12a
0495
(K12a
0495
)
A knot diagram
1
Linearized knot diagam
3 6 12 11 2 10 5 4 1 7 8 9
Solving Sequence
6,10
7
3,11
2 1 5 8 4 9 12
c
6
c
10
c
2
c
1
c
5
c
7
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.50165 × 10
42
u
42
− 3.19414 × 10
44
u
41
+ ··· + 3.84773 × 10
44
b + 2.85090 × 10
44
,
− 3.52358 × 10
44
u
42
− 1.24699 × 10
44
u
41
+ ··· + 3.84773 × 10
44
a + 3.72957 × 10
44
, u
43
+ u
42
+ ··· + 2u − 1i
I
u
2
= h−6.47610 × 10
471
u
99
+ 1.24291 × 10
472
u
98
+ ··· + 1.82398 × 10
472
b + 1.18729 × 10
475
,
1.09026 × 10
476
u
99
− 2.10040 × 10
476
u
98
+ ··· + 7.28496 × 10
475
a − 2.02260 × 10
479
,
u
100
− 3u
99
+ ··· − 14102u + 1997i
I
u
3
= hb + u, −u
3
+ a + u, u
4
+ u
3
− u
2
− u + 1i
I
u
4
= h−9u
12
+ 14u
11
+ 24u
10
− 61u
9
− 18u
8
+ 117u
7
− 19u
6
− 134u
5
+ 56u
4
+ 88u
3
− 58u
2
+ b − 36u + 19,
12u
12
− 19u
11
− 32u
10
+ 83u
9
+ 23u
8
− 160u
7
+ 29u
6
+ 183u
5
− 80u
4
− 120u
3
+ 82u
2
+ a + 48u − 27,
u
13
− 2u
12
− 2u
11
+ 8u
10
− u
9
− 14u
8
+ 8u
7
+ 14u
6
− 13u
5
− 7u
4
+ 11u
3
+ u
2
− 4u + 1i
I
u
5
= hb + 1, a
2
+ a − 4u − 6, u
2
+ u − 1i
* 5 irreducible components of dim
C
= 0, with total 164 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
= h4.50×10
42
u
42
−3.19×10
44
u
41
+· · ·+3.85×10
44
b+2.85×10
44
, −3.52×
10
44
u
42
−1.25×10
44
u
41
+· · ·+3.85×10
44
a+3.73×10
44
, u
43
+u
42
+· · ·+2u−1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
0.915756u
42
+ 0.324085u
41
+ ··· − 8.28487u − 0.969292
−0.0116995u
42
+ 0.830137u
41
+ ··· + 11.5769u − 0.740930
a
11
=
−u
−u
3
+ u
a
2
=
0.904056u
42
+ 1.15422u
41
+ ··· + 3.29201u − 1.71022
−0.0116995u
42
+ 0.830137u
41
+ ··· + 11.5769u − 0.740930
a
1
=
−1
−0.858365u
42
− 0.500568u
41
+ ··· − 0.685046u + 0.703287
a
5
=
−0.0298597u
42
− 0.939789u
41
+ ··· + 24.8126u − 2.91645
0.885896u
42
− 0.615704u
41
+ ··· + 16.5277u − 3.88574
a
8
=
1.25763u
42
+ 0.566937u
41
+ ··· + 7.76709u + 0.365042
−0.359305u
42
+ 0.0358520u
41
+ ··· + 1.77109u + 0.0735383
a
4
=
−0.535897u
42
+ 0.224628u
41
+ ··· + 20.0722u − 1.23522
0.624186u
42
− 0.362368u
41
+ ··· + 17.4211u − 3.89651
a
9
=
u
−0.357797u
42
+ 0.447881u
41
+ ··· − 1.42002u + 0.858365
a
12
=
u
2
− 1
−0.0526870u
42
− 0.367362u
41
+ ··· + 0.888912u + 0.345490
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.11254u
42
+ 0.229872u
41
+ ··· − 39.9613u − 5.19110
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
43
+ 18u
42
+ ··· + 6320u + 256
c
2
, c
5
u
43
+ 12u
42
+ ··· + 204u + 16
c
3
, c
7
u
43
− 2u
42
+ ··· − 11u + 1
c
4
, c
8
u
43
+ 15u
41
+ ··· + 3u + 1
c
6
, c
9
, c
10
c
12
u
43
− u
42
+ ··· + 2u + 1
c
11
u
43
− 18u
42
+ ··· + 8u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
43
+ 18y
42
+ ··· + 23099136y −65536
c
2
, c
5
y
43
− 18y
42
+ ··· + 6320y −256
c
3
, c
7
y
43
+ 2y
42
+ ··· + 49y −1
c
4
, c
8
y
43
+ 30y
42
+ ··· − 51y −1
c
6
, c
9
, c
10
c
12
y
43
− 41y
42
+ ··· + 60y −1
c
11
y
43
− 6y
42
+ ··· + 168y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.117499 + 1.004120I
a = −0.503747 + 1.230070I
b = 0.714886 − 0.696202I
3.79723 − 2.80030I −1.75451 + 2.24956I
u = −0.117499 − 1.004120I
a = −0.503747 − 1.230070I
b = 0.714886 + 0.696202I
3.79723 + 2.80030I −1.75451 − 2.24956I
u = 0.062916 + 1.011790I
a = −0.15608 − 1.47247I
b = 0.928815 + 0.671587I
3.17076 − 8.04245I −3.44286 + 8.35826I
u = 0.062916 − 1.011790I
a = −0.15608 + 1.47247I
b = 0.928815 − 0.671587I
3.17076 + 8.04245I −3.44286 − 8.35826I
u = 1.069580 + 0.138287I
a = 0.792890 − 1.128880I
b = 1.41664 + 0.59320I
−6.25292 − 1.45389I −15.9994 − 2.3137I
u = 1.069580 − 0.138287I
a = 0.792890 + 1.128880I
b = 1.41664 − 0.59320I
−6.25292 + 1.45389I −15.9994 + 2.3137I
u = 1.109200 + 0.079633I
a = −0.211055 − 0.682003I
b = 0.58590 + 1.33812I
−2.84647 − 6.20636I −11.78082 + 7.78840I
u = 1.109200 − 0.079633I
a = −0.211055 + 0.682003I
b = 0.58590 − 1.33812I
−2.84647 + 6.20636I −11.78082 − 7.78840I
u = 0.912089 + 0.720865I
a = −0.10294 − 1.89195I
b = 0.971326 + 0.526994I
−1.90367 − 3.73876I −5.13722 + 7.22741I
u = 0.912089 − 0.720865I
a = −0.10294 + 1.89195I
b = 0.971326 − 0.526994I
−1.90367 + 3.73876I −5.13722 − 7.22741I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.185440 + 0.005135I
a = −0.504645 − 0.907568I
b = 0.532020 + 0.841629I
−5.72482 − 1.57132I −12.72131 + 2.39726I
u = −1.185440 − 0.005135I
a = −0.504645 + 0.907568I
b = 0.532020 − 0.841629I
−5.72482 + 1.57132I −12.72131 − 2.39726I
u = −1.218930 + 0.142311I
a = 0.234566 + 0.991044I
b = 1.22616 − 0.95551I
−5.77798 + 4.07207I −16.1651 − 7.5060I
u = −1.218930 − 0.142311I
a = 0.234566 − 0.991044I
b = 1.22616 + 0.95551I
−5.77798 − 4.07207I −16.1651 + 7.5060I
u = −1.243430 + 0.252908I
a = 0.16597 + 1.57644I
b = 1.066050 − 0.627388I
−7.37478 + 3.89701I −14.05829 + 0.I
u = −1.243430 − 0.252908I
a = 0.16597 − 1.57644I
b = 1.066050 + 0.627388I
−7.37478 − 3.89701I −14.05829 + 0.I
u = 0.481551 + 0.543549I
a = −0.95293 + 1.62097I
b = 0.730477 − 0.458470I
−1.010270 + 0.399925I −5.75032 + 1.08841I
u = 0.481551 − 0.543549I
a = −0.95293 − 1.62097I
b = 0.730477 + 0.458470I
−1.010270 − 0.399925I −5.75032 − 1.08841I
u = 0.661900
a = −1.30419
b = 0.233241
−1.19793 −7.72930
u = 0.019937 + 0.656213I
a = −0.520963 + 0.051706I
b = −0.900796 − 0.188656I
−1.62331 − 3.89803I −10.31136 + 7.16780I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.019937 − 0.656213I
a = −0.520963 − 0.051706I
b = −0.900796 + 0.188656I
−1.62331 + 3.89803I −10.31136 − 7.16780I
u = 1.362940 + 0.240786I
a = −0.500176 − 0.102046I
b = −0.919402 + 0.391596I
−2.88611 + 1.54391I 0
u = 1.362940 − 0.240786I
a = −0.500176 + 0.102046I
b = −0.919402 − 0.391596I
−2.88611 − 1.54391I 0
u = −0.259331 + 0.529204I
a = −0.758126 − 0.463356I
b = 0.039682 + 0.586932I
1.26738 − 1.62023I 0.40000 + 1.60958I
u = −0.259331 − 0.529204I
a = −0.758126 + 0.463356I
b = 0.039682 − 0.586932I
1.26738 + 1.62023I 0.40000 − 1.60958I
u = 1.40146 + 0.24459I
a = −0.412623 − 0.005640I
b = −1.42306 + 0.03312I
−11.2007 − 10.2230I 0
u = 1.40146 − 0.24459I
a = −0.412623 + 0.005640I
b = −1.42306 − 0.03312I
−11.2007 + 10.2230I 0
u = −1.35615 + 0.48076I
a = −0.501656 − 0.811085I
b = 0.448437 + 0.891775I
−6.31477 + 5.74152I 0
u = −1.35615 − 0.48076I
a = −0.501656 + 0.811085I
b = 0.448437 − 0.891775I
−6.31477 − 5.74152I 0
u = 1.37918 + 0.51314I
a = −0.415180 + 0.729199I
b = 0.410344 − 1.035640I
−4.2607 − 13.9202I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.37918 − 0.51314I
a = −0.415180 − 0.729199I
b = 0.410344 + 1.035640I
−4.2607 + 13.9202I 0
u = −1.51469 + 0.21936I
a = −0.447254 + 0.012516I
b = −1.234120 − 0.062522I
−12.36260 + 3.19642I 0
u = −1.51469 − 0.21936I
a = −0.447254 − 0.012516I
b = −1.234120 + 0.062522I
−12.36260 − 3.19642I 0
u = −1.46914 + 0.59124I
a = 0.30263 + 1.47349I
b = 1.133750 − 0.651193I
−8.4013 + 11.4319I 0
u = −1.46914 − 0.59124I
a = 0.30263 − 1.47349I
b = 1.133750 + 0.651193I
−8.4013 − 11.4319I 0
u = 1.49429 + 0.58038I
a = 0.396103 − 1.357230I
b = 1.198150 + 0.678964I
−6.7222 − 20.0860I 0
u = 1.49429 − 0.58038I
a = 0.396103 + 1.357230I
b = 1.198150 − 0.678964I
−6.7222 + 20.0860I 0
u = −1.73149 + 0.11092I
a = −0.507401 + 0.093242I
b = −0.906448 − 0.350335I
−9.79548 − 1.45521I 0
u = −1.73149 − 0.11092I
a = −0.507401 − 0.093242I
b = −0.906448 + 0.350335I
−9.79548 + 1.45521I 0
u = −0.247184 + 0.021411I
a = −0.440997 + 0.191569I
b = −0.907616 − 0.828669I
4.28256 − 3.09500I 12.20187 − 2.50782I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.247184 − 0.021411I
a = −0.440997 − 0.191569I
b = −0.907616 + 0.828669I
4.28256 + 3.09500I 12.20187 + 2.50782I
u = 0.219210 + 0.092274I
a = −3.80430 − 1.49216I
b = 0.772188 + 0.089355I
−1.352550 − 0.324869I −8.63286 + 1.59353I
u = 0.219210 − 0.092274I
a = −3.80430 + 1.49216I
b = 0.772188 − 0.089355I
−1.352550 + 0.324869I −8.63286 − 1.59353I
9
II. I
u
2
= h−6.48 × 10
471
u
99
+ 1.24 × 10
472
u
98
+ · · · + 1.82 × 10
472
b + 1.19 ×
10
475
, 1.09 × 10
476
u
99
− 2.10 × 10
476
u
98
+ · · · + 7.28 × 10
475
a − 2.02 ×
10
479
, u
100
− 3u
99
+ · · · − 14102u + 1997i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
−1.49660u
99
+ 2.88319u
98
+ ··· − 17051.6u + 2776.40
0.355054u
99
− 0.681427u
98
+ ··· + 4015.19u − 650.934
a
11
=
−u
−u
3
+ u
a
2
=
−1.14154u
99
+ 2.20177u
98
+ ··· − 13036.4u + 2125.46
0.355054u
99
− 0.681427u
98
+ ··· + 4015.19u − 650.934
a
1
=
−1.72142u
99
+ 3.30112u
98
+ ··· − 19491.2u + 3175.97
−0.513029u
99
+ 0.985355u
98
+ ··· − 5825.26u + 951.619
a
5
=
0.00681558u
99
+ 0.000928500u
98
+ ··· − 46.7083u + 11.5955
0.622392u
99
− 1.20360u
98
+ ··· + 7159.72u − 1172.37
a
8
=
−1.19879u
99
+ 2.31683u
98
+ ··· − 13648.7u + 2220.10
1.51223u
99
− 2.88894u
98
+ ··· + 16991.6u − 2762.04
a
4
=
−0.666675u
99
+ 1.30122u
98
+ ··· − 7754.81u + 1270.54
0.525452u
99
− 1.01692u
98
+ ··· + 6056.80u − 993.112
a
9
=
−0.793074u
99
+ 1.54287u
98
+ ··· − 9165.38u + 1507.47
1.29836u
99
− 2.48147u
98
+ ··· + 14600.4u − 2373.20
a
12
=
−15.2590u
99
+ 29.3676u
98
+ ··· − 173710.u + 28330.9
−2.90740u
99
+ 5.60560u
98
+ ··· − 33193.5u + 5412.75
(ii) Obstruction class = −1
(iii) Cusp Shapes = −20.4788u
99
+ 39.2181u
98
+ ··· − 231611.u + 37764.1
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
50
+ 24u
49
+ ··· + 50u + 1)
2
c
2
, c
5
(u
50
− 4u
49
+ ··· + 6u + 1)
2
c
3
, c
7
u
100
− 8u
99
+ ··· + 35u − 1
c
4
, c
8
u
100
− 2u
99
+ ··· + 1541u − 1189
c
6
, c
9
, c
10
c
12
u
100
+ 3u
99
+ ··· + 14102u + 1997
c
11
(u
50
+ 12u
49
+ ··· + 16u − 4)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
50
+ 4y
48
+ ··· − 10y + 1)
2
c
2
, c
5
(y
50
− 24y
49
+ ··· − 50y + 1)
2
c
3
, c
7
y
100
− 10y
99
+ ··· − 161y + 1
c
4
, c
8
y
100
+ 2y
99
+ ··· + 65873919y + 1413721
c
6
, c
9
, c
10
c
12
y
100
− 63y
99
+ ··· − 99531630y + 3988009
c
11
(y
50
− 6y
49
+ ··· − 360y + 16)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.656763 + 0.760795I
a = −0.584932 + 1.144110I
b = −0.436168 − 0.694869I
0.427144 + 1.052320I 0
u = 0.656763 − 0.760795I
a = −0.584932 − 1.144110I
b = −0.436168 + 0.694869I
0.427144 − 1.052320I 0
u = 0.905026 + 0.412300I
a = 0.550286 − 0.702215I
b = −0.216437 + 1.063560I
−0.47368 − 5.62173I 0
u = 0.905026 − 0.412300I
a = 0.550286 + 0.702215I
b = −0.216437 − 1.063560I
−0.47368 + 5.62173I 0
u = 0.949536 + 0.348439I
a = −1.218050 − 0.554976I
b = 0.745385 − 0.169931I
−2.44170 − 0.46878I 0
u = 0.949536 − 0.348439I
a = −1.218050 + 0.554976I
b = 0.745385 + 0.169931I
−2.44170 + 0.46878I 0
u = 1.011970 + 0.097016I
a = 1.53769 + 1.22745I
b = −0.736456 − 0.667448I
−3.13684 − 2.46798I 0
u = 1.011970 − 0.097016I
a = 1.53769 − 1.22745I
b = −0.736456 + 0.667448I
−3.13684 + 2.46798I 0
u = 0.085664 + 0.965920I
a = 0.582554 + 1.103620I
b = −1.071100 − 0.607580I
1.01570 − 6.59278I 0
u = 0.085664 − 0.965920I
a = 0.582554 − 1.103620I
b = −1.071100 + 0.607580I
1.01570 + 6.59278I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.860385 + 0.444729I
a = 0.412609 + 0.215003I
b = −0.477882 − 0.757790I
2.77810 + 1.41692I 0
u = −0.860385 − 0.444729I
a = 0.412609 − 0.215003I
b = −0.477882 + 0.757790I
2.77810 − 1.41692I 0
u = 0.917557 + 0.116065I
a = −0.23436 + 2.21973I
b = −0.864244 + 0.414490I
−3.16942 + 1.80253I 0
u = 0.917557 − 0.116065I
a = −0.23436 − 2.21973I
b = −0.864244 − 0.414490I
−3.16942 − 1.80253I 0
u = 1.077360 + 0.004053I
a = −2.55658 + 2.06259I
b = −0.956692 − 0.490395I
−3.53615 − 1.92255I 0
u = 1.077360 − 0.004053I
a = −2.55658 − 2.06259I
b = −0.956692 + 0.490395I
−3.53615 + 1.92255I 0
u = 1.054110 + 0.264782I
a = −0.436059 − 0.507688I
b = 0.174912 − 0.072012I
−2.25288 − 0.54027I 0
u = 1.054110 − 0.264782I
a = −0.436059 + 0.507688I
b = 0.174912 + 0.072012I
−2.25288 + 0.54027I 0
u = −1.079740 + 0.178850I
a = −1.97577 + 0.70292I
b = −0.953268 − 0.231057I
−4.08289 + 7.09407I 0
u = −1.079740 − 0.178850I
a = −1.97577 − 0.70292I
b = −0.953268 + 0.231057I
−4.08289 − 7.09407I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.114640 + 0.127526I
a = 0.882490 − 0.625320I
b = 1.178820 + 0.412170I
−4.49981 + 0.63122I 0
u = −1.114640 − 0.127526I
a = 0.882490 + 0.625320I
b = 1.178820 − 0.412170I
−4.49981 − 0.63122I 0
u = 1.12635
a = 0.310968
b = 1.67865
−7.24677 0
u = 1.123620 + 0.082110I
a = 1.35965 − 1.86945I
b = 1.023230 + 0.261071I
−3.65706 − 0.80100I 0
u = 1.123620 − 0.082110I
a = 1.35965 + 1.86945I
b = 1.023230 − 0.261071I
−3.65706 + 0.80100I 0
u = −0.057481 + 1.129840I
a = 0.027247 − 1.409620I
b = 0.513461 + 0.735910I
0.25096 + 8.19403I 0
u = −0.057481 − 1.129840I
a = 0.027247 + 1.409620I
b = 0.513461 − 0.735910I
0.25096 − 8.19403I 0
u = 0.495922 + 1.020730I
a = 0.594511 − 0.531595I
b = −1.078350 + 0.573559I
−1.46179 + 5.95154I 0
u = 0.495922 − 1.020730I
a = 0.594511 + 0.531595I
b = −1.078350 − 0.573559I
−1.46179 − 5.95154I 0
u = −1.083500 + 0.384657I
a = 0.178705 + 0.589391I
b = 0.215012 − 0.897652I
−1.01117 + 5.33279I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.083500 − 0.384657I
a = 0.178705 − 0.589391I
b = 0.215012 + 0.897652I
−1.01117 − 5.33279I 0
u = −0.552128 + 0.595910I
a = 0.72315 + 2.39951I
b = 0.745385 − 0.169931I
−2.44170 − 0.46878I 0
u = −0.552128 − 0.595910I
a = 0.72315 − 2.39951I
b = 0.745385 + 0.169931I
−2.44170 + 0.46878I 0
u = −1.125100 + 0.381707I
a = −0.83288 − 1.21807I
b = −1.071100 + 0.607580I
1.01570 + 6.59278I 0
u = −1.125100 − 0.381707I
a = −0.83288 + 1.21807I
b = −1.071100 − 0.607580I
1.01570 − 6.59278I 0
u = −1.198300 + 0.018491I
a = 0.731188 + 0.480247I
b = −0.325073 − 0.850938I
−5.49087 + 5.13720I 0
u = −1.198300 − 0.018491I
a = 0.731188 − 0.480247I
b = −0.325073 + 0.850938I
−5.49087 − 5.13720I 0
u = −1.201710 + 0.200589I
a = −0.68018 − 1.78861I
b = −1.156630 + 0.597698I
−7.96986 + 10.48970I 0
u = −1.201710 − 0.200589I
a = −0.68018 + 1.78861I
b = −1.156630 − 0.597698I
−7.96986 − 10.48970I 0
u = −0.140619 + 0.763835I
a = −0.120660 − 1.384640I
b = −0.477882 + 0.757790I
2.77810 − 1.41692I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140619 − 0.763835I
a = −0.120660 + 1.384640I
b = −0.477882 − 0.757790I
2.77810 + 1.41692I 0
u = 1.193770 + 0.368333I
a = 0.0844010 − 0.0070627I
b = −0.436168 + 0.694869I
0.427144 − 1.052320I 0
u = 1.193770 − 0.368333I
a = 0.0844010 + 0.0070627I
b = −0.436168 − 0.694869I
0.427144 + 1.052320I 0
u = −1.25402
a = 0.429329
b = 1.67865
−7.24677 0
u = −1.195240 + 0.384154I
a = 0.360765 + 0.545779I
b = −0.216437 − 1.063560I
−0.47368 + 5.62173I 0
u = −1.195240 − 0.384154I
a = 0.360765 − 0.545779I
b = −0.216437 + 1.063560I
−0.47368 − 5.62173I 0
u = 1.123350 + 0.563061I
a = −0.42110 + 1.45762I
b = −1.243440 − 0.639820I
−3.56043 − 11.64580I 0
u = 1.123350 − 0.563061I
a = −0.42110 − 1.45762I
b = −1.243440 + 0.639820I
−3.56043 + 11.64580I 0
u = −0.395318 + 0.623073I
a = −0.076015 − 1.329850I
b = −0.822433 + 0.736761I
4.01340 + 2.76482I 0
u = −0.395318 − 0.623073I
a = −0.076015 + 1.329850I
b = −0.822433 − 0.736761I
4.01340 − 2.76482I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.235850 + 0.277767I
a = 1.68829 − 1.29789I
b = 0.990030 + 0.443721I
−3.70285 − 3.69603I 0
u = 1.235850 − 0.277767I
a = 1.68829 + 1.29789I
b = 0.990030 − 0.443721I
−3.70285 + 3.69603I 0
u = −0.871034 + 0.966316I
a = 0.799966 + 0.408001I
b = −0.953268 − 0.231057I
−4.08289 + 7.09407I 0
u = −0.871034 − 0.966316I
a = 0.799966 − 0.408001I
b = −0.953268 + 0.231057I
−4.08289 − 7.09407I 0
u = −0.682087
a = 2.52826
b = 1.08337
−2.51173 21.1920
u = 0.097129 + 0.671876I
a = −0.76182 + 1.61317I
b = 0.174912 − 0.072012I
−2.25288 − 0.54027I −6.00000 + 0.I
u = 0.097129 − 0.671876I
a = −0.76182 − 1.61317I
b = 0.174912 + 0.072012I
−2.25288 + 0.54027I −6.00000 + 0.I
u = −0.030312 + 0.651328I
a = 0.635383 + 0.988793I
b = −0.822433 − 0.736761I
4.01340 − 2.76482I 0. + 4.05311I
u = −0.030312 − 0.651328I
a = 0.635383 − 0.988793I
b = −0.822433 + 0.736761I
4.01340 + 2.76482I 0. − 4.05311I
u = −1.256800 + 0.521701I
a = −0.509913 − 0.290009I
b = 0.513461 + 0.735910I
0.25096 + 8.19403I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.256800 − 0.521701I
a = −0.509913 + 0.290009I
b = 0.513461 − 0.735910I
0.25096 − 8.19403I 0
u = −1.308060 + 0.531897I
a = −0.810107 − 1.099470I
b = −1.098390 + 0.355955I
−5.05834 + 8.72078I 0
u = −1.308060 − 0.531897I
a = −0.810107 + 1.099470I
b = −1.098390 − 0.355955I
−5.05834 − 8.72078I 0
u = −0.230728 + 1.395230I
a = −0.446370 + 1.126250I
b = 1.061970 − 0.603466I
−1.39932 + 13.31280I 0
u = −0.230728 − 1.395230I
a = −0.446370 − 1.126250I
b = 1.061970 + 0.603466I
−1.39932 − 13.31280I 0
u = −0.101257 + 0.562966I
a = −3.23307 − 1.40067I
b = 1.023230 + 0.261071I
−3.65706 − 0.80100I −10.8022 − 21.8156I
u = −0.101257 − 0.562966I
a = −3.23307 + 1.40067I
b = 1.023230 − 0.261071I
−3.65706 + 0.80100I −10.8022 + 21.8156I
u = 1.40566 + 0.27667I
a = −0.970218 + 0.838707I
b = −1.078350 − 0.573559I
−1.46179 − 5.95154I 0
u = 1.40566 − 0.27667I
a = −0.970218 − 0.838707I
b = −1.078350 + 0.573559I
−1.46179 + 5.95154I 0
u = −1.36852 + 0.44819I
a = −0.592478 − 1.272930I
b = −1.243440 + 0.639820I
−3.56043 + 11.64580I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36852 − 0.44819I
a = −0.592478 + 1.272930I
b = −1.243440 − 0.639820I
−3.56043 − 11.64580I 0
u = 0.381225 + 0.391402I
a = −0.958951 − 0.206925I
b = 1.178820 − 0.412170I
−4.49981 − 0.63122I −11.53735 + 5.50836I
u = 0.381225 − 0.391402I
a = −0.958951 + 0.206925I
b = 1.178820 + 0.412170I
−4.49981 + 0.63122I −11.53735 − 5.50836I
u = −1.38113 + 0.46979I
a = 0.88861 + 1.34956I
b = 1.061970 − 0.603466I
−1.39932 + 13.31280I 0
u = −1.38113 − 0.46979I
a = 0.88861 − 1.34956I
b = 1.061970 + 0.603466I
−1.39932 − 13.31280I 0
u = −1.46026 + 0.01361I
a = 0.646851 + 0.170646I
b = 1.244560 + 0.218633I
−10.62880 + 1.86401I 0
u = −1.46026 − 0.01361I
a = 0.646851 − 0.170646I
b = 1.244560 − 0.218633I
−10.62880 − 1.86401I 0
u = 1.33803 + 0.59383I
a = 0.375070 − 0.852034I
b = −0.325073 + 0.850938I
−5.49087 − 5.13720I 0
u = 1.33803 − 0.59383I
a = 0.375070 + 0.852034I
b = −0.325073 − 0.850938I
−5.49087 + 5.13720I 0
u = 1.47666 + 0.33344I
a = 0.291071 + 0.286286I
b = 1.244560 − 0.218633I
−10.62880 − 1.86401I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47666 − 0.33344I
a = 0.291071 − 0.286286I
b = 1.244560 + 0.218633I
−10.62880 + 1.86401I 0
u = 0.439430
a = −2.69934
b = 1.08337
−2.51173 21.1920
u = 0.407312 + 0.109649I
a = 1.022410 − 0.594071I
b = 0.215012 − 0.897652I
−1.01117 + 5.33279I −5.08032 − 5.87415I
u = 0.407312 − 0.109649I
a = 1.022410 + 0.594071I
b = 0.215012 + 0.897652I
−1.01117 − 5.33279I −5.08032 + 5.87415I
u = −0.328633 + 0.155733I
a = 3.36879 − 1.60752I
b = −1.098390 − 0.355955I
−5.05834 − 8.72078I −12.2296 + 7.5537I
u = −0.328633 − 0.155733I
a = 3.36879 + 1.60752I
b = −1.098390 + 0.355955I
−5.05834 + 8.72078I −12.2296 − 7.5537I
u = 1.49024 + 0.71508I
a = −0.264914 + 1.352310I
b = −1.156630 − 0.597698I
−7.96986 − 10.48970I 0
u = 1.49024 − 0.71508I
a = −0.264914 − 1.352310I
b = −1.156630 + 0.597698I
−7.96986 + 10.48970I 0
u = −0.63337 + 1.57254I
a = −0.545268 − 0.855325I
b = 0.990030 + 0.443721I
−3.70285 − 3.69603I 0
u = −0.63337 − 1.57254I
a = −0.545268 + 0.855325I
b = 0.990030 − 0.443721I
−3.70285 + 3.69603I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.157018 + 0.237936I
a = −4.63390 − 1.62830I
b = 0.908192 + 0.620745I
−1.86952 − 2.47384I −10.76147 + 0.10199I
u = 0.157018 − 0.237936I
a = −4.63390 + 1.62830I
b = 0.908192 − 0.620745I
−1.86952 + 2.47384I −10.76147 − 0.10199I
u = 1.72720 + 0.06420I
a = 0.181902 − 0.980964I
b = 0.908192 + 0.620745I
−1.86952 − 2.47384I 0
u = 1.72720 − 0.06420I
a = 0.181902 + 0.980964I
b = 0.908192 − 0.620745I
−1.86952 + 2.47384I 0
u = −1.98508 + 0.90307I
a = 0.081396 + 1.085250I
b = −0.736456 − 0.667448I
−3.13684 − 2.46798I 0
u = −1.98508 − 0.90307I
a = 0.081396 − 1.085250I
b = −0.736456 + 0.667448I
−3.13684 + 2.46798I 0
u = 2.48164 + 0.79519I
a = −0.250516 + 0.905817I
b = −0.864244 − 0.414490I
−3.16942 − 1.80253I 0
u = 2.48164 − 0.79519I
a = −0.250516 − 0.905817I
b = −0.864244 + 0.414490I
−3.16942 + 1.80253I 0
u = −0.14812 + 2.77942I
a = 0.223866 − 0.965495I
b = −0.956692 + 0.490395I
−3.53615 + 1.92255I 0
u = −0.14812 − 2.77942I
a = 0.223866 + 0.965495I
b = −0.956692 − 0.490395I
−3.53615 − 1.92255I 0
22
III. I
u
3
= hb + u, −u
3
+ a + u, u
4
+ u
3
− u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
u
3
− u
−u
a
11
=
−u
−u
3
+ u
a
2
=
u
3
− 2u
−u
a
1
=
−1
u
3
− u
a
5
=
−u
3
− u
2
+ u
−u
2
a
8
=
u
u
3
+ u
2
a
4
=
0
−u
3
− u
2
a
9
=
u
u
3
+ 1
a
12
=
u
2
− 1
u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 9u
2
+ 3u − 18
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 3u
3
+ 5u
2
− 3u + 1
c
2
, c
6
, c
9
u
4
+ u
3
− u
2
− u + 1
c
3
, c
5
, c
7
c
10
, c
12
u
4
− u
3
− u
2
+ u + 1
c
4
, c
8
u
4
− 2u
3
+ 2u
2
− u + 1
c
11
(u
2
+ u + 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
+ y
3
+ 9y
2
+ y + 1
c
2
, c
3
, c
5
c
6
, c
7
, c
9
c
10
, c
12
y
4
− 3y
3
+ 5y
2
− 3y + 1
c
4
, c
8
y
4
+ 2y
2
+ 3y + 1
c
11
(y
2
+ y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.692440 + 0.318148I
a = −0.570696 + 0.107280I
b = −0.692440 − 0.318148I
−2.72253 − 1.41376I −12.51838 + 4.91982I
u = 0.692440 − 0.318148I
a = −0.570696 − 0.107280I
b = −0.692440 + 0.318148I
−2.72253 + 1.41376I −12.51838 − 4.91982I
u = −1.192440 + 0.547877I
a = 0.57070 + 1.62477I
b = 1.192440 − 0.547877I
−5.50214 + 11.56320I −11.4816 − 10.1160I
u = −1.192440 − 0.547877I
a = 0.57070 − 1.62477I
b = 1.192440 + 0.547877I
−5.50214 − 11.56320I −11.4816 + 10.1160I
26
IV. I
u
4
=
h−9u
12
+14u
11
+· · ·+b+19, 12u
12
−19u
11
+· · ·+a−27, u
13
−2u
12
+· · ·−4u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
3
=
−12u
12
+ 19u
11
+ ··· − 48u + 27
9u
12
− 14u
11
+ ··· + 36u − 19
a
11
=
−u
−u
3
+ u
a
2
=
−3u
12
+ 5u
11
+ ··· − 12u + 8
9u
12
− 14u
11
+ ··· + 36u − 19
a
1
=
−1
−6u
12
+ 9u
11
+ ··· − 26u + 17
a
5
=
−4u
12
+ 6u
11
+ ··· − 17u + 9
−16u
12
+ 25u
11
+ ··· − 65u + 36
a
8
=
u
3u
12
− 5u
11
+ ··· + 13u − 10
a
4
=
0
−19u
12
+ 29u
11
+ ··· − 78u + 43
a
9
=
u
3u
12
− 6u
11
+ ··· + 8u − 6
a
12
=
u
2
− 1
−6u
12
+ 10u
11
+ ··· − 20u + 14
(ii) Obstruction class = 1
(iii) Cusp Shapes = 75u
12
− 115u
11
− 210u
10
+ 519u
9
+ 167u
8
− 1018u
7
+ 159u
6
+
1178u
5
− 496u
4
− 786u
3
+ 531u
2
+ 311u − 201
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 4u
12
+ ··· + 5u − 1
c
2
u
13
+ 2u
12
+ ··· − 5u − 1
c
3
, c
7
u
13
+ 3u
12
+ ··· + u − 1
c
4
, c
8
u
13
+ 2u
12
+ ··· − u − 1
c
5
u
13
− 2u
12
+ ··· − 5u + 1
c
6
, c
9
u
13
− 2u
12
+ ··· − 4u + 1
c
10
, c
12
u
13
+ 2u
12
+ ··· − 4u − 1
c
11
u
13
+ 11u
12
+ ··· + 128u + 31
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 4y
12
+ ··· − 23y −1
c
2
, c
5
y
13
− 4y
12
+ ··· + 5y −1
c
3
, c
7
y
13
− y
12
+ ··· + 3y −1
c
4
, c
8
y
13
+ 2y
11
+ ··· − 15y −1
c
6
, c
9
, c
10
c
12
y
13
− 8y
12
+ ··· + 14y −1
c
11
y
13
− 5y
12
+ ··· + 6526y −961
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.992701 + 0.282907I
a = −0.435396 − 0.399377I
b = −0.247297 + 1.144110I
−1.69708 + 6.76410I −7.71683 − 11.09769I
u = −0.992701 − 0.282907I
a = −0.435396 + 0.399377I
b = −0.247297 − 1.144110I
−1.69708 − 6.76410I −7.71683 + 11.09769I
u = −0.880123 + 0.552537I
a = −1.41196 − 0.68879I
b = 0.427909 + 0.279082I
−2.50801 + 7.45416I −6.40133 − 6.58220I
u = −0.880123 − 0.552537I
a = −1.41196 + 0.68879I
b = 0.427909 − 0.279082I
−2.50801 − 7.45416I −6.40133 + 6.58220I
u = 0.757953 + 0.778137I
a = −0.67885 + 1.48144I
b = 0.744363 − 0.557876I
−1.73418 + 1.07707I −12.96804 − 4.43209I
u = 0.757953 − 0.778137I
a = −0.67885 − 1.48144I
b = 0.744363 + 0.557876I
−1.73418 − 1.07707I −12.96804 + 4.43209I
u = −1.20134
a = −0.364424
b = −1.74406
−7.84075 −24.5780
u = 1.269840 + 0.347361I
a = −0.500072 − 0.106925I
b = −0.912284 + 0.408885I
−3.32707 + 1.59519I −18.2681 − 5.8552I
u = 1.269840 − 0.347361I
a = −0.500072 + 0.106925I
b = −0.912284 − 0.408885I
−3.32707 − 1.59519I −18.2681 + 5.8552I
u = 0.995567 + 0.866297I
a = −0.16673 − 1.81712I
b = 0.949926 + 0.545728I
−2.41125 − 3.35136I −15.3892 − 0.1863I
30
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.995567 − 0.866297I
a = −0.16673 + 1.81712I
b = 0.949926 − 0.545728I
−2.41125 + 3.35136I −15.3892 + 0.1863I
u = 0.450131 + 0.022096I
a = −0.124781 − 1.167010I
b = 0.909414 + 0.847203I
4.08343 − 3.14937I −25.4676 + 7.5455I
u = 0.450131 − 0.022096I
a = −0.124781 + 1.167010I
b = 0.909414 − 0.847203I
4.08343 + 3.14937I −25.4676 − 7.5455I
31
V. I
u
5
= hb + 1, a
2
+ a − 4u − 6, u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u + 1
a
3
=
a
−1
a
11
=
−u
−u + 1
a
2
=
a − 1
−1
a
1
=
−1
0
a
5
=
a
−1
a
8
=
−au − 2u − 1
−au + a − u + 2
a
4
=
−2au + 2a − u + 1
−3au + 2a − 2u
a
9
=
u
u
a
12
=
−u
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16u − 41
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
4
, c
7
c
8
u
4
+ u
3
+ 3u − 1
c
5
(u + 1)
4
c
6
, c
9
(u
2
+ u − 1)
2
c
10
, c
12
(u
2
− u − 1)
2
c
11
u
4
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
7
c
8
y
4
− y
3
− 8y
2
− 9y + 1
c
6
, c
9
, c
10
c
12
(y
2
− 3y + 1)
2
c
11
y
4
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 2.45333
b = −1.00000
−2.63189 −50.8890
u = 0.618034
a = −3.45333
b = −1.00000
−2.63189 −50.8890
u = −1.61803
a = −0.500000 + 0.471313I
b = −1.00000
−10.5276 −15.1110
u = −1.61803
a = −0.500000 − 0.471313I
b = −1.00000
−10.5276 −15.1110
35
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
4
− 3u
3
+ ··· − 3u + 1)(u
13
− 4u
12
+ ··· + 5u − 1)
· (u
43
+ 18u
42
+ ··· + 6320u + 256)(u
50
+ 24u
49
+ ··· + 50u + 1)
2
c
2
((u − 1)
4
)(u
4
+ u
3
− u
2
− u + 1)(u
13
+ 2u
12
+ ··· − 5u − 1)
· (u
43
+ 12u
42
+ ··· + 204u + 16)(u
50
− 4u
49
+ ··· + 6u + 1)
2
c
3
, c
7
(u
4
− u
3
− u
2
+ u + 1)(u
4
+ u
3
+ 3u − 1)(u
13
+ 3u
12
+ ··· + u − 1)
· (u
43
− 2u
42
+ ··· − 11u + 1)(u
100
− 8u
99
+ ··· + 35u − 1)
c
4
, c
8
(u
4
− 2u
3
+ 2u
2
− u + 1)(u
4
+ u
3
+ 3u − 1)(u
13
+ 2u
12
+ ··· − u − 1)
· (u
43
+ 15u
41
+ ··· + 3u + 1)(u
100
− 2u
99
+ ··· + 1541u − 1189)
c
5
((u + 1)
4
)(u
4
− u
3
− u
2
+ u + 1)(u
13
− 2u
12
+ ··· − 5u + 1)
· (u
43
+ 12u
42
+ ··· + 204u + 16)(u
50
− 4u
49
+ ··· + 6u + 1)
2
c
6
, c
9
((u
2
+ u − 1)
2
)(u
4
+ u
3
− u
2
− u + 1)(u
13
− 2u
12
+ ··· − 4u + 1)
· (u
43
− u
42
+ ··· + 2u + 1)(u
100
+ 3u
99
+ ··· + 14102u + 1997)
c
10
, c
12
((u
2
− u − 1)
2
)(u
4
− u
3
− u
2
+ u + 1)(u
13
+ 2u
12
+ ··· − 4u − 1)
· (u
43
− u
42
+ ··· + 2u + 1)(u
100
+ 3u
99
+ ··· + 14102u + 1997)
c
11
u
4
(u
2
+ u + 1)
2
(u
13
+ 11u
12
+ ··· + 128u + 31)
· (u
43
− 18u
42
+ ··· + 8u + 4)(u
50
+ 12u
49
+ ··· + 16u − 4)
2
36
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
4
)(y
4
+ y
3
+ 9y
2
+ y + 1)(y
13
− 4y
12
+ ··· − 23y −1)
· (y
43
+ 18y
42
+ ··· + 23099136y −65536)
· (y
50
+ 4y
48
+ ··· − 10y + 1)
2
c
2
, c
5
((y −1)
4
)(y
4
− 3y
3
+ ··· − 3y + 1)(y
13
− 4y
12
+ ··· + 5y −1)
· (y
43
− 18y
42
+ ··· + 6320y −256)(y
50
− 24y
49
+ ··· − 50y + 1)
2
c
3
, c
7
(y
4
− 3y
3
+ 5y
2
− 3y + 1)(y
4
− y
3
− 8y
2
− 9y + 1)
· (y
13
− y
12
+ ··· + 3y −1)(y
43
+ 2y
42
+ ··· + 49y −1)
· (y
100
− 10y
99
+ ··· − 161y + 1)
c
4
, c
8
(y
4
+ 2y
2
+ 3y + 1)(y
4
− y
3
− 8y
2
− 9y + 1)(y
13
+ 2y
11
+ ··· − 15y −1)
· (y
43
+ 30y
42
+ ··· − 51y −1)
· (y
100
+ 2y
99
+ ··· + 65873919y + 1413721)
c
6
, c
9
, c
10
c
12
((y
2
− 3y + 1)
2
)(y
4
− 3y
3
+ ··· − 3y + 1)(y
13
− 8y
12
+ ··· + 14y −1)
· (y
43
− 41y
42
+ ··· + 60y −1)
· (y
100
− 63y
99
+ ··· − 99531630y + 3988009)
c
11
y
4
(y
2
+ y + 1)
2
(y
13
− 5y
12
+ ··· + 6526y −961)
· (y
43
− 6y
42
+ ··· + 168y −16)(y
50
− 6y
49
+ ··· − 360y + 16)
2
37
