12a
1221
(K12a
1221
)
A knot diagram
1
Linearized knot diagam
5 6 7 12 2 10 11 4 1 3 8 9
Solving Sequence
1,5
2 6
3,9
10 7 12 4 8 11
c
1
c
5
c
2
c
9
c
6
c
12
c
4
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h6.28820 × 10
367
u
121
− 1.15899 × 10
368
u
120
+ ··· + 2.80418 × 10
367
b + 5.57387 × 10
368
,
6.96628 × 10
366
u
121
− 2.09868 × 10
367
u
120
+ ··· + 1.12167 × 10
367
a + 4.96920 × 10
368
,
u
122
− 2u
121
+ ··· + 47u + 1i
I
u
2
= h−182u
19
− 1044u
18
+ ··· + 101b + 381, 2772u
19
+ 7347u
18
+ ··· + 101a − 2400,
u
20
+ 4u
19
+ ··· − 5u − 1i
I
u
3
= hb, a + 1, u − 1i
I
u
4
= hb + a − 1, a
2
− 2a − 1, u − 1i
I
u
5
= hb + 2a + 2, 2a
2
+ 4a + 1, u − 1i
* 5 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
= h6.29 × 10
367
u
121
− 1.16 × 10
368
u
120
+ · · · + 2.80 × 10
367
b + 5.57 ×
10
368
, 6.97 × 10
366
u
121
− 2.10 × 10
367
u
120
+ · · · + 1.12 × 10
367
a + 4.97 ×
10
368
, u
122
− 2u
121
+ · · · + 47u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
−0.621063u
121
+ 1.87103u
120
+ ··· − 319.578u − 44.3017
−2.24244u
121
+ 4.13307u
120
+ ··· − 767.054u − 19.8770
a
10
=
−2.86350u
121
+ 6.00410u
120
+ ··· − 1086.63u − 64.1787
−2.24244u
121
+ 4.13307u
120
+ ··· − 767.054u − 19.8770
a
7
=
−15.5463u
121
+ 33.3435u
120
+ ··· − 5050.45u − 174.308
1.98458u
121
− 4.93885u
120
+ ··· + 87.1412u − 1.41589
a
12
=
4.21410u
121
− 8.25746u
120
+ ··· + 3320.96u + 137.229
−1.32201u
121
+ 3.30816u
120
+ ··· + 170.879u + 7.81217
a
4
=
−17.4596u
121
+ 36.3324u
120
+ ··· − 6283.25u − 247.315
−2.24708u
121
+ 5.66160u
120
+ ··· − 469.534u − 15.1655
a
8
=
14.2213u
121
− 30.2530u
120
+ ··· + 5516.59u + 223.332
−1.91058u
121
+ 4.28655u
120
+ ··· − 464.676u − 7.01531
a
11
=
−1.13844u
121
+ 3.06041u
120
+ ··· − 402.877u − 46.3036
−2.28437u
121
+ 4.20143u
120
+ ··· − 762.095u − 19.6846
(ii) Obstruction class = −1
(iii) Cusp Shapes = −19.4694u
121
+ 41.3664u
120
+ ··· − 2930.19u − 56.4322
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
122
+ 2u
121
+ ··· − 47u + 1
c
3
u
122
+ 6u
121
+ ··· + 56u − 226
c
4
u
122
− u
121
+ ··· − 4608u + 1408
c
6
u
122
− 5u
121
+ ··· + 33792u + 4096
c
7
, c
11
u
122
+ u
121
+ ··· − 266u − 7
c
8
2(2u
122
− 15u
120
+ ··· − 130u + 4)
c
9
, c
12
u
122
− 39u
120
+ ··· + 24316u − 3428
c
10
2(2u
122
− 6u
121
+ ··· + 323446u − 14731)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
122
− 130y
121
+ ··· − 679y + 1
c
3
y
122
− 8y
121
+ ··· + 969116y + 51076
c
4
y
122
− 29y
121
+ ··· − 133603328y + 1982464
c
6
y
122
+ 9y
121
+ ··· + 167247872y + 16777216
c
7
, c
11
y
122
− 93y
121
+ ··· − 12124y + 49
c
8
4(4y
122
− 60y
121
+ ··· − 9596y + 16)
c
9
, c
12
y
122
− 78y
121
+ ··· − 551516768y + 11751184
c
10
4(4y
122
− 192y
121
+ ··· − 4.02466 × 10
10
y + 2.17002 × 10
8
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.775615 + 0.632204I
a = −0.012407 − 0.325555I
b = 0.177801 + 0.559881I
−4.90234 − 0.58995I 0
u = 0.775615 − 0.632204I
a = −0.012407 + 0.325555I
b = 0.177801 − 0.559881I
−4.90234 + 0.58995I 0
u = 0.866013 + 0.476254I
a = 1.79771 + 0.27061I
b = −1.341600 + 0.061557I
−0.249126 + 0.781997I 0
u = 0.866013 − 0.476254I
a = 1.79771 − 0.27061I
b = −1.341600 − 0.061557I
−0.249126 − 0.781997I 0
u = 0.409705 + 0.898488I
a = −2.12084 − 0.15136I
b = 1.138670 − 0.362404I
−2.10139 − 4.17725I 0
u = 0.409705 − 0.898488I
a = −2.12084 + 0.15136I
b = 1.138670 + 0.362404I
−2.10139 + 4.17725I 0
u = 0.377143 + 0.909077I
a = 1.70164 + 0.27529I
b = −1.031380 + 0.284248I
0.99667 − 3.65957I 0
u = 0.377143 − 0.909077I
a = 1.70164 − 0.27529I
b = −1.031380 − 0.284248I
0.99667 + 3.65957I 0
u = −0.576185 + 0.775295I
a = 1.65486 − 0.51228I
b = −1.313900 − 0.454283I
4.67316 + 8.47858I 0
u = −0.576185 − 0.775295I
a = 1.65486 + 0.51228I
b = −1.313900 + 0.454283I
4.67316 − 8.47858I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.352255 + 0.979492I
a = −1.197070 − 0.034278I
b = 0.697958 − 0.393964I
−3.30086 − 4.68037I 0
u = 0.352255 − 0.979492I
a = −1.197070 + 0.034278I
b = 0.697958 + 0.393964I
−3.30086 + 4.68037I 0
u = −0.522215 + 0.801277I
a = 1.23040 − 0.76678I
b = −1.184080 + 0.229121I
4.85947 − 3.25008I 0
u = −0.522215 − 0.801277I
a = 1.23040 + 0.76678I
b = −1.184080 − 0.229121I
4.85947 + 3.25008I 0
u = 1.07777
a = −0.141435
b = 1.49397
3.19101 0
u = 1.10589
a = −2.28955
b = 1.39337
2.70025 0
u = −0.602865 + 0.935266I
a = −1.71285 + 0.28050I
b = 1.299420 + 0.481580I
−0.62473 + 13.83740I 0
u = −0.602865 − 0.935266I
a = −1.71285 − 0.28050I
b = 1.299420 − 0.481580I
−0.62473 − 13.83740I 0
u = −0.049719 + 0.875632I
a = −1.049620 − 0.568246I
b = 0.306080 + 0.195622I
−2.89309 − 4.76305I 0
u = −0.049719 − 0.875632I
a = −1.049620 + 0.568246I
b = 0.306080 − 0.195622I
−2.89309 + 4.76305I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.665390 + 0.551104I
a = −1.34148 − 0.59374I
b = 0.637287 + 0.501677I
−3.41460 − 0.81571I 0
u = 0.665390 − 0.551104I
a = −1.34148 + 0.59374I
b = 0.637287 − 0.501677I
−3.41460 + 0.81571I 0
u = 1.135200 + 0.110908I
a = −0.96099 − 1.84802I
b = 0.497193 − 0.253165I
−3.50391 − 0.18823I 0
u = 1.135200 − 0.110908I
a = −0.96099 + 1.84802I
b = 0.497193 + 0.253165I
−3.50391 + 0.18823I 0
u = 0.334410 + 0.753180I
a = 2.08267 + 1.27878I
b = −1.196830 + 0.062291I
1.36609 − 5.20020I 0
u = 0.334410 − 0.753180I
a = 2.08267 − 1.27878I
b = −1.196830 − 0.062291I
1.36609 + 5.20020I 0
u = 0.183399 + 0.801278I
a = 1.87377 − 0.08410I
b = −1.221180 + 0.531719I
1.65992 − 6.79751I 0
u = 0.183399 − 0.801278I
a = 1.87377 + 0.08410I
b = −1.221180 − 0.531719I
1.65992 + 6.79751I 0
u = −0.634786 + 0.519164I
a = −0.132228 + 0.412531I
b = −0.107726 − 0.905309I
−4.81458 + 8.89704I 0
u = −0.634786 − 0.519164I
a = −0.132228 − 0.412531I
b = −0.107726 + 0.905309I
−4.81458 − 8.89704I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.079680 + 0.559294I
a = 0.493519 + 0.622655I
b = −1.080810 − 0.323126I
−1.01077 + 2.01579I 0
u = 1.079680 − 0.559294I
a = 0.493519 − 0.622655I
b = −1.080810 + 0.323126I
−1.01077 − 2.01579I 0
u = 1.25560
a = 0.389875
b = −0.314608
−2.51444 0
u = 0.534654 + 0.485640I
a = −0.58809 − 1.87401I
b = 1.160220 + 0.055108I
3.66050 − 1.01718I 0
u = 0.534654 − 0.485640I
a = −0.58809 + 1.87401I
b = 1.160220 − 0.055108I
3.66050 + 1.01718I 0
u = −0.699457 + 0.030386I
a = −0.877174 + 0.157986I
b = −0.425792 + 0.749425I
−4.33581 + 2.94214I 0
u = −0.699457 − 0.030386I
a = −0.877174 − 0.157986I
b = −0.425792 − 0.749425I
−4.33581 − 2.94214I 0
u = −0.655881 + 1.132590I
a = −1.194310 + 0.596089I
b = 1.102520 − 0.298129I
−0.59184 − 7.27143I 0
u = −0.655881 − 1.132590I
a = −1.194310 − 0.596089I
b = 1.102520 + 0.298129I
−0.59184 + 7.27143I 0
u = −0.521410 + 0.441731I
a = −1.20152 + 1.00834I
b = 1.253230 + 0.487875I
2.28849 + 2.28510I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.521410 − 0.441731I
a = −1.20152 − 1.00834I
b = 1.253230 − 0.487875I
2.28849 − 2.28510I 0
u = −1.32238
a = −1.41897
b = 1.53116
−0.257311 0
u = −1.328250 + 0.060654I
a = 0.15467 + 1.49603I
b = −0.751033 + 0.084288I
−5.98529 + 7.30859I 0
u = −1.328250 − 0.060654I
a = 0.15467 − 1.49603I
b = −0.751033 − 0.084288I
−5.98529 − 7.30859I 0
u = 0.269414 + 0.602367I
a = −1.86530 − 0.09639I
b = 1.35185 − 0.42215I
4.65701 − 2.45116I 0
u = 0.269414 − 0.602367I
a = −1.86530 + 0.09639I
b = 1.35185 + 0.42215I
4.65701 + 2.45116I 0
u = −0.650483
a = −0.373699
b = 1.47963
2.70145 0
u = 0.529604 + 0.365891I
a = 0.563202 + 0.174393I
b = −0.223446 − 0.433691I
−1.112900 − 0.711100I 0
u = 0.529604 − 0.365891I
a = 0.563202 − 0.174393I
b = −0.223446 + 0.433691I
−1.112900 + 0.711100I 0
u = 1.360610 + 0.133846I
a = −0.153864 − 1.122460I
b = 0.979497 − 0.324439I
−2.12201 − 2.73849I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.360610 − 0.133846I
a = −0.153864 + 1.122460I
b = 0.979497 + 0.324439I
−2.12201 + 2.73849I 0
u = −1.385680 + 0.016899I
a = −0.85213 − 1.23871I
b = 0.916425 − 0.215658I
−3.09190 + 1.93869I 0
u = −1.385680 − 0.016899I
a = −0.85213 + 1.23871I
b = 0.916425 + 0.215658I
−3.09190 − 1.93869I 0
u = −1.386900 + 0.048999I
a = −0.087279 + 0.288462I
b = −0.42959 + 1.44209I
−6.08375 + 3.17733I 0
u = −1.386900 − 0.048999I
a = −0.087279 − 0.288462I
b = −0.42959 − 1.44209I
−6.08375 − 3.17733I 0
u = 1.343800 + 0.388654I
a = 0.988292 + 0.628203I
b = −0.866388 + 0.201249I
−1.89008 − 1.68640I 0
u = 1.343800 − 0.388654I
a = 0.988292 − 0.628203I
b = −0.866388 − 0.201249I
−1.89008 + 1.68640I 0
u = −1.375060 + 0.269131I
a = 0.937772 − 0.941132I
b = −1.29515 − 0.75871I
−3.27421 + 10.58180I 0
u = −1.375060 − 0.269131I
a = 0.937772 + 0.941132I
b = −1.29515 + 0.75871I
−3.27421 − 10.58180I 0
u = −1.40216
a = 1.49034
b = −1.65967
−1.47514 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.412420 + 0.042054I
a = −0.626521 − 1.114050I
b = 1.107850 − 0.660275I
−4.02464 − 2.49840I 0
u = 1.412420 − 0.042054I
a = −0.626521 + 1.114050I
b = 1.107850 + 0.660275I
−4.02464 + 2.49840I 0
u = −1.401620 + 0.179551I
a = −0.698855 + 0.729456I
b = 1.43467 + 0.80415I
−0.64481 + 5.22887I 0
u = −1.401620 − 0.179551I
a = −0.698855 − 0.729456I
b = 1.43467 − 0.80415I
−0.64481 − 5.22887I 0
u = −0.458320 + 0.348468I
a = −0.0949530 − 0.0671101I
b = 0.194439 + 1.006640I
0.13940 + 3.49220I 0. − 12.87430I
u = −0.458320 − 0.348468I
a = −0.0949530 + 0.0671101I
b = 0.194439 − 1.006640I
0.13940 − 3.49220I 0. + 12.87430I
u = 1.43205 + 0.03528I
a = 0.540368 − 0.440322I
b = −1.53811 − 1.07674I
−7.44291 − 3.45379I 0
u = 1.43205 − 0.03528I
a = 0.540368 + 0.440322I
b = −1.53811 + 1.07674I
−7.44291 + 3.45379I 0
u = 0.508714 + 0.239569I
a = 2.60573 + 0.33058I
b = −0.587170 + 0.278130I
−2.77552 − 0.58498I −3.62976 + 3.41286I
u = 0.508714 − 0.239569I
a = 2.60573 − 0.33058I
b = −0.587170 − 0.278130I
−2.77552 + 0.58498I −3.62976 − 3.41286I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44779 + 0.09474I
a = 0.097142 + 0.363127I
b = −0.878917 + 0.104891I
−2.13759 − 0.15481I 0
u = 1.44779 − 0.09474I
a = 0.097142 − 0.363127I
b = −0.878917 − 0.104891I
−2.13759 + 0.15481I 0
u = 1.45575 + 0.06638I
a = 1.18891 + 1.05501I
b = −1.32791 + 0.51804I
−8.25026 − 8.04187I 0
u = 1.45575 − 0.06638I
a = 1.18891 − 1.05501I
b = −1.32791 − 0.51804I
−8.25026 + 8.04187I 0
u = −1.48757 + 0.06154I
a = 0.990274 − 0.488909I
b = −1.155060 − 0.489600I
−9.29579 + 1.61391I 0
u = −1.48757 − 0.06154I
a = 0.990274 + 0.488909I
b = −1.155060 + 0.489600I
−9.29579 − 1.61391I 0
u = −1.46612 + 0.26963I
a = 0.77863 − 1.33904I
b = −1.097240 − 0.245719I
−4.47333 + 8.88815I 0
u = −1.46612 − 0.26963I
a = 0.77863 + 1.33904I
b = −1.097240 + 0.245719I
−4.47333 − 8.88815I 0
u = −1.48611 + 0.16240I
a = 0.008959 + 0.241734I
b = −0.375407 + 0.897195I
−7.63722 + 2.84798I 0
u = −1.48611 − 0.16240I
a = 0.008959 − 0.241734I
b = −0.375407 − 0.897195I
−7.63722 − 2.84798I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.242556 + 0.442406I
a = −1.39110 + 1.68318I
b = 1.202340 + 0.010553I
2.86252 + 0.62133I 2.53772 − 1.69943I
u = −0.242556 − 0.442406I
a = −1.39110 − 1.68318I
b = 1.202340 − 0.010553I
2.86252 − 0.62133I 2.53772 + 1.69943I
u = 1.50016 + 0.10847I
a = −0.073519 − 0.381663I
b = −0.03023 − 1.54240I
−6.34057 − 5.14980I 0
u = 1.50016 − 0.10847I
a = −0.073519 + 0.381663I
b = −0.03023 + 1.54240I
−6.34057 + 5.14980I 0
u = 0.149489 + 0.450882I
a = 0.946444 + 0.664273I
b = −0.219829 − 0.827303I
−1.41915 − 1.70581I 1.34069 + 2.55747I
u = 0.149489 − 0.450882I
a = 0.946444 − 0.664273I
b = −0.219829 + 0.827303I
−1.41915 + 1.70581I 1.34069 − 2.55747I
u = −1.49245 + 0.31895I
a = 1.027280 − 0.866259I
b = −1.170060 − 0.515570I
−5.07312 + 8.01986I 0
u = −1.49245 − 0.31895I
a = 1.027280 + 0.866259I
b = −1.170060 + 0.515570I
−5.07312 − 8.01986I 0
u = −1.53367 + 0.19129I
a = −0.251954 − 0.057929I
b = 0.662809 − 0.966914I
−10.52910 + 3.59379I 0
u = −1.53367 − 0.19129I
a = −0.251954 + 0.057929I
b = 0.662809 + 0.966914I
−10.52910 − 3.59379I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53459 + 0.18622I
a = −0.063801 + 1.117370I
b = 0.927619 + 0.156942I
−3.19399 + 3.58427I 0
u = −1.53459 − 0.18622I
a = −0.063801 − 1.117370I
b = 0.927619 − 0.156942I
−3.19399 − 3.58427I 0
u = 1.54134 + 0.18413I
a = 0.163454 + 0.200612I
b = 0.019026 + 1.351040I
−11.9581 − 11.5640I 0
u = 1.54134 − 0.18413I
a = 0.163454 − 0.200612I
b = 0.019026 − 1.351040I
−11.9581 + 11.5640I 0
u = −1.52432 + 0.32166I
a = −1.27934 + 0.80575I
b = 1.36327 + 0.48853I
−8.42967 + 8.60750I 0
u = −1.52432 − 0.32166I
a = −1.27934 − 0.80575I
b = 1.36327 − 0.48853I
−8.42967 − 8.60750I 0
u = 1.55237 + 0.13662I
a = −0.296046 − 0.732873I
b = 1.17403 − 0.94577I
−4.71749 − 4.37303I 0
u = 1.55237 − 0.13662I
a = −0.296046 + 0.732873I
b = 1.17403 + 0.94577I
−4.71749 + 4.37303I 0
u = −1.52938 + 0.36250I
a = −0.942365 + 0.603510I
b = 0.972834 + 0.682403I
−9.48023 + 9.55179I 0
u = −1.52938 − 0.36250I
a = −0.942365 − 0.603510I
b = 0.972834 − 0.682403I
−9.48023 − 9.55179I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.57755
a = 0.760465
b = −1.83742
−8.76670 0
u = 1.55696 + 0.27023I
a = 0.827914 + 0.851708I
b = −1.36991 + 0.67143I
−2.31387 − 12.34110I 0
u = 1.55696 − 0.27023I
a = 0.827914 − 0.851708I
b = −1.36991 − 0.67143I
−2.31387 + 12.34110I 0
u = 1.58518 + 0.04671I
a = −0.326598 + 0.280580I
b = −0.085106 + 0.955657I
−12.14960 + 2.68694I 0
u = 1.58518 − 0.04671I
a = −0.326598 − 0.280580I
b = −0.085106 − 0.955657I
−12.14960 − 2.68694I 0
u = −1.58417 + 0.15384I
a = 0.199413 − 0.162583I
b = −0.043572 − 0.968118I
−12.81520 + 3.35893I 0
u = −1.58417 − 0.15384I
a = 0.199413 + 0.162583I
b = −0.043572 + 0.968118I
−12.81520 − 3.35893I 0
u = −0.069562 + 0.389670I
a = 1.41944 + 1.41076I
b = 0.179256 − 0.179773I
1.06508 − 1.32482I 2.58609 + 0.57560I
u = −0.069562 − 0.389670I
a = 1.41944 − 1.41076I
b = 0.179256 + 0.179773I
1.06508 + 1.32482I 2.58609 − 0.57560I
u = 1.57333 + 0.32686I
a = −1.032990 − 0.803924I
b = 1.40890 − 0.65412I
−7.6645 − 18.4585I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57333 − 0.32686I
a = −1.032990 + 0.803924I
b = 1.40890 + 0.65412I
−7.6645 + 18.4585I 0
u = −0.234695 + 0.126837I
a = 5.66815 − 3.74098I
b = −1.054280 − 0.404093I
−2.50341 + 7.21265I −7.10321 − 8.54408I
u = −0.234695 − 0.126837I
a = 5.66815 + 3.74098I
b = −1.054280 + 0.404093I
−2.50341 − 7.21265I −7.10321 + 8.54408I
u = 1.69602 + 0.44408I
a = −0.966528 − 0.261300I
b = 1.100790 − 0.373094I
−8.18869 − 1.41740I 0
u = 1.69602 − 0.44408I
a = −0.966528 + 0.261300I
b = 1.100790 + 0.373094I
−8.18869 + 1.41740I 0
u = −1.79240
a = 0.0608172
b = −0.784497
−12.2055 0
u = −0.154129 + 0.096177I
a = −3.76477 + 6.22858I
b = 0.875629 + 0.355879I
1.19514 + 1.85495I −7.32549 − 0.78497I
u = −0.154129 − 0.096177I
a = −3.76477 − 6.22858I
b = 0.875629 − 0.355879I
1.19514 − 1.85495I −7.32549 + 0.78497I
u = −0.134705 + 0.105396I
a = 1.65107 + 2.11347I
b = −1.09663 + 0.96393I
−2.11552 + 2.94240I −23.5910 − 10.1802I
u = −0.134705 − 0.105396I
a = 1.65107 − 2.11347I
b = −1.09663 − 0.96393I
−2.11552 − 2.94240I −23.5910 + 10.1802I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0403703
a = −31.7055
b = −1.40556
3.28668 1.98650
u = 2.23388
a = −0.642739
b = 0.817082
−10.3119 0
17
II. I
u
2
= h−182u
19
− 1044u
18
+ · · · + 101b + 381, 2772u
19
+ 7347u
18
+ · · · +
101a − 2400, u
20
+ 4u
19
+ · · · − 5u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
−27.4455u
19
− 72.7426u
18
+ ··· + 81.4851u + 23.7624
1.80198u
19
+ 10.3366u
18
+ ··· − 19.6733u − 3.77228
a
10
=
−25.6436u
19
− 62.4059u
18
+ ··· + 61.8119u + 19.9901
1.80198u
19
+ 10.3366u
18
+ ··· − 19.6733u − 3.77228
a
7
=
38.9208u
19
+ 103.535u
18
+ ··· − 113.069u − 35.1089
−10.3564u
19
− 26.5941u
18
+ ··· + 34.1881u + 6.00990
a
12
=
−17.9010u
19
− 51.1683u
18
+ ··· + 53.3366u + 20.3861
108.644u
19
+ 280.406u
18
+ ··· − 327.812u − 74.9901
a
4
=
−43.7921u
19
− 111.653u
18
+ ··· + 146.307u + 22.9109
21.4356u
19
+ 61.0594u
18
+ ··· − 71.1188u − 19.9010
a
8
=
20.3762u
19
+ 53.9604u
18
+ ··· − 52.9208u − 19.7327
−27.7525u
19
− 66.9208u
18
+ ··· + 73.8416u + 15.4653
a
11
=
−23.8020u
19
− 63.3366u
18
+ ··· + 70.6733u + 21.7723
35.0891u
19
+ 97.1485u
18
+ ··· − 122.297u − 27.7525
(ii) Obstruction class = 1
(iii) Cusp Shapes =
25554
101
u
19
+
65517
101
u
18
+ ··· −
76191
101
u −
16954
101
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
20
+ 4u
19
+ ··· − 5u − 1
c
3
u
20
− 4u
19
+ ··· − 3u + 1
c
4
u
20
+ u
19
+ ··· + 7u
2
− 1
c
5
u
20
− 4u
19
+ ··· + 5u − 1
c
6
u
20
+ u
18
+ ··· + 4u − 1
c
7
u
20
− u
19
+ ··· + 10u − 1
c
8
u
20
+ u
19
+ ··· + 2u + 1
c
9
u
20
− u
19
+ ··· + 9u + 1
c
10
u
20
+ 2u
19
+ ··· + 3u
2
− 1
c
11
u
20
+ u
19
+ ··· − 10u − 1
c
12
u
20
+ u
19
+ ··· − 9u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
20
− 28y
19
+ ··· − 17y + 1
c
3
y
20
− 4y
19
+ ··· − 11y + 1
c
4
y
20
− 5y
19
+ ··· − 14y + 1
c
6
y
20
+ 2y
19
+ ··· − 22y + 1
c
7
, c
11
y
20
− 15y
19
+ ··· − 30y + 1
c
8
y
20
− 13y
19
+ ··· − 2y + 1
c
9
, c
12
y
20
− 13y
19
+ ··· − 57y + 1
c
10
y
20
− 14y
19
+ ··· − 6y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.896297
a = −2.38704
b = 0.165507
−3.18441 −30.3070
u = −0.190451 + 0.848378I
a = 2.16621 − 0.76037I
b = −1.017100 + 0.282444I
−1.46247 − 6.35124I −3.54688 + 4.99562I
u = −0.190451 − 0.848378I
a = 2.16621 + 0.76037I
b = −1.017100 − 0.282444I
−1.46247 + 6.35124I −3.54688 − 4.99562I
u = −1.35816
a = −1.59280
b = 1.54937
0.628858 0.350580
u = 0.351813 + 0.459000I
a = −1.81640 − 1.53750I
b = 0.986114 − 0.373835I
1.55707 − 2.40859I −1.25084 + 8.89495I
u = 0.351813 − 0.459000I
a = −1.81640 + 1.53750I
b = 0.986114 + 0.373835I
1.55707 + 2.40859I −1.25084 − 8.89495I
u = −1.39976 + 0.26294I
a = 1.19692 − 1.28439I
b = −1.143190 − 0.481390I
−5.79449 + 9.99089I −6.38131 − 9.42743I
u = −1.39976 − 0.26294I
a = 1.19692 + 1.28439I
b = −1.143190 + 0.481390I
−5.79449 − 9.99089I −6.38131 + 9.42743I
u = −1.43667 + 0.10502I
a = 0.037991 + 0.377660I
b = −0.77311 + 1.27562I
−7.02941 + 4.40536I −8.94199 − 7.44609I
u = −1.43667 − 0.10502I
a = 0.037991 − 0.377660I
b = −0.77311 − 1.27562I
−7.02941 − 4.40536I −8.94199 + 7.44609I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42294 + 0.24818I
a = −0.572321 − 0.786150I
b = 0.842644 − 0.154159I
−2.05407 − 1.07507I −5.19450 − 0.08506I
u = 1.42294 − 0.24818I
a = −0.572321 + 0.786150I
b = 0.842644 + 0.154159I
−2.05407 + 1.07507I −5.19450 + 0.08506I
u = −1.53592 + 0.13806I
a = −0.236351 + 0.848470I
b = 0.988247 + 0.846937I
−5.00654 + 4.48393I −13.2802 − 9.2519I
u = −1.53592 − 0.13806I
a = −0.236351 − 0.848470I
b = 0.988247 − 0.846937I
−5.00654 − 4.48393I −13.2802 + 9.2519I
u = 0.043620 + 0.360386I
a = 0.521847 + 0.623343I
b = −0.892025 − 0.829594I
−1.85170 − 2.88685I 6.13700 + 3.63777I
u = 0.043620 − 0.360386I
a = 0.521847 − 0.623343I
b = −0.892025 + 0.829594I
−1.85170 + 2.88685I 6.13700 − 3.63777I
u = 1.69381
a = 0.798770
b = −1.48154
−8.21233 −2.67880
u = −1.73582
a = −0.482281
b = 0.295154
−12.9390 −14.7530
u = −0.184416
a = 5.50818
b = 1.33928
4.77357 8.94880
u = 2.17715
a = 0.559399
b = −0.850939
−10.1606 17.3570
22
III. I
u
3
= hb, a + 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
a
2
=
1
1
a
6
=
−1
0
a
3
=
0
1
a
9
=
−1
0
a
10
=
−1
0
a
7
=
−1
0
a
12
=
1
0
a
4
=
1
1
a
8
=
−2
−1
a
11
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
u − 1
c
4
, c
5
, c
8
c
10
, c
11
u + 1
c
6
, c
9
, c
12
u
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
10
, c
11
y −1
c
6
, c
9
, c
12
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
26
IV. I
u
4
= hb + a − 1, a
2
− 2a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
a
2
=
1
1
a
6
=
−1
0
a
3
=
0
1
a
9
=
a
−a + 1
a
10
=
1
−a + 1
a
7
=
−a
2
a
12
=
−a
2
a
4
=
2a + 1
−2a + 1
a
8
=
−a − 1
a
a
11
=
1
−a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
10
c
11
(u − 1)
2
c
3
, c
4
u
2
− 2u − 1
c
5
, c
7
, c
8
(u + 1)
2
c
6
, c
9
, c
12
u
2
− 2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
8
, c
10
c
11
(y −1)
2
c
3
, c
4
y
2
− 6y + 1
c
6
, c
9
, c
12
(y −2)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.414214
b = 1.41421
1.64493 −4.00000
u = 1.00000
a = 2.41421
b = −1.41421
1.64493 −4.00000
30
V. I
u
5
= hb + 2a + 2, 2a
2
+ 4a + 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
a
2
=
1
1
a
6
=
−1
0
a
3
=
0
1
a
9
=
a
−2a − 2
a
10
=
−a − 2
−2a − 2
a
7
=
2a + 2
2
a
12
=
2a + 2
2
a
4
=
2
4a + 5
a
8
=
3a + 4
3a + 6
a
11
=
−a − 2
−3a − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
(u − 1)
2
c
3
, c
4
, c
6
c
9
, c
12
u
2
− 2
c
5
, c
7
(u + 1)
2
c
8
2(2u
2
− 4u + 1)
c
10
2(2u
2
+ 4u + 1)
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
11
(y −1)
2
c
3
, c
4
, c
6
c
9
, c
12
(y −2)
2
c
8
, c
10
4(4y
2
− 12y + 1)
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.292893
b = −1.41421
1.64493 −4.00000
u = 1.00000
a = −1.70711
b = 1.41421
1.64493 −4.00000
34
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
5
)(u
20
+ 4u
19
+ ··· − 5u − 1)(u
122
+ 2u
121
+ ··· − 47u + 1)
c
3
(u − 1)(u
2
− 2)(u
2
− 2u − 1)(u
20
− 4u
19
+ ··· − 3u + 1)
· (u
122
+ 6u
121
+ ··· + 56u − 226)
c
4
(u + 1)(u
2
− 2)(u
2
− 2u − 1)(u
20
+ u
19
+ ··· + 7u
2
− 1)
· (u
122
− u
121
+ ··· − 4608u + 1408)
c
5
((u + 1)
5
)(u
20
− 4u
19
+ ··· + 5u − 1)(u
122
+ 2u
121
+ ··· − 47u + 1)
c
6
u(u
2
− 2)
2
(u
20
+ u
18
+ ··· + 4u − 1)
· (u
122
− 5u
121
+ ··· + 33792u + 4096)
c
7
(u − 1)(u + 1)
4
(u
20
− u
19
+ ··· + 10u − 1)(u
122
+ u
121
+ ··· − 266u − 7)
c
8
4(u + 1)
3
(2u
2
− 4u + 1)(u
20
+ u
19
+ ··· + 2u + 1)
· (2u
122
− 15u
120
+ ··· − 130u + 4)
c
9
u(u
2
− 2)
2
(u
20
− u
19
+ ··· + 9u + 1)
· (u
122
− 39u
120
+ ··· + 24316u − 3428)
c
10
4(u − 1)
2
(u + 1)(2u
2
+ 4u + 1)(u
20
+ 2u
19
+ ··· + 3u
2
− 1)
· (2u
122
− 6u
121
+ ··· + 323446u − 14731)
c
11
((u − 1)
4
)(u + 1)(u
20
+ u
19
+ ··· − 10u − 1)(u
122
+ u
121
+ ··· − 266u − 7)
c
12
u(u
2
− 2)
2
(u
20
+ u
19
+ ··· − 9u + 1)
· (u
122
− 39u
120
+ ··· + 24316u − 3428)
35
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
((y −1)
5
)(y
20
− 28y
19
+ ··· − 17y + 1)(y
122
− 130y
121
+ ··· − 679y + 1)
c
3
((y −2)
2
)(y −1)(y
2
− 6y + 1)(y
20
− 4y
19
+ ··· − 11y + 1)
· (y
122
− 8y
121
+ ··· + 969116y + 51076)
c
4
((y −2)
2
)(y −1)(y
2
− 6y + 1)(y
20
− 5y
19
+ ··· − 14y + 1)
· (y
122
− 29y
121
+ ··· − 133603328y + 1982464)
c
6
y(y −2)
4
(y
20
+ 2y
19
+ ··· − 22y + 1)
· (y
122
+ 9y
121
+ ··· + 167247872y + 16777216)
c
7
, c
11
((y −1)
5
)(y
20
− 15y
19
+ ··· − 30y + 1)
· (y
122
− 93y
121
+ ··· − 12124y + 49)
c
8
16(y −1)
3
(4y
2
− 12y + 1)(y
20
− 13y
19
+ ··· − 2y + 1)
· (4y
122
− 60y
121
+ ··· − 9596y + 16)
c
9
, c
12
y(y −2)
4
(y
20
− 13y
19
+ ··· − 57y + 1)
· (y
122
− 78y
121
+ ··· − 551516768y + 11751184)
c
10
16(y −1)
3
(4y
2
− 12y + 1)(y
20
− 14y
19
+ ··· − 6y + 1)
· (4y
122
− 192y
121
+ ··· − 40246645514y + 217002361)
36
