12a
0770
(K12a
0770
)
A knot diagram
1
Linearized knot diagam
3 8 10 12 9 11 2 7 5 1 6 4
Solving Sequence
2,7
8 3 9
1,11
6 12 5 4 10
c
7
c
2
c
8
c
1
c
6
c
11
c
5
c
4
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.65043 × 10
180
u
122
− 4.62248 × 10
181
u
121
+ ··· + 5.34068 × 10
181
b + 2.74124 × 10
183
,
− 7.47255 × 10
182
u
122
− 1.31863 × 10
183
u
121
+ ··· + 6.14178 × 10
182
a + 1.15546 × 10
184
,
u
123
+ u
122
+ ··· + 43u + 23i
I
u
2
= h3u
21
− 3u
20
+ ··· + b + 2u, −5u
21
+ 7u
20
+ ··· + a + 2, u
22
− 2u
21
+ ··· − u + 1i
I
u
3
= h2b − a − 1, a
2
+ 3, u + 1i
* 3 irreducible components of dim
C
= 0, with total 147 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−6.65 × 10
180
u
122
− 4.62 × 10
181
u
121
+ · · · + 5.34 × 10
181
b + 2.74 ×
10
183
, −7.47 × 10
182
u
122
− 1.32 × 10
183
u
121
+ · · · + 6.14 × 10
182
a + 1.16 ×
10
184
, u
123
+ u
122
+ · · · + 43u + 23i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
1.21667u
122
+ 2.14697u
121
+ ··· − 77.9956u − 18.8131
0.124524u
122
+ 0.865522u
121
+ ··· − 67.1265u − 51.3275
a
6
=
−0.0607396u
122
+ 0.475188u
121
+ ··· − 44.6538u − 69.4270
1.67317u
122
+ 0.806668u
121
+ ··· + 5.21204u + 63.7892
a
12
=
1.23243u
122
− 0.911083u
121
+ ··· + 68.7361u + 72.5814
−2.33691u
122
− 2.63772u
121
+ ··· + 131.127u + 1.01620
a
5
=
0.914222u
122
+ 0.748352u
121
+ ··· − 27.3667u − 28.7631
1.49054u
122
+ 0.650958u
121
+ ··· + 16.0082u + 79.3115
a
4
=
−1.54515u
122
− 0.506262u
121
+ ··· − 7.26446u − 50.9718
1.79972u
122
+ 0.979358u
121
+ ··· − 8.27209u + 29.8660
a
10
=
1.17727u
122
+ 1.92689u
121
+ ··· − 54.9908u − 7.68351
−0.328200u
122
+ 0.391498u
121
+ ··· − 57.6916u − 52.2228
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.02390u
122
− 5.22769u
121
+ ··· + 262.256u + 134.644
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
123
+ 37u
122
+ ··· + 8841u + 529
c
2
, c
7
u
123
+ u
122
+ ··· + 43u + 23
c
3
u
123
+ u
122
+ ··· − 438u + 319
c
4
, c
12
u
123
+ 5u
122
+ ··· + 1096u + 193
c
5
, c
9
u
123
− 3u
122
+ ··· − 2u + 1
c
6
, c
11
u
123
− u
122
+ ··· − 2422u + 317
c
10
u
123
− 3u
122
+ ··· + 36u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
123
+ 107y
122
+ ··· − 3332343y −279841
c
2
, c
7
y
123
− 37y
122
+ ··· + 8841y −529
c
3
y
123
+ 23y
122
+ ··· − 8257190y −101761
c
4
, c
12
y
123
+ 87y
122
+ ··· − 679762y −37249
c
5
, c
9
y
123
+ 77y
122
+ ··· − 114y −1
c
6
, c
11
y
123
+ 75y
122
+ ··· + 1511772y −100489
c
10
y
123
− 7y
122
+ ··· − 146y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998038 + 0.111520I
a = −0.618593 − 1.235120I
b = 0.464560 − 0.829256I
−3.64634 − 2.82809I 0
u = 0.998038 − 0.111520I
a = −0.618593 + 1.235120I
b = 0.464560 + 0.829256I
−3.64634 + 2.82809I 0
u = −1.008390 + 0.041848I
a = −0.012986 + 1.238690I
b = 0.74198 + 1.33457I
−5.23839 + 3.65926I 0
u = −1.008390 − 0.041848I
a = −0.012986 − 1.238690I
b = 0.74198 − 1.33457I
−5.23839 − 3.65926I 0
u = 0.747677 + 0.678061I
a = 1.29904 + 1.42318I
b = −1.10040 − 1.00468I
−0.28697 + 3.57568I 0
u = 0.747677 − 0.678061I
a = 1.29904 − 1.42318I
b = −1.10040 + 1.00468I
−0.28697 − 3.57568I 0
u = 0.978634 + 0.099967I
a = −0.575223 − 1.000370I
b = 0.532319 − 0.539416I
−3.62329 − 2.84767I 0
u = 0.978634 − 0.099967I
a = −0.575223 + 1.000370I
b = 0.532319 + 0.539416I
−3.62329 + 2.84767I 0
u = 0.999685 + 0.318338I
a = 0.846148 + 0.812960I
b = 0.02291 + 1.41918I
−8.44641 − 0.32156I 0
u = 0.999685 − 0.318338I
a = 0.846148 − 0.812960I
b = 0.02291 − 1.41918I
−8.44641 + 0.32156I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.694646 + 0.643454I
a = 0.846743 − 0.636508I
b = −0.163630 − 0.059486I
2.48058 − 1.47346I 0
u = 0.694646 − 0.643454I
a = 0.846743 + 0.636508I
b = −0.163630 + 0.059486I
2.48058 + 1.47346I 0
u = −0.718678 + 0.775205I
a = 1.45433 − 0.51245I
b = −0.796471 + 0.555784I
2.25372 − 2.40345I 0
u = −0.718678 − 0.775205I
a = 1.45433 + 0.51245I
b = −0.796471 − 0.555784I
2.25372 + 2.40345I 0
u = −0.828714 + 0.440216I
a = 0.405860 + 0.873938I
b = 0.530574 − 0.657586I
−1.69210 + 2.01686I 0
u = −0.828714 − 0.440216I
a = 0.405860 − 0.873938I
b = 0.530574 + 0.657586I
−1.69210 − 2.01686I 0
u = −0.903346 + 0.243331I
a = 0.0407501 − 0.0294218I
b = −1.183180 − 0.102475I
−1.43303 + 6.80135I 0
u = −0.903346 − 0.243331I
a = 0.0407501 + 0.0294218I
b = −1.183180 + 0.102475I
−1.43303 − 6.80135I 0
u = 1.062020 + 0.073185I
a = −0.736389 − 1.157230I
b = 0.097415 − 0.752583I
−3.59485 − 2.77429I 0
u = 1.062020 − 0.073185I
a = −0.736389 + 1.157230I
b = 0.097415 + 0.752583I
−3.59485 + 2.77429I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.771064 + 0.741605I
a = −0.110952 + 1.386560I
b = 0.516847 − 1.169790I
−1.99581 + 1.48737I 0
u = −0.771064 − 0.741605I
a = −0.110952 − 1.386560I
b = 0.516847 + 1.169790I
−1.99581 − 1.48737I 0
u = −1.040000 + 0.262995I
a = −1.40149 + 0.98571I
b = 0.264976 + 1.307830I
−8.72461 + 5.99285I 0
u = −1.040000 − 0.262995I
a = −1.40149 − 0.98571I
b = 0.264976 − 1.307830I
−8.72461 − 5.99285I 0
u = −0.897567 + 0.593044I
a = 0.702479 − 0.017392I
b = 0.139182 − 0.979590I
−1.12457 + 2.29817I 0
u = −0.897567 − 0.593044I
a = 0.702479 + 0.017392I
b = 0.139182 + 0.979590I
−1.12457 − 2.29817I 0
u = 0.245012 + 0.890518I
a = −0.355572 + 0.069784I
b = 0.419312 − 0.758001I
3.31588 − 1.85610I 0
u = 0.245012 − 0.890518I
a = −0.355572 − 0.069784I
b = 0.419312 + 0.758001I
3.31588 + 1.85610I 0
u = 0.819637 + 0.401676I
a = 0.261319 − 0.494561I
b = −0.539925 + 0.154824I
1.67415 − 2.68529I 0
u = 0.819637 − 0.401676I
a = 0.261319 + 0.494561I
b = −0.539925 − 0.154824I
1.67415 + 2.68529I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.832068 + 0.700606I
a = 2.25867 − 0.20449I
b = −0.161300 − 0.591037I
0.85788 − 2.20310I 0
u = −0.832068 − 0.700606I
a = 2.25867 + 0.20449I
b = −0.161300 + 0.591037I
0.85788 + 2.20310I 0
u = −0.745115 + 0.794136I
a = 1.107990 − 0.745099I
b = −0.633546 + 0.858719I
2.45030 − 2.24805I 0
u = −0.745115 − 0.794136I
a = 1.107990 + 0.745099I
b = −0.633546 − 0.858719I
2.45030 + 2.24805I 0
u = −0.586117 + 0.921962I
a = −0.124249 + 0.255359I
b = 0.423531 − 1.046930I
2.31520 + 1.08669I 0
u = −0.586117 − 0.921962I
a = −0.124249 − 0.255359I
b = 0.423531 + 1.046930I
2.31520 − 1.08669I 0
u = −0.038136 + 0.876287I
a = −0.551055 − 0.730714I
b = 0.513871 + 1.117790I
−1.63003 + 8.62110I 0
u = −0.038136 − 0.876287I
a = −0.551055 + 0.730714I
b = 0.513871 − 1.117790I
−1.63003 − 8.62110I 0
u = 0.862609 + 0.722091I
a = 1.95306 − 0.13787I
b = −0.454401 + 0.739122I
2.80440 − 2.13090I 0
u = 0.862609 − 0.722091I
a = 1.95306 + 0.13787I
b = −0.454401 − 0.739122I
2.80440 + 2.13090I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.961243 + 0.587894I
a = 1.14619 − 0.86535I
b = 0.31694 + 1.38447I
−2.03643 − 1.93180I 0
u = 0.961243 − 0.587894I
a = 1.14619 + 0.86535I
b = 0.31694 − 1.38447I
−2.03643 + 1.93180I 0
u = −0.873179 + 0.719044I
a = −1.56461 − 1.14251I
b = −0.05346 + 2.18005I
−3.82458 + 2.74777I 0
u = −0.873179 − 0.719044I
a = −1.56461 + 1.14251I
b = −0.05346 − 2.18005I
−3.82458 − 2.74777I 0
u = −0.826141 + 0.781445I
a = 1.070400 − 0.503843I
b = −0.612674 + 1.078900I
3.46834 − 2.97155I 0
u = −0.826141 − 0.781445I
a = 1.070400 + 0.503843I
b = −0.612674 − 1.078900I
3.46834 + 2.97155I 0
u = 0.852358 + 0.753126I
a = 0.237441 + 0.203080I
b = −0.436051 − 1.275240I
3.86620 − 1.44750I 0
u = 0.852358 − 0.753126I
a = 0.237441 − 0.203080I
b = −0.436051 + 1.275240I
3.86620 + 1.44750I 0
u = 0.787621 + 0.829507I
a = −1.87946 − 0.52483I
b = 1.41777 − 0.40004I
5.34270 + 5.05268I 0
u = 0.787621 − 0.829507I
a = −1.87946 + 0.52483I
b = 1.41777 + 0.40004I
5.34270 − 5.05268I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.887733 + 0.721472I
a = −0.856295 − 0.891714I
b = 0.560141 + 0.584146I
2.72547 − 3.38209I 0
u = 0.887733 − 0.721472I
a = −0.856295 + 0.891714I
b = 0.560141 − 0.584146I
2.72547 + 3.38209I 0
u = 0.758416 + 0.865706I
a = 0.804802 + 1.078350I
b = −0.408380 − 1.099450I
−1.26568 + 5.11585I 0
u = 0.758416 − 0.865706I
a = 0.804802 − 1.078350I
b = −0.408380 + 1.099450I
−1.26568 − 5.11585I 0
u = −0.916667 + 0.696677I
a = −1.39838 + 0.44542I
b = 0.295926 − 0.386739I
0.58974 + 7.57307I 0
u = −0.916667 − 0.696677I
a = −1.39838 − 0.44542I
b = 0.295926 + 0.386739I
0.58974 − 7.57307I 0
u = 0.706014 + 0.915678I
a = −0.624192 − 0.687267I
b = 0.657698 + 1.214410I
6.59960 + 6.11951I 0
u = 0.706014 − 0.915678I
a = −0.624192 + 0.687267I
b = 0.657698 − 1.214410I
6.59960 − 6.11951I 0
u = −0.718343 + 0.910366I
a = −0.807984 + 0.965034I
b = 0.75916 − 1.30609I
2.36046 − 12.44930I 0
u = −0.718343 − 0.910366I
a = −0.807984 − 0.965034I
b = 0.75916 + 1.30609I
2.36046 + 12.44930I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.900961 + 0.743227I
a = −1.75793 − 0.52878I
b = 0.343286 − 1.313990I
3.71549 − 4.22857I 0
u = 0.900961 − 0.743227I
a = −1.75793 + 0.52878I
b = 0.343286 + 1.313990I
3.71549 + 4.22857I 0
u = 1.140660 + 0.278300I
a = 0.737848 + 1.093620I
b = −0.538495 + 1.302820I
−5.67717 − 12.45260I 0
u = 1.140660 − 0.278300I
a = 0.737848 − 1.093620I
b = −0.538495 − 1.302820I
−5.67717 + 12.45260I 0
u = 0.813009 + 0.120512I
a = −0.23268 − 3.53099I
b = 0.315947 − 0.920401I
−2.01877 − 5.28852I 0
u = 0.813009 − 0.120512I
a = −0.23268 + 3.53099I
b = 0.315947 + 0.920401I
−2.01877 + 5.28852I 0
u = 0.960387 + 0.682857I
a = −2.48484 − 0.60816I
b = 1.10630 − 1.19956I
−0.94330 − 8.86692I 0
u = 0.960387 − 0.682857I
a = −2.48484 + 0.60816I
b = 1.10630 + 1.19956I
−0.94330 + 8.86692I 0
u = −0.813819 + 0.859589I
a = −1.336780 + 0.401490I
b = 1.039350 + 0.325117I
9.35496 − 0.04602I 0
u = −0.813819 − 0.859589I
a = −1.336780 − 0.401490I
b = 1.039350 − 0.325117I
9.35496 + 0.04602I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.936883 + 0.724277I
a = 1.98061 + 0.39240I
b = −0.59881 − 1.36704I
−2.47707 + 4.09068I 0
u = −0.936883 − 0.724277I
a = 1.98061 − 0.39240I
b = −0.59881 + 1.36704I
−2.47707 − 4.09068I 0
u = −0.809882
a = −0.230136
b = 0.468179
−1.31525 −6.85520
u = −0.928238 + 0.754910I
a = −2.30996 + 0.61386I
b = 0.557724 + 1.130270I
3.15268 + 8.76794I 0
u = −0.928238 − 0.754910I
a = −2.30996 − 0.61386I
b = 0.557724 − 1.130270I
3.15268 − 8.76794I 0
u = −0.798815 + 0.045097I
a = 1.24092 + 2.64289I
b = 0.059987 + 1.041400I
−0.780386 + 0.986928I −7.33577 + 0.I
u = −0.798815 − 0.045097I
a = 1.24092 − 2.64289I
b = 0.059987 − 1.041400I
−0.780386 − 0.986928I −7.33577 + 0.I
u = 0.796042 + 0.076675I
a = 1.01452 + 1.61059I
b = −0.22148 + 1.83294I
−7.40333 − 0.39146I −12.24132 − 5.59979I
u = 0.796042 − 0.076675I
a = 1.01452 − 1.61059I
b = −0.22148 − 1.83294I
−7.40333 + 0.39146I −12.24132 + 5.59979I
u = −0.987452 + 0.715297I
a = −1.94054 + 0.76734I
b = 0.827683 + 0.651069I
1.43912 + 8.05022I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.987452 − 0.715297I
a = −1.94054 − 0.76734I
b = 0.827683 − 0.651069I
1.43912 − 8.05022I 0
u = −1.185750 + 0.293560I
a = −0.746021 + 0.436699I
b = −0.298245 + 1.105680I
−5.59178 − 4.46851I 0
u = −1.185750 − 0.293560I
a = −0.746021 − 0.436699I
b = −0.298245 − 1.105680I
−5.59178 + 4.46851I 0
u = 0.482789 + 0.609312I
a = 1.11654 − 1.27200I
b = −0.432805 + 1.108760I
−0.75905 − 2.63678I −4.00000 + 3.70377I
u = 0.482789 − 0.609312I
a = 1.11654 + 1.27200I
b = −0.432805 − 1.108760I
−0.75905 + 2.63678I −4.00000 − 3.70377I
u = 0.892271 + 0.839255I
a = −0.601178 − 1.069560I
b = 0.650357 + 0.349315I
5.44982 − 3.99818I 0
u = 0.892271 − 0.839255I
a = −0.601178 + 1.069560I
b = 0.650357 − 0.349315I
5.44982 + 3.99818I 0
u = 0.909301 + 0.820936I
a = 1.258640 − 0.210367I
b = −0.742377 + 0.414370I
5.38340 − 2.18763I 0
u = 0.909301 − 0.820936I
a = 1.258640 + 0.210367I
b = −0.742377 − 0.414370I
5.38340 + 2.18763I 0
u = −0.986250 + 0.736928I
a = −2.03098 + 0.35816I
b = 0.618675 + 0.939690I
1.71455 + 8.02792I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.986250 − 0.736928I
a = −2.03098 − 0.35816I
b = 0.618675 − 0.939690I
1.71455 − 8.02792I 0
u = −1.203380 + 0.286854I
a = 0.480013 − 0.986726I
b = −0.367702 − 1.128060I
−1.56465 + 5.76869I 0
u = −1.203380 − 0.286854I
a = 0.480013 + 0.986726I
b = −0.367702 + 1.128060I
−1.56465 − 5.76869I 0
u = 0.971042 + 0.769166I
a = 1.20489 + 1.25291I
b = −1.50331 − 0.31741I
4.77387 − 11.03380I 0
u = 0.971042 − 0.769166I
a = 1.20489 − 1.25291I
b = −1.50331 + 0.31741I
4.77387 + 11.03380I 0
u = −0.967816 + 0.798846I
a = 0.910943 − 0.780219I
b = −1.080580 + 0.221639I
8.87149 + 6.21107I 0
u = −0.967816 − 0.798846I
a = 0.910943 + 0.780219I
b = −1.080580 − 0.221639I
8.87149 − 6.21107I 0
u = −0.914060 + 0.864103I
a = 0.496423 + 1.220680I
b = −0.032726 − 0.721159I
6.99072 + 3.20060I 0
u = −0.914060 − 0.864103I
a = 0.496423 − 1.220680I
b = −0.032726 + 0.721159I
6.99072 − 3.20060I 0
u = 1.004730 + 0.776456I
a = −2.08514 + 0.19800I
b = 0.461508 − 1.149300I
−2.03159 − 11.22630I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.004730 − 0.776456I
a = −2.08514 − 0.19800I
b = 0.461508 + 1.149300I
−2.03159 + 11.22630I 0
u = 1.084670 + 0.665154I
a = −0.963426 − 0.321344I
b = 0.016691 − 0.674808I
1.06519 − 3.48213I 0
u = 1.084670 − 0.665154I
a = −0.963426 + 0.321344I
b = 0.016691 + 0.674808I
1.06519 + 3.48213I 0
u = −1.041510 + 0.777555I
a = 2.10475 − 0.28953I
b = −0.76167 − 1.37001I
1.3497 + 18.6828I 0
u = −1.041510 − 0.777555I
a = 2.10475 + 0.28953I
b = −0.76167 + 1.37001I
1.3497 − 18.6828I 0
u = 1.047940 + 0.776322I
a = 1.82971 + 0.37317I
b = −0.63798 + 1.29369I
5.53484 − 12.36040I 0
u = 1.047940 − 0.776322I
a = 1.82971 − 0.37317I
b = −0.63798 − 1.29369I
5.53484 + 12.36040I 0
u = −0.003999 + 0.665189I
a = 0.615883 − 1.217930I
b = −0.089011 + 1.217220I
−5.41204 − 2.84363I −7.09865 + 2.85875I
u = −0.003999 − 0.665189I
a = 0.615883 + 1.217930I
b = −0.089011 − 1.217220I
−5.41204 + 2.84363I −7.09865 − 2.85875I
u = −1.119180 + 0.782046I
a = 1.113900 − 0.291506I
b = −0.324122 − 1.234360I
0.70790 + 5.20301I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.119180 − 0.782046I
a = 1.113900 + 0.291506I
b = −0.324122 + 1.234360I
0.70790 − 5.20301I 0
u = −0.623377 + 0.019768I
a = 2.02034 − 0.18513I
b = −0.509884 − 0.855020I
−0.054548 + 0.657876I −6.69982 + 1.00786I
u = −0.623377 − 0.019768I
a = 2.02034 + 0.18513I
b = −0.509884 + 0.855020I
−0.054548 − 0.657876I −6.69982 − 1.00786I
u = −0.208421 + 0.564251I
a = −0.576081 + 1.185060I
b = 0.727228 + 0.311996I
0.74003 − 3.96476I 0.30467 + 2.31036I
u = −0.208421 − 0.564251I
a = −0.576081 − 1.185060I
b = 0.727228 − 0.311996I
0.74003 + 3.96476I 0.30467 − 2.31036I
u = 0.911037 + 1.074320I
a = −0.318477 + 0.197081I
b = 0.123702 − 0.704600I
4.10003 − 3.80077I 0
u = 0.911037 − 1.074320I
a = −0.318477 − 0.197081I
b = 0.123702 + 0.704600I
4.10003 + 3.80077I 0
u = 0.411020 + 0.290512I
a = 1.85252 + 1.23960I
b = −0.656922 − 0.885889I
−0.90884 + 3.74568I −3.56572 − 0.06650I
u = 0.411020 − 0.290512I
a = 1.85252 − 1.23960I
b = −0.656922 + 0.885889I
−0.90884 − 3.74568I −3.56572 + 0.06650I
u = −0.186545 + 0.438512I
a = 1.41461 + 0.58475I
b = −0.503457 − 0.598022I
−0.199538 + 1.165120I −2.65922 − 3.83622I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.186545 − 0.438512I
a = 1.41461 − 0.58475I
b = −0.503457 + 0.598022I
−0.199538 − 1.165120I −2.65922 + 3.83622I
u = −0.173256 + 0.421315I
a = 1.33171 + 0.56040I
b = −0.414662 − 0.591408I
−0.198990 + 1.167870I −2.84829 − 4.65157I
u = −0.173256 − 0.421315I
a = 1.33171 − 0.56040I
b = −0.414662 + 0.591408I
−0.198990 − 1.167870I −2.84829 + 4.65157I
17
II.
I
u
2
= h3u
21
−3u
20
+· · ·+b+2u, −5u
21
+7u
20
+· · ·+a+2, u
22
−2u
21
+· · ·−u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
5u
21
− 7u
20
+ ··· + u − 2
−3u
21
+ 3u
20
+ ··· − 7u
2
− 2u
a
6
=
10u
21
− 13u
20
+ ··· − 6u − 13
7u
21
− 9u
20
+ ··· − 2u − 8
a
12
=
−u
21
+ 3u
20
+ ··· + 7u + 3
6u
21
− 6u
20
+ ··· + 2u − 6
a
5
=
8u
21
− 10u
20
+ ··· − 4u − 9
8u
21
− 10u
20
+ ··· − u − 8
a
4
=
−u
20
+ 3u
18
+ ··· + 3u − 4
−6u
21
+ 9u
20
+ ··· + 2u + 11
a
10
=
3u
21
− 4u
20
+ ··· + 2u + 1
−5u
21
+ 6u
20
+ ··· − u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 22u
21
−21u
20
−49u
19
+ 64u
18
+ 187u
17
−239u
16
−267u
15
+ 424u
14
+ 527u
13
−792u
12
−
489u
11
+893u
10
+594u
9
−983u
8
−352u
7
+703u
6
+252u
5
−426u
4
−96u
3
+176u
2
+13u−34
18
(iv) u-Polynomials at the component
19
Crossings u-Polynomials at each crossing
c
1
u
22
− 6u
21
+ ··· − 13u + 1
c
2
u
22
+ 2u
21
+ ··· + u + 1
c
3
u
22
+ 2u
21
+ ··· + 6u + 1
c
4
u
22
− u
21
+ ··· + 3u + 1
c
5
u
22
− 3u
21
+ ··· − u + 1
c
6
u
22
+ u
21
+ ··· + 3u + 1
c
7
u
22
− 2u
21
+ ··· − u + 1
c
8
u
22
+ 6u
21
+ ··· + 13u + 1
c
9
u
22
+ 3u
21
+ ··· + u + 1
c
10
u
22
− 7u
21
+ ··· + u + 1
c
11
u
22
− u
21
+ ··· − 3u + 1
c
12
u
22
+ u
21
+ ··· − 3u + 1
20
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
22
+ 26y
21
+ ··· − 5y + 1
c
2
, c
7
y
22
− 6y
21
+ ··· − 13y + 1
c
3
y
22
+ 14y
21
+ ··· + 18y + 1
c
4
, c
12
y
22
+ 23y
21
+ ··· + 3y + 1
c
5
, c
9
y
22
+ 21y
21
+ ··· + 23y + 1
c
6
, c
11
y
22
+ 23y
21
+ ··· + 21y + 1
c
10
y
22
− 7y
21
+ ··· − y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.769117 + 0.740940I
a = 1.78412 + 0.70850I
b = −0.725538 − 0.659027I
1.60497 + 3.45192I −3.17727 − 6.09028I
u = 0.769117 − 0.740940I
a = 1.78412 − 0.70850I
b = −0.725538 + 0.659027I
1.60497 − 3.45192I −3.17727 + 6.09028I
u = −0.646453 + 0.667635I
a = 0.515980 + 0.140540I
b = −0.425444 + 0.948018I
1.60310 + 0.11250I −3.04196 + 0.25217I
u = −0.646453 − 0.667635I
a = 0.515980 − 0.140540I
b = −0.425444 − 0.948018I
1.60310 − 0.11250I −3.04196 − 0.25217I
u = 0.934124 + 0.550703I
a = 1.096320 − 0.327063I
b = 0.150563 + 1.047820I
−0.17866 − 2.06431I −2.43116 + 2.07978I
u = 0.934124 − 0.550703I
a = 1.096320 + 0.327063I
b = 0.150563 − 1.047820I
−0.17866 + 2.06431I −2.43116 − 2.07978I
u = −0.866469 + 0.673571I
a = 1.64928 + 1.35172I
b = 0.04258 − 2.03310I
−4.54136 + 2.60448I −13.17519 − 1.97984I
u = −0.866469 − 0.673571I
a = 1.64928 − 1.35172I
b = 0.04258 + 2.03310I
−4.54136 − 2.60448I −13.17519 + 1.97984I
u = 0.807976 + 0.184434I
a = −0.75843 − 1.44451I
b = 0.12672 − 1.79342I
−7.26807 − 0.81244I −5.49546 + 11.11558I
u = 0.807976 − 0.184434I
a = −0.75843 + 1.44451I
b = 0.12672 + 1.79342I
−7.26807 + 0.81244I −5.49546 − 11.11558I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.958753 + 0.705982I
a = −2.37266 − 0.75742I
b = 0.757131 − 0.744024I
1.01676 − 8.97595I −4.74740 + 12.23569I
u = 0.958753 − 0.705982I
a = −2.37266 + 0.75742I
b = 0.757131 + 0.744024I
1.01676 + 8.97595I −4.74740 − 12.23569I
u = −0.909468 + 0.848093I
a = 0.372174 + 1.170000I
b = −0.020778 − 0.479465I
7.40722 + 3.15191I 9.47301 − 1.45257I
u = −0.909468 − 0.848093I
a = 0.372174 − 1.170000I
b = −0.020778 + 0.479465I
7.40722 − 3.15191I 9.47301 + 1.45257I
u = 0.651600 + 0.333644I
a = 1.57695 − 1.54768I
b = −0.221719 + 0.730024I
0.54600 − 1.55366I −0.61325 + 3.47852I
u = 0.651600 − 0.333644I
a = 1.57695 + 1.54768I
b = −0.221719 − 0.730024I
0.54600 + 1.55366I −0.61325 − 3.47852I
u = −1.074670 + 0.698273I
a = −1.283180 + 0.542936I
b = 0.383628 + 1.145330I
0.22038 + 5.22224I −8.78194 − 6.94109I
u = −1.074670 − 0.698273I
a = −1.283180 − 0.542936I
b = 0.383628 − 1.145330I
0.22038 − 5.22224I −8.78194 + 6.94109I
u = 0.896920 + 1.033760I
a = 0.236079 − 0.292404I
b = −0.087902 + 0.702704I
4.01072 − 3.70076I −18.6298 − 14.4658I
u = 0.896920 − 1.033760I
a = 0.236079 + 0.292404I
b = −0.087902 − 0.702704I
4.01072 + 3.70076I −18.6298 + 14.4658I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.521436 + 0.129813I
a = −0.81663 + 2.70369I
b = −0.479240 − 0.593765I
−1.13120 + 4.68440I −4.87958 − 6.54854I
u = −0.521436 − 0.129813I
a = −0.81663 − 2.70369I
b = −0.479240 + 0.593765I
−1.13120 − 4.68440I −4.87958 + 6.54854I
25
III. I
u
3
= h2b − a − 1, a
2
+ 3, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
7
=
1
0
a
8
=
1
1
a
3
=
1
0
a
9
=
0
1
a
1
=
−1
−1
a
11
=
a
1
2
a +
1
2
a
6
=
1
2
a −
1
2
1
2
a −
1
2
a
12
=
a − 1
1
2
a −
1
2
a
5
=
1
2
a −
1
2
0
a
4
=
1
2
a +
3
2
1
a
10
=
1
2
a +
1
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a − 9
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
(u − 1)
2
c
4
, c
5
, c
11
u
2
+ u + 1
c
6
, c
9
, c
10
c
12
u
2
− u + 1
c
7
, c
8
(u + 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
(y −1)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
c
12
y
2
+ y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.73205I
b = 0.500000 + 0.866025I
−3.28987 + 4.05977I −9.00000 − 6.92820I
u = −1.00000
a = − 1.73205I
b = 0.500000 − 0.866025I
−3.28987 − 4.05977I −9.00000 + 6.92820I
29
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
22
− 6u
21
+ ··· − 13u + 1)
· (u
123
+ 37u
122
+ ··· + 8841u + 529)
c
2
((u − 1)
2
)(u
22
+ 2u
21
+ ··· + u + 1)(u
123
+ u
122
+ ··· + 43u + 23)
c
3
((u − 1)
2
)(u
22
+ 2u
21
+ ··· + 6u + 1)(u
123
+ u
122
+ ··· − 438u + 319)
c
4
(u
2
+ u + 1)(u
22
− u
21
+ ··· + 3u + 1)(u
123
+ 5u
122
+ ··· + 1096u + 193)
c
5
(u
2
+ u + 1)(u
22
− 3u
21
+ ··· − u + 1)(u
123
− 3u
122
+ ··· − 2u + 1)
c
6
(u
2
− u + 1)(u
22
+ u
21
+ ··· + 3u + 1)(u
123
− u
122
+ ··· − 2422u + 317)
c
7
((u + 1)
2
)(u
22
− 2u
21
+ ··· − u + 1)(u
123
+ u
122
+ ··· + 43u + 23)
c
8
((u + 1)
2
)(u
22
+ 6u
21
+ ··· + 13u + 1)
· (u
123
+ 37u
122
+ ··· + 8841u + 529)
c
9
(u
2
− u + 1)(u
22
+ 3u
21
+ ··· + u + 1)(u
123
− 3u
122
+ ··· − 2u + 1)
c
10
(u
2
− u + 1)(u
22
− 7u
21
+ ··· + u + 1)(u
123
− 3u
122
+ ··· + 36u − 1)
c
11
(u
2
+ u + 1)(u
22
− u
21
+ ··· − 3u + 1)(u
123
− u
122
+ ··· − 2422u + 317)
c
12
(u
2
− u + 1)(u
22
+ u
21
+ ··· − 3u + 1)(u
123
+ 5u
122
+ ··· + 1096u + 193)
30
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
((y −1)
2
)(y
22
+ 26y
21
+ ··· − 5y + 1)
· (y
123
+ 107y
122
+ ··· − 3332343y −279841)
c
2
, c
7
((y −1)
2
)(y
22
− 6y
21
+ ··· − 13y + 1)
· (y
123
− 37y
122
+ ··· + 8841y −529)
c
3
((y −1)
2
)(y
22
+ 14y
21
+ ··· + 18y + 1)
· (y
123
+ 23y
122
+ ··· − 8257190y −101761)
c
4
, c
12
(y
2
+ y + 1)(y
22
+ 23y
21
+ ··· + 3y + 1)
· (y
123
+ 87y
122
+ ··· − 679762y −37249)
c
5
, c
9
(y
2
+ y + 1)(y
22
+ 21y
21
+ ··· + 23y + 1)(y
123
+ 77y
122
+ ··· − 114y −1)
c
6
, c
11
(y
2
+ y + 1)(y
22
+ 23y
21
+ ··· + 21y + 1)
· (y
123
+ 75y
122
+ ··· + 1511772y −100489)
c
10
(y
2
+ y + 1)(y
22
− 7y
21
+ ··· − y + 1)(y
123
− 7y
122
+ ··· − 146y −1)
31
