12n
0732
(K12n
0732
)
A knot diagram
1
Linearized knot diagam
4 11 7 12 11 2 1 5 2 7 9 8
Solving Sequence
2,11 3,7
4 1 6 5 10 9 12 8
c
2
c
3
c
1
c
6
c
5
c
10
c
9
c
11
c
8
c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.49919 × 10
429
u
82
− 9.68214 × 10
429
u
81
+ ··· + 4.60228 × 10
434
b + 1.01773 × 10
436
,
2.05304 × 10
436
u
82
− 7.13618 × 10
435
u
81
+ ··· + 1.09384 × 10
440
a − 4.44613 × 10
441
,
u
83
− u
82
+ ··· + 2048046u − 237673i
I
u
2
= h3.26221 × 10
19
u
23
+ 2.15398 × 10
19
u
22
+ ··· + 1.24108 × 10
19
b + 9.39258 × 10
19
,
− 4.34127 × 10
20
u
23
− 2.45018 × 10
20
u
22
+ ··· + 1.24108 × 10
19
a − 9.98705 × 10
20
, u
24
+ u
23
+ ··· + 4u + 1i
I
u
3
= hb − u + 1, a − 1, u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 109 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−3.50 × 10
429
u
82
− 9.68 × 10
429
u
81
+ · · · + 4.60 × 10
434
b + 1.02 ×
10
436
, 2.05 × 10
436
u
82
− 7.14 × 10
435
u
81
+ · · · + 1.09 × 10
440
a − 4.45 ×
10
441
, u
83
− u
82
+ · · · + 2048046u − 237673i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
−0.000187692u
82
+ 0.0000652399u
81
+ ··· − 103.466u + 40.6470
7.60316 × 10
−6
u
82
+ 0.0000210377u
81
+ ··· + 147.358u − 22.1135
a
4
=
−0.000163705u
82
+ 0.000162742u
81
+ ··· + 585.451u − 61.5724
0.0000442704u
82
− 0.0000260632u
81
+ ··· − 70.3579u + 4.73710
a
1
=
−0.000166790u
82
+ 0.0000820861u
81
+ ··· + 162.358u − 3.41475
−0.0000300517u
82
+ 0.0000474903u
81
+ ··· + 260.800u − 37.0113
a
6
=
−0.000180088u
82
+ 0.0000862776u
81
+ ··· + 43.8924u + 18.5335
7.60316 × 10
−6
u
82
+ 0.0000210377u
81
+ ··· + 147.358u − 22.1135
a
5
=
−0.000180088u
82
+ 0.0000862776u
81
+ ··· + 43.8924u + 18.5335
0.0000152790u
82
+ 0.0000407085u
81
+ ··· + 296.685u − 44.4098
a
10
=
−0.000281266u
82
+ 0.000174152u
81
+ ··· + 380.064u − 13.2873
0.0000201427u
82
− 0.0000310990u
81
+ ··· − 119.176u + 13.4499
a
9
=
−0.000261124u
82
+ 0.000143053u
81
+ ··· + 260.888u + 0.162624
0.0000201427u
82
− 0.0000310990u
81
+ ··· − 119.176u + 13.4499
a
12
=
0.000334705u
82
− 0.000159389u
81
+ ··· − 166.178u − 24.0662
−0.0000280200u
82
− 0.0000248455u
81
+ ··· − 290.374u + 47.0998
a
8
=
−0.000362649u
82
+ 0.000164944u
81
+ ··· + 185.086u + 25.2579
−0.0000348471u
82
+ 0.0000542533u
81
+ ··· + 337.625u − 45.7974
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.000301960u
82
+ 0.000391858u
81
+ ··· + 1897.38u − 240.107
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
83
− 11u
82
+ ··· − 3341u + 203
c
2
u
83
+ u
82
+ ··· + 2048046u + 237673
c
3
u
83
+ u
82
+ ··· − 15388u + 2108
c
4
u
83
+ 3u
82
+ ··· − 16u + 1
c
5
u
83
− 15u
81
+ ··· − 663559u + 83839
c
6
u
83
+ 5u
82
+ ··· + 97593u + 5351
c
7
, c
12
u
83
− 3u
82
+ ··· + 1495u + 103
c
8
u
83
+ 6u
82
+ ··· + 322u + 29
c
9
u
83
− 3u
82
+ ··· + 23642902u + 6207563
c
10
u
83
− 2u
82
+ ··· + 130300u + 11257
c
11
u
83
− 12u
82
+ ··· − 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
83
+ 5y
82
+ ··· − 397351y −41209
c
2
y
83
+ 93y
82
+ ··· − 1365124926432y −56488454929
c
3
y
83
+ 15y
82
+ ··· − 56398528y −4443664
c
4
y
83
− 11y
82
+ ··· + 50y −1
c
5
y
83
− 30y
82
+ ··· + 63722693959y −7028977921
c
6
y
83
+ 97y
82
+ ··· − 743094449y −28633201
c
7
, c
12
y
83
+ 59y
82
+ ··· − 208547y −10609
c
8
y
83
− 12y
82
+ ··· + 29850y −841
c
9
y
83
+ 53y
82
+ ··· − 759411803692702y −38533838398969
c
10
y
83
− 98y
82
+ ··· + 5637157808y −126720049
c
11
y
83
+ 22y
82
+ ··· + 68y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.414352 + 0.904844I
a = 0.818742 − 0.835049I
b = −0.234982 + 1.126650I
−0.50253 − 2.71042I 0
u = 0.414352 − 0.904844I
a = 0.818742 + 0.835049I
b = −0.234982 − 1.126650I
−0.50253 + 2.71042I 0
u = −1.028260 + 0.017055I
a = 0.537212 + 0.257597I
b = 1.340570 − 0.138864I
−4.09989 + 1.06646I 0
u = −1.028260 − 0.017055I
a = 0.537212 − 0.257597I
b = 1.340570 + 0.138864I
−4.09989 − 1.06646I 0
u = 0.417263 + 0.866402I
a = 0.318885 − 0.410092I
b = −1.098590 + 0.129272I
−3.34845 − 4.34438I 0. + 7.77500I
u = 0.417263 − 0.866402I
a = 0.318885 + 0.410092I
b = −1.098590 − 0.129272I
−3.34845 + 4.34438I 0. − 7.77500I
u = −0.572659 + 0.744013I
a = 0.505280 − 0.031757I
b = 1.191840 + 0.333632I
−4.39495 − 1.29965I −4.00000 + 3.00721I
u = −0.572659 − 0.744013I
a = 0.505280 + 0.031757I
b = 1.191840 − 0.333632I
−4.39495 + 1.29965I −4.00000 − 3.00721I
u = −1.040930 + 0.307428I
a = −0.273096 − 0.755471I
b = 0.451724 + 0.662973I
−3.60574 − 2.70826I 0
u = −1.040930 − 0.307428I
a = −0.273096 + 0.755471I
b = 0.451724 − 0.662973I
−3.60574 + 2.70826I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637570 + 0.910156I
a = 1.063740 + 0.356958I
b = 0.347803 − 0.186767I
−4.05843 + 0.77081I 0
u = 0.637570 − 0.910156I
a = 1.063740 − 0.356958I
b = 0.347803 + 0.186767I
−4.05843 − 0.77081I 0
u = 0.177985 + 1.106920I
a = 0.489709 − 1.232370I
b = −0.21437 + 1.49408I
−0.48146 − 2.63965I 0
u = 0.177985 − 1.106920I
a = 0.489709 + 1.232370I
b = −0.21437 − 1.49408I
−0.48146 + 2.63965I 0
u = 0.671577 + 0.559435I
a = −0.79653 − 1.25063I
b = 0.100737 + 0.378624I
−4.38490 + 1.02535I −8.49512 + 1.62379I
u = 0.671577 − 0.559435I
a = −0.79653 + 1.25063I
b = 0.100737 − 0.378624I
−4.38490 − 1.02535I −8.49512 − 1.62379I
u = −0.345440 + 0.798324I
a = −1.81170 − 0.41097I
b = 1.42764 + 1.03205I
−0.93031 + 4.30963I −10.3870 − 14.3250I
u = −0.345440 − 0.798324I
a = −1.81170 + 0.41097I
b = 1.42764 − 1.03205I
−0.93031 − 4.30963I −10.3870 + 14.3250I
u = −0.301371 + 0.752449I
a = −1.98642 + 0.02905I
b = 0.321899 − 0.106934I
−3.76643 − 9.37621I −3.18784 + 5.46497I
u = −0.301371 − 0.752449I
a = −1.98642 − 0.02905I
b = 0.321899 + 0.106934I
−3.76643 + 9.37621I −3.18784 − 5.46497I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.773390 + 0.175831I
a = 0.369949 − 0.128530I
b = 0.794235 − 0.233534I
−1.178940 − 0.026902I −2.24486 − 0.66294I
u = 0.773390 − 0.175831I
a = 0.369949 + 0.128530I
b = 0.794235 + 0.233534I
−1.178940 + 0.026902I −2.24486 + 0.66294I
u = 0.379090 + 0.679111I
a = 0.310084 + 0.343934I
b = −1.53351 + 0.59005I
−4.03656 + 9.14747I −3.08929 − 4.48071I
u = 0.379090 − 0.679111I
a = 0.310084 − 0.343934I
b = −1.53351 − 0.59005I
−4.03656 − 9.14747I −3.08929 + 4.48071I
u = −0.585406 + 1.076470I
a = 0.769362 − 0.107344I
b = 0.067450 − 0.608539I
−1.13069 + 3.60924I 0
u = −0.585406 − 1.076470I
a = 0.769362 + 0.107344I
b = 0.067450 + 0.608539I
−1.13069 − 3.60924I 0
u = −0.608231 + 0.426041I
a = 0.659662 + 0.542829I
b = −0.184618 + 0.399153I
2.56481 + 0.56873I 1.41112 − 2.57174I
u = −0.608231 − 0.426041I
a = 0.659662 − 0.542829I
b = −0.184618 − 0.399153I
2.56481 − 0.56873I 1.41112 + 2.57174I
u = 1.064550 + 0.709606I
a = 0.526848 − 0.134656I
b = 0.134105 + 0.347107I
−2.03220 − 2.79313I 0
u = 1.064550 − 0.709606I
a = 0.526848 + 0.134656I
b = 0.134105 − 0.347107I
−2.03220 + 2.79313I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.166100 + 0.526433I
a = −0.305083 + 0.019879I
b = −0.220833 − 0.594073I
1.82630 + 4.81831I 0
u = −1.166100 − 0.526433I
a = −0.305083 − 0.019879I
b = −0.220833 + 0.594073I
1.82630 − 4.81831I 0
u = −0.205221 + 0.687069I
a = 0.768610 − 0.379877I
b = −1.303500 − 0.456175I
1.29077 − 3.56733I 1.02756 + 5.38922I
u = −0.205221 − 0.687069I
a = 0.768610 + 0.379877I
b = −1.303500 + 0.456175I
1.29077 + 3.56733I 1.02756 − 5.38922I
u = −1.239500 + 0.371890I
a = 0.651770 − 0.371480I
b = 0.435731 + 0.296635I
−3.67543 − 1.63059I 0
u = −1.239500 − 0.371890I
a = 0.651770 + 0.371480I
b = 0.435731 − 0.296635I
−3.67543 + 1.63059I 0
u = 0.692399 + 0.077190I
a = 1.163320 − 0.065011I
b = 0.158615 − 0.881612I
−0.69388 + 3.26055I −4.25295 − 4.21550I
u = 0.692399 − 0.077190I
a = 1.163320 + 0.065011I
b = 0.158615 + 0.881612I
−0.69388 − 3.26055I −4.25295 + 4.21550I
u = 0.422423 + 1.314500I
a = −0.553764 + 1.137490I
b = −0.34607 − 1.85608I
4.09935 − 1.72757I 0
u = 0.422423 − 1.314500I
a = −0.553764 − 1.137490I
b = −0.34607 + 1.85608I
4.09935 + 1.72757I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591218
a = 0.492574
b = 0.792557
−1.19065 −5.17470
u = 0.46810 + 1.33998I
a = 0.109017 − 1.294080I
b = −0.29965 + 1.64714I
5.93412 − 1.92291I 0
u = 0.46810 − 1.33998I
a = 0.109017 + 1.294080I
b = −0.29965 − 1.64714I
5.93412 + 1.92291I 0
u = −0.039654 + 0.574075I
a = 1.55657 + 0.40480I
b = −0.354654 + 0.415931I
0.25628 − 1.95793I 0.76700 + 3.94410I
u = −0.039654 − 0.574075I
a = 1.55657 − 0.40480I
b = −0.354654 − 0.415931I
0.25628 + 1.95793I 0.76700 − 3.94410I
u = 0.09161 + 1.49038I
a = 0.157174 + 1.324810I
b = −0.70464 − 1.82638I
5.65852 − 3.30039I 0
u = 0.09161 − 1.49038I
a = 0.157174 − 1.324810I
b = −0.70464 + 1.82638I
5.65852 + 3.30039I 0
u = 0.202641 + 0.448566I
a = −2.95926 − 0.10425I
b = 0.689201 + 0.115151I
0.45787 + 3.68682I 1.09725 − 1.38698I
u = 0.202641 − 0.448566I
a = −2.95926 + 0.10425I
b = 0.689201 − 0.115151I
0.45787 − 3.68682I 1.09725 + 1.38698I
u = 0.330652 + 0.359921I
a = 1.81179 − 0.11132I
b = 1.141310 + 0.719359I
−2.58496 − 1.33025I −4.54267 + 0.24463I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.330652 − 0.359921I
a = 1.81179 + 0.11132I
b = 1.141310 − 0.719359I
−2.58496 + 1.33025I −4.54267 − 0.24463I
u = 1.47401 + 0.34353I
a = −0.530455 − 0.057065I
b = −0.327942 + 0.676870I
−2.11190 − 9.30846I 0
u = 1.47401 − 0.34353I
a = −0.530455 + 0.057065I
b = −0.327942 − 0.676870I
−2.11190 + 9.30846I 0
u = 0.236925 + 0.417535I
a = 1.25133 + 1.31707I
b = 0.011013 + 0.527287I
−0.39541 − 2.01429I −2.84666 + 4.46361I
u = 0.236925 − 0.417535I
a = 1.25133 − 1.31707I
b = 0.011013 − 0.527287I
−0.39541 + 2.01429I −2.84666 − 4.46361I
u = −0.21429 + 1.55945I
a = −0.084526 + 1.258460I
b = 0.28263 − 2.02678I
8.82612 + 3.64300I 0
u = −0.21429 − 1.55945I
a = −0.084526 − 1.258460I
b = 0.28263 + 2.02678I
8.82612 − 3.64300I 0
u = −0.32416 + 1.63100I
a = 0.089654 + 1.094170I
b = −0.26089 − 1.69470I
6.91762 + 0.07901I 0
u = −0.32416 − 1.63100I
a = 0.089654 − 1.094170I
b = −0.26089 + 1.69470I
6.91762 − 0.07901I 0
u = 0.06848 + 1.67430I
a = 0.135743 + 1.110070I
b = −0.22960 − 1.48707I
5.24143 − 2.04516I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06848 − 1.67430I
a = 0.135743 − 1.110070I
b = −0.22960 + 1.48707I
5.24143 + 2.04516I 0
u = −0.43500 + 1.67959I
a = 0.032353 − 1.130650I
b = −0.15356 + 1.52921I
1.75253 + 8.69397I 0
u = −0.43500 − 1.67959I
a = 0.032353 + 1.130650I
b = −0.15356 − 1.52921I
1.75253 − 8.69397I 0
u = −0.38585 + 1.74072I
a = 0.098702 + 0.779884I
b = 0.56146 − 1.98339I
2.44247 + 7.16275I 0
u = −0.38585 − 1.74072I
a = 0.098702 − 0.779884I
b = 0.56146 + 1.98339I
2.44247 − 7.16275I 0
u = −0.19041 + 1.78225I
a = −0.262423 − 0.898122I
b = −0.34219 + 1.82899I
9.74534 − 1.33402I 0
u = −0.19041 − 1.78225I
a = −0.262423 + 0.898122I
b = −0.34219 − 1.82899I
9.74534 + 1.33402I 0
u = −0.41279 + 1.75000I
a = −0.056811 − 1.110350I
b = −0.45263 + 1.93300I
9.4871 + 10.9918I 0
u = −0.41279 − 1.75000I
a = −0.056811 + 1.110350I
b = −0.45263 − 1.93300I
9.4871 − 10.9918I 0
u = 0.21850 + 1.80286I
a = 0.150227 + 0.988006I
b = 0.37037 − 1.50853I
8.03484 + 1.01421I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21850 − 1.80286I
a = 0.150227 − 0.988006I
b = 0.37037 + 1.50853I
8.03484 − 1.01421I 0
u = 0.26361 + 1.80476I
a = −0.127641 − 0.996713I
b = 0.29776 + 1.98890I
7.10818 − 8.02637I 0
u = 0.26361 − 1.80476I
a = −0.127641 + 0.996713I
b = 0.29776 − 1.98890I
7.10818 + 8.02637I 0
u = 0.58577 + 1.80045I
a = −0.096228 + 1.043080I
b = −0.42567 − 1.97742I
4.7687 − 17.1701I 0
u = 0.58577 − 1.80045I
a = −0.096228 − 1.043080I
b = −0.42567 + 1.97742I
4.7687 + 17.1701I 0
u = 0.39418 + 1.91028I
a = 0.097542 − 0.907782I
b = 0.34950 + 1.88034I
6.81458 − 5.87576I 0
u = 0.39418 − 1.91028I
a = 0.097542 + 0.907782I
b = 0.34950 − 1.88034I
6.81458 + 5.87576I 0
u = 0.10550 + 2.05313I
a = 0.113249 − 0.915035I
b = 0.32092 + 1.73513I
7.40347 − 6.14595I 0
u = 0.10550 − 2.05313I
a = 0.113249 + 0.915035I
b = 0.32092 − 1.73513I
7.40347 + 6.14595I 0
u = −0.02637 + 2.06647I
a = −0.139226 + 0.783931I
b = −0.28831 − 1.90761I
6.56568 + 5.36669I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.02637 − 2.06647I
a = −0.139226 − 0.783931I
b = −0.28831 + 1.90761I
6.56568 − 5.36669I 0
u = −0.76454 + 1.92604I
a = 0.178371 + 0.912927I
b = 0.28342 − 1.88805I
4.14225 + 7.38613I 0
u = −0.76454 − 1.92604I
a = 0.178371 − 0.912927I
b = 0.28342 + 1.88805I
4.14225 − 7.38613I 0
13
II.
I
u
2
= h3.26×10
19
u
23
+2.15×10
19
u
22
+· · ·+1.24×10
19
b+9.39×10
19
, −4.34×
10
20
u
23
−2.45×10
20
u
22
+· · ·+1.24×10
19
a−9.99×10
20
, u
24
+u
23
+· · ·+4u+1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u
2
a
7
=
34.9798u
23
+ 19.7424u
22
+ ··· + 137.849u + 80.4708
−2.62853u
23
− 1.73557u
22
+ ··· − 10.2826u − 7.56808
a
4
=
−28.5351u
23
− 15.9884u
22
+ ··· − 112.157u − 63.1806
13.4031u
23
+ 7.72081u
22
+ ··· + 51.6847u + 31.9247
a
1
=
−7.56905u
23
− 4.96424u
22
+ ··· − 27.4653u − 21.4742
−31.2811u
23
− 17.8433u
22
+ ··· − 121.217u − 72.6535
a
6
=
32.3513u
23
+ 18.0068u
22
+ ··· + 127.567u + 72.9027
−2.62853u
23
− 1.73557u
22
+ ··· − 10.2826u − 7.56808
a
5
=
32.3513u
23
+ 18.0068u
22
+ ··· + 127.567u + 72.9027
3.82260u
23
+ 1.83181u
22
+ ··· + 14.7442u + 6.77644
a
10
=
−19.0402u
23
− 11.4933u
22
+ ··· − 72.3152u − 45.7048
−15.6774u
23
− 8.75510u
22
+ ··· − 60.1068u − 36.0819
a
9
=
−34.7175u
23
− 20.2484u
22
+ ··· − 132.422u − 81.7867
−15.6774u
23
− 8.75510u
22
+ ··· − 60.1068u − 36.0819
a
12
=
61.4214u
23
+ 35.0090u
22
+ ··· + 237.201u + 141.518
13.4378u
23
+ 7.40964u
22
+ ··· + 53.9669u + 30.4043
a
8
=
−52.6961u
23
− 29.7451u
22
+ ··· − 204.711u − 119.875
−1.22123u
23
− 0.360132u
22
+ ··· − 6.61842u − 1.30809
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1428788128592264638684
12410773587008329543
u
23
+
812223884015341884174
12410773587008329543
u
22
+ ··· +
5622798522107108947686
12410773587008329543
u +
3194870140513627405289
12410773587008329543
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
24
− 11u
23
+ ··· − 5u + 1
c
2
u
24
+ u
23
+ ··· + 4u + 1
c
3
u
24
− 5u
21
+ ··· − 97u + 31
c
4
u
24
− 3u
23
+ ··· − 12u + 1
c
5
u
24
− 2u
23
+ ··· − 77u + 29
c
6
u
24
+ 7u
23
+ ··· + 143u + 37
c
7
u
24
+ u
23
+ ··· + 9u + 1
c
8
u
24
− 4u
23
+ ··· − 4u + 1
c
9
u
24
− 3u
23
+ ··· + 2u + 1
c
10
u
24
− 5u
22
+ ··· − 2u + 1
c
11
u
24
+ 6u
23
+ ··· + 2u + 1
c
12
u
24
− u
23
+ ··· − 9u + 1
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 7y
23
+ ··· + 19y + 1
c
2
y
24
+ 13y
23
+ ··· − 12y + 1
c
3
y
24
+ 22y
22
+ ··· − 9533y + 961
c
4
y
24
− 11y
23
+ ··· − 38y + 1
c
5
y
24
− 10y
23
+ ··· + 8513y + 841
c
6
y
24
+ 5y
23
+ ··· − 7203y + 1369
c
7
, c
12
y
24
+ 19y
23
+ ··· + 3y + 1
c
8
y
24
+ 14y
22
+ ··· − 6y + 1
c
9
y
24
+ 5y
23
+ ··· − 2y + 1
c
10
y
24
− 10y
23
+ ··· + 24y + 1
c
11
y
24
+ 2y
23
+ ··· − 16y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.809576 + 0.779992I
a = 0.174326 − 0.051460I
b = 0.902583 − 0.266585I
−3.14838 + 2.72704I −10.71163 − 4.00203I
u = −0.809576 − 0.779992I
a = 0.174326 + 0.051460I
b = 0.902583 + 0.266585I
−3.14838 − 2.72704I −10.71163 + 4.00203I
u = 0.635711 + 0.928589I
a = 0.709241 + 0.295340I
b = 0.977518 − 0.338543I
−4.90398 + 1.25886I −19.4212 − 3.3032I
u = 0.635711 − 0.928589I
a = 0.709241 − 0.295340I
b = 0.977518 + 0.338543I
−4.90398 − 1.25886I −19.4212 + 3.3032I
u = 1.141450 + 0.070256I
a = 0.439053 − 0.129771I
b = 1.39180 − 0.55196I
−4.05739 + 0.32269I −8.19576 + 3.10648I
u = 1.141450 − 0.070256I
a = 0.439053 + 0.129771I
b = 1.39180 + 0.55196I
−4.05739 − 0.32269I −8.19576 − 3.10648I
u = −1.080930 + 0.419496I
a = 0.528614 − 0.722136I
b = 0.218156 + 0.631342I
−2.71433 − 1.83987I −0.92922 + 3.25332I
u = −1.080930 − 0.419496I
a = 0.528614 + 0.722136I
b = 0.218156 − 0.631342I
−2.71433 + 1.83987I −0.92922 − 3.25332I
u = −0.291317 + 0.760773I
a = −1.68250 − 0.80233I
b = 1.22598 + 0.77029I
−0.84760 + 3.74018I −4.99835 − 2.41418I
u = −0.291317 − 0.760773I
a = −1.68250 + 0.80233I
b = 1.22598 − 0.77029I
−0.84760 − 3.74018I −4.99835 + 2.41418I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.711004 + 0.229664I
a = 0.784779 − 0.421989I
b = 0.819804 − 0.313488I
−1.41771 − 0.70280I −5.39059 + 6.53110I
u = −0.711004 − 0.229664I
a = 0.784779 + 0.421989I
b = 0.819804 + 0.313488I
−1.41771 + 0.70280I −5.39059 − 6.53110I
u = 0.672936 + 0.306989I
a = 0.19918 − 1.75721I
b = −0.568537 + 0.491944I
−4.68331 + 2.09852I −11.02976 − 3.59872I
u = 0.672936 − 0.306989I
a = 0.19918 + 1.75721I
b = −0.568537 − 0.491944I
−4.68331 − 2.09852I −11.02976 + 3.59872I
u = 0.348106 + 0.501012I
a = 1.65826 + 1.15366I
b = −0.961006 + 0.120617I
0.04901 − 4.35938I −4.33045 + 10.29410I
u = 0.348106 − 0.501012I
a = 1.65826 − 1.15366I
b = −0.961006 − 0.120617I
0.04901 + 4.35938I −4.33045 − 10.29410I
u = −0.26256 + 1.52051I
a = −0.050281 + 1.172670I
b = −0.25452 − 1.65974I
7.65033 + 1.09732I 0.55669 − 1.40274I
u = −0.26256 − 1.52051I
a = −0.050281 − 1.172670I
b = −0.25452 + 1.65974I
7.65033 − 1.09732I 0.55669 + 1.40274I
u = −0.09913 + 1.54901I
a = −0.107671 + 1.228790I
b = 0.61069 − 1.75130I
5.46672 + 3.23345I −16.5379 − 0.7498I
u = −0.09913 − 1.54901I
a = −0.107671 − 1.228790I
b = 0.61069 + 1.75130I
5.46672 − 3.23345I −16.5379 + 0.7498I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.430895 + 0.011507I
a = −0.66609 + 2.28354I
b = −1.102640 − 0.193314I
−5.18556 − 9.79729I −10.06078 + 7.60329I
u = −0.430895 − 0.011507I
a = −0.66609 − 2.28354I
b = −1.102640 + 0.193314I
−5.18556 + 9.79729I −10.06078 − 7.60329I
u = 0.38721 + 2.06635I
a = 0.013086 − 0.855197I
b = 0.24017 + 1.92138I
5.56755 − 7.24275I 0
u = 0.38721 − 2.06635I
a = 0.013086 + 0.855197I
b = 0.24017 − 1.92138I
5.56755 + 7.24275I 0
21
III. I
u
3
= hb − u + 1, a − 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
1
0
a
11
=
0
u
a
3
=
1
u − 1
a
7
=
1
u − 1
a
4
=
1
u − 1
a
1
=
−u + 2
u
a
6
=
u
u − 1
a
5
=
u
u − 2
a
10
=
−u
u + 1
a
9
=
1
u + 1
a
12
=
−u
−u + 1
a
8
=
2u
u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u − 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
, c
11
, c
12
u
2
+ u + 1
c
2
, c
6
, c
7
u
2
− u + 1
c
3
u
2
c
8
, c
9
u
2
+ 3u + 3
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
2
+ y + 1
c
3
y
2
c
8
, c
9
y
2
− 3y + 9
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.00000
b = −0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
u = 0.500000 − 0.866025I
a = 1.00000
b = −0.500000 − 0.866025I
4.05977I 0. − 6.92820I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
24
− 11u
23
+ ··· − 5u + 1)
· (u
83
− 11u
82
+ ··· − 3341u + 203)
c
2
(u
2
− u + 1)(u
24
+ u
23
+ ··· + 4u + 1)
· (u
83
+ u
82
+ ··· + 2048046u + 237673)
c
3
u
2
(u
24
− 5u
21
+ ··· − 97u + 31)(u
83
+ u
82
+ ··· − 15388u + 2108)
c
4
(u
2
+ u + 1)(u
24
− 3u
23
+ ··· − 12u + 1)(u
83
+ 3u
82
+ ··· − 16u + 1)
c
5
(u
2
+ u + 1)(u
24
− 2u
23
+ ··· − 77u + 29)
· (u
83
− 15u
81
+ ··· − 663559u + 83839)
c
6
(u
2
− u + 1)(u
24
+ 7u
23
+ ··· + 143u + 37)
· (u
83
+ 5u
82
+ ··· + 97593u + 5351)
c
7
(u
2
− u + 1)(u
24
+ u
23
+ ··· + 9u + 1)(u
83
− 3u
82
+ ··· + 1495u + 103)
c
8
(u
2
+ 3u + 3)(u
24
− 4u
23
+ ··· − 4u + 1)(u
83
+ 6u
82
+ ··· + 322u + 29)
c
9
(u
2
+ 3u + 3)(u
24
− 3u
23
+ ··· + 2u + 1)
· (u
83
− 3u
82
+ ··· + 23642902u + 6207563)
c
10
(u
2
+ u + 1)(u
24
− 5u
22
+ ··· − 2u + 1)
· (u
83
− 2u
82
+ ··· + 130300u + 11257)
c
11
(u
2
+ u + 1)(u
24
+ 6u
23
+ ··· + 2u + 1)(u
83
− 12u
82
+ ··· − 12u + 1)
c
12
(u
2
+ u + 1)(u
24
− u
23
+ ··· − 9u + 1)(u
83
− 3u
82
+ ··· + 1495u + 103)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
24
− 7y
23
+ ··· + 19y + 1)
· (y
83
+ 5y
82
+ ··· − 397351y −41209)
c
2
(y
2
+ y + 1)(y
24
+ 13y
23
+ ··· − 12y + 1)
· (y
83
+ 93y
82
+ ··· − 1365124926432y −56488454929)
c
3
y
2
(y
24
+ 22y
22
+ ··· − 9533y + 961)
· (y
83
+ 15y
82
+ ··· − 56398528y −4443664)
c
4
(y
2
+ y + 1)(y
24
− 11y
23
+ ··· − 38y + 1)(y
83
− 11y
82
+ ··· + 50y −1)
c
5
(y
2
+ y + 1)(y
24
− 10y
23
+ ··· + 8513y + 841)
· (y
83
− 30y
82
+ ··· + 63722693959y −7028977921)
c
6
(y
2
+ y + 1)(y
24
+ 5y
23
+ ··· − 7203y + 1369)
· (y
83
+ 97y
82
+ ··· − 743094449y −28633201)
c
7
, c
12
(y
2
+ y + 1)(y
24
+ 19y
23
+ ··· + 3y + 1)
· (y
83
+ 59y
82
+ ··· − 208547y −10609)
c
8
(y
2
− 3y + 9)(y
24
+ 14y
22
+ ··· − 6y + 1)
· (y
83
− 12y
82
+ ··· + 29850y −841)
c
9
(y
2
− 3y + 9)(y
24
+ 5y
23
+ ··· − 2y + 1)
· (y
83
+ 53y
82
+ ··· − 759411803692702y −38533838398969)
c
10
(y
2
+ y + 1)(y
24
− 10y
23
+ ··· + 24y + 1)
· (y
83
− 98y
82
+ ··· + 5637157808y −126720049)
c
11
(y
2
+ y + 1)(y
24
+ 2y
23
+ ··· − 16y + 1)(y
83
+ 22y
82
+ ··· + 68y −1)
27
