12a
0480
(K12a
0480
)
A knot diagram
1
Linearized knot diagam
3 6 11 10 2 1 4 5 12 8 7 9
Solving Sequence
5,10 4,12
9 1 8 11 3 2 7 6
c
4
c
9
c
12
c
8
c
10
c
3
c
1
c
7
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.53974 × 10
1782
u
185
− 1.04886 × 10
1782
u
184
+ ··· + 1.94118 × 10
1786
b − 1.46314 × 10
1786
,
− 2.97721 × 10
1785
u
185
+ 6.39771 × 10
1785
u
184
+ ··· + 2.13529 × 10
1787
a + 1.77330 × 10
1787
,
u
186
− 2u
185
+ ··· + 36u + 88i
I
u
2
= h−2.01366 × 10
18
u
38
− 2.85310 × 10
18
u
37
+ ··· + 3.17258 × 10
16
b + 5.50245 × 10
18
,
− 1.58873 × 10
18
u
38
− 1.90932 × 10
18
u
37
+ ··· + 3.17258 × 10
16
a + 3.87866 × 10
18
, u
39
− 8u
37
+ ··· − u + 1i
I
u
3
= h−u
3
− u
2
+ b − 3u, −u
3
+ a − 2u + 1, u
4
+ u
3
+ 3u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 229 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−5.54 × 10
1782
u
185
− 1.05 × 10
1782
u
184
+ · · · + 1.94 × 10
1786
b −
1.46 × 10
1786
, −2.98 × 10
1785
u
185
+ 6.40 × 10
1785
u
184
+ · · · + 2.14 ×
10
1787
a + 1.77 × 10
1787
, u
186
− 2u
185
+ · · · + 36u + 88i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
12
=
0.0139429u
185
− 0.0299617u
184
+ ··· + 27.9469u − 0.830473
0.000285381u
185
+ 0.0000540324u
184
+ ··· − 3.59654u + 0.753738
a
9
=
−0.0142463u
185
+ 0.0252800u
184
+ ··· − 20.5127u − 1.57779
−0.00499165u
185
+ 0.0105584u
184
+ ··· + 3.21433u − 1.41591
a
1
=
0.0267348u
185
− 0.0563542u
184
+ ··· + 62.5196u − 4.69174
−0.00716177u
185
+ 0.0148747u
184
+ ··· − 6.57632u − 1.44609
a
8
=
−0.00925466u
185
+ 0.0147216u
184
+ ··· − 23.7270u − 0.161882
−0.00499165u
185
+ 0.0105584u
184
+ ··· + 3.21433u − 1.41591
a
11
=
0.0282924u
185
− 0.0611872u
184
+ ··· + 48.9451u − 4.17978
−0.00392221u
185
+ 0.00742383u
184
+ ··· − 5.18728u − 0.958823
a
3
=
0.0381994u
185
− 0.0873826u
184
+ ··· + 22.1562u − 17.5234
−0.00538202u
185
+ 0.0115863u
184
+ ··· − 4.88044u − 0.286897
a
2
=
−0.0408306u
185
+ 0.0758692u
184
+ ··· − 42.0542u − 6.21348
−0.000658012u
185
+ 0.00163785u
184
+ ··· − 1.35113u + 0.743251
a
7
=
−0.0152408u
185
+ 0.0271515u
184
+ ··· − 21.4634u − 1.91111
−0.00417663u
185
+ 0.00854602u
184
+ ··· + 3.72464u − 1.45617
a
6
=
−0.0311906u
185
+ 0.0491555u
184
+ ··· − 44.2840u − 15.9001
−0.00170698u
185
+ 0.00411396u
184
+ ··· − 3.64158u + 1.07199
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0273306u
185
+ 0.0429325u
184
+ ··· + 5.94117u − 29.4743
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
186
+ 93u
185
+ ··· + 190u + 1
c
2
, c
5
u
186
+ u
185
+ ··· + 10u − 1
c
3
u
186
+ 5u
185
+ ··· + 305u + 29
c
4
u
186
+ 2u
185
+ ··· − 36u + 88
c
6
u
186
− 9u
185
+ ··· + 133392896u − 8998912
c
7
u
186
+ 4u
185
+ ··· + 96u − 17
c
8
u
186
+ 3u
185
+ ··· + 264890731u + 56493497
c
9
, c
12
u
186
+ 11u
185
+ ··· + 2925u + 459
c
10
u
186
− 12u
185
+ ··· + 104u − 16
c
11
u
186
− 3u
185
+ ··· + 2837302u + 121613
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
186
+ 15y
185
+ ··· − 32898y + 1
c
2
, c
5
y
186
− 93y
185
+ ··· − 190y + 1
c
3
y
186
− y
185
+ ··· + 166641y + 841
c
4
y
186
− 4y
185
+ ··· + 366192y + 7744
c
6
y
186
+ 51y
185
+ ··· − 15721607766212608y + 80980417183744
c
7
y
186
− 6y
185
+ ··· − 20878y + 289
c
8
y
186
− 21y
185
+ ··· − 86383388203073361y + 3191515203289009
c
9
, c
12
y
186
+ 101y
185
+ ··· − 66119733y + 210681
c
10
y
186
+ 2y
185
+ ··· + 15552y + 256
c
11
y
186
+ y
185
+ ··· + 730297573796y + 14789721769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.307193 + 0.967341I
a = 0.781942 − 0.330599I
b = 1.066600 − 0.168179I
0.97519 − 5.05662I 0
u = −0.307193 − 0.967341I
a = 0.781942 + 0.330599I
b = 1.066600 + 0.168179I
0.97519 + 5.05662I 0
u = 0.253390 + 0.990747I
a = −0.242638 + 0.284026I
b = 0.380788 + 0.645948I
−1.86439 − 1.17440I 0
u = 0.253390 − 0.990747I
a = −0.242638 − 0.284026I
b = 0.380788 − 0.645948I
−1.86439 + 1.17440I 0
u = −0.675127 + 0.780576I
a = −0.613719 + 1.037810I
b = 1.07465 + 2.13225I
2.11722 − 10.27940I 0
u = −0.675127 − 0.780576I
a = −0.613719 − 1.037810I
b = 1.07465 − 2.13225I
2.11722 + 10.27940I 0
u = 0.853275 + 0.452540I
a = −0.088030 − 1.280050I
b = 0.45272 − 2.29319I
3.49418 + 6.86248I 0
u = 0.853275 − 0.452540I
a = −0.088030 + 1.280050I
b = 0.45272 + 2.29319I
3.49418 − 6.86248I 0
u = −0.804997 + 0.530431I
a = 0.171471 − 1.314710I
b = −0.40826 − 2.32898I
0.91102 − 12.26790I 0
u = −0.804997 − 0.530431I
a = 0.171471 + 1.314710I
b = −0.40826 + 2.32898I
0.91102 + 12.26790I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083825 + 0.956958I
a = −1.119070 − 0.433268I
b = −1.258870 − 0.213178I
−2.73445 + 10.40150I 0
u = 0.083825 − 0.956958I
a = −1.119070 + 0.433268I
b = −1.258870 + 0.213178I
−2.73445 − 10.40150I 0
u = −0.674689 + 0.681706I
a = −0.598741 + 0.989226I
b = 1.28601 + 1.91959I
0.76354 − 2.80393I 0
u = −0.674689 − 0.681706I
a = −0.598741 − 0.989226I
b = 1.28601 − 1.91959I
0.76354 + 2.80393I 0
u = 0.437848 + 0.842864I
a = 0.147642 + 1.039510I
b = −0.577907 + 0.605984I
−2.56560 − 3.06621I 0
u = 0.437848 − 0.842864I
a = 0.147642 − 1.039510I
b = −0.577907 − 0.605984I
−2.56560 + 3.06621I 0
u = 0.717695 + 0.768921I
a = 0.633626 + 1.017910I
b = −1.02258 + 2.01828I
4.47017 + 5.65374I 0
u = 0.717695 − 0.768921I
a = 0.633626 − 1.017910I
b = −1.02258 − 2.01828I
4.47017 − 5.65374I 0
u = 1.012420 + 0.307233I
a = −1.199850 + 0.186361I
b = 0.364057 − 0.040225I
−2.46023 + 0.04685I 0
u = 1.012420 − 0.307233I
a = −1.199850 − 0.186361I
b = 0.364057 + 0.040225I
−2.46023 − 0.04685I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.572390 + 0.897115I
a = −0.663827 + 0.353353I
b = 0.133217 + 1.285900I
−0.80538 − 2.62868I 0
u = 0.572390 − 0.897115I
a = −0.663827 − 0.353353I
b = 0.133217 − 1.285900I
−0.80538 + 2.62868I 0
u = −0.354982 + 0.861592I
a = −0.305662 + 0.873306I
b = 0.413471 + 0.524540I
−0.32060 − 1.51914I 0
u = −0.354982 − 0.861592I
a = −0.305662 − 0.873306I
b = 0.413471 − 0.524540I
−0.32060 + 1.51914I 0
u = −0.722798 + 0.788914I
a = −0.257287 − 0.728218I
b = 0.363899 − 0.423076I
0.55644 − 3.03027I 0
u = −0.722798 − 0.788914I
a = −0.257287 + 0.728218I
b = 0.363899 + 0.423076I
0.55644 + 3.03027I 0
u = −0.096124 + 1.069100I
a = −0.601379 + 0.578893I
b = 0.467546 − 0.017428I
−0.06484 − 3.30755I 0
u = −0.096124 − 1.069100I
a = −0.601379 − 0.578893I
b = 0.467546 + 0.017428I
−0.06484 + 3.30755I 0
u = −0.138168 + 0.909744I
a = 1.045970 − 0.490376I
b = 1.224420 − 0.250675I
−0.19438 − 5.76200I 0
u = −0.138168 − 0.909744I
a = 1.045970 + 0.490376I
b = 1.224420 + 0.250675I
−0.19438 + 5.76200I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.059355 + 1.086540I
a = 0.788852 + 0.515087I
b = −0.458485 − 0.205965I
−1.89169 + 8.37857I 0
u = −0.059355 − 1.086540I
a = 0.788852 − 0.515087I
b = −0.458485 + 0.205965I
−1.89169 − 8.37857I 0
u = 0.363478 + 1.028510I
a = −0.731178 − 0.148405I
b = −1.038010 − 0.061869I
−0.537922 + 1.129420I 0
u = 0.363478 − 1.028510I
a = −0.731178 + 0.148405I
b = −1.038010 + 0.061869I
−0.537922 − 1.129420I 0
u = 0.824270 + 0.374120I
a = 0.639506 + 0.965348I
b = −1.02094 + 1.02954I
1.83442 + 4.12238I 0
u = 0.824270 − 0.374120I
a = 0.639506 − 0.965348I
b = −1.02094 − 1.02954I
1.83442 − 4.12238I 0
u = −0.314606 + 0.829544I
a = −0.444797 + 0.667757I
b = 0.092191 + 0.608271I
−0.38674 − 1.57867I 0
u = −0.314606 − 0.829544I
a = −0.444797 − 0.667757I
b = 0.092191 − 0.608271I
−0.38674 + 1.57867I 0
u = 0.461175 + 1.019950I
a = −0.443544 + 0.006626I
b = −0.877062 + 0.035310I
−0.59177 + 7.29260I 0
u = 0.461175 − 1.019950I
a = −0.443544 − 0.006626I
b = −0.877062 − 0.035310I
−0.59177 − 7.29260I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.178724 + 1.105860I
a = −0.807341 + 0.478053I
b = −0.069089 + 0.893742I
0.16929 − 1.66192I 0
u = −0.178724 − 1.105860I
a = −0.807341 − 0.478053I
b = −0.069089 − 0.893742I
0.16929 + 1.66192I 0
u = 0.180928 + 1.107630I
a = −0.837168 + 0.470067I
b = −0.052148 + 1.106190I
0.20180 − 2.41331I 0
u = 0.180928 − 1.107630I
a = −0.837168 − 0.470067I
b = −0.052148 − 1.106190I
0.20180 + 2.41331I 0
u = 0.645795 + 0.586749I
a = 0.900189 − 0.344371I
b = 0.662748 + 0.097500I
−1.59920 + 7.23039I 0
u = 0.645795 − 0.586749I
a = 0.900189 + 0.344371I
b = 0.662748 − 0.097500I
−1.59920 − 7.23039I 0
u = 1.118920 + 0.235863I
a = 0.662261 + 1.001360I
b = −0.425293 + 1.057500I
3.68148 − 2.29871I 0
u = 1.118920 − 0.235863I
a = 0.662261 − 1.001360I
b = −0.425293 − 1.057500I
3.68148 + 2.29871I 0
u = 0.793640 + 0.825156I
a = 0.695600 + 0.985737I
b = −0.80313 + 1.93853I
5.36288 + 4.49134I 0
u = 0.793640 − 0.825156I
a = 0.695600 − 0.985737I
b = −0.80313 − 1.93853I
5.36288 − 4.49134I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547707 + 1.009050I
a = 0.0232921 − 0.0858861I
b = 0.626031 + 0.023105I
0.64769 − 3.32832I 0
u = −0.547707 − 1.009050I
a = 0.0232921 + 0.0858861I
b = 0.626031 − 0.023105I
0.64769 + 3.32832I 0
u = −0.854073 + 0.774154I
a = 0.467182 + 0.340599I
b = −0.31259 + 1.45543I
−4.49622 − 0.82832I 0
u = −0.854073 − 0.774154I
a = 0.467182 − 0.340599I
b = −0.31259 − 1.45543I
−4.49622 + 0.82832I 0
u = 0.408699 + 0.733043I
a = 0.422778 + 1.292510I
b = −0.518609 + 0.803977I
−3.93842 + 4.35538I 0
u = 0.408699 − 0.733043I
a = 0.422778 − 1.292510I
b = −0.518609 − 0.803977I
−3.93842 − 4.35538I 0
u = −1.124830 + 0.340404I
a = −0.641335 + 1.005070I
b = 0.497320 + 1.184150I
5.59008 − 2.33345I 0
u = −1.124830 − 0.340404I
a = −0.641335 − 1.005070I
b = 0.497320 − 1.184150I
5.59008 + 2.33345I 0
u = 0.037545 + 0.823907I
a = −1.200190 − 0.581568I
b = −1.326440 − 0.283115I
−4.04651 + 2.52728I 0
u = 0.037545 − 0.823907I
a = −1.200190 + 0.581568I
b = −1.326440 + 0.283115I
−4.04651 − 2.52728I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621603 + 0.537572I
a = −0.786093 − 0.301539I
b = −0.552595 + 0.187397I
0.92510 − 2.38169I 0
u = −0.621603 − 0.537572I
a = −0.786093 + 0.301539I
b = −0.552595 − 0.187397I
0.92510 + 2.38169I 0
u = −0.802130 + 0.868304I
a = −0.750133 + 0.960332I
b = 0.70462 + 1.93410I
3.90480 − 0.23906I 0
u = −0.802130 − 0.868304I
a = −0.750133 − 0.960332I
b = 0.70462 − 1.93410I
3.90480 + 0.23906I 0
u = −0.002919 + 0.805198I
a = 0.815890 + 1.030460I
b = −0.121074 − 0.105187I
−4.49936 + 1.46905I 0
u = −0.002919 − 0.805198I
a = 0.815890 − 1.030460I
b = −0.121074 + 0.105187I
−4.49936 − 1.46905I 0
u = 0.555168 + 0.572524I
a = 0.953028 − 0.052468I
b = 0.794971 + 0.426716I
−3.23830 − 0.80541I 0
u = 0.555168 − 0.572524I
a = 0.953028 + 0.052468I
b = 0.794971 − 0.426716I
−3.23830 + 0.80541I 0
u = −0.715525 + 0.305973I
a = −0.07814 − 1.46534I
b = −0.58982 − 2.36264I
−1.71930 − 3.48624I 0
u = −0.715525 − 0.305973I
a = −0.07814 + 1.46534I
b = −0.58982 + 2.36264I
−1.71930 + 3.48624I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.293268 + 1.195460I
a = −0.670844 + 0.095073I
b = 0.60534 + 1.50815I
0.93337 + 5.95821I 0
u = −0.293268 − 1.195460I
a = −0.670844 − 0.095073I
b = 0.60534 − 1.50815I
0.93337 − 5.95821I 0
u = 0.765582
a = −1.59013
b = 0.345767
−2.40105 0
u = 1.227480 + 0.151731I
a = 0.113179 − 0.892273I
b = 0.44000 − 2.10931I
6.17978 + 3.50042I 0
u = 1.227480 − 0.151731I
a = 0.113179 + 0.892273I
b = 0.44000 + 2.10931I
6.17978 − 3.50042I 0
u = 0.846541 + 0.902891I
a = 0.518287 − 0.568193I
b = −0.138262 − 0.293557I
1.13484 + 7.43949I 0
u = 0.846541 − 0.902891I
a = 0.518287 + 0.568193I
b = −0.138262 + 0.293557I
1.13484 − 7.43949I 0
u = −0.682853 + 1.040320I
a = 0.618865 + 0.451464I
b = −0.066563 + 1.392200I
−3.46205 + 7.14168I 0
u = −0.682853 − 1.040320I
a = 0.618865 − 0.451464I
b = −0.066563 − 1.392200I
−3.46205 − 7.14168I 0
u = −0.639613 + 0.337366I
a = −0.499949 − 0.582165I
b = −0.141593 + 0.133008I
2.53289 − 0.95957I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.639613 − 0.337366I
a = −0.499949 + 0.582165I
b = −0.141593 − 0.133008I
2.53289 + 0.95957I 0
u = −0.101596 + 1.277800I
a = 0.851238 + 0.494891I
b = 0.157976 + 1.074020I
−1.57205 − 1.31987I 0
u = −0.101596 − 1.277800I
a = 0.851238 − 0.494891I
b = 0.157976 − 1.074020I
−1.57205 + 1.31987I 0
u = 0.091246 + 1.279690I
a = 0.858364 + 0.464336I
b = 0.172612 + 0.955527I
−1.60697 + 5.32803I 0
u = 0.091246 − 1.279690I
a = 0.858364 − 0.464336I
b = 0.172612 − 0.955527I
−1.60697 − 5.32803I 0
u = −0.418444 + 0.571193I
a = −0.82281 + 1.84186I
b = 0.565354 + 1.053840I
−3.00011 − 4.21287I 0
u = −0.418444 − 0.571193I
a = −0.82281 − 1.84186I
b = 0.565354 − 1.053840I
−3.00011 + 4.21287I 0
u = −0.611661 + 0.327872I
a = −0.27677 − 1.71708I
b = 0.479420 − 1.082340I
2.32492 − 8.13792I 0
u = −0.611661 − 0.327872I
a = −0.27677 + 1.71708I
b = 0.479420 + 1.082340I
2.32492 + 8.13792I 0
u = −0.435279 + 0.530494I
a = −0.92675 + 2.06327I
b = 0.599255 + 1.119230I
−0.84229 − 11.89770I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.435279 − 0.530494I
a = −0.92675 − 2.06327I
b = 0.599255 − 1.119230I
−0.84229 + 11.89770I 0
u = 0.370947 + 1.267630I
a = 0.654292 + 0.196612I
b = −0.68397 + 1.55861I
3.12360 − 0.94460I 0
u = 0.370947 − 1.267630I
a = 0.654292 − 0.196612I
b = −0.68397 − 1.55861I
3.12360 + 0.94460I 0
u = 0.417987 + 0.530629I
a = 0.98985 + 1.98238I
b = −0.568856 + 1.120570I
1.46747 + 6.91470I 0
u = 0.417987 − 0.530629I
a = 0.98985 − 1.98238I
b = −0.568856 − 1.120570I
1.46747 − 6.91470I 0
u = −1.221560 + 0.514171I
a = −0.597594 + 1.016380I
b = 0.47132 + 1.42236I
5.77218 − 3.85236I 0
u = −1.221560 − 0.514171I
a = −0.597594 − 1.016380I
b = 0.47132 − 1.42236I
5.77218 + 3.85236I 0
u = −0.830250 + 1.038160I
a = −0.716728 + 0.715138I
b = 0.63657 + 1.82484I
3.47498 − 5.76688I 0
u = −0.830250 − 1.038160I
a = −0.716728 − 0.715138I
b = 0.63657 − 1.82484I
3.47498 + 5.76688I 0
u = 0.643271 + 0.161549I
a = 0.461478 − 0.859519I
b = −0.230469 + 0.103148I
1.73882 − 3.43689I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.643271 − 0.161549I
a = 0.461478 + 0.859519I
b = −0.230469 − 0.103148I
1.73882 + 3.43689I 0
u = −1.294190 + 0.363504I
a = 1.108570 + 0.054805I
b = −0.315063 − 0.130755I
−4.88652 − 4.11270I 0
u = −1.294190 − 0.363504I
a = 1.108570 − 0.054805I
b = −0.315063 + 0.130755I
−4.88652 + 4.11270I 0
u = −1.217090 + 0.640607I
a = 0.961568 + 0.094814I
b = −0.466197 − 0.179941I
−5.46535 + 3.31603I 0
u = −1.217090 − 0.640607I
a = 0.961568 − 0.094814I
b = −0.466197 + 0.179941I
−5.46535 − 3.31603I 0
u = −0.697787 + 1.188290I
a = −0.605485 + 0.063395I
b = 0.114003 + 0.399850I
−1.38437 − 1.96944I 0
u = −0.697787 − 1.188290I
a = −0.605485 − 0.063395I
b = 0.114003 − 0.399850I
−1.38437 + 1.96944I 0
u = 0.951603 + 0.997162I
a = 0.719305 − 0.490876I
b = 0.058488 − 0.224399I
−0.72612 + 9.18905I 0
u = 0.951603 − 0.997162I
a = 0.719305 + 0.490876I
b = 0.058488 + 0.224399I
−0.72612 − 9.18905I 0
u = 0.365991 + 0.499289I
a = 1.26815 + 1.82874I
b = −0.480101 + 1.164880I
2.81213 + 4.88759I −4.00000 − 9.10296I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.365991 − 0.499289I
a = 1.26815 − 1.82874I
b = −0.480101 − 1.164880I
2.81213 − 4.88759I −4.00000 + 9.10296I
u = −1.379470 + 0.184451I
a = −0.236400 + 0.685503I
b = −0.27132 + 2.02531I
5.70496 − 2.36563I 0
u = −1.379470 − 0.184451I
a = −0.236400 − 0.685503I
b = −0.27132 − 2.02531I
5.70496 + 2.36563I 0
u = −0.925176 + 1.059580I
a = −0.727097 − 0.395706I
b = −0.068902 − 0.126321I
−5.15090 − 6.14978I 0
u = −0.925176 − 1.059580I
a = −0.727097 + 0.395706I
b = −0.068902 + 0.126321I
−5.15090 + 6.14978I 0
u = −1.238120 + 0.675738I
a = 0.083225 − 0.504729I
b = −1.07876 − 2.46030I
−5.05688 − 0.16003I 0
u = −1.238120 − 0.675738I
a = 0.083225 + 0.504729I
b = −1.07876 + 2.46030I
−5.05688 + 0.16003I 0
u = 0.701301 + 1.225250I
a = 0.671438 + 0.486964I
b = −0.68615 + 1.77249I
4.39661 + 1.22197I 0
u = 0.701301 − 1.225250I
a = 0.671438 − 0.486964I
b = −0.68615 − 1.77249I
4.39661 − 1.22197I 0
u = −0.986305 + 1.010700I
a = −0.769777 − 0.494077I
b = −0.110094 − 0.230099I
−3.2064 − 14.1549I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.986305 − 1.010700I
a = −0.769777 + 0.494077I
b = −0.110094 + 0.230099I
−3.2064 + 14.1549I 0
u = 0.76886 + 1.18718I
a = 0.674711 − 0.081138I
b = −0.004975 + 0.221349I
−5.58145 + 5.26946I 0
u = 0.76886 − 1.18718I
a = 0.674711 + 0.081138I
b = −0.004975 − 0.221349I
−5.58145 − 5.26946I 0
u = 0.68895 + 1.23531I
a = 0.710996 + 0.087797I
b = 0.030842 + 0.439913I
−4.05694 − 2.84491I 0
u = 0.68895 − 1.23531I
a = 0.710996 − 0.087797I
b = 0.030842 − 0.439913I
−4.05694 + 2.84491I 0
u = 0.521128 + 0.254008I
a = 0.22101 − 2.03419I
b = −0.541828 − 1.218760I
4.03353 + 3.21451I 4.49469 − 2.83648I
u = 0.521128 − 0.254008I
a = 0.22101 + 2.03419I
b = −0.541828 + 1.218760I
4.03353 − 3.21451I 4.49469 + 2.83648I
u = 1.30479 + 0.57272I
a = 0.571035 + 1.031390I
b = −0.41150 + 1.50202I
3.96900 + 8.33656I 0
u = 1.30479 − 0.57272I
a = 0.571035 − 1.031390I
b = −0.41150 − 1.50202I
3.96900 − 8.33656I 0
u = −0.330798 + 0.457917I
a = −1.49358 + 1.75805I
b = 0.418440 + 1.208040I
1.80293 − 0.20080I −4.77768 + 1.73588I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.330798 − 0.457917I
a = −1.49358 − 1.75805I
b = 0.418440 − 1.208040I
1.80293 + 0.20080I −4.77768 − 1.73588I
u = 0.533399
a = −0.100301
b = 0.781356
−1.45997 −5.66050
u = −1.12881 + 0.94406I
a = 0.122375 − 0.634524I
b = −0.89438 − 2.45920I
−5.34460 − 9.57074I 0
u = −1.12881 − 0.94406I
a = 0.122375 + 0.634524I
b = −0.89438 + 2.45920I
−5.34460 + 9.57074I 0
u = 1.24756 + 0.79717I
a = 0.517378 + 0.963276I
b = −0.49348 + 1.67529I
2.91136 + 2.09500I 0
u = 1.24756 − 0.79717I
a = 0.517378 − 0.963276I
b = −0.49348 − 1.67529I
2.91136 − 2.09500I 0
u = 1.27668 + 0.87777I
a = −0.143565 − 0.555392I
b = 0.98852 − 2.41560I
−1.26908 + 4.99883I 0
u = 1.27668 − 0.87777I
a = −0.143565 + 0.555392I
b = 0.98852 + 2.41560I
−1.26908 − 4.99883I 0
u = 0.010258 + 0.441700I
a = −1.05374 + 2.72731I
b = −0.224893 − 0.121630I
−5.70613 − 2.53172I −20.3875 + 1.6323I
u = 0.010258 − 0.441700I
a = −1.05374 − 2.72731I
b = −0.224893 + 0.121630I
−5.70613 + 2.53172I −20.3875 − 1.6323I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.13680 + 1.06938I
a = −0.481763 + 0.803075I
b = 0.56686 + 1.83842I
3.55886 − 5.57036I 0
u = −1.13680 − 1.06938I
a = −0.481763 − 0.803075I
b = 0.56686 − 1.83842I
3.55886 + 5.57036I 0
u = 0.400057 + 0.045006I
a = 0.77351 − 2.82258I
b = −0.42683 − 1.45461I
4.19086 + 0.75001I 3.27417 + 0.13817I
u = 0.400057 − 0.045006I
a = 0.77351 + 2.82258I
b = −0.42683 + 1.45461I
4.19086 − 0.75001I 3.27417 − 0.13817I
u = −0.287162 + 0.267129I
a = −1.35562 + 0.56299I
b = 1.80061 − 1.94611I
−4.74316 − 7.71668I −9.96585 − 1.63222I
u = −0.287162 − 0.267129I
a = −1.35562 − 0.56299I
b = 1.80061 + 1.94611I
−4.74316 + 7.71668I −9.96585 + 1.63222I
u = 1.07333 + 1.21138I
a = −0.291230 − 0.806384I
b = 0.65857 − 2.28199I
−2.53426 + 12.40190I 0
u = 1.07333 − 1.21138I
a = −0.291230 + 0.806384I
b = 0.65857 + 2.28199I
−2.53426 − 12.40190I 0
u = −0.369294 + 0.070497I
a = −1.41211 + 2.83552I
b = 0.34832 + 1.45326I
2.68352 − 4.22087I −0.81306 + 5.45920I
u = −0.369294 − 0.070497I
a = −1.41211 − 2.83552I
b = 0.34832 − 1.45326I
2.68352 + 4.22087I −0.81306 − 5.45920I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.07242 + 1.24808I
a = −0.337702 − 0.841266I
b = 0.60871 − 2.24097I
0.1064 + 20.9577I 0
u = 1.07242 − 1.24808I
a = −0.337702 + 0.841266I
b = 0.60871 + 2.24097I
0.1064 − 20.9577I 0
u = −1.08343 + 1.23985I
a = 0.336914 − 0.817093I
b = −0.63477 − 2.23477I
2.6134 − 15.6022I 0
u = −1.08343 − 1.23985I
a = 0.336914 + 0.817093I
b = −0.63477 + 2.23477I
2.6134 + 15.6022I 0
u = −0.229683 + 0.255138I
a = 1.01410 − 2.80851I
b = 0.97055 − 1.73598I
−1.25481 − 1.94131I 8.53453 − 2.73130I
u = −0.229683 − 0.255138I
a = 1.01410 + 2.80851I
b = 0.97055 + 1.73598I
−1.25481 + 1.94131I 8.53453 + 2.73130I
u = 0.256082 + 0.209733I
a = 1.70323 + 0.85487I
b = −1.30025 − 1.74459I
−1.58904 + 3.04262I −6.84058 + 1.82365I
u = 0.256082 − 0.209733I
a = 1.70323 − 0.85487I
b = −1.30025 + 1.74459I
−1.58904 − 3.04262I −6.84058 − 1.82365I
u = −1.13926 + 1.22688I
a = 0.346437 − 0.725370I
b = −0.73699 − 2.19566I
4.92487 − 12.44190I 0
u = −1.13926 − 1.22688I
a = 0.346437 + 0.725370I
b = −0.73699 + 2.19566I
4.92487 + 12.44190I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15454 + 1.67076I
a = −0.449066 + 0.206440I
b = 1.06769 + 1.37615I
−1.61710 − 1.48439I 0
u = −0.15454 − 1.67076I
a = −0.449066 − 0.206440I
b = 1.06769 − 1.37615I
−1.61710 + 1.48439I 0
u = −0.174449 + 0.266572I
a = −2.08380 + 0.09535I
b = 0.99896 − 2.25646I
−5.46277 + 0.97801I −14.5997 − 4.2517I
u = −0.174449 − 0.266572I
a = −2.08380 − 0.09535I
b = 0.99896 + 2.25646I
−5.46277 − 0.97801I −14.5997 + 4.2517I
u = 1.17960 + 1.21445I
a = −0.332414 − 0.673726I
b = 0.80605 − 2.19720I
4.37546 + 6.86401I 0
u = 1.17960 − 1.21445I
a = −0.332414 + 0.673726I
b = 0.80605 + 2.19720I
4.37546 − 6.86401I 0
u = 0.127811 + 0.229812I
a = −1.77834 + 4.57496I
b = 0.314870 − 0.036918I
−2.38230 − 0.30495I −16.3360 + 1.1551I
u = 0.127811 − 0.229812I
a = −1.77834 − 4.57496I
b = 0.314870 + 0.036918I
−2.38230 + 0.30495I −16.3360 − 1.1551I
u = 0.023336 + 0.246033I
a = −1.67282 + 5.52026I
b = −0.337698 − 0.094041I
−4.60142 + 4.66851I −20.3165 − 6.3367I
u = 0.023336 − 0.246033I
a = −1.67282 − 5.52026I
b = −0.337698 + 0.094041I
−4.60142 − 4.66851I −20.3165 + 6.3367I
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37973 + 1.30339I
a = −0.226482 + 0.743299I
b = 0.45514 + 2.02654I
1.16961 − 6.67914I 0
u = −1.37973 − 1.30339I
a = −0.226482 − 0.743299I
b = 0.45514 − 2.02654I
1.16961 + 6.67914I 0
u = −1.80288 + 0.66701I
a = 0.268661 − 0.534707I
b = −0.78407 − 2.08035I
6.29892 + 2.87587I 0
u = −1.80288 − 0.66701I
a = 0.268661 + 0.534707I
b = −0.78407 + 2.08035I
6.29892 − 2.87587I 0
u = 1.43016 + 1.28872I
a = 0.181783 + 0.779872I
b = −0.40479 + 2.02226I
−1.48526 + 11.61390I 0
u = 1.43016 − 1.28872I
a = 0.181783 − 0.779872I
b = −0.40479 − 2.02226I
−1.48526 − 11.61390I 0
u = 1.85916 + 0.60812I
a = −0.188537 − 0.497905I
b = 0.82440 − 2.28050I
5.77448 + 3.00391I 0
u = 1.85916 − 0.60812I
a = −0.188537 + 0.497905I
b = 0.82440 + 2.28050I
5.77448 − 3.00391I 0
u = 1.42988 + 1.40107I
a = 0.164074 + 0.655578I
b = −0.44938 + 2.14186I
−3.19745 + 3.29806I 0
u = 1.42988 − 1.40107I
a = 0.164074 − 0.655578I
b = −0.44938 − 2.14186I
−3.19745 − 3.29806I 0
22
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.77888 + 0.94606I
a = −0.504641 − 0.476537I
b = 0.76720 − 1.58178I
1.42330 − 11.72270I 0
u = 1.77888 − 0.94606I
a = −0.504641 + 0.476537I
b = 0.76720 + 1.58178I
1.42330 + 11.72270I 0
u = −1.80357 + 0.90455I
a = 0.453871 − 0.479591I
b = −0.81713 − 1.67987I
3.90295 + 6.32077I 0
u = −1.80357 − 0.90455I
a = 0.453871 + 0.479591I
b = −0.81713 + 1.67987I
3.90295 − 6.32077I 0
u = 1.95336 + 0.94168I
a = −0.403468 − 0.378015I
b = 1.10730 − 1.68504I
−1.40233 − 3.13589I 0
u = 1.95336 − 0.94168I
a = −0.403468 + 0.378015I
b = 1.10730 + 1.68504I
−1.40233 + 3.13589I 0
23
II.
I
u
2
= h−2.01×10
18
u
38
−2.85×10
18
u
37
+· · ·+3.17×10
16
b+5.50×10
18
, −1.59×
10
18
u
38
−1.91×10
18
u
37
+· · ·+3.17×10
16
a+3.88×10
18
, u
39
−8u
37
+· · ·−u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
12
=
50.0769u
38
+ 60.1821u
37
+ ··· + 0.190740u − 122.256
63.4708u
38
+ 89.9299u
37
+ ··· + 47.2960u − 173.438
a
9
=
−121.065u
38
− 122.256u
37
+ ··· + 47.8502u + 259.551
−49.0769u
38
− 60.1821u
37
+ ··· − 8.19074u + 121.256
a
1
=
307.401u
38
+ 259.551u
37
+ ··· − 223.007u − 576.187
134.459u
38
+ 152.003u
37
+ ··· − 0.744935u − 310.733
a
8
=
−71.9880u
38
− 62.0736u
37
+ ··· + 56.0409u + 138.295
−49.0769u
38
− 60.1821u
37
+ ··· − 8.19074u + 121.256
a
11
=
305.457u
38
+ 179.341u
37
+ ··· − 362.078u − 437.682
114.348u
38
+ 75.2218u
37
+ ··· − 118.116u − 178.341
a
3
=
−437.682u
38
− 305.457u
37
+ ··· + 281.639u + 800.761
−178.341u
38
− 114.348u
37
+ ··· + 132.225u + 296.457
a
2
=
8000.01u
38
+ 4309.48u
37
+ ··· − 7949.09u − 9510.25
2234.16u
38
+ 1562.41u
37
+ ··· − 1396.48u − 3185.54
a
7
=
−93.3820u
38
− 92.8213u
37
+ ··· + 37.9357u + 197.477
−60.0868u
38
− 76.3117u
37
+ ··· − 17.5445u + 152.003
a
6
=
2780.01u
38
+ 1229.69u
37
+ ··· − 3610.28u − 3101.50
574.178u
38
+ 114.004u
37
+ ··· − 1020.43u − 404.066
(ii) Obstruction class = 1
(iii) Cusp Shapes =
85785770042272963235
15862900254506647
u
38
+
359617894200403433821
31725800509013294
u
37
+ ··· +
186894060817789083707
15862900254506647
u −
751272827301618047625
31725800509013294
24
(iv) u-Polynomials at the component
25
Crossings u-Polynomials at each crossing
c
1
u
39
− 20u
38
+ ··· + 10u − 1
c
2
u
39
+ 4u
38
+ ··· − 4u − 1
c
3
u
39
− u
38
+ ··· − 8u
2
+ 1
c
4
u
39
− 8u
37
+ ··· − u + 1
c
5
u
39
− 4u
38
+ ··· − 4u + 1
c
6
u
39
− 12u
38
+ ··· − 116u + 21
c
7
u
39
− u
38
+ ··· − 3u + 1
c
8
u
39
+ 2u
38
+ ··· + 76u − 7
c
9
u
39
− 12u
38
+ ··· + 5u − 1
c
10
u
39
+ 7u
38
+ ··· + 25u + 21
c
11
u
39
+ 2u
38
+ ··· + 40u + 7
c
12
u
39
+ 12u
38
+ ··· + 5u + 1
26
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
+ 8y
38
+ ··· − 10y −1
c
2
, c
5
y
39
− 20y
38
+ ··· + 10y −1
c
3
y
39
− 17y
38
+ ··· + 16y −1
c
4
y
39
− 16y
38
+ ··· + 17y −1
c
6
y
39
+ 4y
38
+ ··· + 5938y −441
c
7
y
39
+ 11y
38
+ ··· + 9y −1
c
8
y
39
+ 12y
38
+ ··· + 6756y −49
c
9
, c
12
y
39
+ 20y
38
+ ··· − 37y −1
c
10
y
39
− 13y
38
+ ··· + 5203y −441
c
11
y
39
− 20y
38
+ ··· + 3574y −49
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.924815 + 0.311925I
a = 0.11561 + 1.43404I
b = 0.42783 + 1.56351I
−0.07877 − 11.10230I −3.74058 + 8.27396I
u = −0.924815 − 0.311925I
a = 0.11561 − 1.43404I
b = 0.42783 − 1.56351I
−0.07877 + 11.10230I −3.74058 − 8.27396I
u = −1.008910 + 0.188119I
a = 0.309077 + 1.135640I
b = 0.25662 + 1.64816I
−2.21558 − 2.89296I −7.37143 + 3.04083I
u = −1.008910 − 0.188119I
a = 0.309077 − 1.135640I
b = 0.25662 − 1.64816I
−2.21558 + 2.89296I −7.37143 − 3.04083I
u = 0.989116 + 0.329453I
a = −0.050509 + 1.281840I
b = −0.42702 + 1.63862I
2.44099 + 6.06191I 0. − 5.19492I
u = 0.989116 − 0.329453I
a = −0.050509 − 1.281840I
b = −0.42702 − 1.63862I
2.44099 − 6.06191I 0. + 5.19492I
u = −0.697260 + 0.646015I
a = 0.438485 − 0.439550I
b = 0.79668 − 1.77678I
−1.15827 − 3.68014I −1.40034 + 6.36118I
u = −0.697260 − 0.646015I
a = 0.438485 + 0.439550I
b = 0.79668 + 1.77678I
−1.15827 + 3.68014I −1.40034 − 6.36118I
u = 0.266485 + 1.020910I
a = −0.597928 − 0.451213I
b = −0.361876 + 0.275235I
−0.15316 + 8.20817I −2.18178 − 11.23071I
u = 0.266485 − 1.020910I
a = −0.597928 + 0.451213I
b = −0.361876 − 0.275235I
−0.15316 − 8.20817I −2.18178 + 11.23071I
29
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.857879 + 0.670338I
a = −0.738335 + 1.154920I
b = 0.69369 + 1.62725I
3.31730 − 0.83841I −4.00000 + 0.I
u = −0.857879 − 0.670338I
a = −0.738335 − 1.154920I
b = 0.69369 − 1.62725I
3.31730 + 0.83841I −4.00000 + 0.I
u = 0.285396 + 0.860515I
a = −0.522568 − 0.526250I
b = −1.019580 + 0.332745I
−1.11714 + 1.99999I −8.19167 − 3.78237I
u = 0.285396 − 0.860515I
a = −0.522568 + 0.526250I
b = −1.019580 − 0.332745I
−1.11714 − 1.99999I −8.19167 + 3.78237I
u = 0.765917 + 0.475113I
a = −0.461266 − 0.452206I
b = −0.42801 − 2.31073I
−4.91010 − 0.66634I −4.08848 − 0.66761I
u = 0.765917 − 0.475113I
a = −0.461266 + 0.452206I
b = −0.42801 + 2.31073I
−4.91010 + 0.66634I −4.08848 + 0.66761I
u = −0.384592 + 0.805398I
a = 0.472005 − 0.488912I
b = 1.300900 − 0.209954I
0.19142 − 5.06118I −8.60265 + 7.14127I
u = −0.384592 − 0.805398I
a = 0.472005 + 0.488912I
b = 1.300900 + 0.209954I
0.19142 + 5.06118I −8.60265 − 7.14127I
u = −0.402380 + 1.051580I
a = 0.538047 − 0.411212I
b = 0.305401 − 0.158350I
1.26027 − 3.77559I 0. + 6.22471I
u = −0.402380 − 1.051580I
a = 0.538047 + 0.411212I
b = 0.305401 + 0.158350I
1.26027 + 3.77559I 0. − 6.22471I
30
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.947825 + 0.627237I
a = 0.535172 + 1.131600I
b = −0.66404 + 1.66961I
4.52388 + 4.83558I 0
u = 0.947825 − 0.627237I
a = 0.535172 − 1.131600I
b = −0.66404 − 1.66961I
4.52388 − 4.83558I 0
u = −0.847256 + 0.806635I
a = −0.827554 + 0.899088I
b = 0.75375 + 1.61764I
3.17795 − 6.62251I 0
u = −0.847256 − 0.806635I
a = −0.827554 − 0.899088I
b = 0.75375 − 1.61764I
3.17795 + 6.62251I 0
u = 0.581387 + 0.571673I
a = −0.433652 − 0.432178I
b = −1.42230 − 2.06228I
−4.53761 + 8.18453I −4.02113 − 11.95988I
u = 0.581387 − 0.571673I
a = −0.433652 + 0.432178I
b = −1.42230 + 2.06228I
−4.53761 − 8.18453I −4.02113 + 11.95988I
u = 0.950084 + 0.865043I
a = 0.684070 + 0.793506I
b = −0.79803 + 1.66370I
4.16853 + 2.84209I 0
u = 0.950084 − 0.865043I
a = 0.684070 − 0.793506I
b = −0.79803 − 1.66370I
4.16853 − 2.84209I 0
u = 0.707436 + 0.020386I
a = −1.71851 + 0.48438I
b = 0.218626 + 0.433517I
−5.05783 + 2.49669I −7.12716 + 1.05845I
u = 0.707436 − 0.020386I
a = −1.71851 − 0.48438I
b = 0.218626 − 0.433517I
−5.05783 − 2.49669I −7.12716 − 1.05845I
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.706508
a = 1.50028
b = −0.586471
−2.80431 −20.6800
u = −0.691067 + 0.008533I
a = 1.97336 + 0.18453I
b = −0.109378 + 0.137192I
−2.00961 + 0.36405I 7.95914 − 5.45782I
u = −0.691067 − 0.008533I
a = 1.97336 − 0.18453I
b = −0.109378 − 0.137192I
−2.00961 − 0.36405I 7.95914 + 5.45782I
u = 0.687085 + 0.019158I
a = −2.07300 + 0.38544I
b = 0.007592 + 0.255466I
−4.17830 − 4.65303I 0.33083 + 7.03077I
u = 0.687085 − 0.019158I
a = −2.07300 − 0.38544I
b = 0.007592 − 0.255466I
−4.17830 + 4.65303I 0.33083 − 7.03077I
u = 1.63181 + 0.14526I
a = −0.060200 + 0.628299I
b = −0.29768 + 2.19968I
5.66252 + 3.73843I 0
u = 1.63181 − 0.14526I
a = −0.060200 − 0.628299I
b = −0.29768 − 2.19968I
5.66252 − 3.73843I 0
u = −1.64513 + 0.19079I
a = 0.167542 − 0.553973I
b = 0.06007 − 2.21301I
5.36554 − 2.30314I 0
u = −1.64513 − 0.19079I
a = 0.167542 + 0.553973I
b = 0.06007 + 2.21301I
5.36554 + 2.30314I 0
32
III. I
u
3
= h−u
3
− u
2
+ b − 3u, −u
3
+ a − 2u + 1, u
4
+ u
3
+ 3u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
12
=
u
3
+ 2u − 1
u
3
+ u
2
+ 3u
a
9
=
u
2
+ u + 2
u
2
+ u + 2
a
1
=
−u
2
− u − 2
−1
a
8
=
0
u
2
+ u + 2
a
11
=
0
u
a
3
=
1
0
a
2
=
−u
2
− u − 1
−1
a
7
=
u
2
+ u + 2
1
a
6
=
u
2
+ u + 2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6u
3
+ 2u
2
+ 7u − 13
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
4
u
4
+ u
3
+ 3u
2
+ u + 1
c
5
(u + 1)
4
c
6
, c
10
u
4
c
7
, c
8
u
4
+ 2u
3
− u + 1
c
9
, c
11
(u
2
− u + 1)
2
c
12
(u
2
+ u + 1)
2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
y
4
+ 5y
3
+ 9y
2
+ 5y + 1
c
6
, c
10
y
4
c
7
, c
8
y
4
− 4y
3
+ 6y
2
− y + 1
c
9
, c
11
, c
12
(y
2
+ y + 1)
2
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.148403 + 0.632502I
a = −1.12196 + 1.05376I
b = −0.64840 + 1.49853I
−1.64493 − 2.02988I −13.74584 + 2.78456I
u = −0.148403 − 0.632502I
a = −1.12196 − 1.05376I
b = −0.64840 − 1.49853I
−1.64493 + 2.02988I −13.74584 − 2.78456I
u = −0.35160 + 1.49853I
a = 0.621964 + 0.187730I
b = −0.851597 + 0.632502I
−1.64493 + 2.02988I −5.75416 − 8.47377I
u = −0.35160 − 1.49853I
a = 0.621964 − 0.187730I
b = −0.851597 − 0.632502I
−1.64493 − 2.02988I −5.75416 + 8.47377I
36
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
39
− 20u
38
+ ··· + 10u − 1)(u
186
+ 93u
185
+ ··· + 190u + 1)
c
2
((u − 1)
4
)(u
39
+ 4u
38
+ ··· − 4u − 1)(u
186
+ u
185
+ ··· + 10u − 1)
c
3
(u
4
+ u
3
+ 3u
2
+ u + 1)(u
39
− u
38
+ ··· − 8u
2
+ 1)
· (u
186
+ 5u
185
+ ··· + 305u + 29)
c
4
(u
4
+ u
3
+ 3u
2
+ u + 1)(u
39
− 8u
37
+ ··· − u + 1)
· (u
186
+ 2u
185
+ ··· − 36u + 88)
c
5
((u + 1)
4
)(u
39
− 4u
38
+ ··· − 4u + 1)(u
186
+ u
185
+ ··· + 10u − 1)
c
6
u
4
(u
39
− 12u
38
+ ··· − 116u + 21)
· (u
186
− 9u
185
+ ··· + 133392896u − 8998912)
c
7
(u
4
+ 2u
3
− u + 1)(u
39
− u
38
+ ··· − 3u + 1)(u
186
+ 4u
185
+ ··· + 96u − 17)
c
8
(u
4
+ 2u
3
− u + 1)(u
39
+ 2u
38
+ ··· + 76u − 7)
· (u
186
+ 3u
185
+ ··· + 264890731u + 56493497)
c
9
((u
2
− u + 1)
2
)(u
39
− 12u
38
+ ··· + 5u − 1)
· (u
186
+ 11u
185
+ ··· + 2925u + 459)
c
10
u
4
(u
39
+ 7u
38
+ ··· + 25u + 21)(u
186
− 12u
185
+ ··· + 104u − 16)
c
11
((u
2
− u + 1)
2
)(u
39
+ 2u
38
+ ··· + 40u + 7)
· (u
186
− 3u
185
+ ··· + 2837302u + 121613)
c
12
((u
2
+ u + 1)
2
)(u
39
+ 12u
38
+ ··· + 5u + 1)
· (u
186
+ 11u
185
+ ··· + 2925u + 459)
37
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
4
)(y
39
+ 8y
38
+ ··· − 10y −1)(y
186
+ 15y
185
+ ··· − 32898y + 1)
c
2
, c
5
((y −1)
4
)(y
39
− 20y
38
+ ··· + 10y −1)(y
186
− 93y
185
+ ··· − 190y + 1)
c
3
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
39
− 17y
38
+ ··· + 16y −1)
· (y
186
− y
185
+ ··· + 166641y + 841)
c
4
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
39
− 16y
38
+ ··· + 17y −1)
· (y
186
− 4y
185
+ ··· + 366192y + 7744)
c
6
y
4
(y
39
+ 4y
38
+ ··· + 5938y −441)
· (y
186
+ 51y
185
+ ··· − 15721607766212608y + 80980417183744)
c
7
(y
4
− 4y
3
+ 6y
2
− y + 1)(y
39
+ 11y
38
+ ··· + 9y −1)
· (y
186
− 6y
185
+ ··· − 20878y + 289)
c
8
(y
4
− 4y
3
+ 6y
2
− y + 1)(y
39
+ 12y
38
+ ··· + 6756y −49)
· (y
186
− 21y
185
+ ··· − 86383388203073361y + 3191515203289009)
c
9
, c
12
((y
2
+ y + 1)
2
)(y
39
+ 20y
38
+ ··· − 37y −1)
· (y
186
+ 101y
185
+ ··· − 66119733y + 210681)
c
10
y
4
(y
39
− 13y
38
+ ··· + 5203y −441)
· (y
186
+ 2y
185
+ ··· + 15552y + 256)
c
11
((y
2
+ y + 1)
2
)(y
39
− 20y
38
+ ··· + 3574y −49)
· (y
186
+ y
185
+ ··· + 730297573796y + 14789721769)
38
