12a
0818
(K12a
0818
)
A knot diagram
1
Linearized knot diagam
4 5 7 2 12 9 3 11 1 6 8 10
Solving Sequence
1,4
2 5
3,9
10 12 6 7 11 8
c
1
c
4
c
2
c
9
c
12
c
5
c
6
c
10
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.70557 × 10
47
u
41
+ 1.02379 × 10
48
u
40
+ ··· + 2.35995 × 10
48
b − 1.46322 × 10
48
,
− 2.68217 × 10
48
u
41
− 8.92209 × 10
48
u
40
+ ··· + 6.29321 × 10
48
a − 9.88859 × 10
49
,
u
42
+ 4u
41
+ ··· + 65u + 16i
I
u
2
= h431u
34
a − 1267u
34
+ ··· + 287a − 903, −3u
34
a + 24u
34
+ ··· + 3a + 14, u
35
+ 4u
34
+ ··· + 3u + 1i
I
u
3
= h16a
3
+ b + 3a − 6, 4a
4
− 3a
3
+ a
2
− 2a + 1, u − 1i
I
u
4
= hb − 1, −2u
3
− 2u
2
+ 2a + 2u + 3, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
I
u
5
= h−a
5
+ 2a
4
+ 8a
3
− 27a
2
+ 11b + 20a + 4, a
6
− 5a
5
+ 9a
4
− 4a
3
− 2a
2
+ a + 1, u − 1i
* 5 irreducible components of dim
C
= 0, with total 127 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
= h4.71 × 10
47
u
41
+ 1.02 × 10
48
u
40
+ · · · + 2.36 × 10
48
b − 1.46 ×
10
48
, −2.68 × 10
48
u
41
− 8.92 × 10
48
u
40
+ · · · + 6.29 × 10
48
a − 9.89 ×
10
49
, u
42
+ 4u
41
+ · · · + 65u + 16i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
0.426201u
41
+ 1.41773u
40
+ ··· + 26.1957u + 15.7131
−0.199393u
41
− 0.433818u
40
+ ··· − 8.03052u + 0.620022
a
10
=
0.226808u
41
+ 0.983916u
40
+ ··· + 18.1651u + 16.3331
−0.199393u
41
− 0.433818u
40
+ ··· − 8.03052u + 0.620022
a
12
=
−0.130478u
41
− 0.589048u
40
+ ··· − 7.93921u − 10.8045
0.214517u
41
+ 0.476122u
40
+ ··· + 8.74596u − 0.0471007
a
6
=
0.00615099u
41
+ 0.0315685u
40
+ ··· + 2.33674u + 0.767602
0.0725771u
41
+ 0.173370u
40
+ ··· + 2.50038u + 1.45174
a
7
=
−0.213738u
41
− 0.514758u
40
+ ··· − 2.95723u − 3.48358
0.0448717u
41
− 0.0100936u
40
+ ··· − 0.439227u − 0.620256
a
11
=
0.382659u
41
+ 1.46025u
40
+ ··· + 24.9207u + 21.9393
0.0557291u
41
+ 0.360679u
40
+ ··· + 2.82601u + 7.24218
a
8
=
0.111846u
41
+ 0.317186u
40
+ ··· + 11.7593u + 0.621293
0.0138015u
41
− 0.0198181u
40
+ ··· − 0.199133u − 0.618692
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.14636u
41
+ 3.75809u
40
+ ··· + 70.7450u + 50.8762
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
42
− 4u
41
+ ··· − 65u + 16
c
3
, c
7
u
42
+ 12u
40
+ ··· + 800u − 256
c
5
, c
6
32(32u
42
− 80u
41
+ ··· − 4u
2
+ 1)
c
8
, c
9
, c
11
c
12
u
42
− 5u
41
+ ··· − 9u − 1
c
10
u
42
+ 6u
41
+ ··· + 23552u + 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
42
− 40y
41
+ ··· − 2401y + 256
c
3
, c
7
y
42
+ 24y
41
+ ··· − 54272y + 65536
c
5
, c
6
1024(1024y
42
− 12544y
41
+ ··· − 8y + 1)
c
8
, c
9
, c
11
c
12
y
42
+ 21y
41
+ ··· − 57y + 1
c
10
y
42
− 12y
41
+ ··· − 370147328y + 16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.382277 + 0.955337I
a = −1.66113 + 0.73518I
b = 0.53625 − 1.35310I
−7.2700 − 13.9728I −5.21740 + 8.75518I
u = 0.382277 − 0.955337I
a = −1.66113 − 0.73518I
b = 0.53625 + 1.35310I
−7.2700 + 13.9728I −5.21740 − 8.75518I
u = 1.036130 + 0.136384I
a = 0.31397 + 1.71197I
b = −0.698855 + 0.209140I
−0.378272 − 0.672845I 8.32593 − 8.18018I
u = 1.036130 − 0.136384I
a = 0.31397 − 1.71197I
b = −0.698855 − 0.209140I
−0.378272 + 0.672845I 8.32593 + 8.18018I
u = −0.176431 + 0.920219I
a = −0.089233 + 0.806500I
b = 0.260719 − 1.022000I
−1.94168 − 4.58363I −2.67478 + 9.67087I
u = −0.176431 − 0.920219I
a = −0.089233 − 0.806500I
b = 0.260719 + 1.022000I
−1.94168 + 4.58363I −2.67478 − 9.67087I
u = 1.16532
a = −0.690948
b = 0.111472
−2.22469 −4.45330
u = 0.906961 + 0.760300I
a = −0.164799 − 0.716064I
b = 0.451974 + 1.333990I
−8.82177 + 8.14344I −7.68661 − 4.52240I
u = 0.906961 − 0.760300I
a = −0.164799 + 0.716064I
b = 0.451974 − 1.333990I
−8.82177 − 8.14344I −7.68661 + 4.52240I
u = −1.201200 + 0.145400I
a = −0.872305 − 0.102731I
b = 0.574673 + 1.022490I
−4.65035 + 8.25878I −8.8821 − 11.5403I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.201200 − 0.145400I
a = −0.872305 + 0.102731I
b = 0.574673 − 1.022490I
−4.65035 − 8.25878I −8.8821 + 11.5403I
u = 0.518201 + 1.133520I
a = 0.589570 − 0.397152I
b = −0.152757 + 1.101360I
−4.92726 − 4.44307I −10.0669 + 11.2674I
u = 0.518201 − 1.133520I
a = 0.589570 + 0.397152I
b = −0.152757 − 1.101360I
−4.92726 + 4.44307I −10.0669 − 11.2674I
u = 0.391460 + 0.629294I
a = 2.37670 + 0.71559I
b = −1.257320 − 0.163098I
1.03974 − 1.89674I −9.71636 + 10.18048I
u = 0.391460 − 0.629294I
a = 2.37670 − 0.71559I
b = −1.257320 + 0.163098I
1.03974 + 1.89674I −9.71636 − 10.18048I
u = 1.28899
a = −0.386397
b = −1.24413
−1.06374 −15.9330
u = −0.520433 + 0.480903I
a = −1.54139 + 0.22846I
b = 0.486493 + 1.206120I
−3.67601 + 8.64693I −1.18407 − 7.85838I
u = −0.520433 − 0.480903I
a = −1.54139 − 0.22846I
b = 0.486493 − 1.206120I
−3.67601 − 8.64693I −1.18407 + 7.85838I
u = −1.369360 + 0.103398I
a = 1.140050 − 0.314674I
b = −1.010040 − 0.754348I
−2.55620 + 3.08969I 0
u = −1.369360 − 0.103398I
a = 1.140050 + 0.314674I
b = −1.010040 + 0.754348I
−2.55620 − 3.08969I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.381130 + 0.223245I
a = −0.587328 + 0.140475I
b = 0.398228 − 0.245218I
−5.21752 + 3.92091I 0
u = −1.381130 − 0.223245I
a = −0.587328 − 0.140475I
b = 0.398228 + 0.245218I
−5.21752 − 3.92091I 0
u = −1.46546 + 0.23954I
a = 0.778883 − 0.741783I
b = −1.44538 + 0.24251I
−4.97209 + 5.11669I 0
u = −1.46546 − 0.23954I
a = 0.778883 + 0.741783I
b = −1.44538 − 0.24251I
−4.97209 − 5.11669I 0
u = 1.22748 + 0.83655I
a = −0.546316 + 0.174607I
b = 0.091410 − 1.130240I
−6.99380 − 2.96639I 0
u = 1.22748 − 0.83655I
a = −0.546316 − 0.174607I
b = 0.091410 + 1.130240I
−6.99380 + 2.96639I 0
u = 0.208756 + 0.468070I
a = −1.034920 − 0.197444I
b = 0.106914 + 0.216906I
−0.189441 − 1.194630I −3.03902 + 4.48079I
u = 0.208756 − 0.468070I
a = −1.034920 + 0.197444I
b = 0.106914 − 0.216906I
−0.189441 + 1.194630I −3.03902 − 4.48079I
u = 1.49536 + 0.19812I
a = −1.070210 − 0.916497I
b = 0.49427 − 1.35780I
−10.2159 − 11.2963I 0
u = 1.49536 − 0.19812I
a = −1.070210 + 0.916497I
b = 0.49427 + 1.35780I
−10.2159 + 11.2963I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50308 + 0.37191I
a = −1.59621 + 0.46175I
b = 0.59118 + 1.39047I
−13.3178 + 18.7741I 0
u = −1.50308 − 0.37191I
a = −1.59621 − 0.46175I
b = 0.59118 − 1.39047I
−13.3178 − 18.7741I 0
u = 0.103524 + 0.426968I
a = 2.10169 − 1.36256I
b = −0.922128 + 0.404344I
2.10350 − 1.31837I 6.89891 − 1.71793I
u = 0.103524 − 0.426968I
a = 2.10169 + 1.36256I
b = −0.922128 − 0.404344I
2.10350 + 1.31837I 6.89891 + 1.71793I
u = −1.56428 + 0.38662I
a = 0.947107 − 0.401179I
b = −0.300179 − 1.217090I
−11.6070 + 9.8095I 0
u = −1.56428 − 0.38662I
a = 0.947107 + 0.401179I
b = −0.300179 + 1.217090I
−11.6070 − 9.8095I 0
u = −0.333406 + 0.020280I
a = −0.65169 + 1.58358I
b = −0.387814 + 0.633347I
0.54776 − 1.46692I 5.66103 + 4.76123I
u = −0.333406 − 0.020280I
a = −0.65169 − 1.58358I
b = −0.387814 − 0.633347I
0.54776 + 1.46692I 5.66103 − 4.76123I
u = −1.67473 + 0.04568I
a = −0.132515 − 0.361034I
b = 0.27984 − 1.41003I
−18.2575 − 5.2882I 0
u = −1.67473 − 0.04568I
a = −0.132515 + 0.361034I
b = 0.27984 + 1.41003I
−18.2575 + 5.2882I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.69220 + 0.30592I
a = 0.394986 + 0.353146I
b = −0.031137 + 1.135330I
−8.08716 − 1.02616I 0
u = 1.69220 − 0.30592I
a = 0.394986 − 0.353146I
b = −0.031137 − 1.135330I
−8.08716 + 1.02616I 0
9
II. I
u
2
= h431u
34
a − 1267u
34
+ · · · + 287a − 903, −3u
34
a + 24u
34
+ · · · + 3a +
14, u
35
+ 4u
34
+ · · · + 3u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
a
−2.59639au
34
+ 7.63253u
34
+ ··· − 1.72892a + 5.43976
a
10
=
−2.59639au
34
+ 7.63253u
34
+ ··· − 0.728916a + 5.43976
−2.59639au
34
+ 7.63253u
34
+ ··· − 1.72892a + 5.43976
a
12
=
−6.19880au
34
− 4.53916u
34
+ ··· − 3.90964a − 4.43675
−6.31627au
34
− 2.84639u
34
+ ··· − 4.71988a − 2.97892
a
6
=
6.56325au
34
− 15.4307u
34
+ ··· + 2.74398a − 3.80422
−0.0391566au
34
− 6.60241u
34
+ ··· + 0.0632530a − 2.68072
a
7
=
−
7
2
u
34
−
17
2
u
33
+ ··· − 9u −
3
2
21
4
u
34
+
57
4
u
33
+ ··· + 9u +
19
4
a
11
=
7.63253au
34
+ 1.94277u
34
+ ··· + 5.43976a + 2.70783
1
a
8
=
7
2
u
34
+
19
2
u
33
+ ··· + 2u +
7
2
31
4
u
34
+
83
4
u
33
+ ··· + 12u +
25
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 10u
34
+
55
2
u
33
+ ··· +
39
2
u +
13
2
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
35
− 4u
34
+ ··· + 3u − 1)
2
c
3
, c
7
(u
35
− u
34
+ ··· − 28u − 8)
2
c
5
, c
6
u
70
− 2u
69
+ ··· − 215264236u + 17305121
c
8
, c
9
, c
11
c
12
u
70
+ 12u
69
+ ··· + 4u + 1
c
10
(u
35
− 2u
34
+ ··· − 2u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
35
− 34y
34
+ ··· + 19y −1)
2
c
3
, c
7
(y
35
+ 21y
34
+ ··· + 16y −64)
2
c
5
, c
6
y
70
− 34y
69
+ ··· − 9709459310743048y + 299467212824641
c
8
, c
9
, c
11
c
12
y
70
+ 46y
69
+ ··· + 60y
2
+ 1
c
10
(y
35
− 12y
34
+ ··· + 10y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.787288 + 0.599387I
a = −0.086494 + 0.987313I
b = −0.409191 − 1.343070I
−4.38053 + 3.19486I −5.71319 − 2.77080I
u = 0.787288 + 0.599387I
a = −1.38411 − 1.00877I
b = 0.940264 + 0.111257I
−4.38053 + 3.19486I −5.71319 − 2.77080I
u = 0.787288 − 0.599387I
a = −0.086494 − 0.987313I
b = −0.409191 + 1.343070I
−4.38053 − 3.19486I −5.71319 + 2.77080I
u = 0.787288 − 0.599387I
a = −1.38411 + 1.00877I
b = 0.940264 − 0.111257I
−4.38053 − 3.19486I −5.71319 + 2.77080I
u = 0.863463 + 0.435553I
a = 0.206812 − 0.579701I
b = −0.094077 + 1.102490I
−3.64066 − 1.76625I −4.73044 + 2.55261I
u = 0.863463 + 0.435553I
a = −0.608026 + 1.260340I
b = 0.255940 − 0.178870I
−3.64066 − 1.76625I −4.73044 + 2.55261I
u = 0.863463 − 0.435553I
a = 0.206812 + 0.579701I
b = −0.094077 − 1.102490I
−3.64066 + 1.76625I −4.73044 − 2.55261I
u = 0.863463 − 0.435553I
a = −0.608026 − 1.260340I
b = 0.255940 + 0.178870I
−3.64066 + 1.76625I −4.73044 − 2.55261I
u = 0.378284 + 0.838154I
a = −1.85036 − 0.34075I
b = 1.101690 + 0.020192I
−3.07931 − 8.20034I −2.93623 + 7.67757I
u = 0.378284 + 0.838154I
a = 1.75417 − 0.92177I
b = −0.56291 + 1.37198I
−3.07931 − 8.20034I −2.93623 + 7.67757I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.378284 − 0.838154I
a = −1.85036 + 0.34075I
b = 1.101690 − 0.020192I
−3.07931 + 8.20034I −2.93623 − 7.67757I
u = 0.378284 − 0.838154I
a = 1.75417 + 0.92177I
b = −0.56291 − 1.37198I
−3.07931 + 8.20034I −2.93623 − 7.67757I
u = 0.535823 + 0.722828I
a = −0.45702 − 1.35557I
b = 0.46606 + 1.42298I
−7.75853 − 2.44036I −9.20394 + 3.90896I
u = 0.535823 + 0.722828I
a = −2.20201 + 0.82058I
b = 0.60727 − 1.30342I
−7.75853 − 2.44036I −9.20394 + 3.90896I
u = 0.535823 − 0.722828I
a = −0.45702 + 1.35557I
b = 0.46606 − 1.42298I
−7.75853 + 2.44036I −9.20394 − 3.90896I
u = 0.535823 − 0.722828I
a = −2.20201 − 0.82058I
b = 0.60727 + 1.30342I
−7.75853 + 2.44036I −9.20394 − 3.90896I
u = 1.11802
a = −6.86583 + 4.96782I
b = 0.077086 − 1.008870I
−5.44402 2.06430
u = 1.11802
a = −6.86583 − 4.96782I
b = 0.077086 + 1.008870I
−5.44402 2.06430
u = 0.334838 + 0.781483I
a = 0.611108 − 0.709436I
b = −0.266376 + 0.028486I
−2.04839 − 2.67684I −0.78426 + 2.93641I
u = 0.334838 + 0.781483I
a = −1.28426 + 0.62029I
b = 0.127641 − 1.040230I
−2.04839 − 2.67684I −0.78426 + 2.93641I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.334838 − 0.781483I
a = 0.611108 + 0.709436I
b = −0.266376 − 0.028486I
−2.04839 + 2.67684I −0.78426 − 2.93641I
u = 0.334838 − 0.781483I
a = −1.28426 − 0.62029I
b = 0.127641 + 1.040230I
−2.04839 + 2.67684I −0.78426 − 2.93641I
u = −1.293330 + 0.022996I
a = −0.965695 − 0.118945I
b = 0.830183 − 0.558253I
−3.19397 + 3.04539I −6.49856 − 3.07346I
u = −1.293330 + 0.022996I
a = 0.672369 + 0.296675I
b = −0.711919 − 0.891888I
−3.19397 + 3.04539I −6.49856 − 3.07346I
u = −1.293330 − 0.022996I
a = −0.965695 + 0.118945I
b = 0.830183 + 0.558253I
−3.19397 − 3.04539I −6.49856 + 3.07346I
u = −1.293330 − 0.022996I
a = 0.672369 − 0.296675I
b = −0.711919 + 0.891888I
−3.19397 − 3.04539I −6.49856 + 3.07346I
u = 1.331630 + 0.151400I
a = 0.358567 − 0.966943I
b = −0.094807 + 0.186756I
−4.74191 − 0.58793I −2.80279 + 0.I
u = 1.331630 + 0.151400I
a = −1.56667 − 1.15669I
b = 0.033995 − 1.083710I
−4.74191 − 0.58793I −2.80279 + 0.I
u = 1.331630 − 0.151400I
a = 0.358567 + 0.966943I
b = −0.094807 − 0.186756I
−4.74191 + 0.58793I −2.80279 + 0.I
u = 1.331630 − 0.151400I
a = −1.56667 + 1.15669I
b = 0.033995 + 1.083710I
−4.74191 + 0.58793I −2.80279 + 0.I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40486
a = −0.474895 + 1.101280I
b = 0.54790 + 1.37862I
−9.85232 −9.92120
u = 1.40486
a = −0.474895 − 1.101280I
b = 0.54790 − 1.37862I
−9.85232 −9.92120
u = 1.403830 + 0.145115I
a = 0.98126 + 1.19495I
b = −0.49226 + 1.38247I
−5.78377 − 5.84473I 0
u = 1.403830 + 0.145115I
a = −0.252994 − 0.344206I
b = 1.053300 − 0.058898I
−5.78377 − 5.84473I 0
u = 1.403830 − 0.145115I
a = 0.98126 − 1.19495I
b = −0.49226 − 1.38247I
−5.78377 + 5.84473I 0
u = 1.403830 − 0.145115I
a = −0.252994 + 0.344206I
b = 1.053300 + 0.058898I
−5.78377 + 5.84473I 0
u = 0.374463 + 0.419722I
a = −2.06448 + 2.38148I
b = −0.028461 + 1.098670I
−3.71944 − 1.17044I −1.16678 + 5.64189I
u = 0.374463 + 0.419722I
a = 4.28644 + 4.59791I
b = −0.059654 − 0.866754I
−3.71944 − 1.17044I −1.16678 + 5.64189I
u = 0.374463 − 0.419722I
a = −2.06448 − 2.38148I
b = −0.028461 − 1.098670I
−3.71944 + 1.17044I −1.16678 − 5.64189I
u = 0.374463 − 0.419722I
a = 4.28644 − 4.59791I
b = −0.059654 + 0.866754I
−3.71944 + 1.17044I −1.16678 − 5.64189I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46236 + 0.17601I
a = 1.51571 − 0.46270I
b = −0.367348 + 0.819468I
−9.77721 + 3.48149I 0
u = −1.46236 + 0.17601I
a = 0.43467 − 1.63292I
b = −0.091480 − 1.230270I
−9.77721 + 3.48149I 0
u = −1.46236 − 0.17601I
a = 1.51571 + 0.46270I
b = −0.367348 − 0.819468I
−9.77721 − 3.48149I 0
u = −1.46236 − 0.17601I
a = 0.43467 + 1.63292I
b = −0.091480 + 1.230270I
−9.77721 − 3.48149I 0
u = −1.45963 + 0.29677I
a = 0.624599 + 0.193615I
b = −0.552157 − 0.070918I
−7.83682 + 6.58963I 0
u = −1.45963 + 0.29677I
a = −1.35152 + 0.58488I
b = 0.249550 + 1.142520I
−7.83682 + 6.58963I 0
u = −1.45963 − 0.29677I
a = 0.624599 − 0.193615I
b = −0.552157 + 0.070918I
−7.83682 − 6.58963I 0
u = −1.45963 − 0.29677I
a = −1.35152 − 0.58488I
b = 0.249550 − 1.142520I
−7.83682 − 6.58963I 0
u = −0.166758 + 0.470101I
a = −1.10634 − 1.04351I
b = −0.266545 + 0.867095I
−0.05478 − 1.72545I 3.36392 + 2.52233I
u = −0.166758 + 0.470101I
a = −1.20153 + 0.96877I
b = 0.368166 + 0.304402I
−0.05478 − 1.72545I 3.36392 + 2.52233I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.166758 − 0.470101I
a = −1.10634 + 1.04351I
b = −0.266545 − 0.867095I
−0.05478 + 1.72545I 3.36392 − 2.52233I
u = −0.166758 − 0.470101I
a = −1.20153 − 0.96877I
b = 0.368166 − 0.304402I
−0.05478 + 1.72545I 3.36392 − 2.52233I
u = −0.261262 + 0.408522I
a = −0.881409 + 0.809220I
b = 0.850553 − 0.149091I
−0.43566 + 3.77887I 2.70186 − 3.89618I
u = −0.261262 + 0.408522I
a = 2.21730 − 0.24123I
b = −0.502121 − 1.163120I
−0.43566 + 3.77887I 2.70186 − 3.89618I
u = −0.261262 − 0.408522I
a = −0.881409 − 0.809220I
b = 0.850553 + 0.149091I
−0.43566 − 3.77887I 2.70186 + 3.89618I
u = −0.261262 − 0.408522I
a = 2.21730 + 0.24123I
b = −0.502121 + 1.163120I
−0.43566 − 3.77887I 2.70186 + 3.89618I
u = −1.48269 + 0.31831I
a = −0.841244 + 0.661850I
b = 1.235650 − 0.053997I
−9.0790 + 12.3988I 0
u = −1.48269 + 0.31831I
a = 1.53656 − 0.44667I
b = −0.65200 − 1.43728I
−9.0790 + 12.3988I 0
u = −1.48269 − 0.31831I
a = −0.841244 − 0.661850I
b = 1.235650 + 0.053997I
−9.0790 − 12.3988I 0
u = −1.48269 − 0.31831I
a = 1.53656 + 0.44667I
b = −0.65200 + 1.43728I
−9.0790 − 12.3988I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52211 + 0.12323I
a = −0.684628 + 0.572571I
b = 1.063560 − 0.479442I
−12.01000 − 1.04091I 0
u = −1.52211 + 0.12323I
a = −0.247279 + 0.320973I
b = −0.24344 + 1.56604I
−12.01000 − 1.04091I 0
u = −1.52211 − 0.12323I
a = −0.684628 − 0.572571I
b = 1.063560 + 0.479442I
−12.01000 + 1.04091I 0
u = −1.52211 − 0.12323I
a = −0.247279 − 0.320973I
b = −0.24344 − 1.56604I
−12.01000 + 1.04091I 0
u = −1.51902 + 0.23855I
a = −1.50135 + 0.36894I
b = 0.78842 + 1.32634I
−14.4705 + 5.9201I 0
u = −1.51902 + 0.23855I
a = 0.181610 + 0.009514I
b = 0.45096 − 1.59114I
−14.4705 + 5.9201I 0
u = −1.51902 − 0.23855I
a = −1.50135 − 0.36894I
b = 0.78842 − 1.32634I
−14.4705 − 5.9201I 0
u = −1.51902 − 0.23855I
a = 0.181610 − 0.009514I
b = 0.45096 + 1.59114I
−14.4705 − 5.9201I 0
u = −0.207771
a = −0.50303 + 3.16268I
b = 0.346555 + 1.166320I
−4.65443 −2.49720
u = −0.207771
a = −0.50303 − 3.16268I
b = 0.346555 − 1.166320I
−4.65443 −2.49720
19
III. I
u
3
= h16a
3
+ b + 3a − 6, 4a
4
− 3a
3
+ a
2
− 2a + 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
3
=
0
1
a
9
=
a
−16a
3
− 3a + 6
a
10
=
−16a
3
− 2a + 6
−16a
3
− 3a + 6
a
12
=
8a
3
− 2a
2
+ 2a − 3
20a
3
− 3a
2
+ 4a − 8
a
6
=
12a
3
− a
2
+ 2a − 5
36a
3
− 3a
2
+ 7a − 13
a
7
=
0
32a
3
− 4a
2
+ 5a − 12
a
11
=
8a
3
− 2a
2
+ 2a − 3
24a
3
− 2a
2
+ 6a − 8
a
8
=
0
32a
3
− 4a
2
+ 5a − 12
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24a
3
+ 5a
2
− 9a + 7
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
6
u
4
− 2u
3
+ 3u
2
− u + 1
c
8
, c
9
u
4
+ u
2
+ u + 1
c
10
u
4
− 3u
3
+ 4u
2
− 3u + 2
c
11
, c
12
u
4
+ u
2
− u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
6
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
8
, c
9
, c
11
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
10
y
4
− y
3
+ 2y
2
+ 7y + 4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.286541 + 0.697356I
b = 0.547424 + 0.585652I
−0.66484 + 1.39709I −1.91043 − 4.25783I
u = 1.00000
a = −0.286541 − 0.697356I
b = 0.547424 − 0.585652I
−0.66484 − 1.39709I −1.91043 + 4.25783I
u = 1.00000
a = 0.661541 + 0.046758I
b = −0.547424 − 1.120870I
−4.26996 + 7.64338I −3.62082 − 1.58240I
u = 1.00000
a = 0.661541 − 0.046758I
b = −0.547424 + 1.120870I
−4.26996 − 7.64338I −3.62082 + 1.58240I
23
IV. I
u
4
= hb − 1, −2u
3
− 2u
2
+ 2a + 2u + 3, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
u
3
+ u
2
− u −
3
2
1
a
10
=
u
3
+ u
2
− u −
1
2
1
a
12
=
u
3
+ u
2
− u +
1
2
1
a
6
=
1
4
u
3
−
3
4
u
−
1
2
u
3
+
1
2
u
a
7
=
u
3
− 2u
−u
3
+ u
a
11
=
u
3
+ u
2
− u −
1
2
1
a
8
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes =
17
4
u
4
+
15
4
u
3
−
17
4
u
2
+
1
2
u +
7
4
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
3
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
4
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
5
32(32u
5
+ 48u
4
+ 32u
3
+ 4u
2
− 2u − 1)
c
6
32(32u
5
− 48u
4
+ 32u
3
− 4u
2
− 2u + 1)
c
7
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
8
, c
9
(u + 1)
5
c
10
u
5
c
11
, c
12
(u − 1)
5
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
3
, c
7
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
5
, c
6
1024(1024y
5
− 256y
4
+ 512y
3
− 48y
2
+ 12y −1)
c
8
, c
9
, c
11
c
12
(y −1)
5
c
10
y
5
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = 0.570903
b = 1.00000
−0.756147 12.1740
u = 0.309916 + 0.549911I
a = −2.26766 − 0.21690I
b = 1.00000
1.31583 − 1.53058I 1.52646 − 1.80092I
u = 0.309916 − 0.549911I
a = −2.26766 + 0.21690I
b = 1.00000
1.31583 + 1.53058I 1.52646 + 1.80092I
u = −1.41878 + 0.21917I
a = −0.767792 + 0.471915I
b = 1.00000
−4.22763 + 4.40083I −2.48831 − 2.71046I
u = −1.41878 − 0.21917I
a = −0.767792 − 0.471915I
b = 1.00000
−4.22763 − 4.40083I −2.48831 + 2.71046I
27
V. I
u
5
=
h−a
5
+2a
4
+8a
3
−27a
2
+11b+20a+4, a
6
−5a
5
+9a
4
−4a
3
−2a
2
+a+1, u−1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
3
=
0
1
a
9
=
a
0.0909091a
5
− 0.181818a
4
+ ··· − 1.81818a − 0.363636
a
10
=
0.0909091a
5
− 0.181818a
4
+ ··· − 0.818182a − 0.363636
0.0909091a
5
− 0.181818a
4
+ ··· − 1.81818a − 0.363636
a
12
=
−0.363636a
5
+ 1.72727a
4
+ ··· + 0.272727a + 0.454545
−0.636364a
5
+ 3.27273a
4
+ ··· + 0.727273a − 0.454545
a
6
=
0.454545a
5
− 1.90909a
4
+ ··· − 1.09091a − 0.818182
−0.181818a
5
+ 1.36364a
4
+ ··· − 1.36364a − 0.272727
a
7
=
0
0.272727a
5
− 0.545455a
4
+ ··· − 1.45455a − 1.09091
a
11
=
−0.363636a
5
+ 1.72727a
4
+ ··· + 0.272727a + 0.454545
−1
a
8
=
0
0.272727a
5
− 0.545455a
4
+ ··· − 1.45455a − 1.09091
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1
11
a
5
+
2
11
a
4
+
30
11
a
3
−
93
11
a
2
+
31
11
a +
15
11
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
6
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
8
, c
9
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
10
(u
3
+ u
2
− 1)
2
c
11
, c
12
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
6
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
8
, c
9
, c
11
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
10
(y
3
− y
2
+ 2y −1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.836473 + 0.439023I
b = −0.713912 + 0.305839I
−1.91067 + 2.82812I −0.28809 − 2.59975I
u = 1.00000
a = 0.836473 − 0.439023I
b = −0.713912 − 0.305839I
−1.91067 − 2.82812I −0.28809 + 2.59975I
u = 1.00000
a = −0.376271 + 0.256441I
b = 0.498832 − 1.001300I
−1.91067 − 2.82812I −0.28809 + 2.59975I
u = 1.00000
a = −0.376271 − 0.256441I
b = 0.498832 + 1.001300I
−1.91067 + 2.82812I −0.28809 − 2.59975I
u = 1.00000
a = 2.03980 + 1.11514I
b = −0.284920 − 1.115140I
−6.04826 −12.42382 + 0.I
u = 1.00000
a = 2.03980 − 1.11514I
b = −0.284920 + 1.115140I
−6.04826 −12.42382 + 0.I
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
10
)(u
5
+ u
4
+ ··· + u − 1)(u
35
− 4u
34
+ ··· + 3u − 1)
2
· (u
42
− 4u
41
+ ··· − 65u + 16)
c
3
u
10
(u
5
− u
4
+ ··· + u − 1)(u
35
− u
34
+ ··· − 28u − 8)
2
· (u
42
+ 12u
40
+ ··· + 800u − 256)
c
4
((u + 1)
10
)(u
5
− u
4
+ ··· + u + 1)(u
35
− 4u
34
+ ··· + 3u − 1)
2
· (u
42
− 4u
41
+ ··· − 65u + 16)
c
5
1024(u
4
− 2u
3
+ 3u
2
− u + 1)(32u
5
+ 48u
4
+ 32u
3
+ 4u
2
− 2u − 1)
· (u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)(32u
42
− 80u
41
+ ··· − 4u
2
+ 1)
· (u
70
− 2u
69
+ ··· − 215264236u + 17305121)
c
6
1024(u
4
− 2u
3
+ 3u
2
− u + 1)(32u
5
− 48u
4
+ 32u
3
− 4u
2
− 2u + 1)
· (u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)(32u
42
− 80u
41
+ ··· − 4u
2
+ 1)
· (u
70
− 2u
69
+ ··· − 215264236u + 17305121)
c
7
u
10
(u
5
+ u
4
+ ··· + u + 1)(u
35
− u
34
+ ··· − 28u − 8)
2
· (u
42
+ 12u
40
+ ··· + 800u − 256)
c
8
, c
9
(u + 1)
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
42
− 5u
41
+ ··· − 9u − 1)(u
70
+ 12u
69
+ ··· + 4u + 1)
c
10
u
5
(u
3
+ u
2
− 1)
2
(u
4
− 3u
3
+ ··· − 3u + 2)(u
35
− 2u
34
+ ··· − 2u + 1)
2
· (u
42
+ 6u
41
+ ··· + 23552u + 4096)
c
11
, c
12
(u − 1)
5
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
42
− 5u
41
+ ··· − 9u − 1)(u
70
+ 12u
69
+ ··· + 4u + 1)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
10
)(y
5
− 5y
4
+ ··· − y −1)(y
35
− 34y
34
+ ··· + 19y −1)
2
· (y
42
− 40y
41
+ ··· − 2401y + 256)
c
3
, c
7
y
10
(y
5
+ 3y
4
+ ··· − y −1)(y
35
+ 21y
34
+ ··· + 16y −64)
2
· (y
42
+ 24y
41
+ ··· − 54272y + 65536)
c
5
, c
6
1048576(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
· (1024y
5
− 256y
4
+ 512y
3
− 48y
2
+ 12y −1)
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)(1024y
42
− 12544y
41
+ ··· − 8y + 1)
· (y
70
− 34y
69
+ ··· − 9709459310743048y + 299467212824641)
c
8
, c
9
, c
11
c
12
(y −1)
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
42
+ 21y
41
+ ··· − 57y + 1)(y
70
+ 46y
69
+ ··· + 60y
2
+ 1)
c
10
y
5
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
35
− 12y
34
+ ··· + 10y −1)
2
· (y
42
− 12y
41
+ ··· − 370147328y + 16777216)
33
