12a
0094
(K12a
0094
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 11 4 12 1 7 6 9
Solving Sequence
8,12
9 1
4,10
3 2 5 7 11 6
c
8
c
12
c
9
c
3
c
1
c
4
c
7
c
10
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.96260 × 10
145
u
95
− 3.70133 × 10
146
u
94
+ ··· + 8.62108 × 10
145
b − 3.66132 × 10
147
,
− 2.18202 × 10
148
u
95
− 7.85274 × 10
148
u
94
+ ··· + 5.43128 × 10
147
a − 7.52984 × 10
149
,
u
96
+ 5u
95
+ ··· − 91u + 49i
I
u
2
= hb, 4u
5
− 2u
4
− 13u
3
+ 3u
2
+ 3a + 8u + 5, u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
I
u
3
= h98a
5
− 302a
4
+ 818a
3
+ 65a
2
+ 1413b + 948a − 1845, a
6
− 4a
5
+ 10a
4
− 2a
3
− 3a
2
− 18a + 27, u + 1i
I
u
4
= ha
2
+ b + 2a + 1, a
3
+ 2a
2
+ a + 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 111 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−9.96 × 10
145
u
95
− 3.70 × 10
146
u
94
+ · · · + 8.62 × 10
145
b − 3.66 ×
10
147
, −2.18 × 10
148
u
95
− 7.85 × 10
148
u
94
+ · · · + 5.43 × 10
147
a − 7.53 ×
10
149
, u
96
+ 5u
95
+ · · · − 91u + 49i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
4.01750u
95
+ 14.4584u
94
+ ··· − 354.098u + 138.638
1.15561u
95
+ 4.29335u
94
+ ··· − 112.037u + 42.4694
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
5.17311u
95
+ 18.7517u
94
+ ··· − 466.134u + 181.108
1.15561u
95
+ 4.29335u
94
+ ··· − 112.037u + 42.4694
a
2
=
3.25211u
95
+ 11.7121u
94
+ ··· − 290.167u + 111.886
1.35247u
95
+ 4.91134u
94
+ ··· − 126.362u + 48.5960
a
5
=
3.49585u
95
+ 12.5870u
94
+ ··· − 305.981u + 121.267
1.35247u
95
+ 4.91134u
94
+ ··· − 126.362u + 48.5960
a
7
=
0.965966u
95
+ 3.49842u
94
+ ··· − 86.5737u + 35.3472
2.93454u
95
+ 10.4708u
94
+ ··· − 255.270u + 99.8370
a
11
=
−2.45974u
95
− 8.79529u
94
+ ··· + 218.176u − 84.7113
3.01300u
95
+ 10.5769u
94
+ ··· − 247.275u + 98.2961
a
6
=
2.19394u
95
+ 7.96817u
94
+ ··· − 194.713u + 77.4488
1.23257u
95
+ 4.56553u
94
+ ··· − 125.028u + 47.0994
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.54253u
95
− 19.5325u
94
+ ··· + 462.052u − 194.600
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
96
+ 46u
95
+ ··· + 6201u + 81
c
2
, c
4
u
96
− 10u
95
+ ··· + 21u + 9
c
3
, c
7
u
96
+ 2u
95
+ ··· − 960u − 576
c
5
u
96
− 2u
95
+ ··· + 37784u − 17960
c
6
, c
10
, c
11
u
96
+ 2u
95
+ ··· − 40u − 8
c
8
, c
9
, c
12
u
96
+ 5u
95
+ ··· − 91u + 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
96
+ 18y
95
+ ··· − 35151813y + 6561
c
2
, c
4
y
96
− 46y
95
+ ··· − 6201y + 81
c
3
, c
7
y
96
+ 48y
95
+ ··· + 958464y + 331776
c
5
y
96
− 8y
95
+ ··· − 4744914496y + 322561600
c
6
, c
10
, c
11
y
96
+ 88y
95
+ ··· − 2240y + 64
c
8
, c
9
, c
12
y
96
− 89y
95
+ ··· + 51009y + 2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.894603 + 0.430427I
a = −0.58259 + 1.60361I
b = −0.799471 − 0.443389I
1.05865 + 1.46642I 0
u = 0.894603 − 0.430427I
a = −0.58259 − 1.60361I
b = −0.799471 + 0.443389I
1.05865 − 1.46642I 0
u = 0.267433 + 0.926258I
a = −0.11021 + 1.94515I
b = −0.675868 − 1.203540I
5.41790 − 12.05450I 0
u = 0.267433 − 0.926258I
a = −0.11021 − 1.94515I
b = −0.675868 + 1.203540I
5.41790 + 12.05450I 0
u = −0.823573 + 0.631077I
a = −0.537201 − 0.568626I
b = 0.466493 + 1.006500I
−1.31559 − 3.10134I 0
u = −0.823573 − 0.631077I
a = −0.537201 + 0.568626I
b = 0.466493 − 1.006500I
−1.31559 + 3.10134I 0
u = 0.587087 + 0.743265I
a = 0.518160 − 0.556696I
b = −0.311553 + 0.850667I
1.94707 − 0.56651I 0
u = 0.587087 − 0.743265I
a = 0.518160 + 0.556696I
b = −0.311553 − 0.850667I
1.94707 + 0.56651I 0
u = −0.942713
a = 2.76097
b = 0.453528
−2.90871 0
u = −0.358924 + 0.854060I
a = 0.26984 + 1.70642I
b = 0.613586 − 1.130970I
0.11990 + 8.22678I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.358924 − 0.854060I
a = 0.26984 − 1.70642I
b = 0.613586 + 1.130970I
0.11990 − 8.22678I 0
u = −0.992667 + 0.428867I
a = 0.646176 + 0.680901I
b = −0.077552 − 0.958487I
−0.004630 + 1.218200I 0
u = −0.992667 − 0.428867I
a = 0.646176 − 0.680901I
b = −0.077552 + 0.958487I
−0.004630 − 1.218200I 0
u = 0.698211 + 0.551668I
a = −0.564768 + 0.843621I
b = −0.309252 − 0.991383I
1.80240 − 4.20818I 0
u = 0.698211 − 0.551668I
a = −0.564768 − 0.843621I
b = −0.309252 + 0.991383I
1.80240 + 4.20818I 0
u = 0.211349 + 0.861415I
a = −0.04386 − 2.14378I
b = 0.493525 + 1.216240I
7.73870 − 6.46946I 0
u = 0.211349 − 0.861415I
a = −0.04386 + 2.14378I
b = 0.493525 − 1.216240I
7.73870 + 6.46946I 0
u = 0.741282 + 0.406653I
a = −0.03057 − 1.82826I
b = −0.490624 + 0.614411I
0.627403 − 0.638866I 0
u = 0.741282 − 0.406653I
a = −0.03057 + 1.82826I
b = −0.490624 − 0.614411I
0.627403 + 0.638866I 0
u = 1.056680 + 0.482012I
a = −0.835691 + 0.839636I
b = 0.358765 − 1.061850I
5.17707 + 1.67004I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.056680 − 0.482012I
a = −0.835691 − 0.839636I
b = 0.358765 + 1.061850I
5.17707 − 1.67004I 0
u = 0.271321 + 0.789087I
a = 0.761633 − 0.541341I
b = −1.023040 + 0.436728I
2.98639 − 5.88754I −12.00000 + 0.I
u = 0.271321 − 0.789087I
a = 0.761633 + 0.541341I
b = −1.023040 − 0.436728I
2.98639 + 5.88754I −12.00000 + 0.I
u = 1.176190 + 0.087795I
a = 2.23771 − 1.12256I
b = 0.653688 − 0.348368I
1.68802 − 0.79999I 0
u = 1.176190 − 0.087795I
a = 2.23771 + 1.12256I
b = 0.653688 + 0.348368I
1.68802 + 0.79999I 0
u = 1.012610 + 0.606707I
a = 0.560411 − 0.684913I
b = −0.589071 + 1.120010I
3.16056 + 6.70309I 0
u = 1.012610 − 0.606707I
a = 0.560411 + 0.684913I
b = −0.589071 − 1.120010I
3.16056 − 6.70309I 0
u = 1.185190 + 0.057003I
a = −0.166385 + 1.005370I
b = −0.15098 − 1.44718I
0.86415 − 3.10882I 0
u = 1.185190 − 0.057003I
a = −0.166385 − 1.005370I
b = −0.15098 + 1.44718I
0.86415 + 3.10882I 0
u = −0.238407 + 0.769442I
a = −0.09177 − 1.88281I
b = −0.404576 + 1.090770I
2.24931 + 3.08732I −8.93943 − 4.55885I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.238407 − 0.769442I
a = −0.09177 + 1.88281I
b = −0.404576 − 1.090770I
2.24931 − 3.08732I −8.93943 + 4.55885I
u = 0.479555 + 0.633842I
a = −0.68905 + 1.25761I
b = −0.437629 − 1.084170I
1.92869 − 4.25628I −8.95478 + 4.66046I
u = 0.479555 − 0.633842I
a = −0.68905 − 1.25761I
b = −0.437629 + 1.084170I
1.92869 + 4.25628I −8.95478 − 4.66046I
u = 0.297926 + 0.713446I
a = −0.26756 + 2.80054I
b = −0.319113 − 0.887092I
2.05700 − 3.39158I −8.19869 + 5.33018I
u = 0.297926 − 0.713446I
a = −0.26756 − 2.80054I
b = −0.319113 + 0.887092I
2.05700 + 3.39158I −8.19869 − 5.33018I
u = −1.274940 + 0.151744I
a = −0.131521 − 1.080050I
b = 0.35236 + 1.51844I
4.83457 − 0.90672I 0
u = −1.274940 − 0.151744I
a = −0.131521 + 1.080050I
b = 0.35236 − 1.51844I
4.83457 + 0.90672I 0
u = 1.263760 + 0.247129I
a = −1.56360 + 0.34158I
b = −0.252571 − 1.050680I
5.57865 − 0.54346I 0
u = 1.263760 − 0.247129I
a = −1.56360 − 0.34158I
b = −0.252571 + 1.050680I
5.57865 + 0.54346I 0
u = −0.334430 + 0.619539I
a = −0.330409 − 0.591868I
b = 0.851796 + 0.434666I
−2.02726 + 2.77817I −15.3604 − 6.1150I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.334430 − 0.619539I
a = −0.330409 + 0.591868I
b = 0.851796 − 0.434666I
−2.02726 − 2.77817I −15.3604 + 6.1150I
u = −1.287070 + 0.218078I
a = 0.372738 + 1.177560I
b = −0.03743 − 1.53555I
5.52415 + 5.61656I 0
u = −1.287070 − 0.218078I
a = 0.372738 − 1.177560I
b = −0.03743 + 1.53555I
5.52415 − 5.61656I 0
u = 0.190244 + 0.645320I
a = 0.67506 − 1.65996I
b = 0.156876 + 1.097660I
3.20723 + 0.61466I −6.11717 − 2.65082I
u = 0.190244 − 0.645320I
a = 0.67506 + 1.65996I
b = 0.156876 − 1.097660I
3.20723 − 0.61466I −6.11717 + 2.65082I
u = 0.228637 + 0.602725I
a = −1.074020 + 0.424384I
b = 0.930502 − 0.044924I
4.17537 − 1.56489I −6.74200 + 0.69028I
u = 0.228637 − 0.602725I
a = −1.074020 − 0.424384I
b = 0.930502 + 0.044924I
4.17537 + 1.56489I −6.74200 − 0.69028I
u = 0.503445 + 0.391937I
a = −0.737578 − 1.066170I
b = 0.527550 + 0.356073I
3.26727 − 1.44940I −6.57025 + 4.96044I
u = 0.503445 − 0.391937I
a = −0.737578 + 1.066170I
b = 0.527550 − 0.356073I
3.26727 + 1.44940I −6.57025 − 4.96044I
u = −1.356770 + 0.230598I
a = 0.968466 + 0.661357I
b = 0.549142 − 0.999132I
−1.63528 + 2.55488I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.356770 − 0.230598I
a = 0.968466 − 0.661357I
b = 0.549142 + 0.999132I
−1.63528 − 2.55488I 0
u = 1.367040 + 0.173042I
a = 1.53440 + 0.00518I
b = 0.531741 + 1.098270I
3.86558 − 5.42020I 0
u = 1.367040 − 0.173042I
a = 1.53440 − 0.00518I
b = 0.531741 − 1.098270I
3.86558 + 5.42020I 0
u = −0.002603 + 0.620958I
a = −1.09699 − 2.51791I
b = −0.104322 + 1.314390I
9.52451 − 2.61831I −2.94788 + 2.70332I
u = −0.002603 − 0.620958I
a = −1.09699 + 2.51791I
b = −0.104322 − 1.314390I
9.52451 + 2.61831I −2.94788 − 2.70332I
u = 1.381080 + 0.124946I
a = −0.255000 + 0.094725I
b = −1.026300 + 0.329559I
−5.66046 − 1.06424I 0
u = 1.381080 − 0.124946I
a = −0.255000 − 0.094725I
b = −1.026300 − 0.329559I
−5.66046 + 1.06424I 0
u = −1.393130 + 0.122971I
a = −0.732186 + 0.046331I
b = −0.893463 − 0.643378I
−5.71954 + 1.65518I 0
u = −1.393130 − 0.122971I
a = −0.732186 − 0.046331I
b = −0.893463 + 0.643378I
−5.71954 − 1.65518I 0
u = −1.398540 + 0.026055I
a = 0.430726 + 0.249827I
b = 0.869514 − 0.594393I
−2.80396 + 2.59732I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.398540 − 0.026055I
a = 0.430726 − 0.249827I
b = 0.869514 + 0.594393I
−2.80396 − 2.59732I 0
u = −0.403865 + 0.443628I
a = 0.83704 + 2.70119I
b = 0.396771 − 0.614354I
−2.61966 + 0.66074I −15.8520 − 7.6803I
u = −0.403865 − 0.443628I
a = 0.83704 − 2.70119I
b = 0.396771 + 0.614354I
−2.61966 − 0.66074I −15.8520 + 7.6803I
u = −1.386340 + 0.239403I
a = 0.082597 + 0.328551I
b = 1.158270 + 0.175859I
−0.96986 + 4.66734I 0
u = −1.386340 − 0.239403I
a = 0.082597 − 0.328551I
b = 1.158270 − 0.175859I
−0.96986 − 4.66734I 0
u = −1.410450 + 0.055569I
a = −1.011580 − 0.863938I
b = −0.661367 + 0.847247I
−6.04305 − 1.02722I 0
u = −1.410450 − 0.055569I
a = −1.011580 + 0.863938I
b = −0.661367 − 0.847247I
−6.04305 + 1.02722I 0
u = 1.42426 + 0.18534I
a = 0.93798 − 1.35215I
b = 0.500115 + 1.007120I
−8.39649 − 3.07099I 0
u = 1.42426 − 0.18534I
a = 0.93798 + 1.35215I
b = 0.500115 − 1.007120I
−8.39649 + 3.07099I 0
u = 1.40527 + 0.29944I
a = −0.912933 + 1.032280I
b = −0.631485 − 1.184960I
−2.99761 − 6.93739I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40527 − 0.29944I
a = −0.912933 − 1.032280I
b = −0.631485 + 1.184960I
−2.99761 + 6.93739I 0
u = 1.42532 + 0.23544I
a = 0.254075 − 0.178935I
b = 1.074790 − 0.581683I
−7.66058 − 5.90482I 0
u = 1.42532 − 0.23544I
a = 0.254075 + 0.178935I
b = 1.074790 + 0.581683I
−7.66058 + 5.90482I 0
u = −1.41882 + 0.27563I
a = −0.88046 − 1.59267I
b = −0.376567 + 1.099430I
−3.42401 + 6.97886I 0
u = −1.41882 − 0.27563I
a = −0.88046 + 1.59267I
b = −0.376567 − 1.099430I
−3.42401 − 6.97886I 0
u = −1.40519 + 0.35580I
a = 0.96762 + 1.26154I
b = 0.61274 − 1.30128I
2.60078 + 10.84870I 0
u = −1.40519 − 0.35580I
a = 0.96762 − 1.26154I
b = 0.61274 + 1.30128I
2.60078 − 10.84870I 0
u = −1.42031 + 0.31148I
a = −0.011770 − 0.343571I
b = −1.168130 − 0.504988I
−2.41478 + 9.86385I 0
u = −1.42031 − 0.31148I
a = −0.011770 + 0.343571I
b = −1.168130 + 0.504988I
−2.41478 − 9.86385I 0
u = −1.46849 + 0.25282I
a = −1.035010 − 0.588551I
b = −0.694605 + 1.088960I
−4.25746 + 7.57273I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46849 − 0.25282I
a = −1.035010 + 0.588551I
b = −0.694605 − 1.088960I
−4.25746 − 7.57273I 0
u = −1.44446 + 0.38146I
a = −1.08702 − 1.20415I
b = −0.76174 + 1.24391I
−0.0342 + 16.7602I 0
u = −1.44446 − 0.38146I
a = −1.08702 + 1.20415I
b = −0.76174 − 1.24391I
−0.0342 − 16.7602I 0
u = 1.46933 + 0.33045I
a = 1.022440 − 0.953412I
b = 0.754824 + 1.171510I
−5.74672 − 12.51240I 0
u = 1.46933 − 0.33045I
a = 1.022440 + 0.953412I
b = 0.754824 − 1.171510I
−5.74672 + 12.51240I 0
u = −0.084665 + 0.465660I
a = 1.95000 + 2.56550I
b = 0.382644 − 1.302200I
8.58074 + 3.10096I −3.84105 − 3.11958I
u = −0.084665 − 0.465660I
a = 1.95000 − 2.56550I
b = 0.382644 + 1.302200I
8.58074 − 3.10096I −3.84105 + 3.11958I
u = −1.56096 + 0.03152I
a = −0.347312 + 0.052373I
b = −0.564388 + 0.773277I
−6.29234 + 5.82359I 0
u = −1.56096 − 0.03152I
a = −0.347312 − 0.052373I
b = −0.564388 − 0.773277I
−6.29234 − 5.82359I 0
u = −1.55744 + 0.20416I
a = 0.092769 − 0.173183I
b = −0.298569 − 0.601193I
−5.22043 + 3.95090I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55744 − 0.20416I
a = 0.092769 + 0.173183I
b = −0.298569 + 0.601193I
−5.22043 − 3.95090I 0
u = 1.58003 + 0.08608I
a = 0.091506 − 0.152694I
b = 0.439553 − 0.654331I
−9.58542 + 0.87825I 0
u = 1.58003 − 0.08608I
a = 0.091506 + 0.152694I
b = 0.439553 + 0.654331I
−9.58542 − 0.87825I 0
u = −0.338118
a = 0.768935
b = −0.339691
−0.610403 −16.1160
u = 0.044589 + 0.274420I
a = −0.230218 + 1.347340I
b = −0.672500 + 0.131387I
−0.925774 − 0.265219I −10.99772 − 1.52988I
u = 0.044589 − 0.274420I
a = −0.230218 − 1.347340I
b = −0.672500 − 0.131387I
−0.925774 + 0.265219I −10.99772 + 1.52988I
14
II.
I
u
2
= hb, 4u
5
−2u
4
−13u
3
+3u
2
+3a+8u+5, u
6
−u
5
−3u
4
+2u
3
+2u
2
+u−1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
−
4
3
u
5
+
2
3
u
4
+ ··· −
8
3
u −
5
3
0
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−
4
3
u
5
+
2
3
u
4
+ ··· −
8
3
u −
5
3
0
a
2
=
−
4
3
u
5
+
2
3
u
4
+ ··· −
11
3
u −
5
3
−u
3
+ u
a
5
=
u
u
3
− u
a
7
=
1
0
a
11
=
u
4
− 3u
2
+ 1
−u
4
+ 2u
2
a
6
=
−u
3
+ 2u
−u
5
+ 3u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
28
9
u
5
+
1
9
u
4
−
46
9
u
3
− u
2
−
34
9
u −
103
9
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
8
, c
9
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
6
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
10
, c
11
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
c
12
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
8
, c
9
c
12
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
c
6
, c
10
, c
11
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493180 + 0.575288I
a = 0.998450 + 0.400249I
b = 0
1.31531 + 1.97241I −11.11410 − 3.48248I
u = −0.493180 − 0.575288I
a = 0.998450 − 0.400249I
b = 0
1.31531 − 1.97241I −11.11410 + 3.48248I
u = 0.483672
a = −2.69889
b = 0
−2.38379 −13.9950
u = 1.52087 + 0.16310I
a = 0.421699 − 0.216810I
b = 0
−5.34051 − 4.59213I −13.8624 + 6.6392I
u = 1.52087 − 0.16310I
a = 0.421699 + 0.216810I
b = 0
−5.34051 + 4.59213I −13.8624 − 6.6392I
u = −1.53904
a = −0.474740
b = 0
−9.30502 −15.6070
18
III. I
u
3
=
h98a
5
+1413b+· · ·+948a−1845, a
6
−4a
5
+10a
4
−2a
3
−3a
2
−18a+27, u +1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
−1
a
9
=
1
1
a
1
=
1
0
a
4
=
a
−0.0693560a
5
+ 0.213730a
4
+ ··· − 0.670913a + 1.30573
a
10
=
0
1
a
3
=
−0.0693560a
5
+ 0.213730a
4
+ ··· + 0.329087a + 1.30573
−0.0693560a
5
+ 0.213730a
4
+ ··· − 0.670913a + 1.30573
a
2
=
−0.0863411a
5
+ 0.177636a
4
+ ··· − 0.188960a + 1.60510
−0.0226469a
5
+ 0.0629866a
4
+ ··· − 0.246285a − 1.26752
a
5
=
−0.0636943a
5
+ 0.114650a
4
+ ··· + 0.0573248a + 0.872611
−0.0226469a
5
+ 0.0629866a
4
+ ··· − 0.246285a − 1.26752
a
7
=
0.0636943a
5
− 0.114650a
4
+ ··· − 0.0573248a − 0.872611
0.0226469a
5
− 0.0629866a
4
+ ··· + 0.246285a + 1.26752
a
11
=
2
−0.122435a
5
+ 0.309271a
4
+ ··· + 0.543524a + 2.86624
a
6
=
−0.0636943a
5
+ 0.114650a
4
+ ··· + 0.0573248a + 0.872611
−0.0863411a
5
+ 0.177636a
4
+ ··· − 0.188960a − 0.394904
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
88
471
a
5
+
284
471
a
4
−
632
471
a
3
−
28
157
a
2
−
800
471
a −
896
157
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
(u
3
+ u
2
+ 2u + 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
10
c
11
(u
2
+ 2)
3
c
8
, c
9
(u + 1)
6
c
12
(u − 1)
6
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
, c
10
c
11
(y + 2)
6
c
8
, c
9
, c
12
(y −1)
6
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.930832 + 0.918189I
b = 0.215080 − 1.307140I
6.31400 + 2.82812I −8.49024 − 2.97945I
u = −1.00000
a = −0.930832 − 0.918189I
b = 0.215080 + 1.307140I
6.31400 − 2.82812I −8.49024 + 2.97945I
u = −1.00000
a = 1.175960 + 0.571534I
b = 0.215080 − 1.307140I
6.31400 + 2.82812I −8.49024 − 2.97945I
u = −1.00000
a = 1.175960 − 0.571534I
b = 0.215080 + 1.307140I
6.31400 − 2.82812I −8.49024 + 2.97945I
u = −1.00000
a = 1.75488 + 2.48177I
b = 0.569840
2.17641 −15.0195 + 0.I
u = −1.00000
a = 1.75488 − 2.48177I
b = 0.569840
2.17641 −15.0195 + 0.I
22
IV. I
u
4
= ha
2
+ b + 2a + 1, a
3
+ 2a
2
+ a + 1, u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
1
a
9
=
1
1
a
1
=
−1
0
a
4
=
a
−a
2
− 2a − 1
a
10
=
0
1
a
3
=
−a
2
− a − 1
−a
2
− 2a − 1
a
2
=
−a
2
− a − 1
−a
2
− a + 1
a
5
=
0
−a
2
− a + 1
a
7
=
0
−a
2
− a + 1
a
11
=
0
1
a
6
=
0
−a
2
− a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2a
2
− 6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
, c
10
c
11
u
3
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
9
(u − 1)
3
c
12
(u + 1)
3
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
y
3
− y
2
+ 2y −1
c
5
, c
6
, c
10
c
11
y
3
c
8
, c
9
, c
12
(y −1)
3
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.122561 + 0.744862I
b = −0.215080 − 1.307140I
1.37919 − 2.82812I −7.07960 − 0.36516I
u = 1.00000
a = −0.122561 − 0.744862I
b = −0.215080 + 1.307140I
1.37919 + 2.82812I −7.07960 + 0.36516I
u = 1.00000
a = −1.75488
b = −0.569840
−2.75839 0.159190
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
3
− u
2
+ 2u − 1)
3
(u
96
+ 46u
95
+ ··· + 6201u + 81)
c
2
((u − 1)
6
)(u
3
+ u
2
− 1)
3
(u
96
− 10u
95
+ ··· + 21u + 9)
c
3
u
6
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
96
+ 2u
95
+ ··· − 960u − 576)
c
4
((u + 1)
6
)(u
3
− u
2
+ 1)
3
(u
96
− 10u
95
+ ··· + 21u + 9)
c
5
u
3
(u
2
+ 2)
3
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
96
− 2u
95
+ ··· + 37784u − 17960)
c
6
u
3
(u
2
+ 2)
3
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
96
+ 2u
95
+ ··· − 40u − 8)
c
7
u
6
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ u
2
+ 2u + 1)(u
96
+ 2u
95
+ ··· − 960u − 576)
c
8
, c
9
(u − 1)
3
(u + 1)
6
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
96
+ 5u
95
+ ··· − 91u + 49)
c
10
, c
11
u
3
(u
2
+ 2)
3
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
96
+ 2u
95
+ ··· − 40u − 8)
c
12
(u − 1)
6
(u + 1)
3
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
96
+ 5u
95
+ ··· − 91u + 49)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
6
(y
3
+ 3y
2
+ 2y −1)
3
· (y
96
+ 18y
95
+ ··· − 35151813y + 6561)
c
2
, c
4
((y −1)
6
)(y
3
− y
2
+ 2y −1)
3
(y
96
− 46y
95
+ ··· − 6201y + 81)
c
3
, c
7
y
6
(y
3
+ 3y
2
+ 2y −1)
3
(y
96
+ 48y
95
+ ··· + 958464y + 331776)
c
5
y
3
(y + 2)
6
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
96
− 8y
95
+ ··· − 4744914496y + 322561600)
c
6
, c
10
, c
11
y
3
(y + 2)
6
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
· (y
96
+ 88y
95
+ ··· − 2240y + 64)
c
8
, c
9
, c
12
(y −1)
9
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
96
− 89y
95
+ ··· + 51009y + 2401)
28
