12a
0292
(K12a
0292
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 11 4 12 7 5 1 9
Solving Sequence
2,5
6
3,11
7 1 10 4 8 9 12
c
5
c
2
c
6
c
1
c
10
c
4
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.95218 × 10
363
u
136
+ 3.07057 × 10
364
u
135
+ ··· + 1.46551 × 10
364
b + 1.37260 × 10
363
,
3.86404 × 10
367
u
136
− 1.31553 × 10
367
u
135
+ ··· + 1.06498 × 10
368
a − 4.78268 × 10
370
,
u
137
+ 3u
136
+ ··· + 3010u − 169i
I
u
2
= h−8u
28
+ 17u
27
+ ··· + b − 27u, −41u
28
+ 97u
27
+ ··· + a + 59, u
29
− 3u
28
+ ··· − 4u + 1i
I
u
3
= hb − 1, a − 2, u + 1i
* 3 irreducible components of dim
C
= 0, with total 167 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
= h8.95 × 10
363
u
136
+ 3.07 × 10
364
u
135
+ · · · + 1.47 × 10
364
b + 1.37 ×
10
363
, 3.86 × 10
367
u
136
− 1.32 × 10
367
u
135
+ · · · + 1.06 × 10
368
a − 4.78 ×
10
370
, u
137
+ 3u
136
+ · · · + 3010u − 169i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
−0.362827u
136
+ 0.123526u
135
+ ··· − 7278.77u + 449.086
−0.610860u
136
− 2.09523u
135
+ ··· − 140.956u − 0.0936606
a
7
=
8.71451u
136
+ 15.9346u
135
+ ··· + 19901.9u − 1151.80
−4.27979u
136
− 6.45501u
135
+ ··· − 1528.53u + 102.101
a
1
=
u
3
u
5
− u
3
+ u
a
10
=
0.248032u
136
+ 2.21876u
135
+ ··· − 7137.82u + 449.179
−0.610860u
136
− 2.09523u
135
+ ··· − 140.956u − 0.0936606
a
4
=
3.38283u
136
+ 5.59457u
135
+ ··· + 10568.1u − 625.048
3.33673u
136
+ 9.05546u
135
+ ··· + 19245.1u − 1033.06
a
8
=
−12.0178u
136
− 33.9406u
135
+ ··· − 50266.6u + 2733.25
13.2592u
136
+ 28.2260u
135
+ ··· + 32710.1u − 1807.05
a
9
=
6.13145u
136
+ 16.8119u
135
+ ··· + 27710.4u − 1478.24
−6.55283u
136
− 15.1761u
135
+ ··· − 17876.4u + 953.654
a
12
=
−2.13161u
136
− 3.37166u
135
+ ··· − 11534.8u + 685.770
0.694888u
136
+ 0.172607u
135
+ ··· + 1710.79u − 115.185
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.91390u
136
+ 17.0980u
135
+ ··· − 4100.08u + 335.512
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
137
+ 53u
136
+ ··· + 3208982u + 28561
c
2
, c
5
u
137
+ 3u
136
+ ··· + 3010u − 169
c
3
, c
7
u
137
+ u
136
+ ··· + 481416u − 77291
c
4
, c
10
u
137
+ 2u
136
+ ··· − 8u − 1
c
6
u
137
− 3u
136
+ ··· + 288732u − 248089
c
8
, c
12
u
137
− 9u
136
+ ··· + 1468u − 271
c
9
u
137
+ 11u
136
+ ··· − 102807486u − 5507323
c
11
u
137
− 63u
136
+ ··· + 597316u − 73441
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
137
+ 75y
136
+ ··· + 4313902139478y −815730721
c
2
, c
5
y
137
− 53y
136
+ ··· + 3208982y −28561
c
3
, c
7
y
137
+ 109y
136
+ ··· − 59701913870y −5973898681
c
4
, c
10
y
137
− 116y
136
+ ··· + 78y −1
c
6
y
137
− 35y
136
+ ··· − 1429947953852y −61548151921
c
8
, c
12
y
137
− 63y
136
+ ··· + 597316y −73441
c
9
y
137
− 43y
136
+ ··· + 1343419781833972y −30330606626329
c
11
y
137
+ 37y
136
+ ··· + 126623191148y −5393580481
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.805157 + 0.597246I
a = 0.94208 − 3.06119I
b = −1.200520 + 0.000228I
7.32539 − 3.28612I 0
u = −0.805157 − 0.597246I
a = 0.94208 + 3.06119I
b = −1.200520 − 0.000228I
7.32539 + 3.28612I 0
u = 0.582366 + 0.820362I
a = 0.513092 − 0.586948I
b = −1.259460 − 0.302714I
3.86691 + 6.57125I 0
u = 0.582366 − 0.820362I
a = 0.513092 + 0.586948I
b = −1.259460 + 0.302714I
3.86691 − 6.57125I 0
u = −0.420350 + 0.891795I
a = 0.470140 + 0.130367I
b = −1.280030 − 0.110876I
6.43121 + 2.64534I 0
u = −0.420350 − 0.891795I
a = 0.470140 − 0.130367I
b = −1.280030 + 0.110876I
6.43121 − 2.64534I 0
u = −0.795381 + 0.579290I
a = −0.049486 − 1.048380I
b = −1.81121 + 0.39041I
3.92418 − 2.12374I 0
u = −0.795381 − 0.579290I
a = −0.049486 + 1.048380I
b = −1.81121 − 0.39041I
3.92418 + 2.12374I 0
u = 0.729232 + 0.657074I
a = −0.115303 + 0.577631I
b = −1.362000 − 0.162869I
3.43840 − 4.29669I 0
u = 0.729232 − 0.657074I
a = −0.115303 − 0.577631I
b = −1.362000 + 0.162869I
3.43840 + 4.29669I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.995976 + 0.219993I
a = 0.48351 + 1.76669I
b = −0.382499 + 0.535032I
−5.05036 − 3.28202I 0
u = 0.995976 − 0.219993I
a = 0.48351 − 1.76669I
b = −0.382499 − 0.535032I
−5.05036 + 3.28202I 0
u = −0.768667 + 0.573669I
a = 1.350920 + 0.170266I
b = −1.321950 − 0.054992I
5.55498 + 3.33530I 0
u = −0.768667 − 0.573669I
a = 1.350920 − 0.170266I
b = −1.321950 + 0.054992I
5.55498 − 3.33530I 0
u = −0.762804 + 0.579753I
a = 0.82594 − 2.36747I
b = −1.50210 − 1.09316I
6.00582 − 0.74830I 0
u = −0.762804 − 0.579753I
a = 0.82594 + 2.36747I
b = −1.50210 + 1.09316I
6.00582 + 0.74830I 0
u = 0.937824 + 0.128756I
a = −0.55983 − 1.91038I
b = 0.328013 − 0.372403I
−4.63559 + 2.51248I 0
u = 0.937824 − 0.128756I
a = −0.55983 + 1.91038I
b = 0.328013 + 0.372403I
−4.63559 − 2.51248I 0
u = 0.460219 + 0.826570I
a = −0.535977 − 0.241258I
b = −0.292622 − 1.001390I
3.86275 + 7.80029I 0
u = 0.460219 − 0.826570I
a = −0.535977 + 0.241258I
b = −0.292622 + 1.001390I
3.86275 − 7.80029I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.835922 + 0.648923I
a = −1.33758 − 0.79335I
b = −0.20053 − 1.62112I
6.59331 − 2.52785I 0
u = 0.835922 − 0.648923I
a = −1.33758 + 0.79335I
b = −0.20053 + 1.62112I
6.59331 + 2.52785I 0
u = −0.536396 + 0.912755I
a = 0.442341 + 0.030875I
b = −1.45528 + 0.40733I
6.77971 − 7.26834I 0
u = −0.536396 − 0.912755I
a = 0.442341 − 0.030875I
b = −1.45528 − 0.40733I
6.77971 + 7.26834I 0
u = 0.756967 + 0.556841I
a = 0.179209 − 0.816030I
b = −1.323400 − 0.283899I
5.45604 + 0.75830I 0
u = 0.756967 − 0.556841I
a = 0.179209 + 0.816030I
b = −1.323400 + 0.283899I
5.45604 − 0.75830I 0
u = −0.613712 + 0.691576I
a = 0.152562 − 0.705237I
b = 0.043581 − 0.708646I
−0.12937 − 2.89825I 0
u = −0.613712 − 0.691576I
a = 0.152562 + 0.705237I
b = 0.043581 + 0.708646I
−0.12937 + 2.89825I 0
u = −0.885459 + 0.249630I
a = −0.638486 + 0.656935I
b = −0.446036 + 0.542795I
−1.49558 + 0.52853I 0
u = −0.885459 − 0.249630I
a = −0.638486 − 0.656935I
b = −0.446036 − 0.542795I
−1.49558 − 0.52853I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.903559 + 0.594068I
a = −1.56952 + 0.00075I
b = 1.321480 + 0.032747I
7.00750 + 7.99825I 0
u = −0.903559 − 0.594068I
a = −1.56952 − 0.00075I
b = 1.321480 − 0.032747I
7.00750 − 7.99825I 0
u = −0.906445 + 0.590629I
a = −0.30300 + 2.22630I
b = 1.76820 + 0.60307I
3.56012 + 6.77597I 0
u = −0.906445 − 0.590629I
a = −0.30300 − 2.22630I
b = 1.76820 − 0.60307I
3.56012 − 6.77597I 0
u = 0.858844 + 0.313988I
a = −0.088619 + 1.069430I
b = 1.361350 + 0.283896I
5.33482 + 3.74361I 0
u = 0.858844 − 0.313988I
a = −0.088619 − 1.069430I
b = 1.361350 − 0.283896I
5.33482 − 3.74361I 0
u = 0.493761 + 0.768951I
a = −0.550981 + 0.376015I
b = 1.232270 + 0.274925I
2.23426 + 1.95781I 0
u = 0.493761 − 0.768951I
a = −0.550981 − 0.376015I
b = 1.232270 − 0.274925I
2.23426 − 1.95781I 0
u = 0.363183 + 0.833917I
a = 0.0355355 + 0.0902461I
b = −1.273840 − 0.188516I
6.39976 + 1.56844I 0
u = 0.363183 − 0.833917I
a = 0.0355355 − 0.0902461I
b = −1.273840 + 0.188516I
6.39976 − 1.56844I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.926008 + 0.591810I
a = 0.876925 + 0.471655I
b = 1.74886 − 0.87662I
5.48126 + 5.41757I 0
u = −0.926008 − 0.591810I
a = 0.876925 − 0.471655I
b = 1.74886 + 0.87662I
5.48126 − 5.41757I 0
u = −0.925435 + 0.610641I
a = −0.35428 + 2.26738I
b = 1.207250 + 0.018699I
5.02673 + 1.38814I 0
u = −0.925435 − 0.610641I
a = −0.35428 − 2.26738I
b = 1.207250 − 0.018699I
5.02673 − 1.38814I 0
u = −0.734042 + 0.502418I
a = 0.94683 − 1.32163I
b = 0.200494 − 0.739966I
1.65290 + 1.27822I 0
u = −0.734042 − 0.502418I
a = 0.94683 + 1.32163I
b = 0.200494 + 0.739966I
1.65290 − 1.27822I 0
u = 0.885695 + 0.672060I
a = −0.322862 − 1.340580I
b = 1.123070 − 0.407962I
2.99396 − 0.90542I 0
u = 0.885695 − 0.672060I
a = −0.322862 + 1.340580I
b = 1.123070 + 0.407962I
2.99396 + 0.90542I 0
u = −0.979547 + 0.531619I
a = 0.129656 − 0.966748I
b = 0.154616 − 0.769501I
0.82013 + 2.94411I 0
u = −0.979547 − 0.531619I
a = 0.129656 + 0.966748I
b = 0.154616 + 0.769501I
0.82013 − 2.94411I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.714460 + 0.857758I
a = −0.197795 + 0.124690I
b = 1.50337 − 0.46402I
12.58990 − 3.92968I 0
u = −0.714460 − 0.857758I
a = −0.197795 − 0.124690I
b = 1.50337 + 0.46402I
12.58990 + 3.92968I 0
u = 0.947528 + 0.599587I
a = 0.25581 − 2.36909I
b = 1.207140 − 0.361511I
4.80636 − 5.39144I 0
u = 0.947528 − 0.599587I
a = 0.25581 + 2.36909I
b = 1.207140 + 0.361511I
4.80636 + 5.39144I 0
u = −1.110130 + 0.161489I
a = −0.47189 + 1.38956I
b = 0.136424 + 0.945028I
−3.43698 − 0.34927I 0
u = −1.110130 − 0.161489I
a = −0.47189 − 1.38956I
b = 0.136424 − 0.945028I
−3.43698 + 0.34927I 0
u = 0.718727 + 0.865772I
a = −0.519296 − 0.193775I
b = −0.024883 + 0.171220I
5.24176 − 4.17178I 0
u = 0.718727 − 0.865772I
a = −0.519296 + 0.193775I
b = −0.024883 − 0.171220I
5.24176 + 4.17178I 0
u = 0.845642 + 0.209874I
a = −0.00020 − 1.47019I
b = 1.48944 − 0.27192I
3.35618 + 0.92289I 0
u = 0.845642 − 0.209874I
a = −0.00020 + 1.47019I
b = 1.48944 + 0.27192I
3.35618 − 0.92289I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.011870 + 0.529443I
a = −0.777769 + 1.148430I
b = −0.080843 + 0.852716I
−3.12449 + 2.84870I 0
u = −1.011870 − 0.529443I
a = −0.777769 − 1.148430I
b = −0.080843 − 0.852716I
−3.12449 − 2.84870I 0
u = −1.140060 + 0.067440I
a = −1.083730 + 0.788776I
b = −0.986959 + 0.326375I
−3.15353 − 0.17714I 0
u = −1.140060 − 0.067440I
a = −1.083730 − 0.788776I
b = −0.986959 − 0.326375I
−3.15353 + 0.17714I 0
u = −0.549630 + 1.013530I
a = −0.369820 − 0.135073I
b = 1.43098 − 0.42597I
9.2405 − 12.8750I 0
u = −0.549630 − 1.013530I
a = −0.369820 + 0.135073I
b = 1.43098 + 0.42597I
9.2405 + 12.8750I 0
u = 1.014690 + 0.547849I
a = −0.390138 + 0.507725I
b = 0.163450 + 0.015988I
0.84620 − 2.97680I 0
u = 1.014690 − 0.547849I
a = −0.390138 − 0.507725I
b = 0.163450 − 0.015988I
0.84620 + 2.97680I 0
u = 0.641887 + 0.551583I
a = 0.388466 + 0.873075I
b = 0.182082 − 0.132393I
1.99070 − 1.46530I 0
u = 0.641887 − 0.551583I
a = 0.388466 − 0.873075I
b = 0.182082 + 0.132393I
1.99070 + 1.46530I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.867742 + 0.770476I
a = 1.39238 − 1.47624I
b = −1.240520 − 0.006387I
8.87079 + 3.84557I 0
u = −0.867742 − 0.770476I
a = 1.39238 + 1.47624I
b = −1.240520 + 0.006387I
8.87079 − 3.84557I 0
u = −1.160450 + 0.022793I
a = 1.22869 + 1.01050I
b = 1.076690 + 0.258704I
−2.25383 + 5.25220I 0
u = −1.160450 − 0.022793I
a = 1.22869 − 1.01050I
b = 1.076690 − 0.258704I
−2.25383 − 5.25220I 0
u = −1.116600 + 0.322148I
a = −0.005519 + 1.177000I
b = −0.179972 + 0.823837I
0.361235 + 0.123400I 0
u = −1.116600 − 0.322148I
a = −0.005519 − 1.177000I
b = −0.179972 − 0.823837I
0.361235 − 0.123400I 0
u = 1.031800 + 0.572120I
a = 0.15905 + 1.64340I
b = −1.216460 + 0.463784I
0.71536 − 5.23431I 0
u = 1.031800 − 0.572120I
a = 0.15905 − 1.64340I
b = −1.216460 − 0.463784I
0.71536 + 5.23431I 0
u = −0.895469 + 0.768409I
a = −1.47837 + 0.48380I
b = 1.285770 + 0.021386I
8.78653 + 1.96366I 0
u = −0.895469 − 0.768409I
a = −1.47837 − 0.48380I
b = 1.285770 − 0.021386I
8.78653 − 1.96366I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.485530 + 0.651974I
a = −0.603509 − 0.363535I
b = 1.186540 + 0.144046I
2.28053 + 0.47722I 0
u = 0.485530 − 0.651974I
a = −0.603509 + 0.363535I
b = 1.186540 − 0.144046I
2.28053 − 0.47722I 0
u = −1.005540 + 0.634699I
a = 0.799485 − 1.090420I
b = 0.064117 − 0.798768I
−1.28991 + 8.03213I 0
u = −1.005540 − 0.634699I
a = 0.799485 + 1.090420I
b = 0.064117 + 0.798768I
−1.28991 − 8.03213I 0
u = 0.790095 + 0.169162I
a = 1.85284 − 0.18452I
b = 1.119750 + 0.581126I
1.46263 + 2.58621I 0
u = 0.790095 − 0.169162I
a = 1.85284 + 0.18452I
b = 1.119750 − 0.581126I
1.46263 − 2.58621I 0
u = 1.041870 + 0.583418I
a = 0.78559 + 1.40487I
b = −0.397212 + 1.265350I
−0.75701 − 7.14868I 0
u = 1.041870 − 0.583418I
a = 0.78559 − 1.40487I
b = −0.397212 − 1.265350I
−0.75701 + 7.14868I 0
u = 0.371154 + 0.691685I
a = −1.114760 − 0.578166I
b = −0.165702 + 0.273462I
4.41381 + 2.76426I 0
u = 0.371154 − 0.691685I
a = −1.114760 + 0.578166I
b = −0.165702 − 0.273462I
4.41381 − 2.76426I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.229050 + 0.049572I
a = 0.341295 − 1.278050I
b = −0.145670 − 0.890855I
−1.99459 − 5.49143I 0
u = −1.229050 − 0.049572I
a = 0.341295 + 1.278050I
b = −0.145670 + 0.890855I
−1.99459 + 5.49143I 0
u = 1.069700 + 0.633929I
a = 0.16348 + 2.01580I
b = −1.251860 + 0.382869I
0.53910 − 7.26662I 0
u = 1.069700 − 0.633929I
a = 0.16348 − 2.01580I
b = −1.251860 − 0.382869I
0.53910 + 7.26662I 0
u = −1.001310 + 0.737994I
a = 0.34453 − 1.90902I
b = −1.50917 − 0.56211I
11.6929 + 9.8554I 0
u = −1.001310 − 0.737994I
a = 0.34453 + 1.90902I
b = −1.50917 + 0.56211I
11.6929 − 9.8554I 0
u = 0.960728 + 0.809195I
a = 0.343260 − 0.121407I
b = −0.0794187 − 0.0837330I
4.55247 − 1.99359I 0
u = 0.960728 − 0.809195I
a = 0.343260 + 0.121407I
b = −0.0794187 + 0.0837330I
4.55247 + 1.99359I 0
u = 0.709570 + 0.222459I
a = −2.90146 + 1.84149I
b = −1.090360 + 0.387055I
5.72206 − 6.07019I 0
u = 0.709570 − 0.222459I
a = −2.90146 − 1.84149I
b = −1.090360 − 0.387055I
5.72206 + 6.07019I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.062540 + 0.686303I
a = −0.26131 − 2.14684I
b = 1.255050 − 0.362414I
2.42242 − 12.22940I 0
u = 1.062540 − 0.686303I
a = −0.26131 + 2.14684I
b = 1.255050 + 0.362414I
2.42242 + 12.22940I 0
u = 0.409639 + 0.609308I
a = 0.540581 − 0.186551I
b = 0.456706 + 0.895631I
0.93405 + 2.42400I 0
u = 0.409639 − 0.609308I
a = 0.540581 + 0.186551I
b = 0.456706 − 0.895631I
0.93405 − 2.42400I 0
u = −0.254762 + 1.241990I
a = −0.199701 + 0.008791I
b = 1.247380 + 0.132801I
8.53970 − 1.11478I 0
u = −0.254762 − 1.241990I
a = −0.199701 − 0.008791I
b = 1.247380 − 0.132801I
8.53970 + 1.11478I 0
u = 1.097110 + 0.646744I
a = −0.70376 − 1.25963I
b = 0.252860 − 1.206560I
1.98292 − 13.29050I 0
u = 1.097110 − 0.646744I
a = −0.70376 + 1.25963I
b = 0.252860 + 1.206560I
1.98292 + 13.29050I 0
u = 1.116560 + 0.618655I
a = 0.466784 − 0.365170I
b = −0.163249 − 0.047506I
2.30974 − 7.87136I 0
u = 1.116560 − 0.618655I
a = 0.466784 + 0.365170I
b = −0.163249 + 0.047506I
2.30974 + 7.87136I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.289420 + 0.076858I
a = 0.890311 − 0.724116I
b = 1.192950 − 0.420831I
−0.17009 − 5.16405I 0
u = 1.289420 − 0.076858I
a = 0.890311 + 0.724116I
b = 1.192950 + 0.420831I
−0.17009 + 5.16405I 0
u = −1.106890 + 0.698920I
a = −0.20055 + 1.86333I
b = 1.49316 + 0.49224I
5.03525 + 13.19610I 0
u = −1.106890 − 0.698920I
a = −0.20055 − 1.86333I
b = 1.49316 − 0.49224I
5.03525 − 13.19610I 0
u = −0.321419 + 0.559035I
a = −0.273484 + 0.554691I
b = 0.062346 + 0.635393I
−1.36775 + 1.38141I 0. − 4.41326I
u = −0.321419 − 0.559035I
a = −0.273484 − 0.554691I
b = 0.062346 − 0.635393I
−1.36775 − 1.38141I 0. + 4.41326I
u = −1.142910 + 0.736349I
a = 0.20080 − 1.79898I
b = −1.46748 − 0.49428I
7.3804 + 19.2113I 0
u = −1.142910 − 0.736349I
a = 0.20080 + 1.79898I
b = −1.46748 + 0.49428I
7.3804 − 19.2113I 0
u = 1.185710 + 0.686622I
a = 0.133152 − 1.238920I
b = 1.185190 − 0.412132I
3.90719 − 7.32035I 0
u = 1.185710 − 0.686622I
a = 0.133152 + 1.238920I
b = 1.185190 + 0.412132I
3.90719 + 7.32035I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.196770 + 0.718402I
a = 0.149705 + 1.161010I
b = 1.213690 + 0.042396I
4.02015 + 3.36119I 0
u = −1.196770 − 0.718402I
a = 0.149705 − 1.161010I
b = 1.213690 − 0.042396I
4.02015 − 3.36119I 0
u = 1.321050 + 0.498827I
a = −0.438041 + 1.112860I
b = −1.185410 + 0.410351I
3.45654 − 4.64334I 0
u = 1.321050 − 0.498827I
a = −0.438041 − 1.112860I
b = −1.185410 − 0.410351I
3.45654 + 4.64334I 0
u = 1.42164 + 0.15931I
a = −0.691557 + 0.763888I
b = −1.190920 + 0.411936I
1.23824 − 10.15100I 0
u = 1.42164 − 0.15931I
a = −0.691557 − 0.763888I
b = −1.190920 − 0.411936I
1.23824 + 10.15100I 0
u = −0.68248 + 1.27758I
a = −0.272928 + 0.233545I
b = 1.233370 + 0.098231I
8.98112 + 5.32815I 0
u = −0.68248 − 1.27758I
a = −0.272928 − 0.233545I
b = 1.233370 − 0.098231I
8.98112 − 5.32815I 0
u = −1.00220 + 1.06603I
a = 0.290030 − 0.582982I
b = −1.227570 − 0.065099I
8.01090 + 2.68717I 0
u = −1.00220 − 1.06603I
a = 0.290030 + 0.582982I
b = −1.227570 + 0.065099I
8.01090 − 2.68717I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.366471 + 0.367463I
a = 0.54726 + 1.57810I
b = −1.358430 + 0.177453I
3.04281 − 4.24622I 4.50858 + 7.18986I
u = 0.366471 − 0.367463I
a = 0.54726 − 1.57810I
b = −1.358430 − 0.177453I
3.04281 + 4.24622I 4.50858 − 7.18986I
u = −1.29583 + 0.81787I
a = −0.162036 − 0.890615I
b = −1.211780 − 0.046617I
5.46588 + 8.34881I 0
u = −1.29583 − 0.81787I
a = −0.162036 + 0.890615I
b = −1.211780 + 0.046617I
5.46588 − 8.34881I 0
u = 0.410919 + 0.066172I
a = −2.96513 + 3.33002I
b = −0.837480 − 0.420112I
4.70642 − 2.26974I 2.90367 + 1.60194I
u = 0.410919 − 0.066172I
a = −2.96513 − 3.33002I
b = −0.837480 + 0.420112I
4.70642 + 2.26974I 2.90367 − 1.60194I
u = 0.117163
a = −4.80110
b = 0.390360
0.993777 11.4450
18
II. I
u
2
= h−8u
28
+ 17u
27
+ · · · + b − 27u, −41u
28
+ 97u
27
+ · · · + a +
59, u
29
− 3u
28
+ · · · − 4u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
11
=
41u
28
− 97u
27
+ ··· + 188u − 59
8u
28
− 17u
27
+ ··· − 31u
2
+ 27u
a
7
=
−32u
28
+ 87u
27
+ ··· − 169u + 79
−u
27
+ 2u
26
+ ··· − 3u − 4
a
1
=
u
3
u
5
− u
3
+ u
a
10
=
33u
28
− 80u
27
+ ··· + 161u − 59
8u
28
− 17u
27
+ ··· − 31u
2
+ 27u
a
4
=
18u
28
− 48u
27
+ ··· + 77u − 41
−3u
28
+ 5u
27
+ ··· − 4u + 2
a
8
=
3u
28
− u
27
+ ··· − 2u + 10
2u
28
− 6u
27
+ ··· + 8u − 3
a
9
=
−28u
28
+ 71u
27
+ ··· − 142u + 49
−8u
28
+ 11u
27
+ ··· + 6u − 13
a
12
=
44u
28
− 103u
27
+ ··· + 178u − 54
u
28
− u
27
+ ··· − 17u + 14
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 28u
28
− 87u
27
− 40u
26
+ 337u
25
+ 150u
24
− 1151u
23
− 268u
22
+ 2767u
21
+ 523u
20
−
5416u
19
−811u
18
+8667u
17
+1018u
16
−11562u
15
−875u
14
+12911u
13
+222u
12
−11986u
11
+
771u
10
+8933u
9
−1377u
8
−5177u
7
+1284u
6
+2201u
5
−789u
4
−578u
3
+265u
2
+66u −34
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
29
− 13u
28
+ ··· + 16u − 1
c
2
u
29
+ 3u
28
+ ··· − 4u − 1
c
3
u
29
+ u
28
+ ··· + 12u − 1
c
4
u
29
− 16u
27
+ ··· + 4u − 1
c
5
u
29
− 3u
28
+ ··· − 4u + 1
c
6
u
29
− u
28
+ ··· + 6u + 1
c
7
u
29
− u
28
+ ··· + 12u + 1
c
8
u
29
+ u
28
+ ··· − 9u
2
+ 1
c
9
u
29
− 3u
28
+ ··· + 7u
2
− 1
c
10
u
29
− 16u
27
+ ··· + 4u + 1
c
11
u
29
+ 15u
28
+ ··· + 18u + 1
c
12
u
29
− u
28
+ ··· + 9u
2
− 1
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 19y
28
+ ··· − 16y −1
c
2
, c
5
y
29
− 13y
28
+ ··· + 16y −1
c
3
, c
7
y
29
+ 29y
28
+ ··· + 36y −1
c
4
, c
10
y
29
− 32y
28
+ ··· − 4y −1
c
6
y
29
− 11y
28
+ ··· + 14y −1
c
8
, c
12
y
29
− 15y
28
+ ··· + 18y −1
c
9
y
29
− 7y
28
+ ··· + 14y −1
c
11
y
29
+ 13y
28
+ ··· + 6y −1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.967038 + 0.280278I
a = −0.084457 + 1.155900I
b = −0.312961 + 0.686323I
−0.296745 + 1.067620I −0.05924 − 2.38455I
u = −0.967038 − 0.280278I
a = −0.084457 − 1.155900I
b = −0.312961 − 0.686323I
−0.296745 − 1.067620I −0.05924 + 2.38455I
u = 0.724808 + 0.641397I
a = −1.175610 + 0.216566I
b = −0.780691 − 0.672622I
5.71475 − 3.07298I 8.76102 + 4.26007I
u = 0.724808 − 0.641397I
a = −1.175610 − 0.216566I
b = −0.780691 + 0.672622I
5.71475 + 3.07298I 8.76102 − 4.26007I
u = −0.721882 + 0.570706I
a = 1.14898 − 2.00806I
b = −1.39520 − 0.58597I
5.46567 − 0.96446I 5.16446 + 1.15272I
u = −0.721882 − 0.570706I
a = 1.14898 + 2.00806I
b = −1.39520 + 0.58597I
5.46567 + 0.96446I 5.16446 − 1.15272I
u = −0.913439 + 0.018373I
a = 0.16138 + 1.94192I
b = −0.012710 + 0.248150I
−4.48876 + 2.86726I 6.09398 − 8.15225I
u = −0.913439 − 0.018373I
a = 0.16138 − 1.94192I
b = −0.012710 − 0.248150I
−4.48876 − 2.86726I 6.09398 + 8.15225I
u = −0.931978 + 0.643484I
a = 0.058006 + 0.883938I
b = 1.58697 − 0.22172I
4.72370 + 5.84549I 6.35142 − 7.61041I
u = −0.931978 − 0.643484I
a = 0.058006 − 0.883938I
b = 1.58697 + 0.22172I
4.72370 − 5.84549I 6.35142 + 7.61041I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.046650 + 0.472512I
a = −0.27787 + 1.73942I
b = −1.33040 + 0.55538I
1.58512 − 6.22697I 3.14633 + 8.23430I
u = 1.046650 − 0.472512I
a = −0.27787 − 1.73942I
b = −1.33040 − 0.55538I
1.58512 + 6.22697I 3.14633 − 8.23430I
u = 0.742031 + 0.392144I
a = 0.659722 − 0.585304I
b = 1.59794 + 0.41386I
2.76371 + 2.65649I 3.93402 − 4.42704I
u = 0.742031 − 0.392144I
a = 0.659722 + 0.585304I
b = 1.59794 − 0.41386I
2.76371 − 2.65649I 3.93402 + 4.42704I
u = −0.722882 + 0.956971I
a = 0.998326 − 0.248538I
b = −1.196040 − 0.096161I
7.97698 + 4.98814I 7.32801 − 6.57414I
u = −0.722882 − 0.956971I
a = 0.998326 + 0.248538I
b = −1.196040 + 0.096161I
7.97698 − 4.98814I 7.32801 + 6.57414I
u = 0.961907 + 0.751097I
a = 0.021825 − 0.641341I
b = 0.517766 − 0.307183I
4.93376 − 2.36104I 10.69221 + 4.58137I
u = 0.961907 − 0.751097I
a = 0.021825 + 0.641341I
b = 0.517766 + 0.307183I
4.93376 + 2.36104I 10.69221 − 4.58137I
u = −0.706452
a = 1.50611
b = 0.240966
0.171122 −1.29850
u = −0.872494 + 0.959691I
a = −0.692521 + 0.286875I
b = 1.212950 + 0.020548I
7.57343 + 1.98494I 6.15109 + 2.40291I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.872494 − 0.959691I
a = −0.692521 − 0.286875I
b = 1.212950 − 0.020548I
7.57343 − 1.98494I 6.15109 − 2.40291I
u = 1.208840 + 0.499911I
a = −0.64239 + 1.28778I
b = −1.142550 + 0.318266I
2.11397 − 4.93239I 2.58479 + 4.33687I
u = 1.208840 − 0.499911I
a = −0.64239 − 1.28778I
b = −1.142550 − 0.318266I
2.11397 + 4.93239I 2.58479 − 4.33687I
u = 0.577602 + 0.264769I
a = −0.25992 + 1.69441I
b = 1.320700 + 0.195004I
4.72095 + 1.57440I 4.23179 − 1.84185I
u = 0.577602 − 0.264769I
a = −0.25992 − 1.69441I
b = 1.320700 − 0.195004I
4.72095 − 1.57440I 4.23179 + 1.84185I
u = 1.233600 + 0.615824I
a = 0.500098 − 1.046340I
b = 1.023240 − 0.296938I
3.44053 − 9.12432I 6.10664 + 9.71442I
u = 1.233600 − 0.615824I
a = 0.500098 + 1.046340I
b = 1.023240 + 0.296938I
3.44053 + 9.12432I 6.10664 − 9.71442I
u = 0.487500 + 0.369200I
a = −2.16863 − 1.66729I
b = −1.209500 − 0.256306I
6.32527 + 4.75434I 9.16276 − 5.13089I
u = 0.487500 − 0.369200I
a = −2.16863 + 1.66729I
b = −1.209500 + 0.256306I
6.32527 − 4.75434I 9.16276 + 5.13089I
26
III. I
u
3
= hb − 1, a − 2, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
11
=
2
1
a
7
=
3
2
a
1
=
−1
−1
a
10
=
1
1
a
4
=
2
1
a
8
=
1
1
a
9
=
−2
−1
a
12
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
8
, c
12
u + 1
c
4
, c
9
, c
10
c
11
u − 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 2.00000
b = 1.00000
1.64493 6.00000
30
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
29
− 13u
28
+ ··· + 16u − 1)
· (u
137
+ 53u
136
+ ··· + 3208982u + 28561)
c
2
(u + 1)(u
29
+ 3u
28
+ ··· − 4u − 1)(u
137
+ 3u
136
+ ··· + 3010u − 169)
c
3
(u + 1)(u
29
+ u
28
+ ··· + 12u − 1)(u
137
+ u
136
+ ··· + 481416u − 77291)
c
4
(u − 1)(u
29
− 16u
27
+ ··· + 4u − 1)(u
137
+ 2u
136
+ ··· − 8u − 1)
c
5
(u + 1)(u
29
− 3u
28
+ ··· − 4u + 1)(u
137
+ 3u
136
+ ··· + 3010u − 169)
c
6
(u + 1)(u
29
− u
28
+ ··· + 6u + 1)
· (u
137
− 3u
136
+ ··· + 288732u − 248089)
c
7
(u + 1)(u
29
− u
28
+ ··· + 12u + 1)(u
137
+ u
136
+ ··· + 481416u − 77291)
c
8
(u + 1)(u
29
+ u
28
+ ··· − 9u
2
+ 1)(u
137
− 9u
136
+ ··· + 1468u − 271)
c
9
(u − 1)(u
29
− 3u
28
+ ··· + 7u
2
− 1)
· (u
137
+ 11u
136
+ ··· − 102807486u − 5507323)
c
10
(u − 1)(u
29
− 16u
27
+ ··· + 4u + 1)(u
137
+ 2u
136
+ ··· − 8u − 1)
c
11
(u − 1)(u
29
+ 15u
28
+ ··· + 18u + 1)
· (u
137
− 63u
136
+ ··· + 597316u − 73441)
c
12
(u + 1)(u
29
− u
28
+ ··· + 9u
2
− 1)(u
137
− 9u
136
+ ··· + 1468u − 271)
31
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
29
+ 19y
28
+ ··· − 16y −1)
· (y
137
+ 75y
136
+ ··· + 4313902139478y −815730721)
c
2
, c
5
(y −1)(y
29
− 13y
28
+ ··· + 16y −1)
· (y
137
− 53y
136
+ ··· + 3208982y −28561)
c
3
, c
7
(y −1)(y
29
+ 29y
28
+ ··· + 36y −1)
· (y
137
+ 109y
136
+ ··· − 59701913870y −5973898681)
c
4
, c
10
(y −1)(y
29
− 32y
28
+ ··· − 4y −1)(y
137
− 116y
136
+ ··· + 78y −1)
c
6
(y −1)(y
29
− 11y
28
+ ··· + 14y −1)
· (y
137
− 35y
136
+ ··· − 1429947953852y −61548151921)
c
8
, c
12
(y −1)(y
29
− 15y
28
+ ··· + 18y −1)
· (y
137
− 63y
136
+ ··· + 597316y −73441)
c
9
(y −1)(y
29
− 7y
28
+ ··· + 14y −1)
· (y
137
− 43y
136
+ ··· + 1343419781833972y −30330606626329)
c
11
(y −1)(y
29
+ 13y
28
+ ··· + 6y −1)
· (y
137
+ 37y
136
+ ··· + 126623191148y −5393580481)
32
