12n
0567
(K12n
0567
)
A knot diagram
1
Linearized knot diagam
3 7 12 10 8 2 11 12 3 5 6 10
Solving Sequence
7,11 3,8
2 6 12 5 10 1 4 9
c
7
c
2
c
6
c
11
c
5
c
10
c
12
c
4
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h5.56281 × 10
317
u
78
− 5.02067 × 10
318
u
77
+ ··· + 8.67837 × 10
319
b + 1.47773 × 10
320
,
− 3.19161 × 10
320
u
78
+ 2.80481 × 10
321
u
77
+ ··· + 1.37986 × 10
322
a + 2.79478 × 10
322
,
u
79
− 9u
78
+ ··· + 734u + 106i
I
u
2
= h2.46309 × 10
21
u
21
− 5.34185 × 10
18
u
20
+ ··· + 1.37105 × 10
22
b + 2.69501 × 10
22
,
− 1.37506 × 10
22
u
21
+ 5.42032 × 10
21
u
20
+ ··· + 5.48420 × 10
22
a − 2.58037 × 10
22
,
u
22
+ 8u
20
+ ··· + 28u + 4i
I
u
3
= hb − 1, a, u + 1i
I
u
4
= hb + 1, a + 1, u + 1i
I
v
1
= ha, b + 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 104 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
= h5.56 × 10
317
u
78
− 5.02 × 10
318
u
77
+ · · · + 8.68 × 10
319
b + 1.48 ×
10
320
, −3.19 × 10
320
u
78
+ 2.80 × 10
321
u
77
+ · · · + 1.38 × 10
322
a + 2.79 ×
10
322
, u
79
− 9u
78
+ · · · + 734u + 106i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
0.0231300u
78
− 0.203268u
77
+ ··· − 11.9417u − 2.02541
−0.00640998u
78
+ 0.0578527u
77
+ ··· − 3.35031u − 1.70277
a
8
=
1
u
2
a
2
=
0.0167200u
78
− 0.145415u
77
+ ··· − 15.2920u − 3.72818
−0.00640998u
78
+ 0.0578527u
77
+ ··· − 3.35031u − 1.70277
a
6
=
0.0133063u
78
− 0.111816u
77
+ ··· + 15.5097u + 0.982850
−0.00879467u
78
+ 0.0756675u
77
+ ··· − 25.5253u − 6.64326
a
12
=
0.0132004u
78
− 0.125171u
77
+ ··· − 25.7839u − 2.94270
−0.00276583u
78
+ 0.0225513u
77
+ ··· − 3.76731u − 0.106117
a
5
=
0.0200166u
78
− 0.171688u
77
+ ··· + 33.7964u + 6.78443
−0.00872034u
78
+ 0.0751173u
77
+ ··· − 26.6187u − 6.69843
a
10
=
0.00488649u
78
− 0.0504017u
77
+ ··· + 3.29564u + 3.47447
−0.00255916u
78
+ 0.0228690u
77
+ ··· − 15.8414u − 4.95528
a
1
=
−0.0145289u
78
+ 0.122760u
77
+ ··· + 14.0823u + 7.64467
−0.0100602u
78
+ 0.0908254u
77
+ ··· − 19.0287u − 7.67271
a
4
=
0.0241505u
78
− 0.223793u
77
+ ··· − 42.8651u − 5.86006
−0.00239155u
78
+ 0.0244554u
77
+ ··· + 2.88597u − 0.413481
a
9
=
0.00650299u
78
− 0.0609618u
77
+ ··· + 2.56028u + 1.33246
−0.00536036u
78
+ 0.0455739u
77
+ ··· − 8.77824u − 1.19157
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.353846u
78
+ 3.26964u
77
+ ··· − 551.965u − 156.813
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
79
+ 43u
78
+ ··· + 457u + 36
c
2
, c
6
u
79
+ u
78
+ ··· − 19u + 6
c
3
u
79
− 6u
78
+ ··· + 3288u − 3153
c
4
, c
10
u
79
+ 3u
78
+ ··· + 39517u + 6618
c
5
u
79
+ 12u
78
+ ··· + 14u + 11
c
7
u
79
+ 9u
78
+ ··· + 734u − 106
c
8
u
79
+ 3u
78
+ ··· + 61u − 6
c
9
u
79
+ u
78
+ ··· + 18402u + 6638
c
11
u
79
− u
78
+ ··· − 21u − 3
c
12
u
79
− 2u
78
+ ··· + 124853u + 21439
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
79
− 15y
78
+ ··· + 33889y −1296
c
2
, c
6
y
79
− 43y
78
+ ··· + 457y −36
c
3
y
79
− 92y
78
+ ··· + 324175002y −9941409
c
4
, c
10
y
79
− 43y
78
+ ··· + 1161720493y −43797924
c
5
y
79
− 36y
78
+ ··· + 2748y −121
c
7
y
79
+ 27y
78
+ ··· − 45092y −11236
c
8
y
79
+ 27y
78
+ ··· + 27889y −36
c
9
y
79
+ 91y
78
+ ··· − 1887671940y −44063044
c
11
y
79
− y
78
+ ··· + 1149y −9
c
12
y
79
+ 72y
78
+ ··· + 5381678245y −459630721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.778248 + 0.684575I
a = 0.496147 + 0.408691I
b = −0.390677 − 0.867183I
−5.37716 + 3.78065I 0
u = −0.778248 − 0.684575I
a = 0.496147 − 0.408691I
b = −0.390677 + 0.867183I
−5.37716 − 3.78065I 0
u = −0.892660
a = −0.278912
b = 1.20837
1.65892 7.72510
u = 0.135677 + 0.874172I
a = 2.18391 + 1.40758I
b = −1.024420 − 0.534790I
−2.76898 − 7.84768I 2.12757 + 8.05813I
u = 0.135677 − 0.874172I
a = 2.18391 − 1.40758I
b = −1.024420 + 0.534790I
−2.76898 + 7.84768I 2.12757 − 8.05813I
u = −0.781273 + 0.304744I
a = 0.842113 − 0.298441I
b = 1.265120 + 0.143006I
−10.97290 + 0.77841I −6.82766 − 0.78518I
u = −0.781273 − 0.304744I
a = 0.842113 + 0.298441I
b = 1.265120 − 0.143006I
−10.97290 − 0.77841I −6.82766 + 0.78518I
u = −0.581646 + 1.006650I
a = −0.240060 − 0.661324I
b = 0.185387 + 0.764265I
4.41709 + 4.52800I 0
u = −0.581646 − 1.006650I
a = −0.240060 + 0.661324I
b = 0.185387 − 0.764265I
4.41709 − 4.52800I 0
u = 0.804957 + 0.173139I
a = −0.302876 − 0.960865I
b = −0.935122 + 0.560283I
−1.36961 + 2.12804I −6.08728 − 3.56903I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.804957 − 0.173139I
a = −0.302876 + 0.960865I
b = −0.935122 − 0.560283I
−1.36961 − 2.12804I −6.08728 + 3.56903I
u = −0.932036 + 0.736879I
a = −0.64902 − 1.47930I
b = −1.146240 + 0.628898I
−7.64208 + 9.32063I 0
u = −0.932036 − 0.736879I
a = −0.64902 + 1.47930I
b = −1.146240 − 0.628898I
−7.64208 − 9.32063I 0
u = −0.305349 + 0.731424I
a = −1.72358 − 0.55517I
b = 0.826923 + 0.741635I
3.38241 − 1.44721I −0.92948 + 7.72706I
u = −0.305349 − 0.731424I
a = −1.72358 + 0.55517I
b = 0.826923 − 0.741635I
3.38241 + 1.44721I −0.92948 − 7.72706I
u = 0.109380 + 0.784726I
a = 2.41586 − 0.71124I
b = −0.784744 + 0.443258I
1.92515 + 0.39107I 4.91566 + 0.78548I
u = 0.109380 − 0.784726I
a = 2.41586 + 0.71124I
b = −0.784744 − 0.443258I
1.92515 − 0.39107I 4.91566 − 0.78548I
u = −0.371146 + 0.688689I
a = 0.49761 + 2.75814I
b = 0.914340 − 0.739129I
3.12020 + 4.18419I −3.46102 − 2.48442I
u = −0.371146 − 0.688689I
a = 0.49761 − 2.75814I
b = 0.914340 + 0.739129I
3.12020 − 4.18419I −3.46102 + 2.48442I
u = −0.478501 + 1.123620I
a = −0.298949 + 0.824219I
b = 0.275465 − 0.433827I
5.17058 + 4.04352I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.478501 − 1.123620I
a = −0.298949 − 0.824219I
b = 0.275465 + 0.433827I
5.17058 − 4.04352I 0
u = 0.395642 + 0.656886I
a = 0.196734 + 0.736150I
b = −0.047600 − 0.467709I
0.165593 − 1.209730I 2.02916 + 5.23119I
u = 0.395642 − 0.656886I
a = 0.196734 − 0.736150I
b = −0.047600 + 0.467709I
0.165593 + 1.209730I 2.02916 − 5.23119I
u = −0.684615 + 1.041570I
a = 0.0285168 + 0.0826745I
b = 0.814198 + 0.338128I
1.57656 − 2.62855I 0
u = −0.684615 − 1.041570I
a = 0.0285168 − 0.0826745I
b = 0.814198 − 0.338128I
1.57656 + 2.62855I 0
u = 0.975838 + 0.782424I
a = 0.657092 − 0.713723I
b = 1.022580 + 0.268605I
−2.94747 − 3.80961I 0
u = 0.975838 − 0.782424I
a = 0.657092 + 0.713723I
b = 1.022580 − 0.268605I
−2.94747 + 3.80961I 0
u = −0.536219 + 1.134980I
a = −0.534763 − 1.106970I
b = −0.506060 + 0.508248I
−4.04856 + 1.41714I 0
u = −0.536219 − 1.134980I
a = −0.534763 + 1.106970I
b = −0.506060 − 0.508248I
−4.04856 − 1.41714I 0
u = −0.741180
a = 0.239372
b = 0.419805
1.79441 4.83380
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.738304 + 1.048750I
a = −0.845945 − 0.269555I
b = 0.998142 − 0.376554I
−3.87655 − 1.76981I 0
u = 0.738304 − 1.048750I
a = −0.845945 + 0.269555I
b = 0.998142 + 0.376554I
−3.87655 + 1.76981I 0
u = 1.105070 + 0.664957I
a = 0.244803 + 0.115320I
b = −1.47554 − 0.01059I
−8.72804 − 7.04097I 0
u = 1.105070 − 0.664957I
a = 0.244803 − 0.115320I
b = −1.47554 + 0.01059I
−8.72804 + 7.04097I 0
u = 1.132430 + 0.621605I
a = 0.49514 − 1.51289I
b = −0.004512 + 0.661734I
−2.89071 + 3.39186I 0
u = 1.132430 − 0.621605I
a = 0.49514 + 1.51289I
b = −0.004512 − 0.661734I
−2.89071 − 3.39186I 0
u = −0.272017 + 0.645577I
a = −0.02750 − 1.78732I
b = −1.24922 + 0.75688I
−3.78506 + 8.40300I 1.55735 − 8.35283I
u = −0.272017 − 0.645577I
a = −0.02750 + 1.78732I
b = −1.24922 − 0.75688I
−3.78506 − 8.40300I 1.55735 + 8.35283I
u = 1.173230 + 0.678550I
a = 1.264070 + 0.058940I
b = 0.672858 + 0.087940I
−2.57246 − 4.30103I 0
u = 1.173230 − 0.678550I
a = 1.264070 − 0.058940I
b = 0.672858 − 0.087940I
−2.57246 + 4.30103I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.365510 + 0.529512I
a = 0.33616 + 1.47447I
b = −0.131837 − 1.340730I
−0.80564 + 1.18538I 10.43073 + 5.93489I
u = 0.365510 − 0.529512I
a = 0.33616 − 1.47447I
b = −0.131837 + 1.340730I
−0.80564 − 1.18538I 10.43073 − 5.93489I
u = −0.372397 + 0.523453I
a = −0.03555 + 2.76231I
b = 0.873019 − 0.750214I
2.81371 + 4.24079I 1.66752 − 8.05004I
u = −0.372397 − 0.523453I
a = −0.03555 − 2.76231I
b = 0.873019 + 0.750214I
2.81371 − 4.24079I 1.66752 + 8.05004I
u = 1.103790 + 0.828086I
a = −0.171841 − 0.938107I
b = 1.31594 + 0.55012I
−5.20033 − 4.93329I 0
u = 1.103790 − 0.828086I
a = −0.171841 + 0.938107I
b = 1.31594 − 0.55012I
−5.20033 + 4.93329I 0
u = −0.609086
a = −1.31379
b = −0.978193
−1.80797 −4.57870
u = −0.917810 + 1.056720I
a = 0.327013 + 1.321270I
b = 1.149280 − 0.560651I
1.73896 + 9.47414I 0
u = −0.917810 − 1.056720I
a = 0.327013 − 1.321270I
b = 1.149280 + 0.560651I
1.73896 − 9.47414I 0
u = 0.313708 + 0.509032I
a = −2.16795 + 3.20848I
b = −0.923339 − 0.452097I
1.45639 − 3.33450I 2.49781 + 7.16900I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.313708 − 0.509032I
a = −2.16795 − 3.20848I
b = −0.923339 + 0.452097I
1.45639 + 3.33450I 2.49781 − 7.16900I
u = −0.51363 + 1.33375I
a = 0.297777 + 0.674355I
b = −0.405830 − 0.317748I
5.04693 + 3.84525I 0
u = −0.51363 − 1.33375I
a = 0.297777 − 0.674355I
b = −0.405830 + 0.317748I
5.04693 − 3.84525I 0
u = 0.92366 + 1.16421I
a = −0.519837 + 1.155040I
b = 0.442033 − 1.069980I
−1.34186 − 10.86070I 0
u = 0.92366 − 1.16421I
a = −0.519837 − 1.155040I
b = 0.442033 + 1.069980I
−1.34186 + 10.86070I 0
u = 0.216721 + 0.462692I
a = 1.19356 − 4.87978I
b = −0.574841 + 0.526921I
−1.37094 − 3.47466I 5.22123 + 1.68240I
u = 0.216721 − 0.462692I
a = 1.19356 + 4.87978I
b = −0.574841 − 0.526921I
−1.37094 + 3.47466I 5.22123 − 1.68240I
u = 0.76744 + 1.37751I
a = 0.741867 − 1.057010I
b = −0.712373 + 0.831700I
3.89746 − 2.86937I 0
u = 0.76744 − 1.37751I
a = 0.741867 + 1.057010I
b = −0.712373 − 0.831700I
3.89746 + 2.86937I 0
u = −0.031530 + 0.417860I
a = −1.64477 − 2.92363I
b = 0.968462 + 0.643997I
2.48038 − 1.25973I 0.414499 − 1.210980I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.031530 − 0.417860I
a = −1.64477 + 2.92363I
b = 0.968462 − 0.643997I
2.48038 + 1.25973I 0.414499 + 1.210980I
u = 0.10747 + 1.58916I
a = −0.00023 − 1.80456I
b = 0.692388 + 0.412184I
−4.62516 − 0.13995I 0
u = 0.10747 − 1.58916I
a = −0.00023 + 1.80456I
b = 0.692388 − 0.412184I
−4.62516 + 0.13995I 0
u = 1.04711 + 1.33119I
a = −0.04905 − 1.52114I
b = 1.204620 + 0.705102I
−3.7393 − 17.2276I 0
u = 1.04711 − 1.33119I
a = −0.04905 + 1.52114I
b = 1.204620 − 0.705102I
−3.7393 + 17.2276I 0
u = 0.90626 + 1.44153I
a = −0.03875 + 1.73006I
b = −1.004110 − 0.729834I
2.99455 − 8.70932I 0
u = 0.90626 − 1.44153I
a = −0.03875 − 1.73006I
b = −1.004110 + 0.729834I
2.99455 + 8.70932I 0
u = −0.84193 + 1.52097I
a = 0.286857 + 0.492815I
b = −1.040030 − 0.466600I
−5.72787 − 2.55886I 0
u = −0.84193 − 1.52097I
a = 0.286857 − 0.492815I
b = −1.040030 + 0.466600I
−5.72787 + 2.55886I 0
u = −1.00763 + 1.43025I
a = −0.079092 − 1.239070I
b = −1.089190 + 0.500708I
2.88288 + 7.82891I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00763 − 1.43025I
a = −0.079092 + 1.239070I
b = −1.089190 − 0.500708I
2.88288 − 7.82891I 0
u = −0.231825 + 0.082340I
a = 1.050750 + 0.434329I
b = −1.97997 − 0.26154I
−0.489628 + 0.006055I −71.0734 − 96.8093I
u = −0.231825 − 0.082340I
a = 1.050750 − 0.434329I
b = −1.97997 + 0.26154I
−0.489628 − 0.006055I −71.0734 + 96.8093I
u = −0.21428 + 1.94197I
a = −0.541939 + 1.278230I
b = 1.006310 − 0.473935I
−5.75770 + 3.61725I 0
u = −0.21428 − 1.94197I
a = −0.541939 − 1.278230I
b = 1.006310 + 0.473935I
−5.75770 − 3.61725I 0
u = 0.99904 + 1.69268I
a = 0.488431 + 1.102260I
b = −1.172360 − 0.431362I
−6.19272 − 0.68993I 0
u = 0.99904 − 1.69268I
a = 0.488431 − 1.102260I
b = −1.172360 + 0.431362I
−6.19272 + 0.68993I 0
u = 2.15231 + 0.64578I
a = −0.203624 + 0.626602I
b = 1.145960 − 0.468340I
−5.94362 + 7.51805I 0
u = 2.15231 − 0.64578I
a = −0.203624 − 0.626602I
b = 1.145960 + 0.468340I
−5.94362 − 7.51805I 0
12
II. I
u
2
= h2.46 × 10
21
u
21
− 5.34 × 10
18
u
20
+ · · · + 1.37 × 10
22
b + 2.70 ×
10
22
, −1.38 × 10
22
u
21
+ 5.42 × 10
21
u
20
+ · · · + 5.48 × 10
22
a − 2.58 ×
10
22
, u
22
+ 8u
20
+ · · · + 28u + 4i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
0.250731u
21
− 0.0988352u
20
+ ··· − 10.6914u + 0.470510
−0.179650u
21
+ 0.000389617u
20
+ ··· + 0.895903u − 1.96565
a
8
=
1
u
2
a
2
=
0.0710809u
21
− 0.0984456u
20
+ ··· − 9.79546u − 1.49514
−0.179650u
21
+ 0.000389617u
20
+ ··· + 0.895903u − 1.96565
a
6
=
−0.0514362u
21
+ 0.155001u
20
+ ··· + 9.60842u + 1.81921
−0.0530987u
21
+ 0.0390748u
20
+ ··· − 0.598343u − 5.10910
a
12
=
0.124929u
21
+ 0.0291947u
20
+ ··· − 0.0790308u − 0.197796
0.00280485u
21
− 0.00661764u
20
+ ··· − 1.41274u − 0.702528
a
5
=
0.101122u
21
+ 0.0831122u
20
+ ··· + 6.07247u + 6.30830
−0.0551212u
21
+ 0.0603063u
20
+ ··· + 0.804315u − 4.82155
a
10
=
0.225471u
21
+ 0.0177999u
20
+ ··· + 0.799370u + 4.38328
−0.115972u
21
+ 0.0000800783u
20
+ ··· − 0.183112u − 4.06652
a
1
=
−0.279252u
21
+ 0.0537237u
20
+ ··· − 0.797291u − 10.8142
0.303972u
21
− 0.0535289u
20
+ ··· − 3.29404u + 8.75698
a
4
=
−0.345499u
21
− 0.199154u
20
+ ··· − 2.78153u + 1.97169
0.0273764u
21
+ 0.148942u
20
+ ··· + 6.18843u − 0.931880
a
9
=
0.125808u
21
+ 0.0250511u
20
+ ··· − 0.0493171u + 0.818347
0.00109520u
21
− 0.0353749u
20
+ ··· − 1.45948u − 0.476329
(ii) Obstruction class = 1
(iii) Cusp Shapes =
127267665923885090334680
13710494354785690079293
u
21
−
20268422342251723240628
13710494354785690079293
u
20
+ ··· −
850893225143436557560740
13710494354785690079293
u +
3955364890476921757575848
13710494354785690079293
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
22
− 17u
21
+ ··· − 13u + 1
c
2
u
22
− u
21
+ ··· + u − 1
c
3
u
22
+ 5u
21
+ ··· − 6u + 1
c
4
u
22
− u
21
+ ··· − 18u + 13
c
5
u
22
− 5u
21
+ ··· + 2u + 1
c
6
u
22
+ u
21
+ ··· − u − 1
c
7
u
22
+ 8u
20
+ ··· + 28u + 4
c
8
u
22
− 5u
21
+ ··· + 43u − 13
c
9
u
22
+ 2u
21
+ ··· − 12u − 4
c
10
u
22
+ u
21
+ ··· + 18u + 13
c
11
u
22
+ u
20
+ ··· + 11u − 1
c
12
u
22
− 5u
21
+ ··· − 5u − 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 25y
21
+ ··· + 11y + 1
c
2
, c
6
y
22
− 17y
21
+ ··· − 13y + 1
c
3
y
22
− 17y
21
+ ··· − 104y + 1
c
4
, c
10
y
22
− 17y
21
+ ··· − 1546y + 169
c
5
y
22
− 33y
21
+ ··· − 14y + 1
c
7
y
22
+ 16y
21
+ ··· − 736y + 16
c
8
y
22
+ 17y
21
+ ··· − 7543y + 169
c
9
y
22
+ 8y
21
+ ··· − 224y + 16
c
11
y
22
+ 2y
21
+ ··· − 163y + 1
c
12
y
22
+ 3y
21
+ ··· − 15y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.868438 + 0.594278I
a = −1.37249 + 0.76619I
b = −0.508292 + 0.207982I
−2.36147 − 3.64249I −0.927282 + 0.923820I
u = 0.868438 − 0.594278I
a = −1.37249 − 0.76619I
b = −0.508292 − 0.207982I
−2.36147 + 3.64249I −0.927282 − 0.923820I
u = −0.450765 + 0.719635I
a = −0.004566 − 0.975016I
b = −0.802503 − 0.300039I
1.20238 − 2.12854I −1.92738 − 0.50157I
u = −0.450765 − 0.719635I
a = −0.004566 + 0.975016I
b = −0.802503 + 0.300039I
1.20238 + 2.12854I −1.92738 + 0.50157I
u = −0.339304 + 1.103900I
a = −0.472119 + 0.708930I
b = 0.487202 − 0.541584I
5.32946 + 4.52303I 7.8508 − 12.4062I
u = −0.339304 − 1.103900I
a = −0.472119 − 0.708930I
b = 0.487202 + 0.541584I
5.32946 − 4.52303I 7.8508 + 12.4062I
u = 0.207309 + 0.757040I
a = −2.32124 + 0.86023I
b = 0.857226 − 0.701147I
3.69847 + 1.13168I 12.69939 + 4.46196I
u = 0.207309 − 0.757040I
a = −2.32124 − 0.86023I
b = 0.857226 + 0.701147I
3.69847 − 1.13168I 12.69939 − 4.46196I
u = 0.275777 + 0.631762I
a = 0.71336 − 3.50085I
b = 0.895803 + 0.700990I
3.57593 − 4.25665I 14.6360 + 6.2434I
u = 0.275777 − 0.631762I
a = 0.71336 + 3.50085I
b = 0.895803 − 0.700990I
3.57593 + 4.25665I 14.6360 − 6.2434I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.682459
a = −0.629458
b = 1.60199
1.37157 −24.7530
u = 1.44377 + 0.06593I
a = 0.196282 − 0.456604I
b = −1.193570 + 0.485737I
−5.37558 + 6.98207I 0.36022 − 4.86270I
u = 1.44377 − 0.06593I
a = 0.196282 + 0.456604I
b = −1.193570 − 0.485737I
−5.37558 − 6.98207I 0.36022 + 4.86270I
u = −0.65206 + 1.38390I
a = 0.646197 + 0.837522I
b = −0.633171 − 0.632803I
5.77602 + 3.37066I 6.81116 + 0.28145I
u = −0.65206 − 1.38390I
a = 0.646197 − 0.837522I
b = −0.633171 + 0.632803I
5.77602 − 3.37066I 6.81116 − 0.28145I
u = −0.38474 + 1.54379I
a = 0.43414 + 1.55487I
b = 0.685386 − 0.269781I
−5.07638 + 1.44838I −7.70492 − 3.87687I
u = −0.38474 − 1.54379I
a = 0.43414 − 1.55487I
b = 0.685386 + 0.269781I
−5.07638 − 1.44838I −7.70492 + 3.87687I
u = −0.92599 + 1.40618I
a = −0.09974 − 1.54439I
b = −1.044280 + 0.642940I
4.47722 + 8.44438I 4.75673 − 6.97687I
u = −0.92599 − 1.40618I
a = −0.09974 + 1.54439I
b = −1.044280 − 0.642940I
4.47722 − 8.44438I 4.75673 + 6.97687I
u = −0.138208
a = 2.10215
b = −2.28799
−0.467985 313.180
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.36790 + 1.93453I
a = −0.456168 − 1.012410I
b = 1.099200 + 0.373608I
−6.76305 − 1.34428I −7.76685 + 2.36036I
u = 0.36790 − 1.93453I
a = −0.456168 + 1.012410I
b = 1.099200 − 0.373608I
−6.76305 + 1.34428I −7.76685 − 2.36036I
20
III. I
u
3
= hb − 1, a, u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
−1
a
3
=
0
1
a
8
=
1
1
a
2
=
1
1
a
6
=
0
−1
a
12
=
0
−1
a
5
=
1
0
a
10
=
1
−1
a
1
=
−1
0
a
4
=
0
1
a
9
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u + 1
c
2
, c
4
, c
6
c
7
, c
8
, c
9
c
10
, c
12
u − 1
c
3
, c
11
u
22
(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
8
, c
9
, c
10
c
12
y −1
c
3
, c
11
y
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = 1.00000
1.64493 6.00000
24
IV. I
u
4
= hb + 1, a + 1, u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
−1
a
3
=
−1
−1
a
8
=
1
1
a
2
=
−2
−1
a
6
=
−1
−1
a
12
=
1
0
a
5
=
−1
−1
a
10
=
1
0
a
1
=
1
0
a
4
=
0
−1
a
9
=
2
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
9
c
10
, c
11
u + 1
c
5
, c
12
u
c
7
, c
8
u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
9
, c
10
c
11
y −1
c
5
, c
12
y
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = −1.00000
−1.64493 −6.00000
28
V. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
−1
0
a
3
=
0
−1
a
8
=
1
0
a
2
=
−1
−1
a
6
=
0
−1
a
12
=
−1
−1
a
5
=
1
−1
a
10
=
0
−1
a
1
=
−1
0
a
4
=
1
0
a
9
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
10
, c
11
, c
12
u − 1
c
3
, c
4
, c
6
c
8
u + 1
c
7
, c
9
u
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
, c
10
, c
11
c
12
y −1
c
7
, c
9
y
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
0 0
32
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u + 1)
2
(u
22
− 17u
21
+ ··· − 13u + 1)
· (u
79
+ 43u
78
+ ··· + 457u + 36)
c
2
((u − 1)
2
)(u + 1)(u
22
− u
21
+ ··· + u − 1)(u
79
+ u
78
+ ··· − 19u + 6)
c
3
u(u + 1)
2
(u
22
+ 5u
21
+ ··· − 6u + 1)(u
79
− 6u
78
+ ··· + 3288u − 3153)
c
4
(u − 1)(u + 1)
2
(u
22
− u
21
+ ··· − 18u + 13)
· (u
79
+ 3u
78
+ ··· + 39517u + 6618)
c
5
u(u − 1)(u + 1)(u
22
− 5u
21
+ ··· + 2u + 1)(u
79
+ 12u
78
+ ··· + 14u + 11)
c
6
(u − 1)(u + 1)
2
(u
22
+ u
21
+ ··· − u − 1)(u
79
+ u
78
+ ··· − 19u + 6)
c
7
u(u − 1)
2
(u
22
+ 8u
20
+ ··· + 28u + 4)(u
79
+ 9u
78
+ ··· + 734u − 106)
c
8
((u − 1)
2
)(u + 1)(u
22
− 5u
21
+ ··· + 43u − 13)(u
79
+ 3u
78
+ ··· + 61u − 6)
c
9
u(u − 1)(u + 1)(u
22
+ 2u
21
+ ··· − 12u − 4)
· (u
79
+ u
78
+ ··· + 18402u + 6638)
c
10
((u − 1)
2
)(u + 1)(u
22
+ u
21
+ ··· + 18u + 13)
· (u
79
+ 3u
78
+ ··· + 39517u + 6618)
c
11
u(u − 1)(u + 1)(u
22
+ u
20
+ ··· + 11u − 1)(u
79
− u
78
+ ··· − 21u − 3)
c
12
u(u − 1)
2
(u
22
− 5u
21
+ ··· − 5u − 1)
· (u
79
− 2u
78
+ ··· + 124853u + 21439)
33
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
3
)(y
22
− 25y
21
+ ··· + 11y + 1)
· (y
79
− 15y
78
+ ··· + 33889y −1296)
c
2
, c
6
((y −1)
3
)(y
22
− 17y
21
+ ··· − 13y + 1)(y
79
− 43y
78
+ ··· + 457y −36)
c
3
y(y −1)
2
(y
22
− 17y
21
+ ··· − 104y + 1)
· (y
79
− 92y
78
+ ··· + 324175002y −9941409)
c
4
, c
10
((y −1)
3
)(y
22
− 17y
21
+ ··· − 1546y + 169)
· (y
79
− 43y
78
+ ··· + 1161720493y −43797924)
c
5
y(y −1)
2
(y
22
− 33y
21
+ ··· − 14y + 1)
· (y
79
− 36y
78
+ ··· + 2748y −121)
c
7
y(y −1)
2
(y
22
+ 16y
21
+ ··· − 736y + 16)
· (y
79
+ 27y
78
+ ··· − 45092y −11236)
c
8
((y −1)
3
)(y
22
+ 17y
21
+ ··· − 7543y + 169)
· (y
79
+ 27y
78
+ ··· + 27889y −36)
c
9
y(y −1)
2
(y
22
+ 8y
21
+ ··· − 224y + 16)
· (y
79
+ 91y
78
+ ··· − 1887671940y −44063044)
c
11
y(y −1)
2
(y
22
+ 2y
21
+ ··· − 163y + 1)(y
79
− y
78
+ ··· + 1149y −9)
c
12
y(y −1)
2
(y
22
+ 3y
21
+ ··· − 15y + 1)
· (y
79
+ 72y
78
+ ··· + 5381678245y −459630721)
34
