12a
0358
(K12a
0358
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 2 1 10 11 12 5 4 7
Solving Sequence
5,10 8,11
9 4 12 3 7 1 2 6
c
10
c
8
c
4
c
11
c
3
c
7
c
12
c
1
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.48000 × 10
182
u
67
+ 2.10373 × 10
182
u
66
+ ··· + 2.76730 × 10
181
b − 5.41435 × 10
182
,
− 2.95579 × 10
182
u
67
+ 4.27734 × 10
182
u
66
+ ··· + 2.76730 × 10
181
a − 3.31608 × 10
183
,
u
68
+ 19u
64
+ ··· − 7u + 1i
I
u
2
= h1.53296 × 10
479
u
85
+ 3.33392 × 10
478
u
84
+ ··· + 2.77033 × 10
479
b + 4.69150 × 10
478
,
1.19862 × 10
480
u
85
+ 1.80990 × 10
479
u
84
+ ··· + 2.77033 × 10
479
a + 4.42171 × 10
479
, u
86
− 4u
84
+ ··· + 43u − 1i
I
u
3
= hu
2
+ b, u
24
+ u
23
+ ··· + a + 6, u
25
− 4u
23
+ ··· + u − 1i
I
u
4
= hb + 1, a − u, u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 181 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
= h−3.48 × 10
182
u
67
+ 2.10 × 10
182
u
66
+ · · · + 2.77 × 10
181
b − 5.41 ×
10
182
, −2.96 × 10
182
u
67
+ 4.28 × 10
182
u
66
+ · · · + 2.77 × 10
181
a − 3.32 ×
10
183
, u
68
+ 19u
64
+ · · · − 7u + 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
8
=
10.6811u
67
− 15.4567u
66
+ ··· − 497.371u + 119.831
12.5754u
67
− 7.60209u
66
+ ··· − 175.533u + 19.5654
a
11
=
1
u
2
a
9
=
17.7268u
67
− 20.5532u
66
+ ··· − 554.027u + 123.940
16.3036u
67
− 10.0984u
66
+ ··· − 218.254u + 24.6619
a
4
=
29.9768u
67
− 19.8927u
66
+ ··· − 442.656u + 71.3591
−3.63379u
67
− 1.04843u
66
+ ··· + 25.3732u + 9.21156
a
12
=
32.7837u
67
− 10.4113u
66
+ ··· − 206.024u − 32.1867
−12.5754u
67
+ 7.60209u
66
+ ··· + 175.533u − 19.5654
a
3
=
9.42361u
67
− 10.6348u
66
+ ··· − 194.629u + 53.6323
−13.7322u
67
+ 4.68970u
66
+ ··· + 164.160u − 7.09202
a
7
=
23.2565u
67
− 23.0588u
66
+ ··· − 672.905u + 139.396
12.5754u
67
− 7.60209u
66
+ ··· − 175.533u + 19.5654
a
1
=
15.3311u
67
− 11.3111u
66
+ ··· − 106.397u + 4.70936
−11.6073u
67
+ 5.60830u
66
+ ··· + 231.455u − 30.3761
a
2
=
15.8016u
67
− 18.6094u
66
+ ··· − 268.617u + 59.5037
15.4207u
67
− 9.11330u
66
+ ··· − 110.867u + 3.78552
a
6
=
−20.4648u
67
+ 7.34855u
66
+ ··· − 44.9005u + 53.2777
−1.24532u
67
+ 3.69828u
66
+ ··· − 32.5923u − 1.47535
(ii) Obstruction class = −1
(iii) Cusp Shapes = 116.467u
67
− 60.5514u
66
+ ··· − 1629.96u + 139.411
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
68
+ 37u
67
+ ··· + 89u + 16
c
2
, c
5
u
68
+ 5u
67
+ ··· + 33u + 4
c
3
, c
10
u
68
+ 19u
64
+ ··· − 7u + 1
c
4
, c
11
u
68
− u
67
+ ··· + 36u
2
+ 1
c
6
, c
12
u
68
+ 15u
67
+ ··· + 233u + 4
c
7
, c
9
u
68
+ 10u
67
+ ··· − 27u + 1
c
8
u
68
+ 38u
67
+ ··· + 17u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
68
− 9y
67
+ ··· + 2287y + 256
c
2
, c
5
y
68
− 37y
67
+ ··· − 89y + 16
c
3
, c
10
y
68
+ 38y
66
+ ··· − 91y + 1
c
4
, c
11
y
68
+ 29y
67
+ ··· + 72y + 1
c
6
, c
12
y
68
+ 55y
67
+ ··· − 4473y + 16
c
7
, c
9
y
68
− 52y
67
+ ··· − 83y + 1
c
8
y
68
+ 68y
66
+ ··· − 69y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.347227 + 0.946466I
a = 0.447675 + 0.190413I
b = 0.419351 − 0.657918I
−3.24328 − 6.62876I 0
u = 0.347227 − 0.946466I
a = 0.447675 − 0.190413I
b = 0.419351 + 0.657918I
−3.24328 + 6.62876I 0
u = 0.852783 + 0.504203I
a = 0.161261 + 0.635469I
b = −1.09501 − 1.03917I
−1.63277 − 6.08911I 0. + 10.34292I
u = 0.852783 − 0.504203I
a = 0.161261 − 0.635469I
b = −1.09501 + 1.03917I
−1.63277 + 6.08911I 0. − 10.34292I
u = 0.445396 + 0.853666I
a = 0.461499 + 0.277653I
b = 0.135076 − 0.753502I
−3.70567 + 1.63808I −5.70574 + 0.I
u = 0.445396 − 0.853666I
a = 0.461499 − 0.277653I
b = 0.135076 + 0.753502I
−3.70567 − 1.63808I −5.70574 + 0.I
u = 0.522673 + 0.800825I
a = 0.919151 + 0.337383I
b = −0.662024 + 0.293325I
−2.09202 + 1.65586I −7.45578 − 5.24528I
u = 0.522673 − 0.800825I
a = 0.919151 − 0.337383I
b = −0.662024 − 0.293325I
−2.09202 − 1.65586I −7.45578 + 5.24528I
u = −1.010070 + 0.356545I
a = −0.031339 − 0.635729I
b = −1.56324 + 1.02397I
−9.15785 + 1.85685I 0
u = −1.010070 − 0.356545I
a = −0.031339 + 0.635729I
b = −1.56324 − 1.02397I
−9.15785 − 1.85685I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.318933 + 0.868215I
a = 0.499987 − 0.196987I
b = 0.296188 + 0.533663I
−0.24152 + 2.17299I 0. − 2.58289I
u = −0.318933 − 0.868215I
a = 0.499987 + 0.196987I
b = 0.296188 − 0.533663I
−0.24152 − 2.17299I 0. + 2.58289I
u = 0.997809 + 0.406411I
a = 0.007684 + 0.619132I
b = −1.47572 − 1.09452I
−5.18332 − 5.99152I 0
u = 0.997809 − 0.406411I
a = 0.007684 − 0.619132I
b = −1.47572 + 1.09452I
−5.18332 + 5.99152I 0
u = −0.734968 + 0.519286I
a = 0.283079 − 0.671507I
b = −0.902944 + 0.866741I
−0.76164 + 1.96482I −4.70279 − 3.62702I
u = −0.734968 − 0.519286I
a = 0.283079 + 0.671507I
b = −0.902944 − 0.866741I
−0.76164 − 1.96482I −4.70279 + 3.62702I
u = −0.069981 + 0.884380I
a = 0.528598 − 0.042048I
b = 0.463855 + 0.116792I
1.87694 + 2.02607I 3.77017 − 4.09968I
u = −0.069981 − 0.884380I
a = 0.528598 + 0.042048I
b = 0.463855 − 0.116792I
1.87694 − 2.02607I 3.77017 + 4.09968I
u = −1.032800 + 0.421146I
a = −0.000941 − 0.590587I
b = −1.51730 + 1.16883I
−8.40560 + 10.79120I 0
u = −1.032800 − 0.421146I
a = −0.000941 + 0.590587I
b = −1.51730 − 1.16883I
−8.40560 − 10.79120I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.876151 + 0.739552I
a = 0.008031 + 1.362540I
b = 0.771843 − 0.443584I
−1.06216 + 2.38167I 0
u = −0.876151 − 0.739552I
a = 0.008031 − 1.362540I
b = 0.771843 + 0.443584I
−1.06216 − 2.38167I 0
u = 0.739570 + 0.231829I
a = 0.020493 + 0.988688I
b = −1.307970 − 0.516340I
−4.93397 − 1.67406I −14.6463 + 4.2905I
u = 0.739570 − 0.231829I
a = 0.020493 − 0.988688I
b = −1.307970 + 0.516340I
−4.93397 + 1.67406I −14.6463 − 4.2905I
u = 0.910659 + 0.868218I
a = −0.085085 − 1.235530I
b = 0.891855 + 0.577721I
0.48086 − 7.22153I 0
u = 0.910659 − 0.868218I
a = −0.085085 + 1.235530I
b = 0.891855 − 0.577721I
0.48086 + 7.22153I 0
u = −0.521019 + 0.514497I
a = 0.622392 − 0.714575I
b = −0.685802 + 0.457243I
−1.09222 + 1.31330I −3.92618 − 4.40458I
u = −0.521019 − 0.514497I
a = 0.622392 + 0.714575I
b = −0.685802 − 0.457243I
−1.09222 − 1.31330I −3.92618 + 4.40458I
u = −1.234770 + 0.419503I
a = 0.397826 + 1.038940I
b = 0.934290 + 0.149605I
−6.52084 + 2.86951I 0
u = −1.234770 − 0.419503I
a = 0.397826 − 1.038940I
b = 0.934290 − 0.149605I
−6.52084 − 2.86951I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.283940 + 0.347168I
a = 0.437743 − 0.982289I
b = 0.923063 − 0.261317I
−10.03860 + 2.02386I 0
u = 1.283940 − 0.347168I
a = 0.437743 + 0.982289I
b = 0.923063 + 0.261317I
−10.03860 − 2.02386I 0
u = 0.134094 + 1.332070I
a = 0.828702 + 0.051317I
b = −1.271790 + 0.131476I
−1.93522 − 1.56682I 0
u = 0.134094 − 1.332070I
a = 0.828702 − 0.051317I
b = −1.271790 − 0.131476I
−1.93522 + 1.56682I 0
u = −0.630096 + 0.186750I
a = 1.175720 − 0.469552I
b = 0.048819 − 0.153786I
−1.77089 + 0.39180I −7.19717 − 1.64300I
u = −0.630096 − 0.186750I
a = 1.175720 + 0.469552I
b = 0.048819 + 0.153786I
−1.77089 − 0.39180I −7.19717 + 1.64300I
u = −0.621936 + 0.161590I
a = −0.81823 + 1.22057I
b = −1.42873 + 0.03945I
−8.62125 − 1.48539I −12.37549 + 3.25891I
u = −0.621936 − 0.161590I
a = −0.81823 − 1.22057I
b = −1.42873 − 0.03945I
−8.62125 + 1.48539I −12.37549 − 3.25891I
u = 1.299580 + 0.492132I
a = 0.331541 − 1.003160I
b = 1.059830 − 0.128516I
−10.55020 − 7.37369I 0
u = 1.299580 − 0.492132I
a = 0.331541 + 1.003160I
b = 1.059830 + 0.128516I
−10.55020 + 7.37369I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.539259 + 0.262076I
a = −1.19117 + 1.19261I
b = −1.346730 + 0.181830I
−7.67223 + 7.31607I −10.44733 − 3.84736I
u = −0.539259 − 0.262076I
a = −1.19117 − 1.19261I
b = −1.346730 − 0.181830I
−7.67223 − 7.31607I −10.44733 + 3.84736I
u = −0.590569 + 0.075856I
a = 2.12977 + 1.15018I
b = 0.197115 + 0.007397I
0.86890 + 6.10828I −3.53214 + 10.54641I
u = −0.590569 − 0.075856I
a = 2.12977 − 1.15018I
b = 0.197115 − 0.007397I
0.86890 − 6.10828I −3.53214 − 10.54641I
u = 0.571423 + 0.027243I
a = 2.24431 − 0.59306I
b = 0.166108 − 0.013277I
2.64938 − 1.14980I 8.50880 − 9.28452I
u = 0.571423 − 0.027243I
a = 2.24431 + 0.59306I
b = 0.166108 + 0.013277I
2.64938 + 1.14980I 8.50880 + 9.28452I
u = 0.95336 + 1.06674I
a = −0.171760 − 1.072920I
b = 1.076150 + 0.805127I
0.95534 − 9.37922I 0
u = 0.95336 − 1.06674I
a = −0.171760 + 1.072920I
b = 1.076150 − 0.805127I
0.95534 + 9.37922I 0
u = 0.55544 + 1.32541I
a = 0.771871 + 0.188431I
b = −1.172570 + 0.565100I
−4.11848 − 0.16698I 0
u = 0.55544 − 1.32541I
a = 0.771871 − 0.188431I
b = −1.172570 − 0.565100I
−4.11848 + 0.16698I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.523872 + 0.189484I
a = −1.06890 − 1.40700I
b = −1.318000 − 0.097191I
−4.58749 − 2.48434I −7.90113 + 0.62149I
u = 0.523872 − 0.189484I
a = −1.06890 + 1.40700I
b = −1.318000 + 0.097191I
−4.58749 + 2.48434I −7.90113 − 0.62149I
u = −1.11339 + 0.93127I
a = −0.013162 + 1.062630I
b = 1.187060 − 0.517921I
−4.71725 + 8.77037I 0
u = −1.11339 − 0.93127I
a = −0.013162 − 1.062630I
b = 1.187060 + 0.517921I
−4.71725 − 8.77037I 0
u = −0.65891 + 1.32082I
a = 0.752740 − 0.214794I
b = −1.131810 − 0.678205I
−7.63638 − 4.19234I 0
u = −0.65891 − 1.32082I
a = 0.752740 + 0.214794I
b = −1.131810 + 0.678205I
−7.63638 + 4.19234I 0
u = −0.98698 + 1.15189I
a = −0.184401 + 1.007490I
b = 1.18008 − 0.89645I
−0.0347 + 14.1725I 0
u = −0.98698 − 1.15189I
a = −0.184401 − 1.007490I
b = 1.18008 + 0.89645I
−0.0347 − 14.1725I 0
u = −0.55908 + 1.42353I
a = 0.746297 − 0.172067I
b = −1.280620 − 0.599655I
−7.54925 + 4.60676I 0
u = −0.55908 − 1.42353I
a = 0.746297 + 0.172067I
b = −1.280620 + 0.599655I
−7.54925 − 4.60676I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.12939 + 1.25688I
a = −0.145720 + 0.908937I
b = 1.45287 − 0.93543I
−4.3166 + 14.8677I 0
u = −1.12939 − 1.25688I
a = −0.145720 − 0.908937I
b = 1.45287 + 0.93543I
−4.3166 − 14.8677I 0
u = 1.17541 + 1.23208I
a = −0.118660 − 0.905590I
b = 1.49689 + 0.86547I
−8.58923 − 10.69630I 0
u = 1.17541 − 1.23208I
a = −0.118660 + 0.905590I
b = 1.49689 − 0.86547I
−8.58923 + 10.69630I 0
u = 1.13734 + 1.29280I
a = −0.152283 − 0.891120I
b = 1.49173 + 0.97919I
−7.5213 − 19.8847I 0
u = 1.13734 − 1.29280I
a = −0.152283 + 0.891120I
b = 1.49173 − 0.97919I
−7.5213 + 19.8847I 0
u = 0.177741 + 0.009631I
a = −0.79472 − 5.50260I
b = −1.031910 + 0.001970I
−1.55668 − 2.08082I −7.56227 + 3.79767I
u = 0.177741 − 0.009631I
a = −0.79472 + 5.50260I
b = −1.031910 − 0.001970I
−1.55668 + 2.08082I −7.56227 − 3.79767I
11
II. I
u
2
= h1.53 × 10
479
u
85
+ 3.33 × 10
478
u
84
+ · · · + 2.77 × 10
479
b + 4.69 ×
10
478
, 1.20 × 10
480
u
85
+ 1.81 × 10
479
u
84
+ · · · + 2.77 × 10
479
a + 4.42 ×
10
479
, u
86
− 4u
84
+ · · · + 43u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
8
=
−4.32663u
85
− 0.653316u
84
+ ··· + 556.356u − 1.59609
−0.553349u
85
− 0.120344u
84
+ ··· + 75.1551u − 0.169348
a
11
=
1
u
2
a
9
=
−4.80547u
85
− 0.752449u
84
+ ··· + 607.745u − 1.11213
−0.557459u
85
− 0.114226u
84
+ ··· + 78.9390u − 0.268481
a
4
=
−11.1333u
85
− 1.42770u
84
+ ··· + 3468.92u − 106.428
−0.525406u
85
− 0.0659176u
84
+ ··· + 192.044u − 6.75608
a
12
=
−9.65501u
85
− 0.976864u
84
+ ··· + 3175.46u − 88.9304
−0.619253u
85
− 0.0501898u
84
+ ··· + 238.716u − 7.36739
a
3
=
−6.98211u
85
− 0.505651u
84
+ ··· + 2960.01u − 79.2322
−0.617382u
85
− 0.00458364u
84
+ ··· + 370.774u − 11.3112
a
7
=
−4.87998u
85
− 0.773659u
84
+ ··· + 631.511u − 1.76544
−0.553349u
85
− 0.120344u
84
+ ··· + 75.1551u − 0.169348
a
1
=
−12.4281u
85
− 1.03198u
84
+ ··· + 4584.43u − 119.627
−1.16547u
85
− 0.0768050u
84
+ ··· + 500.975u − 14.5900
a
2
=
−3.82340u
85
− 0.213777u
84
+ ··· + 2094.49u − 81.9384
−0.0561820u
85
− 0.0158373u
84
+ ··· + 50.6542u − 4.28487
a
6
=
−7.09996u
85
− 0.422945u
84
+ ··· + 3531.19u − 122.826
−0.161542u
85
− 0.0134656u
84
+ ··· + 195.859u − 9.11331
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.65648u
85
+ 0.894392u
84
+ ··· − 1822.38u + 50.8744
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
43
+ 24u
42
+ ··· − 10u
2
+ 1)
2
c
2
, c
5
(u
43
− 2u
42
+ ··· − 4u + 1)
2
c
3
, c
10
u
86
− 4u
84
+ ··· + 43u − 1
c
4
, c
11
u
86
− 2u
85
+ ··· + 15u + 1
c
6
, c
12
(u
43
− 9u
42
+ ··· + 101u − 8)
2
c
7
, c
9
u
86
− 3u
85
+ ··· + 2682u − 617
c
8
(u
43
− 21u
42
+ ··· − u + 2)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
43
− 8y
42
+ ··· + 20y −1)
2
c
2
, c
5
(y
43
− 24y
42
+ ··· + 10y
2
− 1)
2
c
3
, c
10
y
86
− 8y
85
+ ··· − 171y + 1
c
4
, c
11
y
86
− 20y
85
+ ··· − 99y + 1
c
6
, c
12
(y
43
+ 37y
42
+ ··· + 137y −64)
2
c
7
, c
9
y
86
+ 13y
85
+ ··· + 8586034y + 380689
c
8
(y
43
− 3y
42
+ ··· + 85y −4)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.135043 + 0.991220I
a = 0.416179 + 1.100660I
b = 0.38130 − 2.18383I
−4.08710 − 9.94581I 0
u = 0.135043 − 0.991220I
a = 0.416179 − 1.100660I
b = 0.38130 + 2.18383I
−4.08710 + 9.94581I 0
u = −0.062972 + 0.992351I
a = 1.039030 − 0.233873I
b = −0.076390 + 0.215336I
1.81471 + 2.10825I 0
u = −0.062972 − 0.992351I
a = 1.039030 + 0.233873I
b = −0.076390 − 0.215336I
1.81471 − 2.10825I 0
u = 0.070769 + 0.991612I
a = −0.0509758 + 0.1010660I
b = 1.007600 + 0.009789I
1.81471 + 2.10825I 0
u = 0.070769 − 0.991612I
a = −0.0509758 − 0.1010660I
b = 1.007600 − 0.009789I
1.81471 − 2.10825I 0
u = −0.192950 + 0.956508I
a = 0.380551 − 1.131970I
b = 0.30167 + 2.05591I
−0.83965 + 5.42468I 0
u = −0.192950 − 0.956508I
a = 0.380551 + 1.131970I
b = 0.30167 − 2.05591I
−0.83965 − 5.42468I 0
u = −0.402623 + 0.969005I
a = 0.717071 − 1.002420I
b = −0.505618 + 0.811517I
0.21932 + 2.67784I 0
u = −0.402623 − 0.969005I
a = 0.717071 + 1.002420I
b = −0.505618 − 0.811517I
0.21932 − 2.67784I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.231442 + 1.026170I
a = 0.350606 + 1.090360I
b = 0.14722 − 2.15577I
−4.43944 − 1.27982I 0
u = 0.231442 − 1.026170I
a = 0.350606 − 1.090360I
b = 0.14722 + 2.15577I
−4.43944 + 1.27982I 0
u = −0.511836 + 0.926148I
a = 0.232897 − 1.096110I
b = −0.26829 + 1.47381I
−0.09484 + 3.33108I 0
u = −0.511836 − 0.926148I
a = 0.232897 + 1.096110I
b = −0.26829 − 1.47381I
−0.09484 − 3.33108I 0
u = −0.817244 + 0.713826I
a = −0.15969 − 1.56906I
b = −1.62652 + 0.85236I
−9.54476 + 0.88455I 0
u = −0.817244 − 0.713826I
a = −0.15969 + 1.56906I
b = −1.62652 − 0.85236I
−9.54476 − 0.88455I 0
u = 0.600103 + 0.913382I
a = 0.300017 + 1.291380I
b = −0.94980 − 1.18385I
−1.60025 − 6.31849I 0
u = 0.600103 − 0.913382I
a = 0.300017 − 1.291380I
b = −0.94980 + 1.18385I
−1.60025 + 6.31849I 0
u = 0.794728 + 0.769843I
a = −0.07149 + 1.50763I
b = −1.55945 − 0.96649I
−5.60933 − 5.25697I 0
u = 0.794728 − 0.769843I
a = −0.07149 − 1.50763I
b = −1.55945 + 0.96649I
−5.60933 + 5.25697I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.622875 + 0.615661I
a = −0.542486 − 0.027321I
b = 0.849730 + 0.175988I
0.21932 + 2.67784I 0
u = 0.622875 − 0.615661I
a = −0.542486 + 0.027321I
b = 0.849730 − 0.175988I
0.21932 − 2.67784I 0
u = 0.924419 + 0.645626I
a = 0.558379 − 0.730899I
b = 0.545575 + 0.421347I
2.84470 − 1.06861I 0
u = 0.924419 − 0.645626I
a = 0.558379 + 0.730899I
b = 0.545575 − 0.421347I
2.84470 + 1.06861I 0
u = −0.834100 + 0.797541I
a = −0.10490 − 1.43736I
b = −1.64021 + 1.04136I
−9.01796 + 10.05490I 0
u = −0.834100 − 0.797541I
a = −0.10490 + 1.43736I
b = −1.64021 − 1.04136I
−9.01796 − 10.05490I 0
u = 1.168210 + 0.411787I
a = −0.202746 + 0.682337I
b = 0.010873 − 0.421161I
−0.09484 − 3.33108I 0
u = 1.168210 − 0.411787I
a = −0.202746 − 0.682337I
b = 0.010873 + 0.421161I
−0.09484 + 3.33108I 0
u = −0.509587 + 0.554791I
a = −2.21789 − 0.79244I
b = −0.940496 + 0.955675I
−6.03592 + 11.45270I 0
u = −0.509587 − 0.554791I
a = −2.21789 + 0.79244I
b = −0.940496 − 0.955675I
−6.03592 − 11.45270I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373409 + 0.616370I
a = 1.26963 + 2.25666I
b = −0.959002 − 0.382909I
−3.61686 − 0.63537I 0
u = 0.373409 − 0.616370I
a = 1.26963 − 2.25666I
b = −0.959002 + 0.382909I
−3.61686 + 0.63537I 0
u = −0.133892 + 0.679193I
a = 0.44850 − 1.41706I
b = 0.67922 + 1.63183I
1.65498 + 5.98531I 0
u = −0.133892 − 0.679193I
a = 0.44850 + 1.41706I
b = 0.67922 − 1.63183I
1.65498 − 5.98531I 0
u = 0.460697 + 0.511670I
a = −2.41736 + 0.94491I
b = −0.900396 − 0.872655I
−2.79536 − 6.42700I 0
u = 0.460697 − 0.511670I
a = −2.41736 − 0.94491I
b = −0.900396 + 0.872655I
−2.79536 + 6.42700I 0
u = −0.501571 + 0.428164I
a = −2.72044 − 0.65370I
b = −0.998295 + 0.784978I
−7.07086 + 2.20292I 0
u = −0.501571 − 0.428164I
a = −2.72044 + 0.65370I
b = −0.998295 − 0.784978I
−7.07086 − 2.20292I 0
u = −0.564012 + 1.220770I
a = 0.398464 − 0.730231I
b = −0.337136 + 1.080000I
0.40386 + 2.56671I 0
u = −0.564012 − 1.220770I
a = 0.398464 + 0.730231I
b = −0.337136 − 1.080000I
0.40386 − 2.56671I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.379739 + 1.299490I
a = 0.499973 + 0.619835I
b = −0.164409 − 1.079840I
−2.70911 − 6.65745I 0
u = 0.379739 − 1.299490I
a = 0.499973 − 0.619835I
b = −0.164409 + 1.079840I
−2.70911 + 6.65745I 0
u = −1.06348 + 0.95048I
a = 0.263162 + 0.637500I
b = 0.759215 − 0.537136I
1.69172 + 5.85120I 0
u = −1.06348 − 0.95048I
a = 0.263162 − 0.637500I
b = 0.759215 + 0.537136I
1.69172 − 5.85120I 0
u = 0.095879 + 0.532540I
a = −1.52630 + 2.58201I
b = −0.434307 − 0.714196I
1.69172 − 5.85120I 5.42459 + 10.04778I
u = 0.095879 − 0.532540I
a = −1.52630 − 2.58201I
b = −0.434307 + 0.714196I
1.69172 + 5.85120I 5.42459 − 10.04778I
u = −1.40165 + 0.43208I
a = −0.297012 + 0.353990I
b = 0.508820 + 0.088690I
−1.60025 − 6.31849I 0
u = −1.40165 − 0.43208I
a = −0.297012 − 0.353990I
b = 0.508820 − 0.088690I
−1.60025 + 6.31849I 0
u = 0.55750 + 1.37908I
a = 0.381593 + 0.630067I
b = −0.316770 − 1.187940I
−2.72052 + 1.60205I 0
u = 0.55750 − 1.37908I
a = 0.381593 − 0.630067I
b = −0.316770 + 1.187940I
−2.72052 − 1.60205I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.133925 + 0.467599I
a = 0.39940 + 1.87720I
b = 0.84493 − 1.32438I
1.91538 − 2.26464I 4.89318 + 0.67008I
u = 0.133925 − 0.467599I
a = 0.39940 − 1.87720I
b = 0.84493 + 1.32438I
1.91538 + 2.26464I 4.89318 − 0.67008I
u = −0.92753 + 1.21480I
a = 0.189492 − 0.682342I
b = −0.494096 + 0.990526I
1.91538 + 2.26464I 0
u = −0.92753 − 1.21480I
a = 0.189492 + 0.682342I
b = −0.494096 − 0.990526I
1.91538 − 2.26464I 0
u = 0.121668 + 0.429385I
a = 0.05064 − 3.39826I
b = −0.224802 + 0.506766I
2.84470 + 1.06861I 9.63275 − 2.61396I
u = 0.121668 − 0.429385I
a = 0.05064 + 3.39826I
b = −0.224802 − 0.506766I
2.84470 − 1.06861I 9.63275 + 2.61396I
u = 1.13027 + 1.15953I
a = 0.112670 + 0.646613I
b = −0.566638 − 0.833106I
1.65498 − 5.98531I 0
u = 1.13027 − 1.15953I
a = 0.112670 − 0.646613I
b = −0.566638 + 0.833106I
1.65498 + 5.98531I 0
u = 0.000182 + 0.330558I
a = −0.48028 − 1.77090I
b = 1.272210 − 0.422522I
−2.70911 − 6.65745I −2.04943 + 5.57280I
u = 0.000182 − 0.330558I
a = −0.48028 + 1.77090I
b = 1.272210 + 0.422522I
−2.70911 + 6.65745I −2.04943 − 5.57280I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47176 + 1.00374I
a = 0.017821 + 0.579744I
b = −0.638721 − 0.478541I
−0.83965 − 5.42468I 0
u = 1.47176 − 1.00374I
a = 0.017821 − 0.579744I
b = −0.638721 + 0.478541I
−0.83965 + 5.42468I 0
u = 0.197861 + 0.056822I
a = −3.34853 − 0.62754I
b = 1.029320 + 0.674923I
0.40386 + 2.56671I 1.20501 − 1.18142I
u = 0.197861 − 0.056822I
a = −3.34853 + 0.62754I
b = 1.029320 − 0.674923I
0.40386 − 2.56671I 1.20501 + 1.18142I
u = −1.07223 + 1.45621I
a = −0.189500 + 0.114604I
b = 0.926955 + 0.055841I
−3.61686 − 0.63537I 0
u = −1.07223 − 1.45621I
a = −0.189500 − 0.114604I
b = 0.926955 − 0.055841I
−3.61686 + 0.63537I 0
u = −1.81467
a = 0.368861
b = 0.825751
−2.71132 0
u = −1.57653 + 0.93033I
a = −0.006956 − 0.558834I
b = −0.634985 + 0.347651I
−4.43944 + 1.27982I 0
u = −1.57653 − 0.93033I
a = −0.006956 + 0.558834I
b = −0.634985 − 0.347651I
−4.43944 − 1.27982I 0
u = 0.137632
a = −15.0764
b = −0.674497
−2.71132 16.9810
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53268 + 1.08552I
a = 0.031741 − 0.558293I
b = −0.743279 + 0.474657I
−4.08710 + 9.94581I 0
u = −1.53268 − 1.08552I
a = 0.031741 + 0.558293I
b = −0.743279 − 0.474657I
−4.08710 − 9.94581I 0
u = −1.36309 + 1.34142I
a = 0.061627 + 0.465781I
b = 1.132220 − 0.511902I
−2.79536 + 6.42700I 0
u = −1.36309 − 1.34142I
a = 0.061627 − 0.465781I
b = 1.132220 + 0.511902I
−2.79536 − 6.42700I 0
u = 0.0533184 + 0.0393166I
a = 6.49463 − 9.15183I
b = 1.30600 − 0.75689I
−2.72052 + 1.60205I −1.85850 − 1.88019I
u = 0.0533184 − 0.0393166I
a = 6.49463 + 9.15183I
b = 1.30600 + 0.75689I
−2.72052 − 1.60205I −1.85850 + 1.88019I
u = 1.34276 + 1.41745I
a = 0.031233 − 0.470711I
b = 1.186230 + 0.552440I
−6.03592 − 11.45270I 0
u = 1.34276 − 1.41745I
a = 0.031233 + 0.470711I
b = 1.186230 − 0.552440I
−6.03592 + 11.45270I 0
u = 1.47823 + 1.34675I
a = 0.060773 − 0.420842I
b = 1.166350 + 0.424527I
−7.07086 − 2.20292I 0
u = 1.47823 − 1.34675I
a = 0.060773 + 0.420842I
b = 1.166350 − 0.424527I
−7.07086 + 2.20292I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.85370 + 0.87211I
a = −0.178199 + 0.294392I
b = 0.763170 + 0.426147I
−5.60933 − 5.25697I 0
u = −1.85370 − 0.87211I
a = −0.178199 − 0.294392I
b = 0.763170 − 0.426147I
−5.60933 + 5.25697I 0
u = 1.93492 + 0.83629I
a = −0.170878 − 0.304155I
b = 0.742493 − 0.491497I
−9.01796 + 10.05490I 0
u = 1.93492 − 0.83629I
a = −0.170878 + 0.304155I
b = 0.742493 + 0.491497I
−9.01796 − 10.05490I 0
u = 1.88050 + 0.97547I
a = −0.166675 − 0.284634I
b = 0.842891 − 0.432708I
−9.54476 + 0.88455I 0
u = 1.88050 − 0.97547I
a = −0.166675 + 0.284634I
b = 0.842891 + 0.432708I
−9.54476 − 0.88455I 0
23
III. I
u
3
= hu
2
+ b, u
24
+ u
23
+ · · · + a + 6, u
25
− 4u
23
+ · · · + u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
8
=
−u
24
− u
23
+ ··· + u − 6
−u
2
a
11
=
1
u
2
a
9
=
−u
24
− u
23
+ ··· + u − 5
−u
4
a
4
=
−6u
24
− u
23
+ ··· − 12u − 5
0
a
12
=
5u
24
+ 6u
23
+ ··· − 7u + 18
u
2
a
3
=
−5u
24
− u
23
+ ··· − 8u − 4
u
5
a
7
=
−u
24
− u
23
+ ··· + u − 6
−u
2
a
1
=
u
24
+ u
23
+ ··· − u + 5
u
6
− u
4
+ 2u
2
− 1
a
2
=
−u
24
+ 2u
23
+ ··· − 6u + 1
u
16
− 2u
14
+ 4u
12
− 5u
10
+ 6u
8
− 3u
6
+ 2u
4
+ u
2
− 1
a
6
=
2u
24
+ 3u
23
+ ··· − 4u + 3
−u
24
− u
23
+ ··· + u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −30u
24
− 32u
23
+ 110u
22
+ 89u
21
− 323u
20
− 209u
19
+ 673u
18
+
354u
17
−1188u
16
−539u
15
+ 1680u
14
+ 627u
13
−2058u
12
−676u
11
+ 2084u
10
+ 587u
9
−
1801u
8
− 446u
7
+ 1261u
6
+ 285u
5
− 684u
4
− 120u
3
+ 308u
2
+ 29u − 80
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
25
− 14u
24
+ ··· + 4u − 1
c
2
u
25
+ 2u
24
+ ··· − 2u − 1
c
3
, c
10
u
25
− 4u
23
+ ··· + u − 1
c
4
, c
11
u
25
− u
24
+ ··· + 4u
2
− 1
c
5
u
25
− 2u
24
+ ··· − 2u + 1
c
6
u
25
− 6u
24
+ ··· + 18u − 3
c
7
, c
9
u
25
− 8u
24
+ ··· + 11u − 1
c
8
u
25
+ 17u
24
+ ··· + 54u + 3
c
12
u
25
+ 6u
24
+ ··· + 18u + 3
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 2y
24
+ ··· + 8y −1
c
2
, c
5
y
25
− 14y
24
+ ··· + 4y −1
c
3
, c
10
y
25
− 8y
24
+ ··· + 11y −1
c
4
, c
11
y
25
− 11y
24
+ ··· + 8y −1
c
6
, c
12
y
25
+ 18y
24
+ ··· + 120y −9
c
7
, c
9
y
25
+ 12y
24
+ ··· − y −1
c
8
y
25
+ 3y
24
+ ··· + 318y −9
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.610826 + 0.722009I
a = 0.185244 − 1.102610I
b = 0.148188 + 0.882044I
0.89982 + 4.35497I −0.26746 − 7.95573I
u = −0.610826 − 0.722009I
a = 0.185244 + 1.102610I
b = 0.148188 − 0.882044I
0.89982 − 4.35497I −0.26746 + 7.95573I
u = 0.866749 + 0.605406I
a = −0.307936 + 0.839972I
b = −0.384738 − 1.049470I
−0.02193 − 6.28225I −1.99076 + 10.73714I
u = 0.866749 − 0.605406I
a = −0.307936 − 0.839972I
b = −0.384738 + 1.049470I
−0.02193 + 6.28225I −1.99076 − 10.73714I
u = 0.911045
a = −1.20482
b = −0.830003
−3.05968 −13.4490
u = −0.804413 + 0.735073I
a = −0.075710 − 0.838757I
b = −0.106747 + 1.182610I
0.86120 + 2.90391I 0.46167 − 3.52720I
u = −0.804413 − 0.735073I
a = −0.075710 + 0.838757I
b = −0.106747 − 1.182610I
0.86120 − 2.90391I 0.46167 + 3.52720I
u = −0.698525 + 0.854520I
a = 0.163267 − 0.804524I
b = 0.242267 + 1.193810I
−0.18146 + 3.74043I −1.96230 − 6.61607I
u = −0.698525 − 0.854520I
a = 0.163267 + 0.804524I
b = 0.242267 − 1.193810I
−0.18146 − 3.74043I −1.96230 + 6.61607I
u = 0.662716 + 0.900431I
a = 0.237826 + 0.763852I
b = 0.371585 − 1.193460I
−3.34121 − 7.94021I −5.65997 + 10.46423I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.662716 − 0.900431I
a = 0.237826 − 0.763852I
b = 0.371585 + 1.193460I
−3.34121 + 7.94021I −5.65997 − 10.46423I
u = 1.088250 + 0.396616I
a = −0.570588 + 0.479609I
b = −1.026990 − 0.863235I
−3.97672 − 5.50405I −3.54701 + 5.25746I
u = 1.088250 − 0.396616I
a = −0.570588 − 0.479609I
b = −1.026990 + 0.863235I
−3.97672 + 5.50405I −3.54701 − 5.25746I
u = 0.737631 + 0.897881I
a = 0.143747 + 0.726497I
b = 0.262092 − 1.324610I
−3.42891 + 0.36997I −5.20918 + 3.35499I
u = 0.737631 − 0.897881I
a = 0.143747 − 0.726497I
b = 0.262092 + 1.324610I
−3.42891 − 0.36997I −5.20918 − 3.35499I
u = −1.117030 + 0.341780I
a = −0.607367 − 0.410066I
b = −1.130930 + 0.763555I
−7.99502 + 1.22407I −7.96428 − 1.66756I
u = −1.117030 − 0.341780I
a = −0.607367 + 0.410066I
b = −1.130930 − 0.763555I
−7.99502 − 1.22407I −7.96428 + 1.66756I
u = 0.581902 + 0.590759I
a = 0.02197 + 1.45416I
b = 0.010386 − 0.687528I
−0.304045 − 0.962885I −2.10301 − 0.25414I
u = 0.581902 − 0.590759I
a = 0.02197 − 1.45416I
b = 0.010386 + 0.687528I
−0.304045 + 0.962885I −2.10301 + 0.25414I
u = −1.126470 + 0.425200I
a = −0.517741 − 0.455797I
b = −1.08813 + 0.95795I
−7.30177 + 10.34400I −6.20234 − 8.16065I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.126470 − 0.425200I
a = −0.517741 + 0.455797I
b = −1.08813 − 0.95795I
−7.30177 − 10.34400I −6.20234 + 8.16065I
u = −0.702171 + 0.105625I
a = −1.89556 − 0.58349I
b = −0.481887 + 0.148334I
2.44855 + 1.33246I −13.6501 − 10.0463I
u = −0.702171 − 0.105625I
a = −1.89556 + 0.58349I
b = −0.481887 − 0.148334I
2.44855 − 1.33246I −13.6501 + 10.0463I
u = 0.666656 + 0.210572I
a = −1.67474 + 1.17523I
b = −0.400090 − 0.280758I
0.84226 − 6.35848I −6.6808 + 20.7487I
u = 0.666656 − 0.210572I
a = −1.67474 − 1.17523I
b = −0.400090 + 0.280758I
0.84226 + 6.35848I −6.6808 − 20.7487I
29
IV. I
u
4
= hb + 1, a − u, u
2
− u + 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
8
=
u
−1
a
11
=
1
u − 1
a
9
=
u
−1
a
4
=
1
2u − 1
a
12
=
−u + 1
1
a
3
=
0
u
a
7
=
u − 1
−1
a
1
=
−u + 1
1
a
2
=
−u + 1
u + 1
a
6
=
u − 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
9
(u − 1)
2
c
3
, c
4
, c
10
c
11
u
2
− u + 1
c
5
(u + 1)
2
c
6
, c
8
, c
12
u
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
9
(y −1)
2
c
3
, c
4
, c
10
c
11
y
2
+ y + 1
c
6
, c
8
, c
12
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = −1.00000
−3.28987 −9.00000
u = 0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = −1.00000
−3.28987 −9.00000
33
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
25
− 14u
24
+ ··· + 4u − 1)(u
43
+ 24u
42
+ ··· − 10u
2
+ 1)
2
· (u
68
+ 37u
67
+ ··· + 89u + 16)
c
2
((u − 1)
2
)(u
25
+ 2u
24
+ ··· − 2u − 1)(u
43
− 2u
42
+ ··· − 4u + 1)
2
· (u
68
+ 5u
67
+ ··· + 33u + 4)
c
3
, c
10
(u
2
− u + 1)(u
25
− 4u
23
+ ··· + u − 1)(u
68
+ 19u
64
+ ··· − 7u + 1)
· (u
86
− 4u
84
+ ··· + 43u − 1)
c
4
, c
11
(u
2
− u + 1)(u
25
− u
24
+ ··· + 4u
2
− 1)(u
68
− u
67
+ ··· + 36u
2
+ 1)
· (u
86
− 2u
85
+ ··· + 15u + 1)
c
5
((u + 1)
2
)(u
25
− 2u
24
+ ··· − 2u + 1)(u
43
− 2u
42
+ ··· − 4u + 1)
2
· (u
68
+ 5u
67
+ ··· + 33u + 4)
c
6
u
2
(u
25
− 6u
24
+ ··· + 18u − 3)(u
43
− 9u
42
+ ··· + 101u − 8)
2
· (u
68
+ 15u
67
+ ··· + 233u + 4)
c
7
, c
9
((u − 1)
2
)(u
25
− 8u
24
+ ··· + 11u − 1)(u
68
+ 10u
67
+ ··· − 27u + 1)
· (u
86
− 3u
85
+ ··· + 2682u − 617)
c
8
u
2
(u
25
+ 17u
24
+ ··· + 54u + 3)(u
43
− 21u
42
+ ··· − u + 2)
2
· (u
68
+ 38u
67
+ ··· + 17u + 2)
c
12
u
2
(u
25
+ 6u
24
+ ··· + 18u + 3)(u
43
− 9u
42
+ ··· + 101u − 8)
2
· (u
68
+ 15u
67
+ ··· + 233u + 4)
34
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
2
)(y
25
− 2y
24
+ ··· + 8y −1)(y
43
− 8y
42
+ ··· + 20y −1)
2
· (y
68
− 9y
67
+ ··· + 2287y + 256)
c
2
, c
5
((y −1)
2
)(y
25
− 14y
24
+ ··· + 4y −1)(y
43
− 24y
42
+ ··· + 10y
2
− 1)
2
· (y
68
− 37y
67
+ ··· − 89y + 16)
c
3
, c
10
(y
2
+ y + 1)(y
25
− 8y
24
+ ··· + 11y −1)(y
68
+ 38y
66
+ ··· − 91y + 1)
· (y
86
− 8y
85
+ ··· − 171y + 1)
c
4
, c
11
(y
2
+ y + 1)(y
25
− 11y
24
+ ··· + 8y −1)(y
68
+ 29y
67
+ ··· + 72y + 1)
· (y
86
− 20y
85
+ ··· − 99y + 1)
c
6
, c
12
y
2
(y
25
+ 18y
24
+ ··· + 120y −9)(y
43
+ 37y
42
+ ··· + 137y −64)
2
· (y
68
+ 55y
67
+ ··· − 4473y + 16)
c
7
, c
9
((y −1)
2
)(y
25
+ 12y
24
+ ··· − y −1)(y
68
− 52y
67
+ ··· − 83y + 1)
· (y
86
+ 13y
85
+ ··· + 8586034y + 380689)
c
8
y
2
(y
25
+ 3y
24
+ ··· + 318y −9)(y
43
− 3y
42
+ ··· + 85y −4)
2
· (y
68
+ 68y
66
+ ··· − 69y + 4)
35
