12n
0284
(K12n
0284
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 12 2 5 11 7 6 8 10
Solving Sequence
2,7
6 3
4,10
11 1 9 5 8 12
c
6
c
2
c
3
c
10
c
1
c
9
c
4
c
8
c
12
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−157641u
22
+ 1055893u
21
+ ··· + 43337b + 207103,
27883u
22
− 413880u
21
+ ··· + 86674a − 184081, u
23
− 8u
22
+ ··· − 11u + 2i
I
u
2
= hu
8
+ 3u
7
+ 6u
6
+ 7u
5
+ 6u
4
+ 3u
3
+ u
2
+ b − 1,
− u
12
− 6u
11
− 19u
10
− 40u
9
− 61u
8
− 70u
7
− 60u
6
− 37u
5
− 12u
4
+ 5u
3
+ 10u
2
+ a + 8u + 3,
u
13
+ 5u
12
+ 15u
11
+ 30u
10
+ 45u
9
+ 51u
8
+ 45u
7
+ 30u
6
+ 13u
5
+ u
4
− 5u
3
− 5u
2
− 2u − 1i
I
u
3
= h2u
12
a + 29u
12
+ ··· + 2a + 35, 5u
12
a + 9u
12
+ ··· + 3a + 18,
u
13
+ 3u
12
+ 5u
11
+ 4u
10
+ 4u
9
+ 3u
8
+ u
7
− 4u
6
− 2u
5
+ u
3
+ 3u
2
+ 3u + 1i
I
u
4
= ha
3
u + a
3
− a
2
u − au + 4b − 4a − 4u + 1, a
4
+ 2a
2
u − 3a
2
− 2au − 2a − 1, u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 70 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−1.58 × 10
5
u
22
+ 1.06 × 10
6
u
21
+ · · · + 4.33 × 10
4
b + 2.07 ×
10
5
, 27883u
22
−413880u
21
+· · · +86674a − 184081, u
23
−8u
22
+· · · −11u + 2i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
−0.321700u
22
+ 4.77513u
21
+ ··· − 26.2727u + 2.12383
3.63756u
22
− 24.3647u
21
+ ··· + 24.4277u − 4.77890
a
11
=
−0.187911u
22
+ 1.63708u
21
+ ··· − 25.8401u + 2.49965
−2.20154u
22
+ 13.8409u
21
+ ··· + 1.41486u − 0.643399
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
−3.95926u
22
+ 29.1398u
21
+ ··· − 50.7004u + 6.90273
3.63756u
22
− 24.3647u
21
+ ··· + 24.4277u − 4.77890
a
5
=
1.25086u
22
− 9.29017u
21
+ ··· − 1.10816u + 6.18493
−1.69428u
22
+ 12.2032u
21
+ ··· − 15.3776u + 1.78376
a
8
=
−1.06123u
22
+ 8.07276u
21
+ ··· − 14.7681u − 3.81472
0.492097u
22
− 5.85550u
21
+ ··· + 20.7596u − 3.21718
a
12
=
−0.802397u
22
+ 6.76237u
21
+ ··· − 26.6681u + 8.35061
−0.134366u
22
+ 2.76904u
21
+ ··· − 9.99762u + 1.09738
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
52973
43337
u
22
+
121642
43337
u
21
+ ··· +
1232071
43337
u −
582900
43337
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
+ 4u
22
+ ··· − 35u − 4
c
2
, c
6
u
23
− 8u
22
+ ··· − 11u + 2
c
3
u
23
+ 8u
22
+ ··· − 17339u + 16754
c
4
, c
10
u
23
+ 16u
21
+ ··· − 4u − 1
c
5
, c
7
u
23
− 8u
21
+ ··· + 5u − 1
c
8
, c
11
u
23
+ 10u
22
+ ··· − 29u − 4
c
9
, c
12
u
23
+ 3u
22
+ ··· − 10u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 44y
22
+ ··· − 1519y −16
c
2
, c
6
y
23
+ 4y
22
+ ··· − 35y −4
c
3
y
23
+ 84y
22
+ ··· − 4785303843y −280696516
c
4
, c
10
y
23
+ 32y
22
+ ··· + 2y −1
c
5
, c
7
y
23
− 16y
22
+ ··· + 33y −1
c
8
, c
11
y
23
+ 6y
22
+ ··· − 575y −16
c
9
, c
12
y
23
− 39y
22
+ ··· − 196y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.482213 + 0.920645I
a = 0.244578 − 0.919306I
b = 0.0382942 + 0.0881044I
−1.61303 + 2.07315I −0.31329 − 3.51886I
u = 0.482213 − 0.920645I
a = 0.244578 + 0.919306I
b = 0.0382942 − 0.0881044I
−1.61303 − 2.07315I −0.31329 + 3.51886I
u = 0.795198 + 0.518466I
a = 0.729958 + 0.210265I
b = 0.691674 − 0.467858I
−0.22104 + 2.41394I 1.23274 − 2.49732I
u = 0.795198 − 0.518466I
a = 0.729958 − 0.210265I
b = 0.691674 + 0.467858I
−0.22104 − 2.41394I 1.23274 + 2.49732I
u = −0.400101 + 1.050250I
a = 0.662095 + 0.548805I
b = 0.384543 − 1.002950I
−6.34034 − 1.70564I −9.62352 + 2.67791I
u = −0.400101 − 1.050250I
a = 0.662095 − 0.548805I
b = 0.384543 + 1.002950I
−6.34034 + 1.70564I −9.62352 − 2.67791I
u = −0.787767 + 0.322879I
a = 0.846615 − 0.478402I
b = 0.534974 − 0.979772I
−2.52532 + 1.25135I −2.51529 − 0.59191I
u = −0.787767 − 0.322879I
a = 0.846615 + 0.478402I
b = 0.534974 + 0.979772I
−2.52532 − 1.25135I −2.51529 + 0.59191I
u = 0.274775 + 0.733362I
a = 0.596051 + 0.164908I
b = −0.038646 − 0.194454I
−0.352945 + 1.192290I −4.51268 − 5.42631I
u = 0.274775 − 0.733362I
a = 0.596051 − 0.164908I
b = −0.038646 + 0.194454I
−0.352945 − 1.192290I −4.51268 + 5.42631I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.555047 + 1.233680I
a = −0.578619 + 0.250416I
b = 0.773467 + 0.821194I
−5.25580 − 6.48914I −3.11761 + 2.59067I
u = −0.555047 − 1.233680I
a = −0.578619 − 0.250416I
b = 0.773467 − 0.821194I
−5.25580 + 6.48914I −3.11761 − 2.59067I
u = −0.646784
a = −1.86113
b = −1.50954
2.52927 13.5670
u = 1.13690 + 0.99514I
a = 0.847752 − 0.965637I
b = 2.45166 − 0.30632I
8.67002 − 6.60337I 0.16824 + 3.17637I
u = 1.13690 − 0.99514I
a = 0.847752 + 0.965637I
b = 2.45166 + 0.30632I
8.67002 + 6.60337I 0.16824 − 3.17637I
u = 1.02850 + 1.11001I
a = 1.24376 − 0.88643I
b = 2.28163 + 0.96771I
8.2361 + 14.4853I −0.53177 − 7.04602I
u = 1.02850 − 1.11001I
a = 1.24376 + 0.88643I
b = 2.28163 − 0.96771I
8.2361 − 14.4853I −0.53177 + 7.04602I
u = 1.13613 + 1.00401I
a = −1.060840 + 0.748303I
b = −2.47675 − 0.32354I
10.85390 + 6.57430I 0.18173 − 4.98395I
u = 1.13613 − 1.00401I
a = −1.060840 − 0.748303I
b = −2.47675 + 0.32354I
10.85390 − 6.57430I 0.18173 + 4.98395I
u = 1.04311 + 1.14169I
a = −0.869736 + 0.998294I
b = −2.21575 − 0.49458I
10.38880 + 1.40736I −0.548351 + 0.550968I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.04311 − 1.14169I
a = −0.869736 − 0.998294I
b = −2.21575 + 0.49458I
10.38880 − 1.40736I −0.548351 − 0.550968I
u = 0.169482 + 0.280800I
a = −2.98105 − 2.07240I
b = −0.170327 + 1.076150I
−3.36571 + 0.11521I −6.20379 + 0.79398I
u = 0.169482 − 0.280800I
a = −2.98105 + 2.07240I
b = −0.170327 − 1.076150I
−3.36571 − 0.11521I −6.20379 − 0.79398I
7
II. I
u
2
= hu
8
+ 3u
7
+ 6u
6
+ 7u
5
+ 6u
4
+ 3u
3
+ u
2
+ b − 1, −u
12
− 6u
11
+ · · · +
a + 3, u
13
+ 5u
12
+ · · · − 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
u
12
+ 6u
11
+ ··· − 8u − 3
−u
8
− 3u
7
− 6u
6
− 7u
5
− 6u
4
− 3u
3
− u
2
+ 1
a
11
=
u
11
+ 5u
10
+ 14u
9
+ 26u
8
+ 35u
7
+ 35u
6
+ 25u
5
+ 12u
4
− 5u
2
− 5u − 3
u
12
+ 4u
11
+ ··· − u + 1
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
u
12
+ 6u
11
+ ··· − 8u − 4
−u
8
− 3u
7
− 6u
6
− 7u
5
− 6u
4
− 3u
3
− u
2
+ 1
a
5
=
u
12
+ 4u
11
+ ··· + 3u + 3
−u
12
− 5u
11
+ ··· + 4u
2
+ 3u
a
8
=
−u
12
− 4u
11
+ ··· + u − 2
u
11
+ 5u
10
+ 14u
9
+ 25u
8
+ 32u
7
+ 29u
6
+ 19u
5
+ 8u
4
− 4u
2
− 4u − 1
a
12
=
−u
12
− 6u
11
+ ··· + 6u + 2
−u
4
− u
3
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
12
+u
11
+12u
10
+42u
9
+79u
8
+107u
7
+101u
6
+71u
5
+29u
4
−8u
3
−24u
2
−19u −11
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 5u
12
+ ··· − 6u + 1
c
2
u
13
− 5u
12
+ ··· − 2u + 1
c
3
u
13
+ 5u
12
+ ··· + 2u + 5
c
4
, c
10
u
13
+ 5u
11
+ ··· + 2u − 1
c
5
, c
7
u
13
− 3u
11
+ ··· + 3u + 1
c
6
u
13
+ 5u
12
+ ··· − 2u − 1
c
8
u
13
+ 7u
12
+ ··· + 18u + 5
c
9
, c
12
u
13
− 3u
12
+ ··· − 2u − 1
c
11
u
13
− 7u
12
+ ··· + 18u − 5
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
+ 5y
12
+ ··· + 30y −1
c
2
, c
6
y
13
+ 5y
12
+ ··· − 6y −1
c
3
y
13
+ 5y
12
+ ··· − 336y −25
c
4
, c
10
y
13
+ 10y
12
+ ··· − 8y −1
c
5
, c
7
y
13
− 6y
12
+ ··· + 3y −1
c
8
, c
11
y
13
+ 3y
12
+ ··· + 124y −25
c
9
, c
12
y
13
− 13y
12
+ ··· + 6y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.014650 + 0.255879I
a = 0.308979 − 0.014833I
b = 0.725825 + 1.010700I
−1.27099 − 3.82062I −1.40679 + 4.63835I
u = −1.014650 − 0.255879I
a = 0.308979 + 0.014833I
b = 0.725825 − 1.010700I
−1.27099 + 3.82062I −1.40679 − 4.63835I
u = 0.197297 + 0.861440I
a = 0.401352 + 0.826342I
b = −0.709820 + 0.085882I
0.746919 + 0.991007I 3.49980 − 2.09278I
u = 0.197297 − 0.861440I
a = 0.401352 − 0.826342I
b = −0.709820 − 0.085882I
0.746919 − 0.991007I 3.49980 + 2.09278I
u = −0.388828 + 1.189390I
a = −0.898954 − 0.065194I
b = 0.527148 + 0.273002I
−5.76976 − 7.61792I −6.66397 + 8.10409I
u = −0.388828 − 1.189390I
a = −0.898954 + 0.065194I
b = 0.527148 − 0.273002I
−5.76976 + 7.61792I −6.66397 − 8.10409I
u = −0.490814 + 1.270180I
a = 0.514001 + 0.677479I
b = 0.053980 − 0.728775I
−4.83122 − 1.66695I −3.23585 + 1.59270I
u = −0.490814 − 1.270180I
a = 0.514001 − 0.677479I
b = 0.053980 + 0.728775I
−4.83122 + 1.66695I −3.23585 − 1.59270I
u = 0.593865
a = −2.20766
b = −1.60115
2.23989 −14.6790
u = −0.054646 + 0.554847I
a = −0.16877 − 2.22368I
b = 0.907466 + 0.136097I
−2.80544 + 5.20612I −3.31284 − 5.75521I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.054646 − 0.554847I
a = −0.16877 + 2.22368I
b = 0.907466 − 0.136097I
−2.80544 − 5.20612I −3.31284 + 5.75521I
u = −1.04529 + 1.04359I
a = −1.052780 − 0.900847I
b = −2.20403 + 0.34853I
11.16560 − 3.84025I 0.45922 + 2.19131I
u = −1.04529 − 1.04359I
a = −1.052780 + 0.900847I
b = −2.20403 − 0.34853I
11.16560 + 3.84025I 0.45922 − 2.19131I
12
III. I
u
3
=
h2u
12
a+29u
12
+· · ·+2a+35, 5u
12
a+9u
12
+· · ·+3a+18, u
13
+3u
12
+· · ·+3u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
a
−
1
3
u
12
a −
29
6
u
12
+ ··· −
1
3
a −
35
6
a
11
=
1
3
u
12
a +
29
6
u
12
+ ··· +
4
3
a +
35
6
−3u
12
−
13
2
u
11
+ ··· − 6u −
5
2
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
1
3
u
12
a +
29
6
u
12
+ ··· +
4
3
a +
35
6
−
1
3
u
12
a −
29
6
u
12
+ ··· −
1
3
a −
35
6
a
5
=
−3u
12
a − u
12
+ ··· −
5
2
a −
9
2
−
11
6
u
12
a −
1
3
u
12
+ ··· −
10
3
a −
4
3
a
8
=
−
2
3
u
12
a −
7
6
u
12
+ ··· +
5
6
a −
25
6
−
1
3
u
12
a +
1
6
u
12
+ ··· −
5
6
a +
7
6
a
12
=
−4.83333au
12
− 1.33333u
12
+ ··· − 5.83333a − 4.33333
1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 16u
12
+ 41u
11
+ 60u
10
+ 32u
9
+ 40u
8
+ 24u
7
−u
6
−68u
5
−7u
4
+ 11u
3
+ 14u
2
+ 40u + 27
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
13
+ u
12
+ ··· + 3u − 1)
2
c
2
, c
6
(u
13
+ 3u
12
+ ··· + 3u + 1)
2
c
3
(u
13
− 3u
12
+ ··· + 105u + 17)
2
c
4
, c
10
u
26
+ u
25
+ ··· − 1376u + 892
c
5
, c
7
u
26
+ u
25
+ ··· − 16u + 4
c
8
, c
11
(u
13
− 3u
12
+ ··· + 7u − 3)
2
c
9
, c
12
u
26
+ 3u
25
+ ··· + 23978u + 3433
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
13
+ 17y
12
+ ··· + 3y −1)
2
c
2
, c
6
(y
13
+ y
12
+ ··· + 3y −1)
2
c
3
(y
13
+ 33y
12
+ ··· − 4989y −289)
2
c
4
, c
10
y
26
+ 37y
25
+ ··· + 7465488y + 795664
c
5
, c
7
y
26
− 3y
25
+ ··· + 80y + 16
c
8
, c
11
(y
13
+ 7y
12
+ ··· − 47y −9)
2
c
9
, c
12
y
26
− 37y
25
+ ··· + 8143700y + 11785489
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.857473 + 0.279621I
a = 1.146450 + 0.491555I
b = 0.796662 + 0.029542I
0.57111 + 2.96599I 3.40376 − 4.94078I
u = 0.857473 + 0.279621I
a = −0.374853 − 0.402281I
b = −0.42392 − 1.83114I
0.57111 + 2.96599I 3.40376 − 4.94078I
u = 0.857473 − 0.279621I
a = 1.146450 − 0.491555I
b = 0.796662 − 0.029542I
0.57111 − 2.96599I 3.40376 + 4.94078I
u = 0.857473 − 0.279621I
a = −0.374853 + 0.402281I
b = −0.42392 + 1.83114I
0.57111 − 2.96599I 3.40376 + 4.94078I
u = 0.088692 + 0.874872I
a = 0.079744 − 0.117957I
b = 1.001070 + 0.773133I
−4.13282 + 4.47957I −8.13699 − 5.02939I
u = 0.088692 + 0.874872I
a = −1.48441 + 2.01611I
b = 0.206476 − 0.844754I
−4.13282 + 4.47957I −8.13699 − 5.02939I
u = 0.088692 − 0.874872I
a = 0.079744 + 0.117957I
b = 1.001070 − 0.773133I
−4.13282 − 4.47957I −8.13699 + 5.02939I
u = 0.088692 − 0.874872I
a = −1.48441 − 2.01611I
b = 0.206476 + 0.844754I
−4.13282 − 4.47957I −8.13699 + 5.02939I
u = 0.489695 + 1.024820I
a = 0.058476 − 0.727827I
b = 0.304979 − 0.504799I
−1.86631 + 1.44615I 0.486202 − 0.156157I
u = 0.489695 + 1.024820I
a = 1.282050 − 0.518428I
b = −0.296411 + 1.051110I
−1.86631 + 1.44615I 0.486202 − 0.156157I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.489695 − 1.024820I
a = 0.058476 + 0.727827I
b = 0.304979 + 0.504799I
−1.86631 − 1.44615I 0.486202 + 0.156157I
u = 0.489695 − 1.024820I
a = 1.282050 + 0.518428I
b = −0.296411 − 1.051110I
−1.86631 − 1.44615I 0.486202 + 0.156157I
u = −0.561016 + 0.356757I
a = 1.63590 + 0.02743I
b = 1.88883 + 0.58490I
−1.84199 − 6.08937I 0.96961 + 10.45336I
u = −0.561016 + 0.356757I
a = 0.60336 + 2.13477I
b = 0.573289 − 0.541656I
−1.84199 − 6.08937I 0.96961 + 10.45336I
u = −0.561016 − 0.356757I
a = 1.63590 − 0.02743I
b = 1.88883 − 0.58490I
−1.84199 + 6.08937I 0.96961 − 10.45336I
u = −0.561016 − 0.356757I
a = 0.60336 − 2.13477I
b = 0.573289 + 0.541656I
−1.84199 + 6.08937I 0.96961 − 10.45336I
u = −0.621780
a = −1.76823 + 0.25312I
b = −1.361550 − 0.318265I
2.50154 10.0510
u = −0.621780
a = −1.76823 − 0.25312I
b = −1.361550 + 0.318265I
2.50154 10.0510
u = −1.06899 + 0.97779I
a = 0.796159 + 0.828771I
b = 1.98967 + 0.49433I
10.99100 − 1.55475I 0.020480 − 0.977759I
u = −1.06899 + 0.97779I
a = −1.29235 − 0.85739I
b = −2.44763 + 0.61295I
10.99100 − 1.55475I 0.020480 − 0.977759I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.06899 − 0.97779I
a = 0.796159 − 0.828771I
b = 1.98967 − 0.49433I
10.99100 + 1.55475I 0.020480 + 0.977759I
u = −1.06899 − 0.97779I
a = −1.29235 + 0.85739I
b = −2.44763 − 0.61295I
10.99100 + 1.55475I 0.020480 + 0.977759I
u = −0.99496 + 1.07074I
a = 1.26903 + 0.78838I
b = 1.73331 − 0.96676I
10.65510 − 6.00257I −0.76853 + 5.30238I
u = −0.99496 + 1.07074I
a = −0.95131 − 1.16272I
b = −2.46477 + 0.05337I
10.65510 − 6.00257I −0.76853 + 5.30238I
u = −0.99496 − 1.07074I
a = 1.26903 − 0.78838I
b = 1.73331 + 0.96676I
10.65510 + 6.00257I −0.76853 − 5.30238I
u = −0.99496 − 1.07074I
a = −0.95131 + 1.16272I
b = −2.46477 − 0.05337I
10.65510 + 6.00257I −0.76853 − 5.30238I
18
IV. I
u
4
=
ha
3
u+a
3
−a
2
u−au+4b−4a−4u+1, a
4
+2a
2
u−3a
2
−2au−2a−1, u
2
−u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u − 1
a
3
=
u
u − 1
a
4
=
1
u − 1
a
10
=
a
−
1
4
a
3
u +
1
4
a
2
u + ··· + a −
1
4
a
11
=
1
4
a
3
u −
1
4
a
2
u + ··· − a +
1
4
1
4
a
2
u −
7
4
au + ··· +
9
4
a +
1
2
a
1
=
−1
0
a
9
=
1
4
a
3
u −
1
4
a
2
u + ··· +
1
4
a
3
+
1
4
−
1
4
a
3
u +
1
4
a
2
u + ··· + a −
1
4
a
5
=
1
4
a
3
u − a
2
u + ··· +
5
4
a +
7
4
1
4
a
2
u +
1
4
au + ··· −
3
4
a −
3
2
a
8
=
−
1
2
a
2
u +
1
2
au + ··· −
1
2
a − 1
1
2
a
2
u −
1
2
au + ··· +
3
2
a + 2
a
12
=
−
1
4
a
3
u −
1
2
a
2
u + ··· +
1
4
a −
3
4
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u − 4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
4
, c
10
u
8
+ 3u
6
+ 2u
5
+ 7u
4
+ 6u
3
+ 10u
2
+ 4u + 4
c
5
, c
7
u
8
+ 2u
7
− u
6
− 4u
5
+ 3u
4
+ 6u
3
− 6u
2
− 4u + 4
c
8
, c
9
, c
11
c
12
(u
2
+ 1)
4
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y
2
+ y + 1)
4
c
4
, c
10
y
8
+ 6y
7
+ 23y
6
+ 58y
5
+ 93y
4
+ 112y
3
+ 108y
2
+ 64y + 16
c
5
, c
7
y
8
− 6y
7
+ 23y
6
− 58y
5
+ 93y
4
− 112y
3
+ 108y
2
− 64y + 16
c
8
, c
9
, c
11
c
12
(y + 1)
8
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.201767 − 1.028230I
b = − 1.000000I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = −0.204148 + 0.171012I
b = 1.000000I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = −1.53028 + 1.02823I
b = − 1.000000I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = 1.93620 − 0.17101I
b = 1.000000I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = −0.201767 + 1.028230I
b = 1.000000I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −0.204148 − 0.171012I
b = − 1.000000I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −1.53028 − 1.02823I
b = 1.000000I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = 1.93620 + 0.17101I
b = − 1.000000I
−3.28987 − 2.02988I −6.00000 + 3.46410I
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
13
− 5u
12
+ ··· − 6u + 1)(u
13
+ u
12
+ ··· + 3u − 1)
2
· (u
23
+ 4u
22
+ ··· − 35u − 4)
c
2
((u
2
+ u + 1)
4
)(u
13
− 5u
12
+ ··· − 2u + 1)(u
13
+ 3u
12
+ ··· + 3u + 1)
2
· (u
23
− 8u
22
+ ··· − 11u + 2)
c
3
((u
2
− u + 1)
4
)(u
13
− 3u
12
+ ··· + 105u + 17)
2
· (u
13
+ 5u
12
+ ··· + 2u + 5)(u
23
+ 8u
22
+ ··· − 17339u + 16754)
c
4
, c
10
(u
8
+ 3u
6
+ ··· + 4u + 4)(u
13
+ 5u
11
+ ··· + 2u − 1)
· (u
23
+ 16u
21
+ ··· − 4u − 1)(u
26
+ u
25
+ ··· − 1376u + 892)
c
5
, c
7
(u
8
+ 2u
7
− u
6
− 4u
5
+ 3u
4
+ 6u
3
− 6u
2
− 4u + 4)
· (u
13
− 3u
11
+ ··· + 3u + 1)(u
23
− 8u
21
+ ··· + 5u − 1)
· (u
26
+ u
25
+ ··· − 16u + 4)
c
6
((u
2
− u + 1)
4
)(u
13
+ 3u
12
+ ··· + 3u + 1)
2
(u
13
+ 5u
12
+ ··· − 2u − 1)
· (u
23
− 8u
22
+ ··· − 11u + 2)
c
8
((u
2
+ 1)
4
)(u
13
− 3u
12
+ ··· + 7u − 3)
2
(u
13
+ 7u
12
+ ··· + 18u + 5)
· (u
23
+ 10u
22
+ ··· − 29u − 4)
c
9
, c
12
((u
2
+ 1)
4
)(u
13
− 3u
12
+ ··· − 2u − 1)(u
23
+ 3u
22
+ ··· − 10u − 1)
· (u
26
+ 3u
25
+ ··· + 23978u + 3433)
c
11
((u
2
+ 1)
4
)(u
13
− 7u
12
+ ··· + 18u − 5)(u
13
− 3u
12
+ ··· + 7u − 3)
2
· (u
23
+ 10u
22
+ ··· − 29u − 4)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
13
+ 5y
12
+ ··· + 30y −1)
· ((y
13
+ 17y
12
+ ··· + 3y −1)
2
)(y
23
+ 44y
22
+ ··· − 1519y −16)
c
2
, c
6
((y
2
+ y + 1)
4
)(y
13
+ y
12
+ ··· + 3y −1)
2
(y
13
+ 5y
12
+ ··· − 6y −1)
· (y
23
+ 4y
22
+ ··· − 35y −4)
c
3
((y
2
+ y + 1)
4
)(y
13
+ 5y
12
+ ··· − 336y −25)
· (y
13
+ 33y
12
+ ··· − 4989y −289)
2
· (y
23
+ 84y
22
+ ··· − 4785303843y −280696516)
c
4
, c
10
(y
8
+ 6y
7
+ 23y
6
+ 58y
5
+ 93y
4
+ 112y
3
+ 108y
2
+ 64y + 16)
· (y
13
+ 10y
12
+ ··· − 8y −1)(y
23
+ 32y
22
+ ··· + 2y −1)
· (y
26
+ 37y
25
+ ··· + 7465488y + 795664)
c
5
, c
7
(y
8
− 6y
7
+ 23y
6
− 58y
5
+ 93y
4
− 112y
3
+ 108y
2
− 64y + 16)
· (y
13
− 6y
12
+ ··· + 3y −1)(y
23
− 16y
22
+ ··· + 33y −1)
· (y
26
− 3y
25
+ ··· + 80y + 16)
c
8
, c
11
((y + 1)
8
)(y
13
+ 3y
12
+ ··· + 124y −25)(y
13
+ 7y
12
+ ··· − 47y −9)
2
· (y
23
+ 6y
22
+ ··· − 575y −16)
c
9
, c
12
((y + 1)
8
)(y
13
− 13y
12
+ ··· + 6y −1)(y
23
− 39y
22
+ ··· − 196y −1)
· (y
26
− 37y
25
+ ··· + 8143700y + 11785489)
24
