12a
0120
(K12a
0120
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 11 4 7 6 1 9 10
Solving Sequence
4,7
8
9,11
12 3 6 10 1 5 2
c
7
c
8
c
11
c
3
c
6
c
9
c
12
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.75706 × 10
313
u
125
+ 2.01574 × 10
313
u
124
+ ··· + 4.16145 × 10
314
b + 9.40803 × 10
315
,
− 1.92978 × 10
314
u
125
− 2.84524 × 10
314
u
124
+ ··· + 1.66458 × 10
315
a + 4.14260 × 10
316
,
u
126
+ 2u
125
+ ··· + 192u + 64i
I
u
2
= h−2u
2
+ b − u − 3, −7u
2
+ a − 3u − 12, u
3
+ u
2
+ 2u + 1i
I
v
1
= ha, −5v
5
+ 46v
4
− 122v
3
+ 163v
2
+ 69b + 27v + 86, v
6
− 3v
5
+ 6v
4
+ 5v
2
− v + 1i
* 3 irreducible components of dim
C
= 0, with total 135 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−1.76 × 10
313
u
125
+ 2.02 × 10
313
u
124
+ · · · + 4.16 × 10
314
b + 9.41 ×
10
315
, −1.93 × 10
314
u
125
− 2.85 × 10
314
u
124
+ · · · + 1.66 × 10
315
a + 4.14 ×
10
316
, u
126
+ 2u
125
+ · · · + 192u + 64i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
11
=
0.115932u
125
+ 0.170928u
124
+ ··· − 21.4968u − 24.8867
0.0422222u
125
− 0.0484384u
124
+ ··· − 57.8079u − 22.6075
a
12
=
0.0835374u
125
+ 0.170647u
124
+ ··· + 7.57394u − 11.3645
0.0603937u
125
− 0.0175989u
124
+ ··· − 68.0136u − 27.0882
a
3
=
u
u
3
+ u
a
6
=
0.0131721u
125
+ 0.160291u
124
+ ··· + 31.9622u + 2.52399
−0.0309936u
125
− 0.0501114u
124
+ ··· + 21.4480u + 2.89453
a
10
=
0.135778u
125
+ 0.231184u
124
+ ··· − 24.6169u − 20.6261
−0.0157486u
125
− 0.0505249u
124
+ ··· − 45.0908u − 12.3200
a
1
=
0.134423u
125
+ 0.249675u
124
+ ··· − 15.7540u − 12.1955
−0.0161903u
125
− 0.0611574u
124
+ ··· − 50.9747u − 14.3007
a
5
=
0.0842320u
125
+ 0.177889u
124
+ ··· + 30.2985u + 3.33220
−0.0501911u
125
− 0.0717859u
124
+ ··· + 46.0525u + 15.5277
a
2
=
−0.116123u
125
− 0.204715u
124
+ ··· + 22.9544u + 12.7987
0.0366348u
125
+ 0.0898334u
124
+ ··· + 55.3988u + 14.3689
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.597782u
125
− 0.910341u
124
+ ··· − 72.2510u + 19.0666
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
126
+ 68u
125
+ ··· − 17u + 1
c
2
, c
4
u
126
− 8u
125
+ ··· − 9u + 1
c
3
, c
7
u
126
+ 2u
125
+ ··· + 192u + 64
c
5
u
126
+ 4u
125
+ ··· − 1174u − 44
c
6
u
126
− 65u
124
+ ··· + 4405u − 191
c
8
u
126
− 42u
125
+ ··· − 118784u + 4096
c
9
u
126
− 9u
125
+ ··· + 2u − 1
c
10
, c
12
u
126
+ 5u
125
+ ··· − 43u − 1
c
11
u
126
− 20u
125
+ ··· + 124u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
126
− 12y
125
+ ··· − 363y + 1
c
2
, c
4
y
126
− 68y
125
+ ··· + 17y + 1
c
3
, c
7
y
126
+ 42y
125
+ ··· + 118784y + 4096
c
5
y
126
− 122y
125
+ ··· − 141964y + 1936
c
6
y
126
− 130y
125
+ ··· − 3185069y + 36481
c
8
y
126
+ 74y
125
+ ··· − 125829120y + 16777216
c
9
y
126
+ 15y
125
+ ··· − 14y + 1
c
10
, c
12
y
126
− 75y
125
+ ··· − 971y + 1
c
11
y
126
− 24y
125
+ ··· − 8848y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.583149 + 0.813259I
a = −2.27053 − 2.09717I
b = −2.12049 + 0.36398I
0.84437 + 1.77385I 0
u = −0.583149 − 0.813259I
a = −2.27053 + 2.09717I
b = −2.12049 − 0.36398I
0.84437 − 1.77385I 0
u = 0.759752 + 0.658456I
a = 0.990273 − 0.425417I
b = 0.968883 − 0.742231I
−3.19646 + 2.28892I 0
u = 0.759752 − 0.658456I
a = 0.990273 + 0.425417I
b = 0.968883 + 0.742231I
−3.19646 − 2.28892I 0
u = −0.664545 + 0.755167I
a = −1.91116 + 0.31023I
b = −0.266100 + 0.222908I
−1.33049 + 2.05219I 0
u = −0.664545 − 0.755167I
a = −1.91116 − 0.31023I
b = −0.266100 − 0.222908I
−1.33049 − 2.05219I 0
u = 0.638089 + 0.779199I
a = 1.331460 − 0.202093I
b = 1.222590 − 0.051065I
−5.12052 − 2.76244I 0
u = 0.638089 − 0.779199I
a = 1.331460 + 0.202093I
b = 1.222590 + 0.051065I
−5.12052 + 2.76244I 0
u = 1.008890 + 0.070007I
a = −0.673317 + 1.017130I
b = −0.770780 + 0.916567I
2.18854 + 7.22641I 0
u = 1.008890 − 0.070007I
a = −0.673317 − 1.017130I
b = −0.770780 − 0.916567I
2.18854 − 7.22641I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.134506 + 1.012070I
a = 0.668124 + 0.853058I
b = 3.48596 − 0.00064I
3.77115 + 2.20092I 0
u = −0.134506 − 1.012070I
a = 0.668124 − 0.853058I
b = 3.48596 + 0.00064I
3.77115 − 2.20092I 0
u = −0.236806 + 0.993858I
a = 0.318381 + 0.206135I
b = −0.459228 − 0.816560I
1.90248 + 2.83956I 0
u = −0.236806 − 0.993858I
a = 0.318381 − 0.206135I
b = −0.459228 + 0.816560I
1.90248 − 2.83956I 0
u = −0.077039 + 1.019420I
a = 0.301952 − 1.244190I
b = −0.416347 + 0.577211I
2.60094 + 2.12761I 0
u = −0.077039 − 1.019420I
a = 0.301952 + 1.244190I
b = −0.416347 − 0.577211I
2.60094 − 2.12761I 0
u = −0.870239 + 0.437016I
a = 1.087070 + 0.208479I
b = 0.941206 + 0.100996I
−1.62685 − 0.40405I 0
u = −0.870239 − 0.437016I
a = 1.087070 − 0.208479I
b = 0.941206 − 0.100996I
−1.62685 + 0.40405I 0
u = −0.750514 + 0.607886I
a = 1.46168 + 0.08062I
b = 0.039045 − 1.191420I
0.258302 − 1.180800I 0
u = −0.750514 − 0.607886I
a = 1.46168 − 0.08062I
b = 0.039045 + 1.191420I
0.258302 + 1.180800I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.701966 + 0.759826I
a = −1.24534 − 0.98866I
b = −1.35863 − 0.90605I
−3.74921 − 4.56977I 0
u = −0.701966 − 0.759826I
a = −1.24534 + 0.98866I
b = −1.35863 + 0.90605I
−3.74921 + 4.56977I 0
u = 0.745954 + 0.737217I
a = 2.68359 − 2.36502I
b = 2.49265 − 0.33125I
−2.73974 + 0.70736I 0
u = 0.745954 − 0.737217I
a = 2.68359 + 2.36502I
b = 2.49265 + 0.33125I
−2.73974 − 0.70736I 0
u = −0.089485 + 0.946069I
a = −1.249160 − 0.515417I
b = 0.704137 + 0.779201I
0.43085 − 5.09047I 0
u = −0.089485 − 0.946069I
a = −1.249160 + 0.515417I
b = 0.704137 − 0.779201I
0.43085 + 5.09047I 0
u = −0.026963 + 0.943464I
a = −0.023574 − 0.809845I
b = −0.891412 + 0.637060I
2.41442 + 1.40190I 0
u = −0.026963 − 0.943464I
a = −0.023574 + 0.809845I
b = −0.891412 − 0.637060I
2.41442 − 1.40190I 0
u = −1.036680 + 0.220066I
a = −0.464905 + 0.853859I
b = −0.555634 + 0.740553I
1.84155 + 2.77321I 0
u = −1.036680 − 0.220066I
a = −0.464905 − 0.853859I
b = −0.555634 − 0.740553I
1.84155 − 2.77321I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.902790 + 0.575810I
a = −1.07620 + 1.11597I
b = −1.18235 + 1.02995I
0.07212 + 8.10921I 0
u = 0.902790 − 0.575810I
a = −1.07620 − 1.11597I
b = −1.18235 − 1.02995I
0.07212 − 8.10921I 0
u = 0.515649 + 0.940162I
a = 0.384039 − 0.553428I
b = −0.142785 + 1.192870I
4.07539 − 1.91046I 0
u = 0.515649 − 0.940162I
a = 0.384039 + 0.553428I
b = −0.142785 − 1.192870I
4.07539 + 1.91046I 0
u = 0.821210 + 0.696105I
a = −3.79082 + 2.12632I
b = −2.69384 − 0.31365I
−2.64594 + 1.92186I 0
u = 0.821210 − 0.696105I
a = −3.79082 − 2.12632I
b = −2.69384 + 0.31365I
−2.64594 − 1.92186I 0
u = 0.066247 + 1.075380I
a = −0.977182 − 0.775036I
b = −0.333226 + 0.939079I
6.12098 − 0.47562I 0
u = 0.066247 − 1.075380I
a = −0.977182 + 0.775036I
b = −0.333226 − 0.939079I
6.12098 + 0.47562I 0
u = −0.866742 + 0.650126I
a = 1.59684 + 0.84010I
b = 0.366133 + 0.274926I
−1.08056 − 4.64409I 0
u = −0.866742 − 0.650126I
a = 1.59684 − 0.84010I
b = 0.366133 − 0.274926I
−1.08056 + 4.64409I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.164623 + 1.090970I
a = −1.48823 + 0.56829I
b = −0.408591 − 0.765828I
5.90160 − 4.26455I 0
u = 0.164623 − 1.090970I
a = −1.48823 − 0.56829I
b = −0.408591 + 0.765828I
5.90160 + 4.26455I 0
u = −0.612029 + 0.921384I
a = 2.22856 + 2.25864I
b = 2.93767 + 0.27662I
1.22072 + 2.96447I 0
u = −0.612029 − 0.921384I
a = 2.22856 − 2.25864I
b = 2.93767 − 0.27662I
1.22072 − 2.96447I 0
u = 0.608068 + 0.939760I
a = −0.77684 + 1.29711I
b = −1.017590 − 0.210549I
−4.61530 − 2.13294I 0
u = 0.608068 − 0.939760I
a = −0.77684 − 1.29711I
b = −1.017590 + 0.210549I
−4.61530 + 2.13294I 0
u = −0.715251 + 0.862634I
a = −1.98026 − 1.22824I
b = −0.960920 + 0.834792I
−6.56601 + 3.77378I 0
u = −0.715251 − 0.862634I
a = −1.98026 + 1.22824I
b = −0.960920 − 0.834792I
−6.56601 − 3.77378I 0
u = −0.712315 + 0.865143I
a = 1.135870 + 0.516782I
b = 1.122660 + 0.794419I
−6.55718 + 1.68165I 0
u = −0.712315 − 0.865143I
a = 1.135870 − 0.516782I
b = 1.122660 − 0.794419I
−6.55718 − 1.68165I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.283809 + 1.084470I
a = −0.307008 + 1.170970I
b = −0.539369 − 0.764055I
1.79448 − 6.78921I 0
u = 0.283809 − 1.084470I
a = −0.307008 − 1.170970I
b = −0.539369 + 0.764055I
1.79448 + 6.78921I 0
u = −0.837606 + 0.789777I
a = −0.275211 + 0.022470I
b = −0.465135 − 0.192347I
−1.93800 + 2.88339I 0
u = −0.837606 − 0.789777I
a = −0.275211 − 0.022470I
b = −0.465135 + 0.192347I
−1.93800 − 2.88339I 0
u = −0.654600 + 0.951229I
a = 1.32579 + 0.75494I
b = 0.278284 − 0.095007I
−0.71690 + 3.08171I 0
u = −0.654600 − 0.951229I
a = 1.32579 − 0.75494I
b = 0.278284 + 0.095007I
−0.71690 − 3.08171I 0
u = 0.604520 + 0.985901I
a = −1.82381 + 0.04022I
b = −0.458706 − 0.357924I
2.96423 − 5.62025I 0
u = 0.604520 − 0.985901I
a = −1.82381 − 0.04022I
b = −0.458706 + 0.357924I
2.96423 + 5.62025I 0
u = −0.675660 + 0.951102I
a = 2.05437 + 1.09047I
b = 1.25164 − 1.09110I
−3.15580 + 9.87799I 0
u = −0.675660 − 0.951102I
a = 2.05437 − 1.09047I
b = 1.25164 + 1.09110I
−3.15580 − 9.87799I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.778808 + 0.875358I
a = −0.572900 + 0.148261I
b = −0.778626 + 0.292904I
−5.56540 − 7.22095I 0
u = 0.778808 − 0.875358I
a = −0.572900 − 0.148261I
b = −0.778626 − 0.292904I
−5.56540 + 7.22095I 0
u = −0.927777 + 0.716525I
a = 0.915372 + 0.564965I
b = 0.932781 + 0.880195I
−6.29832 − 6.58519I 0
u = −0.927777 − 0.716525I
a = 0.915372 − 0.564965I
b = 0.932781 − 0.880195I
−6.29832 + 6.58519I 0
u = 0.804790 + 0.868133I
a = 0.695000 − 0.451647I
b = 0.419235 + 0.407307I
−5.59394 + 1.30207I 0
u = 0.804790 − 0.868133I
a = 0.695000 + 0.451647I
b = 0.419235 − 0.407307I
−5.59394 − 1.30207I 0
u = −0.728276 + 0.935353I
a = 0.717051 + 0.100206I
b = 0.251817 − 0.678471I
−1.50108 + 2.95525I 0
u = −0.728276 − 0.935353I
a = 0.717051 − 0.100206I
b = 0.251817 + 0.678471I
−1.50108 − 2.95525I 0
u = 0.896738 + 0.785992I
a = −0.048661 + 0.320511I
b = −0.358535 + 0.534392I
−5.47055 + 1.59927I 0
u = 0.896738 − 0.785992I
a = −0.048661 − 0.320511I
b = −0.358535 − 0.534392I
−5.47055 − 1.59927I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.399196 + 0.700132I
a = 1.30026 − 1.13581I
b = −0.0886921 − 0.0654109I
1.88586 + 1.07699I 1.62389 − 3.53502I
u = 0.399196 − 0.700132I
a = 1.30026 + 1.13581I
b = −0.0886921 + 0.0654109I
1.88586 − 1.07699I 1.62389 + 3.53502I
u = 0.700027 + 0.968567I
a = −2.65238 + 1.24312I
b = −2.28063 − 0.74089I
−2.03372 − 6.21937I 0
u = 0.700027 − 0.968567I
a = −2.65238 − 1.24312I
b = −2.28063 + 0.74089I
−2.03372 + 6.21937I 0
u = 0.781482 + 0.172967I
a = 0.808853 + 0.018479I
b = 0.670001 − 0.475989I
−1.45891 + 3.00718I −6.53766 − 7.29173I
u = 0.781482 − 0.172967I
a = 0.808853 − 0.018479I
b = 0.670001 + 0.475989I
−1.45891 − 3.00718I −6.53766 + 7.29173I
u = 1.016950 + 0.656632I
a = 1.127170 − 0.394461I
b = 1.018790 − 0.286886I
−4.10359 + 4.97237I 0
u = 1.016950 − 0.656632I
a = 1.127170 + 0.394461I
b = 1.018790 + 0.286886I
−4.10359 − 4.97237I 0
u = 0.690126 + 1.005750I
a = −1.57769 + 0.94724I
b = −0.878384 − 0.923292I
−2.16358 − 7.80144I 0
u = 0.690126 − 1.005750I
a = −1.57769 − 0.94724I
b = −0.878384 + 0.923292I
−2.16358 + 7.80144I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.678688 + 1.020830I
a = 0.439176 + 0.089131I
b = −0.135909 − 1.297310I
1.45595 + 6.62892I 0
u = −0.678688 − 1.020830I
a = 0.439176 − 0.089131I
b = −0.135909 + 1.297310I
1.45595 − 6.62892I 0
u = −1.006940 + 0.706541I
a = −1.16108 − 1.22610I
b = −1.26556 − 1.14457I
−2.73943 − 12.79060I 0
u = −1.006940 − 0.706541I
a = −1.16108 + 1.22610I
b = −1.26556 + 1.14457I
−2.73943 + 12.79060I 0
u = 0.724342 + 1.011870I
a = 2.42566 − 2.06794I
b = 2.97434 − 0.51864I
−1.67836 − 7.71869I 0
u = 0.724342 − 1.011870I
a = 2.42566 + 2.06794I
b = 2.97434 + 0.51864I
−1.67836 + 7.71869I 0
u = −0.153007 + 1.240150I
a = 0.092403 + 0.405281I
b = 0.712066 − 1.144450I
7.35610 + 6.53099I 0
u = −0.153007 − 1.240150I
a = 0.092403 − 0.405281I
b = 0.712066 + 1.144450I
7.35610 − 6.53099I 0
u = −0.724716 + 1.045350I
a = −1.72340 − 0.01075I
b = −0.555674 + 0.271956I
0.13511 + 10.55390I 0
u = −0.724716 − 1.045350I
a = −1.72340 + 0.01075I
b = −0.555674 − 0.271956I
0.13511 − 10.55390I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.269690 + 1.247800I
a = −0.552188 − 0.177434I
b = 0.337114 − 0.856607I
6.88746 + 2.92032I 0
u = 0.269690 − 1.247800I
a = −0.552188 + 0.177434I
b = 0.337114 + 0.856607I
6.88746 − 2.92032I 0
u = 0.332493 + 1.237100I
a = 0.606989 − 0.510422I
b = 0.87160 + 1.22545I
6.38584 − 11.97810I 0
u = 0.332493 − 1.237100I
a = 0.606989 + 0.510422I
b = 0.87160 − 1.22545I
6.38584 + 11.97810I 0
u = 0.787834 + 1.012220I
a = 0.891993 − 0.032374I
b = 0.404575 + 0.814507I
−4.72827 − 7.84683I 0
u = 0.787834 − 1.012220I
a = 0.891993 + 0.032374I
b = 0.404575 − 0.814507I
−4.72827 + 7.84683I 0
u = 0.715508 + 1.083340I
a = 1.89202 − 0.64242I
b = 1.25623 + 1.21274I
1.6137 − 14.0645I 0
u = 0.715508 − 1.083340I
a = 1.89202 + 0.64242I
b = 1.25623 − 1.21274I
1.6137 + 14.0645I 0
u = −0.776257 + 1.050290I
a = −1.67633 − 0.68364I
b = −0.920719 + 0.994953I
−5.23670 + 12.86370I 0
u = −0.776257 − 1.050290I
a = −1.67633 + 0.68364I
b = −0.920719 − 0.994953I
−5.23670 − 12.86370I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.681519 + 1.116400I
a = −0.953613 − 0.750387I
b = −0.988872 + 0.378489I
0.33688 + 6.13842I 0
u = −0.681519 − 1.116400I
a = −0.953613 + 0.750387I
b = −0.988872 − 0.378489I
0.33688 − 6.13842I 0
u = −0.671958 + 0.032843I
a = 1.134640 + 0.025913I
b = 0.609434 − 0.177023I
−1.094370 + 0.027147I −7.58274 + 0.49956I
u = −0.671958 − 0.032843I
a = 1.134640 − 0.025913I
b = 0.609434 + 0.177023I
−1.094370 − 0.027147I −7.58274 − 0.49956I
u = 0.670945 + 0.001703I
a = 2.03081 − 0.90267I
b = 0.027865 − 0.807747I
2.03745 + 1.42816I 2.53417 − 4.60053I
u = 0.670945 − 0.001703I
a = 2.03081 + 0.90267I
b = 0.027865 + 0.807747I
2.03745 − 1.42816I 2.53417 + 4.60053I
u = 0.092281 + 0.648619I
a = 1.88480 + 2.55860I
b = −0.746614 − 0.345912I
−2.61100 − 1.34807I −3.48651 + 4.76024I
u = 0.092281 − 0.648619I
a = 1.88480 − 2.55860I
b = −0.746614 + 0.345912I
−2.61100 + 1.34807I −3.48651 − 4.76024I
u = −0.455105 + 1.272310I
a = −0.513941 + 0.327642I
b = 0.159968 + 0.682133I
5.46522 + 2.67251I 0
u = −0.455105 − 1.272310I
a = −0.513941 − 0.327642I
b = 0.159968 − 0.682133I
5.46522 − 2.67251I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.802002 + 1.094610I
a = 2.07806 + 0.46476I
b = 1.33080 − 1.24162I
−1.4825 + 19.3861I 0
u = −0.802002 − 1.094610I
a = 2.07806 − 0.46476I
b = 1.33080 + 1.24162I
−1.4825 − 19.3861I 0
u = 0.786293 + 1.115480I
a = −1.219080 + 0.712549I
b = −1.082880 − 0.429394I
−2.63820 − 11.52950I 0
u = 0.786293 − 1.115480I
a = −1.219080 − 0.712549I
b = −1.082880 + 0.429394I
−2.63820 + 11.52950I 0
u = −0.162781 + 1.386730I
a = −0.120667 − 0.112289I
b = −0.572165 + 0.101717I
4.49508 + 2.99438I 0
u = −0.162781 − 1.386730I
a = −0.120667 + 0.112289I
b = −0.572165 − 0.101717I
4.49508 − 2.99438I 0
u = −0.595624
a = 1.09335
b = 0.418065
−1.09586 −8.62110
u = 0.049191 + 0.593330I
a = 1.255130 − 0.115065I
b = 1.148540 − 0.348624I
−2.83015 + 0.66433I −0.80758 + 1.62533I
u = 0.049191 − 0.593330I
a = 1.255130 + 0.115065I
b = 1.148540 + 0.348624I
−2.83015 − 0.66433I −0.80758 − 1.62533I
u = −0.547594
a = −20.8987
b = −4.73364
0.509050 −323.410
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.070102 + 0.510627I
a = −1.029320 + 0.564029I
b = −1.158460 + 0.464443I
−1.24958 + 5.86869I 5.67430 − 9.68755I
u = −0.070102 − 0.510627I
a = −1.029320 − 0.564029I
b = −1.158460 − 0.464443I
−1.24958 − 5.86869I 5.67430 + 9.68755I
u = 0.299663 + 0.400210I
a = 1.60395 − 1.42858I
b = −0.261831 − 0.384133I
1.85257 + 1.11176I 2.15039 − 2.20620I
u = 0.299663 − 0.400210I
a = 1.60395 + 1.42858I
b = −0.261831 + 0.384133I
1.85257 − 1.11176I 2.15039 + 2.20620I
u = −0.259122 + 0.378593I
a = 5.32016 + 5.38456I
b = 0.336456 − 1.106180I
0.359329 − 0.612109I −2.0314 − 16.2217I
u = −0.259122 − 0.378593I
a = 5.32016 − 5.38456I
b = 0.336456 + 1.106180I
0.359329 + 0.612109I −2.0314 + 16.2217I
17
II. I
u
2
= h−2u
2
+ b − u − 3, −7u
2
+ a − 3u − 12, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
11
=
7u
2
+ 3u + 12
2u
2
+ u + 3
a
12
=
7u
2
+ 3u + 12
2u
2
+ u + 3
a
3
=
u
−u
2
− u − 1
a
6
=
−21u
2
− 9u − 36
−5u
2
− 2u − 9
a
10
=
7u
2
+ 3u + 13
3u
2
+ u + 3
a
1
=
−1
−u
2
a
5
=
1
0
a
2
=
−u
2
− 1
−u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 45u
2
+ 24u + 84
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
u
3
− 2u
2
− 3u − 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
9
u
3
− 3u
2
+ 2u + 1
c
10
(u + 1)
3
c
11
u
3
c
12
(u − 1)
3
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
y
3
− y
2
+ 2y −1
c
5
, c
6
y
3
− 10y
2
+ 5y −1
c
8
, c
9
y
3
− 5y
2
+ 10y −1
c
10
, c
12
(y −1)
3
c
11
y
3
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.281752 − 0.014533I
b = −0.539798 + 0.182582I
4.66906 + 2.82812I 4.03193 + 6.06881I
u = −0.215080 − 1.307140I
a = −0.281752 + 0.014533I
b = −0.539798 − 0.182582I
4.66906 − 2.82812I 4.03193 − 6.06881I
u = −0.569840
a = 12.5635
b = 3.07960
0.531480 84.9360
21
III. I
v
1
= ha, −5v
5
+ 46v
4
+ · · · + 69b + 86, v
6
− 3v
5
+ 6v
4
+ 5v
2
− v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
9
=
1
0
a
11
=
0
5
69
v
5
−
2
3
v
4
+ ··· −
9
23
v −
86
69
a
12
=
−
5
69
v
5
+
2
3
v
4
+ ··· +
9
23
v +
86
69
5
69
v
5
−
2
3
v
4
+ ··· −
9
23
v −
86
69
a
3
=
v
0
a
6
=
1
−0.492754v
5
+ 1.33333v
4
+ ··· − 2.73913v − 0.724638
a
10
=
−0.492754v
5
+ 1.33333v
4
+ ··· − 2.73913v + 0.275362
v
5
− 3v
4
+ 6v
3
+ 5v − 1
a
1
=
−0.507246v
5
+ 1.66667v
4
+ ··· − 2.26087v + 0.724638
v
5
− 3v
4
+ 6v
3
+ 5v − 1
a
5
=
35
69
v
5
−
5
3
v
4
+ ··· +
52
23
v −
50
69
−v
5
+ 3v
4
− 6v
3
− 5v + 1
a
2
=
−0.507246v
5
+ 1.66667v
4
+ ··· − 1.26087v + 0.724638
v
5
− 3v
4
+ 6v
3
+ 5v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
17
23
v
5
− 2v
4
+
79
23
v
3
+
53
23
v
2
+
129
23
v −
274
23
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
, c
8
u
6
c
4
(u + 1)
6
c
5
, c
9
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
6
, c
12
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
10
, c
11
u
6
− u
5
− u
4
+ 2u
3
− u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
7
, c
8
y
6
c
5
, c
9
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
6
, c
10
, c
11
c
12
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.344968 + 0.764807I
a = 0
b = 1.002190 + 0.295542I
−3.53554 − 0.92430I −13.12292 + 1.33143I
v = −0.344968 − 0.764807I
a = 0
b = 1.002190 − 0.295542I
−3.53554 + 0.92430I −13.12292 − 1.33143I
v = 0.158836 + 0.437639I
a = 0
b = −1.073950 − 0.558752I
−1.64493 − 5.69302I −11.70582 + 2.69056I
v = 0.158836 − 0.437639I
a = 0
b = −1.073950 + 0.558752I
−1.64493 + 5.69302I −11.70582 − 2.69056I
v = 1.68613 + 1.92635I
a = 0
b = −0.428243 + 0.664531I
0.245672 − 0.924305I −5.17126 + 7.13914I
v = 1.68613 − 1.92635I
a = 0
b = −0.428243 − 0.664531I
0.245672 + 0.924305I −5.17126 − 7.13914I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
3
− u
2
+ 2u − 1)(u
126
+ 68u
125
+ ··· − 17u + 1)
c
2
((u − 1)
6
)(u
3
+ u
2
− 1)(u
126
− 8u
125
+ ··· − 9u + 1)
c
3
u
6
(u
3
− u
2
+ 2u − 1)(u
126
+ 2u
125
+ ··· + 192u + 64)
c
4
((u + 1)
6
)(u
3
− u
2
+ 1)(u
126
− 8u
125
+ ··· − 9u + 1)
c
5
(u
3
− 2u
2
− 3u − 1)(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
126
+ 4u
125
+ ··· − 1174u − 44)
c
6
(u
3
− 2u
2
− 3u − 1)(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
· (u
126
− 65u
124
+ ··· + 4405u − 191)
c
7
u
6
(u
3
+ u
2
+ 2u + 1)(u
126
+ 2u
125
+ ··· + 192u + 64)
c
8
u
6
(u
3
− 3u
2
+ 2u + 1)(u
126
− 42u
125
+ ··· − 118784u + 4096)
c
9
(u
3
− 3u
2
+ 2u + 1)(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
126
− 9u
125
+ ··· + 2u − 1)
c
10
((u + 1)
3
)(u
6
− u
5
+ ··· − u + 1)(u
126
+ 5u
125
+ ··· − 43u − 1)
c
11
u
3
(u
6
− u
5
+ ··· − u + 1)(u
126
− 20u
125
+ ··· + 124u + 8)
c
12
((u − 1)
3
)(u
6
+ u
5
+ ··· + u + 1)(u
126
+ 5u
125
+ ··· − 43u − 1)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
3
+ 3y
2
+ 2y − 1)(y
126
− 12y
125
+ ··· − 363y + 1)
c
2
, c
4
((y − 1)
6
)(y
3
− y
2
+ 2y − 1)(y
126
− 68y
125
+ ··· + 17y + 1)
c
3
, c
7
y
6
(y
3
+ 3y
2
+ 2y − 1)(y
126
+ 42y
125
+ ··· + 118784y + 4096)
c
5
(y
3
− 10y
2
+ 5y − 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
126
− 122y
125
+ ··· − 141964y + 1936)
c
6
(y
3
− 10y
2
+ 5y − 1)(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
126
− 130y
125
+ ··· − 3185069y + 36481)
c
8
y
6
(y
3
− 5y
2
+ 10y − 1)(y
126
+ 74y
125
+ ··· − 1.25829 × 10
8
y + 1.67772 × 10
7
)
c
9
(y
3
− 5y
2
+ 10y − 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
126
+ 15y
125
+ ··· − 14y + 1)
c
10
, c
12
(y − 1)
3
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
126
− 75y
125
+ ··· − 971y + 1)
c
11
y
3
(y
6
− 3y
5
+ ··· − y + 1)(y
126
− 24y
125
+ ··· − 8848y + 64)
27
