12a
0400
(K12a
0400
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 1 12 4 7 5 8 10
Solving Sequence
8,11 5,12
4 9 3 7 10 1 6 2
c
11
c
4
c
8
c
3
c
7
c
10
c
12
c
6
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h26679u
42
+ 790144u
41
+ ··· + 8192b + 610828288,
10603u
42
+ 301637u
41
+ ··· + 8192a + 19992576, u
43
+ 30u
42
+ ··· + 385024u + 16384i
I
u
2
= h−8.60222 × 10
37
a
27
u
2
− 3.77941 × 10
39
a
26
u
2
+ ··· − 2.58200 × 10
42
a − 7.32442 × 10
41
,
2a
27
u
2
− 7a
26
u
2
+ ··· + 3296a + 2157, u
3
− u
2
+ 2u − 1i
I
u
3
= h−9u
25
+ 6u
24
+ ··· + b − 9, 18u
25
− 24u
24
+ ··· + a + 8, u
26
− u
25
+ ··· + u + 1i
* 3 irreducible components of dim
C
= 0, with total 153 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
= h2.67 × 10
4
u
42
+ 7.90 × 10
5
u
41
+ · · · + 8192b + 6.11 × 10
8
, 1.06 × 10
4
u
42
+
3.02 × 10
5
u
41
+ · · · + 8192a + 2.00 × 10
7
, u
43
+ 30u
42
+ · · · + 385024u + 16384i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
5
=
−1.29431u
42
− 36.8209u
41
+ ··· − 81825.5u − 2440.50
−3.25671u
42
− 96.4531u
41
+ ··· − 1.67525 × 10
6
u − 74564
a
12
=
1
u
2
a
4
=
−4.55103u
42
− 133.274u
41
+ ··· − 1757075u − 77004.5
−3.25671u
42
− 96.4531u
41
+ ··· − 1.67525 × 10
6
u − 74564
a
9
=
0.499939u
42
+ 14.4927u
41
+ ··· + 183273.u + 8147
0.505493u
42
+ 14.6592u
41
+ ··· + 184343.u + 8191
a
3
=
−6.94025u
42
− 203.805u
41
+ ··· − 3.09936 × 10
6
u − 137933
−3.15442u
42
− 92.8909u
41
+ ··· − 1.35488 × 10
6
u − 60351
a
7
=
u
u
3
+ u
a
10
=
91
16384
u
42
+
341
2048
u
41
+ ··· +
4275
4
u + 45
−0.505493u
42
− 14.6592u
41
+ ··· − 184342.u − 8191
a
1
=
0.237915u
42
+ 6.90613u
41
+ ··· + 93291.5u + 4151.50
−1.75134u
42
− 51.0520u
41
+ ··· − 736163.u − 32898
a
6
=
3.88507u
42
+ 113.576u
41
+ ··· + 1.71937 × 10
6
u + 76981
0.272095u
42
+ 7.25439u
41
+ ··· − 251149.u − 12291
a
2
=
3.28180u
42
+ 97.8960u
41
+ ··· + 2709292u + 125155.
−2.14587u
42
− 61.9363u
41
+ ··· − 531596u − 22175
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
53359
2048
u
42
−
97463
128
u
41
+ ··· − 12484440u − 560338
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
43
+ 21u
42
+ ··· + 224u + 64
c
2
, c
5
u
43
+ 9u
42
+ ··· + 80u + 8
c
3
, c
4
, c
8
c
10
u
43
+ 18u
41
+ ··· + 2u + 1
c
6
u
43
+ 30u
42
+ ··· + 41536u + 3032
c
7
, c
11
u
43
+ 30u
42
+ ··· + 385024u + 16384
c
9
, c
12
u
43
+ 2u
42
+ ··· + 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
43
+ 3y
42
+ ··· + 39424y −4096
c
2
, c
5
y
43
− 21y
42
+ ··· + 224y −64
c
3
, c
4
, c
8
c
10
y
43
+ 36y
42
+ ··· + 4y −1
c
6
y
43
+ 18y
42
+ ··· + 78220512y −9193024
c
7
, c
11
y
43
+ 30y
42
+ ··· + 2751463424y −268435456
c
9
, c
12
y
43
+ 42y
41
+ ··· + 24y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.141174 + 0.991391I
a = −0.085886 + 0.903257I
b = 0.563509 − 0.402868I
0.045461 − 1.350040I 0
u = −0.141174 − 0.991391I
a = −0.085886 − 0.903257I
b = 0.563509 + 0.402868I
0.045461 + 1.350040I 0
u = −0.321326 + 0.968331I
a = 0.229246 − 0.655333I
b = −0.571811 + 0.178496I
1.45520 + 2.49719I 0
u = −0.321326 − 0.968331I
a = 0.229246 + 0.655333I
b = −0.571811 − 0.178496I
1.45520 − 2.49719I 0
u = −0.628507 + 0.854269I
a = 0.386710 + 0.186990I
b = −0.037084 − 0.487628I
−1.18844 + 2.49867I 0
u = −0.628507 − 0.854269I
a = 0.386710 − 0.186990I
b = −0.037084 + 0.487628I
−1.18844 − 2.49867I 0
u = −0.440030 + 1.016850I
a = 0.487011 − 0.449150I
b = −0.623560 − 0.104987I
0.70092 + 3.36027I 0
u = −0.440030 − 1.016850I
a = 0.487011 + 0.449150I
b = −0.623560 + 0.104987I
0.70092 − 3.36027I 0
u = −0.524536 + 1.018160I
a = −0.595872 + 0.207373I
b = 0.538712 + 0.351178I
−2.68991 + 0.53318I 0
u = −0.524536 − 1.018160I
a = −0.595872 − 0.207373I
b = 0.538712 − 0.351178I
−2.68991 − 0.53318I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.459036 + 1.056680I
a = −0.629338 + 0.454727I
b = 0.728720 + 0.191735I
−1.61281 + 7.80728I 0
u = −0.459036 − 1.056680I
a = −0.629338 − 0.454727I
b = 0.728720 − 0.191735I
−1.61281 − 7.80728I 0
u = −0.727722 + 0.345230I
a = −0.390881 − 0.271091I
b = −0.643766 + 0.587315I
−4.62705 + 4.05996I 0
u = −0.727722 − 0.345230I
a = −0.390881 + 0.271091I
b = −0.643766 − 0.587315I
−4.62705 − 4.05996I 0
u = −1.248100 + 0.323970I
a = 0.171912 + 0.390499I
b = 0.331711 − 1.306820I
1.77506 + 12.52070I 0
u = −1.248100 − 0.323970I
a = 0.171912 − 0.390499I
b = 0.331711 + 1.306820I
1.77506 − 12.52070I 0
u = −0.664252 + 0.222668I
a = −0.449126 − 0.203576I
b = −0.759214 + 0.398613I
−4.00770 − 3.63985I 0
u = −0.664252 − 0.222668I
a = −0.449126 + 0.203576I
b = −0.759214 − 0.398613I
−4.00770 + 3.63985I 0
u = −1.238890 + 0.500023I
a = 0.239069 + 0.432482I
b = 0.279145 − 1.158180I
−1.23780 + 4.03638I 0
u = −1.238890 − 0.500023I
a = 0.239069 − 0.432482I
b = 0.279145 + 1.158180I
−1.23780 − 4.03638I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.584884 + 0.309875I
a = 0.479239 + 0.287501I
b = 0.594121 − 0.396160I
−1.33046 + 0.54618I 0
u = −0.584884 − 0.309875I
a = 0.479239 − 0.287501I
b = 0.594121 + 0.396160I
−1.33046 − 0.54618I 0
u = −1.297050 + 0.349750I
a = −0.170490 − 0.416255I
b = −0.280409 + 1.286670I
4.20709 + 7.07734I 0
u = −1.297050 − 0.349750I
a = −0.170490 + 0.416255I
b = −0.280409 − 1.286670I
4.20709 − 7.07734I 0
u = −0.48161 + 1.51978I
a = −0.47157 − 1.60413I
b = −0.56874 + 1.55957I
7.6153 + 18.5782I 0
u = −0.48161 − 1.51978I
a = −0.47157 + 1.60413I
b = −0.56874 − 1.55957I
7.6153 − 18.5782I 0
u = −0.48644 + 1.53140I
a = 0.47480 + 1.56961I
b = 0.54001 − 1.53934I
10.1557 + 13.2774I 0
u = −0.48644 − 1.53140I
a = 0.47480 − 1.56961I
b = 0.54001 + 1.53934I
10.1557 − 13.2774I 0
u = −0.46452 + 1.54696I
a = −0.41321 − 1.54612I
b = −0.56187 + 1.47570I
5.11499 + 10.03670I 0
u = −0.46452 − 1.54696I
a = −0.41321 + 1.54612I
b = −0.56187 − 1.47570I
5.11499 − 10.03670I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.52604 + 1.57157I
a = 0.51299 + 1.44640I
b = 0.42087 − 1.49118I
12.6114 + 10.3447I 0
u = −0.52604 − 1.57157I
a = 0.51299 − 1.44640I
b = 0.42087 + 1.49118I
12.6114 − 10.3447I 0
u = −0.315713
a = 0.975950
b = 0.450279
−0.825361 −12.5660
u = −0.55239 + 1.60470I
a = −0.51074 − 1.37094I
b = −0.36428 + 1.44514I
12.24020 + 4.85185I 0
u = −0.55239 − 1.60470I
a = −0.51074 + 1.37094I
b = −0.36428 − 1.44514I
12.24020 − 4.85185I 0
u = −1.72863 + 0.24263I
a = −0.072616 − 0.550295I
b = −0.064060 + 1.260030I
6.56444 + 3.14469I 0
u = −1.72863 − 0.24263I
a = −0.072616 + 0.550295I
b = −0.064060 − 1.260030I
6.56444 − 3.14469I 0
u = −1.12384 + 1.56359I
a = 0.462489 + 0.868585I
b = 0.066274 − 1.206250I
4.68041 − 4.47850I 0
u = −1.12384 − 1.56359I
a = 0.462489 − 0.868585I
b = 0.066274 + 1.206250I
4.68041 + 4.47850I 0
u = −0.27940 + 1.95370I
a = 0.225940 + 1.207500I
b = 0.355651 − 1.108640I
2.46971 + 6.73678I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27940 − 1.95370I
a = 0.225940 − 1.207500I
b = 0.355651 + 1.108640I
2.46971 − 6.73678I 0
u = −0.92378 + 1.94706I
a = −0.367644 − 1.032200I
b = −0.169059 + 1.200010I
7.51100 + 1.64842I 0
u = −0.92378 − 1.94706I
a = −0.367644 + 1.032200I
b = −0.169059 − 1.200010I
7.51100 − 1.64842I 0
9
II. I
u
2
= h−8.60 × 10
37
a
27
u
2
− 3.78 × 10
39
a
26
u
2
+ · · · − 2.58 × 10
42
a − 7.32 ×
10
41
, 2a
27
u
2
− 7a
26
u
2
+ · · · + 3296a + 2157, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
5
=
a
0.0000696629a
27
u
2
+ 0.00306066a
26
u
2
+ ··· + 2.09097a + 0.593150
a
12
=
1
u
2
a
4
=
0.0000696629a
27
u
2
+ 0.00306066a
26
u
2
+ ··· + 3.09097a + 0.593150
0.0000696629a
27
u
2
+ 0.00306066a
26
u
2
+ ··· + 2.09097a + 0.593150
a
9
=
−0.00358219a
27
u
2
− 0.00427447a
26
u
2
+ ··· − 0.386814a + 1.56523
−0.00191659a
27
u
2
− 0.00286074a
26
u
2
+ ··· − 0.253071a + 1.66181
a
3
=
−0.00248453a
27
u
2
− 0.00893272a
26
u
2
+ ··· − 13.7006a − 5.06251
−0.00102338a
27
u
2
− 0.00267878a
26
u
2
+ ··· − 5.92254a − 1.61674
a
7
=
u
u
2
− u + 1
a
10
=
−0.00279023a
27
u
2
− 0.00308918a
26
u
2
+ ··· − 0.197048a + 1.19803
−0.000791967a
27
u
2
− 0.00118528a
26
u
2
+ ··· − 0.189767a + 1.56720
a
1
=
0.000696726a
27
u
2
+ 0.00438385a
26
u
2
+ ··· + 4.36618a + 1.76693
0.000391131a
27
u
2
+ 0.00109796a
26
u
2
+ ··· + 1.67363a − 0.773644
a
6
=
−0.00166864a
27
u
2
− 0.000705943a
26
u
2
+ ··· + 2.78062a + 2.34278
−0.00299725a
27
u
2
− 0.00401772a
26
u
2
+ ··· − 7.95573a − 0.515825
a
2
=
−0.00243342a
27
u
2
− 0.00342678a
26
u
2
+ ··· − 7.31203a − 2.87622
−0.00273069a
27
u
2
− 0.00362666a
26
u
2
+ ··· − 2.76642a − 2.34768
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00519361a
27
u
2
− 0.00202993a
26
u
2
+ ··· − 11.2433a − 10.9384
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
14
+ 7u
13
+ ··· + u + 1)
6
c
2
, c
5
(u
14
− u
13
+ ··· − u + 1)
6
c
3
, c
4
, c
8
c
10
u
84
− u
83
+ ··· − 1050404u + 428849
c
6
(u
14
− 3u
13
+ ··· − 7u + 3)
6
c
7
, c
11
(u
3
− u
2
+ 2u − 1)
28
c
9
, c
12
u
84
+ 15u
83
+ ··· + 36868u + 1913
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
14
+ y
13
+ ··· + 7y + 1)
6
c
2
, c
5
(y
14
− 7y
13
+ ··· − y + 1)
6
c
3
, c
4
, c
8
c
10
y
84
+ 75y
83
+ ··· − 72738646416y + 183911464801
c
6
(y
14
+ 5y
13
+ ··· + 23y + 9)
6
c
7
, c
11
(y
3
+ 3y
2
+ 2y − 1)
28
c
9
, c
12
y
84
− 17y
83
+ ··· − 49043376y + 3659569
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.446492 + 0.770300I
b = 0.361715 − 0.283323I
1.89472 + 5.70311I −3.21373 − 3.20086I
u = 0.215080 + 1.307140I
a = −0.153256 + 1.260880I
b = −0.96681 − 1.26598I
6.26422 − 1.42329I −1.99952 + 2.44997I
u = 0.215080 + 1.307140I
a = 0.592822 + 0.277460I
b = −1.57401 − 0.22276I
1.89472 − 11.35940I −3.21373 + 9.15975I
u = 0.215080 + 1.307140I
a = −0.341553 − 0.529574I
b = −0.524254 + 0.160677I
4.44645 + 0.80067I −0.156420 + 0.347190I
u = 0.215080 + 1.307140I
a = 0.976934 − 0.984828I
b = 0.357506 + 0.990276I
6.26422 − 4.23296I −1.99952 + 3.50893I
u = 0.215080 + 1.307140I
a = −0.480742 − 0.271257I
b = 1.46331 + 0.24708I
4.44645 − 6.45691I −0.15642 + 5.61170I
u = 0.215080 + 1.307140I
a = −0.070671 + 0.534043I
b = 0.830538 − 0.324322I
0.13266 − 2.35757I −5.81854 + 3.16294I
u = 0.215080 + 1.307140I
a = −0.29601 + 1.46533I
b = 0.462719 − 1.161180I
1.89472 + 5.70311I −3.21373 − 3.20086I
u = 0.215080 + 1.307140I
a = 0.487475 + 0.072695I
b = −1.412770 − 0.055883I
0.13266 − 3.29867I −5.81854 + 2.79596I
u = 0.215080 + 1.307140I
a = −0.054488 − 0.440320I
b = 1.107410 + 0.500106I
6.51855 − 5.01941I 0.74894 + 6.83663I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.376117 + 0.161014I
b = −0.698326 − 0.355577I
6.51855 − 0.63684I 0.748943 − 0.877732I
u = 0.215080 + 1.307140I
a = −0.07193 + 1.61908I
b = −1.00243 − 1.65746I
7.39513 − 7.89997I 1.18128 + 9.31071I
u = 0.215080 + 1.307140I
a = 0.24055 − 1.62126I
b = −0.295982 + 1.211070I
4.44645 + 0.80067I −0.156420 + 0.347190I
u = 0.215080 + 1.307140I
a = 0.19759 − 1.66051I
b = 0.84511 + 1.67738I
9.32158 − 3.45671I 5.82626 + 4.40196I
u = 0.215080 + 1.307140I
a = 0.02908 + 1.69675I
b = 0.110703 − 1.038360I
0.13266 − 2.35757I −5.81854 + 3.16294I
u = 0.215080 + 1.307140I
a = 0.33218 − 1.81648I
b = 0.61182 + 1.81822I
9.32158 − 2.19954I 5.82626 + 1.55694I
u = 0.215080 + 1.307140I
a = 1.35231 − 1.31410I
b = 0.150003 + 1.159650I
7.39513 + 2.24373I 1.18128 − 3.35182I
u = 0.215080 + 1.307140I
a = −1.22854 + 1.46718I
b = −0.200764 − 1.234310I
9.32158 − 2.19954I 5.82626 + 1.55694I
u = 0.215080 + 1.307140I
a = −0.35716 + 1.90012I
b = −0.52500 − 1.93052I
7.39513 + 2.24373I 1.18128 − 3.35182I
u = 0.215080 + 1.307140I
a = −0.50155 + 1.89040I
b = −0.27989 − 1.74547I
6.26422 − 4.23296I −1.99952 + 3.50893I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.37367 − 1.92287I
b = −0.02323 + 1.44630I
6.51855 − 0.63684I 0
u = 0.215080 + 1.307140I
a = −1.15079 + 1.79049I
b = −0.202204 − 1.366590I
9.32158 − 3.45671I 0
u = 0.215080 + 1.307140I
a = −0.35992 + 2.15275I
b = −0.148313 − 1.389180I
6.51855 − 5.01941I 0
u = 0.215080 + 1.307140I
a = 0.82724 − 2.03016I
b = 0.23424 + 1.46518I
6.26422 − 1.42329I 0
u = 0.215080 + 1.307140I
a = −0.00621 − 2.25135I
b = 0.220990 + 1.205880I
0.13266 − 3.29867I 0
u = 0.215080 + 1.307140I
a = 1.17653 − 1.95613I
b = 0.18091 + 1.41259I
7.39513 − 7.89997I 0
u = 0.215080 + 1.307140I
a = −0.12046 + 2.33883I
b = −0.242929 − 1.279150I
4.44645 − 6.45691I 0
u = 0.215080 + 1.307140I
a = 0.07631 − 2.41590I
b = 0.282528 + 1.270790I
1.89472 − 11.35940I 0
u = 0.215080 − 1.307140I
a = 0.446492 − 0.770300I
b = 0.361715 + 0.283323I
1.89472 − 5.70311I −3.21373 + 3.20086I
u = 0.215080 − 1.307140I
a = −0.153256 − 1.260880I
b = −0.96681 + 1.26598I
6.26422 + 1.42329I −1.99952 − 2.44997I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 − 1.307140I
a = 0.592822 − 0.277460I
b = −1.57401 + 0.22276I
1.89472 + 11.35940I −3.21373 − 9.15975I
u = 0.215080 − 1.307140I
a = −0.341553 + 0.529574I
b = −0.524254 − 0.160677I
4.44645 − 0.80067I −0.156420 − 0.347190I
u = 0.215080 − 1.307140I
a = 0.976934 + 0.984828I
b = 0.357506 − 0.990276I
6.26422 + 4.23296I −1.99952 − 3.50893I
u = 0.215080 − 1.307140I
a = −0.480742 + 0.271257I
b = 1.46331 − 0.24708I
4.44645 + 6.45691I −0.15642 − 5.61170I
u = 0.215080 − 1.307140I
a = −0.070671 − 0.534043I
b = 0.830538 + 0.324322I
0.13266 + 2.35757I −5.81854 − 3.16294I
u = 0.215080 − 1.307140I
a = −0.29601 − 1.46533I
b = 0.462719 + 1.161180I
1.89472 − 5.70311I −3.21373 + 3.20086I
u = 0.215080 − 1.307140I
a = 0.487475 − 0.072695I
b = −1.412770 + 0.055883I
0.13266 + 3.29867I −5.81854 − 2.79596I
u = 0.215080 − 1.307140I
a = −0.054488 + 0.440320I
b = 1.107410 − 0.500106I
6.51855 + 5.01941I 0.74894 − 6.83663I
u = 0.215080 − 1.307140I
a = −0.376117 − 0.161014I
b = −0.698326 + 0.355577I
6.51855 + 0.63684I 0.748943 + 0.877732I
u = 0.215080 − 1.307140I
a = −0.07193 − 1.61908I
b = −1.00243 + 1.65746I
7.39513 + 7.89997I 1.18128 − 9.31071I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 − 1.307140I
a = 0.24055 + 1.62126I
b = −0.295982 − 1.211070I
4.44645 − 0.80067I −0.156420 − 0.347190I
u = 0.215080 − 1.307140I
a = 0.19759 + 1.66051I
b = 0.84511 − 1.67738I
9.32158 + 3.45671I 5.82626 − 4.40196I
u = 0.215080 − 1.307140I
a = 0.02908 − 1.69675I
b = 0.110703 + 1.038360I
0.13266 + 2.35757I −5.81854 − 3.16294I
u = 0.215080 − 1.307140I
a = 0.33218 + 1.81648I
b = 0.61182 − 1.81822I
9.32158 + 2.19954I 5.82626 − 1.55694I
u = 0.215080 − 1.307140I
a = 1.35231 + 1.31410I
b = 0.150003 − 1.159650I
7.39513 − 2.24373I 1.18128 + 3.35182I
u = 0.215080 − 1.307140I
a = −1.22854 − 1.46718I
b = −0.200764 + 1.234310I
9.32158 + 2.19954I 5.82626 − 1.55694I
u = 0.215080 − 1.307140I
a = −0.35716 − 1.90012I
b = −0.52500 + 1.93052I
7.39513 − 2.24373I 1.18128 + 3.35182I
u = 0.215080 − 1.307140I
a = −0.50155 − 1.89040I
b = −0.27989 + 1.74547I
6.26422 + 4.23296I −1.99952 − 3.50893I
u = 0.215080 − 1.307140I
a = 0.37367 + 1.92287I
b = −0.02323 − 1.44630I
6.51855 + 0.63684I 0
u = 0.215080 − 1.307140I
a = −1.15079 − 1.79049I
b = −0.202204 + 1.366590I
9.32158 + 3.45671I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 − 1.307140I
a = −0.35992 − 2.15275I
b = −0.148313 + 1.389180I
6.51855 + 5.01941I 0
u = 0.215080 − 1.307140I
a = 0.82724 + 2.03016I
b = 0.23424 − 1.46518I
6.26422 + 1.42329I 0
u = 0.215080 − 1.307140I
a = −0.00621 + 2.25135I
b = 0.220990 − 1.205880I
0.13266 + 3.29867I 0
u = 0.215080 − 1.307140I
a = 1.17653 + 1.95613I
b = 0.18091 − 1.41259I
7.39513 + 7.89997I 0
u = 0.215080 − 1.307140I
a = −0.12046 − 2.33883I
b = −0.242929 + 1.279150I
4.44645 + 6.45691I 0
u = 0.215080 − 1.307140I
a = 0.07631 + 2.41590I
b = 0.282528 − 1.270790I
1.89472 + 11.35940I 0
u = 0.569840
a = −0.808428 + 0.692390I
b = 0.12559 + 1.44322I
3.25754 + 5.07185I −5.34798 − 6.33126I
u = 0.569840
a = −0.808428 − 0.692390I
b = 0.12559 − 1.44322I
3.25754 − 5.07185I −5.34798 + 6.33126I
u = 0.569840
a = 0.670591 + 0.828888I
b = −0.165610 + 1.371160I
5.18400 − 0.62859I −0.70300 + 1.42251I
u = 0.569840
a = 0.670591 − 0.828888I
b = −0.165610 − 1.371160I
5.18400 + 0.62859I −0.70300 − 1.42251I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569840
a = 0.297525 + 0.697087I
b = 0.156597 − 1.056340I
2.38096 + 2.19128I −5.78032 − 3.85718I
u = 0.569840
a = 0.297525 − 0.697087I
b = 0.156597 + 1.056340I
2.38096 − 2.19128I −5.78032 + 3.85718I
u = 0.569840
a = 0.679371 + 1.079220I
b = 0.499832 − 0.974163I
0.30887 + 3.62879I −6.68569 − 2.63226I
u = 0.569840
a = 0.679371 − 1.079220I
b = 0.499832 + 0.974163I
0.30887 − 3.62879I −6.68569 + 2.63226I
u = 0.569840
a = 0.578384 + 1.152540I
b = −0.287758 + 1.253680I
5.18400 + 0.62859I −0.70300 − 1.42251I
u = 0.569840
a = 0.578384 − 1.152540I
b = −0.287758 − 1.253680I
5.18400 − 0.62859I −0.70300 + 1.42251I
u = 0.569840
a = −0.791512 + 1.118030I
b = −0.581483 − 1.011450I
−2.24286 − 8.53123I −9.74299 + 6.18031I
u = 0.569840
a = −0.791512 − 1.118030I
b = −0.581483 + 1.011450I
−2.24286 + 8.53123I −9.74299 − 6.18031I
u = 0.569840
a = −0.502487 + 0.301443I
b = −0.010694 + 1.353720I
2.12664 − 1.40484I −8.52878 + 0.52948I
u = 0.569840
a = −0.502487 − 0.301443I
b = −0.010694 − 1.353720I
2.12664 + 1.40484I −8.52878 − 0.52948I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569840
a = −0.61948 + 1.27674I
b = −0.570092 − 0.821363I
−4.00492 − 0.47055I −12.34780 − 0.18349I
u = 0.569840
a = −0.61948 − 1.27674I
b = −0.570092 + 0.821363I
−4.00492 + 0.47055I −12.34780 + 0.18349I
u = 0.569840
a = −0.60950 + 1.31572I
b = 0.389110 + 1.216960I
3.25754 − 5.07185I −5.34798 + 6.33126I
u = 0.569840
a = −0.60950 − 1.31572I
b = 0.389110 − 1.216960I
3.25754 + 5.07185I −5.34798 − 6.33126I
u = 0.569840
a = −0.27366 + 1.43244I
b = 0.292431 + 0.943180I
2.12664 + 1.40484I −8.52878 − 0.52948I
u = 0.569840
a = −0.27366 − 1.43244I
b = 0.292431 − 0.943180I
2.12664 − 1.40484I −8.52878 + 0.52948I
u = 0.569840
a = −0.01603 + 1.64904I
b = −0.258777 + 0.204719I
2.38096 + 2.19128I −5.78032 − 3.85718I
u = 0.569840
a = −0.01603 − 1.64904I
b = −0.258777 − 0.204719I
2.38096 − 2.19128I −5.78032 + 3.85718I
u = 0.569840
a = 0.32258 + 1.70088I
b = 0.677865 − 0.259490I
−4.00492 − 0.47055I −12.34780 − 0.18349I
u = 0.569840
a = 0.32258 − 1.70088I
b = 0.677865 + 0.259490I
−4.00492 + 0.47055I −12.34780 + 0.18349I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569840
a = −0.20519 + 1.76940I
b = −0.671957 − 0.059864I
0.30887 + 3.62879I −6.68569 − 2.63226I
u = 0.569840
a = −0.20519 − 1.76940I
b = −0.671957 + 0.059864I
0.30887 − 3.62879I −6.68569 + 2.63226I
u = 0.569840
a = 0.23804 + 1.83570I
b = 0.782388 − 0.060736I
−2.24286 − 8.53123I −9.74299 + 6.18031I
u = 0.569840
a = 0.23804 − 1.83570I
b = 0.782388 + 0.060736I
−2.24286 + 8.53123I −9.74299 − 6.18031I
21
III.
I
u
3
= h−9u
25
+6u
24
+· · ·+b−9, 18u
25
−24u
24
+· · ·+a+8, u
26
−u
25
+· · ·+u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
5
=
−18u
25
+ 24u
24
+ ··· − 20u − 8
9u
25
− 6u
24
+ ··· + 10u + 9
a
12
=
1
u
2
a
4
=
−9u
25
+ 18u
24
+ ··· − 10u + 1
9u
25
− 6u
24
+ ··· + 10u + 9
a
9
=
−u
25
+ 2u
24
+ ··· − 6u + 1
u
25
− u
24
+ ··· + 3u + 1
a
3
=
−8u
25
+ 6u
24
+ ··· − 20u − 11
−5u
25
+ 15u
24
+ ··· − 3u + 17
a
7
=
u
u
3
+ u
a
10
=
−2u
25
+ 3u
24
+ ··· − 8u + 1
u
25
− u
24
+ ··· + 2u + 1
a
1
=
4u
25
− 4u
24
+ ··· + 8u
2
+ 12u
−u
25
− u
24
+ ··· − 5u − 3
a
6
=
4u
25
− 16u
24
+ ··· + u − 15
−10u
25
+ 11u
24
+ ··· − 9u + 1
a
2
=
−5u
25
+ 4u
24
+ ··· + 7u − 4
−3u
25
+ 11u
24
+ ··· + 9u
2
− 9u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 18u
25
− 73u
24
+ 304u
23
− 889u
22
+ 2011u
21
− 4662u
20
+ 7114u
19
− 14178u
18
+
15519u
17
− 28627u
16
+ 22509u
15
− 41212u
14
+ 22013u
13
− 43680u
12
+ 13676u
11
−
34421u
10
+ 4309u
9
−19742u
8
−137u
7
−7608u
6
−379u
5
−1694u
4
+ 8u
3
−197u
2
+ 6u −33
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 14u
25
+ ··· − 8u + 1
c
2
u
26
+ 2u
25
+ ··· + 2u + 1
c
3
, c
10
u
26
+ 14u
24
+ ··· − u + 1
c
4
, c
8
u
26
+ 14u
24
+ ··· + u + 1
c
5
u
26
− 2u
25
+ ··· − 2u + 1
c
6
u
26
− 3u
25
+ ··· − 4u + 1
c
7
u
26
+ u
25
+ ··· − u + 1
c
9
, c
12
u
26
− 2u
25
+ ··· + u + 1
c
11
u
26
− u
25
+ ··· + u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 2y
25
+ ··· + 12y + 1
c
2
, c
5
y
26
− 14y
25
+ ··· − 8y + 1
c
3
, c
4
, c
8
c
10
y
26
+ 28y
25
+ ··· + 11y + 1
c
6
y
26
+ 13y
25
+ ··· + 14y + 1
c
7
, c
11
y
26
+ 27y
25
+ ··· + 13y + 1
c
9
, c
12
y
26
− 4y
25
+ ··· − 5y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.538786 + 0.927958I
a = −0.112900 − 0.570257I
b = 0.222980 + 0.266051I
−1.75224 + 2.38712I −13.9122 − 2.8805I
u = −0.538786 − 0.927958I
a = −0.112900 + 0.570257I
b = 0.222980 − 0.266051I
−1.75224 − 2.38712I −13.9122 + 2.8805I
u = −0.385729 + 0.815157I
a = 0.918364 + 0.023525I
b = −0.433428 + 0.278716I
−2.45237 + 1.53374I −6.64758 − 3.23071I
u = −0.385729 − 0.815157I
a = 0.918364 − 0.023525I
b = −0.433428 − 0.278716I
−2.45237 − 1.53374I −6.64758 + 3.23071I
u = 0.730968 + 0.900749I
a = 0.864910 − 0.641217I
b = 0.051962 + 1.327580I
4.86648 + 3.58079I −0.55619 − 2.13740I
u = 0.730968 − 0.900749I
a = 0.864910 + 0.641217I
b = 0.051962 − 1.327580I
4.86648 − 3.58079I −0.55619 + 2.13740I
u = −0.286870 + 0.746325I
a = 1.41967 − 0.12345I
b = −0.552506 + 0.530432I
−0.58107 + 9.20519I −3.22347 − 8.30608I
u = −0.286870 − 0.746325I
a = 1.41967 + 0.12345I
b = −0.552506 − 0.530432I
−0.58107 − 9.20519I −3.22347 + 8.30608I
u = −0.327261 + 0.703730I
a = −1.312270 + 0.330457I
b = 0.437480 − 0.545304I
1.80693 + 4.30322I 0.37768 − 4.82059I
u = −0.327261 − 0.703730I
a = −1.312270 − 0.330457I
b = 0.437480 + 0.545304I
1.80693 − 4.30322I 0.37768 + 4.82059I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.210837 + 1.210730I
a = 0.85501 − 1.70045I
b = 0.45375 + 1.55359I
6.67132 − 6.55082I −2.32316 + 4.78372I
u = 0.210837 − 1.210730I
a = 0.85501 + 1.70045I
b = 0.45375 − 1.55359I
6.67132 + 6.55082I −2.32316 − 4.78372I
u = 0.158437 + 1.249590I
a = 0.67810 − 1.77851I
b = 0.55249 + 1.49240I
6.25739 + 0.03067I −2.30536 − 3.14986I
u = 0.158437 − 1.249590I
a = 0.67810 + 1.77851I
b = 0.55249 − 1.49240I
6.25739 − 0.03067I −2.30536 + 3.14986I
u = 0.257779 + 1.247520I
a = −0.80164 + 1.55464I
b = −0.40111 − 1.48164I
8.43711 − 2.51138I 0.761345 − 0.589032I
u = 0.257779 − 1.247520I
a = −0.80164 − 1.55464I
b = −0.40111 + 1.48164I
8.43711 + 2.51138I 0.761345 + 0.589032I
u = 0.162202 + 1.315430I
a = −0.56367 + 1.65852I
b = −0.52745 − 1.39209I
7.86913 − 3.31219I 2.10270 + 3.46382I
u = 0.162202 − 1.315430I
a = −0.56367 − 1.65852I
b = −0.52745 + 1.39209I
7.86913 + 3.31219I 2.10270 − 3.46382I
u = −0.333869 + 0.320216I
a = −1.57614 + 1.82817I
b = 0.147799 − 0.800490I
3.50519 + 2.37158I 3.44007 − 4.77951I
u = −0.333869 − 0.320216I
a = −1.57614 − 1.82817I
b = 0.147799 + 0.800490I
3.50519 − 2.37158I 3.44007 + 4.77951I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.279100 + 0.287750I
a = 1.98871 + 1.03413I
b = −0.103078 + 1.153030I
3.19567 − 1.81789I 0.76577 + 3.77634I
u = 0.279100 − 0.287750I
a = 1.98871 − 1.03413I
b = −0.103078 − 1.153030I
3.19567 + 1.81789I 0.76577 − 3.77634I
u = 0.64419 + 1.48810I
a = −0.545796 + 1.078510I
b = −0.222723 − 1.261530I
7.10098 − 1.73215I 0
u = 0.64419 − 1.48810I
a = −0.545796 − 1.078510I
b = −0.222723 + 1.261530I
7.10098 + 1.73215I 0
u = −0.07100 + 1.82525I
a = 0.187650 − 1.267600I
b = 0.373837 + 1.040950I
2.77856 − 6.53404I 0
u = −0.07100 − 1.82525I
a = 0.187650 + 1.267600I
b = 0.373837 − 1.040950I
2.77856 + 6.53404I 0
27
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
14
+ 7u
13
+ ··· + u + 1)
6
)(u
26
− 14u
25
+ ··· − 8u + 1)
· (u
43
+ 21u
42
+ ··· + 224u + 64)
c
2
((u
14
− u
13
+ ··· − u + 1)
6
)(u
26
+ 2u
25
+ ··· + 2u + 1)
· (u
43
+ 9u
42
+ ··· + 80u + 8)
c
3
, c
10
(u
26
+ 14u
24
+ ··· − u + 1)(u
43
+ 18u
41
+ ··· + 2u + 1)
· (u
84
− u
83
+ ··· − 1050404u + 428849)
c
4
, c
8
(u
26
+ 14u
24
+ ··· + u + 1)(u
43
+ 18u
41
+ ··· + 2u + 1)
· (u
84
− u
83
+ ··· − 1050404u + 428849)
c
5
((u
14
− u
13
+ ··· − u + 1)
6
)(u
26
− 2u
25
+ ··· − 2u + 1)
· (u
43
+ 9u
42
+ ··· + 80u + 8)
c
6
((u
14
− 3u
13
+ ··· − 7u + 3)
6
)(u
26
− 3u
25
+ ··· − 4u + 1)
· (u
43
+ 30u
42
+ ··· + 41536u + 3032)
c
7
((u
3
− u
2
+ 2u − 1)
28
)(u
26
+ u
25
+ ··· − u + 1)
· (u
43
+ 30u
42
+ ··· + 385024u + 16384)
c
9
, c
12
(u
26
− 2u
25
+ ··· + u + 1)(u
43
+ 2u
42
+ ··· + 8u + 1)
· (u
84
+ 15u
83
+ ··· + 36868u + 1913)
c
11
((u
3
− u
2
+ 2u − 1)
28
)(u
26
− u
25
+ ··· + u + 1)
· (u
43
+ 30u
42
+ ··· + 385024u + 16384)
28
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
14
+ y
13
+ ··· + 7y + 1)
6
)(y
26
+ 2y
25
+ ··· + 12y + 1)
· (y
43
+ 3y
42
+ ··· + 39424y − 4096)
c
2
, c
5
((y
14
− 7y
13
+ ··· − y + 1)
6
)(y
26
− 14y
25
+ ··· − 8y + 1)
· (y
43
− 21y
42
+ ··· + 224y − 64)
c
3
, c
4
, c
8
c
10
(y
26
+ 28y
25
+ ··· + 11y + 1)(y
43
+ 36y
42
+ ··· + 4y − 1)
· (y
84
+ 75y
83
+ ··· − 72738646416y + 183911464801)
c
6
((y
14
+ 5y
13
+ ··· + 23y + 9)
6
)(y
26
+ 13y
25
+ ··· + 14y + 1)
· (y
43
+ 18y
42
+ ··· + 78220512y − 9193024)
c
7
, c
11
((y
3
+ 3y
2
+ 2y − 1)
28
)(y
26
+ 27y
25
+ ··· + 13y + 1)
· (y
43
+ 30y
42
+ ··· + 2751463424y − 268435456)
c
9
, c
12
(y
26
− 4y
25
+ ··· − 5y + 1)(y
43
+ 42y
41
+ ··· + 24y − 1)
· (y
84
− 17y
83
+ ··· − 49043376y + 3659569)
29
