12a
0560
(K12a
0560
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 11 2 1 4 6 12 5 10
Solving Sequence
2,6
7
3,9
4 10 1 8 12 11 5
c
6
c
2
c
3
c
9
c
1
c
7
c
12
c
10
c
5
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.46746 × 10
81
u
97
− 1.76536 × 10
81
u
96
+ ··· + 5.92140 × 10
81
b − 1.09130 × 10
82
,
4.16618 × 10
81
u
97
+ 1.31352 × 10
81
u
96
+ ··· + 5.92140 × 10
81
a + 7.37637 × 10
81
, u
98
− u
97
+ ··· − u + 1i
I
u
2
= h−u
2
a − u
2
+ b + a, u
3
a
2
− 3a
2
u
2
+ 2u
3
a + a
3
− a
2
u − 5u
2
a + u
3
+ 3a
2
− 2u
2
+ 2a + u − 1, u
4
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 110 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
= h1.47 × 10
81
u
97
− 1.77 × 10
81
u
96
+ · · · + 5.92 × 10
81
b − 1.09 × 10
82
, 4.17 ×
10
81
u
97
+1.31×10
81
u
96
+· · ·+5.92×10
81
a+7.38×10
81
, u
98
−u
97
+· · ·−u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−0.703581u
97
− 0.221826u
96
+ ··· + 2.30148u − 1.24571
−0.247823u
97
+ 0.298133u
96
+ ··· + 0.142766u + 1.84297
a
4
=
2.38586u
97
− 2.00995u
96
+ ··· − 3.05609u − 2.99728
−1.02475u
97
+ 0.625222u
96
+ ··· − 1.33955u + 0.977717
a
10
=
−0.951404u
97
+ 0.0763073u
96
+ ··· + 2.44424u + 0.597258
−0.247823u
97
+ 0.298133u
96
+ ··· + 0.142766u + 1.84297
a
1
=
u
3
u
5
− u
3
+ u
a
8
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
12
=
1.77227u
97
− 1.68697u
96
+ ··· − 6.38178u − 1.90346
−0.845163u
97
+ 0.998105u
96
+ ··· − 1.41033u + 0.784161
a
11
=
0.474727u
97
+ 0.395086u
96
+ ··· + 0.916706u + 0.647928
0.354362u
97
− 0.546426u
96
+ ··· + 0.491807u − 1.27955
a
5
=
1.65331u
97
− 1.49550u
96
+ ··· − 4.34761u − 2.09614
−0.916624u
97
+ 0.581736u
96
+ ··· − 0.992176u + 0.903994
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.96382u
97
− 1.51390u
96
+ ··· + 0.841173u − 1.40563
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
98
+ 49u
97
+ ··· + 7u + 1
c
2
, c
6
u
98
− u
97
+ ··· − u + 1
c
3
, c
4
, c
8
u
98
− u
97
+ ··· + 85u + 25
c
5
, c
11
u
98
+ u
97
+ ··· + 7u + 1
c
7
u
98
− 3u
97
+ ··· − 93143u + 31691
c
9
u
98
− 5u
97
+ ··· − 30007u + 14539
c
10
, c
12
u
98
+ 33u
97
+ ··· − 9u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
98
+ 7y
97
+ ··· + 49y + 1
c
2
, c
6
y
98
− 49y
97
+ ··· − 7y + 1
c
3
, c
4
, c
8
y
98
+ 93y
97
+ ··· − 20825y + 625
c
5
, c
11
y
98
+ 33y
97
+ ··· − 9y + 1
c
7
y
98
+ 35y
97
+ ··· + 1582314577y + 1004319481
c
9
y
98
+ 21y
97
+ ··· − 4470326109y + 211382521
c
10
, c
12
y
98
+ 69y
97
+ ··· + 27y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.698281 + 0.734981I
a = −0.874615 − 0.965911I
b = 0.731025 + 0.877762I
0.24752 + 2.82673I 0
u = −0.698281 − 0.734981I
a = −0.874615 + 0.965911I
b = 0.731025 − 0.877762I
0.24752 − 2.82673I 0
u = −0.946641 + 0.419235I
a = 0.028820 − 0.209134I
b = 0.133572 − 0.403815I
−1.43448 + 1.60642I 0
u = −0.946641 − 0.419235I
a = 0.028820 + 0.209134I
b = 0.133572 + 0.403815I
−1.43448 − 1.60642I 0
u = 0.723311 + 0.768617I
a = −0.938705 + 1.015410I
b = 0.694302 − 1.112160I
−0.67700 − 8.24942I 0
u = 0.723311 − 0.768617I
a = −0.938705 − 1.015410I
b = 0.694302 + 1.112160I
−0.67700 + 8.24942I 0
u = −0.772111 + 0.515798I
a = −0.650090 − 0.932173I
b = 0.244840 + 0.118183I
−1.50656 + 2.09808I 0. − 4.26664I
u = −0.772111 − 0.515798I
a = −0.650090 + 0.932173I
b = 0.244840 − 0.118183I
−1.50656 − 2.09808I 0. + 4.26664I
u = 0.309981 + 0.864468I
a = −1.01439 − 1.42657I
b = 0.84080 + 1.59991I
−3.13766 + 11.40930I 0. − 6.77627I
u = 0.309981 − 0.864468I
a = −1.01439 + 1.42657I
b = 0.84080 − 1.59991I
−3.13766 − 11.40930I 0. + 6.77627I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.038230 + 0.319222I
a = −1.226750 + 0.095271I
b = −0.232277 + 0.027239I
−1.83684 − 4.93742I 0
u = 1.038230 − 0.319222I
a = −1.226750 − 0.095271I
b = −0.232277 − 0.027239I
−1.83684 + 4.93742I 0
u = −0.933178 + 0.561155I
a = −0.19771 + 1.41969I
b = 1.271520 − 0.539820I
3.33056 − 0.96432I 0
u = −0.933178 − 0.561155I
a = −0.19771 − 1.41969I
b = 1.271520 + 0.539820I
3.33056 + 0.96432I 0
u = 0.815439 + 0.727212I
a = −0.81048 + 1.18357I
b = 0.085644 − 1.036660I
−5.05966 − 2.73854I 0
u = 0.815439 − 0.727212I
a = −0.81048 − 1.18357I
b = 0.085644 + 1.036660I
−5.05966 + 2.73854I 0
u = −1.070500 + 0.270114I
a = 0.968021 − 0.509743I
b = 0.457242 − 0.816853I
−0.736308 + 0.805438I 0
u = −1.070500 − 0.270114I
a = 0.968021 + 0.509743I
b = 0.457242 + 0.816853I
−0.736308 − 0.805438I 0
u = −0.647624 + 0.619058I
a = 1.59127 + 0.05416I
b = −1.167280 − 0.786021I
4.16380 + 5.62077I 7.57068 − 6.82410I
u = −0.647624 − 0.619058I
a = 1.59127 − 0.05416I
b = −1.167280 + 0.786021I
4.16380 − 5.62077I 7.57068 + 6.82410I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.307950 + 0.837415I
a = −1.13129 + 1.41921I
b = 0.93785 − 1.45891I
−1.98077 − 5.63221I 2.48540 + 2.18051I
u = −0.307950 − 0.837415I
a = −1.13129 − 1.41921I
b = 0.93785 + 1.45891I
−1.98077 + 5.63221I 2.48540 − 2.18051I
u = 0.232349 + 0.855665I
a = −1.05558 − 1.08467I
b = 0.532748 + 1.218090I
−8.50104 + 5.18557I −4.36390 − 3.55063I
u = 0.232349 − 0.855665I
a = −1.05558 + 1.08467I
b = 0.532748 − 1.218090I
−8.50104 − 5.18557I −4.36390 + 3.55063I
u = 0.961002 + 0.564221I
a = −0.44703 − 1.38158I
b = 1.328800 + 0.254026I
3.62769 − 4.71299I 0
u = 0.961002 − 0.564221I
a = −0.44703 + 1.38158I
b = 1.328800 − 0.254026I
3.62769 + 4.71299I 0
u = 0.605300 + 0.626623I
a = 1.51979 + 0.06738I
b = −1.223730 + 0.519669I
4.66705 + 0.02865I 8.77619 + 0.87832I
u = 0.605300 − 0.626623I
a = 1.51979 − 0.06738I
b = −1.223730 − 0.519669I
4.66705 − 0.02865I 8.77619 − 0.87832I
u = −0.929226 + 0.670090I
a = −0.53068 − 1.33385I
b = −0.588519 + 0.613229I
−0.43509 + 2.50606I 0
u = −0.929226 − 0.670090I
a = −0.53068 + 1.33385I
b = −0.588519 − 0.613229I
−0.43509 − 2.50606I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.915941 + 0.711844I
a = −0.64807 + 1.38100I
b = −0.572020 − 0.910887I
−1.24817 + 2.69565I 0
u = 0.915941 − 0.711844I
a = −0.64807 − 1.38100I
b = −0.572020 + 0.910887I
−1.24817 − 2.69565I 0
u = 1.127030 + 0.285308I
a = 1.064220 + 0.673238I
b = 0.508509 + 1.058380I
−1.74262 + 4.42183I 0
u = 1.127030 − 0.285308I
a = 1.064220 − 0.673238I
b = 0.508509 − 1.058380I
−1.74262 − 4.42183I 0
u = 1.062130 + 0.488743I
a = −1.111330 − 0.750250I
b = 0.557998 − 0.549738I
−0.87096 − 4.56762I 0
u = 1.062130 − 0.488743I
a = −1.111330 + 0.750250I
b = 0.557998 + 0.549738I
−0.87096 + 4.56762I 0
u = 1.081070 + 0.447530I
a = 0.67659 + 1.70831I
b = −2.04138 − 0.47794I
−0.770537 − 0.474142I 0
u = 1.081070 − 0.447530I
a = 0.67659 − 1.70831I
b = −2.04138 + 0.47794I
−0.770537 + 0.474142I 0
u = 0.118232 + 0.819519I
a = −1.229960 − 0.561977I
b = 0.375994 + 0.574642I
−6.10324 − 1.41750I −2.21136 + 2.61331I
u = 0.118232 − 0.819519I
a = −1.229960 + 0.561977I
b = 0.375994 − 0.574642I
−6.10324 + 1.41750I −2.21136 − 2.61331I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.107250 + 0.404686I
a = −1.38453 + 0.31849I
b = −0.137894 + 0.552380I
−2.25294 + 0.52462I 0
u = −1.107250 − 0.404686I
a = −1.38453 − 0.31849I
b = −0.137894 − 0.552380I
−2.25294 − 0.52462I 0
u = 1.115920 + 0.386738I
a = 0.770057 + 0.924879I
b = 0.001644 + 1.122350I
−5.78523 − 1.33156I 0
u = 1.115920 − 0.386738I
a = 0.770057 − 0.924879I
b = 0.001644 − 1.122350I
−5.78523 + 1.33156I 0
u = −1.075130 + 0.491781I
a = 0.321591 − 1.146720I
b = −0.529411 − 0.770162I
−0.78033 + 1.78897I 0
u = −1.075130 − 0.491781I
a = 0.321591 + 1.146720I
b = −0.529411 + 0.770162I
−0.78033 − 1.78897I 0
u = −1.086240 + 0.469331I
a = 1.00483 − 1.65568I
b = −2.08170 + 0.11796I
−0.60469 + 6.62618I 0
u = −1.086240 − 0.469331I
a = 1.00483 + 1.65568I
b = −2.08170 − 0.11796I
−0.60469 − 6.62618I 0
u = 0.800540 + 0.159505I
a = −1.34398 + 0.82795I
b = 0.235141 + 0.634144I
−3.78952 − 0.63574I −7.80030 − 1.07464I
u = 0.800540 − 0.159505I
a = −1.34398 − 0.82795I
b = 0.235141 − 0.634144I
−3.78952 + 0.63574I −7.80030 + 1.07464I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.706846 + 0.404397I
a = 1.025440 + 0.209974I
b = −0.163790 − 0.549676I
−0.92183 + 1.73948I 1.33670 − 5.18470I
u = −0.706846 − 0.404397I
a = 1.025440 − 0.209974I
b = −0.163790 + 0.549676I
−0.92183 − 1.73948I 1.33670 + 5.18470I
u = −0.291710 + 0.746647I
a = 0.913446 − 0.553942I
b = −0.86158 + 1.20273I
2.51136 − 7.38098I 4.67865 + 6.50498I
u = −0.291710 − 0.746647I
a = 0.913446 + 0.553942I
b = −0.86158 − 1.20273I
2.51136 + 7.38098I 4.67865 − 6.50498I
u = −0.204099 + 0.770012I
a = −1.44727 + 0.96788I
b = 0.791296 − 0.812280I
−4.03937 − 2.88714I 1.97779 + 2.63363I
u = −0.204099 − 0.770012I
a = −1.44727 − 0.96788I
b = 0.791296 + 0.812280I
−4.03937 + 2.88714I 1.97779 − 2.63363I
u = 0.324606 + 0.719295I
a = 0.994278 + 0.499389I
b = −0.935589 − 0.987956I
3.41838 + 1.78840I 6.81099 − 1.35188I
u = 0.324606 − 0.719295I
a = 0.994278 − 0.499389I
b = −0.935589 + 0.987956I
3.41838 − 1.78840I 6.81099 + 1.35188I
u = 1.116840 + 0.479179I
a = 0.500971 + 1.225950I
b = −0.546443 + 1.046570I
−1.73593 − 7.03987I 0
u = 1.116840 − 0.479179I
a = 0.500971 − 1.225950I
b = −0.546443 − 1.046570I
−1.73593 + 7.03987I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.202550 + 0.232951I
a = −0.665302 − 0.130075I
b = −0.59992 − 1.56836I
−6.89377 + 2.42700I 0
u = 1.202550 − 0.232951I
a = −0.665302 + 0.130075I
b = −0.59992 + 1.56836I
−6.89377 − 2.42700I 0
u = 1.185840 + 0.328845I
a = −0.159149 + 0.253149I
b = −0.638766 − 1.188740I
−8.21277 − 0.66939I 0
u = 1.185840 − 0.328845I
a = −0.159149 − 0.253149I
b = −0.638766 + 1.188740I
−8.21277 + 0.66939I 0
u = −1.130920 + 0.495066I
a = −1.50190 + 0.76911I
b = 0.357862 + 1.110160I
−5.01226 + 6.39834I 0
u = −1.130920 − 0.495066I
a = −1.50190 − 0.76911I
b = 0.357862 − 1.110160I
−5.01226 − 6.39834I 0
u = 1.117680 + 0.547964I
a = −1.46662 − 1.06692I
b = 0.87922 − 1.22354I
1.10367 − 6.62158I 0
u = 1.117680 − 0.547964I
a = −1.46662 + 1.06692I
b = 0.87922 + 1.22354I
1.10367 + 6.62158I 0
u = −1.230070 + 0.222227I
a = −0.650623 + 0.287213I
b = −0.55993 + 1.63653I
−8.23592 − 8.08821I 0
u = −1.230070 − 0.222227I
a = −0.650623 − 0.287213I
b = −0.55993 − 1.63653I
−8.23592 + 8.08821I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.135920 + 0.548670I
a = −1.56765 + 1.05385I
b = 0.80759 + 1.40097I
0.04166 + 12.27660I 0
u = −1.135920 − 0.548670I
a = −1.56765 − 1.05385I
b = 0.80759 − 1.40097I
0.04166 − 12.27660I 0
u = −1.234570 + 0.289671I
a = −0.280220 + 0.162253I
b = −0.41036 + 1.42432I
−13.20240 − 1.48788I 0
u = −1.234570 − 0.289671I
a = −0.280220 − 0.162253I
b = −0.41036 − 1.42432I
−13.20240 + 1.48788I 0
u = −1.220590 + 0.363156I
a = 0.176181 − 0.092037I
b = −0.400866 + 0.960136I
−10.23010 + 5.45971I 0
u = −1.220590 − 0.363156I
a = 0.176181 + 0.092037I
b = −0.400866 − 0.960136I
−10.23010 − 5.45971I 0
u = −1.162350 + 0.529110I
a = 1.58602 − 0.69662I
b = −1.049770 − 0.884839I
−6.83271 + 7.72442I 0
u = −1.162350 − 0.529110I
a = 1.58602 + 0.69662I
b = −1.049770 + 0.884839I
−6.83271 − 7.72442I 0
u = 1.189490 + 0.501412I
a = 1.304510 + 0.485719I
b = −0.687871 + 0.503380I
−9.27708 − 3.36674I 0
u = 1.189490 − 0.501412I
a = 1.304510 − 0.485719I
b = −0.687871 − 0.503380I
−9.27708 + 3.36674I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.160770 + 0.580972I
a = 2.02321 − 0.58604I
b = −1.04158 − 1.61922I
−4.53003 + 10.88730I 0
u = −1.160770 − 0.580972I
a = 2.02321 + 0.58604I
b = −1.04158 + 1.61922I
−4.53003 − 10.88730I 0
u = 1.169640 + 0.590016I
a = 2.06628 + 0.49634I
b = −0.90929 + 1.73967I
−5.7221 − 16.7702I 0
u = 1.169640 − 0.590016I
a = 2.06628 − 0.49634I
b = −0.90929 − 1.73967I
−5.7221 + 16.7702I 0
u = 1.187170 + 0.556301I
a = 1.77127 + 0.43655I
b = −0.68854 + 1.25154I
−11.3632 − 10.3671I 0
u = 1.187170 − 0.556301I
a = 1.77127 − 0.43655I
b = −0.68854 − 1.25154I
−11.3632 + 10.3671I 0
u = −0.185731 + 0.641811I
a = 0.756552 − 0.283327I
b = −0.232991 + 0.941868I
−2.35932 − 2.00526I −1.48033 + 3.96035I
u = −0.185731 − 0.641811I
a = 0.756552 + 0.283327I
b = −0.232991 − 0.941868I
−2.35932 + 2.00526I −1.48033 − 3.96035I
u = 0.389023 + 0.509805I
a = 1.075130 + 0.144503I
b = −0.544827 − 0.221741I
1.062250 + 0.424517I 8.97355 − 2.01331I
u = 0.389023 − 0.509805I
a = 1.075130 − 0.144503I
b = −0.544827 + 0.221741I
1.062250 − 0.424517I 8.97355 + 2.01331I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.290022 + 0.515209I
a = −0.018168 − 0.781517I
b = 0.879191 − 0.370054I
1.36541 + 2.37978I 3.46852 − 3.41971I
u = −0.290022 − 0.515209I
a = −0.018168 + 0.781517I
b = 0.879191 + 0.370054I
1.36541 − 2.37978I 3.46852 + 3.41971I
u = 0.127475 + 0.564967I
a = 0.312049 + 0.348058I
b = 0.714824 + 0.627954I
0.89060 + 2.90592I 2.23821 − 2.15626I
u = 0.127475 − 0.564967I
a = 0.312049 − 0.348058I
b = 0.714824 − 0.627954I
0.89060 − 2.90592I 2.23821 + 2.15626I
u = 0.445021 + 0.220782I
a = −2.67070 − 2.13843I
b = 1.43176 − 0.52942I
1.36889 − 3.02323I 1.02541 + 1.50693I
u = 0.445021 − 0.220782I
a = −2.67070 + 2.13843I
b = 1.43176 + 0.52942I
1.36889 + 3.02323I 1.02541 − 1.50693I
u = −0.334073 + 0.360832I
a = −2.92777 + 1.91022I
b = 1.54696 + 0.11678I
1.58828 − 2.77548I 2.40050 + 3.94176I
u = −0.334073 − 0.360832I
a = −2.92777 − 1.91022I
b = 1.54696 − 0.11678I
1.58828 + 2.77548I 2.40050 − 3.94176I
14
II. I
u
2
= h−u
2
a − u
2
+ b + a, u
3
a
2
+ 2u
3
a + · · · + 2a − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
a
u
2
a + u
2
− a
a
4
=
u
3
a − u
−au
a
10
=
u
2
a + u
2
u
2
a + u
2
− a
a
1
=
u
3
0
a
8
=
−u
2
+ 1
u
2
a
12
=
u
3
a
2
+ u
3
a + u
3
+ au + u
u
3
a
2
+ 2u
3
a − a
2
u + u
a
11
=
u
3
a
2
+ 2u
2
a − u
3
− a
2
+ 2au + 3u
2
− 3a + 2u − 2
u
3
a
2
+ 2u
3
a − a
2
u − u
2
a + u
3
− u
2
+ a + u
a
5
=
u
3
a
u
3
− au − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
2
u
2
− 4u
3
+ 4au + 8u
2
− 8a + 4u − 12
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
6
c
2
, c
6
, c
7
(u
4
− u
2
+ 1)
3
c
3
, c
4
, c
8
(u
2
+ 1)
6
c
5
, c
11
(u
6
+ u
4
+ 2u
2
+ 1)
2
c
9
(u
6
− 3u
4
+ 2u
2
+ 1)
2
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
2
+ y + 1)
6
c
2
, c
6
, c
7
(y
2
− y + 1)
6
c
3
, c
4
, c
8
(y + 1)
12
c
5
, c
11
(y
3
+ y
2
+ 2y + 1)
4
c
9
(y
3
− 3y
2
+ 2y + 1)
4
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 = 0.866025 + 0.500000I
a = −0.967306 − 0.373532I
b = 1.307140 + 0.215080I
1.37919 + 0.79824I 1.50976 + 0.48465I
u = 0.866025 + 0.500000I
a = −0.006504 + 0.581105I
b = 0.569840I
−2.75839 − 2.02988I −5.01951 + 3.46410I
u = 0.866025 + 0.500000I
a = 0.33984 + 1.89050I
b = −1.307140 + 0.215080I
1.37919 − 4.85801I 1.50976 + 6.44355I
u = 0.866025 − 0.500000I
a = −0.967306 + 0.373532I
b = 1.307140 − 0.215080I
1.37919 − 0.79824I 1.50976 − 0.48465I
u = 0.866025 − 0.500000I
a = −0.006504 − 0.581105I
b = − 0.569840I
−2.75839 + 2.02988I −5.01951 − 3.46410I
u = 0.866025 − 0.500000I
a = 0.33984 − 1.89050I
b = −1.307140 − 0.215080I
1.37919 + 4.85801I 1.50976 − 6.44355I
u = −0.866025 + 0.500000I
a = −1.339840 + 0.158452I
b = 1.307140 + 0.215080I
1.37919 + 4.85801I 1.50976 − 6.44355I
u = −0.866025 + 0.500000I
a = −0.99350 − 1.15095I
b = 0.569840I
−2.75839 + 2.02988I −5.01951 − 3.46410I
u = −0.866025 + 0.500000I
a = −0.03269 − 2.10558I
b = −1.307140 + 0.215080I
1.37919 − 0.79824I 1.50976 − 0.48465I
u = −0.866025 − 0.500000I
a = −1.339840 − 0.158452I
b = 1.307140 − 0.215080I
1.37919 − 4.85801I 1.50976 + 6.44355I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866025 − 0.500000I
a = −0.99350 + 1.15095I
b = − 0.569840I
−2.75839 − 2.02988I −5.01951 + 3.46410I
u = −0.866025 − 0.500000I
a = −0.03269 + 2.10558I
b = −1.307140 − 0.215080I
1.37919 + 0.79824I 1.50976 + 0.48465I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
98
+ 49u
97
+ ··· + 7u + 1)
c
2
, c
6
((u
4
− u
2
+ 1)
3
)(u
98
− u
97
+ ··· − u + 1)
c
3
, c
4
, c
8
((u
2
+ 1)
6
)(u
98
− u
97
+ ··· + 85u + 25)
c
5
, c
11
((u
6
+ u
4
+ 2u
2
+ 1)
2
)(u
98
+ u
97
+ ··· + 7u + 1)
c
7
((u
4
− u
2
+ 1)
3
)(u
98
− 3u
97
+ ··· − 93143u + 31691)
c
9
((u
6
− 3u
4
+ 2u
2
+ 1)
2
)(u
98
− 5u
97
+ ··· − 30007u + 14539)
c
10
((u
3
− u
2
+ 2u − 1)
4
)(u
98
+ 33u
97
+ ··· − 9u + 1)
c
12
((u
3
+ u
2
+ 2u + 1)
4
)(u
98
+ 33u
97
+ ··· − 9u + 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
98
+ 7y
97
+ ··· + 49y + 1)
c
2
, c
6
((y
2
− y + 1)
6
)(y
98
− 49y
97
+ ··· − 7y + 1)
c
3
, c
4
, c
8
((y + 1)
12
)(y
98
+ 93y
97
+ ··· − 20825y + 625)
c
5
, c
11
((y
3
+ y
2
+ 2y + 1)
4
)(y
98
+ 33y
97
+ ··· − 9y + 1)
c
7
((y
2
− y + 1)
6
)(y
98
+ 35y
97
+ ··· + 1.58231 × 10
9
y + 1.00432 × 10
9
)
c
9
(y
3
− 3y
2
+ 2y + 1)
4
· (y
98
+ 21y
97
+ ··· − 4470326109y + 211382521)
c
10
, c
12
((y
3
+ 3y
2
+ 2y − 1)
4
)(y
98
+ 69y
97
+ ··· + 27y + 1)
21
