12a
0799
(K12a
0799
)
A knot diagram
1
Linearized knot diagam
3 8 11 1 12 9 2 7 5 4 6 10
Solving Sequence
1,5 4,10
11 3 2 9 12 6 7 8
c
4
c
10
c
3
c
1
c
9
c
12
c
5
c
6
c
8
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −4.30859 × 10
43
u
34
− 5.23230 × 10
43
u
33
+ ··· + 2.27410 × 10
43
a + 1.99881 × 10
44
,
u
35
+ u
34
+ ··· − 2u − 1i
I
u
2
= h1.34503 × 10
309
u
71
+ 4.07190 × 10
309
u
70
+ ··· + 3.30547 × 10
309
b + 2.52151 × 10
310
,
− 2.10209 × 10
240
u
71
− 6.36722 × 10
240
u
70
+ ··· + 3.89663 × 10
240
a − 1.36055 × 10
242
,
u
72
+ 3u
71
+ ··· + 48u + 1i
I
u
3
= hb + u, −886u
19
− 1725u
18
+ ··· + 2249a + 1906, u
20
+ u
19
+ ··· − 2u + 1i
* 3 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
= hb − u, −4.31 × 10
43
u
34
− 5.23 × 10
43
u
33
+ · · · + 2.27 × 10
43
a +
2.00 × 10
44
, u
35
+ u
34
+ · · · − 2u − 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
10
=
1.89464u
34
+ 2.30083u
33
+ ··· − 29.6286u − 8.78949
u
a
11
=
1.95202u
34
+ 2.28719u
33
+ ··· − 25.9216u − 8.38330
0.0586830u
34
+ 0.0132193u
33
+ ··· + 1.08465u + 0.0710140
a
3
=
1.63631u
34
+ 1.06267u
33
+ ··· − 17.1111u + 4.79896
−0.136168u
34
− 0.222641u
33
+ ··· + 0.865605u + 0.173572
a
2
=
0.267879u
34
+ 1.37848u
33
+ ··· − 3.97515u − 10.7436
−0.167035u
34
− 0.151989u
33
+ ··· + 3.05890u + 0.326704
a
9
=
1.89464u
34
+ 2.30083u
33
+ ··· − 28.6286u − 8.78949
u
a
12
=
2.30439u
34
+ 3.64678u
33
+ ··· − 19.4192u − 18.0743
0.0573800u
34
− 0.0136340u
33
+ ··· + 3.70702u + 0.406189
a
6
=
−4.47995u
34
− 3.38545u
33
+ ··· + 40.8417u + 3.13769
0.112272u
34
+ 0.228464u
33
+ ··· − 1.35463u + 0.400070
a
7
=
0.207182u
34
+ 0.352338u
33
+ ··· − 1.38655u + 0.769048
0.136168u
34
+ 0.222641u
33
+ ··· − 0.865605u − 0.173572
a
8
=
1.04114u
34
+ 1.50676u
33
+ ··· − 16.4681u − 6.55811
−0.167035u
34
− 0.151989u
33
+ ··· + 3.05890u + 0.326704
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8.40302u
34
− 4.98573u
33
+ ··· + 50.7095u − 6.32050
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
35
+ 9u
34
+ ··· + 16u + 64
c
2
, c
7
u
35
+ 7u
34
+ ··· + 20u + 8
c
3
, c
5
, c
10
c
11
u
35
+ 10u
33
+ ··· + 3u + 1
c
4
, c
9
u
35
− u
34
+ ··· − 2u + 1
c
12
u
35
− 27u
34
+ ··· + 73728u − 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
35
+ 35y
34
+ ··· + 34048y −4096
c
2
, c
7
y
35
− 9y
34
+ ··· + 16y −64
c
3
, c
5
, c
10
c
11
y
35
+ 20y
34
+ ··· + y −1
c
4
, c
9
y
35
+ 15y
34
+ ··· − 34y −1
c
12
y
35
− 11y
34
+ ··· + 125829120y −16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591089 + 0.775481I
a = −0.687556 + 0.152845I
b = 0.591089 + 0.775481I
1.33872 − 3.31510I 0.58501 + 5.76749I
u = 0.591089 − 0.775481I
a = −0.687556 − 0.152845I
b = 0.591089 − 0.775481I
1.33872 + 3.31510I 0.58501 − 5.76749I
u = −0.597092 + 0.966307I
a = 1.29984 + 0.98350I
b = −0.597092 + 0.966307I
−3.80954 − 0.35655I −7.72758 − 2.31082I
u = −0.597092 − 0.966307I
a = 1.29984 − 0.98350I
b = −0.597092 − 0.966307I
−3.80954 + 0.35655I −7.72758 + 2.31082I
u = −0.274359 + 0.767854I
a = 0.872835 + 0.188368I
b = −0.274359 + 0.767854I
2.17204 − 0.64743I 3.30372 + 2.66194I
u = −0.274359 − 0.767854I
a = 0.872835 − 0.188368I
b = −0.274359 − 0.767854I
2.17204 + 0.64743I 3.30372 − 2.66194I
u = −0.413251 + 1.183840I
a = 0.674185 + 0.327128I
b = −0.413251 + 1.183840I
9.66329 − 0.96587I 3.05582 + 0.39367I
u = −0.413251 − 1.183840I
a = 0.674185 − 0.327128I
b = −0.413251 − 1.183840I
9.66329 + 0.96587I 3.05582 − 0.39367I
u = 0.419219 + 0.615155I
a = 1.22242 + 1.49117I
b = 0.419219 + 0.615155I
5.07676 − 3.71447I −0.77708 + 4.68220I
u = 0.419219 − 0.615155I
a = 1.22242 − 1.49117I
b = 0.419219 − 0.615155I
5.07676 + 3.71447I −0.77708 − 4.68220I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.466745 + 0.574137I
a = −1.13727 + 1.70318I
b = −0.466745 + 0.574137I
4.38894 + 9.97061I −2.42520 − 9.73459I
u = −0.466745 − 0.574137I
a = −1.13727 − 1.70318I
b = −0.466745 − 0.574137I
4.38894 − 9.97061I −2.42520 + 9.73459I
u = 0.474572 + 1.194770I
a = −0.658032 + 0.313634I
b = 0.474572 + 1.194770I
9.55181 − 5.46707I 2.92000 + 4.74682I
u = 0.474572 − 1.194770I
a = −0.658032 − 0.313634I
b = 0.474572 − 1.194770I
9.55181 + 5.46707I 2.92000 − 4.74682I
u = 0.723524 + 1.111440I
a = −1.045310 + 0.708906I
b = 0.723524 + 1.111440I
−2.05608 − 5.08661I −4.00000 + 6.93227I
u = 0.723524 − 1.111440I
a = −1.045310 − 0.708906I
b = 0.723524 − 1.111440I
−2.05608 + 5.08661I −4.00000 − 6.93227I
u = −0.950167 + 0.965088I
a = 1.212470 + 0.335142I
b = −0.950167 + 0.965088I
−8.23917 + 6.19708I −11.53177 − 4.77423I
u = −0.950167 − 0.965088I
a = 1.212470 − 0.335142I
b = −0.950167 − 0.965088I
−8.23917 − 6.19708I −11.53177 + 4.77423I
u = 0.597400
a = −0.567434
b = 0.597400
−1.22075 −7.22590
u = 0.097938 + 0.514145I
a = 1.96245 + 0.19680I
b = 0.097938 + 0.514145I
0.44134 − 1.63347I 1.73800 + 4.33093I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.097938 − 0.514145I
a = 1.96245 − 0.19680I
b = 0.097938 − 0.514145I
0.44134 + 1.63347I 1.73800 − 4.33093I
u = −0.271525 + 0.415826I
a = −2.75306 + 1.67750I
b = −0.271525 + 0.415826I
−2.74916 + 4.77966I −3.72482 − 10.00221I
u = −0.271525 − 0.415826I
a = −2.75306 − 1.67750I
b = −0.271525 − 0.415826I
−2.74916 − 4.77966I −3.72482 + 10.00221I
u = 1.03004 + 1.11959I
a = −0.999328 + 0.306692I
b = 1.03004 + 1.11959I
−3.63302 − 8.69335I 0
u = 1.03004 − 1.11959I
a = −0.999328 − 0.306692I
b = 1.03004 − 1.11959I
−3.63302 + 8.69335I 0
u = 0.06773 + 1.55270I
a = −0.068133 + 0.960500I
b = 0.06773 + 1.55270I
8.19666 − 3.43452I 0
u = 0.06773 − 1.55270I
a = −0.068133 − 0.960500I
b = 0.06773 − 1.55270I
8.19666 + 3.43452I 0
u = −1.13426 + 1.07638I
a = 1.002730 + 0.193039I
b = −1.13426 + 1.07638I
−6.3568 + 12.9060I 0
u = −1.13426 − 1.07638I
a = 1.002730 − 0.193039I
b = −1.13426 − 1.07638I
−6.3568 − 12.9060I 0
u = −0.067600 + 0.311475I
a = −3.61790 − 2.90700I
b = −0.067600 + 0.311475I
−2.02184 − 1.48778I −5.29371 + 6.36546I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.067600 − 0.311475I
a = −3.61790 + 2.90700I
b = −0.067600 − 0.311475I
−2.02184 + 1.48778I −5.29371 − 6.36546I
u = 1.20419 + 1.21154I
a = −0.874512 + 0.183122I
b = 1.20419 + 1.21154I
2.43884 − 11.28800I 0
u = 1.20419 − 1.21154I
a = −0.874512 − 0.183122I
b = 1.20419 − 1.21154I
2.43884 + 11.28800I 0
u = −1.23200 + 1.19581I
a = 0.877886 + 0.159904I
b = −1.23200 + 1.19581I
1.8345 + 17.7184I 0
u = −1.23200 − 1.19581I
a = 0.877886 − 0.159904I
b = −1.23200 − 1.19581I
1.8345 − 17.7184I 0
8
II. I
u
2
= h1.35 × 10
309
u
71
+ 4.07 × 10
309
u
70
+ · · · + 3.31 × 10
309
b + 2.52 ×
10
310
, −2.10 × 10
240
u
71
− 6.37 × 10
240
u
70
+ · · · + 3.90 × 10
240
a − 1.36 ×
10
242
, u
72
+ 3u
71
+ · · · + 48u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
10
=
0.539465u
71
+ 1.63403u
70
+ ··· + 603.712u + 34.9160
−0.406910u
71
− 1.23187u
70
+ ··· − 242.608u − 7.62829
a
11
=
0.135898u
71
+ 0.410976u
70
+ ··· + 359.814u + 27.2721
−0.433293u
71
− 1.29628u
70
+ ··· − 243.604u − 7.64065
a
3
=
−5.47361u
71
− 15.9771u
70
+ ··· − 3245.98u − 92.7647
0.0926148u
71
+ 0.257322u
70
+ ··· + 41.1552u − 2.78210
a
2
=
−0.130468u
71
− 0.583660u
70
+ ··· − 769.572u − 70.4281
1.03009u
71
+ 3.02070u
70
+ ··· + 634.312u + 21.1555
a
9
=
0.132555u
71
+ 0.402165u
70
+ ··· + 361.104u + 27.2877
−0.406910u
71
− 1.23187u
70
+ ··· − 242.608u − 7.62829
a
12
=
−0.232683u
71
− 0.798062u
70
+ ··· − 461.851u − 26.5601
0.400276u
71
+ 1.09127u
70
+ ··· + 167.198u + 5.35353
a
6
=
4.24388u
71
+ 12.1560u
70
+ ··· + 1995.98u + 55.1998
−0.237755u
71
− 0.677729u
70
+ ··· − 47.8013u + 1.19648
a
7
=
7.24447u
71
+ 21.3193u
70
+ ··· + 4321.80u + 124.943
−0.396176u
71
− 1.16932u
70
+ ··· − 127.116u + 1.79571
a
8
=
0.727709u
71
+ 1.96306u
70
+ ··· − 275.156u − 53.7910
0.803345u
71
+ 2.34508u
70
+ ··· + 560.708u + 19.6459
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.619107u
71
− 1.70406u
70
+ ··· + 144.641u − 5.48872
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
(u
12
+ 3u
11
+ ··· + 2u + 1)
6
c
2
, c
7
(u
12
− u
11
− u
10
+ 2u
9
+ 3u
8
− 4u
7
− 2u
6
+ 4u
5
+ 2u
4
− 3u
3
− u
2
+ 1)
6
c
3
, c
5
, c
10
c
11
u
72
− u
71
+ ··· + 13014u + 2943
c
4
, c
9
u
72
− 3u
71
+ ··· − 48u + 1
c
12
(u
3
+ u
2
− 1)
24
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
(y
12
+ 13y
11
+ ··· + 6y + 1)
6
c
2
, c
7
(y
12
− 3y
11
+ ··· − 2y + 1)
6
c
3
, c
5
, c
10
c
11
y
72
+ 51y
71
+ ··· + 376303320y + 8661249
c
4
, c
9
y
72
− 17y
71
+ ··· − 552y + 1
c
12
(y
3
− y
2
+ 2y −1)
24
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.568176 + 0.839836I
a = −1.093330 − 0.305104I
b = 1.23118 − 1.38930I
6.00451 + 4.31046I 0
u = −0.568176 − 0.839836I
a = −1.093330 + 0.305104I
b = 1.23118 + 1.38930I
6.00451 − 4.31046I 0
u = 0.891554 + 0.489577I
a = 1.108640 + 0.226678I
b = −1.30602 − 0.59539I
−3.34798 − 2.47502I 0
u = 0.891554 − 0.489577I
a = 1.108640 − 0.226678I
b = −1.30602 + 0.59539I
−3.34798 + 2.47502I 0
u = 0.701909 + 0.683885I
a = 1.171710 − 0.080430I
b = −1.28434 − 1.06706I
−1.98742 − 7.07733I 0
u = 0.701909 − 0.683885I
a = 1.171710 + 0.080430I
b = −1.28434 + 1.06706I
−1.98742 + 7.07733I 0
u = 0.977106 + 0.046716I
a = 0.859586 − 0.803411I
b = −0.875721 + 0.368859I
−3.34798 + 3.18123I 0
u = 0.977106 − 0.046716I
a = 0.859586 + 0.803411I
b = −0.875721 − 0.368859I
−3.34798 − 3.18123I 0
u = 0.604256 + 0.853075I
a = 1.066580 − 0.273076I
b = −1.29161 − 1.38021I
5.64748 − 10.62950I 0
u = 0.604256 − 0.853075I
a = 1.066580 + 0.273076I
b = −1.29161 + 1.38021I
5.64748 + 10.62950I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509449 + 0.806111I
a = 1.151870 − 0.360525I
b = −0.302346 − 0.194987I
−0.17094 − 2.11219I 0
u = 0.509449 − 0.806111I
a = 1.151870 + 0.360525I
b = −0.302346 + 0.194987I
−0.17094 + 2.11219I 0
u = −0.875721 + 0.368859I
a = −1.155270 + 0.363964I
b = 0.977106 + 0.046716I
−3.34798 + 3.18123I 0
u = −0.875721 − 0.368859I
a = −1.155270 − 0.363964I
b = 0.977106 − 0.046716I
−3.34798 − 3.18123I 0
u = −0.904826 + 0.206753I
a = 0.792882 + 0.181173I
b = −1.32231 − 1.27743I
−6.12500 + 4.24921I −13.1960 − 6.9831I
u = −0.904826 − 0.206753I
a = 0.792882 − 0.181173I
b = −1.32231 + 1.27743I
−6.12500 − 4.24921I −13.1960 + 6.9831I
u = 1.013100 + 0.432835I
a = −0.630105 + 0.269206I
b = 1.22185 − 0.91863I
−4.30852 − 0.71593I 0
u = 1.013100 − 0.432835I
a = −0.630105 − 0.269206I
b = 1.22185 + 0.91863I
−4.30852 + 0.71593I 0
u = −1.102800 + 0.079429I
a = 0.680979 + 0.049047I
b = −1.75324 − 1.20623I
1.50990 + 7.80134I 0
u = −1.102800 − 0.079429I
a = 0.680979 − 0.049047I
b = −1.75324 + 1.20623I
1.50990 − 7.80134I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.062360 + 0.384623I
a = −0.954650 + 0.355513I
b = 1.52012 − 0.07163I
2.12951 + 5.84119I 0
u = −1.062360 − 0.384623I
a = −0.954650 − 0.355513I
b = 1.52012 + 0.07163I
2.12951 − 5.84119I 0
u = 1.131690 + 0.108519I
a = −0.660959 + 0.063380I
b = 1.74780 − 1.12060I
1.86693 − 1.48234I 0
u = 1.131690 − 0.108519I
a = −0.660959 − 0.063380I
b = 1.74780 + 1.12060I
1.86693 + 1.48234I 0
u = 1.064500 + 0.420736I
a = 0.952102 + 0.323418I
b = −1.55590 − 0.16376I
2.12951 + 0.18495I 0
u = 1.064500 − 0.420736I
a = 0.952102 − 0.323418I
b = −1.55590 + 0.16376I
2.12951 − 0.18495I 0
u = −0.566692 + 0.558756I
a = −1.44223 − 0.10763I
b = 1.00879 − 1.02877I
−0.17094 + 3.54405I −0.53377 − 3.62818I
u = −0.566692 − 0.558756I
a = −1.44223 + 0.10763I
b = 1.00879 + 1.02877I
−0.17094 − 3.54405I −0.53377 + 3.62818I
u = 0.171015 + 1.222870I
a = −0.499006 − 0.787307I
b = −0.313284 − 0.368426I
5.64748 − 4.97322I 0
u = 0.171015 − 1.222870I
a = −0.499006 + 0.787307I
b = −0.313284 + 0.368426I
5.64748 + 4.97322I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.073230 + 1.236080I
a = 0.558583 − 0.742946I
b = 0.246654 − 0.392628I
6.00451 − 1.34579I 0
u = −0.073230 − 1.236080I
a = 0.558583 + 0.742946I
b = 0.246654 + 0.392628I
6.00451 + 1.34579I 0
u = 0.266780 + 0.539724I
a = −0.46331 − 1.85473I
b = −0.331284 + 0.154458I
−1.98742 − 1.42109I −6.66674 + 4.00366I
u = 0.266780 − 0.539724I
a = −0.46331 + 1.85473I
b = −0.331284 − 0.154458I
−1.98742 + 1.42109I −6.66674 − 4.00366I
u = −0.453297 + 0.338937I
a = 1.068140 + 0.798660I
b = −0.62453 − 1.40533I
−7.48556 − 0.35310I −17.6864 + 0.6298I
u = −0.453297 − 0.338937I
a = 1.068140 − 0.798660I
b = −0.62453 + 1.40533I
−7.48556 + 0.35310I −17.6864 − 0.6298I
u = −1.30602 + 0.59539I
a = −0.771502 + 0.218617I
b = 0.891554 − 0.489577I
−3.34798 + 2.47502I 0
u = −1.30602 − 0.59539I
a = −0.771502 − 0.218617I
b = 0.891554 + 0.489577I
−3.34798 − 2.47502I 0
u = 1.00879 + 1.02877I
a = 0.795484 − 0.072863I
b = −0.566692 − 0.558756I
−0.17094 − 3.54405I 0
u = 1.00879 − 1.02877I
a = 0.795484 + 0.072863I
b = −0.566692 + 0.558756I
−0.17094 + 3.54405I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.313284 + 0.368426I
a = −0.00197 − 2.37991I
b = 0.171015 − 1.222870I
5.64748 + 4.97322I −2.12413 − 2.66036I
u = −0.313284 − 0.368426I
a = −0.00197 + 2.37991I
b = 0.171015 + 1.222870I
5.64748 − 4.97322I −2.12413 + 2.66036I
u = 1.52012 + 0.07163I
a = 0.598977 + 0.461776I
b = −1.062360 − 0.384623I
2.12951 − 5.84119I 0
u = 1.52012 − 0.07163I
a = 0.598977 − 0.461776I
b = −1.062360 + 0.384623I
2.12951 + 5.84119I 0
u = 1.22185 + 0.91863I
a = −0.394705 + 0.296753I
b = 1.013100 − 0.432835I
−4.30852 + 0.71593I 0
u = 1.22185 − 0.91863I
a = −0.394705 − 0.296753I
b = 1.013100 + 0.432835I
−4.30852 − 0.71593I 0
u = 0.246654 + 0.392628I
a = −0.35363 − 2.45694I
b = −0.073230 − 1.236080I
6.00451 + 1.34579I −1.33766 − 2.30403I
u = 0.246654 − 0.392628I
a = −0.35363 + 2.45694I
b = −0.073230 + 1.236080I
6.00451 − 1.34579I −1.33766 + 2.30403I
u = −0.62453 + 1.40533I
a = 0.199342 + 0.448567I
b = −0.453297 − 0.338937I
−7.48556 + 0.35310I 0
u = −0.62453 − 1.40533I
a = 0.199342 − 0.448567I
b = −0.453297 + 0.338937I
−7.48556 − 0.35310I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55590 + 0.16376I
a = −0.607599 + 0.414781I
b = 1.064500 − 0.420736I
2.12951 − 0.18495I 0
u = −1.55590 − 0.16376I
a = −0.607599 − 0.414781I
b = 1.064500 + 0.420736I
2.12951 + 0.18495I 0
u = −0.331284 + 0.154458I
a = −3.03677 + 0.83254I
b = 0.266780 + 0.539724I
−1.98742 − 1.42109I −6.66674 + 4.00366I
u = −0.331284 − 0.154458I
a = −3.03677 − 0.83254I
b = 0.266780 − 0.539724I
−1.98742 + 1.42109I −6.66674 − 4.00366I
u = −0.302346 + 0.194987I
a = −3.17175 + 0.41810I
b = 0.509449 − 0.806111I
−0.17094 + 2.11219I −0.53377 − 2.33071I
u = −0.302346 − 0.194987I
a = −3.17175 − 0.41810I
b = 0.509449 + 0.806111I
−0.17094 − 2.11219I −0.53377 + 2.33071I
u = −1.28434 + 1.06706I
a = −0.689254 + 0.007309I
b = 0.701909 − 0.683885I
−1.98742 + 7.07733I 0
u = −1.28434 − 1.06706I
a = −0.689254 − 0.007309I
b = 0.701909 + 0.683885I
−1.98742 − 7.07733I 0
u = −1.32231 + 1.27743I
a = 0.295292 + 0.285269I
b = −0.904826 − 0.206753I
−6.12500 − 4.24921I 0
u = −1.32231 − 1.27743I
a = 0.295292 − 0.285269I
b = −0.904826 + 0.206753I
−6.12500 + 4.24921I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.23118 + 1.38930I
a = 0.613796 − 0.087629I
b = −0.568176 − 0.839836I
6.00451 − 4.31046I 0
u = 1.23118 − 1.38930I
a = 0.613796 + 0.087629I
b = −0.568176 + 0.839836I
6.00451 + 4.31046I 0
u = −1.29161 + 1.38021I
a = −0.604880 − 0.069680I
b = 0.604256 − 0.853075I
5.64748 + 10.62950I 0
u = −1.29161 − 1.38021I
a = −0.604880 + 0.069680I
b = 0.604256 + 0.853075I
5.64748 − 10.62950I 0
u = −0.0431717 + 0.0210889I
a = 14.1169 + 6.8959I
b = −0.07263 − 1.98324I
−2.00808 − 3.01307I −11.65126 + 2.63251I
u = −0.0431717 − 0.0210889I
a = 14.1169 − 6.8959I
b = −0.07263 + 1.98324I
−2.00808 + 3.01307I −11.65126 − 2.63251I
u = −0.07263 + 1.98324I
a = 0.013921 + 0.380119I
b = −0.0431717 − 0.0210889I
−2.00808 + 3.01307I 0
u = −0.07263 − 1.98324I
a = 0.013921 − 0.380119I
b = −0.0431717 + 0.0210889I
−2.00808 − 3.01307I 0
u = 1.74780 + 1.12060I
a = −0.306081 + 0.196243I
b = 1.131690 − 0.108519I
1.86693 + 1.48234I 0
u = 1.74780 − 1.12060I
a = −0.306081 − 0.196243I
b = 1.131690 + 0.108519I
1.86693 − 1.48234I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.75324 + 1.20623I
a = 0.292233 + 0.201057I
b = −1.102800 − 0.079429I
1.50990 − 7.80134I 0
u = −1.75324 − 1.20623I
a = 0.292233 − 0.201057I
b = −1.102800 + 0.079429I
1.50990 + 7.80134I 0
19
III.
I
u
3
= hb + u, −886u
19
− 1725u
18
+ · · · + 2249a + 1906, u
20
+ u
19
+ · · · − 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
10
=
0.393953u
19
+ 0.767008u
18
+ ··· + 2.40907u − 0.847488
−u
a
11
=
1.15918u
19
+ 2.42730u
18
+ ··· + 1.76123u − 1.22054
−0.650067u
19
− 1.04669u
18
+ ··· − 2.02490u + 0.895064
a
3
=
1.10494u
19
+ 1.45487u
18
+ ··· + 2.84260u − 0.234771
−0.498444u
19
− 0.910627u
18
+ ··· − 0.752334u + 0.115162
a
2
=
−0.292574u
19
+ 0.197866u
18
+ ··· − 1.56114u + 2.34949
0.00489106u
19
− 0.576256u
18
+ ··· + 2.49266u − 0.638061
a
9
=
0.393953u
19
+ 0.767008u
18
+ ··· + 1.40907u − 0.847488
−u
a
12
=
1.39395u
19
+ 3.76701u
18
+ ··· − 0.590929u + 1.15251
−0.765229u
19
− 1.66029u
18
+ ··· + 0.647843u + 0.373055
a
6
=
−0.847488u
19
− 1.24144u
18
+ ··· − 1.72877u + 0.285905
0.895064u
19
+ 1.54513u
18
+ ··· + 1.15740u + 0.234771
a
7
=
−0.396621u
19
− 0.634504u
18
+ ··· − 0.405069u − 0.349933
0.498444u
19
+ 0.910627u
18
+ ··· + 0.752334u − 0.115162
a
8
=
0.211650u
19
+ 0.154735u
18
+ ··· + 2.68253u − 1.33793
−0.00489106u
19
+ 0.576256u
18
+ ··· − 2.49266u + 0.638061
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16424
2249
u
19
+
35896
2249
u
18
+ ··· +
2352
2249
u −
32819
2249
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
20
− 6u
19
+ ··· − 11u + 1
c
2
u
20
− 3u
18
+ ··· − u + 1
c
3
, c
11
u
20
+ 10u
18
+ ··· − u + 1
c
4
, c
9
u
20
+ u
19
+ ··· − 2u + 1
c
5
, c
10
u
20
+ 10u
18
+ ··· + u + 1
c
7
u
20
− 3u
18
+ ··· + u + 1
c
8
u
20
+ 6u
19
+ ··· + 11u + 1
c
12
u
20
+ 8u
19
+ ··· − 6u
2
+ 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
20
+ 22y
19
+ ··· + 5y + 1
c
2
, c
7
y
20
− 6y
19
+ ··· − 11y + 1
c
3
, c
5
, c
10
c
11
y
20
+ 20y
19
+ ··· + 19y + 1
c
4
, c
9
y
20
− y
19
+ ··· + 2y + 1
c
12
y
20
− 10y
19
+ ··· − 12y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.803742 + 0.640038I
a = −1.312270 − 0.216838I
b = 0.803742 − 0.640038I
−0.80556 + 3.51175I −5.16057 − 6.47153I
u = −0.803742 − 0.640038I
a = −1.312270 + 0.216838I
b = 0.803742 + 0.640038I
−0.80556 − 3.51175I −5.16057 + 6.47153I
u = 0.109977 + 0.933392I
a = −0.202191 + 0.691646I
b = −0.109977 − 0.933392I
−6.93544 − 0.76917I −4.93268 + 9.83438I
u = 0.109977 − 0.933392I
a = −0.202191 − 0.691646I
b = −0.109977 + 0.933392I
−6.93544 + 0.76917I −4.93268 − 9.83438I
u = 0.025092 + 1.157510I
a = −0.023307 + 0.429548I
b = −0.025092 − 1.157510I
−1.20551 − 3.04014I 0.81171 + 2.97210I
u = 0.025092 − 1.157510I
a = −0.023307 − 0.429548I
b = −0.025092 + 1.157510I
−1.20551 + 3.04014I 0.81171 − 2.97210I
u = 0.838930 + 0.068318I
a = 0.82153 + 1.21370I
b = −0.838930 − 0.068318I
−3.71829 − 4.43650I −12.2519 + 8.7425I
u = 0.838930 − 0.068318I
a = 0.82153 − 1.21370I
b = −0.838930 + 0.068318I
−3.71829 + 4.43650I −12.2519 − 8.7425I
u = −1.130550 + 0.326356I
a = −0.801063 + 0.358429I
b = 1.130550 − 0.326356I
−2.11436 + 2.39551I −2.32396 − 1.51464I
u = −1.130550 − 0.326356I
a = −0.801063 − 0.358429I
b = 1.130550 + 0.326356I
−2.11436 − 2.39551I −2.32396 + 1.51464I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.186100 + 0.148412I
a = 0.238472 − 0.592250I
b = −1.186100 − 0.148412I
3.07275 + 8.15795I −2.68462 − 7.66785I
u = 1.186100 − 0.148412I
a = 0.238472 + 0.592250I
b = −1.186100 + 0.148412I
3.07275 − 8.15795I −2.68462 + 7.66785I
u = −1.231270 + 0.086350I
a = −0.309856 − 0.538687I
b = 1.231270 − 0.086350I
3.39949 − 1.94064I −1.75418 + 2.97120I
u = −1.231270 − 0.086350I
a = −0.309856 + 0.538687I
b = 1.231270 + 0.086350I
3.39949 + 1.94064I −1.75418 − 2.97120I
u = 0.506464 + 0.461594I
a = 2.66341 − 0.41964I
b = −0.506464 − 0.461594I
−2.11393 + 0.95837I −7.35023 + 6.82243I
u = 0.506464 − 0.461594I
a = 2.66341 + 0.41964I
b = −0.506464 + 0.461594I
−2.11393 − 0.95837I −7.35023 − 6.82243I
u = 0.077140 + 0.632787I
a = −0.49697 + 1.73221I
b = −0.077140 − 0.632787I
−4.80805 + 2.38684I −9.41924 − 2.88689I
u = 0.077140 − 0.632787I
a = −0.49697 − 1.73221I
b = −0.077140 + 0.632787I
−4.80805 − 2.38684I −9.41924 + 2.88689I
u = −0.078140 + 1.399020I
a = −0.077754 − 0.975047I
b = 0.078140 − 1.399020I
8.64916 + 3.38003I 6.56566 − 1.45355I
u = −0.078140 − 1.399020I
a = −0.077754 + 0.975047I
b = 0.078140 + 1.399020I
8.64916 − 3.38003I 6.56566 + 1.45355I
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
((u
12
+ 3u
11
+ ··· + 2u + 1)
6
)(u
20
− 6u
19
+ ··· − 11u + 1)
· (u
35
+ 9u
34
+ ··· + 16u + 64)
c
2
(u
12
− u
11
− u
10
+ 2u
9
+ 3u
8
− 4u
7
− 2u
6
+ 4u
5
+ 2u
4
− 3u
3
− u
2
+ 1)
6
· (u
20
− 3u
18
+ ··· − u + 1)(u
35
+ 7u
34
+ ··· + 20u + 8)
c
3
, c
11
(u
20
+ 10u
18
+ ··· − u + 1)(u
35
+ 10u
33
+ ··· + 3u + 1)
· (u
72
− u
71
+ ··· + 13014u + 2943)
c
4
, c
9
(u
20
+ u
19
+ ··· − 2u + 1)(u
35
− u
34
+ ··· − 2u + 1)
· (u
72
− 3u
71
+ ··· − 48u + 1)
c
5
, c
10
(u
20
+ 10u
18
+ ··· + u + 1)(u
35
+ 10u
33
+ ··· + 3u + 1)
· (u
72
− u
71
+ ··· + 13014u + 2943)
c
7
(u
12
− u
11
− u
10
+ 2u
9
+ 3u
8
− 4u
7
− 2u
6
+ 4u
5
+ 2u
4
− 3u
3
− u
2
+ 1)
6
· (u
20
− 3u
18
+ ··· + u + 1)(u
35
+ 7u
34
+ ··· + 20u + 8)
c
8
((u
12
+ 3u
11
+ ··· + 2u + 1)
6
)(u
20
+ 6u
19
+ ··· + 11u + 1)
· (u
35
+ 9u
34
+ ··· + 16u + 64)
c
12
((u
3
+ u
2
− 1)
24
)(u
20
+ 8u
19
+ ··· − 6u
2
+ 1)
· (u
35
− 27u
34
+ ··· + 73728u − 4096)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
((y
12
+ 13y
11
+ ··· + 6y + 1)
6
)(y
20
+ 22y
19
+ ··· + 5y + 1)
· (y
35
+ 35y
34
+ ··· + 34048y −4096)
c
2
, c
7
((y
12
− 3y
11
+ ··· − 2y + 1)
6
)(y
20
− 6y
19
+ ··· − 11y + 1)
· (y
35
− 9y
34
+ ··· + 16y −64)
c
3
, c
5
, c
10
c
11
(y
20
+ 20y
19
+ ··· + 19y + 1)(y
35
+ 20y
34
+ ··· + y −1)
· (y
72
+ 51y
71
+ ··· + 376303320y + 8661249)
c
4
, c
9
(y
20
− y
19
+ ··· + 2y + 1)(y
35
+ 15y
34
+ ··· − 34y −1)
· (y
72
− 17y
71
+ ··· − 552y + 1)
c
12
((y
3
− y
2
+ 2y −1)
24
)(y
20
− 10y
19
+ ··· − 12y + 1)
· (y
35
− 11y
34
+ ··· + 125829120y −16777216)
26
