12a
0058
(K12a
0058
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 8 4 12 11 6 1 9
Solving Sequence
8,12
9
1,4
7 3 2 6 11 10 5
c
8
c
12
c
7
c
3
c
1
c
6
c
11
c
9
c
5
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h9.29564 × 10
38
u
113
− 6.51435 × 10
39
u
112
+ ··· + 2.60710 × 10
37
b − 7.95403 × 10
38
,
− 7.77552 × 10
38
u
113
+ 6.00866 × 10
39
u
112
+ ··· + 2.60710 × 10
37
a + 1.51982 × 10
39
,
u
114
− 8u
113
+ ··· − 8u + 1i
I
u
2
= h−a
5
+ a
4
− 2a
2
+ b + a + 1, a
6
− a
5
+ 2a
3
− a
2
− a + 1, u + 1i
I
u
3
= hb, u
3
− u
2
+ a + 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 126 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
= h9.30 × 10
38
u
113
− 6.51 × 10
39
u
112
+ · · · + 2.61 × 10
37
b − 7.95 ×
10
38
, −7.78 × 10
38
u
113
+ 6.01 × 10
39
u
112
+ · · · + 2.61 × 10
37
a + 1.52 ×
10
39
, u
114
− 8u
113
+ · · · − 8u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
29.8244u
113
− 230.473u
112
+ ··· + 370.662u − 58.2952
−35.6550u
113
+ 249.869u
112
+ ··· − 225.591u + 30.5091
a
7
=
13.8635u
113
− 108.058u
112
+ ··· + 140.743u − 18.9405
19.6275u
113
− 116.224u
112
+ ··· − 51.7393u + 12.4153
a
3
=
0.00677419u
113
− 12.2366u
112
+ ··· + 63.7165u − 10.4574
13.4820u
113
− 101.626u
112
+ ··· + 177.807u − 30.9627
a
2
=
−1.32665u
113
+ 18.2745u
112
+ ··· − 88.4400u + 16.7723
16.0974u
113
− 99.1423u
112
+ ··· − 25.0868u + 8.27723
a
6
=
−5.76401u
113
+ 8.16502u
112
+ ··· + 192.482u − 31.3558
19.6275u
113
− 116.224u
112
+ ··· − 51.7393u + 12.4153
a
11
=
−u
3
u
5
− u
3
+ u
a
10
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
5
=
9.56619u
113
− 88.7065u
112
+ ··· + 213.455u − 33.7200
25.0853u
113
− 158.460u
112
+ ··· + 15.0149u + 1.68646
(ii) Obstruction class = −1
(iii) Cusp Shapes = −164.292u
113
+ 1202.16u
112
+ ··· − 1572.01u + 235.414
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
114
+ 60u
113
+ ··· + 8u + 1
c
2
, c
4
u
114
− 8u
113
+ ··· − 8u + 1
c
3
, c
7
u
114
− 2u
113
+ ··· + 128u + 64
c
5
, c
10
u
114
+ 2u
113
+ ··· − 128u + 64
c
6
u
114
− 42u
113
+ ··· − 90112u + 4096
c
8
, c
12
u
114
+ 8u
113
+ ··· + 8u + 1
c
9
u
114
+ 42u
113
+ ··· + 90112u + 4096
c
11
u
114
− 60u
113
+ ··· − 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
114
− 4y
113
+ ··· + 48y + 1
c
2
, c
4
, c
8
c
12
y
114
− 60y
113
+ ··· − 8y + 1
c
3
, c
5
, c
7
c
10
y
114
− 42y
113
+ ··· − 90112y + 4096
c
6
, c
9
y
114
+ 50y
113
+ ··· + 293601280y + 16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.723700 + 0.681601I
a = −0.935060 + 0.862964I
b = −0.772810 + 0.697186I
−3.83704 − 0.08668I 0
u = 0.723700 − 0.681601I
a = −0.935060 − 0.862964I
b = −0.772810 − 0.697186I
−3.83704 + 0.08668I 0
u = −0.967248 + 0.093961I
a = −0.96783 + 3.05389I
b = 0.226395 + 0.373089I
− 0.435079I 0
u = −0.967248 − 0.093961I
a = −0.96783 − 3.05389I
b = 0.226395 − 0.373089I
0.435079I 0
u = 0.772974 + 0.688687I
a = −0.21472 + 2.21715I
b = 0.794096 + 0.777168I
−7.43467 + 1.22279I 0
u = 0.772974 − 0.688687I
a = −0.21472 − 2.21715I
b = 0.794096 − 0.777168I
−7.43467 − 1.22279I 0
u = −0.866381 + 0.399593I
a = 1.06508 − 0.95635I
b = 0.719217 + 0.040027I
1.63180 − 1.59965I 0
u = −0.866381 − 0.399593I
a = 1.06508 + 0.95635I
b = 0.719217 − 0.040027I
1.63180 + 1.59965I 0
u = 0.730439 + 0.751713I
a = 1.24130 − 0.87403I
b = 0.935189 − 0.716306I
−6.98083 − 4.42168I 0
u = 0.730439 − 0.751713I
a = 1.24130 + 0.87403I
b = 0.935189 + 0.716306I
−6.98083 + 4.42168I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.802021 + 0.683914I
a = 0.92321 − 1.20148I
b = 0.750774 − 0.844212I
−7.35083 + 3.98370I 0
u = 0.802021 − 0.683914I
a = 0.92321 + 1.20148I
b = 0.750774 + 0.844212I
−7.35083 − 3.98370I 0
u = 0.840115 + 0.666403I
a = 0.03898 − 1.90015I
b = −0.887151 − 0.687186I
−3.50334 + 5.22185I 0
u = 0.840115 − 0.666403I
a = 0.03898 + 1.90015I
b = −0.887151 + 0.687186I
−3.50334 − 5.22185I 0
u = 0.249242 + 0.890697I
a = 0.43449 − 1.60639I
b = 1.097690 − 0.748696I
−2.84667 − 12.56330I 0
u = 0.249242 − 0.890697I
a = 0.43449 + 1.60639I
b = 1.097690 + 0.748696I
−2.84667 + 12.56330I 0
u = 0.367954 + 0.843012I
a = 0.920709 + 0.994829I
b = 0.827172 + 0.610541I
−4.89808 + 1.22960I 0
u = 0.367954 − 0.843012I
a = 0.920709 − 0.994829I
b = 0.827172 − 0.610541I
−4.89808 − 1.22960I 0
u = 0.235886 + 0.861061I
a = −0.25004 + 1.40871I
b = −1.071350 + 0.632728I
− 7.33738I 0
u = 0.235886 − 0.861061I
a = −0.25004 − 1.40871I
b = −1.071350 − 0.632728I
7.33738I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.992093 + 0.503554I
a = −1.56593 + 0.29438I
b = −0.878195 − 0.570695I
−0.31630 + 1.75012I 0
u = −0.992093 − 0.503554I
a = −1.56593 − 0.29438I
b = −0.878195 + 0.570695I
−0.31630 − 1.75012I 0
u = 0.262214 + 0.844204I
a = 0.60579 + 1.47194I
b = 0.637492 + 0.960815I
−4.30895 − 6.29751I 0
u = 0.262214 − 0.844204I
a = 0.60579 − 1.47194I
b = 0.637492 − 0.960815I
−4.30895 + 6.29751I 0
u = 0.493882 + 0.731210I
a = −0.770646 − 0.071170I
b = −0.635005 + 0.056742I
−2.73938 − 1.31927I 0
u = 0.493882 − 0.731210I
a = −0.770646 + 0.071170I
b = −0.635005 − 0.056742I
−2.73938 + 1.31927I 0
u = 0.859146 + 0.715227I
a = 0.21037 + 2.02103I
b = 0.985504 + 0.741469I
−6.60278 + 9.89815I 0
u = 0.859146 − 0.715227I
a = 0.21037 − 2.02103I
b = 0.985504 − 0.741469I
−6.60278 − 9.89815I 0
u = 0.279400 + 0.824018I
a = −0.20354 − 1.64945I
b = 0.871980 − 0.608933I
−4.75639 − 3.57361I 0
u = 0.279400 − 0.824018I
a = −0.20354 + 1.64945I
b = 0.871980 + 0.608933I
−4.75639 + 3.57361I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.083270 + 0.372897I
a = 0.530579 + 0.134326I
b = −1.157820 + 0.644547I
2.62178 − 4.12294I 0
u = 1.083270 − 0.372897I
a = 0.530579 − 0.134326I
b = −1.157820 − 0.644547I
2.62178 + 4.12294I 0
u = −1.077570 + 0.400780I
a = 1.070290 + 0.186942I
b = 0.316024 + 0.715565I
2.29165 − 1.37776I 0
u = −1.077570 − 0.400780I
a = 1.070290 − 0.186942I
b = 0.316024 − 0.715565I
2.29165 + 1.37776I 0
u = 1.077400 + 0.437537I
a = 0.566780 − 0.717840I
b = −0.436454 − 0.980206I
0.31630 + 1.75012I 0
u = 1.077400 − 0.437537I
a = 0.566780 + 0.717840I
b = −0.436454 + 0.980206I
0.31630 − 1.75012I 0
u = 0.803613 + 0.228737I
a = 1.047630 − 0.693013I
b = −1.123060 − 0.498549I
1.13197 + 6.36472I 0
u = 0.803613 − 0.228737I
a = 1.047630 + 0.693013I
b = −1.123060 + 0.498549I
1.13197 − 6.36472I 0
u = −1.074570 + 0.459541I
a = 1.51045 + 2.47993I
b = −0.828823 + 0.560918I
−0.48420 − 2.77068I 0
u = −1.074570 − 0.459541I
a = 1.51045 − 2.47993I
b = −0.828823 − 0.560918I
−0.48420 + 2.77068I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.102360 + 0.407324I
a = −0.726243 + 0.007110I
b = 1.153230 − 0.476793I
4.89808 + 1.22960I 0
u = 1.102360 − 0.407324I
a = −0.726243 − 0.007110I
b = 1.153230 + 0.476793I
4.89808 − 1.22960I 0
u = 1.078660 + 0.469830I
a = 1.371390 + 0.222317I
b = −0.870912 + 0.324334I
−0.56892 + 4.18783I 0
u = 1.078660 − 0.469830I
a = 1.371390 − 0.222317I
b = −0.870912 − 0.324334I
−0.56892 − 4.18783I 0
u = −1.136940 + 0.308088I
a = 0.773292 + 0.500000I
b = −0.173577 + 0.728658I
2.51437 − 0.99262I 0
u = −1.136940 − 0.308088I
a = 0.773292 − 0.500000I
b = −0.173577 − 0.728658I
2.51437 + 0.99262I 0
u = 0.285946 + 0.770073I
a = −0.362338 − 1.160650I
b = −0.457760 − 0.768380I
−1.75813 − 2.05566I 0
u = 0.285946 − 0.770073I
a = −0.362338 + 1.160650I
b = −0.457760 + 0.768380I
−1.75813 + 2.05566I 0
u = −1.180940 + 0.074914I
a = 0.688027 + 0.286846I
b = −0.756451 + 0.227484I
2.65024 − 0.27372I 0
u = −1.180940 − 0.074914I
a = 0.688027 − 0.286846I
b = −0.756451 − 0.227484I
2.65024 + 0.27372I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.093160 + 0.476720I
a = −1.45067 − 0.23492I
b = −0.596430 − 0.942263I
− 5.38564I 0
u = −1.093160 − 0.476720I
a = −1.45067 + 0.23492I
b = −0.596430 + 0.942263I
5.38564I 0
u = 1.039270 + 0.592880I
a = −0.306327 − 0.686797I
b = −0.659067 − 0.153585I
−1.13197 + 6.36472I 0
u = 1.039270 − 0.592880I
a = −0.306327 + 0.686797I
b = −0.659067 + 0.153585I
−1.13197 − 6.36472I 0
u = 1.111060 + 0.488310I
a = −0.618644 + 0.545233I
b = 0.113358 + 0.922536I
1.63283 + 5.97986I 0
u = 1.111060 − 0.488310I
a = −0.618644 − 0.545233I
b = 0.113358 − 0.922536I
1.63283 − 5.97986I 0
u = 0.112316 + 0.777931I
a = −0.169940 + 0.169777I
b = −1.184200 + 0.189445I
3.50334 − 5.22185I 0
u = 0.112316 − 0.777931I
a = −0.169940 − 0.169777I
b = −1.184200 − 0.189445I
3.50334 + 5.22185I 0
u = −1.118210 + 0.487349I
a = −1.06729 − 2.29249I
b = 1.074660 − 0.591684I
4.30895 − 6.29751I 0
u = −1.118210 − 0.487349I
a = −1.06729 + 2.29249I
b = 1.074660 + 0.591684I
4.30895 + 6.29751I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.112460 + 0.513795I
a = 0.93605 + 2.47485I
b = −1.102230 + 0.723986I
1.58968 − 11.50070I 0
u = −1.112460 − 0.513795I
a = 0.93605 − 2.47485I
b = −1.102230 − 0.723986I
1.58968 + 11.50070I 0
u = −1.201280 + 0.247663I
a = −1.152390 + 0.563096I
b = 0.767573 + 0.527208I
0.272373I 0
u = −1.201280 − 0.247663I
a = −1.152390 − 0.563096I
b = 0.767573 − 0.527208I
− 0.272373I 0
u = −0.542849 + 0.528773I
a = −1.57978 + 1.93900I
b = −0.962080 + 0.625550I
−1.63283 − 5.97986I 0. + 7.47175I
u = −0.542849 − 0.528773I
a = −1.57978 − 1.93900I
b = −0.962080 − 0.625550I
−1.63283 + 5.97986I 0. − 7.47175I
u = −1.183430 + 0.418904I
a = −0.99759 − 1.35347I
b = 1.195410 − 0.132152I
7.35083 − 3.98370I 0
u = −1.183430 − 0.418904I
a = −0.99759 + 1.35347I
b = 1.195410 + 0.132152I
7.35083 + 3.98370I 0
u = 1.164170 + 0.471096I
a = −0.952649 + 0.792236I
b = 1.256620 − 0.010633I
6.98083 + 4.42168I 0
u = 1.164170 − 0.471096I
a = −0.952649 − 0.792236I
b = 1.256620 + 0.010633I
6.98083 − 4.42168I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.231530 + 0.267297I
a = −0.652314 − 0.692358I
b = 0.566387 − 0.913964I
0.48420 + 2.77068I 0
u = −1.231530 − 0.267297I
a = −0.652314 + 0.692358I
b = 0.566387 + 0.913964I
0.48420 − 2.77068I 0
u = −1.208070 + 0.381842I
a = 0.934726 + 0.877986I
b = −1.191400 − 0.091961I
7.43467 + 1.22279I 0
u = −1.208070 − 0.381842I
a = 0.934726 − 0.877986I
b = −1.191400 + 0.091961I
7.43467 − 1.22279I 0
u = −1.259790 + 0.151116I
a = −0.453722 − 0.495795I
b = 0.930686 − 0.572922I
0.56892 − 4.18783I 0
u = −1.259790 − 0.151116I
a = −0.453722 + 0.495795I
b = 0.930686 + 0.572922I
0.56892 + 4.18783I 0
u = 1.146980 + 0.550556I
a = −0.862666 + 0.240336I
b = −0.415566 + 0.872115I
0.78347 + 7.01604I 0
u = 1.146980 − 0.550556I
a = −0.862666 − 0.240336I
b = −0.415566 − 0.872115I
0.78347 − 7.01604I 0
u = 0.708510 + 0.148960I
a = −1.35933 + 0.48672I
b = 1.111470 + 0.264109I
2.73938 + 1.31927I −1.08879 − 3.18259I
u = 0.708510 − 0.148960I
a = −1.35933 − 0.48672I
b = 1.111470 − 0.264109I
2.73938 − 1.31927I −1.08879 + 3.18259I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.179660 + 0.499614I
a = 0.98803 − 1.15818I
b = −1.258320 − 0.199748I
6.60278 + 9.89815I 0
u = 1.179660 − 0.499614I
a = 0.98803 + 1.15818I
b = −1.258320 + 0.199748I
6.60278 − 9.89815I 0
u = 1.130540 + 0.604539I
a = 0.949298 + 0.166912I
b = 0.771487 − 0.575515I
−2.62178 + 4.12294I 0
u = 1.130540 − 0.604539I
a = 0.949298 − 0.166912I
b = 0.771487 + 0.575515I
−2.62178 − 4.12294I 0
u = 0.043874 + 0.715470I
a = 0.118213 + 0.516293I
b = 1.163740 + 0.031232I
3.83704 − 0.08668I 3.19246 − 0.21288I
u = 0.043874 − 0.715470I
a = 0.118213 − 0.516293I
b = 1.163740 − 0.031232I
3.83704 + 0.08668I 3.19246 + 0.21288I
u = −1.252610 + 0.293273I
a = 0.694772 − 0.089576I
b = −1.066810 − 0.557995I
4.75639 + 3.57361I 0
u = −1.252610 − 0.293273I
a = 0.694772 + 0.089576I
b = −1.066810 + 0.557995I
4.75639 − 3.57361I 0
u = 1.161810 + 0.566216I
a = −1.36434 + 1.96940I
b = 0.923398 + 0.578213I
−2.13189 + 8.72336I 0
u = 1.161810 − 0.566216I
a = −1.36434 − 1.96940I
b = 0.923398 − 0.578213I
−2.13189 − 8.72336I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.594019 + 0.381064I
a = 1.28558 − 1.88876I
b = 0.773477 − 0.453418I
0.86516 − 1.74421I 1.98893 + 4.15175I
u = −0.594019 − 0.381064I
a = 1.28558 + 1.88876I
b = 0.773477 + 0.453418I
0.86516 + 1.74421I 1.98893 − 4.15175I
u = 1.173890 + 0.567584I
a = 1.066740 − 0.224177I
b = 0.626275 − 1.004470I
−1.58968 + 11.50070I 0
u = 1.173890 − 0.567584I
a = 1.066740 + 0.224177I
b = 0.626275 + 1.004470I
−1.58968 − 11.50070I 0
u = −1.279690 + 0.278425I
a = −0.474167 + 0.231706I
b = 1.098150 + 0.703496I
2.13189 + 8.72336I 0
u = −1.279690 − 0.278425I
a = −0.474167 − 0.231706I
b = 1.098150 − 0.703496I
2.13189 − 8.72336I 0
u = −0.280100 + 0.626448I
a = −0.85214 − 2.21498I
b = −1.069570 − 0.680380I
−0.78347 + 7.01604I −1.35162 − 4.29219I
u = −0.280100 − 0.626448I
a = −0.85214 + 2.21498I
b = −1.069570 + 0.680380I
−0.78347 − 7.01604I −1.35162 + 4.29219I
u = 1.187900 + 0.563780I
a = 1.05519 − 1.90418I
b = −1.113560 − 0.642684I
2.84667 + 12.56330I 0
u = 1.187900 − 0.563780I
a = 1.05519 + 1.90418I
b = −1.113560 + 0.642684I
2.84667 − 12.56330I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.195030 + 0.577493I
a = −0.97359 + 2.03917I
b = 1.122560 + 0.759008I
17.9257I 0
u = 1.195030 − 0.577493I
a = −0.97359 − 2.03917I
b = 1.122560 − 0.759008I
− 17.9257I 0
u = 0.541744 + 0.285983I
a = −0.328702 + 0.342755I
b = −0.260966 + 0.836171I
−1.63180 + 1.59965I −5.07271 − 4.39349I
u = 0.541744 − 0.285983I
a = −0.328702 − 0.342755I
b = −0.260966 − 0.836171I
−1.63180 − 1.59965I −5.07271 + 4.39349I
u = 0.200162 + 0.577888I
a = 0.501858 − 1.063660I
b = 0.020575 − 0.802253I
−0.86516 − 1.74421I −1.98893 + 4.15175I
u = 0.200162 − 0.577888I
a = 0.501858 + 1.063660I
b = 0.020575 + 0.802253I
−0.86516 + 1.74421I −1.98893 − 4.15175I
u = −0.194270 + 0.576839I
a = 0.44846 + 2.07334I
b = 1.015950 + 0.510772I
1.75813 + 2.05566I 2.13493 − 0.69938I
u = −0.194270 − 0.576839I
a = 0.44846 − 2.07334I
b = 1.015950 − 0.510772I
1.75813 − 2.05566I 2.13493 + 0.69938I
u = 0.363103 + 0.434065I
a = 2.22430 − 1.23554I
b = −0.689865 − 0.172565I
−2.65024 − 0.27372I −1.41619 − 2.36703I
u = 0.363103 − 0.434065I
a = 2.22430 + 1.23554I
b = −0.689865 + 0.172565I
−2.65024 + 0.27372I −1.41619 + 2.36703I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395058 + 0.375841I
a = −0.58757 − 2.99479I
b = −0.658172 − 0.651342I
−2.51437 − 0.99262I −4.03287 + 1.09288I
u = −0.395058 − 0.375841I
a = −0.58757 + 2.99479I
b = −0.658172 + 0.651342I
−2.51437 + 0.99262I −4.03287 − 1.09288I
u = −0.265974 + 0.454743I
a = −1.50142 + 2.01612I
b = −0.568952 + 0.818115I
−2.29165 + 1.37776I −3.68469 − 0.12674I
u = −0.265974 − 0.454743I
a = −1.50142 − 2.01612I
b = −0.568952 − 0.818115I
−2.29165 − 1.37776I −3.68469 + 0.12674I
16
II. I
u
2
= h−a
5
+ a
4
− 2a
2
+ b + a + 1, a
6
− a
5
+ 2a
3
− a
2
− a + 1, u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
−1
a
9
=
1
−1
a
1
=
−1
0
a
4
=
a
a
5
− a
4
+ 2a
2
− a − 1
a
7
=
0
−a
5
+ a
3
− 2a
2
− a + 2
a
3
=
a
−a
5
− a
2
− a
a
2
=
a
5
− a
3
+ 2a
2
+ a − 2
−2a
5
+ a
3
− 3a
2
− a + 2
a
6
=
a
5
− a
3
+ 2a
2
+ a − 2
−a
5
+ a
3
− 2a
2
− a + 2
a
11
=
1
−1
a
10
=
1
−1
a
5
=
a
5
− a
3
+ 2a
2
+ a − 2
−a
5
+ a
3
− 2a
2
− a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3a
5
+ a
3
+ 6a
2
− 2a + 3
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
, c
9
, c
10
u
6
c
6
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
8
, c
11
(u + 1)
6
c
12
(u − 1)
6
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
7
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
5
, c
9
, c
10
y
6
c
8
, c
11
, c
12
(y −1)
6
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.917982 + 0.270708I
b = 1.002190 + 0.295542I
3.53554 + 0.92430I 8.55174 − 0.47256I
u = −1.00000
a = −0.917982 − 0.270708I
b = 1.002190 − 0.295542I
3.53554 − 0.92430I 8.55174 + 0.47256I
u = −1.00000
a = 0.732786 + 0.381252I
b = −1.073950 + 0.558752I
1.64493 − 5.69302I 3.10838 + 3.92918I
u = −1.00000
a = 0.732786 − 0.381252I
b = −1.073950 − 0.558752I
1.64493 + 5.69302I 3.10838 − 3.92918I
u = −1.00000
a = 0.685196 + 1.063260I
b = −0.428243 + 0.664531I
−0.245672 + 0.924305I −1.66012 − 2.42665I
u = −1.00000
a = 0.685196 − 1.063260I
b = −0.428243 − 0.664531I
−0.245672 − 0.924305I −1.66012 + 2.42665I
20
III. I
u
3
= hb, u
3
− u
2
+ a + 1, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−u
3
+ u
2
− 1
0
a
7
=
1
0
a
3
=
−u
3
+ u
2
− 1
0
a
2
=
−u
3
+ u
2
+ u − 1
−u
3
+ u
a
6
=
1
0
a
11
=
−u
3
u
5
− u
3
+ u
a
10
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
5
=
−u
u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
4
+ 2u
3
+ 5u
2
− 6u − 5
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
6
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
12
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
8
, c
10
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
9
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
11
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
, c
7
y
6
c
5
, c
8
, c
10
c
12
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
9
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 0.66103 − 1.45708I
b = 0
0.245672 − 0.924305I 1.66012 + 2.42665I
u = −1.002190 − 0.295542I
a = 0.66103 + 1.45708I
b = 0
0.245672 + 0.924305I 1.66012 − 2.42665I
u = 0.428243 + 0.664531I
a = −0.769407 + 0.497010I
b = 0
−3.53554 − 0.92430I −8.55174 + 0.47256I
u = 0.428243 − 0.664531I
a = −0.769407 − 0.497010I
b = 0
−3.53554 + 0.92430I −8.55174 − 0.47256I
u = 1.073950 + 0.558752I
a = −0.391622 − 0.558752I
b = 0
−1.64493 + 5.69302I −3.10838 − 3.92918I
u = 1.073950 − 0.558752I
a = −0.391622 + 0.558752I
b = 0
−1.64493 − 5.69302I −3.10838 + 3.92918I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
114
+ 60u
113
+ ··· + 8u + 1)
c
2
((u − 1)
6
)(u
6
+ u
5
+ ··· + u + 1)(u
114
− 8u
113
+ ··· − 8u + 1)
c
3
u
6
(u
6
− u
5
+ ··· − u + 1)(u
114
− 2u
113
+ ··· + 128u + 64)
c
4
((u + 1)
6
)(u
6
− u
5
+ ··· − u + 1)(u
114
− 8u
113
+ ··· − 8u + 1)
c
5
u
6
(u
6
+ u
5
+ ··· + u + 1)(u
114
+ 2u
113
+ ··· − 128u + 64)
c
6
u
6
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
114
− 42u
113
+ ··· − 90112u + 4096)
c
7
u
6
(u
6
+ u
5
+ ··· + u + 1)(u
114
− 2u
113
+ ··· + 128u + 64)
c
8
((u + 1)
6
)(u
6
− u
5
+ ··· − u + 1)(u
114
+ 8u
113
+ ··· + 8u + 1)
c
9
u
6
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
114
+ 42u
113
+ ··· + 90112u + 4096)
c
10
u
6
(u
6
− u
5
+ ··· − u + 1)(u
114
+ 2u
113
+ ··· − 128u + 64)
c
11
(u + 1)
6
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
114
− 60u
113
+ ··· − 8u + 1)
c
12
((u − 1)
6
)(u
6
+ u
5
+ ··· + u + 1)(u
114
+ 8u
113
+ ··· + 8u + 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
((y −1)
6
)(y
6
+ y
5
+ ··· + 3y + 1)(y
114
− 4y
113
+ ··· + 48y + 1)
c
2
, c
4
, c
8
c
12
(y −1)
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
114
− 60y
113
+ ··· − 8y + 1)
c
3
, c
5
, c
7
c
10
y
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
114
− 42y
113
+ ··· − 90112y + 4096)
c
6
, c
9
y
6
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
114
+ 50y
113
+ ··· + 293601280y + 16777216)
26
