12n
0834
(K12n
0834
)
A knot diagram
1
Linearized knot diagam
4 5 12 10 3 9 1 11 5 7 3 8
Solving Sequence
3,5 6,9
7 10 11 12 2 4 1 8
c
5
c
6
c
9
c
10
c
11
c
2
c
4
c
1
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.08966 × 10
500
u
82
− 2.94352 × 10
500
u
81
+ ··· + 5.30022 × 10
505
b − 6.35080 × 10
505
,
− 3.64438 × 10
506
u
82
− 1.00895 × 10
507
u
81
+ ··· + 9.03577 × 10
510
a − 1.96606 × 10
512
,
u
83
+ 3u
82
+ ··· + 2662084u + 170479i
I
u
2
= h−4.04393 × 10
21
u
26
+ 1.97112 × 10
22
u
25
+ ··· + 1.93265 × 10
20
b − 3.76256 × 10
21
,
1.42730 × 10
21
u
26
− 6.73395 × 10
21
u
25
+ ··· + 1.93265 × 10
20
a + 2.32727 × 10
20
, u
27
− 4u
26
+ ··· − 6u + 1i
* 2 irreducible components of dim
C
= 0, with total 110 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−1.09 × 10
500
u
82
− 2.94 × 10
500
u
81
+ · · · + 5.30 × 10
505
b − 6.35 ×
10
505
, −3.64 × 10
506
u
82
− 1.01 × 10
507
u
81
+ · · · + 9.04 × 10
510
a − 1.97 ×
10
512
, u
83
+ 3u
82
+ · · · + 2662084u + 170479i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
9
=
0.0000403328u
82
+ 0.000111662u
81
+ ··· + 301.582u + 21.7586
2.05587 × 10
−6
u
82
+ 5.55358 × 10
−6
u
81
+ ··· + 16.7884u + 1.19821
a
7
=
7.99165 × 10
−6
u
82
+ 0.0000218152u
81
+ ··· + 83.4879u + 11.2783
3.56446 × 10
−6
u
82
+ 8.91911 × 10
−6
u
81
+ ··· + 12.5852u + 1.13575
a
10
=
0.0000382770u
82
+ 0.000106108u
81
+ ··· + 284.794u + 20.5604
2.05587 × 10
−6
u
82
+ 5.55358 × 10
−6
u
81
+ ··· + 16.7884u + 1.19821
a
11
=
0.0000270188u
82
+ 0.0000765238u
81
+ ··· + 263.798u + 21.3036
3.76716 × 10
−6
u
82
+ 9.89186 × 10
−6
u
81
+ ··· + 26.9027u + 2.10980
a
12
=
0.0000270188u
82
+ 0.0000765238u
81
+ ··· + 263.798u + 21.3036
4.37821 × 10
−6
u
82
+ 0.0000117106u
81
+ ··· + 34.3627u + 2.88251
a
2
=
−u
u
a
4
=
−8.47736 × 10
−6
u
82
− 0.0000243217u
81
+ ··· − 110.183u − 10.6747
−2.67993 × 10
−6
u
82
− 6.44923 × 10
−6
u
81
+ ··· − 7.29709u − 0.675289
a
1
=
9.13713 × 10
−6
u
82
+ 0.0000248460u
81
+ ··· + 28.5787u + 2.02038
8.20590 × 10
−6
u
82
+ 0.0000216780u
81
+ ··· + 38.0155u + 2.21423
a
8
=
0.0000343092u
82
+ 0.0000920768u
81
+ ··· + 221.021u + 17.7205
−1.53610 × 10
−6
u
82
− 5.91305 × 10
−6
u
81
+ ··· − 34.4259u − 2.76913
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0000735631u
82
− 0.000207254u
81
+ ··· − 607.762u − 56.2513
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
83
− 3u
82
+ ··· + 348287054u + 1799981
c
2
, c
5
u
83
+ 3u
82
+ ··· + 2662084u + 170479
c
3
, c
11
u
83
+ 2u
82
+ ··· + 6280u + 317
c
4
, c
9
u
83
+ u
82
+ ··· + 355u
2
+ 19
c
6
u
83
− 10u
82
+ ··· − 5710543466u + 554133157
c
7
, c
12
u
83
− u
82
+ ··· − 94u + 421
c
8
u
83
− 2u
82
+ ··· + 2794u + 4489
c
10
u
83
+ u
82
+ ··· − 9u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
83
− 67y
82
+ ··· + 126569059795229812y −3239931600361
c
2
, c
5
y
83
+ 73y
82
+ ··· + 763249377340y −29063089441
c
3
, c
11
y
83
− 52y
82
+ ··· + 9384264y −100489
c
4
, c
9
y
83
+ 25y
82
+ ··· − 13490y −361
c
6
y
83
− 104y
82
+ ··· + 9.99 × 10
18
y −3.07 × 10
17
c
7
, c
12
y
83
+ 51y
82
+ ··· − 4179272y −177241
c
8
y
83
− 14y
82
+ ··· + 313731786y −20151121
c
10
y
83
+ 7y
82
+ ··· + 19y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.460170 + 0.898995I
a = −0.168620 + 0.726275I
b = −0.221048 + 0.705863I
4.26133 − 0.63411I 0
u = 0.460170 − 0.898995I
a = −0.168620 − 0.726275I
b = −0.221048 − 0.705863I
4.26133 + 0.63411I 0
u = −0.941883 + 0.232685I
a = 0.197853 − 0.761878I
b = −0.06542 + 1.55250I
9.22626 − 0.03282I 0
u = −0.941883 − 0.232685I
a = 0.197853 + 0.761878I
b = −0.06542 − 1.55250I
9.22626 + 0.03282I 0
u = 0.151233 + 1.055790I
a = −1.63266 − 0.24668I
b = −0.669200 + 0.693855I
−3.59693 − 0.25964I 0
u = 0.151233 − 1.055790I
a = −1.63266 + 0.24668I
b = −0.669200 − 0.693855I
−3.59693 + 0.25964I 0
u = 0.104503 + 0.894745I
a = −1.48586 + 0.41944I
b = 0.130955 + 0.330576I
−1.93363 + 2.55099I −6.08801 − 4.34231I
u = 0.104503 − 0.894745I
a = −1.48586 − 0.41944I
b = 0.130955 − 0.330576I
−1.93363 − 2.55099I −6.08801 + 4.34231I
u = −0.320146 + 0.834261I
a = 0.32192 − 1.66448I
b = −0.061384 − 0.907535I
2.46760 + 6.12253I −5.10820 − 3.57469I
u = −0.320146 − 0.834261I
a = 0.32192 + 1.66448I
b = −0.061384 + 0.907535I
2.46760 − 6.12253I −5.10820 + 3.57469I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.079120 + 0.323083I
a = −0.102641 − 1.048010I
b = −0.002580 + 0.402975I
4.68534 − 3.54286I 0
u = −1.079120 − 0.323083I
a = −0.102641 + 1.048010I
b = −0.002580 − 0.402975I
4.68534 + 3.54286I 0
u = 0.766720 + 0.305993I
a = −0.152016 + 0.363218I
b = −0.072957 + 1.226830I
7.80934 + 4.18853I 5.53622 − 8.64057I
u = 0.766720 − 0.305993I
a = −0.152016 − 0.363218I
b = −0.072957 − 1.226830I
7.80934 − 4.18853I 5.53622 + 8.64057I
u = 0.361275 + 0.737742I
a = 0.647299 + 0.280234I
b = −0.15977 − 1.58744I
2.95977 − 5.59698I −7.31611 + 4.13920I
u = 0.361275 − 0.737742I
a = 0.647299 − 0.280234I
b = −0.15977 + 1.58744I
2.95977 + 5.59698I −7.31611 − 4.13920I
u = 0.800505 + 0.047194I
a = 0.0794772 − 0.0099353I
b = 0.191222 − 0.999614I
2.00895 + 1.88550I −2.97510 − 3.95787I
u = 0.800505 − 0.047194I
a = 0.0794772 + 0.0099353I
b = 0.191222 + 0.999614I
2.00895 − 1.88550I −2.97510 + 3.95787I
u = 0.153357 + 1.222420I
a = 1.209470 − 0.126486I
b = 0.692358 − 0.502979I
−1.37477 + 2.01127I 0
u = 0.153357 − 1.222420I
a = 1.209470 + 0.126486I
b = 0.692358 + 0.502979I
−1.37477 − 2.01127I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.767881 + 0.006018I
a = 0.684140 − 0.442889I
b = −0.932129 − 0.022458I
−3.25081 − 0.95000I −7.88321 + 7.61599I
u = −0.767881 − 0.006018I
a = 0.684140 + 0.442889I
b = −0.932129 + 0.022458I
−3.25081 + 0.95000I −7.88321 − 7.61599I
u = 0.549190 + 1.115550I
a = 1.300670 − 0.214187I
b = 0.588894 − 0.776860I
−0.96511 + 2.32927I 0
u = 0.549190 − 1.115550I
a = 1.300670 + 0.214187I
b = 0.588894 + 0.776860I
−0.96511 − 2.32927I 0
u = −0.685812 + 0.256869I
a = −0.389456 + 0.622000I
b = 0.786038 − 0.201636I
−2.43520 + 2.07800I −9.07465 − 2.81903I
u = −0.685812 − 0.256869I
a = −0.389456 − 0.622000I
b = 0.786038 + 0.201636I
−2.43520 − 2.07800I −9.07465 + 2.81903I
u = 0.240184 + 1.253840I
a = −1.32154 + 0.54080I
b = −0.669629 + 1.120710I
−2.11921 + 5.33902I 0
u = 0.240184 − 1.253840I
a = −1.32154 − 0.54080I
b = −0.669629 − 1.120710I
−2.11921 − 5.33902I 0
u = −0.452391 + 1.200180I
a = −1.327090 + 0.475985I
b = −1.124410 − 0.597252I
−6.01531 − 1.51859I 0
u = −0.452391 − 1.200180I
a = −1.327090 − 0.475985I
b = −1.124410 + 0.597252I
−6.01531 + 1.51859I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.559073 + 0.326140I
a = −0.091237 − 0.446252I
b = 0.338905 + 1.330250I
1.39029 − 2.51273I −5.26385 − 4.80671I
u = 0.559073 − 0.326140I
a = −0.091237 + 0.446252I
b = 0.338905 − 1.330250I
1.39029 + 2.51273I −5.26385 + 4.80671I
u = 1.262080 + 0.619347I
a = −0.080706 + 0.577363I
b = −0.267607 − 1.101350I
2.47880 + 4.31907I 0
u = 1.262080 − 0.619347I
a = −0.080706 − 0.577363I
b = −0.267607 + 1.101350I
2.47880 − 4.31907I 0
u = −0.303827 + 1.372880I
a = 1.302350 − 0.009523I
b = 1.34178 + 1.06457I
−7.37820 − 4.65827I 0
u = −0.303827 − 1.372880I
a = 1.302350 + 0.009523I
b = 1.34178 − 1.06457I
−7.37820 + 4.65827I 0
u = 0.50902 + 1.34890I
a = −0.938167 − 0.437644I
b = −0.744424 + 1.131700I
−3.23576 + 0.65655I 0
u = 0.50902 − 1.34890I
a = −0.938167 + 0.437644I
b = −0.744424 − 1.131700I
−3.23576 − 0.65655I 0
u = 0.316164 + 0.450393I
a = −2.61551 + 2.38499I
b = −0.515805 + 0.697975I
1.42765 + 8.76014I −8.9252 − 11.6486I
u = 0.316164 − 0.450393I
a = −2.61551 − 2.38499I
b = −0.515805 − 0.697975I
1.42765 − 8.76014I −8.9252 + 11.6486I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.526776 + 0.130625I
a = 1.64907 + 1.42838I
b = −0.063525 + 0.410583I
−1.212250 + 0.458419I −8.45009 + 2.61399I
u = −0.526776 − 0.130625I
a = 1.64907 − 1.42838I
b = −0.063525 − 0.410583I
−1.212250 − 0.458419I −8.45009 − 2.61399I
u = −0.04934 + 1.49667I
a = −0.934626 − 0.361125I
b = −0.95732 − 1.26988I
−4.02002 − 6.07736I 0
u = −0.04934 − 1.49667I
a = −0.934626 + 0.361125I
b = −0.95732 + 1.26988I
−4.02002 + 6.07736I 0
u = 1.42390 + 0.51355I
a = 1.40096 + 0.28358I
b = 0.410299 − 0.847136I
−1.12191 + 2.28952I 0
u = 1.42390 − 0.51355I
a = 1.40096 − 0.28358I
b = 0.410299 + 0.847136I
−1.12191 − 2.28952I 0
u = 0.23379 + 1.55264I
a = 0.938585 + 0.174861I
b = 1.11049 − 0.94048I
−2.12242 − 2.67601I 0
u = 0.23379 − 1.55264I
a = 0.938585 − 0.174861I
b = 1.11049 + 0.94048I
−2.12242 + 2.67601I 0
u = 0.24509 + 1.55456I
a = 1.245430 − 0.100646I
b = 0.481804 − 0.886418I
−0.87721 + 2.01433I 0
u = 0.24509 − 1.55456I
a = 1.245430 + 0.100646I
b = 0.481804 + 0.886418I
−0.87721 − 2.01433I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.51376 + 1.57596I
a = 0.945701 − 0.164051I
b = 1.09511 + 1.11076I
−8.17262 − 4.55804I 0
u = −0.51376 − 1.57596I
a = 0.945701 + 0.164051I
b = 1.09511 − 1.11076I
−8.17262 + 4.55804I 0
u = −0.279421 + 0.154723I
a = −1.57511 − 2.32845I
b = 0.391533 − 1.077430I
0.89383 + 5.51966I −4.81577 − 6.93480I
u = −0.279421 − 0.154723I
a = −1.57511 + 2.32845I
b = 0.391533 + 1.077430I
0.89383 − 5.51966I −4.81577 + 6.93480I
u = −0.77897 + 1.52417I
a = −0.834559 + 0.320224I
b = −0.83894 − 1.21576I
−5.57447 − 8.53577I 0
u = −0.77897 − 1.52417I
a = −0.834559 − 0.320224I
b = −0.83894 + 1.21576I
−5.57447 + 8.53577I 0
u = 1.71458 + 0.23735I
a = 0.024016 + 0.194910I
b = −0.322108 − 0.323947I
4.44720 − 1.98419I 0
u = 1.71458 − 0.23735I
a = 0.024016 − 0.194910I
b = −0.322108 + 0.323947I
4.44720 + 1.98419I 0
u = 0.29319 + 1.73778I
a = −0.832574 + 0.208844I
b = −0.842256 + 0.841665I
−4.08145 + 5.34949I 0
u = 0.29319 − 1.73778I
a = −0.832574 − 0.208844I
b = −0.842256 − 0.841665I
−4.08145 − 5.34949I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.13010 + 1.76314I
a = 0.915724 + 0.008694I
b = 1.25100 + 0.73854I
−7.22965 + 9.66297I 0
u = 0.13010 − 1.76314I
a = 0.915724 − 0.008694I
b = 1.25100 − 0.73854I
−7.22965 − 9.66297I 0
u = −0.142785 + 0.170899I
a = −3.16147 − 4.45029I
b = −0.578288 − 0.452235I
3.08537 − 3.61369I −6.55201 + 5.17838I
u = −0.142785 − 0.170899I
a = −3.16147 + 4.45029I
b = −0.578288 + 0.452235I
3.08537 + 3.61369I −6.55201 − 5.17838I
u = −0.213112
a = 2.54188
b = 0.384068
−0.791810 −12.6720
u = 0.08659 + 1.81227I
a = −0.887978 + 0.026815I
b = −1.057560 − 0.878142I
−10.06270 + 3.27636I 0
u = 0.08659 − 1.81227I
a = −0.887978 − 0.026815I
b = −1.057560 + 0.878142I
−10.06270 − 3.27636I 0
u = −0.19032 + 1.80895I
a = 0.786350 + 0.062928I
b = 1.16484 + 0.96951I
−8.59582 − 3.52880I 0
u = −0.19032 − 1.80895I
a = 0.786350 − 0.062928I
b = 1.16484 − 0.96951I
−8.59582 + 3.52880I 0
u = −1.83255 + 0.07076I
a = −0.200666 + 0.252048I
b = −0.658066 − 0.537500I
0.28249 − 8.18613I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.83255 − 0.07076I
a = −0.200666 − 0.252048I
b = −0.658066 + 0.537500I
0.28249 + 8.18613I 0
u = 0.51163 + 1.76987I
a = 0.879156 − 0.064606I
b = 0.97483 − 1.06910I
−1.63743 + 10.21140I 0
u = 0.51163 − 1.76987I
a = 0.879156 + 0.064606I
b = 0.97483 + 1.06910I
−1.63743 − 10.21140I 0
u = −1.77339 + 0.64608I
a = 0.517134 − 0.144678I
b = 0.519924 + 0.414154I
−2.58248 − 0.86247I 0
u = −1.77339 − 0.64608I
a = 0.517134 + 0.144678I
b = 0.519924 − 0.414154I
−2.58248 + 0.86247I 0
u = 0.03322 + 1.92914I
a = −0.648747 − 0.094426I
b = −1.046470 − 0.645501I
−7.35769 + 1.59908I 0
u = 0.03322 − 1.92914I
a = −0.648747 + 0.094426I
b = −1.046470 + 0.645501I
−7.35769 − 1.59908I 0
u = −0.73084 + 1.79088I
a = 0.969017 − 0.067168I
b = 0.91767 + 1.21902I
−5.6307 − 17.3815I 0
u = −0.73084 − 1.79088I
a = 0.969017 + 0.067168I
b = 0.91767 − 1.21902I
−5.6307 + 17.3815I 0
u = −0.75604 + 1.88383I
a = −0.930165 + 0.071600I
b = −0.922238 − 1.068110I
−9.40953 − 10.47900I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.75604 − 1.88383I
a = −0.930165 − 0.071600I
b = −0.922238 + 1.068110I
−9.40953 + 10.47900I 0
u = −0.17374 + 2.29146I
a = 0.880997 − 0.058898I
b = 0.713431 + 0.936889I
−2.47728 − 2.75627I 0
u = −0.17374 − 2.29146I
a = 0.880997 + 0.058898I
b = 0.713431 − 0.936889I
−2.47728 + 2.75627I 0
13
II.
I
u
2
= h−4.04×10
21
u
26
+1.97×10
22
u
25
+· · ·+1.93×10
20
b−3.76×10
21
, 1.43×
10
21
u
26
−6.73×10
21
u
25
+· · ·+1.93×10
20
a+2.33×10
20
, u
27
−4u
26
+· · ·−6u+1i
(i) Arc colorings
a
3
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
9
=
−7.38521u
26
+ 34.8432u
25
+ ··· + 30.8641u − 1.20419
20.9243u
26
− 101.991u
25
+ ··· − 147.137u + 19.4685
a
7
=
−10.6002u
26
+ 51.6860u
25
+ ··· + 80.1888u − 6.20606
20.9788u
26
− 102.527u
25
+ ··· − 159.836u + 20.2238
a
10
=
−28.3095u
26
+ 136.834u
25
+ ··· + 178.001u − 20.6726
20.9243u
26
− 101.991u
25
+ ··· − 147.137u + 19.4685
a
11
=
−5.40776u
26
+ 26.0671u
25
+ ··· + 41.8757u − 0.657312
−15.4098u
26
+ 76.2735u
25
+ ··· + 115.483u − 18.5009
a
12
=
−5.40776u
26
+ 26.0671u
25
+ ··· + 41.8757u − 0.657312
−18.7489u
26
+ 92.5673u
25
+ ··· + 147.508u − 22.9370
a
2
=
−u
u
a
4
=
58.0982u
26
− 284.534u
25
+ ··· − 452.283u + 58.5015
−37.6519u
26
+ 184.309u
25
+ ··· + 290.925u − 38.6642
a
1
=
−0.594465u
26
+ 3.26250u
25
+ ··· + 17.0575u − 0.276555
−9.02856u
26
+ 44.5812u
25
+ ··· + 69.3910u − 10.7702
a
8
=
8.01099u
26
− 39.0436u
25
+ ··· − 63.6642u + 15.2616
11.1766u
26
− 54.5617u
25
+ ··· − 86.0744u + 9.40541
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
33323838254448526961075
193264588372002970811
u
26
+
164472182050612511766757
193264588372002970811
u
25
+ ··· +
270764044802687883745440
193264588372002970811
u −
41347340969186927752163
193264588372002970811
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
27
− 12u
26
+ ··· − 8u − 229
c
2
u
27
+ 4u
26
+ ··· − 6u − 1
c
3
u
27
− 5u
26
+ ··· − 6u + 1
c
4
u
27
+ 2u
26
+ ··· − 13u
2
− 1
c
5
u
27
− 4u
26
+ ··· − 6u + 1
c
6
u
27
− u
26
+ ··· + 336u − 173
c
7
u
27
− 2u
26
+ ··· + 2u + 1
c
8
u
27
− u
26
+ ··· − 2u − 1
c
9
u
27
− 2u
26
+ ··· + 13u
2
+ 1
c
10
u
27
+ 5u
25
+ ··· + 7u + 1
c
11
u
27
+ 5u
26
+ ··· − 6u − 1
c
12
u
27
+ 2u
26
+ ··· + 2u − 1
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 20y
26
+ ··· + 1415284y −52441
c
2
, c
5
y
27
+ 16y
24
+ ··· + 28y −1
c
3
, c
11
y
27
− 9y
26
+ ··· + 20y −1
c
4
, c
9
y
27
+ 20y
26
+ ··· − 26y −1
c
6
y
27
+ 31y
26
+ ··· + 67570y −29929
c
7
, c
12
y
27
+ 22y
26
+ ··· − 40y
2
− 1
c
8
y
27
+ 9y
26
+ ··· + 6y −1
c
10
y
27
+ 10y
26
+ ··· + 39y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.011508 + 0.960762I
a = −1.59813 + 0.58298I
b = −0.158063 + 0.354673I
−3.28117 + 2.00579I −13.62403 − 3.47473I
u = 0.011508 − 0.960762I
a = −1.59813 − 0.58298I
b = −0.158063 − 0.354673I
−3.28117 − 2.00579I −13.62403 + 3.47473I
u = −1.026840 + 0.248737I
a = −1.107710 − 0.660114I
b = 0.170360 − 0.749462I
2.07996 + 7.57439I −4.21001 − 7.63313I
u = −1.026840 − 0.248737I
a = −1.107710 + 0.660114I
b = 0.170360 + 0.749462I
2.07996 − 7.57439I −4.21001 + 7.63313I
u = −0.910768 + 0.010715I
a = −0.212195 + 0.911198I
b = 0.08610 − 1.55715I
9.18890 − 0.57633I −5.5467 + 13.1274I
u = −0.910768 − 0.010715I
a = −0.212195 − 0.911198I
b = 0.08610 + 1.55715I
9.18890 + 0.57633I −5.5467 − 13.1274I
u = −0.901824
a = −0.122321
b = 0.805064
−3.43153 −12.0740
u = 1.097310 + 0.319632I
a = −0.165655 + 1.075010I
b = −0.017250 − 0.689297I
5.14703 + 3.51083I 3.22862 − 1.62442I
u = 1.097310 − 0.319632I
a = −0.165655 − 1.075010I
b = −0.017250 + 0.689297I
5.14703 − 3.51083I 3.22862 + 1.62442I
u = 0.403986 + 1.079340I
a = −1.27045 − 0.63545I
b = −0.766066 + 0.866289I
−2.36848 − 0.53520I −6.99550 + 1.26697I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.403986 − 1.079340I
a = −1.27045 + 0.63545I
b = −0.766066 − 0.866289I
−2.36848 + 0.53520I −6.99550 − 1.26697I
u = −0.200525 + 1.237720I
a = 1.389760 − 0.042816I
b = 0.471583 − 1.001310I
−0.73876 + 1.53239I −13.14639 + 3.16974I
u = −0.200525 − 1.237720I
a = 1.389760 + 0.042816I
b = 0.471583 + 1.001310I
−0.73876 − 1.53239I −13.14639 − 3.16974I
u = 0.087914 + 1.261540I
a = −1.093090 + 0.703743I
b = −0.713641 + 1.066830I
−1.56049 + 6.01678I −6.76815 − 9.06378I
u = 0.087914 − 1.261540I
a = −1.093090 − 0.703743I
b = −0.713641 − 1.066830I
−1.56049 − 6.01678I −6.76815 + 9.06378I
u = 0.687795 + 0.149655I
a = −1.42021 − 0.58787I
b = 0.046892 + 1.311860I
4.43619 + 6.56592I −2.27593 − 6.29860I
u = 0.687795 − 0.149655I
a = −1.42021 + 0.58787I
b = 0.046892 − 1.311860I
4.43619 − 6.56592I −2.27593 + 6.29860I
u = −0.618893 + 0.275049I
a = −0.079398 − 0.928011I
b = −0.080572 − 1.247090I
7.44583 − 3.94798I −10.42204 − 1.37695I
u = −0.618893 − 0.275049I
a = −0.079398 + 0.928011I
b = −0.080572 + 1.247090I
7.44583 + 3.94798I −10.42204 + 1.37695I
u = −0.33613 + 1.40789I
a = −1.189530 + 0.025816I
b = −1.31239 − 1.09984I
−7.06890 − 4.61624I 1.56312 + 2.77810I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.33613 − 1.40789I
a = −1.189530 − 0.025816I
b = −1.31239 + 1.09984I
−7.06890 + 4.61624I 1.56312 − 2.77810I
u = 1.55547 + 0.37415I
a = −0.203973 + 0.071367I
b = 0.211811 + 0.536233I
4.79550 − 2.02115I 0
u = 1.55547 − 0.37415I
a = −0.203973 − 0.071367I
b = 0.211811 − 0.536233I
4.79550 + 2.02115I 0
u = 0.228176 + 0.104580I
a = 0.20393 − 2.73007I
b = 0.192012 + 1.320610I
1.24796 − 3.09784I −8.17629 + 7.75380I
u = 0.228176 − 0.104580I
a = 0.20393 + 2.73007I
b = 0.192012 − 1.320610I
1.24796 + 3.09784I −8.17629 − 7.75380I
u = 1.47191 + 1.30625I
a = 1.307810 + 0.070078I
b = 0.466693 − 0.859632I
−1.15846 + 2.18965I 0
u = 1.47191 − 1.30625I
a = 1.307810 − 0.070078I
b = 0.466693 + 0.859632I
−1.15846 − 2.18965I 0
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
27
− 12u
26
+ ··· − 8u − 229)
· (u
83
− 3u
82
+ ··· + 348287054u + 1799981)
c
2
(u
27
+ 4u
26
+ ··· − 6u − 1)(u
83
+ 3u
82
+ ··· + 2662084u + 170479)
c
3
(u
27
− 5u
26
+ ··· − 6u + 1)(u
83
+ 2u
82
+ ··· + 6280u + 317)
c
4
(u
27
+ 2u
26
+ ··· − 13u
2
− 1)(u
83
+ u
82
+ ··· + 355u
2
+ 19)
c
5
(u
27
− 4u
26
+ ··· − 6u + 1)(u
83
+ 3u
82
+ ··· + 2662084u + 170479)
c
6
(u
27
− u
26
+ ··· + 336u − 173)
· (u
83
− 10u
82
+ ··· − 5710543466u + 554133157)
c
7
(u
27
− 2u
26
+ ··· + 2u + 1)(u
83
− u
82
+ ··· − 94u + 421)
c
8
(u
27
− u
26
+ ··· − 2u − 1)(u
83
− 2u
82
+ ··· + 2794u + 4489)
c
9
(u
27
− 2u
26
+ ··· + 13u
2
+ 1)(u
83
+ u
82
+ ··· + 355u
2
+ 19)
c
10
(u
27
+ 5u
25
+ ··· + 7u + 1)(u
83
+ u
82
+ ··· − 9u + 1)
c
11
(u
27
+ 5u
26
+ ··· − 6u − 1)(u
83
+ 2u
82
+ ··· + 6280u + 317)
c
12
(u
27
+ 2u
26
+ ··· + 2u − 1)(u
83
− u
82
+ ··· − 94u + 421)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
27
− 20y
26
+ ··· + 1415284y −52441)
· (y
83
− 67y
82
+ ··· + 126569059795229812y −3239931600361)
c
2
, c
5
(y
27
+ 16y
24
+ ··· + 28y −1)
· (y
83
+ 73y
82
+ ··· + 763249377340y −29063089441)
c
3
, c
11
(y
27
− 9y
26
+ ··· + 20y −1)(y
83
− 52y
82
+ ··· + 9384264y −100489)
c
4
, c
9
(y
27
+ 20y
26
+ ··· − 26y −1)(y
83
+ 25y
82
+ ··· − 13490y −361)
c
6
(y
27
+ 31y
26
+ ··· + 67570y −29929)
· (y
83
− 104y
82
+ ··· + 9.99 × 10
18
y −3.07 × 10
17
)
c
7
, c
12
(y
27
+ 22y
26
+ ··· − 40y
2
− 1)
· (y
83
+ 51y
82
+ ··· − 4179272y −177241)
c
8
(y
27
+ 9y
26
+ ··· + 6y −1)
· (y
83
− 14y
82
+ ··· + 313731786y −20151121)
c
10
(y
27
+ 10y
26
+ ··· + 39y −1)(y
83
+ 7y
82
+ ··· + 19y −1)
23
