12a
0478
(K12a
0478
)
A knot diagram
1
Linearized knot diagam
3 6 11 9 7 2 1 12 5 8 4 10
Solving Sequence
4,11 8,12
9 5 3 10 1 2 7 6
c
11
c
8
c
4
c
3
c
10
c
12
c
1
c
7
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h5.33641 × 10
28
u
43
− 9.09644 × 10
28
u
42
+ ··· + 3.03461 × 10
30
b + 1.66297 × 10
30
,
4.33477 × 10
29
u
43
− 4.31353 × 10
28
u
42
+ ··· + 3.03461 × 10
30
a − 1.76199 × 10
30
, u
44
− u
43
+ ··· + u + 1i
I
u
2
= h7.99621 × 10
275
u
83
+ 1.94730 × 10
276
u
82
+ ··· + 8.94216 × 10
276
b − 2.93848 × 10
279
,
− 2.61794 × 10
279
u
83
− 6.34847 × 10
279
u
82
+ ··· + 2.66745 × 10
280
a + 7.68018 × 10
282
,
u
84
+ u
83
+ ··· + 1700u + 2983i
I
u
3
= h−u
2
+ b + 1, u
20
− u
19
+ ··· + a + 2, u
21
− u
20
+ ··· − 3u + 1i
* 3 irreducible components of dim
C
= 0, with total 149 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
= h5.34 × 10
28
u
43
− 9.10 × 10
28
u
42
+ · · · + 3.03 × 10
30
b + 1.66 × 10
30
, 4.33 ×
10
29
u
43
−4.31×10
28
u
42
+· · ·+3.03×10
30
a−1.76×10
30
, u
44
−u
43
+· · ·+u+1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
8
=
−0.142844u
43
+ 0.0142144u
42
+ ··· + 1.40262u + 0.580630
−0.0175851u
43
+ 0.0299756u
42
+ ··· + 1.13114u − 0.548000
a
12
=
1
−u
2
a
9
=
1
−0.142844u
43
+ 0.0142144u
42
+ ··· + 1.40262u − 0.419370
a
5
=
u
−0.128630u
43
+ 0.00337070u
42
+ ··· + 0.723474u + 0.142844
a
3
=
−u
u
a
10
=
−u
2
+ 1
−0.0175851u
43
+ 0.0299756u
42
+ ··· + 1.13114u − 0.548000
a
1
=
−0.000908052u
43
+ 0.108043u
42
+ ··· + 1.12595u + 0.464391
−0.0217088u
43
+ 0.0957979u
42
+ ··· − 1.02492u + 0.655135
a
2
=
−0.0789830u
43
+ 0.152702u
42
+ ··· + 1.28456u + 0.645614
0.0563662u
43
+ 0.0511385u
42
+ ··· − 1.18352u + 0.473911
a
7
=
−0.0789830u
43
+ 0.152702u
42
+ ··· + 1.28456u + 0.645614
−0.0516465u
43
− 0.106716u
42
+ ··· + 1.17971u − 0.547530
a
6
=
−0.234445u
43
+ 0.296776u
42
+ ··· + 0.343682u + 0.0836407
0.219664u
43
− 0.477705u
42
+ ··· + 1.35750u + 0.331150
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.438894u
43
− 1.56601u
42
+ ··· + 5.58366u + 2.74109
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
44
+ 14u
43
+ ··· + 4u + 16
c
2
, c
6
u
44
− 6u
43
+ ··· − 2u − 4
c
3
, c
4
, c
9
c
11
u
44
− u
43
+ ··· + u + 1
c
7
u
44
+ 30u
43
+ ··· − 88022u − 6988
c
8
u
44
+ 40u
43
+ ··· − 42991616u − 2097152
c
10
, c
12
u
44
+ 2u
43
+ ··· + 7u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
44
+ 30y
43
+ ··· + 9744y + 256
c
2
, c
6
y
44
+ 14y
43
+ ··· + 4y + 16
c
3
, c
4
, c
9
c
11
y
44
− 31y
43
+ ··· + y + 1
c
7
y
44
+ 6y
43
+ ··· + 106960964y + 48832144
c
8
y
44
− 2y
43
+ ··· − 7696581394432y + 4398046511104
c
10
, c
12
y
44
− 10y
43
+ ··· − 37y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.963533 + 0.350253I
a = 0.86851 + 1.90330I
b = 0.453390 − 0.216435I
3.18342 + 3.22741I 0.25538 − 6.57497I
u = 0.963533 − 0.350253I
a = 0.86851 − 1.90330I
b = 0.453390 + 0.216435I
3.18342 − 3.22741I 0.25538 + 6.57497I
u = −1.022440 + 0.093582I
a = −0.935498 + 0.358789I
b = −1.034400 − 0.192161I
−1.47417 − 3.43532I 0.66881 + 5.03721I
u = −1.022440 − 0.093582I
a = −0.935498 − 0.358789I
b = −1.034400 + 0.192161I
−1.47417 + 3.43532I 0.66881 − 5.03721I
u = 1.05616
a = −1.31524
b = −0.848120
2.23451 3.56780
u = −0.980841 + 0.478403I
a = 0.65210 − 1.59072I
b = 0.666848 + 0.187542I
1.53255 − 8.57516I 0.51722 + 9.73471I
u = −0.980841 − 0.478403I
a = 0.65210 + 1.59072I
b = 0.666848 − 0.187542I
1.53255 + 8.57516I 0.51722 − 9.73471I
u = 1.139270 + 0.093898I
a = −1.058050 − 0.808186I
b = −0.866999 + 0.460040I
6.02381 + 3.30020I 7.56096 − 4.45656I
u = 1.139270 − 0.093898I
a = −1.058050 + 0.808186I
b = −0.866999 − 0.460040I
6.02381 − 3.30020I 7.56096 + 4.45656I
u = −1.143130 + 0.125355I
a = −0.938693 + 0.792091I
b = −0.953820 − 0.499545I
4.99041 − 9.37474I 6.29693 + 8.40216I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.143130 − 0.125355I
a = −0.938693 − 0.792091I
b = −0.953820 + 0.499545I
4.99041 + 9.37474I 6.29693 − 8.40216I
u = 0.217696 + 0.819184I
a = 0.152694 − 0.527270I
b = −0.940135 − 0.910573I
−0.52383 − 7.78712I 0.00351 + 6.35147I
u = 0.217696 − 0.819184I
a = 0.152694 + 0.527270I
b = −0.940135 + 0.910573I
−0.52383 + 7.78712I 0.00351 − 6.35147I
u = −0.688920 + 0.451970I
a = 1.02687 − 1.08790I
b = 0.426757 − 0.154326I
−2.73346 − 2.08740I −3.07292 + 2.85449I
u = −0.688920 − 0.451970I
a = 1.02687 + 1.08790I
b = 0.426757 + 0.154326I
−2.73346 + 2.08740I −3.07292 − 2.85449I
u = −0.176839 + 0.789101I
a = 0.180681 + 0.508444I
b = −0.854363 + 0.859568I
0.40669 + 2.26076I 1.58718 − 1.55987I
u = −0.176839 − 0.789101I
a = 0.180681 − 0.508444I
b = −0.854363 − 0.859568I
0.40669 − 2.26076I 1.58718 + 1.55987I
u = 0.308970 + 0.711810I
a = 0.086084 − 0.461553I
b = −1.081530 − 0.689213I
−5.25526 − 2.25847I −6.26530 + 1.17443I
u = 0.308970 − 0.711810I
a = 0.086084 + 0.461553I
b = −1.081530 + 0.689213I
−5.25526 + 2.25847I −6.26530 − 1.17443I
u = −0.364868 + 0.635114I
a = 0.660022 − 0.672984I
b = 0.150292 − 0.548954I
0.83408 + 3.47441I 2.06056 − 1.25791I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.364868 − 0.635114I
a = 0.660022 + 0.672984I
b = 0.150292 + 0.548954I
0.83408 − 3.47441I 2.06056 + 1.25791I
u = 0.457923 + 0.566781I
a = −0.044360 − 0.398417I
b = −1.256120 − 0.419833I
−2.07652 + 3.22600I −0.64383 − 7.61023I
u = 0.457923 − 0.566781I
a = −0.044360 + 0.398417I
b = −1.256120 + 0.419833I
−2.07652 − 3.22600I −0.64383 + 7.61023I
u = 0.236575 + 0.631412I
a = 0.581720 + 0.550322I
b = −0.054507 + 0.565134I
1.51179 + 1.75801I 3.42715 − 4.74250I
u = 0.236575 − 0.631412I
a = 0.581720 − 0.550322I
b = −0.054507 − 0.565134I
1.51179 − 1.75801I 3.42715 + 4.74250I
u = 0.645516
a = 2.06097
b = 0.202182
1.23926 13.0470
u = 1.348290 + 0.336035I
a = −0.06962 + 1.61677I
b = 0.514106 − 1.076690I
11.66130 + 2.70389I 0
u = 1.348290 − 0.336035I
a = −0.06962 − 1.61677I
b = 0.514106 + 1.076690I
11.66130 − 2.70389I 0
u = −0.461955 + 0.387848I
a = −0.104836 + 0.279406I
b = −1.198360 + 0.224243I
−1.42861 + 1.53127I 2.46911 + 4.30137I
u = −0.461955 − 0.387848I
a = −0.104836 − 0.279406I
b = −1.198360 − 0.224243I
−1.42861 − 1.53127I 2.46911 − 4.30137I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.31771 + 0.52143I
a = 0.13723 + 1.49979I
b = 0.997246 − 0.885207I
3.63174 + 5.85824I 0
u = 1.31771 − 0.52143I
a = 0.13723 − 1.49979I
b = 0.997246 + 0.885207I
3.63174 − 5.85824I 0
u = −1.37313 + 0.36438I
a = −0.04599 − 1.56888I
b = 0.604568 + 1.134910I
11.8635 − 8.8046I 0
u = −1.37313 − 0.36438I
a = −0.04599 + 1.56888I
b = 0.604568 − 1.134910I
11.8635 + 8.8046I 0
u = −0.153275 + 0.539163I
a = 0.183448 + 0.292807I
b = −0.815929 + 0.401366I
−1.39440 + 1.01413I −2.43614 − 1.49783I
u = −0.153275 − 0.539163I
a = 0.183448 − 0.292807I
b = −0.815929 − 0.401366I
−1.39440 − 1.01413I −2.43614 + 1.49783I
u = −1.38286 + 0.50685I
a = 0.07770 − 1.47027I
b = 1.01010 + 1.07254I
6.12470 − 9.94560I 0
u = −1.38286 − 0.50685I
a = 0.07770 + 1.47027I
b = 1.01010 − 1.07254I
6.12470 + 9.94560I 0
u = 1.40141 + 0.56071I
a = 0.09688 + 1.42482I
b = 1.17626 − 1.07775I
1.86199 + 12.59430I 0
u = 1.40141 − 0.56071I
a = 0.09688 − 1.42482I
b = 1.17626 + 1.07775I
1.86199 − 12.59430I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45240 + 0.53962I
a = 0.057156 − 1.409450I
b = 1.16253 + 1.24292I
8.6839 − 12.8336I 0
u = −1.45240 − 0.53962I
a = 0.057156 + 1.409450I
b = 1.16253 − 1.24292I
8.6839 + 12.8336I 0
u = 1.45843 + 0.55635I
a = 0.063082 + 1.397950I
b = 1.21703 − 1.24520I
7.5897 + 18.7123I 0
u = 1.45843 − 0.55635I
a = 0.063082 − 1.397950I
b = 1.21703 + 1.24520I
7.5897 − 18.7123I 0
9
II. I
u
2
= h8.00 × 10
275
u
83
+ 1.95 × 10
276
u
82
+ · · · + 8.94 × 10
276
b − 2.94 ×
10
279
, −2.62 × 10
279
u
83
− 6.35 × 10
279
u
82
+ · · · + 2.67 × 10
280
a + 7.68 ×
10
282
, u
84
+ u
83
+ · · · + 1700u + 2983i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
8
=
0.0981441u
83
+ 0.237998u
82
+ ··· − 461.448u − 287.922
−0.0894214u
83
− 0.217766u
82
+ ··· + 415.217u + 328.609
a
12
=
1
−u
2
a
9
=
0.0717702u
83
+ 0.154245u
82
+ ··· − 346.149u − 199.348
−0.0466237u
83
− 0.0835566u
82
+ ··· + 238.998u + 157.447
a
5
=
−0.180265u
83
− 0.321728u
82
+ ··· + 766.751u + 328.107
0.174737u
83
+ 0.332085u
82
+ ··· − 717.974u − 456.666
a
3
=
−u
u
a
10
=
−0.180348u
83
− 0.497384u
82
+ ··· + 739.524u + 644.660
0.251112u
83
+ 0.641466u
82
+ ··· − 1096.60u − 894.041
a
1
=
0.170906u
83
+ 0.314317u
82
+ ··· − 852.555u − 530.571
−0.0636915u
83
− 0.0558300u
82
+ ··· + 362.180u + 134.499
a
2
=
0.0385080u
83
− 0.00797016u
82
+ ··· − 275.571u − 79.3238
0.0687064u
83
+ 0.266457u
82
+ ··· − 214.804u − 316.748
a
7
=
−0.0970944u
83
− 0.280754u
82
+ ··· + 381.748u + 372.199
0.285872u
83
+ 0.718243u
82
+ ··· − 1158.87u − 926.093
a
6
=
0.504901u
83
+ 0.999388u
82
+ ··· − 1864.77u − 1209.57
−0.399278u
83
− 0.751070u
82
+ ··· + 1389.21u + 833.181
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.529975u
83
− 1.07671u
82
+ ··· + 1915.72u + 1175.59
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
21
+ 7u
20
+ ··· + 3u − 1)
4
c
2
, c
6
(u
21
+ u
20
+ ··· + u + 1)
4
c
3
, c
4
, c
9
c
11
u
84
+ u
83
+ ··· + 1700u + 2983
c
7
(u
21
− 5u
20
+ ··· − 11u + 3)
4
c
8
(u
2
− u + 1)
42
c
10
, c
12
u
84
− 23u
83
+ ··· − 646u + 37
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
21
+ 15y
20
+ ··· + 27y −1)
4
c
2
, c
6
(y
21
+ 7y
20
+ ··· + 3y −1)
4
c
3
, c
4
, c
9
c
11
y
84
− 69y
83
+ ··· − 605825892y + 8898289
c
7
(y
21
+ 3y
20
+ ··· − 41y −9)
4
c
8
(y
2
+ y + 1)
42
c
10
, c
12
y
84
+ 19y
83
+ ··· + 39856y + 1369
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.601980 + 0.847982I
a = −0.395112 + 0.064605I
b = 0.425024 − 0.439597I
6.30468 + 4.71576I 0
u = 0.601980 − 0.847982I
a = −0.395112 − 0.064605I
b = 0.425024 + 0.439597I
6.30468 − 4.71576I 0
u = −0.768780 + 0.567617I
a = 0.943793 − 0.486452I
b = 0.670826 + 0.088440I
−2.65275 − 2.26732I 0
u = −0.768780 − 0.567617I
a = 0.943793 + 0.486452I
b = 0.670826 − 0.088440I
−2.65275 + 2.26732I 0
u = 1.049670 + 0.081978I
a = −1.04625 − 1.09035I
b = 1.45807 + 0.50805I
2.91326 + 0.43299I 0
u = 1.049670 − 0.081978I
a = −1.04625 + 1.09035I
b = 1.45807 − 0.50805I
2.91326 − 0.43299I 0
u = 0.939509 + 0.083935I
a = 0.84854 + 1.30340I
b = −0.037440 − 0.409098I
1.53708 + 0.23287I 0
u = 0.939509 − 0.083935I
a = 0.84854 − 1.30340I
b = −0.037440 + 0.409098I
1.53708 − 0.23287I 0
u = 0.120597 + 1.085890I
a = 0.324279 − 0.122790I
b = 0.845498 + 0.638091I
−0.209312 − 0.222255I 0
u = 0.120597 − 1.085890I
a = 0.324279 + 0.122790I
b = 0.845498 − 0.638091I
−0.209312 + 0.222255I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.052550 + 0.310061I
a = 0.32578 − 1.84638I
b = −1.034750 + 0.789358I
−0.209312 + 0.222255I 0
u = 1.052550 − 0.310061I
a = 0.32578 + 1.84638I
b = −1.034750 − 0.789358I
−0.209312 − 0.222255I 0
u = 0.081948 + 1.103030I
a = 0.152729 + 0.151629I
b = 0.712209 − 0.710171I
1.53708 + 4.29264I 0
u = 0.081948 − 1.103030I
a = 0.152729 − 0.151629I
b = 0.712209 + 0.710171I
1.53708 − 4.29264I 0
u = −0.872714 + 0.160939I
a = 0.76623 + 1.81920I
b = −0.574764 − 0.257172I
−0.20931 − 3.83751I 0
u = −0.872714 − 0.160939I
a = 0.76623 − 1.81920I
b = −0.574764 + 0.257172I
−0.20931 + 3.83751I 0
u = −0.385745 + 0.789003I
a = 0.771823 + 0.107178I
b = 0.800393 − 0.345438I
−0.20931 + 3.83751I 0
u = −0.385745 − 0.789003I
a = 0.771823 − 0.107178I
b = 0.800393 + 0.345438I
−0.20931 − 3.83751I 0
u = 1.134620 + 0.022935I
a = −1.00246 + 1.31545I
b = 1.85846 − 0.77456I
7.83914 + 4.48847I 0
u = 1.134620 − 0.022935I
a = −1.00246 − 1.31545I
b = 1.85846 + 0.77456I
7.83914 − 4.48847I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.052490 + 0.480961I
a = 0.705316 + 0.737358I
b = 0.628364 − 0.494270I
3.61388 + 2.45396I 0
u = 1.052490 − 0.480961I
a = 0.705316 − 0.737358I
b = 0.628364 + 0.494270I
3.61388 − 2.45396I 0
u = −1.162680 + 0.004240I
a = −0.94957 − 1.31119I
b = 1.79655 + 0.89708I
8.59448 + 1.12879I 0
u = −1.162680 − 0.004240I
a = −0.94957 + 1.31119I
b = 1.79655 − 0.89708I
8.59448 − 1.12879I 0
u = −0.863159 + 0.799142I
a = −0.467671 + 0.197656I
b = 0.277087 + 0.199805I
6.09470 + 0.70163I 0
u = −0.863159 − 0.799142I
a = −0.467671 − 0.197656I
b = 0.277087 − 0.199805I
6.09470 − 0.70163I 0
u = −1.048850 + 0.560595I
a = 0.686771 − 0.663283I
b = 0.740316 + 0.462808I
2.56394 − 8.15338I 0
u = −1.048850 − 0.560595I
a = 0.686771 + 0.663283I
b = 0.740316 − 0.462808I
2.56394 + 8.15338I 0
u = −1.150960 + 0.299655I
a = 0.19965 + 1.74618I
b = −0.95104 − 1.15266I
1.53708 − 4.29264I 0
u = −1.150960 − 0.299655I
a = 0.19965 − 1.74618I
b = −0.95104 + 1.15266I
1.53708 + 4.29264I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.141140 + 0.376776I
a = 0.15415 − 1.85666I
b = −1.27540 + 1.15560I
−2.65275 + 6.32709I 0
u = 1.141140 − 0.376776I
a = 0.15415 + 1.85666I
b = −1.27540 − 1.15560I
−2.65275 − 6.32709I 0
u = −1.227890 + 0.132471I
a = −0.728674 + 1.178950I
b = 1.20230 − 1.12786I
5.75861 − 2.02988I 0
u = −1.227890 − 0.132471I
a = −0.728674 − 1.178950I
b = 1.20230 + 1.12786I
5.75861 + 2.02988I 0
u = 0.710745 + 0.257486I
a = −1.40228 − 0.34636I
b = 0.988633 − 0.200767I
6.09470 + 4.76140I 6.80842 − 5.46594I
u = 0.710745 − 0.257486I
a = −1.40228 + 0.34636I
b = 0.988633 + 0.200767I
6.09470 − 4.76140I 6.80842 + 5.46594I
u = −0.021423 + 1.260760I
a = 0.185863 − 0.033760I
b = 0.797169 + 0.822419I
−2.65275 − 6.32709I 0
u = −0.021423 − 1.260760I
a = 0.185863 + 0.033760I
b = 0.797169 − 0.822419I
−2.65275 + 6.32709I 0
u = −1.205030 + 0.379527I
a = 0.07156 + 1.81786I
b = −1.25638 − 1.44640I
3.61388 − 6.51373I 0
u = −1.205030 − 0.379527I
a = 0.07156 − 1.81786I
b = −1.25638 + 1.44640I
3.61388 + 6.51373I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.200130 + 0.399924I
a = 0.06593 − 1.84627I
b = −1.35668 + 1.43457I
2.56394 + 12.21310I 0
u = 1.200130 − 0.399924I
a = 0.06593 + 1.84627I
b = −1.35668 − 1.43457I
2.56394 − 12.21310I 0
u = 0.155036 + 1.309600I
a = 0.1067750 + 0.0075772I
b = 0.683635 − 0.896570I
3.61388 + 6.51373I 0
u = 0.155036 − 1.309600I
a = 0.1067750 − 0.0075772I
b = 0.683635 + 0.896570I
3.61388 − 6.51373I 0
u = −1.331340 + 0.069009I
a = −0.66571 + 1.39234I
b = 1.42093 − 1.71754I
8.59448 − 2.93098I 0
u = −1.331340 − 0.069009I
a = −0.66571 − 1.39234I
b = 1.42093 + 1.71754I
8.59448 + 2.93098I 0
u = −1.328000 + 0.198818I
a = −0.03686 + 1.42419I
b = −0.18850 − 1.60882I
6.30468 − 4.71576I 0
u = −1.328000 − 0.198818I
a = −0.03686 − 1.42419I
b = −0.18850 + 1.60882I
6.30468 + 4.71576I 0
u = 1.346210 + 0.144723I
a = −0.52346 − 1.32462I
b = 0.92154 + 1.71078I
2.91326 + 3.62678I 0
u = 1.346210 − 0.144723I
a = −0.52346 + 1.32462I
b = 0.92154 − 1.71078I
2.91326 − 3.62678I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.352110 + 0.075673I
a = −0.63529 − 1.41451I
b = 1.36834 + 1.84188I
7.83914 + 8.54824I 0
u = 1.352110 − 0.075673I
a = −0.63529 + 1.41451I
b = 1.36834 − 1.84188I
7.83914 − 8.54824I 0
u = −0.128917 + 1.350010I
a = 0.1223140 + 0.0131157I
b = 0.716321 + 0.932286I
2.56394 − 12.21310I 0
u = −0.128917 − 1.350010I
a = 0.1223140 − 0.0131157I
b = 0.716321 − 0.932286I
2.56394 + 12.21310I 0
u = 1.369380 + 0.196398I
a = −0.199637 − 1.349260I
b = 0.14091 + 1.71944I
6.09470 − 0.70163I 0
u = 1.369380 − 0.196398I
a = −0.199637 + 1.349260I
b = 0.14091 − 1.71944I
6.09470 + 0.70163I 0
u = 1.388100 + 0.034594I
a = 0.160651 − 1.101620I
b = 0.084846 + 1.239850I
6.30468 − 0.65599I 0
u = 1.388100 − 0.034594I
a = 0.160651 + 1.101620I
b = 0.084846 − 1.239850I
6.30468 + 0.65599I 0
u = −0.462900 + 0.338762I
a = −1.48845 − 0.51444I
b = 0.809467 + 0.450405I
6.30468 + 0.65599I 7.85070 − 0.21108I
u = −0.462900 − 0.338762I
a = −1.48845 + 0.51444I
b = 0.809467 − 0.450405I
6.30468 − 0.65599I 7.85070 + 0.21108I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.556631 + 0.039904I
a = 1.80134 + 1.97905I
b = −0.143171 + 0.336012I
−2.65275 + 2.26732I −0.751433 − 0.468938I
u = −0.556631 − 0.039904I
a = 1.80134 − 1.97905I
b = −0.143171 − 0.336012I
−2.65275 − 2.26732I −0.751433 + 0.468938I
u = 0.290742 + 0.440170I
a = 1.61434 − 0.53235I
b = 0.540061 + 0.394688I
1.53708 + 0.23287I 6.12423 + 0.35001I
u = 0.290742 − 0.440170I
a = 1.61434 + 0.53235I
b = 0.540061 − 0.394688I
1.53708 − 0.23287I 6.12423 − 0.35001I
u = −1.48585 + 0.12046I
a = 0.010822 + 0.999659I
b = 0.118412 − 1.322580I
6.09470 − 4.76140I 0
u = −1.48585 − 0.12046I
a = 0.010822 − 0.999659I
b = 0.118412 + 1.322580I
6.09470 + 4.76140I 0
u = −1.31142 + 0.76548I
a = −0.313707 + 0.501417I
b = −0.151011 − 0.332343I
2.91326 − 3.62678I 0
u = −1.31142 − 0.76548I
a = −0.313707 − 0.501417I
b = −0.151011 + 0.332343I
2.91326 + 3.62678I 0
u = 1.46722 + 0.54701I
a = −0.264308 − 0.671365I
b = −0.087745 + 0.802616I
5.75861 + 2.02988I 0
u = 1.46722 − 0.54701I
a = −0.264308 + 0.671365I
b = −0.087745 − 0.802616I
5.75861 − 2.02988I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60465 + 0.36222I
a = −0.133395 + 0.774134I
b = −0.073945 − 1.180800I
2.91326 − 0.43299I 0
u = −1.60465 − 0.36222I
a = −0.133395 − 0.774134I
b = −0.073945 + 1.180800I
2.91326 + 0.43299I 0
u = −0.309551 + 0.107943I
a = 2.95791 + 3.53411I
b = 0.014856 + 0.766229I
2.56394 + 8.15338I 4.74618 − 3.74885I
u = −0.309551 − 0.107943I
a = 2.95791 − 3.53411I
b = 0.014856 − 0.766229I
2.56394 − 8.15338I 4.74618 + 3.74885I
u = 1.51563 + 0.78115I
a = −0.212584 − 0.544293I
b = −0.430203 + 0.555541I
8.59448 + 2.93098I 0
u = 1.51563 − 0.78115I
a = −0.212584 + 0.544293I
b = −0.430203 − 0.555541I
8.59448 − 2.93098I 0
u = −1.49353 + 0.82752I
a = −0.214147 + 0.521007I
b = −0.456812 − 0.468715I
7.83914 − 8.54824I 0
u = −1.49353 − 0.82752I
a = −0.214147 − 0.521007I
b = −0.456812 + 0.468715I
7.83914 + 8.54824I 0
u = 0.277977 + 0.036672I
a = 3.99712 − 3.05760I
b = 0.134175 − 0.715367I
3.61388 − 2.45396I 6.56586 − 0.99058I
u = 0.277977 − 0.036672I
a = 3.99712 + 3.05760I
b = 0.134175 + 0.715367I
3.61388 + 2.45396I 6.56586 + 0.99058I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.68726 + 0.51144I
a = −0.130407 − 0.672426I
b = −0.323367 + 1.097460I
8.59448 + 1.12879I 0
u = 1.68726 − 0.51144I
a = −0.130407 + 0.672426I
b = −0.323367 − 1.097460I
8.59448 − 1.12879I 0
u = −1.71502 + 0.47546I
a = −0.110914 + 0.683286I
b = −0.313187 − 1.170150I
7.83914 + 4.48847I 0
u = −1.71502 − 0.47546I
a = −0.110914 − 0.683286I
b = −0.313187 + 1.170150I
7.83914 − 4.48847I 0
21
III. I
u
3
= h−u
2
+ b + 1, u
20
− u
19
+ · · · + a + 2, u
21
− u
20
+ · · · − 3u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
8
=
−u
20
+ u
19
+ ··· + u − 2
u
2
− 1
a
12
=
1
−u
2
a
9
=
−1
−u
20
+ u
19
+ ··· + u − 1
a
5
=
u
u
19
− u
18
+ ··· + 5u − 1
a
3
=
−u
u
a
10
=
u
2
− 1
−u
4
+ 2u
2
− 1
a
1
=
u
4
− 2u
2
+ 2
−u
6
+ 3u
4
− 4u
2
+ 1
a
2
=
u
8
− 4u
6
+ 7u
4
− 5u
2
+ 2
−u
8
+ 3u
6
− 3u
4
− u
2
+ 1
a
7
=
−u
8
+ 4u
6
− 7u
4
+ 5u
2
− 2
−u
20
+ u
19
+ ··· + u − 1
a
6
=
u
15
− 8u
13
+ 29u
11
− 60u
9
+ 76u
7
− 59u
5
+ 27u
3
− 5u
u
19
− u
18
+ ··· + 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −9u
20
+ 8u
19
+ 94u
18
− 82u
17
− 443u
16
+ 377u
15
+ 1211u
14
− 1007u
13
− 2067u
12
+
1696u
11
+2199u
10
−1826u
9
−1352u
8
+1202u
7
+358u
6
−403u
5
+43u
4
+7u
3
−46u
2
+24u−3
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
21
− 7u
20
+ ··· − 11u + 1
c
2
u
21
− u
20
+ ··· − u + 1
c
3
, c
9
u
21
+ u
20
+ ··· − 3u − 1
c
4
, c
11
u
21
− u
20
+ ··· − 3u + 1
c
6
u
21
+ u
20
+ ··· − u − 1
c
7
u
21
− 5u
20
+ ··· − 3u − 1
c
8
u
21
− 3u
20
+ ··· − 2u − 1
c
10
, c
12
u
21
− 2u
20
+ ··· + 3u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
21
+ 15y
20
+ ··· + 13y −1
c
2
, c
6
y
21
+ 7y
20
+ ··· − 11y −1
c
3
, c
4
, c
9
c
11
y
21
− 23y
20
+ ··· − 3y −1
c
7
y
21
+ 3y
20
+ ··· − 5y −1
c
8
y
21
− 3y
20
+ ··· − 2y −1
c
10
, c
12
y
21
+ 2y
20
+ ··· + 3y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.841520 + 0.362436I
a = −1.76779 + 1.10668I
b = −0.423205 − 0.609994I
3.95731 − 3.50651I 8.68550 + 7.78549I
u = −0.841520 − 0.362436I
a = −1.76779 − 1.10668I
b = −0.423205 + 0.609994I
3.95731 + 3.50651I 8.68550 − 7.78549I
u = 0.798631 + 0.431022I
a = −1.70775 − 0.88920I
b = −0.547968 + 0.688455I
2.76934 + 9.34002I 5.48241 − 11.01139I
u = 0.798631 − 0.431022I
a = −1.70775 + 0.88920I
b = −0.547968 − 0.688455I
2.76934 − 9.34002I 5.48241 + 11.01139I
u = −1.224270 + 0.317561I
a = −0.478386 + 1.019090I
b = 0.397989 − 0.777561I
4.61385 − 1.80955I 5.20830 + 1.73152I
u = −1.224270 − 0.317561I
a = −0.478386 − 1.019090I
b = 0.397989 + 0.777561I
4.61385 + 1.80955I 5.20830 − 1.73152I
u = −0.693036
a = −2.92418
b = −0.519701
0.895273 −12.9680
u = 0.587768 + 0.276453I
a = −2.14228 − 0.50785I
b = −0.730955 + 0.324980I
−2.96854 + 3.18391I −4.89145 − 8.07576I
u = 0.587768 − 0.276453I
a = −2.14228 + 0.50785I
b = −0.730955 − 0.324980I
−2.96854 − 3.18391I −4.89145 + 8.07576I
u = −1.292040 + 0.455283I
a = −0.710775 + 0.736396I
b = 0.462072 − 1.176480I
7.08730 − 3.28052I 10.50843 + 2.68857I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.292040 − 0.455283I
a = −0.710775 − 0.736396I
b = 0.462072 + 1.176480I
7.08730 + 3.28052I 10.50843 − 2.68857I
u = 1.329150 + 0.454382I
a = −0.684013 − 0.681349I
b = 0.560176 + 1.207890I
6.60607 − 2.06273I 8.81350 + 3.56262I
u = 1.329150 − 0.454382I
a = −0.684013 + 0.681349I
b = 0.560176 − 1.207890I
6.60607 + 2.06273I 8.81350 − 3.56262I
u = 1.366990 + 0.357344I
a = −0.507173 − 0.649796I
b = 0.740967 + 0.976970I
2.81576 + 2.43488I 1.83704 − 1.00056I
u = 1.366990 − 0.357344I
a = −0.507173 + 0.649796I
b = 0.740967 − 0.976970I
2.81576 − 2.43488I 1.83704 + 1.00056I
u = −1.40141 + 0.22889I
a = −0.266356 + 0.516321I
b = 0.911562 − 0.641535I
8.10450 − 1.41862I 9.55417 − 0.16796I
u = −1.40141 − 0.22889I
a = −0.266356 − 0.516321I
b = 0.911562 + 0.641535I
8.10450 + 1.41862I 9.55417 + 0.16796I
u = 1.42728 + 0.26030I
a = −0.350186 − 0.498089I
b = 0.969365 + 0.743027I
7.46906 + 7.03476I 8.15699 − 5.23270I
u = 1.42728 − 0.26030I
a = −0.350186 + 0.498089I
b = 0.969365 − 0.743027I
7.46906 − 7.03476I 8.15699 + 5.23270I
u = 0.095937 + 0.298927I
a = −1.92319 − 0.04902I
b = −1.080150 + 0.057356I
−1.42388 − 2.26286I 1.62919 + 4.65561I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.095937 − 0.298927I
a = −1.92319 + 0.04902I
b = −1.080150 − 0.057356I
−1.42388 + 2.26286I 1.62919 − 4.65561I
27
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
21
− 7u
20
+ ··· − 11u + 1)(u
21
+ 7u
20
+ ··· + 3u − 1)
4
· (u
44
+ 14u
43
+ ··· + 4u + 16)
c
2
(u
21
− u
20
+ ··· − u + 1)(u
21
+ u
20
+ ··· + u + 1)
4
· (u
44
− 6u
43
+ ··· − 2u − 4)
c
3
, c
9
(u
21
+ u
20
+ ··· − 3u − 1)(u
44
− u
43
+ ··· + u + 1)
· (u
84
+ u
83
+ ··· + 1700u + 2983)
c
4
, c
11
(u
21
− u
20
+ ··· − 3u + 1)(u
44
− u
43
+ ··· + u + 1)
· (u
84
+ u
83
+ ··· + 1700u + 2983)
c
6
(u
21
+ u
20
+ ··· − u − 1)(u
21
+ u
20
+ ··· + u + 1)
4
· (u
44
− 6u
43
+ ··· − 2u − 4)
c
7
((u
21
− 5u
20
+ ··· − 11u + 3)
4
)(u
21
− 5u
20
+ ··· − 3u − 1)
· (u
44
+ 30u
43
+ ··· − 88022u − 6988)
c
8
((u
2
− u + 1)
42
)(u
21
− 3u
20
+ ··· − 2u − 1)
· (u
44
+ 40u
43
+ ··· − 42991616u − 2097152)
c
10
, c
12
(u
21
− 2u
20
+ ··· + 3u + 1)(u
44
+ 2u
43
+ ··· + 7u − 1)
· (u
84
− 23u
83
+ ··· − 646u + 37)
28
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
21
+ 15y
20
+ ··· + 27y −1)
4
)(y
21
+ 15y
20
+ ··· + 13y −1)
· (y
44
+ 30y
43
+ ··· + 9744y + 256)
c
2
, c
6
(y
21
+ 7y
20
+ ··· − 11y −1)(y
21
+ 7y
20
+ ··· + 3y −1)
4
· (y
44
+ 14y
43
+ ··· + 4y + 16)
c
3
, c
4
, c
9
c
11
(y
21
− 23y
20
+ ··· − 3y −1)(y
44
− 31y
43
+ ··· + y + 1)
· (y
84
− 69y
83
+ ··· − 605825892y + 8898289)
c
7
(y
21
+ 3y
20
+ ··· − 5y −1)(y
21
+ 3y
20
+ ··· − 41y −9)
4
· (y
44
+ 6y
43
+ ··· + 106960964y + 48832144)
c
8
((y
2
+ y + 1)
42
)(y
21
− 3y
20
+ ··· − 2y −1)
· (y
44
− 2y
43
+ ··· − 7696581394432y + 4398046511104)
c
10
, c
12
(y
21
+ 2y
20
+ ··· + 3y −1)(y
44
− 10y
43
+ ··· − 37y + 1)
· (y
84
+ 19y
83
+ ··· + 39856y + 1369)
29
