12a
1169
(K12a
1169
)
A knot diagram
1
Linearized knot diagam
4 10 7 9 11 3 12 1 2 6 5 8
Solving Sequence
3,6
7
4,10
11 2 1 5 12 9 8
c
6
c
3
c
10
c
2
c
1
c
5
c
11
c
9
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3.52939 × 10
358
u
88
− 1.05772 × 10
359
u
87
+ ··· + 6.97081 × 10
361
b + 7.41553 × 10
361
,
2.16674 × 10
361
u
88
− 7.26375 × 10
361
u
87
+ ··· + 7.24268 × 10
364
a − 1.16875 × 10
366
,
u
89
− 2u
88
+ ··· + 21705u + 1039i
I
u
2
= h−14550u
20
+ 40621u
19
+ ··· + 10007b + 23861,
43297u
20
+ 522281u
19
+ ··· + 590413a + 482394, u
21
− 3u
20
+ ··· − 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 110 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
= h3.53 × 10
358
u
88
− 1.06 × 10
359
u
87
+ · · · + 6.97 × 10
361
b + 7.42 ×
10
361
, 2.17 × 10
361
u
88
− 7.26 × 10
361
u
87
+ · · · + 7.24 × 10
364
a − 1.17 ×
10
366
, u
89
− 2u
88
+ · · · + 21705u + 1039i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
−0.000299164u
88
+ 0.00100291u
87
+ ··· + 83.3155u + 16.1369
−0.000506310u
88
+ 0.00151735u
87
+ ··· − 23.7024u − 1.06380
a
11
=
−0.000805473u
88
+ 0.00252026u
87
+ ··· + 59.6131u + 15.0731
−0.000506310u
88
+ 0.00151735u
87
+ ··· − 23.7024u − 1.06380
a
2
=
−0.0000914777u
88
+ 0.000720740u
87
+ ··· + 16.4384u − 11.3057
−0.000933091u
88
+ 0.00300921u
87
+ ··· − 3.26069u − 0.118984
a
1
=
−0.00106155u
88
+ 0.00389260u
87
+ ··· + 1.33023u − 12.0413
−0.00154278u
88
+ 0.00499981u
87
+ ··· − 13.8793u − 0.663133
a
5
=
0.00102463u
88
− 0.00409500u
87
+ ··· − 107.112u − 0.571082
0.000910114u
88
− 0.00293287u
87
+ ··· + 9.31770u + 0.203991
a
12
=
−0.00290304u
88
+ 0.00870923u
87
+ ··· − 80.1138u + 6.30898
−0.00294118u
88
+ 0.00959789u
87
+ ··· − 60.4307u − 3.05496
a
9
=
−0.0000311348u
88
+ 0.00200854u
87
+ ··· + 241.819u + 13.6918
−0.000739385u
88
+ 0.00225940u
87
+ ··· − 11.2394u − 0.123333
a
8
=
0.00306576u
88
− 0.00889713u
87
+ ··· + 170.165u + 9.84182
0.00288924u
88
− 0.00941813u
87
+ ··· + 49.9644u + 2.69032
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00522368u
88
− 0.0168283u
87
+ ··· + 167.584u + 9.76277
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
89
− 10u
88
+ ··· − 12u + 1
c
2
, c
9
u
89
− 41u
87
+ ··· − 51u − 1
c
3
, c
6
u
89
− 2u
88
+ ··· + 21705u + 1039
c
4
u
89
+ 3u
88
+ ··· + 4u + 1
c
5
, c
10
, c
11
u
89
+ u
88
+ ··· − 353u + 43
c
7
, c
8
, c
12
u
89
+ 3u
88
+ ··· + 65u + 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
89
− 2y
88
+ ··· + 104y −1
c
2
, c
9
y
89
− 82y
88
+ ··· + 881y −1
c
3
, c
6
y
89
− 80y
88
+ ··· + 9215419y −1079521
c
4
y
89
+ 3y
88
+ ··· + 496y −1
c
5
, c
10
, c
11
y
89
+ 97y
88
+ ··· − 64419y −1849
c
7
, c
8
, c
12
y
89
− 87y
88
+ ··· − 6453y −361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.931334 + 0.269749I
a = −0.578251 − 0.839253I
b = 0.357409 − 0.353734I
−0.95217 − 3.28642I 0
u = 0.931334 − 0.269749I
a = −0.578251 + 0.839253I
b = 0.357409 + 0.353734I
−0.95217 + 3.28642I 0
u = −0.683702 + 0.782007I
a = 0.88313 + 1.24505I
b = −0.139809 − 1.380880I
−1.63400 + 2.87051I 0
u = −0.683702 − 0.782007I
a = 0.88313 − 1.24505I
b = −0.139809 + 1.380880I
−1.63400 − 2.87051I 0
u = 0.954613
a = 1.56265
b = −0.697507
2.28117 0
u = −0.903684 + 0.289064I
a = 0.0396045 + 0.0524369I
b = 0.275590 − 0.485377I
−1.52290 + 1.04949I 0
u = −0.903684 − 0.289064I
a = 0.0396045 − 0.0524369I
b = 0.275590 + 0.485377I
−1.52290 − 1.04949I 0
u = −0.013811 + 0.942942I
a = 0.18457 − 1.51213I
b = 0.03603 + 1.52937I
−8.35695 − 0.67709I 0
u = −0.013811 − 0.942942I
a = 0.18457 + 1.51213I
b = 0.03603 − 1.52937I
−8.35695 + 0.67709I 0
u = 0.896896 + 0.290740I
a = 0.95110 − 1.13833I
b = −0.039136 − 0.193931I
2.11051 − 1.86504I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.896896 − 0.290740I
a = 0.95110 + 1.13833I
b = −0.039136 + 0.193931I
2.11051 + 1.86504I 0
u = −0.661981 + 0.629334I
a = −0.753931 + 0.280222I
b = 0.403012 + 0.928682I
4.63292 + 1.45826I 0
u = −0.661981 − 0.629334I
a = −0.753931 − 0.280222I
b = 0.403012 − 0.928682I
4.63292 − 1.45826I 0
u = 0.003538 + 1.088700I
a = 0.327210 + 1.020930I
b = −0.477171 − 0.360950I
4.16916 + 6.28701I 0
u = 0.003538 − 1.088700I
a = 0.327210 − 1.020930I
b = −0.477171 + 0.360950I
4.16916 − 6.28701I 0
u = −0.921629 + 0.645105I
a = 0.057292 − 0.134936I
b = −0.503933 + 0.746162I
4.07349 + 3.32852I 0
u = −0.921629 − 0.645105I
a = 0.057292 + 0.134936I
b = −0.503933 − 0.746162I
4.07349 − 3.32852I 0
u = 0.319287 + 0.789276I
a = −0.792411 − 0.134429I
b = 0.722129 + 0.150041I
7.01793 + 2.51150I 9.08872 − 1.49368I
u = 0.319287 − 0.789276I
a = −0.792411 + 0.134429I
b = 0.722129 − 0.150041I
7.01793 − 2.51150I 9.08872 + 1.49368I
u = 1.028410 + 0.522864I
a = 0.505074 + 0.569011I
b = −0.596731 + 0.439235I
4.88850 − 7.23558I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.028410 − 0.522864I
a = 0.505074 − 0.569011I
b = −0.596731 − 0.439235I
4.88850 + 7.23558I 0
u = −0.180579 + 0.814917I
a = −0.646139 − 1.146690I
b = 0.322151 + 0.497476I
−1.47609 + 3.76203I 0. − 9.26829I
u = −0.180579 − 0.814917I
a = −0.646139 + 1.146690I
b = 0.322151 − 0.497476I
−1.47609 − 3.76203I 0. + 9.26829I
u = 1.129070 + 0.306011I
a = −1.210640 + 0.100169I
b = 0.22183 − 1.79891I
−9.28201 − 1.41066I 0
u = 1.129070 − 0.306011I
a = −1.210640 − 0.100169I
b = 0.22183 + 1.79891I
−9.28201 + 1.41066I 0
u = −0.118024 + 0.779790I
a = −0.576335 + 0.141417I
b = 0.307305 − 1.310700I
2.48861 − 6.20764I 5.37925 + 2.59992I
u = −0.118024 − 0.779790I
a = −0.576335 − 0.141417I
b = 0.307305 + 1.310700I
2.48861 + 6.20764I 5.37925 − 2.59992I
u = −1.211940 + 0.104338I
a = 1.08030 − 0.96380I
b = −0.01047 − 1.46876I
−3.62934 − 1.72446I 0
u = −1.211940 − 0.104338I
a = 1.08030 + 0.96380I
b = −0.01047 + 1.46876I
−3.62934 + 1.72446I 0
u = −1.252290 + 0.101314I
a = −1.073640 − 0.032751I
b = 1.152590 − 0.748543I
−0.30805 + 4.24243I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.252290 − 0.101314I
a = −1.073640 + 0.032751I
b = 1.152590 + 0.748543I
−0.30805 − 4.24243I 0
u = −1.26739
a = 0.0280880
b = −0.551997
1.11552 0
u = 1.219740 + 0.369609I
a = −0.106898 − 0.505468I
b = −0.02563 − 1.61339I
−4.49367 − 1.95081I 0
u = 1.219740 − 0.369609I
a = −0.106898 + 0.505468I
b = −0.02563 + 1.61339I
−4.49367 + 1.95081I 0
u = −0.629546 + 0.321594I
a = 1.26046 + 1.53138I
b = −0.208640 − 1.272490I
−1.43898 + 3.12025I −8.35195 − 1.64472I
u = −0.629546 − 0.321594I
a = 1.26046 − 1.53138I
b = −0.208640 + 1.272490I
−1.43898 − 3.12025I −8.35195 + 1.64472I
u = −1.280440 + 0.183298I
a = −0.623520 + 1.073820I
b = 0.09308 + 1.49321I
−7.14221 + 4.80877I 0
u = −1.280440 − 0.183298I
a = −0.623520 − 1.073820I
b = 0.09308 − 1.49321I
−7.14221 − 4.80877I 0
u = 1.299110 + 0.141790I
a = −1.144320 − 0.129659I
b = 0.614468 − 0.550808I
−5.78881 − 2.81212I 0
u = 1.299110 − 0.141790I
a = −1.144320 + 0.129659I
b = 0.614468 + 0.550808I
−5.78881 + 2.81212I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.338370 + 0.002380I
a = 0.997858 − 0.029656I
b = −1.034650 + 0.506155I
−5.71693 + 1.52951I 0
u = −1.338370 − 0.002380I
a = 0.997858 + 0.029656I
b = −1.034650 − 0.506155I
−5.71693 − 1.52951I 0
u = −0.527970 + 0.376833I
a = 1.162140 + 0.211653I
b = −0.093728 − 0.821357I
−0.97885 + 1.56395I 2.29472 − 4.65809I
u = −0.527970 − 0.376833I
a = 1.162140 − 0.211653I
b = −0.093728 + 0.821357I
−0.97885 − 1.56395I 2.29472 + 4.65809I
u = −1.335560 + 0.303573I
a = 0.512156 − 0.850853I
b = −0.18196 − 1.51376I
−1.59230 + 10.01400I 0
u = −1.335560 − 0.303573I
a = 0.512156 + 0.850853I
b = −0.18196 + 1.51376I
−1.59230 − 10.01400I 0
u = −1.185460 + 0.696447I
a = 0.800803 + 0.443584I
b = −0.359156 − 0.783223I
−0.45269 + 3.38593I 0
u = −1.185460 − 0.696447I
a = 0.800803 − 0.443584I
b = −0.359156 + 0.783223I
−0.45269 − 3.38593I 0
u = 0.243696 + 1.356640I
a = −0.306952 + 0.966814I
b = 0.07489 − 1.54016I
−8.39372 − 5.10345I 0
u = 0.243696 − 1.356640I
a = −0.306952 − 0.966814I
b = 0.07489 + 1.54016I
−8.39372 + 5.10345I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.376360 + 0.289133I
a = 1.040330 + 0.010906I
b = −0.836173 + 0.694879I
−6.44455 − 7.59452I 0
u = 1.376360 − 0.289133I
a = 1.040330 − 0.010906I
b = −0.836173 − 0.694879I
−6.44455 + 7.59452I 0
u = 1.397410 + 0.172062I
a = 0.029498 + 0.497892I
b = 0.08139 + 1.53467I
−8.31349 + 0.26560I 0
u = 1.397410 − 0.172062I
a = 0.029498 − 0.497892I
b = 0.08139 − 1.53467I
−8.31349 − 0.26560I 0
u = 1.38142 + 0.39645I
a = −1.007090 + 0.064358I
b = 1.010180 − 0.690416I
−0.37230 − 11.33630I 0
u = 1.38142 − 0.39645I
a = −1.007090 − 0.064358I
b = 1.010180 + 0.690416I
−0.37230 + 11.33630I 0
u = 1.40649 + 0.33533I
a = 0.978871 − 0.037046I
b = −0.33721 + 1.67361I
−13.00830 − 3.83518I 0
u = 1.40649 − 0.33533I
a = 0.978871 + 0.037046I
b = −0.33721 − 1.67361I
−13.00830 + 3.83518I 0
u = −1.45742
a = −0.931036
b = 1.26060
−3.45488 0
u = −1.43613 + 0.30102I
a = −0.860532 − 0.191814I
b = 0.505598 + 0.488318I
−5.59501 + 1.07532I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43613 − 0.30102I
a = −0.860532 + 0.191814I
b = 0.505598 − 0.488318I
−5.59501 − 1.07532I 0
u = −1.39226 + 0.47607I
a = −1.239040 − 0.059772I
b = 0.21041 + 1.54984I
−12.76470 + 5.88731I 0
u = −1.39226 − 0.47607I
a = −1.239040 + 0.059772I
b = 0.21041 − 1.54984I
−12.76470 − 5.88731I 0
u = −0.430277 + 0.288675I
a = −1.14253 − 1.93662I
b = −0.481362 − 0.915091I
2.59466 − 2.91254I 0.554054 + 0.592872I
u = −0.430277 − 0.288675I
a = −1.14253 + 1.93662I
b = −0.481362 + 0.915091I
2.59466 + 2.91254I 0.554054 − 0.592872I
u = 0.213406 + 0.394964I
a = 1.212980 + 0.056615I
b = −0.432414 − 0.150020I
0.917122 + 0.532753I 8.62327 − 2.86690I
u = 0.213406 − 0.394964I
a = 1.212980 − 0.056615I
b = −0.432414 + 0.150020I
0.917122 − 0.532753I 8.62327 + 2.86690I
u = 1.55069 + 0.10378I
a = 0.008176 − 0.478475I
b = −0.18148 − 1.45535I
−3.99790 + 2.66436I 0
u = 1.55069 − 0.10378I
a = 0.008176 + 0.478475I
b = −0.18148 + 1.45535I
−3.99790 − 2.66436I 0
u = −0.118298 + 0.422920I
a = 1.181190 − 0.583974I
b = −0.138944 + 1.287620I
−3.48703 − 2.56442I 2.62635 + 1.28700I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.118298 − 0.422920I
a = 1.181190 + 0.583974I
b = −0.138944 − 1.287620I
−3.48703 + 2.56442I 2.62635 − 1.28700I
u = 1.54299 + 0.24671I
a = −0.911471 − 0.044781I
b = 0.49798 − 1.57958I
−8.75803 − 6.44090I 0
u = 1.54299 − 0.24671I
a = −0.911471 + 0.044781I
b = 0.49798 + 1.57958I
−8.75803 + 6.44090I 0
u = 0.430244
a = 2.54596
b = −0.677536
2.58420 4.24980
u = −1.53841 + 0.53588I
a = 1.045700 + 0.040301I
b = −0.27174 − 1.60793I
−14.0298 + 11.7177I 0
u = −1.53841 − 0.53588I
a = 1.045700 − 0.040301I
b = −0.27174 + 1.60793I
−14.0298 − 11.7177I 0
u = 0.16846 + 1.71362I
a = 0.171565 − 0.782096I
b = −0.13652 + 1.51030I
−2.15977 − 8.41432I 0
u = 0.16846 − 1.71362I
a = 0.171565 + 0.782096I
b = −0.13652 − 1.51030I
−2.15977 + 8.41432I 0
u = −1.61607 + 0.60920I
a = −0.952663 − 0.063958I
b = 0.32947 + 1.63016I
−7.9490 + 16.2760I 0
u = −1.61607 − 0.60920I
a = −0.952663 + 0.063958I
b = 0.32947 − 1.63016I
−7.9490 − 16.2760I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.87983
a = 0.691725
b = −0.206458
−2.91172 0
u = 1.74218 + 0.74698I
a = −0.707757 + 0.147349I
b = 0.12896 − 1.55344I
−12.52120 − 3.24098I 0
u = 1.74218 − 0.74698I
a = −0.707757 − 0.147349I
b = 0.12896 + 1.55344I
−12.52120 + 3.24098I 0
u = −0.0611465 + 0.0620373I
a = 10.86920 + 4.68264I
b = 0.266273 − 0.506645I
−1.45336 + 1.48831I 0.53428 + 3.12329I
u = −0.0611465 − 0.0620373I
a = 10.86920 − 4.68264I
b = 0.266273 + 0.506645I
−1.45336 − 1.48831I 0.53428 − 3.12329I
u = 1.62131 + 1.14628I
a = 0.620849 − 0.287375I
b = −0.10732 + 1.62136I
−8.64981 − 5.17953I 0
u = 1.62131 − 1.14628I
a = 0.620849 + 0.287375I
b = −0.10732 − 1.62136I
−8.64981 + 5.17953I 0
u = 1.97568 + 0.52699I
a = 0.666662 − 0.028414I
b = −0.08012 + 1.45137I
−8.08023 − 1.07339I 0
u = 1.97568 − 0.52699I
a = 0.666662 + 0.028414I
b = −0.08012 − 1.45137I
−8.08023 + 1.07339I 0
13
II. I
u
2
= h−14550u
20
+ 40621u
19
+ · · · + 10007b + 23861, 4.33 × 10
4
u
20
+
5.22 × 10
5
u
19
+ · · · + 5.90 × 10
5
a + 4.82 × 10
5
, u
21
− 3u
20
+ · · · − 3u + 1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
−0.0733334u
20
− 0.884603u
19
+ ··· − 2.10088u − 0.817045
1.45398u
20
− 4.05926u
19
+ ··· + 2.55591u − 2.38443
a
11
=
1.38065u
20
− 4.94386u
19
+ ··· + 0.455036u − 3.20148
1.45398u
20
− 4.05926u
19
+ ··· + 2.55591u − 2.38443
a
2
=
2.42133u
20
− 6.29378u
19
+ ··· + 6.44122u − 3.33218
−1.03482u
20
+ 2.41829u
19
+ ··· − 3.13756u + 3.16651
a
1
=
3.01039u
20
− 7.93884u
19
+ ··· + 6.35545u − 3.68082
−1.59680u
20
+ 4.05130u
19
+ ··· − 3.27446u + 3.39302
a
5
=
−3.16651u
20
+ 8.46472u
19
+ ··· − 5.95194u + 5.36198
−u − 1
a
12
=
2.25590u
20
− 6.37485u
19
+ ··· + 1.61544u − 1.00378
−0.302688u
20
+ 0.718797u
19
+ ··· − 1.97752u + 1.45398
a
9
=
−0.741662u
20
+ 1.03912u
19
+ ··· − 1.93260u − 1.96370
2.47095u
20
− 5.43984u
19
+ ··· + 8.58724u − 3.36947
a
8
=
0.865828u
20
− 2.87756u
19
+ ··· + 1.56930u − 1.46777
0.0250147u
20
− 0.0229416u
19
+ ··· + 0.394827u + 0.0971185
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1401070
590413
u
20
−
5207729
590413
u
19
+ ··· +
12397325
590413
u −
12952837
590413
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 3u
20
+ ··· + 2u − 1
c
2
u
21
+ u
20
+ ··· − u + 3
c
3
u
21
+ 3u
20
+ ··· − 3u − 1
c
4
u
21
+ u
19
+ ··· − 2u − 1
c
5
u
21
+ 12u
19
+ ··· − u + 1
c
6
u
21
− 3u
20
+ ··· − 3u + 1
c
7
, c
8
u
21
− 12u
19
+ ··· + u + 1
c
9
u
21
− u
20
+ ··· − u − 3
c
10
, c
11
u
21
+ 12u
19
+ ··· − u − 1
c
12
u
21
− 12u
19
+ ··· + u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 3y
20
+ ··· − 10y −1
c
2
, c
9
y
21
− 19y
20
+ ··· + 115y −9
c
3
, c
6
y
21
− 21y
20
+ ··· + 13y −1
c
4
y
21
+ 2y
20
+ ··· + 10y −1
c
5
, c
10
, c
11
y
21
+ 24y
20
+ ··· − y −1
c
7
, c
8
, c
12
y
21
− 24y
20
+ ··· + 17y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.930383 + 0.277435I
a = 1.015260 + 0.862529I
b = −0.328952 + 0.421695I
2.08819 + 1.44870I 3.52006 + 4.93432I
u = −0.930383 − 0.277435I
a = 1.015260 − 0.862529I
b = −0.328952 − 0.421695I
2.08819 − 1.44870I 3.52006 − 4.93432I
u = −0.648396 + 0.664203I
a = 0.909055 + 0.463752I
b = 0.447170 − 0.742674I
3.07921 + 4.35618I 0.88528 − 5.41840I
u = −0.648396 − 0.664203I
a = 0.909055 − 0.463752I
b = 0.447170 + 0.742674I
3.07921 − 4.35618I 0.88528 + 5.41840I
u = −1.12254
a = 0.474285
b = 0.350060
0.648902 −6.00040
u = 0.655950 + 0.397506I
a = 1.13303 − 1.90664I
b = −0.153365 + 1.295940I
−1.13185 − 3.22934I 15.8994 + 10.3878I
u = 0.655950 − 0.397506I
a = 1.13303 + 1.90664I
b = −0.153365 − 1.295940I
−1.13185 + 3.22934I 15.8994 − 10.3878I
u = −0.685782 + 0.264566I
a = −1.227390 + 0.116414I
b = −0.219712 + 0.602073I
−1.88174 + 2.05701I −7.23952 − 6.65923I
u = −0.685782 − 0.264566I
a = −1.227390 − 0.116414I
b = −0.219712 − 0.602073I
−1.88174 − 2.05701I −7.23952 + 6.65923I
u = 0.285973 + 0.565869I
a = 0.974671 − 0.799331I
b = 0.243921 − 1.159940I
1.48365 − 6.92231I −1.25656 + 6.03552I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.285973 − 0.565869I
a = 0.974671 + 0.799331I
b = 0.243921 + 1.159940I
1.48365 + 6.92231I −1.25656 − 6.03552I
u = 1.387470 + 0.049356I
a = 0.335276 − 0.492303I
b = 0.01597 − 1.54523I
−5.59782 − 1.13031I −2.89204 + 0.12021I
u = 1.387470 − 0.049356I
a = 0.335276 + 0.492303I
b = 0.01597 + 1.54523I
−5.59782 + 1.13031I −2.89204 − 0.12021I
u = −1.46205
a = −0.918191
b = 0.679742
−5.65099 −6.57830
u = 0.438197 + 0.182945I
a = −1.58094 − 0.53997I
b = −0.076122 + 1.201660I
−4.11956 − 3.06636I −6.09997 + 6.67662I
u = 0.438197 − 0.182945I
a = −1.58094 + 0.53997I
b = −0.076122 − 1.201660I
−4.11956 + 3.06636I −6.09997 − 6.67662I
u = 1.46185 + 0.56955I
a = −0.905072 + 0.140044I
b = 0.18031 − 1.57936I
−11.71150 − 3.26273I −1.60994 + 1.37257I
u = 1.46185 − 0.56955I
a = −0.905072 − 0.140044I
b = 0.18031 + 1.57936I
−11.71150 + 3.26273I −1.60994 − 1.37257I
u = −1.68012
a = 0.744875
b = −0.824696
−1.98125 3.79130
u = 1.66747 + 0.69754I
a = 0.695614 − 0.152518I
b = −0.21177 + 1.64691I
−8.32574 − 4.07513I −1.31294 + 0.55497I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.66747 − 0.69754I
a = 0.695614 + 0.152518I
b = −0.21177 − 1.64691I
−8.32574 + 4.07513I −1.31294 − 0.55497I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 3u
20
+ ··· + 2u − 1)(u
89
− 10u
88
+ ··· − 12u + 1)
c
2
(u
21
+ u
20
+ ··· − u + 3)(u
89
− 41u
87
+ ··· − 51u − 1)
c
3
(u
21
+ 3u
20
+ ··· − 3u − 1)(u
89
− 2u
88
+ ··· + 21705u + 1039)
c
4
(u
21
+ u
19
+ ··· − 2u − 1)(u
89
+ 3u
88
+ ··· + 4u + 1)
c
5
(u
21
+ 12u
19
+ ··· − u + 1)(u
89
+ u
88
+ ··· − 353u + 43)
c
6
(u
21
− 3u
20
+ ··· − 3u + 1)(u
89
− 2u
88
+ ··· + 21705u + 1039)
c
7
, c
8
(u
21
− 12u
19
+ ··· + u + 1)(u
89
+ 3u
88
+ ··· + 65u + 19)
c
9
(u
21
− u
20
+ ··· − u − 3)(u
89
− 41u
87
+ ··· − 51u − 1)
c
10
, c
11
(u
21
+ 12u
19
+ ··· − u − 1)(u
89
+ u
88
+ ··· − 353u + 43)
c
12
(u
21
− 12u
19
+ ··· + u − 1)(u
89
+ 3u
88
+ ··· + 65u + 19)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
− 3y
20
+ ··· − 10y −1)(y
89
− 2y
88
+ ··· + 104y −1)
c
2
, c
9
(y
21
− 19y
20
+ ··· + 115y −9)(y
89
− 82y
88
+ ··· + 881y −1)
c
3
, c
6
(y
21
− 21y
20
+ ··· + 13y −1)
· (y
89
− 80y
88
+ ··· + 9215419y −1079521)
c
4
(y
21
+ 2y
20
+ ··· + 10y −1)(y
89
+ 3y
88
+ ··· + 496y −1)
c
5
, c
10
, c
11
(y
21
+ 24y
20
+ ··· − y −1)(y
89
+ 97y
88
+ ··· − 64419y −1849)
c
7
, c
8
, c
12
(y
21
− 24y
20
+ ··· + 17y −1)(y
89
− 87y
88
+ ··· − 6453y −361)
21
