12a
0129
(K12a
0129
)
A knot diagram
1
Linearized knot diagam
3 5 8 6 2 11 9 4 12 1 7 10
Solving Sequence
9,12
10 1
4,11
8 3 2 7 6 5
c
9
c
12
c
10
c
8
c
3
c
1
c
7
c
6
c
5
c
2
, c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.61547 × 10
58
u
89
− 4.83832 × 10
59
u
88
+ ··· + 1.64419 × 10
56
b + 2.98980 × 10
58
,
− 6.46398 × 10
59
u
89
− 6.85486 × 10
60
u
88
+ ··· + 1.64419 × 10
56
a + 4.63218 × 10
59
,
u
90
+ 12u
89
+ ··· − 6u − 1i
I
u
2
= h3a
8
+ 31a
7
+ 13a
6
+ 178a
5
+ 16a
4
+ 212a
3
− 28a
2
+ 61b + 39a − 18,
a
9
+ 6a
7
+ a
6
+ 9a
5
+ 2a
4
+ 6a
3
+ a
2
+ 2a + 1, u − 1i
I
u
3
= hb, a
2
+ au + 2a + 3u + 5, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 103 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−4.62 × 10
58
u
89
− 4.84 × 10
59
u
88
+ · · · + 1.64 × 10
56
b + 2.99 ×
10
58
, −6.46 × 10
59
u
89
− 6.85 × 10
60
u
88
+ · · · + 1.64 × 10
56
a + 4.63 ×
10
59
, u
90
+ 12u
89
+ · · · − 6u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
3931.41u
89
+ 41691.5u
88
+ ··· − 14878.3u − 2817.31
280.715u
89
+ 2942.68u
88
+ ··· − 973.725u − 181.840
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
−2618.93u
89
− 27889.5u
88
+ ··· + 10177.0u + 1934.72
−5355.91u
89
− 57017.6u
88
+ ··· + 20797.5u + 3951.82
a
3
=
6611.43u
89
+ 70073.2u
88
+ ··· − 24950.5u − 4721.38
7255.63u
89
+ 76897.0u
88
+ ··· − 27351.2u − 5173.98
a
2
=
−5522.62u
89
− 58631.2u
88
+ ··· + 21058.6u + 3993.67
−8007.18u
89
− 85082.8u
88
+ ··· + 30711.5u + 5824.77
a
7
=
2736.97u
89
+ 29128.0u
88
+ ··· − 10620.5u − 2017.09
−5355.91u
89
− 57017.6u
88
+ ··· + 20797.5u + 3951.82
a
6
=
−414.169u
89
− 4382.73u
88
+ ··· + 1550.44u + 294.488
−4375.24u
89
− 46535.3u
88
+ ··· + 16888.5u + 3206.23
a
5
=
5357.29u
89
+ 56777.6u
88
+ ··· − 20209.9u − 3823.63
5572.68u
89
+ 59009.0u
88
+ ··· − 20877.5u − 3945.62
(ii) Obstruction class = −1
(iii) Cusp Shapes = −11889.9u
89
− 126101.u
88
+ ··· + 45065.9u + 8536.51
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
90
+ 32u
89
+ ··· − 34u + 1
c
2
, c
5
u
90
+ 4u
89
+ ··· − 10u + 1
c
3
, c
8
u
90
− 2u
89
+ ··· − 80u − 16
c
6
, c
11
u
90
+ 3u
89
+ ··· + 1024u + 512
c
7
u
90
− 30u
89
+ ··· − 3712u + 256
c
9
, c
10
, c
12
u
90
− 12u
89
+ ··· + 6u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
90
+ 56y
89
+ ··· − 3090y + 1
c
2
, c
5
y
90
+ 32y
89
+ ··· − 34y + 1
c
3
, c
8
y
90
− 30y
89
+ ··· − 3712y + 256
c
6
, c
11
y
90
− 63y
89
+ ··· − 4194304y + 262144
c
7
y
90
+ 54y
89
+ ··· − 4923392y + 65536
c
9
, c
10
, c
12
y
90
− 92y
89
+ ··· + 22y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.636017 + 0.771523I
a = 0.189507 + 0.291046I
b = 0.809550 + 0.779235I
−6.14252 + 0.17816I 0
u = 0.636017 − 0.771523I
a = 0.189507 − 0.291046I
b = 0.809550 − 0.779235I
−6.14252 − 0.17816I 0
u = 0.432828 + 0.882468I
a = 0.666021 + 0.933229I
b = −1.044510 + 0.696314I
0.35982 − 6.42463I 0
u = 0.432828 − 0.882468I
a = 0.666021 − 0.933229I
b = −1.044510 − 0.696314I
0.35982 + 6.42463I 0
u = 0.518572 + 0.830971I
a = −0.817139 − 1.151630I
b = 0.929384 − 0.742004I
−5.77013 − 5.56186I 0
u = 0.518572 − 0.830971I
a = −0.817139 + 1.151630I
b = 0.929384 + 0.742004I
−5.77013 + 5.56186I 0
u = 0.456988 + 0.912736I
a = −0.595801 − 1.004760I
b = 1.056730 − 0.742766I
−0.93673 − 12.04190I 0
u = 0.456988 − 0.912736I
a = −0.595801 + 1.004760I
b = 1.056730 + 0.742766I
−0.93673 + 12.04190I 0
u = 0.780880 + 0.714283I
a = −0.311800 − 0.057546I
b = −0.901778 − 0.603260I
−0.709182 + 0.976820I 0
u = 0.780880 − 0.714283I
a = −0.311800 + 0.057546I
b = −0.901778 + 0.603260I
−0.709182 − 0.976820I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.936431 + 0.058571I
a = 0.16332 + 3.81110I
b = 0.031091 + 0.410222I
−1.33868 − 2.18003I 0
u = 0.936431 − 0.058571I
a = 0.16332 − 3.81110I
b = 0.031091 − 0.410222I
−1.33868 + 2.18003I 0
u = 0.481476 + 0.768915I
a = −0.015198 + 0.457099I
b = 0.658845 + 0.897569I
−2.16958 − 5.97918I 0
u = 0.481476 − 0.768915I
a = −0.015198 − 0.457099I
b = 0.658845 − 0.897569I
−2.16958 + 5.97918I 0
u = 0.776384 + 0.779070I
a = 0.378854 + 0.145892I
b = 0.952795 + 0.670266I
−1.90172 + 6.33365I 0
u = 0.776384 − 0.779070I
a = 0.378854 − 0.145892I
b = 0.952795 − 0.670266I
−1.90172 − 6.33365I 0
u = 0.569713 + 0.687366I
a = −1.21121 − 1.33527I
b = 0.752169 − 0.679210I
−2.52210 + 1.10076I 0
u = 0.569713 − 0.687366I
a = −1.21121 + 1.33527I
b = 0.752169 + 0.679210I
−2.52210 − 1.10076I 0
u = 0.457951 + 0.718324I
a = 1.14669 + 0.97490I
b = −0.867324 + 0.598381I
−0.83297 − 3.71434I 0
u = 0.457951 − 0.718324I
a = 1.14669 − 0.97490I
b = −0.867324 − 0.598381I
−0.83297 + 3.71434I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.478612 + 0.682084I
a = 0.114604 − 0.343684I
b = −0.590308 − 0.817882I
−0.975354 − 0.759900I 0
u = 0.478612 − 0.682084I
a = 0.114604 + 0.343684I
b = −0.590308 + 0.817882I
−0.975354 + 0.759900I 0
u = 1.167340 + 0.055219I
a = −0.02349 − 1.86427I
b = 0.552125 − 0.411305I
−2.59551 − 1.48754I 0
u = 1.167340 − 0.055219I
a = −0.02349 + 1.86427I
b = 0.552125 + 0.411305I
−2.59551 + 1.48754I 0
u = 0.812411
a = 0.583852
b = −0.370124
−1.14251 0
u = 1.150390 + 0.427470I
a = −0.448720 + 0.822247I
b = −0.981187 + 0.022086I
1.90684 + 1.30777I 0
u = 1.150390 − 0.427470I
a = −0.448720 − 0.822247I
b = −0.981187 − 0.022086I
1.90684 − 1.30777I 0
u = 1.210720 + 0.384439I
a = 0.497494 − 0.983806I
b = 0.994018 − 0.128923I
1.77070 − 4.06940I 0
u = 1.210720 − 0.384439I
a = 0.497494 + 0.983806I
b = 0.994018 + 0.128923I
1.77070 + 4.06940I 0
u = 0.627749 + 0.338276I
a = 0.222976 + 0.197509I
b = −0.443744 − 0.400104I
−1.312090 − 0.131479I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.627749 − 0.338276I
a = 0.222976 − 0.197509I
b = −0.443744 + 0.400104I
−1.312090 + 0.131479I 0
u = 0.039569 + 0.707808I
a = 0.731279 − 0.369311I
b = −1.145530 + 0.197235I
5.27989 − 5.41644I 0
u = 0.039569 − 0.707808I
a = 0.731279 + 0.369311I
b = −1.145530 − 0.197235I
5.27989 + 5.41644I 0
u = −1.309680 + 0.123579I
a = 0.148842 + 0.660725I
b = 1.359750 + 0.299237I
1.74727 + 2.35227I 0
u = −1.309680 − 0.123579I
a = 0.148842 − 0.660725I
b = 1.359750 − 0.299237I
1.74727 − 2.35227I 0
u = −1.318240 + 0.160862I
a = −0.150230 − 0.834225I
b = −1.342450 − 0.377499I
1.19065 + 8.38160I 0
u = −1.318240 − 0.160862I
a = −0.150230 + 0.834225I
b = −1.342450 + 0.377499I
1.19065 − 8.38160I 0
u = −0.022892 + 0.662971I
a = −0.708352 + 0.630114I
b = 1.142870 − 0.109683I
5.54649 + 0.24155I 0
u = −0.022892 − 0.662971I
a = −0.708352 − 0.630114I
b = 1.142870 + 0.109683I
5.54649 − 0.24155I 0
u = 1.361180 + 0.016200I
a = 0.56140 − 1.93721I
b = 0.729297 − 0.692212I
−3.02957 − 1.47276I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.361180 − 0.016200I
a = 0.56140 + 1.93721I
b = 0.729297 + 0.692212I
−3.02957 + 1.47276I 0
u = −1.37333
a = −0.302841
b = 1.19993
−2.68158 0
u = −1.384800 + 0.020701I
a = −0.063713 + 1.329510I
b = −0.054613 + 1.170500I
−3.46864 + 2.84931I 0
u = −1.384800 − 0.020701I
a = −0.063713 − 1.329510I
b = −0.054613 − 1.170500I
−3.46864 − 2.84931I 0
u = 1.405530 + 0.038821I
a = −0.65664 − 2.03643I
b = −0.717356 − 0.805436I
−4.45636 − 3.56107I 0
u = 1.405530 − 0.038821I
a = −0.65664 + 2.03643I
b = −0.717356 + 0.805436I
−4.45636 + 3.56107I 0
u = −1.42282 + 0.05396I
a = 0.609449 − 0.428016I
b = −1.074280 − 0.149541I
−6.16448 + 3.67884I 0
u = −1.42282 − 0.05396I
a = 0.609449 + 0.428016I
b = −1.074280 + 0.149541I
−6.16448 − 3.67884I 0
u = −0.456940 + 0.289558I
a = −0.41458 − 1.96666I
b = −1.103730 − 0.551418I
2.86793 + 7.68098I 3.42570 − 7.43251I
u = −0.456940 − 0.289558I
a = −0.41458 + 1.96666I
b = −1.103730 + 0.551418I
2.86793 − 7.68098I 3.42570 + 7.43251I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46262 + 0.04473I
a = −0.76060 + 1.88639I
b = −0.876276 + 0.775532I
−8.11311 − 2.91724I 0
u = 1.46262 − 0.04473I
a = −0.76060 − 1.88639I
b = −0.876276 − 0.775532I
−8.11311 + 2.91724I 0
u = 1.45972 + 0.12783I
a = 0.78050 − 1.73048I
b = 0.967085 − 0.679705I
−2.30309 − 3.84007I 0
u = 1.45972 − 0.12783I
a = 0.78050 + 1.73048I
b = 0.967085 + 0.679705I
−2.30309 + 3.84007I 0
u = −0.397677 + 0.331683I
a = 0.22116 + 1.95582I
b = 1.090830 + 0.464271I
3.76775 + 2.05143I 5.07107 − 2.09109I
u = −0.397677 − 0.331683I
a = 0.22116 − 1.95582I
b = 1.090830 − 0.464271I
3.76775 − 2.05143I 5.07107 + 2.09109I
u = 1.49439 + 0.12104I
a = −0.84201 + 1.75757I
b = −0.997834 + 0.726352I
−3.59781 − 9.32602I 0
u = 1.49439 − 0.12104I
a = −0.84201 − 1.75757I
b = −0.997834 − 0.726352I
−3.59781 + 9.32602I 0
u = −1.50631 + 0.24795I
a = −0.763900 + 1.159780I
b = −0.658885 + 1.041560I
−7.43859 + 4.20013I 0
u = −1.50631 − 0.24795I
a = −0.763900 − 1.159780I
b = −0.658885 − 1.041560I
−7.43859 − 4.20013I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50477 + 0.26124I
a = 0.15880 − 1.64618I
b = −1.059620 − 0.679288I
−7.22418 + 7.32000I 0
u = −1.50477 − 0.26124I
a = 0.15880 + 1.64618I
b = −1.059620 + 0.679288I
−7.22418 − 7.32000I 0
u = −1.51753 + 0.27447I
a = 0.82963 − 1.17068I
b = 0.715559 − 1.054950I
−8.67818 + 9.80003I 0
u = −1.51753 − 0.27447I
a = 0.82963 + 1.17068I
b = 0.715559 + 1.054950I
−8.67818 − 9.80003I 0
u = −1.52668 + 0.23160I
a = −0.31043 + 1.69173I
b = 0.985773 + 0.655534I
−9.35302 + 2.24987I 0
u = −1.52668 − 0.23160I
a = −0.31043 − 1.69173I
b = 0.985773 − 0.655534I
−9.35302 − 2.24987I 0
u = −1.51633 + 0.32829I
a = −0.04771 − 1.76240I
b = −1.120900 − 0.791345I
−5.94645 + 10.83320I 0
u = −1.51633 − 0.32829I
a = −0.04771 + 1.76240I
b = −1.120900 + 0.791345I
−5.94645 − 10.83320I 0
u = −1.56018 + 0.14316I
a = −0.594280 + 0.875331I
b = −0.521495 + 0.785186I
−8.74184 + 1.79743I 0
u = −1.56018 − 0.14316I
a = −0.594280 − 0.875331I
b = −0.521495 − 0.785186I
−8.74184 − 1.79743I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53144 + 0.33920I
a = 0.06718 + 1.81504I
b = 1.114490 + 0.823559I
−7.3686 + 16.6080I 0
u = −1.53144 − 0.33920I
a = 0.06718 − 1.81504I
b = 1.114490 − 0.823559I
−7.3686 − 16.6080I 0
u = −1.54183 + 0.29103I
a = −0.09261 + 1.81241I
b = 1.039290 + 0.771323I
−12.4924 + 9.6696I 0
u = −1.54183 − 0.29103I
a = −0.09261 − 1.81241I
b = 1.039290 − 0.771323I
−12.4924 − 9.6696I 0
u = 0.292842 + 0.291043I
a = 3.26689 − 0.01628I
b = −0.622223 + 0.156782I
−0.74124 − 2.59423I 0.65910 + 9.56095I
u = 0.292842 − 0.291043I
a = 3.26689 + 0.01628I
b = −0.622223 − 0.156782I
−0.74124 + 2.59423I 0.65910 − 9.56095I
u = −1.57556 + 0.23138I
a = 0.830363 − 0.994905I
b = 0.725959 − 0.899964I
−13.48150 + 3.47756I 0
u = −1.57556 − 0.23138I
a = 0.830363 + 0.994905I
b = 0.725959 + 0.899964I
−13.48150 − 3.47756I 0
u = −1.62299 + 0.05733I
a = −0.477773 + 0.438407I
b = −0.425937 + 0.393962I
−8.93658 + 1.58876I 0
u = −1.62299 − 0.05733I
a = −0.477773 − 0.438407I
b = −0.425937 − 0.393962I
−8.93658 − 1.58876I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63443 + 0.16459I
a = 0.809541 − 0.736226I
b = 0.717569 − 0.667754I
−10.19210 − 2.91349I 0
u = −1.63443 − 0.16459I
a = 0.809541 + 0.736226I
b = 0.717569 + 0.667754I
−10.19210 + 2.91349I 0
u = −0.317233 + 0.111582I
a = −0.65770 − 2.68652I
b = −0.806542 − 0.579007I
−2.19525 + 2.29896I −2.08179 − 3.93173I
u = −0.317233 − 0.111582I
a = −0.65770 + 2.68652I
b = −0.806542 + 0.579007I
−2.19525 − 2.29896I −2.08179 + 3.93173I
u = −0.092318 + 0.290712I
a = −1.25011 + 2.47409I
b = 0.825039 + 0.190540I
1.36073 + 0.44955I 6.22502 − 0.98499I
u = −0.092318 − 0.290712I
a = −1.25011 − 2.47409I
b = 0.825039 − 0.190540I
1.36073 − 0.44955I 6.22502 + 0.98499I
u = −0.007194 + 0.281747I
a = 1.96025 − 0.54137I
b = 0.105461 − 0.766955I
0.95724 − 2.17639I 1.30907 + 4.71471I
u = −0.007194 − 0.281747I
a = 1.96025 + 0.54137I
b = 0.105461 + 0.766955I
0.95724 + 2.17639I 1.30907 − 4.71471I
u = −0.149583 + 0.201726I
a = −2.28125 + 1.62624I
b = −0.314053 + 0.763311I
0.57927 + 2.77981I 0.86843 − 2.18416I
u = −0.149583 − 0.201726I
a = −2.28125 − 1.62624I
b = −0.314053 − 0.763311I
0.57927 − 2.77981I 0.86843 + 2.18416I
13
II.
I
u
2
= h3a
8
+61b+· · ·+39a−18, a
9
+6a
7
+a
6
+9a
5
+2a
4
+6a
3
+a
2
+2a+1, u−1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
1
a
10
=
1
1
a
1
=
−1
0
a
4
=
a
−0.0491803a
8
− 0.508197a
7
+ ··· − 0.639344a + 0.295082
a
11
=
0
1
a
8
=
−0.508197a
8
+ 0.0819672a
7
+ ··· + 0.393443a + 1.04918
−0.508197a
8
+ 0.0819672a
7
+ ··· + 0.393443a + 1.04918
a
3
=
−0.0327869a
8
+ 0.327869a
7
+ ··· − 0.426230a − 0.803279
−0.0819672a
8
− 0.180328a
7
+ ··· − 2.06557a − 0.508197
a
2
=
0.114754a
8
− 0.147541a
7
+ ··· − 0.508197a − 0.688525
−0.393443a
8
− 0.0655738a
7
+ ··· − 0.114754a + 0.360656
a
7
=
0
−0.508197a
8
+ 0.0819672a
7
+ ··· + 0.393443a + 1.04918
a
6
=
0
−0.508197a
8
+ 0.0819672a
7
+ ··· + 0.393443a + 1.04918
a
5
=
a
0.311475a
8
− 0.114754a
7
+ ··· + 2.04918a + 1.13115
(ii) Obstruction class = 1
(iii) Cusp Shapes =
160
61
a
8
−
136
61
a
7
+
856
61
a
6
−
592
61
a
5
+
833
61
a
4
−
568
61
a
3
+
540
61
a
2
−
116
61
a +
16
61
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
2
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
3
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
6
, c
11
u
9
c
7
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
8
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
9
, c
10
(u − 1)
9
c
12
(u + 1)
9
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
2
, c
5
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
3
, c
8
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
, c
11
y
9
c
7
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
9
, c
10
, c
12
(y −1)
9
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.450985 + 0.808297I
b = −1.172470 + 0.500383I
1.95319 − 7.08493I −2.55209 + 3.65320I
u = 1.00000
a = −0.450985 − 0.808297I
b = −1.172470 − 0.500383I
1.95319 + 7.08493I −2.55209 − 3.65320I
u = 1.00000
a = 0.128062 + 1.105260I
b = −0.772920 + 0.510351I
−3.42837 − 2.09337I −9.96342 + 4.61282I
u = 1.00000
a = 0.128062 − 1.105260I
b = −0.772920 − 0.510351I
−3.42837 + 2.09337I −9.96342 − 4.61282I
u = 1.00000
a = 0.407341 + 0.647242I
b = 1.173910 + 0.391555I
2.72642 + 1.33617I 0.058077 + 1.140630I
u = 1.00000
a = 0.407341 − 0.647242I
b = 1.173910 − 0.391555I
2.72642 − 1.33617I 0.058077 − 1.140630I
u = 1.00000
a = −0.384820
b = 0.825933
−0.446489 3.26660
u = 1.00000
a = 0.10799 + 2.04391I
b = −0.141484 + 0.739668I
−1.02799 + 2.45442I −3.17587 − 4.82524I
u = 1.00000
a = 0.10799 − 2.04391I
b = −0.141484 − 0.739668I
−1.02799 − 2.45442I −3.17587 + 4.82524I
17
III. I
u
3
= hb, a
2
+ au + 2a + 3u + 5, u
2
+ u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
−u + 1
a
1
=
−u
−u + 1
a
4
=
a
0
a
11
=
u
u
a
8
=
1
0
a
3
=
a
0
a
2
=
a + 2
−u + 1
a
7
=
1
0
a
6
=
u
u − 1
a
5
=
−2au + 2a
−3au + 2a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 13au − 7a + 3u − 5
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
3
, c
7
, c
8
u
4
c
6
, c
9
, c
10
(u
2
+ u − 1)
2
c
11
, c
12
(u
2
− u − 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
2
c
3
, c
7
, c
8
y
4
c
6
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −1.30902 + 2.26728I
b = 0
−0.98696 + 2.02988I −4.50000 + 2.34537I
u = 0.618034
a = −1.30902 − 2.26728I
b = 0
−0.98696 − 2.02988I −4.50000 − 2.34537I
u = −1.61803
a = −0.190983 + 0.330792I
b = 0
−8.88264 + 2.02988I −4.50000 − 9.27358I
u = −1.61803
a = −0.190983 − 0.330792I
b = 0
−8.88264 − 2.02988I −4.50000 + 9.27358I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
− u + 1)
2
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
90
+ 32u
89
+ ··· − 34u + 1)
c
2
(u
2
+ u + 1)
2
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
90
+ 4u
89
+ ··· − 10u + 1)
c
3
u
4
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
90
− 2u
89
+ ··· − 80u − 16)
c
5
(u
2
− u + 1)
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
90
+ 4u
89
+ ··· − 10u + 1)
c
6
u
9
(u
2
+ u − 1)
2
(u
90
+ 3u
89
+ ··· + 1024u + 512)
c
7
u
4
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
90
− 30u
89
+ ··· − 3712u + 256)
c
8
u
4
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
90
− 2u
89
+ ··· − 80u − 16)
c
9
, c
10
((u − 1)
9
)(u
2
+ u − 1)
2
(u
90
− 12u
89
+ ··· + 6u − 1)
c
11
u
9
(u
2
− u − 1)
2
(u
90
+ 3u
89
+ ··· + 1024u + 512)
c
12
((u + 1)
9
)(u
2
− u − 1)
2
(u
90
− 12u
89
+ ··· + 6u − 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
90
+ 56y
89
+ ··· − 3090y + 1)
c
2
, c
5
(y
2
+ y + 1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
90
+ 32y
89
+ ··· − 34y + 1)
c
3
, c
8
y
4
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
90
− 30y
89
+ ··· − 3712y + 256)
c
6
, c
11
y
9
(y
2
− 3y + 1)
2
(y
90
− 63y
89
+ ··· − 4194304y + 262144)
c
7
y
4
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
90
+ 54y
89
+ ··· − 4923392y + 65536)
c
9
, c
10
, c
12
((y −1)
9
)(y
2
− 3y + 1)
2
(y
90
− 92y
89
+ ··· + 22y + 1)
23
