12a
0272
(K12a
0272
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 11 2 9 4 1 12 5 10
Solving Sequence
1,9 4,10
8 3 2 7 5 6 12 11
c
9
c
8
c
3
c
1
c
7
c
4
c
6
c
12
c
10
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.81378 × 10
102
u
92
+ 2.11238 × 10
104
u
91
+ ··· + 4.20120 × 10
103
b + 1.23437 × 10
104
,
1.35442 × 10
104
u
92
− 3.05756 × 10
105
u
91
+ ··· + 4.20120 × 10
103
a − 2.46878 × 10
104
, u
93
− 23u
92
+ ··· − 7u + 1i
I
u
2
= h33a
3
u
2
− 12a
3
u + 42a
2
u
2
+ 28a
3
− 76a
2
u + 165u
2
a + 66a
2
− 60au + 5u
2
+ 167b + 140a − 17u − 16,
2a
3
u
2
+ a
4
− 2a
3
u + 6a
2
u
2
+ 4a
3
− 3a
2
u + 8u
2
a + 11a
2
− 4au + 3u
2
+ 14a − u + 7, u
3
− u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 105 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−8.81 × 10
102
u
92
+ 2.11 × 10
104
u
91
+ · · · + 4.20 × 10
103
b + 1.23 ×
10
104
, 1.35 × 10
104
u
92
− 3.06 × 10
105
u
91
+ · · · + 4.20 × 10
103
a − 2.47 ×
10
104
, u
93
− 23u
92
+ · · · − 7u + 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
−3.22390u
92
+ 72.7783u
91
+ ··· − 42.3730u + 5.87637
0.209792u
92
− 5.02805u
91
+ ··· + 6.01494u − 2.93813
a
10
=
1
u
2
a
8
=
2.05019u
92
− 47.0547u
91
+ ··· + 56.3868u − 6.05494
−1.50087u
92
+ 34.1389u
91
+ ··· − 17.7924u + 4.81082
a
3
=
−1.01350u
92
+ 22.8011u
91
+ ··· + 14.3088u + 1.73659
−0.292693u
92
+ 6.74378u
91
+ ··· − 6.73428u + 0.555834
a
2
=
1.18734u
92
− 26.3170u
91
+ ··· − 26.1202u + 1.75144
0.257687u
92
− 5.95007u
91
+ ··· + 5.55854u − 0.852157
a
7
=
3.55106u
92
− 81.1936u
91
+ ··· + 74.1793u − 10.8658
−1.50087u
92
+ 34.1389u
91
+ ··· − 17.7924u + 4.81082
a
5
=
0.858858u
92
− 19.5520u
91
+ ··· + 20.0064u − 4.50303
−0.127780u
92
+ 2.91765u
91
+ ··· − 0.756148u + 0.591562
a
6
=
0.591562u
92
− 13.4781u
91
+ ··· + 17.7344u − 3.38478
−0.180416u
92
+ 4.10757u
91
+ ··· − 1.20608u + 0.731078
a
12
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.26586u
92
− 96.9345u
91
+ ··· + 57.5150u − 12.9725
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
93
+ 43u
92
+ ··· − 3575u − 625
c
2
, c
6
u
93
− u
92
+ ··· − 35u − 25
c
3
, c
8
u
93
− u
92
+ ··· + u − 1
c
4
u
93
− 3u
92
+ ··· + 22579u − 21009
c
5
, c
11
u
93
+ u
92
+ ··· − u − 1
c
7
u
93
− 47u
92
+ ··· + 7u − 1
c
9
, c
10
, c
12
u
93
+ 23u
92
+ ··· − 7u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
93
+ 27y
92
+ ··· + 30773125y −390625
c
2
, c
6
y
93
+ 43y
92
+ ··· − 3575y −625
c
3
, c
8
y
93
− 47y
92
+ ··· + 7y −1
c
4
y
93
+ 37y
92
+ ··· + 556241131y −441378081
c
5
, c
11
y
93
+ 23y
92
+ ··· − 7y −1
c
7
y
93
+ 5y
92
+ ··· + 35y −1
c
9
, c
10
, c
12
y
93
+ 99y
92
+ ··· + 49y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.975112 + 0.011658I
a = −0.457990 + 1.069300I
b = −1.054870 + 0.383779I
−0.322073 − 1.346820I 0
u = 0.975112 − 0.011658I
a = −0.457990 − 1.069300I
b = −1.054870 − 0.383779I
−0.322073 + 1.346820I 0
u = 0.923458 + 0.251430I
a = 0.274705 − 1.386400I
b = 0.307591 − 0.611476I
−3.59253 + 1.33736I 0
u = 0.923458 − 0.251430I
a = 0.274705 + 1.386400I
b = 0.307591 + 0.611476I
−3.59253 − 1.33736I 0
u = 0.142931 + 0.932629I
a = −0.572352 + 0.952292I
b = 1.015810 + 0.286301I
3.38472 + 0.29711I 0
u = 0.142931 − 0.932629I
a = −0.572352 − 0.952292I
b = 1.015810 − 0.286301I
3.38472 − 0.29711I 0
u = 1.045630 + 0.237932I
a = 0.603596 + 1.269130I
b = 1.102820 + 0.513061I
−1.31714 + 5.79170I 0
u = 1.045630 − 0.237932I
a = 0.603596 − 1.269130I
b = 1.102820 − 0.513061I
−1.31714 − 5.79170I 0
u = 0.574887 + 0.725329I
a = −0.462784 − 0.619036I
b = −0.249615 − 0.631819I
−0.08874 − 2.35747I 0
u = 0.574887 − 0.725329I
a = −0.462784 + 0.619036I
b = −0.249615 + 0.631819I
−0.08874 + 2.35747I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.677583 + 0.571350I
a = 0.84533 − 1.31354I
b = 0.647720 − 0.676775I
−3.74624 − 4.86364I 0
u = 0.677583 − 0.571350I
a = 0.84533 + 1.31354I
b = 0.647720 + 0.676775I
−3.74624 + 4.86364I 0
u = 0.813255 + 0.766947I
a = 0.763480 + 0.944934I
b = 0.310400 + 0.768827I
−2.07581 − 7.04640I 0
u = 0.813255 − 0.766947I
a = 0.763480 − 0.944934I
b = 0.310400 − 0.768827I
−2.07581 + 7.04640I 0
u = 0.704203 + 0.874011I
a = 0.37398 + 1.61333I
b = −1.113560 + 0.500754I
2.35859 − 6.76923I 0
u = 0.704203 − 0.874011I
a = 0.37398 − 1.61333I
b = −1.113560 − 0.500754I
2.35859 + 6.76923I 0
u = 0.704096 + 0.897518I
a = 0.0261087 − 0.0707790I
b = −1.124370 − 0.258362I
2.37106 − 4.17517I 0
u = 0.704096 − 0.897518I
a = 0.0261087 + 0.0707790I
b = −1.124370 + 0.258362I
2.37106 + 4.17517I 0
u = 0.709208 + 0.406138I
a = 1.403280 − 0.030207I
b = 0.502509 + 0.546608I
−4.22922 + 0.22021I 0
u = 0.709208 − 0.406138I
a = 1.403280 + 0.030207I
b = 0.502509 − 0.546608I
−4.22922 − 0.22021I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.879776 + 0.812261I
a = −0.12067 − 1.90804I
b = 1.137730 − 0.559122I
0.36419 − 12.04290I 0
u = 0.879776 − 0.812261I
a = −0.12067 + 1.90804I
b = 1.137730 + 0.559122I
0.36419 + 12.04290I 0
u = −0.235370 + 0.753664I
a = −0.270095 − 0.119388I
b = −1.137830 + 0.440841I
4.28586 − 5.33657I 0
u = −0.235370 − 0.753664I
a = −0.270095 + 0.119388I
b = −1.137830 − 0.440841I
4.28586 + 5.33657I 0
u = 0.581872 + 0.533061I
a = −1.56364 − 2.16916I
b = 1.022280 − 0.523078I
−2.70580 − 4.13046I 0
u = 0.581872 − 0.533061I
a = −1.56364 + 2.16916I
b = 1.022280 + 0.523078I
−2.70580 + 4.13046I 0
u = 0.591243 + 0.477280I
a = 0.31040 + 1.91040I
b = 0.946859 + 0.616173I
−2.86958 + 0.13162I 0
u = 0.591243 − 0.477280I
a = 0.31040 − 1.91040I
b = 0.946859 − 0.616173I
−2.86958 − 0.13162I 0
u = 0.119268 + 1.244880I
a = 0.005877 − 1.232340I
b = −0.538447 − 0.103922I
1.50783 − 2.63535I 0
u = 0.119268 − 1.244880I
a = 0.005877 + 1.232340I
b = −0.538447 + 0.103922I
1.50783 + 2.63535I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.335786 + 1.234390I
a = 0.144944 + 1.027360I
b = −0.958483 + 0.381269I
3.04435 − 5.41546I 0
u = 0.335786 − 1.234390I
a = 0.144944 − 1.027360I
b = −0.958483 − 0.381269I
3.04435 + 5.41546I 0
u = 0.669038 + 0.258538I
a = −0.380219 + 0.996972I
b = −0.667882 + 0.427816I
−1.37927 − 1.72782I 0
u = 0.669038 − 0.258538I
a = −0.380219 − 0.996972I
b = −0.667882 − 0.427816I
−1.37927 + 1.72782I 0
u = 0.467593 + 1.205990I
a = 0.025373 + 0.655972I
b = 1.063500 + 0.423253I
3.13855 + 0.43142I 0
u = 0.467593 − 1.205990I
a = 0.025373 − 0.655972I
b = 1.063500 − 0.423253I
3.13855 − 0.43142I 0
u = 0.309953 + 1.348600I
a = 0.016720 − 1.158940I
b = 0.446130 − 0.271365I
1.22782 − 3.00319I 0
u = 0.309953 − 1.348600I
a = 0.016720 + 1.158940I
b = 0.446130 + 0.271365I
1.22782 + 3.00319I 0
u = −0.347453 + 0.499708I
a = 0.777787 + 0.601514I
b = 1.147950 − 0.329947I
4.27803 − 0.04959I 0
u = −0.347453 − 0.499708I
a = 0.777787 − 0.601514I
b = 1.147950 + 0.329947I
4.27803 + 0.04959I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.342360 + 0.490258I
a = −0.18524 + 2.56638I
b = 1.139310 + 0.443856I
4.26723 + 2.60062I 0
u = −0.342360 − 0.490258I
a = −0.18524 − 2.56638I
b = 1.139310 − 0.443856I
4.26723 − 2.60062I 0
u = −0.469234 + 0.329281I
a = −0.55680 − 2.85165I
b = −1.149110 − 0.527482I
2.92042 + 8.02959I 0
u = −0.469234 − 0.329281I
a = −0.55680 + 2.85165I
b = −1.149110 + 0.527482I
2.92042 − 8.02959I 0
u = 0.17853 + 1.42228I
a = 0.140624 − 0.460282I
b = 0.080958 + 0.460222I
1.54039 − 2.97863I 0
u = 0.17853 − 1.42228I
a = 0.140624 + 0.460282I
b = 0.080958 − 0.460222I
1.54039 + 2.97863I 0
u = −0.122925 + 0.537777I
a = 0.917954 − 0.812454I
b = 0.001615 − 0.645545I
1.17563 − 1.37957I 0
u = −0.122925 − 0.537777I
a = 0.917954 + 0.812454I
b = 0.001615 + 0.645545I
1.17563 + 1.37957I 0
u = 0.03103 + 1.45544I
a = −0.091290 − 1.200980I
b = −0.756943 − 0.749780I
3.42247 + 1.92586I 0
u = 0.03103 − 1.45544I
a = −0.091290 + 1.200980I
b = −0.756943 + 0.749780I
3.42247 − 1.92586I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08873 + 1.46640I
a = −0.213185 + 1.033730I
b = −0.875447 + 0.708452I
3.77833 − 3.56285I 0
u = 0.08873 − 1.46640I
a = −0.213185 − 1.033730I
b = −0.875447 − 0.708452I
3.77833 + 3.56285I 0
u = −0.10165 + 1.48145I
a = −0.668696 + 0.451469I
b = −0.280179 + 0.866951I
6.26975 + 4.86358I 0
u = −0.10165 − 1.48145I
a = −0.668696 − 0.451469I
b = −0.280179 − 0.866951I
6.26975 − 4.86358I 0
u = 0.05789 + 1.48627I
a = 1.77808 − 0.85220I
b = −1.112300 − 0.441488I
4.33913 + 0.66006I 0
u = 0.05789 − 1.48627I
a = 1.77808 + 0.85220I
b = −1.112300 + 0.441488I
4.33913 − 0.66006I 0
u = −0.14250 + 1.48556I
a = 0.83776 − 1.67548I
b = −1.179860 − 0.579243I
8.97443 + 10.18300I 0
u = −0.14250 − 1.48556I
a = 0.83776 + 1.67548I
b = −1.179860 + 0.579243I
8.97443 − 10.18300I 0
u = −0.363573 + 0.318934I
a = −1.48496 + 1.45663I
b = −0.229089 + 0.738206I
0.24940 + 3.26137I 0
u = −0.363573 − 0.318934I
a = −1.48496 − 1.45663I
b = −0.229089 − 0.738206I
0.24940 − 3.26137I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17307 + 1.50827I
a = 0.176430 + 1.102160I
b = 0.898359 + 0.708905I
3.66403 − 2.59876I 0
u = 0.17307 − 1.50827I
a = 0.176430 − 1.102160I
b = 0.898359 − 0.708905I
3.66403 + 2.59876I 0
u = −0.02047 + 1.52637I
a = 0.403798 − 0.365537I
b = 0.162944 − 0.839736I
8.05299 − 0.97235I 0
u = −0.02047 − 1.52637I
a = 0.403798 + 0.365537I
b = 0.162944 + 0.839736I
8.05299 + 0.97235I 0
u = −0.07851 + 1.53623I
a = −0.95802 + 1.33694I
b = 1.195310 + 0.524633I
11.13210 + 4.00565I 0
u = −0.07851 − 1.53623I
a = −0.95802 − 1.33694I
b = 1.195310 − 0.524633I
11.13210 − 4.00565I 0
u = −0.07562 + 1.54400I
a = −0.655071 + 0.225073I
b = 1.237230 − 0.251218I
11.23360 + 1.35764I 0
u = −0.07562 − 1.54400I
a = −0.655071 − 0.225073I
b = 1.237230 + 0.251218I
11.23360 − 1.35764I 0
u = 0.17901 + 1.53877I
a = −1.67539 − 0.97138I
b = 1.114880 − 0.463083I
4.18101 − 6.89019I 0
u = 0.17901 − 1.53877I
a = −1.67539 + 0.97138I
b = 1.114880 + 0.463083I
4.18101 + 6.89019I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21412 + 1.53871I
a = 0.169726 − 1.160300I
b = 0.736350 − 0.761337I
3.18025 − 8.12130I 0
u = 0.21412 − 1.53871I
a = 0.169726 + 1.160300I
b = 0.736350 + 0.761337I
3.18025 + 8.12130I 0
u = 0.00737 + 1.59654I
a = 0.815596 + 0.142705I
b = −1.231300 + 0.340881I
12.40570 − 4.93038I 0
u = 0.00737 − 1.59654I
a = 0.815596 − 0.142705I
b = −1.231300 − 0.340881I
12.40570 + 4.93038I 0
u = 0.20385 + 1.60931I
a = −0.382492 − 0.401970I
b = −0.192162 − 0.840420I
7.77433 − 5.40679I 0
u = 0.20385 − 1.60931I
a = −0.382492 + 0.401970I
b = −0.192162 + 0.840420I
7.77433 + 5.40679I 0
u = 0.14080 + 1.64135I
a = −0.822689 + 0.185322I
b = 1.230600 + 0.321573I
12.24510 − 1.56912I 0
u = 0.14080 − 1.64135I
a = −0.822689 − 0.185322I
b = 1.230600 − 0.321573I
12.24510 + 1.56912I 0
u = 0.27977 + 1.62561I
a = 0.617487 + 0.514179I
b = 0.299812 + 0.868670I
5.79383 − 11.22630I 0
u = 0.27977 − 1.62561I
a = 0.617487 − 0.514179I
b = 0.299812 − 0.868670I
5.79383 + 11.22630I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.220768 + 0.263420I
a = 4.77821 + 0.16986I
b = −0.940242 − 0.399619I
−1.63911 + 1.59917I 5.10383 + 0.18940I
u = 0.220768 − 0.263420I
a = 4.77821 − 0.16986I
b = −0.940242 + 0.399619I
−1.63911 − 1.59917I 5.10383 − 0.18940I
u = 0.23562 + 1.64814I
a = 0.87152 + 1.29779I
b = −1.189830 + 0.537656I
10.7483 − 10.4540I 0
u = 0.23562 − 1.64814I
a = 0.87152 − 1.29779I
b = −1.189830 − 0.537656I
10.7483 + 10.4540I 0
u = 0.22917 + 1.65214I
a = 0.637776 + 0.146711I
b = −1.236400 − 0.233131I
10.86220 − 7.81939I 0
u = 0.22917 − 1.65214I
a = 0.637776 − 0.146711I
b = −1.236400 + 0.233131I
10.86220 + 7.81939I 0
u = 0.30282 + 1.64826I
a = −0.73101 − 1.60141I
b = 1.174680 − 0.587740I
8.4252 − 16.5880I 0
u = 0.30282 − 1.64826I
a = −0.73101 + 1.60141I
b = 1.174680 + 0.587740I
8.4252 + 16.5880I 0
u = 0.202817 + 0.113256I
a = 0.287615 − 1.319100I
b = −0.835540 + 0.577788I
−1.68339 − 2.29491I 4.65059 + 5.45846I
u = 0.202817 − 0.113256I
a = 0.287615 + 1.319100I
b = −0.835540 − 0.577788I
−1.68339 + 2.29491I 4.65059 − 5.45846I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.161038
a = 4.16052
b = 0.723001
0.958624 11.1450
u = −0.0900715 + 0.0809425I
a = −3.33180 − 7.28213I
b = −0.731401 − 0.544627I
−1.85071 + 2.17154I 2.55551 − 3.84587I
u = −0.0900715 − 0.0809425I
a = −3.33180 + 7.28213I
b = −0.731401 + 0.544627I
−1.85071 − 2.17154I 2.55551 + 3.84587I
14
II. I
u
2
=
h33a
3
u
2
+42a
2
u
2
+· · ·+140a−16, 2a
3
u
2
+6a
2
u
2
+· · ·+14a+7, u
3
−u
2
+2u−1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
a
−0.197605a
3
u
2
− 0.251497a
2
u
2
+ ··· − 0.838323a + 0.0958084
a
10
=
1
u
2
a
8
=
0.0838323a
3
u
2
+ 0.197605a
2
u
2
+ ··· + 2.65868a + 2.35329
−0.251497a
3
u
2
− 0.592814a
2
u
2
+ ··· − 1.97605a − 1.05988
a
3
=
−u
2
+ u − 2
0.197605a
3
u
2
+ 0.251497a
2
u
2
+ ··· + 1.83832a + 1.90419
a
2
=
−u
2
+ u − 2
0.197605a
3
u
2
+ 0.251497a
2
u
2
+ ··· + 1.83832a + 1.90419
a
7
=
0.335329a
3
u
2
+ 0.790419a
2
u
2
+ ··· + 4.63473a + 3.41317
−0.251497a
3
u
2
− 0.592814a
2
u
2
+ ··· − 1.97605a − 1.05988
a
5
=
−0.395210a
3
u
2
− 0.502994a
2
u
2
+ ··· − 2.67665a − 1.80838
0
a
6
=
0
0.251497a
3
u
2
+ 0.592814a
2
u
2
+ ··· + 1.97605a + 1.05988
a
12
=
u
u
2
− u + 1
a
11
=
u
2
+ 1
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
168
167
a
3
u
2
−
304
167
a
3
u +
396
167
a
2
u
2
+
264
167
a
3
−
144
167
a
2
u +
840
167
u
2
a +
336
167
a
2
−
184
167
au −
96
167
u
2
+
1320
167
a +
460
167
u +
40
167
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
12
c
2
, c
6
(u
2
+ 1)
6
c
3
, c
4
, c
8
(u
4
− u
2
+ 1)
3
c
5
, c
11
(u
6
+ u
4
+ 2u
2
+ 1)
2
c
7
(u
2
+ u + 1)
6
c
9
, c
10
(u
3
− u
2
+ 2u − 1)
4
c
12
(u
3
+ u
2
+ 2u + 1)
4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
12
c
2
, c
6
(y + 1)
12
c
3
, c
4
, c
8
(y
2
− y + 1)
6
c
5
, c
11
(y
3
+ y
2
+ 2y + 1)
4
c
7
(y
2
+ y + 1)
6
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.706350 − 0.733710I
b = −0.866025 − 0.500000I
1.37919 − 0.79824I 1.50976 − 0.48465I
u = 0.215080 + 1.307140I
a = 0.583789 − 0.521428I
b = 0.866025 − 0.500000I
1.37919 − 4.85801I 1.50976 + 6.44355I
u = 0.215080 + 1.307140I
a = −0.70635 + 1.26629I
b = 0.866025 + 0.500000I
1.37919 − 0.79824I 1.50976 − 0.48465I
u = 0.215080 + 1.307140I
a = 0.58379 + 1.47857I
b = −0.866025 + 0.500000I
1.37919 − 4.85801I 1.50976 + 6.44355I
u = 0.215080 − 1.307140I
a = −0.706350 + 0.733710I
b = −0.866025 + 0.500000I
1.37919 + 0.79824I 1.50976 + 0.48465I
u = 0.215080 − 1.307140I
a = 0.583789 + 0.521428I
b = 0.866025 + 0.500000I
1.37919 + 4.85801I 1.50976 − 6.44355I
u = 0.215080 − 1.307140I
a = −0.70635 − 1.26629I
b = 0.866025 − 0.500000I
1.37919 + 0.79824I 1.50976 + 0.48465I
u = 0.215080 − 1.307140I
a = 0.58379 − 1.47857I
b = −0.866025 − 0.500000I
1.37919 + 4.85801I 1.50976 − 6.44355I
u = 0.569840
a = −0.877439 + 0.519769I
b = 0.866025 − 0.500000I
−2.75839 − 2.02988I −5.01951 + 3.46410I
u = 0.569840
a = −0.877439 − 0.519769I
b = 0.866025 + 0.500000I
−2.75839 + 2.02988I −5.01951 − 3.46410I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569840
a = −0.87744 + 2.51977I
b = −0.866025 + 0.500000I
−2.75839 − 2.02988I −5.01951 + 3.46410I
u = 0.569840
a = −0.87744 − 2.51977I
b = −0.866025 − 0.500000I
−2.75839 + 2.02988I −5.01951 − 3.46410I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
12
)(u
93
+ 43u
92
+ ··· − 3575u − 625)
c
2
, c
6
((u
2
+ 1)
6
)(u
93
− u
92
+ ··· − 35u − 25)
c
3
, c
8
((u
4
− u
2
+ 1)
3
)(u
93
− u
92
+ ··· + u − 1)
c
4
((u
4
− u
2
+ 1)
3
)(u
93
− 3u
92
+ ··· + 22579u − 21009)
c
5
, c
11
((u
6
+ u
4
+ 2u
2
+ 1)
2
)(u
93
+ u
92
+ ··· − u − 1)
c
7
((u
2
+ u + 1)
6
)(u
93
− 47u
92
+ ··· + 7u − 1)
c
9
, c
10
((u
3
− u
2
+ 2u − 1)
4
)(u
93
+ 23u
92
+ ··· − 7u − 1)
c
12
((u
3
+ u
2
+ 2u + 1)
4
)(u
93
+ 23u
92
+ ··· − 7u − 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
12
)(y
93
+ 27y
92
+ ··· + 3.07731 × 10
7
y −390625)
c
2
, c
6
((y + 1)
12
)(y
93
+ 43y
92
+ ··· − 3575y −625)
c
3
, c
8
((y
2
− y + 1)
6
)(y
93
− 47y
92
+ ··· + 7y −1)
c
4
((y
2
− y + 1)
6
)(y
93
+ 37y
92
+ ··· + 5.56241 × 10
8
y −4.41378 × 10
8
)
c
5
, c
11
((y
3
+ y
2
+ 2y + 1)
4
)(y
93
+ 23y
92
+ ··· − 7y −1)
c
7
((y
2
+ y + 1)
6
)(y
93
+ 5y
92
+ ··· + 35y −1)
c
9
, c
10
, c
12
((y
3
+ 3y
2
+ 2y −1)
4
)(y
93
+ 99y
92
+ ··· + 49y −1)
21
