12n
0636
(K12n
0636
)
A knot diagram
1
Linearized knot diagam
3 8 6 12 1 12 9 2 5 4 6 10
Solving Sequence
1,5 6,10
9 12 7 4 3 2 8 11
c
5
c
9
c
12
c
6
c
4
c
3
c
1
c
8
c
11
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 1.29424 × 10
29
u
28
− 4.50885 × 10
29
u
27
+ ··· + 1.80747 × 10
27
a + 2.71900 × 10
29
,
u
29
− 4u
28
+ ··· + 41u
2
− 1i
I
u
2
= hb + u, −1.14135 × 10
17
u
24
+ 9.49047 × 10
15
u
23
+ ··· + 2.50582 × 10
16
a + 3.47140 × 10
17
,
u
25
+ 3u
23
+ ··· − 4u − 1i
I
u
3
= h5.05848 × 10
26
u
23
+ 1.72101 × 10
27
u
22
+ ··· + 1.51027 × 10
28
b − 1.97809 × 10
29
,
1.66317 × 10
24
u
23
+ 5.60162 × 10
24
u
22
+ ··· + 2.05980 × 10
25
a − 6.95407 × 10
26
,
u
24
+ 3u
23
+ ··· − 916u + 152i
I
u
4
= hb + 1, 3u
3
− 8u
2
+ 4a + 9u − 5, u
4
− 4u
3
+ 7u
2
− 7u + 4i
I
u
5
= hb + 1, a
4
− 3a
3
+ 5a
2
− 3a + 2, u + 1i
I
u
6
= h−a
3
− a
2
+ b − a − 1, a
4
+ a
3
+ a
2
+ 1, u + 1i
* 6 irreducible components of dim
C
= 0, with total 90 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
= hb − u, 1.29 × 10
29
u
28
− 4.51 × 10
29
u
27
+ · · · + 1.81 × 10
27
a + 2.72 ×
10
29
, u
29
− 4u
28
+ · · · + 41u
2
− 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
10
=
−71.6051u
28
+ 249.456u
27
+ ··· − 223.148u − 150.431
u
a
9
=
−71.6051u
28
+ 249.456u
27
+ ··· − 224.148u − 150.431
u
a
12
=
−11.9756u
28
+ 39.5117u
27
+ ··· + 56.9931u − 41.0153
−18.4538u
28
+ 64.5320u
27
+ ··· − 70.6051u − 36.9640
a
7
=
7.86693u
28
− 25.7993u
27
+ ··· − 20.9730u + 45.9410
−19.6452u
28
+ 68.7556u
27
+ ··· − 79.1491u − 38.6368
a
4
=
−3.16963u
28
+ 10.4056u
27
+ ··· + 11.0912u − 19.1412
20.6054u
28
− 72.0642u
27
+ ··· + 82.3187u + 40.9096
a
3
=
−22.8148u
28
+ 79.1613u
27
+ ··· − 68.0578u − 57.7779
25.5368u
28
− 89.2904u
27
+ ··· + 101.964u + 50.7349
a
2
=
28.1973u
28
− 97.3373u
27
+ ··· + 82.3877u + 69.1927
−18.7535u
28
+ 65.8134u
27
+ ··· − 77.9114u − 37.4792
a
8
=
−36.1766u
28
+ 127.011u
27
+ ··· − 157.595u − 62.5413
−25.5368u
28
+ 89.2904u
27
+ ··· − 101.964u − 50.7349
a
11
=
−34.4315u
28
+ 118.013u
27
+ ··· − 25.5876u − 86.3700
−12.7801u
28
+ 44.6947u
27
+ ··· − 48.1492u − 25.6417
(ii) Obstruction class = −1
(iii) Cusp Shapes = −362.367u
28
+ 1266.86u
27
+ ··· − 1402.63u − 756.448
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
29
+ 8u
28
+ ··· + 160u − 64
c
2
, c
8
u
29
+ 8u
28
+ ··· + 16u + 8
c
3
u
29
+ 15u
28
+ ··· + 496u + 64
c
4
u
29
+ 2u
28
+ ··· + 5u + 13
c
5
, c
9
u
29
+ 4u
28
+ ··· − 41u
2
+ 1
c
6
, c
10
, c
11
u
29
+ 24u
27
+ ··· + 5u + 1
c
12
u
29
− 13u
28
+ ··· − 100u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
29
+ 24y
28
+ ··· + 94720y − 4096
c
2
, c
8
y
29
+ 8y
28
+ ··· + 160y − 64
c
3
y
29
− 35y
28
+ ··· + 24832y − 4096
c
4
y
29
+ 30y
28
+ ··· − 1041y − 169
c
5
, c
9
y
29
− 20y
28
+ ··· + 82y − 1
c
6
, c
10
, c
11
y
29
+ 48y
28
+ ··· − 15y − 1
c
12
y
29
− 3y
28
+ ··· − 560y − 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.960292 + 0.114322I
a = −0.295102 − 0.789708I
b = 0.960292 + 0.114322I
4.26314 + 5.68742I 0.21225 − 6.40052I
u = 0.960292 − 0.114322I
a = −0.295102 + 0.789708I
b = 0.960292 − 0.114322I
4.26314 − 5.68742I 0.21225 + 6.40052I
u = −0.800224 + 0.473422I
a = −0.020933 + 0.683003I
b = −0.800224 + 0.473422I
1.38041 − 0.94269I 4.60342 + 1.76965I
u = −0.800224 − 0.473422I
a = −0.020933 − 0.683003I
b = −0.800224 − 0.473422I
1.38041 + 0.94269I 4.60342 − 1.76965I
u = 0.214505 + 0.830763I
a = 0.085940 + 0.697105I
b = 0.214505 + 0.830763I
−0.18552 − 2.10133I −2.36676 + 3.80844I
u = 0.214505 − 0.830763I
a = 0.085940 − 0.697105I
b = 0.214505 − 0.830763I
−0.18552 + 2.10133I −2.36676 − 3.80844I
u = 0.834842 + 0.841974I
a = 0.065712 + 0.604077I
b = 0.834842 + 0.841974I
−2.03034 + 3.15669I −2.00000 − 3.13089I
u = 0.834842 − 0.841974I
a = 0.065712 − 0.604077I
b = 0.834842 − 0.841974I
−2.03034 − 3.15669I −2.00000 + 3.13089I
u = −1.170000 + 0.647600I
a = 0.207159 + 1.203770I
b = −1.170000 + 0.647600I
5.63179 − 9.07757I 0
u = −1.170000 − 0.647600I
a = 0.207159 − 1.203770I
b = −1.170000 − 0.647600I
5.63179 + 9.07757I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.322730 + 0.290095I
a = −0.615161 + 1.063240I
b = 1.322730 + 0.290095I
9.61338 + 4.40602I 0
u = 1.322730 − 0.290095I
a = −0.615161 − 1.063240I
b = 1.322730 − 0.290095I
9.61338 − 4.40602I 0
u = −1.151990 + 0.728821I
a = 0.002396 + 0.567381I
b = −1.151990 + 0.728821I
4.32796 − 2.63394I 0
u = −1.151990 − 0.728821I
a = 0.002396 − 0.567381I
b = −1.151990 − 0.728821I
4.32796 + 2.63394I 0
u = −1.171900 + 0.729482I
a = 1.156260 − 0.116734I
b = −1.171900 + 0.729482I
12.9658 − 7.6542I 0
u = −1.171900 − 0.729482I
a = 1.156260 + 0.116734I
b = −1.171900 − 0.729482I
12.9658 + 7.6542I 0
u = 1.29794 + 0.56457I
a = −1.101150 − 0.319489I
b = 1.29794 + 0.56457I
14.08170 + 0.96061I 0
u = 1.29794 − 0.56457I
a = −1.101150 + 0.319489I
b = 1.29794 − 0.56457I
14.08170 − 0.96061I 0
u = 1.16421 + 0.82395I
a = 0.013535 + 0.551844I
b = 1.16421 + 0.82395I
3.49095 + 8.40992I 0
u = 1.16421 − 0.82395I
a = 0.013535 − 0.551844I
b = 1.16421 − 0.82395I
3.49095 − 8.40992I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498483 + 0.001453I
a = 0.228167 − 1.207220I
b = 0.498483 + 0.001453I
−0.76521 + 1.33560I −4.03541 − 5.87673I
u = 0.498483 − 0.001453I
a = 0.228167 + 1.207220I
b = 0.498483 − 0.001453I
−0.76521 − 1.33560I −4.03541 + 5.87673I
u = 0.233111
a = 5.33841
b = 0.233111
−1.74928 −9.97660
u = −0.179695 + 0.046426I
a = −8.32456 − 5.44841I
b = −0.179695 + 0.046426I
−5.01406 − 4.22563I −16.2179 − 14.6298I
u = −0.179695 − 0.046426I
a = −8.32456 + 5.44841I
b = −0.179695 − 0.046426I
−5.01406 + 4.22563I −16.2179 + 14.6298I
u = 1.60072 + 0.97916I
a = −0.124611 + 0.805147I
b = 1.60072 + 0.97916I
14.8695 + 9.1201I 0
u = 1.60072 − 0.97916I
a = −0.124611 − 0.805147I
b = 1.60072 − 0.97916I
14.8695 − 9.1201I 0
u = −1.53648 + 1.11077I
a = 0.053142 + 0.796682I
b = −1.53648 + 1.11077I
13.9120 − 15.6954I 0
u = −1.53648 − 1.11077I
a = 0.053142 − 0.796682I
b = −1.53648 − 1.11077I
13.9120 + 15.6954I 0
7
II. I
u
2
= hb + u, −1.14 × 10
17
u
24
+ 9.49 × 10
15
u
23
+ · · · + 2.51 × 10
16
a +
3.47 × 10
17
, u
25
+ 3u
23
+ · · · − 4u − 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
10
=
4.55481u
24
− 0.378737u
23
+ ··· − 23.2828u − 13.8534
−u
a
9
=
4.55481u
24
− 0.378737u
23
+ ··· − 22.2828u − 13.8534
−u
a
12
=
11.3465u
24
− 3.75211u
23
+ ··· − 53.6177u − 24.6474
0.463760u
24
− 0.563270u
23
+ ··· − 2.03987u + 0.378737
a
7
=
−13.8534u
24
+ 4.55481u
23
+ ··· + 73.9510u + 33.1307
−0.127690u
24
− 0.228930u
23
+ ··· + 1.62932u + 0.250675
a
4
=
−3.62126u
24
+ 1.46376u
23
+ ··· + 17.6341u + 9.44519
0.690960u
24
− 0.0116943u
23
+ ··· − 3.86310u − 1.71443
a
3
=
−3.74895u
24
+ 1.23483u
23
+ ··· + 19.2634u + 9.69586
0.388246u
24
+ 0.192434u
23
+ ··· − 2.81969u − 1.48550
a
2
=
−6.66089u
24
+ 2.95614u
23
+ ··· + 33.1139u + 11.4051
0.871238u
24
− 0.115442u
23
+ ··· − 3.96879u − 1.75674
a
8
=
−2.92829u
24
+ 0.509793u
23
+ ··· + 17.3146u + 9.64795
−0.388246u
24
− 0.192434u
23
+ ··· + 2.81969u + 1.48550
a
11
=
12.5972u
24
− 3.87980u
23
+ ··· − 59.3194u − 28.0208
0.692691u
24
− 0.865985u
23
+ ··· − 2.77978u + 0.506427
(ii) Obstruction class = 1
(iii) Cusp Shapes =
−
141347430048502710
4176363078274867
u
24
+
49486291278266828
4176363078274867
u
23
+···+
739293424200395475
4176363078274867
u+
319470269701535049
4176363078274867
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
25
− 10u
24
+ ··· − 44u + 4
c
2
u
25
+ 5u
23
+ ··· + 11u
2
+ 2
c
3
u
25
+ 19u
24
+ ··· − 21u + 41
c
4
u
25
− u
24
+ ··· − 17u
2
+ 2
c
5
, c
9
u
25
+ 3u
23
+ ··· − 4u − 1
c
6
, c
10
u
25
+ 7u
23
+ ··· − u − 1
c
8
u
25
+ 5u
23
+ ··· − 11u
2
− 2
c
11
u
25
+ 7u
23
+ ··· − u + 1
c
12
u
25
+ 11u
24
+ ··· − 7u
2
+ 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
25
+ 18y
24
+ ··· − 24y − 16
c
2
, c
8
y
25
+ 10y
24
+ ··· − 44y − 4
c
3
y
25
− 35y
24
+ ··· + 70715y − 1681
c
4
y
25
+ 11y
24
+ ··· + 68y − 4
c
5
, c
9
y
25
+ 6y
24
+ ··· + 10y − 1
c
6
, c
10
, c
11
y
25
+ 14y
24
+ ··· + 17y − 1
c
12
y
25
− 3y
24
+ ··· + 14y − 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.796080 + 0.645844I
a = −0.596796 − 0.240010I
b = −0.796080 − 0.645844I
4.84322 − 2.05050I 0.28599 − 1.48631I
u = 0.796080 − 0.645844I
a = −0.596796 + 0.240010I
b = −0.796080 + 0.645844I
4.84322 + 2.05050I 0.28599 + 1.48631I
u = 0.296077 + 0.914388I
a = −0.699710 − 1.211640I
b = −0.296077 − 0.914388I
−2.56141 + 2.33620I −10.59682 − 7.19824I
u = 0.296077 − 0.914388I
a = −0.699710 + 1.211640I
b = −0.296077 + 0.914388I
−2.56141 − 2.33620I −10.59682 + 7.19824I
u = 0.922082 + 0.228189I
a = −0.381519 − 0.872909I
b = −0.922082 − 0.228189I
6.61274 − 0.16294I 8.10933 + 0.42456I
u = 0.922082 − 0.228189I
a = −0.381519 + 0.872909I
b = −0.922082 + 0.228189I
6.61274 + 0.16294I 8.10933 − 0.42456I
u = −0.809953 + 0.096839I
a = 0.363322 − 1.250440I
b = 0.809953 − 0.096839I
5.86968 + 5.30210I 5.18661 − 5.91989I
u = −0.809953 − 0.096839I
a = 0.363322 + 1.250440I
b = 0.809953 + 0.096839I
5.86968 − 5.30210I 5.18661 + 5.91989I
u = −0.687921 + 1.038030I
a = 0.174351 − 0.908552I
b = 0.687921 − 1.038030I
−3.20695 − 4.09541I −9.54085 + 4.81505I
u = −0.687921 − 1.038030I
a = 0.174351 + 0.908552I
b = 0.687921 + 1.038030I
−3.20695 + 4.09541I −9.54085 − 4.81505I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.115530 + 0.661232I
a = 0.315105 − 0.652823I
b = −1.115530 − 0.661232I
3.30766 + 2.48097I −1.93779 − 1.88948I
u = 1.115530 − 0.661232I
a = 0.315105 + 0.652823I
b = −1.115530 + 0.661232I
3.30766 − 2.48097I −1.93779 + 1.88948I
u = 0.343736 + 1.273220I
a = −0.539488 − 0.735855I
b = −0.343736 − 1.273220I
−0.22260 + 5.42341I 0.75618 − 6.73991I
u = 0.343736 − 1.273220I
a = −0.539488 + 0.735855I
b = −0.343736 + 1.273220I
−0.22260 − 5.42341I 0.75618 + 6.73991I
u = 0.675230
a = 2.07673
b = −0.675230
−1.26232 7.41310
u = −1.125130 + 0.793831I
a = −0.199464 − 0.663668I
b = 1.125130 − 0.793831I
2.60794 − 8.42230I −4.02327 + 7.25592I
u = −1.125130 − 0.793831I
a = −0.199464 + 0.663668I
b = 1.125130 + 0.793831I
2.60794 + 8.42230I −4.02327 − 7.25592I
u = −0.454409 + 1.305940I
a = 0.440942 − 0.724830I
b = 0.454409 − 1.305940I
−0.334771 − 0.254683I 0.594711 − 0.383137I
u = −0.454409 − 1.305940I
a = 0.440942 + 0.724830I
b = 0.454409 + 1.305940I
−0.334771 + 0.254683I 0.594711 + 0.383137I
u = −0.440390 + 0.366580I
a = 1.96302 − 0.28081I
b = 0.440390 − 0.366580I
3.32428 − 0.29299I −4.35678 + 0.94699I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.440390 − 0.366580I
a = 1.96302 + 0.28081I
b = 0.440390 + 0.366580I
3.32428 + 0.29299I −4.35678 − 0.94699I
u = 0.11956 + 1.47573I
a = −0.042858 + 0.212628I
b = −0.11956 − 1.47573I
11.63180 − 3.18462I 3.10708 + 2.38160I
u = 0.11956 − 1.47573I
a = −0.042858 − 0.212628I
b = −0.11956 + 1.47573I
11.63180 + 3.18462I 3.10708 − 2.38160I
u = −0.412870 + 0.210392I
a = −2.83528 − 2.84508I
b = 0.412870 − 0.210392I
−4.92153 − 4.38703I 5.2090 + 22.1333I
u = −0.412870 − 0.210392I
a = −2.83528 + 2.84508I
b = 0.412870 + 0.210392I
−4.92153 + 4.38703I 5.2090 − 22.1333I
13
III. I
u
3
=
h5.06×10
26
u
23
+1.72×10
27
u
22
+· · ·+1.51×10
28
b−1.98×10
29
, 1.66×10
24
u
23
+
5.60 × 10
24
u
22
+ · · · + 2.06 × 10
25
a − 6.95 × 10
26
, u
24
+ 3u
23
+ · · · − 916u + 152i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
10
=
−0.0807441u
23
− 0.271949u
22
+ ··· − 112.103u + 33.7608
−0.0334939u
23
− 0.113953u
22
+ ··· − 45.6844u + 13.0976
a
9
=
−0.0472503u
23
− 0.157996u
22
+ ··· − 66.4189u + 20.6632
−0.0334939u
23
− 0.113953u
22
+ ··· − 45.6844u + 13.0976
a
12
=
0.0635809u
23
+ 0.212954u
22
+ ··· + 87.2711u − 27.6880
0.0521176u
23
+ 0.175261u
22
+ ··· + 72.2476u − 22.1390
a
7
=
−0.0561598u
23
− 0.189820u
22
+ ··· − 76.9321u + 22.8112
0.0172861u
23
+ 0.0557112u
22
+ ··· + 25.6034u − 9.48966
a
4
=
0.0388737u
23
+ 0.134109u
22
+ ··· + 51.3287u − 13.3215
−0.0250608u
23
− 0.0822551u
22
+ ··· − 35.7136u + 12.1478
a
3
=
0.0561598u
23
+ 0.189820u
22
+ ··· + 76.9321u − 22.8112
−0.0254832u
23
− 0.0841583u
22
+ ··· − 36.6152u + 12.7335
a
2
=
−0.0472503u
23
− 0.157996u
22
+ ··· − 66.4189u + 20.6632
−0.0278389u
23
− 0.0949127u
22
+ ··· − 35.9862u + 10.6284
a
8
=
−0.0719550u
23
− 0.242039u
22
+ ··· − 98.3636u + 29.8284
−0.0227300u
23
− 0.0785800u
22
+ ··· − 30.8874u + 7.99453
a
11
=
0.123958u
23
+ 0.415686u
22
+ ··· + 170.200u − 53.2032
0.0437678u
23
+ 0.146509u
22
+ ··· + 61.6377u − 18.8555
(ii) Obstruction class = −1
(iii) Cusp Shapes =
789409549397297077238438255
1887837650177179023809147344
u
23
+
5345499614610035395715935423
3775675300354358047618294688
u
22
+
··· +
534181212237586784175387060335
943918825088589511904573672
u −
81677490050712823192860035961
471959412544294755952286836
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
6
c
2
, c
8
(u
4
− u
3
+ u
2
+ 1)
6
c
3
(u
4
− 3u
3
+ u
2
+ 2u + 1)
6
c
4
u
24
− 5u
23
+ ··· − 19608u + 4792
c
5
, c
9
u
24
− 3u
23
+ ··· + 916u + 152
c
6
, c
10
, c
11
u
24
− 6u
23
+ ··· − 2820u + 421
c
12
(u
4
+ u
3
+ u
2
+ 1)
6
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
6
c
2
, c
8
, c
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
c
3
(y
4
− 7y
3
+ 15y
2
− 2y + 1)
6
c
4
y
24
+ 13y
23
+ ··· + 10329632y + 22963264
c
5
, c
9
y
24
+ 9y
23
+ ··· − 295504y + 23104
c
6
, c
10
, c
11
y
24
+ 34y
23
+ ··· − 101592y + 177241
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.451653 + 0.937171I
a = −0.433636 − 1.117900I
b = −0.128858 − 0.863491I
−2.06694 + 1.74886I −1.65348 + 2.34394I
u = 0.451653 − 0.937171I
a = −0.433636 + 1.117900I
b = −0.128858 + 0.863491I
−2.06694 − 1.74886I −1.65348 − 2.34394I
u = 0.727252 + 0.755470I
a = 0.262219 + 0.718105I
b = −1.54826 + 2.15106I
11.93650 + 4.57907I 5.65348 − 7.47354I
u = 0.727252 − 0.755470I
a = 0.262219 − 0.718105I
b = −1.54826 − 2.15106I
11.93650 − 4.57907I 5.65348 + 7.47354I
u = 0.607909 + 0.908003I
a = −0.259320 − 1.111730I
b = −0.615212 − 1.239020I
−2.06694 + 4.57907I −1.65348 − 7.47354I
u = 0.607909 − 0.908003I
a = −0.259320 + 1.111730I
b = −0.615212 + 1.239020I
−2.06694 − 4.57907I −1.65348 + 7.47354I
u = 1.097460 + 0.195307I
a = 0.609099 − 0.938762I
b = −1.56114 − 0.84926I
4.93480 + 6.32793I 2.00000 − 5.12960I
u = 1.097460 − 0.195307I
a = 0.609099 + 0.938762I
b = −1.56114 + 0.84926I
4.93480 − 6.32793I 2.00000 + 5.12960I
u = −0.867738 + 0.717770I
a = −0.166984 + 0.692013I
b = 1.29037 + 2.27278I
11.93650 + 1.74886I 5.65348 + 2.34394I
u = −0.867738 − 0.717770I
a = −0.166984 − 0.692013I
b = 1.29037 − 2.27278I
11.93650 − 1.74886I 5.65348 − 2.34394I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.128858 + 0.863491I
a = 0.88836 − 1.11904I
b = 0.451653 − 0.937171I
−2.06694 − 1.74886I −1.65348 − 2.34394I
u = −0.128858 − 0.863491I
a = 0.88836 + 1.11904I
b = 0.451653 + 0.937171I
−2.06694 + 1.74886I −1.65348 + 2.34394I
u = −0.615212 + 1.239020I
a = 0.316184 − 0.844481I
b = 0.607909 − 0.908003I
−2.06694 − 4.57907I −1.65348 + 7.47354I
u = −0.615212 − 1.239020I
a = 0.316184 + 0.844481I
b = 0.607909 + 0.908003I
−2.06694 + 4.57907I −1.65348 − 7.47354I
u = −1.31086 + 0.82372I
a = 0.439962 − 0.273053I
b = 0.357423 − 0.019370I
4.93480 + 2.83021I 2.00000 − 9.81749I
u = −1.31086 − 0.82372I
a = 0.439962 + 0.273053I
b = 0.357423 + 0.019370I
4.93480 − 2.83021I 2.00000 + 9.81749I
u = 0.357423 + 0.019370I
a = −1.09031 − 1.95629I
b = −1.31086 − 0.82372I
4.93480 − 2.83021I 2.00000 + 9.81749I
u = 0.357423 − 0.019370I
a = −1.09031 + 1.95629I
b = −1.31086 + 0.82372I
4.93480 + 2.83021I 2.00000 − 9.81749I
u = −1.56114 + 0.84926I
a = −0.175996 − 0.679476I
b = 1.097460 − 0.195307I
4.93480 − 6.32793I 2.00000 + 5.12960I
u = −1.56114 − 0.84926I
a = −0.175996 + 0.679476I
b = 1.097460 + 0.195307I
4.93480 + 6.32793I 2.00000 − 5.12960I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.29037 + 2.27278I
a = −0.306144 − 0.019022I
b = −0.867738 + 0.717770I
11.93650 + 1.74886I 0
u = 1.29037 − 2.27278I
a = −0.306144 + 0.019022I
b = −0.867738 − 0.717770I
11.93650 − 1.74886I 0
u = −1.54826 + 2.15106I
a = 0.298140 − 0.051040I
b = 0.727252 + 0.755470I
11.93650 + 4.57907I 0
u = −1.54826 − 2.15106I
a = 0.298140 + 0.051040I
b = 0.727252 − 0.755470I
11.93650 − 4.57907I 0
19
IV. I
u
4
= hb + 1, 3u
3
− 8u
2
+ 4a + 9u − 5, u
4
− 4u
3
+ 7u
2
− 7u + 4i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
10
=
−
3
4
u
3
+ 2u
2
−
9
4
u +
5
4
−1
a
9
=
−
3
4
u
3
+ 2u
2
−
9
4
u +
9
4
−1
a
12
=
−
1
4
u
3
+
1
4
u −
1
4
u
3
− 3u
2
+ 5u − 3
a
7
=
−
1
4
u
3
+
1
4
u −
1
4
−u
3
+ 3u
2
− 3u + 1
a
4
=
5
4
u
3
− 3u
2
+
11
4
u −
3
4
−u
3
+ 3u
2
− 6u + 7
a
3
=
1
4
u
3
−
1
4
u +
1
4
−u
3
+ 2u
2
− 3u + 3
a
2
=
−
3
4
u
3
+ 2u
2
−
9
4
u +
9
4
u
3
− 4u
2
+ 6u − 5
a
8
=
1
2
u
3
− u
2
+
3
2
u −
1
2
−2u
3
+ 5u
2
− 5u + 2
a
11
=
−
5
4
u
3
+ 2u
2
−
3
4
u +
3
4
3u
3
− 11u
2
+ 15u − 11
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
2
, c
8
u
4
− u
3
+ u
2
+ 1
c
3
u
4
− 3u
3
+ u
2
+ 2u + 1
c
4
u
4
+ 3u
3
+ 9u
2
+ 10u + 11
c
5
u
4
+ 4u
3
+ 7u
2
+ 7u + 4
c
6
, c
11
u
4
+ 3u
3
+ 6u
2
+ 8u + 8
c
9
(u − 1)
4
c
10
u
4
+ 2u
3
+ 3u
2
+ 3u + 2
c
12
u
4
+ u
3
+ u
2
+ 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
8
, c
12
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
y
4
− 7y
3
+ 15y
2
− 2y + 1
c
4
y
4
+ 9y
3
+ 43y
2
+ 98y + 121
c
5
y
4
− 2y
3
+ y
2
+ 7y + 16
c
6
, c
11
y
4
+ 3y
3
+ 4y
2
+ 32y + 64
c
9
(y − 1)
4
c
10
y
4
+ 2y
3
+ y
2
+ 3y + 4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.452576 + 1.120870I
a = −0.661541 + 0.046758I
b = −1.00000
4.93480 2.00000
u = 0.452576 − 1.120870I
a = −0.661541 − 0.046758I
b = −1.00000
4.93480 2.00000
u = 1.54742 + 0.58565I
a = 0.286541 − 0.697356I
b = −1.00000
4.93480 2.00000
u = 1.54742 − 0.58565I
a = 0.286541 + 0.697356I
b = −1.00000
4.93480 2.00000
23
V. I
u
5
= hb + 1, a
4
− 3a
3
+ 5a
2
− 3a + 2, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
5
=
1
0
a
6
=
1
−1
a
10
=
a
−1
a
9
=
a + 1
−1
a
12
=
−a
2
a − 1
a
7
=
2a
3
− 4a
2
+ 3a − 1
−a
3
+ 2a
2
− 2a
a
4
=
a
3
− a
2
+ 1
−a
2
+ 2a − 1
a
3
=
a
2
− 2a + 1
a
3
− 3a
2
+ 4a − 1
a
2
=
−a
3
+ a
2
− a − 1
a
2
− 2a + 2
a
8
=
a
3
− 3a
2
+ 4a − 2
−a
3
+ 3a
2
− 4a + 1
a
11
=
−2a
2
+ a − 1
a
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
+ 3u
3
+ 4u
2
+ 4u + 4
c
2
, c
8
u
4
+ u
3
+ 2u
2
+ 2u + 2
c
3
u
4
+ u
3
− 3u
2
− u + 4
c
4
u
4
− u
3
+ 2u
2
− 2u + 2
c
5
, c
9
(u − 1)
4
c
6
, c
10
, c
11
u
4
+ 4u
2
− 2u + 1
c
12
u
4
− 3u
3
+ 5u
2
− 3u + 2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
− y
3
+ 16y + 16
c
2
, c
4
, c
8
y
4
+ 3y
3
+ 4y
2
+ 4y + 4
c
3
y
4
− 7y
3
+ 19y
2
− 25y + 16
c
5
, c
9
(y − 1)
4
c
6
, c
10
, c
11
y
4
+ 8y
3
+ 18y
2
+ 4y + 1
c
12
y
4
+ y
3
+ 11y
2
+ 11y + 4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.219104 + 0.751390I
b = −1.00000
4.93480 2.00000
u = −1.00000
a = 0.219104 − 0.751390I
b = −1.00000
4.93480 2.00000
u = −1.00000
a = 1.28090 + 1.27441I
b = −1.00000
4.93480 2.00000
u = −1.00000
a = 1.28090 − 1.27441I
b = −1.00000
4.93480 2.00000
27
VI. I
u
6
= h−a
3
− a
2
+ b − a − 1, a
4
+ a
3
+ a
2
+ 1, u + 1i
(i) Arc colorings
a
1
=
0
−1
a
5
=
1
0
a
6
=
1
−1
a
10
=
a
a
3
+ a
2
+ a + 1
a
9
=
−a
3
− a
2
− 1
a
3
+ a
2
+ a + 1
a
12
=
−a
2
−a
a
7
=
−a
2
a
3
+ a
2
− 1
a
4
=
−a
3
+ 1
−a
2
a
3
=
a
2
−a
3
− 2a
2
+ 1
a
2
=
−a
3
− a
2
− 1
2a
3
+ 2a
2
+ a
a
8
=
−a
3
− a
a
3
+ a − 1
a
11
=
−2a
2
− a
a
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
2
, c
8
u
4
− u
3
+ u
2
+ 1
c
3
u
4
− 3u
3
+ u
2
+ 2u + 1
c
4
, c
12
u
4
+ u
3
+ u
2
+ 1
c
5
(u − 1)
4
c
6
, c
11
u
4
+ 2u
3
+ 3u
2
+ 3u + 2
c
9
u
4
+ 4u
3
+ 7u
2
+ 7u + 4
c
10
u
4
+ 3u
3
+ 6u
2
+ 8u + 8
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
4
, c
8
c
12
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
y
4
− 7y
3
+ 15y
2
− 2y + 1
c
5
(y − 1)
4
c
6
, c
11
y
4
+ 2y
3
+ y
2
+ 3y + 4
c
9
y
4
− 2y
3
+ y
2
+ 7y + 16
c
10
y
4
+ 3y
3
+ 4y
2
+ 32y + 64
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.351808 + 0.720342I
b = 0.452576 + 1.120870I
4.93480 2.00000
u = −1.00000
a = 0.351808 − 0.720342I
b = 0.452576 − 1.120870I
4.93480 2.00000
u = −1.00000
a = −0.851808 + 0.911292I
b = 1.54742 + 0.58565I
4.93480 2.00000
u = −1.00000
a = −0.851808 − 0.911292I
b = 1.54742 − 0.58565I
4.93480 2.00000
31
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
8
(u
4
+ 3u
3
+ 4u
2
+ 4u + 4)
· (u
25
− 10u
24
+ ··· − 44u + 4)(u
29
+ 8u
28
+ ··· + 160u − 64)
c
2
((u
4
− u
3
+ u
2
+ 1)
8
)(u
4
+ u
3
+ 2u
2
+ 2u + 2)(u
25
+ 5u
23
+ ··· + 11u
2
+ 2)
· (u
29
+ 8u
28
+ ··· + 16u + 8)
c
3
(u
4
− 3u
3
+ u
2
+ 2u + 1)
8
(u
4
+ u
3
− 3u
2
− u + 4)
· (u
25
+ 19u
24
+ ··· − 21u + 41)(u
29
+ 15u
28
+ ··· + 496u + 64)
c
4
(u
4
− u
3
+ 2u
2
− 2u + 2)(u
4
+ u
3
+ u
2
+ 1)(u
4
+ 3u
3
+ ··· + 10u + 11)
· (u
24
− 5u
23
+ ··· − 19608u + 4792)(u
25
− u
24
+ ··· − 17u
2
+ 2)
· (u
29
+ 2u
28
+ ··· + 5u + 13)
c
5
, c
9
((u − 1)
8
)(u
4
+ 4u
3
+ ··· + 7u + 4)(u
24
− 3u
23
+ ··· + 916u + 152)
· (u
25
+ 3u
23
+ ··· − 4u − 1)(u
29
+ 4u
28
+ ··· − 41u
2
+ 1)
c
6
, c
10
(u
4
+ 4u
2
− 2u + 1)(u
4
+ 2u
3
+ ··· + 3u + 2)(u
4
+ 3u
3
+ ··· + 8u + 8)
· (u
24
− 6u
23
+ ··· − 2820u + 421)(u
25
+ 7u
23
+ ··· − u − 1)
· (u
29
+ 24u
27
+ ··· + 5u + 1)
c
8
((u
4
− u
3
+ u
2
+ 1)
8
)(u
4
+ u
3
+ 2u
2
+ 2u + 2)(u
25
+ 5u
23
+ ··· − 11u
2
− 2)
· (u
29
+ 8u
28
+ ··· + 16u + 8)
c
11
(u
4
+ 4u
2
− 2u + 1)(u
4
+ 2u
3
+ ··· + 3u + 2)(u
4
+ 3u
3
+ ··· + 8u + 8)
· (u
24
− 6u
23
+ ··· − 2820u + 421)(u
25
+ 7u
23
+ ··· − u + 1)
· (u
29
+ 24u
27
+ ··· + 5u + 1)
c
12
(u
4
− 3u
3
+ ··· − 3u + 2)(u
4
+ u
3
+ u
2
+ 1)
8
(u
25
+ 11u
24
+ ··· − 7u
2
+ 1)
· (u
29
− 13u
28
+ ··· − 100u + 8)
32
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
4
− y
3
+ 16y + 16)(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
8
· (y
25
+ 18y
24
+ ··· − 24y − 16)(y
29
+ 24y
28
+ ··· + 94720y − 4096)
c
2
, c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
8
(y
4
+ 3y
3
+ 4y
2
+ 4y + 4)
· (y
25
+ 10y
24
+ ··· − 44y − 4)(y
29
+ 8y
28
+ ··· + 160y − 64)
c
3
(y
4
− 7y
3
+ 15y
2
− 2y + 1)
8
(y
4
− 7y
3
+ 19y
2
− 25y + 16)
· (y
25
− 35y
24
+ ··· + 70715y − 1681)
· (y
29
− 35y
28
+ ··· + 24832y − 4096)
c
4
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
4
+ 3y
3
+ 4y
2
+ 4y + 4)
· (y
4
+ 9y
3
+ 43y
2
+ 98y + 121)
· (y
24
+ 13y
23
+ ··· + 10329632y + 22963264)
· (y
25
+ 11y
24
+ ··· + 68y − 4)(y
29
+ 30y
28
+ ··· − 1041y − 169)
c
5
, c
9
(y − 1)
8
(y
4
− 2y
3
+ y
2
+ 7y + 16)
· (y
24
+ 9y
23
+ ··· − 295504y + 23104)(y
25
+ 6y
24
+ ··· + 10y − 1)
· (y
29
− 20y
28
+ ··· + 82y − 1)
c
6
, c
10
, c
11
(y
4
+ 2y
3
+ y
2
+ 3y + 4)(y
4
+ 3y
3
+ 4y
2
+ 32y + 64)
· (y
4
+ 8y
3
+ 18y
2
+ 4y + 1)(y
24
+ 34y
23
+ ··· − 101592y + 177241)
· (y
25
+ 14y
24
+ ··· + 17y − 1)(y
29
+ 48y
28
+ ··· − 15y − 1)
c
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
8
(y
4
+ y
3
+ 11y
2
+ 11y + 4)
· (y
25
− 3y
24
+ ··· + 14y − 1)(y
29
− 3y
28
+ ··· − 560y − 64)
33
