12a
0798
(K12a
0798
)
A knot diagram
1
Linearized knot diagam
3 8 11 1 10 12 9 2 5 7 4 6
Solving Sequence
6,10 1,5
4 9 12 7 8 11 3 2
c
5
c
4
c
9
c
12
c
6
c
7
c
10
c
3
c
2
c
1
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.00309 × 10
43
u
48
− 3.21474 × 10
41
u
47
+ ··· + 9.90975 × 10
43
b − 9.19958 × 10
43
,
− 3.05614 × 10
43
u
48
− 3.56503 × 10
41
u
47
+ ··· + 4.95488 × 10
43
a + 3.30827 × 10
44
, u
49
+ u
48
+ ··· + 8u + 1i
I
u
2
= h2.20369 × 10
113
u
69
+ 5.25148 × 10
112
u
68
+ ··· + 2.19562 × 10
115
b + 2.18119 × 10
115
,
5.47739 × 10
116
u
69
+ 3.09471 × 10
115
u
68
+ ··· + 1.16368 × 10
117
a + 1.96706 × 10
118
,
u
70
+ u
69
+ ··· + 434u + 53i
I
u
3
= h300a
3
+ 95a
2
+ 2260b + 654a − 1651, 25a
4
− 40a
3
− 98a
2
+ 64a + 197, u + 1i
I
u
4
= hb + u, 8a
3
+ 12a
2
u − 4a
2
− 4au − 2a + u, u
2
+ 1i
I
u
5
= h−a
2
+ 8b + 2a + 3, a
3
+ 3a
2
+ 3a + 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 132 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
= h2.00×10
43
u
48
−3.21×10
41
u
47
+· · ·+9.91×10
43
b−9.20×10
43
, −3.06×
10
43
u
48
−3.57×10
41
u
47
+· · ·+4.95×10
43
a+3.31×10
44
, u
49
+u
48
+· · ·+8u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
1
=
0.616794u
48
+ 0.00719500u
47
+ ··· − 24.9481u − 6.67680
−0.202134u
48
+ 0.00324402u
47
+ ··· + 4.56122u + 0.928336
a
5
=
1
−u
2
a
4
=
2.44394u
48
+ 2.29985u
47
+ ··· + 67.1776u + 6.08652
−0.404222u
48
− 0.323237u
47
+ ··· − 9.06575u − 0.414661
a
9
=
u
−u
3
+ u
a
12
=
0.414661u
48
+ 0.0104390u
47
+ ··· − 20.3869u − 5.74847
−0.202134u
48
+ 0.00324402u
47
+ ··· + 4.56122u + 0.928336
a
7
=
−1.53794u
48
− 1.54132u
47
+ ··· − 47.9985u − 3.48227
0.344085u
48
+ 0.255951u
47
+ ··· + 7.86170u + 0.499407
a
8
=
−1.51259u
48
− 1.48491u
47
+ ··· − 47.1606u − 3.63014
0.434697u
48
+ 0.337745u
47
+ ··· + 8.97345u + 0.382603
a
11
=
0.270574u
48
− 0.255160u
47
+ ··· − 33.8519u − 8.19241
−0.121149u
48
+ 0.0602775u
47
+ ··· + 7.38033u + 1.33256
a
3
=
2.96967u
48
+ 2.72241u
47
+ ··· + 77.5346u + 6.35709
−0.585648u
48
− 0.423585u
47
+ ··· − 11.3675u − 0.535810
a
2
=
0.858872u
48
+ 1.20916u
47
+ ··· + 51.2976u + 8.24260
−0.477090u
48
− 0.426611u
47
+ ··· − 15.0209u − 2.17841
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.15453u
48
− 2.18463u
47
+ ··· − 60.6939u − 13.0765
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
49
+ 17u
48
+ ··· − 236u − 100
c
2
, c
8
u
49
− 3u
48
+ ··· + 22u + 10
c
3
, c
5
, c
9
c
11
u
49
+ u
48
+ ··· + 8u + 1
c
4
, c
10
64(64u
49
− 128u
48
+ ··· + 20u + 1)
c
6
, c
12
u
49
+ 3u
48
+ ··· + 186u + 50
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
49
+ 33y
48
+ ··· − 115504y −10000
c
2
, c
8
y
49
+ 17y
48
+ ··· − 236y −100
c
3
, c
5
, c
9
c
11
y
49
− 15y
48
+ ··· − 16y −1
c
4
, c
10
4096(4096y
49
+ 73728y
48
+ ··· − 62y −1)
c
6
, c
12
y
49
+ 21y
48
+ ··· − 112004y −2500
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.981538 + 0.257391I
a = 1.55206 − 0.93078I
b = −1.23894 + 0.72248I
−5.77516 + 2.35068I −11.35180 + 4.63129I
u = 0.981538 − 0.257391I
a = 1.55206 + 0.93078I
b = −1.23894 − 0.72248I
−5.77516 − 2.35068I −11.35180 − 4.63129I
u = −0.810441 + 0.532063I
a = 2.11896 − 0.39965I
b = −0.643779 + 0.920170I
5.03502 + 0.73563I −5.79688 − 4.57205I
u = −0.810441 − 0.532063I
a = 2.11896 + 0.39965I
b = −0.643779 − 0.920170I
5.03502 − 0.73563I −5.79688 + 4.57205I
u = 0.877698 + 0.561491I
a = −2.08820 − 0.30060I
b = 0.653043 + 0.991957I
5.31366 − 7.02170I −5.51690 + 9.17495I
u = 0.877698 − 0.561491I
a = −2.08820 + 0.30060I
b = 0.653043 − 0.991957I
5.31366 + 7.02170I −5.51690 − 9.17495I
u = −0.995699 + 0.372749I
a = −1.36330 − 0.86812I
b = 1.104890 + 0.550579I
−3.06110 + 2.74516I −8.49807 − 6.15151I
u = −0.995699 − 0.372749I
a = −1.36330 + 0.86812I
b = 1.104890 − 0.550579I
−3.06110 − 2.74516I −8.49807 + 6.15151I
u = 0.875340 + 0.605659I
a = 0.219349 + 0.234083I
b = 0.214791 − 1.396630I
5.30349 − 2.15840I −3.93083 + 3.29725I
u = 0.875340 − 0.605659I
a = 0.219349 − 0.234083I
b = 0.214791 + 1.396630I
5.30349 + 2.15840I −3.93083 − 3.29725I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.952373 + 0.520378I
a = −0.168176 + 0.392073I
b = −0.22875 − 1.47692I
4.08293 + 7.70387I −6.80678 − 8.64886I
u = −0.952373 − 0.520378I
a = −0.168176 − 0.392073I
b = −0.22875 + 1.47692I
4.08293 − 7.70387I −6.80678 + 8.64886I
u = 0.452697 + 0.787769I
a = 0.288931 − 0.311418I
b = 0.127804 − 1.164260I
3.71295 − 0.68830I 0.52323 + 2.74701I
u = 0.452697 − 0.787769I
a = 0.288931 + 0.311418I
b = 0.127804 + 1.164260I
3.71295 + 0.68830I 0.52323 − 2.74701I
u = 0.817518 + 0.099039I
a = −2.07999 − 0.26336I
b = 1.288930 + 0.381664I
−4.95390 − 4.13277I −5.04587 + 8.33177I
u = 0.817518 − 0.099039I
a = −2.07999 + 0.26336I
b = 1.288930 − 0.381664I
−4.95390 + 4.13277I −5.04587 − 8.33177I
u = 1.147530 + 0.376229I
a = 1.35388 − 0.64687I
b = −1.218000 + 0.378064I
−8.08094 − 5.83164I −15.5949 + 6.7506I
u = 1.147530 − 0.376229I
a = 1.35388 + 0.64687I
b = −1.218000 − 0.378064I
−8.08094 + 5.83164I −15.5949 − 6.7506I
u = −1.137970 + 0.439927I
a = 1.72337 − 0.29059I
b = −0.79502 + 1.21714I
−3.88494 + 4.95670I −12.24760 − 4.43222I
u = −1.137970 − 0.439927I
a = 1.72337 + 0.29059I
b = −0.79502 − 1.21714I
−3.88494 − 4.95670I −12.24760 + 4.43222I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688687 + 0.308958I
a = −0.878871 + 0.471910I
b = 0.07117 − 1.41606I
−0.16229 + 1.40976I −9.53355 − 4.57288I
u = −0.688687 − 0.308958I
a = −0.878871 − 0.471910I
b = 0.07117 + 1.41606I
−0.16229 − 1.40976I −9.53355 + 4.57288I
u = −0.286451 + 1.239410I
a = 0.020365 − 0.390591I
b = −0.214987 − 0.936488I
1.83503 − 0.92197I −13.0094 + 8.1328I
u = −0.286451 − 1.239410I
a = 0.020365 + 0.390591I
b = −0.214987 + 0.936488I
1.83503 + 0.92197I −13.0094 − 8.1328I
u = 1.156850 + 0.550225I
a = −1.74873 − 0.14409I
b = 0.706757 + 1.215220I
−0.79278 − 9.29438I −8.00000 + 7.50073I
u = 1.156850 − 0.550225I
a = −1.74873 + 0.14409I
b = 0.706757 − 1.215220I
−0.79278 + 9.29438I −8.00000 − 7.50073I
u = −1.163070 + 0.539405I
a = −1.160470 − 0.653820I
b = 1.087680 + 0.283705I
−0.80094 + 6.65775I −8.00000 + 0.I
u = −1.163070 − 0.539405I
a = −1.160470 + 0.653820I
b = 1.087680 − 0.283705I
−0.80094 − 6.65775I −8.00000 + 0.I
u = −0.079925 + 0.692755I
a = −0.057126 − 1.297370I
b = 0.053644 + 0.267090I
4.56105 + 2.90065I −5.11259 − 3.32387I
u = −0.079925 − 0.692755I
a = −0.057126 + 1.297370I
b = 0.053644 − 0.267090I
4.56105 − 2.90065I −5.11259 + 3.32387I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.021549 + 1.328260I
a = 0.023794 − 0.515824I
b = −0.058851 − 0.693519I
5.08062 + 2.68757I −8.00000 + 0.I
u = −0.021549 − 1.328260I
a = 0.023794 + 0.515824I
b = −0.058851 + 0.693519I
5.08062 − 2.68757I −8.00000 + 0.I
u = −0.671080
a = 1.79535
b = −0.940047
−1.58789 −4.29000
u = 1.220900 + 0.538472I
a = 1.155260 − 0.596939I
b = −1.115300 + 0.247129I
−2.05345 − 12.68030I 0
u = 1.220900 − 0.538472I
a = 1.155260 + 0.596939I
b = −1.115300 − 0.247129I
−2.05345 + 12.68030I 0
u = 0.627660 + 1.221110I
a = −0.031390 − 0.235628I
b = 0.331694 − 1.079920I
7.31454 − 0.58694I 0
u = 0.627660 − 1.221110I
a = −0.031390 + 0.235628I
b = 0.331694 + 1.079920I
7.31454 + 0.58694I 0
u = −1.260280 + 0.553994I
a = 1.62317 − 0.09420I
b = −0.69242 + 1.27875I
−5.13578 + 12.53380I 0
u = −1.260280 − 0.553994I
a = 1.62317 + 0.09420I
b = −0.69242 − 1.27875I
−5.13578 − 12.53380I 0
u = −0.58514 + 1.29446I
a = 0.057217 − 0.263592I
b = −0.345871 − 1.041880I
6.79396 − 5.08385I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.58514 − 1.29446I
a = 0.057217 + 0.263592I
b = −0.345871 + 1.041880I
6.79396 + 5.08385I 0
u = 1.25870 + 0.66450I
a = −1.66771 + 0.03866I
b = 0.63511 + 1.26857I
2.30602 − 12.80540I 0
u = 1.25870 − 0.66450I
a = −1.66771 − 0.03866I
b = 0.63511 − 1.26857I
2.30602 + 12.80540I 0
u = −1.29293 + 0.66685I
a = 1.62720 + 0.05274I
b = −0.63273 + 1.28478I
1.2109 + 18.8792I 0
u = −1.29293 − 0.66685I
a = 1.62720 − 0.05274I
b = −0.63273 − 1.28478I
1.2109 − 18.8792I 0
u = −0.208725 + 0.263076I
a = 0.636904 − 0.809965I
b = −0.176417 + 0.283511I
−0.386214 + 0.820546I −8.61529 − 8.26097I
u = −0.208725 − 0.263076I
a = 0.636904 + 0.809965I
b = −0.176417 − 0.283511I
−0.386214 − 0.820546I −8.61529 + 8.26097I
u = −0.097656 + 0.221062I
a = −1.55418 − 4.92473I
b = 0.055569 + 0.876388I
4.71535 + 2.88833I −6.61461 − 3.16484I
u = −0.097656 − 0.221062I
a = −1.55418 + 4.92473I
b = 0.055569 − 0.876388I
4.71535 − 2.88833I −6.61461 + 3.16484I
9
II. I
u
2
= h2.20 × 10
113
u
69
+ 5.25 × 10
112
u
68
+ · · · + 2.20 × 10
115
b + 2.18 ×
10
115
, 5.48 × 10
116
u
69
+ 3.09 × 10
115
u
68
+ · · · + 1.16 × 10
117
a + 1.97 ×
10
118
, u
70
+ u
69
+ · · · + 434u + 53i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
1
=
−0.470697u
69
− 0.0265942u
68
+ ··· − 149.260u − 16.9039
−0.0100368u
69
− 0.00239180u
68
+ ··· − 2.54768u − 0.993431
a
5
=
1
−u
2
a
4
=
−6.01017u
69
+ 0.310008u
68
+ ··· − 2255.61u − 308.627
−0.226244u
69
+ 0.0311423u
68
+ ··· − 77.8654u − 11.1406
a
9
=
u
−u
3
+ u
a
12
=
−0.480734u
69
− 0.0289860u
68
+ ··· − 151.807u − 17.8973
−0.0100368u
69
− 0.00239180u
68
+ ··· − 2.54768u − 0.993431
a
7
=
0.155671u
69
− 0.0389813u
68
+ ··· + 43.7618u + 4.64741
−0.0580571u
69
− 0.00135076u
68
+ ··· − 19.8965u − 2.18136
a
8
=
0.143997u
69
− 0.0275353u
68
+ ··· + 38.2166u + 3.85369
−0.0460225u
69
+ 0.0000400031u
68
+ ··· − 16.0263u − 1.74972
a
11
=
−6.43551u
69
+ 0.0646646u
68
+ ··· − 2338.34u − 323.669
−0.222739u
69
+ 0.0292459u
68
+ ··· − 71.9426u − 10.0199
a
3
=
0.120256u
69
− 0.0236167u
68
+ ··· + 41.4888u + 9.39135
−0.0209187u
69
+ 0.000811014u
68
+ ··· − 9.03896u − 1.96341
a
2
=
0.363436u
69
+ 0.0187985u
68
+ ··· + 118.612u + 19.4997
0.00913425u
69
− 0.000942294u
68
+ ··· + 1.20552u − 0.169703
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0239601u
69
− 0.00841492u
68
+ ··· + 18.6490u − 3.90520
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
35
+ 11u
34
+ ··· − 2u − 1)
2
c
2
, c
8
(u
35
+ u
34
+ ··· + 2u + 1)
2
c
3
, c
5
, c
9
c
11
u
70
+ u
69
+ ··· + 434u + 53
c
4
, c
10
u
70
+ 19u
69
+ ··· + 60600u − 5375
c
6
, c
12
(u
35
− u
34
+ ··· − 2u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
35
+ 27y
34
+ ··· − 22y −1)
2
c
2
, c
8
(y
35
+ 11y
34
+ ··· − 2y −1)
2
c
3
, c
5
, c
9
c
11
y
70
− 41y
69
+ ··· − 86596y + 2809
c
4
, c
10
y
70
− 21y
69
+ ··· − 1096015000y + 28890625
c
6
, c
12
(y
35
+ 19y
34
+ ··· − 2y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.119514 + 1.003680I
a = −0.124946 + 0.339745I
b = 0.491471 + 1.162520I
−1.63653 − 7.02473I −10.39842 + 6.93954I
u = −0.119514 − 1.003680I
a = −0.124946 − 0.339745I
b = 0.491471 − 1.162520I
−1.63653 + 7.02473I −10.39842 − 6.93954I
u = 0.967240 + 0.057432I
a = 2.54114 − 12.61520I
b = 0.030366 − 1.049680I
1.36125 + 2.79178I −2.56555 − 3.12849I
u = 0.967240 − 0.057432I
a = 2.54114 + 12.61520I
b = 0.030366 + 1.049680I
1.36125 − 2.79178I −2.56555 + 3.12849I
u = −1.037220 + 0.046542I
a = −11.49130 − 3.57082I
b = 0.030366 − 1.049680I
1.36125 + 2.79178I −2.56555 − 3.12849I
u = −1.037220 − 0.046542I
a = −11.49130 + 3.57082I
b = 0.030366 + 1.049680I
1.36125 − 2.79178I −2.56555 + 3.12849I
u = 0.992816 + 0.307203I
a = −1.86835 + 0.59825I
b = 0.274169 + 0.754223I
−2.90212 − 1.21814I −7.56786 + 5.43737I
u = 0.992816 − 0.307203I
a = −1.86835 − 0.59825I
b = 0.274169 − 0.754223I
−2.90212 + 1.21814I −7.56786 − 5.43737I
u = 0.812668 + 0.700215I
a = −0.796936 + 1.003470I
b = 0.475306 + 0.917107I
−1.67002 − 2.07827I −8.00000 + 3.40333I
u = 0.812668 − 0.700215I
a = −0.796936 − 1.003470I
b = 0.475306 − 0.917107I
−1.67002 + 2.07827I −8.00000 − 3.40333I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.041410 + 0.270926I
a = −1.52455 + 0.29351I
b = 0.407102 − 1.144230I
−1.01725 + 1.14078I −8.93962 + 0.35223I
u = −1.041410 − 0.270926I
a = −1.52455 − 0.29351I
b = 0.407102 + 1.144230I
−1.01725 − 1.14078I −8.93962 − 0.35223I
u = 0.133172 + 0.888260I
a = −0.513616 + 0.654211I
b = 0.817305 + 0.125028I
1.19431 + 7.52211I −8.37393 − 5.45189I
u = 0.133172 − 0.888260I
a = −0.513616 − 0.654211I
b = 0.817305 − 0.125028I
1.19431 − 7.52211I −8.37393 + 5.45189I
u = −0.977207 + 0.510227I
a = 0.223970 − 0.121731I
b = 0.510838 + 0.446804I
−2.91461 − 1.90476I −11.61760 + 3.26312I
u = −0.977207 − 0.510227I
a = 0.223970 + 0.121731I
b = 0.510838 − 0.446804I
−2.91461 + 1.90476I −11.61760 − 3.26312I
u = −0.895460
a = 1.21237
b = −0.714433
−1.48735 −6.22320
u = −0.744917 + 0.469702I
a = −0.771318 − 0.328880I
b = 0.386425 + 1.221160I
5.25248 + 3.42594I −3.89028 − 2.22817I
u = −0.744917 − 0.469702I
a = −0.771318 + 0.328880I
b = 0.386425 − 1.221160I
5.25248 − 3.42594I −3.89028 + 2.22817I
u = 0.672202 + 0.568802I
a = 0.588099 − 0.277287I
b = −0.402291 + 1.220240I
5.91946 + 2.50696I −2.73890 − 2.94934I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.672202 − 0.568802I
a = 0.588099 + 0.277287I
b = −0.402291 − 1.220240I
5.91946 − 2.50696I −2.73890 + 2.94934I
u = 0.657413 + 0.573036I
a = 1.95056 − 0.17929I
b = −0.402291 − 1.220240I
5.91946 − 2.50696I −2.73890 + 2.94934I
u = 0.657413 − 0.573036I
a = 1.95056 + 0.17929I
b = −0.402291 + 1.220240I
5.91946 + 2.50696I −2.73890 − 2.94934I
u = 0.276214 + 0.810444I
a = 0.0549455 + 0.0810153I
b = −0.453184 + 1.179210I
1.83551 + 4.24996I −3.13542 − 3.77353I
u = 0.276214 − 0.810444I
a = 0.0549455 − 0.0810153I
b = −0.453184 − 1.179210I
1.83551 − 4.24996I −3.13542 + 3.77353I
u = −0.223135 + 0.814237I
a = 0.614394 + 0.692076I
b = −0.812555 + 0.099238I
1.97019 − 1.67857I −6.82266 + 0.36674I
u = −0.223135 − 0.814237I
a = 0.614394 − 0.692076I
b = −0.812555 − 0.099238I
1.97019 + 1.67857I −6.82266 − 0.36674I
u = 0.337448 + 1.122360I
a = 0.279152 + 0.257589I
b = −0.498606 + 1.204550I
5.23403 + 6.46046I 0
u = 0.337448 − 1.122360I
a = 0.279152 − 0.257589I
b = −0.498606 − 1.204550I
5.23403 − 6.46046I 0
u = −1.165920 + 0.188060I
a = 0.066157 − 1.277360I
b = 0.274169 + 0.754223I
−2.90212 − 1.21814I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.165920 − 0.188060I
a = 0.066157 + 1.277360I
b = 0.274169 − 0.754223I
−2.90212 + 1.21814I 0
u = 1.068030 + 0.544420I
a = 1.46092 + 0.01825I
b = −0.453184 − 1.179210I
1.83551 − 4.24996I 0
u = 1.068030 − 0.544420I
a = 1.46092 − 0.01825I
b = −0.453184 + 1.179210I
1.83551 + 4.24996I 0
u = −0.298459 + 1.176530I
a = −0.284974 + 0.293575I
b = 0.509525 + 1.201690I
4.37931 − 12.37660I 0
u = −0.298459 − 1.176530I
a = −0.284974 − 0.293575I
b = 0.509525 − 1.201690I
4.37931 + 12.37660I 0
u = −1.101900 + 0.519411I
a = 0.959687 + 0.178430I
b = −0.812555 − 0.099238I
1.97019 + 1.67857I 0
u = −1.101900 − 0.519411I
a = 0.959687 − 0.178430I
b = −0.812555 + 0.099238I
1.97019 − 1.67857I 0
u = 1.205300 + 0.207889I
a = −1.031590 + 0.049162I
b = 0.703066 − 0.147767I
−4.55305 − 2.51214I 0
u = 1.205300 − 0.207889I
a = −1.031590 − 0.049162I
b = 0.703066 + 0.147767I
−4.55305 + 2.51214I 0
u = −0.931544 + 0.800142I
a = 0.795980 + 0.807318I
b = −0.528952 + 0.892872I
−2.47115 + 7.33485I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.931544 − 0.800142I
a = 0.795980 − 0.807318I
b = −0.528952 − 0.892872I
−2.47115 − 7.33485I 0
u = −0.539710 + 0.522535I
a = −2.20446 − 0.19474I
b = 0.386425 − 1.221160I
5.25248 − 3.42594I −3.89028 + 2.22817I
u = −0.539710 − 0.522535I
a = −2.20446 + 0.19474I
b = 0.386425 + 1.221160I
5.25248 + 3.42594I −3.89028 − 2.22817I
u = −1.138700 + 0.596407I
a = 1.054870 + 0.623315I
b = −0.511218 + 0.765398I
−6.72846 + 2.09817I 0
u = −1.138700 − 0.596407I
a = 1.054870 − 0.623315I
b = −0.511218 − 0.765398I
−6.72846 − 2.09817I 0
u = 1.191760 + 0.514634I
a = −0.940468 + 0.144170I
b = 0.817305 − 0.125028I
1.19431 − 7.52211I 0
u = 1.191760 − 0.514634I
a = −0.940468 − 0.144170I
b = 0.817305 + 0.125028I
1.19431 + 7.52211I 0
u = 1.187310 + 0.528355I
a = 0.012010 − 0.274266I
b = −0.541549 + 0.582168I
−3.33212 − 3.00440I 0
u = 1.187310 − 0.528355I
a = 0.012010 + 0.274266I
b = −0.541549 − 0.582168I
−3.33212 + 3.00440I 0
u = 1.315410 + 0.197168I
a = −1.112060 + 0.162330I
b = 0.510838 + 0.446804I
−2.91461 − 1.90476I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.315410 − 0.197168I
a = −1.112060 − 0.162330I
b = 0.510838 − 0.446804I
−2.91461 + 1.90476I 0
u = −1.262910 + 0.569858I
a = −1.279310 + 0.022571I
b = 0.491471 − 1.162520I
−1.63653 + 7.02473I 0
u = −1.262910 − 0.569858I
a = −1.279310 − 0.022571I
b = 0.491471 + 1.162520I
−1.63653 − 7.02473I 0
u = −1.337050 + 0.368711I
a = 1.090190 + 0.311119I
b = −0.541549 + 0.582168I
−3.33212 − 3.00440I 0
u = −1.337050 − 0.368711I
a = 1.090190 − 0.311119I
b = −0.541549 − 0.582168I
−3.33212 + 3.00440I 0
u = −0.200762 + 0.571555I
a = 0.028580 + 0.953330I
b = 0.703066 + 0.147767I
−4.55305 + 2.51214I −14.0397 − 3.8785I
u = −0.200762 − 0.571555I
a = 0.028580 − 0.953330I
b = 0.703066 − 0.147767I
−4.55305 − 2.51214I −14.0397 + 3.8785I
u = 1.39235 + 0.32069I
a = 0.337466 − 0.509570I
b = −0.511218 + 0.765398I
−6.72846 + 2.09817I 0
u = 1.39235 − 0.32069I
a = 0.337466 + 0.509570I
b = −0.511218 − 0.765398I
−6.72846 − 2.09817I 0
u = −1.42930 + 0.06709I
a = −0.754539 − 0.588624I
b = 0.475306 + 0.917107I
−1.67002 − 2.07827I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42930 − 0.06709I
a = −0.754539 + 0.588624I
b = 0.475306 − 0.917107I
−1.67002 + 2.07827I 0
u = 1.21033 + 0.76716I
a = 1.289950 − 0.141681I
b = −0.498606 − 1.204550I
5.23403 − 6.46046I 0
u = 1.21033 − 0.76716I
a = 1.289950 + 0.141681I
b = −0.498606 + 1.204550I
5.23403 + 6.46046I 0
u = −1.26708 + 0.77421I
a = −1.247750 − 0.134733I
b = 0.509525 − 1.201690I
4.37931 + 12.37660I 0
u = −1.26708 − 0.77421I
a = −1.247750 + 0.134733I
b = 0.509525 + 1.201690I
4.37931 − 12.37660I 0
u = −0.083030 + 0.485962I
a = 0.907222 − 0.069478I
b = 0.407102 + 1.144230I
−1.01725 − 1.14078I −8.93962 − 0.35223I
u = −0.083030 − 0.485962I
a = 0.907222 + 0.069478I
b = 0.407102 − 1.144230I
−1.01725 + 1.14078I −8.93962 + 0.35223I
u = 1.51967 + 0.13036I
a = 0.649262 − 0.463270I
b = −0.528952 + 0.892872I
−2.47115 + 7.33485I 0
u = 1.51967 − 0.13036I
a = 0.649262 + 0.463270I
b = −0.528952 − 0.892872I
−2.47115 − 7.33485I 0
u = −0.183629
a = 4.07848
b = −0.714433
−1.48735 −6.22320
19
III.
I
u
3
= h300a
3
+95a
2
+2260b+654a−1651, 25a
4
−40a
3
−98a
2
+64a+197, u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
−1
a
1
=
a
−0.132743a
3
− 0.0420354a
2
− 0.289381a + 0.730531
a
5
=
1
−1
a
4
=
0.254425a
3
− 0.190265a
2
− 1.07035a − 0.0460177
−0.0221239a
3
+ 0.201327a
2
+ 0.201770a − 0.919912
a
9
=
−1
0
a
12
=
−0.132743a
3
− 0.0420354a
2
+ 0.710619a + 0.730531
−0.132743a
3
− 0.0420354a
2
− 0.289381a + 0.730531
a
7
=
0.0221239a
3
− 0.201327a
2
− 0.201770a + 0.919912
0.276549a
3
+ 0.608407a
2
− 1.27212a − 1.12611
a
8
=
−0.254425a
3
− 0.809735a
2
+ 1.07035a + 2.04602
0.276549a
3
+ 0.608407a
2
− 1.27212a − 1.12611
a
11
=
0.121681a
3
− 0.232301a
2
− 0.359735a + 0.684513
−0.154867a
3
+ 0.159292a
2
− 0.0876106a − 0.189381
a
3
=
0.132743a
3
+ 0.0420354a
2
− 0.710619a − 0.730531
0.132743a
3
+ 0.0420354a
2
+ 0.289381a − 0.730531
a
2
=
−0.265487a
3
− 0.0840708a
2
+ 1.42124a + 0.461062
0.652655a
3
− 0.314159a
2
− 1.70221a − 0.987611
(ii) Obstruction class = 1
(iii) Cusp Shapes =
125
113
a
3
+
275
113
a
2
−
575
113
a −
2769
113
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
2
− 2u + 2)
2
c
2
, c
8
u
4
+ 2u
2
+ 2
c
3
, c
9
(u − 1)
4
c
4
, c
10
25(25u
4
− 40u
3
+ 12u
2
+ 4u + 1)
c
5
, c
11
(u + 1)
4
c
6
, c
12
u
4
− 2u
2
+ 2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
2
+ 4)
2
c
2
, c
8
(y
2
+ 2y + 2)
2
c
3
, c
5
, c
9
c
11
(y −1)
4
c
4
, c
10
625(625y
4
− 1000y
3
+ 514y
2
+ 8y + 1)
c
6
, c
12
(y
2
− 2y + 2)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.229180 + 0.617389I
b = 1.098680 − 0.455090I
−5.75727 + 3.66386I −16.0000 − 4.0000I
u = −1.00000
a = −1.229180 − 0.617389I
b = 1.098680 + 0.455090I
−5.75727 − 3.66386I −16.0000 + 4.0000I
u = −1.00000
a = 2.02918 + 0.21739I
b = −1.098680 − 0.455090I
−5.75727 − 3.66386I −16.0000 + 4.0000I
u = −1.00000
a = 2.02918 − 0.21739I
b = −1.098680 + 0.455090I
−5.75727 + 3.66386I −16.0000 − 4.0000I
23
IV. I
u
4
= hb + u, 8a
3
+ 12a
2
u − 4a
2
− 4au − 2a + u, u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
1
=
a
−u
a
5
=
1
1
a
4
=
a
2
+ au + 1
−au + 2
a
9
=
u
2u
a
12
=
a − u
−u
a
7
=
−au
−1
a
8
=
au − 1
4au − 3
a
11
=
a
2
u
a + u
a
3
=
2a
2
+ au + 1
−2au + 3
a
2
=
−2a
2
u + 2a
2
+ 2au + 3a +
1
2
u
−4a
2
u + 8a + 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16a
2
− 16au + 8a + 4u − 4
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
8
u
6
+ u
4
+ 2u
2
+ 1
c
3
, c
5
, c
6
c
9
, c
11
, c
12
(u
2
+ 1)
3
c
4
, c
10
64(64u
6
+ 64u
5
+ 128u
4
+ 80u
3
+ 44u
2
+ 8u + 1)
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
8
(y
3
+ y
2
+ 2y + 1)
2
c
3
, c
5
, c
6
c
9
, c
11
, c
12
(y + 1)
6
c
4
, c
10
4096(4096y
6
+ 12288y
5
+ 11776y
4
+ 3968y
3
+ 912y
2
+ 24y + 1)
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.107540 − 1.153570I
b = − 1.000000I
6.31400 + 2.82812I −0.49024 − 2.97945I
u = 1.000000I
a = 0.284920 − 0.500000I
b = − 1.000000I
2.17641 −7.01951 + 0.I
u = 1.000000I
a = 0.107540 + 0.153571I
b = − 1.000000I
6.31400 − 2.82812I −0.49024 + 2.97945I
u = − 1.000000I
a = 0.107540 + 1.153570I
b = 1.000000I
6.31400 − 2.82812I −0.49024 + 2.97945I
u = − 1.000000I
a = 0.284920 + 0.500000I
b = 1.000000I
2.17641 −7.01951 + 0.I
u = − 1.000000I
a = 0.107540 − 0.153571I
b = 1.000000I
6.31400 + 2.82812I −0.49024 − 2.97945I
27
V. I
u
5
= h−a
2
+ 8b + 2a + 3, a
3
+ 3a
2
+ 3a + 1, u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
1
=
a
1
8
a
2
−
1
4
a −
3
8
a
5
=
1
−1
a
4
=
−
3
8
a
2
+
3
4
a +
9
8
3
8
a
2
+
1
4
a −
9
8
a
9
=
1
0
a
12
=
1
8
a
2
+
3
4
a −
3
8
1
8
a
2
−
1
4
a −
3
8
a
7
=
−
3
8
a
2
−
1
4
a +
9
8
1
4
a
2
+
1
2
a +
1
4
a
8
=
−
5
8
a
2
−
3
4
a +
7
8
1
4
a
2
+
1
2
a +
1
4
a
11
=
1
2
a
2
−
3
2
−
1
4
a
2
−
1
2
a +
3
4
a
3
=
1
8
a
2
+
3
4
a −
3
8
1
8
a
2
−
1
4
a −
3
8
a
2
=
1
4
a
2
+
3
2
a +
1
4
1
8
a
2
−
1
4
a −
3
8
(ii) Obstruction class = 1
(iii) Cusp Shapes = a
2
+ 2a − 11
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
u
3
c
3
, c
4
, c
9
c
10
(u + 1)
3
c
5
, c
11
(u − 1)
3
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y
3
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y −1)
3
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
u = 1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
u = 1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
3
(u
2
− 2u + 2)
2
(u
3
− u
2
+ 2u − 1)
2
(u
35
+ 11u
34
+ ··· − 2u − 1)
2
· (u
49
+ 17u
48
+ ··· − 236u − 100)
c
2
, c
8
u
3
(u
4
+ 2u
2
+ 2)(u
6
+ u
4
+ 2u
2
+ 1)(u
35
+ u
34
+ ··· + 2u + 1)
2
· (u
49
− 3u
48
+ ··· + 22u + 10)
c
3
, c
9
((u − 1)
4
)(u + 1)
3
(u
2
+ 1)
3
(u
49
+ u
48
+ ··· + 8u + 1)
· (u
70
+ u
69
+ ··· + 434u + 53)
c
4
, c
10
102400(u + 1)
3
(25u
4
− 40u
3
+ 12u
2
+ 4u + 1)
· (64u
6
+ 64u
5
+ 128u
4
+ 80u
3
+ 44u
2
+ 8u + 1)
· (64u
49
− 128u
48
+ ··· + 20u + 1)(u
70
+ 19u
69
+ ··· + 60600u − 5375)
c
5
, c
11
((u − 1)
3
)(u + 1)
4
(u
2
+ 1)
3
(u
49
+ u
48
+ ··· + 8u + 1)
· (u
70
+ u
69
+ ··· + 434u + 53)
c
6
, c
12
u
3
(u
2
+ 1)
3
(u
4
− 2u
2
+ 2)(u
35
− u
34
+ ··· − 2u + 1)
2
· (u
49
+ 3u
48
+ ··· + 186u + 50)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
3
(y
2
+ 4)
2
(y
3
+ 3y
2
+ 2y −1)
2
(y
35
+ 27y
34
+ ··· − 22y −1)
2
· (y
49
+ 33y
48
+ ··· − 115504y −10000)
c
2
, c
8
y
3
(y
2
+ 2y + 2)
2
(y
3
+ y
2
+ 2y + 1)
2
(y
35
+ 11y
34
+ ··· − 2y −1)
2
· (y
49
+ 17y
48
+ ··· − 236y −100)
c
3
, c
5
, c
9
c
11
((y −1)
7
)(y + 1)
6
(y
49
− 15y
48
+ ··· − 16y −1)
· (y
70
− 41y
69
+ ··· − 86596y + 2809)
c
4
, c
10
10485760000(y −1)
3
(625y
4
− 1000y
3
+ 514y
2
+ 8y + 1)
· (4096y
6
+ 12288y
5
+ 11776y
4
+ 3968y
3
+ 912y
2
+ 24y + 1)
· (4096y
49
+ 73728y
48
+ ··· − 62y −1)
· (y
70
− 21y
69
+ ··· − 1096015000y + 28890625)
c
6
, c
12
y
3
(y + 1)
6
(y
2
− 2y + 2)
2
(y
35
+ 19y
34
+ ··· − 2y −1)
2
· (y
49
+ 21y
48
+ ··· − 112004y −2500)
33
