11a
2
(K11a
2
)
A knot diagram
1
Linearized knot diagam
5 1 7 2 3 9 4 11 6 8 10
Solving Sequence
4,7 8,11
9 3 6 5 10 1 2
c
7
c
8
c
3
c
6
c
5
c
10
c
11
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.43741 × 10
171
u
78
− 5.11274 × 10
171
u
77
+ ··· + 1.98334 × 10
172
b − 2.82335 × 10
173
,
− 1.22224 × 10
171
u
78
+ 1.44341 × 10
172
u
77
+ ··· + 1.58667 × 10
173
a + 1.86038 × 10
174
,
u
79
+ 2u
78
+ ··· + 224u + 64i
I
u
2
= hu
2
+ b, u
4
− 2u
3
− u
2
+ a + 3u + 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
v
1
= ha, −18v
5
− 63v
4
− 193v
3
− 63v
2
+ 55b + 27v + 12, v
6
+ 2v
5
+ 7v
4
− 8v
3
+ 7v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 90 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−5.44 × 10
171
u
78
− 5.11 × 10
171
u
77
+ · · · + 1.98 × 10
172
b − 2.82 ×
10
173
, −1.22 × 10
171
u
78
+ 1.44 × 10
172
u
77
+ · · · + 1.59 × 10
173
a + 1.86 ×
10
174
, u
79
+ 2u
78
+ · · · + 224u + 64i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
0.00770315u
78
− 0.0909705u
77
+ ··· − 27.2773u − 11.7250
0.274154u
78
+ 0.257784u
77
+ ··· + 36.6907u + 14.2353
a
9
=
0.0515299u
78
− 0.0134218u
77
+ ··· − 14.2684u − 3.89351
−0.204276u
78
− 0.212923u
77
+ ··· − 35.5855u − 11.5905
a
3
=
u
u
a
6
=
−0.0432551u
78
− 0.0953382u
77
+ ··· − 17.7659u − 9.19854
0.0600517u
78
+ 0.0392781u
77
+ ··· + 5.74611u − 3.52633
a
5
=
−0.0400019u
78
− 0.0348387u
77
+ ··· − 8.25015u − 4.59071
0.0633049u
78
+ 0.0997776u
77
+ ··· + 15.2619u + 1.08150
a
10
=
0.102479u
78
− 0.00813482u
77
+ ··· − 13.9221u − 4.29785
0.401016u
78
+ 0.368694u
77
+ ··· + 54.5295u + 21.0651
a
1
=
−0.103307u
78
− 0.134616u
77
+ ··· − 23.5120u − 5.67221
−0.0633049u
78
− 0.0997776u
77
+ ··· − 15.2619u − 1.08150
a
2
=
0.140138u
78
+ 0.241968u
77
+ ··· + 33.5462u + 15.5291
0.278386u
78
+ 0.429982u
77
+ ··· + 64.6729u + 27.3218
a
2
=
0.140138u
78
+ 0.241968u
77
+ ··· + 33.5462u + 15.5291
0.278386u
78
+ 0.429982u
77
+ ··· + 64.6729u + 27.3218
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0683647u
78
+ 0.114454u
77
+ ··· − 17.3139u − 1.86024
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
79
+ 5u
78
+ ··· + 12u + 1
c
2
u
79
+ 39u
78
+ ··· + 42u − 1
c
3
, c
7
u
79
+ 2u
78
+ ··· + 224u + 64
c
5
u
79
− 5u
78
+ ··· + 14176u + 3137
c
6
, c
9
u
79
− 3u
78
+ ··· − 192u + 32
c
8
, c
10
u
79
− 8u
78
+ ··· − 5u + 1
c
11
u
79
+ 38u
78
+ ··· − 137u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
79
+ 39y
78
+ ··· + 42y −1
c
2
y
79
+ 7y
78
+ ··· + 2238y −1
c
3
, c
7
y
79
− 40y
78
+ ··· + 91136y −4096
c
5
y
79
− 25y
78
+ ··· + 636907866y −9840769
c
6
, c
9
y
79
+ 39y
78
+ ··· − 15872y −1024
c
8
, c
10
y
79
− 38y
78
+ ··· − 137y −1
c
11
y
79
+ 14y
78
+ ··· + 11687y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.853592 + 0.508882I
a = −0.055782 + 1.086980I
b = 0.385053 − 0.112918I
2.66697 − 2.36282I −4.65001 + 1.65972I
u = −0.853592 − 0.508882I
a = −0.055782 − 1.086980I
b = 0.385053 + 0.112918I
2.66697 + 2.36282I −4.65001 − 1.65972I
u = −0.440363 + 0.912546I
a = 0.724174 + 0.449379I
b = −0.699520 − 0.426408I
−0.27585 + 2.15811I −7.00000 − 4.29711I
u = −0.440363 − 0.912546I
a = 0.724174 − 0.449379I
b = −0.699520 + 0.426408I
−0.27585 − 2.15811I −7.00000 + 4.29711I
u = 0.320495 + 0.912395I
a = 0.249632 − 0.939746I
b = 1.37567 + 0.42738I
−2.34704 + 4.31468I −10.21762 − 4.57210I
u = 0.320495 − 0.912395I
a = 0.249632 + 0.939746I
b = 1.37567 − 0.42738I
−2.34704 − 4.31468I −10.21762 + 4.57210I
u = 0.567410 + 0.878865I
a = 0.595821 − 0.532012I
b = −0.237797 + 0.089887I
3.87103 − 0.09665I 0
u = 0.567410 − 0.878865I
a = 0.595821 + 0.532012I
b = −0.237797 − 0.089887I
3.87103 + 0.09665I 0
u = −0.890520 + 0.328701I
a = 0.424564 + 0.261362I
b = 0.946519 + 0.465471I
−1.024930 + 0.378054I −6.69847 + 0.35322I
u = −0.890520 − 0.328701I
a = 0.424564 − 0.261362I
b = 0.946519 − 0.465471I
−1.024930 − 0.378054I −6.69847 − 0.35322I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.913716 + 0.570561I
a = −0.226843 − 0.736350I
b = 0.189637 + 0.143627I
3.68282 − 2.87436I 0
u = 0.913716 − 0.570561I
a = −0.226843 + 0.736350I
b = 0.189637 − 0.143627I
3.68282 + 2.87436I 0
u = −1.045420 + 0.303052I
a = 2.58858 + 0.40116I
b = 1.81492 − 0.66339I
1.18747 + 2.48169I 0
u = −1.045420 − 0.303052I
a = 2.58858 − 0.40116I
b = 1.81492 + 0.66339I
1.18747 − 2.48169I 0
u = −0.809973 + 0.391729I
a = 0.515617 + 0.419812I
b = −0.258885 + 0.774414I
2.91495 + 6.10945I −7.82272 − 8.97445I
u = −0.809973 − 0.391729I
a = 0.515617 − 0.419812I
b = −0.258885 − 0.774414I
2.91495 − 6.10945I −7.82272 + 8.97445I
u = 0.404716 + 1.023830I
a = 0.584705 + 0.288653I
b = −1.81023 + 0.83355I
2.22736 + 5.03014I 0
u = 0.404716 − 1.023830I
a = 0.584705 − 0.288653I
b = −1.81023 − 0.83355I
2.22736 − 5.03014I 0
u = 0.653865 + 0.591272I
a = 0.546637 − 0.447428I
b = −0.313726 − 0.436492I
4.46313 − 1.71758I −1.99294 + 3.91162I
u = 0.653865 − 0.591272I
a = 0.546637 + 0.447428I
b = −0.313726 + 0.436492I
4.46313 + 1.71758I −1.99294 − 3.91162I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.543636 + 0.978739I
a = 0.595952 + 0.594331I
b = −0.143500 − 0.270257I
1.84084 − 4.64712I 0
u = −0.543636 − 0.978739I
a = 0.595952 − 0.594331I
b = −0.143500 + 0.270257I
1.84084 + 4.64712I 0
u = 1.136340 + 0.085967I
a = 0.279099 − 0.088232I
b = 0.651828 − 0.756122I
−4.51217 + 2.77386I 0
u = 1.136340 − 0.085967I
a = 0.279099 + 0.088232I
b = 0.651828 + 0.756122I
−4.51217 − 2.77386I 0
u = 1.067750 + 0.420888I
a = −1.87786 + 0.34577I
b = −0.83129 − 1.54411I
−3.40761 − 2.20375I 0
u = 1.067750 − 0.420888I
a = −1.87786 − 0.34577I
b = −0.83129 + 1.54411I
−3.40761 + 2.20375I 0
u = −0.125465 + 0.835214I
a = −0.10435 − 1.59020I
b = 0.862564 + 0.893320I
−2.81805 − 2.16506I −9.87540 + 5.61737I
u = −0.125465 − 0.835214I
a = −0.10435 + 1.59020I
b = 0.862564 − 0.893320I
−2.81805 + 2.16506I −9.87540 − 5.61737I
u = 1.074320 + 0.446434I
a = 2.33317 − 0.78177I
b = 1.90096 + 0.89090I
1.85989 − 8.01595I 0
u = 1.074320 − 0.446434I
a = 2.33317 + 0.78177I
b = 1.90096 − 0.89090I
1.85989 + 8.01595I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.725121 + 0.392006I
a = −1.90522 − 2.47065I
b = −1.210690 − 0.210584I
−0.64046 + 2.98061I −8.98738 − 7.04047I
u = −0.725121 − 0.392006I
a = −1.90522 + 2.47065I
b = −1.210690 + 0.210584I
−0.64046 − 2.98061I −8.98738 + 7.04047I
u = 1.104970 + 0.414939I
a = 0.283959 − 0.271043I
b = 1.069610 − 0.727261I
−3.45530 − 4.80167I 0
u = 1.104970 − 0.414939I
a = 0.283959 + 0.271043I
b = 1.069610 + 0.727261I
−3.45530 + 4.80167I 0
u = −0.170048 + 1.184850I
a = 0.627452 − 0.278541I
b = −1.99843 − 0.37107I
−1.69051 − 1.86503I 0
u = −0.170048 − 1.184850I
a = 0.627452 + 0.278541I
b = −1.99843 + 0.37107I
−1.69051 + 1.86503I 0
u = −0.441408 + 0.647966I
a = 0.543640 + 0.757595I
b = 1.160190 − 0.111260I
−0.501227 − 0.231040I −6.51195 + 0.36059I
u = −0.441408 − 0.647966I
a = 0.543640 − 0.757595I
b = 1.160190 + 0.111260I
−0.501227 + 0.231040I −6.51195 − 0.36059I
u = −1.101140 + 0.524739I
a = −1.31740 − 1.35522I
b = −1.76932 − 0.29287I
−2.56199 + 4.84000I 0
u = −1.101140 − 0.524739I
a = −1.31740 + 1.35522I
b = −1.76932 + 0.29287I
−2.56199 − 4.84000I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.743273 + 0.192362I
a = 0.523153 − 0.357954I
b = −0.778082 − 1.165960I
2.43852 − 0.18703I −11.37446 − 3.74898I
u = −0.743273 − 0.192362I
a = 0.523153 + 0.357954I
b = −0.778082 + 1.165960I
2.43852 + 0.18703I −11.37446 + 3.74898I
u = −1.214390 + 0.237157I
a = −1.81606 + 0.08423I
b = −1.24455 + 1.45461I
−7.51790 − 0.99407I 0
u = −1.214390 − 0.237157I
a = −1.81606 − 0.08423I
b = −1.24455 − 1.45461I
−7.51790 + 0.99407I 0
u = −1.148700 + 0.510777I
a = −0.065466 + 0.259649I
b = 0.003288 − 0.501341I
−2.69356 + 2.85282I 0
u = −1.148700 − 0.510777I
a = −0.065466 − 0.259649I
b = 0.003288 + 0.501341I
−2.69356 − 2.85282I 0
u = 1.208390 + 0.353192I
a = −1.51238 + 1.05060I
b = −1.79615 + 0.61356I
−7.01716 − 1.79468I 0
u = 1.208390 − 0.353192I
a = −1.51238 − 1.05060I
b = −1.79615 − 0.61356I
−7.01716 + 1.79468I 0
u = −0.484551 + 1.171980I
a = 0.580134 − 0.265852I
b = −2.07365 − 0.94054I
−0.30685 − 9.73004I 0
u = −0.484551 − 1.171980I
a = 0.580134 + 0.265852I
b = −2.07365 + 0.94054I
−0.30685 + 9.73004I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.516322 + 0.514627I
a = 0.550028 + 0.336051I
b = −1.15619 + 1.03408I
3.64506 + 4.10175I −3.50068 + 0.16550I
u = 0.516322 − 0.514627I
a = 0.550028 − 0.336051I
b = −1.15619 − 1.03408I
3.64506 − 4.10175I −3.50068 − 0.16550I
u = 1.098620 + 0.654049I
a = −0.259825 − 0.296004I
b = −0.127365 + 0.305299I
2.17633 − 5.60365I 0
u = 1.098620 − 0.654049I
a = −0.259825 + 0.296004I
b = −0.127365 − 0.305299I
2.17633 + 5.60365I 0
u = −1.187720 + 0.505810I
a = −1.63010 − 0.30290I
b = −0.89789 + 1.80532I
−5.97333 + 6.98094I 0
u = −1.187720 − 0.505810I
a = −1.63010 + 0.30290I
b = −0.89789 − 1.80532I
−5.97333 − 6.98094I 0
u = 1.192530 + 0.590288I
a = −1.17833 + 1.23110I
b = −1.94360 + 0.25893I
−5.05086 − 9.82294I 0
u = 1.192530 − 0.590288I
a = −1.17833 − 1.23110I
b = −1.94360 − 0.25893I
−5.05086 + 9.82294I 0
u = 0.453727 + 0.479176I
a = −1.88077 + 2.61755I
b = 0.031595 − 0.872947I
−1.61075 − 1.37550I 1.06828 + 3.88421I
u = 0.453727 − 0.479176I
a = −1.88077 − 2.61755I
b = 0.031595 + 0.872947I
−1.61075 + 1.37550I 1.06828 − 3.88421I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.160930 + 0.693518I
a = −0.270422 + 0.204754I
b = −0.238385 − 0.350820I
−0.15331 + 10.78920I 0
u = −1.160930 − 0.693518I
a = −0.270422 − 0.204754I
b = −0.238385 + 0.350820I
−0.15331 − 10.78920I 0
u = 1.218660 + 0.679170I
a = 1.73476 − 0.94207I
b = 2.16330 + 1.28301I
−0.31155 − 11.22020I 0
u = 1.218660 − 0.679170I
a = 1.73476 + 0.94207I
b = 2.16330 − 1.28301I
−0.31155 + 11.22020I 0
u = −1.387240 + 0.184587I
a = 1.57267 + 0.32546I
b = 2.17449 − 0.52478I
−4.07832 − 1.19726I 0
u = −1.387240 − 0.184587I
a = 1.57267 − 0.32546I
b = 2.17449 + 0.52478I
−4.07832 + 1.19726I 0
u = −0.195618 + 0.552066I
a = 1.178600 + 0.372591I
b = −0.235368 − 0.239587I
−0.36323 + 1.66196I −2.66065 − 3.49504I
u = −0.195618 − 0.552066I
a = 1.178600 − 0.372591I
b = −0.235368 + 0.239587I
−0.36323 − 1.66196I −2.66065 + 3.49504I
u = −1.32645 + 0.58089I
a = 1.73200 + 0.69897I
b = 2.36240 − 1.10492I
−5.48277 + 8.06356I 0
u = −1.32645 − 0.58089I
a = 1.73200 − 0.69897I
b = 2.36240 + 1.10492I
−5.48277 − 8.06356I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.25392 + 0.74743I
a = 1.60645 + 0.95537I
b = 2.22097 − 1.40824I
−2.7949 + 16.5881I 0
u = −1.25392 − 0.74743I
a = 1.60645 − 0.95537I
b = 2.22097 + 1.40824I
−2.7949 − 16.5881I 0
u = 0.491993 + 0.193491I
a = −4.49599 + 4.27455I
b = −0.856146 + 0.213716I
−1.20246 + 1.70054I −18.7053 + 3.5277I
u = 0.491993 − 0.193491I
a = −4.49599 − 4.27455I
b = −0.856146 − 0.213716I
−1.20246 − 1.70054I −18.7053 − 3.5277I
u = 1.51845 + 0.02075I
a = 1.58759 − 0.09676I
b = 2.61113 + 0.21884I
−8.17783 + 5.50134I 0
u = 1.51845 − 0.02075I
a = 1.58759 + 0.09676I
b = 2.61113 − 0.21884I
−8.17783 − 5.50134I 0
u = 1.49958 + 0.33987I
a = 1.39029 − 0.29970I
b = 2.31492 + 1.03303I
−7.50417 − 3.65998I 0
u = 1.49958 − 0.33987I
a = 1.39029 + 0.29970I
b = 2.31492 − 1.03303I
−7.50417 + 3.65998I 0
u = −0.384773
a = 0.996229
b = 0.763429
−0.986513 −9.91200
12
II. I
u
2
= hu
2
+ b, u
4
− 2u
3
− u
2
+ a + 3u + 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
11
=
−u
4
+ 2u
3
+ u
2
− 3u − 1
−u
2
a
9
=
−u
4
+ 2u
3
+ u
2
− 3u
0
a
3
=
u
u
a
6
=
1
0
a
5
=
−u
2
+ 1
−u
2
a
10
=
−u
4
+ 2u
3
+ u
2
− 3u
0
a
1
=
−1
−u
2
a
2
=
−u
3
+ 2u
−u
4
− u
3
+ u
2
+ 2u + 1
a
2
=
−u
3
+ 2u
−u
4
− u
3
+ u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
+ 7u
3
+ 7u
2
− 13u − 18
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
2
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
3
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
4
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
5
, c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
6
, c
9
u
5
c
8
(u − 1)
5
c
10
, c
11
(u + 1)
5
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
2
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
3
, c
5
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
6
, c
9
y
5
c
8
, c
10
, c
11
(y −1)
5
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −1.67436
b = −1.48288
−4.04602 −8.82740
u = −0.309916 + 0.549911I
a = 0.29977 − 2.14694I
b = 0.206354 + 0.340852I
−1.97403 + 1.53058I −13.5086 − 9.8710I
u = −0.309916 − 0.549911I
a = 0.29977 + 2.14694I
b = 0.206354 − 0.340852I
−1.97403 − 1.53058I −13.5086 + 9.8710I
u = 1.41878 + 0.21917I
a = −1.46259 + 0.14641I
b = −1.96491 − 0.62190I
−7.51750 − 4.40083I −11.07763 + 5.80708I
u = 1.41878 − 0.21917I
a = −1.46259 − 0.14641I
b = −1.96491 + 0.62190I
−7.51750 + 4.40083I −11.07763 − 5.80708I
16
III.
I
v
1
= ha, −18v
5
− 63v
4
+ · · · + 55b + 12, v
6
+ 2v
5
+ 7v
4
− 8v
3
+ 7v
2
− 3v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
0.327273v
5
+ 1.14545v
4
+ ··· − 0.490909v − 0.218182
a
9
=
1
−0.581818v
5
− 2.03636v
4
+ ··· + 0.872727v − 0.945455
a
3
=
v
0
a
6
=
0.581818v
5
+ 2.03636v
4
+ ··· − 0.872727v + 1.94545
0.254545v
5
+ 0.890909v
4
+ ··· − 0.381818v + 2.16364
a
5
=
0.654545v
5
+ 2.29091v
4
+ ··· + 0.0181818v + 1.56364
0.254545v
5
+ 0.890909v
4
+ ··· − 0.381818v + 2.16364
a
10
=
0.327273v
5
+ 1.14545v
4
+ ··· − 0.490909v − 0.218182
0.327273v
5
+ 1.14545v
4
+ ··· − 0.490909v − 0.218182
a
1
=
−0.581818v
5
− 2.03636v
4
+ ··· + 0.872727v − 1.94545
−0.254545v
5
− 0.890909v
4
+ ··· + 0.381818v − 2.16364
a
2
=
−1.74545v
5
− 4.10909v
4
+ ··· − 5.38182v + 1.16364
−1.25455v
5
− 2.89091v
4
+ ··· − 6.61818v + 0.836364
a
2
=
−1.74545v
5
− 4.10909v
4
+ ··· − 5.38182v + 1.16364
−1.25455v
5
− 2.89091v
4
+ ··· − 6.61818v + 0.836364
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
153
55
v
5
−
453
55
v
4
−
1393
55
v
3
+
262
55
v
2
+
37
55
v −
448
55
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
3
c
3
, c
7
u
6
c
4
(u
2
− u + 1)
3
c
6
(u
3
− u
2
+ 2u − 1)
2
c
8
(u
3
+ u
2
− 1)
2
c
9
, c
11
(u
3
+ u
2
+ 2u + 1)
2
c
10
(u
3
− u
2
+ 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
3
c
3
, c
7
y
6
c
6
, c
9
, c
11
(y
3
+ 3y
2
+ 2y − 1)
2
c
8
, c
10
(y
3
− y
2
+ 2y − 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.111778 + 0.558770I
a = 0
b = −0.877439 − 0.744862I
3.02413 − 4.85801I −7.63258 + 5.38377I
v = 0.111778 − 0.558770I
a = 0
b = −0.877439 + 0.744862I
3.02413 + 4.85801I −7.63258 − 5.38377I
v = 0.428020 + 0.376187I
a = 0
b = −0.877439 + 0.744862I
3.02413 + 0.79824I −4.05323 − 2.24743I
v = 0.428020 − 0.376187I
a = 0
b = −0.877439 − 0.744862I
3.02413 − 0.79824I −4.05323 + 2.24743I
v = −1.53980 + 2.66701I
a = 0
b = 0.754878
−1.11345 + 2.02988I −15.8142 − 11.5861I
v = −1.53980 − 2.66701I
a = 0
b = 0.754878
−1.11345 − 2.02988I −15.8142 + 11.5861I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
3
)(u
5
− u
4
+ ··· + u − 1)(u
79
+ 5u
78
+ ··· + 12u + 1)
c
2
((u
2
+ u + 1)
3
)(u
5
+ 3u
4
+ ··· − u − 1)(u
79
+ 39u
78
+ ··· + 42u − 1)
c
3
u
6
(u
5
+ u
4
+ ··· + u − 1)(u
79
+ 2u
78
+ ··· + 224u + 64)
c
4
((u
2
− u + 1)
3
)(u
5
+ u
4
+ ··· + u + 1)(u
79
+ 5u
78
+ ··· + 12u + 1)
c
5
(u
2
+ u + 1)
3
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
· (u
79
− 5u
78
+ ··· + 14176u + 3137)
c
6
u
5
(u
3
− u
2
+ 2u − 1)
2
(u
79
− 3u
78
+ ··· − 192u + 32)
c
7
u
6
(u
5
− u
4
+ ··· + u + 1)(u
79
+ 2u
78
+ ··· + 224u + 64)
c
8
((u − 1)
5
)(u
3
+ u
2
− 1)
2
(u
79
− 8u
78
+ ··· − 5u + 1)
c
9
u
5
(u
3
+ u
2
+ 2u + 1)
2
(u
79
− 3u
78
+ ··· − 192u + 32)
c
10
((u + 1)
5
)(u
3
− u
2
+ 1)
2
(u
79
− 8u
78
+ ··· − 5u + 1)
c
11
((u + 1)
5
)(u
3
+ u
2
+ 2u + 1)
2
(u
79
+ 38u
78
+ ··· − 137u + 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
5
+ 3y
4
+ ··· − y − 1)(y
79
+ 39y
78
+ ··· + 42y − 1)
c
2
(y
2
+ y + 1)
3
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
79
+ 7y
78
+ ··· + 2238y − 1)
c
3
, c
7
y
6
(y
5
− 5y
4
+ ··· − y − 1)(y
79
− 40y
78
+ ··· + 91136y − 4096)
c
5
(y
2
+ y + 1)
3
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
· (y
79
− 25y
78
+ ··· + 636907866y − 9840769)
c
6
, c
9
y
5
(y
3
+ 3y
2
+ 2y − 1)
2
(y
79
+ 39y
78
+ ··· − 15872y − 1024)
c
8
, c
10
((y − 1)
5
)(y
3
− y
2
+ 2y − 1)
2
(y
79
− 38y
78
+ ··· − 137y − 1)
c
11
((y − 1)
5
)(y
3
+ 3y
2
+ 2y − 1)
2
(y
79
+ 14y
78
+ ··· + 11687y − 1)
22
