12a
0474
(K12a
0474
)
A knot diagram
1
Linearized knot diagam
3 6 11 8 9 2 12 1 7 4 10 5
Solving Sequence
2,6
3
7,9
10 1 5 8 4 12 11
c
2
c
6
c
9
c
1
c
5
c
8
c
4
c
12
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1055648117u
31
+ 1559328616u
30
+ ··· + 2272266299b + 2175618217,
1820724774u
31
− 1996711433u
30
+ ··· + 2272266299a − 4457918006, u
32
− u
31
+ ··· − 2u + 1i
I
u
2
= h−7.24825 × 10
482
u
157
− 5.26354 × 10
483
u
156
+ ··· + 2.15540 × 10
482
b − 2.31148 × 10
486
,
− 2.62230 × 10
485
u
157
+ 3.31275 × 10
486
u
156
+ ··· + 9.03111 × 10
484
a + 1.77163 × 10
489
,
u
158
+ 36u
156
+ ··· + 795u + 419i
I
u
3
= h−u
2
+ b + u + 1, a + 1, u
5
+ u
3
+ u
2
+ u + 1i
I
u
4
= h−1984676u
37
+ 1585526u
36
+ ··· + 78131b + 933931, u
37
+ 12u
35
+ ··· + a + 1,
u
38
− u
37
+ ··· + u + 1i
I
u
5
= hu
3
+ u
2
+ b − 1, u
3
+ a, u
4
+ u
3
+ u
2
+ u + 1i
* 5 irreducible components of dim
C
= 0, with total 237 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
= h1.06 × 10
9
u
31
+ 1 .56 × 10
9
u
30
+ · · · + 2.27 × 10
9
b + 2.18 × 10
9
, 1.82 ×
10
9
u
31
− 2.00 × 10
9
u
30
+ · · · + 2.27 × 10
9
a − 4.46 × 10
9
, u
32
− u
31
+ · · · − 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
9
=
−0.801281u
31
+ 0.878731u
30
+ ··· − 4.37539u + 1.96188
−0.464579u
31
− 0.686244u
30
+ ··· + 2.44777u − 0.957466
a
10
=
−0.803867u
31
+ 1.07467u
30
+ ··· − 7.16864u + 3.19015
−0.467165u
31
− 0.490301u
30
+ ··· − 0.345481u + 0.270807
a
1
=
u
2
+ 1
−u
4
a
5
=
0.253688u
31
− 1.40072u
30
+ ··· + 6.07370u − 3.05988
−0.382000u
31
− 0.403712u
30
+ ··· + 0.804118u − 0.994004
a
8
=
−0.773816u
31
+ 0.992632u
30
+ ··· − 4.85623u + 2.88686
−0.520128u
31
− 0.408087u
30
+ ··· + 1.21747u − 0.173024
a
4
=
−0.393606u
31
+ 0.511780u
30
+ ··· + 0.952466u − 0.0779587
−0.664413u
31
+ 0.315422u
30
+ ··· − 0.629955u + 0.118174
a
12
=
−0.454876u
31
+ 1.01874u
30
+ ··· − 4.95799u + 2.52574
0.346405u
31
+ 0.140005u
30
+ ··· − 0.582597u + 0.563860
a
11
=
−0.922041u
31
+ 0.528435u
30
+ ··· − 6.30347u + 2.79655
−0.118174u
31
− 0.546239u
30
+ ··· + 0.865171u − 0.393606
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3072844380
2272266299
u
31
−
8096501151
2272266299
u
30
+ ··· +
41644937217
2272266299
u −
3810236961
2272266299
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
32
+ 15u
31
+ ··· + 6u + 1
c
2
, c
3
, c
6
c
10
u
32
− u
31
+ ··· − 2u + 1
c
4
, c
8
u
32
+ u
31
+ ··· − 9u
2
+ 1
c
5
, c
7
u
32
+ u
31
+ ··· − 4u − 1
c
9
u
32
+ 12u
31
+ ··· − 368u − 320
c
12
u
32
− 19u
31
+ ··· + 76u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
32
+ 3y
31
+ ··· + 6y + 1
c
2
, c
3
, c
6
c
10
y
32
+ 15y
31
+ ··· + 6y + 1
c
4
, c
8
y
32
− 13y
31
+ ··· − 18y + 1
c
5
, c
7
y
32
− 5y
31
+ ··· − 10y + 1
c
9
y
32
− 4y
31
+ ··· − 1748224y + 102400
c
12
y
32
− 5y
31
+ ··· − 784y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.477757 + 0.915446I
a = 0.822115 + 0.863569I
b = 2.29964 − 0.04858I
−3.03094 + 1.03307I 1.81391 − 3.75205I
u = 0.477757 − 0.915446I
a = 0.822115 − 0.863569I
b = 2.29964 + 0.04858I
−3.03094 − 1.03307I 1.81391 + 3.75205I
u = −0.925303 + 0.470201I
a = 0.77272 + 1.27966I
b = −0.0866021 + 0.0749753I
5.40111 + 9.30081I 8.64815 − 4.34110I
u = −0.925303 − 0.470201I
a = 0.77272 − 1.27966I
b = −0.0866021 − 0.0749753I
5.40111 − 9.30081I 8.64815 + 4.34110I
u = 1.06263
a = −0.505330
b = 0.475352
3.35063 −29.5350
u = 0.373274 + 0.995878I
a = −0.659253 + 0.718345I
b = −1.82629 + 1.33122I
−0.05576 + 5.19371I 4.42887 − 7.08711I
u = 0.373274 − 0.995878I
a = −0.659253 − 0.718345I
b = −1.82629 − 1.33122I
−0.05576 − 5.19371I 4.42887 + 7.08711I
u = −0.474535 + 0.969658I
a = −0.744476 + 0.521874I
b = −1.200380 − 0.655213I
−3.34712 − 6.37289I −0.19797 + 8.93417I
u = −0.474535 − 0.969658I
a = −0.744476 − 0.521874I
b = −1.200380 + 0.655213I
−3.34712 + 6.37289I −0.19797 − 8.93417I
u = 0.476166 + 1.040000I
a = −0.853673 + 0.236108I
b = −2.72342 − 0.90132I
−2.54495 + 10.44430I 0.7629 − 14.2377I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.476166 − 1.040000I
a = −0.853673 − 0.236108I
b = −2.72342 + 0.90132I
−2.54495 − 10.44430I 0.7629 + 14.2377I
u = −0.196973 + 1.132120I
a = 0.933768 − 0.180629I
b = 1.58099 − 0.40135I
−7.68853 − 3.19636I −7.98532 + 3.48642I
u = −0.196973 − 1.132120I
a = 0.933768 + 0.180629I
b = 1.58099 + 0.40135I
−7.68853 + 3.19636I −7.98532 − 3.48642I
u = 1.042280 + 0.520937I
a = −0.301819 + 0.612779I
b = 0.408436 + 0.046950I
3.94817 − 0.47576I 7.7925 + 21.6997I
u = 1.042280 − 0.520937I
a = −0.301819 − 0.612779I
b = 0.408436 − 0.046950I
3.94817 + 0.47576I 7.7925 − 21.6997I
u = 0.130483 + 1.162900I
a = −0.770437 − 0.770567I
b = −1.25491 − 1.22831I
−6.42362 − 4.43426I −3.93661 + 3.90816I
u = 0.130483 − 1.162900I
a = −0.770437 + 0.770567I
b = −1.25491 + 1.22831I
−6.42362 + 4.43426I −3.93661 − 3.90816I
u = −0.466499 + 1.079320I
a = 0.058442 + 0.427246I
b = 0.630894 − 0.311585I
−3.17466 − 6.99170I −1.77681 + 6.23178I
u = −0.466499 − 1.079320I
a = 0.058442 − 0.427246I
b = 0.630894 + 0.311585I
−3.17466 + 6.99170I −1.77681 − 6.23178I
u = −0.427864 + 1.109050I
a = 0.567795 + 0.877389I
b = 1.48550 + 0.75181I
−3.53644 − 7.33288I −2.60525 + 8.48950I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.427864 − 1.109050I
a = 0.567795 − 0.877389I
b = 1.48550 − 0.75181I
−3.53644 + 7.33288I −2.60525 − 8.48950I
u = 0.667854 + 1.161150I
a = 1.177840 − 0.492133I
b = 2.41595 − 1.10503I
1.1241 + 21.0689I 3.49932 − 11.71002I
u = 0.667854 − 1.161150I
a = 1.177840 + 0.492133I
b = 2.41595 + 1.10503I
1.1241 − 21.0689I 3.49932 + 11.71002I
u = −0.490346 + 0.432416I
a = 0.130078 − 1.235820I
b = −0.781587 + 0.581190I
0.96043 + 2.38010I 7.46276 − 4.21750I
u = −0.490346 − 0.432416I
a = 0.130078 + 1.235820I
b = −0.781587 − 0.581190I
0.96043 − 2.38010I 7.46276 + 4.21750I
u = −0.683123 + 1.170780I
a = −0.884504 − 0.167122I
b = −1.75324 − 0.73186I
−0.28660 − 12.80370I 1.33394 + 11.29862I
u = −0.683123 − 1.170780I
a = −0.884504 + 0.167122I
b = −1.75324 + 0.73186I
−0.28660 + 12.80370I 1.33394 − 11.29862I
u = −0.219303 + 0.597960I
a = −0.46196 − 1.88067I
b = 0.342049 + 0.528048I
2.71565 − 0.83716I 2.90542 + 8.40033I
u = −0.219303 − 0.597960I
a = −0.46196 + 1.88067I
b = 0.342049 − 0.528048I
2.71565 + 0.83716I 2.90542 − 8.40033I
u = 0.441452 + 0.401358I
a = 0.722248 + 0.018264I
b = 0.438511 + 0.462396I
0.914598 + 0.783161I 7.49019 − 4.89846I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.441452 − 0.401358I
a = 0.722248 − 0.018264I
b = 0.438511 − 0.462396I
0.914598 − 0.783161I 7.49019 + 4.89846I
u = 0.486729
a = 2.48756
b = 0.573576
2.02457 5.26330
8
II. I
u
2
= h−7.25 × 10
482
u
157
− 5.26 × 10
483
u
156
+ · · · + 2.16 × 10
482
b − 2.31 ×
10
486
, −2.62 × 10
485
u
157
+ 3.31 × 10
486
u
156
+ · · · + 9.03 × 10
484
a + 1.77 ×
10
489
, u
158
+ 36u
156
+ · · · + 795u + 419i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
9
=
2.90363u
157
− 36.6816u
156
+ ··· − 56119.5u − 19617.0
3.36284u
157
+ 24.4203u
156
+ ··· + 33100.0u + 10724.2
a
10
=
55.5454u
157
− 42.2460u
156
+ ··· − 104888.u − 45218.7
56.0046u
157
+ 18.8559u
156
+ ··· − 15668.4u − 14877.5
a
1
=
u
2
+ 1
−u
4
a
5
=
38.8314u
157
+ 29.1246u
156
+ ··· + 12999.9u − 2240.90
29.3771u
157
+ 52.6291u
156
+ ··· + 54801.0u + 13658.2
a
8
=
49.9442u
157
− 33.1921u
156
+ ··· − 87278.2u − 38257.9
35.5733u
157
+ 17.8124u
156
+ ··· − 1422.57u − 6532.33
a
4
=
−68.6087u
157
+ 82.8124u
156
+ ··· + 174212.u + 71146.3
−85.6069u
157
− 11.5076u
156
+ ··· + 49001.8u + 31342.5
a
12
=
−42.8030u
157
− 6.55761u
156
+ ··· + 22975.2u + 15153.7
−29.2559u
157
− 60.7310u
156
+ ··· − 66924.7u − 17825.3
a
11
=
−31.0195u
157
− 23.1998u
156
+ ··· − 10016.3u + 1903.58
−52.5109u
157
− 75.9427u
156
+ ··· − 71536.0u − 15388.7
(ii) Obstruction class = −1
(iii) Cusp Shapes = 82.0341u
157
+ 69.2993u
156
+ ··· + 39167.4u − 737.807
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
158
+ 72u
157
+ ··· + 3542053u + 175561
c
2
, c
3
, c
6
c
10
u
158
+ 36u
156
+ ··· + 795u + 419
c
4
, c
8
u
158
+ 4u
157
+ ··· − 84u + 305
c
5
, c
7
u
158
− 7u
156
+ ··· − 1086387u + 160579
c
9
(u
79
− 12u
78
+ ··· − 16031u + 5803)
2
c
12
(u
79
+ 7u
78
+ ··· − u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
158
+ 40y
157
+ ··· − 2099160591827y + 30821664721
c
2
, c
3
, c
6
c
10
y
158
+ 72y
157
+ ··· + 3542053y + 175561
c
4
, c
8
y
158
+ 8y
157
+ ··· − 7749786y + 93025
c
5
, c
7
y
158
− 14y
157
+ ··· − 1110681919919y + 25785615241
c
9
(y
79
− 22y
78
+ ··· + 521006249y −33674809)
2
c
12
(y
79
− y
78
+ ··· + 3y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.310553 + 0.959553I
a = −1.30464 − 0.80619I
b = −2.25826 + 0.33876I
−2.54106 + 5.73014I 0
u = −0.310553 − 0.959553I
a = −1.30464 + 0.80619I
b = −2.25826 − 0.33876I
−2.54106 − 5.73014I 0
u = −0.434056 + 0.885145I
a = 2.01832 − 1.29649I
b = 2.40756 − 0.98414I
−6.62459 − 1.78219I 0
u = −0.434056 − 0.885145I
a = 2.01832 + 1.29649I
b = 2.40756 + 0.98414I
−6.62459 + 1.78219I 0
u = −0.265458 + 0.979005I
a = 0.115623 + 0.809267I
b = 0.465376 + 0.297373I
−4.16298 + 0.24557I 0
u = −0.265458 − 0.979005I
a = 0.115623 − 0.809267I
b = 0.465376 − 0.297373I
−4.16298 − 0.24557I 0
u = −0.568710 + 0.840944I
a = −0.312373 − 1.146900I
b = 0.217198 + 0.226950I
4.11004 − 1.48250I 0
u = −0.568710 − 0.840944I
a = −0.312373 + 1.146900I
b = 0.217198 − 0.226950I
4.11004 + 1.48250I 0
u = −0.091908 + 0.977990I
a = −0.723067 + 0.656630I
b = −1.76400 + 1.68289I
−0.54608 + 4.60609I 0
u = −0.091908 − 0.977990I
a = −0.723067 − 0.656630I
b = −1.76400 − 1.68289I
−0.54608 − 4.60609I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.382591 + 0.899744I
a = 1.68343 − 0.70032I
b = 2.18485 + 0.24223I
0.049532 − 0.236212I 0
u = 0.382591 − 0.899744I
a = 1.68343 + 0.70032I
b = 2.18485 − 0.24223I
0.049532 + 0.236212I 0
u = −0.735318 + 0.710316I
a = −0.380441 − 0.803541I
b = 0.186008 + 0.707821I
5.24621 + 0.61229I 0
u = −0.735318 − 0.710316I
a = −0.380441 + 0.803541I
b = 0.186008 − 0.707821I
5.24621 − 0.61229I 0
u = 0.918664 + 0.319464I
a = 0.719427 − 0.742569I
b = 0.356304 + 0.267336I
0.049532 − 0.236212I 0
u = 0.918664 − 0.319464I
a = 0.719427 + 0.742569I
b = 0.356304 − 0.267336I
0.049532 + 0.236212I 0
u = −0.589770 + 0.841559I
a = 0.881205 + 0.323399I
b = 1.91030 + 0.99055I
4.09867 − 3.13109I 0
u = −0.589770 − 0.841559I
a = 0.881205 − 0.323399I
b = 1.91030 − 0.99055I
4.09867 + 3.13109I 0
u = 0.481337 + 0.916294I
a = −0.773779 + 0.323872I
b = −1.62808 − 1.38929I
−3.00491 + 3.72449I 0
u = 0.481337 − 0.916294I
a = −0.773779 − 0.323872I
b = −1.62808 + 1.38929I
−3.00491 − 3.72449I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.795996 + 0.675080I
a = 0.369650 − 0.699877I
b = −0.105022 + 0.867379I
3.75059 − 5.60386I 0
u = 0.795996 − 0.675080I
a = 0.369650 + 0.699877I
b = −0.105022 − 0.867379I
3.75059 + 5.60386I 0
u = 0.952560 + 0.428199I
a = −0.80810 + 1.25137I
b = 0.0918948 − 0.0588807I
3.3684 − 15.1632I 0
u = 0.952560 − 0.428199I
a = −0.80810 − 1.25137I
b = 0.0918948 + 0.0588807I
3.3684 + 15.1632I 0
u = −0.828714 + 0.636993I
a = 0.56583 + 1.34399I
b = −0.100191 + 0.581741I
6.17644 + 4.30612I 0
u = −0.828714 − 0.636993I
a = 0.56583 − 1.34399I
b = −0.100191 − 0.581741I
6.17644 − 4.30612I 0
u = 0.398177 + 0.863793I
a = 0.409774 − 1.284210I
b = 0.332705 + 0.390561I
0.29819 − 2.09088I 0
u = 0.398177 − 0.863793I
a = 0.409774 + 1.284210I
b = 0.332705 − 0.390561I
0.29819 + 2.09088I 0
u = 0.561309 + 0.748245I
a = −1.108600 + 0.318648I
b = −1.87960 + 0.98263I
1.98199 − 2.11208I 0
u = 0.561309 − 0.748245I
a = −1.108600 − 0.318648I
b = −1.87960 − 0.98263I
1.98199 + 2.11208I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.792422 + 0.720401I
a = −0.424977 + 1.294580I
b = 0.152595 + 0.766920I
4.86883 + 1.98153I 0
u = 0.792422 − 0.720401I
a = −0.424977 − 1.294580I
b = 0.152595 − 0.766920I
4.86883 − 1.98153I 0
u = 0.795505 + 0.456402I
a = −0.79974 + 1.42218I
b = −0.235471 + 0.214744I
−1.14863 − 6.63514I 0
u = 0.795505 − 0.456402I
a = −0.79974 − 1.42218I
b = −0.235471 − 0.214744I
−1.14863 + 6.63514I 0
u = 0.557057 + 0.929299I
a = 0.165136 − 1.250270I
b = −0.354709 − 0.114513I
1.40852 + 6.59786I 0
u = 0.557057 − 0.929299I
a = 0.165136 + 1.250270I
b = −0.354709 + 0.114513I
1.40852 − 6.59786I 0
u = 0.527880 + 0.947283I
a = −1.45741 − 1.53177I
b = −2.25677 − 1.07570I
1.00763 + 5.22007I 0
u = 0.527880 − 0.947283I
a = −1.45741 + 1.53177I
b = −2.25677 + 1.07570I
1.00763 − 5.22007I 0
u = 0.431827 + 0.806322I
a = −0.063102 − 0.407064I
b = 1.73474 − 0.17811I
−2.59007 + 0.08562I 0
u = 0.431827 − 0.806322I
a = −0.063102 + 0.407064I
b = 1.73474 + 0.17811I
−2.59007 − 0.08562I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.432313 + 0.805507I
a = 1.064280 + 0.561916I
b = 1.19099 − 0.88066I
−2.62411 + 2.75813I 0
u = 0.432313 − 0.805507I
a = 1.064280 − 0.561916I
b = 1.19099 + 0.88066I
−2.62411 − 2.75813I 0
u = 0.421077 + 1.001710I
a = −0.20603 + 1.48403I
b = −0.68683 + 1.63297I
−0.40858 + 3.12056I 0
u = 0.421077 − 1.001710I
a = −0.20603 − 1.48403I
b = −0.68683 − 1.63297I
−0.40858 − 3.12056I 0
u = −1.001470 + 0.423311I
a = 0.456088 + 0.775520I
b = −0.335205 − 0.008493I
2.00890 + 6.73082I 0
u = −1.001470 − 0.423311I
a = 0.456088 − 0.775520I
b = −0.335205 + 0.008493I
2.00890 − 6.73082I 0
u = 0.171636 + 0.889290I
a = 0.856525 + 0.617603I
b = 1.29028 + 1.65011I
0.996008 + 0.228208I 0
u = 0.171636 − 0.889290I
a = 0.856525 − 0.617603I
b = 1.29028 − 1.65011I
0.996008 − 0.228208I 0
u = −0.757754 + 0.491337I
a = −0.59566 − 1.77542I
b = 0.238053 + 0.058058I
4.45408 + 5.94036I 0
u = −0.757754 − 0.491337I
a = −0.59566 + 1.77542I
b = 0.238053 − 0.058058I
4.45408 − 5.94036I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.474769 + 1.001460I
a = −0.103439 + 0.715197I
b = −0.421852 + 0.439449I
−0.62943 + 2.99422I 0
u = 0.474769 − 1.001460I
a = −0.103439 − 0.715197I
b = −0.421852 − 0.439449I
−0.62943 − 2.99422I 0
u = −0.395583 + 0.794434I
a = −0.891930 + 0.915396I
b = −2.02916 − 0.04997I
−2.62411 + 2.75813I 0
u = −0.395583 − 0.794434I
a = −0.891930 − 0.915396I
b = −2.02916 + 0.04997I
−2.62411 − 2.75813I 0
u = −0.502570 + 0.996824I
a = −1.369680 − 0.282057I
b = −2.10107 − 0.03500I
−5.64126 − 3.23768I 0
u = −0.502570 − 0.996824I
a = −1.369680 + 0.282057I
b = −2.10107 + 0.03500I
−5.64126 + 3.23768I 0
u = 0.778124 + 0.414904I
a = 1.47017 − 0.37757I
b = 0.048902 − 0.227058I
4.09867 + 3.13109I 0
u = 0.778124 − 0.414904I
a = 1.47017 + 0.37757I
b = 0.048902 + 0.227058I
4.09867 − 3.13109I 0
u = −0.298166 + 1.079110I
a = −0.792936 + 0.759993I
b = −2.26691 + 0.61890I
−2.59007 − 0.08562I 0
u = −0.298166 − 1.079110I
a = −0.792936 − 0.759993I
b = −2.26691 − 0.61890I
−2.59007 + 0.08562I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.484094 + 0.734137I
a = −1.99303 − 1.21164I
b = −2.04533 − 0.41284I
1.72808 − 1.04080I 0
u = 0.484094 − 0.734137I
a = −1.99303 + 1.21164I
b = −2.04533 + 0.41284I
1.72808 + 1.04080I 0
u = −0.086871 + 1.120720I
a = −0.761688 + 0.387029I
b = −1.45240 + 0.20255I
−3.83157 + 0.71992I 0
u = −0.086871 − 1.120720I
a = −0.761688 − 0.387029I
b = −1.45240 − 0.20255I
−3.83157 − 0.71992I 0
u = 0.692083 + 0.535192I
a = 0.71604 − 1.93417I
b = −0.135547 − 0.251225I
5.24621 − 0.61229I 0
u = 0.692083 − 0.535192I
a = 0.71604 + 1.93417I
b = −0.135547 + 0.251225I
5.24621 + 0.61229I 0
u = 0.946963 + 0.614514I
a = −0.730292 + 0.411435I
b = 0.140681 + 0.065288I
6.17644 + 4.30612I 0
u = 0.946963 − 0.614514I
a = −0.730292 − 0.411435I
b = 0.140681 − 0.065288I
6.17644 − 4.30612I 0
u = −0.954405 + 0.609131I
a = −0.553862 − 0.689104I
b = −0.263916 − 0.139116I
1.72808 + 1.04080I 0
u = −0.954405 − 0.609131I
a = −0.553862 + 0.689104I
b = −0.263916 + 0.139116I
1.72808 − 1.04080I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.016630 + 0.510273I
a = 0.613493 − 0.706283I
b = 0.146183 + 0.036293I
1.00763 − 5.22007I 0
u = 1.016630 − 0.510273I
a = 0.613493 + 0.706283I
b = 0.146183 − 0.036293I
1.00763 + 5.22007I 0
u = 0.399897 + 1.066680I
a = 0.798583 + 0.803025I
b = 2.47682 + 0.34607I
−3.00491 − 3.72449I 0
u = 0.399897 − 1.066680I
a = 0.798583 − 0.803025I
b = 2.47682 − 0.34607I
−3.00491 + 3.72449I 0
u = −0.546153 + 1.001830I
a = 1.16381 − 1.42348I
b = 2.12433 − 1.06698I
−0.99488 − 11.48250I 0
u = −0.546153 − 1.001830I
a = 1.16381 + 1.42348I
b = 2.12433 + 1.06698I
−0.99488 + 11.48250I 0
u = 0.688376 + 0.501519I
a = 0.676559 − 0.556792I
b = 0.265065 + 0.560795I
0.996008 + 0.228208I 0
u = 0.688376 − 0.501519I
a = 0.676559 + 0.556792I
b = 0.265065 − 0.560795I
0.996008 − 0.228208I 0
u = −0.341377 + 1.101100I
a = −0.508755 + 0.675606I
b = −1.009930 + 0.460172I
−4.16298 − 0.24557I 0
u = −0.341377 − 1.101100I
a = −0.508755 − 0.675606I
b = −1.009930 − 0.460172I
−4.16298 + 0.24557I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.586174 + 0.997243I
a = 0.850903 + 0.360043I
b = 1.80384 − 0.34155I
−0.46550 − 7.02513I 0
u = −0.586174 − 0.997243I
a = 0.850903 − 0.360043I
b = 1.80384 + 0.34155I
−0.46550 + 7.02513I 0
u = −0.659887 + 0.965771I
a = 0.620572 + 0.228337I
b = 2.05133 + 0.83766I
4.45408 − 5.94036I 0
u = −0.659887 − 0.965771I
a = 0.620572 − 0.228337I
b = 2.05133 − 0.83766I
4.45408 + 5.94036I 0
u = 0.567850 + 1.025580I
a = −0.487372 + 0.413230I
b = −1.69268 + 0.63123I
−0.54608 + 4.60609I 0
u = 0.567850 − 1.025580I
a = −0.487372 − 0.413230I
b = −1.69268 − 0.63123I
−0.54608 − 4.60609I 0
u = −0.942383 + 0.698077I
a = 0.759295 + 0.419727I
b = 0.004151 + 0.164350I
5.00194 − 9.97884I 0
u = −0.942383 − 0.698077I
a = 0.759295 − 0.419727I
b = 0.004151 − 0.164350I
5.00194 + 9.97884I 0
u = 0.687123 + 0.953819I
a = 1.43518 − 0.36327I
b = 1.78713 − 0.72200I
4.14017 + 3.57693I 0
u = 0.687123 − 0.953819I
a = 1.43518 + 0.36327I
b = 1.78713 + 0.72200I
4.14017 − 3.57693I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.420682 + 1.101670I
a = −0.277978 + 0.022640I
b = −0.692295 − 1.062360I
−3.56315 0
u = −0.420682 − 1.101670I
a = −0.277978 − 0.022640I
b = −0.692295 + 1.062360I
−3.56315 0
u = −0.772390 + 0.270072I
a = −1.65475 − 0.34539I
b = 0.161056 − 0.145472I
4.11004 + 1.48250I 0
u = −0.772390 − 0.270072I
a = −1.65475 + 0.34539I
b = 0.161056 + 0.145472I
4.11004 − 1.48250I 0
u = −0.800802 + 0.127364I
a = −1.009110 − 0.405406I
b = −0.661979 + 0.172911I
−0.40858 + 3.12056I 0
u = −0.800802 − 0.127364I
a = −1.009110 + 0.405406I
b = −0.661979 − 0.172911I
−0.40858 − 3.12056I 0
u = −0.714810 + 0.959332I
a = −0.993714 + 0.509602I
b = −1.48592 + 0.18951I
−5.02416 − 2.82268I 0
u = −0.714810 − 0.959332I
a = −0.993714 − 0.509602I
b = −1.48592 − 0.18951I
−5.02416 + 2.82268I 0
u = 0.598092 + 1.038180I
a = −1.61264 + 0.51271I
b = −2.88134 + 1.16487I
3.75059 + 5.60386I 0
u = 0.598092 − 1.038180I
a = −1.61264 − 0.51271I
b = −2.88134 − 1.16487I
3.75059 − 5.60386I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.270415 + 1.170310I
a = 0.560037 − 0.177285I
b = 0.852233 − 1.052720I
−1.13423 + 4.13535I 0
u = 0.270415 − 1.170310I
a = 0.560037 + 0.177285I
b = 0.852233 + 1.052720I
−1.13423 − 4.13535I 0
u = −0.653525 + 0.451009I
a = −0.311978 − 1.140630I
b = −0.568685 + 0.320566I
0.97564 + 2.31172I 0
u = −0.653525 − 0.451009I
a = −0.311978 + 1.140630I
b = −0.568685 − 0.320566I
0.97564 − 2.31172I 0
u = 0.675893 + 1.002900I
a = −0.556998 + 0.202352I
b = −2.14046 + 0.75499I
2.72713 + 11.14780I 0
u = 0.675893 − 1.002900I
a = −0.556998 − 0.202352I
b = −2.14046 − 0.75499I
2.72713 − 11.14780I 0
u = −0.548179 + 1.081710I
a = 0.984157 + 0.311380I
b = 2.63681 + 0.00137I
−0.93553 − 6.97306I 0
u = −0.548179 − 1.081710I
a = 0.984157 − 0.311380I
b = 2.63681 − 0.00137I
−0.93553 + 6.97306I 0
u = −0.501446 + 0.586462I
a = 1.92864 − 1.20508I
b = 1.62944 − 0.12929I
0.26567 + 7.11077I 0
u = −0.501446 − 0.586462I
a = 1.92864 + 1.20508I
b = 1.62944 + 0.12929I
0.26567 − 7.11077I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.691640 + 1.020570I
a = −1.37343 − 0.44280I
b = −1.97075 − 0.90997I
5.00194 − 9.97884I 0
u = −0.691640 − 1.020570I
a = −1.37343 + 0.44280I
b = −1.97075 + 0.90997I
5.00194 + 9.97884I 0
u = −0.613886 + 1.070870I
a = 1.46384 + 0.33278I
b = 2.97199 + 0.98520I
2.72713 − 11.14780I 0
u = −0.613886 − 1.070870I
a = 1.46384 − 0.33278I
b = 2.97199 − 0.98520I
2.72713 + 11.14780I 0
u = −0.430079 + 1.161930I
a = 0.582615 + 0.761725I
b = 1.45091 + 1.71180I
0.29819 − 2.09088I 0
u = −0.430079 − 1.161930I
a = 0.582615 − 0.761725I
b = 1.45091 − 1.71180I
0.29819 + 2.09088I 0
u = 0.627639 + 1.099090I
a = 1.253660 − 0.583782I
b = 2.28599 − 0.89412I
−3.05898 + 11.99430I 0
u = 0.627639 − 1.099090I
a = 1.253660 + 0.583782I
b = 2.28599 + 0.89412I
−3.05898 − 11.99430I 0
u = 0.242663 + 0.690109I
a = −0.488133 − 0.373111I
b = 1.77767 + 1.25045I
−0.93553 − 6.97306I 0
u = 0.242663 − 0.690109I
a = −0.488133 + 0.373111I
b = 1.77767 − 1.25045I
−0.93553 + 6.97306I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.636713 + 0.358715I
a = 0.860813 + 0.227248I
b = −0.525472 − 0.388495I
−1.13423 − 4.13535I 0
u = −0.636713 − 0.358715I
a = 0.860813 − 0.227248I
b = −0.525472 + 0.388495I
−1.13423 + 4.13535I 0
u = 0.607768 + 1.124670I
a = −0.479627 + 0.823560I
b = −0.68480 + 1.53923I
1.98199 + 2.11208I 0
u = 0.607768 − 1.124670I
a = −0.479627 − 0.823560I
b = −0.68480 − 1.53923I
1.98199 − 2.11208I 0
u = −0.712373 + 1.072990I
a = 0.827627 + 0.421722I
b = 1.49660 + 0.42575I
0.26567 − 7.11077I 0
u = −0.712373 − 1.072990I
a = 0.827627 − 0.421722I
b = 1.49660 − 0.42575I
0.26567 + 7.11077I 0
u = −0.833205 + 0.982765I
a = −0.498767 − 0.403098I
b = −0.739078 − 0.793596I
4.14017 + 3.57693I 0
u = −0.833205 − 0.982765I
a = −0.498767 + 0.403098I
b = −0.739078 + 0.793596I
4.14017 − 3.57693I 0
u = −0.014022 + 1.301380I
a = 0.574955 − 0.618539I
b = 1.10680 − 1.39265I
−1.14863 + 6.63514I 0
u = −0.014022 − 1.301380I
a = 0.574955 + 0.618539I
b = 1.10680 + 1.39265I
−1.14863 − 6.63514I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.599739 + 1.165620I
a = −0.818084 + 0.510760I
b = −1.96007 + 0.61164I
−2.54106 + 5.73014I 0
u = 0.599739 − 1.165620I
a = −0.818084 − 0.510760I
b = −1.96007 − 0.61164I
−2.54106 − 5.73014I 0
u = 0.788182 + 1.048400I
a = 0.499498 − 0.312198I
b = 0.882089 − 0.823699I
4.86883 + 1.98153I 0
u = 0.788182 − 1.048400I
a = 0.499498 + 0.312198I
b = 0.882089 + 0.823699I
4.86883 − 1.98153I 0
u = −0.574520 + 1.185810I
a = 0.527043 + 0.816309I
b = 0.86995 + 1.78445I
1.40852 − 6.59786I 0
u = −0.574520 − 1.185810I
a = 0.527043 − 0.816309I
b = 0.86995 − 1.78445I
1.40852 + 6.59786I 0
u = −0.674555 + 1.135350I
a = −1.212950 − 0.494366I
b = −2.32315 − 1.08402I
3.3684 − 15.1632I 0
u = −0.674555 − 1.135350I
a = −1.212950 + 0.494366I
b = −2.32315 + 1.08402I
3.3684 + 15.1632I 0
u = 0.145727 + 1.320420I
a = 0.445515 + 0.388411I
b = 1.093950 + 0.368109I
−5.64126 + 3.23768I 0
u = 0.145727 − 1.320420I
a = 0.445515 − 0.388411I
b = 1.093950 − 0.368109I
−5.64126 − 3.23768I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.713434 + 1.135240I
a = 0.832513 − 0.087903I
b = 1.56300 − 0.61923I
2.00890 + 6.73082I 0
u = 0.713434 − 1.135240I
a = 0.832513 + 0.087903I
b = 1.56300 + 0.61923I
2.00890 − 6.73082I 0
u = 0.072618 + 1.342030I
a = −0.540918 − 0.690908I
b = −1.19943 − 1.46350I
−3.05898 − 11.99430I 0
u = 0.072618 − 1.342030I
a = −0.540918 + 0.690908I
b = −1.19943 + 1.46350I
−3.05898 + 11.99430I 0
u = 0.717837 + 1.150840I
a = −0.812804 + 0.435766I
b = −1.63701 + 0.68784I
−0.99488 + 11.48250I 0
u = 0.717837 − 1.150840I
a = −0.812804 − 0.435766I
b = −1.63701 − 0.68784I
−0.99488 − 11.48250I 0
u = −0.615962 + 0.117735I
a = −0.350383 − 0.326259I
b = −0.680784 + 0.340817I
−0.62943 + 2.99422I 0
u = −0.615962 − 0.117735I
a = −0.350383 + 0.326259I
b = −0.680784 − 0.340817I
−0.62943 − 2.99422I 0
u = −0.506324 + 0.223289I
a = 0.15038 + 1.71230I
b = 0.262077 + 0.264360I
−3.83157 − 0.71992I 0
u = −0.506324 − 0.223289I
a = 0.15038 − 1.71230I
b = 0.262077 − 0.264360I
−3.83157 + 0.71992I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02696 + 1.51625I
a = 0.062685 + 0.348097I
b = 0.195230 + 0.644220I
−6.62459 − 1.78219I 0
u = 0.02696 − 1.51625I
a = 0.062685 − 0.348097I
b = 0.195230 − 0.644220I
−6.62459 + 1.78219I 0
u = −0.09409 + 1.55208I
a = 0.076689 − 0.128034I
b = 0.207284 − 0.560484I
−5.02416 + 2.82268I 0
u = −0.09409 − 1.55208I
a = 0.076689 + 0.128034I
b = 0.207284 + 0.560484I
−5.02416 − 2.82268I 0
u = −0.097038 + 0.425642I
a = 1.50211 − 0.54612I
b = −0.638989 + 1.096140I
0.97564 + 2.31172I 6.81449 − 4.45056I
u = −0.097038 − 0.425642I
a = 1.50211 + 0.54612I
b = −0.638989 − 1.096140I
0.97564 − 2.31172I 6.81449 + 4.45056I
u = 0.360284 + 0.083987I
a = 1.22698 + 2.75279I
b = 0.762809 − 0.918146I
−0.46550 + 7.02513I 4.81797 − 8.69305I
u = 0.360284 − 0.083987I
a = 1.22698 − 2.75279I
b = 0.762809 + 0.918146I
−0.46550 − 7.02513I 4.81797 + 8.69305I
27
III. I
u
3
= h−u
2
+ b + u + 1, a + 1, u
5
+ u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
9
=
−1
u
2
− u − 1
a
10
=
u
4
− u
3
− 1
u
4
− u
3
+ u
2
− u − 1
a
1
=
u
2
+ 1
−u
4
a
5
=
−u
u
3
− u
2
a
8
=
−u
3
− 1
−u
3
− u − 1
a
4
=
u
3
− u
2
− u + 1
u
4
+ 2u
3
− u
2
+ u + 1
a
12
=
−u
4
− u
−u
4
− u + 1
a
11
=
u
2
− u − 1
−u
4
+ u
3
+ u
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
4
− 8u
3
+ 5u
2
− u + 4
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 2u
4
+ 3u
3
− u
2
− u + 1
c
2
, c
5
, c
7
c
10
u
5
+ u
3
+ u
2
+ u + 1
c
3
, c
6
u
5
+ u
3
− u
2
+ u − 1
c
4
, c
8
u
5
− 2u
4
+ 2u
3
− 3u
2
+ 2u + 1
c
9
u
5
− u
4
− 2u
3
+ 5u
2
+ u − 5
c
11
u
5
+ 2u
4
+ 3u
3
+ u
2
− u − 1
c
12
u
5
− u
4
− u
3
+ 3u
2
− 2u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
5
+ 2y
4
+ 3y
3
− 3y
2
+ 3y −1
c
2
, c
3
, c
5
c
6
, c
7
, c
10
y
5
+ 2y
4
+ 3y
3
+ y
2
− y −1
c
4
, c
8
y
5
− 4y
3
+ 3y
2
+ 10y −1
c
9
y
5
− 5y
4
+ 16y
3
− 39y
2
+ 51y −25
c
12
y
5
− 3y
4
+ 3y
3
− 3y
2
− 2y −1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.262247 + 0.873157I
a = −1.00000
b = −1.43138 − 1.33112I
−3.23200 − 4.86949I −1.68901 + 5.80392I
u = −0.262247 − 0.873157I
a = −1.00000
b = −1.43138 + 1.33112I
−3.23200 + 4.86949I −1.68901 − 5.80392I
u = −0.800095
a = −1.00000
b = 0.440247
3.56186 15.3770
u = 0.662294 + 1.032030I
a = −1.00000
b = −2.28874 + 0.33498I
1.45107 + 11.01950I 3.00067 − 9.96957I
u = 0.662294 − 1.032030I
a = −1.00000
b = −2.28874 − 0.33498I
1.45107 − 11.01950I 3.00067 + 9.96957I
31
IV. I
u
4
= h−1.98 × 10
6
u
37
+ 1.59 × 10
6
u
36
+ · · · + 7.81 × 10
4
b + 9.34 ×
10
5
, u
37
+ 12u
35
+ · · · + a + 1, u
38
− u
37
+ · · · + u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
9
=
−u
37
− 12u
35
+ ··· − 15u − 1
25.4019u
37
− 20.2932u
36
+ ··· + 27.4983u − 11.9534
a
10
=
−8.90282u
37
− 8.70708u
36
+ ··· − 47.5106u − 7.10873
17.4991u
37
− 29.0003u
36
+ ··· − 5.01231u − 18.0621
a
1
=
u
2
+ 1
−u
4
a
5
=
2u
37
− 6u
36
+ ··· + 8u − 7
−20.8689u
37
+ 31.3164u
36
+ ··· + 15.2184u + 15.7883
a
8
=
0.0465372u
37
− 6.68628u
36
+ ··· − 26.0102u − 8.56096
17.2296u
37
− 12.7400u
36
+ ··· + 15.9072u − 7.09197
a
4
=
47.5463u
37
− 43.5185u
36
+ ··· + 62.2595u + 6.55671
34.9682u
37
− 21.6243u
36
+ ··· + 45.5719u + 8.68607
a
12
=
−7.11001u
37
+ 34.2559u
36
+ ··· + 51.6108u + 38.2171
−25.1721u
37
+ 35.8190u
36
+ ··· + 1.59311u + 26.1673
a
11
=
−20.8051u
37
+ 29.9356u
36
+ ··· + 11.8040u + 29.6783
0.0692171u
37
− 28.6170u
36
+ ··· − 27.9778u − 16.8464
(ii) Obstruction class = 1
(iii) Cusp Shapes =
684514
78131
u
37
−
1377704
78131
u
36
+ ··· +
565695
78131
u −
4124650
78131
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
− 25u
37
+ ··· − 29u + 1
c
2
, c
10
u
38
− u
37
+ ··· + u + 1
c
3
, c
6
u
38
+ u
37
+ ··· − u + 1
c
4
, c
8
u
38
− u
37
+ ··· + 7u
2
+ 1
c
5
, c
7
u
38
− 3u
37
+ ··· − 11u + 1
c
9
(u
19
− 7u
18
+ ··· + 3u − 1)
2
c
11
u
38
+ 25u
37
+ ··· + 29u + 1
c
12
(u
19
+ 2u
18
+ ··· + u + 1)
2
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
38
− 11y
37
+ ··· − 67y + 1
c
2
, c
3
, c
6
c
10
y
38
+ 25y
37
+ ··· + 29y + 1
c
4
, c
8
y
38
+ y
37
+ ··· + 14y + 1
c
5
, c
7
y
38
+ 15y
37
+ ··· − 39y + 1
c
9
(y
19
+ 3y
18
+ ··· − 13y −1)
2
c
12
(y
19
+ 8y
18
+ ··· + y −1)
2
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.857291 + 0.471939I
a = 0.489725 − 0.735021I
b = 0.521340 + 0.336730I
0.471614 − 0.794306I 3.56373 + 5.07257I
u = 0.857291 − 0.471939I
a = 0.489725 + 0.735021I
b = 0.521340 − 0.336730I
0.471614 + 0.794306I 3.56373 − 5.07257I
u = −0.339881 + 0.974319I
a = −0.674523 + 0.845710I
b = −1.83508 − 0.10903I
−3.73840 + 2.35300I −3.19315 − 1.59794I
u = −0.339881 − 0.974319I
a = −0.674523 − 0.845710I
b = −1.83508 + 0.10903I
−3.73840 − 2.35300I −3.19315 + 1.59794I
u = 0.385555 + 0.887397I
a = 1.98518 + 1.05174I
b = 2.23280 + 1.00987I
−6.80652 + 1.60888I −11.9912 + 9.5186I
u = 0.385555 − 0.887397I
a = 1.98518 − 1.05174I
b = 2.23280 − 1.00987I
−6.80652 − 1.60888I −11.9912 − 9.5186I
u = −0.364564 + 0.968354I
a = −0.708654 + 1.071120I
b = 0.009391 + 1.118890I
0.07884 − 3.73395I 5.32221 + 8.03220I
u = −0.364564 − 0.968354I
a = −0.708654 − 1.071120I
b = 0.009391 − 1.118890I
0.07884 + 3.73395I 5.32221 − 8.03220I
u = 0.300960 + 0.993122I
a = 0.542850 + 0.596656I
b = −0.822378 + 0.266941I
−1.89294 + 8.64589I 2.93385 − 10.21550I
u = 0.300960 − 0.993122I
a = 0.542850 − 0.596656I
b = −0.822378 − 0.266941I
−1.89294 − 8.64589I 2.93385 + 10.21550I
35
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.848401 + 0.610309I
a = 0.226580 − 0.874994I
b = −0.201691 + 0.306571I
2.75263 − 5.40942I 5.53760 + 5.21975I
u = 0.848401 − 0.610309I
a = 0.226580 + 0.874994I
b = −0.201691 − 0.306571I
2.75263 + 5.40942I 5.53760 − 5.21975I
u = 0.259484 + 0.918290I
a = 0.817419 + 0.208348I
b = 0.381830 − 1.357280I
−3.73840 + 2.35300I −3.19315 − 1.59794I
u = 0.259484 − 0.918290I
a = 0.817419 − 0.208348I
b = 0.381830 + 1.357280I
−3.73840 − 2.35300I −3.19315 + 1.59794I
u = −0.348783 + 0.861259I
a = −1.76105 + 0.29227I
b = −2.49906 + 1.14696I
0.471614 + 0.794306I 3.56373 − 5.07257I
u = −0.348783 − 0.861259I
a = −1.76105 − 0.29227I
b = −2.49906 − 1.14696I
0.471614 − 0.794306I 3.56373 + 5.07257I
u = 0.299592 + 0.869774I
a = 1.250900 + 0.117358I
b = 2.79613 + 1.22391I
−1.44854 − 6.15707I 1.62490 + 4.95559I
u = 0.299592 − 0.869774I
a = 1.250900 − 0.117358I
b = 2.79613 − 1.22391I
−1.44854 + 6.15707I 1.62490 − 4.95559I
u = −0.764063 + 0.399289I
a = −0.735506 − 0.785314I
b = −0.783034 + 0.077087I
0.07884 + 3.73395I 5.32221 − 8.03220I
u = −0.764063 − 0.399289I
a = −0.735506 + 0.785314I
b = −0.783034 − 0.077087I
0.07884 − 3.73395I 5.32221 + 8.03220I
36
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.694304 + 0.946157I
a = −1.112440 − 0.529650I
b = −1.58387 − 0.19054I
−4.92954 + 2.76340I 32.6505 + 12.4930I
u = 0.694304 − 0.946157I
a = −1.112440 + 0.529650I
b = −1.58387 + 0.19054I
−4.92954 − 2.76340I 32.6505 − 12.4930I
u = −0.640614 + 1.003430I
a = 1.220570 + 0.008241I
b = 2.23544 + 0.44108I
2.75263 − 5.40942I 4.00000 + 5.21975I
u = −0.640614 − 1.003430I
a = 1.220570 − 0.008241I
b = 2.23544 − 0.44108I
2.75263 + 5.40942I 4.00000 − 5.21975I
u = −0.468792 + 1.102810I
a = 0.379086 + 0.747842I
b = 1.12862 + 1.42597I
0.84871 − 3.68252I 7.53677 + 3.79983I
u = −0.468792 − 1.102810I
a = 0.379086 − 0.747842I
b = 1.12862 − 1.42597I
0.84871 + 3.68252I 7.53677 − 3.79983I
u = −0.561759 + 1.074280I
a = 0.824401 + 0.557811I
b = 1.91991 + 0.06261I
−1.89294 − 8.64589I 4.00000 + 10.21550I
u = −0.561759 − 1.074280I
a = 0.824401 − 0.557811I
b = 1.91991 − 0.06261I
−1.89294 + 8.64589I 4.00000 − 10.21550I
u = 0.602960 + 1.090830I
a = −0.799404 + 0.340668I
b = −2.16981 + 0.04109I
−1.44854 + 6.15707I 0
u = 0.602960 − 1.090830I
a = −0.799404 − 0.340668I
b = −2.16981 − 0.04109I
−1.44854 − 6.15707I 0
37
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.295711 + 0.495304I
a = −1.11636 − 1.55763I
b = 0.226864 + 0.692206I
3.00935 10.02954 + 0.I
u = −0.295711 − 0.495304I
a = −1.11636 + 1.55763I
b = 0.226864 − 0.692206I
3.00935 10.02954 + 0.I
u = 0.01175 + 1.46500I
a = −0.002432 + 0.226165I
b = 0.137257 + 0.136757I
−6.80652 + 1.60888I 0
u = 0.01175 − 1.46500I
a = −0.002432 − 0.226165I
b = 0.137257 − 0.136757I
−6.80652 − 1.60888I 0
u = 0.06718 + 1.55891I
a = −0.016024 + 0.205169I
b = 0.100936 + 0.625989I
−4.92954 − 2.76340I 0
u = 0.06718 − 1.55891I
a = −0.016024 − 0.205169I
b = 0.100936 − 0.625989I
−4.92954 + 2.76340I 0
u = −0.043310 + 0.386385I
a = −0.31032 − 2.49305I
b = −1.295590 + 0.462262I
0.84871 + 3.68252I 7.53677 − 3.79983I
u = −0.043310 − 0.386385I
a = −0.31032 + 2.49305I
b = −1.295590 − 0.462262I
0.84871 − 3.68252I 7.53677 + 3.79983I
38
V. I
u
5
= hu
3
+ u
2
+ b − 1, u
3
+ a, u
4
+ u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
9
=
−u
3
−u
3
− u
2
+ 1
a
10
=
2u
2
+ u + 1
u
2
+ u + 2
a
1
=
u
2
+ 1
u
3
+ u
2
+ u + 1
a
5
=
−u
2
−u
3
− 2u
2
− u − 1
a
8
=
u
2
+ u + 1
u + 1
a
4
=
u
3
+ u
2
+ 2u + 1
−u
3
− u
2
+ u
a
12
=
−u
3
− u
−u
a
11
=
u
2
+ u + 2
−u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
3
+ 7u
2
+ 2u + 6
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
12
u
4
− u
3
+ u
2
− u + 1
c
2
, c
5
, c
7
c
10
, c
11
u
4
+ u
3
+ u
2
+ u + 1
c
4
, c
8
u
4
+ 3u
3
+ 4u
2
+ 2u + 1
c
9
u
4
− 5u + 5
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
4
+ y
3
+ y
2
+ y + 1
c
4
, c
8
y
4
− y
3
+ 6y
2
+ 4y + 1
c
9
y
4
+ 10y
2
− 25y + 25
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309017 + 0.951057I
a = 0.809017 + 0.587785I
b = 2.61803
−3.94784 −5.51722 + 1.31433I
u = 0.309017 − 0.951057I
a = 0.809017 − 0.587785I
b = 2.61803
−3.94784 −5.51722 − 1.31433I
u = −0.809017 + 0.587785I
a = −0.309017 − 0.951057I
b = 0.381966
3.94784 9.01722 + 2.12663I
u = −0.809017 − 0.587785I
a = −0.309017 + 0.951057I
b = 0.381966
3.94784 9.01722 − 2.12663I
42
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ u
2
− u + 1)(u
5
− 2u
4
+ 3u
3
− u
2
− u + 1)
· (u
32
+ 15u
31
+ ··· + 6u + 1)(u
38
− 25u
37
+ ··· − 29u + 1)
· (u
158
+ 72u
157
+ ··· + 3542053u + 175561)
c
2
, c
10
(u
4
+ u
3
+ u
2
+ u + 1)(u
5
+ u
3
+ u
2
+ u + 1)(u
32
− u
31
+ ··· − 2u + 1)
· (u
38
− u
37
+ ··· + u + 1)(u
158
+ 36u
156
+ ··· + 795u + 419)
c
3
, c
6
(u
4
− u
3
+ u
2
− u + 1)(u
5
+ u
3
− u
2
+ u − 1)(u
32
− u
31
+ ··· − 2u + 1)
· (u
38
+ u
37
+ ··· − u + 1)(u
158
+ 36u
156
+ ··· + 795u + 419)
c
4
, c
8
(u
4
+ 3u
3
+ 4u
2
+ 2u + 1)(u
5
− 2u
4
+ 2u
3
− 3u
2
+ 2u + 1)
· (u
32
+ u
31
+ ··· − 9u
2
+ 1)(u
38
− u
37
+ ··· + 7u
2
+ 1)
· (u
158
+ 4u
157
+ ··· − 84u + 305)
c
5
, c
7
(u
4
+ u
3
+ u
2
+ u + 1)(u
5
+ u
3
+ u
2
+ u + 1)(u
32
+ u
31
+ ··· − 4u − 1)
· (u
38
− 3u
37
+ ··· − 11u + 1)(u
158
− 7u
156
+ ··· − 1086387u + 160579)
c
9
(u
4
− 5u + 5)(u
5
− u
4
+ ··· + u − 5)(u
19
− 7u
18
+ ··· + 3u − 1)
2
· (u
32
+ 12u
31
+ ··· − 368u − 320)
· (u
79
− 12u
78
+ ··· − 16031u + 5803)
2
c
11
(u
4
+ u
3
+ u
2
+ u + 1)(u
5
+ 2u
4
+ 3u
3
+ u
2
− u − 1)
· (u
32
+ 15u
31
+ ··· + 6u + 1)(u
38
+ 25u
37
+ ··· + 29u + 1)
· (u
158
+ 72u
157
+ ··· + 3542053u + 175561)
c
12
(u
4
− u
3
+ u
2
− u + 1)(u
5
− u
4
− u
3
+ 3u
2
− 2u + 1)
· ((u
19
+ 2u
18
+ ··· + u + 1)
2
)(u
32
− 19u
31
+ ··· + 76u − 8)
· (u
79
+ 7u
78
+ ··· − u − 1)
2
43
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
4
+ y
3
+ y
2
+ y + 1)(y
5
+ 2y
4
+ 3y
3
− 3y
2
+ 3y −1)
· (y
32
+ 3y
31
+ ··· + 6y + 1)(y
38
− 11y
37
+ ··· − 67y + 1)
· (y
158
+ 40y
157
+ ··· − 2099160591827y + 30821664721)
c
2
, c
3
, c
6
c
10
(y
4
+ y
3
+ y
2
+ y + 1)(y
5
+ 2y
4
+ 3y
3
+ y
2
− y −1)
· (y
32
+ 15y
31
+ ··· + 6y + 1)(y
38
+ 25y
37
+ ··· + 29y + 1)
· (y
158
+ 72y
157
+ ··· + 3542053y + 175561)
c
4
, c
8
(y
4
− y
3
+ 6y
2
+ 4y + 1)(y
5
− 4y
3
+ 3y
2
+ 10y −1)
· (y
32
− 13y
31
+ ··· − 18y + 1)(y
38
+ y
37
+ ··· + 14y + 1)
· (y
158
+ 8y
157
+ ··· − 7749786y + 93025)
c
5
, c
7
(y
4
+ y
3
+ y
2
+ y + 1)(y
5
+ 2y
4
+ 3y
3
+ y
2
− y −1)
· (y
32
− 5y
31
+ ··· − 10y + 1)(y
38
+ 15y
37
+ ··· − 39y + 1)
· (y
158
− 14y
157
+ ··· − 1110681919919y + 25785615241)
c
9
(y
4
+ 10y
2
− 25y + 25)(y
5
− 5y
4
+ 16y
3
− 39y
2
+ 51y −25)
· (y
19
+ 3y
18
+ ··· − 13y −1)
2
· (y
32
− 4y
31
+ ··· − 1748224y + 102400)
· (y
79
− 22y
78
+ ··· + 521006249y −33674809)
2
c
12
(y
4
+ y
3
+ y
2
+ y + 1)(y
5
− 3y
4
+ 3y
3
− 3y
2
− 2y −1)
· ((y
19
+ 8y
18
+ ··· + y −1)
2
)(y
32
− 5y
31
+ ··· − 784y + 64)
· (y
79
− y
78
+ ··· + 3y −1)
2
44
