12a
0397
(K12a
0397
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 1 10 4 12 5 8 7
Solving Sequence
8,11 5,12
4 9 3 10 7 1 6 2
c
11
c
4
c
8
c
3
c
10
c
7
c
12
c
6
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1908269u
44
+ 69257295u
43
+ ··· + 524288b − 1459838517248,
− 6600959u
44
− 250923547u
43
+ ··· + 1048576a − 5495160045568,
u
45
+ 39u
44
+ ··· + 23068672u + 1048576i
I
u
2
= h−4.69815 × 10
233
a
39
u − 6.24002 × 10
233
a
38
u + ··· − 1.03893 × 10
237
a + 1.05559 × 10
236
,
2a
39
u + 21a
38
u + ··· + 142a − 33, u
2
− u + 1i
I
u
3
= h−11u
22
− 8u
21
+ ··· + b + 40, −29u
22
− 83u
21
+ ··· + a + 3, u
23
+ 2u
22
+ ··· − u + 1i
* 3 irreducible components of dim
C
= 0, with total 148 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
= h1.91 × 10
6
u
44
+ 6.93 × 10
7
u
43
+ · · · + 5.24 × 10
5
b − 1.46 ×
10
12
, −6.60 × 10
6
u
44
− 2.51 × 10
8
u
43
+ · · · + 1.05 × 10
6
a − 5.50 ×
10
12
, u
45
+ 39u
44
+ · · · + 23068672u + 1048576i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
5
=
6.29517u
44
+ 239.299u
43
+ ··· + 1.12427 × 10
8
u + 5240593
−3.63973u
44
− 132.098u
43
+ ··· + 5.32322 × 10
7
u + 2784421
a
12
=
1
u
2
a
4
=
2.65543u
44
+ 107.202u
43
+ ··· + 1.65659 × 10
8
u + 8025014
−3.63973u
44
− 132.098u
43
+ ··· + 5.32322 × 10
7
u + 2784421
a
9
=
1
1024
u
43
+
37
1024
u
42
+ ··· + 10752u +
1025
2
−0.000976563u
44
− 0.0361328u
43
+ ··· − 10752u
2
− 511.500u
a
3
=
10.3764u
44
+ 403.507u
43
+ ··· + 3.53442 × 10
8
u + 1.68991 × 10
7
11.0232u
44
+ 424.937u
43
+ ··· + 3.09218 × 10
8
u + 1.46969 × 10
7
a
10
=
−0.000976563u
44
− 0.0371094u
43
+ ··· − 11264.5u − 511.500
1
1024
u
44
+
37
1024
u
43
+ ··· + 10752u
2
+
1025
2
u
a
7
=
1
1024
u
44
+
45
1024
u
43
+ ··· +
388097
4
u + 4608
−
7
1024
u
44
−
17
64
u
43
+ ··· − 154111u − 7168
a
1
=
0.0998535u
44
+ 3.81567u
43
+ ··· + 1630976u + 75265
−0.0717773u
44
− 2.68408u
43
+ ··· − 383232u − 16128
a
6
=
0.245605u
44
+ 8.91406u
43
+ ··· − 2.76384 × 10
6
u − 142464
0.267578u
44
+ 10.4087u
43
+ ··· + 7706241u + 364032
a
2
=
−1.21094u
44
− 46.2363u
43
+ ··· − 2.15274 × 10
7
u − 998527.
−1.38721u
44
− 52.9595u
43
+ ··· − 2.50382 × 10
7
u − 1163264
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1487947
65536
u
44
+
6940087
8192
u
43
+ ··· + 108839472u + 4370874
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ 24u
44
+ ··· + 172u + 16
c
2
, c
5
u
45
+ 6u
44
+ ··· + 38u + 4
c
3
, c
4
, c
8
c
10
u
45
+ 15u
43
+ ··· + 2u + 1
c
6
, c
12
u
45
+ 18u
44
+ ··· + 2834u + 188
c
7
, c
9
u
45
+ u
44
+ ··· − 7u + 1
c
11
u
45
+ 39u
44
+ ··· + 23068672u + 1048576
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 4y
44
+ ··· + 11504y −256
c
2
, c
5
y
45
− 24y
44
+ ··· + 172y −16
c
3
, c
4
, c
8
c
10
y
45
+ 30y
44
+ ··· + 2y −1
c
6
, c
12
y
45
+ 32y
44
+ ··· + 315660y −35344
c
7
, c
9
y
45
− 21y
44
+ ··· + 65y −1
c
11
y
45
− 3y
44
+ ··· + 9345848836096y −1099511627776
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.298816 + 0.989953I
a = −0.117552 − 1.073810I
b = −0.660784 + 0.641263I
−5.72982 − 2.27070I 0
u = −0.298816 − 0.989953I
a = −0.117552 + 1.073810I
b = −0.660784 − 0.641263I
−5.72982 + 2.27070I 0
u = −0.926262 + 0.495766I
a = 0.273491 − 0.286793I
b = −0.759181 − 0.337100I
−4.38180 + 2.50542I 0
u = −0.926262 − 0.495766I
a = 0.273491 + 0.286793I
b = −0.759181 + 0.337100I
−4.38180 − 2.50542I 0
u = −0.919385 + 0.529264I
a = −0.306815 + 0.321928I
b = 0.814984 + 0.335175I
−7.68302 + 7.12344I 0
u = −0.919385 − 0.529264I
a = −0.306815 − 0.321928I
b = 0.814984 − 0.335175I
−7.68302 − 7.12344I 0
u = −0.967769 + 0.504465I
a = −0.313757 + 0.244824I
b = 0.757522 + 0.405488I
−8.11430 − 1.70581I 0
u = −0.967769 − 0.504465I
a = −0.313757 − 0.244824I
b = 0.757522 − 0.405488I
−8.11430 + 1.70581I 0
u = −1.088800 + 0.239432I
a = 0.1243660 − 0.0152569I
b = −0.349735 − 0.420577I
−3.24070 − 0.55670I 0
u = −1.088800 − 0.239432I
a = 0.1243660 + 0.0152569I
b = −0.349735 + 0.420577I
−3.24070 + 0.55670I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198202 + 1.097100I
a = 0.142561 + 1.104920I
b = 0.575831 − 0.709841I
−2.07839 + 2.22551I 0
u = −0.198202 − 1.097100I
a = 0.142561 − 1.104920I
b = 0.575831 + 0.709841I
−2.07839 − 2.22551I 0
u = −0.748453 + 0.420636I
a = 0.044813 − 0.385321I
b = −0.672626 − 0.096659I
−1.42425 + 3.31805I 0
u = −0.748453 − 0.420636I
a = 0.044813 + 0.385321I
b = −0.672626 + 0.096659I
−1.42425 − 3.31805I 0
u = 1.137450 + 0.415999I
a = 0.056535 + 1.223700I
b = 0.076306 − 0.677052I
1.92192 + 2.39939I 0
u = 1.137450 − 0.415999I
a = 0.056535 − 1.223700I
b = 0.076306 + 0.677052I
1.92192 − 2.39939I 0
u = −0.316288 + 1.178330I
a = −0.124276 − 1.126580I
b = −0.636773 + 0.790453I
−5.70018 + 6.82908I 0
u = −0.316288 − 1.178330I
a = −0.124276 + 1.126580I
b = −0.636773 − 0.790453I
−5.70018 − 6.82908I 0
u = −0.489115 + 0.309548I
a = 0.313689 + 0.454525I
b = 0.529742 − 0.075882I
−0.730208 − 0.083656I 0
u = −0.489115 − 0.309548I
a = 0.313689 − 0.454525I
b = 0.529742 + 0.075882I
−0.730208 + 0.083656I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.497869
a = 0.450653
b = 0.446828
−0.768321 0
u = −0.87680 + 1.39604I
a = −0.302809 − 1.259470I
b = −0.61138 + 1.39569I
−1.64377 + 9.31582I 0
u = −0.87680 − 1.39604I
a = −0.302809 + 1.259470I
b = −0.61138 − 1.39569I
−1.64377 − 9.31582I 0
u = −0.90557 + 1.38569I
a = −0.325344 − 1.265460I
b = −0.59960 + 1.43721I
−0.4610 + 18.4165I 0
u = −0.90557 − 1.38569I
a = −0.325344 + 1.265460I
b = −0.59960 − 1.43721I
−0.4610 − 18.4165I 0
u = −0.89990 + 1.39988I
a = 0.319514 + 1.255210I
b = 0.58882 − 1.41851I
2.67201 + 13.38930I 0
u = −0.89990 − 1.39988I
a = 0.319514 − 1.255210I
b = 0.58882 + 1.41851I
2.67201 − 13.38930I 0
u = −1.66275 + 0.46895I
a = −0.248878 − 0.405451I
b = 0.210659 + 0.990181I
−4.73342 − 0.73218I 0
u = −1.66275 − 0.46895I
a = −0.248878 + 0.405451I
b = 0.210659 − 0.990181I
−4.73342 + 0.73218I 0
u = −0.77091 + 1.54748I
a = 0.250065 + 1.181600I
b = 0.520537 − 1.229120I
1.55549 + 7.27021I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.77091 − 1.54748I
a = 0.250065 − 1.181600I
b = 0.520537 + 1.229120I
1.55549 − 7.27021I 0
u = −0.93055 + 1.47612I
a = 0.326629 + 1.202060I
b = 0.49630 − 1.38462I
6.74317 + 12.42830I 0
u = −0.93055 − 1.47612I
a = 0.326629 − 1.202060I
b = 0.49630 + 1.38462I
6.74317 − 12.42830I 0
u = −0.92821 + 1.52975I
a = −0.314902 − 1.176640I
b = −0.46221 + 1.34602I
7.57419 + 7.55749I 0
u = −0.92821 − 1.52975I
a = −0.314902 + 1.176640I
b = −0.46221 − 1.34602I
7.57419 − 7.55749I 0
u = −1.75215 + 0.63639I
a = −0.297374 − 0.502556I
b = 0.198323 + 1.086910I
−3.21485 − 9.54783I 0
u = −1.75215 − 0.63639I
a = −0.297374 + 0.502556I
b = 0.198323 − 1.086910I
−3.21485 + 9.54783I 0
u = −1.80049 + 0.55270I
a = 0.247640 + 0.493732I
b = −0.168749 − 1.056050I
−0.29405 − 4.47039I 0
u = −1.80049 − 0.55270I
a = 0.247640 − 0.493732I
b = −0.168749 + 1.056050I
−0.29405 + 4.47039I 0
u = −0.87811 + 1.69637I
a = −0.272990 − 1.129230I
b = −0.400769 + 1.241740I
6.69869 + 5.23471I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.87811 − 1.69637I
a = −0.272990 + 1.129230I
b = −0.400769 − 1.241740I
6.69869 − 5.23471I 0
u = −0.84113 + 1.84473I
a = 0.248866 + 1.102950I
b = 0.356157 − 1.185750I
4.90627 + 0.20772I 0
u = −0.84113 − 1.84473I
a = 0.248866 − 1.102950I
b = 0.356157 + 1.185750I
4.90627 − 0.20772I 0
u = −2.18886 + 0.16892I
a = 0.051200 + 0.568765I
b = −0.026784 − 1.043710I
2.93772 − 2.57806I 0
u = −2.18886 − 0.16892I
a = 0.051200 − 0.568765I
b = −0.026784 + 1.043710I
2.93772 + 2.57806I 0
9
II. I
u
2
= h−4.70 × 10
233
a
39
u − 6.24 × 10
233
a
38
u + · · · − 1.04 × 10
237
a + 1.06 ×
10
236
, 2a
39
u + 21a
38
u + · · · + 142a − 33, u
2
− u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
5
=
a
0.00205561a
39
u + 0.00273024a
38
u + ··· + 4.54569a − 0.461858
a
12
=
1
u − 1
a
4
=
0.00205561a
39
u + 0.00273024a
38
u + ··· + 5.54569a − 0.461858
0.00205561a
39
u + 0.00273024a
38
u + ··· + 4.54569a − 0.461858
a
9
=
−0.000862208a
39
u + 0.000899759a
38
u + ··· − 0.242076a + 0.813630
−0.000364350a
39
u + 0.00216092a
38
u + ··· + 0.166117a + 0.454919
a
3
=
−0.000192689a
39
u − 0.00330351a
38
u + ··· + 4.35116a + 0.103482
−0.00192222a
39
u + 0.000432146a
38
u + ··· + 1.19703a − 0.0456529
a
10
=
0.000862208a
39
u − 0.000899759a
38
u + ··· + 0.242076a + 1.18637
−0.00308448a
39
u + 0.00143811a
38
u + ··· − 1.13442a − 1.20040
a
7
=
0.000354572a
39
u − 0.000538750a
38
u + ··· − 0.171861a + 0.357600
0.000286009a
39
u + 0.000105031a
38
u + ··· + 0.617988a + 0.351373
a
1
=
−0.0000706296a
39
u − 0.000562200a
38
u + ··· + 0.412914a − 0.859285
0.00181884a
39
u + 0.00345821a
38
u + ··· − 0.844918a − 0.506231
a
6
=
−0.00463429a
39
u − 0.00244524a
38
u + ··· + 1.18427a + 2.37145
0.00370820a
39
u + 0.00576929a
38
u + ··· − 1.20106a − 2.81103
a
2
=
−0.00374070a
39
u + 0.00316369a
38
u + ··· − 8.66531a − 1.32879
−0.00721432a
39
u + 0.00732931a
38
u + ··· − 5.27593a + 1.01325
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0241933a
39
u + 0.0327742a
38
u + ··· + 13.1336a − 21.3800
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
20
+ 11u
19
+ ··· + 2u + 1)
4
c
2
, c
5
(u
20
− u
19
+ ··· + 2u − 1)
4
c
3
, c
4
, c
8
c
10
u
80
− u
79
+ ··· + 35792u + 15097
c
6
, c
12
(u
20
− 3u
19
+ ··· − 12u + 1)
4
c
7
, c
9
u
80
− 21u
79
+ ··· + 36u + 169
c
11
(u
2
− u + 1)
40
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
20
− 3y
19
+ ··· − 6y + 1)
4
c
2
, c
5
(y
20
− 11y
19
+ ··· − 2y + 1)
4
c
3
, c
4
, c
8
c
10
y
80
+ 63y
79
+ ··· + 4240509516y + 227919409
c
6
, c
12
(y
20
+ 17y
19
+ ··· − 62y + 1)
4
c
7
, c
9
y
80
+ 11y
79
+ ··· − 716504y + 28561
c
11
(y
2
+ y + 1)
40
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.223301 − 0.984504I
b = −0.721069 + 0.935523I
−5.08534 + 7.61442I −9.65468 − 2.74133I
u = 0.500000 + 0.866025I
a = −0.161727 + 0.977147I
b = 0.679884 − 0.852689I
−1.84893 + 2.76931I −6.69810 + 0.36946I
u = 0.500000 + 0.866025I
a = −0.872992 + 0.525012I
b = −0.450422 − 1.018540I
3.95796 − 2.02988I −8.93879 + 3.46410I
u = 0.500000 + 0.866025I
a = 0.521612 + 0.826124I
b = 0.311528 − 0.160068I
1.94981 + 2.81121I −5.63163 − 2.91571I
u = 0.500000 + 0.866025I
a = −0.499155 + 0.940951I
b = −0.65006 − 1.49725I
6.19099 − 3.97633I 0.94680 + 8.28286I
u = 0.500000 + 0.866025I
a = 0.171118 − 0.891526I
b = −0.788373 + 0.790387I
−5.88315 − 1.39328I −10.96035 + 3.63399I
u = 0.500000 + 0.866025I
a = −0.417061 + 0.760824I
b = −0.83097 − 1.32637I
4.01885 − 3.83436I −2.82463 + 7.16468I
u = 0.500000 + 0.866025I
a = 0.355095 − 0.780475I
b = 0.90175 + 1.37031I
0.92426 − 8.30305I −6.10015 + 10.00758I
u = 0.500000 + 0.866025I
a = 0.531113 − 1.032670I
b = 0.54401 + 1.57078I
6.19099 − 0.08344I 0.94680 − 1.35465I
u = 0.500000 + 0.866025I
a = 0.375110 − 0.675074I
b = 0.90343 + 1.23362I
0.496471 + 0.114015I −7.45592 + 3.22103I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.528289 + 1.180870I
b = −0.35513 − 1.72050I
0.92426 + 4.24328I −8.00000 + 0.I
u = 0.500000 + 0.866025I
a = 0.560866 − 1.168870I
b = 0.35123 + 1.65493I
4.01885 − 0.22541I 0
u = 0.500000 + 0.866025I
a = −0.455734 − 0.521331I
b = −0.539610 − 0.030941I
2.99206 − 1.44519I −3.20205 + 3.45501I
u = 0.500000 + 0.866025I
a = −0.565033 + 1.216060I
b = −0.26427 − 1.66859I
0.49647 − 4.17378I 0
u = 0.500000 + 0.866025I
a = −0.17739 + 1.40437I
b = 0.160251 − 1.054550I
1.94981 + 2.81121I 0
u = 0.500000 + 0.866025I
a = 0.043628 + 0.507114I
b = 0.928213 − 0.215774I
−1.59840 − 2.02988I −11.89977 + 3.46410I
u = 0.500000 + 0.866025I
a = 0.87299 − 1.27368I
b = 0.234300 + 1.392880I
3.95796 − 2.02988I 0
u = 0.500000 + 0.866025I
a = 1.55443 − 0.33903I
b = 0.022743 + 0.944463I
0.49647 − 4.17378I 0
u = 0.500000 + 0.866025I
a = 0.27721 − 1.58998I
b = 0.019390 + 1.138130I
2.99206 − 1.44519I 0
u = 0.500000 + 0.866025I
a = 0.54980 + 1.52611I
b = −0.151295 − 0.510966I
−1.84893 + 2.76931I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.57372 + 0.50963I
b = −0.035102 − 1.032930I
4.01885 − 0.22541I 0
u = 0.500000 + 0.866025I
a = −0.223415 − 0.228493I
b = −0.909375 − 0.182307I
2.99206 − 2.61458I −3.20205 + 3.47320I
u = 0.500000 + 0.866025I
a = −0.65612 − 1.54780I
b = 0.206465 + 0.455571I
−5.08534 + 7.61442I 0
u = 0.500000 + 0.866025I
a = 0.157128 − 0.259381I
b = −1.328830 + 0.069336I
−5.88315 − 2.66649I −10.96035 + 3.29421I
u = 0.500000 + 0.866025I
a = −0.51135 − 1.66307I
b = 0.221039 + 0.585128I
−5.88315 − 1.39328I 0
u = 0.500000 + 0.866025I
a = −0.132043 + 0.215117I
b = 1.324980 + 0.002145I
−1.84893 − 6.82908I −6.69810 + 6.55874I
u = 0.500000 + 0.866025I
a = 0.161659 − 0.191649I
b = −1.376880 − 0.014061I
−5.08534 − 11.67420I −9.65468 + 9.66953I
u = 0.500000 + 0.866025I
a = 1.69318 − 0.48218I
b = −0.025625 + 1.034880I
0.92426 + 4.24328I 0
u = 0.500000 + 0.866025I
a = −1.56080 + 0.88587I
b = −0.071541 − 1.200140I
6.19099 − 0.08344I 0
u = 0.500000 + 0.866025I
a = 0.068505 + 0.163465I
b = 1.111960 + 0.176330I
1.94981 − 6.87098I −5.63163 + 9.84391I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.52884 − 1.08774I
b = 0.092842 + 1.273400I
6.19099 − 3.97633I 0
u = 0.500000 + 0.866025I
a = −0.04363 + 1.89905I
b = −0.233613 − 0.987309I
−1.59840 − 2.02988I 0
u = 0.500000 + 0.866025I
a = 0.40194 − 1.88281I
b = 0.210631 + 1.186430I
2.99206 − 2.61458I 0
u = 0.500000 + 0.866025I
a = 1.42992 − 1.42006I
b = 0.134239 + 1.363600I
4.01885 − 3.83436I 0
u = 0.500000 + 0.866025I
a = −1.36451 + 1.55210I
b = −0.155551 − 1.386520I
0.496471 + 0.114015I 0
u = 0.500000 + 0.866025I
a = −0.41272 + 2.06703I
b = −0.295962 − 1.192210I
1.94981 − 6.87098I 0
u = 0.500000 + 0.866025I
a = −1.51999 + 1.47916I
b = −0.117609 − 1.383380I
0.92426 − 8.30305I 0
u = 0.500000 + 0.866025I
a = −0.25603 + 2.28814I
b = −0.408313 − 1.141740I
−1.84893 − 6.82908I 0
u = 0.500000 + 0.866025I
a = 0.18310 − 2.29522I
b = 0.421267 + 1.109750I
−5.88315 − 2.66649I 0
u = 0.500000 + 0.866025I
a = 0.27116 − 2.34065I
b = 0.429461 + 1.155270I
−5.08534 − 11.67420I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = 0.223301 + 0.984504I
b = −0.721069 − 0.935523I
−5.08534 − 7.61442I −9.65468 + 2.74133I
u = 0.500000 − 0.866025I
a = −0.161727 − 0.977147I
b = 0.679884 + 0.852689I
−1.84893 − 2.76931I −6.69810 − 0.36946I
u = 0.500000 − 0.866025I
a = −0.872992 − 0.525012I
b = −0.450422 + 1.018540I
3.95796 + 2.02988I −8.93879 − 3.46410I
u = 0.500000 − 0.866025I
a = 0.521612 − 0.826124I
b = 0.311528 + 0.160068I
1.94981 − 2.81121I −5.63163 + 2.91571I
u = 0.500000 − 0.866025I
a = −0.499155 − 0.940951I
b = −0.65006 + 1.49725I
6.19099 + 3.97633I 0.94680 − 8.28286I
u = 0.500000 − 0.866025I
a = 0.171118 + 0.891526I
b = −0.788373 − 0.790387I
−5.88315 + 1.39328I −10.96035 − 3.63399I
u = 0.500000 − 0.866025I
a = −0.417061 − 0.760824I
b = −0.83097 + 1.32637I
4.01885 + 3.83436I −2.82463 − 7.16468I
u = 0.500000 − 0.866025I
a = 0.355095 + 0.780475I
b = 0.90175 − 1.37031I
0.92426 + 8.30305I −6.10015 − 10.00758I
u = 0.500000 − 0.866025I
a = 0.531113 + 1.032670I
b = 0.54401 − 1.57078I
6.19099 + 0.08344I 0.94680 + 1.35465I
u = 0.500000 − 0.866025I
a = 0.375110 + 0.675074I
b = 0.90343 − 1.23362I
0.496471 − 0.114015I −7.45592 − 3.22103I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = −0.528289 − 1.180870I
b = −0.35513 + 1.72050I
0.92426 − 4.24328I −8.00000 + 0.I
u = 0.500000 − 0.866025I
a = 0.560866 + 1.168870I
b = 0.35123 − 1.65493I
4.01885 + 0.22541I 0
u = 0.500000 − 0.866025I
a = −0.455734 + 0.521331I
b = −0.539610 + 0.030941I
2.99206 + 1.44519I −3.20205 − 3.45501I
u = 0.500000 − 0.866025I
a = −0.565033 − 1.216060I
b = −0.26427 + 1.66859I
0.49647 + 4.17378I 0
u = 0.500000 − 0.866025I
a = −0.17739 − 1.40437I
b = 0.160251 + 1.054550I
1.94981 − 2.81121I 0
u = 0.500000 − 0.866025I
a = 0.043628 − 0.507114I
b = 0.928213 + 0.215774I
−1.59840 + 2.02988I −11.89977 − 3.46410I
u = 0.500000 − 0.866025I
a = 0.87299 + 1.27368I
b = 0.234300 − 1.392880I
3.95796 + 2.02988I 0
u = 0.500000 − 0.866025I
a = 1.55443 + 0.33903I
b = 0.022743 − 0.944463I
0.49647 + 4.17378I 0
u = 0.500000 − 0.866025I
a = 0.27721 + 1.58998I
b = 0.019390 − 1.138130I
2.99206 + 1.44519I 0
u = 0.500000 − 0.866025I
a = 0.54980 − 1.52611I
b = −0.151295 + 0.510966I
−1.84893 − 2.76931I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = −1.57372 − 0.50963I
b = −0.035102 + 1.032930I
4.01885 + 0.22541I 0
u = 0.500000 − 0.866025I
a = −0.223415 + 0.228493I
b = −0.909375 + 0.182307I
2.99206 + 2.61458I −3.20205 − 3.47320I
u = 0.500000 − 0.866025I
a = −0.65612 + 1.54780I
b = 0.206465 − 0.455571I
−5.08534 − 7.61442I 0
u = 0.500000 − 0.866025I
a = 0.157128 + 0.259381I
b = −1.328830 − 0.069336I
−5.88315 + 2.66649I −10.96035 − 3.29421I
u = 0.500000 − 0.866025I
a = −0.51135 + 1.66307I
b = 0.221039 − 0.585128I
−5.88315 + 1.39328I 0
u = 0.500000 − 0.866025I
a = −0.132043 − 0.215117I
b = 1.324980 − 0.002145I
−1.84893 + 6.82908I −6.69810 − 6.55874I
u = 0.500000 − 0.866025I
a = 0.161659 + 0.191649I
b = −1.376880 + 0.014061I
−5.08534 + 11.67420I −9.65468 − 9.66953I
u = 0.500000 − 0.866025I
a = 1.69318 + 0.48218I
b = −0.025625 − 1.034880I
0.92426 − 4.24328I 0
u = 0.500000 − 0.866025I
a = −1.56080 − 0.88587I
b = −0.071541 + 1.200140I
6.19099 + 0.08344I 0
u = 0.500000 − 0.866025I
a = 0.068505 − 0.163465I
b = 1.111960 − 0.176330I
1.94981 + 6.87098I −5.63163 − 9.84391I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 − 0.866025I
a = 1.52884 + 1.08774I
b = 0.092842 − 1.273400I
6.19099 + 3.97633I 0
u = 0.500000 − 0.866025I
a = −0.04363 − 1.89905I
b = −0.233613 + 0.987309I
−1.59840 + 2.02988I 0
u = 0.500000 − 0.866025I
a = 0.40194 + 1.88281I
b = 0.210631 − 1.186430I
2.99206 + 2.61458I 0
u = 0.500000 − 0.866025I
a = 1.42992 + 1.42006I
b = 0.134239 − 1.363600I
4.01885 + 3.83436I 0
u = 0.500000 − 0.866025I
a = −1.36451 − 1.55210I
b = −0.155551 + 1.386520I
0.496471 − 0.114015I 0
u = 0.500000 − 0.866025I
a = −0.41272 − 2.06703I
b = −0.295962 + 1.192210I
1.94981 + 6.87098I 0
u = 0.500000 − 0.866025I
a = −1.51999 − 1.47916I
b = −0.117609 + 1.383380I
0.92426 + 8.30305I 0
u = 0.500000 − 0.866025I
a = −0.25603 − 2.28814I
b = −0.408313 + 1.141740I
−1.84893 + 6.82908I 0
u = 0.500000 − 0.866025I
a = 0.18310 + 2.29522I
b = 0.421267 − 1.109750I
−5.88315 + 2.66649I 0
u = 0.500000 − 0.866025I
a = 0.27116 + 2.34065I
b = 0.429461 − 1.155270I
−5.08534 + 11.67420I 0
20
III. I
u
3
=
h−11u
22
−8u
21
+· · ·+b+40, −29u
22
−83u
21
+· · ·+a+3, u
23
+2u
22
+· · ·−u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
5
=
29u
22
+ 83u
21
+ ··· + 45u − 3
11u
22
+ 8u
21
+ ··· − 3u − 40
a
12
=
1
u
2
a
4
=
40u
22
+ 91u
21
+ ··· + 42u − 43
11u
22
+ 8u
21
+ ··· − 3u − 40
a
9
=
−2u
22
− 5u
21
+ ··· − 8u + 1
−u
22
− 2u
21
+ ··· − 6u
2
+ 2
a
3
=
−43u
22
− 126u
21
+ ··· − 67u + 1
−26u
22
− 43u
21
+ ··· − 13u + 54
a
10
=
−u
22
− 3u
21
+ ··· − 5u
2
− 7u
−u
22
− 2u
21
+ ··· − u + 2
a
7
=
−u
21
− 3u
20
+ ··· − 5u − 7
−2u
22
− 5u
21
+ ··· − 7u + 1
a
1
=
−11u
22
− 28u
21
+ ··· − 26u + 6
−5u
22
− 9u
21
+ ··· − 9u
2
+ 16
a
6
=
−14u
22
− 23u
21
+ ··· + 3u + 40
13u
22
+ 39u
21
+ ··· + 40u + 5
a
2
=
30u
22
+ 69u
21
+ ··· + 35u − 32
u
22
− 6u
21
+ ··· − 16u − 21
(ii) Obstruction class = 1
(iii) Cusp Shapes = −101u
22
− 241u
21
− 63u
20
− 438u
19
− 1512u
18
− 929u
17
−
817u
16
− 3145u
15
− 2707u
14
− 726u
13
− 3279u
12
− 3820u
11
− 319u
10
− 1123u
9
−
2832u
8
− 256u
7
+ 468u
6
− 1028u
5
− 293u
4
+ 427u
3
− 102u
2
− 118u + 87
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 13u
22
+ ··· + 5u − 1
c
2
u
23
+ u
22
+ ··· − u − 1
c
3
, c
10
u
23
+ 12u
21
+ ··· + 3u − 1
c
4
, c
8
u
23
+ 12u
21
+ ··· + 3u + 1
c
5
u
23
− u
22
+ ··· − u + 1
c
6
u
23
− 3u
22
+ ··· + 3u + 1
c
7
, c
9
u
23
+ u
22
+ ··· + 2u − 1
c
11
u
23
+ 2u
22
+ ··· − u + 1
c
12
u
23
+ 3u
22
+ ··· + 3u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− y
22
+ ··· + 9y − 1
c
2
, c
5
y
23
− 13y
22
+ ··· + 5y − 1
c
3
, c
4
, c
8
c
10
y
23
+ 24y
22
+ ··· + 5y − 1
c
6
, c
12
y
23
+ 15y
22
+ ··· + 43y − 1
c
7
, c
9
y
23
+ y
22
+ ··· + 4y − 1
c
11
y
23
− 4y
22
+ ··· − y − 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.891523 + 0.539467I
a = −0.465440 − 1.290310I
b = 0.417800 + 0.594568I
−2.06437 − 3.95440I −8.63156 + 6.09948I
u = −0.891523 − 0.539467I
a = −0.465440 + 1.290310I
b = 0.417800 − 0.594568I
−2.06437 + 3.95440I −8.63156 − 6.09948I
u = −0.772619 + 0.561019I
a = 0.52054 + 1.46048I
b = −0.490640 − 0.627106I
−5.20691 − 8.91486I −10.68690 + 8.90274I
u = −0.772619 − 0.561019I
a = 0.52054 − 1.46048I
b = −0.490640 + 0.627106I
−5.20691 + 8.91486I −10.68690 − 8.90274I
u = −0.948923
a = −0.476498
b = 0.232005
−3.06830 −9.64660
u = −0.853358 + 0.383068I
a = 0.687818 + 1.149760I
b = −0.454872 − 0.481247I
−6.25538 + 0.06461I −13.33134 + 1.68019I
u = −0.853358 − 0.383068I
a = 0.687818 − 1.149760I
b = −0.454872 + 0.481247I
−6.25538 − 0.06461I −13.33134 − 1.68019I
u = 0.260940 + 1.058470I
a = 0.74302 − 1.25125I
b = 0.381175 + 1.168270I
3.61187 − 4.35423I −4.17455 + 6.43852I
u = 0.260940 − 1.058470I
a = 0.74302 + 1.25125I
b = 0.381175 − 1.168270I
3.61187 + 4.35423I −4.17455 − 6.43852I
u = 0.755052 + 0.791973I
a = −0.767365 + 0.648951I
b = −0.254019 − 1.301980I
5.36340 − 2.81228I −2.58785 + 3.59508I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.755052 − 0.791973I
a = −0.767365 − 0.648951I
b = −0.254019 + 1.301980I
5.36340 + 2.81228I −2.58785 − 3.59508I
u = 0.357379 + 0.820793I
a = −1.07541 + 1.11627I
b = −0.403716 − 1.268430I
4.71667 − 1.35723I −1.00741 − 1.61688I
u = 0.357379 − 0.820793I
a = −1.07541 − 1.11627I
b = −0.403716 + 1.268430I
4.71667 + 1.35723I −1.00741 + 1.61688I
u = 0.487371 + 0.607807I
a = −1.32119 + 0.63458I
b = −0.36016 − 1.39021I
3.92488 − 2.52107I −3.55346 + 0.94577I
u = 0.487371 − 0.607807I
a = −1.32119 − 0.63458I
b = −0.36016 + 1.39021I
3.92488 + 2.52107I −3.55346 − 0.94577I
u = 0.493262 + 0.533153I
a = 1.42724 − 0.44917I
b = 0.35215 + 1.43492I
0.80414 − 6.84512I −6.80922 + 4.56757I
u = 0.493262 − 0.533153I
a = 1.42724 + 0.44917I
b = 0.35215 − 1.43492I
0.80414 + 6.84512I −6.80922 − 4.56757I
u = 0.412195 + 0.581577I
a = 1.53236 − 0.73131I
b = 0.40701 + 1.40600I
0.56415 + 1.51972I −7.03913 − 2.65885I
u = 0.412195 − 0.581577I
a = 1.53236 + 0.73131I
b = 0.40701 − 1.40600I
0.56415 − 1.51972I −7.03913 + 2.65885I
u = 0.91123 + 1.19260I
a = 0.507332 − 0.834010I
b = 0.219623 + 1.205300I
4.37259 + 1.11056I −5.33341 − 2.98849I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.91123 − 1.19260I
a = 0.507332 + 0.834010I
b = 0.219623 − 1.205300I
4.37259 − 1.11056I −5.33341 + 2.98849I
u = −1.68547 + 0.26457I
a = −0.050661 − 1.036720I
b = 0.069646 + 0.652543I
1.57271 − 2.56456I −19.0218 + 7.7387I
u = −1.68547 − 0.26457I
a = −0.050661 + 1.036720I
b = 0.069646 − 0.652543I
1.57271 + 2.56456I −19.0218 − 7.7387I
26
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
20
+ 11u
19
+ ··· + 2u + 1)
4
)(u
23
− 13u
22
+ ··· + 5u − 1)
· (u
45
+ 24u
44
+ ··· + 172u + 16)
c
2
((u
20
− u
19
+ ··· + 2u − 1)
4
)(u
23
+ u
22
+ ··· − u − 1)
· (u
45
+ 6u
44
+ ··· + 38u + 4)
c
3
, c
10
(u
23
+ 12u
21
+ ··· + 3u − 1)(u
45
+ 15u
43
+ ··· + 2u + 1)
· (u
80
− u
79
+ ··· + 35792u + 15097)
c
4
, c
8
(u
23
+ 12u
21
+ ··· + 3u + 1)(u
45
+ 15u
43
+ ··· + 2u + 1)
· (u
80
− u
79
+ ··· + 35792u + 15097)
c
5
((u
20
− u
19
+ ··· + 2u − 1)
4
)(u
23
− u
22
+ ··· − u + 1)
· (u
45
+ 6u
44
+ ··· + 38u + 4)
c
6
((u
20
− 3u
19
+ ··· − 12u + 1)
4
)(u
23
− 3u
22
+ ··· + 3u + 1)
· (u
45
+ 18u
44
+ ··· + 2834u + 188)
c
7
, c
9
(u
23
+ u
22
+ ··· + 2u − 1)(u
45
+ u
44
+ ··· − 7u + 1)
· (u
80
− 21u
79
+ ··· + 36u + 169)
c
11
((u
2
− u + 1)
40
)(u
23
+ 2u
22
+ ··· − u + 1)
· (u
45
+ 39u
44
+ ··· + 23068672u + 1048576)
c
12
((u
20
− 3u
19
+ ··· − 12u + 1)
4
)(u
23
+ 3u
22
+ ··· + 3u − 1)
· (u
45
+ 18u
44
+ ··· + 2834u + 188)
27
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
20
− 3y
19
+ ··· − 6y + 1)
4
)(y
23
− y
22
+ ··· + 9y − 1)
· (y
45
− 4y
44
+ ··· + 11504y − 256)
c
2
, c
5
((y
20
− 11y
19
+ ··· − 2y + 1)
4
)(y
23
− 13y
22
+ ··· + 5y − 1)
· (y
45
− 24y
44
+ ··· + 172y − 16)
c
3
, c
4
, c
8
c
10
(y
23
+ 24y
22
+ ··· + 5y − 1)(y
45
+ 30y
44
+ ··· + 2y − 1)
· (y
80
+ 63y
79
+ ··· + 4240509516y + 227919409)
c
6
, c
12
((y
20
+ 17y
19
+ ··· − 62y + 1)
4
)(y
23
+ 15y
22
+ ··· + 43y − 1)
· (y
45
+ 32y
44
+ ··· + 315660y − 35344)
c
7
, c
9
(y
23
+ y
22
+ ··· + 4y − 1)(y
45
− 21y
44
+ ··· + 65y − 1)
· (y
80
+ 11y
79
+ ··· − 716504y + 28561)
c
11
((y
2
+ y + 1)
40
)(y
23
− 4y
22
+ ··· − y − 1)
· (y
45
− 3y
44
+ ··· + 9345848836096y − 1099511627776)
28
