12a
0388
(K12a
0388
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 8 2 12 1 11 4 7 5
Solving Sequence
4,11
10 5 9
1,3
8 6 2 12 7
c
10
c
4
c
9
c
3
c
8
c
5
c
2
c
12
c
7
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.10245 × 10
200
u
137
2.70350 × 10
199
u
136
+ ··· + 2.26798 × 10
199
b 2.98834 × 10
200
,
2.02152 × 10
201
u
137
2.45020 × 10
201
u
136
+ ··· + 1.13399 × 10
200
a 5.74431 × 10
201
,
u
138
+ u
137
+ ··· + 2u + 1i
I
u
2
= hu
28
+ 4u
26
+ ··· + b 6, 9u
28
67u
26
+ ··· + a 13, u
30
+ 8u
28
+ ··· + 6u
2
+ 1i
I
u
3
= hu
2
+ b, a 1, u
12
u
11
+ 2u
10
u
9
+ u
7
3u
6
+ 3u
5
2u
4
+ 2u
2
2u + 1i
I
u
4
= hb u 1, a 1, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 182 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
= h1.10 × 10
200
u
137
2.70 × 10
199
u
136
+ · · · + 2.27 × 10
199
b 2.99 ×
10
200
, 2.02 × 10
201
u
137
2.45 × 10
201
u
136
+ · · · + 1.13 × 10
200
a 5.74 ×
10
201
, u
138
+ u
137
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
2
a
1
=
17.8266u
137
+ 21.6069u
136
+ ··· + 72.5125u + 50.6558
4.86092u
137
+ 1.19203u
136
+ ··· 22.3388u + 13.1762
a
3
=
u
5
2u
3
u
u
5
+ u
3
+ u
a
8
=
7.31158u
137
+ 10.8364u
136
+ ··· + 42.2872u + 21.2695
11.0373u
137
10.6810u
136
+ ··· 47.1603u 19.8102
a
6
=
15.0024u
137
+ 5.16035u
136
+ ··· + 39.1591u 6.06825
4.75355u
137
+ 8.15710u
136
+ ··· + 22.1169u + 23.1999
a
2
=
21.6197u
137
+ 26.0663u
136
+ ··· + 86.8487u + 61.5268
9.77139u
137
3.70248u
136
+ ··· 41.5049u + 3.02636
a
12
=
25.2621u
137
+ 27.9992u
136
+ ··· + 102.662u + 62.2454
11.1523u
137
4.87631u
136
+ ··· 47.1386u + 0.543510
a
7
=
10.2508u
137
+ 17.9698u
136
+ ··· + 70.9462u + 35.0066
0.698140u
137
6.12399u
136
+ ··· 5.26299u 19.2641
(ii) Obstruction class = 1
(iii) Cusp Shapes = 1.31574u
137
10.1454u
136
+ ··· 6.22611u 51.1687
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
138
+ 57u
137
+ ··· + 4078944u + 222784
c
2
, c
6
u
138
+ 7u
137
+ ··· + 976u + 472
c
3
u
138
+ u
137
+ ··· + 1500u + 84625
c
4
, c
10
u
138
u
137
+ ··· 2u + 1
c
5
u
138
4u
137
+ ··· 50u + 1
c
7
, c
11
u
138
+ 3u
137
+ ··· + 32098u + 2479
c
8
u
138
u
137
+ ··· 312712u + 21829
c
9
u
138
73u
137
+ ··· 12u + 1
c
12
u
138
3u
137
+ ··· + 126u + 107
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
138
+ 57y
137
+ ··· + 592047023616y + 49632710656
c
2
, c
6
y
138
+ 57y
137
+ ··· + 4078944y + 222784
c
3
y
138
63y
137
+ ··· + 1166513601250y + 7161390625
c
4
, c
10
y
138
+ 73y
137
+ ··· + 12y + 1
c
5
y
138
6y
137
+ ··· 84y + 1
c
7
, c
11
y
138
89y
137
+ ··· 992898284y + 6145441
c
8
y
138
33y
137
+ ··· 25000518340y + 476505241
c
9
y
138
+ 5y
137
+ ··· + 56y + 1
c
12
y
138
+ 13y
137
+ ··· + 1100348y + 11449
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.748280 + 0.644042I
a = 0.610770 0.383166I
b = 0.279919 + 0.054730I
3.23015 1.44711I 0
u = 0.748280 0.644042I
a = 0.610770 + 0.383166I
b = 0.279919 0.054730I
3.23015 + 1.44711I 0
u = 0.932996 + 0.397354I
a = 0.560435 0.059752I
b = 0.675164 0.194043I
0.20912 4.87826I 0
u = 0.932996 0.397354I
a = 0.560435 + 0.059752I
b = 0.675164 + 0.194043I
0.20912 + 4.87826I 0
u = 0.639139 + 0.717002I
a = 0.526322 0.610491I
b = 0.065518 + 0.290224I
3.14704 1.39877I 0
u = 0.639139 0.717002I
a = 0.526322 + 0.610491I
b = 0.065518 0.290224I
3.14704 + 1.39877I 0
u = 0.507689 + 0.814153I
a = 0.460248 0.369612I
b = 0.259173 + 0.658419I
0.62104 2.03888I 0
u = 0.507689 0.814153I
a = 0.460248 + 0.369612I
b = 0.259173 0.658419I
0.62104 + 2.03888I 0
u = 0.657750 + 0.812749I
a = 0.759257 + 0.080546I
b = 0.147457 + 0.240247I
2.90258 + 6.42158I 0
u = 0.657750 0.812749I
a = 0.759257 0.080546I
b = 0.147457 0.240247I
2.90258 6.42158I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.900380 + 0.306762I
a = 0.533987 0.027012I
b = 0.675781 + 0.175122I
0.319495 0.269839I 0
u = 0.900380 0.306762I
a = 0.533987 + 0.027012I
b = 0.675781 0.175122I
0.319495 + 0.269839I 0
u = 0.505496 + 0.784641I
a = 0.155415 0.211164I
b = 0.813512 0.448155I
3.41327 + 2.08249I 0
u = 0.505496 0.784641I
a = 0.155415 + 0.211164I
b = 0.813512 + 0.448155I
3.41327 2.08249I 0
u = 0.002295 + 0.933167I
a = 0.348407 1.168260I
b = 1.02831 + 1.09047I
2.58537 3.57558I 0
u = 0.002295 0.933167I
a = 0.348407 + 1.168260I
b = 1.02831 1.09047I
2.58537 + 3.57558I 0
u = 0.586344 + 0.712656I
a = 0.256709 + 0.327840I
b = 0.216062 1.112430I
0.42447 + 6.42817I 0
u = 0.586344 0.712656I
a = 0.256709 0.327840I
b = 0.216062 + 1.112430I
0.42447 6.42817I 0
u = 0.876763 + 0.277742I
a = 2.01971 + 0.48046I
b = 1.70197 0.89884I
1.8751 14.3871I 0
u = 0.876763 0.277742I
a = 2.01971 0.48046I
b = 1.70197 + 0.89884I
1.8751 + 14.3871I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.675148 + 0.623419I
a = 0.628890 0.768440I
b = 0.218688 0.249187I
7.79238 3.57360I 0
u = 0.675148 0.623419I
a = 0.628890 + 0.768440I
b = 0.218688 + 0.249187I
7.79238 + 3.57360I 0
u = 0.308930 + 1.036300I
a = 0.26750 1.81985I
b = 2.33740 + 0.80264I
2.46898 3.18569I 0
u = 0.308930 1.036300I
a = 0.26750 + 1.81985I
b = 2.33740 0.80264I
2.46898 + 3.18569I 0
u = 0.351642 + 0.833956I
a = 0.842916 0.075164I
b = 0.141774 0.101162I
0.32671 1.54792I 0
u = 0.351642 0.833956I
a = 0.842916 + 0.075164I
b = 0.141774 + 0.101162I
0.32671 + 1.54792I 0
u = 0.762004 + 0.807024I
a = 0.441904 0.113955I
b = 0.141367 0.472899I
5.04826 11.36710I 0
u = 0.762004 0.807024I
a = 0.441904 + 0.113955I
b = 0.141367 + 0.472899I
5.04826 + 11.36710I 0
u = 0.459758 + 1.015400I
a = 1.39876 2.58387I
b = 1.97149 + 1.80899I
2.96281 1.00766I 0
u = 0.459758 1.015400I
a = 1.39876 + 2.58387I
b = 1.97149 1.80899I
2.96281 + 1.00766I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.833669 + 0.246306I
a = 2.07608 0.62945I
b = 1.59871 + 0.86388I
0.18672 + 8.44910I 0
u = 0.833669 0.246306I
a = 2.07608 + 0.62945I
b = 1.59871 0.86388I
0.18672 8.44910I 0
u = 0.631156 + 0.942527I
a = 0.032130 + 0.523672I
b = 0.562343 0.343106I
6.87135 1.44864I 0
u = 0.631156 0.942527I
a = 0.032130 0.523672I
b = 0.562343 + 0.343106I
6.87135 + 1.44864I 0
u = 0.359853 + 0.779267I
a = 1.64500 1.09008I
b = 0.90099 1.77749I
3.04538 + 5.83097I 0
u = 0.359853 0.779267I
a = 1.64500 + 1.09008I
b = 0.90099 + 1.77749I
3.04538 5.83097I 0
u = 0.784849 + 0.833178I
a = 0.336576 + 0.331522I
b = 0.187643 + 0.128653I
4.99993 + 5.64141I 0
u = 0.784849 0.833178I
a = 0.336576 0.331522I
b = 0.187643 0.128653I
4.99993 5.64141I 0
u = 0.055678 + 0.850726I
a = 0.331880 + 0.528641I
b = 0.585870 + 0.867197I
1.17077 1.75880I 0
u = 0.055678 0.850726I
a = 0.331880 0.528641I
b = 0.585870 0.867197I
1.17077 + 1.75880I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.414877 + 1.070120I
a = 0.55316 1.36199I
b = 1.52236 + 0.17162I
1.25960 1.39359I 0
u = 0.414877 1.070120I
a = 0.55316 + 1.36199I
b = 1.52236 0.17162I
1.25960 + 1.39359I 0
u = 0.540226 + 1.032780I
a = 0.60369 2.18713I
b = 2.20825 0.06733I
3.53762 + 6.87962I 0
u = 0.540226 1.032780I
a = 0.60369 + 2.18713I
b = 2.20825 + 0.06733I
3.53762 6.87962I 0
u = 0.437879 + 1.081410I
a = 0.79631 1.65724I
b = 0.25068 + 1.53384I
2.95472 + 0.07846I 0
u = 0.437879 1.081410I
a = 0.79631 + 1.65724I
b = 0.25068 1.53384I
2.95472 0.07846I 0
u = 0.717790 + 0.415508I
a = 1.151190 + 0.406748I
b = 1.206330 0.686473I
4.57232 0.12230I 0
u = 0.717790 0.415508I
a = 1.151190 0.406748I
b = 1.206330 + 0.686473I
4.57232 + 0.12230I 0
u = 0.477056 + 1.070260I
a = 0.53665 + 1.77130I
b = 1.56832 0.83541I
0.02851 3.36557I 0
u = 0.477056 1.070260I
a = 0.53665 1.77130I
b = 1.56832 + 0.83541I
0.02851 + 3.36557I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.646252 + 0.512234I
a = 1.71957 0.10186I
b = 1.71208 0.29986I
5.07463 2.23565I 0
u = 0.646252 0.512234I
a = 1.71957 + 0.10186I
b = 1.71208 + 0.29986I
5.07463 + 2.23565I 0
u = 0.466150 + 1.083490I
a = 1.23938 0.94255I
b = 0.268720 0.691177I
0.09519 + 5.03975I 0
u = 0.466150 1.083490I
a = 1.23938 + 0.94255I
b = 0.268720 + 0.691177I
0.09519 5.03975I 0
u = 0.775971 + 0.259276I
a = 2.06204 + 0.43638I
b = 1.77887 0.94228I
1.75979 + 7.99239I 0
u = 0.775971 0.259276I
a = 2.06204 0.43638I
b = 1.77887 + 0.94228I
1.75979 7.99239I 0
u = 0.608762 + 1.020920I
a = 0.691827 0.686455I
b = 0.699993 0.018161I
2.00844 + 6.60279I 0
u = 0.608762 1.020920I
a = 0.691827 + 0.686455I
b = 0.699993 + 0.018161I
2.00844 6.60279I 0
u = 0.157115 + 1.183080I
a = 0.546397 0.569497I
b = 0.424413 + 0.447750I
5.45597 2.08589I 0
u = 0.157115 1.183080I
a = 0.546397 + 0.569497I
b = 0.424413 0.447750I
5.45597 + 2.08589I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.481072 + 1.093010I
a = 0.697789 0.457258I
b = 1.79379 0.78867I
2.62273 + 7.06472I 0
u = 0.481072 1.093010I
a = 0.697789 + 0.457258I
b = 1.79379 + 0.78867I
2.62273 7.06472I 0
u = 0.426878 + 1.121990I
a = 0.869950 + 0.927785I
b = 2.29389 + 0.55773I
4.24755 0.55395I 0
u = 0.426878 1.121990I
a = 0.869950 0.927785I
b = 2.29389 0.55773I
4.24755 + 0.55395I 0
u = 0.482092 + 1.102240I
a = 0.73817 1.73876I
b = 1.75836 + 1.68519I
0.73692 5.83263I 0
u = 0.482092 1.102240I
a = 0.73817 + 1.73876I
b = 1.75836 1.68519I
0.73692 + 5.83263I 0
u = 0.722215 + 0.333026I
a = 2.60247 + 0.51955I
b = 1.43509 1.10683I
6.52298 5.63767I 6.96561 + 5.54235I
u = 0.722215 0.333026I
a = 2.60247 0.51955I
b = 1.43509 + 1.10683I
6.52298 + 5.63767I 6.96561 5.54235I
u = 0.224822 + 1.184760I
a = 0.639971 + 0.617614I
b = 0.537226 0.485258I
5.44782 3.44229I 0
u = 0.224822 1.184760I
a = 0.639971 0.617614I
b = 0.537226 + 0.485258I
5.44782 + 3.44229I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.294523 + 1.173140I
a = 0.02129 1.59871I
b = 1.75952 + 0.05382I
6.12367 + 4.70777I 0
u = 0.294523 1.173140I
a = 0.02129 + 1.59871I
b = 1.75952 0.05382I
6.12367 4.70777I 0
u = 0.766583 + 0.191365I
a = 1.95474 0.48334I
b = 1.60377 + 0.72697I
3.31803 2.71598I 2.61257 + 1.91367I
u = 0.766583 0.191365I
a = 1.95474 + 0.48334I
b = 1.60377 0.72697I
3.31803 + 2.71598I 2.61257 1.91367I
u = 0.468517 + 1.121520I
a = 0.73584 + 2.02735I
b = 1.05117 1.85791I
3.95618 7.12231I 0
u = 0.468517 1.121520I
a = 0.73584 2.02735I
b = 1.05117 + 1.85791I
3.95618 + 7.12231I 0
u = 0.576038 + 1.083480I
a = 1.07623 + 1.16309I
b = 1.017400 + 0.804040I
2.61627 4.82946I 0
u = 0.576038 1.083480I
a = 1.07623 1.16309I
b = 1.017400 0.804040I
2.61627 + 4.82946I 0
u = 0.340294 + 1.182050I
a = 0.11787 + 1.48216I
b = 1.81420 0.09781I
7.41416 + 0.88258I 0
u = 0.340294 1.182050I
a = 0.11787 1.48216I
b = 1.81420 + 0.09781I
7.41416 0.88258I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.502474 + 1.125750I
a = 1.20050 + 1.00972I
b = 0.396619 + 0.918271I
0.86260 9.72934I 0
u = 0.502474 1.125750I
a = 1.20050 1.00972I
b = 0.396619 0.918271I
0.86260 + 9.72934I 0
u = 0.386148 + 1.172850I
a = 0.35243 1.62014I
b = 0.77820 + 1.44305I
2.87431 + 1.77348I 0
u = 0.386148 1.172850I
a = 0.35243 + 1.62014I
b = 0.77820 1.44305I
2.87431 1.77348I 0
u = 0.547313 + 1.117630I
a = 0.13739 2.31147I
b = 2.28237 + 1.68690I
4.22099 + 10.47690I 0
u = 0.547313 1.117630I
a = 0.13739 + 2.31147I
b = 2.28237 1.68690I
4.22099 10.47690I 0
u = 0.449881 + 1.169470I
a = 0.36792 + 1.45628I
b = 2.09251 0.54636I
5.41259 + 4.06951I 0
u = 0.449881 1.169470I
a = 0.36792 1.45628I
b = 2.09251 + 0.54636I
5.41259 4.06951I 0
u = 0.285497 + 1.221200I
a = 0.230904 + 1.209670I
b = 1.80867 0.03426I
4.83744 + 4.88572I 0
u = 0.285497 1.221200I
a = 0.230904 1.209670I
b = 1.80867 + 0.03426I
4.83744 4.88572I 0
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.730810 + 0.132013I
a = 1.87462 1.41487I
b = 1.236480 + 0.030970I
0.86799 + 5.55501I 2.80187 9.67670I
u = 0.730810 0.132013I
a = 1.87462 + 1.41487I
b = 1.236480 0.030970I
0.86799 5.55501I 2.80187 + 9.67670I
u = 0.448095 + 1.174840I
a = 0.03447 + 1.70384I
b = 1.71767 1.10560I
5.42668 + 4.33154I 0
u = 0.448095 1.174840I
a = 0.03447 1.70384I
b = 1.71767 + 1.10560I
5.42668 4.33154I 0
u = 0.497105 + 1.165690I
a = 0.925864 1.025280I
b = 2.50249 0.12633I
2.09741 10.13010I 0
u = 0.497105 1.165690I
a = 0.925864 + 1.025280I
b = 2.50249 + 0.12633I
2.09741 + 10.13010I 0
u = 0.522583 + 1.164700I
a = 0.22839 + 1.93063I
b = 2.13174 1.04573I
6.15514 + 7.51354I 0
u = 0.522583 1.164700I
a = 0.22839 1.93063I
b = 2.13174 + 1.04573I
6.15514 7.51354I 0
u = 0.548798 + 1.152780I
a = 0.21673 2.09239I
b = 2.39986 + 1.08477I
4.38020 12.94910I 0
u = 0.548798 1.152780I
a = 0.21673 + 2.09239I
b = 2.39986 1.08477I
4.38020 + 12.94910I 0
14
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.248104 + 1.253880I
a = 0.154460 1.192250I
b = 1.67226 + 0.00902I
3.16083 10.80730I 0
u = 0.248104 1.253880I
a = 0.154460 + 1.192250I
b = 1.67226 0.00902I
3.16083 + 10.80730I 0
u = 0.293542 + 1.254710I
a = 0.151828 0.808528I
b = 0.721605 + 0.587668I
4.75967 1.92423I 0
u = 0.293542 1.254710I
a = 0.151828 + 0.808528I
b = 0.721605 0.587668I
4.75967 + 1.92423I 0
u = 0.708822 + 0.004951I
a = 2.10491 0.44492I
b = 1.243620 + 0.135970I
2.11780 0.11834I 5.78477 1.37253I
u = 0.708822 0.004951I
a = 2.10491 + 0.44492I
b = 1.243620 0.135970I
2.11780 + 0.11834I 5.78477 + 1.37253I
u = 0.558720 + 1.175300I
a = 0.13252 + 2.01240I
b = 2.10150 1.22147I
2.95049 13.58640I 0
u = 0.558720 1.175300I
a = 0.13252 2.01240I
b = 2.10150 + 1.22147I
2.95049 + 13.58640I 0
u = 0.429069 + 0.548426I
a = 2.61601 + 1.37717I
b = 1.24058 1.77812I
4.39438 + 4.82308I 10.38560 5.04175I
u = 0.429069 0.548426I
a = 2.61601 1.37717I
b = 1.24058 + 1.77812I
4.39438 4.82308I 10.38560 + 5.04175I
15
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.579159 + 1.177870I
a = 0.024201 + 0.904316I
b = 1.100910 0.321350I
3.00385 5.11858I 0
u = 0.579159 1.177870I
a = 0.024201 0.904316I
b = 1.100910 + 0.321350I
3.00385 + 5.11858I 0
u = 0.543120 + 1.200300I
a = 0.087330 1.019690I
b = 1.43281 + 0.63924I
3.06326 7.20126I 0
u = 0.543120 1.200300I
a = 0.087330 + 1.019690I
b = 1.43281 0.63924I
3.06326 + 7.20126I 0
u = 0.582221 + 1.182340I
a = 0.05040 1.97553I
b = 2.22544 + 1.11961I
0.8461 + 19.7395I 0
u = 0.582221 1.182340I
a = 0.05040 + 1.97553I
b = 2.22544 1.11961I
0.8461 19.7395I 0
u = 0.623937 + 1.174950I
a = 0.062411 0.799544I
b = 1.061170 + 0.303779I
2.22475 + 10.58040I 0
u = 0.623937 1.174950I
a = 0.062411 + 0.799544I
b = 1.061170 0.303779I
2.22475 10.58040I 0
u = 0.624402 + 0.206178I
a = 1.105290 + 0.218004I
b = 0.74744 1.22310I
3.43127 + 5.31891I 6.29076 6.91043I
u = 0.624402 0.206178I
a = 1.105290 0.218004I
b = 0.74744 + 1.22310I
3.43127 5.31891I 6.29076 + 6.91043I
16
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.363913 + 1.298840I
a = 0.105812 + 0.902255I
b = 0.990308 0.484973I
4.60967 + 6.67560I 0
u = 0.363913 1.298840I
a = 0.105812 0.902255I
b = 0.990308 + 0.484973I
4.60967 6.67560I 0
u = 0.499268 + 1.261840I
a = 0.011363 + 1.002050I
b = 1.37029 0.58117I
3.68537 + 3.20150I 0
u = 0.499268 1.261840I
a = 0.011363 1.002050I
b = 1.37029 + 0.58117I
3.68537 3.20150I 0
u = 0.505819 + 0.352651I
a = 1.24079 1.10135I
b = 0.803144 + 0.875121I
1.99560 0.70011I 4.35713 + 1.30447I
u = 0.505819 0.352651I
a = 1.24079 + 1.10135I
b = 0.803144 0.875121I
1.99560 + 0.70011I 4.35713 1.30447I
u = 0.478311 + 0.336035I
a = 0.28167 1.69381I
b = 0.930911 + 0.100143I
0.40745 2.99983I 0.954528 + 0.448338I
u = 0.478311 0.336035I
a = 0.28167 + 1.69381I
b = 0.930911 0.100143I
0.40745 + 2.99983I 0.954528 0.448338I
u = 0.527857 + 0.198947I
a = 1.91461 + 1.02859I
b = 0.736355 1.192170I
1.69466 + 1.71272I 4.34506 3.60692I
u = 0.527857 0.198947I
a = 1.91461 1.02859I
b = 0.736355 + 1.192170I
1.69466 1.71272I 4.34506 + 3.60692I
17
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.539125 + 0.071339I
a = 2.09790 2.35871I
b = 0.948439 + 0.596914I
1.23439 + 3.10248I 2.36075 5.53634I
u = 0.539125 0.071339I
a = 2.09790 + 2.35871I
b = 0.948439 0.596914I
1.23439 3.10248I 2.36075 + 5.53634I
u = 0.356421 + 0.373474I
a = 1.65904 0.72027I
b = 0.337797 + 1.014410I
2.23739 1.23228I 2.80069 + 0.70900I
u = 0.356421 0.373474I
a = 1.65904 + 0.72027I
b = 0.337797 1.014410I
2.23739 + 1.23228I 2.80069 0.70900I
u = 0.207907 + 0.471398I
a = 3.59702 + 1.23551I
b = 0.017720 0.151733I
0.83738 + 3.30070I 3.80847 6.42732I
u = 0.207907 0.471398I
a = 3.59702 1.23551I
b = 0.017720 + 0.151733I
0.83738 3.30070I 3.80847 + 6.42732I
u = 0.273359 + 0.413276I
a = 0.669858 0.328400I
b = 0.32739 1.37687I
2.12218 + 1.58093I 5.81944 0.94709I
u = 0.273359 0.413276I
a = 0.669858 + 0.328400I
b = 0.32739 + 1.37687I
2.12218 1.58093I 5.81944 + 0.94709I
18
II. I
u
2
=
hu
28
+4u
26
+· · ·+b6, 9u
28
67u
26
+· · ·+a13, u
30
+8u
28
+· · ·+6u
2
+1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
2
a
1
=
9u
28
+ 67u
26
+ ··· + 60u
2
+ 13
u
28
4u
26
+ ··· + 18u
2
+ 6
a
3
=
u
5
2u
3
u
u
5
+ u
3
+ u
a
8
=
2u
29
6u
28
+ ··· + u 14
5u
28
+ u
27
+ ··· + u + 7
a
6
=
3u
29
6u
28
+ ··· 13u 8
2u
29
+ u
28
+ ··· + 4u + 1
a
2
=
10u
28
+ 74u
26
+ ··· + 65u
2
+ 14
3u
28
20u
26
+ ··· 3u
2
+ 1
a
12
=
9u
28
+ 68u
26
+ ··· + 68u
2
+ 16
2u
28
12u
26
+ ··· + 7u
2
+ 3
a
7
=
u
29
10u
28
+ ··· + u 20
u
28
+ 8u
26
+ ··· + 17u
4
+ 6u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 7u
29
+19u
28
+50u
27
+150u
26
+180u
25
+600u
24
+418u
23
+1499u
22
+721u
21
+2545u
20
+
1042u
19
+2979u
18
+1396u
17
+2374u
16
+1729u
15
+1223u
14
+1818u
13
+476u
12
+1472u
11
+
389u
10
+ 861u
9
+ 578u
8
+ 343u
7
+ 615u
6
+ 102u
5
+ 474u
4
+ 29u
3
+ 232u
2
+ 12u + 58
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
30
15u
29
+ ··· 17u + 1
c
2
u
30
u
29
+ ··· u + 1
c
3
u
30
8u
28
+ ··· 2u + 1
c
4
u
30
+ 8u
28
+ ··· + 6u
2
+ 1
c
5
u
30
7u
29
+ ··· 4u
2
+ 1
c
6
u
30
+ u
29
+ ··· + u + 1
c
7
u
30
+ 2u
29
+ ··· + 2u + 1
c
8
u
30
+ 5u
28
+ ··· + 4u
4
+ 1
c
9
u
30
+ 16u
29
+ ··· + 12u + 1
c
10
u
30
+ 8u
28
+ ··· + 6u
2
+ 1
c
11
u
30
2u
29
+ ··· 2u + 1
c
12
u
30
+ 4u
28
+ ··· + 4u
2
+ 1
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 15y
29
+ ··· + 5y + 1
c
2
, c
6
y
30
+ 15y
29
+ ··· + 17y + 1
c
3
y
30
16y
29
+ ··· + 22y + 1
c
4
, c
10
y
30
+ 16y
29
+ ··· + 12y + 1
c
5
y
30
7y
29
+ ··· 8y + 1
c
7
, c
11
y
30
22y
29
+ ··· 28y + 1
c
8
y
30
+ 10y
29
+ ··· + 8y
2
+ 1
c
9
y
30
+ 32y
28
+ ··· 4y + 1
c
12
y
30
+ 8y
29
+ ··· + 8y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.362041 + 0.987203I
a = 1.51664 0.38078I
b = 0.375856 0.977584I
0.547482 0.512730I 3.22724 1.51095I
u = 0.362041 0.987203I
a = 1.51664 + 0.38078I
b = 0.375856 + 0.977584I
0.547482 + 0.512730I 3.22724 + 1.51095I
u = 0.413618 + 1.000500I
a = 1.24771 1.67399I
b = 2.04480 + 1.66601I
2.37609 1.81579I 2.08168 + 1.76632I
u = 0.413618 1.000500I
a = 1.24771 + 1.67399I
b = 2.04480 1.66601I
2.37609 + 1.81579I 2.08168 1.76632I
u = 0.894280 + 0.121882I
a = 0.791854 + 0.329906I
b = 0.723001 0.005696I
0.626627 + 0.892293I 3.84481 1.79915I
u = 0.894280 0.121882I
a = 0.791854 0.329906I
b = 0.723001 + 0.005696I
0.626627 0.892293I 3.84481 + 1.79915I
u = 0.666637 + 0.580978I
a = 0.381919 + 0.678655I
b = 0.306802 0.830390I
3.51466 + 0.68129I 6.93877 + 2.81693I
u = 0.666637 0.580978I
a = 0.381919 0.678655I
b = 0.306802 + 0.830390I
3.51466 0.68129I 6.93877 2.81693I
u = 0.806987 + 0.293907I
a = 0.314050 0.712820I
b = 0.542772 + 0.002378I
0.42021 + 4.20885I 3.00114 2.00285I
u = 0.806987 0.293907I
a = 0.314050 + 0.712820I
b = 0.542772 0.002378I
0.42021 4.20885I 3.00114 + 2.00285I
24
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.532069 + 1.023780I
a = 1.56467 1.74925I
b = 1.94201 0.64296I
3.24092 + 7.83132I 3.79845 11.44918I
u = 0.532069 1.023780I
a = 1.56467 + 1.74925I
b = 1.94201 + 0.64296I
3.24092 7.83132I 3.79845 + 11.44918I
u = 0.565384 + 0.601457I
a = 1.27510 1.51897I
b = 1.37657 + 0.62582I
4.58349 3.40871I 6.47467 + 4.45050I
u = 0.565384 0.601457I
a = 1.27510 + 1.51897I
b = 1.37657 0.62582I
4.58349 + 3.40871I 6.47467 4.45050I
u = 0.358138 + 1.123810I
a = 0.693261 1.094840I
b = 0.116361 + 1.243460I
3.61177 + 1.15606I 5.87778 2.10913I
u = 0.358138 1.123810I
a = 0.693261 + 1.094840I
b = 0.116361 1.243460I
3.61177 1.15606I 5.87778 + 2.10913I
u = 0.236290 + 0.784176I
a = 0.323758 1.085050I
b = 0.319778 + 1.248470I
1.44492 2.15650I 1.18067 + 4.86459I
u = 0.236290 0.784176I
a = 0.323758 + 1.085050I
b = 0.319778 1.248470I
1.44492 + 2.15650I 1.18067 4.86459I
u = 0.569463 + 1.038150I
a = 1.245740 + 0.459303I
b = 0.370992 + 0.947636I
2.08324 5.49920I 2.48960 + 5.73420I
u = 0.569463 1.038150I
a = 1.245740 0.459303I
b = 0.370992 0.947636I
2.08324 + 5.49920I 2.48960 5.73420I
25
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.311733 + 0.704205I
a = 1.54901 0.07390I
b = 1.18261 1.89006I
3.50132 + 5.02428I 3.57390 5.95135I
u = 0.311733 0.704205I
a = 1.54901 + 0.07390I
b = 1.18261 + 1.89006I
3.50132 5.02428I 3.57390 + 5.95135I
u = 0.397016 + 1.196750I
a = 0.382753 + 1.247280I
b = 0.94850 1.07461I
4.72226 + 4.99351I 2.97622 5.72956I
u = 0.397016 1.196750I
a = 0.382753 1.247280I
b = 0.94850 + 1.07461I
4.72226 4.99351I 2.97622 + 5.72956I
u = 0.532105 + 1.164830I
a = 0.416740 0.477413I
b = 1.42928 0.07832I
2.27468 9.18953I 1.19515 + 5.88178I
u = 0.532105 1.164830I
a = 0.416740 + 0.477413I
b = 1.42928 + 0.07832I
2.27468 + 9.18953I 1.19515 5.88178I
u = 0.060909 + 0.716731I
a = 2.44743 + 0.13430I
b = 0.977492 + 0.313749I
1.42990 3.22675I 10.31401 + 5.97849I
u = 0.060909 0.716731I
a = 2.44743 0.13430I
b = 0.977492 0.313749I
1.42990 + 3.22675I 10.31401 5.97849I
u = 0.478469 + 1.225040I
a = 0.034275 + 0.929796I
b = 1.36972 0.51567I
4.11229 + 4.02079I 4.19683 5.30760I
u = 0.478469 1.225040I
a = 0.034275 0.929796I
b = 1.36972 + 0.51567I
4.11229 4.02079I 4.19683 + 5.30760I
26
III. I
u
3
= hu
2
+ b, a 1, u
12
u
11
+ · · · 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
2
a
1
=
1
u
2
a
3
=
u
5
2u
3
u
u
5
+ u
3
+ u
a
8
=
u
4
+ u
2
+ 1
u
6
u
2
a
6
=
u
7
2u
3
2u
u
9
u
7
+ u
5
+ 2u
3
+ u
a
2
=
u
11
+ u
10
+ u
9
+ 3u
8
u
7
+ 3u
6
3u
5
3u
2
+ 2u
u
11
u
9
2u
8
+ u
7
3u
6
+ 3u
5
u
4
+ 2u
2
2u + 1
a
12
=
u
2
+ 1
u
4
a
7
=
1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
7
4u
5
+ 4u 2
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)
6
c
2
, c
6
(u
2
u + 1)
6
c
3
, c
5
u
12
u
11
6u
10
+ 3u
9
+ 16u
8
3u
7
13u
6
3u
5
+ 4u
3
+ 8u
2
6u + 1
c
4
, c
10
, c
12
u
12
+ u
11
+ 2u
10
+ u
9
u
7
3u
6
3u
5
2u
4
+ 2u
2
+ 2u + 1
c
7
, c
9
, c
11
u
12
3u
11
+ 2u
10
+ 5u
9
8u
8
u
7
+ 9u
6
3u
5
4u
4
+ 2u
3
+ 1
c
8
u
12
5u
11
+ ··· 8u
2
+ 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
6
c
3
, c
5
y
12
13y
11
+ ··· 20y + 1
c
4
, c
10
, c
12
y
12
+ 3y
11
+ 2y
10
5y
9
8y
8
+ y
7
+ 9y
6
+ 3y
5
4y
4
2y
3
+ 1
c
7
, c
9
, c
11
y
12
5y
11
+ ··· 8y
2
+ 1
c
8
y
12
+ 11y
11
+ ··· 16y + 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 0.975107 + 0.094413I
a = 1.00000
b = 0.941920 + 0.184126I
2.02988I 0. 3.46410I
u = 0.975107 0.094413I
a = 1.00000
b = 0.941920 0.184126I
2.02988I 0. + 3.46410I
u = 0.143629 + 1.043280I
a = 1.00000
b = 1.067800 0.299691I
2.02988I 0. + 3.46410I
u = 0.143629 1.043280I
a = 1.00000
b = 1.067800 + 0.299691I
2.02988I 0. 3.46410I
u = 0.891573 + 0.185983I
a = 1.00000
b = 0.760313 0.331634I
2.02988I 0. 3.46410I
u = 0.891573 0.185983I
a = 1.00000
b = 0.760313 + 0.331634I
2.02988I 0. + 3.46410I
u = 0.453586 + 1.080490I
a = 1.00000
b = 0.961710 + 0.980187I
2.02988I 0. 3.46410I
u = 0.453586 1.080490I
a = 1.00000
b = 0.961710 0.980187I
2.02988I 0. + 3.46410I
u = 0.380623 + 1.119860I
a = 1.00000
b = 1.109210 0.852489I
2.02988I 0. 3.46410I
u = 0.380623 1.119860I
a = 1.00000
b = 1.109210 + 0.852489I
2.02988I 0. + 3.46410I
30
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 0.512868 + 0.571437I
a = 1.00000
b = 0.063506 0.586144I
2.02988I 0. + 3.46410I
u = 0.512868 0.571437I
a = 1.00000
b = 0.063506 + 0.586144I
2.02988I 0. 3.46410I
31
IV. I
u
4
= hb u 1, a 1, u
2
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u + 1
a
5
=
u
u + 1
a
9
=
u
u + 1
a
1
=
1
u + 1
a
3
=
1
0
a
8
=
2u
u + 2
a
6
=
u 2
u
a
2
=
u
u + 1
a
12
=
u + 2
u
a
7
=
1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u + 2
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
8
u
2
+ u + 1
c
2
, c
4
, c
6
c
7
, c
9
, c
10
c
11
, c
12
u
2
u + 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
2
+ y + 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
1(vol +
1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.00000
b = 0.500000 + 0.866025I
2.02988I 0. + 3.46410I
u = 0.500000 0.866025I
a = 1.00000
b = 0.500000 0.866025I
2.02988I 0. 3.46410I
35
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
7
)(u
30
15u
29
+ ··· 17u + 1)
· (u
138
+ 57u
137
+ ··· + 4078944u + 222784)
c
2
((u
2
u + 1)
7
)(u
30
u
29
+ ··· u + 1)(u
138
+ 7u
137
+ ··· + 976u + 472)
c
3
(u
2
+ u + 1)
· (u
12
u
11
6u
10
+ 3u
9
+ 16u
8
3u
7
13u
6
3u
5
+ 4u
3
+ 8u
2
6u + 1)
· (u
30
8u
28
+ ··· 2u + 1)(u
138
+ u
137
+ ··· + 1500u + 84625)
c
4
(u
2
u + 1)(u
12
+ u
11
+ ··· + 2u + 1)
· (u
30
+ 8u
28
+ ··· + 6u
2
+ 1)(u
138
u
137
+ ··· 2u + 1)
c
5
(u
2
+ u + 1)
· (u
12
u
11
6u
10
+ 3u
9
+ 16u
8
3u
7
13u
6
3u
5
+ 4u
3
+ 8u
2
6u + 1)
· (u
30
7u
29
+ ··· 4u
2
+ 1)(u
138
4u
137
+ ··· 50u + 1)
c
6
((u
2
u + 1)
7
)(u
30
+ u
29
+ ··· + u + 1)(u
138
+ 7u
137
+ ··· + 976u + 472)
c
7
(u
2
u + 1)
· (u
12
3u
11
+ 2u
10
+ 5u
9
8u
8
u
7
+ 9u
6
3u
5
4u
4
+ 2u
3
+ 1)
· (u
30
+ 2u
29
+ ··· + 2u + 1)(u
138
+ 3u
137
+ ··· + 32098u + 2479)
c
8
(u
2
+ u + 1)(u
12
5u
11
+ ··· 8u
2
+ 1)(u
30
+ 5u
28
+ ··· + 4u
4
+ 1)
· (u
138
u
137
+ ··· 312712u + 21829)
c
9
(u
2
u + 1)
· (u
12
3u
11
+ 2u
10
+ 5u
9
8u
8
u
7
+ 9u
6
3u
5
4u
4
+ 2u
3
+ 1)
· (u
30
+ 16u
29
+ ··· + 12u + 1)(u
138
73u
137
+ ··· 12u + 1)
c
10
(u
2
u + 1)(u
12
+ u
11
+ ··· + 2u + 1)
· (u
30
+ 8u
28
+ ··· + 6u
2
+ 1)(u
138
u
137
+ ··· 2u + 1)
c
11
(u
2
u + 1)
· (u
12
3u
11
+ 2u
10
+ 5u
9
8u
8
u
7
+ 9u
6
3u
5
4u
4
+ 2u
3
+ 1)
· (u
30
2u
29
+ ··· 2u + 1)(u
138
+ 3u
137
+ ··· + 32098u + 2479)
c
12
(u
2
u + 1)(u
12
+ u
11
+ ··· + 2u + 1)
· (u
30
+ 4u
28
+ ··· + 4u
2
+ 1)(u
138
3u
137
+ ··· + 126u + 107)
36
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
7
)(y
30
+ 15y
29
+ ··· + 5y + 1)
· (y
138
+ 57y
137
+ ··· + 592047023616y + 49632710656)
c
2
, c
6
((y
2
+ y + 1)
7
)(y
30
+ 15y
29
+ ··· + 17y + 1)
· (y
138
+ 57y
137
+ ··· + 4078944y + 222784)
c
3
(y
2
+ y + 1)(y
12
13y
11
+ ··· 20y + 1)(y
30
16y
29
+ ··· + 22y + 1)
· (y
138
63y
137
+ ··· + 1166513601250y + 7161390625)
c
4
, c
10
(y
2
+ y + 1)
· (y
12
+ 3y
11
+ 2y
10
5y
9
8y
8
+ y
7
+ 9y
6
+ 3y
5
4y
4
2y
3
+ 1)
· (y
30
+ 16y
29
+ ··· + 12y + 1)(y
138
+ 73y
137
+ ··· + 12y + 1)
c
5
(y
2
+ y + 1)(y
12
13y
11
+ ··· 20y + 1)(y
30
7y
29
+ ··· 8y + 1)
· (y
138
6y
137
+ ··· 84y + 1)
c
7
, c
11
(y
2
+ y + 1)(y
12
5y
11
+ ··· 8y
2
+ 1)(y
30
22y
29
+ ··· 28y + 1)
· (y
138
89y
137
+ ··· 992898284y + 6145441)
c
8
(y
2
+ y + 1)(y
12
+ 11y
11
+ ··· 16y + 1)(y
30
+ 10y
29
+ ··· + 8y
2
+ 1)
· (y
138
33y
137
+ ··· 25000518340y + 476505241)
c
9
(y
2
+ y + 1)(y
12
5y
11
+ ··· 8y
2
+ 1)(y
30
+ 32y
28
+ ··· 4y + 1)
· (y
138
+ 5y
137
+ ··· + 56y + 1)
c
12
(y
2
+ y + 1)
· (y
12
+ 3y
11
+ 2y
10
5y
9
8y
8
+ y
7
+ 9y
6
+ 3y
5
4y
4
2y
3
+ 1)
· (y
30
+ 8y
29
+ ··· + 8y + 1)(y
138
+ 13y
137
+ ··· + 1100348y + 11449)
37