12a
0162
(K12a
0162
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 11 1 10 4 12 6 8 7
Solving Sequence
2,5 3,11
6 1 7 4 10 8 9 12
c
2
c
5
c
1
c
6
c
4
c
10
c
7
c
8
c
12
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.29523 × 10
304
u
152
− 8.92919 × 10
305
u
151
+ ··· + 1.94694 × 10
303
b + 3.53899 × 10
307
,
5.00929 × 10
304
u
152
+ 5.88603 × 10
305
u
151
+ ··· + 2.72571 × 10
302
a + 2.91301 × 10
305
,
u
153
+ 14u
152
+ ··· − 762u − 49i
I
u
2
= h−7u
23
− 26u
22
+ ··· + b − 8, −6u
23
− 18u
22
+ ··· + a − 4, u
24
+ 4u
23
+ ··· + 3u + 1i
I
u
3
= ha
8
+ 2a
6
+ a
5
+ 4a
4
+ 3a
3
+ 5a
2
+ 7b − 9a + 6, a
9
− a
8
+ 2a
7
− a
6
+ 3a
5
− a
4
+ 2a
3
+ a + 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 186 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
304
u
152
− 8.93 × 10
305
u
151
+ · · · + 1.95 × 10
303
b + 3.54 ×
10
307
, 5.01 × 10
304
u
152
+ 5.89 × 10
305
u
151
+ · · · + 2.73 × 10
302
a + 2.91 ×
10
305
, u
153
+ 14u
152
+ · · · − 762u − 49i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
11
=
−183.779u
152
− 2159.45u
151
+ ··· − 7908.06u − 1068.72
−6.65267u
152
+ 458.628u
151
+ ··· − 255952.u − 18177.2
a
6
=
45.7365u
152
+ 309.760u
151
+ ··· + 116257.u + 8455.45
616.534u
152
+ 7545.94u
151
+ ··· − 118442.u − 6864.99
a
1
=
−u
2
+ 1
−u
4
a
7
=
−446.080u
152
− 6191.45u
151
+ ··· + 446245.u + 30706.7
−74.8796u
152
− 1734.74u
151
+ ··· + 411019.u + 29036.3
a
4
=
u
u
a
10
=
504.654u
152
+ 6286.66u
151
+ ··· − 160897.u − 10329.5
1128.83u
152
+ 14406.8u
151
+ ··· − 512631.u − 33700.1
a
8
=
−220.118u
152
− 2878.28u
151
+ ··· + 137443.u + 9289.07
−350.744u
152
− 4657.56u
151
+ ··· + 250754.u + 16977.6
a
9
=
−296.996u
152
− 3730.32u
151
+ ··· + 106135.u + 6864.24
−427.622u
152
− 5509.60u
151
+ ··· + 219446.u + 14552.8
a
12
=
−632.625u
152
− 8218.23u
151
+ ··· + 354761.u + 23565.6
−617.458u
152
− 8034.34u
151
+ ··· + 357702.u + 23903.3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −424.076u
152
− 5406.81u
151
+ ··· + 203917.u + 13552.6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
153
+ 76u
152
+ ··· + 169142u + 2401
c
2
, c
4
u
153
− 14u
152
+ ··· − 762u + 49
c
3
, c
8
u
153
− u
152
+ ··· − 100352u + 25088
c
5
, c
10
u
153
+ 2u
152
+ ··· + 1528u + 649
c
6
, c
12
u
153
+ 3u
152
+ ··· + 50071u + 3559
c
7
u
153
− 10u
152
+ ··· + 14u + 17
c
9
u
153
− 20u
152
+ ··· + 18213u + 14027
c
11
u
153
− u
152
+ ··· + 118105u + 15199
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
153
+ 16y
152
+ ··· + 4705654178y −5764801
c
2
, c
4
y
153
− 76y
152
+ ··· + 169142y −2401
c
3
, c
8
y
153
+ 69y
152
+ ··· − 16338911232y −629407744
c
5
, c
10
y
153
+ 96y
152
+ ··· − 17206606y −421201
c
6
, c
12
y
153
+ 99y
152
+ ··· − 548780483y −12666481
c
7
y
153
− 8y
152
+ ··· − 9698y −289
c
9
y
153
− 40y
152
+ ··· + 18060550885y −196756729
c
11
y
153
+ 3y
152
+ ··· − 3235076783y −231009601
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.574594 + 0.816890I
a = 1.43644 − 0.31596I
b = 0.611437 − 0.397016I
5.13882 + 1.56779I 0
u = −0.574594 − 0.816890I
a = 1.43644 + 0.31596I
b = 0.611437 + 0.397016I
5.13882 − 1.56779I 0
u = 0.958484 + 0.278909I
a = 0.38766 + 1.64685I
b = 2.38666 + 0.30401I
1.129760 − 0.814632I 0
u = 0.958484 − 0.278909I
a = 0.38766 − 1.64685I
b = 2.38666 − 0.30401I
1.129760 + 0.814632I 0
u = −0.895884 + 0.430701I
a = −0.551403 − 0.393529I
b = −1.57433 + 0.45310I
−2.14959 + 1.73247I 0
u = −0.895884 − 0.430701I
a = −0.551403 + 0.393529I
b = −1.57433 − 0.45310I
−2.14959 − 1.73247I 0
u = −0.985972 + 0.213998I
a = 0.539482 + 1.196150I
b = 1.34686 + 1.00600I
−5.33229 − 6.54252I 0
u = −0.985972 − 0.213998I
a = 0.539482 − 1.196150I
b = 1.34686 − 1.00600I
−5.33229 + 6.54252I 0
u = −0.308239 + 0.976529I
a = 1.08835 − 1.00361I
b = 0.089777 + 0.592784I
2.3368 − 14.2623I 0
u = −0.308239 − 0.976529I
a = 1.08835 + 1.00361I
b = 0.089777 − 0.592784I
2.3368 + 14.2623I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.445994 + 0.851018I
a = −0.73156 + 1.41683I
b = 0.154985 − 0.466806I
4.36623 − 5.28259I 0
u = −0.445994 − 0.851018I
a = −0.73156 − 1.41683I
b = 0.154985 + 0.466806I
4.36623 + 5.28259I 0
u = 0.950665 + 0.433419I
a = 0.438661 − 0.209931I
b = 1.48917 − 0.57495I
−1.93090 − 3.15315I 0
u = 0.950665 − 0.433419I
a = 0.438661 + 0.209931I
b = 1.48917 + 0.57495I
−1.93090 + 3.15315I 0
u = 0.920630 + 0.495323I
a = 1.205590 + 0.584838I
b = 2.53864 − 0.21529I
−0.38761 − 5.07239I 0
u = 0.920630 − 0.495323I
a = 1.205590 − 0.584838I
b = 2.53864 + 0.21529I
−0.38761 + 5.07239I 0
u = −0.322725 + 0.895754I
a = −1.038100 + 0.891150I
b = 0.152242 − 0.790387I
5.83587 − 7.72355I 0
u = −0.322725 − 0.895754I
a = −1.038100 − 0.891150I
b = 0.152242 + 0.790387I
5.83587 + 7.72355I 0
u = 0.418416 + 0.967520I
a = −0.891483 − 0.133621I
b = −0.399415 + 0.176695I
−1.16480 − 4.56244I 0
u = 0.418416 − 0.967520I
a = −0.891483 + 0.133621I
b = −0.399415 − 0.176695I
−1.16480 + 4.56244I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.910466 + 0.237134I
a = 0.618889 + 1.147390I
b = 1.188320 + 0.395835I
−5.78318 + 2.01516I 0
u = −0.910466 − 0.237134I
a = 0.618889 − 1.147390I
b = 1.188320 − 0.395835I
−5.78318 − 2.01516I 0
u = 0.990973 + 0.383908I
a = −0.736554 − 1.003330I
b = −2.52442 − 1.13711I
0.54761 − 1.44300I 0
u = 0.990973 − 0.383908I
a = −0.736554 + 1.003330I
b = −2.52442 + 1.13711I
0.54761 + 1.44300I 0
u = −0.686108 + 0.634402I
a = −1.185060 − 0.533186I
b = −0.873123 + 0.960621I
0.67913 + 5.24901I 0
u = −0.686108 − 0.634402I
a = −1.185060 + 0.533186I
b = −0.873123 − 0.960621I
0.67913 − 5.24901I 0
u = 0.903188 + 0.238495I
a = −0.055343 − 0.756165I
b = −4.52323 + 0.01015I
−2.69283 + 2.12824I 0
u = 0.903188 − 0.238495I
a = −0.055343 + 0.756165I
b = −4.52323 − 0.01015I
−2.69283 − 2.12824I 0
u = −1.003950 + 0.371462I
a = −0.034393 − 0.897261I
b = −1.26131 − 1.05136I
0.011275 − 0.515252I 0
u = −1.003950 − 0.371462I
a = −0.034393 + 0.897261I
b = −1.26131 + 1.05136I
0.011275 + 0.515252I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.462720 + 0.973186I
a = −0.649975 + 0.436879I
b = −0.263586 − 0.603612I
3.60458 − 2.74950I 0
u = −0.462720 − 0.973186I
a = −0.649975 − 0.436879I
b = −0.263586 + 0.603612I
3.60458 + 2.74950I 0
u = 0.835570 + 0.687935I
a = 0.349315 + 0.614531I
b = 1.242750 + 0.025699I
−1.88517 − 2.34362I 0
u = 0.835570 − 0.687935I
a = 0.349315 − 0.614531I
b = 1.242750 − 0.025699I
−1.88517 + 2.34362I 0
u = 1.016760 + 0.370999I
a = 0.645130 + 0.786096I
b = 3.36215 − 1.03847I
−3.53913 − 4.44208I 0
u = 1.016760 − 0.370999I
a = 0.645130 − 0.786096I
b = 3.36215 + 1.03847I
−3.53913 + 4.44208I 0
u = −0.756138 + 0.780095I
a = 1.064490 − 0.701322I
b = 1.207020 − 0.635288I
8.53653 + 4.24665I 0
u = −0.756138 − 0.780095I
a = 1.064490 + 0.701322I
b = 1.207020 + 0.635288I
8.53653 − 4.24665I 0
u = −0.939531 + 0.552017I
a = −0.582454 − 1.069380I
b = −2.08714 − 0.73277I
−0.071240 − 0.591588I 0
u = −0.939531 − 0.552017I
a = −0.582454 + 1.069380I
b = −2.08714 + 0.73277I
−0.071240 + 0.591588I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.475132 + 0.764717I
a = 0.83450 + 1.24262I
b = 0.544227 − 0.336753I
−0.70902 + 7.98208I 0
u = 0.475132 − 0.764717I
a = 0.83450 − 1.24262I
b = 0.544227 + 0.336753I
−0.70902 − 7.98208I 0
u = −0.291130 + 1.063480I
a = 1.008020 − 0.522408I
b = 0.396508 + 0.228257I
2.80976 − 4.80966I 0
u = −0.291130 − 1.063480I
a = 1.008020 + 0.522408I
b = 0.396508 − 0.228257I
2.80976 + 4.80966I 0
u = −0.299280 + 0.841358I
a = −0.63160 − 1.34503I
b = −0.542959 + 0.482245I
−1.60886 − 7.51304I 0
u = −0.299280 − 0.841358I
a = −0.63160 + 1.34503I
b = −0.542959 − 0.482245I
−1.60886 + 7.51304I 0
u = −1.041590 + 0.376605I
a = 1.156170 − 0.184868I
b = 2.13045 − 0.50677I
−6.76823 + 0.15150I 0
u = −1.041590 − 0.376605I
a = 1.156170 + 0.184868I
b = 2.13045 + 0.50677I
−6.76823 − 0.15150I 0
u = 0.752593 + 0.475568I
a = −0.13687 − 1.44830I
b = −0.982498 − 0.298007I
0.157068 + 1.043870I 0
u = 0.752593 − 0.475568I
a = −0.13687 + 1.44830I
b = −0.982498 + 0.298007I
0.157068 − 1.043870I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.086180 + 0.249085I
a = −0.209147 + 0.943972I
b = −1.187340 − 0.203491I
−3.84037 + 2.35778I 0
u = 1.086180 − 0.249085I
a = −0.209147 − 0.943972I
b = −1.187340 + 0.203491I
−3.84037 − 2.35778I 0
u = −0.547399 + 0.690954I
a = 0.807072 + 0.396069I
b = 0.708380 − 0.436182I
3.19945 + 0.72226I 0
u = −0.547399 − 0.690954I
a = 0.807072 − 0.396069I
b = 0.708380 + 0.436182I
3.19945 − 0.72226I 0
u = −0.421737 + 0.773562I
a = 0.441743 + 0.638691I
b = 0.338898 − 0.840790I
2.45307 − 3.31889I 0
u = −0.421737 − 0.773562I
a = 0.441743 − 0.638691I
b = 0.338898 + 0.840790I
2.45307 + 3.31889I 0
u = −0.799180 + 0.340969I
a = −0.448563 + 0.709569I
b = −0.320889 + 1.267110I
0.76492 + 3.31721I 0
u = −0.799180 − 0.340969I
a = −0.448563 − 0.709569I
b = −0.320889 − 1.267110I
0.76492 − 3.31721I 0
u = 0.857796 + 0.098270I
a = −0.665279 − 0.516870I
b = 0.12954 − 2.58752I
−2.79806 − 3.16139I 0
u = 0.857796 − 0.098270I
a = −0.665279 + 0.516870I
b = 0.12954 + 2.58752I
−2.79806 + 3.16139I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.880694 + 0.741742I
a = −0.677390 + 1.004890I
b = −0.475986 + 0.314668I
8.17021 + 1.41350I 0
u = −0.880694 − 0.741742I
a = −0.677390 − 1.004890I
b = −0.475986 − 0.314668I
8.17021 − 1.41350I 0
u = 1.141200 + 0.200987I
a = −0.020466 − 1.001250I
b = −0.29566 − 2.51930I
0.059344 − 0.653379I 0
u = 1.141200 − 0.200987I
a = −0.020466 + 1.001250I
b = −0.29566 + 2.51930I
0.059344 + 0.653379I 0
u = −0.415285 + 0.729352I
a = 1.21677 − 1.36665I
b = −0.363475 + 0.196159I
4.66993 − 1.60864I 0
u = −0.415285 − 0.729352I
a = 1.21677 + 1.36665I
b = −0.363475 − 0.196159I
4.66993 + 1.60864I 0
u = −0.513574 + 0.661509I
a = 0.854458 − 0.718443I
b = 0.264014 + 1.180200I
1.15055 + 2.63661I 0
u = −0.513574 − 0.661509I
a = 0.854458 + 0.718443I
b = 0.264014 − 1.180200I
1.15055 − 2.63661I 0
u = −1.128740 + 0.303775I
a = 0.718205 − 0.479306I
b = 1.17724 − 0.86002I
−6.10563 + 7.70875I 0
u = −1.128740 − 0.303775I
a = 0.718205 + 0.479306I
b = 1.17724 + 0.86002I
−6.10563 − 7.70875I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.473091 + 0.682038I
a = −1.92664 + 0.94089I
b = −0.707865 + 0.663983I
5.01099 − 0.58946I 0
u = −0.473091 − 0.682038I
a = −1.92664 − 0.94089I
b = −0.707865 − 0.663983I
5.01099 + 0.58946I 0
u = −1.053300 + 0.514235I
a = −0.094594 − 1.058760I
b = −1.47704 − 0.34370I
−2.51484 + 2.05166I 0
u = −1.053300 − 0.514235I
a = −0.094594 + 1.058760I
b = −1.47704 + 0.34370I
−2.51484 − 2.05166I 0
u = −1.022370 + 0.574994I
a = 0.306223 + 0.756673I
b = 1.176480 + 0.613540I
1.78661 + 4.16402I 0
u = −1.022370 − 0.574994I
a = 0.306223 − 0.756673I
b = 1.176480 − 0.613540I
1.78661 − 4.16402I 0
u = 1.052340 + 0.530022I
a = 0.759606 + 0.722009I
b = 2.62643 + 1.01096I
1.21069 − 6.89643I 0
u = 1.052340 − 0.530022I
a = 0.759606 − 0.722009I
b = 2.62643 − 1.01096I
1.21069 + 6.89643I 0
u = 1.074240 + 0.485277I
a = −0.864128 + 0.597591I
b = −1.51424 + 0.86371I
−5.98888 − 6.70269I 0
u = 1.074240 − 0.485277I
a = −0.864128 − 0.597591I
b = −1.51424 − 0.86371I
−5.98888 + 6.70269I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.380909 + 0.726311I
a = −1.073540 + 0.909998I
b = −1.047390 − 0.527334I
0.49834 − 4.72614I 0
u = −0.380909 − 0.726311I
a = −1.073540 − 0.909998I
b = −1.047390 + 0.527334I
0.49834 + 4.72614I 0
u = −1.034590 + 0.568304I
a = −0.512156 + 0.536550I
b = −2.40744 + 0.91946I
−0.38974 + 2.15739I 0
u = −1.034590 − 0.568304I
a = −0.512156 − 0.536550I
b = −2.40744 − 0.91946I
−0.38974 − 2.15739I 0
u = 1.175560 + 0.134803I
a = −0.399314 + 0.105905I
b = −1.99799 − 0.23490I
−2.73096 + 1.04396I 0
u = 1.175560 − 0.134803I
a = −0.399314 − 0.105905I
b = −1.99799 + 0.23490I
−2.73096 − 1.04396I 0
u = −1.060810 + 0.573324I
a = 0.59956 − 1.45513I
b = 0.58157 − 1.65500I
3.27382 + 5.45616I 0
u = −1.060810 − 0.573324I
a = 0.59956 + 1.45513I
b = 0.58157 + 1.65500I
3.27382 − 5.45616I 0
u = 1.224400 + 0.068741I
a = −0.532926 + 0.902798I
b = −1.92312 + 1.84736I
−1.47879 + 2.88577I 0
u = 1.224400 − 0.068741I
a = −0.532926 − 0.902798I
b = −1.92312 − 1.84736I
−1.47879 − 2.88577I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.863443 + 0.872751I
a = −0.959659 + 0.533981I
b = −0.949387 + 0.408983I
6.11189 + 9.64087I 0
u = −0.863443 − 0.872751I
a = −0.959659 − 0.533981I
b = −0.949387 − 0.408983I
6.11189 − 9.64087I 0
u = 0.739678 + 0.219151I
a = 0.400872 − 0.401997I
b = −0.135479 − 0.086416I
−0.941917 − 0.128738I 0
u = 0.739678 − 0.219151I
a = 0.400872 + 0.401997I
b = −0.135479 + 0.086416I
−0.941917 + 0.128738I 0
u = −1.035830 + 0.669437I
a = −0.331350 + 1.132300I
b = −0.187671 + 1.352810I
3.75333 + 3.98207I 0
u = −1.035830 − 0.669437I
a = −0.331350 − 1.132300I
b = −0.187671 − 1.352810I
3.75333 − 3.98207I 0
u = −1.089530 + 0.585328I
a = −0.974000 + 0.715575I
b = −2.17476 + 1.70665I
2.69237 + 6.63075I 0
u = −1.089530 − 0.585328I
a = −0.974000 − 0.715575I
b = −2.17476 − 1.70665I
2.69237 − 6.63075I 0
u = −0.837975 + 0.909716I
a = 0.587194 − 0.809108I
b = 0.504659 − 0.451647I
6.21066 − 3.22971I 0
u = −0.837975 − 0.909716I
a = 0.587194 + 0.809108I
b = 0.504659 + 0.451647I
6.21066 + 3.22971I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.099158 + 0.756498I
a = 0.592396 + 0.050813I
b = −0.458333 − 0.104453I
−1.64798 − 2.66834I 0
u = −0.099158 − 0.756498I
a = 0.592396 − 0.050813I
b = −0.458333 + 0.104453I
−1.64798 + 2.66834I 0
u = 1.083140 + 0.603801I
a = −0.966437 − 0.669674I
b = −2.47668 − 0.63380I
−2.53615 − 13.16840I 0
u = 1.083140 − 0.603801I
a = −0.966437 + 0.669674I
b = −2.47668 + 0.63380I
−2.53615 + 13.16840I 0
u = −1.104090 + 0.571992I
a = 0.689921 − 0.744783I
b = 2.26823 − 0.25739I
−1.62186 + 9.68707I 0
u = −1.104090 − 0.571992I
a = 0.689921 + 0.744783I
b = 2.26823 + 0.25739I
−1.62186 − 9.68707I 0
u = −1.093210 + 0.599223I
a = 0.377768 + 0.440427I
b = 1.91811 + 0.21693I
0.47061 + 8.49310I 0
u = −1.093210 − 0.599223I
a = 0.377768 − 0.440427I
b = 1.91811 − 0.21693I
0.47061 − 8.49310I 0
u = 1.181270 + 0.402814I
a = −0.338281 − 0.206291I
b = −0.731939 − 1.066440I
−5.37187 − 1.31466I 0
u = 1.181270 − 0.402814I
a = −0.338281 + 0.206291I
b = −0.731939 + 1.066440I
−5.37187 + 1.31466I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.193610 + 0.397425I
a = 0.049032 − 0.338911I
b = 0.31645 − 1.38718I
−5.39360 − 1.42120I 0
u = 1.193610 − 0.397425I
a = 0.049032 + 0.338911I
b = 0.31645 + 1.38718I
−5.39360 + 1.42120I 0
u = −0.143355 + 0.717544I
a = 0.544841 − 0.795646I
b = −0.615379 + 0.090988I
−1.61580 − 2.44952I 0
u = −0.143355 − 0.717544I
a = 0.544841 + 0.795646I
b = −0.615379 − 0.090988I
−1.61580 + 2.44952I 0
u = 1.243180 + 0.255001I
a = 0.908613 + 0.036004I
b = 2.70401 − 0.44908I
−6.54190 + 4.09896I 0
u = 1.243180 − 0.255001I
a = 0.908613 − 0.036004I
b = 2.70401 + 0.44908I
−6.54190 − 4.09896I 0
u = −1.163740 + 0.522058I
a = −0.577269 − 0.000165I
b = −1.34147 + 0.78759I
−4.47893 + 7.12118I 0
u = −1.163740 − 0.522058I
a = −0.577269 + 0.000165I
b = −1.34147 − 0.78759I
−4.47893 − 7.12118I 0
u = −1.182340 + 0.490261I
a = −0.088343 + 0.277555I
b = 0.056302 + 1.177490I
−4.78165 + 7.26278I 0
u = −1.182340 − 0.490261I
a = −0.088343 − 0.277555I
b = 0.056302 − 1.177490I
−4.78165 − 7.26278I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.114330 + 0.637212I
a = 1.141340 − 0.448009I
b = 2.81103 − 1.10389I
2.35547 + 10.80480I 0
u = −1.114330 − 0.637212I
a = 1.141340 + 0.448009I
b = 2.81103 + 1.10389I
2.35547 − 10.80480I 0
u = 0.453306 + 0.551100I
a = −1.02786 − 1.33674I
b = −0.366857 + 0.794960I
2.95829 + 2.47842I 0
u = 0.453306 − 0.551100I
a = −1.02786 + 1.33674I
b = −0.366857 − 0.794960I
2.95829 − 2.47842I 0
u = 1.061580 + 0.729490I
a = −0.647723 − 0.556979I
b = −1.367820 − 0.089761I
−2.44919 − 3.44783I 0
u = 1.061580 − 0.729490I
a = −0.647723 + 0.556979I
b = −1.367820 + 0.089761I
−2.44919 + 3.44783I 0
u = 1.278810 + 0.211421I
a = −0.133232 + 0.909955I
b = −1.43070 + 1.65004I
0.46000 + 4.24652I 0
u = 1.278810 − 0.211421I
a = −0.133232 − 0.909955I
b = −1.43070 − 1.65004I
0.46000 − 4.24652I 0
u = −1.162650 + 0.587085I
a = −0.895914 − 0.642965I
b = −2.32771 − 0.50967I
−4.17318 + 12.79720I 0
u = −1.162650 − 0.587085I
a = −0.895914 + 0.642965I
b = −2.32771 + 0.50967I
−4.17318 − 12.79720I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.175180 + 0.608421I
a = 0.765208 − 0.611140I
b = 2.49847 − 1.55285I
3.26481 + 13.23710I 0
u = −1.175180 − 0.608421I
a = 0.765208 + 0.611140I
b = 2.49847 + 1.55285I
3.26481 − 13.23710I 0
u = −1.145890 + 0.676573I
a = 0.473936 − 0.365803I
b = 1.81755 − 0.55926I
1.49037 + 8.72661I 0
u = −1.145890 − 0.676573I
a = 0.473936 + 0.365803I
b = 1.81755 + 0.55926I
1.49037 − 8.72661I 0
u = −0.425630 + 0.481298I
a = −1.71107 + 0.19286I
b = −1.03407 + 1.24694I
−0.70464 + 2.18373I 0
u = −0.425630 − 0.481298I
a = −1.71107 − 0.19286I
b = −1.03407 − 1.24694I
−0.70464 − 2.18373I 0
u = −1.210940 + 0.629035I
a = −0.928344 + 0.663982I
b = −2.61075 + 1.33342I
−0.4238 + 20.0703I 0
u = −1.210940 − 0.629035I
a = −0.928344 − 0.663982I
b = −2.61075 − 1.33342I
−0.4238 − 20.0703I 0
u = 1.366400 + 0.224104I
a = 0.295360 − 0.972105I
b = 1.31293 − 1.54767I
−3.40243 + 10.22740I 0
u = 1.366400 − 0.224104I
a = 0.295360 + 0.972105I
b = 1.31293 + 1.54767I
−3.40243 − 10.22740I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.232330 + 0.644358I
a = −0.668575 + 0.689519I
b = −1.77944 + 0.95139I
−0.09625 + 10.86920I 0
u = −1.232330 − 0.644358I
a = −0.668575 − 0.689519I
b = −1.77944 − 0.95139I
−0.09625 − 10.86920I 0
u = 0.229915 + 0.531966I
a = −1.06334 + 1.25276I
b = −0.150349 + 0.347476I
−3.73555 + 2.61983I −8.00000 + 0.I
u = 0.229915 − 0.531966I
a = −1.06334 − 1.25276I
b = −0.150349 − 0.347476I
−3.73555 − 2.61983I −8.00000 + 0.I
u = 1.43890 + 0.08829I
a = 0.154398 − 0.639808I
b = 0.223053 − 0.509205I
−3.80031 + 0.34121I 0
u = 1.43890 − 0.08829I
a = 0.154398 + 0.639808I
b = 0.223053 + 0.509205I
−3.80031 − 0.34121I 0
u = 0.260834 + 0.419052I
a = 2.03463 + 1.18472I
b = 0.391031 − 0.543122I
2.58263 − 1.72264I −1.48426 + 4.56743I
u = 0.260834 − 0.419052I
a = 2.03463 − 1.18472I
b = 0.391031 + 0.543122I
2.58263 + 1.72264I −1.48426 − 4.56743I
u = 1.46397 + 0.47029I
a = 0.216499 + 0.464815I
b = 0.464344 + 0.604489I
−4.60981 − 1.86353I 0
u = 1.46397 − 0.47029I
a = 0.216499 − 0.464815I
b = 0.464344 − 0.604489I
−4.60981 + 1.86353I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.269404
a = 1.56780
b = −0.194159
−0.842074 −11.5210
u = −0.227844 + 0.022165I
a = −2.25639 − 3.86595I
b = −0.857888 − 0.842032I
−0.87309 − 2.36039I −4.63324 + 1.20512I
u = −0.227844 − 0.022165I
a = −2.25639 + 3.86595I
b = −0.857888 + 0.842032I
−0.87309 + 2.36039I −4.63324 − 1.20512I
20
II. I
u
2
=
h−7u
23
−26u
22
+· · ·+b−8, −6u
23
−18u
22
+· · ·+a−4, u
24
+4u
23
+· · ·+3u+1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
11
=
6u
23
+ 18u
22
+ ··· + 12u + 4
7u
23
+ 26u
22
+ ··· + 17u + 8
a
6
=
−4u
23
− 13u
22
+ ··· − 9u − 4
−5u
23
− 21u
22
+ ··· − 14u − 9
a
1
=
−u
2
+ 1
−u
4
a
7
=
−8u
23
− 25u
22
+ ··· − 16u − 7
−7u
23
− 25u
22
+ ··· − 16u − 9
a
4
=
u
u
a
10
=
u
23
+ 4u
22
+ ··· + u + 1
3u
22
+ 11u
21
+ ··· − 2u + 1
a
8
=
−4u
23
− 12u
22
+ ··· − 7u − 3
−4u
23
− 10u
22
+ ··· − 5u − 2
a
9
=
−2u
21
− 2u
20
+ ··· − u − 1
2u
22
+ 2u
21
+ ··· + u
2
+ u
a
12
=
12u
23
+ 36u
22
+ ··· + 24u + 8
13u
23
+ 44u
22
+ ··· + 31u + 14
(ii) Obstruction class = 1
(iii) Cusp Shapes = −29u
23
−91u
22
+ 16u
21
+ 431u
20
+ 459u
19
−678u
18
−1686u
17
−
253u
16
+ 2426u
15
+ 2119u
14
− 1498u
13
− 3180u
12
− 361u
11
+ 2604u
10
+ 1636u
9
−
999u
8
− 1511u
7
− 223u
6
+ 523u
5
+ 331u
4
+ 41u
3
− 43u
2
− 54u − 34
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
24
− 12u
23
+ ··· − u + 1
c
2
u
24
+ 4u
23
+ ··· + 3u + 1
c
3
u
24
+ 6u
22
+ ··· − 3u + 1
c
4
u
24
− 4u
23
+ ··· − 3u + 1
c
5
u
24
+ 12u
22
+ ··· + 3u + 1
c
6
u
24
− 3u
23
+ ··· + 12u
2
+ 1
c
7
u
24
− 5u
21
+ ··· − 3u + 1
c
8
u
24
+ 6u
22
+ ··· + 3u + 1
c
9
u
24
− 6u
22
+ ··· − 12u + 1
c
10
u
24
+ 12u
22
+ ··· − 3u + 1
c
11
u
24
+ 3u
23
+ ··· + 5u
3
+ 1
c
12
u
24
+ 3u
23
+ ··· + 12u
2
+ 1
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 4y
23
+ ··· − 21y + 1
c
2
, c
4
y
24
− 12y
23
+ ··· − y + 1
c
3
, c
8
y
24
+ 12y
23
+ ··· − y + 1
c
5
, c
10
y
24
+ 24y
23
+ ··· + 19y + 1
c
6
, c
12
y
24
+ 19y
23
+ ··· + 24y + 1
c
7
y
24
− 6y
22
+ ··· − 5y + 1
c
9
y
24
− 12y
23
+ ··· − 12y + 1
c
11
y
24
− 5y
23
+ ··· − 6y
2
+ 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.984920 + 0.085434I
a = −0.372048 + 0.752170I
b = −4.80168 − 0.66751I
−3.01331 + 2.64864I −17.2617 − 24.3171I
u = 0.984920 − 0.085434I
a = −0.372048 − 0.752170I
b = −4.80168 + 0.66751I
−3.01331 − 2.64864I −17.2617 + 24.3171I
u = 0.763857 + 0.602118I
a = 0.841603 + 0.511815I
b = 1.30689 − 0.83936I
−1.69057 − 3.87913I −9.47886 + 7.35968I
u = 0.763857 − 0.602118I
a = 0.841603 − 0.511815I
b = 1.30689 + 0.83936I
−1.69057 + 3.87913I −9.47886 − 7.35968I
u = −0.437650 + 0.935412I
a = −0.805664 + 0.841021I
b = −0.324138 − 0.390524I
3.62995 − 4.17688I −4.23406 + 3.79944I
u = −0.437650 − 0.935412I
a = −0.805664 − 0.841021I
b = −0.324138 + 0.390524I
3.62995 + 4.17688I −4.23406 − 3.79944I
u = −0.616062 + 0.730459I
a = 1.41254 − 0.90245I
b = 0.343656 − 0.420784I
5.66713 + 0.57004I −0.69951 − 1.76332I
u = −0.616062 − 0.730459I
a = 1.41254 + 0.90245I
b = 0.343656 + 0.420784I
5.66713 − 0.57004I −0.69951 + 1.76332I
u = −0.957326 + 0.490984I
a = −0.224450 − 0.775238I
b = −1.92308 − 0.21628I
−1.33907 + 0.48887I −9.91527 − 0.20213I
u = −0.957326 − 0.490984I
a = −0.224450 + 0.775238I
b = −1.92308 + 0.21628I
−1.33907 − 0.48887I −9.91527 + 0.20213I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.837264 + 0.198649I
a = −0.35756 − 1.77617I
b = −2.85690 + 0.10461I
1.50297 − 0.47371I −3.53428 − 7.18464I
u = 0.837264 − 0.198649I
a = −0.35756 + 1.77617I
b = −2.85690 − 0.10461I
1.50297 + 0.47371I −3.53428 + 7.18464I
u = −1.011590 + 0.626572I
a = −0.63461 + 1.28046I
b = −0.63821 + 1.76611I
4.46285 + 4.61755I −0.52048 − 4.72657I
u = −1.011590 − 0.626572I
a = −0.63461 − 1.28046I
b = −0.63821 − 1.76611I
4.46285 − 4.61755I −0.52048 + 4.72657I
u = −0.623632 + 0.446968I
a = −0.922814 + 0.255464I
b = −0.62123 + 1.53634I
−0.33081 + 3.49000I −8.88183 − 7.57316I
u = −0.623632 − 0.446968I
a = −0.922814 − 0.255464I
b = −0.62123 − 1.53634I
−0.33081 − 3.49000I −8.88183 + 7.57316I
u = −1.179500 + 0.461469I
a = −0.276345 + 0.356584I
b = −0.068997 + 1.190250I
−4.59064 + 7.57890I −4.1390 − 15.0235I
u = −1.179500 − 0.461469I
a = −0.276345 − 0.356584I
b = −0.068997 − 1.190250I
−4.59064 − 7.57890I −4.1390 + 15.0235I
u = −1.134110 + 0.656648I
a = 0.790631 − 0.482201I
b = 2.29512 − 0.67055I
1.50968 + 9.96183I −8.32009 − 8.52814I
u = −1.134110 − 0.656648I
a = 0.790631 + 0.482201I
b = 2.29512 + 0.67055I
1.50968 − 9.96183I −8.32009 + 8.52814I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38139 + 0.41666I
a = −0.204697 − 0.498796I
b = −0.243831 − 0.830201I
−4.43225 − 1.71576I −1.84111 − 5.35701I
u = 1.38139 − 0.41666I
a = −0.204697 + 0.498796I
b = −0.243831 + 0.830201I
−4.43225 + 1.71576I −1.84111 + 5.35701I
u = −0.007568 + 0.520547I
a = 1.253410 − 0.565225I
b = −0.467606 − 0.786520I
−1.37593 − 3.51457I −7.17387 + 6.69949I
u = −0.007568 − 0.520547I
a = 1.253410 + 0.565225I
b = −0.467606 + 0.786520I
−1.37593 + 3.51457I −7.17387 − 6.69949I
28
III. I
u
3
= ha
8
+ 2a
6
+ a
5
+ 4a
4
+ 3a
3
+ 5a
2
+ 7b − 9a + 6, a
9
− a
8
+ 2a
7
−
a
6
+ 3a
5
− a
4
+ 2a
3
+ a + 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
1
a
3
=
1
1
a
11
=
a
−
1
7
a
8
−
2
7
a
6
+ ··· +
9
7
a −
6
7
a
6
=
−a
2
1
7
a
8
+
2
7
a
6
+ ··· +
5
7
a +
6
7
a
1
=
0
−1
a
7
=
−a
2
1
7
a
8
+
2
7
a
6
+ ··· +
5
7
a +
6
7
a
4
=
1
1
a
10
=
a
3
+ a
−
2
7
a
8
−
4
7
a
6
+ ··· +
4
7
a −
5
7
a
8
=
−a
8
− 2a
6
− 2a
4
− 2a
2
−a
8
− 2a
6
− 2a
4
− 2a
2
a
9
=
−a
8
− 2a
6
− 2a
4
− 2a
2
−a
8
− 2a
6
− 2a
4
− 2a
2
a
12
=
a
4
−
1
7
a
8
−
2
7
a
6
+ ··· +
2
7
a −
6
7
(ii) Obstruction class = 1
(iii) Cusp Shapes =
5
49
a
8
+
40
7
a
7
−
151
49
a
6
+
208
49
a
5
−
85
49
a
4
+
442
49
a
3
−
31
49
a
2
+
95
49
a −
558
49
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
6
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
7
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
11
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
12
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
8
y
9
c
5
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
6
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
9
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.140343 + 0.966856I
b = −0.79086 + 1.50115I
0.13850 + 2.09337I −5.49232 − 4.08340I
u = 1.00000
a = −0.140343 − 0.966856I
b = −0.79086 − 1.50115I
0.13850 − 2.09337I −5.49232 + 4.08340I
u = 1.00000
a = −0.628449 + 0.875112I
b = −1.73338 + 1.49417I
−2.26187 + 2.45442I −12.87375 − 1.42824I
u = 1.00000
a = −0.628449 − 0.875112I
b = −1.73338 − 1.49417I
−2.26187 − 2.45442I −12.87375 + 1.42824I
u = 1.00000
a = 0.796005 + 0.733148I
b = 1.239760 + 0.200327I
−6.01628 + 1.33617I −13.72452 + 1.86826I
u = 1.00000
a = 0.796005 − 0.733148I
b = 1.239760 − 0.200327I
−6.01628 − 1.33617I −13.72452 − 1.86826I
u = 1.00000
a = 0.728966 + 0.986295I
b = 1.19887 + 1.02988I
−5.24306 − 7.08493I −7.53426 + 10.08360I
u = 1.00000
a = 0.728966 − 0.986295I
b = 1.19887 − 1.02988I
−5.24306 + 7.08493I −7.53426 − 10.08360I
u = 1.00000
a = −0.512358
b = −1.68593
−2.84338 −14.1380
32
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
24
− 12u
23
+ ··· − u + 1)
· (u
153
+ 76u
152
+ ··· + 169142u + 2401)
c
2
((u − 1)
9
)(u
24
+ 4u
23
+ ··· + 3u + 1)(u
153
− 14u
152
+ ··· − 762u + 49)
c
3
u
9
(u
24
+ 6u
22
+ ··· − 3u + 1)(u
153
− u
152
+ ··· − 100352u + 25088)
c
4
((u + 1)
9
)(u
24
− 4u
23
+ ··· − 3u + 1)(u
153
− 14u
152
+ ··· − 762u + 49)
c
5
(u
9
+ u
8
+ ··· + u − 1)(u
24
+ 12u
22
+ ··· + 3u + 1)
· (u
153
+ 2u
152
+ ··· + 1528u + 649)
c
6
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
24
− 3u
23
+ ··· + 12u
2
+ 1)(u
153
+ 3u
152
+ ··· + 50071u + 3559)
c
7
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
24
− 5u
21
+ ··· − 3u + 1)(u
153
− 10u
152
+ ··· + 14u + 17)
c
8
u
9
(u
24
+ 6u
22
+ ··· + 3u + 1)(u
153
− u
152
+ ··· − 100352u + 25088)
c
9
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
24
− 6u
22
+ ··· − 12u + 1)(u
153
− 20u
152
+ ··· + 18213u + 14027)
c
10
(u
9
− u
8
+ ··· + u + 1)(u
24
+ 12u
22
+ ··· − 3u + 1)
· (u
153
+ 2u
152
+ ··· + 1528u + 649)
c
11
(u
9
− u
8
+ ··· − u + 1)(u
24
+ 3u
23
+ ··· + 5u
3
+ 1)
· (u
153
− u
152
+ ··· + 118105u + 15199)
c
12
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
24
+ 3u
23
+ ··· + 12u
2
+ 1)(u
153
+ 3u
152
+ ··· + 50071u + 3559)
33
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
24
+ 4y
23
+ ··· − 21y + 1)
· (y
153
+ 16y
152
+ ··· + 4705654178y −5764801)
c
2
, c
4
((y −1)
9
)(y
24
− 12y
23
+ ··· − y + 1)
· (y
153
− 76y
152
+ ··· + 169142y −2401)
c
3
, c
8
y
9
(y
24
+ 12y
23
+ ··· − y + 1)
· (y
153
+ 69y
152
+ ··· − 16338911232y −629407744)
c
5
, c
10
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
24
+ 24y
23
+ ··· + 19y + 1)
· (y
153
+ 96y
152
+ ··· − 17206606y −421201)
c
6
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
24
+ 19y
23
+ ··· + 24y + 1)
· (y
153
+ 99y
152
+ ··· − 548780483y −12666481)
c
7
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
24
− 6y
22
+ ··· − 5y + 1)(y
153
− 8y
152
+ ··· − 9698y −289)
c
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
24
− 12y
23
+ ··· − 12y + 1)
· (y
153
− 40y
152
+ ··· + 18060550885y −196756729)
c
11
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
24
− 5y
23
+ ··· − 6y
2
+ 1)
· (y
153
+ 3y
152
+ ··· − 3235076783y −231009601)
34
