12n
0779
(K12n
0779
)
A knot diagram
1
Linearized knot diagam
4 6 8 12 2 10 1 3 7 6 5 7
Solving Sequence
1,7 3,8
4 9 10 6 2 12 5 11
c
7
c
3
c
8
c
9
c
6
c
2
c
12
c
4
c
11
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.22623 × 10
207
u
76
+ 2.11947 × 10
207
u
75
+ ··· + 3.97389 × 10
208
b − 1.15646 × 10
210
,
− 9.18608 × 10
208
u
76
+ 1.21921 × 10
209
u
75
+ ··· + 1.80256 × 10
210
a + 1.78378 × 10
212
,
u
77
− u
76
+ ··· − 8509u + 567i
I
u
2
= h−457890480u
16
+ 960770667u
15
+ ··· + 1926974837b − 992799855,
702672418u
16
− 1377478673u
15
+ ··· + 1926974837a + 650328159, u
17
− u
16
+ ··· − 4u
2
− 1i
I
u
3
= h10a
3
− 22a
2
+ 93b − 35a − 73, 2a
4
− 4a
3
+ 7a
2
− 16a + 38, u + 1i
I
u
4
= hb + 1, a, u − 1i
* 4 irreducible components of dim
C
= 0, with total 99 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
= h4.23 × 10
207
u
76
+ 2.12 × 10
207
u
75
+ · · · + 3.97 × 10
208
b − 1.16 ×
10
210
, −9.19 × 10
208
u
76
+ 1.22 × 10
209
u
75
+ · · · + 1.80 × 10
210
a + 1.78 ×
10
212
, u
77
− u
76
+ · · · − 8509u + 567i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
3
=
0.0509614u
76
− 0.0676378u
75
+ ··· + 1110.35u − 98.9581
−0.106350u
76
− 0.0533348u
75
+ ··· − 389.322u + 29.1014
a
8
=
1
u
2
a
4
=
0.0271559u
76
− 0.0759271u
75
+ ··· + 891.819u − 79.3123
−0.134886u
76
− 0.0541166u
75
+ ··· − 648.919u + 47.2992
a
9
=
0.178718u
76
+ 0.0499083u
75
+ ··· + 593.550u − 12.1865
0.0572808u
76
− 0.0573505u
75
+ ··· + 977.930u − 74.5360
a
10
=
0.235999u
76
− 0.00744223u
75
+ ··· + 1571.48u − 86.7225
0.0572808u
76
− 0.0573505u
75
+ ··· + 977.930u − 74.5360
a
6
=
0.0765354u
76
+ 0.0880012u
75
+ ··· − 300.208u + 26.0873
0.241208u
76
+ 0.00575286u
75
+ ··· + 1604.13u − 113.055
a
2
=
−0.218018u
76
− 0.108112u
75
+ ··· − 529.500u + 20.8711
−0.377977u
76
− 0.0124606u
75
+ ··· − 2608.00u + 184.881
a
12
=
u
u
a
5
=
0.130908u
76
− 0.113468u
75
+ ··· + 1993.17u − 158.823
−0.0311338u
76
− 0.0916577u
75
+ ··· + 452.432u − 32.2120
a
11
=
−0.102566u
76
+ 0.101738u
75
+ ··· − 1707.65u + 138.806
−0.115613u
76
+ 0.0703324u
75
+ ··· − 1447.07u + 102.159
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.120770u
76
+ 0.0653085u
75
+ ··· − 1789.94u + 132.110
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
+ 3u
76
+ ··· + 140u + 346
c
2
, c
5
u
77
+ u
76
+ ··· − 31u + 3
c
3
, c
8
2(2u
77
+ 2u
76
+ ··· + 45046u + 10309)
c
4
, c
11
2(2u
77
+ 2u
76
+ ··· + 471u − 43)
c
6
, c
9
, c
10
u
77
+ 5u
76
+ ··· − 2468u − 484
c
7
, c
12
u
77
+ u
76
+ ··· − 8509u − 567
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
− 37y
76
+ ··· − 4707452y −119716
c
2
, c
5
y
77
− 21y
76
+ ··· + 409y −9
c
3
, c
8
4(4y
77
+ 168y
76
+ ··· − 2.29225 × 10
9
y −1.06275 × 10
8
)
c
4
, c
11
4(4y
77
+ 256y
76
+ ··· + 124403y −1849)
c
6
, c
9
, c
10
y
77
+ 37y
76
+ ··· − 6355520y −234256
c
7
, c
12
y
77
− 39y
76
+ ··· + 38686993y −321489
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.938209 + 0.312226I
a = 0.45931 − 2.81298I
b = 1.52471 − 1.03894I
2.27562 − 7.70600I 0. + 7.20128I
u = 0.938209 − 0.312226I
a = 0.45931 + 2.81298I
b = 1.52471 + 1.03894I
2.27562 + 7.70600I 0. − 7.20128I
u = −0.875995 + 0.508486I
a = 0.234153 − 0.075791I
b = −1.227120 − 0.007460I
4.70217 + 2.02568I 0
u = −0.875995 − 0.508486I
a = 0.234153 + 0.075791I
b = −1.227120 + 0.007460I
4.70217 − 2.02568I 0
u = 0.968192 + 0.304214I
a = −1.63274 + 0.04834I
b = −1.76494 − 0.36327I
−7.81512 − 1.26226I 0
u = 0.968192 − 0.304214I
a = −1.63274 − 0.04834I
b = −1.76494 + 0.36327I
−7.81512 + 1.26226I 0
u = 1.027380 + 0.057854I
a = 0.78772 − 2.37985I
b = −0.073315 − 0.605421I
−3.36769 + 0.25082I 0
u = 1.027380 − 0.057854I
a = 0.78772 + 2.37985I
b = −0.073315 + 0.605421I
−3.36769 − 0.25082I 0
u = −0.948305 + 0.407949I
a = −1.26321 + 1.04494I
b = −0.398633 + 0.309092I
−11.49710 + 1.71109I 0
u = −0.948305 − 0.407949I
a = −1.26321 − 1.04494I
b = −0.398633 − 0.309092I
−11.49710 − 1.71109I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.959314 + 0.022193I
a = 1.22069 + 1.56847I
b = 1.54319 + 0.33074I
−6.58460 + 0.13649I −5.75334 + 0.I
u = −0.959314 − 0.022193I
a = 1.22069 − 1.56847I
b = 1.54319 − 0.33074I
−6.58460 − 0.13649I −5.75334 + 0.I
u = 0.923083 + 0.484293I
a = −0.463349 − 1.321980I
b = 0.500175 − 0.128105I
−0.99244 − 2.07171I 0
u = 0.923083 − 0.484293I
a = −0.463349 + 1.321980I
b = 0.500175 + 0.128105I
−0.99244 + 2.07171I 0
u = 0.899833 + 0.326890I
a = 0.238006 + 0.627875I
b = −1.47701 − 0.22087I
3.35138 − 2.02606I −4.52965 + 3.33898I
u = 0.899833 − 0.326890I
a = 0.238006 − 0.627875I
b = −1.47701 + 0.22087I
3.35138 + 2.02606I −4.52965 − 3.33898I
u = −0.992418 + 0.445492I
a = −0.580562 − 0.013694I
b = 1.062590 + 0.247665I
2.95780 + 8.95105I 0
u = −0.992418 − 0.445492I
a = −0.580562 + 0.013694I
b = 1.062590 − 0.247665I
2.95780 − 8.95105I 0
u = −0.725676 + 0.550777I
a = −0.06755 − 1.94403I
b = −0.994099 + 0.120889I
5.16680 + 2.21914I 0. − 4.47673I
u = −0.725676 − 0.550777I
a = −0.06755 + 1.94403I
b = −0.994099 − 0.120889I
5.16680 − 2.21914I 0. + 4.47673I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.843064 + 0.306195I
a = −0.51976 + 2.78968I
b = −1.314680 + 0.442050I
3.57992 − 0.75133I −4.75601 + 2.50232I
u = 0.843064 − 0.306195I
a = −0.51976 − 2.78968I
b = −1.314680 − 0.442050I
3.57992 + 0.75133I −4.75601 − 2.50232I
u = 0.752154 + 0.821574I
a = −0.322071 − 0.198011I
b = 0.728252 − 0.076220I
−0.49074 − 2.82293I 0
u = 0.752154 − 0.821574I
a = −0.322071 + 0.198011I
b = 0.728252 + 0.076220I
−0.49074 + 2.82293I 0
u = −0.998042 + 0.507221I
a = −0.58775 + 1.79684I
b = 1.346440 + 0.328851I
−7.03814 + 2.18023I 0
u = −0.998042 − 0.507221I
a = −0.58775 − 1.79684I
b = 1.346440 − 0.328851I
−7.03814 − 2.18023I 0
u = 0.169868 + 1.114180I
a = −0.149610 − 0.014889I
b = 0.580965 − 0.761755I
−0.97528 − 3.93159I 0
u = 0.169868 − 1.114180I
a = −0.149610 + 0.014889I
b = 0.580965 + 0.761755I
−0.97528 + 3.93159I 0
u = 0.171394 + 0.835566I
a = −0.365723 − 0.425611I
b = −0.111115 + 0.835924I
0.31291 − 1.89067I −2.93033 + 6.71981I
u = 0.171394 − 0.835566I
a = −0.365723 + 0.425611I
b = −0.111115 − 0.835924I
0.31291 + 1.89067I −2.93033 − 6.71981I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.767276 + 0.368105I
a = 0.112383 − 0.385376I
b = 1.44666 + 0.61955I
2.76703 + 4.76841I −4.31821 − 0.97191I
u = 0.767276 − 0.368105I
a = 0.112383 + 0.385376I
b = 1.44666 − 0.61955I
2.76703 − 4.76841I −4.31821 + 0.97191I
u = 1.183130 + 0.022965I
a = −0.495265 + 1.183940I
b = 0.162733 + 0.572171I
−3.02318 + 0.57253I 0
u = 1.183130 − 0.022965I
a = −0.495265 − 1.183940I
b = 0.162733 − 0.572171I
−3.02318 − 0.57253I 0
u = −0.759001 + 0.917861I
a = 0.694257 + 0.208347I
b = −0.505991 − 0.128925I
2.22539 + 3.42962I 0
u = −0.759001 − 0.917861I
a = 0.694257 − 0.208347I
b = −0.505991 + 0.128925I
2.22539 − 3.42962I 0
u = −0.572263 + 0.566452I
a = 0.11489 + 2.09983I
b = 0.573464 − 0.556687I
4.23079 − 4.90882I −1.40259 + 0.71127I
u = −0.572263 − 0.566452I
a = 0.11489 − 2.09983I
b = 0.573464 + 0.556687I
4.23079 + 4.90882I −1.40259 − 0.71127I
u = −0.791326
a = 0.816501
b = 1.31849
−2.71373 4.50760
u = −0.502452 + 1.114780I
a = −0.336392 − 0.167540I
b = 0.650114 − 0.208442I
4.35830 − 3.10300I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.502452 − 1.114780I
a = −0.336392 + 0.167540I
b = 0.650114 + 0.208442I
4.35830 + 3.10300I 0
u = −1.225660 + 0.010183I
a = 0.73465 − 1.44720I
b = 1.24124 − 1.30163I
−5.20027 + 0.33103I 0
u = −1.225660 − 0.010183I
a = 0.73465 + 1.44720I
b = 1.24124 + 1.30163I
−5.20027 − 0.33103I 0
u = −1.052070 + 0.697529I
a = 0.419526 − 1.084380I
b = −0.458586 − 0.100923I
1.15545 + 2.60466I 0
u = −1.052070 − 0.697529I
a = 0.419526 + 1.084380I
b = −0.458586 + 0.100923I
1.15545 − 2.60466I 0
u = 0.350389 + 1.238280I
a = 0.302433 + 0.241715I
b = −1.22154 − 1.18957I
2.33286 + 10.04200I 0
u = 0.350389 − 1.238280I
a = 0.302433 − 0.241715I
b = −1.22154 + 1.18957I
2.33286 − 10.04200I 0
u = −0.017094 + 0.709812I
a = −0.015725 − 0.612293I
b = −0.661442 + 0.724504I
0.87207 − 1.63589I 0.91062 + 1.99464I
u = −0.017094 − 0.709812I
a = −0.015725 + 0.612293I
b = −0.661442 − 0.724504I
0.87207 + 1.63589I 0.91062 − 1.99464I
u = 0.586195 + 1.206420I
a = −0.447297 − 0.365209I
b = 1.47980 + 0.94082I
3.06796 + 1.94916I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.586195 − 1.206420I
a = −0.447297 + 0.365209I
b = 1.47980 − 0.94082I
3.06796 − 1.94916I 0
u = 1.053630 + 0.836247I
a = 0.801184 + 1.091560I
b = −1.45091 + 0.28853I
−8.65792 − 3.32546I 0
u = 1.053630 − 0.836247I
a = 0.801184 − 1.091560I
b = −1.45091 − 0.28853I
−8.65792 + 3.32546I 0
u = 1.144550 + 0.762513I
a = 0.469004 + 0.255869I
b = 0.314083 + 0.282253I
−5.17182 − 3.41804I 0
u = 1.144550 − 0.762513I
a = 0.469004 − 0.255869I
b = 0.314083 − 0.282253I
−5.17182 + 3.41804I 0
u = −0.055853 + 1.399210I
a = 0.259596 − 0.566021I
b = −0.71608 + 1.95395I
1.172940 − 0.320324I 0
u = −0.055853 − 1.399210I
a = 0.259596 + 0.566021I
b = −0.71608 − 1.95395I
1.172940 + 0.320324I 0
u = −1.220890 + 0.703647I
a = −0.246045 + 1.136080I
b = 0.830013 + 0.398148I
1.96603 + 9.63339I 0
u = −1.220890 − 0.703647I
a = −0.246045 − 1.136080I
b = 0.830013 − 0.398148I
1.96603 − 9.63339I 0
u = −1.30456 + 0.56803I
a = 0.21222 − 1.61192I
b = −1.66346 − 1.32611I
−3.32087 + 6.55607I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.30456 − 0.56803I
a = 0.21222 + 1.61192I
b = −1.66346 + 1.32611I
−3.32087 − 6.55607I 0
u = −1.36104 + 0.44117I
a = −0.02107 + 1.52062I
b = 1.00390 + 1.20424I
−5.86329 + 9.15412I 0
u = −1.36104 − 0.44117I
a = −0.02107 − 1.52062I
b = 1.00390 − 1.20424I
−5.86329 − 9.15412I 0
u = −1.37113 + 0.45871I
a = 0.26995 − 1.55470I
b = −0.87251 − 1.82313I
−4.46911 + 6.73768I 0
u = −1.37113 − 0.45871I
a = 0.26995 + 1.55470I
b = −0.87251 + 1.82313I
−4.46911 − 6.73768I 0
u = 1.24060 + 0.75166I
a = −0.46366 − 1.44274I
b = 1.57729 − 0.83469I
0.78106 − 8.94267I 0
u = 1.24060 − 0.75166I
a = −0.46366 + 1.44274I
b = 1.57729 + 0.83469I
0.78106 + 8.94267I 0
u = 1.31281 + 0.69335I
a = 0.37601 + 1.53399I
b = −1.54556 + 1.15634I
−0.8032 − 16.8481I 0
u = 1.31281 − 0.69335I
a = 0.37601 − 1.53399I
b = −1.54556 − 1.15634I
−0.8032 + 16.8481I 0
u = −1.48756 + 0.08203I
a = −0.513504 + 1.151500I
b = −0.85673 + 1.70918I
−5.02328 − 5.11535I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48756 − 0.08203I
a = −0.513504 − 1.151500I
b = −0.85673 − 1.70918I
−5.02328 + 5.11535I 0
u = 1.39694 + 0.53346I
a = 0.333447 + 0.773642I
b = −0.167691 + 0.933629I
−5.06385 − 2.26977I 0
u = 1.39694 − 0.53346I
a = 0.333447 − 0.773642I
b = −0.167691 − 0.933629I
−5.06385 + 2.26977I 0
u = 1.45782 + 0.41166I
a = −0.675600 − 1.175820I
b = −0.09665 − 2.25637I
−4.45663 − 5.90917I 0
u = 1.45782 − 0.41166I
a = −0.675600 + 1.175820I
b = −0.09665 + 2.25637I
−4.45663 + 5.90917I 0
u = 0.1384700 + 0.0113495I
a = −4.51798 + 1.81968I
b = 0.353220 − 0.574268I
−1.34082 + 0.63330I −8.08009 − 1.67508I
u = 0.1384700 − 0.0113495I
a = −4.51798 − 1.81968I
b = 0.353220 + 0.574268I
−1.34082 − 0.63330I −8.08009 + 1.67508I
12
II.
I
u
2
= h−4.58 × 10
8
u
16
+ 9.61 × 10
8
u
15
+ · · · + 1.93 × 10
9
b − 9.93 × 10
8
, 7.03 ×
10
8
u
16
−1.38×10
9
u
15
+· · · +1.93×10
9
a+6.50×10
8
, u
17
−u
16
+· · · −4u
2
−1i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
3
=
−0.364651u
16
+ 0.714840u
15
+ ··· − 2.80781u − 0.337487
0.237621u
16
− 0.498590u
15
+ ··· + 0.0910993u + 0.515212
a
8
=
1
u
2
a
4
=
−0.321496u
16
+ 0.509120u
15
+ ··· − 2.35206u − 0.172464
0.241488u
16
− 0.460958u
15
+ ··· + 0.134254u + 0.352647
a
9
=
−0.612409u
16
+ 0.417151u
15
+ ··· + 1.33960u + 3.13400
0.260806u
16
− 0.277899u
15
+ ··· − 1.93236u − 0.505464
a
10
=
−0.351603u
16
+ 0.139252u
15
+ ··· − 0.592762u + 2.62853
0.260806u
16
− 0.277899u
15
+ ··· − 1.93236u − 0.505464
a
6
=
1.09161u
16
− 1.21565u
15
+ ··· − 3.84808u − 0.692045
−0.277769u
16
+ 0.241174u
15
+ ··· + 3.19317u − 0.511629
a
2
=
0.823475u
16
− 0.992964u
15
+ ··· − 3.28510u − 1.09914
−0.437331u
16
+ 0.284935u
15
+ ··· + 3.64726u − 0.593676
a
12
=
u
u
a
5
=
−0.0533608u
16
+ 0.286437u
15
+ ··· − 2.91505u + 0.234630
0.509623u
16
− 0.683642u
15
+ ··· − 0.428729u + 0.759741
a
11
=
−1.03719u
16
+ 1.32400u
15
+ ··· + 5.63586u + 0.710941
0.259310u
16
− 0.177981u
15
+ ··· − 3.97640u + 0.735840
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1861124579
1926974837
u
16
−
1654674004
1926974837
u
15
+ ··· −
8930565079
1926974837
u −
3929061975
1926974837
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− u
16
+ ··· + 8u − 1
c
2
u
17
+ 9u
16
+ ··· − 8u − 1
c
3
u
17
− 2u
16
+ ··· − u − 1
c
4
u
17
− 2u
16
+ ··· − 4u − 1
c
5
u
17
− 9u
16
+ ··· − 8u + 1
c
6
u
17
+ 2u
16
+ ··· + 2u − 1
c
7
u
17
− u
16
+ ··· − 4u
2
− 1
c
8
u
17
+ 2u
16
+ ··· − u + 1
c
9
, c
10
u
17
− 2u
16
+ ··· + 2u + 1
c
11
u
17
+ 2u
16
+ ··· − 4u + 1
c
12
u
17
+ u
16
+ ··· + 4u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 9y
16
+ ··· + 10y −1
c
2
, c
5
y
17
− 11y
16
+ ··· + 16y −1
c
3
, c
8
y
17
+ 6y
16
+ ··· − 5y −1
c
4
, c
11
y
17
+ 8y
16
+ ··· − 8y −1
c
6
, c
9
, c
10
y
17
+ 14y
16
+ ··· + 8y −1
c
7
, c
12
y
17
− 5y
16
+ ··· − 8y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.03643
a = 1.75097
b = −0.373750
−3.19557 −34.5840
u = 0.638800 + 0.863369I
a = −0.525436 + 0.100281I
b = 0.370005 − 0.238052I
−1.00430 − 2.73603I −10.70816 + 0.98270I
u = 0.638800 − 0.863369I
a = −0.525436 − 0.100281I
b = 0.370005 + 0.238052I
−1.00430 + 2.73603I −10.70816 − 0.98270I
u = 0.990121 + 0.590500I
a = 1.114650 + 0.707359I
b = 0.093119 + 0.360372I
−10.87950 − 2.38310I −7.01679 + 4.56060I
u = 0.990121 − 0.590500I
a = 1.114650 − 0.707359I
b = 0.093119 − 0.360372I
−10.87950 + 2.38310I −7.01679 − 4.56060I
u = −0.107060 + 1.320330I
a = 0.021270 − 0.515650I
b = −0.45084 + 1.79379I
1.26487 − 0.95833I −1.73090 + 6.81853I
u = −0.107060 − 1.320330I
a = 0.021270 + 0.515650I
b = −0.45084 − 1.79379I
1.26487 + 0.95833I −1.73090 − 6.81853I
u = −1.107840 + 0.838997I
a = −0.715934 + 1.184300I
b = 1.69244 + 0.40158I
−9.25694 + 3.38423I −13.9467 − 4.2175I
u = −1.107840 − 0.838997I
a = −0.715934 − 1.184300I
b = 1.69244 − 0.40158I
−9.25694 − 3.38423I −13.9467 + 4.2175I
u = 1.25308 + 0.66384I
a = −0.549700 − 0.401706I
b = −0.326738 − 0.665471I
−5.31878 − 3.16732I −16.8676 − 2.7187I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.25308 − 0.66384I
a = −0.549700 + 0.401706I
b = −0.326738 + 0.665471I
−5.31878 + 3.16732I −16.8676 + 2.7187I
u = 0.089248 + 0.443151I
a = −2.74635 − 0.43495I
b = 1.225620 + 0.348844I
4.44461 − 0.57232I −1.120956 + 0.305763I
u = 0.089248 − 0.443151I
a = −2.74635 + 0.43495I
b = 1.225620 − 0.348844I
4.44461 + 0.57232I −1.120956 − 0.305763I
u = −1.47561 + 0.48244I
a = 0.16859 − 1.47094I
b = −1.25909 − 2.03506I
−3.87646 + 7.54083I −4.99133 − 11.97652I
u = −1.47561 − 0.48244I
a = 0.16859 + 1.47094I
b = −1.25909 + 2.03506I
−3.87646 − 7.54083I −4.99133 + 11.97652I
u = −0.298964 + 0.313290I
a = 2.35742 − 1.81709I
b = −1.157640 − 0.738822I
3.19519 + 6.40579I −3.32551 − 4.81825I
u = −0.298964 − 0.313290I
a = 2.35742 + 1.81709I
b = −1.157640 + 0.738822I
3.19519 − 6.40579I −3.32551 + 4.81825I
17
III. I
u
3
= h10a
3
− 22a
2
+ 93b − 35a − 73, 2a
4
− 4a
3
+ 7a
2
− 16a + 38, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
7
=
1
0
a
3
=
a
−0.107527a
3
+ 0.236559a
2
+ 0.376344a + 0.784946
a
8
=
1
1
a
4
=
−0.107527a
3
+ 0.236559a
2
+ 0.376344a + 0.784946
−0.215054a
3
+ 0.473118a
2
− 0.247312a + 1.56989
a
9
=
−0.0215054a
3
+ 0.247312a
2
+ 0.0752688a − 1.04301
0.0645161a
3
+ 0.258065a
2
− 0.225806a + 0.129032
a
10
=
0.0430108a
3
+ 0.505376a
2
− 0.150538a − 0.913978
0.0645161a
3
+ 0.258065a
2
− 0.225806a + 0.129032
a
6
=
0.0430108a
3
− 0.494624a
2
+ 0.849462a − 2.91398
−2
a
2
=
−0.0430108a
3
+ 0.494624a
2
+ 0.150538a + 2.91398
−0.107527a
3
+ 0.236559a
2
+ 0.376344a + 2.78495
a
12
=
−1
−1
a
5
=
a
−0.107527a
3
+ 0.236559a
2
+ 0.376344a + 0.784946
a
11
=
0.0215054a
3
− 0.247312a
2
− 0.0752688a + 1.04301
−0.0645161a
3
− 0.258065a
2
+ 0.225806a − 0.129032
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 2u
3
− 3u
2
+ 4u + 6
c
2
, c
12
(u − 1)
4
c
3
, c
11
2(2u
4
+ 5u
2
+ 2u + 3)
c
4
, c
8
2(2u
4
+ 5u
2
− 2u + 3)
c
5
, c
7
(u + 1)
4
c
6
, c
9
, c
10
(u
2
+ 2)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 10y
3
+ 37y
2
− 52y + 36
c
2
, c
5
, c
7
c
12
(y − 1)
4
c
3
, c
4
, c
8
c
11
4(4y
4
+ 20y
3
+ 37y
2
+ 26y + 9)
c
6
, c
9
, c
10
(y + 2)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.74726 + 1.91261I
b = −1.066450 + 0.451407I
−8.22467 −12.0000
u = −1.00000
a = −0.74726 − 1.91261I
b = −1.066450 − 0.451407I
−8.22467 −12.0000
u = −1.00000
a = 1.74726 + 1.20550I
b = 2.06645 + 0.45141I
−8.22467 −12.0000
u = −1.00000
a = 1.74726 − 1.20550I
b = 2.06645 − 0.45141I
−8.22467 −12.0000
21
IV. I
u
4
= hb + 1, a, u − 1i
(i) Arc colorings
a
1
=
0
1
a
7
=
1
0
a
3
=
0
−1
a
8
=
1
1
a
4
=
−1
−2
a
9
=
1
0
a
10
=
1
0
a
6
=
1
0
a
2
=
−1
−1
a
12
=
1
1
a
5
=
0
−1
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
u − 1
c
5
, c
8
, c
11
c
12
u + 1
c
6
, c
9
, c
10
u
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
11
, c
12
y − 1
c
6
, c
9
, c
10
y
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
4
− 2u
3
+ ··· + 4u + 6)(u
17
− u
16
+ ··· + 8u − 1)
· (u
77
+ 3u
76
+ ··· + 140u + 346)
c
2
((u − 1)
5
)(u
17
+ 9u
16
+ ··· − 8u − 1)(u
77
+ u
76
+ ··· − 31u + 3)
c
3
4(u − 1)(2u
4
+ 5u
2
+ 2u + 3)(u
17
− 2u
16
+ ··· − u − 1)
· (2u
77
+ 2u
76
+ ··· + 45046u + 10309)
c
4
4(u − 1)(2u
4
+ 5u
2
− 2u + 3)(u
17
− 2u
16
+ ··· − 4u − 1)
· (2u
77
+ 2u
76
+ ··· + 471u − 43)
c
5
((u + 1)
5
)(u
17
− 9u
16
+ ··· − 8u + 1)(u
77
+ u
76
+ ··· − 31u + 3)
c
6
u(u
2
+ 2)
2
(u
17
+ 2u
16
+ ··· + 2u − 1)(u
77
+ 5u
76
+ ··· − 2468u − 484)
c
7
(u − 1)(u + 1)
4
(u
17
− u
16
+ ··· − 4u
2
− 1)
· (u
77
+ u
76
+ ··· − 8509u − 567)
c
8
4(u + 1)(2u
4
+ 5u
2
− 2u + 3)(u
17
+ 2u
16
+ ··· − u + 1)
· (2u
77
+ 2u
76
+ ··· + 45046u + 10309)
c
9
, c
10
u(u
2
+ 2)
2
(u
17
− 2u
16
+ ··· + 2u + 1)(u
77
+ 5u
76
+ ··· − 2468u − 484)
c
11
4(u + 1)(2u
4
+ 5u
2
+ 2u + 3)(u
17
+ 2u
16
+ ··· − 4u + 1)
· (2u
77
+ 2u
76
+ ··· + 471u − 43)
c
12
((u − 1)
4
)(u + 1)(u
17
+ u
16
+ ··· + 4u
2
+ 1)
· (u
77
+ u
76
+ ··· − 8509u − 567)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)(y
4
− 10y
3
+ ··· − 52y + 36)(y
17
− 9y
16
+ ··· + 10y − 1)
· (y
77
− 37y
76
+ ··· − 4707452y − 119716)
c
2
, c
5
((y − 1)
5
)(y
17
− 11y
16
+ ··· + 16y − 1)(y
77
− 21y
76
+ ··· + 409y − 9)
c
3
, c
8
16(y − 1)(4y
4
+ 20y
3
+ ··· + 26y + 9)(y
17
+ 6y
16
+ ··· − 5y − 1)
· (4y
77
+ 168y
76
+ ··· − 2292246358y − 106275481)
c
4
, c
11
16(y − 1)(4y
4
+ 20y
3
+ ··· + 26y + 9)(y
17
+ 8y
16
+ ··· − 8y − 1)
· (4y
77
+ 256y
76
+ ··· + 124403y − 1849)
c
6
, c
9
, c
10
y(y + 2)
4
(y
17
+ 14y
16
+ ··· + 8y − 1)
· (y
77
+ 37y
76
+ ··· − 6355520y − 234256)
c
7
, c
12
((y − 1)
5
)(y
17
− 5y
16
+ ··· − 8y − 1)
· (y
77
− 39y
76
+ ··· + 38686993y − 321489)
27
