12a
0829
(K12a
0829
)
A knot diagram
1
Linearized knot diagam
4 5 8 2 10 12 3 11 7 1 9 6
Solving Sequence
3,8 4,11
9 12 7 10 6 1 5 2
c
3
c
8
c
11
c
7
c
9
c
6
c
12
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h7.15195 × 10
399
u
106
− 8.59095 × 10
399
u
105
+ ··· + 3.48006 × 10
400
b − 4.32470 × 10
402
,
3.78913 × 10
398
u
106
− 5.25909 × 10
398
u
105
+ ··· + 4.09419 × 10
399
a − 3.05225 × 10
401
,
u
107
− 2u
106
+ ··· − 512u + 512i
I
u
2
= h22u
2
+ 17b + 2u + 40, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
I
v
1
= ha, 14536v
8
+ 40690v
7
+ ··· + 11959b + 36034,
v
9
+ 3v
8
− 2v
7
− 9v
6
+ 11v
5
+ 25v
4
+ 6v
3
− 2v
2
+ 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 119 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
= h7.15 × 10
399
u
106
− 8.59 × 10
399
u
105
+ · · · + 3.48 × 10
400
b − 4.32 ×
10
402
, 3.79 × 10
398
u
106
− 5.26 × 10
398
u
105
+ · · · + 4.09 × 10
399
a − 3.05 ×
10
401
, u
107
− 2u
106
+ · · · − 512u + 512i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
−0.0925491u
106
+ 0.128453u
105
+ ··· + 27.8911u + 74.5508
−0.205512u
106
+ 0.246862u
105
+ ··· + 10.0191u + 124.271
a
9
=
−0.141762u
106
+ 0.160044u
105
+ ··· − 13.9980u + 76.5882
−0.0579410u
106
+ 0.0583727u
105
+ ··· − 24.6379u + 21.0757
a
12
=
−0.225565u
106
+ 0.289473u
105
+ ··· + 48.0564u + 157.554
−0.280106u
106
+ 0.347672u
105
+ ··· + 48.3843u + 184.903
a
7
=
u
u
a
10
=
−0.192530u
106
+ 0.222762u
105
+ ··· − 4.85824u + 110.365
−0.108709u
106
+ 0.121091u
105
+ ··· − 15.4981u + 54.8520
a
6
=
0.151786u
106
− 0.171743u
105
+ ··· + 15.7215u − 78.5804
0.00714381u
106
− 0.00235302u
105
+ ··· + 22.5669u + 5.72998
a
1
=
0.0917504u
106
− 0.139578u
105
+ ··· − 54.8541u − 83.2245
−0.0193726u
106
+ 0.0291699u
105
+ ··· + 7.73340u + 16.5814
a
5
=
−0.125588u
106
+ 0.200162u
105
+ ··· + 87.0752u + 122.294
−0.0338377u
106
+ 0.0605837u
105
+ ··· + 32.2211u + 39.0699
a
2
=
0.125588u
106
− 0.200162u
105
+ ··· − 87.0752u − 122.294
−0.0267303u
106
+ 0.0296535u
105
+ ··· − 5.96052u + 12.9504
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.991312u
106
− 1.30501u
105
+ ··· − 366.569u − 745.449
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
107
− 11u
106
+ ··· − u − 1
c
3
, c
7
u
107
− 2u
106
+ ··· − 512u + 512
c
5
u
107
+ 2u
106
+ ··· − 10404u + 2312
c
6
, c
12
u
107
+ 3u
106
+ ··· − 3u − 1
c
8
, c
11
u
107
− 5u
106
+ ··· − 5466u − 289
c
9
17(17u
107
+ 96u
106
+ ··· − 2.67194 × 10
8
u + 4.35330 × 10
7
)
c
10
17(17u
107
+ 61u
106
+ ··· + 4.98410 × 10
7
u − 2813417)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
107
− 99y
106
+ ··· − 29y −1
c
3
, c
7
y
107
− 54y
106
+ ··· + 7340032y −262144
c
5
y
107
− 18y
106
+ ··· + 277740560y −5345344
c
6
, c
12
y
107
+ 73y
106
+ ··· + 55y −1
c
8
, c
11
y
107
− 81y
106
+ ··· + 6093612y −83521
c
9
289(289y
107
− 19076y
106
+ ··· + 8.77063 × 10
16
y −1.89512 × 10
15
)
c
10
289
· (289y
107
− 7971y
106
+ ··· + 1153422073109755y −7915315215889)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.931265 + 0.406170I
a = 0.180524 + 0.102775I
b = −0.628756 + 1.070630I
−2.30486 + 1.44330I 0
u = −0.931265 − 0.406170I
a = 0.180524 − 0.102775I
b = −0.628756 − 1.070630I
−2.30486 − 1.44330I 0
u = 0.976707 + 0.115936I
a = 0.599235 + 0.941304I
b = 0.698962 − 0.236650I
−3.84509 + 1.95256I 0
u = 0.976707 − 0.115936I
a = 0.599235 − 0.941304I
b = 0.698962 + 0.236650I
−3.84509 − 1.95256I 0
u = −0.356416 + 0.955461I
a = −0.592799 + 0.220178I
b = −0.938545 + 0.461272I
−1.66924 − 1.97469I 0
u = −0.356416 − 0.955461I
a = −0.592799 − 0.220178I
b = −0.938545 − 0.461272I
−1.66924 + 1.97469I 0
u = −1.012720 + 0.132824I
a = 1.54325 + 0.67120I
b = 2.50954 + 0.63542I
−7.33756 + 0.07613I 0
u = −1.012720 − 0.132824I
a = 1.54325 − 0.67120I
b = 2.50954 − 0.63542I
−7.33756 − 0.07613I 0
u = −0.971497 + 0.327337I
a = 1.094850 + 0.029360I
b = 2.56859 + 0.95662I
−2.56341 + 2.94691I 0
u = −0.971497 − 0.327337I
a = 1.094850 − 0.029360I
b = 2.56859 − 0.95662I
−2.56341 − 2.94691I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.088254 + 0.953155I
a = 0.143294 + 1.178500I
b = 1.132480 − 0.334989I
−4.79638 + 0.98699I 0
u = 0.088254 − 0.953155I
a = 0.143294 − 1.178500I
b = 1.132480 + 0.334989I
−4.79638 − 0.98699I 0
u = 0.933039 + 0.143215I
a = −0.494644 − 1.048140I
b = −0.343321 − 1.127840I
−3.78091 − 2.99219I 0
u = 0.933039 − 0.143215I
a = −0.494644 + 1.048140I
b = −0.343321 + 1.127840I
−3.78091 + 2.99219I 0
u = −0.431800 + 0.976154I
a = −0.668560 − 0.913554I
b = −0.428460 + 0.364883I
−3.77986 + 4.80948I 0
u = −0.431800 − 0.976154I
a = −0.668560 + 0.913554I
b = −0.428460 − 0.364883I
−3.77986 − 4.80948I 0
u = 0.228518 + 0.892361I
a = −0.264082 + 0.338861I
b = 0.70974 + 1.40915I
−4.76982 − 0.36186I 0
u = 0.228518 − 0.892361I
a = −0.264082 − 0.338861I
b = 0.70974 − 1.40915I
−4.76982 + 0.36186I 0
u = −0.092471 + 1.078070I
a = −0.44549 + 1.54366I
b = −0.620069 + 0.456648I
−9.17182 − 2.19773I 0
u = −0.092471 − 1.078070I
a = −0.44549 − 1.54366I
b = −0.620069 − 0.456648I
−9.17182 + 2.19773I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.889247 + 0.203541I
a = −1.189030 + 0.430620I
b = −2.69411 − 0.64847I
−2.97691 − 0.95326I 0
u = 0.889247 − 0.203541I
a = −1.189030 − 0.430620I
b = −2.69411 + 0.64847I
−2.97691 + 0.95326I 0
u = −0.242919 + 0.867268I
a = 0.10892 − 1.53983I
b = 0.090572 + 0.409338I
−4.39157 − 8.45275I 0
u = −0.242919 − 0.867268I
a = 0.10892 + 1.53983I
b = 0.090572 − 0.409338I
−4.39157 + 8.45275I 0
u = 1.061410 + 0.301435I
a = −1.53828 − 0.25745I
b = −2.67895 + 0.02396I
−6.91732 − 4.41662I 0
u = 1.061410 − 0.301435I
a = −1.53828 + 0.25745I
b = −2.67895 − 0.02396I
−6.91732 + 4.41662I 0
u = 0.304573 + 1.063250I
a = 0.997292 + 0.520611I
b = 1.080310 + 0.440969I
−5.05564 + 5.39819I 0
u = 0.304573 − 1.063250I
a = 0.997292 − 0.520611I
b = 1.080310 − 0.440969I
−5.05564 − 5.39819I 0
u = −0.870663 + 0.176776I
a = −0.973907 + 0.679642I
b = −0.531737 − 0.185116I
−0.72189 + 2.74860I 0
u = −0.870663 − 0.176776I
a = −0.973907 − 0.679642I
b = −0.531737 + 0.185116I
−0.72189 − 2.74860I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.015450 + 0.504665I
a = −0.241834 − 0.639622I
b = −0.171049 − 0.300765I
1.09835 − 3.92237I 0
u = 1.015450 − 0.504665I
a = −0.241834 + 0.639622I
b = −0.171049 + 0.300765I
1.09835 + 3.92237I 0
u = 0.526835 + 0.664073I
a = 0.813713 + 0.084744I
b = 0.649668 + 0.235899I
2.60177 − 0.62792I 0
u = 0.526835 − 0.664073I
a = 0.813713 − 0.084744I
b = 0.649668 − 0.235899I
2.60177 + 0.62792I 0
u = −1.076720 + 0.464977I
a = 0.552748 − 0.958127I
b = 0.796377 − 0.842288I
−2.37272 + 7.54825I 0
u = −1.076720 − 0.464977I
a = 0.552748 + 0.958127I
b = 0.796377 + 0.842288I
−2.37272 − 7.54825I 0
u = −0.733065 + 0.330340I
a = 0.064198 − 0.514775I
b = −0.374792 − 0.363000I
−0.769990 − 0.237218I −8.00000 − 1.04777I
u = −0.733065 − 0.330340I
a = 0.064198 + 0.514775I
b = −0.374792 + 0.363000I
−0.769990 + 0.237218I −8.00000 + 1.04777I
u = 0.716753 + 0.360053I
a = −1.124690 + 0.448670I
b = 3.46273 − 0.61131I
−3.50386 − 1.66896I −16.6348 − 15.7652I
u = 0.716753 − 0.360053I
a = −1.124690 − 0.448670I
b = 3.46273 + 0.61131I
−3.50386 + 1.66896I −16.6348 + 15.7652I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.092779 + 0.786586I
a = −0.268044 − 1.184120I
b = −0.075212 + 0.508676I
0.99398 + 2.92097I −2.14055 − 8.38546I
u = 0.092779 − 0.786586I
a = −0.268044 + 1.184120I
b = −0.075212 − 0.508676I
0.99398 − 2.92097I −2.14055 + 8.38546I
u = 0.758308 + 0.133029I
a = −0.372777 + 0.723023I
b = 0.63345 + 1.29744I
−3.58750 + 2.31232I −15.8918 − 2.7555I
u = 0.758308 − 0.133029I
a = −0.372777 − 0.723023I
b = 0.63345 − 1.29744I
−3.58750 − 2.31232I −15.8918 + 2.7555I
u = 0.722730 + 0.161926I
a = 1.58847 + 0.40979I
b = 0.337724 − 0.130488I
−5.80226 − 7.40735I −18.9937 + 9.1512I
u = 0.722730 − 0.161926I
a = 1.58847 − 0.40979I
b = 0.337724 + 0.130488I
−5.80226 + 7.40735I −18.9937 − 9.1512I
u = 1.232030 + 0.307377I
a = −0.310429 + 0.667179I
b = 0.154826 − 0.286118I
−6.76847 − 1.51759I 0
u = 1.232030 − 0.307377I
a = −0.310429 − 0.667179I
b = 0.154826 + 0.286118I
−6.76847 + 1.51759I 0
u = −0.393537 + 0.609625I
a = −1.165490 + 0.721828I
b = −0.669946 + 0.274768I
−0.31883 − 3.28324I −5.60431 + 3.66597I
u = −0.393537 − 0.609625I
a = −1.165490 − 0.721828I
b = −0.669946 − 0.274768I
−0.31883 + 3.28324I −5.60431 − 3.66597I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.212990 + 0.397926I
a = 0.623595 + 0.309847I
b = −0.39774 − 2.98122I
−8.99268 + 4.16407I 0
u = −1.212990 − 0.397926I
a = 0.623595 − 0.309847I
b = −0.39774 + 2.98122I
−8.99268 − 4.16407I 0
u = 1.242800 + 0.298457I
a = 1.168920 + 0.075796I
b = 2.89703 + 0.03063I
−9.14754 − 8.24261I 0
u = 1.242800 − 0.298457I
a = 1.168920 − 0.075796I
b = 2.89703 − 0.03063I
−9.14754 + 8.24261I 0
u = −0.141063 + 1.304170I
a = −0.115873 − 0.757239I
b = −0.172892 + 0.880125I
1.38178 + 2.91494I 0
u = −0.141063 − 1.304170I
a = −0.115873 + 0.757239I
b = −0.172892 − 0.880125I
1.38178 − 2.91494I 0
u = 1.204720 + 0.538302I
a = −0.224257 − 0.099675I
b = 0.245011 + 1.036330I
−7.84058 − 4.80609I 0
u = 1.204720 − 0.538302I
a = −0.224257 + 0.099675I
b = 0.245011 − 1.036330I
−7.84058 + 4.80609I 0
u = −1.309760 + 0.270121I
a = 0.371792 + 1.058620I
b = 0.086820 + 0.488872I
−10.74750 − 1.26365I 0
u = −1.309760 − 0.270121I
a = 0.371792 − 1.058620I
b = 0.086820 − 0.488872I
−10.74750 + 1.26365I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.271700 + 0.434265I
a = 0.883155 − 0.416545I
b = 2.30508 − 0.40191I
−8.58798 + 4.36356I 0
u = 1.271700 − 0.434265I
a = 0.883155 + 0.416545I
b = 2.30508 + 0.40191I
−8.58798 − 4.36356I 0
u = −1.275970 + 0.428836I
a = 0.870350 + 0.396090I
b = 2.57554 − 0.73466I
−9.07128 + 3.71874I 0
u = −1.275970 − 0.428836I
a = 0.870350 − 0.396090I
b = 2.57554 + 0.73466I
−9.07128 − 3.71874I 0
u = 0.441267 + 1.276080I
a = 0.010079 − 1.136560I
b = −0.075031 + 0.587350I
−10.4011 + 11.2730I 0
u = 0.441267 − 1.276080I
a = 0.010079 + 1.136560I
b = −0.075031 − 0.587350I
−10.4011 − 11.2730I 0
u = −1.230600 + 0.564328I
a = −1.137020 − 0.087814I
b = −2.86197 − 0.20383I
−7.4189 + 13.7965I 0
u = −1.230600 − 0.564328I
a = −1.137020 + 0.087814I
b = −2.86197 + 0.20383I
−7.4189 − 13.7965I 0
u = −1.323420 + 0.286711I
a = −0.914417 − 0.024510I
b = −2.58390 + 0.00153I
−4.18081 + 2.37986I 0
u = −1.323420 − 0.286711I
a = −0.914417 + 0.024510I
b = −2.58390 − 0.00153I
−4.18081 − 2.37986I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.278700 + 0.503687I
a = −0.908905 + 0.010734I
b = −2.44601 + 0.82010I
−8.52536 − 6.22901I 0
u = 1.278700 − 0.503687I
a = −0.908905 − 0.010734I
b = −2.44601 − 0.82010I
−8.52536 + 6.22901I 0
u = −1.232670 + 0.616020I
a = 0.285190 − 0.632161I
b = 0.364306 − 0.134856I
−4.44227 + 7.78550I 0
u = −1.232670 − 0.616020I
a = 0.285190 + 0.632161I
b = 0.364306 + 0.134856I
−4.44227 − 7.78550I 0
u = 1.267260 + 0.549056I
a = 0.938331 − 0.109314I
b = 2.60437 − 0.08018I
−2.55413 − 8.13238I 0
u = 1.267260 − 0.549056I
a = 0.938331 + 0.109314I
b = 2.60437 + 0.08018I
−2.55413 + 8.13238I 0
u = −0.613234
a = 0.343678
b = −0.360765
−0.940432 −9.73200
u = −0.429164 + 1.329720I
a = −0.068472 − 0.921024I
b = −0.098161 + 0.749867I
−5.51395 − 5.51248I 0
u = −0.429164 − 1.329720I
a = −0.068472 + 0.921024I
b = −0.098161 − 0.749867I
−5.51395 + 5.51248I 0
u = −0.397402 + 0.438020I
a = 1.19302 + 1.61741I
b = 0.57156 + 4.09559I
−5.90093 − 0.77524I −7.20009 − 8.79210I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.397402 − 0.438020I
a = 1.19302 − 1.61741I
b = 0.57156 − 4.09559I
−5.90093 + 0.77524I −7.20009 + 8.79210I
u = 1.349340 + 0.415520I
a = −1.217360 + 0.693262I
b = −2.01551 + 0.42109I
−13.9537 − 2.9601I 0
u = 1.349340 − 0.415520I
a = −1.217360 − 0.693262I
b = −2.01551 − 0.42109I
−13.9537 + 2.9601I 0
u = 1.27824 + 0.62370I
a = −0.527044 − 0.887663I
b = −0.860085 − 0.585152I
−8.16809 − 11.50410I 0
u = 1.27824 − 0.62370I
a = −0.527044 + 0.887663I
b = −0.860085 + 0.585152I
−8.16809 + 11.50410I 0
u = −0.288463 + 0.497708I
a = 0.665687 − 0.559774I
b = −0.203916 + 0.598819I
−0.62747 + 1.89102I −3.97049 − 2.88595I
u = −0.288463 − 0.497708I
a = 0.665687 + 0.559774I
b = −0.203916 − 0.598819I
−0.62747 − 1.89102I −3.97049 + 2.88595I
u = −1.33200 + 0.52311I
a = 1.312210 − 0.185097I
b = 2.36998 + 0.15644I
−13.1732 + 7.9062I 0
u = −1.33200 − 0.52311I
a = 1.312210 + 0.185097I
b = 2.36998 − 0.15644I
−13.1732 − 7.9062I 0
u = 0.55234 + 1.32267I
a = 0.388265 − 0.819153I
b = 0.481113 + 0.580917I
−9.67010 − 1.15397I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.55234 − 1.32267I
a = 0.388265 + 0.819153I
b = 0.481113 − 0.580917I
−9.67010 + 1.15397I 0
u = −1.29769 + 0.65667I
a = −0.767810 − 0.380695I
b = −2.13616 − 0.22858I
−6.46600 + 1.47782I 0
u = −1.29769 − 0.65667I
a = −0.767810 + 0.380695I
b = −2.13616 + 0.22858I
−6.46600 − 1.47782I 0
u = 1.31949 + 0.75319I
a = 1.044930 − 0.147670I
b = 2.73164 − 0.27623I
−13.2708 − 18.4610I 0
u = 1.31949 − 0.75319I
a = 1.044930 + 0.147670I
b = 2.73164 + 0.27623I
−13.2708 + 18.4610I 0
u = −1.34268 + 0.75552I
a = −0.894702 − 0.162317I
b = −2.54796 − 0.12017I
−8.5253 + 12.8531I 0
u = −1.34268 − 0.75552I
a = −0.894702 + 0.162317I
b = −2.54796 + 0.12017I
−8.5253 − 12.8531I 0
u = −0.399946 + 0.214162I
a = 1.30736 + 1.02540I
b = −0.415975 + 0.038938I
−1.063250 − 0.043134I −7.94611 − 1.24147I
u = −0.399946 − 0.214162I
a = 1.30736 − 1.02540I
b = −0.415975 − 0.038938I
−1.063250 + 0.043134I −7.94611 + 1.24147I
u = 0.149223 + 0.396575I
a = 0.01530 + 3.13817I
b = 0.294661 + 0.448912I
−4.49140 + 1.51008I −9.81598 − 1.55694I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.149223 − 0.396575I
a = 0.01530 − 3.13817I
b = 0.294661 − 0.448912I
−4.49140 − 1.51008I −9.81598 + 1.55694I
u = 1.35595 + 0.81241I
a = 0.749963 − 0.331925I
b = 2.15867 − 0.11610I
−12.32240 − 6.52710I 0
u = 1.35595 − 0.81241I
a = 0.749963 + 0.331925I
b = 2.15867 + 0.11610I
−12.32240 + 6.52710I 0
u = −1.61146 + 0.03604I
a = −0.948244 − 0.190754I
b = −2.56392 − 0.11689I
−18.4193 − 6.1353I 0
u = −1.61146 − 0.03604I
a = −0.948244 + 0.190754I
b = −2.56392 + 0.11689I
−18.4193 + 6.1353I 0
u = 1.65879
a = 0.839440
b = 2.53074
−13.8071 0
u = 0.315785
a = −2.96408
b = −4.94665
−3.02083 −69.6120
15
II. I
u
2
= h22u
2
+ 17b + 2u + 40, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
−u
2
+ u − 2
−
22
17
u
2
−
2
17
u −
40
17
a
9
=
−u
2
+ u − 2
−
22
17
u
2
+
15
17
u −
40
17
a
12
=
0
−u
a
7
=
u
u
a
10
=
−
14
17
u
2
+
8
17
u −
27
17
−
19
17
u
2
+
6
17
u −
33
17
a
6
=
u
u
2
− u + 1
a
1
=
−u
2
+ 2u − 1
u
2
− 2u
a
5
=
u
u
2
− u + 1
a
2
=
u
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2667
289
u
2
−
10925
289
u +
2721
289
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
3
+ u
2
− 1
c
3
u
3
− u
2
+ 2u − 1
c
4
u
3
− u
2
+ 1
c
5
u
3
c
6
u
3
− 3u
2
+ 2u + 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
(u − 1)
3
c
9
17(17u
3
+ 10u
2
− u − 1)
c
10
17(17u
3
− 23u
2
+ 8u − 1)
c
11
(u + 1)
3
c
12
u
3
+ 3u
2
+ 2u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
3
− y
2
+ 2y −1
c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
5
y
3
c
6
, c
12
y
3
− 5y
2
+ 10y −1
c
8
, c
11
(y −1)
3
c
9
289(289y
3
− 134y
2
+ 21y −1)
c
10
289(289y
3
− 257y
2
+ 18y −1)
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.122561 + 0.744862I
b = −0.226957 − 0.881437I
1.37919 − 2.82812I −14.0563 − 44.2246I
u = 0.215080 − 1.307140I
a = −0.122561 − 0.744862I
b = −0.226957 + 0.881437I
1.37919 + 2.82812I −14.0563 + 44.2246I
u = 0.569840
a = −1.75488
b = −2.84020
−2.75839 −9.12970
19
III.
I
v
1
= ha, 14536v
8
+ 40690v
7
+ · · · + 11959b + 36034, v
9
+ 3v
8
+ · · · + 3v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
11
=
0
−1.21549v
8
− 3.40246v
7
+ ··· − 0.204281v −3.01313
a
9
=
v
−0.917468v
8
− 2.75040v
7
+ ··· − 1.68777v −2.76913
a
12
=
0.298018v
8
+ 0.652061v
7
+ ··· − 0.483485v + 0.244000
−0.705410v
8
− 1.67138v
7
+ ··· + 2.87842v −0.490008
a
7
=
v
0
a
10
=
0.109374v
8
+ 0.367255v
7
+ ··· + 0.0885526v + 0.00200686
−0.917468v
8
− 2.75040v
7
+ ··· − 1.68777v −2.76913
a
6
=
−0.120495v
8
− 0.294506v
7
+ ··· + 0.670792v + 0.0803579
0.198846v
8
+ 0.759428v
7
+ ··· + 1.00962v −0.427544
a
1
=
−0.244000v
8
− 0.433983v
7
+ ··· − 0.633331v −0.215486
−1
a
5
=
0.244000v
8
+ 0.433983v
7
+ ··· + 0.633331v + 0.215486
1
a
2
=
−0.244000v
8
− 0.433983v
7
+ ··· − 0.633331v + 0.784514
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
30669
11959
v
8
+
76868
11959
v
7
−
100871
11959
v
6
−
237835
11959
v
5
+
437462
11959
v
4
+
579948
11959
v
3
−
66654
11959
v
2
−
147944
11959
v −
72837
11959
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
, c
10
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
8
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
9
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ 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
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
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
8
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
9
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.924205 + 0.223068I
a = 0
b = −0.037875 + 0.791187I
−2.26187 + 2.45442I −8.53903 − 2.82066I
v = −0.924205 − 0.223068I
a = 0
b = −0.037875 − 0.791187I
−2.26187 − 2.45442I −8.53903 + 2.82066I
v = 0.295822 + 0.390531I
a = 0
b = 0.80973 − 2.39258I
−6.01628 + 1.33617I −16.4774 − 4.4812I
v = 0.295822 − 0.390531I
a = 0
b = 0.80973 + 2.39258I
−6.01628 − 1.33617I −16.4774 + 4.4812I
v = −0.280601
a = 0
b = −2.94345
−2.84338 −3.87310
v = 1.47927 + 0.93319I
a = 0
b = −0.218072 + 0.482572I
0.13850 + 2.09337I −6.02684 − 1.69698I
v = 1.47927 − 0.93319I
a = 0
b = −0.218072 − 0.482572I
0.13850 − 2.09337I −6.02684 + 1.69698I
v = −2.21059 + 0.69487I
a = 0
b = 0.417942 + 0.357732I
−5.24306 − 7.08493I −9.02021 + 2.94778I
v = −2.21059 − 0.69487I
a = 0
b = 0.417942 − 0.357732I
−5.24306 + 7.08493I −9.02021 − 2.94778I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
9
)(u
3
+ u
2
− 1)(u
107
− 11u
106
+ ··· − u − 1)
c
3
u
9
(u
3
− u
2
+ 2u − 1)(u
107
− 2u
106
+ ··· − 512u + 512)
c
4
((u + 1)
9
)(u
3
− u
2
+ 1)(u
107
− 11u
106
+ ··· − u − 1)
c
5
u
3
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
107
+ 2u
106
+ ··· − 10404u + 2312)
c
6
(u
3
− 3u
2
+ 2u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
107
+ 3u
106
+ ··· − 3u − 1)
c
7
u
9
(u
3
+ u
2
+ 2u + 1)(u
107
− 2u
106
+ ··· − 512u + 512)
c
8
(u − 1)
3
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
107
− 5u
106
+ ··· − 5466u − 289)
c
9
289(17u
3
+ 10u
2
− u − 1)
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (17u
107
+ 96u
106
+ ··· − 267194040u + 43532959)
c
10
289(17u
3
− 23u
2
+ 8u − 1)(u
9
+ u
8
+ ··· + u − 1)
· (17u
107
+ 61u
106
+ ··· + 49840983u − 2813417)
c
11
(u + 1)
3
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
107
− 5u
106
+ ··· − 5466u − 289)
c
12
(u
3
+ 3u
2
+ 2u − 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
107
+ 3u
106
+ ··· − 3u − 1)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
9
)(y
3
− y
2
+ 2y −1)(y
107
− 99y
106
+ ··· − 29y −1)
c
3
, c
7
y
9
(y
3
+ 3y
2
+ 2y −1)(y
107
− 54y
106
+ ··· + 7340032y −262144)
c
5
y
3
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
107
− 18y
106
+ ··· + 277740560y −5345344)
c
6
, c
12
(y
3
− 5y
2
+ 10y −1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
107
+ 73y
106
+ ··· + 55y −1)
c
8
, c
11
(y −1)
3
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
107
− 81y
106
+ ··· + 6093612y −83521)
c
9
83521(289y
3
− 134y
2
+ 21y −1)
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (289y
107
− 1.91 × 10
4
y
106
+ ··· + 8.77 × 10
16
y −1.90 × 10
15
)
c
10
83521(289y
3
− 257y
2
+ 18y −1)
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (289y
107
− 7971y
106
+ ··· + 1153422073109755y −7915315215889)
25
