12a
0001
(K12a
0001
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 9 11 4 12 7 1 10
Solving Sequence
9,12
10
1,4
8 5 11 7 6 3 2
c
9
c
12
c
8
c
4
c
11
c
7
c
6
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.90724 × 10
78
u
127
− 4.51726 × 10
79
u
126
+ ··· + 5.58481 × 10
75
b − 1.43118 × 10
78
,
4.97117 × 10
78
u
127
− 5.50418 × 10
79
u
126
+ ··· + 5.58481 × 10
75
a + 9.59232 × 10
77
, u
128
− 13u
127
+ ··· − 3u + 1i
I
u
2
= hb, −u
5
+ u
3
a + 2u
4
− u
2
a + a
2
− 2u
2
+ a + u, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
I
u
3
= ha
2
+ b + a − 1, a
4
+ a
3
− 2a
2
− a + 2, u + 1i
I
u
4
= ha
5
− 3a
4
+ 4a
2
+ b + a − 1, a
6
− 3a
5
+ 5a
3
− a
2
− 2a + 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 150 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
= h3.91 × 10
78
u
127
− 4.52 × 10
79
u
126
+ · · · + 5.58 × 10
75
b − 1.43 ×
10
78
, 4.97 × 10
78
u
127
− 5.50 × 10
79
u
126
+ · · · + 5.58 × 10
75
a + 9.59 ×
10
77
, u
128
− 13u
127
+ · · · − 3u + 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
=
−890.124u
127
+ 9855.63u
126
+ ··· − 533.258u − 171.757
−699.620u
127
+ 8088.48u
126
+ ··· − 995.384u + 256.262
a
8
=
726.036u
127
− 9831.86u
126
+ ··· + 2699.13u − 1698.98
534.963u
127
− 4792.44u
126
+ ··· − 933.777u + 1212.53
a
5
=
−1886.04u
127
+ 22618.7u
126
+ ··· − 3435.20u + 1391.46
−473.156u
127
+ 3944.04u
126
+ ··· + 1228.16u − 1364.18
a
11
=
−u
3
u
5
− u
3
+ u
a
7
=
1184.26u
127
− 16846.3u
126
+ ··· + 5432.79u − 3580.45
421.670u
127
− 3154.11u
126
+ ··· − 1503.13u + 1602.68
a
6
=
1605.93u
127
− 20000.5u
126
+ ··· + 3929.65u − 1977.77
421.670u
127
− 3154.11u
126
+ ··· − 1503.13u + 1602.68
a
3
=
−1994.18u
127
+ 23589.1u
126
+ ··· − 3282.53u + 1117.67
−165.031u
127
+ 388.300u
126
+ ··· + 1669.75u − 1431.77
a
2
=
−1938.13u
127
+ 22466.1u
126
+ ··· − 2775.51u + 659.657
490.496u
127
− 6640.18u
126
+ ··· + 1926.70u − 1129.42
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4093.96u
127
+ 45529.3u
126
+ ··· − 3370.47u − 481.481
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
128
+ 64u
127
+ ··· + 8u + 1
c
2
, c
5
u
128
+ 8u
127
+ ··· + 8u + 1
c
3
u
128
− 8u
127
+ ··· − 97068u + 41508
c
4
, c
8
u
128
− 2u
127
+ ··· + 8192u + 4096
c
6
u
128
− 4u
127
+ ··· − 59111052u + 3579401
c
7
, c
10
u
128
+ 3u
127
+ ··· + 6144u + 1024
c
9
, c
12
u
128
+ 13u
127
+ ··· + 3u + 1
c
11
u
128
− 59u
127
+ ··· + 37u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
128
+ 8y
127
+ ··· + 64y + 1
c
2
, c
5
y
128
+ 64y
127
+ ··· + 8y + 1
c
3
y
128
− 48y
127
+ ··· + 110992594392y + 1722914064
c
4
, c
8
y
128
+ 70y
127
+ ··· + 520093696y + 16777216
c
6
y
128
− 56y
127
+ ··· − 158438371667520y + 12812111518801
c
7
, c
10
y
128
− 69y
127
+ ··· − 27787264y + 1048576
c
9
, c
12
y
128
− 59y
127
+ ··· + 37y + 1
c
11
y
128
+ 33y
127
+ ··· − 4663y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.467216 + 0.888765I
a = −0.262139 − 0.326352I
b = −1.174290 − 0.314881I
−5.57599 − 5.97894I 0
u = 0.467216 − 0.888765I
a = −0.262139 + 0.326352I
b = −1.174290 + 0.314881I
−5.57599 + 5.97894I 0
u = 0.884815 + 0.447263I
a = 0.736525 + 0.098393I
b = −0.646072 + 0.807347I
1.78444 + 0.33658I 0
u = 0.884815 − 0.447263I
a = 0.736525 − 0.098393I
b = −0.646072 − 0.807347I
1.78444 − 0.33658I 0
u = 0.903432 + 0.456730I
a = 1.332140 − 0.440260I
b = −0.785831 − 0.652425I
1.86792 + 3.29651I 0
u = 0.903432 − 0.456730I
a = 1.332140 + 0.440260I
b = −0.785831 + 0.652425I
1.86792 − 3.29651I 0
u = 0.549415 + 0.856556I
a = −0.314902 − 0.196049I
b = −1.170170 + 0.054456I
−6.12700 + 1.81309I 0
u = 0.549415 − 0.856556I
a = −0.314902 + 0.196049I
b = −1.170170 − 0.054456I
−6.12700 − 1.81309I 0
u = 0.421809 + 0.932088I
a = −0.16666 − 1.56984I
b = 0.574257 − 1.264840I
−6.12043 − 7.30221I 0
u = 0.421809 − 0.932088I
a = −0.16666 + 1.56984I
b = 0.574257 + 1.264840I
−6.12043 + 7.30221I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.465799 + 0.851706I
a = −0.17541 − 2.04875I
b = 0.259022 − 1.027760I
−3.31867 − 4.55381I 0
u = 0.465799 − 0.851706I
a = −0.17541 + 2.04875I
b = 0.259022 + 1.027760I
−3.31867 + 4.55381I 0
u = −0.926528 + 0.448937I
a = −0.503695 + 0.895385I
b = −0.775401 − 0.266682I
1.78403 − 1.66122I 0
u = −0.926528 − 0.448937I
a = −0.503695 − 0.895385I
b = −0.775401 + 0.266682I
1.78403 + 1.66122I 0
u = 0.506875 + 0.826946I
a = −0.08559 + 2.23069I
b = −0.064227 + 0.999070I
−3.61244 + 0.86916I 0
u = 0.506875 − 0.826946I
a = −0.08559 − 2.23069I
b = −0.064227 − 0.999070I
−3.61244 − 0.86916I 0
u = −0.737819 + 0.621082I
a = 0.93612 + 2.04262I
b = 0.268137 + 1.346520I
−6.39276 − 1.42340I 0
u = −0.737819 − 0.621082I
a = 0.93612 − 2.04262I
b = 0.268137 − 1.346520I
−6.39276 + 1.42340I 0
u = 0.408451 + 0.952232I
a = 0.14412 + 1.47260I
b = −0.66863 + 1.31884I
−8.8015 − 12.5693I 0
u = 0.408451 − 0.952232I
a = 0.14412 − 1.47260I
b = −0.66863 − 1.31884I
−8.8015 + 12.5693I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.862643 + 0.428421I
a = −1.21199 − 2.91585I
b = 0.062599 − 0.793471I
1.108160 + 0.710643I 0
u = −0.862643 − 0.428421I
a = −1.21199 + 2.91585I
b = 0.062599 + 0.793471I
1.108160 − 0.710643I 0
u = −0.919358 + 0.483575I
a = 1.59445 + 2.58825I
b = −0.285476 + 0.894692I
1.44266 − 4.40723I 0
u = −0.919358 − 0.483575I
a = 1.59445 − 2.58825I
b = −0.285476 − 0.894692I
1.44266 + 4.40723I 0
u = 0.918229 + 0.497793I
a = −0.788010 − 0.432152I
b = 0.615333 − 0.754332I
0.54839 + 5.39329I 0
u = 0.918229 − 0.497793I
a = −0.788010 + 0.432152I
b = 0.615333 + 0.754332I
0.54839 − 5.39329I 0
u = 0.472353 + 0.826605I
a = 0.199203 + 0.250333I
b = 0.943077 + 0.193062I
−2.84693 − 1.72799I 0
u = 0.472353 − 0.826605I
a = 0.199203 − 0.250333I
b = 0.943077 − 0.193062I
−2.84693 + 1.72799I 0
u = 0.460270 + 0.946554I
a = 0.01204 + 1.62062I
b = −0.44420 + 1.39719I
−11.01500 − 3.84928I 0
u = 0.460270 − 0.946554I
a = 0.01204 − 1.62062I
b = −0.44420 − 1.39719I
−11.01500 + 3.84928I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.831926 + 0.448912I
a = −1.55091 + 0.63092I
b = 0.825714 + 0.605979I
0.17233 − 1.51959I 0
u = 0.831926 − 0.448912I
a = −1.55091 − 0.63092I
b = 0.825714 − 0.605979I
0.17233 + 1.51959I 0
u = −0.910580 + 0.533390I
a = 0.623441 − 1.010220I
b = 1.072100 + 0.299027I
−0.61836 − 5.74521I 0
u = −0.910580 − 0.533390I
a = 0.623441 + 1.010220I
b = 1.072100 − 0.299027I
−0.61836 + 5.74521I 0
u = −1.056700 + 0.121003I
a = 1.40180 − 2.12162I
b = −0.246674 − 0.447064I
1.97936 − 2.35936I 0
u = −1.056700 − 0.121003I
a = 1.40180 + 2.12162I
b = −0.246674 + 0.447064I
1.97936 + 2.35936I 0
u = −0.782301 + 0.501067I
a = 0.514821 − 1.161720I
b = 1.024760 − 0.105409I
−1.05662 + 1.51276I 0
u = −0.782301 − 0.501067I
a = 0.514821 + 1.161720I
b = 1.024760 + 0.105409I
−1.05662 − 1.51276I 0
u = 0.637614 + 0.871450I
a = −0.50478 + 1.83058I
b = 0.380560 + 1.312160I
−7.55837 + 2.76750I 0
u = 0.637614 − 0.871450I
a = −0.50478 − 1.83058I
b = 0.380560 − 1.312160I
−7.55837 − 2.76750I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.664691 + 0.620912I
a = 0.0740313 − 0.0478021I
b = 0.641222 − 0.618829I
−3.24131 + 0.01631I 0
u = 0.664691 − 0.620912I
a = 0.0740313 + 0.0478021I
b = 0.641222 + 0.618829I
−3.24131 − 0.01631I 0
u = −0.642929 + 0.634338I
a = 0.70955 + 1.92950I
b = 0.539215 + 1.287990I
−4.76631 + 7.04658I 0
u = −0.642929 − 0.634338I
a = 0.70955 − 1.92950I
b = 0.539215 − 1.287990I
−4.76631 − 7.04658I 0
u = 0.608648 + 0.912650I
a = 0.39418 − 1.78668I
b = −0.23220 − 1.45855I
−12.00690 − 1.08932I 0
u = 0.608648 − 0.912650I
a = 0.39418 + 1.78668I
b = −0.23220 + 1.45855I
−12.00690 + 1.08932I 0
u = −0.926319 + 0.604861I
a = −1.47167 − 2.09294I
b = 0.394748 − 1.334950I
−5.81461 − 3.40517I 0
u = −0.926319 − 0.604861I
a = −1.47167 + 2.09294I
b = 0.394748 + 1.334950I
−5.81461 + 3.40517I 0
u = 0.929829 + 0.599892I
a = −0.826514 + 0.810044I
b = 0.838781 + 0.511078I
−2.49531 + 4.79440I 0
u = 0.929829 − 0.599892I
a = −0.826514 − 0.810044I
b = 0.838781 − 0.511078I
−2.49531 − 4.79440I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.834599 + 0.317293I
a = 0.607611 − 0.429842I
b = −0.607666 + 0.987525I
0.79205 − 1.96703I 0
u = 0.834599 − 0.317293I
a = 0.607611 + 0.429842I
b = −0.607666 − 0.987525I
0.79205 + 1.96703I 0
u = 0.848804 + 0.266513I
a = −0.632048 + 0.603499I
b = 0.613884 − 1.086290I
−1.41894 − 6.93011I 0
u = 0.848804 − 0.266513I
a = −0.632048 − 0.603499I
b = 0.613884 + 1.086290I
−1.41894 + 6.93011I 0
u = −0.667096 + 0.585551I
a = −0.72206 − 2.07304I
b = −0.429340 − 1.193630I
−2.01099 + 2.08594I 0
u = −0.667096 − 0.585551I
a = −0.72206 + 2.07304I
b = −0.429340 + 1.193630I
−2.01099 − 2.08594I 0
u = 0.671246 + 0.887919I
a = 0.52699 − 1.75239I
b = −0.50667 − 1.39349I
−10.56640 + 7.80081I 0
u = 0.671246 − 0.887919I
a = 0.52699 + 1.75239I
b = −0.50667 + 1.39349I
−10.56640 − 7.80081I 0
u = −1.040140 + 0.399543I
a = −0.640041 + 0.567994I
b = −0.394283 − 0.566210I
2.19825 − 1.39363I 0
u = −1.040140 − 0.399543I
a = −0.640041 − 0.567994I
b = −0.394283 + 0.566210I
2.19825 + 1.39363I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.016570 + 0.457027I
a = 1.032610 − 0.035620I
b = −0.575478 − 0.767072I
1.86462 + 5.09781I 0
u = 1.016570 − 0.457027I
a = 1.032610 + 0.035620I
b = −0.575478 + 0.767072I
1.86462 − 5.09781I 0
u = −0.965962 + 0.579568I
a = 1.61748 + 2.11047I
b = −0.544207 + 1.210720I
−1.10137 − 6.74666I 0
u = −0.965962 − 0.579568I
a = 1.61748 − 2.11047I
b = −0.544207 − 1.210720I
−1.10137 + 6.74666I 0
u = −0.983318 + 0.599046I
a = −1.62754 − 2.03045I
b = 0.63195 − 1.28165I
−3.74035 − 11.90180I 0
u = −0.983318 − 0.599046I
a = −1.62754 + 2.03045I
b = 0.63195 + 1.28165I
−3.74035 + 11.90180I 0
u = 1.065750 + 0.442801I
a = −0.997127 − 0.204455I
b = 0.456080 + 0.926673I
0.00932 + 9.64129I 0
u = 1.065750 − 0.442801I
a = −0.997127 + 0.204455I
b = 0.456080 − 0.926673I
0.00932 − 9.64129I 0
u = −1.162860 + 0.135909I
a = −1.323840 − 0.086207I
b = 0.645634 − 0.381020I
2.61757 − 0.40705I 0
u = −1.162860 − 0.135909I
a = −1.323840 + 0.086207I
b = 0.645634 + 0.381020I
2.61757 + 0.40705I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.150830 + 0.264016I
a = −1.040540 + 0.117585I
b = 0.346991 − 0.669629I
2.55173 − 0.89115I 0
u = −1.150830 − 0.264016I
a = −1.040540 − 0.117585I
b = 0.346991 + 0.669629I
2.55173 + 0.89115I 0
u = 0.347912 + 0.738078I
a = −0.054770 + 0.273114I
b = 0.424981 + 0.531973I
−1.87900 − 1.84140I 0
u = 0.347912 − 0.738078I
a = −0.054770 − 0.273114I
b = 0.424981 − 0.531973I
−1.87900 + 1.84140I 0
u = −1.181750 + 0.099439I
a = −0.883504 + 0.917778I
b = 0.300620 + 0.738938I
2.43308 + 2.28422I 0
u = −1.181750 − 0.099439I
a = −0.883504 − 0.917778I
b = 0.300620 − 0.738938I
2.43308 − 2.28422I 0
u = −1.142850 + 0.407232I
a = 0.938805 − 0.516089I
b = 0.189205 + 0.995087I
0.18861 + 2.20753I 0
u = −1.142850 − 0.407232I
a = 0.938805 + 0.516089I
b = 0.189205 − 0.995087I
0.18861 − 2.20753I 0
u = 1.118090 + 0.519341I
a = −0.561461 − 0.424753I
b = −0.082616 + 0.814985I
−0.91707 + 3.27060I 0
u = 1.118090 − 0.519341I
a = −0.561461 + 0.424753I
b = −0.082616 − 0.814985I
−0.91707 − 3.27060I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.202380 + 0.331291I
a = 1.105400 − 0.337621I
b = −0.266903 + 1.018850I
0.37432 − 4.83030I 0
u = −1.202380 − 0.331291I
a = 1.105400 + 0.337621I
b = −0.266903 − 1.018850I
0.37432 + 4.83030I 0
u = −1.248640 + 0.065178I
a = 1.45455 − 0.01017I
b = −0.988655 + 0.241802I
0.56813 + 3.46508I 0
u = −1.248640 − 0.065178I
a = 1.45455 + 0.01017I
b = −0.988655 − 0.241802I
0.56813 − 3.46508I 0
u = 1.112560 + 0.572551I
a = 0.226403 + 0.533712I
b = 0.456794 − 0.519543I
0.34343 + 6.81837I 0
u = 1.112560 − 0.572551I
a = 0.226403 − 0.533712I
b = 0.456794 + 0.519543I
0.34343 − 6.81837I 0
u = 1.022840 + 0.725245I
a = 0.796455 − 1.101220I
b = 0.283234 − 1.322490I
−6.38720 + 3.12375I 0
u = 1.022840 − 0.725245I
a = 0.796455 + 1.101220I
b = 0.283234 + 1.322490I
−6.38720 − 3.12375I 0
u = 1.006350 + 0.755132I
a = −0.805448 + 0.924099I
b = −0.42006 + 1.40957I
−9.54640 − 1.76865I 0
u = 1.006350 − 0.755132I
a = −0.805448 − 0.924099I
b = −0.42006 − 1.40957I
−9.54640 + 1.76865I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.088460 + 0.649545I
a = 1.19797 − 1.79880I
b = −0.188248 − 1.021790I
−1.85825 + 4.64991I 0
u = 1.088460 − 0.649545I
a = 1.19797 + 1.79880I
b = −0.188248 + 1.021790I
−1.85825 − 4.64991I 0
u = 1.073230 + 0.677577I
a = 0.175564 − 0.949380I
b = −1.171710 + 0.054354I
−4.53924 + 3.88030I 0
u = 1.073230 − 0.677577I
a = 0.175564 + 0.949380I
b = −1.171710 − 0.054354I
−4.53924 − 3.88030I 0
u = 1.103920 + 0.641568I
a = −0.018596 + 0.835541I
b = 0.991239 − 0.304457I
−0.95037 + 7.21793I 0
u = 1.103920 − 0.641568I
a = −0.018596 − 0.835541I
b = 0.991239 + 0.304457I
−0.95037 − 7.21793I 0
u = 0.678394 + 0.228741I
a = −0.177693 + 0.606218I
b = 0.329747 − 0.994777I
−3.53910 + 0.43298I 0
u = 0.678394 − 0.228741I
a = −0.177693 − 0.606218I
b = 0.329747 + 0.994777I
−3.53910 − 0.43298I 0
u = 1.112960 + 0.648845I
a = −1.44793 + 1.70769I
b = 0.353521 + 1.057330I
−1.37015 + 10.13200I 0
u = 1.112960 − 0.648845I
a = −1.44793 − 1.70769I
b = 0.353521 − 1.057330I
−1.37015 − 10.13200I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.059890 + 0.738559I
a = −1.01328 + 1.11251I
b = −0.14030 + 1.46845I
−10.63320 + 7.14080I 0
u = 1.059890 − 0.738559I
a = −1.01328 − 1.11251I
b = −0.14030 − 1.46845I
−10.63320 − 7.14080I 0
u = 0.117684 + 0.685153I
a = 0.413155 − 0.527878I
b = −0.050087 − 1.018590I
−3.55848 + 1.17274I 0
u = 0.117684 − 0.685153I
a = 0.413155 + 0.527878I
b = −0.050087 + 1.018590I
−3.55848 − 1.17274I 0
u = 1.123940 + 0.663598I
a = −0.023494 − 0.950137I
b = −1.178890 + 0.396849I
−3.58743 + 11.70610I 0
u = 1.123940 − 0.663598I
a = −0.023494 + 0.950137I
b = −1.178890 − 0.396849I
−3.58743 − 11.70610I 0
u = −1.308590 + 0.115968I
a = −0.696518 − 0.024469I
b = 0.503697 + 1.177980I
0.02376 + 4.17701I 0
u = −1.308590 − 0.115968I
a = −0.696518 + 0.024469I
b = 0.503697 − 1.177980I
0.02376 − 4.17701I 0
u = −1.328070 + 0.073496I
a = 0.423249 + 0.065006I
b = −0.336189 − 1.309520I
−4.50996 + 0.84886I 0
u = −1.328070 − 0.073496I
a = 0.423249 − 0.065006I
b = −0.336189 + 1.309520I
−4.50996 − 0.84886I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.651715 + 0.142686I
a = −0.14238 + 1.83709I
b = −0.532495 + 0.403697I
0.73525 − 1.44550I 0
u = −0.651715 − 0.142686I
a = −0.14238 − 1.83709I
b = −0.532495 − 0.403697I
0.73525 + 1.44550I 0
u = 1.157540 + 0.662046I
a = −1.64394 + 1.41344I
b = 0.626325 + 1.249550I
−3.88140 + 13.13440I 0
u = 1.157540 − 0.662046I
a = −1.64394 − 1.41344I
b = 0.626325 − 1.249550I
−3.88140 − 13.13440I 0
u = 1.148410 + 0.683905I
a = 1.52729 − 1.35239I
b = −0.50851 − 1.37155I
−8.91379 + 9.80389I 0
u = 1.148410 − 0.683905I
a = 1.52729 + 1.35239I
b = −0.50851 + 1.37155I
−8.91379 − 9.80389I 0
u = −1.332240 + 0.128823I
a = 0.716970 + 0.179971I
b = −0.593328 − 1.265060I
−2.61751 + 9.23119I 0
u = −1.332240 − 0.128823I
a = 0.716970 − 0.179971I
b = −0.593328 + 1.265060I
−2.61751 − 9.23119I 0
u = 1.170360 + 0.663622I
a = 1.68279 − 1.35634I
b = −0.70945 − 1.29439I
−6.4759 + 18.4604I 0
u = 1.170360 − 0.663622I
a = 1.68279 + 1.35634I
b = −0.70945 + 1.29439I
−6.4759 − 18.4604I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.097770 + 0.629296I
a = 0.672848 − 0.846263I
b = 0.345787 − 1.103930I
−2.87414 − 6.16357I 0
u = −0.097770 − 0.629296I
a = 0.672848 + 0.846263I
b = 0.345787 + 1.103930I
−2.87414 + 6.16357I 0
u = −0.058852 + 0.480634I
a = −0.976506 + 0.713958I
b = −0.320328 + 0.882356I
−0.41306 − 1.86476I −0.08533 + 4.23574I
u = −0.058852 − 0.480634I
a = −0.976506 − 0.713958I
b = −0.320328 − 0.882356I
−0.41306 + 1.86476I −0.08533 − 4.23574I
u = −0.237248 + 0.001998I
a = −1.10814 − 3.21322I
b = −0.481437 − 0.479931I
0.67709 + 1.37274I 2.95642 − 4.45072I
u = −0.237248 − 0.001998I
a = −1.10814 + 3.21322I
b = −0.481437 + 0.479931I
0.67709 − 1.37274I 2.95642 + 4.45072I
u = 0.014595 + 0.145747I
a = −3.38942 + 4.27535I
b = 0.580802 + 0.221013I
−0.25476 − 2.59885I 1.68242 + 3.17530I
u = 0.014595 − 0.145747I
a = −3.38942 − 4.27535I
b = 0.580802 − 0.221013I
−0.25476 + 2.59885I 1.68242 − 3.17530I
17
II.
I
u
2
= hb, −u
5
+ u
3
a + 2u
4
− u
2
a + a
2
− 2u
2
+ a + u, u
6
− u
5
− u
4
+ 2u
3
− u + 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
=
a
0
a
8
=
1
0
a
5
=
a
0
a
11
=
−u
3
u
5
− u
3
+ u
a
7
=
−u
3
u
3
− u
a
6
=
−u
u
3
− u
a
3
=
u
4
a − u
2
a + a
−u
5
a + u
4
a + 2u
3
a − u
2
a − au + a
a
2
=
u
4
a − u
2
a + u
3
− u
2
+ a + 1
−u
5
a + u
4
a + 2u
3
a − u
2
a − au + a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
5
a + u
4
a − u
5
+ 8u
3
a − 2u
4
−3u
2
a − 5au + 2u
2
+ 3a −3u −2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
8
u
12
c
6
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
7
, c
12
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
9
, c
10
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
11
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
6
c
4
, c
8
y
12
c
6
, c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
7
, c
9
, c
10
c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = −0.93136 − 1.30101I
b = 0
1.89061 + 1.10558I 6.66783 − 4.72351I
u = −1.002190 + 0.295542I
a = 1.59239 − 0.15607I
b = 0
1.89061 − 2.95419I 2.82220 + 4.67955I
u = −1.002190 − 0.295542I
a = −0.93136 + 1.30101I
b = 0
1.89061 − 1.10558I 6.66783 + 4.72351I
u = −1.002190 − 0.295542I
a = 1.59239 + 0.15607I
b = 0
1.89061 + 2.95419I 2.82220 − 4.67955I
u = 0.428243 + 0.664531I
a = 0.045720 + 0.914831I
b = 0
−1.89061 − 2.95419I −2.90246 + 4.54482I
u = 0.428243 + 0.664531I
a = −0.815127 − 0.417821I
b = 0
−1.89061 + 1.10558I 0.30406 − 2.63469I
u = 0.428243 − 0.664531I
a = 0.045720 − 0.914831I
b = 0
−1.89061 + 2.95419I −2.90246 − 4.54482I
u = 0.428243 − 0.664531I
a = −0.815127 + 0.417821I
b = 0
−1.89061 − 1.10558I 0.30406 + 2.63469I
u = 1.073950 + 0.558752I
a = −0.679704 + 0.059778I
b = 0
3.66314I 3.68173 − 3.33422I
u = 1.073950 + 0.558752I
a = 0.288082 − 0.618530I
b = 0
7.72290I −0.57335 − 9.26831I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = −0.679704 − 0.059778I
b = 0
− 3.66314I 3.68173 + 3.33422I
u = 1.073950 − 0.558752I
a = 0.288082 + 0.618530I
b = 0
− 7.72290I −0.57335 + 9.26831I
22
III. I
u
3
= ha
2
+ b + a − 1, a
4
+ a
3
− 2a
2
− a + 2, u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
−1
a
10
=
1
−1
a
1
=
−1
0
a
4
=
a
−a
2
− a + 1
a
8
=
−a
3
− a
2
+ a + 1
a
3
+ a
2
− a − 1
a
5
=
−1
−a
2
+ 2
a
11
=
1
−1
a
7
=
−a
3
− a
2
+ a + 1
a
3
+ a
2
− a − 1
a
6
=
0
a
3
+ a
2
− a − 1
a
3
=
a
a
3
+ a
2
− a − 1
a
2
=
−a
2
+ 1
a
3
+ 2a
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5a
3
− 6a
2
+ a + 6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
4
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
, c
8
u
4
+ u
2
− u + 1
c
7
, c
10
u
4
c
9
, c
11
(u + 1)
4
c
12
(u − 1)
4
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
4
, c
5
c
8
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
7
, c
10
y
4
c
9
, c
11
, c
12
(y −1)
4
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.899232 + 0.400532I
b = −0.547424 − 1.120870I
−0.98010 + 7.64338I 1.53830 − 8.45840I
u = −1.00000
a = 0.899232 − 0.400532I
b = −0.547424 + 1.120870I
−0.98010 − 7.64338I 1.53830 + 8.45840I
u = −1.00000
a = −1.39923 + 0.32564I
b = 0.547424 + 0.585652I
2.62503 + 1.39709I 4.96170 − 3.59727I
u = −1.00000
a = −1.39923 − 0.32564I
b = 0.547424 − 0.585652I
2.62503 − 1.39709I 4.96170 + 3.59727I
26
IV. I
u
4
= ha
5
− 3a
4
+ 4a
2
+ b + a − 1, a
6
− 3a
5
+ 5a
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
−a
5
+ 3a
4
− 4a
2
− a + 1
a
8
=
a
3
− 2a
2
− a + 2
−a
3
+ 2a
2
+ a − 2
a
5
=
−a
5
+ 2a
4
+ 2a
3
− 3a
2
− 2a + 1
a
4
− 2a
3
− a
2
+ 2a
a
11
=
1
−1
a
7
=
a
3
− 2a
2
− a + 2
−a
3
+ 2a
2
+ a − 2
a
6
=
0
−a
3
+ 2a
2
+ a − 2
a
3
=
a
a
3
− a
2
− 2a
a
2
=
−a
4
+ a
3
+ 2a
2
− 1
−a
5
+ 3a
4
+ a
3
− 5a
2
− 2a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3a
4
+ 8a
3
− 8a + 4
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
4
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
5
, c
8
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
7
, c
10
u
6
c
9
, c
11
(u + 1)
6
c
12
(u − 1)
6
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
4
, c
5
c
8
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y −1)
2
c
7
, c
10
y
6
c
9
, c
11
, c
12
(y −1)
6
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.897438 + 0.201182I
b = 0.498832 − 1.001300I
1.37919 − 2.82812I 4.90478 + 3.87141I
u = −1.00000
a = −0.897438 − 0.201182I
b = 0.498832 + 1.001300I
1.37919 + 2.82812I 4.90478 − 3.87141I
u = −1.00000
a = 0.500000 + 0.273346I
b = −0.284920 − 1.115140I
−2.75839 0.235367 − 0.997558I
u = −1.00000
a = 0.500000 − 0.273346I
b = −0.284920 + 1.115140I
−2.75839 0.235367 + 0.997558I
u = −1.00000
a = 1.89744 + 0.20118I
b = −0.713912 + 0.305839I
1.37919 + 2.82812I 5.35985 − 0.59776I
u = −1.00000
a = 1.89744 − 0.20118I
b = −0.713912 − 0.305839I
1.37919 − 2.82812I 5.35985 + 0.59776I
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
128
+ 64u
127
+ ··· + 8u + 1)
c
2
(u
2
+ u + 1)
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
128
+ 8u
127
+ ··· + 8u + 1)
c
3
(u
2
− u + 1)
6
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
128
− 8u
127
+ ··· − 97068u + 41508)
c
4
u
12
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
128
− 2u
127
+ ··· + 8192u + 4096)
c
5
(u
2
− u + 1)
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
128
+ 8u
127
+ ··· + 8u + 1)
c
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
128
− 4u
127
+ ··· − 59111052u + 3579401)
c
7
u
10
(u
6
+ u
5
+ ··· + u + 1)
2
(u
128
+ 3u
127
+ ··· + 6144u + 1024)
c
8
u
12
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
128
− 2u
127
+ ··· + 8192u + 4096)
c
9
((u + 1)
10
)(u
6
− u
5
+ ··· − u + 1)
2
(u
128
+ 13u
127
+ ··· + 3u + 1)
c
10
u
10
(u
6
− u
5
+ ··· − u + 1)
2
(u
128
+ 3u
127
+ ··· + 6144u + 1024)
c
11
(u + 1)
10
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
· (u
128
− 59u
127
+ ··· + 37u + 1)
c
12
((u − 1)
10
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
128
+ 13u
127
+ ··· + 3u + 1)
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
4
+ 2y
3
+ ··· + 5y + 1)(y
6
− y
5
+ ··· + 8y
2
+ 1)
· (y
128
+ 8y
127
+ ··· + 64y + 1)
c
2
, c
5
(y
2
+ y + 1)
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
128
+ 64y
127
+ ··· + 8y + 1)
c
3
(y
2
+ y + 1)
6
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
128
− 48y
127
+ ··· + 110992594392y + 1722914064)
c
4
, c
8
y
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
128
+ 70y
127
+ ··· + 520093696y + 16777216)
c
6
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
128
− 56y
127
+ ··· − 158438371667520y + 12812111518801)
c
7
, c
10
y
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
128
− 69y
127
+ ··· − 27787264y + 1048576)
c
9
, c
12
(y −1)
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
128
− 59y
127
+ ··· + 37y + 1)
c
11
(y −1)
10
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
128
+ 33y
127
+ ··· − 4663y + 1)
32
