12a
0109
(K12a
0109
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 10 4 12 7 6 1 9
Solving Sequence
5,11 3,6
2 1 4 10 7 8 9 12
c
5
c
2
c
1
c
4
c
10
c
6
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.02927 × 10
100
u
87
− 6.39816 × 10
100
u
86
+ ··· + 3.58918 × 10
101
b + 2.49262 × 10
101
,
7.25285 × 10
101
u
87
+ 1.13095 × 10
102
u
86
+ ··· + 2.15351 × 10
102
a − 5.93535 × 10
102
, u
88
+ 2u
87
+ ··· − 40u − 8i
I
u
2
= hb + 1, −4u
4
− 3u
3
− 16u
2
+ 3a − 8u − 10, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
I
u
3
= h4a
2
u − 6a
2
− 8au + 17b + 12a + 2u − 20, 4a
3
+ 6a
2
u − 8a
2
− 2au − u − 6, u
2
+ 2i
I
v
1
= ha, −v
2
+ b + 3v + 1, v
3
− 2v
2
− 3v −1i
* 4 irreducible components of dim
C
= 0, with total 102 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−5.03 × 10
100
u
87
− 6.40 × 10
100
u
86
+ · · · + 3.59 × 10
101
b + 2.49 ×
10
101
, 7.25 × 10
101
u
87
+ 1.13 × 10
102
u
86
+ · · · + 2.15 × 10
102
a − 5.94 ×
10
102
, u
88
+ 2u
87
+ · · · − 40u − 8i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−0.336792u
87
− 0.525165u
86
+ ··· + 5.92456u + 2.75613
0.140123u
87
+ 0.178262u
86
+ ··· − 3.22318u − 0.694480
a
6
=
1
−u
2
a
2
=
−0.196669u
87
− 0.346903u
86
+ ··· + 2.70138u + 2.06165
0.140123u
87
+ 0.178262u
86
+ ··· − 3.22318u − 0.694480
a
1
=
−0.0645847u
87
− 0.103802u
86
+ ··· − 3.32912u − 1.32103
−0.0244135u
87
− 0.0970148u
86
+ ··· + 5.00657u + 1.44969
a
4
=
−0.0540904u
87
− 0.114055u
86
+ ··· − 2.19327u + 2.15068
−0.157753u
87
− 0.184210u
86
+ ··· + 5.70265u + 0.193558
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
−0.0379577u
87
− 0.0552205u
86
+ ··· + 5.05922u + 1.39579
0.00232376u
87
+ 0.0655726u
86
+ ··· − 3.90590u − 1.43269
a
9
=
−u
3
− 2u
u
5
+ 3u
3
+ u
a
12
=
−0.173051u
87
− 0.352789u
86
+ ··· + 2.21047u − 0.306496
−0.0357757u
87
− 0.0453033u
86
+ ··· + 2.09794u + 0.712500
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.162012u
87
+ 0.0691568u
86
+ ··· + 10.5321u − 2.78961
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 43u
87
+ ··· + 5850u + 81
c
2
, c
4
u
88
− 9u
87
+ ··· + 12u + 9
c
3
, c
7
u
88
+ 2u
87
+ ··· − 192u − 288
c
5
, c
6
, c
9
c
10
u
88
+ 2u
87
+ ··· − 40u − 8
c
8
, c
12
u
88
− 5u
87
+ ··· − 525u + 49
c
11
u
88
− 41u
87
+ ··· − 246519u + 2401
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
88
+ 13y
87
+ ··· − 26338446y + 6561
c
2
, c
4
y
88
− 43y
87
+ ··· − 5850y + 81
c
3
, c
7
y
88
+ 42y
87
+ ··· + 59904y + 82944
c
5
, c
6
, c
9
c
10
y
88
+ 104y
87
+ ··· − 448y + 64
c
8
, c
12
y
88
− 41y
87
+ ··· − 246519y + 2401
c
11
y
88
+ 23y
87
+ ··· − 42416044391y + 5764801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.544232 + 0.801981I
a = 0.45727 + 1.70633I
b = 1.122770 − 0.558543I
−1.95733 + 7.43628I 0
u = 0.544232 − 0.801981I
a = 0.45727 − 1.70633I
b = 1.122770 + 0.558543I
−1.95733 − 7.43628I 0
u = −0.639200 + 0.724714I
a = 0.19749 − 2.03333I
b = 1.172430 + 0.616645I
0.25275 − 13.11110I 0
u = −0.639200 − 0.724714I
a = 0.19749 + 2.03333I
b = 1.172430 − 0.616645I
0.25275 + 13.11110I 0
u = 0.425748 + 0.993580I
a = 0.064085 + 0.159980I
b = 0.957165 + 0.380322I
−3.21813 + 0.79813I 0
u = 0.425748 − 0.993580I
a = 0.064085 − 0.159980I
b = 0.957165 − 0.380322I
−3.21813 − 0.79813I 0
u = −0.589414 + 0.668596I
a = −0.901108 + 0.955267I
b = 0.339571 − 0.905352I
2.77273 − 7.53893I 0
u = −0.589414 − 0.668596I
a = −0.901108 − 0.955267I
b = 0.339571 + 0.905352I
2.77273 + 7.53893I 0
u = 0.521144 + 0.708575I
a = 0.09047 − 2.35621I
b = −1.035090 + 0.541644I
−1.93302 + 6.75586I 0
u = 0.521144 − 0.708575I
a = 0.09047 + 2.35621I
b = −1.035090 − 0.541644I
−1.93302 − 6.75586I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.454359 + 0.719803I
a = 0.108044 + 0.326009I
b = −1.287330 + 0.187629I
−2.77018 − 4.12176I 0. + 7.16112I
u = −0.454359 − 0.719803I
a = 0.108044 − 0.326009I
b = −1.287330 − 0.187629I
−2.77018 + 4.12176I 0. − 7.16112I
u = 0.189661 + 0.796762I
a = −0.421221 + 0.469754I
b = −1.170030 − 0.256475I
−4.00054 − 0.43094I −4.62005 − 1.23771I
u = 0.189661 − 0.796762I
a = −0.421221 − 0.469754I
b = −1.170030 + 0.256475I
−4.00054 + 0.43094I −4.62005 + 1.23771I
u = 0.476204 + 0.665286I
a = −0.583867 − 0.579072I
b = 0.308494 + 0.733628I
0.39849 + 2.53090I 2.00000 − 3.36549I
u = 0.476204 − 0.665286I
a = −0.583867 + 0.579072I
b = 0.308494 − 0.733628I
0.39849 − 2.53090I 2.00000 + 3.36549I
u = −0.325850 + 0.749057I
a = −0.33571 + 2.12266I
b = −1.063440 − 0.409718I
−3.62884 − 1.93734I −4.67467 + 2.40265I
u = −0.325850 − 0.749057I
a = −0.33571 − 2.12266I
b = −1.063440 + 0.409718I
−3.62884 + 1.93734I −4.67467 − 2.40265I
u = −0.764680 + 0.260523I
a = −1.01456 + 1.01023I
b = 1.121010 − 0.587805I
1.64540 + 8.43286I 2.93830 − 6.25674I
u = −0.764680 − 0.260523I
a = −1.01456 − 1.01023I
b = 1.121010 + 0.587805I
1.64540 − 8.43286I 2.93830 + 6.25674I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.209318 + 1.208190I
a = 0.464577 + 0.697157I
b = 0.852854 − 0.450479I
−3.00819 + 4.00876I 0
u = 0.209318 − 1.208190I
a = 0.464577 − 0.697157I
b = 0.852854 + 0.450479I
−3.00819 − 4.00876I 0
u = 0.367904 + 0.650557I
a = 1.28515 + 1.07932I
b = −0.523066 − 0.570388I
−0.39958 + 2.25212I 1.06124 − 3.79280I
u = 0.367904 − 0.650557I
a = 1.28515 − 1.07932I
b = −0.523066 + 0.570388I
−0.39958 − 2.25212I 1.06124 + 3.79280I
u = −0.295855 + 1.218520I
a = 0.010588 + 0.192785I
b = 1.046980 − 0.516890I
−3.02122 + 4.63137I 0
u = −0.295855 − 1.218520I
a = 0.010588 − 0.192785I
b = 1.046980 + 0.516890I
−3.02122 − 4.63137I 0
u = 0.736276 + 0.098653I
a = −0.817831 − 0.970106I
b = 1.025650 + 0.511792I
0.17226 − 3.17277I 1.85523 + 2.82339I
u = 0.736276 − 0.098653I
a = −0.817831 + 0.970106I
b = 1.025650 − 0.511792I
0.17226 + 3.17277I 1.85523 − 2.82339I
u = −0.674195 + 0.305262I
a = 0.11126 − 1.73615I
b = 0.372533 + 0.786143I
3.86256 + 3.27144I 6.73775 − 1.69394I
u = −0.674195 − 0.305262I
a = 0.11126 + 1.73615I
b = 0.372533 − 0.786143I
3.86256 − 3.27144I 6.73775 + 1.69394I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.034179 + 0.718127I
a = 0.764549 − 0.742243I
b = −0.184555 + 0.451760I
−1.22278 + 1.55214I −0.78508 − 5.01782I
u = 0.034179 − 0.718127I
a = 0.764549 + 0.742243I
b = −0.184555 − 0.451760I
−1.22278 − 1.55214I −0.78508 + 5.01782I
u = −0.317676 + 0.640571I
a = 1.74066 − 1.75496I
b = 1.001370 + 0.622107I
3.82065 − 4.46578I 2.93072 + 6.78920I
u = −0.317676 − 0.640571I
a = 1.74066 + 1.75496I
b = 1.001370 − 0.622107I
3.82065 + 4.46578I 2.93072 − 6.78920I
u = −0.440566 + 0.518571I
a = −1.302340 − 0.305908I
b = 0.590084 − 0.713658I
5.03768 + 0.64765I 6.53702 + 1.45121I
u = −0.440566 − 0.518571I
a = −1.302340 + 0.305908I
b = 0.590084 + 0.713658I
5.03768 − 0.64765I 6.53702 − 1.45121I
u = 0.617215 + 0.203807I
a = 1.68584 + 1.45481I
b = −1.002130 − 0.427316I
−0.43590 − 2.88040I 1.88878 + 2.99748I
u = 0.617215 − 0.203807I
a = 1.68584 − 1.45481I
b = −1.002130 + 0.427316I
−0.43590 + 2.88040I 1.88878 − 2.99748I
u = 0.594706 + 0.256396I
a = −0.073072 + 1.290030I
b = 0.553067 − 0.541679I
1.61593 + 1.10166I 4.49842 − 4.17125I
u = 0.594706 − 0.256396I
a = −0.073072 − 1.290030I
b = 0.553067 + 0.541679I
1.61593 − 1.10166I 4.49842 + 4.17125I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.037223 + 1.354310I
a = 1.29186 + 1.33974I
b = −0.935436 − 0.213125I
−4.84743 − 0.66518I 0
u = 0.037223 − 1.354310I
a = 1.29186 − 1.33974I
b = −0.935436 + 0.213125I
−4.84743 + 0.66518I 0
u = −0.184148 + 1.365040I
a = 0.520576 − 0.880021I
b = 0.481633 + 0.586417I
−1.360140 + 0.220167I 0
u = −0.184148 − 1.365040I
a = 0.520576 + 0.880021I
b = 0.481633 − 0.586417I
−1.360140 − 0.220167I 0
u = −0.396296 + 0.432190I
a = −0.49246 − 1.73630I
b = 0.740300 + 0.830855I
5.31869 − 3.65991I 6.10187 + 9.13654I
u = −0.396296 − 0.432190I
a = −0.49246 + 1.73630I
b = 0.740300 − 0.830855I
5.31869 + 3.65991I 6.10187 − 9.13654I
u = −0.542158 + 0.117917I
a = 1.37098 + 1.98919I
b = −1.142410 − 0.181756I
−1.021790 + 0.705294I 3.49954 − 4.37901I
u = −0.542158 − 0.117917I
a = 1.37098 − 1.98919I
b = −1.142410 + 0.181756I
−1.021790 − 0.705294I 3.49954 + 4.37901I
u = 0.03018 + 1.52198I
a = −2.04233 − 1.47340I
b = −1.045690 + 0.315482I
−5.53360 + 1.03148I 0
u = 0.03018 − 1.52198I
a = −2.04233 + 1.47340I
b = −1.045690 − 0.315482I
−5.53360 − 1.03148I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04131 + 1.52824I
a = −0.061906 + 0.831333I
b = 0.962138 − 0.868668I
−1.82017 + 1.37348I 0
u = −0.04131 − 1.52824I
a = −0.061906 − 0.831333I
b = 0.962138 + 0.868668I
−1.82017 − 1.37348I 0
u = −0.11035 + 1.53163I
a = −0.149288 − 0.272362I
b = 0.368366 − 0.654466I
−1.82032 − 1.29038I 0
u = −0.11035 − 1.53163I
a = −0.149288 + 0.272362I
b = 0.368366 + 0.654466I
−1.82032 + 1.29038I 0
u = −0.08013 + 1.53516I
a = 0.071720 − 0.991753I
b = 0.806978 + 0.935865I
−1.34895 − 5.18025I 0
u = −0.08013 − 1.53516I
a = 0.071720 + 0.991753I
b = 0.806978 − 0.935865I
−1.34895 + 5.18025I 0
u = −0.262252 + 0.372162I
a = −0.93452 + 1.46801I
b = 0.950259 − 0.771844I
4.71038 + 2.27505I 2.87495 + 6.92818I
u = −0.262252 − 0.372162I
a = −0.93452 − 1.46801I
b = 0.950259 + 0.771844I
4.71038 − 2.27505I 2.87495 − 6.92818I
u = 0.280491 + 0.286926I
a = −0.03250 − 5.56793I
b = −0.763793 + 0.248992I
0.742521 + 0.263079I 1.89432 − 10.85247I
u = 0.280491 − 0.286926I
a = −0.03250 + 5.56793I
b = −0.763793 − 0.248992I
0.742521 − 0.263079I 1.89432 + 10.85247I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10435 + 1.59638I
a = 0.597044 + 0.707359I
b = −0.520082 − 0.766678I
−8.09429 + 3.99340I 0
u = 0.10435 − 1.59638I
a = 0.597044 − 0.707359I
b = −0.520082 + 0.766678I
−8.09429 − 3.99340I 0
u = 0.13215 + 1.59776I
a = −0.287968 − 0.352186I
b = 0.216304 + 0.908312I
−7.29353 + 4.75365I 0
u = 0.13215 − 1.59776I
a = −0.287968 + 0.352186I
b = 0.216304 − 0.908312I
−7.29353 − 4.75365I 0
u = −0.09037 + 1.60143I
a = 1.44988 − 0.84143I
b = 1.091120 + 0.543357I
−3.91219 − 5.96968I 0
u = −0.09037 − 1.60143I
a = 1.44988 + 0.84143I
b = 1.091120 − 0.543357I
−3.91219 + 5.96968I 0
u = −0.17781 + 1.59504I
a = −0.539469 + 0.440389I
b = 0.314437 − 0.996490I
−4.83782 − 10.38830I 0
u = −0.17781 − 1.59504I
a = −0.539469 − 0.440389I
b = 0.314437 + 0.996490I
−4.83782 + 10.38830I 0
u = −0.02758 + 1.60517I
a = 0.427081 − 0.575629I
b = −0.297892 + 0.763089I
−9.20407 + 1.33304I 0
u = −0.02758 − 1.60517I
a = 0.427081 + 0.575629I
b = −0.297892 − 0.763089I
−9.20407 − 1.33304I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15240 + 1.60919I
a = −0.50275 − 1.61138I
b = −1.078540 + 0.619975I
−9.79087 + 9.27121I 0
u = 0.15240 − 1.60919I
a = −0.50275 + 1.61138I
b = −1.078540 − 0.619975I
−9.79087 − 9.27121I 0
u = −0.13042 + 1.61198I
a = −0.665204 + 0.200185I
b = −1.377650 + 0.211486I
−10.71360 − 6.30775I 0
u = −0.13042 − 1.61198I
a = −0.665204 − 0.200185I
b = −1.377650 − 0.211486I
−10.71360 + 6.30775I 0
u = −0.09497 + 1.61734I
a = −0.71777 + 1.37284I
b = −1.140320 − 0.532443I
−11.73680 − 3.53945I 0
u = −0.09497 − 1.61734I
a = −0.71777 − 1.37284I
b = −1.140320 + 0.532443I
−11.73680 + 3.53945I 0
u = 0.378309
a = 1.75496
b = −0.125481
1.01782 11.4040
u = 0.06578 + 1.62137I
a = −0.858345 + 0.218227I
b = −1.316490 − 0.299557I
−12.27180 + 0.62227I 0
u = 0.06578 − 1.62137I
a = −0.858345 − 0.218227I
b = −1.316490 + 0.299557I
−12.27180 − 0.62227I 0
u = −0.19926 + 1.61688I
a = 0.81358 − 1.44253I
b = 1.218140 + 0.634975I
−7.6180 − 16.2777I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19926 − 1.61688I
a = 0.81358 + 1.44253I
b = 1.218140 − 0.634975I
−7.6180 + 16.2777I 0
u = 0.15988 + 1.63933I
a = 0.89920 + 1.16202I
b = 1.204800 − 0.573189I
−10.2649 + 10.1230I 0
u = 0.15988 − 1.63933I
a = 0.89920 − 1.16202I
b = 1.204800 + 0.573189I
−10.2649 − 10.1230I 0
u = −0.00661 + 1.70566I
a = 0.785461 + 0.141099I
b = 1.083240 − 0.305675I
−13.33910 + 4.11275I 0
u = −0.00661 − 1.70566I
a = 0.785461 − 0.141099I
b = 1.083240 + 0.305675I
−13.33910 − 4.11275I 0
u = 0.09125 + 1.70355I
a = 0.686106 + 0.124440I
b = 0.983741 + 0.219632I
−12.68530 + 2.74860I 0
u = 0.09125 − 1.70355I
a = 0.686106 − 0.124440I
b = 0.983741 − 0.219632I
−12.68530 − 2.74860I 0
u = −0.227971
a = 3.59324
b = −0.877499
−1.26625 −9.48720
13
II.
I
u
2
= hb + 1, −4u
4
− 3u
3
− 16u
2
+ 3a − 8u − 10, u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
4
3
u
4
+ u
3
+
16
3
u
2
+
8
3
u +
10
3
−1
a
6
=
1
−u
2
a
2
=
4
3
u
4
+ u
3
+
16
3
u
2
+
8
3
u +
7
3
−1
a
1
=
−1
0
a
4
=
4
3
u
4
+ u
3
+
16
3
u
2
+
8
3
u +
10
3
−1
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−u
3
− 2u
−u
4
− u
3
− 3u
2
− 2u − 1
a
12
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
58
9
u
4
+
13
3
u
3
+
211
9
u
2
+
128
9
u +
115
9
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
7
u
5
c
4
(u + 1)
5
c
5
, c
6
, c
11
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
8
u
5
+ u
4
− u
2
+ u + 1
c
9
, c
10
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
12
u
5
− u
4
+ u
2
+ u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
7
y
5
c
5
, c
6
, c
9
c
10
, c
11
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
8
, c
12
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233677 + 0.885557I
a = −0.162657 + 0.410020I
b = −1.00000
−3.46474 − 2.21397I −2.99716 + 4.40290I
u = −0.233677 − 0.885557I
a = −0.162657 − 0.410020I
b = −1.00000
−3.46474 + 2.21397I −2.99716 − 4.40290I
u = −0.416284
a = 3.11537
b = −1.00000
−0.762751 10.8010
u = −0.05818 + 1.69128I
a = −0.728361 + 0.139255I
b = −1.00000
−12.60320 − 3.33174I −0.51443 + 5.79761I
u = −0.05818 − 1.69128I
a = −0.728361 − 0.139255I
b = −1.00000
−12.60320 + 3.33174I −0.51443 − 5.79761I
17
III. I
u
3
=
h4a
2
u−6a
2
−8au+17b +12a +2u − 20, 4a
3
+6a
2
u−8a
2
−2au−u −6, u
2
+2i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
a
−0.235294a
2
u + 0.470588au + ··· − 0.705882a + 1.17647
a
6
=
1
2
a
2
=
−0.235294a
2
u + 0.470588au + ··· + 0.294118a + 1.17647
−0.235294a
2
u + 0.470588au + ··· − 0.705882a + 1.17647
a
1
=
−
1
2
u
−0.352941a
2
u − 0.294118au + ··· + 0.941176a + 1.76471
a
4
=
0.411765a
2
u − 0.823529au + ··· + 0.235294a − 0.0588235
−0.117647a
2
u − 0.764706au + ··· + 1.64706a − 0.411765
a
10
=
−u
−u
a
7
=
−1
0
a
8
=
−
1
2
u
−0.352941a
2
u − 0.294118au + ··· + 0.941176a + 1.76471
a
9
=
0
−u
a
12
=
−
1
2
u
−0.352941a
2
u − 0.294118au + ··· + 0.941176a + 1.76471
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
16
17
a
2
u +
24
17
a
2
+
32
17
au −
48
17
a −
8
17
u +
80
17
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
(u
3
+ u
2
+ 2u + 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
9
c
10
(u
2
+ 2)
3
c
8
(u − 1)
6
c
11
, c
12
(u + 1)
6
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
, c
9
c
10
(y + 2)
6
c
8
, c
11
, c
12
(y −1)
6
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.520153 − 0.983610I
b = 0.877439 + 0.744862I
−0.26574 − 2.82812I 3.50976 + 2.97945I
u = 1.414210I
a = −0.275030 + 0.506114I
b = 0.877439 − 0.744862I
−0.26574 + 2.82812I 3.50976 − 2.97945I
u = 1.414210I
a = 1.75488 − 1.64382I
b = −0.754878
−4.40332 −3.01951 + 0.I
u = − 1.414210I
a = 0.520153 + 0.983610I
b = 0.877439 − 0.744862I
−0.26574 + 2.82812I 3.50976 − 2.97945I
u = − 1.414210I
a = −0.275030 − 0.506114I
b = 0.877439 + 0.744862I
−0.26574 − 2.82812I 3.50976 + 2.97945I
u = − 1.414210I
a = 1.75488 + 1.64382I
b = −0.754878
−4.40332 −3.01951 + 0.I
21
IV. I
v
1
= ha, −v
2
+ b + 3v + 1, v
3
− 2v
2
− 3v − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
v
0
a
3
=
0
v
2
− 3v − 1
a
6
=
1
0
a
2
=
v
2
− 3v − 1
v
2
− 3v − 1
a
1
=
v
2
− 3v − 1
−v
2
+ 2v + 3
a
4
=
−2v
2
+ 5v + 4
−2v
2
+ 5v + 3
a
10
=
v
0
a
7
=
1
0
a
8
=
−v
2
+ 3v + 1
v
2
− 2v − 3
a
9
=
v
0
a
12
=
v
2
− 2v − 1
−v
2
+ 2v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8v
2
− 26v − 14
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
, c
9
c
10
u
3
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
11
(u + 1)
3
c
12
(u − 1)
3
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y − 1
c
2
, c
4
y
3
− y
2
+ 2y − 1
c
5
, c
6
, c
9
c
10
y
3
c
8
, c
11
, c
12
(y − 1)
3
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.539798 + 0.182582I
a = 0
b = 0.877439 − 0.744862I
4.66906 + 2.82812I 2.09911 − 6.32406I
v = −0.539798 − 0.182582I
a = 0
b = 0.877439 + 0.744862I
4.66906 − 2.82812I 2.09911 + 6.32406I
v = 3.07960
a = 0
b = −0.754878
0.531480 −18.1980
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
3
− u
2
+ 2u − 1)
3
(u
88
+ 43u
87
+ ··· + 5850u + 81)
c
2
((u − 1)
5
)(u
3
+ u
2
− 1)
3
(u
88
− 9u
87
+ ··· + 12u + 9)
c
3
u
5
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
88
+ 2u
87
+ ··· − 192u − 288)
c
4
((u + 1)
5
)(u
3
− u
2
+ 1)
3
(u
88
− 9u
87
+ ··· + 12u + 9)
c
5
, c
6
u
3
(u
2
+ 2)
3
(u
5
+ u
4
+ ··· + 3u + 1)(u
88
+ 2u
87
+ ··· − 40u − 8)
c
7
u
5
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ u
2
+ 2u + 1)(u
88
+ 2u
87
+ ··· − 192u − 288)
c
8
((u − 1)
6
)(u + 1)
3
(u
5
+ u
4
+ ··· + u + 1)(u
88
− 5u
87
+ ··· − 525u + 49)
c
9
, c
10
u
3
(u
2
+ 2)
3
(u
5
− u
4
+ ··· + 3u − 1)(u
88
+ 2u
87
+ ··· − 40u − 8)
c
11
(u + 1)
9
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
· (u
88
− 41u
87
+ ··· − 246519u + 2401)
c
12
((u − 1)
3
)(u + 1)
6
(u
5
− u
4
+ ··· + u − 1)(u
88
− 5u
87
+ ··· − 525u + 49)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
5
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
88
+ 13y
87
+ ··· − 26338446y + 6561)
c
2
, c
4
((y − 1)
5
)(y
3
− y
2
+ 2y − 1)
3
(y
88
− 43y
87
+ ··· − 5850y + 81)
c
3
, c
7
y
5
(y
3
+ 3y
2
+ 2y − 1)
3
(y
88
+ 42y
87
+ ··· + 59904y + 82944)
c
5
, c
6
, c
9
c
10
y
3
(y + 2)
6
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y − 1)
· (y
88
+ 104y
87
+ ··· − 448y + 64)
c
8
, c
12
(y − 1)
9
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y − 1)
· (y
88
− 41y
87
+ ··· − 246519y + 2401)
c
11
(y − 1)
9
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y − 1)
· (y
88
+ 23y
87
+ ··· − 42416044391y + 5764801)
27
