12a
0906
(K12a
0906
)
A knot diagram
1
Linearized knot diagam
4 6 8 1 10 3 11 2 12 7 5 9
Solving Sequence
1,4
2
5,9
8 3 12 10 6 11 7
c
1
c
4
c
8
c
3
c
12
c
9
c
5
c
11
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.04772 × 10
856
u
165
+ 2.15325 × 10
857
u
164
+ ··· + 7.14027 × 10
856
b − 2.56483 × 10
859
,
− 5.81109 × 10
862
u
165
− 3.21459 × 10
863
u
164
+ ··· + 1.88142 × 10
863
a + 1.42202 × 10
866
,
u
166
+ 8u
165
+ ··· + 2632u + 872i
I
u
2
= h−2.55124 × 10
30
u
37
+ 8.73175 × 10
29
u
36
+ ··· + 2.16094 × 10
30
b − 2.67181 × 10
30
,
8.56010 × 10
31
u
37
+ 4.54227 × 10
31
u
36
+ ··· + 3.94371 × 10
31
a + 2.76795 × 10
32
, u
38
− u
37
+ ··· − 8u + 1i
I
u
3
= hb
2
+ bu + u
2
− b − u + 2, −u
2
+ a − 1, u
3
− u
2
+ 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 210 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
= h3.05 × 10
856
u
165
+ 2.15 × 10
857
u
164
+ · · · + 7.14 × 10
856
b − 2.56 ×
10
859
, −5.81 × 10
862
u
165
− 3.21 × 10
863
u
164
+ · · · + 1.88 × 10
863
a + 1.42 ×
10
866
, u
166
+ 8u
165
+ · · · + 2632u + 872i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
a
9
=
0.308868u
165
+ 1.70860u
164
+ ··· − 1647.45u − 755.823
−0.426835u
165
− 3.01565u
164
+ ··· + 488.904u + 359.207
a
8
=
0.709267u
165
+ 5.10475u
164
+ ··· − 399.199u − 450.266
−0.801687u
165
− 6.07418u
164
+ ··· − 368.114u + 190.946
a
3
=
1.66949u
165
+ 12.4962u
164
+ ··· + 514.887u − 490.226
−1.29994u
165
− 9.74217u
164
+ ··· − 506.050u + 346.274
a
12
=
1.00412u
165
+ 8.54831u
164
+ ··· + 3623.57u + 937.744
−0.586007u
165
− 5.28118u
164
+ ··· − 2908.83u − 836.491
a
10
=
−1.54406u
165
− 10.8649u
164
+ ··· + 1675.08u + 1229.26
1.57472u
165
+ 11.1056u
164
+ ··· − 1400.65u − 1149.74
a
6
=
1.25092u
165
+ 9.70100u
164
+ ··· + 1430.93u + 76.9177
−1.55368u
165
− 12.0162u
164
+ ··· − 1799.48u − 58.1751
a
11
=
0.700034u
165
+ 6.28921u
164
+ ··· + 3463.72u + 1005.58
−0.281919u
165
− 3.02209u
164
+ ··· − 2748.98u − 904.325
a
7
=
0.277983u
165
+ 3.57812u
164
+ ··· + 4227.48u + 1464.30
−1.07064u
165
− 9.95430u
164
+ ··· − 5989.86u − 1805.10
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.81941u
165
− 45.7526u
164
+ ··· − 8806.53u − 906.143
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
166
− 8u
165
+ ··· − 2632u + 872
c
2
, c
6
u
166
− 6u
165
+ ··· − 44364u + 15032
c
3
u
166
+ u
165
+ ··· + 77004800u + 37093376
c
5
u
166
− u
165
+ ··· − 77004800u + 37093376
c
7
, c
10
u
166
+ 6u
165
+ ··· + 44364u + 15032
c
8
u
166
− 2u
165
+ ··· + 23296u + 6376
c
9
, c
12
u
166
+ 8u
165
+ ··· + 2632u + 872
c
11
u
166
+ 2u
165
+ ··· − 23296u + 6376
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
9
c
12
y
166
+ 112y
165
+ ··· + 54967136y + 760384
c
2
, c
6
, c
7
c
10
y
166
− 88y
165
+ ··· − 10772707536y + 225961024
c
3
, c
5
y
166
− 37y
165
+ ··· − 110732919839916032y + 1375918543077376
c
8
, c
11
y
166
− 4y
165
+ ··· + 2251132064y + 40653376
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972169 + 0.218898I
a = −0.128892 + 0.159914I
b = 0.234140 + 1.328490I
−7.28993 − 0.80501I 0
u = 0.972169 − 0.218898I
a = −0.128892 − 0.159914I
b = 0.234140 − 1.328490I
−7.28993 + 0.80501I 0
u = −0.241874 + 0.958464I
a = −1.81538 + 0.81812I
b = 1.106070 − 0.249313I
−1.26280 + 2.02558I 0
u = −0.241874 − 0.958464I
a = −1.81538 − 0.81812I
b = 1.106070 + 0.249313I
−1.26280 − 2.02558I 0
u = −0.330909 + 0.958382I
a = 1.234160 + 0.600276I
b = −0.56010 − 1.49269I
0.64081 + 2.61414I 0
u = −0.330909 − 0.958382I
a = 1.234160 − 0.600276I
b = −0.56010 + 1.49269I
0.64081 − 2.61414I 0
u = 0.613798 + 0.813224I
a = −0.69358 − 1.37041I
b = 0.116888 − 1.252910I
−5.25563 − 2.26754I 0
u = 0.613798 − 0.813224I
a = −0.69358 + 1.37041I
b = 0.116888 + 1.252910I
−5.25563 + 2.26754I 0
u = −0.030127 + 1.025620I
a = −1.74054 − 0.44163I
b = 0.161139 − 0.843990I
4.56133 + 2.80842I 0
u = −0.030127 − 1.025620I
a = −1.74054 + 0.44163I
b = 0.161139 + 0.843990I
4.56133 − 2.80842I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.885024 + 0.524345I
a = 0.143825 + 0.269554I
b = −0.451443 + 0.448364I
1.42629 − 4.21693I 0
u = −0.885024 − 0.524345I
a = 0.143825 − 0.269554I
b = −0.451443 − 0.448364I
1.42629 + 4.21693I 0
u = −0.127639 + 0.955130I
a = −0.939256 + 0.779728I
b = 0.16705 + 1.40981I
−4.33829 + 4.25319I 0
u = −0.127639 − 0.955130I
a = −0.939256 − 0.779728I
b = 0.16705 − 1.40981I
−4.33829 − 4.25319I 0
u = −0.225299 + 0.936493I
a = 1.352360 + 0.100036I
b = −0.486351 − 1.236260I
0.64887 + 2.89892I 0
u = −0.225299 − 0.936493I
a = 1.352360 − 0.100036I
b = −0.486351 + 1.236260I
0.64887 − 2.89892I 0
u = 0.209745 + 1.023240I
a = 1.02484 − 1.59523I
b = −0.249301 + 1.027720I
−1.94689 − 3.53576I 0
u = 0.209745 − 1.023240I
a = 1.02484 + 1.59523I
b = −0.249301 − 1.027720I
−1.94689 + 3.53576I 0
u = 0.152380 + 0.931757I
a = −0.88458 − 1.19968I
b = 0.78153 + 1.70359I
−2.50839 − 0.97139I 0
u = 0.152380 − 0.931757I
a = −0.88458 + 1.19968I
b = 0.78153 − 1.70359I
−2.50839 + 0.97139I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.249301 + 1.027720I
a = 0.454155 + 0.833480I
b = −0.209745 + 1.023240I
1.94689 − 3.53576I 0
u = 0.249301 − 1.027720I
a = 0.454155 − 0.833480I
b = −0.209745 − 1.023240I
1.94689 + 3.53576I 0
u = 0.035069 + 1.059860I
a = 2.26454 − 0.47380I
b = −0.582937 + 0.928006I
4.95016 − 2.52119I 0
u = 0.035069 − 1.059860I
a = 2.26454 + 0.47380I
b = −0.582937 − 0.928006I
4.95016 + 2.52119I 0
u = −0.651241 + 0.667306I
a = 0.575706 + 0.364985I
b = 0.339015 − 1.328620I
−6.62966 − 2.49532I 0
u = −0.651241 − 0.667306I
a = 0.575706 − 0.364985I
b = 0.339015 + 1.328620I
−6.62966 + 2.49532I 0
u = −0.447824 + 0.970612I
a = −1.72043 − 0.13388I
b = 0.63804 + 1.35560I
−5.64838 + 6.76788I 0
u = −0.447824 − 0.970612I
a = −1.72043 + 0.13388I
b = 0.63804 − 1.35560I
−5.64838 − 6.76788I 0
u = 1.047770 + 0.258314I
a = −0.212607 + 0.061679I
b = −0.330148 − 1.199420I
−3.34359 + 1.96570I 0
u = 1.047770 − 0.258314I
a = −0.212607 − 0.061679I
b = −0.330148 + 1.199420I
−3.34359 − 1.96570I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.860323 + 0.669737I
a = 0.037789 − 0.360133I
b = 0.461677 + 1.274220I
−4.59764 + 5.27559I 0
u = 0.860323 − 0.669737I
a = 0.037789 + 0.360133I
b = 0.461677 − 1.274220I
−4.59764 − 5.27559I 0
u = 0.061638 + 0.907243I
a = 0.780592 − 0.464704I
b = −0.23918 − 1.46071I
−2.66064 + 2.48196I 0
u = 0.061638 − 0.907243I
a = 0.780592 + 0.464704I
b = −0.23918 + 1.46071I
−2.66064 − 2.48196I 0
u = 0.582937 + 0.928006I
a = 1.59448 + 0.54639I
b = −0.035069 + 1.059860I
−4.95016 − 2.52119I 0
u = 0.582937 − 0.928006I
a = 1.59448 − 0.54639I
b = −0.035069 − 1.059860I
−4.95016 + 2.52119I 0
u = 0.130373 + 1.088470I
a = −2.40675 − 0.57766I
b = 0.363797 − 1.133890I
1.31493 − 9.17596I 0
u = 0.130373 − 1.088470I
a = −2.40675 + 0.57766I
b = 0.363797 + 1.133890I
1.31493 + 9.17596I 0
u = −0.142227 + 0.890446I
a = −0.24139 + 1.58897I
b = 0.32729 − 2.09186I
−2.01341 + 6.35063I 0
u = −0.142227 − 0.890446I
a = −0.24139 − 1.58897I
b = 0.32729 + 2.09186I
−2.01341 − 6.35063I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.101570 + 0.069081I
a = 0.228295 − 0.259670I
b = −0.385385 − 1.286770I
−1.48964 + 7.78003I 0
u = −1.101570 − 0.069081I
a = 0.228295 + 0.259670I
b = −0.385385 + 1.286770I
−1.48964 − 7.78003I 0
u = 1.109350 + 0.049474I
a = 0.002103 + 0.278265I
b = −0.240939 + 1.226760I
−4.28618 − 2.77563I 0
u = 1.109350 − 0.049474I
a = 0.002103 − 0.278265I
b = −0.240939 − 1.226760I
−4.28618 + 2.77563I 0
u = 0.401620 + 0.778058I
a = −1.78845 − 0.73107I
b = 0.832421 + 0.085376I
−0.645618 + 0.585336I 0
u = 0.401620 − 0.778058I
a = −1.78845 + 0.73107I
b = 0.832421 − 0.085376I
−0.645618 − 0.585336I 0
u = −1.106070 + 0.249313I
a = −0.162926 − 0.775764I
b = 0.241874 − 0.958464I
1.26280 − 2.02558I 0
u = −1.106070 − 0.249313I
a = −0.162926 + 0.775764I
b = 0.241874 + 0.958464I
1.26280 + 2.02558I 0
u = 0.083335 + 0.860633I
a = −2.07119 + 1.07012I
b = 1.32235 − 0.96830I
−2.88532 − 0.42811I 0
u = 0.083335 − 0.860633I
a = −2.07119 − 1.07012I
b = 1.32235 + 0.96830I
−2.88532 + 0.42811I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.161139 + 0.843990I
a = 2.10569 + 1.21665I
b = 0.030127 − 1.025620I
−4.56133 − 2.80842I 0
u = −0.161139 − 0.843990I
a = 2.10569 − 1.21665I
b = 0.030127 + 1.025620I
−4.56133 + 2.80842I 0
u = 0.614309 + 0.973766I
a = −1.68275 + 0.10562I
b = 0.73446 − 1.26312I
−3.55161 − 10.76260I 0
u = 0.614309 − 0.973766I
a = −1.68275 − 0.10562I
b = 0.73446 + 1.26312I
−3.55161 + 10.76260I 0
u = 0.696817 + 0.928767I
a = −0.069883 − 0.256345I
b = −0.116062 − 0.135620I
−1.19072 − 1.66992I 0
u = 0.696817 − 0.928767I
a = −0.069883 + 0.256345I
b = −0.116062 + 0.135620I
−1.19072 + 1.66992I 0
u = −0.832421 + 0.085376I
a = 0.018474 + 1.207020I
b = −0.401620 + 0.778058I
0.645618 + 0.585336I 0
u = −0.832421 − 0.085376I
a = 0.018474 − 1.207020I
b = −0.401620 − 0.778058I
0.645618 − 0.585336I 0
u = 0.788236 + 0.244072I
a = 0.012371 + 0.586664I
b = 0.494958 − 0.132987I
−3.03351 − 3.67994I 0
u = 0.788236 − 0.244072I
a = 0.012371 − 0.586664I
b = 0.494958 + 0.132987I
−3.03351 + 3.67994I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.034081 + 0.821473I
a = 3.09960 − 0.54004I
b = 0.034081 + 0.821473I
8.51377I 0
u = −0.034081 − 0.821473I
a = 3.09960 + 0.54004I
b = 0.034081 − 0.821473I
− 8.51377I 0
u = 0.303969 + 1.143130I
a = 1.37878 − 0.74323I
b = −0.78329 + 1.51303I
0.84891 − 6.85717I 0
u = 0.303969 − 1.143130I
a = 1.37878 + 0.74323I
b = −0.78329 − 1.51303I
0.84891 + 6.85717I 0
u = −0.363797 + 1.133890I
a = 2.36613 + 0.64895I
b = −0.130373 − 1.088470I
−1.31493 + 9.17596I 0
u = −0.363797 − 1.133890I
a = 2.36613 − 0.64895I
b = −0.130373 + 1.088470I
−1.31493 − 9.17596I 0
u = 0.198308 + 1.176710I
a = 1.71393 − 0.52899I
b = −1.123230 + 0.576311I
4.15083 − 3.32222I 0
u = 0.198308 − 1.176710I
a = 1.71393 + 0.52899I
b = −1.123230 − 0.576311I
4.15083 + 3.32222I 0
u = −0.233186 + 0.768133I
a = −1.86686 − 1.12090I
b = 0.87930 + 1.27832I
−2.05570 − 4.32127I 0
u = −0.233186 − 0.768133I
a = −1.86686 + 1.12090I
b = 0.87930 − 1.27832I
−2.05570 + 4.32127I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.160540 + 0.784851I
a = −1.48487 − 0.10512I
b = 0.160540 + 0.784851I
− 0.664448I 0
u = −0.160540 − 0.784851I
a = −1.48487 + 0.10512I
b = 0.160540 − 0.784851I
0.664448I 0
u = −0.743499 + 0.235712I
a = −0.662425 − 0.472261I
b = 0.304555 − 0.177362I
3.05344 − 0.37163I 0
u = −0.743499 − 0.235712I
a = −0.662425 + 0.472261I
b = 0.304555 + 0.177362I
3.05344 + 0.37163I 0
u = 0.330148 + 1.199420I
a = 1.091160 + 0.071251I
b = −1.047770 − 0.258314I
3.34359 − 1.96570I 0
u = 0.330148 − 1.199420I
a = 1.091160 − 0.071251I
b = −1.047770 + 0.258314I
3.34359 + 1.96570I 0
u = −0.719261 + 0.232376I
a = 0.020514 − 0.471466I
b = 0.385001 − 1.327700I
−7.76532 − 3.84221I 0
u = −0.719261 − 0.232376I
a = 0.020514 + 0.471466I
b = 0.385001 + 1.327700I
−7.76532 + 3.84221I 0
u = 0.240939 + 1.226760I
a = 1.353480 − 0.010847I
b = −1.109350 + 0.049474I
4.28618 − 2.77563I 0
u = 0.240939 − 1.226760I
a = 1.353480 + 0.010847I
b = −1.109350 − 0.049474I
4.28618 + 2.77563I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.116888 + 1.252910I
a = 1.77651 + 1.25446I
b = −0.613798 − 0.813224I
5.25563 + 2.26754I 0
u = −0.116888 − 1.252910I
a = 1.77651 − 1.25446I
b = −0.613798 + 0.813224I
5.25563 − 2.26754I 0
u = 1.123230 + 0.576311I
a = 0.211423 + 0.518704I
b = −0.198308 + 1.176710I
−4.15083 − 3.32222I 0
u = 1.123230 − 0.576311I
a = 0.211423 − 0.518704I
b = −0.198308 − 1.176710I
−4.15083 + 3.32222I 0
u = −0.310070 + 1.224610I
a = 1.61977 − 0.31229I
b = −1.348560 + 0.102625I
6.97620 + 6.78564I 0
u = −0.310070 − 1.224610I
a = 1.61977 + 0.31229I
b = −1.348560 − 0.102625I
6.97620 − 6.78564I 0
u = −0.686445 + 0.265915I
a = −1.052380 − 0.012259I
b = −0.069590 + 1.294380I
−1.29336 + 1.14631I 0
u = −0.686445 − 0.265915I
a = −1.052380 + 0.012259I
b = −0.069590 − 1.294380I
−1.29336 − 1.14631I 0
u = −0.406135 + 1.201730I
a = −1.87282 − 0.36960I
b = 0.58817 + 1.29969I
−4.73323 + 8.05445I 0
u = −0.406135 − 1.201730I
a = −1.87282 + 0.36960I
b = 0.58817 − 1.29969I
−4.73323 − 8.05445I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.714302 + 0.140698I
a = −0.166511 − 1.038200I
b = 0.714302 + 0.140698I
9.66190I 0
u = −0.714302 − 0.140698I
a = −0.166511 + 1.038200I
b = 0.714302 − 0.140698I
− 9.66190I 0
u = −1.280860 + 0.073525I
a = −0.177460 − 0.212483I
b = 0.409078 − 1.266050I
−4.1077 − 13.8043I 0
u = −1.280860 − 0.073525I
a = −0.177460 + 0.212483I
b = 0.409078 + 1.266050I
−4.1077 + 13.8043I 0
u = 0.069590 + 1.294380I
a = −0.925594 + 0.281853I
b = 0.686445 + 0.265915I
1.29336 + 1.14631I 0
u = 0.069590 − 1.294380I
a = −0.925594 − 0.281853I
b = 0.686445 − 0.265915I
1.29336 − 1.14631I 0
u = 0.067307 + 1.322720I
a = −0.774104 − 1.111060I
b = 0.482054 + 0.306015I
3.80938 − 5.65587I 0
u = 0.067307 − 1.322720I
a = −0.774104 + 1.111060I
b = 0.482054 − 0.306015I
3.80938 + 5.65587I 0
u = 0.486351 + 1.236260I
a = −0.986871 + 0.314652I
b = 0.225299 − 0.936493I
−0.64887 − 2.89892I 0
u = 0.486351 − 1.236260I
a = −0.986871 − 0.314652I
b = 0.225299 + 0.936493I
−0.64887 + 2.89892I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.409078 + 1.266050I
a = −1.41004 + 0.30714I
b = 1.280860 − 0.073525I
4.1077 + 13.8043I 0
u = −0.409078 − 1.266050I
a = −1.41004 − 0.30714I
b = 1.280860 + 0.073525I
4.1077 − 13.8043I 0
u = 0.534347 + 1.228490I
a = −1.57597 + 0.40557I
b = 0.525199 − 1.270700I
−4.11997 − 4.57380I 0
u = 0.534347 − 1.228490I
a = −1.57597 − 0.40557I
b = 0.525199 + 1.270700I
−4.11997 + 4.57380I 0
u = 0.385385 + 1.286770I
a = −1.266930 − 0.161940I
b = 1.101570 − 0.069081I
1.48964 − 7.78003I 0
u = 0.385385 − 1.286770I
a = −1.266930 + 0.161940I
b = 1.101570 + 0.069081I
1.48964 + 7.78003I 0
u = −0.234140 + 1.328490I
a = 1.044440 − 0.352307I
b = −0.972169 + 0.218898I
7.28993 − 0.80501I 0
u = −0.234140 − 1.328490I
a = 1.044440 + 0.352307I
b = −0.972169 − 0.218898I
7.28993 + 0.80501I 0
u = 1.348560 + 0.102625I
a = −0.105012 + 0.302490I
b = 0.310070 + 1.224610I
−6.97620 + 6.78564I 0
u = 1.348560 − 0.102625I
a = −0.105012 − 0.302490I
b = 0.310070 − 1.224610I
−6.97620 − 6.78564I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.461677 + 1.274220I
a = 0.731739 − 0.408347I
b = −0.860323 + 0.669737I
4.59764 + 5.27559I 0
u = −0.461677 − 1.274220I
a = 0.731739 + 0.408347I
b = −0.860323 − 0.669737I
4.59764 − 5.27559I 0
u = 0.451443 + 0.448364I
a = −0.766158 − 1.003790I
b = 0.885024 + 0.524345I
−1.42629 − 4.21693I 0
u = 0.451443 − 0.448364I
a = −0.766158 + 1.003790I
b = 0.885024 − 0.524345I
−1.42629 + 4.21693I 0
u = −0.339015 + 1.328620I
a = −0.866270 + 0.256667I
b = 0.651241 − 0.667306I
6.62966 + 2.49532I 0
u = −0.339015 − 1.328620I
a = −0.866270 − 0.256667I
b = 0.651241 + 0.667306I
6.62966 − 2.49532I 0
u = −0.525199 + 1.270700I
a = 1.317640 − 0.150072I
b = −0.534347 − 1.228490I
4.11997 + 4.57380I 0
u = −0.525199 − 1.270700I
a = 1.317640 + 0.150072I
b = −0.534347 + 1.228490I
4.11997 − 4.57380I 0
u = −0.385001 + 1.327700I
a = −0.939073 + 0.367520I
b = 0.719261 − 0.232376I
7.76532 + 3.84221I 0
u = −0.385001 − 1.327700I
a = −0.939073 − 0.367520I
b = 0.719261 + 0.232376I
7.76532 − 3.84221I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.16705 + 1.40981I
a = −0.87657 − 1.30961I
b = 0.127639 + 0.955130I
4.33829 + 4.25319I 0
u = −0.16705 − 1.40981I
a = −0.87657 + 1.30961I
b = 0.127639 − 0.955130I
4.33829 − 4.25319I 0
u = −0.58817 + 1.29969I
a = −1.399390 + 0.174731I
b = 0.406135 + 1.201730I
4.73323 + 8.05445I 0
u = −0.58817 − 1.29969I
a = −1.399390 − 0.174731I
b = 0.406135 − 1.201730I
4.73323 − 8.05445I 0
u = −0.482054 + 0.306015I
a = 1.13197 + 1.63236I
b = −0.067307 + 1.322720I
−3.80938 − 5.65587I 0
u = −0.482054 − 0.306015I
a = 1.13197 − 1.63236I
b = −0.067307 − 1.322720I
−3.80938 + 5.65587I 0
u = 0.61776 + 1.30687I
a = 1.200820 − 0.231807I
b = −0.61776 + 1.30687I
− 7.98531I 0
u = 0.61776 − 1.30687I
a = 1.200820 + 0.231807I
b = −0.61776 − 1.30687I
7.98531I 0
u = −0.73446 + 1.26312I
a = 1.154390 − 0.240091I
b = −0.614309 − 0.973766I
3.55161 + 10.76260I 0
u = −0.73446 − 1.26312I
a = 1.154390 + 0.240091I
b = −0.614309 + 0.973766I
3.55161 − 10.76260I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.55984 + 1.35269I
a = 1.277190 − 0.263601I
b = −0.55984 + 1.35269I
− 8.66768I 0
u = 0.55984 − 1.35269I
a = 1.277190 + 0.263601I
b = −0.55984 − 1.35269I
8.66768I 0
u = −0.52831 + 1.36936I
a = 1.49399 + 0.31411I
b = −0.63120 − 1.36963I
2.96539 + 13.50520I 0
u = −0.52831 − 1.36936I
a = 1.49399 − 0.31411I
b = −0.63120 + 1.36963I
2.96539 − 13.50520I 0
u = 0.23918 + 1.46071I
a = −0.442710 + 1.146230I
b = −0.061638 − 0.907243I
2.66064 − 2.48196I 0
u = 0.23918 − 1.46071I
a = −0.442710 − 1.146230I
b = −0.061638 + 0.907243I
2.66064 + 2.48196I 0
u = −0.494958 + 0.132987I
a = 0.301143 + 1.053580I
b = −0.788236 − 0.244072I
3.03351 + 3.67994I 0
u = −0.494958 − 0.132987I
a = 0.301143 − 1.053580I
b = −0.788236 + 0.244072I
3.03351 − 3.67994I 0
u = −0.63804 + 1.35560I
a = −1.164130 + 0.030727I
b = 0.447824 + 0.970612I
5.64838 + 6.76788I 0
u = −0.63804 − 1.35560I
a = −1.164130 − 0.030727I
b = 0.447824 − 0.970612I
5.64838 − 6.76788I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.63120 + 1.36963I
a = −1.321960 + 0.113276I
b = 0.52831 − 1.36936I
−2.96539 − 13.50520I 0
u = 0.63120 − 1.36963I
a = −1.321960 − 0.113276I
b = 0.52831 + 1.36936I
−2.96539 + 13.50520I 0
u = −0.61818 + 1.37844I
a = −1.43618 − 0.18376I
b = 0.61818 + 1.37844I
20.3606I 0
u = −0.61818 − 1.37844I
a = −1.43618 + 0.18376I
b = 0.61818 − 1.37844I
− 20.3606I 0
u = 0.373681 + 0.268102I
a = −3.14053 − 2.43672I
b = −0.068273 − 0.202972I
−0.091634 + 0.759404I 0
u = 0.373681 − 0.268102I
a = −3.14053 + 2.43672I
b = −0.068273 + 0.202972I
−0.091634 − 0.759404I 0
u = −0.87930 + 1.27832I
a = −0.382366 + 0.348568I
b = 0.233186 + 0.768133I
2.05570 − 4.32127I 0
u = −0.87930 − 1.27832I
a = −0.382366 − 0.348568I
b = 0.233186 − 0.768133I
2.05570 + 4.32127I 0
u = 0.56010 + 1.49269I
a = −0.692095 + 0.163853I
b = 0.330909 − 0.958382I
−0.64081 − 2.61414I 0
u = 0.56010 − 1.49269I
a = −0.692095 − 0.163853I
b = 0.330909 + 0.958382I
−0.64081 + 2.61414I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.174652 + 0.334054I
a = −1.004240 − 0.737722I
b = −0.174652 + 0.334054I
− 0.928350I 0. + 6.99737I
u = 0.174652 − 0.334054I
a = −1.004240 + 0.737722I
b = −0.174652 − 0.334054I
0.928350I 0. − 6.99737I
u = −1.32235 + 0.96830I
a = 0.155400 − 0.367164I
b = −0.083335 − 0.860633I
2.88532 + 0.42811I 0
u = −1.32235 − 0.96830I
a = 0.155400 + 0.367164I
b = −0.083335 + 0.860633I
2.88532 − 0.42811I 0
u = −0.304555 + 0.177362I
a = 0.45862 + 1.57601I
b = 0.743499 − 0.235712I
−3.05344 + 0.37163I −4.41447 + 2.91552I
u = −0.304555 − 0.177362I
a = 0.45862 − 1.57601I
b = 0.743499 + 0.235712I
−3.05344 − 0.37163I −4.41447 − 2.91552I
u = 0.78329 + 1.51303I
a = 0.665389 − 0.117496I
b = −0.303969 + 1.143130I
−0.84891 − 6.85717I 0
u = 0.78329 − 1.51303I
a = 0.665389 + 0.117496I
b = −0.303969 − 1.143130I
−0.84891 + 6.85717I 0
u = 0.068273 + 0.202972I
a = 8.90502 + 0.57452I
b = −0.373681 − 0.268102I
0.091634 − 0.759404I 12.21539 + 1.68846I
u = 0.068273 − 0.202972I
a = 8.90502 − 0.57452I
b = −0.373681 + 0.268102I
0.091634 + 0.759404I 12.21539 − 1.68846I
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.116062 + 0.135620I
a = 1.04351 + 2.62194I
b = −0.696817 − 0.928767I
1.19072 + 1.66992I −12.48819 + 2.15812I
u = 0.116062 − 0.135620I
a = 1.04351 − 2.62194I
b = −0.696817 + 0.928767I
1.19072 − 1.66992I −12.48819 − 2.15812I
u = −0.78153 + 1.70359I
a = −0.117275 − 0.231026I
b = −0.152380 + 0.931757I
2.50839 − 0.97139I 0
u = −0.78153 − 1.70359I
a = −0.117275 + 0.231026I
b = −0.152380 − 0.931757I
2.50839 + 0.97139I 0
u = −0.32729 + 2.09186I
a = −0.037266 + 0.214055I
b = 0.142227 − 0.890446I
2.01341 − 6.35063I 0
u = −0.32729 − 2.09186I
a = −0.037266 − 0.214055I
b = 0.142227 + 0.890446I
2.01341 + 6.35063I 0
21
II.
I
u
2
= h−2.55×10
30
u
37
+8.73×10
29
u
36
+· · ·+2.16×10
30
b−2.67×10
30
, 8.56×
10
31
u
37
+4.54×10
31
u
36
+· · ·+3.94×10
31
a+2.77×10
32
, u
38
−u
37
+· · ·−8u+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
a
9
=
−2.17057u
37
− 1.15178u
36
+ ··· + 11.1508u − 7.01865
1.18062u
37
− 0.404072u
36
+ ··· − 9.36136u + 1.23641
a
8
=
−4.29415u
37
+ 0.467845u
36
+ ··· − 3.89602u − 4.93272
2.19941u
37
− 0.907133u
36
+ ··· − 11.2694u + 1.74037
a
3
=
−13.1177u
37
+ 8.80233u
36
+ ··· − 254.288u + 47.5716
1.57959u
37
+ 0.284487u
36
+ ··· + 0.995340u + 0.792686
a
12
=
1.53749u
37
− 2.23026u
36
+ ··· + 9.06011u − 2.36862
−2.13981u
37
+ 1.55284u
36
+ ··· − 14.4874u + 1.49894
a
10
=
−3.18350u
37
+ 3.79407u
36
+ ··· − 40.7575u − 0.708877
−0.0996288u
37
− 2.44960u
36
+ ··· + 13.6914u − 1.36519
a
6
=
−17.2790u
37
+ 16.2247u
36
+ ··· − 315.662u + 52.6626
1.88153u
37
− 3.83957u
36
+ ··· + 23.6180u − 2.10771
a
11
=
0.135992u
37
− 0.829652u
36
+ ··· − 0.575461u − 1.08889
−0.738310u
37
+ 0.152234u
36
+ ··· − 4.85187u + 0.219207
a
7
=
−7.36042u
37
+ 4.46863u
36
+ ··· − 45.7297u + 1.47141
0.834513u
37
− 2.31566u
36
+ ··· + 12.6154u − 1.63493
(ii) Obstruction class = 1
(iii) Cusp Shapes = 31.5312u
37
− 19.9178u
36
+ ··· + 569.219u − 68.4921
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
38
− u
37
+ ··· − 8u + 1
c
2
, c
10
u
38
− u
37
+ ··· − 3u + 1
c
3
u
38
− 2u
37
+ ··· + 14u + 28
c
4
, c
9
u
38
+ u
37
+ ··· + 8u + 1
c
5
u
38
+ 2u
37
+ ··· − 14u + 28
c
6
, c
7
u
38
+ u
37
+ ··· + 3u + 1
c
8
u
38
+ u
37
+ ··· + 4u + 1
c
11
u
38
− u
37
+ ··· − 4u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
9
c
12
y
38
+ 29y
37
+ ··· + 14y + 1
c
2
, c
6
, c
7
c
10
y
38
− 23y
37
+ ··· − 29y + 1
c
3
, c
5
y
38
− 40y
36
+ ··· − 2380y + 784
c
8
, c
11
y
38
− 3y
37
+ ··· + 32y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.933085 + 0.407912I
a = 0.221568 − 0.665433I
b = 0.185024 − 1.212340I
−4.23539 − 2.76947I −5.70457 − 0.94630I
u = 0.933085 − 0.407912I
a = 0.221568 + 0.665433I
b = 0.185024 + 1.212340I
−4.23539 + 2.76947I −5.70457 + 0.94630I
u = −0.340511 + 0.973127I
a = 2.81883 − 0.44021I
b = −0.340511 − 0.973127I
9.77424I 0. − 11.74663I
u = −0.340511 − 0.973127I
a = 2.81883 + 0.44021I
b = −0.340511 + 0.973127I
− 9.77424I 0. + 11.74663I
u = −0.908887 + 0.069929I
a = −0.477828 + 0.623256I
b = 0.302700 + 0.834985I
2.02629 + 1.51983I 3.65866 − 2.81426I
u = −0.908887 − 0.069929I
a = −0.477828 − 0.623256I
b = 0.302700 − 0.834985I
2.02629 − 1.51983I 3.65866 + 2.81426I
u = −0.069019 + 0.885914I
a = 0.819102 − 0.967431I
b = −0.27953 + 1.78152I
−1.84829 + 5.92717I 0.866897 − 1.032654I
u = −0.069019 − 0.885914I
a = 0.819102 + 0.967431I
b = −0.27953 − 1.78152I
−1.84829 − 5.92717I 0.866897 + 1.032654I
u = 0.302700 + 0.834985I
a = 1.39394 + 0.57384I
b = −0.908887 + 0.069929I
−2.02629 − 1.51983I −3.65866 + 2.81426I
u = 0.302700 − 0.834985I
a = 1.39394 − 0.57384I
b = −0.908887 − 0.069929I
−2.02629 + 1.51983I −3.65866 − 2.81426I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083005 + 0.879285I
a = 1.85347 + 1.11055I
b = −1.00387 − 1.29195I
−2.80877 − 0.42407I −6.63080 + 0.12335I
u = 0.083005 − 0.879285I
a = 1.85347 − 1.11055I
b = −1.00387 + 1.29195I
−2.80877 + 0.42407I −6.63080 − 0.12335I
u = 0.599807 + 0.979180I
a = 0.520410 − 0.236654I
b = −0.092209 + 0.471920I
−1.57677 − 1.71782I −8.52291 + 0.I
u = 0.599807 − 0.979180I
a = 0.520410 + 0.236654I
b = −0.092209 − 0.471920I
−1.57677 + 1.71782I −8.52291 + 0.I
u = 0.402827 + 1.115830I
a = 1.82813 − 0.31574I
b = −0.63829 + 1.30833I
−4.77406 − 7.12992I 0. + 3.49375I
u = 0.402827 − 1.115830I
a = 1.82813 + 0.31574I
b = −0.63829 − 1.30833I
−4.77406 + 7.12992I 0. − 3.49375I
u = 0.185024 + 1.212340I
a = −1.41955 + 0.72810I
b = 0.933085 − 0.407912I
4.23539 − 2.76947I 5.70457 + 0.I
u = 0.185024 − 1.212340I
a = −1.41955 − 0.72810I
b = 0.933085 + 0.407912I
4.23539 + 2.76947I 5.70457 + 0.I
u = 0.576577 + 0.514480I
a = −0.585116 + 0.217032I
b = −0.373316 − 1.341120I
−6.71738 + 3.21759I −3.21108 − 5.05543I
u = 0.576577 − 0.514480I
a = −0.585116 − 0.217032I
b = −0.373316 + 1.341120I
−6.71738 − 3.21759I −3.21108 + 5.05543I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.157862 + 1.249940I
a = −1.55615 − 1.09990I
b = 0.421901 + 0.531771I
5.78678 + 4.10535I 9.77321 + 0.I
u = −0.157862 − 1.249940I
a = −1.55615 + 1.09990I
b = 0.421901 − 0.531771I
5.78678 − 4.10535I 9.77321 + 0.I
u = 0.421901 + 0.531771I
a = 0.71850 + 2.24216I
b = −0.157862 + 1.249940I
−5.78678 − 4.10535I −9.77321 + 6.22329I
u = 0.421901 − 0.531771I
a = 0.71850 − 2.24216I
b = −0.157862 − 1.249940I
−5.78678 + 4.10535I −9.77321 − 6.22329I
u = −0.373316 + 1.341120I
a = −0.784797 + 0.237629I
b = 0.576577 − 0.514480I
6.71738 + 3.21759I 0
u = −0.373316 − 1.341120I
a = −0.784797 − 0.237629I
b = 0.576577 + 0.514480I
6.71738 − 3.21759I 0
u = −0.63829 + 1.30833I
a = −1.255780 + 0.132452I
b = 0.402827 + 1.115830I
4.77406 + 7.12992I 0
u = −0.63829 − 1.30833I
a = −1.255780 − 0.132452I
b = 0.402827 − 1.115830I
4.77406 − 7.12992I 0
u = 0.59606 + 1.34379I
a = −1.124550 + 0.305279I
b = 0.59606 − 1.34379I
− 8.35939I 0
u = 0.59606 − 1.34379I
a = −1.124550 − 0.305279I
b = 0.59606 + 1.34379I
8.35939I 0
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.092209 + 0.471920I
a = −1.133270 + 0.277519I
b = 0.599807 + 0.979180I
1.57677 + 1.71782I 8.52291 − 0.80662I
u = −0.092209 − 0.471920I
a = −1.133270 − 0.277519I
b = 0.599807 − 0.979180I
1.57677 − 1.71782I 8.52291 + 0.80662I
u = −1.00387 + 1.29195I
a = 0.439538 − 0.163487I
b = 0.083005 − 0.879285I
2.80877 − 0.42407I 0
u = −1.00387 − 1.29195I
a = 0.439538 + 0.163487I
b = 0.083005 + 0.879285I
2.80877 + 0.42407I 0
u = 0.262503 + 0.185193I
a = −4.48019 − 6.07184I
b = 0.262503 − 0.185193I
0.606687I 0. + 51.5656I
u = 0.262503 − 0.185193I
a = −4.48019 + 6.07184I
b = 0.262503 + 0.185193I
− 0.606687I 0. − 51.5656I
u = −0.27953 + 1.78152I
a = −0.296286 − 0.379246I
b = −0.069019 + 0.885914I
1.84829 − 5.92717I 0
u = −0.27953 − 1.78152I
a = −0.296286 + 0.379246I
b = −0.069019 − 0.885914I
1.84829 + 5.92717I 0
28
III. I
u
3
= hb
2
+ bu + u
2
− b − u + 2, −u
2
+ a − 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
a
9
=
u
2
+ 1
b
a
8
=
u
2
− b − u + 2
−u
2
b + b + 2u − 1
a
3
=
u
2
b − bu − u
2
+ 2b + u − 1
bu + u
2
− b − u
a
12
=
u
2
b + b + 1
−bu − u
2
+ b + u − 2
a
10
=
bu + b − 1
−bu − u
2
+ u − 1
a
6
=
u
2
b − bu + 2b
−u
2
+ u − 1
a
11
=
u
2
b + bu + u
2
+ b − u + 1
−2bu − 2u
2
+ b + 2u − 2
a
7
=
−bu + u
2
+ b + 2
bu − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4bu − 8u
2
+ 8u − 8
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
12
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
3
, c
10
(u
3
+ u
2
− 1)
2
c
4
, c
9
, c
11
(u
3
+ u
2
+ 2u + 1)
2
c
5
, c
6
, c
7
(u
3
− u
2
+ 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
c
9
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
3
, c
5
c
6
, c
7
, c
10
(y
3
− y
2
+ 2y −1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.662359 + 0.562280I
b = 0.215080 − 1.307140I
− 5.65624I 0. + 5.95889I
u = 0.215080 + 1.307140I
a = −0.662359 + 0.562280I
b = 0.569840
4.13758 − 2.82812I 6.52927 + 2.97945I
u = 0.215080 − 1.307140I
a = −0.662359 − 0.562280I
b = 0.215080 + 1.307140I
5.65624I 0. − 5.95889I
u = 0.215080 − 1.307140I
a = −0.662359 − 0.562280I
b = 0.569840
4.13758 + 2.82812I 6.52927 − 2.97945I
u = 0.569840
a = 1.32472
b = 0.215080 + 1.307140I
−4.13758 + 2.82812I −6.52927 − 2.97945I
u = 0.569840
a = 1.32472
b = 0.215080 − 1.307140I
−4.13758 − 2.82812I −6.52927 + 2.97945I
32
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
− u
2
+ 2u − 1)
2
)(u
38
− u
37
+ ··· − 8u + 1)
· (u
166
− 8u
165
+ ··· − 2632u + 872)
c
2
((u
3
+ u
2
− 1)
2
)(u
38
− u
37
+ ··· − 3u + 1)
· (u
166
− 6u
165
+ ··· − 44364u + 15032)
c
3
((u
3
+ u
2
− 1)
2
)(u
38
− 2u
37
+ ··· + 14u + 28)
· (u
166
+ u
165
+ ··· + 77004800u + 37093376)
c
4
((u
3
+ u
2
+ 2u + 1)
2
)(u
38
+ u
37
+ ··· + 8u + 1)
· (u
166
− 8u
165
+ ··· − 2632u + 872)
c
5
((u
3
− u
2
+ 1)
2
)(u
38
+ 2u
37
+ ··· − 14u + 28)
· (u
166
− u
165
+ ··· − 77004800u + 37093376)
c
6
((u
3
− u
2
+ 1)
2
)(u
38
+ u
37
+ ··· + 3u + 1)
· (u
166
− 6u
165
+ ··· − 44364u + 15032)
c
7
((u
3
− u
2
+ 1)
2
)(u
38
+ u
37
+ ··· + 3u + 1)
· (u
166
+ 6u
165
+ ··· + 44364u + 15032)
c
8
((u
3
− u
2
+ 2u − 1)
2
)(u
38
+ u
37
+ ··· + 4u + 1)
· (u
166
− 2u
165
+ ··· + 23296u + 6376)
c
9
((u
3
+ u
2
+ 2u + 1)
2
)(u
38
+ u
37
+ ··· + 8u + 1)
· (u
166
+ 8u
165
+ ··· + 2632u + 872)
c
10
((u
3
+ u
2
− 1)
2
)(u
38
− u
37
+ ··· − 3u + 1)
· (u
166
+ 6u
165
+ ··· + 44364u + 15032)
c
11
((u
3
+ u
2
+ 2u + 1)
2
)(u
38
− u
37
+ ··· − 4u + 1)
· (u
166
+ 2u
165
+ ··· − 23296u + 6376)
c
12
((u
3
− u
2
+ 2u − 1)
2
)(u
38
− u
37
+ ··· − 8u + 1)
· (u
166
+ 8u
165
+ ··· + 2632u + 872)
33
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
9
c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
38
+ 29y
37
+ ··· + 14y + 1)
· (y
166
+ 112y
165
+ ··· + 54967136y + 760384)
c
2
, c
6
, c
7
c
10
((y
3
− y
2
+ 2y −1)
2
)(y
38
− 23y
37
+ ··· − 29y + 1)
· (y
166
− 88y
165
+ ··· − 10772707536y + 225961024)
c
3
, c
5
((y
3
− y
2
+ 2y −1)
2
)(y
38
− 40y
36
+ ··· − 2380y + 784)
· (y
166
− 37y
165
+ ··· − 110732919839916032y + 1375918543077376)
c
8
, c
11
((y
3
+ 3y
2
+ 2y −1)
2
)(y
38
− 3y
37
+ ··· + 32y + 1)
· (y
166
− 4y
165
+ ··· + 2251132064y + 40653376)
34
