12a
0639
(K12a
0639
)
A knot diagram
1
Linearized knot diagam
3 7 10 11 8 2 5 6 12 1 9 4
Solving Sequence
5,8
6
9,11
12 4 1 7 10 3 2
c
5
c
8
c
11
c
4
c
12
c
7
c
10
c
3
c
2
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h6.85776 × 10
89
u
105
− 3.83253 × 10
90
u
104
+ ··· + 1.08124 × 10
88
b − 4.80658 × 10
89
,
4.70720 × 10
88
u
105
− 2.64592 × 10
89
u
104
+ ··· + 6.75773 × 10
86
a − 3.15249 × 10
88
, u
106
− 7u
105
+ ··· − u
2
+ 1i
I
u
2
= hb
5
+ b
4
− 2b
3
− b
2
+ b − 1, a + 1, u − 1i
I
u
3
= hb − u − 2, a + u + 1, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 113 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
= h6.86 × 10
89
u
105
− 3.83 × 10
90
u
104
+ · · · + 1.08 × 10
88
b − 4.81 ×
10
89
, 4.71 × 10
88
u
105
− 2.65 × 10
89
u
104
+ · · · + 6.76 × 10
86
a − 3.15 ×
10
88
, u
106
− 7u
105
+ · · · − u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
6
=
1
u
2
a
9
=
−u
−u
3
+ u
a
11
=
−69.6565u
105
+ 391.540u
104
+ ··· + 13.0928u + 46.6502
−63.4251u
105
+ 354.458u
104
+ ··· + 29.6271u + 44.4544
a
12
=
−69.5768u
105
+ 390.512u
104
+ ··· + 13.1350u + 46.3658
−64.8453u
105
+ 361.946u
104
+ ··· + 29.5052u + 45.2086
a
4
=
−284.662u
105
+ 1597.59u
104
+ ··· + 118.715u + 201.545
−311.105u
105
+ 1745.83u
104
+ ··· + 155.762u + 224.822
a
1
=
−91.6179u
105
+ 515.563u
104
+ ··· + 31.6304u + 63.6344
−95.0632u
105
+ 536.170u
104
+ ··· + 47.1533u + 69.1269
a
7
=
u
u
a
10
=
−71.5437u
105
+ 403.178u
104
+ ··· + 13.5283u + 47.5824
−65.3971u
105
+ 366.683u
104
+ ··· + 30.9677u + 46.7591
a
3
=
−72.6372u
105
+ 410.221u
104
+ ··· + 24.5715u + 50.5987
−127.336u
105
+ 721.871u
104
+ ··· + 67.1446u + 94.7937
a
2
=
−166.039u
105
+ 941.534u
104
+ ··· + 79.2707u + 121.844
−220.738u
105
+ 1253.18u
104
+ ··· + 121.844u + 166.039
(ii) Obstruction class = −1
(iii) Cusp Shapes = −117.650u
105
+ 684.548u
104
+ ··· + 74.1017u + 98.6648
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
106
+ 36u
105
+ ··· + 15872u + 1024
c
2
, c
6
u
106
− 2u
105
+ ··· − 32u − 32
c
3
u
106
+ 5u
105
+ ··· + 117392u + 6541
c
4
u
106
+ u
105
+ ··· + 294900u − 153931
c
5
, c
7
, c
8
u
106
− 7u
105
+ ··· − u
2
+ 1
c
9
, c
11
u
106
+ 4u
105
+ ··· + 63u + 1
c
10
u
106
− 18u
105
+ ··· − 64u + 4
c
12
u
106
+ 9u
105
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
106
+ 60y
105
+ ··· − 50987008y + 1048576
c
2
, c
6
y
106
− 36y
105
+ ··· − 15872y + 1024
c
3
y
106
+ 119y
105
+ ··· − 11945791032y + 42784681
c
4
y
106
+ 47y
105
+ ··· − 1112070735948y + 23694752761
c
5
, c
7
, c
8
y
106
− 89y
105
+ ··· − 2y + 1
c
9
, c
11
y
106
− 80y
105
+ ··· − 5699y + 1
c
10
y
106
+ 18y
105
+ ··· − 888y + 16
c
12
y
106
− 25y
105
+ ··· − 20y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.676515 + 0.691802I
a = 0.664912 + 0.408543I
b = 0.718628 − 0.395544I
0.39517 − 2.43050I 0
u = −0.676515 − 0.691802I
a = 0.664912 − 0.408543I
b = 0.718628 + 0.395544I
0.39517 + 2.43050I 0
u = −0.155047 + 0.936670I
a = −0.360203 + 0.420878I
b = 0.845813 + 0.632251I
6.24033 + 5.37724I 0
u = −0.155047 − 0.936670I
a = −0.360203 − 0.420878I
b = 0.845813 − 0.632251I
6.24033 − 5.37724I 0
u = −0.154727 + 0.905545I
a = −0.913842 + 0.473543I
b = 1.47585 + 1.03011I
7.1033 + 13.7991I 0
u = −0.154727 − 0.905545I
a = −0.913842 − 0.473543I
b = 1.47585 − 1.03011I
7.1033 − 13.7991I 0
u = −0.545270 + 0.721728I
a = −0.008138 + 0.528724I
b = 0.884430 + 0.673476I
0.75431 + 7.41963I 0
u = −0.545270 − 0.721728I
a = −0.008138 − 0.528724I
b = 0.884430 − 0.673476I
0.75431 − 7.41963I 0
u = −0.900430
a = 2.61743
b = −1.68822
0.491361 0
u = −1.086680 + 0.311551I
a = 0.817502 − 0.738946I
b = −0.656324 − 0.563923I
−0.608988 + 0.539453I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.086680 − 0.311551I
a = 0.817502 + 0.738946I
b = −0.656324 + 0.563923I
−0.608988 − 0.539453I 0
u = 1.107130 + 0.281035I
a = −0.821941 + 0.041902I
b = −1.314860 − 0.139803I
4.76987 − 4.98668I 0
u = 1.107130 − 0.281035I
a = −0.821941 − 0.041902I
b = −1.314860 + 0.139803I
4.76987 + 4.98668I 0
u = −1.147060 + 0.071642I
a = 3.68942 + 0.33716I
b = 0.463816 − 0.751777I
−0.503326 + 1.106790I 0
u = −1.147060 − 0.071642I
a = 3.68942 − 0.33716I
b = 0.463816 + 0.751777I
−0.503326 − 1.106790I 0
u = −0.143266 + 0.836626I
a = 1.373120 − 0.108253I
b = −0.948240 − 0.538305I
2.20961 + 7.79473I 0
u = −0.143266 − 0.836626I
a = 1.373120 + 0.108253I
b = −0.948240 + 0.538305I
2.20961 − 7.79473I 0
u = −1.095120 + 0.407068I
a = 0.320212 − 0.383419I
b = −0.782798 + 0.522188I
−0.70354 − 3.31461I 0
u = −1.095120 − 0.407068I
a = 0.320212 + 0.383419I
b = −0.782798 − 0.522188I
−0.70354 + 3.31461I 0
u = −0.088609 + 0.814986I
a = 0.762436 − 0.880723I
b = −0.794822 − 0.574538I
6.58986 + 4.90925I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.088609 − 0.814986I
a = 0.762436 + 0.880723I
b = −0.794822 + 0.574538I
6.58986 − 4.90925I 0
u = 0.162273 + 0.798920I
a = 0.316274 + 0.790393I
b = −0.995395 + 0.354943I
7.55362 + 0.96837I 0
u = 0.162273 − 0.798920I
a = 0.316274 − 0.790393I
b = −0.995395 − 0.354943I
7.55362 − 0.96837I 0
u = 1.149890 + 0.305354I
a = −0.939292 + 0.135464I
b = −1.58279 − 0.61339I
5.12337 + 3.69187I 0
u = 1.149890 − 0.305354I
a = −0.939292 − 0.135464I
b = −1.58279 + 0.61339I
5.12337 − 3.69187I 0
u = −0.149263 + 0.789775I
a = 0.787740 − 0.502854I
b = −1.000220 + 0.355985I
2.21730 + 3.52862I 0
u = −0.149263 − 0.789775I
a = 0.787740 + 0.502854I
b = −1.000220 − 0.355985I
2.21730 − 3.52862I 0
u = 0.116906 + 0.784426I
a = 1.027520 + 0.758088I
b = −1.48580 + 0.84073I
8.23030 − 7.68453I 0
u = 0.116906 − 0.784426I
a = 1.027520 − 0.758088I
b = −1.48580 − 0.84073I
8.23030 + 7.68453I 0
u = −0.043513 + 0.784836I
a = −1.13155 − 0.86536I
b = 0.974851 − 0.492494I
6.79678 + 0.76185I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.043513 − 0.784836I
a = −1.13155 + 0.86536I
b = 0.974851 + 0.492494I
6.79678 − 0.76185I 0
u = −0.090918 + 0.770718I
a = 0.001017 + 1.326850I
b = 0.06005 − 3.53436I
4.25332 + 2.68884I 0
u = −0.090918 − 0.770718I
a = 0.001017 − 1.326850I
b = 0.06005 + 3.53436I
4.25332 − 2.68884I 0
u = −1.188560 + 0.302224I
a = −3.89588 + 2.92318I
b = 0.00036 + 3.50411I
0.93309 + 1.21144I 0
u = −1.188560 − 0.302224I
a = −3.89588 − 2.92318I
b = 0.00036 − 3.50411I
0.93309 − 1.21144I 0
u = −1.175320 + 0.364112I
a = −0.270216 + 0.548089I
b = −0.889921 + 0.420737I
3.26694 − 0.64913I 0
u = −1.175320 − 0.364112I
a = −0.270216 − 0.548089I
b = −0.889921 − 0.420737I
3.26694 + 0.64913I 0
u = −1.126180 + 0.508705I
a = 0.898946 + 0.172086I
b = 1.39497 − 0.91788I
4.14016 − 8.79112I 0
u = −1.126180 − 0.508705I
a = 0.898946 − 0.172086I
b = 1.39497 + 0.91788I
4.14016 + 8.79112I 0
u = −0.561852 + 0.496019I
a = 1.115350 − 0.527225I
b = −0.500955 − 0.811935I
−2.53589 + 3.13368I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.561852 − 0.496019I
a = 1.115350 + 0.527225I
b = −0.500955 + 0.811935I
−2.53589 − 3.13368I 0
u = −1.136020 + 0.558855I
a = 0.617174 − 0.047762I
b = 0.798355 − 0.402245I
3.25541 − 0.12582I 0
u = −1.136020 − 0.558855I
a = 0.617174 + 0.047762I
b = 0.798355 + 0.402245I
3.25541 + 0.12582I 0
u = 0.011550 + 0.728370I
a = −1.54002 − 0.02128I
b = 0.811948 − 0.385158I
2.92007 − 2.23216I 0
u = 0.011550 − 0.728370I
a = −1.54002 + 0.02128I
b = 0.811948 + 0.385158I
2.92007 + 2.23216I 0
u = −1.230720 + 0.336990I
a = −0.36663 + 2.32265I
b = 0.792864 + 0.474315I
3.14368 + 3.28642I 0
u = −1.230720 − 0.336990I
a = −0.36663 − 2.32265I
b = 0.792864 − 0.474315I
3.14368 − 3.28642I 0
u = −1.247910 + 0.266698I
a = 0.768384 + 0.760013I
b = 0.824777 − 0.350711I
−0.96936 + 1.83401I 0
u = −1.247910 − 0.266698I
a = 0.768384 − 0.760013I
b = 0.824777 + 0.350711I
−0.96936 − 1.83401I 0
u = −1.287610 + 0.041503I
a = 0.66975 − 2.02910I
b = 0.387490 − 0.867901I
−4.21617 − 1.15380I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.287610 − 0.041503I
a = 0.66975 + 2.02910I
b = 0.387490 + 0.867901I
−4.21617 + 1.15380I 0
u = −0.053183 + 0.707999I
a = −0.903055 − 0.778769I
b = 0.902577 + 0.767060I
2.69570 + 1.67604I 0
u = −0.053183 − 0.707999I
a = −0.903055 + 0.778769I
b = 0.902577 − 0.767060I
2.69570 − 1.67604I 0
u = 1.30027
a = 0.0462337
b = 1.30766
−1.62200 0
u = −0.408373 + 0.567951I
a = −0.0891000 − 0.0161191I
b = −0.260164 + 0.867072I
−2.10687 + 0.70084I 0
u = −0.408373 − 0.567951I
a = −0.0891000 + 0.0161191I
b = −0.260164 − 0.867072I
−2.10687 − 0.70084I 0
u = 1.273780 + 0.296345I
a = −0.390302 − 0.625295I
b = 0.790325 + 0.164732I
−0.99913 − 1.45852I 0
u = 1.273780 − 0.296345I
a = −0.390302 + 0.625295I
b = 0.790325 − 0.164732I
−0.99913 + 1.45852I 0
u = −1.283820 + 0.305322I
a = −0.76594 + 1.50433I
b = 0.872259 + 0.566446I
−1.11938 + 5.96884I 0
u = −1.283820 − 0.305322I
a = −0.76594 − 1.50433I
b = 0.872259 − 0.566446I
−1.11938 − 5.96884I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.327730 + 0.070439I
a = −0.62997 + 1.44422I
b = −0.014472 + 0.282945I
−3.44617 − 3.59566I 0
u = 1.327730 − 0.070439I
a = −0.62997 − 1.44422I
b = −0.014472 − 0.282945I
−3.44617 + 3.59566I 0
u = 1.298730 + 0.338989I
a = 0.285583 + 0.380830I
b = 1.123630 + 0.504102I
2.60474 − 4.81260I 0
u = 1.298730 − 0.338989I
a = 0.285583 − 0.380830I
b = 1.123630 − 0.504102I
2.60474 + 4.81260I 0
u = 1.309800 + 0.298572I
a = −0.55339 − 1.32739I
b = 1.11367 − 1.09988I
−1.58451 − 5.32615I 0
u = 1.309800 − 0.298572I
a = −0.55339 + 1.32739I
b = 1.11367 + 1.09988I
−1.58451 + 5.32615I 0
u = 1.355400 + 0.028503I
a = 0.01751 + 3.16477I
b = 0.45318 + 2.49341I
−4.83518 − 0.65583I 0
u = 1.355400 − 0.028503I
a = 0.01751 − 3.16477I
b = 0.45318 − 2.49341I
−4.83518 + 0.65583I 0
u = 1.326120 + 0.332619I
a = 2.48237 + 2.50089I
b = 0.19652 + 3.55328I
−0.19585 − 6.67821I 0
u = 1.326120 − 0.332619I
a = 2.48237 − 2.50089I
b = 0.19652 − 3.55328I
−0.19585 + 6.67821I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.326560 + 0.356381I
a = 0.29521 + 1.92543I
b = −0.708338 + 0.686086I
2.15213 − 9.12723I 0
u = 1.326560 − 0.356381I
a = 0.29521 − 1.92543I
b = −0.708338 − 0.686086I
2.15213 + 9.12723I 0
u = −1.341230 + 0.339352I
a = −0.09526 − 2.46363I
b = −1.41486 − 0.99307I
3.64308 + 11.74720I 0
u = −1.341230 − 0.339352I
a = −0.09526 + 2.46363I
b = −1.41486 + 0.99307I
3.64308 − 11.74720I 0
u = 1.358860 + 0.338855I
a = −0.512927 + 0.834676I
b = −1.155300 − 0.186797I
−2.53934 − 7.60969I 0
u = 1.358860 − 0.338855I
a = −0.512927 − 0.834676I
b = −1.155300 + 0.186797I
−2.53934 + 7.60969I 0
u = 0.592031 + 0.074392I
a = −1.51424 + 0.39595I
b = −1.226890 + 0.278103I
4.78736 − 4.50881I 6.94966 + 4.99876I
u = 0.592031 − 0.074392I
a = −1.51424 − 0.39595I
b = −1.226890 − 0.278103I
4.78736 + 4.50881I 6.94966 − 4.99876I
u = −1.404270 + 0.042876I
a = −1.48733 − 1.04364I
b = −0.760017 − 0.566211I
−1.42389 + 4.99446I 0
u = −1.404270 − 0.042876I
a = −1.48733 + 1.04364I
b = −0.760017 + 0.566211I
−1.42389 − 4.99446I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.359400 + 0.362607I
a = 0.56802 + 1.29682I
b = −1.050780 + 0.591009I
−2.52295 − 12.11160I 0
u = 1.359400 − 0.362607I
a = 0.56802 − 1.29682I
b = −1.050780 − 0.591009I
−2.52295 + 12.11160I 0
u = 1.400470 + 0.183938I
a = −0.54835 − 1.40528I
b = −0.153428 − 1.096360I
−7.82829 − 3.32815I 0
u = 1.400470 − 0.183938I
a = −0.54835 + 1.40528I
b = −0.153428 + 1.096360I
−7.82829 + 3.32815I 0
u = −0.583612
a = 0.544793
b = −0.336523
−0.970312 −9.97770
u = −1.37079 + 0.35678I
a = −0.24834 − 1.41725I
b = −0.773940 − 0.533648I
2.71114 + 3.22315I 0
u = −1.37079 − 0.35678I
a = −0.24834 + 1.41725I
b = −0.773940 + 0.533648I
2.71114 − 3.22315I 0
u = 1.41732 + 0.10081I
a = 0.00873 + 1.70382I
b = −0.708506 + 0.990413I
−8.87200 − 4.93818I 0
u = 1.41732 − 0.10081I
a = 0.00873 − 1.70382I
b = −0.708506 − 0.990413I
−8.87200 + 4.93818I 0
u = 1.37888 + 0.39639I
a = −0.11288 − 2.22988I
b = 1.50035 − 1.13284I
2.2683 − 18.4659I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.37888 − 0.39639I
a = −0.11288 + 2.22988I
b = 1.50035 + 1.13284I
2.2683 + 18.4659I 0
u = 1.38164 + 0.41269I
a = −0.09672 − 1.47557I
b = 0.833671 − 0.803272I
1.40270 − 10.20110I 0
u = 1.38164 − 0.41269I
a = −0.09672 + 1.47557I
b = 0.833671 + 0.803272I
1.40270 + 10.20110I 0
u = 1.44978
a = −0.106761
b = −0.407994
−7.46939 0
u = 1.46808 + 0.17386I
a = 0.70037 − 1.61769I
b = 0.855289 − 1.015720I
−5.89344 − 10.41290I 0
u = 1.46808 − 0.17386I
a = 0.70037 + 1.61769I
b = 0.855289 + 1.015720I
−5.89344 + 10.41290I 0
u = −0.472359 + 0.148831I
a = −0.57944 + 1.97008I
b = −1.08911 − 2.05565I
0.670260 + 0.135177I 27.0189 − 4.6847I
u = −0.472359 − 0.148831I
a = −0.57944 − 1.97008I
b = −1.08911 + 2.05565I
0.670260 − 0.135177I 27.0189 + 4.6847I
u = −0.299380 + 0.376191I
a = −0.56926 − 2.18333I
b = −0.435451 + 0.189258I
1.54060 + 2.24837I −0.25150 − 8.36036I
u = −0.299380 − 0.376191I
a = −0.56926 + 2.18333I
b = −0.435451 − 0.189258I
1.54060 − 2.24837I −0.25150 + 8.36036I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.56011 + 0.03449I
a = 0.560796 + 0.026578I
b = 0.216786 + 0.072352I
−7.36096 + 0.00988I 0
u = 1.56011 − 0.03449I
a = 0.560796 − 0.026578I
b = 0.216786 − 0.072352I
−7.36096 − 0.00988I 0
u = 0.172518 + 0.021543I
a = 1.06469 + 2.51398I
b = 0.347391 + 0.606245I
0.08921 + 1.51284I 0.39009 − 4.24743I
u = 0.172518 − 0.021543I
a = 1.06469 − 2.51398I
b = 0.347391 − 0.606245I
0.08921 − 1.51284I 0.39009 + 4.24743I
u = −0.024614 + 0.157392I
a = −3.01966 − 7.50084I
b = 1.126090 + 0.073113I
2.53457 − 0.11622I 3.70952 − 2.56780I
u = −0.024614 − 0.157392I
a = −3.01966 + 7.50084I
b = 1.126090 − 0.073113I
2.53457 + 0.11622I 3.70952 + 2.56780I
15
II. I
u
2
= hb
5
+ b
4
− 2b
3
− b
2
+ b − 1, a + 1, u − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
1
a
6
=
1
1
a
9
=
−1
0
a
11
=
−1
b
a
12
=
b − 1
b
a
4
=
−b + 1
b
2
a
1
=
b
4
− b
3
− b
2
+ 2b − 1
b
4
− b
3
− b
2
+ 2b − 1
a
7
=
1
1
a
10
=
b
2
− b − 1
b
2
a
3
=
b
4
− b
3
− b
2
+ 2b − 1
b
4
− b
3
− b
2
+ 2b − 1
a
2
=
b
4
− b
3
− b
2
+ 2b − 1
b
4
− b
3
− b
2
+ 2b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3b
4
+ 7b
3
− 2b
2
− 6b − 5
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
5
c
3
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
4
, c
11
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
5
(u − 1)
5
c
7
, c
8
(u + 1)
5
c
9
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
10
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
12
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
5
c
3
, c
10
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
4
, c
9
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
5
, c
7
, c
8
(y −1)
5
c
12
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 1.21774
0.756147 3.96490
u = 1.00000
a = −1.00000
b = 0.309916 + 0.549911I
−1.31583 + 1.53058I −8.42731 − 4.45807I
u = 1.00000
a = −1.00000
b = 0.309916 − 0.549911I
−1.31583 − 1.53058I −8.42731 + 4.45807I
u = 1.00000
a = −1.00000
b = −1.41878 + 0.21917I
4.22763 − 4.40083I −8.55516 + 1.78781I
u = 1.00000
a = −1.00000
b = −1.41878 − 0.21917I
4.22763 + 4.40083I −8.55516 − 1.78781I
19
III. I
u
3
= hb − u − 2, a + u + 1, u
2
+ u − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
6
=
1
−u + 1
a
9
=
−u
−u + 1
a
11
=
−u − 1
u + 2
a
12
=
−1
2u + 1
a
4
=
−2u − 2
3u + 5
a
1
=
2u − 1
u − 1
a
7
=
u
u
a
10
=
−u − 1
u + 2
a
3
=
1
0
a
2
=
u
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 41
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
12
u
2
− 3u + 1
c
2
, c
5
u
2
+ u − 1
c
6
, c
7
, c
8
u
2
− u − 1
c
9
(u + 1)
2
c
10
u
2
c
11
(u − 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
12
y
2
− 7y + 1
c
2
, c
5
, c
6
c
7
, c
8
y
2
− 3y + 1
c
9
, c
11
(y −1)
2
c
10
y
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −1.61803
b = 2.61803
0.657974 41.0000
u = −1.61803
a = 0.618034
b = 0.381966
−7.23771 41.0000
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
5
(u
2
− 3u + 1)(u
106
+ 36u
105
+ ··· + 15872u + 1024)
c
2
u
5
(u
2
+ u − 1)(u
106
− 2u
105
+ ··· − 32u − 32)
c
3
(u
2
− 3u + 1)(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
· (u
106
+ 5u
105
+ ··· + 117392u + 6541)
c
4
(u
2
− 3u + 1)(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
106
+ u
105
+ ··· + 294900u − 153931)
c
5
((u − 1)
5
)(u
2
+ u − 1)(u
106
− 7u
105
+ ··· − u
2
+ 1)
c
6
u
5
(u
2
− u − 1)(u
106
− 2u
105
+ ··· − 32u − 32)
c
7
, c
8
((u + 1)
5
)(u
2
− u − 1)(u
106
− 7u
105
+ ··· − u
2
+ 1)
c
9
((u + 1)
2
)(u
5
− u
4
+ ··· + u + 1)(u
106
+ 4u
105
+ ··· + 63u + 1)
c
10
u
2
(u
5
+ u
4
+ ··· + u + 1)(u
106
− 18u
105
+ ··· − 64u + 4)
c
11
((u − 1)
2
)(u
5
+ u
4
+ ··· + u − 1)(u
106
+ 4u
105
+ ··· + 63u + 1)
c
12
(u
2
− 3u + 1)(u
5
+ 3u
4
+ ··· − u − 1)(u
106
+ 9u
105
+ ··· − 2u − 1)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
5
(y
2
− 7y + 1)(y
106
+ 60y
105
+ ··· − 5.09870 × 10
7
y + 1048576)
c
2
, c
6
y
5
(y
2
− 3y + 1)(y
106
− 36y
105
+ ··· − 15872y + 1024)
c
3
(y
2
− 7y + 1)(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
106
+ 119y
105
+ ··· − 11945791032y + 42784681)
c
4
(y
2
− 7y + 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
106
+ 47y
105
+ ··· − 1112070735948y + 23694752761)
c
5
, c
7
, c
8
((y −1)
5
)(y
2
− 3y + 1)(y
106
− 89y
105
+ ··· − 2y + 1)
c
9
, c
11
((y −1)
2
)(y
5
− 5y
4
+ ··· − y −1)(y
106
− 80y
105
+ ··· − 5699y + 1)
c
10
y
2
(y
5
+ 3y
4
+ ··· − y −1)(y
106
+ 18y
105
+ ··· − 888y + 16)
c
12
(y
2
− 7y + 1)(y
5
− y
4
+ ··· + 3y −1)(y
106
− 25y
105
+ ··· − 20y + 1)
25
