12a
0036
(K12a
0036
)
A knot diagram
1
Linearized knot diagam
3 5 6 10 2 12 1 11 4 8 9 7
Solving Sequence
4,9
10
5,7,12
1 6 3 2 11 8
c
9
c
4
c
12
c
6
c
3
c
2
c
11
c
8
c
1
, c
5
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.71327 × 10
48
u
35
+ 4.04621 × 10
50
u
34
+ ··· + 1.08619 × 10
53
d − 2.28969 × 10
52
,
5.92442 × 10
49
u
35
− 1.37260 × 10
51
u
34
+ ··· + 2.17237 × 10
53
c − 1.61328 × 10
53
,
1.56429 × 10
50
u
35
− 1.90035 × 10
51
u
34
+ ··· + 1.08619 × 10
53
b + 1.05897 × 10
53
,
− 1.77635 × 10
50
u
35
+ 8.48997 × 10
50
u
34
+ ··· + 1.08619 × 10
53
a − 1.56178 × 10
53
,
u
36
− 3u
35
+ ··· − 64u + 32i
I
u
2
= h1.13466 × 10
15
au
27
− 3.06796 × 10
15
u
27
+ ··· + 2.79964 × 10
15
a − 1.43321 × 10
16
,
− 6.13592 × 10
15
au
27
− 7.57070 × 10
15
u
27
+ ··· − 2.86643 × 10
16
a − 2.56902 × 10
16
, b + 1,
2.13254 × 10
15
au
27
+ 1.47729 × 10
16
u
27
+ ··· + 2.93914 × 10
16
a + 7.21477 × 10
16
, u
28
+ u
27
+ ··· + 8u + 4i
I
v
1
= ha, d, c − 1, b + 1, v
2
+ v + 1i
I
v
2
= ha, d − 1, c + a, b + 1, v
2
+ v + 1i
I
v
3
= ha, d − 1, c + a + 1, b + 1, v + 1i
I
v
4
= hc, d − 1, cb − a − 1, v
2
ba + v
2
c + v
2
b + 2v
2
a + cv + av + 2v
2
+ c + v, b
2
v
2
+ 2v
2
b + bv + v
2
+ v + 1i
* 5 irreducible components of dim
C
= 0, with total 97 representations.
* 1 irreducible components of dim
C
= 1
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−3.71 × 10
48
u
35
+ 4.05 × 10
50
u
34
+ · · · + 1.09 × 10
53
d − 2.29 ×
10
52
, 5.92 × 10
49
u
35
− 1.37 × 10
51
u
34
+ · · · + 2.17 × 10
53
c − 1.61 × 10
53
, 1.56 ×
10
50
u
35
− 1.90 × 10
51
u
34
+ · · · + 1.09 × 10
53
b + 1.06 × 10
53
, −1.78 × 10
50
u
35
+
8.49 × 10
50
u
34
+ · · · + 1.09 × 10
53
a − 1.56 × 10
53
, u
36
− 3u
35
+ · · · − 64u + 32i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
7
=
0.00163541u
35
− 0.00781632u
34
+ ··· − 1.02250u + 1.43786
−0.00144017u
35
+ 0.0174956u
34
+ ··· + 2.23968u − 0.974944
a
12
=
−0.000272717u
35
+ 0.00631846u
34
+ ··· + 0.563935u + 0.742637
0.0000341864u
35
− 0.00372516u
34
+ ··· − 0.444645u + 0.210801
a
1
=
−0.0000432971u
35
+ 0.0122726u
34
+ ··· + 1.33646u + 0.416353
0.00188305u
35
− 0.0189570u
34
+ ··· − 2.03361u + 0.857265
a
6
=
0.000904113u
35
− 0.00884304u
34
+ ··· − 1.47566u + 1.66218
−0.000947410u
35
+ 0.0211156u
34
+ ··· + 2.81213u − 1.24583
a
3
=
0.00194611u
35
− 0.00144413u
34
+ ··· + 2.53686u − 0.189589
0.0137165u
35
− 0.0449480u
34
+ ··· − 0.634013u + 0.309094
a
2
=
0.00349030u
35
− 0.000257565u
34
+ ··· + 3.44348u − 0.336815
0.0131839u
35
− 0.0436398u
34
+ ··· − 1.21762u + 0.270108
a
11
=
−0.000238531u
35
+ 0.00259330u
34
+ ··· + 0.119290u + 0.953438
0.0000341864u
35
− 0.00372516u
34
+ ··· − 0.444645u + 0.210801
a
8
=
−0.000238531u
35
+ 0.00259330u
34
+ ··· + 0.119290u + 0.953438
0.000492763u
35
+ 0.00362002u
34
+ ··· + 0.572452u − 0.270888
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0805025u
35
− 0.242112u
34
+ ··· + 5.72407u − 9.52193
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
36
+ 17u
35
+ ··· − 120u + 16
c
2
, c
5
u
36
+ u
35
+ ··· + 16u + 4
c
3
u
36
− u
35
+ ··· − 104u + 1252
c
4
, c
9
u
36
+ 3u
35
+ ··· + 64u + 32
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
36
− 5u
35
+ ··· + 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
+ 5y
35
+ ··· − 27936y + 256
c
2
, c
5
y
36
+ 17y
35
+ ··· − 120y + 16
c
3
y
36
− 7y
35
+ ··· − 22103608y + 1567504
c
4
, c
9
y
36
− 15y
35
+ ··· − 1024y + 1024
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
36
− 41y
35
+ ··· − 21y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.956534 + 0.246505I
a = −0.0142428 + 0.0350628I
b = 0.595799 − 0.651291I
c = 0.141093 − 0.856670I
d = 0.446161 + 0.609262I
−2.56616 − 0.65266I −13.12638 + 3.31133I
u = 0.956534 − 0.246505I
a = −0.0142428 − 0.0350628I
b = 0.595799 + 0.651291I
c = 0.141093 + 0.856670I
d = 0.446161 − 0.609262I
−2.56616 + 0.65266I −13.12638 − 3.31133I
u = −0.935949 + 0.527292I
a = −0.118634 + 0.273971I
b = 0.711040 + 0.301202I
c = 0.364553 + 1.079240I
d = 0.236726 − 0.726179I
1.36964 + 3.10356I −5.16268 − 4.71165I
u = −0.935949 − 0.527292I
a = −0.118634 − 0.273971I
b = 0.711040 − 0.301202I
c = 0.364553 − 1.079240I
d = 0.236726 + 0.726179I
1.36964 − 3.10356I −5.16268 + 4.71165I
u = −0.651308 + 0.620650I
a = 0.088381 + 0.613358I
b = 0.525117 + 0.024485I
c = 0.711979 + 1.024680I
d = 0.018859 − 0.596676I
2.25394 + 1.43184I −2.05632 − 3.52848I
u = −0.651308 − 0.620650I
a = 0.088381 − 0.613358I
b = 0.525117 − 0.024485I
c = 0.711979 − 1.024680I
d = 0.018859 + 0.596676I
2.25394 − 1.43184I −2.05632 + 3.52848I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.134519 + 0.831817I
a = −2.49461 + 0.46036I
b = 5.38486 − 0.94232I
c = −0.800905 − 0.073407I
d = 1.245840 + 0.061269I
−4.07214 − 2.53804I −12.12047 + 3.16226I
u = −0.134519 − 0.831817I
a = −2.49461 − 0.46036I
b = 5.38486 + 0.94232I
c = −0.800905 + 0.073407I
d = 1.245840 − 0.061269I
−4.07214 + 2.53804I −12.12047 − 3.16226I
u = 0.488093 + 0.675929I
a = 0.219986 − 0.913847I
b = 0.439268 + 0.155961I
c = 0.951048 − 1.034360I
d = −0.119169 + 0.531960I
0.92725 + 3.15352I −4.07893 − 3.45921I
u = 0.488093 − 0.675929I
a = 0.219986 + 0.913847I
b = 0.439268 − 0.155961I
c = 0.951048 + 1.034360I
d = −0.119169 − 0.531960I
0.92725 − 3.15352I −4.07893 + 3.45921I
u = 1.066500 + 0.529753I
a = −0.230642 − 0.205554I
b = 0.835462 − 0.357382I
c = 0.257325 − 1.157650I
d = 0.296959 + 0.811036I
−0.85359 − 7.85577I −9.34096 + 8.43490I
u = 1.066500 − 0.529753I
a = −0.230642 + 0.205554I
b = 0.835462 + 0.357382I
c = 0.257325 + 1.157650I
d = 0.296959 − 0.811036I
−0.85359 + 7.85577I −9.34096 − 8.43490I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.471804 + 1.201650I
a = −1.55056 + 0.44817I
b = 3.43387 − 0.95934I
c = −1.009840 − 0.265513I
d = 1.41953 + 0.22707I
−6.92260 − 4.39379I −12.55418 + 2.40542I
u = −0.471804 − 1.201650I
a = −1.55056 − 0.44817I
b = 3.43387 + 0.95934I
c = −1.009840 + 0.265513I
d = 1.41953 − 0.22707I
−6.92260 + 4.39379I −12.55418 − 2.40542I
u = 1.232210 + 0.408112I
a = 1.16290 − 2.88555I
b = 3.50484 − 0.82980I
c = −0.478569 + 1.058540I
d = −1.43441 − 0.19589I
−8.11992 − 1.67660I −15.7568 + 0.9806I
u = 1.232210 − 0.408112I
a = 1.16290 + 2.88555I
b = 3.50484 + 0.82980I
c = −0.478569 − 1.058540I
d = −1.43441 + 0.19589I
−8.11992 + 1.67660I −15.7568 − 0.9806I
u = −1.223950 + 0.516090I
a = 0.35261 + 3.02077I
b = 3.33397 + 0.96426I
c = −0.310513 − 1.254720I
d = −1.43061 + 0.24878I
−7.33125 + 7.52384I −14.0983 − 6.1679I
u = −1.223950 − 0.516090I
a = 0.35261 − 3.02077I
b = 3.33397 − 0.96426I
c = −0.310513 + 1.254720I
d = −1.43061 − 0.24878I
−7.33125 − 7.52384I −14.0983 + 6.1679I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.666134 + 0.068993I
a = 0.780189 + 0.682100I
b = −0.90161 − 1.52116I
c = −0.128853 − 0.268419I
d = 0.706776 + 0.200522I
−2.77509 − 2.72721I −16.6085 + 5.9652I
u = −0.666134 − 0.068993I
a = 0.780189 − 0.682100I
b = −0.90161 + 1.52116I
c = −0.128853 + 0.268419I
d = 0.706776 − 0.200522I
−2.77509 + 2.72721I −16.6085 − 5.9652I
u = 0.318666 + 1.335800I
a = −1.57860 − 0.26349I
b = 3.47760 + 0.56643I
c = −1.083360 + 0.176981I
d = 1.48437 − 0.15238I
−11.42670 + 0.95860I −17.6650 + 0.2050I
u = 0.318666 − 1.335800I
a = −1.57860 + 0.26349I
b = 3.47760 − 0.56643I
c = −1.083360 − 0.176981I
d = 1.48437 + 0.15238I
−11.42670 − 0.95860I −17.6650 − 0.2050I
u = 0.568640 + 1.285090I
a = −1.44127 − 0.41824I
b = 3.20069 + 0.90828I
c = −1.059710 + 0.318993I
d = 1.46105 − 0.27427I
−9.63713 + 9.42250I −15.4804 − 5.9490I
u = 0.568640 − 1.285090I
a = −1.44127 + 0.41824I
b = 3.20069 − 0.90828I
c = −1.059710 − 0.318993I
d = 1.46105 + 0.27427I
−9.63713 − 9.42250I −15.4804 + 5.9490I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.579877
a = 0.700882
b = −0.382079
c = 0.313536
d = 0.400496
−0.811618 −12.0290
u = −1.27702 + 0.74720I
a = −0.79571 + 2.33781I
b = 2.94232 + 0.99996I
c = 0.11920 − 1.42161I
d = −1.45945 + 0.36293I
−9.5381 + 11.3478I −13.0594 − 5.6672I
u = −1.27702 − 0.74720I
a = −0.79571 − 2.33781I
b = 2.94232 − 0.99996I
c = 0.11920 + 1.42161I
d = −1.45945 − 0.36293I
−9.5381 − 11.3478I −13.0594 + 5.6672I
u = 1.51924
a = 1.38331
b = 3.36154
c = −0.179172
d = −1.57128
−14.8609 −15.8600
u = 1.29117 + 0.81558I
a = −0.98989 − 2.12524I
b = 2.84808 − 0.99055I
c = 0.22492 + 1.45088I
d = −1.46798 − 0.39682I
−12.0349 − 16.8809I −15.3736 + 9.2575I
u = 1.29117 − 0.81558I
a = −0.98989 + 2.12524I
b = 2.84808 + 0.99055I
c = 0.22492 − 1.45088I
d = −1.46798 + 0.39682I
−12.0349 + 16.8809I −15.3736 − 9.2575I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.111921 + 0.451208I
a = 1.46514 − 0.45120I
b = −0.0451061 + 0.0894307I
c = 1.40357 − 0.27941I
d = −0.190856 + 0.111820I
−0.30692 − 1.79670I −2.13838 + 3.34715I
u = 0.111921 − 0.451208I
a = 1.46514 + 0.45120I
b = −0.0451061 − 0.0894307I
c = 1.40357 + 0.27941I
d = −0.190856 − 0.111820I
−0.30692 + 1.79670I −2.13838 − 3.34715I
u = 1.38860 + 0.67758I
a = −0.35175 − 2.03094I
b = 2.99578 − 0.83109I
c = 0.126360 + 1.208340I
d = −1.51341 − 0.32643I
−15.0030 − 8.0885I −18.3300 + 3.8436I
u = 1.38860 − 0.67758I
a = −0.35175 + 2.03094I
b = 2.99578 + 0.83109I
c = 0.126360 − 1.208340I
d = −1.51341 + 0.32643I
−15.0030 + 8.0885I −18.3300 − 3.8436I
u = −1.61122 + 0.12770I
a = 0.954593 + 0.434273I
b = 3.22829 + 0.14916I
c = 0.004513 − 0.218310I
d = −1.61501 + 0.06033I
−18.8051 + 4.7571I −19.1049 − 3.2273I
u = −1.61122 − 0.12770I
a = 0.954593 − 0.434273I
b = 3.22829 − 0.14916I
c = 0.004513 + 0.218310I
d = −1.61501 − 0.06033I
−18.8051 − 4.7571I −19.1049 + 3.2273I
10
II.
I
u
2
= h1.13×10
15
au
27
−3.07×10
15
u
27
+· · ·+2.80×10
15
a−1.43×10
16
, −6.14×
10
15
au
27
− 7.57 × 10
15
u
27
+ · · · − 2.87 × 10
16
a − 2.57 × 10
16
, b + 1, 2.13 ×
10
15
au
27
+1.48×10
16
u
27
+· · ·+2.94×10
16
a+7.21×10
16
, u
28
+u
27
+· · ·+8u+4i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
7
=
a
−1
a
12
=
2.97137au
27
+ 3.66617u
27
+ ··· + 13.8809a + 12.4407
−1.09893au
27
+ 2.97137u
27
+ ··· − 2.71150a + 13.8809
a
1
=
−1.87244u
27
− 0.749749u
26
+ ··· − 7.03105u − 11.1694
1.09893u
27
− 0.185171u
26
+ ··· + 5.48839u + 2.71150
a
6
=
−0.333289u
27
− 0.505230u
26
+ ··· − 0.0509032u − 3.96717
−1.53915u
27
− 0.244519u
26
+ ··· − 6.98014u − 7.20224
a
3
=
−3.54326u
27
− 0.280326u
26
+ ··· − 16.6119u − 14.7552
0.187465u
27
− 0.126714u
26
+ ··· + 1.72320u + 0.0904714
a
2
=
−2.49289u
27
− 0.296873u
26
+ ··· − 11.3968u − 10.5619
0.0560178u
27
− 0.0365360u
26
+ ··· + 0.841877u + 0.164880
a
11
=
1.87244au
27
+ 6.63754u
27
+ ··· + 11.1694a + 26.3216
−1.09893au
27
+ 2.97137u
27
+ ··· − 2.71150a + 13.8809
a
8
=
1.87244au
27
+ 6.63754u
27
+ ··· + 11.1694a + 26.3216
1.53915au
27
+ 1.87244u
27
+ ··· + 7.20224a + 9.16941
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
37274533074785
129063433504426
u
27
+
53621307092165
129063433504426
u
26
+ ··· +
660629047616669
129063433504426
u −
645502044434670
64531716752213
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
28
+ 14u
27
+ ··· + 2u + 1)
2
c
2
, c
5
(u
28
+ 2u
27
+ ··· + 2u + 1)
2
c
3
(u
28
− 2u
27
+ ··· − 22u + 17)
2
c
4
, c
9
(u
28
− u
27
+ ··· − 8u + 4)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
56
− 3u
55
+ ··· + 72u + 16
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 2y
27
+ ··· + 14y + 1)
2
c
2
, c
5
(y
28
+ 14y
27
+ ··· + 2y + 1)
2
c
3
(y
28
− 10y
27
+ ··· − 246y + 289)
2
c
4
, c
9
(y
28
− 15y
27
+ ··· − 88y + 16)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
56
− 43y
55
+ ··· + 736y + 256
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.910131 + 0.395689I
a = −1.02788 + 1.10315I
b = −1.00000
c = −1.20522 + 1.86019I
d = −1.276980 − 0.186733I
−1.72215 − 4.24816I −10.11355 + 6.97904I
u = 0.910131 + 0.395689I
a = −0.01361 + 2.44534I
b = −1.00000
c = 0.300677 − 0.944242I
d = 0.313357 + 0.643423I
−1.72215 − 4.24816I −10.11355 + 6.97904I
u = 0.910131 − 0.395689I
a = −1.02788 − 1.10315I
b = −1.00000
c = −1.20522 − 1.86019I
d = −1.276980 + 0.186733I
−1.72215 + 4.24816I −10.11355 − 6.97904I
u = 0.910131 − 0.395689I
a = −0.01361 − 2.44534I
b = −1.00000
c = 0.300677 + 0.944242I
d = 0.313357 − 0.643423I
−1.72215 + 4.24816I −10.11355 − 6.97904I
u = −0.017123 + 0.961380I
a = 0.177063 − 0.402321I
b = −1.00000
c = −0.873117 − 0.009489I
d = 1.306640 + 0.007988I
−4.61196 + 1.34593I −13.91932 − 0.66126I
u = −0.017123 + 0.961380I
a = 1.58097 + 1.51341I
b = −1.00000
c = 1.50836 + 1.81823I
d = −0.638546 − 0.533764I
−4.61196 + 1.34593I −13.91932 − 0.66126I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.017123 − 0.961380I
a = 0.177063 + 0.402321I
b = −1.00000
c = −0.873117 + 0.009489I
d = 1.306640 − 0.007988I
−4.61196 − 1.34593I −13.91932 + 0.66126I
u = −0.017123 − 0.961380I
a = 1.58097 − 1.51341I
b = −1.00000
c = 1.50836 − 1.81823I
d = −0.638546 + 0.533764I
−4.61196 − 1.34593I −13.91932 + 0.66126I
u = −0.907099 + 0.252760I
a = 0.971495 + 0.463170I
b = −1.00000
c = 0.186210 + 0.817511I
d = 0.419544 − 0.572998I
−2.63794 + 3.28147I −13.2327 − 4.9939I
u = −0.907099 + 0.252760I
a = 0.704043 − 0.365524I
b = −1.00000
c = −0.351737 − 0.579401I
d = 0.859190 + 0.455166I
−2.63794 + 3.28147I −13.2327 − 4.9939I
u = −0.907099 − 0.252760I
a = 0.971495 − 0.463170I
b = −1.00000
c = 0.186210 − 0.817511I
d = 0.419544 + 0.572998I
−2.63794 − 3.28147I −13.2327 + 4.9939I
u = −0.907099 − 0.252760I
a = 0.704043 + 0.365524I
b = −1.00000
c = −0.351737 + 0.579401I
d = 0.859190 − 0.455166I
−2.63794 − 3.28147I −13.2327 + 4.9939I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387411 + 0.832689I
a = 0.365520 + 0.349527I
b = −1.00000
c = −0.795695 + 0.216194I
d = 1.239370 − 0.180444I
−1.43770 + 1.40144I −7.30053 − 1.74630I
u = 0.387411 + 0.832689I
a = 1.42688 − 0.89203I
b = −1.00000
c = 1.11790 − 1.26235I
d = −0.279611 + 0.583432I
−1.43770 + 1.40144I −7.30053 − 1.74630I
u = 0.387411 − 0.832689I
a = 0.365520 − 0.349527I
b = −1.00000
c = −0.795695 − 0.216194I
d = 1.239370 + 0.180444I
−1.43770 − 1.40144I −7.30053 + 1.74630I
u = 0.387411 − 0.832689I
a = 1.42688 + 0.89203I
b = −1.00000
c = 1.11790 + 1.26235I
d = −0.279611 − 0.583432I
−1.43770 − 1.40144I −7.30053 + 1.74630I
u = −0.387502 + 1.047530I
a = 0.340954 − 0.431763I
b = −1.00000
c = −0.920428 − 0.218491I
d = 1.344350 + 0.185032I
−3.70255 − 5.75423I −11.89302 + 5.96655I
u = −0.387502 + 1.047530I
a = 1.27979 + 1.06278I
b = −1.00000
c = 1.05142 + 1.53293I
d = −0.382179 − 0.735842I
−3.70255 − 5.75423I −11.89302 + 5.96655I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.387502 − 1.047530I
a = 0.340954 + 0.431763I
b = −1.00000
c = −0.920428 + 0.218491I
d = 1.344350 − 0.185032I
−3.70255 + 5.75423I −11.89302 − 5.96655I
u = −0.387502 − 1.047530I
a = 1.27979 − 1.06278I
b = −1.00000
c = 1.05142 − 1.53293I
d = −0.382179 + 0.735842I
−3.70255 + 5.75423I −11.89302 − 5.96655I
u = −0.802767 + 0.244916I
a = −2.05210 − 1.27314I
b = −1.00000
c = −2.29143 − 1.82037I
d = −1.229860 + 0.111546I
−2.32218 − 0.90628I −12.59768 − 1.67094I
u = −0.802767 + 0.244916I
a = −0.72932 − 2.54382I
b = −1.00000
c = 0.273098 + 0.711267I
d = 0.374376 − 0.483492I
−2.32218 − 0.90628I −12.59768 − 1.67094I
u = −0.802767 − 0.244916I
a = −2.05210 + 1.27314I
b = −1.00000
c = −2.29143 + 1.82037I
d = −1.229860 − 0.111546I
−2.32218 + 0.90628I −12.59768 + 1.67094I
u = −0.802767 − 0.244916I
a = −0.72932 + 2.54382I
b = −1.00000
c = 0.273098 − 0.711267I
d = 0.374376 + 0.483492I
−2.32218 + 0.90628I −12.59768 + 1.67094I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.147340 + 0.340892I
a = −0.224291 + 1.144170I
b = −1.00000
c = −0.471254 − 0.771751I
d = 0.938913 + 0.621780I
−5.81300 + 1.47542I −13.29345 − 0.59666I
u = −1.147340 + 0.340892I
a = −1.07497 − 1.33487I
b = −1.00000
c = −0.776477 − 1.062760I
d = −1.393270 + 0.163069I
−5.81300 + 1.47542I −13.29345 − 0.59666I
u = −1.147340 − 0.340892I
a = −0.224291 − 1.144170I
b = −1.00000
c = −0.471254 + 0.771751I
d = 0.938913 − 0.621780I
−5.81300 − 1.47542I −13.29345 + 0.59666I
u = −1.147340 − 0.340892I
a = −1.07497 + 1.33487I
b = −1.00000
c = −0.776477 + 1.062760I
d = −1.393270 − 0.163069I
−5.81300 − 1.47542I −13.29345 + 0.59666I
u = 0.611767 + 0.458091I
a = 1.235620 − 0.499323I
b = −1.00000
c = 0.669435 − 0.799308I
d = 0.099411 + 0.470368I
−0.887541 + 0.644142I −7.64602 + 1.30683I
u = 0.611767 + 0.458091I
a = 0.552061 + 0.278825I
b = −1.00000
c = −0.542285 + 0.331792I
d = 1.027130 − 0.267751I
−0.887541 + 0.644142I −7.64602 + 1.30683I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.611767 − 0.458091I
a = 1.235620 + 0.499323I
b = −1.00000
c = 0.669435 + 0.799308I
d = 0.099411 − 0.470368I
−0.887541 − 0.644142I −7.64602 − 1.30683I
u = 0.611767 − 0.458091I
a = 0.552061 − 0.278825I
b = −1.00000
c = −0.542285 − 0.331792I
d = 1.027130 + 0.267751I
−0.887541 − 0.644142I −7.64602 − 1.30683I
u = 1.175470 + 0.589984I
a = −0.299231 + 0.442331I
b = −1.00000
c = −0.23958 + 1.44120I
d = −1.40691 − 0.28559I
−3.88965 − 6.77427I −10.22594 + 4.95962I
u = 1.175470 + 0.589984I
a = 0.42258 + 1.93124I
b = −1.00000
c = 0.209555 − 1.262070I
d = 0.307742 + 0.904345I
−3.88965 − 6.77427I −10.22594 + 4.95962I
u = 1.175470 − 0.589984I
a = −0.299231 − 0.442331I
b = −1.00000
c = −0.23958 − 1.44120I
d = −1.40691 + 0.28559I
−3.88965 + 6.77427I −10.22594 − 4.95962I
u = 1.175470 − 0.589984I
a = 0.42258 − 1.93124I
b = −1.00000
c = 0.209555 + 1.262070I
d = 0.307742 − 0.904345I
−3.88965 + 6.77427I −10.22594 − 4.95962I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.312590 + 0.177484I
a = −0.920187 + 0.871890I
b = −1.00000
c = −0.575440 + 0.451407I
d = −1.47301 − 0.08468I
−9.90219 + 2.08114I −17.7960 − 2.7886I
u = 1.312590 + 0.177484I
a = −0.113586 − 1.304510I
b = −1.00000
c = −0.391157 + 0.943404I
d = 0.853841 − 0.754977I
−9.90219 + 2.08114I −17.7960 − 2.7886I
u = 1.312590 − 0.177484I
a = −0.920187 − 0.871890I
b = −1.00000
c = −0.575440 − 0.451407I
d = −1.47301 + 0.08468I
−9.90219 − 2.08114I −17.7960 + 2.7886I
u = 1.312590 − 0.177484I
a = −0.113586 + 1.304510I
b = −1.00000
c = −0.391157 − 0.943404I
d = 0.853841 + 0.754977I
−9.90219 − 2.08114I −17.7960 + 2.7886I
u = 1.262900 + 0.460239I
a = −0.110303 − 1.099220I
b = −1.00000
c = −0.584732 + 0.832898I
d = 1.027590 − 0.683591I
−8.61088 − 6.23266I −16.1498 + 4.3008I
u = 1.262900 + 0.460239I
a = −0.73910 + 1.34519I
b = −1.00000
c = −0.341352 + 1.102730I
d = −1.44949 − 0.22125I
−8.61088 − 6.23266I −16.1498 + 4.3008I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.262900 − 0.460239I
a = −0.110303 + 1.099220I
b = −1.00000
c = −0.584732 − 0.832898I
d = 1.027590 + 0.683591I
−8.61088 + 6.23266I −16.1498 − 4.3008I
u = 1.262900 − 0.460239I
a = −0.73910 − 1.34519I
b = −1.00000
c = −0.341352 − 1.102730I
d = −1.44949 + 0.22125I
−8.61088 + 6.23266I −16.1498 − 4.3008I
u = −1.280370 + 0.446560I
a = −0.502612 − 0.171924I
b = −1.00000
c = −0.332736 − 1.053240I
d = −1.45797 + 0.21451I
−8.68474 + 3.62399I −16.2087 − 2.7619I
u = −1.280370 + 0.446560I
a = 0.25189 − 1.78789I
b = −1.00000
c = 0.059654 + 1.225020I
d = 0.436936 − 0.910395I
−8.68474 + 3.62399I −16.2087 − 2.7619I
u = −1.280370 − 0.446560I
a = −0.502612 + 0.171924I
b = −1.00000
c = −0.332736 + 1.053240I
d = −1.45797 − 0.21451I
−8.68474 − 3.62399I −16.2087 + 2.7619I
u = −1.280370 − 0.446560I
a = 0.25189 + 1.78789I
b = −1.00000
c = 0.059654 − 1.225020I
d = 0.436936 + 0.910395I
−8.68474 − 3.62399I −16.2087 + 2.7619I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.376924 + 0.508425I
a = −0.304778 + 0.396413I
b = −1.00000
c = −0.608002 − 0.187738I
d = 1.085050 + 0.152783I
−3.51302 + 1.43304I −13.5823 − 4.9760I
u = −0.376924 + 0.508425I
a = 0.96605 − 5.26986I
b = −1.00000
c = 1.01842 − 5.30238I
d = −0.999265 + 0.195824I
−3.51302 + 1.43304I −13.5823 − 4.9760I
u = −0.376924 − 0.508425I
a = −0.304778 − 0.396413I
b = −1.00000
c = −0.608002 + 0.187738I
d = 1.085050 − 0.152783I
−3.51302 − 1.43304I −13.5823 + 4.9760I
u = −0.376924 − 0.508425I
a = 0.96605 + 5.26986I
b = −1.00000
c = 1.01842 + 5.30238I
d = −0.999265 − 0.195824I
−3.51302 − 1.43304I −13.5823 + 4.9760I
u = −1.241130 + 0.661367I
a = −0.160346 − 0.333380I
b = −1.00000
c = −0.043949 − 1.401630I
d = −1.44024 + 0.32064I
−6.41692 + 11.95450I −13.0412 − 8.3222I
u = −1.241130 + 0.661367I
a = 0.49740 − 1.83602I
b = −1.00000
c = 0.199842 + 1.344140I
d = 0.293882 − 0.972896I
−6.41692 + 11.95450I −13.0412 − 8.3222I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.241130 − 0.661367I
a = −0.160346 + 0.333380I
b = −1.00000
c = −0.043949 + 1.401630I
d = −1.44024 − 0.32064I
−6.41692 − 11.95450I −13.0412 + 8.3222I
u = −1.241130 − 0.661367I
a = 0.49740 + 1.83602I
b = −1.00000
c = 0.199842 − 1.344140I
d = 0.293882 + 0.972896I
−6.41692 − 11.95450I −13.0412 + 8.3222I
23
III. I
v
1
= ha, d, c − 1, b + 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
10
=
1
0
a
5
=
v
0
a
7
=
0
−1
a
12
=
1
0
a
1
=
1
1
a
6
=
−1
−1
a
3
=
0
−v
a
2
=
1
−v
a
11
=
1
0
a
8
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 11
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
8
, c
9
c
10
, c
11
u
2
c
6
, c
7
(u − 1)
2
c
12
(u + 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
8
, c
9
c
10
, c
11
y
2
c
6
, c
7
, c
12
(y − 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −1.00000
c = 1.00000
d = 0
−1.64493 + 2.02988I −9.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −1.00000
c = 1.00000
d = 0
−1.64493 − 2.02988I −9.00000 + 3.46410I
27
IV. I
v
2
= ha, d − 1, c + a, b + 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
10
=
1
0
a
5
=
v
0
a
7
=
0
−1
a
12
=
0
1
a
1
=
0
1
a
6
=
0
−1
a
3
=
v
−v
a
2
=
v + 1
−v
a
11
=
1
1
a
8
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 11
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
6
, c
7
c
9
, c
12
u
2
c
8
(u − 1)
2
c
10
, c
11
(u + 1)
2
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
6
, c
7
c
9
, c
12
y
2
c
8
, c
10
, c
11
(y − 1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −1.00000
c = 0
d = 1.00000
−1.64493 + 2.02988I −9.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −1.00000
c = 0
d = 1.00000
−1.64493 − 2.02988I −9.00000 + 3.46410I
31
V. I
v
3
= ha, d − 1, c + a + 1, b + 1, v + 1i
(i) Arc colorings
a
4
=
−1
0
a
9
=
1
0
a
10
=
1
0
a
5
=
−1
0
a
7
=
0
−1
a
12
=
−1
1
a
1
=
−1
0
a
6
=
−1
0
a
3
=
−1
0
a
2
=
−1
0
a
11
=
0
1
a
8
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
u
c
6
, c
7
, c
10
c
11
u + 1
c
8
, c
12
u − 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
y
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y − 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
c = −1.00000
d = 1.00000
−3.28987 −12.0000
35
VI.
I
v
4
= hc, d − 1, cb − a − 1, v
2
ba + v
2
c + · · · + c + v, b
2
v
2
+ 2v
2
b + · · · + v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
10
=
1
0
a
5
=
v
0
a
7
=
−1
b
a
12
=
0
1
a
1
=
−1
b + 1
a
6
=
−1
b + 1
a
3
=
bv + 2v
−b
2
v − 2bv − v
a
2
=
−v
2
b + bv − v
2
+ v
−b
2
v − 2bv − v
a
11
=
1
1
a
8
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = b
3
v + 3b
2
v − bv + v
2
− 3v − 16
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
36
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−3.28987 − 2.02988I −14.5770 − 3.5248I
37
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
(u
28
+ 14u
27
+ ··· + 2u + 1)
2
· (u
36
+ 17u
35
+ ··· − 120u + 16)
c
2
u(u
2
+ u + 1)
2
(u
28
+ 2u
27
+ ··· + 2u + 1)
2
(u
36
+ u
35
+ ··· + 16u + 4)
c
3
u(u
2
− u + 1)
2
(u
28
− 2u
27
+ ··· − 22u + 17)
2
· (u
36
− u
35
+ ··· − 104u + 1252)
c
4
, c
9
u
5
(u
28
− u
27
+ ··· − 8u + 4)
2
(u
36
+ 3u
35
+ ··· + 64u + 32)
c
5
u(u
2
− u + 1)
2
(u
28
+ 2u
27
+ ··· + 2u + 1)
2
(u
36
+ u
35
+ ··· + 16u + 4)
c
6
, c
7
u
2
(u − 1)
2
(u + 1)(u
36
− 5u
35
+ ··· + 3u − 1)
· (u
56
− 3u
55
+ ··· + 72u + 16)
c
8
u
2
(u − 1)
3
(u
36
− 5u
35
+ ··· + 3u − 1)(u
56
− 3u
55
+ ··· + 72u + 16)
c
10
, c
11
u
2
(u + 1)
3
(u
36
− 5u
35
+ ··· + 3u − 1)(u
56
− 3u
55
+ ··· + 72u + 16)
c
12
u
2
(u − 1)(u + 1)
2
(u
36
− 5u
35
+ ··· + 3u − 1)
· (u
56
− 3u
55
+ ··· + 72u + 16)
38
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
(y
28
+ 2y
27
+ ··· + 14y + 1)
2
· (y
36
+ 5y
35
+ ··· − 27936y + 256)
c
2
, c
5
y(y
2
+ y + 1)
2
(y
28
+ 14y
27
+ ··· + 2y + 1)
2
· (y
36
+ 17y
35
+ ··· − 120y + 16)
c
3
y(y
2
+ y + 1)
2
(y
28
− 10y
27
+ ··· − 246y + 289)
2
· (y
36
− 7y
35
+ ··· − 22103608y + 1567504)
c
4
, c
9
y
5
(y
28
− 15y
27
+ ··· − 88y + 16)
2
· (y
36
− 15y
35
+ ··· − 1024y + 1024)
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
2
(y − 1)
3
(y
36
− 41y
35
+ ··· − 21y + 1)
· (y
56
− 43y
55
+ ··· + 736y + 256)
39
