12a
0117
(K12a
0117
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 10 4 11 7 9 1 6
Solving Sequence
3,8 4,11 5,9
2 1 12 7 10 6
c
3
c
8
c
2
c
1
c
11
c
7
c
10
c
6
c
4
, c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3.99437 × 10
56
u
42
− 1.17694 × 10
57
u
41
+ ··· + 1.61592 × 10
58
d + 3.40126 × 10
57
,
3.31530 × 10
55
u
42
− 3.28100 × 10
56
u
41
+ ··· + 3.23183 × 10
58
c + 4.23971 × 10
58
,
− 4.23475 × 10
55
u
42
+ 5.01357 × 10
55
u
41
+ ··· + 1.61592 × 10
58
b − 1.64157 × 10
57
,
1.77513 × 10
55
u
42
− 8.50273 × 10
55
u
41
+ ··· + 3.23183 × 10
58
a − 3.36911 × 10
58
, u
43
− 3u
42
+ ··· + 64u − 32i
I
u
2
= h5.02544 × 10
17
u
34
− 6.24095 × 10
17
u
33
+ ··· + 3.02602 × 10
18
d + 2.19741 × 10
18
,
− 6.42534 × 10
19
u
34
− 3.74850 × 10
19
u
33
+ ··· + 4.84163 × 10
19
c + 2.56918 × 10
19
,
4.96996 × 10
18
au
34
− 6.75491 × 10
18
u
34
+ ··· − 1.88128 × 10
19
a − 4.81090 × 10
19
,
− 5.09108 × 10
19
au
34
− 2.42015 × 10
19
u
34
+ ··· − 1.99866 × 10
19
a − 6.67500 × 10
19
, u
35
+ u
34
+ ··· − 8u − 4i
I
v
1
= hc, d + 1, b, a − 1, v
2
+ v + 1i
I
v
2
= ha, d + 1, c + a, b − 1, v
2
+ v + 1i
I
v
3
= ha, d, c + 1, b − 1, v + 1i
I
v
4
= ha, d
2
v
2
− dv + 1, v
2
dc − v
2
d − cv + a + v, da − c + 1, c
2
v
2
− cav − 2v
2
c + a
2
+ av + v
2
, b − 1i
* 5 irreducible components of dim
C
= 0, with total 118 representations.
* 1 irreducible components of dim
C
= 1
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
= h3.99 × 10
56
u
42
− 1.18× 10
57
u
41
+ · · · + 1.62 × 10
58
d +3.40 × 10
57
, 3.32 ×
10
55
u
42
− 3.28 × 10
56
u
41
+ · · · + 3.23 × 10
58
c + 4.24 × 10
58
, −4.23 ×
10
55
u
42
+ 5.01 × 10
55
u
41
+ · · · + 1.62 × 10
58
b − 1.64 × 10
57
, 1.78 × 10
55
u
42
−
8.50 × 10
55
u
41
+ · · · + 3.23 × 10
58
a − 3.37 × 10
58
, u
43
− 3u
42
+ · · · + 64u − 32i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
−0.00102583u
42
+ 0.0101521u
41
+ ··· − 0.345721u − 1.31186
−0.0247189u
42
+ 0.0728342u
41
+ ··· − 0.100365u − 0.210485
a
5
=
−0.000549265u
42
+ 0.00263093u
41
+ ··· + 0.260997u + 1.04248
0.00262065u
42
− 0.00310262u
41
+ ··· − 0.582583u + 0.101587
a
9
=
0.0176645u
42
− 0.0450742u
41
+ ··· − 2.28416u − 0.505300
−0.0151840u
42
+ 0.0606156u
41
+ ··· + 2.05478u − 1.00258
a
2
=
−0.000549265u
42
+ 0.00263093u
41
+ ··· + 0.260997u + 1.04248
−0.00664203u
42
+ 0.00629753u
41
+ ··· + 0.502086u − 0.0701269
a
1
=
−0.00719130u
42
+ 0.00892846u
41
+ ··· + 0.763083u + 0.972348
−0.00664203u
42
+ 0.00629753u
41
+ ··· + 0.502086u − 0.0701269
a
12
=
−0.00209131u
42
+ 0.0152778u
41
+ ··· − 0.305485u − 1.53809
−0.0237130u
42
+ 0.0774882u
41
+ ··· − 0.381714u − 0.292656
a
7
=
u
u
3
+ u
a
10
=
0.0268260u
42
− 0.0643618u
41
+ ··· − 3.05990u − 0.696376
0.000919890u
42
+ 0.0297984u
41
+ ··· + 1.04761u − 0.931356
a
6
=
−0.0236931u
42
+ 0.0626821u
41
+ ··· + 0.245356u + 1.10137
−0.0252351u
42
+ 0.0753290u
41
+ ··· − 0.321126u − 0.479194
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.141642u
42
+ 0.373966u
41
+ ··· + 18.4912u − 10.3634
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
43
+ 19u
42
+ ··· + 11u + 1
c
2
, c
4
, c
5
c
12
u
43
− 5u
42
+ ··· − 5u + 1
c
3
, c
7
u
43
+ 3u
42
+ ··· + 64u + 32
c
6
, c
9
u
43
+ u
42
+ ··· + 8u + 4
c
8
, c
10
u
43
+ 15u
42
+ ··· + 88u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
43
+ 21y
42
+ ··· − 117y − 1
c
2
, c
4
, c
5
c
12
y
43
− 19y
42
+ ··· + 11y − 1
c
3
, c
7
y
43
+ 15y
42
+ ··· − 1024y − 1024
c
6
, c
9
y
43
+ 15y
42
+ ··· + 88y − 16
c
8
, c
10
y
43
+ 27y
42
+ ··· + 18208y − 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.083173 + 0.999400I
a = 0.72843 − 1.47481I
b = −0.730777 + 0.545079I
c = 0.847687 + 0.941729I
d = −0.167389 − 0.931774I
−0.05445 + 4.88438I −6.23953 − 8.26907I
u = −0.083173 − 0.999400I
a = 0.72843 + 1.47481I
b = −0.730777 − 0.545079I
c = 0.847687 − 0.941729I
d = −0.167389 + 0.931774I
−0.05445 − 4.88438I −6.23953 + 8.26907I
u = −0.853926 + 0.430623I
a = 0.481539 − 0.101502I
b = 0.988333 + 0.419116I
c = −0.433251 + 0.229265I
d = −1.40759 + 0.95521I
−2.38574 − 3.27178I −9.17419 + 4.94523I
u = −0.853926 − 0.430623I
a = 0.481539 + 0.101502I
b = 0.988333 − 0.419116I
c = −0.433251 − 0.229265I
d = −1.40759 − 0.95521I
−2.38574 + 3.27178I −9.17419 − 4.94523I
u = 1.033880 + 0.177916I
a = 0.555689 − 0.233546I
b = 0.529415 + 0.642786I
c = −0.074981 + 1.239350I
d = −0.257235 + 0.960210I
2.18783 + 1.46576I −4.39540 + 0.53246I
u = 1.033880 − 0.177916I
a = 0.555689 + 0.233546I
b = 0.529415 − 0.642786I
c = −0.074981 − 1.239350I
d = −0.257235 − 0.960210I
2.18783 − 1.46576I −4.39540 − 0.53246I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073470 + 0.049653I
a = 0.530276 + 0.204737I
b = 0.641163 − 0.633645I
c = 0.195783 − 1.125570I
d = −0.132889 − 0.974636I
2.38615 + 4.03105I −4.49490 − 6.55598I
u = −1.073470 − 0.049653I
a = 0.530276 − 0.204737I
b = 0.641163 + 0.633645I
c = 0.195783 + 1.125570I
d = −0.132889 + 0.974636I
2.38615 − 4.03105I −4.49490 + 6.55598I
u = −0.118650 + 1.091750I
a = 0.665477 + 1.093120I
b = −0.593668 − 0.667444I
c = 0.042888 − 0.446984I
d = −0.181308 + 1.017000I
3.02575 − 1.21250I −0.81942 + 2.86814I
u = −0.118650 − 1.091750I
a = 0.665477 − 1.093120I
b = −0.593668 + 0.667444I
c = 0.042888 + 0.446984I
d = −0.181308 − 1.017000I
3.02575 + 1.21250I −0.81942 − 2.86814I
u = 0.359241 + 0.820253I
a = 0.870329 − 0.688965I
b = −0.293648 + 0.559159I
c = −0.888721 + 0.717011I
d = −0.421777 − 0.556156I
−0.40821 − 1.76300I −5.68682 + 2.17312I
u = 0.359241 − 0.820253I
a = 0.870329 + 0.688965I
b = −0.293648 − 0.559159I
c = −0.888721 − 0.717011I
d = −0.421777 + 0.556156I
−0.40821 + 1.76300I −5.68682 − 2.17312I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.910628 + 0.648287I
a = 0.449928 + 0.096871I
b = 1.124110 − 0.457326I
c = −0.725195 + 0.750875I
d = −2.15758 + 0.22862I
−6.78885 + 5.21532I −15.4874 − 4.9651I
u = 0.910628 − 0.648287I
a = 0.449928 − 0.096871I
b = 1.124110 + 0.457326I
c = −0.725195 − 0.750875I
d = −2.15758 − 0.22862I
−6.78885 − 5.21532I −15.4874 + 4.9651I
u = 0.653698 + 0.530431I
a = 0.474331 + 0.068978I
b = 1.064570 − 0.300236I
c = −1.46607 − 0.52025I
d = −2.88991 − 1.78080I
−4.07070 − 1.09789I −13.44053 + 1.40134I
u = 0.653698 − 0.530431I
a = 0.474331 − 0.068978I
b = 1.064570 + 0.300236I
c = −1.46607 + 0.52025I
d = −2.88991 + 1.78080I
−4.07070 + 1.09789I −13.44053 − 1.40134I
u = 0.576447 + 1.031310I
a = −0.28667 + 1.83591I
b = −1.083030 − 0.531725I
c = 0.534742 + 1.166610I
d = −1.301930 − 0.329738I
−2.58520 − 3.71825I −9.87585 + 4.37570I
u = 0.576447 − 1.031310I
a = −0.28667 − 1.83591I
b = −1.083030 + 0.531725I
c = 0.534742 − 1.166610I
d = −1.301930 + 0.329738I
−2.58520 + 3.71825I −9.87585 − 4.37570I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.098260 + 0.588414I
a = 0.444497 − 0.121481I
b = 1.093370 + 0.572119I
c = 0.249890 − 0.823067I
d = −1.021840 − 0.591171I
−0.56681 − 5.57701I −7.91552 + 3.90122I
u = −1.098260 − 0.588414I
a = 0.444497 + 0.121481I
b = 1.093370 − 0.572119I
c = 0.249890 + 0.823067I
d = −1.021840 + 0.591171I
−0.56681 + 5.57701I −7.91552 − 3.90122I
u = −0.614898 + 1.118930I
a = −0.31373 − 1.65536I
b = −1.110520 + 0.583151I
c = 0.160557 − 0.564023I
d = −0.993758 + 0.779989I
−0.28043 + 8.69625I −6.61034 − 7.94559I
u = −0.614898 − 1.118930I
a = −0.31373 + 1.65536I
b = −1.110520 − 0.583151I
c = 0.160557 + 0.564023I
d = −0.993758 − 0.779989I
−0.28043 − 8.69625I −6.61034 + 7.94559I
u = 1.109210 + 0.657844I
a = 0.436604 + 0.117557I
b = 1.135580 − 0.575012I
c = 0.205444 + 1.179480I
d = −1.16587 + 0.97462I
−1.67059 + 11.25340I −9.77881 − 8.46956I
u = 1.109210 − 0.657844I
a = 0.436604 − 0.117557I
b = 1.135580 + 0.575012I
c = 0.205444 − 1.179480I
d = −1.16587 − 0.97462I
−1.67059 − 11.25340I −9.77881 + 8.46956I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.724262 + 1.081360I
a = −0.51124 + 1.64089I
b = −1.173080 − 0.555502I
c = −0.733855 + 0.745817I
d = −1.52033 − 1.25212I
−5.40682 − 11.27400I −13.1483 + 8.7166I
u = 0.724262 − 1.081360I
a = −0.51124 − 1.64089I
b = −1.173080 + 0.555502I
c = −0.733855 − 0.745817I
d = −1.52033 + 1.25212I
−5.40682 + 11.27400I −13.1483 − 8.7166I
u = −0.460216 + 1.229810I
a = 0.522317 + 0.781774I
b = −0.409134 − 0.884374I
c = −0.886956 + 0.201557I
d = −0.82278 + 1.35195I
6.33622 + 1.07199I −1.20689 + 1.13710I
u = −0.460216 − 1.229810I
a = 0.522317 − 0.781774I
b = −0.409134 + 0.884374I
c = −0.886956 − 0.201557I
d = −0.82278 − 1.35195I
6.33622 − 1.07199I −1.20689 − 1.13710I
u = 0.548223 + 1.211710I
a = 0.521334 − 0.726495I
b = −0.347993 + 0.908591I
c = −1.151280 − 0.142674I
d = −1.06491 − 1.27360I
5.47474 − 6.91618I −2.74163 + 4.17963I
u = 0.548223 − 1.211710I
a = 0.521334 + 0.726495I
b = −0.347993 − 0.908591I
c = −1.151280 + 0.142674I
d = −1.06491 + 1.27360I
5.47474 + 6.91618I −2.74163 − 4.17963I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.168268 + 1.366960I
a = 0.219555 + 1.223470I
b = −0.857901 − 0.791847I
c = 0.981919 + 0.112942I
d = 0.509117 + 0.733224I
7.94604 − 2.88039I −2.40290 + 2.87135I
u = 0.168268 − 1.366960I
a = 0.219555 − 1.223470I
b = −0.857901 + 0.791847I
c = 0.981919 − 0.112942I
d = 0.509117 − 0.733224I
7.94604 + 2.88039I −2.40290 − 2.87135I
u = 0.620383
a = 0.635515
b = 0.573528
c = 0.187133
d = 0.872137
−1.07886 −8.06050
u = −0.256404 + 1.367180I
a = 0.141032 − 1.272300I
b = −0.913934 + 0.776435I
c = 1.080980 − 0.022426I
d = 0.549850 − 0.430577I
7.59831 + 8.92002I −3.37196 − 8.11870I
u = −0.256404 − 1.367180I
a = 0.141032 + 1.272300I
b = −0.913934 − 0.776435I
c = 1.080980 + 0.022426I
d = 0.549850 + 0.430577I
7.59831 − 8.92002I −3.37196 + 8.11870I
u = 0.170237 + 0.574659I
a = 1.248050 − 0.407611I
b = −0.275978 + 0.236465I
c = −1.39991 + 0.71798I
d = 0.022364 − 0.261910I
−0.37797 − 1.66748I −2.59196 + 2.78569I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.170237 − 0.574659I
a = 1.248050 + 0.407611I
b = −0.275978 − 0.236465I
c = −1.39991 − 0.71798I
d = 0.022364 + 0.261910I
−0.37797 + 1.66748I −2.59196 − 2.78569I
u = −0.766704 + 1.185140I
a = −0.48729 − 1.47075I
b = −1.202990 + 0.612671I
c = −0.773518 + 0.191669I
d = −1.04186 + 1.80633I
1.37987 + 12.30340I −8.00000 − 6.92563I
u = −0.766704 − 1.185140I
a = −0.48729 + 1.47075I
b = −1.202990 − 0.612671I
c = −0.773518 − 0.191669I
d = −1.04186 − 1.80633I
1.37987 − 12.30340I −8.00000 + 6.92563I
u = 0.80758 + 1.17123I
a = −0.54459 + 1.45657I
b = −1.225210 − 0.602344I
c = −1.124940 − 0.247998I
d = −1.24308 − 2.01707I
0.0200 − 18.1731I −8.00000 + 11.31467I
u = 0.80758 − 1.17123I
a = −0.54459 − 1.45657I
b = −1.225210 + 0.602344I
c = −1.124940 + 0.247998I
d = −1.24308 + 2.01707I
0.0200 + 18.1731I −8.00000 − 11.31467I
u = −0.546169 + 0.144967I
a = 0.536373 − 0.039062I
b = 0.854540 + 0.135059I
c = 0.76523 + 1.50364I
d = 1.77463 + 3.06017I
−2.99504 − 2.52590I −15.3721 + 4.9240I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.546169 − 0.144967I
a = 0.536373 + 0.039062I
b = 0.854540 − 0.135059I
c = 0.76523 − 1.50364I
d = 1.77463 − 3.06017I
−2.99504 + 2.52590I −15.3721 − 4.9240I
12
II.
I
u
2
= h5.03×10
17
u
34
−6.24×10
17
u
33
+· · ·+3.03×10
18
d+2.20×10
18
, −6.43×
10
19
u
34
− 3.75 × 10
19
u
33
+ · · · + 4.84 × 10
19
c + 2.57 × 10
19
, 4.97 × 10
18
au
34
−
6.75 × 10
18
u
34
+ · · · − 1.88 × 10
19
a − 4.81 × 10
19
, −5.09 × 10
19
au
34
− 2.42 ×
10
19
u
34
+ · · · − 2.00 × 10
19
a − 6.67 × 10
19
, u
35
+ u
34
+ · · · − 8u − 4i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
1.32710u
34
+ 0.774224u
33
+ ··· − 7.47663u − 0.530644
−0.166074u
34
+ 0.206243u
33
+ ··· + 0.520915u − 0.726173
a
5
=
a
−0.410603au
34
+ 0.558070u
34
+ ··· + 1.55425a + 3.97461
a
9
=
1.21768u
34
+ 0.482146u
33
+ ··· − 5.66991u + 0.141282
0.232442u
34
+ 1.70045u
33
+ ··· − 8.44317u − 6.53055
a
2
=
a
0.410603au
34
− 0.558070u
34
+ ··· − 1.55425a − 3.97461
a
1
=
0.410603au
34
− 0.558070u
34
+ ··· − 0.554254a − 3.97461
0.410603au
34
− 0.558070u
34
+ ··· − 1.55425a − 3.97461
a
12
=
−0.558070au
34
+ 2.05125u
34
+ ··· − 3.97461a + 4.17014
1
a
7
=
u
u
3
+ u
a
10
=
0.654987u
34
− 0.535216u
33
+ ··· + 1.28424u + 4.11539
0.556375u
34
+ 1.25106u
33
+ ··· − 7.37715u − 4.37512
a
6
=
−1.49318u
34
− 0.567981u
33
+ ··· + 7.99754u − 0.195529
0.558070u
34
− 0.392605u
33
+ ··· + 1.94978u + 2.97461
(ii) Obstruction class = −1
(iii) Cusp Shapes =
22672372767718895251
6052032860907500938
u
34
+
26762652226596727431
6052032860907500938
u
33
+ ··· −
270510416900889983975
6052032860907500938
u −
78654406032569267566
3026016430453750469
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
70
+ 39u
69
+ ··· + 2336u + 256
c
2
, c
5
u
70
− 3u
69
+ ··· − 56u + 16
c
3
(u
35
− u
34
+ ··· − 8u + 4)
2
c
4
, c
12
u
70
+ 3u
69
+ ··· + 56u + 16
c
6
(u
35
+ 2u
34
+ ··· − 2u
2
+ 1)
2
c
7
(u
35
+ u
34
+ ··· − 8u − 4)
2
c
8
(u
35
+ 12u
34
+ ··· + 4u − 1)
2
c
9
(u
35
− 2u
34
+ ··· + 2u
2
− 1)
2
c
10
(u
35
− 12u
34
+ ··· + 4u + 1)
2
c
11
u
70
− 39u
69
+ ··· − 2336u + 256
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
70
− 19y
69
+ ··· − 1270272y + 65536
c
2
, c
4
, c
5
c
12
y
70
− 39y
69
+ ··· − 2336y + 256
c
3
, c
7
(y
35
+ 15y
34
+ ··· − 72y − 16)
2
c
6
, c
9
(y
35
+ 12y
34
+ ··· + 4y − 1)
2
c
8
, c
10
(y
35
+ 24y
34
+ ··· + 40y − 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.207372 + 0.975503I
a = 0.810975 − 0.957053I
b = −0.484647 + 0.608181I
c = 1.062090 + 0.321806I
d = 1.38172 + 0.97448I
0.32534 + 1.86508I −3.98051 − 2.70414I
u = 0.207372 + 0.975503I
a = 0.431780 + 0.018192I
b = 1.311890 − 0.097404I
c = 1.062090 + 0.321806I
d = 1.38172 + 0.97448I
0.32534 + 1.86508I −3.98051 − 2.70414I
u = 0.207372 − 0.975503I
a = 0.810975 + 0.957053I
b = −0.484647 − 0.608181I
c = 1.062090 − 0.321806I
d = 1.38172 − 0.97448I
0.32534 − 1.86508I −3.98051 + 2.70414I
u = 0.207372 − 0.975503I
a = 0.431780 − 0.018192I
b = 1.311890 + 0.097404I
c = 1.062090 − 0.321806I
d = 1.38172 − 0.97448I
0.32534 − 1.86508I −3.98051 + 2.70414I
u = −0.325740 + 0.904391I
a = 0.825073 + 0.782270I
b = −0.361740 − 0.605148I
c = −0.713255 + 1.217410I
d = 0.786266 − 0.470892I
−0.525136 − 0.811264I −5.97406 − 0.21615I
u = −0.325740 + 0.904391I
a = 0.40485 − 2.13305I
b = −0.914115 + 0.452512I
c = −0.713255 + 1.217410I
d = 0.786266 − 0.470892I
−0.525136 − 0.811264I −5.97406 − 0.21615I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.325740 − 0.904391I
a = 0.825073 − 0.782270I
b = −0.361740 + 0.605148I
c = −0.713255 − 1.217410I
d = 0.786266 + 0.470892I
−0.525136 + 0.811264I −5.97406 + 0.21615I
u = −0.325740 − 0.904391I
a = 0.40485 + 2.13305I
b = −0.914115 − 0.452512I
c = −0.713255 − 1.217410I
d = 0.786266 + 0.470892I
−0.525136 + 0.811264I −5.97406 + 0.21615I
u = −0.365087 + 0.973537I
a = 0.740296 + 0.786236I
b = −0.365209 − 0.674183I
c = 1.302500 − 0.057465I
d = 1.76334 − 0.68298I
−0.19294 + 3.49535I −5.62111 − 3.75014I
u = −0.365087 + 0.973537I
a = 0.430751 − 0.032296I
b = 1.308550 + 0.173084I
c = 1.302500 − 0.057465I
d = 1.76334 − 0.68298I
−0.19294 + 3.49535I −5.62111 − 3.75014I
u = −0.365087 − 0.973537I
a = 0.740296 − 0.786236I
b = −0.365209 + 0.674183I
c = 1.302500 + 0.057465I
d = 1.76334 + 0.68298I
−0.19294 − 3.49535I −5.62111 + 3.75014I
u = −0.365087 − 0.973537I
a = 0.430751 + 0.032296I
b = 1.308550 − 0.173084I
c = 1.302500 + 0.057465I
d = 1.76334 + 0.68298I
−0.19294 − 3.49535I −5.62111 + 3.75014I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.655999 + 0.827108I
a = 0.439925 + 0.062584I
b = 1.228020 − 0.316960I
c = −0.742711 + 0.708889I
d = −1.277850 − 0.434606I
−7.12278 − 2.53588I −15.8469 + 3.8333I
u = 0.655999 + 0.827108I
a = −0.70483 + 2.22687I
b = −1.129190 − 0.408170I
c = −0.742711 + 0.708889I
d = −1.277850 − 0.434606I
−7.12278 − 2.53588I −15.8469 + 3.8333I
u = 0.655999 − 0.827108I
a = 0.439925 − 0.062584I
b = 1.228020 + 0.316960I
c = −0.742711 − 0.708889I
d = −1.277850 + 0.434606I
−7.12278 + 2.53588I −15.8469 − 3.8333I
u = 0.655999 − 0.827108I
a = −0.70483 − 2.22687I
b = −1.129190 + 0.408170I
c = −0.742711 − 0.708889I
d = −1.277850 + 0.434606I
−7.12278 + 2.53588I −15.8469 − 3.8333I
u = −0.705852 + 0.611410I
a = 0.700829 + 0.414305I
b = 0.057360 − 0.625074I
c = 0.666953 + 0.717828I
d = 1.37809 + 0.36840I
−3.90189 − 1.16771I −12.59463 + 0.48242I
u = −0.705852 + 0.611410I
a = 0.462699 − 0.073809I
b = 1.107600 + 0.336202I
c = 0.666953 + 0.717828I
d = 1.37809 + 0.36840I
−3.90189 − 1.16771I −12.59463 + 0.48242I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.705852 − 0.611410I
a = 0.700829 − 0.414305I
b = 0.057360 + 0.625074I
c = 0.666953 − 0.717828I
d = 1.37809 − 0.36840I
−3.90189 + 1.16771I −12.59463 − 0.48242I
u = −0.705852 − 0.611410I
a = 0.462699 + 0.073809I
b = 1.107600 − 0.336202I
c = 0.666953 − 0.717828I
d = 1.37809 − 0.36840I
−3.90189 + 1.16771I −12.59463 − 0.48242I
u = 1.045080 + 0.368116I
a = 0.564228 − 0.293694I
b = 0.394500 + 0.725871I
c = −0.295299 − 0.937240I
d = 0.623699 − 0.729903I
1.47991 + 0.62379I −5.11442 + 0.32782I
u = 1.045080 + 0.368116I
a = 0.475227 + 0.134196I
b = 0.948855 − 0.550324I
c = −0.295299 − 0.937240I
d = 0.623699 − 0.729903I
1.47991 + 0.62379I −5.11442 + 0.32782I
u = 1.045080 − 0.368116I
a = 0.564228 + 0.293694I
b = 0.394500 − 0.725871I
c = −0.295299 + 0.937240I
d = 0.623699 + 0.729903I
1.47991 − 0.62379I −5.11442 − 0.32782I
u = 1.045080 − 0.368116I
a = 0.475227 − 0.134196I
b = 0.948855 + 0.550324I
c = −0.295299 + 0.937240I
d = 0.623699 + 0.729903I
1.47991 − 0.62379I −5.11442 − 0.32782I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.713294 + 0.504864I
a = 0.476506 + 0.077725I
b = 1.044220 − 0.333440I
c = 0.25773 + 1.47872I
d = −0.679626 + 0.385702I
−3.98776 + 3.19845I −13.06265 − 3.08489I
u = 0.713294 + 0.504864I
a = −2.05407 + 2.74671I
b = −1.174610 − 0.233492I
c = 0.25773 + 1.47872I
d = −0.679626 + 0.385702I
−3.98776 + 3.19845I −13.06265 − 3.08489I
u = 0.713294 − 0.504864I
a = 0.476506 − 0.077725I
b = 1.044220 + 0.333440I
c = 0.25773 − 1.47872I
d = −0.679626 − 0.385702I
−3.98776 − 3.19845I −13.06265 + 3.08489I
u = 0.713294 − 0.504864I
a = −2.05407 − 2.74671I
b = −1.174610 + 0.233492I
c = 0.25773 − 1.47872I
d = −0.679626 − 0.385702I
−3.98776 − 3.19845I −13.06265 + 3.08489I
u = 0.413724 + 1.080130I
a = 0.635679 − 0.786411I
b = −0.378327 + 0.769084I
c = −0.137887 − 0.497562I
d = 0.633660 + 0.873788I
1.87781 − 3.59908I −3.00767 + 3.96847I
u = 0.413724 + 1.080130I
a = 0.05598 + 1.74978I
b = −0.981735 − 0.570915I
c = −0.137887 − 0.497562I
d = 0.633660 + 0.873788I
1.87781 − 3.59908I −3.00767 + 3.96847I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.413724 − 1.080130I
a = 0.635679 + 0.786411I
b = −0.378327 − 0.769084I
c = −0.137887 + 0.497562I
d = 0.633660 − 0.873788I
1.87781 + 3.59908I −3.00767 − 3.96847I
u = 0.413724 − 1.080130I
a = 0.05598 − 1.74978I
b = −0.981735 + 0.570915I
c = −0.137887 + 0.497562I
d = 0.633660 − 0.873788I
1.87781 + 3.59908I −3.00767 − 3.96847I
u = −0.511698 + 1.037850I
a = 0.422963 − 0.044547I
b = 1.338330 + 0.246276I
c = −0.851453 + 0.290444I
d = −1.12077 + 1.41710I
−1.31903 + 2.68874I −7.41111 − 2.89622I
u = −0.511698 + 1.037850I
a = −0.14705 − 1.84591I
b = −1.042890 + 0.538322I
c = −0.851453 + 0.290444I
d = −1.12077 + 1.41710I
−1.31903 + 2.68874I −7.41111 − 2.89622I
u = −0.511698 − 1.037850I
a = 0.422963 + 0.044547I
b = 1.338330 − 0.246276I
c = −0.851453 − 0.290444I
d = −1.12077 − 1.41710I
−1.31903 − 2.68874I −7.41111 + 2.89622I
u = −0.511698 − 1.037850I
a = −0.14705 + 1.84591I
b = −1.042890 − 0.538322I
c = −0.851453 − 0.290444I
d = −1.12077 − 1.41710I
−1.31903 − 2.68874I −7.41111 + 2.89622I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.060110 + 0.482223I
a = 0.558487 + 0.331278I
b = 0.324518 − 0.785666I
c = −0.126269 + 1.234200I
d = 0.801891 + 0.960827I
0.71766 − 6.15318I −6.72324 + 5.00692I
u = −1.060110 + 0.482223I
a = 0.459428 − 0.125654I
b = 1.025140 + 0.553877I
c = −0.126269 + 1.234200I
d = 0.801891 + 0.960827I
0.71766 − 6.15318I −6.72324 + 5.00692I
u = −1.060110 − 0.482223I
a = 0.558487 − 0.331278I
b = 0.324518 + 0.785666I
c = −0.126269 − 1.234200I
d = 0.801891 − 0.960827I
0.71766 + 6.15318I −6.72324 − 5.00692I
u = −1.060110 − 0.482223I
a = 0.459428 + 0.125654I
b = 1.025140 − 0.553877I
c = −0.126269 − 1.234200I
d = 0.801891 − 0.960827I
0.71766 + 6.15318I −6.72324 − 5.00692I
u = −0.600323 + 1.020000I
a = 0.612638 + 0.649478I
b = −0.231461 − 0.814754I
c = 0.755428 + 0.748346I
d = 1.13345 − 1.05223I
−2.63440 + 6.20108I −10.04876 − 5.89177I
u = −0.600323 + 1.020000I
a = −0.34236 − 1.84493I
b = −1.097230 + 0.523982I
c = 0.755428 + 0.748346I
d = 1.13345 − 1.05223I
−2.63440 + 6.20108I −10.04876 − 5.89177I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.600323 − 1.020000I
a = 0.612638 − 0.649478I
b = −0.231461 + 0.814754I
c = 0.755428 − 0.748346I
d = 1.13345 + 1.05223I
−2.63440 − 6.20108I −10.04876 + 5.89177I
u = −0.600323 − 1.020000I
a = −0.34236 + 1.84493I
b = −1.097230 − 0.523982I
c = 0.755428 − 0.748346I
d = 1.13345 + 1.05223I
−2.63440 − 6.20108I −10.04876 + 5.89177I
u = 0.597289 + 1.062760I
a = 0.419111 + 0.051606I
b = 1.350370 − 0.289408I
c = −1.213230 − 0.187249I
d = −1.51066 − 1.39568I
−2.31683 − 8.24742I −9.43055 + 7.59916I
u = 0.597289 + 1.062760I
a = −0.31098 + 1.76298I
b = −1.097030 − 0.550106I
c = −1.213230 − 0.187249I
d = −1.51066 − 1.39568I
−2.31683 − 8.24742I −9.43055 + 7.59916I
u = 0.597289 − 1.062760I
a = 0.419111 − 0.051606I
b = 1.350370 + 0.289408I
c = −1.213230 + 0.187249I
d = −1.51066 + 1.39568I
−2.31683 + 8.24742I −9.43055 − 7.59916I
u = 0.597289 − 1.062760I
a = −0.31098 − 1.76298I
b = −1.097030 + 0.550106I
c = −1.213230 + 0.187249I
d = −1.51066 + 1.39568I
−2.31683 + 8.24742I −9.43055 − 7.59916I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.329730 + 0.664757I
a = 0.460522 − 0.030841I
b = 1.161750 + 0.144773I
c = 0.263271 − 0.249266I
d = −0.242861 + 0.429341I
−3.05354 + 1.15463I −8.48725 − 5.51426I
u = −0.329730 + 0.664757I
a = 0.74666 − 3.40319I
b = −0.938492 + 0.280347I
c = 0.263271 − 0.249266I
d = −0.242861 + 0.429341I
−3.05354 + 1.15463I −8.48725 − 5.51426I
u = −0.329730 − 0.664757I
a = 0.460522 + 0.030841I
b = 1.161750 − 0.144773I
c = 0.263271 + 0.249266I
d = −0.242861 − 0.429341I
−3.05354 − 1.15463I −8.48725 + 5.51426I
u = −0.329730 − 0.664757I
a = 0.74666 + 3.40319I
b = −0.938492 − 0.280347I
c = 0.263271 + 0.249266I
d = −0.242861 − 0.429341I
−3.05354 − 1.15463I −8.48725 + 5.51426I
u = 0.047497 + 1.362920I
a = 0.362035 − 1.073040I
b = −0.717707 + 0.836690I
c = −1.045080 + 0.054003I
d = −0.534004 + 0.168050I
8.17684 − 3.01120I −1.89563 + 2.75790I
u = 0.047497 + 1.362920I
a = 0.310277 + 1.144270I
b = −0.779261 − 0.814064I
c = −1.045080 + 0.054003I
d = −0.534004 + 0.168050I
8.17684 − 3.01120I −1.89563 + 2.75790I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.047497 − 1.362920I
a = 0.362035 + 1.073040I
b = −0.717707 − 0.836690I
c = −1.045080 − 0.054003I
d = −0.534004 − 0.168050I
8.17684 + 3.01120I −1.89563 − 2.75790I
u = 0.047497 − 1.362920I
a = 0.310277 − 1.144270I
b = −0.779261 + 0.814064I
c = −1.045080 − 0.054003I
d = −0.534004 − 0.168050I
8.17684 + 3.01120I −1.89563 − 2.75790I
u = 0.642257 + 1.206250I
a = 0.508332 − 0.676520I
b = −0.290119 + 0.944754I
c = 0.815617 + 0.201286I
d = 0.92631 + 1.64279I
4.15268 − 6.65019I −3.95665 + 3.46663I
u = 0.642257 + 1.206250I
a = −0.31655 + 1.51284I
b = −1.132510 − 0.633283I
c = 0.815617 + 0.201286I
d = 0.92631 + 1.64279I
4.15268 − 6.65019I −3.95665 + 3.46663I
u = 0.642257 − 1.206250I
a = 0.508332 + 0.676520I
b = −0.290119 − 0.944754I
c = 0.815617 − 0.201286I
d = 0.92631 − 1.64279I
4.15268 + 6.65019I −3.95665 − 3.46663I
u = 0.642257 − 1.206250I
a = −0.31655 − 1.51284I
b = −1.132510 + 0.633283I
c = 0.815617 − 0.201286I
d = 0.92631 − 1.64279I
4.15268 + 6.65019I −3.95665 − 3.46663I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.626561
a = 0.632339 + 0.026645I
b = 0.578626 − 0.066519I
c = 0.191221
d = 0.884921
−1.07873 −7.97520
u = 0.626561
a = 0.632339 − 0.026645I
b = 0.578626 + 0.066519I
c = 0.191221
d = 0.884921
−1.07873 −7.97520
u = −0.532829 + 0.309500I
a = 0.506148 − 0.049944I
b = 0.956655 + 0.193071I
c = 1.018580 − 0.903408I
d = −0.157037 − 0.201603I
−3.17896 + 1.46996I −12.94917 − 3.34118I
u = −0.532829 + 0.309500I
a = −3.92552 − 4.75017I
b = −1.103370 + 0.125091I
c = 1.018580 − 0.903408I
d = −0.157037 − 0.201603I
−3.17896 + 1.46996I −12.94917 − 3.34118I
u = −0.532829 − 0.309500I
a = 0.506148 + 0.049944I
b = 0.956655 − 0.193071I
c = 1.018580 + 0.903408I
d = −0.157037 + 0.201603I
−3.17896 − 1.46996I −12.94917 + 3.34118I
u = −0.532829 − 0.309500I
a = −3.92552 + 4.75017I
b = −1.103370 − 0.125091I
c = 1.018580 + 0.903408I
d = −0.157037 + 0.201603I
−3.17896 − 1.46996I −12.94917 + 3.34118I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.704423 + 1.193170I
a = 0.502880 + 0.645463I
b = −0.248885 − 0.964082I
c = 1.137410 − 0.208123I
d = 1.15191 − 1.72817I
2.99525 + 12.51090I −5.90812 − 8.16035I
u = −0.704423 + 1.193170I
a = −0.40526 − 1.50005I
b = −1.167850 + 0.621297I
c = 1.137410 − 0.208123I
d = 1.15191 − 1.72817I
2.99525 + 12.51090I −5.90812 − 8.16035I
u = −0.704423 − 1.193170I
a = 0.502880 − 0.645463I
b = −0.248885 + 0.964082I
c = 1.137410 + 0.208123I
d = 1.15191 + 1.72817I
2.99525 − 12.51090I −5.90812 + 8.16035I
u = −0.704423 − 1.193170I
a = −0.40526 + 1.50005I
b = −1.167850 − 0.621297I
c = 1.137410 + 0.208123I
d = 1.15191 + 1.72817I
2.99525 − 12.51090I −5.90812 + 8.16035I
27
III. I
v
1
= hc, d + 1, b, a − 1, v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
11
=
0
−1
a
5
=
1
0
a
9
=
v
v
a
2
=
1
0
a
1
=
1
0
a
12
=
1
−1
a
7
=
v
0
a
10
=
v + 1
v
a
6
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 11
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
u
2
c
5
(u + 1)
2
c
6
, c
10
u
2
+ u + 1
c
8
, c
9
u
2
− u + 1
c
11
, c
12
(u − 1)
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
y
2
c
5
, c
11
, c
12
(y − 1)
2
c
6
, c
8
, c
9
c
10
y
2
+ y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 1.00000
b = 0
c = 0
d = −1.00000
−1.64493 + 2.02988I −9.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 1.00000
b = 0
c = 0
d = −1.00000
−1.64493 − 2.02988I −9.00000 + 3.46410I
31
IV. I
v
2
= ha, d + 1, c + a, b − 1, v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
11
=
0
−1
a
5
=
0
1
a
9
=
v
v
a
2
=
1
−1
a
1
=
0
−1
a
12
=
0
−1
a
7
=
v
0
a
10
=
v + 1
v
a
6
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 11
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
5
, c
7
c
11
, c
12
u
2
c
4
(u + 1)
2
c
6
, c
10
u
2
+ u + 1
c
8
, c
9
u
2
− u + 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
5
, c
7
c
11
, c
12
y
2
c
6
, c
8
, c
9
c
10
y
2
+ y + 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 1.00000
c = 0
d = −1.00000
−1.64493 + 2.02988I −9.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 1.00000
c = 0
d = −1.00000
−1.64493 − 2.02988I −9.00000 + 3.46410I
35
V. I
v
3
= ha, d, c + 1, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
−1
0
a
4
=
1
0
a
11
=
−1
0
a
5
=
0
1
a
9
=
−1
0
a
2
=
1
−1
a
1
=
0
−1
a
12
=
−1
−1
a
7
=
−1
0
a
10
=
−1
0
a
6
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
11
u − 1
c
3
, c
6
, c
7
c
8
, c
9
, c
10
u
c
4
, c
12
u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
11
, c
12
y − 1
c
3
, c
6
, c
7
c
8
, c
9
, c
10
y
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
c = −1.00000
d = 0
−3.28987 −12.0000
39
VI. I
v
4
= ha, d
2
v
2
− dv + 1, v
2
dc − v
2
d + · · · + a + v, da − c + 1, c
2
v
2
−
2v
2
c + · · · + a
2
+ av, b − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
11
=
1
d
a
5
=
0
1
a
9
=
dv + v
d
2
v
a
2
=
1
−1
a
1
=
0
−1
a
12
=
1
d + 1
a
7
=
v
0
a
10
=
v
2
d + dv
d
2
v
a
6
=
−1
−d
(ii) Obstruction class = −1
(iii) Cusp Shapes = −d
3
v + 4dv + v
2
− 16
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
40
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−3.28987 + 2.02988I −13.38669 + 2.91767I
41
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
u
2
(u − 1)
3
(u
43
+ 19u
42
+ ··· + 11u + 1)
c
2
u
2
(u − 1)
3
(u
43
− 5u
42
+ ··· − 5u + 1)
c
3
, c
7
u
5
(u
43
+ 3u
42
+ ··· + 64u + 32)
c
4
u
2
(u + 1)
3
(u
43
− 5u
42
+ ··· − 5u + 1)
c
5
u
2
(u − 1)(u + 1)
2
(u
43
− 5u
42
+ ··· − 5u + 1)
c
6
u(u
2
+ u + 1)
2
(u
43
+ u
42
+ ··· + 8u + 4)
c
8
u(u
2
− u + 1)
2
(u
43
+ 15u
42
+ ··· + 88u − 16)
c
9
u(u
2
− u + 1)
2
(u
43
+ u
42
+ ··· + 8u + 4)
c
10
u(u
2
+ u + 1)
2
(u
43
+ 15u
42
+ ··· + 88u − 16)
c
12
u
2
(u − 1)
2
(u + 1)(u
43
− 5u
42
+ ··· − 5u + 1)
42
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
2
(y − 1)
3
(y
43
+ 21y
42
+ ··· − 117y − 1)
c
2
, c
4
, c
5
c
12
y
2
(y − 1)
3
(y
43
− 19y
42
+ ··· + 11y − 1)
c
3
, c
7
y
5
(y
43
+ 15y
42
+ ··· − 1024y − 1024)
c
6
, c
9
y(y
2
+ y + 1)
2
(y
43
+ 15y
42
+ ··· + 88y − 16)
c
8
, c
10
y(y
2
+ y + 1)
2
(y
43
+ 27y
42
+ ··· + 18208y − 256)
43
