12a
1181
(K12a
1181
)
A knot diagram
1
Linearized knot diagam
4 10 8 1 9 11 3 12 2 7 6 5
Solving Sequence
3,7
8
4,10
11 2 1 6 12 9 5
c
7
c
3
c
10
c
2
c
1
c
6
c
11
c
9
c
5
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−14254847226477u
26
+ 36513086551233u
25
+ ··· + 25218582104246b + 69411294847385,
a − 1, u
27
− 2u
26
+ ··· − u + 1i
I
u
2
= h1.54251 × 10
20
u
23
− 1.34594 × 10
20
u
22
+ ··· + 4.03018 × 10
21
b + 1.66567 × 10
20
,
2.09874 × 10
23
u
23
+ 2.15950 × 10
23
u
22
+ ··· + 7.08424 × 10
25
a − 6.56169 × 10
25
, u
24
− 7u
22
+ ··· − 17u + 44i
I
u
3
= h−2706u
15
+ 399u
14
+ ··· + 2389b + 1730, a + 1,
u
16
− 8u
14
+ 28u
12
− u
11
− 50u
10
+ 3u
9
+ 46u
8
− 2u
7
− 23u
6
− u
5
+ 12u
4
+ 4u
3
− 4u
2
− u + 1i
I
u
4
= h2.71133 × 10
33
u
31
− 1.79455 × 10
33
u
30
+ ··· + 1.73517 × 10
36
b + 3.10903 × 10
35
,
− 1.46619 × 10
42
u
31
− 3.55764 × 10
42
u
30
+ ··· + 1.02938 × 10
44
a − 1.96344 × 10
44
,
u
32
+ u
31
+ ··· + 556u + 109i
* 4 irreducible components of dim
C
= 0, with total 99 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−1.43 × 10
13
u
26
+ 3.65 × 10
13
u
25
+ · · · + 2.52 × 10
13
b + 6.94 ×
10
13
, a − 1, u
27
− 2u
26
+ · · · − u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
1
0.565252u
26
− 1.44786u
25
+ ··· + 3.67612u − 2.75239
a
11
=
0.565252u
26
− 1.44786u
25
+ ··· + 3.67612u − 1.75239
0.565252u
26
− 1.44786u
25
+ ··· + 3.67612u − 2.75239
a
2
=
u
−0.317361u
26
+ 0.398104u
25
+ ··· − 1.18714u − 0.565252
a
1
=
0.0683574u
26
− 0.219861u
25
+ ··· + 1.08074u + 0.236618
−0.398080u
26
+ 0.502028u
25
+ ··· − 1.41938u − 0.718723
a
6
=
−1.04115u
26
+ 1.62303u
25
+ ··· − 4.19819u − 1.11991
−1.60640u
26
+ 3.07090u
25
+ ··· − 7.87431u + 0.632474
a
12
=
−0.337903u
26
+ 0.670668u
25
+ ··· − 1.19240u − 0.372411
0.703245u
26
− 0.952366u
25
+ ··· + 3.00579u + 0.747502
a
9
=
−u
2
+ 1
0.801869u
26
− 1.98946u
25
+ ··· + 4.55874u − 3.06975
a
5
=
−0.0367769u
26
− 0.0781692u
25
+ ··· − 0.950528u − 0.0601984
−0.265354u
26
+ 0.386964u
25
+ ··· − 0.436197u − 0.0643596
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
32741796610216
12609291052123
u
26
+
41485402060855
12609291052123
u
25
+ ··· −
145165804658306
12609291052123
u −
32798700861086
12609291052123
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
27
− 13u
26
+ ··· + 240u − 16
c
2
, c
3
, c
7
c
9
u
27
− 2u
26
+ ··· − u + 1
c
5
, c
8
u
27
− u
25
+ ··· − 4u − 1
c
6
, c
10
, c
11
u
27
− 15u
26
+ ··· + 1792u − 128
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
27
+ 23y
26
+ ··· + 384y −256
c
2
, c
3
, c
7
c
9
y
27
− 24y
26
+ ··· − 13y −1
c
5
, c
8
y
27
− 2y
26
+ ··· + 32y −1
c
6
, c
10
, c
11
y
27
+ 23y
26
+ ··· + 49152y −16384
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.606808 + 0.696344I
a = 1.00000
b = −0.420246 + 0.658451I
5.31904 − 1.53633I 0.97752 + 4.58695I
u = 0.606808 − 0.696344I
a = 1.00000
b = −0.420246 − 0.658451I
5.31904 + 1.53633I 0.97752 − 4.58695I
u = −0.414460 + 0.742322I
a = 1.00000
b = −0.633985 + 0.290639I
6.49491 − 2.15245I 3.36843 + 1.56518I
u = −0.414460 − 0.742322I
a = 1.00000
b = −0.633985 − 0.290639I
6.49491 + 2.15245I 3.36843 − 1.56518I
u = −1.171460 + 0.136751I
a = 1.00000
b = −1.05498 − 1.55972I
−3.97655 + 0.54664I 30.5727 + 2.7472I
u = −1.171460 − 0.136751I
a = 1.00000
b = −1.05498 + 1.55972I
−3.97655 − 0.54664I 30.5727 − 2.7472I
u = −1.19268
a = 1.00000
b = −1.69791
−4.06015 36.8660
u = 1.237680 + 0.193185I
a = 1.00000
b = −1.049080 − 0.332758I
1.45272 − 6.00981I −2.55081 + 5.00274I
u = 1.237680 − 0.193185I
a = 1.00000
b = −1.049080 + 0.332758I
1.45272 + 6.00981I −2.55081 − 5.00274I
u = 0.272498 + 0.656447I
a = 1.00000
b = −0.232111 − 1.384450I
1.19387 + 5.26918I −1.87715 − 0.41400I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.272498 − 0.656447I
a = 1.00000
b = −0.232111 + 1.384450I
1.19387 − 5.26918I −1.87715 + 0.41400I
u = −0.544239 + 0.357222I
a = 1.00000
b = −0.039400 − 1.138300I
−1.49429 + 1.37539I −1.96403 − 5.12263I
u = −0.544239 − 0.357222I
a = 1.00000
b = −0.039400 + 1.138300I
−1.49429 − 1.37539I −1.96403 + 5.12263I
u = 1.327650 + 0.303823I
a = 1.00000
b = −0.890497 + 0.845146I
−5.92020 − 7.30574I −7.23638 + 8.13726I
u = 1.327650 − 0.303823I
a = 1.00000
b = −0.890497 − 0.845146I
−5.92020 + 7.30574I −7.23638 − 8.13726I
u = −1.38999 + 0.44746I
a = 1.00000
b = −0.810708 − 0.774977I
0.07846 + 12.01660I −3.25285 − 8.03502I
u = −1.38999 − 0.44746I
a = 1.00000
b = −0.810708 + 0.774977I
0.07846 − 12.01660I −3.25285 + 8.03502I
u = 1.41817 + 0.42518I
a = 1.00000
b = −0.29217 + 1.70490I
−13.2741 − 6.0424I −9.03644 + 3.94723I
u = 1.41817 − 0.42518I
a = 1.00000
b = −0.29217 − 1.70490I
−13.2741 + 6.0424I −9.03644 − 3.94723I
u = 0.145479 + 0.452208I
a = 1.00000
b = −0.507451 − 0.168459I
1.007930 + 0.745055I 5.32116 − 2.57707I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.145479 − 0.452208I
a = 1.00000
b = −0.507451 + 0.168459I
1.007930 − 0.745055I 5.32116 + 2.57707I
u = 0.050720 + 0.437517I
a = 1.00000
b = −0.189311 + 1.341130I
−3.75311 − 3.26931I 1.67169 + 1.70953I
u = 0.050720 − 0.437517I
a = 1.00000
b = −0.189311 − 1.341130I
−3.75311 + 3.26931I 1.67169 − 1.70953I
u = −1.53697 + 0.51725I
a = 1.00000
b = −0.27260 − 1.65847I
−14.1771 + 11.6933I −8.79505 − 6.96759I
u = −1.53697 − 0.51725I
a = 1.00000
b = −0.27260 + 1.65847I
−14.1771 − 11.6933I −8.79505 + 6.96759I
u = 1.59445 + 0.61058I
a = 1.00000
b = −0.25851 + 1.63892I
−7.9325 − 16.0663I −5.13174 + 7.30628I
u = 1.59445 − 0.61058I
a = 1.00000
b = −0.25851 − 1.63892I
−7.9325 + 16.0663I −5.13174 − 7.30628I
7
II. I
u
2
=
h1.54×10
20
u
23
−1.35×10
20
u
22
+· · ·+4.03×10
21
b+1.67×10
20
, 2.10×10
23
u
23
+
2.16 × 10
23
u
22
+ · · · + 7.08 × 10
25
a − 6.56 × 10
25
, u
24
− 7u
22
+ · · · − 17u + 44i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
−0.00296255u
23
− 0.00304832u
22
+ ··· − 3.93361u + 0.926237
−0.0382739u
23
+ 0.0333965u
22
+ ··· − 0.105335u − 0.0413300
a
11
=
−0.0412365u
23
+ 0.0303482u
22
+ ··· − 4.03895u + 0.884907
−0.0382739u
23
+ 0.0333965u
22
+ ··· − 0.105335u − 0.0413300
a
2
=
−0.0201774u
23
+ 0.0155738u
22
+ ··· − 2.72579u − 1.70248
0.00503082u
23
+ 0.000302895u
22
+ ··· + 0.272744u + 0.00411174
a
1
=
0.00116113u
23
− 0.00701763u
22
+ ··· − 3.72064u − 0.461882
0.00950900u
23
− 0.00681322u
22
+ ··· − 0.0553531u − 0.242466
a
6
=
−0.0490673u
23
+ 0.0343037u
22
+ ··· − 0.624915u − 1.18574
−0.0489739u
23
+ 0.0292729u
22
+ ··· + 1.76740u − 1.46007
a
12
=
−0.0210466u
23
− 0.0368566u
22
+ ··· − 3.26892u − 0.0171514
0.0163096u
23
− 0.0531254u
22
+ ··· − 0.469008u + 1.01208
a
9
=
0.0467094u
23
− 0.0349497u
22
+ ··· − 2.97974u + 3.81507
0.0190281u
23
+ 0.00280066u
22
+ ··· − 1.24120u + 1.26645
a
5
=
−0.0201710u
23
+ 0.0209149u
22
+ ··· + 0.277876u + 1.39317
−0.0172295u
23
+ 0.0179602u
22
+ ··· + 1.65187u − 1.28904
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
512825581100401728988
1610055529353491698290907
u
23
+
269382744526795906872124
1610055529353491698290907
u
22
+
··· +
11701910792187320542488702
1610055529353491698290907
u −
14358907726484786548966942
1610055529353491698290907
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u
3
+ 2u − 1)
8
c
2
, c
3
, c
7
c
9
u
24
− 7u
22
+ ··· − 17u + 44
c
5
, c
8
u
24
− 2u
23
+ ··· − 3u + 2
c
6
, c
10
, c
11
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
3
+ 4y
2
+ 4y −1)
8
c
2
, c
3
, c
7
c
9
y
24
− 14y
23
+ ··· + 1383y + 1936
c
5
, c
8
y
24
− 2y
23
+ ··· + 363y + 4
c
6
, c
10
, c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
6
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.010910 + 0.464639I
a = −0.456815 + 0.921980I
b = 0.395123 + 0.506844I
4.71694 + 6.55305I −0.85533 − 8.11776I
u = −1.010910 − 0.464639I
a = −0.456815 − 0.921980I
b = 0.395123 − 0.506844I
4.71694 − 6.55305I −0.85533 + 8.11776I
u = 0.033411 + 1.144290I
a = −0.431476 + 0.870839I
b = 0.395123 − 0.506844I
4.71694 − 6.55305I −0.85533 + 8.11776I
u = 0.033411 − 1.144290I
a = −0.431476 − 0.870839I
b = 0.395123 + 0.506844I
4.71694 + 6.55305I −0.85533 − 8.11776I
u = 0.891188 + 0.733300I
a = −0.044870 − 0.389755I
b = 0.395123 + 0.506844I
4.71694 − 3.72284I −0.85533 − 1.69972I
u = 0.891188 − 0.733300I
a = −0.044870 + 0.389755I
b = 0.395123 − 0.506844I
4.71694 + 3.72284I −0.85533 + 1.69972I
u = −1.114270 + 0.395229I
a = 0.515228 − 0.399147I
b = 0.10488 − 1.55249I
−2.28481 + 1.97398I −4.50880 − 0.64422I
u = −1.114270 − 0.395229I
a = 0.515228 + 0.399147I
b = 0.10488 + 1.55249I
−2.28481 − 1.97398I −4.50880 + 0.64422I
u = −0.416348 + 0.648391I
a = 1.21293 + 0.93966I
b = 0.10488 − 1.55249I
−2.28481 + 1.97398I −4.50880 − 0.64422I
u = −0.416348 − 0.648391I
a = 1.21293 − 0.93966I
b = 0.10488 + 1.55249I
−2.28481 − 1.97398I −4.50880 + 0.64422I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.272640 + 0.033718I
a = −1.132040 − 0.253135I
b = 0.395123 − 0.506844I
−5.51100 − 1.41510I −12.80913 + 4.90874I
u = 1.272640 − 0.033718I
a = −1.132040 + 0.253135I
b = 0.395123 + 0.506844I
−5.51100 + 1.41510I −12.80913 − 4.90874I
u = 1.290960 + 0.234627I
a = −0.340402 − 1.248340I
b = 0.10488 − 1.55249I
−2.28481 − 8.30190I −4.50880 + 5.77382I
u = 1.290960 − 0.234627I
a = −0.340402 + 1.248340I
b = 0.10488 + 1.55249I
−2.28481 + 8.30190I −4.50880 − 5.77382I
u = −1.348220 + 0.322916I
a = −1.340340 + 0.224947I
b = 0.10488 + 1.55249I
−12.51270 + 3.16396I −16.4626 − 2.5648I
u = −1.348220 − 0.322916I
a = −1.340340 − 0.224947I
b = 0.10488 − 1.55249I
−12.51270 − 3.16396I −16.4626 + 2.5648I
u = −1.43214 + 0.36032I
a = −0.841292 − 0.188121I
b = 0.395123 + 0.506844I
−5.51100 + 1.41510I −12.80913 − 4.90874I
u = −1.43214 − 0.36032I
a = −0.841292 + 0.188121I
b = 0.395123 − 0.506844I
−5.51100 − 1.41510I −12.80913 + 4.90874I
u = 0.245820 + 0.380248I
a = −0.29151 − 2.53215I
b = 0.395123 − 0.506844I
4.71694 + 3.72284I −0.85533 + 1.69972I
u = 0.245820 − 0.380248I
a = −0.29151 + 2.53215I
b = 0.395123 + 0.506844I
4.71694 − 3.72284I −0.85533 − 1.69972I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14655 + 1.69142I
a = −0.203319 − 0.745623I
b = 0.10488 + 1.55249I
−2.28481 + 8.30190I −4.50880 − 5.77382I
u = −0.14655 − 1.69142I
a = −0.203319 + 0.745623I
b = 0.10488 − 1.55249I
−2.28481 − 8.30190I −4.50880 + 5.77382I
u = 1.73443 + 0.73609I
a = −0.725643 + 0.121784I
b = 0.10488 − 1.55249I
−12.51270 − 3.16396I −16.4626 + 2.5648I
u = 1.73443 − 0.73609I
a = −0.725643 − 0.121784I
b = 0.10488 + 1.55249I
−12.51270 + 3.16396I −16.4626 − 2.5648I
13
III.
I
u
3
= h−2706u
15
+ 399u
14
+ · · · + 2389b + 1730, a + 1, u
16
− 8u
14
+ · · · − u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
−1
1.13269u
15
− 0.167015u
14
+ ··· − 0.808288u − 0.724152
a
11
=
1.13269u
15
− 0.167015u
14
+ ··· − 0.808288u − 1.72415
1.13269u
15
− 0.167015u
14
+ ··· − 0.808288u − 0.724152
a
2
=
u
0.167015u
15
− 0.626622u
14
+ ··· + 0.591461u + 1.13269
a
1
=
0.463792u
15
− 0.356635u
14
+ ··· + 0.206362u + 0.626622
0.161574u
15
− 0.651319u
14
+ ··· + 0.564671u + 0.862704
a
6
=
−1.61741u
15
+ 0.120971u
14
+ ··· + 1.11427u + 0.136040
−0.484722u
15
− 0.0460444u
14
+ ··· + 0.305986u − 1.58811
a
12
=
1.87484u
15
− 0.568020u
14
+ ··· − 2.61616u + 1.79029
0.257430u
15
− 0.447049u
14
+ ··· − 1.50188u + 1.92633
a
9
=
u
2
− 1
0.506069u
15
+ 0.296777u
14
+ ··· + 0.491419u − 0.891168
a
5
=
−0.948514u
15
+ 0.310590u
14
+ ··· + 1.09962u − 1.21473
−0.513604u
15
+ 0.438259u
14
+ ··· + 1.93303u − 1.17497
(ii) Obstruction class = 1
(iii) Cusp Shapes =
9756
2389
u
15
−
3319
2389
u
14
+ ··· −
7285
2389
u −
36203
2389
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
16
− 2u
15
+ ··· + 7u
2
+ 1
c
2
, c
7
u
16
− 8u
14
+ ··· − u + 1
c
3
, c
9
u
16
− 8u
14
+ ··· + u + 1
c
4
u
16
+ 2u
15
+ ··· + 7u
2
+ 1
c
5
, c
8
u
16
+ u
14
+ ··· + 11u
2
+ 1
c
6
u
16
+ 9u
14
+ ··· + u
2
+ 1
c
10
, c
11
u
16
+ 9u
14
+ ··· + u
2
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
16
+ 16y
15
+ ··· + 14y + 1
c
2
, c
3
, c
7
c
9
y
16
− 16y
15
+ ··· − 9y + 1
c
5
, c
8
y
16
+ 2y
15
+ ··· + 22y + 1
c
6
, c
10
, c
11
y
16
+ 18y
15
+ ··· + 2y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.567370 + 0.557169I
a = −1.00000
b = −0.350298 − 0.269016I
4.56619 − 4.78505I −2.52350 + 6.12027I
u = 0.567370 − 0.557169I
a = −1.00000
b = −0.350298 + 0.269016I
4.56619 + 4.78505I −2.52350 − 6.12027I
u = −1.240320 + 0.109568I
a = −1.00000
b = 0.749404 + 0.967609I
−4.25143 + 0.43751I −7.44687 + 1.86427I
u = −1.240320 − 0.109568I
a = −1.00000
b = 0.749404 − 0.967609I
−4.25143 − 0.43751I −7.44687 − 1.86427I
u = −0.711481 + 0.187291I
a = −1.00000
b = −0.575792 + 1.022690I
−2.13756 + 0.75149I −18.1027 + 5.6218I
u = −0.711481 − 0.187291I
a = −1.00000
b = −0.575792 − 1.022690I
−2.13756 − 0.75149I −18.1027 − 5.6218I
u = −0.360345 + 0.597726I
a = −1.00000
b = −0.133891 − 1.312560I
0.93102 + 6.43898I −3.84687 − 6.35084I
u = −0.360345 − 0.597726I
a = −1.00000
b = −0.133891 + 1.312560I
0.93102 − 6.43898I −3.84687 + 6.35084I
u = 1.43665 + 0.28361I
a = −1.00000
b = 0.284706 − 0.275286I
−1.58557 − 2.35863I −5.77026 + 0.78709I
u = 1.43665 − 0.28361I
a = −1.00000
b = 0.284706 + 0.275286I
−1.58557 + 2.35863I −5.77026 − 0.78709I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455839 + 0.238502I
a = −1.00000
b = −0.177159 + 1.256650I
−4.35783 − 3.47301I −11.51010 + 5.67528I
u = 0.455839 − 0.238502I
a = −1.00000
b = −0.177159 − 1.256650I
−4.35783 + 3.47301I −11.51010 − 5.67528I
u = 1.45191 + 0.49519I
a = −1.00000
b = 0.11799 − 1.56046I
−11.63570 − 3.03892I −5.31317 + 0.93772I
u = 1.45191 − 0.49519I
a = −1.00000
b = 0.11799 + 1.56046I
−11.63570 + 3.03892I −5.31317 − 0.93772I
u = −1.59962 + 0.58103I
a = −1.00000
b = 0.08504 + 1.51659I
−7.84805 + 3.64236I −4.98656 − 1.05999I
u = −1.59962 − 0.58103I
a = −1.00000
b = 0.08504 − 1.51659I
−7.84805 − 3.64236I −4.98656 + 1.05999I
18
IV. I
u
4
= h2.71 × 10
33
u
31
− 1.79 × 10
33
u
30
+ · · · + 1.74 × 10
36
b + 3.11 ×
10
35
, −1.47 × 10
42
u
31
− 3.56 × 10
42
u
30
+ · · · + 1.03 × 10
44
a − 1.96 ×
10
44
, u
32
+ u
31
+ · · · + 556u + 109i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
10
=
0.0142434u
31
+ 0.0345611u
30
+ ··· − 3.14382u + 1.90740
−0.00156258u
31
+ 0.00103422u
30
+ ··· − 2.55221u − 0.179177
a
11
=
0.0126809u
31
+ 0.0355953u
30
+ ··· − 5.69604u + 1.72823
−0.00156258u
31
+ 0.00103422u
30
+ ··· − 2.55221u − 0.179177
a
2
=
−0.0288608u
31
− 0.0239141u
30
+ ··· + 6.84731u − 1.96427
0.0443958u
31
+ 0.0998783u
30
+ ··· − 20.0671u − 3.81402
a
1
=
−0.00956947u
31
+ 0.0263152u
30
+ ··· − 8.14313u − 4.57850
0.0471154u
31
+ 0.107494u
30
+ ··· − 24.3809u − 4.57202
a
6
=
0.0592026u
31
+ 0.131424u
30
+ ··· − 43.2460u − 4.52615
0.0242115u
31
+ 0.0520369u
30
+ ··· − 21.9865u − 3.91407
a
12
=
−0.0243945u
31
+ 0.0127569u
30
+ ··· − 9.24622u + 1.14300
0.00302978u
31
+ 0.0360437u
30
+ ··· − 20.7583u − 3.80929
a
9
=
0.0368542u
31
+ 0.0548895u
30
+ ··· + 24.5846u + 4.62265
0.0980429u
31
+ 0.175742u
30
+ ··· − 37.0173u − 5.77455
a
5
=
−0.0574811u
31
− 0.141022u
30
+ ··· + 37.3394u + 8.60492
−0.0219826u
31
− 0.0224361u
30
+ ··· + 13.9060u + 1.79852
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00776588u
31
− 0.0131084u
30
+ ··· − 13.8916u − 5.66401
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
8
c
2
, c
3
, c
7
c
9
u
32
+ u
31
+ ··· + 556u + 109
c
5
, c
8
u
32
− 5u
31
+ ··· − 6u + 1
c
6
, c
10
, c
11
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
8
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
4
+ 3y
3
+ 2y
2
+ 1)
8
c
2
, c
3
, c
7
c
9
y
32
− 35y
31
+ ··· + 34650y + 11881
c
5
, c
8
y
32
+ 9y
31
+ ··· + 114y + 1
c
6
, c
10
, c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
8
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.005860 + 0.246476I
a = −0.283234 − 0.719828I
b = 0.395123 − 0.506844I
−1.43393 − 3.44499I −4.17326 + 8.37284I
u = 1.005860 − 0.246476I
a = −0.283234 + 0.719828I
b = 0.395123 + 0.506844I
−1.43393 + 3.44499I −4.17326 − 8.37284I
u = −0.082071 + 0.902659I
a = −0.02831 − 1.52235I
b = 0.10488 + 1.55249I
−8.43568 + 1.13408I −7.82674 + 0.89930I
u = −0.082071 − 0.902659I
a = −0.02831 + 1.52235I
b = 0.10488 − 1.55249I
−8.43568 − 1.13408I −7.82674 − 0.89930I
u = −1.091330 + 0.132649I
a = −1.45196 − 0.32329I
b = 0.395123 − 0.506844I
−1.43393 + 0.61478I −4.17326 + 1.44464I
u = −1.091330 − 0.132649I
a = −1.45196 + 0.32329I
b = 0.395123 + 0.506844I
−1.43393 − 0.61478I −4.17326 − 1.44464I
u = 1.089690 + 0.255963I
a = −1.84888 + 0.02386I
b = 0.10488 − 1.55249I
−8.43568 − 1.13408I −7.82674 − 0.89930I
u = 1.089690 − 0.255963I
a = −1.84888 − 0.02386I
b = 0.10488 + 1.55249I
−8.43568 + 1.13408I −7.82674 + 0.89930I
u = −0.838428 + 0.177804I
a = 0.213205 − 0.186384I
b = 0.395123 − 0.506844I
−1.43393 + 0.61478I −4.17326 + 1.44464I
u = −0.838428 − 0.177804I
a = 0.213205 + 0.186384I
b = 0.395123 + 0.506844I
−1.43393 − 0.61478I −4.17326 − 1.44464I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.107472 + 0.793853I
a = −0.473340 − 1.202980I
b = 0.395123 + 0.506844I
−1.43393 + 3.44499I −4.17326 − 8.37284I
u = −0.107472 − 0.793853I
a = −0.473340 + 1.202980I
b = 0.395123 − 0.506844I
−1.43393 − 3.44499I −4.17326 + 8.37284I
u = −1.360610 + 0.125651I
a = −0.290211 + 0.965098I
b = 0.10488 + 1.55249I
−8.43568 + 5.19385I −7.82674 − 6.02890I
u = −1.360610 − 0.125651I
a = −0.290211 − 0.965098I
b = 0.10488 − 1.55249I
−8.43568 − 5.19385I −7.82674 + 6.02890I
u = 0.273598 + 1.349590I
a = −0.285743 + 0.950240I
b = 0.10488 − 1.55249I
−8.43568 − 5.19385I −7.82674 + 6.02890I
u = 0.273598 − 1.349590I
a = −0.285743 − 0.950240I
b = 0.10488 + 1.55249I
−8.43568 + 5.19385I −7.82674 − 6.02890I
u = 1.376490 + 0.099387I
a = −0.012211 + 0.656651I
b = 0.10488 + 1.55249I
−8.43568 + 1.13408I −7.82674 + 0.89930I
u = 1.376490 − 0.099387I
a = −0.012211 − 0.656651I
b = 0.10488 − 1.55249I
−8.43568 − 1.13408I −7.82674 − 0.89930I
u = −1.409760 + 0.075274I
a = −0.952995 + 0.430152I
b = 0.395123 + 0.506844I
−1.43393 + 3.44499I −4.17326 − 8.37284I
u = −1.409760 − 0.075274I
a = −0.952995 − 0.430152I
b = 0.395123 − 0.506844I
−1.43393 − 3.44499I −4.17326 + 8.37284I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.31112 + 0.67815I
a = −0.871724 + 0.393469I
b = 0.395123 − 0.506844I
−1.43393 − 3.44499I −4.17326 + 8.37284I
u = 1.31112 − 0.67815I
a = −0.871724 − 0.393469I
b = 0.395123 + 0.506844I
−1.43393 + 3.44499I −4.17326 − 8.37284I
u = 1.47337 + 0.23175I
a = −1.182970 − 0.610498I
b = 0.10488 − 1.55249I
−8.43568 − 5.19385I −7.82674 + 6.02890I
u = 1.47337 − 0.23175I
a = −1.182970 + 0.610498I
b = 0.10488 + 1.55249I
−8.43568 + 5.19385I −7.82674 − 6.02890I
u = 1.62744 + 0.16021I
a = −0.656194 + 0.146107I
b = 0.395123 − 0.506844I
−1.43393 + 0.61478I −4.17326 + 1.44464I
u = 1.62744 − 0.16021I
a = −0.656194 − 0.146107I
b = 0.395123 + 0.506844I
−1.43393 − 0.61478I −4.17326 − 1.44464I
u = −0.145617 + 0.194178I
a = 2.65857 + 2.32413I
b = 0.395123 − 0.506844I
−1.43393 + 0.61478I −4.17326 + 1.44464I
u = −0.145617 − 0.194178I
a = 2.65857 − 2.32413I
b = 0.395123 + 0.506844I
−1.43393 − 0.61478I −4.17326 − 1.44464I
u = −1.60147 + 1.17365I
a = −0.667544 − 0.344501I
b = 0.10488 + 1.55249I
−8.43568 + 5.19385I 0
u = −1.60147 − 1.17365I
a = −0.667544 + 0.344501I
b = 0.10488 − 1.55249I
−8.43568 − 5.19385I 0
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −2.02081 + 0.44725I
a = −0.540778 + 0.006978I
b = 0.10488 + 1.55249I
−8.43568 + 1.13408I 0
u = −2.02081 − 0.44725I
a = −0.540778 − 0.006978I
b = 0.10488 − 1.55249I
−8.43568 − 1.13408I 0
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
((u
3
+ 2u − 1)
8
)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
8
(u
16
− 2u
15
+ ··· + 7u
2
+ 1)
· (u
27
− 13u
26
+ ··· + 240u − 16)
c
2
, c
7
(u
16
− 8u
14
+ ··· − u + 1)(u
24
− 7u
22
+ ··· − 17u + 44)
· (u
27
− 2u
26
+ ··· − u + 1)(u
32
+ u
31
+ ··· + 556u + 109)
c
3
, c
9
(u
16
− 8u
14
+ ··· + u + 1)(u
24
− 7u
22
+ ··· − 17u + 44)
· (u
27
− 2u
26
+ ··· − u + 1)(u
32
+ u
31
+ ··· + 556u + 109)
c
4
((u
3
+ 2u − 1)
8
)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
8
(u
16
+ 2u
15
+ ··· + 7u
2
+ 1)
· (u
27
− 13u
26
+ ··· + 240u − 16)
c
5
, c
8
(u
16
+ u
14
+ ··· + 11u
2
+ 1)(u
24
− 2u
23
+ ··· − 3u + 2)
· (u
27
− u
25
+ ··· − 4u − 1)(u
32
− 5u
31
+ ··· − 6u + 1)
c
6
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
14
)(u
16
+ 9u
14
+ ··· + u
2
+ 1)
· (u
27
− 15u
26
+ ··· + 1792u − 128)
c
10
, c
11
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
14
)(u
16
+ 9u
14
+ ··· + u
2
+ 1)
· (u
27
− 15u
26
+ ··· + 1792u − 128)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
3
+ 4y
2
+ 4y −1)
8
(y
4
+ 3y
3
+ 2y
2
+ 1)
8
· (y
16
+ 16y
15
+ ··· + 14y + 1)(y
27
+ 23y
26
+ ··· + 384y −256)
c
2
, c
3
, c
7
c
9
(y
16
− 16y
15
+ ··· − 9y + 1)(y
24
− 14y
23
+ ··· + 1383y + 1936)
· (y
27
− 24y
26
+ ··· − 13y −1)(y
32
− 35y
31
+ ··· + 34650y + 11881)
c
5
, c
8
(y
16
+ 2y
15
+ ··· + 22y + 1)(y
24
− 2y
23
+ ··· + 363y + 4)
· (y
27
− 2y
26
+ ··· + 32y −1)(y
32
+ 9y
31
+ ··· + 114y + 1)
c
6
, c
10
, c
11
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
14
)(y
16
+ 18y
15
+ ··· + 2y + 1)
· (y
27
+ 23y
26
+ ··· + 49152y −16384)
27
