12a
0049
(K12a
0049
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 12 4 11 1 6 8 10
Solving Sequence
4,8
7
3,12
6 11 9 5 2 10 1
c
7
c
3
c
6
c
11
c
8
c
5
c
2
c
10
c
12
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.20260 × 10
103
u
47
+ 1.71175 × 10
103
u
46
+ ··· + 6.39981 × 10
106
b − 1.52221 × 10
105
,
3.79806 × 10
106
u
47
+ 1.55054 × 10
106
u
46
+ ··· + 1.02397 × 10
108
a − 1.21535 × 10
109
,
u
48
− 9u
46
+ ··· − 688u + 128i
I
u
2
= h−1.12143 × 10
21
au
39
− 8.51510 × 10
20
u
39
+ ··· + 5.02212 × 10
21
a − 6.07964 × 10
21
,
1.50092 × 10
21
au
39
+ 7.38054 × 10
22
u
39
+ ··· + 1.98528 × 10
22
a + 5.64927 × 10
23
, u
40
− u
39
+ ··· + 8u + 4i
I
u
3
= hb + 1, 2u
5
− 4u
3
− 2u
2
+ 2a + 4u + 3, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
v
1
= ha, −20v
2
+ 13b + 69v −1, 4v
3
− 13v
2
− v −1i
I
v
2
= ha, b
2
− bv −b + v + 1, v
2
+ v + 1i
* 5 irreducible components of dim
C
= 0, with total 141 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
= h2.20 × 10
103
u
47
+ 1.71 × 10
103
u
46
+ · · · + 6.40 × 10
106
b − 1.52 ×
10
105
, 3.80 × 10
106
u
47
+ 1.55 × 10
106
u
46
+ · · · + 1.02 × 10
108
a − 1.22 ×
10
109
, u
48
− 9u
46
+ · · · − 688u + 128i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
12
=
−0.0370915u
47
− 0.0151424u
46
+ ··· − 33.2399u + 11.8690
−0.000344167u
47
− 0.000267469u
46
+ ··· − 1.40675u + 0.0237852
a
6
=
−0.0117969u
47
− 0.00536501u
46
+ ··· − 11.1030u + 4.23953
−0.00240170u
47
+ 0.000899905u
46
+ ··· − 1.74418u + 0.851220
a
11
=
−0.0367474u
47
− 0.0148750u
46
+ ··· − 31.8331u + 11.8452
−0.000344167u
47
− 0.000267469u
46
+ ··· − 1.40675u + 0.0237852
a
9
=
−0.0214507u
47
− 0.00655382u
46
+ ··· − 18.8650u + 7.82073
−0.00136402u
47
− 0.00245258u
46
+ ··· − 1.53193u + 0.301599
a
5
=
−0.0154147u
47
− 0.00689804u
46
+ ··· − 13.6620u + 4.47307
−0.00168960u
47
+ 0.000640698u
46
+ ··· − 2.79942u + 1.14559
a
2
=
0.0150232u
47
+ 0.00593756u
46
+ ··· + 13.6887u − 4.73571
0.00403224u
47
+ 0.00287074u
46
+ ··· + 2.13541u − 0.497366
a
10
=
−0.0322794u
47
− 0.0132920u
46
+ ··· − 29.5231u + 11.3082
−0.00393259u
47
+ 0.000672538u
46
+ ··· − 1.57848u + 0.378010
a
1
=
−0.0171043u
47
− 0.00625734u
46
+ ··· − 16.4614u + 5.61866
−0.00177483u
47
− 0.00220211u
46
+ ··· + 0.683721u − 0.344650
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0972185u
47
+ 0.0505623u
46
+ ··· + 105.606u − 17.3444
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
+ 25u
47
+ ··· + 42145u + 256
c
2
, c
4
u
48
− 3u
47
+ ··· + 257u − 16
c
3
, c
7
u
48
− 9u
46
+ ··· − 688u + 128
c
5
, c
6
64(64u
48
− 96u
47
+ ··· − 2u − 1)
c
8
, c
9
, c
11
c
12
u
48
− 6u
47
+ ··· + 8u + 1
c
10
u
48
+ 6u
47
+ ··· − 61440u − 16384
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
− y
47
+ ··· − 1631257409y + 65536
c
2
, c
4
y
48
− 25y
47
+ ··· − 42145y + 256
c
3
, c
7
y
48
− 18y
47
+ ··· − 312576y + 16384
c
5
, c
6
4096(4096y
48
+ 82944y
47
+ ··· + 10y + 1)
c
8
, c
9
, c
11
c
12
y
48
+ 26y
47
+ ··· − 20y + 1
c
10
y
48
+ 14y
47
+ ··· + 6325010432y + 268435456
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.957590 + 0.423594I
a = −1.29646 − 0.87018I
b = −1.285560 − 0.248171I
3.25118 − 1.53806I 3.77848 + 7.20641I
u = −0.957590 − 0.423594I
a = −1.29646 + 0.87018I
b = −1.285560 + 0.248171I
3.25118 + 1.53806I 3.77848 − 7.20641I
u = −1.054240 + 0.079852I
a = −1.58480 − 0.04060I
b = −1.030710 + 0.545069I
4.42263 − 0.15820I 11.64093 − 4.40181I
u = −1.054240 − 0.079852I
a = −1.58480 + 0.04060I
b = −1.030710 − 0.545069I
4.42263 + 0.15820I 11.64093 + 4.40181I
u = 0.539276 + 0.712411I
a = −0.41290 + 1.57537I
b = −1.240410 − 0.075216I
−0.534230 − 1.086180I −9.30458 + 4.94087I
u = 0.539276 − 0.712411I
a = −0.41290 − 1.57537I
b = −1.240410 + 0.075216I
−0.534230 + 1.086180I −9.30458 − 4.94087I
u = 1.107360 + 0.212049I
a = 0.660042 − 0.139690I
b = 0.236042 − 0.336040I
2.16805 + 0.31460I 6.33607 + 1.41060I
u = 1.107360 − 0.212049I
a = 0.660042 + 0.139690I
b = 0.236042 + 0.336040I
2.16805 − 0.31460I 6.33607 − 1.41060I
u = 1.088870 + 0.336703I
a = −1.347020 + 0.378216I
b = −0.880248 − 0.712038I
3.50226 + 4.89574I 9.61286 − 4.76181I
u = 1.088870 − 0.336703I
a = −1.347020 − 0.378216I
b = −0.880248 + 0.712038I
3.50226 − 4.89574I 9.61286 + 4.76181I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.480846 + 1.096760I
a = 0.179702 − 0.206085I
b = 0.438927 + 1.307300I
−6.90844 + 7.54006I 2.09002 − 3.97280I
u = −0.480846 − 1.096760I
a = 0.179702 + 0.206085I
b = 0.438927 − 1.307300I
−6.90844 − 7.54006I 2.09002 + 3.97280I
u = 0.516195 + 0.591350I
a = 0.170724 + 0.199358I
b = 0.33722 − 1.45953I
−11.66740 − 4.83794I −3.17102 − 3.25316I
u = 0.516195 − 0.591350I
a = 0.170724 − 0.199358I
b = 0.33722 + 1.45953I
−11.66740 + 4.83794I −3.17102 + 3.25316I
u = 1.040010 + 0.629240I
a = −0.950394 + 0.827169I
b = −1.42981 + 0.19688I
0.92737 + 6.25196I −0.25642 − 8.29589I
u = 1.040010 − 0.629240I
a = −0.950394 − 0.827169I
b = −1.42981 − 0.19688I
0.92737 − 6.25196I −0.25642 + 8.29589I
u = 1.075020 + 0.599638I
a = 2.02582 + 0.19826I
b = 0.47642 + 1.34836I
−9.94682 + 9.68628I 0.23852 − 6.37320I
u = 1.075020 − 0.599638I
a = 2.02582 − 0.19826I
b = 0.47642 − 1.34836I
−9.94682 − 9.68628I 0.23852 + 6.37320I
u = −1.117060 + 0.522418I
a = 0.656913 + 0.175589I
b = 0.349783 + 0.203417I
0.57085 − 5.30713I 1.46323 + 3.65514I
u = −1.117060 − 0.522418I
a = 0.656913 − 0.175589I
b = 0.349783 − 0.203417I
0.57085 + 5.30713I 1.46323 − 3.65514I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.337526 + 0.625207I
a = 0.846555 + 0.378329I
b = 0.1056360 − 0.0894509I
−1.73027 + 0.78678I −2.85510 − 1.12813I
u = −0.337526 − 0.625207I
a = 0.846555 − 0.378329I
b = 0.1056360 + 0.0894509I
−1.73027 − 0.78678I −2.85510 + 1.12813I
u = 0.150119 + 0.692868I
a = 0.848244 − 0.604603I
b = −0.790495 + 0.329232I
0.444741 − 1.185570I 12.13150 − 0.87372I
u = 0.150119 − 0.692868I
a = 0.848244 + 0.604603I
b = −0.790495 − 0.329232I
0.444741 + 1.185570I 12.13150 + 0.87372I
u = 0.666823 + 1.114180I
a = 0.183212 + 0.199747I
b = 0.51177 − 1.35591I
−9.3008 − 12.7131I 0. + 7.50345I
u = 0.666823 − 1.114180I
a = 0.183212 − 0.199747I
b = 0.51177 + 1.35591I
−9.3008 + 12.7131I 0. − 7.50345I
u = −1.189830 + 0.719252I
a = 1.68887 + 0.05904I
b = 0.55588 − 1.34810I
−4.6404 − 14.0060I 0. + 7.65759I
u = −1.189830 − 0.719252I
a = 1.68887 − 0.05904I
b = 0.55588 + 1.34810I
−4.6404 + 14.0060I 0. − 7.65759I
u = −0.394792 + 0.449338I
a = 0.167205 + 0.201068I
b = 0.16139 − 1.45643I
−11.31320 − 5.43128I −4.9444 + 14.3480I
u = −0.394792 − 0.449338I
a = 0.167205 − 0.201068I
b = 0.16139 + 1.45643I
−11.31320 + 5.43128I −4.9444 − 14.3480I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16364 + 0.81469I
a = 1.67765 − 0.26000I
b = 0.57752 + 1.39189I
−7.6620 + 19.6586I 0
u = 1.16364 − 0.81469I
a = 1.67765 + 0.26000I
b = 0.57752 − 1.39189I
−7.6620 − 19.6586I 0
u = −1.13709 + 0.91603I
a = −0.944068 − 0.205418I
b = −0.269760 + 1.216300I
−5.92456 − 10.57000I 0
u = −1.13709 − 0.91603I
a = −0.944068 + 0.205418I
b = −0.269760 − 1.216300I
−5.92456 + 10.57000I 0
u = −1.42500 + 0.33439I
a = 1.031810 − 0.494343I
b = 0.461071 − 1.095760I
0.42166 − 10.24840I 0
u = −1.42500 − 0.33439I
a = 1.031810 + 0.494343I
b = 0.461071 + 1.095760I
0.42166 + 10.24840I 0
u = 0.13578 + 1.48549I
a = 0.130130 − 0.207768I
b = 0.145425 + 1.101620I
−5.16976 + 4.06955I 0
u = 0.13578 − 1.48549I
a = 0.130130 + 0.207768I
b = 0.145425 − 1.101620I
−5.16976 − 4.06955I 0
u = 1.48360 + 0.19570I
a = 0.703584 + 0.513498I
b = 0.348493 + 0.991064I
1.36851 + 3.98875I 0
u = 1.48360 − 0.19570I
a = 0.703584 − 0.513498I
b = 0.348493 − 0.991064I
1.36851 − 3.98875I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16364 + 0.98340I
a = −0.703120 + 0.177219I
b = −0.210046 − 1.081920I
−2.27888 + 4.80151I 0
u = 1.16364 − 0.98340I
a = −0.703120 − 0.177219I
b = −0.210046 + 1.081920I
−2.27888 − 4.80151I 0
u = 0.429264
a = −5.96055
b = −0.657110
−0.607601 32.9320
u = −1.50494 + 0.56039I
a = −0.413804 + 0.508854I
b = 0.023784 + 1.127520I
−7.87585 + 0.96622I 0
u = −1.50494 − 0.56039I
a = −0.413804 − 0.508854I
b = 0.023784 − 1.127520I
−7.87585 − 0.96622I 0
u = −0.88669 + 1.37679I
a = 0.183944 + 0.141300I
b = −0.077780 − 1.115500I
−7.01684 + 2.73591I 0
u = −0.88669 − 1.37679I
a = 0.183944 − 0.141300I
b = −0.077780 + 1.115500I
−7.01684 − 2.73591I 0
u = 0.281260
a = 0.863091
b = −0.371991
0.702877 14.4650
9
II.
I
u
2
= h−1.12×10
21
au
39
−8.52×10
20
u
39
+· · ·+5.02×10
21
a−6.08×10
21
, 1.50×
10
21
au
39
+7.38×10
22
u
39
+· · ·+1.99×10
22
a+5.65×10
23
, u
40
−u
39
+· · ·+8u+4i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
12
=
a
0.708220au
39
+ 0.537755u
39
+ ··· − 3.17162a + 3.83948
a
6
=
0.120603au
39
− 2.74256u
39
+ ··· + 4.39726a − 2.76323
1.41383au
39
− 1.53443u
39
+ ··· + 2.40579a − 6.80305
a
11
=
−0.708220au
39
− 0.537755u
39
+ ··· + 4.17162a − 3.83948
0.708220au
39
+ 0.537755u
39
+ ··· − 3.17162a + 3.83948
a
9
=
1.41953au
39
− 1.36509u
39
+ ··· + 2.87891a − 2.03774
−1.25231au
39
+ 1.24660u
39
+ ··· − 0.943647a + 0.470529
a
5
=
0.251077u
39
− 0.352373u
38
+ ··· − 5.77817u + 0.265295
−0.778868u
39
+ 1.36370u
38
+ ··· + 0.172609u − 3.83835
a
2
=
0.188503u
39
− 1.22854u
38
+ ··· + 5.41162u + 3.97824
−0.433588u
39
+ 1.32667u
38
+ ··· + 7.93281u − 0.0833981
a
10
=
0.537755au
39
− 1.09578u
39
+ ··· + 3.83948a − 0.770437
1
a
1
=
−0.527790u
39
+ 1.01132u
38
+ ··· − 5.60556u − 3.57306
0.370531u
39
− 1.20473u
38
+ ··· − 1.92971u + 1.90422
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2251146475259849438263
791727160734421751198
u
39
−
5566663425698706915383
791727160734421751198
u
38
+ ··· +
20269146053632003308639
791727160734421751198
u +
11942328350242228350160
395863580367210875599
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
40
+ 21u
39
+ ··· + 3u + 1)
2
c
2
, c
4
(u
40
− 3u
39
+ ··· − 3u + 1)
2
c
3
, c
7
(u
40
− u
39
+ ··· + 8u + 4)
2
c
5
, c
6
u
80
+ 2u
79
+ ··· + 418062244u + 41568281
c
8
, c
9
, c
11
c
12
u
80
+ 14u
79
+ ··· + 4u + 1
c
10
(u
40
− 2u
39
+ ··· + 4u
2
+ 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
40
− y
39
+ ··· + 17y + 1)
2
c
2
, c
4
(y
40
− 21y
39
+ ··· − 3y + 1)
2
c
3
, c
7
(y
40
− 15y
39
+ ··· − 120y + 16)
2
c
5
, c
6
y
80
+ 42y
79
+ ··· + 5456149534708088y + 1727921985294961
c
8
, c
9
, c
11
c
12
y
80
+ 54y
79
+ ··· − 32y
2
+ 1
c
10
(y
40
+ 14y
39
+ ··· + 8y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.826955 + 0.557830I
a = 0.745274 − 0.624480I
b = 1.094300 − 0.379023I
−5.66453 + 0.03317I 1.69926 − 1.92960I
u = 0.826955 + 0.557830I
a = 0.186356 − 0.161443I
b = −0.31800 + 1.54704I
−5.66453 + 0.03317I 1.69926 − 1.92960I
u = 0.826955 − 0.557830I
a = 0.745274 + 0.624480I
b = 1.094300 + 0.379023I
−5.66453 − 0.03317I 1.69926 + 1.92960I
u = 0.826955 − 0.557830I
a = 0.186356 + 0.161443I
b = −0.31800 − 1.54704I
−5.66453 − 0.03317I 1.69926 + 1.92960I
u = −0.833045 + 0.611078I
a = −0.083268 + 0.377413I
b = 0.40800 + 1.44338I
−5.61480 − 2.41163I 1.66429 + 3.34704I
u = −0.833045 + 0.611078I
a = 1.95871 + 0.08818I
b = 0.639652 − 1.245220I
−5.61480 − 2.41163I 1.66429 + 3.34704I
u = −0.833045 − 0.611078I
a = −0.083268 − 0.377413I
b = 0.40800 − 1.44338I
−5.61480 + 2.41163I 1.66429 − 3.34704I
u = −0.833045 − 0.611078I
a = 1.95871 − 0.08818I
b = 0.639652 + 1.245220I
−5.61480 + 2.41163I 1.66429 − 3.34704I
u = 0.877394 + 0.558636I
a = 1.49199 − 0.93722I
b = 1.010680 + 0.081201I
−5.50165 + 4.43619I 2.27094 − 5.48285I
u = 0.877394 + 0.558636I
a = −2.48197 − 0.03741I
b = −0.45899 − 1.36850I
−5.50165 + 4.43619I 2.27094 − 5.48285I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877394 − 0.558636I
a = 1.49199 + 0.93722I
b = 1.010680 − 0.081201I
−5.50165 − 4.43619I 2.27094 + 5.48285I
u = 0.877394 − 0.558636I
a = −2.48197 + 0.03741I
b = −0.45899 + 1.36850I
−5.50165 − 4.43619I 2.27094 + 5.48285I
u = −0.519708 + 0.927909I
a = −0.193562 − 1.010920I
b = −0.171268 − 0.115232I
−3.92955 + 1.74616I 3.95570 − 1.25758I
u = −0.519708 + 0.927909I
a = 0.282445 − 0.802919I
b = 0.070922 + 1.063730I
−3.92955 + 1.74616I 3.95570 − 1.25758I
u = −0.519708 − 0.927909I
a = −0.193562 + 1.010920I
b = −0.171268 + 0.115232I
−3.92955 − 1.74616I 3.95570 + 1.25758I
u = −0.519708 − 0.927909I
a = 0.282445 + 0.802919I
b = 0.070922 − 1.063730I
−3.92955 − 1.74616I 3.95570 + 1.25758I
u = 0.724966 + 0.781823I
a = −0.388682 − 0.372042I
b = 0.57153 − 1.34706I
−9.29673 − 1.32070I −3.28134 + 0.72610I
u = 0.724966 + 0.781823I
a = 2.12006 − 0.70707I
b = 0.51317 + 1.39627I
−9.29673 − 1.32070I −3.28134 + 0.72610I
u = 0.724966 − 0.781823I
a = −0.388682 + 0.372042I
b = 0.57153 + 1.34706I
−9.29673 + 1.32070I −3.28134 − 0.72610I
u = 0.724966 − 0.781823I
a = 2.12006 + 0.70707I
b = 0.51317 − 1.39627I
−9.29673 + 1.32070I −3.28134 − 0.72610I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.868850 + 0.239262I
a = −1.01430 + 2.67027I
b = −0.101637 − 1.117380I
−1.81418 + 0.52119I 10.28438 − 0.91978I
u = 0.868850 + 0.239262I
a = −3.13476 + 0.46944I
b = −0.187234 + 0.916488I
−1.81418 + 0.52119I 10.28438 − 0.91978I
u = 0.868850 − 0.239262I
a = −1.01430 − 2.67027I
b = −0.101637 + 1.117380I
−1.81418 − 0.52119I 10.28438 + 0.91978I
u = 0.868850 − 0.239262I
a = −3.13476 − 0.46944I
b = −0.187234 − 0.916488I
−1.81418 − 0.52119I 10.28438 + 0.91978I
u = −0.779818 + 0.432918I
a = −0.42623 + 1.61459I
b = 0.043388 + 0.215741I
−4.54874 + 0.68759I 4.54360 + 0.75970I
u = −0.779818 + 0.432918I
a = 2.73004 − 0.74211I
b = −0.014553 − 1.091010I
−4.54874 + 0.68759I 4.54360 + 0.75970I
u = −0.779818 − 0.432918I
a = −0.42623 − 1.61459I
b = 0.043388 − 0.215741I
−4.54874 − 0.68759I 4.54360 − 0.75970I
u = −0.779818 − 0.432918I
a = 2.73004 + 0.74211I
b = −0.014553 + 1.091010I
−4.54874 − 0.68759I 4.54360 − 0.75970I
u = −0.968267 + 0.542322I
a = −0.17528 − 1.48716I
b = −0.051937 + 1.220780I
−3.68787 − 4.72692I 5.63267 + 6.05913I
u = −0.968267 + 0.542322I
a = −1.45149 − 0.86027I
b = −0.338370 − 0.740909I
−3.68787 − 4.72692I 5.63267 + 6.05913I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.968267 − 0.542322I
a = −0.17528 + 1.48716I
b = −0.051937 − 1.220780I
−3.68787 + 4.72692I 5.63267 − 6.05913I
u = −0.968267 − 0.542322I
a = −1.45149 + 0.86027I
b = −0.338370 + 0.740909I
−3.68787 + 4.72692I 5.63267 − 6.05913I
u = −0.360998 + 0.803267I
a = 0.546303 + 0.788949I
b = 0.843917 + 0.082387I
−2.68067 + 2.86826I 5.22261 − 1.95241I
u = −0.360998 + 0.803267I
a = 0.216150 + 0.304597I
b = −0.379813 − 1.278460I
−2.68067 + 2.86826I 5.22261 − 1.95241I
u = −0.360998 − 0.803267I
a = 0.546303 − 0.788949I
b = 0.843917 − 0.082387I
−2.68067 − 2.86826I 5.22261 + 1.95241I
u = −0.360998 − 0.803267I
a = 0.216150 − 0.304597I
b = −0.379813 + 1.278460I
−2.68067 − 2.86826I 5.22261 + 1.95241I
u = 0.603619 + 0.975261I
a = 0.539104 − 0.656174I
b = 1.074420 − 0.024887I
−4.97042 − 7.12390I 2.15087 + 6.13601I
u = 0.603619 + 0.975261I
a = 0.142310 − 0.265040I
b = −0.52253 + 1.37829I
−4.97042 − 7.12390I 2.15087 + 6.13601I
u = 0.603619 − 0.975261I
a = 0.539104 + 0.656174I
b = 1.074420 + 0.024887I
−4.97042 + 7.12390I 2.15087 − 6.13601I
u = 0.603619 − 0.975261I
a = 0.142310 + 0.265040I
b = −0.52253 − 1.37829I
−4.97042 + 7.12390I 2.15087 − 6.13601I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.151618 + 0.823207I
a = 0.293631 + 1.015830I
b = 0.361538 + 0.026553I
−2.21633 + 2.17702I 6.16670 − 4.43587I
u = 0.151618 + 0.823207I
a = 0.314260 + 0.523562I
b = −0.173897 − 1.060920I
−2.21633 + 2.17702I 6.16670 − 4.43587I
u = 0.151618 − 0.823207I
a = 0.293631 − 1.015830I
b = 0.361538 − 0.026553I
−2.21633 − 2.17702I 6.16670 + 4.43587I
u = 0.151618 − 0.823207I
a = 0.314260 − 0.523562I
b = −0.173897 + 1.060920I
−2.21633 − 2.17702I 6.16670 + 4.43587I
u = 0.977999 + 0.696966I
a = 1.61826 − 0.26074I
b = 0.75429 + 1.35354I
−8.50566 + 6.90989I −1.24227 − 6.39245I
u = 0.977999 + 0.696966I
a = −0.127765 − 0.211953I
b = 0.48300 − 1.56700I
−8.50566 + 6.90989I −1.24227 − 6.39245I
u = 0.977999 − 0.696966I
a = 1.61826 + 0.26074I
b = 0.75429 − 1.35354I
−8.50566 − 6.90989I −1.24227 + 6.39245I
u = 0.977999 − 0.696966I
a = −0.127765 + 0.211953I
b = 0.48300 + 1.56700I
−8.50566 − 6.90989I −1.24227 + 6.39245I
u = 1.094140 + 0.530959I
a = −0.452032 − 0.389965I
b = −0.355050 + 0.041453I
0.43018 + 2.44717I 8.96365 − 1.04542I
u = 1.094140 + 0.530959I
a = 1.44357 − 0.11719I
b = 0.188082 + 1.024920I
0.43018 + 2.44717I 8.96365 − 1.04542I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.094140 − 0.530959I
a = −0.452032 + 0.389965I
b = −0.355050 − 0.041453I
0.43018 − 2.44717I 8.96365 + 1.04542I
u = 1.094140 − 0.530959I
a = 1.44357 + 0.11719I
b = 0.188082 − 1.024920I
0.43018 − 2.44717I 8.96365 + 1.04542I
u = 1.221120 + 0.063847I
a = 1.125980 − 0.196059I
b = 0.593163 + 0.475031I
2.92122 − 0.22925I 9.84725 − 0.24543I
u = 1.221120 + 0.063847I
a = −0.471814 + 0.677278I
b = −0.495029 + 0.827389I
2.92122 − 0.22925I 9.84725 − 0.24543I
u = 1.221120 − 0.063847I
a = 1.125980 + 0.196059I
b = 0.593163 − 0.475031I
2.92122 + 0.22925I 9.84725 + 0.24543I
u = 1.221120 − 0.063847I
a = −0.471814 − 0.677278I
b = −0.495029 − 0.827389I
2.92122 + 0.22925I 9.84725 + 0.24543I
u = −1.226770 + 0.155149I
a = −0.981671 + 0.701822I
b = −0.583486 + 1.021390I
2.73470 − 5.56367I 9.18066 + 6.01609I
u = −1.226770 + 0.155149I
a = 1.261620 − 0.006116I
b = 0.810598 + 0.350769I
2.73470 − 5.56367I 9.18066 + 6.01609I
u = −1.226770 − 0.155149I
a = −0.981671 − 0.701822I
b = −0.583486 − 1.021390I
2.73470 + 5.56367I 9.18066 − 6.01609I
u = −1.226770 − 0.155149I
a = 1.261620 + 0.006116I
b = 0.810598 − 0.350769I
2.73470 + 5.56367I 9.18066 − 6.01609I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.098500 + 0.611090I
a = 1.183730 + 0.618523I
b = 1.122820 + 0.061689I
−0.58338 − 8.09252I 6.94350 + 6.08172I
u = −1.098500 + 0.611090I
a = −1.75069 − 0.00735I
b = −0.59867 + 1.36346I
−0.58338 − 8.09252I 6.94350 + 6.08172I
u = −1.098500 − 0.611090I
a = 1.183730 − 0.618523I
b = 1.122820 − 0.061689I
−0.58338 + 8.09252I 6.94350 − 6.08172I
u = −1.098500 − 0.611090I
a = −1.75069 + 0.00735I
b = −0.59867 − 1.36346I
−0.58338 + 8.09252I 6.94350 − 6.08172I
u = −0.719231 + 0.070906I
a = 1.19660 − 0.78457I
b = 0.790261 − 0.723503I
−4.03832 − 2.81821I 5.95524 + 6.55211I
u = −0.719231 + 0.070906I
a = 0.326838 + 0.027869I
b = −0.00782 + 1.46891I
−4.03832 − 2.81821I 5.95524 + 6.55211I
u = −0.719231 − 0.070906I
a = 1.19660 + 0.78457I
b = 0.790261 + 0.723503I
−4.03832 + 2.81821I 5.95524 − 6.55211I
u = −0.719231 − 0.070906I
a = 0.326838 − 0.027869I
b = −0.00782 − 1.46891I
−4.03832 + 2.81821I 5.95524 − 6.55211I
u = −1.114950 + 0.686791I
a = −0.724507 + 0.285455I
b = −0.501222 + 0.106408I
−2.08664 − 7.65538I 6.00000 + 4.86252I
u = −1.114950 + 0.686791I
a = 1.44363 + 0.43879I
b = 0.213807 − 1.140070I
−2.08664 − 7.65538I 6.00000 + 4.86252I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.114950 − 0.686791I
a = −0.724507 − 0.285455I
b = −0.501222 − 0.106408I
−2.08664 + 7.65538I 6.00000 − 4.86252I
u = −1.114950 − 0.686791I
a = 1.44363 − 0.43879I
b = 0.213807 + 1.140070I
−2.08664 + 7.65538I 6.00000 − 4.86252I
u = 1.116090 + 0.737773I
a = 1.021870 − 0.676642I
b = 1.219170 − 0.027895I
−3.34357 + 13.38520I 3.57925 − 9.35928I
u = 1.116090 + 0.737773I
a = −1.65187 + 0.26409I
b = −0.62712 − 1.44018I
−3.34357 + 13.38520I 3.57925 − 9.35928I
u = 1.116090 − 0.737773I
a = 1.021870 + 0.676642I
b = 1.219170 + 0.027895I
−3.34357 − 13.38520I 3.57925 + 9.35928I
u = 1.116090 − 0.737773I
a = −1.65187 − 0.26409I
b = −0.62712 + 1.44018I
−3.34357 − 13.38520I 3.57925 + 9.35928I
u = −0.341463 + 0.518277I
a = −4.34533 + 6.66745I
b = 0.049617 + 0.912810I
−5.04535 + 0.68997I −0.176606 + 0.164918I
u = −0.341463 + 0.518277I
a = 10.66650 + 3.71569I
b = 0.030298 − 1.072820I
−5.04535 + 0.68997I −0.176606 + 0.164918I
u = −0.341463 − 0.518277I
a = −4.34533 − 6.66745I
b = 0.049617 − 0.912810I
−5.04535 − 0.68997I −0.176606 − 0.164918I
u = −0.341463 − 0.518277I
a = 10.66650 − 3.71569I
b = 0.030298 + 1.072820I
−5.04535 − 0.68997I −0.176606 − 0.164918I
20
III. I
u
3
= hb + 1, 2u
5
− 4u
3
− 2u
2
+ 2a + 4u + 3, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
12
=
−u
5
+ 2u
3
+ u
2
− 2u −
3
2
−1
a
6
=
−
1
4
u
2
+
1
2
1
2
u
2
a
11
=
−u
5
+ 2u
3
+ u
2
− 2u −
1
2
−1
a
9
=
−u
5
+ 2u
3
+ u
2
− 2u +
1
2
−1
a
5
=
−u
2
+ 1
u
2
a
2
=
−u
4
+ u
2
− 1
u
5
+ u
4
− 2u
3
− u
2
+ u + 1
a
10
=
−u
5
+ 2u
3
+ u
2
− 2u −
1
2
−1
a
1
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
5
+
15
4
u
4
− 4u
3
− 8u
2
+ 4u + 14
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
64(64u
6
+ 96u
5
+ 80u
4
+ 32u
3
+ 8u
2
+ 2u + 1)
c
6
64(64u
6
− 96u
5
+ 80u
4
− 32u
3
+ 8u
2
− 2u + 1)
c
8
, c
9
(u + 1)
6
c
10
u
6
c
11
, c
12
(u − 1)
6
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
7
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
5
, c
6
4096(4096y
6
+ 1024y
5
+ 1280y
4
+ 96y
2
+ 12y + 1)
c
8
, c
9
, c
11
c
12
(y − 1)
6
c
10
y
6
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −1.269410 + 0.497010I
b = −1.00000
3.53554 + 0.92430I 10.21433 + 1.99338I
u = 1.002190 − 0.295542I
a = −1.269410 − 0.497010I
b = −1.00000
3.53554 − 0.92430I 10.21433 − 1.99338I
u = −0.428243 + 0.664531I
a = 0.16103 − 1.45708I
b = −1.00000
−0.245672 + 0.924305I 11.09213 + 6.83768I
u = −0.428243 − 0.664531I
a = 0.16103 + 1.45708I
b = −1.00000
−0.245672 − 0.924305I 11.09213 − 6.83768I
u = −1.073950 + 0.558752I
a = −0.891622 − 0.558752I
b = −1.00000
1.64493 − 5.69302I 8.81854 + 4.26477I
u = −1.073950 − 0.558752I
a = −0.891622 + 0.558752I
b = −1.00000
1.64493 + 5.69302I 8.81854 − 4.26477I
24
IV. I
v
1
= ha, −20v
2
+ 13b + 69v − 1, 4v
3
− 13v
2
− v − 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
7
=
1
0
a
3
=
v
0
a
12
=
0
20
13
v
2
−
69
13
v +
1
13
a
6
=
1
12
13
v
2
−
31
13
v −
28
13
a
11
=
−
20
13
v
2
+
69
13
v −
1
13
20
13
v
2
−
69
13
v +
1
13
a
9
=
12
13
v
2
−
31
13
v −
15
13
−
12
13
v
2
+
31
13
v +
28
13
a
5
=
−
20
13
v
2
+
69
13
v −
1
13
4v
2
− 13v − 1
a
2
=
20
13
v
2
−
56
13
v +
1
13
−4v
2
+ 13v + 1
a
10
=
1
−
8
13
v
2
+
38
13
v −
42
13
a
1
=
20
13
v
2
−
69
13
v +
1
13
−4v
2
+ 13v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
7
13
v
2
−
69
13
v +
118
13
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
8
c
9
u
3
+ 2u + 1
c
10
u
3
− 3u
2
+ 5u − 2
c
11
, c
12
u
3
+ 2u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
8
c
9
, c
11
, c
12
y
3
+ 4y
2
+ 4y − 1
c
10
y
3
+ y
2
+ 13y − 4
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.048505 + 0.268962I
a = 0
b = 0.22670 − 1.46771I
−11.08570 − 5.13794I 9.29669 − 1.44162I
v = −0.048505 − 0.268962I
a = 0
b = 0.22670 + 1.46771I
−11.08570 + 5.13794I 9.29669 + 1.44162I
v = 3.34701
a = 0
b = −0.453398
−0.857735 −2.65590
28
V. I
v
2
= ha, b
2
− bv − b + v + 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
7
=
1
0
a
3
=
v
0
a
12
=
0
b
a
6
=
1
bv + b − v − 1
a
11
=
−b
b
a
9
=
bv + b − v
−bv − b + v + 1
a
5
=
bv + v + 2
−v − 1
a
2
=
−bv − 2
v + 1
a
10
=
−b + v
1
a
1
=
−bv − v − 2
v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 3
29
(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
, c
8
c
9
u
4
− u
3
+ 2u
2
− 2u + 1
c
10
(u
2
+ u + 1)
2
c
11
, c
12
u
4
+ u
3
+ 2u
2
+ 2u + 1
30
(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
, c
8
c
9
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
10
(y
2
+ y + 1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.621744 − 0.440597I
−4.93480 − 2.02988I 1.0000 + 3.46410I
v = −0.500000 + 0.866025I
a = 0
b = −0.121744 + 1.306620I
−4.93480 − 2.02988I 1.0000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 0.621744 + 0.440597I
−4.93480 + 2.02988I 1.0000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −0.121744 − 1.306620I
−4.93480 + 2.02988I 1.0000 − 3.46410I
32
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
7
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· ((u
40
+ 21u
39
+ ··· + 3u + 1)
2
)(u
48
+ 25u
47
+ ··· + 42145u + 256)
c
2
((u − 1)
7
)(u
6
+ u
5
+ ··· + u + 1)(u
40
− 3u
39
+ ··· − 3u + 1)
2
· (u
48
− 3u
47
+ ··· + 257u − 16)
c
3
u
7
(u
6
− u
5
+ ··· − u + 1)(u
40
− u
39
+ ··· + 8u + 4)
2
· (u
48
− 9u
46
+ ··· − 688u + 128)
c
4
((u + 1)
7
)(u
6
− u
5
+ ··· − u + 1)(u
40
− 3u
39
+ ··· − 3u + 1)
2
· (u
48
− 3u
47
+ ··· + 257u − 16)
c
5
4096(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (64u
6
+ 96u
5
+ 80u
4
+ 32u
3
+ 8u
2
+ 2u + 1)
· (64u
48
− 96u
47
+ ··· − 2u − 1)
· (u
80
+ 2u
79
+ ··· + 418062244u + 41568281)
c
6
4096(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (64u
6
− 96u
5
+ 80u
4
− 32u
3
+ 8u
2
− 2u + 1)
· (64u
48
− 96u
47
+ ··· − 2u − 1)
· (u
80
+ 2u
79
+ ··· + 418062244u + 41568281)
c
7
u
7
(u
6
+ u
5
+ ··· + u + 1)(u
40
− u
39
+ ··· + 8u + 4)
2
· (u
48
− 9u
46
+ ··· − 688u + 128)
c
8
, c
9
((u + 1)
6
)(u
3
+ 2u + 1)(u
4
− u
3
+ ··· − 2u + 1)(u
48
− 6u
47
+ ··· + 8u + 1)
· (u
80
+ 14u
79
+ ··· + 4u + 1)
c
10
u
6
(u
2
+ u + 1)
2
(u
3
− 3u
2
+ 5u − 2)(u
40
− 2u
39
+ ··· + 4u
2
+ 1)
2
· (u
48
+ 6u
47
+ ··· − 61440u − 16384)
c
11
, c
12
((u − 1)
6
)(u
3
+ 2u − 1)(u
4
+ u
3
+ ··· + 2u + 1)(u
48
− 6u
47
+ ··· + 8u + 1)
· (u
80
+ 14u
79
+ ··· + 4u + 1)
33
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
7
)(y
6
+ y
5
+ ··· + 3y + 1)(y
40
− y
39
+ ··· + 17y + 1)
2
· (y
48
− y
47
+ ··· − 1631257409y + 65536)
c
2
, c
4
(y − 1)
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· ((y
40
− 21y
39
+ ··· − 3y + 1)
2
)(y
48
− 25y
47
+ ··· − 42145y + 256)
c
3
, c
7
y
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
40
− 15y
39
+ ··· − 120y + 16)
2
· (y
48
− 18y
47
+ ··· − 312576y + 16384)
c
5
, c
6
16777216(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (4096y
6
+ 1024y
5
+ 1280y
4
+ 96y
2
+ 12y + 1)
· (4096y
48
+ 82944y
47
+ ··· + 10y + 1)
· (y
80
+ 42y
79
+ ··· + 5456149534708088y + 1727921985294961)
c
8
, c
9
, c
11
c
12
(y − 1)
6
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
48
+ 26y
47
+ ··· − 20y + 1)(y
80
+ 54y
79
+ ··· − 32y
2
+ 1)
c
10
y
6
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y − 4)(y
40
+ 14y
39
+ ··· + 8y + 1)
2
· (y
48
+ 14y
47
+ ··· + 6325010432y + 268435456)
34
