12a
0637
(K12a
0637
)
A knot diagram
1
Linearized knot diagam
3 7 10 9 12 2 11 5 1 6 8 4
Solving Sequence
4,9 1,5
10 3 2 8 12 6 11 7
c
4
c
9
c
3
c
1
c
8
c
12
c
5
c
11
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.80686 × 10
608
u
135
+ 4.59267 × 10
609
u
134
+ ··· + 3.53132 × 10
611
b + 7.99940 × 10
610
,
− 1.21400 × 10
609
u
135
− 1.85289 × 10
611
u
134
+ ··· + 1.45844 × 10
614
a − 4.86124 × 10
614
,
u
136
− 5u
135
+ ··· − 1764u − 392i
I
u
2
= h3127351u
18
− 1101560u
17
+ ··· + 3308497b − 3526485,
4211238u
18
− 9238417u
17
+ ··· + 3308497a + 6322815, u
19
− u
18
+ ··· − 11u
2
− 1i
I
u
3
= hb, a + u, u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 157 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−7.81 × 10
608
u
135
+ 4.59 × 10
609
u
134
+ · · · + 3.53 × 10
611
b + 8.00 ×
10
610
, −1.21 × 10
609
u
135
− 1.85 × 10
611
u
134
+ · · · + 1.46 × 10
614
a − 4.86 ×
10
614
, u
136
− 5u
135
+ · · · − 1764u − 392i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
1
=
8.32400 × 10
−6
u
135
+ 0.00127046u
134
+ ··· + 11.7711u + 3.33319
0.00221075u
135
− 0.0130055u
134
+ ··· + 2.35289u − 0.226527
a
5
=
1
u
2
a
10
=
−0.00320519u
135
+ 0.0124770u
134
+ ··· − 18.1541u − 2.63362
0.00190447u
135
− 0.0132405u
134
+ ··· + 4.84713u + 1.75434
a
3
=
0.00961782u
135
− 0.0513213u
134
+ ··· + 2.39397u + 4.01892
0.00525886u
135
− 0.0201863u
134
+ ··· − 7.87142u − 0.761178
a
2
=
−0.0132748u
135
+ 0.0673620u
134
+ ··· − 21.5615u − 2.98098
−0.000837063u
135
− 0.00318599u
134
+ ··· + 7.32115u + 1.47992
a
8
=
u
u
3
+ u
a
12
=
−0.00220242u
135
+ 0.0142760u
134
+ ··· + 9.41817u + 3.55971
0.00221075u
135
− 0.0130055u
134
+ ··· + 2.35289u − 0.226527
a
6
=
−0.00128220u
135
+ 0.0191494u
134
+ ··· − 15.4030u + 2.71700
−0.00302398u
135
+ 0.0113216u
134
+ ··· + 5.21126u + 0.327390
a
11
=
0.00108998u
135
− 0.00277045u
134
+ ··· + 8.16182u + 3.74680
0.000603983u
135
− 0.00470337u
134
+ ··· + 1.35625u − 0.268539
a
7
=
−0.00620299u
135
+ 0.0265644u
134
+ ··· + 29.1434u + 7.44215
0.00106340u
135
− 0.00871337u
134
+ ··· + 5.45011u + 0.321834
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00348385u
135
− 0.0403883u
134
+ ··· + 22.9816u + 11.3314
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
136
+ 52u
135
+ ··· + 9209u + 529
c
2
, c
6
u
136
− 2u
135
+ ··· − 89u − 23
c
3
u
136
+ 7u
135
+ ··· − 20u − 1
c
4
, c
8
u
136
+ 5u
135
+ ··· + 1764u − 392
c
5
u
136
− 3u
135
+ ··· − 10733u + 829
c
7
, c
11
u
136
− 3u
135
+ ··· − 5775u + 244
c
9
u
136
− 4u
135
+ ··· − 59182u − 17287
c
10
u
136
+ 4u
135
+ ··· + 113947u − 42193
c
12
u
136
+ 15u
135
+ ··· − 36u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
136
+ 68y
135
+ ··· + 1258572891y + 279841
c
2
, c
6
y
136
− 52y
135
+ ··· − 9209y + 529
c
3
y
136
+ 5y
135
+ ··· − 32y + 1
c
4
, c
8
y
136
+ 109y
135
+ ··· − 1223824y + 153664
c
5
y
136
− 47y
135
+ ··· − 19505819y + 687241
c
7
, c
11
y
136
− 113y
135
+ ··· − 9614305y + 59536
c
9
y
136
− 42y
135
+ ··· + 9263767506y + 298840369
c
10
y
136
− 30y
135
+ ··· − 52468465753y + 1780249249
c
12
y
136
− 11y
135
+ ··· − 1776y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.981483 + 0.194710I
a = 0.487582 − 1.061820I
b = 0.684933 − 0.932359I
−3.02456 − 6.65628I 0
u = 0.981483 − 0.194710I
a = 0.487582 + 1.061820I
b = 0.684933 + 0.932359I
−3.02456 + 6.65628I 0
u = −0.302840 + 0.950578I
a = 1.44682 − 0.22641I
b = −0.296701 − 0.506353I
−0.76134 + 6.16481I 0
u = −0.302840 − 0.950578I
a = 1.44682 + 0.22641I
b = −0.296701 + 0.506353I
−0.76134 − 6.16481I 0
u = −0.979464 + 0.038146I
a = 1.046020 − 0.701042I
b = 0.722445 − 0.812577I
−1.52856 − 8.54158I 0
u = −0.979464 − 0.038146I
a = 1.046020 + 0.701042I
b = 0.722445 + 0.812577I
−1.52856 + 8.54158I 0
u = 0.151638 + 1.012050I
a = 0.161145 − 0.868688I
b = 3.41324 + 0.54552I
3.12305 + 2.06608I 0
u = 0.151638 − 1.012050I
a = 0.161145 + 0.868688I
b = 3.41324 − 0.54552I
3.12305 − 2.06608I 0
u = −0.979982 + 0.309514I
a = −0.25551 − 1.41166I
b = 0.136556 − 0.747463I
3.04388 − 0.52509I 0
u = −0.979982 − 0.309514I
a = −0.25551 + 1.41166I
b = 0.136556 + 0.747463I
3.04388 + 0.52509I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.914350 + 0.469337I
a = 0.15902 − 1.71081I
b = −0.083275 − 0.829333I
2.05985 + 5.50935I 0
u = 0.914350 − 0.469337I
a = 0.15902 + 1.71081I
b = −0.083275 + 0.829333I
2.05985 − 5.50935I 0
u = 0.958608 + 0.066625I
a = −0.946811 + 0.693056I
b = −0.632110 + 0.752174I
−0.27138 − 3.15703I 0
u = 0.958608 − 0.066625I
a = −0.946811 − 0.693056I
b = −0.632110 − 0.752174I
−0.27138 + 3.15703I 0
u = −0.135717 + 0.938317I
a = 1.171490 + 0.784766I
b = −0.114192 − 0.199226I
−2.52392 − 0.14907I 0
u = −0.135717 − 0.938317I
a = 1.171490 − 0.784766I
b = −0.114192 + 0.199226I
−2.52392 + 0.14907I 0
u = 0.152114 + 1.047540I
a = −0.301370 − 0.233899I
b = 1.141520 + 0.689819I
1.60169 − 2.91819I 0
u = 0.152114 − 1.047540I
a = −0.301370 + 0.233899I
b = 1.141520 − 0.689819I
1.60169 + 2.91819I 0
u = 0.252270 + 1.037820I
a = −0.869697 − 0.126533I
b = 0.479427 − 0.271272I
0.86648 − 2.06124I 0
u = 0.252270 − 1.037820I
a = −0.869697 + 0.126533I
b = 0.479427 + 0.271272I
0.86648 + 2.06124I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.837404 + 0.322705I
a = −0.694951 + 0.286572I
b = −0.015978 + 0.547591I
1.94190 + 0.55872I 0
u = −0.837404 − 0.322705I
a = −0.694951 − 0.286572I
b = −0.015978 − 0.547591I
1.94190 − 0.55872I 0
u = −0.008280 + 1.119830I
a = −0.159799 − 1.114960I
b = 0.03210 − 1.75361I
3.45662 + 1.19333I 0
u = −0.008280 − 1.119830I
a = −0.159799 + 1.114960I
b = 0.03210 + 1.75361I
3.45662 − 1.19333I 0
u = 0.304821 + 1.112420I
a = −0.720839 − 0.703542I
b = 0.834018 − 0.531603I
0.89236 − 2.44414I 0
u = 0.304821 − 1.112420I
a = −0.720839 + 0.703542I
b = 0.834018 + 0.531603I
0.89236 + 2.44414I 0
u = 0.219062 + 1.152790I
a = 1.77534 − 0.55054I
b = −0.206015 + 0.078298I
1.23659 − 2.47274I 0
u = 0.219062 − 1.152790I
a = 1.77534 + 0.55054I
b = −0.206015 − 0.078298I
1.23659 + 2.47274I 0
u = 0.013238 + 1.173740I
a = −0.045455 − 1.349070I
b = −0.02527 − 1.93660I
5.17420 − 2.39055I 0
u = 0.013238 − 1.173740I
a = −0.045455 + 1.349070I
b = −0.02527 + 1.93660I
5.17420 + 2.39055I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.150212 + 0.805508I
a = 0.407311 − 0.763432I
b = −0.569199 + 0.927037I
2.15127 − 0.79768I 0
u = −0.150212 − 0.805508I
a = 0.407311 + 0.763432I
b = −0.569199 − 0.927037I
2.15127 + 0.79768I 0
u = −0.145982 + 1.194190I
a = 0.136926 − 0.910700I
b = −1.40298 − 1.12621I
4.37821 + 1.69238I 0
u = −0.145982 − 1.194190I
a = 0.136926 + 0.910700I
b = −1.40298 + 1.12621I
4.37821 − 1.69238I 0
u = 0.462490 + 1.116580I
a = 1.38294 + 0.78397I
b = −0.217676 + 0.469481I
4.19712 − 10.61180I 0
u = 0.462490 − 1.116580I
a = 1.38294 − 0.78397I
b = −0.217676 − 0.469481I
4.19712 + 10.61180I 0
u = −0.023411 + 1.233580I
a = −0.346728 + 0.323039I
b = 1.44932 + 1.29738I
1.82787 − 2.48174I 0
u = −0.023411 − 1.233580I
a = −0.346728 − 0.323039I
b = 1.44932 − 1.29738I
1.82787 + 2.48174I 0
u = −0.120685 + 0.750153I
a = −0.04422 + 2.21426I
b = 0.032281 + 1.095470I
−3.50794 + 1.54063I 0
u = −0.120685 − 0.750153I
a = −0.04422 − 2.21426I
b = 0.032281 − 1.095470I
−3.50794 − 1.54063I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.167440 + 0.424522I
a = −0.542033 − 0.916711I
b = −0.665908 − 0.868794I
4.09156 + 7.55900I 0
u = −1.167440 − 0.424522I
a = −0.542033 + 0.916711I
b = −0.665908 + 0.868794I
4.09156 − 7.55900I 0
u = −0.014597 + 1.243110I
a = −0.80318 + 1.33274I
b = 0.959566 + 0.810599I
7.97959 + 8.79008I 0
u = −0.014597 − 1.243110I
a = −0.80318 − 1.33274I
b = 0.959566 − 0.810599I
7.97959 − 8.79008I 0
u = 0.141849 + 1.249280I
a = −1.103230 + 0.039500I
b = 1.352340 − 0.028688I
1.98199 − 0.92146I 0
u = 0.141849 − 1.249280I
a = −1.103230 − 0.039500I
b = 1.352340 + 0.028688I
1.98199 + 0.92146I 0
u = −0.653080 + 0.349813I
a = −0.306707 − 0.977063I
b = −0.697548 − 1.012470I
1.91773 + 3.55207I 0
u = −0.653080 − 0.349813I
a = −0.306707 + 0.977063I
b = −0.697548 + 1.012470I
1.91773 − 3.55207I 0
u = −0.019016 + 1.261740I
a = 0.751852 + 1.066740I
b = −1.124570 + 0.761603I
9.92861 − 2.36642I 0
u = −0.019016 − 1.261740I
a = 0.751852 − 1.066740I
b = −1.124570 − 0.761603I
9.92861 + 2.36642I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.707639 + 0.069066I
a = 1.048460 − 0.912240I
b = 0.544976 − 1.018770I
−5.75265 − 2.32928I −7.06110 + 0.I
u = −0.707639 − 0.069066I
a = 1.048460 + 0.912240I
b = 0.544976 + 1.018770I
−5.75265 + 2.32928I −7.06110 + 0.I
u = −0.329536 + 1.247580I
a = −0.390138 + 0.881909I
b = 1.21962 + 1.27645I
−2.08160 + 6.15361I 0
u = −0.329536 − 1.247580I
a = −0.390138 − 0.881909I
b = 1.21962 − 1.27645I
−2.08160 − 6.15361I 0
u = 1.242020 + 0.355992I
a = 0.591318 − 0.930230I
b = 0.697845 − 0.861755I
2.76128 − 13.52910I 0
u = 1.242020 − 0.355992I
a = 0.591318 + 0.930230I
b = 0.697845 + 0.861755I
2.76128 + 13.52910I 0
u = 0.620441 + 0.339642I
a = −0.487855 + 1.037950I
b = −0.187055 + 0.767608I
−1.16016 − 1.33965I 0. + 4.37094I
u = 0.620441 − 0.339642I
a = −0.487855 − 1.037950I
b = −0.187055 − 0.767608I
−1.16016 + 1.33965I 0. − 4.37094I
u = −0.395929 + 1.235260I
a = −1.043790 + 0.358024I
b = 0.430408 + 0.345386I
6.26159 + 5.53325I 0
u = −0.395929 − 1.235260I
a = −1.043790 − 0.358024I
b = 0.430408 − 0.345386I
6.26159 − 5.53325I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.299723 + 1.266030I
a = 0.313961 − 1.170680I
b = −0.991635 − 0.913823I
5.50999 + 3.17286I 0
u = −0.299723 − 1.266030I
a = 0.313961 + 1.170680I
b = −0.991635 + 0.913823I
5.50999 − 3.17286I 0
u = 0.360206 + 1.251930I
a = −0.402774 − 1.311800I
b = 0.891393 − 0.912140I
4.19605 − 8.46266I 0
u = 0.360206 − 1.251930I
a = −0.402774 + 1.311800I
b = 0.891393 + 0.912140I
4.19605 + 8.46266I 0
u = −0.096363 + 1.311080I
a = 0.112577 + 0.636063I
b = −1.53192 + 1.01243I
10.78600 + 4.00364I 0
u = −0.096363 − 1.311080I
a = 0.112577 − 0.636063I
b = −1.53192 − 1.01243I
10.78600 − 4.00364I 0
u = 0.120369 + 1.316730I
a = 0.009938 + 0.607473I
b = 1.56232 + 1.04618I
9.27217 − 10.26780I 0
u = 0.120369 − 1.316730I
a = 0.009938 − 0.607473I
b = 1.56232 − 1.04618I
9.27217 + 10.26780I 0
u = −0.475031 + 0.481180I
a = 0.08954 + 1.69963I
b = −0.062215 + 1.043550I
−2.16643 − 2.81238I −3.01505 + 1.45077I
u = −0.475031 − 0.481180I
a = 0.08954 − 1.69963I
b = −0.062215 − 1.043550I
−2.16643 + 2.81238I −3.01505 − 1.45077I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.446508 + 0.480371I
a = 0.58535 − 2.82648I
b = 0.068908 − 0.700380I
−0.909099 − 0.180096I −7.02104 + 1.48725I
u = 0.446508 − 0.480371I
a = 0.58535 + 2.82648I
b = 0.068908 + 0.700380I
−0.909099 + 0.180096I −7.02104 − 1.48725I
u = −0.448880 + 1.284280I
a = −0.223147 + 1.091730I
b = 1.30927 + 1.19959I
2.37424 + 13.57830I 0
u = −0.448880 − 1.284280I
a = −0.223147 − 1.091730I
b = 1.30927 − 1.19959I
2.37424 − 13.57830I 0
u = 0.418918 + 1.320840I
a = 0.189697 + 0.999987I
b = −1.25953 + 1.17196I
4.06395 − 8.01371I 0
u = 0.418918 − 1.320840I
a = 0.189697 − 0.999987I
b = −1.25953 − 1.17196I
4.06395 + 8.01371I 0
u = 0.187089 + 1.379670I
a = 0.175273 + 0.611190I
b = −1.02046 + 1.35278I
4.38987 − 3.93870I 0
u = 0.187089 − 1.379670I
a = 0.175273 − 0.611190I
b = −1.02046 − 1.35278I
4.38987 + 3.93870I 0
u = 0.542183 + 0.233446I
a = 0.326843 + 1.194970I
b = 0.418948 + 0.663812I
−1.58591 − 0.97043I −3.82761 + 0.82785I
u = 0.542183 − 0.233446I
a = 0.326843 − 1.194970I
b = 0.418948 − 0.663812I
−1.58591 + 0.97043I −3.82761 − 0.82785I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.113950 + 1.409110I
a = −0.129708 − 0.732051I
b = 0.684952 − 0.571355I
9.67053 + 2.96947I 0
u = −0.113950 − 1.409110I
a = −0.129708 + 0.732051I
b = 0.684952 + 0.571355I
9.67053 − 2.96947I 0
u = 0.04442 + 1.41384I
a = 0.029133 − 0.828842I
b = −0.807755 − 0.795601I
9.41264 + 2.80994I 0
u = 0.04442 − 1.41384I
a = 0.029133 + 0.828842I
b = −0.807755 + 0.795601I
9.41264 − 2.80994I 0
u = 0.020718 + 0.570454I
a = 0.30280 − 1.96398I
b = 0.172294 + 1.235970I
3.09116 + 2.32307I 16.3107 − 9.3430I
u = 0.020718 − 0.570454I
a = 0.30280 + 1.96398I
b = 0.172294 − 1.235970I
3.09116 − 2.32307I 16.3107 + 9.3430I
u = −0.188756 + 0.521521I
a = −0.77392 − 1.94014I
b = −0.686102 + 1.002950I
3.12603 + 2.39225I 9.06902 + 6.97086I
u = −0.188756 − 0.521521I
a = −0.77392 + 1.94014I
b = −0.686102 − 1.002950I
3.12603 − 2.39225I 9.06902 − 6.97086I
u = 0.554146 + 0.001366I
a = 1.40120 + 1.38461I
b = 0.813546 + 0.203203I
0.58990 + 4.81521I 2.24613 − 4.54598I
u = 0.554146 − 0.001366I
a = 1.40120 − 1.38461I
b = 0.813546 − 0.203203I
0.58990 − 4.81521I 2.24613 + 4.54598I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.26750 + 1.43200I
a = 0.427874 − 0.570118I
b = −1.45292 − 1.11592I
7.59293 + 6.96607I 0
u = −0.26750 − 1.43200I
a = 0.427874 + 0.570118I
b = −1.45292 + 1.11592I
7.59293 − 6.96607I 0
u = 0.41398 + 1.40485I
a = −0.470805 − 0.916175I
b = 1.16045 − 1.09565I
2.01977 − 11.60480I 0
u = 0.41398 − 1.40485I
a = −0.470805 + 0.916175I
b = 1.16045 + 1.09565I
2.01977 + 11.60480I 0
u = −0.52593 + 1.37345I
a = −0.477581 + 0.796148I
b = 0.712392 + 0.676730I
6.69236 + 5.85561I 0
u = −0.52593 − 1.37345I
a = −0.477581 − 0.796148I
b = 0.712392 − 0.676730I
6.69236 − 5.85561I 0
u = −0.09714 + 1.49933I
a = −0.071954 − 0.867007I
b = 0.049673 − 0.681225I
9.83192 + 3.09070I 0
u = −0.09714 − 1.49933I
a = −0.071954 + 0.867007I
b = 0.049673 + 0.681225I
9.83192 − 3.09070I 0
u = −0.470347 + 0.080046I
a = −1.65155 − 1.26100I
b = −0.757551 − 0.030920I
1.64170 + 0.05442I 5.97527 + 1.38963I
u = −0.470347 − 0.080046I
a = −1.65155 + 1.26100I
b = −0.757551 + 0.030920I
1.64170 − 0.05442I 5.97527 − 1.38963I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.49465 + 1.47050I
a = 0.059995 + 0.843739I
b = −1.073900 + 0.819905I
6.03289 − 6.64676I 0
u = 0.49465 − 1.47050I
a = 0.059995 − 0.843739I
b = −1.073900 − 0.819905I
6.03289 + 6.64676I 0
u = 0.432510 + 0.063513I
a = 0.11485 + 1.62720I
b = 0.883673 + 0.580622I
−1.58709 − 1.21163I −6.61256 + 2.97902I
u = 0.432510 − 0.063513I
a = 0.11485 − 1.62720I
b = 0.883673 − 0.580622I
−1.58709 + 1.21163I −6.61256 − 2.97902I
u = −0.45128 + 1.49782I
a = 0.085533 + 0.478688I
b = 1.208830 + 0.435841I
10.34880 + 4.82983I 0
u = −0.45128 − 1.49782I
a = 0.085533 − 0.478688I
b = 1.208830 − 0.435841I
10.34880 − 4.82983I 0
u = −0.45991 + 1.50482I
a = 0.241280 − 0.983791I
b = −1.17364 − 1.19814I
10.0833 + 13.2815I 0
u = −0.45991 − 1.50482I
a = 0.241280 + 0.983791I
b = −1.17364 + 1.19814I
10.0833 − 13.2815I 0
u = 0.47838 + 1.49979I
a = −0.138710 + 0.592243I
b = −1.271910 + 0.531645I
9.9440 − 10.1934I 0
u = 0.47838 − 1.49979I
a = −0.138710 − 0.592243I
b = −1.271910 − 0.531645I
9.9440 + 10.1934I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.49218 + 1.49924I
a = −0.242029 − 1.053330I
b = 1.15827 − 1.21100I
8.5267 − 19.5613I 0
u = 0.49218 − 1.49924I
a = −0.242029 + 1.053330I
b = 1.15827 + 1.21100I
8.5267 + 19.5613I 0
u = −1.57603 + 0.08027I
a = 0.304884 − 0.492135I
b = 0.398436 − 0.338581I
4.33355 − 1.53454I 0
u = −1.57603 − 0.08027I
a = 0.304884 + 0.492135I
b = 0.398436 + 0.338581I
4.33355 + 1.53454I 0
u = −0.03752 + 1.58102I
a = 0.065601 + 0.381998I
b = 0.325751 + 0.605320I
3.79404 − 2.92444I 0
u = −0.03752 − 1.58102I
a = 0.065601 − 0.381998I
b = 0.325751 − 0.605320I
3.79404 + 2.92444I 0
u = −0.60722 + 1.48945I
a = −0.219673 + 1.106620I
b = 0.820425 + 0.979066I
9.07956 + 8.72345I 0
u = −0.60722 − 1.48945I
a = −0.219673 − 1.106620I
b = 0.820425 − 0.979066I
9.07956 − 8.72345I 0
u = 0.57774 + 1.52044I
a = 0.132585 + 1.074160I
b = −0.892428 + 0.986481I
9.10013 − 3.61859I 0
u = 0.57774 − 1.52044I
a = 0.132585 − 1.074160I
b = −0.892428 − 0.986481I
9.10013 + 3.61859I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.68138 + 0.13540I
a = −0.390625 − 0.331214I
b = −0.432528 − 0.212299I
4.02922 − 3.69499I 0
u = 1.68138 − 0.13540I
a = −0.390625 + 0.331214I
b = −0.432528 + 0.212299I
4.02922 + 3.69499I 0
u = −0.103201 + 0.267919I
a = 0.862791 − 0.147655I
b = 0.33344 − 1.57915I
−1.20642 + 3.24458I −8.2723 − 20.7502I
u = −0.103201 − 0.267919I
a = 0.862791 + 0.147655I
b = 0.33344 + 1.57915I
−1.20642 − 3.24458I −8.2723 + 20.7502I
u = −0.285406
a = −3.03677
b = −0.492714
1.12272 11.1750
u = 0.154924 + 0.158169I
a = −0.70155 + 5.64423I
b = 0.985387 + 0.089326I
4.60181 − 9.00523I 5.96633 + 6.29175I
u = 0.154924 − 0.158169I
a = −0.70155 − 5.64423I
b = 0.985387 − 0.089326I
4.60181 + 9.00523I 5.96633 − 6.29175I
u = −0.172847 + 0.101959I
a = 2.55233 + 4.57931I
b = −1.063350 + 0.110520I
6.29043 + 2.89211I 9.29484 − 3.33568I
u = −0.172847 − 0.101959I
a = 2.55233 − 4.57931I
b = −1.063350 − 0.110520I
6.29043 − 2.89211I 9.29484 + 3.33568I
u = 0.06647 + 1.86571I
a = 0.045489 − 0.299436I
b = 0.207167 − 0.910907I
6.41462 + 3.31930I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06647 − 1.86571I
a = 0.045489 + 0.299436I
b = 0.207167 + 0.910907I
6.41462 − 3.31930I 0
u = 0.54569 + 1.80298I
a = 0.1058470 − 0.0004980I
b = 0.346493 + 0.019407I
0.204133 + 0.345609I 0
u = 0.54569 − 1.80298I
a = 0.1058470 + 0.0004980I
b = 0.346493 − 0.019407I
0.204133 − 0.345609I 0
u = 0.37057 + 1.87912I
a = −0.053079 + 0.309370I
b = −0.090046 + 0.323901I
3.85824 − 2.87616I 0
u = 0.37057 − 1.87912I
a = −0.053079 − 0.309370I
b = −0.090046 − 0.323901I
3.85824 + 2.87616I 0
u = 2.37630
a = −0.147560
b = −0.179765
0.265457 0
18
II. I
u
2
= h3.13 × 10
6
u
18
− 1.10 × 10
6
u
17
+ · · · + 3.31 × 10
6
b − 3.53 × 10
6
, 4.21 ×
10
6
u
18
−9.24×10
6
u
17
+· · ·+3.31×10
6
a+6.32×10
6
, u
19
−u
18
+· · ·−11u
2
−1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
1
=
−1.27286u
18
+ 2.79233u
17
+ ··· + 4.29462u − 1.91108
−0.945248u
18
+ 0.332949u
17
+ ··· + 6.33620u + 1.06589
a
5
=
1
u
2
a
10
=
1.78390u
18
− 3.89595u
17
+ ··· − 3.55434u + 5.85116
0.272855u
18
− 1.79233u
17
+ ··· − 1.29462u + 1.91108
a
3
=
4.59659u
18
− 2.45413u
17
+ ··· − 11.4683u − 3.09754
−1.19512u
18
+ 3.53428u
17
+ ··· + 0.332158u − 1.39731
a
2
=
4.33044u
18
− 2.54928u
17
+ ··· − 15.2205u − 3.03308
1.11517u
18
+ 0.702346u
17
+ ··· + 3.75157u − 1.21611
a
8
=
u
u
3
+ u
a
12
=
−0.327607u
18
+ 2.45938u
17
+ ··· − 2.04158u − 2.97697
−0.945248u
18
+ 0.332949u
17
+ ··· + 6.33620u + 1.06589
a
6
=
−2.16422u
18
+ 0.900143u
17
+ ··· + 3.03373u + 1.36677
−0.339438u
18
+ 0.0707176u
17
+ ··· + 1.38102u + 3.43889
a
11
=
−0.638042u
18
+ 1.85344u
17
+ ··· − 1.31443u − 1.45750
−0.657270u
18
− 0.380493u
17
+ ··· + 6.75291u + 1.66899
a
7
=
−0.343425u
18
− 0.352256u
17
+ ··· + 2.84501u − 0.982824
2.26422u
18
− 0.278842u
17
+ ··· − 5.85220u − 3.65684
(ii) Obstruction class = 1
(iii) Cusp Shapes =
113731721
3308497
u
18
−
122304285
3308497
u
17
+ ··· −
167222314
3308497
u +
63097751
3308497
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
19
− 9u
18
+ ··· + 5u − 1
c
2
u
19
+ u
18
+ ··· + u − 1
c
3
u
19
+ 3u
18
+ ··· − 7u − 1
c
4
u
19
− u
18
+ ··· − 11u
2
− 1
c
5
u
19
− 2u
18
+ ··· − u + 1
c
6
u
19
− u
18
+ ··· + u + 1
c
7
u
19
− 9u
17
+ ··· + 3u + 1
c
8
u
19
+ u
18
+ ··· + 11u
2
+ 1
c
9
u
19
− 4u
18
+ ··· + 3u + 1
c
10
u
19
+ 2u
18
+ ··· − 4u + 1
c
11
u
19
− 9u
17
+ ··· + 3u − 1
c
12
u
19
− 4u
18
+ ··· + 26u + 3
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 3y
18
+ ··· − 7y −1
c
2
, c
6
y
19
− 9y
18
+ ··· + 5y −1
c
3
y
19
+ 5y
18
+ ··· − y −1
c
4
, c
8
y
19
+ 17y
18
+ ··· − 22y −1
c
5
y
19
− 8y
18
+ ··· + 3y −1
c
7
, c
11
y
19
− 18y
18
+ ··· − 39y −1
c
9
y
19
− 6y
18
+ ··· + 13y −1
c
10
y
19
− 6y
18
+ ··· + 12y −1
c
12
y
19
− 2y
18
+ ··· + 502y −9
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.209559 + 0.919561I
a = −0.320802 − 0.929595I
b = −2.08658 + 1.36801I
3.12378 − 2.11694I 57.0161 + 27.7352I
u = −0.209559 − 0.919561I
a = −0.320802 + 0.929595I
b = −2.08658 − 1.36801I
3.12378 + 2.11694I 57.0161 − 27.7352I
u = 0.080519 + 1.201710I
a = 1.014420 − 0.537793I
b = −1.181480 − 0.601693I
1.85150 − 1.54249I 1.31428 + 3.08095I
u = 0.080519 − 1.201710I
a = 1.014420 + 0.537793I
b = −1.181480 + 0.601693I
1.85150 + 1.54249I 1.31428 − 3.08095I
u = 0.457848 + 1.145640I
a = 0.67044 + 1.28336I
b = −0.908367 + 0.507401I
5.46703 − 11.02550I 7.17011 + 10.31199I
u = 0.457848 − 1.145640I
a = 0.67044 − 1.28336I
b = −0.908367 − 0.507401I
5.46703 + 11.02550I 7.17011 − 10.31199I
u = −0.406841 + 0.496089I
a = −0.973347 − 0.198277I
b = 0.008411 + 0.993515I
1.43371 + 1.41487I 0.12878 − 4.93178I
u = −0.406841 − 0.496089I
a = −0.973347 + 0.198277I
b = 0.008411 − 0.993515I
1.43371 − 1.41487I 0.12878 + 4.93178I
u = 0.054364 + 0.611975I
a = 0.36972 + 2.57617I
b = −0.121498 + 1.013670I
−3.80331 − 1.24964I −9.17184 − 3.81648I
u = 0.054364 − 0.611975I
a = 0.36972 − 2.57617I
b = −0.121498 − 1.013670I
−3.80331 + 1.24964I −9.17184 + 3.81648I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38771
a = 0.400151
b = 0.133551
0.193725 −12.5530
u = −0.53503 + 1.34304I
a = −0.310997 + 0.953953I
b = 0.908177 + 0.662487I
7.58058 + 6.03645I 10.36733 − 4.64724I
u = −0.53503 − 1.34304I
a = −0.310997 − 0.953953I
b = 0.908177 − 0.662487I
7.58058 − 6.03645I 10.36733 + 4.64724I
u = −0.37531 + 1.44384I
a = −0.353748 + 0.662766I
b = 1.071250 + 0.856488I
7.81625 + 6.23436I 9.05553 − 3.81843I
u = −0.37531 − 1.44384I
a = −0.353748 − 0.662766I
b = 1.071250 − 0.856488I
7.81625 − 6.23436I 9.05553 + 3.81843I
u = 0.099924 + 0.408537I
a = 0.550806 + 1.158770I
b = −0.25181 + 1.44431I
−1.06564 + 3.01949I 8.76905 + 4.80187I
u = 0.099924 − 0.408537I
a = 0.550806 − 1.158770I
b = −0.25181 − 1.44431I
−1.06564 − 3.01949I 8.76905 − 4.80187I
u = 0.64023 + 1.56852I
a = 0.153442 − 0.355010I
b = 0.495130 − 0.339869I
3.81818 − 3.04500I 8.6274 + 18.2900I
u = 0.64023 − 1.56852I
a = 0.153442 + 0.355010I
b = 0.495130 + 0.339869I
3.81818 + 3.04500I 8.6274 − 18.2900I
25
III. I
u
3
= hb, a + u, u
2
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
1
=
−u
0
a
5
=
1
u − 1
a
10
=
−1
u
a
3
=
−u + 1
u − 1
a
2
=
−2u + 1
u − 1
a
8
=
u
u − 1
a
12
=
−u
0
a
6
=
−u + 1
u − 1
a
11
=
0
u − 1
a
7
=
u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
(u − 1)
2
c
3
, c
4
u
2
− u + 1
c
5
, c
6
, c
7
(u + 1)
2
c
8
, c
9
, c
10
u
2
+ u + 1
c
12
u
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
11
(y −1)
2
c
3
, c
4
, c
8
c
9
, c
10
y
2
+ y + 1
c
12
y
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = 0
0 3.00000
u = 0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = 0
0 3.00000
29
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
19
− 9u
18
+ ··· + 5u − 1)(u
136
+ 52u
135
+ ··· + 9209u + 529)
c
2
((u − 1)
2
)(u
19
+ u
18
+ ··· + u − 1)(u
136
− 2u
135
+ ··· − 89u − 23)
c
3
(u
2
− u + 1)(u
19
+ 3u
18
+ ··· − 7u − 1)(u
136
+ 7u
135
+ ··· − 20u − 1)
c
4
(u
2
− u + 1)(u
19
− u
18
+ ··· − 11u
2
− 1)(u
136
+ 5u
135
+ ··· + 1764u − 392)
c
5
((u + 1)
2
)(u
19
− 2u
18
+ ··· − u + 1)(u
136
− 3u
135
+ ··· − 10733u + 829)
c
6
((u + 1)
2
)(u
19
− u
18
+ ··· + u + 1)(u
136
− 2u
135
+ ··· − 89u − 23)
c
7
((u + 1)
2
)(u
19
− 9u
17
+ ··· + 3u + 1)(u
136
− 3u
135
+ ··· − 5775u + 244)
c
8
(u
2
+ u + 1)(u
19
+ u
18
+ ··· + 11u
2
+ 1)(u
136
+ 5u
135
+ ··· + 1764u − 392)
c
9
(u
2
+ u + 1)(u
19
− 4u
18
+ ··· + 3u + 1)
· (u
136
− 4u
135
+ ··· − 59182u − 17287)
c
10
(u
2
+ u + 1)(u
19
+ 2u
18
+ ··· − 4u + 1)
· (u
136
+ 4u
135
+ ··· + 113947u − 42193)
c
11
((u − 1)
2
)(u
19
− 9u
17
+ ··· + 3u − 1)(u
136
− 3u
135
+ ··· − 5775u + 244)
c
12
u
2
(u
19
− 4u
18
+ ··· + 26u + 3)(u
136
+ 15u
135
+ ··· − 36u + 8)
30
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
2
)(y
19
+ 3y
18
+ ··· − 7y −1)
· (y
136
+ 68y
135
+ ··· + 1258572891y + 279841)
c
2
, c
6
((y −1)
2
)(y
19
− 9y
18
+ ··· + 5y −1)(y
136
− 52y
135
+ ··· − 9209y + 529)
c
3
(y
2
+ y + 1)(y
19
+ 5y
18
+ ··· − y −1)(y
136
+ 5y
135
+ ··· − 32y + 1)
c
4
, c
8
(y
2
+ y + 1)(y
19
+ 17y
18
+ ··· − 22y −1)
· (y
136
+ 109y
135
+ ··· − 1223824y + 153664)
c
5
((y −1)
2
)(y
19
− 8y
18
+ ··· + 3y −1)
· (y
136
− 47y
135
+ ··· − 19505819y + 687241)
c
7
, c
11
((y −1)
2
)(y
19
− 18y
18
+ ··· − 39y −1)
· (y
136
− 113y
135
+ ··· − 9614305y + 59536)
c
9
(y
2
+ y + 1)(y
19
− 6y
18
+ ··· + 13y −1)
· (y
136
− 42y
135
+ ··· + 9263767506y + 298840369)
c
10
(y
2
+ y + 1)(y
19
− 6y
18
+ ··· + 12y −1)
· (y
136
− 30y
135
+ ··· − 52468465753y + 1780249249)
c
12
y
2
(y
19
− 2y
18
+ ··· + 502y −9)(y
136
− 11y
135
+ ··· − 1776y + 64)
31
