12n
0879
(K12n
0879
)
A knot diagram
1
Linearized knot diagam
4 9 10 11 2 3 1 11 6 7 4 8
Solving Sequence
3,10 4,6
7 11 9 2 1 5 8 12
c
3
c
6
c
10
c
9
c
2
c
1
c
5
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.18451 × 10
18
u
23
− 3.11362 × 10
18
u
22
+ ··· + 1.10562 × 10
17
b + 1.21069 × 10
18
, a − 1,
3u
24
− 3u
23
+ ··· + u + 1i
I
u
2
= h2.45436 × 10
314
u
67
− 2.51900 × 10
313
u
66
+ ··· + 3.33912 × 10
315
b − 2.97612 × 10
315
,
5.14656 × 10
314
u
67
+ 3.56618 × 10
314
u
66
+ ··· + 6.67823 × 10
315
a − 2.19657 × 10
315
,
8u
68
+ 40u
66
+ ··· − 270u + 50i
I
u
3
= h83485020528u
16
− 39219382232u
15
+ ··· + 2862203951b + 39645537732, a + 1,
4u
17
− 4u
16
+ ··· + 3u − 1i
I
u
4
= h−18u
3
+ 24u
2
+ b − 21u + 8, −30u
3
+ 42u
2
+ 2a − 41u + 17, 6u
4
− 12u
3
+ 13u
2
− 8u + 2i
* 4 irreducible components of dim
C
= 0, with total 113 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
= h2.18 × 10
18
u
23
− 3.11 × 10
18
u
22
+ · · · + 1.11 × 10
17
b + 1.21 ×
10
18
, a − 1, 3u
24
− 3u
23
+ · · · + u + 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
1
−19.7583u
23
+ 28.1618u
22
+ ··· + 11.4162u − 10.9504
a
7
=
−19.7583u
23
+ 28.1618u
22
+ ··· + 11.4162u − 9.95035
−19.7583u
23
+ 28.1618u
22
+ ··· + 11.4162u − 10.9504
a
11
=
−3.47015u
23
+ 5.78314u
22
+ ··· − 3.89407u + 1.41709
−11.8736u
23
+ 19.3044u
22
+ ··· + 0.470185u − 5.16901
a
9
=
u
8.40348u
23
− 13.5213u
22
+ ··· − 3.36425u + 6.58610
a
2
=
−5.11782u
23
+ 8.44910u
22
+ ··· + 3.78494u − 1.80116
2.31299u
23
− 4.48479u
22
+ ··· + 2.57381u + 1.15672
a
1
=
−0.316894u
23
− 0.861176u
22
+ ··· + 5.76323u + 0.465985
5.20333u
23
− 8.76032u
22
+ ··· + 2.47662u + 2.65983
a
5
=
−8.28934u
23
+ 7.65842u
22
+ ··· + 6.46724u − 3.91525
−27.1673u
23
+ 42.5966u
22
+ ··· + 5.38232u − 13.8780
a
8
=
−18.0653u
23
+ 25.7028u
22
+ ··· + 5.14347u − 6.60098
−18.6559u
23
+ 29.0833u
22
+ ··· + 3.56041u − 6.94383
a
12
=
13.1720u
23
− 21.8361u
22
+ ··· + 3.80961u + 2.98092
17.5768u
23
− 28.7733u
22
+ ··· − 1.58709u + 7.28605
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
10401411537800859069
110561902854140359
u
23
+
17169214705690460772
110561902854140359
u
22
+ ··· +
2497259999525294046
110561902854140359
u −
6190596405972712460
110561902854140359
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
3(3u
24
− 3u
23
+ ··· − 19u + 1)
c
2
, c
10
u
24
+ u
23
+ ··· − 3u − 3
c
3
, c
9
3(3u
24
+ 3u
23
+ ··· − u + 1)
c
4
, c
11
3(3u
24
− 3u
23
+ ··· + 2u + 1)
c
5
u
24
− 3u
23
+ ··· − 33u + 3
c
6
u
24
− 17u
23
+ ··· + 448u − 64
c
7
, c
12
u
24
− 11u
23
+ ··· − 192u + 32
c
8
9(9u
24
+ 168u
23
+ ··· − 30720u − 4096)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
9(9y
24
+ 201y
23
+ ··· − 165y + 1)
c
2
, c
10
y
24
− 5y
23
+ ··· + 21y + 9
c
3
, c
9
9(9y
24
− 51y
23
+ ··· − 17y + 1)
c
4
, c
11
9(9y
24
− 267y
23
+ ··· − 18y + 1)
c
5
y
24
+ 11y
23
+ ··· − 69y + 9
c
6
y
24
+ 7y
23
+ ··· − 36864y + 4096
c
7
, c
12
y
24
+ 9y
23
+ ··· + 4608y + 1024
c
8
81(81y
24
− 558y
23
+ ··· − 4.40402 × 10
7
y + 1.67772 × 10
7
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.532676 + 0.913923I
a = 1.00000
b = −0.790735 + 0.557429I
0.60856 − 1.63023I 4.46172 + 2.19213I
u = 0.532676 − 0.913923I
a = 1.00000
b = −0.790735 − 0.557429I
0.60856 + 1.63023I 4.46172 − 2.19213I
u = −0.706049 + 0.814568I
a = 1.00000
b = −1.19229 − 0.96975I
3.12317 + 4.41220I 8.88741 − 6.41775I
u = −0.706049 − 0.814568I
a = 1.00000
b = −1.19229 + 0.96975I
3.12317 − 4.41220I 8.88741 + 6.41775I
u = 1.077440 + 0.425171I
a = 1.00000
b = −0.372534 + 0.567998I
0.51482 − 4.14942I 0.15057 + 3.98630I
u = 1.077440 − 0.425171I
a = 1.00000
b = −0.372534 − 0.567998I
0.51482 + 4.14942I 0.15057 − 3.98630I
u = 0.799855 + 0.085298I
a = 1.00000
b = 0.479827 + 0.465785I
−2.57731 + 3.83319I 9.74735 − 1.51258I
u = 0.799855 − 0.085298I
a = 1.00000
b = 0.479827 − 0.465785I
−2.57731 − 3.83319I 9.74735 + 1.51258I
u = 0.968057 + 0.775960I
a = 1.00000
b = −1.25250 + 1.11203I
−2.68123 − 8.44569I 4.87208 + 6.96290I
u = 0.968057 − 0.775960I
a = 1.00000
b = −1.25250 − 1.11203I
−2.68123 + 8.44569I 4.87208 − 6.96290I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.712863
a = 1.00000
b = 0.384370
1.52481 8.20500
u = −0.899468 + 0.933589I
a = 1.00000
b = −0.534071 − 0.239788I
1.44603 − 1.35473I 0.81221 + 4.49282I
u = −0.899468 − 0.933589I
a = 1.00000
b = −0.534071 + 0.239788I
1.44603 + 1.35473I 0.81221 − 4.49282I
u = −0.603700 + 0.327165I
a = 1.00000
b = −0.64481 + 1.66099I
3.38556 + 9.86546I 0.31403 − 9.36723I
u = −0.603700 − 0.327165I
a = 1.00000
b = −0.64481 − 1.66099I
3.38556 − 9.86546I 0.31403 + 9.36723I
u = −0.676903
a = 1.00000
b = −1.90202
4.28877 −4.23850
u = −0.502333 + 0.277465I
a = 1.00000
b = −0.22982 − 1.47598I
−4.98881 + 0.86817I −1.31263 − 8.38596I
u = −0.502333 − 0.277465I
a = 1.00000
b = −0.22982 + 1.47598I
−4.98881 − 0.86817I −1.31263 + 8.38596I
u = 0.417523 + 0.252999I
a = 1.00000
b = −0.67427 − 1.95408I
4.92870 − 2.24110I −2.79694 + 9.86890I
u = 0.417523 − 0.252999I
a = 1.00000
b = −0.67427 + 1.95408I
4.92870 + 2.24110I −2.79694 − 9.86890I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.13728 + 1.04931I
a = 1.00000
b = −1.26137 − 0.99901I
6.84073 + 11.26200I 6.34322 − 5.87609I
u = −1.13728 − 1.04931I
a = 1.00000
b = −1.26137 + 0.99901I
6.84073 − 11.26200I 6.34322 + 5.87609I
u = 1.24817 + 1.05440I
a = 1.00000
b = −1.26861 + 0.96825I
5.4097 − 18.4597I 4.00000 + 9.52264I
u = 1.24817 − 1.05440I
a = 1.00000
b = −1.26861 − 0.96825I
5.4097 + 18.4597I 4.00000 − 9.52264I
7
II. I
u
2
= h2.45 × 10
314
u
67
− 2.52 × 10
313
u
66
+ · · · + 3.34 × 10
315
b − 2.98 ×
10
315
, 5.15 × 10
314
u
67
+ 3.57 × 10
314
u
66
+ · · · + 6.68 × 10
315
a − 2.20 ×
10
315
, 8u
68
+ 40u
66
+ · · · − 270u + 50i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−0.0770647u
67
− 0.0534000u
66
+ ··· − 16.8229u + 0.328914
−0.0735034u
67
+ 0.00754390u
66
+ ··· + 2.00619u + 0.891289
a
7
=
−0.150568u
67
− 0.0458561u
66
+ ··· − 14.8167u + 1.22020
−0.0735034u
67
+ 0.00754390u
66
+ ··· + 2.00619u + 0.891289
a
11
=
0.994747u
67
+ 0.163784u
66
+ ··· + 31.3491u − 25.1360
0.0657230u
67
− 0.00810655u
66
+ ··· − 4.39556u − 0.739629
a
9
=
0.893408u
67
+ 0.167359u
66
+ ··· + 39.7338u − 23.1675
0.0356157u
67
+ 0.00453081u
66
+ ··· − 1.98921u − 1.22896
a
2
=
−0.482326u
67
− 0.145242u
66
+ ··· − 39.3734u + 10.6341
−0.0384659u
67
− 0.0181689u
66
+ ··· − 0.0483855u + 1.94402
a
1
=
−0.469780u
67
− 0.153990u
66
+ ··· − 37.5345u + 11.6703
−0.0365482u
67
− 0.0214924u
66
+ ··· − 0.422063u + 1.99869
a
5
=
1.82905u
67
+ 0.339241u
66
+ ··· + 48.1219u − 49.9002
−0.0247642u
67
− 0.00963364u
66
+ ··· − 0.636979u − 0.894487
a
8
=
0.699429u
67
+ 0.125955u
66
+ ··· + 11.4056u − 22.0627
−0.0339967u
67
− 0.00175580u
66
+ ··· + 0.286722u + 0.383406
a
12
=
−0.955082u
67
− 0.162043u
66
+ ··· − 27.6430u + 24.8520
−0.0707061u
67
+ 0.0132240u
66
+ ··· + 4.20640u + 0.728749
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.623974u
67
+ 0.335986u
66
+ ··· + 24.1020u − 21.7293
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
8(8u
68
+ 172u
66
+ ··· + 1.91280 × 10
9
u + 3.08885 × 10
8
)
c
2
, c
10
2(2u
68
− 7u
66
+ ··· + 10344u + 1196)
c
3
, c
9
8(8u
68
+ 40u
66
+ ··· + 270u + 50)
c
4
, c
11
8(8u
68
− 184u
66
+ ··· + 3891182u + 266986)
c
5
2(2u
68
+ 21u
66
+ ··· − 27024u + 18932)
c
6
(u
34
+ 8u
33
+ ··· + 10u + 2)
2
c
7
, c
12
(u
34
+ 6u
33
+ ··· + 6u + 2)
2
c
8
16(4u
34
− 54u
33
+ ··· + 2256u + 523)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
64(64y
68
+ 2752y
67
+ ··· − 2.42039 × 10
16
y + 9.54099 × 10
16
)
c
2
, c
10
4(4y
68
− 28y
67
+ ··· − 1.47963 × 10
7
y + 1430416)
c
3
, c
9
64(64y
68
+ 640y
67
+ ··· − 109200y + 2500)
c
4
, c
11
64(64y
68
− 2944y
67
+ ··· − 3.77367 × 10
12
y + 7.12815 × 10
10
)
c
5
4(4y
68
+ 84y
67
+ ··· + 2.03431 × 10
9
y + 3.58421 × 10
8
)
c
6
(y
34
− 4y
33
+ ··· − 64y + 4)
2
c
7
, c
12
(y
34
+ 10y
33
+ ··· + 80y + 4)
2
c
8
256(16y
34
− 524y
33
+ ··· − 8625016y + 273529)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.468826 + 0.852869I
a = −0.77391 + 1.59871I
b = 0.693022 + 0.186434I
7.51890 + 2.81171I 10.32503 − 3.98363I
u = −0.468826 − 0.852869I
a = −0.77391 − 1.59871I
b = 0.693022 − 0.186434I
7.51890 − 2.81171I 10.32503 + 3.98363I
u = 0.995301 + 0.297202I
a = −0.609910 + 0.291744I
b = 0.649286 − 0.866728I
−3.82331 + 0.42771I −2.75863 + 0.I
u = 0.995301 − 0.297202I
a = −0.609910 − 0.291744I
b = 0.649286 + 0.866728I
−3.82331 − 0.42771I −2.75863 + 0.I
u = 0.680400 + 0.673865I
a = −0.898666 − 0.635347I
b = 1.09735 − 1.13898I
6.73817 − 0.34876I 9.87930 + 1.23396I
u = 0.680400 − 0.673865I
a = −0.898666 + 0.635347I
b = 1.09735 + 1.13898I
6.73817 + 0.34876I 9.87930 − 1.23396I
u = −0.183314 + 1.037870I
a = −0.741922 − 0.524531I
b = 1.09735 + 1.13898I
6.73817 + 0.34876I 9.87930 − 1.23396I
u = −0.183314 − 1.037870I
a = −0.741922 + 0.524531I
b = 1.09735 − 1.13898I
6.73817 − 0.34876I 9.87930 + 1.23396I
u = 0.799744 + 0.356609I
a = −0.633337 + 0.028903I
b = 0.724976 + 0.995650I
−2.27163 − 2.86243I 4.65330 + 7.44714I
u = 0.799744 − 0.356609I
a = −0.633337 − 0.028903I
b = 0.724976 − 0.995650I
−2.27163 + 2.86243I 4.65330 − 7.44714I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.525695 + 1.012530I
a = −0.95830 − 1.27829I
b = 0.719391 − 0.178386I
6.92940 − 9.49005I 0
u = 0.525695 − 1.012530I
a = −0.95830 + 1.27829I
b = 0.719391 + 0.178386I
6.92940 + 9.49005I 0
u = −0.783891 + 0.272664I
a = 1.81278 − 0.91048I
b = −0.628715 − 0.960903I
2.54618 + 9.70408I 1.30183 − 8.87741I
u = −0.783891 − 0.272664I
a = 1.81278 + 0.91048I
b = −0.628715 + 0.960903I
2.54618 − 9.70408I 1.30183 + 8.87741I
u = −0.845838 + 0.808955I
a = −0.940084 + 0.472817I
b = 1.13687 + 1.03425I
7.05120 + 7.79983I 0
u = −0.845838 − 0.808955I
a = −0.940084 − 0.472817I
b = 1.13687 − 1.03425I
7.05120 − 7.79983I 0
u = 0.124602 + 1.176870I
a = 1.086090 + 0.366101I
b = −0.709035 + 0.133102I
1.08787 − 1.51029I 0
u = 0.124602 − 1.176870I
a = 1.086090 − 0.366101I
b = −0.709035 − 0.133102I
1.08787 + 1.51029I 0
u = 0.733204 + 0.331461I
a = 1.74987 + 1.06963I
b = −0.515136 + 0.944106I
3.57407 − 2.76213I 2.69378 + 6.04053I
u = 0.733204 − 0.331461I
a = 1.74987 − 1.06963I
b = −0.515136 − 0.944106I
3.57407 + 2.76213I 2.69378 − 6.04053I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.056350 + 0.633111I
a = 0.285872 − 0.364191I
b = −1.132560 + 0.289085I
6.45659 − 2.10452I 0
u = −1.056350 − 0.633111I
a = 0.285872 + 0.364191I
b = −1.132560 − 0.289085I
6.45659 + 2.10452I 0
u = 0.412671 + 1.160410I
a = −0.848977 + 0.426994I
b = 1.13687 − 1.03425I
7.05120 − 7.79983I 0
u = 0.412671 − 1.160410I
a = −0.848977 − 0.426994I
b = 1.13687 + 1.03425I
7.05120 + 7.79983I 0
u = 1.201900 + 0.270973I
a = 0.229366 + 0.205547I
b = −1.330840 − 0.425024I
5.18347 − 3.76978I 0
u = 1.201900 − 0.270973I
a = 0.229366 − 0.205547I
b = −1.330840 + 0.425024I
5.18347 + 3.76978I 0
u = −0.693751 + 0.109107I
a = −1.33429 − 0.63824I
b = 0.649286 − 0.866728I
−3.82331 + 0.42771I −2.75863 + 0.63001I
u = −0.693751 − 0.109107I
a = −1.33429 + 0.63824I
b = 0.649286 + 0.866728I
−3.82331 − 0.42771I −2.75863 − 0.63001I
u = −0.055320 + 0.688385I
a = 0.213319 + 0.886260I
b = 0.23733 − 1.44997I
−4.86346 + 0.65866I 2.97197 − 10.93905I
u = −0.055320 − 0.688385I
a = 0.213319 − 0.886260I
b = 0.23733 + 1.44997I
−4.86346 − 0.65866I 2.97197 + 10.93905I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.077309 + 0.640233I
a = 3.17254 − 1.64334I
b = −0.339874 + 0.241600I
−0.169612 − 0.106946I 2.05478 − 7.99940I
u = −0.077309 − 0.640233I
a = 3.17254 + 1.64334I
b = −0.339874 − 0.241600I
−0.169612 + 0.106946I 2.05478 + 7.99940I
u = −0.295523 + 1.323800I
a = 0.826792 − 0.278697I
b = −0.709035 + 0.133102I
1.08787 − 1.51029I 0
u = −0.295523 − 1.323800I
a = 0.826792 + 0.278697I
b = −0.709035 − 0.133102I
1.08787 + 1.51029I 0
u = −0.323505 + 0.550313I
a = −2.09178 − 1.20192I
b = 0.714129 + 0.426902I
−1.73503 + 4.63424I 1.41391 − 8.73652I
u = −0.323505 − 0.550313I
a = −2.09178 + 1.20192I
b = 0.714129 − 0.426902I
−1.73503 − 4.63424I 1.41391 + 8.73652I
u = −0.621889 + 0.097818I
a = 0.256714 − 1.066550I
b = 0.23733 − 1.44997I
−4.86346 + 0.65866I 2.97197 − 10.93905I
u = −0.621889 − 0.097818I
a = 0.256714 + 1.066550I
b = 0.23733 + 1.44997I
−4.86346 − 0.65866I 2.97197 + 10.93905I
u = −1.058490 + 0.909565I
a = −1.136770 − 0.125774I
b = 1.134040 + 0.771245I
−2.27862 + 6.60178I 0
u = −1.058490 − 0.909565I
a = −1.136770 + 0.125774I
b = 1.134040 − 0.771245I
−2.27862 − 6.60178I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.071407 + 0.565700I
a = 1.33362 + 1.69899I
b = −1.132560 + 0.289085I
6.45659 − 2.10452I 9.49776 + 3.04081I
u = −0.071407 − 0.565700I
a = 1.33362 − 1.69899I
b = −1.132560 − 0.289085I
6.45659 + 2.10452I 9.49776 − 3.04081I
u = −0.516815 + 0.202739I
a = −1.57566 + 0.07191I
b = 0.724976 − 0.995650I
−2.27163 + 2.86243I 4.65330 − 7.44714I
u = −0.516815 − 0.202739I
a = −1.57566 − 0.07191I
b = 0.724976 + 0.995650I
−2.27163 − 2.86243I 4.65330 + 7.44714I
u = 1.33813 + 0.76231I
a = −0.359403 − 0.206510I
b = 0.714129 − 0.426902I
−1.73503 − 4.63424I 0
u = 1.33813 − 0.76231I
a = −0.359403 + 0.206510I
b = 0.714129 + 0.426902I
−1.73503 + 4.63424I 0
u = −1.21633 + 0.94957I
a = −1.051920 + 0.120713I
b = 1.094950 + 0.826706I
−1.10719 + 9.53077I 0
u = −1.21633 − 0.94957I
a = −1.051920 − 0.120713I
b = 1.094950 − 0.826706I
−1.10719 − 9.53077I 0
u = 1.31766 + 0.90084I
a = −0.869045 − 0.096152I
b = 1.134040 − 0.771245I
−2.27862 − 6.60178I 0
u = 1.31766 − 0.90084I
a = −0.869045 + 0.096152I
b = 1.134040 + 0.771245I
−2.27862 + 6.60178I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.219976 + 0.309198I
a = 2.41799 − 2.16689I
b = −1.330840 − 0.425024I
5.18347 − 3.76978I 7.61093 + 4.09207I
u = 0.219976 − 0.309198I
a = 2.41799 + 2.16689I
b = −1.330840 + 0.425024I
5.18347 + 3.76978I 7.61093 − 4.09207I
u = 1.16486 + 1.14571I
a = −0.938285 + 0.107673I
b = 1.094950 − 0.826706I
−1.10719 − 9.53077I 0
u = 1.16486 − 1.14571I
a = −0.938285 − 0.107673I
b = 1.094950 + 0.826706I
−1.10719 + 9.53077I 0
u = 0.92847 + 1.36427I
a = 0.416025 − 0.254301I
b = −0.515136 + 0.944106I
3.57407 − 2.76213I 0
u = 0.92847 − 1.36427I
a = 0.416025 + 0.254301I
b = −0.515136 − 0.944106I
3.57407 + 2.76213I 0
u = −1.17276 + 1.20800I
a = 0.440515 + 0.221252I
b = −0.628715 − 0.960903I
2.54618 + 9.70408I 0
u = −1.17276 − 1.20800I
a = 0.440515 − 0.221252I
b = −0.628715 + 0.960903I
2.54618 − 9.70408I 0
u = −1.00066 + 1.40956I
a = −0.245311 + 0.506752I
b = 0.693022 − 0.186434I
7.51890 − 2.81171I 0
u = −1.00066 − 1.40956I
a = −0.245311 − 0.506752I
b = 0.693022 + 0.186434I
7.51890 + 2.81171I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.195791 + 0.026637I
a = −9.61408 − 3.32356I
b = 0.454798 − 0.372120I
0.416750 − 0.601408I 1.43686 + 9.41286I
u = 0.195791 − 0.026637I
a = −9.61408 + 3.32356I
b = 0.454798 + 0.372120I
0.416750 + 0.601408I 1.43686 − 9.41286I
u = 0.79054 + 1.64230I
a = −0.375455 − 0.500826I
b = 0.719391 + 0.178386I
6.92940 + 9.49005I 0
u = 0.79054 − 1.64230I
a = −0.375455 + 0.500826I
b = 0.719391 − 0.178386I
6.92940 − 9.49005I 0
u = −1.79382 + 0.90682I
a = −0.0929107 − 0.0321190I
b = 0.454798 + 0.372120I
0.416750 + 0.601408I 0
u = −1.79382 − 0.90682I
a = −0.0929107 + 0.0321190I
b = 0.454798 − 0.372120I
0.416750 − 0.601408I 0
u = 0.80685 + 2.15821I
a = 0.248523 + 0.128732I
b = −0.339874 + 0.241600I
−0.169612 − 0.106946I 0
u = 0.80685 − 2.15821I
a = 0.248523 − 0.128732I
b = −0.339874 − 0.241600I
−0.169612 + 0.106946I 0
17
III. I
u
3
= h8.35 × 10
10
u
16
− 3.92 × 10
10
u
15
+ · · · + 2.86 × 10
9
b + 3.96 ×
10
10
, a + 1, 4u
17
− 4u
16
+ · · · + 3u − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−1
−29.1681u
16
+ 13.7025u
15
+ ··· + 14.5094u − 13.8514
a
7
=
−29.1681u
16
+ 13.7025u
15
+ ··· + 14.5094u − 14.8514
−29.1681u
16
+ 13.7025u
15
+ ··· + 14.5094u − 13.8514
a
11
=
21.2708u
16
− 11.2975u
15
+ ··· − 9.62148u + 12.5516
5.80518u
16
− 4.26392u
15
+ ··· − 1.59682u + 5.25961
a
9
=
u
15.4656u
16
− 7.03360u
15
+ ··· − 7.02466u + 7.29202
a
2
=
8.43198u
16
− 3.84679u
15
+ ··· − 4.30716u + 4.86639
9.97324u
16
− 6.25135u
15
+ ··· − 3.40144u + 5.31769
a
1
=
15.6935u
16
− 8.45787u
15
+ ··· − 6.37770u + 9.03779
11.1387u
16
− 7.65532u
15
+ ··· − 3.57388u + 5.98030
a
5
=
−19.9888u
16
+ 9.79709u
15
+ ··· + 8.99838u − 11.5058
−19.9888u
16
+ 9.79709u
15
+ ··· + 8.99838u − 11.5058
a
8
=
−30.4245u
16
+ 11.4764u
15
+ ··· + 18.1218u − 18.7023
−8.55005u
16
+ 2.81847u
15
+ ··· + 6.03957u − 7.50334
a
12
=
23.3540u
16
− 14.1281u
15
+ ··· − 9.05605u + 15.3179
5.11652u
16
− 4.84615u
15
+ ··· − 0.515530u + 5.07278
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
232960675924
2862203951
u
16
−
140394778628
2862203951
u
15
+ ··· −
87916155015
2862203951
u +
138818591522
2862203951
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
17
− 16u
16
+ ··· − 345u + 89)
c
2
, c
10
u
17
− u
16
+ ··· − 4u − 4
c
3
, c
9
4(4u
17
− 4u
16
+ ··· + 3u − 1)
c
4
4(4u
17
+ 4u
16
+ ··· − 4u − 1)
c
5
u
17
+ u
16
+ ··· − 48u − 28
c
6
u
17
+ 6u
16
+ ··· + 5u − 1
c
7
u
17
− 2u
16
+ ··· − u − 1
c
8
16(16u
17
+ 64u
16
+ ··· + 276u + 149)
c
11
4(4u
17
− 4u
16
+ ··· − 4u + 1)
c
12
u
17
+ 2u
16
+ ··· − u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(16y
17
+ 32y
16
+ ··· + 31449y −7921)
c
2
, c
10
y
17
− 5y
16
+ ··· − 32y −16
c
3
, c
9
16(16y
17
− 96y
16
+ ··· + 13y −1)
c
4
, c
11
16(16y
17
− 96y
16
+ ··· − 18y −1)
c
5
y
17
− y
16
+ ··· + 4432y −784
c
6
y
17
+ 4y
16
+ ··· + 21y −1
c
7
, c
12
y
17
+ 10y
16
+ ··· + y −1
c
8
256(256y
17
− 1664y
16
+ ··· − 129146y −22201)
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.349992 + 0.941594I
a = −1.00000
b = 0.382221 − 1.039030I
4.86685 − 9.32651I 5.41608 + 7.90457I
u = 0.349992 − 0.941594I
a = −1.00000
b = 0.382221 + 1.039030I
4.86685 + 9.32651I 5.41608 − 7.90457I
u = −0.925285 + 0.049672I
a = −1.00000
b = −0.324837 + 0.399070I
−3.01855 − 3.88143I −8.52830 + 3.72764I
u = −0.925285 − 0.049672I
a = −1.00000
b = −0.324837 − 0.399070I
−3.01855 + 3.88143I −8.52830 − 3.72764I
u = 1.105130 + 0.043646I
a = −1.00000
b = −0.289360 − 0.016387I
0.282501 − 0.033649I −0.021483 − 0.214659I
u = 1.105130 − 0.043646I
a = −1.00000
b = −0.289360 + 0.016387I
0.282501 + 0.033649I −0.021483 + 0.214659I
u = −0.779267 + 0.338902I
a = −1.00000
b = 0.869461 − 0.624268I
−3.27381 + 2.66022I −5.11049 − 5.19029I
u = −0.779267 − 0.338902I
a = −1.00000
b = 0.869461 + 0.624268I
−3.27381 − 2.66022I −5.11049 + 5.19029I
u = −0.181322 + 0.635600I
a = −1.00000
b = 0.097483 + 1.352810I
5.51202 + 1.96200I 8.78340 − 3.00810I
u = −0.181322 − 0.635600I
a = −1.00000
b = 0.097483 − 1.352810I
5.51202 − 1.96200I 8.78340 + 3.00810I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.138810 + 0.797369I
a = −1.00000
b = 1.18485 + 0.98213I
−4.13204 + 8.52148I −2.44134 − 7.06872I
u = −1.138810 − 0.797369I
a = −1.00000
b = 1.18485 − 0.98213I
−4.13204 − 8.52148I −2.44134 + 7.06872I
u = 0.589412 + 0.054615I
a = −1.00000
b = 0.72146 − 1.54093I
−5.44098 + 0.16624I −9.87770 − 0.33991I
u = 0.589412 − 0.054615I
a = −1.00000
b = 0.72146 + 1.54093I
−5.44098 − 0.16624I −9.87770 + 0.33991I
u = 0.393230
a = −1.00000
b = −1.47554
4.97612 9.22450
u = 1.28353 + 1.07729I
a = −1.00000
b = 1.096500 − 0.719832I
−2.21885 − 8.19478I 0.16759 + 8.21222I
u = 1.28353 − 1.07729I
a = −1.00000
b = 1.096500 + 0.719832I
−2.21885 + 8.19478I 0.16759 − 8.21222I
22
IV. I
u
4
= h−18u
3
+ 24u
2
+ b − 21u + 8, −30u
3
+ 42u
2
+ 2a − 41u +
17, 6u
4
− 12u
3
+ 13u
2
− 8u + 2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
15u
3
− 21u
2
+
41
2
u −
17
2
18u
3
− 24u
2
+ 21u − 8
a
7
=
33u
3
− 45u
2
+
83
2
u −
33
2
18u
3
− 24u
2
+ 21u − 8
a
11
=
−
39
2
u
3
+ 21u
2
−
85
4
u + 5
−6u
3
+ 6u
2
− 6u + 1
a
9
=
−
15
2
u
3
+ 9u
2
−
37
4
u + 3
−6u
3
+ 6u
2
− 4u + 1
a
2
=
21
2
u
3
− 15u
2
+
55
4
u − 4
3u
2
− 1
a
1
=
15
2
u
3
− 9u
2
+
37
4
u − 3
2u
3
+ u − 1
a
5
=
75
2
u
3
−
111
2
u
2
+
205
4
u −
87
4
15u
3
− 21u
2
+
41
2
u − 9
a
8
=
51u
3
− 72u
2
+
133
2
u − 27
16u
3
− 24u
2
+ 24u − 10
a
12
=
−
21
2
u
3
+ 9u
2
−
39
4
u
−2u
3
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
6(6u
4
− 24u
3
+ 31u
2
− 10u + 1)
c
2
, c
5
, c
10
2(2u
4
+ 5u
2
+ 6u + 3)
c
3
, c
9
, c
11
6(6u
4
− 12u
3
+ 13u
2
− 8u + 2)
c
4
6(6u
4
+ 12u
3
+ 13u
2
+ 8u + 2)
c
6
, c
7
, c
12
(u
2
+ 2)
2
c
8
9(3u
2
+ 2u + 3)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
36(36y
4
− 204y
3
+ 493y
2
− 38y + 1)
c
2
, c
5
, c
10
4(4y
4
+ 20y
3
+ 37y
2
− 6y + 9)
c
3
, c
4
, c
9
c
11
36(36y
4
+ 12y
3
+ y
2
− 12y + 4)
c
6
, c
7
, c
12
(y + 2)
4
c
8
81(9y
2
+ 14y + 9)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.375454 + 0.826676I
a = −0.164544 + 0.680759I
b = − 1.414210I
−4.93480 0
u = 0.375454 − 0.826676I
a = −0.164544 − 0.680759I
b = 1.414210I
−4.93480 0
u = 0.624546 + 0.119569I
a = −0.33546 + 1.38787I
b = 1.414210I
−4.93480 0
u = 0.624546 − 0.119569I
a = −0.33546 − 1.38787I
b = − 1.414210I
−4.93480 0
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
576(6u
4
− 24u
3
+ ··· − 10u + 1)(4u
17
− 16u
16
+ ··· − 345u + 89)
· (3u
24
− 3u
23
+ ··· − 19u + 1)
· (8u
68
+ 172u
66
+ ··· + 1912799780u + 308884925)
c
2
, c
10
4(2u
4
+ 5u
2
+ 6u + 3)(u
17
− u
16
+ ··· − 4u − 4)(u
24
+ u
23
+ ··· − 3u − 3)
· (2u
68
− 7u
66
+ ··· + 10344u + 1196)
c
3
, c
9
576(6u
4
− 12u
3
+ ··· − 8u + 2)(4u
17
− 4u
16
+ ··· + 3u − 1)
· (3u
24
+ 3u
23
+ ··· − u + 1)(8u
68
+ 40u
66
+ ··· + 270u + 50)
c
4
576(6u
4
+ 12u
3
+ ··· + 8u + 2)(4u
17
+ 4u
16
+ ··· − 4u − 1)
· (3u
24
− 3u
23
+ ··· + 2u + 1)
· (8u
68
− 184u
66
+ ··· + 3891182u + 266986)
c
5
4(2u
4
+ 5u
2
+ 6u + 3)(u
17
+ u
16
+ ··· − 48u − 28)
· (u
24
− 3u
23
+ ··· − 33u + 3)(2u
68
+ 21u
66
+ ··· − 27024u + 18932)
c
6
((u
2
+ 2)
2
)(u
17
+ 6u
16
+ ··· + 5u − 1)(u
24
− 17u
23
+ ··· + 448u − 64)
· (u
34
+ 8u
33
+ ··· + 10u + 2)
2
c
7
((u
2
+ 2)
2
)(u
17
− 2u
16
+ ··· − u − 1)(u
24
− 11u
23
+ ··· − 192u + 32)
· (u
34
+ 6u
33
+ ··· + 6u + 2)
2
c
8
20736(3u
2
+ 2u + 3)
2
(16u
17
+ 64u
16
+ ··· + 276u + 149)
· (9u
24
+ 168u
23
+ ··· − 30720u − 4096)
· (4u
34
− 54u
33
+ ··· + 2256u + 523)
2
c
11
576(6u
4
− 12u
3
+ ··· − 8u + 2)(4u
17
− 4u
16
+ ··· − 4u + 1)
· (3u
24
− 3u
23
+ ··· + 2u + 1)
· (8u
68
− 184u
66
+ ··· + 3891182u + 266986)
c
12
((u
2
+ 2)
2
)(u
17
+ 2u
16
+ ··· − u + 1)(u
24
− 11u
23
+ ··· − 192u + 32)
· (u
34
+ 6u
33
+ ··· + 6u + 2)
2
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
331776(36y
4
− 204y
3
+ 493y
2
− 38y + 1)
· (16y
17
+ 32y
16
+ ··· + 31449y −7921)
· (9y
24
+ 201y
23
+ ··· − 165y + 1)
· (64y
68
+ 2752y
67
+ ··· − 2.42 × 10
16
y + 9.54 × 10
16
)
c
2
, c
10
16(4y
4
+ 20y
3
+ ··· − 6y + 9)(y
17
− 5y
16
+ ··· − 32y −16)
· (y
24
− 5y
23
+ ··· + 21y + 9)
· (4y
68
− 28y
67
+ ··· − 14796304y + 1430416)
c
3
, c
9
331776(36y
4
+ 12y
3
+ ··· − 12y + 4)(16y
17
− 96y
16
+ ··· + 13y −1)
· (9y
24
− 51y
23
+ ··· − 17y + 1)
· (64y
68
+ 640y
67
+ ··· − 109200y + 2500)
c
4
, c
11
331776(36y
4
+ 12y
3
+ ··· − 12y + 4)(16y
17
− 96y
16
+ ··· − 18y −1)
· (9y
24
− 267y
23
+ ··· − 18y + 1)
· (64y
68
− 2944y
67
+ ··· − 3773667301888y + 71281524196)
c
5
16(4y
4
+ 20y
3
+ ··· − 6y + 9)(y
17
− y
16
+ ··· + 4432y −784)
· (y
24
+ 11y
23
+ ··· − 69y + 9)
· (4y
68
+ 84y
67
+ ··· + 2034305520y + 358420624)
c
6
((y + 2)
4
)(y
17
+ 4y
16
+ ··· + 21y −1)
· (y
24
+ 7y
23
+ ··· − 36864y + 4096)(y
34
− 4y
33
+ ··· − 64y + 4)
2
c
7
, c
12
((y + 2)
4
)(y
17
+ 10y
16
+ ··· + y −1)(y
24
+ 9y
23
+ ··· + 4608y + 1024)
· (y
34
+ 10y
33
+ ··· + 80y + 4)
2
c
8
429981696(9y
2
+ 14y + 9)
2
· (256y
17
− 1664y
16
+ ··· − 129146y −22201)
· (81y
24
− 558y
23
+ ··· − 44040192y + 16777216)
· (16y
34
− 524y
33
+ ··· − 8625016y + 273529)
2
28
