12a
0608
(K12a
0608
)
A knot diagram
1
Linearized knot diagam
3 7 9 12 10 2 11 1 6 5 8 4
Solving Sequence
2,6
7
3,9
4 10 1 5 11 8 12
c
6
c
2
c
3
c
9
c
1
c
5
c
10
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.91359 × 10
294
u
122
− 4.52981 × 10
294
u
121
+ ··· + 3.88967 × 10
294
b − 2.98604 × 10
296
,
− 9.79728 × 10
295
u
122
− 2.24169 × 10
296
u
121
+ ··· + 4.00636 × 10
296
a − 7.79915 × 10
297
,
u
123
+ 3u
122
+ ··· + 118u + 103i
I
u
2
= h88u
27
+ 45u
26
+ ··· + 23b − 99, −10u
27
+ 78u
26
+ ··· + 23a − 144, u
28
− 7u
26
+ ··· − 8u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 151 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−1.91 × 10
294
u
122
− 4.53 × 10
294
u
121
+ · · · + 3.89 × 10
294
b − 2.99 ×
10
296
, −9.80 × 10
295
u
122
− 2.24 × 10
296
u
121
+ · · · + 4.01 × 10
296
a − 7.80 ×
10
297
, u
123
+ 3u
122
+ · · · + 118u + 103i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
0.244543u
122
+ 0.559534u
121
+ ··· − 28.9145u + 19.4669
0.491968u
122
+ 1.16457u
121
+ ··· + 4.25457u + 76.7685
a
4
=
−1.06929u
122
− 2.35492u
121
+ ··· − 11.6245u − 175.307
−0.153231u
122
− 0.387862u
121
+ ··· + 11.1290u − 2.47162
a
10
=
0.736511u
122
+ 1.72411u
121
+ ··· − 24.6599u + 96.2354
0.491968u
122
+ 1.16457u
121
+ ··· + 4.25457u + 76.7685
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
0.415775u
122
+ 0.783733u
121
+ ··· + 11.3829u + 77.3969
−0.364639u
122
− 0.941621u
121
+ ··· + 18.7141u − 45.2372
a
11
=
0.366534u
122
+ 0.922878u
121
+ ··· − 25.4284u + 50.5634
0.319860u
122
+ 0.705880u
121
+ ··· − 17.4424u + 46.0162
a
8
=
0.408604u
122
+ 0.923887u
121
+ ··· − 20.1527u + 36.3808
0.573783u
122
+ 1.34367u
121
+ ··· + 3.16407u + 79.2098
a
12
=
0.168150u
122
+ 0.451184u
121
+ ··· + 10.0432u + 61.5193
0.0421304u
122
+ 0.0512572u
121
+ ··· + 8.54951u + 21.5981
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0861323u
122
+ 0.301447u
121
+ ··· − 68.2666u + 155.020
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
123
+ 55u
122
+ ··· + 363300u + 10609
c
2
, c
6
u
123
− 3u
122
+ ··· + 118u − 103
c
3
u
123
− u
122
+ ··· + 87046u − 12899
c
4
, c
12
u
123
+ 7u
122
+ ··· − 111u − 43
c
5
, c
9
, c
10
u
123
− u
122
+ ··· + u − 19
c
7
, c
11
u
123
+ 3u
122
+ ··· − 752u − 187
c
8
u
123
+ 2u
122
+ ··· + 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
123
+ 41y
122
+ ··· + 2225325352y −112550881
c
2
, c
6
y
123
− 55y
122
+ ··· + 363300y −10609
c
3
y
123
+ 27y
122
+ ··· − 6188058542y −166384201
c
4
, c
12
y
123
+ 91y
122
+ ··· − 18639y −1849
c
5
, c
9
, c
10
y
123
+ 123y
122
+ ··· − 47879y −361
c
7
, c
11
y
123
− 69y
122
+ ··· + 1826632y −34969
c
8
y
123
− 10y
122
+ ··· + 136y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.787312 + 0.611782I
a = 1.347980 − 0.063462I
b = −0.704765 + 0.157248I
2.06112 − 0.67907I 0
u = −0.787312 − 0.611782I
a = 1.347980 + 0.063462I
b = −0.704765 − 0.157248I
2.06112 + 0.67907I 0
u = 0.948530 + 0.334543I
a = 1.52357 + 0.72529I
b = −1.032510 + 0.448117I
−2.63821 + 1.05482I 0
u = 0.948530 − 0.334543I
a = 1.52357 − 0.72529I
b = −1.032510 − 0.448117I
−2.63821 − 1.05482I 0
u = 0.407053 + 0.920884I
a = −0.282292 + 0.316166I
b = 0.397219 − 0.046853I
1.20818 − 4.13474I 0
u = 0.407053 − 0.920884I
a = −0.282292 − 0.316166I
b = 0.397219 + 0.046853I
1.20818 + 4.13474I 0
u = −0.515334 + 0.875291I
a = 0.506060 − 1.177120I
b = −0.15168 + 1.45970I
−7.77774 − 4.96669I 0
u = −0.515334 − 0.875291I
a = 0.506060 + 1.177120I
b = −0.15168 − 1.45970I
−7.77774 + 4.96669I 0
u = 0.742368 + 0.694050I
a = −1.144460 − 0.407527I
b = 0.473434 − 0.779230I
4.20707 − 2.00630I 0
u = 0.742368 − 0.694050I
a = −1.144460 + 0.407527I
b = 0.473434 + 0.779230I
4.20707 + 2.00630I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.899456 + 0.386524I
a = −1.205040 − 0.331370I
b = −0.07659 − 1.90314I
−11.55850 − 1.59415I 0
u = 0.899456 − 0.386524I
a = −1.205040 + 0.331370I
b = −0.07659 + 1.90314I
−11.55850 + 1.59415I 0
u = −0.940419 + 0.400277I
a = 2.58071 − 1.55175I
b = 0.022898 − 1.315310I
−4.61342 − 3.20939I 0
u = −0.940419 − 0.400277I
a = 2.58071 + 1.55175I
b = 0.022898 + 1.315310I
−4.61342 + 3.20939I 0
u = −0.547983 + 0.864160I
a = −0.831442 + 0.465828I
b = 0.716478 − 0.312874I
5.66260 − 2.23601I 0
u = −0.547983 − 0.864160I
a = −0.831442 − 0.465828I
b = 0.716478 + 0.312874I
5.66260 + 2.23601I 0
u = 0.499148 + 0.825004I
a = −1.173990 − 0.748238I
b = 0.899665 + 0.392483I
1.63268 + 7.95122I 0
u = 0.499148 − 0.825004I
a = −1.173990 + 0.748238I
b = 0.899665 − 0.392483I
1.63268 − 7.95122I 0
u = 1.003890 + 0.321587I
a = −0.164326 − 0.143765I
b = 0.175029 + 0.466402I
−1.66108 − 1.47407I 0
u = 1.003890 − 0.321587I
a = −0.164326 + 0.143765I
b = 0.175029 − 0.466402I
−1.66108 + 1.47407I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.042520 + 0.171631I
a = −0.238632 − 0.296052I
b = 0.433016 − 0.822238I
−5.79252 − 1.16404I 0
u = −1.042520 − 0.171631I
a = −0.238632 + 0.296052I
b = 0.433016 + 0.822238I
−5.79252 + 1.16404I 0
u = −0.945639 + 0.472768I
a = −1.54105 + 1.40262I
b = 0.13061 + 1.51319I
−3.11222 + 3.71000I 0
u = −0.945639 − 0.472768I
a = −1.54105 − 1.40262I
b = 0.13061 − 1.51319I
−3.11222 − 3.71000I 0
u = −1.068950 + 0.027148I
a = −0.065840 + 0.370856I
b = −0.516622 − 0.708624I
−4.17554 + 6.43085I 0
u = −1.068950 − 0.027148I
a = −0.065840 − 0.370856I
b = −0.516622 + 0.708624I
−4.17554 − 6.43085I 0
u = 0.964494 + 0.465733I
a = 2.41393 + 0.37226I
b = −0.089867 + 1.348840I
−3.08837 − 1.58092I 0
u = 0.964494 − 0.465733I
a = 2.41393 − 0.37226I
b = −0.089867 − 1.348840I
−3.08837 + 1.58092I 0
u = −0.875483 + 0.638970I
a = −1.16011 + 1.11661I
b = 0.585032 + 0.257556I
1.80755 + 5.59259I 0
u = −0.875483 − 0.638970I
a = −1.16011 − 1.11661I
b = 0.585032 − 0.257556I
1.80755 − 5.59259I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.437385 + 0.992590I
a = −0.508035 + 0.885387I
b = 0.33220 − 1.49038I
−4.42863 − 12.37890I 0
u = −0.437385 − 0.992590I
a = −0.508035 − 0.885387I
b = 0.33220 + 1.49038I
−4.42863 + 12.37890I 0
u = 1.029890 + 0.363744I
a = −0.735917 − 0.877515I
b = 1.005630 − 0.051546I
−2.96783 − 3.24228I 0
u = 1.029890 − 0.363744I
a = −0.735917 + 0.877515I
b = 1.005630 + 0.051546I
−2.96783 + 3.24228I 0
u = −0.859174 + 0.266582I
a = −0.864643 + 1.047260I
b = −0.122746 − 1.028840I
−4.11003 + 6.16993I 0
u = −0.859174 − 0.266582I
a = −0.864643 − 1.047260I
b = −0.122746 + 1.028840I
−4.11003 − 6.16993I 0
u = 0.866442 + 0.686571I
a = 0.021204 − 0.798522I
b = −0.082816 − 0.345180I
3.81153 − 2.64755I 0
u = 0.866442 − 0.686571I
a = 0.021204 + 0.798522I
b = −0.082816 + 0.345180I
3.81153 + 2.64755I 0
u = −0.457246 + 0.766444I
a = 0.295154 + 1.361580I
b = 0.10777 − 1.49701I
−8.07051 + 1.26448I 0
u = −0.457246 − 0.766444I
a = 0.295154 − 1.361580I
b = 0.10777 + 1.49701I
−8.07051 − 1.26448I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.782458 + 0.421266I
a = 0.492123 + 0.259294I
b = −0.25826 + 1.42214I
−2.49887 + 0.02070I 0
u = −0.782458 − 0.421266I
a = 0.492123 − 0.259294I
b = −0.25826 − 1.42214I
−2.49887 − 0.02070I 0
u = 0.923397 + 0.629238I
a = 0.459018 + 0.164260I
b = −0.621856 − 0.578750I
3.64481 − 3.09137I 0
u = 0.923397 − 0.629238I
a = 0.459018 − 0.164260I
b = −0.621856 + 0.578750I
3.64481 + 3.09137I 0
u = 0.980910 + 0.535352I
a = −2.34185 − 1.18607I
b = 0.22577 − 1.42603I
−3.65229 − 8.55997I 0
u = 0.980910 − 0.535352I
a = −2.34185 + 1.18607I
b = 0.22577 + 1.42603I
−3.65229 + 8.55997I 0
u = 0.385592 + 1.050480I
a = −0.281760 − 0.585327I
b = 0.24772 + 1.43250I
0.06289 + 5.69076I 0
u = 0.385592 − 1.050480I
a = −0.281760 + 0.585327I
b = 0.24772 − 1.43250I
0.06289 − 5.69076I 0
u = 0.169806 + 0.859437I
a = 0.524015 + 0.315294I
b = 0.018135 − 1.235180I
−2.18571 + 2.40188I 0
u = 0.169806 − 0.859437I
a = 0.524015 − 0.315294I
b = 0.018135 + 1.235180I
−2.18571 − 2.40188I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.003390 + 0.537040I
a = −1.171840 + 0.574067I
b = 0.616372 + 0.213805I
−0.26082 + 4.36982I 0
u = −1.003390 − 0.537040I
a = −1.171840 − 0.574067I
b = 0.616372 − 0.213805I
−0.26082 − 4.36982I 0
u = 0.660571 + 0.541819I
a = 1.171540 + 0.572811I
b = −0.270269 − 1.340010I
−2.63800 + 4.19479I 0
u = 0.660571 − 0.541819I
a = 1.171540 − 0.572811I
b = −0.270269 + 1.340010I
−2.63800 − 4.19479I 0
u = −1.005150 + 0.553399I
a = 0.353317 − 0.779011I
b = −1.022200 + 0.905486I
−1.13521 + 6.72211I 0
u = −1.005150 − 0.553399I
a = 0.353317 + 0.779011I
b = −1.022200 − 0.905486I
−1.13521 − 6.72211I 0
u = −1.114370 + 0.289346I
a = 0.331211 − 0.959738I
b = 0.160740 − 1.382660I
−6.91836 − 0.04737I 0
u = −1.114370 − 0.289346I
a = 0.331211 + 0.959738I
b = 0.160740 + 1.382660I
−6.91836 + 0.04737I 0
u = 0.889597 + 0.768873I
a = 0.626789 − 0.957771I
b = 0.043016 + 0.993124I
−0.21937 − 2.90174I 0
u = 0.889597 − 0.768873I
a = 0.626789 + 0.957771I
b = 0.043016 − 0.993124I
−0.21937 + 2.90174I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.602560 + 0.561546I
a = −2.00071 + 0.52026I
b = 0.795831 + 0.968113I
0.10275 − 2.20920I 0
u = −0.602560 − 0.561546I
a = −2.00071 − 0.52026I
b = 0.795831 − 0.968113I
0.10275 + 2.20920I 0
u = −1.074070 + 0.485368I
a = −0.610249 + 0.910638I
b = 0.924230 − 0.351363I
−2.13614 + 3.57490I 0
u = −1.074070 − 0.485368I
a = −0.610249 − 0.910638I
b = 0.924230 + 0.351363I
−2.13614 − 3.57490I 0
u = 0.639090 + 0.504053I
a = 1.077930 − 0.580036I
b = −0.192648 + 0.630385I
−0.71618 − 1.90859I 0
u = 0.639090 − 0.504053I
a = 1.077930 + 0.580036I
b = −0.192648 − 0.630385I
−0.71618 + 1.90859I 0
u = −1.045760 + 0.568872I
a = 1.73537 + 0.12208I
b = −0.25881 − 1.60054I
−9.82983 + 3.72484I 0
u = −1.045760 − 0.568872I
a = 1.73537 − 0.12208I
b = −0.25881 + 1.60054I
−9.82983 − 3.72484I 0
u = 0.933199 + 0.740178I
a = 0.904231 − 0.486103I
b = −0.234717 + 0.833476I
−0.29508 − 2.93135I 0
u = 0.933199 − 0.740178I
a = 0.904231 + 0.486103I
b = −0.234717 − 0.833476I
−0.29508 + 2.93135I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.050600 + 0.576898I
a = −1.59175 − 0.34367I
b = 0.555747 − 0.459906I
−3.28631 − 7.76450I 0
u = 1.050600 − 0.576898I
a = −1.59175 + 0.34367I
b = 0.555747 + 0.459906I
−3.28631 + 7.76450I 0
u = 1.199430 + 0.018650I
a = −0.326384 + 0.958707I
b = 0.07865 + 1.59809I
−13.9909 + 2.9581I 0
u = 1.199430 − 0.018650I
a = −0.326384 − 0.958707I
b = 0.07865 − 1.59809I
−13.9909 − 2.9581I 0
u = −0.883489 + 0.823866I
a = 0.85913 + 1.40259I
b = −0.032006 − 1.331310I
0.14542 + 3.06178I 0
u = −0.883489 − 0.823866I
a = 0.85913 − 1.40259I
b = −0.032006 + 1.331310I
0.14542 − 3.06178I 0
u = 1.167860 + 0.351487I
a = 0.650199 + 0.290683I
b = 0.25318 + 1.56328I
−8.82881 + 0.83224I 0
u = 1.167860 − 0.351487I
a = 0.650199 − 0.290683I
b = 0.25318 − 1.56328I
−8.82881 − 0.83224I 0
u = −1.127710 + 0.480498I
a = −1.82337 + 0.51238I
b = 0.47357 + 1.49368I
−7.99189 + 8.84719I 0
u = −1.127710 − 0.480498I
a = −1.82337 − 0.51238I
b = 0.47357 − 1.49368I
−7.99189 − 8.84719I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.110470 + 0.559884I
a = −1.99586 − 0.47824I
b = 0.290942 − 1.342730I
−5.10181 − 7.59480I 0
u = 1.110470 − 0.559884I
a = −1.99586 + 0.47824I
b = 0.290942 + 1.342730I
−5.10181 + 7.59480I 0
u = 0.434198 + 0.618590I
a = 1.41844 + 0.70439I
b = −0.314285 − 0.489036I
−1.57370 + 3.01462I 4.59125 − 4.24141I
u = 0.434198 − 0.618590I
a = 1.41844 − 0.70439I
b = −0.314285 + 0.489036I
−1.57370 − 3.01462I 4.59125 + 4.24141I
u = 0.327812 + 0.669357I
a = 0.856891 + 0.912817I
b = −0.245218 − 1.287400I
−2.89276 + 2.80570I 3.21371 − 1.63988I
u = 0.327812 − 0.669357I
a = 0.856891 − 0.912817I
b = −0.245218 + 1.287400I
−2.89276 − 2.80570I 3.21371 + 1.63988I
u = 1.180670 + 0.436343I
a = −0.322934 + 0.042889I
b = 0.0067332 + 0.1318550I
−1.80294 − 1.34025I 0
u = 1.180670 − 0.436343I
a = −0.322934 − 0.042889I
b = 0.0067332 − 0.1318550I
−1.80294 + 1.34025I 0
u = 1.088750 + 0.642007I
a = 1.30896 + 0.59178I
b = −1.013580 + 0.497805I
−0.14887 − 13.43410I 0
u = 1.088750 − 0.642007I
a = 1.30896 − 0.59178I
b = −1.013580 − 0.497805I
−0.14887 + 13.43410I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.071670 + 0.673655I
a = 1.093560 − 0.442170I
b = −0.778925 − 0.479486I
4.06812 + 7.92542I 0
u = −1.071670 − 0.673655I
a = 1.093560 + 0.442170I
b = −0.778925 + 0.479486I
4.06812 − 7.92542I 0
u = −0.571980 + 0.454559I
a = 1.43695 − 0.31602I
b = −0.480902 + 0.025130I
1.042310 − 0.100714I 11.05953 + 0.92262I
u = −0.571980 − 0.454559I
a = 1.43695 + 0.31602I
b = −0.480902 − 0.025130I
1.042310 + 0.100714I 11.05953 − 0.92262I
u = −0.719247 + 0.031000I
a = 2.25126 − 0.47542I
b = −0.335275 − 0.453348I
0.559631 − 0.028225I 3.73353 − 0.43145I
u = −0.719247 − 0.031000I
a = 2.25126 + 0.47542I
b = −0.335275 + 0.453348I
0.559631 + 0.028225I 3.73353 + 0.43145I
u = 1.157130 + 0.565388I
a = −1.79624 − 0.50897I
b = 0.184128 − 1.295580I
−4.99442 − 7.50414I 0
u = 1.157130 − 0.565388I
a = −1.79624 + 0.50897I
b = 0.184128 + 1.295580I
−4.99442 + 7.50414I 0
u = −0.080053 + 0.706651I
a = 0.84526 − 1.32254I
b = −0.33809 + 1.42370I
−5.09434 − 4.55628I 2.46367 + 3.11245I
u = −0.080053 − 0.706651I
a = 0.84526 + 1.32254I
b = −0.33809 − 1.42370I
−5.09434 + 4.55628I 2.46367 − 3.11245I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.601004 + 0.369751I
a = 0.214027 − 1.384130I
b = −0.084763 + 1.173690I
−2.02990 − 2.08563I 5.03397 + 5.10620I
u = 0.601004 − 0.369751I
a = 0.214027 + 1.384130I
b = −0.084763 − 1.173690I
−2.02990 + 2.08563I 5.03397 − 5.10620I
u = −1.109200 + 0.675081I
a = −1.99957 − 0.13886I
b = 0.22139 + 1.48235I
−9.5852 + 10.7219I 0
u = −1.109200 − 0.675081I
a = −1.99957 + 0.13886I
b = 0.22139 − 1.48235I
−9.5852 − 10.7219I 0
u = −0.566260 + 1.196990I
a = −0.276390 − 0.583794I
b = 0.100971 + 1.374480I
−3.41479 + 5.75686I 0
u = −0.566260 − 1.196990I
a = −0.276390 + 0.583794I
b = 0.100971 − 1.374480I
−3.41479 − 5.75686I 0
u = −1.173470 + 0.678874I
a = 1.79527 − 0.22317I
b = −0.37084 − 1.54686I
−6.7118 + 18.4340I 0
u = −1.173470 − 0.678874I
a = 1.79527 + 0.22317I
b = −0.37084 + 1.54686I
−6.7118 − 18.4340I 0
u = 1.365480 + 0.021506I
a = 0.060189 − 0.750509I
b = −0.19493 − 1.52083I
−11.2418 + 9.1333I 0
u = 1.365480 − 0.021506I
a = 0.060189 + 0.750509I
b = −0.19493 + 1.52083I
−11.2418 − 9.1333I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.192050 + 0.677817I
a = 1.55469 + 0.34247I
b = −0.28776 + 1.51874I
−2.42897 − 11.84450I 0
u = 1.192050 − 0.677817I
a = 1.55469 − 0.34247I
b = −0.28776 − 1.51874I
−2.42897 + 11.84450I 0
u = −1.41597 + 0.14452I
a = 0.086654 − 0.817722I
b = −0.06727 − 1.46117I
−7.57822 + 1.85934I 0
u = −1.41597 − 0.14452I
a = 0.086654 + 0.817722I
b = −0.06727 + 1.46117I
−7.57822 − 1.85934I 0
u = −0.214793 + 0.534884I
a = 1.87361 + 0.18083I
b = −0.762942 − 0.220779I
0.126458 + 0.501413I 6.99069 − 0.97875I
u = −0.214793 − 0.534884I
a = 1.87361 − 0.18083I
b = −0.762942 + 0.220779I
0.126458 − 0.501413I 6.99069 + 0.97875I
u = −1.31658 + 0.67345I
a = −0.997522 + 0.205714I
b = −0.002765 + 1.373410I
−6.18745 + 1.32084I 0
u = −1.31658 − 0.67345I
a = −0.997522 − 0.205714I
b = −0.002765 − 1.373410I
−6.18745 − 1.32084I 0
u = 0.497375 + 0.069997I
a = 2.44253 + 1.50473I
b = 0.220366 − 0.429480I
−1.30719 + 2.77377I 2.12105 − 5.40265I
u = 0.497375 − 0.069997I
a = 2.44253 − 1.50473I
b = 0.220366 + 0.429480I
−1.30719 − 2.77377I 2.12105 + 5.40265I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.477236
a = 1.85229
b = −0.355196
0.885419 11.9600
u = −1.22203 + 0.90973I
a = 0.851154 + 0.087020I
b = −0.07295 − 1.57142I
−8.03343 + 4.00605I 0
u = −1.22203 − 0.90973I
a = 0.851154 − 0.087020I
b = −0.07295 + 1.57142I
−8.03343 − 4.00605I 0
17
II. I
u
2
= h88u
27
+ 45u
26
+ · · · + 23b − 99, −10u
27
+ 78u
26
+ · · · + 23a −
144, u
28
− 7u
26
+ · · · − 8u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
0.434783u
27
− 3.39130u
26
+ ··· + 3.04348u + 6.26087
−3.82609u
27
− 1.95652u
26
+ ··· + 8.21739u + 4.30435
a
4
=
−12.9565u
27
+ 3.26087u
26
+ ··· + 14.3043u + 7.82609
−3.82609u
27
− 0.956522u
26
+ ··· + 10.2174u − 0.695652
a
10
=
−3.39130u
27
− 5.34783u
26
+ ··· + 11.2609u + 10.5652
−3.82609u
27
− 1.95652u
26
+ ··· + 8.21739u + 4.30435
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−1.30435u
27
− 4.82609u
26
+ ··· + 0.869565u + 11.2174
7.69565u
27
− 3.82609u
26
+ ··· − 14.1304u + 4.21739
a
11
=
6.30435u
27
− 1.17391u
26
+ ··· − 21.8696u + 8.78261
−4.26087u
27
+ 7.43478u
26
+ ··· + 0.173913u − 5.95652
a
8
=
−0.565217u
27
− 2.39130u
26
+ ··· + 4.04348u + 5.26087
−3.82609u
27
− 1.95652u
26
+ ··· + 8.21739u + 4.30435
a
12
=
8.34783u
27
+ 0.0869565u
26
+ ··· − 8.56522u − 3.39130
−4.91304u
27
+ 3.52174u
26
+ ··· + 7.60870u − 1.34783
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
424
23
u
27
+
492
23
u
26
+ ··· −
461
23
u +
247
23
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
− 14u
27
+ ··· − 16u + 1
c
2
u
28
− 7u
26
+ ··· − 8u
2
+ 1
c
3
u
28
+ 4u
26
+ ··· − 2u + 1
c
4
u
28
+ 14u
26
+ ··· + u + 3
c
5
u
28
+ 16u
26
+ ··· + u + 1
c
6
u
28
− 7u
26
+ ··· − 8u
2
+ 1
c
7
u
28
− 4u
27
+ ··· − 4u + 1
c
8
u
28
+ u
27
+ ··· + 2u
2
+ 1
c
9
, c
10
u
28
+ 16u
26
+ ··· − u + 1
c
11
u
28
+ 4u
27
+ ··· + 4u + 1
c
12
u
28
+ 14u
26
+ ··· − u + 3
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 14y
27
+ ··· + 4y
2
+ 1
c
2
, c
6
y
28
− 14y
27
+ ··· − 16y + 1
c
3
y
28
+ 8y
27
+ ··· − 2y + 1
c
4
, c
12
y
28
+ 28y
27
+ ··· + 167y + 9
c
5
, c
9
, c
10
y
28
+ 32y
27
+ ··· + 11y + 1
c
7
, c
11
y
28
− 24y
27
+ ··· − 28y + 1
c
8
y
28
− 9y
27
+ ··· + 4y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.915167 + 0.306798I
a = 1.314090 − 0.376918I
b = 0.04802 − 1.85125I
−11.84290 + 1.28681I −6.01173 + 4.88233I
u = −0.915167 − 0.306798I
a = 1.314090 + 0.376918I
b = 0.04802 + 1.85125I
−11.84290 − 1.28681I −6.01173 − 4.88233I
u = −0.691639 + 0.777864I
a = −0.350646 − 0.392835I
b = −0.310148 + 0.468429I
0.53145 + 3.71930I 4.55046 − 6.69924I
u = −0.691639 − 0.777864I
a = −0.350646 + 0.392835I
b = −0.310148 − 0.468429I
0.53145 − 3.71930I 4.55046 + 6.69924I
u = 0.432723 + 0.827633I
a = −0.041836 − 0.321263I
b = −0.133766 + 1.289080I
−2.53211 − 5.32903I 6.12582 + 4.95903I
u = 0.432723 − 0.827633I
a = −0.041836 + 0.321263I
b = −0.133766 − 1.289080I
−2.53211 + 5.32903I 6.12582 − 4.95903I
u = 1.011290 + 0.423393I
a = −0.713876 − 1.070590I
b = 0.718901 + 0.516702I
−2.27853 − 5.05967I 3.47459 + 6.66316I
u = 1.011290 − 0.423393I
a = −0.713876 + 1.070590I
b = 0.718901 − 0.516702I
−2.27853 + 5.05967I 3.47459 − 6.66316I
u = 0.872702 + 0.686844I
a = −0.185565 − 0.657965I
b = −0.044753 − 0.637567I
3.35795 − 2.64859I −1.69884 + 2.56363I
u = 0.872702 − 0.686844I
a = −0.185565 + 0.657965I
b = −0.044753 + 0.637567I
3.35795 + 2.64859I −1.69884 − 2.56363I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.876358 + 0.765551I
a = 0.92195 + 1.58625I
b = −0.020666 − 1.224370I
1.10467 + 2.89033I 11.40955 − 2.13475I
u = −0.876358 − 0.765551I
a = 0.92195 − 1.58625I
b = −0.020666 + 1.224370I
1.10467 − 2.89033I 11.40955 + 2.13475I
u = −0.792613 + 0.235951I
a = 2.12050 + 0.25249I
b = −0.278257 − 0.359878I
0.641193 + 0.799954I 5.77042 − 9.13013I
u = −0.792613 − 0.235951I
a = 2.12050 − 0.25249I
b = −0.278257 + 0.359878I
0.641193 − 0.799954I 5.77042 + 9.13013I
u = 0.725232 + 0.348379I
a = 2.44478 + 1.12149I
b = −0.600308 + 0.657620I
−1.18482 + 1.75585I 2.86033 + 0.77633I
u = 0.725232 − 0.348379I
a = 2.44478 − 1.12149I
b = −0.600308 − 0.657620I
−1.18482 − 1.75585I 2.86033 − 0.77633I
u = −1.091580 + 0.500735I
a = −2.22274 + 0.92875I
b = 0.278546 + 1.320190I
−5.34404 + 8.60711I −0.70812 − 11.02230I
u = −1.091580 − 0.500735I
a = −2.22274 − 0.92875I
b = 0.278546 − 1.320190I
−5.34404 − 8.60711I −0.70812 + 11.02230I
u = −1.124270 + 0.494821I
a = −0.416217 + 0.360770I
b = 0.510017 + 0.131165I
−1.39313 + 1.57288I 8.43595 − 4.38584I
u = −1.124270 − 0.494821I
a = −0.416217 − 0.360770I
b = 0.510017 − 0.131165I
−1.39313 − 1.57288I 8.43595 + 4.38584I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.202310 + 0.304809I
a = 0.584754 + 0.812487I
b = 0.13513 + 1.40947I
−6.19136 + 0.59628I 2.45660 − 2.03049I
u = 1.202310 − 0.304809I
a = 0.584754 − 0.812487I
b = 0.13513 − 1.40947I
−6.19136 − 0.59628I 2.45660 + 2.03049I
u = −0.562984 + 0.396371I
a = 2.03466 − 1.32651I
b = −0.227724 + 1.238680I
−3.44400 − 4.66789I 0.91589 + 5.91609I
u = −0.562984 − 0.396371I
a = 2.03466 + 1.32651I
b = −0.227724 − 1.238680I
−3.44400 + 4.66789I 0.91589 − 5.91609I
u = 0.599089 + 0.115219I
a = 1.93413 − 0.42370I
b = −0.173110 − 1.310390I
−2.88560 + 1.01731I 1.33365 − 1.59890I
u = 0.599089 − 0.115219I
a = 1.93413 + 0.42370I
b = −0.173110 + 1.310390I
−2.88560 − 1.01731I 1.33365 + 1.59890I
u = 1.21127 + 0.83460I
a = −0.923981 + 0.029523I
b = 0.09811 − 1.57477I
−8.01715 − 3.84216I 3.0854 − 16.7816I
u = 1.21127 − 0.83460I
a = −0.923981 − 0.029523I
b = 0.09811 + 1.57477I
−8.01715 + 3.84216I 3.0854 + 16.7816I
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 14u
27
+ ··· − 16u + 1)(u
123
+ 55u
122
+ ··· + 363300u + 10609)
c
2
(u
28
− 7u
26
+ ··· − 8u
2
+ 1)(u
123
− 3u
122
+ ··· + 118u − 103)
c
3
(u
28
+ 4u
26
+ ··· − 2u + 1)(u
123
− u
122
+ ··· + 87046u − 12899)
c
4
(u
28
+ 14u
26
+ ··· + u + 3)(u
123
+ 7u
122
+ ··· − 111u − 43)
c
5
(u
28
+ 16u
26
+ ··· + u + 1)(u
123
− u
122
+ ··· + u − 19)
c
6
(u
28
− 7u
26
+ ··· − 8u
2
+ 1)(u
123
− 3u
122
+ ··· + 118u − 103)
c
7
(u
28
− 4u
27
+ ··· − 4u + 1)(u
123
+ 3u
122
+ ··· − 752u − 187)
c
8
(u
28
+ u
27
+ ··· + 2u
2
+ 1)(u
123
+ 2u
122
+ ··· + 2u − 1)
c
9
, c
10
(u
28
+ 16u
26
+ ··· − u + 1)(u
123
− u
122
+ ··· + u − 19)
c
11
(u
28
+ 4u
27
+ ··· + 4u + 1)(u
123
+ 3u
122
+ ··· − 752u − 187)
c
12
(u
28
+ 14u
26
+ ··· − u + 3)(u
123
+ 7u
122
+ ··· − 111u − 43)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 14y
27
+ ··· + 4y
2
+ 1)
· (y
123
+ 41y
122
+ ··· + 2225325352y −112550881)
c
2
, c
6
(y
28
− 14y
27
+ ··· − 16y + 1)(y
123
− 55y
122
+ ··· + 363300y −10609)
c
3
(y
28
+ 8y
27
+ ··· − 2y + 1)
· (y
123
+ 27y
122
+ ··· − 6188058542y −166384201)
c
4
, c
12
(y
28
+ 28y
27
+ ··· + 167y + 9)(y
123
+ 91y
122
+ ··· − 18639y −1849)
c
5
, c
9
, c
10
(y
28
+ 32y
27
+ ··· + 11y + 1)(y
123
+ 123y
122
+ ··· − 47879y −361)
c
7
, c
11
(y
28
− 24y
27
+ ··· − 28y + 1)
· (y
123
− 69y
122
+ ··· + 1826632y −34969)
c
8
(y
28
− 9y
27
+ ··· + 4y + 1)(y
123
− 10y
122
+ ··· + 136y −1)
25
