12a
0754
(K12a
0754
)
A knot diagram
1
Linearized knot diagam
3 8 10 9 1 11 2 6 12 7 4 5
Solving Sequence
2,7
8 3
1,11
6 9 5 10 4 12
c
7
c
2
c
1
c
6
c
8
c
5
c
10
c
3
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.46501 × 10
559
u
176
3.76087 × 10
559
u
175
+ ··· + 3.16375 × 10
560
b 5.29003 × 10
561
,
1.55061 × 10
560
u
176
1.24993 × 10
560
u
175
+ ··· + 6.89926 × 10
560
a 2.74571 × 10
562
,
u
177
+ u
176
+ ··· 113u + 181i
I
u
2
= h77050238748u
45
49060443352u
44
+ ··· + 31929802369b 481900138262,
331992933622u
45
546861658639u
44
+ ··· + 31929802369a + 478475058213,
u
46
14u
44
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 223 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−4.47 × 10
559
u
176
3.76 × 10
559
u
175
+ · · · + 3.16 × 10
560
b 5.29 ×
10
561
, 1.55 × 10
560
u
176
1.25 × 10
560
u
175
+ · · · + 6.90 × 10
560
a 2.75 ×
10
562
, u
177
+ u
176
+ · · · 113u + 181i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
u
3
+ u
a
11
=
0.224751u
176
+ 0.181169u
175
+ ··· 91.7426u + 39.7972
0.141130u
176
+ 0.118874u
175
+ ··· 50.5273u + 16.7208
a
6
=
0.0966568u
176
+ 0.154708u
175
+ ··· + 73.3219u 43.4893
0.0682880u
176
+ 0.0385578u
175
+ ··· + 40.6569u 20.0654
a
9
=
0.110994u
176
+ 0.0695990u
175
+ ··· 132.292u + 49.7926
0.0211045u
176
0.0878728u
175
+ ··· 73.3585u + 41.7302
a
5
=
0.00914328u
176
+ 0.00801270u
175
+ ··· + 86.7261u 33.6343
0.0205661u
176
0.0320211u
175
+ ··· + 30.3503u 4.79365
a
10
=
0.0836203u
176
+ 0.0622956u
175
+ ··· 41.2152u + 23.0764
0.141130u
176
+ 0.118874u
175
+ ··· 50.5273u + 16.7208
a
4
=
0.0277595u
176
+ 0.180289u
175
+ ··· 6.60090u 14.9261
0.0125667u
176
+ 0.0103138u
175
+ ··· 29.9452u + 3.75498
a
12
=
0.0206965u
176
0.105243u
175
+ ··· + 42.4728u + 20.1661
0.121159u
176
+ 0.164325u
175
+ ··· + 14.5812u 26.0587
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.724599u
176
+ 1.40135u
175
+ ··· 17.4844u 116.459
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
177
+ 89u
176
+ ··· + 1149811u + 32761
c
2
, c
7
u
177
+ u
176
+ ··· 113u + 181
c
3
u
177
+ 16u
175
+ ··· + 2770141136u + 148430897
c
4
u
177
+ 2u
176
+ ··· 118u 47
c
5
, c
12
u
177
68u
175
+ ··· 8904u + 467
c
6
, c
10
u
177
+ 51u
175
+ ··· + 1008921u + 96053
c
8
u
177
10u
176
+ ··· + 224156u + 83191
c
9
u
177
+ 13u
176
+ ··· 3396057u 216341
c
11
u
177
4u
176
+ ··· 500u + 41
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
177
+ 15y
176
+ ··· + 55508891787y 1073283121
c
2
, c
7
y
177
89y
176
+ ··· + 1149811y 32761
c
3
y
177
+ 32y
176
+ ··· 268829528448372104y 22031731184224609
c
4
y
177
32y
176
+ ··· + 102002y 2209
c
5
, c
12
y
177
136y
176
+ ··· 143543164y 218089
c
6
, c
10
y
177
+ 102y
176
+ ··· 436351764825y 9226178809
c
8
y
177
30y
176
+ ··· + 663714149210y 6920742481
c
9
y
177
+ 43y
176
+ ··· 5046528559981y 46803428281
c
11
y
177
14y
176
+ ··· + 185384y 1681
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.974325 + 0.222085I
a = 0.81562 + 2.35721I
b = 0.09517 + 1.55029I
6.50033 2.27440I 0
u = 0.974325 0.222085I
a = 0.81562 2.35721I
b = 0.09517 1.55029I
6.50033 + 2.27440I 0
u = 0.995811 + 0.113591I
a = 0.03619 2.56105I
b = 0.210574 1.363500I
6.60802 + 1.95285I 0
u = 0.995811 0.113591I
a = 0.03619 + 2.56105I
b = 0.210574 + 1.363500I
6.60802 1.95285I 0
u = 0.891267 + 0.464106I
a = 1.80760 1.69279I
b = 0.148991 0.762299I
0.290980 + 0.835797I 0
u = 0.891267 0.464106I
a = 1.80760 + 1.69279I
b = 0.148991 + 0.762299I
0.290980 0.835797I 0
u = 0.932751 + 0.374408I
a = 0.347062 0.824795I
b = 1.238490 + 0.232968I
0.20430 + 1.61888I 0
u = 0.932751 0.374408I
a = 0.347062 + 0.824795I
b = 1.238490 0.232968I
0.20430 1.61888I 0
u = 0.249112 + 0.975833I
a = 0.059917 0.579235I
b = 0.401271 1.184370I
5.10078 + 5.95524I 0
u = 0.249112 0.975833I
a = 0.059917 + 0.579235I
b = 0.401271 + 1.184370I
5.10078 5.95524I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.659460 + 0.739964I
a = 0.265306 0.602206I
b = 0.602881 0.581728I
0.50499 5.98199I 0
u = 0.659460 0.739964I
a = 0.265306 + 0.602206I
b = 0.602881 + 0.581728I
0.50499 + 5.98199I 0
u = 0.960156 + 0.320973I
a = 2.51324 + 3.47680I
b = 0.036699 + 0.860470I
4.97745 3.70596I 0
u = 0.960156 0.320973I
a = 2.51324 3.47680I
b = 0.036699 0.860470I
4.97745 + 3.70596I 0
u = 0.327466 + 0.959605I
a = 0.373522 + 0.507460I
b = 0.623318 + 1.250290I
3.9652 14.7921I 0
u = 0.327466 0.959605I
a = 0.373522 0.507460I
b = 0.623318 1.250290I
3.9652 + 14.7921I 0
u = 0.873905 + 0.453283I
a = 0.18625 + 1.54037I
b = 1.080860 + 0.499009I
0.24529 4.90883I 0
u = 0.873905 0.453283I
a = 0.18625 1.54037I
b = 1.080860 0.499009I
0.24529 + 4.90883I 0
u = 0.407136 + 0.876029I
a = 0.228493 0.230111I
b = 0.625577 1.213760I
0.65768 + 8.86127I 0
u = 0.407136 0.876029I
a = 0.228493 + 0.230111I
b = 0.625577 + 1.213760I
0.65768 8.86127I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.929681 + 0.252073I
a = 1.98508 1.54026I
b = 0.101282 + 0.438544I
4.69188 + 6.03218I 0
u = 0.929681 0.252073I
a = 1.98508 + 1.54026I
b = 0.101282 0.438544I
4.69188 6.03218I 0
u = 0.891310 + 0.531806I
a = 0.659025 + 0.106796I
b = 0.613693 + 0.630340I
0.962538 + 0.626000I 0
u = 0.891310 0.531806I
a = 0.659025 0.106796I
b = 0.613693 0.630340I
0.962538 0.626000I 0
u = 0.484590 + 0.828041I
a = 0.455710 0.186890I
b = 0.390296 1.060170I
1.27015 3.46858I 0
u = 0.484590 0.828041I
a = 0.455710 + 0.186890I
b = 0.390296 + 1.060170I
1.27015 + 3.46858I 0
u = 0.981309 + 0.356252I
a = 0.0327071 0.1150610I
b = 0.825548 + 0.833562I
4.80627 + 0.53223I 0
u = 0.981309 0.356252I
a = 0.0327071 + 0.1150610I
b = 0.825548 0.833562I
4.80627 0.53223I 0
u = 0.801643 + 0.676667I
a = 0.535505 0.017695I
b = 0.469122 0.536520I
3.06544 2.33212I 0
u = 0.801643 0.676667I
a = 0.535505 + 0.017695I
b = 0.469122 + 0.536520I
3.06544 + 2.33212I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.997233 + 0.341494I
a = 1.00789 + 1.50673I
b = 0.56095 + 1.59851I
7.10045 + 0.18077I 0
u = 0.997233 0.341494I
a = 1.00789 1.50673I
b = 0.56095 1.59851I
7.10045 0.18077I 0
u = 0.425461 + 0.839516I
a = 0.655201 + 0.424317I
b = 0.541164 + 0.346849I
1.55079 0.51771I 0
u = 0.425461 0.839516I
a = 0.655201 0.424317I
b = 0.541164 0.346849I
1.55079 + 0.51771I 0
u = 0.672996 + 0.819837I
a = 0.809570 0.195709I
b = 0.293941 + 0.657252I
0.20302 1.64601I 0
u = 0.672996 0.819837I
a = 0.809570 + 0.195709I
b = 0.293941 0.657252I
0.20302 + 1.64601I 0
u = 0.936300
a = 1.21722
b = 0.597295
2.21006 0
u = 0.546028 + 0.739177I
a = 0.91845 + 1.25629I
b = 0.353663 + 0.981728I
1.28885 + 4.62079I 0
u = 0.546028 0.739177I
a = 0.91845 1.25629I
b = 0.353663 0.981728I
1.28885 4.62079I 0
u = 0.652726 + 0.646500I
a = 0.619657 + 0.655257I
b = 0.623344 + 0.968272I
0.26043 + 4.06910I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.652726 0.646500I
a = 0.619657 0.655257I
b = 0.623344 0.968272I
0.26043 4.06910I 0
u = 0.865311 + 0.268129I
a = 1.34391 + 3.02315I
b = 0.518492 + 1.045400I
4.20869 3.12674I 0
u = 0.865311 0.268129I
a = 1.34391 3.02315I
b = 0.518492 1.045400I
4.20869 + 3.12674I 0
u = 0.019928 + 0.897306I
a = 1.023540 0.325536I
b = 0.438641 0.962197I
4.15749 1.66209I 0
u = 0.019928 0.897306I
a = 1.023540 + 0.325536I
b = 0.438641 + 0.962197I
4.15749 + 1.66209I 0
u = 0.984173 + 0.497443I
a = 0.525993 + 0.587716I
b = 0.548453 0.164878I
0.21065 4.60175I 0
u = 0.984173 0.497443I
a = 0.525993 0.587716I
b = 0.548453 + 0.164878I
0.21065 + 4.60175I 0
u = 0.870051 + 0.679152I
a = 0.313124 + 0.500964I
b = 0.323064 0.402527I
2.87655 2.88564I 0
u = 0.870051 0.679152I
a = 0.313124 0.500964I
b = 0.323064 + 0.402527I
2.87655 + 2.88564I 0
u = 1.023420 + 0.414546I
a = 0.59669 + 2.65233I
b = 0.25466 + 1.43283I
8.30031 2.14999I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.023420 0.414546I
a = 0.59669 2.65233I
b = 0.25466 1.43283I
8.30031 + 2.14999I 0
u = 1.003530 + 0.468682I
a = 1.007460 0.720630I
b = 1.249210 + 0.598406I
0.280054 + 0.456269I 0
u = 1.003530 0.468682I
a = 1.007460 + 0.720630I
b = 1.249210 0.598406I
0.280054 0.456269I 0
u = 0.982907 + 0.512624I
a = 1.30656 2.51647I
b = 0.358370 1.078470I
0.86960 + 5.99499I 0
u = 0.982907 0.512624I
a = 1.30656 + 2.51647I
b = 0.358370 + 1.078470I
0.86960 5.99499I 0
u = 0.664022 + 0.902110I
a = 0.268917 + 0.282201I
b = 0.314378 + 0.879919I
2.10337 4.61954I 0
u = 0.664022 0.902110I
a = 0.268917 0.282201I
b = 0.314378 0.879919I
2.10337 + 4.61954I 0
u = 0.352863 + 1.065400I
a = 0.443332 + 0.605358I
b = 0.486671 + 1.071910I
3.61595 + 4.69476I 0
u = 0.352863 1.065400I
a = 0.443332 0.605358I
b = 0.486671 1.071910I
3.61595 4.69476I 0
u = 0.367583 + 0.796928I
a = 0.589023 + 0.487069I
b = 1.048850 + 0.291504I
0.95048 + 8.79821I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.367583 0.796928I
a = 0.589023 0.487069I
b = 1.048850 0.291504I
0.95048 8.79821I 0
u = 1.123410 + 0.148227I
a = 0.147814 + 0.129479I
b = 0.463378 0.322398I
6.76781 1.75341I 0
u = 1.123410 0.148227I
a = 0.147814 0.129479I
b = 0.463378 + 0.322398I
6.76781 + 1.75341I 0
u = 0.861289 + 0.741903I
a = 0.87342 1.18739I
b = 0.441231 0.715211I
0.091216 + 0.552522I 0
u = 0.861289 0.741903I
a = 0.87342 + 1.18739I
b = 0.441231 + 0.715211I
0.091216 0.552522I 0
u = 1.086500 + 0.349977I
a = 0.21485 2.17760I
b = 0.020473 1.231930I
8.19104 3.38162I 0
u = 1.086500 0.349977I
a = 0.21485 + 2.17760I
b = 0.020473 + 1.231930I
8.19104 + 3.38162I 0
u = 1.027750 + 0.501132I
a = 2.55206 + 1.43844I
b = 0.338256 + 1.215810I
7.70017 8.42877I 0
u = 1.027750 0.501132I
a = 2.55206 1.43844I
b = 0.338256 1.215810I
7.70017 + 8.42877I 0
u = 1.012670 + 0.531949I
a = 0.213014 + 1.212140I
b = 1.113660 + 0.102945I
0.56443 5.15617I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.012670 0.531949I
a = 0.213014 1.212140I
b = 1.113660 0.102945I
0.56443 + 5.15617I 0
u = 1.135000 + 0.178422I
a = 0.406463 + 0.890434I
b = 0.901111 0.067709I
5.88446 6.20711I 0
u = 1.135000 0.178422I
a = 0.406463 0.890434I
b = 0.901111 + 0.067709I
5.88446 + 6.20711I 0
u = 1.115390 + 0.308103I
a = 0.91644 + 1.59936I
b = 0.400309 + 1.255670I
3.51682 0.04625I 0
u = 1.115390 0.308103I
a = 0.91644 1.59936I
b = 0.400309 1.255670I
3.51682 + 0.04625I 0
u = 1.138060 + 0.232237I
a = 0.93177 2.34296I
b = 0.365094 1.318450I
6.43755 + 3.41743I 0
u = 1.138060 0.232237I
a = 0.93177 + 2.34296I
b = 0.365094 + 1.318450I
6.43755 3.41743I 0
u = 0.330093 + 0.769389I
a = 0.390812 0.649588I
b = 0.57301 1.31805I
1.84585 6.20965I 0
u = 0.330093 0.769389I
a = 0.390812 + 0.649588I
b = 0.57301 + 1.31805I
1.84585 + 6.20965I 0
u = 0.390387 + 0.731665I
a = 0.0947310 + 0.0770864I
b = 0.311756 + 1.136680I
2.02526 + 0.37726I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.390387 0.731665I
a = 0.0947310 0.0770864I
b = 0.311756 1.136680I
2.02526 0.37726I 0
u = 1.039380 + 0.546545I
a = 0.498307 + 0.650794I
b = 1.293830 0.347290I
1.66142 + 7.48678I 0
u = 1.039380 0.546545I
a = 0.498307 0.650794I
b = 1.293830 + 0.347290I
1.66142 7.48678I 0
u = 0.648891 + 0.507118I
a = 0.732167 0.973907I
b = 0.518833 0.948226I
1.93320 1.79902I 0
u = 0.648891 0.507118I
a = 0.732167 + 0.973907I
b = 0.518833 + 0.948226I
1.93320 + 1.79902I 0
u = 1.104650 + 0.426014I
a = 1.48771 1.81697I
b = 0.462698 1.325560I
9.81624 + 0.99624I 0
u = 1.104650 0.426014I
a = 1.48771 + 1.81697I
b = 0.462698 + 1.325560I
9.81624 0.99624I 0
u = 1.096900 + 0.446500I
a = 0.95320 1.83733I
b = 0.25057 1.58336I
9.69077 + 8.37862I 0
u = 1.096900 0.446500I
a = 0.95320 + 1.83733I
b = 0.25057 + 1.58336I
9.69077 8.37862I 0
u = 1.051180 + 0.550355I
a = 1.12587 + 1.48729I
b = 0.88961 + 1.25216I
5.57613 + 6.49569I 0
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.051180 0.550355I
a = 1.12587 1.48729I
b = 0.88961 1.25216I
5.57613 6.49569I 0
u = 1.055240 + 0.551970I
a = 0.003634 + 0.617367I
b = 1.025790 + 0.254662I
3.27346 + 6.74423I 0
u = 1.055240 0.551970I
a = 0.003634 0.617367I
b = 1.025790 0.254662I
3.27346 6.74423I 0
u = 0.799610 + 0.891804I
a = 0.145253 0.185821I
b = 0.312267 0.830509I
0.33983 3.80682I 0
u = 0.799610 0.891804I
a = 0.145253 + 0.185821I
b = 0.312267 + 0.830509I
0.33983 + 3.80682I 0
u = 0.468435 + 0.645537I
a = 0.070806 0.956949I
b = 0.708818 + 0.071839I
1.54515 2.05417I 0
u = 0.468435 0.645537I
a = 0.070806 + 0.956949I
b = 0.708818 0.071839I
1.54515 + 2.05417I 0
u = 1.055420 + 0.594328I
a = 1.51699 + 2.46869I
b = 0.268183 + 1.081570I
2.85988 9.70816I 0
u = 1.055420 0.594328I
a = 1.51699 2.46869I
b = 0.268183 1.081570I
2.85988 + 9.70816I 0
u = 0.504912 + 0.601844I
a = 0.569631 0.252506I
b = 0.925046 0.071562I
2.03264 + 0.63861I 0
14
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.504912 0.601844I
a = 0.569631 + 0.252506I
b = 0.925046 + 0.071562I
2.03264 0.63861I 0
u = 0.495482 + 0.608806I
a = 0.863460 1.011800I
b = 1.028980 0.423868I
3.26580 2.89404I 0
u = 0.495482 0.608806I
a = 0.863460 + 1.011800I
b = 1.028980 + 0.423868I
3.26580 + 2.89404I 0
u = 0.488278 + 0.604002I
a = 0.041005 0.887723I
b = 0.666559 + 1.091920I
3.90652 1.88381I 0
u = 0.488278 0.604002I
a = 0.041005 + 0.887723I
b = 0.666559 1.091920I
3.90652 + 1.88381I 0
u = 0.858231 + 0.873414I
a = 0.628898 0.604327I
b = 0.450774 0.932398I
0.49636 + 10.15920I 0
u = 0.858231 0.873414I
a = 0.628898 + 0.604327I
b = 0.450774 + 0.932398I
0.49636 10.15920I 0
u = 1.108730 + 0.520242I
a = 1.85998 0.96803I
b = 0.056669 0.926003I
6.97607 + 3.98114I 0
u = 1.108730 0.520242I
a = 1.85998 + 0.96803I
b = 0.056669 + 0.926003I
6.97607 3.98114I 0
u = 1.006440 + 0.702596I
a = 0.171521 0.425462I
b = 0.243608 + 0.604162I
1.23044 + 7.33913I 0
15
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.006440 0.702596I
a = 0.171521 + 0.425462I
b = 0.243608 0.604162I
1.23044 7.33913I 0
u = 1.109580 + 0.528391I
a = 1.06762 + 2.02611I
b = 0.74657 + 1.25686I
2.05189 7.59547I 0
u = 1.109580 0.528391I
a = 1.06762 2.02611I
b = 0.74657 1.25686I
2.05189 + 7.59547I 0
u = 1.092170 + 0.571577I
a = 1.15218 + 1.62123I
b = 0.47571 + 1.36734I
4.07554 + 4.57508I 0
u = 1.092170 0.571577I
a = 1.15218 1.62123I
b = 0.47571 1.36734I
4.07554 4.57508I 0
u = 1.232800 + 0.072488I
a = 0.49681 1.83437I
b = 0.365136 1.277640I
5.16632 6.17185I 0
u = 1.232800 0.072488I
a = 0.49681 + 1.83437I
b = 0.365136 + 1.277640I
5.16632 + 6.17185I 0
u = 1.123220 + 0.525229I
a = 0.940313 0.153598I
b = 0.849477 0.529011I
1.90407 1.49651I 0
u = 1.123220 0.525229I
a = 0.940313 + 0.153598I
b = 0.849477 + 0.529011I
1.90407 + 1.49651I 0
u = 1.181400 + 0.391639I
a = 1.08787 1.59805I
b = 0.616078 0.970757I
8.04591 + 5.92997I 0
16
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.181400 0.391639I
a = 1.08787 + 1.59805I
b = 0.616078 + 0.970757I
8.04591 5.92997I 0
u = 1.150320 + 0.481785I
a = 0.86476 + 1.60291I
b = 0.307482 + 0.713035I
0.76423 4.87203I 0
u = 1.150320 0.481785I
a = 0.86476 1.60291I
b = 0.307482 0.713035I
0.76423 + 4.87203I 0
u = 1.190060 + 0.392650I
a = 0.196292 1.353840I
b = 0.323882 1.130810I
8.00674 2.72764I 0
u = 1.190060 0.392650I
a = 0.196292 + 1.353840I
b = 0.323882 + 1.130810I
8.00674 + 2.72764I 0
u = 0.289758 + 0.686660I
a = 0.048601 + 1.169220I
b = 0.415124 + 0.681082I
2.52438 + 1.38836I 0
u = 0.289758 0.686660I
a = 0.048601 1.169220I
b = 0.415124 0.681082I
2.52438 1.38836I 0
u = 1.129010 + 0.569138I
a = 1.34235 2.26774I
b = 0.58130 1.42417I
4.19561 + 11.24720I 0
u = 1.129010 0.569138I
a = 1.34235 + 2.26774I
b = 0.58130 + 1.42417I
4.19561 11.24720I 0
u = 1.101480 + 0.628453I
a = 1.42731 1.47585I
b = 0.489541 1.175260I
3.15575 + 8.91297I 0
17
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.101480 0.628453I
a = 1.42731 + 1.47585I
b = 0.489541 + 1.175260I
3.15575 8.91297I 0
u = 1.125620 + 0.588687I
a = 0.500913 0.659325I
b = 1.207430 + 0.247995I
3.2014 13.9871I 0
u = 1.125620 0.588687I
a = 0.500913 + 0.659325I
b = 1.207430 0.247995I
3.2014 + 13.9871I 0
u = 1.143270 + 0.562048I
a = 0.65089 + 1.88526I
b = 0.260346 + 0.998301I
0.04894 + 3.45668I 0
u = 1.143270 0.562048I
a = 0.65089 1.88526I
b = 0.260346 0.998301I
0.04894 3.45668I 0
u = 1.126510 + 0.610015I
a = 0.118234 0.285480I
b = 0.792595 + 0.256486I
3.69589 + 5.91340I 0
u = 1.126510 0.610015I
a = 0.118234 + 0.285480I
b = 0.792595 0.256486I
3.69589 5.91340I 0
u = 0.656573 + 0.282210I
a = 0.620116 + 0.326275I
b = 0.347383 + 0.425260I
1.177830 + 0.554388I 0
u = 0.656573 0.282210I
a = 0.620116 0.326275I
b = 0.347383 0.425260I
1.177830 0.554388I 0
u = 0.588577 + 0.394784I
a = 1.076990 + 0.908184I
b = 1.084690 + 0.721689I
1.60264 + 3.32934I 6.18548 + 0.I
18
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.588577 0.394784I
a = 1.076990 0.908184I
b = 1.084690 0.721689I
1.60264 3.32934I 6.18548 + 0.I
u = 0.293072 + 0.641560I
a = 1.120390 + 0.162745I
b = 0.159484 0.959539I
4.63986 + 0.55817I 7.38860 + 0.I
u = 0.293072 0.641560I
a = 1.120390 0.162745I
b = 0.159484 + 0.959539I
4.63986 0.55817I 7.38860 + 0.I
u = 1.222950 + 0.433474I
a = 0.28423 2.07272I
b = 0.633102 0.875296I
2.88698 + 6.94632I 0
u = 1.222950 0.433474I
a = 0.28423 + 2.07272I
b = 0.633102 + 0.875296I
2.88698 6.94632I 0
u = 0.566261 + 0.415378I
a = 1.21392 1.40032I
b = 0.156391 + 1.137680I
6.21863 + 4.42335I 7.46789 4.16553I
u = 0.566261 0.415378I
a = 1.21392 + 1.40032I
b = 0.156391 1.137680I
6.21863 4.42335I 7.46789 + 4.16553I
u = 1.137420 + 0.627599I
a = 1.11869 1.75008I
b = 0.69310 1.31971I
1.5528 14.4058I 0
u = 1.137420 0.627599I
a = 1.11869 + 1.75008I
b = 0.69310 + 1.31971I
1.5528 + 14.4058I 0
u = 0.255198 + 0.648434I
a = 0.457656 + 0.115156I
b = 0.665608 + 1.080140I
0.32056 + 3.02657I 0. 3.29197I
19
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.255198 0.648434I
a = 0.457656 0.115156I
b = 0.665608 1.080140I
0.32056 3.02657I 0. + 3.29197I
u = 1.029950 + 0.820102I
a = 0.554770 + 0.389034I
b = 0.106143 + 0.814593I
1.04908 1.65636I 0
u = 1.029950 0.820102I
a = 0.554770 0.389034I
b = 0.106143 0.814593I
1.04908 + 1.65636I 0
u = 0.352816 + 0.565392I
a = 0.774383 + 0.366800I
b = 0.570908 + 0.286454I
1.61658 + 0.72125I 4.21730 + 1.21229I
u = 0.352816 0.565392I
a = 0.774383 0.366800I
b = 0.570908 0.286454I
1.61658 0.72125I 4.21730 1.21229I
u = 0.626810 + 0.177672I
a = 0.47870 + 2.91880I
b = 0.08431 + 1.44003I
6.76022 + 5.20834I 4.82259 5.76207I
u = 0.626810 0.177672I
a = 0.47870 2.91880I
b = 0.08431 1.44003I
6.76022 5.20834I 4.82259 + 5.76207I
u = 1.196370 + 0.629202I
a = 1.12787 + 1.90257I
b = 0.65973 + 1.32275I
6.6187 + 20.5544I 0
u = 1.196370 0.629202I
a = 1.12787 1.90257I
b = 0.65973 1.32275I
6.6187 20.5544I 0
u = 1.216300 + 0.605604I
a = 0.90718 1.80818I
b = 0.443883 1.322900I
8.0436 11.6343I 0
20
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.216300 0.605604I
a = 0.90718 + 1.80818I
b = 0.443883 + 1.322900I
8.0436 + 11.6343I 0
u = 1.354970 + 0.189238I
a = 0.49967 + 1.73518I
b = 0.472680 + 1.253910I
9.7829 + 10.9783I 0
u = 1.354970 0.189238I
a = 0.49967 1.73518I
b = 0.472680 1.253910I
9.7829 10.9783I 0
u = 0.107722 + 0.611553I
a = 0.028426 0.735003I
b = 0.818313 0.725481I
0.70511 2.94977I 0.77816 + 5.38546I
u = 0.107722 0.611553I
a = 0.028426 + 0.735003I
b = 0.818313 + 0.725481I
0.70511 + 2.94977I 0.77816 5.38546I
u = 1.230940 + 0.664853I
a = 1.07152 + 1.65269I
b = 0.545595 + 1.159180I
6.36772 10.89210I 0
u = 1.230940 0.664853I
a = 1.07152 1.65269I
b = 0.545595 1.159180I
6.36772 + 10.89210I 0
u = 1.42005 + 0.27195I
a = 0.50841 1.59082I
b = 0.179495 1.147660I
10.65500 1.52947I 0
u = 1.42005 0.27195I
a = 0.50841 + 1.59082I
b = 0.179495 + 1.147660I
10.65500 + 1.52947I 0
u = 0.007192 + 0.508226I
a = 1.48448 + 0.16026I
b = 0.172573 1.339150I
6.97969 4.66343I 6.67994 + 4.47542I
21
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.007192 0.508226I
a = 1.48448 0.16026I
b = 0.172573 + 1.339150I
6.97969 + 4.66343I 6.67994 4.47542I
u = 1.48292 + 0.18695I
a = 0.15328 + 1.62185I
b = 0.297661 + 1.043810I
10.10840 0.30685I 0
u = 1.48292 0.18695I
a = 0.15328 1.62185I
b = 0.297661 1.043810I
10.10840 + 0.30685I 0
u = 1.53362 + 0.04871I
a = 0.07298 1.45600I
b = 0.080460 0.876805I
8.91789 + 1.28366I 0
u = 1.53362 0.04871I
a = 0.07298 + 1.45600I
b = 0.080460 + 0.876805I
8.91789 1.28366I 0
u = 0.353993 + 0.091545I
a = 0.576585 + 0.325449I
b = 0.777233 0.742897I
0.89957 2.81238I 4.80695 + 6.22775I
u = 0.353993 0.091545I
a = 0.576585 0.325449I
b = 0.777233 + 0.742897I
0.89957 + 2.81238I 4.80695 6.22775I
22
II. I
u
2
= h7.71 × 10
10
u
45
4.91 × 10
10
u
44
+ · · · + 3.19 × 10
10
b 4.82 ×
10
11
, 3.32 × 10
11
u
45
5.47 × 10
11
u
44
+ · · · + 3.19 × 10
10
a + 4.78 ×
10
11
, u
46
14u
44
+ · · · + 3u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
u
3
+ u
a
11
=
10.3976u
45
+ 17.1270u
44
+ ··· 50.0506u 14.9852
2.41311u
45
+ 1.53651u
44
+ ··· + 59.7551u + 15.0925
a
6
=
37.3731u
45
+ 48.7727u
44
+ ··· 145.343u 43.4124
17.5615u
45
+ 18.0553u
44
+ ··· 107.919u 29.7649
a
9
=
4.18561u
45
29.3387u
44
+ ··· 71.3477u 11.7973
10.8236u
45
1.23253u
44
+ ··· 34.6891u 9.05060
a
5
=
15.1278u
45
+ 38.0763u
44
+ ··· 65.2261u 25.2324
1.25081u
45
+ 9.13970u
44
+ ··· 56.0878u 16.6770
a
10
=
12.8107u
45
+ 15.5905u
44
+ ··· 109.806u 30.0777
2.41311u
45
+ 1.53651u
44
+ ··· + 59.7551u + 15.0925
a
4
=
56.1218u
45
+ 33.8772u
44
+ ··· 294.780u 73.6228
20.4014u
45
+ 12.0171u
44
+ ··· 24.1839u 3.82965
a
12
=
6.58372u
45
11.4548u
44
+ ··· + 99.8440u + 25.0471
27.9650u
45
35.3715u
44
+ ··· + 98.8917u + 27.0793
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
89030218431
31929802369
u
45
+
970483410583
31929802369
u
44
+ ··· +
11015325856943
31929802369
u +
2629114158335
31929802369
23
(iv) u-Polynomials at the component
24
Crossings u-Polynomials at each crossing
c
1
u
46
28u
45
+ ··· 17u + 1
c
2
u
46
14u
44
+ ··· 3u + 1
c
3
u
46
+ u
45
+ ··· + 132u + 11
c
4
u
46
+ u
45
+ ··· + 4u + 1
c
5
u
46
u
45
+ ··· + 18u + 1
c
6
u
46
u
45
+ ··· + 3u + 1
c
7
u
46
14u
44
+ ··· + 3u + 1
c
8
u
46
+ 3u
45
+ ··· + 12u + 1
c
9
u
46
+ 4u
45
+ ··· u + 1
c
10
u
46
+ u
45
+ ··· 3u + 1
c
11
u
46
u
45
+ ··· 2u + 1
c
12
u
46
+ u
45
+ ··· 18u + 1
25
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
46
4y
45
+ ··· + 47y + 1
c
2
, c
7
y
46
28y
45
+ ··· 17y + 1
c
3
y
46
7y
45
+ ··· 10582y + 121
c
4
y
46
19y
45
+ ··· + 4y + 1
c
5
, c
12
y
46
43y
45
+ ··· 98y + 1
c
6
, c
10
y
46
+ 27y
45
+ ··· + 35y + 1
c
8
y
46
21y
45
+ ··· + 68y + 1
c
9
y
46
+ 12y
45
+ ··· + 23y + 1
c
11
y
46
9y
45
+ ··· 10y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.967242 + 0.259496I
a = 1.05380 3.35382I
b = 0.125565 1.393460I
8.03600 3.76090I 11.49389 + 4.80109I
u = 0.967242 0.259496I
a = 1.05380 + 3.35382I
b = 0.125565 + 1.393460I
8.03600 + 3.76090I 11.49389 4.80109I
u = 0.429921 + 0.906941I
a = 0.440586 0.686873I
b = 0.422994 1.122700I
2.69565 + 4.90056I 4.75531 6.01424I
u = 0.429921 0.906941I
a = 0.440586 + 0.686873I
b = 0.422994 + 1.122700I
2.69565 4.90056I 4.75531 + 6.01424I
u = 0.725204 + 0.693954I
a = 0.276536 + 0.224180I
b = 0.245515 + 0.502452I
2.33974 3.60285I 0.61269 + 4.95954I
u = 0.725204 0.693954I
a = 0.276536 0.224180I
b = 0.245515 0.502452I
2.33974 + 3.60285I 0.61269 4.95954I
u = 0.939292 + 0.214126I
a = 0.670956 1.221050I
b = 0.006621 1.329610I
7.85483 + 5.69821I 11.15488 7.28120I
u = 0.939292 0.214126I
a = 0.670956 + 1.221050I
b = 0.006621 + 1.329610I
7.85483 5.69821I 11.15488 + 7.28120I
u = 0.988081 + 0.348862I
a = 0.65953 + 1.62479I
b = 0.49449 + 1.47775I
6.77873 + 0.13867I 0.84845 + 1.77413I
u = 0.988081 0.348862I
a = 0.65953 1.62479I
b = 0.49449 1.47775I
6.77873 0.13867I 0.84845 1.77413I
28
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.041620 + 0.309578I
a = 2.14648 2.83300I
b = 0.204092 0.739022I
5.19056 6.65225I 9.73982 + 9.73034I
u = 1.041620 0.309578I
a = 2.14648 + 2.83300I
b = 0.204092 + 0.739022I
5.19056 + 6.65225I 9.73982 9.73034I
u = 0.996864 + 0.468531I
a = 1.127250 0.469028I
b = 1.183350 + 0.615781I
0.239315 0.043472I 0. 8.33527I
u = 0.996864 0.468531I
a = 1.127250 + 0.469028I
b = 1.183350 0.615781I
0.239315 + 0.043472I 0. + 8.33527I
u = 0.856514 + 0.251703I
a = 0.62668 + 2.79288I
b = 0.24475 + 1.47466I
6.12295 2.65789I 5.21741 + 10.16383I
u = 0.856514 0.251703I
a = 0.62668 2.79288I
b = 0.24475 1.47466I
6.12295 + 2.65789I 5.21741 10.16383I
u = 0.996485 + 0.490399I
a = 0.151455 + 1.401610I
b = 1.109930 + 0.263672I
0.37946 + 5.76027I 2.0000 14.3388I
u = 0.996485 0.490399I
a = 0.151455 1.401610I
b = 1.109930 0.263672I
0.37946 5.76027I 2.0000 + 14.3388I
u = 0.729085 + 0.854559I
a = 0.972569 0.204713I
b = 0.177552 0.646493I
0.55218 2.11050I 6.77517 + 6.77743I
u = 0.729085 0.854559I
a = 0.972569 + 0.204713I
b = 0.177552 + 0.646493I
0.55218 + 2.11050I 6.77517 6.77743I
29
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.805306 + 0.280716I
a = 1.96923 + 2.19082I
b = 0.194423 0.603030I
4.28569 + 4.16900I 0.96371 4.22019I
u = 0.805306 0.280716I
a = 1.96923 2.19082I
b = 0.194423 + 0.603030I
4.28569 4.16900I 0.96371 + 4.22019I
u = 0.688261 + 0.466101I
a = 0.594536 0.754409I
b = 0.820598 + 0.244677I
1.44422 1.78366I 2.52994 + 3.89108I
u = 0.688261 0.466101I
a = 0.594536 + 0.754409I
b = 0.820598 0.244677I
1.44422 + 1.78366I 2.52994 3.89108I
u = 1.058940 + 0.544011I
a = 1.18927 + 1.32788I
b = 0.787281 + 1.122690I
5.22806 + 6.48862I 0
u = 1.058940 0.544011I
a = 1.18927 1.32788I
b = 0.787281 1.122690I
5.22806 6.48862I 0
u = 0.962805 + 0.706764I
a = 0.375508 + 0.233471I
b = 0.065716 0.538154I
1.28663 + 7.88982I 0
u = 0.962805 0.706764I
a = 0.375508 0.233471I
b = 0.065716 + 0.538154I
1.28663 7.88982I 0
u = 0.665853 + 0.423392I
a = 0.557072 + 0.755875I
b = 0.999022 + 0.734436I
1.36692 3.73506I 1.74396 + 12.46346I
u = 0.665853 0.423392I
a = 0.557072 0.755875I
b = 0.999022 0.734436I
1.36692 + 3.73506I 1.74396 12.46346I
30
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.140820 + 0.451564I
a = 0.74590 + 2.11225I
b = 0.430389 + 0.932359I
0.89501 + 5.66556I 0
u = 1.140820 0.451564I
a = 0.74590 2.11225I
b = 0.430389 0.932359I
0.89501 5.66556I 0
u = 1.008510 + 0.746406I
a = 0.628091 + 0.548655I
b = 0.075039 + 0.606986I
1.47367 1.93340I 0
u = 1.008510 0.746406I
a = 0.628091 0.548655I
b = 0.075039 0.606986I
1.47367 + 1.93340I 0
u = 1.130090 + 0.619557I
a = 1.39088 1.92423I
b = 0.460826 1.277380I
4.86841 10.47860I 0
u = 1.130090 0.619557I
a = 1.39088 + 1.92423I
b = 0.460826 + 1.277380I
4.86841 + 10.47860I 0
u = 0.538641 + 0.383684I
a = 1.055000 + 0.512454I
b = 0.594032 + 0.752150I
1.23640 2.06191I 2.40525 + 1.66559I
u = 0.538641 0.383684I
a = 1.055000 0.512454I
b = 0.594032 0.752150I
1.23640 + 2.06191I 2.40525 1.66559I
u = 0.272756 + 0.568907I
a = 0.977129 0.948003I
b = 0.524855 + 0.934111I
3.33196 1.98343I 1.28839 + 4.06659I
u = 0.272756 0.568907I
a = 0.977129 + 0.948003I
b = 0.524855 0.934111I
3.33196 + 1.98343I 1.28839 4.06659I
31
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.48090 + 0.03553I
a = 0.017265 + 1.379330I
b = 0.165014 + 0.984511I
9.38977 0.36803I 0
u = 1.48090 0.03553I
a = 0.017265 1.379330I
b = 0.165014 0.984511I
9.38977 + 0.36803I 0
u = 1.47989 + 0.12531I
a = 0.13181 1.74157I
b = 0.168012 0.978347I
9.37086 1.69923I 0
u = 1.47989 0.12531I
a = 0.13181 + 1.74157I
b = 0.168012 + 0.978347I
9.37086 + 1.69923I 0
u = 0.354643 + 0.364408I
a = 0.63642 2.05065I
b = 0.539342 + 0.857540I
3.32459 2.00115I 2.41651 + 4.47631I
u = 0.354643 0.364408I
a = 0.63642 + 2.05065I
b = 0.539342 0.857540I
3.32459 + 2.00115I 2.41651 4.47631I
32
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
46
28u
45
+ ··· 17u + 1)
· (u
177
+ 89u
176
+ ··· + 1149811u + 32761)
c
2
(u
46
14u
44
+ ··· 3u + 1)(u
177
+ u
176
+ ··· 113u + 181)
c
3
(u
46
+ u
45
+ ··· + 132u + 11)
· (u
177
+ 16u
175
+ ··· + 2770141136u + 148430897)
c
4
(u
46
+ u
45
+ ··· + 4u + 1)(u
177
+ 2u
176
+ ··· 118u 47)
c
5
(u
46
u
45
+ ··· + 18u + 1)(u
177
68u
175
+ ··· 8904u + 467)
c
6
(u
46
u
45
+ ··· + 3u + 1)(u
177
+ 51u
175
+ ··· + 1008921u + 96053)
c
7
(u
46
14u
44
+ ··· + 3u + 1)(u
177
+ u
176
+ ··· 113u + 181)
c
8
(u
46
+ 3u
45
+ ··· + 12u + 1)(u
177
10u
176
+ ··· + 224156u + 83191)
c
9
(u
46
+ 4u
45
+ ··· u + 1)(u
177
+ 13u
176
+ ··· 3396057u 216341)
c
10
(u
46
+ u
45
+ ··· 3u + 1)(u
177
+ 51u
175
+ ··· + 1008921u + 96053)
c
11
(u
46
u
45
+ ··· 2u + 1)(u
177
4u
176
+ ··· 500u + 41)
c
12
(u
46
+ u
45
+ ··· 18u + 1)(u
177
68u
175
+ ··· 8904u + 467)
33
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
46
4y
45
+ ··· + 47y + 1)
· (y
177
+ 15y
176
+ ··· + 55508891787y 1073283121)
c
2
, c
7
(y
46
28y
45
+ ··· 17y + 1)
· (y
177
89y
176
+ ··· + 1149811y 32761)
c
3
(y
46
7y
45
+ ··· 10582y + 121)
· (y
177
+ 32y
176
+ ··· 268829528448372104y 22031731184224609)
c
4
(y
46
19y
45
+ ··· + 4y + 1)(y
177
32y
176
+ ··· + 102002y 2209)
c
5
, c
12
(y
46
43y
45
+ ··· 98y + 1)
· (y
177
136y
176
+ ··· 143543164y 218089)
c
6
, c
10
(y
46
+ 27y
45
+ ··· + 35y + 1)
· (y
177
+ 102y
176
+ ··· 436351764825y 9226178809)
c
8
(y
46
21y
45
+ ··· + 68y + 1)
· (y
177
30y
176
+ ··· + 663714149210y 6920742481)
c
9
(y
46
+ 12y
45
+ ··· + 23y + 1)
· (y
177
+ 43y
176
+ ··· 5046528559981y 46803428281)
c
11
(y
46
9y
45
+ ··· 10y + 1)(y
177
14y
176
+ ··· + 185384y 1681)
34