12n
0776
(K12n
0776
)
A knot diagram
1
Linearized knot diagam
4 6 10 11 12 2 5 1 4 8 7 10
Solving Sequence
5,11 4,8
7 12 6 10 1 3 2 9
c
4
c
7
c
11
c
5
c
10
c
12
c
3
c
2
c
9
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h1.30447 × 10
408
u
82
+ 1.37413 × 10
409
u
81
+ ··· + 8.60439 × 10
408
b − 2.49025 × 10
408
,
− 1.05688 × 10
410
u
82
− 1.12073 × 10
411
u
81
+ ··· + 1.29066 × 10
410
a + 2.26537 × 10
410
,
u
83
+ 11u
82
+ ··· − 13u − 3i
I
u
2
= h1.25634 × 10
54
u
29
+ 1.27322 × 10
55
u
28
+ ··· + 2.61825 × 10
54
b + 1.66292 × 10
54
,
2.32992 × 10
54
u
29
+ 2.36472 × 10
55
u
28
+ ··· + 3.00141 × 10
54
a + 8.04364 × 10
54
, u
30
+ 10u
29
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 113 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
= h1.30 × 10
408
u
82
+ 1.37 × 10
409
u
81
+ · · · + 8.60 × 10
408
b − 2.49 ×
10
408
, −1.06 × 10
410
u
82
− 1.12 × 10
411
u
81
+ · · · + 1.29 × 10
410
a + 2.27 ×
10
410
, u
83
+ 11u
82
+ · · · − 13u − 3i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
8
=
0.818869u
82
+ 8.68343u
81
+ ··· + 28.1044u − 1.75521
−0.151605u
82
− 1.59701u
81
+ ··· + 2.31640u + 0.289416
a
7
=
0.970473u
82
+ 10.2804u
81
+ ··· + 25.7880u − 2.04462
−0.151605u
82
− 1.59701u
81
+ ··· + 2.31640u + 0.289416
a
12
=
−0.751807u
82
− 7.77308u
81
+ ··· + 119.279u + 25.5349
−0.0208145u
82
− 0.206503u
81
+ ··· − 1.29505u − 1.10729
a
6
=
0.0172443u
82
− 0.0375127u
81
+ ··· − 126.673u − 18.4506
−0.0490051u
82
− 0.539643u
81
+ ··· + 3.70028u + 1.39331
a
10
=
−0.731904u
82
− 7.54031u
81
+ ··· + 113.239u + 23.1711
0.0407173u
82
+ 0.439275u
81
+ ··· − 2.74464u − 1.25654
a
1
=
−1.19729u
82
− 12.6448u
81
+ ··· + 1.47287u + 12.3678
−0.0211191u
82
− 0.198672u
81
+ ··· + 2.33013u − 0.629956
a
3
=
−2.19019u
82
− 23.7541u
81
+ ··· + 139.252u + 18.1407
0.108002u
82
+ 1.16613u
81
+ ··· − 5.31878u − 1.13687
a
2
=
−1.26772u
82
− 13.4375u
81
+ ··· + 2.38069u + 14.5739
−0.00603930u
82
− 0.0390650u
81
+ ··· + 1.88614u − 0.683654
a
9
=
−0.532288u
82
− 5.37650u
81
+ ··· + 106.052u + 20.3826
0.0409161u
82
+ 0.446102u
81
+ ··· − 2.56150u − 1.35247
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.65712u
82
+ 17.5491u
81
+ ··· − 136.696u − 33.9475
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
83
+ u
82
+ ··· − 53405u + 3225
c
2
, c
6
u
83
+ 2u
82
+ ··· + 217u − 67
c
3
, c
9
u
83
+ 10u
82
+ ··· + 34163451u − 6221089
c
4
u
83
+ 11u
82
+ ··· − 13u − 3
c
5
u
83
− 15u
81
+ ··· − 486505u + 43627
c
7
u
83
+ 5u
82
+ ··· − 6u − 1
c
8
u
83
− 51u
81
+ ··· + 17717265u − 4973081
c
10
u
83
+ 11u
82
+ ··· + 1754u + 107
c
11
u
83
+ 7u
82
+ ··· − 3609u + 331
c
12
u
83
− 11u
82
+ ··· + 133746194u + 15906677
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
83
− 131y
82
+ ··· − 220531175y −10400625
c
2
, c
6
y
83
+ 60y
82
+ ··· − 303187y −4489
c
3
, c
9
y
83
− 126y
82
+ ··· − 86541304996979y −38701948345921
c
4
y
83
− 15y
82
+ ··· + 7y −9
c
5
y
83
− 30y
82
+ ··· + 62663810995y −1903315129
c
7
y
83
+ 13y
82
+ ··· − 96y −1
c
8
y
83
− 102y
82
+ ··· − 98203788924489y −24731534632561
c
10
y
83
+ 17y
82
+ ··· − 583740y −11449
c
11
y
83
+ 5y
82
+ ··· + 2855899y −109561
c
12
y
83
− 303y
82
+ ··· − 13069623167467982y −253022373182329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.709906 + 0.690044I
a = −0.927762 + 0.065003I
b = −1.090150 + 0.433533I
−0.98312 + 1.83332I 0
u = 0.709906 − 0.690044I
a = −0.927762 − 0.065003I
b = −1.090150 − 0.433533I
−0.98312 − 1.83332I 0
u = 0.261828 + 0.930528I
a = −0.764997 + 0.206710I
b = −0.298237 + 0.061397I
−0.40627 + 1.72494I 0
u = 0.261828 − 0.930528I
a = −0.764997 − 0.206710I
b = −0.298237 − 0.061397I
−0.40627 − 1.72494I 0
u = −0.894847 + 0.518321I
a = 1.59094 − 0.23930I
b = 1.118840 − 0.816514I
3.48501 − 4.70122I 0
u = −0.894847 − 0.518321I
a = 1.59094 + 0.23930I
b = 1.118840 + 0.816514I
3.48501 + 4.70122I 0
u = −0.362153 + 0.892735I
a = 1.38780 + 0.53803I
b = −0.181923 − 0.485373I
−3.04231 + 1.75204I 0
u = −0.362153 − 0.892735I
a = 1.38780 − 0.53803I
b = −0.181923 + 0.485373I
−3.04231 − 1.75204I 0
u = −0.740237 + 0.744539I
a = −0.421844 + 0.182382I
b = −0.823000 + 0.195896I
−0.28428 + 2.31145I 0
u = −0.740237 − 0.744539I
a = −0.421844 − 0.182382I
b = −0.823000 − 0.195896I
−0.28428 − 2.31145I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.270866 + 1.053850I
a = 1.49395 − 0.74055I
b = 0.081067 + 0.787778I
−13.4588 + 7.1690I 0
u = 0.270866 − 1.053850I
a = 1.49395 + 0.74055I
b = 0.081067 − 0.787778I
−13.4588 − 7.1690I 0
u = −0.758010 + 0.437224I
a = −1.44879 − 1.65189I
b = −0.791564 + 0.668716I
−9.72538 − 8.72357I 0
u = −0.758010 − 0.437224I
a = −1.44879 + 1.65189I
b = −0.791564 − 0.668716I
−9.72538 + 8.72357I 0
u = −0.516399 + 0.659806I
a = −0.798299 + 0.327613I
b = −0.75838 + 1.49622I
−5.06876 − 0.94779I 0
u = −0.516399 − 0.659806I
a = −0.798299 − 0.327613I
b = −0.75838 − 1.49622I
−5.06876 + 0.94779I 0
u = −0.602229 + 0.994072I
a = −1.45123 − 0.15027I
b = −0.92859 + 1.10832I
−14.0609 − 2.5251I 0
u = −0.602229 − 0.994072I
a = −1.45123 + 0.15027I
b = −0.92859 − 1.10832I
−14.0609 + 2.5251I 0
u = 0.803341 + 0.845356I
a = −0.913620 − 0.197343I
b = −0.280226 − 0.440104I
−0.29002 + 2.15185I 0
u = 0.803341 − 0.845356I
a = −0.913620 + 0.197343I
b = −0.280226 + 0.440104I
−0.29002 − 2.15185I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.680380 + 0.437401I
a = 0.501491 − 0.074945I
b = 0.824171 + 0.728489I
1.37263 + 1.70785I 0
u = 0.680380 − 0.437401I
a = 0.501491 + 0.074945I
b = 0.824171 − 0.728489I
1.37263 − 1.70785I 0
u = −0.233492 + 0.754653I
a = −1.000650 + 0.119961I
b = 0.060779 + 0.557525I
−1.09485 + 1.14990I 0
u = −0.233492 − 0.754653I
a = −1.000650 − 0.119961I
b = 0.060779 − 0.557525I
−1.09485 − 1.14990I 0
u = −0.577250 + 0.501896I
a = −1.42505 + 0.21771I
b = −1.60916 − 0.88816I
−10.73260 − 8.88187I 0. + 8.54488I
u = −0.577250 − 0.501896I
a = −1.42505 − 0.21771I
b = −1.60916 + 0.88816I
−10.73260 + 8.88187I 0. − 8.54488I
u = 0.777187 + 1.003380I
a = −1.057860 − 0.100809I
b = −1.08433 − 1.22178I
−4.76888 + 8.66641I 0
u = 0.777187 − 1.003380I
a = −1.057860 + 0.100809I
b = −1.08433 + 1.22178I
−4.76888 − 8.66641I 0
u = 0.064315 + 1.270220I
a = −0.687278 − 0.229993I
b = −1.19350 − 1.01922I
−13.2417 + 5.2799I 0
u = 0.064315 − 1.270220I
a = −0.687278 + 0.229993I
b = −1.19350 + 1.01922I
−13.2417 − 5.2799I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.680427 + 0.042583I
a = 1.38569 + 0.95422I
b = 1.098090 − 0.661662I
3.67022 − 0.24922I 11.72806 − 2.38470I
u = −0.680427 − 0.042583I
a = 1.38569 − 0.95422I
b = 1.098090 + 0.661662I
3.67022 + 0.24922I 11.72806 + 2.38470I
u = 0.948869 + 0.927196I
a = 0.689941 + 0.118533I
b = 0.820966 + 1.116060I
0.03269 + 4.50461I 0
u = 0.948869 − 0.927196I
a = 0.689941 − 0.118533I
b = 0.820966 − 1.116060I
0.03269 − 4.50461I 0
u = −0.574607 + 0.326079I
a = 1.81871 − 0.33275I
b = 1.25086 − 1.16436I
2.26604 − 3.57767I −8.97068 + 8.43068I
u = −0.574607 − 0.326079I
a = 1.81871 + 0.33275I
b = 1.25086 + 1.16436I
2.26604 + 3.57767I −8.97068 − 8.43068I
u = 0.927408 + 0.976224I
a = −0.319524 − 0.705776I
b = 0.160830 − 0.946290I
−8.05970 − 2.70904I 0
u = 0.927408 − 0.976224I
a = −0.319524 + 0.705776I
b = 0.160830 + 0.946290I
−8.05970 + 2.70904I 0
u = 0.373196 + 0.449963I
a = 1.72772 + 1.13860I
b = 0.447128 − 1.280330I
−10.82210 + 1.04215I −8.95659 − 0.64479I
u = 0.373196 − 0.449963I
a = 1.72772 − 1.13860I
b = 0.447128 + 1.280330I
−10.82210 − 1.04215I −8.95659 + 0.64479I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.02114 + 1.01195I
a = 1.165700 + 0.230472I
b = 0.99942 + 1.24394I
−7.91150 + 10.06580I 0
u = 1.02114 − 1.01195I
a = 1.165700 − 0.230472I
b = 0.99942 − 1.24394I
−7.91150 − 10.06580I 0
u = −0.165432 + 0.479272I
a = 1.74495 − 1.61770I
b = −0.331671 + 0.790672I
−2.95336 − 5.09545I −6.33229 + 9.13394I
u = −0.165432 − 0.479272I
a = 1.74495 + 1.61770I
b = −0.331671 − 0.790672I
−2.95336 + 5.09545I −6.33229 − 9.13394I
u = 0.504156
a = 5.40046
b = 0.696000
−4.71616 10.6220
u = 0.10860 + 1.51156I
a = 0.484440 + 0.127681I
b = 1.002370 + 0.085521I
0.309078 + 0.377421I 0
u = 0.10860 − 1.51156I
a = 0.484440 − 0.127681I
b = 1.002370 − 0.085521I
0.309078 − 0.377421I 0
u = −1.31990 + 0.75395I
a = 0.861735 − 0.367052I
b = 0.90290 − 1.18899I
2.06751 − 7.02731I 0
u = −1.31990 − 0.75395I
a = 0.861735 + 0.367052I
b = 0.90290 + 1.18899I
2.06751 + 7.02731I 0
u = −1.03049 + 1.12737I
a = −0.670023 + 0.083173I
b = −0.799015 + 1.128390I
−2.24741 − 9.70482I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.03049 − 1.12737I
a = −0.670023 − 0.083173I
b = −0.799015 − 1.128390I
−2.24741 + 9.70482I 0
u = −1.02629 + 1.15598I
a = −0.816028 + 0.211399I
b = −0.677550 + 0.597699I
−5.06471 − 5.76701I 0
u = −1.02629 − 1.15598I
a = −0.816028 − 0.211399I
b = −0.677550 − 0.597699I
−5.06471 + 5.76701I 0
u = 1.36893 + 0.74159I
a = 0.399726 − 0.420329I
b = 0.578099 + 0.577904I
−5.53407 + 1.96330I 0
u = 1.36893 − 0.74159I
a = 0.399726 + 0.420329I
b = 0.578099 − 0.577904I
−5.53407 − 1.96330I 0
u = 0.043734 + 0.437894I
a = 1.37494 − 0.86927I
b = 1.80634 − 1.67583I
−6.61873 + 0.72943I −27.0371 − 3.0253I
u = 0.043734 − 0.437894I
a = 1.37494 + 0.86927I
b = 1.80634 + 1.67583I
−6.61873 − 0.72943I −27.0371 + 3.0253I
u = −1.48630 + 0.49749I
a = −0.184899 − 0.725570I
b = −0.514333 − 1.079950I
−11.23120 − 3.55868I 0
u = −1.48630 − 0.49749I
a = −0.184899 + 0.725570I
b = −0.514333 + 1.079950I
−11.23120 + 3.55868I 0
u = 1.17287 + 1.06491I
a = −0.948428 − 0.052602I
b = −0.770986 − 1.135900I
−2.90730 + 8.25650I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.17287 − 1.06491I
a = −0.948428 + 0.052602I
b = −0.770986 + 1.135900I
−2.90730 − 8.25650I 0
u = 1.60080 + 0.00259I
a = −0.308479 + 0.601802I
b = −0.512848 + 0.469068I
−2.12534 − 2.73496I 0
u = 1.60080 − 0.00259I
a = −0.308479 − 0.601802I
b = −0.512848 − 0.469068I
−2.12534 + 2.73496I 0
u = −0.275291 + 0.221049I
a = −0.64665 + 1.27043I
b = −1.054180 − 0.813914I
−0.89305 − 2.92243I −9.70267 + 2.02248I
u = −0.275291 − 0.221049I
a = −0.64665 − 1.27043I
b = −1.054180 + 0.813914I
−0.89305 + 2.92243I −9.70267 − 2.02248I
u = −0.318817 + 0.131695I
a = −3.73118 − 2.56355I
b = 0.0551272 + 0.0990377I
−2.40668 − 0.00982I −16.7035 − 7.8985I
u = −0.318817 − 0.131695I
a = −3.73118 + 2.56355I
b = 0.0551272 − 0.0990377I
−2.40668 + 0.00982I −16.7035 + 7.8985I
u = 0.252941 + 0.222750I
a = −1.61194 − 2.97824I
b = −0.203176 − 1.245190I
−7.63133 − 1.98716I −11.03642 + 4.01004I
u = 0.252941 − 0.222750I
a = −1.61194 + 2.97824I
b = −0.203176 + 1.245190I
−7.63133 + 1.98716I −11.03642 − 4.01004I
u = −1.20089 + 1.18117I
a = −0.951427 + 0.190149I
b = −0.97977 + 1.25279I
−12.3596 − 17.5347I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.20089 − 1.18117I
a = −0.951427 − 0.190149I
b = −0.97977 − 1.25279I
−12.3596 + 17.5347I 0
u = 0.40829 + 1.64602I
a = 0.252064 − 0.072091I
b = −0.082371 + 0.853035I
−4.39323 + 0.59906I 0
u = 0.40829 − 1.64602I
a = 0.252064 + 0.072091I
b = −0.082371 − 0.853035I
−4.39323 − 0.59906I 0
u = 0.133270 + 0.145455I
a = 1.89268 + 13.71840I
b = −0.154111 − 0.408727I
−2.72551 − 0.66144I −24.1115 − 31.0038I
u = 0.133270 − 0.145455I
a = 1.89268 − 13.71840I
b = −0.154111 + 0.408727I
−2.72551 + 0.66144I −24.1115 + 31.0038I
u = −1.57118 + 0.94094I
a = 0.451176 − 0.364575I
b = 0.294701 − 0.688444I
−2.17859 − 4.62625I 0
u = −1.57118 − 0.94094I
a = 0.451176 + 0.364575I
b = 0.294701 + 0.688444I
−2.17859 + 4.62625I 0
u = 1.16083 + 1.45232I
a = 0.665646 + 0.142507I
b = 1.033180 + 0.595503I
−8.06942 + 7.08098I 0
u = 1.16083 − 1.45232I
a = 0.665646 − 0.142507I
b = 1.033180 − 0.595503I
−8.06942 − 7.08098I 0
u = −1.20226 + 1.73624I
a = 0.213848 − 0.358282I
b = −0.247627 − 0.670148I
−12.8693 + 7.8727I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.20226 − 1.73624I
a = 0.213848 + 0.358282I
b = −0.247627 + 0.670148I
−12.8693 − 7.8727I 0
u = −3.30429 + 0.71948I
a = −0.0507409 + 0.0686539I
b = −0.016178 + 1.084750I
−4.67503 + 0.08868I 0
u = −3.30429 − 0.71948I
a = −0.0507409 − 0.0686539I
b = −0.016178 − 1.084750I
−4.67503 − 0.08868I 0
13
II. I
u
2
=
h1.26×10
54
u
29
+1.27×10
55
u
28
+· · ·+2.62×10
54
b+1.66×10
54
, 2.33×10
54
u
29
+
2.36 × 10
55
u
28
+ · · · + 3.00 × 10
54
a + 8.04 × 10
54
, u
30
+ 10u
29
+ · · · − 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
8
=
−0.776274u
29
− 7.87870u
28
+ ··· − 14.4332u − 2.67995
−0.479840u
29
− 4.86287u
28
+ ··· − 10.1187u − 0.635126
a
7
=
−0.296434u
29
− 3.01583u
28
+ ··· − 4.31447u − 2.04483
−0.479840u
29
− 4.86287u
28
+ ··· − 10.1187u − 0.635126
a
12
=
−0.784936u
29
− 7.49694u
28
+ ··· − 11.5746u + 2.88220
0.0540488u
29
+ 0.600763u
28
+ ··· − 0.892560u + 0.854988
a
6
=
−0.659512u
29
− 6.25109u
28
+ ··· − 11.4807u + 3.31022
−0.0591853u
29
− 0.587345u
28
+ ··· − 1.73211u + 0.912115
a
10
=
−0.630267u
29
− 5.81988u
28
+ ··· − 13.4474u + 5.43172
0.100621u
29
+ 1.07630u
28
+ ··· + 1.01977u + 1.69453
a
1
=
0.329607u
29
+ 3.29915u
28
+ ··· + 9.75861u − 4.93015
−0.120600u
29
− 1.28428u
28
+ ··· − 1.86892u − 2.01908
a
3
=
−0.214937u
29
− 2.65604u
28
+ ··· + 11.2629u − 6.81042
−0.155969u
29
− 1.70352u
28
+ ··· − 2.05754u − 3.24115
a
2
=
0.443524u
29
+ 4.48675u
28
+ ··· + 11.3041u − 2.91414
−0.137180u
29
− 1.45673u
28
+ ··· − 1.88598u − 2.06751
a
9
=
−0.686563u
29
− 6.30933u
28
+ ··· − 14.0235u + 7.60903
0.0905133u
29
+ 0.965512u
28
+ ··· + 1.22311u + 1.62101
(ii) Obstruction class = 1
(iii) Cusp Shapes = 1.96657u
29
+ 20.4621u
28
+ ··· + 47.8697u − 2.01729
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
30
− 22u
29
+ ··· − 3284u + 361
c
2
u
30
+ u
29
+ ··· + 4u + 1
c
3
u
30
+ 9u
29
+ ··· − 2u + 1
c
4
u
30
+ 10u
29
+ ··· − 2u + 1
c
5
u
30
+ 3u
29
+ ··· − 8u + 1
c
6
u
30
− u
29
+ ··· − 4u + 1
c
7
u
30
− 6u
29
+ ··· + u + 1
c
8
u
30
+ u
29
+ ··· − 4u + 1
c
9
u
30
− 9u
29
+ ··· + 2u + 1
c
10
u
30
− 10u
29
+ ··· − 11u + 1
c
11
u
30
− 6u
29
+ ··· + 2u + 1
c
12
u
30
− 10u
29
+ ··· + 3u + 1
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 46y
29
+ ··· − 1581322y + 130321
c
2
, c
6
y
30
+ 13y
29
+ ··· + 22y + 1
c
3
, c
9
y
30
− 25y
29
+ ··· + 26y + 1
c
4
y
30
− 18y
29
+ ··· + 52y + 1
c
5
y
30
+ 7y
29
+ ··· − 28y + 1
c
7
y
30
+ 2y
29
+ ··· − y + 1
c
8
y
30
− 13y
29
+ ··· + 20y + 1
c
10
y
30
− 2y
29
+ ··· + 27y + 1
c
11
y
30
+ 14y
29
+ ··· + 20y + 1
c
12
y
30
+ 366y
29
+ ··· + 121y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.264851 + 0.986255I
a = 0.361756 − 0.958759I
b = 0.850957 + 0.097098I
−11.54740 + 7.22206I −5.65155 − 4.25847I
u = −0.264851 − 0.986255I
a = 0.361756 + 0.958759I
b = 0.850957 − 0.097098I
−11.54740 − 7.22206I −5.65155 + 4.25847I
u = 0.895499 + 0.582838I
a = −1.56633 − 0.03026I
b = −1.10896 − 0.91654I
3.13872 + 5.11649I −3.26050 − 11.10481I
u = 0.895499 − 0.582838I
a = −1.56633 + 0.03026I
b = −1.10896 + 0.91654I
3.13872 − 5.11649I −3.26050 + 11.10481I
u = 0.758092 + 0.267664I
a = −1.34276 − 0.62428I
b = −1.22987 − 0.94219I
2.67470 + 3.26845I 3.47425 + 0.31137I
u = 0.758092 − 0.267664I
a = −1.34276 + 0.62428I
b = −1.22987 + 0.94219I
2.67470 − 3.26845I 3.47425 − 0.31137I
u = −0.808579 + 1.008580I
a = 0.625296 − 0.162400I
b = 0.973062 − 0.124636I
−0.52735 + 1.51415I −4.01431 + 0.97590I
u = −0.808579 − 1.008580I
a = 0.625296 + 0.162400I
b = 0.973062 + 0.124636I
−0.52735 − 1.51415I −4.01431 − 0.97590I
u = 0.705784 + 0.035899I
a = −1.21686 + 0.99456I
b = −1.078060 − 0.731623I
3.20399 + 0.36138I −6.01046 − 1.13377I
u = 0.705784 − 0.035899I
a = −1.21686 − 0.99456I
b = −1.078060 + 0.731623I
3.20399 − 0.36138I −6.01046 + 1.13377I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.513887 + 0.484747I
a = 0.612259 + 0.049795I
b = 0.700776 + 1.052900I
−0.42743 − 3.33155I −0.36861 + 10.50639I
u = −0.513887 − 0.484747I
a = 0.612259 − 0.049795I
b = 0.700776 − 1.052900I
−0.42743 + 3.33155I −0.36861 − 10.50639I
u = −1.293000 + 0.211113I
a = 0.340213 − 0.765814I
b = 0.365797 − 0.255677I
−1.29420 − 4.26619I 1.65207 + 7.58449I
u = −1.293000 − 0.211113I
a = 0.340213 + 0.765814I
b = 0.365797 + 0.255677I
−1.29420 + 4.26619I 1.65207 − 7.58449I
u = −0.201020 + 0.524745I
a = 1.17021 − 2.68289I
b = −0.213535 + 0.311118I
−2.36627 − 0.24882I −12.5512 + 12.1355I
u = −0.201020 − 0.524745I
a = 1.17021 + 2.68289I
b = −0.213535 − 0.311118I
−2.36627 + 0.24882I −12.5512 − 12.1355I
u = −1.10174 + 1.00955I
a = 0.825015 − 0.016778I
b = 0.822575 − 1.114390I
−1.14409 − 9.85717I −0.89607 + 8.10159I
u = −1.10174 − 1.00955I
a = 0.825015 + 0.016778I
b = 0.822575 + 1.114390I
−1.14409 + 9.85717I −0.89607 − 8.10159I
u = 0.119635 + 0.409700I
a = −2.66687 + 3.75712I
b = 0.302007 − 0.395775I
−2.76195 + 0.87026I −16.3868 − 3.1307I
u = 0.119635 − 0.409700I
a = −2.66687 − 3.75712I
b = 0.302007 + 0.395775I
−2.76195 − 0.87026I −16.3868 + 3.1307I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.12733 + 1.57632I
a = −0.435438 + 0.098878I
b = −0.895542 + 0.150896I
0.587144 + 1.284410I 3.15676 − 3.79447I
u = 0.12733 − 1.57632I
a = −0.435438 − 0.098878I
b = −0.895542 − 0.150896I
0.587144 − 1.284410I 3.15676 + 3.79447I
u = 1.36990 + 0.80876I
a = −0.798991 − 0.342128I
b = −0.88374 − 1.17376I
1.79152 + 6.79652I −9.91993 + 0.I
u = 1.36990 − 0.80876I
a = −0.798991 + 0.342128I
b = −0.88374 + 1.17376I
1.79152 − 6.79652I −9.91993 + 0.I
u = −1.13078 + 1.22918I
a = −0.737364 + 0.226659I
b = −0.737518 + 0.702723I
−4.93858 − 6.22716I 0. + 12.49688I
u = −1.13078 − 1.22918I
a = −0.737364 − 0.226659I
b = −0.737518 − 0.702723I
−4.93858 + 6.22716I 0. − 12.49688I
u = 0.027817 + 0.207011I
a = −3.21790 − 2.28750I
b = −0.90341 − 1.73353I
−6.32991 − 0.83665I −2.04581 + 8.27979I
u = 0.027817 − 0.207011I
a = −3.21790 + 2.28750I
b = −0.90341 + 1.73353I
−6.32991 + 0.83665I −2.04581 − 8.27979I
u = −3.69021 + 2.18082I
a = 0.0477690 − 0.0382406I
b = 0.035454 − 1.049530I
−4.73294 + 0.11525I 0
u = −3.69021 − 2.18082I
a = 0.0477690 + 0.0382406I
b = 0.035454 + 1.049530I
−4.73294 − 0.11525I 0
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
30
− 22u
29
+ ··· − 3284u + 361)(u
83
+ u
82
+ ··· − 53405u + 3225)
c
2
(u
30
+ u
29
+ ··· + 4u + 1)(u
83
+ 2u
82
+ ··· + 217u − 67)
c
3
(u
30
+ 9u
29
+ ··· − 2u + 1)
· (u
83
+ 10u
82
+ ··· + 34163451u − 6221089)
c
4
(u
30
+ 10u
29
+ ··· − 2u + 1)(u
83
+ 11u
82
+ ··· − 13u − 3)
c
5
(u
30
+ 3u
29
+ ··· − 8u + 1)(u
83
− 15u
81
+ ··· − 486505u + 43627)
c
6
(u
30
− u
29
+ ··· − 4u + 1)(u
83
+ 2u
82
+ ··· + 217u − 67)
c
7
(u
30
− 6u
29
+ ··· + u + 1)(u
83
+ 5u
82
+ ··· − 6u − 1)
c
8
(u
30
+ u
29
+ ··· − 4u + 1)(u
83
− 51u
81
+ ··· + 1.77173 × 10
7
u − 4973081)
c
9
(u
30
− 9u
29
+ ··· + 2u + 1)
· (u
83
+ 10u
82
+ ··· + 34163451u − 6221089)
c
10
(u
30
− 10u
29
+ ··· − 11u + 1)(u
83
+ 11u
82
+ ··· + 1754u + 107)
c
11
(u
30
− 6u
29
+ ··· + 2u + 1)(u
83
+ 7u
82
+ ··· − 3609u + 331)
c
12
(u
30
− 10u
29
+ ··· + 3u + 1)
· (u
83
− 11u
82
+ ··· + 133746194u + 15906677)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
30
− 46y
29
+ ··· − 1581322y + 130321)
· (y
83
− 131y
82
+ ··· − 220531175y −10400625)
c
2
, c
6
(y
30
+ 13y
29
+ ··· + 22y + 1)(y
83
+ 60y
82
+ ··· − 303187y −4489)
c
3
, c
9
(y
30
− 25y
29
+ ··· + 26y + 1)
· (y
83
− 126y
82
+ ··· − 86541304996979y −38701948345921)
c
4
(y
30
− 18y
29
+ ··· + 52y + 1)(y
83
− 15y
82
+ ··· + 7y −9)
c
5
(y
30
+ 7y
29
+ ··· − 28y + 1)
· (y
83
− 30y
82
+ ··· + 62663810995y −1903315129)
c
7
(y
30
+ 2y
29
+ ··· − y + 1)(y
83
+ 13y
82
+ ··· − 96y −1)
c
8
(y
30
− 13y
29
+ ··· + 20y + 1)
· (y
83
− 102y
82
+ ··· − 98203788924489y −24731534632561)
c
10
(y
30
− 2y
29
+ ··· + 27y + 1)(y
83
+ 17y
82
+ ··· − 583740y −11449)
c
11
(y
30
+ 14y
29
+ ··· + 20y + 1)(y
83
+ 5y
82
+ ··· + 2855899y −109561)
c
12
(y
30
+ 366y
29
+ ··· + 121y + 1)
· (y
83
− 303y
82
+ ··· − 13069623167467982y −253022373182329)
23
