12a
0082
(K12a
0082
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 11 4 1 6 12 7 10
Solving Sequence
6,11 4,7
8 12 3 10 1 9 5 2
c
6
c
7
c
11
c
3
c
10
c
12
c
9
c
5
c
2
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
102
+ u
101
+ ··· + b − 1, −u
99
+ 16u
97
+ ··· + a + 2u, u
103
+ 2u
102
+ ··· + 6u
2
− 1i
I
u
2
= hu
7
− u
5
+ 2u
3
+ b − u + 1, u
7
− u
5
+ u
4
+ 2u
3
− u
2
+ a + 2, u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 111 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
=
hu
102
+u
101
+· · ·+b−1, −u
99
+16u
97
+· · ·+a+2u, u
103
+2u
102
+· · ·+6u
2
−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
u
99
− 16u
97
+ ··· − 3u
2
− 2u
−u
102
− u
101
+ ··· + u + 1
a
7
=
1
u
2
a
8
=
−u
17
+ 2u
15
− 5u
13
+ 6u
11
− 7u
9
+ 6u
7
− 2u
5
+ 2u
3
+ u
−u
19
+ 3u
17
− 8u
15
+ 13u
13
− 17u
11
+ 17u
9
− 12u
7
+ 8u
5
− 3u
3
+ u
a
12
=
−u
−u
3
+ u
a
3
=
−2u
102
− 2u
101
+ ··· − 3u + 1
−u
102
− u
101
+ ··· − 4u
2
+ 1
a
10
=
u
3
u
5
− u
3
+ u
a
1
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
a
9
=
u
5
+ u
u
5
− u
3
+ u
a
5
=
−u
10
+ u
8
− 2u
6
+ u
4
− u
2
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
2
=
−u
102
− u
101
+ ··· − 2u + 1
−u
102
− u
101
+ ··· + u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11u
102
+ 10u
101
+ ··· − 4u − 21
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
103
+ 49u
102
+ ··· + 72u + 1
c
2
, c
4
u
103
− 9u
102
+ ··· − 2u + 1
c
3
, c
7
u
103
+ u
102
+ ··· + 896u + 256
c
5
, c
9
u
103
+ 2u
102
+ ··· + 126u + 9
c
6
, c
11
u
103
− 2u
102
+ ··· − 6u
2
+ 1
c
8
u
103
− 8u
102
+ ··· + 326018u + 52865
c
10
, c
12
u
103
+ 36u
102
+ ··· + 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
103
+ 19y
102
+ ··· + 1672y −1
c
2
, c
4
y
103
− 49y
102
+ ··· + 72y −1
c
3
, c
7
y
103
+ 51y
102
+ ··· − 1130496y −65536
c
5
, c
9
y
103
− 68y
102
+ ··· − 22536y −81
c
6
, c
11
y
103
− 36y
102
+ ··· + 12y −1
c
8
y
103
+ 16y
102
+ ··· − 53970185116y −2794708225
c
10
, c
12
y
103
+ 64y
102
+ ··· − 68y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.912335 + 0.408500I
a = 2.31902 − 0.54728I
b = 0.584528 − 0.968145I
0.08009 + 7.90391I 0
u = −0.912335 − 0.408500I
a = 2.31902 + 0.54728I
b = 0.584528 + 0.968145I
0.08009 − 7.90391I 0
u = 0.616846 + 0.780917I
a = 0.639980 + 0.490478I
b = −1.65356 + 0.05660I
−0.99710 + 5.42375I 0
u = 0.616846 − 0.780917I
a = 0.639980 − 0.490478I
b = −1.65356 − 0.05660I
−0.99710 − 5.42375I 0
u = −0.881449 + 0.484517I
a = −1.60696 + 0.38647I
b = −0.254925 + 0.557993I
1.89796 + 2.95652I 0
u = −0.881449 − 0.484517I
a = −1.60696 − 0.38647I
b = −0.254925 − 0.557993I
1.89796 − 2.95652I 0
u = 1.005320 + 0.087510I
a = 0.54041 + 1.59055I
b = 0.289073 + 0.524898I
−0.23823 − 2.28486I 0
u = 1.005320 − 0.087510I
a = 0.54041 − 1.59055I
b = 0.289073 − 0.524898I
−0.23823 + 2.28486I 0
u = −0.624209 + 0.794738I
a = −1.097790 + 0.679494I
b = 1.43840 + 2.14786I
3.77337 − 6.03756I 0
u = −0.624209 − 0.794738I
a = −1.097790 − 0.679494I
b = 1.43840 − 2.14786I
3.77337 + 6.03756I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.613526 + 0.803225I
a = 1.31576 − 0.53967I
b = −1.56697 − 2.36415I
1.44101 − 11.65940I 0
u = −0.613526 − 0.803225I
a = 1.31576 + 0.53967I
b = −1.56697 + 2.36415I
1.44101 + 11.65940I 0
u = −0.614579 + 0.767089I
a = 1.15511 − 1.33576I
b = −1.84696 − 1.71453I
−1.91217 − 2.88103I 0
u = −0.614579 − 0.767089I
a = 1.15511 + 1.33576I
b = −1.84696 + 1.71453I
−1.91217 + 2.88103I 0
u = 0.631063 + 0.747905I
a = −0.656987 − 0.310998I
b = 1.314400 − 0.477130I
0.307513 + 1.061580I 0
u = 0.631063 − 0.747905I
a = −0.656987 + 0.310998I
b = 1.314400 + 0.477130I
0.307513 − 1.061580I 0
u = −0.672704 + 0.770186I
a = −0.233235 + 0.783530I
b = 0.75052 + 1.40903I
5.58134 − 2.28100I 0
u = −0.672704 − 0.770186I
a = −0.233235 − 0.783530I
b = 0.75052 − 1.40903I
5.58134 + 2.28100I 0
u = −0.702746 + 0.759112I
a = −0.085346 − 0.728100I
b = −0.403150 − 1.083490I
4.66987 + 3.22738I 0
u = −0.702746 − 0.759112I
a = −0.085346 + 0.728100I
b = −0.403150 + 1.083490I
4.66987 − 3.22738I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.559939 + 0.767741I
a = 0.186132 + 0.629586I
b = −0.911639 − 0.783862I
−2.37667 − 0.08774I 0
u = 0.559939 − 0.767741I
a = 0.186132 − 0.629586I
b = −0.911639 + 0.783862I
−2.37667 + 0.08774I 0
u = 0.934664 + 0.166620I
a = 0.25189 − 1.89766I
b = 0.409310 − 0.451135I
−1.07874 + 2.57674I 0
u = 0.934664 − 0.166620I
a = 0.25189 + 1.89766I
b = 0.409310 + 0.451135I
−1.07874 − 2.57674I 0
u = −0.853017 + 0.633169I
a = −0.533821 + 0.009715I
b = −0.1065160 + 0.0398102I
1.77380 + 2.47815I 0
u = −0.853017 − 0.633169I
a = −0.533821 − 0.009715I
b = −0.1065160 − 0.0398102I
1.77380 − 2.47815I 0
u = −1.067130 + 0.027007I
a = 2.20309 + 0.64129I
b = 1.68580 + 0.39940I
−5.25977 + 0.42586I 0
u = −1.067130 − 0.027007I
a = 2.20309 − 0.64129I
b = 1.68580 − 0.39940I
−5.25977 − 0.42586I 0
u = 1.085050 + 0.040939I
a = −2.07495 − 0.29647I
b = −1.99607 + 0.35332I
−7.69423 − 2.11350I 0
u = 1.085050 − 0.040939I
a = −2.07495 + 0.29647I
b = −1.99607 − 0.35332I
−7.69423 + 2.11350I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.089270 + 0.053148I
a = −2.37201 − 1.44590I
b = −1.97109 − 0.94572I
−6.91666 + 4.67542I 0
u = −1.089270 − 0.053148I
a = −2.37201 + 1.44590I
b = −1.97109 + 0.94572I
−6.91666 − 4.67542I 0
u = 1.091240 + 0.069455I
a = 2.22714 + 1.29507I
b = 1.93126 + 0.69834I
−2.30120 − 5.35216I 0
u = 1.091240 − 0.069455I
a = 2.22714 − 1.29507I
b = 1.93126 − 0.69834I
−2.30120 + 5.35216I 0
u = 0.606096 + 0.662511I
a = −0.798963 + 0.126546I
b = 0.649948 − 0.932632I
−0.302081 + 0.540644I 0
u = 0.606096 − 0.662511I
a = −0.798963 − 0.126546I
b = 0.649948 + 0.932632I
−0.302081 − 0.540644I 0
u = 0.511993 + 0.732368I
a = 0.343675 − 0.709475I
b = 0.044302 + 1.277450I
−2.69016 + 2.77408I 0
u = 0.511993 − 0.732368I
a = 0.343675 + 0.709475I
b = 0.044302 − 1.277450I
−2.69016 − 2.77408I 0
u = 1.106320 + 0.068441I
a = −2.68986 − 1.37616I
b = −2.38599 − 0.90186I
−4.70352 − 10.84140I 0
u = 1.106320 − 0.068441I
a = −2.68986 + 1.37616I
b = −2.38599 + 0.90186I
−4.70352 + 10.84140I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.842412 + 0.726529I
a = −0.178651 − 0.729133I
b = 0.0579763 − 0.1150040I
3.07344 + 0.63735I 0
u = −0.842412 − 0.726529I
a = −0.178651 + 0.729133I
b = 0.0579763 + 0.1150040I
3.07344 − 0.63735I 0
u = −1.116010 + 0.016772I
a = −0.84995 − 1.85919I
b = −0.75181 − 1.51606I
−8.11122 − 1.30695I 0
u = −1.116010 − 0.016772I
a = −0.84995 + 1.85919I
b = −0.75181 + 1.51606I
−8.11122 + 1.30695I 0
u = 0.859325 + 0.712441I
a = 0.75900 − 2.33832I
b = 3.00650 − 0.45544I
1.60340 − 2.72171I 0
u = 0.859325 − 0.712441I
a = 0.75900 + 2.33832I
b = 3.00650 + 0.45544I
1.60340 + 2.72171I 0
u = 0.823392 + 0.756871I
a = 0.218483 − 0.973336I
b = 1.78019 − 1.08683I
6.43694 + 4.87550I 0
u = 0.823392 − 0.756871I
a = 0.218483 + 0.973336I
b = 1.78019 + 1.08683I
6.43694 − 4.87550I 0
u = 0.770289 + 0.411262I
a = 1.47793 − 0.96752I
b = 0.440891 + 0.958529I
−2.10537 − 2.84140I 0
u = 0.770289 − 0.411262I
a = 1.47793 + 0.96752I
b = 0.440891 − 0.958529I
−2.10537 + 2.84140I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.841098 + 0.751122I
a = −0.506788 + 1.209090I
b = −1.90230 + 0.81017I
8.10016 − 0.78832I 0
u = 0.841098 − 0.751122I
a = −0.506788 − 1.209090I
b = −1.90230 − 0.81017I
8.10016 + 0.78832I 0
u = −0.876875 + 0.722197I
a = −0.091761 + 0.802743I
b = −0.0013840 + 0.0733994I
2.96916 + 4.87835I 0
u = −0.876875 − 0.722197I
a = −0.091761 − 0.802743I
b = −0.0013840 − 0.0733994I
2.96916 − 4.87835I 0
u = 0.885183 + 0.741783I
a = −1.39537 + 1.55461I
b = −2.03510 − 0.19569I
7.96620 − 4.86085I 0
u = 0.885183 − 0.741783I
a = −1.39537 − 1.55461I
b = −2.03510 + 0.19569I
7.96620 + 4.86085I 0
u = 0.901166 + 0.740058I
a = 1.66978 − 1.57705I
b = 1.97824 + 0.55475I
6.20092 − 10.53630I 0
u = 0.901166 − 0.740058I
a = 1.66978 + 1.57705I
b = 1.97824 − 0.55475I
6.20092 + 10.53630I 0
u = −1.005990 + 0.592232I
a = 0.167955 + 1.051150I
b = 0.878165 − 0.601426I
0.848394 + 1.048560I 0
u = −1.005990 − 0.592232I
a = 0.167955 − 1.051150I
b = 0.878165 + 0.601426I
0.848394 − 1.048560I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.011120 + 0.612755I
a = −2.26014 + 0.37543I
b = −0.99132 − 2.03559I
−3.51458 − 1.68605I 0
u = 1.011120 − 0.612755I
a = −2.26014 − 0.37543I
b = −0.99132 + 2.03559I
−3.51458 + 1.68605I 0
u = −1.026270 + 0.590666I
a = −0.53736 − 1.42442I
b = −1.44389 + 0.79586I
−1.50754 − 4.20851I 0
u = −1.026270 − 0.590666I
a = −0.53736 + 1.42442I
b = −1.44389 − 0.79586I
−1.50754 + 4.20851I 0
u = −1.012950 + 0.625812I
a = −0.700288 − 0.186711I
b = −0.19292 + 1.59502I
−4.11619 + 4.19240I 0
u = −1.012950 − 0.625812I
a = −0.700288 + 0.186711I
b = −0.19292 − 1.59502I
−4.11619 − 4.19240I 0
u = 1.007840 + 0.644172I
a = 1.61422 − 0.67239I
b = 1.06573 + 1.37400I
−1.46823 − 5.66596I 0
u = 1.007840 − 0.644172I
a = 1.61422 + 0.67239I
b = 1.06573 − 1.37400I
−1.46823 + 5.66596I 0
u = −0.516513 + 0.614538I
a = 1.61419 + 1.13685I
b = 0.114440 − 0.378217I
−2.79751 + 0.75492I −13.18461 − 4.17377I
u = −0.516513 − 0.614538I
a = 1.61419 − 1.13685I
b = 0.114440 + 0.378217I
−2.79751 − 0.75492I −13.18461 + 4.17377I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.984760 + 0.696068I
a = −1.354280 + 0.257551I
b = −0.630888 + 0.742129I
3.81659 + 2.30298I 0
u = −0.984760 − 0.696068I
a = −1.354280 − 0.257551I
b = −0.630888 − 0.742129I
3.81659 − 2.30298I 0
u = −0.392378 + 0.674009I
a = 1.55257 + 0.40077I
b = −0.903906 + 0.236031I
0.18178 + 8.98054I −11.00021 − 7.46838I
u = −0.392378 − 0.674009I
a = 1.55257 − 0.40077I
b = −0.903906 − 0.236031I
0.18178 − 8.98054I −11.00021 + 7.46838I
u = −1.004500 + 0.695052I
a = 1.79376 + 0.08698I
b = 1.12781 − 1.16810I
4.58233 + 7.83910I 0
u = −1.004500 − 0.695052I
a = 1.79376 − 0.08698I
b = 1.12781 + 1.16810I
4.58233 − 7.83910I 0
u = 1.042120 + 0.637671I
a = −1.61249 − 0.63861I
b = 0.17740 − 1.77018I
−4.20496 − 7.99344I 0
u = 1.042120 − 0.637671I
a = −1.61249 + 0.63861I
b = 0.17740 + 1.77018I
−4.20496 + 7.99344I 0
u = 1.018180 + 0.675918I
a = 0.96849 − 1.49648I
b = 1.68010 + 0.59427I
−0.84382 − 6.49823I 0
u = 1.018180 − 0.675918I
a = 0.96849 + 1.49648I
b = 1.68010 − 0.59427I
−0.84382 + 6.49823I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.028310 + 0.678590I
a = −2.41921 − 1.22556I
b = −2.79352 + 1.71272I
−3.14095 + 8.37153I 0
u = −1.028310 − 0.678590I
a = −2.41921 + 1.22556I
b = −2.79352 − 1.71272I
−3.14095 − 8.37153I 0
u = 1.044270 + 0.661570I
a = 0.50721 + 1.38026I
b = −1.25248 + 0.85970I
−3.79812 − 5.32874I 0
u = 1.044270 − 0.661570I
a = 0.50721 − 1.38026I
b = −1.25248 − 0.85970I
−3.79812 + 5.32874I 0
u = 1.031540 + 0.683934I
a = −0.62182 + 1.93629I
b = −2.05487 − 0.18548I
−2.23392 − 10.96790I 0
u = 1.031540 − 0.683934I
a = −0.62182 − 1.93629I
b = −2.05487 + 0.18548I
−2.23392 + 10.96790I 0
u = −1.033220 + 0.691226I
a = 2.77565 + 0.66832I
b = 2.07476 − 2.34471I
2.54734 + 11.64380I 0
u = −1.033220 − 0.691226I
a = 2.77565 − 0.66832I
b = 2.07476 + 2.34471I
2.54734 − 11.64380I 0
u = 0.443432 + 0.610668I
a = 0.886007 − 0.667581I
b = −0.730589 + 1.052200I
−2.10237 − 3.12059I −13.26982 + 4.81629I
u = 0.443432 − 0.610668I
a = 0.886007 + 0.667581I
b = −0.730589 − 1.052200I
−2.10237 + 3.12059I −13.26982 − 4.81629I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.040030 + 0.690804I
a = −3.04535 − 0.73216I
b = −2.19998 + 2.72089I
0.1621 + 17.2846I 0
u = −1.040030 − 0.690804I
a = −3.04535 + 0.73216I
b = −2.19998 − 2.72089I
0.1621 − 17.2846I 0
u = −0.378402 + 0.630093I
a = −1.33629 − 0.55236I
b = 0.523829 − 0.380248I
2.41042 + 3.58130I −7.69186 − 3.73533I
u = −0.378402 − 0.630093I
a = −1.33629 + 0.55236I
b = 0.523829 + 0.380248I
2.41042 − 3.58130I −7.69186 + 3.73533I
u = −0.658769 + 0.304586I
a = 2.31140 + 1.30466I
b = 0.923181 + 0.133554I
−2.64550 + 0.77211I −15.5455 − 7.3829I
u = −0.658769 − 0.304586I
a = 2.31140 − 1.30466I
b = 0.923181 − 0.133554I
−2.64550 − 0.77211I −15.5455 + 7.3829I
u = −0.218526 + 0.537148I
a = −0.408550 − 0.675362I
b = −0.241540 − 0.913033I
3.54467 + 0.53496I −5.34128 − 2.54226I
u = −0.218526 − 0.537148I
a = −0.408550 + 0.675362I
b = −0.241540 + 0.913033I
3.54467 − 0.53496I −5.34128 + 2.54226I
u = −0.135378 + 0.544021I
a = 0.020276 + 0.569777I
b = 0.550133 + 1.008990I
2.18579 − 4.67641I −7.53230 + 3.53464I
u = −0.135378 − 0.544021I
a = 0.020276 − 0.569777I
b = 0.550133 − 1.008990I
2.18579 + 4.67641I −7.53230 − 3.53464I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.468563
a = −0.888738
b = 0.195924
−0.660128 −14.9900
u = 0.240493 + 0.334959I
a = −1.106550 + 0.760023I
b = 0.648529 − 0.094589I
−0.875975 + 0.268582I −10.54321 + 1.26230I
u = 0.240493 − 0.334959I
a = −1.106550 − 0.760023I
b = 0.648529 + 0.094589I
−0.875975 − 0.268582I −10.54321 − 1.26230I
15
II. I
u
2
= hu
7
− u
5
+ 2u
3
+ b − u + 1, u
7
− u
5
+ u
4
+ 2u
3
− u
2
+ a + 2, u
8
−
u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
−u
7
+ u
5
− u
4
− 2u
3
+ u
2
− 2
−u
7
+ u
5
− 2u
3
+ u − 1
a
7
=
1
u
2
a
8
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
−u
7
+ u
5
− u
4
− 2u
3
+ u
2
− 2
−u
7
+ u
5
− 2u
3
+ u − 1
a
10
=
u
3
u
5
− u
3
+ u
a
1
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
a
9
=
u
5
+ u
u
5
− u
3
+ u
a
5
=
u
5
+ u
u
7
− u
5
+ 2u
3
− u
a
2
=
−u
7
− u
4
− 2u
3
+ u
2
− u − 2
−2u
7
+ 2u
5
− 4u
3
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
7
− u
6
+ 5u
5
− 5u
3
+ u
2
+ 4u − 17
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
, c
8
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
6
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
9
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
10
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
11
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
12
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
8
, c
9
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
6
, c
11
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
10
, c
12
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 + 0.730671I
a = −0.805639 − 0.183365I
b = 0.320534 − 0.633953I
−2.68559 + 1.13123I −13.47926 − 0.84929I
u = 0.570868 − 0.730671I
a = −0.805639 + 0.183365I
b = 0.320534 + 0.633953I
−2.68559 − 1.13123I −13.47926 + 0.84929I
u = −0.855237 + 0.665892I
a = −0.189481 − 1.310380I
b = −1.54709 − 0.16160I
0.51448 + 2.57849I −14.5054 − 3.2330I
u = −0.855237 − 0.665892I
a = −0.189481 + 1.310380I
b = −1.54709 + 0.16160I
0.51448 − 2.57849I −14.5054 + 3.2330I
u = −1.09818
a = 0.729394
b = 0.879647
−8.14766 −19.4520
u = 1.031810 + 0.655470I
a = 0.708845 − 0.169402I
b = 0.679246 + 0.851242I
−4.02461 − 6.44354I −15.2754 + 5.9053I
u = 1.031810 − 0.655470I
a = 0.708845 + 0.169402I
b = 0.679246 − 0.851242I
−4.02461 + 6.44354I −15.2754 − 5.9053I
u = 0.603304
a = −2.15684
b = −0.785038
−2.48997 −15.0280
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
103
+ 49u
102
+ ··· + 72u + 1)
c
2
((u − 1)
8
)(u
103
− 9u
102
+ ··· − 2u + 1)
c
3
, c
7
u
8
(u
103
+ u
102
+ ··· + 896u + 256)
c
4
((u + 1)
8
)(u
103
− 9u
102
+ ··· − 2u + 1)
c
5
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)(u
103
+ 2u
102
+ ··· + 126u + 9)
c
6
(u
8
− u
7
+ ··· + 2u − 1)(u
103
− 2u
102
+ ··· − 6u
2
+ 1)
c
8
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
103
− 8u
102
+ ··· + 326018u + 52865)
c
9
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)(u
103
+ 2u
102
+ ··· + 126u + 9)
c
10
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
103
+ 36u
102
+ ··· + 12u + 1)
c
11
(u
8
+ u
7
+ ··· − 2u − 1)(u
103
− 2u
102
+ ··· − 6u
2
+ 1)
c
12
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
103
+ 36u
102
+ ··· + 12u + 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
8
)(y
103
+ 19y
102
+ ··· + 1672y −1)
c
2
, c
4
((y −1)
8
)(y
103
− 49y
102
+ ··· + 72y −1)
c
3
, c
7
y
8
(y
103
+ 51y
102
+ ··· − 1130496y −65536)
c
5
, c
9
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
103
− 68y
102
+ ··· − 22536y −81)
c
6
, c
11
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
103
− 36y
102
+ ··· + 12y −1)
c
8
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
103
+ 16y
102
+ ··· − 53970185116y −2794708225)
c
10
, c
12
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
103
+ 64y
102
+ ··· − 68y −1)
21
