12n
0869
(K12n
0869
)
A knot diagram
1
Linearized knot diagam
4 6 12 11 8 2 10 1 6 5 2 9
Solving Sequence
1,4 2,9
8 12 3 11 5 6 7 10
c
1
c
8
c
12
c
3
c
11
c
4
c
5
c
6
c
10
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.67975 × 10
46
u
38
− 3.90240 × 10
46
u
37
+ ··· + 3.59901 × 10
48
b + 1.25329 × 10
48
,
2.81649 × 10
48
u
38
+ 3.45577 × 10
48
u
37
+ ··· + 4.40879 × 10
49
a − 4.18324 × 10
48
, u
39
+ u
38
+ ··· + 30u − 14i
I
u
2
= h−3.36074 × 10
194
u
63
− 8.92084 × 10
194
u
62
+ ··· + 3.64648 × 10
194
b − 7.25439 × 10
195
,
− 6.74789 × 10
193
u
63
− 1.33622 × 10
194
u
62
+ ··· + 7.29297 × 10
194
a − 8.82411 × 10
193
,
u
64
+ 3u
63
+ ··· − 4u + 8i
I
u
3
= h−3.66786 × 10
26
u
23
+ 2.73754 × 10
27
u
22
+ ··· + 1.22821 × 10
25
b + 4.47903 × 10
27
,
− 4.10017 × 10
27
u
23
+ 3.02216 × 10
28
u
22
+ ··· + 8.59744 × 10
25
a + 4.48658 × 10
28
,
u
24
− 8u
23
+ ··· − 70u + 7i
I
u
4
= h−u
5
+ u
4
− u
2
+ b + 1, u
5
− u
4
+ u
2
+ a, u
6
− u
5
+ 2u
3
− u + 1i
I
u
5
= h−u
4
+ 4u
3
− 4u
2
+ b + 1, −u
5
+ 6u
4
− 11u
3
+ 6u
2
+ 2a − u, u
6
− 6u
5
+ 11u
4
− 4u
3
− 5u
2
+ 2u + 2i
* 5 irreducible components of dim
C
= 0, with total 139 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−3.68 × 10
46
u
38
− 3.90 × 10
46
u
37
+ · · · + 3.60 × 10
48
b + 1.25 ×
10
48
, 2.82 × 10
48
u
38
+ 3.46 × 10
48
u
37
+ · · · + 4.41 × 10
49
a − 4.18 ×
10
48
, u
39
+ u
38
+ · · · + 30u − 14i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
−0.0638836u
38
− 0.0783836u
37
+ ··· + 6.35623u + 0.0948842
0.0102244u
38
+ 0.0108430u
37
+ ··· − 1.45245u − 0.348231
a
8
=
−0.0536593u
38
− 0.0675406u
37
+ ··· + 4.90378u − 0.253347
0.0102244u
38
+ 0.0108430u
37
+ ··· − 1.45245u − 0.348231
a
12
=
−0.0313510u
38
− 0.00602783u
37
+ ··· + 4.96444u − 1.10367
0.00245578u
38
− 0.00214837u
37
+ ··· − 1.62023u + 0.291758
a
3
=
0.00526533u
38
− 0.0380235u
37
+ ··· − 0.721536u + 3.89543
−0.00646705u
38
+ 0.00362817u
37
+ ··· + 1.41883u − 1.00701
a
11
=
−0.0408173u
38
− 0.0178341u
37
+ ··· + 4.54283u − 1.16643
−0.0000418849u
38
− 0.000707613u
37
+ ··· − 1.68255u + 0.258997
a
5
=
0.0191976u
38
− 0.00946661u
37
+ ··· − 2.44735u + 3.14453
−0.0138813u
38
− 0.00112472u
37
+ ··· + 1.35643u − 0.751230
a
6
=
0.0330789u
38
− 0.00834188u
37
+ ··· − 3.80378u + 3.89576
−0.0144999u
38
+ 0.00138800u
37
+ ··· + 2.01139u − 0.894371
a
7
=
0.0412254u
38
+ 0.00641291u
37
+ ··· − 3.49811u + 3.58128
−0.0161200u
38
+ 0.000315430u
37
+ ··· + 1.92720u − 0.801856
a
10
=
0.0421366u
38
+ 0.120763u
37
+ ··· − 0.319502u − 4.70818
0.00470461u
38
− 0.0208136u
37
+ ··· − 1.77613u + 1.38625
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.201895u
38
− 0.184513u
37
+ ··· + 13.2872u − 8.60911
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
39
− u
38
+ ··· + 30u + 14
c
2
, c
6
u
39
− 4u
38
+ ··· + 338u + 250
c
3
, c
9
7(7u
39
− 23u
38
+ ··· + 3790u + 397)
c
4
, c
10
7(7u
39
− 9u
38
+ ··· + 704u + 128)
c
7
, c
11
u
39
− 2u
38
+ ··· − 256u + 112
c
8
, c
12
u
39
+ 3u
38
+ ··· + 144u + 26
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
39
− 5y
38
+ ··· + 508y −196
c
2
, c
6
y
39
− 26y
38
+ ··· + 1469244y −62500
c
3
, c
9
49(49y
39
+ 1473y
38
+ ··· + 1541000y −157609)
c
4
, c
10
49(49y
39
+ 885y
38
+ ··· + 167936y −16384)
c
7
, c
11
y
39
+ 18y
38
+ ··· − 65280y −12544
c
8
, c
12
y
39
+ 23y
38
+ ··· + 1392y −676
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.381563 + 0.926690I
a = −0.14741 − 1.42857I
b = 0.47478 + 1.47845I
9.75422 − 0.22436I 4.24092 − 0.06868I
u = −0.381563 − 0.926690I
a = −0.14741 + 1.42857I
b = 0.47478 − 1.47845I
9.75422 + 0.22436I 4.24092 + 0.06868I
u = 0.215256 + 0.903029I
a = 0.317687 + 0.450207I
b = 1.333880 − 0.292850I
−3.37895 − 1.11916I −6.71537 + 6.25818I
u = 0.215256 − 0.903029I
a = 0.317687 − 0.450207I
b = 1.333880 + 0.292850I
−3.37895 + 1.11916I −6.71537 − 6.25818I
u = 0.917716 + 0.575117I
a = −0.152269 − 0.405561I
b = −0.719237 + 0.977922I
−3.37369 − 0.44904I −6.52041 + 1.93090I
u = 0.917716 − 0.575117I
a = −0.152269 + 0.405561I
b = −0.719237 − 0.977922I
−3.37369 + 0.44904I −6.52041 − 1.93090I
u = 0.699403 + 0.556885I
a = 0.518684 + 0.096121I
b = 0.472369 − 0.181298I
−0.91086 − 1.79017I −2.80280 + 6.23617I
u = 0.699403 − 0.556885I
a = 0.518684 − 0.096121I
b = 0.472369 + 0.181298I
−0.91086 + 1.79017I −2.80280 − 6.23617I
u = −0.779933 + 0.820657I
a = −0.118076 + 0.420776I
b = 1.099400 + 0.118017I
4.74644 + 5.48396I −1.77561 − 5.39681I
u = −0.779933 − 0.820657I
a = −0.118076 − 0.420776I
b = 1.099400 − 0.118017I
4.74644 − 5.48396I −1.77561 + 5.39681I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.204110 + 0.288939I
a = −1.18779 − 0.84508I
b = 0.155560 + 1.078100I
7.44242 − 0.75014I −6.49122 − 1.47517I
u = −1.204110 − 0.288939I
a = −1.18779 + 0.84508I
b = 0.155560 − 1.078100I
7.44242 + 0.75014I −6.49122 + 1.47517I
u = −0.688870 + 0.136185I
a = −1.224570 − 0.143786I
b = −0.736776 + 0.868265I
−1.58257 + 2.78797I −3.07729 − 3.24624I
u = −0.688870 − 0.136185I
a = −1.224570 + 0.143786I
b = −0.736776 − 0.868265I
−1.58257 − 2.78797I −3.07729 + 3.24624I
u = 1.142330 + 0.620428I
a = −0.730432 + 0.151211I
b = −0.501259 − 0.114342I
−4.62069 − 5.39762I −8.35878 + 5.66526I
u = 1.142330 − 0.620428I
a = −0.730432 − 0.151211I
b = −0.501259 + 0.114342I
−4.62069 + 5.39762I −8.35878 − 5.66526I
u = 1.142510 + 0.628521I
a = −0.864650 + 0.458202I
b = −0.482270 − 0.570367I
−4.57295 − 5.51103I −8.91990 + 5.09219I
u = 1.142510 − 0.628521I
a = −0.864650 − 0.458202I
b = −0.482270 + 0.570367I
−4.57295 + 5.51103I −8.91990 − 5.09219I
u = −0.543197 + 1.207720I
a = 0.184124 + 0.980020I
b = −0.34670 − 1.76350I
6.72679 + 4.10592I 0. − 4.04035I
u = −0.543197 − 1.207720I
a = 0.184124 − 0.980020I
b = −0.34670 + 1.76350I
6.72679 − 4.10592I 0. + 4.04035I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.958594 + 0.924625I
a = 0.98980 + 1.44113I
b = 0.60517 − 1.32684I
8.4720 + 11.5395I −0.99707 − 7.84282I
u = −0.958594 − 0.924625I
a = 0.98980 − 1.44113I
b = 0.60517 + 1.32684I
8.4720 − 11.5395I −0.99707 + 7.84282I
u = −1.004680 + 0.940267I
a = −0.082278 − 0.283040I
b = −1.41652 − 0.13516I
0.20771 + 11.31300I −4.80272 − 7.49455I
u = −1.004680 − 0.940267I
a = −0.082278 + 0.283040I
b = −1.41652 + 0.13516I
0.20771 − 11.31300I −4.80272 + 7.49455I
u = −0.985001 + 0.972060I
a = 0.767766 + 1.016360I
b = −0.102004 − 1.296790I
6.36005 − 2.77187I −3.05581 + 2.62484I
u = −0.985001 − 0.972060I
a = 0.767766 − 1.016360I
b = −0.102004 + 1.296790I
6.36005 + 2.77187I −3.05581 − 2.62484I
u = −0.200200 + 0.572516I
a = 1.70301 − 0.18917I
b = −0.220388 − 0.392976I
1.45570 − 1.51861I 4.04545 + 0.43743I
u = −0.200200 − 0.572516I
a = 1.70301 + 0.18917I
b = −0.220388 + 0.392976I
1.45570 + 1.51861I 4.04545 − 0.43743I
u = 0.66362 + 1.25439I
a = 0.192642 − 1.214670I
b = 0.354197 + 1.305910I
0.92156 − 6.68525I −7.23472 + 7.95810I
u = 0.66362 − 1.25439I
a = 0.192642 + 1.214670I
b = 0.354197 − 1.305910I
0.92156 + 6.68525I −7.23472 − 7.95810I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.08738 + 1.00044I
a = 0.786836 − 1.127920I
b = 0.299996 + 1.227280I
2.31687 − 4.92337I 1.27355 + 1.21908I
u = 1.08738 − 1.00044I
a = 0.786836 + 1.127920I
b = 0.299996 − 1.227280I
2.31687 + 4.92337I 1.27355 − 1.21908I
u = 0.138711 + 0.396343I
a = 0.59039 + 5.18828I
b = −0.372749 − 0.989227I
1.78029 − 1.83280I −12.0868 + 10.8163I
u = 0.138711 − 0.396343I
a = 0.59039 − 5.18828I
b = −0.372749 + 0.989227I
1.78029 + 1.83280I −12.0868 − 10.8163I
u = 1.38806 + 0.78702I
a = −0.871934 + 1.031450I
b = −0.354934 − 1.319140I
−0.20142 − 9.10069I 0. + 6.60524I
u = 1.38806 − 0.78702I
a = −0.871934 − 1.031450I
b = −0.354934 + 1.319140I
−0.20142 + 9.10069I 0. − 6.60524I
u = −1.29140 + 0.99260I
a = −0.808947 − 1.125780I
b = −0.66663 + 1.44205I
4.4225 + 18.5144I 0
u = −1.29140 − 0.99260I
a = −0.808947 + 1.125780I
b = −0.66663 − 1.44205I
4.4225 − 18.5144I 0
u = 0.285108
a = 1.07076
b = −0.751755
−1.19853 −5.08320
8
II. I
u
2
= h−3.36 × 10
194
u
63
− 8.92 × 10
194
u
62
+ · · · + 3.65 × 10
194
b − 7.25 ×
10
195
, −6.75 × 10
193
u
63
− 1.34 × 10
194
u
62
+ · · · + 7.29 × 10
194
a − 8.82 ×
10
193
, u
64
+ 3u
63
+ · · · − 4u + 8i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
0.0925260u
63
+ 0.183221u
62
+ ··· + 18.9131u + 0.120995
0.921637u
63
+ 2.44642u
62
+ ··· − 64.8386u + 19.8942
a
8
=
1.01416u
63
+ 2.62964u
62
+ ··· − 45.9255u + 20.0152
0.921637u
63
+ 2.44642u
62
+ ··· − 64.8386u + 19.8942
a
12
=
−0.397732u
63
− 1.12402u
62
+ ··· + 58.4066u − 10.9114
−1.83192u
63
− 4.71054u
62
+ ··· + 88.6071u − 34.2118
a
3
=
0.0634086u
63
+ 0.178584u
62
+ ··· − 6.51378u + 3.34814
−0.551562u
63
− 1.42402u
62
+ ··· + 15.6615u − 8.04679
a
11
=
−2.20658u
63
− 5.78972u
62
+ ··· + 143.555u − 44.5698
−2.13061u
63
− 5.49360u
62
+ ··· + 106.121u − 40.2985
a
5
=
−0.311343u
63
− 0.637742u
62
+ ··· − 34.6103u + 4.87894
0.0177322u
63
+ 0.195921u
62
+ ··· − 38.6360u + 7.30043
a
6
=
0.614335u
63
+ 1.75383u
62
+ ··· − 69.6491u + 19.7599
−0.488015u
63
− 1.30063u
62
+ ··· + 26.8103u − 9.30122
a
7
=
0.134912u
63
+ 0.474640u
62
+ ··· − 37.5674u + 9.74525
−0.536387u
63
− 1.43131u
62
+ ··· + 31.2820u − 10.5739
a
10
=
1.42624u
63
+ 3.50879u
62
+ ··· − 18.5106u + 18.6991
0.774717u
63
+ 2.02597u
62
+ ··· − 37.7653u + 13.6468
(ii) Obstruction class = −1
(iii) Cusp Shapes = 9.79898u
63
+ 24.5723u
62
+ ··· − 364.680u + 147.102
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
64
− 3u
63
+ ··· + 4u + 8
c
2
, c
6
(u
32
+ 3u
31
+ ··· − 197u − 17)
2
c
3
, c
9
u
64
− 5u
62
+ ··· − 151551u + 109156
c
4
, c
10
(u
32
+ 9u
30
+ ··· − 159u − 39)
2
c
7
, c
11
u
64
− 13u
63
+ ··· − 14192u + 1088
c
8
, c
12
(u
32
− u
31
+ ··· + 15u − 43)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
64
− 35y
63
+ ··· − 6000y + 64
c
2
, c
6
(y
32
− 23y
31
+ ··· − 11065y + 289)
2
c
3
, c
9
y
64
− 10y
63
+ ··· − 162341142769y + 11915032336
c
4
, c
10
(y
32
+ 18y
31
+ ··· − 1335y + 1521)
2
c
7
, c
11
y
64
− 19y
63
+ ··· − 30831872y + 1183744
c
8
, c
12
(y
32
+ 29y
31
+ ··· + 37013y + 1849)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.962163 + 0.307932I
a = 1.023170 + 0.750197I
b = −0.159347 + 1.088400I
2.79274 + 0.13431I 0
u = 0.962163 − 0.307932I
a = 1.023170 − 0.750197I
b = −0.159347 − 1.088400I
2.79274 − 0.13431I 0
u = 0.567766 + 0.841359I
a = −0.190788 + 1.398060I
b = −0.51244 − 1.54462I
4.76515 − 4.52869I 0
u = 0.567766 − 0.841359I
a = −0.190788 − 1.398060I
b = −0.51244 + 1.54462I
4.76515 + 4.52869I 0
u = −0.835940 + 0.661381I
a = 1.33252 + 1.70530I
b = 0.431770 − 1.307820I
8.30164 + 4.57817I 0
u = −0.835940 − 0.661381I
a = 1.33252 − 1.70530I
b = 0.431770 + 1.307820I
8.30164 − 4.57817I 0
u = −0.852457 + 0.644467I
a = 0.121717 + 0.824750I
b = 0.837919
4.27386 0
u = −0.852457 − 0.644467I
a = 0.121717 − 0.824750I
b = 0.837919
4.27386 0
u = 0.304243 + 0.870445I
a = 0.10646 − 1.95520I
b = −0.092714 + 1.263860I
3.20379 + 2.62478I 0
u = 0.304243 − 0.870445I
a = 0.10646 + 1.95520I
b = −0.092714 − 1.263860I
3.20379 − 2.62478I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.057070 + 0.257547I
a = 0.723741 − 0.991040I
b = 0.085775 − 0.685758I
−7.23053 + 1.36356I 0
u = −1.057070 − 0.257547I
a = 0.723741 + 0.991040I
b = 0.085775 + 0.685758I
−7.23053 − 1.36356I 0
u = −0.830673 + 0.245387I
a = 0.942042 − 0.010162I
b = 0.773851 − 0.896847I
−4.87430 + 7.62655I 4.31752 − 8.08508I
u = −0.830673 − 0.245387I
a = 0.942042 + 0.010162I
b = 0.773851 + 0.896847I
−4.87430 − 7.62655I 4.31752 + 8.08508I
u = 1.138500 + 0.231412I
a = 0.635480 + 0.873812I
b = 0.159878 + 1.184480I
0.75589 − 7.24896I 0
u = 1.138500 − 0.231412I
a = 0.635480 − 0.873812I
b = 0.159878 − 1.184480I
0.75589 + 7.24896I 0
u = −0.717888 + 0.402459I
a = −0.002746 − 0.413003I
b = −1.255360 + 0.575196I
−0.07972 + 4.30514I −8.18803 − 7.69807I
u = −0.717888 − 0.402459I
a = −0.002746 + 0.413003I
b = −1.255360 − 0.575196I
−0.07972 − 4.30514I −8.18803 + 7.69807I
u = 0.613650 + 0.497367I
a = −0.74700 − 1.34855I
b = −0.137426 + 0.889581I
−3.31895 + 0.38088I −5.16361 − 0.66528I
u = 0.613650 − 0.497367I
a = −0.74700 + 1.34855I
b = −0.137426 − 0.889581I
−3.31895 − 0.38088I −5.16361 + 0.66528I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.553469 + 1.089310I
a = −0.39672 − 1.79627I
b = −0.159347 + 1.088400I
2.79274 + 0.13431I 0
u = −0.553469 − 1.089310I
a = −0.39672 + 1.79627I
b = −0.159347 − 1.088400I
2.79274 − 0.13431I 0
u = 0.078535 + 0.684285I
a = 1.50952 + 2.16696I
b = −0.247516 − 0.737755I
1.63215 − 1.59930I 8.69923 + 5.57276I
u = 0.078535 − 0.684285I
a = 1.50952 − 2.16696I
b = −0.247516 + 0.737755I
1.63215 + 1.59930I 8.69923 − 5.57276I
u = 0.781902 + 1.082280I
a = −0.237406 + 1.366770I
b = −0.092714 − 1.263860I
3.20379 − 2.62478I 0
u = 0.781902 − 1.082280I
a = −0.237406 − 1.366770I
b = −0.092714 + 1.263860I
3.20379 + 2.62478I 0
u = −1.227480 + 0.548653I
a = 0.017111 − 0.166181I
b = 0.067014 + 0.530835I
−1.69750 + 6.00434I 0
u = −1.227480 − 0.548653I
a = 0.017111 + 0.166181I
b = 0.067014 − 0.530835I
−1.69750 − 6.00434I 0
u = −0.984891 + 0.940001I
a = −0.59554 − 1.37878I
b = −0.41680 + 1.48230I
6.29446 + 9.80876I 0
u = −0.984891 − 0.940001I
a = −0.59554 + 1.37878I
b = −0.41680 − 1.48230I
6.29446 − 9.80876I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.358390 + 0.208893I
a = −0.156424 + 0.051080I
b = −0.137426 − 0.889581I
−3.31895 − 0.38088I 0
u = 1.358390 − 0.208893I
a = −0.156424 − 0.051080I
b = −0.137426 + 0.889581I
−3.31895 + 0.38088I 0
u = −1.06126 + 0.95614I
a = −0.316580 − 0.936481I
b = 0.431770 + 1.307820I
8.30164 − 4.57817I 0
u = −1.06126 − 0.95614I
a = −0.316580 + 0.936481I
b = 0.431770 − 1.307820I
8.30164 + 4.57817I 0
u = 0.379181 + 0.402833I
a = 4.91958 + 1.55487I
b = 0.067014 − 0.530835I
−1.69750 − 6.00434I −0.30980 − 1.55337I
u = 0.379181 − 0.402833I
a = 4.91958 − 1.55487I
b = 0.067014 + 0.530835I
−1.69750 + 6.00434I −0.30980 + 1.55337I
u = −1.22729 + 0.77360I
a = −0.644581 − 0.481013I
b = −1.255360 − 0.575196I
−0.07972 − 4.30514I 0
u = −1.22729 − 0.77360I
a = −0.644581 + 0.481013I
b = −1.255360 + 0.575196I
−0.07972 + 4.30514I 0
u = −0.427674 + 0.203192I
a = 1.40918 − 1.88213I
b = 0.140828 + 1.344780I
−4.86785 + 0.69304I −7.98362 − 8.67364I
u = −0.427674 − 0.203192I
a = 1.40918 + 1.88213I
b = 0.140828 − 1.344780I
−4.86785 − 0.69304I −7.98362 + 8.67364I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24246 + 0.93806I
a = 0.56665 + 1.30040I
b = 0.159878 − 1.184480I
0.75589 + 7.24896I 0
u = −1.24246 − 0.93806I
a = 0.56665 − 1.30040I
b = 0.159878 + 1.184480I
0.75589 − 7.24896I 0
u = −0.437498 + 0.041928I
a = 1.138190 − 0.255230I
b = 0.93620 + 1.06098I
−4.77928 + 1.38633I −2.68608 + 9.80464I
u = −0.437498 − 0.041928I
a = 1.138190 + 0.255230I
b = 0.93620 − 1.06098I
−4.77928 − 1.38633I −2.68608 − 9.80464I
u = 0.421812
a = 0.674343
b = −0.730697
−1.19702 −5.68960
u = 0.391711 + 0.125725I
a = 1.11338 − 1.90605I
b = 0.67267 + 1.66748I
4.14362 − 6.62538I −11.58727 + 8.02056I
u = 0.391711 − 0.125725I
a = 1.11338 + 1.90605I
b = 0.67267 − 1.66748I
4.14362 + 6.62538I −11.58727 − 8.02056I
u = −0.327963 + 0.245285I
a = 2.32590 − 2.13065I
b = −0.247516 − 0.737755I
1.63215 − 1.59930I 8.69923 + 5.57276I
u = −0.327963 − 0.245285I
a = 2.32590 + 2.13065I
b = −0.247516 + 0.737755I
1.63215 + 1.59930I 8.69923 − 5.57276I
u = 1.18216 + 1.12588I
a = 0.74131 − 1.29069I
b = 0.773851 + 0.896847I
−4.87430 − 7.62655I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.18216 − 1.12588I
a = 0.74131 + 1.29069I
b = 0.773851 − 0.896847I
−4.87430 + 7.62655I 0
u = −1.12922 + 1.18467I
a = −0.715216 − 0.916920I
b = −0.51244 + 1.54462I
4.76515 + 4.52869I 0
u = −1.12922 − 1.18467I
a = −0.715216 + 0.916920I
b = −0.51244 − 1.54462I
4.76515 − 4.52869I 0
u = −0.76984 + 1.57512I
a = 0.211433 + 0.967103I
b = −0.41680 − 1.48230I
6.29446 − 9.80876I 0
u = −0.76984 − 1.57512I
a = 0.211433 − 0.967103I
b = −0.41680 + 1.48230I
6.29446 + 9.80876I 0
u = 0.135489
a = 2.38464
b = −0.730697
−1.19702 −5.68960
u = 1.51575 + 1.17913I
a = 0.042233 + 0.244506I
b = 0.93620 − 1.06098I
−4.77928 − 1.38633I 0
u = 1.51575 − 1.17913I
a = 0.042233 − 0.244506I
b = 0.93620 + 1.06098I
−4.77928 + 1.38633I 0
u = 2.00508 + 0.27337I
a = 0.274454 + 1.030460I
b = 0.085775 − 0.685758I
−7.23053 + 1.36356I 0
u = 2.00508 − 0.27337I
a = 0.274454 − 1.030460I
b = 0.085775 + 0.685758I
−7.23053 − 1.36356I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.71775 + 1.10513I
a = 0.679279 + 0.675093I
b = 0.67267 − 1.66748I
4.14362 + 6.62538I 0
u = −1.71775 − 1.10513I
a = 0.679279 − 0.675093I
b = 0.67267 + 1.66748I
4.14362 − 6.62538I 0
u = 2.34314 + 0.12518I
a = 0.140145 + 0.427493I
b = 0.140828 − 1.344780I
−4.86785 − 0.69304I 0
u = 2.34314 − 0.12518I
a = 0.140145 − 0.427493I
b = 0.140828 + 1.344780I
−4.86785 + 0.69304I 0
18
III. I
u
3
= h−3.67 × 10
26
u
23
+ 2.74 × 10
27
u
22
+ · · · + 1.23 × 10
25
b + 4.48 ×
10
27
, −4.10 × 10
27
u
23
+ 3.02 × 10
28
u
22
+ · · · + 8.60 × 10
25
a + 4.49 ×
10
28
, u
24
− 8u
23
+ · · · − 70u + 7i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
47.6906u
23
− 351.519u
22
+ ··· + 4424.76u − 521.851
29.8636u
23
− 222.890u
22
+ ··· + 3056.38u − 364.681
a
8
=
77.5542u
23
− 574.408u
22
+ ··· + 7481.14u − 886.532
29.8636u
23
− 222.890u
22
+ ··· + 3056.38u − 364.681
a
12
=
−12.8106u
23
+ 100.818u
22
+ ··· − 2044.21u + 269.129
−9.95501u
23
+ 73.3208u
22
+ ··· − 763.480u + 77.2798
a
3
=
0.138784u
23
+ 11.3623u
22
+ ··· − 1638.59u + 246.874
11.4161u
23
− 83.1833u
22
+ ··· + 940.881u − 107.944
a
11
=
−25.1908u
23
+ 190.223u
22
+ ··· − 2780.72u + 334.744
−16.0870u
23
+ 118.943u
22
+ ··· − 1351.40u + 144.738
a
5
=
−20.9624u
23
+ 168.401u
22
+ ··· − 3767.42u + 499.102
−9.94567u
23
+ 81.2009u
22
+ ··· − 1999.72u + 267.949
a
6
=
−32.1987u
23
+ 250.704u
22
+ ··· − 4728.32u + 612.544
13.1750u
23
− 94.7433u
22
+ ··· + 874.407u − 89.4725
a
7
=
−22.3595u
23
+ 176.188u
22
+ ··· − 3597.32u + 474.872
14.4092u
23
− 104.761u
22
+ ··· + 1099.33u − 118.852
a
10
=
27.2400u
23
− 184.739u
22
+ ··· + 294.311u + 43.5055
30.5534u
23
− 223.504u
22
+ ··· + 2557.59u − 289.562
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
2413990051504396952568557713
12282052756577788766591881
u
23
+
17843697385323316380752630998
12282052756577788766591881
u
22
+ ··· −
217680263277212179414137521046
12282052756577788766591881
u +
24555062877957345779880593656
12282052756577788766591881
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
24
− 8u
23
+ ··· − 70u + 7
c
2
(u
12
− 5u
11
+ ··· − u + 1)
2
c
3
, c
9
7(7u
24
− 7u
23
+ ··· + 75u + 5)
c
4
, c
10
7(7u
24
+ 60u
22
+ ··· + 22427u
2
+ 4717)
c
6
(u
12
+ 5u
11
+ ··· + u + 1)
2
c
7
, c
11
u
24
− 3u
22
+ ··· − 112u + 28
c
8
(u
12
+ 3u
11
+ ··· − u + 1)
2
c
12
(u
12
− 3u
11
+ ··· + u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
24
− 16y
23
+ ··· − 476y + 49
c
2
, c
6
(y
12
− 3y
11
+ ··· + 5y + 1)
2
c
3
, c
9
49(49y
24
− 1071y
23
+ ··· − 1875y + 25)
c
4
, c
10
49(7y
12
+ 60y
11
+ ··· + 22427y + 4717)
2
c
7
, c
11
y
24
− 6y
23
+ ··· − 2240y + 784
c
8
, c
12
(y
12
+ 9y
11
+ ··· + 11y + 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.990360 + 0.229959I
a = 0.772033 − 0.008329I
b = 0.696956 + 0.905272I
−5.24399 − 7.57487I −16.9266 + 5.7019I
u = 0.990360 − 0.229959I
a = 0.772033 + 0.008329I
b = 0.696956 − 0.905272I
−5.24399 + 7.57487I −16.9266 − 5.7019I
u = −1.052190 + 0.204446I
a = −0.671428 + 1.062710I
b = −0.194327 + 0.818955I
−7.05899 + 1.71829I −5.19858 − 10.93231I
u = −1.052190 − 0.204446I
a = −0.671428 − 1.062710I
b = −0.194327 − 0.818955I
−7.05899 − 1.71829I −5.19858 + 10.93231I
u = −0.005493 + 0.852422I
a = 1.09872 + 1.76399I
b = −0.272473 − 0.732142I
1.24358 − 1.53174I −12.33823 + 2.51319I
u = −0.005493 − 0.852422I
a = 1.09872 − 1.76399I
b = −0.272473 + 0.732142I
1.24358 + 1.53174I −12.33823 − 2.51319I
u = 0.670567 + 0.451392I
a = −3.10489 − 1.25043I
b = −0.220204 − 0.443899I
−1.92697 − 6.43714I −7.7705 + 12.2950I
u = 0.670567 − 0.451392I
a = −3.10489 + 1.25043I
b = −0.220204 + 0.443899I
−1.92697 + 6.43714I −7.7705 − 12.2950I
u = −1.176230 + 0.572580I
a = −0.287366 − 0.389151I
b = −0.220204 + 0.443899I
−1.92697 + 6.43714I −7.7705 − 12.2950I
u = −1.176230 − 0.572580I
a = −0.287366 + 0.389151I
b = −0.220204 − 0.443899I
−1.92697 − 6.43714I −7.7705 + 12.2950I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.107516 + 0.630369I
a = −0.54125 − 1.37593I
b = 0.48403 + 1.67729I
4.71142 − 6.53437I 1.95402 + 5.88343I
u = 0.107516 − 0.630369I
a = −0.54125 + 1.37593I
b = 0.48403 − 1.67729I
4.71142 + 6.53437I 1.95402 − 5.88343I
u = 0.577516 + 0.093224I
a = 0.70516 + 2.89509I
b = −0.272473 + 0.732142I
1.24358 + 1.53174I −12.33823 − 2.51319I
u = 0.577516 − 0.093224I
a = 0.70516 − 2.89509I
b = −0.272473 − 0.732142I
1.24358 − 1.53174I −12.33823 + 2.51319I
u = 0.497811 + 0.172649I
a = 0.228512 + 0.377817I
b = 1.00602 − 1.16447I
−4.88453 − 1.63304I −15.7201 + 17.9154I
u = 0.497811 − 0.172649I
a = 0.228512 − 0.377817I
b = 1.00602 + 1.16447I
−4.88453 + 1.63304I −15.7201 − 17.9154I
u = 1.21458 + 1.13879I
a = 0.73104 − 1.29369I
b = 0.696956 + 0.905272I
−5.24399 − 7.57487I 0
u = 1.21458 − 1.13879I
a = 0.73104 + 1.29369I
b = 0.696956 − 0.905272I
−5.24399 + 7.57487I 0
u = −1.43744 + 1.24436I
a = 0.580978 + 0.823510I
b = 0.48403 − 1.67729I
4.71142 + 6.53437I 0
u = −1.43744 − 1.24436I
a = 0.580978 − 0.823510I
b = 0.48403 + 1.67729I
4.71142 − 6.53437I 0
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 2.01097 + 0.27938I
a = −0.149660 − 1.076590I
b = −0.194327 + 0.818955I
−7.05899 + 1.71829I 0
u = 2.01097 − 0.27938I
a = −0.149660 + 1.076590I
b = −0.194327 − 0.818955I
−7.05899 − 1.71829I 0
u = 1.60204 + 1.39782I
a = 0.066724 + 0.280616I
b = 1.00602 − 1.16447I
−4.88453 − 1.63304I 0
u = 1.60204 − 1.39782I
a = 0.066724 − 0.280616I
b = 1.00602 + 1.16447I
−4.88453 + 1.63304I 0
24
IV. I
u
4
= h−u
5
+ u
4
− u
2
+ b + 1, u
5
− u
4
+ u
2
+ a, u
6
− u
5
+ 2u
3
− u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
−u
5
+ u
4
− u
2
u
5
− u
4
+ u
2
− 1
a
8
=
−1
u
5
− u
4
+ u
2
− 1
a
12
=
u
3
− u
2
+ 1
u
5
− u
4
− u
3
+ 2u
2
− 1
a
3
=
u
2
− u + 1
u
4
− u
3
+ 2u − 1
a
11
=
0
−u
3
+ u
2
− 1
a
5
=
0
u
a
6
=
−u
−u
3
+ u − 1
a
7
=
−1
−u
2
+ u − 1
a
10
=
0
−u
3
+ u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
5
− 3u
4
+ u
3
+ 8u
2
+ u − 5
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
6
− u
5
+ 2u
3
− u + 1
c
2
u
6
+ 5u
5
+ 10u
4
+ 12u
3
+ 11u
2
+ 6u + 2
c
3
, c
9
u
6
− u
5
+ 3u
4
+ u
3
+ u
2
+ 2u + 1
c
4
, c
10
u
6
c
6
u
6
− 5u
5
+ 10u
4
− 12u
3
+ 11u
2
− 6u + 2
c
7
, c
11
u
6
+ 2u
4
− 2u
2
+ 1
c
8
u
6
− 2u
5
+ 4u
4
− 5u
3
+ 5u
2
− 4u + 2
c
12
u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 5u
2
+ 4u + 2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
6
− y
5
+ 4y
4
− 4y
3
+ 4y
2
− y + 1
c
2
, c
6
y
6
− 5y
5
+ 2y
4
+ 20y
3
+ 17y
2
+ 8y + 4
c
3
, c
9
y
6
+ 5y
5
+ 13y
4
+ 11y
3
+ 3y
2
− 2y + 1
c
4
, c
10
y
6
c
7
, c
11
(y
3
+ 2y
2
− 2y + 1)
2
c
8
, c
12
y
6
+ 4y
5
+ 6y
4
+ 3y
3
+ y
2
+ 4y + 4
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.915589 + 0.402116I
a = −1.23898 − 1.13846I
b = 0.238984 + 1.138460I
8.28528 − 1.18132I 1.33896 + 1.96041I
u = −0.915589 − 0.402116I
a = −1.23898 + 1.13846I
b = 0.238984 − 1.138460I
8.28528 + 1.18132I 1.33896 − 1.96041I
u = 0.510869 + 0.551075I
a = −0.137977 − 0.412869I
b = −0.862023 + 0.412869I
−1.44750 − 0.78507I −4.75532 + 4.67080I
u = 0.510869 − 0.551075I
a = −0.137977 + 0.412869I
b = −0.862023 − 0.412869I
−1.44750 + 0.78507I −4.75532 − 4.67080I
u = 0.904720 + 0.975923I
a = −0.623039 + 1.214800I
b = −0.376961 − 1.214800I
1.38689 − 5.20040I −7.08364 + 4.17423I
u = 0.904720 − 0.975923I
a = −0.623039 − 1.214800I
b = −0.376961 + 1.214800I
1.38689 + 5.20040I −7.08364 − 4.17423I
28
V. I
u
5
= h−u
4
+ 4u
3
− 4u
2
+ b + 1, −u
5
+ 6u
4
− 11u
3
+ 6u
2
+ 2a − u, u
6
−
6u
5
+ 11u
4
− 4u
3
− 5u
2
+ 2u + 2i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
9
=
1
2
u
5
− 3u
4
+
11
2
u
3
− 3u
2
+
1
2
u
u
4
− 4u
3
+ 4u
2
− 1
a
8
=
1
2
u
5
− 2u
4
+
3
2
u
3
+ u
2
+
1
2
u − 1
u
4
− 4u
3
+ 4u
2
− 1
a
12
=
−
1
2
u
5
+ 3u
4
−
11
2
u
3
+ 2u
2
+
5
2
u − 1
u
2
− 2u + 1
a
3
=
−
1
2
u
5
+ 3u
4
−
11
2
u
3
+ 2u
2
+
5
2
u − 1
u
2
− u + 1
a
11
=
−
1
2
u
5
+ 3u
4
−
11
2
u
3
+ 3u
2
−
1
2
u
u
4
− 3u
3
+ 2u
2
− 2u + 1
a
5
=
1
2
u
5
− 3u
4
+
11
2
u
3
− 2u
2
−
5
2
u + 1
u
5
− 6u
4
+ 11u
3
− 5u
2
− 2u + 1
a
6
=
1
2
u
5
− 3u
4
+
11
2
u
3
− 3u
2
+
1
2
u
−u
3
+ 3u
2
− u − 1
a
7
=
1
2
u
5
− 2u
4
+
3
2
u
3
+ u
2
+
1
2
u − 1
2u
5
− 7u
4
+ 3u
3
+ 7u
2
− 3u − 3
a
10
=
0
u
4
− 3u
3
+ u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
6
− 6u
5
+ 11u
4
− 4u
3
− 5u
2
+ 2u + 2
c
2
, c
12
(u
3
+ 2u − 1)
2
c
3
, c
9
(u + 1)
6
c
4
, c
10
(u
2
+ 1)
3
c
6
, c
8
(u
3
+ 2u + 1)
2
c
7
, c
11
u
6
+ 2u
5
− 5u
4
− 6u
3
+ 18u
2
− 12u + 4
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
6
− 14y
5
+ 63y
4
− 98y
3
+ 85y
2
− 24y + 4
c
2
, c
6
, c
8
c
12
(y
3
+ 4y
2
+ 4y −1)
2
c
3
, c
9
(y −1)
6
c
4
, c
10
(y + 1)
6
c
7
, c
11
y
6
− 14y
5
+ 85y
4
− 160y
3
+ 140y
2
+ 16
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000 + 0.453398I
a = 0.376086 + 0.829484I
b = 0.453398
−4.93480 −12.0000
u = 1.000000 − 0.453398I
a = 0.376086 − 0.829484I
b = 0.453398
−4.93480 −12.0000
u = −0.467712 + 0.226699I
a = −0.83917 + 1.73133I
b = −0.22670 − 1.46771I
−4.93480 −12.0000
u = −0.467712 − 0.226699I
a = −0.83917 − 1.73133I
b = −0.22670 + 1.46771I
−4.93480 −12.0000
u = 2.46771 + 0.22670I
a = −0.036916 − 0.401842I
b = −0.22670 + 1.46771I
−4.93480 −12.0000
u = 2.46771 − 0.22670I
a = −0.036916 + 0.401842I
b = −0.22670 − 1.46771I
−4.93480 −12.0000
32
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
6
− 6u
5
+ 11u
4
− 4u
3
− 5u
2
+ 2u + 2)(u
6
− u
5
+ 2u
3
− u + 1)
· (u
24
− 8u
23
+ ··· − 70u + 7)(u
39
− u
38
+ ··· + 30u + 14)
· (u
64
− 3u
63
+ ··· + 4u + 8)
c
2
(u
3
+ 2u − 1)
2
(u
6
+ 5u
5
+ 10u
4
+ 12u
3
+ 11u
2
+ 6u + 2)
· ((u
12
− 5u
11
+ ··· − u + 1)
2
)(u
32
+ 3u
31
+ ··· − 197u − 17)
2
· (u
39
− 4u
38
+ ··· + 338u + 250)
c
3
, c
9
49(u + 1)
6
(u
6
− u
5
+ 3u
4
+ u
3
+ u
2
+ 2u + 1)
· (7u
24
− 7u
23
+ ··· + 75u + 5)(7u
39
− 23u
38
+ ··· + 3790u + 397)
· (u
64
− 5u
62
+ ··· − 151551u + 109156)
c
4
, c
10
49u
6
(u
2
+ 1)
3
(7u
24
+ 60u
22
+ ··· + 22427u
2
+ 4717)
· ((u
32
+ 9u
30
+ ··· − 159u − 39)
2
)(7u
39
− 9u
38
+ ··· + 704u + 128)
c
6
(u
3
+ 2u + 1)
2
(u
6
− 5u
5
+ 10u
4
− 12u
3
+ 11u
2
− 6u + 2)
· ((u
12
+ 5u
11
+ ··· + u + 1)
2
)(u
32
+ 3u
31
+ ··· − 197u − 17)
2
· (u
39
− 4u
38
+ ··· + 338u + 250)
c
7
, c
11
(u
6
+ 2u
4
− 2u
2
+ 1)(u
6
+ 2u
5
− 5u
4
− 6u
3
+ 18u
2
− 12u + 4)
· (u
24
− 3u
22
+ ··· − 112u + 28)(u
39
− 2u
38
+ ··· − 256u + 112)
· (u
64
− 13u
63
+ ··· − 14192u + 1088)
c
8
(u
3
+ 2u + 1)
2
(u
6
− 2u
5
+ 4u
4
− 5u
3
+ 5u
2
− 4u + 2)
· ((u
12
+ 3u
11
+ ··· − u + 1)
2
)(u
32
− u
31
+ ··· + 15u − 43)
2
· (u
39
+ 3u
38
+ ··· + 144u + 26)
c
12
(u
3
+ 2u − 1)
2
(u
6
+ 2u
5
+ 4u
4
+ 5u
3
+ 5u
2
+ 4u + 2)
· ((u
12
− 3u
11
+ ··· + u + 1)
2
)(u
32
− u
31
+ ··· + 15u − 43)
2
· (u
39
+ 3u
38
+ ··· + 144u + 26)
33
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
6
− 14y
5
+ 63y
4
− 98y
3
+ 85y
2
− 24y + 4)
· (y
6
− y
5
+ 4y
4
− 4y
3
+ 4y
2
− y + 1)(y
24
− 16y
23
+ ··· − 476y + 49)
· (y
39
− 5y
38
+ ··· + 508y −196)(y
64
− 35y
63
+ ··· − 6000y + 64)
c
2
, c
6
(y
3
+ 4y
2
+ 4y −1)
2
(y
6
− 5y
5
+ 2y
4
+ 20y
3
+ 17y
2
+ 8y + 4)
· ((y
12
− 3y
11
+ ··· + 5y + 1)
2
)(y
32
− 23y
31
+ ··· − 11065y + 289)
2
· (y
39
− 26y
38
+ ··· + 1469244y −62500)
c
3
, c
9
2401(y −1)
6
(y
6
+ 5y
5
+ 13y
4
+ 11y
3
+ 3y
2
− 2y + 1)
· (49y
24
− 1071y
23
+ ··· − 1875y + 25)
· (49y
39
+ 1473y
38
+ ··· + 1541000y −157609)
· (y
64
− 10y
63
+ ··· − 162341142769y + 11915032336)
c
4
, c
10
2401y
6
(y + 1)
6
(7y
12
+ 60y
11
+ ··· + 22427y + 4717)
2
· (y
32
+ 18y
31
+ ··· − 1335y + 1521)
2
· (49y
39
+ 885y
38
+ ··· + 167936y −16384)
c
7
, c
11
(y
3
+ 2y
2
− 2y + 1)
2
(y
6
− 14y
5
+ 85y
4
− 160y
3
+ 140y
2
+ 16)
· (y
24
− 6y
23
+ ··· − 2240y + 784)
· (y
39
+ 18y
38
+ ··· − 65280y −12544)
· (y
64
− 19y
63
+ ··· − 30831872y + 1183744)
c
8
, c
12
(y
3
+ 4y
2
+ 4y −1)
2
(y
6
+ 4y
5
+ 6y
4
+ 3y
3
+ y
2
+ 4y + 4)
· (y
12
+ 9y
11
+ ··· + 11y + 1)
2
· (y
32
+ 29y
31
+ ··· + 37013y + 1849)
2
· (y
39
+ 23y
38
+ ··· + 1392y −676)
34
