12a
0702
(K12a
0702
)
A knot diagram
1
Linearized knot diagam
3 8 6 10 1 11 9 2 12 4 7 5
Solving Sequence
4,10
5
7,11
12 1 6 3 9 8 2
c
4
c
10
c
11
c
12
c
6
c
3
c
9
c
7
c
2
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.19038 × 10
83
u
40
+ 4.26853 × 10
83
u
39
+ ··· + 1.55480 × 10
86
b − 1.07861 × 10
86
,
− 5.72981 × 10
85
u
40
+ 1.60933 × 10
86
u
39
+ ··· + 3.88699 × 10
87
a − 9.00245 × 10
87
,
u
41
− 3u
40
+ ··· − 434u + 50i
I
u
2
= h−u
2
a + b + 1, −2u
26
a − 2u
25
a + ··· − 3a + 6, u
27
+ u
26
+ ··· + 2u − 1i
I
u
3
= hu
3
− u
2
+ 5b + 2u + 3, 3u
3
+ 2u
2
+ 10a − 14u − 6, u
4
− 2u
2
+ 2i
I
u
4
= hb + a − 1, 8a
3
+ 4a
2
u − 12a
2
− 4au + 2a + 1, u
2
+ 1i
I
v
1
= ha, b + 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 106 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−1.19 × 10
83
u
40
+ 4.27 × 10
83
u
39
+ · · · + 1.55 × 10
86
b − 1.08 ×
10
86
, −5.73 × 10
85
u
40
+ 1.61 × 10
86
u
39
+ · · · + 3.89 × 10
87
a − 9.00 ×
10
87
, u
41
− 3u
40
+ · · · − 434u + 50i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
7
=
0.0147410u
40
− 0.0414030u
39
+ ··· + 31.9284u + 2.31605
0.000765620u
40
− 0.00274539u
39
+ ··· + 1.07683u + 0.693733
a
11
=
−u
u
a
12
=
0.0115033u
40
− 0.0353806u
39
+ ··· + 46.5023u − 6.32310
0.00230652u
40
− 0.00672063u
39
+ ··· + 8.78658u − 0.731794
a
1
=
0.0138747u
40
− 0.0423896u
39
+ ··· + 56.2419u − 7.09843
0.00281990u
40
− 0.00776945u
39
+ ··· + 8.71363u − 0.737049
a
6
=
0.0146359u
40
− 0.0416011u
39
+ ··· + 31.6745u + 2.43461
0.000870716u
40
− 0.00254730u
39
+ ··· + 1.33067u + 0.575165
a
3
=
0.0128297u
40
− 0.0366995u
39
+ ··· + 28.5656u + 1.49810
0.00113437u
40
− 0.00267356u
39
+ ··· + 2.04755u + 0.246021
a
9
=
0.00492043u
40
− 0.0158956u
39
+ ··· + 24.8003u − 4.18302
0.00178970u
40
− 0.00537829u
39
+ ··· + 7.06620u − 0.641486
a
8
=
−0.000300319u
40
+ 0.00224674u
39
+ ··· − 9.20295u + 3.52338
−0.00108526u
40
+ 0.00257937u
39
+ ··· − 2.40758u + 0.183564
a
2
=
0.00367128u
40
− 0.00992859u
39
+ ··· + 5.43318u + 0.814239
0.00134579u
40
− 0.00361819u
39
+ ··· + 3.39304u + 0.0150160
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0228051u
40
+ 0.0718802u
39
+ ··· − 38.8520u + 4.20733
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
41
+ 13u
40
+ ··· − 1260u − 100
c
2
, c
8
u
41
+ 3u
40
+ ··· − 10u + 10
c
3
, c
9
64(64u
41
+ 256u
40
+ ··· − 13u
2
− 1)
c
4
, c
10
u
41
− 3u
40
+ ··· − 434u + 50
c
5
, c
6
, c
11
c
12
u
41
− u
40
+ ··· + 14u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
41
+ 33y
40
+ ··· − 489200y −10000
c
2
, c
8
y
41
+ 13y
40
+ ··· − 1260y −100
c
3
, c
9
4096(4096y
41
− 147456y
40
+ ··· − 26y −1)
c
4
, c
10
y
41
+ 25y
40
+ ··· − 199044y −2500
c
5
, c
6
, c
11
c
12
y
41
− 31y
40
+ ··· − 96y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455951 + 0.852881I
a = 0.728739 + 0.291805I
b = 0.139910 − 0.558255I
0.86494 + 1.62805I 5.67415 − 3.58289I
u = 0.455951 − 0.852881I
a = 0.728739 − 0.291805I
b = 0.139910 + 0.558255I
0.86494 − 1.62805I 5.67415 + 3.58289I
u = −0.021368 + 1.036750I
a = 1.161860 + 0.121316I
b = −1.236090 − 0.167032I
4.65548 + 2.80230I 13.48887 − 2.99820I
u = −0.021368 − 1.036750I
a = 1.161860 − 0.121316I
b = −1.236090 + 0.167032I
4.65548 − 2.80230I 13.48887 + 2.99820I
u = −0.850702 + 0.604796I
a = 1.089290 − 0.351516I
b = −0.364276 + 0.545866I
−0.16962 + 2.89326I 2.19290 − 0.10248I
u = −0.850702 − 0.604796I
a = 1.089290 + 0.351516I
b = −0.364276 − 0.545866I
−0.16962 − 2.89326I 2.19290 + 0.10248I
u = −0.471844 + 0.764313I
a = −0.121231 + 0.155243I
b = 0.127637 − 0.862325I
1.00547 + 1.41725I 6.32483 − 4.75240I
u = −0.471844 − 0.764313I
a = −0.121231 − 0.155243I
b = 0.127637 + 0.862325I
1.00547 − 1.41725I 6.32483 + 4.75240I
u = 0.676505 + 0.580935I
a = −0.636641 + 0.057470I
b = 0.388189 + 0.860067I
−0.01909 − 5.83785I 3.11476 + 10.68510I
u = 0.676505 − 0.580935I
a = −0.636641 − 0.057470I
b = 0.388189 − 0.860067I
−0.01909 + 5.83785I 3.11476 − 10.68510I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.106757 + 1.119200I
a = 0.407888 + 0.094333I
b = 0.707134 − 0.209548I
−0.743392 − 0.853731I 8.26894 + 8.56558I
u = 0.106757 − 1.119200I
a = 0.407888 − 0.094333I
b = 0.707134 + 0.209548I
−0.743392 + 0.853731I 8.26894 − 8.56558I
u = −0.135573 + 0.750401I
a = 0.497918 + 0.003694I
b = −0.087550 − 0.403450I
0.517216 + 0.980568I 7.41204 − 7.03124I
u = −0.135573 − 0.750401I
a = 0.497918 − 0.003694I
b = −0.087550 + 0.403450I
0.517216 − 0.980568I 7.41204 + 7.03124I
u = 0.015207 + 1.271930I
a = 0.258817 + 0.015105I
b = 1.052190 − 0.036306I
4.96111 − 3.02863I 13.36303 + 2.94764I
u = 0.015207 − 1.271930I
a = 0.258817 − 0.015105I
b = 1.052190 + 0.036306I
4.96111 + 3.02863I 13.36303 − 2.94764I
u = 1.267430 + 0.165148I
a = −1.57147 − 0.04495I
b = 0.523699 + 0.462735I
10.5970 − 11.3672I 9.96311 + 7.10557I
u = 1.267430 − 0.165148I
a = −1.57147 + 0.04495I
b = 0.523699 − 0.462735I
10.5970 + 11.3672I 9.96311 − 7.10557I
u = −1.303430 + 0.145939I
a = −1.59455 + 0.04931I
b = 0.546188 − 0.390643I
11.47150 + 4.79100I 11.44614 − 2.44954I
u = −1.303430 − 0.145939I
a = −1.59455 − 0.04931I
b = 0.546188 + 0.390643I
11.47150 − 4.79100I 11.44614 + 2.44954I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48598
a = −1.70628
b = 0.809440
6.30192 14.4050
u = 0.346910 + 0.359461I
a = −0.044452 + 0.984431I
b = 0.444124 + 0.546475I
−2.78156 − 0.97104I −4.60139 + 3.38415I
u = 0.346910 − 0.359461I
a = −0.044452 − 0.984431I
b = 0.444124 − 0.546475I
−2.78156 + 0.97104I −4.60139 − 3.38415I
u = 1.54269 + 0.18278I
a = −1.72780 − 0.12223I
b = 0.941440 + 0.289062I
2.02994 − 4.70447I 11.23439 + 5.82932I
u = 1.54269 − 0.18278I
a = −1.72780 + 0.12223I
b = 0.941440 − 0.289062I
2.02994 + 4.70447I 11.23439 − 5.82932I
u = 0.52762 + 1.47752I
a = −0.21972 + 1.74763I
b = 0.20870 − 2.77021I
15.8147 − 17.6250I 0
u = 0.52762 − 1.47752I
a = −0.21972 − 1.74763I
b = 0.20870 + 2.77021I
15.8147 + 17.6250I 0
u = −0.53754 + 1.48742I
a = −0.19175 − 1.71682I
b = 0.21292 + 2.73453I
16.6893 + 11.2011I 0
u = −0.53754 − 1.48742I
a = −0.19175 + 1.71682I
b = 0.21292 − 2.73453I
16.6893 − 11.2011I 0
u = 0.50522 + 1.54544I
a = −0.04761 + 1.80771I
b = 0.06833 − 2.69458I
7.92273 − 11.59880I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50522 − 1.54544I
a = −0.04761 − 1.80771I
b = 0.06833 + 2.69458I
7.92273 + 11.59880I 0
u = −0.56045 + 1.56650I
a = 0.03187 − 1.69887I
b = 0.08948 + 2.57599I
11.62590 + 7.27779I 0
u = −0.56045 − 1.56650I
a = 0.03187 + 1.69887I
b = 0.08948 − 2.57599I
11.62590 − 7.27779I 0
u = −0.68168 + 1.55704I
a = 0.25317 − 1.45413I
b = 0.08907 + 2.25581I
15.8034 + 2.5637I 0
u = −0.68168 − 1.55704I
a = 0.25317 + 1.45413I
b = 0.08907 − 2.25581I
15.8034 − 2.5637I 0
u = 0.71972 + 1.54565I
a = 0.34306 + 1.40038I
b = 0.04686 − 2.15261I
14.6951 + 4.0355I 0
u = 0.71972 − 1.54565I
a = 0.34306 − 1.40038I
b = 0.04686 + 2.15261I
14.6951 − 4.0355I 0
u = 0.58769 + 1.64814I
a = 0.20254 + 1.74524I
b = −0.04962 − 2.50192I
7.14307 − 3.31046I 0
u = 0.58769 − 1.64814I
a = 0.20254 − 1.74524I
b = −0.04962 + 2.50192I
7.14307 + 3.31046I 0
u = 0.053861 + 0.132763I
a = 4.65323 + 2.55602I
b = 0.746943 + 0.099019I
1.42567 + 2.78320I 0.79755 − 2.69383I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.053861 − 0.132763I
a = 4.65323 − 2.55602I
b = 0.746943 − 0.099019I
1.42567 − 2.78320I 0.79755 + 2.69383I
9
II.
I
u
2
= h−u
2
a + b + 1, −2u
26
a − 2u
25
a + · · · − 3a + 6, u
27
+ u
26
+ · · · + 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
7
=
a
u
2
a − 1
a
11
=
−u
u
a
12
=
u
26
+ 3u
25
+ ··· + 2au − 4u
−2u
25
− 2u
24
+ ··· − u + 2
a
1
=
u
26
+ 3u
25
+ ··· + au − 2u
−2u
25
− 2u
24
+ ··· − u + 2
a
6
=
−u
4
a − u
2
a + u
2
+ a
u
4
a + 2u
2
a − u
2
− 1
a
3
=
−2u
26
a + 4u
26
+ ··· − a + 5
2u
26
a − 2u
26
+ ··· + 8u − 1
a
9
=
2u
25
a − 3u
26
+ ··· − 2a + 2
−2u
25
a + 2u
26
+ ··· + 2a − 2
a
8
=
−2u
26
a + 4u
26
+ ··· + a + 3
2u
26
a − 2u
26
+ ··· + 8u − 3
a
2
=
2u
25
a − u
26
+ ··· − 2a + 6
−2u
25
a + 2u
26
+ ··· + 2a − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
25
− 4u
24
− 44u
23
− 40u
22
− 208u
21
− 168u
20
− 536u
19
−
372u
18
− 772u
17
− 432u
16
− 508u
15
− 184u
14
+ 100u
13
+ 92u
12
+ 340u
11
+ 72u
10
+
68u
9
− 48u
8
− 144u
7
− 28u
6
− 76u
5
+ 12u
4
+ 16u
3
+ 20u + 2
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
27
+ 7u
26
+ ··· − 2u − 1)
2
c
2
, c
8
(u
27
− u
26
+ ··· − u
2
− 1)
2
c
3
, c
9
u
54
− 7u
53
+ ··· − 168722854u − 19874761
c
4
, c
10
(u
27
+ u
26
+ ··· + 2u − 1)
2
c
5
, c
6
, c
11
c
12
u
54
− u
53
+ ··· − 532u − 53
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
27
+ 27y
26
+ ··· + 14y −1)
2
c
2
, c
8
(y
27
+ 7y
26
+ ··· − 2y −1)
2
c
3
, c
9
y
54
− 37y
53
+ ··· − 8208746653844232y + 395006124807121
c
4
, c
10
(y
27
+ 23y
26
+ ··· − 2y −1)
2
c
5
, c
6
, c
11
c
12
y
54
− 41y
53
+ ··· − 143528y + 2809
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.278071 + 0.956556I
a = 2.36487 + 0.60631I
b = −2.65845 − 1.76596I
7.99009 − 3.05015I 9.08831 + 1.99178I
u = −0.278071 + 0.956556I
a = −0.31543 + 2.83300I
b = 0.77133 − 2.20533I
7.99009 − 3.05015I 9.08831 + 1.99178I
u = −0.278071 − 0.956556I
a = 2.36487 − 0.60631I
b = −2.65845 + 1.76596I
7.99009 + 3.05015I 9.08831 − 1.99178I
u = −0.278071 − 0.956556I
a = −0.31543 − 2.83300I
b = 0.77133 + 2.20533I
7.99009 + 3.05015I 9.08831 − 1.99178I
u = 0.260338 + 0.833668I
a = 2.60824 + 0.53025I
b = −2.86613 + 0.79958I
8.16912 − 2.83072I 9.79804 + 3.74350I
u = 0.260338 + 0.833668I
a = 0.66908 − 3.18206I
b = −0.03843 + 2.28630I
8.16912 − 2.83072I 9.79804 + 3.74350I
u = 0.260338 − 0.833668I
a = 2.60824 − 0.53025I
b = −2.86613 − 0.79958I
8.16912 + 2.83072I 9.79804 − 3.74350I
u = 0.260338 − 0.833668I
a = 0.66908 + 3.18206I
b = −0.03843 − 2.28630I
8.16912 + 2.83072I 9.79804 − 3.74350I
u = −0.768863 + 0.186622I
a = 0.767167 − 0.556376I
b = −0.732874 − 0.529681I
5.58232 + 7.02686I 5.81546 − 6.08794I
u = −0.768863 + 0.186622I
a = 1.47566 + 0.78554I
b = 0.0463708 + 0.0135400I
5.58232 + 7.02686I 5.81546 − 6.08794I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768863 − 0.186622I
a = 0.767167 + 0.556376I
b = −0.732874 + 0.529681I
5.58232 − 7.02686I 5.81546 + 6.08794I
u = −0.768863 − 0.186622I
a = 1.47566 − 0.78554I
b = 0.0463708 − 0.0135400I
5.58232 − 7.02686I 5.81546 + 6.08794I
u = 0.738973 + 0.201195I
a = 0.724890 + 0.569525I
b = −0.802846 + 0.503503I
6.04391 − 0.96140I 6.72916 + 1.18503I
u = 0.738973 + 0.201195I
a = 1.55361 − 0.82203I
b = 0.0299440 + 0.0463562I
6.04391 − 0.96140I 6.72916 + 1.18503I
u = 0.738973 − 0.201195I
a = 0.724890 − 0.569525I
b = −0.802846 − 0.503503I
6.04391 + 0.96140I 6.72916 − 1.18503I
u = 0.738973 − 0.201195I
a = 1.55361 + 0.82203I
b = 0.0299440 − 0.0463562I
6.04391 + 0.96140I 6.72916 − 1.18503I
u = −0.291604 + 1.207020I
a = −0.661099 + 0.685256I
b = 0.389321 − 0.474702I
2.46677 + 0.98697I 3.17341 + 0.25321I
u = −0.291604 + 1.207020I
a = 0.48769 + 1.53601I
b = −0.58778 − 2.45051I
2.46677 + 0.98697I 3.17341 + 0.25321I
u = −0.291604 − 1.207020I
a = −0.661099 − 0.685256I
b = 0.389321 + 0.474702I
2.46677 − 0.98697I 3.17341 − 0.25321I
u = −0.291604 − 1.207020I
a = 0.48769 − 1.53601I
b = −0.58778 + 2.45051I
2.46677 − 0.98697I 3.17341 − 0.25321I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.750412 + 0.064416I
a = 0.856575 − 0.332457I
b = −0.553343 − 0.268644I
−1.00899 + 2.79673I −0.25981 − 4.61920I
u = −0.750412 + 0.064416I
a = 1.42141 + 0.41171I
b = −0.165674 + 0.092715I
−1.00899 + 2.79673I −0.25981 − 4.61920I
u = −0.750412 − 0.064416I
a = 0.856575 + 0.332457I
b = −0.553343 + 0.268644I
−1.00899 − 2.79673I −0.25981 + 4.61920I
u = −0.750412 − 0.064416I
a = 1.42141 − 0.41171I
b = −0.165674 − 0.092715I
−1.00899 − 2.79673I −0.25981 + 4.61920I
u = 0.082485 + 1.285040I
a = −1.23688 + 0.88472I
b = 0.84651 − 1.71714I
7.63181 − 2.01066I 12.08108 + 3.90758I
u = 0.082485 + 1.285040I
a = −0.56330 − 1.80575I
b = 0.30916 + 2.85016I
7.63181 − 2.01066I 12.08108 + 3.90758I
u = 0.082485 − 1.285040I
a = −1.23688 − 0.88472I
b = 0.84651 + 1.71714I
7.63181 + 2.01066I 12.08108 − 3.90758I
u = 0.082485 − 1.285040I
a = −0.56330 + 1.80575I
b = 0.30916 − 2.85016I
7.63181 + 2.01066I 12.08108 − 3.90758I
u = 0.257867 + 1.292320I
a = −0.657719 − 0.061377I
b = 0.095618 − 0.339940I
5.83412 − 3.27708I 11.27794 + 2.87566I
u = 0.257867 + 1.292320I
a = 0.16467 − 1.58727I
b = −0.20616 + 2.65508I
5.83412 − 3.27708I 11.27794 + 2.87566I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.257867 − 1.292320I
a = −0.657719 + 0.061377I
b = 0.095618 + 0.339940I
5.83412 + 3.27708I 11.27794 − 2.87566I
u = 0.257867 − 1.292320I
a = 0.16467 + 1.58727I
b = −0.20616 − 2.65508I
5.83412 + 3.27708I 11.27794 − 2.87566I
u = −0.317436 + 1.304880I
a = 0.20283 + 1.46123I
b = −0.11439 − 2.50885I
3.27233 + 6.65682I 5.19788 − 7.22011I
u = −0.317436 + 1.304880I
a = −0.350883 + 0.118774I
b = −0.339506 + 0.100412I
3.27233 + 6.65682I 5.19788 − 7.22011I
u = −0.317436 − 1.304880I
a = 0.20283 − 1.46123I
b = −0.11439 + 2.50885I
3.27233 − 6.65682I 5.19788 + 7.22011I
u = −0.317436 − 1.304880I
a = −0.350883 − 0.118774I
b = −0.339506 − 0.100412I
3.27233 − 6.65682I 5.19788 + 7.22011I
u = 0.649647
a = 0.553820
b = −0.766265
1.77816 5.74170
u = 0.649647
a = 1.85261
b = −0.218123
1.77816 5.74170
u = 0.307012 + 1.374630I
a = 0.11853 − 1.41160I
b = −0.02134 + 2.63436I
11.02600 − 4.75862I 11.32590 + 2.41055I
u = 0.307012 + 1.374630I
a = −0.301203 + 0.156502I
b = −0.591333 − 0.535207I
11.02600 − 4.75862I 11.32590 + 2.41055I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.307012 − 1.374630I
a = 0.11853 + 1.41160I
b = −0.02134 − 2.63436I
11.02600 + 4.75862I 11.32590 − 2.41055I
u = 0.307012 − 1.374630I
a = −0.301203 − 0.156502I
b = −0.591333 + 0.535207I
11.02600 + 4.75862I 11.32590 − 2.41055I
u = −0.322115 + 1.372980I
a = 0.135135 + 1.402660I
b = −0.00005 − 2.61810I
10.5129 + 10.9775I 10.31167 − 7.27184I
u = −0.322115 + 1.372980I
a = −0.257057 − 0.132543I
b = −0.659339 + 0.463470I
10.5129 + 10.9775I 10.31167 − 7.27184I
u = −0.322115 − 1.372980I
a = 0.135135 − 1.402660I
b = −0.00005 + 2.61810I
10.5129 − 10.9775I 10.31167 + 7.27184I
u = −0.322115 − 1.372980I
a = −0.257057 + 0.132543I
b = −0.659339 − 0.463470I
10.5129 − 10.9775I 10.31167 + 7.27184I
u = 0.01000 + 1.42794I
a = −0.476092 + 1.070440I
b = −0.05987 − 2.19612I
15.0119 − 3.1530I 13.82291 + 2.60032I
u = 0.01000 + 1.42794I
a = −0.447560 − 1.123330I
b = −0.05538 + 2.27757I
15.0119 − 3.1530I 13.82291 + 2.60032I
u = 0.01000 − 1.42794I
a = −0.476092 − 1.070440I
b = −0.05987 + 2.19612I
15.0119 + 3.1530I 13.82291 − 2.60032I
u = 0.01000 − 1.42794I
a = −0.447560 + 1.123330I
b = −0.05538 − 2.27757I
15.0119 + 3.1530I 13.82291 − 2.60032I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.247000 + 0.300914I
a = 0.24147 + 2.21936I
b = −1.337040 − 0.029666I
2.93764 − 0.95364I 5.76719 + 7.10310I
u = 0.247000 + 0.300914I
a = 2.77217 − 2.52780I
b = −0.706130 + 0.486758I
2.93764 − 0.95364I 5.76719 + 7.10310I
u = 0.247000 − 0.300914I
a = 0.24147 − 2.21936I
b = −1.337040 + 0.029666I
2.93764 + 0.95364I 5.76719 − 7.10310I
u = 0.247000 − 0.300914I
a = 2.77217 + 2.52780I
b = −0.706130 − 0.486758I
2.93764 + 0.95364I 5.76719 − 7.10310I
18
III. I
u
3
= hu
3
− u
2
+ 5b + 2u + 3, 3u
3
+ 2u
2
+ 10a − 14u − 6, u
4
− 2u
2
+ 2i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
7
=
−
3
10
u
3
−
1
5
u
2
+
7
5
u +
3
5
−
1
5
u
3
+
1
5
u
2
−
2
5
u −
3
5
a
11
=
−u
u
a
12
=
−
3
10
u
3
−
1
5
u
2
+
2
5
u +
3
5
−
1
5
u
3
+
1
5
u
2
+
3
5
u −
3
5
a
1
=
−
3
10
u
3
−
1
5
u
2
+
2
5
u −
2
5
−
1
5
u
3
−
4
5
u
2
+
3
5
u −
3
5
a
6
=
−
3
10
u
3
−
1
5
u
2
+
2
5
u +
3
5
−
1
5
u
3
+
1
5
u
2
+
3
5
u −
3
5
a
3
=
−
1
50
u
3
+
4
25
u + 1
8
25
u
3
−
1
5
u
2
−
14
25
u +
3
5
a
9
=
3
10
u
3
+
8
25
u
2
−
2
5
u −
14
25
−
3
25
u
2
+ u −
1
25
a
8
=
−
1
10
u
3
−
3
25
u
2
+
4
5
u −
1
25
4
5
u
3
−
2
25
u
2
−
2
5
u −
9
25
a
2
=
−
9
50
u
3
+
4
5
u
2
+
11
25
u −
2
5
−
3
25
u
3
−
3
5
u
2
−
1
25
u −
1
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
+ 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
− 2u + 2)
2
c
2
, c
8
u
4
+ 2u
2
+ 2
c
3
, c
9
25(25u
4
+ 40u
3
+ 12u
2
− 4u + 1)
c
4
, c
10
u
4
− 2u
2
+ 2
c
5
, c
11
(u + 1)
4
c
6
, c
12
(u − 1)
4
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
+ 4)
2
c
2
, c
8
(y
2
+ 2y + 2)
2
c
3
, c
9
625(625y
4
− 1000y
3
+ 514y
2
+ 8y + 1)
c
4
, c
10
(y
2
− 2y + 2)
2
c
5
, c
6
, c
11
c
12
(y −1)
4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098680 + 0.455090I
a = 1.74508 − 0.02901I
b = −0.968192 − 0.292791I
0.82247 − 3.66386I 8.00000 + 4.00000I
u = 1.098680 − 0.455090I
a = 1.74508 + 0.02901I
b = −0.968192 + 0.292791I
0.82247 + 3.66386I 8.00000 − 4.00000I
u = −1.098680 + 0.455090I
a = −0.945079 + 0.370994I
b = 0.168192 − 0.692791I
0.82247 + 3.66386I 8.00000 − 4.00000I
u = −1.098680 − 0.455090I
a = −0.945079 − 0.370994I
b = 0.168192 + 0.692791I
0.82247 − 3.66386I 8.00000 + 4.00000I
22
IV. I
u
4
= hb + a − 1, 8a
3
+ 4a
2
u − 12a
2
− 4au + 2a + 1, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−1
a
7
=
a
−a + 1
a
11
=
−u
u
a
12
=
au − u
−au + 2u
a
1
=
au
−au + u
a
6
=
a + 1
−a
a
3
=
−a
2
− a + 1
a
2
a
9
=
a
2
u − 2au + u
−a
2
u + 3au − u
a
8
=
a
2
u + 2a
2
− au −
5
2
a +
5
4
−a
2
u − 4a
2
+ au +
7
2
a −
1
4
a
2
=
−4a
2
u − a
2
+
9
2
au + a −
3
4
u
2a
2
u + a
2
−
3
2
au − a +
3
4
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 16a
2
+ 8au − 16a − 4u + 4
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
8
u
6
+ u
4
+ 2u
2
+ 1
c
3
, c
9
64(64u
6
+ 192u
5
+ 192u
4
+ 64u
3
− 4u
2
− 4u + 1)
c
4
, c
5
, c
6
c
10
, c
11
, c
12
(u
2
+ 1)
3
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
8
(y
3
+ y
2
+ 2y + 1)
2
c
3
, c
9
4096(4096y
6
− 12288y
5
+ 11776y
4
− 3968y
3
+ 912y
2
− 24y + 1)
c
4
, c
5
, c
6
c
10
, c
11
, c
12
(y + 1)
6
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.153570 − 0.107540I
b = −0.153571 + 0.107540I
3.02413 − 2.82812I 7.50976 + 2.97945I
u = 1.000000I
a = 0.500000 − 0.284920I
b = 0.500000 + 0.284920I
−1.11345 − 60.980489 + 0.10I
u = 1.000000I
a = −0.153571 − 0.107540I
b = 1.153570 + 0.107540I
3.02413 + 2.82812I 7.50976 − 2.97945I
u = − 1.000000I
a = 1.153570 + 0.107540I
b = −0.153571 − 0.107540I
3.02413 + 2.82812I 7.50976 − 2.97945I
u = − 1.000000I
a = 0.500000 + 0.284920I
b = 0.500000 − 0.284920I
−1.11345 − 60.980489 + 0.10I
u = − 1.000000I
a = −0.153571 + 0.107540I
b = 1.153570 − 0.107540I
3.02413 − 2.82812I 7.50976 + 2.97945I
26
V. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
−1
0
a
5
=
1
0
a
7
=
0
−1
a
11
=
−1
0
a
12
=
−1
1
a
1
=
0
1
a
6
=
1
−1
a
3
=
0
1
a
9
=
0
−1
a
8
=
0
−1
a
2
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
u
c
3
, c
6
, c
9
c
12
u + 1
c
5
, c
11
u − 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
8
, c
10
y
c
3
, c
5
, c
6
c
9
, c
11
, c
12
y −1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
3.28987 12.0000
30
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u(u
2
− 2u + 2)
2
(u
3
− u
2
+ 2u − 1)
2
(u
27
+ 7u
26
+ ··· − 2u − 1)
2
· (u
41
+ 13u
40
+ ··· − 1260u − 100)
c
2
, c
8
u(u
4
+ 2u
2
+ 2)(u
6
+ u
4
+ 2u
2
+ 1)(u
27
− u
26
+ ··· − u
2
− 1)
2
· (u
41
+ 3u
40
+ ··· − 10u + 10)
c
3
, c
9
102400(u + 1)(25u
4
+ 40u
3
+ 12u
2
− 4u + 1)
· (64u
6
+ 192u
5
+ 192u
4
+ 64u
3
− 4u
2
− 4u + 1)
· (64u
41
+ 256u
40
+ ··· − 13u
2
− 1)
· (u
54
− 7u
53
+ ··· − 168722854u − 19874761)
c
4
, c
10
u(u
2
+ 1)
3
(u
4
− 2u
2
+ 2)(u
27
+ u
26
+ ··· + 2u − 1)
2
· (u
41
− 3u
40
+ ··· − 434u + 50)
c
5
, c
11
(u − 1)(u + 1)
4
(u
2
+ 1)
3
(u
41
− u
40
+ ··· + 14u − 1)
· (u
54
− u
53
+ ··· − 532u − 53)
c
6
, c
12
((u − 1)
4
)(u + 1)(u
2
+ 1)
3
(u
41
− u
40
+ ··· + 14u − 1)
· (u
54
− u
53
+ ··· − 532u − 53)
31
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y(y
2
+ 4)
2
(y
3
+ 3y
2
+ 2y −1)
2
(y
27
+ 27y
26
+ ··· + 14y −1)
2
· (y
41
+ 33y
40
+ ··· − 489200y −10000)
c
2
, c
8
y(y
2
+ 2y + 2)
2
(y
3
+ y
2
+ 2y + 1)
2
(y
27
+ 7y
26
+ ··· − 2y −1)
2
· (y
41
+ 13y
40
+ ··· − 1260y −100)
c
3
, c
9
10485760000(y −1)(625y
4
− 1000y
3
+ 514y
2
+ 8y + 1)
· (4096y
6
− 12288y
5
+ 11776y
4
− 3968y
3
+ 912y
2
− 24y + 1)
· (4096y
41
− 147456y
40
+ ··· − 26y −1)
· (y
54
− 37y
53
+ ··· − 8208746653844232y + 395006124807121)
c
4
, c
10
y(y + 1)
6
(y
2
− 2y + 2)
2
(y
27
+ 23y
26
+ ··· − 2y −1)
2
· (y
41
+ 25y
40
+ ··· − 199044y −2500)
c
5
, c
6
, c
11
c
12
((y −1)
5
)(y + 1)
6
(y
41
− 31y
40
+ ··· − 96y −1)
· (y
54
− 41y
53
+ ··· − 143528y + 2809)
32
