12a
0858
(K12a
0858
)
A knot diagram
1
Linearized knot diagam
4 5 9 12 11 10 3 1 7 6 2 8
Solving Sequence
5,11 3,6
2 12 4 1 10 7 8 9
c
5
c
2
c
11
c
4
c
1
c
10
c
6
c
7
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.29209 × 10
154
u
103
− 9.15492 × 10
154
u
102
+ ··· + 1.10622 × 10
155
b − 5.83673 × 10
155
,
− 5.85136 × 10
155
u
103
− 1.74496 × 10
156
u
102
+ ··· + 1.10622 × 10
155
a − 7.67740 × 10
156
,
u
104
+ 3u
103
+ ··· + 31u + 1i
I
u
2
= h−u
21
− u
20
+ ··· + b − 3, 2u
21
+ 4u
20
+ ··· + a + 3, u
22
+ 2u
21
+ ··· + 8u + 1i
* 2 irreducible components of dim
C
= 0, with total 126 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−4.29 × 10
154
u
103
− 9.15 × 10
154
u
102
+ · · · + 1.11 × 10
155
b − 5.84 ×
10
155
, −5.85 × 10
155
u
103
− 1.74 × 10
156
u
102
+ · · · + 1.11 × 10
155
a − 7.68 ×
10
156
, u
104
+ 3u
103
+ · · · + 31u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
5.28950u
103
+ 15.7740u
102
+ ··· + 1359.16u + 69.4021
0.387996u
103
+ 0.827586u
102
+ ··· + 112.043u + 5.27628
a
6
=
1
−u
2
a
2
=
4.90151u
103
+ 14.9465u
102
+ ··· + 1247.12u + 64.1258
0.387996u
103
+ 0.827586u
102
+ ··· + 112.043u + 5.27628
a
12
=
−5.09955u
103
− 15.8273u
102
+ ··· − 1348.62u − 60.5142
−0.268969u
103
− 1.64114u
102
+ ··· − 126.625u − 4.31384
a
4
=
5.26176u
103
+ 16.1541u
102
+ ··· + 1390.45u + 70.8132
0.154109u
103
+ 0.372863u
102
+ ··· + 117.159u + 5.24451
a
1
=
4.09794u
103
+ 11.9682u
102
+ ··· + 106.242u − 9.40838
−0.0216898u
103
− 0.0878425u
102
+ ··· − 77.7280u − 4.38713
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
−1.82974u
103
− 4.02329u
102
+ ··· − 596.508u − 12.8099
0.420981u
103
+ 1.67225u
102
+ ··· + 54.8748u + 3.69402
a
9
=
−u
3
− 2u
u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.19505u
103
− 3.04834u
102
+ ··· − 478.535u − 23.6887
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
104
+ 8u
103
+ ··· + 14156u + 5744
c
2
u
104
+ 14u
102
+ ··· + 11537u + 1378
c
3
u
104
− u
103
+ ··· + 1584164u + 498521
c
4
u
104
+ 7u
102
+ ··· − 38u + 1
c
5
, c
6
, c
9
c
10
u
104
+ 3u
103
+ ··· + 31u + 1
c
7
u
104
− u
103
+ ··· − 487679u + 95891
c
8
, c
12
u
104
− u
103
+ ··· − 125u + 142
c
11
u
104
+ 10u
103
+ ··· + 18056u + 1169
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
104
− 32y
103
+ ··· − 1389779440y + 32993536
c
2
y
104
+ 28y
103
+ ··· − 10876525y + 1898884
c
3
y
104
+ 49y
103
+ ··· + 10000134915712y + 248523187441
c
4
y
104
+ 14y
103
+ ··· − 30y + 1
c
5
, c
6
, c
9
c
10
y
104
+ 131y
103
+ ··· − 163y + 1
c
7
y
104
+ 37y
103
+ ··· + 307454898715y + 9195083881
c
8
, c
12
y
104
− 61y
103
+ ··· − 477693y + 20164
c
11
y
104
+ 38y
103
+ ··· + 142466966y + 1366561
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.502898 + 0.916877I
a = 0.731786 + 1.022940I
b = −0.612116 + 0.969487I
−7.90140 − 3.33837I 0
u = −0.502898 − 0.916877I
a = 0.731786 − 1.022940I
b = −0.612116 − 0.969487I
−7.90140 + 3.33837I 0
u = −0.141268 + 0.942566I
a = −0.379999 − 0.233920I
b = −1.335470 − 0.351793I
−5.49881 + 1.95923I 0
u = −0.141268 − 0.942566I
a = −0.379999 + 0.233920I
b = −1.335470 + 0.351793I
−5.49881 − 1.95923I 0
u = −0.570868 + 0.880506I
a = −0.618818 − 0.625987I
b = 0.116597 − 1.104840I
−7.41549 − 5.38278I 0
u = −0.570868 − 0.880506I
a = −0.618818 + 0.625987I
b = 0.116597 + 1.104840I
−7.41549 + 5.38278I 0
u = 0.162376 + 1.044170I
a = 0.684256 + 0.359913I
b = 0.791948 + 0.317582I
−1.40281 + 2.16908I 0
u = 0.162376 − 1.044170I
a = 0.684256 − 0.359913I
b = 0.791948 − 0.317582I
−1.40281 − 2.16908I 0
u = 0.132711 + 1.052880I
a = 1.278520 − 0.335968I
b = 0.238919 − 0.386711I
−5.03707 − 0.16972I 0
u = 0.132711 − 1.052880I
a = 1.278520 + 0.335968I
b = 0.238919 + 0.386711I
−5.03707 + 0.16972I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328304 + 0.862251I
a = 0.165679 + 1.388680I
b = 0.874529 + 0.960461I
−1.19082 + 2.99470I 0
u = 0.328304 − 0.862251I
a = 0.165679 − 1.388680I
b = 0.874529 − 0.960461I
−1.19082 − 2.99470I 0
u = −0.276342 + 0.874409I
a = −0.07809 − 1.99438I
b = 0.92580 − 1.20926I
−2.01960 − 5.44676I 0
u = −0.276342 − 0.874409I
a = −0.07809 + 1.99438I
b = 0.92580 + 1.20926I
−2.01960 + 5.44676I 0
u = 0.538764 + 0.944968I
a = 0.404249 − 1.083240I
b = −0.929614 − 0.978308I
−2.34922 + 8.42032I 0
u = 0.538764 − 0.944968I
a = 0.404249 + 1.083240I
b = −0.929614 + 0.978308I
−2.34922 − 8.42032I 0
u = −0.532031 + 0.950553I
a = 0.364609 + 1.272250I
b = −1.00220 + 1.14405I
−5.9219 − 14.4505I 0
u = −0.532031 − 0.950553I
a = 0.364609 − 1.272250I
b = −1.00220 − 1.14405I
−5.9219 + 14.4505I 0
u = −0.691545 + 0.883155I
a = −0.626007 + 0.058674I
b = −0.303448 − 0.699022I
−5.06268 + 5.04824I 0
u = −0.691545 − 0.883155I
a = −0.626007 − 0.058674I
b = −0.303448 + 0.699022I
−5.06268 − 5.04824I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.840047 + 0.076471I
a = 0.327363 + 0.245393I
b = −0.594520 − 0.700938I
0.76666 + 3.88111I 0
u = 0.840047 − 0.076471I
a = 0.327363 − 0.245393I
b = −0.594520 + 0.700938I
0.76666 − 3.88111I 0
u = 0.048893 + 0.839271I
a = −1.16896 + 2.29985I
b = 0.394853 + 0.947867I
−6.18765 + 5.05686I 0
u = 0.048893 − 0.839271I
a = −1.16896 − 2.29985I
b = 0.394853 − 0.947867I
−6.18765 − 5.05686I 0
u = 0.054307 + 0.830716I
a = 0.212346 + 1.076540I
b = −0.601861 + 1.043040I
−2.87472 + 1.68657I 0
u = 0.054307 − 0.830716I
a = 0.212346 − 1.076540I
b = −0.601861 − 1.043040I
−2.87472 − 1.68657I 0
u = −0.811464 + 0.083411I
a = 0.275473 − 0.260082I
b = −0.747402 + 0.862488I
−2.77324 − 9.99543I 0
u = −0.811464 − 0.083411I
a = 0.275473 + 0.260082I
b = −0.747402 − 0.862488I
−2.77324 + 9.99543I 0
u = −0.103146 + 0.808046I
a = −0.38687 − 1.52545I
b = −1.11179 − 1.59842I
−5.86231 − 5.76260I 0
u = −0.103146 − 0.808046I
a = −0.38687 + 1.52545I
b = −1.11179 + 1.59842I
−5.86231 + 5.76260I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.409728 + 0.673140I
a = −0.58461 + 1.34596I
b = 0.83524 + 1.36856I
−2.13658 + 6.08917I 0
u = 0.409728 − 0.673140I
a = −0.58461 − 1.34596I
b = 0.83524 − 1.36856I
−2.13658 − 6.08917I 0
u = −0.769636 + 0.053062I
a = 0.375105 − 0.232095I
b = −0.229831 + 0.894662I
−4.92977 + 0.88276I 0
u = −0.769636 − 0.053062I
a = 0.375105 + 0.232095I
b = −0.229831 − 0.894662I
−4.92977 − 0.88276I 0
u = 0.679892 + 1.028790I
a = −0.305880 + 0.158737I
b = 0.003951 + 0.615735I
−1.87702 + 1.33803I 0
u = 0.679892 − 1.028790I
a = −0.305880 − 0.158737I
b = 0.003951 − 0.615735I
−1.87702 − 1.33803I 0
u = −0.298746 + 0.693724I
a = −0.06811 + 2.41205I
b = −0.412342 + 0.182178I
−3.49112 − 6.57213I 0
u = −0.298746 − 0.693724I
a = −0.06811 − 2.41205I
b = −0.412342 − 0.182178I
−3.49112 + 6.57213I 0
u = −0.237343 + 0.668959I
a = −0.60277 − 1.51902I
b = 1.00094 − 1.13669I
−0.73294 − 3.33904I 0
u = −0.237343 − 0.668959I
a = −0.60277 + 1.51902I
b = 1.00094 + 1.13669I
−0.73294 + 3.33904I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.489607 + 0.472391I
a = 1.186520 − 0.254661I
b = −0.543846 − 0.236945I
0.80233 + 1.78889I 4.00000 + 2.53482I
u = 0.489607 − 0.472391I
a = 1.186520 + 0.254661I
b = −0.543846 + 0.236945I
0.80233 − 1.78889I 4.00000 − 2.53482I
u = −0.056856 + 0.667069I
a = −1.026160 − 0.899272I
b = 1.082170 − 0.479825I
−0.78029 − 2.45975I 1.56496 + 4.60534I
u = −0.056856 − 0.667069I
a = −1.026160 + 0.899272I
b = 1.082170 + 0.479825I
−0.78029 + 2.45975I 1.56496 − 4.60534I
u = 0.079539 + 0.659669I
a = 1.21852 + 1.18832I
b = 0.487415 + 0.558178I
−1.04432 + 1.94452I 0.44759 − 4.35481I
u = 0.079539 − 0.659669I
a = 1.21852 − 1.18832I
b = 0.487415 − 0.558178I
−1.04432 − 1.94452I 0.44759 + 4.35481I
u = −0.034529 + 1.367220I
a = 1.251690 − 0.268262I
b = 0.739942 − 0.073109I
−5.06693 − 0.49368I 0
u = −0.034529 − 1.367220I
a = 1.251690 + 0.268262I
b = 0.739942 + 0.073109I
−5.06693 + 0.49368I 0
u = 0.384071 + 0.487436I
a = 0.751499 − 1.132160I
b = −0.280619 + 0.013695I
0.74823 + 1.41717I 7.99103 − 4.76808I
u = 0.384071 − 0.487436I
a = 0.751499 + 1.132160I
b = −0.280619 − 0.013695I
0.74823 − 1.41717I 7.99103 + 4.76808I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570445 + 0.227108I
a = 0.724932 + 0.725809I
b = 0.712694 − 0.892078I
−0.80561 − 2.69224I 0.86014 + 3.46707I
u = 0.570445 − 0.227108I
a = 0.724932 − 0.725809I
b = 0.712694 + 0.892078I
−0.80561 + 2.69224I 0.86014 − 3.46707I
u = −0.397156 + 0.323544I
a = 0.93708 − 1.37258I
b = 0.822579 + 0.535327I
0.221336 + 1.123620I 1.97465 + 3.42457I
u = −0.397156 − 0.323544I
a = 0.93708 + 1.37258I
b = 0.822579 − 0.535327I
0.221336 − 1.123620I 1.97465 − 3.42457I
u = 0.506465 + 0.002396I
a = −0.105042 − 0.152201I
b = 0.804872 + 0.250234I
1.43831 + 0.12872I 9.00370 + 1.16576I
u = 0.506465 − 0.002396I
a = −0.105042 + 0.152201I
b = 0.804872 − 0.250234I
1.43831 − 0.12872I 9.00370 − 1.16576I
u = 0.11093 + 1.51234I
a = 0.523741 − 0.597490I
b = −0.777182 − 0.293338I
−5.75279 + 3.87407I 0
u = 0.11093 − 1.51234I
a = 0.523741 + 0.597490I
b = −0.777182 + 0.293338I
−5.75279 − 3.87407I 0
u = −0.450202 + 0.168694I
a = 1.57697 − 0.98184I
b = −0.849531 − 0.131713I
−1.99105 + 3.91633I 4.79400 − 3.67932I
u = −0.450202 − 0.168694I
a = 1.57697 + 0.98184I
b = −0.849531 + 0.131713I
−1.99105 − 3.91633I 4.79400 + 3.67932I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.408993 + 0.061968I
a = −0.870341 + 0.284115I
b = 0.920328 − 0.783783I
0.80123 − 3.04052I 6.83565 + 8.73795I
u = −0.408993 − 0.061968I
a = −0.870341 − 0.284115I
b = 0.920328 + 0.783783I
0.80123 + 3.04052I 6.83565 − 8.73795I
u = 0.06184 + 1.59500I
a = 0.23501 − 1.40430I
b = −0.076351 − 0.495907I
−6.51615 + 2.69010I 0
u = 0.06184 − 1.59500I
a = 0.23501 + 1.40430I
b = −0.076351 + 0.495907I
−6.51615 − 2.69010I 0
u = −0.00686 + 1.59874I
a = 0.49443 + 1.47750I
b = 0.070839 + 0.929945I
−8.76444 + 2.10610I 0
u = −0.00686 − 1.59874I
a = 0.49443 − 1.47750I
b = 0.070839 − 0.929945I
−8.76444 − 2.10610I 0
u = 0.09071 + 1.62099I
a = 0.38141 + 2.24288I
b = 1.04947 + 1.86313I
−10.04900 + 7.81578I 0
u = 0.09071 − 1.62099I
a = 0.38141 − 2.24288I
b = 1.04947 − 1.86313I
−10.04900 − 7.81578I 0
u = −0.05613 + 1.63119I
a = 0.57924 − 1.96031I
b = 1.30610 − 1.53456I
−8.81712 − 4.37016I 0
u = −0.05613 − 1.63119I
a = 0.57924 + 1.96031I
b = 1.30610 + 1.53456I
−8.81712 + 4.37016I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.01126 + 1.63337I
a = 0.360804 − 0.737559I
b = 1.43899 − 0.49323I
−8.92043 − 2.68470I 0
u = −0.01126 − 1.63337I
a = 0.360804 + 0.737559I
b = 1.43899 + 0.49323I
−8.92043 + 2.68470I 0
u = −0.06741 + 1.63246I
a = −0.29501 + 1.81166I
b = −0.151442 + 0.454421I
−11.61330 − 7.84388I 0
u = −0.06741 − 1.63246I
a = −0.29501 − 1.81166I
b = −0.151442 − 0.454421I
−11.61330 + 7.84388I 0
u = −0.02728 + 1.66296I
a = −1.15006 − 2.07477I
b = −1.55205 − 1.96957I
−14.5853 − 6.2594I 0
u = −0.02728 − 1.66296I
a = −1.15006 + 2.07477I
b = −1.55205 + 1.96957I
−14.5853 + 6.2594I 0
u = 0.01513 + 1.66372I
a = −0.59500 + 1.59738I
b = −1.07841 + 1.42400I
−11.65700 + 1.95959I 0
u = 0.01513 − 1.66372I
a = −0.59500 − 1.59738I
b = −1.07841 − 1.42400I
−11.65700 − 1.95959I 0
u = 0.01664 + 1.66945I
a = −0.28312 + 1.86519I
b = 0.674892 + 1.040730I
−15.0505 + 5.3333I 0
u = 0.01664 − 1.66945I
a = −0.28312 − 1.86519I
b = 0.674892 − 1.040730I
−15.0505 − 5.3333I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08409 + 1.67730I
a = 0.62495 + 1.93763I
b = 1.02211 + 1.51213I
−10.09910 + 4.56839I 0
u = 0.08409 − 1.67730I
a = 0.62495 − 1.93763I
b = 1.02211 − 1.51213I
−10.09910 − 4.56839I 0
u = −0.07088 + 1.68001I
a = 0.47194 − 2.25156I
b = 0.94189 − 1.58874I
−11.00560 − 6.77939I 0
u = −0.07088 − 1.68001I
a = 0.47194 + 2.25156I
b = 0.94189 + 1.58874I
−11.00560 + 6.77939I 0
u = −0.16505 + 1.67970I
a = −0.30640 − 1.49193I
b = 0.32631 − 1.38443I
−16.2170 − 8.2628I 0
u = −0.16505 − 1.67970I
a = −0.30640 + 1.49193I
b = 0.32631 + 1.38443I
−16.2170 + 8.2628I 0
u = −0.14240 + 1.68308I
a = 0.07083 + 1.53547I
b = −0.87679 + 1.11168I
−16.8778 − 5.8754I 0
u = −0.14240 − 1.68308I
a = 0.07083 − 1.53547I
b = −0.87679 − 1.11168I
−16.8778 + 5.8754I 0
u = −0.02267 + 1.69173I
a = −1.205200 − 0.631112I
b = −1.77192 − 0.61321I
−14.8104 + 1.4077I 0
u = −0.02267 − 1.69173I
a = −1.205200 + 0.631112I
b = −1.77192 + 0.61321I
−14.8104 − 1.4077I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15326 + 1.69277I
a = −0.25585 − 1.64137I
b = −1.14981 − 1.22068I
−11.4479 + 11.1627I 0
u = 0.15326 − 1.69277I
a = −0.25585 + 1.64137I
b = −1.14981 + 1.22068I
−11.4479 − 11.1627I 0
u = 0.01869 + 1.70226I
a = 0.422433 − 0.545258I
b = −0.425173 − 0.406842I
−14.6931 + 0.3069I 0
u = 0.01869 − 1.70226I
a = 0.422433 + 0.545258I
b = −0.425173 + 0.406842I
−14.6931 − 0.3069I 0
u = −0.15215 + 1.69617I
a = −0.29351 + 1.85137I
b = −1.17227 + 1.39675I
−15.0671 − 17.1743I 0
u = −0.15215 − 1.69617I
a = −0.29351 − 1.85137I
b = −1.17227 − 1.39675I
−15.0671 + 17.1743I 0
u = 0.13765 + 1.71554I
a = 0.141859 + 1.187960I
b = 0.617032 + 1.085440I
−11.58530 + 4.29339I 0
u = 0.13765 − 1.71554I
a = 0.141859 − 1.187960I
b = 0.617032 − 1.085440I
−11.58530 − 4.29339I 0
u = −0.135262 + 0.224383I
a = 1.70040 − 2.96158I
b = 0.335448 + 0.496452I
0.13864 + 1.58495I 1.31807 − 1.97880I
u = −0.135262 − 0.224383I
a = 1.70040 + 2.96158I
b = 0.335448 − 0.496452I
0.13864 − 1.58495I 1.31807 + 1.97880I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19178 + 1.74653I
a = −0.156767 − 0.694979I
b = 0.304116 − 0.753836I
−14.2097 + 1.3446I 0
u = −0.19178 − 1.74653I
a = −0.156767 + 0.694979I
b = 0.304116 + 0.753836I
−14.2097 − 1.3446I 0
u = −0.0819509 + 0.0317781I
a = 4.88891 + 11.43510I
b = −0.253995 + 1.080020I
−3.58644 + 4.97389I 1.73611 − 5.61537I
u = −0.0819509 − 0.0317781I
a = 4.88891 − 11.43510I
b = −0.253995 − 1.080020I
−3.58644 − 4.97389I 1.73611 + 5.61537I
15
II.
I
u
2
= h−u
21
−u
20
+· · ·+b−3, 2u
21
+4u
20
+· · ·+a+3, u
22
+2u
21
+· · ·+8u+1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−2u
21
− 4u
20
+ ··· − 30u − 3
u
21
+ u
20
+ ··· + 12u + 3
a
6
=
1
−u
2
a
2
=
−3u
21
− 5u
20
+ ··· − 42u − 6
u
21
+ u
20
+ ··· + 12u + 3
a
12
=
−u
21
− 15u
19
+ ··· − 9u + 1
2u
21
+ 3u
20
+ ··· + 23u + 3
a
4
=
−3u
21
− 5u
20
+ ··· − 42u − 5
2u
21
+ 3u
20
+ ··· + 25u + 5
a
1
=
−2u
21
− 3u
20
+ ··· − 40u
2
− 14u
2u
21
+ 3u
20
+ ··· + 25u + 4
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
u
21
+ u
20
+ ··· + 17u + 2
−u
21
− 2u
20
+ ··· − 15u − 3
a
9
=
−u
3
− 2u
u
5
+ 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
−10u
21
−7u
20
−141u
19
−90u
18
−840u
17
−473u
16
−2754u
15
−1311u
14
−5433u
13
−2083u
12
−
6642u
11
−1999u
10
−5017u
9
−1297u
8
−2278u
7
−654u
6
−592u
5
−202u
4
−84u
3
−22u
2
−19u+4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 13u
21
+ ··· − 11u + 1
c
2
u
22
+ 9u
21
+ ··· + 5u + 1
c
3
u
22
+ 4u
20
+ ··· + u + 1
c
4
u
22
+ u
21
+ ··· + u + 1
c
5
, c
6
u
22
+ 2u
21
+ ··· + 8u + 1
c
7
u
22
+ 4u
20
+ ··· + 2u + 1
c
8
u
22
− 5u
20
+ ··· − u + 1
c
9
, c
10
u
22
− 2u
21
+ ··· − 8u + 1
c
11
u
22
+ u
21
+ ··· + u + 1
c
12
u
22
− 5u
20
+ ··· + u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 3y
21
+ ··· + 23y + 1
c
2
y
22
+ 7y
21
+ ··· + 11y + 1
c
3
y
22
+ 8y
21
+ ··· + 19y + 1
c
4
y
22
+ 13y
21
+ ··· + 9y + 1
c
5
, c
6
, c
9
c
10
y
22
+ 30y
21
+ ··· + 52y
2
+ 1
c
7
y
22
+ 8y
21
+ ··· − 10y + 1
c
8
, c
12
y
22
− 10y
21
+ ··· − 15y + 1
c
11
y
22
+ 9y
21
+ ··· + 13y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.260039 + 0.814231I
a = −0.07282 − 1.69631I
b = 1.02045 − 1.27936I
−1.50865 − 4.06278I −1.73350 + 7.43931I
u = −0.260039 − 0.814231I
a = −0.07282 + 1.69631I
b = 1.02045 + 1.27936I
−1.50865 + 4.06278I −1.73350 − 7.43931I
u = −0.513392 + 1.101110I
a = 0.331724 − 0.097201I
b = 0.009125 + 0.374583I
−1.54750 − 1.16736I 6.12536 − 5.58688I
u = −0.513392 − 1.101110I
a = 0.331724 + 0.097201I
b = 0.009125 − 0.374583I
−1.54750 + 1.16736I 6.12536 + 5.58688I
u = 0.342694 + 0.691677I
a = −0.037082 + 0.398376I
b = −0.351209 − 0.606327I
−4.42431 − 3.92780I −1.78221 + 1.52974I
u = 0.342694 − 0.691677I
a = −0.037082 − 0.398376I
b = −0.351209 + 0.606327I
−4.42431 + 3.92780I −1.78221 − 1.52974I
u = 0.225543 + 0.680682I
a = −1.11825 + 2.21918I
b = −0.051851 + 1.135470I
−4.53032 + 5.87417I −3.21531 − 7.87829I
u = 0.225543 − 0.680682I
a = −1.11825 − 2.21918I
b = −0.051851 − 1.135470I
−4.53032 − 5.87417I −3.21531 + 7.87829I
u = −0.04968 + 1.42999I
a = 1.348280 + 0.372464I
b = 0.996629 + 0.422487I
−4.80045 + 1.01728I 2.84745 − 8.71021I
u = −0.04968 − 1.42999I
a = 1.348280 − 0.372464I
b = 0.996629 − 0.422487I
−4.80045 − 1.01728I 2.84745 + 8.71021I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.421916 + 0.289657I
a = −1.71025 + 0.48258I
b = 0.603986 − 0.426323I
0.74603 − 2.40280I 5.79656 + 9.33997I
u = −0.421916 − 0.289657I
a = −1.71025 − 0.48258I
b = 0.603986 + 0.426323I
0.74603 + 2.40280I 5.79656 − 9.33997I
u = −0.08819 + 1.52280I
a = −0.597078 − 0.689567I
b = 0.816795 − 0.301665I
−5.54671 − 3.96043I 17.2601 + 10.8631I
u = −0.08819 − 1.52280I
a = −0.597078 + 0.689567I
b = 0.816795 + 0.301665I
−5.54671 + 3.96043I 17.2601 − 10.8631I
u = 0.06151 + 1.64708I
a = −0.21693 + 2.25230I
b = 0.12336 + 1.51523I
−12.7952 + 6.9466I −4.71884 − 5.98802I
u = 0.06151 − 1.64708I
a = −0.21693 − 2.25230I
b = 0.12336 − 1.51523I
−12.7952 − 6.9466I −4.71884 + 5.98802I
u = −0.07021 + 1.67025I
a = 0.67086 − 2.16616I
b = 1.18851 − 1.72785I
−10.26870 − 5.32986I −2.59736 + 6.54048I
u = −0.07021 − 1.67025I
a = 0.67086 + 2.16616I
b = 1.18851 + 1.72785I
−10.26870 + 5.32986I −2.59736 − 6.54048I
u = −0.283622 + 0.162602I
a = 1.20764 − 1.85056I
b = 0.937792 + 0.676253I
0.54699 + 1.98347I 7.55461 − 2.60545I
u = −0.283622 − 0.162602I
a = 1.20764 + 1.85056I
b = 0.937792 − 0.676253I
0.54699 − 1.98347I 7.55461 + 2.60545I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05730 + 1.72809I
a = −0.306085 + 0.092293I
b = −0.793590 − 0.075830I
−13.44380 − 2.19567I −2.03687 + 5.18624I
u = 0.05730 − 1.72809I
a = −0.306085 − 0.092293I
b = −0.793590 + 0.075830I
−13.44380 + 2.19567I −2.03687 − 5.18624I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 13u
21
+ ··· − 11u + 1)(u
104
+ 8u
103
+ ··· + 14156u + 5744)
c
2
(u
22
+ 9u
21
+ ··· + 5u + 1)(u
104
+ 14u
102
+ ··· + 11537u + 1378)
c
3
(u
22
+ 4u
20
+ ··· + u + 1)(u
104
− u
103
+ ··· + 1584164u + 498521)
c
4
(u
22
+ u
21
+ ··· + u + 1)(u
104
+ 7u
102
+ ··· − 38u + 1)
c
5
, c
6
(u
22
+ 2u
21
+ ··· + 8u + 1)(u
104
+ 3u
103
+ ··· + 31u + 1)
c
7
(u
22
+ 4u
20
+ ··· + 2u + 1)(u
104
− u
103
+ ··· − 487679u + 95891)
c
8
(u
22
− 5u
20
+ ··· − u + 1)(u
104
− u
103
+ ··· − 125u + 142)
c
9
, c
10
(u
22
− 2u
21
+ ··· − 8u + 1)(u
104
+ 3u
103
+ ··· + 31u + 1)
c
11
(u
22
+ u
21
+ ··· + u + 1)(u
104
+ 10u
103
+ ··· + 18056u + 1169)
c
12
(u
22
− 5u
20
+ ··· + u + 1)(u
104
− u
103
+ ··· − 125u + 142)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
+ 3y
21
+ ··· + 23y + 1)
· (y
104
− 32y
103
+ ··· − 1389779440y + 32993536)
c
2
(y
22
+ 7y
21
+ ··· + 11y + 1)
· (y
104
+ 28y
103
+ ··· − 10876525y + 1898884)
c
3
(y
22
+ 8y
21
+ ··· + 19y + 1)
· (y
104
+ 49y
103
+ ··· + 10000134915712y + 248523187441)
c
4
(y
22
+ 13y
21
+ ··· + 9y + 1)(y
104
+ 14y
103
+ ··· − 30y + 1)
c
5
, c
6
, c
9
c
10
(y
22
+ 30y
21
+ ··· + 52y
2
+ 1)(y
104
+ 131y
103
+ ··· − 163y + 1)
c
7
(y
22
+ 8y
21
+ ··· − 10y + 1)
· (y
104
+ 37y
103
+ ··· + 307454898715y + 9195083881)
c
8
, c
12
(y
22
− 10y
21
+ ··· − 15y + 1)(y
104
− 61y
103
+ ··· − 477693y + 20164)
c
11
(y
22
+ 9y
21
+ ··· + 13y + 1)
· (y
104
+ 38y
103
+ ··· + 142466966y + 1366561)
23
