12n
0537
(K12n
0537
)
A knot diagram
1
Linearized knot diagam
3 5 7 12 2 11 10 5 4 3 9 8
Solving Sequence
4,12 5,9
10 8 1 7 3 2 6 11
c
4
c
9
c
8
c
12
c
7
c
3
c
2
c
5
c
11
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.81893 × 10
17
u
27
− 6.03500 × 10
17
u
26
+ ··· + 5.35730 × 10
17
b − 3.43509 × 10
18
,
− 3.83926 × 10
18
u
27
+ 2.85325 × 10
18
u
26
+ ··· + 5.35730 × 10
17
a − 4.31215 × 10
18
, u
28
+ 2u
26
+ ··· + 2u + 1i
I
u
2
= h6.36861 × 10
214
u
67
+ 1.23983 × 10
215
u
66
+ ··· + 2.21361 × 10
214
b + 4.99066 × 10
215
,
− 6.89986 × 10
215
u
67
− 1.24081 × 10
216
u
66
+ ··· + 2.21361 × 10
214
a − 3.68206 × 10
216
,
u
68
+ 2u
67
+ ··· + 21u + 1i
I
u
3
= h−2.25962 × 10
48
u
35
− 8.58758 × 10
47
u
34
+ ··· + 1.17942 × 10
46
b + 5.94065 × 10
48
,
− 1.61303 × 10
48
u
35
− 6.16039 × 10
47
u
34
+ ··· + 1.17942 × 10
46
a + 4.20101 × 10
48
, u
36
+ 5u
34
+ ··· − 6u
2
+ 1i
I
u
4
= hb, 2u
4
+ u
3
+ 3u
2
+ a − u − 2, u
5
+ u
3
− u
2
− u + 1i
I
u
5
= hb − 1, a + 1, u
2
− u + 1i
* 5 irreducible components of dim
C
= 0, with total 139 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−4.82×10
17
u
27
−6.04×10
17
u
26
+· · ·+5.36×10
17
b−3.44×10
18
, −3.84×
10
18
u
27
+2.85×10
18
u
26
+· · ·+5.36×10
17
a−4.31×10
18
, u
28
+2u
26
+· · ·+2u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
7.16640u
27
− 5.32591u
26
+ ··· + 6.13836u + 8.04910
0.899507u
27
+ 1.12650u
26
+ ··· + 4.01358u + 6.41197
a
10
=
8.06591u
27
− 4.19941u
26
+ ··· + 10.1519u + 14.4611
0.899507u
27
+ 1.12650u
26
+ ··· + 4.01358u + 6.41197
a
8
=
5.18943u
27
− 2.77194u
26
+ ··· + 6.66653u + 9.13517
0.163984u
27
+ 0.536152u
26
+ ··· + 0.882630u + 3.85801
a
1
=
6.83813u
27
− 3.91955u
26
+ ··· + 6.32359u + 12.0959
−1.93722u
27
+ 1.48121u
26
+ ··· − 1.00772u − 2.61673
a
7
=
−14.1808u
27
+ 9.53294u
26
+ ··· − 9.14159u − 22.3381
u
a
3
=
−9.53294u
27
+ 6.37147u
26
+ ··· − 6.02353u − 13.1808
−u
2
a
2
=
−13.4897u
27
+ 8.98078u
26
+ ··· − 9.23353u − 19.5523
−1.82185u
27
+ 1.25415u
26
+ ··· − 1.26190u − 2.60931
a
6
=
5.48144u
27
− 3.48713u
26
+ ··· + 3.70672u + 8.83761
1.93722u
27
− 1.48121u
26
+ ··· + 1.00772u + 2.61673
a
11
=
19.2062u
27
− 12.8410u
26
+ ··· + 15.9255u + 27.6152
0.163984u
27
+ 0.536152u
26
+ ··· + 0.882630u + 3.85801
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
18680269678576763267
535729943333344787
u
27
+
8598753415343829290
535729943333344787
u
26
+ ··· −
35223182169748815025
535729943333344787
u −
23029573736888830965
535729943333344787
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
+ 27u
27
+ ··· + 13748u + 1296
c
2
, c
5
u
28
+ 3u
27
+ ··· + 2u + 36
c
3
, c
4
u
28
+ 2u
26
+ ··· + 2u + 1
c
6
, c
12
u
28
+ 8u
27
+ ··· + 224u + 32
c
7
, c
11
u
28
+ 3u
27
+ ··· + 13u + 1
c
8
, c
10
u
28
+ u
27
+ ··· − 3u + 1
c
9
u
28
+ 5u
27
+ ··· + 320u + 128
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 49y
27
+ ··· − 825712y + 1679616
c
2
, c
5
y
28
+ 27y
27
+ ··· + 13748y + 1296
c
3
, c
4
y
28
+ 4y
27
+ ··· + 6y + 1
c
6
, c
12
y
28
+ 30y
27
+ ··· + 29696y + 1024
c
7
, c
11
y
28
− y
27
+ ··· − y + 1
c
8
, c
10
y
28
− 29y
27
+ ··· − 45y + 1
c
9
y
28
− y
27
+ ··· + 233472y + 16384
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.668779 + 0.723827I
a = −1.042480 + 0.230333I
b = 0.533282 + 0.983247I
−0.10356 + 2.64453I 1.22282 − 3.18892I
u = −0.668779 − 0.723827I
a = −1.042480 − 0.230333I
b = 0.533282 − 0.983247I
−0.10356 − 2.64453I 1.22282 + 3.18892I
u = 0.635506 + 0.698040I
a = 1.370710 + 0.155616I
b = −2.42228 − 0.22270I
−8.72712 − 8.29781I −3.70457 + 10.88184I
u = 0.635506 − 0.698040I
a = 1.370710 − 0.155616I
b = −2.42228 + 0.22270I
−8.72712 + 8.29781I −3.70457 − 10.88184I
u = 0.048408 + 0.902686I
a = 1.55642 − 0.39395I
b = −0.456492 + 0.690736I
−6.94969 − 1.95373I 0.13138 + 3.39783I
u = 0.048408 − 0.902686I
a = 1.55642 + 0.39395I
b = −0.456492 − 0.690736I
−6.94969 + 1.95373I 0.13138 − 3.39783I
u = 0.983916 + 0.634599I
a = 0.837957 + 0.541891I
b = −0.560930 + 1.151500I
−2.43111 − 6.54317I −6.80530 + 6.55208I
u = 0.983916 − 0.634599I
a = 0.837957 − 0.541891I
b = −0.560930 − 1.151500I
−2.43111 + 6.54317I −6.80530 − 6.55208I
u = −0.278802 + 0.692018I
a = −1.019280 − 0.484379I
b = 2.06902 + 0.53469I
−0.15480 + 3.78570I 3.46312 − 12.68951I
u = −0.278802 − 0.692018I
a = −1.019280 + 0.484379I
b = 2.06902 − 0.53469I
−0.15480 − 3.78570I 3.46312 + 12.68951I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.262782 + 0.616933I
a = 0.103884 − 0.340572I
b = −0.836041 + 0.476997I
0.01742 + 1.41732I −1.09305 − 2.14471I
u = −0.262782 − 0.616933I
a = 0.103884 + 0.340572I
b = −0.836041 − 0.476997I
0.01742 − 1.41732I −1.09305 + 2.14471I
u = −0.659524 + 0.003319I
a = −2.13553 + 2.39966I
b = 0.278963 + 0.671140I
−9.47298 + 2.59610I −14.8510 − 6.7959I
u = −0.659524 − 0.003319I
a = −2.13553 − 2.39966I
b = 0.278963 − 0.671140I
−9.47298 − 2.59610I −14.8510 + 6.7959I
u = 0.572072 + 0.249132I
a = 2.09983 + 0.65588I
b = −0.562847 + 0.942357I
−2.94382 − 1.92479I −11.20798 + 2.16356I
u = 0.572072 − 0.249132I
a = 2.09983 − 0.65588I
b = −0.562847 − 0.942357I
−2.94382 + 1.92479I −11.20798 − 2.16356I
u = −0.163734 + 0.512554I
a = −0.561467 − 0.153031I
b = −0.152593 + 0.805696I
0.027219 + 1.275630I 0.54017 − 5.75782I
u = −0.163734 − 0.512554I
a = −0.561467 + 0.153031I
b = −0.152593 − 0.805696I
0.027219 − 1.275630I 0.54017 + 5.75782I
u = −0.20976 + 1.48222I
a = −0.275606 − 0.434449I
b = 0.209091 + 0.559595I
2.42708 + 1.71113I −8.50690 − 8.37300I
u = −0.20976 − 1.48222I
a = −0.275606 + 0.434449I
b = 0.209091 − 0.559595I
2.42708 − 1.71113I −8.50690 + 8.37300I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.15979 + 1.04033I
a = 1.179480 + 0.124327I
b = −0.87720 − 1.53540I
−12.9356 + 18.0876I −5.50986 − 8.24727I
u = −1.15979 − 1.04033I
a = 1.179480 − 0.124327I
b = −0.87720 + 1.53540I
−12.9356 − 18.0876I −5.50986 + 8.24727I
u = 1.14462 + 1.07762I
a = −0.343283 + 0.540527I
b = 0.060499 − 1.217480I
−12.42660 + 1.51018I −8.64520 + 0.I
u = 1.14462 − 1.07762I
a = −0.343283 − 0.540527I
b = 0.060499 + 1.217480I
−12.42660 − 1.51018I −8.64520 + 0.I
u = −1.15228 + 1.07906I
a = 0.632964 + 0.320798I
b = −0.526893 − 1.288980I
−4.70997 + 4.71020I −6.97281 − 3.71311I
u = −1.15228 − 1.07906I
a = 0.632964 − 0.320798I
b = −0.526893 + 1.288980I
−4.70997 − 4.71020I −6.97281 + 3.71311I
u = 1.17094 + 1.06658I
a = −0.903598 + 0.197693I
b = 0.74443 − 1.44446I
−4.94640 − 12.28330I −5.06082 + 8.01009I
u = 1.17094 − 1.06658I
a = −0.903598 − 0.197693I
b = 0.74443 + 1.44446I
−4.94640 + 12.28330I −5.06082 − 8.01009I
7
II. I
u
2
= h6.37 × 10
214
u
67
+ 1.24 × 10
215
u
66
+ · · · + 2.21 × 10
214
b + 4.99 ×
10
215
, −6.90 × 10
215
u
67
− 1.24 × 10
216
u
66
+ · · · + 2.21 × 10
214
a − 3.68 ×
10
216
, u
68
+ 2u
67
+ · · · + 21u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
31.1702u
67
+ 56.0539u
66
+ ··· + 2647.88u + 166.338
−2.87703u
67
− 5.60095u
66
+ ··· − 328.693u − 22.5454
a
10
=
28.2932u
67
+ 50.4529u
66
+ ··· + 2319.19u + 143.792
−2.87703u
67
− 5.60095u
66
+ ··· − 328.693u − 22.5454
a
8
=
26.7127u
67
+ 47.8406u
66
+ ··· + 2218.34u + 137.506
−2.95446u
67
− 5.72854u
66
+ ··· − 338.974u − 23.2473
a
1
=
88.0011u
67
+ 162.387u
66
+ ··· + 8091.09u + 542.171
−5.68870u
67
− 10.3246u
66
+ ··· − 569.445u − 41.1034
a
7
=
5.00717u
67
+ 8.61197u
66
+ ··· + 214.047u − 9.36045
−3.79980u
67
− 7.12911u
66
+ ··· − 372.019u − 24.6242
a
3
=
−63.6091u
67
− 117.431u
66
+ ··· − 5857.97u − 389.038
4.84840u
67
+ 8.68921u
66
+ ··· + 432.644u + 30.6341
a
2
=
−69.4105u
67
− 128.375u
66
+ ··· − 6432.53u − 429.459
4.85010u
67
+ 8.61831u
66
+ ··· + 424.612u + 29.9753
a
6
=
−63.3932u
67
− 117.128u
66
+ ··· − 6447.05u − 489.180
−3.77612u
67
− 6.57578u
66
+ ··· − 244.295u − 13.6639
a
11
=
102.661u
67
+ 190.241u
66
+ ··· + 9665.96u + 654.485
−5.94412u
67
− 11.0219u
66
+ ··· − 591.464u − 42.5143
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.381385u
67
+ 4.09349u
66
+ ··· + 460.637u + 29.8348
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
34
+ 44u
33
+ ··· + 211167u + 11664)
2
c
2
, c
5
(u
34
− 2u
33
+ ··· − 27u + 108)
2
c
3
, c
4
u
68
+ 2u
67
+ ··· + 21u + 1
c
6
, c
12
u
68
− 6u
67
+ ··· + 218203862u + 59673407
c
7
, c
11
u
68
+ 3u
67
+ ··· + 311u + 59
c
8
, c
10
u
68
+ u
67
+ ··· + 927119u + 1344671
c
9
(u
34
− u
33
+ ··· − 71u + 209)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
34
− 92y
33
+ ··· + 1741335327y + 136048896)
2
c
2
, c
5
(y
34
+ 44y
33
+ ··· + 211167y + 11664)
2
c
3
, c
4
y
68
− 2y
67
+ ··· − 119y + 1
c
6
, c
12
y
68
+ 24y
67
+ ··· + 109187012423296144y + 3560915502987649
c
7
, c
11
y
68
− 35y
67
+ ··· + 19745y + 3481
c
8
, c
10
y
68
− 13y
67
+ ··· − 6278009008341y + 1808140098241
c
9
(y
34
+ 27y
33
+ ··· + 812985y + 43681)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.988229 + 0.036641I
a = 0.541719 − 0.076017I
b = −0.092881 + 0.993847I
−2.68708 + 3.24701I −7.49713 − 2.56448I
u = −0.988229 − 0.036641I
a = 0.541719 + 0.076017I
b = −0.092881 − 0.993847I
−2.68708 − 3.24701I −7.49713 + 2.56448I
u = 1.048190 + 0.084796I
a = −0.740063 + 0.401409I
b = 0.74542 − 1.31472I
−11.74950 + 0.99052I 0
u = 1.048190 − 0.084796I
a = −0.740063 − 0.401409I
b = 0.74542 + 1.31472I
−11.74950 − 0.99052I 0
u = 0.897611 + 0.299654I
a = 0.81753 − 2.31884I
b = 0.899935 − 0.657412I
−10.05820 + 4.24924I −11.45347 − 2.51859I
u = 0.897611 − 0.299654I
a = 0.81753 + 2.31884I
b = 0.899935 + 0.657412I
−10.05820 − 4.24924I −11.45347 + 2.51859I
u = 0.316205 + 1.016990I
a = −1.18839 + 1.71559I
b = 0.263043 − 1.081580I
−7.73519 − 5.04941I 0
u = 0.316205 − 1.016990I
a = −1.18839 − 1.71559I
b = 0.263043 + 1.081580I
−7.73519 + 5.04941I 0
u = 0.685355 + 0.849666I
a = 0.268449 + 0.431117I
b = 0.223062 + 0.797775I
−6.57994 − 2.99755I 0
u = 0.685355 − 0.849666I
a = 0.268449 − 0.431117I
b = 0.223062 − 0.797775I
−6.57994 + 2.99755I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.468927 + 0.753341I
a = 1.82075 + 0.71765I
b = −0.601383 − 0.937913I
0.30115 + 6.48305I 2.75382 − 11.37072I
u = −0.468927 − 0.753341I
a = 1.82075 − 0.71765I
b = −0.601383 + 0.937913I
0.30115 − 6.48305I 2.75382 + 11.37072I
u = −0.247431 + 0.841447I
a = −0.006812 − 0.392523I
b = −0.608249 + 1.119590I
0.134730 + 1.289890I 2.62841 − 5.51442I
u = −0.247431 − 0.841447I
a = −0.006812 + 0.392523I
b = −0.608249 − 1.119590I
0.134730 − 1.289890I 2.62841 + 5.51442I
u = −0.799604 + 0.350430I
a = −1.359860 − 0.075744I
b = 0.899935 − 0.657412I
−10.05820 + 4.24924I −11.45347 − 2.51859I
u = −0.799604 − 0.350430I
a = −1.359860 + 0.075744I
b = 0.899935 + 0.657412I
−10.05820 − 4.24924I −11.45347 + 2.51859I
u = −0.863696 + 0.007111I
a = −1.55464 + 0.90908I
b = −0.360465 + 0.686126I
−3.46175 + 1.42507I −10.51067 − 4.72604I
u = −0.863696 − 0.007111I
a = −1.55464 − 0.90908I
b = −0.360465 − 0.686126I
−3.46175 − 1.42507I −10.51067 + 4.72604I
u = −0.790910 + 0.123927I
a = 1.041290 + 0.463826I
b = −1.26373 − 1.89895I
−12.11020 + 6.39851I −11.48496 − 5.28007I
u = −0.790910 − 0.123927I
a = 1.041290 − 0.463826I
b = −1.26373 + 1.89895I
−12.11020 − 6.39851I −11.48496 + 5.28007I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.744234 + 0.181720I
a = −0.77241 + 1.52342I
b = −0.404490 + 0.921778I
−2.66841 − 5.52402I −9.8516 + 10.9069I
u = 0.744234 − 0.181720I
a = −0.77241 − 1.52342I
b = −0.404490 − 0.921778I
−2.66841 + 5.52402I −9.8516 − 10.9069I
u = −0.139920 + 1.247210I
a = 0.063353 + 1.141210I
b = 0.059202 − 0.623325I
4.42322 + 2.94331I 0
u = −0.139920 − 1.247210I
a = 0.063353 − 1.141210I
b = 0.059202 + 0.623325I
4.42322 − 2.94331I 0
u = 1.089210 + 0.651528I
a = 1.127320 + 0.267005I
b = −0.404490 + 0.921778I
−2.66841 − 5.52402I 0
u = 1.089210 − 0.651528I
a = 1.127320 − 0.267005I
b = −0.404490 − 0.921778I
−2.66841 + 5.52402I 0
u = 0.559625 + 0.428522I
a = −1.65845 − 0.12542I
b = 0.86109 − 1.26732I
−1.33870 − 6.60010I −6.29119 + 6.93498I
u = 0.559625 − 0.428522I
a = −1.65845 + 0.12542I
b = 0.86109 + 1.26732I
−1.33870 + 6.60010I −6.29119 − 6.93498I
u = −0.641696 + 1.127080I
a = 0.464741 − 0.402605I
b = −1.078840 + 0.695928I
0.362177 + 0.737675I 0
u = −0.641696 − 1.127080I
a = 0.464741 + 0.402605I
b = −1.078840 − 0.695928I
0.362177 − 0.737675I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.692090 + 0.104185I
a = 1.62625 − 0.34239I
b = −0.360465 − 0.686126I
−3.46175 − 1.42507I −10.51067 + 4.72604I
u = 0.692090 − 0.104185I
a = 1.62625 + 0.34239I
b = −0.360465 + 0.686126I
−3.46175 + 1.42507I −10.51067 − 4.72604I
u = −0.630362 + 1.147050I
a = −0.606718 − 0.469413I
b = 0.89698 + 1.81746I
−1.23903 + 3.47975I 0
u = −0.630362 − 1.147050I
a = −0.606718 + 0.469413I
b = 0.89698 − 1.81746I
−1.23903 − 3.47975I 0
u = −1.214430 + 0.596977I
a = −1.203930 + 0.263018I
b = 0.624993 + 0.841916I
−10.68940 + 6.84316I 0
u = −1.214430 − 0.596977I
a = −1.203930 − 0.263018I
b = 0.624993 − 0.841916I
−10.68940 − 6.84316I 0
u = −1.055410 + 0.872464I
a = −0.935528 − 0.245342I
b = −0.092881 + 0.993847I
−2.68708 + 3.24701I 0
u = −1.055410 − 0.872464I
a = −0.935528 + 0.245342I
b = −0.092881 − 0.993847I
−2.68708 − 3.24701I 0
u = −0.505178 + 0.289459I
a = 1.303920 − 0.401547I
b = −1.078840 − 0.695928I
0.362177 − 0.737675I −3.01494 − 2.57610I
u = −0.505178 − 0.289459I
a = 1.303920 + 0.401547I
b = −1.078840 + 0.695928I
0.362177 + 0.737675I −3.01494 + 2.57610I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.03822 + 0.97416I
a = 1.292760 − 0.248045I
b = −1.26373 + 1.89895I
−12.11020 − 6.39851I 0
u = 1.03822 − 0.97416I
a = 1.292760 + 0.248045I
b = −1.26373 − 1.89895I
−12.11020 + 6.39851I 0
u = 0.95320 + 1.07772I
a = 0.470263 − 1.062870I
b = 0.74542 + 1.31472I
−11.74950 − 0.99052I 0
u = 0.95320 − 1.07772I
a = 0.470263 + 1.062870I
b = 0.74542 − 1.31472I
−11.74950 + 0.99052I 0
u = 0.541931 + 0.113704I
a = −0.169744 − 0.186828I
b = 0.89698 + 1.81746I
−1.23903 + 3.47975I −11.86128 + 7.58185I
u = 0.541931 − 0.113704I
a = −0.169744 + 0.186828I
b = 0.89698 − 1.81746I
−1.23903 − 3.47975I −11.86128 − 7.58185I
u = −0.486109 + 0.250377I
a = 0.54394 + 5.66734I
b = 0.624993 + 0.841916I
−10.68940 + 6.84316I −13.1700 − 13.6418I
u = −0.486109 − 0.250377I
a = 0.54394 − 5.66734I
b = 0.624993 − 0.841916I
−10.68940 − 6.84316I −13.1700 + 13.6418I
u = −1.20413 + 0.91553I
a = −0.977470 + 0.362937I
b = 0.86109 + 1.26732I
−1.33870 + 6.60010I 0
u = −1.20413 − 0.91553I
a = −0.977470 − 0.362937I
b = 0.86109 − 1.26732I
−1.33870 − 6.60010I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.10477 + 1.07329I
a = −1.038600 + 0.326925I
b = 0.543096 − 1.209800I
−12.3962 − 9.6578I 0
u = 1.10477 − 1.07329I
a = −1.038600 − 0.326925I
b = 0.543096 + 1.209800I
−12.3962 + 9.6578I 0
u = −1.15749 + 1.06627I
a = 0.773036 + 0.369354I
b = −0.206787 − 1.043190I
−4.75446 + 3.62192I 0
u = −1.15749 − 1.06627I
a = 0.773036 − 0.369354I
b = −0.206787 + 1.043190I
−4.75446 − 3.62192I 0
u = 1.36128 + 0.87098I
a = 0.679421 + 0.350166I
b = −0.601383 + 0.937913I
0.30115 − 6.48305I 0
u = 1.36128 − 0.87098I
a = 0.679421 − 0.350166I
b = −0.601383 − 0.937913I
0.30115 + 6.48305I 0
u = −1.12817 + 1.27635I
a = 0.150045 + 0.627835I
b = 0.543096 − 1.209800I
−12.3962 − 9.6578I 0
u = −1.12817 − 1.27635I
a = 0.150045 − 0.627835I
b = 0.543096 + 1.209800I
−12.3962 + 9.6578I 0
u = 1.26466 + 1.16633I
a = −0.449381 + 0.416092I
b = −0.206787 − 1.043190I
−4.75446 + 3.62192I 0
u = 1.26466 − 1.16633I
a = −0.449381 − 0.416092I
b = −0.206787 + 1.043190I
−4.75446 − 3.62192I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.173722 + 0.166663I
a = −2.01494 + 0.17662I
b = −0.608249 + 1.119590I
0.134730 + 1.289890I 2.62841 − 5.51442I
u = −0.173722 − 0.166663I
a = −2.01494 − 0.17662I
b = −0.608249 − 1.119590I
0.134730 − 1.289890I 2.62841 + 5.51442I
u = −0.145879 + 0.018683I
a = −12.29330 + 6.13439I
b = 0.223062 − 0.797775I
−6.57994 + 2.99755I −2.94535 + 1.14914I
u = −0.145879 − 0.018683I
a = −12.29330 − 6.13439I
b = 0.223062 + 0.797775I
−6.57994 − 2.99755I −2.94535 − 1.14914I
u = −1.41912 + 1.21972I
a = −0.491669 − 0.178009I
b = 0.263043 + 1.081580I
−7.73519 + 5.04941I 0
u = −1.41912 − 1.21972I
a = −0.491669 + 0.178009I
b = 0.263043 − 1.081580I
−7.73519 − 5.04941I 0
u = 0.76383 + 2.23790I
a = −0.0228934 − 0.0620777I
b = 0.059202 + 0.623325I
4.42322 − 2.94331I 0
u = 0.76383 − 2.23790I
a = −0.0228934 + 0.0620777I
b = 0.059202 − 0.623325I
4.42322 + 2.94331I 0
17
III. I
u
3
= h−2.26 × 10
48
u
35
− 8.59 × 10
47
u
34
+ · · · + 1.18 × 10
46
b + 5.94 ×
10
48
, −1.61 × 10
48
u
35
− 6.16 × 10
47
u
34
+ · · · + 1.18 × 10
46
a + 4.20 ×
10
48
, u
36
+ 5u
34
+ · · · − 6u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
136.764u
35
+ 52.2322u
34
+ ··· − 952.902u − 356.192
191.587u
35
+ 72.8118u
34
+ ··· − 1328.03u − 503.692
a
10
=
328.351u
35
+ 125.044u
34
+ ··· − 2280.93u − 859.884
191.587u
35
+ 72.8118u
34
+ ··· − 1328.03u − 503.692
a
8
=
308.702u
35
+ 117.542u
34
+ ··· − 2144.16u − 807.652
216.358u
35
+ 82.1742u
34
+ ··· − 1499.96u − 569.001
a
1
=
−94.9256u
35
− 37.8952u
34
+ ··· + 692.912u + 256.406
−197.524u
35
− 75.3883u
34
+ ··· + 1369.87u + 521.602
a
7
=
33.4401u
35
+ 13.3311u
34
+ ··· − 236.732u − 93.2582
127.909u
35
+ 48.6370u
34
+ ··· − 883.973u − 337.364
a
3
=
−190.561u
35
− 71.5139u
34
+ ··· + 1300.58u + 496.970
−140.950u
35
− 53.2913u
34
+ ··· + 973.267u + 369.632
a
2
=
−76.8688u
35
− 28.4927u
34
+ ··· + 517.870u + 198.851
−124.568u
35
− 47.0802u
34
+ ··· + 859.575u + 326.611
a
6
=
38.5133u
35
+ 14.5614u
34
+ ··· − 273.354u − 91.8404
164.276u
35
+ 62.5988u
34
+ ··· − 1139.07u − 430.370
a
11
=
97.5697u
35
+ 35.9068u
34
+ ··· − 647.165u − 251.689
5.06363u
35
+ 1.65514u
34
+ ··· − 30.4338u − 11.5181
(ii) Obstruction class = 1
(iii) Cusp Shapes = 1809.72u
35
+ 688.118u
34
+ ··· − 12501.2u − 4762.85
18
(iv) u-Polynomials at the component
19
Crossings u-Polynomials at each crossing
c
1
(u
18
− 17u
17
+ ··· − 56u + 4)
2
c
2
(u
18
+ u
17
+ ··· + 6u + 2)
2
c
3
u
36
+ 5u
34
+ ··· − 6u
2
+ 1
c
4
u
36
+ 5u
34
+ ··· − 6u
2
+ 1
c
5
(u
18
− u
17
+ ··· − 6u + 2)
2
c
6
u
36
− 7u
35
+ ··· + 192u + 32
c
7
u
36
− 11u
35
+ ··· − 12u + 1
c
8
u
36
+ u
35
+ ··· + 4u + 1
c
9
u
36
+ 8u
34
+ ··· + 2720u
2
+ 329
c
10
u
36
− u
35
+ ··· − 4u + 1
c
11
u
36
+ 11u
35
+ ··· + 12u + 1
c
12
u
36
+ 7u
35
+ ··· − 192u + 32
20
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 19y
17
+ ··· + 360y + 16)
2
c
2
, c
5
(y
18
+ 17y
17
+ ··· + 56y + 4)
2
c
3
, c
4
y
36
+ 10y
35
+ ··· − 12y + 1
c
6
, c
12
y
36
− 17y
35
+ ··· + 13312y + 1024
c
7
, c
11
y
36
− 3y
35
+ ··· − 12y + 1
c
8
, c
10
y
36
+ 3y
35
+ ··· + 14y + 1
c
9
(y
18
+ 8y
17
+ ··· + 2720y + 329)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387110 + 0.887771I
a = −0.817383 + 0.149910I
b = 1.087400 + 0.195941I
1.90337 + 1.03056I 1.286140 − 0.538382I
u = 0.387110 − 0.887771I
a = −0.817383 − 0.149910I
b = 1.087400 − 0.195941I
1.90337 − 1.03056I 1.286140 + 0.538382I
u = 0.694269 + 0.635190I
a = −1.61256 − 0.33667I
b = 0.680806 − 1.107480I
−1.04528 − 7.85103I −2.06789 + 11.86645I
u = 0.694269 − 0.635190I
a = −1.61256 + 0.33667I
b = 0.680806 + 1.107480I
−1.04528 + 7.85103I −2.06789 − 11.86645I
u = 0.908151 + 0.000867I
a = −0.328700 − 0.385035I
b = −0.351407 − 1.092420I
−2.07175 + 4.73666I −4.27691 − 4.63834I
u = 0.908151 − 0.000867I
a = −0.328700 + 0.385035I
b = −0.351407 + 1.092420I
−2.07175 − 4.73666I −4.27691 + 4.63834I
u = −0.640781 + 0.916918I
a = 0.911491 − 0.266288I
b = −1.087400 − 0.195941I
1.90337 + 1.03056I − 61.286140 + 0.10I
u = −0.640781 − 0.916918I
a = 0.911491 + 0.266288I
b = −1.087400 + 0.195941I
1.90337 − 1.03056I − 61.286140 + 0.10I
u = −0.315914 + 0.788474I
a = 1.25754 + 0.95575I
b = −0.750098 − 0.946970I
−0.18706 + 5.80137I −2.95659 − 3.22264I
u = −0.315914 − 0.788474I
a = 1.25754 − 0.95575I
b = −0.750098 + 0.946970I
−0.18706 − 5.80137I −2.95659 + 3.22264I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.549127 + 1.040930I
a = −0.774918 − 0.449602I
b = 1.20331 + 1.55588I
−1.12744 + 3.79285I 0. − 14.6968I
u = −0.549127 − 1.040930I
a = −0.774918 + 0.449602I
b = 1.20331 − 1.55588I
−1.12744 − 3.79285I 0. + 14.6968I
u = −0.421922 + 1.103170I
a = 0.087462 − 0.569260I
b = −0.86966 + 1.32584I
−0.394276 + 1.096290I −12.74294 + 0.I
u = −0.421922 − 1.103170I
a = 0.087462 + 0.569260I
b = −0.86966 − 1.32584I
−0.394276 − 1.096290I −12.74294 + 0.I
u = 0.577450 + 0.561844I
a = 2.83116 − 0.64804I
b = −0.038303 + 0.828326I
−6.65751 − 3.75744I −5.03414 + 7.76355I
u = 0.577450 − 0.561844I
a = 2.83116 + 0.64804I
b = −0.038303 − 0.828326I
−6.65751 + 3.75744I −5.03414 − 7.76355I
u = −0.098370 + 1.269320I
a = −0.078604 − 1.138060I
b = 0.039244 + 0.664656I
4.35413 + 3.10586I 0. − 23.8029I
u = −0.098370 − 1.269320I
a = −0.078604 + 1.138060I
b = 0.039244 − 0.664656I
4.35413 − 3.10586I 0. + 23.8029I
u = −1.032540 + 0.761277I
a = −0.051147 + 0.482440I
b = 0.038303 + 0.828326I
−6.65751 + 3.75744I 0
u = −1.032540 − 0.761277I
a = −0.051147 − 0.482440I
b = 0.038303 − 0.828326I
−6.65751 − 3.75744I 0
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.012960 + 0.802948I
a = −1.149180 + 0.015549I
b = 0.351407 + 1.092420I
−2.07175 + 4.73666I 0
u = −1.012960 − 0.802948I
a = −1.149180 − 0.015549I
b = 0.351407 − 1.092420I
−2.07175 − 4.73666I 0
u = 1.099210 + 0.703645I
a = 1.215140 + 0.060923I
b = −0.912449 + 0.842826I
−10.40110 − 6.30737I 0
u = 1.099210 − 0.703645I
a = 1.215140 − 0.060923I
b = −0.912449 − 0.842826I
−10.40110 + 6.30737I 0
u = −0.573544 + 0.103977I
a = −0.792146 − 0.118092I
b = 0.86966 + 1.32584I
−0.394276 − 1.096290I −12.74294 + 0.28360I
u = −0.573544 − 0.103977I
a = −0.792146 + 0.118092I
b = 0.86966 − 1.32584I
−0.394276 + 1.096290I −12.74294 − 0.28360I
u = −1.24415 + 0.89531I
a = −0.814673 + 0.309886I
b = 0.750098 + 0.946970I
−0.18706 + 5.80137I 0
u = −1.24415 − 0.89531I
a = −0.814673 − 0.309886I
b = 0.750098 − 0.946970I
−0.18706 − 5.80137I 0
u = 1.33512 + 0.86016I
a = 0.718294 + 0.467996I
b = −0.680806 + 1.107480I
−1.04528 − 7.85103I 0
u = 1.33512 − 0.86016I
a = 0.718294 − 0.467996I
b = −0.680806 − 1.107480I
−1.04528 + 7.85103I 0
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.380464 + 0.000200I
a = 0.92076 + 1.11017I
b = −1.20331 + 1.55588I
−1.12744 − 3.79285I −3.8135 + 14.6968I
u = 0.380464 − 0.000200I
a = 0.92076 − 1.11017I
b = −1.20331 − 1.55588I
−1.12744 + 3.79285I −3.8135 − 14.6968I
u = −0.199060 + 0.249576I
a = 5.86236 − 1.19720I
b = 0.912449 − 0.842826I
−10.40110 − 6.30737I −5.57429 + 2.02371I
u = −0.199060 − 0.249576I
a = 5.86236 + 1.19720I
b = 0.912449 + 0.842826I
−10.40110 + 6.30737I −5.57429 − 2.02371I
u = 0.70660 + 2.28427I
a = 0.115104 − 0.112014I
b = −0.039244 + 0.664656I
4.35413 − 3.10586I 0
u = 0.70660 − 2.28427I
a = 0.115104 + 0.112014I
b = −0.039244 − 0.664656I
4.35413 + 3.10586I 0
26
IV. I
u
4
= hb, 2u
4
+ u
3
+ 3u
2
+ a − u − 2, u
5
+ u
3
− u
2
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
−2u
4
− u
3
− 3u
2
+ u + 2
0
a
10
=
−2u
4
− u
3
− 3u
2
+ u + 2
0
a
8
=
−u
4
− u
3
− 2u
2
+ 1
−u
a
1
=
−u − 1
u
4
+ u
2
+ u − 1
a
7
=
2u
4
+ u
3
+ 3u
2
− 1
−u
a
3
=
u
4
+ u
3
+ 2u
2
+ u − 1
−u
2
a
2
=
2u
4
+ 2u
3
+ 4u
2
+ u − 2
u
4
− 1
a
6
=
3u
4
+ u
3
+ 3u
2
− 2u − 4
−u
4
− u
2
− u + 1
a
11
=
−3u
4
− 2u
3
− 5u
2
+ 2
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
4
+ 3u
3
+ 3u − 9
27
(iv) u-Polynomials at the component
28
Crossings u-Polynomials at each crossing
c
1
u
5
− 6u
4
+ 13u
3
− 12u
2
+ 4u + 1
c
2
u
5
+ 3u
3
+ 2u − 1
c
3
u
5
+ u
3
+ u
2
− u − 1
c
4
u
5
+ u
3
− u
2
− u + 1
c
5
u
5
+ 3u
3
+ 2u + 1
c
6
u
5
+ 2u
4
+ u
3
+ 2u
2
+ 2u − 1
c
7
u
5
− 3u
4
+ 3u
3
+ u
2
− 2u − 1
c
8
u
5
− u
4
− u
3
+ u
2
+ 1
c
9
u
5
c
10
u
5
+ u
4
− u
3
− u
2
− 1
c
11
u
5
+ 3u
4
+ 3u
3
− u
2
− 2u + 1
c
12
u
5
− 2u
4
+ u
3
− 2u
2
+ 2u + 1
29
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− 10y
4
+ 33y
3
− 28y
2
+ 40y −1
c
2
, c
5
y
5
+ 6y
4
+ 13y
3
+ 12y
2
+ 4y −1
c
3
, c
4
y
5
+ 2y
4
− y
3
− 3y
2
+ 3y −1
c
6
, c
12
y
5
− 2y
4
− 3y
3
+ 4y
2
+ 8y −1
c
7
, c
11
y
5
− 3y
4
+ 11y
3
− 19y
2
+ 6y −1
c
8
, c
10
y
5
− 3y
4
+ 3y
3
+ y
2
− 2y −1
c
9
y
5
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.862442
a = −1.55887
b = 0
−3.66375 −11.8520
u = 0.717360 + 0.267040I
a = 1.07233 − 1.95491I
b = 0
−9.07644 + 2.10101I −6.05167 + 2.99980I
u = 0.717360 − 0.267040I
a = 1.07233 + 1.95491I
b = 0
−9.07644 − 2.10101I −6.05167 − 2.99980I
u = −0.286139 + 1.377340I
a = 0.207102 + 0.293496I
b = 0
2.68365 + 1.36579I 2.97770 + 5.89289I
u = −0.286139 − 1.377340I
a = 0.207102 − 0.293496I
b = 0
2.68365 − 1.36579I 2.97770 − 5.89289I
32
V. I
u
5
= hb − 1, a + 1, u
2
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u − 1
a
9
=
−1
1
a
10
=
0
1
a
8
=
u − 1
0
a
1
=
−u + 1
u
a
7
=
u − 1
−u + 1
a
3
=
−u + 1
u
a
2
=
−u + 1
u
a
6
=
1
u − 1
a
11
=
u
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
2
c
3
, c
4
, c
7
c
8
, c
10
, c
11
u
2
− u + 1
c
6
, c
9
, c
12
(u − 1)
2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
2
c
3
, c
4
, c
7
c
8
, c
10
, c
11
y
2
+ y + 1
c
6
, c
9
, c
12
(y −1)
2
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.00000
b = 1.00000
3.28987 6.00000
u = 0.500000 − 0.866025I
a = −1.00000
b = 1.00000
3.28987 6.00000
36
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u
5
− 6u
4
+ ··· + 4u + 1)(u
18
− 17u
17
+ ··· − 56u + 4)
2
· (u
28
+ 27u
27
+ ··· + 13748u + 1296)
· (u
34
+ 44u
33
+ ··· + 211167u + 11664)
2
c
2
u
2
(u
5
+ 3u
3
+ 2u − 1)(u
18
+ u
17
+ ··· + 6u + 2)
2
· (u
28
+ 3u
27
+ ··· + 2u + 36)(u
34
− 2u
33
+ ··· − 27u + 108)
2
c
3
(u
2
− u + 1)(u
5
+ u
3
+ u
2
− u − 1)(u
28
+ 2u
26
+ ··· + 2u + 1)
· (u
36
+ 5u
34
+ ··· − 6u
2
+ 1)(u
68
+ 2u
67
+ ··· + 21u + 1)
c
4
(u
2
− u + 1)(u
5
+ u
3
− u
2
− u + 1)(u
28
+ 2u
26
+ ··· + 2u + 1)
· (u
36
+ 5u
34
+ ··· − 6u
2
+ 1)(u
68
+ 2u
67
+ ··· + 21u + 1)
c
5
u
2
(u
5
+ 3u
3
+ 2u + 1)(u
18
− u
17
+ ··· − 6u + 2)
2
· (u
28
+ 3u
27
+ ··· + 2u + 36)(u
34
− 2u
33
+ ··· − 27u + 108)
2
c
6
((u − 1)
2
)(u
5
+ 2u
4
+ ··· + 2u − 1)(u
28
+ 8u
27
+ ··· + 224u + 32)
· (u
36
− 7u
35
+ ··· + 192u + 32)
· (u
68
− 6u
67
+ ··· + 218203862u + 59673407)
c
7
(u
2
− u + 1)(u
5
− 3u
4
+ ··· − 2u − 1)(u
28
+ 3u
27
+ ··· + 13u + 1)
· (u
36
− 11u
35
+ ··· − 12u + 1)(u
68
+ 3u
67
+ ··· + 311u + 59)
c
8
(u
2
− u + 1)(u
5
− u
4
− u
3
+ u
2
+ 1)(u
28
+ u
27
+ ··· − 3u + 1)
· (u
36
+ u
35
+ ··· + 4u + 1)(u
68
+ u
67
+ ··· + 927119u + 1344671)
c
9
u
5
(u − 1)
2
(u
28
+ 5u
27
+ ··· + 320u + 128)
· ((u
34
− u
33
+ ··· − 71u + 209)
2
)(u
36
+ 8u
34
+ ··· + 2720u
2
+ 329)
c
10
(u
2
− u + 1)(u
5
+ u
4
− u
3
− u
2
− 1)(u
28
+ u
27
+ ··· − 3u + 1)
· (u
36
− u
35
+ ··· − 4u + 1)(u
68
+ u
67
+ ··· + 927119u + 1344671)
c
11
(u
2
− u + 1)(u
5
+ 3u
4
+ ··· − 2u + 1)(u
28
+ 3u
27
+ ··· + 13u + 1)
· (u
36
+ 11u
35
+ ··· + 12u + 1)(u
68
+ 3u
67
+ ··· + 311u + 59)
c
12
((u − 1)
2
)(u
5
− 2u
4
+ ··· + 2u + 1)(u
28
+ 8u
27
+ ··· + 224u + 32)
· (u
36
+ 7u
35
+ ··· − 192u + 32)
· (u
68
− 6u
67
+ ··· + 218203862u + 59673407)
37
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y
5
− 10y
4
+ 33y
3
− 28y
2
+ 40y −1)
· (y
18
− 19y
17
+ ··· + 360y + 16)
2
· (y
28
− 49y
27
+ ··· − 825712y + 1679616)
· (y
34
− 92y
33
+ ··· + 1741335327y + 136048896)
2
c
2
, c
5
y
2
(y
5
+ 6y
4
+ ··· + 4y −1)(y
18
+ 17y
17
+ ··· + 56y + 4)
2
· (y
28
+ 27y
27
+ ··· + 13748y + 1296)
· (y
34
+ 44y
33
+ ··· + 211167y + 11664)
2
c
3
, c
4
(y
2
+ y + 1)(y
5
+ 2y
4
+ ··· + 3y −1)(y
28
+ 4y
27
+ ··· + 6y + 1)
· (y
36
+ 10y
35
+ ··· − 12y + 1)(y
68
− 2y
67
+ ··· − 119y + 1)
c
6
, c
12
(y −1)
2
(y
5
− 2y
4
− 3y
3
+ 4y
2
+ 8y −1)
· (y
28
+ 30y
27
+ ··· + 29696y + 1024)
· (y
36
− 17y
35
+ ··· + 13312y + 1024)
· (y
68
+ 24y
67
+ ··· + 109187012423296144y + 3560915502987649)
c
7
, c
11
(y
2
+ y + 1)(y
5
− 3y
4
+ ··· + 6y −1)(y
28
− y
27
+ ··· − y + 1)
· (y
36
− 3y
35
+ ··· − 12y + 1)(y
68
− 35y
67
+ ··· + 19745y + 3481)
c
8
, c
10
(y
2
+ y + 1)(y
5
− 3y
4
+ ··· − 2y −1)(y
28
− 29y
27
+ ··· − 45y + 1)
· (y
36
+ 3y
35
+ ··· + 14y + 1)
· (y
68
− 13y
67
+ ··· − 6278009008341y + 1808140098241)
c
9
y
5
(y −1)
2
(y
18
+ 8y
17
+ ··· + 2720y + 329)
2
· (y
28
− y
27
+ ··· + 233472y + 16384)
· (y
34
+ 27y
33
+ ··· + 812985y + 43681)
2
38
