12n
0283
(K12n
0283
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 9 2 12 11 12 5 4 9
Solving Sequence
4,8 5,11
9 6 12 1 7 3 2 10
c
4
c
8
c
5
c
11
c
12
c
7
c
3
c
2
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −3.85888 × 10
16
u
31
+ 4.26003 × 10
16
u
30
+ ··· + 3.07647 × 10
15
a − 2.04981 × 10
16
,
u
32
− u
31
+ ··· + 13u
2
+ 1i
I
u
2
= hb + u, 3u
16
− 3u
15
+ ··· + a − 1,
u
17
− u
16
− u
15
+ 2u
14
+ 4u
13
− 6u
12
− 3u
11
+ 8u
10
+ 5u
9
− 11u
8
− 2u
7
+ 10u
6
+ 2u
5
− 7u
4
− u
3
+ 4u
2
− 1i
I
u
3
= h−1.04996 × 10
43
u
31
+ 4.71287 × 10
42
u
30
+ ··· + 1.47931 × 10
44
b − 3.76971 × 10
43
,
3.26424 × 10
44
u
31
− 3.75981 × 10
44
u
30
+ ··· + 2.51482 × 10
45
a + 1.97058 × 10
44
, u
32
− 2u
31
+ ··· − 3u + 17i
I
u
4
= h−u
3
+ u
2
+ b − 3u + 1, a, u
4
− u
3
+ 3u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 85 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, −3.86 × 10
16
u
31
+ 4.26 × 10
16
u
30
+ · · · + 3.08 × 10
15
a −
2.05 × 10
16
, u
32
− u
31
+ · · · + 13u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
11
=
12.5432u
31
− 13.8471u
30
+ ··· + 13.5866u + 6.66287
u
a
9
=
−16.8410u
31
+ 25.7996u
30
+ ··· − 50.1828u + 26.0290
−6.20203u
31
+ 7.81804u
30
+ ··· − 11.5432u + 1.30392
a
6
=
−14.3847u
31
+ 10.0771u
30
+ ··· − 25.7395u − 5.74332
−4.59634u
31
+ 4.24837u
30
+ ··· − 16.7216u − 4.58421
a
12
=
12.5432u
31
− 13.8471u
30
+ ··· + 14.5866u + 6.66287
u
a
1
=
16.0624u
31
− 21.2113u
30
+ ··· + 41.6901u − 20.5255
2.18153u
31
− 4.28474u
30
+ ··· + 13.9678u − 8.31557
a
7
=
−29.2451u
31
+ 41.4357u
30
+ ··· − 75.2692u + 28.6368
−6.20203u
31
+ 7.81804u
30
+ ··· − 11.5432u + 1.30392
a
3
=
−2.97045u
31
− 12.5885u
30
+ ··· + 19.9046u − 19.7914
1.28508u
31
− 4.38219u
30
+ ··· + 9.58280u − 4.01243
a
2
=
4.67800u
31
− 35.4901u
30
+ ··· − 6.88392u − 73.8593
5.30418u
31
− 11.1266u
30
+ ··· + 18.0833u − 20.0632
a
10
=
6.34118u
31
− 6.02908u
30
+ ··· + 2.04336u + 7.96679
−2.32875u
31
+ 3.30173u
30
+ ··· − 5.20203u + 1.61602
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
137669939372982157
3076468870904633
u
31
−
10255547182342868
3076468870904633
u
30
+···+
105136250462441589
3076468870904633
u+
471315500834574952
3076468870904633
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
+ 19u
31
+ ··· + 7u + 16
c
2
, c
6
u
32
− 5u
31
+ ··· − 7u + 4
c
3
u
32
+ 5u
31
+ ··· + 89u + 4
c
4
, c
11
u
32
− u
31
+ ··· + 13u
2
+ 1
c
5
u
32
− 32u
30
+ ··· + u + 1
c
7
u
32
+ 35u
31
+ ··· + 147456u + 16384
c
8
u
32
+ 22u
31
+ ··· + 21u + 2
c
9
, c
12
u
32
+ 2u
31
+ ··· − 17u + 1
c
10
u
32
− 12u
30
+ ··· − 17u + 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
− 9y
31
+ ··· − 1425y + 256
c
2
, c
6
y
32
+ 19y
31
+ ··· + 7y + 16
c
3
y
32
− 37y
31
+ ··· − 3673y + 16
c
4
, c
11
y
32
+ 13y
31
+ ··· + 26y + 1
c
5
y
32
− 64y
31
+ ··· + 3y + 1
c
7
y
32
− 17y
31
+ ··· + 3623878656y + 268435456
c
8
y
32
+ 60y
30
+ ··· + 19y + 4
c
9
, c
12
y
32
− 60y
31
+ ··· − 9y + 1
c
10
y
32
− 24y
31
+ ··· − 5117y + 289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.800209 + 0.679293I
a = −0.512896 − 0.056292I
b = 0.800209 + 0.679293I
1.24992 + 2.03308I −1.46651 − 1.63420I
u = 0.800209 − 0.679293I
a = −0.512896 + 0.056292I
b = 0.800209 − 0.679293I
1.24992 − 2.03308I −1.46651 + 1.63420I
u = −0.855632 + 0.391807I
a = 0.459557 − 0.032989I
b = −0.855632 + 0.391807I
0.16119 + 2.51789I −0.56583 − 5.72451I
u = −0.855632 − 0.391807I
a = 0.459557 + 0.032989I
b = −0.855632 − 0.391807I
0.16119 − 2.51789I −0.56583 + 5.72451I
u = 0.152358 + 1.111590I
a = −0.201254 − 0.208299I
b = 0.152358 + 1.111590I
−3.34829 − 0.12486I −9.98571 − 0.34747I
u = 0.152358 − 1.111590I
a = −0.201254 + 0.208299I
b = 0.152358 − 1.111590I
−3.34829 + 0.12486I −9.98571 + 0.34747I
u = −0.092710 + 0.862384I
a = −0.384305 + 0.955600I
b = −0.092710 + 0.862384I
−3.61750 + 1.08846I −11.50895 − 1.14763I
u = −0.092710 − 0.862384I
a = −0.384305 − 0.955600I
b = −0.092710 − 0.862384I
−3.61750 − 1.08846I −11.50895 + 1.14763I
u = 0.428817 + 0.727273I
a = −0.07660 + 2.49273I
b = 0.428817 + 0.727273I
−11.71580 − 3.61170I −9.63478 − 2.16413I
u = 0.428817 − 0.727273I
a = −0.07660 − 2.49273I
b = 0.428817 − 0.727273I
−11.71580 + 3.61170I −9.63478 + 2.16413I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.386380 + 0.705787I
a = −0.23876 + 2.54670I
b = −0.386380 + 0.705787I
−7.99069 − 1.31704I −7.26287 + 5.35092I
u = −0.386380 − 0.705787I
a = −0.23876 − 2.54670I
b = −0.386380 − 0.705787I
−7.99069 + 1.31704I −7.26287 − 5.35092I
u = 0.391478 + 0.659853I
a = 0.32637 + 2.90203I
b = 0.391478 + 0.659853I
−11.93460 + 6.10252I −10.79983 − 9.08073I
u = 0.391478 − 0.659853I
a = 0.32637 − 2.90203I
b = 0.391478 − 0.659853I
−11.93460 − 6.10252I −10.79983 + 9.08073I
u = −0.699668 + 1.103420I
a = 0.639142 − 0.193517I
b = −0.699668 + 1.103420I
−5.32466 − 1.51971I −9.09663 + 1.51246I
u = −0.699668 − 1.103420I
a = 0.639142 + 0.193517I
b = −0.699668 − 1.103420I
−5.32466 + 1.51971I −9.09663 − 1.51246I
u = 0.008513 + 0.657799I
a = 1.162970 + 0.228615I
b = 0.008513 + 0.657799I
−0.99449 + 1.29399I −3.54121 − 4.20952I
u = 0.008513 − 0.657799I
a = 1.162970 − 0.228615I
b = 0.008513 − 0.657799I
−0.99449 − 1.29399I −3.54121 + 4.20952I
u = 0.868024 + 1.029180I
a = −0.658984 − 0.058816I
b = 0.868024 + 1.029180I
−0.05539 + 4.40246I −4.33829 − 3.27958I
u = 0.868024 − 1.029180I
a = −0.658984 + 0.058816I
b = 0.868024 − 1.029180I
−0.05539 − 4.40246I −4.33829 + 3.27958I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.125746 + 0.622773I
a = −1.88454 + 0.92438I
b = −0.125746 + 0.622773I
−3.33065 − 4.80034I −9.65737 + 7.89620I
u = −0.125746 − 0.622773I
a = −1.88454 − 0.92438I
b = −0.125746 − 0.622773I
−3.33065 + 4.80034I −9.65737 − 7.89620I
u = −0.91505 + 1.10566I
a = 0.731772 − 0.024127I
b = −0.91505 + 1.10566I
−2.06182 − 9.69561I 0. + 8.25119I
u = −0.91505 − 1.10566I
a = 0.731772 + 0.024127I
b = −0.91505 − 1.10566I
−2.06182 + 9.69561I 0. − 8.25119I
u = −0.034652 + 0.486523I
a = 0.705466 − 0.923628I
b = −0.034652 + 0.486523I
−0.06748 + 1.56172I 0.05355 − 4.52111I
u = −0.034652 − 0.486523I
a = 0.705466 + 0.923628I
b = −0.034652 − 0.486523I
−0.06748 − 1.56172I 0.05355 + 4.52111I
u = −0.95977 + 1.23861I
a = 1.033700 − 0.023141I
b = −0.95977 + 1.23861I
−9.7261 − 10.4089I 0
u = −0.95977 − 1.23861I
a = 1.033700 + 0.023141I
b = −0.95977 − 1.23861I
−9.7261 + 10.4089I 0
u = 0.94787 + 1.25221I
a = −1.027830 − 0.077389I
b = 0.94787 + 1.25221I
−14.1870 + 5.4411I 0
u = 0.94787 − 1.25221I
a = −1.027830 + 0.077389I
b = 0.94787 − 1.25221I
−14.1870 − 5.4411I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.97234 + 1.24005I
a = −1.073810 − 0.004329I
b = 0.97234 + 1.24005I
−13.4156 + 15.8053I 0
u = 0.97234 − 1.24005I
a = −1.073810 + 0.004329I
b = 0.97234 − 1.24005I
−13.4156 − 15.8053I 0
8
II. I
u
2
= hb + u, 3u
16
− 3u
15
+ · · · + a − 1, u
17
− u
16
+ · · · + 4u
2
− 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
11
=
−3u
16
+ 3u
15
+ ··· − 5u + 1
−u
a
9
=
2u
16
− 3u
15
+ ··· + 5u − 4
u
16
− u
15
+ ··· − u
2
+ 4u
a
6
=
−6u
16
+ 11u
15
+ ··· − 13u + 15
−u
16
+ 4u
15
+ ··· − 5u + 6
a
12
=
−3u
16
+ 3u
15
+ ··· − 6u + 1
−u
a
1
=
−8u
16
+ 12u
15
+ ··· − 23u + 10
−4u
16
+ 4u
15
+ ··· − 10u + 1
a
7
=
4u
16
− 5u
15
+ ··· + 11u − 4
u
16
− u
15
+ ··· − u
2
+ 4u
a
3
=
4u
16
− 9u
15
+ ··· + 12u − 12
−u
15
+ u
14
+ ··· + u − 4
a
2
=
14u
16
− 22u
15
+ ··· + 26u − 17
6u
16
− 10u
15
+ ··· + 12u − 11
a
10
=
−4u
16
+ 4u
15
+ ··· − 9u + 1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
16
+ 4u
15
− 4u
14
− 4u
13
+ 3u
12
+ 17u
11
− 25u
10
− 11u
9
+
23u
8
+ 23u
7
− 48u
6
− 5u
5
+ 30u
4
+ 11u
3
− 33u
2
− 3u + 8
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 10u
16
+ ··· − 4u + 1
c
2
u
17
− 2u
16
+ ··· + 2u − 1
c
3
u
17
+ 2u
16
+ ··· − 6u
2
− 1
c
4
, c
11
u
17
− u
16
+ ··· + 4u
2
− 1
c
5
u
17
+ 2u
16
+ ··· + 3u − 1
c
6
u
17
+ 2u
16
+ ··· + 2u + 1
c
7
u
17
+ 6u
16
+ ··· − 3u − 1
c
8
u
17
+ 9u
16
+ ··· − 118u − 21
c
9
u
17
− 8u
16
+ ··· + 3u − 1
c
10
u
17
− 4u
15
+ ··· + u − 1
c
12
u
17
+ 8u
16
+ ··· + 3u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 2y
16
+ ··· + 74y
3
− 1
c
2
, c
6
y
17
+ 10y
16
+ ··· − 4y −1
c
3
y
17
− 14y
16
+ ··· − 12y −1
c
4
, c
11
y
17
− 3y
16
+ ··· + 8y −1
c
5
y
17
− 8y
16
+ ··· − y −1
c
7
y
17
− 16y
16
+ ··· − 5y −1
c
8
y
17
− 5y
16
+ ··· + 946y −441
c
9
, c
12
y
17
− 4y
16
+ ··· − 17y −1
c
10
y
17
− 8y
16
+ ··· + 3y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621825 + 0.705881I
a = −1.69701 − 0.12364I
b = 0.621825 − 0.705881I
0.16835 − 3.69444I −3.43345 + 6.20569I
u = −0.621825 − 0.705881I
a = −1.69701 + 0.12364I
b = 0.621825 + 0.705881I
0.16835 + 3.69444I −3.43345 − 6.20569I
u = 0.985112 + 0.472102I
a = 0.650559 + 0.351279I
b = −0.985112 − 0.472102I
0.03052 − 1.55891I −2.18552 − 2.08462I
u = 0.985112 − 0.472102I
a = 0.650559 − 0.351279I
b = −0.985112 + 0.472102I
0.03052 + 1.55891I −2.18552 + 2.08462I
u = −0.924919 + 0.614200I
a = −0.886710 + 0.219548I
b = 0.924919 − 0.614200I
1.80526 − 3.09805I 2.71378 + 6.00667I
u = −0.924919 − 0.614200I
a = −0.886710 − 0.219548I
b = 0.924919 + 0.614200I
1.80526 + 3.09805I 2.71378 − 6.00667I
u = 0.700967 + 0.501936I
a = 1.39448 + 0.81847I
b = −0.700967 − 0.501936I
−1.94678 + 5.32379I −4.18293 − 7.79972I
u = 0.700967 − 0.501936I
a = 1.39448 − 0.81847I
b = −0.700967 + 0.501936I
−1.94678 − 5.32379I −4.18293 + 7.79972I
u = 0.677004 + 0.917206I
a = 1.157990 − 0.482730I
b = −0.677004 − 0.917206I
−1.93385 + 1.63299I −5.94728 − 2.28105I
u = 0.677004 − 0.917206I
a = 1.157990 + 0.482730I
b = −0.677004 + 0.917206I
−1.93385 − 1.63299I −5.94728 + 2.28105I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856536 + 0.852054I
a = −0.984611 − 0.179626I
b = 0.856536 − 0.852054I
1.50462 − 4.39558I 2.29329 + 4.97306I
u = −0.856536 − 0.852054I
a = −0.984611 + 0.179626I
b = 0.856536 + 0.852054I
1.50462 + 4.39558I 2.29329 − 4.97306I
u = 0.707184
a = −1.41344
b = −0.707184
−7.59564 −3.54960
u = 0.863394 + 0.964445I
a = 0.890585 − 0.307806I
b = −0.863394 − 0.964445I
−0.71548 + 8.94334I −2.29262 − 7.34583I
u = 0.863394 − 0.964445I
a = 0.890585 + 0.307806I
b = −0.863394 + 0.964445I
−0.71548 − 8.94334I −2.29262 + 7.34583I
u = −0.676789 + 0.041582I
a = 1.68144 + 0.49673I
b = 0.676789 − 0.041582I
−11.56420 − 5.02914I −6.69047 + 2.68447I
u = −0.676789 − 0.041582I
a = 1.68144 − 0.49673I
b = 0.676789 + 0.041582I
−11.56420 + 5.02914I −6.69047 − 2.68447I
13
III. I
u
3
= h−1.05 × 10
43
u
31
+ 4.71 × 10
42
u
30
+ · · · + 1.48 × 10
44
b − 3.77 ×
10
43
, 3.26 × 10
44
u
31
− 3.76 × 10
44
u
30
+ · · · + 2.51 × 10
45
a + 1.97 ×
10
44
, u
32
− 2u
31
+ · · · − 3u + 17i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
11
=
−0.129800u
31
+ 0.149506u
30
+ ··· − 7.89817u − 0.0783584
0.0709764u
31
− 0.0318586u
30
+ ··· + 0.0746396u + 0.254829
a
9
=
−0.112910u
31
+ 0.209924u
30
+ ··· − 2.19568u + 1.23577
−0.0168898u
31
− 0.0604187u
30
+ ··· − 4.70249u − 1.31413
a
6
=
−0.00441307u
31
− 0.108854u
30
+ ··· − 2.15238u − 2.06675
0.143271u
31
− 0.0431300u
30
+ ··· + 3.60055u + 2.54054
a
12
=
−0.0588235u
31
+ 0.117647u
30
+ ··· − 7.82353u + 0.176471
0.0709764u
31
− 0.0318586u
30
+ ··· + 0.0746396u + 0.254829
a
1
=
−0.0706474u
31
+ 0.301908u
30
+ ··· − 1.93782u + 2.98528
−0.0346426u
31
+ 0.271751u
30
+ ··· + 2.53465u + 3.05041
a
7
=
−0.0588235u
31
+ 0.117647u
30
+ ··· − 7.82353u + 0.176471
0.0709764u
31
− 0.0318586u
30
+ ··· + 1.07464u + 0.254829
a
3
=
0.0149899u
31
− 0.100956u
30
+ ··· − 5.35030u − 0.119609
−0.127897u
31
+ 0.0824258u
30
+ ··· − 7.92285u − 3.64080
a
2
=
0.182759u
31
− 0.207627u
30
+ ··· + 5.96598u + 4.51980
−0.230768u
31
+ 0.589230u
30
+ ··· − 6.71849u + 4.83964
a
10
=
−0.101574u
31
+ 0.282734u
30
+ ··· − 5.94721u + 2.04807
−0.0632789u
31
+ 0.328608u
30
+ ··· − 0.0145611u + 3.47938
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.112903u
31
− 0.364793u
30
+ ··· − 1.27394u − 15.4783
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
16
+ 10u
15
+ ··· + 4u + 1)
2
c
2
, c
6
(u
16
+ 2u
15
+ ··· + 2u
2
+ 1)
2
c
3
(u
16
− 2u
15
+ ··· − 4u + 1)
2
c
4
, c
11
u
32
− 2u
31
+ ··· − 3u + 17
c
5
u
32
− 20u
30
+ ··· + 147u + 11483
c
7
(u − 1)
32
c
8
(u
16
− 5u
15
+ ··· − 10u + 4)
2
c
9
, c
12
u
32
+ 5u
31
+ ··· − 40346u + 7837
c
10
u
32
− 10u
30
+ ··· − 52147u + 13057
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
16
− 6y
15
+ ··· + 52y
2
+ 1)
2
c
2
, c
6
(y
16
+ 10y
15
+ ··· + 4y + 1)
2
c
3
(y
16
− 22y
15
+ ··· + 4y + 1)
2
c
4
, c
11
y
32
+ 46y
30
+ ··· + 4513y + 289
c
5
y
32
− 40y
31
+ ··· + 4819370525y + 131859289
c
7
(y −1)
32
c
8
(y
16
+ 5y
15
+ ··· + 84y + 16)
2
c
9
, c
12
y
32
− 37y
31
+ ··· − 3847924y + 61418569
c
10
y
32
− 20y
31
+ ··· − 1430609823y + 170485249
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.595671 + 0.842379I
a = −1.48043 − 0.22659I
b = 0.920809 − 0.564799I
−0.08555 − 5.00887I −2.04817 + 9.54125I
u = −0.595671 − 0.842379I
a = −1.48043 + 0.22659I
b = 0.920809 + 0.564799I
−0.08555 + 5.00887I −2.04817 − 9.54125I
u = 0.445704 + 0.827008I
a = −1.006630 + 0.127867I
b = 1.51162 − 1.06489I
−12.05440 + 7.15239I −8.17635 − 6.88764I
u = 0.445704 − 0.827008I
a = −1.006630 − 0.127867I
b = 1.51162 + 1.06489I
−12.05440 − 7.15239I −8.17635 + 6.88764I
u = 0.920809 + 0.564799I
a = 1.38479 + 0.35836I
b = −0.595671 − 0.842379I
−0.08555 + 5.00887I −2.04817 − 9.54125I
u = 0.920809 − 0.564799I
a = 1.38479 − 0.35836I
b = −0.595671 + 0.842379I
−0.08555 − 5.00887I −2.04817 + 9.54125I
u = 0.304893 + 0.861352I
a = −1.122090 + 0.066210I
b = 1.48728 − 1.09791I
−12.74750 − 3.22124I −9.99417 + 0.06529I
u = 0.304893 − 0.861352I
a = −1.122090 − 0.066210I
b = 1.48728 + 1.09791I
−12.74750 + 3.22124I −9.99417 − 0.06529I
u = −0.371450 + 0.797625I
a = 1.037300 + 0.063551I
b = −1.51710 − 1.09383I
−8.33008 − 1.76073I −6.56613 + 3.85252I
u = −0.371450 − 0.797625I
a = 1.037300 − 0.063551I
b = −1.51710 + 1.09383I
−8.33008 + 1.76073I −6.56613 − 3.85252I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.702474 + 0.876922I
a = 1.195520 − 0.248497I
b = −0.639086 − 0.446115I
0.59866 + 2.73963I 0.340477 + 0.446917I
u = 0.702474 − 0.876922I
a = 1.195520 + 0.248497I
b = −0.639086 + 0.446115I
0.59866 − 2.73963I 0.340477 − 0.446917I
u = 0.275864 + 0.794362I
a = 1.52812 − 0.20094I
b = −1.13799 − 0.92245I
−3.72434 + 5.60445I −9.51726 − 7.00610I
u = 0.275864 − 0.794362I
a = 1.52812 + 0.20094I
b = −1.13799 + 0.92245I
−3.72434 − 5.60445I −9.51726 + 7.00610I
u = −0.639086 + 0.446115I
a = −1.75455 + 0.14252I
b = 0.702474 − 0.876922I
0.59866 − 2.73963I 0.340477 − 0.446917I
u = −0.639086 − 0.446115I
a = −1.75455 − 0.14252I
b = 0.702474 + 0.876922I
0.59866 + 2.73963I 0.340477 + 0.446917I
u = 0.865485 + 1.019380I
a = 0.834505 − 0.032645I
b = −0.350507 − 0.537414I
0.10305 + 2.86220I −3.06555 − 3.98366I
u = 0.865485 − 1.019380I
a = 0.834505 + 0.032645I
b = −0.350507 + 0.537414I
0.10305 − 2.86220I −3.06555 + 3.98366I
u = −0.350507 + 0.537414I
a = −1.71691 − 0.28607I
b = 0.865485 − 1.019380I
0.10305 − 2.86220I −3.06555 + 3.98366I
u = −0.350507 − 0.537414I
a = −1.71691 + 0.28607I
b = 0.865485 + 1.019380I
0.10305 + 2.86220I −3.06555 − 3.98366I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.13799 + 0.92245I
a = −0.806166 + 0.364503I
b = 0.275864 − 0.794362I
−3.72434 − 5.60445I −9.51726 + 7.00610I
u = −1.13799 − 0.92245I
a = −0.806166 − 0.364503I
b = 0.275864 + 0.794362I
−3.72434 + 5.60445I −9.51726 − 7.00610I
u = 0.086773 + 0.477663I
a = 1.35727 − 0.63772I
b = −0.98910 − 1.38893I
−1.59332 − 1.36627I −7.47286 − 3.74224I
u = 0.086773 − 0.477663I
a = 1.35727 + 0.63772I
b = −0.98910 + 1.38893I
−1.59332 + 1.36627I −7.47286 + 3.74224I
u = −0.98910 + 1.38893I
a = −0.426970 − 0.000051I
b = 0.086773 − 0.477663I
−1.59332 + 1.36627I −7.47286 + 3.74224I
u = −0.98910 − 1.38893I
a = −0.426970 + 0.000051I
b = 0.086773 + 0.477663I
−1.59332 − 1.36627I −7.47286 − 3.74224I
u = 1.48728 + 1.09791I
a = 0.130314 + 0.540083I
b = 0.304893 − 0.861352I
−12.74750 + 3.22124I 0
u = 1.48728 − 1.09791I
a = 0.130314 − 0.540083I
b = 0.304893 + 0.861352I
−12.74750 − 3.22124I 0
u = 1.51162 + 1.06489I
a = −0.003578 + 0.515545I
b = 0.445704 − 0.827008I
−12.05440 − 7.15239I 0
u = 1.51162 − 1.06489I
a = −0.003578 − 0.515545I
b = 0.445704 + 0.827008I
−12.05440 + 7.15239I 0
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51710 + 1.09383I
a = −0.062247 + 0.484928I
b = −0.371450 − 0.797625I
−8.33008 + 1.76073I 0
u = −1.51710 − 1.09383I
a = −0.062247 − 0.484928I
b = −0.371450 + 0.797625I
−8.33008 − 1.76073I 0
20
IV. I
u
4
= h−u
3
+ u
2
+ b − 3u + 1, a, u
4
− u
3
+ 3u
2
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
11
=
0
u
3
− u
2
+ 3u − 1
a
9
=
0
u
a
6
=
1
0
a
12
=
u
3
− u
2
+ 3u − 1
u
3
− u
2
+ 3u − 1
a
1
=
u
3
− u
2
+ 3u − 1
u
3
− u
2
+ 2u − 1
a
7
=
−u
3
+ u
2
− 3u + 1
−u
3
+ u
2
− 2u + 1
a
3
=
u
3
+ 2u + 2
u
3
− u
2
+ 2u
a
2
=
u
2
+ 2
u
3
− u
2
+ 2u
a
10
=
u
3
− u
2
+ 3u − 1
u
3
− u
2
+ 4u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9u
3
+ 9u
2
− 18u − 3
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
4
, c
5
, c
10
c
11
u
4
− u
3
+ 3u
2
− u + 1
c
7
, c
9
(u − 1)
4
c
8
u
4
c
12
(u + 1)
4
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y
2
+ y + 1)
2
c
4
, c
5
, c
10
c
11
y
4
+ 5y
3
+ 9y
2
+ 5y + 1
c
7
, c
9
, c
12
(y −1)
4
c
8
y
4
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.148403 + 0.632502I
a = 0
b = −0.35160 + 1.49853I
−1.64493 + 2.02988I −7.50000 − 7.79423I
u = 0.148403 − 0.632502I
a = 0
b = −0.35160 − 1.49853I
−1.64493 − 2.02988I −7.50000 + 7.79423I
u = 0.35160 + 1.49853I
a = 0
b = −0.148403 + 0.632502I
−1.64493 − 2.02988I −7.50000 + 7.79423I
u = 0.35160 − 1.49853I
a = 0
b = −0.148403 − 0.632502I
−1.64493 + 2.02988I −7.50000 − 7.79423I
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
16
+ 10u
15
+ ··· + 4u + 1)
2
· (u
17
− 10u
16
+ ··· − 4u + 1)(u
32
+ 19u
31
+ ··· + 7u + 16)
c
2
((u
2
+ u + 1)
2
)(u
16
+ 2u
15
+ ··· + 2u
2
+ 1)
2
(u
17
− 2u
16
+ ··· + 2u − 1)
· (u
32
− 5u
31
+ ··· − 7u + 4)
c
3
((u
2
− u + 1)
2
)(u
16
− 2u
15
+ ··· − 4u + 1)
2
(u
17
+ 2u
16
+ ··· − 6u
2
− 1)
· (u
32
+ 5u
31
+ ··· + 89u + 4)
c
4
, c
11
(u
4
− u
3
+ 3u
2
− u + 1)(u
17
− u
16
+ ··· + 4u
2
− 1)
· (u
32
− 2u
31
+ ··· − 3u + 17)(u
32
− u
31
+ ··· + 13u
2
+ 1)
c
5
(u
4
− u
3
+ 3u
2
− u + 1)(u
17
+ 2u
16
+ ··· + 3u − 1)
· (u
32
− 32u
30
+ ··· + u + 1)(u
32
− 20u
30
+ ··· + 147u + 11483)
c
6
((u
2
− u + 1)
2
)(u
16
+ 2u
15
+ ··· + 2u
2
+ 1)
2
(u
17
+ 2u
16
+ ··· + 2u + 1)
· (u
32
− 5u
31
+ ··· − 7u + 4)
c
7
((u − 1)
36
)(u
17
+ 6u
16
+ ··· − 3u − 1)
· (u
32
+ 35u
31
+ ··· + 147456u + 16384)
c
8
u
4
(u
16
− 5u
15
+ ··· − 10u + 4)
2
(u
17
+ 9u
16
+ ··· − 118u − 21)
· (u
32
+ 22u
31
+ ··· + 21u + 2)
c
9
((u − 1)
4
)(u
17
− 8u
16
+ ··· + 3u − 1)(u
32
+ 2u
31
+ ··· − 17u + 1)
· (u
32
+ 5u
31
+ ··· − 40346u + 7837)
c
10
(u
4
− u
3
+ 3u
2
− u + 1)(u
17
− 4u
15
+ ··· + u − 1)
· (u
32
− 12u
30
+ ··· − 17u + 17)(u
32
− 10u
30
+ ··· − 52147u + 13057)
c
12
((u + 1)
4
)(u
17
+ 8u
16
+ ··· + 3u + 1)(u
32
+ 2u
31
+ ··· − 17u + 1)
· (u
32
+ 5u
31
+ ··· − 40346u + 7837)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
16
− 6y
15
+ ··· + 52y
2
+ 1)
2
· (y
17
− 2y
16
+ ··· + 74y
3
− 1)(y
32
− 9y
31
+ ··· − 1425y + 256)
c
2
, c
6
((y
2
+ y + 1)
2
)(y
16
+ 10y
15
+ ··· + 4y + 1)
2
· (y
17
+ 10y
16
+ ··· − 4y −1)(y
32
+ 19y
31
+ ··· + 7y + 16)
c
3
((y
2
+ y + 1)
2
)(y
16
− 22y
15
+ ··· + 4y + 1)
2
· (y
17
− 14y
16
+ ··· − 12y −1)(y
32
− 37y
31
+ ··· − 3673y + 16)
c
4
, c
11
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
17
− 3y
16
+ ··· + 8y −1)
· (y
32
+ 46y
30
+ ··· + 4513y + 289)(y
32
+ 13y
31
+ ··· + 26y + 1)
c
5
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
17
− 8y
16
+ ··· − y −1)
· (y
32
− 64y
31
+ ··· + 3y + 1)
· (y
32
− 40y
31
+ ··· + 4819370525y + 131859289)
c
7
((y −1)
36
)(y
17
− 16y
16
+ ··· − 5y −1)
· (y
32
− 17y
31
+ ··· + 3623878656y + 268435456)
c
8
y
4
(y
16
+ 5y
15
+ ··· + 84y + 16)
2
(y
17
− 5y
16
+ ··· + 946y −441)
· (y
32
+ 60y
30
+ ··· + 19y + 4)
c
9
, c
12
((y −1)
4
)(y
17
− 4y
16
+ ··· − 17y −1)(y
32
− 60y
31
+ ··· − 9y + 1)
· (y
32
− 37y
31
+ ··· − 3847924y + 61418569)
c
10
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
17
− 8y
16
+ ··· + 3y −1)
· (y
32
− 24y
31
+ ··· − 5117y + 289)
· (y
32
− 20y
31
+ ··· − 1430609823y + 170485249)
26
