12n
0828
(K12n
0828
)
A knot diagram
1
Linearized knot diagam
4 6 12 8 10 11 2 12 5 3 7 8
Solving Sequence
6,11
7
3,12
2 8 10 5 4 1 9
c
6
c
11
c
2
c
7
c
10
c
5
c
4
c
1
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4.86488 × 10
164
u
74
+ 2.61870 × 10
164
u
73
+ ··· + 7.00921 × 10
164
b + 5.62454 × 10
165
,
1.09347 × 10
165
u
74
+ 1.00292 × 10
165
u
73
+ ··· + 2.10276 × 10
165
a + 1.21416 × 10
166
,
u
75
− 26u
73
+ ··· − 29u − 11i
I
u
2
= h3565784u
20
+ 1758543u
19
+ ··· + 4587301b + 16185776,
− 848187u
20
+ 33456238u
19
+ ··· + 22936505a − 154067073, u
21
+ u
20
+ ··· − 6u + 5i
* 2 irreducible components of dim
C
= 0, with total 96 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
= h4.86 × 10
164
u
74
+ 2.62 × 10
164
u
73
+ · · · + 7.01 × 10
164
b + 5.62 ×
10
165
, 1.09 × 10
165
u
74
+ 1.00 × 10
165
u
73
+ · · · + 2.10 × 10
165
a + 1.21 ×
10
166
, u
75
− 26u
73
+ · · · − 29u − 11i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
3
=
−0.520016u
74
− 0.476954u
73
+ ··· + 17.4523u − 5.77412
−0.694069u
74
− 0.373608u
73
+ ··· − 32.7082u − 8.02450
a
12
=
u
−u
3
+ u
a
2
=
0.174054u
74
− 0.103346u
73
+ ··· + 50.1605u + 2.25038
−0.694069u
74
− 0.373608u
73
+ ··· − 32.7082u − 8.02450
a
8
=
0.492874u
74
+ 0.989732u
73
+ ··· + 37.5192u + 6.43908
−0.533362u
74
− 0.574794u
73
+ ··· − 25.1238u − 7.74220
a
10
=
0.232330u
74
+ 0.157784u
73
+ ··· + 85.2464u + 7.12576
0.332393u
74
+ 0.264914u
73
+ ··· + 8.68473u + 1.62379
a
5
=
0.118936u
74
− 0.271370u
73
+ ··· + 78.1808u + 7.39601
0.581180u
74
+ 0.461009u
73
+ ··· + 26.2919u + 6.63202
a
4
=
−0.0260069u
74
− 0.241627u
73
+ ··· + 43.5597u − 0.0222318
−0.483810u
74
− 0.266665u
73
+ ··· − 18.8593u − 4.86120
a
1
=
−0.608923u
74
− 0.434802u
73
+ ··· − 30.3780u − 3.65550
−0.433540u
74
− 0.348757u
73
+ ··· − 25.2954u − 5.66632
a
9
=
0.194330u
74
+ 0.575188u
73
+ ··· + 19.9609u + 1.00031
−0.583866u
74
− 0.672134u
73
+ ··· − 27.3764u − 8.62099
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.00721u
74
− 1.40524u
73
+ ··· − 209.477u − 50.8854
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
75
+ 4u
74
+ ··· + 19778u + 1511
c
2
u
75
− 7u
74
+ ··· + 18u + 1
c
3
u
75
− 2u
74
+ ··· − 264568u + 145247
c
4
u
75
+ u
74
+ ··· − 4794u − 103
c
5
, c
9
u
75
− 3u
74
+ ··· + 4690u − 3812
c
6
, c
11
u
75
− 26u
73
+ ··· − 29u + 11
c
7
u
75
+ u
74
+ ··· + 1531u − 221
c
8
, c
12
u
75
− 5u
74
+ ··· + 6535u + 1379
c
10
u
75
− 2u
74
+ ··· − 27u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
75
+ 72y
74
+ ··· − 34177216y −2283121
c
2
y
75
+ 11y
74
+ ··· + 92y −1
c
3
y
75
+ 36y
74
+ ··· + 220857023174y −21096691009
c
4
y
75
+ 85y
74
+ ··· + 17227620y −10609
c
5
, c
9
y
75
− 45y
74
+ ··· + 350201676y −14531344
c
6
, c
11
y
75
− 52y
74
+ ··· + 6627y −121
c
7
y
75
+ 37y
74
+ ··· + 884919y −48841
c
8
, c
12
y
75
− 87y
74
+ ··· + 99190065y −1901641
c
10
y
75
+ 8y
74
+ ··· − 2407y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.013866 + 0.992612I
a = 0.692135 + 0.718908I
b = 0.400349 + 1.084530I
−6.17619 + 2.37907I 0
u = −0.013866 − 0.992612I
a = 0.692135 − 0.718908I
b = 0.400349 − 1.084530I
−6.17619 − 2.37907I 0
u = 0.939254 + 0.315999I
a = 0.018888 + 0.438631I
b = −0.664173 + 0.848941I
−1.07144 + 2.44545I 0
u = 0.939254 − 0.315999I
a = 0.018888 − 0.438631I
b = −0.664173 − 0.848941I
−1.07144 − 2.44545I 0
u = −0.938498 + 0.408238I
a = 0.13100 + 1.90136I
b = −0.330038 + 0.911612I
−1.29527 − 3.07415I 0
u = −0.938498 − 0.408238I
a = 0.13100 − 1.90136I
b = −0.330038 − 0.911612I
−1.29527 + 3.07415I 0
u = −0.960972 + 0.048035I
a = −0.544278 + 1.052270I
b = 0.903732 + 0.646873I
1.079070 − 0.291978I 0
u = −0.960972 − 0.048035I
a = −0.544278 − 1.052270I
b = 0.903732 − 0.646873I
1.079070 + 0.291978I 0
u = −0.966822 + 0.378367I
a = 1.94521 − 0.03260I
b = −0.084333 + 0.363747I
2.57495 − 7.43580I 0
u = −0.966822 − 0.378367I
a = 1.94521 + 0.03260I
b = −0.084333 − 0.363747I
2.57495 + 7.43580I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.034730 + 0.129185I
a = 0.145476 − 0.953838I
b = −0.87885 − 1.88423I
5.36144 − 1.41166I 0
u = −1.034730 − 0.129185I
a = 0.145476 + 0.953838I
b = −0.87885 + 1.88423I
5.36144 + 1.41166I 0
u = 0.907268 + 0.075300I
a = 0.94549 − 2.12345I
b = −0.523555 − 0.950514I
−3.93565 + 1.98540I 0. + 3.06730I
u = 0.907268 − 0.075300I
a = 0.94549 + 2.12345I
b = −0.523555 + 0.950514I
−3.93565 − 1.98540I 0. − 3.06730I
u = 1.110880 + 0.165795I
a = −0.047261 − 0.317334I
b = 2.14672 − 0.81505I
5.56938 + 6.51079I 0
u = 1.110880 − 0.165795I
a = −0.047261 + 0.317334I
b = 2.14672 + 0.81505I
5.56938 − 6.51079I 0
u = −1.160340 + 0.126685I
a = 0.282949 + 0.314124I
b = −0.837413 + 0.239299I
2.25915 − 0.14325I 0
u = −1.160340 − 0.126685I
a = 0.282949 − 0.314124I
b = −0.837413 − 0.239299I
2.25915 + 0.14325I 0
u = 0.206317 + 1.155090I
a = −0.603459 + 0.707647I
b = −0.521027 + 0.818222I
−4.61919 − 3.44875I 0
u = 0.206317 − 1.155090I
a = −0.603459 − 0.707647I
b = −0.521027 − 0.818222I
−4.61919 + 3.44875I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.114000 + 0.368961I
a = −1.019900 + 0.719651I
b = 0.988836 + 0.744888I
4.35958 + 4.55603I 0
u = 1.114000 − 0.368961I
a = −1.019900 − 0.719651I
b = 0.988836 − 0.744888I
4.35958 − 4.55603I 0
u = 0.760290 + 0.301132I
a = −1.63953 − 0.05711I
b = −0.341483 + 0.350286I
−3.59837 − 0.23339I 3.34922 − 1.64513I
u = 0.760290 − 0.301132I
a = −1.63953 + 0.05711I
b = −0.341483 − 0.350286I
−3.59837 + 0.23339I 3.34922 + 1.64513I
u = −0.002744 + 1.189670I
a = 0.701533 − 0.828624I
b = 0.653223 − 1.002770I
−0.08499 − 10.49950I 0
u = −0.002744 − 1.189670I
a = 0.701533 + 0.828624I
b = 0.653223 + 1.002770I
−0.08499 + 10.49950I 0
u = 1.172170 + 0.305565I
a = 0.523471 + 0.816282I
b = −0.132271 − 0.058421I
−1.80185 + 2.16906I 0
u = 1.172170 − 0.305565I
a = 0.523471 − 0.816282I
b = −0.132271 + 0.058421I
−1.80185 − 2.16906I 0
u = 1.173800 + 0.362759I
a = −0.378650 + 0.861125I
b = 1.099170 + 0.869923I
3.34164 + 4.17608I 0
u = 1.173800 − 0.362759I
a = −0.378650 − 0.861125I
b = 1.099170 − 0.869923I
3.34164 − 4.17608I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.052071 + 0.743666I
a = −1.22281 − 1.12361I
b = −0.525972 − 1.114410I
−6.07542 + 3.12385I −2.56319 − 4.01706I
u = −0.052071 − 0.743666I
a = −1.22281 + 1.12361I
b = −0.525972 + 1.114410I
−6.07542 − 3.12385I −2.56319 + 4.01706I
u = 0.647746 + 0.356319I
a = −0.52809 + 1.45131I
b = 1.33036 + 0.69475I
3.40846 + 5.43996I −0.90178 − 5.14570I
u = 0.647746 − 0.356319I
a = −0.52809 − 1.45131I
b = 1.33036 − 0.69475I
3.40846 − 5.43996I −0.90178 + 5.14570I
u = −1.237780 + 0.300983I
a = −0.68099 − 1.37162I
b = 0.955357 − 0.902724I
7.74101 − 8.12655I 0
u = −1.237780 − 0.300983I
a = −0.68099 + 1.37162I
b = 0.955357 + 0.902724I
7.74101 + 8.12655I 0
u = −0.404055 + 0.594522I
a = 0.79451 − 1.92548I
b = 0.006207 − 1.108050I
1.03252 + 3.60544I −4.06380 − 1.82140I
u = −0.404055 − 0.594522I
a = 0.79451 + 1.92548I
b = 0.006207 + 1.108050I
1.03252 − 3.60544I −4.06380 + 1.82140I
u = 0.686004
a = 1.77921
b = −1.18115
−2.50904 −13.2560
u = −1.337960 + 0.048610I
a = 0.085328 + 0.223266I
b = 0.89019 + 1.54950I
6.53570 − 1.10775I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.337960 − 0.048610I
a = 0.085328 − 0.223266I
b = 0.89019 − 1.54950I
6.53570 + 1.10775I 0
u = −1.278100 + 0.422698I
a = 0.395219 + 1.012020I
b = −1.09039 + 1.47215I
−2.27515 − 7.48919I 0
u = −1.278100 − 0.422698I
a = 0.395219 − 1.012020I
b = −1.09039 − 1.47215I
−2.27515 + 7.48919I 0
u = −0.630165 + 0.173633I
a = 1.17934 − 1.10273I
b = −0.690665 + 0.543583I
4.27365 − 0.04437I 3.14115 + 2.61297I
u = −0.630165 − 0.173633I
a = 1.17934 + 1.10273I
b = −0.690665 − 0.543583I
4.27365 + 0.04437I 3.14115 − 2.61297I
u = 0.201905 + 0.589482I
a = 0.41957 − 1.35572I
b = 0.678636 − 1.018540I
1.71568 − 0.87377I −4.45101 − 0.59244I
u = 0.201905 − 0.589482I
a = 0.41957 + 1.35572I
b = 0.678636 + 1.018540I
1.71568 + 0.87377I −4.45101 + 0.59244I
u = 1.255700 + 0.619721I
a = 0.150657 − 0.302176I
b = −0.850030 − 0.371842I
−1.71673 + 3.48360I 0
u = 1.255700 − 0.619721I
a = 0.150657 + 0.302176I
b = −0.850030 + 0.371842I
−1.71673 − 3.48360I 0
u = 1.373600 + 0.302564I
a = 0.148834 − 0.958574I
b = −0.831950 − 0.610118I
11.26350 + 2.23040I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.373600 − 0.302564I
a = 0.148834 + 0.958574I
b = −0.831950 + 0.610118I
11.26350 − 2.23040I 0
u = 1.277590 + 0.602915I
a = 0.361233 − 1.084430I
b = −1.00616 − 1.06220I
−1.23702 + 9.55268I 0
u = 1.277590 − 0.602915I
a = 0.361233 + 1.084430I
b = −1.00616 + 1.06220I
−1.23702 − 9.55268I 0
u = −0.53023 + 1.32146I
a = −0.371566 + 0.232025I
b = −0.602848 − 0.069339I
4.94966 + 2.13138I 0
u = −0.53023 − 1.32146I
a = −0.371566 − 0.232025I
b = −0.602848 + 0.069339I
4.94966 − 2.13138I 0
u = −1.33869 + 0.49079I
a = −0.297532 − 0.830875I
b = 1.12359 − 1.40728I
−2.01665 − 7.67344I 0
u = −1.33869 − 0.49079I
a = −0.297532 + 0.830875I
b = 1.12359 + 1.40728I
−2.01665 + 7.67344I 0
u = 1.43679 + 0.09756I
a = −0.060747 + 0.750626I
b = 0.00253 + 2.18189I
7.07352 − 1.46642I 0
u = 1.43679 − 0.09756I
a = −0.060747 − 0.750626I
b = 0.00253 − 2.18189I
7.07352 + 1.46642I 0
u = 1.04085 + 1.02337I
a = 0.404301 + 0.100962I
b = 0.686049 − 0.445349I
3.77545 + 0.13140I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.04085 − 1.02337I
a = 0.404301 − 0.100962I
b = 0.686049 + 0.445349I
3.77545 − 0.13140I 0
u = −0.520472
a = −3.56024
b = −0.196479
−2.81755 −5.84520
u = 1.37763 + 0.57274I
a = −0.327901 + 1.049300I
b = 1.16712 + 1.26375I
4.2230 + 16.6469I 0
u = 1.37763 − 0.57274I
a = −0.327901 − 1.049300I
b = 1.16712 − 1.26375I
4.2230 − 16.6469I 0
u = −1.29659 + 0.76159I
a = −0.040832 − 0.596066I
b = 0.645843 − 0.482141I
0.41911 − 3.99968I 0
u = −1.29659 − 0.76159I
a = −0.040832 + 0.596066I
b = 0.645843 + 0.482141I
0.41911 + 3.99968I 0
u = −1.37317 + 0.63897I
a = 0.030652 + 0.763246I
b = −1.163710 + 0.673853I
8.47631 − 9.19794I 0
u = −1.37317 − 0.63897I
a = 0.030652 − 0.763246I
b = −1.163710 − 0.673853I
8.47631 + 9.19794I 0
u = 0.399944 + 0.225942I
a = −0.97127 + 2.25690I
b = 1.265320 + 0.451196I
3.42078 + 5.42017I −0.67147 − 4.81273I
u = 0.399944 − 0.225942I
a = −0.97127 − 2.25690I
b = 1.265320 − 0.451196I
3.42078 − 5.42017I −0.67147 + 4.81273I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.047641 + 0.411386I
a = 1.018950 − 0.899310I
b = 0.382640 − 0.474799I
−0.012233 − 1.006120I −0.14669 + 6.62242I
u = −0.047641 − 0.411386I
a = 1.018950 + 0.899310I
b = 0.382640 + 0.474799I
−0.012233 + 1.006120I −0.14669 − 6.62242I
u = −0.167122
a = −8.32002
b = −0.479306
−2.84829 −2.66050
u = −1.79051 + 0.67497I
a = 0.228770 − 0.140811I
b = 0.177471 + 0.154132I
4.72272 + 3.49376I 0
u = −1.79051 − 0.67497I
a = 0.228770 + 0.140811I
b = 0.177471 − 0.154132I
4.72272 − 3.49376I 0
12
II.
I
u
2
= h3.57 × 10
6
u
20
+ 1.76 × 10
6
u
19
+ · · · + 4.59 × 10
6
b + 1.62 × 10
7
, −8.48 ×
10
5
u
20
+ 3.35 × 10
7
u
19
+ · · · + 2.29 × 10
7
a − 1.54 × 10
8
, u
21
+ u
20
+ · · · − 6u + 5i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
3
=
0.0369798u
20
− 1.45865u
19
+ ··· − 13.1245u + 6.71711
−0.777316u
20
− 0.383350u
19
+ ··· + 6.41390u − 3.52839
a
12
=
u
−u
3
+ u
a
2
=
0.814296u
20
− 1.07530u
19
+ ··· − 19.5384u + 10.2455
−0.777316u
20
− 0.383350u
19
+ ··· + 6.41390u − 3.52839
a
8
=
−0.252921u
20
− 0.758060u
19
+ ··· − 2.49621u + 5.84126
−0.495626u
20
− 0.795075u
19
+ ··· + 1.93899u + 0.815101
a
10
=
0.860543u
20
+ 1.73551u
19
+ ··· + 11.3000u − 9.27095
0.326407u
20
+ 0.988228u
19
+ ··· + 1.22673u − 2.67701
a
5
=
0.00585499u
20
− 0.951995u
19
+ ··· − 14.0920u + 3.66552
0.210010u
20
+ 0.171345u
19
+ ··· + 0.699044u − 2.11466
a
4
=
0.965535u
20
− 1.09140u
19
+ ··· − 22.6790u + 10.0385
−0.611923u
20
− 0.730373u
19
+ ··· + 4.87009u − 3.01351
a
1
=
−0.244683u
20
− 0.311053u
19
+ ··· − 2.38142u + 3.17549
−0.128348u
20
− 0.518938u
19
+ ··· + 0.357854u + 0.856290
a
9
=
−0.422140u
20
− 0.564907u
19
+ ··· + 0.669517u + 2.97935
−0.534291u
20
− 0.622926u
19
+ ··· + 2.08439u − 0.234950
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2314838
4587301
u
20
−
20496911
4587301
u
19
+ ··· −
242100829
4587301
u +
93801989
4587301
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
21
− 5u
20
+ ··· − 3u − 1
c
2
u
21
+ 5u
19
+ ··· + u − 1
c
3
u
21
− 3u
20
+ ··· + 47u + 43
c
4
u
21
+ 6u
19
+ ··· + 7u + 1
c
5
u
21
− 9u
19
+ ··· − 10u − 4
c
6
u
21
+ u
20
+ ··· − 6u + 5
c
7
u
21
+ 8u
19
+ ··· − 6u − 7
c
8
u
21
− 8u
19
+ ··· + 4u − 1
c
9
u
21
− 9u
19
+ ··· − 10u + 4
c
10
u
21
− u
20
+ ··· + 4u − 1
c
11
u
21
− u
20
+ ··· − 6u − 5
c
12
u
21
− 8u
19
+ ··· + 4u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 11y
20
+ ··· + 11y −1
c
2
y
21
+ 10y
20
+ ··· − 5y −1
c
3
y
21
+ 27y
20
+ ··· + 11153y −1849
c
4
y
21
+ 12y
20
+ ··· − 17y −1
c
5
, c
9
y
21
− 18y
20
+ ··· + 268y −16
c
6
, c
11
y
21
− 17y
20
+ ··· + 226y −25
c
7
y
21
+ 16y
20
+ ··· − 370y −49
c
8
, c
12
y
21
− 16y
20
+ ··· − 20y −1
c
10
y
21
+ 3y
20
+ ··· − 4y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.001020 + 0.262420I
a = −0.921736 − 0.575279I
b = 1.64460 − 0.25263I
4.36516 − 6.59975I 1.05252 + 8.07459I
u = −1.001020 − 0.262420I
a = −0.921736 + 0.575279I
b = 1.64460 + 0.25263I
4.36516 + 6.59975I 1.05252 − 8.07459I
u = −0.137847 + 0.949067I
a = −0.852631 − 0.775856I
b = −0.503361 − 1.102010I
−7.38286 + 2.58162I −9.14346 − 2.28449I
u = −0.137847 − 0.949067I
a = −0.852631 + 0.775856I
b = −0.503361 + 1.102010I
−7.38286 − 2.58162I −9.14346 + 2.28449I
u = 0.933976 + 0.190871I
a = 0.53801 − 2.33404I
b = −0.338970 − 0.954357I
−3.93389 + 2.54020I −4.26332 − 10.43284I
u = 0.933976 − 0.190871I
a = 0.53801 + 2.33404I
b = −0.338970 + 0.954357I
−3.93389 − 2.54020I −4.26332 + 10.43284I
u = −0.983637 + 0.420576I
a = 0.057658 − 0.984094I
b = 0.000605 − 0.667761I
−0.01096 − 2.31575I 2.89116 + 3.13951I
u = −0.983637 − 0.420576I
a = 0.057658 + 0.984094I
b = 0.000605 + 0.667761I
−0.01096 + 2.31575I 2.89116 − 3.13951I
u = 0.686384 + 0.325532I
a = −2.10424 + 0.04632I
b = −0.267232 + 0.305573I
−4.27917 − 0.25341I −10.22146 − 1.60946I
u = 0.686384 − 0.325532I
a = −2.10424 − 0.04632I
b = −0.267232 − 0.305573I
−4.27917 + 0.25341I −10.22146 + 1.60946I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.753934
a = 2.10025
b = −0.921449
−2.13830 10.8270
u = 0.476315 + 0.539233I
a = −0.302885 − 0.739305I
b = −0.310507 + 0.873261I
3.63985 + 1.20269I 0.11227 − 2.52581I
u = 0.476315 − 0.539233I
a = −0.302885 + 0.739305I
b = −0.310507 − 0.873261I
3.63985 − 1.20269I 0.11227 + 2.52581I
u = 1.370620 + 0.034901I
a = −0.117613 − 0.704260I
b = 0.02178 − 2.18523I
7.55445 + 0.17379I 6.36834 + 1.10559I
u = 1.370620 − 0.034901I
a = −0.117613 + 0.704260I
b = 0.02178 + 2.18523I
7.55445 − 0.17379I 6.36834 − 1.10559I
u = −1.314580 + 0.500777I
a = 0.351230 + 0.955966I
b = −1.05469 + 1.43008I
−3.61843 − 7.80961I −5.08756 + 5.98059I
u = −1.314580 − 0.500777I
a = 0.351230 − 0.955966I
b = −1.05469 − 1.43008I
−3.61843 + 7.80961I −5.08756 − 5.98059I
u = 1.31032 + 0.74608I
a = −0.083874 + 0.426133I
b = 0.761324 + 0.466956I
−1.66929 + 3.96809I −0.71858 − 12.39534I
u = 1.31032 − 0.74608I
a = −0.083874 − 0.426133I
b = 0.761324 − 0.466956I
−1.66929 − 3.96809I −0.71858 + 12.39534I
u = −1.46356 + 0.64846I
a = 0.185956 − 0.063411I
b = 0.507174 − 0.292801I
4.75936 + 3.16555I 4.09678 + 3.29546I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46356 − 0.64846I
a = 0.185956 + 0.063411I
b = 0.507174 + 0.292801I
4.75936 − 3.16555I 4.09678 − 3.29546I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 5u
20
+ ··· − 3u − 1)(u
75
+ 4u
74
+ ··· + 19778u + 1511)
c
2
(u
21
+ 5u
19
+ ··· + u − 1)(u
75
− 7u
74
+ ··· + 18u + 1)
c
3
(u
21
− 3u
20
+ ··· + 47u + 43)(u
75
− 2u
74
+ ··· − 264568u + 145247)
c
4
(u
21
+ 6u
19
+ ··· + 7u + 1)(u
75
+ u
74
+ ··· − 4794u − 103)
c
5
(u
21
− 9u
19
+ ··· − 10u − 4)(u
75
− 3u
74
+ ··· + 4690u − 3812)
c
6
(u
21
+ u
20
+ ··· − 6u + 5)(u
75
− 26u
73
+ ··· − 29u + 11)
c
7
(u
21
+ 8u
19
+ ··· − 6u − 7)(u
75
+ u
74
+ ··· + 1531u − 221)
c
8
(u
21
− 8u
19
+ ··· + 4u − 1)(u
75
− 5u
74
+ ··· + 6535u + 1379)
c
9
(u
21
− 9u
19
+ ··· − 10u + 4)(u
75
− 3u
74
+ ··· + 4690u − 3812)
c
10
(u
21
− u
20
+ ··· + 4u − 1)(u
75
− 2u
74
+ ··· − 27u + 7)
c
11
(u
21
− u
20
+ ··· − 6u − 5)(u
75
− 26u
73
+ ··· − 29u + 11)
c
12
(u
21
− 8u
19
+ ··· + 4u + 1)(u
75
− 5u
74
+ ··· + 6535u + 1379)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ 11y
20
+ ··· + 11y −1)
· (y
75
+ 72y
74
+ ··· − 34177216y −2283121)
c
2
(y
21
+ 10y
20
+ ··· − 5y −1)(y
75
+ 11y
74
+ ··· + 92y −1)
c
3
(y
21
+ 27y
20
+ ··· + 11153y −1849)
· (y
75
+ 36y
74
+ ··· + 220857023174y −21096691009)
c
4
(y
21
+ 12y
20
+ ··· − 17y −1)
· (y
75
+ 85y
74
+ ··· + 17227620y −10609)
c
5
, c
9
(y
21
− 18y
20
+ ··· + 268y −16)
· (y
75
− 45y
74
+ ··· + 350201676y −14531344)
c
6
, c
11
(y
21
− 17y
20
+ ··· + 226y −25)(y
75
− 52y
74
+ ··· + 6627y −121)
c
7
(y
21
+ 16y
20
+ ··· − 370y −49)
· (y
75
+ 37y
74
+ ··· + 884919y −48841)
c
8
, c
12
(y
21
− 16y
20
+ ··· − 20y −1)
· (y
75
− 87y
74
+ ··· + 99190065y −1901641)
c
10
(y
21
+ 3y
20
+ ··· − 4y −1)(y
75
+ 8y
74
+ ··· − 2407y −49)
22
