12a
0324
(K12a
0324
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 10 1 4 7 12 5 9
Solving Sequence
4,11
5
9,12
1 8 3 2 7 10 6
c
4
c
11
c
12
c
8
c
3
c
1
c
7
c
10
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.97705 × 10
454
u
150
+ 5.44321 × 10
453
u
149
+ ··· + 1.74550 × 10
455
b + 3.85569 × 10
456
,
1.24527 × 10
457
u
150
− 4.69754 × 10
456
u
149
+ ··· + 1.02984 × 10
457
a − 1.13363 × 10
459
,
u
151
− u
150
+ ··· − 347u + 59i
I
u
2
= h−6960094u
37
− 14517025u
36
+ ··· + 2084882b + 33128019,
100284480u
37
+ 64266775u
36
+ ··· + 2084882a − 144370152, u
38
− 10u
36
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 189 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−5.98 × 10
454
u
150
+ 5.44 × 10
453
u
149
+ · · · + 1.75 × 10
455
b + 3.86 ×
10
456
, 1.25 × 10
457
u
150
− 4.70 × 10
456
u
149
+ · · · + 1.03 × 10
457
a − 1.13 ×
10
459
, u
151
− u
150
+ · · · − 347u + 59i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
9
=
−1.20919u
150
+ 0.456142u
149
+ ··· − 509.338u + 110.078
0.342427u
150
− 0.0311843u
149
+ ··· + 107.848u − 22.0893
a
12
=
u
−u
3
+ u
a
1
=
0.0321236u
150
− 0.160065u
149
+ ··· + 124.646u − 27.6243
0.560103u
150
− 0.0814844u
149
+ ··· + 176.427u − 36.0766
a
8
=
−1.55162u
150
+ 0.487326u
149
+ ··· − 617.186u + 132.167
0.342427u
150
− 0.0311843u
149
+ ··· + 107.848u − 22.0893
a
3
=
0.415768u
150
− 0.161858u
149
+ ··· + 122.308u − 31.5806
−0.307673u
150
− 0.0169399u
149
+ ··· − 73.6657u + 14.9648
a
2
=
−0.945289u
150
+ 0.0486104u
149
+ ··· − 261.709u + 50.8717
0.543340u
150
− 0.113382u
149
+ ··· + 173.488u − 36.6489
a
7
=
0.234863u
150
+ 0.182289u
149
+ ··· + 20.9259u + 2.63592
−0.188680u
150
+ 0.118465u
149
+ ··· − 71.2589u + 15.7347
a
10
=
−u
3
u
5
− u
3
+ u
a
6
=
0.597935u
150
+ 0.103993u
149
+ ··· + 141.486u − 21.8592
−0.407732u
150
+ 0.124190u
149
+ ··· − 134.008u + 27.5308
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.875815u
150
+ 0.572195u
149
+ ··· + 22.1449u + 33.7195
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
151
+ 59u
150
+ ··· − 241657u + 120409
c
2
, c
5
u
151
+ 3u
150
+ ··· + 1193u − 347
c
3
, c
8
u
151
+ u
150
+ ··· − 3953u − 319
c
4
, c
11
u
151
+ u
150
+ ··· − 347u − 59
c
6
, c
9
u
151
− 6u
150
+ ··· + 220218u − 26057
c
7
u
151
− 2u
150
+ ··· − 15334096u + 82036477
c
10
u
151
− 73u
150
+ ··· + 62943u − 3481
c
12
u
151
+ 10u
150
+ ··· − 194288u − 9629
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
151
+ 85y
150
+ ··· + 4342105053167y −14498327281
c
2
, c
5
y
151
− 59y
150
+ ··· − 241657y −120409
c
3
, c
8
y
151
− 101y
150
+ ··· + 16937937y −101761
c
4
, c
11
y
151
− 73y
150
+ ··· + 62943y −3481
c
6
, c
9
y
151
+ 94y
150
+ ··· − 24366231410y −678967249
c
7
y
151
− 58y
150
+ ··· + 432393903636177302y −6729983558571529
c
10
y
151
+ 27y
150
+ ··· − 2959833961y −12117361
c
12
y
151
− 34y
150
+ ··· + 5136926742y −92717641
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.266173 + 0.955595I
a = −0.039639 − 0.162305I
b = −1.001740 − 0.126781I
0.0393853 + 0.0284279I 0
u = −0.266173 − 0.955595I
a = −0.039639 + 0.162305I
b = −1.001740 + 0.126781I
0.0393853 − 0.0284279I 0
u = 0.180807 + 0.968414I
a = 0.186766 + 0.331168I
b = 0.627417 + 0.335459I
−1.59974 − 1.64062I 0
u = 0.180807 − 0.968414I
a = 0.186766 − 0.331168I
b = 0.627417 − 0.335459I
−1.59974 + 1.64062I 0
u = −0.301843 + 0.933657I
a = 0.663027 + 0.942111I
b = 1.332720 + 0.459969I
6.43799 + 7.51813I 0
u = −0.301843 − 0.933657I
a = 0.663027 − 0.942111I
b = 1.332720 − 0.459969I
6.43799 − 7.51813I 0
u = −0.767737 + 0.609881I
a = −0.64597 − 1.64540I
b = 0.729574 − 0.844251I
−4.00055 − 4.07728I 0
u = −0.767737 − 0.609881I
a = −0.64597 + 1.64540I
b = 0.729574 + 0.844251I
−4.00055 + 4.07728I 0
u = 0.910083 + 0.463641I
a = 0.028649 + 0.538279I
b = −0.115994 + 0.705686I
−0.568526 − 0.503686I 0
u = 0.910083 − 0.463641I
a = 0.028649 − 0.538279I
b = −0.115994 − 0.705686I
−0.568526 + 0.503686I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.966948 + 0.094963I
a = −1.59959 − 0.17797I
b = 1.361200 + 0.067293I
6.58926 + 1.11575I 0
u = 0.966948 − 0.094963I
a = −1.59959 + 0.17797I
b = 1.361200 − 0.067293I
6.58926 − 1.11575I 0
u = 0.592643 + 0.763145I
a = 0.845780 − 0.577160I
b = 0.871487 − 0.507063I
−3.36943 − 0.94507I 0
u = 0.592643 − 0.763145I
a = 0.845780 + 0.577160I
b = 0.871487 + 0.507063I
−3.36943 + 0.94507I 0
u = −0.430995 + 0.861059I
a = 0.40197 + 1.41723I
b = −0.133292 + 1.137370I
0.79172 + 7.55240I 0
u = −0.430995 − 0.861059I
a = 0.40197 − 1.41723I
b = −0.133292 − 1.137370I
0.79172 − 7.55240I 0
u = −0.919760 + 0.265609I
a = −0.866660 + 0.895930I
b = 1.289860 + 0.314682I
3.71338 + 4.23491I 0
u = −0.919760 − 0.265609I
a = −0.866660 − 0.895930I
b = 1.289860 − 0.314682I
3.71338 − 4.23491I 0
u = 0.979888 + 0.358398I
a = −1.81724 + 3.44611I
b = 1.048720 − 0.040840I
7.20102 − 2.66249I 0
u = 0.979888 − 0.358398I
a = −1.81724 − 3.44611I
b = 1.048720 + 0.040840I
7.20102 + 2.66249I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.917889 + 0.265686I
a = 0.299366 − 0.613944I
b = −1.57710 + 0.03351I
6.03966 + 2.57566I 0
u = 0.917889 − 0.265686I
a = 0.299366 + 0.613944I
b = −1.57710 − 0.03351I
6.03966 − 2.57566I 0
u = 1.001240 + 0.305391I
a = −0.720437 + 0.860784I
b = 1.57230 − 0.23343I
6.37377 − 0.39083I 0
u = 1.001240 − 0.305391I
a = −0.720437 − 0.860784I
b = 1.57230 + 0.23343I
6.37377 + 0.39083I 0
u = −1.000190 + 0.314909I
a = 1.84864 + 0.49240I
b = −1.302810 + 0.197550I
4.12322 − 6.46883I 0
u = −1.000190 − 0.314909I
a = 1.84864 − 0.49240I
b = −1.302810 − 0.197550I
4.12322 + 6.46883I 0
u = 0.703455 + 0.795491I
a = 0.312828 + 0.491077I
b = 0.863591 + 0.357054I
−0.52833 + 5.15862I 0
u = 0.703455 − 0.795491I
a = 0.312828 − 0.491077I
b = 0.863591 − 0.357054I
−0.52833 − 5.15862I 0
u = 0.338545 + 1.008360I
a = −0.661891 + 0.816396I
b = −1.33310 + 0.58227I
4.5955 − 13.6183I 0
u = 0.338545 − 1.008360I
a = −0.661891 − 0.816396I
b = −1.33310 − 0.58227I
4.5955 + 13.6183I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.875174 + 0.610615I
a = −0.724669 − 0.751453I
b = −0.592619 − 1.014440I
−3.68787 − 0.71977I 0
u = −0.875174 − 0.610615I
a = −0.724669 + 0.751453I
b = −0.592619 + 1.014440I
−3.68787 + 0.71977I 0
u = 0.501332 + 0.783748I
a = −1.24533 + 0.89065I
b = −1.036630 + 0.336659I
−0.84542 − 5.01805I 0
u = 0.501332 − 0.783748I
a = −1.24533 − 0.89065I
b = −1.036630 − 0.336659I
−0.84542 + 5.01805I 0
u = 0.893044 + 0.174620I
a = −2.32937 + 1.21022I
b = −0.674592 − 0.255096I
6.46346 + 5.05998I 0
u = 0.893044 − 0.174620I
a = −2.32937 − 1.21022I
b = −0.674592 + 0.255096I
6.46346 − 5.05998I 0
u = −0.871275 + 0.658385I
a = 0.40610 − 1.46892I
b = 1.093100 − 0.210104I
2.28620 − 4.36380I 0
u = −0.871275 − 0.658385I
a = 0.40610 + 1.46892I
b = 1.093100 + 0.210104I
2.28620 + 4.36380I 0
u = 0.778150 + 0.461026I
a = 0.62429 − 1.45200I
b = −0.127338 − 0.705983I
−1.33743 + 1.95041I 0
u = 0.778150 − 0.461026I
a = 0.62429 + 1.45200I
b = −0.127338 + 0.705983I
−1.33743 − 1.95041I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.016730 + 0.418997I
a = 1.43056 − 0.81313I
b = 0.098771 − 1.382640I
−0.150897 + 0.660964I 0
u = 1.016730 − 0.418997I
a = 1.43056 + 0.81313I
b = 0.098771 + 1.382640I
−0.150897 − 0.660964I 0
u = 0.947218 + 0.569441I
a = −0.223187 − 0.298072I
b = 0.183102 + 0.116630I
−0.39913 + 4.66537I 0
u = 0.947218 − 0.569441I
a = −0.223187 + 0.298072I
b = 0.183102 − 0.116630I
−0.39913 − 4.66537I 0
u = −1.11091
a = 0.661856
b = −1.06563
2.32313 0
u = −0.629888 + 0.619321I
a = −0.801701 + 0.244034I
b = −0.970989 + 0.084603I
1.70144 − 0.57477I 0
u = −0.629888 − 0.619321I
a = −0.801701 − 0.244034I
b = −0.970989 − 0.084603I
1.70144 + 0.57477I 0
u = −0.994623 + 0.523909I
a = 0.697019 + 1.019290I
b = 0.394830 + 0.808059I
−1.27413 − 5.76219I 0
u = −0.994623 − 0.523909I
a = 0.697019 − 1.019290I
b = 0.394830 − 0.808059I
−1.27413 + 5.76219I 0
u = 0.110888 + 0.868680I
a = 0.0181099 + 0.0004230I
b = 0.979038 + 0.216597I
−0.52350 + 4.20011I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.110888 − 0.868680I
a = 0.0181099 − 0.0004230I
b = 0.979038 − 0.216597I
−0.52350 − 4.20011I 0
u = 0.308405 + 0.817889I
a = −0.27040 + 1.39730I
b = −0.097431 + 0.989247I
2.00775 − 2.44556I 0
u = 0.308405 − 0.817889I
a = −0.27040 − 1.39730I
b = −0.097431 − 0.989247I
2.00775 + 2.44556I 0
u = −1.059500 + 0.381466I
a = 0.54761 + 2.32470I
b = −1.31172 + 0.66617I
9.18330 − 0.52130I 0
u = −1.059500 − 0.381466I
a = 0.54761 − 2.32470I
b = −1.31172 − 0.66617I
9.18330 + 0.52130I 0
u = 1.128790 + 0.037842I
a = −1.057410 − 0.005475I
b = −0.243625 + 0.731530I
6.53089 − 5.31320I 0
u = 1.128790 − 0.037842I
a = −1.057410 + 0.005475I
b = −0.243625 − 0.731530I
6.53089 + 5.31320I 0
u = −0.574701 + 0.972850I
a = −0.081660 − 0.440805I
b = −0.668104 − 0.626425I
0.12280 − 3.17215I 0
u = −0.574701 − 0.972850I
a = −0.081660 + 0.440805I
b = −0.668104 + 0.626425I
0.12280 + 3.17215I 0
u = −0.826640 + 0.269393I
a = 0.117716 − 0.139831I
b = −0.414105 + 0.081390I
1.291060 − 0.430892I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.826640 − 0.269393I
a = 0.117716 + 0.139831I
b = −0.414105 − 0.081390I
1.291060 + 0.430892I 0
u = 1.046410 + 0.432532I
a = 1.92962 + 0.02145I
b = −1.303460 + 0.078059I
8.74522 + 1.30880I 0
u = 1.046410 − 0.432532I
a = 1.92962 − 0.02145I
b = −1.303460 − 0.078059I
8.74522 − 1.30880I 0
u = −1.039470 + 0.454804I
a = 0.89826 + 3.43900I
b = −1.145480 + 0.088957I
8.61733 − 5.26654I 0
u = −1.039470 − 0.454804I
a = 0.89826 − 3.43900I
b = −1.145480 − 0.088957I
8.61733 + 5.26654I 0
u = 0.638241 + 0.943667I
a = −0.540211 − 0.467559I
b = −0.816241 − 0.025741I
−0.828545 + 0.993806I 0
u = 0.638241 − 0.943667I
a = −0.540211 + 0.467559I
b = −0.816241 + 0.025741I
−0.828545 − 0.993806I 0
u = 0.347928 + 0.780527I
a = 0.994860 − 0.850067I
b = 1.32562 − 0.60153I
0.94328 − 7.91215I 0
u = 0.347928 − 0.780527I
a = 0.994860 + 0.850067I
b = 1.32562 + 0.60153I
0.94328 + 7.91215I 0
u = 0.716511 + 0.900284I
a = 0.050177 − 0.584960I
b = 0.327357 − 0.673022I
−0.383606 − 1.084060I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.716511 − 0.900284I
a = 0.050177 + 0.584960I
b = 0.327357 + 0.673022I
−0.383606 + 1.084060I 0
u = −1.131230 + 0.233881I
a = 0.614960 + 0.638025I
b = −1.42700 − 0.39113I
5.59107 + 5.20508I 0
u = −1.131230 − 0.233881I
a = 0.614960 − 0.638025I
b = −1.42700 + 0.39113I
5.59107 − 5.20508I 0
u = −1.042720 + 0.502832I
a = −1.227280 − 0.618588I
b = −0.27177 − 1.45018I
−0.78836 − 5.67597I 0
u = −1.042720 − 0.502832I
a = −1.227280 + 0.618588I
b = −0.27177 + 1.45018I
−0.78836 + 5.67597I 0
u = −1.023990 + 0.550827I
a = −1.96687 − 1.22263I
b = 1.288210 − 0.133366I
5.81086 − 8.61662I 0
u = −1.023990 − 0.550827I
a = −1.96687 + 1.22263I
b = 1.288210 + 0.133366I
5.81086 + 8.61662I 0
u = −0.614586 + 0.548729I
a = 0.72044 + 1.89368I
b = −0.519949 + 0.584103I
−2.44864 + 1.41961I 0
u = −0.614586 − 0.548729I
a = 0.72044 − 1.89368I
b = −0.519949 − 0.584103I
−2.44864 − 1.41961I 0
u = 1.062050 + 0.508661I
a = −0.001809 − 0.567709I
b = −1.62642 + 0.48517I
8.31071 + 6.27709I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.062050 − 0.508661I
a = −0.001809 + 0.567709I
b = −1.62642 − 0.48517I
8.31071 − 6.27709I 0
u = −1.166650 + 0.181169I
a = 0.662822 + 0.059320I
b = 0.315986 + 0.844423I
6.95108 − 0.49917I 0
u = −1.166650 − 0.181169I
a = 0.662822 − 0.059320I
b = 0.315986 − 0.844423I
6.95108 + 0.49917I 0
u = 1.119040 + 0.389516I
a = −0.93816 + 2.01771I
b = 1.25759 + 0.75804I
9.21506 + 6.57820I 0
u = 1.119040 − 0.389516I
a = −0.93816 − 2.01771I
b = 1.25759 − 0.75804I
9.21506 − 6.57820I 0
u = −0.560895 + 0.573182I
a = 1.042140 − 0.673495I
b = −1.280270 − 0.258116I
4.40854 + 4.07935I 0
u = −0.560895 − 0.573182I
a = 1.042140 + 0.673495I
b = −1.280270 + 0.258116I
4.40854 − 4.07935I 0
u = −0.387958 + 0.679259I
a = −1.172130 − 0.757981I
b = −1.289050 − 0.429734I
2.50388 + 2.38188I 0
u = −0.387958 − 0.679259I
a = −1.172130 + 0.757981I
b = −1.289050 + 0.429734I
2.50388 − 2.38188I 0
u = −1.085440 + 0.552366I
a = −0.45780 − 2.03848I
b = 1.41138 − 0.53145I
4.53178 − 7.14521I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.085440 − 0.552366I
a = −0.45780 + 2.03848I
b = 1.41138 + 0.53145I
4.53178 + 7.14521I 0
u = 0.727980 + 0.284832I
a = 0.93112 − 1.82809I
b = −0.232317 − 1.101530I
−1.38151 + 2.46089I 0
u = 0.727980 − 0.284832I
a = 0.93112 + 1.82809I
b = −0.232317 + 1.101530I
−1.38151 − 2.46089I 0
u = 1.022460 + 0.666560I
a = 0.17775 − 1.61356I
b = −1.035590 − 0.560045I
−2.09793 + 6.35631I 0
u = 1.022460 − 0.666560I
a = 0.17775 + 1.61356I
b = −1.035590 + 0.560045I
−2.09793 − 6.35631I 0
u = 1.072220 + 0.612814I
a = 0.05312 + 2.11181I
b = 1.089490 + 0.417302I
0.87929 + 10.27800I 0
u = 1.072220 − 0.612814I
a = 0.05312 − 2.11181I
b = 1.089490 − 0.417302I
0.87929 − 10.27800I 0
u = 1.119310 + 0.524215I
a = 0.62470 − 1.50339I
b = −1.025990 − 0.022052I
2.27446 + 0.58633I 0
u = 1.119310 − 0.524215I
a = 0.62470 + 1.50339I
b = −1.025990 + 0.022052I
2.27446 − 0.58633I 0
u = −1.128380 + 0.514252I
a = −0.064006 + 0.139002I
b = 0.342622 + 0.417812I
3.73858 − 2.82652I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.128380 − 0.514252I
a = −0.064006 − 0.139002I
b = 0.342622 − 0.417812I
3.73858 + 2.82652I 0
u = −1.142800 + 0.484256I
a = 0.034324 − 0.476906I
b = 1.44649 + 0.58783I
8.54536 − 1.24048I 0
u = −1.142800 − 0.484256I
a = 0.034324 + 0.476906I
b = 1.44649 − 0.58783I
8.54536 + 1.24048I 0
u = 1.129510 + 0.576855I
a = 0.61495 − 1.88717I
b = −1.43606 − 0.65679I
3.25734 + 13.01480I 0
u = 1.129510 − 0.576855I
a = 0.61495 + 1.88717I
b = −1.43606 + 0.65679I
3.25734 − 13.01480I 0
u = 1.141410 + 0.569329I
a = −0.892689 + 0.878577I
b = 0.110140 + 1.092760I
4.48661 + 7.57578I 0
u = 1.141410 − 0.569329I
a = −0.892689 − 0.878577I
b = 0.110140 − 1.092760I
4.48661 − 7.57578I 0
u = −1.257330 + 0.219490I
a = −0.281673 − 0.236119I
b = 1.126470 − 0.004721I
5.60164 − 4.17808I 0
u = −1.257330 − 0.219490I
a = −0.281673 + 0.236119I
b = 1.126470 + 0.004721I
5.60164 + 4.17808I 0
u = 0.001164 + 0.713788I
a = 0.129995 + 0.819265I
b = −0.462542 + 0.444744I
0.80713 − 1.54342I 3.62434 + 4.97368I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.001164 − 0.713788I
a = 0.129995 − 0.819265I
b = −0.462542 − 0.444744I
0.80713 + 1.54342I 3.62434 − 4.97368I
u = −1.127370 + 0.626934I
a = 0.854578 + 0.802560I
b = 0.035326 + 1.277960I
2.90700 − 13.06440I 0
u = −1.127370 − 0.626934I
a = 0.854578 − 0.802560I
b = 0.035326 − 1.277960I
2.90700 + 13.06440I 0
u = 1.212730 + 0.480193I
a = −0.826730 + 1.008040I
b = 0.696510 + 0.513744I
4.26305 + 6.00567I 0
u = 1.212730 − 0.480193I
a = −0.826730 − 1.008040I
b = 0.696510 − 0.513744I
4.26305 − 6.00567I 0
u = −1.148850 + 0.634497I
a = −0.50496 − 1.33818I
b = 1.174070 − 0.173092I
2.58694 − 5.73432I 0
u = −1.148850 − 0.634497I
a = −0.50496 + 1.33818I
b = 1.174070 + 0.173092I
2.58694 + 5.73432I 0
u = −0.175956 + 0.664223I
a = −0.53812 + 1.75140I
b = −1.31971 + 0.54145I
5.77286 − 3.16618I 5.94206 + 3.29527I
u = −0.175956 − 0.664223I
a = −0.53812 − 1.75140I
b = −1.31971 − 0.54145I
5.77286 + 3.16618I 5.94206 − 3.29527I
u = −0.493879 + 0.472580I
a = −0.63891 − 1.83433I
b = 0.360525 − 1.196920I
−2.44983 + 1.54099I 1.35815 − 5.08517I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493879 − 0.472580I
a = −0.63891 + 1.83433I
b = 0.360525 + 1.196920I
−2.44983 − 1.54099I 1.35815 + 5.08517I
u = 0.664726 + 0.141815I
a = −0.39588 − 2.29330I
b = 0.1384260 + 0.0284114I
−0.78196 + 2.78750I 9.43682 − 6.77718I
u = 0.664726 − 0.141815I
a = −0.39588 + 2.29330I
b = 0.1384260 − 0.0284114I
−0.78196 − 2.78750I 9.43682 + 6.77718I
u = −1.190470 + 0.611840I
a = 0.58877 + 1.87555I
b = −1.37974 + 0.49688I
9.1314 − 13.1308I 0
u = −1.190470 − 0.611840I
a = 0.58877 − 1.87555I
b = −1.37974 − 0.49688I
9.1314 + 13.1308I 0
u = 1.158250 + 0.685906I
a = 0.251647 + 0.021577I
b = −0.254537 + 0.116977I
1.10518 + 7.69617I 0
u = 1.158250 − 0.685906I
a = 0.251647 − 0.021577I
b = −0.254537 − 0.116977I
1.10518 − 7.69617I 0
u = −1.204770 + 0.608589I
a = 0.466183 + 0.990085I
b = −1.083040 + 0.482008I
2.05221 − 3.73821I 0
u = −1.204770 − 0.608589I
a = 0.466183 − 0.990085I
b = −1.083040 − 0.482008I
2.05221 + 3.73821I 0
u = 1.344910 + 0.206006I
a = 0.681521 − 0.052152I
b = −1.351160 + 0.355856I
12.02940 − 3.69313I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.344910 − 0.206006I
a = 0.681521 + 0.052152I
b = −1.351160 − 0.355856I
12.02940 + 3.69313I 0
u = −0.618615 + 0.154062I
a = 3.07962 + 2.34354I
b = 1.035340 − 0.151371I
6.86850 + 1.92294I 7.01924 − 1.26116I
u = −0.618615 − 0.154062I
a = 3.07962 − 2.34354I
b = 1.035340 + 0.151371I
6.86850 − 1.92294I 7.01924 + 1.26116I
u = 1.209920 + 0.647265I
a = −0.58496 + 1.71551I
b = 1.41069 + 0.59610I
7.2814 + 19.5798I 0
u = 1.209920 − 0.647265I
a = −0.58496 − 1.71551I
b = 1.41069 − 0.59610I
7.2814 − 19.5798I 0
u = −1.072150 + 0.858021I
a = −0.259497 − 0.987287I
b = 1.038200 − 0.500709I
1.59114 − 3.42886I 0
u = −1.072150 − 0.858021I
a = −0.259497 + 0.987287I
b = 1.038200 + 0.500709I
1.59114 + 3.42886I 0
u = 0.999392 + 0.941873I
a = 0.170208 − 0.756920I
b = −0.777511 − 0.495042I
0.44844 + 7.68666I 0
u = 0.999392 − 0.941873I
a = 0.170208 + 0.756920I
b = −0.777511 + 0.495042I
0.44844 − 7.68666I 0
u = 0.412582 + 0.411865I
a = −0.46992 + 2.27122I
b = 1.48300 + 0.26877I
6.42856 − 2.14920I 5.88821 + 3.25514I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.412582 − 0.411865I
a = −0.46992 − 2.27122I
b = 1.48300 − 0.26877I
6.42856 + 2.14920I 5.88821 − 3.25514I
u = −1.42305 + 0.15920I
a = −0.565903 − 0.081802I
b = 1.283480 + 0.423406I
10.8172 + 9.5544I 0
u = −1.42305 − 0.15920I
a = −0.565903 + 0.081802I
b = 1.283480 − 0.423406I
10.8172 − 9.5544I 0
u = 1.34747 + 0.49188I
a = −0.703756 + 0.809388I
b = 1.008220 + 0.090448I
4.90929 + 4.95614I 0
u = 1.34747 − 0.49188I
a = −0.703756 − 0.809388I
b = 1.008220 − 0.090448I
4.90929 − 4.95614I 0
u = −1.35767 + 0.56506I
a = 0.627188 + 0.795642I
b = −1.168900 + 0.214784I
3.88655 − 9.53027I 0
u = −1.35767 − 0.56506I
a = 0.627188 − 0.795642I
b = −1.168900 − 0.214784I
3.88655 + 9.53027I 0
u = 0.021922 + 0.464940I
a = −0.0739811 + 0.0609871I
b = 0.376905 + 0.582632I
−1.62666 − 1.27118I −1.93388 − 0.65553I
u = 0.021922 − 0.464940I
a = −0.0739811 − 0.0609871I
b = 0.376905 − 0.582632I
−1.62666 + 1.27118I −1.93388 + 0.65553I
u = 0.176008 + 0.224005I
a = −4.32723 + 1.57990I
b = 1.312990 − 0.103475I
6.58871 + 2.03230I 7.98619 − 3.34032I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.176008 − 0.224005I
a = −4.32723 − 1.57990I
b = 1.312990 + 0.103475I
6.58871 − 2.03230I 7.98619 + 3.34032I
20
II.
I
u
2
= h−6.96 × 10
6
u
37
− 1.45 × 10
7
u
36
+ · · · + 2.08 × 10
6
b + 3.31 × 10
7
, 1.00 ×
10
8
u
37
+6.43×10
7
u
36
+· · ·+2.08×10
6
a−1.44×10
8
, u
38
−10u
36
+· · ·−2u+1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
9
=
−48.1008u
37
− 30.8251u
36
+ ··· − 58.8735u + 69.2462
3.33836u
37
+ 6.96300u
36
+ ··· + 16.7005u − 15.8896
a
12
=
u
−u
3
+ u
a
1
=
78.4681u
37
+ 39.3080u
36
+ ··· + 35.5827u − 76.6318
−11.4818u
37
+ 3.10017u
36
+ ··· + 0.310773u + 13.6024
a
8
=
−51.4392u
37
− 37.7881u
36
+ ··· − 75.5740u + 85.1358
3.33836u
37
+ 6.96300u
36
+ ··· + 16.7005u − 15.8896
a
3
=
−38.9546u
37
− 16.1203u
36
+ ··· − 31.5668u + 30.7708
32.1084u
37
+ 12.8650u
36
+ ··· + 25.0202u − 43.1165
a
2
=
−12.4976u
37
+ 12.5424u
36
+ ··· + 49.5414u − 5.88595
9.43326u
37
− 5.48016u
36
+ ··· − 20.5475u − 14.4989
a
7
=
−15.4635u
37
− 17.6621u
36
+ ··· − 32.1753u + 42.2745
−26.0272u
37
− 27.5754u
36
+ ··· − 48.9256u + 23.2119
a
10
=
−u
3
u
5
− u
3
+ u
a
6
=
−9.02470u
37
− 5.25605u
36
+ ··· − 23.2549u + 40.5975
−19.9853u
37
− 29.8409u
36
+ ··· − 44.3911u + 10.7593
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
443066941
2084882
u
37
−
528025979
2084882
u
36
+ ··· −
347974495
1042441
u +
312998335
2084882
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
38
− 18u
37
+ ··· − 22u + 1
c
2
u
38
+ 2u
37
+ ··· + 2u + 1
c
3
u
38
− 12u
36
+ ··· − 2u + 1
c
4
u
38
− 10u
36
+ ··· − 2u + 1
c
5
u
38
− 2u
37
+ ··· − 2u + 1
c
6
u
38
− 7u
37
+ ··· − 7u + 1
c
7
u
38
− u
37
+ ··· − u + 1
c
8
u
38
− 12u
36
+ ··· + 2u + 1
c
9
u
38
+ 7u
37
+ ··· + 7u + 1
c
10
u
38
+ 20u
37
+ ··· + 14u + 1
c
11
u
38
− 10u
36
+ ··· + 2u + 1
c
12
u
38
− 3u
37
+ ··· − 7u + 1
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
+ 22y
37
+ ··· + 18y + 1
c
2
, c
5
y
38
− 18y
37
+ ··· − 22y + 1
c
3
, c
8
y
38
− 24y
37
+ ··· − 16y + 1
c
4
, c
11
y
38
− 20y
37
+ ··· − 14y + 1
c
6
, c
9
y
38
+ 19y
37
+ ··· + 19y + 1
c
7
y
38
− 9y
37
+ ··· − 17y + 1
c
10
y
38
+ 12y
37
+ ··· + 10y + 1
c
12
y
38
− 5y
37
+ ··· + 19y + 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.969625 + 0.291098I
a = 0.585516 + 0.702920I
b = 1.246660 + 0.247660I
7.98711 − 3.33140I 11.04134 + 4.17388I
u = −0.969625 − 0.291098I
a = 0.585516 − 0.702920I
b = 1.246660 − 0.247660I
7.98711 + 3.33140I 11.04134 − 4.17388I
u = −0.909102 + 0.283433I
a = 2.52203 + 2.18260I
b = −1.281690 + 0.185860I
7.75366 + 0.97119I 11.22990 + 0.77185I
u = −0.909102 − 0.283433I
a = 2.52203 − 2.18260I
b = −1.281690 − 0.185860I
7.75366 − 0.97119I 11.22990 − 0.77185I
u = 0.965169 + 0.415284I
a = 1.41398 − 0.81072I
b = 0.019707 − 1.017520I
−0.764006 + 0.486262I −1.52398 + 1.36642I
u = 0.965169 − 0.415284I
a = 1.41398 + 0.81072I
b = 0.019707 + 1.017520I
−0.764006 − 0.486262I −1.52398 − 1.36642I
u = −0.717170 + 0.569540I
a = −0.379433 − 1.043820I
b = −0.035636 − 1.020860I
−2.52710 + 0.48218I −0.737542 + 1.120850I
u = −0.717170 − 0.569540I
a = −0.379433 + 1.043820I
b = −0.035636 + 1.020860I
−2.52710 − 0.48218I −0.737542 − 1.120850I
u = 1.035960 + 0.339022I
a = −2.23962 + 2.19472I
b = 1.072280 + 0.310836I
7.25600 + 6.07680I 8.73339 − 8.10413I
u = 1.035960 − 0.339022I
a = −2.23962 − 2.19472I
b = 1.072280 − 0.310836I
7.25600 − 6.07680I 8.73339 + 8.10413I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.980873 + 0.545549I
a = −0.923221 − 0.600509I
b = −0.004188 − 0.980185I
−1.64410 − 4.95385I 0. + 4.81570I
u = −0.980873 − 0.545549I
a = −0.923221 + 0.600509I
b = −0.004188 + 0.980185I
−1.64410 + 4.95385I 0. − 4.81570I
u = 0.831171 + 0.268269I
a = −1.82636 + 2.42242I
b = −0.998402 + 0.348706I
6.40421 − 3.57024I 6.95194 + 3.49908I
u = 0.831171 − 0.268269I
a = −1.82636 − 2.42242I
b = −0.998402 − 0.348706I
6.40421 + 3.57024I 6.95194 − 3.49908I
u = −0.499890 + 1.014760I
a = −0.076153 − 0.180110I
b = −0.590547 − 0.173073I
−1.47254 − 0.41673I −4.21513 + 0.I
u = −0.499890 − 1.014760I
a = −0.076153 + 0.180110I
b = −0.590547 + 0.173073I
−1.47254 + 0.41673I −4.21513 + 0.I
u = −1.104790 + 0.312508I
a = −0.511874 − 0.540228I
b = 1.41499 + 0.08876I
7.01013 − 3.11838I 10.60055 + 3.92869I
u = −1.104790 − 0.312508I
a = −0.511874 + 0.540228I
b = 1.41499 − 0.08876I
7.01013 + 3.11838I 10.60055 − 3.92869I
u = 0.722724 + 0.337213I
a = 0.53159 − 1.97962I
b = −0.047100 − 0.927769I
−1.62680 + 2.79836I −4.51266 − 12.65381I
u = 0.722724 − 0.337213I
a = 0.53159 + 1.97962I
b = −0.047100 + 0.927769I
−1.62680 − 2.79836I −4.51266 + 12.65381I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.118320 + 0.481398I
a = 1.108200 − 0.694887I
b = −1.300970 − 0.104228I
4.59587 + 7.86572I 0. − 7.16447I
u = 1.118320 − 0.481398I
a = 1.108200 + 0.694887I
b = −1.300970 + 0.104228I
4.59587 − 7.86572I 0. + 7.16447I
u = −0.747518 + 0.188283I
a = 0.904238 + 0.947692I
b = −1.54470 − 0.04905I
5.50079 + 0.97987I 1.75374 + 0.22526I
u = −0.747518 − 0.188283I
a = 0.904238 − 0.947692I
b = −1.54470 + 0.04905I
5.50079 − 0.97987I 1.75374 − 0.22526I
u = 0.031944 + 0.748782I
a = −0.300436 + 0.268385I
b = 0.493431 − 0.222525I
−1.46400 + 2.53482I −0.72301 − 4.85420I
u = 0.031944 − 0.748782I
a = −0.300436 − 0.268385I
b = 0.493431 + 0.222525I
−1.46400 − 2.53482I −0.72301 + 4.85420I
u = 0.670883 + 0.322552I
a = −1.41201 − 0.14583I
b = 1.338280 − 0.260057I
2.77937 − 4.46570I −0.13807 + 4.09528I
u = 0.670883 − 0.322552I
a = −1.41201 + 0.14583I
b = 1.338280 + 0.260057I
2.77937 + 4.46570I −0.13807 − 4.09528I
u = −0.967882 + 0.845121I
a = 0.132208 − 0.985298I
b = 0.946922 − 0.396098I
−0.22400 − 6.23705I 0
u = −0.967882 − 0.845121I
a = 0.132208 + 0.985298I
b = 0.946922 + 0.396098I
−0.22400 + 6.23705I 0
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.087000 + 0.797543I
a = 0.238397 − 1.005030I
b = −1.095670 − 0.419101I
0.72404 + 3.45537I 0
u = 1.087000 − 0.797543I
a = 0.238397 + 1.005030I
b = −1.095670 + 0.419101I
0.72404 − 3.45537I 0
u = −1.198180 + 0.684453I
a = −0.048070 + 0.824017I
b = −0.717388 + 0.175683I
1.72500 − 8.21836I 0
u = −1.198180 − 0.684453I
a = −0.048070 − 0.824017I
b = −0.717388 − 0.175683I
1.72500 + 8.21836I 0
u = 1.317020 + 0.482479I
a = −0.701987 + 0.671161I
b = 0.723019 + 0.337464I
3.84086 + 5.19868I 0
u = 1.317020 − 0.482479I
a = −0.701987 − 0.671161I
b = 0.723019 − 0.337464I
3.84086 − 5.19868I 0
u = 0.314855 + 0.456776I
a = −1.016990 − 0.675621I
b = 0.360995 − 0.466501I
−1.44128 + 2.49020I −1.48894 − 3.44933I
u = 0.314855 − 0.456776I
a = −1.016990 + 0.675621I
b = 0.360995 + 0.466501I
−1.44128 − 2.49020I −1.48894 + 3.44933I
29
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
38
− 18u
37
+ ··· − 22u + 1)
· (u
151
+ 59u
150
+ ··· − 241657u + 120409)
c
2
(u
38
+ 2u
37
+ ··· + 2u + 1)(u
151
+ 3u
150
+ ··· + 1193u − 347)
c
3
(u
38
− 12u
36
+ ··· − 2u + 1)(u
151
+ u
150
+ ··· − 3953u − 319)
c
4
(u
38
− 10u
36
+ ··· − 2u + 1)(u
151
+ u
150
+ ··· − 347u − 59)
c
5
(u
38
− 2u
37
+ ··· − 2u + 1)(u
151
+ 3u
150
+ ··· + 1193u − 347)
c
6
(u
38
− 7u
37
+ ··· − 7u + 1)(u
151
− 6u
150
+ ··· + 220218u − 26057)
c
7
(u
38
− u
37
+ ··· − u + 1)(u
151
− 2u
150
+ ··· − 1.53341 × 10
7
u + 8.20365 × 10
7
)
c
8
(u
38
− 12u
36
+ ··· + 2u + 1)(u
151
+ u
150
+ ··· − 3953u − 319)
c
9
(u
38
+ 7u
37
+ ··· + 7u + 1)(u
151
− 6u
150
+ ··· + 220218u − 26057)
c
10
(u
38
+ 20u
37
+ ··· + 14u + 1)(u
151
− 73u
150
+ ··· + 62943u − 3481)
c
11
(u
38
− 10u
36
+ ··· + 2u + 1)(u
151
+ u
150
+ ··· − 347u − 59)
c
12
(u
38
− 3u
37
+ ··· − 7u + 1)(u
151
+ 10u
150
+ ··· − 194288u − 9629)
30
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
38
+ 22y
37
+ ··· + 18y + 1)
· (y
151
+ 85y
150
+ ··· + 4342105053167y −14498327281)
c
2
, c
5
(y
38
− 18y
37
+ ··· − 22y + 1)
· (y
151
− 59y
150
+ ··· − 241657y −120409)
c
3
, c
8
(y
38
− 24y
37
+ ··· − 16y + 1)
· (y
151
− 101y
150
+ ··· + 16937937y −101761)
c
4
, c
11
(y
38
− 20y
37
+ ··· − 14y + 1)(y
151
− 73y
150
+ ··· + 62943y −3481)
c
6
, c
9
(y
38
+ 19y
37
+ ··· + 19y + 1)
· (y
151
+ 94y
150
+ ··· − 24366231410y −678967249)
c
7
(y
38
− 9y
37
+ ··· − 17y + 1)
· (y
151
− 58y
150
+ ··· + 432393903636177302y −6729983558571529)
c
10
(y
38
+ 12y
37
+ ··· + 10y + 1)
· (y
151
+ 27y
150
+ ··· − 2959833961y −12117361)
c
12
(y
38
− 5y
37
+ ··· + 19y + 1)
· (y
151
− 34y
150
+ ··· + 5136926742y −92717641)
31
