12a
0414
(K12a
0414
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 7 2 5 11 1 4 8 10
Solving Sequence
8,11
9
4,12
5 3 7 6 2 10 1
c
8
c
11
c
4
c
3
c
7
c
5
c
2
c
10
c
12
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h5989u
32
− 10457u
31
+ ··· + 131072b − 109701, 4909u
32
− 21209u
31
+ ··· + 8192a − 2485,
u
33
− 4u
32
+ ··· − 5u − 1i
I
u
2
= h−1.96974 × 10
53
u
47
− 1.99921 × 10
54
u
46
+ ··· + 5.08812 × 10
53
b − 4.24069 × 10
53
,
− 5.78567 × 10
53
u
47
− 4.93093 × 10
54
u
46
+ ··· + 5.08812 × 10
53
a − 2.96282 × 10
54
,
u
48
+ 9u
47
+ ··· + 64u
2
+ 1i
I
u
3
= h16b
4
+ 8b
3
+ 12b
2
+ 4b + 1, a, u − 1i
I
u
4
= hau + b − u + 1, a
2
− a + 1, u
2
+ 1i
* 4 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
= h5989u
32
− 10457u
31
+ · · · + 131072b − 109701, 4909u
32
−
21209u
31
+ · · · + 8192a − 2485, u
33
− 4u
32
+ · · · − 5u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
4
=
−0.599243u
32
+ 2.58899u
31
+ ··· + 10.0874u + 0.303345
−0.0456924u
32
+ 0.0797806u
31
+ ··· + 2.44522u + 0.836952
a
12
=
−u
u
a
5
=
−0.470421u
32
+ 1.90313u
31
+ ··· + 10.2872u + 0.214317
−0.174515u
32
+ 0.765640u
31
+ ··· + 2.24542u + 0.925980
a
3
=
−0.688271u
32
+ 3.07392u
31
+ ··· + 12.1718u + 0.948280
−0.216263u
32
+ 0.632584u
31
+ ··· + 3.00031u + 0.965775
a
7
=
−0.0625076u
32
+ 0.312538u
31
+ ··· − 3.24997u + 1.93751
0.0625153u
32
− 0.312576u
31
+ ··· − 0.750061u + 0.0624847
a
6
=
0.183983u
32
− 0.905144u
31
+ ··· + 6.21585u − 1.95071
0.0234833u
32
− 0.0922699u
31
+ ··· + 0.322815u − 0.177536
a
2
=
−7.62939 × 10
−6
u
32
+ 0.0000381470u
31
+ ··· + 2.00003u − 0.999992
−0.0000152588u
32
+ 0.0000762939u
31
+ ··· + 2.00006u + 0.0000152588
a
10
=
1
16
u
32
−
3
16
u
31
+ ··· −
3
8
u +
15
16
−
1
16
u
32
+
3
16
u
31
+ ··· +
3
8
u +
1
16
a
1
=
−
1
16
u
32
+
5
16
u
31
+ ··· −
9
4
u −
1
16
1
16
u
32
−
5
16
u
31
+ ··· +
5
4
u +
1
16
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
522847
262144
u
32
+
2155227
262144
u
31
+ ··· +
1440543
65536
u −
304289
262144
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
33
+ 8u
32
+ ··· + 113u − 16
c
2
, c
6
u
33
− 2u
32
+ ··· + 9u + 4
c
3
, c
4
16(16u
33
+ 8u
32
+ ··· + 4u + 4)
c
8
, c
9
, c
11
c
12
u
33
+ 4u
32
+ ··· − 5u + 1
c
10
u
33
− 3u
32
+ ··· − 384u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
33
+ 36y
32
+ ··· + 55265y −256
c
2
, c
6
y
33
+ 8y
32
+ ··· + 113y −16
c
3
, c
4
256(256y
33
+ 6464y
32
+ ··· − 32y −16)
c
8
, c
9
, c
11
c
12
y
33
+ 24y
32
+ ··· − 7y −1
c
10
y
33
+ 7y
32
+ ··· − 4210688y −262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.810506 + 0.397174I
a = 0.471042 − 0.576203I
b = 0.031782 + 0.156283I
−2.63885 − 1.50470I −17.6118 + 0.9903I
u = 0.810506 − 0.397174I
a = 0.471042 + 0.576203I
b = 0.031782 − 0.156283I
−2.63885 + 1.50470I −17.6118 − 0.9903I
u = 0.459603 + 0.737094I
a = 0.563800 − 1.220850I
b = −0.026160 + 0.652384I
1.91133 − 4.13194I −6.69421 + 7.53600I
u = 0.459603 − 0.737094I
a = 0.563800 + 1.220850I
b = −0.026160 − 0.652384I
1.91133 + 4.13194I −6.69421 − 7.53600I
u = 1.196360 + 0.133535I
a = 0.087023 − 0.413184I
b = 0.0413995 − 0.0359861I
−1.64834 + 1.66934I 3.56607 − 13.11303I
u = 1.196360 − 0.133535I
a = 0.087023 + 0.413184I
b = 0.0413995 + 0.0359861I
−1.64834 − 1.66934I 3.56607 + 13.11303I
u = −0.056738 + 1.254160I
a = −1.46678 − 1.15743I
b = 2.16586 + 1.14828I
5.46091 − 1.66598I 1.53418 + 0.83103I
u = −0.056738 − 1.254160I
a = −1.46678 + 1.15743I
b = 2.16586 − 1.14828I
5.46091 + 1.66598I 1.53418 − 0.83103I
u = 0.289788 + 0.681289I
a = −0.86769 + 1.37314I
b = 0.375820 − 0.719083I
1.78168 + 1.19316I −7.53573 + 1.61269I
u = 0.289788 − 0.681289I
a = −0.86769 − 1.37314I
b = 0.375820 + 0.719083I
1.78168 − 1.19316I −7.53573 − 1.61269I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.270166 + 1.241020I
a = −1.48489 − 0.50819I
b = 2.34742 + 0.73110I
3.11523 + 5.84648I −4.56559 − 6.45729I
u = −0.270166 − 1.241020I
a = −1.48489 + 0.50819I
b = 2.34742 − 0.73110I
3.11523 − 5.84648I −4.56559 + 6.45729I
u = −0.141430 + 1.333060I
a = 1.31942 + 0.84469I
b = −2.15460 − 0.87222I
8.30753 + 3.24726I 2.97336 − 3.54656I
u = −0.141430 − 1.333060I
a = 1.31942 − 0.84469I
b = −2.15460 + 0.87222I
8.30753 − 3.24726I 2.97336 + 3.54656I
u = 0.162413 + 1.369390I
a = −0.78771 − 1.24953I
b = 1.53033 + 0.98573I
15.1953 − 7.1498I 0. + 4.85816I
u = 0.162413 − 1.369390I
a = −0.78771 + 1.24953I
b = 1.53033 − 0.98573I
15.1953 + 7.1498I 0. − 4.85816I
u = 0.118253 + 1.392890I
a = 0.86034 + 1.18437I
b = −1.63148 − 0.95130I
15.7605 − 0.3593I 0
u = 0.118253 − 1.392890I
a = 0.86034 − 1.18437I
b = −1.63148 + 0.95130I
15.7605 + 0.3593I 0
u = −0.439636 + 1.342260I
a = −1.183190 − 0.355879I
b = 2.28590 + 0.59287I
6.8551 + 12.3830I 0. − 9.37412I
u = −0.439636 − 1.342260I
a = −1.183190 + 0.355879I
b = 2.28590 − 0.59287I
6.8551 − 12.3830I 0. + 9.37412I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.35672 + 1.37871I
a = 1.194790 + 0.473103I
b = −2.24033 − 0.62807I
8.96151 + 7.45389I 0
u = −0.35672 − 1.37871I
a = 1.194790 − 0.473103I
b = −2.24033 + 0.62807I
8.96151 − 7.45389I 0
u = 0.522632
a = −1.04517
b = 0.171255
−0.864315 −11.0710
u = 1.49341 + 0.02296I
a = 0.004827 − 0.505215I
b = 0.009296 − 0.149192I
6.08983 + 3.23170I 0
u = 1.49341 − 0.02296I
a = 0.004827 + 0.505215I
b = 0.009296 + 0.149192I
6.08983 − 3.23170I 0
u = −0.53426 + 1.45932I
a = −1.028710 − 0.344760I
b = 2.27296 + 0.51516I
16.3788 + 16.6342I 0
u = −0.53426 − 1.45932I
a = −1.028710 + 0.344760I
b = 2.27296 − 0.51516I
16.3788 − 16.6342I 0
u = −0.51174 + 1.47115I
a = 1.030260 + 0.366604I
b = −2.25941 − 0.51779I
16.8347 + 9.9710I 0
u = −0.51174 − 1.47115I
a = 1.030260 − 0.366604I
b = −2.25941 + 0.51779I
16.8347 − 9.9710I 0
u = −0.373254 + 0.022102I
a = −0.06596 + 1.42063I
b = 0.074590 + 1.162160I
6.15660 − 3.12287I 1.67109 + 2.42125I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.373254 − 0.022102I
a = −0.06596 − 1.42063I
b = 0.074590 − 1.162160I
6.15660 + 3.12287I 1.67109 − 2.42125I
u = −0.107703 + 0.140066I
a = −1.12399 + 2.11844I
b = 0.341008 + 0.397575I
−0.346424 − 1.198420I −4.36203 + 5.18223I
u = −0.107703 − 0.140066I
a = −1.12399 − 2.11844I
b = 0.341008 − 0.397575I
−0.346424 + 1.198420I −4.36203 − 5.18223I
8
II. I
u
2
= h−1.97 × 10
53
u
47
− 2.00 × 10
54
u
46
+ · · · + 5.09 × 10
53
b − 4.24 ×
10
53
, −5.79 × 10
53
u
47
− 4.93 × 10
54
u
46
+ · · · + 5.09 × 10
53
a − 2.96 ×
10
54
, u
48
+ 9u
47
+ · · · + 64u
2
+ 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
u
2
a
4
=
1.13709u
47
+ 9.69105u
46
+ ··· + 70.0607u + 5.82301
0.387125u
47
+ 3.92917u
46
+ ··· + 7.46630u + 0.833448
a
12
=
−u
u
a
5
=
1.55344u
47
+ 13.7027u
46
+ ··· + 71.5849u + 5.72526
−0.0292178u
47
− 0.0824765u
46
+ ··· + 5.94208u + 0.931194
a
3
=
1.32966u
47
+ 11.7305u
46
+ ··· + 78.6641u + 6.11366
−0.241681u
47
− 1.88232u
46
+ ··· + 7.27373u + 0.527099
a
7
=
−1.59496u
47
− 14.2055u
46
+ ··· − 56.3536u + 1.75782
0.0247441u
47
+ 0.125308u
46
+ ··· − 6.45255u − 0.262204
a
6
=
2.51207u
47
+ 22.2488u
46
+ ··· + 63.3921u − 0.943478
0.00312394u
47
+ 0.0401568u
46
+ ··· + 7.57257u + 0.426062
a
2
=
0.572309u
47
+ 5.04293u
46
+ ··· + 0.200411u − 0.779680
0.282861u
47
+ 2.34564u
46
+ ··· − 0.371898u + 0.328173
a
10
=
−0.294021u
47
− 2.25196u
46
+ ··· − 36.4484u − 8.21659
−1
a
1
=
−u
47
− 9u
46
+ ··· − 620u
2
− 64u
0.394226u
47
+ 3.26397u
46
+ ··· − 8.21659u + 0.294021
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0194241u
47
+ 0.274555u
46
+ ··· + 24.2369u − 5.45603
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
(u
24
+ 5u
23
+ ··· + 4u + 1)
2
c
2
, c
6
(u
24
− u
23
+ ··· − 2u + 1)
2
c
3
, c
4
u
48
− 5u
47
+ ··· − 226208u + 1237879
c
8
, c
9
, c
11
c
12
u
48
− 9u
47
+ ··· + 64u
2
+ 1
c
10
(u
24
+ u
23
+ ··· − 2u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y
24
+ 29y
23
+ ··· + 20y + 1)
2
c
2
, c
6
(y
24
+ 5y
23
+ ··· + 4y + 1)
2
c
3
, c
4
y
48
+ 31y
47
+ ··· + 24673685371492y + 1532344418641
c
8
, c
9
, c
11
c
12
y
48
+ 35y
47
+ ··· + 128y + 1
c
10
(y
24
+ 9y
23
+ ··· + 4y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.980744 + 0.033066I
a = 0.710121 − 0.970033I
b = −0.0139690 + 0.0292733I
2.50043 + 7.34378I −8.00000 − 8.70536I
u = −0.980744 − 0.033066I
a = 0.710121 + 0.970033I
b = −0.0139690 − 0.0292733I
2.50043 − 7.34378I −8.00000 + 8.70536I
u = −0.018560 + 1.043510I
a = −0.640429 + 0.680961I
b = 1.46692 + 0.06389I
1.62658 + 2.08350I 0
u = −0.018560 − 1.043510I
a = −0.640429 − 0.680961I
b = 1.46692 − 0.06389I
1.62658 − 2.08350I 0
u = −0.882259 + 0.224615I
a = −0.891979 + 0.856342I
b = 0.114179 − 0.194204I
3.92390 + 3.08008I −1.95703 − 2.82964I
u = −0.882259 − 0.224615I
a = −0.891979 − 0.856342I
b = 0.114179 + 0.194204I
3.92390 − 3.08008I −1.95703 + 2.82964I
u = 0.010763 + 1.094900I
a = 0.290435 − 0.328937I
b = −3.08197 − 0.34616I
3.08573 − 1.11019I 0
u = 0.010763 − 1.094900I
a = 0.290435 + 0.328937I
b = −3.08197 + 0.34616I
3.08573 + 1.11019I 0
u = 0.319322 + 1.080060I
a = −0.894805 + 0.364573I
b = 1.53223 − 0.32727I
−0.47750 − 2.61939I 0
u = 0.319322 − 1.080060I
a = −0.894805 − 0.364573I
b = 1.53223 + 0.32727I
−0.47750 + 2.61939I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.022326 + 0.866430I
a = −0.351897 − 0.428351I
b = −0.42856 − 2.75599I
3.08573 + 1.11019I −7.08627 − 5.87957I
u = 0.022326 − 0.866430I
a = −0.351897 + 0.428351I
b = −0.42856 + 2.75599I
3.08573 − 1.11019I −7.08627 + 5.87957I
u = 0.070364 + 1.192310I
a = 0.653251 − 0.404984I
b = −1.73332 + 0.20487I
3.18351 − 1.48443I 0
u = 0.070364 − 1.192310I
a = 0.653251 + 0.404984I
b = −1.73332 − 0.20487I
3.18351 + 1.48443I 0
u = −0.112411 + 1.231810I
a = −0.366402 + 0.690629I
b = 1.46512 + 0.56427I
9.74478 + 4.87894I 0
u = −0.112411 − 1.231810I
a = −0.366402 − 0.690629I
b = 1.46512 − 0.56427I
9.74478 − 4.87894I 0
u = −0.080284 + 1.240960I
a = 0.359527 − 0.665336I
b = −1.52951 − 0.59847I
9.92570 − 1.57218I 0
u = −0.080284 − 1.240960I
a = 0.359527 + 0.665336I
b = −1.52951 + 0.59847I
9.92570 + 1.57218I 0
u = −1.246030 + 0.166941I
a = −0.622701 + 0.776104I
b = 0.215883 + 0.099436I
11.61100 + 3.84160I 0
u = −1.246030 − 0.166941I
a = −0.622701 − 0.776104I
b = 0.215883 − 0.099436I
11.61100 − 3.84160I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.255490 + 0.121911I
a = 0.603893 − 0.792963I
b = −0.189376 − 0.121790I
11.3504 + 10.3945I 0
u = −1.255490 − 0.121911I
a = 0.603893 + 0.792963I
b = −0.189376 + 0.121790I
11.3504 − 10.3945I 0
u = −0.546001 + 1.213640I
a = −0.687726 + 0.249352I
b = 1.208230 − 0.558353I
6.78312 + 2.24409I 0
u = −0.546001 − 1.213640I
a = −0.687726 − 0.249352I
b = 1.208230 + 0.558353I
6.78312 − 2.24409I 0
u = 0.465585 + 0.444846I
a = 0.35870 − 1.41573I
b = −1.06906 − 1.22858I
9.92570 + 1.57218I −4.12166 − 2.29522I
u = 0.465585 − 0.444846I
a = 0.35870 + 1.41573I
b = −1.06906 + 1.22858I
9.92570 − 1.57218I −4.12166 + 2.29522I
u = 0.487951 + 0.375365I
a = −0.51836 + 1.48283I
b = 1.07574 + 1.16660I
9.74478 − 4.87894I −4.44407 + 2.58342I
u = 0.487951 − 0.375365I
a = −0.51836 − 1.48283I
b = 1.07574 − 1.16660I
9.74478 + 4.87894I −4.44407 − 2.58342I
u = 0.322137 + 1.361350I
a = 0.762790 − 0.256280I
b = −1.64722 + 0.35851I
3.92390 − 3.08008I 0
u = 0.322137 − 1.361350I
a = 0.762790 + 0.256280I
b = −1.64722 − 0.35851I
3.92390 + 3.08008I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.471832 + 1.328370I
a = −0.809389 + 0.212649I
b = 1.63311 − 0.39683I
2.50043 − 7.34378I 0
u = 0.471832 − 1.328370I
a = −0.809389 − 0.212649I
b = 1.63311 + 0.39683I
2.50043 + 7.34378I 0
u = −0.391141 + 1.355140I
a = 0.646964 − 0.240514I
b = −1.43489 + 0.51946I
6.78312 − 2.24409I 0
u = −0.391141 − 1.355140I
a = 0.646964 + 0.240514I
b = −1.43489 − 0.51946I
6.78312 + 2.24409I 0
u = −0.580158 + 0.075111I
a = 0.96535 + 1.59014I
b = 0.294807 − 0.258255I
−0.47750 − 2.61939I −12.11481 + 3.60921I
u = −0.580158 − 0.075111I
a = 0.96535 − 1.59014I
b = 0.294807 + 0.258255I
−0.47750 + 2.61939I −12.11481 − 3.60921I
u = −0.353776 + 0.398658I
a = −1.71158 + 0.19235I
b = −0.050547 − 0.825568I
3.18351 + 1.48443I −2.66287 − 3.68159I
u = −0.353776 − 0.398658I
a = −1.71158 − 0.19235I
b = −0.050547 + 0.825568I
3.18351 − 1.48443I −2.66287 + 3.68159I
u = 0.54994 + 1.53645I
a = −0.753450 + 0.160860I
b = 1.68785 − 0.40537I
11.3504 − 10.3945I 0
u = 0.54994 − 1.53645I
a = −0.753450 − 0.160860I
b = 1.68785 + 0.40537I
11.3504 + 10.3945I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.51674 + 1.55141I
a = 0.746313 − 0.168037I
b = −1.68832 + 0.39730I
11.61100 − 3.84160I 0
u = 0.51674 − 1.55141I
a = 0.746313 + 0.168037I
b = −1.68832 − 0.39730I
11.61100 + 3.84160I 0
u = −0.68305 + 1.51479I
a = −0.636165 + 0.279673I
b = 1.309160 − 0.286833I
15.6992 + 3.3032I 0
u = −0.68305 − 1.51479I
a = −0.636165 − 0.279673I
b = 1.309160 + 0.286833I
15.6992 − 3.3032I 0
u = −0.65013 + 1.53993I
a = 0.633866 − 0.274677I
b = −1.336370 + 0.290398I
15.6992 − 3.3032I 0
u = −0.65013 − 1.53993I
a = 0.633866 + 0.274677I
b = −1.336370 − 0.290398I
15.6992 + 3.3032I 0
u = 0.0430770 + 0.0919701I
a = 3.15367 + 9.07419I
b = 0.699871 + 0.813700I
1.62658 − 2.08350I −8.24893 + 3.59251I
u = 0.0430770 − 0.0919701I
a = 3.15367 − 9.07419I
b = 0.699871 − 0.813700I
1.62658 + 2.08350I −8.24893 − 3.59251I
16
III. I
u
3
= h16b
4
+ 8b
3
+ 12b
2
+ 4b + 1, a, u − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
1
a
9
=
1
1
a
4
=
0
b
a
12
=
−1
1
a
5
=
−b
2b
a
3
=
b
2b
a
7
=
2b
2
+ 1
−4b
2
a
6
=
−4b
3
− 3b
8b
3
+ 2b
a
2
=
−2b
2
− 1
−4b
2
a
10
=
0
1
a
1
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 32b
3
+ b
2
+ 16b − 10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
3
16(16u
4
− 8u
3
+ 12u
2
− 4u + 1)
c
4
16(16u
4
+ 8u
3
+ 12u
2
+ 4u + 1)
c
6
u
4
+ u
3
+ u
2
+ 1
c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
, c
9
(u − 1)
4
c
10
u
4
c
11
, c
12
(u + 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
6
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
, c
4
256(256y
4
+ 320y
3
+ 112y
2
+ 8y + 1)
c
8
, c
9
, c
11
c
12
(y −1)
4
c
10
y
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −0.052438 + 0.776246I
5.14581 + 3.16396I −8.41011 − 2.42402I
u = 1.00000
a = 0
b = −0.052438 − 0.776246I
5.14581 − 3.16396I −8.41011 + 2.42402I
u = 1.00000
a = 0
b = −0.197562 + 0.253422I
−1.85594 + 1.41510I −12.21489 + 4.38336I
u = 1.00000
a = 0
b = −0.197562 − 0.253422I
−1.85594 − 1.41510I −12.21489 − 4.38336I
20
IV. I
u
4
= hau + b − u + 1, a
2
− a + 1, u
2
+ 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
9
=
1
−1
a
4
=
a
−au + u − 1
a
12
=
−u
u
a
5
=
−au + 2a + u − 1
−a
a
3
=
−au + 2a + u − 1
−a
a
7
=
a + u − 1
−a + 1
a
6
=
2a + u − 2
−a + 1
a
2
=
−1
0
a
10
=
au − u
−au + u − 1
a
1
=
−a − u + 1
a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a − 4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
(u
2
− u + 1)
2
c
2
, c
7
(u
2
+ u + 1)
2
c
3
u
4
− 2u
3
+ 2u
2
− 4u + 4
c
4
u
4
+ 2u
3
+ 2u
2
+ 4u + 4
c
8
, c
9
, c
11
c
12
(u
2
+ 1)
2
c
10
u
4
− u
2
+ 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
(y
2
+ y + 1)
2
c
3
, c
4
y
4
− 4y
2
+ 16
c
8
, c
9
, c
11
c
12
(y + 1)
4
c
10
(y
2
− y + 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.500000 + 0.866025I
b = −0.133975 + 0.500000I
3.28987 − 2.02988I −2.00000 + 3.46410I
u = 1.000000I
a = 0.500000 − 0.866025I
b = −1.86603 + 0.50000I
3.28987 + 2.02988I −2.00000 − 3.46410I
u = − 1.000000I
a = 0.500000 + 0.866025I
b = −1.86603 − 0.50000I
3.28987 − 2.02988I −2.00000 + 3.46410I
u = − 1.000000I
a = 0.500000 − 0.866025I
b = −0.133975 − 0.500000I
3.28987 + 2.02988I −2.00000 − 3.46410I
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
2
− u + 1)
2
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
24
+ 5u
23
+ ··· + 4u + 1)
2
· (u
33
+ 8u
32
+ ··· + 113u − 16)
c
2
((u
2
+ u + 1)
2
)(u
4
− u
3
+ u
2
+ 1)(u
24
− u
23
+ ··· − 2u + 1)
2
· (u
33
− 2u
32
+ ··· + 9u + 4)
c
3
256(u
4
− 2u
3
+ 2u
2
− 4u + 4)(16u
4
− 8u
3
+ 12u
2
− 4u + 1)
· (16u
33
+ 8u
32
+ ··· + 4u + 4)(u
48
− 5u
47
+ ··· − 226208u + 1237879)
c
4
256(u
4
+ 2u
3
+ 2u
2
+ 4u + 4)(16u
4
+ 8u
3
+ 12u
2
+ 4u + 1)
· (16u
33
+ 8u
32
+ ··· + 4u + 4)(u
48
− 5u
47
+ ··· − 226208u + 1237879)
c
6
((u
2
− u + 1)
2
)(u
4
+ u
3
+ u
2
+ 1)(u
24
− u
23
+ ··· − 2u + 1)
2
· (u
33
− 2u
32
+ ··· + 9u + 4)
c
7
((u
2
+ u + 1)
2
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
24
+ 5u
23
+ ··· + 4u + 1)
2
· (u
33
+ 8u
32
+ ··· + 113u − 16)
c
8
, c
9
((u − 1)
4
)(u
2
+ 1)
2
(u
33
+ 4u
32
+ ··· − 5u + 1)
· (u
48
− 9u
47
+ ··· + 64u
2
+ 1)
c
10
u
4
(u
4
− u
2
+ 1)(u
24
+ u
23
+ ··· − 2u + 1)
2
· (u
33
− 3u
32
+ ··· − 384u + 512)
c
11
, c
12
((u + 1)
4
)(u
2
+ 1)
2
(u
33
+ 4u
32
+ ··· − 5u + 1)
· (u
48
− 9u
47
+ ··· + 64u
2
+ 1)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
((y
2
+ y + 1)
2
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
24
+ 29y
23
+ ··· + 20y + 1)
2
· (y
33
+ 36y
32
+ ··· + 55265y −256)
c
2
, c
6
((y
2
+ y + 1)
2
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
24
+ 5y
23
+ ··· + 4y + 1)
2
· (y
33
+ 8y
32
+ ··· + 113y −16)
c
3
, c
4
65536(y
4
− 4y
2
+ 16)(256y
4
+ 320y
3
+ 112y
2
+ 8y + 1)
· (256y
33
+ 6464y
32
+ ··· − 32y −16)
· (y
48
+ 31y
47
+ ··· + 24673685371492y + 1532344418641)
c
8
, c
9
, c
11
c
12
((y −1)
4
)(y + 1)
4
(y
33
+ 24y
32
+ ··· − 7y −1)
· (y
48
+ 35y
47
+ ··· + 128y + 1)
c
10
y
4
(y
2
− y + 1)
2
(y
24
+ 9y
23
+ ··· + 4y + 1)
2
· (y
33
+ 7y
32
+ ··· − 4210688y −262144)
26
