12n
0800
(K12n
0800
)
A knot diagram
1
Linearized knot diagam
4 6 10 11 8 3 1 5 1 2 9 8
Solving Sequence
1,4 2,11
5 10 3 9 12 8 6 7
c
1
c
4
c
10
c
3
c
9
c
11
c
8
c
5
c
6
c
2
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.92227 × 10
321
u
86
− 3.69003 × 10
322
u
85
+ ··· + 2.21292 × 10
323
b − 4.49196 × 10
322
,
− 5.95683 × 10
322
u
86
− 2.93141 × 10
323
u
85
+ ··· + 2.21292 × 10
323
a − 2.78972 × 10
323
,
u
87
+ 5u
86
+ ··· + 4u + 4i
I
u
2
= h−3.25868 × 10
30
u
29
+ 3.07384 × 10
31
u
28
+ ··· + 2.27509 × 10
31
b + 1.25975 × 10
31
,
9.91315 × 10
31
u
29
− 7.89725 × 10
32
u
28
+ ··· + 2.27509 × 10
31
a + 6.40206 × 10
32
, u
30
− 8u
29
+ ··· + 5u + 1i
* 2 irreducible components of dim
C
= 0, with total 117 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−7.92 × 10
321
u
86
− 3.69 × 10
322
u
85
+ · · · + 2.21 × 10
323
b − 4.49 ×
10
322
, −5.96 × 10
322
u
86
− 2.93 × 10
323
u
85
+ · · · + 2.21 × 10
323
a − 2.79 ×
10
323
, u
87
+ 5u
86
+ · · · + 4u + 4i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
11
=
0.269184u
86
+ 1.32468u
85
+ ··· − 19.4374u + 1.26065
0.0358000u
86
+ 0.166749u
85
+ ··· − 8.38995u + 0.202988
a
5
=
−0.680199u
86
− 3.41770u
85
+ ··· − 15.4169u − 3.56450
0.111567u
86
+ 0.524563u
85
+ ··· − 0.0651331u − 1.20855
a
10
=
0.222580u
86
+ 1.11462u
85
+ ··· − 12.0392u + 1.14263
0.0130509u
86
+ 0.0574080u
85
+ ··· − 8.29540u + 0.111121
a
3
=
−0.825564u
86
− 4.14608u
85
+ ··· − 9.76061u − 1.75430
0.0999887u
86
+ 0.508035u
85
+ ··· + 2.57177u − 0.461771
a
9
=
0.235631u
86
+ 1.17203u
85
+ ··· − 20.3346u + 1.25375
0.0130509u
86
+ 0.0574080u
85
+ ··· − 8.29540u + 0.111121
a
12
=
0.395173u
86
+ 1.73507u
85
+ ··· − 7.11517u + 0.677846
−0.0892168u
86
− 0.463239u
85
+ ··· − 8.03508u − 0.827379
a
8
=
0.323432u
86
+ 1.78313u
85
+ ··· − 27.4861u − 4.51913
0.0981978u
86
+ 0.425811u
85
+ ··· − 5.99692u + 0.687737
a
6
=
−0.356479u
86
− 2.16611u
85
+ ··· + 3.37461u + 3.34404
−0.187301u
86
− 0.872331u
85
+ ··· + 0.697416u − 2.13808
a
7
=
−0.225234u
86
− 1.35732u
85
+ ··· + 21.4892u + 5.20687
−0.0981978u
86
− 0.425811u
85
+ ··· + 5.99692u − 0.687737
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.150725u
86
+ 0.590384u
85
+ ··· − 62.7762u + 6.33261
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
87
− 5u
86
+ ··· + 4u − 4
c
2
, c
6
u
87
+ u
86
+ ··· − 352u − 43
c
3
u
87
− 10u
85
+ ··· − 133313u − 18803
c
4
u
87
− 2u
86
+ ··· + 6903u − 691
c
5
, c
8
u
87
+ 4u
86
+ ··· − 156u − 29
c
7
, c
12
u
87
− 40u
85
+ ··· + 41988135u − 3861113
c
9
u
87
− 3u
86
+ ··· − 1157278u − 318509
c
10
u
87
− 7u
86
+ ··· + 884u + 71
c
11
u
87
− 2u
86
+ ··· + 141578544u + 6358336
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
87
− 21y
86
+ ··· + 632y −16
c
2
, c
6
y
87
− 63y
86
+ ··· + 52954y −1849
c
3
y
87
− 20y
86
+ ··· + 6084674411y −353552809
c
4
y
87
− 36y
86
+ ··· + 6991587y −477481
c
5
, c
8
y
87
+ 24y
86
+ ··· − 20150y −841
c
7
, c
12
y
87
− 80y
86
+ ··· − 64642179821373y −14908193598769
c
9
y
87
+ 49y
86
+ ··· − 124754575690068y −101447983081
c
10
y
87
− y
86
+ ··· + 1220520y −5041
c
11
y
87
+ 42y
86
+ ··· + 15642609176560384y −40428436688896
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.912192 + 0.401975I
a = 1.71620 + 0.38603I
b = 1.218770 + 0.339427I
2.78525 − 8.03445I 0
u = 0.912192 − 0.401975I
a = 1.71620 − 0.38603I
b = 1.218770 − 0.339427I
2.78525 + 8.03445I 0
u = 0.063304 + 1.009710I
a = −0.384643 − 1.145980I
b = −0.348157 − 0.850557I
5.78686 + 4.25193I 0
u = 0.063304 − 1.009710I
a = −0.384643 + 1.145980I
b = −0.348157 + 0.850557I
5.78686 − 4.25193I 0
u = 0.453234 + 0.912797I
a = −0.028386 − 1.020130I
b = 0.41597 − 1.37970I
5.44822 − 2.84020I 0
u = 0.453234 − 0.912797I
a = −0.028386 + 1.020130I
b = 0.41597 + 1.37970I
5.44822 + 2.84020I 0
u = −0.694539 + 0.782085I
a = −0.64714 + 1.25869I
b = 0.410123 − 0.062150I
9.43262 + 3.01438I 0
u = −0.694539 − 0.782085I
a = −0.64714 − 1.25869I
b = 0.410123 + 0.062150I
9.43262 − 3.01438I 0
u = −0.416393 + 0.963809I
a = 0.339992 + 0.197096I
b = 0.467908 + 0.587539I
3.48674 + 2.87950I 0
u = −0.416393 − 0.963809I
a = 0.339992 − 0.197096I
b = 0.467908 − 0.587539I
3.48674 − 2.87950I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.785521 + 0.699014I
a = 0.993051 + 0.291711I
b = 1.49665 + 0.40739I
−3.25758 + 8.20249I 0
u = −0.785521 − 0.699014I
a = 0.993051 − 0.291711I
b = 1.49665 − 0.40739I
−3.25758 − 8.20249I 0
u = 0.816587 + 0.473890I
a = 1.81569 + 0.51492I
b = 0.719364 + 0.598319I
3.76903 − 1.56318I 4.00000 + 3.26305I
u = 0.816587 − 0.473890I
a = 1.81569 − 0.51492I
b = 0.719364 − 0.598319I
3.76903 + 1.56318I 4.00000 − 3.26305I
u = 0.147112 + 1.065990I
a = −0.401964 + 0.609701I
b = 0.111488 + 0.446761I
2.45312 − 4.65946I 0
u = 0.147112 − 1.065990I
a = −0.401964 − 0.609701I
b = 0.111488 − 0.446761I
2.45312 + 4.65946I 0
u = 0.931256 + 0.572305I
a = 0.785536 − 0.187780I
b = 1.57831 − 0.64495I
−3.96504 − 1.92363I 0
u = 0.931256 − 0.572305I
a = 0.785536 + 0.187780I
b = 1.57831 + 0.64495I
−3.96504 + 1.92363I 0
u = 0.892042 + 0.148083I
a = −0.422634 + 0.204443I
b = −0.593358 − 1.050630I
−2.69372 − 2.16255I −0.88908 + 4.42862I
u = 0.892042 − 0.148083I
a = −0.422634 − 0.204443I
b = −0.593358 + 1.050630I
−2.69372 + 2.16255I −0.88908 − 4.42862I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.548120 + 0.988311I
a = 0.701455 − 0.520019I
b = −0.165990 − 0.329990I
2.34699 − 1.37288I 0
u = −0.548120 − 0.988311I
a = 0.701455 + 0.520019I
b = −0.165990 + 0.329990I
2.34699 + 1.37288I 0
u = −0.484874 + 1.021390I
a = 0.250420 − 0.050777I
b = 0.290233 + 0.553102I
3.50028 + 2.86892I 0
u = −0.484874 − 1.021390I
a = 0.250420 + 0.050777I
b = 0.290233 − 0.553102I
3.50028 − 2.86892I 0
u = 0.460721 + 0.683739I
a = 0.915361 + 0.110361I
b = 0.160669 − 0.135663I
0.11406 − 1.55831I 1.29774 + 4.43942I
u = 0.460721 − 0.683739I
a = 0.915361 − 0.110361I
b = 0.160669 + 0.135663I
0.11406 + 1.55831I 1.29774 − 4.43942I
u = −0.787268 + 0.887666I
a = −0.817774 + 1.041560I
b = 0.518701 + 0.366589I
9.35877 + 9.75636I 0
u = −0.787268 − 0.887666I
a = −0.817774 − 1.041560I
b = 0.518701 − 0.366589I
9.35877 − 9.75636I 0
u = −1.007710 + 0.645864I
a = −1.177580 − 0.334928I
b = −2.65128 + 0.45417I
−2.03670 + 4.04341I 0
u = −1.007710 − 0.645864I
a = −1.177580 + 0.334928I
b = −2.65128 − 0.45417I
−2.03670 − 4.04341I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.377151 + 1.147650I
a = −0.483019 − 0.604530I
b = 0.545999 + 0.569923I
4.00465 + 2.11919I 0
u = 0.377151 − 1.147650I
a = −0.483019 + 0.604530I
b = 0.545999 − 0.569923I
4.00465 − 2.11919I 0
u = −1.106240 + 0.490549I
a = −0.947435 − 0.589082I
b = −1.36762 + 0.53535I
−1.29962 + 1.65088I 0
u = −1.106240 − 0.490549I
a = −0.947435 + 0.589082I
b = −1.36762 − 0.53535I
−1.29962 − 1.65088I 0
u = −1.170960 + 0.382675I
a = 0.706683 − 0.206861I
b = 2.42929 − 1.12143I
7.91042 + 1.84125I 0
u = −1.170960 − 0.382675I
a = 0.706683 + 0.206861I
b = 2.42929 + 1.12143I
7.91042 − 1.84125I 0
u = 0.281224 + 0.709242I
a = −0.89796 + 1.43996I
b = −0.892007 − 0.507078I
−2.20998 − 5.06993I 1.66963 + 6.40826I
u = 0.281224 − 0.709242I
a = −0.89796 − 1.43996I
b = −0.892007 + 0.507078I
−2.20998 + 5.06993I 1.66963 − 6.40826I
u = −0.657198 + 0.307147I
a = 1.88727 + 0.07366I
b = 1.51953 − 0.47787I
−0.87663 + 6.37484I 6.19951 + 2.37879I
u = −0.657198 − 0.307147I
a = 1.88727 − 0.07366I
b = 1.51953 + 0.47787I
−0.87663 − 6.37484I 6.19951 − 2.37879I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.155190 + 0.687197I
a = 0.719993 − 0.282618I
b = 1.68780 − 1.60413I
8.22587 − 3.64595I 0
u = −1.155190 − 0.687197I
a = 0.719993 + 0.282618I
b = 1.68780 + 1.60413I
8.22587 + 3.64595I 0
u = 0.643999 + 0.109479I
a = 1.061680 + 0.694693I
b = −0.030351 − 0.437816I
−3.39381 − 0.96598I 0.39517 + 7.21957I
u = 0.643999 − 0.109479I
a = 1.061680 − 0.694693I
b = −0.030351 + 0.437816I
−3.39381 + 0.96598I 0.39517 − 7.21957I
u = −0.566702 + 0.198795I
a = −1.98171 − 0.36620I
b = −1.39477 + 0.43507I
−2.60998 + 1.32687I 0.720881 − 0.280633I
u = −0.566702 − 0.198795I
a = −1.98171 + 0.36620I
b = −1.39477 − 0.43507I
−2.60998 − 1.32687I 0.720881 + 0.280633I
u = 0.741085 + 1.188570I
a = −0.341339 − 0.507587I
b = 0.647963 + 0.071670I
3.72251 − 4.38135I 0
u = 0.741085 − 1.188570I
a = −0.341339 + 0.507587I
b = 0.647963 − 0.071670I
3.72251 + 4.38135I 0
u = −0.572023 + 0.086882I
a = 1.75123 − 0.18932I
b = 0.202750 + 0.708885I
−3.14226 − 4.80021I 6.02675 + 3.57707I
u = −0.572023 − 0.086882I
a = 1.75123 + 0.18932I
b = 0.202750 − 0.708885I
−3.14226 + 4.80021I 6.02675 − 3.57707I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.440749 + 0.367901I
a = 1.71358 + 0.03534I
b = 0.574482 − 0.388650I
1.47462 − 0.14531I 7.13969 + 3.49282I
u = −0.440749 − 0.367901I
a = 1.71358 − 0.03534I
b = 0.574482 + 0.388650I
1.47462 + 0.14531I 7.13969 − 3.49282I
u = −1.22331 + 0.82785I
a = −0.855548 + 0.140813I
b = −1.58797 + 1.11307I
0.27819 + 8.09027I 0
u = −1.22331 − 0.82785I
a = −0.855548 − 0.140813I
b = −1.58797 − 1.11307I
0.27819 − 8.09027I 0
u = −1.06015 + 1.03363I
a = 0.999482 + 0.206134I
b = 1.76783 − 0.88695I
6.94845 + 10.55380I 0
u = −1.06015 − 1.03363I
a = 0.999482 − 0.206134I
b = 1.76783 + 0.88695I
6.94845 − 10.55380I 0
u = 1.14479 + 1.03666I
a = 0.815763 − 0.109466I
b = 1.54275 + 1.18017I
2.52234 − 3.55910I 0
u = 1.14479 − 1.03666I
a = 0.815763 + 0.109466I
b = 1.54275 − 1.18017I
2.52234 + 3.55910I 0
u = −1.05813 + 1.12751I
a = 0.145464 + 0.730331I
b = 1.087400 − 0.008770I
7.10114 − 2.70607I 0
u = −1.05813 − 1.12751I
a = 0.145464 − 0.730331I
b = 1.087400 + 0.008770I
7.10114 + 2.70607I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32042 + 0.82197I
a = −0.533477 − 0.058376I
b = −1.75928 + 0.27907I
0.77190 + 4.16807I 0
u = −1.32042 − 0.82197I
a = −0.533477 + 0.058376I
b = −1.75928 − 0.27907I
0.77190 − 4.16807I 0
u = −0.437998
a = 1.57305
b = 0.228308
1.19704 7.87590
u = 1.24751 + 0.95031I
a = −0.736747 + 0.461163I
b = −2.02741 − 0.23872I
−6.47758 − 2.96918I 0
u = 1.24751 − 0.95031I
a = −0.736747 − 0.461163I
b = −2.02741 + 0.23872I
−6.47758 + 2.96918I 0
u = −1.18844 + 1.02512I
a = 1.004850 + 0.214529I
b = 2.19066 − 1.08284I
5.7235 + 17.6063I 0
u = −1.18844 − 1.02512I
a = 1.004850 − 0.214529I
b = 2.19066 + 1.08284I
5.7235 − 17.6063I 0
u = −1.09223 + 1.13307I
a = −0.662443 − 0.450886I
b = −2.15973 + 0.59397I
−0.10678 + 5.66380I 0
u = −1.09223 − 1.13307I
a = −0.662443 + 0.450886I
b = −2.15973 − 0.59397I
−0.10678 − 5.66380I 0
u = −0.112776 + 0.384345I
a = 5.57611 − 5.50713I
b = −1.006150 + 0.062796I
−0.0371163 − 0.0367021I −8.4334 − 13.9645I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.112776 − 0.384345I
a = 5.57611 + 5.50713I
b = −1.006150 − 0.062796I
−0.0371163 + 0.0367021I −8.4334 + 13.9645I
u = 1.35698 + 0.93075I
a = 0.814355 − 0.101972I
b = 2.29464 + 1.25421I
1.14531 − 9.78347I 0
u = 1.35698 − 0.93075I
a = 0.814355 + 0.101972I
b = 2.29464 − 1.25421I
1.14531 + 9.78347I 0
u = −0.094411 + 0.338574I
a = 0.87849 − 1.44245I
b = 2.05669 + 0.94373I
8.05058 + 0.40994I 18.7140 + 3.3872I
u = −0.094411 − 0.338574I
a = 0.87849 + 1.44245I
b = 2.05669 − 0.94373I
8.05058 − 0.40994I 18.7140 − 3.3872I
u = 0.312702 + 0.159104I
a = 2.77994 − 0.20053I
b = 2.32458 + 2.43420I
5.59090 − 6.35630I −0.1485 + 15.1289I
u = 0.312702 − 0.159104I
a = 2.77994 + 0.20053I
b = 2.32458 − 2.43420I
5.59090 + 6.35630I −0.1485 − 15.1289I
u = −0.95311 + 1.37768I
a = 0.053807 + 0.760361I
b = 1.327890 − 0.448270I
6.72564 − 9.19457I 0
u = −0.95311 − 1.37768I
a = 0.053807 − 0.760361I
b = 1.327890 + 0.448270I
6.72564 + 9.19457I 0
u = 1.18578 + 1.18641I
a = −0.730372 + 0.476175I
b = −1.79404 − 0.86269I
−5.77689 − 5.71907I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.18578 − 1.18641I
a = −0.730372 − 0.476175I
b = −1.79404 + 0.86269I
−5.77689 + 5.71907I 0
u = 0.233582 + 0.040081I
a = −6.96917 − 1.14129I
b = −0.838345 + 0.317215I
0.311077 − 0.458631I 2.75665 + 5.13065I
u = 0.233582 − 0.040081I
a = −6.96917 + 1.14129I
b = −0.838345 − 0.317215I
0.311077 + 0.458631I 2.75665 − 5.13065I
u = 1.92037 + 0.28539I
a = −0.599470 + 0.151895I
b = −3.00149 − 0.04689I
−7.66564 − 0.71189I 0
u = 1.92037 − 0.28539I
a = −0.599470 − 0.151895I
b = −3.00149 + 0.04689I
−7.66564 + 0.71189I 0
u = 2.09382 + 0.09189I
a = −0.344115 − 0.080336I
b = −2.08465 − 0.48560I
−5.77352 − 2.12518I 0
u = 2.09382 − 0.09189I
a = −0.344115 + 0.080336I
b = −2.08465 + 0.48560I
−5.77352 + 2.12518I 0
13
II.
I
u
2
= h−3.26×10
30
u
29
+3.07×10
31
u
28
+· · ·+2.28×10
31
b+1.26×10
31
, 9.91×
10
31
u
29
−7.90×10
32
u
28
+· · ·+2.28×10
31
a+6.40×10
32
, u
30
−8u
29
+· · ·+5u+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
11
=
−4.35726u
29
+ 34.7118u
28
+ ··· − 11.4934u − 28.1398
0.143233u
29
− 1.35109u
28
+ ··· + 2.21771u − 0.553715
a
5
=
32.4699u
29
− 264.608u
28
+ ··· + 107.589u + 152.261
1.04679u
29
− 8.54165u
28
+ ··· + 1.93436u + 6.39287
a
10
=
−3.45609u
29
+ 26.9760u
28
+ ··· − 8.62249u − 27.4399
0.637967u
29
− 5.66845u
28
+ ··· + 3.94896u − 0.0272306
a
3
=
29.2569u
29
− 235.969u
28
+ ··· + 90.1819u + 149.419
−1.19067u
29
+ 11.3015u
28
+ ··· − 10.4421u + 3.21100
a
9
=
−2.81812u
29
+ 21.3075u
28
+ ··· − 4.67353u − 27.4671
0.637967u
29
− 5.66845u
28
+ ··· + 3.94896u − 0.0272306
a
12
=
2.38336u
29
− 20.9011u
28
+ ··· + 12.2620u + 4.97176
1.70365u
29
− 14.7732u
28
+ ··· + 7.33375u + 2.02151
a
8
=
−5.57532u
29
+ 48.4654u
28
+ ··· − 32.7344u − 13.3998
0.313551u
29
− 2.67450u
28
+ ··· + 2.41495u + 0.394386
a
6
=
36.6261u
29
− 301.275u
28
+ ··· + 128.389u + 157.033
1.01379u
29
− 8.31609u
28
+ ··· + 2.17156u + 6.40119
a
7
=
−5.88887u
29
+ 51.1399u
28
+ ··· − 35.1493u − 13.7942
0.313551u
29
− 2.67450u
28
+ ··· + 2.41495u + 0.394386
(ii) Obstruction class = 1
(iii) Cusp Shapes = −73.4402u
29
+ 601.455u
28
+ ··· − 270.631u − 331.472
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
30
− 8u
29
+ ··· + 5u + 1
c
2
u
30
− 2u
29
+ ··· − u + 1
c
3
u
30
+ 7u
29
+ ··· − 2u + 1
c
4
u
30
+ 7u
29
+ ··· − 4u + 17
c
5
u
30
+ 7u
29
+ ··· + 11u + 1
c
6
u
30
+ 2u
29
+ ··· + u + 1
c
7
u
30
− u
29
+ ··· − 22u + 1
c
8
u
30
− 7u
29
+ ··· − 11u + 1
c
9
u
30
+ 6u
29
+ ··· + 3u + 1
c
10
u
30
+ 4u
28
+ ··· + 9u + 1
c
11
u
30
+ 5u
29
+ ··· + 702u + 324
c
12
u
30
+ u
29
+ ··· + 22u + 1
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 16y
29
+ ··· − 27y + 1
c
2
, c
6
y
30
− 14y
29
+ ··· − 13y + 1
c
3
y
30
− 27y
29
+ ··· − 10y + 1
c
4
y
30
− 51y
29
+ ··· − 5762y + 289
c
5
, c
8
y
30
+ 13y
29
+ ··· − 17y + 1
c
7
, c
12
y
30
+ y
29
+ ··· − 162y + 1
c
9
y
30
+ 10y
29
+ ··· + 221y + 1
c
10
y
30
+ 8y
29
+ ··· − 103y + 1
c
11
y
30
+ 7y
29
+ ··· + 1799172y + 104976
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.922928 + 0.587538I
a = −0.945123 − 0.371366I
b = −2.12791 − 0.57187I
−3.96611 + 7.21759I −0.87488 − 5.62385I
u = −0.922928 − 0.587538I
a = −0.945123 + 0.371366I
b = −2.12791 + 0.57187I
−3.96611 − 7.21759I −0.87488 + 5.62385I
u = 0.704491 + 0.496236I
a = 1.57500 − 0.31600I
b = 1.46524 + 0.51141I
−1.00133 − 6.83745I 2.05753 + 13.48275I
u = 0.704491 − 0.496236I
a = 1.57500 + 0.31600I
b = 1.46524 − 0.51141I
−1.00133 + 6.83745I 2.05753 − 13.48275I
u = 0.386560 + 1.109940I
a = −0.051401 − 0.462394I
b = 0.304135 − 0.577341I
2.50276 − 3.64171I 2.92014 + 2.19640I
u = 0.386560 − 1.109940I
a = −0.051401 + 0.462394I
b = 0.304135 + 0.577341I
2.50276 + 3.64171I 2.92014 − 2.19640I
u = −0.263153 + 1.160860I
a = −0.431578 − 0.621044I
b = −0.407030 − 0.132485I
2.87178 + 3.78144I 6.31019 − 4.19604I
u = −0.263153 − 1.160860I
a = −0.431578 + 0.621044I
b = −0.407030 + 0.132485I
2.87178 − 3.78144I 6.31019 + 4.19604I
u = 0.500940 + 0.629952I
a = 1.68166 − 0.06066I
b = 0.303310 + 0.498258I
1.43876 − 0.76884I 6.64471 + 4.27009I
u = 0.500940 − 0.629952I
a = 1.68166 + 0.06066I
b = 0.303310 − 0.498258I
1.43876 + 0.76884I 6.64471 − 4.27009I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.743487 + 0.011194I
a = −1.58893 + 0.46371I
b = −0.672210 − 0.441056I
−3.76793 − 4.74109I −6.96064 + 3.57575I
u = −0.743487 − 0.011194I
a = −1.58893 − 0.46371I
b = −0.672210 + 0.441056I
−3.76793 + 4.74109I −6.96064 − 3.57575I
u = 0.641333 + 0.136681I
a = −0.906364 + 1.074960I
b = −0.329411 − 0.850433I
−3.51250 + 0.24334I −1.82124 + 2.49290I
u = 0.641333 − 0.136681I
a = −0.906364 − 1.074960I
b = −0.329411 + 0.850433I
−3.51250 − 0.24334I −1.82124 − 2.49290I
u = −0.609580 + 0.204219I
a = 0.407913 + 0.650635I
b = 2.23585 + 0.71430I
7.62000 + 0.50528I 0.258078 − 0.196315I
u = −0.609580 − 0.204219I
a = 0.407913 − 0.650635I
b = 2.23585 − 0.71430I
7.62000 − 0.50528I 0.258078 + 0.196315I
u = −0.573695
a = −3.33723
b = −0.970491
−0.112514 −7.33930
u = −0.234236 + 0.490295I
a = −0.02926 + 1.74200I
b = 1.79609 + 1.69689I
5.83320 − 6.00958I 10.35590 + 0.19003I
u = −0.234236 − 0.490295I
a = −0.02926 − 1.74200I
b = 1.79609 − 1.69689I
5.83320 + 6.00958I 10.35590 − 0.19003I
u = 1.17894 + 0.89891I
a = −0.806852 + 0.440198I
b = −1.97344 − 0.14521I
−6.51184 − 2.43468I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.17894 − 0.89891I
a = −0.806852 − 0.440198I
b = −1.97344 + 0.14521I
−6.51184 + 2.43468I 0
u = −1.24538 + 0.97708I
a = −0.714351 − 0.298346I
b = −2.34521 + 0.62696I
−0.25045 + 5.04299I 0
u = −1.24538 − 0.97708I
a = −0.714351 + 0.298346I
b = −2.34521 − 0.62696I
−0.25045 − 5.04299I 0
u = 1.15151 + 1.21077I
a = −0.710752 + 0.517304I
b = −1.70800 − 0.84973I
−5.59793 − 5.98728I 0
u = 1.15151 − 1.21077I
a = −0.710752 − 0.517304I
b = −1.70800 + 0.84973I
−5.59793 + 5.98728I 0
u = −0.245930
a = −19.5202
b = −1.01937
0.0131283 −196.150
u = 1.88508 + 0.17326I
a = −0.620542 + 0.087183I
b = −3.08908 + 0.19184I
−7.58112 − 1.13122I 0
u = 1.88508 − 0.17326I
a = −0.620542 − 0.087183I
b = −3.08908 − 0.19184I
−7.58112 + 1.13122I 0
u = 1.97973 + 0.12368I
a = −0.430688 − 0.048129I
b = −1.95742 − 0.56422I
−6.12186 − 2.02764I 0
u = 1.97973 − 0.12368I
a = −0.430688 + 0.048129I
b = −1.95742 + 0.56422I
−6.12186 + 2.02764I 0
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
30
− 8u
29
+ ··· + 5u + 1)(u
87
− 5u
86
+ ··· + 4u − 4)
c
2
(u
30
− 2u
29
+ ··· − u + 1)(u
87
+ u
86
+ ··· − 352u − 43)
c
3
(u
30
+ 7u
29
+ ··· − 2u + 1)(u
87
− 10u
85
+ ··· − 133313u − 18803)
c
4
(u
30
+ 7u
29
+ ··· − 4u + 17)(u
87
− 2u
86
+ ··· + 6903u − 691)
c
5
(u
30
+ 7u
29
+ ··· + 11u + 1)(u
87
+ 4u
86
+ ··· − 156u − 29)
c
6
(u
30
+ 2u
29
+ ··· + u + 1)(u
87
+ u
86
+ ··· − 352u − 43)
c
7
(u
30
− u
29
+ ··· − 22u + 1)
· (u
87
− 40u
85
+ ··· + 41988135u − 3861113)
c
8
(u
30
− 7u
29
+ ··· − 11u + 1)(u
87
+ 4u
86
+ ··· − 156u − 29)
c
9
(u
30
+ 6u
29
+ ··· + 3u + 1)(u
87
− 3u
86
+ ··· − 1157278u − 318509)
c
10
(u
30
+ 4u
28
+ ··· + 9u + 1)(u
87
− 7u
86
+ ··· + 884u + 71)
c
11
(u
30
+ 5u
29
+ ··· + 702u + 324)
· (u
87
− 2u
86
+ ··· + 141578544u + 6358336)
c
12
(u
30
+ u
29
+ ··· + 22u + 1)
· (u
87
− 40u
85
+ ··· + 41988135u − 3861113)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
30
− 16y
29
+ ··· − 27y + 1)(y
87
− 21y
86
+ ··· + 632y −16)
c
2
, c
6
(y
30
− 14y
29
+ ··· − 13y + 1)(y
87
− 63y
86
+ ··· + 52954y −1849)
c
3
(y
30
− 27y
29
+ ··· − 10y + 1)
· (y
87
− 20y
86
+ ··· + 6084674411y −353552809)
c
4
(y
30
− 51y
29
+ ··· − 5762y + 289)
· (y
87
− 36y
86
+ ··· + 6991587y −477481)
c
5
, c
8
(y
30
+ 13y
29
+ ··· − 17y + 1)(y
87
+ 24y
86
+ ··· − 20150y −841)
c
7
, c
12
(y
30
+ y
29
+ ··· − 162y + 1)
· (y
87
− 80y
86
+ ··· − 64642179821373y −14908193598769)
c
9
(y
30
+ 10y
29
+ ··· + 221y + 1)
· (y
87
+ 49y
86
+ ··· − 124754575690068y −101447983081)
c
10
(y
30
+ 8y
29
+ ··· − 103y + 1)(y
87
− y
86
+ ··· + 1220520y −5041)
c
11
(y
30
+ 7y
29
+ ··· + 1799172y + 104976)
· (y
87
+ 42y
86
+ ··· + 15642609176560384y −40428436688896)
23
