12a
0807
(K12a
0807
)
A knot diagram
1
Linearized knot diagam
4 5 6 9 10 12 1 11 2 3 8 7
Solving Sequence
1,8
7 12
3,6
4 2 11 9 10 5
c
7
c
12
c
6
c
3
c
1
c
11
c
8
c
10
c
5
c
2
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h49791514u
59
+ 185733104u
58
+ ··· + 664747b + 436245750,
5475421u
59
+ 31624832u
58
+ ··· + 7312217a + 58998547, u
60
+ 5u
59
+ ··· − 38u + 11i
I
u
2
= h−2861u
38
a − 1053u
38
+ ··· − 2113a − 517, −u
38
a + u
38
+ ··· − 3a − 5, u
39
− 2u
38
+ ··· + 2u − 1i
I
u
3
= h3u
21
− 2u
20
+ ··· + b − 2, −u
21
+ u
20
+ ··· + a + 4, u
22
− 2u
21
+ ··· + u + 1i
I
u
4
= hb
2
+ b − 1, a − 1, u + 1i
I
v
1
= ha, b + 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 163 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
= h4.98 × 10
7
u
59
+ 1 .86 × 10
8
u
58
+ · · · + 6.65 × 10
5
b + 4.36 × 10
8
, 5.48 ×
10
6
u
59
+3.16×10
7
u
58
+· · ·+7.31×10
6
a+5.90×10
7
, u
60
+5u
59
+· · ·−38u+11i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
−0.748805u
59
− 4.32493u
58
+ ··· + 52.3418u − 8.06849
−74.9030u
59
− 279.404u
58
+ ··· + 2793.44u − 656.258
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
42.7214u
59
+ 157.014u
58
+ ··· − 1466.48u + 353.804
−102.962u
59
− 379.700u
58
+ ··· + 3682.85u − 871.934
a
2
=
−34.9557u
59
− 124.857u
58
+ ··· + 1080.98u − 269.488
46.2308u
59
+ 165.630u
58
+ ··· − 1559.60u + 373.881
a
11
=
u
3
− 2u
−u
3
+ u
a
9
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
10
=
4.60523u
59
+ 17.8774u
58
+ ··· − 165.454u + 35.6621
−42.1101u
59
− 161.731u
58
+ ··· + 1740.73u − 400.478
a
5
=
7.80133u
59
+ 27.2592u
58
+ ··· − 208.204u + 54.6615
−73.4028u
59
− 275.257u
58
+ ··· + 2770.22u − 651.201
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
121118688
664747
u
59
−
439577769
664747
u
58
+ ··· +
4220306946
664747
u −
1004828410
664747
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
60
+ 8u
59
+ ··· − 27u + 1
c
2
u
60
+ 34u
59
+ ··· − 87u − 11
c
4
, c
10
u
60
+ 17u
56
+ ··· + 7u + 1
c
5
, c
9
u
60
− u
59
+ ··· + 4u − 1
c
6
, c
7
, c
12
u
60
− 5u
59
+ ··· + 38u + 11
c
8
, c
11
u
60
+ 15u
59
+ ··· − 25484u − 1639
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
60
− 44y
59
+ ··· − 175y + 1
c
2
y
60
+ 58y
58
+ ··· − 1409y + 121
c
4
, c
10
y
60
+ 34y
58
+ ··· − 55y + 1
c
5
, c
9
y
60
− 25y
59
+ ··· − 66y + 1
c
6
, c
7
, c
12
y
60
− 51y
59
+ ··· − 674y + 121
c
8
, c
11
y
60
+ 41y
59
+ ··· − 39182108y + 2686321
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.060897 + 0.868711I
a = 1.74244 + 0.72857I
b = −1.61713 − 0.67161I
−8.13893 − 2.83634I −3.79343 + 3.27629I
u = 0.060897 − 0.868711I
a = 1.74244 − 0.72857I
b = −1.61713 + 0.67161I
−8.13893 + 2.83634I −3.79343 − 3.27629I
u = 0.128834 + 0.848151I
a = 3.09604 − 0.05310I
b = −2.55532 + 0.53851I
−5.9522 + 14.9479I 0. − 8.67429I
u = 0.128834 − 0.848151I
a = 3.09604 + 0.05310I
b = −2.55532 − 0.53851I
−5.9522 − 14.9479I 0. + 8.67429I
u = 0.095160 + 0.812795I
a = −3.40389 + 0.06404I
b = 2.60895 − 0.21567I
−6.77759 + 6.06790I −6.89903 − 8.29238I
u = 0.095160 − 0.812795I
a = −3.40389 − 0.06404I
b = 2.60895 + 0.21567I
−6.77759 − 6.06790I −6.89903 + 8.29238I
u = 1.139700 + 0.336402I
a = 1.40739 + 0.67616I
b = −1.16674 + 1.01101I
−3.09648 + 1.54338I 0
u = 1.139700 − 0.336402I
a = 1.40739 − 0.67616I
b = −1.16674 − 1.01101I
−3.09648 − 1.54338I 0
u = 0.121157 + 0.797619I
a = −2.01479 − 1.24838I
b = 1.55370 + 0.68878I
−6.18372 + 2.58960I −4.84200 − 1.19126I
u = 0.121157 − 0.797619I
a = −2.01479 + 1.24838I
b = 1.55370 − 0.68878I
−6.18372 − 2.58960I −4.84200 + 1.19126I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.123550 + 0.412628I
a = −0.72460 − 1.64385I
b = 2.25070 + 0.01928I
−2.90687 − 10.41390I 0
u = 1.123550 − 0.412628I
a = −0.72460 + 1.64385I
b = 2.25070 − 0.01928I
−2.90687 + 10.41390I 0
u = −1.205960 + 0.012637I
a = −0.103629 − 0.111372I
b = 0.787825 + 0.838109I
2.13388 − 0.44264I 0
u = −1.205960 − 0.012637I
a = −0.103629 + 0.111372I
b = 0.787825 − 0.838109I
2.13388 + 0.44264I 0
u = −0.011128 + 0.786562I
a = −2.68629 − 0.56383I
b = 1.94930 + 0.99862I
−5.66611 − 0.17773I −4.38219 − 0.43593I
u = −0.011128 − 0.786562I
a = −2.68629 + 0.56383I
b = 1.94930 − 0.99862I
−5.66611 + 0.17773I −4.38219 + 0.43593I
u = 1.166760 + 0.357089I
a = 0.97029 + 1.86168I
b = −2.17056 + 0.36127I
−3.50603 − 1.83244I 0
u = 1.166760 − 0.357089I
a = 0.97029 − 1.86168I
b = −2.17056 − 0.36127I
−3.50603 + 1.83244I 0
u = 0.548543 + 0.502233I
a = 0.206746 + 0.433608I
b = 0.745089 + 0.097408I
−0.86790 + 10.42950I 3.00610 − 9.66598I
u = 0.548543 − 0.502233I
a = 0.206746 − 0.433608I
b = 0.745089 − 0.097408I
−0.86790 − 10.42950I 3.00610 + 9.66598I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.431078 + 0.588336I
a = 0.023424 + 0.774923I
b = −0.107206 + 0.378275I
−1.26191 − 6.52666I 1.65444 + 4.13374I
u = 0.431078 − 0.588336I
a = 0.023424 − 0.774923I
b = −0.107206 − 0.378275I
−1.26191 + 6.52666I 1.65444 − 4.13374I
u = −1.250750 + 0.253692I
a = −0.602712 + 0.147425I
b = 1.166760 + 0.424599I
1.80106 − 1.18068I 0
u = −1.250750 − 0.253692I
a = −0.602712 − 0.147425I
b = 1.166760 − 0.424599I
1.80106 + 1.18068I 0
u = −0.077320 + 0.719425I
a = 1.32124 − 0.56354I
b = −1.066300 − 0.127595I
−1.73557 − 2.28005I 2.10056 + 2.97528I
u = −0.077320 − 0.719425I
a = 1.32124 + 0.56354I
b = −1.066300 + 0.127595I
−1.73557 + 2.28005I 2.10056 − 2.97528I
u = 1.206360 + 0.420533I
a = −1.030210 − 0.819652I
b = 1.26332 − 1.06914I
−4.61140 + 7.45006I 0
u = 1.206360 − 0.420533I
a = −1.030210 + 0.819652I
b = 1.26332 + 1.06914I
−4.61140 − 7.45006I 0
u = 1.27903
a = 1.93254
b = 0.333489
2.37328 0
u = −1.261350 + 0.340608I
a = 0.411479 − 1.290950I
b = −2.32788 + 0.56589I
−1.79214 − 3.88409I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.261350 − 0.340608I
a = 0.411479 + 1.290950I
b = −2.32788 − 0.56589I
−1.79214 + 3.88409I 0
u = −0.385617 + 0.575805I
a = 0.355886 + 0.193509I
b = 0.088406 − 0.407822I
0.93949 − 1.79577I 8.38505 − 1.97163I
u = −0.385617 − 0.575805I
a = 0.355886 − 0.193509I
b = 0.088406 + 0.407822I
0.93949 + 1.79577I 8.38505 + 1.97163I
u = 1.278460 + 0.340753I
a = 1.26291 + 1.54365I
b = −1.52939 + 1.35909I
−1.65511 + 4.23939I 0
u = 1.278460 − 0.340753I
a = 1.26291 − 1.54365I
b = −1.52939 − 1.35909I
−1.65511 − 4.23939I 0
u = −1.350340 + 0.079844I
a = 0.354882 − 0.159748I
b = 0.55689 + 1.39046I
3.39876 − 4.42651I 0
u = −1.350340 − 0.079844I
a = 0.354882 + 0.159748I
b = 0.55689 − 1.39046I
3.39876 + 4.42651I 0
u = 1.317550 + 0.310044I
a = −0.263784 − 1.093550I
b = 0.991089 − 0.453216I
2.64360 + 6.02566I 0
u = 1.317550 − 0.310044I
a = −0.263784 + 1.093550I
b = 0.991089 + 0.453216I
2.64360 − 6.02566I 0
u = 1.35461
a = −0.906395
b = −0.361301
6.51449 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.311420 + 0.396696I
a = −0.189189 + 1.092900I
b = 1.76017 − 0.21463I
−3.85452 − 1.69969I 0
u = −1.311420 − 0.396696I
a = −0.189189 − 1.092900I
b = 1.76017 + 0.21463I
−3.85452 + 1.69969I 0
u = −1.330390 + 0.355574I
a = 1.26040 − 1.73128I
b = −2.83443 − 0.72331I
−2.30463 − 10.27760I 0
u = −1.330390 − 0.355574I
a = 1.26040 + 1.73128I
b = −2.83443 + 0.72331I
−2.30463 + 10.27760I 0
u = −1.38309
a = 0.187317
b = 1.04622
3.23568 0
u = −1.346470 + 0.343806I
a = 0.20565 − 1.42562I
b = −1.73002 + 0.40643I
−1.56255 − 6.70988I 0
u = −1.346470 − 0.343806I
a = 0.20565 + 1.42562I
b = −1.73002 − 0.40643I
−1.56255 + 6.70988I 0
u = −1.354300 + 0.371721I
a = −1.20650 + 1.73448I
b = 2.62599 + 0.98286I
−1.2861 − 19.3357I 0
u = −1.354300 − 0.371721I
a = −1.20650 − 1.73448I
b = 2.62599 − 0.98286I
−1.2861 + 19.3357I 0
u = −1.41652 + 0.11414I
a = −0.669108 + 0.142685I
b = −0.682724 − 0.737781I
5.40592 − 12.35690I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41652 − 0.11414I
a = −0.669108 − 0.142685I
b = −0.682724 + 0.737781I
5.40592 + 12.35690I 0
u = −1.41428 + 0.17772I
a = 0.134372 + 0.588151I
b = −0.272154 + 0.118060I
4.63496 + 3.89220I 0
u = −1.41428 − 0.17772I
a = 0.134372 − 0.588151I
b = −0.272154 − 0.118060I
4.63496 − 3.89220I 0
u = 1.44039 + 0.21474I
a = −0.309129 − 0.085453I
b = −0.134108 − 0.270569I
6.80384 + 4.70309I 0
u = 1.44039 − 0.21474I
a = −0.309129 + 0.085453I
b = −0.134108 + 0.270569I
6.80384 − 4.70309I 0
u = 0.403727 + 0.360380I
a = −0.263367 − 1.336380I
b = −0.475150 + 0.280630I
−2.00858 + 3.05776I −2.14055 − 8.96943I
u = 0.403727 − 0.360380I
a = −0.263367 + 1.336380I
b = −0.475150 − 0.280630I
−2.00858 − 3.05776I −2.14055 + 8.96943I
u = 0.359656 + 0.302824I
a = 1.024700 − 0.936645I
b = −0.472574 − 0.106407I
−2.06170 − 0.42298I −2.32972 − 0.96462I
u = 0.359656 − 0.302824I
a = 1.024700 + 0.936645I
b = −0.472574 + 0.106407I
−2.06170 + 0.42298I −2.32972 + 0.96462I
u = −0.462483
a = 0.619787
b = 0.568615
1.01644 10.3330
10
II. I
u
2
= h−2861u
38
a − 1053u
38
+ · · · − 2113a − 517, −u
38
a + u
38
+ · · · −
3a − 5, u
39
− 2u
38
+ · · · + 2u − 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
a
7.18844au
38
+ 2.64573u
38
+ ··· + 5.30905a + 1.29899
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−4.36683au
38
+ 0.929648u
38
+ ··· − 2.32161a + 1.92462
9.67588au
38
+ 2.36935u
38
+ ··· + 7.18844a + 1.64573
a
2
=
−0.798995au
38
+ 0.422111u
38
+ ··· − 2.07035a + 0.452261
3.57538au
38
− 3.84171u
38
+ ··· + 3.22362a − 3.58040
a
11
=
u
3
− 2u
−u
3
+ u
a
9
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
10
=
2.22362au
38
− 3.58040u
38
+ ··· + 0.846734a − 4.87186
−3.03266au
38
− 1.21859u
38
+ ··· − 2.21357a + 0.801508
a
5
=
−3.21357au
38
+ 1.80151u
38
+ ··· − 1.55025a + 1.39447
7.18844au
38
+ 4.64573u
38
+ ··· + 5.30905a + 3.29899
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11u
38
− 9u
37
+ ··· + 13u + 23
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
78
− 3u
77
+ ··· − 2666u + 199
c
2
(u
39
− 19u
38
+ ··· + 3u − 2)
2
c
4
, c
10
u
78
− 2u
77
+ ··· + 35u + 1
c
5
, c
9
u
78
− 2u
77
+ ··· + 15u + 1
c
6
, c
7
, c
12
(u
39
+ 2u
38
+ ··· + 2u + 1)
2
c
8
, c
11
(u
39
− 9u
38
+ ··· + 41u − 8)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
78
+ 13y
77
+ ··· − 2946466y + 39601
c
2
(y
39
− 3y
38
+ ··· + 85y −4)
2
c
4
, c
10
y
78
+ 4y
77
+ ··· − 251y + 1
c
5
, c
9
y
78
+ 16y
77
+ ··· − 159y + 1
c
6
, c
7
, c
12
(y
39
− 32y
38
+ ··· + 14y −1)
2
c
8
, c
11
(y
39
+ 29y
38
+ ··· + 1473y −64)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.123651 + 0.855009I
a = −1.77146 − 0.28783I
b = 1.355350 + 0.397482I
−4.43189 − 6.50037I 3.53586 + 10.69545I
u = −0.123651 + 0.855009I
a = 2.68416 − 0.08902I
b = −2.40063 − 0.44845I
−4.43189 − 6.50037I 3.53586 + 10.69545I
u = −0.123651 − 0.855009I
a = −1.77146 + 0.28783I
b = 1.355350 − 0.397482I
−4.43189 + 6.50037I 3.53586 − 10.69545I
u = −0.123651 − 0.855009I
a = 2.68416 + 0.08902I
b = −2.40063 + 0.44845I
−4.43189 + 6.50037I 3.53586 − 10.69545I
u = −0.063917 + 0.838666I
a = 2.25814 − 1.13574I
b = −2.20893 + 1.16309I
−7.20996 − 5.30080I −6.54147 + 5.87182I
u = −0.063917 + 0.838666I
a = −3.01341 − 0.84137I
b = 2.27518 + 0.86812I
−7.20996 − 5.30080I −6.54147 + 5.87182I
u = −0.063917 − 0.838666I
a = 2.25814 + 1.13574I
b = −2.20893 − 1.16309I
−7.20996 + 5.30080I −6.54147 − 5.87182I
u = −0.063917 − 0.838666I
a = −3.01341 + 0.84137I
b = 2.27518 − 0.86812I
−7.20996 + 5.30080I −6.54147 − 5.87182I
u = −1.133230 + 0.422673I
a = 0.381507 − 0.944409I
b = −1.052720 + 0.111590I
−1.33992 + 1.91665I 7.11970 − 8.94516I
u = −1.133230 + 0.422673I
a = −0.64409 + 1.36564I
b = 2.18676 + 0.19276I
−1.33992 + 1.91665I 7.11970 − 8.94516I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.133230 − 0.422673I
a = 0.381507 + 0.944409I
b = −1.052720 − 0.111590I
−1.33992 − 1.91665I 7.11970 + 8.94516I
u = −1.133230 − 0.422673I
a = −0.64409 − 1.36564I
b = 2.18676 − 0.19276I
−1.33992 − 1.91665I 7.11970 + 8.94516I
u = −0.757825 + 0.192035I
a = 0.862379 + 0.191207I
b = 0.357929 − 0.065164I
0.481717 + 0.049103I 13.22495 − 2.86756I
u = −0.757825 + 0.192035I
a = −0.367173 + 0.260313I
b = 1.42082 − 0.18186I
0.481717 + 0.049103I 13.22495 − 2.86756I
u = −0.757825 − 0.192035I
a = 0.862379 − 0.191207I
b = 0.357929 + 0.065164I
0.481717 − 0.049103I 13.22495 + 2.86756I
u = −0.757825 − 0.192035I
a = −0.367173 − 0.260313I
b = 1.42082 + 0.18186I
0.481717 − 0.049103I 13.22495 + 2.86756I
u = 0.049569 + 0.770909I
a = 0.07625 + 2.42180I
b = −0.215843 − 1.013410I
−2.37878 + 5.47730I 1.04994 − 8.31805I
u = 0.049569 + 0.770909I
a = −3.71600 + 0.97162I
b = 3.06226 − 1.06664I
−2.37878 + 5.47730I 1.04994 − 8.31805I
u = 0.049569 − 0.770909I
a = 0.07625 − 2.42180I
b = −0.215843 + 1.013410I
−2.37878 − 5.47730I 1.04994 + 8.31805I
u = 0.049569 − 0.770909I
a = −3.71600 − 0.97162I
b = 3.06226 + 1.06664I
−2.37878 − 5.47730I 1.04994 + 8.31805I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.506814 + 0.542713I
a = 0.481931 − 0.063254I
b = 0.377429 − 0.519249I
1.05104 − 1.97403I 16.0074 + 7.0550I
u = −0.506814 + 0.542713I
a = 0.127230 + 0.318204I
b = −0.144855 − 0.286684I
1.05104 − 1.97403I 16.0074 + 7.0550I
u = −0.506814 − 0.542713I
a = 0.481931 + 0.063254I
b = 0.377429 + 0.519249I
1.05104 + 1.97403I 16.0074 − 7.0550I
u = −0.506814 − 0.542713I
a = 0.127230 − 0.318204I
b = −0.144855 + 0.286684I
1.05104 + 1.97403I 16.0074 − 7.0550I
u = −1.206090 + 0.389767I
a = −1.25389 + 1.13808I
b = 1.55489 + 1.67996I
−3.69786 + 0.88565I −3.87253 − 2.40555I
u = −1.206090 + 0.389767I
a = 0.43407 − 1.76270I
b = −2.10776 + 0.41811I
−3.69786 + 0.88565I −3.87253 − 2.40555I
u = −1.206090 − 0.389767I
a = −1.25389 − 1.13808I
b = 1.55489 − 1.67996I
−3.69786 − 0.88565I −3.87253 + 2.40555I
u = −1.206090 − 0.389767I
a = 0.43407 + 1.76270I
b = −2.10776 − 0.41811I
−3.69786 − 0.88565I −3.87253 + 2.40555I
u = 1.233670 + 0.316469I
a = −1.15724 + 0.96995I
b = 0.421855 − 0.995500I
1.25464 − 1.55345I 4.26613 + 4.65636I
u = 1.233670 + 0.316469I
a = 0.32061 + 2.14479I
b = −3.21372 − 0.03357I
1.25464 − 1.55345I 4.26613 + 4.65636I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.233670 − 0.316469I
a = −1.15724 − 0.96995I
b = 0.421855 + 0.995500I
1.25464 + 1.55345I 4.26613 − 4.65636I
u = 1.233670 − 0.316469I
a = 0.32061 − 2.14479I
b = −3.21372 + 0.03357I
1.25464 + 1.55345I 4.26613 − 4.65636I
u = 1.273050 + 0.106169I
a = 0.608908 − 0.637834I
b = 0.296458 − 1.362430I
3.32972 + 5.12862I 3.60822 − 7.93881I
u = 1.273050 + 0.106169I
a = 0.327473 − 1.231730I
b = 0.41014 + 1.38736I
3.32972 + 5.12862I 3.60822 − 7.93881I
u = 1.273050 − 0.106169I
a = 0.608908 + 0.637834I
b = 0.296458 + 1.362430I
3.32972 − 5.12862I 3.60822 + 7.93881I
u = 1.273050 − 0.106169I
a = 0.327473 + 1.231730I
b = 0.41014 − 1.38736I
3.32972 − 5.12862I 3.60822 + 7.93881I
u = 0.007878 + 0.698911I
a = 0.412394 − 0.002485I
b = −0.533870 − 0.726362I
−1.02896 − 2.54522I 3.65939 + 1.47176I
u = 0.007878 + 0.698911I
a = 3.23412 − 1.35354I
b = −1.86056 + 0.74398I
−1.02896 − 2.54522I 3.65939 + 1.47176I
u = 0.007878 − 0.698911I
a = 0.412394 + 0.002485I
b = −0.533870 + 0.726362I
−1.02896 + 2.54522I 3.65939 − 1.47176I
u = 0.007878 − 0.698911I
a = 3.23412 + 1.35354I
b = −1.86056 − 0.74398I
−1.02896 + 2.54522I 3.65939 − 1.47176I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.288800 + 0.298775I
a = 0.0834285 − 0.1010380I
b = 1.053860 − 0.550749I
3.03679 − 1.08193I 9.39220 + 0.I
u = −1.288800 + 0.298775I
a = −1.87346 + 1.27639I
b = 2.09459 + 1.34584I
3.03679 − 1.08193I 9.39220 + 0.I
u = −1.288800 − 0.298775I
a = 0.0834285 + 0.1010380I
b = 1.053860 + 0.550749I
3.03679 + 1.08193I 9.39220 + 0.I
u = −1.288800 − 0.298775I
a = −1.87346 − 1.27639I
b = 2.09459 − 1.34584I
3.03679 + 1.08193I 9.39220 + 0.I
u = −1.324220 + 0.023221I
a = −1.004440 + 0.507659I
b = −0.67432 + 1.84418I
6.27729 − 4.23327I 13.4928 + 5.6612I
u = −1.324220 + 0.023221I
a = 1.192020 − 0.491264I
b = −0.073206 + 1.385530I
6.27729 − 4.23327I 13.4928 + 5.6612I
u = −1.324220 − 0.023221I
a = −1.004440 − 0.507659I
b = −0.67432 − 1.84418I
6.27729 + 4.23327I 13.4928 − 5.6612I
u = −1.324220 − 0.023221I
a = 1.192020 + 0.491264I
b = −0.073206 − 1.385530I
6.27729 + 4.23327I 13.4928 − 5.6612I
u = 1.299180 + 0.291471I
a = −0.127194 − 0.519240I
b = 0.101917 − 0.905492I
3.04618 + 6.08935I 9.11052 − 5.32314I
u = 1.299180 + 0.291471I
a = −0.58286 − 1.84086I
b = 1.88079 − 0.04494I
3.04618 + 6.08935I 9.11052 − 5.32314I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.299180 − 0.291471I
a = −0.127194 + 0.519240I
b = 0.101917 + 0.905492I
3.04618 − 6.08935I 9.11052 + 5.32314I
u = 1.299180 − 0.291471I
a = −0.58286 + 1.84086I
b = 1.88079 + 0.04494I
3.04618 − 6.08935I 9.11052 + 5.32314I
u = −1.303360 + 0.334319I
a = 1.15816 + 1.12222I
b = 0.006325 − 1.085460I
1.85272 − 9.46925I 0. + 10.60799I
u = −1.303360 + 0.334319I
a = 1.61855 − 1.77976I
b = −2.89602 − 1.91883I
1.85272 − 9.46925I 0. + 10.60799I
u = −1.303360 − 0.334319I
a = 1.15816 − 1.12222I
b = 0.006325 + 1.085460I
1.85272 + 9.46925I 0. − 10.60799I
u = −1.303360 − 0.334319I
a = 1.61855 + 1.77976I
b = −2.89602 + 1.91883I
1.85272 + 9.46925I 0. − 10.60799I
u = 1.36287
a = −0.974911
b = −0.855309
6.48774 13.8410
u = 1.36287
a = −0.873301
b = 0.0714531
6.48774 13.8410
u = 1.313580 + 0.373944I
a = 0.02364 − 1.49562I
b = 2.63616 + 0.57247I
−2.90240 + 9.65793I 0
u = 1.313580 + 0.373944I
a = 1.59640 + 1.39253I
b = −2.30070 + 1.28293I
−2.90240 + 9.65793I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.313580 − 0.373944I
a = 0.02364 + 1.49562I
b = 2.63616 − 0.57247I
−2.90240 − 9.65793I 0
u = 1.313580 − 0.373944I
a = 1.59640 − 1.39253I
b = −2.30070 − 1.28293I
−2.90240 − 9.65793I 0
u = 1.352090 + 0.376162I
a = 0.912749 + 0.851853I
b = −1.48397 + 0.70255I
0.20827 + 10.92560I 0
u = 1.352090 + 0.376162I
a = −0.96319 − 1.60889I
b = 2.36793 − 0.95704I
0.20827 + 10.92560I 0
u = 1.352090 − 0.376162I
a = 0.912749 − 0.851853I
b = −1.48397 − 0.70255I
0.20827 − 10.92560I 0
u = 1.352090 − 0.376162I
a = −0.96319 + 1.60889I
b = 2.36793 + 0.95704I
0.20827 − 10.92560I 0
u = 1.40890 + 0.13092I
a = −0.713500 − 0.184447I
b = −0.272694 + 0.261424I
7.17527 + 4.13148I 0
u = 1.40890 + 0.13092I
a = 0.125998 − 0.164559I
b = 0.094521 − 0.700099I
7.17527 + 4.13148I 0
u = 1.40890 − 0.13092I
a = −0.713500 + 0.184447I
b = −0.272694 − 0.261424I
7.17527 − 4.13148I 0
u = 1.40890 − 0.13092I
a = 0.125998 + 0.164559I
b = 0.094521 + 0.700099I
7.17527 − 4.13148I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.218111 + 0.511499I
a = −0.096291 + 0.207038I
b = −0.582754 − 0.545183I
−1.06178 − 3.07962I −0.39349 + 8.73887I
u = −0.218111 + 0.511499I
a = 1.70766 − 1.62859I
b = −0.685003 − 0.101681I
−1.06178 − 3.07962I −0.39349 + 8.73887I
u = −0.218111 − 0.511499I
a = −0.096291 − 0.207038I
b = −0.582754 + 0.545183I
−1.06178 + 3.07962I −0.39349 − 8.73887I
u = −0.218111 − 0.511499I
a = 1.70766 + 1.62859I
b = −0.685003 + 0.101681I
−1.06178 + 3.07962I −0.39349 − 8.73887I
u = 0.306674 + 0.085981I
a = 0.77627 − 1.78794I
b = 0.74393 + 1.20863I
1.31871 + 3.86348I 13.1636 − 8.7518I
u = 0.306674 + 0.085981I
a = −2.69574 − 2.71187I
b = −0.599614 + 0.140224I
1.31871 + 3.86348I 13.1636 − 8.7518I
u = 0.306674 − 0.085981I
a = 0.77627 + 1.78794I
b = 0.74393 − 1.20863I
1.31871 − 3.86348I 13.1636 + 8.7518I
u = 0.306674 − 0.085981I
a = −2.69574 + 2.71187I
b = −0.599614 − 0.140224I
1.31871 − 3.86348I 13.1636 + 8.7518I
21
III.
I
u
3
= h3u
21
−2u
20
+· · ·+b−2, −u
21
+u
20
+· · ·+a+4, u
22
−2u
21
+· · ·+u+1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
u
21
− u
20
+ ··· − 2u − 4
−3u
21
+ 2u
20
+ ··· + 21u
2
+ 2
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
3u
21
− 3u
20
+ ··· − u − 5
−6u
21
+ 4u
20
+ ··· + 3u + 4
a
2
=
u
20
− u
19
+ ··· − 11u − 2
−2u
21
+ u
20
+ ··· + 4u + 2
a
11
=
u
3
− 2u
−u
3
+ u
a
9
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
10
=
u
20
− u
19
+ ··· − 11u + 1
−4u
21
+ 3u
20
+ ··· + 10u + 4
a
5
=
2u
21
− 2u
20
+ ··· − 2u − 4
−3u
21
+ 2u
20
+ ··· − u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −18u
21
+12u
20
+164u
19
−73u
18
−631u
17
+113u
16
+1249u
15
+212u
14
−1109u
13
−922u
12
−
246u
11
+972u
10
+1326u
9
+140u
8
−690u
7
−782u
6
−335u
5
+134u
4
+253u
3
+234u
2
+51u+19
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
22
− 7u
21
+ ··· − 10u + 1
c
2
u
22
+ 15u
21
+ ··· + 62u + 5
c
4
, c
10
u
22
+ u
21
+ ··· + 5u
2
+ 1
c
5
, c
9
u
22
+ 5u
20
+ ··· − u + 1
c
6
, c
7
u
22
− 2u
21
+ ··· + u + 1
c
8
u
22
+ 6u
21
+ ··· + 21u + 5
c
11
u
22
− 6u
21
+ ··· − 21u + 5
c
12
u
22
+ 2u
21
+ ··· − u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
22
+ 11y
21
+ ··· − 2y + 1
c
2
y
22
+ 3y
21
+ ··· − 84y + 25
c
4
, c
10
y
22
+ 7y
21
+ ··· + 10y + 1
c
5
, c
9
y
22
+ 10y
21
+ ··· + 7y + 1
c
6
, c
7
, c
12
y
22
− 20y
21
+ ··· + 23y + 1
c
8
, c
11
y
22
+ 12y
21
+ ··· + 529y + 25
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.083765 + 0.835376I
a = −2.53587 − 0.25325I
b = 2.09538 + 0.30590I
−5.58210 − 5.56224I −0.33278 + 5.61076I
u = −0.083765 − 0.835376I
a = −2.53587 + 0.25325I
b = 2.09538 − 0.30590I
−5.58210 + 5.56224I −0.33278 − 5.61076I
u = −0.475591 + 0.593446I
a = −0.242359 + 0.230281I
b = −0.154285 + 0.239343I
0.59401 − 2.04789I −6.78919 + 8.33532I
u = −0.475591 − 0.593446I
a = −0.242359 − 0.230281I
b = −0.154285 − 0.239343I
0.59401 + 2.04789I −6.78919 − 8.33532I
u = −1.179230 + 0.391528I
a = 0.59508 − 1.38345I
b = −1.73243 − 0.23268I
−2.22170 + 1.14853I 2.14445 − 1.86985I
u = −1.179230 − 0.391528I
a = 0.59508 + 1.38345I
b = −1.73243 + 0.23268I
−2.22170 − 1.14853I 2.14445 + 1.86985I
u = 0.011243 + 0.717282I
a = 2.12798 + 1.49333I
b = −1.68397 − 0.42028I
−1.64583 + 3.75609I 0.57652 − 6.79053I
u = 0.011243 − 0.717282I
a = 2.12798 − 1.49333I
b = −1.68397 + 0.42028I
−1.64583 − 3.75609I 0.57652 + 6.79053I
u = 1.300670 + 0.072382I
a = 0.256368 + 0.166926I
b = −0.30681 − 1.72598I
4.80274 + 4.89641I 9.74683 − 7.87967I
u = 1.300670 − 0.072382I
a = 0.256368 − 0.166926I
b = −0.30681 + 1.72598I
4.80274 − 4.89641I 9.74683 + 7.87967I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.273250 + 0.294154I
a = −1.192430 − 0.456556I
b = 1.92456 − 0.89194I
2.27717 − 0.10563I 6.12462 + 3.49316I
u = 1.273250 − 0.294154I
a = −1.192430 + 0.456556I
b = 1.92456 + 0.89194I
2.27717 + 0.10563I 6.12462 − 3.49316I
u = −1.311820 + 0.109771I
a = −0.355234 − 1.013560I
b = −0.423319 − 0.141616I
4.72723 + 2.17924I 8.35049 − 2.29721I
u = −1.311820 − 0.109771I
a = −0.355234 + 1.013560I
b = −0.423319 + 0.141616I
4.72723 − 2.17924I 8.35049 + 2.29721I
u = −1.289130 + 0.294586I
a = 0.17593 + 1.69035I
b = 1.51498 + 0.02014I
2.41432 − 7.40770I 5.29212 + 9.89233I
u = −1.289130 − 0.294586I
a = 0.17593 − 1.69035I
b = 1.51498 − 0.02014I
2.41432 + 7.40770I 5.29212 − 9.89233I
u = 1.324580 + 0.368590I
a = 1.07391 + 1.27879I
b = −2.26492 + 0.82769I
−1.17021 + 9.88984I 4.50443 − 8.10827I
u = 1.324580 − 0.368590I
a = 1.07391 − 1.27879I
b = −2.26492 − 0.82769I
−1.17021 − 9.88984I 4.50443 + 8.10827I
u = 1.44830 + 0.20263I
a = 0.269630 + 0.177889I
b = 0.1028190 + 0.0400194I
6.74015 + 4.85997I −3.8232 − 25.0005I
u = 1.44830 − 0.20263I
a = 0.269630 − 0.177889I
b = 0.1028190 − 0.0400194I
6.74015 − 4.85997I −3.8232 + 25.0005I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.018493 + 0.294318I
a = −3.17301 − 0.51149I
b = 0.428003 − 0.695837I
0.57876 − 3.67907I 0.70568 + 5.96025I
u = −0.018493 − 0.294318I
a = −3.17301 + 0.51149I
b = 0.428003 + 0.695837I
0.57876 + 3.67907I 0.70568 − 5.96025I
27
IV. I
u
4
= hb
2
+ b − 1, a − 1, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
8
=
1
0
a
7
=
1
1
a
12
=
1
0
a
3
=
1
b
a
6
=
0
1
a
4
=
1
b + 1
a
2
=
1
b
a
11
=
1
0
a
9
=
1
0
a
10
=
b + 1
−b + 1
a
5
=
b + 2
b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
12
(u − 1)
2
c
2
, c
8
, c
11
u
2
c
4
, c
5
, c
9
c
10
u
2
+ u − 1
c
6
, c
7
(u + 1)
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
12
(y −1)
2
c
2
, c
8
, c
11
y
2
c
4
, c
5
, c
9
c
10
y
2
− 3y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 0.618034
0 −5.00000
u = −1.00000
a = 1.00000
b = −1.61803
0 −5.00000
31
V. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
1
=
1
0
a
8
=
1
0
a
7
=
1
0
a
12
=
1
0
a
3
=
0
−1
a
6
=
1
0
a
4
=
1
−1
a
2
=
0
1
a
11
=
1
0
a
9
=
1
0
a
10
=
1
1
a
5
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
9
, c
10
u + 1
c
2
, c
6
, c
7
c
8
, c
11
, c
12
u
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
9
, c
10
y −1
c
2
, c
6
, c
7
c
8
, c
11
, c
12
y
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
−1.64493 −6.00000
35
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
((u − 1)
2
)(u + 1)(u
22
− 7u
21
+ ··· − 10u + 1)(u
60
+ 8u
59
+ ··· − 27u + 1)
· (u
78
− 3u
77
+ ··· − 2666u + 199)
c
2
u
3
(u
22
+ 15u
21
+ ··· + 62u + 5)(u
39
− 19u
38
+ ··· + 3u − 2)
2
· (u
60
+ 34u
59
+ ··· − 87u − 11)
c
4
, c
10
(u + 1)(u
2
+ u − 1)(u
22
+ u
21
+ ··· + 5u
2
+ 1)(u
60
+ 17u
56
+ ··· + 7u + 1)
· (u
78
− 2u
77
+ ··· + 35u + 1)
c
5
, c
9
(u + 1)(u
2
+ u − 1)(u
22
+ 5u
20
+ ··· − u + 1)(u
60
− u
59
+ ··· + 4u − 1)
· (u
78
− 2u
77
+ ··· + 15u + 1)
c
6
, c
7
u(u + 1)
2
(u
22
− 2u
21
+ ··· + u + 1)(u
39
+ 2u
38
+ ··· + 2u + 1)
2
· (u
60
− 5u
59
+ ··· + 38u + 11)
c
8
u
3
(u
22
+ 6u
21
+ ··· + 21u + 5)(u
39
− 9u
38
+ ··· + 41u − 8)
2
· (u
60
+ 15u
59
+ ··· − 25484u − 1639)
c
11
u
3
(u
22
− 6u
21
+ ··· − 21u + 5)(u
39
− 9u
38
+ ··· + 41u − 8)
2
· (u
60
+ 15u
59
+ ··· − 25484u − 1639)
c
12
u(u − 1)
2
(u
22
+ 2u
21
+ ··· − u + 1)(u
39
+ 2u
38
+ ··· + 2u + 1)
2
· (u
60
− 5u
59
+ ··· + 38u + 11)
36
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
3
)(y
22
+ 11y
21
+ ··· − 2y + 1)(y
60
− 44y
59
+ ··· − 175y + 1)
· (y
78
+ 13y
77
+ ··· − 2946466y + 39601)
c
2
y
3
(y
22
+ 3y
21
+ ··· − 84y + 25)(y
39
− 3y
38
+ ··· + 85y −4)
2
· (y
60
+ 58y
58
+ ··· − 1409y + 121)
c
4
, c
10
(y −1)(y
2
− 3y + 1)(y
22
+ 7y
21
+ ··· + 10y + 1)
· (y
60
+ 34y
58
+ ··· − 55y + 1)(y
78
+ 4y
77
+ ··· − 251y + 1)
c
5
, c
9
(y −1)(y
2
− 3y + 1)(y
22
+ 10y
21
+ ··· + 7y + 1)
· (y
60
− 25y
59
+ ··· − 66y + 1)(y
78
+ 16y
77
+ ··· − 159y + 1)
c
6
, c
7
, c
12
y(y −1)
2
(y
22
− 20y
21
+ ··· + 23y + 1)
· ((y
39
− 32y
38
+ ··· + 14y −1)
2
)(y
60
− 51y
59
+ ··· − 674y + 121)
c
8
, c
11
y
3
(y
22
+ 12y
21
+ ··· + 529y + 25)(y
39
+ 29y
38
+ ··· + 1473y −64)
2
· (y
60
+ 41y
59
+ ··· − 39182108y + 2686321)
37
