12a
0389
(K12a
0389
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 11 2 5 1 12 8 7 4
Solving Sequence
2,6
3
7,11
12 1 5 8 9 10 4
c
2
c
6
c
11
c
1
c
5
c
7
c
8
c
10
c
4
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.76018 × 10
52
u
42
− 8.19007 × 10
53
u
41
+ ··· + 4.22162 × 10
54
b − 1.94678 × 10
55
,
− 3.03721 × 10
54
u
42
− 1.54819 × 10
55
u
41
+ ··· + 5.91027 × 10
55
a − 2.03913 × 10
56
,
u
43
+ 4u
42
+ ··· + 134u + 28i
I
u
2
= h−5.79031 × 10
80
au
81
+ 2.67049 × 10
81
u
81
+ ··· − 6.08145 × 10
81
a − 7.04436 × 10
79
,
2.08713 × 10
81
au
81
− 4.14790 × 10
81
u
81
+ ··· + 2.02533 × 10
82
a − 9.22667 × 10
81
,
u
82
+ 16u
80
+ ··· + 28u − 5i
I
u
3
= h690655u
20
a − 666179u
20
+ ··· + 1599444a + 1444642,
− 242859u
20
a + 48196u
20
+ ··· + 583206a − 231757, u
21
+ u
20
+ ··· − u + 1i
I
u
4
= h−u
7
+ 2u
4
− u
3
+ u
2
+ b + u + 1, u
5
+ u
4
+ u
3
+ a + u + 1, u
8
+ u
7
+ 2u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 257 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
= h−9.76 × 10
52
u
42
− 8.19 × 10
53
u
41
+ · · · + 4.22 × 10
54
b − 1.95 ×
10
55
, −3.04 × 10
54
u
42
− 1.55 × 10
55
u
41
+ · · · + 5.91 × 10
55
a − 2.04 ×
10
56
, u
43
+ 4u
42
+ · · · + 134u + 28i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
11
=
0.0513888u
42
+ 0.261949u
41
+ ··· + 20.1928u + 3.45016
0.0231195u
42
+ 0.194003u
41
+ ··· + 18.1185u + 4.61145
a
12
=
0.0159210u
42
+ 0.131374u
41
+ ··· + 14.9367u + 2.18649
−0.0123483u
42
+ 0.0634275u
41
+ ··· + 12.8625u + 3.34778
a
1
=
u
2
+ 1
−u
4
a
5
=
0.155651u
42
+ 0.702946u
41
+ ··· + 35.1812u + 7.23755
0.101892u
42
+ 0.546709u
41
+ ··· + 38.4993u + 9.13509
a
8
=
0.0518738u
42
+ 0.267566u
41
+ ··· + 17.9695u + 3.60481
0.0142301u
42
+ 0.0907475u
41
+ ··· + 9.44885u + 2.12776
a
9
=
0.108301u
42
+ 0.464706u
41
+ ··· + 26.4079u + 5.38944
0.0305975u
42
+ 0.135562u
41
+ ··· + 10.6899u + 2.32099
a
10
=
0.143779u
42
+ 0.616717u
41
+ ··· + 31.4209u + 5.08925
0.0671918u
42
+ 0.363732u
41
+ ··· + 23.7776u + 5.19067
a
4
=
−0.245909u
42
− 1.05925u
41
+ ··· − 50.3183u − 9.57685
−0.147417u
42
− 0.635759u
41
+ ··· − 30.6375u − 6.47544
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.10962u
42
+ 3.30125u
41
+ ··· + 55.8783u + 10.2094
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
43
+ 12u
42
+ ··· − 8532u − 784
c
2
, c
6
u
43
− 4u
42
+ ··· + 134u − 28
c
3
, c
5
3(3u
43
+ 18u
42
+ ··· − 9u − 1)
c
4
3(3u
43
+ 3u
42
+ ··· + 6656u − 1024)
c
7
, c
12
u
43
+ 2u
42
+ ··· − 21u − 3
c
8
, c
11
u
43
+ 10u
42
+ ··· − 66u − 6
c
9
, c
10
u
43
+ 6u
42
+ ··· + u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
43
+ 8y
42
+ ··· + 30513904y −614656
c
2
, c
6
y
43
+ 12y
42
+ ··· − 8532y −784
c
3
, c
5
9(9y
43
− 60y
42
+ ··· + 19y −1)
c
4
9(9y
43
− 33y
42
+ ··· + 1.70394 × 10
7
y −1048576)
c
7
, c
12
y
43
− 16y
42
+ ··· + 159y −9
c
8
, c
11
y
43
− 10y
42
+ ··· − 588y −36
c
9
, c
10
y
43
+ 4y
42
+ ··· + 19y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.718182 + 0.751745I
a = −0.522759 − 0.163186I
b = −0.933915 − 0.789766I
−1.03885 + 5.59083I −0.80296 − 8.20049I
u = 0.718182 − 0.751745I
a = −0.522759 + 0.163186I
b = −0.933915 + 0.789766I
−1.03885 − 5.59083I −0.80296 + 8.20049I
u = −0.431183 + 0.848497I
a = 0.90051 + 2.07304I
b = 1.21180 + 1.76142I
−1.55530 − 2.02522I −12.2265 + 20.7180I
u = −0.431183 − 0.848497I
a = 0.90051 − 2.07304I
b = 1.21180 − 1.76142I
−1.55530 + 2.02522I −12.2265 − 20.7180I
u = 0.771623 + 0.728064I
a = 0.365410 − 0.767846I
b = 0.283036 + 0.562453I
3.84055 − 0.99267I 9.49500 + 4.60211I
u = 0.771623 − 0.728064I
a = 0.365410 + 0.767846I
b = 0.283036 − 0.562453I
3.84055 + 0.99267I 9.49500 − 4.60211I
u = −0.046594 + 0.908670I
a = 1.164645 − 0.012772I
b = 2.12526 − 0.65917I
−4.88607 − 2.08508I −7.79096 + 3.96252I
u = −0.046594 − 0.908670I
a = 1.164645 + 0.012772I
b = 2.12526 + 0.65917I
−4.88607 + 2.08508I −7.79096 − 3.96252I
u = −0.630009 + 0.893960I
a = −1.30697 + 0.78142I
b = −2.04729 + 0.27572I
−1.74768 − 2.41654I 9.67963 + 4.40868I
u = −0.630009 − 0.893960I
a = −1.30697 − 0.78142I
b = −2.04729 − 0.27572I
−1.74768 + 2.41654I 9.67963 − 4.40868I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.583673 + 0.688264I
a = 0.382832 + 0.752482I
b = −0.72882 − 1.38224I
3.88646 − 0.96920I 6.32905 − 0.22884I
u = −0.583673 − 0.688264I
a = 0.382832 − 0.752482I
b = −0.72882 + 1.38224I
3.88646 + 0.96920I 6.32905 + 0.22884I
u = −0.999781 + 0.479062I
a = 0.485799 + 0.279788I
b = −0.313320 − 0.267661I
5.03993 − 1.05509I 21.5749 + 4.0861I
u = −0.999781 − 0.479062I
a = 0.485799 − 0.279788I
b = −0.313320 + 0.267661I
5.03993 + 1.05509I 21.5749 − 4.0861I
u = 0.939472 + 0.598164I
a = −0.504756 + 1.300037I
b = −0.162293 + 0.284453I
6.13585 − 6.88234I 10.41111 + 6.89791I
u = 0.939472 − 0.598164I
a = −0.504756 − 1.300037I
b = −0.162293 − 0.284453I
6.13585 + 6.88234I 10.41111 − 6.89791I
u = 0.009492 + 0.842049I
a = −0.027024 + 0.454273I
b = 1.013011 + 0.223049I
−1.68203 − 1.83995I 2.74369 + 3.75799I
u = 0.009492 − 0.842049I
a = −0.027024 − 0.454273I
b = 1.013011 − 0.223049I
−1.68203 + 1.83995I 2.74369 − 3.75799I
u = −0.987577 + 0.624297I
a = −0.456506 − 1.224878I
b = −0.105049 + 0.116560I
2.7441 + 15.6580I 5.64449 − 7.99170I
u = −0.987577 − 0.624297I
a = −0.456506 + 1.224878I
b = −0.105049 − 0.116560I
2.7441 − 15.6580I 5.64449 + 7.99170I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.167516 + 0.159688I
a = 0.674624 + 0.558725I
b = 0.164428 − 0.018115I
−0.04862 + 9.36863I 3.31258 − 12.56283I
u = 1.167516 − 0.159688I
a = 0.674624 − 0.558725I
b = 0.164428 + 0.018115I
−0.04862 − 9.36863I 3.31258 + 12.56283I
u = −0.634457 + 1.002920I
a = −0.489863 − 0.256674I
b = −1.94366 − 1.06319I
2.84002 − 3.91305I 5.13045 + 1.88768I
u = −0.634457 − 1.002920I
a = −0.489863 + 0.256674I
b = −1.94366 + 1.06319I
2.84002 + 3.91305I 5.13045 − 1.88768I
u = 0.711454 + 0.981552I
a = −0.676420 + 0.324738I
b = −1.97645 + 0.33283I
3.06667 + 6.61548I 9.05531 − 10.31718I
u = 0.711454 − 0.981552I
a = −0.676420 − 0.324738I
b = −1.97645 − 0.33283I
3.06667 − 6.61548I 9.05531 + 10.31718I
u = −0.212615 + 1.246801I
a = −1.024712 − 0.267774I
b = −1.58785 − 0.53969I
−1.60269 − 5.36815I 5.92946 + 11.43526I
u = −0.212615 − 1.246801I
a = −1.024712 + 0.267774I
b = −1.58785 + 0.53969I
−1.60269 + 5.36815I 5.92946 − 11.43526I
u = 0.731768 + 1.094416I
a = 1.282193 − 0.414778I
b = 2.24528 − 0.60925I
4.59586 + 13.00720I 7.74298 − 11.37761I
u = 0.731768 − 1.094416I
a = 1.282193 + 0.414778I
b = 2.24528 + 0.60925I
4.59586 − 13.00720I 7.74298 + 11.37761I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.225826 + 1.299835I
a = −0.890318 + 0.539751I
b = −1.86420 + 0.91662I
−5.5253 + 13.9644I 0. − 10.27847I
u = 0.225826 − 1.299835I
a = −0.890318 − 0.539751I
b = −1.86420 − 0.91662I
−5.5253 − 13.9644I 0. + 10.27847I
u = −1.327786 + 0.119699I
a = 0.000010 + 0.488521I
b = −0.158759 + 0.237886I
3.44804 + 0.36999I 0. − 20.7347I
u = −1.327786 − 0.119699I
a = 0.000010 − 0.488521I
b = −0.158759 − 0.237886I
3.44804 − 0.36999I 0. + 20.7347I
u = −0.759592 + 1.110308I
a = 1.158564 + 0.362113I
b = 2.45406 + 0.61030I
1.2097 − 22.0263I 4.00000 + 11.67686I
u = −0.759592 − 1.110308I
a = 1.158564 − 0.362113I
b = 2.45406 − 0.61030I
1.2097 + 22.0263I 4.00000 − 11.67686I
u = −0.745632 + 1.187640I
a = −0.455074 − 0.199741I
b = −1.042660 − 0.779445I
2.82111 − 5.29573I 12.9987 + 26.5587I
u = −0.745632 − 1.187640I
a = −0.455074 + 0.199741I
b = −1.042660 + 0.779445I
2.82111 + 5.29573I 12.9987 − 26.5587I
u = 0.31165 + 1.39193I
a = 0.533862 + 0.359501I
b = 1.059394 + 0.479960I
−4.74380 − 3.59234I 0
u = 0.31165 − 1.39193I
a = 0.533862 − 0.359501I
b = 1.059394 − 0.479960I
−4.74380 + 3.59234I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.000647 + 0.512790I
a = −0.893952 + 0.888550I
b = 0.483093 + 0.313857I
−1.62700 − 1.83193I 0.64526 + 1.98343I
u = −0.000647 − 0.512790I
a = −0.893952 − 0.888550I
b = 0.483093 − 0.313857I
−1.62700 + 1.83193I 0.64526 − 1.98343I
u = −0.454864
a = −1.32876
b = −0.350197
0.911852 11.1470
9
II. I
u
2
= h−5.79 × 10
80
au
81
+ 2.67 × 10
81
u
81
+ · · · − 6.08 × 10
81
a − 7.04 ×
10
79
, 2.09 × 10
81
au
81
− 4.15 × 10
81
u
81
+ · · · + 2.03 × 10
82
a − 9.23 ×
10
81
, u
82
+ 16u
80
+ · · · + 28u − 5i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
11
=
a
1.23135au
81
− 5.67900u
81
+ ··· + 12.9327a + 0.149804
a
12
=
−2.40596au
81
− 3.18384u
81
+ ··· − 4.39682a − 33.6869
−1.17460au
81
− 8.86285u
81
+ ··· + 7.53586a − 33.5371
a
1
=
u
2
+ 1
−u
4
a
5
=
0.545671au
81
− 2.08186u
81
+ ··· + 4.43845a − 8.82082
4.41200au
81
− 2.28183u
81
+ ··· + 19.8861a − 3.34871
a
8
=
−0.320223au
81
+ 2.73715u
81
+ ··· + 1.83764a + 11.9926
−0.704980au
81
− 2.34180u
81
+ ··· − 6.73521a − 1.53151
a
9
=
2.58654au
81
+ 1.32806u
81
+ ··· + 7.71066a − 7.65206
1.07936au
81
− 4.43683u
81
+ ··· − 6.15677a − 19.7556
a
10
=
−5.37003au
81
− 2.54125u
81
+ ··· − 11.4774a − 6.65226
−4.00792au
81
− 4.43184u
81
+ ··· − 1.14834a − 10.4356
a
4
=
−4.83881au
81
− 5.00401u
81
+ ··· − 6.64032a − 14.9366
0.673184au
81
− 4.49704u
81
+ ··· + 22.1841a − 9.34371
(ii) Obstruction class = −1
(iii) Cusp Shapes = 19.7809u
81
+ 4.18064u
80
+ ··· − 495.369u + 83.1513
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
82
+ 32u
81
+ ··· + 686u + 25)
2
c
2
(u
82
+ 16u
80
+ ··· − 28u − 5)
2
c
3
, c
5
u
164
+ u
163
+ ··· − 362858u + 42877
c
4
(u
82
+ 2u
81
+ ··· − 662u + 76)
2
c
6
(u
82
+ 16u
80
+ ··· + 28u − 5)
2
c
7
, c
12
u
164
− 12u
163
+ ··· − 28u + 1
c
8
, c
11
u
164
+ 11u
163
+ ··· + 11062u + 3389
c
9
u
164
− u
163
+ ··· − 3078u + 373
c
10
u
164
+ u
163
+ ··· + 3078u + 373
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
82
+ 48y
81
+ ··· − 151346y + 625)
2
c
2
, c
6
(y
82
+ 32y
81
+ ··· + 686y + 25)
2
c
3
, c
5
y
164
− 45y
163
+ ··· − 178661607030y + 1838437129
c
4
(y
82
− 36y
81
+ ··· − 265724y + 5776)
2
c
7
, c
12
y
164
+ 24y
163
+ ··· − 146y + 1
c
8
, c
11
y
164
− 35y
163
+ ··· − 1545612284y + 11485321
c
9
, c
10
y
164
− 15y
163
+ ··· − 11486792y + 139129
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.102379 + 0.987009I
a = 0.317278 − 0.873673I
b = 0.756126 + 1.189239I
−1.74735 + 6.05585I 0
u = −0.102379 + 0.987009I
a = 0.493436 − 0.973937I
b = 1.42885 − 1.67251I
−1.74735 + 6.05585I 0
u = −0.102379 − 0.987009I
a = 0.317278 + 0.873673I
b = 0.756126 − 1.189239I
−1.74735 − 6.05585I 0
u = −0.102379 − 0.987009I
a = 0.493436 + 0.973937I
b = 1.42885 + 1.67251I
−1.74735 − 6.05585I 0
u = −0.688378 + 0.711449I
a = 0.44220 + 1.37172I
b = 0.317278 − 0.376478I
2.53761 + 6.16310I 0
u = −0.688378 + 0.711449I
a = 0.337930 + 0.263236I
b = 2.63563 + 0.58402I
2.53761 + 6.16310I 0
u = −0.688378 − 0.711449I
a = 0.44220 − 1.37172I
b = 0.317278 + 0.376478I
2.53761 − 6.16310I 0
u = −0.688378 − 0.711449I
a = 0.337930 − 0.263236I
b = 2.63563 − 0.58402I
2.53761 − 6.16310I 0
u = 0.081643 + 1.021795I
a = −0.574735 + 0.127492I
b = −2.31102 + 0.84132I
−4.98297 + 6.06099I 0
u = 0.081643 + 1.021795I
a = 1.15680 − 0.87879I
b = 1.96133 − 1.27439I
−4.98297 + 6.06099I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.081643 − 1.021795I
a = −0.574735 − 0.127492I
b = −2.31102 − 0.84132I
−4.98297 − 6.06099I 0
u = 0.081643 − 1.021795I
a = 1.15680 + 0.87879I
b = 1.96133 + 1.27439I
−4.98297 − 6.06099I 0
u = 0.222975 + 0.949050I
a = −0.849225 − 0.071882I
b = −1.56892 − 0.96744I
−5.31896 + 2.25086I 0
u = 0.222975 + 0.949050I
a = 1.49418 − 0.54414I
b = 2.35863 − 0.72524I
−5.31896 + 2.25086I 0
u = 0.222975 − 0.949050I
a = −0.849225 + 0.071882I
b = −1.56892 + 0.96744I
−5.31896 − 2.25086I 0
u = 0.222975 − 0.949050I
a = 1.49418 + 0.54414I
b = 2.35863 + 0.72524I
−5.31896 − 2.25086I 0
u = −0.171387 + 0.956518I
a = 0.599720 + 0.762281I
b = 1.43154 + 0.91842I
−1.81006 − 2.10708I 0
u = −0.171387 + 0.956518I
a = 0.704891 + 0.841467I
b = 1.263282 + 0.237449I
−1.81006 − 2.10708I 0
u = −0.171387 − 0.956518I
a = 0.599720 − 0.762281I
b = 1.43154 − 0.91842I
−1.81006 + 2.10708I 0
u = −0.171387 − 0.956518I
a = 0.704891 − 0.841467I
b = 1.263282 − 0.237449I
−1.81006 + 2.10708I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.783796 + 0.687106I
a = 0.211946 − 0.816504I
b = 0.783680 + 0.913408I
0.93884 + 6.00467I 0
u = −0.783796 + 0.687106I
a = 0.46250 + 1.48455I
b = 0.365251 + 0.119121I
0.93884 + 6.00467I 0
u = −0.783796 − 0.687106I
a = 0.211946 + 0.816504I
b = 0.783680 − 0.913408I
0.93884 − 6.00467I 0
u = −0.783796 − 0.687106I
a = 0.46250 − 1.48455I
b = 0.365251 − 0.119121I
0.93884 − 6.00467I 0
u = 0.615325 + 0.729924I
a = −0.698457 + 0.164535I
b = −0.672941 − 0.947419I
−1.05465 + 5.50459I 0
u = 0.615325 + 0.729924I
a = −0.276711 − 0.595308I
b = −1.08058 − 0.94515I
−1.05465 + 5.50459I 0
u = 0.615325 − 0.729924I
a = −0.698457 − 0.164535I
b = −0.672941 + 0.947419I
−1.05465 − 5.50459I 0
u = 0.615325 − 0.729924I
a = −0.276711 + 0.595308I
b = −1.08058 + 0.94515I
−1.05465 − 5.50459I 0
u = 0.588823 + 0.751386I
a = 0.540619 − 0.898618I
b = −0.369589 + 0.471258I
4.68710 + 1.89704I 0
u = 0.588823 + 0.751386I
a = −0.566521 + 0.334837I
b = −2.39469 + 1.10008I
4.68710 + 1.89704I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.588823 − 0.751386I
a = 0.540619 + 0.898618I
b = −0.369589 − 0.471258I
4.68710 − 1.89704I 0
u = 0.588823 − 0.751386I
a = −0.566521 − 0.334837I
b = −2.39469 − 1.10008I
4.68710 − 1.89704I 0
u = 0.759373 + 0.724307I
a = 0.435025 − 1.130379I
b = 0.197944 + 0.289395I
4.14795 − 1.48215I 0
u = 0.759373 + 0.724307I
a = 0.351078 − 0.603944I
b = 1.253359 + 0.360196I
4.14795 − 1.48215I 0
u = 0.759373 − 0.724307I
a = 0.435025 + 1.130379I
b = 0.197944 − 0.289395I
4.14795 + 1.48215I 0
u = 0.759373 − 0.724307I
a = 0.351078 + 0.603944I
b = 1.253359 − 0.360196I
4.14795 + 1.48215I 0
u = 0.592504 + 0.873679I
a = 0.916767 + 0.661132I
b = 1.92566 − 0.35296I
−3.55448 + 2.33523I 0
u = 0.592504 + 0.873679I
a = −1.33631 − 1.11053I
b = −1.54585 − 1.13215I
−3.55448 + 2.33523I 0
u = 0.592504 − 0.873679I
a = 0.916767 − 0.661132I
b = 1.92566 + 0.35296I
−3.55448 − 2.33523I 0
u = 0.592504 − 0.873679I
a = −1.33631 + 1.11053I
b = −1.54585 + 1.13215I
−3.55448 − 2.33523I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.497907 + 0.791181I
a = −0.09313 − 1.79644I
b = 0.40229 − 1.37398I
−0.77152 − 1.64761I 0
u = −0.497907 + 0.791181I
a = −1.19243 − 1.61276I
b = −1.68357 − 0.85158I
−0.77152 − 1.64761I 0
u = −0.497907 − 0.791181I
a = −0.09313 + 1.79644I
b = 0.40229 + 1.37398I
−0.77152 + 1.64761I 0
u = −0.497907 − 0.791181I
a = −1.19243 + 1.61276I
b = −1.68357 + 0.85158I
−0.77152 + 1.64761I 0
u = −0.656153 + 0.855523I
a = −0.16967 − 1.59996I
b = 0.031540 − 0.452918I
5.26864 − 2.54846I 0
u = −0.656153 + 0.855523I
a = 1.57834 + 0.35247I
b = 2.55673 + 0.64010I
5.26864 − 2.54846I 0
u = −0.656153 − 0.855523I
a = −0.16967 + 1.59996I
b = 0.031540 + 0.452918I
5.26864 + 2.54846I 0
u = −0.656153 − 0.855523I
a = 1.57834 − 0.35247I
b = 2.55673 − 0.64010I
5.26864 + 2.54846I 0
u = 0.734731 + 0.552895I
a = −0.50407 + 1.56637I
b = −0.050639 + 0.140593I
0.78675 − 7.63610I 0
u = 0.734731 + 0.552895I
a = 1.46961 + 0.95629I
b = 1.44160 + 0.52221I
0.78675 − 7.63610I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.734731 − 0.552895I
a = −0.50407 − 1.56637I
b = −0.050639 − 0.140593I
0.78675 + 7.63610I 0
u = 0.734731 − 0.552895I
a = 1.46961 − 0.95629I
b = 1.44160 − 0.52221I
0.78675 + 7.63610I 0
u = 0.580213 + 0.698978I
a = 0.035627 + 1.300327I
b = 0.688348 − 0.437352I
−1.30751 − 3.63367I 0
u = 0.580213 + 0.698978I
a = 0.90301 − 1.19516I
b = 1.85953 − 0.02021I
−1.30751 − 3.63367I 0
u = 0.580213 − 0.698978I
a = 0.035627 − 1.300327I
b = 0.688348 + 0.437352I
−1.30751 + 3.63367I 0
u = 0.580213 − 0.698978I
a = 0.90301 + 1.19516I
b = 1.85953 + 0.02021I
−1.30751 + 3.63367I 0
u = 0.147604 + 1.096332I
a = 0.692277 + 1.077089I
b = 1.54129 + 0.89857I
−5.00549 − 2.29441I 0
u = 0.147604 + 1.096332I
a = −0.517297 − 0.433151I
b = −1.15443 − 1.19525I
−5.00549 − 2.29441I 0
u = 0.147604 − 1.096332I
a = 0.692277 − 1.077089I
b = 1.54129 − 0.89857I
−5.00549 + 2.29441I 0
u = 0.147604 − 1.096332I
a = −0.517297 + 0.433151I
b = −1.15443 + 1.19525I
−5.00549 + 2.29441I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.492160 + 1.000696I
a = 1.053691 + 0.382790I
b = 1.39710 + 0.59856I
−1.43135 − 2.33882I 0
u = −0.492160 + 1.000696I
a = 1.10522 + 1.16722I
b = 1.80366 + 0.79472I
−1.43135 − 2.33882I 0
u = −0.492160 − 1.000696I
a = 1.053691 − 0.382790I
b = 1.39710 − 0.59856I
−1.43135 + 2.33882I 0
u = −0.492160 − 1.000696I
a = 1.10522 − 1.16722I
b = 1.80366 − 0.79472I
−1.43135 + 2.33882I 0
u = −0.831555 + 0.747005I
a = −0.794981 − 0.573537I
b = −1.96782 + 0.04826I
2.09965 − 5.22800I 0
u = −0.831555 + 0.747005I
a = 0.536603 + 0.282820I
b = −0.008492 − 0.407778I
2.09965 − 5.22800I 0
u = −0.831555 − 0.747005I
a = −0.794981 + 0.573537I
b = −1.96782 − 0.04826I
2.09965 + 5.22800I 0
u = −0.831555 − 0.747005I
a = 0.536603 − 0.282820I
b = −0.008492 + 0.407778I
2.09965 + 5.22800I 0
u = 0.558931 + 0.971274I
a = 0.189922 − 0.781054I
b = −0.255754 + 1.246243I
3.98782 + 2.66971I 0
u = 0.558931 + 0.971274I
a = −0.518881 + 0.482099I
b = −1.35483 + 1.45301I
3.98782 + 2.66971I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.558931 − 0.971274I
a = 0.189922 + 0.781054I
b = −0.255754 − 1.246243I
3.98782 − 2.66971I 0
u = 0.558931 − 0.971274I
a = −0.518881 − 0.482099I
b = −1.35483 − 1.45301I
3.98782 − 2.66971I 0
u = −0.875737
a = −0.905996 + 0.765010I
b = −0.074026 − 0.240770I
−1.58426 2.71380
u = −0.875737
a = −0.905996 − 0.765010I
b = −0.074026 + 0.240770I
−1.58426 2.71380
u = 0.745313 + 0.865190I
a = −0.670864 + 0.774770I
b = −0.403118 + 0.284988I
4.09671 + 7.97160I 0
u = 0.745313 + 0.865190I
a = −1.282899 + 0.103611I
b = −2.46294 + 0.52288I
4.09671 + 7.97160I 0
u = 0.745313 − 0.865190I
a = −0.670864 − 0.774770I
b = −0.403118 − 0.284988I
4.09671 − 7.97160I 0
u = 0.745313 − 0.865190I
a = −1.282899 − 0.103611I
b = −2.46294 − 0.52288I
4.09671 − 7.97160I 0
u = 0.631098 + 0.962390I
a = −0.680616 − 0.717661I
b = −0.742658 − 0.622932I
−1.79456 − 0.57489I 0
u = 0.631098 + 0.962390I
a = 0.217567 − 0.140312I
b = 1.55805 + 0.36586I
−1.79456 − 0.57489I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.631098 − 0.962390I
a = −0.680616 + 0.717661I
b = −0.742658 + 0.622932I
−1.79456 + 0.57489I 0
u = 0.631098 − 0.962390I
a = 0.217567 + 0.140312I
b = 1.55805 − 0.36586I
−1.79456 + 0.57489I 0
u = 0.776367 + 0.858693I
a = 0.655709 − 0.601697I
b = 0.880515 − 0.641390I
4.12981 − 2.24537I 0
u = 0.776367 + 0.858693I
a = 0.092585 − 1.227344I
b = −0.241282 + 0.114546I
4.12981 − 2.24537I 0
u = 0.776367 − 0.858693I
a = 0.655709 + 0.601697I
b = 0.880515 + 0.641390I
4.12981 + 2.24537I 0
u = 0.776367 − 0.858693I
a = 0.092585 + 1.227344I
b = −0.241282 − 0.114546I
4.12981 + 2.24537I 0
u = 0.020717 + 1.158741I
a = −0.838570 − 0.618427I
b = −1.46709 − 1.15879I
−4.72203 − 6.11748I 0
u = 0.020717 + 1.158741I
a = −1.05996 + 1.14441I
b = −1.77762 + 0.77517I
−4.72203 − 6.11748I 0
u = 0.020717 − 1.158741I
a = −0.838570 + 0.618427I
b = −1.46709 + 1.15879I
−4.72203 + 6.11748I 0
u = 0.020717 − 1.158741I
a = −1.05996 − 1.14441I
b = −1.77762 − 0.77517I
−4.72203 + 6.11748I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.610056 + 0.985518I
a = 1.038962 − 0.159001I
b = 2.41965 − 0.82510I
−2.23730 + 8.40928I 0
u = 0.610056 + 0.985518I
a = −0.990136 + 0.973592I
b = −2.05440 + 0.32984I
−2.23730 + 8.40928I 0
u = 0.610056 − 0.985518I
a = 1.038962 + 0.159001I
b = 2.41965 + 0.82510I
−2.23730 − 8.40928I 0
u = 0.610056 − 0.985518I
a = −0.990136 − 0.973592I
b = −2.05440 − 0.32984I
−2.23730 − 8.40928I 0
u = 1.019344 + 0.563448I
a = 0.508278 − 1.119809I
b = 0.147529 + 0.199846I
4.20151 − 7.22862I 0
u = 1.019344 + 0.563448I
a = −0.525991 + 0.481685I
b = 0.134773 − 0.128980I
4.20151 − 7.22862I 0
u = 1.019344 − 0.563448I
a = 0.508278 + 1.119809I
b = 0.147529 − 0.199846I
4.20151 + 7.22862I 0
u = 1.019344 − 0.563448I
a = −0.525991 − 0.481685I
b = 0.134773 + 0.128980I
4.20151 + 7.22862I 0
u = −0.658563 + 0.976376I
a = −1.125343 − 0.516263I
b = −2.64625 − 0.72623I
1.72208 − 11.38300I 0
u = −0.658563 + 0.976376I
a = −0.243734 − 0.487896I
b = −0.11099 + 1.68510I
1.72208 − 11.38300I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.658563 − 0.976376I
a = −1.125343 + 0.516263I
b = −2.64625 + 0.72623I
1.72208 + 11.38300I 0
u = −0.658563 − 0.976376I
a = −0.243734 + 0.487896I
b = −0.11099 − 1.68510I
1.72208 + 11.38300I 0
u = −0.692637 + 0.420238I
a = −1.084930 − 0.530335I
b = −0.184382 + 0.053809I
2.24532 + 0.18686I 7.18291 − 3.86145I
u = −0.692637 + 0.420238I
a = −1.11979 + 1.05165I
b = −1.045952 + 0.506656I
2.24532 + 0.18686I 7.18291 − 3.86145I
u = −0.692637 − 0.420238I
a = −1.084930 + 0.530335I
b = −0.184382 − 0.053809I
2.24532 − 0.18686I 7.18291 + 3.86145I
u = −0.692637 − 0.420238I
a = −1.11979 − 1.05165I
b = −1.045952 − 0.506656I
2.24532 − 0.18686I 7.18291 + 3.86145I
u = −0.837347 + 0.866979I
a = −0.767843 − 0.092615I
b = −1.110011 − 0.332522I
2.87654 − 3.09038I 0
u = −0.837347 + 0.866979I
a = 0.241720 + 0.641911I
b = −0.179630 + 0.176942I
2.87654 − 3.09038I 0
u = −0.837347 − 0.866979I
a = −0.767843 + 0.092615I
b = −1.110011 + 0.332522I
2.87654 + 3.09038I 0
u = −0.837347 − 0.866979I
a = 0.241720 − 0.641911I
b = −0.179630 − 0.176942I
2.87654 + 3.09038I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.713163 + 0.977639I
a = −0.968035 + 0.415291I
b = −2.27874 + 0.60272I
3.38769 + 7.07961I 0
u = 0.713163 + 0.977639I
a = −0.575501 + 0.436867I
b = −1.51526 − 0.47494I
3.38769 + 7.07961I 0
u = 0.713163 − 0.977639I
a = −0.968035 − 0.415291I
b = −2.27874 − 0.60272I
3.38769 − 7.07961I 0
u = 0.713163 − 0.977639I
a = −0.575501 − 0.436867I
b = −1.51526 + 0.47494I
3.38769 − 7.07961I 0
u = −0.764471 + 0.945268I
a = 0.302137 + 0.924075I
b = 0.622130 − 0.311227I
1.51925 − 0.72010I 0
u = −0.764471 + 0.945268I
a = −0.230770 − 0.252512I
b = −1.056167 − 0.501436I
1.51925 − 0.72010I 0
u = −0.764471 − 0.945268I
a = 0.302137 − 0.924075I
b = 0.622130 + 0.311227I
1.51925 + 0.72010I 0
u = −0.764471 − 0.945268I
a = −0.230770 + 0.252512I
b = −1.056167 + 0.501436I
1.51925 + 0.72010I 0
u = −0.706304 + 1.005042I
a = 0.701144 − 0.166413I
b = 2.43829 + 0.47911I
−0.02479 − 11.64150I 0
u = −0.706304 + 1.005042I
a = −1.33325 − 0.49801I
b = −2.54711 − 0.56416I
−0.02479 − 11.64150I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.706304 − 1.005042I
a = 0.701144 + 0.166413I
b = 2.43829 − 0.47911I
−0.02479 + 11.64150I 0
u = −0.706304 − 1.005042I
a = −1.33325 + 0.49801I
b = −2.54711 + 0.56416I
−0.02479 + 11.64150I 0
u = 0.656134 + 1.044523I
a = 1.299897 − 0.397065I
b = 2.47031 − 0.71567I
−0.64011 + 12.97150I 0
u = 0.656134 + 1.044523I
a = 0.90076 + 1.31218I
b = 1.35150 + 1.10801I
−0.64011 + 12.97150I 0
u = 0.656134 − 1.044523I
a = 1.299897 + 0.397065I
b = 2.47031 + 0.71567I
−0.64011 − 12.97150I 0
u = 0.656134 − 1.044523I
a = 0.90076 − 1.31218I
b = 1.35150 − 1.10801I
−0.64011 − 12.97150I 0
u = −0.638373 + 1.080172I
a = 0.518988 + 0.461647I
b = 1.134453 + 0.760897I
0.41887 − 5.36607I 0
u = −0.638373 + 1.080172I
a = −0.871436 + 1.009610I
b = −1.36179 + 0.79319I
0.41887 − 5.36607I 0
u = −0.638373 − 1.080172I
a = 0.518988 − 0.461647I
b = 1.134453 − 0.760897I
0.41887 + 5.36607I 0
u = −0.638373 − 1.080172I
a = −0.871436 − 1.009610I
b = −1.36179 − 0.79319I
0.41887 + 5.36607I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.121030 + 0.584998I
a = 0.244141 + 1.147393I
b = −0.007370 + 0.431276I
3.95679 − 0.35266I 0
u = −1.121030 + 0.584998I
a = −0.504941 − 0.081075I
b = −0.219157 + 0.038383I
3.95679 − 0.35266I 0
u = −1.121030 − 0.584998I
a = 0.244141 − 1.147393I
b = −0.007370 − 0.431276I
3.95679 + 0.35266I 0
u = −1.121030 − 0.584998I
a = −0.504941 + 0.081075I
b = −0.219157 − 0.038383I
3.95679 + 0.35266I 0
u = −0.367565 + 1.222032I
a = 0.878996 + 0.455684I
b = 2.08893 + 0.84142I
−5.51762 − 4.38107I 0
u = −0.367565 + 1.222032I
a = −0.364829 + 0.496811I
b = −1.002012 + 0.885954I
−5.51762 − 4.38107I 0
u = −0.367565 − 1.222032I
a = 0.878996 − 0.455684I
b = 2.08893 − 0.84142I
−5.51762 + 4.38107I 0
u = −0.367565 − 1.222032I
a = −0.364829 − 0.496811I
b = −1.002012 − 0.885954I
−5.51762 + 4.38107I 0
u = 0.749973 + 1.139258I
a = −1.073570 + 0.371491I
b = −2.39232 + 0.60804I
2.40195 + 13.63020I 0
u = 0.749973 + 1.139258I
a = 0.581656 − 0.336374I
b = 1.30562 − 0.82900I
2.40195 + 13.63020I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.749973 − 1.139258I
a = −1.073570 − 0.371491I
b = −2.39232 − 0.60804I
2.40195 − 13.63020I 0
u = 0.749973 − 1.139258I
a = 0.581656 + 0.336374I
b = 1.30562 + 0.82900I
2.40195 − 13.63020I 0
u = −0.845881 + 1.115257I
a = −1.334105 − 0.344236I
b = −2.16679 − 0.37211I
2.33444 − 6.63695I 0
u = −0.845881 + 1.115257I
a = 0.355867 + 0.289833I
b = 0.719952 + 0.270282I
2.33444 − 6.63695I 0
u = −0.845881 − 1.115257I
a = −1.334105 + 0.344236I
b = −2.16679 + 0.37211I
2.33444 + 6.63695I 0
u = −0.845881 − 1.115257I
a = 0.355867 − 0.289833I
b = 0.719952 − 0.270282I
2.33444 + 6.63695I 0
u = −0.097362 + 0.536746I
a = −1.32055 + 1.00516I
b = −0.86089 + 1.87657I
2.58479 − 0.09865I 1.75768 − 0.41334I
u = −0.097362 + 0.536746I
a = −0.94357 − 1.92962I
b = −0.349717 + 0.124457I
2.58479 − 0.09865I 1.75768 − 0.41334I
u = −0.097362 − 0.536746I
a = −1.32055 − 1.00516I
b = −0.86089 − 1.87657I
2.58479 + 0.09865I 1.75768 + 0.41334I
u = −0.097362 − 0.536746I
a = −0.94357 + 1.92962I
b = −0.349717 − 0.124457I
2.58479 + 0.09865I 1.75768 + 0.41334I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06857 + 1.47022I
a = 0.742540 + 0.512047I
b = 1.64947 + 0.63887I
−3.79732 − 4.23788I 0
u = −0.06857 + 1.47022I
a = 0.041539 − 0.179639I
b = −0.051292 − 0.478297I
−3.79732 − 4.23788I 0
u = −0.06857 − 1.47022I
a = 0.742540 − 0.512047I
b = 1.64947 − 0.63887I
−3.79732 + 4.23788I 0
u = −0.06857 − 1.47022I
a = 0.041539 + 0.179639I
b = −0.051292 + 0.478297I
−3.79732 + 4.23788I 0
u = 0.454458 + 0.039085I
a = 1.63283 + 0.91663I
b = 0.576929 − 0.958945I
−1.49447 + 4.52523I 3.99817 − 7.04316I
u = 0.454458 + 0.039085I
a = −2.00901 − 1.21433I
b = 0.226960 − 0.320503I
−1.49447 + 4.52523I 3.99817 − 7.04316I
u = 0.454458 − 0.039085I
a = 1.63283 − 0.91663I
b = 0.576929 + 0.958945I
−1.49447 − 4.52523I 3.99817 + 7.04316I
u = 0.454458 − 0.039085I
a = −2.00901 + 1.21433I
b = 0.226960 + 0.320503I
−1.49447 − 4.52523I 3.99817 + 7.04316I
u = 0.415034
a = −1.09706 + 1.83796I
b = 0.217401 + 0.303171I
−2.77257 −0.265100
u = 0.415034
a = −1.09706 − 1.83796I
b = 0.217401 − 0.303171I
−2.77257 −0.265100
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.006580 + 0.328712I
a = 2.24112 + 0.27424I
b = 0.67653 + 2.68161I
0.57540 − 6.78088I −5.17076 + 2.86152I
u = −0.006580 + 0.328712I
a = 1.59061 + 3.52804I
b = −0.291550 + 0.252885I
0.57540 − 6.78088I −5.17076 + 2.86152I
u = −0.006580 − 0.328712I
a = 2.24112 − 0.27424I
b = 0.67653 − 2.68161I
0.57540 + 6.78088I −5.17076 − 2.86152I
u = −0.006580 − 0.328712I
a = 1.59061 − 3.52804I
b = −0.291550 − 0.252885I
0.57540 + 6.78088I −5.17076 − 2.86152I
29
III.
I
u
3
= h6.91 × 10
5
au
20
− 6.66 × 10
5
u
20
+ · · · + 1.60 × 10
6
a + 1.44 × 10
6
, −2.43 ×
10
5
au
20
+ 4.82 ×10
4
u
20
+ · · · +5.83 × 10
5
a − 2.32× 10
5
, u
21
+ u
20
+ · · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
11
=
a
−1.49504au
20
+ 1.44206u
20
+ ··· − 3.46226a − 3.12717
a
12
=
1.31468au
20
− 0.100016u
20
+ ··· + 2.62870a + 2.24404
−0.180362au
20
+ 1.34204u
20
+ ··· − 1.83356a − 0.883125
a
1
=
u
2
+ 1
−u
4
a
5
=
0.784475au
20
+ 0.397685u
20
+ ··· + 0.876181a − 0.173880
−1.63738au
20
+ 0.594672u
20
+ ··· − 2.58527a − 4.63963
a
8
=
−2.34472au
20
− 2.06949u
20
+ ··· + 0.364785a − 3.64135
−1.61997au
20
− 3.60148u
20
+ ··· + 2.45790a − 3.66334
a
9
=
−3.46226au
20
− 3.22343u
20
+ ··· + 0.545147a − 5.91816
−1.62870au
20
− 3.07689u
20
+ ··· + 1.49504a − 3.50155
a
10
=
−2.58608au
20
− 1.05697u
20
+ ··· − 0.558930a − 4.49851
−2.29916au
20
+ 0.531631u
20
+ ··· − 1.87552a − 5.20908
a
4
=
−2.62537au
20
− 4.11397u
20
+ ··· + 3.22343a − 3.47995
−1.04097au
20
− 3.02197u
20
+ ··· + 3.07689a − 0.910587
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
573826
92393
u
20
−
655818
92393
u
19
+ ··· −
280213
13199
u +
259652
92393
30
(iv) u-Polynomials at the component
31
Crossings u-Polynomials at each crossing
c
1
(u
21
− 9u
20
+ ··· − 5u + 1)
2
c
2
(u
21
+ u
20
+ ··· − u + 1)
2
c
3
3(3u
42
− 25u
40
+ ··· + 8u
2
+ 1)
c
4
3(3u
42
− 28u
40
+ ··· − 79585u
2
+ 13342)
c
5
3(3u
42
− 25u
40
+ ··· + 8u
2
+ 1)
c
6
(u
21
− u
20
+ ··· − u − 1)
2
c
7
u
42
+ u
41
+ ··· − 10u
2
+ 3
c
8
u
42
− 2u
41
+ ··· + 72u + 6
c
9
u
42
− 6u
41
+ ··· + 4u + 1
c
10
u
42
+ 6u
41
+ ··· − 4u + 1
c
11
u
42
+ 2u
41
+ ··· − 72u + 6
c
12
u
42
− u
41
+ ··· − 10u
2
+ 3
32
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ y
20
+ ··· − 13y −1)
2
c
2
, c
6
(y
21
+ 9y
20
+ ··· − 5y −1)
2
c
3
, c
5
9(9y
42
− 150y
41
+ ··· + 16y + 1)
c
4
9(3y
21
− 28y
20
+ ··· − 79585y + 13342)
2
c
7
, c
12
y
42
− 9y
41
+ ··· − 60y + 9
c
8
, c
11
y
42
− 26y
41
+ ··· + 84y + 36
c
9
, c
10
y
42
− 8y
41
+ ··· − 10y + 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.881576 + 0.418831I
a = −0.361683 − 1.121333I
b = 0.207870 − 0.378663I
3.78339 − 0.04138I 10.41762 − 3.81109I
u = −0.881576 + 0.418831I
a = −0.730949 + 0.005543I
b = −0.278195 + 0.434952I
3.78339 − 0.04138I 10.41762 − 3.81109I
u = −0.881576 − 0.418831I
a = −0.361683 + 1.121333I
b = 0.207870 + 0.378663I
3.78339 + 0.04138I 10.41762 + 3.81109I
u = −0.881576 − 0.418831I
a = −0.730949 − 0.005543I
b = −0.278195 − 0.434952I
3.78339 + 0.04138I 10.41762 + 3.81109I
u = −0.975689
a = −0.557318 + 0.589892I
b = 0.049772 + 0.442736I
3.74666 15.9220
u = −0.975689
a = −0.557318 − 0.589892I
b = 0.049772 − 0.442736I
3.74666 15.9220
u = 0.698370 + 0.650268I
a = −0.355980 − 0.686589I
b = −1.79122 + 0.32674I
1.83840 − 6.35244I 4.81759 + 6.65061I
u = 0.698370 + 0.650268I
a = −0.52515 + 1.49030I
b = −0.393589 − 0.091413I
1.83840 − 6.35244I 4.81759 + 6.65061I
u = 0.698370 − 0.650268I
a = −0.355980 + 0.686589I
b = −1.79122 − 0.32674I
1.83840 + 6.35244I 4.81759 − 6.65061I
u = 0.698370 − 0.650268I
a = −0.52515 − 1.49030I
b = −0.393589 + 0.091413I
1.83840 + 6.35244I 4.81759 − 6.65061I
35
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.476537 + 0.936351I
a = 1.80266 + 0.94454I
b = 2.16809 + 0.95721I
−1.68581 − 1.86148I −7.79878 − 2.15039I
u = −0.476537 + 0.936351I
a = −2.16341 − 1.13374I
b = −2.63982 − 0.90534I
−1.68581 − 1.86148I −7.79878 − 2.15039I
u = −0.476537 − 0.936351I
a = 1.80266 − 0.94454I
b = 2.16809 − 0.95721I
−1.68581 + 1.86148I −7.79878 + 2.15039I
u = −0.476537 − 0.936351I
a = −2.16341 + 1.13374I
b = −2.63982 + 0.90534I
−1.68581 + 1.86148I −7.79878 + 2.15039I
u = −0.104938 + 1.045834I
a = −0.996552 − 0.618015I
b = −1.78863 − 1.21314I
−4.18470 − 5.21358I −0.79665 + 4.22153I
u = −0.104938 + 1.045834I
a = 0.368788 − 0.683066I
b = 1.39495 − 0.29757I
−4.18470 − 5.21358I −0.79665 + 4.22153I
u = −0.104938 − 1.045834I
a = −0.996552 + 0.618015I
b = −1.78863 + 1.21314I
−4.18470 + 5.21358I −0.79665 − 4.22153I
u = −0.104938 − 1.045834I
a = 0.368788 + 0.683066I
b = 1.39495 + 0.29757I
−4.18470 + 5.21358I −0.79665 − 4.22153I
u = 0.561052 + 0.893013I
a = −0.235455 + 0.765228I
b = 0.526202 − 1.267104I
3.43041 + 2.23267I 3.41392 − 1.50119I
u = 0.561052 + 0.893013I
a = 0.486006 − 0.367781I
b = 1.77426 − 1.54792I
3.43041 + 2.23267I 3.41392 − 1.50119I
36
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.561052 − 0.893013I
a = −0.235455 − 0.765228I
b = 0.526202 + 1.267104I
3.43041 − 2.23267I 3.41392 + 1.50119I
u = 0.561052 − 0.893013I
a = 0.486006 + 0.367781I
b = 1.77426 + 1.54792I
3.43041 − 2.23267I 3.41392 + 1.50119I
u = 0.674245 + 1.017385I
a = 1.235031 − 0.519035I
b = 2.52854 − 0.64889I
0.72594 + 11.68850I 5.01313 − 11.04581I
u = 0.674245 + 1.017385I
a = −0.576962 − 0.288535I
b = −1.59779 + 0.81587I
0.72594 + 11.68850I 5.01313 − 11.04581I
u = 0.674245 − 1.017385I
a = 1.235031 + 0.519035I
b = 2.52854 + 0.64889I
0.72594 − 11.68850I 5.01313 + 11.04581I
u = 0.674245 − 1.017385I
a = −0.576962 + 0.288535I
b = −1.59779 − 0.81587I
0.72594 − 11.68850I 5.01313 + 11.04581I
u = −0.094129 + 0.709191I
a = −0.252055 + 1.030204I
b = −1.86324 + 1.58970I
−2.65904 + 4.24204I −3.54332 − 5.59638I
u = −0.094129 + 0.709191I
a = −0.69175 + 1.33662I
b = −0.766515 − 0.680615I
−2.65904 + 4.24204I −3.54332 − 5.59638I
u = −0.094129 − 0.709191I
a = −0.252055 − 1.030204I
b = −1.86324 − 1.58970I
−2.65904 − 4.24204I −3.54332 + 5.59638I
u = −0.094129 − 0.709191I
a = −0.69175 − 1.33662I
b = −0.766515 + 0.680615I
−2.65904 − 4.24204I −3.54332 + 5.59638I
37
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.826136 + 1.029522I
a = 1.184032 + 0.362526I
b = 2.14999 + 0.37191I
2.33522 − 6.36054I 8.63011 − 1.69394I
u = −0.826136 + 1.029522I
a = 0.379736 + 0.331436I
b = 0.695524 + 0.033648I
2.33522 − 6.36054I 8.63011 − 1.69394I
u = −0.826136 − 1.029522I
a = 1.184032 − 0.362526I
b = 2.14999 − 0.37191I
2.33522 + 6.36054I 8.63011 + 1.69394I
u = −0.826136 − 1.029522I
a = 0.379736 − 0.331436I
b = 0.695524 − 0.033648I
2.33522 + 6.36054I 8.63011 + 1.69394I
u = −0.00985 + 1.43426I
a = −0.729901 − 0.526288I
b = −1.58381 − 0.67192I
−3.92414 − 4.32422I −12.5168 + 20.5203I
u = −0.00985 + 1.43426I
a = 0.172191 + 0.049366I
b = 0.305401 + 0.349487I
−3.92414 − 4.32422I −12.5168 + 20.5203I
u = −0.00985 − 1.43426I
a = −0.729901 + 0.526288I
b = −1.58381 + 0.67192I
−3.92414 + 4.32422I −12.5168 − 20.5203I
u = −0.00985 − 1.43426I
a = 0.172191 − 0.049366I
b = 0.305401 − 0.349487I
−3.92414 + 4.32422I −12.5168 − 20.5203I
u = 0.447345 + 0.344431I
a = 1.004017 + 0.416329I
b = 0.40170 + 2.22779I
0.93439 + 7.02753I 10.9024 − 13.2309I
u = 0.447345 + 0.344431I
a = −1.95530 + 0.54442I
b = 0.000501 + 0.269681I
0.93439 + 7.02753I 10.9024 − 13.2309I
38
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.447345 − 0.344431I
a = 1.004017 − 0.416329I
b = 0.40170 − 2.22779I
0.93439 − 7.02753I 10.9024 + 13.2309I
u = 0.447345 − 0.344431I
a = −1.95530 − 0.54442I
b = 0.000501 − 0.269681I
0.93439 − 7.02753I 10.9024 + 13.2309I
39
IV. I
u
4
= h−u
7
+ 2u
4
− u
3
+ u
2
+ b + u + 1, u
5
+ u
4
+ u
3
+ a + u + 1, u
8
+
u
7
+ 2u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
11
=
−u
5
− u
4
− u
3
− u − 1
u
7
− 2u
4
+ u
3
− u
2
− u − 1
a
12
=
−u
5
− u
4
− u
3
+ u
2
− u
u
7
− 2u
4
+ u
3
− u
a
1
=
u
2
+ 1
−u
4
a
5
=
−u
6
− u
5
− 2u
4
− u
3
− 3u
2
− 2u − 1
−u
7
− u
6
− 2u
5
− u
4
− 3u
3
− 3u
2
− 2u − 1
a
8
=
−u
5
− u
4
− u
3
− 1
u
7
− u
4
+ u
3
a
9
=
u
7
+ u
6
+ u
5
+ u
3
+ 2u
2
u
7
+ u
5
− u
4
+ 2u
3
a
10
=
u
7
− u
5
− 3u
4
+ u
2
− 1
u
7
− u
6
− 2u
5
− 5u
4
− u
3
− 2u
2
− 2u − 2
a
4
=
−u
6
− u
5
− 2u
4
− u
3
− 3u
2
− 2u − 1
−u
7
− u
6
− 2u
5
− u
4
− 3u
3
− 3u
2
− 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10u
7
+ 11u
6
+ 16u
5
+ 9u
4
+ 21u
3
+ 20u
2
+ 4u + 7
40
(iv) u-Polynomials at the component
41
Crossings u-Polynomials at each crossing
c
1
u
8
− 3u
7
+ 8u
6
− 11u
5
+ 13u
4
− 10u
3
+ 6u
2
− 3u + 1
c
2
u
8
+ u
7
+ 2u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u + 1
c
3
u
8
+ 3u
6
− u
5
+ u
4
− 2u
3
− u
2
+ 1
c
4
u
8
c
5
u
8
+ 3u
6
+ u
5
+ u
4
+ 2u
3
− u
2
+ 1
c
6
u
8
− u
7
+ 2u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u + 1
c
7
u
8
− u
6
− 2u
5
+ u
4
− u
3
+ 3u
2
+ 1
c
8
u
8
+ 2u
7
− 3u
6
− 7u
5
+ 3u
4
+ 8u
3
− 2u
2
− 3u + 2
c
9
u
8
− 6u
7
+ 11u
6
− 3u
5
− 7u
4
+ 3u
2
+ 2u + 1
c
10
u
8
+ 6u
7
+ 11u
6
+ 3u
5
− 7u
4
+ 3u
2
− 2u + 1
c
11
u
8
− 2u
7
− 3u
6
+ 7u
5
+ 3u
4
− 8u
3
− 2u
2
+ 3u + 2
c
12
u
8
− u
6
+ 2u
5
+ u
4
+ u
3
+ 3u
2
+ 1
42
43
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
+ 7y
7
+ 24y
6
+ 39y
5
+ 29y
4
+ 6y
3
+ 2y
2
+ 3y + 1
c
2
, c
6
y
8
+ 3y
7
+ 8y
6
+ 11y
5
+ 13y
4
+ 10y
3
+ 6y
2
+ 3y + 1
c
3
, c
5
y
8
+ 6y
7
+ 11y
6
+ 3y
5
− 7y
4
+ 3y
2
− 2y + 1
c
4
y
8
c
7
, c
12
y
8
− 2y
7
+ 3y
6
− 7y
4
+ 3y
3
+ 11y
2
+ 6y + 1
c
8
, c
11
y
8
− 10y
7
+ 43y
6
− 103y
5
+ 149y
4
− 130y
3
+ 64y
2
− 17y + 4
c
9
, c
10
y
8
− 14y
7
+ 71y
6
− 157y
5
+ 141y
4
− 8y
3
− 5y
2
+ 2y + 1
44
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.671852 + 0.866239I
a = 1.049991 + 0.870539I
b = 1.84297 + 0.06459I
−2.27367 + 2.59903I −5.01492 − 5.67257I
u = 0.671852 − 0.866239I
a = 1.049991 − 0.870539I
b = 1.84297 − 0.06459I
−2.27367 − 2.59903I −5.01492 + 5.67257I
u = −0.636169 + 0.536939I
a = −0.577120 − 0.732862I
b = 0.665259 + 0.689606I
4.52677 − 0.45848I 12.52054 − 4.29850I
u = −0.636169 − 0.536939I
a = −0.577120 + 0.732862I
b = 0.665259 − 0.689606I
4.52677 + 0.45848I 12.52054 + 4.29850I
u = 0.187636 + 0.807559I
a = −1.47208 − 0.15531I
b = −1.77788 − 0.79675I
−4.97144 + 0.82384I −7.26579 + 2.83996I
u = 0.187636 − 0.807559I
a = −1.47208 + 0.15531I
b = −1.77788 + 0.79675I
−4.97144 − 0.82384I −7.26579 − 2.83996I
u = −0.723319 + 1.106196I
a = 0.499208 + 0.180900I
b = 1.26966 + 0.70532I
2.71833 − 5.01867I 3.26018 + 0.33670I
u = −0.723319 − 1.106196I
a = 0.499208 − 0.180900I
b = 1.26966 − 0.70532I
2.71833 + 5.01867I 3.26018 − 0.33670I
45
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
8
− 3u
7
+ 8u
6
− 11u
5
+ 13u
4
− 10u
3
+ 6u
2
− 3u + 1)
· ((u
21
− 9u
20
+ ··· − 5u + 1)
2
)(u
43
+ 12u
42
+ ··· − 8532u − 784)
c
2
(u
8
+ u
7
+ ··· + u + 1)(u
21
+ u
20
+ ··· − u + 1)
2
· (u
43
− 4u
42
+ ··· + 134u − 28)
c
3
9(u
8
+ 3u
6
+ ··· − u
2
+ 1)(3u
42
− 25u
40
+ ··· + 8u
2
+ 1)
· (3u
43
+ 18u
42
+ ··· − 9u − 1)
c
4
9u
8
(3u
42
− 28u
40
+ ··· − 79585u
2
+ 13342)
· (3u
43
+ 3u
42
+ ··· + 6656u − 1024)
c
5
9(u
8
+ 3u
6
+ ··· − u
2
+ 1)(3u
42
− 25u
40
+ ··· + 8u
2
+ 1)
· (3u
43
+ 18u
42
+ ··· − 9u − 1)
c
6
(u
8
− u
7
+ ··· − u + 1)(u
21
− u
20
+ ··· − u − 1)
2
· (u
43
− 4u
42
+ ··· + 134u − 28)
c
7
(u
8
− u
6
− 2u
5
+ u
4
− u
3
+ 3u
2
+ 1)(u
42
+ u
41
+ ··· − 10u
2
+ 3)
· (u
43
+ 2u
42
+ ··· − 21u − 3)
c
8
(u
8
+ 2u
7
− 3u
6
− 7u
5
+ 3u
4
+ 8u
3
− 2u
2
− 3u + 2)
· (u
42
− 2u
41
+ ··· + 72u + 6)(u
43
+ 10u
42
+ ··· − 66u − 6)
c
9
(u
8
− 6u
7
+ ··· + 2u + 1)(u
42
− 6u
41
+ ··· + 4u + 1)
· (u
43
+ 6u
42
+ ··· + u − 1)
c
10
(u
8
+ 6u
7
+ ··· − 2u + 1)(u
42
+ 6u
41
+ ··· − 4u + 1)
· (u
43
+ 6u
42
+ ··· + u − 1)
c
11
(u
8
− 2u
7
− 3u
6
+ 7u
5
+ 3u
4
− 8u
3
− 2u
2
+ 3u + 2)
· (u
42
+ 2u
41
+ ··· − 72u + 6)(u
43
+ 10u
42
+ ··· − 66u − 6)
c
12
(u
8
− u
6
+ 2u
5
+ u
4
+ u
3
+ 3u
2
+ 1)(u
42
− u
41
+ ··· − 10u
2
+ 3)
· (u
43
+ 2u
42
+ ··· − 21u − 3)
46
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
8
+ 7y
7
+ 24y
6
+ 39y
5
+ 29y
4
+ 6y
3
+ 2y
2
+ 3y + 1)
· (y
21
+ y
20
+ ··· − 13y −1)
2
· (y
43
+ 8y
42
+ ··· + 30513904y −614656)
c
2
, c
6
(y
8
+ 3y
7
+ 8y
6
+ 11y
5
+ 13y
4
+ 10y
3
+ 6y
2
+ 3y + 1)
· ((y
21
+ 9y
20
+ ··· − 5y −1)
2
)(y
43
+ 12y
42
+ ··· − 8532y −784)
c
3
, c
5
81(y
8
+ 6y
7
+ 11y
6
+ 3y
5
− 7y
4
+ 3y
2
− 2y + 1)
· (9y
42
− 150y
41
+ ··· + 16y + 1)(9y
43
− 60y
42
+ ··· + 19y −1)
c
4
81y
8
(3y
21
− 28y
20
+ ··· − 79585y + 13342)
2
· (9y
43
− 33y
42
+ ··· + 17039360y −1048576)
c
7
, c
12
(y
8
− 2y
7
+ 3y
6
− 7y
4
+ 3y
3
+ 11y
2
+ 6y + 1)
· (y
42
− 9y
41
+ ··· − 60y + 9)(y
43
− 16y
42
+ ··· + 159y −9)
c
8
, c
11
(y
8
− 10y
7
+ 43y
6
− 103y
5
+ 149y
4
− 130y
3
+ 64y
2
− 17y + 4)
· (y
42
− 26y
41
+ ··· + 84y + 36)(y
43
− 10y
42
+ ··· − 588y −36)
c
9
, c
10
(y
8
− 14y
7
+ 71y
6
− 157y
5
+ 141y
4
− 8y
3
− 5y
2
+ 2y + 1)
· (y
42
− 8y
41
+ ··· − 10y + 1)(y
43
+ 4y
42
+ ··· + 19y −1)
47
