12a
0066
(K12a
0066
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 12 9 4 11 1 6 8 10
Solving Sequence
4,8
7
3,12
11 9 6 5 2 10 1
c
7
c
3
c
11
c
8
c
6
c
5
c
2
c
10
c
12
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h6.80476 × 10
108
u
49
+ 2.19909 × 10
108
u
48
+ ··· + 1.95260 × 10
111
b − 2.72720 × 10
111
,
− 4.84605 × 10
110
u
49
− 1.94945 × 10
110
u
48
+ ··· + 1.24966 × 10
113
a + 4.21327 × 10
112
,
u
50
− 12u
48
+ ··· + 288u + 256i
I
u
2
= h−1.95324 × 10
37
au
41
+ 1.89496 × 10
37
u
41
+ ··· + 2.35403 × 10
38
a − 3.16022 × 10
38
,
1.51510 × 10
33
au
41
+ 3.94443 × 10
33
u
41
+ ··· − 3.53502 × 10
34
a + 1.31758 × 10
33
, u
42
− u
41
+ ··· − 28u + 8i
I
u
3
= hb − 1, −2u
5
+ 4u
3
+ 2u
2
+ 2a − 4u + 1, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
v
1
= ha, 4v
3
+ 7v
2
+ 3b + 6v + 1, 4v
4
+ 7v
3
+ 2v
2
− v + 1i
I
v
2
= ha, v
2
b + b
2
− 2bv + v
2
+ b − v, v
3
− 2v
2
+ v −1i
* 5 irreducible components of dim
C
= 0, with total 150 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
= h6.80 × 10
108
u
49
+ 2.20 × 10
108
u
48
+ · · · + 1.95 × 10
111
b − 2.73 ×
10
111
, −4.85 × 10
110
u
49
− 1.95 × 10
110
u
48
+ · · · + 1.25 × 10
113
a + 4.21 ×
10
112
, u
50
− 12u
48
+ · · · + 288u + 256i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
12
=
0.00387789u
49
+ 0.00155998u
48
+ ··· + 1.14208u − 0.337153
−0.00348498u
49
− 0.00112624u
48
+ ··· − 0.0926115u + 1.39671
a
11
=
0.000392909u
49
+ 0.000433746u
48
+ ··· + 1.04946u + 1.05955
−0.00348498u
49
− 0.00112624u
48
+ ··· − 0.0926115u + 1.39671
a
9
=
0.00111006u
49
+ 0.000131981u
48
+ ··· − 1.27976u + 0.512699
0.00140446u
49
+ 0.00290843u
48
+ ··· − 5.70099u − 1.73217
a
6
=
0.00201779u
49
+ 0.00143250u
48
+ ··· − 0.109009u + 0.480487
−0.00781200u
49
− 0.00431636u
48
+ ··· + 5.00237u + 1.88446
a
5
=
0.00484500u
49
− 0.000170753u
48
+ ··· − 3.72519u − 1.11366
−0.00778716u
49
− 0.000940792u
48
+ ··· + 8.29788u + 2.19949
a
2
=
0.00532065u
49
+ 5.33603 × 10
−6
u
48
+ ··· − 5.76383u − 1.04212
−0.00949931u
49
− 0.00114275u
48
+ ··· + 8.12540u + 2.15441
a
10
=
0.00121926u
49
− 0.00119597u
48
+ ··· − 2.16726u − 0.00363201
0.00360994u
49
+ 0.00427773u
48
+ ··· − 1.54167u + 0.244495
a
1
=
−0.00294216u
49
− 0.00111155u
48
+ ··· + 4.57269u + 1.08583
0.00749971u
49
+ 0.000932472u
48
+ ··· − 7.22456u − 1.91494
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0110690u
49
− 0.00700300u
48
+ ··· + 18.6252u + 7.32722
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
+ 24u
49
+ ··· − 3807u + 256
c
2
, c
4
u
50
− 4u
49
+ ··· − 129u + 16
c
3
, c
7
u
50
− 12u
48
+ ··· + 288u + 256
c
5
, c
6
64(64u
50
+ 160u
49
+ ··· + 14u
2
+ 1)
c
8
, c
9
, c
11
c
12
u
50
+ 6u
49
+ ··· + 2u + 1
c
10
u
50
− 6u
49
+ ··· − 94208u + 16384
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
+ 8y
49
+ ··· − 4265025y + 65536
c
2
, c
4
y
50
− 24y
49
+ ··· + 3807y + 256
c
3
, c
7
y
50
− 24y
49
+ ··· − 971776y + 65536
c
5
, c
6
4096(4096y
50
− 31744y
49
+ ··· + 28y + 1)
c
8
, c
9
, c
11
c
12
y
50
+ 22y
49
+ ··· + 50y + 1
c
10
y
50
− 14y
49
+ ··· − 3875536896y + 268435456
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.898117 + 0.279435I
a = 0.671077 + 0.045381I
b = −0.247217 − 0.158952I
1.50673 + 0.62503I 6.47419 − 0.03134I
u = 0.898117 − 0.279435I
a = 0.671077 − 0.045381I
b = −0.247217 + 0.158952I
1.50673 − 0.62503I 6.47419 + 0.03134I
u = 0.965194 + 0.442129I
a = −1.61017 − 0.22648I
b = 1.071190 − 0.624443I
−2.71273 + 4.53515I −2.87509 − 2.93075I
u = 0.965194 − 0.442129I
a = −1.61017 + 0.22648I
b = 1.071190 + 0.624443I
−2.71273 − 4.53515I −2.87509 + 2.93075I
u = −0.815600 + 0.692403I
a = 0.972370 + 0.356228I
b = −0.469378 − 0.920279I
−0.49128 − 8.69321I −1.67470 + 11.86102I
u = −0.815600 − 0.692403I
a = 0.972370 − 0.356228I
b = −0.469378 + 0.920279I
−0.49128 + 8.69321I −1.67470 − 11.86102I
u = 0.391611 + 0.792627I
a = −2.56595 − 0.65373I
b = 1.172710 − 0.211438I
−3.48472 − 1.30066I 1.53330 + 11.98211I
u = 0.391611 − 0.792627I
a = −2.56595 + 0.65373I
b = 1.172710 + 0.211438I
−3.48472 + 1.30066I 1.53330 − 11.98211I
u = −1.113190 + 0.328139I
a = −0.766999 + 0.669164I
b = 1.346160 − 0.166657I
0.75440 − 1.33711I 8.60470 + 4.56613I
u = −1.113190 − 0.328139I
a = −0.766999 − 0.669164I
b = 1.346160 + 0.166657I
0.75440 + 1.33711I 8.60470 − 4.56613I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.003630 + 0.588097I
a = 0.616489 − 0.235311I
b = −0.351193 + 0.342652I
−0.52997 − 5.02287I 1.42361 + 2.95767I
u = −1.003630 − 0.588097I
a = 0.616489 + 0.235311I
b = −0.351193 − 0.342652I
−0.52997 + 5.02287I 1.42361 − 2.95767I
u = 1.112250 + 0.378181I
a = 1.37497 + 1.15202I
b = −0.511869 + 1.290650I
3.14115 + 10.05270I 1.54666 − 6.99924I
u = 1.112250 − 0.378181I
a = 1.37497 − 1.15202I
b = −0.511869 − 1.290650I
3.14115 − 10.05270I 1.54666 + 6.99924I
u = −0.195744 + 1.173710I
a = 0.764863 − 0.753983I
b = −0.460044 + 1.282800I
5.62294 + 7.71288I 3.01131 − 4.10494I
u = −0.195744 − 1.173710I
a = 0.764863 + 0.753983I
b = −0.460044 − 1.282800I
5.62294 − 7.71288I 3.01131 + 4.10494I
u = −0.778976 + 0.095167I
a = −1.011110 − 0.147769I
b = 0.774047 − 0.742819I
−1.54304 + 0.82047I −0.34103 + 1.51386I
u = −0.778976 − 0.095167I
a = −1.011110 + 0.147769I
b = 0.774047 + 0.742819I
−1.54304 − 0.82047I −0.34103 − 1.51386I
u = 0.546215 + 0.490567I
a = −0.47633 − 2.47862I
b = 1.002780 + 0.289724I
−3.92674 − 0.66017I −8.3250 − 13.1911I
u = 0.546215 − 0.490567I
a = −0.47633 + 2.47862I
b = 1.002780 − 0.289724I
−3.92674 + 0.66017I −8.3250 + 13.1911I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.502657 + 1.174230I
a = 0.840947 + 0.823851I
b = −0.53623 − 1.31854I
4.16035 − 12.95250I 0.95450 + 8.17982I
u = 0.502657 − 1.174230I
a = 0.840947 − 0.823851I
b = −0.53623 + 1.31854I
4.16035 + 12.95250I 0.95450 − 8.17982I
u = 1.151050 + 0.579567I
a = −1.12350 − 0.93703I
b = 1.379840 + 0.292717I
−1.15010 + 6.50993I 2.90407 − 9.24766I
u = 1.151050 − 0.579567I
a = −1.12350 + 0.93703I
b = 1.379840 − 0.292717I
−1.15010 − 6.50993I 2.90407 + 9.24766I
u = −1.241740 + 0.418945I
a = 0.523890 − 0.607495I
b = 0.048258 − 0.824590I
−1.051330 + 0.854717I −9.88678 − 3.08419I
u = −1.241740 − 0.418945I
a = 0.523890 + 0.607495I
b = 0.048258 + 0.824590I
−1.051330 − 0.854717I −9.88678 + 3.08419I
u = 0.570734 + 0.264073I
a = 0.981699 + 0.648623I
b = −0.598386 − 1.137800I
1.13411 − 7.11668I 4.00252 − 2.15626I
u = 0.570734 − 0.264073I
a = 0.981699 − 0.648623I
b = −0.598386 + 1.137800I
1.13411 + 7.11668I 4.00252 + 2.15626I
u = −0.370485 + 0.488941I
a = 1.40100 + 0.26552I
b = 0.059670 − 0.170060I
−1.77807 + 0.66799I −4.16532 + 0.83627I
u = −0.370485 − 0.488941I
a = 1.40100 − 0.26552I
b = 0.059670 + 0.170060I
−1.77807 − 0.66799I −4.16532 − 0.83627I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.795488 + 1.154490I
a = 0.594105 − 0.281157I
b = −0.222609 + 1.026440I
3.64839 + 4.61933I 3.31531 − 11.47051I
u = 0.795488 − 1.154490I
a = 0.594105 + 0.281157I
b = −0.222609 − 1.026440I
3.64839 − 4.61933I 3.31531 + 11.47051I
u = −0.19057 + 1.41148I
a = −0.189641 + 0.204297I
b = 0.183449 − 0.960795I
1.12888 + 3.74820I 0. − 12.89354I
u = −0.19057 − 1.41148I
a = −0.189641 − 0.204297I
b = 0.183449 + 0.960795I
1.12888 − 3.74820I 0. + 12.89354I
u = −1.30509 + 0.60711I
a = 1.50657 − 0.37542I
b = −0.55176 − 1.36199I
9.1915 − 13.9309I 0. + 7.22655I
u = −1.30509 − 0.60711I
a = 1.50657 + 0.37542I
b = −0.55176 + 1.36199I
9.1915 + 13.9309I 0. − 7.22655I
u = −0.92121 + 1.12031I
a = −0.177275 − 0.218827I
b = −0.126991 + 0.884845I
−0.38233 + 2.45424I 0. − 9.83894I
u = −0.92121 − 1.12031I
a = −0.177275 + 0.218827I
b = −0.126991 − 0.884845I
−0.38233 − 2.45424I 0. + 9.83894I
u = 1.25070 + 0.75757I
a = 1.76373 + 0.19301I
b = −0.59610 + 1.35908I
6.5813 + 19.8578I 0
u = 1.25070 − 0.75757I
a = 1.76373 − 0.19301I
b = −0.59610 − 1.35908I
6.5813 − 19.8578I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428127 + 0.285395I
a = −0.800907 + 0.886390I
b = 0.694592 + 0.408886I
−1.23082 − 1.07266I −4.68345 + 2.46317I
u = −0.428127 − 0.285395I
a = −0.800907 − 0.886390I
b = 0.694592 − 0.408886I
−1.23082 + 1.07266I −4.68345 − 2.46317I
u = −1.52390 + 0.01972I
a = 0.334754 − 0.368783I
b = −0.356016 − 1.353720I
12.2277 − 8.7964I 0
u = −1.52390 − 0.01972I
a = 0.334754 + 0.368783I
b = −0.356016 + 1.353720I
12.2277 + 8.7964I 0
u = −1.35309 + 0.74274I
a = −1.014570 + 0.310379I
b = 0.334802 + 1.144640I
4.61279 − 11.08970I 0
u = −1.35309 − 0.74274I
a = −1.014570 − 0.310379I
b = 0.334802 − 1.144640I
4.61279 + 11.08970I 0
u = 1.55085 + 0.24154I
a = −0.024960 − 0.231338I
b = −0.262084 − 1.311530I
11.83750 − 2.26957I 0
u = 1.55085 − 0.24154I
a = −0.024960 + 0.231338I
b = −0.262084 + 1.311530I
11.83750 + 2.26957I 0
u = 1.50650 + 0.58645I
a = −0.663181 − 0.347229I
b = 0.222382 − 1.119540I
7.01611 + 4.67438I 0
u = 1.50650 − 0.58645I
a = −0.663181 + 0.347229I
b = 0.222382 + 1.119540I
7.01611 − 4.67438I 0
9
II. I
u
2
= h−1.95 × 10
37
au
41
+ 1.89 × 10
37
u
41
+ · · · + 2.35 × 10
38
a − 3.16 ×
10
38
, 1.52 × 10
33
au
41
+ 3.94 × 10
33
u
41
+ · · · − 3.54 × 10
34
a + 1.32 ×
10
33
, u
42
− u
41
+ · · · − 28u + 8i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
12
=
a
0.420527au
41
− 0.407981u
41
+ ··· − 5.06818a + 6.80388
a
11
=
0.420527au
41
− 0.407981u
41
+ ··· − 4.06818a + 6.80388
0.420527au
41
− 0.407981u
41
+ ··· − 5.06818a + 6.80388
a
9
=
0.154531au
41
− 2.43911u
41
+ ··· − 3.26279a + 32.6290
−0.282246au
41
− 0.279866u
41
+ ··· + 1.49713a + 0.975049
a
6
=
−0.729646au
41
− 0.107181u
41
+ ··· + 11.1484a − 9.07282
−0.190720au
41
− 0.538926u
41
+ ··· + 1.43722a + 9.71123
a
5
=
−0.600678u
41
+ 0.244644u
40
+ ··· − 16.9635u + 8.41409
−0.578537u
41
+ 0.112322u
40
+ ··· − 9.27967u + 4.53403
a
2
=
1.08667u
41
− 0.309169u
40
+ ··· + 21.0796u − 10.0999
0.105021u
41
− 0.110845u
40
+ ··· + 8.96049u − 4.53423
a
10
=
0.407981au
41
− 2.35024u
41
+ ··· − 6.80388a + 31.7051
−1
a
1
=
−1.17921u
41
+ 0.356966u
40
+ ··· − 26.2432u + 12.9481
0.0287964u
41
+ 0.00828293u
40
+ ··· − 4.30958u + 2.04396
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.13855u
41
− 0.644766u
40
+ ··· + 69.1611u − 17.9282
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
42
+ 20u
41
+ ··· + 39u + 1)
2
c
2
, c
4
(u
42
− 4u
41
+ ··· + 7u − 1)
2
c
3
, c
7
(u
42
− u
41
+ ··· − 28u + 8)
2
c
5
, c
6
u
84
+ 2u
83
+ ··· + 581438984u + 60886121
c
8
, c
9
, c
11
c
12
u
84
− 14u
83
+ ··· − 4u + 1
c
10
(u
42
+ 2u
41
+ ··· − 2u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
42
+ 8y
41
+ ··· − 999y + 1)
2
c
2
, c
4
(y
42
− 20y
41
+ ··· − 39y + 1)
2
c
3
, c
7
(y
42
− 21y
41
+ ··· − 784y + 64)
2
c
5
, c
6
y
84
− 38y
83
+ ··· − 58401168007787376y + 3707119730426641
c
8
, c
9
, c
11
c
12
y
84
+ 54y
83
+ ··· − 60y
2
+ 1
c
10
(y
42
− 14y
41
+ ··· + 2y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.232737 + 0.958770I
a = 1.51165 − 1.20059I
b = −0.41354 + 1.37451I
4.96975 − 2.03798I 4.18964 + 3.67578I
u = 0.232737 + 0.958770I
a = 1.47814 + 1.41134I
b = −0.564224 − 1.240190I
4.96975 − 2.03798I 4.18964 + 3.67578I
u = 0.232737 − 0.958770I
a = 1.51165 + 1.20059I
b = −0.41354 − 1.37451I
4.96975 + 2.03798I 4.18964 − 3.67578I
u = 0.232737 − 0.958770I
a = 1.47814 − 1.41134I
b = −0.564224 + 1.240190I
4.96975 + 2.03798I 4.18964 − 3.67578I
u = 0.912821 + 0.370122I
a = 0.081154 + 0.848484I
b = −0.964211 − 0.072097I
−0.63969 + 4.75718I −1.27952 − 5.86296I
u = 0.912821 + 0.370122I
a = −1.76377 − 1.53546I
b = 0.522152 − 1.265870I
−0.63969 + 4.75718I −1.27952 − 5.86296I
u = 0.912821 − 0.370122I
a = 0.081154 − 0.848484I
b = −0.964211 + 0.072097I
−0.63969 − 4.75718I −1.27952 + 5.86296I
u = 0.912821 − 0.370122I
a = −1.76377 + 1.53546I
b = 0.522152 + 1.265870I
−0.63969 − 4.75718I −1.27952 + 5.86296I
u = −0.834355 + 0.450716I
a = 0.496950 − 0.930335I
b = −0.051378 − 0.222509I
−1.30280 + 0.70618I −3.37702 + 0.55676I
u = −0.834355 + 0.450716I
a = 1.80822 − 0.48836I
b = 0.034418 − 0.871050I
−1.30280 + 0.70618I −3.37702 + 0.55676I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.834355 − 0.450716I
a = 0.496950 + 0.930335I
b = −0.051378 + 0.222509I
−1.30280 − 0.70618I −3.37702 − 0.55676I
u = −0.834355 − 0.450716I
a = 1.80822 + 0.48836I
b = 0.034418 + 0.871050I
−1.30280 − 0.70618I −3.37702 − 0.55676I
u = −0.497589 + 0.958024I
a = −0.323160 + 0.697370I
b = 0.183345 + 0.113079I
−0.62266 + 1.78828I −3.96378 − 1.37373I
u = −0.497589 + 0.958024I
a = 0.401410 − 0.545035I
b = −0.107100 + 0.951359I
−0.62266 + 1.78828I −3.96378 − 1.37373I
u = −0.497589 − 0.958024I
a = −0.323160 − 0.697370I
b = 0.183345 − 0.113079I
−0.62266 − 1.78828I −3.96378 + 1.37373I
u = −0.497589 − 0.958024I
a = 0.401410 + 0.545035I
b = −0.107100 − 0.951359I
−0.62266 − 1.78828I −3.96378 + 1.37373I
u = −0.134308 + 0.909932I
a = −0.589936 + 1.116220I
b = 0.411288 − 1.253390I
1.66534 + 2.94974I 0.00088 − 1.92478I
u = −0.134308 + 0.909932I
a = 1.55526 − 0.61214I
b = −0.848427 + 0.025203I
1.66534 + 2.94974I 0.00088 − 1.92478I
u = −0.134308 − 0.909932I
a = −0.589936 − 1.116220I
b = 0.411288 + 1.253390I
1.66534 − 2.94974I 0.00088 + 1.92478I
u = −0.134308 − 0.909932I
a = 1.55526 + 0.61214I
b = −0.848427 − 0.025203I
1.66534 − 2.94974I 0.00088 + 1.92478I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.086850 + 0.154461I
a = 0.49387 − 1.92438I
b = 0.034469 − 1.177150I
5.32687 + 0.16365I 1.74023 − 0.29295I
u = 1.086850 + 0.154461I
a = −1.72226 − 1.23616I
b = 0.217618 + 0.718151I
5.32687 + 0.16365I 1.74023 − 0.29295I
u = 1.086850 − 0.154461I
a = 0.49387 + 1.92438I
b = 0.034469 + 1.177150I
5.32687 − 0.16365I 1.74023 + 0.29295I
u = 1.086850 − 0.154461I
a = −1.72226 + 1.23616I
b = 0.217618 − 0.718151I
5.32687 − 0.16365I 1.74023 + 0.29295I
u = −0.798766 + 0.403013I
a = 1.009400 − 0.071564I
b = −0.638014 + 0.604613I
−1.44979 − 4.32552I −2.33469 + 7.57694I
u = −0.798766 + 0.403013I
a = −0.758354 − 0.408384I
b = 0.594014 + 0.749718I
−1.44979 − 4.32552I −2.33469 + 7.57694I
u = −0.798766 − 0.403013I
a = 1.009400 + 0.071564I
b = −0.638014 − 0.604613I
−1.44979 + 4.32552I −2.33469 − 7.57694I
u = −0.798766 − 0.403013I
a = −0.758354 + 0.408384I
b = 0.594014 − 0.749718I
−1.44979 + 4.32552I −2.33469 − 7.57694I
u = 0.465404 + 1.033510I
a = −0.776621 − 1.132340I
b = 0.56253 + 1.31912I
0.23764 − 7.32917I −1.90854 + 6.67478I
u = 0.465404 + 1.033510I
a = 1.70092 + 0.38646I
b = −1.050300 + 0.064111I
0.23764 − 7.32917I −1.90854 + 6.67478I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.465404 − 1.033510I
a = −0.776621 + 1.132340I
b = 0.56253 − 1.31912I
0.23764 + 7.32917I −1.90854 − 6.67478I
u = 0.465404 − 1.033510I
a = 1.70092 − 0.38646I
b = −1.050300 − 0.064111I
0.23764 + 7.32917I −1.90854 − 6.67478I
u = 0.755565 + 0.337157I
a = −0.856993 − 0.803825I
b = 0.671995 + 1.050850I
−1.18242 − 1.63203I −1.08702 − 2.62995I
u = 0.755565 + 0.337157I
a = 1.399160 + 0.102365I
b = −0.912786 + 0.392807I
−1.18242 − 1.63203I −1.08702 − 2.62995I
u = 0.755565 − 0.337157I
a = −0.856993 + 0.803825I
b = 0.671995 − 1.050850I
−1.18242 + 1.63203I −1.08702 + 2.62995I
u = 0.755565 − 0.337157I
a = 1.399160 − 0.102365I
b = −0.912786 − 0.392807I
−1.18242 + 1.63203I −1.08702 + 2.62995I
u = 0.265196 + 0.777853I
a = −0.132473 + 0.867658I
b = 0.199134 − 1.031900I
1.22766 + 2.20756I −0.91183 − 4.39193I
u = 0.265196 + 0.777853I
a = 0.798380 − 0.862355I
b = −0.377178 − 0.039196I
1.22766 + 2.20756I −0.91183 − 4.39193I
u = 0.265196 − 0.777853I
a = −0.132473 − 0.867658I
b = 0.199134 + 1.031900I
1.22766 − 2.20756I −0.91183 + 4.39193I
u = 0.265196 − 0.777853I
a = 0.798380 + 0.862355I
b = −0.377178 + 0.039196I
1.22766 − 2.20756I −0.91183 + 4.39193I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.791058
a = 0.20284 + 2.66753I
b = −0.440001 + 1.257300I
3.61503 7.17890
u = 0.791058
a = 0.20284 − 2.66753I
b = −0.440001 − 1.257300I
3.61503 7.17890
u = −1.119440 + 0.484001I
a = −1.93177 + 0.44893I
b = 0.291230 − 0.895374I
3.92176 − 5.08816I −1.48038 + 5.57765I
u = −1.119440 + 0.484001I
a = −0.97311 + 1.76409I
b = 0.122020 + 1.178420I
3.92176 − 5.08816I −1.48038 + 5.57765I
u = −1.119440 − 0.484001I
a = −1.93177 − 0.44893I
b = 0.291230 + 0.895374I
3.92176 + 5.08816I −1.48038 − 5.57765I
u = −1.119440 − 0.484001I
a = −0.97311 − 1.76409I
b = 0.122020 − 1.178420I
3.92176 + 5.08816I −1.48038 − 5.57765I
u = 1.136730 + 0.486401I
a = −0.500617 + 0.509781I
b = 0.353261 − 0.070116I
3.85619 + 2.39851I 1.004040 − 0.878657I
u = 1.136730 + 0.486401I
a = 1.40932 + 0.50529I
b = −0.158839 + 1.079200I
3.85619 + 2.39851I 1.004040 − 0.878657I
u = 1.136730 − 0.486401I
a = −0.500617 − 0.509781I
b = 0.353261 + 0.070116I
3.85619 − 2.39851I 1.004040 + 0.878657I
u = 1.136730 − 0.486401I
a = 1.40932 − 0.50529I
b = −0.158839 − 1.079200I
3.85619 − 2.39851I 1.004040 + 0.878657I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.207670 + 0.341373I
a = 0.813751 + 0.915422I
b = −0.900058 − 0.532369I
6.14713 + 1.06689I 3.69538 − 0.36183I
u = 1.207670 + 0.341373I
a = 0.554985 + 0.079494I
b = 0.15484 + 1.48362I
6.14713 + 1.06689I 3.69538 − 0.36183I
u = 1.207670 − 0.341373I
a = 0.813751 − 0.915422I
b = −0.900058 + 0.532369I
6.14713 − 1.06689I 3.69538 + 0.36183I
u = 1.207670 − 0.341373I
a = 0.554985 − 0.079494I
b = 0.15484 − 1.48362I
6.14713 − 1.06689I 3.69538 + 0.36183I
u = −1.263970 + 0.066052I
a = 0.665062 − 0.472891I
b = −0.986879 + 0.316168I
6.95353 + 4.35155I 4.59858 − 5.33139I
u = −1.263970 + 0.066052I
a = −0.038901 − 0.425858I
b = 0.31332 − 1.45728I
6.95353 + 4.35155I 4.59858 − 5.33139I
u = −1.263970 − 0.066052I
a = 0.665062 + 0.472891I
b = −0.986879 − 0.316168I
6.95353 − 4.35155I 4.59858 + 5.33139I
u = −1.263970 − 0.066052I
a = −0.038901 + 0.425858I
b = 0.31332 + 1.45728I
6.95353 − 4.35155I 4.59858 + 5.33139I
u = −1.253490 + 0.315421I
a = 1.44870 − 0.39303I
b = −0.68021 − 1.31927I
9.87960 − 1.93798I 7.95326 + 1.38361I
u = −1.253490 + 0.315421I
a = 0.0176087 + 0.0774925I
b = −0.46769 + 1.49281I
9.87960 − 1.93798I 7.95326 + 1.38361I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.253490 − 0.315421I
a = 1.44870 + 0.39303I
b = −0.68021 + 1.31927I
9.87960 + 1.93798I 7.95326 − 1.38361I
u = −1.253490 − 0.315421I
a = 0.0176087 − 0.0774925I
b = −0.46769 − 1.49281I
9.87960 + 1.93798I 7.95326 − 1.38361I
u = −0.329380 + 0.607670I
a = 1.91830 − 6.31824I
b = 0.045154 − 1.052520I
1.56112 + 0.76607I −7.12845 − 1.30178I
u = −0.329380 + 0.607670I
a = −10.62400 − 2.53492I
b = 0.061950 + 0.947949I
1.56112 + 0.76607I −7.12845 − 1.30178I
u = −0.329380 − 0.607670I
a = 1.91830 + 6.31824I
b = 0.045154 + 1.052520I
1.56112 − 0.76607I −7.12845 + 1.30178I
u = −0.329380 − 0.607670I
a = −10.62400 + 2.53492I
b = 0.061950 − 0.947949I
1.56112 − 0.76607I −7.12845 + 1.30178I
u = −1.213380 + 0.511337I
a = 0.867787 − 0.552784I
b = −1.143420 + 0.023396I
4.97652 − 7.98804I 2.75545 + 5.63639I
u = −1.213380 + 0.511337I
a = −1.49756 + 0.40473I
b = 0.58597 + 1.39555I
4.97652 − 7.98804I 2.75545 + 5.63639I
u = −1.213380 − 0.511337I
a = 0.867787 + 0.552784I
b = −1.143420 − 0.023396I
4.97652 + 7.98804I 2.75545 − 5.63639I
u = −1.213380 − 0.511337I
a = −1.49756 − 0.40473I
b = 0.58597 − 1.39555I
4.97652 + 7.98804I 2.75545 − 5.63639I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.165920 + 0.667088I
a = −0.577892 − 0.133773I
b = 0.515914 − 0.043918I
1.51197 − 7.76497I 0. + 4.74518I
u = −1.165920 + 0.667088I
a = 1.47345 − 0.28081I
b = −0.273480 − 1.072760I
1.51197 − 7.76497I 0. + 4.74518I
u = −1.165920 − 0.667088I
a = −0.577892 + 0.133773I
b = 0.515914 + 0.043918I
1.51197 + 7.76497I 0. − 4.74518I
u = −1.165920 − 0.667088I
a = 1.47345 + 0.28081I
b = −0.273480 + 1.072760I
1.51197 + 7.76497I 0. − 4.74518I
u = 1.239790 + 0.555518I
a = −0.267910 + 0.337001I
b = −0.38688 − 1.55484I
8.15282 + 7.53350I 5.04295 − 6.51119I
u = 1.239790 + 0.555518I
a = 1.85937 + 0.13321I
b = −0.76662 + 1.24734I
8.15282 + 7.53350I 5.04295 − 6.51119I
u = 1.239790 − 0.555518I
a = −0.267910 − 0.337001I
b = −0.38688 + 1.55484I
8.15282 − 7.53350I 5.04295 + 6.51119I
u = 1.239790 − 0.555518I
a = 1.85937 − 0.13321I
b = −0.76662 − 1.24734I
8.15282 − 7.53350I 5.04295 + 6.51119I
u = 1.205450 + 0.688309I
a = 1.094510 + 0.734681I
b = −1.193570 − 0.100733I
2.60047 + 13.58860I 0. − 9.29837I
u = 1.205450 + 0.688309I
a = −1.77964 − 0.13933I
b = 0.65954 − 1.38657I
2.60047 + 13.58860I 0. − 9.29837I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.205450 − 0.688309I
a = 1.094510 − 0.734681I
b = −1.193570 + 0.100733I
2.60047 − 13.58860I 0. + 9.29837I
u = 1.205450 − 0.688309I
a = −1.77964 + 0.13933I
b = 0.65954 + 1.38657I
2.60047 − 13.58860I 0. + 9.29837I
u = 0.413714
a = 2.80478 + 2.11582I
b = −0.209348 − 1.063710I
4.17299 7.72600
u = 0.413714
a = 2.80478 − 2.11582I
b = −0.209348 + 1.063710I
4.17299 7.72600
21
III. I
u
3
= hb − 1, −2u
5
+ 4u
3
+ 2u
2
+ 2a − 4u + 1, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
12
=
u
5
− 2u
3
− u
2
+ 2u −
1
2
1
a
11
=
u
5
− 2u
3
− u
2
+ 2u +
1
2
1
a
9
=
u
5
− 2u
3
− u
2
+ 2u +
3
2
1
a
6
=
−
1
4
u
2
+
1
2
1
2
u
2
a
5
=
−u
2
+ 1
u
2
a
2
=
−u
4
+ u
2
− 1
u
5
+ u
4
− 2u
3
− u
2
+ u + 1
a
10
=
u
5
− 2u
3
− u
2
+ 2u +
1
2
1
a
1
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
5
+
15
4
u
4
− 4u
3
− 8u
2
+ 4u + 2
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
64(64u
6
− 96u
5
+ 80u
4
− 32u
3
+ 8u
2
− 2u + 1)
c
6
64(64u
6
+ 96u
5
+ 80u
4
+ 32u
3
+ 8u
2
+ 2u + 1)
c
8
, c
9
(u − 1)
6
c
10
u
6
c
11
, c
12
(u + 1)
6
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
3
, c
4
c
7
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
5
, c
6
4096(4096y
6
+ 1024y
5
+ 1280y
4
+ 96y
2
+ 12y + 1)
c
8
, c
9
, c
11
c
12
(y −1)
6
c
10
y
6
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.730593 − 0.497010I
b = 1.00000
0.245672 + 0.924305I −1.78567 + 1.99338I
u = 1.002190 − 0.295542I
a = −0.730593 + 0.497010I
b = 1.00000
0.245672 − 0.924305I −1.78567 − 1.99338I
u = −0.428243 + 0.664531I
a = −2.16103 + 1.45708I
b = 1.00000
−3.53554 + 0.92430I −0.90787 + 6.83768I
u = −0.428243 − 0.664531I
a = −2.16103 − 1.45708I
b = 1.00000
−3.53554 − 0.92430I −0.90787 − 6.83768I
u = −1.073950 + 0.558752I
a = −1.108380 + 0.558752I
b = 1.00000
−1.64493 − 5.69302I −3.18146 + 4.26477I
u = −1.073950 − 0.558752I
a = −1.108380 − 0.558752I
b = 1.00000
−1.64493 + 5.69302I −3.18146 − 4.26477I
25
IV. I
v
1
= ha, 4v
3
+ 7v
2
+ 3b + 6v + 1, 4v
4
+ 7v
3
+ 2v
2
− v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
7
=
1
0
a
3
=
v
0
a
12
=
0
−
4
3
v
3
−
7
3
v
2
− 2v −
1
3
a
11
=
−
4
3
v
3
−
7
3
v
2
− 2v −
1
3
−
4
3
v
3
−
7
3
v
2
− 2v −
1
3
a
9
=
4
3
v
3
+
11
3
v
2
+
5
3
v
4
3
v
3
+
11
3
v
2
+
5
3
v − 1
a
6
=
−
4
3
v
3
−
7
3
v
2
− 2v −
1
3
−
8
3
v
3
− 6v
2
−
11
3
v −
1
3
a
5
=
−
4
3
v
3
−
7
3
v
2
− 2v −
1
3
−4v
3
− 7v
2
− 2v + 1
a
2
=
4
3
v
3
+
7
3
v
2
+ 3v +
1
3
4v
3
+ 7v
2
+ 2v − 1
a
10
=
1
8
3
v
2
+
10
3
v +
4
3
a
1
=
4
3
v
3
+
7
3
v
2
+ 2v +
1
3
4v
3
+ 7v
2
+ 2v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v
3
+
62
3
v
2
+
67
3
v −
11
3
26
(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
27
(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
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.112690 + 0.371716I
a = 0
b = 0.547424 − 0.585652I
−2.62503 + 1.39709I −9.45081 − 3.47689I
v = −1.112690 − 0.371716I
a = 0
b = 0.547424 + 0.585652I
−2.62503 − 1.39709I −9.45081 + 3.47689I
v = 0.237691 + 0.353773I
a = 0
b = −0.547424 − 1.120870I
0.98010 − 7.64338I −0.08044 + 11.43934I
v = 0.237691 − 0.353773I
a = 0
b = −0.547424 + 1.120870I
0.98010 + 7.64338I −0.08044 − 11.43934I
29
V. I
v
2
= ha, v
2
b + b
2
− 2bv + v
2
+ b − v, v
3
− 2v
2
+ v − 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
7
=
1
0
a
3
=
v
0
a
12
=
0
b
a
11
=
b
b
a
9
=
−v
2
b + 2bv − v
2
− b + v + 1
−v
2
b + 2bv − v
2
− b + v
a
6
=
bv − b + 1
v
2
b − bv + v
2
− v
a
5
=
bv − b + 1
v
2
− 2v + 1
a
2
=
−bv + b + v − 1
−v
2
+ 2v − 1
a
10
=
−v
2
b + 2bv − v + 1
−1
a
1
=
−bv + b − 1
−v
2
+ 2v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2v
2
+ 5v − 5
30
(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
31
(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
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.122561 + 0.744862I
a = 0
b = 0.498832 + 1.001300I
−1.37919 − 2.82812I −3.30760 + 3.35914I
v = 0.122561 + 0.744862I
a = 0
b = −0.713912 + 0.305839I
−1.37919 − 2.82812I −3.30760 + 3.35914I
v = 0.122561 − 0.744862I
a = 0
b = 0.498832 − 1.001300I
−1.37919 + 2.82812I −3.30760 − 3.35914I
v = 0.122561 − 0.744862I
a = 0
b = −0.713912 − 0.305839I
−1.37919 + 2.82812I −3.30760 − 3.35914I
v = 1.75488
a = 0
b = −0.284920 + 1.115140I
2.75839 −2.38480
v = 1.75488
a = 0
b = −0.284920 − 1.115140I
2.75839 −2.38480
33
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· ((u
42
+ 20u
41
+ ··· + 39u + 1)
2
)(u
50
+ 24u
49
+ ··· − 3807u + 256)
c
2
((u − 1)
10
)(u
6
+ u
5
+ ··· + u + 1)(u
42
− 4u
41
+ ··· + 7u − 1)
2
· (u
50
− 4u
49
+ ··· − 129u + 16)
c
3
u
10
(u
6
− u
5
+ ··· − u + 1)(u
42
− u
41
+ ··· − 28u + 8)
2
· (u
50
− 12u
48
+ ··· + 288u + 256)
c
4
((u + 1)
10
)(u
6
− u
5
+ ··· − u + 1)(u
42
− 4u
41
+ ··· + 7u − 1)
2
· (u
50
− 4u
49
+ ··· − 129u + 16)
c
5
4096(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (64u
6
− 96u
5
+ 80u
4
− 32u
3
+ 8u
2
− 2u + 1)
· (64u
50
+ 160u
49
+ ··· + 14u
2
+ 1)
· (u
84
+ 2u
83
+ ··· + 581438984u + 60886121)
c
6
4096(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (64u
6
+ 96u
5
+ 80u
4
+ 32u
3
+ 8u
2
+ 2u + 1)
· (64u
50
+ 160u
49
+ ··· + 14u
2
+ 1)
· (u
84
+ 2u
83
+ ··· + 581438984u + 60886121)
c
7
u
10
(u
6
+ u
5
+ ··· + u + 1)(u
42
− u
41
+ ··· − 28u + 8)
2
· (u
50
− 12u
48
+ ··· + 288u + 256)
c
8
, c
9
(u − 1)
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
50
+ 6u
49
+ ··· + 2u + 1)(u
84
− 14u
83
+ ··· − 4u + 1)
c
10
u
6
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ ··· + 3u + 2)(u
42
+ 2u
41
+ ··· − 2u − 1)
2
· (u
50
− 6u
49
+ ··· − 94208u + 16384)
c
11
, c
12
(u + 1)
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
50
+ 6u
49
+ ··· + 2u + 1)(u
84
− 14u
83
+ ··· − 4u + 1)
34
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
10
)(y
6
+ y
5
+ ··· + 3y + 1)(y
42
+ 8y
41
+ ··· − 999y + 1)
2
· (y
50
+ 8y
49
+ ··· − 4265025y + 65536)
c
2
, c
4
(y − 1)
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· ((y
42
− 20y
41
+ ··· − 39y + 1)
2
)(y
50
− 24y
49
+ ··· + 3807y + 256)
c
3
, c
7
y
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
42
− 21y
41
+ ··· − 784y + 64)
2
· (y
50
− 24y
49
+ ··· − 971776y + 65536)
c
5
, c
6
16777216(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (4096y
6
+ 1024y
5
+ 1280y
4
+ 96y
2
+ 12y + 1)
· (4096y
50
− 31744y
49
+ ··· + 28y + 1)
· (y
84
− 38y
83
+ ··· − 58401168007787376y + 3707119730426641)
c
8
, c
9
, c
11
c
12
(y − 1)
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
50
+ 22y
49
+ ··· + 50y + 1)(y
84
+ 54y
83
+ ··· − 60y
2
+ 1)
c
10
y
6
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
42
− 14y
41
+ ··· + 2y + 1)
2
· (y
50
− 14y
49
+ ··· − 3875536896y + 268435456)
35
