12n
0632
(K12n
0632
)
A knot diagram
1
Linearized knot diagam
3 8 6 11 9 10 11 2 4 1 4 7
Solving Sequence
2,8 3,6
4 9 10 1 11 5 7 12
c
2
c
3
c
8
c
9
c
1
c
10
c
5
c
7
c
12
c
4
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.90187 × 10
41
u
47
− 3.78001 × 10
41
u
46
+ ··· + 1.28153 × 10
42
b + 4.17139 × 10
42
,
3.62446 × 10
41
u
47
− 9.89184 × 10
41
u
46
+ ··· + 5.12610 × 10
42
a + 3.33997 × 10
42
, u
48
− 3u
47
+ ··· − 72u + 16i
I
u
2
= h−2.03008 × 10
16
au
32
+ 2.90523 × 10
16
u
32
+ ··· − 2.34244 × 10
17
a + 2.23321 × 10
17
,
− 1.75837 × 10
15
au
32
− 3.99178 × 10
16
u
32
+ ··· − 3.28264 × 10
17
a + 3.99087 × 10
17
,
u
33
+ u
32
+ ··· − 7u + 11i
I
u
3
= h825341u
37
+ 1493u
36
+ ··· + 121486b − 2500187,
2974391u
37
− 2651575u
36
+ ··· + 607430a − 22087770, u
38
+ 11u
36
+ ··· + 12u
2
+ 5i
I
v
1
= ha, v
2
+ b + 2v, v
3
+ 3v
2
+ 2v + 1i
* 4 irreducible components of dim
C
= 0, with total 155 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
=
h2.90×10
41
u
47
−3.78×10
41
u
46
+· · ·+1.28×10
42
b+4.17×10
42
, 3.62×10
41
u
47
−
9.89 × 10
41
u
46
+ · · · + 5.13 × 10
42
a + 3.34 × 10
42
, u
48
− 3u
47
+ · · · − 72u + 16i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
6
=
−0.0707059u
47
+ 0.192970u
46
+ ··· + 2.02201u − 0.651561
−0.226439u
47
+ 0.294962u
46
+ ··· + 10.9693u − 3.25501
a
4
=
−0.510598u
47
+ 1.08091u
46
+ ··· − 13.9117u + 2.18945
−0.454714u
47
+ 0.887793u
46
+ ··· + 1.07657u − 2.81659
a
9
=
u
u
a
10
=
−0.294663u
47
+ 0.316302u
46
+ ··· + 9.54700u − 3.10520
0.0653557u
47
− 0.679568u
46
+ ··· + 37.0059u − 9.89112
a
1
=
u
2
+ 1
−u
4
a
11
=
−0.155733u
47
+ 0.101992u
46
+ ··· + 8.94734u − 2.60345
−0.0000489054u
47
− 0.477796u
46
+ ··· + 34.7725u − 9.09833
a
5
=
0.155684u
47
− 0.579788u
46
+ ··· + 25.8252u − 6.49488
−0.0000489054u
47
− 0.477796u
46
+ ··· + 34.7725u − 9.09833
a
7
=
0.700023u
47
− 1.69491u
46
+ ··· + 31.7696u − 6.01626
0.500164u
47
− 1.27854u
46
+ ··· + 19.1631u − 1.82344
a
12
=
0.569045u
47
− 0.934017u
46
+ ··· + 6.75968u + 0.801632
−0.0171747u
47
+ 0.560556u
46
+ ··· − 33.6917u + 10.3628
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.71002u
47
+ 7.94048u
46
+ ··· − 215.263u + 55.9379
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
+ 23u
47
+ ··· + 832u + 256
c
2
, c
8
u
48
+ 3u
47
+ ··· + 72u + 16
c
3
, c
10
u
48
− u
47
+ ··· − 3u + 1
c
4
, c
11
u
48
− 5u
47
+ ··· − 1329u + 160
c
5
, c
7
u
48
− 22u
46
+ ··· + 700u + 200
c
6
u
48
+ 6u
47
+ ··· − 2475u + 918
c
9
, c
12
u
48
− 16u
46
+ ··· − 154u + 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
+ 11y
47
+ ··· + 675840y + 65536
c
2
, c
8
y
48
+ 23y
47
+ ··· + 832y + 256
c
3
, c
10
y
48
− y
47
+ ··· + 27y + 1
c
4
, c
11
y
48
− 37y
47
+ ··· − 197281y + 25600
c
5
, c
7
y
48
− 44y
47
+ ··· + 2167600y + 40000
c
6
y
48
+ 2y
47
+ ··· − 1509921y + 842724
c
9
, c
12
y
48
− 32y
47
+ ··· − 15386y + 289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.072234 + 1.009590I
a = −1.22324 + 0.93575I
b = −0.322776 + 0.234343I
−3.79904 + 3.93017I −1.59134 − 4.51288I
u = −0.072234 − 1.009590I
a = −1.22324 − 0.93575I
b = −0.322776 − 0.234343I
−3.79904 − 3.93017I −1.59134 + 4.51288I
u = −0.750282 + 0.624427I
a = 0.877939 − 0.849112I
b = 1.83705 + 0.04183I
1.29000 + 4.48373I 7.58276 − 2.87666I
u = −0.750282 − 0.624427I
a = 0.877939 + 0.849112I
b = 1.83705 − 0.04183I
1.29000 − 4.48373I 7.58276 + 2.87666I
u = 0.613049 + 0.734079I
a = 0.34365 + 2.29466I
b = 1.075750 + 0.555261I
6.97125 + 0.95587I 6.61091 − 4.11301I
u = 0.613049 − 0.734079I
a = 0.34365 − 2.29466I
b = 1.075750 − 0.555261I
6.97125 − 0.95587I 6.61091 + 4.11301I
u = 0.713580 + 0.617959I
a = 0.903291 + 0.979506I
b = 1.020980 + 0.018093I
1.77056 − 2.17781I 4.82468 + 3.78261I
u = 0.713580 − 0.617959I
a = 0.903291 − 0.979506I
b = 1.020980 − 0.018093I
1.77056 + 2.17781I 4.82468 − 3.78261I
u = −0.106932 + 1.050970I
a = 0.513607 + 0.490726I
b = −0.13366 + 1.43900I
2.12023 + 1.00595I 5.23912 − 2.50505I
u = −0.106932 − 1.050970I
a = 0.513607 − 0.490726I
b = −0.13366 − 1.43900I
2.12023 − 1.00595I 5.23912 + 2.50505I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998142 + 0.481752I
a = −0.639140 − 1.033170I
b = −1.61536 + 0.35291I
7.2965 − 12.6756I 6.45387 + 5.95608I
u = 0.998142 − 0.481752I
a = −0.639140 + 1.033170I
b = −1.61536 − 0.35291I
7.2965 + 12.6756I 6.45387 − 5.95608I
u = −0.745488 + 0.467501I
a = −0.40070 + 1.92827I
b = −1.63796 − 0.07983I
7.04207 + 2.69361I 12.38588 − 5.07908I
u = −0.745488 − 0.467501I
a = −0.40070 − 1.92827I
b = −1.63796 + 0.07983I
7.04207 − 2.69361I 12.38588 + 5.07908I
u = 0.364690 + 1.059660I
a = −0.117822 − 0.681542I
b = 0.234019 − 0.185992I
−3.73555 + 0.62051I 0
u = 0.364690 − 1.059660I
a = −0.117822 + 0.681542I
b = 0.234019 + 0.185992I
−3.73555 − 0.62051I 0
u = 0.451904 + 1.026910I
a = −1.33410 − 1.30797I
b = −1.32090 − 0.59244I
−3.32273 + 6.10549I 0. − 6.61286I
u = 0.451904 − 1.026910I
a = −1.33410 + 1.30797I
b = −1.32090 + 0.59244I
−3.32273 − 6.10549I 0. + 6.61286I
u = 0.640017 + 0.942419I
a = −0.820679 − 0.511384I
b = −1.96429 − 0.04776I
6.31587 + 4.00200I 6.45296 − 3.11892I
u = 0.640017 − 0.942419I
a = −0.820679 + 0.511384I
b = −1.96429 + 0.04776I
6.31587 − 4.00200I 6.45296 + 3.11892I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.298498 + 0.789976I
a = 0.379370 + 0.964150I
b = 1.56784 + 1.18772I
−2.12114 − 2.96147I −3.25494 + 1.48217I
u = 0.298498 − 0.789976I
a = 0.379370 − 0.964150I
b = 1.56784 − 1.18772I
−2.12114 + 2.96147I −3.25494 − 1.48217I
u = −0.463720 + 1.068040I
a = 0.874078 − 0.695825I
b = 0.872961 − 0.051243I
−1.10916 − 3.41423I 0
u = −0.463720 − 1.068040I
a = 0.874078 + 0.695825I
b = 0.872961 + 0.051243I
−1.10916 + 3.41423I 0
u = 0.637391 + 0.990955I
a = −0.45612 − 1.38999I
b = −1.52449 − 1.28957I
0.68173 + 7.36598I 0. − 8.55059I
u = 0.637391 − 0.990955I
a = −0.45612 + 1.38999I
b = −1.52449 + 1.28957I
0.68173 − 7.36598I 0. + 8.55059I
u = −0.663005 + 1.024610I
a = −0.75487 + 1.93333I
b = −1.74471 + 1.01235I
0.08239 − 9.87726I 0
u = −0.663005 − 1.024610I
a = −0.75487 − 1.93333I
b = −1.74471 − 1.01235I
0.08239 + 9.87726I 0
u = −1.056260 + 0.636872I
a = −0.032565 − 1.010660I
b = 0.789001 − 0.401945I
8.12208 − 6.43854I 0
u = −1.056260 − 0.636872I
a = −0.032565 + 1.010660I
b = 0.789001 + 0.401945I
8.12208 + 6.43854I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.606495 + 1.075940I
a = 1.00711 − 1.81965I
b = 2.69461 − 1.04799I
5.24428 − 7.84216I 0
u = −0.606495 − 1.075940I
a = 1.00711 + 1.81965I
b = 2.69461 + 1.04799I
5.24428 + 7.84216I 0
u = 0.648933 + 0.372189I
a = −1.15793 + 1.69242I
b = 0.844553 + 0.510508I
6.95234 + 0.39618I 12.53507 − 4.08831I
u = 0.648933 − 0.372189I
a = −1.15793 − 1.69242I
b = 0.844553 − 0.510508I
6.95234 − 0.39618I 12.53507 + 4.08831I
u = 0.563635 + 1.174740I
a = −0.951010 − 0.642156I
b = −1.75643 + 0.28005I
4.46125 + 4.40033I 0
u = 0.563635 − 1.174740I
a = −0.951010 + 0.642156I
b = −1.75643 − 0.28005I
4.46125 − 4.40033I 0
u = 0.705215 + 1.162730I
a = 0.82971 + 1.66340I
b = 2.21819 + 1.08373I
5.1858 + 18.8530I 0
u = 0.705215 − 1.162730I
a = 0.82971 − 1.66340I
b = 2.21819 − 1.08373I
5.1858 − 18.8530I 0
u = 0.613806 + 0.078399I
a = 0.529727 − 0.797181I
b = 0.548360 − 0.505925I
−0.74503 + 2.83022I 7.38869 − 2.36983I
u = 0.613806 − 0.078399I
a = 0.529727 + 0.797181I
b = 0.548360 + 0.505925I
−0.74503 − 2.83022I 7.38869 + 2.36983I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500797 + 0.350954I
a = 0.320846 + 0.457891I
b = −0.431234 + 0.483909I
0.956146 − 0.504632I 9.17940 + 3.83818I
u = −0.500797 − 0.350954I
a = 0.320846 − 0.457891I
b = −0.431234 − 0.483909I
0.956146 + 0.504632I 9.17940 − 3.83818I
u = 0.001378 + 1.393570I
a = 0.499786 + 0.079532I
b = 0.035284 − 0.688867I
0.18184 − 9.53195I 0
u = 0.001378 − 1.393570I
a = 0.499786 − 0.079532I
b = 0.035284 + 0.688867I
0.18184 + 9.53195I 0
u = −0.870155 + 1.110250I
a = −0.623696 + 0.359289I
b = −1.309200 + 0.026773I
6.69908 − 0.43812I 0
u = −0.870155 − 1.110250I
a = −0.623696 − 0.359289I
b = −1.309200 − 0.026773I
6.69908 + 0.43812I 0
u = 0.08513 + 1.42831I
a = 0.182771 − 0.302780I
b = 0.522416 − 0.131488I
−4.72528 − 0.59037I 0
u = 0.08513 − 1.42831I
a = 0.182771 + 0.302780I
b = 0.522416 + 0.131488I
−4.72528 + 0.59037I 0
9
II. I
u
2
= h−2.03 × 10
16
au
32
+ 2.91 × 10
16
u
32
+ · · · − 2.34 × 10
17
a + 2.23 ×
10
17
, −1.76 × 10
15
au
32
− 3.99 × 10
16
u
32
+ · · · − 3.28 × 10
17
a + 3.99 ×
10
17
, u
33
+ u
32
+ · · · − 7u + 11i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
6
=
a
0.391169au
32
− 0.559799u
32
+ ··· + 4.51357a − 4.30309
a
4
=
0.364219au
32
+ 0.464300u
32
+ ··· + 2.24836a − 22.1496
0.234314au
32
+ 0.527041u
32
+ ··· − 0.198158a − 16.6316
a
9
=
u
u
a
10
=
−0.264790au
32
+ 0.618972u
32
+ ··· − 2.62489a − 3.56836
−0.780172au
32
− 0.142686u
32
+ ··· − 8.71610a − 3.79069
a
1
=
u
2
+ 1
−u
4
a
11
=
−0.391169au
32
− 0.114073u
32
+ ··· − 3.51357a − 4.91800
−0.908717au
32
− 0.584667u
32
+ ··· − 9.91583a + 0.416754
a
5
=
0.517548au
32
+ 0.341193u
32
+ ··· + 6.40225a − 2.21651
0.908717au
32
− 0.218606u
32
+ ··· + 9.91583a − 6.51960
a
7
=
0.908250au
32
+ 2.38664u
32
+ ··· + 5.60633a + 2.84026
0.989039au
32
+ 2.76675u
32
+ ··· + 0.911866a − 0.529176
a
12
=
−0.620353au
32
+ 0.737707u
32
+ ··· + 10.6936a + 9.69735
0.315026au
32
+ 1.68970u
32
+ ··· + 17.0382a + 7.83841
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
903243108544774
625274099350525
u
32
+
1805117122242941
625274099350525
u
31
+ ··· +
4314310509574099
125054819870105
u −
11096996532907333
625274099350525
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
33
+ 13u
32
+ ··· − 941u − 121)
2
c
2
, c
8
(u
33
− u
32
+ ··· − 7u − 11)
2
c
3
, c
10
u
66
− 7u
65
+ ··· + 47u + 29
c
4
, c
11
(u
33
+ 2u
32
+ ··· − 8u − 1)
2
c
5
, c
7
u
66
+ 12u
64
+ ··· − 1048425u − 638825
c
6
(u
33
− u
32
+ ··· − 4u − 1)
2
c
9
, c
12
u
66
− 2u
65
+ ··· − 52649u − 9793
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
33
+ 17y
32
+ ··· + 5327y −14641)
2
c
2
, c
8
(y
33
+ 13y
32
+ ··· − 941y −121)
2
c
3
, c
10
y
66
− 31y
65
+ ··· − 76101y + 841
c
4
, c
11
(y
33
− 28y
32
+ ··· + 16y −1)
2
c
5
, c
7
y
66
+ 24y
65
+ ··· − 2888276776775y + 408097380625
c
6
(y
33
+ 11y
32
+ ··· − 36y −1)
2
c
9
, c
12
y
66
+ 14y
65
+ ··· − 2701564289y + 95902849
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00045
a = −0.729229
b = 0.0710552
4.51725 −4.11620
u = −1.00045
a = 0.192294
b = −1.64543
4.51725 −4.11620
u = −0.597418 + 0.770414I
a = −1.47977 − 0.11392I
b = 0.64936 − 1.68170I
2.56250 + 2.10521I 4.05719 − 1.95522I
u = −0.597418 + 0.770414I
a = −1.65555 + 0.70942I
b = −2.06179 − 0.12173I
2.56250 + 2.10521I 4.05719 − 1.95522I
u = −0.597418 − 0.770414I
a = −1.47977 + 0.11392I
b = 0.64936 + 1.68170I
2.56250 − 2.10521I 4.05719 + 1.95522I
u = −0.597418 − 0.770414I
a = −1.65555 − 0.70942I
b = −2.06179 + 0.12173I
2.56250 − 2.10521I 4.05719 + 1.95522I
u = −0.342707 + 0.887603I
a = −0.117440 − 0.661580I
b = −0.933048 + 0.344357I
0.46246 + 2.22160I −0.67965 + 7.70078I
u = −0.342707 + 0.887603I
a = 1.15472 + 3.54214I
b = −1.18973 + 3.08181I
0.46246 + 2.22160I −0.67965 + 7.70078I
u = −0.342707 − 0.887603I
a = −0.117440 + 0.661580I
b = −0.933048 − 0.344357I
0.46246 − 2.22160I −0.67965 − 7.70078I
u = −0.342707 − 0.887603I
a = 1.15472 − 3.54214I
b = −1.18973 − 3.08181I
0.46246 − 2.22160I −0.67965 − 7.70078I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.465782 + 0.820583I
a = −0.460215 − 0.465452I
b = 0.728090 + 0.267934I
−3.34705 + 1.85137I 0.37014 − 4.45962I
u = 0.465782 + 0.820583I
a = 0.56208 − 1.48869I
b = −0.199876 − 1.369340I
−3.34705 + 1.85137I 0.37014 − 4.45962I
u = 0.465782 − 0.820583I
a = −0.460215 + 0.465452I
b = 0.728090 − 0.267934I
−3.34705 − 1.85137I 0.37014 + 4.45962I
u = 0.465782 − 0.820583I
a = 0.56208 + 1.48869I
b = −0.199876 + 1.369340I
−3.34705 − 1.85137I 0.37014 + 4.45962I
u = 0.340868 + 0.868108I
a = 1.72849 − 0.71719I
b = −0.26299 − 1.56255I
−6.94338 + 1.45144I −11.05813 + 8.16791I
u = 0.340868 + 0.868108I
a = 0.56285 − 2.49869I
b = 0.96111 − 1.98923I
−6.94338 + 1.45144I −11.05813 + 8.16791I
u = 0.340868 − 0.868108I
a = 1.72849 + 0.71719I
b = −0.26299 + 1.56255I
−6.94338 − 1.45144I −11.05813 − 8.16791I
u = 0.340868 − 0.868108I
a = 0.56285 + 2.49869I
b = 0.96111 + 1.98923I
−6.94338 − 1.45144I −11.05813 − 8.16791I
u = 0.877130 + 0.632782I
a = −0.859094 − 0.991814I
b = −1.58978 + 0.49196I
7.73449 − 4.44776I 7.97575 + 3.52690I
u = 0.877130 + 0.632782I
a = 0.12562 + 1.63949I
b = 0.732208 + 0.525068I
7.73449 − 4.44776I 7.97575 + 3.52690I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877130 − 0.632782I
a = −0.859094 + 0.991814I
b = −1.58978 − 0.49196I
7.73449 + 4.44776I 7.97575 − 3.52690I
u = 0.877130 − 0.632782I
a = 0.12562 − 1.63949I
b = 0.732208 − 0.525068I
7.73449 + 4.44776I 7.97575 − 3.52690I
u = −0.589753 + 0.928082I
a = −1.73599 − 0.14226I
b = 0.09197 − 1.95154I
2.05867 − 6.80913I 1.26696 + 6.58532I
u = −0.589753 + 0.928082I
a = 0.65806 − 2.31545I
b = 1.65447 − 1.66316I
2.05867 − 6.80913I 1.26696 + 6.58532I
u = −0.589753 − 0.928082I
a = −1.73599 + 0.14226I
b = 0.09197 + 1.95154I
2.05867 + 6.80913I 1.26696 − 6.58532I
u = −0.589753 − 0.928082I
a = 0.65806 + 2.31545I
b = 1.65447 + 1.66316I
2.05867 + 6.80913I 1.26696 − 6.58532I
u = −0.707500 + 0.842770I
a = 1.083330 − 0.781583I
b = 1.53847 + 0.05298I
2.97003 − 2.70098I 7.24456 + 2.95734I
u = −0.707500 + 0.842770I
a = −0.19373 + 1.60853I
b = −1.31935 + 1.13429I
2.97003 − 2.70098I 7.24456 + 2.95734I
u = −0.707500 − 0.842770I
a = 1.083330 + 0.781583I
b = 1.53847 − 0.05298I
2.97003 + 2.70098I 7.24456 − 2.95734I
u = −0.707500 − 0.842770I
a = −0.19373 − 1.60853I
b = −1.31935 − 1.13429I
2.97003 + 2.70098I 7.24456 − 2.95734I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.652684 + 0.906130I
a = −0.764661 + 1.011010I
b = 0.41659 + 1.49322I
−5.08911 + 2.59734I 20.4704 − 1.6035I
u = 0.652684 + 0.906130I
a = 0.32173 − 1.51230I
b = 0.595386 − 0.907775I
−5.08911 + 2.59734I 20.4704 − 1.6035I
u = 0.652684 − 0.906130I
a = −0.764661 − 1.011010I
b = 0.41659 − 1.49322I
−5.08911 − 2.59734I 20.4704 + 1.6035I
u = 0.652684 − 0.906130I
a = 0.32173 + 1.51230I
b = 0.595386 + 0.907775I
−5.08911 − 2.59734I 20.4704 + 1.6035I
u = −0.158057 + 0.822377I
a = 1.068300 − 0.739457I
b = −0.127946 − 0.917269I
0.67336 − 4.65501I 6.88596 + 4.94477I
u = −0.158057 + 0.822377I
a = 2.34677 + 1.51286I
b = 1.23347 + 2.33699I
0.67336 − 4.65501I 6.88596 + 4.94477I
u = −0.158057 − 0.822377I
a = 1.068300 + 0.739457I
b = −0.127946 + 0.917269I
0.67336 + 4.65501I 6.88596 − 4.94477I
u = −0.158057 − 0.822377I
a = 2.34677 − 1.51286I
b = 1.23347 − 2.33699I
0.67336 + 4.65501I 6.88596 − 4.94477I
u = −0.328934 + 1.152340I
a = 0.342623 − 0.656443I
b = −0.167331 − 0.931796I
0.28979 − 4.24121I −0.93669 + 2.38496I
u = −0.328934 + 1.152340I
a = 1.69573 − 0.60375I
b = 1.77371 + 0.88068I
0.28979 − 4.24121I −0.93669 + 2.38496I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.328934 − 1.152340I
a = 0.342623 + 0.656443I
b = −0.167331 + 0.931796I
0.28979 + 4.24121I −0.93669 − 2.38496I
u = −0.328934 − 1.152340I
a = 1.69573 + 0.60375I
b = 1.77371 − 0.88068I
0.28979 + 4.24121I −0.93669 − 2.38496I
u = 0.746312 + 0.156222I
a = 0.68113 + 1.59984I
b = 0.968791 − 0.000898I
−0.88161 − 3.55819I 10.41631 + 1.44599I
u = 0.746312 + 0.156222I
a = 0.189806 − 0.098680I
b = −0.662830 − 0.345267I
−0.88161 − 3.55819I 10.41631 + 1.44599I
u = 0.746312 − 0.156222I
a = 0.68113 − 1.59984I
b = 0.968791 + 0.000898I
−0.88161 + 3.55819I 10.41631 − 1.44599I
u = 0.746312 − 0.156222I
a = 0.189806 + 0.098680I
b = −0.662830 + 0.345267I
−0.88161 + 3.55819I 10.41631 − 1.44599I
u = 0.517462 + 1.145100I
a = 0.978528 + 0.630302I
b = 1.030270 − 0.240789I
−3.68423 + 8.21577I 11.87745 − 6.40774I
u = 0.517462 + 1.145100I
a = −1.09370 − 1.69249I
b = −2.08161 − 1.71106I
−3.68423 + 8.21577I 11.87745 − 6.40774I
u = 0.517462 − 1.145100I
a = 0.978528 − 0.630302I
b = 1.030270 + 0.240789I
−3.68423 − 8.21577I 11.87745 + 6.40774I
u = 0.517462 − 1.145100I
a = −1.09370 + 1.69249I
b = −2.08161 + 1.71106I
−3.68423 − 8.21577I 11.87745 + 6.40774I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.313499 + 1.230020I
a = 0.636502 + 0.239794I
b = 0.588471 − 0.064522I
−5.04001 + 0.17984I 5.54847 − 5.83488I
u = 0.313499 + 1.230020I
a = 0.107016 − 0.514574I
b = 0.875372 − 0.007078I
−5.04001 + 0.17984I 5.54847 − 5.83488I
u = 0.313499 − 1.230020I
a = 0.636502 − 0.239794I
b = 0.588471 + 0.064522I
−5.04001 − 0.17984I 5.54847 + 5.83488I
u = 0.313499 − 1.230020I
a = 0.107016 + 0.514574I
b = 0.875372 + 0.007078I
−5.04001 − 0.17984I 5.54847 + 5.83488I
u = 0.713732 + 1.055730I
a = −1.058950 − 0.263864I
b = −1.93542 + 0.00811I
6.42259 + 10.34510I 5.95668 − 7.97490I
u = 0.713732 + 1.055730I
a = 0.47134 + 1.74355I
b = 1.98496 + 1.22183I
6.42259 + 10.34510I 5.95668 − 7.97490I
u = 0.713732 − 1.055730I
a = −1.058950 + 0.263864I
b = −1.93542 − 0.00811I
6.42259 − 10.34510I 5.95668 + 7.97490I
u = 0.713732 − 1.055730I
a = 0.47134 − 1.74355I
b = 1.98496 − 1.22183I
6.42259 − 10.34510I 5.95668 + 7.97490I
u = −1.120990 + 0.632875I
a = −0.589746 + 0.616213I
b = −1.66096 + 0.05310I
4.75175 + 1.67559I −5.3856 − 18.6967I
u = −1.120990 + 0.632875I
a = 0.363061 − 0.260468I
b = 0.410493 + 0.504110I
4.75175 + 1.67559I −5.3856 − 18.6967I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.120990 − 0.632875I
a = −0.589746 − 0.616213I
b = −1.66096 − 0.05310I
4.75175 − 1.67559I −5.3856 + 18.6967I
u = −1.120990 − 0.632875I
a = 0.363061 + 0.260468I
b = 0.410493 − 0.504110I
4.75175 − 1.67559I −5.3856 + 18.6967I
u = −0.781881 + 1.147150I
a = −0.013605 + 0.873166I
b = −0.973573 + 1.021480I
3.02581 − 8.44326I 2.04839 + 11.24887I
u = −0.781881 + 1.147150I
a = 0.80411 − 1.41781I
b = 1.72024 − 0.59211I
3.02581 − 8.44326I 2.04839 + 11.24887I
u = −0.781881 − 1.147150I
a = −0.013605 − 0.873166I
b = −0.973573 − 1.021480I
3.02581 + 8.44326I 2.04839 − 11.24887I
u = −0.781881 − 1.147150I
a = 0.80411 + 1.41781I
b = 1.72024 + 0.59211I
3.02581 + 8.44326I 2.04839 − 11.24887I
19
III.
I
u
3
= h8.25 × 10
5
u
37
+ 1493u
36
+ · · · + 1.21 × 10
5
b − 2.50 × 10
6
, 2.97 × 10
6
u
37
−
2.65 × 10
6
u
36
+ · · · + 6.07 × 10
5
a − 2.21 × 10
7
, u
38
+ 11u
36
+ · · · + 12u
2
+ 5i
(i) Arc colorings
a
2
=
1
0
a
8
=
0
u
a
3
=
1
−u
2
a
6
=
−4.89668u
37
+ 4.36524u
36
+ ··· − 4.73488u + 36.3627
−6.79371u
37
− 0.0122895u
36
+ ··· − 19.1902u + 20.5800
a
4
=
0.750223u
37
+ 0.126130u
36
+ ··· + 27.5052u + 19.7683
−0.470779u
37
+ 3.34656u
36
+ ··· + 11.7018u + 38.8313
a
9
=
u
u
a
10
=
−0.246216u
37
+ 4.43502u
36
+ ··· − 3.76343u + 19.1382
−4.19156u
37
+ 3.25454u
36
+ ··· − 15.0226u + 3.70453
a
1
=
u
2
+ 1
−u
4
a
11
=
−1.89703u
37
+ 4.37752u
36
+ ··· − 14.4553u + 15.7826
−7.39878u
37
+ 3.17167u
36
+ ··· − 28.6753u + 1.30758
a
5
=
−5.50175u
37
+ 1.20586u
36
+ ··· − 14.2200u + 14.4750
−7.39878u
37
− 3.17167u
36
+ ··· − 28.6753u − 1.30758
a
7
=
4.83075u
37
+ 2.32200u
36
+ ··· + 10.4724u + 54.5491
1.36238u
37
+ 6.38517u
36
+ ··· − 36.9868u + 69.3406
a
12
=
−9.34683u
37
− u
36
+ ··· − 3u
2
− 75.0552u
−12.7102u
37
− 1.25452u
36
+ ··· − 80.7911u − 20.9993
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1814189
60743
u
36
+
20378303
60743
u
34
+ ··· +
23815231
60743
u
2
+
17876866
60743
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
19
− 11u
18
+ ··· + 12u − 5)
2
c
2
, c
8
u
38
+ 11u
36
+ ··· + 12u
2
+ 5
c
3
, c
10
u
38
− 12u
37
+ ··· − 13u + 1
c
4
(u
19
+ u
18
+ ··· + 5u + 1)
2
c
5
, c
7
u
38
− 3u
37
+ ··· − 111u + 17
c
6
(u
19
+ u
18
+ ··· − 4u + 1)
2
c
9
, c
12
u
38
+ 3u
37
+ ··· + 3u + 1
c
11
(u
19
− u
18
+ ··· + 5u − 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
19
+ 3y
18
+ ··· + 264y −25)
2
c
2
, c
8
(y
19
+ 11y
18
+ ··· + 12y + 5)
2
c
3
, c
10
y
38
− 26y
37
+ ··· + 5y + 1
c
4
, c
11
(y
19
− 5y
18
+ ··· + y −1)
2
c
5
, c
7
y
38
+ 31y
37
+ ··· + 1857y + 289
c
6
(y
19
+ 5y
18
+ ··· + 26y −1)
2
c
9
, c
12
y
38
+ 21y
37
+ ··· + 23y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.412022 + 0.881902I
a = 0.91095 − 2.39633I
b = 0.93616 − 2.12443I
−6.74183 + 1.70912I 4.33338 − 10.64212I
u = 0.412022 − 0.881902I
a = 0.91095 + 2.39633I
b = 0.93616 + 2.12443I
−6.74183 − 1.70912I 4.33338 + 10.64212I
u = −0.412022 + 0.881902I
a = 1.76553 + 0.44609I
b = −0.18455 + 1.63121I
−6.74183 − 1.70912I 4.33338 + 10.64212I
u = −0.412022 − 0.881902I
a = 1.76553 − 0.44609I
b = −0.18455 − 1.63121I
−6.74183 + 1.70912I 4.33338 − 10.64212I
u = 0.308023 + 0.983770I
a = −2.99688 + 0.63338I
b = −1.76257 + 2.08605I
0.11792 + 5.16769I −1.68971 − 10.61691I
u = 0.308023 − 0.983770I
a = −2.99688 − 0.63338I
b = −1.76257 − 2.08605I
0.11792 − 5.16769I −1.68971 + 10.61691I
u = −0.308023 + 0.983770I
a = 0.987481 − 0.977692I
b = 0.298884 − 1.033670I
0.11792 − 5.16769I −1.68971 + 10.61691I
u = −0.308023 − 0.983770I
a = 0.987481 + 0.977692I
b = 0.298884 + 1.033670I
0.11792 + 5.16769I −1.68971 − 10.61691I
u = 0.301511 + 0.867567I
a = −1.44033 + 3.01293I
b = 1.08165 + 3.15481I
0.54600 − 2.63207I 2.61608 + 10.31253I
u = 0.301511 − 0.867567I
a = −1.44033 − 3.01293I
b = 1.08165 − 3.15481I
0.54600 + 2.63207I 2.61608 − 10.31253I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.301511 + 0.867567I
a = −0.396244 − 0.323286I
b = −1.246010 + 0.558485I
0.54600 + 2.63207I 2.61608 − 10.31253I
u = −0.301511 − 0.867567I
a = −0.396244 + 0.323286I
b = −1.246010 − 0.558485I
0.54600 − 2.63207I 2.61608 + 10.31253I
u = 0.654757 + 0.936084I
a = 0.218014 − 1.382120I
b = 0.626544 − 0.757798I
−5.29049 + 2.63486I −18.6643 − 8.9200I
u = 0.654757 − 0.936084I
a = 0.218014 + 1.382120I
b = 0.626544 + 0.757798I
−5.29049 − 2.63486I −18.6643 + 8.9200I
u = −0.654757 + 0.936084I
a = −0.612791 − 1.018590I
b = 0.42764 − 1.38058I
−5.29049 − 2.63486I −18.6643 + 8.9200I
u = −0.654757 − 0.936084I
a = −0.612791 + 1.018590I
b = 0.42764 + 1.38058I
−5.29049 + 2.63486I −18.6643 − 8.9200I
u = 0.988310 + 0.636554I
a = 0.420116 + 0.468776I
b = 0.415480 − 0.511395I
4.92585 − 1.43262I 11.51701 − 4.11370I
u = 0.988310 − 0.636554I
a = 0.420116 − 0.468776I
b = 0.415480 + 0.511395I
4.92585 + 1.43262I 11.51701 + 4.11370I
u = −0.988310 + 0.636554I
a = −0.626874 + 0.768484I
b = −1.65233 + 0.05159I
4.92585 + 1.43262I 11.51701 + 4.11370I
u = −0.988310 − 0.636554I
a = −0.626874 − 0.768484I
b = −1.65233 − 0.05159I
4.92585 − 1.43262I 11.51701 − 4.11370I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180900I
a = −0.262609 − 0.624739I
b = 0.444400 − 0.583923I
−5.22359 −7.30670
u = − 1.180900I
a = −0.262609 + 0.624739I
b = 0.444400 + 0.583923I
−5.22359 −7.30670
u = 0.518632 + 1.121930I
a = −1.11559 − 1.77534I
b = −2.03858 − 1.72144I
−4.06549 + 8.24393I −9.26811 − 8.48381I
u = 0.518632 − 1.121930I
a = −1.11559 + 1.77534I
b = −2.03858 + 1.72144I
−4.06549 − 8.24393I −9.26811 + 8.48381I
u = −0.518632 + 1.121930I
a = −0.986285 + 0.809459I
b = −1.023710 − 0.070351I
−4.06549 − 8.24393I −9.26811 + 8.48381I
u = −0.518632 − 1.121930I
a = −0.986285 − 0.809459I
b = −1.023710 + 0.070351I
−4.06549 + 8.24393I −9.26811 − 8.48381I
u = 0.680045 + 1.043770I
a = 0.133297 − 1.121200I
b = −1.35595 − 1.37943I
3.55683 + 7.38660I 5.87432 − 6.02042I
u = 0.680045 − 1.043770I
a = 0.133297 + 1.121200I
b = −1.35595 + 1.37943I
3.55683 − 7.38660I 5.87432 + 6.02042I
u = −0.680045 + 1.043770I
a = 0.84713 − 1.68780I
b = 1.94384 − 0.96634I
3.55683 − 7.38660I 5.87432 + 6.02042I
u = −0.680045 − 1.043770I
a = 0.84713 + 1.68780I
b = 1.94384 + 0.96634I
3.55683 + 7.38660I 5.87432 − 6.02042I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.282784 + 1.238480I
a = 0.155319 − 0.640260I
b = 0.832997 − 0.212290I
−5.36306 − 0.09786I −9.78999 + 5.82362I
u = 0.282784 − 1.238480I
a = 0.155319 + 0.640260I
b = 0.832997 + 0.212290I
−5.36306 + 0.09786I −9.78999 − 5.82362I
u = −0.282784 + 1.238480I
a = −0.415626 + 0.102162I
b = −0.048557 − 0.183010I
−5.36306 + 0.09786I −9.78999 − 5.82362I
u = −0.282784 − 1.238480I
a = −0.415626 − 0.102162I
b = −0.048557 + 0.183010I
−5.36306 − 0.09786I −9.78999 + 5.82362I
u = 0.552086 + 0.135216I
a = 0.81856 + 1.97918I
b = 1.060820 + 0.290884I
−1.52328 − 3.84579I −0.27531 + 6.74900I
u = 0.552086 − 0.135216I
a = 0.81856 − 1.97918I
b = 1.060820 − 0.290884I
−1.52328 + 3.84579I −0.27531 − 6.74900I
u = −0.552086 + 0.135216I
a = 0.096843 + 0.214273I
b = 0.743843 − 0.536748I
−1.52328 + 3.84579I −0.27531 − 6.74900I
u = −0.552086 − 0.135216I
a = 0.096843 − 0.214273I
b = 0.743843 + 0.536748I
−1.52328 − 3.84579I −0.27531 + 6.74900I
26
IV. I
v
1
= ha, v
2
+ b + 2v , v
3
+ 3v
2
+ 2v + 1i
(i) Arc colorings
a
2
=
1
0
a
8
=
v
0
a
3
=
1
0
a
6
=
0
−v
2
− 2v
a
4
=
1
−v
2
− 3v − 1
a
9
=
v
0
a
10
=
−1
v
2
+ 2v
a
1
=
1
0
a
11
=
−v
2
− 2v − 1
v
2
+ 2v
a
5
=
v
2
+ v + 1
−v
2
− 2v
a
7
=
v
2
+ 2v
v + 1
a
12
=
0
v
2
+ 2v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6v
2
− 17v − 5
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
8
u
3
c
3
, c
6
, c
10
u
3
− u
2
+ 1
c
4
u
3
− 2u
2
+ u − 1
c
5
, c
7
, c
11
u
3
+ 2u
2
+ u + 1
c
9
, c
12
u
3
− u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
8
y
3
c
3
, c
6
, c
10
y
3
− y
2
+ 2y − 1
c
4
, c
5
, c
7
c
11
y
3
− 2y
2
− 3y − 1
c
9
, c
12
y
3
− 2y
2
+ y − 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.337641 + 0.562280I
a = 0
b = 0.877439 − 0.744862I
−1.45094 + 3.77083I 1.95284 − 7.28057I
v = −0.337641 − 0.562280I
a = 0
b = 0.877439 + 0.744862I
−1.45094 − 3.77083I 1.95284 + 7.28057I
v = −2.32472
a = 0
b = −0.754878
6.19175 2.09430
30
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
3
(u
19
− 11u
18
+ ··· + 12u − 5)
2
(u
33
+ 13u
32
+ ··· − 941u − 121)
2
· (u
48
+ 23u
47
+ ··· + 832u + 256)
c
2
, c
8
u
3
(u
33
− u
32
+ ··· − 7u − 11)
2
(u
38
+ 11u
36
+ ··· + 12u
2
+ 5)
· (u
48
+ 3u
47
+ ··· + 72u + 16)
c
3
, c
10
(u
3
− u
2
+ 1)(u
38
− 12u
37
+ ··· − 13u + 1)(u
48
− u
47
+ ··· − 3u + 1)
· (u
66
− 7u
65
+ ··· + 47u + 29)
c
4
(u
3
− 2u
2
+ u − 1)(u
19
+ u
18
+ ··· + 5u + 1)
2
· ((u
33
+ 2u
32
+ ··· − 8u − 1)
2
)(u
48
− 5u
47
+ ··· − 1329u + 160)
c
5
, c
7
(u
3
+ 2u
2
+ u + 1)(u
38
− 3u
37
+ ··· − 111u + 17)
· (u
48
− 22u
46
+ ··· + 700u + 200)
· (u
66
+ 12u
64
+ ··· − 1048425u − 638825)
c
6
(u
3
− u
2
+ 1)(u
19
+ u
18
+ ··· − 4u + 1)
2
(u
33
− u
32
+ ··· − 4u − 1)
2
· (u
48
+ 6u
47
+ ··· − 2475u + 918)
c
9
, c
12
(u
3
− u + 1)(u
38
+ 3u
37
+ ··· + 3u + 1)(u
48
− 16u
46
+ ··· − 154u + 17)
· (u
66
− 2u
65
+ ··· − 52649u − 9793)
c
11
(u
3
+ 2u
2
+ u + 1)(u
19
− u
18
+ ··· + 5u − 1)
2
· ((u
33
+ 2u
32
+ ··· − 8u − 1)
2
)(u
48
− 5u
47
+ ··· − 1329u + 160)
31
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
3
(y
19
+ 3y
18
+ ··· + 264y − 25)
2
· (y
33
+ 17y
32
+ ··· + 5327y − 14641)
2
· (y
48
+ 11y
47
+ ··· + 675840y + 65536)
c
2
, c
8
y
3
(y
19
+ 11y
18
+ ··· + 12y + 5)
2
(y
33
+ 13y
32
+ ··· − 941y − 121)
2
· (y
48
+ 23y
47
+ ··· + 832y + 256)
c
3
, c
10
(y
3
− y
2
+ 2y − 1)(y
38
− 26y
37
+ ··· + 5y + 1)(y
48
− y
47
+ ··· + 27y + 1)
· (y
66
− 31y
65
+ ··· − 76101y + 841)
c
4
, c
11
(y
3
− 2y
2
− 3y − 1)(y
19
− 5y
18
+ ··· + y − 1)
2
· (y
33
− 28y
32
+ ··· + 16y − 1)
2
· (y
48
− 37y
47
+ ··· − 197281y + 25600)
c
5
, c
7
(y
3
− 2y
2
− 3y − 1)(y
38
+ 31y
37
+ ··· + 1857y + 289)
· (y
48
− 44y
47
+ ··· + 2167600y + 40000)
· (y
66
+ 24y
65
+ ··· − 2888276776775y + 408097380625)
c
6
(y
3
− y
2
+ 2y − 1)(y
19
+ 5y
18
+ ··· + 26y − 1)
2
· (y
33
+ 11y
32
+ ··· − 36y − 1)
2
· (y
48
+ 2y
47
+ ··· − 1509921y + 842724)
c
9
, c
12
(y
3
− 2y
2
+ y − 1)(y
38
+ 21y
37
+ ··· + 23y + 1)
· (y
48
− 32y
47
+ ··· − 15386y + 289)
· (y
66
+ 14y
65
+ ··· − 2701564289y + 95902849)
32
