12a
0386
(K12a
0386
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 8 2 11 1 4 12 7 5
Solving Sequence
2,7
6 3
1,12
11 8 9 5 10 4
c
6
c
2
c
1
c
11
c
7
c
8
c
5
c
10
c
4
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −13623u
25
− 12794u
24
+ ··· + 24374a + 5797, u
26
− u
25
+ ··· + 2u − 1i
I
u
2
= h7.39786 × 10
132
u
91
+ 1.99769 × 10
133
u
90
+ ··· + 5.07101 × 10
132
b − 1.01915 × 10
133
,
− 1.78004 × 10
132
u
91
+ 4.64745 × 10
131
u
90
+ ··· + 2.53550 × 10
132
a − 2.75480 × 10
133
,
u
92
+ 2u
91
+ ··· + 41u + 2i
I
u
3
= hb + u, u
11
+ u
10
+ 2u
9
+ u
8
+ 3u
7
+ 3u
6
+ 2u
5
+ u
4
+ 3u
2
+ a,
u
12
+ u
11
+ 3u
10
+ 2u
9
+ 6u
8
+ 4u
7
+ 7u
6
+ 3u
5
+ 6u
4
+ 3u
3
+ 3u
2
+ u + 1i
I
u
4
= h−u
11
− u
10
− 3u
9
− 2u
8
− 6u
7
− 4u
6
− 7u
5
− 4u
4
− 6u
3
− 2u
2
+ b − 3u − 1,
u
11
+ u
10
+ 2u
9
+ u
8
+ 3u
7
+ 3u
6
+ 2u
5
+ 2u
4
+ u
2
+ a + 1,
u
12
+ u
11
+ 3u
10
+ 2u
9
+ 6u
8
+ 4u
7
+ 7u
6
+ 4u
5
+ 6u
4
+ 2u
3
+ 3u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 142 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
= hb−u, −13623u
25
−12794u
24
+· · ·+24374a+5797, u
26
−u
25
+· · ·+2u−1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
0.558915u
25
+ 0.524904u
24
+ ··· − 3.21010u − 0.237835
u
a
11
=
0.558915u
25
+ 0.524904u
24
+ ··· − 4.21010u − 0.237835
u
a
8
=
−1.08382u
25
+ 0.646673u
24
+ ··· + 1.35567u + 0.441085
−u
2
a
9
=
−0.785263u
25
+ 0.970296u
24
+ ··· + 2.12210u − 0.0820546
−0.102035u
25
− 0.0894396u
24
+ ··· + 0.193608u + 0.103758
a
5
=
−0.677936u
25
+ 0.0100927u
24
+ ··· − 0.814967u + 1.36490
0.140108u
25
+ 0.375728u
24
+ ··· + 1.05502u − 0.948265
a
10
=
0.996061u
25
− 0.753754u
24
+ ··· − 5.81882u + 0.845983
u
3
+ u
a
4
=
−0.294617u
25
+ 0.430130u
24
+ ··· + 4.05239u − 0.322844
0.102035u
25
+ 0.0894396u
24
+ ··· − 0.193608u − 0.103758
(ii) Obstruction class = −1
(iii) Cusp Shapes =
26279
12187
u
25
−
14751
12187
u
24
+ ··· −
2321
12187
u +
143807
12187
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
26
+ 11u
25
+ ··· − 8u + 1
c
2
, c
6
, c
7
c
11
u
26
− u
25
+ ··· + 2u − 1
c
3
, c
4
, c
9
u
26
+ 11u
25
+ ··· − 8u − 32
c
5
u
26
− 24u
25
+ ··· − 29184u + 2048
c
8
, c
12
u
26
− 6u
24
+ ··· + u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
26
+ 15y
25
+ ··· − 156y + 1
c
2
, c
6
, c
7
c
11
y
26
+ 11y
25
+ ··· − 8y + 1
c
3
, c
4
, c
9
y
26
− 25y
25
+ ··· − 1344y + 1024
c
5
y
26
+ 58y
24
+ ··· − 138674176y + 4194304
c
8
, c
12
y
26
− 12y
25
+ ··· + 63y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.807615 + 0.620588I
a = −1.41594 + 0.44568I
b = −0.807615 + 0.620588I
4.61940 + 2.42366I 11.49135 − 1.87928I
u = −0.807615 − 0.620588I
a = −1.41594 − 0.44568I
b = −0.807615 − 0.620588I
4.61940 − 2.42366I 11.49135 + 1.87928I
u = 0.685911 + 0.758379I
a = 1.50210 + 1.14201I
b = 0.685911 + 0.758379I
2.96984 + 2.94472I 13.74154 − 2.94116I
u = 0.685911 − 0.758379I
a = 1.50210 − 1.14201I
b = 0.685911 − 0.758379I
2.96984 − 2.94472I 13.74154 + 2.94116I
u = 0.329454 + 0.917116I
a = 2.49009 − 1.59537I
b = 0.329454 + 0.917116I
−2.86243 + 2.69103I 3.21966 − 6.77085I
u = 0.329454 − 0.917116I
a = 2.49009 + 1.59537I
b = 0.329454 − 0.917116I
−2.86243 − 2.69103I 3.21966 + 6.77085I
u = −0.664437 + 0.829427I
a = −3.39426 − 0.66607I
b = −0.664437 + 0.829427I
9.68736 − 2.24802I 12.39075 + 4.49177I
u = −0.664437 − 0.829427I
a = −3.39426 + 0.66607I
b = −0.664437 − 0.829427I
9.68736 + 2.24802I 12.39075 − 4.49177I
u = −0.144028 + 1.075630I
a = −0.93960 − 1.40239I
b = −0.144028 + 1.075630I
−5.86362 + 0.20015I −4.19232 − 0.64656I
u = −0.144028 − 1.075630I
a = −0.93960 + 1.40239I
b = −0.144028 − 1.075630I
−5.86362 − 0.20015I −4.19232 + 0.64656I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.941091 + 0.622014I
a = 1.67976 + 0.31359I
b = 0.941091 + 0.622014I
12.33100 − 5.65494I 13.25979 + 1.47273I
u = 0.941091 − 0.622014I
a = 1.67976 − 0.31359I
b = 0.941091 − 0.622014I
12.33100 + 5.65494I 13.25979 − 1.47273I
u = −0.718112 + 0.900060I
a = −2.12467 + 0.83966I
b = −0.718112 + 0.900060I
9.28845 − 8.45450I 12.1791 + 8.6146I
u = −0.718112 − 0.900060I
a = −2.12467 − 0.83966I
b = −0.718112 − 0.900060I
9.28845 + 8.45450I 12.1791 − 8.6146I
u = 0.643874 + 0.975926I
a = 2.71464 − 1.15433I
b = 0.643874 + 0.975926I
1.56867 + 7.39409I 9.80460 − 8.29279I
u = 0.643874 − 0.975926I
a = 2.71464 + 1.15433I
b = 0.643874 − 0.975926I
1.56867 − 7.39409I 9.80460 + 8.29279I
u = 0.043255 + 1.216790I
a = 0.450845 − 0.826169I
b = 0.043255 + 1.216790I
−1.24232 − 2.12927I 4.01236 + 3.25160I
u = 0.043255 − 1.216790I
a = 0.450845 + 0.826169I
b = 0.043255 − 1.216790I
−1.24232 + 2.12927I 4.01236 − 3.25160I
u = 0.186488 + 0.738957I
a = −0.359062 − 0.571045I
b = 0.186488 + 0.738957I
−1.43325 + 1.76515I 5.03671 − 5.93425I
u = 0.186488 − 0.738957I
a = −0.359062 + 0.571045I
b = 0.186488 − 0.738957I
−1.43325 − 1.76515I 5.03671 + 5.93425I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688964 + 1.070760I
a = −2.23446 − 0.81457I
b = −0.688964 + 1.070760I
1.85165 − 13.77330I 6.97647 + 10.67636I
u = −0.688964 − 1.070760I
a = −2.23446 + 0.81457I
b = −0.688964 − 1.070760I
1.85165 + 13.77330I 6.97647 − 10.67636I
u = 0.752694 + 1.118140I
a = 2.15761 − 0.51442I
b = 0.752694 + 1.118140I
9.2507 + 18.1776I 9.30289 − 9.71516I
u = 0.752694 − 1.118140I
a = 2.15761 + 0.51442I
b = 0.752694 − 1.118140I
9.2507 − 18.1776I 9.30289 + 9.71516I
u = −0.417843
a = 3.42500
b = −0.417843
7.84141 10.0650
u = 0.298624
a = −0.479073
b = 0.298624
0.653973 15.4890
7
II. I
u
2
= h7.40 × 10
132
u
91
+ 2.00 × 10
133
u
90
+ · · · + 5.07 × 10
132
b − 1.02 ×
10
133
, −1.78 × 10
132
u
91
+ 4.65 × 10
131
u
90
+ · · · + 2.54 × 10
132
a − 2.75 ×
10
133
, u
92
+ 2u
91
+ · · · + 41u + 2i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
0.702046u
91
− 0.183295u
90
+ ··· + 154.391u + 10.8649
−1.45885u
91
− 3.93944u
90
+ ··· + 25.5277u + 2.00976
a
11
=
2.16090u
91
+ 3.75615u
90
+ ··· + 128.863u + 8.85514
−1.45885u
91
− 3.93944u
90
+ ··· + 25.5277u + 2.00976
a
8
=
−3.09629u
91
− 8.80027u
90
+ ··· − 2.33000u + 4.74136
−2.50890u
91
− 5.76206u
90
+ ··· + 44.4508u + 2.16426
a
9
=
−7.54762u
91
− 19.0382u
90
+ ··· + 155.289u + 12.3751
−4.02479u
91
− 7.82729u
90
+ ··· + 170.044u + 8.14333
a
5
=
2.83666u
91
+ 4.59685u
90
+ ··· + 45.4045u + 9.16643
−1.97405u
91
− 5.81218u
90
+ ··· + 0.126535u + 1.64984
a
10
=
−4.87434u
91
− 12.3841u
90
+ ··· + 343.215u + 9.88688
−1.98056u
91
− 4.31566u
90
+ ··· + 93.1840u + 3.95306
a
4
=
−1.99202u
91
+ 0.293742u
90
+ ··· + 406.348u + 22.5493
4.42433u
91
+ 15.5293u
90
+ ··· + 114.784u + 5.48884
(ii) Obstruction class = −1
(iii) Cusp Shapes = −11.6941u
91
− 28.4552u
90
+ ··· + 63.6053u + 5.57785
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
92
+ 32u
91
+ ··· − 225u + 4
c
2
, c
6
, c
7
c
11
u
92
+ 2u
91
+ ··· + 41u + 2
c
3
, c
4
, c
9
(u
46
− 5u
45
+ ··· − u + 1)
2
c
5
(u
46
+ 11u
45
+ ··· − 11u − 1)
2
c
8
, c
12
u
92
− 5u
91
+ ··· − 169896u + 138881
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
92
+ 60y
91
+ ··· + 881743y + 16
c
2
, c
6
, c
7
c
11
y
92
+ 32y
91
+ ··· − 225y + 4
c
3
, c
4
, c
9
(y
46
− 51y
45
+ ··· − 43y + 1)
2
c
5
(y
46
+ 11y
45
+ ··· + y + 1)
2
c
8
, c
12
y
92
− 31y
91
+ ··· − 535870573466y + 19287932161
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.384275 + 0.922259I
a = −0.196400 − 0.647605I
b = −0.107571 + 0.785518I
−1.49826 + 1.86565I 0
u = 0.384275 − 0.922259I
a = −0.196400 + 0.647605I
b = −0.107571 − 0.785518I
−1.49826 − 1.86565I 0
u = 0.104954 + 0.988208I
a = 0.06006 + 1.83739I
b = 0.527133 − 0.897374I
−1.74949 − 1.99664I 0
u = 0.104954 − 0.988208I
a = 0.06006 − 1.83739I
b = 0.527133 + 0.897374I
−1.74949 + 1.99664I 0
u = 0.672129 + 0.755146I
a = −0.97156 + 1.44268I
b = −1.199970 + 0.386947I
10.12620 + 0.27578I 0
u = 0.672129 − 0.755146I
a = −0.97156 − 1.44268I
b = −1.199970 − 0.386947I
10.12620 − 0.27578I 0
u = −0.845063 + 0.559528I
a = −1.40890 − 0.46109I
b = −0.693227 − 1.033110I
3.38247 + 8.06038I 0
u = −0.845063 − 0.559528I
a = −1.40890 + 0.46109I
b = −0.693227 + 1.033110I
3.38247 − 8.06038I 0
u = 0.894041 + 0.372500I
a = −1.172930 + 0.459245I
b = −0.633260 + 0.846876I
3.07336 − 0.96915I 0
u = 0.894041 − 0.372500I
a = −1.172930 − 0.459245I
b = −0.633260 − 0.846876I
3.07336 + 0.96915I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.527133 + 0.897374I
a = −1.08952 + 1.37635I
b = 0.104954 − 0.988208I
−1.74949 + 1.99664I 0
u = 0.527133 − 0.897374I
a = −1.08952 − 1.37635I
b = 0.104954 + 0.988208I
−1.74949 − 1.99664I 0
u = 0.657222 + 0.697436I
a = 1.98616 − 0.38406I
b = 0.671820 − 0.937942I
2.42160 − 2.30364I 0
u = 0.657222 − 0.697436I
a = 1.98616 + 0.38406I
b = 0.671820 + 0.937942I
2.42160 + 2.30364I 0
u = −0.641745 + 0.838715I
a = 1.44102 + 0.26317I
b = 0.917442 − 0.560673I
3.10180 − 4.01845I 0
u = −0.641745 − 0.838715I
a = 1.44102 − 0.26317I
b = 0.917442 + 0.560673I
3.10180 + 4.01845I 0
u = −0.633260 + 0.846876I
a = 0.670798 + 0.938661I
b = 0.894041 + 0.372500I
3.07336 − 0.96915I 0
u = −0.633260 − 0.846876I
a = 0.670798 − 0.938661I
b = 0.894041 − 0.372500I
3.07336 + 0.96915I 0
u = 0.138860 + 1.051530I
a = −0.181379 − 0.286249I
b = −0.517894 + 0.472786I
−1.73726 + 1.92631I 0
u = 0.138860 − 1.051530I
a = −0.181379 + 0.286249I
b = −0.517894 − 0.472786I
−1.73726 − 1.92631I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.651474 + 0.855223I
a = −0.722091 + 1.065280I
b = −0.87344 + 1.16989I
7.65487 − 2.41625I 0
u = 0.651474 − 0.855223I
a = −0.722091 − 1.065280I
b = −0.87344 − 1.16989I
7.65487 + 2.41625I 0
u = 0.917442 + 0.560673I
a = −1.41331 − 0.26957I
b = −0.641745 − 0.838715I
3.10180 + 4.01845I 0
u = 0.917442 − 0.560673I
a = −1.41331 + 0.26957I
b = −0.641745 + 0.838715I
3.10180 − 4.01845I 0
u = 0.647081 + 0.859138I
a = −2.46993 + 0.50078I
b = −0.83829 − 1.22663I
7.64236 + 7.46930I 0
u = 0.647081 − 0.859138I
a = −2.46993 − 0.50078I
b = −0.83829 + 1.22663I
7.64236 − 7.46930I 0
u = 0.668613 + 0.872921I
a = −0.516254 + 0.171332I
b = −0.0592993 + 0.0462954I
1.01357 + 2.58423I 0
u = 0.668613 − 0.872921I
a = −0.516254 − 0.171332I
b = −0.0592993 − 0.0462954I
1.01357 − 2.58423I 0
u = −0.737043 + 0.826535I
a = −0.63108 − 2.02908I
b = −0.669007 − 0.884235I
9.51681 + 2.91709I 0
u = −0.737043 − 0.826535I
a = −0.63108 + 2.02908I
b = −0.669007 + 0.884235I
9.51681 − 2.91709I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.669007 + 0.884235I
a = −1.86616 − 1.01078I
b = −0.737043 − 0.826535I
9.51681 − 2.91709I 0
u = −0.669007 − 0.884235I
a = −1.86616 + 1.01078I
b = −0.737043 + 0.826535I
9.51681 + 2.91709I 0
u = −0.568462 + 0.683326I
a = 0.734078 + 0.955365I
b = 0.770591 + 1.030330I
1.73892 + 2.14972I 0
u = −0.568462 − 0.683326I
a = 0.734078 − 0.955365I
b = 0.770591 − 1.030330I
1.73892 − 2.14972I 0
u = 0.773550 + 0.436944I
a = 0.292921 + 0.784690I
b = −0.243248 + 1.241290I
4.40684 − 4.36446I 0
u = 0.773550 − 0.436944I
a = 0.292921 − 0.784690I
b = −0.243248 − 1.241290I
4.40684 + 4.36446I 0
u = −0.898218 + 0.678865I
a = 0.179251 + 0.632745I
b = 0.014143 + 0.836013I
5.97757 − 0.66120I 0
u = −0.898218 − 0.678865I
a = 0.179251 − 0.632745I
b = 0.014143 − 0.836013I
5.97757 + 0.66120I 0
u = −0.585246 + 0.976451I
a = 1.99761 + 0.67960I
b = 0.692044 − 1.145060I
0.81481 − 6.80898I 0
u = −0.585246 − 0.976451I
a = 1.99761 − 0.67960I
b = 0.692044 + 1.145060I
0.81481 + 6.80898I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.659061 + 0.934255I
a = −1.62301 + 0.40053I
b = −1.208270 − 0.529614I
9.57845 + 4.88836I 0
u = 0.659061 − 0.934255I
a = −1.62301 − 0.40053I
b = −1.208270 + 0.529614I
9.57845 − 4.88836I 0
u = 0.671820 + 0.937942I
a = −0.00420 − 1.68031I
b = 0.657222 − 0.697436I
2.42160 + 2.30364I 0
u = 0.671820 − 0.937942I
a = −0.00420 + 1.68031I
b = 0.657222 + 0.697436I
2.42160 − 2.30364I 0
u = 0.993762 + 0.598379I
a = 1.33362 − 0.67978I
b = 0.742562 − 1.087310I
10.8811 − 11.8282I 0
u = 0.993762 − 0.598379I
a = 1.33362 + 0.67978I
b = 0.742562 + 1.087310I
10.8811 + 11.8282I 0
u = 0.014143 + 0.836013I
a = −0.546063 + 0.697155I
b = −0.898218 + 0.678865I
5.97757 − 0.66120I 6.00000 + 0.I
u = 0.014143 − 0.836013I
a = −0.546063 − 0.697155I
b = −0.898218 − 0.678865I
5.97757 + 0.66120I 6.00000 + 0.I
u = −0.586521 + 1.010100I
a = 1.119650 + 0.692976I
b = 0.075243 − 1.202660I
−3.13888 − 6.52644I 0
u = −0.586521 − 1.010100I
a = 1.119650 − 0.692976I
b = 0.075243 + 1.202660I
−3.13888 + 6.52644I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.075243 + 1.202660I
a = −0.670379 + 1.086120I
b = −0.586521 − 1.010100I
−3.13888 + 6.52644I 0
u = 0.075243 − 1.202660I
a = −0.670379 − 1.086120I
b = −0.586521 + 1.010100I
−3.13888 − 6.52644I 0
u = −0.107571 + 0.785518I
a = −0.626612 − 0.578450I
b = 0.384275 + 0.922259I
−1.49826 + 1.86565I 3.52037 − 4.33930I
u = −0.107571 − 0.785518I
a = −0.626612 + 0.578450I
b = 0.384275 − 0.922259I
−1.49826 − 1.86565I 3.52037 + 4.33930I
u = −0.693227 + 1.033110I
a = −0.382680 − 1.145400I
b = −0.845063 − 0.559528I
3.38247 − 8.06038I 0
u = −0.693227 − 1.033110I
a = −0.382680 + 1.145400I
b = −0.845063 + 0.559528I
3.38247 + 8.06038I 0
u = 0.634075 + 1.073450I
a = −1.232080 + 0.266868I
b = −0.216288 − 1.390700I
2.60520 + 9.64233I 0
u = 0.634075 − 1.073450I
a = −1.232080 − 0.266868I
b = −0.216288 + 1.390700I
2.60520 − 9.64233I 0
u = 0.282265 + 0.698034I
a = 0.85393 − 2.11174I
b = 0.282265 − 0.698034I
−1.99436 6.54077 + 0.I
u = 0.282265 − 0.698034I
a = 0.85393 + 2.11174I
b = 0.282265 + 0.698034I
−1.99436 6.54077 + 0.I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.199970 + 0.386947I
a = 1.372760 + 0.245997I
b = 0.672129 + 0.755146I
10.12620 + 0.27578I 0
u = −1.199970 − 0.386947I
a = 1.372760 − 0.245997I
b = 0.672129 − 0.755146I
10.12620 − 0.27578I 0
u = −0.243248 + 1.241290I
a = 0.587897 − 0.021533I
b = 0.773550 + 0.436944I
4.40684 − 4.36446I 0
u = −0.243248 − 1.241290I
a = 0.587897 + 0.021533I
b = 0.773550 − 0.436944I
4.40684 + 4.36446I 0
u = 0.099062 + 0.726030I
a = −1.58207 + 0.49349I
b = −0.774589 − 1.024930I
4.93750 + 5.50082I 6.95120 − 5.88210I
u = 0.099062 − 0.726030I
a = −1.58207 − 0.49349I
b = −0.774589 + 1.024930I
4.93750 − 5.50082I 6.95120 + 5.88210I
u = −0.774589 + 1.024930I
a = 0.924639 − 0.196309I
b = 0.099062 − 0.726030I
4.93750 − 5.50082I 0
u = −0.774589 − 1.024930I
a = 0.924639 + 0.196309I
b = 0.099062 + 0.726030I
4.93750 + 5.50082I 0
u = 0.770591 + 1.030330I
a = −0.523962 + 0.646747I
b = −0.568462 + 0.683326I
1.73892 + 2.14972I 0
u = 0.770591 − 1.030330I
a = −0.523962 − 0.646747I
b = −0.568462 − 0.683326I
1.73892 − 2.14972I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.517894 + 0.472786I
a = −0.512074 − 0.022450I
b = 0.138860 + 1.051530I
−1.73726 + 1.92631I 3.89432 − 4.39576I
u = −0.517894 − 0.472786I
a = −0.512074 + 0.022450I
b = 0.138860 − 1.051530I
−1.73726 − 1.92631I 3.89432 + 4.39576I
u = 0.197229 + 0.661581I
a = 1.75065 − 0.31294I
b = −0.614599 + 1.163900I
5.26525 − 4.46279I 2.29672 + 4.19886I
u = 0.197229 − 0.661581I
a = 1.75065 + 0.31294I
b = −0.614599 − 1.163900I
5.26525 + 4.46279I 2.29672 − 4.19886I
u = −0.614599 + 1.163900I
a = 0.540716 − 0.760064I
b = 0.197229 + 0.661581I
5.26525 − 4.46279I 0
u = −0.614599 − 1.163900I
a = 0.540716 + 0.760064I
b = 0.197229 − 0.661581I
5.26525 + 4.46279I 0
u = 0.742562 + 1.087310I
a = 0.665074 − 1.138780I
b = 0.993762 − 0.598379I
10.8811 + 11.8282I 0
u = 0.742562 − 1.087310I
a = 0.665074 + 1.138780I
b = 0.993762 + 0.598379I
10.8811 − 11.8282I 0
u = −1.208270 + 0.529614I
a = 1.38348 − 0.43005I
b = 0.659061 − 0.934255I
9.57845 − 4.88836I 0
u = −1.208270 − 0.529614I
a = 1.38348 + 0.43005I
b = 0.659061 + 0.934255I
9.57845 + 4.88836I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.692044 + 1.145060I
a = −1.70181 + 0.57199I
b = −0.585246 − 0.976451I
0.81481 + 6.80898I 0
u = 0.692044 − 1.145060I
a = −1.70181 − 0.57199I
b = −0.585246 + 0.976451I
0.81481 − 6.80898I 0
u = −0.357390 + 0.546281I
a = 2.16190 + 3.30453I
b = −0.357390 − 0.546281I
7.61775 4.49295 + 0.I
u = −0.357390 − 0.546281I
a = 2.16190 − 3.30453I
b = −0.357390 + 0.546281I
7.61775 4.49295 + 0.I
u = −0.216288 + 1.390700I
a = 0.926336 + 0.623675I
b = 0.634075 − 1.073450I
2.60520 − 9.64233I 0
u = −0.216288 − 1.390700I
a = 0.926336 − 0.623675I
b = 0.634075 + 1.073450I
2.60520 + 9.64233I 0
u = −0.87344 + 1.16989I
a = 0.608052 + 0.726893I
b = 0.651474 + 0.855223I
7.65487 − 2.41625I 0
u = −0.87344 − 1.16989I
a = 0.608052 − 0.726893I
b = 0.651474 − 0.855223I
7.65487 + 2.41625I 0
u = −0.83829 + 1.22663I
a = 1.76949 + 0.44441I
b = 0.647081 − 0.859138I
7.64236 − 7.46930I 0
u = −0.83829 − 1.22663I
a = 1.76949 − 0.44441I
b = 0.647081 + 0.859138I
7.64236 + 7.46930I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0592993 + 0.0462954I
a = 2.43438 + 7.56829I
b = 0.668613 + 0.872921I
1.01357 + 2.58423I 2.71428 − 4.03968I
u = −0.0592993 − 0.0462954I
a = 2.43438 − 7.56829I
b = 0.668613 − 0.872921I
1.01357 − 2.58423I 2.71428 + 4.03968I
20
III. I
u
3
= hb + u, u
11
+ u
10
+ · · · + 3u
2
+ a, u
12
+ u
11
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−u
11
− u
10
− 2u
9
− u
8
− 3u
7
− 3u
6
− 2u
5
− u
4
− 3u
2
−u
a
11
=
−u
11
− u
10
− 2u
9
− u
8
− 3u
7
− 3u
6
− 2u
5
− u
4
− 3u
2
+ u
−u
a
8
=
u
10
+ u
9
+ 3u
8
+ u
7
+ 5u
6
+ 2u
5
+ 6u
4
+ 4u
2
+ u + 2
−u
2
a
9
=
u
10
+ u
9
+ 3u
8
+ u
7
+ 6u
6
+ 2u
5
+ 7u
4
+ 5u
2
+ u + 2
u
8
+ 2u
6
+ 3u
4
+ u
2
+ 1
a
5
=
−u
10
− u
9
− 3u
8
− 2u
7
− 6u
6
− 4u
5
− 7u
4
− 2u
3
− 5u
2
− 2u − 2
u
11
+ u
10
+ 2u
9
+ u
8
+ 3u
7
+ 2u
6
+ 2u
5
+ u
3
+ 2u
2
a
10
=
u
9
+ 2u
7
− u
6
+ 4u
5
− u
4
+ 3u
3
− 2u
2
+ 2u
−u
3
− u
a
4
=
−u
11
− 3u
9
− 6u
7
− 7u
5
− 6u
3
+ u
2
− 3u
−u
8
− 2u
6
− 3u
4
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 7u
11
+ 4u
10
+ 16u
9
+ 4u
8
+ 31u
7
+ 7u
6
+ 26u
5
− 5u
4
+ 23u
3
− 3u
2
+ u + 3
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
12
− 5u
11
+ ··· − 5u + 1
c
2
, c
7
u
12
− u
11
+ ··· − u + 1
c
3
, c
4
u
12
+ 2u
11
+ ··· + 2u + 1
c
5
u
12
− u
11
− 2u
9
+ 4u
6
− 2u
5
− u
4
+ 3u
2
+ 2u + 1
c
6
, c
11
u
12
+ u
11
+ ··· + u + 1
c
8
, c
12
u
12
− u
10
− u
9
− 3u
8
+ u
7
+ 3u
6
+ 2u
5
+ u
4
− 2u
3
− u
2
+ 1
c
9
u
12
− 2u
11
+ ··· − 2u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
12
+ 9y
11
+ ··· + 5y + 1
c
2
, c
6
, c
7
c
11
y
12
+ 5y
11
+ ··· + 5y + 1
c
3
, c
4
, c
9
y
12
− 14y
11
+ ··· + 2y + 1
c
5
y
12
− y
11
+ ··· + 2y + 1
c
8
, c
12
y
12
− 2y
11
+ ··· − 2y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.655102 + 0.736440I
a = −1.251530 − 0.398490I
b = −0.655102 − 0.736440I
1.97845 + 3.67934I 6.30875 − 7.16034I
u = 0.655102 − 0.736440I
a = −1.251530 + 0.398490I
b = −0.655102 + 0.736440I
1.97845 − 3.67934I 6.30875 + 7.16034I
u = −0.793413 + 0.890052I
a = 2.01108 − 0.02373I
b = 0.793413 − 0.890052I
8.13868 − 5.95932I 11.90060 + 5.23042I
u = −0.793413 − 0.890052I
a = 2.01108 + 0.02373I
b = 0.793413 + 0.890052I
8.13868 + 5.95932I 11.90060 − 5.23042I
u = 0.592825 + 1.034570I
a = −1.95190 + 0.82796I
b = −0.592825 − 1.034570I
0.03780 + 6.13395I 3.34772 − 4.32128I
u = 0.592825 − 1.034570I
a = −1.95190 − 0.82796I
b = −0.592825 + 1.034570I
0.03780 − 6.13395I 3.34772 + 4.32128I
u = −0.554835 + 0.511693I
a = 0.11463 + 1.76794I
b = 0.554835 − 0.511693I
8.17744 − 0.96019I 12.36505 + 4.95398I
u = −0.554835 − 0.511693I
a = 0.11463 − 1.76794I
b = 0.554835 + 0.511693I
8.17744 + 0.96019I 12.36505 − 4.95398I
u = 0.147187 + 0.720863I
a = 1.32897 − 0.99098I
b = −0.147187 − 0.720863I
−2.42991 + 1.27964I 0.05150 − 3.21690I
u = 0.147187 − 0.720863I
a = 1.32897 + 0.99098I
b = −0.147187 + 0.720863I
−2.42991 − 1.27964I 0.05150 + 3.21690I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.546865 + 1.162890I
a = 1.248760 + 0.553949I
b = 0.546865 − 1.162890I
3.83675 − 8.25339I 10.02638 + 7.06157I
u = −0.546865 − 1.162890I
a = 1.248760 − 0.553949I
b = 0.546865 + 1.162890I
3.83675 + 8.25339I 10.02638 − 7.06157I
25
IV.
I
u
4
= h−u
11
− u
10
+ · · · + b − 1, u
11
+ u
10
+ · · · + a + 1, u
12
+ u
11
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−u
11
− u
10
− 2u
9
− u
8
− 3u
7
− 3u
6
− 2u
5
− 2u
4
− u
2
− 1
u
11
+ u
10
+ 3u
9
+ 2u
8
+ 6u
7
+ 4u
6
+ 7u
5
+ 4u
4
+ 6u
3
+ 2u
2
+ 3u + 1
a
11
=
−2u
11
− 2u
10
+ ··· − 3u − 2
u
11
+ u
10
+ 3u
9
+ 2u
8
+ 6u
7
+ 4u
6
+ 7u
5
+ 4u
4
+ 6u
3
+ 2u
2
+ 3u + 1
a
8
=
2u
11
+ 4u
9
− u
8
+ 9u
7
− u
6
+ 7u
5
− u
4
+ 6u
3
− 2u
2
+ 3u
−u
11
− 2u
9
+ u
8
− 4u
7
+ 2u
6
− 3u
5
+ 3u
4
− 2u
3
+ 4u
2
− u + 2
a
9
=
2u
11
+ 4u
9
− u
8
+ 9u
7
− u
6
+ 7u
5
+ 6u
3
− u
2
+ 3u + 1
u
6
+ 2u
4
+ 3u
2
+ 2
a
5
=
−u
10
− u
9
− 3u
8
− 2u
7
− 6u
6
− 4u
5
− 7u
4
− 3u
3
− 5u
2
− u − 2
u
11
+ u
10
+ 2u
9
+ u
8
+ 3u
7
+ 2u
6
+ 2u
5
+ u
4
+ u
3
+ 1
a
10
=
−3u
11
− 2u
10
+ ··· − 4u − 1
−u
11
− 2u
10
− 3u
9
− 4u
8
− 5u
7
− 8u
6
− 5u
5
− 7u
4
− 3u
3
− 4u
2
+ u − 2
a
4
=
−2u
11
− 2u
10
+ ··· − 4u − 2
u
11
− u
10
+ 2u
9
− 3u
8
+ 4u
7
− 6u
6
+ 3u
5
− 5u
4
+ u
3
− 4u
2
+ 2u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 5u
11
+ 7u
10
+ 13u
9
+ 11u
8
+ 23u
7
+ 23u
6
+ 21u
5
+ 15u
4
+ 17u
3
+ 8u
2
+ 12
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
12
− 5u
11
+ ··· − 5u + 1
c
2
, c
7
u
12
− u
11
+ ··· − u + 1
c
3
, c
4
(u
6
− u
5
− 3u
4
+ 3u
3
+ u
2
− u + 1)
2
c
5
(u
6
− u
5
+ u
4
+ u
3
− u
2
+ u − 1)
2
c
6
, c
11
u
12
+ u
11
+ ··· + u + 1
c
8
, c
12
u
12
− u
10
+ 2u
9
+ 3u
8
− 5u
7
+ 7u
6
− u
5
− 2u
4
+ 4u
3
− u
2
+ 1
c
9
(u
6
+ u
5
− 3u
4
− 3u
3
+ u
2
+ u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
12
+ 9y
11
+ ··· + 9y + 1
c
2
, c
6
, c
7
c
11
y
12
+ 5y
11
+ ··· + 5y + 1
c
3
, c
4
, c
9
(y
6
− 7y
5
+ 17y
4
− 15y
3
+ y
2
+ y + 1)
2
c
5
(y
6
+ y
5
+ y
4
− 3y
3
− 3y
2
+ y + 1)
2
c
8
, c
12
y
12
− 2y
11
+ ··· − 2y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.140919 + 0.990021I
a = 0.28280 − 1.98683I
b = −0.140919 + 0.990021I
−3.57493 − 60.206728 + 0.10I
u = 0.140919 − 0.990021I
a = 0.28280 + 1.98683I
b = −0.140919 − 0.990021I
−3.57493 − 60.206728 + 0.10I
u = −0.751292 + 0.659970I
a = 1.54227 + 1.35480I
b = 0.751292 + 0.659970I
8.82105 12.00884 + 0.I
u = −0.751292 − 0.659970I
a = 1.54227 − 1.35480I
b = 0.751292 − 0.659970I
8.82105 12.00884 + 0.I
u = 0.508444 + 0.678069I
a = −1.215690 + 0.720457I
b = −0.707850 + 0.944001I
1.30433 − 1.63935I 4.91398 − 3.40744I
u = 0.508444 − 0.678069I
a = −1.215690 − 0.720457I
b = −0.707850 − 0.944001I
1.30433 + 1.63935I 4.91398 + 3.40744I
u = 0.707850 + 0.944001I
a = −0.252097 + 0.983240I
b = −0.508444 + 0.678069I
1.30433 + 1.63935I 4.91398 + 3.40744I
u = 0.707850 − 0.944001I
a = −0.252097 − 0.983240I
b = −0.508444 − 0.678069I
1.30433 − 1.63935I 4.91398 − 3.40744I
u = −0.383361 + 0.619349I
a = −0.549407 + 0.130797I
b = 0.722560 + 1.167350I
5.94221 + 4.33255I 14.4782 − 1.9451I
u = −0.383361 − 0.619349I
a = −0.549407 − 0.130797I
b = 0.722560 − 1.167350I
5.94221 − 4.33255I 14.4782 + 1.9451I
29
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.722560 + 1.167350I
a = 0.192116 − 0.229946I
b = 0.383361 + 0.619349I
5.94221 − 4.33255I 14.4782 + 1.9451I
u = −0.722560 − 1.167350I
a = 0.192116 + 0.229946I
b = 0.383361 − 0.619349I
5.94221 + 4.33255I 14.4782 − 1.9451I
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
12
− 5u
11
+ ··· − 5u + 1)(u
12
− 5u
11
+ ··· − 5u + 1)
· (u
26
+ 11u
25
+ ··· − 8u + 1)(u
92
+ 32u
91
+ ··· − 225u + 4)
c
2
, c
7
(u
12
− u
11
+ ··· − u + 1)(u
12
− u
11
+ ··· − u + 1)(u
26
− u
25
+ ··· + 2u − 1)
· (u
92
+ 2u
91
+ ··· + 41u + 2)
c
3
, c
4
((u
6
− u
5
− 3u
4
+ 3u
3
+ u
2
− u + 1)
2
)(u
12
+ 2u
11
+ ··· + 2u + 1)
· (u
26
+ 11u
25
+ ··· − 8u − 32)(u
46
− 5u
45
+ ··· − u + 1)
2
c
5
(u
6
− u
5
+ u
4
+ u
3
− u
2
+ u − 1)
2
· (u
12
− u
11
− 2u
9
+ 4u
6
− 2u
5
− u
4
+ 3u
2
+ 2u + 1)
· (u
26
− 24u
25
+ ··· − 29184u + 2048)(u
46
+ 11u
45
+ ··· − 11u − 1)
2
c
6
, c
11
(u
12
+ u
11
+ ··· + u + 1)(u
12
+ u
11
+ ··· + u + 1)(u
26
− u
25
+ ··· + 2u − 1)
· (u
92
+ 2u
91
+ ··· + 41u + 2)
c
8
, c
12
(u
12
− u
10
− u
9
− 3u
8
+ u
7
+ 3u
6
+ 2u
5
+ u
4
− 2u
3
− u
2
+ 1)
· (u
12
− u
10
+ 2u
9
+ 3u
8
− 5u
7
+ 7u
6
− u
5
− 2u
4
+ 4u
3
− u
2
+ 1)
· (u
26
− 6u
24
+ ··· + u − 2)(u
92
− 5u
91
+ ··· − 169896u + 138881)
c
9
((u
6
+ u
5
− 3u
4
− 3u
3
+ u
2
+ u + 1)
2
)(u
12
− 2u
11
+ ··· − 2u + 1)
· (u
26
+ 11u
25
+ ··· − 8u − 32)(u
46
− 5u
45
+ ··· − u + 1)
2
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
12
+ 9y
11
+ ··· + 9y + 1)(y
12
+ 9y
11
+ ··· + 5y + 1)
· (y
26
+ 15y
25
+ ··· − 156y + 1)(y
92
+ 60y
91
+ ··· + 881743y + 16)
c
2
, c
6
, c
7
c
11
(y
12
+ 5y
11
+ ··· + 5y + 1)(y
12
+ 5y
11
+ ··· + 5y + 1)
· (y
26
+ 11y
25
+ ··· − 8y + 1)(y
92
+ 32y
91
+ ··· − 225y + 4)
c
3
, c
4
, c
9
((y
6
− 7y
5
+ ··· + y + 1)
2
)(y
12
− 14y
11
+ ··· + 2y + 1)
· (y
26
− 25y
25
+ ··· − 1344y + 1024)(y
46
− 51y
45
+ ··· − 43y + 1)
2
c
5
((y
6
+ y
5
+ y
4
− 3y
3
− 3y
2
+ y + 1)
2
)(y
12
− y
11
+ ··· + 2y + 1)
· (y
26
+ 58y
24
+ ··· − 138674176y + 4194304)
· (y
46
+ 11y
45
+ ··· + y + 1)
2
c
8
, c
12
(y
12
− 2y
11
+ ··· − 2y + 1)(y
12
− 2y
11
+ ··· − 2y + 1)
· (y
26
− 12y
25
+ ··· + 63y + 4)
· (y
92
− 31y
91
+ ··· − 535870573466y + 19287932161)
32
