12n
0140
(K12n
0140
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 9 3 11 1 6 8 10
Solving Sequence
8,11
9
3,12
7 6 5 2 1 10 4
c
8
c
11
c
7
c
6
c
5
c
2
c
1
c
9
c
4
c
3
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−219034042585u
29
+ 477658347892u
28
+ ··· + 4962190966784b + 2219335787081,
− 1283291111693u
29
+ 4041034486657u
28
+ ··· + 2481095483392a + 21380565133380,
u
30
− 3u
29
+ ··· − 14u − 1i
I
u
2
= h9.19271 × 10
50
u
41
+ 6.53340 × 10
51
u
40
+ ··· + 1.68743 × 10
52
b + 4.76895 × 10
52
,
− 4.05666 × 10
51
u
41
− 1.46559 × 10
52
u
40
+ ··· + 1.18120 × 10
53
a − 9.05537 × 10
53
,
u
42
+ 8u
41
+ ··· + 406u + 49i
I
u
3
= hb, −u
3
+ u
2
+ 4a + 2u + 3, u
4
+ u
2
− u + 1i
I
u
4
= h8a
2
+ b + 18a + 4, 8a
3
+ 20a
2
+ 8a + 1, u − 1i
I
u
5
= hb, −u
3
+ a − u − 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
I
u
6
= hau + 4b + a + u − 5, a
2
+ 4au − 2a + 6u − 3, u
2
+ 1i
* 6 irreducible components of dim
C
= 0, with total 89 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−2.19 × 10
11
u
29
+ 4.78 × 10
11
u
28
+ · · · + 4.96 × 10
12
b + 2.22 ×
10
12
, −1.28 × 10
12
u
29
+ 4.04 × 10
12
u
28
+ · · · + 2.48 × 10
12
a + 2.14 ×
10
13
, u
30
− 3u
29
+ · · · − 14u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
3
=
0.517228u
29
− 1.62873u
28
+ ··· + 26.8709u − 8.61739
0.0441406u
29
− 0.0962596u
28
+ ··· + 1.16893u − 0.447249
a
12
=
−u
u
a
7
=
0.146114u
29
− 0.558009u
28
+ ··· + 11.5186u − 3.67862
0.114897u
29
− 0.286853u
28
+ ··· − 0.242495u − 0.299101
a
6
=
0.120091u
29
− 0.480458u
28
+ ··· + 10.2319u − 3.49919
0.0593413u
29
− 0.0838619u
28
+ ··· − 0.275735u − 0.299617
a
5
=
0.120607u
29
− 0.426449u
28
+ ··· + 10.4168u − 3.47317
0.0588257u
29
− 0.137871u
28
+ ··· − 0.460615u − 0.325639
a
2
=
0.366931u
29
− 1.21295u
28
+ ··· + 20.1769u − 5.68931
0.0588257u
29
− 0.137871u
28
+ ··· − 0.460615u − 0.325639
a
1
=
−0.0625000u
29
+ 0.125000u
28
+ ··· + 2.93750u + 0.0625000
1
16
u
29
−
1
8
u
28
+ ··· −
31
16
u −
1
16
a
10
=
1
16
u
29
−
1
4
u
28
+ ··· +
13
16
u +
17
16
−0.0625000u
29
+ 0.250000u
28
+ ··· − 0.812500u − 0.0625000
a
4
=
0.473087u
29
− 1.53247u
28
+ ··· + 25.7020u − 8.17014
0.0441406u
29
− 0.0962596u
28
+ ··· + 1.16893u − 0.447249
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
29246499640993
39697527734272
u
29
+
4877178426605
2481095483392
u
28
+ ··· −
648015885883539
39697527734272
u −
374986321947515
39697527734272
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 14u
29
+ ··· − 2399u + 256
c
2
, c
4
u
30
− 6u
29
+ ··· − 31u + 16
c
3
, c
7
u
30
− 2u
29
+ ··· − 96u − 256
c
5
, c
6
8(8u
30
+ 20u
29
+ ··· + 12u + 4)
c
8
, c
9
, c
11
c
12
u
30
+ 3u
29
+ ··· + 14u − 1
c
10
u
30
− 6u
29
+ ··· + 64u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 10y
29
+ ··· − 6849345y + 65536
c
2
, c
4
y
30
− 14y
29
+ ··· + 2399y + 256
c
3
, c
7
y
30
+ 18y
29
+ ··· + 76800y + 65536
c
5
, c
6
64(64y
30
− 1360y
29
+ ··· − 192y + 16)
c
8
, c
9
, c
11
c
12
y
30
+ 23y
29
+ ··· − 290y + 1
c
10
y
30
+ 6y
29
+ ··· − 1789952y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.151717 + 0.986186I
a = −1.190140 − 0.027428I
b = 1.54321 − 0.20318I
−5.68347 − 0.58233I −8.3451 + 12.8590I
u = 0.151717 − 0.986186I
a = −1.190140 + 0.027428I
b = 1.54321 + 0.20318I
−5.68347 + 0.58233I −8.3451 − 12.8590I
u = 0.783732 + 0.743673I
a = 0.631228 − 0.256038I
b = −0.083764 + 0.794094I
−1.33282 − 2.23553I −4.59779 + 3.41546I
u = 0.783732 − 0.743673I
a = 0.631228 + 0.256038I
b = −0.083764 − 0.794094I
−1.33282 + 2.23553I −4.59779 − 3.41546I
u = 1.09098
a = 1.70930
b = 0.608605
−2.65754 30.3480
u = −0.576049 + 1.073970I
a = −0.261951 − 0.195372I
b = −0.151381 + 0.594028I
1.34016 + 8.01200I 2.34579 − 12.49324I
u = −0.576049 − 1.073970I
a = −0.261951 + 0.195372I
b = −0.151381 − 0.594028I
1.34016 − 8.01200I 2.34579 + 12.49324I
u = 0.625133 + 0.199278I
a = 1.38297 + 2.15219I
b = 0.386290 − 0.372621I
−2.83148 − 0.66530I −18.2240 − 6.7846I
u = 0.625133 − 0.199278I
a = 1.38297 − 2.15219I
b = 0.386290 + 0.372621I
−2.83148 + 0.66530I −18.2240 + 6.7846I
u = −0.117957 + 1.367060I
a = 0.699932 − 0.475481I
b = −1.78516 + 0.43773I
6.76007 + 1.66777I 0.57274 − 1.46728I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.117957 − 1.367060I
a = 0.699932 + 0.475481I
b = −1.78516 − 0.43773I
6.76007 − 1.66777I 0.57274 + 1.46728I
u = −0.244597 + 1.352860I
a = 0.31073 + 1.77800I
b = −0.22783 − 1.65229I
5.09939 + 5.42433I −0.68852 − 4.20178I
u = −0.244597 − 1.352860I
a = 0.31073 − 1.77800I
b = −0.22783 + 1.65229I
5.09939 − 5.42433I −0.68852 + 4.20178I
u = 0.259417 + 1.365310I
a = −0.19856 + 1.74019I
b = −0.91810 − 1.71117I
10.78970 − 8.07891I −0.53452 + 5.22614I
u = 0.259417 − 1.365310I
a = −0.19856 − 1.74019I
b = −0.91810 + 1.71117I
10.78970 + 8.07891I −0.53452 − 5.22614I
u = −0.35445 + 1.40429I
a = −0.544865 + 0.390463I
b = 1.65162 + 0.07394I
7.38806 + 8.84406I −1.28461 − 6.03116I
u = −0.35445 − 1.40429I
a = −0.544865 − 0.390463I
b = 1.65162 − 0.07394I
7.38806 − 8.84406I −1.28461 + 6.03116I
u = 0.06550 + 1.45294I
a = −0.04154 − 1.68423I
b = 0.69837 + 1.94525I
13.33180 − 0.21203I 1.73134 + 0.I
u = 0.06550 − 1.45294I
a = −0.04154 + 1.68423I
b = 0.69837 − 1.94525I
13.33180 + 0.21203I 1.73134 + 0.I
u = 0.339570 + 0.379677I
a = 0.592119 + 0.913683I
b = −0.452974 − 0.318485I
−0.505428 − 1.105530I −5.83661 + 6.57696I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339570 − 0.379677I
a = 0.592119 − 0.913683I
b = −0.452974 + 0.318485I
−0.505428 + 1.105530I −5.83661 − 6.57696I
u = 1.52530 + 0.11249I
a = 0.155403 + 0.304847I
b = 0.24118 − 1.48607I
2.40331 + 3.17859I 0. − 3.79440I
u = 1.52530 − 0.11249I
a = 0.155403 − 0.304847I
b = 0.24118 + 1.48607I
2.40331 − 3.17859I 0. + 3.79440I
u = −0.58141 + 1.45298I
a = 0.76540 + 1.55713I
b = 0.78764 − 1.58037I
12.0126 + 17.2447I −2.29441 − 8.43337I
u = −0.58141 − 1.45298I
a = 0.76540 − 1.55713I
b = 0.78764 + 1.58037I
12.0126 − 17.2447I −2.29441 + 8.43337I
u = −0.414284 + 0.113025I
a = 0.170265 − 1.051000I
b = −0.229191 − 1.205720I
2.31731 − 2.61856I 1.56244 + 2.01080I
u = −0.414284 − 0.113025I
a = 0.170265 + 1.051000I
b = −0.229191 + 1.205720I
2.31731 + 2.61856I 1.56244 − 2.01080I
u = −0.47748 + 1.50384I
a = −0.58934 − 1.58578I
b = −0.50245 + 1.81791I
14.1647 + 9.9224I 0. − 4.39684I
u = −0.47748 − 1.50384I
a = −0.58934 + 1.58578I
b = −0.50245 − 1.81791I
14.1647 − 9.9224I 0. + 4.39684I
u = −0.0592723
a = −10.2226
b = −0.523532
−1.19030 −8.24210
7
II. I
u
2
= h9.19 × 10
50
u
41
+ 6.53 × 10
51
u
40
+ · · · + 1.69 × 10
52
b + 4.77 ×
10
52
, −4.06 × 10
51
u
41
− 1.47 × 10
52
u
40
+ · · · + 1.18 × 10
53
a − 9.06 ×
10
53
, u
42
+ 8u
41
+ · · · + 406u + 49i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
3
=
0.0343435u
41
+ 0.124076u
40
+ ··· + 50.6244u + 7.66624
−0.0544776u
41
− 0.387181u
40
+ ··· − 17.0063u − 2.82616
a
12
=
−u
u
a
7
=
−0.137949u
41
− 1.03303u
40
+ ··· − 26.6535u − 2.02469
−0.0157309u
41
− 0.0881611u
40
+ ··· + 22.8491u + 3.77512
a
6
=
−0.162962u
41
− 1.21826u
40
+ ··· − 71.3909u − 9.25731
−0.0118963u
41
− 0.0998927u
40
+ ··· + 18.0364u + 3.04637
a
5
=
−0.146119u
41
− 1.10192u
40
+ ··· − 47.1902u − 5.30246
−0.0287391u
41
− 0.216234u
40
+ ··· − 6.16428u − 0.908484
a
2
=
0.187628u
41
+ 1.31124u
40
+ ··· + 100.721u + 14.2062
−0.0287391u
41
− 0.216234u
40
+ ··· − 6.16428u − 0.908484
a
1
=
0.0204082u
41
+ 0.163265u
40
+ ··· + 36.6122u + 8.28571
0.0941921u
41
+ 0.708146u
40
+ ··· + 54.1974u + 8.58973
a
10
=
0.175301u
41
+ 1.30821u
40
+ ··· + 114.966u + 16.9746
−1
a
4
=
0.0888211u
41
+ 0.511257u
40
+ ··· + 67.6307u + 10.4924
−0.0544776u
41
− 0.387181u
40
+ ··· − 17.0063u − 2.82616
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.137513u
41
− 1.10677u
40
+ ··· − 86.1411u − 17.7083
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
21
+ 6u
20
+ ··· − 2u + 1)
2
c
2
, c
4
(u
21
− 4u
20
+ ··· − 2u + 1)
2
c
3
, c
7
(u
21
− u
20
+ ··· + 4u + 8)
2
c
5
, c
6
u
42
+ 8u
41
+ ··· + 859266u + 387139
c
8
, c
9
, c
11
c
12
u
42
− 8u
41
+ ··· − 406u + 49
c
10
(u
21
+ 2u
20
+ ··· + u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ 22y
20
+ ··· + 66y −1)
2
c
2
, c
4
(y
21
− 6y
20
+ ··· − 2y −1)
2
c
3
, c
7
(y
21
+ 21y
20
+ ··· − 176y −64)
2
c
5
, c
6
y
42
− 26y
41
+ ··· − 934716639340y + 149876605321
c
8
, c
9
, c
11
c
12
y
42
+ 30y
41
+ ··· + 10976y + 2401
c
10
(y
21
− 8y
20
+ ··· + 17y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.041887 + 1.002630I
a = −8.74756 − 5.85633I
b = −0.492750
2.07989 −13.37190 + 0.I
u = −0.041887 − 1.002630I
a = −8.74756 + 5.85633I
b = −0.492750
2.07989 −13.37190 + 0.I
u = −0.870370 + 0.220126I
a = 1.199530 − 0.425810I
b = 1.088250 − 0.021385I
2.22124 + 4.45806I −4.43689 − 6.14529I
u = −0.870370 − 0.220126I
a = 1.199530 + 0.425810I
b = 1.088250 + 0.021385I
2.22124 − 4.45806I −4.43689 + 6.14529I
u = −0.769906 + 0.433901I
a = 0.483221 − 0.092871I
b = −0.006772 − 0.621655I
−0.56968 − 2.93752I −1.02400 + 3.43881I
u = −0.769906 − 0.433901I
a = 0.483221 + 0.092871I
b = −0.006772 + 0.621655I
−0.56968 + 2.93752I −1.02400 − 3.43881I
u = 0.600601 + 0.944887I
a = −0.154802 + 0.082043I
b = −0.006772 − 0.621655I
−0.56968 − 2.93752I 0. + 3.43881I
u = 0.600601 − 0.944887I
a = −0.154802 − 0.082043I
b = −0.006772 + 0.621655I
−0.56968 + 2.93752I 0. − 3.43881I
u = −0.475850 + 1.016220I
a = 0.272799 + 0.705259I
b = 0.528856 + 0.467306I
4.75904 + 0.34630I 1.96536 + 0.I
u = −0.475850 − 1.016220I
a = 0.272799 − 0.705259I
b = 0.528856 − 0.467306I
4.75904 − 0.34630I 1.96536 + 0.I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.053090 + 1.155400I
a = −0.058655 − 0.325592I
b = −0.899194 − 0.226112I
1.45515 − 0.21101I −6.00000 + 0.I
u = 0.053090 − 1.155400I
a = −0.058655 + 0.325592I
b = −0.899194 + 0.226112I
1.45515 + 0.21101I −6.00000 + 0.I
u = 0.216321 + 1.202960I
a = −0.33507 − 2.15389I
b = −0.157544 + 0.891019I
0.26332 − 2.36605I 0
u = 0.216321 − 1.202960I
a = −0.33507 + 2.15389I
b = −0.157544 − 0.891019I
0.26332 + 2.36605I 0
u = 0.474335 + 0.591031I
a = 1.05367 + 1.22545I
b = 0.00145 + 1.46011I
6.58039 + 1.36266I −4.18856 − 2.27516I
u = 0.474335 − 0.591031I
a = 1.05367 − 1.22545I
b = 0.00145 − 1.46011I
6.58039 − 1.36266I −4.18856 + 2.27516I
u = −0.185639 + 1.238440I
a = −0.70977 − 2.01041I
b = −0.45321 + 1.45865I
5.71484 + 4.94435I 0
u = −0.185639 − 1.238440I
a = −0.70977 + 2.01041I
b = −0.45321 − 1.45865I
5.71484 − 4.94435I 0
u = −0.021801 + 1.271800I
a = 0.50394 + 2.30405I
b = 0.00145 − 1.46011I
6.58039 − 1.36266I 0
u = −0.021801 − 1.271800I
a = 0.50394 − 2.30405I
b = 0.00145 + 1.46011I
6.58039 + 1.36266I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.252620 + 0.261440I
a = −0.093957 − 0.166544I
b = −0.15224 + 1.62071I
8.50490 + 3.89686I 0
u = −1.252620 − 0.261440I
a = −0.093957 + 0.166544I
b = −0.15224 − 1.62071I
8.50490 − 3.89686I 0
u = −1.302650 + 0.047271I
a = 0.370885 + 0.223986I
b = 0.55439 − 1.54207I
7.25306 + 10.68720I 0
u = −1.302650 − 0.047271I
a = 0.370885 − 0.223986I
b = 0.55439 + 1.54207I
7.25306 − 10.68720I 0
u = −0.226174 + 1.289570I
a = 0.560692 + 0.745306I
b = 0.528856 − 0.467306I
4.75904 − 0.34630I 0
u = −0.226174 − 1.289570I
a = 0.560692 − 0.745306I
b = 0.528856 + 0.467306I
4.75904 + 0.34630I 0
u = 0.588336 + 0.271246I
a = −0.350608 − 1.017080I
b = −0.45321 − 1.45865I
5.71484 − 4.94435I −5.24866 + 2.70559I
u = 0.588336 − 0.271246I
a = −0.350608 + 1.017080I
b = −0.45321 + 1.45865I
5.71484 + 4.94435I −5.24866 − 2.70559I
u = 0.319588 + 1.353120I
a = −0.014969 − 0.198168I
b = 1.088250 + 0.021385I
2.22124 − 4.45806I 0
u = 0.319588 − 1.353120I
a = −0.014969 + 0.198168I
b = 1.088250 − 0.021385I
2.22124 + 4.45806I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.579219 + 0.187158I
a = −1.56373 + 0.83045I
b = −0.157544 − 0.891019I
0.26332 + 2.36605I −4.59037 − 2.67274I
u = −0.579219 − 0.187158I
a = −1.56373 − 0.83045I
b = −0.157544 + 0.891019I
0.26332 − 2.36605I −4.59037 + 2.67274I
u = −0.239978 + 0.362151I
a = −3.20155 + 1.86451I
b = −0.899194 + 0.226112I
1.45515 + 0.21101I −7.18710 − 0.57244I
u = −0.239978 − 0.362151I
a = −3.20155 − 1.86451I
b = −0.899194 − 0.226112I
1.45515 − 0.21101I −7.18710 + 0.57244I
u = 0.62069 + 1.53093I
a = 0.66906 − 1.34449I
b = 0.55439 + 1.54207I
7.25306 − 10.68720I 0
u = 0.62069 − 1.53093I
a = 0.66906 + 1.34449I
b = 0.55439 − 1.54207I
7.25306 + 10.68720I 0
u = 0.45894 + 1.59821I
a = −0.42722 + 1.36484I
b = −0.15224 − 1.62071I
8.50490 − 3.89686I 0
u = 0.45894 − 1.59821I
a = −0.42722 − 1.36484I
b = −0.15224 + 1.62071I
8.50490 + 3.89686I 0
u = −0.76320 + 1.48676I
a = 0.794802 + 1.042100I
b = 0.24239 − 1.67299I
12.12580 + 3.51416I 0
u = −0.76320 − 1.48676I
a = 0.794802 − 1.042100I
b = 0.24239 + 1.67299I
12.12580 − 3.51416I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.60260 + 1.60806I
a = −0.536403 − 1.053510I
b = 0.24239 + 1.67299I
12.12580 − 3.51416I 0
u = −0.60260 − 1.60806I
a = −0.536403 + 1.053510I
b = 0.24239 − 1.67299I
12.12580 + 3.51416I 0
15
III. I
u
3
= hb, −u
3
+ u
2
+ 4a + 2u + 3, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
3
=
1
4
u
3
−
1
4
u
2
−
1
2
u −
3
4
0
a
12
=
−u
u
a
7
=
1
0
a
6
=
u
2
+ 1
−u
2
+ u − 1
a
5
=
−u
3
+ u
2
+ 1
u
3
− u
2
+ u − 1
a
2
=
5
4
u
3
−
5
4
u
2
−
1
2
u −
7
4
−u
3
+ u
2
− u + 1
a
1
=
u
3
− u
2
− 1
−u
3
+ u
2
− u + 1
a
10
=
−u
3
− u
2
u
3
+ u
2
+ 1
a
4
=
1
4
u
3
−
1
4
u
2
−
1
2
u −
3
4
0
(ii) Obstruction class = 1
(iii) Cusp Shapes =
49
16
u
3
+
43
16
u
2
+
21
8
u −
163
16
16
(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
17
(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
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −1.112690 − 0.371716I
b = 0
−2.62503 − 1.39709I −10.08957 + 4.25783I
u = 0.547424 − 0.585652I
a = −1.112690 + 0.371716I
b = 0
−2.62503 + 1.39709I −10.08957 − 4.25783I
u = −0.547424 + 1.120870I
a = 0.237691 − 0.353773I
b = 0
0.98010 + 7.64338I −8.37918 − 1.58240I
u = −0.547424 − 1.120870I
a = 0.237691 + 0.353773I
b = 0
0.98010 − 7.64338I −8.37918 + 1.58240I
19
IV. I
u
4
= h8a
2
+ b + 18a + 4, 8a
3
+ 20a
2
+ 8a + 1, u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
1
a
9
=
1
1
a
3
=
a
−8a
2
− 18a − 4
a
12
=
−1
1
a
7
=
−2a
2
− 4a
−4a
2
− 8a
a
6
=
0
−2a
2
− 4a
a
5
=
2a
2
+ 4a
−4a
2
− 8a
a
2
=
−2a
2
− 4a − 2
−4a
2
− 8a
a
1
=
−1
0
a
10
=
0
1
a
4
=
8a
2
+ 19a + 4
−8a
2
− 18a − 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3a
2
+
61
2
a −
5
4
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
8(8u
3
− 12u
2
+ 4u + 1)
c
6
8(8u
3
+ 12u
2
+ 4u − 1)
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
9
(u − 1)
3
c
10
u
3
c
11
, c
12
(u + 1)
3
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
y
3
− y
2
+ 2y −1
c
5
, c
6
64(64y
3
− 80y
2
+ 40y −1)
c
8
, c
9
, c
11
c
12
(y −1)
3
c
10
y
3
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.230101 + 0.091291I
b = −0.215080 − 1.307140I
1.37919 − 2.82812I −8.13425 + 2.65834I
u = 1.00000
a = −0.230101 − 0.091291I
b = −0.215080 + 1.307140I
1.37919 + 2.82812I −8.13425 − 2.65834I
u = 1.00000
a = −2.03980
b = −0.569840
−2.75839 −50.9820
23
V. I
u
5
= hb, −u
3
+ a − u − 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
3
=
u
3
+ u + 1
0
a
12
=
−u
u
a
7
=
1
0
a
6
=
u
2
+ 1
u
4
a
5
=
u
5
+ u
4
+ 2u
3
+ 2u
2
+ 2u + 2
−u
5
− 2u
3
− u
2
− 2u − 1
a
2
=
−u
5
− u
4
− u
3
− 2u
2
− u − 1
u
5
+ 2u
3
+ u
2
+ 2u + 1
a
1
=
−u
5
− u
4
− 2u
3
− 2u
2
− 2u − 2
u
5
+ 2u
3
+ u
2
+ 2u + 1
a
10
=
−u
5
− 2u
3
− u
−1
a
4
=
u
3
+ u + 1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
5
+ 3u
3
− 2u
2
+ 3u − 8
24
(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
25
(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
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = 0.122561 + 0.744862I
b = 0
−1.37919 − 2.82812I −11.71191 + 2.59975I
u = 0.498832 − 1.001300I
a = 0.122561 − 0.744862I
b = 0
−1.37919 + 2.82812I −11.71191 − 2.59975I
u = −0.284920 + 1.115140I
a = 1.75488
b = 0
2.75839 − 60.423824 + 0.10I
u = −0.284920 − 1.115140I
a = 1.75488
b = 0
2.75839 − 60.423824 + 0.10I
u = −0.713912 + 0.305839I
a = 0.122561 + 0.744862I
b = 0
−1.37919 − 2.82812I −11.71191 + 2.59975I
u = −0.713912 − 0.305839I
a = 0.122561 − 0.744862I
b = 0
−1.37919 + 2.82812I −11.71191 − 2.59975I
27
VI. I
u
6
= hau + 4b + a + u − 5, a
2
+ 4au − 2a + 6u − 3, u
2
+ 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−1
a
3
=
a
−
1
4
au −
1
4
a −
1
4
u +
5
4
a
12
=
−u
u
a
7
=
−
1
4
au +
1
4
a −
3
4
u +
13
4
1
4
au +
1
4
a +
1
4
u −
9
4
a
6
=
−
1
4
au −
1
4
a −
1
4
u +
9
4
1
4
au +
3
4
a −
1
4
u −
5
4
a
5
=
−
1
4
au +
1
4
a −
3
4
u +
13
4
1
4
au +
1
4
a +
1
4
u −
9
4
a
2
=
−
1
2
au − u +
7
2
1
4
au +
1
4
a +
1
4
u −
9
4
a
1
=
−
3
4
au −
3
4
a −
7
4
u +
23
4
3
4
au +
3
4
a +
3
4
u −
23
4
a
10
=
3
4
au −
3
4
a −
23
4
u −
3
4
−
3
4
au +
3
4
a +
23
4
u −
1
4
a
4
=
1
4
au +
5
4
a +
1
4
u −
5
4
−
1
4
au −
1
4
a −
1
4
u +
5
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− 3u + 1)
2
c
2
, c
3
(u
2
+ u − 1)
2
c
4
, c
7
(u
2
− u − 1)
2
c
5
u
4
− 6u
3
+ 18u
2
− 12u + 4
c
6
u
4
+ 6u
3
+ 18u
2
+ 12u + 4
c
8
, c
9
, c
11
c
12
(u
2
+ 1)
2
c
10
u
4
+ 7u
2
+ 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 7y + 1)
2
c
2
, c
3
, c
4
c
7
(y
2
− 3y + 1)
2
c
5
, c
6
y
4
+ 188y
2
+ 16
c
8
, c
9
, c
11
c
12
(y + 1)
4
c
10
(y
2
+ 7y + 1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.236070 + 0.236068I
b = 1.61803
−5.59278 −4.00000
u = 1.000000I
a = 3.23607 − 4.23607I
b = −0.618034
2.30291 −4.00000
u = − 1.000000I
a = −1.236070 − 0.236068I
b = 1.61803
−5.59278 −4.00000
u = − 1.000000I
a = 3.23607 + 4.23607I
b = −0.618034
2.30291 −4.00000
31
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
2
− 3u + 1)
2
(u
3
− u
2
+ 2u − 1)(u
21
+ 6u
20
+ ··· − 2u + 1)
2
· (u
30
+ 14u
29
+ ··· − 2399u + 256)
c
2
((u − 1)
10
)(u
2
+ u − 1)
2
(u
3
+ u
2
− 1)(u
21
− 4u
20
+ ··· − 2u + 1)
2
· (u
30
− 6u
29
+ ··· − 31u + 16)
c
3
u
10
(u
2
+ u − 1)
2
(u
3
− u
2
+ 2u − 1)(u
21
− u
20
+ ··· + 4u + 8)
2
· (u
30
− 2u
29
+ ··· − 96u − 256)
c
4
((u + 1)
10
)(u
2
− u − 1)
2
(u
3
− u
2
+ 1)(u
21
− 4u
20
+ ··· − 2u + 1)
2
· (u
30
− 6u
29
+ ··· − 31u + 16)
c
5
64(8u
3
− 12u
2
+ 4u + 1)(u
4
− 6u
3
+ 18u
2
− 12u + 4)
· (u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (8u
30
+ 20u
29
+ ··· + 12u + 4)(u
42
+ 8u
41
+ ··· + 859266u + 387139)
c
6
64(8u
3
+ 12u
2
+ 4u − 1)(u
4
+ 2u
3
+ 3u
2
+ u + 1)
· (u
4
+ 6u
3
+ 18u
2
+ 12u + 4)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (8u
30
+ 20u
29
+ ··· + 12u + 4)(u
42
+ 8u
41
+ ··· + 859266u + 387139)
c
7
u
10
(u
2
− u − 1)
2
(u
3
+ u
2
+ 2u + 1)(u
21
− u
20
+ ··· + 4u + 8)
2
· (u
30
− 2u
29
+ ··· − 96u − 256)
c
8
, c
9
((u − 1)
3
)(u
2
+ 1)
2
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ ··· + 2u + 1)
· (u
30
+ 3u
29
+ ··· + 14u − 1)(u
42
− 8u
41
+ ··· − 406u + 49)
c
10
u
3
(u
3
− u
2
+ 1)
2
(u
4
+ 7u
2
+ 1)(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· ((u
21
+ 2u
20
+ ··· + u − 1)
2
)(u
30
− 6u
29
+ ··· + 64u + 256)
c
11
, c
12
((u + 1)
3
)(u
2
+ 1)
2
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ ··· − 2u + 1)
· (u
30
+ 3u
29
+ ··· + 14u − 1)(u
42
− 8u
41
+ ··· − 406u + 49)
32
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
10
(y
2
− 7y + 1)
2
(y
3
+ 3y
2
+ 2y −1)
· (y
21
+ 22y
20
+ ··· + 66y −1)
2
· (y
30
+ 10y
29
+ ··· − 6849345y + 65536)
c
2
, c
4
((y −1)
10
)(y
2
− 3y + 1)
2
(y
3
− y
2
+ 2y −1)(y
21
− 6y
20
+ ··· − 2y −1)
2
· (y
30
− 14y
29
+ ··· + 2399y + 256)
c
3
, c
7
y
10
(y
2
− 3y + 1)
2
(y
3
+ 3y
2
+ 2y −1)(y
21
+ 21y
20
+ ··· − 176y −64)
2
· (y
30
+ 18y
29
+ ··· + 76800y + 65536)
c
5
, c
6
4096(64y
3
− 80y
2
+ 40y −1)(y
4
+ 188y
2
+ 16)(y
4
+ 2y
3
+ ··· + 5y + 1)
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)(64y
30
− 1360y
29
+ ··· − 192y + 16)
· (y
42
− 26y
41
+ ··· − 934716639340y + 149876605321)
c
8
, c
9
, c
11
c
12
((y −1)
3
)(y + 1)
4
(y
4
+ 2y
3
+ ··· + y + 1)(y
6
+ 3y
5
+ ··· + 2y
3
+ 1)
· (y
30
+ 23y
29
+ ··· − 290y + 1)(y
42
+ 30y
41
+ ··· + 10976y + 2401)
c
10
y
3
(y
2
+ 7y + 1)
2
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· ((y
21
− 8y
20
+ ··· + 17y −1)
2
)(y
30
+ 6y
29
+ ··· − 1789952y + 65536)
33
