12a
0959
(K12a
0959
)
A knot diagram
1
Linearized knot diagam
4 6 10 9 12 3 11 1 2 8 7 5
Solving Sequence
7,11
8
3,12
6 2 5 10 4 1 9
c
7
c
11
c
6
c
2
c
5
c
10
c
3
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h8.35200 × 10
510
u
141
− 4.09385 × 10
511
u
140
+ ··· + 2.45826 × 10
513
b − 8.83000 × 10
512
,
6.00094 × 10
514
u
141
− 2.96953 × 10
515
u
140
+ ··· + 2.13869 × 10
515
a − 1.26630 × 10
517
,
u
142
− 5u
141
+ ··· − 332u + 29i
I
u
2
= h75418015u
30
+ 613925564u
29
+ ··· + 89877703b − 104428676,
227579646u
30
+ 1595720565u
29
+ ··· + 89877703a + 471832864, u
31
+ 6u
30
+ ··· + 27u
2
− 1i
I
u
3
= hb − 1, 3a − u + 1, u
2
+ u + 1i
I
u
4
= hb − 1, a + u, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 177 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
= h8.35 × 10
510
u
141
− 4.09 × 10
511
u
140
+ · · · + 2.46 × 10
513
b − 8.83 ×
10
512
, 6.00 × 10
514
u
141
− 2.97 × 10
515
u
140
+ · · · + 2.14 × 10
515
a − 1.27 ×
10
517
, u
142
− 5u
141
+ · · · − 332u + 29i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
−0.280590u
141
+ 1.38848u
140
+ ··· − 228.267u + 59.2090
−0.00339752u
141
+ 0.0166534u
140
+ ··· + 1.73708u + 0.359197
a
12
=
u
u
a
6
=
−0.161778u
141
+ 0.754742u
140
+ ··· − 182.653u + 47.6645
0.0494736u
141
− 0.275149u
140
+ ··· + 7.41354u − 0.302281
a
2
=
0.000859398u
141
+ 0.0173947u
140
+ ··· − 87.6362u + 22.3884
0.0988280u
141
− 0.484196u
140
+ ··· − 0.641859u + 0.706963
a
5
=
−0.174032u
141
+ 0.814178u
140
+ ··· − 185.281u + 48.4292
0.0372198u
141
− 0.215713u
140
+ ··· + 4.78579u + 0.462379
a
10
=
−u
u
3
+ u
a
4
=
−0.267746u
141
+ 1.28141u
140
+ ··· − 216.097u + 57.4617
−0.00572144u
141
− 0.00711253u
140
+ ··· + 4.17014u + 0.863544
a
1
=
0.400381u
141
− 1.89645u
140
+ ··· + 318.441u − 68.7080
0.0321004u
141
− 0.116898u
140
+ ··· − 13.3500u + 3.03495
a
9
=
0.228624u
141
− 1.18663u
140
+ ··· + 64.1107u − 11.5201
0.199469u
141
− 1.13061u
140
+ ··· + 19.9646u − 0.792164
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.49543u
141
− 12.0492u
140
+ ··· + 2253.52u − 500.102
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
3(3u
142
− 20u
140
+ ··· + 29u − 1)
c
2
, c
6
u
142
+ 2u
141
+ ··· − 356u + 304
c
3
3(3u
142
− 6u
141
+ ··· − 261246u − 14332)
c
4
u
142
+ 2u
141
+ ··· + 32895u − 13173
c
5
, c
12
3(3u
142
+ 12u
141
+ ··· − 1.16737 × 10
7
u − 729697)
c
7
, c
10
, c
11
u
142
− 5u
141
+ ··· − 332u + 29
c
8
u
142
+ 22u
140
+ ··· + 3840u + 576
c
9
u
142
− 2u
141
+ ··· + 29864u − 11279
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
9(9y
142
− 120y
141
+ ··· − 57y + 1)
c
2
, c
6
y
142
− 62y
141
+ ··· + 425936y + 92416
c
3
9(9y
142
− 138y
141
+ ··· + 2.20180 × 10
10
y + 2.05406 × 10
8
)
c
4
y
142
+ 26y
141
+ ··· + 7659337353y + 173527929
c
5
, c
12
9(9y
142
+ 852y
141
+ ··· + 1.69390 × 10
13
y + 5.32458 × 10
11
)
c
7
, c
10
, c
11
y
142
+ 139y
141
+ ··· − 94158y + 841
c
8
y
142
+ 44y
141
+ ··· − 2230272y + 331776
c
9
y
142
+ 2y
141
+ ··· − 7484772366y + 127215841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.642590 + 0.816128I
a = 0.017475 − 0.603353I
b = −1.090570 − 0.186235I
2.74568 + 3.72052I 0
u = 0.642590 − 0.816128I
a = 0.017475 + 0.603353I
b = −1.090570 + 0.186235I
2.74568 − 3.72052I 0
u = 0.943307 + 0.013606I
a = 0.523454 − 0.510396I
b = −0.918496 − 0.691900I
0.70494 + 2.70160I 0
u = 0.943307 − 0.013606I
a = 0.523454 + 0.510396I
b = −0.918496 + 0.691900I
0.70494 − 2.70160I 0
u = −0.966558 + 0.452108I
a = −0.535878 − 0.706338I
b = 1.158380 − 0.655861I
−1.3841 − 14.7096I 0
u = −0.966558 − 0.452108I
a = −0.535878 + 0.706338I
b = 1.158380 + 0.655861I
−1.3841 + 14.7096I 0
u = 0.875728 + 0.317953I
a = 0.439140 − 0.569516I
b = −1.044380 − 0.109811I
4.26985 + 1.50980I 0
u = 0.875728 − 0.317953I
a = 0.439140 + 0.569516I
b = −1.044380 + 0.109811I
4.26985 − 1.50980I 0
u = 0.493472 + 0.961325I
a = −0.340616 − 0.322389I
b = 1.089300 − 0.079315I
1.53464 + 2.38535I 0
u = 0.493472 − 0.961325I
a = −0.340616 + 0.322389I
b = 1.089300 + 0.079315I
1.53464 − 2.38535I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.790119 + 0.452760I
a = −1.356870 − 0.396797I
b = 0.728522 − 0.516306I
−3.29487 + 4.30574I 0
u = −0.790119 − 0.452760I
a = −1.356870 + 0.396797I
b = 0.728522 + 0.516306I
−3.29487 − 4.30574I 0
u = 0.208817 + 1.079900I
a = −0.223436 + 0.626423I
b = −0.429029 + 0.204141I
−2.34458 + 3.04452I 0
u = 0.208817 − 1.079900I
a = −0.223436 − 0.626423I
b = −0.429029 − 0.204141I
−2.34458 − 3.04452I 0
u = 1.020410 + 0.442473I
a = −0.521102 + 0.238186I
b = 1.088850 + 0.444342I
0.64936 + 4.75757I 0
u = 1.020410 − 0.442473I
a = −0.521102 − 0.238186I
b = 1.088850 − 0.444342I
0.64936 − 4.75757I 0
u = 0.707431 + 0.499654I
a = −0.386233 + 0.646196I
b = 1.219560 + 0.648628I
−1.03167 + 5.58242I 0
u = 0.707431 − 0.499654I
a = −0.386233 − 0.646196I
b = 1.219560 − 0.648628I
−1.03167 − 5.58242I 0
u = 0.749048 + 0.402762I
a = −0.087163 + 1.372770I
b = 0.981884 + 0.276958I
3.02954 + 2.04599I 0
u = 0.749048 − 0.402762I
a = −0.087163 − 1.372770I
b = 0.981884 − 0.276958I
3.02954 − 2.04599I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.737530 + 0.384331I
a = 0.857728 + 0.749010I
b = −1.154610 + 0.661050I
−2.52747 − 7.11688I 0
u = −0.737530 − 0.384331I
a = 0.857728 − 0.749010I
b = −1.154610 − 0.661050I
−2.52747 + 7.11688I 0
u = −0.643956 + 0.508889I
a = −0.338789 + 0.319747I
b = 0.376743 + 0.950292I
−3.72501 − 8.90092I 0
u = −0.643956 − 0.508889I
a = −0.338789 − 0.319747I
b = 0.376743 − 0.950292I
−3.72501 + 8.90092I 0
u = 1.065310 + 0.522095I
a = 0.583609 − 0.675353I
b = −0.995320 − 0.551462I
0.87974 + 5.44723I 0
u = 1.065310 − 0.522095I
a = 0.583609 + 0.675353I
b = −0.995320 + 0.551462I
0.87974 − 5.44723I 0
u = −0.693685 + 0.398764I
a = 0.451970 + 1.337320I
b = −1.211880 + 0.404517I
3.98949 − 8.94716I 0
u = −0.693685 − 0.398764I
a = 0.451970 − 1.337320I
b = −1.211880 − 0.404517I
3.98949 + 8.94716I 0
u = 0.340372 + 1.157210I
a = 0.34956 − 2.02425I
b = −0.821720 − 0.784733I
−2.82768 + 7.38570I 0
u = 0.340372 − 1.157210I
a = 0.34956 + 2.02425I
b = −0.821720 + 0.784733I
−2.82768 − 7.38570I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.333359 + 0.713404I
a = −0.475634 + 0.135045I
b = −1.303340 − 0.251159I
3.04704 + 5.02224I 0
u = −0.333359 − 0.713404I
a = −0.475634 − 0.135045I
b = −1.303340 + 0.251159I
3.04704 − 5.02224I 0
u = −0.240579 + 1.193860I
a = 0.932308 − 0.268323I
b = 1.380920 + 0.175400I
0.47775 − 3.33774I 0
u = −0.240579 − 1.193860I
a = 0.932308 + 0.268323I
b = 1.380920 − 0.175400I
0.47775 + 3.33774I 0
u = 0.548703 + 1.091500I
a = −0.527923 + 0.273988I
b = −0.823315 + 0.539077I
−2.62567 + 2.51585I 0
u = 0.548703 − 1.091500I
a = −0.527923 − 0.273988I
b = −0.823315 − 0.539077I
−2.62567 − 2.51585I 0
u = 0.853051 + 0.882884I
a = 0.186871 + 0.078567I
b = −0.689713 + 0.477853I
−0.187221 + 1.160760I 0
u = 0.853051 − 0.882884I
a = 0.186871 − 0.078567I
b = −0.689713 − 0.477853I
−0.187221 − 1.160760I 0
u = −0.163374 + 1.218340I
a = −1.02663 − 1.89218I
b = −0.092596 − 0.262769I
−4.71635 − 7.36833I 0
u = −0.163374 − 1.218340I
a = −1.02663 + 1.89218I
b = −0.092596 + 0.262769I
−4.71635 + 7.36833I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.871082 + 0.873688I
a = 0.224041 − 0.128263I
b = 0.956294 + 0.527645I
−2.54329 + 8.54907I 0
u = −0.871082 − 0.873688I
a = 0.224041 + 0.128263I
b = 0.956294 − 0.527645I
−2.54329 − 8.54907I 0
u = −0.509071 + 0.547445I
a = −0.157483 + 0.680723I
b = −0.867139 − 0.575732I
−3.33250 + 2.82467I 0
u = −0.509071 − 0.547445I
a = −0.157483 − 0.680723I
b = −0.867139 + 0.575732I
−3.33250 − 2.82467I 0
u = 0.328825 + 0.657498I
a = 0.704188 + 0.606675I
b = −0.008280 + 0.398492I
−0.40637 + 1.82781I 0
u = 0.328825 − 0.657498I
a = 0.704188 − 0.606675I
b = −0.008280 − 0.398492I
−0.40637 − 1.82781I 0
u = 0.097968 + 1.268690I
a = 0.78424 + 1.56513I
b = 0.746783 + 0.781991I
−1.52986 + 2.94544I 0
u = 0.097968 − 1.268690I
a = 0.78424 − 1.56513I
b = 0.746783 − 0.781991I
−1.52986 − 2.94544I 0
u = −0.006619 + 1.292480I
a = 0.13050 + 2.44173I
b = −0.133227 + 1.311720I
−7.54127 + 0.89803I 0
u = −0.006619 − 1.292480I
a = 0.13050 − 2.44173I
b = −0.133227 − 1.311720I
−7.54127 − 0.89803I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.168089 + 1.283240I
a = −0.94002 + 1.07137I
b = −0.964706 + 0.361388I
−1.70264 + 3.21989I 0
u = −0.168089 − 1.283240I
a = −0.94002 − 1.07137I
b = −0.964706 − 0.361388I
−1.70264 − 3.21989I 0
u = 0.057100 + 1.324370I
a = 0.345602 − 0.380089I
b = 1.49368 − 0.11239I
−1.23352 + 0.72597I 0
u = 0.057100 − 1.324370I
a = 0.345602 + 0.380089I
b = 1.49368 + 0.11239I
−1.23352 − 0.72597I 0
u = −0.201131 + 1.310480I
a = 0.39729 − 1.76605I
b = 1.119060 − 0.706966I
−0.30789 − 2.94943I 0
u = −0.201131 − 1.310480I
a = 0.39729 + 1.76605I
b = 1.119060 + 0.706966I
−0.30789 + 2.94943I 0
u = 0.558574 + 0.358142I
a = 0.31244 + 1.61475I
b = 0.941529 − 0.330493I
−0.83700 − 1.33766I 0
u = 0.558574 − 0.358142I
a = 0.31244 − 1.61475I
b = 0.941529 + 0.330493I
−0.83700 + 1.33766I 0
u = −0.189121 + 1.325790I
a = −0.71099 − 1.70974I
b = −0.176301 − 0.714324I
−4.63200 − 7.40725I 0
u = −0.189121 − 1.325790I
a = −0.71099 + 1.70974I
b = −0.176301 + 0.714324I
−4.63200 + 7.40725I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.873456 + 1.020830I
a = 0.035777 + 0.409646I
b = 0.752464 − 0.266551I
−0.90582 + 1.76298I 0
u = 0.873456 − 1.020830I
a = 0.035777 − 0.409646I
b = 0.752464 + 0.266551I
−0.90582 − 1.76298I 0
u = −0.635804 + 0.150451I
a = 1.47210 − 0.05433I
b = −0.755655 + 0.592582I
−3.68254 − 1.82520I 0
u = −0.635804 − 0.150451I
a = 1.47210 + 0.05433I
b = −0.755655 − 0.592582I
−3.68254 + 1.82520I 0
u = −0.044396 + 1.351350I
a = −0.18490 + 1.64708I
b = −1.23408 + 0.78519I
−7.00217 − 3.33315I 0
u = −0.044396 − 1.351350I
a = −0.18490 − 1.64708I
b = −1.23408 − 0.78519I
−7.00217 + 3.33315I 0
u = −0.645165 + 0.054390I
a = −0.806804 − 0.445214I
b = 1.229590 − 0.404665I
3.92422 + 0.06439I 0
u = −0.645165 − 0.054390I
a = −0.806804 + 0.445214I
b = 1.229590 + 0.404665I
3.92422 − 0.06439I 0
u = −0.055605 + 1.354360I
a = −0.858508 + 0.157201I
b = −1.85397 + 0.05924I
−1.07564 − 6.31405I 0
u = −0.055605 − 1.354360I
a = −0.858508 − 0.157201I
b = −1.85397 − 0.05924I
−1.07564 + 6.31405I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.109009 + 1.360100I
a = 0.50860 + 1.62021I
b = 0.503762 + 0.129477I
−5.96355 + 0.91867I 0
u = 0.109009 − 1.360100I
a = 0.50860 − 1.62021I
b = 0.503762 − 0.129477I
−5.96355 − 0.91867I 0
u = 0.094013 + 1.373090I
a = 0.50435 − 1.56561I
b = 0.835374 − 0.604403I
−3.21335 + 1.13985I 0
u = 0.094013 − 1.373090I
a = 0.50435 + 1.56561I
b = 0.835374 + 0.604403I
−3.21335 − 1.13985I 0
u = 0.047673 + 1.382060I
a = −0.53024 + 2.46707I
b = 0.939459 + 0.260395I
−5.11402 + 0.68211I 0
u = 0.047673 − 1.382060I
a = −0.53024 − 2.46707I
b = 0.939459 − 0.260395I
−5.11402 − 0.68211I 0
u = 0.226425 + 0.574051I
a = 2.05635 − 2.42714I
b = −0.780073 − 0.475319I
−2.86698 + 6.92930I 3.42159 − 10.37880I
u = 0.226425 − 0.574051I
a = 2.05635 + 2.42714I
b = −0.780073 + 0.475319I
−2.86698 − 6.92930I 3.42159 + 10.37880I
u = −0.065349 + 1.385010I
a = 0.21400 + 1.57674I
b = −0.408080 + 0.684531I
−6.89459 + 0.86791I 0
u = −0.065349 − 1.385010I
a = 0.21400 − 1.57674I
b = −0.408080 − 0.684531I
−6.89459 − 0.86791I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.575616 + 0.208751I
a = −0.488825 − 0.593288I
b = 0.034455 − 0.837209I
0.18610 − 4.61045I 6.00000 + 7.28544I
u = −0.575616 − 0.208751I
a = −0.488825 + 0.593288I
b = 0.034455 + 0.837209I
0.18610 + 4.61045I 6.00000 − 7.28544I
u = −0.33407 + 1.38157I
a = 0.330549 + 1.362890I
b = −1.059480 + 0.676117I
−8.45107 − 5.56059I 0
u = −0.33407 − 1.38157I
a = 0.330549 − 1.362890I
b = −1.059480 − 0.676117I
−8.45107 + 5.56059I 0
u = −0.397175 + 0.416339I
a = 0.0397112 + 0.0396057I
b = −0.419872 − 1.036180I
−4.82118 − 1.14145I −3.17765 + 7.01904I
u = −0.397175 − 0.416339I
a = 0.0397112 − 0.0396057I
b = −0.419872 + 1.036180I
−4.82118 + 1.14145I −3.17765 − 7.01904I
u = −0.225495 + 0.507809I
a = 1.16640 + 1.00371I
b = 0.048260 + 0.563484I
−1.14702 + 1.78911I 1.00281 − 1.12035I
u = −0.225495 − 0.507809I
a = 1.16640 − 1.00371I
b = 0.048260 − 0.563484I
−1.14702 − 1.78911I 1.00281 + 1.12035I
u = 0.34333 + 1.41646I
a = −0.152141 − 1.211710I
b = −0.979069 − 0.395764I
−1.20544 + 5.88296I 0
u = 0.34333 − 1.41646I
a = −0.152141 + 1.211710I
b = −0.979069 + 0.395764I
−1.20544 − 5.88296I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.16196 + 1.45079I
a = −0.77757 − 1.41013I
b = −0.61496 − 1.31797I
−10.82780 − 3.31481I 0
u = −0.16196 − 1.45079I
a = −0.77757 + 1.41013I
b = −0.61496 + 1.31797I
−10.82780 + 3.31481I 0
u = 0.11893 + 1.45940I
a = 0.48863 − 1.65260I
b = 0.53766 − 1.56090I
−10.21780 + 0.80786I 0
u = 0.11893 − 1.45940I
a = 0.48863 + 1.65260I
b = 0.53766 + 1.56090I
−10.21780 − 0.80786I 0
u = −0.10051 + 1.46785I
a = 0.89905 − 1.63901I
b = 0.992133 − 0.444265I
−4.24703 − 1.99121I 0
u = −0.10051 − 1.46785I
a = 0.89905 + 1.63901I
b = 0.992133 + 0.444265I
−4.24703 + 1.99121I 0
u = −0.28003 + 1.47044I
a = −0.19310 + 1.71437I
b = −1.27509 + 0.81538I
−8.51253 − 10.83600I 0
u = −0.28003 − 1.47044I
a = −0.19310 − 1.71437I
b = −1.27509 − 0.81538I
−8.51253 + 10.83600I 0
u = −0.25470 + 1.48414I
a = −0.54064 + 1.72717I
b = −1.137500 + 0.588329I
−2.14091 − 12.41600I 0
u = −0.25470 − 1.48414I
a = −0.54064 − 1.72717I
b = −1.137500 − 0.588329I
−2.14091 + 12.41600I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19637 + 1.50341I
a = −0.551614 − 0.650419I
b = −0.595444 − 0.816822I
−9.87357 + 0.03826I 0
u = −0.19637 − 1.50341I
a = −0.551614 + 0.650419I
b = −0.595444 + 0.816822I
−9.87357 − 0.03826I 0
u = −0.23545 + 1.49943I
a = 0.59355 + 1.34991I
b = 0.517545 + 1.305810I
−10.2251 − 12.1553I 0
u = −0.23545 − 1.49943I
a = 0.59355 − 1.34991I
b = 0.517545 − 1.305810I
−10.2251 + 12.1553I 0
u = 0.27997 + 1.49439I
a = 0.49688 + 1.51195I
b = 0.857275 + 0.575483I
−3.16407 + 5.81342I 0
u = 0.27997 − 1.49439I
a = 0.49688 − 1.51195I
b = 0.857275 − 0.575483I
−3.16407 − 5.81342I 0
u = 0.11388 + 1.51903I
a = −0.224209 − 1.221250I
b = −0.158453 − 1.159590I
−10.04230 + 3.46563I 0
u = 0.11388 − 1.51903I
a = −0.224209 + 1.221250I
b = −0.158453 + 1.159590I
−10.04230 − 3.46563I 0
u = 0.467947 + 0.082376I
a = 0.20095 + 1.61703I
b = 1.061320 + 0.299676I
2.49343 + 0.76222I 8.97618 + 6.78934I
u = 0.467947 − 0.082376I
a = 0.20095 − 1.61703I
b = 1.061320 − 0.299676I
2.49343 − 0.76222I 8.97618 − 6.78934I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.16019 + 1.51773I
a = 0.161334 − 1.389530I
b = −1.165360 − 0.532914I
−9.81043 + 8.85249I 0
u = 0.16019 − 1.51773I
a = 0.161334 + 1.389530I
b = −1.165360 + 0.532914I
−9.81043 − 8.85249I 0
u = 0.471529 + 0.034714I
a = 0.724237 + 0.854589I
b = 0.189168 + 0.252378I
1.130630 + 0.395757I 9.73572 − 1.85939I
u = 0.471529 − 0.034714I
a = 0.724237 − 0.854589I
b = 0.189168 − 0.252378I
1.130630 − 0.395757I 9.73572 + 1.85939I
u = 0.27262 + 1.51013I
a = 0.43826 + 1.57436I
b = 1.33352 + 0.92106I
−7.55128 + 9.24082I 0
u = 0.27262 − 1.51013I
a = 0.43826 − 1.57436I
b = 1.33352 − 0.92106I
−7.55128 − 9.24082I 0
u = 0.15346 + 1.53004I
a = −0.688242 − 1.214960I
b = −1.080210 − 0.654743I
−4.94512 + 6.18384I 0
u = 0.15346 − 1.53004I
a = −0.688242 + 1.214960I
b = −1.080210 + 0.654743I
−4.94512 − 6.18384I 0
u = 0.36147 + 1.51681I
a = 0.213386 + 1.183390I
b = 1.35152 + 0.64187I
−5.64604 + 9.68033I 0
u = 0.36147 − 1.51681I
a = 0.213386 − 1.183390I
b = 1.35152 − 0.64187I
−5.64604 − 9.68033I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.25466 + 1.54065I
a = −0.151629 − 1.104120I
b = 1.137050 − 0.553487I
−9.93865 + 0.42751I 0
u = −0.25466 − 1.54065I
a = −0.151629 + 1.104120I
b = 1.137050 + 0.553487I
−9.93865 − 0.42751I 0
u = −0.36101 + 1.52897I
a = 0.17111 − 1.60929I
b = 1.26889 − 0.80370I
−7.7580 − 19.5165I 0
u = −0.36101 − 1.52897I
a = 0.17111 + 1.60929I
b = 1.26889 + 0.80370I
−7.7580 + 19.5165I 0
u = 0.22488 + 1.55770I
a = −0.388858 + 1.130520I
b = −0.442685 + 0.996940I
−8.08216 + 4.56639I 0
u = 0.22488 − 1.55770I
a = −0.388858 − 1.130520I
b = −0.442685 − 0.996940I
−8.08216 − 4.56639I 0
u = −0.259450 + 0.296585I
a = −0.43913 − 2.89349I
b = 1.105900 − 0.177648I
1.65486 − 0.64880I 1.44968 − 4.85704I
u = −0.259450 − 0.296585I
a = −0.43913 + 2.89349I
b = 1.105900 + 0.177648I
1.65486 + 0.64880I 1.44968 + 4.85704I
u = 0.38304 + 1.57313I
a = −0.07108 − 1.44660I
b = −1.164860 − 0.701696I
−5.88179 + 10.70490I 0
u = 0.38304 − 1.57313I
a = −0.07108 + 1.44660I
b = −1.164860 + 0.701696I
−5.88179 − 10.70490I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.114533 + 0.357347I
a = −1.35824 + 1.81438I
b = −0.768213 − 0.676906I
−3.17629 + 2.69246I −0.28093 − 4.84720I
u = −0.114533 − 0.357347I
a = −1.35824 − 1.81438I
b = −0.768213 + 0.676906I
−3.17629 − 2.69246I −0.28093 + 4.84720I
u = 0.199086 + 0.312708I
a = −1.043320 − 0.040655I
b = 0.206884 − 1.238140I
−4.26384 − 0.61629I −0.55814 − 8.09106I
u = 0.199086 − 0.312708I
a = −1.043320 + 0.040655I
b = 0.206884 + 1.238140I
−4.26384 + 0.61629I −0.55814 + 8.09106I
u = −0.300707 + 0.176178I
a = −0.73109 + 1.94677I
b = −1.42436 − 0.01880I
2.99963 + 5.36465I 12.00185 − 5.42830I
u = −0.300707 − 0.176178I
a = −0.73109 − 1.94677I
b = −1.42436 + 0.01880I
2.99963 − 5.36465I 12.00185 + 5.42830I
u = 0.05719 + 1.68348I
a = −0.506400 + 0.609047I
b = −0.347661 + 0.495378I
−12.33570 + 4.40392I 0
u = 0.05719 − 1.68348I
a = −0.506400 − 0.609047I
b = −0.347661 − 0.495378I
−12.33570 − 4.40392I 0
u = −0.06429 + 1.75109I
a = 0.275749 + 0.446728I
b = 0.439231 + 0.416422I
−12.19390 + 4.78155I 0
u = −0.06429 − 1.75109I
a = 0.275749 − 0.446728I
b = 0.439231 − 0.416422I
−12.19390 − 4.78155I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.142557
a = −21.6522
b = 0.835651
−0.427188 291.940
u = 0.113032
a = 7.26839
b = 0.697821
1.16360 10.1550
19
II. I
u
2
= h7.54 × 10
7
u
30
+ 6.14 × 10
8
u
29
+ · · · + 8.99 × 10
7
b − 1.04 × 10
8
, 2.28 ×
10
8
u
30
+1.60×10
9
u
29
+· · ·+8.99×10
7
a+4.72×10
8
, u
31
+6u
30
+· · ·+27u
2
−1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
3
=
−2.53210u
30
− 17.7544u
29
+ ··· − 71.3633u − 5.24972
−0.839118u
30
− 6.83068u
29
+ ··· + 1.62587u + 1.16190
a
12
=
u
u
a
6
=
−2.17968u
30
− 9.31290u
29
+ ··· − 59.8579u − 8.18588
−1.28897u
30
− 4.20054u
29
+ ··· + 7.12225u − 3.10181
a
2
=
−2.83987u
30
− 19.0985u
29
+ ··· − 29.4731u + 1.62448
−0.256171u
30
− 3.06243u
29
+ ··· − 1.50377u − 0.879822
a
5
=
−1.26989u
30
− 4.98483u
29
+ ··· − 60.7486u − 7.95395
−0.379172u
30
+ 0.127534u
29
+ ··· + 6.23153u − 2.86988
a
10
=
−u
u
3
+ u
a
4
=
−2.80831u
30
− 20.0829u
29
+ ··· − 70.3192u − 4.37596
−0.645109u
30
− 5.78072u
29
+ ··· + 0.857948u + 0.959447
a
1
=
1.97743u
30
+ 11.1095u
29
+ ··· + 127.357u + 18.0892
1.02402u
30
+ 5.42485u
29
+ ··· − 5.14949u − 0.162049
a
9
=
−0.603868u
30
− 5.03515u
29
+ ··· + 36.8306u + 1.93288
−0.686689u
30
− 5.47183u
29
+ ··· − 4.98451u + 3.10493
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1461514683
89877703
u
30
−
8086163338
89877703
u
29
+ ··· −
51551548380
89877703
u −
5515258640
89877703
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
− 12u
30
+ ··· − 3u
2
− 1
c
2
u
31
− 7u
30
+ ··· − 10u + 1
c
3
u
31
− 2u
30
+ ··· − u + 13
c
4
u
31
+ 4u
29
+ ··· − 2u + 1
c
5
u
31
+ 6u
30
+ ··· − 12u + 1
c
6
u
31
+ 7u
30
+ ··· − 10u − 1
c
7
u
31
+ 6u
30
+ ··· + 27u
2
− 1
c
8
u
31
+ u
30
+ ··· + 156u + 49
c
9
u
31
+ u
30
+ ··· − 15u
2
− 1
c
10
, c
11
u
31
− 6u
30
+ ··· − 27u
2
+ 1
c
12
u
31
− 6u
30
+ ··· − 12u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
− 22y
30
+ ··· − 6y −1
c
2
, c
6
y
31
− 13y
30
+ ··· + 28y −1
c
3
y
31
− 18y
30
+ ··· − 1455y −169
c
4
y
31
+ 8y
30
+ ··· + 16y
2
− 1
c
5
, c
12
y
31
+ 10y
30
+ ··· + 16y −1
c
7
, c
10
, c
11
y
31
+ 34y
30
+ ··· + 54y −1
c
8
y
31
+ 29y
30
+ ··· + 39722y −2401
c
9
y
31
+ 17y
30
+ ··· − 30y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.965390 + 0.529714I
a = 0.556150 + 0.489722I
b = −1.061210 + 0.508762I
0.10637 − 5.02110I 3.13722 + 7.80756I
u = −0.965390 − 0.529714I
a = 0.556150 − 0.489722I
b = −1.061210 − 0.508762I
0.10637 + 5.02110I 3.13722 − 7.80756I
u = 0.032221 + 1.171400I
a = −1.386770 + 0.084190I
b = −1.60455 − 0.07381I
0.43030 + 5.74357I 6.00000 − 5.60976I
u = 0.032221 − 1.171400I
a = −1.386770 − 0.084190I
b = −1.60455 + 0.07381I
0.43030 − 5.74357I 6.00000 + 5.60976I
u = 0.195145 + 1.193150I
a = 1.10190 − 2.35628I
b = −0.566095 − 0.444169I
−4.60693 + 8.02154I 0. − 13.88052I
u = 0.195145 − 1.193150I
a = 1.10190 + 2.35628I
b = −0.566095 + 0.444169I
−4.60693 − 8.02154I 0. + 13.88052I
u = −0.211598 + 1.206560I
a = 0.410374 + 0.203269I
b = 1.275200 + 0.226168I
−0.08729 − 1.73503I 6.00000 + 4.05768I
u = −0.211598 − 1.206560I
a = 0.410374 − 0.203269I
b = 1.275200 − 0.226168I
−0.08729 + 1.73503I 6.00000 − 4.05768I
u = −0.003155 + 0.730855I
a = 0.035636 + 0.575912I
b = −1.44512 + 0.15145I
2.13309 − 5.55164I 2.31699 + 7.15311I
u = −0.003155 − 0.730855I
a = 0.035636 − 0.575912I
b = −1.44512 − 0.15145I
2.13309 + 5.55164I 2.31699 − 7.15311I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.687065 + 0.208171I
a = −0.297047 − 1.061110I
b = 0.970172 − 0.301221I
2.86190 − 1.36449I 13.50429 + 1.58498I
u = −0.687065 − 0.208171I
a = −0.297047 + 1.061110I
b = 0.970172 + 0.301221I
2.86190 + 1.36449I 13.50429 − 1.58498I
u = 0.375229 + 0.609839I
a = 0.47768 − 2.17422I
b = −0.513348 + 0.224655I
−2.53264 − 5.92324I 6.56403 + 3.62035I
u = 0.375229 − 0.609839I
a = 0.47768 + 2.17422I
b = −0.513348 − 0.224655I
−2.53264 + 5.92324I 6.56403 − 3.62035I
u = −0.040678 + 1.288960I
a = 0.22049 + 2.54227I
b = 0.142465 + 1.248760I
−7.66939 + 0.31322I 0
u = −0.040678 − 1.288960I
a = 0.22049 − 2.54227I
b = 0.142465 − 1.248760I
−7.66939 − 0.31322I 0
u = −0.865616 + 0.997186I
a = −0.032189 + 0.145586I
b = −0.754831 − 0.389568I
−1.14639 − 1.39055I 0
u = −0.865616 − 0.997186I
a = −0.032189 − 0.145586I
b = −0.754831 + 0.389568I
−1.14639 + 1.39055I 0
u = 0.054834 + 1.398650I
a = 0.14781 + 2.40858I
b = 0.844242 + 0.251626I
−5.28196 + 0.64943I 0
u = 0.054834 − 1.398650I
a = 0.14781 − 2.40858I
b = 0.844242 − 0.251626I
−5.28196 − 0.64943I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.33057 + 1.39092I
a = 0.214549 − 1.335150I
b = 0.755038 − 0.537490I
−2.25696 − 5.16117I 0
u = −0.33057 − 1.39092I
a = 0.214549 + 1.335150I
b = 0.755038 + 0.537490I
−2.25696 + 5.16117I 0
u = −0.11973 + 1.47233I
a = −0.31732 − 1.39329I
b = −0.287392 − 1.344580I
−10.07670 − 2.28079I 0
u = −0.11973 − 1.47233I
a = −0.31732 + 1.39329I
b = −0.287392 + 1.344580I
−10.07670 + 2.28079I 0
u = −0.30019 + 1.52833I
a = −0.27317 + 1.40504I
b = −1.30238 + 0.74131I
−6.61918 − 9.43308I 0
u = −0.30019 − 1.52833I
a = −0.27317 − 1.40504I
b = −1.30238 − 0.74131I
−6.61918 + 9.43308I 0
u = −0.175986 + 0.238164I
a = 1.20947 + 0.74353I
b = −0.020359 − 1.200950I
−4.12466 − 0.99187I 8.09761 + 9.09408I
u = −0.175986 − 0.238164I
a = 1.20947 − 0.74353I
b = −0.020359 + 1.200950I
−4.12466 + 0.99187I 8.09761 − 9.09408I
u = −0.01650 + 1.74532I
a = −0.292008 − 0.300798I
b = −0.342131 − 0.079341I
−11.90070 − 4.45233I 0
u = −0.01650 − 1.74532I
a = −0.292008 + 0.300798I
b = −0.342131 + 0.079341I
−11.90070 + 4.45233I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.118124
a = −24.5511
b = 0.820564
−0.443607 −199.230
26
III. I
u
3
= hb − 1, 3a − u + 1, u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u + 1
a
3
=
1
3
u −
1
3
1
a
12
=
u
u
a
6
=
1
3
u +
2
3
1
a
2
=
−1
0
a
5
=
2
3
u +
4
3
1
3
u +
5
3
a
10
=
−u
u + 1
a
4
=
5
3
u +
1
3
−
2
3
u −
1
3
a
1
=
1
3
u
−0.333333
a
9
=
1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
44
9
u +
91
9
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
12
3(3u
2
+ 1)
c
2
(u + 1)
2
c
3
3(3u
2
+ 6u + 4)
c
4
u
2
+ 3u + 3
c
6
(u − 1)
2
c
7
u
2
+ u + 1
c
8
u
2
c
9
, c
10
, c
11
u
2
− u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
12
9(3y + 1)
2
c
2
, c
6
(y −1)
2
c
3
9(9y
2
− 12y + 16)
c
4
y
2
− 3y + 9
c
7
, c
9
, c
10
c
11
y
2
+ y + 1
c
8
y
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.500000 + 0.288675I
b = 1.00000
1.64493 − 2.02988I 12.55556 − 4.23390I
u = −0.500000 − 0.866025I
a = −0.500000 − 0.288675I
b = 1.00000
1.64493 + 2.02988I 12.55556 + 4.23390I
30
IV. I
u
4
= hb − 1, a + u, u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u + 1
a
3
=
−u
1
a
12
=
u
u
a
6
=
−u + 1
1
a
2
=
−1
0
a
5
=
−u
0
a
10
=
−u
u + 1
a
4
=
−u + 1
u + 1
a
1
=
u + 1
u
a
9
=
1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u + 11
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
12
u
2
+ u + 1
c
2
(u + 1)
2
c
3
, c
5
, c
9
c
10
, c
11
u
2
− u + 1
c
4
, c
6
(u − 1)
2
c
8
u
2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
, c
10
c
11
, c
12
y
2
+ y + 1
c
2
, c
4
, c
6
(y −1)
2
c
8
y
2
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 1.00000
1.64493 − 2.02988I 9.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 1.00000
1.64493 + 2.02988I 9.00000 − 3.46410I
34
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
9(u
2
+ u + 1)(3u
2
+ 1)(u
31
− 12u
30
+ ··· − 3u
2
− 1)
· (3u
142
− 20u
140
+ ··· + 29u − 1)
c
2
((u + 1)
4
)(u
31
− 7u
30
+ ··· − 10u + 1)(u
142
+ 2u
141
+ ··· − 356u + 304)
c
3
9(u
2
− u + 1)(3u
2
+ 6u + 4)(u
31
− 2u
30
+ ··· − u + 13)
· (3u
142
− 6u
141
+ ··· − 261246u − 14332)
c
4
((u − 1)
2
)(u
2
+ 3u + 3)(u
31
+ 4u
29
+ ··· − 2u + 1)
· (u
142
+ 2u
141
+ ··· + 32895u − 13173)
c
5
9(u
2
− u + 1)(3u
2
+ 1)(u
31
+ 6u
30
+ ··· − 12u + 1)
· (3u
142
+ 12u
141
+ ··· − 11673715u − 729697)
c
6
((u − 1)
4
)(u
31
+ 7u
30
+ ··· − 10u − 1)(u
142
+ 2u
141
+ ··· − 356u + 304)
c
7
((u
2
+ u + 1)
2
)(u
31
+ 6u
30
+ ··· + 27u
2
− 1)
· (u
142
− 5u
141
+ ··· − 332u + 29)
c
8
u
4
(u
31
+ u
30
+ ··· + 156u + 49)(u
142
+ 22u
140
+ ··· + 3840u + 576)
c
9
((u
2
− u + 1)
2
)(u
31
+ u
30
+ ··· − 15u
2
− 1)
· (u
142
− 2u
141
+ ··· + 29864u − 11279)
c
10
, c
11
((u
2
− u + 1)
2
)(u
31
− 6u
30
+ ··· − 27u
2
+ 1)
· (u
142
− 5u
141
+ ··· − 332u + 29)
c
12
9(u
2
+ u + 1)(3u
2
+ 1)(u
31
− 6u
30
+ ··· − 12u − 1)
· (3u
142
+ 12u
141
+ ··· − 11673715u − 729697)
35
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
81(3y + 1)
2
(y
2
+ y + 1)(y
31
− 22y
30
+ ··· − 6y −1)
· (9y
142
− 120y
141
+ ··· − 57y + 1)
c
2
, c
6
((y −1)
4
)(y
31
− 13y
30
+ ··· + 28y −1)
· (y
142
− 62y
141
+ ··· + 425936y + 92416)
c
3
81(y
2
+ y + 1)(9y
2
− 12y + 16)(y
31
− 18y
30
+ ··· − 1455y −169)
· (9y
142
− 138y
141
+ ··· + 22018021060y + 205406224)
c
4
((y −1)
2
)(y
2
− 3y + 9)(y
31
+ 8y
30
+ ··· + 16y
2
− 1)
· (y
142
+ 26y
141
+ ··· + 7659337353y + 173527929)
c
5
, c
12
81(3y + 1)
2
(y
2
+ y + 1)(y
31
+ 10y
30
+ ··· + 16y −1)
· (9y
142
+ 852y
141
+ ··· + 16938989993629y + 532457711809)
c
7
, c
10
, c
11
((y
2
+ y + 1)
2
)(y
31
+ 34y
30
+ ··· + 54y −1)
· (y
142
+ 139y
141
+ ··· − 94158y + 841)
c
8
y
4
(y
31
+ 29y
30
+ ··· + 39722y −2401)
· (y
142
+ 44y
141
+ ··· − 2230272y + 331776)
c
9
((y
2
+ y + 1)
2
)(y
31
+ 17y
30
+ ··· − 30y −1)
· (y
142
+ 2y
141
+ ··· − 7484772366y + 127215841)
36
