12a
0357
(K12a
0357
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 2 12 5 10 4 1 7 11
Solving Sequence
4,9 1,10
11 3 2 8 5 6 7 12
c
9
c
10
c
3
c
1
c
8
c
4
c
5
c
7
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.53983 × 10
51
u
99
+ 4.05833 × 10
51
u
98
+ ··· + 2.11035 × 10
51
b − 1.02725 × 10
52
,
− 1.15475 × 10
51
u
99
− 3.57142 × 10
51
u
98
+ ··· + 2.11035 × 10
51
a + 1.63343 × 10
52
, u
100
+ u
99
+ ··· − 4u + 4i
I
u
2
= hu
3
+ 2b + 2a − 2u, −2u
3
a + 2u
2
a − u
3
+ 2a
2
+ u
2
− 2a + 2u − 4, u
4
− 2u
2
+ 2i
I
v
1
= ha, b − v −1, v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 110 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
= h1.54×10
51
u
99
+4.06×10
51
u
98
+· · ·+2.11×10
51
b−1.03×10
52
, −1.15×
10
51
u
99
−3.57×10
51
u
98
+· · ·+2.11×10
51
a+1.63×10
52
, u
100
+u
99
+· · ·−4u+4i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
1
=
0.547186u
99
+ 1.69233u
98
+ ··· + 4.11499u − 7.74008
−0.729657u
99
− 1.92306u
98
+ ··· + 4.44039u + 4.86768
a
10
=
1
−u
2
a
11
=
−1.79863u
99
+ 1.22296u
98
+ ··· + 1.87484u − 7.99017
1.88775u
99
− 1.11746u
98
+ ··· − 10.4758u + 12.6756
a
3
=
−u
u
a
2
=
0.178071u
99
+ 1.82811u
98
+ ··· + 3.57812u − 7.93309
−0.360542u
99
− 2.05883u
98
+ ··· + 4.97727u + 5.06069
a
8
=
−u
2
+ 1
u
4
a
5
=
−u
5
+ 2u
3
− u
u
7
− u
5
+ u
a
6
=
1.21054u
99
+ 0.764246u
98
+ ··· − 22.5600u + 8.32879
−0.674548u
99
− 2.17762u
98
+ ··· + 14.7440u − 0.641411
a
7
=
−u
8
+ 3u
6
− 3u
4
+ 1
u
10
− 2u
8
+ u
6
+ 2u
4
− u
2
a
12
=
−1.59623u
99
+ 0.969406u
98
+ ··· + 3.93582u − 7.28650
1.46440u
99
− 1.22984u
98
+ ··· − 9.77743u + 11.7646
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.789187u
99
− 6.38881u
98
+ ··· − 5.66830u + 22.0670
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
100
+ 45u
99
+ ··· + 75u + 1
c
2
, c
5
u
100
+ 3u
99
+ ··· − 17u + 1
c
3
, c
9
u
100
− u
99
+ ··· + 4u + 4
c
4
, c
7
u
100
− 3u
99
+ ··· + 3612u + 748
c
6
, c
11
u
100
− 2u
99
+ ··· + 12u + 5
c
8
u
100
− 55u
99
+ ··· − 80u + 16
c
10
, c
12
u
100
+ 32u
99
+ ··· + 46u + 25
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
100
+ 35y
99
+ ··· − 3619y + 1
c
2
, c
5
y
100
− 45y
99
+ ··· − 75y + 1
c
3
, c
9
y
100
− 55y
99
+ ··· − 80y + 16
c
4
, c
7
y
100
+ 85y
99
+ ··· − 21196752y + 559504
c
6
, c
11
y
100
+ 32y
99
+ ··· + 46y + 25
c
8
y
100
− 15y
99
+ ··· − 5376y + 256
c
10
, c
12
y
100
+ 80y
99
+ ··· + 107034y + 625
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.912469 + 0.405577I
a = 1.019230 + 0.409473I
b = −0.55692 − 1.37489I
−0.20776 + 3.79756I 0
u = 0.912469 − 0.405577I
a = 1.019230 − 0.409473I
b = −0.55692 + 1.37489I
−0.20776 − 3.79756I 0
u = −0.841778 + 0.519872I
a = −2.00523 + 0.30647I
b = 1.66830 − 1.62048I
−4.20715 − 5.65114I 0
u = −0.841778 − 0.519872I
a = −2.00523 − 0.30647I
b = 1.66830 + 1.62048I
−4.20715 + 5.65114I 0
u = −0.909434 + 0.598251I
a = −2.21700 − 0.75018I
b = 2.31160 − 0.62141I
1.14788 − 11.04990I 0
u = −0.909434 − 0.598251I
a = −2.21700 + 0.75018I
b = 2.31160 + 0.62141I
1.14788 + 11.04990I 0
u = −0.892846 + 0.148332I
a = 0.874246 − 0.052986I
b = −0.880061 + 0.446449I
1.50372 − 0.38043I 6.35087 + 0.58790I
u = −0.892846 − 0.148332I
a = 0.874246 + 0.052986I
b = −0.880061 − 0.446449I
1.50372 + 0.38043I 6.35087 − 0.58790I
u = 0.934036 + 0.577393I
a = 1.83094 − 0.79317I
b = −1.93636 − 0.41442I
1.95982 + 5.33714I 0
u = 0.934036 − 0.577393I
a = 1.83094 + 0.79317I
b = −1.93636 + 0.41442I
1.95982 − 5.33714I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.814912 + 0.386226I
a = −2.91863 + 1.07511I
b = 1.36240 − 1.22807I
−1.73172 − 3.82124I −3.99607 + 6.81813I
u = −0.814912 − 0.386226I
a = −2.91863 − 1.07511I
b = 1.36240 + 1.22807I
−1.73172 + 3.82124I −3.99607 − 6.81813I
u = −0.610558 + 0.655440I
a = −0.29458 + 1.91836I
b = −1.14490 − 1.51664I
0.28832 + 6.20529I −3.10468 − 4.98772I
u = −0.610558 − 0.655440I
a = −0.29458 − 1.91836I
b = −1.14490 + 1.51664I
0.28832 − 6.20529I −3.10468 + 4.98772I
u = −1.055440 + 0.366629I
a = 1.177940 − 0.074014I
b = −1.014110 + 0.235891I
3.00378 − 1.28109I 0
u = −1.055440 − 0.366629I
a = 1.177940 + 0.074014I
b = −1.014110 − 0.235891I
3.00378 + 1.28109I 0
u = 0.763559 + 0.437417I
a = −1.122190 − 0.545518I
b = 0.871896 + 0.806261I
−1.57401 + 1.88920I −4.68601 − 4.44810I
u = 0.763559 − 0.437417I
a = −1.122190 + 0.545518I
b = 0.871896 − 0.806261I
−1.57401 − 1.88920I −4.68601 + 4.44810I
u = 0.984201 + 0.538389I
a = −1.63348 + 0.33461I
b = 1.78287 + 0.23609I
2.74500 + 6.04482I 0
u = 0.984201 − 0.538389I
a = −1.63348 − 0.33461I
b = 1.78287 − 0.23609I
2.74500 − 6.04482I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.131300 + 0.031645I
a = 0.391679 − 0.793695I
b = −0.398613 − 0.311538I
6.37271 + 0.11350I 0
u = −1.131300 − 0.031645I
a = 0.391679 + 0.793695I
b = −0.398613 + 0.311538I
6.37271 − 0.11350I 0
u = −0.781213 + 0.377020I
a = −1.19190 + 1.27616I
b = 0.50457 − 2.37511I
−1.84014 + 0.43513I −4.52284 + 3.06310I
u = −0.781213 − 0.377020I
a = −1.19190 − 1.27616I
b = 0.50457 + 2.37511I
−1.84014 − 0.43513I −4.52284 − 3.06310I
u = −0.150097 + 0.854140I
a = −1.35989 + 0.76503I
b = −0.66687 − 1.38476I
5.33031 + 11.95280I −1.22194 − 7.32364I
u = −0.150097 − 0.854140I
a = −1.35989 − 0.76503I
b = −0.66687 + 1.38476I
5.33031 − 11.95280I −1.22194 + 7.32364I
u = 0.128935 + 0.855015I
a = 1.244510 + 0.598650I
b = 0.741965 − 1.096350I
6.34419 − 5.84958I 0.46765 + 2.69584I
u = 0.128935 − 0.855015I
a = 1.244510 − 0.598650I
b = 0.741965 + 1.096350I
6.34419 + 5.84958I 0.46765 − 2.69584I
u = −0.681105 + 0.527016I
a = −1.59641 + 1.60846I
b = 0.07953 − 1.62701I
−4.66816 + 1.38516I −10.24072 − 0.52045I
u = −0.681105 − 0.527016I
a = −1.59641 − 1.60846I
b = 0.07953 + 1.62701I
−4.66816 − 1.38516I −10.24072 + 0.52045I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.097937 + 0.853235I
a = −0.842921 − 0.573169I
b = −0.359480 + 1.282810I
7.38468 − 5.80677I 1.37130 + 3.23085I
u = 0.097937 − 0.853235I
a = −0.842921 + 0.573169I
b = −0.359480 − 1.282810I
7.38468 + 5.80677I 1.37130 − 3.23085I
u = 0.564718 + 0.646983I
a = 0.12930 + 1.50881I
b = 1.12507 − 1.09493I
0.901266 − 0.586971I −1.67720 + 0.I
u = 0.564718 − 0.646983I
a = 0.12930 − 1.50881I
b = 1.12507 + 1.09493I
0.901266 + 0.586971I −1.67720 + 0.I
u = 1.139570 + 0.076692I
a = −0.102816 − 0.836460I
b = 0.238969 − 0.353591I
6.08791 + 5.84929I 0
u = 1.139570 − 0.076692I
a = −0.102816 + 0.836460I
b = 0.238969 + 0.353591I
6.08791 − 5.84929I 0
u = −0.069488 + 0.854881I
a = 0.807259 − 0.508489I
b = 0.524439 + 1.090280I
7.98792 − 0.33942I 2.27380 + 1.86979I
u = −0.069488 − 0.854881I
a = 0.807259 + 0.508489I
b = 0.524439 − 1.090280I
7.98792 + 0.33942I 2.27380 − 1.86979I
u = 1.085200 + 0.397109I
a = 0.720541 + 0.454709I
b = 0.019567 − 1.119010I
0.18495 + 3.60808I 0
u = 1.085200 − 0.397109I
a = 0.720541 − 0.454709I
b = 0.019567 + 1.119010I
0.18495 − 3.60808I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.793988 + 0.262883I
a = 2.82288 + 0.48559I
b = −1.208080 − 0.604939I
−0.988788 − 0.952734I −0.15661 − 1.44604I
u = 0.793988 − 0.262883I
a = 2.82288 − 0.48559I
b = −1.208080 + 0.604939I
−0.988788 + 0.952734I −0.15661 + 1.44604I
u = −1.041020 + 0.542940I
a = 1.36561 + 0.86394I
b = −1.81769 − 0.34870I
2.88537 − 0.64653I 0
u = −1.041020 − 0.542940I
a = 1.36561 − 0.86394I
b = −1.81769 + 0.34870I
2.88537 + 0.64653I 0
u = 1.083910 + 0.462365I
a = −0.918572 − 0.375609I
b = 0.937185 + 0.367758I
2.44049 + 5.71324I 0
u = 1.083910 − 0.462365I
a = −0.918572 + 0.375609I
b = 0.937185 − 0.367758I
2.44049 − 5.71324I 0
u = −0.426174 + 0.689734I
a = −0.33089 − 1.61078I
b = 1.140840 + 0.629451I
1.09924 − 4.09171I −1.69507 + 5.63411I
u = −0.426174 − 0.689734I
a = −0.33089 + 1.61078I
b = 1.140840 − 0.629451I
1.09924 + 4.09171I −1.69507 − 5.63411I
u = 0.807716 + 0.067600I
a = −0.749405 + 0.499425I
b = 1.29639 − 0.97122I
−0.64641 + 2.78439I 1.21161 − 6.73563I
u = 0.807716 − 0.067600I
a = −0.749405 − 0.499425I
b = 1.29639 + 0.97122I
−0.64641 − 2.78439I 1.21161 + 6.73563I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.475387 + 0.654531I
a = 0.03470 − 1.55956I
b = −0.770329 + 0.879847I
1.27228 − 1.41798I −1.021987 + 0.105675I
u = 0.475387 − 0.654531I
a = 0.03470 + 1.55956I
b = −0.770329 − 0.879847I
1.27228 + 1.41798I −1.021987 − 0.105675I
u = 0.050429 + 0.795903I
a = 1.255810 − 0.182945I
b = 0.201445 − 0.051960I
2.95290 − 2.61250I 1.60904 + 3.16874I
u = 0.050429 − 0.795903I
a = 1.255810 + 0.182945I
b = 0.201445 + 0.051960I
2.95290 + 2.61250I 1.60904 − 3.16874I
u = −0.119249 + 0.780742I
a = −1.72510 + 0.11892I
b = 0.152712 − 0.741542I
−1.15099 + 5.81538I −5.00175 − 6.04754I
u = −0.119249 − 0.780742I
a = −1.72510 − 0.11892I
b = 0.152712 + 0.741542I
−1.15099 − 5.81538I −5.00175 + 6.04754I
u = −1.127070 + 0.498863I
a = −0.02921 + 1.49604I
b = −1.00419 − 1.48775I
−0.61092 − 3.91398I 0
u = −1.127070 − 0.498863I
a = −0.02921 − 1.49604I
b = −1.00419 + 1.48775I
−0.61092 + 3.91398I 0
u = −0.028534 + 0.756569I
a = −0.125642 − 0.736579I
b = 0.20550 − 1.68728I
0.52074 + 2.75335I −1.11486 − 3.14721I
u = −0.028534 − 0.756569I
a = −0.125642 + 0.736579I
b = 0.20550 + 1.68728I
0.52074 − 2.75335I −1.11486 + 3.14721I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.197390 + 0.397927I
a = 0.005516 − 0.546579I
b = 0.66877 + 1.28063I
2.71082 − 1.81383I 0
u = 1.197390 − 0.397927I
a = 0.005516 + 0.546579I
b = 0.66877 − 1.28063I
2.71082 + 1.81383I 0
u = 1.181700 + 0.455217I
a = −1.05213 − 0.98897I
b = 1.23536 + 1.54269I
3.30802 + 5.60701I 0
u = 1.181700 − 0.455217I
a = −1.05213 + 0.98897I
b = 1.23536 − 1.54269I
3.30802 − 5.60701I 0
u = −1.184150 + 0.456831I
a = 0.328157 + 0.804933I
b = −0.24589 − 1.53400I
3.29330 − 2.94534I 0
u = −1.184150 − 0.456831I
a = 0.328157 − 0.804933I
b = −0.24589 + 1.53400I
3.29330 + 2.94534I 0
u = 1.195820 + 0.443985I
a = 1.37811 + 1.50021I
b = 0.05336 − 2.03271I
4.03956 + 1.53093I 0
u = 1.195820 − 0.443985I
a = 1.37811 − 1.50021I
b = 0.05336 + 2.03271I
4.03956 − 1.53093I 0
u = −1.194680 + 0.465648I
a = −1.20311 + 1.79616I
b = −0.28010 − 2.17430I
3.88377 − 7.20029I 0
u = −1.194680 − 0.465648I
a = −1.20311 − 1.79616I
b = −0.28010 + 2.17430I
3.88377 + 7.20029I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.010080 + 0.715576I
a = −1.24270 − 0.73378I
b = 0.308954 + 0.451098I
−0.028264 − 1.352720I −1.88211 + 0.54543I
u = −0.010080 − 0.715576I
a = −1.24270 + 0.73378I
b = 0.308954 − 0.451098I
−0.028264 + 1.352720I −1.88211 − 0.54543I
u = −1.212120 + 0.432274I
a = 0.766667 − 0.450671I
b = −1.14266 + 1.29226I
6.66680 − 1.70631I 0
u = −1.212120 − 0.432274I
a = 0.766667 + 0.450671I
b = −1.14266 − 1.29226I
6.66680 + 1.70631I 0
u = −1.191240 + 0.499876I
a = −1.15247 + 1.32228I
b = 1.04357 − 2.42873I
1.98773 − 10.53560I 0
u = −1.191240 − 0.499876I
a = −1.15247 − 1.32228I
b = 1.04357 + 2.42873I
1.98773 + 10.53560I 0
u = 1.206990 + 0.476857I
a = 0.580406 + 0.543183I
b = −0.72477 − 1.55496I
6.34811 + 7.22914I 0
u = 1.206990 − 0.476857I
a = 0.580406 − 0.543183I
b = −0.72477 + 1.55496I
6.34811 − 7.22914I 0
u = 1.245050 + 0.367022I
a = 0.263536 + 0.632197I
b = 0.658637 + 0.468363I
9.64537 − 7.82161I 0
u = 1.245050 − 0.367022I
a = 0.263536 − 0.632197I
b = 0.658637 − 0.468363I
9.64537 + 7.82161I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.246200 + 0.382136I
a = 0.038717 + 0.547358I
b = −0.842986 + 0.574957I
10.57580 + 1.62455I 0
u = −1.246200 − 0.382136I
a = 0.038717 − 0.547358I
b = −0.842986 − 0.574957I
10.57580 − 1.62455I 0
u = −1.245340 + 0.402553I
a = 0.662864 − 0.742768I
b = 0.114048 + 0.113661I
11.48720 + 1.46496I 0
u = −1.245340 − 0.402553I
a = 0.662864 + 0.742768I
b = 0.114048 − 0.113661I
11.48720 − 1.46496I 0
u = −0.229275 + 0.647029I
a = −0.579282 − 1.224090I
b = 0.829861 − 0.556928I
−3.17453 − 0.52670I −9.02712 + 0.52794I
u = −0.229275 − 0.647029I
a = −0.579282 + 1.224090I
b = 0.829861 + 0.556928I
−3.17453 + 0.52670I −9.02712 − 0.52794I
u = 1.245450 + 0.419803I
a = −0.382581 − 0.719643I
b = −0.330973 − 0.038714I
11.98730 + 4.79103I 0
u = 1.245450 − 0.419803I
a = −0.382581 + 0.719643I
b = −0.330973 + 0.038714I
11.98730 − 4.79103I 0
u = −1.210620 + 0.527810I
a = −2.25559 + 0.82338I
b = 2.14131 − 2.26366I
8.4995 − 16.9935I 0
u = −1.210620 − 0.527810I
a = −2.25559 − 0.82338I
b = 2.14131 + 2.26366I
8.4995 + 16.9935I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.216030 + 0.519338I
a = 1.99835 + 0.60348I
b = −1.97723 − 2.00701I
9.5945 + 10.8498I 0
u = 1.216030 − 0.519338I
a = 1.99835 − 0.60348I
b = −1.97723 + 2.00701I
9.5945 − 10.8498I 0
u = 1.221780 + 0.505858I
a = −1.83357 − 0.90573I
b = 1.52263 + 1.79888I
10.7454 + 10.7319I 0
u = 1.221780 − 0.505858I
a = −1.83357 + 0.90573I
b = 1.52263 − 1.79888I
10.7454 − 10.7319I 0
u = −1.227710 + 0.493367I
a = 1.76734 − 0.69562I
b = −1.57118 + 1.65545I
11.45740 − 4.52311I 0
u = −1.227710 − 0.493367I
a = 1.76734 + 0.69562I
b = −1.57118 − 1.65545I
11.45740 + 4.52311I 0
u = 0.451798 + 0.412784I
a = 1.286600 − 0.192388I
b = −0.151873 − 0.415600I
−1.49122 − 0.27727I −6.33963 + 0.19121I
u = 0.451798 − 0.412784I
a = 1.286600 + 0.192388I
b = −0.151873 + 0.415600I
−1.49122 + 0.27727I −6.33963 − 0.19121I
u = 0.147589 + 0.554230I
a = −0.385611 − 0.500096I
b = 0.283515 + 0.578313I
−0.05525 − 1.76673I −0.22399 + 3.93080I
u = 0.147589 − 0.554230I
a = −0.385611 + 0.500096I
b = 0.283515 − 0.578313I
−0.05525 + 1.76673I −0.22399 − 3.93080I
14
II.
I
u
2
= hu
3
+2b+2a−2u, −2u
3
a+2u
2
a−u
3
+2a
2
+u
2
−2a+2u−4, u
4
−2u
2
+2i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
1
=
a
−
1
2
u
3
− a + u
a
10
=
1
−u
2
a
11
=
1
2
u
3
a −
1
2
u
3
− au +
3
2
u
2
+ a
1
2
u
3
+ au − 3u
2
− a + 2
a
3
=
−u
u
a
2
=
a − u
−
1
2
u
3
− a + 2u
a
8
=
−u
2
+ 1
2u
2
− 2
a
5
=
u
−u
a
6
=
a
−
1
2
u
3
− a + u
a
7
=
−1
u
2
a
12
=
1
2
u
3
a + u
2
a − u
3
− au +
3
2
u
2
+ u − 1
−u
2
a +
1
2
u
3
+ au − 2u
2
+ a − u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
a − 2u
3
− 4u
2
− 4a + 4u
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
8
c
2
(u + 1)
8
c
3
, c
9
(u
4
− 2u
2
+ 2)
2
c
4
, c
7
(u
4
+ 2u
2
+ 2)
2
c
6
, c
10
(u
2
− u + 1)
4
c
8
(u
2
+ 2u + 2)
4
c
11
, c
12
(u
2
+ u + 1)
4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
8
c
3
, c
9
(y
2
− 2y + 2)
4
c
4
, c
7
(y
2
+ 2y + 2)
4
c
6
, c
10
, c
11
c
12
(y
2
+ y + 1)
4
c
8
(y
2
+ 4)
4
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098680 + 0.455090I
a = 1.187820 + 0.276887I
b = −0.410936 − 0.598684I
0.82247 + 1.63398I −2.00000 − 0.53590I
u = 1.098680 + 0.455090I
a = −0.544228 + 0.276887I
b = 1.32112 − 0.59868I
0.82247 + 5.69375I −2.00000 − 7.46410I
u = 1.098680 − 0.455090I
a = 1.187820 − 0.276887I
b = −0.410936 + 0.598684I
0.82247 − 1.63398I −2.00000 + 0.53590I
u = 1.098680 − 0.455090I
a = −0.544228 − 0.276887I
b = 1.32112 + 0.59868I
0.82247 − 5.69375I −2.00000 + 7.46410I
u = −1.098680 + 0.455090I
a = 0.544228 + 1.276890I
b = −1.32112 − 1.59868I
0.82247 − 1.63398I −2.00000 + 0.53590I
u = −1.098680 + 0.455090I
a = −1.18782 + 1.27689I
b = 0.41094 − 1.59868I
0.82247 − 5.69375I −2.00000 + 7.46410I
u = −1.098680 − 0.455090I
a = 0.544228 − 1.276890I
b = −1.32112 + 1.59868I
0.82247 + 1.63398I −2.00000 − 0.53590I
u = −1.098680 − 0.455090I
a = −1.18782 − 1.27689I
b = 0.41094 + 1.59868I
0.82247 + 5.69375I −2.00000 − 7.46410I
18
III. I
v
1
= ha, b − v − 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
1
=
0
v + 1
a
10
=
1
0
a
11
=
1
v
a
3
=
v
0
a
2
=
v
v + 1
a
8
=
1
0
a
5
=
v
0
a
6
=
0
−v − 1
a
7
=
1
0
a
12
=
v + 1
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
4
, c
7
c
8
, c
9
u
2
c
5
(u + 1)
2
c
6
, c
12
u
2
+ u + 1
c
10
, c
11
u
2
− u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
2
c
3
, c
4
, c
7
c
8
, c
9
y
2
c
6
, c
10
, c
11
c
12
y
2
+ y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
−1.64493 − 2.02988I −6.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
−1.64493 + 2.02988I −6.00000 − 3.46410I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
100
+ 45u
99
+ ··· + 75u + 1)
c
2
((u − 1)
2
)(u + 1)
8
(u
100
+ 3u
99
+ ··· − 17u + 1)
c
3
, c
9
u
2
(u
4
− 2u
2
+ 2)
2
(u
100
− u
99
+ ··· + 4u + 4)
c
4
, c
7
u
2
(u
4
+ 2u
2
+ 2)
2
(u
100
− 3u
99
+ ··· + 3612u + 748)
c
5
((u − 1)
8
)(u + 1)
2
(u
100
+ 3u
99
+ ··· − 17u + 1)
c
6
((u
2
− u + 1)
4
)(u
2
+ u + 1)(u
100
− 2u
99
+ ··· + 12u + 5)
c
8
u
2
(u
2
+ 2u + 2)
4
(u
100
− 55u
99
+ ··· − 80u + 16)
c
10
((u
2
− u + 1)
5
)(u
100
+ 32u
99
+ ··· + 46u + 25)
c
11
(u
2
− u + 1)(u
2
+ u + 1)
4
(u
100
− 2u
99
+ ··· + 12u + 5)
c
12
((u
2
+ u + 1)
5
)(u
100
+ 32u
99
+ ··· + 46u + 25)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
10
)(y
100
+ 35y
99
+ ··· − 3619y + 1)
c
2
, c
5
((y − 1)
10
)(y
100
− 45y
99
+ ··· − 75y + 1)
c
3
, c
9
y
2
(y
2
− 2y + 2)
4
(y
100
− 55y
99
+ ··· − 80y + 16)
c
4
, c
7
y
2
(y
2
+ 2y + 2)
4
(y
100
+ 85y
99
+ ··· − 2.11968 × 10
7
y + 559504)
c
6
, c
11
((y
2
+ y + 1)
5
)(y
100
+ 32y
99
+ ··· + 46y + 25)
c
8
y
2
(y
2
+ 4)
4
(y
100
− 15y
99
+ ··· − 5376y + 256)
c
10
, c
12
((y
2
+ y + 1)
5
)(y
100
+ 80y
99
+ ··· + 107034y + 625)
24
