12a
0395
(K12a
0395
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 10 1 12 5 7 4 8
Solving Sequence
8,12
9
1,4
3 2 7 11 5 10 6
c
8
c
12
c
3
c
1
c
7
c
11
c
4
c
10
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.65404 × 10
344
u
118
− 3.71960 × 10
344
u
117
+ ··· + 1.51948 × 10
345
b − 8.39541 × 10
345
,
− 4.85729 × 10
345
u
118
− 1.06056 × 10
346
u
117
+ ··· + 1.51948 × 10
345
a + 4.54469 × 10
346
,
u
119
+ 2u
118
+ ··· − 26u + 1i
I
u
2
= h−u
27
+ 18u
26
+ ··· + b + 13, −5u
26
+ 5u
25
+ ··· + a − 5, u
28
− u
27
+ ··· + 6u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 147 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
= h2.65 × 10
344
u
118
− 3.72 × 10
344
u
117
+ · · · + 1.52 × 10
345
b − 8.40 ×
10
345
, −4.86 × 10
345
u
118
− 1.06 × 10
346
u
117
+ · · · + 1.52 × 10
345
a + 4.54 ×
10
346
, u
119
+ 2u
118
+ · · · − 26u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
4
=
3.19669u
118
+ 6.97979u
117
+ ··· + 513.032u − 29.9096
−0.174668u
118
+ 0.244795u
117
+ ··· − 62.1195u + 5.52519
a
3
=
3.45928u
118
+ 7.64632u
117
+ ··· + 563.101u − 34.8483
−0.208279u
118
+ 0.424943u
117
+ ··· − 65.5319u + 5.66654
a
2
=
−1.55048u
118
− 3.05586u
117
+ ··· − 520.403u + 40.2446
0.373680u
118
+ 0.462149u
117
+ ··· − 61.8390u + 3.46753
a
7
=
u
2
+ 1
u
2
a
11
=
−3.38646u
118
− 6.55223u
117
+ ··· − 668.355u + 47.2932
−0.293160u
118
+ 0.510861u
117
+ ··· − 51.3704u + 2.09553
a
5
=
1.68383u
118
+ 3.07028u
117
+ ··· + 512.719u − 38.2522
−0.497398u
118
− 1.60028u
117
+ ··· + 16.7133u − 0.0504918
a
10
=
−3.52942u
118
− 7.11188u
117
+ ··· − 628.685u + 45.7434
−1.04054u
118
− 1.58837u
117
+ ··· − 43.3753u + 1.76478
a
6
=
1.84545u
118
+ 3.19677u
117
+ ··· + 336.654u − 40.3459
0.339358u
118
− 0.259898u
117
+ ··· + 120.671u − 6.71138
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.64123u
118
− 5.23612u
117
+ ··· − 267.516u + 30.7025
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
119
+ 51u
118
+ ··· + 26772u + 361
c
2
, c
5
u
119
+ 7u
118
+ ··· − 208u − 19
c
3
u
119
− u
118
+ ··· − 25185412u − 11522837
c
4
, c
11
u
119
− 3u
118
+ ··· − 2732u − 8803
c
6
, c
10
u
119
+ 3u
118
+ ··· − 4107u − 2939
c
7
, c
8
, c
12
u
119
− 2u
118
+ ··· − 26u − 1
c
9
u
119
+ u
118
+ ··· + 8910u − 1089
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
119
+ 49y
118
+ ··· + 68785416y −130321
c
2
, c
5
y
119
− 51y
118
+ ··· + 26772y −361
c
3
y
119
+ 43y
118
+ ··· − 5505345069862148y −132775772528569
c
4
, c
11
y
119
+ 95y
118
+ ··· − 90407930y −77492809
c
6
, c
10
y
119
− 75y
118
+ ··· + 495977351y −8637721
c
7
, c
8
, c
12
y
119
+ 120y
118
+ ··· + 210y −1
c
9
y
119
− 13y
118
+ ··· − 26164314y −1185921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.355122 + 0.928118I
a = 0.550756 − 0.398938I
b = 1.14338 − 0.84841I
3.73858 + 1.09865I 0
u = 0.355122 − 0.928118I
a = 0.550756 + 0.398938I
b = 1.14338 + 0.84841I
3.73858 − 1.09865I 0
u = 0.437780 + 0.889964I
a = −0.413334 + 0.259923I
b = −1.15550 + 0.89782I
2.52193 − 4.36091I 0
u = 0.437780 − 0.889964I
a = −0.413334 − 0.259923I
b = −1.15550 − 0.89782I
2.52193 + 4.36091I 0
u = −0.845759 + 0.501522I
a = 1.092950 − 0.875220I
b = 0.953716 + 0.274130I
1.93927 − 7.77593I 0
u = −0.845759 − 0.501522I
a = 1.092950 + 0.875220I
b = 0.953716 − 0.274130I
1.93927 + 7.77593I 0
u = 0.875445 + 0.381861I
a = 0.405474 + 1.234410I
b = 0.313119 − 0.353758I
−2.76497 − 2.55600I 0
u = 0.875445 − 0.381861I
a = 0.405474 − 1.234410I
b = 0.313119 + 0.353758I
−2.76497 + 2.55600I 0
u = −0.705215 + 0.782711I
a = −1.117440 + 0.448086I
b = −1.055030 − 0.080011I
−4.11674 − 5.83144I 0
u = −0.705215 − 0.782711I
a = −1.117440 − 0.448086I
b = −1.055030 + 0.080011I
−4.11674 + 5.83144I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.757241 + 0.738794I
a = 0.530380 − 0.966180I
b = 0.964868 − 0.113031I
1.31392 + 2.27943I 0
u = −0.757241 − 0.738794I
a = 0.530380 + 0.966180I
b = 0.964868 + 0.113031I
1.31392 − 2.27943I 0
u = −0.951437 + 0.538602I
a = −0.954025 + 0.834561I
b = −1.006380 − 0.310638I
0.09823 − 13.43470I 0
u = −0.951437 − 0.538602I
a = −0.954025 − 0.834561I
b = −1.006380 + 0.310638I
0.09823 + 13.43470I 0
u = 0.695269 + 0.547167I
a = 1.12801 + 0.86039I
b = 1.313030 + 0.247781I
−3.35283 + 7.39480I 0
u = 0.695269 − 0.547167I
a = 1.12801 − 0.86039I
b = 1.313030 − 0.247781I
−3.35283 − 7.39480I 0
u = 1.112250 + 0.084793I
a = 0.065711 + 1.222590I
b = 0.053847 − 0.423809I
−3.19379 + 1.91472I 0
u = 1.112250 − 0.084793I
a = 0.065711 − 1.222590I
b = 0.053847 + 0.423809I
−3.19379 − 1.91472I 0
u = −1.081990 + 0.417768I
a = −0.237717 + 0.919197I
b = −0.527929 − 0.155026I
−2.65576 − 0.04297I 0
u = −1.081990 − 0.417768I
a = −0.237717 − 0.919197I
b = −0.527929 + 0.155026I
−2.65576 + 0.04297I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.641878 + 0.455011I
a = −1.12839 − 1.00439I
b = −1.134130 − 0.121220I
−1.97592 + 2.57078I 0
u = 0.641878 − 0.455011I
a = −1.12839 + 1.00439I
b = −1.134130 + 0.121220I
−1.97592 − 2.57078I 0
u = 0.675053 + 0.328204I
a = 1.136430 − 0.608303I
b = 0.237290 + 0.356326I
4.09882 + 8.36988I 0
u = 0.675053 − 0.328204I
a = 1.136430 + 0.608303I
b = 0.237290 − 0.356326I
4.09882 − 8.36988I 0
u = 0.634326 + 0.392829I
a = −0.81207 − 1.22851I
b = −0.611921 + 0.198271I
−1.91605 + 1.49481I 0
u = 0.634326 − 0.392829I
a = −0.81207 + 1.22851I
b = −0.611921 − 0.198271I
−1.91605 − 1.49481I 0
u = −0.240172 + 1.238760I
a = −0.556332 + 0.086031I
b = −0.113358 + 1.141540I
−0.726114 − 0.980196I 0
u = −0.240172 − 1.238760I
a = −0.556332 − 0.086031I
b = −0.113358 − 1.141540I
−0.726114 + 0.980196I 0
u = −0.484304 + 0.554618I
a = −0.606336 − 0.560699I
b = −0.616895 + 0.079272I
0.41624 − 4.00939I 0
u = −0.484304 − 0.554618I
a = −0.606336 + 0.560699I
b = −0.616895 − 0.079272I
0.41624 + 4.00939I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.264408 + 1.242480I
a = 0.477396 − 0.193983I
b = −0.348744 − 0.889733I
−1.11104 − 6.19546I 0
u = −0.264408 − 1.242480I
a = 0.477396 + 0.193983I
b = −0.348744 + 0.889733I
−1.11104 + 6.19546I 0
u = −0.964873 + 0.827467I
a = −0.468445 + 0.848498I
b = −0.992484 − 0.116628I
−0.55827 + 7.05368I 0
u = −0.964873 − 0.827467I
a = −0.468445 − 0.848498I
b = −0.992484 + 0.116628I
−0.55827 − 7.05368I 0
u = 0.095017 + 1.278750I
a = −0.650456 − 0.592085I
b = −0.693055 + 0.490549I
−1.97975 − 4.57227I 0
u = 0.095017 − 1.278750I
a = −0.650456 + 0.592085I
b = −0.693055 − 0.490549I
−1.97975 + 4.57227I 0
u = −0.225905 + 1.265030I
a = −0.537859 − 0.450634I
b = −0.724965 + 0.412460I
−1.26041 − 0.68479I 0
u = −0.225905 − 1.265030I
a = −0.537859 + 0.450634I
b = −0.724965 − 0.412460I
−1.26041 + 0.68479I 0
u = −0.699562 + 0.012160I
a = 0.572503 − 0.802595I
b = 0.331384 − 0.700904I
2.66598 + 2.68142I 0
u = −0.699562 − 0.012160I
a = 0.572503 + 0.802595I
b = 0.331384 + 0.700904I
2.66598 − 2.68142I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.453308 + 0.523255I
a = −1.017620 − 0.478761I
b = −0.985184 + 0.688651I
−1.41515 + 1.44928I 0
u = 0.453308 − 0.523255I
a = −1.017620 + 0.478761I
b = −0.985184 − 0.688651I
−1.41515 − 1.44928I 0
u = 0.428626 + 0.530864I
a = 1.64427 + 0.93701I
b = 0.865572 + 0.646236I
−6.41806 + 1.42312I 0
u = 0.428626 − 0.530864I
a = 1.64427 − 0.93701I
b = 0.865572 − 0.646236I
−6.41806 − 1.42312I 0
u = −0.305414 + 0.597967I
a = 0.95867 − 1.19353I
b = 1.014210 − 0.576340I
1.23996 + 1.80948I 6.00000 + 0.I
u = −0.305414 − 0.597967I
a = 0.95867 + 1.19353I
b = 1.014210 + 0.576340I
1.23996 − 1.80948I 6.00000 + 0.I
u = 0.623047 + 0.229109I
a = −1.41218 + 0.62072I
b = −0.188966 − 0.236767I
5.77681 + 2.48293I 12.94457 − 3.64631I
u = 0.623047 − 0.229109I
a = −1.41218 − 0.62072I
b = −0.188966 + 0.236767I
5.77681 − 2.48293I 12.94457 + 3.64631I
u = −0.565817 + 0.318993I
a = 0.626424 + 0.495344I
b = 0.530615 + 0.076115I
1.123500 + 0.392328I 10.23388 + 0.I
u = −0.565817 − 0.318993I
a = 0.626424 − 0.495344I
b = 0.530615 − 0.076115I
1.123500 − 0.392328I 10.23388 + 0.I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.230407 + 1.346620I
a = 0.081429 − 0.280356I
b = −0.329335 − 0.132775I
−3.97108 − 2.43584I 0
u = −0.230407 − 1.346620I
a = 0.081429 + 0.280356I
b = −0.329335 + 0.132775I
−3.97108 + 2.43584I 0
u = −0.071954 + 1.381730I
a = −0.149743 − 0.485375I
b = −0.590332 − 0.059182I
−3.85572 − 1.71095I 0
u = −0.071954 − 1.381730I
a = −0.149743 + 0.485375I
b = −0.590332 + 0.059182I
−3.85572 + 1.71095I 0
u = −0.185869 + 1.371190I
a = 0.560257 + 0.491962I
b = 0.755665 − 0.451477I
−1.51610 − 4.94231I 0
u = −0.185869 − 1.371190I
a = 0.560257 − 0.491962I
b = 0.755665 + 0.451477I
−1.51610 + 4.94231I 0
u = 0.022030 + 1.384840I
a = 1.283010 − 0.173050I
b = 3.44123 + 0.33674I
−5.42143 + 3.44426I 0
u = 0.022030 − 1.384840I
a = 1.283010 + 0.173050I
b = 3.44123 − 0.33674I
−5.42143 − 3.44426I 0
u = −0.611413 + 0.036672I
a = −0.625202 + 1.115140I
b = −0.071919 + 0.898469I
2.99131 − 2.19855I 11.46185 + 4.70957I
u = −0.611413 − 0.036672I
a = −0.625202 − 1.115140I
b = −0.071919 − 0.898469I
2.99131 + 2.19855I 11.46185 − 4.70957I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.009442 + 1.389940I
a = 0.597050 + 0.553267I
b = 0.726809 − 0.497772I
−1.90973 − 0.74900I 0
u = 0.009442 − 1.389940I
a = 0.597050 − 0.553267I
b = 0.726809 + 0.497772I
−1.90973 + 0.74900I 0
u = 0.068252 + 1.395030I
a = 0.799590 − 0.024691I
b = 4.16098 − 0.65705I
−2.63776 + 7.11139I 0
u = 0.068252 − 1.395030I
a = 0.799590 + 0.024691I
b = 4.16098 + 0.65705I
−2.63776 − 7.11139I 0
u = 0.019788 + 1.405330I
a = −0.787884 + 0.025430I
b = −3.83254 + 1.05902I
−2.12066 + 1.34209I 0
u = 0.019788 − 1.405330I
a = −0.787884 − 0.025430I
b = −3.83254 − 1.05902I
−2.12066 − 1.34209I 0
u = 0.178838 + 1.397610I
a = 0.280190 − 0.972222I
b = 0.514942 − 1.214260I
0.59675 + 5.29093I 0
u = 0.178838 − 1.397610I
a = 0.280190 + 0.972222I
b = 0.514942 + 1.214260I
0.59675 − 5.29093I 0
u = −0.02863 + 1.43149I
a = −1.263290 + 0.492520I
b = −3.09033 + 0.24494I
−6.34108 − 3.66733I 0
u = −0.02863 − 1.43149I
a = −1.263290 − 0.492520I
b = −3.09033 − 0.24494I
−6.34108 + 3.66733I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22631 + 1.45071I
a = −0.223160 + 0.875930I
b = −0.421321 + 0.944082I
−1.66872 + 11.59560I 0
u = 0.22631 − 1.45071I
a = −0.223160 − 0.875930I
b = −0.421321 − 0.944082I
−1.66872 − 11.59560I 0
u = 0.41059 + 1.41053I
a = 0.976432 + 0.144840I
b = 2.63906 + 0.49267I
−7.57844 + 3.50049I 0
u = 0.41059 − 1.41053I
a = 0.976432 − 0.144840I
b = 2.63906 − 0.49267I
−7.57844 − 3.50049I 0
u = −0.334922 + 0.409655I
a = 2.57491 − 0.45039I
b = 0.640329 + 0.086594I
1.54320 − 3.79998I 8.38218 + 10.90850I
u = −0.334922 − 0.409655I
a = 2.57491 + 0.45039I
b = 0.640329 − 0.086594I
1.54320 + 3.79998I 8.38218 − 10.90850I
u = 0.234996 + 0.472015I
a = −0.34460 − 1.75071I
b = −0.324245 + 0.319005I
−1.57985 + 1.04137I −2.49531 − 4.65112I
u = 0.234996 − 0.472015I
a = −0.34460 + 1.75071I
b = −0.324245 − 0.319005I
−1.57985 − 1.04137I −2.49531 + 4.65112I
u = 0.05301 + 1.48085I
a = 0.200024 + 0.748713I
b = 0.770060 + 0.614245I
−7.97482 + 1.97792I 0
u = 0.05301 − 1.48085I
a = 0.200024 − 0.748713I
b = 0.770060 − 0.614245I
−7.97482 − 1.97792I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24021 + 1.46852I
a = 0.906336 + 0.004574I
b = 3.10374 + 0.45869I
−7.97429 + 4.79171I 0
u = 0.24021 − 1.46852I
a = 0.906336 − 0.004574I
b = 3.10374 − 0.45869I
−7.97429 − 4.79171I 0
u = −0.09971 + 1.48504I
a = −1.160300 − 0.419905I
b = −3.26243 − 0.52300I
−4.72540 − 5.35859I 0
u = −0.09971 − 1.48504I
a = −1.160300 + 0.419905I
b = −3.26243 + 0.52300I
−4.72540 + 5.35859I 0
u = 0.271717 + 0.433378I
a = −0.466330 − 1.189350I
b = −0.348299 + 0.415435I
−1.63518 + 1.00896I −1.29963 − 2.42841I
u = 0.271717 − 0.433378I
a = −0.466330 + 1.189350I
b = −0.348299 − 0.415435I
−1.63518 − 1.00896I −1.29963 + 2.42841I
u = −0.12626 + 1.49477I
a = 0.013608 + 0.543832I
b = 0.445315 + 0.158551I
−6.28755 − 6.10241I 0
u = −0.12626 − 1.49477I
a = 0.013608 − 0.543832I
b = 0.445315 − 0.158551I
−6.28755 + 6.10241I 0
u = 0.22981 + 1.48820I
a = 0.902472 − 0.130756I
b = 2.98391 + 0.80464I
−8.28790 + 5.77299I 0
u = 0.22981 − 1.48820I
a = 0.902472 + 0.130756I
b = 2.98391 − 0.80464I
−8.28790 − 5.77299I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04426 + 1.50840I
a = 0.643066 + 0.821993I
b = 1.88275 + 0.98824I
−8.16537 + 1.90483I 0
u = 0.04426 − 1.50840I
a = 0.643066 − 0.821993I
b = 1.88275 − 0.98824I
−8.16537 − 1.90483I 0
u = 0.14469 + 1.52320I
a = −0.967546 + 0.219590I
b = −2.84342 − 0.59009I
−13.27470 + 3.56498I 0
u = 0.14469 − 1.52320I
a = −0.967546 − 0.219590I
b = −2.84342 + 0.59009I
−13.27470 − 3.56498I 0
u = 0.25073 + 1.52669I
a = −0.873917 + 0.166504I
b = −2.84533 − 0.88143I
−10.1029 + 10.9021I 0
u = 0.25073 − 1.52669I
a = −0.873917 − 0.166504I
b = −2.84533 + 0.88143I
−10.1029 − 10.9021I 0
u = −0.441308
a = 0.675392
b = 0.301982
0.688149 14.7620
u = −0.29831 + 1.53296I
a = −0.998556 − 0.171879I
b = −3.13214 + 0.19790I
−4.67706 − 11.94260I 0
u = −0.29831 − 1.53296I
a = −0.998556 + 0.171879I
b = −3.13214 − 0.19790I
−4.67706 + 11.94260I 0
u = −0.20448 + 1.55923I
a = −0.716104 + 0.017362I
b = −2.44493 + 0.76882I
−6.20797 − 0.89847I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.20448 − 1.55923I
a = −0.716104 − 0.017362I
b = −2.44493 − 0.76882I
−6.20797 + 0.89847I 0
u = 0.45511 + 1.52515I
a = −0.909756 − 0.162932I
b = −2.61224 − 0.30017I
−8.52565 + 7.69322I 0
u = 0.45511 − 1.52515I
a = −0.909756 + 0.162932I
b = −2.61224 + 0.30017I
−8.52565 − 7.69322I 0
u = −0.33515 + 1.55812I
a = 0.973849 + 0.152157I
b = 3.06529 − 0.26544I
−6.6898 − 18.1097I 0
u = −0.33515 − 1.55812I
a = 0.973849 − 0.152157I
b = 3.06529 + 0.26544I
−6.6898 + 18.1097I 0
u = −0.20626 + 1.59303I
a = 0.956730 + 0.259520I
b = 2.97480 + 0.00679I
−11.9612 − 9.1487I 0
u = −0.20626 − 1.59303I
a = 0.956730 − 0.259520I
b = 2.97480 − 0.00679I
−11.9612 + 9.1487I 0
u = 0.28238 + 1.61861I
a = −0.846541 − 0.096461I
b = −2.83405 − 0.09721I
−9.60077 + 2.12615I 0
u = 0.28238 − 1.61861I
a = −0.846541 + 0.096461I
b = −2.83405 + 0.09721I
−9.60077 − 2.12615I 0
u = −0.07462 + 1.67704I
a = 0.724399 + 0.036666I
b = 2.69499 − 0.47686I
−10.05180 + 3.11146I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07462 − 1.67704I
a = 0.724399 − 0.036666I
b = 2.69499 + 0.47686I
−10.05180 − 3.11146I 0
u = −0.34792 + 1.64698I
a = 0.672940 − 0.035628I
b = 2.25801 − 0.47892I
−9.61907 − 5.52901I 0
u = −0.34792 − 1.64698I
a = 0.672940 + 0.035628I
b = 2.25801 + 0.47892I
−9.61907 + 5.52901I 0
u = 0.263141 + 0.010603I
a = −1.52722 − 3.15353I
b = −1.49486 + 0.84774I
2.12025 + 6.04650I 10.1944 − 10.1636I
u = 0.263141 − 0.010603I
a = −1.52722 + 3.15353I
b = −1.49486 − 0.84774I
2.12025 − 6.04650I 10.1944 + 10.1636I
u = −0.0385712 + 0.1131690I
a = 12.04120 − 6.17358I
b = −0.105353 + 0.558006I
−1.02856 − 3.32615I −5.3149 + 16.6260I
u = −0.0385712 − 0.1131690I
a = 12.04120 + 6.17358I
b = −0.105353 − 0.558006I
−1.02856 + 3.32615I −5.3149 − 16.6260I
u = 0.0748114 + 0.0173435I
a = 7.05820 + 9.61837I
b = 1.30770 − 1.07243I
2.76609 + 1.01918I 12.85545 − 4.57171I
u = 0.0748114 − 0.0173435I
a = 7.05820 − 9.61837I
b = 1.30770 + 1.07243I
2.76609 − 1.01918I 12.85545 + 4.57171I
16
II. I
u
2
=
h−u
27
+18u
26
+· · ·+b+13, −5u
26
+5u
25
+· · ·+a−5, u
28
−u
27
+· · ·+6u
2
+1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
u
a
4
=
5u
26
− 5u
25
+ ··· − 5u + 5
u
27
− 18u
26
+ ··· + 6u − 13
a
3
=
−u
27
+ 31u
26
+ ··· − 11u + 23
7u
27
+ 10u
26
+ ··· + 5u + 12
a
2
=
−4u
27
+ 18u
26
+ ··· − 8u + 9
7u
26
− 8u
25
+ ··· + u + 3
a
7
=
u
2
+ 1
u
2
a
11
=
−u
27
− 14u
25
+ ··· − 2u − 3
2u
27
− 5u
26
+ ··· + 3u − 2
a
5
=
−u
27
+ 4u
26
+ ··· + 5u + 4
5u
27
− 6u
26
+ ··· + 6u − 2
a
10
=
−u
27
− 14u
25
+ ··· − 2u − 2
2u
27
− 4u
26
+ ··· + 3u − 1
a
6
=
u
26
+ 14u
24
+ ··· + 2u + 4
u
27
− 4u
26
+ ··· − 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −46u
27
+54u
26
−647u
25
+688u
24
−3899u
23
+3914u
22
−13105u
21
+13115u
20
−26703u
19
+
28504u
18
−33608u
17
+40977u
16
−26441u
15
+36742u
14
−16280u
13
+15756u
12
−14162u
11
−
2456u
10
−12262u
9
−4716u
8
−5384u
7
−524u
6
−876u
5
+ 402u
4
−191u
3
+ 10u
2
−61u −3
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
− 14u
27
+ ··· − 14u + 1
c
2
u
28
− 7u
26
+ ··· − 7u
2
+ 1
c
3
u
28
+ 4u
25
+ ··· − u
2
+ 1
c
4
u
28
+ 14u
26
+ ··· + 2u + 1
c
5
u
28
− 7u
26
+ ··· − 7u
2
+ 1
c
6
u
28
− 4u
27
+ ··· − u + 1
c
7
, c
8
u
28
− u
27
+ ··· + 6u
2
+ 1
c
9
u
28
+ 2u
26
+ ··· + 2u + 1
c
10
u
28
+ 4u
27
+ ··· + u + 1
c
11
u
28
+ 14u
26
+ ··· − 2u + 1
c
12
u
28
+ u
27
+ ··· + 6u
2
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 14y
27
+ ··· + 22y + 1
c
2
, c
5
y
28
− 14y
27
+ ··· − 14y + 1
c
3
y
28
+ 16y
26
+ ··· − 2y + 1
c
4
, c
11
y
28
+ 28y
27
+ ··· + 36y + 1
c
6
, c
10
y
28
− 22y
27
+ ··· − 25y + 1
c
7
, c
8
, c
12
y
28
+ 29y
27
+ ··· + 12y + 1
c
9
y
28
+ 4y
27
+ ··· + 8y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.057970 + 0.166282I
a = −0.208823 − 1.175340I
b = −0.112755 + 0.344968I
−3.97772 + 1.20140I −2.85140 + 0.11450I
u = 1.057970 − 0.166282I
a = −0.208823 + 1.175340I
b = −0.112755 − 0.344968I
−3.97772 − 1.20140I −2.85140 − 0.11450I
u = −0.139257 + 1.222350I
a = −0.540849 − 0.166027I
b = 1.046250 + 0.304982I
−0.73942 − 7.06380I 6.87825 + 9.81843I
u = −0.139257 − 1.222350I
a = −0.540849 + 0.166027I
b = 1.046250 − 0.304982I
−0.73942 + 7.06380I 6.87825 − 9.81843I
u = −0.109455 + 1.235990I
a = 0.581933 + 0.254472I
b = −0.608729 − 0.841553I
−0.11256 − 1.80905I 8.89618 + 4.13642I
u = −0.109455 − 1.235990I
a = 0.581933 − 0.254472I
b = −0.608729 + 0.841553I
−0.11256 + 1.80905I 8.89618 − 4.13642I
u = −0.309375 + 0.661931I
a = −0.840544 + 0.816321I
b = −1.90631 + 0.13994I
1.43275 + 5.42505I 2.75477 − 4.39975I
u = −0.309375 − 0.661931I
a = −0.840544 − 0.816321I
b = −1.90631 − 0.13994I
1.43275 − 5.42505I 2.75477 + 4.39975I
u = −0.046105 + 1.293450I
a = 0.722624 + 0.538641I
b = 1.213690 − 0.485372I
−1.64140 − 3.06077I 3.78856 + 1.96073I
u = −0.046105 − 1.293450I
a = 0.722624 − 0.538641I
b = 1.213690 + 0.485372I
−1.64140 + 3.06077I 3.78856 − 1.96073I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.234718 + 1.284670I
a = −0.243223 + 0.065777I
b = 0.001021 − 0.413753I
−4.35783 − 2.56470I −7.06193 + 4.48383I
u = −0.234718 − 1.284670I
a = −0.243223 − 0.065777I
b = 0.001021 + 0.413753I
−4.35783 + 2.56470I −7.06193 − 4.48383I
u = −0.223370 + 0.627076I
a = 1.067160 − 0.873388I
b = 1.72440 − 0.74819I
2.23223 + 0.57114I 3.41868 + 3.39984I
u = −0.223370 − 0.627076I
a = 1.067160 + 0.873388I
b = 1.72440 + 0.74819I
2.23223 − 0.57114I 3.41868 − 3.39984I
u = −0.577599 + 0.286788I
a = 0.060532 + 0.910181I
b = −0.609362 − 0.366066I
−0.913262 − 0.484116I 6.63213 − 1.77950I
u = −0.577599 − 0.286788I
a = 0.060532 − 0.910181I
b = −0.609362 + 0.366066I
−0.913262 + 0.484116I 6.63213 + 1.77950I
u = 0.11418 + 1.43429I
a = −1.252930 + 0.057473I
b = −3.46724 + 0.07220I
−5.51846 + 4.88137I 0. − 6.63417I
u = 0.11418 − 1.43429I
a = −1.252930 − 0.057473I
b = −3.46724 − 0.07220I
−5.51846 − 4.88137I 0. + 6.63417I
u = 0.34785 + 1.42900I
a = −0.921646 − 0.108794I
b = −2.78620 − 0.61422I
−8.38147 + 3.80359I −4.21890 + 0.I
u = 0.34785 − 1.42900I
a = −0.921646 + 0.108794I
b = −2.78620 + 0.61422I
−8.38147 − 3.80359I −4.21890 + 0.I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.094690 + 0.468230I
a = 1.82899 − 1.34340I
b = 0.601135 − 0.815470I
1.46551 + 2.52456I 5.53353 − 6.54159I
u = −0.094690 − 0.468230I
a = 1.82899 + 1.34340I
b = 0.601135 + 0.815470I
1.46551 − 2.52456I 5.53353 + 6.54159I
u = −0.03077 + 1.53379I
a = 0.773157 − 0.656502I
b = 2.24154 − 0.84097I
−7.92937 − 2.20751I 5.54405 + 8.63255I
u = −0.03077 − 1.53379I
a = 0.773157 + 0.656502I
b = 2.24154 + 0.84097I
−7.92937 + 2.20751I 5.54405 − 8.63255I
u = 0.398184 + 0.210426I
a = −1.82799 − 2.67857I
b = 0.055600 + 0.215565I
−0.82870 − 3.05974I 10.34175 − 2.88215I
u = 0.398184 − 0.210426I
a = −1.82799 + 2.67857I
b = 0.055600 − 0.215565I
−0.82870 + 3.05974I 10.34175 + 2.88215I
u = 0.34716 + 1.61506I
a = 0.801609 + 0.007769I
b = 2.60695 + 0.24121I
−10.20870 + 6.58276I 0
u = 0.34716 − 1.61506I
a = 0.801609 − 0.007769I
b = 2.60695 − 0.24121I
−10.20870 − 6.58276I 0
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 14u
27
+ ··· − 14u + 1)(u
119
+ 51u
118
+ ··· + 26772u + 361)
c
2
(u
28
− 7u
26
+ ··· − 7u
2
+ 1)(u
119
+ 7u
118
+ ··· − 208u − 19)
c
3
(u
28
+ 4u
25
+ ··· − u
2
+ 1)(u
119
− u
118
+ ··· − 2.51854 × 10
7
u − 1.15228 × 10
7
)
c
4
(u
28
+ 14u
26
+ ··· + 2u + 1)(u
119
− 3u
118
+ ··· − 2732u − 8803)
c
5
(u
28
− 7u
26
+ ··· − 7u
2
+ 1)(u
119
+ 7u
118
+ ··· − 208u − 19)
c
6
(u
28
− 4u
27
+ ··· − u + 1)(u
119
+ 3u
118
+ ··· − 4107u − 2939)
c
7
, c
8
(u
28
− u
27
+ ··· + 6u
2
+ 1)(u
119
− 2u
118
+ ··· − 26u − 1)
c
9
(u
28
+ 2u
26
+ ··· + 2u + 1)(u
119
+ u
118
+ ··· + 8910u − 1089)
c
10
(u
28
+ 4u
27
+ ··· + u + 1)(u
119
+ 3u
118
+ ··· − 4107u − 2939)
c
11
(u
28
+ 14u
26
+ ··· − 2u + 1)(u
119
− 3u
118
+ ··· − 2732u − 8803)
c
12
(u
28
+ u
27
+ ··· + 6u
2
+ 1)(u
119
− 2u
118
+ ··· − 26u − 1)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 14y
27
+ ··· + 22y + 1)
· (y
119
+ 49y
118
+ ··· + 68785416y −130321)
c
2
, c
5
(y
28
− 14y
27
+ ··· − 14y + 1)(y
119
− 51y
118
+ ··· + 26772y −361)
c
3
(y
28
+ 16y
26
+ ··· − 2y + 1)
· (y
119
+ 43y
118
+ ··· − 5505345069862148y −132775772528569)
c
4
, c
11
(y
28
+ 28y
27
+ ··· + 36y + 1)
· (y
119
+ 95y
118
+ ··· − 90407930y −77492809)
c
6
, c
10
(y
28
− 22y
27
+ ··· − 25y + 1)
· (y
119
− 75y
118
+ ··· + 495977351y −8637721)
c
7
, c
8
, c
12
(y
28
+ 29y
27
+ ··· + 12y + 1)(y
119
+ 120y
118
+ ··· + 210y −1)
c
9
(y
28
+ 4y
27
+ ··· + 8y + 1)
· (y
119
− 13y
118
+ ··· − 26164314y −1185921)
24
