12a
0288
(K12a
0288
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 12 2 10 11 7 4 1 5
Solving Sequence
3,6
2
7,10
8 4 11 1 12 5 9
c
2
c
6
c
7
c
3
c
10
c
1
c
11
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.31109 × 10
21
u
55
− 7.82504 × 10
21
u
54
+ ··· + 5.87982 × 10
21
b − 7.54174 × 10
21
,
3.46636 × 10
21
u
55
+ 5.58656 × 10
21
u
54
+ ··· + 3.91988 × 10
21
a + 2.03288 × 10
22
, u
56
+ u
55
+ ··· + 5u + 1i
I
u
2
= h−4.48511 × 10
91
u
83
+ 8.27522 × 10
90
u
82
+ ··· + 5.10117 × 10
93
b − 6.71976 × 10
93
,
2.37745 × 10
94
u
83
+ 9.35836 × 10
93
u
82
+ ··· + 8.67198 × 10
94
a + 1.23067 × 10
95
, u
84
+ u
83
+ ··· + 88u + 17i
I
u
3
= h12a
5
u + 50a
4
u + 60a
4
− 58a
3
u + 200a
3
− 345a
2
u + 66a
2
− 132au + 13b − 290a + 125u − 56,
a
6
− 6a
5
u + 5a
5
− 25a
4
u − 6a
4
− 16a
3
u − 48a
3
+ 44a
2
u − 41a
2
+ 34au + 20a − 4u + 11, u
2
+ 1i
I
u
4
= h2b − 3, 4a − 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 153 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−6.31×10
21
u
55
−7.83×10
21
u
54
+· · ·+5.88×10
21
b−7.54×10
21
, 3.47×
10
21
u
55
+5.59×10
21
u
54
+· · ·+3.92×10
21
a+2.03×10
22
, u
56
+u
55
+· · ·+5u+1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
10
=
−0.884303u
55
− 1.42519u
54
+ ··· − 11.7187u − 5.18607
1.07335u
55
+ 1.33083u
54
+ ··· + 10.5900u + 1.28265
a
8
=
0.398819u
55
+ 0.264821u
54
+ ··· − 1.50716u − 4.14726
−0.293268u
55
− 0.142370u
54
+ ··· + 7.15161u + 1.04151
a
4
=
1.12125u
55
+ 0.795368u
54
+ ··· − 1.21708u + 3.71105
0.728912u
55
+ 0.645449u
54
+ ··· + 5.28443u + 0.988456
a
11
=
−u
4
− u
2
− 1
−0.0156250u
55
− 0.0156250u
54
+ ··· − 2.07813u
2
− 0.0156250u
a
1
=
u
2
+ 1
u
2
a
12
=
−1
−0.0156250u
55
− 0.0156250u
54
+ ··· − 2.07813u
2
− 0.0156250u
a
5
=
−u
0.0156250u
54
+ 0.0156250u
53
+ ··· + 1.07813u + 0.0156250
a
9
=
−0.338735u
55
− 0.642358u
54
+ ··· − 7.14616u − 4.61240
1.28465u
55
+ 1.74616u
54
+ ··· + 13.4307u + 1.61906
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
29125476928318618116311
15679520968247263985664
u
55
+
44772161939557650505
122496257564431749888
u
54
+ ··· +
47342986975139852519811
1306626747353938665472
u +
168360984603466865896361
15679520968247263985664
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
56
+ 23u
55
+ ··· + 7u + 1
c
2
, c
5
, c
6
c
12
u
56
− u
55
+ ··· − 5u + 1
c
3
2(2u
56
− 7u
55
+ ··· − 1408u + 568)
c
4
2(2u
56
+ 5u
55
+ ··· − 12415u − 1814)
c
7
, c
9
u
56
+ 2u
55
+ ··· + 111u − 16
c
8
u
56
− 9u
55
+ ··· − 108u + 32
c
10
u
56
− 11u
55
+ ··· + 12u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
56
+ 27y
55
+ ··· − 281y + 1
c
2
, c
5
, c
6
c
12
y
56
+ 23y
55
+ ··· + 7y + 1
c
3
4(4y
56
+ 203y
55
+ ··· + 8791360y + 322624)
c
4
4(4y
56
+ 203y
55
+ ··· − 6.38349 × 10
7
y + 3290596)
c
7
, c
9
y
56
− 34y
55
+ ··· − 3873y + 256
c
8
y
56
− 9y
55
+ ··· − 14928y + 1024
c
10
y
56
− 13y
55
+ ··· − 56y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.641354 + 0.766924I
a = 0.694797 − 0.010474I
b = −0.411989 + 0.253331I
1.69613 + 5.88626I 6.59882 − 10.04911I
u = 0.641354 − 0.766924I
a = 0.694797 + 0.010474I
b = −0.411989 − 0.253331I
1.69613 − 5.88626I 6.59882 + 10.04911I
u = 0.890495 + 0.394781I
a = 0.56585 + 1.71637I
b = 0.77307 + 2.16329I
5.23278 − 8.75525I 9.12590 + 4.28286I
u = 0.890495 − 0.394781I
a = 0.56585 − 1.71637I
b = 0.77307 − 2.16329I
5.23278 + 8.75525I 9.12590 − 4.28286I
u = 0.680820 + 0.645893I
a = −0.27069 − 1.56272I
b = −0.429081 − 1.133110I
5.34241 + 3.10303I 13.5555 − 6.2410I
u = 0.680820 − 0.645893I
a = −0.27069 + 1.56272I
b = −0.429081 + 1.133110I
5.34241 − 3.10303I 13.5555 + 6.2410I
u = 0.391841 + 0.990849I
a = 0.108165 + 1.215430I
b = −1.272990 − 0.612251I
−5.11253 + 3.37715I −0.88601 − 5.46141I
u = 0.391841 − 0.990849I
a = 0.108165 − 1.215430I
b = −1.272990 + 0.612251I
−5.11253 − 3.37715I −0.88601 + 5.46141I
u = −0.356333 + 1.031000I
a = 0.112919 + 1.134410I
b = 1.06758 − 1.21699I
−3.74795 + 3.70678I 1.07262 + 1.48118I
u = −0.356333 − 1.031000I
a = 0.112919 − 1.134410I
b = 1.06758 + 1.21699I
−3.74795 − 3.70678I 1.07262 − 1.48118I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.567758 + 0.703113I
a = −0.048537 + 0.661451I
b = 0.909520 + 0.756625I
1.47606 − 2.14860I 6.53813 + 2.61588I
u = −0.567758 − 0.703113I
a = −0.048537 − 0.661451I
b = 0.909520 − 0.756625I
1.47606 + 2.14860I 6.53813 − 2.61588I
u = −1.004770 + 0.465676I
a = −0.752461 + 1.121390I
b = −1.11019 + 2.22948I
3.88963 + 0.18068I 12.1686 − 14.3132I
u = −1.004770 − 0.465676I
a = −0.752461 − 1.121390I
b = −1.11019 − 2.22948I
3.88963 − 0.18068I 12.1686 + 14.3132I
u = 0.699427 + 0.539052I
a = −0.43783 − 2.08391I
b = 0.185339 − 1.303870I
5.10282 − 0.74752I 13.56172 + 0.84027I
u = 0.699427 − 0.539052I
a = −0.43783 + 2.08391I
b = 0.185339 + 1.303870I
5.10282 + 0.74752I 13.56172 − 0.84027I
u = −1.13520
a = −0.599595
b = −2.22015
3.17493 −46.8580
u = −0.443116 + 1.068040I
a = −0.294627 + 0.330709I
b = −0.701327 + 0.323759I
−6.12718 − 2.42607I 0. + 3.46050I
u = −0.443116 − 1.068040I
a = −0.294627 − 0.330709I
b = −0.701327 − 0.323759I
−6.12718 + 2.42607I 0. − 3.46050I
u = −0.604422 + 0.580004I
a = 1.67133 − 3.65644I
b = 0.06407 − 4.02240I
2.96769 − 1.32540I −18.6606 + 10.9069I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.604422 − 0.580004I
a = 1.67133 + 3.65644I
b = 0.06407 + 4.02240I
2.96769 + 1.32540I −18.6606 − 10.9069I
u = 0.727400 + 0.390596I
a = −0.558491 − 0.668115I
b = 0.155223 − 0.051892I
0.86120 − 3.19371I 6.98585 + 3.47955I
u = 0.727400 − 0.390596I
a = −0.558491 + 0.668115I
b = 0.155223 + 0.051892I
0.86120 + 3.19371I 6.98585 − 3.47955I
u = 0.798907 + 0.863165I
a = 1.08626 + 1.62924I
b = −0.25509 + 2.32871I
6.92651 + 10.55710I 8.79807 − 9.19219I
u = 0.798907 − 0.863165I
a = 1.08626 − 1.62924I
b = −0.25509 − 2.32871I
6.92651 − 10.55710I 8.79807 + 9.19219I
u = −0.546311 + 1.045040I
a = −0.004162 − 0.200042I
b = −0.618017 + 0.983572I
−0.04707 − 3.40862I 0
u = −0.546311 − 1.045040I
a = −0.004162 + 0.200042I
b = −0.618017 − 0.983572I
−0.04707 + 3.40862I 0
u = 0.422043 + 1.122130I
a = 0.259194 + 0.525303I
b = 0.143647 − 0.242320I
−5.00479 + 8.23366I 0. − 10.38982I
u = 0.422043 − 1.122130I
a = 0.259194 − 0.525303I
b = 0.143647 + 0.242320I
−5.00479 − 8.23366I 0. + 10.38982I
u = 0.541495 + 1.089460I
a = 1.35077 − 1.05139I
b = 1.28833 + 2.18214I
−1.20159 + 6.69686I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.541495 − 1.089460I
a = 1.35077 + 1.05139I
b = 1.28833 − 2.18214I
−1.20159 − 6.69686I 0
u = −0.799984 + 0.939547I
a = −1.30937 + 1.40522I
b = 0.57203 + 2.16000I
6.49526 − 1.44027I 0
u = −0.799984 − 0.939547I
a = −1.30937 − 1.40522I
b = 0.57203 − 2.16000I
6.49526 + 1.44027I 0
u = −0.051851 + 0.762889I
a = 0.282476 + 1.053620I
b = −0.690965 − 0.883742I
−2.27089 − 5.91381I 7.94668 + 7.27969I
u = −0.051851 − 0.762889I
a = 0.282476 − 1.053620I
b = −0.690965 + 0.883742I
−2.27089 + 5.91381I 7.94668 − 7.27969I
u = −0.591203 + 1.092780I
a = 1.31016 − 1.25263I
b = −0.930688 − 0.609508I
2.45649 − 6.90794I 0
u = −0.591203 − 1.092780I
a = 1.31016 + 1.25263I
b = −0.930688 + 0.609508I
2.45649 + 6.90794I 0
u = 0.568843 + 1.123960I
a = −3.35816 − 1.22273I
b = 0.85524 − 3.67514I
−0.61428 + 8.19980I 0
u = 0.568843 − 1.123960I
a = −3.35816 + 1.22273I
b = 0.85524 + 3.67514I
−0.61428 − 8.19980I 0
u = −0.594804 + 1.135650I
a = 1.55919 − 1.02268I
b = −0.21013 − 1.56219I
1.33863 − 10.96070I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.594804 − 1.135650I
a = 1.55919 + 1.02268I
b = −0.21013 + 1.56219I
1.33863 + 10.96070I 0
u = −0.559956 + 0.434306I
a = −0.589021 − 0.157164I
b = −0.697701 + 0.414035I
1.163170 − 0.747921I 7.34726 + 4.22076I
u = −0.559956 − 0.434306I
a = −0.589021 + 0.157164I
b = −0.697701 − 0.414035I
1.163170 + 0.747921I 7.34726 − 4.22076I
u = 0.551322 + 1.170130I
a = 0.065982 + 0.333605I
b = −0.706084 − 0.227289I
−3.52575 + 8.58144I 0
u = 0.551322 − 1.170130I
a = 0.065982 − 0.333605I
b = −0.706084 + 0.227289I
−3.52575 − 8.58144I 0
u = 0.061371 + 0.690777I
a = −0.450846 + 0.828076I
b = 0.897751 − 0.266212I
−3.81337 − 0.64970I 3.11741 − 0.92674I
u = 0.061371 − 0.690777I
a = −0.450846 − 0.828076I
b = 0.897751 + 0.266212I
−3.81337 + 0.64970I 3.11741 + 0.92674I
u = −0.582882 + 1.176740I
a = 0.049432 − 0.569260I
b = 0.047888 − 0.543291I
−3.89165 − 13.47290I 0
u = −0.582882 − 1.176740I
a = 0.049432 + 0.569260I
b = 0.047888 + 0.543291I
−3.89165 + 13.47290I 0
u = −0.609351 + 1.211770I
a = −1.98054 + 1.28391I
b = 1.22737 + 2.10225I
0.1196 − 20.0021I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.609351 − 1.211770I
a = −1.98054 − 1.28391I
b = 1.22737 − 2.10225I
0.1196 + 20.0021I 0
u = 0.631153 + 1.210450I
a = 1.59641 + 1.30244I
b = −1.48858 + 1.76082I
−0.97220 + 12.02980I 0
u = 0.631153 − 1.210450I
a = 1.59641 − 1.30244I
b = −1.48858 − 1.76082I
−0.97220 − 12.02980I 0
u = −0.101342 + 0.410395I
a = −1.242190 − 0.632064I
b = 0.097330 + 1.042940I
0.89200 − 1.30649I 6.20526 + 4.80910I
u = −0.101342 − 0.410395I
a = −1.242190 + 0.632064I
b = 0.097330 − 1.042940I
0.89200 + 1.30649I 6.20526 − 4.80910I
u = −0.249581
a = −4.98248
b = −0.802957
2.23670 0.606960
10
II. I
u
2
= h−4.49 × 10
91
u
83
+ 8.28 × 10
90
u
82
+ · · · + 5.10 × 10
93
b − 6.72 ×
10
93
, 2.38 × 10
94
u
83
+ 9.36 × 10
93
u
82
+ · · · + 8.67 × 10
94
a + 1.23 ×
10
95
, u
84
+ u
83
+ · · · + 88u + 17i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
10
=
−0.274153u
83
− 0.107915u
82
+ ··· − 4.50932u − 1.41914
0.00879232u
83
− 0.00162222u
82
+ ··· + 2.60942u + 1.31730
a
8
=
−0.0179921u
83
+ 0.241722u
82
+ ··· + 45.6550u + 13.6692
0.00995629u
83
+ 0.0822915u
82
+ ··· + 8.95606u + 2.13864
a
4
=
−0.375221u
83
− 0.209923u
82
+ ··· − 12.2704u − 2.30297
−0.150797u
83
− 0.0987334u
82
+ ··· − 1.35636u − 0.733590
a
11
=
−0.132863u
83
− 0.0894160u
82
+ ··· − 20.7215u − 5.84894
−0.0224294u
83
− 0.0235312u
82
+ ··· + 0.893970u + 1.39768
a
1
=
u
2
+ 1
u
2
a
12
=
−0.178939u
83
− 0.110997u
82
+ ··· − 24.5523u − 8.40162
1
a
5
=
−0.126765u
83
− 0.0582595u
82
+ ··· − 18.5803u − 8.21843
−0.0679413u
83
+ 0.000564076u
82
+ ··· − 6.34498u − 3.04196
a
9
=
−0.285202u
83
− 0.171429u
82
+ ··· − 9.87160u − 3.03135
0.0104337u
83
− 0.0117629u
82
+ ··· + 2.05195u + 0.597007
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0168362u
83
+ 0.405628u
82
+ ··· + 25.2983u + 3.62973
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
84
+ 47u
83
+ ··· − 672u + 289
c
2
, c
5
, c
6
c
12
u
84
− u
83
+ ··· − 88u + 17
c
3
(u
42
+ u
41
+ ··· + 10u + 4)
2
c
4
(u
42
− u
41
+ ··· − 21u + 1)
2
c
7
, c
9
(u
42
+ u
41
+ ··· + 7u + 1)
2
c
8
(u
42
− 7u
41
+ ··· − u + 1)
2
c
10
(u
42
+ 3u
41
+ ··· + u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
84
− 21y
83
+ ··· − 9557396y + 83521
c
2
, c
5
, c
6
c
12
y
84
+ 47y
83
+ ··· − 672y + 289
c
3
(y
42
+ 41y
41
+ ··· + 308y + 16)
2
c
4
(y
42
+ 33y
41
+ ··· − 247y + 1)
2
c
7
, c
9
(y
42
− 27y
41
+ ··· − 7y + 1)
2
c
8
(y
42
− 3y
41
+ ··· − 7y + 1)
2
c
10
(y
42
− 7y
41
+ ··· − 3y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.951872 + 0.276744I
a = −0.39157 + 1.57246I
b = −1.04779 + 2.14004I
2.9646 + 14.3413I 4.00000 − 8.28932I
u = −0.951872 − 0.276744I
a = −0.39157 − 1.57246I
b = −1.04779 − 2.14004I
2.9646 − 14.3413I 4.00000 + 8.28932I
u = 0.531874 + 0.814655I
a = −0.235436 − 0.176088I
b = 0.428289 + 0.678050I
1.56120 − 1.20148I 7.68187 + 4.16647I
u = 0.531874 − 0.814655I
a = −0.235436 + 0.176088I
b = 0.428289 − 0.678050I
1.56120 + 1.20148I 7.68187 − 4.16647I
u = 0.987080 + 0.316254I
a = 0.582224 + 1.121970I
b = 1.30000 + 1.90393I
1.77491 − 6.18924I 0
u = 0.987080 − 0.316254I
a = 0.582224 − 1.121970I
b = 1.30000 − 1.90393I
1.77491 + 6.18924I 0
u = −0.472668 + 0.925828I
a = −1.38938 − 0.57724I
b = −0.85123 + 1.67366I
0.88637 − 2.06372I 0
u = −0.472668 − 0.925828I
a = −1.38938 + 0.57724I
b = −0.85123 − 1.67366I
0.88637 + 2.06372I 0
u = −0.365634 + 0.990499I
a = 2.37994 − 2.01802I
b = −0.146160 − 1.186050I
−1.39551 − 2.76342I 0
u = −0.365634 − 0.990499I
a = 2.37994 + 2.01802I
b = −0.146160 + 1.186050I
−1.39551 + 2.76342I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.166361 + 1.064190I
a = 0.222499 + 0.775256I
b = 0.501062 − 0.154481I
−3.70167 − 1.01542I 0
u = 0.166361 − 1.064190I
a = 0.222499 − 0.775256I
b = 0.501062 + 0.154481I
−3.70167 + 1.01542I 0
u = −0.861223 + 0.274631I
a = 0.447664 − 0.841230I
b = −0.101282 − 0.359060I
−1.20076 + 8.16087I 3.94706 − 7.65229I
u = −0.861223 − 0.274631I
a = 0.447664 + 0.841230I
b = −0.101282 + 0.359060I
−1.20076 − 8.16087I 3.94706 + 7.65229I
u = −0.219257 + 0.874467I
a = 3.40559 − 2.71073I
b = 0.020182 − 0.631523I
−0.621946 + 0.257129I 8.13768 + 2.68186I
u = −0.219257 − 0.874467I
a = 3.40559 + 2.71073I
b = 0.020182 + 0.631523I
−0.621946 − 0.257129I 8.13768 − 2.68186I
u = 0.307330 + 1.066780I
a = −5.67618 − 0.22144I
b = 0.08332 − 2.91001I
−2.80543 + 0.38762I 0
u = 0.307330 − 1.066780I
a = −5.67618 + 0.22144I
b = 0.08332 + 2.91001I
−2.80543 − 0.38762I 0
u = −0.816869 + 0.351666I
a = 0.02403 − 1.83361I
b = 0.05111 − 1.46523I
3.66382 + 5.70185I 10.61456 − 6.99288I
u = −0.816869 − 0.351666I
a = 0.02403 + 1.83361I
b = 0.05111 + 1.46523I
3.66382 − 5.70185I 10.61456 + 6.99288I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.585604 + 0.948707I
a = −1.32890 − 1.58654I
b = 0.668874 − 0.815038I
4.44406 + 1.79873I 0
u = 0.585604 − 0.948707I
a = −1.32890 + 1.58654I
b = 0.668874 + 0.815038I
4.44406 − 1.79873I 0
u = −0.855194 + 0.715858I
a = −0.76816 + 1.52285I
b = −0.13960 + 2.24229I
7.14323 − 4.60033I 0
u = −0.855194 − 0.715858I
a = −0.76816 − 1.52285I
b = −0.13960 − 2.24229I
7.14323 + 4.60033I 0
u = 0.568046 + 0.959810I
a = 1.37749 + 1.72915I
b = −0.76692 + 1.63638I
−4.13754 + 2.24209I 0
u = 0.568046 − 0.959810I
a = 1.37749 − 1.72915I
b = −0.76692 − 1.63638I
−4.13754 − 2.24209I 0
u = −0.758844 + 0.419717I
a = −0.287572 − 1.117020I
b = 0.668874 − 0.815038I
4.44406 + 1.79873I 12.47510 − 0.83291I
u = −0.758844 − 0.419717I
a = −0.287572 + 1.117020I
b = 0.668874 + 0.815038I
4.44406 − 1.79873I 12.47510 + 0.83291I
u = −0.537381 + 1.003410I
a = 3.69954 − 1.88396I
b = −0.46119 − 3.74468I
1.69916 − 3.19900I 0
u = −0.537381 − 1.003410I
a = 3.69954 + 1.88396I
b = −0.46119 + 3.74468I
1.69916 + 3.19900I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.826710 + 0.792492I
a = 1.19449 + 1.56505I
b = −0.13960 + 2.24229I
7.14323 − 4.60033I 0
u = 0.826710 − 0.792492I
a = 1.19449 − 1.56505I
b = −0.13960 − 2.24229I
7.14323 + 4.60033I 0
u = −0.093008 + 1.146880I
a = 1.30559 + 0.60076I
b = 0.020182 + 0.631523I
−0.621946 − 0.257129I 0
u = −0.093008 − 1.146880I
a = 1.30559 − 0.60076I
b = 0.020182 − 0.631523I
−0.621946 + 0.257129I 0
u = −0.441120 + 1.073580I
a = −0.313016 − 0.998766I
b = −0.145380 − 0.195788I
−6.13332 − 4.53919I 0
u = −0.441120 − 1.073580I
a = −0.313016 + 0.998766I
b = −0.145380 + 0.195788I
−6.13332 + 4.53919I 0
u = 0.015777 + 1.168210I
a = 0.254753 + 1.283830I
b = 0.259413 − 0.533713I
−3.54870 − 1.34243I 0
u = 0.015777 − 1.168210I
a = 0.254753 − 1.283830I
b = 0.259413 + 0.533713I
−3.54870 + 1.34243I 0
u = 0.246543 + 1.147790I
a = 2.96006 − 1.66756I
b = 0.08332 + 2.91001I
−2.80543 − 0.38762I 0
u = 0.246543 − 1.147790I
a = 2.96006 + 1.66756I
b = 0.08332 − 2.91001I
−2.80543 + 0.38762I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.790539 + 0.233655I
a = 0.254852 − 0.304931I
b = 0.744215 − 0.026824I
−0.77775 − 3.57467I 2.99358 + 1.46864I
u = 0.790539 − 0.233655I
a = 0.254852 + 0.304931I
b = 0.744215 + 0.026824I
−0.77775 + 3.57467I 2.99358 − 1.46864I
u = 0.753325 + 0.332759I
a = −0.52004 − 2.83483I
b = −0.46119 − 3.74468I
1.69916 − 3.19900I −4.91732 − 10.84472I
u = 0.753325 − 0.332759I
a = −0.52004 + 2.83483I
b = −0.46119 + 3.74468I
1.69916 + 3.19900I −4.91732 + 10.84472I
u = 0.587978 + 1.024140I
a = −1.45243 − 1.33342I
b = 0.05111 − 1.46523I
3.66382 + 5.70185I 0
u = 0.587978 − 1.024140I
a = −1.45243 + 1.33342I
b = 0.05111 + 1.46523I
3.66382 − 5.70185I 0
u = −0.537462 + 1.060840I
a = −2.06677 + 1.86366I
b = 0.87584 + 1.89908I
−2.44680 − 10.28750I 0
u = −0.537462 − 1.060840I
a = −2.06677 − 1.86366I
b = 0.87584 − 1.89908I
−2.44680 + 10.28750I 0
u = −0.620482 + 0.509254I
a = −0.955022 + 0.401385I
b = 0.428289 + 0.678050I
1.56120 − 1.20148I 7.68187 + 4.16647I
u = −0.620482 − 0.509254I
a = −0.955022 − 0.401385I
b = 0.428289 − 0.678050I
1.56120 + 1.20148I 7.68187 − 4.16647I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.510672 + 1.083630I
a = −0.114052 + 0.483358I
b = 0.744215 − 0.026824I
−0.77775 − 3.57467I 0
u = −0.510672 − 1.083630I
a = −0.114052 − 0.483358I
b = 0.744215 + 0.026824I
−0.77775 + 3.57467I 0
u = −0.197785 + 1.208910I
a = −0.388972 + 0.092186I
b = −0.146160 + 1.186050I
−1.39551 + 2.76342I 0
u = −0.197785 − 1.208910I
a = −0.388972 − 0.092186I
b = −0.146160 − 1.186050I
−1.39551 − 2.76342I 0
u = 0.358263 + 1.176890I
a = 0.438284 + 0.625720I
b = −0.576547
−4.99175 0
u = 0.358263 − 1.176890I
a = 0.438284 − 0.625720I
b = −0.576547
−4.99175 0
u = 0.574474 + 1.095730I
a = 0.156893 − 0.575244I
b = −0.101282 − 0.359060I
−1.20076 + 8.16087I 0
u = 0.574474 − 1.095730I
a = 0.156893 + 0.575244I
b = −0.101282 + 0.359060I
−1.20076 − 8.16087I 0
u = −0.578971 + 0.461942I
a = −0.82324 + 2.49340I
b = −0.47444 + 1.70352I
−0.66943 + 5.77796I 4.70723 − 3.77194I
u = −0.578971 − 0.461942I
a = −0.82324 − 2.49340I
b = −0.47444 − 1.70352I
−0.66943 − 5.77796I 4.70723 + 3.77194I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.716730 + 0.176249I
a = −0.540642 + 0.599446I
b = 0.379962 + 0.861183I
−1.62437 + 4.60168I 1.92175 − 9.10658I
u = 0.716730 − 0.176249I
a = −0.540642 − 0.599446I
b = 0.379962 − 0.861183I
−1.62437 − 4.60168I 1.92175 + 9.10658I
u = 0.633608 + 0.363234I
a = 0.414127 + 0.949449I
b = −0.85123 + 1.67366I
0.88637 − 2.06372I 7.58768 + 6.20553I
u = 0.633608 − 0.363234I
a = 0.414127 − 0.949449I
b = −0.85123 − 1.67366I
0.88637 + 2.06372I 7.58768 − 6.20553I
u = −0.277378 + 1.257970I
a = −0.335234 + 0.865928I
b = 0.379962 − 0.861183I
−1.62437 − 4.60168I 0
u = −0.277378 − 1.257970I
a = −0.335234 − 0.865928I
b = 0.379962 + 0.861183I
−1.62437 + 4.60168I 0
u = −0.270661 + 1.259850I
a = −0.593163 + 0.562481I
b = −0.145380 + 0.195788I
−6.13332 + 4.53919I 0
u = −0.270661 − 1.259850I
a = −0.593163 − 0.562481I
b = −0.145380 − 0.195788I
−6.13332 − 4.53919I 0
u = 0.100542 + 1.292600I
a = −0.145253 + 1.056930I
b = −0.47444 − 1.70352I
−0.66943 − 5.77796I 0
u = 0.100542 − 1.292600I
a = −0.145253 − 1.056930I
b = −0.47444 + 1.70352I
−0.66943 + 5.77796I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629938 + 1.144520I
a = 1.88349 + 1.45771I
b = −1.04779 + 2.14004I
2.9646 + 14.3413I 0
u = 0.629938 − 1.144520I
a = 1.88349 − 1.45771I
b = −1.04779 − 2.14004I
2.9646 − 14.3413I 0
u = 0.425157 + 1.241880I
a = 0.709496 + 0.661172I
b = −0.780021
−4.89562 0
u = 0.425157 − 1.241880I
a = 0.709496 − 0.661172I
b = −0.780021
−4.89562 0
u = 0.164634 + 0.664229I
a = 1.79299 + 0.74893I
b = 0.259413 + 0.533713I
−3.54870 + 1.34243I 1.03679 − 4.26706I
u = 0.164634 − 0.664229I
a = 1.79299 − 0.74893I
b = 0.259413 − 0.533713I
−3.54870 − 1.34243I 1.03679 + 4.26706I
u = −0.673733 + 1.141180I
a = −1.49035 + 1.37377I
b = 1.30000 + 1.90393I
1.77491 − 6.18924I 0
u = −0.673733 − 1.141180I
a = −1.49035 − 1.37377I
b = 1.30000 − 1.90393I
1.77491 + 6.18924I 0
u = −0.260548 + 1.338350I
a = 0.141594 + 1.088570I
b = 0.87584 − 1.89908I
−2.44680 + 10.28750I 0
u = −0.260548 − 1.338350I
a = 0.141594 − 1.088570I
b = 0.87584 + 1.89908I
−2.44680 − 10.28750I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.182393 + 1.356620I
a = 0.071105 + 1.273620I
b = −0.76692 − 1.63638I
−4.13754 − 2.24209I 0
u = 0.182393 − 1.356620I
a = 0.071105 − 1.273620I
b = −0.76692 + 1.63638I
−4.13754 + 2.24209I 0
u = −0.352141 + 0.038419I
a = 1.45162 − 1.80927I
b = 0.501062 + 0.154481I
−3.70167 + 1.01542I 0.525020 − 1.212964I
u = −0.352141 − 0.038419I
a = 1.45162 + 1.80927I
b = 0.501062 − 0.154481I
−3.70167 − 1.01542I 0.525020 + 1.212964I
22
III.
I
u
3
= h12a
5
u +50a
4
u +· · ·− 290a −56, −6a
5
u −25a
4
u +· · ·+ 20a +11, u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−1
a
7
=
u
0
a
10
=
a
−0.923077a
5
u − 3.84615a
4
u + ··· + 22.3077a + 4.30769
a
8
=
−0.923077a
5
u − 7.69231a
4
u + ··· + 8.84615a + 10.1538
0.615385a
5
u + 2.23077a
4
u + ··· − 17.5385a − 1.53846
a
4
=
0.307692a
5
u + 5.84615a
4
u + ··· + 7.53846a − 8
−3.46154a
4
u − 13.5385a
3
u + ··· − 13.6154a + 2.46154
a
11
=
−1
−2.30769a
5
u − 10.6154a
4
u + ··· + 42.7692a + 15.7692
a
1
=
0
−1
a
12
=
−1
−2.30769a
5
u − 10.6154a
4
u + ··· + 42.7692a + 14.7692
a
5
=
−u
−11.5385a
4
u − 42.4615a
3
u + ··· − 40.3846a + 13.5385
a
9
=
−0.923077a
5
u − 3.84615a
4
u + ··· + 23.3077a + 4.30769
−0.923077a
5
u − 3.84615a
4
u + ··· + 22.3077a + 4.30769
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
20
13
a
5
−
100
13
a
4
u +
92
13
a
4
−
368
13
a
3
u −
36
13
a
3
−
292
13
a
2
u −
484
13
a
2
+
232
13
au −
324
13
a +
76
13
u −
4
13
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u − 1)
12
c
2
, c
5
, c
6
c
12
(u
2
+ 1)
6
c
3
, c
10
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
4
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
7
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
8
, c
9
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y −1)
12
c
2
, c
5
, c
6
c
12
(y + 1)
12
c
3
, c
10
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
4
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
7
, c
8
, c
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.655968 + 0.901719I
b = −0.664531 − 0.428243I
−5.18047 + 0.92430I −5.71672 − 0.79423I
u = 1.000000I
a = 0.415113 + 0.618748I
b = 0.558752 − 1.073950I
−3.28987 + 5.69302I −2.00000 − 5.51057I
u = 1.000000I
a = −0.655968 + 1.098280I
b = 0.664531 − 0.428243I
−5.18047 − 0.92430I −5.71672 + 0.79423I
u = 1.000000I
a = 0.41511 + 1.38125I
b = −0.558752 − 1.073950I
−3.28987 − 5.69302I −2.00000 + 5.51057I
u = 1.000000I
a = −2.25915 − 0.43225I
b = 0.295542 + 1.002190I
−1.39926 − 0.92430I 1.71672 + 0.79423I
u = 1.000000I
a = −2.25915 + 2.43225I
b = −0.295542 + 1.002190I
−1.39926 + 0.92430I 1.71672 − 0.79423I
u = − 1.000000I
a = −0.655968 − 0.901719I
b = −0.664531 + 0.428243I
−5.18047 − 0.92430I −5.71672 + 0.79423I
u = − 1.000000I
a = 0.415113 − 0.618748I
b = 0.558752 + 1.073950I
−3.28987 − 5.69302I −2.00000 + 5.51057I
u = − 1.000000I
a = −0.655968 − 1.098280I
b = 0.664531 + 0.428243I
−5.18047 + 0.92430I −5.71672 − 0.79423I
u = − 1.000000I
a = 0.41511 − 1.38125I
b = −0.558752 + 1.073950I
−3.28987 + 5.69302I −2.00000 − 5.51057I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = −2.25915 + 0.43225I
b = 0.295542 − 1.002190I
−1.39926 + 0.92430I 1.71672 − 0.79423I
u = − 1.000000I
a = −2.25915 − 2.43225I
b = −0.295542 − 1.002190I
−1.39926 − 0.92430I 1.71672 + 0.79423I
27
IV. I
u
4
= h2b − 3, 4a − 1, u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
−1
a
2
=
1
1
a
7
=
−1
−2
a
10
=
0.25
1.5
a
8
=
−0.75
−0.5
a
4
=
1.375
0.25
a
11
=
3
2
a
1
=
2
1
a
12
=
1
1
a
5
=
1
0
a
9
=
−0.75
−0.5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 26.0625
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
11
, c
12
u + 1
c
3
, c
4
2(2u + 1)
c
5
, c
6
, c
9
u − 1
c
8
u
c
10
u + 2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
9
c
11
, c
12
y −1
c
3
, c
4
4(4y −1)
c
8
y
c
10
y −4
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.250000
b = 1.50000
3.28987 26.0630
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
((u − 1)
12
)(u + 1)(u
56
+ 23u
55
+ ··· + 7u + 1)
· (u
84
+ 47u
83
+ ··· − 672u + 289)
c
2
, c
12
(u + 1)(u
2
+ 1)
6
(u
56
− u
55
+ ··· − 5u + 1)(u
84
− u
83
+ ··· − 88u + 17)
c
3
4(2u + 1)(u
12
− u
10
+ ··· − 3u
2
+ 1)(u
42
+ u
41
+ ··· + 10u + 4)
2
· (2u
56
− 7u
55
+ ··· − 1408u + 568)
c
4
4(2u + 1)(u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1)
· ((u
42
− u
41
+ ··· − 21u + 1)
2
)(2u
56
+ 5u
55
+ ··· − 12415u − 1814)
c
5
, c
6
(u − 1)(u
2
+ 1)
6
(u
56
− u
55
+ ··· − 5u + 1)(u
84
− u
83
+ ··· − 88u + 17)
c
7
(u + 1)(u
6
− u
5
+ ··· − u + 1)
2
(u
42
+ u
41
+ ··· + 7u + 1)
2
· (u
56
+ 2u
55
+ ··· + 111u − 16)
c
8
u(u
6
+ u
5
+ ··· + u + 1)
2
(u
42
− 7u
41
+ ··· − u + 1)
2
· (u
56
− 9u
55
+ ··· − 108u + 32)
c
9
(u − 1)(u
6
+ u
5
+ ··· + u + 1)
2
(u
42
+ u
41
+ ··· + 7u + 1)
2
· (u
56
+ 2u
55
+ ··· + 111u − 16)
c
10
(u + 2)(u
12
− u
10
+ ··· − 3u
2
+ 1)(u
42
+ 3u
41
+ ··· + u + 1)
2
· (u
56
− 11u
55
+ ··· + 12u − 4)
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y −1)
13
)(y
56
+ 27y
55
+ ··· − 281y + 1)
· (y
84
− 21y
83
+ ··· − 9557396y + 83521)
c
2
, c
5
, c
6
c
12
(y −1)(y + 1)
12
(y
56
+ 23y
55
+ ··· + 7y + 1)
· (y
84
+ 47y
83
+ ··· − 672y + 289)
c
3
16(4y −1)(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
· (y
42
+ 41y
41
+ ··· + 308y + 16)
2
· (4y
56
+ 203y
55
+ ··· + 8791360y + 322624)
c
4
16(4y −1)(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
· (y
42
+ 33y
41
+ ··· − 247y + 1)
2
· (4y
56
+ 203y
55
+ ··· − 63834933y + 3290596)
c
7
, c
9
(y −1)(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· ((y
42
− 27y
41
+ ··· − 7y + 1)
2
)(y
56
− 34y
55
+ ··· − 3873y + 256)
c
8
y(y
6
− 3y
5
+ ··· − y + 1)
2
(y
42
− 3y
41
+ ··· − 7y + 1)
2
· (y
56
− 9y
55
+ ··· − 14928y + 1024)
c
10
(y −4)(y
6
− y
5
+ ··· − 3y + 1)
2
(y
42
− 7y
41
+ ··· − 3y + 1)
2
· (y
56
− 13y
55
+ ··· − 56y + 16)
33
