12a
0426
(K12a
0426
)
A knot diagram
1
Linearized knot diagam
3 6 10 7 2 9 11 5 1 12 8 4
Solving Sequence
7,11 5,8
9 12 4 1 6 10 3 2
c
7
c
8
c
11
c
4
c
12
c
6
c
10
c
3
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h5u
17
− 11u
16
+ ··· + 3b − 11, u
17
+ u
16
+ ··· + 2a + 4, u
18
− 3u
17
+ ··· − 6u + 2i
I
u
2
= h2.93297 × 10
19
u
49
− 3.08421 × 10
20
u
48
+ ··· + 4.46875 × 10
17
b − 5.17754 × 10
20
,
− 2.95147 × 10
19
u
49
+ 6.16285 × 10
20
u
48
+ ··· + 5.80937 × 10
18
a + 6.41388 × 10
21
,
u
50
− 11u
49
+ ··· − 165u + 13i
I
u
3
= h−u
5
a − u
5
+ 2u
3
a + u
3
− 2au + b − u + 1, 2u
4
a + u
3
a − 3u
4
− 2u
2
a − 2u
3
+ a
2
− 2au + u
2
+ 3u + 2,
u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
4
= hu
5
− u
3
+ b + u, u
3
+ a, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
5
= h−2u
43
a − 4u
42
a + ··· + 4b − 65, 50u
43
a − 95u
43
+ ··· − 468a + 943, u
44
+ 3u
43
+ ··· − 14u − 1i
I
u
6
= h3u
15
+ 5u
14
− 4u
13
− 18u
12
− 11u
11
+ 4u
10
+ 4u
9
+ u
8
+ 21u
7
+ 32u
6
+ 22u
5
+ 9u
4
+ 10u
3
+ 5u
2
+ b − u − 1,
− 7u
15
− 28u
14
+ ··· + 2a − 22, u
16
+ 4u
15
+ ··· + 8u + 2i
I
u
7
= h−u
2
a + b − 1, a
2
+ 2au + 2u
2
+ a + 3u + 2, u
3
+ u
2
− 1i
I
u
8
= h−u
3
a − u
2
a − u
3
+ au + 2b + 1, −u
2
a + u
3
+ a
2
+ au − 2u
2
+ a − u + 2, u
4
− u
2
+ 1i
I
u
9
= h−71757a
7
+ 7931089b + ··· − 9811314a + 3141666,
a
8
+ 6a
6
− 6a
5
+ 26a
4
− 18a
3
+ 87a
2
− 60a + 73, u − 1i
* 9 irreducible components of dim
C
= 0, with total 212 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
1
I.
I
u
1
= h5u
17
−11u
16
+· · ·+3b −11, u
17
+u
16
+· · ·+2a +4, u
18
−3u
17
+· · ·−6u +2i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
5
=
−
1
2
u
17
−
1
2
u
16
+ ··· −
3
2
u
2
− 2
−
5
3
u
17
+
11
3
u
16
+ ··· −
23
3
u +
11
3
a
8
=
1
u
2
a
9
=
1
2
u
17
−
5
2
u
16
+ ··· + 5u − 3
−
5
3
u
17
+
11
3
u
16
+ ··· −
23
3
u +
11
3
a
12
=
−u
−u
3
+ u
a
4
=
7
6
u
17
−
25
6
u
16
+ ··· +
23
3
u −
17
3
−
5
3
u
17
+
11
3
u
16
+ ··· −
23
3
u +
11
3
a
1
=
19
6
u
17
−
37
6
u
16
+ ··· +
32
3
u −
14
3
−
2
3
u
17
+
2
3
u
16
+ ··· +
1
3
u −
1
3
a
6
=
−
7
6
u
17
+
25
6
u
16
+ ··· −
23
3
u +
17
3
2
3
u
17
−
2
3
u
16
+ ··· +
2
3
u +
1
3
a
10
=
u
3
u
5
− u
3
+ u
a
3
=
−
5
2
u
17
+
7
2
u
16
+ ··· − 7u + 1
−3.33333u
17
+ 7.33333u
16
+ ··· − 13.3333u + 6.33333
a
2
=
−1.83333u
17
+ 3.83333u
16
+ ··· − 8.33333u + 3.33333
−2u
17
+ 5u
16
+ ··· − 9u + 5
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
17
+ 14u
16
+ 12u
15
− 50u
14
− 2u
13
+ 94u
12
− 40u
11
−
130u
10
+ 112u
9
+ 86u
8
− 140u
7
− 22u
6
+ 106u
5
− 20u
4
− 36u
3
+ 24u
2
− 14u + 6
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
18
+ 7u
17
+ ··· − 4u + 4
c
2
, c
5
, c
7
c
11
u
18
+ 3u
17
+ ··· + 6u + 2
c
3
, c
8
u
18
− 9u
17
+ ··· − 16u + 8
c
4
, c
6
, c
9
c
12
u
18
+ 5u
16
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
18
+ 13y
17
+ ··· − 272y + 16
c
2
, c
5
, c
7
c
11
y
18
− 7y
17
+ ··· + 4y + 4
c
3
, c
8
y
18
− 9y
17
+ ··· − 480y + 64
c
4
, c
6
, c
9
c
12
y
18
+ 10y
17
+ ··· + y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.929188 + 0.427848I
a = 1.45891 + 0.96005I
b = −0.612958 + 0.694927I
−2.52393 − 4.60971I −3.54545 + 10.13031I
u = 0.929188 − 0.427848I
a = 1.45891 − 0.96005I
b = −0.612958 − 0.694927I
−2.52393 + 4.60971I −3.54545 − 10.13031I
u = −0.880851 + 0.560750I
a = −0.83772 + 1.88459I
b = −0.21871 + 1.48927I
−1.22474 + 4.46780I −2.01264 − 5.91058I
u = −0.880851 − 0.560750I
a = −0.83772 − 1.88459I
b = −0.21871 − 1.48927I
−1.22474 − 4.46780I −2.01264 + 5.91058I
u = 0.582973 + 0.940039I
a = −0.268767 − 0.004991I
b = −1.09278 − 1.05818I
5.24090 + 8.44951I 3.89928 − 4.02582I
u = 0.582973 − 0.940039I
a = −0.268767 + 0.004991I
b = −1.09278 + 1.05818I
5.24090 − 8.44951I 3.89928 + 4.02582I
u = 0.829747 + 0.331402I
a = −0.543141 − 1.062640I
b = 0.506778 + 0.049880I
−1.42597 − 1.89978I −0.27303 + 2.78097I
u = 0.829747 − 0.331402I
a = −0.543141 + 1.062640I
b = 0.506778 − 0.049880I
−1.42597 + 1.89978I −0.27303 − 2.78097I
u = −1.174310 + 0.030732I
a = 0.73424 + 1.60100I
b = 0.540765 + 1.144710I
−8.44772 + 5.23335I −9.78688 − 5.32435I
u = −1.174310 − 0.030732I
a = 0.73424 − 1.60100I
b = 0.540765 − 1.144710I
−8.44772 − 5.23335I −9.78688 + 5.32435I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.933002 + 0.761436I
a = 0.373106 − 0.772716I
b = 0.113921 − 0.679581I
4.32570 + 5.86053I 5.28493 − 4.51200I
u = −0.933002 − 0.761436I
a = 0.373106 + 0.772716I
b = 0.113921 + 0.679581I
4.32570 − 5.86053I 5.28493 + 4.51200I
u = 0.969925 + 0.853431I
a = 0.717351 + 0.406552I
b = 0.005204 + 1.085600I
1.61741 − 6.44223I −7.21121 + 5.93194I
u = 0.969925 − 0.853431I
a = 0.717351 − 0.406552I
b = 0.005204 − 1.085600I
1.61741 + 6.44223I −7.21121 − 5.93194I
u = 1.120310 + 0.718189I
a = −0.54198 − 1.83396I
b = 1.13133 − 1.27977I
1.8659 − 20.6729I −0.25702 + 11.54258I
u = 1.120310 − 0.718189I
a = −0.54198 + 1.83396I
b = 1.13133 + 1.27977I
1.8659 + 20.6729I −0.25702 − 11.54258I
u = 0.056018 + 0.547940I
a = −0.591992 − 0.492924I
b = −0.373557 + 0.433371I
0.572438 − 1.277810I 3.90202 + 5.68169I
u = 0.056018 − 0.547940I
a = −0.591992 + 0.492924I
b = −0.373557 − 0.433371I
0.572438 + 1.277810I 3.90202 − 5.68169I
6
II. I
u
2
= h2.93 × 10
19
u
49
− 3.08 × 10
20
u
48
+ · · · + 4.47 × 10
17
b − 5.18 ×
10
20
, −2.95 × 10
19
u
49
+ 6.16 × 10
20
u
48
+ · · · + 5.81 × 10
18
a + 6.41 ×
10
21
, u
50
− 11u
49
+ · · · − 165u + 13i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
5
=
5.08053u
49
− 106.085u
48
+ ··· + 11433.4u − 1104.06
−65.6329u
49
+ 690.174u
48
+ ··· − 13362.0u + 1158.61
a
8
=
1
u
2
a
9
=
3.20250u
49
− 44.5872u
48
+ ··· + 545.377u − 12.0177
−22.0074u
49
+ 211.526u
48
+ ··· − 924.850u + 52.1829
a
12
=
−u
−u
3
+ u
a
4
=
70.7134u
49
− 796.258u
48
+ ··· + 24795.5u − 2262.67
−65.6329u
49
+ 690.174u
48
+ ··· − 13362.0u + 1158.61
a
1
=
6.69943u
49
− 28.5149u
48
+ ··· − 5493.60u + 527.935
20.4159u
49
− 227.260u
48
+ ··· + 5735.08u − 500.233
a
6
=
−71.2237u
49
+ 730.489u
48
+ ··· − 12363.3u + 1079.94
3.20274u
49
− 17.3842u
48
+ ··· − 795.115u + 58.9383
a
10
=
u
3
u
5
− u
3
+ u
a
3
=
7.76879u
49
− 154.326u
48
+ ··· + 14845.3u − 1429.50
−84.9603u
49
+ 868.882u
48
+ ··· − 13592.6u + 1152.16
a
2
=
36.0253u
49
− 376.781u
48
+ ··· + 8948.18u − 832.007
−29.2879u
49
+ 282.012u
48
+ ··· − 2240.06u + 176.845
(ii) Obstruction class = −1
(iii) Cusp Shapes =
9871134219706577536
446874893374714199
u
49
−
123797457722876187653
446874893374714199
u
48
+ ··· +
6910675158351158980446
446874893374714199
u −
601472827700807026450
446874893374714199
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
50
+ 19u
49
+ ··· + 5099u + 169
c
2
, c
5
, c
7
c
11
u
50
+ 11u
49
+ ··· + 165u + 13
c
3
, c
8
(u
25
+ 4u
24
+ ··· + 3u + 1)
2
c
4
, c
6
, c
9
c
12
u
50
+ 5u
49
+ ··· + 4u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
50
+ 13y
49
+ ··· − 3709039y + 28561
c
2
, c
5
, c
7
c
11
y
50
− 19y
49
+ ··· − 5099y + 169
c
3
, c
8
(y
25
− 8y
24
+ ··· + y − 1)
2
c
4
, c
6
, c
9
c
12
y
50
+ 21y
49
+ ··· + 52y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.553707 + 0.832806I
a = 0.043757 − 0.161962I
b = 1.07602 + 1.01172I
−2.22763 + 6.76528I 0. − 5.55124I
u = 0.553707 − 0.832806I
a = 0.043757 + 0.161962I
b = 1.07602 − 1.01172I
−2.22763 − 6.76528I 0. + 5.55124I
u = −0.837139 + 0.557385I
a = 0.79159 − 1.91622I
b = 0.14846 − 1.48629I
−1.07852 0
u = −0.837139 − 0.557385I
a = 0.79159 + 1.91622I
b = 0.14846 + 1.48629I
−1.07852 0
u = 0.558430 + 0.809571I
a = −0.1049370 − 0.0051426I
b = 0.475534 − 0.512990I
−2.54415 − 3.36836I 0. + 11.53583I
u = 0.558430 − 0.809571I
a = −0.1049370 + 0.0051426I
b = 0.475534 + 0.512990I
−2.54415 + 3.36836I 0. − 11.53583I
u = −0.917168 + 0.480093I
a = −0.86443 + 1.71315I
b = −0.316452 + 1.330430I
−2.28095 + 0.36934I 0
u = −0.917168 − 0.480093I
a = −0.86443 − 1.71315I
b = −0.316452 − 1.330430I
−2.28095 − 0.36934I 0
u = 0.933200 + 0.451504I
a = −0.748966 − 0.796862I
b = 0.496615 − 0.374938I
−1.46923 − 1.71043I 0
u = 0.933200 − 0.451504I
a = −0.748966 + 0.796862I
b = 0.496615 + 0.374938I
−1.46923 + 1.71043I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855986 + 0.425974I
a = 0.52160 − 1.79372I
b = 0.054829 − 1.272590I
−1.96570 + 3.34746I 0. − 8.41971I
u = −0.855986 − 0.425974I
a = 0.52160 + 1.79372I
b = 0.054829 + 1.272590I
−1.96570 − 3.34746I 0. + 8.41971I
u = −0.947983 + 0.107928I
a = −0.39264 − 2.05984I
b = −0.334947 − 1.326910I
−2.54415 + 3.36836I −3.18716 − 11.53583I
u = −0.947983 − 0.107928I
a = −0.39264 + 2.05984I
b = −0.334947 + 1.326910I
−2.54415 − 3.36836I −3.18716 + 11.53583I
u = −0.932177 + 0.127667I
a = 1.17876 − 2.00119I
b = 0.66990 − 1.34941I
−4.36972 + 2.52616I −17.6949 − 8.8137I
u = −0.932177 − 0.127667I
a = 1.17876 + 2.00119I
b = 0.66990 + 1.34941I
−4.36972 − 2.52616I −17.6949 + 8.8137I
u = 0.705776 + 0.790233I
a = −0.379152 + 0.570875I
b = −1.29001 − 1.06513I
3.42082 + 2.87486I 0
u = 0.705776 − 0.790233I
a = −0.379152 − 0.570875I
b = −1.29001 + 1.06513I
3.42082 − 2.87486I 0
u = 0.848218 + 0.375573I
a = 1.68167 + 0.17265I
b = −0.434516 + 0.694240I
−2.28095 + 0.36934I −1.79998 + 1.57281I
u = 0.848218 − 0.375573I
a = 1.68167 − 0.17265I
b = −0.434516 − 0.694240I
−2.28095 − 0.36934I −1.79998 − 1.57281I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.903202 + 0.595706I
a = −0.66474 − 1.60449I
b = 1.44211 − 0.54229I
−1.79493 − 2.26748I 0
u = 0.903202 − 0.595706I
a = −0.66474 + 1.60449I
b = 1.44211 + 0.54229I
−1.79493 + 2.26748I 0
u = 0.553438 + 0.956996I
a = 0.240338 + 0.074404I
b = 1.09277 + 1.06584I
3.6258 + 14.5513I 0
u = 0.553438 − 0.956996I
a = 0.240338 − 0.074404I
b = 1.09277 − 1.06584I
3.6258 − 14.5513I 0
u = −0.805706 + 0.801297I
a = −0.487390 + 0.656086I
b = −0.193006 + 0.633975I
4.71625 0
u = −0.805706 − 0.801297I
a = −0.487390 − 0.656086I
b = −0.193006 − 0.633975I
4.71625 0
u = 0.251795 + 1.124930I
a = −0.254137 + 0.049386I
b = −0.423621 + 0.366735I
3.42082 − 2.87486I 0
u = 0.251795 − 1.124930I
a = −0.254137 − 0.049386I
b = −0.423621 − 0.366735I
3.42082 + 2.87486I 0
u = 0.731346 + 0.379553I
a = −1.245790 + 0.394727I
b = 0.369373 − 0.633955I
−1.96570 − 3.34746I 0. + 8.41971I
u = 0.731346 − 0.379553I
a = −1.245790 − 0.394727I
b = 0.369373 + 0.633955I
−1.96570 + 3.34746I 0. − 8.41971I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.370215 + 1.168900I
a = 0.223126 − 0.084389I
b = 0.462705 − 0.346414I
2.53033 − 8.55334I 0
u = 0.370215 − 1.168900I
a = 0.223126 + 0.084389I
b = 0.462705 + 0.346414I
2.53033 + 8.55334I 0
u = 0.997780 + 0.713374I
a = 0.85559 + 1.68166I
b = −1.31365 + 1.39313I
2.53033 − 8.55334I 0
u = 0.997780 − 0.713374I
a = 0.85559 − 1.68166I
b = −1.31365 − 1.39313I
2.53033 + 8.55334I 0
u = −1.249550 + 0.152177I
a = −0.58334 − 1.39167I
b = −0.482964 − 1.010150I
−2.22763 + 6.76528I 0
u = −1.249550 − 0.152177I
a = −0.58334 + 1.39167I
b = −0.482964 + 1.010150I
−2.22763 − 6.76528I 0
u = 0.948687 + 0.830787I
a = −0.602613 − 0.618497I
b = 0.388518 − 1.079670I
1.63367 0
u = 0.948687 − 0.830787I
a = −0.602613 + 0.618497I
b = 0.388518 + 1.079670I
1.63367 0
u = 1.072930 + 0.680011I
a = −0.71338 − 1.81412I
b = 1.16504 − 1.24505I
−3.78504 − 12.42080I 0
u = 1.072930 − 0.680011I
a = −0.71338 + 1.81412I
b = 1.16504 + 1.24505I
−3.78504 + 12.42080I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.296060 + 0.117362I
a = 0.67390 + 1.34621I
b = 0.541462 + 0.992346I
−3.78504 + 12.42080I 0
u = −1.296060 − 0.117362I
a = 0.67390 − 1.34621I
b = 0.541462 − 0.992346I
−3.78504 − 12.42080I 0
u = 1.102950 + 0.724130I
a = 0.56636 + 1.78230I
b = −1.13689 + 1.28166I
3.6258 − 14.5513I 0
u = 1.102950 − 0.724130I
a = 0.56636 − 1.78230I
b = −1.13689 − 1.28166I
3.6258 + 14.5513I 0
u = 1.304940 + 0.232629I
a = 0.177583 + 0.626392I
b = −0.065583 + 0.228032I
−1.79493 + 2.26748I 0
u = 1.304940 − 0.232629I
a = 0.177583 − 0.626392I
b = −0.065583 − 0.228032I
−1.79493 − 2.26748I 0
u = 1.166690 + 0.634912I
a = 0.454441 + 0.458068I
b = −0.102112 + 0.474616I
−4.36972 − 2.52616I 0
u = 1.166690 − 0.634912I
a = 0.454441 − 0.458068I
b = −0.102112 − 0.474616I
−4.36972 + 2.52616I 0
u = 0.338458 + 0.034083I
a = −0.59797 + 2.01326I
b = 0.210423 − 0.573227I
−1.46923 + 1.71043I −1.72966 − 1.33913I
u = 0.338458 − 0.034083I
a = −0.59797 − 2.01326I
b = 0.210423 + 0.573227I
−1.46923 − 1.71043I −1.72966 + 1.33913I
14
III. I
u
3
= h−u
5
a − u
5
+ 2u
3
a + u
3
− 2au + b − u + 1, 2u
4
a − 3u
4
+ · · · + a
2
+
2, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
5
=
a
u
5
a + u
5
− 2u
3
a − u
3
+ 2au + u − 1
a
8
=
1
u
2
a
9
=
u
5
a − u
5
− 2u
3
a + u
3
+ 2au + a − u − 1
u
5
a + u
5
− 2u
3
a − u
3
+ 2au + u − 1
a
12
=
−u
−u
3
+ u
a
4
=
−u
5
a − u
5
+ 2u
3
a + u
3
− 2au + a − u + 1
u
5
a + u
5
− 2u
3
a − u
3
+ 2au + u − 1
a
1
=
−u
5
a + u
3
a + 2u
4
+ u
3
− au − 2u
2
+ a − 2u
−1
a
6
=
u
5
a + u
5
− 2u
3
a + 2u
4
− u
2
a + u
3
+ 2au − 2u
2
+ a − u − 1
−u
5
a − u
5
+ 2u
3
a + u
2
a + 3u
3
− 2au − 3u − 1
a
10
=
u
3
u
5
− u
3
+ u
a
3
=
−u
5
a + u
3
a + u
3
− au + a + 1
−u
5
a − u
4
a + u
5
+ u
3
a + 2u
2
a + u
2
− a − 1
a
2
=
−2u
5
a − u
4
a + u
5
+ 2u
3
a + 2u
4
+ 2u
2
a + u
3
− au − u
2
− 2u
2u
5
+ 2u
4
− 2u
3
+ au − 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u
4
− 8u
2
− 8u − 2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
c
2
, c
5
, c
7
c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
3
, c
8
u
12
− 9u
11
+ ··· − 104u + 17
c
4
, c
6
, c
9
c
12
u
12
+ u
11
+ 2u
10
− 2u
9
+ 3u
8
− 3u
7
+ 17u
6
− 9u
5
+ 19u
4
− 5u
3
+ 6u
2
+ 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
5
, c
7
c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
3
, c
8
y
12
+ 3y
11
+ ··· + 64y + 289
c
4
, c
6
, c
9
c
12
y
12
+ 3y
11
+ ··· + 12y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 1.72095 + 1.00813I
b = 0.51345 + 1.52069I
−5.42615 − 1.84861I −13.43343 + 1.58845I
u = 1.002190 + 0.295542I
a = 0.39343 − 2.26995I
b = −0.085204 − 0.856161I
−5.42615 − 1.84861I −13.43343 + 1.58845I
u = 1.002190 − 0.295542I
a = 1.72095 − 1.00813I
b = 0.51345 − 1.52069I
−5.42615 + 1.84861I −13.43343 − 1.58845I
u = 1.002190 − 0.295542I
a = 0.39343 + 2.26995I
b = −0.085204 + 0.856161I
−5.42615 + 1.84861I −13.43343 − 1.58845I
u = −0.428243 + 0.664531I
a = −1.071180 − 0.131182I
b = 0.170133 − 0.403810I
2.13628 − 1.84861I 1.43343 + 1.58845I
u = −0.428243 + 0.664531I
a = −0.275983 − 0.338083I
b = −1.172330 + 0.699352I
2.13628 − 1.84861I 1.43343 + 1.58845I
u = −0.428243 − 0.664531I
a = −1.071180 + 0.131182I
b = 0.170133 + 0.403810I
2.13628 + 1.84861I 1.43343 − 1.58845I
u = −0.428243 − 0.664531I
a = −0.275983 + 0.338083I
b = −1.172330 − 0.699352I
2.13628 + 1.84861I 1.43343 − 1.58845I
u = −1.073950 + 0.558752I
a = 1.34873 − 1.14126I
b = −0.344080 − 0.571978I
−1.64493 + 11.38600I −6.00000 − 11.02114I
u = −1.073950 + 0.558752I
a = −0.11594 + 2.13765I
b = 1.41803 + 1.13073I
−1.64493 + 11.38600I −6.00000 − 11.02114I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = 1.34873 + 1.14126I
b = −0.344080 + 0.571978I
−1.64493 − 11.38600I −6.00000 + 11.02114I
u = −1.073950 − 0.558752I
a = −0.11594 − 2.13765I
b = 1.41803 − 1.13073I
−1.64493 − 11.38600I −6.00000 + 11.02114I
19
IV. I
u
4
= hu
5
− u
3
+ b + u, u
3
+ a, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
5
=
−u
3
−u
5
+ u
3
− u
a
8
=
1
u
2
a
9
=
−u
5
+ 2u
3
− u
u
5
− u
3
+ u
a
12
=
−u
−u
3
+ u
a
4
=
u
5
− 2u
3
+ u
−u
5
+ u
3
− u
a
1
=
−1
0
a
6
=
u
u
3
− u
a
10
=
u
3
u
5
− u
3
+ u
a
3
=
−1
−u
2
a
2
=
−u
2
− 1
−u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
4
− 8u
2
− 8u + 4
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
8
c
10
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
4
, c
5
, c
6
c
9
, c
11
, c
12
u
6
− u
5
− u
4
+ 2u
3
− u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
8
c
10
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
4
, c
5
c
6
, c
7
, c
9
c
11
, c
12
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.743983 − 0.864704I
b = −0.428243 − 0.664531I
−3.78121 − 1.84861I −7.43343 + 1.58845I
u = 1.002190 − 0.295542I
a = −0.743983 + 0.864704I
b = −0.428243 + 0.664531I
−3.78121 + 1.84861I −7.43343 − 1.58845I
u = −0.428243 + 0.664531I
a = −0.488802 − 0.072152I
b = 1.002190 − 0.295542I
3.78121 − 1.84861I 7.43343 + 1.58845I
u = −0.428243 − 0.664531I
a = −0.488802 + 0.072152I
b = 1.002190 + 0.295542I
3.78121 + 1.84861I 7.43343 − 1.58845I
u = −1.073950 + 0.558752I
a = 0.23279 − 1.75889I
b = −1.073950 − 0.558752I
11.3860I 0. − 11.02114I
u = −1.073950 − 0.558752I
a = 0.23279 + 1.75889I
b = −1.073950 + 0.558752I
− 11.3860I 0. + 11.02114I
23
V. I
u
5
= h−2u
43
a − 4u
42
a + · · · + 4b − 65, 50u
43
a − 95u
43
+ · · · − 468a +
943, u
44
+ 3u
43
+ · · · − 14u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
5
=
a
1
2
u
43
a + u
42
a + ··· + 163u +
65
4
a
8
=
1
u
2
a
9
=
7u
43
a +
7
8
u
43
+ ··· −
5
2
a −
91
8
9
4
u
43
a +
9
4
u
42
a + ··· +
7
2
a − 1
a
12
=
−u
−u
3
+ u
a
4
=
−
1
2
u
43
a − u
42
a + ··· + a −
65
4
1
2
u
43
a + u
42
a + ··· + 163u +
65
4
a
1
=
21
4
u
42
a + 2u
43
+ ··· −
65
4
a +
23
2
−1
a
6
=
49
2
u
43
a + 2u
43
+ ··· −
139
4
a +
21
2
−
5
2
u
43
a −
1
8
u
43
+ ··· +
1
4
a −
7
8
a
10
=
u
3
u
5
− u
3
+ u
a
3
=
−
9
2
u
43
−
19
4
u
42
+ ··· + a −
41
4
−
1
2
u
43
a − 6u
43
+ ··· + 226u +
83
4
a
2
=
−
95
4
u
43
a +
13
8
u
43
+ ··· + 29a +
79
8
7
4
u
43
a +
11
8
u
43
+ ··· −
5
2
a −
11
8
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
97
4
u
43
− 54u
42
+ ··· +
1089
4
u +
51
4
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
44
+ 19u
43
+ ··· + 70u + 1)
2
c
2
, c
5
, c
7
c
11
(u
44
− 3u
43
+ ··· + 14u − 1)
2
c
3
, c
8
(u
44
+ u
43
+ ··· + 840u + 271)
2
c
4
, c
6
, c
9
c
12
u
88
+ 11u
87
+ ··· + 20u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
44
+ 17y
43
+ ··· − 3330y + 1)
2
c
2
, c
5
, c
7
c
11
(y
44
− 19y
43
+ ··· − 70y + 1)
2
c
3
, c
8
(y
44
− 7y
43
+ ··· − 1090962y + 73441)
2
c
4
, c
6
, c
9
c
12
y
88
− 39y
87
+ ··· − 250y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.767481 + 0.649572I
a = −0.209749 + 0.455086I
b = 1.050190 + 0.737585I
3.61742 + 6.06223I 4.09868 − 3.56729I
u = 0.767481 + 0.649572I
a = −0.69676 − 2.08757I
b = 1.35788 − 1.16717I
3.61742 + 6.06223I 4.09868 − 3.56729I
u = 0.767481 − 0.649572I
a = −0.209749 − 0.455086I
b = 1.050190 − 0.737585I
3.61742 − 6.06223I 4.09868 + 3.56729I
u = 0.767481 − 0.649572I
a = −0.69676 + 2.08757I
b = 1.35788 + 1.16717I
3.61742 − 6.06223I 4.09868 + 3.56729I
u = 0.803659 + 0.647731I
a = 0.091655 − 0.132248I
b = −1.193190 − 0.680438I
5.35656 + 0.02685I 6.61609 + 1.70053I
u = 0.803659 + 0.647731I
a = 0.66010 + 2.10096I
b = −1.33111 + 1.04031I
5.35656 + 0.02685I 6.61609 + 1.70053I
u = 0.803659 − 0.647731I
a = 0.091655 + 0.132248I
b = −1.193190 + 0.680438I
5.35656 − 0.02685I 6.61609 − 1.70053I
u = 0.803659 − 0.647731I
a = 0.66010 − 2.10096I
b = −1.33111 − 1.04031I
5.35656 − 0.02685I 6.61609 − 1.70053I
u = 0.851089 + 0.590714I
a = 0.07497 − 1.50979I
b = 1.84927 − 0.00718I
−1.70735 − 2.34151I 6.14112 + 4.86696I
u = 0.851089 + 0.590714I
a = −0.93452 − 1.56224I
b = 1.150410 − 0.258778I
−1.70735 − 2.34151I 6.14112 + 4.86696I
27
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.851089 − 0.590714I
a = 0.07497 + 1.50979I
b = 1.84927 + 0.00718I
−1.70735 + 2.34151I 6.14112 − 4.86696I
u = 0.851089 − 0.590714I
a = −0.93452 + 1.56224I
b = 1.150410 + 0.258778I
−1.70735 + 2.34151I 6.14112 − 4.86696I
u = −0.473872 + 0.833820I
a = −0.325630 − 0.110420I
b = 0.598560 − 0.485867I
2.48681 − 1.78904I −1.77660 + 1.34347I
u = −0.473872 + 0.833820I
a = −0.181027 − 0.089265I
b = −1.054730 + 0.566967I
2.48681 − 1.78904I −1.77660 + 1.34347I
u = −0.473872 − 0.833820I
a = −0.325630 + 0.110420I
b = 0.598560 + 0.485867I
2.48681 + 1.78904I −1.77660 − 1.34347I
u = −0.473872 − 0.833820I
a = −0.181027 + 0.089265I
b = −1.054730 − 0.566967I
2.48681 + 1.78904I −1.77660 − 1.34347I
u = −0.503143 + 0.946145I
a = 0.120712 − 0.412859I
b = 0.808803 − 0.791262I
5.08140 − 5.03772I 5.56121 + 5.67665I
u = −0.503143 + 0.946145I
a = −0.128920 − 0.292183I
b = −1.123420 + 0.229540I
5.08140 − 5.03772I 5.56121 + 5.67665I
u = −0.503143 − 0.946145I
a = 0.120712 + 0.412859I
b = 0.808803 + 0.791262I
5.08140 + 5.03772I 5.56121 − 5.67665I
u = −0.503143 − 0.946145I
a = −0.128920 + 0.292183I
b = −1.123420 − 0.229540I
5.08140 + 5.03772I 5.56121 − 5.67665I
28
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.542619 + 0.934381I
a = −0.217567 + 0.342060I
b = −0.878871 + 0.768623I
5.35656 − 0.02685I 6.61609 − 1.70053I
u = −0.542619 + 0.934381I
a = 0.055966 + 0.360352I
b = 1.039850 − 0.142869I
5.35656 − 0.02685I 6.61609 − 1.70053I
u = −0.542619 − 0.934381I
a = −0.217567 − 0.342060I
b = −0.878871 − 0.768623I
5.35656 + 0.02685I 6.61609 + 1.70053I
u = −0.542619 − 0.934381I
a = 0.055966 − 0.360352I
b = 1.039850 + 0.142869I
5.35656 + 0.02685I 6.61609 + 1.70053I
u = 0.892273 + 0.637275I
a = −0.798485 + 0.407722I
b = −1.70312 − 0.82985I
5.08140 − 5.03772I 5.56121 + 5.67665I
u = 0.892273 + 0.637275I
a = 0.79044 + 2.21552I
b = −0.931912 + 0.821648I
5.08140 − 5.03772I 5.56121 + 5.67665I
u = 0.892273 − 0.637275I
a = −0.798485 − 0.407722I
b = −1.70312 + 0.82985I
5.08140 + 5.03772I 5.56121 − 5.67665I
u = 0.892273 − 0.637275I
a = 0.79044 − 2.21552I
b = −0.931912 − 0.821648I
5.08140 + 5.03772I 5.56121 − 5.67665I
u = −0.802626 + 0.757447I
a = −0.492685 + 1.009980I
b = 0.379182 + 0.670238I
4.62114 5.54727 + 0.I
u = −0.802626 + 0.757447I
a = −0.458276 + 0.324516I
b = −0.733776 + 0.580087I
4.62114 5.54727 + 0.I
29
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.802626 − 0.757447I
a = −0.492685 − 1.009980I
b = 0.379182 − 0.670238I
4.62114 5.54727 + 0.I
u = −0.802626 − 0.757447I
a = −0.458276 − 0.324516I
b = −0.733776 − 0.580087I
4.62114 5.54727 + 0.I
u = 0.918693 + 0.631895I
a = 1.086560 − 0.368999I
b = 1.77703 + 0.97307I
3.15038 − 11.06350I 2.31684 + 10.51224I
u = 0.918693 + 0.631895I
a = −0.79220 − 2.32690I
b = 0.801722 − 0.841787I
3.15038 − 11.06350I 2.31684 + 10.51224I
u = 0.918693 − 0.631895I
a = 1.086560 + 0.368999I
b = 1.77703 − 0.97307I
3.15038 + 11.06350I 2.31684 − 10.51224I
u = 0.918693 − 0.631895I
a = −0.79220 + 2.32690I
b = 0.801722 + 0.841787I
3.15038 + 11.06350I 2.31684 − 10.51224I
u = 1.11703
a = −0.559527 + 1.206560I
b = −0.064688 + 0.847977I
−3.19687 −5.88290
u = 1.11703
a = −0.559527 − 1.206560I
b = −0.064688 − 0.847977I
−3.19687 −5.88290
u = −0.972088 + 0.562819I
a = 1.63782 − 0.13643I
b = −0.300509 − 0.254450I
−3.73793 + 3.81466I −6.30765 − 8.57961I
u = −0.972088 + 0.562819I
a = −0.71054 + 2.33938I
b = 1.35813 + 1.69326I
−3.73793 + 3.81466I −6.30765 − 8.57961I
30
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.972088 − 0.562819I
a = 1.63782 + 0.13643I
b = −0.300509 + 0.254450I
−3.73793 − 3.81466I −6.30765 + 8.57961I
u = −0.972088 − 0.562819I
a = −0.71054 − 2.33938I
b = 1.35813 − 1.69326I
−3.73793 − 3.81466I −6.30765 + 8.57961I
u = −0.714060 + 0.501949I
a = 1.34919 + 0.68585I
b = 1.59813 − 1.14955I
−2.85723 + 0.57531I −2.18655 + 5.07930I
u = −0.714060 + 0.501949I
a = 1.59862 − 1.48482I
b = 0.0868291 − 0.0247619I
−2.85723 + 0.57531I −2.18655 + 5.07930I
u = −0.714060 − 0.501949I
a = 1.34919 − 0.68585I
b = 1.59813 + 1.14955I
−2.85723 − 0.57531I −2.18655 − 5.07930I
u = −0.714060 − 0.501949I
a = 1.59862 + 1.48482I
b = 0.0868291 + 0.0247619I
−2.85723 − 0.57531I −2.18655 − 5.07930I
u = 1.182370 + 0.249072I
a = 1.33410 + 0.52761I
b = 0.716253 + 0.936843I
−3.73793 + 3.81466I −6.30765 − 8.57961I
u = 1.182370 + 0.249072I
a = −0.04691 − 1.87311I
b = −0.139509 − 0.906647I
−3.73793 + 3.81466I −6.30765 − 8.57961I
u = 1.182370 − 0.249072I
a = 1.33410 − 0.52761I
b = 0.716253 − 0.936843I
−3.73793 − 3.81466I −6.30765 + 8.57961I
u = 1.182370 − 0.249072I
a = −0.04691 + 1.87311I
b = −0.139509 + 0.906647I
−3.73793 − 3.81466I −6.30765 + 8.57961I
31
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.044760 + 0.613681I
a = −0.947346 + 0.792517I
b = 0.530131 + 0.447375I
0.48539 + 6.82448I 0. − 6.22925I
u = −1.044760 + 0.613681I
a = 0.34576 − 1.93178I
b = −1.17630 − 1.20444I
0.48539 + 6.82448I 0. − 6.22925I
u = −1.044760 − 0.613681I
a = −0.947346 − 0.792517I
b = 0.530131 − 0.447375I
0.48539 − 6.82448I 0. + 6.22925I
u = −1.044760 − 0.613681I
a = 0.34576 + 1.93178I
b = −1.17630 + 1.20444I
0.48539 − 6.82448I 0. + 6.22925I
u = 1.215330 + 0.165372I
a = −1.025870 − 0.466462I
b = −0.541188 − 0.729277I
−2.85723 − 0.57531I 0
u = 1.215330 + 0.165372I
a = 0.04140 + 1.59807I
b = 0.156527 + 0.829153I
−2.85723 − 0.57531I 0
u = 1.215330 − 0.165372I
a = −1.025870 + 0.466462I
b = −0.541188 + 0.729277I
−2.85723 + 0.57531I 0
u = 1.215330 − 0.165372I
a = 0.04140 − 1.59807I
b = 0.156527 − 0.829153I
−2.85723 + 0.57531I 0
u = −0.695081 + 0.217967I
a = 0.305437 + 1.080750I
b = 1.56163 − 0.21982I
0.57189 − 7.31268I −5.07151 + 6.33709I
u = −0.695081 + 0.217967I
a = 3.07338 − 0.83141I
b = 0.347865 − 0.007131I
0.57189 − 7.31268I −5.07151 + 6.33709I
32
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.695081 − 0.217967I
a = 0.305437 − 1.080750I
b = 1.56163 + 0.21982I
0.57189 + 7.31268I −5.07151 − 6.33709I
u = −0.695081 − 0.217967I
a = 3.07338 + 0.83141I
b = 0.347865 + 0.007131I
0.57189 + 7.31268I −5.07151 − 6.33709I
u = −1.109330 + 0.644832I
a = −0.65014 + 1.36464I
b = 0.683547 + 0.755743I
0.57189 + 7.31268I 0
u = −1.109330 + 0.644832I
a = 0.09902 − 1.63155I
b = −1.15242 − 0.87299I
0.57189 + 7.31268I 0
u = −1.109330 − 0.644832I
a = −0.65014 − 1.36464I
b = 0.683547 − 0.755743I
0.57189 − 7.31268I 0
u = −1.109330 − 0.644832I
a = 0.09902 + 1.63155I
b = −1.15242 + 0.87299I
0.57189 − 7.31268I 0
u = 1.318490 + 0.024433I
a = 0.150294 + 0.994451I
b = 0.127511 + 0.470493I
−1.70735 + 2.34151I 0
u = 1.318490 + 0.024433I
a = −0.274504 + 0.224235I
b = −0.188454 − 0.112226I
−1.70735 + 2.34151I 0
u = 1.318490 − 0.024433I
a = 0.150294 − 0.994451I
b = 0.127511 − 0.470493I
−1.70735 − 2.34151I 0
u = 1.318490 − 0.024433I
a = −0.274504 − 0.224235I
b = −0.188454 + 0.112226I
−1.70735 − 2.34151I 0
33
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.110670 + 0.713391I
a = 0.113297 + 1.048100I
b = 1.135860 + 0.456326I
3.61742 + 6.06223I 0
u = −1.110670 + 0.713391I
a = 0.44380 − 1.68331I
b = −0.806935 − 1.052440I
3.61742 + 6.06223I 0
u = −1.110670 − 0.713391I
a = 0.113297 − 1.048100I
b = 1.135860 − 0.456326I
3.61742 − 6.06223I 0
u = −1.110670 − 0.713391I
a = 0.44380 + 1.68331I
b = −0.806935 + 1.052440I
3.61742 − 6.06223I 0
u = −0.235182 + 0.635023I
a = 1.24503 + 0.86650I
b = 0.016785 + 0.660631I
0.48539 − 6.82448I −1.22382 + 6.22925I
u = −0.235182 + 0.635023I
a = −0.118272 + 0.377558I
b = 1.207550 − 0.716047I
0.48539 − 6.82448I −1.22382 + 6.22925I
u = −0.235182 − 0.635023I
a = 1.24503 − 0.86650I
b = 0.016785 − 0.660631I
0.48539 + 6.82448I −1.22382 − 6.22925I
u = −0.235182 − 0.635023I
a = −0.118272 − 0.377558I
b = 1.207550 + 0.716047I
0.48539 + 6.82448I −1.22382 − 6.22925I
u = −1.133930 + 0.701691I
a = −0.187501 − 1.213320I
b = −1.214170 − 0.539939I
3.15038 + 11.06350I 0
u = −1.133930 + 0.701691I
a = −0.50414 + 1.69437I
b = 0.748726 + 1.033840I
3.15038 + 11.06350I 0
34
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.133930 − 0.701691I
a = −0.187501 + 1.213320I
b = −1.214170 + 0.539939I
3.15038 − 11.06350I 0
u = −1.133930 − 0.701691I
a = −0.50414 − 1.69437I
b = 0.748726 − 1.033840I
3.15038 − 11.06350I 0
u = −0.604720 + 0.161152I
a = −0.485397 − 0.758391I
b = −1.382110 + 0.218862I
2.48681 − 1.78904I −1.77660 + 1.34347I
u = −0.604720 + 0.161152I
a = −3.01193 + 0.44916I
b = −0.403113 − 0.055546I
2.48681 − 1.78904I −1.77660 + 1.34347I
u = −0.604720 − 0.161152I
a = −0.485397 + 0.758391I
b = −1.382110 − 0.218862I
2.48681 + 1.78904I −1.77660 − 1.34347I
u = −0.604720 − 0.161152I
a = −3.01193 − 0.44916I
b = −0.403113 + 0.055546I
2.48681 + 1.78904I −1.77660 − 1.34347I
u = −0.131617
a = 5.64036 + 4.49230I
b = 0.731173 − 0.579698I
−3.19687 −5.88290
u = −0.131617
a = 5.64036 − 4.49230I
b = 0.731173 + 0.579698I
−3.19687 −5.88290
35
VI. I
u
6
=
h3u
15
+5u
14
+· · ·+b−1, −7u
15
−28u
14
+· · ·+2a−22, u
16
+4u
15
+· · ·+8u+2i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
5
=
7
2
u
15
+ 14u
14
+ ··· +
59
2
u + 11
−3u
15
− 5u
14
+ ··· + u + 1
a
8
=
1
u
2
a
9
=
−
11
2
u
15
− 17u
14
+ ··· −
67
2
u − 8
u
15
+ 3u
14
+ ··· + 7u + 1
a
12
=
−u
−u
3
+ u
a
4
=
13
2
u
15
+ 19u
14
+ ··· +
57
2
u + 10
−3u
15
− 5u
14
+ ··· + u + 1
a
1
=
−
13
2
u
15
− 20u
14
+ ··· −
67
2
u − 11
4u
15
+ 9u
14
+ ··· + 7u + 1
a
6
=
17
2
u
15
+ 30u
14
+ ··· +
143
2
u + 24
−4u
15
− 13u
14
+ ··· − 30u − 9
a
10
=
u
3
u
5
− u
3
+ u
a
3
=
3
2
u
15
+ 4u
14
+ ··· +
5
2
u + 2
−4u
15
− 11u
14
+ ··· − 18u − 5
a
2
=
13
2
u
15
+ 26u
14
+ ··· +
139
2
u + 25
−7u
15
− 21u
14
+ ··· − 41u − 11
(ii) Obstruction class = 1
(iii) Cusp Shapes = −38u
15
− 69u
14
+ 46u
13
+ 251u
12
+ 175u
11
− 71u
10
− 114u
9
−
26u
8
− 246u
7
− 430u
6
− 310u
5
− 60u
4
− 64u
3
− 35u
2
+ 26u + 42
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
16
− 6u
15
+ ··· + 4u + 4
c
2
, c
7
u
16
+ 4u
15
+ ··· + 8u + 2
c
3
, c
8
(u
8
+ 2u
7
+ 2u
6
+ u
2
+ u + 1)
2
c
4
, c
6
, c
9
c
12
u
16
− 6u
14
+ ··· − u
2
+ 1
c
5
, c
11
u
16
− 4u
15
+ ··· − 8u + 2
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
16
+ 2y
15
+ ··· + 152y + 16
c
2
, c
5
, c
7
c
11
y
16
− 6y
15
+ ··· + 4y + 4
c
3
, c
8
(y
8
+ 4y
6
+ 2y
5
+ 2y
4
+ 4y
3
+ y
2
+ y + 1)
2
c
4
, c
6
, c
9
c
12
y
16
− 12y
15
+ ··· − 2y + 1
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.484640 + 0.846797I
a = −0.680045 + 0.269791I
b = −0.618812 − 0.101203I
2.47558 − 7.94608I 0.92481 + 5.79314I
u = 0.484640 − 0.846797I
a = −0.680045 − 0.269791I
b = −0.618812 + 0.101203I
2.47558 + 7.94608I 0.92481 − 5.79314I
u = −0.620876 + 0.837136I
a = 0.129335 + 0.230266I
b = 0.980946 − 0.677334I
3.68697 − 2.14875I 5.80448 + 2.27366I
u = −0.620876 − 0.837136I
a = 0.129335 − 0.230266I
b = 0.980946 + 0.677334I
3.68697 + 2.14875I 5.80448 − 2.27366I
u = −0.868732 + 0.620313I
a = 0.43706 − 1.78935I
b = −1.81641 − 0.27594I
−2.07294 + 2.43245I −21.6315 − 8.0683I
u = −0.868732 − 0.620313I
a = 0.43706 + 1.78935I
b = −1.81641 + 0.27594I
−2.07294 − 2.43245I −21.6315 + 8.0683I
u = −0.597300 + 0.462977I
a = 1.26482 − 0.64500I
b = −1.184110 + 0.133480I
1.66766 − 7.05131I 3.40216 + 4.97138I
u = −0.597300 − 0.462977I
a = 1.26482 + 0.64500I
b = −1.184110 − 0.133480I
1.66766 + 7.05131I 3.40216 − 4.97138I
u = −1.034390 + 0.719349I
a = −0.62644 + 1.38546I
b = 0.99042 + 1.11066I
2.47558 + 7.94608I 0.92481 − 5.79314I
u = −1.034390 − 0.719349I
a = −0.62644 − 1.38546I
b = 0.99042 − 1.11066I
2.47558 − 7.94608I 0.92481 + 5.79314I
39
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.125140 + 0.624650I
a = −0.20300 + 1.50281I
b = 0.927126 + 0.676564I
1.66766 + 7.05131I 3.40216 − 4.97138I
u = −1.125140 − 0.624650I
a = −0.20300 − 1.50281I
b = 0.927126 − 0.676564I
1.66766 − 7.05131I 3.40216 + 4.97138I
u = 0.270172 + 0.658282I
a = 0.744963 − 0.703702I
b = 0.764226 + 0.048273I
3.68697 − 2.14875I 5.80448 + 2.27366I
u = 0.270172 − 0.658282I
a = 0.744963 + 0.703702I
b = 0.764226 − 0.048273I
3.68697 + 2.14875I 5.80448 − 2.27366I
u = 1.49163 + 0.08776I
a = −0.066697 − 0.588457I
b = −0.043384 − 0.465221I
−2.07294 + 2.43245I −21.6315 − 8.0683I
u = 1.49163 − 0.08776I
a = −0.066697 + 0.588457I
b = −0.043384 + 0.465221I
−2.07294 − 2.43245I −21.6315 + 8.0683I
40
VII. I
u
7
= h−u
2
a + b − 1, a
2
+ 2au + 2u
2
+ a + 3u + 2, u
3
+ u
2
− 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
5
=
a
u
2
a + 1
a
8
=
1
u
2
a
9
=
−a + 1
−u
2
a + u
2
− 1
a
12
=
−u
u
2
+ u − 1
a
4
=
−u
2
a + a − 1
u
2
a + 1
a
1
=
−a − 2u − 1
−1
a
6
=
−u
2
a − a − 2u − 1
−u
2
a − au − u
2
+ a − 1
a
10
=
−u
2
+ 1
u
2
a
3
=
−u
2
a + u
2
+ a − 2
u
2
a − u
2
+ 1
a
2
=
−au − u
2
− u − 2
u
2
a + au − a − u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u − 2
41
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
3
+ u
2
+ 2u + 1)
2
c
2
, c
5
, c
7
c
11
(u
3
− u
2
+ 1)
2
c
3
, c
8
(u + 1)
6
c
4
, c
6
, c
9
c
12
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
42
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
3
+ 3y
2
+ 2y − 1)
2
c
2
, c
5
, c
7
c
11
(y
3
− y
2
+ 2y − 1)
2
c
3
, c
8
(y − 1)
6
c
4
, c
6
, c
9
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
43
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.562133 − 1.239140I
b = −0.498832 − 1.001300I
4.40332 + 5.65624I 5.01951 − 5.95889I
u = −0.877439 + 0.744862I
a = 0.192744 − 0.250580I
b = 0.713912 − 0.305839I
4.40332 + 5.65624I 5.01951 − 5.95889I
u = −0.877439 − 0.744862I
a = 0.562133 + 1.239140I
b = −0.498832 + 1.001300I
4.40332 − 5.65624I 5.01951 + 5.95889I
u = −0.877439 − 0.744862I
a = 0.192744 + 0.250580I
b = 0.713912 + 0.305839I
4.40332 − 5.65624I 5.01951 + 5.95889I
u = 0.754878
a = −1.25488 + 1.95694I
b = 0.284920 + 1.115140I
−3.87184 −8.03900
u = 0.754878
a = −1.25488 − 1.95694I
b = 0.284920 − 1.115140I
−3.87184 −8.03900
44
VIII. I
u
8
=
h−u
3
a−u
2
a−u
3
+au+2b+1, −u
2
a+u
3
+a
2
+au−2u
2
+a−u+2, u
4
−u
2
+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
5
=
a
1
2
u
3
a +
1
2
u
3
+ ··· −
1
2
au −
1
2
a
8
=
1
u
2
a
9
=
−
1
2
u
3
a + u
3
+ ··· −
1
2
a +
1
2
u
3
a
12
=
−u
−u
3
+ u
a
4
=
−
1
2
u
3
a −
1
2
u
3
+ ··· + a +
1
2
1
2
u
3
a +
1
2
u
3
+ ··· −
1
2
au −
1
2
a
1
=
1
2
u
3
a −
1
2
u
2
+ ··· −
1
2
a +
1
2
1
a
6
=
−
1
2
u
3
a +
1
2
u
2
+ ··· +
1
2
a −
1
2
−1
a
10
=
u
3
0
a
3
=
a
1
2
u
3
a +
1
2
u
3
+ ··· −
1
2
au −
1
2
a
2
=
1
2
u
3
a −
1
2
u
2
+ ··· +
1
2
a +
1
2
1
2
u
3
a +
1
2
u
3
+ ··· −
1
2
au +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 8
45
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
8
u
8
− 2u
6
+ 2u
5
+ 2u
4
− 2u
3
+ 3u
2
+ 4u + 1
c
4
, c
12
u
8
− 4u
7
+ 10u
6
− 16u
5
+ 18u
4
− 14u
3
+ 7u
2
− 2u + 1
c
5
(u + 1)
8
c
6
, c
9
(u
2
+ 1)
4
c
7
, c
11
(u
4
− u
2
+ 1)
2
c
10
(u
2
− u + 1)
4
46
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
8
c
3
, c
8
y
8
− 4y
7
+ 8y
6
− 6y
5
+ 2y
4
− 12y
3
+ 29y
2
− 10y + 1
c
4
, c
12
y
8
+ 4y
7
+ 8y
6
+ 6y
5
+ 2y
4
+ 12y
3
+ 29y
2
+ 10y + 1
c
6
, c
9
(y + 1)
8
c
7
, c
11
(y
2
− y + 1)
4
c
10
(y
2
+ y + 1)
4
47
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 0.131115 + 0.786143I
b = −1.060940 + 0.445679I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = 0.866025 + 0.500000I
a = −1.49714 − 0.42012I
b = 0.060942 − 0.445679I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = 0.866025 − 0.500000I
a = 0.131115 − 0.786143I
b = −1.060940 − 0.445679I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = −1.49714 + 0.42012I
b = 0.060942 + 0.445679I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = −0.866025 + 0.500000I
a = −0.553254 + 1.002550I
b = −0.69440 + 1.28601I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = −0.866025 + 0.500000I
a = 0.91928 − 2.36858I
b = −0.305600 − 1.286010I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = −0.866025 − 0.500000I
a = −0.553254 − 1.002550I
b = −0.69440 − 1.28601I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = 0.91928 + 2.36858I
b = −0.305600 + 1.286010I
−3.28987 − 2.02988I −6.00000 + 3.46410I
48
IX. I
u
9
= h7.93 × 10
6
b − 7.18 × 10
4
a
7
+ · · · − 9.81 × 10
6
a + 3.14 × 10
6
, a
8
+
6a
6
+ · · · − 60a + 73, u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
1
a
5
=
a
0.00904756a
7
+ 0.00216843a
6
+ ··· + 1.23707a − 0.396120
a
8
=
1
1
a
9
=
−0.00216843a
7
− 0.00652609a
6
+ ··· − 0.146733a + 1.66047
0.00216843a
7
+ 0.00652609a
6
+ ··· + 0.146733a + 1.33953
a
12
=
−1
0
a
4
=
−0.00904756a
7
− 0.00216843a
6
+ ··· − 0.237070a + 0.396120
0.00904756a
7
+ 0.00216843a
6
+ ··· + 1.23707a − 0.396120
a
1
=
0.00216843a
7
+ 0.00652609a
6
+ ··· + 0.146733a − 0.660472
−1
a
6
=
0.000900759a
7
+ 0.0124795a
6
+ ··· + 0.0865369a + 3.18407
0.00867371a
7
+ 0.0261044a
6
+ ··· + 0.586933a + 1.35811
a
10
=
1
1
a
3
=
−0.0271427a
7
− 0.00650529a
6
+ ··· − 1.71121a + 1.18836
−0.00904756a
7
− 0.00216843a
6
+ ··· − 0.237070a + 0.396120
a
2
=
−0.0242196a
7
− 0.0533541a
6
+ ··· − 1.58772a − 0.706203
−0.00994138a
7
− 0.0201510a
6
+ ··· − 0.647129a − 0.513573
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
864
10477
a
7
−
144
10477
a
6
−
5208
10477
a
5
+
4316
10477
a
4
−
14760
10477
a
3
+
13092
10477
a
2
−
52032
10477
a −
40648
10477
49
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
4
c
2
, c
5
(u
4
− u
2
+ 1)
2
c
3
, c
8
u
8
− 2u
6
+ 2u
5
+ 2u
4
− 2u
3
+ 3u
2
+ 4u + 1
c
4
, c
12
(u
2
+ 1)
4
c
6
, c
9
u
8
− 4u
7
+ 10u
6
− 16u
5
+ 18u
4
− 14u
3
+ 7u
2
− 2u + 1
c
7
, c
10
(u − 1)
8
c
11
(u + 1)
8
50
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
4
c
2
, c
5
(y
2
− y + 1)
4
c
3
, c
8
y
8
− 4y
7
+ 8y
6
− 6y
5
+ 2y
4
− 12y
3
+ 29y
2
− 10y + 1
c
4
, c
12
(y + 1)
8
c
6
, c
9
y
8
+ 4y
7
+ 8y
6
+ 6y
5
+ 2y
4
+ 12y
3
+ 29y
2
+ 10y + 1
c
7
, c
10
, c
11
(y − 1)
8
51
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.445679 + 0.939058I
b = 1.000000I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = 1.00000
a = 0.445679 − 0.939058I
b = − 1.000000I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = 1.28601 + 1.30560I
b = 1.000000I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = 1.28601 − 1.30560I
b = − 1.000000I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = 1.00000
a = −0.44568 + 2.06094I
b = 1.000000I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = 1.00000
a = −0.44568 − 2.06094I
b = − 1.000000I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = −1.28601 + 1.69440I
b = 1.000000I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = −1.28601 − 1.69440I
b = − 1.000000I
−3.28987 + 2.02988I −6.00000 − 3.46410I
52
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u − 1)
8
(u
2
− u + 1)
4
(u
3
+ u
2
+ 2u + 1)
2
· (u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· ((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
)(u
16
− 6u
15
+ ··· + 4u + 4)
· (u
18
+ 7u
17
+ ··· − 4u + 4)(u
44
+ 19u
43
+ ··· + 70u + 1)
2
· (u
50
+ 19u
49
+ ··· + 5099u + 169)
c
2
, c
7
(u − 1)
8
(u
3
− u
2
+ 1)
2
(u
4
− u
2
+ 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
· (u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
16
+ 4u
15
+ ··· + 8u + 2)
· (u
18
+ 3u
17
+ ··· + 6u + 2)(u
44
− 3u
43
+ ··· + 14u − 1)
2
· (u
50
+ 11u
49
+ ··· + 165u + 13)
c
3
, c
8
(u + 1)
6
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
8
− 2u
6
+ 2u
5
+ 2u
4
− 2u
3
+ 3u
2
+ 4u + 1)
2
· ((u
8
+ 2u
7
+ 2u
6
+ u
2
+ u + 1)
2
)(u
12
− 9u
11
+ ··· − 104u + 17)
· (u
18
− 9u
17
+ ··· − 16u + 8)(u
25
+ 4u
24
+ ··· + 3u + 1)
2
· (u
44
+ u
43
+ ··· + 840u + 271)
2
c
4
, c
6
, c
9
c
12
((u
2
+ 1)
4
)(u
6
− u
5
+ ··· − u + 1)(u
6
+ u
5
+ ··· + 2u + 1)
· (u
8
− 4u
7
+ 10u
6
− 16u
5
+ 18u
4
− 14u
3
+ 7u
2
− 2u + 1)
· (u
12
+ u
11
+ 2u
10
− 2u
9
+ 3u
8
− 3u
7
+ 17u
6
− 9u
5
+ 19u
4
− 5u
3
+ 6u
2
+ 1)
· (u
16
− 6u
14
+ ··· − u
2
+ 1)(u
18
+ 5u
16
+ ··· + u + 1)
· (u
50
+ 5u
49
+ ··· + 4u + 1)(u
88
+ 11u
87
+ ··· + 20u + 1)
c
5
, c
11
(u + 1)
8
(u
3
− u
2
+ 1)
2
(u
4
− u
2
+ 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
· (u
16
− 4u
15
+ ··· − 8u + 2)(u
18
+ 3u
17
+ ··· + 6u + 2)
· ((u
44
− 3u
43
+ ··· + 14u − 1)
2
)(u
50
+ 11u
49
+ ··· + 165u + 13)
53
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y − 1)
8
(y
2
+ y + 1)
4
(y
3
+ 3y
2
+ 2y − 1)
2
· ((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
)(y
16
+ 2y
15
+ ··· + 152y + 16)
· (y
18
+ 13y
17
+ ··· − 272y + 16)(y
44
+ 17y
43
+ ··· − 3330y + 1)
2
· (y
50
+ 13y
49
+ ··· − 3709039y + 28561)
c
2
, c
5
, c
7
c
11
(y − 1)
8
(y
2
− y + 1)
4
(y
3
− y
2
+ 2y − 1)
2
· ((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
)(y
16
− 6y
15
+ ··· + 4y + 4)
· (y
18
− 7y
17
+ ··· + 4y + 4)(y
44
− 19y
43
+ ··· − 70y + 1)
2
· (y
50
− 19y
49
+ ··· − 5099y + 169)
c
3
, c
8
(y − 1)
6
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
8
+ 4y
6
+ 2y
5
+ 2y
4
+ 4y
3
+ y
2
+ y + 1)
2
· (y
8
− 4y
7
+ 8y
6
− 6y
5
+ 2y
4
− 12y
3
+ 29y
2
− 10y + 1)
2
· (y
12
+ 3y
11
+ ··· + 64y + 289)(y
18
− 9y
17
+ ··· − 480y + 64)
· (y
25
− 8y
24
+ ··· + y − 1)
2
· (y
44
− 7y
43
+ ··· − 1090962y + 73441)
2
c
4
, c
6
, c
9
c
12
((y + 1)
8
)(y
6
− 3y
5
+ ··· − y + 1)(y
6
+ 3y
5
+ ··· + 2y
3
+ 1)
· (y
8
+ 4y
7
+ 8y
6
+ 6y
5
+ 2y
4
+ 12y
3
+ 29y
2
+ 10y + 1)
· (y
12
+ 3y
11
+ ··· + 12y + 1)(y
16
− 12y
15
+ ··· − 2y + 1)
· (y
18
+ 10y
17
+ ··· + y + 1)(y
50
+ 21y
49
+ ··· + 52y + 1)
· (y
88
− 39y
87
+ ··· − 250y + 1)
54
