12a
0916
(K12a
0916
)
A knot diagram
1
Linearized knot diagam
4 6 9 10 2 11 12 3 1 5 7 8
Solving Sequence
7,11
12
3,8
9 4 1 6 2 5 10
c
11
c
7
c
8
c
3
c
12
c
6
c
2
c
5
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.91980 × 10
108
u
81
− 4.29606 × 10
108
u
80
+ ··· + 1.92612 × 10
108
b + 3.19210 × 10
108
,
− 5.04794 × 10
108
u
81
− 7.50428 × 10
108
u
80
+ ··· + 1.92612 × 10
108
a − 1.67695 × 10
109
,
u
82
+ u
81
+ ··· + 10u − 1i
I
u
2
= h−u
12
+ 8u
10
+ 2u
9
− 23u
8
− 10u
7
+ 27u
6
+ 13u
5
− 11u
4
− u
3
+ 4u
2
+ b − 1,
− 2u
13
+ u
12
+ 20u
11
− 5u
10
− 80u
9
+ u
8
+ 158u
7
+ 30u
6
− 150u
5
− 50u
4
+ 53u
3
+ 23u
2
+ a − 4u − 8,
u
14
− 10u
12
− 2u
11
+ 39u
10
+ 15u
9
− 73u
8
− 40u
7
+ 63u
6
+ 44u
5
− 17u
4
− 18u
3
− 2u
2
+ 4u + 1i
I
u
3
= hu
2
+ b, a − 1, u
6
+ u
5
− 2u
4
− 2u
3
− 1i
I
u
4
= hb + 1, a − 1, u − 1i
I
u
5
= hb + a − 1, a
2
− a − 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 105 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−2.92 × 10
108
u
81
− 4.30 × 10
108
u
80
+ · · · + 1.93 × 10
108
b + 3.19 ×
10
108
, −5.05 × 10
108
u
81
− 7.50 × 10
108
u
80
+ · · · + 1.93 × 10
108
a − 1.68 ×
10
109
, u
82
+ u
81
+ · · · + 10u − 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
3
=
2.62078u
81
+ 3.89606u
80
+ ··· − 39.6810u + 8.70635
1.51590u
81
+ 2.23043u
80
+ ··· − 9.19417u − 1.65727
a
8
=
u
−u
3
+ u
a
9
=
−6.70590u
81
− 12.1721u
80
+ ··· + 90.0743u − 10.7546
2.72204u
81
+ 5.57368u
80
+ ··· − 61.2733u + 9.72272
a
4
=
6.65029u
81
+ 6.12344u
80
+ ··· − 81.0522u + 16.1926
−3.69683u
81
− 2.01061u
80
+ ··· + 53.9722u − 8.26479
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
−u
u
a
2
=
3.92048u
81
+ 5.03730u
80
+ ··· − 55.4423u + 10.6962
0.216200u
81
+ 1.08919u
80
+ ··· + 6.56719u − 3.64708
a
5
=
6.01645u
81
+ 9.73383u
80
+ ··· − 69.8702u + 4.28812
−2.02257u
81
− 2.95608u
80
+ ··· + 24.6648u − 4.64477
a
10
=
−7.90580u
81
− 13.4568u
80
+ ··· + 100.376u − 9.65178
3.61742u
81
+ 6.47329u
80
+ ··· − 70.8432u + 10.9055
(ii) Obstruction class = −1
(iii) Cusp Shapes = 36.4294u
81
+ 55.9906u
80
+ ··· − 576.502u + 76.1479
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
82
− 3u
81
+ ··· + 15u − 1
c
2
, c
5
u
82
+ u
81
+ ··· − 138u + 33
c
3
, c
8
u
82
− 22u
80
+ ··· − 4101u − 607
c
4
, c
10
u
82
+ 5u
81
+ ··· + 112u − 8
c
6
, c
7
, c
11
c
12
u
82
+ u
81
+ ··· + 10u − 1
c
9
u
82
− 2u
81
+ ··· − 24u + 12
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
82
− 13y
81
+ ··· − 27y + 1
c
2
, c
5
y
82
− 39y
81
+ ··· − 42804y + 1089
c
3
, c
8
y
82
− 44y
81
+ ··· − 14225097y + 368449
c
4
, c
10
y
82
− 51y
81
+ ··· − 13728y + 64
c
6
, c
7
, c
11
c
12
y
82
− 101y
81
+ ··· − 110y + 1
c
9
y
82
− 8y
81
+ ··· − 216y + 144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.984782 + 0.188624I
a = −0.141871 + 0.097301I
b = −0.334414 + 0.658720I
5.90211 − 2.33787I 0
u = −0.984782 − 0.188624I
a = −0.141871 − 0.097301I
b = −0.334414 − 0.658720I
5.90211 + 2.33787I 0
u = 0.843614 + 0.550628I
a = 0.787898 + 0.115680I
b = 0.1163850 − 0.0010731I
2.79780 − 0.42396I 0
u = 0.843614 − 0.550628I
a = 0.787898 − 0.115680I
b = 0.1163850 + 0.0010731I
2.79780 + 0.42396I 0
u = −1.02284
a = 1.47383
b = −0.331000
0.462297 0
u = −0.783113 + 0.549508I
a = 0.0588211 + 0.1268950I
b = −0.86879 − 1.12637I
−4.73426 − 7.26403I 0
u = −0.783113 − 0.549508I
a = 0.0588211 − 0.1268950I
b = −0.86879 + 1.12637I
−4.73426 + 7.26403I 0
u = 0.887115 + 0.337671I
a = 0.155583 − 0.193486I
b = 1.042270 − 0.535647I
−3.35923 + 0.42248I 0
u = 0.887115 − 0.337671I
a = 0.155583 + 0.193486I
b = 1.042270 + 0.535647I
−3.35923 − 0.42248I 0
u = 0.811426 + 0.677149I
a = 0.0288692 + 0.0472312I
b = −0.527577 + 1.199900I
−0.39025 + 13.28170I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.811426 − 0.677149I
a = 0.0288692 − 0.0472312I
b = −0.527577 − 1.199900I
−0.39025 − 13.28170I 0
u = 0.188934 + 0.907176I
a = −0.616856 + 0.715162I
b = −0.157446 + 0.338454I
−2.29134 − 8.09229I 0
u = 0.188934 − 0.907176I
a = −0.616856 − 0.715162I
b = −0.157446 − 0.338454I
−2.29134 + 8.09229I 0
u = 0.585370 + 0.706438I
a = 0.0863636 − 0.0965957I
b = 0.083043 − 1.114300I
2.00602 + 4.30322I 0
u = 0.585370 − 0.706438I
a = 0.0863636 + 0.0965957I
b = 0.083043 + 1.114300I
2.00602 − 4.30322I 0
u = −0.795599 + 0.407080I
a = −0.817039 + 0.266032I
b = −0.02769 − 1.43627I
3.45231 − 7.58300I 0
u = −0.795599 − 0.407080I
a = −0.817039 − 0.266032I
b = −0.02769 + 1.43627I
3.45231 + 7.58300I 0
u = 0.770296 + 0.366086I
a = −1.102450 − 0.449931I
b = 0.209050 − 0.713360I
2.67572 + 6.81110I 0
u = 0.770296 − 0.366086I
a = −1.102450 + 0.449931I
b = 0.209050 + 0.713360I
2.67572 − 6.81110I 0
u = 1.17627
a = 0.260420
b = 0.996259
−3.39624 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.657045 + 0.470711I
a = −0.122567 + 0.464530I
b = 0.656971 + 1.206150I
−2.18416 − 4.72064I 0
u = −0.657045 − 0.470711I
a = −0.122567 − 0.464530I
b = 0.656971 − 1.206150I
−2.18416 + 4.72064I 0
u = 0.695887 + 0.178695I
a = 0.331121 − 1.049200I
b = −1.52202 + 1.38533I
−0.296974 + 0.337709I −14.6453 + 19.7980I
u = 0.695887 − 0.178695I
a = 0.331121 + 1.049200I
b = −1.52202 − 1.38533I
−0.296974 − 0.337709I −14.6453 − 19.7980I
u = −0.561252 + 0.447215I
a = −0.597055 − 0.069631I
b = 0.304635 + 0.996919I
−0.76027 − 3.85816I 0. + 6.83350I
u = −0.561252 − 0.447215I
a = −0.597055 + 0.069631I
b = 0.304635 − 0.996919I
−0.76027 + 3.85816I 0. − 6.83350I
u = −0.126025 + 0.701569I
a = −0.59662 − 1.32241I
b = 0.114296 − 0.377897I
−6.70258 + 3.06709I −5.21302 − 2.47341I
u = −0.126025 − 0.701569I
a = −0.59662 + 1.32241I
b = 0.114296 + 0.377897I
−6.70258 − 3.06709I −5.21302 + 2.47341I
u = −0.236388 + 0.598256I
a = 0.294774 − 0.609135I
b = 0.426322 + 1.024910I
−0.07658 − 4.13532I 0.75722 + 4.26107I
u = −0.236388 − 0.598256I
a = 0.294774 + 0.609135I
b = 0.426322 − 1.024910I
−0.07658 + 4.13532I 0.75722 − 4.26107I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.28955 + 0.58878I
a = −0.0523594 + 0.0124131I
b = 0.706077 + 0.030045I
2.14333 + 2.89478I 0
u = −1.28955 − 0.58878I
a = −0.0523594 − 0.0124131I
b = 0.706077 − 0.030045I
2.14333 − 2.89478I 0
u = 0.113038 + 0.567992I
a = −0.569049 − 0.821467I
b = −0.095569 − 0.935559I
0.88681 + 4.41440I 3.03410 − 4.57971I
u = 0.113038 − 0.567992I
a = −0.569049 + 0.821467I
b = −0.095569 + 0.935559I
0.88681 − 4.41440I 3.03410 + 4.57971I
u = 0.558549 + 0.147764I
a = 0.621866 + 0.196056I
b = −0.456183 − 0.414679I
0.998059 + 0.188402I 10.40306 − 0.95041I
u = 0.558549 − 0.147764I
a = 0.621866 − 0.196056I
b = −0.456183 + 0.414679I
0.998059 − 0.188402I 10.40306 + 0.95041I
u = −0.234783 + 0.515407I
a = 1.32426 + 1.53813I
b = 0.365229 + 0.093260I
−3.40619 + 1.28533I −2.46945 + 0.12060I
u = −0.234783 − 0.515407I
a = 1.32426 − 1.53813I
b = 0.365229 − 0.093260I
−3.40619 − 1.28533I −2.46945 − 0.12060I
u = 0.502065 + 0.126289I
a = −2.39872 − 0.92369I
b = 0.61945 + 1.69002I
−0.834967 + 0.544419I −9.5439 + 23.8545I
u = 0.502065 − 0.126289I
a = −2.39872 + 0.92369I
b = 0.61945 − 1.69002I
−0.834967 − 0.544419I −9.5439 − 23.8545I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.284642 + 0.381065I
a = 1.48853 + 0.50264I
b = 0.008733 − 0.426456I
−1.50630 + 0.84820I −1.82690 − 0.01242I
u = −0.284642 − 0.381065I
a = 1.48853 − 0.50264I
b = 0.008733 + 0.426456I
−1.50630 − 0.84820I −1.82690 + 0.01242I
u = −1.52579 + 0.01939I
a = −0.08285 + 2.43592I
b = −0.54993 − 3.11467I
6.46065 − 4.82598I 0
u = −1.52579 − 0.01939I
a = −0.08285 − 2.43592I
b = −0.54993 + 3.11467I
6.46065 + 4.82598I 0
u = 1.52787 + 0.06405I
a = 0.02483 − 2.22735I
b = 0.25321 + 2.46288I
5.88122 + 5.76712I 0
u = 1.52787 − 0.06405I
a = 0.02483 + 2.22735I
b = 0.25321 − 2.46288I
5.88122 − 5.76712I 0
u = 1.54225 + 0.03034I
a = 0.49740 + 1.73264I
b = −1.12629 − 2.23338I
4.80677 − 0.09764I 0
u = 1.54225 − 0.03034I
a = 0.49740 − 1.73264I
b = −1.12629 + 2.23338I
4.80677 + 0.09764I 0
u = 0.438034
a = 4.33297
b = 0.243064
−5.42434 13.3340
u = 1.55488 + 0.14908I
a = −0.15289 − 2.05569I
b = −0.07056 + 2.52598I
6.30459 + 6.05965I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55488 − 0.14908I
a = −0.15289 + 2.05569I
b = −0.07056 − 2.52598I
6.30459 − 6.05965I 0
u = −1.56931 + 0.07915I
a = −0.504205 + 1.215630I
b = 0.11412 − 1.46849I
8.22114 − 1.25008I 0
u = −1.56931 − 0.07915I
a = −0.504205 − 1.215630I
b = 0.11412 + 1.46849I
8.22114 + 1.25008I 0
u = −1.57829 + 0.02432I
a = 0.83255 − 2.02283I
b = −0.10047 + 2.25438I
6.44108 − 1.01444I 0
u = −1.57829 − 0.02432I
a = 0.83255 + 2.02283I
b = −0.10047 − 2.25438I
6.44108 + 1.01444I 0
u = 1.59304 + 0.13349I
a = 0.48960 − 2.30928I
b = −1.09569 + 3.07315I
5.44937 + 6.93869I 0
u = 1.59304 − 0.13349I
a = 0.48960 + 2.30928I
b = −1.09569 − 3.07315I
5.44937 − 6.93869I 0
u = −1.61613 + 0.05731I
a = −0.86864 − 2.17772I
b = 1.34031 + 2.38505I
7.71340 − 1.27145I 0
u = −1.61613 − 0.05731I
a = −0.86864 + 2.17772I
b = 1.34031 − 2.38505I
7.71340 + 1.27145I 0
u = −1.60197 + 0.23933I
a = −0.21626 + 1.64990I
b = −0.42879 − 2.17532I
9.34734 − 7.89119I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60197 − 0.23933I
a = −0.21626 − 1.64990I
b = −0.42879 + 2.17532I
9.34734 + 7.89119I 0
u = −1.62865 + 0.10885I
a = −0.27752 + 1.88885I
b = 0.60651 − 2.82092I
10.91440 − 8.63897I 0
u = −1.62865 − 0.10885I
a = −0.27752 − 1.88885I
b = 0.60651 + 2.82092I
10.91440 + 8.63897I 0
u = 1.63599 + 0.11853I
a = 0.13839 + 1.88321I
b = 0.63901 − 2.35405I
11.7947 + 9.5991I 0
u = 1.63599 − 0.11853I
a = 0.13839 − 1.88321I
b = 0.63901 + 2.35405I
11.7947 − 9.5991I 0
u = 1.63569 + 0.16394I
a = −0.60372 + 1.93511I
b = 1.25447 − 2.32571I
3.49190 + 9.98671I 0
u = 1.63569 − 0.16394I
a = −0.60372 − 1.93511I
b = 1.25447 + 2.32571I
3.49190 − 9.98671I 0
u = −1.64218 + 0.10635I
a = 1.02828 + 1.40183I
b = −1.70059 − 1.85899I
5.25941 − 2.18573I 0
u = −1.64218 − 0.10635I
a = 1.02828 − 1.40183I
b = −1.70059 + 1.85899I
5.25941 + 2.18573I 0
u = 1.64631 + 0.13035I
a = −0.166642 − 1.110980I
b = −0.64066 + 1.48754I
10.14690 + 2.43534I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.64631 − 0.13035I
a = −0.166642 + 1.110980I
b = −0.64066 − 1.48754I
10.14690 − 2.43534I 0
u = −1.64774 + 0.20688I
a = −0.28445 − 1.94616I
b = 1.02920 + 2.54457I
7.8970 − 16.6675I 0
u = −1.64774 − 0.20688I
a = −0.28445 + 1.94616I
b = 1.02920 − 2.54457I
7.8970 + 16.6675I 0
u = −1.65858 + 0.12298I
a = 0.110901 − 1.131240I
b = −0.41531 + 1.65555I
11.51240 − 2.00269I 0
u = −1.65858 − 0.12298I
a = 0.110901 + 1.131240I
b = −0.41531 − 1.65555I
11.51240 + 2.00269I 0
u = 1.68232 + 0.02867I
a = −0.34423 − 1.51184I
b = 0.47995 + 2.19462I
15.2504 + 3.0857I 0
u = 1.68232 − 0.02867I
a = −0.34423 + 1.51184I
b = 0.47995 − 2.19462I
15.2504 − 3.0857I 0
u = −0.232323 + 0.118937I
a = 2.05401 + 1.65947I
b = 0.558019 + 0.573483I
−1.47682 − 0.41930I −7.12572 − 0.42040I
u = −0.232323 − 0.118937I
a = 2.05401 − 1.65947I
b = 0.558019 − 0.573483I
−1.47682 + 0.41930I −7.12572 + 0.42040I
u = 0.139756 + 0.051773I
a = 5.40801 + 1.65564I
b = −0.39225 + 1.47645I
0.34771 − 4.65375I 6.29780 + 2.05720I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.139756 − 0.051773I
a = 5.40801 − 1.65564I
b = −0.39225 − 1.47645I
0.34771 + 4.65375I 6.29780 − 2.05720I
u = 1.88800
a = 0.440654
b = −0.742379
14.6724 0
13
II.
I
u
2
= h−u
12
+8u
10
+· · ·+b−1, −2u
13
+u
12
+· · ·+a−8, u
14
−10u
12
+· · ·+4u+1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
3
=
2u
13
− u
12
+ ··· + 4u + 8
u
12
− 8u
10
− 2u
9
+ 23u
8
+ 10u
7
− 27u
6
− 13u
5
+ 11u
4
+ u
3
− 4u
2
+ 1
a
8
=
u
−u
3
+ u
a
9
=
3u
13
− u
12
+ ··· + 6u + 11
−u
12
− u
11
+ ··· + u + 1
a
4
=
−u
13
+ 11u
11
+ ··· + 19u
2
− 6
−u
13
+ 9u
11
+ ··· + 4u
2
+ 2u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
−u
u
a
2
=
2u
13
− 20u
11
+ ··· + 2u + 8
−u
7
+ 5u
5
+ 2u
4
− 7u
3
− 5u
2
+ 2u + 1
a
5
=
−4u
13
+ 40u
11
+ ··· − 2u − 15
−u
13
+ 9u
11
+ ··· + 7u
2
− 1
a
10
=
3u
13
− 2u
12
+ ··· + 7u + 13
u
3
− 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
13
+ 6u
12
+ 53u
11
− 42u
10
− 226u
9
+ 93u
8
+ 475u
7
− 51u
6
−
478u
5
− 45u
4
+ 177u
3
+ 40u
2
− 9u − 18
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− 5u
13
+ ··· + 8u − 1
c
2
u
14
+ 6u
13
+ ··· + 6u + 1
c
3
u
14
− 3u
12
− u
11
+ u
10
+ 2u
9
+ 4u
8
− 4u
6
− u
5
− u
4
+ u
3
+ 3u
2
− 1
c
4
u
14
− 3u
12
+ u
11
+ u
10
− u
9
+ 4u
8
− 4u
6
+ 2u
5
− u
4
− u
3
+ 3u
2
− 1
c
5
u
14
− 6u
13
+ ··· − 6u + 1
c
6
, c
7
u
14
− 10u
12
+ ··· − 4u + 1
c
8
u
14
− 3u
12
+ u
11
+ u
10
− 2u
9
+ 4u
8
− 4u
6
+ u
5
− u
4
− u
3
+ 3u
2
− 1
c
9
u
14
− 3u
13
+ ··· + 9u + 5
c
10
u
14
− 3u
12
− u
11
+ u
10
+ u
9
+ 4u
8
− 4u
6
− 2u
5
− u
4
+ u
3
+ 3u
2
− 1
c
11
, c
12
u
14
− 10u
12
+ ··· + 4u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− 7y
13
+ ··· − 16y + 1
c
2
, c
5
y
14
− 14y
13
+ ··· − 14y + 1
c
3
, c
8
y
14
− 6y
13
+ ··· − 6y + 1
c
4
, c
10
y
14
− 6y
13
+ ··· − 6y + 1
c
6
, c
7
, c
11
c
12
y
14
− 20y
13
+ ··· − 20y + 1
c
9
y
14
− 9y
13
+ ··· − 381y + 25
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.22387
a = 0.572038
b = 0.757485
−2.53458 6.54520
u = −1.162790 + 0.439090I
a = 0.523471 − 0.653534I
b = −0.040336 + 0.575626I
2.80440 + 2.09868I 6.54061 − 1.90346I
u = −1.162790 − 0.439090I
a = 0.523471 + 0.653534I
b = −0.040336 − 0.575626I
2.80440 − 2.09868I 6.54061 + 1.90346I
u = 0.596998 + 0.186070I
a = 1.073280 + 0.589812I
b = 0.271776 − 1.277540I
−0.545174 + 0.639000I 3.99401 + 1.44845I
u = 0.596998 − 0.186070I
a = 1.073280 − 0.589812I
b = 0.271776 + 1.277540I
−0.545174 − 0.639000I 3.99401 − 1.44845I
u = −0.325168 + 0.425935I
a = −0.322223 + 0.016593I
b = 0.09995 + 1.63147I
0.08308 − 5.23699I 1.10474 + 13.13886I
u = −0.325168 − 0.425935I
a = −0.322223 − 0.016593I
b = 0.09995 − 1.63147I
0.08308 + 5.23699I 1.10474 − 13.13886I
u = 1.51899
a = 1.45349
b = −2.86372
0.601067 −4.00870
u = 1.54617 + 0.13024I
a = −0.06551 − 2.57810I
b = −0.34874 + 3.21051I
6.64288 + 7.22347I 7.90690 − 8.98242I
u = 1.54617 − 0.13024I
a = −0.06551 + 2.57810I
b = −0.34874 − 3.21051I
6.64288 − 7.22347I 7.90690 + 8.98242I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59813 + 0.06557I
a = 0.15257 + 1.71766I
b = −0.75191 − 2.00442I
7.12099 − 1.61991I 3.99923 − 0.01293I
u = −1.59813 − 0.06557I
a = 0.15257 − 1.71766I
b = −0.75191 + 2.00442I
7.12099 + 1.61991I 3.99923 + 0.01293I
u = −0.270493
a = 6.33895
b = 0.754277
−5.70613 −15.7570
u = 1.86121
a = −0.0876364
b = −0.109531
14.9057 23.1290
18
III. I
u
3
= hu
2
+ b, a − 1, u
6
+ u
5
− 2u
4
− 2u
3
− 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
3
=
1
−u
2
a
8
=
u
−u
3
+ u
a
9
=
0
u
a
4
=
1
0
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
−u
u
a
2
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
5
=
u
5
− 2u
3
+ u − 1
1
a
10
=
u
5
− 2u
3
+ u
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ u
5
− 2u
3
+ 2u
2
− 4u + 1
c
2
, c
5
, c
9
u
6
− 5u
4
− 2u
3
+ 4u
2
− 3
c
3
, c
6
, c
7
c
8
, c
11
, c
12
u
6
+ u
5
− 2u
4
− 2u
3
− 1
c
4
, c
10
(u − 1)
6
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− y
5
+ 8y
4
+ 6y
3
− 12y
2
− 12y + 1
c
2
, c
5
, c
9
y
6
− 10y
5
+ 33y
4
− 50y
3
+ 46y
2
− 24y + 9
c
3
, c
6
, c
7
c
8
, c
11
, c
12
y
6
− 5y
5
+ 8y
4
− 6y
3
+ 4y
2
+ 1
c
4
, c
10
(y −1)
6
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.819901 + 0.541369I
a = 1.00000
b = −0.379157 + 0.887737I
1.64493 6.00000
u = −0.819901 − 0.541369I
a = 1.00000
b = −0.379157 − 0.887737I
1.64493 6.00000
u = 0.373850 + 0.559427I
a = 1.00000
b = 0.173195 − 0.418284I
1.64493 6.00000
u = 0.373850 − 0.559427I
a = 1.00000
b = 0.173195 + 0.418284I
1.64493 6.00000
u = 1.45970
a = 1.00000
b = −2.13072
1.64493 6.00000
u = −1.56760
a = 1.00000
b = −2.45736
1.64493 6.00000
22
IV. I
u
4
= hb + 1, a − 1, u − 1i
(i) Arc colorings
a
7
=
0
1
a
11
=
1
0
a
12
=
1
−1
a
3
=
1
−1
a
8
=
1
0
a
9
=
0
1
a
4
=
1
0
a
1
=
0
−1
a
6
=
−1
1
a
2
=
1
−1
a
5
=
−1
1
a
10
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u + 1
c
2
, c
5
, c
9
u
c
3
, c
4
, c
6
c
7
, c
8
, c
10
c
11
, c
12
u − 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y −1
c
2
, c
5
, c
9
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = −1.00000
1.64493 6.00000
26
V. I
u
5
= hb + a − 1, a
2
− a − 1, u − 1i
(i) Arc colorings
a
7
=
0
1
a
11
=
1
0
a
12
=
1
−1
a
3
=
a
−a + 1
a
8
=
1
0
a
9
=
0
−a + 2
a
4
=
a
a − 2
a
1
=
0
−1
a
6
=
−1
1
a
2
=
a + 1
−a
a
5
=
a
−a + 1
a
10
=
0
−a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
u
2
− u − 1
c
2
, c
11
, c
12
(u − 1)
2
c
3
, c
4
u
2
+ u − 1
c
5
, c
6
, c
7
(u + 1)
2
c
9
u
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
10
y
2
− 3y + 1
c
2
, c
5
, c
6
c
7
, c
11
, c
12
(y −1)
2
c
9
y
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.618034
b = 1.61803
0 −5.00000
u = 1.00000
a = 1.61803
b = −0.618034
0 −5.00000
30
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
2
− u − 1)(u
6
+ u
5
+ ··· − 4u + 1)(u
14
− 5u
13
+ ··· + 8u − 1)
· (u
82
− 3u
81
+ ··· + 15u − 1)
c
2
u(u − 1)
2
(u
6
− 5u
4
+ ··· + 4u
2
− 3)(u
14
+ 6u
13
+ ··· + 6u + 1)
· (u
82
+ u
81
+ ··· − 138u + 33)
c
3
(u − 1)(u
2
+ u − 1)(u
6
+ u
5
− 2u
4
− 2u
3
− 1)
· (u
14
− 3u
12
− u
11
+ u
10
+ 2u
9
+ 4u
8
− 4u
6
− u
5
− u
4
+ u
3
+ 3u
2
− 1)
· (u
82
− 22u
80
+ ··· − 4101u − 607)
c
4
(u − 1)
7
(u
2
+ u − 1)
· (u
14
− 3u
12
+ u
11
+ u
10
− u
9
+ 4u
8
− 4u
6
+ 2u
5
− u
4
− u
3
+ 3u
2
− 1)
· (u
82
+ 5u
81
+ ··· + 112u − 8)
c
5
u(u + 1)
2
(u
6
− 5u
4
+ ··· + 4u
2
− 3)(u
14
− 6u
13
+ ··· − 6u + 1)
· (u
82
+ u
81
+ ··· − 138u + 33)
c
6
, c
7
(u − 1)(u + 1)
2
(u
6
+ u
5
+ ··· − 2u
3
− 1)(u
14
− 10u
12
+ ··· − 4u + 1)
· (u
82
+ u
81
+ ··· + 10u − 1)
c
8
(u − 1)(u
2
− u − 1)(u
6
+ u
5
− 2u
4
− 2u
3
− 1)
· (u
14
− 3u
12
+ u
11
+ u
10
− 2u
9
+ 4u
8
− 4u
6
+ u
5
− u
4
− u
3
+ 3u
2
− 1)
· (u
82
− 22u
80
+ ··· − 4101u − 607)
c
9
u
3
(u
6
− 5u
4
+ ··· + 4u
2
− 3)(u
14
− 3u
13
+ ··· + 9u + 5)
· (u
82
− 2u
81
+ ··· − 24u + 12)
c
10
(u − 1)
7
(u
2
− u − 1)
· (u
14
− 3u
12
− u
11
+ u
10
+ u
9
+ 4u
8
− 4u
6
− 2u
5
− u
4
+ u
3
+ 3u
2
− 1)
· (u
82
+ 5u
81
+ ··· + 112u − 8)
c
11
, c
12
((u − 1)
3
)(u
6
+ u
5
− 2u
4
− 2u
3
− 1)(u
14
− 10u
12
+ ··· + 4u + 1)
· (u
82
+ u
81
+ ··· + 10u − 1)
31
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
2
− 3y + 1)(y
6
− y
5
+ 8y
4
+ 6y
3
− 12y
2
− 12y + 1)
· (y
14
− 7y
13
+ ··· − 16y + 1)(y
82
− 13y
81
+ ··· − 27y + 1)
c
2
, c
5
y(y −1)
2
(y
6
− 10y
5
+ 33y
4
− 50y
3
+ 46y
2
− 24y + 9)
· (y
14
− 14y
13
+ ··· − 14y + 1)(y
82
− 39y
81
+ ··· − 42804y + 1089)
c
3
, c
8
(y −1)(y
2
− 3y + 1)(y
6
− 5y
5
+ 8y
4
− 6y
3
+ 4y
2
+ 1)
· (y
14
− 6y
13
+ ··· − 6y + 1)(y
82
− 44y
81
+ ··· − 1.42251 × 10
7
y + 368449)
c
4
, c
10
((y −1)
7
)(y
2
− 3y + 1)(y
14
− 6y
13
+ ··· − 6y + 1)
· (y
82
− 51y
81
+ ··· − 13728y + 64)
c
6
, c
7
, c
11
c
12
((y −1)
3
)(y
6
− 5y
5
+ ··· + 4y
2
+ 1)(y
14
− 20y
13
+ ··· − 20y + 1)
· (y
82
− 101y
81
+ ··· − 110y + 1)
c
9
y
3
(y
6
− 10y
5
+ 33y
4
− 50y
3
+ 46y
2
− 24y + 9)
· (y
14
− 9y
13
+ ··· − 381y + 25)(y
82
− 8y
81
+ ··· − 216y + 144)
32
