12n
0052
(K12n
0052
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 10 12 4 7 6 1 7
Solving Sequence
2,6
5 3 4
1,11
10 7 9 8 12
c
5
c
2
c
3
c
1
c
10
c
6
c
9
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−31828697846u
32
+ 114828956540u
31
+ ··· + 560421961026b + 532030527306,
− 197273519317u
32
+ 385887384126u
31
+ ··· + 1120843922052a + 266870259643,
u
33
− 2u
32
+ ··· + 5u + 4i
I
u
2
= h−u
19
a + 2u
19
+ ··· + 2a + 1, −2u
19
+ 3u
18
+ ··· − 4a + 3, u
20
− u
19
+ ··· − 2u + 1i
I
u
3
= h−u
4
a − 2u
2
a + u
3
+ au + b − a + u − 1, 2u
4
a + 4u
3
a + 6u
2
a − 3u
3
+ a
2
+ 4au − 5u
2
+ 2a − 8u − 4,
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
I
u
4
= hb + 1, 2a − 2u + 3, u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 85 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−3.18×10
10
u
32
+1.15×10
11
u
31
+· · ·+5.60×10
11
b+5.32×10
11
, −1.97×
10
11
u
32
+3.86×10
11
u
31
+· · ·+1.12×10
12
a+2.67×10
11
, u
33
−2u
32
+· · ·+5u+4i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
0.176004u
32
− 0.344283u
31
+ ··· − 1.32385u − 0.238098
0.0567942u
32
− 0.204897u
31
+ ··· − 0.869757u − 0.949339
a
10
=
0.119210u
32
− 0.139386u
31
+ ··· − 0.454097u + 0.711242
0.0567942u
32
− 0.204897u
31
+ ··· − 0.869757u − 0.949339
a
7
=
0.207329u
32
− 0.154336u
31
+ ··· − 0.127694u + 1.18034
0.00997898u
32
− 0.246238u
31
+ ··· − 1.25132u − 0.881877
a
9
=
0.322990u
32
− 0.306718u
31
+ ··· + 0.284165u + 1.39874
0.0620557u
32
− 0.436306u
31
+ ··· − 2.88278u − 1.94300
a
8
=
0.442680u
32
− 0.385581u
31
+ ··· + 0.406459u + 1.30251
0.00301080u
32
− 0.502789u
31
+ ··· − 2.70870u − 1.78276
a
12
=
0.203780u
32
− 0.167332u
31
+ ··· + 0.738262u + 0.687499
0.00526157u
32
− 0.231409u
31
+ ··· − 1.01302u − 0.993665
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
299977318733
280210980513
u
32
−
1019459365581
373614640684
u
31
+ ··· −
12370860698239
1120843922052
u +
1142458947067
280210980513
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
33
+ 16u
32
+ ··· + 145u − 16
c
2
, c
5
u
33
+ 2u
32
+ ··· + 5u − 4
c
3
u
33
− 2u
32
+ ··· + 317u − 292
c
4
, c
8
u
33
− 3u
32
+ ··· + 88u − 32
c
6
, c
7
, c
9
c
10
, c
12
u
33
− 2u
32
+ ··· − u − 1
c
11
u
33
+ 8u
32
+ ··· + 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
33
+ 4y
32
+ ··· + 42945y −256
c
2
, c
5
y
33
+ 16y
32
+ ··· + 145y −16
c
3
y
33
− 8y
32
+ ··· + 1520193y −85264
c
4
, c
8
y
33
+ 15y
32
+ ··· − 10048y −1024
c
6
, c
7
, c
9
c
10
, c
12
y
33
+ 8y
32
+ ··· + 3y −1
c
11
y
33
+ 32y
32
+ ··· + 43y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.245925 + 0.967546I
a = 0.251909 − 0.983582I
b = −0.187676 + 0.479329I
−1.41636 − 2.05180I 2.48876 + 5.93206I
u = −0.245925 − 0.967546I
a = 0.251909 + 0.983582I
b = −0.187676 − 0.479329I
−1.41636 + 2.05180I 2.48876 − 5.93206I
u = −0.575427 + 0.852009I
a = 0.942155 + 0.274666I
b = 0.340349 − 0.122054I
0.45731 − 2.27972I 1.08128 + 4.27119I
u = −0.575427 − 0.852009I
a = 0.942155 − 0.274666I
b = 0.340349 + 0.122054I
0.45731 + 2.27972I 1.08128 − 4.27119I
u = −0.812937 + 0.631708I
a = 1.47975 − 0.44818I
b = 0.743424 − 1.002600I
2.94313 − 7.42925I 5.70373 + 7.47980I
u = −0.812937 − 0.631708I
a = 1.47975 + 0.44818I
b = 0.743424 + 1.002600I
2.94313 + 7.42925I 5.70373 − 7.47980I
u = 0.409753 + 0.871693I
a = −1.12499 + 1.08600I
b = −1.204130 − 0.140549I
1.31683 + 1.72852I −4.93752 + 4.67154I
u = 0.409753 − 0.871693I
a = −1.12499 − 1.08600I
b = −1.204130 + 0.140549I
1.31683 − 1.72852I −4.93752 − 4.67154I
u = 0.867555 + 0.396268I
a = 1.30056 − 0.58396I
b = 0.737799 − 1.175390I
1.52939 − 11.12300I 4.95685 + 6.43500I
u = 0.867555 − 0.396268I
a = 1.30056 + 0.58396I
b = 0.737799 + 1.175390I
1.52939 + 11.12300I 4.95685 − 6.43500I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.686118 + 0.578359I
a = −1.88566 − 0.06922I
b = −0.982967 − 0.781621I
4.40316 + 1.88813I 8.98813 − 1.20865I
u = 0.686118 − 0.578359I
a = −1.88566 + 0.06922I
b = −0.982967 + 0.781621I
4.40316 − 1.88813I 8.98813 + 1.20865I
u = 0.864975 + 0.034660I
a = 0.331594 − 0.009701I
b = 0.305266 + 0.786195I
−4.64239 + 1.30030I 4.70025 − 5.48240I
u = 0.864975 − 0.034660I
a = 0.331594 + 0.009701I
b = 0.305266 − 0.786195I
−4.64239 − 1.30030I 4.70025 + 5.48240I
u = −0.783314 + 0.350967I
a = −1.325760 − 0.086765I
b = −0.755107 − 0.967847I
3.18749 + 4.30240I 7.11828 − 3.25713I
u = −0.783314 − 0.350967I
a = −1.325760 + 0.086765I
b = −0.755107 + 0.967847I
3.18749 − 4.30240I 7.11828 + 3.25713I
u = −0.240711 + 1.138690I
a = 0.218446 + 1.066860I
b = −0.589322 − 0.850975I
−1.47063 + 1.54484I 2.00175 − 2.84762I
u = −0.240711 − 1.138690I
a = 0.218446 − 1.066860I
b = −0.589322 + 0.850975I
−1.47063 − 1.54484I 2.00175 + 2.84762I
u = 0.591437 + 1.006810I
a = −0.445351 + 1.131670I
b = −1.117370 + 0.693565I
3.12726 + 3.05094I 6.17471 − 5.64978I
u = 0.591437 − 1.006810I
a = −0.445351 − 1.131670I
b = −1.117370 − 0.693565I
3.12726 − 3.05094I 6.17471 + 5.64978I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.698987 + 0.997819I
a = 0.090751 + 0.887560I
b = 0.721939 + 0.913335I
1.84788 + 1.79409I 4.29068 − 3.01350I
u = −0.698987 − 0.997819I
a = 0.090751 − 0.887560I
b = 0.721939 − 0.913335I
1.84788 − 1.79409I 4.29068 + 3.01350I
u = 0.130978 + 1.224260I
a = 0.086555 + 0.842104I
b = 0.639885 − 1.138090I
−4.05878 − 8.31071I −0.77091 + 5.89193I
u = 0.130978 − 1.224260I
a = 0.086555 − 0.842104I
b = 0.639885 + 1.138090I
−4.05878 + 8.31071I −0.77091 − 5.89193I
u = −0.582339 + 1.132530I
a = −1.72579 − 1.27163I
b = −0.702978 + 1.047320I
0.87531 − 9.44053I 3.45057 + 7.37353I
u = −0.582339 − 1.132530I
a = −1.72579 + 1.27163I
b = −0.702978 − 1.047320I
0.87531 + 9.44053I 3.45057 − 7.37353I
u = 0.625502 + 1.141600I
a = 2.00848 − 0.87462I
b = 0.73439 + 1.22624I
−0.7160 + 16.6422I 2.25690 − 10.10185I
u = 0.625502 − 1.141600I
a = 2.00848 + 0.87462I
b = 0.73439 − 1.22624I
−0.7160 − 16.6422I 2.25690 + 10.10185I
u = 0.428870 + 1.244810I
a = 0.598711 − 0.990983I
b = 0.322959 + 0.874255I
−8.56638 + 5.85952I 0.43324 − 9.30798I
u = 0.428870 − 1.244810I
a = 0.598711 + 0.990983I
b = 0.322959 − 0.874255I
−8.56638 − 5.85952I 0.43324 + 9.30798I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.472894 + 1.232170I
a = −0.522556 + 0.573461I
b = 0.226689 − 0.797235I
−8.26141 + 3.47041I 2.59273 + 2.52733I
u = 0.472894 − 1.232170I
a = −0.522556 − 0.573461I
b = 0.226689 + 0.797235I
−8.26141 − 3.47041I 2.59273 − 2.52733I
u = −0.276882
a = 0.692398
b = −0.466299
0.794015 12.6910
8
II. I
u
2
=
h−u
19
a+2u
19
+· · ·+2a+1, −2u
19
+3u
18
+· · ·−4a+3, u
20
−u
19
+· · ·−2u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
a
u
19
a − 2u
19
+ ··· − 2a − 1
a
10
=
−u
19
a + 2u
19
+ ··· + 3a + 1
u
19
a − 2u
19
+ ··· − 2a − 1
a
7
=
−5u
19
a − u
19
+ ··· − 3a + 5
3u
19
a + u
19
+ ··· + 2a − 1
a
9
=
−u
13
− 2u
11
− 3u
9
− 2u
7
− 2u
5
− 2u
3
− u
−u
15
− 3u
13
− 6u
11
− 7u
9
− 6u
7
− 4u
5
− 2u
3
− u
a
8
=
−u
18
− 3u
16
− 6u
14
− 7u
12
− 7u
10
− 7u
8
− 6u
6
− 4u
4
− u
2
− 1
−u
19
+ u
18
+ ··· − 2u + 1
a
12
=
4u
19
a − 3u
19
+ ··· − 2a − 2
−3u
19
a + u
19
+ ··· + a + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
18
+ 4u
17
−16u
16
+ 16u
15
−36u
14
+ 40u
13
−52u
12
+ 60u
11
−
56u
10
+ 64u
9
− 56u
8
+ 52u
7
− 48u
6
+ 40u
5
− 32u
4
+ 32u
3
− 12u
2
+ 12u − 2
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
20
+ 9u
19
+ ··· + 2u + 1)
2
c
2
, c
5
(u
20
+ u
19
+ ··· + 2u + 1)
2
c
3
(u
20
− u
19
+ ··· − 4u + 1)
2
c
4
, c
8
(u
20
+ u
19
+ ··· + u
2
+ 1)
2
c
6
, c
7
, c
9
c
10
, c
12
u
40
+ 5u
39
+ ··· + 390u + 73
c
11
u
40
+ 19u
39
+ ··· + 61352u + 5329
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 5y
19
+ ··· + 10y + 1)
2
c
2
, c
5
(y
20
+ 9y
19
+ ··· + 2y + 1)
2
c
3
(y
20
+ y
19
+ ··· + 18y + 1)
2
c
4
, c
8
(y
20
+ 5y
19
+ ··· + 2y + 1)
2
c
6
, c
7
, c
9
c
10
, c
12
y
40
+ 19y
39
+ ··· + 61352y + 5329
c
11
y
40
+ 3y
39
+ ··· − 70175632y + 28398241
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.781348 + 0.506112I
a = −1.170880 + 0.568217I
b = −0.805258 + 0.766657I
3.79920 − 1.55876I 8.11661 + 2.37917I
u = −0.781348 + 0.506112I
a = 1.325460 + 0.373843I
b = 0.821640 + 0.721695I
3.79920 − 1.55876I 8.11661 + 2.37917I
u = −0.781348 − 0.506112I
a = −1.170880 − 0.568217I
b = −0.805258 − 0.766657I
3.79920 + 1.55876I 8.11661 − 2.37917I
u = −0.781348 − 0.506112I
a = 1.325460 − 0.373843I
b = 0.821640 − 0.721695I
3.79920 + 1.55876I 8.11661 − 2.37917I
u = −0.487491 + 0.960535I
a = 1.02921 + 2.67375I
b = −0.088535 − 1.136560I
−3.54419 − 2.59904I 5.59387 + 3.16627I
u = −0.487491 + 0.960535I
a = −3.93581 + 0.32426I
b = −0.199008 + 0.878501I
−3.54419 − 2.59904I 5.59387 + 3.16627I
u = −0.487491 − 0.960535I
a = 1.02921 − 2.67375I
b = −0.088535 + 1.136560I
−3.54419 + 2.59904I 5.59387 − 3.16627I
u = −0.487491 − 0.960535I
a = −3.93581 − 0.32426I
b = −0.199008 − 0.878501I
−3.54419 + 2.59904I 5.59387 − 3.16627I
u = 0.795114 + 0.464423I
a = −1.22649 + 0.85458I
b = −0.828035 + 1.035210I
3.56254 − 4.70967I 7.63739 + 2.80351I
u = 0.795114 + 0.464423I
a = 1.57933 + 0.22784I
b = 1.029860 + 0.526311I
3.56254 − 4.70967I 7.63739 + 2.80351I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.795114 − 0.464423I
a = −1.22649 − 0.85458I
b = −0.828035 − 1.035210I
3.56254 + 4.70967I 7.63739 − 2.80351I
u = 0.795114 − 0.464423I
a = 1.57933 − 0.22784I
b = 1.029860 − 0.526311I
3.56254 + 4.70967I 7.63739 − 2.80351I
u = 0.331938 + 1.037100I
a = 0.385330 − 0.198340I
b = 0.566703 − 1.063780I
−6.92523 + 0.74806I −3.88926 − 0.17223I
u = 0.331938 + 1.037100I
a = 1.54638 − 1.04589I
b = 0.261397 + 1.361890I
−6.92523 + 0.74806I −3.88926 − 0.17223I
u = 0.331938 − 1.037100I
a = 0.385330 + 0.198340I
b = 0.566703 + 1.063780I
−6.92523 − 0.74806I −3.88926 + 0.17223I
u = 0.331938 − 1.037100I
a = 1.54638 + 1.04589I
b = 0.261397 − 1.361890I
−6.92523 − 0.74806I −3.88926 + 0.17223I
u = 0.044359 + 1.100970I
a = 0.144451 − 0.727954I
b = 0.783482 + 0.369003I
−1.86599 − 2.89577I 1.68771 + 2.74717I
u = 0.044359 + 1.100970I
a = 0.120658 − 0.668355I
b = −0.575520 + 0.995344I
−1.86599 − 2.89577I 1.68771 + 2.74717I
u = 0.044359 − 1.100970I
a = 0.144451 + 0.727954I
b = 0.783482 − 0.369003I
−1.86599 + 2.89577I 1.68771 − 2.74717I
u = 0.044359 − 1.100970I
a = 0.120658 + 0.668355I
b = −0.575520 − 0.995344I
−1.86599 + 2.89577I 1.68771 − 2.74717I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.502129 + 1.070060I
a = −1.196860 + 0.433804I
b = 0.02454 − 1.45386I
−5.78161 + 6.06247I −0.39660 − 7.82928I
u = 0.502129 + 1.070060I
a = 1.81174 − 0.26469I
b = 0.753263 + 0.761883I
−5.78161 + 6.06247I −0.39660 − 7.82928I
u = 0.502129 − 1.070060I
a = −1.196860 − 0.433804I
b = 0.02454 + 1.45386I
−5.78161 − 6.06247I −0.39660 + 7.82928I
u = 0.502129 − 1.070060I
a = 1.81174 + 0.26469I
b = 0.753263 − 0.761883I
−5.78161 − 6.06247I −0.39660 + 7.82928I
u = −0.455846 + 0.648892I
a = 1.182610 − 0.667439I
b = 0.000037 + 1.148130I
−2.61010 − 1.37271I 7.12015 + 4.43993I
u = −0.455846 + 0.648892I
a = −0.69832 − 3.01113I
b = 0.000279 − 0.680563I
−2.61010 − 1.37271I 7.12015 + 4.43993I
u = −0.455846 − 0.648892I
a = 1.182610 + 0.667439I
b = 0.000037 − 1.148130I
−2.61010 + 1.37271I 7.12015 − 4.43993I
u = −0.455846 − 0.648892I
a = −0.69832 + 3.01113I
b = 0.000279 + 0.680563I
−2.61010 + 1.37271I 7.12015 − 4.43993I
u = −0.628268 + 1.065390I
a = 0.062803 − 0.923190I
b = −0.801152 − 0.631202I
2.12977 − 3.75485I 5.74318 + 2.44199I
u = −0.628268 + 1.065390I
a = 1.69799 + 0.89596I
b = 0.734017 − 0.821832I
2.12977 − 3.75485I 5.74318 + 2.44199I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.628268 − 1.065390I
a = 0.062803 + 0.923190I
b = −0.801152 + 0.631202I
2.12977 + 3.75485I 5.74318 − 2.44199I
u = −0.628268 − 1.065390I
a = 1.69799 − 0.89596I
b = 0.734017 + 0.821832I
2.12977 + 3.75485I 5.74318 − 2.44199I
u = 0.621367 + 1.089770I
a = 0.450132 − 1.108290I
b = 1.111620 − 0.461350I
1.69596 + 10.03250I 4.83081 − 7.28178I
u = 0.621367 + 1.089770I
a = −1.94152 + 0.70857I
b = −0.838812 − 1.128460I
1.69596 + 10.03250I 4.83081 − 7.28178I
u = 0.621367 − 1.089770I
a = 0.450132 + 1.108290I
b = 1.111620 + 0.461350I
1.69596 − 10.03250I 4.83081 + 7.28178I
u = 0.621367 − 1.089770I
a = −1.94152 − 0.70857I
b = −0.838812 + 1.128460I
1.69596 − 10.03250I 4.83081 + 7.28178I
u = 0.558047 + 0.271580I
a = 0.714003 + 0.735342I
b = 0.041067 + 1.303980I
−3.61982 − 1.83292I 3.55614 + 4.26331I
u = 0.558047 + 0.271580I
a = 1.61977 − 1.74347I
b = 0.508409 − 0.727923I
−3.61982 − 1.83292I 3.55614 + 4.26331I
u = 0.558047 − 0.271580I
a = 0.714003 − 0.735342I
b = 0.041067 − 1.303980I
−3.61982 + 1.83292I 3.55614 − 4.26331I
u = 0.558047 − 0.271580I
a = 1.61977 + 1.74347I
b = 0.508409 + 0.727923I
−3.61982 + 1.83292I 3.55614 − 4.26331I
15
III. I
u
3
= h−u
4
a − 2u
2
a + u
3
+ au + b − a + u − 1, 2u
4
a + 4u
3
a + · · · + 2a −
4, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
−u
4
− u
3
− u
2
− 1
a
11
=
a
u
4
a + 2u
2
a − u
3
− au + a − u + 1
a
10
=
−u
4
a − 2u
2
a + u
3
+ au + u − 1
u
4
a + 2u
2
a − u
3
− au + a − u + 1
a
7
=
−u
3
a + 2u
4
+ 3u
3
− au + 6u
2
+ a + 4u + 2
1
a
9
=
−u
4
a − 2u
2
a + u
3
+ au − a + u − 1
0
a
8
=
−u
4
a − u
3
a − u
2
a − a − 1
−u
4
a − u
4
− 3u
2
a + au − 2u
2
− 2a + u − 1
a
12
=
u
3
+ a
u
4
a − u
4
+ 2u
2
a − 2u
3
− au − u
2
+ a − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 4u − 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
3
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
4
, c
8
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
6
, c
7
, c
9
c
10
, c
12
(u
2
+ 1)
5
c
11
(u − 1)
10
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
c
2
, c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
c
3
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
c
4
, c
8
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
6
, c
7
, c
9
c
10
, c
12
(y + 1)
10
c
11
(y − 1)
10
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = 2.33905 − 0.71839I
b = − 1.000000I
−3.61897 + 1.53058I −0.51511 − 4.43065I
u = 0.339110 + 0.822375I
a = 0.26050 − 3.57549I
b = 1.000000I
−3.61897 + 1.53058I −0.51511 − 4.43065I
u = 0.339110 − 0.822375I
a = 2.33905 + 0.71839I
b = 1.000000I
−3.61897 − 1.53058I −0.51511 + 4.43065I
u = 0.339110 − 0.822375I
a = 0.26050 + 3.57549I
b = − 1.000000I
−3.61897 − 1.53058I −0.51511 + 4.43065I
u = −0.766826
a = −0.674363 + 0.304077I
b = 1.000000I
−5.69095 −1.48110
u = −0.766826
a = −0.674363 − 0.304077I
b = − 1.000000I
−5.69095 −1.48110
u = −0.455697 + 1.200150I
a = 0.265647 + 0.869899I
b = − 1.000000I
−9.16243 − 4.40083I −4.74431 + 3.49859I
u = −0.455697 + 1.200150I
a = −1.190830 − 0.577079I
b = 1.000000I
−9.16243 − 4.40083I −4.74431 + 3.49859I
u = −0.455697 − 1.200150I
a = 0.265647 − 0.869899I
b = 1.000000I
−9.16243 + 4.40083I −4.74431 − 3.49859I
u = −0.455697 − 1.200150I
a = −1.190830 + 0.577079I
b = − 1.000000I
−9.16243 + 4.40083I −4.74431 − 3.49859I
19
IV. I
u
4
= hb + 1, 2a − 2u + 3, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u − 1
a
3
=
u
u − 1
a
4
=
1
u − 1
a
1
=
−1
0
a
11
=
u −
3
2
−1
a
10
=
u −
1
2
−1
a
7
=
u +
1
2
−1
a
9
=
2u
−2
a
8
=
2u
−2
a
12
=
u −
1
2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
31
4
u + 14
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
8
u
2
c
6
, c
7
, c
11
(u + 1)
2
c
9
, c
10
, c
12
(u − 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
8
y
2
c
6
, c
7
, c
9
c
10
, c
11
, c
12
(y − 1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.000000 + 0.866025I
b = −1.00000
1.64493 + 2.02988I 10.12500 − 6.71170I
u = 0.500000 − 0.866025I
a = −1.000000 − 0.866025I
b = −1.00000
1.64493 − 2.02988I 10.12500 + 6.71170I
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
5
− 3u
4
+ ··· − u + 1)
2
(u
20
+ 9u
19
+ ··· + 2u + 1)
2
· (u
33
+ 16u
32
+ ··· + 145u − 16)
c
2
(u
2
+ u + 1)(u
5
− u
4
+ ··· + u − 1)
2
(u
20
+ u
19
+ ··· + 2u + 1)
2
· (u
33
+ 2u
32
+ ··· + 5u − 4)
c
3
(u
2
− u + 1)(u
5
+ u
4
+ ··· + u − 1)
2
(u
20
− u
19
+ ··· − 4u + 1)
2
· (u
33
− 2u
32
+ ··· + 317u − 292)
c
4
, c
8
u
2
(u
10
+ 5u
8
+ ··· − u
2
+ 1)(u
20
+ u
19
+ ··· + u
2
+ 1)
2
· (u
33
− 3u
32
+ ··· + 88u − 32)
c
5
(u
2
− u + 1)(u
5
+ u
4
+ ··· + u + 1)
2
(u
20
+ u
19
+ ··· + 2u + 1)
2
· (u
33
+ 2u
32
+ ··· + 5u − 4)
c
6
, c
7
((u + 1)
2
)(u
2
+ 1)
5
(u
33
− 2u
32
+ ··· − u − 1)
· (u
40
+ 5u
39
+ ··· + 390u + 73)
c
9
, c
10
, c
12
((u − 1)
2
)(u
2
+ 1)
5
(u
33
− 2u
32
+ ··· − u − 1)
· (u
40
+ 5u
39
+ ··· + 390u + 73)
c
11
((u − 1)
10
)(u + 1)
2
(u
33
+ 8u
32
+ ··· + 3u − 1)
· (u
40
+ 19u
39
+ ··· + 61352u + 5329)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
· ((y
20
+ 5y
19
+ ··· + 10y + 1)
2
)(y
33
+ 4y
32
+ ··· + 42945y − 256)
c
2
, c
5
(y
2
+ y + 1)(y
5
+ 3y
4
+ ··· − y − 1)
2
(y
20
+ 9y
19
+ ··· + 2y + 1)
2
· (y
33
+ 16y
32
+ ··· + 145y − 16)
c
3
(y
2
+ y + 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· ((y
20
+ y
19
+ ··· + 18y + 1)
2
)(y
33
− 8y
32
+ ··· + 1520193y − 85264)
c
4
, c
8
y
2
(y
5
+ 5y
4
+ ··· − y + 1)
2
(y
20
+ 5y
19
+ ··· + 2y + 1)
2
· (y
33
+ 15y
32
+ ··· − 10048y − 1024)
c
6
, c
7
, c
9
c
10
, c
12
((y − 1)
2
)(y + 1)
10
(y
33
+ 8y
32
+ ··· + 3y − 1)
· (y
40
+ 19y
39
+ ··· + 61352y + 5329)
c
11
((y − 1)
12
)(y
33
+ 32y
32
+ ··· + 43y − 1)
· (y
40
+ 3y
39
+ ··· − 70175632y + 28398241)
25
