12a
1055
(K12a
1055
)
A knot diagram
1
Linearized knot diagam
4 7 9 10 12 3 11 2 1 8 6 5
Solving Sequence
2,7 3,11
8 9 4 1 6 12 5 10
c
2
c
7
c
8
c
3
c
1
c
6
c
11
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.17270 × 10
674
u
143
+ 1.84276 × 10
675
u
142
+ ··· + 2.58449 × 10
677
b + 5.69888 × 10
678
,
5.38072 × 10
678
u
143
+ 8.23180 × 10
678
u
142
+ ··· + 2.55606 × 10
680
a − 2.46598 × 10
681
,
u
144
+ u
143
+ ··· − 5896u + 989i
I
u
2
= h2.35537 × 10
30
u
39
+ 1.05919 × 10
30
u
38
+ ··· + 2.44460 × 10
29
b − 7.09475 × 10
30
,
− 7.27177 × 10
30
u
39
− 1.23813 × 10
31
u
38
+ ··· + 2.44460 × 10
29
a + 2.34572 × 10
30
, u
40
+ 2u
39
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 184 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−2.17 × 10
674
u
143
+ 1.84 × 10
675
u
142
+ · · · + 2.58 × 10
677
b + 5.70 ×
10
678
, 5.38 × 10
678
u
143
+ 8.23 × 10
678
u
142
+ · · · + 2.56 × 10
680
a − 2.47 ×
10
681
, u
144
+ u
143
+ · · · − 5896u + 989i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
−0.0210508u
143
− 0.0322050u
142
+ ··· − 109.801u + 9.64757
0.000840669u
143
− 0.00713005u
142
+ ··· + 103.422u − 22.0503
a
8
=
0.0253537u
143
+ 0.0104650u
142
+ ··· + 455.891u − 94.6977
0.00283709u
143
+ 0.00148924u
142
+ ··· + 18.9687u − 4.22269
a
9
=
0.0225166u
143
+ 0.00897573u
142
+ ··· + 436.922u − 90.4750
0.00283709u
143
+ 0.00148924u
142
+ ··· + 18.9687u − 4.22269
a
4
=
−0.0196348u
143
− 0.0664906u
142
+ ··· + 301.113u − 86.8414
−0.0258564u
143
− 0.0394073u
142
+ ··· − 111.551u + 11.5497
a
1
=
−0.0676036u
143
− 0.105365u
142
+ ··· − 317.722u + 28.5588
−0.00635388u
143
+ 0.00430054u
142
+ ··· − 146.861u + 30.0276
a
6
=
u
u
3
+ u
a
12
=
−0.0281418u
143
− 0.0439491u
142
+ ··· − 131.963u + 9.36949
−0.00598204u
143
− 0.0163303u
142
+ ··· + 60.8374u − 17.7264
a
5
=
−0.0195811u
143
+ 0.00160936u
142
+ ··· − 476.589u + 101.810
−0.000614508u
143
+ 0.000419443u
142
+ ··· − 14.7609u + 5.86952
a
10
=
0.0796632u
143
+ 0.130380u
142
+ ··· + 238.971u − 3.85049
0.0103227u
143
+ 0.00404013u
142
+ ··· + 172.885u − 34.7918
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0628033u
143
+ 0.00950011u
142
+ ··· + 1209.64u − 250.992
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
144
− 5u
143
+ ··· − 106u + 17
c
2
, c
6
u
144
− u
143
+ ··· + 5896u + 989
c
3
u
144
+ u
143
+ ··· − 431616u + 85504
c
4
u
144
− u
143
+ ··· + 545u + 307
c
5
, c
11
, c
12
u
144
− u
143
+ ··· + 2435u + 193
c
7
, c
10
u
144
− 7u
143
+ ··· + 126358u + 11033
c
8
u
144
+ u
143
+ ··· + 222158u + 28393
c
9
u
144
− 3u
143
+ ··· − 94488u + 22681
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
144
+ 17y
143
+ ··· + 8926y + 289
c
2
, c
6
y
144
+ 65y
143
+ ··· + 23149068y + 978121
c
3
y
144
− 5y
143
+ ··· − 279517724672y + 7310934016
c
4
y
144
+ 51y
143
+ ··· + 4212805y + 94249
c
5
, c
11
, c
12
y
144
+ 161y
143
+ ··· + 3654383y + 37249
c
7
, c
10
y
144
+ 87y
143
+ ··· + 4474494936y + 121727089
c
8
y
144
+ 25y
143
+ ··· + 51876294512y + 806162449
c
9
y
144
+ 37y
143
+ ··· + 31337234260y + 514427761
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.517855 + 0.858761I
a = 1.07131 − 1.17568I
b = 0.422535 − 0.489625I
−1.32577 − 2.09615I 0
u = 0.517855 − 0.858761I
a = 1.07131 + 1.17568I
b = 0.422535 + 0.489625I
−1.32577 + 2.09615I 0
u = −0.355540 + 0.926995I
a = −0.92831 − 1.29737I
b = 0.284858 − 0.363499I
−2.00130 + 1.43707I 0
u = −0.355540 − 0.926995I
a = −0.92831 + 1.29737I
b = 0.284858 + 0.363499I
−2.00130 − 1.43707I 0
u = −0.228469 + 0.962555I
a = −0.523580 − 1.184250I
b = −0.509620 − 0.276973I
4.12127 + 0.74656I 0
u = −0.228469 − 0.962555I
a = −0.523580 + 1.184250I
b = −0.509620 + 0.276973I
4.12127 − 0.74656I 0
u = 0.063001 + 1.022290I
a = 0.375022 − 1.209370I
b = −0.184033 − 0.290733I
4.32694 + 0.06920I 0
u = 0.063001 − 1.022290I
a = 0.375022 + 1.209370I
b = −0.184033 + 0.290733I
4.32694 − 0.06920I 0
u = −0.424519 + 0.872191I
a = 0.956076 − 0.683640I
b = −0.09268 − 2.12496I
−3.24788 + 4.70970I 0
u = −0.424519 − 0.872191I
a = 0.956076 + 0.683640I
b = −0.09268 + 2.12496I
−3.24788 − 4.70970I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.427690 + 0.843847I
a = −1.149220 + 0.698741I
b = 1.25378 + 1.49091I
−3.33926 − 1.12138I 0
u = −0.427690 − 0.843847I
a = −1.149220 − 0.698741I
b = 1.25378 − 1.49091I
−3.33926 + 1.12138I 0
u = −1.013940 + 0.328197I
a = 0.700021 − 0.866564I
b = −0.01062 − 1.73100I
−3.04638 − 8.74887I 0
u = −1.013940 − 0.328197I
a = 0.700021 + 0.866564I
b = −0.01062 + 1.73100I
−3.04638 + 8.74887I 0
u = 1.027860 + 0.283936I
a = −0.400907 − 0.889539I
b = 0.36679 − 1.72986I
−4.61579 + 0.14727I 0
u = 1.027860 − 0.283936I
a = −0.400907 + 0.889539I
b = 0.36679 + 1.72986I
−4.61579 − 0.14727I 0
u = −0.442077 + 0.972988I
a = 1.158990 − 0.636061I
b = −1.026780 − 0.947011I
−2.97543 + 5.01417I 0
u = −0.442077 − 0.972988I
a = 1.158990 + 0.636061I
b = −1.026780 + 0.947011I
−2.97543 − 5.01417I 0
u = 1.000520 + 0.384416I
a = 0.84725 + 1.13480I
b = 0.11867 + 1.47304I
−7.85810 + 4.18783I 0
u = 1.000520 − 0.384416I
a = 0.84725 − 1.13480I
b = 0.11867 − 1.47304I
−7.85810 − 4.18783I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.633669 + 0.876521I
a = 0.299556 − 0.921499I
b = −1.00999 − 1.36150I
1.75567 + 4.34220I 0
u = −0.633669 − 0.876521I
a = 0.299556 + 0.921499I
b = −1.00999 + 1.36150I
1.75567 − 4.34220I 0
u = −0.708842 + 0.572621I
a = 1.30572 − 0.88155I
b = −0.339536 − 0.635963I
−10.40510 + 0.69580I 0
u = −0.708842 − 0.572621I
a = 1.30572 + 0.88155I
b = −0.339536 + 0.635963I
−10.40510 − 0.69580I 0
u = 0.610838 + 0.902898I
a = 0.715158 + 0.400766I
b = 0.03549 + 1.68791I
−0.92355 − 1.16423I 0
u = 0.610838 − 0.902898I
a = 0.715158 − 0.400766I
b = 0.03549 − 1.68791I
−0.92355 + 1.16423I 0
u = 0.560258 + 0.696446I
a = −0.570660 − 0.624073I
b = 1.002330 − 0.488793I
−0.96818 − 1.42189I 0
u = 0.560258 − 0.696446I
a = −0.570660 + 0.624073I
b = 1.002330 + 0.488793I
−0.96818 + 1.42189I 0
u = −0.303732 + 1.066140I
a = −0.733376 − 0.446451I
b = −0.088832 + 0.426032I
2.36848 − 0.79913I 0
u = −0.303732 − 1.066140I
a = −0.733376 + 0.446451I
b = −0.088832 − 0.426032I
2.36848 + 0.79913I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.266885 + 1.078750I
a = −0.276052 + 0.400419I
b = 0.076490 + 0.488818I
1.10377 − 2.05634I 0
u = 0.266885 − 1.078750I
a = −0.276052 − 0.400419I
b = 0.076490 − 0.488818I
1.10377 + 2.05634I 0
u = −0.456686 + 0.759218I
a = −0.931926 + 1.023090I
b = −0.14489 + 1.45922I
−3.62940 − 1.30889I 0
u = −0.456686 − 0.759218I
a = −0.931926 − 1.023090I
b = −0.14489 − 1.45922I
−3.62940 + 1.30889I 0
u = 0.125732 + 1.107930I
a = 0.837788 + 0.386447I
b = −1.47232 + 0.33107I
−1.85603 + 5.07461I 0
u = 0.125732 − 1.107930I
a = 0.837788 − 0.386447I
b = −1.47232 − 0.33107I
−1.85603 − 5.07461I 0
u = 0.494450 + 0.726951I
a = −0.85345 − 1.22710I
b = 1.39694 − 1.24451I
−1.60214 − 3.42664I 0
u = 0.494450 − 0.726951I
a = −0.85345 + 1.22710I
b = 1.39694 + 1.24451I
−1.60214 + 3.42664I 0
u = 0.127020 + 1.114490I
a = 0.455851 − 0.633263I
b = 1.097710 + 0.273582I
1.16957 + 1.11750I 0
u = 0.127020 − 1.114490I
a = 0.455851 + 0.633263I
b = 1.097710 − 0.273582I
1.16957 − 1.11750I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.168145 + 1.127140I
a = −0.158159 − 0.844049I
b = −0.125944 − 0.188979I
3.53079 − 2.66328I 0
u = 0.168145 − 1.127140I
a = −0.158159 + 0.844049I
b = −0.125944 + 0.188979I
3.53079 + 2.66328I 0
u = 0.700144 + 0.900884I
a = 1.145280 − 0.297858I
b = 0.146788 + 0.452565I
−3.29013 + 0.66050I 0
u = 0.700144 − 0.900884I
a = 1.145280 + 0.297858I
b = 0.146788 − 0.452565I
−3.29013 − 0.66050I 0
u = −0.390874 + 1.081960I
a = 0.750270 − 0.412185I
b = 0.96387 − 1.56771I
−6.93969 + 2.57610I 0
u = −0.390874 − 1.081960I
a = 0.750270 + 0.412185I
b = 0.96387 + 1.56771I
−6.93969 − 2.57610I 0
u = 0.482016 + 1.049150I
a = 0.858899 + 0.746632I
b = −1.51305 + 1.73571I
0.24985 − 7.82066I 0
u = 0.482016 − 1.049150I
a = 0.858899 − 0.746632I
b = −1.51305 − 1.73571I
0.24985 + 7.82066I 0
u = −1.131750 + 0.241574I
a = 0.100307 − 1.130640I
b = −0.678773 − 1.219620I
−10.25730 + 3.14256I 0
u = −1.131750 − 0.241574I
a = 0.100307 + 1.130640I
b = −0.678773 + 1.219620I
−10.25730 − 3.14256I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.214027 + 0.813486I
a = 1.10150 − 1.09864I
b = −0.814823 − 1.152660I
1.16885 + 3.08474I 0
u = −0.214027 − 0.813486I
a = 1.10150 + 1.09864I
b = −0.814823 + 1.152660I
1.16885 − 3.08474I 0
u = −0.649790 + 0.510668I
a = 0.773497 + 0.135585I
b = −0.186296 + 0.931616I
−7.21083 − 0.39117I 0
u = −0.649790 − 0.510668I
a = 0.773497 − 0.135585I
b = −0.186296 − 0.931616I
−7.21083 + 0.39117I 0
u = −0.579659 + 1.036620I
a = 0.742083 − 1.006530I
b = −1.06629 − 1.75122I
0.33040 + 7.23718I 0
u = −0.579659 − 1.036620I
a = 0.742083 + 1.006530I
b = −1.06629 + 1.75122I
0.33040 − 7.23718I 0
u = −0.608949 + 1.025090I
a = 0.555994 + 0.603439I
b = −0.091363 + 0.327585I
−5.72956 + 5.36982I 0
u = −0.608949 − 1.025090I
a = 0.555994 − 0.603439I
b = −0.091363 − 0.327585I
−5.72956 − 5.36982I 0
u = −0.436203 + 1.112580I
a = −0.541794 + 0.639987I
b = 1.04481 + 1.09676I
2.76565 − 0.81161I 0
u = −0.436203 − 1.112580I
a = −0.541794 − 0.639987I
b = 1.04481 − 1.09676I
2.76565 + 0.81161I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.613093 + 0.516769I
a = −1.17848 + 0.78233I
b = 0.04086 + 1.47264I
−1.18560 − 2.48718I 0
u = −0.613093 − 0.516769I
a = −1.17848 − 0.78233I
b = 0.04086 − 1.47264I
−1.18560 + 2.48718I 0
u = 0.575581 + 1.054390I
a = −0.750827 + 0.918826I
b = −0.207997 + 0.084971I
−4.32792 − 12.04850I 0
u = 0.575581 − 1.054390I
a = −0.750827 − 0.918826I
b = −0.207997 − 0.084971I
−4.32792 + 12.04850I 0
u = 0.814552 + 0.918703I
a = 0.010307 − 1.024020I
b = 0.74676 − 1.67595I
−3.37246 − 6.44630I 0
u = 0.814552 − 0.918703I
a = 0.010307 + 1.024020I
b = 0.74676 + 1.67595I
−3.37246 + 6.44630I 0
u = 0.573243 + 0.511294I
a = −1.154820 + 0.608881I
b = −0.199791 + 1.255340I
−5.97031 + 7.35454I 0
u = 0.573243 − 0.511294I
a = −1.154820 − 0.608881I
b = −0.199791 − 1.255340I
−5.97031 − 7.35454I 0
u = 0.448637 + 1.149920I
a = −0.735635 − 0.876913I
b = 0.75668 − 1.20545I
1.30780 − 6.55447I 0
u = 0.448637 − 1.149920I
a = −0.735635 + 0.876913I
b = 0.75668 + 1.20545I
1.30780 + 6.55447I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.505675 + 1.126910I
a = 0.854993 + 0.881546I
b = 0.07486 + 1.46044I
−9.64904 + 1.20544I 0
u = 0.505675 − 1.126910I
a = 0.854993 − 0.881546I
b = 0.07486 − 1.46044I
−9.64904 − 1.20544I 0
u = −0.625956 + 1.065260I
a = −0.464025 + 0.929483I
b = 0.04685 + 1.50346I
−8.88424 + 4.46607I 0
u = −0.625956 − 1.065260I
a = −0.464025 − 0.929483I
b = 0.04685 − 1.50346I
−8.88424 − 4.46607I 0
u = 0.415061 + 1.164620I
a = −0.808416 + 0.297906I
b = 0.578523 − 0.123155I
0.541665 + 0.674438I 0
u = 0.415061 − 1.164620I
a = −0.808416 − 0.297906I
b = 0.578523 + 0.123155I
0.541665 − 0.674438I 0
u = −0.391320 + 1.176750I
a = 0.419634 + 0.768388I
b = 0.281154 + 0.101537I
3.12719 + 8.75276I 0
u = −0.391320 − 1.176750I
a = 0.419634 − 0.768388I
b = 0.281154 − 0.101537I
3.12719 − 8.75276I 0
u = 0.529117 + 0.515088I
a = 0.17738 + 1.41004I
b = 0.07309 + 1.65251I
−1.80834 − 4.97274I 0
u = 0.529117 − 0.515088I
a = 0.17738 − 1.41004I
b = 0.07309 − 1.65251I
−1.80834 + 4.97274I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.552350 + 1.142960I
a = −0.842810 − 0.662161I
b = −0.16534 − 1.82352I
−10.03460 − 9.32684I 0
u = 0.552350 − 1.142960I
a = −0.842810 + 0.662161I
b = −0.16534 + 1.82352I
−10.03460 + 9.32684I 0
u = −0.249519 + 0.685647I
a = −1.81767 + 0.54432I
b = 1.85314 + 0.14047I
−8.55206 + 0.30724I 0
u = −0.249519 − 0.685647I
a = −1.81767 − 0.54432I
b = 1.85314 − 0.14047I
−8.55206 − 0.30724I 0
u = −0.544172 + 1.165270I
a = −0.373268 − 0.595968I
b = 0.341746 − 0.006999I
−3.71802 + 3.39018I 0
u = −0.544172 − 1.165270I
a = −0.373268 + 0.595968I
b = 0.341746 + 0.006999I
−3.71802 − 3.39018I 0
u = −1.295510 + 0.079139I
a = −0.050953 + 0.456006I
b = −0.18642 + 2.25352I
−7.70149 − 1.28594I 0
u = −1.295510 − 0.079139I
a = −0.050953 − 0.456006I
b = −0.18642 − 2.25352I
−7.70149 + 1.28594I 0
u = 0.644292 + 0.276965I
a = −0.625586 − 0.286812I
b = 0.0650896 − 0.0924493I
−1.13811 − 1.22929I 0
u = 0.644292 − 0.276965I
a = −0.625586 + 0.286812I
b = 0.0650896 + 0.0924493I
−1.13811 + 1.22929I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.589086 + 1.163640I
a = 0.679726 + 0.674196I
b = −0.94054 + 1.88497I
−1.89596 − 5.69212I 0
u = 0.589086 − 1.163640I
a = 0.679726 − 0.674196I
b = −0.94054 − 1.88497I
−1.89596 + 5.69212I 0
u = 0.416142 + 0.544802I
a = −0.526173 − 0.598536I
b = 0.880180 + 0.038644I
−0.94869 − 1.38584I 0. + 4.67960I
u = 0.416142 − 0.544802I
a = −0.526173 + 0.598536I
b = 0.880180 − 0.038644I
−0.94869 + 1.38584I 0. − 4.67960I
u = 0.564918 + 0.383332I
a = 1.45545 + 1.93888I
b = −0.708421 + 1.011680I
−12.34290 + 4.70339I −8.84051 + 0.I
u = 0.564918 − 0.383332I
a = 1.45545 − 1.93888I
b = −0.708421 − 1.011680I
−12.34290 − 4.70339I −8.84051 + 0.I
u = 1.279420 + 0.322188I
a = 0.265884 + 0.709923I
b = 0.05481 + 1.79871I
−4.14898 + 0.36457I 0
u = 1.279420 − 0.322188I
a = 0.265884 − 0.709923I
b = 0.05481 − 1.79871I
−4.14898 − 0.36457I 0
u = −0.679447 + 0.013049I
a = 0.864948 − 0.181389I
b = 0.387957 − 0.800762I
−0.31375 + 4.79943I 1.02873 − 5.75401I
u = −0.679447 − 0.013049I
a = 0.864948 + 0.181389I
b = 0.387957 + 0.800762I
−0.31375 − 4.79943I 1.02873 + 5.75401I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.343291 + 0.582586I
a = −1.136990 − 0.510742I
b = −0.05655 − 2.15459I
−1.38479 + 4.08308I 0. − 2.31629I
u = 0.343291 − 0.582586I
a = −1.136990 + 0.510742I
b = −0.05655 + 2.15459I
−1.38479 − 4.08308I 0. + 2.31629I
u = 0.724269 + 1.110850I
a = 0.357258 + 0.703821I
b = −0.60736 + 1.54911I
0.27215 − 4.05186I 0
u = 0.724269 − 1.110850I
a = 0.357258 − 0.703821I
b = −0.60736 − 1.54911I
0.27215 + 4.05186I 0
u = −0.645742 + 1.189570I
a = −0.644003 + 0.838531I
b = 1.15957 + 1.85202I
−0.4180 + 14.6536I 0
u = −0.645742 − 1.189570I
a = −0.644003 − 0.838531I
b = 1.15957 − 1.85202I
−0.4180 − 14.6536I 0
u = 0.216745 + 1.340300I
a = −0.114024 + 0.270673I
b = −0.450190 + 0.108923I
3.89757 − 4.36674I 0
u = 0.216745 − 1.340300I
a = −0.114024 − 0.270673I
b = −0.450190 − 0.108923I
3.89757 + 4.36674I 0
u = 0.679467 + 1.184370I
a = −0.685854 − 1.021870I
b = 0.74889 − 1.82687I
−5.42868 − 10.24140I 0
u = 0.679467 − 1.184370I
a = −0.685854 + 1.021870I
b = 0.74889 + 1.82687I
−5.42868 + 10.24140I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.279570 + 0.508697I
a = −0.655421 − 0.757776I
b = 0.00347 − 1.65050I
−10.4575 + 12.0914I 0
u = 1.279570 − 0.508697I
a = −0.655421 + 0.757776I
b = 0.00347 + 1.65050I
−10.4575 − 12.0914I 0
u = 0.706563 + 1.209930I
a = −0.648502 − 0.723443I
b = 1.15299 − 1.47961I
−1.31805 − 7.01165I 0
u = 0.706563 − 1.209930I
a = −0.648502 + 0.723443I
b = 1.15299 + 1.47961I
−1.31805 + 7.01165I 0
u = 0.326041 + 0.497146I
a = −2.80161 − 1.47093I
b = 0.374915 − 0.577320I
−11.86600 − 5.10117I −3.31976 + 13.71604I
u = 0.326041 − 0.497146I
a = −2.80161 + 1.47093I
b = 0.374915 + 0.577320I
−11.86600 + 5.10117I −3.31976 − 13.71604I
u = −0.80836 + 1.16532I
a = −0.428291 + 0.441966I
b = −0.12334 + 1.63999I
−7.67134 + 3.64800I 0
u = −0.80836 − 1.16532I
a = −0.428291 − 0.441966I
b = −0.12334 − 1.63999I
−7.67134 − 3.64800I 0
u = −1.27764 + 0.63566I
a = 0.600340 − 0.644348I
b = −0.35571 − 1.53116I
−11.12240 − 3.61652I 0
u = −1.27764 − 0.63566I
a = 0.600340 + 0.644348I
b = −0.35571 + 1.53116I
−11.12240 + 3.61652I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.60116 + 1.35195I
a = 0.663090 − 0.813046I
b = −0.72253 − 1.22270I
−5.60159 + 9.06894I 0
u = −0.60116 − 1.35195I
a = 0.663090 + 0.813046I
b = −0.72253 + 1.22270I
−5.60159 − 9.06894I 0
u = −0.81198 + 1.24526I
a = −0.496488 + 0.794285I
b = 0.77989 + 1.88384I
−8.9761 + 11.0061I 0
u = −0.81198 − 1.24526I
a = −0.496488 − 0.794285I
b = 0.77989 − 1.88384I
−8.9761 − 11.0061I 0
u = −0.00068 + 1.48664I
a = 0.398547 + 0.239482I
b = −0.445922 + 0.044881I
3.77813 − 4.67524I 0
u = −0.00068 − 1.48664I
a = 0.398547 − 0.239482I
b = −0.445922 − 0.044881I
3.77813 + 4.67524I 0
u = 0.79017 + 1.26045I
a = 0.539243 + 0.899260I
b = −0.96322 + 1.86450I
−7.9951 − 19.3312I 0
u = 0.79017 − 1.26045I
a = 0.539243 − 0.899260I
b = −0.96322 − 1.86450I
−7.9951 + 19.3312I 0
u = 0.15580 + 1.48534I
a = 0.648674 − 0.013151I
b = 0.140672 + 0.486657I
−1.344860 + 0.071059I 0
u = 0.15580 − 1.48534I
a = 0.648674 + 0.013151I
b = 0.140672 − 0.486657I
−1.344860 − 0.071059I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.259274 + 0.426424I
a = −1.47486 + 0.23951I
b = 0.93919 − 1.44304I
−6.46196 + 0.59813I −2.28013 + 2.06602I
u = −0.259274 − 0.426424I
a = −1.47486 − 0.23951I
b = 0.93919 + 1.44304I
−6.46196 − 0.59813I −2.28013 − 2.06602I
u = 0.378100 + 0.315438I
a = 0.061691 + 0.566245I
b = −1.44940 − 1.89731I
−5.55648 − 7.76279I −8.80485 + 0.13382I
u = 0.378100 − 0.315438I
a = 0.061691 − 0.566245I
b = −1.44940 + 1.89731I
−5.55648 + 7.76279I −8.80485 − 0.13382I
u = 0.460230 + 0.031925I
a = 0.68579 − 2.15652I
b = 0.662368 − 0.658317I
−1.89889 − 2.91214I −2.97212 + 3.96953I
u = 0.460230 − 0.031925I
a = 0.68579 + 2.15652I
b = 0.662368 + 0.658317I
−1.89889 + 2.91214I −2.97212 − 3.96953I
u = −0.294915 + 0.277240I
a = −1.249540 − 0.321400I
b = −0.336044 + 0.469231I
1.112250 − 0.672938I 6.55539 + 1.55226I
u = −0.294915 − 0.277240I
a = −1.249540 + 0.321400I
b = −0.336044 − 0.469231I
1.112250 + 0.672938I 6.55539 − 1.55226I
u = −1.54620 + 0.49174I
a = −0.377594 + 0.642257I
b = 0.07544 + 1.72310I
−10.29290 − 0.46791I 0
u = −1.54620 − 0.49174I
a = −0.377594 − 0.642257I
b = 0.07544 − 1.72310I
−10.29290 + 0.46791I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.89165 + 1.36360I
a = 0.481026 − 0.723766I
b = −1.06851 − 1.68449I
−7.39010 + 8.78873I 0
u = −0.89165 − 1.36360I
a = 0.481026 + 0.723766I
b = −1.06851 + 1.68449I
−7.39010 − 8.78873I 0
u = −0.07002 + 1.81798I
a = −0.515105 + 0.073071I
b = 0.412978 + 0.054824I
−1.39947 + 6.49457I 0
u = −0.07002 − 1.81798I
a = −0.515105 − 0.073071I
b = 0.412978 − 0.054824I
−1.39947 − 6.49457I 0
19
II.
I
u
2
= h2.36×10
30
u
39
+1.06×10
30
u
38
+· · ·+2.44×10
29
b−7.09×10
30
, −7.27×
10
30
u
39
−1.24×10
31
u
38
+· · ·+2.44×10
29
a+2.35×10
30
, u
40
+2u
39
+· · ·+2u+1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
11
=
29.7463u
39
+ 50.6475u
38
+ ··· + 65.2894u − 9.59554
−9.63502u
39
− 4.33277u
38
+ ··· + 7.83294u + 29.0222
a
8
=
−6.24409u
39
− 19.3595u
38
+ ··· + 35.8114u − 21.5391
−6.23997u
39
− 2.63691u
38
+ ··· + 0.390048u + 18.6882
a
9
=
−0.00411436u
39
− 16.7226u
38
+ ··· + 35.4213u − 40.2272
−6.23997u
39
− 2.63691u
38
+ ··· + 0.390048u + 18.6882
a
4
=
29.0169u
39
+ 84.8647u
38
+ ··· + 187.391u + 59.9064
−17.1156u
39
− 44.1846u
38
+ ··· − 71.6652u − 38.0551
a
1
=
−72.8815u
39
− 101.235u
38
+ ··· − 85.0283u + 64.7378
31.8632u
39
+ 60.5309u
38
+ ··· + 81.9156u + 25.0931
a
6
=
u
u
3
+ u
a
12
=
36.4409u
39
+ 55.0238u
38
+ ··· + 61.2585u − 27.0313
−2.59464u
39
+ 4.41572u
38
+ ··· + 15.1332u + 20.5992
a
5
=
7.52128u
39
+ 43.4975u
38
+ ··· + 15.2571u + 72.4110
−5.11574u
39
− 24.7981u
38
+ ··· − 55.2528u − 40.9312
a
10
=
−10.4023u
39
− 4.14132u
38
+ ··· + 31.3326u + 66.7682
11.3636u
39
+ 21.2245u
38
+ ··· + 27.9945u + 10.6085
(ii) Obstruction class = 1
(iii) Cusp Shapes = −56.6554u
39
− 56.7530u
38
+ ··· − 43.5485u + 78.1331
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
− 6u
39
+ ··· + 2u + 1
c
2
u
40
+ 2u
39
+ ··· + 2u + 1
c
3
u
40
+ 7u
38
+ ··· + 22u
2
+ 1
c
4
u
40
+ 15u
38
+ ··· + u + 1
c
5
u
40
+ 26u
38
+ ··· − 7u + 3
c
6
u
40
− 2u
39
+ ··· − 2u + 1
c
7
u
40
+ 12u
39
+ ··· + 6u + 1
c
8
u
40
− 2u
39
+ ··· − 8u + 33
c
9
u
40
− 4u
39
+ ··· − 2u + 1
c
10
u
40
− 12u
39
+ ··· − 6u + 1
c
11
, c
12
u
40
+ 26u
38
+ ··· + 7u + 3
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
+ 8y
39
+ ··· + 10y + 1
c
2
, c
6
y
40
+ 20y
39
+ ··· + 36y + 1
c
3
y
40
+ 14y
39
+ ··· + 44y + 1
c
4
y
40
+ 30y
39
+ ··· + 25y + 1
c
5
, c
11
, c
12
y
40
+ 52y
39
+ ··· + 59y + 9
c
7
, c
10
y
40
+ 22y
39
+ ··· + 32y + 1
c
8
y
40
+ 16y
39
+ ··· + 1256y + 1089
c
9
y
40
+ 8y
39
+ ··· + 20y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.444550 + 0.914413I
a = −0.96905 − 1.21576I
b = −0.041558 − 0.359931I
−2.29584 + 1.76861I −3.60737 − 6.50436I
u = −0.444550 − 0.914413I
a = −0.96905 + 1.21576I
b = −0.041558 + 0.359931I
−2.29584 − 1.76861I −3.60737 + 6.50436I
u = 0.187273 + 0.932085I
a = 0.430639 − 1.322430I
b = 0.317986 − 0.324879I
3.81470 − 0.78259I −4.44356 + 8.12416I
u = 0.187273 − 0.932085I
a = 0.430639 + 1.322430I
b = 0.317986 + 0.324879I
3.81470 + 0.78259I −4.44356 − 8.12416I
u = 0.103709 + 1.052920I
a = 0.162735 − 0.717732I
b = −1.002300 − 0.109719I
0.606419 − 0.422920I 5.92451 − 2.14116I
u = 0.103709 − 1.052920I
a = 0.162735 + 0.717732I
b = −1.002300 + 0.109719I
0.606419 + 0.422920I 5.92451 + 2.14116I
u = −0.157513 + 1.141160I
a = −0.625253 − 0.411431I
b = −0.882706 + 0.389542I
0.72327 − 1.31147I −2.43030 + 8.28751I
u = −0.157513 − 1.141160I
a = −0.625253 + 0.411431I
b = −0.882706 − 0.389542I
0.72327 + 1.31147I −2.43030 − 8.28751I
u = −0.459495 + 1.059880I
a = −0.624357 + 0.471625I
b = −0.79266 + 1.50891I
−6.49496 + 2.48742I 4.09239 − 0.50324I
u = −0.459495 − 1.059880I
a = −0.624357 − 0.471625I
b = −0.79266 − 1.50891I
−6.49496 − 2.48742I 4.09239 + 0.50324I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.327736 + 0.747107I
a = 0.98982 − 1.25683I
b = −1.34302 − 0.87753I
−0.91572 + 3.34905I 6.49485 − 6.47835I
u = −0.327736 − 0.747107I
a = 0.98982 + 1.25683I
b = −1.34302 + 0.87753I
−0.91572 − 3.34905I 6.49485 + 6.47835I
u = −1.186900 + 0.062909I
a = −0.097888 + 0.552757I
b = −0.09909 + 2.48425I
−7.89709 + 0.96908I −11.70952 + 7.02494I
u = −1.186900 − 0.062909I
a = −0.097888 − 0.552757I
b = −0.09909 − 2.48425I
−7.89709 − 0.96908I −11.70952 − 7.02494I
u = 0.722017 + 0.952058I
a = −0.344851 − 0.919898I
b = 0.64926 − 1.60763I
0.15202 − 5.01084I 2.00000 + 7.80911I
u = 0.722017 − 0.952058I
a = −0.344851 + 0.919898I
b = 0.64926 + 1.60763I
0.15202 + 5.01084I 2.00000 − 7.80911I
u = 0.443692 + 1.109600I
a = 0.766187 − 0.292369I
b = −0.430106 + 0.246966I
0.970237 − 0.012243I 3.33159 + 1.87657I
u = 0.443692 − 1.109600I
a = 0.766187 + 0.292369I
b = −0.430106 − 0.246966I
0.970237 + 0.012243I 3.33159 − 1.87657I
u = 0.571025 + 1.110320I
a = −0.766465 − 0.758843I
b = 1.08906 − 1.59059I
−0.71028 − 6.28155I 0. + 6.09192I
u = 0.571025 − 1.110320I
a = −0.766465 + 0.758843I
b = 1.08906 + 1.59059I
−0.71028 + 6.28155I 0. − 6.09192I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.296920 + 0.169850I
a = −0.281347 + 0.913459I
b = −0.126023 + 1.368710I
−10.33980 − 2.19096I 0
u = −1.296920 − 0.169850I
a = −0.281347 − 0.913459I
b = −0.126023 − 1.368710I
−10.33980 + 2.19096I 0
u = 1.302850 + 0.214110I
a = 0.230499 + 0.678527I
b = −0.02376 + 1.81092I
−3.88043 + 0.67833I 0. − 11.89725I
u = 1.302850 − 0.214110I
a = 0.230499 − 0.678527I
b = −0.02376 − 1.81092I
−3.88043 − 0.67833I 0. + 11.89725I
u = −0.200667 + 0.644596I
a = 1.98028 − 0.41743I
b = −1.72532 + 0.25249I
−8.54079 + 0.70829I −5.06182 − 12.00760I
u = −0.200667 − 0.644596I
a = 1.98028 + 0.41743I
b = −1.72532 − 0.25249I
−8.54079 − 0.70829I −5.06182 + 12.00760I
u = 0.412690 + 0.533656I
a = 0.035749 + 0.927287I
b = 1.01970 + 2.36762I
−5.34256 − 8.10456I 1.6796 + 16.4619I
u = 0.412690 − 0.533656I
a = 0.035749 − 0.927287I
b = 1.01970 − 2.36762I
−5.34256 + 8.10456I 1.6796 − 16.4619I
u = 0.233922 + 0.618882I
a = 1.60397 + 0.80050I
b = −0.36236 + 1.48237I
−3.18342 + 2.49347I −1.92849 − 5.48708I
u = 0.233922 − 0.618882I
a = 1.60397 − 0.80050I
b = −0.36236 − 1.48237I
−3.18342 − 2.49347I −1.92849 + 5.48708I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.218148 + 0.583018I
a = −0.91360 + 1.11345I
b = 0.21487 + 2.03800I
−0.98005 + 4.91747I 5.03116 − 8.96155I
u = −0.218148 − 0.583018I
a = −0.91360 − 1.11345I
b = 0.21487 − 2.03800I
−0.98005 − 4.91747I 5.03116 + 8.96155I
u = 0.15771 + 1.47078I
a = 0.346555 + 0.069621I
b = −0.180229 − 0.167427I
3.41178 − 4.33900I 0
u = 0.15771 − 1.47078I
a = 0.346555 − 0.069621I
b = −0.180229 + 0.167427I
3.41178 + 4.33900I 0
u = −0.69434 + 1.33473I
a = 0.638877 − 0.782571I
b = −0.81248 − 1.50925I
−6.41075 + 9.08001I 0
u = −0.69434 − 1.33473I
a = 0.638877 + 0.782571I
b = −0.81248 + 1.50925I
−6.41075 − 9.08001I 0
u = −0.09140 + 1.58151I
a = −0.228927 + 0.057448I
b = 1.188430 − 0.153311I
−0.20447 + 6.13649I 0
u = −0.09140 − 1.58151I
a = −0.228927 − 0.057448I
b = 1.188430 + 0.153311I
−0.20447 − 6.13649I 0
u = −0.057220 + 0.367746I
a = −4.83357 + 0.87437I
b = 0.342300 + 0.508522I
−11.69990 − 4.70526I 5.02386 − 2.74606I
u = −0.057220 − 0.367746I
a = −4.83357 − 0.87437I
b = 0.342300 − 0.508522I
−11.69990 + 4.70526I 5.02386 + 2.74606I
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
40
− 6u
39
+ ··· + 2u + 1)(u
144
− 5u
143
+ ··· − 106u + 17)
c
2
(u
40
+ 2u
39
+ ··· + 2u + 1)(u
144
− u
143
+ ··· + 5896u + 989)
c
3
(u
40
+ 7u
38
+ ··· + 22u
2
+ 1)(u
144
+ u
143
+ ··· − 431616u + 85504)
c
4
(u
40
+ 15u
38
+ ··· + u + 1)(u
144
− u
143
+ ··· + 545u + 307)
c
5
(u
40
+ 26u
38
+ ··· − 7u + 3)(u
144
− u
143
+ ··· + 2435u + 193)
c
6
(u
40
− 2u
39
+ ··· − 2u + 1)(u
144
− u
143
+ ··· + 5896u + 989)
c
7
(u
40
+ 12u
39
+ ··· + 6u + 1)(u
144
− 7u
143
+ ··· + 126358u + 11033)
c
8
(u
40
− 2u
39
+ ··· − 8u + 33)(u
144
+ u
143
+ ··· + 222158u + 28393)
c
9
(u
40
− 4u
39
+ ··· − 2u + 1)(u
144
− 3u
143
+ ··· − 94488u + 22681)
c
10
(u
40
− 12u
39
+ ··· − 6u + 1)(u
144
− 7u
143
+ ··· + 126358u + 11033)
c
11
, c
12
(u
40
+ 26u
38
+ ··· + 7u + 3)(u
144
− u
143
+ ··· + 2435u + 193)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
40
+ 8y
39
+ ··· + 10y + 1)(y
144
+ 17y
143
+ ··· + 8926y + 289)
c
2
, c
6
(y
40
+ 20y
39
+ ··· + 36y + 1)
· (y
144
+ 65y
143
+ ··· + 23149068y + 978121)
c
3
(y
40
+ 14y
39
+ ··· + 44y + 1)
· (y
144
− 5y
143
+ ··· − 279517724672y + 7310934016)
c
4
(y
40
+ 30y
39
+ ··· + 25y + 1)
· (y
144
+ 51y
143
+ ··· + 4212805y + 94249)
c
5
, c
11
, c
12
(y
40
+ 52y
39
+ ··· + 59y + 9)
· (y
144
+ 161y
143
+ ··· + 3654383y + 37249)
c
7
, c
10
(y
40
+ 22y
39
+ ··· + 32y + 1)
· (y
144
+ 87y
143
+ ··· + 4474494936y + 121727089)
c
8
(y
40
+ 16y
39
+ ··· + 1256y + 1089)
· (y
144
+ 25y
143
+ ··· + 51876294512y + 806162449)
c
9
(y
40
+ 8y
39
+ ··· + 20y + 1)
· (y
144
+ 37y
143
+ ··· + 31337234260y + 514427761)
28
