12a
0846
(K12a
0846
)
A knot diagram
1
Linearized knot diagam
4 5 9 2 11 1 10 3 12 6 8 7
Solving Sequence
1,4
2
5,11
6 7 10 8 12 9 3
c
1
c
4
c
5
c
6
c
10
c
7
c
12
c
9
c
3
c
2
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.09278 × 10
260
u
129
− 1.32449 × 10
261
u
128
+ ··· + 3.80012 × 10
256
b + 2.54286 × 10
261
,
5.57550 × 10
259
u
129
+ 8.45930 × 10
260
u
128
+ ··· + 7.60023 × 10
256
a − 5.21843 × 10
261
,
u
130
+ 14u
129
+ ··· − 35u − 49i
I
u
2
= h5u
19
+ 12u
18
+ ··· + b + 5, 3u
19
+ 11u
18
+ ··· + a + 11u, u
20
+ 4u
19
+ ··· − 5u + 1i
I
u
3
= h18445a
8
− 60477a
7
+ 69483a
6
− 21043a
5
− 6071a
4
− 11267a
3
+ 12888a
2
+ 1627b − 373a − 4047,
7a
9
− 20a
8
+ 16a
7
+ 5a
6
− 7a
5
− 6a
4
+ 4a
3
+ 3a
2
− 2a − 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 159 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−1.09 × 10
260
u
129
− 1.32 × 10
261
u
128
+ · · · + 3.80 × 10
256
b + 2.54 ×
10
261
, 5.58 × 10
259
u
129
+ 8.46 × 10
260
u
128
+ · · · + 7.60 × 10
256
a − 5.22 ×
10
261
, u
130
+ 14u
129
+ · · · − 35u − 49i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
11
=
−733.595u
129
− 11130.3u
128
+ ··· − 27344.6u + 68661.4
2875.66u
129
+ 34853.9u
128
+ ··· − 23132.5u − 66915.3
a
6
=
2327.78u
129
+ 29108.4u
128
+ ··· − 4815.65u − 75259.4
4875.30u
129
+ 60798.0u
128
+ ··· − 13534.6u − 153050.
a
7
=
−2547.52u
129
− 31689.7u
128
+ ··· + 8718.97u + 77790.6
4875.30u
129
+ 60798.0u
128
+ ··· − 13534.6u − 153050.
a
10
=
2968.38u
129
+ 38020.6u
128
+ ··· + 6385.70u − 116156.
214.488u
129
+ 2233.99u
128
+ ··· − 7504.88u + 3687.50
a
8
=
−709.800u
129
− 8902.49u
128
+ ··· + 1399.03u + 23362.7
1166.71u
129
+ 14805.6u
128
+ ··· + 1012.59u − 42841.9
a
12
=
−3174.46u
129
− 40879.9u
128
+ ··· − 10269.3u + 129353.
2950.79u
129
+ 36205.8u
128
+ ··· − 16869.5u − 79058.2
a
9
=
681.193u
129
+ 8778.25u
128
+ ··· + 3329.62u − 28655.4
−2590.23u
129
− 32855.2u
128
+ ··· − 2287.68u + 95049.6
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5605.17u
129
− 69784.3u
128
+ ··· + 15066.8u + 174873.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
130
− 14u
129
+ ··· + 35u − 49
c
3
, c
8
u
130
+ u
129
+ ··· − 60928u + 25088
c
5
, c
10
u
130
− 2u
129
+ ··· − 4232u − 4232
c
6
, c
12
u
130
− 3u
129
+ ··· + 4534u − 71
c
7
u
130
+ 10u
129
+ ··· − 27u − 9
c
9
u
130
+ 18u
129
+ ··· − 8409u + 1079
c
11
u
130
+ u
129
+ ··· − 15153510u − 893777
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
130
− 122y
129
+ ··· − 5929y + 2401
c
3
, c
8
y
130
− 69y
129
+ ··· − 11984437248y + 629407744
c
5
, c
10
y
130
+ 86y
129
+ ··· + 519774240y + 17909824
c
6
, c
12
y
130
+ 81y
129
+ ··· − 16239788y + 5041
c
7
y
130
− 6y
129
+ ··· + 2151y + 81
c
9
y
130
− 26y
129
+ ··· − 102045441y + 1164241
c
11
y
130
+ 13y
129
+ ··· + 20581982318772y + 798837325729
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328537 + 0.951554I
a = 1.274030 − 0.038467I
b = −1.19741 + 1.89741I
−0.4865 − 14.3089I 0
u = 0.328537 − 0.951554I
a = 1.274030 + 0.038467I
b = −1.19741 − 1.89741I
−0.4865 + 14.3089I 0
u = 0.925732 + 0.424462I
a = −0.347303 − 1.192700I
b = 0.225774 + 0.575562I
1.39635 + 3.23709I 0
u = 0.925732 − 0.424462I
a = −0.347303 + 1.192700I
b = 0.225774 − 0.575562I
1.39635 − 3.23709I 0
u = 0.858665 + 0.587059I
a = 1.116190 + 0.421322I
b = −0.18571 + 1.68368I
−5.66140 + 2.87702I 0
u = 0.858665 − 0.587059I
a = 1.116190 − 0.421322I
b = −0.18571 − 1.68368I
−5.66140 − 2.87702I 0
u = 1.074370 + 0.067387I
a = 2.71351 + 0.00240I
b = 0.93774 + 1.10701I
−0.42547 + 2.53758I 0
u = 1.074370 − 0.067387I
a = 2.71351 − 0.00240I
b = 0.93774 − 1.10701I
−0.42547 − 2.53758I 0
u = 1.017690 + 0.363111I
a = 0.750109 + 0.218017I
b = −0.612129 − 0.557038I
−4.78176 − 1.13220I 0
u = 1.017690 − 0.363111I
a = 0.750109 − 0.218017I
b = −0.612129 + 0.557038I
−4.78176 + 1.13220I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.326397 + 0.853815I
a = −0.843130 + 0.307087I
b = 0.13566 − 1.88854I
−4.00841 − 7.89339I 0
u = 0.326397 − 0.853815I
a = −0.843130 − 0.307087I
b = 0.13566 + 1.88854I
−4.00841 + 7.89339I 0
u = 0.547123 + 0.943513I
a = −0.894553 + 0.625707I
b = 0.10167 − 2.32803I
−1.42660 − 2.83814I 0
u = 0.547123 − 0.943513I
a = −0.894553 − 0.625707I
b = 0.10167 + 2.32803I
−1.42660 + 2.83814I 0
u = −0.378985 + 0.820019I
a = −1.070330 − 0.449410I
b = 0.28653 + 1.41351I
3.12587 − 4.37430I 0
u = −0.378985 − 0.820019I
a = −1.070330 + 0.449410I
b = 0.28653 − 1.41351I
3.12587 + 4.37430I 0
u = 0.613683 + 0.661203I
a = 1.223980 + 0.253281I
b = −0.026339 + 1.164490I
−2.89630 + 0.85409I 0
u = 0.613683 − 0.661203I
a = 1.223980 − 0.253281I
b = −0.026339 − 1.164490I
−2.89630 − 0.85409I 0
u = 0.456890 + 0.755947I
a = −0.566371 − 0.319790I
b = 0.30403 − 1.47097I
−2.38061 − 5.66774I 0
u = 0.456890 − 0.755947I
a = −0.566371 + 0.319790I
b = 0.30403 + 1.47097I
−2.38061 + 5.66774I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.310871 + 1.087400I
a = 1.53844 − 0.09507I
b = −2.17790 + 1.71738I
−0.99196 − 4.71706I 0
u = 0.310871 − 1.087400I
a = 1.53844 + 0.09507I
b = −2.17790 − 1.71738I
−0.99196 + 4.71706I 0
u = 0.281124 + 0.804317I
a = −0.815269 + 0.700780I
b = 0.302176 − 0.112938I
3.35673 − 7.72625I 0
u = 0.281124 − 0.804317I
a = −0.815269 − 0.700780I
b = 0.302176 + 0.112938I
3.35673 + 7.72625I 0
u = −1.163870 + 0.069350I
a = −0.404045 + 0.135763I
b = −0.768918 − 0.712141I
1.52846 + 7.35278I 0
u = −1.163870 − 0.069350I
a = −0.404045 − 0.135763I
b = −0.768918 + 0.712141I
1.52846 − 7.35278I 0
u = 0.820783
a = 1.05160
b = 0.0364198
−1.15012 0
u = 0.967020 + 0.706799I
a = −0.876124 + 0.280697I
b = −0.88322 − 1.97107I
−2.38605 + 8.61930I 0
u = 0.967020 − 0.706799I
a = −0.876124 − 0.280697I
b = −0.88322 + 1.97107I
−2.38605 − 8.61930I 0
u = 1.164850 + 0.314678I
a = 0.726113 − 0.266537I
b = 0.492041 − 0.078387I
−0.131132 − 1.178100I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.164850 − 0.314678I
a = 0.726113 + 0.266537I
b = 0.492041 + 0.078387I
−0.131132 + 1.178100I 0
u = 0.391027 + 0.684289I
a = 0.461372 + 0.327658I
b = −0.370357 − 0.824880I
−0.63869 − 3.79000I 0
u = 0.391027 − 0.684289I
a = 0.461372 − 0.327658I
b = −0.370357 + 0.824880I
−0.63869 + 3.79000I 0
u = 0.079052 + 0.768633I
a = 0.00874662 + 0.00398131I
b = 0.544900 − 0.096774I
3.19605 − 2.75030I 0
u = 0.079052 − 0.768633I
a = 0.00874662 − 0.00398131I
b = 0.544900 + 0.096774I
3.19605 + 2.75030I 0
u = 1.190180 + 0.318430I
a = 0.674856 − 0.624355I
b = 0.456322 − 0.062958I
−0.169062 − 1.292200I 0
u = 1.190180 − 0.318430I
a = 0.674856 + 0.624355I
b = 0.456322 + 0.062958I
−0.169062 + 1.292200I 0
u = −1.243070 + 0.082316I
a = −0.477105 + 0.673366I
b = −0.918203 − 0.239906I
1.95452 − 0.73217I 0
u = −1.243070 − 0.082316I
a = −0.477105 − 0.673366I
b = −0.918203 + 0.239906I
1.95452 + 0.73217I 0
u = 0.108093 + 0.744850I
a = −0.125117 + 0.426426I
b = 0.625444 − 0.004175I
3.14662 − 2.57828I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.108093 − 0.744850I
a = −0.125117 − 0.426426I
b = 0.625444 + 0.004175I
3.14662 + 2.57828I 0
u = 1.252820 + 0.043823I
a = 1.08094 + 2.93788I
b = 0.467723 + 0.557245I
−5.23503 − 0.36072I 0
u = 1.252820 − 0.043823I
a = 1.08094 − 2.93788I
b = 0.467723 − 0.557245I
−5.23503 + 0.36072I 0
u = 1.252870 + 0.067833I
a = 0.64482 − 4.73420I
b = 1.04580 − 1.78608I
−1.20363 − 3.45389I 0
u = 1.252870 − 0.067833I
a = 0.64482 + 4.73420I
b = 1.04580 + 1.78608I
−1.20363 + 3.45389I 0
u = −0.442581 + 0.598153I
a = 1.078450 − 0.503730I
b = −0.75287 − 1.55009I
2.56590 + 8.61563I 0
u = −0.442581 − 0.598153I
a = 1.078450 + 0.503730I
b = −0.75287 + 1.55009I
2.56590 − 8.61563I 0
u = 0.343983 + 0.636102I
a = 0.676314 + 0.731561I
b = 0.226933 + 0.763022I
−2.96488 − 2.11966I 0
u = 0.343983 − 0.636102I
a = 0.676314 − 0.731561I
b = 0.226933 − 0.763022I
−2.96488 + 2.11966I 0
u = −1.278240 + 0.076549I
a = 0.688761 − 0.362001I
b = 0.635930 − 0.936669I
−4.78653 − 1.59407I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.278240 − 0.076549I
a = 0.688761 + 0.362001I
b = 0.635930 + 0.936669I
−4.78653 + 1.59407I 0
u = 0.310436 + 0.645987I
a = −1.89400 − 0.01713I
b = 1.33565 − 1.76018I
1.16491 − 5.17903I 0
u = 0.310436 − 0.645987I
a = −1.89400 + 0.01713I
b = 1.33565 + 1.76018I
1.16491 + 5.17903I 0
u = 0.546564 + 0.459359I
a = 1.066240 + 0.221282I
b = −0.289619 + 0.130137I
−1.385150 − 0.269456I 0
u = 0.546564 − 0.459359I
a = 1.066240 − 0.221282I
b = −0.289619 − 0.130137I
−1.385150 + 0.269456I 0
u = 1.315590 + 0.071467I
a = −0.112675 − 0.790590I
b = −0.398404 − 0.494567I
−2.97910 − 1.77302I 0
u = 1.315590 − 0.071467I
a = −0.112675 + 0.790590I
b = −0.398404 + 0.494567I
−2.97910 + 1.77302I 0
u = 0.987474 + 0.878597I
a = 0.894909 − 0.344556I
b = 0.32266 + 2.47963I
−2.45297 − 3.70553I 0
u = 0.987474 − 0.878597I
a = 0.894909 + 0.344556I
b = 0.32266 − 2.47963I
−2.45297 + 3.70553I 0
u = 1.326740 + 0.196563I
a = −0.613407 + 0.123183I
b = 0.363905 − 0.317078I
0.47369 − 5.68832I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.326740 − 0.196563I
a = −0.613407 − 0.123183I
b = 0.363905 + 0.317078I
0.47369 + 5.68832I 0
u = −1.35728
a = 1.14882
b = 1.52745
−2.56238 0
u = −1.317810 + 0.326766I
a = 0.479988 + 0.466680I
b = 0.628510 + 0.171659I
−1.18088 + 6.70646I 0
u = −1.317810 − 0.326766I
a = 0.479988 − 0.466680I
b = 0.628510 − 0.171659I
−1.18088 − 6.70646I 0
u = 0.366768 + 0.520839I
a = −2.23423 − 1.57920I
b = 0.801086 − 0.369711I
−3.37537 − 1.30670I 0
u = 0.366768 − 0.520839I
a = −2.23423 + 1.57920I
b = 0.801086 + 0.369711I
−3.37537 + 1.30670I 0
u = 0.406976 + 0.459261I
a = 0.631498 − 0.737431I
b = 0.67086 + 1.79575I
0.47179 + 1.76850I 0
u = 0.406976 − 0.459261I
a = 0.631498 + 0.737431I
b = 0.67086 − 1.79575I
0.47179 − 1.76850I 0
u = −1.377590 + 0.183136I
a = 1.034860 + 0.508253I
b = 1.76292 − 0.74576I
−3.08113 + 0.81431I 0
u = −1.377590 − 0.183136I
a = 1.034860 − 0.508253I
b = 1.76292 + 0.74576I
−3.08113 − 0.81431I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.361960 + 0.297233I
a = 0.612441 − 0.128457I
b = 0.825978 − 0.180047I
−1.53269 + 6.33362I 0
u = −1.361960 − 0.297233I
a = 0.612441 + 0.128457I
b = 0.825978 + 0.180047I
−1.53269 − 6.33362I 0
u = 1.395060 + 0.057125I
a = 0.21679 − 2.46918I
b = 0.109256 − 1.376090I
−4.71583 − 3.31857I 0
u = 1.395060 − 0.057125I
a = 0.21679 + 2.46918I
b = 0.109256 + 1.376090I
−4.71583 + 3.31857I 0
u = 1.395630 + 0.187546I
a = −1.21124 − 2.32835I
b = −0.04024 − 1.84969I
−6.87980 − 5.59995I 0
u = 1.395630 − 0.187546I
a = −1.21124 + 2.32835I
b = −0.04024 + 1.84969I
−6.87980 + 5.59995I 0
u = −0.130721 + 0.564242I
a = −0.81966 − 1.40814I
b = −0.174294 + 0.402763I
5.03065 + 2.91197I 0
u = −0.130721 − 0.564242I
a = −0.81966 + 1.40814I
b = −0.174294 − 0.402763I
5.03065 − 2.91197I 0
u = −0.476447 + 0.316086I
a = 0.493099 − 0.642060I
b = −0.731484 − 1.186380I
3.62319 − 0.56871I 0
u = −0.476447 − 0.316086I
a = 0.493099 + 0.642060I
b = −0.731484 + 1.186380I
3.62319 + 0.56871I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43415 + 0.18496I
a = 1.53348 − 2.15932I
b = 0.47839 − 2.33301I
−5.39383 + 0.67456I 0
u = −1.43415 − 0.18496I
a = 1.53348 + 2.15932I
b = 0.47839 + 2.33301I
−5.39383 − 0.67456I 0
u = −1.44236 + 0.10379I
a = 0.263305 − 0.348512I
b = 1.089260 − 0.781730I
−5.37237 − 2.41269I 0
u = −1.44236 − 0.10379I
a = 0.263305 + 0.348512I
b = 1.089260 + 0.781730I
−5.37237 + 2.41269I 0
u = −1.42708 + 0.25184I
a = −0.34989 + 2.76349I
b = 1.61491 + 2.06056I
−4.41116 + 8.47604I 0
u = −1.42708 − 0.25184I
a = −0.34989 − 2.76349I
b = 1.61491 − 2.06056I
−4.41116 − 8.47604I 0
u = −1.43628 + 0.20856I
a = −0.22358 + 1.73503I
b = 1.196200 + 0.638607I
−9.16387 + 4.05703I 0
u = −1.43628 − 0.20856I
a = −0.22358 − 1.73503I
b = 1.196200 − 0.638607I
−9.16387 − 4.05703I 0
u = −1.44630 + 0.17990I
a = −0.165006 − 0.086158I
b = −0.853185 + 0.249209I
−7.57713 + 2.60992I 0
u = −1.44630 − 0.17990I
a = −0.165006 + 0.086158I
b = −0.853185 − 0.249209I
−7.57713 − 2.60992I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44080 + 0.23751I
a = 0.97728 − 1.53055I
b = 0.233743 − 1.166650I
−8.72321 + 5.31358I 0
u = −1.44080 − 0.23751I
a = 0.97728 + 1.53055I
b = 0.233743 + 1.166650I
−8.72321 − 5.31358I 0
u = −1.43345 + 0.31707I
a = −0.146080 − 0.442910I
b = 0.451725 − 0.171945I
−2.13477 + 11.78310I 0
u = −1.43345 − 0.31707I
a = −0.146080 + 0.442910I
b = 0.451725 + 0.171945I
−2.13477 − 11.78310I 0
u = −1.45299 + 0.24669I
a = −0.670793 + 0.589860I
b = −0.83242 + 1.14754I
−6.57708 + 7.15153I 0
u = −1.45299 − 0.24669I
a = −0.670793 − 0.589860I
b = −0.83242 − 1.14754I
−6.57708 − 7.15153I 0
u = −0.220048 + 0.470245I
a = −1.45606 + 0.27415I
b = 0.132066 + 1.362320I
−1.67452 + 3.13091I 0. − 4.61042I
u = −0.220048 − 0.470245I
a = −1.45606 − 0.27415I
b = 0.132066 − 1.362320I
−1.67452 − 3.13091I 0. + 4.61042I
u = 0.169375 + 0.489161I
a = −2.69024 − 0.96416I
b = 1.33643 + 1.10743I
1.88655 + 1.65023I 0
u = 0.169375 − 0.489161I
a = −2.69024 + 0.96416I
b = 1.33643 − 1.10743I
1.88655 − 1.65023I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46709 + 0.23777I
a = 0.37141 + 2.44450I
b = −1.06288 + 1.98251I
−3.56917 − 11.75340I 0
u = 1.46709 − 0.23777I
a = 0.37141 − 2.44450I
b = −1.06288 − 1.98251I
−3.56917 + 11.75340I 0
u = −1.45682 + 0.33683I
a = −1.25834 + 1.75821I
b = 0.29126 + 2.12439I
−9.7181 + 12.1998I 0
u = −1.45682 − 0.33683I
a = −1.25834 − 1.75821I
b = 0.29126 − 2.12439I
−9.7181 − 12.1998I 0
u = −1.49467 + 0.27154I
a = −0.60073 + 1.97944I
b = 0.42932 + 1.82551I
−8.70050 + 9.40227I 0
u = −1.49467 − 0.27154I
a = −0.60073 − 1.97944I
b = 0.42932 − 1.82551I
−8.70050 − 9.40227I 0
u = −1.47646 + 0.38036I
a = 0.69606 − 2.10476I
b = −1.44135 − 1.94162I
−6.2538 + 19.1081I 0
u = −1.47646 − 0.38036I
a = 0.69606 + 2.10476I
b = −1.44135 + 1.94162I
−6.2538 − 19.1081I 0
u = −1.48158 + 0.40940I
a = 0.33044 − 1.94155I
b = −2.04237 − 1.49424I
−6.71754 + 9.96409I 0
u = −1.48158 − 0.40940I
a = 0.33044 + 1.94155I
b = −2.04237 + 1.49424I
−6.71754 − 9.96409I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52583 + 0.19237I
a = 0.48679 − 1.40099I
b = −0.634984 − 1.180570I
−9.92744 + 2.15814I 0
u = −1.52583 − 0.19237I
a = 0.48679 + 1.40099I
b = −0.634984 + 1.180570I
−9.92744 − 2.15814I 0
u = −1.55026 + 0.04901I
a = −0.28086 − 2.10795I
b = −0.88426 − 1.97881I
−13.95940 − 1.16927I 0
u = −1.55026 − 0.04901I
a = −0.28086 + 2.10795I
b = −0.88426 + 1.97881I
−13.95940 + 1.16927I 0
u = 0.435611 + 0.084902I
a = −2.50008 + 2.78780I
b = 0.626643 − 1.059520I
0.75859 − 3.24972I −3.33882 + 7.37039I
u = 0.435611 − 0.084902I
a = −2.50008 − 2.78780I
b = 0.626643 + 1.059520I
0.75859 + 3.24972I −3.33882 − 7.37039I
u = −1.53409 + 0.31891I
a = −0.77421 + 1.73372I
b = 0.64737 + 2.34212I
−8.13468 + 7.32693I 0
u = −1.53409 − 0.31891I
a = −0.77421 − 1.73372I
b = 0.64737 − 2.34212I
−8.13468 − 7.32693I 0
u = 1.49661 + 0.46709I
a = −0.04787 + 1.76466I
b = −2.70406 + 0.98122I
−4.64544 − 1.87466I 0
u = 1.49661 − 0.46709I
a = −0.04787 − 1.76466I
b = −2.70406 − 0.98122I
−4.64544 + 1.87466I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59096 + 0.14068I
a = −0.54729 − 1.96960I
b = 0.13724 − 2.60910I
−4.06225 + 0.19731I 0
u = 1.59096 − 0.14068I
a = −0.54729 + 1.96960I
b = 0.13724 + 2.60910I
−4.06225 − 0.19731I 0
u = −0.073283 + 0.370574I
a = 2.38317 − 0.06342I
b = −0.043622 − 0.725438I
−1.62444 − 1.37557I −2.92985 + 3.86022I
u = −0.073283 − 0.370574I
a = 2.38317 + 0.06342I
b = −0.043622 + 0.725438I
−1.62444 + 1.37557I −2.92985 − 3.86022I
u = −1.64351 + 0.02769I
a = −0.24515 − 2.01215I
b = −0.46408 − 2.57352I
−12.25150 + 6.55987I 0
u = −1.64351 − 0.02769I
a = −0.24515 + 2.01215I
b = −0.46408 + 2.57352I
−12.25150 − 6.55987I 0
u = −0.097591 + 0.291894I
a = −0.039504 + 1.142780I
b = 0.411801 + 0.371975I
1.35306 + 0.46632I 5.92593 − 0.52773I
u = −0.097591 − 0.291894I
a = −0.039504 − 1.142780I
b = 0.411801 − 0.371975I
1.35306 − 0.46632I 5.92593 + 0.52773I
u = −0.194799 + 0.102366I
a = 0.35736 + 4.32856I
b = 0.522501 + 0.963381I
0.38694 + 2.59415I 0.37875 − 4.06475I
u = −0.194799 − 0.102366I
a = 0.35736 − 4.32856I
b = 0.522501 − 0.963381I
0.38694 − 2.59415I 0.37875 + 4.06475I
17
II. I
u
2
=
h5u
19
+12u
18
+· · ·+b+5, 3u
19
+11u
18
+· · ·+a+11u, u
20
+4u
19
+· · ·−5u+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
11
=
−3u
19
− 11u
18
+ ··· − u
2
− 11u
−5u
19
− 12u
18
+ ··· + 31u − 5
a
6
=
9u
19
+ 28u
18
+ ··· + 70u
2
− 9u
6u
19
+ 16u
18
+ ··· − 34u + 7
a
7
=
3u
19
+ 12u
18
+ ··· + 25u − 7
6u
19
+ 16u
18
+ ··· − 34u + 7
a
10
=
−5u
19
− 15u
18
+ ··· − 7u + 1
−5u
19
− 12u
18
+ ··· + 31u − 6
a
8
=
−4u
19
− 10u
18
+ ··· + 21u − 5
−u
19
− u
18
+ ··· − 10u
3
+ u
a
12
=
−2u
19
− 9u
18
+ ··· − 26u + 4
−9u
19
− 24u
18
+ ··· + 52u − 9
a
9
=
2u
19
+ 4u
18
+ ··· − 4u − 1
4u
19
+ 12u
18
+ ··· − 21u + 4
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 23u
19
+ 65u
18
−128u
17
−417u
16
+ 349u
15
+ 1036u
14
−842u
13
−1095u
12
+ 1813u
11
+
107u
10
−2150u
9
+ 923u
8
+ 698u
7
−773u
6
+ 630u
5
−157u
4
−294u
3
+ 329u
2
−131u + 25
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
20
+ 4u
19
+ ··· − 5u + 1
c
3
u
20
− 6u
18
+ ··· − 3u + 1
c
4
u
20
− 4u
19
+ ··· + 5u + 1
c
5
u
20
+ 10u
18
+ ··· − 3u + 1
c
6
u
20
+ 3u
19
+ ··· + 10u
2
+ 1
c
7
u
20
− 5u
17
+ ··· + 3u + 1
c
8
u
20
− 6u
18
+ ··· + 3u + 1
c
9
u
20
− 4u
18
+ ··· + 5u + 1
c
10
u
20
+ 10u
18
+ ··· + 3u + 1
c
11
u
20
− 3u
19
+ ··· + 5u
3
+ 1
c
12
u
20
− 3u
19
+ ··· + 10u
2
+ 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
20
− 20y
19
+ ··· − y + 1
c
3
, c
8
y
20
− 12y
19
+ ··· − 9y + 1
c
5
, c
10
y
20
+ 20y
19
+ ··· + 15y + 1
c
6
, c
12
y
20
+ 15y
19
+ ··· + 20y + 1
c
7
y
20
+ 6y
18
+ ··· − 5y + 1
c
9
y
20
− 8y
19
+ ··· − 5y + 1
c
11
y
20
− 5y
19
+ ··· + 6y
2
+ 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.027230 + 0.081684I
a = −2.30351 − 3.13842I
b = 0.72152 − 1.23039I
−0.30091 − 3.00431I 3.31212 − 12.78342I
u = 1.027230 − 0.081684I
a = −2.30351 + 3.13842I
b = 0.72152 + 1.23039I
−0.30091 + 3.00431I 3.31212 + 12.78342I
u = 0.501873 + 0.929654I
a = −1.211620 + 0.118420I
b = 1.07976 − 2.08773I
−1.53784 − 4.32358I −6.41394 + 6.31106I
u = 0.501873 − 0.929654I
a = −1.211620 − 0.118420I
b = 1.07976 + 2.08773I
−1.53784 + 4.32358I −6.41394 − 6.31106I
u = −0.071739 + 0.688234I
a = 0.585949 + 0.746078I
b = 0.214773 − 0.950720I
2.73376 − 3.43447I −1.29601 + 4.99499I
u = −0.071739 − 0.688234I
a = 0.585949 − 0.746078I
b = 0.214773 + 0.950720I
2.73376 + 3.43447I −1.29601 − 4.99499I
u = −1.295880 + 0.302541I
a = 0.191219 + 0.525405I
b = 0.596979 + 0.576684I
−1.21585 + 7.07402I −6.1302 − 16.7431I
u = −1.295880 − 0.302541I
a = 0.191219 − 0.525405I
b = 0.596979 − 0.576684I
−1.21585 − 7.07402I −6.1302 + 16.7431I
u = 0.549802 + 0.356787I
a = 0.35379 + 1.94005I
b = 0.343585 + 0.431490I
−3.72172 − 0.64910I −8.97978 − 3.00915I
u = 0.549802 − 0.356787I
a = 0.35379 − 1.94005I
b = 0.343585 − 0.431490I
−3.72172 + 0.64910I −8.97978 + 3.00915I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.366330 + 0.095115I
a = 1.164800 − 0.430480I
b = 1.33275 − 1.03209I
−3.84276 − 1.04802I −4.21027 + 1.93550I
u = −1.366330 − 0.095115I
a = 1.164800 + 0.430480I
b = 1.33275 + 1.03209I
−3.84276 + 1.04802I −4.21027 − 1.93550I
u = 1.44756 + 0.28033I
a = −0.08490 − 2.03707I
b = 1.62005 − 1.28338I
−4.47222 − 1.54255I −4.86257 − 3.43959I
u = 1.44756 − 0.28033I
a = −0.08490 + 2.03707I
b = 1.62005 + 1.28338I
−4.47222 + 1.54255I −4.86257 + 3.43959I
u = −1.49847 + 0.16427I
a = 0.55236 − 1.52265I
b = −0.358673 − 1.026630I
−10.40230 + 2.81932I −12.19450 − 3.27289I
u = −1.49847 − 0.16427I
a = 0.55236 + 1.52265I
b = −0.358673 + 1.026630I
−10.40230 − 2.81932I −12.19450 + 3.27289I
u = −1.50968 + 0.30012I
a = −0.53456 + 2.05169I
b = 0.99430 + 2.10528I
−8.01378 + 8.58732I −5.27072 − 5.92160I
u = −1.50968 − 0.30012I
a = −0.53456 − 2.05169I
b = 0.99430 − 2.10528I
−8.01378 − 8.58732I −5.27072 + 5.92160I
u = 0.215636 + 0.242909I
a = −3.21354 − 1.93336I
b = 0.95496 + 1.28199I
1.16478 + 2.39395I 1.54588 − 3.97709I
u = 0.215636 − 0.242909I
a = −3.21354 + 1.93336I
b = 0.95496 − 1.28199I
1.16478 − 2.39395I 1.54588 + 3.97709I
22
III.
I
u
3
= h18445a
8
+ 1627b + · · · − 373a − 4047, 7a
9
− 20a
8
+ · · · − 2a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
11
=
a
−11.3368a
8
+ 37.1709a
7
+ ··· + 0.229256a + 2.48740
a
6
=
4.77996a
8
− 16.7935a
7
+ ··· − 0.751690a − 2.61955
16.1168a
8
− 53.9644a
7
+ ··· + 0.0190535a − 5.10695
a
7
=
−11.3368a
8
+ 37.1709a
7
+ ··· − 0.770744a + 2.48740
16.1168a
8
− 53.9644a
7
+ ··· + 0.0190535a − 5.10695
a
10
=
3.42041a
8
− 10.2717a
7
+ ··· + 0.268593a − 0.185003
−19.2532a
8
+ 64.0701a
7
+ ··· − 1.27289a + 5.78980
a
8
=
0
4.47019a
8
− 14.0670a
7
+ ··· − 1.94960a − 0.799017
a
12
=
a
11.8359a
8
− 40.0080a
7
+ ··· − 2.02151a − 2.97603
a
9
=
0
4.47019a
8
− 14.0670a
7
+ ··· − 1.94960a − 0.799017
a
3
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
29652
1627
a
8
+
116724
1627
a
7
−
144460
1627
a
6
+
30924
1627
a
5
+
45947
1627
a
4
+
20832
1627
a
3
−
45328
1627
a
2
−
8640
1627
a +
14276
1627
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
6
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
7
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
9
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
10
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
11
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
8
y
9
c
5
, c
10
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
6
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
9
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.650520 + 0.534295I
b = 0.140343 + 0.966856I
−3.42837 + 2.09337I −6.52230 − 4.24226I
u = 1.00000
a = 0.650520 − 0.534295I
b = 0.140343 − 0.966856I
−3.42837 − 2.09337I −6.52230 + 4.24226I
u = 1.00000
a = 1.17358
b = 0.512358
−0.446489 3.16660
u = 1.00000
a = 1.104930 + 0.619057I
b = 0.628449 + 0.875112I
−1.02799 + 2.45442I −8.21790 − 4.39771I
u = 1.00000
a = 1.104930 − 0.619057I
b = 0.628449 − 0.875112I
−1.02799 − 2.45442I −8.21790 + 4.39771I
u = 1.00000
a = −0.443756 + 0.532821I
b = −0.796005 − 0.733148I
2.72642 − 1.33617I 0.84367 + 3.27176I
u = 1.00000
a = −0.443756 − 0.532821I
b = −0.796005 + 0.733148I
2.72642 + 1.33617I 0.84367 − 3.27176I
u = 1.00000
a = −0.469909 + 0.043588I
b = −0.728966 + 0.986295I
1.95319 − 7.08493I 3.61934 + 1.74309I
u = 1.00000
a = −0.469909 − 0.043588I
b = −0.728966 − 0.986295I
1.95319 + 7.08493I 3.61934 − 1.74309I
26
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
9
)(u
20
+ 4u
19
+ ··· − 5u + 1)(u
130
− 14u
129
+ ··· + 35u − 49)
c
3
u
9
(u
20
− 6u
18
+ ··· − 3u + 1)(u
130
+ u
129
+ ··· − 60928u + 25088)
c
4
((u + 1)
9
)(u
20
− 4u
19
+ ··· + 5u + 1)(u
130
− 14u
129
+ ··· + 35u − 49)
c
5
(u
9
− u
8
+ ··· + u + 1)(u
20
+ 10u
18
+ ··· − 3u + 1)
· (u
130
− 2u
129
+ ··· − 4232u − 4232)
c
6
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
20
+ 3u
19
+ ··· + 10u
2
+ 1)(u
130
− 3u
129
+ ··· + 4534u − 71)
c
7
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
20
− 5u
17
+ ··· + 3u + 1)(u
130
+ 10u
129
+ ··· − 27u − 9)
c
8
u
9
(u
20
− 6u
18
+ ··· + 3u + 1)(u
130
+ u
129
+ ··· − 60928u + 25088)
c
9
(u
9
− u
8
+ ··· − u + 1)(u
20
− 4u
18
+ ··· + 5u + 1)
· (u
130
+ 18u
129
+ ··· − 8409u + 1079)
c
10
(u
9
+ u
8
+ ··· + u − 1)(u
20
+ 10u
18
+ ··· + 3u + 1)
· (u
130
− 2u
129
+ ··· − 4232u − 4232)
c
11
(u
9
+ u
8
+ ··· − u − 1)(u
20
− 3u
19
+ ··· + 5u
3
+ 1)
· (u
130
+ u
129
+ ··· − 15153510u − 893777)
c
12
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
20
− 3u
19
+ ··· + 10u
2
+ 1)(u
130
− 3u
129
+ ··· + 4534u − 71)
27
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
9
)(y
20
− 20y
19
+ ··· − y + 1)
· (y
130
− 122y
129
+ ··· − 5929y + 2401)
c
3
, c
8
y
9
(y
20
− 12y
19
+ ··· − 9y + 1)
· (y
130
− 69y
129
+ ··· − 11984437248y + 629407744)
c
5
, c
10
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
20
+ 20y
19
+ ··· + 15y + 1)
· (y
130
+ 86y
129
+ ··· + 519774240y + 17909824)
c
6
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
20
+ 15y
19
+ ··· + 20y + 1)
· (y
130
+ 81y
129
+ ··· − 16239788y + 5041)
c
7
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
20
+ 6y
18
+ ··· − 5y + 1)(y
130
− 6y
129
+ ··· + 2151y + 81)
c
9
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
20
− 8y
19
+ ··· − 5y + 1)
· (y
130
− 26y
129
+ ··· − 102045441y + 1164241)
c
11
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
20
− 5y
19
+ ··· + 6y
2
+ 1)
· (y
130
+ 13y
129
+ ··· + 20581982318772y + 798837325729)
28
