12a
0211
(K12a
0211
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 2 5 11 4 12 1 8 10
Solving Sequence
4,8
9
5,12
10 1 11 7 3 6 2
c
8
c
4
c
9
c
12
c
11
c
7
c
3
c
6
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.86194 × 10
263
u
97
+ 1.50956 × 10
264
u
96
+ ··· + 4.00373 × 10
264
b + 1.42422 × 10
266
,
1.21954 × 10
264
u
97
− 1.97917 × 10
264
u
96
+ ··· + 8.00746 × 10
264
a − 1.99719 × 10
266
,
u
98
− 2u
97
+ ··· − 160u + 64i
I
u
2
= hb, 2u
7
− 3u
6
− 5u
5
+ 7u
4
+ 4u
3
− 3u
2
+ a − 4, u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1i
I
v
1
= ha, 26v
5
− 33v
4
+ 317v
3
− 123v
2
+ 413b + 89v −685, v
6
− 3v
5
+ 15v
4
− 24v
3
+ 11v
2
− 6v + 1i
* 3 irreducible components of dim
C
= 0, with total 112 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−9.86 × 10
263
u
97
+ 1.51 × 10
264
u
96
+ · · · + 4.00 × 10
264
b + 1.42 ×
10
266
, 1.22 × 10
264
u
97
− 1.98 × 10
264
u
96
+ · · · + 8.01 × 10
264
a − 2.00 ×
10
266
, u
98
− 2u
97
+ · · · − 160u + 64i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
5
=
−u
−u
3
+ u
a
12
=
−0.152300u
97
+ 0.247165u
96
+ ··· − 4.59357u + 24.9416
0.246319u
97
− 0.377039u
96
+ ··· + 7.83550u − 35.5724
a
10
=
−0.0398059u
97
+ 0.0702429u
96
+ ··· − 3.05431u + 8.48553
−0.411031u
97
+ 0.653363u
96
+ ··· − 7.40277u + 62.7622
a
1
=
0.00297584u
97
− 0.00863836u
96
+ ··· + 1.05873u − 0.848853
−0.411031u
97
+ 0.653363u
96
+ ··· − 7.40277u + 62.7622
a
11
=
−0.398619u
97
+ 0.624205u
96
+ ··· − 12.4291u + 60.5140
0.246319u
97
− 0.377039u
96
+ ··· + 7.83550u − 35.5724
a
7
=
−0.402842u
97
+ 0.642002u
96
+ ··· − 5.72372u + 61.7414
0.405818u
97
− 0.650640u
96
+ ··· + 6.78245u − 62.5902
a
3
=
0.0603712u
97
− 0.0945033u
96
+ ··· + 3.51045u − 8.93865
−0.286712u
97
+ 0.446756u
96
+ ··· − 6.09763u + 42.5150
a
6
=
−0.402533u
97
+ 0.632225u
96
+ ··· − 6.75744u + 60.4412
0.389959u
97
− 0.628287u
96
+ ··· + 6.33110u − 60.7040
a
2
=
0.0840663u
97
− 0.138202u
96
+ ··· + 6.02197u − 11.8518
−0.634821u
97
+ 0.986175u
96
+ ··· − 17.0563u + 92.8076
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.75154u
97
+ 2.69397u
96
+ ··· − 90.1293u + 259.318
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
98
+ 32u
97
+ ··· + 46u + 1
c
2
, c
5
u
98
+ 4u
97
+ ··· + 14u + 1
c
3
u
98
− 4u
97
+ ··· + 19016u + 4129
c
4
, c
8
u
98
+ 2u
97
+ ··· + 160u + 64
c
7
, c
11
u
98
− 4u
97
+ ··· − 128u + 256
c
9
, c
10
, c
12
u
98
+ 12u
97
+ ··· − 31u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
98
+ 72y
97
+ ··· − 2334y + 1
c
2
, c
5
y
98
− 32y
97
+ ··· − 46y + 1
c
3
y
98
+ 76y
96
+ ··· − 284998790y + 17048641
c
4
, c
8
y
98
− 42y
97
+ ··· − 87040y + 4096
c
7
, c
11
y
98
− 60y
97
+ ··· − 3457024y + 65536
c
9
, c
10
, c
12
y
98
− 96y
97
+ ··· − 903y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.836034 + 0.535484I
a = −0.62066 − 1.46991I
b = −0.276978 − 1.030340I
2.71965 − 2.17187I 0
u = 0.836034 − 0.535484I
a = −0.62066 + 1.46991I
b = −0.276978 + 1.030340I
2.71965 + 2.17187I 0
u = 1.007890 + 0.057843I
a = 0.515193 + 1.015350I
b = 0.482660 + 0.606015I
−1.69730 − 0.04707I 0
u = 1.007890 − 0.057843I
a = 0.515193 − 1.015350I
b = 0.482660 − 0.606015I
−1.69730 + 0.04707I 0
u = 0.988943 + 0.038650I
a = 0.298767 + 1.109500I
b = −0.915779 + 0.645889I
0.81536 + 3.65505I 0
u = 0.988943 − 0.038650I
a = 0.298767 − 1.109500I
b = −0.915779 − 0.645889I
0.81536 − 3.65505I 0
u = 0.640994 + 0.748545I
a = −1.24753 − 1.31283I
b = 0.099282 − 1.047820I
6.60141 − 1.31084I 0
u = 0.640994 − 0.748545I
a = −1.24753 + 1.31283I
b = 0.099282 + 1.047820I
6.60141 + 1.31084I 0
u = 0.958058 + 0.352709I
a = 0.462382 + 0.808485I
b = −1.122110 + 0.350042I
−1.92679 − 1.50494I 0
u = 0.958058 − 0.352709I
a = 0.462382 − 0.808485I
b = −1.122110 − 0.350042I
−1.92679 + 1.50494I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.945192 + 0.184243I
a = 0.063153 + 1.354140I
b = −0.690539 + 0.806870I
1.09894 − 0.93181I 0
u = −0.945192 − 0.184243I
a = 0.063153 − 1.354140I
b = −0.690539 − 0.806870I
1.09894 + 0.93181I 0
u = −0.566049 + 0.872784I
a = 0.561625 − 0.370323I
b = −1.047790 + 0.313579I
4.33302 − 0.85349I 0
u = −0.566049 − 0.872784I
a = 0.561625 + 0.370323I
b = −1.047790 − 0.313579I
4.33302 + 0.85349I 0
u = −0.577362 + 0.766403I
a = −1.41361 + 1.28993I
b = 0.174263 + 1.005380I
6.01938 − 4.43105I 0
u = −0.577362 − 0.766403I
a = −1.41361 − 1.28993I
b = 0.174263 − 1.005380I
6.01938 + 4.43105I 0
u = −0.413184 + 0.978752I
a = 0.192652 − 0.001510I
b = 1.327370 − 0.296247I
8.16464 − 2.11391I 0
u = −0.413184 − 0.978752I
a = 0.192652 + 0.001510I
b = 1.327370 + 0.296247I
8.16464 + 2.11391I 0
u = 0.523046 + 0.927802I
a = 0.550866 + 0.336203I
b = −1.026850 − 0.381970I
3.59665 + 6.49124I 0
u = 0.523046 − 0.927802I
a = 0.550866 − 0.336203I
b = −1.026850 + 0.381970I
3.59665 − 6.49124I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.945040 + 0.577805I
a = 0.464812 − 0.635543I
b = −1.252900 − 0.141177I
3.98973 + 1.09003I 0
u = −0.945040 − 0.577805I
a = 0.464812 + 0.635543I
b = −1.252900 + 0.141177I
3.98973 − 1.09003I 0
u = −0.685394 + 0.556168I
a = −0.51862 + 2.07030I
b = 0.966579 + 0.148747I
4.79276 + 3.49348I 0. − 7.89856I
u = −0.685394 − 0.556168I
a = −0.51862 − 2.07030I
b = 0.966579 − 0.148747I
4.79276 − 3.49348I 0. + 7.89856I
u = 0.295338 + 0.821202I
a = 0.653295 + 0.245041I
b = −0.779521 − 0.351251I
−1.36442 + 1.59603I −6.13954 − 4.68221I
u = 0.295338 − 0.821202I
a = 0.653295 − 0.245041I
b = −0.779521 + 0.351251I
−1.36442 − 1.59603I −6.13954 + 4.68221I
u = 1.072730 + 0.347020I
a = 0.084885 − 1.334090I
b = 0.898101 − 0.581765I
−2.07276 − 0.59423I 0
u = 1.072730 − 0.347020I
a = 0.084885 + 1.334090I
b = 0.898101 + 0.581765I
−2.07276 + 0.59423I 0
u = −1.009660 + 0.504740I
a = −0.429556 + 1.236740I
b = −0.466522 + 1.159040I
−0.85776 + 4.36308I 0
u = −1.009660 − 0.504740I
a = −0.429556 − 1.236740I
b = −0.466522 − 1.159040I
−0.85776 − 4.36308I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.004060 + 0.523832I
a = −0.16333 + 1.43855I
b = 1.054600 + 0.456626I
0.08244 + 4.26327I 0
u = −1.004060 − 0.523832I
a = −0.16333 − 1.43855I
b = 1.054600 − 0.456626I
0.08244 − 4.26327I 0
u = 1.003640 + 0.555239I
a = 0.429213 + 0.654904I
b = −1.293330 + 0.197292I
3.15484 − 6.74893I 0
u = 1.003640 − 0.555239I
a = 0.429213 − 0.654904I
b = −1.293330 − 0.197292I
3.15484 + 6.74893I 0
u = −0.645737 + 0.552571I
a = 0.191518 + 0.001250I
b = 1.66186 − 0.25832I
12.53660 − 1.88182I 4.98464 − 2.28984I
u = −0.645737 − 0.552571I
a = 0.191518 − 0.001250I
b = 1.66186 + 0.25832I
12.53660 + 1.88182I 4.98464 + 2.28984I
u = 1.036730 + 0.499877I
a = −0.97362 + 1.91004I
b = −1.310510 + 0.383002I
10.82510 − 0.18571I 0
u = 1.036730 − 0.499877I
a = −0.97362 − 1.91004I
b = −1.310510 − 0.383002I
10.82510 + 0.18571I 0
u = −0.097083 + 0.832554I
a = 0.645250 + 0.020161I
b = −0.410288 − 0.453030I
1.80058 − 2.93404I −2.97782 + 1.88762I
u = −0.097083 − 0.832554I
a = 0.645250 − 0.020161I
b = −0.410288 + 0.453030I
1.80058 + 2.93404I −2.97782 − 1.88762I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.213026 + 1.154770I
a = 0.189633 + 0.002822I
b = 1.149250 + 0.171052I
6.34419 − 1.80278I 0
u = 0.213026 − 1.154770I
a = 0.189633 − 0.002822I
b = 1.149250 − 0.171052I
6.34419 + 1.80278I 0
u = −1.040490 + 0.550713I
a = −0.76305 − 1.93141I
b = −1.327380 − 0.426303I
11.23540 + 6.34533I 0
u = −1.040490 − 0.550713I
a = −0.76305 + 1.93141I
b = −1.327380 + 0.426303I
11.23540 − 6.34533I 0
u = 1.109200 + 0.410240I
a = 0.405843 + 0.678327I
b = 0.187608 + 0.716386I
−0.53991 − 1.97315I 0
u = 1.109200 − 0.410240I
a = 0.405843 − 0.678327I
b = 0.187608 − 0.716386I
−0.53991 + 1.97315I 0
u = 0.674999 + 0.448882I
a = 0.191020 − 0.001236I
b = 1.71246 + 0.21779I
12.08790 − 3.77750I 2.50485 + 8.33450I
u = 0.674999 − 0.448882I
a = 0.191020 + 0.001236I
b = 1.71246 − 0.21779I
12.08790 + 3.77750I 2.50485 − 8.33450I
u = −1.193260 + 0.019414I
a = 0.299196 + 1.016150I
b = 0.586869 + 0.776976I
−3.03641 + 4.53724I 0
u = −1.193260 − 0.019414I
a = 0.299196 − 1.016150I
b = 0.586869 − 0.776976I
−3.03641 − 4.53724I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.004200 + 0.653502I
a = −0.602734 − 1.133920I
b = −0.326421 − 1.294080I
5.49575 − 4.02919I 0
u = 1.004200 − 0.653502I
a = −0.602734 + 1.133920I
b = −0.326421 + 1.294080I
5.49575 + 4.02919I 0
u = 0.600377 + 0.503296I
a = −0.54654 − 2.46979I
b = 0.890404 − 0.099731I
4.41694 + 2.33204I 2.30899 + 3.70876I
u = 0.600377 − 0.503296I
a = −0.54654 + 2.46979I
b = 0.890404 + 0.099731I
4.41694 − 2.33204I 2.30899 − 3.70876I
u = 0.238587 + 0.745701I
a = 0.669615 + 0.070375I
b = −0.264277 + 0.421377I
2.12182 − 2.26046I −2.69224 + 4.33377I
u = 0.238587 − 0.745701I
a = 0.669615 − 0.070375I
b = −0.264277 − 0.421377I
2.12182 + 2.26046I −2.69224 − 4.33377I
u = −1.204290 + 0.213731I
a = 0.350525 − 0.833986I
b = 0.353431 − 0.806311I
−6.24882 + 1.48049I 0
u = −1.204290 − 0.213731I
a = 0.350525 + 0.833986I
b = 0.353431 + 0.806311I
−6.24882 − 1.48049I 0
u = −1.046130 + 0.645338I
a = −0.560990 + 1.100540I
b = −0.373512 + 1.324650I
4.59791 + 9.79417I 0
u = −1.046130 − 0.645338I
a = −0.560990 − 1.100540I
b = −0.373512 − 1.324650I
4.59791 − 9.79417I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.635410 + 1.087650I
a = 0.196297 − 0.001060I
b = 1.32653 − 0.52109I
10.54050 − 4.32714I 0
u = −0.635410 − 1.087650I
a = 0.196297 + 0.001060I
b = 1.32653 + 0.52109I
10.54050 + 4.32714I 0
u = 0.493999 + 1.159450I
a = 0.194594 + 0.003965I
b = 1.200110 + 0.420492I
4.11910 + 4.28811I 0
u = 0.493999 − 1.159450I
a = 0.194594 − 0.003965I
b = 1.200110 − 0.420492I
4.11910 − 4.28811I 0
u = 1.130640 + 0.562921I
a = −0.178921 − 1.268500I
b = 1.139660 − 0.572230I
−3.85649 − 6.65841I 0
u = 1.130640 − 0.562921I
a = −0.178921 + 1.268500I
b = 1.139660 + 0.572230I
−3.85649 + 6.65841I 0
u = −0.571342 + 0.450763I
a = 0.799690 − 0.588134I
b = −0.876514 − 0.040008I
1.381480 − 0.079256I 5.31373 − 0.44192I
u = −0.571342 − 0.450763I
a = 0.799690 + 0.588134I
b = −0.876514 + 0.040008I
1.381480 + 0.079256I 5.31373 + 0.44192I
u = −1.202490 + 0.418464I
a = 0.338934 − 0.689561I
b = 0.169739 − 0.787709I
−1.65592 + 7.43184I 0
u = −1.202490 − 0.418464I
a = 0.338934 + 0.689561I
b = 0.169739 + 0.787709I
−1.65592 − 7.43184I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.085590 + 0.676848I
a = −0.316501 + 1.272240I
b = 1.241290 + 0.481735I
2.71709 + 6.60282I 0
u = −1.085590 − 0.676848I
a = −0.316501 − 1.272240I
b = 1.241290 − 0.481735I
2.71709 − 6.60282I 0
u = 0.647434 + 1.135080I
a = 0.197276 + 0.001542I
b = 1.289260 + 0.557225I
9.53500 + 10.09170I 0
u = 0.647434 − 1.135080I
a = 0.197276 − 0.001542I
b = 1.289260 − 0.557225I
9.53500 − 10.09170I 0
u = 1.123060 + 0.685056I
a = −0.305837 − 1.231590I
b = 1.265010 − 0.517604I
1.72661 − 12.41470I 0
u = 1.123060 − 0.685056I
a = −0.305837 + 1.231590I
b = 1.265010 + 0.517604I
1.72661 + 12.41470I 0
u = −1.172330 + 0.684132I
a = −0.29816 − 1.53310I
b = −1.273590 − 0.614310I
5.85743 + 8.14777I 0
u = −1.172330 − 0.684132I
a = −0.29816 + 1.53310I
b = −1.273590 + 0.614310I
5.85743 − 8.14777I 0
u = 1.232490 + 0.616049I
a = −0.45590 + 1.35591I
b = −1.172930 + 0.574754I
3.06376 − 4.20801I 0
u = 1.232490 − 0.616049I
a = −0.45590 − 1.35591I
b = −1.172930 − 0.574754I
3.06376 + 4.20801I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.161510 + 0.793472I
a = −0.02680 − 1.54017I
b = −1.35879 − 0.71390I
8.8284 + 11.1189I 0
u = −1.161510 − 0.793472I
a = −0.02680 + 1.54017I
b = −1.35879 + 0.71390I
8.8284 − 11.1189I 0
u = −0.395569 + 0.441362I
a = −1.83851 + 3.13114I
b = 0.042317 + 0.538401I
0.744221 − 0.347993I −10.77580 − 1.35993I
u = −0.395569 − 0.441362I
a = −1.83851 − 3.13114I
b = 0.042317 − 0.538401I
0.744221 + 0.347993I −10.77580 + 1.35993I
u = 1.42094 + 0.14910I
a = −1.037220 + 0.312565I
b = −0.917859 + 0.126132I
1.73398 − 1.68885I 0
u = 1.42094 − 0.14910I
a = −1.037220 − 0.312565I
b = −0.917859 − 0.126132I
1.73398 + 1.68885I 0
u = 1.22262 + 0.74228I
a = −0.15511 + 1.41210I
b = −1.25942 + 0.70773I
1.75267 − 11.04810I 0
u = 1.22262 − 0.74228I
a = −0.15511 − 1.41210I
b = −1.25942 − 0.70773I
1.75267 + 11.04810I 0
u = 1.17840 + 0.81196I
a = 0.00730 + 1.49544I
b = −1.35718 + 0.74462I
7.7850 − 17.0818I 0
u = 1.17840 − 0.81196I
a = 0.00730 − 1.49544I
b = −1.35718 − 0.74462I
7.7850 + 17.0818I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50976 + 0.23215I
a = −0.815003 − 0.384063I
b = −0.836256 − 0.194442I
0.01719 + 7.01679I 0
u = −1.50976 − 0.23215I
a = −0.815003 + 0.384063I
b = −0.836256 + 0.194442I
0.01719 − 7.01679I 0
u = −1.56343
a = −0.832965
b = −0.802385
−4.01787 0
u = 0.428199
a = 0.190716
b = 1.68418
7.58133 −22.6420
u = 0.410800
a = 1.26130
b = 0.180308
−0.884136 −11.8670
u = 0.002190 + 0.400188I
a = −8.30916 − 0.20003I
b = 0.448143 + 0.052970I
4.27018 + 2.77355I 35.2011 − 5.5393I
u = 0.002190 − 0.400188I
a = −8.30916 + 0.20003I
b = 0.448143 − 0.052970I
4.27018 − 2.77355I 35.2011 + 5.5393I
u = −0.372816
a = 2.12859
b = −0.521179
1.14364 10.4810
14
II. I
u
2
=
hb, 2u
7
−3u
6
−5u
5
+7u
4
+4u
3
−3u
2
+a−4, u
8
−u
7
−3u
6
+2u
5
+3u
4
−2u−1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
5
=
−u
−u
3
+ u
a
12
=
−2u
7
+ 3u
6
+ 5u
5
− 7u
4
− 4u
3
+ 3u
2
+ 4
0
a
10
=
−2u
7
+ 3u
6
+ 5u
5
− 7u
4
− 4u
3
+ 3u
2
+ 5
u
2
a
1
=
−1
−u
2
a
11
=
−2u
7
+ 3u
6
+ 5u
5
− 7u
4
− 4u
3
+ 3u
2
+ 4
0
a
7
=
1
0
a
3
=
u
u
a
6
=
−u
4
+ u
2
+ 1
−u
6
+ 2u
4
− u
2
a
2
=
u
4
− u
2
− 1
u
4
− 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
7
− 16u
6
− 18u
5
+ 36u
4
+ 15u
3
− 13u
2
− 4u − 25
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
2
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
3
, c
4
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
5
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
6
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
7
, c
11
u
8
c
8
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
9
, c
10
(u + 1)
8
c
12
(u − 1)
8
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
2
, c
5
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
3
, c
4
, c
8
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
7
, c
11
y
8
c
9
, c
10
, c
12
(y −1)
8
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180120 + 0.268597I
a = 0.615431 + 0.295452I
b = 0
0.604279 + 1.131230I −1.048604 + 0.799861I
u = −1.180120 − 0.268597I
a = 0.615431 − 0.295452I
b = 0
0.604279 − 1.131230I −1.048604 − 0.799861I
u = −0.108090 + 0.747508I
a = −1.68119 + 0.49658I
b = 0
3.80435 + 2.57849I 0.86993 − 2.07507I
u = −0.108090 − 0.747508I
a = −1.68119 − 0.49658I
b = 0
3.80435 − 2.57849I 0.86993 + 2.07507I
u = 1.37100
a = 0.532015
b = 0
−4.85780 −9.68010
u = 1.334530 + 0.318930I
a = 0.473764 − 0.240160I
b = 0
−0.73474 − 6.44354I −3.69048 + 2.66284I
u = 1.334530 − 0.318930I
a = 0.473764 + 0.240160I
b = 0
−0.73474 + 6.44354I −3.69048 − 2.66284I
u = −0.463640
a = 4.65198
b = 0
0.799899 −25.5820
18
III.
I
v
1
= ha, 26v
5
−33v
4
+· · · +413b − 685, v
6
−3v
5
+15v
4
−24v
3
+11v
2
−6v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
9
=
1
0
a
5
=
v
0
a
12
=
0
−0.0629540v
5
+ 0.0799031v
4
+ ··· − 0.215496v + 1.65860
a
10
=
1
0.0629540v
5
− 0.0799031v
4
+ ··· + 0.215496v −2.65860
a
1
=
−0.0629540v
5
+ 0.0799031v
4
+ ··· − 0.215496v + 1.65860
0.0629540v
5
− 0.0799031v
4
+ ··· + 0.215496v −2.65860
a
11
=
0.0629540v
5
− 0.0799031v
4
+ ··· + 0.215496v −1.65860
−0.0629540v
5
+ 0.0799031v
4
+ ··· − 0.215496v + 1.65860
a
7
=
0.0629540v
5
− 0.0799031v
4
+ ··· + 0.215496v −1.65860
−0.0629540v
5
+ 0.0799031v
4
+ ··· − 0.215496v + 2.65860
a
3
=
−0.217918v
5
+ 0.353511v
4
+ ··· + 4.56174v + 0.125908
0.326877v
5
− 0.530266v
4
+ ··· − 5.84262v −0.188862
a
6
=
−0.0871671v
5
+ 0.341404v
4
+ ··· − 0.375303v −1.54964
−0.0629540v
5
+ 0.0799031v
4
+ ··· − 0.215496v + 2.65860
a
2
=
−0.963680v
5
+ 2.60775v
4
+ ··· − 3.76029v + 2.31235
1.26392v
5
− 3.45036v
4
+ ··· + 4.94189v −3.53027
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1914
413
v
5
+
5225
413
v
4
−
27339
413
v
3
+
38886
413
v
2
−
10650
413
v +
9063
413
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
, c
8
u
6
c
5
(u
3
− u
2
+ 1)
2
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
9
, c
10
(u
2
− u − 1)
3
c
11
, c
12
(u
2
+ u − 1)
3
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
5
(y
3
− y
2
+ 2y −1)
2
c
4
, c
8
y
6
c
7
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
3
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.49186
a = 0
b = −0.618034
−0.126494 1.65540
v = 0.082153 + 0.499284I
a = 0
b = 1.61803
11.90680 − 2.82812I 1.56739 + 1.81005I
v = 0.082153 − 0.499284I
a = 0
b = 1.61803
11.90680 + 2.82812I 1.56739 − 1.81005I
v = 0.217660
a = 0
b = 1.61803
7.76919 20.1360
v = 0.56309 + 3.42214I
a = 0
b = −0.618034
4.01109 − 2.82812I −5.96298 + 6.80673I
v = 0.56309 − 3.42214I
a = 0
b = −0.618034
4.01109 + 2.82812I −5.96298 − 6.80673I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
2
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
98
+ 32u
97
+ ··· + 46u + 1)
c
2
(u
3
+ u
2
− 1)
2
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
98
+ 4u
97
+ ··· + 14u + 1)
c
3
(u
3
− u
2
+ 2u − 1)
2
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
98
− 4u
97
+ ··· + 19016u + 4129)
c
4
u
6
(u
8
+ u
7
+ ··· + 2u − 1)(u
98
+ 2u
97
+ ··· + 160u + 64)
c
5
(u
3
− u
2
+ 1)
2
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
98
+ 4u
97
+ ··· + 14u + 1)
c
6
(u
3
+ u
2
+ 2u + 1)
2
· (u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
98
+ 32u
97
+ ··· + 46u + 1)
c
7
u
8
(u
2
− u − 1)
3
(u
98
− 4u
97
+ ··· − 128u + 256)
c
8
u
6
(u
8
− u
7
+ ··· − 2u − 1)(u
98
+ 2u
97
+ ··· + 160u + 64)
c
9
, c
10
((u + 1)
8
)(u
2
− u − 1)
3
(u
98
+ 12u
97
+ ··· − 31u + 1)
c
11
u
8
(u
2
+ u − 1)
3
(u
98
− 4u
97
+ ··· − 128u + 256)
c
12
((u − 1)
8
)(u
2
+ u − 1)
3
(u
98
+ 12u
97
+ ··· − 31u + 1)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
98
+ 72y
97
+ ··· − 2334y + 1)
c
2
, c
5
(y
3
− y
2
+ 2y −1)
2
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
98
− 32y
97
+ ··· − 46y + 1)
c
3
(y
3
+ 3y
2
+ 2y −1)
2
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
98
+ 76y
96
+ ··· − 284998790y + 17048641)
c
4
, c
8
y
6
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
98
− 42y
97
+ ··· − 87040y + 4096)
c
7
, c
11
y
8
(y
2
− 3y + 1)
3
(y
98
− 60y
97
+ ··· − 3457024y + 65536)
c
9
, c
10
, c
12
((y −1)
8
)(y
2
− 3y + 1)
3
(y
98
− 96y
97
+ ··· − 903y + 1)
24
