12n
0712
(K12n
0712
)
A knot diagram
1
Linearized knot diagam
4 10 11 10 12 3 4 12 1 7 6 9
Solving Sequence
3,11 4,7
8 6 12 5 10 2 1 9
c
3
c
7
c
6
c
11
c
5
c
10
c
2
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h7.16436 × 10
249
u
75
+ 2.01743 × 10
250
u
74
+ ··· + 3.69252 × 10
250
b − 9.34607 × 10
250
,
8.19251 × 10
249
u
75
+ 2.51790 × 10
250
u
74
+ ··· + 3.69252 × 10
250
a − 2.00281 × 10
251
, u
76
+ 3u
75
+ ··· − 40u − 8i
I
u
2
= h−6040320u
16
+ 4996901u
15
+ ··· + 9996367b − 9918960,
1258838u
16
− 20888294u
15
+ ··· + 9996367a + 50252931, u
17
+ 3u
15
+ ··· + u − 1i
* 2 irreducible components of dim
C
= 0, with total 93 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
= h7.16 × 10
249
u
75
+ 2.02 × 10
250
u
74
+ · · · + 3.69 × 10
250
b − 9.35 ×
10
250
, 8.19 × 10
249
u
75
+ 2.52 × 10
250
u
74
+ · · · + 3.69 × 10
250
a − 2.00 ×
10
251
, u
76
+ 3u
75
+ · · · − 40u − 8i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
7
=
−0.221867u
75
− 0.681890u
74
+ ··· + 21.9887u + 5.42396
−0.194023u
75
− 0.546355u
74
+ ··· + 17.3170u + 2.53108
a
8
=
−0.444577u
75
− 1.31396u
74
+ ··· + 41.7321u + 8.08534
−0.189585u
75
− 0.533144u
74
+ ··· + 16.9775u + 2.81951
a
6
=
−0.415891u
75
− 1.22824u
74
+ ··· + 39.3057u + 7.95504
−0.194023u
75
− 0.546355u
74
+ ··· + 17.3170u + 2.53108
a
12
=
−0.0622434u
75
− 0.0455723u
74
+ ··· − 33.2165u − 8.05740
−0.0439022u
75
− 0.116446u
74
+ ··· + 1.87201u + 1.57885
a
5
=
0.651878u
75
+ 1.92544u
74
+ ··· − 51.0468u − 2.30852
−0.0179655u
75
− 0.0546002u
74
+ ··· + 3.42243u + 2.09091
a
10
=
−0.0294076u
75
+ 0.0381562u
74
+ ··· − 28.1824u − 9.55530
0.0110664u
75
+ 0.0327171u
74
+ ··· − 4.90611u − 0.0809515
a
2
=
−0.317501u
75
− 0.942464u
74
+ ··· + 28.4231u + 3.04039
0.0616004u
75
+ 0.175235u
74
+ ··· − 5.56085u − 2.01059
a
1
=
−0.299536u
75
− 0.887864u
74
+ ··· + 25.0007u + 0.949486
0.0645846u
75
+ 0.181799u
74
+ ··· − 5.38898u − 2.00496
a
9
=
−0.442676u
75
− 1.15751u
74
+ ··· + 2.36444u − 4.96056
−0.0699751u
75
− 0.183763u
74
+ ··· + 4.34691u + 0.572363
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.982921u
75
+ 2.54015u
74
+ ··· − 83.5290u − 1.53183
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ 5u
75
+ ··· + 14139u + 307
c
2
u
76
+ 16u
74
+ ··· − 417u + 9
c
3
u
76
− 3u
75
+ ··· + 40u − 8
c
4
u
76
+ 25u
74
+ ··· − 40832u − 9472
c
5
, c
11
u
76
+ 21u
74
+ ··· − 7422u − 4041
c
6
u
76
+ 5u
75
+ ··· − 14u + 1
c
7
u
76
+ u
75
+ ··· + 280u − 19
c
8
, c
9
, c
12
u
76
− 32u
74
+ ··· − 141u + 19
c
10
u
76
− 4u
75
+ ··· + 100u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
− 57y
75
+ ··· − 374836851y + 94249
c
2
y
76
+ 32y
75
+ ··· − 151605y + 81
c
3
y
76
+ 13y
75
+ ··· + 1568y + 64
c
4
y
76
+ 50y
75
+ ··· + 4136583168y + 89718784
c
5
, c
11
y
76
+ 42y
75
+ ··· + 335290680y + 16329681
c
6
y
76
+ 9y
75
+ ··· − 22y + 1
c
7
y
76
+ 17y
75
+ ··· − 28924y + 361
c
8
, c
9
, c
12
y
76
− 64y
75
+ ··· + 5199y + 361
c
10
y
76
+ 10y
75
+ ··· − 8956y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.988673 + 0.157879I
a = 0.210479 − 0.611484I
b = −0.77585 + 1.64641I
0.29226 + 5.94254I 0
u = −0.988673 − 0.157879I
a = 0.210479 + 0.611484I
b = −0.77585 − 1.64641I
0.29226 − 5.94254I 0
u = −0.856136 + 0.519729I
a = 0.138708 + 0.873657I
b = −0.09153 − 1.49560I
0.21542 + 4.69032I 0
u = −0.856136 − 0.519729I
a = 0.138708 − 0.873657I
b = −0.09153 + 1.49560I
0.21542 − 4.69032I 0
u = −0.791352 + 0.617036I
a = 0.037093 + 1.016310I
b = 0.642295 − 1.104590I
0.55399 + 4.14989I 0
u = −0.791352 − 0.617036I
a = 0.037093 − 1.016310I
b = 0.642295 + 1.104590I
0.55399 − 4.14989I 0
u = 0.274686 + 0.996744I
a = −0.488851 − 0.812735I
b = −0.457165 + 0.633310I
6.38323 − 2.69065I 0
u = 0.274686 − 0.996744I
a = −0.488851 + 0.812735I
b = −0.457165 − 0.633310I
6.38323 + 2.69065I 0
u = −0.836004 + 0.659794I
a = 0.06104 − 1.56008I
b = −0.880984 + 0.616441I
−6.58488 + 4.99744I 0
u = −0.836004 − 0.659794I
a = 0.06104 + 1.56008I
b = −0.880984 − 0.616441I
−6.58488 − 4.99744I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.347092 + 0.856959I
a = 1.28732 + 1.16537I
b = 0.451088 − 0.953532I
3.58206 + 8.75485I 8.32937 − 7.77105I
u = −0.347092 − 0.856959I
a = 1.28732 − 1.16537I
b = 0.451088 + 0.953532I
3.58206 − 8.75485I 8.32937 + 7.77105I
u = 0.878556 + 0.200637I
a = 0.238847 − 0.740853I
b = −0.40970 + 1.78620I
−3.57909 + 0.60336I −2.63945 + 2.67457I
u = 0.878556 − 0.200637I
a = 0.238847 + 0.740853I
b = −0.40970 − 1.78620I
−3.57909 − 0.60336I −2.63945 − 2.67457I
u = 0.699124 + 0.554855I
a = 0.15882 + 1.84694I
b = −0.853372 − 0.594063I
−2.66450 + 0.00138I 0.99118 + 2.31235I
u = 0.699124 − 0.554855I
a = 0.15882 − 1.84694I
b = −0.853372 + 0.594063I
−2.66450 − 0.00138I 0.99118 − 2.31235I
u = 0.644694 + 0.906666I
a = −0.091006 − 1.240470I
b = 1.00187 + 1.51947I
9.65535 − 5.48513I 0
u = 0.644694 − 0.906666I
a = −0.091006 + 1.240470I
b = 1.00187 − 1.51947I
9.65535 + 5.48513I 0
u = 0.394933 + 0.781994I
a = 1.36967 − 1.13329I
b = 0.361605 + 0.847407I
−1.42075 − 4.05339I 4.25074 + 6.84714I
u = 0.394933 − 0.781994I
a = 1.36967 + 1.13329I
b = 0.361605 − 0.847407I
−1.42075 + 4.05339I 4.25074 − 6.84714I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.723650 + 0.459547I
a = 0.035116 − 0.774350I
b = 0.655940 + 0.546441I
−1.18749 − 1.04073I −2.87515 + 1.88476I
u = 0.723650 − 0.459547I
a = 0.035116 + 0.774350I
b = 0.655940 − 0.546441I
−1.18749 + 1.04073I −2.87515 − 1.88476I
u = 0.802133 + 0.883320I
a = −0.451106 − 0.482056I
b = −0.418768 − 0.183701I
6.65595 − 3.01746I 0
u = 0.802133 − 0.883320I
a = −0.451106 + 0.482056I
b = −0.418768 + 0.183701I
6.65595 + 3.01746I 0
u = 0.925583 + 0.764929I
a = 0.027137 + 1.376180I
b = −0.895559 − 0.641011I
−2.50803 − 9.92376I 0
u = 0.925583 − 0.764929I
a = 0.027137 − 1.376180I
b = −0.895559 + 0.641011I
−2.50803 + 9.92376I 0
u = −0.464123 + 0.622645I
a = 1.42148 + 1.07836I
b = 0.249050 − 0.626220I
1.25423 − 0.69104I 7.01445 − 3.43740I
u = −0.464123 − 0.622645I
a = 1.42148 − 1.07836I
b = 0.249050 + 0.626220I
1.25423 + 0.69104I 7.01445 + 3.43740I
u = −1.24798
a = 0.00845205
b = 0.614730
2.40053 0
u = −0.245836 + 0.608610I
a = −1.01333 + 1.76814I
b = −0.189251 − 0.380413I
1.92153 + 0.94962I −2.98543 − 0.44875I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.245836 − 0.608610I
a = −1.01333 − 1.76814I
b = −0.189251 + 0.380413I
1.92153 − 0.94962I −2.98543 + 0.44875I
u = 0.079389 + 0.643195I
a = 1.88748 − 1.54979I
b = −0.427883 + 0.986505I
9.02338 + 2.28669I 0.66173 + 6.35182I
u = 0.079389 − 0.643195I
a = 1.88748 + 1.54979I
b = −0.427883 − 0.986505I
9.02338 − 2.28669I 0.66173 − 6.35182I
u = 0.659231 + 1.237980I
a = −0.029277 + 0.560989I
b = −0.983298 − 0.893974I
8.19481 − 3.33586I 0
u = 0.659231 − 1.237980I
a = −0.029277 − 0.560989I
b = −0.983298 + 0.893974I
8.19481 + 3.33586I 0
u = −0.98850 + 1.01710I
a = −0.138103 + 0.999293I
b = 1.06198 − 1.21767I
−0.46066 + 6.48918I 0
u = −0.98850 − 1.01710I
a = −0.138103 − 0.999293I
b = 1.06198 + 1.21767I
−0.46066 − 6.48918I 0
u = −0.328939 + 0.463886I
a = 1.55302 + 0.64027I
b = −0.053887 − 0.497588I
1.328470 − 0.474798I 6.36942 − 0.30577I
u = −0.328939 − 0.463886I
a = 1.55302 − 0.64027I
b = −0.053887 + 0.497588I
1.328470 + 0.474798I 6.36942 + 0.30577I
u = 0.534569 + 0.150336I
a = −0.376119 − 1.361820I
b = 1.31070 + 0.63115I
−2.20215 − 2.11422I −3.95825 + 2.02066I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.534569 − 0.150336I
a = −0.376119 + 1.361820I
b = 1.31070 − 0.63115I
−2.20215 + 2.11422I −3.95825 − 2.02066I
u = 0.526151
a = 4.68059
b = 0.222446
3.74373 −111.560
u = −0.97016 + 1.10954I
a = 0.091135 − 0.575325I
b = −0.885716 + 1.032580I
3.43380 + 4.26674I 0
u = −0.97016 − 1.10954I
a = 0.091135 + 0.575325I
b = −0.885716 − 1.032580I
3.43380 − 4.26674I 0
u = −0.281385 + 0.377115I
a = −1.73924 + 1.56042I
b = −0.465609 + 0.236668I
1.70817 + 1.12824I 3.87173 − 6.48533I
u = −0.281385 − 0.377115I
a = −1.73924 − 1.56042I
b = −0.465609 − 0.236668I
1.70817 − 1.12824I 3.87173 + 6.48533I
u = 0.130457 + 0.443544I
a = 0.83864 + 1.48325I
b = 1.53456 − 1.51852I
1.75853 − 7.50443I 7.50202 + 11.32011I
u = 0.130457 − 0.443544I
a = 0.83864 − 1.48325I
b = 1.53456 + 1.51852I
1.75853 + 7.50443I 7.50202 − 11.32011I
u = −0.43167 + 1.47701I
a = −0.497084 − 0.041859I
b = 1.065130 + 0.173695I
−4.34097 + 0.35523I 0
u = −0.43167 − 1.47701I
a = −0.497084 + 0.041859I
b = 1.065130 − 0.173695I
−4.34097 − 0.35523I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.03967 + 1.15434I
a = −0.175674 − 0.949551I
b = 1.10780 + 1.18726I
−3.18134 − 11.88140I 0
u = 1.03967 − 1.15434I
a = −0.175674 + 0.949551I
b = 1.10780 − 1.18726I
−3.18134 + 11.88140I 0
u = −1.07256 + 1.16076I
a = 0.518563 − 0.163208I
b = −0.354403 − 0.325175I
−0.346472 + 1.021960I 0
u = −1.07256 − 1.16076I
a = 0.518563 + 0.163208I
b = −0.354403 + 0.325175I
−0.346472 − 1.021960I 0
u = −0.065520 + 0.389048I
a = −3.90518 + 0.23427I
b = −0.663122 − 0.134399I
3.88542 + 0.95380I −0.53894 + 3.77835I
u = −0.065520 − 0.389048I
a = −3.90518 − 0.23427I
b = −0.663122 + 0.134399I
3.88542 − 0.95380I −0.53894 − 3.77835I
u = 0.91249 + 1.33131I
a = 0.152639 + 0.727902I
b = −0.806727 − 0.838803I
2.28311 − 5.16223I 0
u = 0.91249 − 1.33131I
a = 0.152639 − 0.727902I
b = −0.806727 + 0.838803I
2.28311 + 5.16223I 0
u = 0.18899 + 1.60874I
a = −0.579596 + 0.139074I
b = 1.208120 − 0.259339I
0.43258 − 3.98462I 0
u = 0.18899 − 1.60874I
a = −0.579596 − 0.139074I
b = 1.208120 + 0.259339I
0.43258 + 3.98462I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.03600 + 1.25835I
a = −0.207314 + 0.919011I
b = 1.13468 − 1.16952I
1.8826 + 16.8363I 0
u = −1.03600 − 1.25835I
a = −0.207314 − 0.919011I
b = 1.13468 + 1.16952I
1.8826 − 16.8363I 0
u = −0.95108 + 1.32857I
a = 0.036047 − 0.766370I
b = −0.884370 + 0.831483I
6.15358 + 7.92208I 0
u = −0.95108 − 1.32857I
a = 0.036047 + 0.766370I
b = −0.884370 − 0.831483I
6.15358 − 7.92208I 0
u = 0.82591 + 1.43030I
a = −0.368712 − 0.006518I
b = 0.909492 − 0.149096I
−0.90960 + 3.32063I 0
u = 0.82591 − 1.43030I
a = −0.368712 + 0.006518I
b = 0.909492 + 0.149096I
−0.90960 − 3.32063I 0
u = −0.196925 + 0.198557I
a = 0.87584 − 2.14816I
b = 1.92387 + 1.05055I
−3.96027 + 2.48444I −5.35559 − 12.59159I
u = −0.196925 − 0.198557I
a = 0.87584 + 2.14816I
b = 1.92387 − 1.05055I
−3.96027 − 2.48444I −5.35559 + 12.59159I
u = 1.27946 + 1.20751I
a = 0.135069 + 0.566822I
b = −0.726578 − 1.080900I
6.23257 − 5.85237I 0
u = 1.27946 − 1.20751I
a = 0.135069 − 0.566822I
b = −0.726578 + 1.080900I
6.23257 + 5.85237I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.94793 + 1.50677I
a = 0.230301 − 0.619665I
b = −0.682958 + 0.866149I
5.82633 + 2.70104I 0
u = −0.94793 − 1.50677I
a = 0.230301 + 0.619665I
b = −0.682958 − 0.866149I
5.82633 − 2.70104I 0
u = 1.50227 + 0.97016I
a = 0.381804 + 0.242487I
b = −0.322820 + 0.301588I
−4.02902 + 3.33307I 0
u = 1.50227 − 0.97016I
a = 0.381804 − 0.242487I
b = −0.322820 − 0.301588I
−4.02902 − 3.33307I 0
u = −1.83497 + 0.74700I
a = 0.279823 − 0.271827I
b = −0.307214 − 0.279280I
0.17127 − 7.70833I 0
u = −1.83497 − 0.74700I
a = 0.279823 + 0.271827I
b = −0.307214 + 0.279280I
0.17127 + 7.70833I 0
12
II.
I
u
2
= h−6.04 × 10
6
u
16
+ 5.00 × 10
6
u
15
+ · · · + 1.00 × 10
7
b − 9.92 × 10
6
, 1.26 ×
10
6
u
16
− 2.09 × 10
7
u
15
+ · · · + 1.00 × 10
7
a + 5.03 × 10
7
, u
17
+ 3u
15
+ · · · + u − 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
7
=
−0.125930u
16
+ 2.08959u
15
+ ··· + 10.3993u − 5.02712
0.604252u
16
− 0.499872u
15
+ ··· − 2.52114u + 0.992256
a
8
=
0.138953u
16
+ 1.97910u
15
+ ··· + 10.0937u − 6.12445
0.331276u
16
− 0.372219u
15
+ ··· − 2.14577u + 0.881767
a
6
=
0.478322u
16
+ 1.58972u
15
+ ··· + 7.87816u − 4.03486
0.604252u
16
− 0.499872u
15
+ ··· − 2.52114u + 0.992256
a
12
=
2.93753u
16
− 0.213439u
15
+ ··· − 8.94162u − 5.24626
−1.08959u
16
− 0.339369u
15
+ ··· + 0.901190u + 1.12593
a
5
=
6.72458u
16
− 0.347814u
15
+ ··· − 15.9518u + 7.15302
−0.0964454u
16
+ 0.0683699u
15
+ ··· + 1.11139u − 0.589717
a
10
=
5.12838u
16
+ 0.385878u
15
+ ··· − 9.07212u − 7.23639
−1.10126u
16
− 0.259949u
15
+ ··· + 1.22931u + 0.864200
a
2
=
−1.44840u
16
− 0.264495u
15
+ ··· + 4.16177u − 1.79318
0.915875u
16
+ 0.244253u
15
+ ··· − 2.29530u + 0.325222
a
1
=
−1.35195u
16
− 0.332865u
15
+ ··· + 3.05037u − 1.20347
0.981428u
16
+ 0.333098u
15
+ ··· − 2.13048u + 0.256852
a
9
=
0.0890174u
16
− 0.254122u
15
+ ··· + 1.05583u − 5.67538
0.942381u
16
+ 0.210599u
15
+ ··· − 2.25734u + 0.290593
(ii) Obstruction class = 1
(iii) Cusp Shapes =
23991057
9996367
u
16
+
18751596
9996367
u
15
+ ··· +
16790502
9996367
u +
371933198
9996367
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 8u
16
+ ··· − 7u + 1
c
2
u
17
− u
16
+ ··· + 85u − 11
c
3
u
17
+ 3u
15
+ ··· + u − 1
c
4
u
17
− u
16
+ ··· − u − 1
c
5
u
17
− u
16
+ ··· − 8u − 5
c
6
u
17
+ 3u
15
+ ··· + 6u + 1
c
7
u
17
+ 4u
16
+ ··· + 6u − 5
c
8
, c
9
u
17
− u
16
+ ··· − 3u + 1
c
10
u
17
+ 3u
16
+ ··· + 3u
2
+ 1
c
11
u
17
+ u
16
+ ··· − 8u + 5
c
12
u
17
+ u
16
+ ··· − 3u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 14y
15
+ ··· + 5y −1
c
2
y
17
+ 9y
16
+ ··· + 2407y −121
c
3
y
17
+ 6y
16
+ ··· − 9y −1
c
4
y
17
− y
16
+ ··· + 15y −1
c
5
, c
11
y
17
+ 11y
16
+ ··· − 186y −25
c
6
y
17
+ 6y
16
+ ··· + 20y −1
c
7
y
17
+ 6y
16
+ ··· + 46y −25
c
8
, c
9
, c
12
y
17
− 19y
16
+ ··· + 23y −1
c
10
y
17
− y
16
+ ··· − 6y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972003 + 0.212018I
a = −0.488289 − 0.271559I
b = 0.336060 + 1.308020I
1.01866 + 6.81301I 4.54269 − 5.97212I
u = 0.972003 − 0.212018I
a = −0.488289 + 0.271559I
b = 0.336060 − 1.308020I
1.01866 − 6.81301I 4.54269 + 5.97212I
u = 0.192968 + 1.105900I
a = −0.631721 + 0.168013I
b = 0.883233 + 0.254108I
−0.82435 − 2.10930I 2.15224 + 0.70653I
u = 0.192968 − 1.105900I
a = −0.631721 − 0.168013I
b = 0.883233 − 0.254108I
−0.82435 + 2.10930I 2.15224 − 0.70653I
u = −0.506977 + 0.637369I
a = −0.605526 + 0.069770I
b = 1.09502 − 0.93131I
−3.76213 − 1.93723I 0.705082 + 0.084395I
u = −0.506977 − 0.637369I
a = −0.605526 − 0.069770I
b = 1.09502 + 0.93131I
−3.76213 + 1.93723I 0.705082 − 0.084395I
u = −0.637103 + 1.057460I
a = 0.126961 − 1.026520I
b = −1.02655 + 1.38119I
10.56410 + 5.07740I 12.18176 − 3.44506I
u = −0.637103 − 1.057460I
a = 0.126961 + 1.026520I
b = −1.02655 − 1.38119I
10.56410 − 5.07740I 12.18176 + 3.44506I
u = 0.030058 + 0.707978I
a = −1.63369 − 1.72427I
b = 0.275529 + 0.997923I
9.31524 − 2.53943I 17.0890 + 7.0986I
u = 0.030058 − 0.707978I
a = −1.63369 + 1.72427I
b = 0.275529 − 0.997923I
9.31524 + 2.53943I 17.0890 − 7.0986I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.632350
a = 3.11676
b = 0.186461
3.79508 54.1520
u = −0.114173 + 0.525642I
a = −2.08531 + 2.37442I
b = −0.061878 − 0.492319I
2.27870 + 0.92922I 21.3078 + 0.7119I
u = −0.114173 − 0.525642I
a = −2.08531 − 2.37442I
b = −0.061878 + 0.492319I
2.27870 − 0.92922I 21.3078 − 0.7119I
u = 0.95698 + 1.17980I
a = 0.103371 + 0.669932I
b = −0.831065 − 1.058980I
3.84695 − 4.69977I 8.87800 + 7.79886I
u = 0.95698 − 1.17980I
a = 0.103371 − 0.669932I
b = −0.831065 + 1.058980I
3.84695 + 4.69977I 8.87800 − 7.79886I
u = −1.20993 + 1.50887I
a = 0.155831 − 0.457656I
b = −0.763587 + 0.778846I
6.91907 + 4.78852I 9.06731 − 5.35952I
u = −1.20993 − 1.50887I
a = 0.155831 + 0.457656I
b = −0.763587 − 0.778846I
6.91907 − 4.78852I 9.06731 + 5.35952I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
− 8u
16
+ ··· − 7u + 1)(u
76
+ 5u
75
+ ··· + 14139u + 307)
c
2
(u
17
− u
16
+ ··· + 85u − 11)(u
76
+ 16u
74
+ ··· − 417u + 9)
c
3
(u
17
+ 3u
15
+ ··· + u − 1)(u
76
− 3u
75
+ ··· + 40u − 8)
c
4
(u
17
− u
16
+ ··· − u − 1)(u
76
+ 25u
74
+ ··· − 40832u − 9472)
c
5
(u
17
− u
16
+ ··· − 8u − 5)(u
76
+ 21u
74
+ ··· − 7422u − 4041)
c
6
(u
17
+ 3u
15
+ ··· + 6u + 1)(u
76
+ 5u
75
+ ··· − 14u + 1)
c
7
(u
17
+ 4u
16
+ ··· + 6u − 5)(u
76
+ u
75
+ ··· + 280u − 19)
c
8
, c
9
(u
17
− u
16
+ ··· − 3u + 1)(u
76
− 32u
74
+ ··· − 141u + 19)
c
10
(u
17
+ 3u
16
+ ··· + 3u
2
+ 1)(u
76
− 4u
75
+ ··· + 100u − 1)
c
11
(u
17
+ u
16
+ ··· − 8u + 5)(u
76
+ 21u
74
+ ··· − 7422u − 4041)
c
12
(u
17
+ u
16
+ ··· − 3u − 1)(u
76
− 32u
74
+ ··· − 141u + 19)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
− 14y
15
+ ··· + 5y −1)
· (y
76
− 57y
75
+ ··· − 374836851y + 94249)
c
2
(y
17
+ 9y
16
+ ··· + 2407y −121)(y
76
+ 32y
75
+ ··· − 151605y + 81)
c
3
(y
17
+ 6y
16
+ ··· − 9y −1)(y
76
+ 13y
75
+ ··· + 1568y + 64)
c
4
(y
17
− y
16
+ ··· + 15y −1)
· (y
76
+ 50y
75
+ ··· + 4136583168y + 89718784)
c
5
, c
11
(y
17
+ 11y
16
+ ··· − 186y −25)
· (y
76
+ 42y
75
+ ··· + 335290680y + 16329681)
c
6
(y
17
+ 6y
16
+ ··· + 20y −1)(y
76
+ 9y
75
+ ··· − 22y + 1)
c
7
(y
17
+ 6y
16
+ ··· + 46y −25)(y
76
+ 17y
75
+ ··· − 28924y + 361)
c
8
, c
9
, c
12
(y
17
− 19y
16
+ ··· + 23y −1)(y
76
− 64y
75
+ ··· + 5199y + 361)
c
10
(y
17
− y
16
+ ··· − 6y −1)(y
76
+ 10y
75
+ ··· − 8956y + 1)
19
