12a
0688
(K12a
0688
)
A knot diagram
1
Linearized knot diagam
3 7 12 11 8 2 5 6 4 1 9 10
Solving Sequence
5,8
6
9,11
12 4 10 1 3 7 2
c
5
c
8
c
11
c
4
c
9
c
12
c
3
c
7
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.68453 × 10
93
u
111
+ 1.11304 × 10
94
u
110
+ ··· + 1.28372 × 10
91
b + 1.22997 × 10
93
,
9.04813 × 10
92
u
111
+ 6.05101 × 10
93
u
110
+ ··· + 6.41862 × 10
90
a + 6.86529 × 10
92
, u
112
+ 8u
111
+ ··· + 7u + 1i
I
u
2
= h−3a
5
− 13a
4
− 7a
3
+ 17a
2
+ 13b − 21a − 7, a
6
+ 6a
5
+ 11a
4
+ 4a
3
− a
2
+ a + 1, u − 1i
I
u
3
= hb − u − 2, a + 2u + 3, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 120 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
= h1.68 × 10
93
u
111
+ 1.11 × 10
94
u
110
+ · · · + 1.28 × 10
91
b + 1.23 ×
10
93
, 9.05 × 10
92
u
111
+ 6.05 × 10
93
u
110
+ · · · + 6.42 × 10
90
a + 6.87 ×
10
92
, u
112
+ 8u
111
+ · · · + 7u + 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
6
=
1
u
2
a
9
=
−u
−u
3
+ u
a
11
=
−140.967u
111
− 942.728u
110
+ ··· − 600.909u − 106.959
−131.222u
111
− 867.039u
110
+ ··· − 599.242u − 95.8125
a
12
=
−213.060u
111
− 1409.07u
110
+ ··· − 894.420u − 152.892
−224.762u
111
− 1481.90u
110
+ ··· − 1006.45u − 160.281
a
4
=
395.197u
111
+ 2586.54u
110
+ ··· + 1658.16u + 259.193
480.110u
111
+ 3139.69u
110
+ ··· + 2114.70u + 332.176
a
10
=
−222.614u
111
− 1474.78u
110
+ ··· − 971.574u − 159.791
−210.094u
111
− 1388.78u
110
+ ··· − 955.661u − 152.161
a
1
=
29.6253u
111
+ 191.679u
110
+ ··· + 147.724u + 18.3331
27.7910u
111
+ 186.215u
110
+ ··· + 132.979u + 21.1686
a
3
=
−11.9578u
111
− 90.3909u
110
+ ··· − 110.147u − 13.3668
−1.04928u
111
− 18.2756u
110
+ ··· − 40.6199u − 7.10602
a
7
=
u
u
a
2
=
8.04702u
111
+ 45.4206u
110
+ ··· − 14.9838u + 1.78624
18.9556u
111
+ 117.536u
110
+ ··· + 54.5429u + 8.04702
(ii) Obstruction class = −1
(iii) Cusp Shapes = 725.208u
111
+ 4779.01u
110
+ ··· + 3630.85u + 563.580
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
112
+ 42u
111
+ ··· + 36864u + 4096
c
2
, c
6
u
112
− 2u
111
+ ··· + 192u + 64
c
3
u
112
− 9u
111
+ ··· + 2324u − 121
c
4
u
112
− 5u
111
+ ··· − 32u + 161
c
5
, c
7
, c
8
u
112
− 8u
111
+ ··· − 7u + 1
c
9
u
112
+ 9u
111
+ ··· + 2u + 1
c
10
, c
12
u
112
− 4u
111
+ ··· − 35u + 1
c
11
u
112
+ 18u
111
+ ··· − 48u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
112
+ 46y
111
+ ··· + 1719664640y + 16777216
c
2
, c
6
y
112
− 42y
111
+ ··· − 36864y + 4096
c
3
y
112
− 109y
111
+ ··· − 1162588y + 14641
c
4
y
112
− 109y
111
+ ··· − 254760y + 25921
c
5
, c
7
, c
8
y
112
− 96y
111
+ ··· + 115y + 1
c
9
y
112
+ 11y
111
+ ··· − 8y + 1
c
10
, c
12
y
112
− 68y
111
+ ··· − 815y + 1
c
11
y
112
− 18y
111
+ ··· − 1464y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972143 + 0.332867I
a = −1.362640 − 0.348523I
b = 0.160167 + 0.470619I
−3.76699 + 1.68644I 0
u = 0.972143 − 0.332867I
a = −1.362640 + 0.348523I
b = 0.160167 − 0.470619I
−3.76699 − 1.68644I 0
u = 0.647072 + 0.675313I
a = 0.310613 + 0.510412I
b = −0.698002 + 0.997090I
−5.03852 − 7.34388I 0
u = 0.647072 − 0.675313I
a = 0.310613 − 0.510412I
b = −0.698002 − 0.997090I
−5.03852 + 7.34388I 0
u = 0.548793 + 0.737316I
a = −0.661657 + 0.301680I
b = −0.474652 − 0.832338I
−4.72741 + 2.38013I 0
u = 0.548793 − 0.737316I
a = −0.661657 − 0.301680I
b = −0.474652 + 0.832338I
−4.72741 − 2.38013I 0
u = 0.227920 + 0.890098I
a = −0.597510 − 0.463491I
b = 0.986400 − 0.352157I
1.39228 − 6.23151I 0
u = 0.227920 − 0.890098I
a = −0.597510 + 0.463491I
b = 0.986400 + 0.352157I
1.39228 + 6.23151I 0
u = 0.189834 + 0.893590I
a = 1.083890 + 0.384288I
b = −1.25320 + 1.19672I
0.0844 − 14.1422I 0
u = 0.189834 − 0.893590I
a = 1.083890 − 0.384288I
b = −1.25320 − 1.19672I
0.0844 + 14.1422I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.997496 + 0.551038I
a = 0.193992 − 0.279188I
b = 0.861494 + 0.198796I
−0.97322 + 1.18405I 0
u = 0.997496 − 0.551038I
a = 0.193992 + 0.279188I
b = 0.861494 − 0.198796I
−0.97322 − 1.18405I 0
u = 1.113020 + 0.261600I
a = −0.66056 + 3.72609I
b = −2.25960 − 0.15223I
−2.52074 − 0.67374I 0
u = 1.113020 − 0.261600I
a = −0.66056 − 3.72609I
b = −2.25960 + 0.15223I
−2.52074 + 0.67374I 0
u = 0.157978 + 0.840183I
a = −0.955571 − 0.661158I
b = 0.891203 − 0.911299I
3.81295 − 7.90390I 0
u = 0.157978 − 0.840183I
a = −0.955571 + 0.661158I
b = 0.891203 + 0.911299I
3.81295 + 7.90390I 0
u = 0.099726 + 0.831030I
a = 0.241531 + 0.125256I
b = −0.278553 + 0.649349I
3.10964 − 3.02719I 0
u = 0.099726 − 0.831030I
a = 0.241531 − 0.125256I
b = −0.278553 − 0.649349I
3.10964 + 3.02719I 0
u = 1.086720 + 0.423280I
a = 0.458631 + 0.411155I
b = 0.878136 + 0.769471I
0.97833 + 3.36110I 0
u = 1.086720 − 0.423280I
a = 0.458631 − 0.411155I
b = 0.878136 − 0.769471I
0.97833 − 3.36110I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.161640 + 0.221560I
a = 0.693593 − 0.043378I
b = 1.31955 − 0.74333I
−1.46335 − 4.79145I 0
u = −1.161640 − 0.221560I
a = 0.693593 + 0.043378I
b = 1.31955 + 0.74333I
−1.46335 + 4.79145I 0
u = −0.019986 + 0.809418I
a = −0.259392 + 0.443642I
b = 0.492698 + 0.239422I
3.50998 − 2.86593I 0
u = −0.019986 − 0.809418I
a = −0.259392 − 0.443642I
b = 0.492698 − 0.239422I
3.50998 + 2.86593I 0
u = 1.075340 + 0.518822I
a = −0.726902 + 0.037922I
b = −1.14674 − 1.11271I
−2.61261 + 9.14928I 0
u = 1.075340 − 0.518822I
a = −0.726902 − 0.037922I
b = −1.14674 + 1.11271I
−2.61261 − 9.14928I 0
u = 0.186766 + 0.778487I
a = −1.61668 + 0.23169I
b = 0.429062 − 0.334358I
−1.33438 − 5.79082I 0
u = 0.186766 − 0.778487I
a = −1.61668 − 0.23169I
b = 0.429062 + 0.334358I
−1.33438 + 5.79082I 0
u = 0.719187 + 0.318145I
a = −2.22822 − 0.73581I
b = 0.088142 − 0.899059I
−4.28499 − 1.36074I 0
u = 0.719187 − 0.318145I
a = −2.22822 + 0.73581I
b = 0.088142 + 0.899059I
−4.28499 + 1.36074I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.227110 + 0.002061I
a = −1.66017 + 1.94116I
b = −0.560265 + 0.316560I
−2.72849 − 1.53038I 0
u = 1.227110 − 0.002061I
a = −1.66017 − 1.94116I
b = −0.560265 − 0.316560I
−2.72849 + 1.53038I 0
u = −1.214510 + 0.193657I
a = −0.331320 − 0.319809I
b = −1.255610 − 0.094001I
−0.04609 + 2.27832I 0
u = −1.214510 − 0.193657I
a = −0.331320 + 0.319809I
b = −1.255610 + 0.094001I
−0.04609 − 2.27832I 0
u = 0.142386 + 0.756030I
a = 2.22149 + 0.27721I
b = −2.86360 − 0.28993I
0.35372 − 3.11615I 0
u = 0.142386 − 0.756030I
a = 2.22149 − 0.27721I
b = −2.86360 + 0.28993I
0.35372 + 3.11615I 0
u = 1.217360 + 0.250346I
a = 1.70418 − 3.04656I
b = 2.85131 + 0.00560I
−2.76825 − 1.54043I 0
u = 1.217360 − 0.250346I
a = 1.70418 + 3.04656I
b = 2.85131 − 0.00560I
−2.76825 + 1.54043I 0
u = 1.239890 + 0.163213I
a = −0.51282 − 2.72556I
b = −0.113281 − 1.084940I
−5.29466 − 0.57195I 0
u = 1.239890 − 0.163213I
a = −0.51282 + 2.72556I
b = −0.113281 + 1.084940I
−5.29466 + 0.57195I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.143570 + 0.726883I
a = −1.27103 + 0.68455I
b = 1.22226 + 1.00947I
1.47470 + 8.28591I 0
u = −0.143570 − 0.726883I
a = −1.27103 − 0.68455I
b = 1.22226 − 1.00947I
1.47470 − 8.28591I 0
u = −1.225750 + 0.333086I
a = 0.461927 − 0.047089I
b = 0.855537 − 0.095153I
−0.18525 + 6.98643I 0
u = −1.225750 − 0.333086I
a = 0.461927 + 0.047089I
b = 0.855537 + 0.095153I
−0.18525 − 6.98643I 0
u = −1.245720 + 0.276383I
a = −0.429395 + 0.363064I
b = −1.165230 + 0.702845I
0.97470 + 1.25354I 0
u = −1.245720 − 0.276383I
a = −0.429395 − 0.363064I
b = −1.165230 − 0.702845I
0.97470 − 1.25354I 0
u = −0.039317 + 0.720481I
a = 1.30484 − 0.79273I
b = −0.993124 − 0.771280I
4.67418 + 2.34341I 0
u = −0.039317 − 0.720481I
a = 1.30484 + 0.79273I
b = −0.993124 + 0.771280I
4.67418 − 2.34341I 0
u = 0.192939 + 0.694349I
a = −0.264401 + 0.563665I
b = 0.102997 + 1.191740I
−2.51350 − 2.16509I 0
u = 0.192939 − 0.694349I
a = −0.264401 − 0.563665I
b = 0.102997 − 1.191740I
−2.51350 + 2.16509I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.232290 + 0.347470I
a = −0.490318 − 0.822966I
b = 0.110576 − 0.543663I
−0.359065 − 1.357260I 0
u = 1.232290 − 0.347470I
a = −0.490318 + 0.822966I
b = 0.110576 + 0.543663I
−0.359065 + 1.357260I 0
u = 1.211410 + 0.426352I
a = −0.258603 − 0.333714I
b = −0.201500 − 0.178702I
−0.28499 − 1.43055I 0
u = 1.211410 − 0.426352I
a = −0.258603 + 0.333714I
b = −0.201500 + 0.178702I
−0.28499 + 1.43055I 0
u = 0.089830 + 0.703854I
a = −2.00704 − 0.17497I
b = 2.26623 − 0.37498I
0.63350 − 1.90492I 0
u = 0.089830 − 0.703854I
a = −2.00704 + 0.17497I
b = 2.26623 + 0.37498I
0.63350 + 1.90492I 0
u = 1.271470 + 0.237024I
a = 1.57652 + 0.70957I
b = −0.349469 + 0.426717I
−4.39307 − 4.01879I 0
u = 1.271470 − 0.237024I
a = 1.57652 − 0.70957I
b = −0.349469 − 0.426717I
−4.39307 + 4.01879I 0
u = 0.690432
a = −0.298400
b = 0.429439
−1.01489 0
u = 0.502927 + 0.470467I
a = −0.219491 − 1.265850I
b = 0.584208 − 0.484004I
−0.94679 − 3.25376I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.502927 − 0.470467I
a = −0.219491 + 1.265850I
b = 0.584208 + 0.484004I
−0.94679 + 3.25376I 0
u = 1.293630 + 0.299459I
a = 0.48591 + 2.44283I
b = −0.853382 + 0.851081I
0.51258 − 6.03565I 0
u = 1.293630 − 0.299459I
a = 0.48591 − 2.44283I
b = −0.853382 − 0.851081I
0.51258 + 6.03565I 0
u = −0.154665 + 0.643514I
a = 0.555855 − 0.975061I
b = −1.026540 − 0.095270I
3.07753 + 0.68921I 0
u = −0.154665 − 0.643514I
a = 0.555855 + 0.975061I
b = −1.026540 + 0.095270I
3.07753 − 0.68921I 0
u = −1.330400 + 0.260515I
a = 0.95297 − 1.04827I
b = −0.196988 − 0.216176I
−5.01539 + 2.29068I 0
u = −1.330400 − 0.260515I
a = 0.95297 + 1.04827I
b = −0.196988 + 0.216176I
−5.01539 − 2.29068I 0
u = −1.328060 + 0.294821I
a = 0.36738 + 2.37866I
b = 2.08275 + 0.80093I
−3.83391 + 5.53172I 0
u = −1.328060 − 0.294821I
a = 0.36738 − 2.37866I
b = 2.08275 − 0.80093I
−3.83391 − 5.53172I 0
u = 0.055623 + 0.622634I
a = 1.57566 + 0.78961I
b = −0.137389 − 0.136164I
−0.591650 + 0.928319I −6.00000 + 0.I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.055623 − 0.622634I
a = 1.57566 − 0.78961I
b = −0.137389 + 0.136164I
−0.591650 − 0.928319I −6.00000 + 0.I
u = −1.374060 + 0.048611I
a = 0.89533 − 1.47816I
b = 0.705292 − 0.964759I
−6.88250 + 0.95679I 0
u = −1.374060 − 0.048611I
a = 0.89533 + 1.47816I
b = 0.705292 + 0.964759I
−6.88250 − 0.95679I 0
u = 1.352330 + 0.307047I
a = −0.28491 − 2.46921I
b = 1.18789 − 1.17802I
−3.24903 − 12.04520I 0
u = 1.352330 − 0.307047I
a = −0.28491 + 2.46921I
b = 1.18789 + 1.17802I
−3.24903 + 12.04520I 0
u = 0.529509 + 0.306312I
a = −0.037220 + 0.172357I
b = 0.588740 + 0.308270I
−1.135370 − 0.042892I −9.77824 + 0.I
u = 0.529509 − 0.306312I
a = −0.037220 − 0.172357I
b = 0.588740 − 0.308270I
−1.135370 + 0.042892I −9.77824 + 0.I
u = −1.351740 + 0.319952I
a = −1.69444 − 1.70373I
b = −3.09935 + 0.46402I
−4.35845 + 7.01409I 0
u = −1.351740 − 0.319952I
a = −1.69444 + 1.70373I
b = −3.09935 − 0.46402I
−4.35845 − 7.01409I 0
u = −1.341910 + 0.359550I
a = 0.532957 − 1.118490I
b = −0.305901 − 0.888362I
−1.43150 + 7.30797I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.341910 − 0.359550I
a = 0.532957 + 1.118490I
b = −0.305901 + 0.888362I
−1.43150 − 7.30797I 0
u = −1.39348
a = −3.37932
b = −3.54740
−8.60113 0
u = −1.366310 + 0.293948I
a = 0.59315 − 1.75824I
b = 0.197409 − 1.284420I
−7.43290 + 5.78346I 0
u = −1.366310 − 0.293948I
a = 0.59315 + 1.75824I
b = 0.197409 + 1.284420I
−7.43290 − 5.78346I 0
u = 1.375700 + 0.272901I
a = −0.484234 + 1.243210I
b = −0.900349 + 0.307525I
−1.81857 − 4.04926I 0
u = 1.375700 − 0.272901I
a = −0.484234 − 1.243210I
b = −0.900349 − 0.307525I
−1.81857 + 4.04926I 0
u = 1.404160 + 0.033715I
a = 1.25531 + 1.44669I
b = 0.566275 + 0.948690I
−6.89574 + 4.83025I 0
u = 1.404160 − 0.033715I
a = 1.25531 − 1.44669I
b = 0.566275 − 0.948690I
−6.89574 − 4.83025I 0
u = −1.373030 + 0.326241I
a = −1.007360 + 0.555305I
b = 0.590165 + 0.343631I
−6.26355 + 9.78611I 0
u = −1.373030 − 0.326241I
a = −1.007360 − 0.555305I
b = 0.590165 − 0.343631I
−6.26355 − 9.78611I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.409010 + 0.080595I
a = 0.47214 + 1.91564I
b = 0.390502 + 0.770194I
−7.09262 + 4.86963I 0
u = −1.409010 − 0.080595I
a = 0.47214 − 1.91564I
b = 0.390502 − 0.770194I
−7.09262 − 4.86963I 0
u = −1.36882 + 0.35973I
a = −0.52300 + 2.04764I
b = 0.869024 + 1.011960I
−1.00529 + 12.22180I 0
u = −1.36882 − 0.35973I
a = −0.52300 − 2.04764I
b = 0.869024 − 1.011960I
−1.00529 − 12.22180I 0
u = −1.42521 + 0.02285I
a = −0.59418 + 1.59160I
b = 0.468045 + 0.892905I
−10.99840 + 2.00997I 0
u = −1.42521 − 0.02285I
a = −0.59418 − 1.59160I
b = 0.468045 − 0.892905I
−10.99840 − 2.00997I 0
u = −1.39493 + 0.38237I
a = 0.45776 − 2.15262I
b = −1.30054 − 1.28561I
−4.9272 + 18.7232I 0
u = −1.39493 − 0.38237I
a = 0.45776 + 2.15262I
b = −1.30054 + 1.28561I
−4.9272 − 18.7232I 0
u = 0.541504
a = 6.40334
b = −4.23756
−2.58861 158.370
u = −1.41117 + 0.37622I
a = 0.095495 + 1.289910I
b = 1.036730 + 0.484104I
−3.79919 + 10.78570I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41117 − 0.37622I
a = 0.095495 − 1.289910I
b = 1.036730 − 0.484104I
−3.79919 − 10.78570I 0
u = −0.497821 + 0.137020I
a = 1.51035 − 0.27858I
b = 0.911716 − 0.662167I
−0.90850 − 5.42294I −1.43047 + 4.96614I
u = −0.497821 − 0.137020I
a = 1.51035 + 0.27858I
b = 0.911716 + 0.662167I
−0.90850 + 5.42294I −1.43047 − 4.96614I
u = −1.49258 + 0.12612I
a = −0.46867 − 1.85261I
b = −0.75840 − 1.30183I
−12.2107 + 9.8962I 0
u = −1.49258 − 0.12612I
a = −0.46867 + 1.85261I
b = −0.75840 + 1.30183I
−12.2107 − 9.8962I 0
u = −1.50703 + 0.17644I
a = −0.659597 + 0.817640I
b = −0.105634 + 0.883669I
−11.58490 + 0.78846I 0
u = −1.50703 − 0.17644I
a = −0.659597 − 0.817640I
b = −0.105634 − 0.883669I
−11.58490 − 0.78846I 0
u = −1.63690
a = 0.332409
b = 0.414031
−10.4601 0
u = −0.244806 + 0.102225I
a = −1.67402 − 2.35307I
b = −0.866434 − 0.319209I
1.46476 + 1.15131I 2.56362 − 1.63144I
u = −0.244806 − 0.102225I
a = −1.67402 + 2.35307I
b = −0.866434 + 0.319209I
1.46476 − 1.15131I 2.56362 + 1.63144I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0392826 + 0.0876665I
a = −3.58914 + 5.96550I
b = 0.439969 + 0.844782I
−1.92777 − 0.81004I −4.48759 + 0.13033I
u = −0.0392826 − 0.0876665I
a = −3.58914 − 5.96550I
b = 0.439969 − 0.844782I
−1.92777 + 0.81004I −4.48759 − 0.13033I
16
II. I
u
2
=
h−3a
5
−13a
4
−7a
3
+17a
2
+13b−21a−7, a
6
+6a
5
+11a
4
+4a
3
−a
2
+a+1, u−1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
1
a
6
=
1
1
a
9
=
−1
0
a
11
=
a
3
13
a
5
+ a
4
+ ··· +
21
13
a +
7
13
a
12
=
3
13
a
5
+ a
4
+ ··· +
34
13
a +
7
13
3
13
a
5
+ a
4
+ ··· +
21
13
a +
7
13
a
4
=
−
5
13
a
5
− 2a
4
+ ··· +
4
13
a +
10
13
−1.15385a
5
− 6a
4
+ ··· + 0.923077a − 0.692308
a
10
=
−2.30769a
5
− 12a
4
+ ··· + 1.84615a − 3.38462
−2.07692a
5
− 11a
4
+ ··· + 2.46154a − 2.84615
a
1
=
−2.07692a
5
− 11a
4
+ ··· + 2.46154a − 2.84615
−2.07692a
5
− 11a
4
+ ··· + 2.46154a − 2.84615
a
3
=
−2.07692a
5
− 11a
4
+ ··· + 2.46154a − 2.84615
−2.07692a
5
− 11a
4
+ ··· + 2.46154a − 2.84615
a
7
=
1
1
a
2
=
−2.07692a
5
− 11a
4
+ ··· + 2.46154a − 2.84615
−2.07692a
5
− 11a
4
+ ··· + 2.46154a − 2.84615
(ii) Obstruction class = 1
(iii) Cusp Shapes =
92
13
a
5
+ 37a
4
+
622
13
a
3
−
179
13
a
2
+
20
13
a +
24
13
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
6
c
3
, c
9
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
4
, c
10
, c
11
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
5
(u − 1)
6
c
7
, c
8
(u + 1)
6
c
12
u
6
− u
5
− u
4
+ 2u
3
− u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
6
c
3
, c
9
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
4
, c
10
, c
11
c
12
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
5
, c
7
, c
8
(y −1)
6
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.658836 + 0.177500I
b = −1.073950 + 0.558752I
−1.64493 − 5.69302I −11.7058 + 8.3306I
u = 1.00000
a = −0.658836 − 0.177500I
b = −1.073950 − 0.558752I
−1.64493 + 5.69302I −11.7058 − 8.3306I
u = 1.00000
a = 0.346225 + 0.393823I
b = 1.002190 + 0.295542I
0.245672 + 0.924305I −5.68949 − 0.25702I
u = 1.00000
a = 0.346225 − 0.393823I
b = 1.002190 − 0.295542I
0.245672 − 0.924305I −5.68949 + 0.25702I
u = 1.00000
a = −2.68739 + 0.76772I
b = −0.428243 − 0.664531I
−3.53554 − 0.92430I −12.60470 − 5.55069I
u = 1.00000
a = −2.68739 − 0.76772I
b = −0.428243 + 0.664531I
−3.53554 + 0.92430I −12.60470 + 5.55069I
20
III. I
u
3
= hb − u − 2, a + 2u + 3, u
2
+ u − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
6
=
1
−u + 1
a
9
=
−u
−u + 1
a
11
=
−2u − 3
u + 2
a
12
=
−2u − 3
u + 2
a
4
=
−5u − 7
3u + 5
a
10
=
−4u − 2
3
a
1
=
2u − 1
u − 1
a
3
=
1
0
a
7
=
u
u
a
2
=
u
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −61
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
2
− 3u + 1
c
2
, c
5
u
2
+ u − 1
c
6
, c
7
, c
8
u
2
− u − 1
c
9
u
2
+ 3u + 1
c
10
(u − 1)
2
c
11
u
2
c
12
(u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
9
y
2
− 7y + 1
c
2
, c
5
, c
6
c
7
, c
8
y
2
− 3y + 1
c
10
, c
12
(y −1)
2
c
11
y
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −4.23607
b = 2.61803
−2.63189 −61.0000
u = −1.61803
a = 0.236068
b = 0.381966
−10.5276 −61.0000
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
6
(u
2
− 3u + 1)(u
112
+ 42u
111
+ ··· + 36864u + 4096)
c
2
u
6
(u
2
+ u − 1)(u
112
− 2u
111
+ ··· + 192u + 64)
c
3
(u
2
− 3u + 1)(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
112
− 9u
111
+ ··· + 2324u − 121)
c
4
(u
2
− 3u + 1)(u
6
+ u
5
+ ··· + u + 1)(u
112
− 5u
111
+ ··· − 32u + 161)
c
5
((u − 1)
6
)(u
2
+ u − 1)(u
112
− 8u
111
+ ··· − 7u + 1)
c
6
u
6
(u
2
− u − 1)(u
112
− 2u
111
+ ··· + 192u + 64)
c
7
, c
8
((u + 1)
6
)(u
2
− u − 1)(u
112
− 8u
111
+ ··· − 7u + 1)
c
9
(u
2
+ 3u + 1)(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
112
+ 9u
111
+ ··· + 2u + 1)
c
10
((u − 1)
2
)(u
6
+ u
5
+ ··· + u + 1)(u
112
− 4u
111
+ ··· − 35u + 1)
c
11
u
2
(u
6
+ u
5
+ ··· + u + 1)(u
112
+ 18u
111
+ ··· − 48u + 4)
c
12
((u + 1)
2
)(u
6
− u
5
+ ··· − u + 1)(u
112
− 4u
111
+ ··· − 35u + 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
6
(y
2
− 7y + 1)(y
112
+ 46y
111
+ ··· + 1.71966 × 10
9
y + 1.67772 × 10
7
)
c
2
, c
6
y
6
(y
2
− 3y + 1)(y
112
− 42y
111
+ ··· − 36864y + 4096)
c
3
(y
2
− 7y + 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
112
− 109y
111
+ ··· − 1162588y + 14641)
c
4
(y
2
− 7y + 1)(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
112
− 109y
111
+ ··· − 254760y + 25921)
c
5
, c
7
, c
8
((y −1)
6
)(y
2
− 3y + 1)(y
112
− 96y
111
+ ··· + 115y + 1)
c
9
(y
2
− 7y + 1)(y
6
+ y
5
+ ··· + 3y + 1)(y
112
+ 11y
111
+ ··· − 8y + 1)
c
10
, c
12
(y −1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
112
− 68y
111
+ ··· − 815y + 1)
c
11
y
2
(y
6
− 3y
5
+ ··· − y + 1)(y
112
− 18y
111
+ ··· − 1464y + 16)
26
