 0.750414I
7.39577 + 2.70914I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50959 − 0.30643I
a = 0.553270 + 0.283027I
b = −0.041798 + 0.750414I
7.39577 − 2.70914I 0
u = −0.307962 + 0.334683I
a = −0.646318 + 0.777154I
b = −0.200980 + 0.371837I
0.196594 − 0.980812I 3.31524 + 7.18006I
u = −0.307962 − 0.334683I
a = −0.646318 − 0.777154I
b = −0.200980 − 0.371837I
0.196594 + 0.980812I 3.31524 − 7.18006I
u = −1.48923 + 0.44102I
a = 0.162313 + 0.201835I
b = −0.980839 − 0.621887I
13.5295 − 9.1720I 0
u = −1.48923 − 0.44102I
a = 0.162313 − 0.201835I
b = −0.980839 + 0.621887I
13.5295 + 9.1720I 0
u = 0.128136 + 0.410429I
a = −1.29668 + 0.78147I
b = −0.560999 + 0.890607I
0.19847 − 2.17667I 0.68586 + 2.94537I
u = 0.128136 − 0.410429I
a = −1.29668 − 0.78147I
b = −0.560999 − 0.890607I
0.19847 + 2.17667I 0.68586 − 2.94537I
u = −1.52256 + 0.50776I
a = 1.08603 + 1.06504I
b = −0.758307 + 1.104120I
12.0155 − 15.5095I 0
u = −1.52256 − 0.50776I
a = 1.08603 − 1.06504I
b = −0.758307 − 1.104120I
12.0155 + 15.5095I 0
u = 0.046763 + 0.307117I
a = 0.04254 − 2.41858I
b = 0.820849 + 0.561471I
7.58253 + 0.63888I 6.93084 − 2.84898I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.046763 − 0.307117I
a = 0.04254 + 2.41858I
b = 0.820849 − 0.561471I
7.58253 − 0.63888I 6.93084 + 2.84898I
u = −0.198912 + 0.077556I
a = −0.94110 + 2.54372I
b = 0.706486 − 1.065940I
6.10007 − 5.08359I 5.69636 + 1.21643I
u = −0.198912 − 0.077556I
a = −0.94110 − 2.54372I
b = 0.706486 + 1.065940I
6.10007 + 5.08359I 5.69636 − 1.21643I
u = 1.65753 + 0.77266I
a = 0.897263 − 1.007730I
b = −0.679271 − 0.835623I
10.85990 + 4.67168I 0
u = 1.65753 − 0.77266I
a = 0.897263 + 1.007730I
b = −0.679271 + 0.835623I
10.85990 − 4.67168I 0
u = 1.74322 + 0.63886I
a = 0.245971 + 0.281094I
b = −0.676138 + 0.881444I
10.71770 − 0.56043I 0
u = 1.74322 − 0.63886I
a = 0.245971 − 0.281094I
b = −0.676138 − 0.881444I
10.71770 + 0.56043I 0
11
II. I
u
2
= hu
6
− u
5
− 3u
4
+ 3u
3
+ 3u
2
+ b − 2u − 1, −u
11
+ 2u
10
+ · · · + 2a −
9, u
12
− 2u
11
+ · · · + 5u + 2i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
2
=
1
2
u
11
− u
10
+ ··· + 5u +
9
2
−u
6
+ u
5
+ 3u
4
− 3u
3
− 3u
2
+ 2u + 1
a
11
=
u
−u
3
+ u
a
1
=
1
2
u
11
− u
10
+ ··· + 3u +
7
2
−u
6
+ u
5
+ 3u
4
− 3u
3
− 3u
2
+ 2u + 1
a
3
=
u
11
− 2u
10
+ ··· + 3u + 2
−u
8
+ u
7
+ 3u
6
− 3u
5
− 3u
4
+ 2u
3
+ u
2
+ u
a
5
=
1
2
u
11
− 2u
10
+ ··· + 7u +
3
2
u
7
− u
6
− 3u
5
+ 3u
4
+ 3u
3
− 2u
2
− u − 1
a
4
=
1
2
u
11
− 2u
10
+ ··· + 6u +
3
2
u
11
− u
10
+ ··· − 2u − 1
a
9
=
−
1
2
u
11
+ u
10
+ ··· − u −
7
2
−u
4
+ u
3
+ 2u
2
− u − 1
a
8
=
1
2
u
11
−
7
2
u
9
+ ··· − 7u −
7
2
−u
11
+ u
10
+ ··· + 5u + 1
a
8
=
1
2
u
11
−
7
2
u
9
+ ··· − 7u −
7
2
−u
11
+ u
10
+ ··· + 5u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
11
+ u
10
+ 7u
9
− 6u
8
− 24u
7
+ 18u
6
+ 43u
5
− 27u
4
− 41u
3
+ 17u
2
+ 20u + 4
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− u
11
+ ··· − u + 1
c
2
u
12
+ 5u
11
+ ··· + 5u + 1
c
3
u
12
+ 7u
10
+ 17u
8
+ u
7
+ 15u
6
+ 4u
5
+ u
4
+ 4u
3
− u
2
+ 1
c
4
u
12
− u
10
− 3u
9
− u
8
+ 3u
7
+ 4u
6
+ u
5
− 2u
3
− u
2
+ 1
c
5
u
12
+ u
11
+ ··· + u + 1
c
6
u
12
− 2u
11
− 5u
10
+ 12u
9
+ 9u
8
− 29u
7
− 6u
6
+ 35u
5
− 21u
3
+ 5u + 2
c
7
, c
8
u
12
+ 7u
10
+ 17u
8
− u
7
+ 15u
6
− 4u
5
+ u
4
− 4u
3
− u
2
+ 1
c
9
u
12
− u
10
− 2u
9
+ u
7
+ 4u
6
+ 3u
5
− u
4
− 3u
3
− u
2
+ 1
c
10
u
12
+ 2u
11
− 5u
10
− 12u
9
+ 9u
8
+ 29u
7
− 6u
6
− 35u
5
+ 21u
3
− 5u + 2
c
11
u
12
− 2u
11
+ ··· − 2u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
12
+ 5y
11
+ ··· + 5y + 1
c
2
y
12
+ 9y
11
+ ··· + 9y + 1
c
3
, c
7
, c
8
y
12
+ 14y
11
+ ··· − 2y + 1
c
4
y
12
− 2y
11
+ ··· − 2y + 1
c
6
, c
10
y
12
− 14y
11
+ ··· − 25y + 4
c
9
y
12
− 2y
11
+ ··· − 2y + 1
c
11
y
12
+ 2y
11
− y
10
− 4y
9
+ 9y
8
+ 5y
7
− 9y
6
− 6y
5
+ 9y
4
− y
2
+ 2y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972521 + 0.508215I
a = 0.443552 − 1.155780I
b = −0.620586 − 1.173980I
6.48178 + 6.40598I 7.80646 − 6.33972I
u = 0.972521 − 0.508215I
a = 0.443552 + 1.155780I
b = −0.620586 + 1.173980I
6.48178 − 6.40598I 7.80646 + 6.33972I
u = −1.105730 + 0.306025I
a = −1.22523 − 1.12382I
b = 0.652038 − 1.006000I
2.33148 − 3.99686I 1.50375 + 2.05925I
u = −1.105730 − 0.306025I
a = −1.22523 + 1.12382I
b = 0.652038 + 1.006000I
2.33148 + 3.99686I 1.50375 − 2.05925I
u = −1.310620 + 0.162001I
a = −0.148721 − 0.157045I
b = 0.585728 + 0.681872I
3.42377 + 0.95171I 2.37059 − 4.65710I
u = −1.310620 − 0.162001I
a = −0.148721 + 0.157045I
b = 0.585728 − 0.681872I
3.42377 − 0.95171I 2.37059 + 4.65710I
u = 1.300570 + 0.543594I
a = −0.080694 + 0.988779I
b = −0.438411 + 0.562405I
8.75961 + 1.92614I 9.97632 + 1.04911I
u = 1.300570 − 0.543594I
a = −0.080694 − 0.988779I
b = −0.438411 − 0.562405I
8.75961 − 1.92614I 9.97632 − 1.04911I
u = 1.45085 + 0.16539I
a = 0.856836 − 0.213098I
b = −0.811300 − 0.781246I
10.26960 + 3.07498I 8.16546 − 2.75495I
u = 1.45085 − 0.16539I
a = 0.856836 + 0.213098I
b = −0.811300 + 0.781246I
10.26960 − 3.07498I 8.16546 + 2.75495I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.307597 + 0.275985I
a = 1.90426 + 3.57986I
b = 0.132531 + 0.859925I
−1.65743 + 0.58036I −2.32258 + 0.32607I
u = −0.307597 − 0.275985I
a = 1.90426 − 3.57986I
b = 0.132531 − 0.859925I
−1.65743 − 0.58036I −2.32258 − 0.32607I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
12
− u
11
+ ··· − u + 1)(u
67
+ 12u
65
+ ··· + 23u + 1)
c
2
(u
12
+ 5u
11
+ ··· + 5u + 1)(u
67
+ 24u
66
+ ··· + 655u − 1)
c
3
(u
12
+ 7u
10
+ 17u
8
+ u
7
+ 15u
6
+ 4u
5
+ u
4
+ 4u
3
− u
2
+ 1)
· (u
67
+ u
66
+ ··· + 34u − 11)
c
4
(u
12
− u
10
− 3u
9
− u
8
+ 3u
7
+ 4u
6
+ u
5
− 2u
3
− u
2
+ 1)
· (u
67
− 3u
66
+ ··· − 56360u + 14843)
c
5
(u
12
+ u
11
+ ··· + u + 1)(u
67
+ 12u
65
+ ··· + 23u + 1)
c
6
(u
12
− 2u
11
− 5u
10
+ 12u
9
+ 9u
8
− 29u
7
− 6u
6
+ 35u
5
− 21u
3
+ 5u + 2)
· (u
67
+ u
66
+ ··· + 178u − 14)
c
7
, c
8
(u
12
+ 7u
10
+ 17u
8
− u
7
+ 15u
6
− 4u
5
+ u
4
− 4u
3
− u
2
+ 1)
· (u
67
+ u
66
+ ··· + 34u − 11)
c
9
(u
12
− u
10
− 2u
9
+ u
7
+ 4u
6
+ 3u
5
− u
4
− 3u
3
− u
2
+ 1)
· (u
67
+ u
66
+ ··· + 1218u − 523)
c
10
(u
12
+ 2u
11
− 5u
10
− 12u
9
+ 9u
8
+ 29u
7
− 6u
6
− 35u
5
+ 21u
3
− 5u + 2)
· (u
67
+ u
66
+ ··· + 178u − 14)
c
11
(u
12
− 2u
11
+ ··· − 2u + 1)(u
67
− 11u
66
+ ··· + 19734u − 3697)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
12
+ 5y
11
+ ··· + 5y + 1)(y
67
+ 24y
66
+ ··· + 655y −1)
c
2
(y
12
+ 9y
11
+ ··· + 9y + 1)(y
67
+ 44y
66
+ ··· + 467315y −1)
c
3
, c
7
, c
8
(y
12
+ 14y
11
+ ··· − 2y + 1)(y
67
+ 73y
66
+ ··· − 5026y −121)
c
4
(y
12
− 2y
11
+ ··· − 2y + 1)
· (y
67
− 31y
66
+ ··· + 4845129346y −220314649)
c
6
, c
10
(y
12
− 14y
11
+ ··· − 25y + 4)(y
67
− 59y
66
+ ··· + 2144y −196)
c
9
(y
12
− 2y
11
+ ··· − 2y + 1)(y
67
− 19y
66
+ ··· + 1068262y −273529)
c
11
(y
12
+ 2y
11
− y
10
− 4y
9
+ 9y
8
+ 5y
7
− 9y
6
− 6y
5
+ 9y
4
− y
2
+ 2y + 1)
· (y
67
+ 25y
66
+ ··· − 401527606y −13667809)
18
