12a
0771
(K12a
0771
)
A knot diagram
1
Linearized knot diagam
3 8 10 12 9 11 2 1 5 7 4 6
Solving Sequence
2,7
8
3,10
4 11 1 9 6 5 12
c
7
c
2
c
3
c
10
c
1
c
8
c
6
c
5
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.94153 × 10
27
u
43
+ 1.81790 × 10
28
u
42
+ ··· + 2.63209 × 10
28
b − 4.42452 × 10
28
,
− 1.06493 × 10
29
u
43
− 2.17847 × 10
29
u
42
+ ··· + 1.05284 × 10
29
a − 5.20010 × 10
29
,
u
44
+ 3u
43
+ ··· + 12u + 8i
I
u
2
= h−2u
35
a + 2u
35
+ ··· + 3a + 2, 30u
35
a − 138u
35
+ ··· − 15a + 144, u
36
− u
35
+ ··· − u
2
+ 1i
I
u
3
= hb − 1, −u
3
+ 4u
2
+ 4a − 2, u
4
− 2u
2
+ 2i
I
v
1
= ha, b + 1, 2v + 1i
* 4 irreducible components of dim
C
= 0, with total 121 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
= h8.94 × 10
27
u
43
+ 1.82 × 10
28
u
42
+ · · · + 2.63 × 10
28
b − 4.42 ×
10
28
, −1.06 × 10
29
u
43
− 2.18 × 10
29
u
42
+ · · · + 1.05 × 10
29
a − 5.20 ×
10
29
, u
44
+ 3u
43
+ · · · + 12u + 8i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
1.01148u
43
+ 2.06914u
42
+ ··· + 6.75356u + 4.93913
−0.339712u
43
− 0.690668u
42
+ ··· + 0.899245u + 1.68099
a
4
=
−0.491722u
43
− 1.08414u
42
+ ··· − 5.99398u − 7.66894
0.0371897u
43
+ 0.0225085u
42
+ ··· + 0.0962924u + 0.243944
a
11
=
0.671771u
43
+ 1.37847u
42
+ ··· + 7.65281u + 6.62012
−0.339712u
43
− 0.690668u
42
+ ··· + 0.899245u + 1.68099
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
6
=
−0.410209u
43
− 0.680680u
42
+ ··· − 5.44836u − 3.15716
−0.585333u
43
− 1.56699u
42
+ ··· − 0.199466u − 3.32612
a
5
=
−0.395067u
43
− 0.647681u
42
+ ··· − 7.86724u − 6.66270
−0.214121u
43
− 0.720629u
42
+ ··· + 0.874054u − 0.939898
a
12
=
0.454683u
43
+ 0.926181u
42
+ ··· + 6.06159u + 5.75581
−0.205670u
43
− 0.268381u
42
+ ··· − 0.997900u + 1.21691
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.954565u
43
+ 3.18813u
42
+ ··· − 26.7876u + 6.14997
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 23u
43
+ ··· + 272u + 64
c
2
, c
7
u
44
+ 3u
43
+ ··· + 12u + 8
c
3
, c
12
128(128u
44
+ 64u
43
+ ··· − 11u − 1)
c
4
, c
11
u
44
− 13u
42
+ ··· + 647u − 416
c
5
, c
6
, c
9
c
10
u
44
+ u
43
+ ··· − 16u − 5
c
8
u
44
+ 9u
43
+ ··· + 42988u + 25384
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
− 3y
43
+ ··· − 12544y + 4096
c
2
, c
7
y
44
− 23y
43
+ ··· − 272y + 64
c
3
, c
12
16384(16384y
44
+ 151552y
43
+ ··· − 55y + 1)
c
4
, c
11
y
44
− 26y
43
+ ··· − 5622769y + 173056
c
5
, c
6
, c
9
c
10
y
44
+ 17y
43
+ ··· − 146y + 25
c
8
y
44
+ 29y
43
+ ··· − 8202497168y + 644347456
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.884944 + 0.456342I
a = 1.76169 − 1.31420I
b = −0.815843 − 0.660997I
3.80422 + 3.00198I 9.87086 − 5.43823I
u = −0.884944 − 0.456342I
a = 1.76169 + 1.31420I
b = −0.815843 + 0.660997I
3.80422 − 3.00198I 9.87086 + 5.43823I
u = −0.670238 + 0.750027I
a = −0.384753 + 1.126000I
b = 0.459752 − 1.089540I
0.43707 − 6.38433I 5.82179 + 5.84528I
u = −0.670238 − 0.750027I
a = −0.384753 − 1.126000I
b = 0.459752 + 1.089540I
0.43707 + 6.38433I 5.82179 − 5.84528I
u = −0.601725 + 0.830742I
a = −0.529924 − 0.448858I
b = 0.184705 + 0.860484I
−0.47398 + 2.76828I 9.57507 − 9.72155I
u = −0.601725 − 0.830742I
a = −0.529924 + 0.448858I
b = 0.184705 − 0.860484I
−0.47398 − 2.76828I 9.57507 + 9.72155I
u = 0.186329 + 0.936259I
a = −0.0808606 − 0.0791166I
b = −0.073120 + 0.812347I
0.435225 − 0.901619I 13.9955 + 4.4616I
u = 0.186329 − 0.936259I
a = −0.0808606 + 0.0791166I
b = −0.073120 − 0.812347I
0.435225 + 0.901619I 13.9955 − 4.4616I
u = 0.191787 + 0.913705I
a = 0.872159 + 0.565110I
b = −0.381936 − 1.276420I
−7.62519 + 7.08844I 1.23316 − 4.93509I
u = 0.191787 − 0.913705I
a = 0.872159 − 0.565110I
b = −0.381936 + 1.276420I
−7.62519 − 7.08844I 1.23316 + 4.93509I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.208206 + 0.873746I
a = 1.33288 − 0.57705I
b = −0.57707 + 1.33359I
−4.2603 − 13.7418I 4.56439 + 7.35664I
u = −0.208206 − 0.873746I
a = 1.33288 + 0.57705I
b = −0.57707 − 1.33359I
−4.2603 + 13.7418I 4.56439 − 7.35664I
u = −1.004180 + 0.480691I
a = −0.017302 − 0.166511I
b = −0.289315 + 0.457341I
−1.31781 + 1.99895I 3.76651 + 1.75105I
u = −1.004180 − 0.480691I
a = −0.017302 + 0.166511I
b = −0.289315 − 0.457341I
−1.31781 − 1.99895I 3.76651 − 1.75105I
u = −0.891355 + 0.676843I
a = 1.80496 + 0.33828I
b = −0.524580 − 1.162410I
−0.21415 + 11.72470I 5.05083 − 10.25102I
u = −0.891355 − 0.676843I
a = 1.80496 − 0.33828I
b = −0.524580 + 1.162410I
−0.21415 − 11.72470I 5.05083 + 10.25102I
u = 1.064910 + 0.482421I
a = 0.874561 + 0.554909I
b = −0.432078 + 0.243913I
−1.04936 − 4.41613I 4.34936 + 8.68385I
u = 1.064910 − 0.482421I
a = 0.874561 − 0.554909I
b = −0.432078 − 0.243913I
−1.04936 + 4.41613I 4.34936 − 8.68385I
u = −0.667044 + 0.444211I
a = −1.60584 + 0.60607I
b = 1.020760 − 0.533523I
4.44990 + 0.84092I 12.07181 − 5.13739I
u = −0.667044 − 0.444211I
a = −1.60584 − 0.60607I
b = 1.020760 + 0.533523I
4.44990 − 0.84092I 12.07181 + 5.13739I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.136530 + 0.421684I
a = 0.606451 + 1.237990I
b = −1.389530 + 0.221504I
−0.17714 − 2.64557I − 60.10 − 1.179168I
u = 1.136530 − 0.421684I
a = 0.606451 − 1.237990I
b = −1.389530 − 0.221504I
−0.17714 + 2.64557I − 60.10 + 1.179168I
u = −1.146090 + 0.479405I
a = 0.239075 − 1.309680I
b = −1.39337 + 0.38888I
0.24666 + 5.31593I 2.56328 − 8.44742I
u = −1.146090 − 0.479405I
a = 0.239075 + 1.309680I
b = −1.39337 − 0.38888I
0.24666 − 5.31593I 2.56328 + 8.44742I
u = 1.082540 + 0.685582I
a = 1.011040 + 0.097761I
b = −0.193861 + 0.889333I
−2.02935 − 4.79440I 7.24675 + 10.74676I
u = 1.082540 − 0.685582I
a = 1.011040 − 0.097761I
b = −0.193861 − 0.889333I
−2.02935 + 4.79440I 7.24675 − 10.74676I
u = 1.259910 + 0.315100I
a = 0.091904 + 0.628273I
b = 0.52009 + 1.36003I
−8.94132 + 9.79930I 0. − 4.91774I
u = 1.259910 − 0.315100I
a = 0.091904 − 0.628273I
b = 0.52009 − 1.36003I
−8.94132 − 9.79930I 0. + 4.91774I
u = 0.685053
a = −1.66669
b = −0.374180
2.00566 3.54950
u = −1.201480 + 0.555428I
a = −2.04851 + 0.88093I
b = 0.60384 + 1.36202I
−7.2417 + 18.9627I 0. − 10.45856I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.201480 − 0.555428I
a = −2.04851 − 0.88093I
b = 0.60384 − 1.36202I
−7.2417 − 18.9627I 0. + 10.45856I
u = −1.298400 + 0.319915I
a = 0.224279 − 0.600246I
b = 0.287147 − 1.310910I
−12.44790 − 2.88689I −3.91928 + 0.I
u = −1.298400 − 0.319915I
a = 0.224279 + 0.600246I
b = 0.287147 + 1.310910I
−12.44790 + 2.88689I −3.91928 + 0.I
u = 1.330060 + 0.160088I
a = 0.223696 + 0.671956I
b = −0.211250 + 1.150130I
−7.05764 − 5.66751I −3.71453 + 8.78354I
u = 1.330060 − 0.160088I
a = 0.223696 − 0.671956I
b = −0.211250 − 1.150130I
−7.05764 + 5.66751I −3.71453 − 8.78354I
u = 1.219740 + 0.558773I
a = −1.69862 − 0.67374I
b = 0.423980 − 1.324410I
−10.7383 − 12.4231I 0. + 7.73932I
u = 1.219740 − 0.558773I
a = −1.69862 + 0.67374I
b = 0.423980 + 1.324410I
−10.7383 + 12.4231I 0. − 7.73932I
u = −0.126816 + 0.631710I
a = −1.75809 − 0.34785I
b = 1.283540 + 0.336498I
3.08765 − 1.01915I 6.08245 + 6.44104I
u = −0.126816 − 0.631710I
a = −1.75809 + 0.34785I
b = 1.283540 − 0.336498I
3.08765 + 1.01915I 6.08245 − 6.44104I
u = 0.643966
a = −1.64514
b = 1.21259
2.74899 −5.75340
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.378525 + 0.481692I
a = −1.018580 − 0.068518I
b = 0.389924 + 0.119878I
0.917264 + 0.353906I 10.71011 − 2.76595I
u = 0.378525 − 0.481692I
a = −1.018580 + 0.068518I
b = 0.389924 − 0.119878I
0.917264 − 0.353906I 10.71011 + 2.76595I
u = −1.314340 + 0.508817I
a = −0.744288 + 0.705700I
b = 0.189010 + 1.009770I
−3.99655 + 6.00812I 0
u = −1.314340 − 0.508817I
a = −0.744288 − 0.705700I
b = 0.189010 − 1.009770I
−3.99655 − 6.00812I 0
9
II. I
u
2
= h−2u
35
a + 2u
35
+ · · · + 3a + 2, 30u
35
a − 138u
35
+ · · · − 15a +
144, u
36
− u
35
+ · · · − u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
a
2
5
u
35
a −
2
5
u
35
+ ··· −
3
5
a −
2
5
a
4
=
−1.20000au
35
− 3.12000u
35
+ ··· − 9.52000u − 1.84000
−
8
5
u
35
a +
9
5
u
35
+ ··· +
2
5
a − 2
a
11
=
2
5
u
35
a −
2
5
u
35
+ ··· +
2
5
a −
2
5
2
5
u
35
a −
2
5
u
35
+ ··· −
3
5
a −
2
5
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
6
=
−2u
34
a +
4
5
u
35
+ ··· + 2a +
3
5
−
2
5
u
35
a +
2
5
u
35
+ ··· +
8
5
a −
8
5
a
5
=
2
5
u
35
a +
2
5
u
35
+ ··· +
2
5
a +
1
5
−1
a
12
=
−0.600000au
35
− 3.68000u
35
+ ··· + 1.20000a − 2.56000
6
5
u
35
a −
2
5
u
35
+ ··· −
4
5
a +
2
5
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
35
−40u
33
+ 4u
32
+ 192u
31
−36u
30
−564u
29
+ 156u
28
+ 1092u
27
−412u
26
−1380u
25
+
712u
24
+ 980u
23
−792u
22
−16u
21
+ 480u
20
−732u
19
+ 16u
18
+ 680u
17
−280u
16
−112u
15
+
188u
14
−272u
13
+ 12u
12
+ 216u
11
−80u
10
+ 36u
8
−80u
7
+ 8u
6
+ 32u
5
−8u
4
+ 4u
3
−8u + 2
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
36
+ 19u
35
+ ··· + 2u + 1)
2
c
2
, c
4
, c
7
c
11
(u
36
− u
35
+ ··· − u
2
+ 1)
2
c
3
, c
12
25(25u
72
+ 245u
71
+ ··· + 2.03078 × 10
7
u + 8751347)
c
5
, c
6
, c
9
c
10
u
72
− 3u
71
+ ··· − 8u + 1
c
8
(u
36
− 3u
35
+ ··· − 22u + 5)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
36
− 3y
35
+ ··· + 2y + 1)
2
c
2
, c
4
, c
7
c
11
(y
36
− 19y
35
+ ··· − 2y + 1)
2
c
3
, c
12
625
· (625y
72
+ 21875y
71
+ ··· + 1173257570845272y + 76586074314409)
c
5
, c
6
, c
9
c
10
y
72
+ 47y
71
+ ··· + 16y + 1
c
8
(y
36
+ 25y
35
+ ··· − 154y + 25)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805609 + 0.585926I
a = 1.34736 + 0.54821I
b = −0.879869 − 0.290902I
2.49525 − 6.60899I 9.22618 + 6.99003I
u = 0.805609 + 0.585926I
a = −1.78646 + 0.60897I
b = 0.594572 − 1.095950I
2.49525 − 6.60899I 9.22618 + 6.99003I
u = 0.805609 − 0.585926I
a = 1.34736 − 0.54821I
b = −0.879869 + 0.290902I
2.49525 + 6.60899I 9.22618 − 6.99003I
u = 0.805609 − 0.585926I
a = −1.78646 − 0.60897I
b = 0.594572 + 1.095950I
2.49525 + 6.60899I 9.22618 − 6.99003I
u = −0.973666 + 0.342560I
a = 0.447907 + 0.107396I
b = −0.011489 + 1.238060I
−3.28987 + 3.75301I 4.00000 − 6.73664I
u = −0.973666 + 0.342560I
a = 1.28533 + 1.62124I
b = −0.381887 − 0.646554I
−3.28987 + 3.75301I 4.00000 − 6.73664I
u = −0.973666 − 0.342560I
a = 0.447907 − 0.107396I
b = −0.011489 − 1.238060I
−3.28987 − 3.75301I 4.00000 + 6.73664I
u = −0.973666 − 0.342560I
a = 1.28533 − 1.62124I
b = −0.381887 + 0.646554I
−3.28987 − 3.75301I 4.00000 + 6.73664I
u = −0.771553 + 0.550437I
a = −1.162210 − 0.407110I
b = 0.234332 + 0.882807I
−0.80333 + 2.21040I 6.18679 − 3.72055I
u = −0.771553 + 0.550437I
a = 0.386775 + 0.087230I
b = −0.335627 + 0.268806I
−0.80333 + 2.21040I 6.18679 − 3.72055I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.771553 − 0.550437I
a = −1.162210 + 0.407110I
b = 0.234332 − 0.882807I
−0.80333 − 2.21040I 6.18679 + 3.72055I
u = −0.771553 − 0.550437I
a = 0.386775 − 0.087230I
b = −0.335627 − 0.268806I
−0.80333 − 2.21040I 6.18679 + 3.72055I
u = 0.733643 + 0.592284I
a = −0.04384 + 1.44725I
b = −0.505467 − 0.969491I
2.70142 + 1.96554I 10.00564 − 0.22737I
u = 0.733643 + 0.592284I
a = −1.66783 − 0.73754I
b = 0.697085 − 0.342379I
2.70142 + 1.96554I 10.00564 − 0.22737I
u = 0.733643 − 0.592284I
a = −0.04384 − 1.44725I
b = −0.505467 + 0.969491I
2.70142 − 1.96554I 10.00564 + 0.22737I
u = 0.733643 − 0.592284I
a = −1.66783 + 0.73754I
b = 0.697085 + 0.342379I
2.70142 − 1.96554I 10.00564 + 0.22737I
u = 0.879174 + 0.103222I
a = 0.891367 − 0.781604I
b = −0.198899 − 1.224140I
−4.77876 − 0.27307I −2.50261 + 0.38004I
u = 0.879174 + 0.103222I
a = 1.81483 − 0.20231I
b = −0.386040 + 0.988207I
−4.77876 − 0.27307I −2.50261 + 0.38004I
u = 0.879174 − 0.103222I
a = 0.891367 + 0.781604I
b = −0.198899 + 1.224140I
−4.77876 + 0.27307I −2.50261 − 0.38004I
u = 0.879174 − 0.103222I
a = 1.81483 + 0.20231I
b = −0.386040 − 0.988207I
−4.77876 + 0.27307I −2.50261 − 0.38004I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.079360 + 0.331184I
a = 0.473951 + 0.743199I
b = 0.049864 + 1.153020I
−3.28987 + 3.70794I 4.00000 − 4.78665I
u = −1.079360 + 0.331184I
a = 0.28883 + 1.39170I
b = −0.226916 − 0.363024I
−3.28987 + 3.70794I 4.00000 − 4.78665I
u = −1.079360 − 0.331184I
a = 0.473951 − 0.743199I
b = 0.049864 − 1.153020I
−3.28987 − 3.70794I 4.00000 + 4.78665I
u = −1.079360 − 0.331184I
a = 0.28883 − 1.39170I
b = −0.226916 + 0.363024I
−3.28987 − 3.70794I 4.00000 + 4.78665I
u = 0.193860 + 0.787757I
a = −1.35011 − 0.68528I
b = 0.63317 + 1.34153I
−0.40442 + 7.72472I 7.24945 − 5.61903I
u = 0.193860 + 0.787757I
a = 1.54997 − 0.17570I
b = −1.130270 + 0.112171I
−0.40442 + 7.72472I 7.24945 − 5.61903I
u = 0.193860 − 0.787757I
a = −1.35011 + 0.68528I
b = 0.63317 − 1.34153I
−0.40442 − 7.72472I 7.24945 + 5.61903I
u = 0.193860 − 0.787757I
a = 1.54997 + 0.17570I
b = −1.130270 − 0.112171I
−0.40442 − 7.72472I 7.24945 + 5.61903I
u = 1.169940 + 0.367759I
a = −0.568021 − 0.939849I
b = −0.194502 − 1.387160I
−7.19868 − 0.64400I −1.19682 + 0.84878I
u = 1.169940 + 0.367759I
a = −0.308788 − 0.720856I
b = 0.802333 + 0.406586I
−7.19868 − 0.64400I −1.19682 + 0.84878I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.169940 − 0.367759I
a = −0.568021 + 0.939849I
b = −0.194502 + 1.387160I
−7.19868 + 0.64400I −1.19682 − 0.84878I
u = 1.169940 − 0.367759I
a = −0.308788 + 0.720856I
b = 0.802333 − 0.406586I
−7.19868 + 0.64400I −1.19682 − 0.84878I
u = −0.176866 + 0.751609I
a = −0.952710 + 0.470829I
b = 0.298605 − 1.284180I
−3.28987 − 2.99647I 4.00000 + 2.49060I
u = −0.176866 + 0.751609I
a = 1.328940 − 0.404023I
b = −0.769681 + 0.178507I
−3.28987 − 2.99647I 4.00000 + 2.49060I
u = −0.176866 − 0.751609I
a = −0.952710 − 0.470829I
b = 0.298605 + 1.284180I
−3.28987 + 2.99647I 4.00000 − 2.49060I
u = −0.176866 − 0.751609I
a = 1.328940 + 0.404023I
b = −0.769681 − 0.178507I
−3.28987 + 2.99647I 4.00000 − 2.49060I
u = 0.241156 + 0.725408I
a = −0.685379 − 0.494659I
b = −0.082118 + 0.888085I
0.618939 − 0.643996I 9.19682 + 0.84878I
u = 0.241156 + 0.725408I
a = −0.402951 + 0.714998I
b = 0.125392 + 0.204531I
0.618939 − 0.643996I 9.19682 + 0.84878I
u = 0.241156 − 0.725408I
a = −0.685379 + 0.494659I
b = −0.082118 − 0.888085I
0.618939 + 0.643996I 9.19682 − 0.84878I
u = 0.241156 − 0.725408I
a = −0.402951 − 0.714998I
b = 0.125392 − 0.204531I
0.618939 + 0.643996I 9.19682 − 0.84878I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.188280 + 0.342283I
a = −0.257826 + 0.747976I
b = 1.125280 − 0.027064I
−4.56945 − 4.07135I 2.11548 + 2.88119I
u = −1.188280 + 0.342283I
a = −0.422122 + 0.546791I
b = −0.54628 + 1.40974I
−4.56945 − 4.07135I 2.11548 + 2.88119I
u = −1.188280 − 0.342283I
a = −0.257826 − 0.747976I
b = 1.125280 + 0.027064I
−4.56945 + 4.07135I 2.11548 − 2.88119I
u = −1.188280 − 0.342283I
a = −0.422122 − 0.546791I
b = −0.54628 − 1.40974I
−4.56945 + 4.07135I 2.11548 − 2.88119I
u = −0.038116 + 0.743633I
a = 0.769766 + 0.614159I
b = −0.35364 − 1.45234I
−5.77640 − 2.21040I 1.81321 + 3.72055I
u = −0.038116 + 0.743633I
a = 1.55350 − 0.71846I
b = −0.659913 + 1.186540I
−5.77640 − 2.21040I 1.81321 + 3.72055I
u = −0.038116 − 0.743633I
a = 0.769766 − 0.614159I
b = −0.35364 + 1.45234I
−5.77640 + 2.21040I 1.81321 − 3.72055I
u = −0.038116 − 0.743633I
a = 1.55350 + 0.71846I
b = −0.659913 − 1.186540I
−5.77640 + 2.21040I 1.81321 − 3.72055I
u = 1.143830 + 0.521070I
a = 0.057559 + 0.543208I
b = 0.176175 + 0.122923I
−2.01029 − 4.07135I 5.88452 + 2.88119I
u = 1.143830 + 0.521070I
a = 1.70412 + 0.57551I
b = −0.104231 + 0.944623I
−2.01029 − 4.07135I 5.88452 + 2.88119I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.143830 − 0.521070I
a = 0.057559 − 0.543208I
b = 0.176175 − 0.122923I
−2.01029 + 4.07135I 5.88452 − 2.88119I
u = 1.143830 − 0.521070I
a = 1.70412 − 0.57551I
b = −0.104231 − 0.944623I
−2.01029 + 4.07135I 5.88452 − 2.88119I
u = 1.184710 + 0.434081I
a = 0.270936 − 0.001720I
b = 0.64951 + 1.30606I
−9.28116 − 1.96554I −2.00564 + 0.22737I
u = 1.184710 + 0.434081I
a = −1.66650 − 1.05864I
b = 0.46135 − 1.46236I
−9.28116 − 1.96554I −2.00564 + 0.22737I
u = 1.184710 − 0.434081I
a = 0.270936 + 0.001720I
b = 0.64951 − 1.30606I
−9.28116 + 1.96554I −2.00564 − 0.22737I
u = 1.184710 − 0.434081I
a = −1.66650 + 1.05864I
b = 0.46135 + 1.46236I
−9.28116 + 1.96554I −2.00564 − 0.22737I
u = −1.184420 + 0.463218I
a = 0.927533 − 0.364029I
b = 0.34103 − 1.54824I
−9.07499 + 6.60899I −1.22618 − 6.99003I
u = −1.184420 + 0.463218I
a = −1.85045 + 0.91774I
b = 0.77145 + 1.19452I
−9.07499 + 6.60899I −1.22618 − 6.99003I
u = −1.184420 − 0.463218I
a = 0.927533 + 0.364029I
b = 0.34103 + 1.54824I
−9.07499 − 6.60899I −1.22618 + 6.99003I
u = −1.184420 − 0.463218I
a = −1.85045 − 0.91774I
b = 0.77145 − 1.19452I
−9.07499 − 6.60899I −1.22618 + 6.99003I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.168380 + 0.513346I
a = −0.844950 + 0.649405I
b = 0.915189 + 0.166444I
−6.17532 + 7.72472I 0.75055 − 5.61903I
u = −1.168380 + 0.513346I
a = 1.85055 − 0.85235I
b = −0.367709 − 1.354240I
−6.17532 + 7.72472I 0.75055 − 5.61903I
u = −1.168380 − 0.513346I
a = −0.844950 − 0.649405I
b = 0.915189 − 0.166444I
−6.17532 − 7.72472I 0.75055 + 5.61903I
u = −1.168380 − 0.513346I
a = 1.85055 + 0.85235I
b = −0.367709 + 1.354240I
−6.17532 − 7.72472I 0.75055 + 5.61903I
u = 1.175040 + 0.526945I
a = −0.565080 − 1.163500I
b = 1.214090 + 0.120279I
−3.28987 − 12.60260I 4.00000 + 8.81146I
u = 1.175040 + 0.526945I
a = 2.03424 + 0.94384I
b = −0.68262 + 1.38913I
−3.28987 − 12.60260I 4.00000 + 8.81146I
u = 1.175040 − 0.526945I
a = −0.565080 + 1.163500I
b = 1.214090 − 0.120279I
−3.28987 + 12.60260I 4.00000 − 8.81146I
u = 1.175040 − 0.526945I
a = 2.03424 − 0.94384I
b = −0.68262 − 1.38913I
−3.28987 + 12.60260I 4.00000 − 8.81146I
u = −0.446315 + 0.412227I
a = −5.77405 − 3.06455I
b = 0.091090 + 1.080300I
−1.80097 − 0.27307I 10.50261 + 0.38004I
u = −0.446315 + 0.412227I
a = −2.07421 + 6.71218I
b = 0.136632 − 0.945269I
−1.80097 − 0.27307I 10.50261 + 0.38004I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.446315 − 0.412227I
a = −5.77405 + 3.06455I
b = 0.091090 − 1.080300I
−1.80097 + 0.27307I 10.50261 − 0.38004I
u = −0.446315 − 0.412227I
a = −2.07421 − 6.71218I
b = 0.136632 + 0.945269I
−1.80097 + 0.27307I 10.50261 − 0.38004I
20
III. I
u
3
= hb − 1, −u
3
+ 4u
2
+ 4a − 2, u
4
− 2u
2
+ 2i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
1
4
u
3
− u
2
+
1
2
1
a
4
=
−
1
8
u
3
−
1
2
u
2
−
1
4
u
−
1
2
u
3
+
1
2
u +
1
2
a
11
=
1
4
u
3
− u
2
+
3
2
1
a
1
=
u
3
u
3
− u
a
9
=
−1
0
a
6
=
1
4
u
3
− u
2
+
5
2
1
a
5
=
1
4
u
3
− u
2
+
3
2
1
a
12
=
3
8
u
3
−
1
2
u
2
+
1
4
u +
3
2
1
2
u
3
−
1
2
u +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
+ 4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− 2u + 2)
2
c
2
, c
7
u
4
− 2u
2
+ 2
c
3
16(16u
4
+ 32u
3
+ 32u
2
+ 16u + 5)
c
4
, c
9
, c
10
(u + 1)
4
c
5
, c
6
, c
11
(u − 1)
4
c
8
u
4
+ 2u
2
+ 2
c
12
16(16u
4
− 32u
3
+ 32u
2
− 16u + 5)
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ 4)
2
c
2
, c
7
(y
2
− 2y + 2)
2
c
3
, c
12
256(256y
4
+ 160y
2
+ 64y + 25)
c
4
, c
5
, c
6
c
9
, c
10
, c
11
(y −1)
4
c
8
(y
2
+ 2y + 2)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098680 + 0.455090I
a = −0.339101 − 0.611557I
b = 1.00000
0.82247 − 3.66386I 8.00000 + 4.00000I
u = 1.098680 − 0.455090I
a = −0.339101 + 0.611557I
b = 1.00000
0.82247 + 3.66386I 8.00000 − 4.00000I
u = −1.098680 + 0.455090I
a = −0.66090 + 1.38844I
b = 1.00000
0.82247 + 3.66386I 8.00000 − 4.00000I
u = −1.098680 − 0.455090I
a = −0.66090 − 1.38844I
b = 1.00000
0.82247 − 3.66386I 8.00000 + 4.00000I
24
IV. I
v
1
= ha, b + 1, 2v + 1i
(i) Arc colorings
a
2
=
−0.5
0
a
7
=
1
0
a
8
=
1
0
a
3
=
−0.5
0
a
10
=
0
−1
a
4
=
−0.5
0.5
a
11
=
−1
−1
a
1
=
−0.5
0
a
9
=
1
0
a
6
=
2
1
a
5
=
1
1
a
12
=
−1.5
−0.5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
c
3
2(2u − 1)
c
4
, c
9
, c
10
u − 1
c
5
, c
6
, c
11
u + 1
c
12
2(2u + 1)
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
c
3
, c
12
4(4y −1)
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y −1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000
a = 0
b = −1.00000
3.28987 12.0000
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− 2u + 2)
2
(u
36
+ 19u
35
+ ··· + 2u + 1)
2
· (u
44
+ 23u
43
+ ··· + 272u + 64)
c
2
, c
7
u(u
4
− 2u
2
+ 2)(u
36
− u
35
+ ··· − u
2
+ 1)
2
(u
44
+ 3u
43
+ ··· + 12u + 8)
c
3
102400(2u − 1)(16u
4
+ 32u
3
+ 32u
2
+ 16u + 5)
· (128u
44
+ 64u
43
+ ··· − 11u − 1)
· (25u
72
+ 245u
71
+ ··· + 20307804u + 8751347)
c
4
(u − 1)(u + 1)
4
(u
36
− u
35
+ ··· − u
2
+ 1)
2
· (u
44
− 13u
42
+ ··· + 647u − 416)
c
5
, c
6
((u − 1)
4
)(u + 1)(u
44
+ u
43
+ ··· − 16u − 5)(u
72
− 3u
71
+ ··· − 8u + 1)
c
8
u(u
4
+ 2u
2
+ 2)(u
36
− 3u
35
+ ··· − 22u + 5)
2
· (u
44
+ 9u
43
+ ··· + 42988u + 25384)
c
9
, c
10
(u − 1)(u + 1)
4
(u
44
+ u
43
+ ··· − 16u − 5)(u
72
− 3u
71
+ ··· − 8u + 1)
c
11
((u − 1)
4
)(u + 1)(u
36
− u
35
+ ··· − u
2
+ 1)
2
· (u
44
− 13u
42
+ ··· + 647u − 416)
c
12
102400(2u + 1)(16u
4
− 32u
3
+ 32u
2
− 16u + 5)
· (128u
44
+ 64u
43
+ ··· − 11u − 1)
· (25u
72
+ 245u
71
+ ··· + 20307804u + 8751347)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ 4)
2
(y
36
− 3y
35
+ ··· + 2y + 1)
2
· (y
44
− 3y
43
+ ··· − 12544y + 4096)
c
2
, c
7
y(y
2
− 2y + 2)
2
(y
36
− 19y
35
+ ··· − 2y + 1)
2
· (y
44
− 23y
43
+ ··· − 272y + 64)
c
3
, c
12
10485760000(4y −1)(256y
4
+ 160y
2
+ 64y + 25)
· (16384y
44
+ 151552y
43
+ ··· − 55y + 1)
· (625y
72
+ 21875y
71
+ ··· + 1173257570845272y + 76586074314409)
c
4
, c
11
((y −1)
5
)(y
36
− 19y
35
+ ··· − 2y + 1)
2
· (y
44
− 26y
43
+ ··· − 5622769y + 173056)
c
5
, c
6
, c
9
c
10
((y −1)
5
)(y
44
+ 17y
43
+ ··· − 146y + 25)(y
72
+ 47y
71
+ ··· + 16y + 1)
c
8
y(y
2
+ 2y + 2)
2
(y
36
+ 25y
35
+ ··· − 154y + 25)
2
· (y
44
+ 29y
43
+ ··· − 8202497168y + 644347456)
30
