12n
0614
(K12n
0614
)
A knot diagram
1
Linearized knot diagam
3 8 12 1 3 11 1 2 5 4 6 10
Solving Sequence
10,12 1,4
5 3 2 6 9 8 7 11
c
12
c
4
c
3
c
1
c
5
c
9
c
8
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.58062 × 10
138
u
65
+ 4.69453 × 10
138
u
64
+ ··· + 1.96428 × 10
138
b − 6.10934 × 10
138
,
− 5.77959 × 10
138
u
65
+ 1.53536 × 10
139
u
64
+ ··· + 1.96428 × 10
138
a − 8.78790 × 10
138
, u
66
− 3u
65
+ ··· − u + 1i
I
u
2
= h−2.51011 × 10
19
u
29
− 1.59153 × 10
20
u
28
+ ··· + 4.01614 × 10
18
b + 6.48608 × 10
19
,
9.77600 × 10
19
u
29
+ 6.23565 × 10
20
u
28
+ ··· + 4.01614 × 10
18
a − 2.61075 × 10
20
, u
30
+ 6u
29
+ ··· − 5u + 1i
* 2 irreducible components of dim
C
= 0, with total 96 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−2.58 × 10
138
u
65
+ 4.69 × 10
138
u
64
+ · · · + 1.96 × 10
138
b − 6.11 ×
10
138
, −5.78 × 10
138
u
65
+ 1.54 × 10
139
u
64
+ · · · + 1.96 × 10
138
a − 8.79 ×
10
138
, u
66
− 3u
65
+ · · · − u + 1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
2.94235u
65
− 7.81641u
64
+ ··· + 25.6075u + 4.47386
1.31378u
65
− 2.38995u
64
+ ··· − 2.35764u + 3.11022
a
5
=
1.35304u
65
− 5.33630u
64
+ ··· + 26.0334u + 0.352996
1.00899u
65
− 0.212160u
64
+ ··· − 3.05615u + 5.39804
a
3
=
1.62857u
65
− 5.42646u
64
+ ··· + 27.9652u + 1.36363
1.31378u
65
− 2.38995u
64
+ ··· − 2.35764u + 3.11022
a
2
=
2.67431u
65
− 6.60681u
64
+ ··· + 7.51766u + 0.766700
−1.06116u
65
+ 2.61339u
64
+ ··· − 4.02289u + 2.44879
a
6
=
2.56600u
65
− 6.01019u
64
+ ··· + 22.5310u + 4.35095
0.291260u
65
− 1.82499u
64
+ ··· − 2.83835u − 0.458853
a
9
=
−1.65301u
65
+ 3.65430u
64
+ ··· − 1.56313u + 1.16438
0.868094u
65
− 1.36078u
64
+ ··· + 2.50443u − 0.692763
a
8
=
−2.32081u
65
+ 5.95599u
64
+ ··· − 22.5004u + 1.37356
2.29981u
65
− 4.87483u
64
+ ··· + 9.45129u − 0.967867
a
7
=
0.411567u
65
− 0.846993u
64
+ ··· − 14.3635u − 0.600756
1.53761u
65
− 4.15828u
64
+ ··· + 8.11307u − 2.36203
a
11
=
−0.387409u
65
− 0.881551u
64
+ ··· + 2.81929u − 2.83069
−0.986797u
65
+ 2.57596u
64
+ ··· + 2.56990u + 0.0462032
(ii) Obstruction class = −1
(iii) Cusp Shapes = 10.6441u
65
− 22.9856u
64
+ ··· + 3.38658u + 10.7302
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ 15u
65
+ ··· − 3u + 1
c
2
, c
8
u
66
+ u
65
+ ··· + 15u + 1
c
3
u
66
+ 3u
65
+ ··· + 17224u + 1571
c
4
u
66
+ 2u
65
+ ··· − 19824143u + 13993901
c
5
u
66
− 8u
65
+ ··· + 438u + 29
c
6
, c
11
u
66
+ 28u
64
+ ··· − 13u + 1
c
7
u
66
− u
65
+ ··· + 296940149u + 21005497
c
9
u
66
− 4u
65
+ ··· − 10934824u + 2425663
c
10
u
66
− u
65
+ ··· + 10841u + 4167
c
12
u
66
− 3u
65
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
+ 87y
65
+ ··· + 221y + 1
c
2
, c
8
y
66
+ 15y
65
+ ··· − 3y + 1
c
3
y
66
− 25y
65
+ ··· − 67947428y + 2468041
c
4
y
66
+ 52y
65
+ ··· − 1605005892392269y + 195829265197801
c
5
y
66
− 102y
65
+ ··· − 73060y + 841
c
6
, c
11
y
66
+ 56y
65
+ ··· − 55y + 1
c
7
y
66
+ 165y
65
+ ··· + 9982498502631681y + 441230904217009
c
9
y
66
+ 96y
65
+ ··· − 208158950639894y + 5883840989569
c
10
y
66
− 21y
65
+ ··· + 301897937y + 17363889
c
12
y
66
+ 7y
65
+ ··· + 93y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.249527 + 0.973850I
a = −0.269984 + 0.352199I
b = −1.284520 − 0.093761I
3.79747 + 2.06731I 0
u = 0.249527 − 0.973850I
a = −0.269984 − 0.352199I
b = −1.284520 + 0.093761I
3.79747 − 2.06731I 0
u = 0.615318 + 0.828344I
a = −0.02105 + 1.59803I
b = −0.727846 + 0.496461I
0.55976 − 4.92526I 0
u = 0.615318 − 0.828344I
a = −0.02105 − 1.59803I
b = −0.727846 − 0.496461I
0.55976 + 4.92526I 0
u = −0.437096 + 0.815557I
a = 0.405639 − 1.190780I
b = 1.26009 − 1.96901I
12.42740 + 5.70029I 3.74452 − 6.12160I
u = −0.437096 − 0.815557I
a = 0.405639 + 1.190780I
b = 1.26009 + 1.96901I
12.42740 − 5.70029I 3.74452 + 6.12160I
u = 0.033859 + 0.905828I
a = 0.686387 + 0.796402I
b = −0.999476 − 0.290107I
3.53265 + 0.97150I 4.91841 + 0.I
u = 0.033859 − 0.905828I
a = 0.686387 − 0.796402I
b = −0.999476 + 0.290107I
3.53265 − 0.97150I 4.91841 + 0.I
u = −0.682349 + 0.882535I
a = 0.466401 − 1.133650I
b = −0.374389 − 1.078440I
−0.80690 + 2.71270I 0
u = −0.682349 − 0.882535I
a = 0.466401 + 1.133650I
b = −0.374389 + 1.078440I
−0.80690 − 2.71270I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.289401 + 0.832892I
a = −0.352656 + 1.319950I
b = −1.34067 + 1.94518I
13.15070 − 1.94186I 5.70542 − 1.07468I
u = −0.289401 − 0.832892I
a = −0.352656 − 1.319950I
b = −1.34067 − 1.94518I
13.15070 + 1.94186I 5.70542 + 1.07468I
u = 0.359145 + 0.783685I
a = 1.054300 − 0.565207I
b = −0.734467 − 0.404994I
7.06668 + 1.57189I 4.29931 − 7.86449I
u = 0.359145 − 0.783685I
a = 1.054300 + 0.565207I
b = −0.734467 + 0.404994I
7.06668 − 1.57189I 4.29931 + 7.86449I
u = 0.682707 + 0.513106I
a = 0.24428 − 2.03609I
b = 1.067660 − 0.541710I
1.63963 − 5.80606I −5.45360 + 9.71206I
u = 0.682707 − 0.513106I
a = 0.24428 + 2.03609I
b = 1.067660 + 0.541710I
1.63963 + 5.80606I −5.45360 − 9.71206I
u = 0.342573 + 0.774825I
a = −0.00166 + 1.68586I
b = −0.98226 + 1.11174I
3.76909 − 6.48056I 5.17385 + 9.06963I
u = 0.342573 − 0.774825I
a = −0.00166 − 1.68586I
b = −0.98226 − 1.11174I
3.76909 + 6.48056I 5.17385 − 9.06963I
u = 0.409070 + 0.741183I
a = −0.977149 + 0.697862I
b = 0.686979 + 0.481839I
6.87593 − 4.70790I 1.11470 − 3.72537I
u = 0.409070 − 0.741183I
a = −0.977149 − 0.697862I
b = 0.686979 − 0.481839I
6.87593 + 4.70790I 1.11470 + 3.72537I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.601095 + 0.581351I
a = 0.556911 − 0.409109I
b = 1.025200 − 0.590189I
0.136895 + 0.733623I −2.74494 + 0.I
u = 0.601095 − 0.581351I
a = 0.556911 + 0.409109I
b = 1.025200 + 0.590189I
0.136895 − 0.733623I −2.74494 + 0.I
u = −0.428271 + 0.713032I
a = 3.10687 − 0.23646I
b = −0.770827 − 0.716616I
12.07670 − 2.21337I 4.41985 − 2.89857I
u = −0.428271 − 0.713032I
a = 3.10687 + 0.23646I
b = −0.770827 + 0.716616I
12.07670 + 2.21337I 4.41985 + 2.89857I
u = −0.666391 + 0.960759I
a = 0.586302 − 0.825625I
b = −0.342142 − 0.858442I
−0.64111 + 2.45300I 0
u = −0.666391 − 0.960759I
a = 0.586302 + 0.825625I
b = −0.342142 + 0.858442I
−0.64111 − 2.45300I 0
u = −1.178240 + 0.061260I
a = 0.663485 + 0.224665I
b = 0.362141 + 0.169931I
−2.39687 − 0.04300I 0
u = −1.178240 − 0.061260I
a = 0.663485 − 0.224665I
b = 0.362141 − 0.169931I
−2.39687 + 0.04300I 0
u = −0.978455 + 0.724029I
a = −0.184249 + 0.739258I
b = 0.158181 + 1.022200I
−3.11037 + 0.52815I 0
u = −0.978455 − 0.724029I
a = −0.184249 − 0.739258I
b = 0.158181 − 1.022200I
−3.11037 − 0.52815I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.248792 + 0.713501I
a = 0.350874 − 1.113190I
b = −0.795609 − 0.732164I
1.05108 + 1.79441I 1.95797 − 4.33085I
u = −0.248792 − 0.713501I
a = 0.350874 + 1.113190I
b = −0.795609 + 0.732164I
1.05108 − 1.79441I 1.95797 + 4.33085I
u = −0.362005 + 0.647934I
a = −3.73012 − 0.37278I
b = 0.704011 + 0.655660I
12.40550 + 4.61805I 6.00525 − 8.48089I
u = −0.362005 − 0.647934I
a = −3.73012 + 0.37278I
b = 0.704011 − 0.655660I
12.40550 − 4.61805I 6.00525 + 8.48089I
u = 0.766631 + 1.026940I
a = −0.522622 + 0.702186I
b = −1.51898 + 0.65915I
6.16026 − 1.87831I 0
u = 0.766631 − 1.026940I
a = −0.522622 − 0.702186I
b = −1.51898 − 0.65915I
6.16026 + 1.87831I 0
u = 0.983808 + 0.839486I
a = 0.647660 − 1.216280I
b = 1.115270 − 0.152332I
5.26486 − 4.65376I 0
u = 0.983808 − 0.839486I
a = 0.647660 + 1.216280I
b = 1.115270 + 0.152332I
5.26486 + 4.65376I 0
u = 0.053565 + 0.677699I
a = 0.06723 − 2.16764I
b = 0.732638 + 0.191707I
3.59207 + 4.61001I 4.03017 − 6.08936I
u = 0.053565 − 0.677699I
a = 0.06723 + 2.16764I
b = 0.732638 − 0.191707I
3.59207 − 4.61001I 4.03017 + 6.08936I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.887350 + 1.047850I
a = −0.389145 + 0.768196I
b = 0.633717 + 0.991445I
−2.15650 + 6.27128I 0
u = −0.887350 − 1.047850I
a = −0.389145 − 0.768196I
b = 0.633717 − 0.991445I
−2.15650 − 6.27128I 0
u = 0.935204 + 1.043390I
a = 0.322460 − 0.784777I
b = 1.47663 − 0.84266I
3.09240 − 7.98201I 0
u = 0.935204 − 1.043390I
a = 0.322460 + 0.784777I
b = 1.47663 + 0.84266I
3.09240 + 7.98201I 0
u = 0.189006 + 0.539851I
a = −0.14714 − 1.49703I
b = 1.65589 − 1.01498I
1.81042 − 2.05249I 3.67407 + 5.51602I
u = 0.189006 − 0.539851I
a = −0.14714 + 1.49703I
b = 1.65589 + 1.01498I
1.81042 + 2.05249I 3.67407 − 5.51602I
u = 0.98278 + 1.07695I
a = −0.374561 + 0.803029I
b = −0.920434 − 0.084883I
2.95941 + 0.54302I 0
u = 0.98278 − 1.07695I
a = −0.374561 − 0.803029I
b = −0.920434 + 0.084883I
2.95941 − 0.54302I 0
u = 0.96734 + 1.18586I
a = −0.189609 + 1.218970I
b = −1.52025 + 1.03660I
15.3119 − 8.5854I 0
u = 0.96734 − 1.18586I
a = −0.189609 − 1.218970I
b = −1.52025 − 1.03660I
15.3119 + 8.5854I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.97648 + 1.18488I
a = 0.075593 − 1.252430I
b = 1.46536 − 1.04892I
14.4678 − 15.9965I 0
u = 0.97648 − 1.18488I
a = 0.075593 + 1.252430I
b = 1.46536 + 1.04892I
14.4678 + 15.9965I 0
u = 1.28242 + 1.00513I
a = 0.884168 − 0.187959I
b = 1.226060 + 0.549068I
14.3264 + 0.4250I 0
u = 1.28242 − 1.00513I
a = 0.884168 + 0.187959I
b = 1.226060 − 0.549068I
14.3264 − 0.4250I 0
u = 1.30509 + 0.99681I
a = −0.812511 + 0.031797I
b = −1.167660 − 0.660772I
13.4708 + 7.8026I 0
u = 1.30509 − 0.99681I
a = −0.812511 − 0.031797I
b = −1.167660 + 0.660772I
13.4708 − 7.8026I 0
u = −1.13183 + 1.26806I
a = 0.337985 + 0.720296I
b = 1.196830 + 0.393471I
9.15397 + 8.21782I 0
u = −1.13183 − 1.26806I
a = 0.337985 − 0.720296I
b = 1.196830 − 0.393471I
9.15397 − 8.21782I 0
u = 0.045507 + 0.282776I
a = −2.19269 + 1.53645I
b = 0.730632 + 0.344719I
−0.20859 − 1.52213I −3.23626 + 4.72897I
u = 0.045507 − 0.282776I
a = −2.19269 − 1.53645I
b = 0.730632 − 0.344719I
−0.20859 + 1.52213I −3.23626 − 4.72897I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.16315 + 1.29787I
a = −0.388674 − 0.556758I
b = −1.166830 − 0.246261I
9.09525 + 0.92745I 0
u = −1.16315 − 1.29787I
a = −0.388674 + 0.556758I
b = −1.166830 + 0.246261I
9.09525 − 0.92745I 0
u = −0.064829 + 0.176117I
a = 3.07467 − 0.79403I
b = 0.307561 − 0.497960I
−0.217612 + 1.382700I −2.39310 − 4.83328I
u = −0.064829 − 0.176117I
a = 3.07467 + 0.79403I
b = 0.307561 + 0.497960I
−0.217612 − 1.382700I −2.39310 + 4.83328I
u = −1.76296 + 0.61380I
a = 0.0226134 − 0.1199730I
b = 0.341515 − 0.207501I
−4.80865 + 3.88403I 0
u = −1.76296 − 0.61380I
a = 0.0226134 + 0.1199730I
b = 0.341515 + 0.207501I
−4.80865 − 3.88403I 0
11
II.
I
u
2
= h−2.51×10
19
u
29
−1.59×10
20
u
28
+· · ·+4.02×10
18
b+6.49×10
19
, 9.78×
10
19
u
29
+6.24×10
20
u
28
+· · ·+4.02×10
18
a−2.61×10
20
, u
30
+6u
29
+· · ·−5u+1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
−24.3418u
29
− 155.265u
28
+ ··· − 150.976u + 65.0064
6.25007u
29
+ 39.6284u
28
+ ··· + 37.3973u − 16.1500
a
5
=
−33.8102u
29
− 215.601u
28
+ ··· − 210.102u + 90.3706
4.95851u
29
+ 31.7341u
28
+ ··· + 29.2380u − 12.6245
a
3
=
−30.5919u
29
− 194.893u
28
+ ··· − 188.373u + 81.1565
6.25007u
29
+ 39.6284u
28
+ ··· + 37.3973u − 16.1500
a
2
=
−12.1917u
29
− 76.9619u
28
+ ··· − 72.9374u + 39.5688
−0.602753u
29
− 4.04941u
28
+ ··· − 4.64126u + 0.893751
a
6
=
30.2018u
29
+ 191.789u
28
+ ··· + 184.852u − 79.1727
−8.03538u
29
− 51.0463u
28
+ ··· − 51.8658u + 22.2080
a
9
=
28.9293u
29
+ 182.939u
28
+ ··· + 176.262u − 85.9815
−0.978784u
29
− 5.60749u
28
+ ··· − 5.70367u + 3.91752
a
8
=
−44.5210u
29
− 283.726u
28
+ ··· − 280.369u + 118.761
8.60468u
29
+ 54.5709u
28
+ ··· + 55.9046u − 23.6544
a
7
=
−29.1421u
29
− 186.256u
28
+ ··· − 185.982u + 78.5055
10.7566u
29
+ 68.7177u
28
+ ··· + 66.5121u − 28.8516
a
11
=
20.6148u
29
+ 130.865u
28
+ ··· + 127.785u − 60.3047
−1.36890u
29
− 8.61147u
28
+ ··· − 7.61980u + 5.21974
(ii) Obstruction class = 1
(iii) Cusp Shapes =
39236244732154106120
4016136176896476131
u
29
+
247548470797569329746
4016136176896476131
u
28
+ ··· +
198693521190973939460
4016136176896476131
u −
83331556397087838785
4016136176896476131
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
30
− 14u
29
+ ··· − 11u + 1
c
2
u
30
+ 7u
28
+ ··· + u + 1
c
3
u
30
+ 2u
29
+ ··· − 2u + 1
c
4
u
30
+ 5u
29
+ ··· − 3u + 1
c
5
u
30
− 19u
29
+ ··· − 1154u + 131
c
6
u
30
− u
29
+ ··· − u + 1
c
7
u
30
+ 14u
28
+ ··· − 11u + 1
c
8
u
30
+ 7u
28
+ ··· − u + 1
c
9
u
30
+ u
29
+ ··· − 8u
2
+ 1
c
10
u
30
+ 3u
28
+ ··· − u + 1
c
11
u
30
+ u
29
+ ··· + u + 1
c
12
u
30
+ 6u
29
+ ··· − 5u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 18y
29
+ ··· + 27y + 1
c
2
, c
8
y
30
+ 14y
29
+ ··· + 11y + 1
c
3
y
30
− 2y
29
+ ··· − 22y + 1
c
4
y
30
+ 3y
29
+ ··· − 11y + 1
c
5
y
30
− 31y
29
+ ··· − 199614y + 17161
c
6
, c
11
y
30
+ 15y
29
+ ··· + 23y + 1
c
7
y
30
+ 28y
29
+ ··· − 13y + 1
c
9
y
30
+ 7y
29
+ ··· − 16y + 1
c
10
y
30
+ 6y
29
+ ··· − 29y + 1
c
12
y
30
− 2y
29
+ ··· − 9y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.603204 + 0.809374I
a = 0.29660 + 1.47876I
b = −1.094550 + 0.548167I
2.13900 − 4.35109I 1.69957 + 4.49340I
u = 0.603204 − 0.809374I
a = 0.29660 − 1.47876I
b = −1.094550 − 0.548167I
2.13900 + 4.35109I 1.69957 − 4.49340I
u = −0.383848 + 0.902790I
a = −0.618153 − 0.806863I
b = 0.628202 − 0.320445I
6.99548 + 5.21560I 5.06626 − 10.74725I
u = −0.383848 − 0.902790I
a = −0.618153 + 0.806863I
b = 0.628202 + 0.320445I
6.99548 − 5.21560I 5.06626 + 10.74725I
u = −0.648514 + 0.822215I
a = 0.414253 − 1.192590I
b = −0.129028 − 1.014040I
−0.78908 + 3.42720I −3.11722 − 9.43783I
u = −0.648514 − 0.822215I
a = 0.414253 + 1.192590I
b = −0.129028 + 1.014040I
−0.78908 − 3.42720I −3.11722 + 9.43783I
u = −0.404378 + 0.985375I
a = 0.681647 + 0.534909I
b = −0.628799 + 0.188622I
6.97379 − 0.97936I 2.14380 − 4.42680I
u = −0.404378 − 0.985375I
a = 0.681647 − 0.534909I
b = −0.628799 − 0.188622I
6.97379 + 0.97936I 2.14380 + 4.42680I
u = 0.867346 + 0.275922I
a = 0.913209 − 0.704051I
b = 0.930244 − 0.872725I
0.53572 − 1.51138I −2.28158 + 1.95408I
u = 0.867346 − 0.275922I
a = 0.913209 + 0.704051I
b = 0.930244 + 0.872725I
0.53572 + 1.51138I −2.28158 − 1.95408I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.829579 + 0.745332I
a = −0.323807 + 0.916399I
b = 0.20554 + 1.41759I
−2.31096 + 0.01849I −1.78366 + 1.48028I
u = −0.829579 − 0.745332I
a = −0.323807 − 0.916399I
b = 0.20554 − 1.41759I
−2.31096 − 0.01849I −1.78366 − 1.48028I
u = 0.871359 + 0.821323I
a = −0.009677 − 1.032930I
b = 1.180320 − 0.719837I
0.73610 − 8.24067I −2.72267 + 8.70598I
u = 0.871359 − 0.821323I
a = −0.009677 + 1.032930I
b = 1.180320 + 0.719837I
0.73610 + 8.24067I −2.72267 − 8.70598I
u = −0.676814 + 0.987894I
a = 0.735824 − 0.965341I
b = −0.526597 − 0.964939I
−0.22435 + 1.69315I 0.69403 + 2.03206I
u = −0.676814 − 0.987894I
a = 0.735824 + 0.965341I
b = −0.526597 + 0.964939I
−0.22435 − 1.69315I 0.69403 − 2.03206I
u = 0.360737 + 1.177760I
a = −0.017033 + 0.332514I
b = −0.927662 − 0.292814I
2.29381 + 2.51402I −1.19591 − 4.68195I
u = 0.360737 − 1.177760I
a = −0.017033 − 0.332514I
b = −0.927662 + 0.292814I
2.29381 − 2.51402I −1.19591 + 4.68195I
u = −1.231720 + 0.234032I
a = −0.614860 − 0.337013I
b = −0.485297 − 0.003569I
−2.15146 − 0.25175I 6.19891 + 8.76841I
u = −1.231720 − 0.234032I
a = −0.614860 + 0.337013I
b = −0.485297 + 0.003569I
−2.15146 + 0.25175I 6.19891 − 8.76841I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.552473 + 0.462183I
a = −0.98654 + 2.16131I
b = −0.851162 + 0.664272I
2.62025 − 5.69940I 1.20393 + 7.78726I
u = 0.552473 − 0.462183I
a = −0.98654 − 2.16131I
b = −0.851162 − 0.664272I
2.62025 + 5.69940I 1.20393 − 7.78726I
u = −0.800290 + 1.036500I
a = −0.619656 + 0.792306I
b = 0.649238 + 1.178040I
−1.40700 + 6.10902I 2.06343 − 6.00727I
u = −0.800290 − 1.036500I
a = −0.619656 − 0.792306I
b = 0.649238 − 1.178040I
−1.40700 − 6.10902I 2.06343 + 6.00727I
u = 0.172255 + 0.578149I
a = 0.133471 − 0.699001I
b = 1.68863 + 0.23144I
1.73768 + 1.21323I 1.59734 + 2.38690I
u = 0.172255 − 0.578149I
a = 0.133471 + 0.699001I
b = 1.68863 − 0.23144I
1.73768 − 1.21323I 1.59734 − 2.38690I
u = 0.368737 + 0.013777I
a = −1.13147 − 4.66059I
b = −0.111152 + 1.120390I
12.18670 − 3.59085I 2.96392 + 1.72170I
u = 0.368737 − 0.013777I
a = −1.13147 + 4.66059I
b = −0.111152 − 1.120390I
12.18670 + 3.59085I 2.96392 − 1.72170I
u = −1.82097 + 0.60339I
a = 0.146187 + 0.168237I
b = 0.472070 + 0.019838I
−4.66165 + 4.05235I 0
u = −1.82097 − 0.60339I
a = 0.146187 − 0.168237I
b = 0.472070 − 0.019838I
−4.66165 − 4.05235I 0
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
30
− 14u
29
+ ··· − 11u + 1)(u
66
+ 15u
65
+ ··· − 3u + 1)
c
2
(u
30
+ 7u
28
+ ··· + u + 1)(u
66
+ u
65
+ ··· + 15u + 1)
c
3
(u
30
+ 2u
29
+ ··· − 2u + 1)(u
66
+ 3u
65
+ ··· + 17224u + 1571)
c
4
(u
30
+ 5u
29
+ ··· − 3u + 1)
· (u
66
+ 2u
65
+ ··· − 19824143u + 13993901)
c
5
(u
30
− 19u
29
+ ··· − 1154u + 131)(u
66
− 8u
65
+ ··· + 438u + 29)
c
6
(u
30
− u
29
+ ··· − u + 1)(u
66
+ 28u
64
+ ··· − 13u + 1)
c
7
(u
30
+ 14u
28
+ ··· − 11u + 1)
· (u
66
− u
65
+ ··· + 296940149u + 21005497)
c
8
(u
30
+ 7u
28
+ ··· − u + 1)(u
66
+ u
65
+ ··· + 15u + 1)
c
9
(u
30
+ u
29
+ ··· − 8u
2
+ 1)(u
66
− 4u
65
+ ··· − 1.09348 × 10
7
u + 2425663)
c
10
(u
30
+ 3u
28
+ ··· − u + 1)(u
66
− u
65
+ ··· + 10841u + 4167)
c
11
(u
30
+ u
29
+ ··· + u + 1)(u
66
+ 28u
64
+ ··· − 13u + 1)
c
12
(u
30
+ 6u
29
+ ··· − 5u + 1)(u
66
− 3u
65
+ ··· − u + 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
30
+ 18y
29
+ ··· + 27y + 1)(y
66
+ 87y
65
+ ··· + 221y + 1)
c
2
, c
8
(y
30
+ 14y
29
+ ··· + 11y + 1)(y
66
+ 15y
65
+ ··· − 3y + 1)
c
3
(y
30
− 2y
29
+ ··· − 22y + 1)
· (y
66
− 25y
65
+ ··· − 67947428y + 2468041)
c
4
(y
30
+ 3y
29
+ ··· − 11y + 1)
· (y
66
+ 52y
65
+ ··· − 1605005892392269y + 195829265197801)
c
5
(y
30
− 31y
29
+ ··· − 199614y + 17161)
· (y
66
− 102y
65
+ ··· − 73060y + 841)
c
6
, c
11
(y
30
+ 15y
29
+ ··· + 23y + 1)(y
66
+ 56y
65
+ ··· − 55y + 1)
c
7
(y
30
+ 28y
29
+ ··· − 13y + 1)
· (y
66
+ 165y
65
+ ··· + 9982498502631681y + 441230904217009)
c
9
(y
30
+ 7y
29
+ ··· − 16y + 1)
· (y
66
+ 96y
65
+ ··· − 208158950639894y + 5883840989569)
c
10
(y
30
+ 6y
29
+ ··· − 29y + 1)
· (y
66
− 21y
65
+ ··· + 301897937y + 17363889)
c
12
(y
30
− 2y
29
+ ··· − 9y + 1)(y
66
+ 7y
65
+ ··· + 93y + 1)
21
