12a
0675
(K12a
0675
)
A knot diagram
1
Linearized knot diagam
3 7 11 10 8 2 5 6 12 1 9 4
Solving Sequence
3,11 4,7
2 1 6 10 5 8 12 9
c
3
c
2
c
1
c
6
c
10
c
4
c
7
c
12
c
9
c
5
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.64413 × 10
873
u
111
− 4.69059 × 10
874
u
110
+ ··· + 2.10211 × 10
875
b + 3.17682 × 10
876
,
2.94142 × 10
875
u
111
− 1.73846 × 10
876
u
110
+ ··· + 3.38440 × 10
877
a + 5.18415 × 10
878
,
u
112
− 5u
111
+ ··· − 32u + 161i
I
u
2
= hb, u
5
+ 2u
4
− u
3
− 3u
2
+ a + 2, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
3
= hb + u + 2, a − 1, u
2
+ 3u + 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
= h8.64 × 10
873
u
111
− 4.69 × 10
874
u
110
+ · · · + 2.10 × 10
875
b + 3.18 ×
10
876
, 2.94 × 10
875
u
111
− 1.74 × 10
876
u
110
+ · · · + 3.38 × 10
877
a + 5.18 ×
10
878
, u
112
− 5u
111
+ · · · − 32u + 161i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
−0.00869112u
111
+ 0.0513670u
110
+ ··· − 22.1084u − 15.3178
−0.0411212u
111
+ 0.223137u
110
+ ··· + 49.0131u − 15.1125
a
2
=
0.0417015u
111
− 0.223931u
110
+ ··· − 1.70906u + 19.4928
−0.0475784u
111
+ 0.258130u
110
+ ··· + 41.4609u − 18.2032
a
1
=
−0.00587685u
111
+ 0.0341992u
110
+ ··· + 39.7519u + 1.28959
−0.0475784u
111
+ 0.258130u
110
+ ··· + 41.4609u − 18.2032
a
6
=
−0.0777167u
111
+ 0.428161u
110
+ ··· + 64.6212u − 43.6433
0.0560739u
111
− 0.303666u
110
+ ··· − 49.2634u + 20.8838
a
10
=
−0.0139652u
111
+ 0.0715977u
110
+ ··· + 10.2906u + 6.50129
0.0156815u
111
− 0.0832120u
110
+ ··· − 16.6168u + 3.89101
a
5
=
0.00952388u
111
− 0.0439959u
110
+ ··· + 1.32330u − 3.32008
0.000290774u
111
− 0.00392329u
110
+ ··· + 0.729889u + 1.77651
a
8
=
0.0324993u
111
− 0.172787u
110
+ ··· − 30.0523u + 8.35382
−0.0466259u
111
+ 0.252618u
110
+ ··· + 49.2139u − 17.8341
a
12
=
0.0424410u
111
− 0.227744u
110
+ ··· − 2.80931u + 20.2680
−0.0567134u
111
+ 0.307789u
110
+ ··· + 49.8914u − 21.4801
a
9
=
0.0353301u
111
− 0.195586u
110
+ ··· − 74.1382u + 16.7074
−0.0486125u
111
+ 0.264384u
110
+ ··· + 48.8205u − 20.2064
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.30472u
111
− 7.06537u
110
+ ··· − 1339.89u + 498.199
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
− 5u
111
+ ··· − 32u + 161
c
4
u
112
− 9u
111
+ ··· + 2324u − 121
c
5
, c
7
, c
8
u
112
− 8u
111
+ ··· − 7u + 1
c
9
, c
11
u
112
− 4u
111
+ ··· − 35u + 1
c
10
u
112
+ 18u
111
+ ··· − 48u + 4
c
12
u
112
+ 9u
111
+ ··· + 2u + 1
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
+ ··· − 254760y + 25921
c
4
y
112
− 109y
111
+ ··· − 1162588y + 14641
c
5
, c
7
, c
8
y
112
− 96y
111
+ ··· + 115y + 1
c
9
, c
11
y
112
− 68y
111
+ ··· − 815y + 1
c
10
y
112
− 18y
111
+ ··· − 1464y + 16
c
12
y
112
+ 11y
111
+ ··· − 8y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.468045 + 0.892905I
a = −0.13957 − 1.52043I
b = 1.212340 + 0.047993I
−10.99840 − 2.00997I 0
u = −0.468045 − 0.892905I
a = −0.13957 + 1.52043I
b = 1.212340 − 0.047993I
−10.99840 + 2.00997I 0
u = 1.026540 + 0.095270I
a = 0.531056 + 0.969905I
b = −0.541459 − 0.797677I
3.07753 + 0.68921I 0
u = 1.026540 − 0.095270I
a = 0.531056 − 0.969905I
b = −0.541459 + 0.797677I
3.07753 − 0.68921I 0
u = 0.474652 + 0.832338I
a = 0.501877 − 0.671501I
b = 1.149220 + 0.205342I
−4.72741 + 2.38013I 0
u = 0.474652 − 0.832338I
a = 0.501877 + 0.671501I
b = 1.149220 − 0.205342I
−4.72741 − 2.38013I 0
u = −0.986400 + 0.352157I
a = −0.06333 + 1.49320I
b = −1.095380 − 0.664874I
1.39228 − 6.23151I 0
u = −0.986400 − 0.352157I
a = −0.06333 − 1.49320I
b = −1.095380 + 0.664874I
1.39228 + 6.23151I 0
u = −0.439969 + 0.844782I
a = 0.750760 + 0.662615I
b = 0.168122 − 0.261520I
−1.92777 + 0.81004I 0
u = −0.439969 − 0.844782I
a = 0.750760 − 0.662615I
b = 0.168122 + 0.261520I
−1.92777 − 0.81004I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.900349 + 0.307525I
a = −0.58166 − 1.29875I
b = 0.564295 + 1.113070I
−1.81857 + 4.04926I 0
u = 0.900349 − 0.307525I
a = −0.58166 + 1.29875I
b = 0.564295 − 1.113070I
−1.81857 − 4.04926I 0
u = 0.305901 + 0.888362I
a = 0.236205 + 1.086070I
b = 1.045770 − 0.734544I
−1.43150 + 7.30797I 0
u = 0.305901 − 0.888362I
a = 0.236205 − 1.086070I
b = 1.045770 + 0.734544I
−1.43150 − 7.30797I 0
u = 0.866434 + 0.319209I
a = 0.281117 + 0.511404I
b = −0.085748 − 0.495139I
1.46476 + 1.15131I 0
u = 0.866434 − 0.319209I
a = 0.281117 − 0.511404I
b = −0.085748 + 0.495139I
1.46476 − 1.15131I 0
u = 0.113281 + 1.084940I
a = −1.16785 − 1.00702I
b = −0.351973 + 0.831284I
−5.29466 − 0.57195I 0
u = 0.113281 − 1.084940I
a = −1.16785 + 1.00702I
b = −0.351973 − 0.831284I
−5.29466 + 0.57195I 0
u = −0.088142 + 0.899059I
a = −1.61631 + 1.18838I
b = −0.757971 + 0.094539I
−4.28499 − 1.36074I 0
u = −0.088142 − 0.899059I
a = −1.61631 − 1.18838I
b = −0.757971 − 0.094539I
−4.28499 + 1.36074I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.566275 + 0.948690I
a = 0.209851 + 1.205160I
b = −0.070911 − 1.168160I
−6.89574 − 4.83025I 0
u = −0.566275 − 0.948690I
a = 0.209851 − 1.205160I
b = −0.070911 + 1.168160I
−6.89574 + 4.83025I 0
u = 0.105634 + 0.883669I
a = 0.142577 + 0.894261I
b = −1.38242 − 0.36899I
−11.58490 − 0.78846I 0
u = 0.105634 − 0.883669I
a = 0.142577 − 0.894261I
b = −1.38242 + 0.36899I
−11.58490 + 0.78846I 0
u = −0.861494 + 0.198796I
a = 0.369814 − 1.123050I
b = 1.052340 + 0.440204I
−0.97322 − 1.18405I 0
u = −0.861494 − 0.198796I
a = 0.369814 + 1.123050I
b = 1.052340 − 0.440204I
−0.97322 + 1.18405I 0
u = −0.911716 + 0.662167I
a = −0.114233 − 0.615496I
b = 0.029697 + 0.635113I
−0.90850 − 5.42294I 0
u = −0.911716 − 0.662167I
a = −0.114233 + 0.615496I
b = 0.029697 − 0.635113I
−0.90850 + 5.42294I 0
u = −0.390502 + 0.770194I
a = 1.182600 − 0.418464I
b = 1.178770 + 0.169202I
−7.09262 − 4.86963I 0
u = −0.390502 − 0.770194I
a = 1.182600 + 0.418464I
b = 1.178770 − 0.169202I
−7.09262 + 4.86963I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855537 + 0.095153I
a = −0.736687 + 0.424172I
b = 0.824062 − 0.686417I
−0.18525 + 6.98643I 0
u = −0.855537 − 0.095153I
a = −0.736687 − 0.424172I
b = 0.824062 + 0.686417I
−0.18525 − 6.98643I 0
u = −1.036730 + 0.484104I
a = −0.15871 − 1.57266I
b = 1.180290 + 0.770211I
−3.79919 − 10.78570I 0
u = −1.036730 − 0.484104I
a = −0.15871 + 1.57266I
b = 1.180290 − 0.770211I
−3.79919 + 10.78570I 0
u = −0.878136 + 0.769471I
a = −1.03073 + 1.75744I
b = −0.854510 − 0.585436I
0.97833 − 3.36110I 0
u = −0.878136 − 0.769471I
a = −1.03073 − 1.75744I
b = −0.854510 + 0.585436I
0.97833 + 3.36110I 0
u = −0.705292 + 0.964759I
a = −0.134401 + 0.171016I
b = −1.104990 + 0.102541I
−6.88250 + 0.95679I 0
u = −0.705292 − 0.964759I
a = −0.134401 − 0.171016I
b = −1.104990 − 0.102541I
−6.88250 − 0.95679I 0
u = −0.102997 + 1.191740I
a = 0.718781 + 0.113606I
b = 0.872881 − 0.545073I
−2.51350 + 2.16509I 0
u = −0.102997 − 1.191740I
a = 0.718781 − 0.113606I
b = 0.872881 + 0.545073I
−2.51350 − 2.16509I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.853382 + 0.851081I
a = 0.666579 + 0.635943I
b = −0.618439 − 0.951660I
0.51258 + 6.03565I 0
u = 0.853382 − 0.851081I
a = 0.666579 − 0.635943I
b = −0.618439 + 0.951660I
0.51258 − 6.03565I 0
u = 0.698002 + 0.997090I
a = −0.616237 − 0.033041I
b = −1.124740 + 0.060024I
−5.03852 + 7.34388I 0
u = 0.698002 − 0.997090I
a = −0.616237 + 0.033041I
b = −1.124740 − 0.060024I
−5.03852 − 7.34388I 0
u = −0.584208 + 0.484004I
a = −1.85886 + 0.99076I
b = −0.852044 − 0.127697I
−0.94679 − 3.25376I 0
u = −0.584208 − 0.484004I
a = −1.85886 − 0.99076I
b = −0.852044 + 0.127697I
−0.94679 + 3.25376I 0
u = 0.993124 + 0.771280I
a = −0.761129 − 0.522135I
b = 0.705432 + 0.773381I
4.67418 + 2.34341I 0
u = 0.993124 − 0.771280I
a = −0.761129 + 0.522135I
b = 0.705432 − 0.773381I
4.67418 − 2.34341I 0
u = 1.255610 + 0.094001I
a = −0.781393 + 0.562496I
b = 0.784331 − 0.418208I
−0.04609 + 2.27832I 0
u = 1.255610 − 0.094001I
a = −0.781393 − 0.562496I
b = 0.784331 + 0.418208I
−0.04609 − 2.27832I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.891203 + 0.911299I
a = 0.67375 − 1.67146I
b = 0.985762 + 0.695082I
3.81295 − 7.90390I 0
u = −0.891203 − 0.911299I
a = 0.67375 + 1.67146I
b = 0.985762 − 0.695082I
3.81295 + 7.90390I 0
u = 0.278553 + 0.649349I
a = −0.543784 − 1.113530I
b = −0.927060 + 0.744372I
3.10964 + 3.02719I 0
u = 0.278553 − 0.649349I
a = −0.543784 + 1.113530I
b = −0.927060 − 0.744372I
3.10964 − 3.02719I 0
u = −0.197409 + 1.284420I
a = −0.223939 − 0.085915I
b = −1.094380 + 0.606228I
−7.43290 + 5.78346I 0
u = −0.197409 − 1.284420I
a = −0.223939 + 0.085915I
b = −1.094380 − 0.606228I
−7.43290 − 5.78346I 0
u = −0.590165 + 0.343631I
a = 1.47450 + 2.91661I
b = −1.107300 − 0.670157I
−6.26355 − 9.78611I 0
u = −0.590165 − 0.343631I
a = 1.47450 − 2.91661I
b = −1.107300 + 0.670157I
−6.26355 + 9.78611I 0
u = −0.869024 + 1.011960I
a = −0.47159 + 1.56244I
b = −1.098070 − 0.735726I
−1.00529 − 12.22180I 0
u = −0.869024 − 1.011960I
a = −0.47159 − 1.56244I
b = −1.098070 + 0.735726I
−1.00529 + 12.22180I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.588740 + 0.308270I
a = 1.42258 − 0.40347I
b = 0.730002 − 0.053014I
−1.135370 + 0.042892I 0
u = −0.588740 − 0.308270I
a = 1.42258 + 0.40347I
b = 0.730002 + 0.053014I
−1.135370 − 0.042892I 0
u = 0.560265 + 0.316560I
a = −1.042770 − 0.669832I
b = 0.004601 + 0.787819I
−2.72849 + 1.53038I 0
u = 0.560265 − 0.316560I
a = −1.042770 + 0.669832I
b = 0.004601 − 0.787819I
−2.72849 − 1.53038I 0
u = 1.165230 + 0.702845I
a = 0.891880 + 0.374546I
b = −0.857228 − 0.576973I
0.97470 − 1.25354I 0
u = 1.165230 − 0.702845I
a = 0.891880 − 0.374546I
b = −0.857228 + 0.576973I
0.97470 + 1.25354I 0
u = −0.110576 + 0.543663I
a = 0.300944 + 0.690223I
b = 0.712854 − 0.837133I
−0.359065 − 1.357260I −4.82662 + 0.I
u = −0.110576 − 0.543663I
a = 0.300944 − 0.690223I
b = 0.712854 + 0.837133I
−0.359065 + 1.357260I −4.82662 + 0.I
u = 0.349469 + 0.426717I
a = 2.77883 + 2.17565I
b = −0.497376 − 0.903947I
−4.39307 + 4.01879I −13.0394 − 6.3418I
u = 0.349469 − 0.426717I
a = 2.77883 − 2.17565I
b = −0.497376 + 0.903947I
−4.39307 − 4.01879I −13.0394 + 6.3418I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.492698 + 0.239422I
a = 0.549744 − 0.276436I
b = −0.800248 + 0.836455I
3.50998 + 2.86593I −0.44864 − 5.27046I
u = −0.492698 − 0.239422I
a = 0.549744 + 0.276436I
b = −0.800248 − 0.836455I
3.50998 − 2.86593I −0.44864 + 5.27046I
u = −0.429062 + 0.334358I
a = −1.24655 − 3.63053I
b = 0.948423 + 0.616190I
−1.33438 − 5.79082I −9.77157 + 8.99738I
u = −0.429062 − 0.334358I
a = −1.24655 + 3.63053I
b = 0.948423 − 0.616190I
−1.33438 + 5.79082I −9.77157 − 8.99738I
u = −0.160167 + 0.470619I
a = −0.97937 + 4.21410I
b = −0.729051 − 0.393657I
−3.76699 − 1.68644I −14.6816 + 6.6415I
u = −0.160167 − 0.470619I
a = −0.97937 − 4.21410I
b = −0.729051 + 0.393657I
−3.76699 + 1.68644I −14.6816 − 6.6415I
u = 0.75840 + 1.30183I
a = 0.020758 + 0.437342I
b = 1.353180 − 0.264117I
−12.2107 + 9.8962I 0
u = 0.75840 − 1.30183I
a = 0.020758 − 0.437342I
b = 1.353180 + 0.264117I
−12.2107 − 9.8962I 0
u = −1.31955 + 0.74333I
a = 0.615027 − 0.525764I
b = −0.685413 + 0.484737I
−1.46335 − 4.79145I 0
u = −1.31955 − 0.74333I
a = 0.615027 + 0.525764I
b = −0.685413 − 0.484737I
−1.46335 + 4.79145I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.429439
a = 1.79353
b = 0.601087
−1.01489 −10.1760
u = −1.22226 + 1.00947I
a = −0.531918 + 0.901402I
b = 0.616280 − 0.864859I
1.47470 − 8.28591I 0
u = −1.22226 − 1.00947I
a = −0.531918 − 0.901402I
b = 0.616280 + 0.864859I
1.47470 + 8.28591I 0
u = −0.414031
a = 0.710994
b = −1.65804
−10.4601 57.7740
u = 1.14674 + 1.11271I
a = −0.460592 − 1.320060I
b = −1.009770 + 0.565159I
−2.61261 + 9.14928I 0
u = 1.14674 − 1.11271I
a = −0.460592 + 1.320060I
b = −1.009770 − 0.565159I
−2.61261 − 9.14928I 0
u = −1.18789 + 1.17802I
a = 0.543314 − 1.107150I
b = −0.632118 + 1.066720I
−3.24903 − 12.04520I 0
u = −1.18789 − 1.17802I
a = 0.543314 + 1.107150I
b = −0.632118 − 1.066720I
−3.24903 + 12.04520I 0
u = 0.196988 + 0.216176I
a = −1.69062 − 5.29146I
b = −1.022500 + 0.540394I
−5.01539 + 2.29068I −12.66920 + 0.63312I
u = 0.196988 − 0.216176I
a = −1.69062 + 5.29146I
b = −1.022500 − 0.540394I
−5.01539 − 2.29068I −12.66920 − 0.63312I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.201500 + 0.178702I
a = 1.82535 + 1.36786I
b = 0.857519 − 0.800677I
−0.28499 − 1.43055I −2.82816 + 2.44341I
u = 0.201500 − 0.178702I
a = 1.82535 − 1.36786I
b = 0.857519 + 0.800677I
−0.28499 + 1.43055I −2.82816 − 2.44341I
u = 1.25320 + 1.19672I
a = 0.19298 + 1.48373I
b = 1.067090 − 0.707773I
0.0844 + 14.1422I 0
u = 1.25320 − 1.19672I
a = 0.19298 − 1.48373I
b = 1.067090 + 0.707773I
0.0844 − 14.1422I 0
u = 0.137389 + 0.136164I
a = −7.22185 − 4.14942I
b = 0.702404 + 0.610926I
−0.591650 + 0.928319I −7.08998 − 2.83075I
u = 0.137389 − 0.136164I
a = −7.22185 + 4.14942I
b = 0.702404 − 0.610926I
−0.591650 − 0.928319I −7.08998 + 2.83075I
u = 1.30054 + 1.28561I
a = 0.00089 − 1.50453I
b = −1.148010 + 0.781264I
−4.9272 + 18.7232I 0
u = 1.30054 − 1.28561I
a = 0.00089 + 1.50453I
b = −1.148010 − 0.781264I
−4.9272 − 18.7232I 0
u = −2.08275 + 0.80093I
a = −0.267916 − 1.307150I
b = 1.018830 + 0.608303I
−3.83391 − 5.53172I 0
u = −2.08275 − 0.80093I
a = −0.267916 + 1.307150I
b = 1.018830 − 0.608303I
−3.83391 + 5.53172I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.25960 + 0.15223I
a = 0.04322 + 1.60132I
b = 0.572900 − 0.604567I
−2.52074 − 0.67374I 0
u = 2.25960 − 0.15223I
a = 0.04322 − 1.60132I
b = 0.572900 + 0.604567I
−2.52074 + 0.67374I 0
u = −2.26623 + 0.37498I
a = 0.08634 + 1.50403I
b = −0.800557 − 0.646744I
0.63350 − 1.90492I 0
u = −2.26623 − 0.37498I
a = 0.08634 − 1.50403I
b = −0.800557 + 0.646744I
0.63350 + 1.90492I 0
u = −2.85131 + 0.00560I
a = −0.00878 − 1.82788I
b = 0.529918 + 0.799159I
−2.76825 + 1.54043I 0
u = −2.85131 − 0.00560I
a = −0.00878 + 1.82788I
b = 0.529918 − 0.799159I
−2.76825 − 1.54043I 0
u = 2.86360 + 0.28993I
a = 0.325586 + 1.203530I
b = −0.891220 − 0.640795I
0.35372 − 3.11615I 0
u = 2.86360 − 0.28993I
a = 0.325586 − 1.203530I
b = −0.891220 + 0.640795I
0.35372 + 3.11615I 0
u = 3.09935 + 0.46402I
a = −0.548660 − 1.086970I
b = 1.065510 + 0.657494I
−4.35845 − 7.01409I 0
u = 3.09935 − 0.46402I
a = −0.548660 + 1.086970I
b = 1.065510 − 0.657494I
−4.35845 + 7.01409I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 3.54740
a = 0.397758
b = −1.14559
−8.60113 0
u = 4.23756
a = 0.938274
b = 0.618644
−2.58861 0
16
II. I
u
2
= hb, u
5
+ 2u
4
− u
3
− 3u
2
+ a + 2, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
−u
5
− 2u
4
+ u
3
+ 3u
2
− 2
0
a
2
=
1
0
a
1
=
1
0
a
6
=
−u
5
− 2u
4
+ u
3
+ 3u
2
− 2
0
a
10
=
−u
u
a
5
=
u
4
− u
2
+ 1
−u
4
a
8
=
−u
5
− 3u
4
+ u
3
+ 4u
2
− 3
u
4
a
12
=
−u
2
+ 1
u
4
a
9
=
−u
4
+ u
2
− 1
u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
5
− u
4
− 4u
3
− 3u
2
+ 8u − 8
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
+ u
5
− u
4
− 2u
3
+ u + 1
c
4
, c
12
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
5
(u − 1)
6
c
7
, c
8
(u + 1)
6
c
10
, c
11
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
, c
10
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
4
, c
12
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 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 = 1.002190 + 0.295542I
a = 0.344968 − 0.764807I
b = 0
0.245672 + 0.924305I −5.68949 − 0.25702I
u = 1.002190 − 0.295542I
a = 0.344968 + 0.764807I
b = 0
0.245672 − 0.924305I −5.68949 + 0.25702I
u = −0.428243 + 0.664531I
a = −1.68613 − 1.92635I
b = 0
−3.53554 + 0.92430I −12.60470 + 5.55069I
u = −0.428243 − 0.664531I
a = −1.68613 + 1.92635I
b = 0
−3.53554 − 0.92430I −12.60470 − 5.55069I
u = −1.073950 + 0.558752I
a = −0.158836 + 0.437639I
b = 0
−1.64493 − 5.69302I −11.7058 + 8.3306I
u = −1.073950 − 0.558752I
a = −0.158836 − 0.437639I
b = 0
−1.64493 + 5.69302I −11.7058 − 8.3306I
20
III. I
u
3
= hb + u + 2, a − 1, u
2
+ 3u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
3u + 1
a
7
=
1
−u − 2
a
2
=
u + 3
−u − 3
a
1
=
0
−u − 3
a
6
=
−2u − 4
u + 3
a
10
=
0
u
a
5
=
1
0
a
8
=
u + 3
−u − 2
a
12
=
u + 3
−3
a
9
=
−u − 3
u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −61
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
2
− 3u + 1
c
2
, c
5
u
2
+ u − 1
c
3
, c
4
u
2
+ 3u + 1
c
6
, c
7
, c
8
u
2
− u − 1
c
9
(u − 1)
2
c
10
u
2
c
11
(u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
12
y
2
− 7y + 1
c
2
, c
5
, c
6
c
7
, c
8
y
2
− 3y + 1
c
9
, c
11
(y −1)
2
c
10
y
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.381966
a = 1.00000
b = −1.61803
−10.5276 −61.0000
u = −2.61803
a = 1.00000
b = 0.618034
−2.63189 −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
+ u
5
+ ··· + u + 1)(u
112
− 5u
111
+ ··· − 32u + 161)
c
4
(u
2
+ 3u + 1)(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
112
− 9u
111
+ ··· + 2324u − 121)
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 − 1)
2
)(u
6
+ u
5
+ ··· + u + 1)(u
112
− 4u
111
+ ··· − 35u + 1)
c
10
u
2
(u
6
− u
5
+ ··· − u + 1)(u
112
+ 18u
111
+ ··· − 48u + 4)
c
11
((u + 1)
2
)(u
6
− u
5
+ ··· − u + 1)(u
112
− 4u
111
+ ··· − 35u + 1)
c
12
(u
2
− 3u + 1)(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
112
+ 9u
111
+ ··· + 2u + 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
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
112
− 109y
111
+ ··· − 254760y + 25921)
c
4
(y
2
− 7y + 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
112
− 109y
111
+ ··· − 1162588y + 14641)
c
5
, c
7
, c
8
((y −1)
6
)(y
2
− 3y + 1)(y
112
− 96y
111
+ ··· + 115y + 1)
c
9
, c
11
(y −1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
112
− 68y
111
+ ··· − 815y + 1)
c
10
y
2
(y
6
− 3y
5
+ ··· − y + 1)(y
112
− 18y
111
+ ··· − 1464y + 16)
c
12
(y
2
− 7y + 1)(y
6
+ y
5
+ ··· + 3y + 1)(y
112
+ 11y
111
+ ··· − 8y + 1)
26
