12n
0521
(K12n
0521
)
A knot diagram
1
Linearized knot diagam
3 6 10 1 12 2 10 5 6 1 9 8
Solving Sequence
2,6 3,10
4 7 8 1 11 9 12 5
c
2
c
3
c
6
c
7
c
1
c
10
c
9
c
12
c
5
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h432917u
27
+ 3841573u
26
+ ··· + 262964b + 2783376,
413130u
27
+ 3479001u
26
+ ··· + 262964a + 1217429, u
28
+ 9u
27
+ ··· + 124u + 16i
I
u
2
= h−87u
16
+ 385u
15
+ ··· + 77b − 41, −190u
16
+ 693u
15
+ ··· + 231a − 163, u
17
− 4u
16
+ ··· − 6u
2
− 1i
I
u
3
= h343u
10
a
3
+ 5345u
10
a
2
+ ··· + 5127a + 18129, u
10
a
3
− 3u
10
a
2
+ ··· + 26a + 1,
u
11
− 2u
10
+ 6u
9
− 8u
8
+ 12u
7
− 13u
6
+ 12u
5
− 13u
4
+ 9u
3
− 8u
2
+ 4u − 1i
I
u
4
= hb − a + u, a
2
+ a − u − 1, u
2
+ u + 1i
I
u
5
= hb − a + 1, a
2
− au − a + 1, u
2
+ u + 1i
* 5 irreducible components of dim
C
= 0, with total 97 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
= h4.33 × 10
5
u
27
+ 3 .84 × 10
6
u
26
+ · · · + 2.63 × 10
5
b + 2.78 × 10
6
, 4.13 ×
10
5
u
27
+3.48×10
6
u
26
+· · ·+2.63×10
5
a+1.22×10
6
, u
28
+9u
27
+· · ·+124u+16i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
−1.57105u
27
− 13.2300u
26
+ ··· − 55.0012u − 4.62964
−1.64630u
27
− 14.6087u
26
+ ··· − 102.538u − 10.5846
a
4
=
0.956809u
27
+ 9.01001u
26
+ ··· + 2.45249u − 3.84208
1.67232u
27
+ 15.4625u
26
+ ··· + 188.238u + 21.6886
a
7
=
u
u
a
8
=
−0.715515u
27
− 6.45245u
26
+ ··· − 184.785u − 26.5307
0.687566u
27
+ 5.41127u
26
+ ··· − 74.2301u − 11.6532
a
1
=
u
2
+ 1
−u
4
a
11
=
−0.693057u
27
− 6.09592u
26
+ ··· + 30.7434u + 7.11420
−2.14571u
27
− 18.5603u
26
+ ··· − 94.5924u − 9.92361
a
9
=
−1.57105u
27
− 13.2300u
26
+ ··· − 55.0012u − 4.62964
−2.38308u
27
− 20.2951u
26
+ ··· − 14.8953u + 3.96757
a
12
=
−1.33446u
27
− 10.2494u
26
+ ··· − 6.34518u + 1.73776
1.02850u
27
+ 9.08118u
26
+ ··· + 212.265u + 31.6255
a
5
=
2.39557u
27
+ 20.4749u
26
+ ··· + 148.520u + 18.4022
1.49590u
27
+ 15.8334u
26
+ ··· + 111.117u + 8.74080
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
394167
65741
u
27
−
3195674
65741
u
26
+ ··· −
10576918
65741
u −
485930
65741
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
+ 17u
27
+ ··· + 1360u + 256
c
2
, c
6
u
28
− 9u
27
+ ··· − 124u + 16
c
3
, c
9
u
28
+ u
27
+ ··· + u + 1
c
4
u
28
− 2u
27
+ ··· − 45u + 25
c
5
, c
8
u
28
+ u
26
+ ··· + 3u + 1
c
7
, c
10
u
28
+ u
27
+ ··· + 21u + 1
c
11
u
28
− 28u
27
+ ··· − 50u + 4
c
12
u
28
− 26u
27
+ ··· − 5120u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 11y
27
+ ··· + 264448y + 65536
c
2
, c
6
y
28
+ 17y
27
+ ··· + 1360y + 256
c
3
, c
9
y
28
− 31y
27
+ ··· − 7y + 1
c
4
y
28
− 16y
27
+ ··· − 10575y + 625
c
5
, c
8
y
28
+ 2y
27
+ ··· + y + 1
c
7
, c
10
y
28
− 39y
27
+ ··· − 197y + 1
c
11
y
28
− 22y
27
+ ··· − 188y + 16
c
12
y
28
− 6y
27
+ ··· − 1310720y + 262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.029760 + 1.024060I
a = −0.76705 + 1.20618I
b = 0.33513 + 2.03849I
−1.70801 + 1.93955I −4.01504 − 3.31370I
u = −0.029760 − 1.024060I
a = −0.76705 − 1.20618I
b = 0.33513 − 2.03849I
−1.70801 − 1.93955I −4.01504 + 3.31370I
u = −0.205800 + 0.952470I
a = −0.890270 − 0.134444I
b = −1.028510 + 0.354995I
−1.87676 − 2.57239I −5.76873 + 3.90772I
u = −0.205800 − 0.952470I
a = −0.890270 + 0.134444I
b = −1.028510 − 0.354995I
−1.87676 + 2.57239I −5.76873 − 3.90772I
u = 0.703844 + 0.651022I
a = 0.364061 + 0.072255I
b = −0.169040 − 0.626677I
2.58954 − 1.93444I 4.44360 + 1.82417I
u = 0.703844 − 0.651022I
a = 0.364061 − 0.072255I
b = −0.169040 + 0.626677I
2.58954 + 1.93444I 4.44360 − 1.82417I
u = −0.233119 + 1.022850I
a = 0.432125 − 0.884732I
b = 0.046325 − 1.319720I
−0.84729 − 2.02401I −1.05491 + 4.41629I
u = −0.233119 − 1.022850I
a = 0.432125 + 0.884732I
b = 0.046325 + 1.319720I
−0.84729 + 2.02401I −1.05491 − 4.41629I
u = −0.592728 + 0.886067I
a = 0.419564 − 0.328119I
b = 0.484607 − 0.267874I
0.19636 − 2.32367I 1.59759 + 0.30167I
u = −0.592728 − 0.886067I
a = 0.419564 + 0.328119I
b = 0.484607 + 0.267874I
0.19636 + 2.32367I 1.59759 − 0.30167I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.126080 + 0.017717I
a = 1.48097 − 0.28232I
b = −0.203539 + 0.072850I
−9.14619 + 10.60730I −4.00237 − 5.50977I
u = −1.126080 − 0.017717I
a = 1.48097 + 0.28232I
b = −0.203539 − 0.072850I
−9.14619 − 10.60730I −4.00237 + 5.50977I
u = −1.213710 + 0.122756I
a = −1.169300 − 0.161303I
b = 0.313944 − 0.165481I
−6.88343 + 0.76194I −9.63760 − 8.88824I
u = −1.213710 − 0.122756I
a = −1.169300 + 0.161303I
b = 0.313944 + 0.165481I
−6.88343 − 0.76194I −9.63760 + 8.88824I
u = 0.134895 + 0.764791I
a = 0.249686 − 0.929537I
b = −0.794879 − 0.643863I
−1.33224 − 1.70353I −4.58528 + 4.79833I
u = 0.134895 − 0.764791I
a = 0.249686 + 0.929537I
b = −0.794879 + 0.643863I
−1.33224 + 1.70353I −4.58528 − 4.79833I
u = 0.679542 + 1.054720I
a = −0.182005 + 0.228644I
b = 0.574163 + 0.446259I
1.38884 + 7.31481I −0.62097 − 4.93244I
u = 0.679542 − 1.054720I
a = −0.182005 − 0.228644I
b = 0.574163 − 0.446259I
1.38884 − 7.31481I −0.62097 + 4.93244I
u = −0.460065 + 0.249682I
a = 0.997340 − 0.899044I
b = 0.291991 − 0.299264I
1.23290 − 0.94981I 4.62875 + 1.98787I
u = −0.460065 − 0.249682I
a = 0.997340 + 0.899044I
b = 0.291991 + 0.299264I
1.23290 + 0.94981I 4.62875 − 1.98787I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.55190 + 1.37856I
a = −0.123948 − 1.306340I
b = −0.07928 − 2.82342I
−13.4242 − 16.5538I 0. + 7.97631I
u = −0.55190 − 1.37856I
a = −0.123948 + 1.306340I
b = −0.07928 + 2.82342I
−13.4242 + 16.5538I 0. − 7.97631I
u = −0.52857 + 1.41990I
a = −0.376449 − 1.012200I
b = −0.77064 − 2.32349I
−13.6922 + 4.6715I 0
u = −0.52857 − 1.41990I
a = −0.376449 + 1.012200I
b = −0.77064 + 2.32349I
−13.6922 − 4.6715I 0
u = −0.61460 + 1.40685I
a = 0.274785 + 0.995117I
b = 0.28808 + 2.29388I
−10.96370 − 7.28590I 0
u = −0.61460 − 1.40685I
a = 0.274785 − 0.995117I
b = 0.28808 − 2.29388I
−10.96370 + 7.28590I 0
u = −0.46195 + 1.47320I
a = 0.040494 + 1.014100I
b = 0.21165 + 2.44842I
−12.15350 − 5.19576I −13.77473 + 0.I
u = −0.46195 − 1.47320I
a = 0.040494 − 1.014100I
b = 0.21165 − 2.44842I
−12.15350 + 5.19576I −13.77473 + 0.I
7
II. I
u
2
= h−87u
16
+ 385u
15
+ · · · + 77b − 41, −190u
16
+ 693u
15
+ · · · +
231a − 163, u
17
− 4u
16
+ · · · − 6u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
0.822511u
16
− 3u
15
+ ··· + 1.92641u + 0.705628
87
77
u
16
− 5u
15
+ ··· −
9
77
u +
41
77
a
4
=
0.307359u
16
− 3u
15
+ ··· − 2.04329u + 2.82684
−1.68831u
16
+ 5u
15
+ ··· + 1.51948u + 2.07792
a
7
=
u
u
a
8
=
−1.99567u
16
+ 8u
15
+ ··· + 4.56277u + 0.251082
−1.05195u
16
+ 5u
15
+ ··· + 3.24675u − 2.01299
a
1
=
u
2
+ 1
−u
4
a
11
=
0.722944u
16
− 2u
15
+ ··· + 0.982684u + 0.930736
46
33
u
16
− 5u
15
+ ··· −
26
33
u −
5
33
a
9
=
0.822511u
16
− 3u
15
+ ··· + 1.92641u + 0.705628
65
33
u
16
− 8u
15
+ ··· −
31
33
u +
8
33
a
12
=
0.995671u
16
− 3u
15
+ ··· + 0.437229u − 2.25108
0.757576u
16
− 3u
15
+ ··· − 4.51515u − 0.0606061
a
5
=
0.601732u
16
− 4u
15
+ ··· − 1.77489u + 1.90043
−1.12121u
16
+ 2u
15
+ ··· + 1.24242u + 2.96970
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
733
231
u
16
+ 12u
15
+ ··· −
1504
231
u −
2089
231
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 10u
16
+ ··· − 12u + 1
c
2
u
17
− 4u
16
+ ··· − 6u
2
− 1
c
3
, c
9
u
17
− u
16
+ ··· + 3u + 1
c
4
u
17
+ 2u
16
+ ··· + 9u + 3
c
5
, c
8
u
17
+ 3u
15
+ ··· − u + 1
c
6
u
17
+ 4u
16
+ ··· + 6u
2
+ 1
c
7
, c
10
u
17
− 7u
16
+ ··· + 3u − 1
c
11
u
17
+ 11u
16
+ ··· − 3066u − 441
c
12
u
17
+ 5u
16
+ ··· − 2u − 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 2y
16
+ ··· − 72y −1
c
2
, c
6
y
17
+ 10y
16
+ ··· − 12y −1
c
3
, c
9
y
17
− 15y
16
+ ··· − 5y −1
c
4
y
17
− 8y
16
+ ··· − 69y −9
c
5
, c
8
y
17
+ 6y
16
+ ··· − y −1
c
7
, c
10
y
17
− 15y
16
+ ··· − 7y −1
c
11
y
17
− 17y
16
+ ··· + 1120140y −194481
c
12
y
17
− 7y
16
+ ··· + 10y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.681671 + 0.839345I
a = −0.122858 + 0.250052I
b = −0.441734 − 0.354193I
−0.38004 − 2.63462I −9.27234 + 5.42347I
u = −0.681671 − 0.839345I
a = −0.122858 − 0.250052I
b = −0.441734 + 0.354193I
−0.38004 + 2.63462I −9.27234 − 5.42347I
u = 0.140165 + 1.110590I
a = 0.71958 + 1.33512I
b = −0.09285 + 2.38278I
−4.67353 + 6.46548I −8.36385 − 4.08762I
u = 0.140165 − 1.110590I
a = 0.71958 − 1.33512I
b = −0.09285 − 2.38278I
−4.67353 − 6.46548I −8.36385 + 4.08762I
u = 0.826686 + 0.794603I
a = −0.711849 + 0.393093I
b = −0.347366 + 0.674089I
1.46643 − 2.44849I −3.63614 + 3.80526I
u = 0.826686 − 0.794603I
a = −0.711849 − 0.393093I
b = −0.347366 − 0.674089I
1.46643 + 2.44849I −3.63614 − 3.80526I
u = 1.16029
a = −1.30387
b = 0.242504
−6.83994 −5.94510
u = 0.760360 + 0.946681I
a = 0.216684 − 0.748655I
b = −0.135378 − 0.914178I
0.99165 + 8.38015I −2.49309 − 10.10429I
u = 0.760360 − 0.946681I
a = 0.216684 + 0.748655I
b = −0.135378 + 0.914178I
0.99165 − 8.38015I −2.49309 + 10.10429I
u = 0.123423 + 0.767586I
a = 1.31748 − 1.02145I
b = 1.50929 + 0.04931I
−3.32631 − 5.28974I −7.90203 + 5.12286I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.123423 − 0.767586I
a = 1.31748 + 1.02145I
b = 1.50929 − 0.04931I
−3.32631 + 5.28974I −7.90203 − 5.12286I
u = −0.063406 + 1.278620I
a = −0.358068 − 0.728040I
b = 0.48768 − 1.65706I
−6.36689 − 2.53679I −10.96403 + 3.03478I
u = −0.063406 − 1.278620I
a = −0.358068 + 0.728040I
b = 0.48768 + 1.65706I
−6.36689 + 2.53679I −10.96403 − 3.03478I
u = 0.52000 + 1.40243I
a = 0.163383 − 1.128450I
b = 0.29881 − 2.51025I
−11.37900 + 5.95622I −6.44408 − 3.49025I
u = 0.52000 − 1.40243I
a = 0.163383 + 1.128450I
b = 0.29881 + 2.51025I
−11.37900 − 5.95622I −6.44408 + 3.49025I
u = −0.205705 + 0.307610I
a = 1.42758 + 1.56792I
b = −0.899718 + 0.379291I
−2.52117 + 1.45550I −12.95189 − 5.06302I
u = −0.205705 − 0.307610I
a = 1.42758 − 1.56792I
b = −0.899718 − 0.379291I
−2.52117 − 1.45550I −12.95189 + 5.06302I
12
III. I
u
3
= h343u
10
a
3
+ 5345u
10
a
2
+ · · · + 5127a + 18129, u
10
a
3
− 3u
10
a
2
+
· · · + 26a + 1, u
11
− 2u
10
+ · · · + 4u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
a
−0.0262373a
3
u
10
− 0.408858a
2
u
10
+ ··· − 0.392182a − 1.38675
a
4
=
0.318825a
3
u
10
− 0.142507a
2
u
10
+ ··· − 0.164385a + 1.37895
1.32211a
3
u
10
+ 0.701752a
2
u
10
+ ··· − 0.826589a + 0.354548
a
7
=
u
u
a
8
=
0.360514a
3
u
10
− 0.000152987a
2
u
10
+ ··· − 0.115582a + 0.209210
1.27721a
3
u
10
+ 1.06035a
2
u
10
+ ··· + 1.09699a − 0.0332747
a
1
=
u
2
+ 1
−u
4
a
11
=
0.156276a
3
u
10
+ 0.274918a
2
u
10
+ ··· + 0.700375a + 0.0499503
0.639180a
3
u
10
+ 0.619292a
2
u
10
+ ··· − 0.125143a − 1.88136
a
9
=
a
−0.0262373a
3
u
10
− 0.408858a
2
u
10
+ ··· − 0.392182a − 1.38675
a
12
=
0.156276a
3
u
10
+ 0.274918a
2
u
10
+ ··· + 0.700375a + 0.0499503
0.890691a
3
u
10
+ 1.68729a
2
u
10
+ ··· − 0.249063a − 2.37512
a
5
=
0.538591a
3
u
10
− 0.338866a
2
u
10
+ ··· − 0.0135394a + 1.39976
1.48596a
3
u
10
+ 1.15299a
2
u
10
+ ··· − 0.418267a − 0.209822
(ii) Obstruction class = −1
(iii) Cusp Shapes =
18852
13073
u
10
a
3
−
8
13073
u
10
a
2
+ ··· −
6044
13073
a +
50159
13073
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
11
+ 8u
10
+ ··· − 18u
2
− 1)
4
c
2
, c
6
(u
11
+ 2u
10
+ ··· + 4u + 1)
4
c
3
, c
9
u
44
− 25u
42
+ ··· + 193u + 1
c
4
u
44
− 6u
43
+ ··· − 351984u + 130591
c
5
, c
8
u
44
− 2u
43
+ ··· + 95u + 25
c
7
, c
10
u
44
+ 5u
43
+ ··· + 281670u + 28225
c
11
(u
11
+ 5u
10
+ ··· − 10u − 4)
4
c
12
(u
2
+ u + 1)
22
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
11
− 8y
10
+ ··· − 36y −1)
4
c
2
, c
6
(y
11
+ 8y
10
+ ··· − 18y
2
− 1)
4
c
3
, c
9
y
44
− 50y
43
+ ··· + 33239y + 1
c
4
y
44
− 44y
43
+ ··· + 412133171800y + 17054009281
c
5
, c
8
y
44
+ 10y
43
+ ··· + 21775y + 625
c
7
, c
10
y
44
− 53y
43
+ ··· − 30404080600y + 796650625
c
11
(y
11
− 5y
10
+ ··· + 108y −16)
4
c
12
(y
2
+ y + 1)
22
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.617799 + 0.778228I
a = 0.589454 + 0.528793I
b = 0.540084 − 0.380969I
−0.43565 − 4.46673I −8.45208 + 10.60791I
u = −0.617799 + 0.778228I
a = −0.056046 − 0.700162I
b = −0.643608 − 0.688149I
−0.435652 − 0.406964I −8.45208 + 3.67970I
u = −0.617799 + 0.778228I
a = −0.439822 − 1.326850I
b = 0.597857 − 1.109030I
−0.435652 − 0.406964I −8.45208 + 3.67970I
u = −0.617799 + 0.778228I
a = 1.41393 + 0.05528I
b = 1.03920 + 1.23994I
−0.43565 − 4.46673I −8.45208 + 10.60791I
u = −0.617799 − 0.778228I
a = 0.589454 − 0.528793I
b = 0.540084 + 0.380969I
−0.43565 + 4.46673I −8.45208 − 10.60791I
u = −0.617799 − 0.778228I
a = −0.056046 + 0.700162I
b = −0.643608 + 0.688149I
−0.435652 + 0.406964I −8.45208 − 3.67970I
u = −0.617799 − 0.778228I
a = −0.439822 + 1.326850I
b = 0.597857 + 1.109030I
−0.435652 + 0.406964I −8.45208 − 3.67970I
u = −0.617799 − 0.778228I
a = 1.41393 − 0.05528I
b = 1.03920 − 1.23994I
−0.43565 + 4.46673I −8.45208 − 10.60791I
u = 1.06351
a = −1.49958 + 0.14846I
b = −0.022831 + 0.204938I
−7.98334 + 2.02988I −7.16744 − 3.46410I
u = 1.06351
a = −1.49958 − 0.14846I
b = −0.022831 − 0.204938I
−7.98334 − 2.02988I −7.16744 + 3.46410I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.06351
a = 1.61628 + 0.35059I
b = −0.233271 − 0.238643I
−7.98334 − 2.02988I −7.16744 + 3.46410I
u = 1.06351
a = 1.61628 − 0.35059I
b = −0.233271 + 0.238643I
−7.98334 + 2.02988I −7.16744 − 3.46410I
u = 0.221199 + 1.131890I
a = −0.282121 − 1.073420I
b = 0.52445 − 3.15670I
−4.38744 + 7.66724I −6.48609 − 11.64165I
u = 0.221199 + 1.131890I
a = −0.722841 − 0.452983I
b = 0.335223 − 0.182775I
−4.38744 + 3.60747I −6.48609 − 4.71344I
u = 0.221199 + 1.131890I
a = −0.253046 + 1.234040I
b = −0.04671 + 2.56573I
−4.38744 + 3.60747I −6.48609 − 4.71344I
u = 0.221199 + 1.131890I
a = 1.44648 + 1.52804I
b = 1.39498 + 1.71537I
−4.38744 + 7.66724I −6.48609 − 11.64165I
u = 0.221199 − 1.131890I
a = −0.282121 + 1.073420I
b = 0.52445 + 3.15670I
−4.38744 − 7.66724I −6.48609 + 11.64165I
u = 0.221199 − 1.131890I
a = −0.722841 + 0.452983I
b = 0.335223 + 0.182775I
−4.38744 − 3.60747I −6.48609 + 4.71344I
u = 0.221199 − 1.131890I
a = −0.253046 − 1.234040I
b = −0.04671 − 2.56573I
−4.38744 − 3.60747I −6.48609 + 4.71344I
u = 0.221199 − 1.131890I
a = 1.44648 − 1.52804I
b = 1.39498 − 1.71537I
−4.38744 − 7.66724I −6.48609 + 11.64165I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.029838 + 1.264780I
a = −0.177967 + 0.946487I
b = −0.42614 + 2.84232I
−6.65088 − 0.57787I −11.49826 − 1.42165I
u = −0.029838 + 1.264780I
a = −1.062190 − 0.030421I
b = −0.504118 + 0.124524I
−6.65088 − 0.57787I −11.49826 − 1.42165I
u = −0.029838 + 1.264780I
a = −0.11469 − 1.68739I
b = 0.13874 − 2.62771I
−6.65088 − 4.63764I −11.49826 + 5.50656I
u = −0.029838 + 1.264780I
a = −0.058572 + 0.155353I
b = −2.24297 + 0.33866I
−6.65088 − 4.63764I −11.49826 + 5.50656I
u = −0.029838 − 1.264780I
a = −0.177967 − 0.946487I
b = −0.42614 − 2.84232I
−6.65088 + 0.57787I −11.49826 + 1.42165I
u = −0.029838 − 1.264780I
a = −1.062190 + 0.030421I
b = −0.504118 − 0.124524I
−6.65088 + 0.57787I −11.49826 + 1.42165I
u = −0.029838 − 1.264780I
a = −0.11469 + 1.68739I
b = 0.13874 + 2.62771I
−6.65088 + 4.63764I −11.49826 − 5.50656I
u = −0.029838 − 1.264780I
a = −0.058572 − 0.155353I
b = −2.24297 − 0.33866I
−6.65088 + 4.63764I −11.49826 − 5.50656I
u = 0.52365 + 1.35993I
a = −0.440908 + 1.028850I
b = −1.08236 + 2.43446I
−12.23950 + 3.61593I −9.10897 − 0.19933I
u = 0.52365 + 1.35993I
a = 0.052366 − 1.202380I
b = 0.35777 − 2.45711I
−12.2395 + 7.6757I −9.10897 − 7.12753I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.52365 + 1.35993I
a = 0.337952 − 1.232570I
b = 0.40689 − 2.36204I
−12.23950 + 3.61593I −9.10897 − 0.19933I
u = 0.52365 + 1.35993I
a = −0.177318 + 1.393410I
b = 0.04268 + 3.00587I
−12.2395 + 7.6757I −9.10897 − 7.12753I
u = 0.52365 − 1.35993I
a = −0.440908 − 1.028850I
b = −1.08236 − 2.43446I
−12.23950 − 3.61593I −9.10897 + 0.19933I
u = 0.52365 − 1.35993I
a = 0.052366 + 1.202380I
b = 0.35777 + 2.45711I
−12.2395 − 7.6757I −9.10897 + 7.12753I
u = 0.52365 − 1.35993I
a = 0.337952 + 1.232570I
b = 0.40689 + 2.36204I
−12.23950 − 3.61593I −9.10897 + 0.19933I
u = 0.52365 − 1.35993I
a = −0.177318 − 1.393410I
b = 0.04268 − 3.00587I
−12.2395 − 7.6757I −9.10897 + 7.12753I
u = 0.371033 + 0.270161I
a = 0.01049750 + 0.00431977I
b = −1.009870 − 0.210773I
−1.90371 − 1.10694I −0.37088 − 1.58915I
u = 0.371033 + 0.270161I
a = 2.04632 − 0.92835I
b = −0.321194 − 0.354636I
−1.90371 − 1.10694I −0.37088 − 1.58915I
u = 0.371033 + 0.270161I
a = −2.71130 + 0.68471I
b = −0.187627 − 0.749850I
−1.90371 − 5.16670I −0.37088 + 5.33905I
u = 0.371033 + 0.270161I
a = 2.48312 + 1.55855I
b = 1.342820 − 0.120180I
−1.90371 − 5.16670I −0.37088 + 5.33905I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.371033 − 0.270161I
a = 0.01049750 − 0.00431977I
b = −1.009870 + 0.210773I
−1.90371 + 1.10694I −0.37088 + 1.58915I
u = 0.371033 − 0.270161I
a = 2.04632 + 0.92835I
b = −0.321194 + 0.354636I
−1.90371 + 1.10694I −0.37088 + 1.58915I
u = 0.371033 − 0.270161I
a = −2.71130 − 0.68471I
b = −0.187627 + 0.749850I
−1.90371 + 5.16670I −0.37088 − 5.33905I
u = 0.371033 − 0.270161I
a = 2.48312 − 1.55855I
b = 1.342820 + 0.120180I
−1.90371 + 5.16670I −0.37088 − 5.33905I
20
IV. I
u
4
= hb − a + u, a
2
+ a − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u + 1
a
10
=
a
a − u
a
4
=
2
−au − a + 1
a
7
=
u
u
a
8
=
au + a + u
au + a + u + 1
a
1
=
−u
−u
a
11
=
a + 1
a − u + 1
a
9
=
a
au + 2a − u
a
12
=
a + 1
a − u + 1
a
5
=
−au − u + 1
−2au − a − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u + 3
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
10
, c
12
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
3
, c
5
, c
8
c
9
u
4
− u
3
+ 2u + 1
c
4
u
4
− 3u + 3
c
11
u
4
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
10
, c
12
(y
2
+ y + 1)
2
c
3
, c
5
, c
8
c
9
y
4
− y
3
+ 6y
2
− 4y + 1
c
4
y
4
+ 6y
2
− 9y + 9
c
11
y
4
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.473561 + 0.444772I
b = 0.973561 − 0.421254I
− 4.05977I 1.50000 + 2.59808I
u = −0.500000 + 0.866025I
a = −1.47356 − 0.44477I
b = −0.97356 − 1.31080I
− 4.05977I 1.50000 + 2.59808I
u = −0.500000 − 0.866025I
a = 0.473561 − 0.444772I
b = 0.973561 + 0.421254I
4.05977I 1.50000 − 2.59808I
u = −0.500000 − 0.866025I
a = −1.47356 + 0.44477I
b = −0.97356 + 1.31080I
4.05977I 1.50000 − 2.59808I
24
V. I
u
5
= hb − a + 1, a
2
− au − a + 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u + 1
a
10
=
a
a − 1
a
4
=
u + 1
au + 2u + 2
a
7
=
u
u
a
8
=
−au + u
−au + 2u
a
1
=
−u
−u
a
11
=
a − u − 1
a − u − 2
a
9
=
a
au + 2a − 1
a
12
=
a − u − 1
a − u − 2
a
5
=
−a + 2u + 1
au − a + 3u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u − 1
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
10
, c
12
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
3
, c
5
, c
8
c
9
u
4
+ 2u
3
− u + 1
c
4
u
4
+ 3u
3
+ 3u
2
+ 3u + 3
c
11
u
4
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
10
, c
12
(y
2
+ y + 1)
2
c
3
, c
5
, c
8
c
9
y
4
− 4y
3
+ 6y
2
− y + 1
c
4
y
4
− 3y
3
− 3y
2
+ 9y + 9
c
11
y
4
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.148403 − 0.632502I
b = −0.851597 − 0.632502I
0 1.50000 − 4.33013I
u = −0.500000 + 0.866025I
a = 0.35160 + 1.49853I
b = −0.64840 + 1.49853I
0 1.50000 − 4.33013I
u = −0.500000 − 0.866025I
a = 0.148403 + 0.632502I
b = −0.851597 + 0.632502I
0 1.50000 + 4.33013I
u = −0.500000 − 0.866025I
a = 0.35160 − 1.49853I
b = −0.64840 − 1.49853I
0 1.50000 + 4.33013I
28
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
11
+ 8u
10
+ ··· − 18u
2
− 1)
4
· (u
17
− 10u
16
+ ··· − 12u + 1)(u
28
+ 17u
27
+ ··· + 1360u + 256)
c
2
((u
2
+ u + 1)
4
)(u
11
+ 2u
10
+ ··· + 4u + 1)
4
(u
17
− 4u
16
+ ··· − 6u
2
− 1)
· (u
28
− 9u
27
+ ··· − 124u + 16)
c
3
, c
9
(u
4
− u
3
+ 2u + 1)(u
4
+ 2u
3
− u + 1)(u
17
− u
16
+ ··· + 3u + 1)
· (u
28
+ u
27
+ ··· + u + 1)(u
44
− 25u
42
+ ··· + 193u + 1)
c
4
(u
4
− 3u + 3)(u
4
+ 3u
3
+ ··· + 3u + 3)(u
17
+ 2u
16
+ ··· + 9u + 3)
· (u
28
− 2u
27
+ ··· − 45u + 25)(u
44
− 6u
43
+ ··· − 351984u + 130591)
c
5
, c
8
(u
4
− u
3
+ 2u + 1)(u
4
+ 2u
3
− u + 1)(u
17
+ 3u
15
+ ··· − u + 1)
· (u
28
+ u
26
+ ··· + 3u + 1)(u
44
− 2u
43
+ ··· + 95u + 25)
c
6
((u
2
− u + 1)
4
)(u
11
+ 2u
10
+ ··· + 4u + 1)
4
(u
17
+ 4u
16
+ ··· + 6u
2
+ 1)
· (u
28
− 9u
27
+ ··· − 124u + 16)
c
7
, c
10
((u
2
− u + 1)
4
)(u
17
− 7u
16
+ ··· + 3u − 1)(u
28
+ u
27
+ ··· + 21u + 1)
· (u
44
+ 5u
43
+ ··· + 281670u + 28225)
c
11
u
8
(u
11
+ 5u
10
+ ··· − 10u − 4)
4
(u
17
+ 11u
16
+ ··· − 3066u − 441)
· (u
28
− 28u
27
+ ··· − 50u + 4)
c
12
((u
2
− u + 1)
4
)(u
2
+ u + 1)
22
(u
17
+ 5u
16
+ ··· − 2u − 1)
· (u
28
− 26u
27
+ ··· − 5120u + 512)
29
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
11
− 8y
10
+ ··· − 36y −1)
4
· (y
17
− 2y
16
+ ··· − 72y −1)(y
28
− 11y
27
+ ··· + 264448y + 65536)
c
2
, c
6
((y
2
+ y + 1)
4
)(y
11
+ 8y
10
+ ··· − 18y
2
− 1)
4
· (y
17
+ 10y
16
+ ··· − 12y −1)(y
28
+ 17y
27
+ ··· + 1360y + 256)
c
3
, c
9
(y
4
− 4y
3
+ 6y
2
− y + 1)(y
4
− y
3
+ 6y
2
− 4y + 1)
· (y
17
− 15y
16
+ ··· − 5y −1)(y
28
− 31y
27
+ ··· − 7y + 1)
· (y
44
− 50y
43
+ ··· + 33239y + 1)
c
4
(y
4
+ 6y
2
− 9y + 9)(y
4
− 3y
3
+ ··· + 9y + 9)(y
17
− 8y
16
+ ··· − 69y −9)
· (y
28
− 16y
27
+ ··· − 10575y + 625)
· (y
44
− 44y
43
+ ··· + 412133171800y + 17054009281)
c
5
, c
8
(y
4
− 4y
3
+ 6y
2
− y + 1)(y
4
− y
3
+ 6y
2
− 4y + 1)(y
17
+ 6y
16
+ ··· − y −1)
· (y
28
+ 2y
27
+ ··· + y + 1)(y
44
+ 10y
43
+ ··· + 21775y + 625)
c
7
, c
10
((y
2
+ y + 1)
4
)(y
17
− 15y
16
+ ··· − 7y −1)
· (y
28
− 39y
27
+ ··· − 197y + 1)
· (y
44
− 53y
43
+ ··· − 30404080600y + 796650625)
c
11
y
8
(y
11
− 5y
10
+ ··· + 108y −16)
4
· (y
17
− 17y
16
+ ··· + 1120140y −194481)
· (y
28
− 22y
27
+ ··· − 188y + 16)
c
12
((y
2
+ y + 1)
26
)(y
17
− 7y
16
+ ··· + 10y −1)
· (y
28
− 6y
27
+ ··· − 1310720y + 262144)
30
