12a
0949
(K12a
0949
)
A knot diagram
1
Linearized knot diagam
4 6 10 8 11 3 5 12 1 2 7 9
Solving Sequence
8,12
9 1
5,10
4 2 3 7 6 11
c
8
c
12
c
9
c
4
c
1
c
3
c
7
c
6
c
11
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.31639 × 10
422
u
132
+ 1.53310 × 10
423
u
131
+ ··· + 1.77653 × 10
424
b + 1.30059 × 10
424
,
− 3.70487 × 10
424
u
132
+ 1.90525 × 10
425
u
131
+ ··· + 2.13183 × 10
424
a + 4.70733 × 10
425
,
u
133
− 5u
132
+ ··· − 56u − 3i
I
u
2
= h6761534u
24
+ 25064228u
23
+ ··· + 32603b − 5175546,
− 3451225u
24
− 12321594u
23
+ ··· + 32603a + 2498173, u
25
+ 5u
24
+ ··· − 7u − 1i
I
u
3
= h−6a
3
+ 2a
2
+ b − 27a − 9, 2a
4
+ 9a
2
+ 6a + 1, u − 1i
I
u
4
= hb, a − 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 163 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−2.32 × 10
422
u
132
+ 1.53 × 10
423
u
131
+ · · · + 1.78 × 10
424
b + 1.30 ×
10
424
, −3.70 × 10
424
u
132
+ 1.91 × 10
425
u
131
+ · · · + 2.13 × 10
424
a + 4.71 ×
10
425
, u
133
− 5u
132
+ · · · − 56u − 3i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
5
=
1.73788u
132
− 8.93715u
131
+ ··· − 298.967u − 22.0812
0.0130389u
132
− 0.0862979u
131
+ ··· − 11.5157u − 0.732099
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
1.75092u
132
− 9.02344u
131
+ ··· − 310.482u − 22.8133
0.0130389u
132
− 0.0862979u
131
+ ··· − 11.5157u − 0.732099
a
2
=
−1.63049u
132
+ 8.15688u
131
+ ··· + 595.484u + 44.4192
0.356925u
132
− 1.97497u
131
+ ··· − 21.3742u − 0.805447
a
3
=
1.81952u
132
− 9.36921u
131
+ ··· − 327.425u − 24.1733
0.000295256u
132
− 0.0526861u
131
+ ··· − 14.0734u − 0.887146
a
7
=
0.0524645u
132
− 0.199611u
131
+ ··· − 69.0014u − 6.56518
−0.0372953u
132
+ 0.479760u
131
+ ··· + 8.11647u + 0.646970
a
6
=
0.956137u
132
− 4.71492u
131
+ ··· − 444.889u − 30.0851
−0.322208u
132
+ 1.81509u
131
+ ··· + 5.03229u − 0.932874
a
11
=
−3.25930u
132
+ 16.4774u
131
+ ··· + 738.406u + 42.2610
−0.130790u
132
+ 0.834469u
131
+ ··· + 87.2420u + 6.33965
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.17653u
132
− 5.26495u
131
+ ··· − 634.853u − 55.6689
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
133
− 15u
132
+ ··· + 11068u − 1172
c
2
, c
6
u
133
− 3u
132
+ ··· − 17081u + 1539
c
3
2(2u
133
+ 2u
132
+ ··· + 11264u + 2048)
c
4
, c
7
u
133
− 9u
132
+ ··· − 24896u + 1952
c
5
2(2u
133
+ 2u
132
+ ··· + 7848686u + 3253981)
c
8
, c
9
, c
12
u
133
+ 5u
132
+ ··· − 56u + 3
c
10
u
133
+ 7u
132
+ ··· + 62070u + 9146
c
11
u
133
+ 7u
130
+ ··· + 14366u + 3254
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
133
− 7y
132
+ ··· − 104928320y −1373584
c
2
, c
6
y
133
− 77y
132
+ ··· + 162555355y −2368521
c
3
4(4y
133
+ 192y
132
+ ··· − 1.10100 × 10
8
y −4194304)
c
4
, c
7
y
133
+ 93y
132
+ ··· − 337168896y −3810304
c
5
4(4y
133
+ 240y
132
+ ··· − 5.32285 × 10
14
y −1.05884 × 10
13
)
c
8
, c
9
, c
12
y
133
− 137y
132
+ ··· − 56y −9
c
10
y
133
− 51y
132
+ ··· + 15173548824y −83649316
c
11
y
133
+ 108y
131
+ ··· − 2741332040y −10588516
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.574211 + 0.806522I
a = −0.47135 − 1.68203I
b = −0.458336 + 1.314170I
2.92527 + 8.52139I 0
u = −0.574211 − 0.806522I
a = −0.47135 + 1.68203I
b = −0.458336 − 1.314170I
2.92527 − 8.52139I 0
u = 0.378103 + 0.906879I
a = 0.33971 − 2.11105I
b = 0.293973 + 1.167940I
2.16623 − 4.99446I 0
u = 0.378103 − 0.906879I
a = 0.33971 + 2.11105I
b = 0.293973 − 1.167940I
2.16623 + 4.99446I 0
u = 0.329684 + 0.964221I
a = 0.01448 + 1.45443I
b = −0.445410 − 0.888166I
1.46652 − 5.73875I 0
u = 0.329684 − 0.964221I
a = 0.01448 − 1.45443I
b = −0.445410 + 0.888166I
1.46652 + 5.73875I 0
u = −0.494919 + 0.893036I
a = 0.71500 + 1.26830I
b = −0.238880 − 1.154660I
3.16581 − 3.01226I 0
u = −0.494919 − 0.893036I
a = 0.71500 − 1.26830I
b = −0.238880 + 1.154660I
3.16581 + 3.01226I 0
u = 0.924375 + 0.465795I
a = 0.341741 − 0.191628I
b = −0.437473 + 0.302466I
−0.783926 + 0.529519I 0
u = 0.924375 − 0.465795I
a = 0.341741 + 0.191628I
b = −0.437473 − 0.302466I
−0.783926 − 0.529519I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.014880 + 0.249045I
a = 0.26982 − 2.02091I
b = 0.025828 + 1.409670I
4.71692 + 1.38176I 0
u = 1.014880 − 0.249045I
a = 0.26982 + 2.02091I
b = 0.025828 − 1.409670I
4.71692 − 1.38176I 0
u = 0.373883 + 0.866496I
a = −0.02527 + 1.93367I
b = −0.332906 − 1.081600I
1.43426 − 2.64312I 0
u = 0.373883 − 0.866496I
a = −0.02527 − 1.93367I
b = −0.332906 + 1.081600I
1.43426 + 2.64312I 0
u = −0.532921 + 0.915024I
a = 0.33759 + 1.80539I
b = 0.482952 − 1.319860I
6.2072 + 14.4323I 0
u = −0.532921 − 0.915024I
a = 0.33759 − 1.80539I
b = 0.482952 + 1.319860I
6.2072 − 14.4323I 0
u = 0.989465 + 0.379484I
a = −0.80123 + 1.55516I
b = 0.091704 − 0.713483I
0.263606 − 0.184369I 0
u = 0.989465 − 0.379484I
a = −0.80123 − 1.55516I
b = 0.091704 + 0.713483I
0.263606 + 0.184369I 0
u = 0.415346 + 0.990925I
a = 0.386696 − 1.313430I
b = 0.157988 + 0.867765I
0.46372 − 2.33810I 0
u = 0.415346 − 0.990925I
a = 0.386696 + 1.313430I
b = 0.157988 − 0.867765I
0.46372 + 2.33810I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.704660 + 0.550275I
a = 1.200850 − 0.552040I
b = −0.097070 + 1.128250I
2.06026 − 1.40425I 0
u = 0.704660 − 0.550275I
a = 1.200850 + 0.552040I
b = −0.097070 − 1.128250I
2.06026 + 1.40425I 0
u = −0.696078 + 0.514809I
a = −0.723227 − 0.979580I
b = 0.215798 + 1.326840I
7.58706 + 0.38056I 0
u = −0.696078 − 0.514809I
a = −0.723227 + 0.979580I
b = 0.215798 − 1.326840I
7.58706 − 0.38056I 0
u = 0.566105 + 0.614307I
a = −0.0235346 − 0.0690271I
b = 0.441384 − 0.059551I
−1.03448 − 2.04846I 0
u = 0.566105 − 0.614307I
a = −0.0235346 + 0.0690271I
b = 0.441384 + 0.059551I
−1.03448 + 2.04846I 0
u = 0.794351 + 0.230141I
a = −0.43059 + 1.98792I
b = 0.204220 − 0.503604I
0.237202 − 0.167348I 0
u = 0.794351 − 0.230141I
a = −0.43059 − 1.98792I
b = 0.204220 + 0.503604I
0.237202 + 0.167348I 0
u = 1.109050 + 0.393892I
a = −0.521767 + 0.393448I
b = 0.343256 − 1.259130I
4.40836 + 2.54732I 0
u = 1.109050 − 0.393892I
a = −0.521767 − 0.393448I
b = 0.343256 + 1.259130I
4.40836 − 2.54732I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.403984 + 0.683130I
a = 0.84329 + 1.84290I
b = 0.417585 − 1.322650I
8.44013 + 3.83414I 0
u = −0.403984 − 0.683130I
a = 0.84329 − 1.84290I
b = 0.417585 + 1.322650I
8.44013 − 3.83414I 0
u = −0.537463 + 0.563850I
a = −0.450237 + 0.016524I
b = 0.964956 − 0.103893I
1.89345 + 9.32259I 0
u = −0.537463 − 0.563850I
a = −0.450237 − 0.016524I
b = 0.964956 + 0.103893I
1.89345 − 9.32259I 0
u = −0.727912 + 0.988878I
a = −0.651866 − 1.171610I
b = 0.320963 + 1.149250I
5.78280 − 8.24577I 0
u = −0.727912 − 0.988878I
a = −0.651866 + 1.171610I
b = 0.320963 − 1.149250I
5.78280 + 8.24577I 0
u = −0.224218 + 0.729839I
a = −0.653937 + 1.176690I
b = 0.355795 − 0.141174I
2.87171 − 5.33242I 0
u = −0.224218 − 0.729839I
a = −0.653937 − 1.176690I
b = 0.355795 + 0.141174I
2.87171 + 5.33242I 0
u = 0.497368 + 0.554874I
a = 0.613055 − 1.117160I
b = −0.633997 + 0.494336I
0.34427 − 1.51811I 0
u = 0.497368 − 0.554874I
a = 0.613055 + 1.117160I
b = −0.633997 − 0.494336I
0.34427 + 1.51811I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.114871 + 0.720135I
a = −0.03182 − 1.98080I
b = 0.550237 + 1.300370I
7.41576 − 6.58321I 0
u = 0.114871 − 0.720135I
a = −0.03182 + 1.98080I
b = 0.550237 − 1.300370I
7.41576 + 6.58321I 0
u = 0.351793 + 0.590951I
a = −0.10506 + 1.82082I
b = −0.360927 − 1.349490I
3.01841 − 2.63877I 0
u = 0.351793 − 0.590951I
a = −0.10506 − 1.82082I
b = −0.360927 + 1.349490I
3.01841 + 2.63877I 0
u = −1.327140 + 0.014584I
a = −1.88231 + 0.42302I
b = −0.053802 − 0.861572I
0.47041 + 6.74381I 0
u = −1.327140 − 0.014584I
a = −1.88231 − 0.42302I
b = −0.053802 + 0.861572I
0.47041 − 6.74381I 0
u = 0.262945 + 0.616414I
a = −2.10232 + 2.36683I
b = 0.015632 − 1.219980I
6.85021 − 4.66073I 0
u = 0.262945 − 0.616414I
a = −2.10232 − 2.36683I
b = 0.015632 + 1.219980I
6.85021 + 4.66073I 0
u = 1.329540 + 0.095124I
a = 0.929518 − 0.191850I
b = 1.000780 − 0.423256I
−0.607150 − 1.109740I 0
u = 1.329540 − 0.095124I
a = 0.929518 + 0.191850I
b = 1.000780 + 0.423256I
−0.607150 + 1.109740I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.333530 + 0.040329I
a = 0.587200 + 0.036810I
b = 1.35622 − 1.13947I
1.19011 − 1.90299I 0
u = −1.333530 − 0.040329I
a = 0.587200 − 0.036810I
b = 1.35622 + 1.13947I
1.19011 + 1.90299I 0
u = −1.333000 + 0.230008I
a = 1.054960 + 0.765005I
b = 0.81399 − 1.29343I
2.88699 + 9.95019I 0
u = −1.333000 − 0.230008I
a = 1.054960 − 0.765005I
b = 0.81399 + 1.29343I
2.88699 − 9.95019I 0
u = 1.341420 + 0.193854I
a = 0.903653 − 0.557086I
b = 0.275026 + 0.815619I
−1.95121 − 1.33658I 0
u = 1.341420 − 0.193854I
a = 0.903653 + 0.557086I
b = 0.275026 − 0.815619I
−1.95121 + 1.33658I 0
u = 1.358650 + 0.106966I
a = −0.904994 − 0.219653I
b = −0.194170 − 1.017110I
1.65394 − 1.39071I 0
u = 1.358650 − 0.106966I
a = −0.904994 + 0.219653I
b = −0.194170 + 1.017110I
1.65394 + 1.39071I 0
u = −0.592092 + 0.221364I
a = 0.052072 + 1.246130I
b = 0.662794 + 0.347988I
2.24208 + 3.37065I −4.00000 − 5.75675I
u = −0.592092 − 0.221364I
a = 0.052072 − 1.246130I
b = 0.662794 − 0.347988I
2.24208 − 3.37065I −4.00000 + 5.75675I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.371290 + 0.051878I
a = 0.065385 + 0.438714I
b = 0.61251 − 2.18568I
0.93911 − 3.98308I 0
u = 1.371290 − 0.051878I
a = 0.065385 − 0.438714I
b = 0.61251 + 2.18568I
0.93911 + 3.98308I 0
u = −1.372810 + 0.037798I
a = 0.03694 + 1.45996I
b = −0.05136 − 1.62620I
2.21593 + 0.54322I 0
u = −1.372810 − 0.037798I
a = 0.03694 − 1.45996I
b = −0.05136 + 1.62620I
2.21593 − 0.54322I 0
u = −0.476540 + 0.391755I
a = 0.155313 − 0.074410I
b = −0.987024 + 0.180034I
−1.57068 + 3.54785I −6.35480 − 10.17340I
u = −0.476540 − 0.391755I
a = 0.155313 + 0.074410I
b = −0.987024 − 0.180034I
−1.57068 − 3.54785I −6.35480 + 10.17340I
u = −1.385030 + 0.101265I
a = −0.429680 − 1.218680I
b = −0.302767 + 1.261620I
−3.45355 + 3.71222I 0
u = −1.385030 − 0.101265I
a = −0.429680 + 1.218680I
b = −0.302767 − 1.261620I
−3.45355 − 3.71222I 0
u = 0.609207
a = 0.540750
b = −0.447332
−1.11415 −9.92320
u = −1.404830 + 0.005344I
a = 1.004270 − 0.956018I
b = 0.274246 + 0.967774I
−4.96359 + 2.05422I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.404830 − 0.005344I
a = 1.004270 + 0.956018I
b = 0.274246 − 0.967774I
−4.96359 − 2.05422I 0
u = −1.40742 + 0.14663I
a = −0.635566 − 0.606471I
b = −0.85324 + 1.52041I
−2.53143 + 5.14360I 0
u = −1.40742 − 0.14663I
a = −0.635566 + 0.606471I
b = −0.85324 − 1.52041I
−2.53143 − 5.14360I 0
u = 1.41489 + 0.04091I
a = −1.101290 + 0.645661I
b = −0.663322 − 1.121380I
−5.66604 − 2.49553I 0
u = 1.41489 − 0.04091I
a = −1.101290 − 0.645661I
b = −0.663322 + 1.121380I
−5.66604 + 2.49553I 0
u = 1.43348 + 0.07898I
a = 1.40726 − 1.33578I
b = 0.412663 + 1.258010I
−1.28880 − 8.09029I 0
u = 1.43348 − 0.07898I
a = 1.40726 + 1.33578I
b = 0.412663 − 1.258010I
−1.28880 + 8.09029I 0
u = −1.43702 + 0.20766I
a = −1.74439 − 0.47596I
b = −0.131205 + 1.056820I
1.32313 + 7.60879I 0
u = −1.43702 − 0.20766I
a = −1.74439 + 0.47596I
b = −0.131205 − 1.056820I
1.32313 − 7.60879I 0
u = −0.135763 + 0.492747I
a = −0.419702 + 0.679952I
b = 0.980114 − 0.157893I
3.83136 − 0.94632I 3.69353 − 2.08963I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.135763 − 0.492747I
a = −0.419702 − 0.679952I
b = 0.980114 + 0.157893I
3.83136 + 0.94632I 3.69353 + 2.08963I
u = 0.163689 + 0.480709I
a = 0.65194 + 2.56615I
b = −0.140064 − 0.870618I
1.41412 − 1.82766I −0.64360 + 4.68630I
u = 0.163689 − 0.480709I
a = 0.65194 − 2.56615I
b = −0.140064 + 0.870618I
1.41412 + 1.82766I −0.64360 − 4.68630I
u = 1.48897 + 0.14295I
a = −0.366890 + 0.148135I
b = −1.42428 + 0.08068I
−8.02010 − 5.56867I 0
u = 1.48897 − 0.14295I
a = −0.366890 − 0.148135I
b = −1.42428 − 0.08068I
−8.02010 + 5.56867I 0
u = 1.47816 + 0.23264I
a = 1.144460 − 0.645255I
b = 0.609383 + 1.267820I
2.32170 − 7.14117I 0
u = 1.47816 − 0.23264I
a = 1.144460 + 0.645255I
b = 0.609383 − 1.267820I
2.32170 + 7.14117I 0
u = −1.49434 + 0.20747I
a = −0.0467668 + 0.1043070I
b = −1.016830 − 0.565966I
−6.12896 + 4.38413I 0
u = −1.49434 − 0.20747I
a = −0.0467668 − 0.1043070I
b = −1.016830 + 0.565966I
−6.12896 − 4.38413I 0
u = 1.51233 + 0.07051I
a = −0.850042 − 0.283965I
b = −0.727153 − 0.665675I
−7.05549 − 3.14594I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51233 − 0.07051I
a = −0.850042 + 0.283965I
b = −0.727153 + 0.665675I
−7.05549 + 3.14594I 0
u = 1.50792 + 0.20095I
a = 0.248901 − 0.248007I
b = 1.341120 − 0.039708I
−4.77289 − 12.16840I 0
u = 1.50792 − 0.20095I
a = 0.248901 + 0.248007I
b = 1.341120 + 0.039708I
−4.77289 + 12.16840I 0
u = −1.51476 + 0.14502I
a = 0.264739 − 0.299134I
b = 0.796126 + 0.659011I
−6.95112 + 2.06444I 0
u = −1.51476 − 0.14502I
a = 0.264739 + 0.299134I
b = 0.796126 − 0.659011I
−6.95112 − 2.06444I 0
u = −1.52400 + 0.10670I
a = −0.184813 − 0.090273I
b = −1.056070 − 0.115666I
−8.52441 + 1.00167I 0
u = −1.52400 − 0.10670I
a = −0.184813 + 0.090273I
b = −1.056070 + 0.115666I
−8.52441 − 1.00167I 0
u = −1.50178 + 0.29232I
a = −0.758450 − 1.138580I
b = −0.56217 + 1.31818I
−4.76063 + 6.76009I 0
u = −1.50178 − 0.29232I
a = −0.758450 + 1.138580I
b = −0.56217 − 1.31818I
−4.76063 − 6.76009I 0
u = −1.50017 + 0.33374I
a = 0.94585 + 1.25725I
b = 0.423389 − 1.318380I
−3.92143 + 9.46474I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50017 − 0.33374I
a = 0.94585 − 1.25725I
b = 0.423389 + 1.318380I
−3.92143 − 9.46474I 0
u = −1.49391 + 0.36272I
a = −0.691558 − 1.038670I
b = −0.682500 + 1.081280I
−4.43943 + 10.49490I 0
u = −1.49391 − 0.36272I
a = −0.691558 + 1.038670I
b = −0.682500 − 1.081280I
−4.43943 − 10.49490I 0
u = −1.53296 + 0.19544I
a = 0.303820 + 0.201082I
b = 0.770547 + 0.026111I
−7.97843 + 5.01067I 0
u = −1.53296 − 0.19544I
a = 0.303820 − 0.201082I
b = 0.770547 − 0.026111I
−7.97843 − 5.01067I 0
u = −1.52256 + 0.31925I
a = 0.783366 + 0.821509I
b = 0.505391 − 0.986115I
−5.89368 + 6.90189I 0
u = −1.52256 − 0.31925I
a = 0.783366 − 0.821509I
b = 0.505391 + 0.986115I
−5.89368 − 6.90189I 0
u = 1.55573 + 0.00457I
a = 0.285248 − 0.546406I
b = 0.637687 − 0.017128I
−4.97142 − 4.01378I 0
u = 1.55573 − 0.00457I
a = 0.285248 + 0.546406I
b = 0.637687 + 0.017128I
−4.97142 + 4.01378I 0
u = 1.54949 + 0.28403I
a = −0.883549 + 0.876103I
b = −0.65702 − 1.37402I
−3.98685 − 12.53700I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54949 − 0.28403I
a = −0.883549 − 0.876103I
b = −0.65702 + 1.37402I
−3.98685 + 12.53700I 0
u = −0.401690 + 0.132674I
a = −1.72929 + 0.28563I
b = −0.574527 + 0.827043I
−0.54692 + 2.29604I 1.45935 + 11.26789I
u = −0.401690 − 0.132674I
a = −1.72929 − 0.28563I
b = −0.574527 − 0.827043I
−0.54692 − 2.29604I 1.45935 − 11.26789I
u = 0.116136 + 0.405794I
a = 1.51229 − 0.51428I
b = −0.010360 − 0.160570I
−0.252568 − 1.384130I −3.29769 + 2.91676I
u = 0.116136 − 0.405794I
a = 1.51229 + 0.51428I
b = −0.010360 + 0.160570I
−0.252568 + 1.384130I −3.29769 − 2.91676I
u = 1.54587 + 0.32785I
a = 0.902165 − 1.036600I
b = 0.63663 + 1.40336I
−0.5079 − 18.9585I 0
u = 1.54587 − 0.32785I
a = 0.902165 + 1.036600I
b = 0.63663 − 1.40336I
−0.5079 + 18.9585I 0
u = −1.60227 + 0.10254I
a = 0.595130 − 0.352778I
b = 0.069326 − 0.869851I
−5.91736 + 3.60682I 0
u = −1.60227 − 0.10254I
a = 0.595130 + 0.352778I
b = 0.069326 + 0.869851I
−5.91736 − 3.60682I 0
u = 1.59497 + 0.36952I
a = 0.307920 − 0.895269I
b = 0.399654 + 0.950414I
−2.57319 + 0.53784I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59497 − 0.36952I
a = 0.307920 + 0.895269I
b = 0.399654 − 0.950414I
−2.57319 − 0.53784I 0
u = 1.56695 + 0.57517I
a = −0.321654 + 1.049090I
b = −0.251618 − 1.040620I
−2.96796 − 4.31699I 0
u = 1.56695 − 0.57517I
a = −0.321654 − 1.049090I
b = −0.251618 + 1.040620I
−2.96796 + 4.31699I 0
u = 0.014572 + 0.263358I
a = 0.64043 − 1.81306I
b = 0.72079 + 1.59382I
5.42384 + 3.02086I 25.2643 − 7.3345I
u = 0.014572 − 0.263358I
a = 0.64043 + 1.81306I
b = 0.72079 − 1.59382I
5.42384 − 3.02086I 25.2643 + 7.3345I
u = −0.186558 + 0.174265I
a = 3.89098 + 7.58041I
b = 0.318668 − 1.060700I
4.17910 + 7.06432I −5.3223 − 13.1258I
u = −0.186558 − 0.174265I
a = 3.89098 − 7.58041I
b = 0.318668 + 1.060700I
4.17910 − 7.06432I −5.3223 + 13.1258I
u = −0.105013 + 0.170958I
a = −5.70928 + 0.50634I
b = −0.032596 + 1.383050I
6.60511 + 0.07586I 6.10031 − 0.13311I
u = −0.105013 − 0.170958I
a = −5.70928 − 0.50634I
b = −0.032596 − 1.383050I
6.60511 − 0.07586I 6.10031 + 0.13311I
u = −0.144821 + 0.087119I
a = −5.75700 − 3.52265I
b = −0.383727 + 0.842523I
−0.46416 + 1.91834I −10.08682 − 1.92617I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.144821 − 0.087119I
a = −5.75700 + 3.52265I
b = −0.383727 − 0.842523I
−0.46416 − 1.91834I −10.08682 + 1.92617I
u = 1.94618 + 0.18830I
a = 0.069663 − 0.568994I
b = −0.014874 + 0.793607I
−4.42032 − 2.85190I 0
u = 1.94618 − 0.18830I
a = 0.069663 + 0.568994I
b = −0.014874 − 0.793607I
−4.42032 + 2.85190I 0
18
II.
I
u
2
= h6.76 × 10
6
u
24
+ 2.51 × 10
7
u
23
+ · · · + 3.26 × 10
4
b − 5.18 × 10
6
, −3.45 ×
10
6
u
24
−1.23×10
7
u
23
+· · · +3.26×10
4
a+2.50×10
6
, u
25
+5u
24
+· · · − 7u −1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
5
=
105.856u
24
+ 377.928u
23
+ ··· − 471.470u − 76.6240
−207.390u
24
− 768.771u
23
+ ··· + 989.824u + 158.744
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−101.534u
24
− 390.842u
23
+ ··· + 518.354u + 82.1204
−207.390u
24
− 768.771u
23
+ ··· + 989.824u + 158.744
a
2
=
−126.101u
24
− 428.768u
23
+ ··· + 505.785u + 79.1843
−110.665u
24
− 377.553u
23
+ ··· + 441.192u + 67.7447
a
3
=
104.413u
24
+ 375.596u
23
+ ··· − 470.119u − 76.7317
−366.857u
24
− 1339.83u
23
+ ··· + 1696.98u + 271.157
a
7
=
34.6235u
24
+ 142.131u
23
+ ··· − 212.691u − 32.7237
585.335u
24
+ 2117.45u
23
+ ··· − 2654.81u − 420.255
a
6
=
250.131u
24
+ 911.029u
23
+ ··· − 1160.99u − 185.716
−44.7226u
24
− 177.047u
23
+ ··· + 241.920u + 41.1168
a
11
=
8.33571u
24
+ 27.3502u
23
+ ··· − 30.3192u − 3.78842
−31.9865u
24
− 139.417u
23
+ ··· + 217.641u + 34.6235
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16873930
32603
u
24
+
57225794
32603
u
23
+ ··· −
65295295
32603
u −
10504251
32603
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 2u
24
+ ··· + 8u − 1
c
2
u
25
+ 3u
24
+ ··· − 9u
2
+ 1
c
3
u
25
− 2u
24
+ ··· + u − 1
c
4
u
25
− 2u
24
+ ··· − 4u + 1
c
5
u
25
− 2u
24
+ ··· − u − 1
c
6
u
25
− 3u
24
+ ··· + 9u
2
− 1
c
7
u
25
+ 2u
24
+ ··· − 4u − 1
c
8
, c
9
u
25
+ 5u
24
+ ··· − 7u − 1
c
10
u
25
− 5u
24
+ ··· + 5u − 1
c
11
u
25
+ 2u
23
+ ··· + 3u + 1
c
12
u
25
− 5u
24
+ ··· − 7u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 6y
24
+ ··· + 16y −1
c
2
, c
6
y
25
− 11y
24
+ ··· + 18y −1
c
3
y
25
+ 12y
24
+ ··· − 17y −1
c
4
, c
7
y
25
+ 22y
24
+ ··· − 2y −1
c
5
y
25
+ 4y
24
+ ··· − 15y −1
c
8
, c
9
, c
12
y
25
− 31y
24
+ ··· + 31y −1
c
10
y
25
− 3y
24
+ ··· − 5y −1
c
11
y
25
+ 4y
24
+ ··· + 3y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.298541 + 1.027340I
a = −0.06383 + 1.76347I
b = −0.275475 − 1.053730I
1.21436 − 3.36231I −4.23447 + 8.76870I
u = 0.298541 − 1.027340I
a = −0.06383 − 1.76347I
b = −0.275475 + 1.053730I
1.21436 + 3.36231I −4.23447 − 8.76870I
u = 0.661162 + 0.586105I
a = 0.374120 − 1.007700I
b = −0.285215 + 0.529958I
−0.390506 − 0.796360I −8.99184 + 1.29305I
u = 0.661162 − 0.586105I
a = 0.374120 + 1.007700I
b = −0.285215 − 0.529958I
−0.390506 + 0.796360I −8.99184 − 1.29305I
u = 1.11819
a = 1.82102
b = 0.341509
−0.134992 10.0610
u = −1.366610 + 0.028855I
a = 0.515700 − 0.511164I
b = 0.72419 + 1.80510I
0.98406 + 3.43301I − 60.10 + 0.511542I
u = −1.366610 − 0.028855I
a = 0.515700 + 0.511164I
b = 0.72419 − 1.80510I
0.98406 − 3.43301I − 60.10 − 0.511542I
u = −1.398330 + 0.168604I
a = 1.74303 + 0.87672I
b = 0.460302 − 1.077380I
0.16949 + 8.89961I −4.00000 − 9.54946I
u = −1.398330 − 0.168604I
a = 1.74303 − 0.87672I
b = 0.460302 + 1.077380I
0.16949 − 8.89961I −4.00000 + 9.54946I
u = 1.40218 + 0.24784I
a = −0.430179 + 0.875308I
b = −0.329714 − 1.227330I
−2.17602 − 3.60162I −4.00000 + 1.95348I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40218 − 0.24784I
a = −0.430179 − 0.875308I
b = −0.329714 + 1.227330I
−2.17602 + 3.60162I −4.00000 − 1.95348I
u = −0.169775 + 0.539626I
a = −1.32853 − 3.37395I
b = 0.279532 + 1.025430I
4.59302 − 6.54943I 2.35710 + 3.53999I
u = −0.169775 − 0.539626I
a = −1.32853 + 3.37395I
b = 0.279532 − 1.025430I
4.59302 + 6.54943I 2.35710 − 3.53999I
u = −1.52649 + 0.08191I
a = −0.709019 + 0.514080I
b = −0.540835 + 0.432994I
−7.20434 + 3.67523I −12.3858 − 8.5099I
u = −1.52649 − 0.08191I
a = −0.709019 − 0.514080I
b = −0.540835 − 0.432994I
−7.20434 − 3.67523I −12.3858 + 8.5099I
u = 0.411616 + 0.217187I
a = −1.81390 − 0.21549I
b = −0.514630 − 0.717296I
−0.61285 − 2.55011I −7.6321 + 17.9745I
u = 0.411616 − 0.217187I
a = −1.81390 + 0.21549I
b = −0.514630 + 0.717296I
−0.61285 + 2.55011I −7.6321 − 17.9745I
u = −1.53548 + 0.16663I
a = −0.215309 + 0.195137I
b = −0.708315 − 0.330475I
−7.56957 + 3.45249I 0
u = −1.53548 − 0.16663I
a = −0.215309 − 0.195137I
b = −0.708315 + 0.330475I
−7.56957 − 3.45249I 0
u = −1.50652 + 0.34579I
a = −0.790881 − 1.108830I
b = −0.486612 + 1.227370I
−4.77229 + 8.14428I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50652 − 0.34579I
a = −0.790881 + 1.108830I
b = −0.486612 − 1.227370I
−4.77229 − 8.14428I 0
u = −0.178079 + 0.099223I
a = −1.40410 − 0.68529I
b = 0.49534 − 1.50963I
5.20429 − 3.01827I −11.79399 + 6.31118I
u = −0.178079 − 0.099223I
a = −1.40410 + 0.68529I
b = 0.49534 + 1.50963I
5.20429 + 3.01827I −11.79399 − 6.31118I
u = 1.84870 + 0.23184I
a = 0.212393 − 0.429879I
b = 0.010682 + 0.845722I
−4.17657 − 2.99878I 0
u = 1.84870 − 0.23184I
a = 0.212393 + 0.429879I
b = 0.010682 − 0.845722I
−4.17657 + 2.99878I 0
24
III. I
u
3
= h−6a
3
+ 2a
2
+ b − 27a − 9, 2a
4
+ 9a
2
+ 6a + 1, u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
1
a
9
=
1
1
a
1
=
−1
0
a
5
=
a
6a
3
− 2a
2
+ 27a + 9
a
10
=
0
1
a
4
=
6a
3
− 2a
2
+ 28a + 9
6a
3
− 2a
2
+ 27a + 9
a
2
=
2a
3
+ 9a + 4
2
a
3
=
6a
3
− 2a
2
+ 28a + 9
12a
3
− 4a
2
+ 55a + 18
a
7
=
2a
3
+ 9a + 4
2
a
6
=
−4a
3
+ 2a
2
− 19a − 5
−12a
3
+ 4a
2
− 55a − 16
a
11
=
4a
3
− 2a
2
+ 18a + 7
4a
3
+ 18a + 9
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
(u
2
+ 2)
2
c
2
, c
8
, c
9
(u − 1)
4
c
3
2(2u
4
+ 5u
2
− 2u + 3)
c
5
2(2u
4
+ 5u
2
+ 2u + 3)
c
6
, c
12
(u + 1)
4
c
10
, c
11
u
4
− 2u
3
− 3u
2
+ 4u + 6
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
(y + 2)
4
c
2
, c
6
, c
8
c
9
, c
12
(y −1)
4
c
3
, c
5
4(4y
4
+ 20y
3
+ 37y
2
+ 26y + 9)
c
10
, c
11
y
4
− 10y
3
+ 37y
2
− 52y + 36
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.319193 + 0.046988I
b = 1.414210I
4.93480 0
u = 1.00000
a = −0.319193 − 0.046988I
b = − 1.414210I
4.93480 0
u = 1.00000
a = 0.31919 + 2.16831I
b = − 1.414210I
4.93480 0
u = 1.00000
a = 0.31919 − 2.16831I
b = 1.414210I
4.93480 0
28
IV. I
u
4
= hb, a − 1, u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
1
a
9
=
1
1
a
1
=
−1
0
a
5
=
1
0
a
10
=
0
1
a
4
=
1
0
a
2
=
−1
0
a
3
=
1
1
a
7
=
1
0
a
6
=
2
1
a
11
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
u
c
2
, c
11
, c
12
u + 1
c
3
, c
5
, c
6
c
8
, c
9
, c
10
u − 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
y
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
10
, c
11
, c
12
y −1
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0
0 0
32
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
+ 2)
2
(u
25
− 2u
24
+ ··· + 8u − 1)
· (u
133
− 15u
132
+ ··· + 11068u − 1172)
c
2
((u − 1)
4
)(u + 1)(u
25
+ 3u
24
+ ··· − 9u
2
+ 1)
· (u
133
− 3u
132
+ ··· − 17081u + 1539)
c
3
4(u − 1)(2u
4
+ 5u
2
− 2u + 3)(u
25
− 2u
24
+ ··· + u − 1)
· (2u
133
+ 2u
132
+ ··· + 11264u + 2048)
c
4
u(u
2
+ 2)
2
(u
25
− 2u
24
+ ··· − 4u + 1)
· (u
133
− 9u
132
+ ··· − 24896u + 1952)
c
5
4(u − 1)(2u
4
+ 5u
2
+ 2u + 3)(u
25
− 2u
24
+ ··· − u − 1)
· (2u
133
+ 2u
132
+ ··· + 7848686u + 3253981)
c
6
(u − 1)(u + 1)
4
(u
25
− 3u
24
+ ··· + 9u
2
− 1)
· (u
133
− 3u
132
+ ··· − 17081u + 1539)
c
7
u(u
2
+ 2)
2
(u
25
+ 2u
24
+ ··· − 4u − 1)
· (u
133
− 9u
132
+ ··· − 24896u + 1952)
c
8
, c
9
((u − 1)
5
)(u
25
+ 5u
24
+ ··· − 7u − 1)(u
133
+ 5u
132
+ ··· − 56u + 3)
c
10
(u − 1)(u
4
− 2u
3
+ ··· + 4u + 6)(u
25
− 5u
24
+ ··· + 5u − 1)
· (u
133
+ 7u
132
+ ··· + 62070u + 9146)
c
11
(u + 1)(u
4
− 2u
3
+ ··· + 4u + 6)(u
25
+ 2u
23
+ ··· + 3u + 1)
· (u
133
+ 7u
130
+ ··· + 14366u + 3254)
c
12
((u + 1)
5
)(u
25
− 5u
24
+ ··· − 7u + 1)(u
133
+ 5u
132
+ ··· − 56u + 3)
33
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y + 2)
4
(y
25
− 6y
24
+ ··· + 16y −1)
· (y
133
− 7y
132
+ ··· − 104928320y −1373584)
c
2
, c
6
((y −1)
5
)(y
25
− 11y
24
+ ··· + 18y −1)
· (y
133
− 77y
132
+ ··· + 162555355y −2368521)
c
3
16(y −1)(4y
4
+ 20y
3
+ ··· + 26y + 9)(y
25
+ 12y
24
+ ··· − 17y −1)
· (4y
133
+ 192y
132
+ ··· − 110100480y −4194304)
c
4
, c
7
y(y + 2)
4
(y
25
+ 22y
24
+ ··· − 2y −1)
· (y
133
+ 93y
132
+ ··· − 337168896y −3810304)
c
5
16(y −1)(4y
4
+ 20y
3
+ ··· + 26y + 9)(y
25
+ 4y
24
+ ··· − 15y −1)
· (4y
133
+ 240y
132
+ ··· − 532285298173316y −10588392348361)
c
8
, c
9
, c
12
((y −1)
5
)(y
25
− 31y
24
+ ··· + 31y −1)(y
133
− 137y
132
+ ··· − 56y −9)
c
10
(y −1)(y
4
− 10y
3
+ ··· − 52y + 36)(y
25
− 3y
24
+ ··· − 5y −1)
· (y
133
− 51y
132
+ ··· + 15173548824y −83649316)
c
11
(y −1)(y
4
− 10y
3
+ ··· − 52y + 36)(y
25
+ 4y
24
+ ··· + 3y −1)
· (y
133
+ 108y
131
+ ··· − 2741332040y −10588516)
34
