12a
0589
(K12a
0589
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 12 2 11 1 4 6 8 5
Solving Sequence
5,10
4 9
1,3
2 8 12 6 11 7
c
4
c
9
c
3
c
1
c
8
c
12
c
5
c
10
c
7
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.11582 × 10
221
u
99
− 8.63174 × 10
221
u
98
+ ··· + 1.62343 × 10
221
b − 3.59350 × 10
222
,
− 4.74270 × 10
224
u
99
− 5.73839 × 10
224
u
98
+ ··· + 3.73389 × 10
222
a − 2.20342 × 10
225
,
u
100
+ u
99
+ ··· + 14u − 1i
I
u
2
= hu
3
+ b, −u
3
+ 2u
2
+ 3a + 2u − 1, u
4
− u
2
+ 1i
I
u
3
= hu
3
+ b, −u
3
− u
2
+ 3a + 2u − 1, u
4
− u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 108 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−7.12 × 10
221
u
99
− 8.63 × 10
221
u
98
+ · · · + 1.62 × 10
221
b − 3.59 ×
10
222
, −4.74 × 10
224
u
99
− 5.74 × 10
224
u
98
+ · · · + 3.73 × 10
222
a − 2.20 ×
10
225
, u
100
+ u
99
+ · · · + 14u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
9
=
−u
−u
3
+ u
a
1
=
127.018u
99
+ 153.684u
98
+ ··· − 5600.34u + 590.115
4.38320u
99
+ 5.31698u
98
+ ··· − 199.270u + 22.1353
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
133.223u
99
+ 161.070u
98
+ ··· − 5878.58u + 619.701
4.83883u
99
+ 5.87137u
98
+ ··· − 222.047u + 24.6627
a
8
=
508.169u
99
+ 596.373u
98
+ ··· − 24295.6u + 2806.67
7.84464u
99
+ 8.68358u
98
+ ··· − 428.049u + 56.5824
a
12
=
122.634u
99
+ 148.367u
98
+ ··· − 5401.07u + 567.979
4.38320u
99
+ 5.31698u
98
+ ··· − 199.270u + 22.1353
a
6
=
55.7325u
99
+ 63.3082u
98
+ ··· − 2893.42u + 361.738
0.770246u
99
+ 1.01289u
98
+ ··· − 36.2687u + 5.09196
a
11
=
621.926u
99
+ 735.391u
98
+ ··· − 29150.1u + 3301.04
12.8285u
99
+ 14.6903u
98
+ ··· − 658.830u + 81.8685
a
7
=
−96.2686u
99
− 119.321u
98
+ ··· + 3938.19u − 382.399
−6.04319u
99
− 7.28700u
98
+ ··· + 275.012u − 29.1983
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.33253u
99
− 12.0749u
98
+ ··· − 581.309u + 160.926
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
100
+ 35u
99
+ ··· + 5314u + 169
c
2
, c
6
u
100
− 3u
99
+ ··· − 20u + 13
c
3
, c
4
, c
9
u
100
− u
99
+ ··· − 14u − 1
c
5
, c
12
u
100
− 3u
99
+ ··· − 128u + 52
c
7
, c
11
u
100
− 5u
99
+ ··· + 22u − 1
c
8
529(529u
100
+ 2323u
99
+ ··· − 5.59128 × 10
7
u − 3.11681 × 10
7
)
c
10
529(529u
100
+ 3841u
99
+ ··· + 8995520u − 970300)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
100
+ 65y
99
+ ··· − 6927358y + 28561
c
2
, c
6
y
100
− 35y
99
+ ··· − 5314y + 169
c
3
, c
4
, c
9
y
100
− 95y
99
+ ··· − 58y + 1
c
5
, c
12
y
100
+ 53y
99
+ ··· − 89080y + 2704
c
7
, c
11
y
100
− 55y
99
+ ··· − 82y + 1
c
8
279841(279841y
100
− 5042957y
99
+ ··· − 6.77314 × 10
16
y + 9.71451 × 10
14
)
c
10
279841
· (279841y
100
− 18269015y
99
+ ··· − 953537733200y + 941482090000)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.494564 + 0.868297I
a = 0.957136 − 0.711585I
b = 0.595137 + 1.233490I
1.56718 + 13.70260I 0
u = 0.494564 − 0.868297I
a = 0.957136 + 0.711585I
b = 0.595137 − 1.233490I
1.56718 − 13.70260I 0
u = −0.594360 + 0.794669I
a = −0.315966 − 0.050179I
b = 0.519602 + 1.007160I
3.10737 + 2.58864I 0
u = −0.594360 − 0.794669I
a = −0.315966 + 0.050179I
b = 0.519602 − 1.007160I
3.10737 − 2.58864I 0
u = 0.546169 + 0.879548I
a = −0.641283 + 0.597330I
b = −0.371361 − 0.967519I
−1.19926 + 1.95519I 0
u = 0.546169 − 0.879548I
a = −0.641283 − 0.597330I
b = −0.371361 + 0.967519I
−1.19926 − 1.95519I 0
u = −0.529573 + 0.783995I
a = −0.952631 − 0.685469I
b = −0.603749 + 1.220150I
2.97162 − 7.84264I 0
u = −0.529573 − 0.783995I
a = −0.952631 + 0.685469I
b = −0.603749 − 1.220150I
2.97162 + 7.84264I 0
u = −0.435240 + 0.977287I
a = 0.608130 + 0.654085I
b = 0.430468 − 1.039270I
−2.05758 − 7.06500I 0
u = −0.435240 − 0.977287I
a = 0.608130 − 0.654085I
b = 0.430468 + 1.039270I
−2.05758 + 7.06500I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.721353 + 0.811301I
a = 0.168237 + 0.016183I
b = −0.529096 + 1.067270I
2.19181 − 8.06866I 0
u = 0.721353 − 0.811301I
a = 0.168237 − 0.016183I
b = −0.529096 − 1.067270I
2.19181 + 8.06866I 0
u = 0.787367 + 0.395930I
a = 0.003217 + 0.657953I
b = −0.347285 + 1.118780I
−2.34706 − 2.72684I 0
u = 0.787367 − 0.395930I
a = 0.003217 − 0.657953I
b = −0.347285 − 1.118780I
−2.34706 + 2.72684I 0
u = −0.559331 + 0.641843I
a = 0.395096 + 0.141503I
b = 0.990205 + 0.205441I
4.69005 − 8.03457I 0
u = −0.559331 − 0.641843I
a = 0.395096 − 0.141503I
b = 0.990205 − 0.205441I
4.69005 + 8.03457I 0
u = 0.881092 + 0.739200I
a = −0.183885 + 0.313689I
b = 0.171550 − 0.635394I
−0.32711 + 3.86344I 0
u = 0.881092 − 0.739200I
a = −0.183885 − 0.313689I
b = 0.171550 + 0.635394I
−0.32711 − 3.86344I 0
u = −0.388057 + 0.754681I
a = −0.438833 − 1.099830I
b = −0.639728 + 0.405220I
4.11149 + 3.49119I 0
u = −0.388057 − 0.754681I
a = −0.438833 + 1.099830I
b = −0.639728 − 0.405220I
4.11149 − 3.49119I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.220257 + 0.785544I
a = 0.174053 − 1.140200I
b = 0.598970 + 0.513921I
4.54056 + 1.86436I 0
u = 0.220257 − 0.785544I
a = 0.174053 + 1.140200I
b = 0.598970 − 0.513921I
4.54056 − 1.86436I 0
u = −0.172179 + 0.766268I
a = 0.649580 + 0.848586I
b = 0.319532 − 1.179920I
−5.75809 − 1.64364I 0
u = −0.172179 − 0.766268I
a = 0.649580 − 0.848586I
b = 0.319532 + 1.179920I
−5.75809 + 1.64364I 0
u = −1.120250 + 0.487086I
a = 0.268645 − 0.225715I
b = −0.195130 − 1.131990I
−2.96999 − 2.86139I 0
u = −1.120250 − 0.487086I
a = 0.268645 + 0.225715I
b = −0.195130 + 1.131990I
−2.96999 + 2.86139I 0
u = 0.640737 + 0.436206I
a = 0.392007 + 0.728401I
b = 0.265180 + 0.020545I
−0.00920 + 3.88649I 0
u = 0.640737 − 0.436206I
a = 0.392007 − 0.728401I
b = 0.265180 − 0.020545I
−0.00920 − 3.88649I 0
u = 0.612405 + 0.473798I
a = −0.386204 + 0.113587I
b = −0.994841 + 0.198747I
6.02810 + 2.15602I 0
u = 0.612405 − 0.473798I
a = −0.386204 − 0.113587I
b = −0.994841 − 0.198747I
6.02810 − 2.15602I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.985471 + 0.762198I
a = 0.128101 + 0.137545I
b = −0.306861 − 0.793029I
−0.490285 + 0.995813I 0
u = −0.985471 − 0.762198I
a = 0.128101 − 0.137545I
b = −0.306861 + 0.793029I
−0.490285 − 0.995813I 0
u = 0.297954 + 0.690813I
a = 1.047450 − 0.622152I
b = 0.577725 + 1.176240I
−3.86712 + 6.69392I 0. − 7.62154I
u = 0.297954 − 0.690813I
a = 1.047450 + 0.622152I
b = 0.577725 − 1.176240I
−3.86712 − 6.69392I 0. + 7.62154I
u = 0.598781 + 0.454455I
a = −1.030130 + 0.238005I
b = −0.144324 − 1.036660I
−2.01635 + 1.81696I 6.00000 − 4.70771I
u = 0.598781 − 0.454455I
a = −1.030130 − 0.238005I
b = −0.144324 + 1.036660I
−2.01635 − 1.81696I 6.00000 + 4.70771I
u = −1.319190 + 0.001997I
a = −1.73316 − 0.25842I
b = −1.114860 − 0.217275I
2.06676 − 0.04063I 0
u = −1.319190 − 0.001997I
a = −1.73316 + 0.25842I
b = −1.114860 + 0.217275I
2.06676 + 0.04063I 0
u = −1.320980 + 0.094418I
a = −2.08249 − 0.88815I
b = −0.299976 + 0.950759I
4.18219 − 2.56239I 0
u = −1.320980 − 0.094418I
a = −2.08249 + 0.88815I
b = −0.299976 − 0.950759I
4.18219 + 2.56239I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.338530 + 0.032041I
a = −1.57595 + 1.15586I
b = −0.97364 + 1.31873I
2.35208 + 2.63289I 0
u = 1.338530 − 0.032041I
a = −1.57595 − 1.15586I
b = −0.97364 − 1.31873I
2.35208 − 2.63289I 0
u = 1.34563
a = 0.292417
b = −0.308446
6.43420 0
u = 1.368210 + 0.031204I
a = −1.170500 + 0.572561I
b = −0.418859 + 1.321610I
2.43343 + 2.34353I 0
u = 1.368210 − 0.031204I
a = −1.170500 − 0.572561I
b = −0.418859 − 1.321610I
2.43343 − 2.34353I 0
u = −1.377550 + 0.076292I
a = 0.277805 − 1.369850I
b = 0.03758 − 1.95221I
3.92135 − 4.66086I 0
u = −1.377550 − 0.076292I
a = 0.277805 + 1.369850I
b = 0.03758 + 1.95221I
3.92135 + 4.66086I 0
u = 1.363690 + 0.248056I
a = −1.62981 − 0.29969I
b = −0.524954 − 1.166630I
−0.90590 + 5.22564I 0
u = 1.363690 − 0.248056I
a = −1.62981 + 0.29969I
b = −0.524954 + 1.166630I
−0.90590 − 5.22564I 0
u = −0.611023 + 0.040869I
a = −1.051260 + 0.666639I
b = −0.381510 + 0.069285I
0.818668 + 0.063255I 12.29924 + 0.65938I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.611023 − 0.040869I
a = −1.051260 − 0.666639I
b = −0.381510 − 0.069285I
0.818668 − 0.063255I 12.29924 − 0.65938I
u = 1.43265 + 0.11313I
a = 1.83238 + 0.76058I
b = 1.15364 + 1.26329I
7.20401 + 5.59825I 0
u = 1.43265 − 0.11313I
a = 1.83238 − 0.76058I
b = 1.15364 − 1.26329I
7.20401 − 5.59825I 0
u = −1.41877 + 0.23880I
a = −1.88730 + 0.46425I
b = −0.80880 + 1.16573I
1.63204 − 10.03090I 0
u = −1.41877 − 0.23880I
a = −1.88730 − 0.46425I
b = −0.80880 − 1.16573I
1.63204 + 10.03090I 0
u = −1.43734 + 0.07599I
a = 1.43588 − 0.53919I
b = 0.482283 − 1.151980I
4.24349 − 2.96705I 0
u = −1.43734 − 0.07599I
a = 1.43588 + 0.53919I
b = 0.482283 + 1.151980I
4.24349 + 2.96705I 0
u = 1.44484 + 0.07008I
a = 1.302600 + 0.430128I
b = 0.216338 + 0.513954I
6.58552 + 0.25931I 0
u = 1.44484 − 0.07008I
a = 1.302600 − 0.430128I
b = 0.216338 − 0.513954I
6.58552 − 0.25931I 0
u = −1.45805 + 0.02122I
a = 1.77281 + 2.58470I
b = 0.180425 + 0.937246I
4.70273 + 2.17240I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45805 − 0.02122I
a = 1.77281 − 2.58470I
b = 0.180425 − 0.937246I
4.70273 − 2.17240I 0
u = −0.271871 + 0.439056I
a = −2.15900 − 0.28952I
b = 0.291940 + 0.860441I
1.11878 + 1.37649I 6.33692 + 2.07286I
u = −0.271871 − 0.439056I
a = −2.15900 + 0.28952I
b = 0.291940 − 0.860441I
1.11878 − 1.37649I 6.33692 − 2.07286I
u = −0.350138 + 0.374779I
a = −0.833386 − 0.521069I
b = −0.682826 + 1.206250I
1.47798 − 3.83735I 9.5830 + 10.7537I
u = −0.350138 − 0.374779I
a = −0.833386 + 0.521069I
b = −0.682826 − 1.206250I
1.47798 + 3.83735I 9.5830 − 10.7537I
u = −1.44495 + 0.36811I
a = −1.191740 − 0.398723I
b = −0.641528 + 0.893391I
9.82550 − 6.20178I 0
u = −1.44495 − 0.36811I
a = −1.191740 + 0.398723I
b = −0.641528 − 0.893391I
9.82550 + 6.20178I 0
u = −1.51367 + 0.15493I
a = 1.57679 + 0.51951I
b = 1.38997 + 0.31490I
12.94730 − 4.46201I 0
u = −1.51367 − 0.15493I
a = 1.57679 − 0.51951I
b = 1.38997 − 0.31490I
12.94730 + 4.46201I 0
u = 1.50470 + 0.30800I
a = 1.213970 − 0.300886I
b = 0.645180 + 0.817793I
10.20430 + 0.51681I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50470 − 0.30800I
a = 1.213970 + 0.300886I
b = 0.645180 − 0.817793I
10.20430 − 0.51681I 0
u = −0.463361
a = −1.22093
b = −0.338405
0.744582 13.7610
u = 1.52183 + 0.21651I
a = −1.43233 + 0.55988I
b = −1.274880 + 0.268665I
11.4877 + 11.1816I 0
u = 1.52183 − 0.21651I
a = −1.43233 − 0.55988I
b = −1.274880 − 0.268665I
11.4877 − 11.1816I 0
u = −1.53535 + 0.19283I
a = −1.099040 − 0.202970I
b = −0.877186 − 0.233897I
7.16720 − 6.52031I 0
u = −1.53535 − 0.19283I
a = −1.099040 + 0.202970I
b = −0.877186 + 0.233897I
7.16720 + 6.52031I 0
u = 1.54781 + 0.10756I
a = 1.127950 − 0.138482I
b = 0.816167 − 0.259682I
8.26390 + 0.91408I 0
u = 1.54781 − 0.10756I
a = 1.127950 + 0.138482I
b = 0.816167 + 0.259682I
8.26390 − 0.91408I 0
u = 1.53130 + 0.27358I
a = 1.65900 + 0.28363I
b = 0.73536 + 1.33153I
9.6817 + 11.7095I 0
u = 1.53130 − 0.27358I
a = 1.65900 − 0.28363I
b = 0.73536 − 1.33153I
9.6817 − 11.7095I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53199 + 0.31297I
a = −1.69028 + 0.19186I
b = −0.69130 + 1.32348I
8.1368 − 18.0090I 0
u = −1.53199 − 0.31297I
a = −1.69028 − 0.19186I
b = −0.69130 − 1.32348I
8.1368 + 18.0090I 0
u = −1.53930 + 0.28493I
a = 1.353570 − 0.191387I
b = 0.577835 − 1.165050I
5.60463 − 6.09906I 0
u = −1.53930 − 0.28493I
a = 1.353570 + 0.191387I
b = 0.577835 + 1.165050I
5.60463 + 6.09906I 0
u = 0.031819 + 0.432835I
a = 0.673328 + 0.407362I
b = 0.524926 + 0.467278I
−1.59343 − 1.35865I −0.15444 + 1.54135I
u = 0.031819 − 0.432835I
a = 0.673328 − 0.407362I
b = 0.524926 − 0.467278I
−1.59343 + 1.35865I −0.15444 − 1.54135I
u = 1.53179 + 0.35023I
a = −1.378750 − 0.101122I
b = −0.578888 − 1.190700I
4.32081 + 11.84680I 0
u = 1.53179 − 0.35023I
a = −1.378750 + 0.101122I
b = −0.578888 + 1.190700I
4.32081 − 11.84680I 0
u = 0.000582 + 0.412245I
a = 0.844273 + 0.142581I
b = 0.683194 + 0.703089I
−1.60023 − 1.33130I −2.66231 + 0.62507I
u = 0.000582 − 0.412245I
a = 0.844273 − 0.142581I
b = 0.683194 − 0.703089I
−1.60023 + 1.33130I −2.66231 − 0.62507I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57713 + 0.22259I
a = −0.512379 + 0.491015I
b = −0.671814 + 0.691220I
10.41410 + 1.15655I 0
u = 1.57713 − 0.22259I
a = −0.512379 − 0.491015I
b = −0.671814 − 0.691220I
10.41410 − 1.15655I 0
u = 0.147452 + 0.360979I
a = 0.246092 + 0.907450I
b = 0.23079 − 1.53364I
−0.88848 + 3.18787I −0.85305 − 11.96812I
u = 0.147452 − 0.360979I
a = 0.246092 − 0.907450I
b = 0.23079 + 1.53364I
−0.88848 − 3.18787I −0.85305 + 11.96812I
u = −1.62268 + 0.16552I
a = 0.627568 + 0.513142I
b = 0.657699 + 0.776414I
10.32470 + 4.49901I 0
u = −1.62268 − 0.16552I
a = 0.627568 − 0.513142I
b = 0.657699 − 0.776414I
10.32470 − 4.49901I 0
u = 0.250122 + 0.070148I
a = −4.22464 + 0.58722I
b = −0.102242 − 1.039580I
−1.51133 + 2.06989I 5.39582 − 3.50708I
u = 0.250122 − 0.070148I
a = −4.22464 − 0.58722I
b = −0.102242 + 1.039580I
−1.51133 − 2.06989I 5.39582 + 3.50708I
u = 0.203055 + 0.029017I
a = −13.9313 − 20.5765I
b = −0.092638 − 1.025750I
−0.10500 − 2.04747I 48.5669 − 10.4108I
u = 0.203055 − 0.029017I
a = −13.9313 + 20.5765I
b = −0.092638 + 1.025750I
−0.10500 + 2.04747I 48.5669 + 10.4108I
14
II. I
u
2
= hu
3
+ b, −u
3
+ 2u
2
+ 3a + 2u − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
9
=
−u
−u
3
+ u
a
1
=
1
3
u
3
−
2
3
u
2
−
2
3
u +
1
3
−u
3
a
3
=
−u
2
+ 1
u
2
+ 1
a
2
=
1
3
u
3
−
5
3
u
2
−
2
3
u +
1
3
−u
3
− u
2
+ 2
a
8
=
−
2
3
u
3
−
1
3
u
2
−
2
3
u +
1
3
−
4
3
u
3
−
1
3
u
2
+
5
3
u +
2
3
a
12
=
4
3
u
3
−
2
3
u
2
−
2
3
u +
1
3
−u
3
a
6
=
−
1
3
u
3
−
2
3
u
2
+
2
3
u +
1
3
1
a
11
=
−
2
3
u
2
+
2
3
−
2
3
u
3
+
1
3
u
2
+
4
3
u +
1
3
a
7
=
−
2
3
u
3
−
1
3
u
2
−
2
3
u −
1
3
−2u
3
− u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
+ 8
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
6
, c
9
u
4
− u
2
+ 1
c
5
, c
12
(u
2
+ 1)
2
c
7
(u
2
+ u + 1)
2
c
8
9(9u
4
+ 9u
2
+ 6u + 1)
c
10
9(9u
4
+ 18u
3
+ 18u
2
+ 12u + 4)
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
11
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
6
, c
9
(y
2
− y + 1)
2
c
5
, c
12
(y + 1)
4
c
8
81(81y
4
+ 162y
3
+ 99y
2
− 18y + 1)
c
10
81(81y
4
− 36y
2
+ 16)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.577350 − 0.577350I
b = − 1.000000I
−1.64493 + 4.05977I 4.00000 − 6.92820I
u = 0.866025 − 0.500000I
a = −0.577350 + 0.577350I
b = 1.000000I
−1.64493 − 4.05977I 4.00000 + 6.92820I
u = −0.866025 + 0.500000I
a = 0.577350 + 0.577350I
b = − 1.000000I
−1.64493 − 4.05977I 4.00000 + 6.92820I
u = −0.866025 − 0.500000I
a = 0.577350 − 0.577350I
b = 1.000000I
−1.64493 + 4.05977I 4.00000 − 6.92820I
18
III. I
u
3
= hu
3
+ b, −u
3
− u
2
+ 3a + 2u − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
9
=
−u
−u
3
+ u
a
1
=
1
3
u
3
+
1
3
u
2
−
2
3
u +
1
3
−u
3
a
3
=
−u
2
+ 1
u
2
+ 1
a
2
=
1
3
u
3
+
1
3
u
2
−
2
3
u +
4
3
−u
3
+ 2u
2
− 1
a
8
=
−
1
3
u
3
+
1
3
u
2
−
4
3
u
−
4
3
u
3
+
2
3
u
2
+
5
3
u −
1
3
a
12
=
4
3
u
3
+
1
3
u
2
−
2
3
u +
1
3
−u
3
a
6
=
2
3
u
3
−
2
3
u
2
−
1
3
u +
1
3
1
a
11
=
−
1
3
u
3
+
2
3
u
2
−
1
3
u
−
2
3
u
3
+
1
3
u
2
+
4
3
u −
2
3
a
7
=
1
3
u
3
−
1
3
u
2
−
5
3
u +
2
3
−2u
3
+ u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
2
− u + 1)
2
c
2
, c
3
, c
4
c
6
, c
9
u
4
− u
2
+ 1
c
5
, c
12
(u
2
+ 1)
2
c
7
(u
2
+ u + 1)
2
c
8
9(9u
4
+ 4)
c
10
9(9u
4
− 18u
3
+ 18u
2
− 6u + 1)
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
11
(y
2
+ y + 1)
2
c
2
, c
3
, c
4
c
6
, c
9
(y
2
− y + 1)
2
c
5
, c
12
(y + 1)
4
c
8
81(9y
2
+ 4)
2
c
10
81(81y
4
+ 126y
2
+ 1)
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.077350 + 0.288675I
b = − 1.000000I
−1.64493 4.00000
u = 0.866025 − 0.500000I
a = −0.077350 − 0.288675I
b = 1.000000I
−1.64493 4.00000
u = −0.866025 + 0.500000I
a = 1.077350 − 0.288675I
b = − 1.000000I
−1.64493 4.00000
u = −0.866025 − 0.500000I
a = 1.077350 + 0.288675I
b = 1.000000I
−1.64493 4.00000
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
100
+ 35u
99
+ ··· + 5314u + 169)
c
2
, c
6
((u
4
− u
2
+ 1)
2
)(u
100
− 3u
99
+ ··· − 20u + 13)
c
3
, c
4
, c
9
((u
4
− u
2
+ 1)
2
)(u
100
− u
99
+ ··· − 14u − 1)
c
5
, c
12
((u
2
+ 1)
4
)(u
100
− 3u
99
+ ··· − 128u + 52)
c
7
((u
2
+ u + 1)
4
)(u
100
− 5u
99
+ ··· + 22u − 1)
c
8
42849(9u
4
+ 4)(9u
4
+ 9u
2
+ 6u + 1)
· (529u
100
+ 2323u
99
+ ··· − 55912752u − 31168112)
c
10
42849(9u
4
− 18u
3
+ ··· − 6u + 1)(9u
4
+ 18u
3
+ ··· + 12u + 4)
· (529u
100
+ 3841u
99
+ ··· + 8995520u − 970300)
c
11
((u
2
− u + 1)
4
)(u
100
− 5u
99
+ ··· + 22u − 1)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
100
+ 65y
99
+ ··· − 6927358y + 28561)
c
2
, c
6
((y
2
− y + 1)
4
)(y
100
− 35y
99
+ ··· − 5314y + 169)
c
3
, c
4
, c
9
((y
2
− y + 1)
4
)(y
100
− 95y
99
+ ··· − 58y + 1)
c
5
, c
12
((y + 1)
8
)(y
100
+ 53y
99
+ ··· − 89080y + 2704)
c
7
, c
11
((y
2
+ y + 1)
4
)(y
100
− 55y
99
+ ··· − 82y + 1)
c
8
1836036801(9y
2
+ 4)
2
(81y
4
+ 162y
3
+ 99y
2
− 18y + 1)
· (2.80 × 10
5
y
100
− 5.04 × 10
6
y
99
+ ··· − 6.77 × 10
16
y + 9.71 × 10
14
)
c
10
1836036801(81y
4
− 36y
2
+ 16)(81y
4
+ 126y
2
+ 1)
· (279841y
100
− 18269015y
99
+ ··· − 953537733200y + 941482090000)
24
