12a
0276
(K12a
0276
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 11 5 4 12 1 7 10
Solving Sequence
4,9 5,12
10 1 8 3 2 7 11 6
c
4
c
9
c
12
c
8
c
3
c
1
c
7
c
11
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.34258 × 10
83
u
91
− 8.81488 × 10
83
u
90
+ ··· + 2.17711 × 10
84
b − 2.38406 × 10
84
,
6.19627 × 10
83
u
91
− 1.41945 × 10
84
u
90
+ ··· + 2.17711 × 10
84
a − 5.54877 × 10
83
, u
92
− 2u
91
+ ··· + 12u + 4i
I
u
2
= h−u
7
+ u
6
+ 2u
5
− 3u
4
+ 2u
2
+ b − 2u + 2, u
7
+ u
6
− 3u
5
− 2u
4
+ 3u
3
+ a + 2,
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
I
u
3
= hau + b − 2a − u − 1, 2a
2
− au − 1, u
2
− 2i
I
v
1
= ha, b + v + 2, v
2
+ 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 106 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
=
h3.34×10
83
u
91
−8.81×10
83
u
90
+· · ·+2.18×10
84
b−2.38×10
84
, 6.20×10
83
u
91
−
1.42 × 10
84
u
90
+ · · · + 2.18 × 10
84
a − 5.55 × 10
83
, u
92
− 2u
91
+ · · · + 12u + 4i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
−0.284611u
91
+ 0.651991u
90
+ ··· − 6.71279u + 0.254869
−0.153533u
91
+ 0.404890u
90
+ ··· − 1.63656u + 1.09506
a
10
=
0.850284u
91
− 1.32698u
90
+ ··· − 1.86531u + 2.15950
1.33947u
91
− 1.25204u
90
+ ··· − 11.3059u − 1.45062
a
1
=
0.225091u
91
− 0.817064u
90
+ ··· + 8.33508u + 3.68616
−0.466743u
91
− 0.0372697u
90
+ ··· + 5.80110u + 2.57471
a
8
=
u
u
a
3
=
−u
2
+ 1
−u
2
a
2
=
0.615650u
91
− 1.09071u
90
+ ··· + 3.61981u + 0.972754
0.240176u
91
− 0.305085u
90
+ ··· − 3.12691u + 0.0205266
a
7
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
11
=
−0.489371u
91
+ 0.911075u
90
+ ··· − 4.78614u + 1.45037
−0.651264u
91
+ 0.696436u
90
+ ··· + 2.84926u + 2.67873
a
6
=
−0.375474u
91
+ 0.785620u
90
+ ··· − 6.74672u − 0.952228
0.240176u
91
− 0.305085u
90
+ ··· − 3.12691u + 0.0205266
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.63469u
91
+ 5.95903u
90
+ ··· + 9.38857u − 43.1013
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
92
+ 48u
91
+ ··· + 1755u + 81
c
2
, c
5
u
92
+ 4u
91
+ ··· − 69u − 9
c
3
, c
4
, c
8
u
92
+ 2u
91
+ ··· − 12u + 4
c
6
, c
11
u
92
− 2u
91
+ ··· − 1920u + 256
c
7
u
92
− 6u
91
+ ··· + 6260u + 380
c
9
, c
10
, c
12
u
92
− 12u
91
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
92
+ 72y
90
+ ··· − 662499y + 6561
c
2
, c
5
y
92
− 48y
91
+ ··· − 1755y + 81
c
3
, c
4
, c
8
y
92
− 86y
91
+ ··· − 240y + 16
c
6
, c
11
y
92
− 60y
91
+ ··· − 5947392y + 65536
c
7
y
92
− 14y
91
+ ··· − 25869360y + 144400
c
9
, c
10
, c
12
y
92
− 92y
91
+ ··· + 74y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.969583 + 0.107648I
a = −0.003539 − 0.526904I
b = 0.459221 + 0.068074I
−0.513504 + 0.030259I 0
u = 0.969583 − 0.107648I
a = −0.003539 + 0.526904I
b = 0.459221 − 0.068074I
−0.513504 − 0.030259I 0
u = −1.03762
a = −1.39452
b = −0.0725617
−11.4153 0
u = −0.674626 + 0.619008I
a = −0.97265 − 1.31507I
b = −0.927957 + 0.305099I
−8.21616 − 7.69201I 0
u = −0.674626 − 0.619008I
a = −0.97265 + 1.31507I
b = −0.927957 − 0.305099I
−8.21616 + 7.69201I 0
u = 0.741480 + 0.527661I
a = 1.14534 − 1.08640I
b = 0.880522 + 0.160216I
−5.81043 + 2.35579I 0
u = 0.741480 − 0.527661I
a = 1.14534 + 1.08640I
b = 0.880522 − 0.160216I
−5.81043 − 2.35579I 0
u = −0.390955 + 0.781852I
a = −1.10343 − 1.35509I
b = −1.50467 + 0.09620I
−7.2837 + 12.4485I −16.5634 − 8.5018I
u = −0.390955 − 0.781852I
a = −1.10343 + 1.35509I
b = −1.50467 − 0.09620I
−7.2837 − 12.4485I −16.5634 + 8.5018I
u = 0.063829 + 0.858332I
a = 0.17179 − 1.48729I
b = 0.216749 − 0.221340I
−0.63733 − 3.04639I −16.3980 + 3.8542I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.063829 − 0.858332I
a = 0.17179 + 1.48729I
b = 0.216749 + 0.221340I
−0.63733 + 3.04639I −16.3980 − 3.8542I
u = 0.330243 + 0.776749I
a = 0.97602 − 1.44162I
b = 1.296880 − 0.073620I
−4.46168 − 6.88858I −13.9256 + 5.1752I
u = 0.330243 − 0.776749I
a = 0.97602 + 1.44162I
b = 1.296880 + 0.073620I
−4.46168 + 6.88858I −13.9256 − 5.1752I
u = −1.180620 + 0.049140I
a = 0.905051 + 0.405129I
b = 1.71434 − 0.47461I
−4.02322 + 0.72103I 0
u = −1.180620 − 0.049140I
a = 0.905051 − 0.405129I
b = 1.71434 + 0.47461I
−4.02322 − 0.72103I 0
u = −0.341347 + 0.720746I
a = 1.198680 − 0.029660I
b = 0.788988 − 0.152649I
−1.23377 + 8.07113I −13.5538 − 8.5121I
u = −0.341347 − 0.720746I
a = 1.198680 + 0.029660I
b = 0.788988 + 0.152649I
−1.23377 − 8.07113I −13.5538 + 8.5121I
u = −1.184720 + 0.249629I
a = 0.146188 − 0.546688I
b = 0.0273490 + 0.0956059I
−0.85249 + 4.72720I 0
u = −1.184720 − 0.249629I
a = 0.146188 + 0.546688I
b = 0.0273490 − 0.0956059I
−0.85249 − 4.72720I 0
u = −0.616721 + 0.490885I
a = −0.221693 + 1.040660I
b = −0.229638 + 0.292595I
−2.26213 − 3.90874I −15.3859 + 3.7108I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.616721 − 0.490885I
a = −0.221693 − 1.040660I
b = −0.229638 − 0.292595I
−2.26213 + 3.90874I −15.3859 − 3.7108I
u = 1.210350 + 0.144980I
a = −1.027120 − 0.175344I
b = −2.53696 + 0.78808I
−4.28970 − 3.40044I 0
u = 1.210350 − 0.144980I
a = −1.027120 + 0.175344I
b = −2.53696 − 0.78808I
−4.28970 + 3.40044I 0
u = 1.146230 + 0.420367I
a = 1.010760 − 0.337976I
b = 1.263380 − 0.483375I
−3.97193 − 1.52452I 0
u = 1.146230 − 0.420367I
a = 1.010760 + 0.337976I
b = 1.263380 + 0.483375I
−3.97193 + 1.52452I 0
u = 0.341585 + 0.668395I
a = −1.05640 + 1.61061I
b = −1.30954 − 0.55648I
−3.99403 − 5.59592I −15.4677 + 6.2129I
u = 0.341585 − 0.668395I
a = −1.05640 − 1.61061I
b = −1.30954 + 0.55648I
−3.99403 + 5.59592I −15.4677 − 6.2129I
u = 0.188441 + 0.708555I
a = 0.638248 − 0.300259I
b = 0.471116 + 0.361008I
1.75825 − 3.49258I −7.18786 + 5.15359I
u = 0.188441 − 0.708555I
a = 0.638248 + 0.300259I
b = 0.471116 − 0.361008I
1.75825 + 3.49258I −7.18786 − 5.15359I
u = −0.279771 + 0.668738I
a = −1.02400 − 1.79888I
b = −1.37269 − 0.62207I
−9.80694 + 2.97546I −17.9875 − 3.6008I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.279771 − 0.668738I
a = −1.02400 + 1.79888I
b = −1.37269 + 0.62207I
−9.80694 − 2.97546I −17.9875 + 3.6008I
u = 0.252374 + 0.668121I
a = −1.118440 + 0.021493I
b = −0.759308 + 0.065796I
1.14826 − 3.17312I −9.30715 + 5.02148I
u = 0.252374 − 0.668121I
a = −1.118440 − 0.021493I
b = −0.759308 − 0.065796I
1.14826 + 3.17312I −9.30715 − 5.02148I
u = 1.273630 + 0.242181I
a = 0.285414 + 0.261261I
b = 1.316700 + 0.008357I
−1.34793 − 2.04566I 0
u = 1.273630 − 0.242181I
a = 0.285414 − 0.261261I
b = 1.316700 − 0.008357I
−1.34793 + 2.04566I 0
u = 0.508498 + 0.473897I
a = −1.32056 + 1.41639I
b = −1.73251 − 0.27223I
−4.75530 + 1.78277I −17.3380 + 0.3544I
u = 0.508498 − 0.473897I
a = −1.32056 − 1.41639I
b = −1.73251 + 0.27223I
−4.75530 − 1.78277I −17.3380 − 0.3544I
u = −0.300885 + 0.616253I
a = −0.35830 + 1.49912I
b = −0.158598 − 0.016331I
−2.55198 + 2.76644I −15.5409 − 4.4573I
u = −0.300885 − 0.616253I
a = −0.35830 − 1.49912I
b = −0.158598 + 0.016331I
−2.55198 − 2.76644I −15.5409 + 4.4573I
u = −0.030654 + 0.683608I
a = −0.780875 − 0.127083I
b = −0.481566 + 0.327235I
2.66095 − 1.28667I −5.71389 + 2.78365I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.030654 − 0.683608I
a = −0.780875 + 0.127083I
b = −0.481566 − 0.327235I
2.66095 + 1.28667I −5.71389 − 2.78365I
u = 0.666845 + 0.068325I
a = −0.075581 + 0.622950I
b = 0.422885 + 0.072774I
−0.523648 − 0.094088I −11.87057 + 0.12396I
u = 0.666845 − 0.068325I
a = −0.075581 − 0.622950I
b = 0.422885 − 0.072774I
−0.523648 + 0.094088I −11.87057 − 0.12396I
u = −1.270790 + 0.395450I
a = −0.962888 − 0.190034I
b = −1.70094 − 0.74003I
−4.78582 + 7.53244I 0
u = −1.270790 − 0.395450I
a = −0.962888 + 0.190034I
b = −1.70094 + 0.74003I
−4.78582 − 7.53244I 0
u = −1.33936
a = −1.25475
b = −3.76057
−14.2652 0
u = −1.354420 + 0.050875I
a = −0.0211295 + 0.0997711I
b = −1.50291 − 0.41520I
−6.43271 + 0.08678I 0
u = −1.354420 − 0.050875I
a = −0.0211295 − 0.0997711I
b = −1.50291 + 0.41520I
−6.43271 − 0.08678I 0
u = −1.375350 + 0.176357I
a = 0.525875 + 0.521338I
b = 0.890304 + 0.387213I
−5.48308 + 1.43317I 0
u = −1.375350 − 0.176357I
a = 0.525875 − 0.521338I
b = 0.890304 − 0.387213I
−5.48308 − 1.43317I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.363580 + 0.289426I
a = −0.378679 + 0.156042I
b = −1.58342 + 0.01614I
−3.14548 + 7.11465I 0
u = −1.363580 − 0.289426I
a = −0.378679 − 0.156042I
b = −1.58342 − 0.01614I
−3.14548 − 7.11465I 0
u = −0.252729 + 0.545556I
a = 1.12490 + 1.80734I
b = 1.195530 − 0.220149I
−1.55180 + 1.30485I −10.68807 − 2.05814I
u = −0.252729 − 0.545556I
a = 1.12490 − 1.80734I
b = 1.195530 + 0.220149I
−1.55180 − 1.30485I −10.68807 + 2.05814I
u = 1.40328
a = −0.707097
b = 17.9866
−8.20346 0
u = 1.40268 + 0.21970I
a = −1.000470 + 0.047291I
b = −4.06076 + 1.13846I
−6.86940 − 4.15900I 0
u = 1.40268 − 0.21970I
a = −1.000470 − 0.047291I
b = −4.06076 − 1.13846I
−6.86940 + 4.15900I 0
u = −1.40166 + 0.25943I
a = 0.369957 − 0.538443I
b = 1.406840 − 0.025933I
−4.13348 + 6.54909I 0
u = −1.40166 − 0.25943I
a = 0.369957 + 0.538443I
b = 1.406840 + 0.025933I
−4.13348 − 6.54909I 0
u = 1.41699 + 0.18942I
a = −0.397552 − 0.451392I
b = −1.82800 + 0.67940I
−8.80343 − 2.85042I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41699 − 0.18942I
a = −0.397552 + 0.451392I
b = −1.82800 − 0.67940I
−8.80343 + 2.85042I 0
u = 1.42092 + 0.16882I
a = 1.142530 − 0.249164I
b = 3.80818 − 0.16162I
−16.6231 − 2.4062I 0
u = 1.42092 − 0.16882I
a = 1.142530 + 0.249164I
b = 3.80818 + 0.16162I
−16.6231 + 2.4062I 0
u = 1.41759 + 0.24025I
a = −0.462209 + 0.634966I
b = −1.046820 + 0.817846I
−8.05484 − 5.91545I 0
u = 1.41759 − 0.24025I
a = −0.462209 − 0.634966I
b = −1.046820 − 0.817846I
−8.05484 + 5.91545I 0
u = 1.41612 + 0.26230I
a = 1.057140 − 0.017947I
b = 3.10624 − 2.03685I
−15.2379 − 6.3798I 0
u = 1.41612 − 0.26230I
a = 1.057140 + 0.017947I
b = 3.10624 + 2.03685I
−15.2379 + 6.3798I 0
u = −0.352318 + 0.432951I
a = 1.375020 + 0.227128I
b = 1.314630 + 0.274086I
−3.18353 + 0.42138I −17.5159 − 5.9857I
u = −0.352318 − 0.432951I
a = 1.375020 − 0.227128I
b = 1.314630 − 0.274086I
−3.18353 − 0.42138I −17.5159 + 5.9857I
u = −1.45707
a = 0.181182
b = −0.725800
−6.80909 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43616 + 0.25685I
a = 1.031140 + 0.086193I
b = 4.33596 + 0.85538I
−9.69388 + 8.97902I 0
u = −1.43616 − 0.25685I
a = 1.031140 − 0.086193I
b = 4.33596 − 0.85538I
−9.69388 − 8.97902I 0
u = −1.45252 + 0.16856I
a = 0.936630 + 0.094115I
b = 4.57825 + 1.58709I
−10.98590 + 0.55352I 0
u = −1.45252 − 0.16856I
a = 0.936630 − 0.094115I
b = 4.57825 − 1.58709I
−10.98590 − 0.55352I 0
u = 1.44182 + 0.27820I
a = −0.413431 − 0.565984I
b = −1.66846 − 0.35397I
−6.95051 − 11.70980I 0
u = 1.44182 − 0.27820I
a = −0.413431 + 0.565984I
b = −1.66846 + 0.35397I
−6.95051 + 11.70980I 0
u = −1.44321 + 0.30242I
a = −1.030120 + 0.007492I
b = −3.35638 − 1.37897I
−10.1396 + 10.8027I 0
u = −1.44321 − 0.30242I
a = −1.030120 − 0.007492I
b = −3.35638 + 1.37897I
−10.1396 − 10.8027I 0
u = 0.050008 + 0.517890I
a = 0.52093 + 1.97586I
b = 0.517556 − 0.009269I
−0.827089 + 0.874579I −11.22500 − 0.78875I
u = 0.050008 − 0.517890I
a = 0.52093 − 1.97586I
b = 0.517556 + 0.009269I
−0.827089 − 0.874579I −11.22500 + 0.78875I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47977 + 0.13837I
a = −0.310364 + 0.480653I
b = −0.254435 + 0.836932I
−9.00130 + 1.76478I 0
u = 1.47977 − 0.13837I
a = −0.310364 − 0.480653I
b = −0.254435 − 0.836932I
−9.00130 − 1.76478I 0
u = −0.370766 + 0.343538I
a = −2.20808 − 2.27788I
b = −0.417615 + 0.286970I
−10.92680 + 0.27845I −21.2584 − 7.9964I
u = −0.370766 − 0.343538I
a = −2.20808 + 2.27788I
b = −0.417615 − 0.286970I
−10.92680 − 0.27845I −21.2584 + 7.9964I
u = 1.47215 + 0.29827I
a = 1.040950 + 0.028454I
b = 3.74721 − 1.28908I
−13.2764 − 16.3796I 0
u = 1.47215 − 0.29827I
a = 1.040950 − 0.028454I
b = 3.74721 + 1.28908I
−13.2764 + 16.3796I 0
u = −1.51807 + 0.07871I
a = −0.987795 − 0.122501I
b = −3.57890 − 0.15397I
−13.33100 − 0.52768I 0
u = −1.51807 − 0.07871I
a = −0.987795 + 0.122501I
b = −3.57890 + 0.15397I
−13.33100 + 0.52768I 0
u = 1.54513 + 0.15028I
a = 0.951588 − 0.239832I
b = 3.61495 − 0.33639I
−15.6075 + 5.0247I 0
u = 1.54513 − 0.15028I
a = 0.951588 + 0.239832I
b = 3.61495 + 0.33639I
−15.6075 − 5.0247I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.386082
a = −0.548617
b = 0.295418
−0.651274 −14.9140
u = −0.284058
a = 3.08613
b = 2.55351
−2.87845 −51.1960
14
II. I
u
2
= h−u
7
+ u
6
+ 2u
5
− 3u
4
+ 2u
2
+ b − 2u + 2, u
7
+ u
6
− 3u
5
− 2u
4
+
3u
3
+ a + 2, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
−u
7
− u
6
+ 3u
5
+ 2u
4
− 3u
3
− 2
u
7
− u
6
− 2u
5
+ 3u
4
− 2u
2
+ 2u − 2
a
10
=
−u
7
− u
6
+ 3u
5
+ 2u
4
− 3u
3
− 2
u
7
− u
6
− 2u
5
+ 3u
4
− 2u
2
+ 3u − 2
a
1
=
0
−u
a
8
=
u
u
a
3
=
−u
2
+ 1
−u
2
a
2
=
u
5
− 2u
3
+ u
u
5
− u
3
− u
a
7
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
11
=
−u
7
− u
6
+ 3u
5
+ 2u
4
− 3u
3
− 2
u
7
− u
6
− 2u
5
+ 3u
4
− 2u
2
+ 2u − 2
a
6
=
−u
3
+ 2u
−u
5
+ u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
7
+ u
6
+ 10u
5
− 3u
4
− 6u
3
+ 2u
2
− 4u − 11
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
2
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
3
, c
4
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
5
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
6
, c
11
u
8
c
7
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
8
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
9
, c
10
(u − 1)
8
c
12
(u + 1)
8
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
2
, c
5
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
3
, c
4
, c
8
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
6
, c
11
y
8
c
9
, c
10
, c
12
(y −1)
8
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = −0.805639 + 0.183365I
b = −1.217260 + 0.361920I
−2.68559 − 1.13123I −13.44913 − 0.23763I
u = 1.180120 − 0.268597I
a = −0.805639 − 0.183365I
b = −1.217260 − 0.361920I
−2.68559 + 1.13123I −13.44913 + 0.23763I
u = 0.108090 + 0.747508I
a = −0.189481 + 1.310380I
b = −0.190969 + 0.055172I
0.51448 − 2.57849I −10.29693 + 2.50491I
u = 0.108090 − 0.747508I
a = −0.189481 − 1.310380I
b = −0.190969 − 0.055172I
0.51448 + 2.57849I −10.29693 − 2.50491I
u = −1.37100
a = 0.729394
b = −3.96004
−8.14766 −2.27260
u = −1.334530 + 0.318930I
a = 0.708845 + 0.169402I
b = 1.59435 + 0.51399I
−4.02461 + 6.44354I −17.1399 − 2.7122I
u = −1.334530 − 0.318930I
a = 0.708845 − 0.169402I
b = 1.59435 − 0.51399I
−4.02461 − 6.44354I −17.1399 + 2.7122I
u = 0.463640
a = −2.15684
b = −1.41219
−2.48997 −12.9560
18
III. I
u
3
= hau + b − 2a − u − 1, 2a
2
− au − 1, u
2
− 2i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
2
a
12
=
a
−au + 2a + u + 1
a
10
=
−a −
1
2
u
−4a + 1
a
1
=
−a −
1
2
u
−2a − u + 1
a
8
=
u
u
a
3
=
−1
−2
a
2
=
−a −
1
2
u − 1
−2a − u − 1
a
7
=
0
−u
a
11
=
a
−au + u + 1
a
6
=
−a −
1
2
u
−2a − u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
4
c
2
(u + 1)
4
c
3
, c
4
, c
7
c
8
(u
2
− 2)
2
c
6
, c
12
(u
2
− u − 1)
2
c
9
, c
10
, c
11
(u
2
+ u − 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
7
c
8
(y −2)
4
c
6
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 1.14412
b = 3.08443
−15.4624 −24.0000
u = 1.41421
a = −0.437016
b = 2.15822
−7.56670 −24.0000
u = −1.41421
a = −1.14412
b = −4.32049
−15.4624 −24.0000
u = −1.41421
a = 0.437016
b = 1.07785
−7.56670 −24.0000
22
IV. I
v
1
= ha, b + v + 2, v
2
+ 3v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
5
=
1
0
a
12
=
0
−v − 2
a
10
=
v
−1
a
1
=
2v + 1
−1
a
8
=
v
0
a
3
=
1
0
a
2
=
2v + 2
−1
a
7
=
v
0
a
11
=
−2v − 1
−v − 2
a
6
=
−2v − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
4
, c
7
c
8
u
2
c
5
(u + 1)
2
c
6
, c
9
, c
10
u
2
+ u − 1
c
11
, c
12
u
2
− u − 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
2
c
3
, c
4
, c
7
c
8
y
2
c
6
, c
9
, c
10
c
11
, c
12
y
2
− 3y + 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.381966
a = 0
b = −1.61803
−2.63189 −6.00000
v = −2.61803
a = 0
b = 0.618034
−10.5276 −6.00000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
92
+ 48u
91
+ ··· + 1755u + 81)
c
2
(u − 1)
2
(u + 1)
4
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
92
+ 4u
91
+ ··· − 69u − 9)
c
3
, c
4
u
2
(u
2
− 2)
2
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
92
+ 2u
91
+ ··· − 12u + 4)
c
5
(u − 1)
4
(u + 1)
2
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
92
+ 4u
91
+ ··· − 69u − 9)
c
6
u
8
(u
2
− u − 1)
2
(u
2
+ u − 1)(u
92
− 2u
91
+ ··· − 1920u + 256)
c
7
u
2
(u
2
− 2)
2
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
92
− 6u
91
+ ··· + 6260u + 380)
c
8
u
2
(u
2
− 2)
2
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
92
+ 2u
91
+ ··· − 12u + 4)
c
9
, c
10
((u − 1)
8
)(u
2
+ u − 1)
3
(u
92
− 12u
91
+ ··· + 6u + 1)
c
11
u
8
(u
2
− u − 1)(u
2
+ u − 1)
2
(u
92
− 2u
91
+ ··· − 1920u + 256)
c
12
((u + 1)
8
)(u
2
− u − 1)
3
(u
92
− 12u
91
+ ··· + 6u + 1)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
6
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
92
+ 72y
90
+ ··· − 662499y + 6561)
c
2
, c
5
(y − 1)
6
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
92
− 48y
91
+ ··· − 1755y + 81)
c
3
, c
4
, c
8
y
2
(y − 2)
4
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
92
− 86y
91
+ ··· − 240y + 16)
c
6
, c
11
y
8
(y
2
− 3y + 1)
3
(y
92
− 60y
91
+ ··· − 5947392y + 65536)
c
7
y
2
(y − 2)
4
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
92
− 14y
91
+ ··· − 25869360y + 144400)
c
9
, c
10
, c
12
((y − 1)
8
)(y
2
− 3y + 1)
3
(y
92
− 92y
91
+ ··· + 74y + 1)
28
