12a
0706
(K12a
0706
)
A knot diagram
1
Linearized knot diagam
3 8 6 12 9 11 2 1 5 7 4 10
Solving Sequence
2,7
8 3 1
9,11
6 4 5 10 12
c
7
c
2
c
1
c
8
c
6
c
3
c
5
c
10
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.77122 × 10
31
u
42
+ 1.28986 × 10
32
u
41
+ ··· + 6.23372 × 10
32
b − 4.00675 × 10
32
,
4.66471 × 10
32
u
42
− 7.74777 × 10
32
u
41
+ ··· + 2.49349 × 10
33
a + 4.88238 × 10
33
, u
43
− 3u
42
+ ··· − 28u + 8i
I
u
2
= h−338u
34
a + 751u
34
+ ··· + 2112a − 1193, 90u
34
a − 8u
34
+ ··· + 5a + 274, u
35
+ u
34
+ ··· + 2u + 1i
I
u
3
= hb + 1, −u
3
− 4u
2
+ 4a + 6, u
4
− 2u
2
+ 2i
I
v
1
= ha, b − 1, 2v −1i
* 4 irreducible components of dim
C
= 0, with total 118 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−8.77 × 10
31
u
42
+ 1.29 × 10
32
u
41
+ · · · + 6.23 × 10
32
b − 4.01 ×
10
32
, 4.66 × 10
32
u
42
− 7.75 × 10
32
u
41
+ · · · + 2.49 × 10
33
a + 4.88 ×
10
33
, u
43
− 3u
42
+ · · · − 28u + 8i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
11
=
−0.187076u
42
+ 0.310720u
41
+ ··· − 1.10826u − 1.95805
0.140706u
42
− 0.206917u
41
+ ··· + 0.489729u + 0.642754
a
6
=
−0.0109355u
42
+ 0.0220436u
41
+ ··· − 0.0604385u + 0.806906
−0.00913229u
42
− 0.0157531u
41
+ ··· − 0.674511u + 0.907667
a
4
=
0.0216414u
42
− 0.0230274u
41
+ ··· + 0.532942u − 0.0730053
0.0852608u
42
− 0.239690u
41
+ ··· + 2.60820u − 0.0463949
a
5
=
−0.0643673u
42
+ 0.170970u
41
+ ··· − 2.78169u + 2.70928
−0.0198900u
42
− 0.0117962u
41
+ ··· − 0.613345u + 0.548201
a
10
=
−0.0463696u
42
+ 0.103803u
41
+ ··· − 0.618528u − 1.31530
0.140706u
42
− 0.206917u
41
+ ··· + 0.489729u + 0.642754
a
12
=
−0.157589u
42
+ 0.303639u
41
+ ··· − 3.64692u + 0.181125
0.0870361u
42
− 0.136522u
41
+ ··· + 1.11816u + 0.638551
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.255497u
42
− 0.304541u
41
+ ··· + 16.6870u + 2.47466
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
43
+ 21u
42
+ ··· + 272u + 64
c
2
, c
7
u
43
− 3u
42
+ ··· − 28u + 8
c
3
, c
12
128(128u
43
+ 576u
42
+ ··· + u + 1)
c
4
, c
11
u
43
− 18u
41
+ ··· + 889u + 416
c
5
, c
6
, c
9
c
10
u
43
− u
42
+ ··· − 24u + 5
c
8
u
43
− 9u
42
+ ··· + 2332u + 2968
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
43
+ 3y
42
+ ··· − 36608y −4096
c
2
, c
7
y
43
− 21y
42
+ ··· + 272y −64
c
3
, c
12
16384(16384y
43
− 274432y
42
+ ··· + 75y −1)
c
4
, c
11
y
43
− 36y
42
+ ··· + 989169y −173056
c
5
, c
6
, c
9
c
10
y
43
+ 19y
42
+ ··· + 126y −25
c
8
y
43
+ 15y
42
+ ··· + 81561488y −8809024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.364395 + 0.877924I
a = 0.04638 − 1.82403I
b = 0.391782 + 1.198260I
4.01698 − 7.46652I 3.11751 + 6.34023I
u = −0.364395 − 0.877924I
a = 0.04638 + 1.82403I
b = 0.391782 − 1.198260I
4.01698 + 7.46652I 3.11751 − 6.34023I
u = 0.756742 + 0.762090I
a = 0.61467 − 2.10710I
b = 0.38983 + 1.39078I
12.3032 − 10.3019I 6.09134 + 7.29034I
u = 0.756742 − 0.762090I
a = 0.61467 + 2.10710I
b = 0.38983 − 1.39078I
12.3032 + 10.3019I 6.09134 − 7.29034I
u = 0.309821 + 0.864620I
a = 0.23217 + 1.87818I
b = 0.54746 − 1.38673I
9.6780 + 13.4175I 4.66358 − 6.56976I
u = 0.309821 − 0.864620I
a = 0.23217 − 1.87818I
b = 0.54746 + 1.38673I
9.6780 − 13.4175I 4.66358 + 6.56976I
u = 0.263698 + 1.077760I
a = 0.063581 + 1.403550I
b = −0.030867 − 1.141810I
7.30362 − 1.07498I 16.0017 + 3.6754I
u = 0.263698 − 1.077760I
a = 0.063581 − 1.403550I
b = −0.030867 + 1.141810I
7.30362 + 1.07498I 16.0017 − 3.6754I
u = −1.045620 + 0.374301I
a = 1.32312 + 1.26742I
b = 1.240050 − 0.457624I
−2.30003 + 1.95260I −1.79739 + 0.90426I
u = −1.045620 − 0.374301I
a = 1.32312 − 1.26742I
b = 1.240050 + 0.457624I
−2.30003 − 1.95260I −1.79739 − 0.90426I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.044540 + 0.384315I
a = 0.304099 + 0.657915I
b = −0.100329 − 0.404925I
−0.22935 − 3.67460I −0.89632 + 6.35112I
u = 1.044540 − 0.384315I
a = 0.304099 − 0.657915I
b = −0.100329 + 0.404925I
−0.22935 + 3.67460I −0.89632 − 6.35112I
u = −0.846910 + 0.182966I
a = 0.062155 + 0.638512I
b = −0.715260 − 0.471235I
−0.998880 + 0.351600I −6.01917 − 1.74255I
u = −0.846910 − 0.182966I
a = 0.062155 − 0.638512I
b = −0.715260 + 0.471235I
−0.998880 − 0.351600I −6.01917 + 1.74255I
u = 0.867602 + 0.745647I
a = 0.99486 − 1.48397I
b = −0.307161 + 1.363000I
11.98760 + 4.69062I 6.27466 − 2.28196I
u = 0.867602 − 0.745647I
a = 0.99486 + 1.48397I
b = −0.307161 − 1.363000I
11.98760 − 4.69062I 6.27466 + 2.28196I
u = 1.079400 + 0.517359I
a = −0.01844 − 1.52789I
b = 1.49377 − 0.29947I
−1.25135 − 4.90293I 2.46086 + 7.07158I
u = 1.079400 − 0.517359I
a = −0.01844 + 1.52789I
b = 1.49377 + 0.29947I
−1.25135 + 4.90293I 2.46086 − 7.07158I
u = −0.790225 + 0.907782I
a = 0.45900 + 1.60463I
b = 0.082408 − 1.150310I
6.23041 + 3.24342I 11.79096 − 7.78462I
u = −0.790225 − 0.907782I
a = 0.45900 − 1.60463I
b = 0.082408 + 1.150310I
6.23041 − 3.24342I 11.79096 + 7.78462I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.136540 + 0.399301I
a = 1.014030 − 0.675093I
b = 0.799216 + 0.538229I
−4.92648 − 4.54280I −9.30891 + 6.68648I
u = 1.136540 − 0.399301I
a = 1.014030 + 0.675093I
b = 0.799216 − 0.538229I
−4.92648 + 4.54280I −9.30891 − 6.68648I
u = 1.217380 + 0.123691I
a = −0.278389 − 0.273065I
b = −0.417369 + 1.014720I
−1.53276 + 4.52647I −3.84680 − 6.77592I
u = 1.217380 − 0.123691I
a = −0.278389 + 0.273065I
b = −0.417369 − 1.014720I
−1.53276 − 4.52647I −3.84680 + 6.77592I
u = −1.127830 + 0.474826I
a = 0.096382 + 0.762504I
b = 0.864085 + 0.359880I
−4.41300 + 3.28480I −9.46585 − 1.64947I
u = −1.127830 − 0.474826I
a = 0.096382 − 0.762504I
b = 0.864085 − 0.359880I
−4.41300 − 3.28480I −9.46585 + 1.64947I
u = −1.238660 + 0.218673I
a = −0.381217 − 0.075299I
b = −0.53587 − 1.30966I
4.54892 − 10.07780I −0.39399 + 5.36382I
u = −1.238660 − 0.218673I
a = −0.381217 + 0.075299I
b = −0.53587 + 1.30966I
4.54892 + 10.07780I −0.39399 − 5.36382I
u = −1.153790 + 0.610907I
a = −1.48361 − 1.48093I
b = −0.458133 + 1.229980I
1.62850 + 12.94670I 0. − 9.56767I
u = −1.153790 − 0.610907I
a = −1.48361 + 1.48093I
b = −0.458133 − 1.229980I
1.62850 − 12.94670I 0. + 9.56767I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.694049
a = −0.0645283
b = −0.550881
−1.02637 −10.0280
u = 1.167800 + 0.591087I
a = −1.86194 + 1.44933I
b = −0.58874 − 1.39305I
7.1025 − 18.7791I 1.67063 + 10.13873I
u = 1.167800 − 0.591087I
a = −1.86194 − 1.44933I
b = −0.58874 + 1.39305I
7.1025 + 18.7791I 1.67063 − 10.13873I
u = 0.370173 + 0.562820I
a = 0.890218 + 0.191663I
b = −1.40761 − 0.15779I
0.787413 + 0.515759I 8.15856 − 2.76240I
u = 0.370173 − 0.562820I
a = 0.890218 − 0.191663I
b = −1.40761 + 0.15779I
0.787413 − 0.515759I 8.15856 + 2.76240I
u = −0.085379 + 0.627851I
a = 0.241341 − 0.446824I
b = −0.728213 + 0.394310I
−1.60222 + 0.88694I −6.18860 − 3.12820I
u = −0.085379 − 0.627851I
a = 0.241341 + 0.446824I
b = −0.728213 − 0.394310I
−1.60222 − 0.88694I −6.18860 + 3.12820I
u = 1.208770 + 0.701017I
a = −0.901694 + 1.038270I
b = −0.114387 − 1.123360I
4.48482 − 5.24026I 9.16270 + 10.48846I
u = 1.208770 − 0.701017I
a = −0.901694 − 1.038270I
b = −0.114387 + 1.123360I
4.48482 + 5.24026I 9.16270 − 10.48846I
u = −1.342780 + 0.405991I
a = 0.590693 + 0.381161I
b = 0.193810 − 1.053580I
2.11212 + 6.10939I 0. − 12.47941I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.342780 − 0.405991I
a = 0.590693 − 0.381161I
b = 0.193810 + 1.053580I
2.11212 − 6.10939I 0. + 12.47941I
u = 0.420151 + 0.385137I
a = −1.47515 + 0.40144I
b = 0.176966 − 0.117588I
1.51091 + 0.21948I 6.61608 − 0.74738I
u = 0.420151 − 0.385137I
a = −1.47515 − 0.40144I
b = 0.176966 + 0.117588I
1.51091 − 0.21948I 6.61608 + 0.74738I
9
II. I
u
2
= h−338u
34
a + 751u
34
+ · · · + 2112a − 1193, 90u
34
a − 8u
34
+ · · · +
5a + 274, u
35
+ u
34
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
11
=
a
0.0725789au
34
− 0.161263u
34
+ ··· − 0.453511a + 0.256174
a
6
=
−0.161263au
34
+ 1.98020u
34
+ ··· + 0.256174a − 0.298776
0.120464au
34
+ 0.0725789u
34
+ ··· + 0.0283444a + 0.546489
a
4
=
−2.63629au
34
− 1.29937u
34
+ ··· − 0.973245a − 4.98809
0.000858922au
34
− 2.41374u
34
+ ··· − 0.0586214a − 0.862057
a
5
=
−0.161263au
34
+ 1.98020u
34
+ ··· + 0.256174a − 1.29878
1
a
10
=
0.0725789au
34
− 0.161263u
34
+ ··· + 0.546489a + 0.256174
0.0725789au
34
− 0.161263u
34
+ ··· − 0.453511a + 0.256174
a
12
=
−2.41374au
34
− 0.700116u
34
+ ··· − 0.862057a − 2.24709
0.439768au
34
− 2.63629u
34
+ ··· − 0.0141722a − 0.973245
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
33
−32u
31
−4u
30
+ 132u
29
+ 28u
28
−348u
27
−100u
26
+ 644u
25
+ 224u
24
−868u
23
−
344u
22
+ 880u
21
+ 376u
20
− 700u
19
− 312u
18
+ 488u
17
+ 228u
16
− 336u
15
− 180u
14
+
232u
13
+140u
12
−136u
11
−88u
10
+72u
9
+44u
8
−32u
7
−24u
6
+16u
5
+16u
4
−4u
3
−8u
2
+6
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
35
+ 17u
34
+ ··· + 2u + 1)
2
c
2
, c
7
(u
35
+ u
34
+ ··· + 2u + 1)
2
c
3
, c
12
25(25u
70
− 165u
69
+ ··· + 4.75915 × 10
8
u + 3.82582 × 10
7
)
c
4
, c
11
(u
35
− u
34
+ ··· + u
2
− 1)
2
c
5
, c
6
, c
9
c
10
u
70
+ 3u
69
+ ··· + 8u + 1
c
8
(u
35
+ 3u
34
+ ··· + 58u + 7)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
35
+ 3y
34
+ ··· − 14y −1)
2
c
2
, c
7
(y
35
− 17y
34
+ ··· + 2y −1)
2
c
3
, c
12
625(625y
70
− 23125y
69
+ ··· − 1.79208 × 10
16
y + 1.46369 × 10
15
)
c
4
, c
11
(y
35
− 29y
34
+ ··· + 2y −1)
2
c
5
, c
6
, c
9
c
10
y
70
+ 47y
69
+ ··· + 16y + 1
c
8
(y
35
+ 11y
34
+ ··· + 1446y −49)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.890522 + 0.542191I
a = 0.420148 − 1.134650I
b = −0.887010 − 0.496104I
6.32924 − 0.83862I 3.46140 − 0.32367I
u = −0.890522 + 0.542191I
a = −1.81892 − 1.34506I
b = 0.17214 + 1.46425I
6.32924 − 0.83862I 3.46140 − 0.32367I
u = −0.890522 − 0.542191I
a = 0.420148 + 1.134650I
b = −0.887010 + 0.496104I
6.32924 + 0.83862I 3.46140 + 0.32367I
u = −0.890522 − 0.542191I
a = −1.81892 + 1.34506I
b = 0.17214 − 1.46425I
6.32924 + 0.83862I 3.46140 + 0.32367I
u = 0.996188 + 0.423828I
a = −0.787246 + 0.845478I
b = −0.352524 + 0.767455I
1.75221 − 1.71623I −3.26691 − 0.12597I
u = 0.996188 + 0.423828I
a = −1.23437 + 1.84232I
b = −0.064633 − 1.226040I
1.75221 − 1.71623I −3.26691 − 0.12597I
u = 0.996188 − 0.423828I
a = −0.787246 − 0.845478I
b = −0.352524 − 0.767455I
1.75221 + 1.71623I −3.26691 + 0.12597I
u = 0.996188 − 0.423828I
a = −1.23437 − 1.84232I
b = −0.064633 + 1.226040I
1.75221 + 1.71623I −3.26691 + 0.12597I
u = −0.665614 + 0.623440I
a = −0.439114 + 0.434345I
b = 1.033840 − 0.288357I
6.99216 + 5.45820I 4.60996 − 5.96309I
u = −0.665614 + 0.623440I
a = −0.40352 − 2.35368I
b = −0.34875 + 1.47367I
6.99216 + 5.45820I 4.60996 − 5.96309I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.665614 − 0.623440I
a = −0.439114 − 0.434345I
b = 1.033840 + 0.288357I
6.99216 − 5.45820I 4.60996 + 5.96309I
u = −0.665614 − 0.623440I
a = −0.40352 + 2.35368I
b = −0.34875 − 1.47367I
6.99216 − 5.45820I 4.60996 + 5.96309I
u = −0.903342
a = −1.89131 + 1.48396I
b = −0.344219 + 1.164240I
5.63430 0.141130
u = −0.903342
a = −1.89131 − 1.48396I
b = −0.344219 − 1.164240I
5.63430 0.141130
u = 0.688085 + 0.531421I
a = 0.212009 + 0.451127I
b = 0.336278 + 0.239728I
2.50904 − 2.01862I −1.09133 + 4.63726I
u = 0.688085 + 0.531421I
a = −0.88597 + 2.22330I
b = −0.108999 − 1.142220I
2.50904 − 2.01862I −1.09133 + 4.63726I
u = 0.688085 − 0.531421I
a = 0.212009 − 0.451127I
b = 0.336278 − 0.239728I
2.50904 + 2.01862I −1.09133 − 4.63726I
u = 0.688085 − 0.531421I
a = −0.88597 − 2.22330I
b = −0.108999 + 1.142220I
2.50904 + 2.01862I −1.09133 − 4.63726I
u = −1.059800 + 0.502369I
a = 0.26147 + 1.61880I
b = −0.234288 − 1.162630I
2.48084 + 4.67146I −0.51273 − 7.37463I
u = −1.059800 + 0.502369I
a = −2.79747 − 1.54656I
b = −0.319958 + 1.048700I
2.48084 + 4.67146I −0.51273 − 7.37463I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.059800 − 0.502369I
a = 0.26147 − 1.61880I
b = −0.234288 + 1.162630I
2.48084 − 4.67146I −0.51273 + 7.37463I
u = −1.059800 − 0.502369I
a = −2.79747 + 1.54656I
b = −0.319958 − 1.048700I
2.48084 − 4.67146I −0.51273 + 7.37463I
u = 1.146120 + 0.254789I
a = −1.037470 + 0.622193I
b = −1.044800 − 0.117101I
0.76959 + 4.45397I −3.15239 − 2.81525I
u = 1.146120 + 0.254789I
a = 0.169760 − 0.407579I
b = 0.59055 − 1.28795I
0.76959 + 4.45397I −3.15239 − 2.81525I
u = 1.146120 − 0.254789I
a = −1.037470 − 0.622193I
b = −1.044800 + 0.117101I
0.76959 − 4.45397I −3.15239 + 2.81525I
u = 1.146120 − 0.254789I
a = 0.169760 + 0.407579I
b = 0.59055 + 1.28795I
0.76959 − 4.45397I −3.15239 + 2.81525I
u = −0.308085 + 0.766136I
a = −0.588916 − 0.042005I
b = 1.177980 + 0.012281I
5.25576 − 7.38977I 3.01566 + 5.00078I
u = −0.308085 + 0.766136I
a = −0.10013 + 1.93999I
b = −0.58139 − 1.43466I
5.25576 − 7.38977I 3.01566 + 5.00078I
u = −0.308085 − 0.766136I
a = −0.588916 + 0.042005I
b = 1.177980 − 0.012281I
5.25576 + 7.38977I 3.01566 − 5.00078I
u = −0.308085 − 0.766136I
a = −0.10013 − 1.93999I
b = −0.58139 + 1.43466I
5.25576 + 7.38977I 3.01566 − 5.00078I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.142990 + 0.287310I
a = −0.674948 − 0.484137I
b = −0.687825 + 0.345199I
−3.52386 − 0.30557I −7.68573 + 0.05854I
u = −1.142990 + 0.287310I
a = 0.277824 + 0.046595I
b = 0.500699 + 0.963199I
−3.52386 − 0.30557I −7.68573 + 0.05854I
u = −1.142990 − 0.287310I
a = −0.674948 + 0.484137I
b = −0.687825 − 0.345199I
−3.52386 + 0.30557I −7.68573 − 0.05854I
u = −1.142990 − 0.287310I
a = 0.277824 − 0.046595I
b = 0.500699 − 0.963199I
−3.52386 + 0.30557I −7.68573 − 0.05854I
u = 0.460984 + 0.678579I
a = −0.07948 + 1.72676I
b = 0.69761 − 1.36017I
10.08710 + 1.04155I 7.85373 − 0.57295I
u = 0.460984 + 0.678579I
a = 0.11349 − 2.12206I
b = 0.50150 + 1.51702I
10.08710 + 1.04155I 7.85373 − 0.57295I
u = 0.460984 − 0.678579I
a = −0.07948 − 1.72676I
b = 0.69761 + 1.36017I
10.08710 − 1.04155I 7.85373 + 0.57295I
u = 0.460984 − 0.678579I
a = 0.11349 + 2.12206I
b = 0.50150 − 1.51702I
10.08710 − 1.04155I 7.85373 + 0.57295I
u = 1.141570 + 0.325389I
a = 0.336135 + 0.693863I
b = 0.278779 − 0.228359I
−0.03490 − 3.85709I −4.01107 + 3.91391I
u = 1.141570 + 0.325389I
a = −0.0437808 + 0.0663890I
b = −0.186633 − 0.896468I
−0.03490 − 3.85709I −4.01107 + 3.91391I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.141570 − 0.325389I
a = 0.336135 − 0.693863I
b = 0.278779 + 0.228359I
−0.03490 + 3.85709I −4.01107 − 3.91391I
u = 1.141570 − 0.325389I
a = −0.0437808 − 0.0663890I
b = −0.186633 + 0.896468I
−0.03490 + 3.85709I −4.01107 − 3.91391I
u = 1.053770 + 0.564883I
a = 1.44332 − 0.58846I
b = −0.41775 + 1.60635I
8.34984 − 5.85664I 4.52563 + 5.76903I
u = 1.053770 + 0.564883I
a = −1.89148 + 1.53790I
b = −0.81409 − 1.29517I
8.34984 − 5.85664I 4.52563 + 5.76903I
u = 1.053770 − 0.564883I
a = 1.44332 + 0.58846I
b = −0.41775 − 1.60635I
8.34984 + 5.85664I 4.52563 − 5.76903I
u = 1.053770 − 0.564883I
a = −1.89148 − 1.53790I
b = −0.81409 + 1.29517I
8.34984 + 5.85664I 4.52563 − 5.76903I
u = 0.276974 + 0.740238I
a = −0.352310 − 0.333827I
b = 0.706334 + 0.106935I
0.71532 + 3.36312I −1.83397 − 3.13288I
u = 0.276974 + 0.740238I
a = −0.34322 − 1.79653I
b = −0.401602 + 1.116130I
0.71532 + 3.36312I −1.83397 − 3.13288I
u = 0.276974 − 0.740238I
a = −0.352310 + 0.333827I
b = 0.706334 − 0.106935I
0.71532 − 3.36312I −1.83397 + 3.13288I
u = 0.276974 − 0.740238I
a = −0.34322 + 1.79653I
b = −0.401602 − 1.116130I
0.71532 − 3.36312I −1.83397 + 3.13288I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.131430 + 0.520956I
a = −0.415635 + 0.780636I
b = −0.159300 + 0.136630I
1.28903 + 4.02658I −2.00000 − 2.90516I
u = −1.131430 + 0.520956I
a = 2.00512 + 0.91973I
b = 0.063369 − 1.070960I
1.28903 + 4.02658I −2.00000 − 2.90516I
u = −1.131430 − 0.520956I
a = −0.415635 − 0.780636I
b = −0.159300 − 0.136630I
1.28903 − 4.02658I −2.00000 + 2.90516I
u = −1.131430 − 0.520956I
a = 2.00512 − 0.91973I
b = 0.063369 + 1.070960I
1.28903 − 4.02658I −2.00000 + 2.90516I
u = 1.134810 + 0.545503I
a = −0.088444 + 0.629026I
b = −0.834149 + 0.124912I
−1.77646 − 8.22097I −4.85255 + 6.68822I
u = 1.134810 + 0.545503I
a = 1.72527 − 1.36047I
b = 0.480581 + 1.168070I
−1.77646 − 8.22097I −4.85255 + 6.68822I
u = 1.134810 − 0.545503I
a = −0.088444 − 0.629026I
b = −0.834149 − 0.124912I
−1.77646 + 8.22097I −4.85255 − 6.68822I
u = 1.134810 − 0.545503I
a = 1.72527 + 1.36047I
b = 0.480581 − 1.168070I
−1.77646 + 8.22097I −4.85255 − 6.68822I
u = −1.134940 + 0.561389I
a = −0.215432 − 1.235000I
b = −1.249680 − 0.050047I
2.82939 + 12.38410I −0.15786 − 8.57579I
u = −1.134940 + 0.561389I
a = 1.90003 + 1.45902I
b = 0.65668 − 1.44821I
2.82939 + 12.38410I −0.15786 − 8.57579I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.134940 − 0.561389I
a = −0.215432 + 1.235000I
b = −1.249680 + 0.050047I
2.82939 − 12.38410I −0.15786 + 8.57579I
u = −1.134940 − 0.561389I
a = 1.90003 − 1.45902I
b = 0.65668 + 1.44821I
2.82939 − 12.38410I −0.15786 + 8.57579I
u = −0.217277 + 0.699987I
a = 0.157163 + 1.157450I
b = −0.113324 + 0.190551I
3.88220 + 0.59945I 1.29885 − 0.74081I
u = −0.217277 + 0.699987I
a = −1.27039 + 1.48005I
b = 0.040324 − 1.086570I
3.88220 + 0.59945I 1.29885 − 0.74081I
u = −0.217277 − 0.699987I
a = 0.157163 − 1.157450I
b = −0.113324 − 0.190551I
3.88220 − 0.59945I 1.29885 + 0.74081I
u = −0.217277 − 0.699987I
a = −1.27039 − 1.48005I
b = 0.040324 + 1.086570I
3.88220 − 0.59945I 1.29885 + 0.74081I
u = −0.396163 + 0.521609I
a = 2.00625 − 2.76320I
b = 0.222362 + 1.035550I
4.38168 − 0.44632I 4.73891 + 2.08073I
u = −0.396163 + 0.521609I
a = 1.53155 + 3.40113I
b = 0.191906 − 1.087580I
4.38168 − 0.44632I 4.73891 + 2.08073I
u = −0.396163 − 0.521609I
a = 2.00625 + 2.76320I
b = 0.222362 − 1.035550I
4.38168 + 0.44632I 4.73891 − 2.08073I
u = −0.396163 − 0.521609I
a = 1.53155 − 3.40113I
b = 0.191906 + 1.087580I
4.38168 + 0.44632I 4.73891 − 2.08073I
19
III. I
u
3
= hb + 1, −u
3
− 4u
2
+ 4a + 6, u
4
− 2u
2
+ 2i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
3
− u
a
9
=
−1
0
a
11
=
1
4
u
3
+ u
2
−
3
2
−1
a
6
=
1
4
u
3
+ u
2
−
1
2
−1
a
4
=
−
1
8
u
3
+
1
2
u
2
−
1
4
u
−
1
2
u
3
+
1
2
u −
1
2
a
5
=
1
4
u
3
+ u
2
−
3
2
−1
a
10
=
1
4
u
3
+ u
2
−
5
2
−1
a
12
=
3
8
u
3
+
1
2
u
2
+
1
4
u −
3
2
1
2
u
3
−
1
2
u −
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
− 8
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− 2u + 2)
2
c
2
, c
7
u
4
− 2u
2
+ 2
c
3
16(16u
4
+ 32u
3
+ 32u
2
+ 16u + 5)
c
4
, c
5
, c
6
(u + 1)
4
c
8
u
4
+ 2u
2
+ 2
c
9
, c
10
, c
11
(u − 1)
4
c
12
16(16u
4
− 32u
3
+ 32u
2
− 16u + 5)
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ 4)
2
c
2
, c
7
(y
2
− 2y + 2)
2
c
3
, c
12
256(256y
4
+ 160y
2
+ 64y + 25)
c
4
, c
5
, c
6
c
9
, c
10
, c
11
(y −1)
4
c
8
(y
2
+ 2y + 2)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098680 + 0.455090I
a = −0.33910 + 1.38844I
b = −1.00000
−2.46740 − 3.66386I −4.00000 + 4.00000I
u = 1.098680 − 0.455090I
a = −0.33910 − 1.38844I
b = −1.00000
−2.46740 + 3.66386I −4.00000 − 4.00000I
u = −1.098680 + 0.455090I
a = −0.660899 − 0.611557I
b = −1.00000
−2.46740 + 3.66386I −4.00000 − 4.00000I
u = −1.098680 − 0.455090I
a = −0.660899 + 0.611557I
b = −1.00000
−2.46740 − 3.66386I −4.00000 + 4.00000I
23
IV. I
v
1
= ha, b − 1, 2v − 1i
(i) Arc colorings
a
2
=
0.5
0
a
7
=
1
0
a
8
=
1
0
a
3
=
0.5
0
a
1
=
0.5
0
a
9
=
1
0
a
11
=
0
1
a
6
=
1
−1
a
4
=
1
−0.5
a
5
=
0
−1
a
10
=
1
1
a
12
=
1
0.5
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
c
3
2(2u + 1)
c
4
, c
5
, c
6
u − 1
c
9
, c
10
, c
11
u + 1
c
12
2(2u − 1)
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
c
3
, c
12
4(4y −1)
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y −1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000
a = 0
b = 1.00000
0 0
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− 2u + 2)
2
(u
35
+ 17u
34
+ ··· + 2u + 1)
2
· (u
43
+ 21u
42
+ ··· + 272u + 64)
c
2
, c
7
u(u
4
− 2u
2
+ 2)(u
35
+ u
34
+ ··· + 2u + 1)
2
(u
43
− 3u
42
+ ··· − 28u + 8)
c
3
102400(2u + 1)(16u
4
+ 32u
3
+ 32u
2
+ 16u + 5)
· (128u
43
+ 576u
42
+ ··· + u + 1)
· (25u
70
− 165u
69
+ ··· + 475915454u + 38258189)
c
4
(u − 1)(u + 1)
4
(u
35
− u
34
+ ··· + u
2
− 1)
2
· (u
43
− 18u
41
+ ··· + 889u + 416)
c
5
, c
6
(u − 1)(u + 1)
4
(u
43
− u
42
+ ··· − 24u + 5)(u
70
+ 3u
69
+ ··· + 8u + 1)
c
8
u(u
4
+ 2u
2
+ 2)(u
35
+ 3u
34
+ ··· + 58u + 7)
2
· (u
43
− 9u
42
+ ··· + 2332u + 2968)
c
9
, c
10
((u − 1)
4
)(u + 1)(u
43
− u
42
+ ··· − 24u + 5)(u
70
+ 3u
69
+ ··· + 8u + 1)
c
11
((u − 1)
4
)(u + 1)(u
35
− u
34
+ ··· + u
2
− 1)
2
· (u
43
− 18u
41
+ ··· + 889u + 416)
c
12
102400(2u − 1)(16u
4
− 32u
3
+ 32u
2
− 16u + 5)
· (128u
43
+ 576u
42
+ ··· + u + 1)
· (25u
70
− 165u
69
+ ··· + 475915454u + 38258189)
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ 4)
2
(y
35
+ 3y
34
+ ··· − 14y −1)
2
· (y
43
+ 3y
42
+ ··· − 36608y −4096)
c
2
, c
7
y(y
2
− 2y + 2)
2
(y
35
− 17y
34
+ ··· + 2y −1)
2
· (y
43
− 21y
42
+ ··· + 272y −64)
c
3
, c
12
10485760000(4y −1)(256y
4
+ 160y
2
+ 64y + 25)
· (16384y
43
− 274432y
42
+ ··· + 75y −1)
· (625y
70
− 2.31 × 10
4
y
69
+ ··· − 1.79 × 10
16
y + 1.46 × 10
15
)
c
4
, c
11
((y −1)
5
)(y
35
− 29y
34
+ ··· + 2y −1)
2
· (y
43
− 36y
42
+ ··· + 989169y −173056)
c
5
, c
6
, c
9
c
10
((y −1)
5
)(y
43
+ 19y
42
+ ··· + 126y −25)(y
70
+ 47y
69
+ ··· + 16y + 1)
c
8
y(y
2
+ 2y + 2)
2
(y
35
+ 11y
34
+ ··· + 1446y −49)
2
· (y
43
+ 15y
42
+ ··· + 81561488y −8809024)
29
