12a
1269
(K12a
1269
)
A knot diagram
1
Linearized knot diagam
5 7 11 9 2 10 1 12 6 4 3 8
Solving Sequence
4,10
11 3
7,12
2 6 9 5 1 8
c
10
c
3
c
11
c
2
c
6
c
9
c
4
c
1
c
8
c
5
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5.85714 × 10
181
u
95
+ 9.69877 × 10
181
u
94
+ ··· + 1.18195 × 10
183
b + 3.37065 × 10
183
,
2.93871 × 10
183
u
95
− 7.16174 × 10
183
u
94
+ ··· + 5.42517 × 10
185
a + 2.14826 × 10
185
,
u
96
+ 2u
95
+ ··· + 252u + 36i
I
u
2
= hb + 1, 3a
2
+ 4au − 2a + 2u − 1, u
2
− u + 1i
I
u
3
= hau + 17b − 10a + 2u − 3, 6a
2
− 3au − 6a + 4u + 13, u
2
+ 2i
I
u
4
= hb − 1, 3a + 2u + 1, u
2
+ u + 1i
I
v
1
= ha, b + 3v −2, 3v
2
− 3v + 1i
* 5 irreducible components of dim
C
= 0, with total 108 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
= h5.86 × 10
181
u
95
+ 9.70 × 10
181
u
94
+ · · · + 1.18 × 10
183
b + 3.37 ×
10
183
, 2.94 × 10
183
u
95
− 7.16 × 10
183
u
94
+ · · · + 5.43 × 10
185
a + 2.15 ×
10
185
, u
96
+ 2u
95
+ · · · + 252u + 36i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
3
=
−u
u
3
+ u
a
7
=
−0.00541682u
95
+ 0.0132010u
94
+ ··· + 0.00687780u − 0.395980
−0.0495547u
95
− 0.0820571u
94
+ ··· − 14.3667u − 2.85176
a
12
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
0.0992526u
95
− 0.0551318u
94
+ ··· − 32.0600u − 5.27325
−0.0122200u
95
+ 0.0105278u
94
+ ··· − 4.85256u − 1.05968
a
6
=
0.0441379u
95
+ 0.0952581u
94
+ ··· + 14.3735u + 2.45578
−0.0495547u
95
− 0.0820571u
94
+ ··· − 14.3667u − 2.85176
a
9
=
0.0234885u
95
+ 0.0658944u
94
+ ··· + 3.68018u + 1.26869
0.0283007u
95
+ 0.0420807u
94
+ ··· + 8.03772u + 0.727400
a
5
=
−0.00746047u
95
+ 0.233084u
94
+ ··· + 48.9621u + 6.70772
−0.0189892u
95
− 0.0718124u
94
+ ··· − 16.8541u − 3.26791
a
1
=
0.000359993u
95
+ 0.0337391u
94
+ ··· − 1.28875u + 0.181747
−0.0229557u
95
− 0.0459877u
94
+ ··· − 15.6594u − 3.01831
a
8
=
0.0411489u
95
+ 0.0905918u
94
+ ··· + 9.90432u + 1.92132
0.0139742u
95
+ 0.0146067u
94
+ ··· + 3.23336u − 0.117667
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.231161u
95
+ 0.357393u
94
+ ··· + 149.917u + 38.0944
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
96
+ 6u
95
+ ··· + 1513u + 171
c
2
153(153u
96
− 1122u
95
+ ··· − 2319325u + 211775)
c
3
, c
10
, c
11
u
96
− 2u
95
+ ··· − 252u + 36
c
4
153(153u
96
+ 1122u
95
+ ··· + 2319325u + 211775)
c
6
, c
9
u
96
− 6u
95
+ ··· − 1513u + 171
c
7
, c
8
, c
12
u
96
+ 2u
95
+ ··· + 252u + 36
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
96
− 46y
95
+ ··· + 91835y + 29241
c
2
, c
4
23409
· (23409y
96
+ 3597030y
95
+ ··· − 1268367547525y + 44848650625)
c
3
, c
7
, c
8
c
10
, c
11
, c
12
y
96
+ 88y
95
+ ··· − 11088y + 1296
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.898765 + 0.388007I
a = 0.739120 + 0.992025I
b = −1.235350 + 0.570498I
6.02898 − 12.74240I 0
u = −0.898765 − 0.388007I
a = 0.739120 − 0.992025I
b = −1.235350 − 0.570498I
6.02898 + 12.74240I 0
u = 0.995441 + 0.279700I
a = 0.714209 − 0.582579I
b = −1.124380 − 0.433724I
8.63109 + 5.94668I 0
u = 0.995441 − 0.279700I
a = 0.714209 + 0.582579I
b = −1.124380 + 0.433724I
8.63109 − 5.94668I 0
u = 0.633864 + 0.676593I
a = 0.239952 + 0.307233I
b = 1.052140 − 0.445178I
−0.86556 − 4.10831I 0
u = 0.633864 − 0.676593I
a = 0.239952 − 0.307233I
b = 1.052140 + 0.445178I
−0.86556 + 4.10831I 0
u = −0.803922 + 0.356543I
a = −0.710014 − 0.698458I
b = 1.083670 − 0.332758I
2.95364 − 3.29863I 0
u = −0.803922 − 0.356543I
a = −0.710014 + 0.698458I
b = 1.083670 + 0.332758I
2.95364 + 3.29863I 0
u = −0.727281 + 0.856999I
a = −0.137909 + 0.040758I
b = −1.129590 − 0.494296I
4.65404 + 7.20641I 0
u = −0.727281 − 0.856999I
a = −0.137909 − 0.040758I
b = −1.129590 + 0.494296I
4.65404 − 7.20641I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.622703 + 0.939235I
a = −0.089094 − 0.350289I
b = 0.898679 + 0.116727I
1.38070 − 1.74472I 0
u = −0.622703 − 0.939235I
a = −0.089094 + 0.350289I
b = 0.898679 − 0.116727I
1.38070 + 1.74472I 0
u = 0.772268 + 0.400857I
a = −0.680381 + 0.997728I
b = 1.209110 + 0.583849I
8.87949I 0
u = 0.772268 − 0.400857I
a = −0.680381 − 0.997728I
b = 1.209110 − 0.583849I
− 8.87949I 0
u = 0.771982 + 0.827937I
a = 0.499341 − 0.487132I
b = −0.685204 − 0.234958I
5.13290 + 2.78667I 0
u = 0.771982 − 0.827937I
a = 0.499341 + 0.487132I
b = −0.685204 + 0.234958I
5.13290 − 2.78667I 0
u = −0.599657 + 0.611070I
a = 1.007420 + 0.784394I
b = −0.226957 + 0.654074I
2.06768 + 2.77783I 0
u = −0.599657 − 0.611070I
a = 1.007420 − 0.784394I
b = −0.226957 − 0.654074I
2.06768 − 2.77783I 0
u = −0.115335 + 1.147880I
a = 0.70778 − 2.07964I
b = 1.075860 − 0.501278I
5.12486 − 0.13689I 0
u = −0.115335 − 1.147880I
a = 0.70778 + 2.07964I
b = 1.075860 + 0.501278I
5.12486 + 0.13689I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.731552 + 0.384410I
a = −0.166488 − 0.411126I
b = −0.189877 − 0.960843I
2.83495 − 7.24042I 0. + 6.11797I
u = −0.731552 − 0.384410I
a = −0.166488 + 0.411126I
b = −0.189877 + 0.960843I
2.83495 + 7.24042I 0. − 6.11797I
u = 0.094206 + 1.189270I
a = −0.704909 − 0.522742I
b = −1.41025 − 0.11210I
−0.35798 + 2.04659I 0
u = 0.094206 − 1.189270I
a = −0.704909 + 0.522742I
b = −1.41025 + 0.11210I
−0.35798 − 2.04659I 0
u = 0.690098 + 0.374922I
a = 0.409026 + 0.343398I
b = −0.032781 + 0.521090I
5.76012 + 2.17547I 3.26535 − 2.63718I
u = 0.690098 − 0.374922I
a = 0.409026 − 0.343398I
b = −0.032781 − 0.521090I
5.76012 − 2.17547I 3.26535 + 2.63718I
u = −0.745206 + 0.120913I
a = 0.924044 + 0.512942I
b = −0.733266 − 0.498563I
0.35798 + 2.04659I 1.48192 − 2.96266I
u = −0.745206 − 0.120913I
a = 0.924044 − 0.512942I
b = −0.733266 + 0.498563I
0.35798 − 2.04659I 1.48192 + 2.96266I
u = 0.180320 + 1.232950I
a = 0.446556 − 0.664547I
b = 1.319160 − 0.321760I
4.76539 + 1.42946I 0
u = 0.180320 − 1.232950I
a = 0.446556 + 0.664547I
b = 1.319160 + 0.321760I
4.76539 − 1.42946I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.230955 + 1.258120I
a = 0.72711 + 2.09836I
b = 0.859426 + 0.697175I
4.30438 + 4.69669I 0
u = 0.230955 − 1.258120I
a = 0.72711 − 2.09836I
b = 0.859426 − 0.697175I
4.30438 − 4.69669I 0
u = −0.021775 + 1.313750I
a = −0.37597 + 1.84316I
b = −0.361222 + 1.172990I
−5.13290 − 2.78667I 0
u = −0.021775 − 1.313750I
a = −0.37597 − 1.84316I
b = −0.361222 − 1.172990I
−5.13290 + 2.78667I 0
u = −0.611848 + 0.300748I
a = 0.569630 + 1.018580I
b = −1.163290 + 0.599792I
0.86556 − 4.10831I 1.82293 + 5.09276I
u = −0.611848 − 0.300748I
a = 0.569630 − 1.018580I
b = −1.163290 − 0.599792I
0.86556 + 4.10831I 1.82293 − 5.09276I
u = 0.702614 + 1.125330I
a = −0.0295038 − 0.1080650I
b = −0.973030 + 0.351499I
6.16313 − 0.02021I 0
u = 0.702614 − 1.125330I
a = −0.0295038 + 0.1080650I
b = −0.973030 − 0.351499I
6.16313 + 0.02021I 0
u = −0.655989 + 0.132783I
a = −0.948654 + 0.445473I
b = 1.340740 + 0.306672I
7.91688 − 2.81601I 6.90503 + 4.39381I
u = −0.655989 − 0.132783I
a = −0.948654 − 0.445473I
b = 1.340740 − 0.306672I
7.91688 + 2.81601I 6.90503 − 4.39381I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.256339 + 1.318950I
a = 0.665064 − 0.142114I
b = 1.47305 + 0.18637I
3.36976 − 6.13494I 0
u = −0.256339 − 1.318950I
a = 0.665064 + 0.142114I
b = 1.47305 − 0.18637I
3.36976 + 6.13494I 0
u = −0.359991 + 1.294920I
a = 0.573791 + 1.214200I
b = −0.986026 + 0.574325I
−3.36976 − 6.13494I 0
u = −0.359991 − 1.294920I
a = 0.573791 − 1.214200I
b = −0.986026 − 0.574325I
−3.36976 + 6.13494I 0
u = 0.637602 + 0.042374I
a = −0.47840 + 1.35636I
b = 1.078260 + 0.495005I
8.31265 + 1.52094I 7.32059 − 4.39774I
u = 0.637602 − 0.042374I
a = −0.47840 − 1.35636I
b = 1.078260 − 0.495005I
8.31265 − 1.52094I 7.32059 + 4.39774I
u = −0.130737 + 1.364780I
a = −0.95405 − 1.65292I
b = −0.763978 − 1.168780I
−6.16313 − 0.02021I 0
u = −0.130737 − 1.364780I
a = −0.95405 + 1.65292I
b = −0.763978 + 1.168780I
−6.16313 + 0.02021I 0
u = 0.508376 + 0.346831I
a = 0.128091 − 0.445554I
b = 0.255309 − 0.983307I
−2.95364 + 3.29863I −2.80092 − 7.63925I
u = 0.508376 − 0.346831I
a = 0.128091 + 0.445554I
b = 0.255309 + 0.983307I
−2.95364 − 3.29863I −2.80092 + 7.63925I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.177340 + 1.373420I
a = −0.42613 − 1.58338I
b = −1.158410 − 0.525755I
−2.06768 + 2.77783I 0
u = 0.177340 − 1.373420I
a = −0.42613 + 1.58338I
b = −1.158410 + 0.525755I
−2.06768 − 2.77783I 0
u = −0.033664 + 1.385440I
a = −5.74699 + 0.73017I
b = 1.080390 + 0.068609I
− 0.114059I 0
u = −0.033664 − 1.385440I
a = −5.74699 − 0.73017I
b = 1.080390 − 0.068609I
0.114059I 0
u = 0.536972 + 0.238240I
a = −1.67659 + 0.43396I
b = 0.403646 + 0.441604I
−2.71476 − 0.30303I −4.15215 − 2.67445I
u = 0.536972 − 0.238240I
a = −1.67659 − 0.43396I
b = 0.403646 − 0.441604I
−2.71476 + 0.30303I −4.15215 + 2.67445I
u = −0.06941 + 1.42120I
a = −0.91484 + 1.81338I
b = −0.696526 + 0.120728I
−5.64754 − 0.25291I 0
u = −0.06941 − 1.42120I
a = −0.91484 − 1.81338I
b = −0.696526 − 0.120728I
−5.64754 + 0.25291I 0
u = 0.25699 + 1.40638I
a = −0.38879 + 1.36849I
b = 0.857469 + 0.535742I
−7.91688 + 2.81601I 0
u = 0.25699 − 1.40638I
a = −0.38879 − 1.36849I
b = 0.857469 − 0.535742I
−7.91688 − 2.81601I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11330 + 1.42657I
a = 0.203225 + 1.240760I
b = 0.165447 + 0.846099I
−5.76012 − 2.17547I 0
u = −0.11330 − 1.42657I
a = 0.203225 − 1.240760I
b = 0.165447 − 0.846099I
−5.76012 + 2.17547I 0
u = −0.23382 + 1.41996I
a = −0.47373 + 1.88036I
b = −1.16760 + 0.81853I
−4.65404 − 7.20641I 0
u = −0.23382 − 1.41996I
a = −0.47373 − 1.88036I
b = −1.16760 − 0.81853I
−4.65404 + 7.20641I 0
u = 0.19947 + 1.42576I
a = 0.77078 − 1.51148I
b = 0.463426 − 1.194690I
−8.63109 + 5.94668I 0
u = 0.19947 − 1.42576I
a = 0.77078 + 1.51148I
b = 0.463426 + 1.194690I
−8.63109 − 5.94668I 0
u = −0.24407 + 1.41963I
a = −0.435799 − 0.272544I
b = −0.488637 − 0.633305I
−4.76539 − 1.42946I 0
u = −0.24407 − 1.41963I
a = −0.435799 + 0.272544I
b = −0.488637 + 0.633305I
−4.76539 + 1.42946I 0
u = 0.26655 + 1.43615I
a = −0.310306 + 1.108040I
b = −0.179542 + 0.892827I
5.67688I 0
u = 0.26655 − 1.43615I
a = −0.310306 − 1.108040I
b = −0.179542 − 0.892827I
− 5.67688I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.524036 + 0.118018I
a = 1.187280 − 0.725665I
b = −1.214580 − 0.185845I
2.71476 + 0.30303I 4.15215 + 2.67445I
u = 0.524036 − 0.118018I
a = 1.187280 + 0.725665I
b = −1.214580 + 0.185845I
2.71476 − 0.30303I 4.15215 − 2.67445I
u = −0.29633 + 1.45000I
a = 0.19603 − 1.49186I
b = 1.175980 − 0.547847I
−2.83495 − 7.24042I 0
u = −0.29633 − 1.45000I
a = 0.19603 + 1.49186I
b = 1.175980 + 0.547847I
−2.83495 + 7.24042I 0
u = −0.297510 + 0.424068I
a = −1.76121 + 1.51699I
b = −0.975998 − 0.255863I
0.990478I 0. + 7.11271I
u = −0.297510 − 0.424068I
a = −1.76121 − 1.51699I
b = −0.975998 + 0.255863I
− 0.990478I 0. − 7.11271I
u = −0.27765 + 1.45892I
a = −0.70912 − 1.33877I
b = −0.298273 − 1.124210I
−3.08590 − 10.91640I 0
u = −0.27765 − 1.45892I
a = −0.70912 + 1.33877I
b = −0.298273 + 1.124210I
−3.08590 + 10.91640I 0
u = 0.29051 + 1.47268I
a = 0.29548 + 1.81215I
b = 1.25358 + 0.72493I
−6.02898 + 12.74240I 0
u = 0.29051 − 1.47268I
a = 0.29548 − 1.81215I
b = 1.25358 − 0.72493I
−6.02898 − 12.74240I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.39714 + 1.45835I
a = −0.03856 − 1.48788I
b = −1.209130 − 0.553068I
3.08590 + 10.91640I 0
u = 0.39714 − 1.45835I
a = −0.03856 + 1.48788I
b = −1.209130 + 0.553068I
3.08590 − 10.91640I 0
u = −0.34566 + 1.48991I
a = −0.14552 + 1.81713I
b = −1.27576 + 0.65676I
− 17.2440I 0
u = −0.34566 − 1.48991I
a = −0.14552 − 1.81713I
b = −1.27576 − 0.65676I
17.2440I 0
u = −0.036347 + 0.467928I
a = 2.38863 − 4.44522I
b = 1.049490 − 0.176177I
5.64754 + 0.25291I −1.00897 + 2.63613I
u = −0.036347 − 0.467928I
a = 2.38863 + 4.44522I
b = 1.049490 + 0.176177I
5.64754 − 0.25291I −1.00897 − 2.63613I
u = 0.13518 + 1.53492I
a = 0.708724 − 0.527451I
b = 0.723646 − 0.536849I
−8.31265 − 1.52094I 0
u = 0.13518 − 1.53492I
a = 0.708724 + 0.527451I
b = 0.723646 + 0.536849I
−8.31265 + 1.52094I 0
u = −0.13446 + 1.53766I
a = 0.039219 + 1.258400I
b = −0.592833 + 0.577440I
−5.12486 + 0.13689I 0
u = −0.13446 − 1.53766I
a = 0.039219 − 1.258400I
b = −0.592833 − 0.577440I
−5.12486 − 0.13689I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.250207 + 0.339089I
a = −0.402030 + 0.539333I
b = −0.103366 + 0.303393I
− 0.799053I 0. + 8.48530I
u = −0.250207 − 0.339089I
a = −0.402030 − 0.539333I
b = −0.103366 − 0.303393I
0.799053I 0. − 8.48530I
u = −0.05000 + 1.60773I
a = −0.614107 − 0.858616I
b = −0.894979 − 0.572244I
−4.30438 + 4.69669I 0
u = −0.05000 − 1.60773I
a = −0.614107 + 0.858616I
b = −0.894979 + 0.572244I
−4.30438 − 4.69669I 0
u = −0.338391 + 0.110245I
a = −0.043652 − 0.574113I
b = −0.547622 − 1.025950I
−1.38070 + 1.74472I 9.50332 + 6.81540I
u = −0.338391 − 0.110245I
a = −0.043652 + 0.574113I
b = −0.547622 + 1.025950I
−1.38070 − 1.74472I 9.50332 − 6.81540I
14
II. I
u
2
= hb + 1, 3a
2
+ 4au − 2a + 2u − 1, u
2
− u + 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
−u + 1
a
3
=
−u
u − 1
a
7
=
a
−1
a
12
=
u
−u + 2
a
2
=
−
1
3
au +
2
3
a −
2
3
u +
1
3
−au + a + 2u − 1
a
6
=
a + 1
−1
a
9
=
−a
1
a
5
=
−
2
3
au +
4
3
a −
1
3
u +
2
3
−au + u
a
1
=
au
−au + 2a + 2u − 2
a
8
=
au + u − 1
−3au + 3a + u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u + 8
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
11
(u
2
− u + 1)
2
c
2
3(3u
4
+ 4u
2
+ 4u + 1)
c
3
, c
5
(u
2
+ u + 1)
2
c
4
3(3u
4
− 6u
3
+ u
2
+ 2u + 1)
c
6
(u − 1)
4
c
7
, c
8
, c
12
(u
2
+ 2)
2
c
9
(u + 1)
4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
10
, c
11
(y
2
+ y + 1)
2
c
2
9(9y
4
+ 24y
3
+ 22y
2
− 8y + 1)
c
4
9(9y
4
− 30y
3
+ 31y
2
− 2y + 1)
c
6
, c
9
(y −1)
4
c
7
, c
8
, c
12
(y + 2)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.408248 − 1.284460I
b = −1.00000
6.57974 + 2.02988I 6.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = −0.408248 + 0.129757I
b = −1.00000
6.57974 + 2.02988I 6.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = 0.408248 + 1.284460I
b = −1.00000
6.57974 − 2.02988I 6.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −0.408248 − 0.129757I
b = −1.00000
6.57974 − 2.02988I 6.00000 + 3.46410I
18
III. I
u
3
= hau + 17b − 10a + 2u − 3, 6a
2
− 3au − 6a + 4u + 13, u
2
+ 2i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
2
a
3
=
−u
−u
a
7
=
a
−0.0588235au + 0.588235a − 0.117647u + 0.176471
a
12
=
−1
0
a
2
=
−0.176471au + 0.764706a − 0.186275u − 0.803922
−0.235294au + 0.352941a − 0.470588u − 0.294118
a
6
=
0.0588235au + 0.411765a + 0.117647u − 0.176471
−0.0588235au + 0.588235a − 0.117647u + 0.176471
a
9
=
0.176471au + 0.235294a − 0.147059u + 0.470588
−0.0588235au + 0.588235a − 0.117647u − 0.823529
a
5
=
0.235294au − 0.352941a + 0.303922u + 0.627451
0.176471au + 0.235294a + 0.352941u + 0.470588
a
1
=
0.0588235au + 0.411765a + 0.117647u − 0.176471
−0.0588235au + 0.588235a − 0.117647u + 0.176471
a
8
=
0.117647au + 0.823529a − 0.264706u − 0.352941
−0.0588235au + 0.588235a − 0.117647u − 0.823529
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4
17
au −
40
17
a +
8
17
u −
80
17
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u + 1)
4
c
2
3(3u
4
+ 6u
3
+ u
2
− 2u + 1)
c
3
, c
10
, c
11
(u
2
+ 2)
2
c
4
3(3u
4
+ 4u
2
− 4u + 1)
c
5
(u − 1)
4
c
6
, c
7
, c
8
(u
2
+ u + 1)
2
c
9
, c
12
(u
2
− u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)
4
c
2
9(9y
4
− 30y
3
+ 31y
2
− 2y + 1)
c
3
, c
10
, c
11
(y + 2)
4
c
4
9(9y
4
+ 24y
3
+ 22y
2
− 8y + 1)
c
6
, c
7
, c
8
c
9
, c
12
(y
2
+ y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.704124 − 1.089820I
b = 0.500000 − 0.866025I
−6.57974 − 2.02988I −6.00000 + 3.46410I
u = 1.414210I
a = 0.29588 + 1.79693I
b = 0.500000 + 0.866025I
−6.57974 + 2.02988I −6.00000 − 3.46410I
u = − 1.414210I
a = 0.704124 + 1.089820I
b = 0.500000 + 0.866025I
−6.57974 + 2.02988I −6.00000 − 3.46410I
u = − 1.414210I
a = 0.29588 − 1.79693I
b = 0.500000 − 0.866025I
−6.57974 − 2.02988I −6.00000 + 3.46410I
22
IV. I
u
4
= hb − 1, 3a + 2u + 1, u
2
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
u + 1
a
3
=
−u
u + 1
a
7
=
−
2
3
u −
1
3
1
a
12
=
−u
u + 2
a
2
=
−u +
1
3
5
3
u +
4
3
a
6
=
−
2
3
u −
4
3
1
a
9
=
−
2
3
u −
1
3
1
a
5
=
−
1
3
u
4
3
u +
2
3
a
1
=
−u
u + 2
a
8
=
−
2
3
u −
1
3
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
28
3
u + 10
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
2
− u + 1
c
2
3(3u
2
+ 1)
c
4
3(3u
2
+ 3u + 1)
c
5
, c
10
, c
11
u
2
+ u + 1
c
6
(u + 1)
2
c
7
, c
8
, c
12
u
2
c
9
(u − 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
10
, c
11
y
2
+ y + 1
c
2
9(3y + 1)
2
c
4
9(9y
2
− 3y + 1)
c
6
, c
9
(y −1)
2
c
7
, c
8
, c
12
y
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = − 0.577350I
b = 1.00000
1.64493 − 2.02988I 5.33333 + 8.08290I
u = −0.500000 − 0.866025I
a = 0.577350I
b = 1.00000
1.64493 + 2.02988I 5.33333 − 8.08290I
26
V. I
v
1
= ha, b + 3v − 2, 3v
2
− 3v + 1i
(i) Arc colorings
a
4
=
v
0
a
10
=
1
0
a
11
=
1
0
a
3
=
v
0
a
7
=
0
−3v + 2
a
12
=
1
0
a
2
=
v
2v − 1
a
6
=
3v − 2
−3v + 2
a
9
=
3v
−3v + 1
a
5
=
4v − 2
−v + 1
a
1
=
−3v + 2
3v − 2
a
8
=
1
−3v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 28v −
58
3
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
3(3u
2
− 3u + 1)
c
3
, c
10
, c
11
u
2
c
4
3(3u
2
+ 1)
c
5
(u + 1)
2
c
6
, c
12
u
2
+ u + 1
c
7
, c
8
, c
9
u
2
− u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y − 1)
2
c
2
9(9y
2
− 3y + 1)
c
3
, c
10
, c
11
y
2
c
4
9(3y + 1)
2
c
6
, c
7
, c
8
c
9
, c
12
y
2
+ y + 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.288675I
a = 0
b = 0.500000 − 0.866025I
−1.64493 − 2.02988I −5.33333 + 8.08290I
v = 0.500000 − 0.288675I
a = 0
b = 0.500000 + 0.866025I
−1.64493 + 2.02988I −5.33333 − 8.08290I
30
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u + 1)
4
(u
2
− u + 1)
3
(u
96
+ 6u
95
+ ··· + 1513u + 171)
c
2
12393(3u
2
+ 1)(3u
2
− 3u + 1)(3u
4
+ 4u
2
+ 4u + 1)
· (3u
4
+ 6u
3
+ u
2
− 2u + 1)
· (153u
96
− 1122u
95
+ ··· − 2319325u + 211775)
c
3
u
2
(u
2
+ 2)
2
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
96
− 2u
95
+ ··· − 252u + 36)
c
4
12393(3u
2
+ 1)(3u
2
+ 3u + 1)(3u
4
+ 4u
2
− 4u + 1)
· (3u
4
− 6u
3
+ u
2
+ 2u + 1)
· (153u
96
+ 1122u
95
+ ··· + 2319325u + 211775)
c
5
((u − 1)
4
)(u + 1)
2
(u
2
+ u + 1)
3
(u
96
+ 6u
95
+ ··· + 1513u + 171)
c
6
((u − 1)
4
)(u + 1)
2
(u
2
+ u + 1)
3
(u
96
− 6u
95
+ ··· − 1513u + 171)
c
7
, c
8
u
2
(u
2
+ 2)
2
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
96
+ 2u
95
+ ··· + 252u + 36)
c
9
((u − 1)
2
)(u + 1)
4
(u
2
− u + 1)
3
(u
96
− 6u
95
+ ··· − 1513u + 171)
c
10
, c
11
u
2
(u
2
+ 2)
2
(u
2
− u + 1)
2
(u
2
+ u + 1)(u
96
− 2u
95
+ ··· − 252u + 36)
c
12
u
2
(u
2
+ 2)
2
(u
2
− u + 1)
2
(u
2
+ u + 1)(u
96
+ 2u
95
+ ··· + 252u + 36)
31
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
((y − 1)
6
)(y
2
+ y + 1)
3
(y
96
− 46y
95
+ ··· + 91835y + 29241)
c
2
, c
4
153586449(3y + 1)
2
(9y
2
− 3y + 1)(9y
4
− 30y
3
+ 31y
2
− 2y + 1)
· (9y
4
+ 24y
3
+ 22y
2
− 8y + 1)
· (23409y
96
+ 3597030y
95
+ ··· − 1268367547525y + 44848650625)
c
3
, c
7
, c
8
c
10
, c
11
, c
12
y
2
(y + 2)
4
(y
2
+ y + 1)
3
(y
96
+ 88y
95
+ ··· − 11088y + 1296)
32
