12a
0784
(K12a
0784
)
A knot diagram
1
Linearized knot diagam
3 8 11 9 12 10 2 7 5 1 4 6
Solving Sequence
5,12 6,9
10 7 1 4 8 11 3 2
c
5
c
9
c
6
c
12
c
4
c
8
c
11
c
3
c
2
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.63739 × 10
482
u
126
+ 1.73298 × 10
482
u
125
+ ··· + 2.05419 × 10
482
b − 2.00818 × 10
485
,
− 1.32661 × 10
485
u
126
− 1.40289 × 10
485
u
125
+ ··· + 2.36848 × 10
485
a + 1.00544 × 10
488
,
u
127
+ u
126
+ ··· − 6672u − 1153i
I
u
2
= h−286200551u
28
− 494699359u
27
+ ··· + 112090025b + 67634672,
− 816612824u
28
− 1336630466u
27
+ ··· + 112090025a + 558878203, u
29
+ u
28
+ ··· − u + 1i
I
u
3
= hb − u + 1, a, u
2
− u − 1i
* 3 irreducible components of dim
C
= 0, with total 158 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
= h2.64 × 10
482
u
126
+ 1.73 × 10
482
u
125
+ · · · + 2.05 × 10
482
b − 2.01 ×
10
485
, −1.33 × 10
485
u
126
− 1.40 × 10
485
u
125
+ · · · + 2.37 × 10
485
a + 1.01 ×
10
488
, u
127
+ u
126
+ · · · − 6672u − 1153i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
0.560111u
126
+ 0.592315u
125
+ ··· − 752.208u − 424.508
−1.28391u
126
− 0.843635u
125
+ ··· + 3591.97u + 977.602
a
10
=
1.84402u
126
+ 1.43595u
125
+ ··· − 4344.18u − 1402.11
−1.28391u
126
− 0.843635u
125
+ ··· + 3591.97u + 977.602
a
7
=
−0.934886u
126
− 0.344702u
125
+ ··· + 5811.23u + 1302.90
−0.433227u
126
+ 0.455790u
125
+ ··· + 8089.02u + 1593.55
a
1
=
u
−u
3
+ u
a
4
=
−0.0709417u
126
− 0.649720u
125
+ ··· − 6676.29u − 1248.62
2.42115u
126
+ 0.505784u
125
+ ··· − 14133.4u − 3134.64
a
8
=
−0.0120408u
126
+ 0.123095u
125
+ ··· + 4476.63u + 997.946
1.42633u
126
− 0.415950u
125
+ ··· − 13110.2u − 2621.56
a
11
=
0.546467u
126
+ 0.457767u
125
+ ··· − 1204.38u − 453.814
−1.74298u
126
− 1.01022u
125
+ ··· + 6097.02u + 1557.66
a
3
=
1.03181u
126
+ 0.0803714u
125
+ ··· − 7342.95u − 1545.08
1.99899u
126
+ 0.207011u
125
+ ··· − 13754.8u − 2953.24
a
2
=
0.601134u
126
− 0.502581u
125
+ ··· − 4109.22u − 598.688
3.57670u
126
+ 0.360615u
125
+ ··· − 21584.6u − 4600.97
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.36102u
126
− 0.802747u
125
+ ··· + 30637.4u + 6600.82
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
127
+ 39u
126
+ ··· + 1944u + 81
c
2
, c
7
u
127
+ u
126
+ ··· + 18u − 9
c
3
, c
11
u
127
− 2u
126
+ ··· − 91249u + 90319
c
4
, c
9
u
127
+ 2u
126
+ ··· − 15u − 1
c
5
, c
12
u
127
+ u
126
+ ··· − 6672u − 1153
c
6
u
127
− 2u
126
+ ··· − 934469u + 281173
c
10
u
127
+ 6u
126
+ ··· + 1248715953u + 143741087
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
127
+ 109y
126
+ ··· + 84564y −6561
c
2
, c
7
y
127
− 39y
126
+ ··· + 1944y −81
c
3
, c
11
y
127
− 106y
126
+ ··· + 204122256495y −8157521761
c
4
, c
9
y
127
− 66y
126
+ ··· + 191y −1
c
5
, c
12
y
127
− 83y
126
+ ··· + 49166786y −1329409
c
6
y
127
+ 22y
126
+ ··· − 2134776124149y −79058255929
c
10
y
127
− 58y
126
+ ··· + 427269195188756631y −20661500091941569
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.899609 + 0.424992I
a = −1.10629 − 0.94682I
b = −1.11918 + 0.90820I
−1.07536 + 5.17840I 0
u = 0.899609 − 0.424992I
a = −1.10629 + 0.94682I
b = −1.11918 − 0.90820I
−1.07536 − 5.17840I 0
u = −0.969383 + 0.217043I
a = −0.242095 + 0.716577I
b = −1.108500 − 0.431288I
−2.20885 − 0.84555I 0
u = −0.969383 − 0.217043I
a = −0.242095 − 0.716577I
b = −1.108500 + 0.431288I
−2.20885 + 0.84555I 0
u = 0.975700 + 0.058998I
a = −1.50968 − 0.43039I
b = −1.39756 + 0.26312I
1.86265 + 1.12684I 0
u = 0.975700 − 0.058998I
a = −1.50968 + 0.43039I
b = −1.39756 − 0.26312I
1.86265 − 1.12684I 0
u = −0.833264 + 0.468989I
a = −0.481761 + 0.814515I
b = −1.350000 + 0.031703I
1.37120 + 3.57194I 0
u = −0.833264 − 0.468989I
a = −0.481761 − 0.814515I
b = −1.350000 − 0.031703I
1.37120 − 3.57194I 0
u = 0.785879 + 0.517921I
a = 0.504803 + 0.816321I
b = 1.361010 + 0.150128I
1.55196 + 1.85604I 0
u = 0.785879 − 0.517921I
a = 0.504803 − 0.816321I
b = 1.361010 − 0.150128I
1.55196 − 1.85604I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.921369
a = 1.14442
b = 1.76452
−3.14048 0
u = 0.941710 + 0.530939I
a = −1.091830 − 0.862514I
b = −1.00896 + 1.08502I
3.99006 + 8.76786I 0
u = 0.941710 − 0.530939I
a = −1.091830 + 0.862514I
b = −1.00896 − 1.08502I
3.99006 − 8.76786I 0
u = 0.465741 + 0.983160I
a = 1.42474 − 0.17082I
b = 1.038660 − 0.084011I
−3.47260 + 4.47855I 0
u = 0.465741 − 0.983160I
a = 1.42474 + 0.17082I
b = 1.038660 + 0.084011I
−3.47260 − 4.47855I 0
u = 0.910313 + 0.030662I
a = −0.115819 − 0.906180I
b = 0.615448 + 0.407124I
1.46568 + 0.43178I 0
u = 0.910313 − 0.030662I
a = −0.115819 + 0.906180I
b = 0.615448 − 0.407124I
1.46568 − 0.43178I 0
u = 0.885847 + 0.205046I
a = −1.11298 − 0.88899I
b = −1.33628 + 0.72164I
1.31135 + 1.25389I 0
u = 0.885847 − 0.205046I
a = −1.11298 + 0.88899I
b = −1.33628 − 0.72164I
1.31135 − 1.25389I 0
u = 1.086360 + 0.116517I
a = 0.035013 + 0.516038I
b = 0.885902 − 0.829996I
2.98971 + 0.94847I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.086360 − 0.116517I
a = 0.035013 − 0.516038I
b = 0.885902 + 0.829996I
2.98971 − 0.94847I 0
u = −1.066830 + 0.244598I
a = 1.21273 − 1.16451I
b = 1.105170 + 0.598534I
1.54996 − 5.14937I 0
u = −1.066830 − 0.244598I
a = 1.21273 + 1.16451I
b = 1.105170 − 0.598534I
1.54996 + 5.14937I 0
u = −0.898348 + 0.070569I
a = 1.075500 − 0.494864I
b = 1.65418 + 0.50089I
0.62635 − 5.91693I 0
u = −0.898348 − 0.070569I
a = 1.075500 + 0.494864I
b = 1.65418 − 0.50089I
0.62635 + 5.91693I 0
u = −0.965308 + 0.528116I
a = 1.070340 − 0.856967I
b = 0.95027 + 1.08029I
4.24976 − 3.00059I 0
u = −0.965308 − 0.528116I
a = 1.070340 + 0.856967I
b = 0.95027 − 1.08029I
4.24976 + 3.00059I 0
u = −1.090420 + 0.156147I
a = −0.131377 + 0.486924I
b = −1.074270 − 0.867636I
2.02042 − 6.23432I 0
u = −1.090420 − 0.156147I
a = −0.131377 − 0.486924I
b = −1.074270 + 0.867636I
2.02042 + 6.23432I 0
u = 1.106460 + 0.094367I
a = −1.97773 − 1.38977I
b = −0.993385 + 0.393640I
8.69249 + 0.96192I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.106460 − 0.094367I
a = −1.97773 + 1.38977I
b = −0.993385 − 0.393640I
8.69249 − 0.96192I 0
u = 1.071220 + 0.326687I
a = −0.670886 − 0.787907I
b = 0.118526 + 0.756860I
6.62998 + 0.44766I 0
u = 1.071220 − 0.326687I
a = −0.670886 + 0.787907I
b = 0.118526 − 0.756860I
6.62998 − 0.44766I 0
u = −1.117830 + 0.106521I
a = 1.85098 − 1.49346I
b = 0.986138 + 0.434205I
8.52486 − 7.18622I 0
u = −1.117830 − 0.106521I
a = 1.85098 + 1.49346I
b = 0.986138 − 0.434205I
8.52486 + 7.18622I 0
u = 0.534383 + 0.689920I
a = 0.478682 + 0.686201I
b = 1.160460 + 0.697958I
2.82278 − 4.08425I 0
u = 0.534383 − 0.689920I
a = 0.478682 − 0.686201I
b = 1.160460 − 0.697958I
2.82278 + 4.08425I 0
u = −1.067680 + 0.371245I
a = 0.733164 − 0.800903I
b = −0.003651 + 0.784977I
6.42520 − 6.45218I 0
u = −1.067680 − 0.371245I
a = 0.733164 + 0.800903I
b = −0.003651 − 0.784977I
6.42520 + 6.45218I 0
u = 0.620487 + 0.589256I
a = 0.548489 + 0.759148I
b = 1.217960 + 0.436850I
−1.83228 − 1.08155I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.620487 − 0.589256I
a = 0.548489 − 0.759148I
b = 1.217960 − 0.436850I
−1.83228 + 1.08155I 0
u = −1.045130 + 0.469194I
a = 0.946605 − 0.934179I
b = 0.788954 + 0.736081I
0.47688 − 4.49237I 0
u = −1.045130 − 0.469194I
a = 0.946605 + 0.934179I
b = 0.788954 − 0.736081I
0.47688 + 4.49237I 0
u = −0.502135 + 0.687224I
a = −0.472241 + 0.657894I
b = −1.092990 + 0.722258I
2.92596 − 1.65726I 0
u = −0.502135 − 0.687224I
a = −0.472241 − 0.657894I
b = −1.092990 − 0.722258I
2.92596 + 1.65726I 0
u = −0.435982 + 0.722667I
a = −1.396900 − 0.103093I
b = −0.943841 + 0.061516I
−1.65126 + 0.13326I 0
u = −0.435982 − 0.722667I
a = −1.396900 + 0.103093I
b = −0.943841 − 0.061516I
−1.65126 − 0.13326I 0
u = 0.256758 + 0.792899I
a = −1.52637 − 0.60838I
b = −0.400374 − 0.677480I
7.42361 + 0.98363I 0
u = 0.256758 − 0.792899I
a = −1.52637 + 0.60838I
b = −0.400374 + 0.677480I
7.42361 − 0.98363I 0
u = 0.158435 + 0.811000I
a = 1.58987 − 0.20219I
b = 1.186190 + 0.129187I
−5.85707 − 1.88338I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.158435 − 0.811000I
a = 1.58987 + 0.20219I
b = 1.186190 − 0.129187I
−5.85707 + 1.88338I 0
u = 0.110570 + 1.195880I
a = −1.335490 − 0.397774I
b = −1.073010 − 0.594550I
5.53142 − 5.95429I 0
u = 0.110570 − 1.195880I
a = −1.335490 + 0.397774I
b = −1.073010 + 0.594550I
5.53142 + 5.95429I 0
u = −0.089749 + 1.201270I
a = 1.339290 − 0.390590I
b = 1.122270 − 0.584605I
4.52673 + 12.24300I 0
u = −0.089749 − 1.201270I
a = 1.339290 + 0.390590I
b = 1.122270 + 0.584605I
4.52673 − 12.24300I 0
u = −1.118870 + 0.449295I
a = 0.878072 − 1.027960I
b = 0.920268 + 0.556646I
0.54978 − 4.62144I 0
u = −1.118870 − 0.449295I
a = 0.878072 + 1.027960I
b = 0.920268 − 0.556646I
0.54978 + 4.62144I 0
u = −0.745220 + 0.204465I
a = 0.07001 − 1.44950I
b = −0.394495 + 0.100817I
−0.32061 − 3.50677I 0
u = −0.745220 − 0.204465I
a = 0.07001 + 1.44950I
b = −0.394495 − 0.100817I
−0.32061 + 3.50677I 0
u = −0.728800 + 0.172451I
a = 1.41642 − 2.53956I
b = −0.269398 − 0.042175I
6.73042 − 6.79692I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728800 − 0.172451I
a = 1.41642 + 2.53956I
b = −0.269398 + 0.042175I
6.73042 + 6.79692I 0
u = −0.223887 + 0.712552I
a = 1.63558 − 0.63068I
b = 0.283171 − 0.714554I
6.85744 − 7.23141I 0
u = −0.223887 − 0.712552I
a = 1.63558 + 0.63068I
b = 0.283171 + 0.714554I
6.85744 + 7.23141I 0
u = 0.315325 + 1.215630I
a = −1.272500 − 0.456206I
b = −0.851784 − 0.462480I
1.67897 − 1.92022I 0
u = 0.315325 − 1.215630I
a = −1.272500 + 0.456206I
b = −0.851784 + 0.462480I
1.67897 + 1.92022I 0
u = 0.713232 + 0.155152I
a = −1.72331 − 2.33254I
b = 0.267307 − 0.045218I
7.03336 + 0.58707I 0
u = 0.713232 − 0.155152I
a = −1.72331 + 2.33254I
b = 0.267307 + 0.045218I
7.03336 − 0.58707I 0
u = 1.284030 + 0.310582I
a = −0.0338741 + 0.0205357I
b = −0.258211 − 1.200890I
4.42676 + 6.00018I 0
u = 1.284030 − 0.310582I
a = −0.0338741 − 0.0205357I
b = −0.258211 + 1.200890I
4.42676 − 6.00018I 0
u = −0.030399 + 0.678002I
a = 1.82967 − 0.36505I
b = 1.264820 + 0.355903I
−0.64284 − 7.09594I −5.07346 + 6.77744I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.030399 − 0.678002I
a = 1.82967 + 0.36505I
b = 1.264820 − 0.355903I
−0.64284 + 7.09594I −5.07346 − 6.77744I
u = 1.175060 + 0.609769I
a = −0.762664 − 0.880020I
b = −0.872464 + 0.252078I
−1.06435 + 1.29725I 0
u = 1.175060 − 0.609769I
a = −0.762664 + 0.880020I
b = −0.872464 − 0.252078I
−1.06435 − 1.29725I 0
u = −1.272320 + 0.367407I
a = 0.68412 − 1.26924I
b = 1.135280 + 0.549511I
3.93987 − 5.23803I 0
u = −1.272320 − 0.367407I
a = 0.68412 + 1.26924I
b = 1.135280 − 0.549511I
3.93987 + 5.23803I 0
u = 1.269610 + 0.394723I
a = 0.0409520 − 0.0525356I
b = −0.50725 − 1.32126I
11.1187 + 11.2500I 0
u = 1.269610 − 0.394723I
a = 0.0409520 + 0.0525356I
b = −0.50725 + 1.32126I
11.1187 − 11.2500I 0
u = −0.427878 + 0.513104I
a = −0.835560 + 0.459521I
b = −0.854553 + 0.377787I
−1.286080 + 0.455261I −7.70736 + 1.32907I
u = −0.427878 − 0.513104I
a = −0.835560 − 0.459521I
b = −0.854553 − 0.377787I
−1.286080 − 0.455261I −7.70736 − 1.32907I
u = 1.250100 + 0.466607I
a = −0.683965 − 1.073830I
b = −1.075790 + 0.420354I
−2.44640 + 6.61908I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.250100 − 0.466607I
a = −0.683965 + 1.073830I
b = −1.075790 − 0.420354I
−2.44640 − 6.61908I 0
u = −0.158795 + 1.330380I
a = 1.283370 − 0.378700I
b = 1.006120 − 0.419750I
−2.71266 + 5.78701I 0
u = −0.158795 − 1.330380I
a = 1.283370 + 0.378700I
b = 1.006120 + 0.419750I
−2.71266 − 5.78701I 0
u = 1.290630 + 0.383162I
a = −0.637761 − 1.244490I
b = −1.159890 + 0.528856I
3.39980 + 11.12530I 0
u = 1.290630 − 0.383162I
a = −0.637761 + 1.244490I
b = −1.159890 − 0.528856I
3.39980 − 11.12530I 0
u = −1.289890 + 0.395097I
a = −0.0207285 − 0.0679971I
b = 0.524654 − 1.259980I
11.90370 − 5.14638I 0
u = −1.289890 − 0.395097I
a = −0.0207285 + 0.0679971I
b = 0.524654 + 1.259980I
11.90370 + 5.14638I 0
u = −1.217590 + 0.670566I
a = −1.61163 + 0.39154I
b = −0.946882 − 0.528758I
9.26360 + 1.80665I 0
u = −1.217590 − 0.670566I
a = −1.61163 − 0.39154I
b = −0.946882 + 0.528758I
9.26360 − 1.80665I 0
u = −0.030368 + 0.608580I
a = −0.032047 + 0.352615I
b = −0.059994 + 0.820870I
3.49662 + 2.89047I −0.32814 − 2.83025I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.030368 − 0.608580I
a = −0.032047 − 0.352615I
b = −0.059994 − 0.820870I
3.49662 − 2.89047I −0.32814 + 2.83025I
u = −1.368090 + 0.313616I
a = 0.1135650 − 0.0396663I
b = 0.356367 − 0.956192I
7.68279 − 2.73588I 0
u = −1.368090 − 0.313616I
a = 0.1135650 + 0.0396663I
b = 0.356367 + 0.956192I
7.68279 + 2.73588I 0
u = 1.397660 + 0.141411I
a = −0.261924 + 0.078658I
b = 0.047609 − 0.650115I
4.27409 − 0.09782I 0
u = 1.397660 − 0.141411I
a = −0.261924 − 0.078658I
b = 0.047609 + 0.650115I
4.27409 + 0.09782I 0
u = −0.001739 + 0.590856I
a = −1.99205 − 0.28236I
b = −1.178080 + 0.395962I
0.06673 + 1.46934I −3.77347 − 1.94821I
u = −0.001739 − 0.590856I
a = −1.99205 + 0.28236I
b = −1.178080 − 0.395962I
0.06673 − 1.46934I −3.77347 + 1.94821I
u = −0.584488 + 1.282970I
a = 1.156800 − 0.490604I
b = 0.794712 − 0.304872I
−1.74040 − 2.72976I 0
u = −0.584488 − 1.282970I
a = 1.156800 + 0.490604I
b = 0.794712 + 0.304872I
−1.74040 + 2.72976I 0
u = 1.25413 + 0.65584I
a = 1.56004 + 0.46546I
b = 0.982720 − 0.572883I
10.07250 + 4.68382I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.25413 − 0.65584I
a = 1.56004 − 0.46546I
b = 0.982720 + 0.572883I
10.07250 − 4.68382I 0
u = 1.43785 + 0.04048I
a = −0.535512 − 0.137324I
b = 0.713551 + 0.400227I
9.48279 + 3.64685I 0
u = 1.43785 − 0.04048I
a = −0.535512 + 0.137324I
b = 0.713551 − 0.400227I
9.48279 − 3.64685I 0
u = 0.553209 + 0.067349I
a = −1.098260 − 0.704150I
b = 0.358204 − 0.037734I
1.291040 + 0.409621I 6.92214 − 0.12402I
u = 0.553209 − 0.067349I
a = −1.098260 + 0.704150I
b = 0.358204 + 0.037734I
1.291040 − 0.409621I 6.92214 + 0.12402I
u = −1.45221 + 0.03510I
a = 0.549371 − 0.108937I
b = −0.751998 + 0.326051I
9.62150 + 2.15278I 0
u = −1.45221 − 0.03510I
a = 0.549371 + 0.108937I
b = −0.751998 − 0.326051I
9.62150 − 2.15278I 0
u = −0.370734 + 0.393926I
a = −0.429653 − 0.083886I
b = −0.494247 + 0.281919I
−1.210000 + 0.364522I −7.31156 − 0.42344I
u = −0.370734 − 0.393926I
a = −0.429653 + 0.083886I
b = −0.494247 − 0.281919I
−1.210000 − 0.364522I −7.31156 + 0.42344I
u = −1.46400
a = 0.528721
b = −0.689013
5.43041 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36214 + 0.59920I
a = 1.23814 + 0.71467I
b = 1.24462 − 0.77204I
9.5011 + 12.2560I 0
u = 1.36214 − 0.59920I
a = 1.23814 − 0.71467I
b = 1.24462 + 0.77204I
9.5011 − 12.2560I 0
u = −1.36570 + 0.59786I
a = −1.211510 + 0.722450I
b = −1.27196 − 0.77970I
8.5561 − 18.5437I 0
u = −1.36570 − 0.59786I
a = −1.211510 − 0.722450I
b = −1.27196 + 0.77970I
8.5561 + 18.5437I 0
u = 1.35288 + 0.63179I
a = 1.30740 + 0.57713I
b = 1.176410 − 0.646957I
5.19449 + 8.54254I 0
u = 1.35288 − 0.63179I
a = 1.30740 − 0.57713I
b = 1.176410 + 0.646957I
5.19449 − 8.54254I 0
u = −1.37309 + 0.61522I
a = −1.212770 + 0.607975I
b = −1.26327 − 0.66728I
1.28295 − 12.44340I 0
u = −1.37309 − 0.61522I
a = −1.212770 − 0.607975I
b = −1.26327 + 0.66728I
1.28295 + 12.44340I 0
u = −1.36625 + 0.67954I
a = −1.304500 + 0.449717I
b = −1.166820 − 0.541799I
1.26955 − 4.49210I 0
u = −1.36625 − 0.67954I
a = −1.304500 − 0.449717I
b = −1.166820 + 0.541799I
1.26955 + 4.49210I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55952
a = −0.369842
b = −0.107026
4.40346 0
u = −1.53003 + 0.40063I
a = 0.239958 − 0.198517I
b = 0.672186 − 0.604197I
11.05410 − 0.02645I 0
u = −1.53003 − 0.40063I
a = 0.239958 + 0.198517I
b = 0.672186 + 0.604197I
11.05410 + 0.02645I 0
u = −0.392255 + 0.133279I
a = 1.09057 − 2.12779I
b = −0.415248 − 0.317817I
−0.33314 − 3.44474I −1.95232 + 7.26627I
u = −0.392255 − 0.133279I
a = 1.09057 + 2.12779I
b = −0.415248 + 0.317817I
−0.33314 + 3.44474I −1.95232 − 7.26627I
u = 1.57828 + 0.43033I
a = −0.289281 − 0.232214I
b = −0.729025 − 0.506644I
9.98593 − 6.02268I 0
u = 1.57828 − 0.43033I
a = −0.289281 + 0.232214I
b = −0.729025 + 0.506644I
9.98593 + 6.02268I 0
17
II.
I
u
2
= h−2.86 × 10
8
u
28
− 4.95 × 10
8
u
27
+ · · · + 1.12 × 10
8
b + 6.76 × 10
7
, −8.17 ×
10
8
u
28
− 1.34 × 10
9
u
27
+ · · · + 1.12 × 10
8
a + 5.59 × 10
8
, u
29
+ u
28
+ · · · − u + 1 i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
7.28533u
28
+ 11.9246u
27
+ ··· + 3.04539u − 4.98598
2.55331u
28
+ 4.41341u
27
+ ··· + 3.99911u − 0.603396
a
10
=
4.73202u
28
+ 7.51120u
27
+ ··· − 0.953725u − 4.38258
2.55331u
28
+ 4.41341u
27
+ ··· + 3.99911u − 0.603396
a
7
=
−2.17231u
28
− 4.24622u
27
+ ··· − 0.543133u + 11.1661
u
27
+ u
26
+ ··· + 2u
2
+ u
a
1
=
u
−u
3
+ u
a
4
=
0.603396u
28
+ 2.15671u
27
+ ··· − 1.36969u + 3.39572
−3.77918u
28
− 10.9579u
27
+ ··· − 5.34944u + 8.73202
a
8
=
−4.46408u
28
− 9.63668u
27
+ ··· − 7.21401u + 7.77398
−1.75545u
28
− 0.547472u
27
+ ··· + 10.0792u − 0.00136247
a
11
=
5.73202u
28
+ 8.51120u
27
+ ··· − 0.953725u − 4.38258
2.55331u
28
+ 4.41341u
27
+ ··· + 4.99911u − 0.603396
a
3
=
−1.71156u
28
− 2.73546u
27
+ ··· − 0.661777u + 6.75592
−1.91908u
28
− 6.68368u
27
+ ··· − 4.39953u + 8.17871
a
2
=
−8.68370u
28
− 14.2212u
27
+ ··· − 0.542786u + 6.59926
2.44891u
28
− 0.130150u
27
+ ··· − 11.8599u + 2.56577
(ii) Obstruction class = 1
(iii) Cusp Shapes =
101871452
22418005
u
28
+
257938703
22418005
u
27
+ ··· +
351259376
22418005
u −
510075814
22418005
18
(iv) u-Polynomials at the component
19
Crossings u-Polynomials at each crossing
c
1
u
29
− 10u
28
+ ··· + 10u − 1
c
2
u
29
− 2u
28
+ ··· − 2u + 1
c
3
u
29
+ 2u
28
+ ··· − 10u
2
+ 1
c
4
u
29
− 10u
27
+ ··· + 2u + 1
c
5
u
29
+ u
28
+ ··· − u + 1
c
6
u
29
− 5u
28
+ ··· − 3u − 1
c
7
u
29
+ 2u
28
+ ··· − 2u − 1
c
8
u
29
+ 10u
28
+ ··· + 10u + 1
c
9
u
29
− 10u
27
+ ··· + 2u − 1
c
10
u
29
+ 10u
28
+ ··· − 12u − 1
c
11
u
29
− 2u
28
+ ··· + 10u
2
− 1
c
12
u
29
− u
28
+ ··· − u − 1
20
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
29
+ 26y
28
+ ··· − 6y −1
c
2
, c
7
y
29
− 10y
28
+ ··· + 10y −1
c
3
, c
11
y
29
− 28y
28
+ ··· + 20y −1
c
4
, c
9
y
29
− 20y
28
+ ··· + 28y −1
c
5
, c
12
y
29
− 17y
28
+ ··· + 7y −1
c
6
y
29
− y
28
+ ··· + 17y −1
c
10
y
29
+ 2y
27
+ ··· + 12y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.717329 + 0.639076I
a = 0.835365 + 0.632972I
b = 0.944147 + 0.381573I
−0.49913 − 1.32873I −0.11938 + 3.61914I
u = 0.717329 − 0.639076I
a = 0.835365 − 0.632972I
b = 0.944147 − 0.381573I
−0.49913 + 1.32873I −0.11938 − 3.61914I
u = 0.971101 + 0.390171I
a = −1.06836 − 1.27741I
b = −0.831437 + 0.726843I
0.14499 + 5.23557I −2.62383 − 11.25511I
u = 0.971101 − 0.390171I
a = −1.06836 + 1.27741I
b = −0.831437 − 0.726843I
0.14499 − 5.23557I −2.62383 + 11.25511I
u = 0.219513 + 1.090680I
a = −1.54205 + 0.42138I
b = −0.972784 + 0.254874I
−2.51265 + 4.70394I −0.95489 − 4.11722I
u = 0.219513 − 1.090680I
a = −1.54205 − 0.42138I
b = −0.972784 − 0.254874I
−2.51265 − 4.70394I −0.95489 + 4.11722I
u = 1.068400 + 0.338347I
a = −0.669211 − 0.895117I
b = −1.03410 + 0.97557I
2.25935 + 2.55675I 0.21907 − 3.50060I
u = 1.068400 − 0.338347I
a = −0.669211 + 0.895117I
b = −1.03410 − 0.97557I
2.25935 − 2.55675I 0.21907 + 3.50060I
u = 0.787446 + 0.344627I
a = −2.41393 − 1.87520I
b = −0.674591 + 0.430681I
6.61601 + 7.49632I 0.75406 − 11.77555I
u = 0.787446 − 0.344627I
a = −2.41393 + 1.87520I
b = −0.674591 − 0.430681I
6.61601 − 7.49632I 0.75406 + 11.77555I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.110140 + 0.349021I
a = 0.724328 − 0.749361I
b = 1.16818 + 0.92442I
1.89518 − 7.59700I 0.23689 + 9.81031I
u = −1.110140 − 0.349021I
a = 0.724328 + 0.749361I
b = 1.16818 − 0.92442I
1.89518 + 7.59700I 0.23689 − 9.81031I
u = −0.741037 + 0.349545I
a = 2.75181 − 1.61634I
b = 0.698318 + 0.378783I
6.79683 − 1.24647I 0.17790 + 6.35109I
u = −0.741037 − 0.349545I
a = 2.75181 + 1.61634I
b = 0.698318 − 0.378783I
6.79683 + 1.24647I 0.17790 − 6.35109I
u = −1.077370 + 0.524252I
a = 1.179200 − 0.687396I
b = 1.075340 + 0.596166I
−0.46459 − 3.20098I −3.62932 + 1.91041I
u = −1.077370 − 0.524252I
a = 1.179200 + 0.687396I
b = 1.075340 − 0.596166I
−0.46459 + 3.20098I −3.62932 − 1.91041I
u = 0.701084 + 0.230911I
a = 0.353519 + 0.284777I
b = 1.37458 + 0.58598I
0.823771 + 0.029925I −2.16055 − 2.77865I
u = 0.701084 − 0.230911I
a = 0.353519 − 0.284777I
b = 1.37458 − 0.58598I
0.823771 − 0.029925I −2.16055 + 2.77865I
u = −0.709684 + 0.161413I
a = −0.259884 + 0.183138I
b = −1.58614 + 0.56071I
0.08985 + 5.26986I −5.32900 − 1.52833I
u = −0.709684 − 0.161413I
a = −0.259884 − 0.183138I
b = −1.58614 − 0.56071I
0.08985 − 5.26986I −5.32900 + 1.52833I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.682387 + 1.121540I
a = −1.015240 + 0.547779I
b = −0.918132 + 0.262247I
−2.34299 − 2.57657I −7.69899 + 0.14437I
u = −0.682387 − 1.121540I
a = −1.015240 − 0.547779I
b = −0.918132 − 0.262247I
−2.34299 + 2.57657I −7.69899 − 0.14437I
u = −1.399970 + 0.152116I
a = 0.361293 + 0.773973I
b = −0.529293 + 0.096178I
9.65667 − 1.04707I 3.49346 − 0.44914I
u = −1.399970 − 0.152116I
a = 0.361293 − 0.773973I
b = −0.529293 − 0.096178I
9.65667 + 1.04707I 3.49346 + 0.44914I
u = −1.41919
a = 0.677909
b = −0.520773
5.72976 16.4330
u = 1.41200 + 0.20655I
a = −0.106841 + 0.820821I
b = 0.551900 + 0.121988I
9.15952 − 4.90987I 1.56419 + 4.39302I
u = 1.41200 − 0.20655I
a = −0.106841 − 0.820821I
b = 0.551900 − 0.121988I
9.15952 + 4.90987I 1.56419 − 4.39302I
u = 0.053312 + 0.478165I
a = 1.53105 + 1.74843I
b = 0.994390 + 0.198323I
0.055929 − 0.701152I −0.646183 + 0.411566I
u = 0.053312 − 0.478165I
a = 1.53105 − 1.74843I
b = 0.994390 − 0.198323I
0.055929 + 0.701152I −0.646183 − 0.411566I
25
III. I
u
3
= hb − u + 1, a, u
2
− u − 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u − 1
a
9
=
0
u − 1
a
10
=
−u + 1
u − 1
a
7
=
u
−2u
a
1
=
u
−u − 1
a
4
=
1
u − 2
a
8
=
u
−u − 1
a
11
=
−u
2u − 1
a
3
=
−u
2u
a
2
=
0
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −13
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u − 1)
2
c
2
, c
6
, c
8
(u + 1)
2
c
3
, c
5
, c
9
u
2
− u − 1
c
4
, c
10
, c
11
c
12
u
2
+ u − 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
(y −1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
c
12
y
2
− 3y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 0
b = −1.61803
−3.94784 −13.0000
u = 1.61803
a = 0
b = 0.618034
3.94784 −13.0000
29
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
29
− 10u
28
+ ··· + 10u − 1)
· (u
127
+ 39u
126
+ ··· + 1944u + 81)
c
2
((u + 1)
2
)(u
29
− 2u
28
+ ··· − 2u + 1)(u
127
+ u
126
+ ··· + 18u − 9)
c
3
(u
2
− u − 1)(u
29
+ 2u
28
+ ··· − 10u
2
+ 1)
· (u
127
− 2u
126
+ ··· − 91249u + 90319)
c
4
(u
2
+ u − 1)(u
29
− 10u
27
+ ··· + 2u + 1)(u
127
+ 2u
126
+ ··· − 15u − 1)
c
5
(u
2
− u − 1)(u
29
+ u
28
+ ··· − u + 1)(u
127
+ u
126
+ ··· − 6672u − 1153)
c
6
((u + 1)
2
)(u
29
− 5u
28
+ ··· − 3u − 1)
· (u
127
− 2u
126
+ ··· − 934469u + 281173)
c
7
((u − 1)
2
)(u
29
+ 2u
28
+ ··· − 2u − 1)(u
127
+ u
126
+ ··· + 18u − 9)
c
8
((u + 1)
2
)(u
29
+ 10u
28
+ ··· + 10u + 1)
· (u
127
+ 39u
126
+ ··· + 1944u + 81)
c
9
(u
2
− u − 1)(u
29
− 10u
27
+ ··· + 2u − 1)(u
127
+ 2u
126
+ ··· − 15u − 1)
c
10
(u
2
+ u − 1)(u
29
+ 10u
28
+ ··· − 12u − 1)
· (u
127
+ 6u
126
+ ··· + 1248715953u + 143741087)
c
11
(u
2
+ u − 1)(u
29
− 2u
28
+ ··· + 10u
2
− 1)
· (u
127
− 2u
126
+ ··· − 91249u + 90319)
c
12
(u
2
+ u − 1)(u
29
− u
28
+ ··· − u − 1)(u
127
+ u
126
+ ··· − 6672u − 1153)
30
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
((y −1)
2
)(y
29
+ 26y
28
+ ··· − 6y −1)
· (y
127
+ 109y
126
+ ··· + 84564y −6561)
c
2
, c
7
((y −1)
2
)(y
29
− 10y
28
+ ··· + 10y −1)
· (y
127
− 39y
126
+ ··· + 1944y −81)
c
3
, c
11
(y
2
− 3y + 1)(y
29
− 28y
28
+ ··· + 20y −1)
· (y
127
− 106y
126
+ ··· + 204122256495y −8157521761)
c
4
, c
9
(y
2
− 3y + 1)(y
29
− 20y
28
+ ··· + 28y −1)
· (y
127
− 66y
126
+ ··· + 191y −1)
c
5
, c
12
(y
2
− 3y + 1)(y
29
− 17y
28
+ ··· + 7y −1)
· (y
127
− 83y
126
+ ··· + 49166786y −1329409)
c
6
((y −1)
2
)(y
29
− y
28
+ ··· + 17y −1)
· (y
127
+ 22y
126
+ ··· − 2134776124149y −79058255929)
c
10
(y
2
− 3y + 1)(y
29
+ 2y
27
+ ··· + 12y −1)
· (y
127
− 58y
126
+ ··· + 427269195188756631y −20661500091941569)
31
