12a
0223
(K12a
0223
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 11 2 10 12 4 1 5 8
Solving Sequence
8,12 4,9
5 10 1 7 3 11 6 2
c
8
c
4
c
9
c
12
c
7
c
3
c
11
c
5
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h769u
45
+ 22195u
44
+ ··· + 2048b + 18618368, −1645u
45
− 50133u
44
+ ··· + 8192a − 21766144,
u
46
+ 29u
45
+ ··· + 172032u + 8192i
I
u
2
= h−5.15204 × 10
18
a
19
u
2
− 9.61919 × 10
18
a
18
u
2
+ ··· − 5.70417 × 10
21
a − 2.02099 × 10
21
,
− 2a
19
u
2
− 5a
18
u
2
+ ··· + 389a + 155, u
3
− u
2
+ 2u − 1i
I
u
3
= h4u
29
+ u
28
+ ··· + b + 33, −29u
29
+ 70u
28
+ ··· + 2a − 55, u
30
− 2u
29
+ ··· + u + 2i
I
u
4
= h67a
5
u
2
+ 102a
4
u
2
+ ··· + 362a + 422, −2a
4
u
2
− 2a
3
u
2
+ ··· − 11a + 1, u
3
− u
2
+ 2u − 1i
* 4 irreducible components of dim
C
= 0, with total 154 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
= h769u
45
+ 22195u
44
+ · · · + 2048b + 18618368, −1645u
45
− 5.01 ×
10
4
u
44
+ · · · + 8192a − 2.18 × 10
7
, u
46
+ 29u
45
+ · · · + 172032u + 8192i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
0.200806u
45
+ 6.11975u
44
+ ··· + 46599.5u + 2657
−0.375488u
45
− 10.8374u
44
+ ··· − 180404u − 9091
a
9
=
1
−u
2
a
5
=
−1.40613u
45
− 39.1708u
44
+ ··· − 186438.u − 8862
−0.296387u
45
− 7.36377u
44
+ ··· + 31888u + 1645
a
10
=
1
8192
u
45
+
119
8192
u
44
+ ··· + 933u + 46
0.505615u
45
+ 14.1682u
44
+ ··· + 82866u + 4141
a
1
=
u
u
a
7
=
−0.274048u
45
− 7.68079u
44
+ ··· − 42145.5u − 2100
0.982910u
45
+ 27.7881u
44
+ ··· + 203839u + 10297
a
3
=
−2.30249u
45
− 65.0942u
44
+ ··· − 648664.u − 33111
1.45679u
45
+ 41.2253u
44
+ ··· + 186450u + 9592
a
11
=
−0.494507u
45
− 13.8463u
44
+ ··· − 81908u − 4096
45
4096
u
45
+
1259
4096
u
44
+ ··· + 25u − 1
a
6
=
−2.72314u
45
− 76.9080u
44
+ ··· − 541748.u − 26895
0.812256u
45
+ 23.5637u
44
+ ··· + 155986u + 7758
a
2
=
−5.37744u
45
− 152.656u
44
+ ··· − 1.53361 × 10
6
u − 79260.5
1.09839u
45
+ 31.0549u
44
+ ··· + 140452.u + 7392
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5013
1024
u
45
−
144727
1024
u
44
+ ··· − 1843566u − 96850
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
46
+ 23u
45
+ ··· + 160u + 64
c
2
, c
6
u
46
− 9u
45
+ ··· − 80u + 8
c
3
u
46
+ 9u
45
+ ··· + 48000u + 8768
c
4
, c
5
, c
9
c
11
u
46
+ 22u
44
+ ··· + 2u + 1
c
7
, c
10
u
46
− 3u
45
+ ··· + 15u + 1
c
8
, c
12
u
46
− 29u
45
+ ··· − 172032u + 8192
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
+ 3y
45
+ ··· + 34304y + 4096
c
2
, c
6
y
46
+ 23y
45
+ ··· + 160y + 64
c
3
y
46
− 17y
45
+ ··· + 657339392y + 76877824
c
4
, c
5
, c
9
c
11
y
46
+ 44y
45
+ ··· + 2y + 1
c
7
, c
10
y
46
− 21y
45
+ ··· − 131y + 1
c
8
, c
12
y
46
+ 23y
45
+ ··· − 301989888y + 67108864
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.799771 + 0.573925I
a = 0.364393 + 0.335556I
b = −0.066790 − 0.489318I
0.23982 − 5.32921I 0
u = −0.799771 − 0.573925I
a = 0.364393 − 0.335556I
b = −0.066790 + 0.489318I
0.23982 + 5.32921I 0
u = 0.893801 + 0.251608I
a = 0.044626 + 1.229910I
b = 0.58367 − 1.51957I
1.15969 + 2.64455I 0
u = 0.893801 − 0.251608I
a = 0.044626 − 1.229910I
b = 0.58367 + 1.51957I
1.15969 − 2.64455I 0
u = −0.512458 + 0.963987I
a = −0.430313 + 0.180490I
b = −0.0655666 − 0.0544458I
0.14368 − 3.22065I 0
u = −0.512458 − 0.963987I
a = −0.430313 − 0.180490I
b = −0.0655666 + 0.0544458I
0.14368 + 3.22065I 0
u = −0.388129 + 1.023260I
a = −0.426674 + 0.589584I
b = −0.183361 + 0.160958I
−1.19630 − 3.09642I 0
u = −0.388129 − 1.023260I
a = −0.426674 − 0.589584I
b = −0.183361 − 0.160958I
−1.19630 + 3.09642I 0
u = −0.324185 + 1.064380I
a = 0.399633 − 0.786327I
b = 0.197166 − 0.347962I
−4.51131 + 0.55103I 0
u = −0.324185 − 1.064380I
a = 0.399633 + 0.786327I
b = 0.197166 + 0.347962I
−4.51131 − 0.55103I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.636420 + 0.928507I
a = 0.487473 + 0.128530I
b = −0.118282 + 0.098125I
−0.796799 + 0.099834I 0
u = −0.636420 − 0.928507I
a = 0.487473 − 0.128530I
b = −0.118282 − 0.098125I
−0.796799 − 0.099834I 0
u = −0.400449 + 1.071460I
a = 0.563394 − 0.645136I
b = 0.312197 − 0.165596I
−4.04848 − 7.39004I 0
u = −0.400449 − 1.071460I
a = 0.563394 + 0.645136I
b = 0.312197 + 0.165596I
−4.04848 + 7.39004I 0
u = −0.065239 + 0.801819I
a = 0.118295 + 0.879729I
b = 0.403205 + 0.174145I
−1.90599 − 1.35920I 0
u = −0.065239 − 0.801819I
a = 0.118295 − 0.879729I
b = 0.403205 − 0.174145I
−1.90599 + 1.35920I 0
u = −0.636988 + 0.468513I
a = −0.399061 − 0.335733I
b = −0.186385 + 0.345366I
1.55277 − 1.12061I 0
u = −0.636988 − 0.468513I
a = −0.399061 + 0.335733I
b = −0.186385 − 0.345366I
1.55277 + 1.12061I 0
u = −1.293830 + 0.240209I
a = −0.125234 − 0.391120I
b = 0.17398 + 1.95216I
−9.2090 − 11.8951I 0
u = −1.293830 − 0.240209I
a = −0.125234 + 0.391120I
b = 0.17398 − 1.95216I
−9.2090 + 11.8951I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.343470 + 0.254073I
a = 0.121901 + 0.415510I
b = −0.26873 − 2.00701I
−6.15188 − 6.52811I 0
u = −1.343470 − 0.254073I
a = 0.121901 − 0.415510I
b = −0.26873 + 2.00701I
−6.15188 + 6.52811I 0
u = −1.374360 + 0.172869I
a = −0.081685 − 0.416558I
b = 0.18781 + 2.15232I
−11.06560 − 2.43248I 0
u = −1.374360 − 0.172869I
a = −0.081685 + 0.416558I
b = 0.18781 − 2.15232I
−11.06560 + 2.43248I 0
u = −0.597343 + 0.091283I
a = 0.532629 + 0.097217I
b = 0.581340 − 0.128594I
−1.30110 + 3.67557I 0
u = −0.597343 − 0.091283I
a = 0.532629 − 0.097217I
b = 0.581340 + 0.128594I
−1.30110 − 3.67557I 0
u = −0.474804 + 0.228895I
a = −0.606283 − 0.281711I
b = −0.394151 + 0.170715I
1.036500 − 0.329167I 9.79847 + 0.I
u = −0.474804 − 0.228895I
a = −0.606283 + 0.281711I
b = −0.394151 − 0.170715I
1.036500 + 0.329167I 9.79847 + 0.I
u = −0.50438 + 1.51379I
a = 0.54133 + 1.59621I
b = −0.81797 + 2.47099I
−14.8126 − 18.1675I 0
u = −0.50438 − 1.51379I
a = 0.54133 − 1.59621I
b = −0.81797 − 2.47099I
−14.8126 + 18.1675I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.50748 + 1.52626I
a = −0.53256 − 1.55965I
b = 0.81772 − 2.47947I
−11.8567 − 12.9387I 0
u = −0.50748 − 1.52626I
a = −0.53256 + 1.55965I
b = 0.81772 + 2.47947I
−11.8567 + 12.9387I 0
u = −0.52920 + 1.52540I
a = 0.58432 + 1.52852I
b = −0.83326 + 2.47604I
−16.5662 − 9.0443I 0
u = −0.52920 − 1.52540I
a = 0.58432 − 1.52852I
b = −0.83326 − 2.47604I
−16.5662 + 9.0443I 0
u = −0.49940 + 1.60831I
a = −0.43900 − 1.41526I
b = 0.80667 − 2.59864I
−7.89455 − 10.71430I 0
u = −0.49940 − 1.60831I
a = −0.43900 + 1.41526I
b = 0.80667 + 2.59864I
−7.89455 + 10.71430I 0
u = −0.66884 + 1.57562I
a = −0.632758 − 1.225720I
b = 1.10252 − 2.37452I
−15.5284 − 5.1709I 0
u = −0.66884 − 1.57562I
a = −0.632758 + 1.225720I
b = 1.10252 + 2.37452I
−15.5284 + 5.1709I 0
u = −0.79157 + 1.55497I
a = −0.635987 − 1.056940I
b = 1.37706 − 2.08974I
−12.99410 + 4.22647I 0
u = −0.79157 − 1.55497I
a = −0.635987 + 1.056940I
b = 1.37706 + 2.08974I
−12.99410 − 4.22647I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.53627 + 1.66484I
a = 0.439767 + 1.323980I
b = −0.90517 + 2.71062I
−7.40589 − 5.18365I 0
u = −0.53627 − 1.66484I
a = 0.439767 − 1.323980I
b = −0.90517 − 2.71062I
−7.40589 + 5.18365I 0
u = −1.75426 + 0.12015I
a = 0.035438 + 0.550581I
b = −0.30850 − 2.94126I
−1.59220 − 3.11488I 0
u = −1.75426 − 0.12015I
a = 0.035438 − 0.550581I
b = −0.30850 + 2.94126I
−1.59220 + 3.11488I 0
u = −0.75494 + 1.61988I
a = 0.576352 + 1.115620I
b = −1.39518 + 2.33963I
−10.17990 − 1.41035I 0
u = −0.75494 − 1.61988I
a = 0.576352 − 1.115620I
b = −1.39518 − 2.33963I
−10.17990 + 1.41035I 0
9
II. I
u
2
= h−5.15 × 10
18
a
19
u
2
− 9.62 × 10
18
a
18
u
2
+ · · · − 5.70 × 10
21
a − 2.02 ×
10
21
, −2a
19
u
2
− 5a
18
u
2
+ · · · + 389a + 155, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
a
0.00624366a
19
u
2
+ 0.0116573a
18
u
2
+ ··· + 6.91278a + 2.44921
a
9
=
1
−u
2
a
5
=
0.00624366a
19
u
2
+ 0.0116573a
18
u
2
+ ··· + 7.91278a + 2.44921
0.00589498a
19
u
2
+ 0.00970531a
18
u
2
+ ··· + 4.98347a + 1.02435
a
10
=
−0.0222268a
19
u
2
+ 0.0385989a
18
u
2
+ ··· − 1.52939a + 3.00132
1
5
a
2
u
2
+
2
5
u
2
+ ··· +
4
5
a
2
+
8
5
a
1
=
u
u
a
7
=
0.0255730a
19
u
2
− 0.0386005a
18
u
2
+ ··· − 4.61675a − 5.17283
−0.280000a
4
u
2
− 1.12000a
2
u
2
+ ··· − 2.08000a
2
− 2.08000
a
3
=
0.00811715a
19
u
2
− 0.0185732a
18
u
2
+ ··· + 2.73016a + 0.0448430
0.00840339a
19
u
2
− 0.0245270a
18
u
2
+ ··· − 2.51095a − 3.00433
a
11
=
−0.0300738a
19
u
2
+ 0.0495554a
18
u
2
+ ··· − 1.67353a + 3.99775
−0.00784700a
19
u
2
+ 0.0109564a
18
u
2
+ ··· − 0.144142a + 2.59644
a
6
=
0.0116152a
19
u
2
− 0.0203774a
18
u
2
+ ··· − 6.28641a − 7.47013
1
5
a
3
u
2
+
2
5
u
2
a + ··· −
1
5
a
3
−
2
5
a
a
2
=
0.00249033a
19
u
2
+ 0.0238687a
18
u
2
+ ··· + 12.0177a + 7.16327
−0.00531474a
19
u
2
+ 0.0136319a
18
u
2
+ ··· − 0.592585a + 0.0240514
(ii) Obstruction class = −1
(iii) Cusp Shapes =
21229213881407898776
825162189597541015625
a
19
u
2
−
99261565058430515616
825162189597541015625
a
18
u
2
+ ··· −
4819014882020878281412
825162189597541015625
a −
14886800916766629307678
825162189597541015625
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
10
+ 5u
9
+ 13u
8
+ 19u
7
+ 17u
6
+ 7u
5
− 2u
3
+ u
2
+ 2u + 1)
6
c
2
, c
6
(u
10
+ u
9
+ 3u
8
+ 3u
7
+ 5u
6
+ 5u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 2u + 1)
6
c
3
(u
10
+ 2u
9
− u
8
− 5u
7
− 3u
6
+ 4u
5
+ 12u
4
+ 13u
3
+ 5u
2
+ u + 2)
6
c
4
, c
5
, c
9
c
11
u
60
+ u
59
+ ··· − 626u + 3383
c
7
, c
10
u
60
− 11u
59
+ ··· − 53768u + 6593
c
8
, c
12
(u
3
+ u
2
+ 2u + 1)
20
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
10
+ y
9
+ 13y
8
+ 11y
7
+ 45y
6
+ 35y
5
+ 12y
4
+ 2y
3
+ 9y
2
− 2y + 1)
6
c
2
, c
6
(y
10
+ 5y
9
+ 13y
8
+ 19y
7
+ 17y
6
+ 7y
5
− 2y
3
+ y
2
+ 2y + 1)
6
c
3
(y
10
− 6y
9
+ ··· + 19y + 4)
6
c
4
, c
5
, c
9
c
11
y
60
+ 55y
59
+ ··· − 363644884y + 11444689
c
7
, c
10
y
60
− 17y
59
+ ··· + 11794588y + 43467649
c
8
, c
12
(y
3
+ 3y
2
+ 2y − 1)
20
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.753681 − 0.475251I
b = −1.78844 − 0.37957I
−8.34008 − 5.45819I −3.68536 + 3.16937I
u = 0.215080 + 1.307140I
a = −0.546194 − 0.474142I
b = 0.403352 − 0.051960I
−8.34008 + 11.11440I −3.68536 − 9.12826I
u = 0.215080 + 1.307140I
a = 0.574901 + 0.335993I
b = 1.57210 + 0.28523I
−5.54533 − 0.65027I −0.314721 − 0.184301I
u = 0.215080 + 1.307140I
a = −0.285753 + 1.351650I
b = −0.543510 + 1.072600I
−8.40699 + 4.05981I −4.41153 − 8.42852I
u = 0.215080 + 1.307140I
a = 0.428457 + 0.424908I
b = −0.499901 + 0.057312I
−5.54533 + 6.30651I −0.31472 − 5.77459I
u = 0.215080 + 1.307140I
a = 0.91047 − 1.17250I
b = 1.24405 − 1.35425I
−8.40699 + 1.59643I −4.41153 + 2.46963I
u = 0.215080 + 1.307140I
a = 0.46161 − 1.63922I
b = −0.57315 − 1.54354I
−8.34008 − 5.45819I −3.68536 + 3.16937I
u = 0.215080 + 1.307140I
a = −0.37848 + 1.70556I
b = 0.61872 + 1.65480I
−5.54533 − 0.65027I −0.314721 − 0.184301I
u = 0.215080 + 1.307140I
a = 0.249866 + 0.028485I
b = −0.749845 − 0.180326I
−3.02174 + 5.13818I 1.35393 − 6.50078I
u = 0.215080 + 1.307140I
a = 0.12162 − 1.79476I
b = 0.097878 − 1.186300I
−12.8356 + 6.9740I −8.49110 − 6.95545I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.065417 + 0.174229I
b = 0.948493 + 0.296744I
−3.02174 + 0.51807I 1.35393 + 0.54188I
u = 0.215080 + 1.307140I
a = 0.22681 − 1.88180I
b = 0.054342 − 1.297810I
−12.83560 − 1.31773I −8.49110 + 0.99655I
u = 0.215080 + 1.307140I
a = −0.50665 + 1.84019I
b = −0.17308 + 1.65844I
−8.40699 + 1.59643I −4.41153 + 2.46963I
u = 0.215080 + 1.307140I
a = −0.09218 + 1.91765I
b = 0.92173 + 2.04017I
−3.02174 + 0.51807I 1.35393 + 0.54188I
u = 0.215080 + 1.307140I
a = 0.83452 − 1.90639I
b = 0.57676 − 2.18544I
−8.40699 + 4.05981I −4.41153 − 8.42852I
u = 0.215080 + 1.307140I
a = 0.08612 − 2.09921I
b = −0.91359 − 2.30802I
−3.02174 + 5.13818I 1.35393 − 6.50078I
u = 0.215080 + 1.307140I
a = −1.44111 + 1.58193I
b = −1.61358 + 2.16592I
−12.83560 − 1.31773I −8.49110 + 0.99655I
u = 0.215080 + 1.307140I
a = −1.37238 + 1.80234I
b = −1.39612 + 2.41080I
−12.8356 + 6.9740I −8.49110 − 6.95545I
u = 0.215080 + 1.307140I
a = 0.23996 − 2.36391I
b = −0.68840 − 2.73151I
−5.54533 + 6.30651I −0.31472 − 5.77459I
u = 0.215080 + 1.307140I
a = −0.23228 + 2.46167I
b = 0.71727 + 2.88385I
−8.34008 + 11.11440I −3.68536 − 9.12826I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 − 1.307140I
a = −0.753681 + 0.475251I
b = −1.78844 + 0.37957I
−8.34008 + 5.45819I −3.68536 − 3.16937I
u = 0.215080 − 1.307140I
a = −0.546194 + 0.474142I
b = 0.403352 + 0.051960I
−8.34008 − 11.11440I −3.68536 + 9.12826I
u = 0.215080 − 1.307140I
a = 0.574901 − 0.335993I
b = 1.57210 − 0.28523I
−5.54533 + 0.65027I −0.314721 + 0.184301I
u = 0.215080 − 1.307140I
a = −0.285753 − 1.351650I
b = −0.543510 − 1.072600I
−8.40699 − 4.05981I −4.41153 + 8.42852I
u = 0.215080 − 1.307140I
a = 0.428457 − 0.424908I
b = −0.499901 − 0.057312I
−5.54533 − 6.30651I −0.31472 + 5.77459I
u = 0.215080 − 1.307140I
a = 0.91047 + 1.17250I
b = 1.24405 + 1.35425I
−8.40699 − 1.59643I −4.41153 − 2.46963I
u = 0.215080 − 1.307140I
a = 0.46161 + 1.63922I
b = −0.57315 + 1.54354I
−8.34008 + 5.45819I −3.68536 − 3.16937I
u = 0.215080 − 1.307140I
a = −0.37848 − 1.70556I
b = 0.61872 − 1.65480I
−5.54533 + 0.65027I −0.314721 + 0.184301I
u = 0.215080 − 1.307140I
a = 0.249866 − 0.028485I
b = −0.749845 + 0.180326I
−3.02174 − 5.13818I 1.35393 + 6.50078I
u = 0.215080 − 1.307140I
a = 0.12162 + 1.79476I
b = 0.097878 + 1.186300I
−12.8356 − 6.9740I −8.49110 + 6.95545I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 − 1.307140I
a = −0.065417 − 0.174229I
b = 0.948493 − 0.296744I
−3.02174 − 0.51807I 1.35393 − 0.54188I
u = 0.215080 − 1.307140I
a = 0.22681 + 1.88180I
b = 0.054342 + 1.297810I
−12.83560 + 1.31773I −8.49110 − 0.99655I
u = 0.215080 − 1.307140I
a = −0.50665 − 1.84019I
b = −0.17308 − 1.65844I
−8.40699 − 1.59643I −4.41153 − 2.46963I
u = 0.215080 − 1.307140I
a = −0.09218 − 1.91765I
b = 0.92173 − 2.04017I
−3.02174 − 0.51807I 1.35393 − 0.54188I
u = 0.215080 − 1.307140I
a = 0.83452 + 1.90639I
b = 0.57676 + 2.18544I
−8.40699 − 4.05981I −4.41153 + 8.42852I
u = 0.215080 − 1.307140I
a = 0.08612 + 2.09921I
b = −0.91359 + 2.30802I
−3.02174 − 5.13818I 1.35393 + 6.50078I
u = 0.215080 − 1.307140I
a = −1.44111 − 1.58193I
b = −1.61358 − 2.16592I
−12.83560 + 1.31773I −8.49110 − 0.99655I
u = 0.215080 − 1.307140I
a = −1.37238 − 1.80234I
b = −1.39612 − 2.41080I
−12.8356 − 6.9740I −8.49110 + 6.95545I
u = 0.215080 − 1.307140I
a = 0.23996 + 2.36391I
b = −0.68840 + 2.73151I
−5.54533 − 6.30651I −0.31472 + 5.77459I
u = 0.215080 − 1.307140I
a = −0.23228 − 2.46167I
b = 0.71727 − 2.88385I
−8.34008 − 11.11440I −3.68536 + 9.12826I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569840
a = −0.691753 + 0.900274I
b = −0.198932 − 1.368010I
−1.40774 + 3.47839I 6.21454 − 2.79515I
u = 0.569840
a = −0.691753 − 0.900274I
b = −0.198932 + 1.368010I
−1.40774 − 3.47839I 6.21454 + 2.79515I
u = 0.569840
a = 0.833453 + 0.905620I
b = 0.22342 − 1.43186I
−4.20250 − 8.28632I 2.84391 + 6.14881I
u = 0.569840
a = 0.833453 − 0.905620I
b = 0.22342 + 1.43186I
−4.20250 + 8.28632I 2.84391 − 6.14881I
u = 0.569840
a = 0.869132 + 0.956638I
b = −0.535562 + 1.131840I
−8.69800 + 4.14585I −1.96183 − 3.97600I
u = 0.569840
a = 0.869132 − 0.956638I
b = −0.535562 − 1.131840I
−8.69800 − 4.14585I −1.96183 + 3.97600I
u = 0.569840
a = −0.254094 + 1.301160I
b = 0.288722 + 0.604570I
−4.26940 + 1.23169I 2.11774 − 5.44908I
u = 0.569840
a = −0.254094 − 1.301160I
b = 0.288722 − 0.604570I
−4.26940 − 1.23169I 2.11774 + 5.44908I
u = 0.569840
a = −0.363696 + 1.279380I
b = −0.262040 − 1.092640I
1.11584 + 2.31006I 7.88320 − 3.52133I
u = 0.569840
a = −0.363696 − 1.279380I
b = −0.262040 + 1.092640I
1.11584 − 2.31006I 7.88320 + 3.52133I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569840
a = −0.389163 + 0.475675I
b = 0.153653 + 1.172260I
−4.26940 − 1.23169I 2.11774 + 5.44908I
u = 0.569840
a = −0.389163 − 0.475675I
b = 0.153653 − 1.172260I
−4.26940 + 1.23169I 2.11774 − 5.44908I
u = 0.569840
a = 0.795483 + 1.164250I
b = −0.609211 + 0.989056I
−8.69800 − 4.14585I −1.96183 + 3.97600I
u = 0.569840
a = 0.795483 − 1.164250I
b = −0.609211 − 0.989056I
−8.69800 + 4.14585I −1.96183 − 3.97600I
u = 0.569840
a = 0.24323 + 1.53155I
b = 0.344886 − 0.840470I
1.11584 + 2.31006I 7.88320 − 3.52133I
u = 0.569840
a = 0.24323 − 1.53155I
b = 0.344886 + 0.840470I
1.11584 − 2.31006I 7.88320 + 3.52133I
u = 0.569840
a = 0.10774 + 1.78772I
b = 0.600562 − 0.480557I
−1.40774 + 3.47839I 6.21454 − 2.79515I
u = 0.569840
a = 0.10774 − 1.78772I
b = 0.600562 + 0.480557I
−1.40774 − 3.47839I 6.21454 + 2.79515I
u = 0.569840
a = −0.11054 + 1.86439I
b = −0.720573 − 0.473098I
−4.20250 − 8.28632I 2.84391 + 6.14881I
u = 0.569840
a = −0.11054 − 1.86439I
b = −0.720573 + 0.473098I
−4.20250 + 8.28632I 2.84391 − 6.14881I
18
III. I
u
3
=
h4u
29
+u
28
+· · ·+b+33, −29u
29
+70u
28
+· · ·+2a−55, u
30
−2u
29
+· · ·+u+2i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
29
2
u
29
− 35u
28
+ ··· + 58u +
55
2
−4u
29
− u
28
+ ··· + 19u − 33
a
9
=
1
−u
2
a
5
=
21
2
u
29
− 25u
28
+ ··· + 54u +
13
2
−6u
29
+ 12u
28
+ ··· + 13u − 29
a
10
=
−
3
2
u
29
+ 2u
28
+ ··· − 12u −
3
2
−u
29
+ 2u
28
+ ··· − 2u + 1
a
1
=
u
u
a
7
=
1
2
u
29
+ 3u
28
+ ··· + 17u +
21
2
2u
29
− 2u
28
+ ··· + 8u + 3
a
3
=
−
3
2
u
29
+ 10u
28
+ ··· − 4u +
53
2
4u
29
− 2u
28
+ ··· − 3u + 37
a
11
=
−
3
2
u
29
+ 3u
28
+ ··· − 10u +
1
2
−u
29
+ 3u
28
+ ··· + 12u
2
+ 3
a
6
=
15u
29
− 31u
28
+ ··· + 33u + 19
8u
29
− 28u
28
+ ··· + 50u − 40
a
2
=
33
2
u
29
− 19u
28
+ ··· + 54u +
159
2
24u
29
− 57u
28
+ ··· + 105u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −47u
29
+ 95u
28
− 548u
27
+ 913u
26
− 2523u
25
+ 3700u
24
−
5843u
23
+ 8328u
22
− 6732u
21
+ 11019u
20
− 2264u
19
+ 5985u
18
+ 726u
17
− 9012u
16
−
9505u
15
− 26913u
14
− 30055u
13
− 34426u
12
− 40817u
11
− 25858u
10
− 31373u
9
−
10806u
8
− 14162u
7
− 2007u
6
− 3834u
5
− 328u
4
− 894u
3
− 340u
2
− 176u − 76
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
− 16u
29
+ ··· − 8u + 1
c
2
u
30
− 2u
29
+ ··· − 2u + 1
c
3
u
30
+ 2u
29
+ ··· + 9u + 2
c
4
, c
11
u
30
+ 17u
28
+ ··· − u + 1
c
5
, c
9
u
30
+ 17u
28
+ ··· + u + 1
c
6
u
30
+ 2u
29
+ ··· + 2u + 1
c
7
, c
10
u
30
− 3u
29
+ ··· − 10u + 1
c
8
u
30
− 2u
29
+ ··· + u + 2
c
12
u
30
+ 2u
29
+ ··· − u + 2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 4y
29
+ ··· − 12y + 1
c
2
, c
6
y
30
+ 16y
29
+ ··· + 8y + 1
c
3
y
30
− 8y
29
+ ··· + 51y + 4
c
4
, c
5
, c
9
c
11
y
30
+ 34y
29
+ ··· − 9y + 1
c
7
, c
10
y
30
− 7y
29
+ ··· − 30y + 1
c
8
, c
12
y
30
+ 20y
29
+ ··· + 63y + 4
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.954358 + 0.210669I
a = −0.157797 + 1.396290I
b = −0.42289 − 1.97188I
0.90437 − 2.79385I −11.1621 + 9.0861I
u = −0.954358 − 0.210669I
a = −0.157797 − 1.396290I
b = −0.42289 + 1.97188I
0.90437 + 2.79385I −11.1621 − 9.0861I
u = −0.487760 + 0.913151I
a = 0.282967 + 0.414413I
b = −0.469527 + 0.371738I
−0.262375 − 0.129830I 7.66829 + 1.39620I
u = −0.487760 − 0.913151I
a = 0.282967 − 0.414413I
b = −0.469527 − 0.371738I
−0.262375 + 0.129830I 7.66829 − 1.39620I
u = −0.452089 + 0.844145I
a = −0.552166 − 0.021065I
b = 0.009729 − 0.587148I
−0.00756 − 3.73651I 0.40463 + 10.05332I
u = −0.452089 − 0.844145I
a = −0.552166 + 0.021065I
b = 0.009729 + 0.587148I
−0.00756 + 3.73651I 0.40463 − 10.05332I
u = 0.395534 + 1.115610I
a = 1.05638 − 1.22612I
b = 0.257277 − 0.768700I
−11.11260 − 2.62022I −4.33545 + 2.54697I
u = 0.395534 − 1.115610I
a = 1.05638 + 1.22612I
b = 0.257277 + 0.768700I
−11.11260 + 2.62022I −4.33545 − 2.54697I
u = 0.282007 + 1.171250I
a = 0.99630 − 1.51825I
b = 0.609476 − 1.061230I
−11.60570 + 5.64781I −4.91183 − 3.78174I
u = 0.282007 − 1.171250I
a = 0.99630 + 1.51825I
b = 0.609476 + 1.061230I
−11.60570 − 5.64781I −4.91183 + 3.78174I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.194470 + 1.267770I
a = −0.69601 + 1.67138I
b = −0.75988 + 1.50055I
−8.33239 + 3.05072I −3.41230 − 0.35327I
u = 0.194470 − 1.267770I
a = −0.69601 − 1.67138I
b = −0.75988 − 1.50055I
−8.33239 − 3.05072I −3.41230 + 0.35327I
u = −0.220342 + 0.677642I
a = 1.72214 − 0.32654I
b = 0.274742 + 1.101150I
−5.82568 − 8.71515I −4.10097 + 7.30655I
u = −0.220342 − 0.677642I
a = 1.72214 + 0.32654I
b = 0.274742 − 1.101150I
−5.82568 + 8.71515I −4.10097 − 7.30655I
u = 0.374108 + 1.234240I
a = −0.84930 + 1.32789I
b = −0.232711 + 1.180040I
−8.13358 + 1.89857I − 60.10 − 0.703598I
u = 0.374108 − 1.234240I
a = −0.84930 − 1.32789I
b = −0.232711 − 1.180040I
−8.13358 − 1.89857I − 60.10 + 0.703598I
u = 0.113491 + 1.305880I
a = 0.48876 − 1.74372I
b = 0.90956 − 1.71662I
−10.39040 + 0.41896I −6.15304 + 1.26264I
u = 0.113491 − 1.305880I
a = 0.48876 + 1.74372I
b = 0.90956 + 1.71662I
−10.39040 − 0.41896I −6.15304 − 1.26264I
u = −0.265692 + 0.625254I
a = −1.61215 + 0.54381I
b = −0.279464 − 1.065660I
−2.88017 − 3.92346I −1.21214 + 4.26144I
u = −0.265692 − 0.625254I
a = −1.61215 − 0.54381I
b = −0.279464 + 1.065660I
−2.88017 + 3.92346I −1.21214 − 4.26144I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05808 + 1.41627I
a = 0.30999 − 1.58553I
b = 0.92701 − 2.00489I
−9.22090 + 7.68788I −4.49738 − 6.93831I
u = 0.05808 − 1.41627I
a = 0.30999 + 1.58553I
b = 0.92701 + 2.00489I
−9.22090 − 7.68788I −4.49738 + 6.93831I
u = −0.160117 + 0.556209I
a = 2.02259 − 0.64113I
b = 0.298497 + 1.049780I
−6.93501 − 0.20087I −6.34680 + 0.65586I
u = −0.160117 − 0.556209I
a = 2.02259 + 0.64113I
b = 0.298497 − 1.049780I
−6.93501 + 0.20087I −6.34680 − 0.65586I
u = 0.17114 + 1.44043I
a = −0.44043 + 1.48846I
b = −0.63512 + 1.99041I
−7.14969 + 3.03258I 0. − 2.04340I
u = 0.17114 − 1.44043I
a = −0.44043 − 1.48846I
b = −0.63512 − 1.99041I
−7.14969 − 3.03258I 0. + 2.04340I
u = 0.446808 + 0.301559I
a = −1.211930 − 0.717774I
b = 0.006603 − 0.798556I
−5.10854 − 0.65478I −7.03551 − 0.27211I
u = 0.446808 − 0.301559I
a = −1.211930 + 0.717774I
b = 0.006603 + 0.798556I
−5.10854 + 0.65478I −7.03551 + 0.27211I
u = 1.50472 + 0.21618I
a = −0.109336 + 0.422908I
b = 0.50671 − 2.07597I
−1.12126 + 2.86817I 0
u = 1.50472 − 0.21618I
a = −0.109336 − 0.422908I
b = 0.50671 + 2.07597I
−1.12126 − 2.86817I 0
24
IV. I
u
4
= h67a
5
u
2
+ 102a
4
u
2
+ · · · + 362a + 422, −2a
4
u
2
− 2a
3
u
2
+ · · · −
11a + 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
a
−0.116522a
5
u
2
− 0.177391a
4
u
2
+ ··· − 0.629565a − 0.733913
a
9
=
1
−u
2
a
5
=
−0.116522a
5
u
2
− 0.177391a
4
u
2
+ ··· + 0.370435a − 0.733913
−0.147826a
5
u
2
− 0.0608696a
4
u
2
+ ··· − 1.84348a − 1.40870
a
10
=
0.177391a
5
u
2
− 0.00695652a
4
u
2
+ ··· + 0.212174a + 0.0104348
1
5
a
2
u
2
+
2
5
u
2
+ ··· +
4
5
a
2
+
8
5
a
1
=
u
u
a
7
=
−0.177391a
5
u
2
+ 0.00695652a
4
u
2
+ ··· + 0.787826a + 0.389565
−0.280000a
4
u
2
− 1.12000a
2
u
2
+ ··· − 2.08000a
2
− 2.08000
a
3
=
0.177391a
5
u
2
− 0.00695652a
4
u
2
+ ··· + 0.212174a − 0.389565
−0.116522a
5
u
2
+ 0.102609a
4
u
2
+ ··· − 0.629565a + 1.34609
a
11
=
0.293913a
5
u
2
− 0.109565a
4
u
2
+ ··· + 0.841739a + 1.06435
0.116522a
5
u
2
− 0.102609a
4
u
2
+ ··· + 0.629565a + 2.65391
a
6
=
1
5
a
3
u
2
+
2
5
u
2
a + ··· −
2
5
a + 2
1
5
a
3
u
2
+
2
5
u
2
a + ··· −
1
5
a
3
−
2
5
a
a
2
=
0.0608696a
5
u
2
− 0.0243478a
4
u
2
+ ··· + 0.582609a − 0.963478
−0.349565a
5
u
2
− 0.0921739a
4
u
2
+ ··· − 1.88870a + 0.0382609
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
− 4u + 2
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ 2u
2
+ u − 1)
6
c
2
, c
6
(u
3
+ u − 1)
6
c
3
(u − 1)
18
c
4
, c
5
, c
9
c
11
u
18
+ 10u
16
+ ··· − 106u + 23
c
7
, c
10
u
18
− 4u
17
+ ··· − 292u + 89
c
8
, c
12
(u
3
+ u
2
+ 2u + 1)
6
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 2y
2
+ 5y − 1)
6
c
2
, c
6
(y
3
+ 2y
2
+ y − 1)
6
c
3
(y − 1)
18
c
4
, c
5
, c
9
c
11
y
18
+ 20y
17
+ ··· + 356y + 529
c
7
, c
10
y
18
− 12y
17
+ ··· − 77788y + 7921
c
8
, c
12
(y
3
+ 3y
2
+ 2y − 1)
6
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.784997 − 0.039230I
b = −1.69200 + 0.07253I
−9.60386 + 2.82812I −5.50976 − 2.97945I
u = 0.215080 + 1.307140I
a = −0.330614 − 0.633892I
b = 0.492761 − 0.237412I
−9.60386 + 2.82812I −5.50976 − 2.97945I
u = 0.215080 + 1.307140I
a = −0.22941 + 1.78152I
b = −0.145783 + 1.273280I
−9.60386 + 2.82812I −5.50976 − 2.97945I
u = 0.215080 + 1.307140I
a = 0.47175 − 1.81160I
b = −0.43525 − 1.69984I
−9.60386 + 2.82812I −5.50976 − 2.97945I
u = 0.215080 + 1.307140I
a = 1.28006 − 1.65694I
b = 1.36368 − 2.16518I
−9.60386 + 2.82812I −5.50976 − 2.97945I
u = 0.215080 + 1.307140I
a = −0.40679 + 2.36014I
b = 0.41659 + 2.75662I
−9.60386 + 2.82812I −5.50976 − 2.97945I
u = 0.215080 − 1.307140I
a = −0.784997 + 0.039230I
b = −1.69200 − 0.07253I
−9.60386 − 2.82812I −5.50976 + 2.97945I
u = 0.215080 − 1.307140I
a = −0.330614 + 0.633892I
b = 0.492761 + 0.237412I
−9.60386 − 2.82812I −5.50976 + 2.97945I
u = 0.215080 − 1.307140I
a = −0.22941 − 1.78152I
b = −0.145783 − 1.273280I
−9.60386 − 2.82812I −5.50976 + 2.97945I
u = 0.215080 − 1.307140I
a = 0.47175 + 1.81160I
b = −0.43525 + 1.69984I
−9.60386 − 2.82812I −5.50976 + 2.97945I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 − 1.307140I
a = 1.28006 + 1.65694I
b = 1.36368 + 2.16518I
−9.60386 − 2.82812I −5.50976 + 2.97945I
u = 0.215080 − 1.307140I
a = −0.40679 − 2.36014I
b = 0.41659 − 2.75662I
−9.60386 − 2.82812I −5.50976 + 2.97945I
u = 0.569840
a = 0.693291 + 0.635785I
b = 0.094590 − 1.402580I
−5.46628 1.01950
u = 0.569840
a = 0.693291 − 0.635785I
b = 0.094590 + 1.402580I
−5.46628 1.01950
u = 0.569840
a = −0.709483 + 1.021010I
b = 0.487919 + 1.021010I
−5.46628 1.01950
u = 0.569840
a = −0.709483 − 1.021010I
b = 0.487919 − 1.021010I
−5.46628 1.01950
u = 0.569840
a = 0.01619 + 1.77975I
b = −0.582509 − 0.258612I
−5.46628 1.01950
u = 0.569840
a = 0.01619 − 1.77975I
b = −0.582509 + 0.258612I
−5.46628 1.01950
29
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ 2u
2
+ u − 1)
6
· (u
10
+ 5u
9
+ 13u
8
+ 19u
7
+ 17u
6
+ 7u
5
− 2u
3
+ u
2
+ 2u + 1)
6
· (u
30
− 16u
29
+ ··· − 8u + 1)(u
46
+ 23u
45
+ ··· + 160u + 64)
c
2
(u
3
+ u − 1)
6
· (u
10
+ u
9
+ 3u
8
+ 3u
7
+ 5u
6
+ 5u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 2u + 1)
6
· (u
30
− 2u
29
+ ··· − 2u + 1)(u
46
− 9u
45
+ ··· − 80u + 8)
c
3
(u − 1)
18
· (u
10
+ 2u
9
− u
8
− 5u
7
− 3u
6
+ 4u
5
+ 12u
4
+ 13u
3
+ 5u
2
+ u + 2)
6
· (u
30
+ 2u
29
+ ··· + 9u + 2)(u
46
+ 9u
45
+ ··· + 48000u + 8768)
c
4
, c
11
(u
18
+ 10u
16
+ ··· − 106u + 23)(u
30
+ 17u
28
+ ··· − u + 1)
· (u
46
+ 22u
44
+ ··· + 2u + 1)(u
60
+ u
59
+ ··· − 626u + 3383)
c
5
, c
9
(u
18
+ 10u
16
+ ··· − 106u + 23)(u
30
+ 17u
28
+ ··· + u + 1)
· (u
46
+ 22u
44
+ ··· + 2u + 1)(u
60
+ u
59
+ ··· − 626u + 3383)
c
6
(u
3
+ u − 1)
6
· (u
10
+ u
9
+ 3u
8
+ 3u
7
+ 5u
6
+ 5u
5
+ 4u
4
+ 4u
3
+ 3u
2
+ 2u + 1)
6
· (u
30
+ 2u
29
+ ··· + 2u + 1)(u
46
− 9u
45
+ ··· − 80u + 8)
c
7
, c
10
(u
18
− 4u
17
+ ··· − 292u + 89)(u
30
− 3u
29
+ ··· − 10u + 1)
· (u
46
− 3u
45
+ ··· + 15u + 1)(u
60
− 11u
59
+ ··· − 53768u + 6593)
c
8
((u
3
+ u
2
+ 2u + 1)
26
)(u
30
− 2u
29
+ ··· + u + 2)
· (u
46
− 29u
45
+ ··· − 172032u + 8192)
c
12
((u
3
+ u
2
+ 2u + 1)
26
)(u
30
+ 2u
29
+ ··· − u + 2)
· (u
46
− 29u
45
+ ··· − 172032u + 8192)
30
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 2y
2
+ 5y − 1)
6
· (y
10
+ y
9
+ 13y
8
+ 11y
7
+ 45y
6
+ 35y
5
+ 12y
4
+ 2y
3
+ 9y
2
− 2y + 1)
6
· (y
30
+ 4y
29
+ ··· − 12y + 1)(y
46
+ 3y
45
+ ··· + 34304y + 4096)
c
2
, c
6
(y
3
+ 2y
2
+ y − 1)
6
· (y
10
+ 5y
9
+ 13y
8
+ 19y
7
+ 17y
6
+ 7y
5
− 2y
3
+ y
2
+ 2y + 1)
6
· (y
30
+ 16y
29
+ ··· + 8y + 1)(y
46
+ 23y
45
+ ··· + 160y + 64)
c
3
((y − 1)
18
)(y
10
− 6y
9
+ ··· + 19y + 4)
6
(y
30
− 8y
29
+ ··· + 51y + 4)
· (y
46
− 17y
45
+ ··· + 657339392y + 76877824)
c
4
, c
5
, c
9
c
11
(y
18
+ 20y
17
+ ··· + 356y + 529)(y
30
+ 34y
29
+ ··· − 9y + 1)
· (y
46
+ 44y
45
+ ··· + 2y + 1)
· (y
60
+ 55y
59
+ ··· − 363644884y + 11444689)
c
7
, c
10
(y
18
− 12y
17
+ ··· − 77788y + 7921)(y
30
− 7y
29
+ ··· − 30y + 1)
· (y
46
− 21y
45
+ ··· − 131y + 1)
· (y
60
− 17y
59
+ ··· + 11794588y + 43467649)
c
8
, c
12
((y
3
+ 3y
2
+ 2y − 1)
26
)(y
30
+ 20y
29
+ ··· + 63y + 4)
· (y
46
+ 23y
45
+ ··· − 301989888y + 67108864)
31
