12n
0862
(K12n
0862
)
A knot diagram
1
Linearized knot diagam
4 7 10 11 2 9 1 3 6 1 5 7
Solving Sequence
7,12
1
5,8
11 4 2 3 6 10 9
c
12
c
7
c
11
c
4
c
1
c
2
c
5
c
10
c
9
c
3
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.13423 × 10
545
u
98
− 8.41031 × 10
545
u
97
+ ··· + 7.71729 × 10
546
b − 9.78140 × 10
546
,
5.62354 × 10
545
u
98
+ 8.39082 × 10
545
u
97
+ ··· + 7.71729 × 10
546
a − 1.14457 × 10
547
, u
99
+ 2u
98
+ ··· − 14u − 1i
I
u
2
= h1.44391 × 10
37
u
35
− 2.21652 × 10
37
u
34
+ ··· + 7.10926 × 10
36
b − 1.15603 × 10
37
,
− 2.43176 × 10
37
u
35
+ 4.52865 × 10
37
u
34
+ ··· + 7.10926 × 10
36
a − 4.98348 × 10
37
, u
36
− u
35
+ ··· − 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 135 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−4.13 × 10
545
u
98
− 8.41 × 10
545
u
97
+ · · · + 7.72 × 10
546
b − 9.78 ×
10
546
, 5.62 × 10
545
u
98
+ 8.39 × 10
545
u
97
+ · · · + 7.72 × 10
546
a − 1.14 ×
10
547
, u
99
+ 2u
98
+ · · · − 14u − 1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
−0.0728693u
98
− 0.108728u
97
+ ··· − 13.0659u + 1.48313
0.0535710u
98
+ 0.108980u
97
+ ··· − 0.601675u + 1.26747
a
8
=
−u
−u
3
+ u
a
11
=
0.0740548u
98
+ 0.178821u
97
+ ··· − 11.5713u + 4.30161
0.0862112u
98
+ 0.164238u
97
+ ··· + 2.60025u + 1.58172
a
4
=
−0.334497u
98
− 0.626075u
97
+ ··· − 12.9486u − 5.18044
−0.0392665u
98
− 0.0482840u
97
+ ··· − 9.63437u − 0.506867
a
2
=
−0.0956699u
98
− 0.257464u
97
+ ··· + 10.1109u − 5.80856
0.00747297u
98
+ 0.0566310u
97
+ ··· − 21.3422u − 3.34556
a
3
=
−0.0956699u
98
− 0.257464u
97
+ ··· + 10.1109u − 5.80856
0.0249836u
98
+ 0.0918021u
97
+ ··· − 22.3636u − 3.41168
a
6
=
0.787689u
98
+ 1.52752u
97
+ ··· − 69.5405u − 9.45597
0.0462208u
98
+ 0.110462u
97
+ ··· − 15.8136u − 2.79226
a
10
=
−0.0192983u
98
+ 0.000252513u
97
+ ··· − 13.6676u + 2.75060
0.0886812u
98
+ 0.169088u
97
+ ··· + 2.62084u + 1.58986
a
9
=
0.509611u
98
+ 0.950444u
97
+ ··· − 68.2325u + 2.11639
0.396273u
98
+ 0.765808u
97
+ ··· − 26.1751u − 0.792660
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.730846u
98
− 1.26329u
97
+ ··· − 88.2611u − 10.4029
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
99
+ 8u
98
+ ··· + 36u − 5
c
2
u
99
− u
98
+ ··· − 20407938u − 31437685
c
3
u
99
− 2u
98
+ ··· − 309043u + 44933
c
4
, c
11
u
99
+ 2u
98
+ ··· + 66361u + 6341
c
5
u
99
− 3u
98
+ ··· − 439231u − 28927
c
6
, c
9
u
99
− 5u
98
+ ··· − 544u + 88
c
7
, c
12
u
99
+ 2u
98
+ ··· − 14u − 1
c
8
u
99
+ u
98
+ ··· + 1415210u − 900451
c
10
u
99
+ 6u
98
+ ··· − 11704u + 191
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
99
− 10y
98
+ ··· − 294y −25
c
2
y
99
+ 41y
98
+ ··· − 24026013786433826y −988328038159225
c
3
y
99
+ 10y
98
+ ··· − 1343708331y −2018974489
c
4
, c
11
y
99
− 90y
98
+ ··· + 1567376929y −40208281
c
5
y
99
+ 47y
98
+ ··· + 82222035835y −836771329
c
6
, c
9
y
99
+ 59y
98
+ ··· − 190880y −7744
c
7
, c
12
y
99
+ 88y
98
+ ··· − 138y −1
c
8
y
99
+ 33y
98
+ ··· − 28122811583158y −810812003401
c
10
y
99
− 46y
98
+ ··· + 118391676y −36481
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.841907 + 0.665859I
a = −0.480654 − 1.217040I
b = 1.174250 − 0.039744I
2.49130 − 4.74543I 0
u = 0.841907 − 0.665859I
a = −0.480654 + 1.217040I
b = 1.174250 + 0.039744I
2.49130 + 4.74543I 0
u = −0.558882 + 0.663005I
a = −0.546261 − 1.222320I
b = 0.502565 + 0.043849I
0.13656 + 4.34462I 0
u = −0.558882 − 0.663005I
a = −0.546261 + 1.222320I
b = 0.502565 − 0.043849I
0.13656 − 4.34462I 0
u = −0.131669 + 1.135030I
a = 0.223696 − 0.439525I
b = −0.458676 + 0.424837I
2.27045 + 1.29976I 0
u = −0.131669 − 1.135030I
a = 0.223696 + 0.439525I
b = −0.458676 − 0.424837I
2.27045 − 1.29976I 0
u = −1.138660 + 0.274741I
a = 0.737094 − 0.887941I
b = 0.330996 − 0.935799I
−2.60891 + 0.42160I 0
u = −1.138660 − 0.274741I
a = 0.737094 + 0.887941I
b = 0.330996 + 0.935799I
−2.60891 − 0.42160I 0
u = 0.025254 + 1.180590I
a = 0.307410 + 0.482375I
b = −0.329710 − 0.747157I
3.11063 − 2.43594I 0
u = 0.025254 − 1.180590I
a = 0.307410 − 0.482375I
b = −0.329710 + 0.747157I
3.11063 + 2.43594I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.806800 + 0.101225I
a = 2.51629 − 0.95511I
b = 0.383951 − 0.268064I
−0.33641 − 6.65531I 0
u = 0.806800 − 0.101225I
a = 2.51629 + 0.95511I
b = 0.383951 + 0.268064I
−0.33641 + 6.65531I 0
u = 1.130000 + 0.503781I
a = −0.02556 − 1.90378I
b = 0.912448 − 0.703140I
−0.94367 − 6.59640I 0
u = 1.130000 − 0.503781I
a = −0.02556 + 1.90378I
b = 0.912448 + 0.703140I
−0.94367 + 6.59640I 0
u = −0.749780
a = 3.85347
b = 0.507829
−4.28603 0
u = −0.172092 + 1.243830I
a = −0.174890 − 0.489493I
b = −0.361805 − 0.145036I
2.59575 + 2.23609I 0
u = −0.172092 − 1.243830I
a = −0.174890 + 0.489493I
b = −0.361805 + 0.145036I
2.59575 − 2.23609I 0
u = 0.734114
a = −2.17128
b = 0.731388
−2.34784 0
u = −0.678779 + 0.269082I
a = 1.23135 + 0.81607I
b = 1.272410 − 0.203025I
−0.912418 − 0.160739I 0
u = −0.678779 − 0.269082I
a = 1.23135 − 0.81607I
b = 1.272410 + 0.203025I
−0.912418 + 0.160739I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.275020 + 0.163285I
a = −0.897049 + 0.290257I
b = 0.813600 + 0.085835I
−3.31462 − 1.01409I 0
u = 1.275020 − 0.163285I
a = −0.897049 − 0.290257I
b = 0.813600 − 0.085835I
−3.31462 + 1.01409I 0
u = 0.366152 + 0.612502I
a = 0.495378 + 0.200281I
b = −0.961051 + 0.092169I
3.17315 + 0.57771I 0
u = 0.366152 − 0.612502I
a = 0.495378 − 0.200281I
b = −0.961051 − 0.092169I
3.17315 − 0.57771I 0
u = 0.320047 + 0.620159I
a = 0.497009 − 0.267226I
b = −0.981853 − 0.461824I
1.49843 + 1.71620I 0
u = 0.320047 − 0.620159I
a = 0.497009 + 0.267226I
b = −0.981853 + 0.461824I
1.49843 − 1.71620I 0
u = −1.364920 + 0.022663I
a = −0.660886 + 0.261525I
b = 0.914002 + 0.084661I
−2.92110 + 1.72300I 0
u = −1.364920 − 0.022663I
a = −0.660886 − 0.261525I
b = 0.914002 − 0.084661I
−2.92110 − 1.72300I 0
u = −0.077138 + 1.372770I
a = 0.091199 − 0.752761I
b = −0.705516 − 0.513272I
2.36200 + 2.20848I 0
u = −0.077138 − 1.372770I
a = 0.091199 + 0.752761I
b = −0.705516 + 0.513272I
2.36200 − 2.20848I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.115603 + 1.381960I
a = 0.71542 + 1.29686I
b = −1.037720 + 0.412533I
7.34093 − 7.61660I 0
u = 0.115603 − 1.381960I
a = 0.71542 − 1.29686I
b = −1.037720 − 0.412533I
7.34093 + 7.61660I 0
u = −1.390590 + 0.253299I
a = 0.504938 − 0.165887I
b = −1.340510 − 0.191286I
7.70793 − 0.30774I 0
u = −1.390590 − 0.253299I
a = 0.504938 + 0.165887I
b = −1.340510 + 0.191286I
7.70793 + 0.30774I 0
u = 0.34035 + 1.37755I
a = −0.206775 + 0.498668I
b = −0.096627 + 0.445266I
6.77160 − 6.21356I 0
u = 0.34035 − 1.37755I
a = −0.206775 − 0.498668I
b = −0.096627 − 0.445266I
6.77160 + 6.21356I 0
u = −0.526678
a = 0.943179
b = 0.689513
−0.952013 −10.9550
u = 0.35927 + 1.43517I
a = 0.373171 − 0.175529I
b = −0.178657 + 1.370660I
7.48264 − 0.43702I 0
u = 0.35927 − 1.43517I
a = 0.373171 + 0.175529I
b = −0.178657 − 1.370660I
7.48264 + 0.43702I 0
u = 0.487130 + 0.161889I
a = 2.74918 − 1.16574I
b = 1.359750 − 0.032280I
3.15153 + 5.69737I 0.323090 − 1.093045I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.487130 − 0.161889I
a = 2.74918 + 1.16574I
b = 1.359750 + 0.032280I
3.15153 − 5.69737I 0.323090 + 1.093045I
u = 0.503721 + 0.078772I
a = 1.59142 − 0.27337I
b = 0.217966 − 0.535658I
2.94519 + 2.79350I −5.37825 − 2.60185I
u = 0.503721 − 0.078772I
a = 1.59142 + 0.27337I
b = 0.217966 + 0.535658I
2.94519 − 2.79350I −5.37825 + 2.60185I
u = −0.283860 + 0.380766I
a = 1.212560 + 0.571324I
b = 0.640597 − 0.599069I
−1.100560 − 0.006892I −10.45174 + 0.21085I
u = −0.283860 − 0.380766I
a = 1.212560 − 0.571324I
b = 0.640597 + 0.599069I
−1.100560 + 0.006892I −10.45174 − 0.21085I
u = 0.14706 + 1.52666I
a = −0.012539 + 0.419450I
b = −0.413730 + 0.752092I
5.56058 + 3.23730I 0
u = 0.14706 − 1.52666I
a = −0.012539 − 0.419450I
b = −0.413730 − 0.752092I
5.56058 − 3.23730I 0
u = 0.12041 + 1.55906I
a = 1.71311 + 0.59107I
b = −1.364850 + 0.053351I
11.04790 + 4.75147I 0
u = 0.12041 − 1.55906I
a = 1.71311 − 0.59107I
b = −1.364850 − 0.053351I
11.04790 − 4.75147I 0
u = 1.59446 + 0.11781I
a = 0.470296 − 0.148956I
b = −1.42228 − 0.28677I
3.02276 + 3.67171I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59446 − 0.11781I
a = 0.470296 + 0.148956I
b = −1.42228 + 0.28677I
3.02276 − 3.67171I 0
u = 0.04772 + 1.60438I
a = 1.367460 + 0.152126I
b = −1.54935 + 0.63664I
12.06290 − 7.00092I 0
u = 0.04772 − 1.60438I
a = 1.367460 − 0.152126I
b = −1.54935 − 0.63664I
12.06290 + 7.00092I 0
u = −0.01871 + 1.60873I
a = −1.61348 + 0.03894I
b = 1.58139 − 0.02708I
10.52470 − 0.08002I 0
u = −0.01871 − 1.60873I
a = −1.61348 − 0.03894I
b = 1.58139 + 0.02708I
10.52470 + 0.08002I 0
u = −0.04319 + 1.61215I
a = 1.90412 − 0.14400I
b = −1.240570 + 0.030624I
5.52663 − 2.36605I 0
u = −0.04319 − 1.61215I
a = 1.90412 + 0.14400I
b = −1.240570 − 0.030624I
5.52663 + 2.36605I 0
u = 0.09411 + 1.62140I
a = 1.57411 + 0.01957I
b = −1.311230 − 0.324208I
6.50816 + 6.43237I 0
u = 0.09411 − 1.62140I
a = 1.57411 − 0.01957I
b = −1.311230 + 0.324208I
6.50816 − 6.43237I 0
u = −0.40126 + 1.58028I
a = 0.315133 + 0.055054I
b = −0.25564 − 1.43131I
2.35561 + 5.41845I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.40126 − 1.58028I
a = 0.315133 − 0.055054I
b = −0.25564 + 1.43131I
2.35561 − 5.41845I 0
u = −0.09574 + 1.63425I
a = 1.65669 − 0.13609I
b = −1.297230 + 0.168492I
5.38317 − 3.33321I 0
u = −0.09574 − 1.63425I
a = 1.65669 + 0.13609I
b = −1.297230 − 0.168492I
5.38317 + 3.33321I 0
u = 0.32785 + 1.60601I
a = 0.245188 − 0.074585I
b = −0.27399 + 1.39829I
5.94803 − 11.21930I 0
u = 0.32785 − 1.60601I
a = 0.245188 + 0.074585I
b = −0.27399 − 1.39829I
5.94803 + 11.21930I 0
u = −0.15468 + 1.66146I
a = 1.374040 − 0.309901I
b = −1.52586 + 0.10620I
7.11961 − 5.54819I 0
u = −0.15468 − 1.66146I
a = 1.374040 + 0.309901I
b = −1.52586 − 0.10620I
7.11961 + 5.54819I 0
u = −0.71253 + 1.55073I
a = −1.36949 + 0.72327I
b = 1.48889 + 0.52726I
12.8693 + 6.8764I 0
u = −0.71253 − 1.55073I
a = −1.36949 − 0.72327I
b = 1.48889 − 0.52726I
12.8693 − 6.8764I 0
u = −0.04063 + 1.70758I
a = 1.278400 − 0.060583I
b = −1.75827 − 0.48827I
7.56157 + 3.30858I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04063 − 1.70758I
a = 1.278400 + 0.060583I
b = −1.75827 + 0.48827I
7.56157 − 3.30858I 0
u = 0.09804 + 1.70887I
a = 1.322810 + 0.138996I
b = −1.58383 − 0.20996I
6.40985 + 3.35174I 0
u = 0.09804 − 1.70887I
a = 1.322810 − 0.138996I
b = −1.58383 + 0.20996I
6.40985 − 3.35174I 0
u = −0.078333 + 0.268938I
a = 2.24092 − 1.99047I
b = 0.835453 + 0.478092I
−0.24867 + 4.16049I −7.66355 − 7.49884I
u = −0.078333 − 0.268938I
a = 2.24092 + 1.99047I
b = 0.835453 − 0.478092I
−0.24867 − 4.16049I −7.66355 + 7.49884I
u = 0.21066 + 1.72405I
a = 1.165180 + 0.153518I
b = −1.94902 + 0.92546I
9.84065 + 2.24703I 0
u = 0.21066 − 1.72405I
a = 1.165180 − 0.153518I
b = −1.94902 − 0.92546I
9.84065 − 2.24703I 0
u = 0.206008 + 0.095507I
a = 4.40218 + 1.16103I
b = 1.149320 − 0.378794I
5.56039 − 6.41977I −1.64714 + 6.90816I
u = 0.206008 − 0.095507I
a = 4.40218 − 1.16103I
b = 1.149320 + 0.378794I
5.56039 + 6.41977I −1.64714 − 6.90816I
u = 0.76917 + 1.60242I
a = −1.173590 − 0.564908I
b = 1.392800 − 0.185453I
8.15426 − 4.21056I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.76917 − 1.60242I
a = −1.173590 + 0.564908I
b = 1.392800 + 0.185453I
8.15426 + 4.21056I 0
u = −0.110856 + 0.169303I
a = 1.76909 − 0.13498I
b = 0.382443 + 0.713139I
−1.02164 − 2.30830I −7.48322 − 1.56595I
u = −0.110856 − 0.169303I
a = 1.76909 + 0.13498I
b = 0.382443 − 0.713139I
−1.02164 + 2.30830I −7.48322 + 1.56595I
u = −0.063091 + 0.187939I
a = 1.72582 + 0.32469I
b = 0.494125 − 0.690437I
−1.67668 − 0.04041I −5.30445 + 0.32910I
u = −0.063091 − 0.187939I
a = 1.72582 − 0.32469I
b = 0.494125 + 0.690437I
−1.67668 + 0.04041I −5.30445 − 0.32910I
u = −1.82926 + 0.02603I
a = 0.482654 − 0.123459I
b = −1.47654 − 0.21993I
6.01817 + 9.10369I 0
u = −1.82926 − 0.02603I
a = 0.482654 + 0.123459I
b = −1.47654 + 0.21993I
6.01817 − 9.10369I 0
u = 0.76157 + 1.67204I
a = −1.25771 − 0.64738I
b = 1.52331 − 0.55961I
7.9115 − 12.2028I 0
u = 0.76157 − 1.67204I
a = −1.25771 + 0.64738I
b = 1.52331 + 0.55961I
7.9115 + 12.2028I 0
u = −0.71606 + 1.72620I
a = −1.261790 + 0.582601I
b = 1.54412 + 0.55478I
11.6473 + 17.9875I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.71606 − 1.72620I
a = −1.261790 − 0.582601I
b = 1.54412 − 0.55478I
11.6473 − 17.9875I 0
u = −0.0974023 + 0.0623725I
a = 3.28317 + 1.01195I
b = 1.107660 − 0.597656I
1.08848 − 7.32595I 2.34406 + 1.32437I
u = −0.0974023 − 0.0623725I
a = 3.28317 − 1.01195I
b = 1.107660 + 0.597656I
1.08848 + 7.32595I 2.34406 − 1.32437I
u = −0.0066835 + 0.1147270I
a = 3.13072 − 1.30877I
b = 1.024890 + 0.566210I
−0.11428 + 4.80264I −3.65062 − 12.30393I
u = −0.0066835 − 0.1147270I
a = 3.13072 + 1.30877I
b = 1.024890 − 0.566210I
−0.11428 − 4.80264I −3.65062 + 12.30393I
u = −0.61470 + 1.78428I
a = −1.201800 + 0.424412I
b = 1.48580 + 0.18410I
11.96160 + 0.01213I 0
u = −0.61470 − 1.78428I
a = −1.201800 − 0.424412I
b = 1.48580 − 0.18410I
11.96160 − 0.01213I 0
u = −0.89738 + 1.67398I
a = −1.097410 + 0.546329I
b = 1.377410 + 0.235887I
11.5998 + 8.9491I 0
u = −0.89738 − 1.67398I
a = −1.097410 − 0.546329I
b = 1.377410 − 0.235887I
11.5998 − 8.9491I 0
14
II.
I
u
2
= h1.44×10
37
u
35
−2.22×10
37
u
34
+· · ·+7.11×10
36
b−1.16×10
37
, −2.43×
10
37
u
35
+4.53×10
37
u
34
+· · ·+7.11×10
36
a−4.98×10
37
, u
36
−u
35
+· · ·−2u−1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
3.42056u
35
− 6.37007u
34
+ ··· − 9.08919u + 7.00984
−2.03103u
35
+ 3.11780u
34
+ ··· + 2.58945u + 1.62609
a
8
=
−u
−u
3
+ u
a
11
=
−0.641007u
35
+ 2.22410u
34
+ ··· + 5.52246u − 8.65232
−1.31983u
35
+ 2.36282u
34
+ ··· + 1.54791u + 1.56671
a
4
=
3.24316u
35
− 4.97900u
34
+ ··· − 4.88135u − 0.259154
−1.85425u
35
+ 2.56540u
34
+ ··· + 1.97687u + 3.65637
a
2
=
−5.75723u
35
+ 8.87108u
34
+ ··· + 5.24889u + 6.22644
2.65462u
35
− 4.56701u
34
+ ··· − 3.04349u − 1.83423
a
3
=
−5.75723u
35
+ 8.87108u
34
+ ··· + 5.24889u + 6.22644
0.831439u
35
− 1.97606u
34
+ ··· − 2.57303u + 1.27961
a
6
=
−6.11435u
35
+ 8.23226u
34
+ ··· − 1.34294u + 17.7253
3.05021u
35
− 5.25482u
34
+ ··· − 2.82856u − 3.66053
a
10
=
−1.38953u
35
+ 3.25228u
34
+ ··· + 6.49974u − 8.63593
−1.45293u
35
+ 2.48165u
34
+ ··· + 1.35868u + 1.84636
a
9
=
5.02428u
35
− 7.81497u
34
+ ··· − 8.04860u − 10.1028
1.31065u
35
− 1.56847u
34
+ ··· + 0.857942u − 3.37089
(ii) Obstruction class = 1
(iii) Cusp Shapes = 27.4389u
35
− 44.6719u
34
+ ··· − 34.3494u − 47.9556
15
(iv) u-Polynomials at the component
16
Crossings u-Polynomials at each crossing
c
1
u
36
− 21u
35
+ ··· + 2u − 1
c
2
u
36
− 7u
34
+ ··· + 11u
2
− 1
c
3
u
36
− 3u
35
+ ··· + 3u + 1
c
4
u
36
− u
35
+ ··· − u − 1
c
5
u
36
+ 2u
34
+ ··· − 49u − 5
c
6
u
36
− 8u
35
+ ··· − 52u + 8
c
7
u
36
+ u
35
+ ··· + 2u − 1
c
8
u
36
− 9u
34
+ ··· − 2u + 1
c
9
u
36
+ 8u
35
+ ··· + 52u + 8
c
10
u
36
+ 11u
35
+ ··· − 6u − 1
c
11
u
36
+ u
35
+ ··· + u − 1
c
12
u
36
− u
35
+ ··· − 2u − 1
17
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
− 17y
35
+ ··· − 18y + 1
c
2
y
36
− 14y
35
+ ··· − 22y + 1
c
3
y
36
− 13y
35
+ ··· − y + 1
c
4
, c
11
y
36
− 33y
35
+ ··· − 17y + 1
c
5
y
36
+ 4y
35
+ ··· + 329y + 25
c
6
, c
9
y
36
+ 20y
35
+ ··· + 816y + 64
c
7
, c
12
y
36
+ 13y
35
+ ··· − 18y + 1
c
8
y
36
− 18y
35
+ ··· − 10y + 1
c
10
y
36
− 13y
35
+ ··· − 16y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.933978 + 0.264392I
a = −0.951125 + 0.787457I
b = −0.110086 + 0.813600I
−3.05609 + 0.45050I −16.5545 − 1.0085I
u = −0.933978 − 0.264392I
a = −0.951125 − 0.787457I
b = −0.110086 − 0.813600I
−3.05609 − 0.45050I −16.5545 + 1.0085I
u = −0.843660
a = −1.17925
b = 0.380590
−3.07766 −15.7190
u = −0.000828 + 1.169490I
a = 0.489625 − 0.413020I
b = −0.197521 + 0.366303I
1.98881 + 1.75644I −9.99638 − 6.31597I
u = −0.000828 − 1.169490I
a = 0.489625 + 0.413020I
b = −0.197521 − 0.366303I
1.98881 − 1.75644I −9.99638 + 6.31597I
u = −0.079255 + 0.798291I
a = 0.40042 + 1.42271I
b = −0.588235 − 0.406172I
4.41221 − 2.72786I 2.45795 + 3.77656I
u = −0.079255 − 0.798291I
a = 0.40042 − 1.42271I
b = −0.588235 + 0.406172I
4.41221 + 2.72786I 2.45795 − 3.77656I
u = 1.042160 + 0.604650I
a = 0.35792 + 2.09607I
b = −0.966126 + 0.621760I
−1.12414 − 6.38280I −14.9037 − 4.1510I
u = 1.042160 − 0.604650I
a = 0.35792 − 2.09607I
b = −0.966126 − 0.621760I
−1.12414 + 6.38280I −14.9037 + 4.1510I
u = 0.504737 + 0.607203I
a = −0.956754 + 0.326325I
b = 0.631344 + 0.573526I
−0.80766 − 3.25952I −5.28373 + 4.58456I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.504737 − 0.607203I
a = −0.956754 − 0.326325I
b = 0.631344 − 0.573526I
−0.80766 + 3.25952I −5.28373 − 4.58456I
u = −0.741509 + 0.266947I
a = −1.49012 − 0.26016I
b = −1.45690 + 0.59412I
−0.806411 − 0.462384I 4.6062 + 18.2130I
u = −0.741509 − 0.266947I
a = −1.49012 + 0.26016I
b = −1.45690 − 0.59412I
−0.806411 + 0.462384I 4.6062 − 18.2130I
u = 0.730985 + 0.222082I
a = −1.40211 + 1.09483I
b = −1.385760 + 0.151946I
2.86751 − 6.34395I −4.36129 + 11.79304I
u = 0.730985 − 0.222082I
a = −1.40211 − 1.09483I
b = −1.385760 − 0.151946I
2.86751 + 6.34395I −4.36129 − 11.79304I
u = −1.248490 + 0.269258I
a = −0.845857 − 0.140881I
b = 0.848036 − 0.217008I
−3.42093 + 0.63578I −11.32870 + 7.98607I
u = −1.248490 − 0.269258I
a = −0.845857 + 0.140881I
b = 0.848036 + 0.217008I
−3.42093 − 0.63578I −11.32870 − 7.98607I
u = 0.178545 + 1.294760I
a = −0.439829 − 0.979967I
b = 0.985010 − 0.410304I
7.82429 − 7.37095I 5.35667 + 5.36931I
u = 0.178545 − 1.294760I
a = −0.439829 + 0.979967I
b = 0.985010 + 0.410304I
7.82429 + 7.37095I 5.35667 − 5.36931I
u = −0.028226 + 1.317640I
a = 0.355990 + 0.458054I
b = 0.604381 + 0.375933I
2.38848 + 2.70269I −8.6681 − 13.6821I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.028226 − 1.317640I
a = 0.355990 − 0.458054I
b = 0.604381 − 0.375933I
2.38848 − 2.70269I −8.6681 + 13.6821I
u = 0.529165 + 0.370552I
a = −0.460011 + 0.394367I
b = 1.100350 + 0.576229I
−0.24462 + 4.33021I −7.90307 + 3.12935I
u = 0.529165 − 0.370552I
a = −0.460011 − 0.394367I
b = 1.100350 − 0.576229I
−0.24462 − 4.33021I −7.90307 − 3.12935I
u = −0.581297 + 0.258694I
a = −0.520779 + 0.436766I
b = 1.077910 + 0.535598I
0.72055 + 7.65074I −10.2916 − 12.5302I
u = −0.581297 − 0.258694I
a = −0.520779 − 0.436766I
b = 1.077910 − 0.535598I
0.72055 − 7.65074I −10.2916 + 12.5302I
u = 1.49418 + 0.18399I
a = −0.703476 + 0.117939I
b = 1.064640 + 0.190926I
−2.63110 + 2.23325I 0
u = 1.49418 − 0.18399I
a = −0.703476 − 0.117939I
b = 1.064640 − 0.190926I
−2.63110 − 2.23325I 0
u = −0.461663 + 0.164231I
a = 5.34764 + 2.96273I
b = −0.785476 − 0.073442I
0.32040 + 6.52647I −1.05599 − 6.20509I
u = −0.461663 − 0.164231I
a = 5.34764 − 2.96273I
b = −0.785476 + 0.073442I
0.32040 − 6.52647I −1.05599 + 6.20509I
u = 0.25924 + 1.49913I
a = 1.50473 + 0.43312I
b = −1.42803 − 0.15494I
8.15186 + 4.94827I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25924 − 1.49913I
a = 1.50473 − 0.43312I
b = −1.42803 + 0.15494I
8.15186 − 4.94827I 0
u = 0.452642
a = 7.57265
b = −0.803257
−3.75887 −7.14540
u = 0.13856 + 1.70888I
a = −1.240340 − 0.207170I
b = 1.81020 − 0.51076I
9.42435 + 2.44760I 0
u = 0.13856 − 1.70888I
a = −1.240340 + 0.207170I
b = 1.81020 + 0.51076I
9.42435 − 2.44760I 0
u = −0.10682 + 1.77968I
a = 1.357380 − 0.135941I
b = −1.49240 + 0.18207I
7.01957 − 4.09701I 0
u = −0.10682 − 1.77968I
a = 1.357380 + 0.135941I
b = −1.49240 − 0.18207I
7.01957 + 4.09701I 0
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
36
− 21u
35
+ ··· + 2u − 1)(u
99
+ 8u
98
+ ··· + 36u − 5)
c
2
(u
36
− 7u
34
+ ··· + 11u
2
− 1)
· (u
99
− u
98
+ ··· − 20407938u − 31437685)
c
3
(u
36
− 3u
35
+ ··· + 3u + 1)(u
99
− 2u
98
+ ··· − 309043u + 44933)
c
4
(u
36
− u
35
+ ··· − u − 1)(u
99
+ 2u
98
+ ··· + 66361u + 6341)
c
5
(u
36
+ 2u
34
+ ··· − 49u − 5)(u
99
− 3u
98
+ ··· − 439231u − 28927)
c
6
(u
36
− 8u
35
+ ··· − 52u + 8)(u
99
− 5u
98
+ ··· − 544u + 88)
c
7
(u
36
+ u
35
+ ··· + 2u − 1)(u
99
+ 2u
98
+ ··· − 14u − 1)
c
8
(u
36
− 9u
34
+ ··· − 2u + 1)(u
99
+ u
98
+ ··· + 1415210u − 900451)
c
9
(u
36
+ 8u
35
+ ··· + 52u + 8)(u
99
− 5u
98
+ ··· − 544u + 88)
c
10
(u
36
+ 11u
35
+ ··· − 6u − 1)(u
99
+ 6u
98
+ ··· − 11704u + 191)
c
11
(u
36
+ u
35
+ ··· + u − 1)(u
99
+ 2u
98
+ ··· + 66361u + 6341)
c
12
(u
36
− u
35
+ ··· − 2u − 1)(u
99
+ 2u
98
+ ··· − 14u − 1)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
36
− 17y
35
+ ··· − 18y + 1)(y
99
− 10y
98
+ ··· − 294y −25)
c
2
(y
36
− 14y
35
+ ··· − 22y + 1)
· (y
99
+ 41y
98
+ ··· − 24026013786433826y −988328038159225)
c
3
(y
36
− 13y
35
+ ··· − y + 1)
· (y
99
+ 10y
98
+ ··· − 1343708331y −2018974489)
c
4
, c
11
(y
36
− 33y
35
+ ··· − 17y + 1)
· (y
99
− 90y
98
+ ··· + 1567376929y −40208281)
c
5
(y
36
+ 4y
35
+ ··· + 329y + 25)
· (y
99
+ 47y
98
+ ··· + 82222035835y −836771329)
c
6
, c
9
(y
36
+ 20y
35
+ ··· + 816y + 64)(y
99
+ 59y
98
+ ··· − 190880y −7744)
c
7
, c
12
(y
36
+ 13y
35
+ ··· − 18y + 1)(y
99
+ 88y
98
+ ··· − 138y −1)
c
8
(y
36
− 18y
35
+ ··· − 10y + 1)
· (y
99
+ 33y
98
+ ··· − 28122811583158y −810812003401)
c
10
(y
36
− 13y
35
+ ··· − 16y + 1)
· (y
99
− 46y
98
+ ··· + 118391676y −36481)
25
