12a
0108
(K12a
0108
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 10 4 7 12 1 9 6
Solving Sequence
4,7
8
9,12
10 3 6 1 2 11 5
c
7
c
8
c
9
c
3
c
6
c
12
c
1
c
11
c
5
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.77659 × 10
312
u
125
− 1.54560 × 10
313
u
124
+ ··· + 7.56628 × 10
313
b − 1.03264 × 10
314
,
− 1.29367 × 10
314
u
125
− 2.52409 × 10
314
u
124
+ ··· + 1.66458 × 10
315
a + 2.23551 × 10
316
,
u
126
+ 2u
125
+ ··· + 192u + 64i
I
u
2
= h3u
2
+ b + u + 3, 6u
2
+ a + 2u + 10, u
3
+ u
2
+ 2u + 1i
I
v
1
= ha, 31v
5
− 92v
4
+ 163v
3
+ 52v
2
+ 69b + 81v −64, 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−7.78 × 10
312
u
125
− 1.55 × 10
313
u
124
+ · · · + 7.57 × 10
313
b − 1.03 ×
10
314
, −1.29 × 10
314
u
125
− 2.52 × 10
314
u
124
+ · · · + 1.66 × 10
315
a + 2.24 ×
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
12
=
0.0777175u
125
+ 0.151635u
124
+ ··· − 12.0430u − 13.4298
0.102780u
125
+ 0.204274u
124
+ ··· + 21.2752u + 1.36479
a
10
=
−0.251458u
125
− 0.504776u
124
+ ··· − 62.6343u − 15.8172
−0.125368u
125
− 0.296640u
124
+ ··· − 55.2984u − 10.6403
a
3
=
u
u
3
+ u
a
6
=
0.184749u
125
+ 0.229941u
124
+ ··· + 26.0397u − 4.61527
0.128633u
125
+ 0.222528u
124
+ ··· + 38.3890u + 5.67195
a
1
=
0.134423u
125
+ 0.249675u
124
+ ··· − 15.7540u − 12.1955
−0.0161903u
125
− 0.0611574u
124
+ ··· − 50.9747u − 14.3007
a
2
=
0.116123u
125
+ 0.204715u
124
+ ··· − 22.9544u − 12.7987
−0.0366348u
125
− 0.0898334u
124
+ ··· − 55.3988u − 14.3689
a
11
=
0.0236074u
125
+ 0.0498670u
124
+ ··· − 20.2156u − 13.1289
0.150252u
125
+ 0.329184u
124
+ ··· + 32.2910u + 2.86962
a
5
=
0.0842320u
125
+ 0.177889u
124
+ ··· + 30.2985u + 3.33220
−0.0501911u
125
− 0.0717859u
124
+ ··· + 46.0525u + 15.5277
(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
− 65u
124
+ ··· + 4405u − 191
c
6
u
126
+ 4u
125
+ ··· − 1174u − 44
c
8
u
126
− 42u
125
+ ··· − 118784u + 4096
c
9
, c
11
u
126
+ 5u
125
+ ··· − 43u − 1
c
10
u
126
− 20u
125
+ ··· + 124u + 8
c
12
u
126
− 9u
125
+ ··· + 2u − 1
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
− 130y
125
+ ··· − 3185069y + 36481
c
6
y
126
− 122y
125
+ ··· − 141964y + 1936
c
8
y
126
+ 74y
125
+ ··· − 125829120y + 16777216
c
9
, c
11
y
126
− 75y
125
+ ··· − 971y + 1
c
10
y
126
− 24y
125
+ ··· − 8848y + 64
c
12
y
126
+ 15y
125
+ ··· − 14y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.583149 + 0.813259I
a = −2.40429 − 0.88467I
b = −2.36089 + 0.71738I
0.84437 + 1.77385I 0
u = −0.583149 − 0.813259I
a = −2.40429 + 0.88467I
b = −2.36089 − 0.71738I
0.84437 − 1.77385I 0
u = 0.759752 + 0.658456I
a = 0.411118 + 0.209764I
b = −0.228083 − 0.339879I
−3.19646 + 2.28892I 0
u = 0.759752 − 0.658456I
a = 0.411118 − 0.209764I
b = −0.228083 + 0.339879I
−3.19646 − 2.28892I 0
u = −0.664545 + 0.755167I
a = −0.12102 + 2.46179I
b = 1.225020 + 0.310188I
−1.33049 + 2.05219I 0
u = −0.664545 − 0.755167I
a = −0.12102 − 2.46179I
b = 1.225020 − 0.310188I
−1.33049 − 2.05219I 0
u = 0.638089 + 0.779199I
a = 1.54419 + 1.11191I
b = 0.88077 + 1.29949I
−5.12052 − 2.76244I 0
u = 0.638089 − 0.779199I
a = 1.54419 − 1.11191I
b = 0.88077 − 1.29949I
−5.12052 + 2.76244I 0
u = 1.008890 + 0.070007I
a = 2.21899 + 0.03163I
b = 1.73462 + 0.26110I
2.18854 + 7.22641I 0
u = 1.008890 − 0.070007I
a = 2.21899 − 0.03163I
b = 1.73462 − 0.26110I
2.18854 − 7.22641I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.134506 + 1.012070I
a = −0.72834 + 1.25076I
b = 4.00557 + 0.08173I
3.77115 + 2.20092I 0
u = −0.134506 − 1.012070I
a = −0.72834 − 1.25076I
b = 4.00557 − 0.08173I
3.77115 − 2.20092I 0
u = −0.236806 + 0.993858I
a = 0.049581 − 0.414116I
b = −0.407535 − 0.842117I
1.90248 + 2.83956I 0
u = −0.236806 − 0.993858I
a = 0.049581 + 0.414116I
b = −0.407535 + 0.842117I
1.90248 − 2.83956I 0
u = −0.077039 + 1.019420I
a = −0.395957 − 0.895205I
b = −0.345162 − 0.284694I
2.60094 + 2.12761I 0
u = −0.077039 − 1.019420I
a = −0.395957 + 0.895205I
b = −0.345162 + 0.284694I
2.60094 − 2.12761I 0
u = −0.870239 + 0.437016I
a = 2.01350 − 0.73003I
b = 1.27645 − 0.83997I
−1.62685 − 0.40405I 0
u = −0.870239 − 0.437016I
a = 2.01350 + 0.73003I
b = 1.27645 + 0.83997I
−1.62685 + 0.40405I 0
u = −0.750514 + 0.607886I
a = −0.48073 + 2.04336I
b = −0.174005 + 0.510313I
0.258302 − 1.180800I 0
u = −0.750514 − 0.607886I
a = −0.48073 − 2.04336I
b = −0.174005 − 0.510313I
0.258302 + 1.180800I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.701966 + 0.759826I
a = 1.88316 − 0.88061I
b = 1.45456 − 1.13212I
−3.74921 − 4.56977I 0
u = −0.701966 − 0.759826I
a = 1.88316 + 0.88061I
b = 1.45456 + 1.13212I
−3.74921 + 4.56977I 0
u = 0.745954 + 0.737217I
a = 2.05866 − 4.11011I
b = 2.80767 − 0.70209I
−2.73974 + 0.70736I 0
u = 0.745954 − 0.737217I
a = 2.05866 + 4.11011I
b = 2.80767 + 0.70209I
−2.73974 − 0.70736I 0
u = −0.089485 + 0.946069I
a = 1.28925 − 1.00533I
b = −1.55692 + 0.09969I
0.43085 − 5.09047I 0
u = −0.089485 − 0.946069I
a = 1.28925 + 1.00533I
b = −1.55692 − 0.09969I
0.43085 + 5.09047I 0
u = −0.026963 + 0.943464I
a = −0.404065 + 0.007320I
b = −0.922484 + 0.758848I
2.41442 + 1.40190I 0
u = −0.026963 − 0.943464I
a = −0.404065 − 0.007320I
b = −0.922484 − 0.758848I
2.41442 − 1.40190I 0
u = −1.036680 + 0.220066I
a = 2.08600 − 0.38383I
b = 1.56493 − 0.14601I
1.84155 + 2.77321I 0
u = −1.036680 − 0.220066I
a = 2.08600 + 0.38383I
b = 1.56493 + 0.14601I
1.84155 − 2.77321I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.902790 + 0.575810I
a = 2.16135 + 0.69093I
b = 1.72111 + 0.92699I
0.07212 + 8.10921I 0
u = 0.902790 − 0.575810I
a = 2.16135 − 0.69093I
b = 1.72111 − 0.92699I
0.07212 − 8.10921I 0
u = 0.515649 + 0.940162I
a = −0.80683 − 1.94203I
b = 0.490259 − 0.645229I
4.07539 − 1.91046I 0
u = 0.515649 − 0.940162I
a = −0.80683 + 1.94203I
b = 0.490259 + 0.645229I
4.07539 + 1.91046I 0
u = 0.821210 + 0.696105I
a = −3.79378 + 1.02212I
b = −3.05665 − 0.68146I
−2.64594 + 1.92186I 0
u = 0.821210 − 0.696105I
a = −3.79378 − 1.02212I
b = −3.05665 + 0.68146I
−2.64594 − 1.92186I 0
u = 0.066247 + 1.075380I
a = −1.104920 − 0.720837I
b = 1.083610 − 0.383367I
6.12098 − 0.47562I 0
u = 0.066247 − 1.075380I
a = −1.104920 + 0.720837I
b = 1.083610 + 0.383367I
6.12098 + 0.47562I 0
u = −0.866742 + 0.650126I
a = −0.929827 + 0.051878I
b = −1.310250 + 0.281104I
−1.08056 − 4.64409I 0
u = −0.866742 − 0.650126I
a = −0.929827 − 0.051878I
b = −1.310250 − 0.281104I
−1.08056 + 4.64409I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.164623 + 1.090970I
a = −0.937838 − 0.153506I
b = 1.274750 + 0.205009I
5.90160 − 4.26455I 0
u = 0.164623 − 1.090970I
a = −0.937838 + 0.153506I
b = 1.274750 − 0.205009I
5.90160 + 4.26455I 0
u = −0.612029 + 0.921384I
a = 1.39754 + 3.67655I
b = 3.36533 + 0.62198I
1.22072 + 2.96447I 0
u = −0.612029 − 0.921384I
a = 1.39754 − 3.67655I
b = 3.36533 − 0.62198I
1.22072 − 2.96447I 0
u = 0.608068 + 0.939760I
a = 0.48099 + 2.26771I
b = −1.36323 + 1.12639I
−4.61530 − 2.13294I 0
u = 0.608068 − 0.939760I
a = 0.48099 − 2.26771I
b = −1.36323 − 1.12639I
−4.61530 + 2.13294I 0
u = −0.715251 + 0.862634I
a = −0.756830 + 0.170735I
b = 0.355188 + 0.261563I
−6.56601 + 3.77378I 0
u = −0.715251 − 0.862634I
a = −0.756830 − 0.170735I
b = 0.355188 − 0.261563I
−6.56601 − 3.77378I 0
u = −0.712315 + 0.865143I
a = 0.170620 + 0.028930I
b = −0.416168 + 0.527299I
−6.55718 + 1.68165I 0
u = −0.712315 − 0.865143I
a = 0.170620 − 0.028930I
b = −0.416168 − 0.527299I
−6.55718 − 1.68165I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.283809 + 1.084470I
a = −0.430557 + 0.774152I
b = −0.040161 + 0.255290I
1.79448 − 6.78921I 0
u = 0.283809 − 1.084470I
a = −0.430557 − 0.774152I
b = −0.040161 − 0.255290I
1.79448 + 6.78921I 0
u = −0.837606 + 0.789777I
a = 0.715847 − 0.779366I
b = 0.193028 − 0.396166I
−1.93800 + 2.88339I 0
u = −0.837606 − 0.789777I
a = 0.715847 + 0.779366I
b = 0.193028 + 0.396166I
−1.93800 − 2.88339I 0
u = −0.654600 + 0.951229I
a = −0.832909 + 0.532511I
b = −1.137890 + 0.549091I
−0.71690 + 3.08171I 0
u = −0.654600 − 0.951229I
a = −0.832909 − 0.532511I
b = −1.137890 − 0.549091I
−0.71690 − 3.08171I 0
u = 0.604520 + 0.985901I
a = −0.16855 − 1.64248I
b = 1.39968 − 0.21265I
2.96423 − 5.62025I 0
u = 0.604520 − 0.985901I
a = −0.16855 + 1.64248I
b = 1.39968 + 0.21265I
2.96423 + 5.62025I 0
u = −0.675660 + 0.951102I
a = 0.11728 − 2.78463I
b = −1.78102 − 1.05893I
−3.15580 + 9.87799I 0
u = −0.675660 − 0.951102I
a = 0.11728 + 2.78463I
b = −1.78102 + 1.05893I
−3.15580 − 9.87799I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.778808 + 0.875358I
a = 0.546248 + 0.475768I
b = 0.0584220 + 0.0928196I
−5.56540 − 7.22095I 0
u = 0.778808 − 0.875358I
a = 0.546248 − 0.475768I
b = 0.0584220 − 0.0928196I
−5.56540 + 7.22095I 0
u = −0.927777 + 0.716525I
a = 0.181729 − 0.399959I
b = −0.398777 + 0.187696I
−6.29832 − 6.58519I 0
u = −0.927777 − 0.716525I
a = 0.181729 + 0.399959I
b = −0.398777 − 0.187696I
−6.29832 + 6.58519I 0
u = 0.804790 + 0.868133I
a = 0.076332 + 0.809767I
b = −0.017738 + 0.432056I
−5.59394 + 1.30207I 0
u = 0.804790 − 0.868133I
a = 0.076332 − 0.809767I
b = −0.017738 − 0.432056I
−5.59394 − 1.30207I 0
u = −0.728276 + 0.935353I
a = 0.292431 − 0.682258I
b = 0.088734 − 0.582632I
−1.50108 + 2.95525I 0
u = −0.728276 − 0.935353I
a = 0.292431 + 0.682258I
b = 0.088734 + 0.582632I
−1.50108 − 2.95525I 0
u = 0.896738 + 0.785992I
a = 0.482925 + 0.897178I
b = −0.052130 + 0.488664I
−5.47055 + 1.59927I 0
u = 0.896738 − 0.785992I
a = 0.482925 − 0.897178I
b = −0.052130 − 0.488664I
−5.47055 − 1.59927I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.399196 + 0.700132I
a = −0.418821 − 0.419802I
b = −0.997317 − 0.308529I
1.88586 + 1.07699I 1.62389 − 3.53502I
u = 0.399196 − 0.700132I
a = −0.418821 + 0.419802I
b = −0.997317 + 0.308529I
1.88586 − 1.07699I 1.62389 + 3.53502I
u = 0.700027 + 0.968567I
a = −2.77865 + 0.09884I
b = −2.51167 − 1.19272I
−2.03372 − 6.21937I 0
u = 0.700027 − 0.968567I
a = −2.77865 − 0.09884I
b = −2.51167 + 1.19272I
−2.03372 + 6.21937I 0
u = 0.781482 + 0.172967I
a = 1.29236 + 0.58740I
b = 0.330603 − 0.091888I
−1.45891 + 3.00718I −6.53766 − 7.29173I
u = 0.781482 − 0.172967I
a = 1.29236 − 0.58740I
b = 0.330603 + 0.091888I
−1.45891 − 3.00718I −6.53766 + 7.29173I
u = 1.016950 + 0.656632I
a = 2.14399 + 1.13198I
b = 1.47418 + 1.22457I
−4.10359 + 4.97237I 0
u = 1.016950 − 0.656632I
a = 2.14399 − 1.13198I
b = 1.47418 − 1.22457I
−4.10359 − 4.97237I 0
u = 0.690126 + 1.005750I
a = −0.447053 + 0.050891I
b = 0.418051 − 0.078612I
−2.16358 − 7.80144I 0
u = 0.690126 − 1.005750I
a = −0.447053 − 0.050891I
b = 0.418051 + 0.078612I
−2.16358 + 7.80144I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.678688 + 1.020830I
a = −0.61288 + 1.97507I
b = 0.387426 + 0.911011I
1.45595 + 6.62892I 0
u = −0.678688 − 1.020830I
a = −0.61288 − 1.97507I
b = 0.387426 − 0.911011I
1.45595 − 6.62892I 0
u = −1.006940 + 0.706541I
a = 2.28472 − 0.87519I
b = 1.85509 − 1.10457I
−2.73943 − 12.79060I 0
u = −1.006940 − 0.706541I
a = 2.28472 + 0.87519I
b = 1.85509 + 1.10457I
−2.73943 + 12.79060I 0
u = 0.724342 + 1.011870I
a = 1.80502 − 3.43113I
b = 3.42838 − 0.94214I
−1.67836 − 7.71869I 0
u = 0.724342 − 1.011870I
a = 1.80502 + 3.43113I
b = 3.42838 + 0.94214I
−1.67836 + 7.71869I 0
u = −0.153007 + 1.240150I
a = 0.118355 − 0.383852I
b = −2.10059 − 0.27454I
7.35610 + 6.53099I 0
u = −0.153007 − 1.240150I
a = 0.118355 + 0.383852I
b = −2.10059 + 0.27454I
7.35610 − 6.53099I 0
u = −0.724716 + 1.045350I
a = 0.20991 + 1.64245I
b = 1.48746 + 0.30734I
0.13511 + 10.55390I 0
u = −0.724716 − 1.045350I
a = 0.20991 − 1.64245I
b = 1.48746 − 0.30734I
0.13511 − 10.55390I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.269690 + 1.247800I
a = −0.109494 + 1.094990I
b = −1.85754 + 0.41849I
6.88746 + 2.92032I 0
u = 0.269690 − 1.247800I
a = −0.109494 − 1.094990I
b = −1.85754 − 0.41849I
6.88746 − 2.92032I 0
u = 0.332493 + 1.237100I
a = −0.006022 + 1.079100I
b = −2.15220 + 0.54761I
6.38584 − 11.97810I 0
u = 0.332493 − 1.237100I
a = −0.006022 − 1.079100I
b = −2.15220 − 0.54761I
6.38584 + 11.97810I 0
u = 0.787834 + 1.012220I
a = 0.291926 + 0.593782I
b = 0.226779 + 0.567475I
−4.72827 − 7.84683I 0
u = 0.787834 − 1.012220I
a = 0.291926 − 0.593782I
b = 0.226779 − 0.567475I
−4.72827 + 7.84683I 0
u = 0.715508 + 1.083340I
a = −0.25215 + 2.51710I
b = −1.96241 + 1.12186I
1.6137 − 14.0645I 0
u = 0.715508 − 1.083340I
a = −0.25215 − 2.51710I
b = −1.96241 − 1.12186I
1.6137 + 14.0645I 0
u = −0.776257 + 1.050290I
a = −0.261775 + 0.072130I
b = 0.551281 + 0.082118I
−5.23670 + 12.86370I 0
u = −0.776257 − 1.050290I
a = −0.261775 − 0.072130I
b = 0.551281 − 0.082118I
−5.23670 − 12.86370I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.681519 + 1.116400I
a = −0.06483 − 2.22505I
b = −1.62801 − 1.29676I
0.33688 + 6.13842I 0
u = −0.681519 − 1.116400I
a = −0.06483 + 2.22505I
b = −1.62801 + 1.29676I
0.33688 − 6.13842I 0
u = −0.671958 + 0.032843I
a = 1.73322 − 0.09355I
b = 0.586846 − 0.184878I
−1.094370 + 0.027147I −7.58274 + 0.49956I
u = −0.671958 − 0.032843I
a = 1.73322 + 0.09355I
b = 0.586846 + 0.184878I
−1.094370 − 0.027147I −7.58274 − 0.49956I
u = 0.670945 + 0.001703I
a = −0.118845 + 0.786074I
b = −0.901209 − 0.015610I
2.03745 + 1.42816I 2.53417 − 4.60053I
u = 0.670945 − 0.001703I
a = −0.118845 − 0.786074I
b = −0.901209 + 0.015610I
2.03745 − 1.42816I 2.53417 + 4.60053I
u = 0.092281 + 0.648619I
a = 0.23936 + 1.95343I
b = −0.460292 − 0.261821I
−2.61100 − 1.34807I −3.48651 + 4.76024I
u = 0.092281 − 0.648619I
a = 0.23936 − 1.95343I
b = −0.460292 + 0.261821I
−2.61100 + 1.34807I −3.48651 − 4.76024I
u = −0.455105 + 1.272310I
a = −0.29244 − 1.52392I
b = −1.72190 − 0.80643I
5.46522 + 2.67251I 0
u = −0.455105 − 1.272310I
a = −0.29244 + 1.52392I
b = −1.72190 + 0.80643I
5.46522 − 2.67251I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.802002 + 1.094610I
a = −0.45501 − 2.65767I
b = −1.97178 − 1.24834I
−1.4825 + 19.3861I 0
u = −0.802002 − 1.094610I
a = −0.45501 + 2.65767I
b = −1.97178 + 1.24834I
−1.4825 − 19.3861I 0
u = 0.786293 + 1.115480I
a = −0.16433 + 2.46206I
b = −1.58922 + 1.46628I
−2.63820 − 11.52950I 0
u = 0.786293 − 1.115480I
a = −0.16433 − 2.46206I
b = −1.58922 − 1.46628I
−2.63820 + 11.52950I 0
u = −0.162781 + 1.386730I
a = −0.661077 − 0.561639I
b = −2.34852 − 0.39218I
4.49508 + 2.99438I 0
u = −0.162781 − 1.386730I
a = −0.661077 + 0.561639I
b = −2.34852 + 0.39218I
4.49508 − 2.99438I 0
u = −0.595624
a = 1.50825
b = 0.418502
−1.09586 −8.62110
u = 0.049191 + 0.593330I
a = 0.955093 − 0.531289I
b = 0.253912 − 0.874200I
−2.83015 + 0.66433I −0.80758 + 1.62533I
u = 0.049191 − 0.593330I
a = 0.955093 + 0.531289I
b = 0.253912 + 0.874200I
−2.83015 − 0.66433I −0.80758 − 1.62533I
u = −0.547594
a = −18.2084
b = −4.97465
0.509050 −323.410
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.070102 + 0.510627I
a = 1.358090 + 0.350014I
b = 0.903119 + 0.640568I
−1.24958 + 5.86869I 5.67430 − 9.68755I
u = −0.070102 − 0.510627I
a = 1.358090 − 0.350014I
b = 0.903119 − 0.640568I
−1.24958 − 5.86869I 5.67430 + 9.68755I
u = 0.299663 + 0.400210I
a = −0.051668 − 0.210161I
b = −1.024470 − 0.220592I
1.85257 + 1.11176I 2.15039 − 2.20620I
u = 0.299663 − 0.400210I
a = −0.051668 + 0.210161I
b = −1.024470 + 0.220592I
1.85257 − 1.11176I 2.15039 + 2.20620I
u = −0.259122 + 0.378593I
a = 0.48178 + 8.59597I
b = 0.691501 − 0.498616I
0.359329 − 0.612109I −2.0314 − 16.2217I
u = −0.259122 − 0.378593I
a = 0.48178 − 8.59597I
b = 0.691501 + 0.498616I
0.359329 + 0.612109I −2.0314 + 16.2217I
17
II. I
u
2
= h3u
2
+ b + u + 3, 6u
2
+ a + 2u + 10, 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
12
=
−6u
2
− 2u − 10
−3u
2
− u − 3
a
10
=
−5u
2
− 2u − 9
−2u
2
− u − 3
a
3
=
u
−u
2
− u − 1
a
6
=
16u
2
+ 7u + 29
5u
2
+ 2u + 9
a
1
=
−1
−u
2
a
2
=
−u
2
− 1
−u
2
− u − 1
a
11
=
−5u
2
− 2u − 9
−2u
2
− u − 3
a
5
=
1
0
(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
u
3
− 3u
2
+ 2u + 1
c
9
(u + 1)
3
c
10
u
3
c
11
(u − 1)
3
c
12
u
3
+ 3u
2
+ 2u − 1
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
12
y
3
− 5y
2
+ 10y −1
c
9
, c
11
(y −1)
3
c
10
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 = 0.404314 + 0.759395I
b = 2.20216 + 0.37970I
4.66906 + 2.82812I 4.03193 + 6.06881I
u = −0.215080 − 1.307140I
a = 0.404314 − 0.759395I
b = 2.20216 − 0.37970I
4.66906 − 2.82812I 4.03193 − 6.06881I
u = −0.569840
a = −10.8086
b = −3.40431
0.531480 84.9360
21
III. I
v
1
= ha, 31v
5
− 92v
4
+ · · · + 69b − 64, 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
12
=
0
−0.449275v
5
+ 1.33333v
4
+ ··· − 1.17391v + 0.927536
a
10
=
1
55
69
v
5
−
7
3
v
4
+ ··· +
62
23
v −
49
69
a
3
=
v
0
a
6
=
55
69
v
5
−
7
3
v
4
+ ··· +
62
23
v +
20
69
−0.782609v
5
+ 2v
4
+ ··· − 4.17391v − 0.739130
a
1
=
−1.01449v
5
+ 3.33333v
4
+ ··· − 3.52174v + 1.44928
v
5
− 3v
4
+ 6v
3
+ 5v − 1
a
2
=
−1.01449v
5
+ 3.33333v
4
+ ··· − 2.52174v + 1.44928
v
5
− 3v
4
+ 6v
3
+ 5v − 1
a
11
=
31
69
v
5
−
4
3
v
4
+ ··· +
27
23
v −
64
69
−0.449275v
5
+ 1.33333v
4
+ ··· − 1.17391v + 0.927536
a
5
=
1.01449v
5
− 3.33333v
4
+ ··· + 3.52174v − 1.44928
−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
10
, c
11
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
6
, c
12
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
9
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
, c
10
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
6
, c
12
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 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 = 0.428243 + 0.664531I
−3.53554 − 0.92430I −13.12292 + 1.33143I
v = −0.344968 − 0.764807I
a = 0
b = 0.428243 − 0.664531I
−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 = −1.002190 + 0.295542I
0.245672 − 0.924305I −5.17126 + 7.13914I
v = 1.68613 − 1.92635I
a = 0
b = −1.002190 − 0.295542I
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
+ u
5
− u
4
− 2u
3
+ u + 1)
· (u
126
− 65u
124
+ ··· + 4405u − 191)
c
6
(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
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 + 1)
3
)(u
6
− u
5
+ ··· − u + 1)(u
126
+ 5u
125
+ ··· − 43u − 1)
c
10
u
3
(u
6
+ u
5
+ ··· + u + 1)(u
126
− 20u
125
+ ··· + 124u + 8)
c
11
((u − 1)
3
)(u
6
+ u
5
+ ··· + u + 1)(u
126
+ 5u
125
+ ··· − 43u − 1)
c
12
(u
3
+ 3u
2
+ 2u − 1)(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
126
− 9u
125
+ ··· + 2u − 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
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
126
− 130y
125
+ ··· − 3185069y + 36481)
c
6
(y
3
− 10y
2
+ 5y − 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
126
− 122y
125
+ ··· − 141964y + 1936)
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
, c
11
(y − 1)
3
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
126
− 75y
125
+ ··· − 971y + 1)
c
10
y
3
(y
6
− 3y
5
+ ··· − y + 1)(y
126
− 24y
125
+ ··· − 8848y + 64)
c
12
(y
3
− 5y
2
+ 10y − 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
126
+ 15y
125
+ ··· − 14y + 1)
27
