12a
0739
(K12a
0739
)
A knot diagram
1
Linearized knot diagam
3 8 9 11 12 10 1 2 6 7 5 4
Solving Sequence
2,9
8 3
4,11
5 1 7 10 12 6
c
8
c
2
c
3
c
4
c
1
c
7
c
10
c
12
c
5
c
6
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
31
+ 6u
30
+ ··· + b + 3, −7u
31
− 17u
30
+ ··· + 2a − 6, u
32
+ 3u
31
+ ··· + 6u + 2i
I
u
2
= hu
23
a + 7u
23
+ ··· − a − 50, 2u
23
a − u
23
+ ··· + a
2
− a, u
24
− u
23
+ ··· − 2u + 1i
I
u
3
= hb − 1, u
3
+ 2u
2
+ 2a + 4, u
4
+ 2u
2
+ 2i
I
v
1
= ha, b − 1, v + 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
=
h3u
31
+6u
30
+· · ·+b+3, −7u
31
−17u
30
+· · ·+2a−6, u
32
+3u
31
+· · ·+6u+2i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
11
=
7
2
u
31
+
17
2
u
30
+ ··· + 10u + 3
−3u
31
− 6u
30
+ ··· − 6u − 3
a
5
=
−
1
2
u
31
−
3
2
u
30
+ ··· − 2u − 1
−u
29
− u
28
+ ··· − u − 1
a
1
=
u
3
u
5
+ u
3
+ u
a
7
=
−u
6
− u
4
+ 1
−u
8
− 2u
6
− 2u
4
a
10
=
3
2
u
31
+
7
2
u
30
+ ··· + 4u + 2
−u
31
− 2u
30
+ ··· − 2u − 1
a
12
=
u
11
+ 2u
9
+ 2u
7
+ u
3
−u
11
− 3u
9
− 4u
7
− u
5
+ u
3
+ u
a
6
=
−
1
2
u
31
−
3
2
u
30
+ ··· − 4u − 3
−u
29
− u
28
+ ··· − 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
30
+ 6u
29
+ 24u
28
+ 48u
27
+ 118u
26
+ 184u
25
+ 346u
24
+ 442u
23
+ 680u
22
+ 734u
21
+
948u
20
+ 882u
19
+ 940u
18
+ 750u
17
+ 614u
16
+ 384u
15
+ 160u
14
− 26u
13
− 174u
12
−
266u
11
− 274u
10
− 286u
9
− 220u
8
− 170u
7
− 92u
6
− 46u
5
− 16u
4
− 6u
3
+ 12u
2
+ 14u
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
+ 17u
31
+ ··· + 4u + 4
c
2
, c
8
u
32
− 3u
31
+ ··· − 6u + 2
c
3
, c
7
u
32
+ 3u
31
+ ··· + 186u + 34
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
32
+ u
31
+ ··· − 2u − 1
c
12
u
32
− 3u
31
+ ··· + 256u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
− 3y
31
+ ··· − 240y + 16
c
2
, c
8
y
32
+ 17y
31
+ ··· + 4y + 4
c
3
, c
7
y
32
− 23y
31
+ ··· + 1988y + 1156
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y
32
− 35y
31
+ ··· − 8y + 1
c
12
y
32
+ y
31
+ ··· − 1441792y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.530176 + 0.767965I
a = −0.333698 + 1.088190I
b = −1.227720 − 0.174945I
3.24325 + 2.15228I −1.95940 − 4.22418I
u = 0.530176 − 0.767965I
a = −0.333698 − 1.088190I
b = −1.227720 + 0.174945I
3.24325 − 2.15228I −1.95940 + 4.22418I
u = 0.600367 + 0.882410I
a = 1.053060 − 0.667414I
b = 0.99155 + 1.32550I
−5.84755 + 9.45240I −12.6198 − 8.2074I
u = 0.600367 − 0.882410I
a = 1.053060 + 0.667414I
b = 0.99155 − 1.32550I
−5.84755 − 9.45240I −12.6198 + 8.2074I
u = 0.646120 + 0.645507I
a = −0.580073 − 1.083300I
b = 0.852194 − 1.117410I
−5.16481 − 4.62443I −11.58848 + 2.31548I
u = 0.646120 − 0.645507I
a = −0.580073 + 1.083300I
b = 0.852194 + 1.117410I
−5.16481 + 4.62443I −11.58848 − 2.31548I
u = −0.131686 + 1.135040I
a = −0.83751 + 1.33294I
b = 0.240682 − 1.143010I
−11.15830 − 4.71723I −19.1935 + 3.5978I
u = −0.131686 − 1.135040I
a = −0.83751 − 1.33294I
b = 0.240682 + 1.143010I
−11.15830 + 4.71723I −19.1935 − 3.5978I
u = −0.837356 + 0.165249I
a = 0.404130 − 0.561898I
b = 1.02549 + 1.88978I
−9.6605 + 10.4842I −13.3472 − 5.6777I
u = −0.837356 − 0.165249I
a = 0.404130 + 0.561898I
b = 1.02549 − 1.88978I
−9.6605 − 10.4842I −13.3472 + 5.6777I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.850182
a = −0.699857
b = −0.827456
−14.5114 −16.1110
u = −0.716975 + 0.384483I
a = −0.620707 − 0.541693I
b = 0.537816 − 0.772266I
−6.35392 − 2.54841I −12.91352 + 2.61370I
u = −0.716975 − 0.384483I
a = −0.620707 + 0.541693I
b = 0.537816 + 0.772266I
−6.35392 + 2.54841I −12.91352 − 2.61370I
u = −0.556688 + 1.075410I
a = −1.58889 + 0.49107I
b = 0.474528 + 0.553995I
−8.36419 − 2.29995I −16.4016 + 1.9872I
u = −0.556688 − 1.075410I
a = −1.58889 − 0.49107I
b = 0.474528 − 0.553995I
−8.36419 + 2.29995I −16.4016 − 1.9872I
u = 0.446730 + 1.133610I
a = −0.174401 − 0.268039I
b = 0.451030 − 0.097453I
−4.05143 + 3.92335I −11.83314 − 4.97716I
u = 0.446730 − 1.133610I
a = −0.174401 + 0.268039I
b = 0.451030 + 0.097453I
−4.05143 − 3.92335I −11.83314 + 4.97716I
u = −0.385111 + 1.156080I
a = 1.50345 + 1.00275I
b = −0.605346 − 0.873356I
−2.81095 − 0.89291I −9.61808 − 1.56697I
u = −0.385111 − 1.156080I
a = 1.50345 − 1.00275I
b = −0.605346 + 0.873356I
−2.81095 + 0.89291I −9.61808 + 1.56697I
u = −0.727485 + 0.163192I
a = 0.025322 + 0.657062I
b = −0.937084 − 0.752441I
0.91865 + 2.74283I −4.47712 − 4.42713I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.727485 − 0.163192I
a = 0.025322 − 0.657062I
b = −0.937084 + 0.752441I
0.91865 − 2.74283I −4.47712 + 4.42713I
u = −0.156809 + 0.717859I
a = 0.551971 − 0.300182I
b = 0.009711 + 0.252381I
−0.500387 − 0.882970I −9.10822 + 7.52488I
u = −0.156809 − 0.717859I
a = 0.551971 + 0.300182I
b = 0.009711 − 0.252381I
−0.500387 + 0.882970I −9.10822 − 7.52488I
u = −0.502524 + 1.164790I
a = −0.02663 − 2.31078I
b = −1.016320 + 0.969217I
−1.97783 − 7.36348I −8.22078 + 7.59115I
u = −0.502524 − 1.164790I
a = −0.02663 + 2.31078I
b = −1.016320 − 0.969217I
−1.97783 + 7.36348I −8.22078 − 7.59115I
u = −0.355660 + 1.231240I
a = −1.84106 − 2.12601I
b = 0.82482 + 1.97592I
−13.9647 + 6.4949I −17.9768 − 2.7490I
u = −0.355660 − 1.231240I
a = −1.84106 + 2.12601I
b = 0.82482 − 1.97592I
−13.9647 − 6.4949I −17.9768 + 2.7490I
u = −0.529210 + 1.200000I
a = 1.21068 + 3.02446I
b = 1.12053 − 2.00398I
−12.7401 − 15.4900I −16.2477 + 8.8219I
u = −0.529210 − 1.200000I
a = 1.21068 − 3.02446I
b = 1.12053 + 2.00398I
−12.7401 + 15.4900I −16.2477 − 8.8219I
u = 0.455444 + 1.234730I
a = 0.384015 + 0.486298I
b = −0.986970 + 0.213554I
−18.2324 + 4.6426I −19.4334 − 3.2455I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455444 − 1.234730I
a = 0.384015 − 0.486298I
b = −0.986970 − 0.213554I
−18.2324 − 4.6426I −19.4334 + 3.2455I
u = 0.591155
a = 0.440555
b = 0.317636
−1.06479 −10.0120
8
II.
I
u
2
= hu
23
a+7u
23
+· · ·−a−50, 2u
23
a−u
23
+· · ·+a
2
−a, u
24
−u
23
+· · ·−2u+1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
11
=
a
−0.0232558au
23
− 0.162791u
23
+ ··· + 0.0232558a + 1.16279
a
5
=
−0.162791au
23
− 0.139535u
23
+ ··· − 0.837209a + 0.139535
0.186047au
23
+ 0.302326u
23
+ ··· − 0.186047a + 0.697674
a
1
=
u
3
u
5
+ u
3
+ u
a
7
=
−u
6
− u
4
+ 1
−u
8
− 2u
6
− 2u
4
a
10
=
−0.0232558au
23
− 0.162791u
23
+ ··· + 1.02326a + 1.16279
−0.139535au
23
+ 0.0232558u
23
+ ··· + 0.139535a + 0.976744
a
12
=
u
11
+ 2u
9
+ 2u
7
+ u
3
−u
11
− 3u
9
− 4u
7
− u
5
+ u
3
+ u
a
6
=
−0.0232558au
23
− 0.162791u
23
+ ··· − 0.976744a + 0.162791
0.0232558au
23
+ 0.162791u
23
+ ··· − 0.0232558a + 0.837209
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
23
+ 4u
22
− 24u
21
+ 20u
20
− 68u
19
+ 52u
18
− 108u
17
+ 80u
16
− 96u
15
+ 84u
14
−
32u
13
+ 52u
12
+ 24u
11
+ 8u
10
+ 32u
9
− 28u
8
+ 16u
7
− 20u
6
− 4u
4
+ 4u
3
+ 4u
2
− 4u − 6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
24
+ 13u
23
+ ··· − 2u
2
+ 1)
2
c
2
, c
8
(u
24
+ u
23
+ ··· + 2u + 1)
2
c
3
, c
7
(u
24
− u
23
+ ··· − 10u + 1)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
48
+ u
47
+ ··· − 4u + 1
c
12
(u
24
− 3u
23
+ ··· − 4u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
24
− 3y
23
+ ··· − 4y + 1)
2
c
2
, c
8
(y
24
+ 13y
23
+ ··· − 2y
2
+ 1)
2
c
3
, c
7
(y
24
− 19y
23
+ ··· − 48y + 1)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y
48
− 37y
47
+ ··· + 20y + 1
c
12
(y
24
+ y
23
+ ··· + 20y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.539628 + 0.849352I
a = −0.810554 − 0.445397I
b = −1.20576 + 0.87004I
−0.84994 − 5.71321I −7.89177 + 7.50361I
u = −0.539628 + 0.849352I
a = 0.69898 + 1.48637I
b = 1.20415 − 0.78961I
−0.84994 − 5.71321I −7.89177 + 7.50361I
u = −0.539628 − 0.849352I
a = −0.810554 + 0.445397I
b = −1.20576 − 0.87004I
−0.84994 + 5.71321I −7.89177 − 7.50361I
u = −0.539628 − 0.849352I
a = 0.69898 − 1.48637I
b = 1.20415 + 0.78961I
−0.84994 + 5.71321I −7.89177 − 7.50361I
u = 0.096397 + 0.986281I
a = 0.335716 + 0.777902I
b = 0.148186 − 1.237850I
−5.03371 + 2.05721I −16.2730 − 4.0179I
u = 0.096397 + 0.986281I
a = −1.83300 − 0.82815I
b = 0.584267 + 0.297623I
−5.03371 + 2.05721I −16.2730 − 4.0179I
u = 0.096397 − 0.986281I
a = 0.335716 − 0.777902I
b = 0.148186 + 1.237850I
−5.03371 − 2.05721I −16.2730 + 4.0179I
u = 0.096397 − 0.986281I
a = −1.83300 + 0.82815I
b = 0.584267 − 0.297623I
−5.03371 − 2.05721I −16.2730 + 4.0179I
u = 0.414627 + 0.808476I
a = 0.562342 − 0.117972I
b = 1.45444 + 0.06431I
−3.34583 + 1.77225I −12.01088 − 4.04184I
u = 0.414627 + 0.808476I
a = −0.18786 − 2.56978I
b = 1.160570 + 0.339960I
−3.34583 + 1.77225I −12.01088 − 4.04184I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.414627 − 0.808476I
a = 0.562342 + 0.117972I
b = 1.45444 − 0.06431I
−3.34583 − 1.77225I −12.01088 + 4.04184I
u = 0.414627 − 0.808476I
a = −0.18786 + 2.56978I
b = 1.160570 − 0.339960I
−3.34583 − 1.77225I −12.01088 + 4.04184I
u = −0.542169 + 0.664263I
a = −0.013199 + 0.714741I
b = 1.221860 + 0.515853I
−0.325618 + 1.343200I −5.97036 − 0.62000I
u = −0.542169 + 0.664263I
a = 0.35358 − 1.62117I
b = −0.898839 − 0.548932I
−0.325618 + 1.343200I −5.97036 − 0.62000I
u = −0.542169 − 0.664263I
a = −0.013199 − 0.714741I
b = 1.221860 − 0.515853I
−0.325618 − 1.343200I −5.97036 + 0.62000I
u = −0.542169 − 0.664263I
a = 0.35358 + 1.62117I
b = −0.898839 + 0.548932I
−0.325618 − 1.343200I −5.97036 + 0.62000I
u = 0.796432 + 0.144602I
a = −0.024899 + 0.947038I
b = 0.86856 − 1.22361I
−4.08687 − 6.17959I −10.21479 + 5.04555I
u = 0.796432 + 0.144602I
a = −0.352028 − 0.405762I
b = −1.41700 + 1.69394I
−4.08687 − 6.17959I −10.21479 + 5.04555I
u = 0.796432 − 0.144602I
a = −0.024899 − 0.947038I
b = 0.86856 + 1.22361I
−4.08687 + 6.17959I −10.21479 − 5.04555I
u = 0.796432 − 0.144602I
a = −0.352028 + 0.405762I
b = −1.41700 − 1.69394I
−4.08687 + 6.17959I −10.21479 − 5.04555I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.472424 + 1.121720I
a = 0.617013 + 0.630854I
b = −0.105671 − 0.147261I
−4.03801 + 3.77265I −10.10807 − 3.49106I
u = 0.472424 + 1.121720I
a = −0.87913 − 1.24478I
b = 1.079170 + 0.069000I
−4.03801 + 3.77265I −10.10807 − 3.49106I
u = 0.472424 − 1.121720I
a = 0.617013 − 0.630854I
b = −0.105671 + 0.147261I
−4.03801 − 3.77265I −10.10807 + 3.49106I
u = 0.472424 − 1.121720I
a = −0.87913 + 1.24478I
b = 1.079170 − 0.069000I
−4.03801 − 3.77265I −10.10807 + 3.49106I
u = −0.766849 + 0.083191I
a = −0.847511 − 0.813506I
b = 0.475866 + 0.640007I
−5.92424 + 1.18290I −13.39246 − 0.39910I
u = −0.766849 + 0.083191I
a = 0.381935 − 0.210219I
b = 1.81850 + 1.06364I
−5.92424 + 1.18290I −13.39246 − 0.39910I
u = −0.766849 − 0.083191I
a = −0.847511 + 0.813506I
b = 0.475866 − 0.640007I
−5.92424 − 1.18290I −13.39246 + 0.39910I
u = −0.766849 − 0.083191I
a = 0.381935 + 0.210219I
b = 1.81850 − 1.06364I
−5.92424 − 1.18290I −13.39246 + 0.39910I
u = 0.376287 + 1.204930I
a = −1.74160 + 1.67094I
b = 0.647235 − 1.204540I
−8.11968 − 2.24524I −15.0270 + 1.8938I
u = 0.376287 + 1.204930I
a = 2.37658 − 1.59469I
b = −1.20203 + 1.95399I
−8.11968 − 2.24524I −15.0270 + 1.8938I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.376287 − 1.204930I
a = −1.74160 − 1.67094I
b = 0.647235 + 1.204540I
−8.11968 + 2.24524I −15.0270 − 1.8938I
u = 0.376287 − 1.204930I
a = 2.37658 + 1.59469I
b = −1.20203 − 1.95399I
−8.11968 + 2.24524I −15.0270 − 1.8938I
u = −0.413902 + 1.197930I
a = −1.53766 − 0.93732I
b = 0.235526 + 0.577363I
−9.64981 − 2.92383I −17.2902 + 3.2930I
u = −0.413902 + 1.197930I
a = −2.50614 − 0.27466I
b = 1.77795 + 1.42801I
−9.64981 − 2.92383I −17.2902 + 3.2930I
u = −0.413902 − 1.197930I
a = −1.53766 + 0.93732I
b = 0.235526 − 0.577363I
−9.64981 + 2.92383I −17.2902 − 3.2930I
u = −0.413902 − 1.197930I
a = −2.50614 + 0.27466I
b = 1.77795 − 1.42801I
−9.64981 + 2.92383I −17.2902 − 3.2930I
u = −0.486243 + 1.189530I
a = −0.30991 + 1.87168I
b = 0.445465 − 0.845894I
−9.13493 − 5.78082I −16.3753 + 3.7263I
u = −0.486243 + 1.189530I
a = −0.56299 + 2.89522I
b = 2.11445 − 1.07258I
−9.13493 − 5.78082I −16.3753 + 3.7263I
u = −0.486243 − 1.189530I
a = −0.30991 − 1.87168I
b = 0.445465 + 0.845894I
−9.13493 + 5.78082I −16.3753 − 3.7263I
u = −0.486243 − 1.189530I
a = −0.56299 − 2.89522I
b = 2.11445 + 1.07258I
−9.13493 + 5.78082I −16.3753 − 3.7263I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.512242 + 1.189930I
a = 0.47428 − 2.72028I
b = 0.88509 + 1.37979I
−7.16211 + 11.00000I −13.3183 − 8.0528I
u = 0.512242 + 1.189930I
a = −0.56654 + 3.23218I
b = −1.62178 − 1.80958I
−7.16211 + 11.00000I −13.3183 − 8.0528I
u = 0.512242 − 1.189930I
a = 0.47428 + 2.72028I
b = 0.88509 − 1.37979I
−7.16211 − 11.00000I −13.3183 + 8.0528I
u = 0.512242 − 1.189930I
a = −0.56654 − 3.23218I
b = −1.62178 + 1.80958I
−7.16211 − 11.00000I −13.3183 + 8.0528I
u = 0.580381 + 0.259924I
a = 0.972618 − 0.860339I
b = −0.239708 − 0.201327I
−1.54689 + 0.40841I −6.12800 − 0.75563I
u = 0.580381 + 0.259924I
a = −0.100026 + 0.215685I
b = 1.069500 + 0.131935I
−1.54689 + 0.40841I −6.12800 − 0.75563I
u = 0.580381 − 0.259924I
a = 0.972618 + 0.860339I
b = −0.239708 + 0.201327I
−1.54689 − 0.40841I −6.12800 + 0.75563I
u = 0.580381 − 0.259924I
a = −0.100026 − 0.215685I
b = 1.069500 − 0.131935I
−1.54689 − 0.40841I −6.12800 + 0.75563I
16
III. I
u
3
= hb − 1, u
3
+ 2u
2
+ 2a + 4, u
4
+ 2u
2
+ 2i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
11
=
−
1
2
u
3
− u
2
− 2
1
a
5
=
−
3
2
u
3
− u
2
− 2
u
3
+ u + 1
a
1
=
u
3
−u
3
− u
a
7
=
−1
0
a
10
=
−
1
2
u
3
− u
2
− 1
1
a
12
=
u
3
−u
3
− u
a
6
=
−
1
2
u
3
− u
2
− 2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 20
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− 2u + 2)
2
c
2
, c
8
u
4
+ 2u
2
+ 2
c
3
, c
7
u
4
− 2u
2
+ 2
c
4
, c
5
, c
9
c
10
(u − 1)
4
c
6
, c
11
(u + 1)
4
c
12
u
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ 4)
2
c
2
, c
8
(y
2
+ 2y + 2)
2
c
3
, c
7
(y
2
− 2y + 2)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
(y −1)
4
c
12
y
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455090 + 1.098680I
a = −0.223113 − 0.678203I
b = 1.00000
−5.75727 + 3.66386I −16.0000 − 4.0000I
u = 0.455090 − 1.098680I
a = −0.223113 + 0.678203I
b = 1.00000
−5.75727 − 3.66386I −16.0000 + 4.0000I
u = −0.455090 + 1.098680I
a = −1.77689 + 1.32180I
b = 1.00000
−5.75727 − 3.66386I −16.0000 + 4.0000I
u = −0.455090 − 1.098680I
a = −1.77689 − 1.32180I
b = 1.00000
−5.75727 + 3.66386I −16.0000 − 4.0000I
20
IV. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
2
=
−1
0
a
9
=
1
0
a
8
=
1
0
a
3
=
−1
0
a
4
=
−1
0
a
11
=
0
1
a
5
=
−1
−1
a
1
=
−1
0
a
7
=
1
0
a
10
=
1
1
a
12
=
−1
0
a
6
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
12
u
c
4
, c
5
, c
9
c
10
u + 1
c
6
, c
11
u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
12
y
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y − 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− 2u + 2)
2
(u
24
+ 13u
23
+ ··· − 2u
2
+ 1)
2
· (u
32
+ 17u
31
+ ··· + 4u + 4)
c
2
, c
8
u(u
4
+ 2u
2
+ 2)(u
24
+ u
23
+ ··· + 2u + 1)
2
(u
32
− 3u
31
+ ··· − 6u + 2)
c
3
, c
7
u(u
4
− 2u
2
+ 2)(u
24
− u
23
+ ··· − 10u + 1)
2
· (u
32
+ 3u
31
+ ··· + 186u + 34)
c
4
, c
5
, c
9
c
10
((u − 1)
4
)(u + 1)(u
32
+ u
31
+ ··· − 2u − 1)(u
48
+ u
47
+ ··· − 4u + 1)
c
6
, c
11
(u − 1)(u + 1)
4
(u
32
+ u
31
+ ··· − 2u − 1)(u
48
+ u
47
+ ··· − 4u + 1)
c
12
u
5
(u
24
− 3u
23
+ ··· − 4u + 1)
2
(u
32
− 3u
31
+ ··· + 256u + 256)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ 4)
2
(y
24
− 3y
23
+ ··· − 4y + 1)
2
(y
32
− 3y
31
+ ··· − 240y + 16)
c
2
, c
8
y(y
2
+ 2y + 2)
2
(y
24
+ 13y
23
+ ··· − 2y
2
+ 1)
2
· (y
32
+ 17y
31
+ ··· + 4y + 4)
c
3
, c
7
y(y
2
− 2y + 2)
2
(y
24
− 19y
23
+ ··· − 48y + 1)
2
· (y
32
− 23y
31
+ ··· + 1988y + 1156)
c
4
, c
5
, c
6
c
9
, c
10
, c
11
((y − 1)
5
)(y
32
− 35y
31
+ ··· − 8y + 1)(y
48
− 37y
47
+ ··· + 20y + 1)
c
12
y
5
(y
24
+ y
23
+ ··· + 20y + 1)
2
(y
32
+ y
31
+ ··· − 1441792y + 65536)
26
