12a
0431
(K12a
0431
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 11 4 12 5 1 9 7
Solving Sequence
8,12 5,9
10 4 3 7 1 11 6 2
c
8
c
9
c
4
c
3
c
7
c
12
c
11
c
6
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.08221 × 10
1017
u
182
+ 1.35395 × 10
1018
u
181
+ ··· + 2.55657 × 10
1018
b + 6.03949 × 10
1020
,
6.03054 × 10
1019
u
182
8.16888 × 10
1020
u
181
+ ··· + 2.10491 × 10
1020
a + 2.67814 × 10
1023
,
u
183
13u
182
+ ··· + 6260u 3952i
I
u
2
= h−5.30317 × 10
15
u
45
+ 9.11536 × 10
16
u
44
+ ··· + 9.18144 × 10
14
b 6.45933 × 10
16
,
1.83232 × 10
17
u
45
3.25201 × 10
18
u
44
+ ··· + 6.42701 × 10
15
a + 4.76357 × 10
17
, u
46
18u
45
+ ··· 97u + 7i
* 2 irreducible components of dim
C
= 0, with total 229 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
= h−1.08 × 10
1017
u
182
+ 1.35 × 10
1018
u
181
+ · · · + 2.56 × 10
1018
b +
6.04 × 10
1020
, 6.03 × 10
1019
u
182
8.17 × 10
1020
u
181
+ · · · + 2.10 × 10
1020
a +
2.68 × 10
1023
, u
183
13u
182
+ · · · + 6260u 3952i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
5
=
0.286499u
182
+ 3.88088u
181
+ ··· + 4569.49u 1272.33
0.0423306u
182
0.529598u
181
+ ··· + 222.058u 236.235
a
9
=
1
u
2
a
10
=
0.387179u
182
4.99816u
181
+ ··· 1287.11u 949.545
0.0501010u
182
0.653556u
181
+ ··· 265.486u 132.693
a
4
=
0.244169u
182
+ 3.35128u
181
+ ··· + 4791.55u 1508.57
0.0423306u
182
0.529598u
181
+ ··· + 222.058u 236.235
a
3
=
0.117373u
182
+ 1.35855u
181
+ ··· 1035.35u + 1306.01
0.111769u
182
+ 1.45629u
181
+ ··· + 1217.32u 0.425868
a
7
=
0.150852u
182
+ 1.98096u
181
+ ··· + 1225.75u + 102.938
0.00953673u
182
0.157843u
181
+ ··· 704.908u + 345.154
a
1
=
0.119555u
182
+ 1.73225u
181
+ ··· + 3788.50u 1319.55
0.0310668u
182
+ 0.464528u
181
+ ··· + 1509.59u 561.843
a
11
=
u
u
3
+ u
a
6
=
0.193264u
182
+ 2.55272u
181
+ ··· + 1827.85u 18.6801
0.0164454u
182
+ 0.188229u
181
+ ··· 398.097u + 304.139
a
2
=
0.0929241u
182
1.36603u
181
+ ··· 2642.26u + 1101.99
0.0701137u
182
+ 0.884804u
181
+ ··· + 214.247u + 298.614
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.0678249u
182
+ 0.743225u
181
+ ··· 2271.57u + 1265.71
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
183
+ 82u
182
+ ··· + 16u + 1
c
2
, c
5
u
183
+ 4u
182
+ ··· + 20u + 1
c
3
u
183
+ 2u
182
+ ··· + 136040u + 44287
c
4
, c
7
u
183
+ 2u
182
+ ··· + 30967u + 8921
c
6
u
183
2u
182
+ ··· + 10862u + 527
c
8
, c
11
u
183
+ 13u
182
+ ··· + 6260u + 3952
c
9
u
183
u
182
+ ··· + 36530383u + 15439309
c
10
u
183
13u
182
+ ··· + 808u + 1
c
12
u
183
+ 8u
182
+ ··· 9354518u + 728723
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
183
+ 50y
182
+ ··· + 4624y 1
c
2
, c
5
y
183
82y
182
+ ··· + 16y 1
c
3
y
183
+ 4y
182
+ ··· 261117339144y 1961338369
c
4
, c
7
y
183
100y
182
+ ··· + 3828341213y 79584241
c
6
y
183
+ 26y
182
+ ··· 28715838y 277729
c
8
, c
11
y
183
+ 99y
182
+ ··· 447121808y 15618304
c
9
y
183
y
182
+ ··· + 6862895901260619y 238372262397481
c
10
y
183
+ 15y
182
+ ··· + 315098y 1
c
12
y
183
+ 2y
182
+ ··· 44241446103030y 531037210729
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.109145 + 1.004260I
a = 0.32645 + 1.94373I
b = 0.46884 1.59401I
5.73632 + 2.61032I 0
u = 0.109145 1.004260I
a = 0.32645 1.94373I
b = 0.46884 + 1.59401I
5.73632 2.61032I 0
u = 0.474605 + 0.855807I
a = 0.16105 1.96522I
b = 0.936293 + 0.779716I
0.11444 4.46856I 0
u = 0.474605 0.855807I
a = 0.16105 + 1.96522I
b = 0.936293 0.779716I
0.11444 + 4.46856I 0
u = 0.787313 + 0.573287I
a = 0.481590 + 0.075837I
b = 1.200510 0.275493I
3.41227 6.64607I 0
u = 0.787313 0.573287I
a = 0.481590 0.075837I
b = 1.200510 + 0.275493I
3.41227 + 6.64607I 0
u = 0.431412 + 0.951554I
a = 0.61887 1.92842I
b = 1.197510 + 0.388597I
6.95643 + 2.58003I 0
u = 0.431412 0.951554I
a = 0.61887 + 1.92842I
b = 1.197510 0.388597I
6.95643 2.58003I 0
u = 0.224766 + 0.923643I
a = 0.29247 + 1.45607I
b = 0.967832 0.499646I
0.203430 + 0.797452I 0
u = 0.224766 0.923643I
a = 0.29247 1.45607I
b = 0.967832 + 0.499646I
0.203430 0.797452I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.146019 + 1.045120I
a = 0.70016 1.67400I
b = 0.296606 + 1.315740I
5.88429 2.90843I 0
u = 0.146019 1.045120I
a = 0.70016 + 1.67400I
b = 0.296606 1.315740I
5.88429 + 2.90843I 0
u = 0.089576 + 1.061220I
a = 0.03862 1.84294I
b = 0.11882 + 1.47999I
5.79090 3.15817I 0
u = 0.089576 1.061220I
a = 0.03862 + 1.84294I
b = 0.11882 1.47999I
5.79090 + 3.15817I 0
u = 0.491782 + 0.787874I
a = 0.63547 1.75863I
b = 1.234790 + 0.402039I
3.35915 5.35503I 0
u = 0.491782 0.787874I
a = 0.63547 + 1.75863I
b = 1.234790 0.402039I
3.35915 + 5.35503I 0
u = 0.398828 + 0.831123I
a = 0.05013 1.70457I
b = 1.65689 + 0.06147I
8.67420 + 1.70955I 0
u = 0.398828 0.831123I
a = 0.05013 + 1.70457I
b = 1.65689 0.06147I
8.67420 1.70955I 0
u = 0.042485 + 0.916931I
a = 0.07239 + 2.04280I
b = 1.083850 0.608952I
1.34148 + 3.84832I 0
u = 0.042485 0.916931I
a = 0.07239 2.04280I
b = 1.083850 + 0.608952I
1.34148 3.84832I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.253570 + 1.056280I
a = 0.675074 + 0.822827I
b = 0.397454 0.735287I
2.06637 1.14443I 0
u = 0.253570 1.056280I
a = 0.675074 0.822827I
b = 0.397454 + 0.735287I
2.06637 + 1.14443I 0
u = 0.303028 + 1.053370I
a = 0.74779 + 2.44925I
b = 1.151140 0.297713I
0.37592 + 4.43107I 0
u = 0.303028 1.053370I
a = 0.74779 2.44925I
b = 1.151140 + 0.297713I
0.37592 4.43107I 0
u = 0.398687 + 0.798508I
a = 0.56518 + 1.73812I
b = 1.225740 0.381156I
1.337870 + 0.050450I 0
u = 0.398687 0.798508I
a = 0.56518 1.73812I
b = 1.225740 + 0.381156I
1.337870 0.050450I 0
u = 0.434704 + 1.025960I
a = 0.391022 + 1.152800I
b = 0.452956 0.741335I
0.139475 0.478764I 0
u = 0.434704 1.025960I
a = 0.391022 1.152800I
b = 0.452956 + 0.741335I
0.139475 + 0.478764I 0
u = 0.458957 + 0.752394I
a = 0.73148 + 1.43664I
b = 0.972081 0.615995I
0.094435 + 0.634449I 0
u = 0.458957 0.752394I
a = 0.73148 1.43664I
b = 0.972081 + 0.615995I
0.094435 0.634449I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.702531 + 0.872299I
a = 0.202738 0.517122I
b = 0.998318 + 0.365025I
2.20573 4.10299I 0
u = 0.702531 0.872299I
a = 0.202738 + 0.517122I
b = 0.998318 0.365025I
2.20573 + 4.10299I 0
u = 1.130090 + 0.012260I
a = 0.087064 0.118191I
b = 1.135540 0.226140I
4.63431 0.29028I 0
u = 1.130090 0.012260I
a = 0.087064 + 0.118191I
b = 1.135540 + 0.226140I
4.63431 + 0.29028I 0
u = 0.353012 + 0.788504I
a = 0.608945 0.237573I
b = 1.64585 0.07715I
3.49751 + 8.99933I 0
u = 0.353012 0.788504I
a = 0.608945 + 0.237573I
b = 1.64585 + 0.07715I
3.49751 8.99933I 0
u = 0.283921 + 1.106070I
a = 0.70475 + 1.43336I
b = 0.308285 1.271040I
6.91633 + 3.38590I 0
u = 0.283921 1.106070I
a = 0.70475 1.43336I
b = 0.308285 + 1.271040I
6.91633 3.38590I 0
u = 1.067610 + 0.423916I
a = 0.1193080 0.0260623I
b = 1.186720 + 0.496387I
6.24789 6.13386I 0
u = 1.067610 0.423916I
a = 0.1193080 + 0.0260623I
b = 1.186720 0.496387I
6.24789 + 6.13386I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.113524 + 0.842312I
a = 0.07623 2.18664I
b = 1.056900 + 0.627645I
0.986054 0.412804I 0
u = 0.113524 0.842312I
a = 0.07623 + 2.18664I
b = 1.056900 0.627645I
0.986054 + 0.412804I 0
u = 0.399422 + 1.080510I
a = 0.67177 1.48623I
b = 0.773473 0.007435I
1.24957 1.07670I 0
u = 0.399422 1.080510I
a = 0.67177 + 1.48623I
b = 0.773473 + 0.007435I
1.24957 + 1.07670I 0
u = 0.254841 + 1.124830I
a = 0.89046 1.87820I
b = 1.027580 + 0.329027I
4.20286 4.07396I 0
u = 0.254841 1.124830I
a = 0.89046 + 1.87820I
b = 1.027580 0.329027I
4.20286 + 4.07396I 0
u = 0.019531 + 0.843861I
a = 0.808548 0.403324I
b = 0.506373 + 0.692372I
1.46987 4.37845I 0
u = 0.019531 0.843861I
a = 0.808548 + 0.403324I
b = 0.506373 0.692372I
1.46987 + 4.37845I 0
u = 1.052910 + 0.481840I
a = 0.611221 + 0.357938I
b = 0.910693 + 0.163806I
3.51368 + 0.79772I 0
u = 1.052910 0.481840I
a = 0.611221 0.357938I
b = 0.910693 0.163806I
3.51368 0.79772I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.345762 + 1.107380I
a = 0.93334 2.22617I
b = 1.119480 + 0.339824I
1.45556 + 10.63760I 0
u = 0.345762 1.107380I
a = 0.93334 + 2.22617I
b = 1.119480 0.339824I
1.45556 10.63760I 0
u = 0.511654 + 0.642564I
a = 0.529780 + 0.454081I
b = 1.051550 0.416862I
0.678419 + 0.466821I 0
u = 0.511654 0.642564I
a = 0.529780 0.454081I
b = 1.051550 + 0.416862I
0.678419 0.466821I 0
u = 0.318264 + 0.750714I
a = 0.562016 + 0.468041I
b = 1.58856 + 0.01371I
1.60032 + 3.27151I 0
u = 0.318264 0.750714I
a = 0.562016 0.468041I
b = 1.58856 0.01371I
1.60032 3.27151I 0
u = 0.804315 + 0.124211I
a = 0.138450 0.772152I
b = 0.093252 + 0.370978I
2.30567 + 1.61661I 0
u = 0.804315 0.124211I
a = 0.138450 + 0.772152I
b = 0.093252 0.370978I
2.30567 1.61661I 0
u = 0.659084 + 0.477297I
a = 0.420291 0.946191I
b = 0.350893 + 0.419700I
1.61613 3.71425I 0
u = 0.659084 0.477297I
a = 0.420291 + 0.946191I
b = 0.350893 0.419700I
1.61613 + 3.71425I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.730801 + 0.939627I
a = 0.867974 + 1.090830I
b = 0.668981 0.612045I
2.31740 + 8.92866I 0
u = 0.730801 0.939627I
a = 0.867974 1.090830I
b = 0.668981 + 0.612045I
2.31740 8.92866I 0
u = 0.474103 + 1.094950I
a = 0.642206 1.143190I
b = 0.361960 + 1.207710I
0.72684 + 5.65398I 0
u = 0.474103 1.094950I
a = 0.642206 + 1.143190I
b = 0.361960 1.207710I
0.72684 5.65398I 0
u = 0.431482 + 1.114870I
a = 0.01943 + 1.78821I
b = 1.33997 0.62582I
2.33597 + 3.67582I 0
u = 0.431482 1.114870I
a = 0.01943 1.78821I
b = 1.33997 + 0.62582I
2.33597 3.67582I 0
u = 0.646738 + 1.007510I
a = 0.744686 1.114610I
b = 0.748352 + 0.577690I
4.67821 + 3.49103I 0
u = 0.646738 1.007510I
a = 0.744686 + 1.114610I
b = 0.748352 0.577690I
4.67821 3.49103I 0
u = 1.170530 + 0.252592I
a = 0.199498 + 0.185514I
b = 1.180860 0.500188I
0.60107 8.67171I 0
u = 1.170530 0.252592I
a = 0.199498 0.185514I
b = 1.180860 + 0.500188I
0.60107 + 8.67171I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.797110 + 0.076706I
a = 1.120170 + 0.608336I
b = 0.099356 0.740353I
0.41690 9.52197I 0
u = 0.797110 0.076706I
a = 1.120170 0.608336I
b = 0.099356 + 0.740353I
0.41690 + 9.52197I 0
u = 0.788029 + 0.129530I
a = 0.654235 0.039991I
b = 1.144920 0.475116I
0.53003 5.27967I 0
u = 0.788029 0.129530I
a = 0.654235 + 0.039991I
b = 1.144920 + 0.475116I
0.53003 + 5.27967I 0
u = 0.798323 + 0.932992I
a = 0.07037 + 1.58809I
b = 1.006650 0.609707I
2.86365 8.03010I 0
u = 0.798323 0.932992I
a = 0.07037 1.58809I
b = 1.006650 + 0.609707I
2.86365 + 8.03010I 0
u = 1.175730 + 0.358109I
a = 0.411681 + 0.018031I
b = 0.976199 + 0.219898I
3.41980 + 0.72619I 0
u = 1.175730 0.358109I
a = 0.411681 0.018031I
b = 0.976199 0.219898I
3.41980 0.72619I 0
u = 0.372457 + 0.671523I
a = 0.042280 0.317881I
b = 1.48840 0.13772I
7.90926 + 0.91624I 0
u = 0.372457 0.671523I
a = 0.042280 + 0.317881I
b = 1.48840 + 0.13772I
7.90926 0.91624I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.532725 + 1.114590I
a = 0.635982 0.234884I
b = 0.892669 + 0.739734I
1.69874 + 3.76399I 0
u = 0.532725 1.114590I
a = 0.635982 + 0.234884I
b = 0.892669 0.739734I
1.69874 3.76399I 0
u = 0.316657 + 1.201900I
a = 0.502826 + 1.087630I
b = 0.281956 0.866275I
3.12234 5.83694I 0
u = 0.316657 1.201900I
a = 0.502826 1.087630I
b = 0.281956 + 0.866275I
3.12234 + 5.83694I 0
u = 0.052081 + 0.754387I
a = 0.28394 3.64393I
b = 0.688567 + 0.068851I
2.46103 + 2.56983I 0
u = 0.052081 0.754387I
a = 0.28394 + 3.64393I
b = 0.688567 0.068851I
2.46103 2.56983I 0
u = 0.309349 + 1.213200I
a = 0.158221 0.960573I
b = 0.190956 + 0.682689I
2.60658 2.53272I 0
u = 0.309349 1.213200I
a = 0.158221 + 0.960573I
b = 0.190956 0.682689I
2.60658 + 2.53272I 0
u = 0.287985 + 1.221130I
a = 0.56421 + 1.81954I
b = 1.023200 0.378284I
3.40119 9.63122I 0
u = 0.287985 1.221130I
a = 0.56421 1.81954I
b = 1.023200 + 0.378284I
3.40119 + 9.63122I 0
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.271230 + 1.227850I
a = 0.374753 1.132670I
b = 0.191130 + 0.893619I
3.78481 1.52233I 0
u = 0.271230 1.227850I
a = 0.374753 + 1.132670I
b = 0.191130 0.893619I
3.78481 + 1.52233I 0
u = 0.723508 + 0.027656I
a = 1.114770 0.447162I
b = 0.112143 + 0.739716I
2.46625 4.03969I 0
u = 0.723508 0.027656I
a = 1.114770 + 0.447162I
b = 0.112143 0.739716I
2.46625 + 4.03969I 0
u = 0.351815 + 1.228810I
a = 0.572380 + 0.339024I
b = 0.754831 0.618004I
4.65134 1.22493I 0
u = 0.351815 1.228810I
a = 0.572380 0.339024I
b = 0.754831 + 0.618004I
4.65134 + 1.22493I 0
u = 0.368231 + 1.230390I
a = 0.56519 1.46369I
b = 1.30650 + 0.80006I
2.72777 5.38077I 0
u = 0.368231 1.230390I
a = 0.56519 + 1.46369I
b = 1.30650 0.80006I
2.72777 + 5.38077I 0
u = 1.253930 + 0.286644I
a = 0.135769 0.216636I
b = 1.183810 + 0.500442I
2.6809 14.1536I 0
u = 1.253930 0.286644I
a = 0.135769 + 0.216636I
b = 1.183810 0.500442I
2.6809 + 14.1536I 0
14
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.467277 + 1.199050I
a = 0.543327 + 1.242050I
b = 0.318009 1.205300I
5.82307 + 8.46174I 0
u = 0.467277 1.199050I
a = 0.543327 1.242050I
b = 0.318009 + 1.205300I
5.82307 8.46174I 0
u = 1.153870 + 0.571829I
a = 0.059652 0.287124I
b = 1.018420 + 0.298492I
4.13877 + 1.34883I 0
u = 1.153870 0.571829I
a = 0.059652 + 0.287124I
b = 1.018420 0.298492I
4.13877 1.34883I 0
u = 0.514708 + 1.188900I
a = 0.00545 1.68380I
b = 1.31368 + 0.66694I
3.60772 + 10.08900I 0
u = 0.514708 1.188900I
a = 0.00545 + 1.68380I
b = 1.31368 0.66694I
3.60772 10.08900I 0
u = 0.054175 + 0.685608I
a = 0.51808 + 3.97083I
b = 0.629872 0.097015I
0.66321 + 8.31222I 0
u = 0.054175 0.685608I
a = 0.51808 3.97083I
b = 0.629872 + 0.097015I
0.66321 8.31222I 0
u = 0.506043 + 1.215480I
a = 0.504501 1.225330I
b = 0.313126 + 1.193960I
3.7377 + 14.3343I 0
u = 0.506043 1.215480I
a = 0.504501 + 1.225330I
b = 0.313126 1.193960I
3.7377 14.3343I 0
15
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.486321 + 1.228590I
a = 0.510957 1.020370I
b = 0.813686 + 0.465520I
5.78014 + 0.41286I 0
u = 0.486321 1.228590I
a = 0.510957 + 1.020370I
b = 0.813686 0.465520I
5.78014 0.41286I 0
u = 0.546514 + 0.397402I
a = 1.95929 + 1.33528I
b = 0.727239 + 0.164143I
3.54777 + 0.93531I 0
u = 0.546514 0.397402I
a = 1.95929 1.33528I
b = 0.727239 0.164143I
3.54777 0.93531I 0
u = 1.332810 + 0.174266I
a = 0.446401 + 0.471452I
b = 0.969672 0.309326I
4.87780 + 3.81110I 0
u = 1.332810 0.174266I
a = 0.446401 0.471452I
b = 0.969672 + 0.309326I
4.87780 3.81110I 0
u = 0.425880 + 0.495966I
a = 0.156712 0.002836I
b = 0.331826 + 0.747219I
1.68304 4.25771I 0
u = 0.425880 0.495966I
a = 0.156712 + 0.002836I
b = 0.331826 0.747219I
1.68304 + 4.25771I 0
u = 0.477424 + 1.265660I
a = 0.424691 + 1.023380I
b = 0.387518 0.643458I
1.19681 6.24940I 0
u = 0.477424 1.265660I
a = 0.424691 1.023380I
b = 0.387518 + 0.643458I
1.19681 + 6.24940I 0
16
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.415418 + 1.306020I
a = 0.442663 + 0.980641I
b = 0.828008 0.438106I
4.34402 4.90681I 0
u = 0.415418 1.306020I
a = 0.442663 0.980641I
b = 0.828008 + 0.438106I
4.34402 + 4.90681I 0
u = 0.344518 + 1.331030I
a = 0.442440 0.818560I
b = 0.344799 + 0.522779I
2.37133 2.38494I 0
u = 0.344518 1.331030I
a = 0.442440 + 0.818560I
b = 0.344799 0.522779I
2.37133 + 2.38494I 0
u = 0.397657 + 1.316400I
a = 0.54626 + 1.32460I
b = 1.35181 0.72427I
1.94394 10.46340I 0
u = 0.397657 1.316400I
a = 0.54626 1.32460I
b = 1.35181 + 0.72427I
1.94394 + 10.46340I 0
u = 0.669803 + 1.204120I
a = 0.04594 + 1.54936I
b = 1.29166 0.68988I
3.74950 + 12.34900I 0
u = 0.669803 1.204120I
a = 0.04594 1.54936I
b = 1.29166 + 0.68988I
3.74950 12.34900I 0
u = 0.125365 + 0.602866I
a = 1.63023 + 0.53483I
b = 1.301450 + 0.164867I
1.29014 2.00406I 21.7805 + 0.I
u = 0.125365 0.602866I
a = 1.63023 0.53483I
b = 1.301450 0.164867I
1.29014 + 2.00406I 21.7805 + 0.I
17
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.614088 + 1.240630I
a = 0.336906 + 0.967331I
b = 0.805910 0.029245I
0.98162 5.70269I 0
u = 0.614088 1.240630I
a = 0.336906 0.967331I
b = 0.805910 + 0.029245I
0.98162 + 5.70269I 0
u = 0.146516 + 1.378940I
a = 1.235180 + 0.504746I
b = 0.639378 0.273765I
5.54116 1.26847I 0
u = 0.146516 1.378940I
a = 1.235180 0.504746I
b = 0.639378 + 0.273765I
5.54116 + 1.26847I 0
u = 0.518714 + 0.322835I
a = 1.31956 + 2.49608I
b = 0.703637 0.519861I
3.58538 1.09348I 21.7391 + 0.I
u = 0.518714 0.322835I
a = 1.31956 2.49608I
b = 0.703637 + 0.519861I
3.58538 + 1.09348I 21.7391 + 0.I
u = 0.566763 + 0.220863I
a = 1.67423 + 0.55409I
b = 0.091554 0.741119I
3.11477 1.50552I 16.4873 + 3.6407I
u = 0.566763 0.220863I
a = 1.67423 0.55409I
b = 0.091554 + 0.741119I
3.11477 + 1.50552I 16.4873 3.6407I
u = 0.013734 + 0.603834I
a = 0.39739 2.50833I
b = 1.000060 + 0.601318I
0.40914 + 3.96289I 10.29324 6.29056I
u = 0.013734 0.603834I
a = 0.39739 + 2.50833I
b = 1.000060 0.601318I
0.40914 3.96289I 10.29324 + 6.29056I
18
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.766595 + 1.172660I
a = 0.124982 0.832007I
b = 1.242430 + 0.389858I
2.46228 4.69197I 0
u = 0.766595 1.172660I
a = 0.124982 + 0.832007I
b = 1.242430 0.389858I
2.46228 + 4.69197I 0
u = 1.391360 + 0.228907I
a = 0.113769 0.171494I
b = 1.083860 0.153683I
5.14793 + 3.11046I 0
u = 1.391360 0.228907I
a = 0.113769 + 0.171494I
b = 1.083860 + 0.153683I
5.14793 3.11046I 0
u = 0.63153 + 1.27627I
a = 0.020531 + 1.229020I
b = 1.182700 0.495337I
0.32456 7.07139I 0
u = 0.63153 1.27627I
a = 0.020531 1.229020I
b = 1.182700 + 0.495337I
0.32456 + 7.07139I 0
u = 0.18170 + 1.42855I
a = 1.022300 0.674010I
b = 0.592432 + 0.352205I
4.80356 6.37770I 0
u = 0.18170 1.42855I
a = 1.022300 + 0.674010I
b = 0.592432 0.352205I
4.80356 + 6.37770I 0
u = 1.37397 + 0.43638I
a = 0.221802 + 0.374664I
b = 0.999430 0.293615I
4.89879 1.87482I 0
u = 1.37397 0.43638I
a = 0.221802 0.374664I
b = 0.999430 + 0.293615I
4.89879 + 1.87482I 0
19
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.496533 + 0.253809I
a = 0.466070 0.196336I
b = 0.215534 0.709071I
3.23792 + 0.82542I 6.89615 2.38411I
u = 0.496533 0.253809I
a = 0.466070 + 0.196336I
b = 0.215534 + 0.709071I
3.23792 0.82542I 6.89615 + 2.38411I
u = 0.64896 + 1.29851I
a = 0.03387 1.54317I
b = 1.28982 + 0.67958I
2.7112 + 15.0738I 0
u = 0.64896 1.29851I
a = 0.03387 + 1.54317I
b = 1.28982 0.67958I
2.7112 15.0738I 0
u = 0.76731 + 1.25750I
a = 0.05192 1.44891I
b = 1.094440 + 0.573842I
2.09983 5.48874I 0
u = 0.76731 1.25750I
a = 0.05192 + 1.44891I
b = 1.094440 0.573842I
2.09983 + 5.48874I 0
u = 1.38692 + 0.49888I
a = 0.192033 0.307439I
b = 1.015820 0.109600I
4.78336 2.61030I 0
u = 1.38692 0.49888I
a = 0.192033 + 0.307439I
b = 1.015820 + 0.109600I
4.78336 + 2.61030I 0
u = 0.16564 + 1.47662I
a = 0.531337 0.455411I
b = 0.652875 + 0.220274I
1.60056 2.69066I 0
u = 0.16564 1.47662I
a = 0.531337 + 0.455411I
b = 0.652875 0.220274I
1.60056 + 2.69066I 0
20
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.68289 + 1.32024I
a = 0.04204 + 1.51465I
b = 1.28754 0.67942I
0.6343 + 20.9175I 0
u = 0.68289 1.32024I
a = 0.04204 1.51465I
b = 1.28754 + 0.67942I
0.6343 20.9175I 0
u = 0.60498 + 1.36829I
a = 0.05591 + 1.45303I
b = 1.097990 0.508722I
0.17372 6.69047I 0
u = 0.60498 1.36829I
a = 0.05591 1.45303I
b = 1.097990 + 0.508722I
0.17372 + 6.69047I 0
u = 0.63166 + 1.35633I
a = 0.235837 + 1.100380I
b = 1.291270 0.533265I
0.50588 6.57404I 0
u = 0.63166 1.35633I
a = 0.235837 1.100380I
b = 1.291270 + 0.533265I
0.50588 + 6.57404I 0
u = 0.275847 + 0.407167I
a = 1.313260 + 0.497056I
b = 1.361700 0.253712I
3.66517 7.66196I 18.6801 + 1.6819I
u = 0.275847 0.407167I
a = 1.313260 0.497056I
b = 1.361700 + 0.253712I
3.66517 + 7.66196I 18.6801 1.6819I
u = 0.205389 + 0.430760I
a = 0.74249 + 1.21447I
b = 0.620928 0.135571I
0.447847 + 0.185650I 12.14694 + 0.21668I
u = 0.205389 0.430760I
a = 0.74249 1.21447I
b = 0.620928 + 0.135571I
0.447847 0.185650I 12.14694 0.21668I
21
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.73692 + 1.35526I
a = 0.161369 0.932804I
b = 1.303480 + 0.460573I
1.53863 10.41700I 0
u = 0.73692 1.35526I
a = 0.161369 + 0.932804I
b = 1.303480 0.460573I
1.53863 + 10.41700I 0
u = 0.410475 + 0.152923I
a = 0.448222 + 1.123910I
b = 1.201530 + 0.302554I
1.08479 2.28739I 14.2740 + 2.5495I
u = 0.410475 0.152923I
a = 0.448222 1.123910I
b = 1.201530 0.302554I
1.08479 + 2.28739I 14.2740 2.5495I
u = 0.68759 + 1.40627I
a = 0.01422 1.46818I
b = 1.088640 + 0.536050I
0.85640 10.87850I 0
u = 0.68759 1.40627I
a = 0.01422 + 1.46818I
b = 1.088640 0.536050I
0.85640 + 10.87850I 0
u = 0.19606 + 1.57358I
a = 0.474004 + 0.387596I
b = 0.777694 0.405568I
5.95156 3.30419I 0
u = 0.19606 1.57358I
a = 0.474004 0.387596I
b = 0.777694 + 0.405568I
5.95156 + 3.30419I 0
u = 0.347973 + 0.210206I
a = 1.12522 + 1.40603I
b = 1.040380 + 0.353947I
0.224627 0.064113I 9.97227 + 1.02683I
u = 0.347973 0.210206I
a = 1.12522 1.40603I
b = 1.040380 0.353947I
0.224627 + 0.064113I 9.97227 1.02683I
22
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.12611 + 1.68152I
a = 0.452111 0.405072I
b = 0.794743 + 0.354300I
4.54856 8.35215I 0
u = 0.12611 1.68152I
a = 0.452111 + 0.405072I
b = 0.794743 0.354300I
4.54856 + 8.35215I 0
u = 0.267414
a = 1.42355
b = 0.334187
0.620927 15.7220
23
II. I
u
2
= h−5.30 × 10
15
u
45
+ 9.12 × 10
16
u
44
+ · · · + 9.18 × 10
14
b 6.46 ×
10
16
, 1.83 × 10
17
u
45
3.25 × 10
18
u
44
+ · · · + 6.43 × 10
15
a + 4.76 ×
10
17
, u
46
18u
45
+ · · · 97u + 7i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
5
=
28.5097u
45
+ 505.991u
44
+ ··· + 886.309u 74.1180
5.77597u
45
99.2802u
44
+ ··· 994.275u + 70.3521
a
9
=
1
u
2
a
10
=
15.0747u
45
268.348u
44
+ ··· + 554.289u 21.2840
7.43867u
45
134.635u
44
+ ··· + 839.080u 54.1122
a
4
=
22.7338u
45
+ 406.710u
44
+ ··· 107.966u 3.76591
5.77597u
45
99.2802u
44
+ ··· 994.275u + 70.3521
a
3
=
24.2349u
45
+ 449.377u
44
+ ··· 3504.79u + 236.916
24.6720u
45
428.236u
44
+ ··· 2642.82u + 207.513
a
7
=
20.8875u
45
+ 376.575u
44
+ ··· 1374.44u + 74.0263
0.599368u
45
+ 3.82512u
44
+ ··· 2048.07u + 152.213
a
1
=
16.8674u
45
+ 319.430u
44
+ ··· 3591.66u + 250.074
0.599368u
45
+ 3.82512u
44
+ ··· 2041.07u + 152.213
a
11
=
u
u
3
+ u
a
6
=
21.6262u
45
+ 383.716u
44
+ ··· 611.001u + 14.9556
2.41597u
45
+ 55.0604u
44
+ ··· 1876.51u + 136.229
a
2
=
1.32204u
45
+ 18.4605u
44
+ ··· + 1429.06u 105.726
1.56461u
45
+ 42.1820u
44
+ ··· 2068.46u + 142.873
(ii) Obstruction class = 1
(iii) Cusp Shapes =
95792388053740867
918144026274199
u
45
1807087590774948112
918144026274199
u
44
+ ··· +
16196303759661442603
918144026274199
u
1172152646790843432
918144026274199
24
(iv) u-Polynomials at the component
25
Crossings u-Polynomials at each crossing
c
1
u
46
25u
45
+ ··· 35u + 1
c
2
u
46
+ 3u
45
+ ··· + 7u 1
c
3
u
46
u
45
+ ··· u 1
c
4
u
46
+ u
45
+ ··· + 20u
2
1
c
5
u
46
3u
45
+ ··· 7u 1
c
6
u
46
u
45
+ ··· + u 1
c
7
u
46
u
45
+ ··· + 20u
2
1
c
8
u
46
18u
45
+ ··· 97u + 7
c
9
u
46
+ 6u
44
+ ··· 46u + 7
c
10
u
46
4u
45
+ ··· 3u + 1
c
11
u
46
+ 18u
45
+ ··· + 97u + 7
c
12
u
46
7u
45
+ ··· + 27u 7
26
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
+ 3y
45
+ ··· 67y + 1
c
2
, c
5
y
46
25y
45
+ ··· 35y + 1
c
3
y
46
19y
45
+ ··· + y + 1
c
4
, c
7
y
46
27y
45
+ ··· 40y + 1
c
6
y
46
+ 23y
45
+ ··· + 15y + 1
c
8
, c
11
y
46
+ 24y
45
+ ··· + 657y + 49
c
9
y
46
+ 12y
45
+ ··· 3642y + 49
c
10
y
46
12y
45
+ ··· + 35y + 1
c
12
y
46
21y
45
+ ··· 281y + 49
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.161201 + 1.010030I
a = 0.15965 + 1.90225I
b = 0.00231 1.56197I
5.69748 3.64709I 0
u = 0.161201 1.010030I
a = 0.15965 1.90225I
b = 0.00231 + 1.56197I
5.69748 + 3.64709I 0
u = 0.147064 + 0.934830I
a = 0.56971 2.07224I
b = 0.38183 + 1.58226I
5.39271 + 2.38484I 0
u = 0.147064 0.934830I
a = 0.56971 + 2.07224I
b = 0.38183 1.58226I
5.39271 2.38484I 0
u = 0.390365 + 0.833934I
a = 0.07708 1.73979I
b = 1.66920 + 0.07137I
8.64527 1.68385I 0
u = 0.390365 0.833934I
a = 0.07708 + 1.73979I
b = 1.66920 0.07137I
8.64527 + 1.68385I 0
u = 1.128490 + 0.017970I
a = 0.502983 0.095250I
b = 0.893352 + 0.127136I
2.95664 + 0.13475I 0
u = 1.128490 0.017970I
a = 0.502983 + 0.095250I
b = 0.893352 0.127136I
2.95664 0.13475I 0
u = 0.247199 + 0.779763I
a = 0.87119 3.23577I
b = 0.754240 + 0.261816I
2.41680 + 3.37824I 0
u = 0.247199 0.779763I
a = 0.87119 + 3.23577I
b = 0.754240 0.261816I
2.41680 3.37824I 0
29
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.365182 + 0.727919I
a = 1.18396 + 3.13974I
b = 0.689378 0.215443I
0.52681 + 8.99486I 0
u = 0.365182 0.727919I
a = 1.18396 3.13974I
b = 0.689378 + 0.215443I
0.52681 8.99486I 0
u = 0.035139 + 0.807159I
a = 0.11432 1.77557I
b = 1.136010 + 0.593494I
0.68717 + 2.04100I 0
u = 0.035139 0.807159I
a = 0.11432 + 1.77557I
b = 1.136010 0.593494I
0.68717 2.04100I 0
u = 0.152031 + 1.198330I
a = 0.794584 + 0.852769I
b = 0.539929 0.557970I
2.56334 2.50675I 0
u = 0.152031 1.198330I
a = 0.794584 0.852769I
b = 0.539929 + 0.557970I
2.56334 + 2.50675I 0
u = 0.369769 + 1.158630I
a = 0.31893 + 1.69472I
b = 1.260290 0.477165I
1.47815 4.23898I 0
u = 0.369769 1.158630I
a = 0.31893 1.69472I
b = 1.260290 + 0.477165I
1.47815 + 4.23898I 0
u = 0.473559 + 1.177910I
a = 0.399000 0.568405I
b = 0.519783 + 0.733946I
0.73688 4.35112I 0
u = 0.473559 1.177910I
a = 0.399000 + 0.568405I
b = 0.519783 0.733946I
0.73688 + 4.35112I 0
30
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.722715
a = 0.901668
b = 0.357360
2.60560 12.0000
u = 0.071164 + 0.689648I
a = 0.488407 + 0.954185I
b = 1.392370 + 0.117735I
0.91429 + 2.18439I 0
u = 0.071164 0.689648I
a = 0.488407 0.954185I
b = 1.392370 0.117735I
0.91429 2.18439I 0
u = 0.424745 + 1.318440I
a = 0.323154 1.374540I
b = 1.226680 + 0.502394I
0.92317 9.69617I 0
u = 0.424745 1.318440I
a = 0.323154 + 1.374540I
b = 1.226680 0.502394I
0.92317 + 9.69617I 0
u = 0.006183 + 1.390720I
a = 0.772448 0.725439I
b = 0.608232 + 0.017464I
5.24284 1.96480I 0
u = 0.006183 1.390720I
a = 0.772448 + 0.725439I
b = 0.608232 0.017464I
5.24284 + 1.96480I 0
u = 0.060647 + 0.596741I
a = 0.164880 0.885796I
b = 1.45808 0.11795I
3.07499 + 8.07629I 9.56631 6.66944I
u = 0.060647 0.596741I
a = 0.164880 + 0.885796I
b = 1.45808 + 0.11795I
3.07499 8.07629I 9.56631 + 6.66944I
u = 1.285340 + 0.557109I
a = 0.153701 0.082501I
b = 0.996480 + 0.292406I
3.74166 + 1.85997I 0
31
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.285340 0.557109I
a = 0.153701 + 0.082501I
b = 0.996480 0.292406I
3.74166 1.85997I 0
u = 1.42783 + 0.04521I
a = 0.354262 + 0.235727I
b = 0.918573 0.249081I
4.19186 + 3.80881I 0
u = 1.42783 0.04521I
a = 0.354262 0.235727I
b = 0.918573 + 0.249081I
4.19186 3.80881I 0
u = 0.29952 + 1.42582I
a = 0.259863 + 0.459733I
b = 0.439838 0.275947I
1.85604 2.01319I 0
u = 0.29952 1.42582I
a = 0.259863 0.459733I
b = 0.439838 + 0.275947I
1.85604 + 2.01319I 0
u = 0.76366 + 1.25343I
a = 0.070074 + 1.184620I
b = 1.131970 0.537323I
1.30729 9.05066I 0
u = 0.76366 1.25343I
a = 0.070074 1.184620I
b = 1.131970 + 0.537323I
1.30729 + 9.05066I 0
u = 0.057885 + 0.526494I
a = 0.61500 + 4.47144I
b = 0.486904 0.449428I
3.06413 + 1.15341I 4.48050 7.14460I
u = 0.057885 0.526494I
a = 0.61500 4.47144I
b = 0.486904 + 0.449428I
3.06413 1.15341I 4.48050 + 7.14460I
u = 0.03744 + 1.49501I
a = 0.493033 + 0.711832I
b = 0.594880 0.087702I
4.23209 6.98802I 0
32
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.03744 1.49501I
a = 0.493033 0.711832I
b = 0.594880 + 0.087702I
4.23209 + 6.98802I 0
u = 1.47046 + 0.40220I
a = 0.213563 + 0.169355I
b = 0.962670 0.272821I
4.39013 1.65137I 0
u = 1.47046 0.40220I
a = 0.213563 0.169355I
b = 0.962670 + 0.272821I
4.39013 + 1.65137I 0
u = 0.67745 + 1.37172I
a = 0.082112 1.173210I
b = 1.167440 + 0.503445I
0.82242 5.74929I 0
u = 0.67745 1.37172I
a = 0.082112 + 1.173210I
b = 1.167440 0.503445I
0.82242 + 5.74929I 0
u = 0.236842
a = 2.72539
b = 1.36364
7.84349 19.3370
33
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
46
25u
45
+ ··· 35u + 1)(u
183
+ 82u
182
+ ··· + 16u + 1)
c
2
(u
46
+ 3u
45
+ ··· + 7u 1)(u
183
+ 4u
182
+ ··· + 20u + 1)
c
3
(u
46
u
45
+ ··· u 1)(u
183
+ 2u
182
+ ··· + 136040u + 44287)
c
4
(u
46
+ u
45
+ ··· + 20u
2
1)(u
183
+ 2u
182
+ ··· + 30967u + 8921)
c
5
(u
46
3u
45
+ ··· 7u 1)(u
183
+ 4u
182
+ ··· + 20u + 1)
c
6
(u
46
u
45
+ ··· + u 1)(u
183
2u
182
+ ··· + 10862u + 527)
c
7
(u
46
u
45
+ ··· + 20u
2
1)(u
183
+ 2u
182
+ ··· + 30967u + 8921)
c
8
(u
46
18u
45
+ ··· 97u + 7)(u
183
+ 13u
182
+ ··· + 6260u + 3952)
c
9
(u
46
+ 6u
44
+ ··· 46u + 7)
· (u
183
u
182
+ ··· + 36530383u + 15439309)
c
10
(u
46
4u
45
+ ··· 3u + 1)(u
183
13u
182
+ ··· + 808u + 1)
c
11
(u
46
+ 18u
45
+ ··· + 97u + 7)(u
183
+ 13u
182
+ ··· + 6260u + 3952)
c
12
(u
46
7u
45
+ ··· + 27u 7)(u
183
+ 8u
182
+ ··· 9354518u + 728723)
34
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
46
+ 3y
45
+ ··· 67y + 1)(y
183
+ 50y
182
+ ··· + 4624y 1)
c
2
, c
5
(y
46
25y
45
+ ··· 35y + 1)(y
183
82y
182
+ ··· + 16y 1)
c
3
(y
46
19y
45
+ ··· + y + 1)
· (y
183
+ 4y
182
+ ··· 261117339144y 1961338369)
c
4
, c
7
(y
46
27y
45
+ ··· 40y + 1)
· (y
183
100y
182
+ ··· + 3828341213y 79584241)
c
6
(y
46
+ 23y
45
+ ··· + 15y + 1)
· (y
183
+ 26y
182
+ ··· 28715838y 277729)
c
8
, c
11
(y
46
+ 24y
45
+ ··· + 657y + 49)
· (y
183
+ 99y
182
+ ··· 447121808y 15618304)
c
9
(y
46
+ 12y
45
+ ··· 3642y + 49)
· (y
183
y
182
+ ··· + 6862895901260619y 238372262397481)
c
10
(y
46
12y
45
+ ··· + 35y + 1)(y
183
+ 15y
182
+ ··· + 315098y 1)
c
12
(y
46
21y
45
+ ··· 281y + 49)
· (y
183
+ 2y
182
+ ··· 44241446103030y 531037210729)
35