12a
0043
(K12a
0043
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 4 10 12 6 1 8 11
Solving Sequence
5,9
6
3,10
2 1 11 4 7 12 8
c
5
c
9
c
2
c
1
c
10
c
4
c
6
c
12
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.12989 × 10
299
u
117
− 1.16841 × 10
300
u
116
+ ··· + 4.70875 × 10
301
b + 1.53055 × 10
303
,
3.83387 × 10
299
u
117
+ 8.89420 × 10
298
u
116
+ ··· + 2.35437 × 10
301
a − 5.12301 × 10
302
,
u
118
− 2u
117
+ ··· + 2560u − 512i
I
u
2
= hb + 1, 2u
7
+ 3u
6
− 5u
5
− 7u
4
+ 4u
3
+ 3u
2
+ a + 4, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
I
v
1
= ha, b − v −1, v
3
+ 2v
2
+ v + 1i
I
v
2
= ha, −89v
5
− 27v
4
− 1425v
3
+ 1434v
2
+ 80b − 1060v + 163, v
6
+ 16v
4
− 21v
3
+ 18v
2
− 7v + 1i
* 4 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
= h1.13 × 10
299
u
117
− 1.17 × 10
300
u
116
+ · · · + 4.71 × 10
301
b + 1.53 ×
10
303
, 3.83 × 10
299
u
117
+ 8.89 × 10
298
u
116
+ · · · + 2.35 × 10
301
a − 5.12 ×
10
302
, u
118
− 2u
117
+ · · · + 2560u − 512i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
3
=
−0.0162840u
117
− 0.00377773u
116
+ ··· + 7.00670u + 21.7596
−0.00239956u
117
+ 0.0248136u
116
+ ··· + 64.2202u − 32.5045
a
10
=
−u
−u
3
+ u
a
2
=
−0.0186836u
117
+ 0.0210359u
116
+ ··· + 71.2269u − 10.7449
−0.00239956u
117
+ 0.0248136u
116
+ ··· + 64.2202u − 32.5045
a
1
=
0.239969u
117
− 0.352060u
116
+ ··· − 716.486u + 221.132
−0.292188u
117
+ 0.424993u
116
+ ··· + 866.378u − 258.873
a
11
=
−0.131955u
117
+ 0.204289u
116
+ ··· + 413.640u − 128.922
0.221589u
117
− 0.335927u
116
+ ··· − 682.434u + 206.678
a
4
=
0.0733908u
117
− 0.115200u
116
+ ··· − 209.169u + 71.7653
−0.172469u
117
+ 0.223238u
116
+ ··· + 440.130u − 109.957
a
7
=
−0.0522189u
117
+ 0.0729326u
116
+ ··· + 149.893u − 37.7416
0.277615u
117
− 0.398424u
116
+ ··· − 812.461u + 242.743
a
12
=
0.265862u
117
− 0.404606u
116
+ ··· − 827.746u + 260.201
−0.364450u
117
+ 0.560905u
116
+ ··· + 1155.73u − 356.859
a
8
=
−0.116915u
117
+ 0.172605u
116
+ ··· + 354.396u − 103.215
0.331573u
117
− 0.477354u
116
+ ··· − 974.009u + 293.000
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.80808u
117
− 2.59255u
116
+ ··· − 5062.88u + 1486.83
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
118
+ 56u
117
+ ··· + 165u + 1
c
2
, c
4
u
118
− 12u
117
+ ··· + 13u + 1
c
3
, c
6
u
118
− 4u
117
+ ··· + 1664u − 256
c
5
, c
9
u
118
+ 2u
117
+ ··· − 2560u − 512
c
7
u
118
− 5u
117
+ ··· − 42339u + 2017
c
8
, c
11
u
118
+ 5u
117
+ ··· + 11u + 1
c
10
, c
12
u
118
+ 39u
117
+ ··· − 19u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
118
+ 24y
117
+ ··· − 12937y + 1
c
2
, c
4
y
118
− 56y
117
+ ··· − 165y + 1
c
3
, c
6
y
118
+ 60y
117
+ ··· − 1228800y + 65536
c
5
, c
9
y
118
− 56y
117
+ ··· − 9306112y + 262144
c
7
y
118
− 11y
117
+ ··· + 141591059y + 4068289
c
8
, c
11
y
118
− 39y
117
+ ··· + 19y + 1
c
10
, c
12
y
118
+ 85y
117
+ ··· − 157y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.968041 + 0.257958I
a = −1.095610 + 0.036404I
b = −1.208900 − 0.211455I
−3.20568 + 0.98478I 0
u = −0.968041 − 0.257958I
a = −1.095610 − 0.036404I
b = −1.208900 + 0.211455I
−3.20568 − 0.98478I 0
u = 0.829247 + 0.549290I
a = −0.865086 − 0.372811I
b = 0.553838 − 0.724684I
6.32463 + 3.26581I 0
u = 0.829247 − 0.549290I
a = −0.865086 + 0.372811I
b = 0.553838 + 0.724684I
6.32463 − 3.26581I 0
u = −0.415238 + 0.916584I
a = 1.23962 + 1.28903I
b = −0.981130 − 0.446334I
0.99666 − 5.77439I 0
u = −0.415238 − 0.916584I
a = 1.23962 − 1.28903I
b = −0.981130 + 0.446334I
0.99666 + 5.77439I 0
u = 0.482135 + 0.901109I
a = 0.214333 − 1.168030I
b = 0.447969 + 0.621910I
0.099568 + 0.954515I 0
u = 0.482135 − 0.901109I
a = 0.214333 + 1.168030I
b = 0.447969 − 0.621910I
0.099568 − 0.954515I 0
u = 0.249986 + 0.944644I
a = −0.120617 − 0.867968I
b = 0.793060 + 0.496364I
1.78559 − 4.11675I 0
u = 0.249986 − 0.944644I
a = −0.120617 + 0.867968I
b = 0.793060 − 0.496364I
1.78559 + 4.11675I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.799310 + 0.561370I
a = −0.196431 + 1.338860I
b = 0.715155 − 0.892572I
6.93896 + 1.81575I 0
u = −0.799310 − 0.561370I
a = −0.196431 − 1.338860I
b = 0.715155 + 0.892572I
6.93896 − 1.81575I 0
u = 0.843723 + 0.487342I
a = −0.237848 − 1.342180I
b = 0.748925 + 0.908083I
6.30583 − 7.44643I 0
u = 0.843723 − 0.487342I
a = −0.237848 + 1.342180I
b = 0.748925 − 0.908083I
6.30583 + 7.44643I 0
u = 0.478089 + 0.846590I
a = 1.25380 − 1.23453I
b = −0.930674 + 0.453400I
1.68529 + 0.26296I 0
u = 0.478089 − 0.846590I
a = 1.25380 + 1.23453I
b = −0.930674 − 0.453400I
1.68529 − 0.26296I 0
u = −0.853323 + 0.583684I
a = −0.906160 + 0.157216I
b = 0.528021 + 0.758724I
6.75979 + 2.72376I 0
u = −0.853323 − 0.583684I
a = −0.906160 − 0.157216I
b = 0.528021 − 0.758724I
6.75979 − 2.72376I 0
u = 0.972715 + 0.354059I
a = 1.75870 − 1.27137I
b = 1.028880 + 0.606831I
4.90526 − 1.82621I 0
u = 0.972715 − 0.354059I
a = 1.75870 + 1.27137I
b = 1.028880 − 0.606831I
4.90526 + 1.82621I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.985328 + 0.420063I
a = 1.57530 + 1.48448I
b = 1.049240 − 0.617926I
5.20076 + 7.94162I 0
u = −0.985328 − 0.420063I
a = 1.57530 − 1.48448I
b = 1.049240 + 0.617926I
5.20076 − 7.94162I 0
u = −0.520970 + 0.762195I
a = −0.023391 + 1.189300I
b = 0.622197 − 0.716300I
3.44231 + 1.13448I 0
u = −0.520970 − 0.762195I
a = −0.023391 − 1.189300I
b = 0.622197 + 0.716300I
3.44231 − 1.13448I 0
u = 1.016500 + 0.411656I
a = −0.57750 + 1.92773I
b = −1.025370 − 0.473801I
−2.56259 − 3.40175I 0
u = 1.016500 − 0.411656I
a = −0.57750 − 1.92773I
b = −1.025370 + 0.473801I
−2.56259 + 3.40175I 0
u = −1.068630 + 0.250244I
a = 0.732536 + 0.841832I
b = −0.410454 − 0.655638I
−4.72278 + 0.90000I 0
u = −1.068630 − 0.250244I
a = 0.732536 − 0.841832I
b = −0.410454 + 0.655638I
−4.72278 − 0.90000I 0
u = 0.990053 + 0.499135I
a = 0.921702 − 0.978841I
b = −0.598504 + 0.641847I
0.972070 − 0.862575I 0
u = 0.990053 − 0.499135I
a = 0.921702 + 0.978841I
b = −0.598504 − 0.641847I
0.972070 + 0.862575I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.243622 + 0.854934I
a = −0.381125 − 0.936603I
b = 0.975067 + 0.617838I
2.38535 − 3.97142I 0
u = −0.243622 − 0.854934I
a = −0.381125 + 0.936603I
b = 0.975067 − 0.617838I
2.38535 + 3.97142I 0
u = −1.114060 + 0.037982I
a = 0.446073 − 0.685881I
b = −0.171434 + 0.680603I
−1.57653 + 4.72128I 0
u = −1.114060 − 0.037982I
a = 0.446073 + 0.685881I
b = −0.171434 − 0.680603I
−1.57653 − 4.72128I 0
u = 1.027390 + 0.442691I
a = −0.166893 + 0.306639I
b = 0.252493 − 0.709156I
−0.506538 − 0.358617I 0
u = 1.027390 − 0.442691I
a = −0.166893 − 0.306639I
b = 0.252493 + 0.709156I
−0.506538 + 0.358617I 0
u = 0.861028 + 0.151410I
a = 0.522984 + 0.294298I
b = −0.049918 − 0.430497I
−0.628133 − 0.111774I 0
u = 0.861028 − 0.151410I
a = 0.522984 − 0.294298I
b = −0.049918 + 0.430497I
−0.628133 + 0.111774I 0
u = −0.614884 + 0.943203I
a = 0.117724 + 1.369210I
b = 0.448785 − 0.808428I
6.24801 − 0.38665I 0
u = −0.614884 − 0.943203I
a = 0.117724 − 1.369210I
b = 0.448785 + 0.808428I
6.24801 + 0.38665I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.031010 + 1.128990I
a = −0.316506 + 0.783217I
b = 0.963150 − 0.484891I
1.155310 − 0.197698I 0
u = 0.031010 − 1.128990I
a = −0.316506 − 0.783217I
b = 0.963150 + 0.484891I
1.155310 + 0.197698I 0
u = 0.268922 + 0.827360I
a = 0.72388 + 1.84885I
b = −1.168050 − 0.164940I
0.29288 + 3.57986I 0
u = 0.268922 − 0.827360I
a = 0.72388 − 1.84885I
b = −1.168050 + 0.164940I
0.29288 − 3.57986I 0
u = 0.590336 + 0.982576I
a = 0.167145 − 1.387410I
b = 0.403326 + 0.803323I
5.42643 + 6.09310I 0
u = 0.590336 − 0.982576I
a = 0.167145 + 1.387410I
b = 0.403326 − 0.803323I
5.42643 − 6.09310I 0
u = 0.777956 + 0.330194I
a = −0.458677 + 1.167580I
b = 0.981131 − 0.822526I
5.61296 − 1.12841I 0
u = 0.777956 − 0.330194I
a = −0.458677 − 1.167580I
b = 0.981131 + 0.822526I
5.61296 + 1.12841I 0
u = −0.718794 + 0.438941I
a = −0.466394 − 1.130240I
b = 0.996581 + 0.793604I
6.09920 − 4.36602I 0
u = −0.718794 − 0.438941I
a = −0.466394 + 1.130240I
b = 0.996581 − 0.793604I
6.09920 + 4.36602I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.139670 + 0.233858I
a = −0.64291 − 1.42563I
b = −1.125200 + 0.435963I
−4.44670 − 0.52239I 0
u = −1.139670 − 0.233858I
a = −0.64291 + 1.42563I
b = −1.125200 − 0.435963I
−4.44670 + 0.52239I 0
u = 1.165730 + 0.117225I
a = −0.711644 − 0.603236I
b = −1.233320 + 0.315637I
−4.75315 + 3.18722I 0
u = 1.165730 − 0.117225I
a = −0.711644 + 0.603236I
b = −1.233320 − 0.315637I
−4.75315 − 3.18722I 0
u = −0.377624 + 0.735819I
a = 0.37330 − 1.98922I
b = −1.174320 + 0.104126I
0.77652 + 1.81636I −12.00000 + 0.I
u = −0.377624 − 0.735819I
a = 0.37330 + 1.98922I
b = −1.174320 − 0.104126I
0.77652 − 1.81636I −12.00000 + 0.I
u = −1.072760 + 0.484709I
a = 0.860812 + 1.003010I
b = −0.574193 − 0.692752I
0.05864 + 6.41739I 0
u = −1.072760 − 0.484709I
a = 0.860812 − 1.003010I
b = −0.574193 + 0.692752I
0.05864 − 6.41739I 0
u = 0.336930 + 1.138880I
a = −0.462918 + 0.832786I
b = 1.062340 − 0.556419I
−1.69323 + 5.63066I 0
u = 0.336930 − 1.138880I
a = −0.462918 − 0.832786I
b = 1.062340 + 0.556419I
−1.69323 − 5.63066I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.537139 + 1.064810I
a = −0.528088 − 0.903093I
b = 1.097750 + 0.625048I
4.31525 − 5.75325I 0
u = −0.537139 − 1.064810I
a = −0.528088 + 0.903093I
b = 1.097750 − 0.625048I
4.31525 + 5.75325I 0
u = −1.037560 + 0.589522I
a = −0.548931 − 0.411253I
b = 0.357729 + 0.832116I
1.88903 + 3.97132I 0
u = −1.037560 − 0.589522I
a = −0.548931 + 0.411253I
b = 0.357729 − 0.832116I
1.88903 − 3.97132I 0
u = −0.132287 + 0.795513I
a = 1.35850 + 1.53988I
b = −1.023230 − 0.290062I
−3.52217 − 0.96416I −19.6651 + 0.I
u = −0.132287 − 0.795513I
a = 1.35850 − 1.53988I
b = −1.023230 + 0.290062I
−3.52217 + 0.96416I −19.6651 + 0.I
u = −1.085610 + 0.543986I
a = −0.356479 − 0.308822I
b = −1.327980 − 0.156554I
−1.30186 + 2.99365I 0
u = −1.085610 − 0.543986I
a = −0.356479 + 0.308822I
b = −1.327980 + 0.156554I
−1.30186 − 2.99365I 0
u = 1.167610 + 0.373716I
a = −0.483262 − 0.069876I
b = −1.305780 + 0.232105I
−7.40438 − 2.81707I 0
u = 1.167610 − 0.373716I
a = −0.483262 + 0.069876I
b = −1.305780 − 0.232105I
−7.40438 + 2.81707I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.540828 + 1.135790I
a = −0.544870 + 0.876987I
b = 1.116380 − 0.608106I
3.30849 + 11.38200I 0
u = 0.540828 − 1.135790I
a = −0.544870 − 0.876987I
b = 1.116380 + 0.608106I
3.30849 − 11.38200I 0
u = −1.174780 + 0.476913I
a = −0.28290 − 1.74882I
b = −1.074940 + 0.543544I
−6.67400 + 5.57881I 0
u = −1.174780 − 0.476913I
a = −0.28290 + 1.74882I
b = −1.074940 − 0.543544I
−6.67400 − 5.57881I 0
u = 1.110890 + 0.615385I
a = −0.14456 + 1.95078I
b = −1.013080 − 0.587449I
−0.28581 − 5.70221I 0
u = 1.110890 − 0.615385I
a = −0.14456 − 1.95078I
b = −1.013080 + 0.587449I
−0.28581 + 5.70221I 0
u = 1.150860 + 0.554359I
a = −0.260357 + 0.219493I
b = −1.350640 + 0.171559I
−2.33167 − 8.63976I 0
u = 1.150860 − 0.554359I
a = −0.260357 − 0.219493I
b = −1.350640 − 0.171559I
−2.33167 + 8.63976I 0
u = 0.557305 + 0.449357I
a = −0.51930 + 3.80205I
b = −0.801649 − 0.340065I
2.29990 − 3.21991I −11.6454 + 9.3303I
u = 0.557305 − 0.449357I
a = −0.51930 − 3.80205I
b = −0.801649 + 0.340065I
2.29990 + 3.21991I −11.6454 − 9.3303I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.141930 + 0.609772I
a = −0.486454 + 0.645626I
b = 0.299791 − 0.906005I
−2.05151 − 6.52131I 0
u = 1.141930 − 0.609772I
a = −0.486454 − 0.645626I
b = 0.299791 + 0.906005I
−2.05151 + 6.52131I 0
u = −1.106120 + 0.710751I
a = −0.695103 − 0.696708I
b = 0.373079 + 0.947396I
4.66095 + 6.47958I 0
u = −1.106120 − 0.710751I
a = −0.695103 + 0.696708I
b = 0.373079 − 0.947396I
4.66095 − 6.47958I 0
u = −1.160330 + 0.627826I
a = −0.09864 − 1.89218I
b = −1.031920 + 0.604757I
−1.32480 + 11.44640I 0
u = −1.160330 − 0.627826I
a = −0.09864 + 1.89218I
b = −1.031920 − 0.604757I
−1.32480 − 11.44640I 0
u = −1.197040 + 0.583092I
a = 0.75573 + 1.45880I
b = 1.142950 − 0.603629I
−0.44954 + 9.31105I 0
u = −1.197040 − 0.583092I
a = 0.75573 − 1.45880I
b = 1.142950 + 0.603629I
−0.44954 − 9.31105I 0
u = 1.334630 + 0.023307I
a = 0.778731 + 0.175399I
b = 1.001030 − 0.399951I
−3.08028 + 2.84861I 0
u = 1.334630 − 0.023307I
a = 0.778731 − 0.175399I
b = 1.001030 + 0.399951I
−3.08028 − 2.84861I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.138450 + 0.719642I
a = −0.667790 + 0.755929I
b = 0.358664 − 0.967401I
3.65490 − 12.33480I 0
u = 1.138450 − 0.719642I
a = −0.667790 − 0.755929I
b = 0.358664 + 0.967401I
3.65490 + 12.33480I 0
u = 1.276910 + 0.487951I
a = 0.749851 − 1.177460I
b = 1.139720 + 0.557439I
−3.01548 − 5.22865I 0
u = 1.276910 − 0.487951I
a = 0.749851 + 1.177460I
b = 1.139720 − 0.557439I
−3.01548 + 5.22865I 0
u = 1.333150 + 0.335645I
a = 0.532133 − 0.147238I
b = 0.902286 − 0.299866I
−2.37987 − 0.21837I 0
u = 1.333150 − 0.335645I
a = 0.532133 + 0.147238I
b = 0.902286 + 0.299866I
−2.37987 + 0.21837I 0
u = 0.606553 + 0.136516I
a = −0.323621 − 1.210050I
b = 0.858468 + 0.822607I
1.55699 − 3.04585I −22.2897 + 7.2245I
u = 0.606553 − 0.136516I
a = −0.323621 + 1.210050I
b = 0.858468 − 0.822607I
1.55699 + 3.04585I −22.2897 − 7.2245I
u = −1.194310 + 0.735932I
a = 0.49361 + 1.67781I
b = 1.179130 − 0.645250I
2.20206 + 12.28150I 0
u = −1.194310 − 0.735932I
a = 0.49361 − 1.67781I
b = 1.179130 + 0.645250I
2.20206 − 12.28150I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.032258 + 0.593857I
a = 1.85959 − 0.38959I
b = −0.164637 + 0.077592I
2.37401 − 2.69643I −3.59687 + 2.70387I
u = 0.032258 − 0.593857I
a = 1.85959 + 0.38959I
b = −0.164637 − 0.077592I
2.37401 + 2.69643I −3.59687 − 2.70387I
u = −0.453797 + 0.354290I
a = −0.97607 − 5.19517I
b = −0.790637 + 0.250799I
2.05724 − 2.52902I −14.1044 − 7.2590I
u = −0.453797 − 0.354290I
a = −0.97607 + 5.19517I
b = −0.790637 − 0.250799I
2.05724 + 2.52902I −14.1044 + 7.2590I
u = 1.27377 + 0.66046I
a = 0.51916 − 1.45394I
b = 1.182920 + 0.605604I
−4.71019 − 12.03970I 0
u = 1.27377 − 0.66046I
a = 0.51916 + 1.45394I
b = 1.182920 − 0.605604I
−4.71019 + 12.03970I 0
u = 1.22016 + 0.76098I
a = 0.42193 − 1.65996I
b = 1.192000 + 0.646097I
1.1052 − 18.1923I 0
u = 1.22016 − 0.76098I
a = 0.42193 + 1.65996I
b = 1.192000 − 0.646097I
1.1052 + 18.1923I 0
u = −1.44666 + 0.06158I
a = 0.640057 + 0.341446I
b = 1.060440 − 0.388230I
−4.87122 + 7.86476I 0
u = −1.44666 − 0.06158I
a = 0.640057 − 0.341446I
b = 1.060440 + 0.388230I
−4.87122 − 7.86476I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.524803
a = 0.867240
b = −0.0932121
−0.780063 −12.4920
u = −1.42325 + 0.40242I
a = 0.440992 + 0.117684I
b = 0.917187 + 0.253600I
−3.84346 + 5.72004I 0
u = −1.42325 − 0.40242I
a = 0.440992 − 0.117684I
b = 0.917187 − 0.253600I
−3.84346 − 5.72004I 0
u = −1.47689 + 0.17377I
a = 0.528339 − 0.069385I
b = 0.995495 + 0.310761I
−8.36236 − 1.00432I 0
u = −1.47689 − 0.17377I
a = 0.528339 + 0.069385I
b = 0.995495 − 0.310761I
−8.36236 + 1.00432I 0
u = 0.408179 + 0.268119I
a = 1.59911 − 0.55685I
b = −0.676846 + 0.186588I
−0.945116 + 0.083072I −9.62237 + 0.87598I
u = 0.408179 − 0.268119I
a = 1.59911 + 0.55685I
b = −0.676846 − 0.186588I
−0.945116 − 0.083072I −9.62237 − 0.87598I
u = −0.319264
a = −11.9462
b = −0.971561
−2.59067 −102.670
16
II. I
u
2
=
hb+1, 2u
7
+3u
6
−5u
5
−7u
4
+4u
3
+3u
2
+a+4, u
8
+u
7
−3u
6
−2u
5
+3u
4
+2u−1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
3
=
−2u
7
− 3u
6
+ 5u
5
+ 7u
4
− 4u
3
− 3u
2
− 4
−1
a
10
=
−u
−u
3
+ u
a
2
=
−2u
7
− 3u
6
+ 5u
5
+ 7u
4
− 4u
3
− 3u
2
− 5
−1
a
1
=
−1
0
a
11
=
u
3
− 2u
−u
3
+ u
a
4
=
−2u
7
− 3u
6
+ 5u
5
+ 7u
4
− 4u
3
− 3u
2
− 4
−1
a
7
=
1
u
2
a
12
=
−u
6
+ 3u
4
− 2u
2
− 1
u
6
− 2u
4
+ u
2
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
7
+ 8u
6
− 18u
5
− 12u
4
+ 7u
3
− 3u
2
+ 12u − 3
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
6
u
8
c
4
(u + 1)
8
c
5
, c
7
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
8
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
9
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
10
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
11
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
12
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
6
y
8
c
5
, c
7
, c
9
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
8
, c
11
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
10
, c
12
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = −0.615431 + 0.295452I
b = −1.00000
−2.68559 − 1.13123I −13.78185 + 1.82144I
u = 1.180120 − 0.268597I
a = −0.615431 − 0.295452I
b = −1.00000
−2.68559 + 1.13123I −13.78185 − 1.82144I
u = 0.108090 + 0.747508I
a = 1.68119 + 0.49658I
b = −1.00000
0.51448 − 2.57849I −9.42408 + 5.06085I
u = 0.108090 − 0.747508I
a = 1.68119 − 0.49658I
b = −1.00000
0.51448 + 2.57849I −9.42408 − 5.06085I
u = −1.37100
a = −0.532015
b = −1.00000
−8.14766 −18.0480
u = −1.334530 + 0.318930I
a = −0.473764 − 0.240160I
b = −1.00000
−4.02461 + 6.44354I −15.1664 − 7.9255I
u = −1.334530 − 0.318930I
a = −0.473764 + 0.240160I
b = −1.00000
−4.02461 − 6.44354I −15.1664 + 7.9255I
u = 0.463640
a = −4.65198
b = −1.00000
−2.48997 1.79260
20
III. I
v
1
= ha, b − v − 1, v
3
+ 2v
2
+ v + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
v
0
a
6
=
1
0
a
3
=
0
v + 1
a
10
=
v
0
a
2
=
v + 1
v + 1
a
1
=
v + 1
−v
2
− v + 1
a
11
=
v
2
+ 3v
v
2
+ 3v + 2
a
4
=
−v
2
− 2v
−v
2
− 2v − 1
a
7
=
−v − 1
v
2
+ v − 1
a
12
=
−2
v
2
+ 2v
a
8
=
−v − 2
v
2
+ v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2v
2
+ 9v − 7
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
10
u
3
− u
2
+ 2u − 1
c
2
, c
8
u
3
+ u
2
− 1
c
4
, c
11
u
3
− u
2
+ 1
c
5
, c
9
u
3
c
6
, c
12
u
3
+ u
2
+ 2u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
12
y
3
+ 3y
2
+ 2y − 1
c
2
, c
4
, c
8
c
11
y
3
− y
2
+ 2y − 1
c
5
, c
9
y
3
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.122561 + 0.744862I
a = 0
b = 0.877439 + 0.744862I
6.04826 − 5.65624I −9.18265 + 6.33859I
v = −0.122561 − 0.744862I
a = 0
b = 0.877439 − 0.744862I
6.04826 + 5.65624I −9.18265 − 6.33859I
v = −1.75488
a = 0
b = −0.754878
−2.22691 −16.6350
24
IV.
I
v
2
= ha, −89v
5
− 27v
4
+ · · · + 80b + 163, v
6
+ 16v
4
− 21v
3
+ 18v
2
− 7v + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
v
0
a
6
=
1
0
a
3
=
0
1.11250v
5
+ 0.337500v
4
+ ··· + 13.2500v − 2.03750
a
10
=
v
0
a
2
=
1.11250v
5
+ 0.337500v
4
+ ··· + 13.2500v − 2.03750
1.11250v
5
+ 0.337500v
4
+ ··· + 13.2500v − 2.03750
a
1
=
1.11250v
5
+ 0.337500v
4
+ ··· + 13.2500v − 2.03750
−0.837500v
5
− 0.262500v
4
+ ··· − 10v + 3.86250
a
11
=
27
80
v
5
+
1
80
v
4
+ ··· +
31
4
v −
89
80
−0.862500v
5
− 0.0875000v
4
+ ··· − 9.75000v + 2.78750
a
4
=
−1.95000v
5
− 0.600000v
4
+ ··· − 23.2500v + 5.90000
−1.95000v
5
− 0.600000v
4
+ ··· − 23.2500v + 4.90000
a
7
=
−1.11250v
5
− 0.337500v
4
+ ··· − 13.2500v + 2.03750
0.837500v
5
+ 0.262500v
4
+ ··· + 10v − 3.86250
a
12
=
1.05000v
5
+ 0.650000v
4
+ ··· + 12.5000v − 1.85000
−1.02500v
5
+ 0.175000v
4
+ ··· − 17.7500v + 5.92500
a
8
=
−1.15000v
5
− 0.200000v
4
+ ··· − 14.2500v + 2.30000
0.837500v
5
+ 0.262500v
4
+ ··· + 10v − 3.86250
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
13
4
v
5
−
3
4
v
4
−
209
4
v
3
+
115
2
v
2
− 47v +
19
4
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
10
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
8
(u
3
+ u
2
− 1)
2
c
4
, c
11
(u
3
− u
2
+ 1)
2
c
5
, c
9
u
6
c
6
, c
12
(u
3
+ u
2
+ 2u + 1)
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
12
(y
3
+ 3y
2
+ 2y − 1)
2
c
2
, c
4
, c
8
c
11
(y
3
− y
2
+ 2y − 1)
2
c
5
, c
9
y
6
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.354760 + 0.666322I
a = 0
b = 0.877439 − 0.744862I
6.04826 −8.27833 − 0.98317I
v = 0.354760 − 0.666322I
a = 0
b = 0.877439 + 0.744862I
6.04826 −8.27833 + 0.98317I
v = 0.307599 + 0.104043I
a = 0
b = 0.877439 + 0.744862I
1.91067 − 2.82812I −5.88933 − 2.71361I
v = 0.307599 − 0.104043I
a = 0
b = 0.877439 − 0.744862I
1.91067 + 2.82812I −5.88933 + 2.71361I
v = −0.66236 + 4.02547I
a = 0
b = −0.754878
1.91067 + 2.82812I −29.3323 − 8.2928I
v = −0.66236 − 4.02547I
a = 0
b = −0.754878
1.91067 − 2.82812I −29.3323 + 8.2928I
28
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
3
− u
2
+ 2u − 1)
3
(u
118
+ 56u
117
+ ··· + 165u + 1)
c
2
((u − 1)
8
)(u
3
+ u
2
− 1)
3
(u
118
− 12u
117
+ ··· + 13u + 1)
c
3
u
8
(u
3
− u
2
+ 2u − 1)
3
(u
118
− 4u
117
+ ··· + 1664u − 256)
c
4
((u + 1)
8
)(u
3
− u
2
+ 1)
3
(u
118
− 12u
117
+ ··· + 13u + 1)
c
5
u
9
(u
8
+ u
7
+ ··· + 2u − 1)(u
118
+ 2u
117
+ ··· − 2560u − 512)
c
6
u
8
(u
3
+ u
2
+ 2u + 1)
3
(u
118
− 4u
117
+ ··· + 1664u − 256)
c
7
(u
3
− u
2
+ 2u − 1)
3
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
118
− 5u
117
+ ··· − 42339u + 2017)
c
8
(u
3
+ u
2
− 1)
3
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
118
+ 5u
117
+ ··· + 11u + 1)
c
9
u
9
(u
8
− u
7
+ ··· − 2u − 1)(u
118
+ 2u
117
+ ··· − 2560u − 512)
c
10
(u
3
− u
2
+ 2u − 1)
3
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
118
+ 39u
117
+ ··· − 19u + 1)
c
11
(u
3
− u
2
+ 1)
3
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
118
+ 5u
117
+ ··· + 11u + 1)
c
12
(u
3
+ u
2
+ 2u + 1)
3
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
118
+ 39u
117
+ ··· − 19u + 1)
29
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
8
)(y
3
+ 3y
2
+ 2y − 1)
3
(y
118
+ 24y
117
+ ··· − 12937y + 1)
c
2
, c
4
((y − 1)
8
)(y
3
− y
2
+ 2y − 1)
3
(y
118
− 56y
117
+ ··· − 165y + 1)
c
3
, c
6
y
8
(y
3
+ 3y
2
+ 2y − 1)
3
(y
118
+ 60y
117
+ ··· − 1228800y + 65536)
c
5
, c
9
y
9
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
118
− 56y
117
+ ··· − 9306112y + 262144)
c
7
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
118
− 11y
117
+ ··· + 141591059y + 4068289)
c
8
, c
11
(y
3
− y
2
+ 2y − 1)
3
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
118
− 39y
117
+ ··· + 19y + 1)
c
10
, c
12
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
118
+ 85y
117
+ ··· − 157y + 1)
30
