12a
0419
(K12a
0419
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 10 2 5 11 7 1 4 8
Solving Sequence
4,12 5,8
1 7 11 9 3 10 6 2
c
4
c
12
c
7
c
11
c
8
c
3
c
10
c
5
c
2
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9.88459 × 10
1013
u
181
+ 1.80208 × 10
1014
u
180
+ ··· + 2.42399 × 10
1014
b + 3.99849 × 10
1014
,
2.88553 × 10
1013
u
181
4.79670 × 10
1013
u
180
+ ··· + 1.27578 × 10
1013
a 1.17798 × 10
1014
,
u
182
+ 2u
181
+ ··· + 18u + 1i
I
u
2
= h−1.15838 × 10
33
u
42
1.70244 × 10
33
u
41
+ ··· + 2.11466 × 10
32
b 1.33001 × 10
33
,
1.28770 × 10
33
u
42
+ 1.62157 × 10
32
u
41
+ ··· + 2.11466 × 10
32
a 6.36585 × 10
33
, u
43
+ u
42
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 225 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
= h9.88 × 10
1013
u
181
+ 1.80 × 10
1014
u
180
+ · · · + 2.42 × 10
1014
b + 4.00 ×
10
1014
, 2.89 × 10
1013
u
181
4.80 × 10
1013
u
180
+ · · · + 1.28 × 10
1013
a
1.18 × 10
1014
, u
182
+ 2u
181
+ · · · + 18u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
8
=
2.26177u
181
+ 3.75981u
180
+ ··· + 147.770u + 9.23341
0.407782u
181
0.743438u
180
+ ··· 27.0959u 1.64955
a
1
=
3.27635u
181
5.34779u
180
+ ··· 141.246u 8.30418
0.0374048u
181
+ 0.441289u
180
+ ··· + 39.6804u + 3.60649
a
7
=
3.24310u
181
+ 4.95955u
180
+ ··· + 186.351u + 11.6467
0.352908u
181
0.162965u
180
+ ··· 14.3448u 0.886637
a
11
=
u
u
a
9
=
2.89776u
181
+ 4.31013u
180
+ ··· + 160.146u + 10.0693
0.228210u
181
0.193110u
180
+ ··· 14.7200u 0.813692
a
3
=
3.44546u
181
+ 6.53680u
180
+ ··· + 327.617u + 24.9418
0.447829u
181
0.305439u
180
+ ··· + 2.78794u + 0.556196
a
10
=
4.22856u
181
7.89659u
180
+ ··· 295.726u 32.9946
0.193692u
181
+ 0.370684u
180
+ ··· + 18.9442u + 1.19168
a
6
=
5.48557u
181
10.1286u
180
+ ··· 548.088u 44.6091
0.455170u
181
0.262679u
180
+ ··· 12.6569u 1.01401
a
2
=
1.47936u
181
3.47355u
180
+ ··· 84.2762u 8.47404
0.452183u
181
+ 0.416483u
180
+ ··· + 37.1423u + 2.46176
(ii) Obstruction class = 1
(iii) Cusp Shapes = 1.74311u
181
3.28687u
180
+ ··· 161.807u 22.4706
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
182
+ 80u
181
+ ··· 14u + 1
c
2
, c
6
u
182
+ 40u
180
+ ··· + 4u + 1
c
3
u
182
+ u
181
+ ··· + 173061562687u + 50838216514
c
4
, c
11
u
182
+ 2u
181
+ ··· + 18u + 1
c
5
u
182
6u
180
+ ··· 29u + 1
c
7
u
182
+ 16u
181
+ ··· + 107815334379u + 9487345129
c
8
u
182
+ 18u
181
+ ··· + 37740592u + 2302703
c
9
u
182
+ 8u
181
+ ··· 16483u + 704
c
10
u
182
+ 17u
181
+ ··· + 1894916324u + 143269799
c
12
u
182
u
181
+ ··· 233173107u + 23453042
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
182
+ 60y
181
+ ··· 458y + 1
c
2
, c
6
y
182
+ 80y
181
+ ··· 14y + 1
c
3
y
182
+ 83y
181
+ ··· + 1.73 × 10
23
y + 2.58 × 10
21
c
4
, c
11
y
182
126y
181
+ ··· 110y + 1
c
5
y
182
12y
181
+ ··· + 393y + 1
c
7
y
182
+ 100y
181
+ ··· + 4.51 × 10
21
y + 9.00 × 10
19
c
8
y
182
52y
181
+ ··· 245956311483672y + 5302441106209
c
9
y
182
26y
181
+ ··· 28999369y + 495616
c
10
y
182
+ 35y
181
+ ··· + 2524246924058369408y + 20526235305500401
c
12
y
182
59y
181
+ ··· 11000196487083765y + 550045179053764
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.009030 + 0.141856I
a = 0.313299 + 0.401315I
b = 2.13016 + 0.32049I
5.55107 0.59106I 0
u = 1.009030 0.141856I
a = 0.313299 0.401315I
b = 2.13016 0.32049I
5.55107 + 0.59106I 0
u = 1.023890 + 0.011929I
a = 0.29832 1.57682I
b = 0.078867 0.465740I
0.0137628 + 0.0482185I 0
u = 1.023890 0.011929I
a = 0.29832 + 1.57682I
b = 0.078867 + 0.465740I
0.0137628 0.0482185I 0
u = 0.947856 + 0.399001I
a = 1.162700 + 0.604371I
b = 0.790022 + 0.241060I
2.28558 1.78667I 0
u = 0.947856 0.399001I
a = 1.162700 0.604371I
b = 0.790022 0.241060I
2.28558 + 1.78667I 0
u = 0.968734 + 0.024336I
a = 0.61065 + 1.41694I
b = 0.383892 + 0.156040I
0.77817 5.28244I 0
u = 0.968734 0.024336I
a = 0.61065 1.41694I
b = 0.383892 0.156040I
0.77817 + 5.28244I 0
u = 0.166608 + 1.034190I
a = 0.473620 0.611144I
b = 0.201200 + 0.046334I
1.04142 + 2.04374I 0
u = 0.166608 1.034190I
a = 0.473620 + 0.611144I
b = 0.201200 0.046334I
1.04142 2.04374I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.006100 + 0.315489I
a = 2.10865 + 0.05491I
b = 2.57152 0.31924I
0.31160 + 5.57110I 0
u = 1.006100 0.315489I
a = 2.10865 0.05491I
b = 2.57152 + 0.31924I
0.31160 5.57110I 0
u = 0.948274 + 0.465858I
a = 0.096936 + 0.389458I
b = 0.783343 + 0.021851I
0.49949 + 2.11576I 0
u = 0.948274 0.465858I
a = 0.096936 0.389458I
b = 0.783343 0.021851I
0.49949 2.11576I 0
u = 0.043615 + 0.939743I
a = 0.608201 + 1.043260I
b = 0.449289 + 0.142500I
1.83925 + 2.77276I 0
u = 0.043615 0.939743I
a = 0.608201 1.043260I
b = 0.449289 0.142500I
1.83925 2.77276I 0
u = 0.103365 + 1.075060I
a = 0.257832 0.925480I
b = 0.401416 + 0.172859I
3.03083 5.08964I 0
u = 0.103365 1.075060I
a = 0.257832 + 0.925480I
b = 0.401416 0.172859I
3.03083 + 5.08964I 0
u = 0.209631 + 0.891648I
a = 0.323876 1.187200I
b = 0.534672 0.053449I
2.06496 + 1.86441I 0
u = 0.209631 0.891648I
a = 0.323876 + 1.187200I
b = 0.534672 + 0.053449I
2.06496 1.86441I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.913511 + 0.026956I
a = 1.094780 0.583268I
b = 1.78144 1.29355I
0.75830 5.61050I 0
u = 0.913511 0.026956I
a = 1.094780 + 0.583268I
b = 1.78144 + 1.29355I
0.75830 + 5.61050I 0
u = 1.021910 + 0.394620I
a = 0.755643 + 0.301443I
b = 1.49429 + 0.79233I
1.67984 1.70771I 0
u = 1.021910 0.394620I
a = 0.755643 0.301443I
b = 1.49429 0.79233I
1.67984 + 1.70771I 0
u = 1.021630 + 0.404588I
a = 1.80591 + 0.17101I
b = 2.35188 0.35534I
1.56593 11.13020I 0
u = 1.021630 0.404588I
a = 1.80591 0.17101I
b = 2.35188 + 0.35534I
1.56593 + 11.13020I 0
u = 0.494596 + 0.746564I
a = 0.04206 1.46230I
b = 0.846040 0.356835I
0.07980 + 6.70477I 0
u = 0.494596 0.746564I
a = 0.04206 + 1.46230I
b = 0.846040 + 0.356835I
0.07980 6.70477I 0
u = 0.409772 + 0.792393I
a = 0.659545 + 0.416504I
b = 0.094912 + 0.880997I
0.62119 2.88256I 0
u = 0.409772 0.792393I
a = 0.659545 0.416504I
b = 0.094912 0.880997I
0.62119 + 2.88256I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.439928 + 1.017320I
a = 0.469839 + 0.363233I
b = 0.101180 + 0.549735I
1.16243 + 3.40220I 0
u = 0.439928 1.017320I
a = 0.469839 0.363233I
b = 0.101180 0.549735I
1.16243 3.40220I 0
u = 0.473109 + 0.745843I
a = 0.989975 + 0.029769I
b = 0.1102610 + 0.0785284I
0.03558 + 2.02814I 0
u = 0.473109 0.745843I
a = 0.989975 0.029769I
b = 0.1102610 0.0785284I
0.03558 2.02814I 0
u = 0.122766 + 0.871575I
a = 0.547664 + 0.475647I
b = 0.110992 + 0.599971I
1.00419 + 2.17891I 0
u = 0.122766 0.871575I
a = 0.547664 0.475647I
b = 0.110992 0.599971I
1.00419 2.17891I 0
u = 0.872659 + 0.021473I
a = 0.955023 + 0.863297I
b = 1.61678 + 1.28554I
0.544965 0.181606I 0
u = 0.872659 0.021473I
a = 0.955023 0.863297I
b = 1.61678 1.28554I
0.544965 + 0.181606I 0
u = 1.061940 + 0.387693I
a = 0.752968 + 0.326112I
b = 1.68899 + 0.74071I
2.65927 3.49415I 0
u = 1.061940 0.387693I
a = 0.752968 0.326112I
b = 1.68899 0.74071I
2.65927 + 3.49415I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.029820 + 0.471134I
a = 0.695018 + 0.627876I
b = 2.05239 + 0.07516I
4.91072 + 2.60056I 0
u = 1.029820 0.471134I
a = 0.695018 0.627876I
b = 2.05239 0.07516I
4.91072 2.60056I 0
u = 1.042850 + 0.445106I
a = 1.117350 + 0.501463I
b = 0.974232 + 0.390855I
2.44187 + 5.72625I 0
u = 1.042850 0.445106I
a = 1.117350 0.501463I
b = 0.974232 0.390855I
2.44187 5.72625I 0
u = 0.313703 + 0.804817I
a = 0.642167 + 0.426873I
b = 0.155789 + 0.796728I
0.232400 0.983727I 0
u = 0.313703 0.804817I
a = 0.642167 0.426873I
b = 0.155789 0.796728I
0.232400 + 0.983727I 0
u = 1.135020 + 0.096203I
a = 1.39768 1.41526I
b = 2.03788 1.09850I
3.52324 + 2.42981I 0
u = 1.135020 0.096203I
a = 1.39768 + 1.41526I
b = 2.03788 + 1.09850I
3.52324 2.42981I 0
u = 1.094990 + 0.347334I
a = 0.614598 + 0.358300I
b = 2.47322 + 0.66744I
2.12331 + 12.08440I 0
u = 1.094990 0.347334I
a = 0.614598 0.358300I
b = 2.47322 0.66744I
2.12331 12.08440I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.087640 + 0.370755I
a = 0.658927 + 0.390268I
b = 2.25881 + 0.57503I
0.45219 6.49738I 0
u = 1.087640 0.370755I
a = 0.658927 0.390268I
b = 2.25881 0.57503I
0.45219 + 6.49738I 0
u = 0.383925 + 0.758280I
a = 0.949582 + 0.691523I
b = 0.0585502 0.0482950I
3.66110 + 5.98563I 0
u = 0.383925 0.758280I
a = 0.949582 0.691523I
b = 0.0585502 + 0.0482950I
3.66110 5.98563I 0
u = 1.150780 + 0.071912I
a = 0.446515 + 0.363356I
b = 1.26845 1.89681I
8.05622 + 2.42918I 0
u = 1.150780 0.071912I
a = 0.446515 0.363356I
b = 1.26845 + 1.89681I
8.05622 2.42918I 0
u = 0.523690 + 0.664837I
a = 0.656045 + 0.384686I
b = 0.151256 + 0.873918I
0.63709 + 1.91849I 0
u = 0.523690 0.664837I
a = 0.656045 0.384686I
b = 0.151256 0.873918I
0.63709 1.91849I 0
u = 0.077307 + 1.152530I
a = 0.610762 + 0.832657I
b = 0.1026890 + 0.0288167I
6.59732 6.52254I 0
u = 0.077307 1.152530I
a = 0.610762 0.832657I
b = 0.1026890 0.0288167I
6.59732 + 6.52254I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.157490 + 0.074157I
a = 0.895828 + 0.135122I
b = 2.06913 0.93311I
4.87734 1.50235I 0
u = 1.157490 0.074157I
a = 0.895828 0.135122I
b = 2.06913 + 0.93311I
4.87734 + 1.50235I 0
u = 0.512743 + 0.655907I
a = 1.290390 + 0.139531I
b = 0.0081725 + 0.1250560I
0.99697 6.30001I 0
u = 0.512743 0.655907I
a = 1.290390 0.139531I
b = 0.0081725 0.1250560I
0.99697 + 6.30001I 0
u = 0.358868 + 0.747225I
a = 0.912763 + 0.764350I
b = 0.0315625 0.0820181I
4.83309 0.72593I 0
u = 0.358868 0.747225I
a = 0.912763 0.764350I
b = 0.0315625 + 0.0820181I
4.83309 + 0.72593I 0
u = 1.171230 + 0.078145I
a = 1.23232 1.98992I
b = 1.71566 1.63366I
3.09865 + 4.77084I 0
u = 1.171230 0.078145I
a = 1.23232 + 1.98992I
b = 1.71566 + 1.63366I
3.09865 4.77084I 0
u = 1.145480 + 0.264663I
a = 0.824884 + 0.488640I
b = 1.45286 0.24358I
2.18439 4.50657I 0
u = 1.145480 0.264663I
a = 0.824884 0.488640I
b = 1.45286 + 0.24358I
2.18439 + 4.50657I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.178790 + 0.109097I
a = 1.03810 1.91406I
b = 1.61342 1.50768I
5.16369 10.73600I 0
u = 1.178790 0.109097I
a = 1.03810 + 1.91406I
b = 1.61342 + 1.50768I
5.16369 + 10.73600I 0
u = 0.350762 + 0.736423I
a = 0.824471 + 1.077340I
b = 0.476660 0.249754I
2.71377 + 2.34753I 0
u = 0.350762 0.736423I
a = 0.824471 1.077340I
b = 0.476660 + 0.249754I
2.71377 2.34753I 0
u = 0.074986 + 1.184210I
a = 0.611288 + 0.771304I
b = 0.0221398 + 0.0372648I
0.18248 + 9.21724I 0
u = 0.074986 1.184210I
a = 0.611288 0.771304I
b = 0.0221398 0.0372648I
0.18248 9.21724I 0
u = 1.182310 + 0.109853I
a = 0.980182 + 0.264074I
b = 2.24126 0.83390I
6.13126 + 5.46331I 0
u = 1.182310 0.109853I
a = 0.980182 0.264074I
b = 2.24126 + 0.83390I
6.13126 5.46331I 0
u = 0.084791 + 1.190600I
a = 0.633586 + 0.768477I
b = 0.0385920 0.0115308I
2.2740 15.0260I 0
u = 0.084791 1.190600I
a = 0.633586 0.768477I
b = 0.0385920 + 0.0115308I
2.2740 + 15.0260I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.521370 + 0.614871I
a = 0.14023 1.66409I
b = 0.805733 0.557452I
1.10086 1.82815I 0
u = 0.521370 0.614871I
a = 0.14023 + 1.66409I
b = 0.805733 + 0.557452I
1.10086 + 1.82815I 0
u = 1.191350 + 0.124175I
a = 0.608850 + 0.381822I
b = 1.61182 1.21452I
3.52865 5.52089I 0
u = 1.191350 0.124175I
a = 0.608850 0.381822I
b = 1.61182 + 1.21452I
3.52865 + 5.52089I 0
u = 1.199570 + 0.020586I
a = 0.950215 0.946839I
b = 1.96369 0.36176I
6.97409 + 1.38401I 0
u = 1.199570 0.020586I
a = 0.950215 + 0.946839I
b = 1.96369 + 0.36176I
6.97409 1.38401I 0
u = 0.009940 + 1.202340I
a = 0.152701 0.721877I
b = 0.162865 + 0.233313I
3.37095 + 1.01527I 0
u = 0.009940 1.202340I
a = 0.152701 + 0.721877I
b = 0.162865 0.233313I
3.37095 1.01527I 0
u = 0.006295 + 1.206770I
a = 0.414908 + 0.867625I
b = 0.130140 + 0.293336I
0.77508 + 4.01705I 0
u = 0.006295 1.206770I
a = 0.414908 0.867625I
b = 0.130140 0.293336I
0.77508 4.01705I 0
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.214870 + 0.084740I
a = 0.885085 + 0.447815I
b = 2.17241 0.50810I
7.02455 0.37232I 0
u = 1.214870 0.084740I
a = 0.885085 0.447815I
b = 2.17241 + 0.50810I
7.02455 + 0.37232I 0
u = 1.136840 + 0.448961I
a = 0.039366 + 0.246237I
b = 0.894431 0.344364I
2.02741 7.04890I 0
u = 1.136840 0.448961I
a = 0.039366 0.246237I
b = 0.894431 + 0.344364I
2.02741 + 7.04890I 0
u = 1.222220 + 0.038878I
a = 0.665158 + 0.138449I
b = 1.83516 0.86764I
5.17211 1.79123I 0
u = 1.222220 0.038878I
a = 0.665158 0.138449I
b = 1.83516 + 0.86764I
5.17211 + 1.79123I 0
u = 1.179980 + 0.332676I
a = 0.979830 + 0.385264I
b = 1.39508 + 0.31645I
2.90773 + 1.67823I 0
u = 1.179980 0.332676I
a = 0.979830 0.385264I
b = 1.39508 0.31645I
2.90773 1.67823I 0
u = 1.222950 + 0.098574I
a = 0.611746 + 0.306596I
b = 1.91149 1.35410I
5.88701 + 10.52240I 0
u = 1.222950 0.098574I
a = 0.611746 0.306596I
b = 1.91149 + 1.35410I
5.88701 10.52240I 0
14
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.337983 + 0.683082I
a = 0.90210 + 1.18684I
b = 0.508297 0.479779I
0.15922 8.16631I 0
u = 0.337983 0.683082I
a = 0.90210 1.18684I
b = 0.508297 + 0.479779I
0.15922 + 8.16631I 0
u = 1.232460 + 0.170914I
a = 1.40923 0.77204I
b = 2.36457 0.75685I
7.17036 6.09836I 0
u = 1.232460 0.170914I
a = 1.40923 + 0.77204I
b = 2.36457 + 0.75685I
7.17036 + 6.09836I 0
u = 1.247090 + 0.055355I
a = 1.23653 1.45284I
b = 1.81286 1.27652I
9.93442 2.22963I 0
u = 1.247090 0.055355I
a = 1.23653 + 1.45284I
b = 1.81286 + 1.27652I
9.93442 + 2.22963I 0
u = 1.259070 + 0.111332I
a = 0.487282 + 0.213669I
b = 1.63698 0.76567I
5.41124 1.66385I 0
u = 1.259070 0.111332I
a = 0.487282 0.213669I
b = 1.63698 + 0.76567I
5.41124 + 1.66385I 0
u = 0.553673 + 0.474572I
a = 0.599887 + 0.333001I
b = 0.399140 + 0.634231I
0.22539 + 1.84351I 0
u = 0.553673 0.474572I
a = 0.599887 0.333001I
b = 0.399140 0.634231I
0.22539 1.84351I 0
15
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.461654 + 0.558096I
a = 0.650106 + 0.513933I
b = 0.095947 + 0.375961I
0.22902 + 1.47887I 0
u = 0.461654 0.558096I
a = 0.650106 0.513933I
b = 0.095947 0.375961I
0.22902 1.47887I 0
u = 1.279310 + 0.047906I
a = 1.38215 + 0.74820I
b = 1.88606 + 0.71650I
3.66448 + 0.68864I 0
u = 1.279310 0.047906I
a = 1.38215 0.74820I
b = 1.88606 0.71650I
3.66448 0.68864I 0
u = 1.299630 + 0.079845I
a = 0.585065 + 0.006843I
b = 1.76128 + 0.99090I
7.48248 + 1.01387I 0
u = 1.299630 0.079845I
a = 0.585065 0.006843I
b = 1.76128 0.99090I
7.48248 1.01387I 0
u = 1.347770 + 0.042179I
a = 0.502688 + 0.054756I
b = 1.66603 0.97379I
6.85153 + 5.21485I 0
u = 1.347770 0.042179I
a = 0.502688 0.054756I
b = 1.66603 + 0.97379I
6.85153 5.21485I 0
u = 1.352340 + 0.019957I
a = 1.002800 + 0.867738I
b = 1.56720 + 0.87016I
5.93701 6.27570I 0
u = 1.352340 0.019957I
a = 1.002800 0.867738I
b = 1.56720 0.87016I
5.93701 + 6.27570I 0
16
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.311700 + 0.469067I
a = 0.609227 + 0.018349I
b = 1.48382 + 0.51985I
7.59726 0.05302I 0
u = 1.311700 0.469067I
a = 0.609227 0.018349I
b = 1.48382 0.51985I
7.59726 + 0.05302I 0
u = 1.319020 + 0.487375I
a = 1.136060 0.088242I
b = 2.16649 0.55772I
5.69234 6.96557I 0
u = 1.319020 0.487375I
a = 1.136060 + 0.088242I
b = 2.16649 + 0.55772I
5.69234 + 6.96557I 0
u = 1.32202 + 0.51370I
a = 0.977648 0.376818I
b = 1.62556 0.30335I
5.90649 7.98073I 0
u = 1.32202 0.51370I
a = 0.977648 + 0.376818I
b = 1.62556 + 0.30335I
5.90649 + 7.98073I 0
u = 1.39490 + 0.29190I
a = 1.138630 0.515829I
b = 2.25135 0.91332I
7.73023 + 4.29582I 0
u = 1.39490 0.29190I
a = 1.138630 + 0.515829I
b = 2.25135 + 0.91332I
7.73023 4.29582I 0
u = 1.37105 + 0.42048I
a = 1.081160 0.264992I
b = 2.08465 0.67973I
5.87340 7.08858I 0
u = 1.37105 0.42048I
a = 1.081160 + 0.264992I
b = 2.08465 + 0.67973I
5.87340 + 7.08858I 0
17
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.35398 + 0.54659I
a = 1.037700 + 0.010983I
b = 2.18551 0.46064I
7.02366 + 10.93540I 0
u = 1.35398 0.54659I
a = 1.037700 0.010983I
b = 2.18551 + 0.46064I
7.02366 10.93540I 0
u = 1.39012 + 0.46177I
a = 0.983149 0.103026I
b = 1.56692 0.06387I
4.12378 + 1.84628I 0
u = 1.39012 0.46177I
a = 0.983149 + 0.103026I
b = 1.56692 + 0.06387I
4.12378 1.84628I 0
u = 0.077822 + 0.517192I
a = 0.042973 + 1.153600I
b = 0.442844 + 0.516492I
0.79313 + 1.54992I 0
u = 0.077822 0.517192I
a = 0.042973 1.153600I
b = 0.442844 0.516492I
0.79313 1.54992I 0
u = 1.38794 + 0.52494I
a = 1.151980 + 0.364855I
b = 2.03780 + 0.50960I
3.74007 9.98254I 0
u = 1.38794 0.52494I
a = 1.151980 0.364855I
b = 2.03780 0.50960I
3.74007 + 9.98254I 0
u = 1.35907 + 0.60513I
a = 1.175010 + 0.561048I
b = 2.01499 + 0.38181I
5.44353 + 2.80424I 0
u = 1.35907 0.60513I
a = 1.175010 0.561048I
b = 2.01499 0.38181I
5.44353 2.80424I 0
18
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.40097 + 0.51596I
a = 1.101200 + 0.346640I
b = 2.20239 + 0.57007I
11.2687 + 12.3565I 0
u = 1.40097 0.51596I
a = 1.101200 0.346640I
b = 2.20239 0.57007I
11.2687 12.3565I 0
u = 1.37195 + 0.59278I
a = 0.587596 0.055233I
b = 1.264170 + 0.153162I
4.72161 + 4.05361I 0
u = 1.37195 0.59278I
a = 0.587596 + 0.055233I
b = 1.264170 0.153162I
4.72161 4.05361I 0
u = 1.40620 + 0.53059I
a = 1.113250 + 0.329635I
b = 2.17755 + 0.67040I
4.8525 15.1923I 0
u = 1.40620 0.53059I
a = 1.113250 0.329635I
b = 2.17755 0.67040I
4.8525 + 15.1923I 0
u = 1.47078 + 0.33869I
a = 0.982642 0.510574I
b = 2.02199 1.05158I
7.22827 + 10.15400I 0
u = 1.47078 0.33869I
a = 0.982642 + 0.510574I
b = 2.02199 + 1.05158I
7.22827 10.15400I 0
u = 1.41339 + 0.53128I
a = 1.108950 + 0.323663I
b = 2.21661 + 0.69429I
6.9974 + 21.0296I 0
u = 1.41339 0.53128I
a = 1.108950 0.323663I
b = 2.21661 0.69429I
6.9974 21.0296I 0
19
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.41657 + 0.52796I
a = 0.894339 0.034315I
b = 2.04741 0.31774I
7.99671 + 5.07222I 0
u = 1.41657 0.52796I
a = 0.894339 + 0.034315I
b = 2.04741 + 0.31774I
7.99671 5.07222I 0
u = 1.42832 + 0.51696I
a = 0.707537 0.038113I
b = 1.72162 + 0.02398I
8.05429 7.15608I 0
u = 1.42832 0.51696I
a = 0.707537 + 0.038113I
b = 1.72162 0.02398I
8.05429 + 7.15608I 0
u = 1.48600 + 0.40235I
a = 0.881448 0.423908I
b = 1.79299 0.92209I
6.16462 6.52287I 0
u = 1.48600 0.40235I
a = 0.881448 + 0.423908I
b = 1.79299 + 0.92209I
6.16462 + 6.52287I 0
u = 0.329528 + 0.311108I
a = 2.64729 0.01620I
b = 0.202174 0.266844I
2.28250 1.41843I 10.96887 + 3.04728I
u = 0.329528 0.311108I
a = 2.64729 + 0.01620I
b = 0.202174 + 0.266844I
2.28250 + 1.41843I 10.96887 3.04728I
u = 1.46134 + 0.56591I
a = 0.675399 0.199345I
b = 1.298770 0.275770I
10.94210 + 0.13111I 0
u = 1.46134 0.56591I
a = 0.675399 + 0.199345I
b = 1.298770 + 0.275770I
10.94210 0.13111I 0
20
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.54826 + 0.54683I
a = 0.575383 0.080483I
b = 1.111390 0.198391I
4.75456 2.53354I 0
u = 1.54826 0.54683I
a = 0.575383 + 0.080483I
b = 1.111390 + 0.198391I
4.75456 + 2.53354I 0
u = 1.58891 + 0.50038I
a = 0.589038 0.384733I
b = 1.138810 0.782176I
3.39578 10.81060I 0
u = 1.58891 0.50038I
a = 0.589038 + 0.384733I
b = 1.138810 + 0.782176I
3.39578 + 10.81060I 0
u = 1.55817 + 0.58962I
a = 0.523360 0.123280I
b = 1.070320 0.289966I
6.74069 + 8.23797I 0
u = 1.55817 0.58962I
a = 0.523360 + 0.123280I
b = 1.070320 + 0.289966I
6.74069 8.23797I 0
u = 1.57877 + 0.55933I
a = 0.550205 0.299586I
b = 1.069390 0.562308I
2.39409 + 5.65869I 0
u = 1.57877 0.55933I
a = 0.550205 + 0.299586I
b = 1.069390 + 0.562308I
2.39409 5.65869I 0
u = 0.244994 + 0.019428I
a = 2.82334 1.75655I
b = 0.720345 + 1.197780I
5.53952 1.76841I 6.31054 + 0.53214I
u = 0.244994 0.019428I
a = 2.82334 + 1.75655I
b = 0.720345 1.197780I
5.53952 + 1.76841I 6.31054 0.53214I
21
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.220248 + 0.058584I
a = 2.06030 3.56868I
b = 0.018963 0.770201I
1.06632 1.46141I 4.65838 + 2.99597I
u = 0.220248 0.058584I
a = 2.06030 + 3.56868I
b = 0.018963 + 0.770201I
1.06632 + 1.46141I 4.65838 2.99597I
u = 0.136256 + 0.050619I
a = 7.86888 + 1.63778I
b = 0.201382 0.626587I
3.04957 + 4.66149I 12.8011 6.5761I
u = 0.136256 0.050619I
a = 7.86888 1.63778I
b = 0.201382 + 0.626587I
3.04957 4.66149I 12.8011 + 6.5761I
u = 0.0073798 + 0.1121080I
a = 1.72286 8.23141I
b = 0.076112 + 0.803118I
3.48377 + 1.26062I 14.5556 1.8178I
u = 0.0073798 0.1121080I
a = 1.72286 + 8.23141I
b = 0.076112 0.803118I
3.48377 1.26062I 14.5556 + 1.8178I
u = 0.0530995 + 0.0941323I
a = 0.84618 + 9.22200I
b = 0.873013 + 1.012040I
0.00983 + 4.32982I 0.237716 1.379884I
u = 0.0530995 0.0941323I
a = 0.84618 9.22200I
b = 0.873013 1.012040I
0.00983 4.32982I 0.237716 + 1.379884I
u = 0.0894092 + 0.0264817I
a = 11.35930 2.50398I
b = 0.91861 1.11978I
2.05940 + 9.80001I 2.85598 5.19981I
u = 0.0894092 0.0264817I
a = 11.35930 + 2.50398I
b = 0.91861 + 1.11978I
2.05940 9.80001I 2.85598 + 5.19981I
22
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.16005 + 1.96875I
a = 0.032187 0.195560I
b = 0.0105251 0.0206240I
3.42714 + 2.86954I 0
u = 0.16005 1.96875I
a = 0.032187 + 0.195560I
b = 0.0105251 + 0.0206240I
3.42714 2.86954I 0
23
II.
I
u
2
= h−1.16×10
33
u
42
1.70×10
33
u
41
+· · ·+2.11×10
32
b1.33×10
33
, 1.29×
10
33
u
42
+1.62×10
32
u
41
+· · ·+2.11×10
32
a6.37×10
33
, u
43
+u
42
+· · ·+2u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
8
=
6.08938u
42
0.766824u
41
+ ··· 31.8497u + 30.1034
5.47783u
42
+ 8.05062u
41
+ ··· 16.3644u + 6.28948
a
1
=
11.6126u
42
11.7491u
41
+ ··· + 55.7010u 26.7564
2.53628u
42
1.15504u
41
+ ··· + 14.9692u 10.3714
a
7
=
2.64422u
42
18.4919u
41
+ ··· 7.86228u + 30.6701
5.19016u
42
16.9115u
41
+ ··· + 10.3522u + 15.2810
a
11
=
u
u
a
9
=
1.37536u
42
19.1784u
41
+ ··· 13.6032u + 39.5324
1.98691u
42
10.3609u
41
+ ··· + 1.88209u + 15.7185
a
3
=
5.79164u
42
+ 6.04583u
41
+ ··· + 27.8521u 48.5369
0.473205u
42
+ 5.61577u
41
+ ··· + 9.24257u 18.5165
a
10
=
10.8379u
42
+ 7.04368u
41
+ ··· 51.2332u + 35.4218
6.31427u
42
+ 8.49903u
41
+ ··· 21.1023u + 11.1387
a
6
=
0.275980u
42
+ 7.73119u
41
+ ··· + 5.59083u 28.0925
0.492532u
42
+ 4.72372u
41
+ ··· + 2.85792u 10.9713
a
2
=
12.4950u
42
4.85510u
41
+ ··· + 52.5668u 49.4783
2.07591u
42
+ 4.38430u
41
+ ··· + 11.6898u 21.5923
(ii) Obstruction class = 1
(iii) Cusp Shapes = 10.8171u
42
22.5095u
41
+ ··· + 7.87998u + 8.10939
24
(iv) u-Polynomials at the component
25
Crossings u-Polynomials at each crossing
c
1
u
43
21u
42
+ ··· 28u + 1
c
2
u
43
u
42
+ ··· 2u 1
c
3
u
43
+ 10u
41
+ ··· + 46u 19
c
4
u
43
+ u
42
+ ··· + 2u + 1
c
5
u
43
+ u
42
+ ··· + 5u 1
c
6
u
43
+ u
42
+ ··· 2u + 1
c
7
u
43
+ 5u
42
+ ··· + u 1
c
8
u
43
19u
42
+ ··· + 20u 1
c
9
u
43
+ 17u
42
+ ··· 2u + 1
c
10
u
43
+ 4u
42
+ ··· + 12u 1
c
11
u
43
u
42
+ ··· + 2u 1
c
12
u
43
2u
42
+ ··· + 26u 5
26
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
43
+ 17y
42
+ ··· + 12y 1
c
2
, c
6
y
43
+ 21y
42
+ ··· 28y 1
c
3
y
43
+ 20y
42
+ ··· 11906y 361
c
4
, c
11
y
43
25y
42
+ ··· + 20y 1
c
5
y
43
7y
42
+ ··· 55y 1
c
7
y
43
+ 29y
42
+ ··· + 29y 1
c
8
y
43
11y
42
+ ··· + 46y 1
c
9
y
43
17y
42
+ ··· 12y 1
c
10
y
43
12y
42
+ ··· + 146y 1
c
12
y
43
14y
42
+ ··· + 866y 25
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.565151 + 0.800616I
a = 0.185627 + 0.542499I
b = 0.274493 + 0.668369I
0.686696 + 0.673462I 5.67919 + 1.84612I
u = 0.565151 0.800616I
a = 0.185627 0.542499I
b = 0.274493 0.668369I
0.686696 0.673462I 5.67919 1.84612I
u = 0.914332 + 0.229073I
a = 1.050760 0.761962I
b = 2.18027 0.99698I
3.07780 10.54400I 7.92431 + 8.70011I
u = 0.914332 0.229073I
a = 1.050760 + 0.761962I
b = 2.18027 + 0.99698I
3.07780 + 10.54400I 7.92431 8.70011I
u = 0.917630 + 0.211655I
a = 1.41256 0.56579I
b = 2.22258 0.87483I
1.05238 + 4.95322I 6.38591 4.44936I
u = 0.917630 0.211655I
a = 1.41256 + 0.56579I
b = 2.22258 + 0.87483I
1.05238 4.95322I 6.38591 + 4.44936I
u = 0.887205 + 0.201480I
a = 0.830229 0.066285I
b = 1.73340 1.40424I
6.39188 2.42893I 11.24732 + 5.26931I
u = 0.887205 0.201480I
a = 0.830229 + 0.066285I
b = 1.73340 + 1.40424I
6.39188 + 2.42893I 11.24732 5.26931I
u = 0.196540 + 1.135610I
a = 0.492451 0.676345I
b = 0.137904 0.282759I
0.71795 + 3.69642I 9.20992 + 0.I
u = 0.196540 1.135610I
a = 0.492451 + 0.676345I
b = 0.137904 + 0.282759I
0.71795 3.69642I 9.20992 + 0.I
29
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.126640 + 0.320280I
a = 0.831118 + 0.686523I
b = 0.912029 + 0.260840I
2.44112 + 3.38307I 5.07283 4.00845I
u = 1.126640 0.320280I
a = 0.831118 0.686523I
b = 0.912029 0.260840I
2.44112 3.38307I 5.07283 + 4.00845I
u = 1.197860 + 0.008892I
a = 0.379046 0.493992I
b = 0.405921 + 0.960135I
7.97372 + 1.44568I 12.67725 + 0.I
u = 1.197860 0.008892I
a = 0.379046 + 0.493992I
b = 0.405921 0.960135I
7.97372 1.44568I 12.67725 + 0.I
u = 1.196420 + 0.113382I
a = 0.646564 + 0.031567I
b = 2.36000 0.87609I
6.25020 + 1.44230I 16.0171 3.2552I
u = 1.196420 0.113382I
a = 0.646564 0.031567I
b = 2.36000 + 0.87609I
6.25020 1.44230I 16.0171 + 3.2552I
u = 0.011133 + 0.758671I
a = 0.430596 0.830453I
b = 0.030419 + 0.422050I
2.25228 + 1.16332I 5.50591 1.22848I
u = 0.011133 0.758671I
a = 0.430596 + 0.830453I
b = 0.030419 0.422050I
2.25228 1.16332I 5.50591 + 1.22848I
u = 1.268520 + 0.067807I
a = 0.136821 + 0.967894I
b = 0.026150 + 0.431672I
2.96494 + 3.70265I 0
u = 1.268520 0.067807I
a = 0.136821 0.967894I
b = 0.026150 0.431672I
2.96494 3.70265I 0
30
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.27569
a = 1.38622
b = 2.07324
4.00337 13.2720
u = 0.047233 + 0.717801I
a = 0.73180 1.30877I
b = 0.307807 + 0.084455I
2.11862 4.88343I 2.05264 + 6.77099I
u = 0.047233 0.717801I
a = 0.73180 + 1.30877I
b = 0.307807 0.084455I
2.11862 + 4.88343I 2.05264 6.77099I
u = 1.297710 + 0.049111I
a = 0.958357 + 0.058286I
b = 2.23720 0.24341I
7.42479 3.50502I 0
u = 1.297710 0.049111I
a = 0.958357 0.058286I
b = 2.23720 + 0.24341I
7.42479 + 3.50502I 0
u = 1.330900 + 0.006653I
a = 0.134334 0.718223I
b = 0.230826 0.150354I
4.95626 + 8.95445I 0
u = 1.330900 0.006653I
a = 0.134334 + 0.718223I
b = 0.230826 + 0.150354I
4.95626 8.95445I 0
u = 0.044207 + 0.632858I
a = 0.97806 1.46172I
b = 0.429288 0.128050I
1.48097 + 1.36518I 0.320270 + 0.970120I
u = 0.044207 0.632858I
a = 0.97806 + 1.46172I
b = 0.429288 + 0.128050I
1.48097 1.36518I 0.320270 0.970120I
u = 1.31304 + 0.58058I
a = 1.096960 0.552633I
b = 2.00716 0.36957I
5.36677 + 2.82669I 0
31
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.31304 0.58058I
a = 1.096960 + 0.552633I
b = 2.00716 + 0.36957I
5.36677 2.82669I 0
u = 1.41096 + 0.40220I
a = 0.979847 0.277139I
b = 2.09731 0.73887I
6.82418 + 9.25279I 0
u = 1.41096 0.40220I
a = 0.979847 + 0.277139I
b = 2.09731 + 0.73887I
6.82418 9.25279I 0
u = 1.40238 + 0.47077I
a = 1.055200 0.221287I
b = 1.83349 0.51367I
4.54693 9.04995I 0
u = 1.40238 0.47077I
a = 1.055200 + 0.221287I
b = 1.83349 + 0.51367I
4.54693 + 9.04995I 0
u = 1.42623 + 0.42710I
a = 0.983914 0.267954I
b = 1.97665 0.77167I
6.24794 5.75781I 0
u = 1.42623 0.42710I
a = 0.983914 + 0.267954I
b = 1.97665 + 0.77167I
6.24794 + 5.75781I 0
u = 0.310676 + 0.013099I
a = 1.66167 + 3.52268I
b = 0.597416 + 1.075280I
1.67338 + 0.10116I 4.79649 0.11122I
u = 0.310676 0.013099I
a = 1.66167 3.52268I
b = 0.597416 1.075280I
1.67338 0.10116I 4.79649 + 0.11122I
u = 0.183489 + 0.205725I
a = 1.03544 4.14597I
b = 0.688486 0.794377I
0.70925 + 5.27416I 1.94196 5.03576I
32
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.183489 0.205725I
a = 1.03544 + 4.14597I
b = 0.688486 + 0.794377I
0.70925 5.27416I 1.94196 + 5.03576I
u = 0.18252 + 1.89544I
a = 0.011085 + 0.142621I
b = 0.036578 + 0.247131I
3.51628 + 2.83574I 0
u = 0.18252 1.89544I
a = 0.011085 0.142621I
b = 0.036578 0.247131I
3.51628 2.83574I 0
33
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
43
21u
42
+ ··· 28u + 1)(u
182
+ 80u
181
+ ··· 14u + 1)
c
2
(u
43
u
42
+ ··· 2u 1)(u
182
+ 40u
180
+ ··· + 4u + 1)
c
3
(u
43
+ 10u
41
+ ··· + 46u 19)
· (u
182
+ u
181
+ ··· + 173061562687u + 50838216514)
c
4
(u
43
+ u
42
+ ··· + 2u + 1)(u
182
+ 2u
181
+ ··· + 18u + 1)
c
5
(u
43
+ u
42
+ ··· + 5u 1)(u
182
6u
180
+ ··· 29u + 1)
c
6
(u
43
+ u
42
+ ··· 2u + 1)(u
182
+ 40u
180
+ ··· + 4u + 1)
c
7
(u
43
+ 5u
42
+ ··· + u 1)
· (u
182
+ 16u
181
+ ··· + 107815334379u + 9487345129)
c
8
(u
43
19u
42
+ ··· + 20u 1)
· (u
182
+ 18u
181
+ ··· + 37740592u + 2302703)
c
9
(u
43
+ 17u
42
+ ··· 2u + 1)(u
182
+ 8u
181
+ ··· 16483u + 704)
c
10
(u
43
+ 4u
42
+ ··· + 12u 1)
· (u
182
+ 17u
181
+ ··· + 1894916324u + 143269799)
c
11
(u
43
u
42
+ ··· + 2u 1)(u
182
+ 2u
181
+ ··· + 18u + 1)
c
12
(u
43
2u
42
+ ··· + 26u 5)
· (u
182
u
181
+ ··· 233173107u + 23453042)
34
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
43
+ 17y
42
+ ··· + 12y 1)(y
182
+ 60y
181
+ ··· 458y + 1)
c
2
, c
6
(y
43
+ 21y
42
+ ··· 28y 1)(y
182
+ 80y
181
+ ··· 14y + 1)
c
3
(y
43
+ 20y
42
+ ··· 11906y 361)
· (y
182
+ 83y
181
+ ··· + 1.73 × 10
23
y + 2.58 × 10
21
)
c
4
, c
11
(y
43
25y
42
+ ··· + 20y 1)(y
182
126y
181
+ ··· 110y + 1)
c
5
(y
43
7y
42
+ ··· 55y 1)(y
182
12y
181
+ ··· + 393y + 1)
c
7
(y
43
+ 29y
42
+ ··· + 29y 1)
· (y
182
+ 100y
181
+ ··· + 4.51 × 10
21
y + 9.00 × 10
19
)
c
8
(y
43
11y
42
+ ··· + 46y 1)
· (y
182
52y
181
+ ··· 245956311483672y + 5302441106209)
c
9
(y
43
17y
42
+ ··· 12y 1)
· (y
182
26y
181
+ ··· 28999369y + 495616)
c
10
(y
43
12y
42
+ ··· + 146y 1)
· (y
182
+ 35y
181
+ ··· + 2524246924058369408y + 20526235305500401)
c
12
(y
43
14y
42
+ ··· + 866y 25)
· (y
182
59y
181
+ ··· 11000196487083765y + 550045179053764)
35