12a
0942
(K12a
0942
)
A knot diagram
1
Linearized knot diagam
4 6 9 1 10 3 11 12 2 8 7 5
Solving Sequence
7,11
8 12
3,9
4 6 2 1 10 5
c
7
c
11
c
8
c
3
c
6
c
2
c
1
c
10
c
5
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.67572 × 10
88
u
91
+ 2.35834 × 10
89
u
90
+ ··· + 2.42279 × 10
90
b + 9.70979 × 10
89
,
1.80595 × 10
90
u
91
+ 3.65341 × 10
90
u
90
+ ··· + 2.18051 × 10
91
a + 1.03035 × 10
91
, u
92
+ 3u
91
+ ··· + 49u + 9i
I
u
2
= h−9u
2
a − 18au − 3u
2
+ 23b − 3a − 6u − 1, −3u
2
a + 3a
2
+ 3au + 3u
2
− 3a + 4, u
3
− u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 98 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−6.68 × 10
88
u
91
+ 2.36 × 10
89
u
90
+ · · · + 2.42 × 10
90
b + 9.71 ×
10
89
, 1.81 × 10
90
u
91
+ 3.65 × 10
90
u
90
+ · · · + 2.18 × 10
91
a + 1.03 ×
10
91
, u
92
+ 3u
91
+ · · · + 49u + 9i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
12
=
−u
u
a
3
=
−0.0828225u
91
− 0.167548u
90
+ ··· − 3.52927u − 0.472529
0.0275538u
91
− 0.0973397u
90
+ ··· − 1.86772u − 0.400769
a
9
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
4
=
0.0509100u
91
+ 0.622642u
90
+ ··· + 12.8628u + 2.47080
−0.324534u
91
− 1.12865u
90
+ ··· − 16.5700u − 3.59604
a
6
=
0.000609590u
91
+ 0.892534u
90
+ ··· − 5.59951u − 1.33977
−1.01318u
91
− 2.80973u
90
+ ··· − 41.4443u − 9.83553
a
2
=
−0.210669u
91
− 0.186692u
90
+ ··· − 7.66553u − 4.08858
−0.171606u
91
− 0.788526u
90
+ ··· − 11.2024u − 3.44047
a
1
=
0.0567726u
91
+ 0.233111u
90
+ ··· + 5.88148u + 1.02278
0.283527u
91
+ 0.499883u
90
+ ··· + 13.4607u + 2.66381
a
10
=
u
u
3
+ u
a
5
=
−0.161712u
91
+ 0.315650u
90
+ ··· − 3.68445u − 0.838694
−0.539534u
91
− 1.79824u
90
+ ··· − 33.6623u − 8.52519
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.692795u
91
− 2.25332u
90
+ ··· − 40.8738u − 9.09423
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
92
− 4u
91
+ ··· − 4u + 1
c
2
, c
6
u
92
− 4u
91
+ ··· − 4u + 1
c
3
27(27u
92
− 27u
91
+ ··· + 133643u − 6581)
c
5
27(27u
92
− 54u
91
+ ··· + 1430027u + 751139)
c
7
, c
10
, c
11
u
92
− 3u
91
+ ··· − 49u + 9
c
8
u
92
+ 3u
91
+ ··· + 30601u + 21969
c
9
u
92
+ 3u
91
+ ··· + 4320u + 5184
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
92
+ 88y
91
+ ··· − 10y + 1
c
2
, c
6
y
92
− 52y
91
+ ··· − 10y + 1
c
3
729(729y
92
− 38313y
91
+ ··· − 6.42023 × 10
9
y + 4.33096 × 10
7
)
c
5
729
· (729y
92
+ 16362y
91
+ ··· + 15225683884841y + 564209797321)
c
7
, c
10
, c
11
y
92
+ 83y
91
+ ··· − 169y + 81
c
8
y
92
− y
91
+ ··· + 12026870567y + 482636961
c
9
y
92
− 35y
91
+ ··· − 347120640y + 26873856
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.582390 + 0.791689I
a = 0.753577 − 0.347209I
b = −1.251090 + 0.475634I
9.25726 − 8.18208I 0
u = −0.582390 − 0.791689I
a = 0.753577 + 0.347209I
b = −1.251090 − 0.475634I
9.25726 + 8.18208I 0
u = 0.736262 + 0.628121I
a = 1.049820 + 0.457055I
b = −0.887252 + 0.284095I
3.94303 − 3.83126I 0
u = 0.736262 − 0.628121I
a = 1.049820 − 0.457055I
b = −0.887252 − 0.284095I
3.94303 + 3.83126I 0
u = 0.926342 + 0.164936I
a = 0.460377 + 0.377356I
b = −0.729328 + 0.179095I
2.52480 − 1.25642I 0
u = 0.926342 − 0.164936I
a = 0.460377 − 0.377356I
b = −0.729328 − 0.179095I
2.52480 + 1.25642I 0
u = 0.323996 + 1.013050I
a = 0.630042 − 0.069778I
b = −0.265885 − 0.472333I
5.03694 − 3.16909I 0
u = 0.323996 − 1.013050I
a = 0.630042 + 0.069778I
b = −0.265885 + 0.472333I
5.03694 + 3.16909I 0
u = −0.094010 + 1.097530I
a = −1.038130 + 0.233071I
b = 0.418611 + 0.766435I
0.233678 − 0.500797I 0
u = −0.094010 − 1.097530I
a = −1.038130 − 0.233071I
b = 0.418611 − 0.766435I
0.233678 + 0.500797I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.818478 + 0.331482I
a = 0.76020 − 1.33742I
b = −1.295560 − 0.541975I
7.8020 + 13.0110I 0. − 8.15881I
u = −0.818478 − 0.331482I
a = 0.76020 + 1.33742I
b = −1.295560 + 0.541975I
7.8020 − 13.0110I 0. + 8.15881I
u = −0.437432 + 0.765002I
a = −0.719368 + 0.448533I
b = 1.213080 − 0.455397I
2.95349 − 4.88268I −4.00000 + 4.50142I
u = −0.437432 − 0.765002I
a = −0.719368 − 0.448533I
b = 1.213080 + 0.455397I
2.95349 + 4.88268I −4.00000 − 4.50142I
u = 0.000013 + 1.147790I
a = 0.344767 − 0.348258I
b = −0.829604 + 0.540806I
3.51439 − 1.54001I 0
u = 0.000013 − 1.147790I
a = 0.344767 + 0.348258I
b = −0.829604 − 0.540806I
3.51439 + 1.54001I 0
u = 0.374112 + 1.092450I
a = −0.830199 − 0.416954I
b = 0.927867 − 0.309390I
1.93950 − 4.31636I 0
u = 0.374112 − 1.092450I
a = −0.830199 + 0.416954I
b = 0.927867 + 0.309390I
1.93950 + 4.31636I 0
u = −0.374410 + 0.730981I
a = 0.902557 − 0.188982I
b = −0.056183 − 0.815962I
5.65365 − 3.41644I −0.205199 + 1.266815I
u = −0.374410 − 0.730981I
a = 0.902557 + 0.188982I
b = −0.056183 + 0.815962I
5.65365 + 3.41644I −0.205199 − 1.266815I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.819573
a = 0.0197403
b = 0.744911
−1.38150 −13.5870
u = −0.760866 + 0.288446I
a = −0.62010 + 1.40146I
b = 1.286890 + 0.560835I
1.36094 + 9.14769I −3.11665 − 8.62512I
u = −0.760866 − 0.288446I
a = −0.62010 − 1.40146I
b = 1.286890 − 0.560835I
1.36094 − 9.14769I −3.11665 + 8.62512I
u = 0.756425 + 0.260905I
a = 0.485720 + 0.109400I
b = −0.302020 − 0.238032I
2.69497 − 1.07990I −4.94046 + 1.01805I
u = 0.756425 − 0.260905I
a = 0.485720 − 0.109400I
b = −0.302020 + 0.238032I
2.69497 + 1.07990I −4.94046 − 1.01805I
u = 0.703199 + 0.371330I
a = −0.929795 − 0.803087I
b = 0.871833 − 0.211011I
−0.61831 − 2.08055I −9.77125 + 9.25183I
u = 0.703199 − 0.371330I
a = −0.929795 + 0.803087I
b = 0.871833 + 0.211011I
−0.61831 + 2.08055I −9.77125 − 9.25183I
u = −0.736185 + 0.281983I
a = −0.479375 + 0.643889I
b = −0.102011 + 1.017520I
4.08651 + 7.45020I −2.56752 − 6.27902I
u = −0.736185 − 0.281983I
a = −0.479375 − 0.643889I
b = −0.102011 − 1.017520I
4.08651 − 7.45020I −2.56752 + 6.27902I
u = −0.142124 + 1.263210I
a = 1.52577 − 0.30777I
b = −0.745186 − 0.965258I
2.80330 + 4.03627I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.142124 − 1.263210I
a = 1.52577 + 0.30777I
b = −0.745186 + 0.965258I
2.80330 − 4.03627I 0
u = 0.164963 + 1.270790I
a = 0.050965 − 0.698499I
b = −0.577119 − 0.165305I
3.85258 − 2.03665I 0
u = 0.164963 − 1.270790I
a = 0.050965 + 0.698499I
b = −0.577119 + 0.165305I
3.85258 + 2.03665I 0
u = −0.656857 + 0.267157I
a = 0.44312 − 1.61945I
b = −1.248510 − 0.587775I
1.84603 + 4.13199I −1.86475 − 5.14943I
u = −0.656857 − 0.267157I
a = 0.44312 + 1.61945I
b = −1.248510 + 0.587775I
1.84603 − 4.13199I −1.86475 + 5.14943I
u = 0.128671 + 1.295620I
a = −3.84498 + 0.47312I
b = 1.203540 − 0.042147I
9.63383 − 2.00341I 0
u = 0.128671 − 1.295620I
a = −3.84498 − 0.47312I
b = 1.203540 + 0.042147I
9.63383 + 2.00341I 0
u = −0.581029 + 0.359352I
a = −0.222451 + 0.196065I
b = 1.348550 − 0.386647I
8.85704 + 2.47164I 3.01205 − 4.35204I
u = −0.581029 − 0.359352I
a = −0.222451 − 0.196065I
b = 1.348550 + 0.386647I
8.85704 − 2.47164I 3.01205 + 4.35204I
u = −0.642174 + 0.199804I
a = 0.535662 − 0.867543I
b = 0.182287 − 1.052460I
−2.15457 + 3.40976I −5.90227 − 8.24087I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.642174 − 0.199804I
a = 0.535662 + 0.867543I
b = 0.182287 + 1.052460I
−2.15457 − 3.40976I −5.90227 + 8.24087I
u = 0.671704
a = −0.310781
b = 0.215837
−1.55032 −7.74090
u = 0.259605 + 1.309660I
a = −0.247077 + 0.013717I
b = 0.097376 + 0.288479I
2.60983 − 3.35368I 0
u = 0.259605 − 1.309660I
a = −0.247077 − 0.013717I
b = 0.097376 − 0.288479I
2.60983 + 3.35368I 0
u = −0.516057 + 0.400667I
a = −0.76365 + 2.13859I
b = 1.185740 + 0.507231I
9.09275 + 1.02296I 3.55453 − 4.18776I
u = −0.516057 − 0.400667I
a = −0.76365 − 2.13859I
b = 1.185740 − 0.507231I
9.09275 − 1.02296I 3.55453 + 4.18776I
u = 0.503851 + 1.248960I
a = 1.103600 + 0.557191I
b = −0.967384 + 0.312417I
6.83291 − 6.37350I 0
u = 0.503851 − 1.248960I
a = 1.103600 − 0.557191I
b = −0.967384 − 0.312417I
6.83291 + 6.37350I 0
u = 0.163438 + 1.344350I
a = −0.54876 + 2.14293I
b = 0.884445 + 0.234151I
10.19730 − 2.39866I 0
u = 0.163438 − 1.344350I
a = −0.54876 − 2.14293I
b = 0.884445 − 0.234151I
10.19730 + 2.39866I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.223299 + 1.351700I
a = 2.70863 + 1.95015I
b = −1.068200 + 0.141951I
5.06193 − 3.40170I 0
u = 0.223299 − 1.351700I
a = 2.70863 − 1.95015I
b = −1.068200 − 0.141951I
5.06193 + 3.40170I 0
u = −0.188713 + 1.361780I
a = −0.486402 − 0.868672I
b = −0.389728 + 1.216040I
3.87314 + 0.69064I 0
u = −0.188713 − 1.361780I
a = −0.486402 + 0.868672I
b = −0.389728 − 1.216040I
3.87314 − 0.69064I 0
u = −0.251021 + 1.379070I
a = 0.729238 + 0.669618I
b = 0.135336 − 1.223050I
2.87331 + 6.66260I 0
u = −0.251021 − 1.379070I
a = 0.729238 − 0.669618I
b = 0.135336 + 1.223050I
2.87331 − 6.66260I 0
u = 0.574264 + 0.111966I
a = 0.22466 + 2.92931I
b = −0.931822 + 0.094872I
0.395763 − 0.494287I 4.29552 − 12.70736I
u = 0.574264 − 0.111966I
a = 0.22466 − 2.92931I
b = −0.931822 − 0.094872I
0.395763 + 0.494287I 4.29552 + 12.70736I
u = −0.14834 + 1.40864I
a = 2.08410 − 0.83521I
b = −1.48389 + 0.31155I
8.76204 + 0.97088I 0
u = −0.14834 − 1.40864I
a = 2.08410 + 0.83521I
b = −1.48389 − 0.31155I
8.76204 − 0.97088I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.28623 + 1.39773I
a = 0.315348 + 0.116776I
b = −0.023245 − 0.439811I
7.95406 − 4.80757I 0
u = 0.28623 − 1.39773I
a = 0.315348 − 0.116776I
b = −0.023245 + 0.439811I
7.95406 + 4.80757I 0
u = −0.25957 + 1.40499I
a = 2.14568 − 1.00660I
b = −1.35135 − 0.65463I
7.18270 + 7.48451I 0
u = −0.25957 − 1.40499I
a = 2.14568 + 1.00660I
b = −1.35135 + 0.65463I
7.18270 − 7.48451I 0
u = −0.08596 + 1.43421I
a = 0.312598 + 0.534930I
b = 0.323835 − 0.877940I
12.34400 − 2.20430I 0
u = −0.08596 − 1.43421I
a = 0.312598 − 0.534930I
b = 0.323835 + 0.877940I
12.34400 + 2.20430I 0
u = −0.19682 + 1.42934I
a = −2.02321 + 0.96049I
b = 1.239090 + 0.674351I
14.9149 + 3.6571I 0
u = −0.19682 − 1.42934I
a = −2.02321 − 0.96049I
b = 1.239090 − 0.674351I
14.9149 − 3.6571I 0
u = −0.22102 + 1.42800I
a = −1.79058 + 0.83116I
b = 1.47155 − 0.43333I
14.5709 + 5.4197I 0
u = −0.22102 − 1.42800I
a = −1.79058 − 0.83116I
b = 1.47155 + 0.43333I
14.5709 − 5.4197I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.29049 + 1.41717I
a = −0.693518 − 0.523001I
b = −0.075269 + 1.125750I
9.5099 + 11.1778I 0
u = −0.29049 − 1.41717I
a = −0.693518 + 0.523001I
b = −0.075269 − 1.125750I
9.5099 − 11.1778I 0
u = −0.313193 + 0.456137I
a = 0.441752 − 0.760209I
b = −1.228750 + 0.322684I
3.01576 − 0.85496I 1.23119 − 2.52327I
u = −0.313193 − 0.456137I
a = 0.441752 + 0.760209I
b = −1.228750 − 0.322684I
3.01576 + 0.85496I 1.23119 + 2.52327I
u = −0.30153 + 1.42217I
a = −2.13521 + 1.07097I
b = 1.35800 + 0.59500I
6.8199 + 13.0005I 0
u = −0.30153 − 1.42217I
a = −2.13521 − 1.07097I
b = 1.35800 − 0.59500I
6.8199 − 13.0005I 0
u = 0.29153 + 1.43750I
a = −1.85744 − 0.85644I
b = 1.076850 − 0.249443I
5.14012 − 5.77360I 0
u = 0.29153 − 1.43750I
a = −1.85744 + 0.85644I
b = 1.076850 + 0.249443I
5.14012 + 5.77360I 0
u = −0.05758 + 1.46635I
a = −2.22236 + 0.47583I
b = 1.352440 − 0.274412I
10.15940 − 3.63892I 0
u = −0.05758 − 1.46635I
a = −2.22236 − 0.47583I
b = 1.352440 + 0.274412I
10.15940 + 3.63892I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.32315 + 1.44956I
a = 2.11174 − 1.09178I
b = −1.34379 − 0.56775I
13.4980 + 17.1470I 0
u = −0.32315 − 1.44956I
a = 2.11174 + 1.09178I
b = −1.34379 + 0.56775I
13.4980 − 17.1470I 0
u = −0.491340 + 0.087310I
a = −0.82486 + 1.36513I
b = −0.518685 + 1.021610I
−0.82443 − 1.77338I 6.58787 − 6.08701I
u = −0.491340 − 0.087310I
a = −0.82486 − 1.36513I
b = −0.518685 − 1.021610I
−0.82443 + 1.77338I 6.58787 + 6.08701I
u = 0.475028 + 0.043866I
a = −5.16609 + 4.98938I
b = 1.030210 + 0.088639I
5.75586 − 0.13073I −4.90020 − 5.98483I
u = 0.475028 − 0.043866I
a = −5.16609 − 4.98938I
b = 1.030210 − 0.088639I
5.75586 + 0.13073I −4.90020 + 5.98483I
u = 0.29258 + 1.53406I
a = 1.83456 + 0.50035I
b = −1.107870 + 0.294999I
10.88590 − 7.72340I 0
u = 0.29258 − 1.53406I
a = 1.83456 − 0.50035I
b = −1.107870 − 0.294999I
10.88590 + 7.72340I 0
u = −0.06461 + 1.56283I
a = 2.00684 − 0.32098I
b = −1.306820 + 0.337330I
17.3400 − 6.1869I 0
u = −0.06461 − 1.56283I
a = 2.00684 + 0.32098I
b = −1.306820 − 0.337330I
17.3400 + 6.1869I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.105890 + 0.334666I
a = −1.150010 − 0.432779I
b = −0.001375 + 0.424041I
−0.176718 − 0.984073I −3.51434 + 6.22041I
u = 0.105890 − 0.334666I
a = −1.150010 + 0.432779I
b = −0.001375 − 0.424041I
−0.176718 + 0.984073I −3.51434 − 6.22041I
14
II. I
u
2
= h−9u
2
a − 18au − 3u
2
+ 23b − 3a − 6u − 1, −3u
2
a + 3a
2
+ 3au +
3u
2
− 3a + 4, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
12
=
−u
u
a
3
=
a
0.391304au
2
+ 0.130435u
2
+ ··· + 0.130435a + 0.0434783
a
9
=
u
u
2
− u + 1
a
4
=
0.521739au
2
+ 0.173913u
2
+ ··· + 1.17391a + 0.391304
−0.391304au
2
− 0.130435u
2
+ ··· − 0.130435a − 0.0434783
a
6
=
−0.130435au
2
− 1.04348u
2
+ ··· + 0.956522a − 0.347826
0.391304au
2
+ 0.130435u
2
+ ··· + 0.130435a − 0.956522
a
2
=
−0.260870au
2
+ 0.913043u
2
+ ··· + 0.913043a + 1.30435
0.391304au
2
+ 0.130435u
2
+ ··· + 0.130435a + 1.04348
a
1
=
−0.652174au
2
− 0.217391u
2
+ ··· + 0.782609a + 0.260870
0.782609au
2
+ 0.260870u
2
+ ··· + 0.260870a + 0.0869565
a
10
=
u
u
2
− u + 1
a
5
=
0.130435au
2
− 0.956522u
2
+ ··· + 1.04348a − 0.652174
au − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
36
23
u
2
a −
95
23
au −
104
23
u
2
−
81
23
a +
158
69
u −
165
23
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
12
(u
2
− u + 1)
3
c
2
, c
4
(u
2
+ u + 1)
3
c
3
27(27u
6
+ 9u
4
+ 6u
2
+ 1)
c
5
27(27u
6
+ 27u
5
+ 9u
4
− 3u
2
+ 1)
c
7
(u
3
− u
2
+ 2u − 1)
2
c
8
(u
3
+ u
2
− 1)
2
c
9
u
6
c
10
, c
11
(u
3
+ u
2
+ 2u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
12
(y
2
+ y + 1)
3
c
3
729(27y
3
+ 9y
2
+ 6y + 1)
2
c
5
729(729y
6
− 243y
5
− 81y
4
+ 27y
2
− 6y + 1)
c
7
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
8
(y
3
− y
2
+ 2y −1)
2
c
9
y
6
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −1.083790 − 0.189897I
b = 0.500000 − 0.866025I
3.02413 − 4.85801I 1.60261 + 7.59932I
u = 0.215080 + 1.307140I
a = 0.206350 − 0.554965I
b = 0.500000 + 0.866025I
3.02413 − 0.79824I −3.02248 + 0.15845I
u = 0.215080 − 1.307140I
a = −1.083790 + 0.189897I
b = 0.500000 + 0.866025I
3.02413 + 4.85801I 1.60261 − 7.59932I
u = 0.215080 − 1.307140I
a = 0.206350 + 0.554965I
b = 0.500000 − 0.866025I
3.02413 + 0.79824I −3.02248 − 0.15845I
u = 0.569840
a = 0.377439 + 1.231090I
b = 0.500000 + 0.866025I
−1.11345 + 2.02988I −9.74680 − 7.85891I
u = 0.569840
a = 0.377439 − 1.231090I
b = 0.500000 − 0.866025I
−1.11345 − 2.02988I −9.74680 + 7.85891I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
((u
2
− u + 1)
3
)(u
92
− 4u
91
+ ··· − 4u + 1)
c
2
((u
2
+ u + 1)
3
)(u
92
− 4u
91
+ ··· − 4u + 1)
c
3
729(27u
6
+ 9u
4
+ 6u
2
+ 1)(27u
92
− 27u
91
+ ··· + 133643u − 6581)
c
4
((u
2
+ u + 1)
3
)(u
92
− 4u
91
+ ··· − 4u + 1)
c
5
729(27u
6
+ 27u
5
+ 9u
4
− 3u
2
+ 1)
· (27u
92
− 54u
91
+ ··· + 1430027u + 751139)
c
6
((u
2
− u + 1)
3
)(u
92
− 4u
91
+ ··· − 4u + 1)
c
7
((u
3
− u
2
+ 2u − 1)
2
)(u
92
− 3u
91
+ ··· − 49u + 9)
c
8
((u
3
+ u
2
− 1)
2
)(u
92
+ 3u
91
+ ··· + 30601u + 21969)
c
9
u
6
(u
92
+ 3u
91
+ ··· + 4320u + 5184)
c
10
, c
11
((u
3
+ u
2
+ 2u + 1)
2
)(u
92
− 3u
91
+ ··· − 49u + 9)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
((y
2
+ y + 1)
3
)(y
92
+ 88y
91
+ ··· − 10y + 1)
c
2
, c
6
((y
2
+ y + 1)
3
)(y
92
− 52y
91
+ ··· − 10y + 1)
c
3
531441(27y
3
+ 9y
2
+ 6y + 1)
2
· (729y
92
− 38313y
91
+ ··· − 6420225317y + 43309561)
c
5
531441(729y
6
− 243y
5
− 81y
4
+ 27y
2
− 6y + 1)
· (729y
92
+ 16362y
91
+ ··· + 15225683884841y + 564209797321)
c
7
, c
10
, c
11
((y
3
+ 3y
2
+ 2y −1)
2
)(y
92
+ 83y
91
+ ··· − 169y + 81)
c
8
((y
3
− y
2
+ 2y −1)
2
)(y
92
− y
91
+ ··· + 1.20269 × 10
10
y + 4.82637 × 10
8
)
c
9
y
6
(y
92
− 35y
91
+ ··· − 3.47121 × 10
8
y + 2.68739 × 10
7
)
20
