12a
0628
(K12a
0628
)
A knot diagram
1
Linearized knot diagam
3 7 10 9 8 2 6 11 12 1 5 4
Solving Sequence
9,12 5,10
4 1 3 2 11 8 6 7
c
9
c
4
c
12
c
3
c
1
c
11
c
8
c
5
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.07461 × 10
68
u
46
+ 1.87630 × 10
70
u
45
+ ··· + 3.58440 × 10
69
b + 2.42033 × 10
69
,
− 4.03525 × 10
69
u
46
+ 9.96490 × 10
70
u
45
+ ··· + 7.16879 × 10
69
a − 2.41381 × 10
70
,
u
47
− 25u
46
+ ··· + 9u − 2i
I
u
2
= h2u
34
a + 9u
34
+ ··· − 16a − 66, 74u
34
a + 11u
34
+ ··· − 1408a − 380, u
35
+ 17u
34
+ ··· − 36u − 8i
I
u
3
= h−u
13
− 11u
12
+ ··· + b − 69, −50u
13
− 600u
12
+ ··· + 119a − 5520, u
14
+ 12u
13
+ ··· + 753u + 119i
I
v
1
= ha, 6v
5
− 52v
4
+ 157v
3
− 196v
2
+ b + 114v −20, v
6
− 9v
5
+ 29v
4
− 41v
3
+ 29v
2
− 9v + 1i
* 4 irreducible components of dim
C
= 0, with total 137 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−8.07 × 10
68
u
46
+ 1.88 × 10
70
u
45
+ · · · + 3.58 × 10
69
b + 2.42 ×
10
69
, −4.04 × 10
69
u
46
+ 9.96 × 10
70
u
45
+ · · · + 7.17 × 10
69
a − 2.41 ×
10
70
, u
47
− 25u
46
+ · · · + 9u − 2i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
5
=
0.562891u
46
− 13.9004u
45
+ ··· − 5.16569u + 3.36710
0.225271u
46
− 5.23462u
45
+ ··· − 1.00376u − 0.675240
a
10
=
1
−u
2
a
4
=
0.337620u
46
− 8.66577u
45
+ ··· − 4.16193u + 4.04234
0.225271u
46
− 5.23462u
45
+ ··· − 1.00376u − 0.675240
a
1
=
0.169203u
46
− 4.28920u
45
+ ··· − 7.93593u + 2.72071
0.0591214u
46
− 1.09993u
45
+ ··· − 0.197882u − 0.338406
a
3
=
0.165732u
46
− 4.51075u
45
+ ··· − 2.46301u + 2.91656
0.435105u
46
− 10.3002u
45
+ ··· − 1.93948u − 0.390908
a
2
=
0.0648503u
46
− 1.39194u
45
+ ··· − 14.5959u + 2.04861
−0.131505u
46
+ 3.30763u
45
+ ··· − 0.786389u + 0.0263510
a
11
=
−0.0906579u
46
+ 2.39136u
45
+ ··· − 9.46119u + 1.92565
−0.318982u
46
+ 7.78049u
45
+ ··· + 0.672616u − 0.456649
a
8
=
0.242494u
46
− 6.10090u
45
+ ··· + 14.2499u − 0.538109
0.220995u
46
− 5.44044u
45
+ ··· + 0.632902u + 0.206826
a
6
=
0.593189u
46
− 14.8971u
45
+ ··· + 5.69357u + 1.97676
0.561061u
46
− 13.2944u
45
+ ··· − 0.319039u − 0.574337
a
7
=
0.784381u
46
− 19.6156u
45
+ ··· + 14.2320u + 1.32228
0.322833u
46
− 7.50881u
45
+ ··· + 2.82860u − 0.790986
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.442403u
46
− 9.99419u
45
+ ··· − 2.55500u − 6.13236
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
47
+ 11u
46
+ ··· + 129u + 16
c
2
, c
6
u
47
− 5u
46
+ ··· + 5u + 4
c
3
, c
11
u
47
+ 9u
45
+ ··· − 6u + 1
c
4
, c
12
u
47
+ 3u
46
+ ··· + 3u + 1
c
8
, c
10
u
47
+ 8u
46
+ ··· + 14u − 1
c
9
u
47
+ 25u
46
+ ··· + 9u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
47
+ 53y
46
+ ··· − 12319y −256
c
2
, c
6
y
47
− 11y
46
+ ··· + 129y −16
c
3
, c
11
y
47
+ 18y
46
+ ··· + 24y −1
c
4
, c
12
y
47
+ 29y
46
+ ··· − 53y −1
c
8
, c
10
y
47
− 6y
46
+ ··· + 316y −1
c
9
y
47
− 3y
46
+ ··· + 109y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.986892 + 0.257612I
a = −0.240592 + 0.022595I
b = −0.105712 + 0.949661I
−1.56579 + 2.13171I 0
u = 0.986892 − 0.257612I
a = −0.240592 − 0.022595I
b = −0.105712 − 0.949661I
−1.56579 − 2.13171I 0
u = −0.830353 + 0.249534I
a = 0.156117 − 0.996332I
b = −0.000476 − 0.473342I
1.96281 − 2.11633I 0. + 4.02661I
u = −0.830353 − 0.249534I
a = 0.156117 + 0.996332I
b = −0.000476 + 0.473342I
1.96281 + 2.11633I 0. − 4.02661I
u = 1.045570 + 0.455359I
a = 0.231147 − 0.651269I
b = −1.13460 − 1.29557I
−1.01169 + 1.42980I 0
u = 1.045570 − 0.455359I
a = 0.231147 + 0.651269I
b = −1.13460 + 1.29557I
−1.01169 − 1.42980I 0
u = 0.779229 + 0.975300I
a = −0.537680 + 0.259174I
b = −0.166184 + 0.726379I
−4.20569 − 1.69908I 0
u = 0.779229 − 0.975300I
a = −0.537680 − 0.259174I
b = −0.166184 − 0.726379I
−4.20569 + 1.69908I 0
u = 0.183042 + 0.680484I
a = 0.931695 − 0.444316I
b = −0.009062 − 0.684052I
−0.97551 − 1.07913I −5.53069 + 4.56519I
u = 0.183042 − 0.680484I
a = 0.931695 + 0.444316I
b = −0.009062 + 0.684052I
−0.97551 + 1.07913I −5.53069 − 4.56519I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.202810 + 0.603274I
a = −0.086506 + 0.756693I
b = 0.99713 + 1.26439I
1.79955 + 5.97631I 0
u = 1.202810 − 0.603274I
a = −0.086506 − 0.756693I
b = 0.99713 − 1.26439I
1.79955 − 5.97631I 0
u = 1.104270 + 0.787113I
a = 0.119630 − 0.908657I
b = −0.99509 − 1.20831I
−3.04962 + 8.17588I 0
u = 1.104270 − 0.787113I
a = 0.119630 + 0.908657I
b = −0.99509 + 1.20831I
−3.04962 − 8.17588I 0
u = 0.304094 + 1.336820I
a = 0.542187 − 0.423730I
b = 0.126684 − 0.613012I
−0.33080 − 2.07585I 0
u = 0.304094 − 1.336820I
a = 0.542187 + 0.423730I
b = 0.126684 + 0.613012I
−0.33080 + 2.07585I 0
u = 0.137187 + 0.560954I
a = 1.24351 − 1.45572I
b = −0.540535 − 0.928428I
4.33642 − 2.76626I −6.11765 + 1.36219I
u = 0.137187 − 0.560954I
a = 1.24351 + 1.45572I
b = −0.540535 + 0.928428I
4.33642 + 2.76626I −6.11765 − 1.36219I
u = 1.41903 + 0.21089I
a = 0.072584 + 0.499229I
b = 0.68921 + 1.38028I
9.20338 + 2.61174I 0
u = 1.41903 − 0.21089I
a = 0.072584 − 0.499229I
b = 0.68921 − 1.38028I
9.20338 − 2.61174I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.084908 + 0.552003I
a = −1.33147 + 1.55641I
b = 0.487600 + 0.952889I
4.42276 + 3.42689I −5.94446 − 4.00737I
u = 0.084908 − 0.552003I
a = −1.33147 − 1.55641I
b = 0.487600 − 0.952889I
4.42276 − 3.42689I −5.94446 + 4.00737I
u = 1.43830 + 0.13063I
a = −0.098758 − 0.457306I
b = −0.59129 − 1.35386I
8.76706 − 4.19529I 0
u = 1.43830 − 0.13063I
a = −0.098758 + 0.457306I
b = −0.59129 + 1.35386I
8.76706 + 4.19529I 0
u = 1.26461 + 0.85093I
a = 0.000444 + 0.909791I
b = 0.97549 + 1.21247I
2.31156 + 9.58565I 0
u = 1.26461 − 0.85093I
a = 0.000444 − 0.909791I
b = 0.97549 − 1.21247I
2.31156 − 9.58565I 0
u = 1.22930 + 0.93502I
a = −0.000607 − 0.968672I
b = −0.97798 − 1.20771I
0.2553 + 14.2440I 0
u = 1.22930 − 0.93502I
a = −0.000607 + 0.968672I
b = −0.97798 + 1.20771I
0.2553 − 14.2440I 0
u = −1.55593 + 0.05191I
a = 0.012590 − 0.744758I
b = 0.001750 − 0.453593I
10.52640 − 3.28012I 0
u = −1.55593 − 0.05191I
a = 0.012590 + 0.744758I
b = 0.001750 + 0.453593I
10.52640 + 3.28012I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.383960 + 0.015221I
a = −0.09489 + 4.37068I
b = 0.008396 + 1.213720I
5.31991 − 3.17818I −5.96055 + 2.51448I
u = −0.383960 − 0.015221I
a = −0.09489 − 4.37068I
b = 0.008396 − 1.213720I
5.31991 + 3.17818I −5.96055 − 2.51448I
u = 0.61115 + 1.50375I
a = −0.493409 + 0.370823I
b = −0.182737 + 0.618606I
−1.63385 − 6.10019I 0
u = 0.61115 − 1.50375I
a = −0.493409 − 0.370823I
b = −0.182737 − 0.618606I
−1.63385 + 6.10019I 0
u = 0.014272 + 0.328823I
a = −2.70355 + 1.41748I
b = 0.196161 + 0.946775I
−1.97861 + 1.49292I −10.70609 − 5.87130I
u = 0.014272 − 0.328823I
a = −2.70355 − 1.41748I
b = 0.196161 − 0.946775I
−1.97861 − 1.49292I −10.70609 + 5.87130I
u = 1.34828 + 1.00110I
a = 0.083860 + 0.974442I
b = 0.97814 + 1.20179I
9.8115 + 11.7454I 0
u = 1.34828 − 1.00110I
a = 0.083860 − 0.974442I
b = 0.97814 − 1.20179I
9.8115 − 11.7454I 0
u = 1.33518 + 1.02090I
a = −0.081979 − 0.988201I
b = −0.97956 − 1.20259I
9.3683 + 18.3359I 0
u = 1.33518 − 1.02090I
a = −0.081979 + 0.988201I
b = −0.97956 + 1.20259I
9.3683 − 18.3359I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.256430
a = 1.88104
b = −0.648700
−1.19524 −8.00760
u = −0.199176 + 0.097478I
a = −1.91491 + 5.71249I
b = 0.056148 + 1.109040I
−1.82406 − 1.46144I −9.84747 + 4.59178I
u = −0.199176 − 0.097478I
a = −1.91491 − 5.71249I
b = 0.056148 − 1.109040I
−1.82406 + 1.46144I −9.84747 − 4.59178I
u = 0.38526 + 1.94699I
a = 0.437854 − 0.407305I
b = 0.183052 − 0.551742I
7.14509 − 2.45592I 0
u = 0.38526 − 1.94699I
a = 0.437854 + 0.407305I
b = 0.183052 + 0.551742I
7.14509 + 2.45592I 0
u = 0.46782 + 1.95962I
a = −0.437774 + 0.397887I
b = −0.192176 + 0.554586I
6.91812 − 8.96525I 0
u = 0.46782 − 1.95962I
a = −0.437774 − 0.397887I
b = −0.192176 − 0.554586I
6.91812 + 8.96525I 0
9
II. I
u
2
= h2u
34
a + 9u
34
+ · · · − 16a − 66, 74u
34
a + 11u
34
+ · · · − 1408a −
380, u
35
+ 17u
34
+ · · · − 36u − 8i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
5
=
a
−u
34
a −
9
2
u
34
+ ··· + 8a + 33
a
10
=
1
−u
2
a
4
=
u
34
a +
9
2
u
34
+ ··· − 7a − 33
−u
34
a −
9
2
u
34
+ ··· + 8a + 33
a
1
=
9
2
u
34
a −
7
8
u
34
+ ··· − 33a +
5
2
−1
a
3
=
u
34
a + 16u
33
a + ··· − 7a + 4
−u
34
a −
7
2
u
34
+ ··· + 8a + 21
a
2
=
5
2
u
34
a +
1
8
u
34
+ ··· − 12a −
11
2
1
2
u
34
a −
3
4
u
34
+ ··· − 12a − 2
a
11
=
9
2
u
34
a +
1
8
u
34
+ ··· − 37a −
11
2
−2u
33
a + u
34
+ ··· − 4a − 7
a
8
=
3
2
u
34
a −
7
8
u
34
+ ··· − 53a +
5
2
u
34
a + u
34
+ ··· − 16a − 9
a
6
=
−
3
4
u
34
a −
33
8
u
34
+ ··· +
349
2
u + 68
−
9
2
u
34
−
151
2
u
33
+ ··· + 116u + 54
a
7
=
−
5
4
u
34
a − u
34
+ ··· + 12a + 32
1
2
u
34
a +
1
2
u
34
+ ··· + 4a + 7
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
13
4
u
34
−
227
4
u
33
+ ··· −
895
2
u − 65
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
(u
35
+ 8u
34
+ ··· + 6u + 1)
2
c
2
, c
6
(u
35
+ 2u
34
+ ··· − 2u + 1)
2
c
3
, c
11
u
70
+ 2u
69
+ ··· − 10925u + 8375
c
4
, c
12
u
70
+ 4u
69
+ ··· + 9u + 1
c
8
, c
10
u
70
− 7u
69
+ ··· − 1398u + 103
c
9
(u
35
− 17u
34
+ ··· − 36u + 8)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y
35
+ 40y
34
+ ··· − 6y −1)
2
c
2
, c
6
(y
35
− 8y
34
+ ··· + 6y −1)
2
c
3
, c
11
y
70
+ 20y
69
+ ··· + 3013313125y + 70140625
c
4
, c
12
y
70
− 8y
69
+ ··· + 13y + 1
c
8
, c
10
y
70
+ 33y
69
+ ··· + 275134y + 10609
c
9
(y
35
− 7y
34
+ ··· + 1424y −64)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.964127 + 0.262445I
a = 0.117573 − 1.015810I
b = 0.350664 − 1.060490I
1.94444 − 2.29540I 0.91018 + 4.37550I
u = −0.964127 + 0.262445I
a = 0.404381 − 0.827637I
b = −0.213001 + 0.104258I
1.94444 − 2.29540I 0.91018 + 4.37550I
u = −0.964127 − 0.262445I
a = 0.117573 + 1.015810I
b = 0.350664 + 1.060490I
1.94444 + 2.29540I 0.91018 − 4.37550I
u = −0.964127 − 0.262445I
a = 0.404381 + 0.827637I
b = −0.213001 − 0.104258I
1.94444 + 2.29540I 0.91018 − 4.37550I
u = −0.545063 + 0.930286I
a = −0.422586 + 0.935328I
b = −1.05299 + 1.06043I
−1.74570 − 6.26407I −12.1310 + 10.5895I
u = −0.545063 + 0.930286I
a = −1.11507 − 1.00008I
b = 0.227226 − 0.654642I
−1.74570 − 6.26407I −12.1310 + 10.5895I
u = −0.545063 − 0.930286I
a = −0.422586 − 0.935328I
b = −1.05299 − 1.06043I
−1.74570 + 6.26407I −12.1310 − 10.5895I
u = −0.545063 − 0.930286I
a = −1.11507 + 1.00008I
b = 0.227226 + 0.654642I
−1.74570 + 6.26407I −12.1310 − 10.5895I
u = −0.769928 + 0.815144I
a = 0.290344 − 0.925570I
b = 0.852648 − 1.015970I
0.08222 − 3.07227I −4.95653 + 3.77311I
u = −0.769928 + 0.815144I
a = 0.821612 + 0.458607I
b = −0.359248 + 0.527956I
0.08222 − 3.07227I −4.95653 + 3.77311I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.769928 − 0.815144I
a = 0.290344 + 0.925570I
b = 0.852648 + 1.015970I
0.08222 + 3.07227I −4.95653 − 3.77311I
u = −0.769928 − 0.815144I
a = 0.821612 − 0.458607I
b = −0.359248 − 0.527956I
0.08222 + 3.07227I −4.95653 − 3.77311I
u = −0.520349 + 0.616898I
a = −0.348333 + 1.069510I
b = −0.90908 + 1.30588I
−3.03157 − 1.36849I −14.2578 + 4.5888I
u = −0.520349 + 0.616898I
a = −1.81715 − 0.28667I
b = 0.145968 − 0.468917I
−3.03157 − 1.36849I −14.2578 + 4.5888I
u = −0.520349 − 0.616898I
a = −0.348333 − 1.069510I
b = −0.90908 − 1.30588I
−3.03157 + 1.36849I −14.2578 − 4.5888I
u = −0.520349 − 0.616898I
a = −1.81715 + 0.28667I
b = 0.145968 + 0.468917I
−3.03157 + 1.36849I −14.2578 − 4.5888I
u = 0.773064 + 0.207728I
a = 0.029702 − 1.290000I
b = 1.35908 − 0.77271I
11.23360 + 3.62608I 1.44054 − 2.93370I
u = 0.773064 + 0.207728I
a = −0.46892 + 2.04886I
b = 0.920239 + 0.676047I
11.23360 + 3.62608I 1.44054 − 2.93370I
u = 0.773064 − 0.207728I
a = 0.029702 + 1.290000I
b = 1.35908 + 0.77271I
11.23360 − 3.62608I 1.44054 + 2.93370I
u = 0.773064 − 0.207728I
a = −0.46892 − 2.04886I
b = 0.920239 − 0.676047I
11.23360 − 3.62608I 1.44054 + 2.93370I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.763132 + 0.228871I
a = −0.059405 + 1.268730I
b = −1.37969 + 0.78187I
10.7852 + 10.1738I 0.60965 − 7.87359I
u = 0.763132 + 0.228871I
a = 0.48070 − 2.11119I
b = −0.896123 − 0.673718I
10.7852 + 10.1738I 0.60965 − 7.87359I
u = 0.763132 − 0.228871I
a = −0.059405 − 1.268730I
b = −1.37969 − 0.78187I
10.7852 − 10.1738I 0.60965 + 7.87359I
u = 0.763132 − 0.228871I
a = 0.48070 + 2.11119I
b = −0.896123 + 0.673718I
10.7852 − 10.1738I 0.60965 + 7.87359I
u = −0.557804 + 1.163430I
a = −0.504376 + 0.846367I
b = −1.15064 + 0.93090I
5.85934 − 9.40637I 0
u = −0.557804 + 1.163430I
a = −0.77400 − 1.29127I
b = 0.262140 − 0.799037I
5.85934 − 9.40637I 0
u = −0.557804 − 1.163430I
a = −0.504376 − 0.846367I
b = −1.15064 − 0.93090I
5.85934 + 9.40637I 0
u = −0.557804 − 1.163430I
a = −0.77400 + 1.29127I
b = 0.262140 + 0.799037I
5.85934 + 9.40637I 0
u = 0.696782 + 0.078059I
a = −0.286945 − 1.206990I
b = 1.29659 − 0.59850I
4.06992 + 1.58553I 3.88029 − 1.71972I
u = 0.696782 + 0.078059I
a = −0.68685 + 1.60178I
b = 1.055880 + 0.547593I
4.06992 + 1.58553I 3.88029 − 1.71972I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.696782 − 0.078059I
a = −0.286945 + 1.206990I
b = 1.29659 + 0.59850I
4.06992 − 1.58553I 3.88029 + 1.71972I
u = 0.696782 − 0.078059I
a = −0.68685 − 1.60178I
b = 1.055880 − 0.547593I
4.06992 − 1.58553I 3.88029 + 1.71972I
u = −0.597263 + 1.172270I
a = 0.495613 − 0.826184I
b = 1.13743 − 0.90879I
6.09123 − 3.06029I 0
u = −0.597263 + 1.172270I
a = 0.72146 + 1.25846I
b = −0.286492 + 0.801724I
6.09123 − 3.06029I 0
u = −0.597263 − 1.172270I
a = 0.495613 + 0.826184I
b = 1.13743 + 0.90879I
6.09123 + 3.06029I 0
u = −0.597263 − 1.172270I
a = 0.72146 − 1.25846I
b = −0.286492 − 0.801724I
6.09123 + 3.06029I 0
u = 0.657111 + 0.150265I
a = 0.104447 + 1.068260I
b = −1.42166 + 0.62739I
1.93432 + 6.05072I −0.26965 − 8.65398I
u = 0.657111 + 0.150265I
a = 0.91193 − 1.89650I
b = −0.936571 − 0.519018I
1.93432 + 6.05072I −0.26965 − 8.65398I
u = 0.657111 − 0.150265I
a = 0.104447 − 1.068260I
b = −1.42166 − 0.62739I
1.93432 − 6.05072I −0.26965 + 8.65398I
u = 0.657111 − 0.150265I
a = 0.91193 + 1.89650I
b = −0.936571 + 0.519018I
1.93432 − 6.05072I −0.26965 + 8.65398I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.928482 + 1.034750I
a = 0.291145 + 0.812770I
b = −0.538881 + 0.711044I
0.13523 − 3.41860I 0
u = −0.928482 + 1.034750I
a = 0.236386 − 0.711345I
b = 0.875925 − 0.764420I
0.13523 − 3.41860I 0
u = −0.928482 − 1.034750I
a = 0.291145 − 0.812770I
b = −0.538881 − 0.711044I
0.13523 + 3.41860I 0
u = −0.928482 − 1.034750I
a = 0.236386 + 0.711345I
b = 0.875925 + 0.764420I
0.13523 + 3.41860I 0
u = −1.404630 + 0.025943I
a = 0.134206 − 0.793052I
b = 0.445608 − 0.484188I
10.47460 − 3.26575I 0
u = −1.404630 + 0.025943I
a = −0.121919 − 0.764495I
b = −0.445417 − 0.425761I
10.47460 − 3.26575I 0
u = −1.404630 − 0.025943I
a = 0.134206 + 0.793052I
b = 0.445608 + 0.484188I
10.47460 + 3.26575I 0
u = −1.404630 − 0.025943I
a = −0.121919 + 0.764495I
b = −0.445417 + 0.425761I
10.47460 + 3.26575I 0
u = 0.594216
a = 0.833572 + 0.866110I
b = −1.220660 + 0.322827I
−0.882038 −0.340160
u = 0.594216
a = 0.833572 − 0.866110I
b = −1.220660 − 0.322827I
−0.882038 −0.340160
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.514940 + 0.140607I
a = −0.122479 + 1.275520I
b = −0.31441 + 1.76661I
1.66264 + 2.69554I 5.85968 + 3.62149I
u = −0.514940 + 0.140607I
a = −1.41021 + 2.75765I
b = 0.029782 − 0.279871I
1.66264 + 2.69554I 5.85968 + 3.62149I
u = −0.514940 − 0.140607I
a = −0.122479 − 1.275520I
b = −0.31441 − 1.76661I
1.66264 − 2.69554I 5.85968 − 3.62149I
u = −0.514940 − 0.140607I
a = −1.41021 − 2.75765I
b = 0.029782 + 0.279871I
1.66264 − 2.69554I 5.85968 − 3.62149I
u = −1.17020 + 0.97515I
a = 0.075112 − 0.995428I
b = 0.658256 − 0.866374I
2.08927 − 2.26390I 0
u = −1.17020 + 0.97515I
a = −0.112153 + 0.257338I
b = −0.808245 + 0.417634I
2.08927 − 2.26390I 0
u = −1.17020 − 0.97515I
a = 0.075112 + 0.995428I
b = 0.658256 + 0.866374I
2.08927 + 2.26390I 0
u = −1.17020 − 0.97515I
a = −0.112153 − 0.257338I
b = −0.808245 − 0.417634I
2.08927 + 2.26390I 0
u = −1.12595 + 1.09745I
a = 0.024734 + 1.034540I
b = −0.615985 + 0.860331I
1.71476 − 5.96924I 0
u = −1.12595 + 1.09745I
a = 0.250124 − 0.388618I
b = 0.912598 − 0.507009I
1.71476 − 5.96924I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.12595 − 1.09745I
a = 0.024734 − 1.034540I
b = −0.615985 − 0.860331I
1.71476 + 5.96924I 0
u = −1.12595 − 1.09745I
a = 0.250124 + 0.388618I
b = 0.912598 + 0.507009I
1.71476 + 5.96924I 0
u = −1.30130 + 1.11600I
a = 0.076914 − 1.114750I
b = 0.645923 − 0.905225I
9.79528 − 1.36327I 0
u = −1.30130 + 1.11600I
a = −0.344518 + 0.206810I
b = −0.974282 + 0.362355I
9.79528 − 1.36327I 0
u = −1.30130 − 1.11600I
a = 0.076914 + 1.114750I
b = 0.645923 + 0.905225I
9.79528 + 1.36327I 0
u = −1.30130 − 1.11600I
a = −0.344518 − 0.206810I
b = −0.974282 − 0.362355I
9.79528 + 1.36327I 0
u = −1.28716 + 1.13850I
a = −0.063233 + 1.123160I
b = −0.639600 + 0.907852I
9.72328 − 7.82412I 0
u = −1.28716 + 1.13850I
a = 0.358190 − 0.229933I
b = 0.987003 − 0.379060I
9.72328 − 7.82412I 0
u = −1.28716 − 1.13850I
a = −0.063233 − 1.123160I
b = −0.639600 − 0.907852I
9.72328 + 7.82412I 0
u = −1.28716 − 1.13850I
a = 0.358190 + 0.229933I
b = 0.987003 + 0.379060I
9.72328 + 7.82412I 0
19
III. I
u
3
= h−u
13
− 11u
12
+ · · · + b − 69, −50u
13
− 600u
12
+ · · · + 119a −
5520, u
14
+ 12u
13
+ · · · + 753u + 119i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
5
=
0.420168u
13
+ 5.04202u
12
+ ··· + 261.403u + 46.3866
u
13
+ 11u
12
+ ··· + 414u + 69
a
10
=
1
−u
2
a
4
=
−0.579832u
13
− 5.95798u
12
+ ··· − 152.597u − 22.6134
u
13
+ 11u
12
+ ··· + 414u + 69
a
1
=
0.991597u
13
+ 10.8992u
12
+ ··· + 614.832u + 111.672
−u
13
− 11u
12
+ ··· − 634u − 118
a
3
=
−0.579832u
13
− 6.95798u
12
+ ··· − 422.597u − 72.6134
−u
13
− 11u
12
+ ··· − 339u − 50
a
2
=
0.00840336u
13
+ 0.100840u
12
+ ··· + 18.1681u + 3.32773
u
4
+ 2u
3
+ 2u
2
− 1
a
11
=
−0.00840336u
13
− 0.100840u
12
+ ··· − 20.1681u − 5.32773
u + 1
a
8
=
0.00840336u
13
+ 0.100840u
12
+ ··· + 19.1681u + 5.32773
−u
2
− 2u − 1
a
6
=
0.260504u
13
+ 3.12605u
12
+ ··· + 213.210u + 39.1597
u
13
+ 12u
12
+ ··· + 546u + 88
a
7
=
−0.941176u
13
− 10.2941u
12
+ ··· − 506.824u − 85.7059
u
13
+ 11u
12
+ ··· + 620u + 112
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
12
− 21u
11
− 117u
10
− 440u
9
− 1225u
8
− 2638u
7
− 4481u
6
−
6034u
5
− 6384u
4
− 5178u
3
− 3060u
2
− 1183u − 227
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
14
− 4u
13
+ ··· − 5u + 1
c
2
u
14
− 2u
13
+ ··· − u + 1
c
3
, c
11
u
14
− u
12
− u
11
+ 4u
10
+ u
9
− 3u
7
+ 3u
6
+ 3u
4
− u
3
+ u
2
− u + 1
c
4
, c
12
u
14
− u
13
+ u
12
− u
11
+ 3u
10
+ 3u
8
− 3u
7
+ u
5
+ 4u
4
− u
3
− u
2
+ 1
c
6
u
14
+ 2u
13
+ ··· + u + 1
c
7
u
14
+ 4u
13
+ ··· + 5u + 1
c
8
, c
10
u
14
− 2u
13
+ ··· + u + 1
c
9
u
14
+ 12u
13
+ ··· + 753u + 119
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
14
+ 16y
13
+ ··· + 19y + 1
c
2
, c
6
y
14
− 4y
13
+ ··· − 5y + 1
c
3
, c
11
y
14
− 2y
13
+ ··· + y + 1
c
4
, c
12
y
14
+ y
13
+ ··· − 2y + 1
c
8
, c
10
y
14
+ 14y
13
+ ··· + 9y + 1
c
9
y
14
+ 4y
13
+ ··· + 4191y + 14161
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.898365 + 0.466164I
a = 0.274587 + 0.624794I
b = −1.12748 + 0.90814I
−0.807946 − 1.069820I −0.115639 − 0.754165I
u = −0.898365 − 0.466164I
a = 0.274587 − 0.624794I
b = −1.12748 − 0.90814I
−0.807946 + 1.069820I −0.115639 + 0.754165I
u = −0.522055 + 1.037080I
a = −0.094737 + 0.915476I
b = −0.788118 + 0.504575I
−0.10349 − 6.22523I −5.98500 + 10.70028I
u = −0.522055 − 1.037080I
a = −0.094737 − 0.915476I
b = −0.788118 − 0.504575I
−0.10349 + 6.22523I −5.98500 − 10.70028I
u = −1.17778 + 0.86403I
a = −0.032784 − 0.642146I
b = 0.672741 − 0.825252I
1.12503 − 4.25284I −2.67238 + 7.72503I
u = −1.17778 − 0.86403I
a = −0.032784 + 0.642146I
b = 0.672741 + 0.825252I
1.12503 + 4.25284I −2.67238 − 7.72503I
u = −0.89755 + 1.20623I
a = 0.075475 − 0.727886I
b = 0.669316 − 0.614876I
1.06641 − 2.99350I −1.88418 + 3.44945I
u = −0.89755 − 1.20623I
a = 0.075475 + 0.727886I
b = 0.669316 + 0.614876I
1.06641 + 2.99350I −1.88418 − 3.44945I
u = −0.39747 + 1.53501I
a = −0.273895 + 0.762140I
b = −0.643425 + 0.438659I
7.82970 − 9.13196I −0.21746 + 9.07167I
u = −0.39747 − 1.53501I
a = −0.273895 − 0.762140I
b = −0.643425 − 0.438659I
7.82970 + 9.13196I −0.21746 − 9.07167I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62637 + 0.08568I
a = −0.007488 − 0.488153I
b = 0.085422 − 1.254780I
9.17104 − 3.40642I 0.11216 + 4.03009I
u = −1.62637 − 0.08568I
a = −0.007488 + 0.488153I
b = 0.085422 + 1.254780I
9.17104 + 3.40642I 0.11216 − 4.03009I
u = −0.48042 + 1.56468I
a = 0.252119 − 0.742861I
b = 0.631541 − 0.455736I
8.03821 − 2.69363I 0.26249 + 4.46966I
u = −0.48042 − 1.56468I
a = 0.252119 + 0.742861I
b = 0.631541 + 0.455736I
8.03821 + 2.69363I 0.26249 − 4.46966I
24
IV. I
v
1
= ha, 6v
5
− 52v
4
+ · · · + b − 20, v
6
− 9v
5
+ 29v
4
− 41v
3
+ 29v
2
− 9v + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
v
0
a
5
=
0
−6v
5
+ 52v
4
− 157v
3
+ 196v
2
− 114v + 20
a
10
=
1
0
a
4
=
6v
5
− 52v
4
+ 157v
3
− 196v
2
+ 114v −20
−6v
5
+ 52v
4
− 157v
3
+ 196v
2
− 114v + 20
a
1
=
v −1
1
a
3
=
0
−6v
5
+ 52v
4
− 157v
3
+ 196v
2
− 114v + 20
a
2
=
v −1
−v
5
+ 9v
4
− 29v
3
+ 41v
2
− 29v + 9
a
11
=
v
1
a
8
=
−v + 1
−1
a
6
=
3v
5
− 26v
4
+ 79v
3
− 100v
2
+ 58v −10
−10v
5
+ 87v
4
− 264v
3
+ 332v
2
− 194v + 34
a
7
=
v
5
− 9v
4
+ 29v
3
− 40v
2
+ 25v −5
−2v
5
+ 18v
4
− 58v
3
+ 82v
2
− 57v + 14
(ii) Obstruction class = 1
(iii) Cusp Shapes = 21v
5
− 184v
4
+ 564v
3
− 721v
2
+ 428v −94
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
, c
4
, c
11
c
12
u
6
− u
5
+ 5u
4
− 3u
3
+ 5u
2
− u + 1
c
6
(u
3
− u
2
+ 1)
2
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
8
, c
10
(u − 1)
6
c
9
u
6
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
6
(y
3
− y
2
+ 2y −1)
2
c
3
, c
4
, c
11
c
12
y
6
+ 9y
5
+ 29y
4
+ 41y
3
+ 29y
2
+ 9y + 1
c
8
, c
10
(y −1)
6
c
9
y
6
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.837641 + 0.546221I
a = 0
b = −0.284920 − 0.958551I
−2.75839 −13.82608 + 0.I
v = 0.837641 − 0.546221I
a = 0
b = −0.284920 + 0.958551I
−2.75839 −13.82608 + 0.I
v = 0.286741 + 0.052196I
a = 0
b = −0.16654 − 1.84482I
1.37919 − 2.82812I −17.5870 + 7.0980I
v = 0.286741 − 0.052196I
a = 0
b = −0.16654 + 1.84482I
1.37919 + 2.82812I −17.5870 − 7.0980I
v = 3.37562 + 0.61448I
a = 0
b = −0.048539 − 0.537677I
1.37919 + 2.82812I −17.5870 − 7.0980I
v = 3.37562 − 0.61448I
a = 0
b = −0.048539 + 0.537677I
1.37919 − 2.82812I −17.5870 + 7.0980I
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
3
− u
2
+ 2u − 1)
2
)(u
14
− 4u
13
+ ··· − 5u + 1)
· ((u
35
+ 8u
34
+ ··· + 6u + 1)
2
)(u
47
+ 11u
46
+ ··· + 129u + 16)
c
2
((u
3
+ u
2
− 1)
2
)(u
14
− 2u
13
+ ··· − u + 1)(u
35
+ 2u
34
+ ··· − 2u + 1)
2
· (u
47
− 5u
46
+ ··· + 5u + 4)
c
3
, c
11
(u
6
− u
5
+ 5u
4
− 3u
3
+ 5u
2
− u + 1)
· (u
14
− u
12
− u
11
+ 4u
10
+ u
9
− 3u
7
+ 3u
6
+ 3u
4
− u
3
+ u
2
− u + 1)
· (u
47
+ 9u
45
+ ··· − 6u + 1)(u
70
+ 2u
69
+ ··· − 10925u + 8375)
c
4
, c
12
(u
6
− u
5
+ 5u
4
− 3u
3
+ 5u
2
− u + 1)
· (u
14
− u
13
+ u
12
− u
11
+ 3u
10
+ 3u
8
− 3u
7
+ u
5
+ 4u
4
− u
3
− u
2
+ 1)
· (u
47
+ 3u
46
+ ··· + 3u + 1)(u
70
+ 4u
69
+ ··· + 9u + 1)
c
6
((u
3
− u
2
+ 1)
2
)(u
14
+ 2u
13
+ ··· + u + 1)(u
35
+ 2u
34
+ ··· − 2u + 1)
2
· (u
47
− 5u
46
+ ··· + 5u + 4)
c
7
((u
3
+ u
2
+ 2u + 1)
2
)(u
14
+ 4u
13
+ ··· + 5u + 1)
· ((u
35
+ 8u
34
+ ··· + 6u + 1)
2
)(u
47
+ 11u
46
+ ··· + 129u + 16)
c
8
, c
10
((u − 1)
6
)(u
14
− 2u
13
+ ··· + u + 1)(u
47
+ 8u
46
+ ··· + 14u − 1)
· (u
70
− 7u
69
+ ··· − 1398u + 103)
c
9
u
6
(u
14
+ 12u
13
+ ··· + 753u + 119)(u
35
− 17u
34
+ ··· − 36u + 8)
2
· (u
47
+ 25u
46
+ ··· + 9u + 2)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
((y
3
+ 3y
2
+ 2y −1)
2
)(y
14
+ 16y
13
+ ··· + 19y + 1)
· ((y
35
+ 40y
34
+ ··· − 6y −1)
2
)(y
47
+ 53y
46
+ ··· − 12319y −256)
c
2
, c
6
((y
3
− y
2
+ 2y −1)
2
)(y
14
− 4y
13
+ ··· − 5y + 1)
· ((y
35
− 8y
34
+ ··· + 6y −1)
2
)(y
47
− 11y
46
+ ··· + 129y −16)
c
3
, c
11
(y
6
+ 9y
5
+ ··· + 9y + 1)(y
14
− 2y
13
+ ··· + y + 1)
· (y
47
+ 18y
46
+ ··· + 24y −1)
· (y
70
+ 20y
69
+ ··· + 3013313125y + 70140625)
c
4
, c
12
(y
6
+ 9y
5
+ ··· + 9y + 1)(y
14
+ y
13
+ ··· − 2y + 1)
· (y
47
+ 29y
46
+ ··· − 53y −1)(y
70
− 8y
69
+ ··· + 13y + 1)
c
8
, c
10
((y −1)
6
)(y
14
+ 14y
13
+ ··· + 9y + 1)(y
47
− 6y
46
+ ··· + 316y −1)
· (y
70
+ 33y
69
+ ··· + 275134y + 10609)
c
9
y
6
(y
14
+ 4y
13
+ ··· + 4191y + 14161)
· ((y
35
− 7y
34
+ ··· + 1424y −64)
2
)(y
47
− 3y
46
+ ··· + 109y −4)
30
