12n
0396
(K12n
0396
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 9 2 12 1 12 4 8 5
Solving Sequence
5,12 1,10
4 9 6 8 3 2 7 11
c
12
c
4
c
9
c
5
c
8
c
3
c
2
c
6
c
11
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.96098 × 10
119
u
60
− 8.03566 × 10
119
u
59
+ ··· + 1.57498 × 10
117
b − 7.94333 × 10
120
,
− 4.40897 × 10
120
u
60
− 1.19687 × 10
121
u
59
+ ··· + 2.99247 × 10
118
a − 1.18579 × 10
122
,
u
61
+ 2u
60
+ ··· − 76u − 19i
I
u
2
= h−1.15866 × 10
17
u
27
+ 2.41753 × 10
17
u
26
+ ··· + 7.07730 × 10
17
b + 1.02954 × 10
18
,
3.01367 × 10
17
u
27
+ 5.60690 × 10
16
u
26
+ ··· + 7.07730 × 10
17
a + 1.80278 × 10
18
, u
28
− u
27
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 89 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−2.96 × 10
119
u
60
− 8.04 × 10
119
u
59
+ · · · + 1.57 × 10
117
b − 7.94 ×
10
120
, −4.41 × 10
120
u
60
− 1.20 × 10
121
u
59
+ · · · + 2.99 × 10
118
a − 1.19 ×
10
122
, u
61
+ 2u
60
+ · · · − 76u − 19i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
10
=
147.336u
60
+ 399.962u
59
+ ··· + 21361.8u + 3962.58
188.001u
60
+ 510.206u
59
+ ··· + 27232.1u + 5043.44
a
4
=
39.5209u
60
+ 107.101u
59
+ ··· + 5741.11u + 1070.30
182.349u
60
+ 493.732u
59
+ ··· + 26284.5u + 4863.37
a
9
=
−40.6653u
60
− 110.244u
59
+ ··· − 5870.31u − 1080.86
188.001u
60
+ 510.206u
59
+ ··· + 27232.1u + 5043.44
a
6
=
76.4909u
60
+ 207.985u
59
+ ··· + 11163.0u + 2075.69
−219.319u
60
− 594.616u
59
+ ··· − 31704.4u − 5868.76
a
8
=
126.765u
60
+ 344.336u
59
+ ··· + 18391.7u + 3413.23
103.129u
60
+ 279.972u
59
+ ··· + 14952.3u + 2768.79
a
3
=
43.5638u
60
+ 118.466u
59
+ ··· + 6304.28u + 1174.55
105.291u
60
+ 285.368u
59
+ ··· + 15160.1u + 2799.38
a
2
=
−28.7474u
60
− 81.0140u
59
+ ··· − 4637.56u − 879.035
16.0573u
60
+ 44.4956u
59
+ ··· + 2463.99u + 460.188
a
7
=
−23.6360u
60
− 64.3645u
59
+ ··· − 3439.43u − 644.437
−103.129u
60
− 279.972u
59
+ ··· − 14952.3u − 2768.79
a
11
=
86.9161u
60
+ 235.789u
59
+ ··· + 12531.9u + 2321.16
223.821u
60
+ 605.501u
59
+ ··· + 32142.9u + 5936.73
(ii) Obstruction class = −1
(iii) Cusp Shapes = 21.9680u
60
+ 64.0290u
59
+ ··· + 3263.11u + 632.215
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
61
+ 25u
60
+ ··· + 1370u − 1
c
2
, c
6
u
61
− u
60
+ ··· + 34u + 1
c
3
u
61
− u
60
+ ··· + 4446u − 457
c
4
, c
10
u
61
− u
60
+ ··· − 1806u − 419
c
5
u
61
− 4u
60
+ ··· + 1708u − 491
c
7
, c
11
u
61
+ u
60
+ ··· + 99546436u − 13493731
c
8
u
61
+ 5u
60
+ ··· − 3032u − 3995
c
9
u
61
+ 14u
60
+ ··· − 96977u − 34681
c
12
u
61
− 2u
60
+ ··· − 76u + 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
61
+ 37y
60
+ ··· + 1971254y −1
c
2
, c
6
y
61
+ 25y
60
+ ··· + 1370y −1
c
3
y
61
+ 121y
60
+ ··· + 5985624y −208849
c
4
, c
10
y
61
+ 89y
60
+ ··· − 560482y −175561
c
5
y
61
− 16y
60
+ ··· − 1860166y −241081
c
7
, c
11
y
61
− 103y
60
+ ··· − 592149097680014y −182080776300361
c
8
y
61
+ 15y
60
+ ··· − 71386126y −15960025
c
9
y
61
− 50y
60
+ ··· + 15117817107y −1202771761
c
12
y
61
− 8y
60
+ ··· + 11324y −361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.726966 + 0.679000I
a = −0.230767 − 0.059357I
b = −1.380190 + 0.112865I
−0.39695 + 7.20473I 0
u = 0.726966 − 0.679000I
a = −0.230767 + 0.059357I
b = −1.380190 − 0.112865I
−0.39695 − 7.20473I 0
u = −0.875047 + 0.392404I
a = −0.47290 + 2.04945I
b = −1.125280 − 0.174220I
13.1897 − 5.2499I 0
u = −0.875047 − 0.392404I
a = −0.47290 − 2.04945I
b = −1.125280 + 0.174220I
13.1897 + 5.2499I 0
u = −0.686697 + 0.668109I
a = −0.142029 − 0.279533I
b = −0.950069 − 0.505344I
0.97517 − 2.05582I 0
u = −0.686697 − 0.668109I
a = −0.142029 + 0.279533I
b = −0.950069 + 0.505344I
0.97517 + 2.05582I 0
u = −0.771408 + 0.558902I
a = 0.855387 + 0.424717I
b = −0.529958 + 0.377542I
1.45455 − 2.20607I 0
u = −0.771408 − 0.558902I
a = 0.855387 − 0.424717I
b = −0.529958 − 0.377542I
1.45455 + 2.20607I 0
u = 0.869455 + 0.365490I
a = −0.68027 − 2.08352I
b = −0.861856 + 0.200205I
13.34180 − 0.97900I 0
u = 0.869455 − 0.365490I
a = −0.68027 + 2.08352I
b = −0.861856 − 0.200205I
13.34180 + 0.97900I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.705296 + 0.787110I
a = 0.365472 − 0.248330I
b = −0.616614 − 0.573787I
−3.39919 + 1.16742I 0
u = 0.705296 − 0.787110I
a = 0.365472 + 0.248330I
b = −0.616614 + 0.573787I
−3.39919 − 1.16742I 0
u = 0.812877 + 0.431384I
a = 0.549432 − 0.418684I
b = −0.504160 − 0.006726I
0.36729 − 2.80634I 0
u = 0.812877 − 0.431384I
a = 0.549432 + 0.418684I
b = −0.504160 + 0.006726I
0.36729 + 2.80634I 0
u = −0.780322 + 0.432313I
a = −0.74003 + 1.52918I
b = −1.62681 + 0.60427I
7.59223 − 1.75046I 0. + 3.23996I
u = −0.780322 − 0.432313I
a = −0.74003 − 1.52918I
b = −1.62681 − 0.60427I
7.59223 + 1.75046I 0. − 3.23996I
u = −0.782122 + 0.813062I
a = 0.920690 − 0.309572I
b = 0.090638 + 0.459504I
−0.92589 − 1.49460I 0
u = −0.782122 − 0.813062I
a = 0.920690 + 0.309572I
b = 0.090638 − 0.459504I
−0.92589 + 1.49460I 0
u = 0.766937 + 0.356712I
a = −0.78300 − 1.73528I
b = −0.748000 − 1.154520I
7.96502 + 1.47006I 1.19768 − 5.86407I
u = 0.766937 − 0.356712I
a = −0.78300 + 1.73528I
b = −0.748000 + 1.154520I
7.96502 − 1.47006I 1.19768 + 5.86407I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.820762 + 0.035126I
a = 0.025762 − 1.070560I
b = 0.96419 − 1.42306I
2.72013 − 4.69538I 8.21020 + 6.35662I
u = −0.820762 − 0.035126I
a = 0.025762 + 1.070560I
b = 0.96419 + 1.42306I
2.72013 + 4.69538I 8.21020 − 6.35662I
u = −0.668997 + 0.434762I
a = −1.35708 + 1.70611I
b = −2.67172 + 1.77247I
12.42490 + 1.87507I 8.22328 + 3.06573I
u = −0.668997 − 0.434762I
a = −1.35708 − 1.70611I
b = −2.67172 − 1.77247I
12.42490 − 1.87507I 8.22328 − 3.06573I
u = 0.663299 + 0.399729I
a = −1.23402 − 1.94571I
b = −2.27338 − 2.29267I
12.56990 + 4.12429I 8.83070 − 8.92853I
u = 0.663299 − 0.399729I
a = −1.23402 + 1.94571I
b = −2.27338 + 2.29267I
12.56990 − 4.12429I 8.83070 + 8.92853I
u = −0.999522 + 0.784828I
a = 0.339017 − 0.929172I
b = 1.18055 − 1.23638I
−0.26229 − 4.50672I 0
u = −0.999522 − 0.784828I
a = 0.339017 + 0.929172I
b = 1.18055 + 1.23638I
−0.26229 + 4.50672I 0
u = −0.673114 + 0.229923I
a = −1.17312 + 1.10043I
b = 1.004440 − 0.010897I
1.87484 − 5.76780I 8.27915 + 6.01369I
u = −0.673114 − 0.229923I
a = −1.17312 − 1.10043I
b = 1.004440 + 0.010897I
1.87484 + 5.76780I 8.27915 − 6.01369I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.711299 + 0.000372I
a = 0.176203 + 0.946068I
b = 1.49076 + 1.19282I
3.84612 − 0.01760I 12.41131 + 0.33539I
u = 0.711299 − 0.000372I
a = 0.176203 − 0.946068I
b = 1.49076 − 1.19282I
3.84612 + 0.01760I 12.41131 − 0.33539I
u = 0.690752 + 0.149932I
a = −1.24503 − 0.94277I
b = 1.053100 + 0.036616I
3.60663 + 0.64270I 10.66774 − 1.11520I
u = 0.690752 − 0.149932I
a = −1.24503 + 0.94277I
b = 1.053100 − 0.036616I
3.60663 − 0.64270I 10.66774 + 1.11520I
u = 0.666210
a = −0.620179
b = 1.36454
2.55102 −1.40580
u = 1.091640 + 0.786832I
a = 0.082122 + 0.498308I
b = 0.739742 + 0.883315I
−2.15310 + 4.74224I 0
u = 1.091640 − 0.786832I
a = 0.082122 − 0.498308I
b = 0.739742 − 0.883315I
−2.15310 − 4.74224I 0
u = 1.079410 + 0.861460I
a = −0.087453 + 1.131980I
b = 1.16805 + 1.07452I
4.14492 + 9.07328I 0
u = 1.079410 − 0.861460I
a = −0.087453 − 1.131980I
b = 1.16805 − 1.07452I
4.14492 − 9.07328I 0
u = −1.101140 + 0.886669I
a = 0.120210 − 1.120340I
b = 1.123830 − 0.809916I
4.47537 − 2.71866I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.101140 − 0.886669I
a = 0.120210 + 1.120340I
b = 1.123830 + 0.809916I
4.47537 + 2.71866I 0
u = −1.00173 + 1.00324I
a = 0.864058 − 0.327243I
b = 1.50512 + 0.06717I
3.99030 − 4.68111I 0
u = −1.00173 − 1.00324I
a = 0.864058 + 0.327243I
b = 1.50512 − 0.06717I
3.99030 + 4.68111I 0
u = −0.284071 + 0.480320I
a = 0.653928 − 0.889307I
b = 0.192049 − 0.368264I
0.126806 − 1.131010I 1.48638 + 6.15892I
u = −0.284071 − 0.480320I
a = 0.653928 + 0.889307I
b = 0.192049 + 0.368264I
0.126806 + 1.131010I 1.48638 − 6.15892I
u = 0.96181 + 1.10808I
a = 0.850926 + 0.018700I
b = 1.121250 − 0.516410I
3.31319 − 1.80350I 0
u = 0.96181 − 1.10808I
a = 0.850926 − 0.018700I
b = 1.121250 + 0.516410I
3.31319 + 1.80350I 0
u = −1.19981 + 0.95170I
a = −0.586023 + 1.122640I
b = −1.74762 + 1.13918I
14.2638 − 15.4086I 0
u = −1.19981 − 0.95170I
a = −0.586023 − 1.122640I
b = −1.74762 − 1.13918I
14.2638 + 15.4086I 0
u = −0.413783 + 0.174153I
a = −1.22718 + 1.44451I
b = 0.779070 + 0.027625I
−0.577442 + 0.867661I 3.54220 − 1.55941I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.413783 − 0.174153I
a = −1.22718 − 1.44451I
b = 0.779070 − 0.027625I
−0.577442 − 0.867661I 3.54220 + 1.55941I
u = 1.21410 + 1.00732I
a = −0.684959 − 1.075550I
b = −1.74677 − 0.90885I
16.2354 + 8.5140I 0
u = 1.21410 − 1.00732I
a = −0.684959 + 1.075550I
b = −1.74677 + 0.90885I
16.2354 − 8.5140I 0
u = −0.94282 + 1.34692I
a = −1.065560 + 0.485760I
b = −1.079560 − 0.281696I
13.0287 + 7.2582I 0
u = −0.94282 − 1.34692I
a = −1.065560 − 0.485760I
b = −1.079560 + 0.281696I
13.0287 − 7.2582I 0
u = 1.10472 + 1.30488I
a = −0.983159 − 0.647679I
b = −1.302950 + 0.023682I
15.3849 + 0.0125I 0
u = 1.10472 − 1.30488I
a = −0.983159 + 0.647679I
b = −1.302950 − 0.023682I
15.3849 − 0.0125I 0
u = −1.38674 + 1.15686I
a = −0.681273 + 0.791297I
b = −1.232310 + 0.599781I
7.54707 − 4.86571I 0
u = −1.38674 − 1.15686I
a = −0.681273 − 0.791297I
b = −1.232310 − 0.599781I
7.54707 + 4.86571I 0
u = 0.65643 + 1.91854I
a = 0.380740 + 0.457124I
b = 0.302176 + 0.330402I
−5.84281 + 2.46686I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.65643 − 1.91854I
a = 0.380740 − 0.457124I
b = 0.302176 − 0.330402I
−5.84281 − 2.46686I 0
11
II.
I
u
2
= h−1.16×10
17
u
27
+2.42×10
17
u
26
+· · ·+7.08×10
17
b+1.03×10
18
, 3.01×
10
17
u
27
+5.61×10
16
u
26
+· · ·+7.08×10
17
a+1.80×10
18
, u
28
−u
27
+· · ·−u+1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
10
=
−0.425822u
27
− 0.0792238u
26
+ ··· − 3.95926u − 2.54727
0.163715u
27
− 0.341590u
26
+ ··· − 1.74850u − 1.45471
a
4
=
2.75982u
27
− 2.52025u
26
+ ··· + 11.4180u − 4.43000
1.63228u
27
− 1.16592u
26
+ ··· + 7.03643u − 1.81633
a
9
=
−0.589537u
27
+ 0.262366u
26
+ ··· − 2.21075u − 1.09257
0.163715u
27
− 0.341590u
26
+ ··· − 1.74850u − 1.45471
a
6
=
0.226629u
27
− 0.385302u
26
+ ··· + 3.03735u − 1.54642
0.900907u
27
− 0.969026u
26
+ ··· + 3.34424u − 1.06726
a
8
=
−0.816329u
27
+ 0.184047u
26
+ ··· − 3.69689u − 2.22010
0.239570u
27
− 0.350091u
26
+ ··· − 1.67019u − 1.75982
a
3
=
−0.816986u
27
+ 0.686655u
26
+ ··· − 2.11709u + 1.42597
−0.505046u
27
+ 0.265362u
26
+ ··· − 2.97310u + 0.425822
a
2
=
−0.533956u
27
+ 0.229556u
26
+ ··· − 3.31604u − 0.492592
−0.246269u
27
− 0.205594u
26
+ ··· − 1.24312u − 1.67842
a
7
=
−1.05590u
27
+ 0.534138u
26
+ ··· − 2.02670u − 0.460285
0.239570u
27
− 0.350091u
26
+ ··· − 1.67019u − 1.75982
a
11
=
1.42582u
27
+ 0.0792238u
26
+ ··· + 10.9593u + 5.54727
0.186139u
27
+ 0.260571u
26
+ ··· + 3.88003u + 4.05232
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1324489982334781349
707729639082377921
u
27
+
406096222270673532
707729639082377921
u
26
+ ··· −
701121119184732213
707729639082377921
u +
6006310912169242997
707729639082377921
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
28
− 18u
27
+ ··· − 119u + 9
c
2
u
28
+ 9u
26
+ ··· + u + 3
c
3
u
28
+ 15u
26
+ ··· − 309u + 99
c
4
u
28
+ 15u
26
+ ··· + 3u + 1
c
5
u
28
− u
27
+ ··· − 7u + 1
c
6
u
28
+ 9u
26
+ ··· − u + 3
c
7
u
28
− 2u
27
+ ··· + 7u + 1
c
8
u
28
− 4u
26
+ ··· + 3u + 1
c
9
u
28
+ 7u
27
+ ··· + 6u + 1
c
10
u
28
+ 15u
26
+ ··· − 3u + 1
c
11
u
28
+ 2u
27
+ ··· − 7u + 1
c
12
u
28
− u
27
+ ··· − u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 2y
27
+ ··· + 563y + 81
c
2
, c
6
y
28
+ 18y
27
+ ··· + 119y + 9
c
3
y
28
+ 30y
27
+ ··· + 57969y + 9801
c
4
, c
10
y
28
+ 30y
27
+ ··· + 27y + 1
c
5
y
28
+ y
27
+ ··· − 25y + 1
c
7
, c
11
y
28
− 14y
27
+ ··· + 15y + 1
c
8
y
28
− 8y
27
+ ··· + 15y + 1
c
9
y
28
− 21y
27
+ ··· + 10y + 1
c
12
y
28
+ y
27
+ ··· + 5y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.702052 + 0.710332I
a = 0.857396 − 0.334821I
b = −0.263227 + 0.411890I
−1.74769 − 0.16344I 0.141433 − 0.136539I
u = −0.702052 − 0.710332I
a = 0.857396 + 0.334821I
b = −0.263227 − 0.411890I
−1.74769 + 0.16344I 0.141433 + 0.136539I
u = 0.929799 + 0.320741I
a = 0.096618 + 0.339668I
b = 1.032050 − 0.370405I
1.14047 − 3.70350I 4.84363 + 4.23194I
u = 0.929799 − 0.320741I
a = 0.096618 − 0.339668I
b = 1.032050 + 0.370405I
1.14047 + 3.70350I 4.84363 − 4.23194I
u = 0.807818 + 0.736725I
a = 0.702139 + 0.301480I
b = 0.004590 − 0.562515I
−1.67195 + 2.90344I 1.31719 − 4.53689I
u = 0.807818 − 0.736725I
a = 0.702139 − 0.301480I
b = 0.004590 + 0.562515I
−1.67195 − 2.90344I 1.31719 + 4.53689I
u = 0.161477 + 0.864236I
a = 1.125520 − 0.462351I
b = 0.303103 + 0.274488I
2.01588 + 0.05500I 4.86588 − 0.08812I
u = 0.161477 − 0.864236I
a = 1.125520 + 0.462351I
b = 0.303103 − 0.274488I
2.01588 − 0.05500I 4.86588 + 0.08812I
u = 0.871653 + 0.745728I
a = 0.338920 + 0.812501I
b = 1.55229 + 0.65793I
0.59797 + 8.54813I 3.23391 − 9.48208I
u = 0.871653 − 0.745728I
a = 0.338920 − 0.812501I
b = 1.55229 − 0.65793I
0.59797 − 8.54813I 3.23391 + 9.48208I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.816267 + 0.837532I
a = 0.357595 − 0.800294I
b = 1.265940 − 0.477611I
2.12233 − 3.64186I 4.74207 + 4.00458I
u = −0.816267 − 0.837532I
a = 0.357595 + 0.800294I
b = 1.265940 + 0.477611I
2.12233 + 3.64186I 4.74207 − 4.00458I
u = 0.777892 + 0.262089I
a = −0.52453 − 1.82829I
b = −1.23714 − 1.08838I
8.42193 + 1.08621I 12.97797 + 3.21719I
u = 0.777892 − 0.262089I
a = −0.52453 + 1.82829I
b = −1.23714 + 1.08838I
8.42193 − 1.08621I 12.97797 − 3.21719I
u = −0.402909 + 0.676482I
a = 1.371320 − 0.071287I
b = −0.186336 − 0.319339I
0.62992 − 5.52513I 1.53066 + 4.97462I
u = −0.402909 − 0.676482I
a = 1.371320 + 0.071287I
b = −0.186336 + 0.319339I
0.62992 + 5.52513I 1.53066 − 4.97462I
u = 0.999978 + 0.725902I
a = 0.311176 + 0.821553I
b = 1.34379 + 1.18837I
−1.03388 + 2.66855I 3.05978 − 0.97697I
u = 0.999978 − 0.725902I
a = 0.311176 − 0.821553I
b = 1.34379 − 1.18837I
−1.03388 − 2.66855I 3.05978 + 0.97697I
u = −1.132400 + 0.517279I
a = −0.584826 + 1.142560I
b = −0.898312 + 0.872745I
6.57826 − 3.10189I 4.06886 + 3.92167I
u = −1.132400 − 0.517279I
a = −0.584826 − 1.142560I
b = −0.898312 − 0.872745I
6.57826 + 3.10189I 4.06886 − 3.92167I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.678921 + 0.199447I
a = −0.374227 − 0.491947I
b = 1.340810 + 0.233735I
2.95059 − 0.55691I 5.48175 + 6.90028I
u = −0.678921 − 0.199447I
a = −0.374227 + 0.491947I
b = 1.340810 − 0.233735I
2.95059 + 0.55691I 5.48175 − 6.90028I
u = −1.089850 + 0.744629I
a = 0.280576 − 0.817045I
b = 1.00656 − 1.25835I
−0.47467 − 5.44176I 1.37883 + 9.36383I
u = −1.089850 − 0.744629I
a = 0.280576 + 0.817045I
b = 1.00656 + 1.25835I
−0.47467 + 5.44176I 1.37883 − 9.36383I
u = 0.115959 + 0.392417I
a = −4.32508 − 1.45221I
b = −2.18796 − 0.36120I
12.51090 + 3.10926I 6.97168 − 1.87926I
u = 0.115959 − 0.392417I
a = −4.32508 + 1.45221I
b = −2.18796 + 0.36120I
12.51090 − 3.10926I 6.97168 + 1.87926I
u = 0.65783 + 1.97053I
a = 0.367396 + 0.471354I
b = 0.423846 + 0.324990I
−5.72113 + 2.57039I 0
u = 0.65783 − 1.97053I
a = 0.367396 − 0.471354I
b = 0.423846 − 0.324990I
−5.72113 − 2.57039I 0
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 18u
27
+ ··· − 119u + 9)(u
61
+ 25u
60
+ ··· + 1370u − 1)
c
2
(u
28
+ 9u
26
+ ··· + u + 3)(u
61
− u
60
+ ··· + 34u + 1)
c
3
(u
28
+ 15u
26
+ ··· − 309u + 99)(u
61
− u
60
+ ··· + 4446u − 457)
c
4
(u
28
+ 15u
26
+ ··· + 3u + 1)(u
61
− u
60
+ ··· − 1806u − 419)
c
5
(u
28
− u
27
+ ··· − 7u + 1)(u
61
− 4u
60
+ ··· + 1708u − 491)
c
6
(u
28
+ 9u
26
+ ··· − u + 3)(u
61
− u
60
+ ··· + 34u + 1)
c
7
(u
28
− 2u
27
+ ··· + 7u + 1)(u
61
+ u
60
+ ··· + 9.95464 × 10
7
u − 1.34937 × 10
7
)
c
8
(u
28
− 4u
26
+ ··· + 3u + 1)(u
61
+ 5u
60
+ ··· − 3032u − 3995)
c
9
(u
28
+ 7u
27
+ ··· + 6u + 1)(u
61
+ 14u
60
+ ··· − 96977u − 34681)
c
10
(u
28
+ 15u
26
+ ··· − 3u + 1)(u
61
− u
60
+ ··· − 1806u − 419)
c
11
(u
28
+ 2u
27
+ ··· − 7u + 1)(u
61
+ u
60
+ ··· + 9.95464 × 10
7
u − 1.34937 × 10
7
)
c
12
(u
28
− u
27
+ ··· − u + 1)(u
61
− 2u
60
+ ··· − 76u + 19)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
− 2y
27
+ ··· + 563y + 81)(y
61
+ 37y
60
+ ··· + 1971254y −1)
c
2
, c
6
(y
28
+ 18y
27
+ ··· + 119y + 9)(y
61
+ 25y
60
+ ··· + 1370y −1)
c
3
(y
28
+ 30y
27
+ ··· + 57969y + 9801)
· (y
61
+ 121y
60
+ ··· + 5985624y −208849)
c
4
, c
10
(y
28
+ 30y
27
+ ··· + 27y + 1)(y
61
+ 89y
60
+ ··· − 560482y −175561)
c
5
(y
28
+ y
27
+ ··· − 25y + 1)(y
61
− 16y
60
+ ··· − 1860166y −241081)
c
7
, c
11
(y
28
− 14y
27
+ ··· + 15y + 1)
· (y
61
− 103y
60
+ ··· − 592149097680014y −182080776300361)
c
8
(y
28
− 8y
27
+ ··· + 15y + 1)
· (y
61
+ 15y
60
+ ··· − 71386126y −15960025)
c
9
(y
28
− 21y
27
+ ··· + 10y + 1)
· (y
61
− 50y
60
+ ··· + 15117817107y −1202771761)
c
12
(y
28
+ y
27
+ ··· + 5y + 1)(y
61
− 8y
60
+ ··· + 11324y −361)
21
