12a
0053
(K12a
0053
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 4 11 12 1 6 9 8
Solving Sequence
5,10
6
3,11
2 1 4 7 8 9 12
c
5
c
10
c
2
c
1
c
4
c
6
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.63164 × 10
260
u
101
+ 2.67815 × 10
260
u
100
+ ··· + 1.75319 × 10
262
b − 2.53854 × 10
263
,
− 1.79420 × 10
261
u
101
+ 8.56337 × 10
260
u
100
+ ··· + 7.01276 × 10
262
a − 7.92227 × 10
263
,
u
102
− 2u
101
+ ··· − 1024u − 512i
I
u
2
= hb + 1, u
5
− 4u
3
− u
2
+ a + 4u + 3, u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
I
v
1
= ha, v
2
+ b + 2v, v
3
+ 3v
2
+ 2v + 1i
I
v
2
= ha, −6v
5
+ 29v
4
− 57v
3
− 43v
2
+ 10b + 2v −1, v
6
− 5v
5
+ 10v
4
+ 7v
3
− 4v
2
− 2v + 1i
* 4 irreducible components of dim
C
= 0, with total 117 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−3.63 × 10
260
u
101
+ 2.68 × 10
260
u
100
+ · · · + 1.75 × 10
262
b − 2.54 ×
10
263
, −1.79 × 10
261
u
101
+ 8.56 × 10
260
u
100
+ · · · + 7.01 × 10
262
a − 7.92 ×
10
263
, u
102
− 2u
101
+ · · · − 1024u − 512i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
0.0255848u
101
− 0.0122111u
100
+ ··· + 83.4661u + 11.2969
0.0207145u
101
− 0.0152759u
100
+ ··· + 31.4829u + 14.4796
a
11
=
−u
−u
3
+ u
a
2
=
0.0462992u
101
− 0.0274870u
100
+ ··· + 114.949u + 25.7765
0.0207145u
101
− 0.0152759u
100
+ ··· + 31.4829u + 14.4796
a
1
=
−0.0274317u
101
+ 0.0331153u
100
+ ··· − 44.0458u − 25.7039
0.0488757u
101
− 0.0591895u
100
+ ··· + 95.3012u + 28.8088
a
4
=
0.0272415u
101
− 0.00262615u
100
+ ··· + 74.8617u + 22.1520
0.0457661u
101
− 0.0510031u
100
+ ··· + 104.242u + 36.2491
a
7
=
0.0214440u
101
− 0.0260743u
100
+ ··· + 51.2554u + 3.10487
−0.0386065u
101
+ 0.0480052u
100
+ ··· − 67.1046u − 20.2002
a
8
=
0.0429892u
101
− 0.0538624u
100
+ ··· + 87.5705u + 14.2399
−0.0455989u
101
+ 0.0579958u
100
+ ··· − 76.7190u − 23.5004
a
9
=
0.0657508u
101
− 0.101129u
100
+ ··· + 110.895u + 1.93899
−0.0556268u
101
+ 0.0657875u
100
+ ··· − 118.941u − 39.5496
a
12
=
−0.0157934u
101
+ 0.0415356u
100
+ ··· + 36.6963u + 23.0326
0.00311735u
101
+ 0.00656623u
100
+ ··· − 7.45847u + 6.07217
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0103007u
101
+ 0.100685u
100
+ ··· − 40.1004u + 18.3924
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
102
+ 50u
101
+ ··· + 200u + 1
c
2
, c
4
u
102
− 10u
101
+ ··· − 100u
2
+ 1
c
3
, c
6
u
102
− 4u
101
+ ··· + 384u − 64
c
5
, c
10
u
102
− 2u
101
+ ··· − 1024u − 512
c
7
, c
9
u
102
+ 5u
101
+ ··· + 22859u + 3137
c
8
, c
11
, c
12
u
102
− 5u
101
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
102
+ 14y
101
+ ··· − 37224y + 1
c
2
, c
4
y
102
− 50y
101
+ ··· − 200y + 1
c
3
, c
6
y
102
+ 48y
101
+ ··· − 24576y + 4096
c
5
, c
10
y
102
− 56y
101
+ ··· − 10878976y + 262144
c
7
, c
9
y
102
− 71y
101
+ ··· + 595599577y + 9840769
c
8
, c
11
, c
12
y
102
+ 85y
101
+ ··· + 57y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.469735 + 0.883162I
a = 0.286453 − 0.882567I
b = 0.479220 + 0.391058I
2.77045 − 2.21678I 0
u = 0.469735 − 0.883162I
a = 0.286453 + 0.882567I
b = 0.479220 − 0.391058I
2.77045 + 2.21678I 0
u = −0.965899 + 0.256296I
a = −0.99583 − 1.74154I
b = −1.049970 + 0.394446I
−2.68165 + 2.67345I 0
u = −0.965899 − 0.256296I
a = −0.99583 + 1.74154I
b = −1.049970 − 0.394446I
−2.68165 − 2.67345I 0
u = −0.896724 + 0.456096I
a = −0.092216 + 0.231496I
b = 0.429580 + 0.543361I
0.100178 − 0.283803I 0
u = −0.896724 − 0.456096I
a = −0.092216 − 0.231496I
b = 0.429580 − 0.543361I
0.100178 + 0.283803I 0
u = 0.859646 + 0.497283I
a = −0.52080 + 2.39634I
b = −0.930896 − 0.466209I
3.08017 − 4.18267I 0
u = 0.859646 − 0.497283I
a = −0.52080 − 2.39634I
b = −0.930896 + 0.466209I
3.08017 + 4.18267I 0
u = −0.664667 + 0.756869I
a = −0.053899 + 1.310560I
b = 0.606787 − 0.823071I
8.69978 + 0.83422I 0
u = −0.664667 − 0.756869I
a = −0.053899 − 1.310560I
b = 0.606787 + 0.823071I
8.69978 − 0.83422I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.255024 + 0.958228I
a = 1.22671 + 1.38675I
b = −1.047270 − 0.391591I
0.18214 − 4.88214I 0
u = −0.255024 − 0.958228I
a = 1.22671 − 1.38675I
b = −1.047270 + 0.391591I
0.18214 + 4.88214I 0
u = 0.852957 + 0.467639I
a = −0.358332 − 0.587928I
b = 0.558508 − 0.610769I
5.28770 + 3.54945I 0
u = 0.852957 − 0.467639I
a = −0.358332 + 0.587928I
b = 0.558508 + 0.610769I
5.28770 − 3.54945I 0
u = −0.458068 + 0.947743I
a = 0.328346 + 1.239270I
b = 0.341772 − 0.633589I
−0.30629 − 1.47045I 0
u = −0.458068 − 0.947743I
a = 0.328346 − 1.239270I
b = 0.341772 + 0.633589I
−0.30629 + 1.47045I 0
u = 0.678873 + 0.626121I
a = 1.18836 − 1.02645I
b = −0.757090 + 0.486265I
3.62452 − 0.25444I −12.00000 + 0.I
u = 0.678873 − 0.626121I
a = 1.18836 + 1.02645I
b = −0.757090 − 0.486265I
3.62452 + 0.25444I −12.00000 + 0.I
u = 0.119286 + 0.909951I
a = 1.22475 − 1.50418I
b = −1.071070 + 0.323375I
−3.94455 + 1.08858I −17.6433 + 0.I
u = 0.119286 − 0.909951I
a = 1.22475 + 1.50418I
b = −1.071070 − 0.323375I
−3.94455 − 1.08858I −17.6433 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.054683 + 0.909702I
a = 1.07662 + 1.64430I
b = −1.126830 − 0.260614I
−0.13399 + 2.63215I −12.00000 − 4.25973I
u = 0.054683 − 0.909702I
a = 1.07662 − 1.64430I
b = −1.126830 + 0.260614I
−0.13399 − 2.63215I −12.00000 + 4.25973I
u = −0.552950 + 0.718959I
a = −0.470014 − 1.024770I
b = 1.024520 + 0.708766I
7.46771 − 4.86452I −5.39463 + 0.I
u = −0.552950 − 0.718959I
a = −0.470014 + 1.024770I
b = 1.024520 − 0.708766I
7.46771 + 4.86452I −5.39463 + 0.I
u = 1.077250 + 0.202520I
a = 1.49875 − 0.60317I
b = 1.007730 + 0.542878I
3.95319 − 1.01949I 0
u = 1.077250 − 0.202520I
a = 1.49875 + 0.60317I
b = 1.007730 − 0.542878I
3.95319 + 1.01949I 0
u = 0.847792 + 0.305277I
a = −0.306504 − 1.308290I
b = 0.816745 + 0.899720I
5.48740 − 6.77518I −12.0000 + 8.1278I
u = 0.847792 − 0.305277I
a = −0.306504 + 1.308290I
b = 0.816745 − 0.899720I
5.48740 + 6.77518I −12.0000 − 8.1278I
u = 0.505238 + 0.996875I
a = 0.276220 − 1.351900I
b = 0.335981 + 0.733204I
4.20848 + 5.36069I 0
u = 0.505238 − 0.996875I
a = 0.276220 + 1.351900I
b = 0.335981 − 0.733204I
4.20848 − 5.36069I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.879562 + 0.061987I
a = −1.67185 − 0.65129I
b = −1.118850 + 0.248432I
−3.01354 − 0.43650I −16.9920 + 5.6265I
u = 0.879562 − 0.061987I
a = −1.67185 + 0.65129I
b = −1.118850 − 0.248432I
−3.01354 + 0.43650I −16.9920 − 5.6265I
u = 1.010690 + 0.491378I
a = −0.304624 + 0.260791I
b = 0.311768 − 0.732223I
1.33313 − 3.20923I 0
u = 1.010690 − 0.491378I
a = −0.304624 − 0.260791I
b = 0.311768 + 0.732223I
1.33313 + 3.20923I 0
u = −0.697298 + 0.512897I
a = −0.85017 − 1.31278I
b = −1.203620 − 0.053436I
2.04651 + 2.09519I −6.28035 − 5.02967I
u = −0.697298 − 0.512897I
a = −0.85017 + 1.31278I
b = −1.203620 + 0.053436I
2.04651 − 2.09519I −6.28035 + 5.02967I
u = 0.415660 + 0.730923I
a = −0.077135 − 1.102180I
b = 0.691438 + 0.664577I
3.13379 − 1.41013I −5.75364 + 1.93454I
u = 0.415660 − 0.730923I
a = −0.077135 + 1.102180I
b = 0.691438 − 0.664577I
3.13379 + 1.41013I −5.75364 − 1.93454I
u = −0.978284 + 0.623736I
a = −0.719027 − 0.315629I
b = 0.422219 + 0.829820I
7.68710 + 4.41199I 0
u = −0.978284 − 0.623736I
a = −0.719027 + 0.315629I
b = 0.422219 − 0.829820I
7.68710 − 4.41199I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.804564 + 0.094462I
a = −0.412124 + 1.223020I
b = 0.928475 − 0.856899I
5.15559 − 0.37233I −13.56324 + 1.75422I
u = 0.804564 − 0.094462I
a = −0.412124 − 1.223020I
b = 0.928475 + 0.856899I
5.15559 + 0.37233I −13.56324 − 1.75422I
u = −1.183540 + 0.152520I
a = 0.584352 + 0.866013I
b = −0.327386 − 0.735963I
−1.90155 − 2.90937I 0
u = −1.183540 − 0.152520I
a = 0.584352 − 0.866013I
b = −0.327386 + 0.735963I
−1.90155 + 2.90937I 0
u = 1.167870 + 0.278365I
a = 0.687171 − 0.928053I
b = −0.421218 + 0.731632I
−5.42236 − 1.22087I 0
u = 1.167870 − 0.278365I
a = 0.687171 + 0.928053I
b = −0.421218 − 0.731632I
−5.42236 + 1.22087I 0
u = −1.161710 + 0.380863I
a = 0.754334 + 0.984612I
b = −0.493125 − 0.737361I
−1.13135 + 5.34314I 0
u = −1.161710 − 0.380863I
a = 0.754334 − 0.984612I
b = −0.493125 + 0.737361I
−1.13135 − 5.34314I 0
u = −0.760304 + 0.132527I
a = −0.345603 + 1.251750I
b = 0.865317 − 0.863222I
1.28913 + 3.15635I −18.6926 − 4.9567I
u = −0.760304 − 0.132527I
a = −0.345603 − 1.251750I
b = 0.865317 + 0.863222I
1.28913 − 3.15635I −18.6926 + 4.9567I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.118500 + 0.552200I
a = 0.95395 + 1.54284I
b = 1.114870 − 0.615352I
5.60729 + 9.79157I 0
u = −1.118500 − 0.552200I
a = 0.95395 − 1.54284I
b = 1.114870 + 0.615352I
5.60729 − 9.79157I 0
u = −1.226270 + 0.279300I
a = 1.044130 + 0.778399I
b = 1.067550 − 0.516419I
−1.78322 + 4.05653I 0
u = −1.226270 − 0.279300I
a = 1.044130 − 0.778399I
b = 1.067550 + 0.516419I
−1.78322 − 4.05653I 0
u = 0.341376 + 0.658757I
a = 0.850121 − 0.679018I
b = 0.134755 + 0.186887I
2.73869 − 2.12194I −5.45556 + 2.97058I
u = 0.341376 − 0.658757I
a = 0.850121 + 0.679018I
b = 0.134755 − 0.186887I
2.73869 + 2.12194I −5.45556 − 2.97058I
u = 0.237869 + 1.242390I
a = −0.439691 + 0.766188I
b = 1.059290 − 0.500801I
0.93403 + 1.83086I 0
u = 0.237869 − 1.242390I
a = −0.439691 − 0.766188I
b = 1.059290 + 0.500801I
0.93403 − 1.83086I 0
u = 0.131680 + 0.704994I
a = −0.328865 + 0.986806I
b = 0.921623 − 0.644162I
2.47180 + 3.64125I −5.93260 − 6.08823I
u = 0.131680 − 0.704994I
a = −0.328865 − 0.986806I
b = 0.921623 + 0.644162I
2.47180 − 3.64125I −5.93260 + 6.08823I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.364857 + 1.236950I
a = −0.495662 − 0.796350I
b = 1.095170 + 0.535588I
−2.46443 − 6.07420I 0
u = −0.364857 − 1.236950I
a = −0.495662 + 0.796350I
b = 1.095170 − 0.535588I
−2.46443 + 6.07420I 0
u = 1.258950 + 0.297340I
a = −0.401660 − 0.297563I
b = −1.314010 + 0.281641I
−4.86882 + 0.96261I 0
u = 1.258950 − 0.297340I
a = −0.401660 + 0.297563I
b = −1.314010 − 0.281641I
−4.86882 − 0.96261I 0
u = 0.458497 + 1.227020I
a = −0.532964 + 0.821965I
b = 1.118460 − 0.562936I
1.92668 + 10.29270I 0
u = 0.458497 − 1.227020I
a = −0.532964 − 0.821965I
b = 1.118460 + 0.562936I
1.92668 − 10.29270I 0
u = 1.187880 + 0.553524I
a = −0.355130 + 0.685776I
b = 0.239674 − 0.902710I
0.19904 − 3.04869I 0
u = 1.187880 − 0.553524I
a = −0.355130 − 0.685776I
b = 0.239674 + 0.902710I
0.19904 + 3.04869I 0
u = −1.251460 + 0.405072I
a = −0.311122 + 0.114315I
b = −1.340840 − 0.245232I
−8.19580 + 3.31639I 0
u = −1.251460 − 0.405072I
a = −0.311122 − 0.114315I
b = −1.340840 + 0.245232I
−8.19580 − 3.31639I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.250310 + 0.409568I
a = −0.27505 − 1.58198I
b = −1.122860 + 0.534778I
−4.28336 + 1.91291I 0
u = −1.250310 − 0.409568I
a = −0.27505 + 1.58198I
b = −1.122860 − 0.534778I
−4.28336 − 1.91291I 0
u = 1.245540 + 0.444122I
a = 0.86118 − 1.13024I
b = 1.119470 + 0.554114I
−1.00865 − 8.08532I 0
u = 1.245540 − 0.444122I
a = 0.86118 + 1.13024I
b = 1.119470 − 0.554114I
−1.00865 + 8.08532I 0
u = 1.238600 + 0.485737I
a = −0.238880 + 0.015588I
b = −1.358710 + 0.216589I
−3.76353 − 7.55514I 0
u = 1.238600 − 0.485737I
a = −0.238880 − 0.015588I
b = −1.358710 − 0.216589I
−3.76353 + 7.55514I 0
u = 1.248460 + 0.507912I
a = −0.17120 + 1.69208I
b = −1.098050 − 0.574579I
−7.44285 − 6.21744I 0
u = 1.248460 − 0.507912I
a = −0.17120 − 1.69208I
b = −1.098050 + 0.574579I
−7.44285 + 6.21744I 0
u = −1.199110 + 0.632919I
a = −0.476470 − 0.759573I
b = 0.281258 + 0.951290I
−2.72286 + 7.32646I 0
u = −1.199110 − 0.632919I
a = −0.476470 + 0.759573I
b = 0.281258 − 0.951290I
−2.72286 − 7.32646I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.236410 + 0.575925I
a = −0.10670 − 1.76523I
b = −1.076880 + 0.600242I
−2.88830 + 10.46490I 0
u = −1.236410 − 0.575925I
a = −0.10670 + 1.76523I
b = −1.076880 − 0.600242I
−2.88830 − 10.46490I 0
u = 1.192890 + 0.683328I
a = −0.556877 + 0.795127I
b = 0.311441 − 0.974383I
1.98421 − 11.53410I 0
u = 1.192890 − 0.683328I
a = −0.556877 − 0.795127I
b = 0.311441 + 0.974383I
1.98421 + 11.53410I 0
u = 1.34180 + 0.63995I
a = 0.457492 − 1.332140I
b = 1.196990 + 0.583051I
−2.67024 − 8.45023I 0
u = 1.34180 − 0.63995I
a = 0.457492 + 1.332140I
b = 1.196990 − 0.583051I
−2.67024 + 8.45023I 0
u = 1.28912 + 0.75340I
a = 0.36121 − 1.54178I
b = 1.209450 + 0.627942I
−0.7652 − 17.3335I 0
u = 1.28912 − 0.75340I
a = 0.36121 + 1.54178I
b = 1.209450 − 0.627942I
−0.7652 + 17.3335I 0
u = −1.31875 + 0.71144I
a = 0.38934 + 1.45200I
b = 1.207890 − 0.609037I
−5.54444 + 12.98070I 0
u = −1.31875 − 0.71144I
a = 0.38934 − 1.45200I
b = 1.207890 + 0.609037I
−5.54444 − 12.98070I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.497844
a = 0.865204
b = −0.0717077
−0.675799 −14.6910
u = −0.326069 + 0.266750I
a = 1.77180 + 0.55149I
b = −0.719427 − 0.150406I
−0.978110 − 0.104240I −10.05546 − 1.12981I
u = −0.326069 − 0.266750I
a = 1.77180 − 0.55149I
b = −0.719427 + 0.150406I
−0.978110 + 0.104240I −10.05546 + 1.12981I
u = −0.400500 + 0.102762I
a = −7.18535 − 4.89337I
b = −0.879416 + 0.112735I
1.77306 − 2.64662I −33.5126 − 4.0993I
u = −0.400500 − 0.102762I
a = −7.18535 + 4.89337I
b = −0.879416 − 0.112735I
1.77306 + 2.64662I −33.5126 + 4.0993I
u = −1.59121 + 0.07207I
a = 0.446162 − 0.200488I
b = 1.058940 + 0.304432I
−5.92991 − 5.44719I 0
u = −1.59121 − 0.07207I
a = 0.446162 + 0.200488I
b = 1.058940 − 0.304432I
−5.92991 + 5.44719I 0
u = −1.58344 + 0.30802I
a = 0.395590 − 0.007776I
b = 0.988167 + 0.243027I
−5.46115 + 3.91765I 0
u = −1.58344 − 0.30802I
a = 0.395590 + 0.007776I
b = 0.988167 − 0.243027I
−5.46115 − 3.91765I 0
u = 1.60314 + 0.19201I
a = 0.413865 + 0.095304I
b = 1.025450 − 0.268432I
−9.63402 + 0.74509I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60314 − 0.19201I
a = 0.413865 − 0.095304I
b = 1.025450 + 0.268432I
−9.63402 − 0.74509I 0
u = 0.341325
a = −10.9115
b = −0.954265
−2.53188 −77.9360
15
II. I
u
2
= hb + 1, u
5
− 4u
3
− u
2
+ a + 4u + 3, u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
3
=
−u
5
+ 4u
3
+ u
2
− 4u − 3
−1
a
11
=
−u
−u
3
+ u
a
2
=
−u
5
+ 4u
3
+ u
2
− 4u − 4
−1
a
1
=
−1
0
a
4
=
−u
5
+ 4u
3
+ u
2
− 4u − 3
−1
a
7
=
1
u
2
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
u
u
a
12
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
5
− 3u
4
− 19u
3
+ 5u
2
+ 8u − 6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
6
u
6
c
4
(u + 1)
6
c
5
, c
7
, c
9
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
8
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
10
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
c
11
, c
12
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
y
6
c
5
, c
7
, c
9
c
10
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
c
8
, c
11
, c
12
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493180 + 0.575288I
a = 0.26610 − 1.72116I
b = −1.00000
1.31531 + 1.97241I −15.7816 − 4.5012I
u = −0.493180 − 0.575288I
a = 0.26610 + 1.72116I
b = −1.00000
1.31531 − 1.97241I −15.7816 + 4.5012I
u = 0.483672
a = −4.27462
b = −1.00000
−2.38379 −3.08970
u = 1.52087 + 0.16310I
a = −0.417699 + 0.090629I
b = −1.00000
−5.34051 − 4.59213I −11.43321 + 5.39767I
u = 1.52087 − 0.16310I
a = −0.417699 − 0.090629I
b = −1.00000
−5.34051 + 4.59213I −11.43321 − 5.39767I
u = −1.53904
a = −0.422181
b = −1.00000
−9.30502 −14.4810
19
III. I
v
1
= ha, v
2
+ b + 2v , v
3
+ 3v
2
+ 2v + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
6
=
1
0
a
3
=
0
−v
2
− 2v
a
11
=
v
0
a
2
=
−v
2
− 2v
−v
2
− 2v
a
1
=
−v
2
− 2v
v + 2
a
4
=
v
2
+ 3v + 2
v
2
+ 3v + 1
a
7
=
v
2
+ 2v
−v − 2
a
8
=
−1
−v − 2
a
9
=
−v
2
− 2v − 1
−v
2
− 2v + 1
a
12
=
v + 1
2v
2
+ 6v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5v
2
− 11v − 13
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
8
u
3
− u
2
+ 2u − 1
c
2
, c
7
, c
9
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
10
u
3
c
6
, c
11
, c
12
u
3
+ u
2
+ 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
, c
11
, c
12
y
3
+ 3y
2
+ 2y − 1
c
2
, c
4
, c
7
c
9
y
3
− y
2
+ 2y − 1
c
5
, c
10
y
3
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.337641 + 0.562280I
a = 0
b = 0.877439 − 0.744862I
6.04826 + 5.65624I −8.27516 − 4.28659I
v = −0.337641 − 0.562280I
a = 0
b = 0.877439 + 0.744862I
6.04826 − 5.65624I −8.27516 + 4.28659I
v = −2.32472
a = 0
b = −0.754878
−2.22691 −14.4500
23
IV. I
v
2
=
ha, −6v
5
+29v
4
−57v
3
−43v
2
+10b+2v −1, v
6
−5v
5
+10v
4
+7v
3
−4v
2
−2v+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
6
=
1
0
a
3
=
0
3
5
v
5
−
29
10
v
4
+ ··· −
1
5
v +
1
10
a
11
=
v
0
a
2
=
3
5
v
5
−
29
10
v
4
+ ··· −
1
5
v +
1
10
3
5
v
5
−
29
10
v
4
+ ··· −
1
5
v +
1
10
a
1
=
3
5
v
5
−
29
10
v
4
+ ··· −
1
5
v +
1
10
−
9
20
v
5
+
11
5
v
4
+ ··· +
3
20
v +
9
4
a
4
=
−1.05000v
5
+ 5.10000v
4
+ ··· + 0.350000v + 2.15000
−1.05000v
5
+ 5.10000v
4
+ ··· + 0.350000v + 1.15000
a
7
=
−
3
5
v
5
+
29
10
v
4
+ ··· +
1
5
v −
1
10
9
20
v
5
−
11
5
v
4
+ ··· −
3
20
v −
9
4
a
8
=
−0.650000v
5
+ 3.30000v
4
+ ··· + 0.550000v − 0.0500000
9
20
v
5
−
11
5
v
4
+ ··· −
3
20
v −
9
4
a
9
=
−
1
10
v
5
+
3
10
v
4
+ ··· −
13
10
v +
3
5
1
5
v
5
−
7
10
v
4
+ ··· −
7
5
v −
3
2
a
12
=
1
4
v
5
−
13
10
v
4
+ ··· +
5
4
v −
3
20
7
20
v
5
−
21
10
v
4
+ ··· −
49
20
v +
7
4
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3
5
v
5
−
17
5
v
4
+
41
5
v
3
+
4
5
v
2
−
26
5
v −
37
5
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
8
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
7
, c
9
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
10
u
6
c
6
, c
11
, c
12
(u
3
+ u
2
+ 2u + 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y − 1)
2
c
2
, c
4
, c
7
c
9
(y
3
− y
2
+ 2y − 1)
2
c
5
, c
10
y
6
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.609638 + 0.241870I
a = 0
b = 0.877439 + 0.744862I
6.04826 −4.97493 + 1.29886I
v = −0.609638 − 0.241870I
a = 0
b = 0.877439 − 0.744862I
6.04826 −4.97493 − 1.29886I
v = 0.407481 + 0.137827I
a = 0
b = 0.877439 + 0.744862I
1.91067 − 2.82812I −9.06804 − 0.18883I
v = 0.407481 − 0.137827I
a = 0
b = 0.877439 − 0.744862I
1.91067 + 2.82812I −9.06804 + 0.18883I
v = 2.70216 + 2.29387I
a = 0
b = −0.754878
1.91067 − 2.82812I −11.4570 + 15.2977I
v = 2.70216 − 2.29387I
a = 0
b = −0.754878
1.91067 + 2.82812I −11.4570 − 15.2977I
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
3
− u
2
+ 2u − 1)
3
(u
102
+ 50u
101
+ ··· + 200u + 1)
c
2
((u − 1)
6
)(u
3
+ u
2
− 1)
3
(u
102
− 10u
101
+ ··· − 100u
2
+ 1)
c
3
u
6
(u
3
− u
2
+ 2u − 1)
3
(u
102
− 4u
101
+ ··· + 384u − 64)
c
4
((u + 1)
6
)(u
3
− u
2
+ 1)
3
(u
102
− 10u
101
+ ··· − 100u
2
+ 1)
c
5
u
9
(u
6
− u
5
+ ··· + u − 1)(u
102
− 2u
101
+ ··· − 1024u − 512)
c
6
u
6
(u
3
+ u
2
+ 2u + 1)
3
(u
102
− 4u
101
+ ··· + 384u − 64)
c
7
, c
9
(u
3
+ u
2
− 1)
3
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
102
+ 5u
101
+ ··· + 22859u + 3137)
c
8
(u
3
− u
2
+ 2u − 1)
3
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
102
− 5u
101
+ ··· + 3u + 1)
c
10
u
9
(u
6
+ u
5
+ ··· − u − 1)(u
102
− 2u
101
+ ··· − 1024u − 512)
c
11
, c
12
(u
3
+ u
2
+ 2u + 1)
3
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
102
− 5u
101
+ ··· + 3u + 1)
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
3
+ 3y
2
+ 2y − 1)
3
(y
102
+ 14y
101
+ ··· − 37224y + 1)
c
2
, c
4
((y − 1)
6
)(y
3
− y
2
+ 2y − 1)
3
(y
102
− 50y
101
+ ··· − 200y + 1)
c
3
, c
6
y
6
(y
3
+ 3y
2
+ 2y − 1)
3
(y
102
+ 48y
101
+ ··· − 24576y + 4096)
c
5
, c
10
y
9
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
102
− 56y
101
+ ··· − 10878976y + 262144)
c
7
, c
9
(y
3
− y
2
+ 2y − 1)
3
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
102
− 71y
101
+ ··· + 595599577y + 9840769)
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y − 1)
3
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
· (y
102
+ 85y
101
+ ··· + 57y + 1)
29
