12a
0231
(K12a
0231
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 12 2 4 11 1 5 8 10
Solving Sequence
1,9 5,10
11 4 8 7 3 12 6 2
c
9
c
10
c
4
c
8
c
7
c
3
c
12
c
5
c
2
c
1
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6651u
44
+ 145618u
43
+ ··· + 524288b − 466223,
524233u
44
− 2692162u
43
+ ··· + 524288a − 643773, u
45
− 5u
44
+ ··· − 4u − 1i
I
u
2
= h1.55401 × 10
94
u
69
+ 1.52437 × 10
95
u
68
+ ··· + 1.07854 × 10
94
b + 7.18821 × 10
93
,
− 1.16571 × 10
94
u
69
− 1.26580 × 10
95
u
68
+ ··· + 1.07854 × 10
94
a − 8.60428 × 10
94
,
u
70
+ 11u
69
+ ··· + 16u + 1i
I
u
3
= hb − a, 32a
5
− 16a
4
− 16a
3
+ 4a
2
+ 2a + 1, u − 1i
I
u
4
= hau + b + a − u + 1, a
2
− 2au − a + u, u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 124 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
= h6651u
44
+ 145618u
43
+ · · · + 524288b − 466223, 5.24 × 10
5
u
44
−
2.69 × 10
6
u
43
+ · · · + 5.24 × 10
5
a − 6.44 × 10
5
, u
45
− 5u
44
+ · · · − 4u − 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
−0.999895u
44
+ 5.13489u
43
+ ··· + 14.6410u + 1.22790
−0.0126858u
44
− 0.277744u
43
+ ··· + 3.08293u + 0.889250
a
10
=
1
u
2
a
11
=
1
16
u
44
−
5
16
u
43
+ ··· −
1
4
u
2
+
31
16
u
u
a
4
=
−1.01258u
44
+ 4.85715u
43
+ ··· + 17.7239u + 2.11715
−0.0126858u
44
− 0.277744u
43
+ ··· + 3.08293u + 0.889250
a
8
=
1
16
u
43
−
5
16
u
42
+ ··· −
1
4
u +
15
16
−u
2
a
7
=
9.53674 × 10
−7
u
44
− 5.72205 × 10
−6
u
43
+ ··· − 5.00000u + 2.00000
4.76837 × 10
−7
u
44
− 2.86102 × 10
−6
u
43
+ ··· − 1.00000u − 4.76837 × 10
−7
a
3
=
0.132458u
44
− 0.552269u
43
+ ··· + 10.2747u + 0.660954
−0.193096u
44
+ 1.22194u
43
+ ··· + 1.49102u + 0.299046
a
12
=
u
u
3
+ u
a
6
=
−0.658722u
44
+ 3.16490u
43
+ ··· + 13.8025u + 1.24059
0.332701u
44
− 1.98454u
43
+ ··· + 1.52910u + 0.637812
a
2
=
−0.0177879u
44
+ 0.166283u
43
+ ··· + 9.80950u − 1.04152
−0.00756836u
44
+ 0.106544u
43
+ ··· + 1.77556u − 0.0534439
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
853951
4194304
u
44
+
1865277
2097152
u
43
+ ··· +
22965053
4194304
u −
24110657
4194304
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ 24u
44
+ ··· + 145u − 16
c
2
, c
6
u
45
− 2u
44
+ ··· + 5u + 4
c
3
, c
7
u
45
+ 2u
44
+ ··· + 621u + 292
c
4
, c
5
32(32u
45
− 16u
44
+ ··· + 12u + 4)
c
8
, c
9
, c
11
c
12
u
45
+ 5u
44
+ ··· − 4u + 1
c
10
u
45
+ 3u
44
+ ··· + 5632u + 2048
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 4y
44
+ ··· + 44993y −256
c
2
, c
6
y
45
+ 24y
44
+ ··· + 145y −16
c
3
, c
7
y
45
− 32y
44
+ ··· + 1265729y −85264
c
4
, c
5
1024(1024y
45
− 5376y
44
+ ··· + 320y −16)
c
8
, c
9
, c
11
c
12
y
45
+ 17y
44
+ ··· − 1030y
2
− 1
c
10
y
45
+ 9y
44
+ ··· − 83623936y −4194304
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.520727 + 0.939578I
a = 0.758964 + 0.066469I
b = 0.779771 + 0.243421I
−4.56636 − 1.73156I −11.99281 + 3.31846I
u = 0.520727 − 0.939578I
a = 0.758964 − 0.066469I
b = 0.779771 − 0.243421I
−4.56636 + 1.73156I −11.99281 − 3.31846I
u = 0.420339 + 0.991396I
a = −0.974005 − 0.017820I
b = −0.710296 − 0.326186I
−0.21603 − 5.35749I −6.20050 + 6.92376I
u = 0.420339 − 0.991396I
a = −0.974005 + 0.017820I
b = −0.710296 + 0.326186I
−0.21603 + 5.35749I −6.20050 − 6.92376I
u = 0.776889 + 0.479998I
a = −0.168820 − 0.167222I
b = −0.630907 + 0.111072I
−2.93036 − 1.75870I −17.4213 + 1.7562I
u = 0.776889 − 0.479998I
a = −0.168820 + 0.167222I
b = −0.630907 − 0.111072I
−2.93036 + 1.75870I −17.4213 − 1.7562I
u = 0.217946 + 0.864786I
a = −1.40293 − 0.70903I
b = −0.536590 − 0.217455I
2.55612 − 3.52730I −8.10907 + 10.18535I
u = 0.217946 − 0.864786I
a = −1.40293 + 0.70903I
b = −0.536590 + 0.217455I
2.55612 + 3.52730I −8.10907 − 10.18535I
u = 0.442791 + 1.050870I
a = 0.933478 − 0.112856I
b = 0.753141 + 0.378689I
−3.07301 − 10.38100I −8.00000 + 9.73173I
u = 0.442791 − 1.050870I
a = 0.933478 + 0.112856I
b = 0.753141 − 0.378689I
−3.07301 + 10.38100I −8.00000 − 9.73173I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.297785 + 1.113910I
a = 0.03350 + 2.19997I
b = 0.673195 − 0.752405I
4.65659 − 0.00210I −3.78722 − 3.26916I
u = −0.297785 − 1.113910I
a = 0.03350 − 2.19997I
b = 0.673195 + 0.752405I
4.65659 + 0.00210I −3.78722 + 3.26916I
u = 0.113962 + 0.805614I
a = 1.38924 + 1.35506I
b = 0.518517 + 0.141686I
2.17122 + 1.50395I −11.94091 + 1.99102I
u = 0.113962 − 0.805614I
a = 1.38924 − 1.35506I
b = 0.518517 − 0.141686I
2.17122 − 1.50395I −11.94091 − 1.99102I
u = −0.412048 + 0.695424I
a = −0.61411 − 2.35550I
b = −1.116650 − 0.046522I
−6.28912 + 6.14694I −10.86325 − 8.13273I
u = −0.412048 − 0.695424I
a = −0.61411 + 2.35550I
b = −1.116650 + 0.046522I
−6.28912 − 6.14694I −10.86325 + 8.13273I
u = 1.198270 + 0.098629I
a = −0.0225006 + 0.0343167I
b = −0.159457 + 0.519154I
−1.73909 + 1.72292I 5.26680 − 11.72526I
u = 1.198270 − 0.098629I
a = −0.0225006 − 0.0343167I
b = −0.159457 − 0.519154I
−1.73909 − 1.72292I 5.26680 + 11.72526I
u = −0.354317 + 1.160890I
a = −0.08135 − 2.03091I
b = −0.760215 + 0.900488I
6.42066 + 5.09294I 0. − 6.60661I
u = −0.354317 − 1.160890I
a = −0.08135 + 2.03091I
b = −0.760215 − 0.900488I
6.42066 − 5.09294I 0. + 6.60661I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.470835 + 1.120420I
a = 0.30475 + 1.97067I
b = 1.051690 − 0.899049I
1.14313 + 7.15516I −8.00000 − 7.04629I
u = −0.470835 − 1.120420I
a = 0.30475 − 1.97067I
b = 1.051690 + 0.899049I
1.14313 − 7.15516I −8.00000 + 7.04629I
u = −0.334613 + 0.649816I
a = 0.57160 + 2.36102I
b = 0.967229 + 0.125022I
−2.56741 + 1.44381I −7.78555 − 4.48019I
u = −0.334613 − 0.649816I
a = 0.57160 − 2.36102I
b = 0.967229 − 0.125022I
−2.56741 − 1.44381I −7.78555 + 4.48019I
u = 1.224740 + 0.401588I
a = −0.1045230 + 0.0475191I
b = −0.584434 + 0.569316I
−4.17784 + 0.91994I 0
u = 1.224740 − 0.401588I
a = −0.1045230 − 0.0475191I
b = −0.584434 − 0.569316I
−4.17784 − 0.91994I 0
u = 1.217570 + 0.485388I
a = 0.1307500 − 0.0531710I
b = 0.691032 − 0.549753I
−7.82065 − 3.25322I 0
u = 1.217570 − 0.485388I
a = 0.1307500 + 0.0531710I
b = 0.691032 + 0.549753I
−7.82065 + 3.25322I 0
u = −0.375360 + 0.563080I
a = −0.54767 − 2.43496I
b = −1.010960 − 0.292068I
−6.31075 − 3.17495I −10.44526 − 1.01574I
u = −0.375360 − 0.563080I
a = −0.54767 + 2.43496I
b = −1.010960 + 0.292068I
−6.31075 + 3.17495I −10.44526 + 1.01574I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.445965 + 1.253320I
a = −0.15883 − 1.79924I
b = −0.89148 + 1.18060I
7.27138 + 7.55038I 0
u = −0.445965 − 1.253320I
a = −0.15883 + 1.79924I
b = −0.89148 − 1.18060I
7.27138 − 7.55038I 0
u = 1.294890 + 0.408163I
a = 0.1009240 − 0.0680235I
b = 0.600371 − 0.662127I
−7.44445 + 5.45779I 0
u = 1.294890 − 0.408163I
a = 0.1009240 + 0.0680235I
b = 0.600371 + 0.662127I
−7.44445 − 5.45779I 0
u = −0.492198 + 1.284080I
a = 0.20751 + 1.72707I
b = 0.97106 − 1.28854I
6.42111 + 12.47940I 0
u = −0.492198 − 1.284080I
a = 0.20751 − 1.72707I
b = 0.97106 + 1.28854I
6.42111 − 12.47940I 0
u = −0.615203 + 1.260530I
a = −0.37637 − 1.68251I
b = −1.27509 + 1.33680I
−2.09321 + 9.43737I 0
u = −0.615203 − 1.260530I
a = −0.37637 + 1.68251I
b = −1.27509 − 1.33680I
−2.09321 − 9.43737I 0
u = −0.60014 + 1.29188I
a = 0.33986 + 1.65539I
b = 1.21338 − 1.39737I
2.26103 + 13.52680I 0
u = −0.60014 − 1.29188I
a = 0.33986 − 1.65539I
b = 1.21338 + 1.39737I
2.26103 − 13.52680I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.61764 + 1.30754I
a = −0.35102 − 1.62737I
b = −1.24080 + 1.44894I
−0.8748 + 18.5817I 0
u = −0.61764 − 1.30754I
a = −0.35102 + 1.62737I
b = −1.24080 − 1.44894I
−0.8748 − 18.5817I 0
u = 0.440279
a = −0.481278
b = 0.451961
−0.780322 −12.5880
u = −0.132173 + 0.113061I
a = −0.47781 + 3.06580I
b = 0.221516 + 0.422164I
−0.50223 − 1.35791I −4.98318 + 4.28434I
u = −0.132173 − 0.113061I
a = −0.47781 − 3.06580I
b = 0.221516 − 0.422164I
−0.50223 + 1.35791I −4.98318 − 4.28434I
9
II. I
u
2
= h1.55 × 10
94
u
69
+ 1.52 × 10
95
u
68
+ · · · + 1.08 × 10
94
b + 7.19 ×
10
93
, −1.17 × 10
94
u
69
− 1.27 × 10
95
u
68
+ · · · + 1.08 × 10
94
a − 8.60 ×
10
94
, u
70
+ 11u
69
+ · · · + 16u + 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
1.08082u
69
+ 11.7362u
68
+ ··· + 184.359u + 7.97770
−1.44084u
69
− 14.1336u
68
+ ··· − 20.0415u − 0.666475
a
10
=
1
u
2
a
11
=
u
69
+ 11u
68
+ ··· + 192u + 16
−3.20315u
69
− 32.5737u
68
+ ··· − 83.3945u − 5.63546
a
4
=
−0.360027u
69
− 2.39747u
68
+ ··· + 164.318u + 7.31122
−1.44084u
69
− 14.1336u
68
+ ··· − 20.0415u − 0.666475
a
8
=
5.63546u
69
+ 58.7869u
68
+ ··· + 224.368u + 7.77279
2.66095u
69
+ 26.7961u
68
+ ··· + 45.6150u + 4.20315
a
7
=
1.64927u
69
+ 17.2776u
68
+ ··· + 79.4458u + 5.23781
0.564864u
69
+ 5.72230u
68
+ ··· + 3.88670u + 0.373194
a
3
=
−0.216460u
69
− 0.984352u
68
+ ··· + 187.162u + 7.45450
−0.144073u
69
− 1.84384u
68
+ ··· − 21.7810u − 0.688465
a
12
=
u
u
3
+ u
a
6
=
1.51593u
69
+ 16.2137u
68
+ ··· + 203.870u + 9.30832
0.761879u
69
+ 7.92472u
68
+ ··· + 3.97357u + 0.972847
a
2
=
−0.132976u
69
− 0.100144u
68
+ ··· + 61.5717u − 5.48447
−0.306015u
69
− 3.25379u
68
+ ··· + 8.43607u + 1.65974
(ii) Obstruction class = −1
(iii) Cusp Shapes = −17.4050u
69
− 175.428u
68
+ ··· − 209.459u − 22.1259
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
35
+ 19u
34
+ ··· − 2u − 1)
2
c
2
, c
6
(u
35
− u
34
+ ··· − 2u + 1)
2
c
3
, c
7
(u
35
+ u
34
+ ··· + 10u + 1)
2
c
4
, c
5
u
70
− 3u
69
+ ··· + 116244u + 29257
c
8
, c
9
, c
11
c
12
u
70
− 11u
69
+ ··· − 16u + 1
c
10
(u
35
− u
34
+ ··· + 2u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
35
− 5y
34
+ ··· + 2y −1)
2
c
2
, c
6
(y
35
+ 19y
34
+ ··· − 2y −1)
2
c
3
, c
7
(y
35
− 29y
34
+ ··· − 50y −1)
2
c
4
, c
5
y
70
+ 27y
69
+ ··· + 28203718484y + 855972049
c
8
, c
9
, c
11
c
12
y
70
+ 43y
69
+ ··· + 128y + 1
c
10
(y
35
+ 11y
34
+ ··· − 2y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.362102 + 0.951729I
a = −0.100504 − 1.012000I
b = −1.45453 + 0.12725I
−5.23403 + 6.46046I 0
u = −0.362102 − 0.951729I
a = −0.100504 + 1.012000I
b = −1.45453 − 0.12725I
−5.23403 − 6.46046I 0
u = −0.971172 + 0.001234I
a = 0.0134351 + 0.0212814I
b = 0.686282 − 0.949474I
2.47115 + 7.33485I 0
u = −0.971172 − 0.001234I
a = 0.0134351 − 0.0212814I
b = 0.686282 + 0.949474I
2.47115 − 7.33485I 0
u = 0.016391 + 1.047640I
a = −0.02718 + 1.43210I
b = 0.660206 − 0.876545I
1.67002 + 2.07827I 0
u = 0.016391 − 1.047640I
a = −0.02718 − 1.43210I
b = 0.660206 + 0.876545I
1.67002 − 2.07827I 0
u = 0.231464 + 1.027880I
a = −1.95974 + 1.25976I
b = 2.01738 − 2.24983I
−1.83551 + 4.24996I 0
u = 0.231464 − 1.027880I
a = −1.95974 − 1.25976I
b = 2.01738 + 2.24983I
−1.83551 − 4.24996I 0
u = 0.171370 + 1.043120I
a = 1.97007 − 1.59447I
b = −2.10116 + 2.39246I
1.48735 0
u = 0.171370 − 1.043120I
a = 1.97007 + 1.59447I
b = −2.10116 − 2.39246I
1.48735 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.330094 + 0.880242I
a = 0.185222 + 1.053900I
b = 1.304500 − 0.071629I
−1.97019 + 1.67857I 0
u = −0.330094 − 0.880242I
a = 0.185222 − 1.053900I
b = 1.304500 + 0.071629I
−1.97019 − 1.67857I 0
u = −0.428006 + 0.831185I
a = −0.240025 − 0.928202I
b = −1.365590 − 0.121653I
−5.91946 − 2.50696I 0
u = −0.428006 − 0.831185I
a = −0.240025 + 0.928202I
b = −1.365590 + 0.121653I
−5.91946 + 2.50696I 0
u = 0.001993 + 1.099100I
a = 0.16754 − 2.73997I
b = −0.54348 + 2.96665I
2.90212 − 1.21814I 0
u = 0.001993 − 1.099100I
a = 0.16754 + 2.73997I
b = −0.54348 − 2.96665I
2.90212 + 1.21814I 0
u = 0.455946 + 1.002640I
a = −0.226037 + 1.393280I
b = −0.359584 − 0.449294I
−1.36125 − 2.79178I 0
u = 0.455946 − 1.002640I
a = −0.226037 − 1.393280I
b = −0.359584 + 0.449294I
−1.36125 + 2.79178I 0
u = −1.077150 + 0.256650I
a = −0.073618 − 0.180904I
b = −0.93877 − 1.13745I
−5.25248 − 3.42594I 0
u = −1.077150 − 0.256650I
a = −0.073618 + 0.180904I
b = −0.93877 + 1.13745I
−5.25248 + 3.42594I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.094680 + 0.191898I
a = 0.045501 + 0.148806I
b = 0.85647 + 1.14457I
−1.19431 − 7.52211I 0
u = −1.094680 − 0.191898I
a = 0.045501 − 0.148806I
b = 0.85647 − 1.14457I
−1.19431 + 7.52211I 0
u = 0.189786 + 1.097990I
a = −1.64670 + 1.49396I
b = 1.95456 − 2.37976I
−1.83551 − 4.24996I 0
u = 0.189786 − 1.097990I
a = −1.64670 − 1.49396I
b = 1.95456 + 2.37976I
−1.83551 + 4.24996I 0
u = 0.004361 + 0.856181I
a = 3.11503 − 0.27313I
b = −2.63446 + 0.56745I
2.90212 + 1.21814I 0
u = 0.004361 − 0.856181I
a = 3.11503 + 0.27313I
b = −2.63446 − 0.56745I
2.90212 − 1.21814I 0
u = −0.702120 + 0.906516I
a = −0.796718 − 0.252448I
b = 0.222896 + 0.142326I
1.01725 − 1.14078I 0
u = −0.702120 − 0.906516I
a = −0.796718 + 0.252448I
b = 0.222896 − 0.142326I
1.01725 + 1.14078I 0
u = −1.142550 + 0.196557I
a = −0.022298 − 0.165856I
b = −0.84945 − 1.20442I
−4.37931 − 12.37660I 0
u = −1.142550 − 0.196557I
a = −0.022298 + 0.165856I
b = −0.84945 + 1.20442I
−4.37931 + 12.37660I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.835497 + 0.076887I
a = −0.014110 − 0.190842I
b = −0.675470 + 0.801354I
3.33212 + 3.00440I 0
u = −0.835497 − 0.076887I
a = −0.014110 + 0.190842I
b = −0.675470 − 0.801354I
3.33212 − 3.00440I 0
u = 0.183998 + 1.157830I
a = 0.002222 − 1.388870I
b = −0.018988 + 1.000380I
2.91461 − 1.90476I 0
u = 0.183998 − 1.157830I
a = 0.002222 + 1.388870I
b = −0.018988 − 1.000380I
2.91461 + 1.90476I 0
u = −0.658098 + 1.076360I
a = 0.777615 + 0.453828I
b = −0.105220 − 0.453813I
4.55305 + 2.51214I 0
u = −0.658098 − 1.076360I
a = 0.777615 − 0.453828I
b = −0.105220 + 0.453813I
4.55305 − 2.51214I 0
u = −0.671200 + 0.272239I
a = 0.507154 + 0.106964I
b = 0.964036 + 0.723303I
−1.36125 − 2.79178I −13.43445 + 0.I
u = −0.671200 − 0.272239I
a = 0.507154 − 0.106964I
b = 0.964036 − 0.723303I
−1.36125 + 2.79178I −13.43445 + 0.I
u = 0.528808 + 0.431959I
a = 0.83458 − 1.89090I
b = 0.114478 − 0.558335I
−5.91946 − 2.50696I −13.26110 + 2.94934I
u = 0.528808 − 0.431959I
a = 0.83458 + 1.89090I
b = 0.114478 + 0.558335I
−5.91946 + 2.50696I −13.26110 − 2.94934I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.752093 + 1.088900I
a = −0.689822 − 0.417214I
b = −0.049160 + 0.362378I
1.63653 + 7.02473I 0
u = −0.752093 − 1.088900I
a = −0.689822 + 0.417214I
b = −0.049160 − 0.362378I
1.63653 − 7.02473I 0
u = 0.378678 + 1.271580I
a = 0.082986 − 1.247180I
b = 0.437616 + 0.986037I
3.33212 − 3.00440I 0
u = 0.378678 − 1.271580I
a = 0.082986 + 1.247180I
b = 0.437616 − 0.986037I
3.33212 + 3.00440I 0
u = −0.532938 + 1.273710I
a = 0.700808 + 0.699873I
b = −0.025749 − 0.896753I
6.72846 + 2.09817I 0
u = −0.532938 − 1.273710I
a = 0.700808 − 0.699873I
b = −0.025749 + 0.896753I
6.72846 − 2.09817I 0
u = 0.484898 + 1.307290I
a = −0.136066 + 1.194180I
b = −0.639871 − 0.963047I
2.47115 − 7.33485I 0
u = 0.484898 − 1.307290I
a = −0.136066 − 1.194180I
b = −0.639871 + 0.963047I
2.47115 + 7.33485I 0
u = 0.532064 + 0.260484I
a = 1.27588 − 1.99852I
b = −0.006289 − 0.802486I
−5.23403 + 6.46046I −12.19651 − 3.55460I
u = 0.532064 − 0.260484I
a = 1.27588 + 1.99852I
b = −0.006289 + 0.802486I
−5.23403 − 6.46046I −12.19651 + 3.55460I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.691259 + 1.229650I
a = 0.270821 − 1.165160I
b = 0.942516 + 0.685241I
−5.25248 − 3.42594I 0
u = 0.691259 − 1.229650I
a = 0.270821 + 1.165160I
b = 0.942516 − 0.685241I
−5.25248 + 3.42594I 0
u = −0.44836 + 1.34906I
a = −0.642320 − 0.809577I
b = 0.022505 + 1.096370I
6.72846 − 2.09817I 0
u = −0.44836 − 1.34906I
a = −0.642320 + 0.809577I
b = 0.022505 − 1.096370I
6.72846 + 2.09817I 0
u = 0.66211 + 1.27675I
a = −0.239531 + 1.153130I
b = −0.923043 − 0.788287I
−1.19431 − 7.52211I 0
u = 0.66211 − 1.27675I
a = −0.239531 − 1.153130I
b = −0.923043 + 0.788287I
−1.19431 + 7.52211I 0
u = 0.450658 + 0.322883I
a = −1.02214 + 2.21324I
b = 0.070264 + 0.659054I
−1.97019 + 1.67857I −9.17734 − 0.36674I
u = 0.450658 − 0.322883I
a = −1.02214 − 2.21324I
b = 0.070264 − 0.659054I
−1.97019 − 1.67857I −9.17734 + 0.36674I
u = −0.12997 + 1.44563I
a = 0.393709 + 1.099040I
b = −0.12084 − 1.47133I
1.01725 + 1.14078I 0
u = −0.12997 − 1.44563I
a = 0.393709 − 1.099040I
b = −0.12084 + 1.47133I
1.01725 − 1.14078I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.26268 + 1.43599I
a = −0.502802 − 0.992024I
b = 0.069674 + 1.379420I
4.55305 − 2.51214I 0
u = −0.26268 − 1.43599I
a = −0.502802 + 0.992024I
b = 0.069674 − 1.379420I
4.55305 + 2.51214I 0
u = 0.69145 + 1.30334I
a = 0.244252 − 1.130360I
b = 0.992491 + 0.815615I
−4.37931 − 12.37660I 0
u = 0.69145 − 1.30334I
a = 0.244252 + 1.130360I
b = 0.992491 − 0.815615I
−4.37931 + 12.37660I 0
u = −0.479440 + 0.166521I
a = 0.003513 − 1.058800I
b = −0.776200 + 0.600848I
2.91461 + 1.90476I −4.38240 − 3.26312I
u = −0.479440 − 0.166521I
a = 0.003513 + 1.058800I
b = −0.776200 − 0.600848I
2.91461 − 1.90476I −4.38240 + 3.26312I
u = −0.25835 + 1.51265I
a = 0.433847 + 0.954857I
b = −0.01097 − 1.43398I
1.63653 − 7.02473I 0
u = −0.25835 − 1.51265I
a = 0.433847 − 0.954857I
b = −0.01097 + 1.43398I
1.63653 + 7.02473I 0
u = −0.0387239 + 0.1019520I
a = −4.68457 + 7.81727I
b = 0.782958 − 0.728346I
1.67002 − 2.07827I −8.18960 + 3.40333I
u = −0.0387239 − 0.1019520I
a = −4.68457 − 7.81727I
b = 0.782958 + 0.728346I
1.67002 + 2.07827I −8.18960 − 3.40333I
19
III. I
u
3
= hb − a, 32a
5
− 16a
4
− 16a
3
+ 4a
2
+ 2a + 1, u − 1i
(i) Arc colorings
a
1
=
0
1
a
9
=
1
0
a
5
=
a
a
a
10
=
1
1
a
11
=
1
1
a
4
=
2a
a
a
8
=
0
−1
a
7
=
−4a
2
−2a
2
− 1
a
3
=
−8a
3
+ 2a
−4a
3
− a
a
12
=
1
2
a
6
=
2a
3a
a
2
=
−16a
4
− 8a
3
+ 4a
2
+ 4a + 1
−24a
4
− 4a
3
+ 6a
2
+ 2a +
3
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 64a
4
− 32a
3
− 15a
2
+ 8a − 14
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
4
32(32u
5
+ 16u
4
− 16u
3
− 4u
2
+ 2u − 1)
c
5
32(32u
5
− 16u
4
− 16u
3
+ 4u
2
+ 2u + 1)
c
6
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
, c
9
(u − 1)
5
c
10
u
5
c
11
, c
12
(u + 1)
5
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
2
, c
6
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
3
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
4
, c
5
1024(1024y
5
− 1280y
4
+ 512y
3
− 48y
2
− 4y −1)
c
8
, c
9
, c
11
c
12
(y −1)
5
c
10
y
5
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.709392 + 0.109583I
b = 0.709392 + 0.109583I
−7.51750 − 4.40083I −12.40273 + 3.06842I
u = 1.00000
a = 0.709392 − 0.109583I
b = 0.709392 − 0.109583I
−7.51750 + 4.40083I −12.40273 − 3.06842I
u = 1.00000
a = −0.608868
b = −0.608868
−4.04602 −8.41300
u = 1.00000
a = −0.154958 + 0.274955I
b = −0.154958 + 0.274955I
−1.97403 + 1.53058I −15.7658 + 4.0719I
u = 1.00000
a = −0.154958 − 0.274955I
b = −0.154958 − 0.274955I
−1.97403 − 1.53058I −15.7658 − 4.0719I
23
IV. I
u
4
= hau + b + a − u + 1, a
2
− 2au − a + u, u
2
+ 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
5
=
a
−au − a + u − 1
a
10
=
1
−1
a
11
=
a
−u
a
4
=
−au + u − 1
−au − a + u − 1
a
8
=
au + 1
1
a
7
=
0
−u
a
3
=
−au + u − 1
−2au − a + 2u − 2
a
12
=
u
0
a
6
=
−au + u − 1
−au − a + u − 1
a
2
=
−au − 1
−au − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a + 4u
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
(u
2
− u + 1)
2
c
2
, c
7
(u
2
+ u + 1)
2
c
4
u
4
− 2u
3
+ 2u
2
− 4u + 4
c
5
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
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
(y
2
+ y + 1)
2
c
4
, c
5
y
4
− 4y
2
+ 16
c
8
, c
9
, c
11
c
12
(y + 1)
4
c
10
(y
2
− y + 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.500000 + 0.133975I
b = −1.36603 + 0.36603I
3.28987 − 2.02988I −2.00000 + 3.46410I
u = 1.000000I
a = 0.50000 + 1.86603I
b = 0.36603 − 1.36603I
3.28987 + 2.02988I −2.00000 − 3.46410I
u = − 1.000000I
a = 0.500000 − 0.133975I
b = −1.36603 − 0.36603I
3.28987 + 2.02988I −2.00000 − 3.46410I
u = − 1.000000I
a = 0.50000 − 1.86603I
b = 0.36603 + 1.36603I
3.28987 − 2.02988I −2.00000 + 3.46410I
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
· ((u
35
+ 19u
34
+ ··· − 2u − 1)
2
)(u
45
+ 24u
44
+ ··· + 145u − 16)
c
2
((u
2
+ u + 1)
2
)(u
5
− u
4
+ ··· + u − 1)(u
35
− u
34
+ ··· − 2u + 1)
2
· (u
45
− 2u
44
+ ··· + 5u + 4)
c
3
((u
2
− u + 1)
2
)(u
5
+ u
4
+ ··· + u − 1)(u
35
+ u
34
+ ··· + 10u + 1)
2
· (u
45
+ 2u
44
+ ··· + 621u + 292)
c
4
1024(u
4
− 2u
3
+ ··· − 4u + 4)(32u
5
+ 16u
4
+ ··· + 2u − 1)
· (32u
45
− 16u
44
+ ··· + 12u + 4)(u
70
− 3u
69
+ ··· + 116244u + 29257)
c
5
1024(u
4
+ 2u
3
+ ··· + 4u + 4)(32u
5
− 16u
4
+ ··· + 2u + 1)
· (32u
45
− 16u
44
+ ··· + 12u + 4)(u
70
− 3u
69
+ ··· + 116244u + 29257)
c
6
((u
2
− u + 1)
2
)(u
5
+ u
4
+ ··· + u + 1)(u
35
− u
34
+ ··· − 2u + 1)
2
· (u
45
− 2u
44
+ ··· + 5u + 4)
c
7
((u
2
+ u + 1)
2
)(u
5
− u
4
+ ··· + u + 1)(u
35
+ u
34
+ ··· + 10u + 1)
2
· (u
45
+ 2u
44
+ ··· + 621u + 292)
c
8
, c
9
((u − 1)
5
)(u
2
+ 1)
2
(u
45
+ 5u
44
+ ··· − 4u + 1)
· (u
70
− 11u
69
+ ··· − 16u + 1)
c
10
u
5
(u
4
− u
2
+ 1)(u
35
− u
34
+ ··· + 2u − 1)
2
· (u
45
+ 3u
44
+ ··· + 5632u + 2048)
c
11
, c
12
((u + 1)
5
)(u
2
+ 1)
2
(u
45
+ 5u
44
+ ··· − 4u + 1)
· (u
70
− 11u
69
+ ··· − 16u + 1)
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
· ((y
35
− 5y
34
+ ··· + 2y −1)
2
)(y
45
− 4y
44
+ ··· + 44993y −256)
c
2
, c
6
(y
2
+ y + 1)
2
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· ((y
35
+ 19y
34
+ ··· − 2y −1)
2
)(y
45
+ 24y
44
+ ··· + 145y −16)
c
3
, c
7
(y
2
+ y + 1)
2
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
35
− 29y
34
+ ··· − 50y −1)
2
· (y
45
− 32y
44
+ ··· + 1265729y −85264)
c
4
, c
5
1048576(y
4
− 4y
2
+ 16)(1024y
5
− 1280y
4
+ ··· − 4y −1)
· (1024y
45
− 5376y
44
+ ··· + 320y −16)
· (y
70
+ 27y
69
+ ··· + 28203718484y + 855972049)
c
8
, c
9
, c
11
c
12
((y −1)
5
)(y + 1)
4
(y
45
+ 17y
44
+ ··· − 1030y
2
− 1)
· (y
70
+ 43y
69
+ ··· + 128y + 1)
c
10
y
5
(y
2
− y + 1)
2
(y
35
+ 11y
34
+ ··· − 2y −1)
2
· (y
45
+ 9y
44
+ ··· − 83623936y −4194304)
29
