12a
0445
(K12a
0445
)
A knot diagram
1
Linearized knot diagam
3 6 10 9 2 12 1 5 11 4 8 7
Solving Sequence
4,11
10
2,3
1 9 5 6 8 12 7
c
10
c
3
c
1
c
9
c
4
c
5
c
8
c
11
c
7
c
2
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
60
+ 16u
58
+ ··· + 4b + 4, 2u
64
− 34u
62
+ ··· + 4a − 2, u
65
− 2u
64
+ ··· + 4u − 2i
I
u
2
= h−7u
8
a
2
+ 2u
8
a + ··· − 8a + 8, −3u
8
a − u
8
+ ··· − a − 1, u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
I
u
3
= hu
3
+ b − u + 1, −u
3
− 2u
2
+ 2a + 2u + 2, u
4
− 2u
2
+ 2i
I
v
1
= ha, b + 1, v −1i
* 4 irreducible components of dim
C
= 0, with total 97 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−u
60
+16u
58
+· · ·+4b+4, 2u
64
−34u
62
+· · ·+4a−2, u
65
−2u
64
+· · ·+4u−2i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
2
=
−
1
2
u
64
+
17
2
u
62
+ ··· − 2u
2
+
1
2
1
4
u
60
− 4u
58
+ ··· +
3
2
u − 1
a
3
=
−u
−u
3
+ u
a
1
=
−
1
2
u
64
+
17
2
u
62
+ ··· + u +
1
2
3
4
u
57
−
45
4
u
55
+ ··· +
1
2
u − 1
a
9
=
−u
2
+ 1
u
2
a
5
=
−u
5
+ 2u
3
− u
u
5
− u
3
+ u
a
6
=
−
1
2
u
64
+ u
63
+ ··· −
1
2
u
2
−
1
2
u
64
− u
63
+ ··· −
3
2
u + 1
a
8
=
−u
8
+ 3u
6
− 3u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
12
=
u
16
− 5u
14
+ 11u
12
− 12u
10
+ 5u
8
+ 2u
6
− 2u
4
+ 1
−u
16
+ 4u
14
− 8u
12
+ 8u
10
− 4u
8
a
7
=
−
1
4
u
47
+ 3u
45
+ ··· −
1
2
u + 1
−
1
4
u
49
+
13
4
u
47
+ ··· +
1
2
u
2
+
1
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
64
− 34u
62
+ ··· + 4u
2
+ 2u
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
+ 30u
64
+ ··· + 341u + 25
c
2
, c
5
u
65
+ 2u
64
+ ··· − u − 5
c
3
, c
10
u
65
− 2u
64
+ ··· + 4u − 2
c
4
, c
8
u
65
− 6u
64
+ ··· + 800u − 128
c
6
, c
7
, c
12
u
65
− 2u
64
+ ··· − 29u − 5
c
9
u
65
− 34u
64
+ ··· + 8u − 4
c
11
u
65
+ 6u
64
+ ··· − 38400u − 6400
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
+ 18y
64
+ ··· − 5119y −625
c
2
, c
5
y
65
− 30y
64
+ ··· + 341y −25
c
3
, c
10
y
65
− 34y
64
+ ··· + 8y −4
c
4
, c
8
y
65
+ 46y
64
+ ··· − 449536y −16384
c
6
, c
7
, c
12
y
65
− 62y
64
+ ··· + 101y −25
c
9
y
65
− 6y
64
+ ··· − 96y −16
c
11
y
65
+ 18y
64
+ ··· + 928972800y −40960000
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.817592 + 0.566504I
a = 1.001660 + 0.499146I
b = −0.803784 − 0.901222I
−4.82306 + 6.28510I −3.32278 − 7.59393I
u = 0.817592 − 0.566504I
a = 1.001660 − 0.499146I
b = −0.803784 + 0.901222I
−4.82306 − 6.28510I −3.32278 + 7.59393I
u = −0.953679 + 0.230396I
a = 0.530015 + 0.857835I
b = −0.234736 − 1.236490I
0.22966 − 3.35008I 3.44223 + 7.37445I
u = −0.953679 − 0.230396I
a = 0.530015 − 0.857835I
b = −0.234736 + 1.236490I
0.22966 + 3.35008I 3.44223 − 7.37445I
u = 0.867814 + 0.546058I
a = −1.086670 − 0.445288I
b = 0.772557 − 0.231724I
2.45054 + 5.49911I 5.13183 − 6.08008I
u = 0.867814 − 0.546058I
a = −1.086670 + 0.445288I
b = 0.772557 + 0.231724I
2.45054 − 5.49911I 5.13183 + 6.08008I
u = −0.851343 + 0.598329I
a = −0.993809 + 0.234050I
b = 0.744150 − 0.677275I
−0.19697 − 10.34520I 2.00000 + 9.33633I
u = −0.851343 − 0.598329I
a = −0.993809 − 0.234050I
b = 0.744150 + 0.677275I
−0.19697 + 10.34520I 2.00000 − 9.33633I
u = −1.063320 + 0.100601I
a = 0.569690 − 0.407670I
b = 0.152388 + 0.523402I
6.87892 − 1.28336I 11.91682 + 0.I
u = −1.063320 − 0.100601I
a = 0.569690 + 0.407670I
b = 0.152388 − 0.523402I
6.87892 + 1.28336I 11.91682 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.682675 + 0.625842I
a = −1.037510 + 0.885110I
b = 0.086909 + 0.270043I
−0.68166 + 5.57497I 0.67648 − 3.36542I
u = −0.682675 − 0.625842I
a = −1.037510 − 0.885110I
b = 0.086909 − 0.270043I
−0.68166 − 5.57497I 0.67648 + 3.36542I
u = 0.714787 + 0.573135I
a = 1.30327 + 0.78179I
b = −0.082774 + 0.462333I
−5.11709 − 1.75235I −4.58587 + 0.58883I
u = 0.714787 − 0.573135I
a = 1.30327 − 0.78179I
b = −0.082774 − 0.462333I
−5.11709 + 1.75235I −4.58587 − 0.58883I
u = 1.111470 + 0.181688I
a = −0.544169 + 0.744719I
b = 0.054698 − 1.212870I
5.34190 + 6.22052I 0
u = 1.111470 − 0.181688I
a = −0.544169 − 0.744719I
b = 0.054698 + 1.212870I
5.34190 − 6.22052I 0
u = −1.079780 + 0.393400I
a = 0.586713 + 0.500350I
b = −0.287866 − 1.175110I
0.29352 − 3.61296I 0
u = −1.079780 − 0.393400I
a = 0.586713 − 0.500350I
b = −0.287866 + 1.175110I
0.29352 + 3.61296I 0
u = 1.036050 + 0.514389I
a = −0.176619 − 0.238402I
b = 0.242683 − 0.667917I
4.33017 + 4.75138I 0
u = 1.036050 − 0.514389I
a = −0.176619 + 0.238402I
b = 0.242683 + 0.667917I
4.33017 − 4.75138I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.179248 + 0.820504I
a = −2.76924 − 0.28927I
b = 2.56160 + 0.44968I
3.24662 + 11.46570I 3.08775 − 7.01203I
u = −0.179248 − 0.820504I
a = −2.76924 + 0.28927I
b = 2.56160 − 0.44968I
3.24662 − 11.46570I 3.08775 + 7.01203I
u = 0.622403 + 0.560318I
a = −0.757931 − 0.804055I
b = 0.716714 + 0.206450I
1.76971 − 1.06987I 3.74931 − 0.57518I
u = 0.622403 − 0.560318I
a = −0.757931 + 0.804055I
b = 0.716714 − 0.206450I
1.76971 + 1.06987I 3.74931 + 0.57518I
u = 0.148042 + 0.807692I
a = −1.272480 + 0.105470I
b = 1.252900 + 0.245176I
5.88305 − 6.01895I 6.28213 + 3.41956I
u = 0.148042 − 0.807692I
a = −1.272480 − 0.105470I
b = 1.252900 − 0.245176I
5.88305 + 6.01895I 6.28213 − 3.41956I
u = 0.026559 + 0.816830I
a = 2.05792 − 0.30407I
b = −1.92568 + 0.54969I
8.97867 − 2.80576I 7.60406 + 2.92369I
u = 0.026559 − 0.816830I
a = 2.05792 + 0.30407I
b = −1.92568 − 0.54969I
8.97867 + 2.80576I 7.60406 − 2.92369I
u = 0.173965 + 0.785851I
a = 2.80856 − 0.43408I
b = −2.62242 + 0.58225I
−1.84850 − 7.14370I −0.88487 + 6.10212I
u = 0.173965 − 0.785851I
a = 2.80856 + 0.43408I
b = −2.62242 − 0.58225I
−1.84850 + 7.14370I −0.88487 − 6.10212I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.328214 + 0.717210I
a = 0.33358 − 1.68604I
b = −0.533884 + 0.706902I
0.88497 − 3.76157I 1.92305 + 4.45594I
u = −0.328214 − 0.717210I
a = 0.33358 + 1.68604I
b = −0.533884 − 0.706902I
0.88497 + 3.76157I 1.92305 − 4.45594I
u = −1.104700 + 0.540023I
a = 1.152340 + 0.185689I
b = −0.775860 − 1.007390I
3.14622 − 1.01880I 0
u = −1.104700 − 0.540023I
a = 1.152340 − 0.185689I
b = −0.775860 + 1.007390I
3.14622 + 1.01880I 0
u = −1.191410 + 0.358120I
a = −0.22902 − 2.04791I
b = −2.78366 + 0.30989I
2.23292 + 3.39189I 0
u = −1.191410 − 0.358120I
a = −0.22902 + 2.04791I
b = −2.78366 − 0.30989I
2.23292 − 3.39189I 0
u = 1.136920 + 0.509754I
a = −1.073520 + 0.346110I
b = 0.693931 − 1.151840I
−0.67611 + 3.99514I 0
u = 1.136920 − 0.509754I
a = −1.073520 − 0.346110I
b = 0.693931 + 1.151840I
−0.67611 − 3.99514I 0
u = 0.744579
a = −1.05480
b = 0.775268
1.14707 9.24630
u = −1.176550 + 0.440517I
a = 1.21001 + 1.35680I
b = 1.76452 − 1.56292I
5.27296 − 5.60632I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.176550 − 0.440517I
a = 1.21001 − 1.35680I
b = 1.76452 + 1.56292I
5.27296 + 5.60632I 0
u = 1.169190 + 0.459982I
a = −0.82847 − 1.76090I
b = 1.90826 − 0.72975I
5.13635 + 2.80309I 0
u = 1.169190 − 0.459982I
a = −0.82847 + 1.76090I
b = 1.90826 + 0.72975I
5.13635 − 2.80309I 0
u = 0.403097 + 0.615636I
a = 0.0208537 + 0.1192870I
b = 0.456874 + 0.195401I
2.53638 − 0.30236I 4.66642 + 1.23466I
u = 0.403097 − 0.615636I
a = 0.0208537 − 0.1192870I
b = 0.456874 − 0.195401I
2.53638 + 0.30236I 4.66642 − 1.23466I
u = 1.216740 + 0.346923I
a = 0.16322 − 1.82772I
b = 2.64947 + 0.36051I
7.52621 − 7.61146I 0
u = 1.216740 − 0.346923I
a = 0.16322 + 1.82772I
b = 2.64947 − 0.36051I
7.52621 + 7.61146I 0
u = −1.212450 + 0.371030I
a = 0.463224 + 0.616052I
b = 1.36963 − 0.52285I
9.98584 + 2.06282I 0
u = −1.212450 − 0.371030I
a = 0.463224 − 0.616052I
b = 1.36963 + 0.52285I
9.98584 − 2.06282I 0
u = 0.238477 + 0.691626I
a = −0.14363 − 1.82861I
b = 0.377761 + 0.729301I
−3.27706 + 0.59453I −4.21283 − 0.89914I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.238477 − 0.691626I
a = −0.14363 + 1.82861I
b = 0.377761 − 0.729301I
−3.27706 − 0.59453I −4.21283 + 0.89914I
u = 1.179570 + 0.519770I
a = 0.01991 + 2.86759I
b = −3.20110 − 0.82584I
1.10514 + 11.98050I 0
u = 1.179570 − 0.519770I
a = 0.01991 − 2.86759I
b = −3.20110 + 0.82584I
1.10514 − 11.98050I 0
u = 0.014596 + 0.706342I
a = −1.49992 − 0.84941I
b = 1.45112 + 1.05511I
1.90823 + 1.44788I 5.13064 − 4.21767I
u = 0.014596 − 0.706342I
a = −1.49992 + 0.84941I
b = 1.45112 − 1.05511I
1.90823 − 1.44788I 5.13064 + 4.21767I
u = −1.219250 + 0.439359I
a = 0.36557 − 1.86792I
b = −2.20444 − 0.03684I
12.68970 − 1.63450I 0
u = −1.219250 − 0.439359I
a = 0.36557 + 1.86792I
b = −2.20444 + 0.03684I
12.68970 + 1.63450I 0
u = 1.192660 + 0.515912I
a = −0.38726 − 1.49439I
b = 1.405220 − 0.098495I
8.96580 + 10.88390I 0
u = 1.192660 − 0.515912I
a = −0.38726 + 1.49439I
b = 1.405220 + 0.098495I
8.96580 − 10.88390I 0
u = 1.215800 + 0.464785I
a = −0.38312 + 1.70536I
b = −2.30596 − 0.95072I
12.5099 + 7.4058I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.215800 − 0.464785I
a = −0.38312 − 1.70536I
b = −2.30596 + 0.95072I
12.5099 − 7.4058I 0
u = −1.190160 + 0.530226I
a = −0.24352 + 2.69698I
b = 3.08085 − 0.66725I
6.2428 − 16.4359I 0
u = −1.190160 − 0.530226I
a = −0.24352 − 2.69698I
b = 3.08085 + 0.66725I
6.2428 + 16.4359I 0
u = −0.425252 + 0.383889I
a = −1.132260 − 0.775726I
b = −0.367711 + 0.340835I
−1.51336 + 0.22253I −6.47259 − 0.43196I
u = −0.425252 − 0.383889I
a = −1.132260 + 0.775726I
b = −0.367711 − 0.340835I
−1.51336 − 0.22253I −6.47259 + 0.43196I
11
II. I
u
2
= h−7u
8
a
2
+ 2u
8
a + · · · − 8a + 8, −3u
8
a − u
8
+ · · · − a − 1, u
9
+ u
8
−
2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
2
=
a
0.368421a
2
u
8
− 0.105263au
8
+ ··· + 0.421053a − 0.421053
a
3
=
−u
−u
3
+ u
a
1
=
0.210526a
2
u
8
− 0.631579au
8
+ ··· + 1.52632a − 0.526316
0.421053a
2
u
8
− 1.26316au
8
+ ··· − 0.947368a − 1.05263
a
9
=
−u
2
+ 1
u
2
a
5
=
−u
5
+ 2u
3
− u
u
5
− u
3
+ u
a
6
=
−0.526316a
2
u
8
− 0.421053au
8
+ ··· − 1.31579a + 0.315789
0.157895a
2
u
8
+ 0.526316au
8
+ ··· − 0.105263a + 0.105263
a
8
=
−u
8
+ 3u
6
− 3u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
12
=
u
u
3
− u
a
7
=
0.210526a
2
u
8
− 0.631579au
8
+ ··· − 0.473684a + 1.47368
0.842105a
2
u
8
− 0.526316au
8
+ ··· − 0.894737a − 0.105263
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
7
− 8u
5
− 4u
4
+ 8u
3
+ 4u
2
+ 4u + 2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
+ 18u
26
+ ··· + u + 1
c
2
, c
5
, c
6
c
7
, c
12
u
27
− 9u
25
+ ··· − u + 1
c
3
, c
10
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
c
4
, c
8
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
c
9
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
3
c
11
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 18y
26
+ ··· + 9y − 1
c
2
, c
5
, c
6
c
7
, c
12
y
27
− 18y
26
+ ··· + y − 1
c
3
, c
10
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
c
4
, c
8
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
c
9
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
3
c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = 0.938233 − 0.549595I
b = −0.700495 − 0.037445I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = −0.772920 + 0.510351I
a = −0.951167 + 0.931060I
b = 0.82536 − 1.27735I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = −0.772920 + 0.510351I
a = −1.69872 + 0.67925I
b = 0.044903 + 0.772033I
−1.78344 − 2.09337I −0.51499 + 4.16283I
u = −0.772920 − 0.510351I
a = 0.938233 + 0.549595I
b = −0.700495 + 0.037445I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = −0.772920 − 0.510351I
a = −0.951167 − 0.931060I
b = 0.82536 + 1.27735I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = −0.772920 − 0.510351I
a = −1.69872 − 0.67925I
b = 0.044903 − 0.772033I
−1.78344 + 2.09337I −0.51499 − 4.16283I
u = 0.825933
a = −1.009920 + 0.483068I
b = 0.666865 − 0.540481I
1.19845 8.65230
u = 0.825933
a = −1.009920 − 0.483068I
b = 0.666865 + 0.540481I
1.19845 8.65230
u = 0.825933
a = 1.69414
b = 1.19129
1.19845 8.65230
u = 1.173910 + 0.391555I
a = −0.791730 + 0.659033I
b = 0.37946 − 1.36702I
4.37135 + 1.33617I 7.28409 − 0.70175I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.173910 + 0.391555I
a = −0.860718 + 0.617604I
b = −1.13913 − 0.93448I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = 1.173910 + 0.391555I
a = −0.05333 − 2.41062I
b = 2.95190 − 0.03287I
4.37135 + 1.33617I 7.28409 − 0.70175I
u = 1.173910 − 0.391555I
a = −0.791730 − 0.659033I
b = 0.37946 + 1.36702I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = 1.173910 − 0.391555I
a = −0.860718 − 0.617604I
b = −1.13913 + 0.93448I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = 1.173910 − 0.391555I
a = −0.05333 + 2.41062I
b = 2.95190 + 0.03287I
4.37135 − 1.33617I 7.28409 + 0.70175I
u = −0.141484 + 0.739668I
a = 1.078680 − 0.155169I
b = −1.098540 + 0.450597I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = −0.141484 + 0.739668I
a = 0.11499 − 2.02771I
b = −0.242725 + 0.851614I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = −0.141484 + 0.739668I
a = −2.74674 − 0.75294I
b = 2.59952 + 0.89764I
0.61694 + 2.45442I 2.32792 − 2.91298I
u = −0.141484 − 0.739668I
a = 1.078680 + 0.155169I
b = −1.098540 − 0.450597I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = −0.141484 − 0.739668I
a = 0.11499 + 2.02771I
b = −0.242725 − 0.851614I
0.61694 − 2.45442I 2.32792 + 2.91298I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.141484 − 0.739668I
a = −2.74674 + 0.75294I
b = 2.59952 − 0.89764I
0.61694 − 2.45442I 2.32792 + 2.91298I
u = −1.172470 + 0.500383I
a = 1.091800 + 0.484704I
b = −0.69350 − 1.28119I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = −1.172470 + 0.500383I
a = 0.54475 − 1.43728I
b = −1.40261 − 0.36766I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = −1.172470 + 0.500383I
a = 0.49679 + 2.90848I
b = 3.21334 − 1.22706I
3.59813 − 7.08493I 5.57680 + 5.91335I
u = −1.172470 − 0.500383I
a = 1.091800 − 0.484704I
b = −0.69350 + 1.28119I
3.59813 + 7.08493I 5.57680 − 5.91335I
u = −1.172470 − 0.500383I
a = 0.54475 + 1.43728I
b = −1.40261 + 0.36766I
3.59813 + 7.08493I 5.57680 − 5.91335I
u = −1.172470 − 0.500383I
a = 0.49679 − 2.90848I
b = 3.21334 + 1.22706I
3.59813 + 7.08493I 5.57680 − 5.91335I
17
III. I
u
3
= hu
3
+ b − u + 1, −u
3
− 2u
2
+ 2a + 2u + 2, u
4
− 2u
2
+ 2i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
2
=
1
2
u
3
+ u
2
− u − 1
−u
3
+ u − 1
a
3
=
−u
−u
3
+ u
a
1
=
1
2
u
3
+ u
2
− 1
−1
a
9
=
−u
2
+ 1
u
2
a
5
=
u
u
3
− u
a
6
=
1
2
u
3
+ u
2
− 1
−1
a
8
=
−1
0
a
12
=
1
0
a
7
=
1
2
u
3
+ u
2
− 2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 8
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
(u − 1)
4
c
2
, c
12
(u + 1)
4
c
3
, c
10
u
4
− 2u
2
+ 2
c
4
, c
8
u
4
+ 2u
2
+ 2
c
9
(u
2
+ 2u + 2)
2
c
11
u
4
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
(y − 1)
4
c
3
, c
10
(y
2
− 2y + 2)
2
c
4
, c
8
(y
2
+ 2y + 2)
2
c
9
(y
2
+ 4)
2
c
11
y
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098680 + 0.455090I
a = −0.77689 + 1.32180I
b = −0.544910 − 1.098680I
2.46740 + 3.66386I 4.00000 − 4.00000I
u = 1.098680 − 0.455090I
a = −0.77689 − 1.32180I
b = −0.544910 + 1.098680I
2.46740 − 3.66386I 4.00000 + 4.00000I
u = −1.098680 + 0.455090I
a = 0.776887 − 0.678203I
b = −1.45509 − 1.09868I
2.46740 − 3.66386I 4.00000 + 4.00000I
u = −1.098680 − 0.455090I
a = 0.776887 + 0.678203I
b = −1.45509 + 1.09868I
2.46740 + 3.66386I 4.00000 − 4.00000I
21
IV. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
1
0
a
10
=
1
0
a
2
=
0
−1
a
3
=
1
0
a
1
=
−1
−1
a
9
=
1
0
a
5
=
1
0
a
6
=
1
1
a
8
=
1
0
a
12
=
1
0
a
7
=
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
u
c
5
, c
6
, c
7
u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
y − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
y
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
0 0
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
27
+ 18u
26
+ ··· + u + 1)(u
65
+ 30u
64
+ ··· + 341u + 25)
c
2
(u − 1)(u + 1)
4
(u
27
− 9u
25
+ ··· − u + 1)(u
65
+ 2u
64
+ ··· − u − 5)
c
3
, c
10
u(u
4
− 2u
2
+ 2)(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
3
· (u
65
− 2u
64
+ ··· + 4u − 2)
c
4
, c
8
u(u
4
+ 2u
2
+ 2)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
3
· (u
65
− 6u
64
+ ··· + 800u − 128)
c
5
((u − 1)
4
)(u + 1)(u
27
− 9u
25
+ ··· − u + 1)(u
65
+ 2u
64
+ ··· − u − 5)
c
6
, c
7
((u − 1)
4
)(u + 1)(u
27
− 9u
25
+ ··· − u + 1)(u
65
− 2u
64
+ ··· − 29u − 5)
c
9
u(u
2
+ 2u + 2)
2
· (u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
3
· (u
65
− 34u
64
+ ··· + 8u − 4)
c
11
u
5
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
3
· (u
65
+ 6u
64
+ ··· − 38400u − 6400)
c
12
(u − 1)(u + 1)
4
(u
27
− 9u
25
+ ··· − u + 1)(u
65
− 2u
64
+ ··· − 29u − 5)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
5
)(y
27
− 18y
26
+ ··· + 9y − 1)(y
65
+ 18y
64
+ ··· − 5119y − 625)
c
2
, c
5
((y − 1)
5
)(y
27
− 18y
26
+ ··· + y − 1)(y
65
− 30y
64
+ ··· + 341y − 25)
c
3
, c
10
y(y
2
− 2y + 2)
2
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
3
· (y
65
− 34y
64
+ ··· + 8y − 4)
c
4
, c
8
y(y
2
+ 2y + 2)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
3
· (y
65
+ 46y
64
+ ··· − 449536y − 16384)
c
6
, c
7
, c
12
((y − 1)
5
)(y
27
− 18y
26
+ ··· + y − 1)(y
65
− 62y
64
+ ··· + 101y − 25)
c
9
y(y
2
+ 4)
2
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
3
· (y
65
− 6y
64
+ ··· − 96y − 16)
c
11
y
5
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
3
· (y
65
+ 18y
64
+ ··· + 928972800y − 40960000)
27
