12a
0190
(K12a
0190
)
A knot diagram
1
Linearized knot diagam
3 5 9 8 2 10 11 1 12 7 6 4
Solving Sequence
6,10
7 11 8
2,12
5 3 1 4 9
c
6
c
10
c
7
c
11
c
5
c
2
c
1
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.67377 × 10
71
u
109
− 5.17463 × 10
71
u
108
+ ··· + 4.10404 × 10
71
b + 5.42742 × 10
71
,
− 9.81616 × 10
71
u
109
+ 1.63462 × 10
72
u
108
+ ··· + 2.05202 × 10
71
a − 7.57506 × 10
71
,
u
110
− 3u
109
+ ··· + 8u − 1i
I
u
2
= h2b − a − 1, a
2
+ 3, u + 1i
* 2 irreducible components of dim
C
= 0, with total 112 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
= h2.67 × 10
71
u
109
− 5.17 × 10
71
u
108
+ · · · + 4.10 × 10
71
b + 5.43 ×
10
71
, −9.82 × 10
71
u
109
+ 1.63 × 10
72
u
108
+ · · · + 2.05 × 10
71
a − 7.58 ×
10
71
, u
110
− 3u
109
+ · · · + 8u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u
2
a
11
=
u
−u
3
+ u
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
4.78366u
109
− 7.96591u
108
+ ··· − 16.2149u + 3.69151
−0.651497u
109
+ 1.26086u
108
+ ··· + 10.2507u − 1.32246
a
12
=
−u
3
+ 2u
−u
3
+ u
a
5
=
−14.0684u
109
+ 25.6715u
108
+ ··· + 96.8437u − 13.6523
−0.875843u
109
+ 1.66189u
108
+ ··· + 11.1520u − 2.38600
a
3
=
−13.3409u
109
+ 24.7528u
108
+ ··· + 99.6560u − 15.0161
−1.58470u
109
+ 2.94901u
108
+ ··· + 15.5277u − 3.08164
a
1
=
2.29763u
109
− 3.93043u
108
+ ··· − 9.56518u − 0.0651181
0.683728u
109
− 0.838824u
108
+ ··· − 0.453193u − 0.136203
a
4
=
−11.4285u
109
+ 22.4100u
108
+ ··· + 92.0592u − 13.8943
3.48936u
109
− 5.81189u
108
+ ··· − 16.2207u + 1.70832
a
9
=
u
7
− 4u
5
+ 4u
3
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 82.9086u
109
− 149.372u
108
+ ··· − 520.277u + 76.7509
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
110
+ 42u
109
+ ··· − 41u + 1
c
2
, c
5
u
110
+ 2u
109
+ ··· − 5u + 1
c
3
u
110
+ 2u
109
+ ··· + 102407u − 11029
c
4
u
110
+ 4u
109
+ ··· − 120613u + 16231
c
6
, c
7
, c
10
u
110
− 3u
109
+ ··· + 8u − 1
c
8
u
110
− 7u
109
+ ··· + 4u
2
− 1
c
9
u
110
− 21u
109
+ ··· − 3668038u + 132529
c
11
u
110
+ 3u
109
+ ··· − 60672u + 14144
c
12
u
110
+ 11u
109
+ ··· − 4u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
110
+ 54y
109
+ ··· − 249y + 1
c
2
, c
5
y
110
+ 42y
109
+ ··· − 41y + 1
c
3
y
110
− 142y
109
+ ··· − 10478723377y + 121638841
c
4
y
110
− 90y
109
+ ··· − 24945269141y + 263445361
c
6
, c
7
, c
10
y
110
− 101y
109
+ ··· − 8y + 1
c
8
y
110
− 13y
109
+ ··· − 8y + 1
c
9
y
110
+ 63y
109
+ ··· + 713896960236y + 17563935841
c
11
y
110
− 23y
109
+ ··· − 7863217792y + 200052736
c
12
y
110
− 15y
109
+ ··· − 264y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.042430 + 0.304760I
a = 0.69080 − 1.25394I
b = −0.490951 − 0.711163I
1.73683 + 1.13820I 0
u = 1.042430 − 0.304760I
a = 0.69080 + 1.25394I
b = −0.490951 + 0.711163I
1.73683 − 1.13820I 0
u = 0.709787 + 0.529952I
a = 0.094658 + 0.769532I
b = −0.612347 + 0.859094I
3.00793 − 1.60581I 0
u = 0.709787 − 0.529952I
a = 0.094658 − 0.769532I
b = −0.612347 − 0.859094I
3.00793 + 1.60581I 0
u = 0.633711 + 0.588741I
a = 0.668832 − 1.023250I
b = −0.615338 − 0.830644I
3.09579 + 3.22900I 0
u = 0.633711 − 0.588741I
a = 0.668832 + 1.023250I
b = −0.615338 + 0.830644I
3.09579 − 3.22900I 0
u = −1.136620 + 0.182300I
a = −0.14401 − 1.78120I
b = −0.070153 − 1.175620I
−2.43949 − 3.79745I 0
u = −1.136620 − 0.182300I
a = −0.14401 + 1.78120I
b = −0.070153 + 1.175620I
−2.43949 + 3.79745I 0
u = 0.356416 + 0.767376I
a = 0.95148 − 1.95836I
b = −0.613775 − 0.920723I
1.82712 + 6.13376I 0
u = 0.356416 − 0.767376I
a = 0.95148 + 1.95836I
b = −0.613775 + 0.920723I
1.82712 − 6.13376I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.406637 + 0.732719I
a = −0.474129 + 0.329964I
b = −0.605411 + 0.753946I
2.34496 + 1.30819I 0
u = 0.406637 − 0.732719I
a = −0.474129 − 0.329964I
b = −0.605411 − 0.753946I
2.34496 − 1.30819I 0
u = −0.631106 + 0.523418I
a = 0.063499 − 0.929955I
b = −0.693197 − 1.091710I
3.03970 + 10.45680I 0
u = −0.631106 − 0.523418I
a = 0.063499 + 0.929955I
b = −0.693197 + 1.091710I
3.03970 − 10.45680I 0
u = −0.357210 + 0.732588I
a = 1.23601 + 2.38787I
b = −0.697975 + 1.114660I
2.0566 − 14.7635I 0
u = −0.357210 − 0.732588I
a = 1.23601 − 2.38787I
b = −0.697975 − 1.114660I
2.0566 + 14.7635I 0
u = −0.365820 + 0.709983I
a = −0.877302 + 0.431752I
b = −0.924219 − 0.528395I
3.85584 − 8.80943I 6.00000 + 6.63181I
u = −0.365820 − 0.709983I
a = −0.877302 − 0.431752I
b = −0.924219 + 0.528395I
3.85584 + 8.80943I 6.00000 − 6.63181I
u = 1.196860 + 0.125400I
a = 0.679124 − 0.504764I
b = −0.287494 − 0.066047I
1.85030 + 0.56407I 0
u = 1.196860 − 0.125400I
a = 0.679124 + 0.504764I
b = −0.287494 + 0.066047I
1.85030 − 0.56407I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.207530 + 0.036111I
a = −2.05692 + 4.49642I
b = 0.475367 + 0.904372I
2.18862 + 2.29145I 0
u = 1.207530 − 0.036111I
a = −2.05692 − 4.49642I
b = 0.475367 − 0.904372I
2.18862 − 2.29145I 0
u = −0.585644 + 0.524890I
a = 0.307417 + 0.678703I
b = −0.887496 + 0.553841I
4.68466 + 4.61363I 10.47045 + 0.I
u = −0.585644 − 0.524890I
a = 0.307417 − 0.678703I
b = −0.887496 − 0.553841I
4.68466 − 4.61363I 10.47045 + 0.I
u = 1.167380 + 0.336331I
a = −0.364740 + 0.861422I
b = −0.564442 + 0.983855I
0.77242 − 3.22559I 0
u = 1.167380 − 0.336331I
a = −0.364740 − 0.861422I
b = −0.564442 − 0.983855I
0.77242 + 3.22559I 0
u = 0.022669 + 0.764528I
a = −0.28681 − 2.41502I
b = −0.590058 − 1.033690I
−2.73847 + 7.20991I 2.16879 − 8.38863I
u = 0.022669 − 0.764528I
a = −0.28681 + 2.41502I
b = −0.590058 + 1.033690I
−2.73847 − 7.20991I 2.16879 + 8.38863I
u = −1.240340 + 0.100015I
a = −0.54389 − 1.88615I
b = 0.554895 − 1.160570I
2.33423 − 4.86971I 0
u = −1.240340 − 0.100015I
a = −0.54389 + 1.88615I
b = 0.554895 + 1.160570I
2.33423 + 4.86971I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.214290 + 0.306199I
a = 1.03227 + 1.77137I
b = −0.618109 + 1.069640I
1.06963 − 11.08770I 0
u = −1.214290 − 0.306199I
a = 1.03227 − 1.77137I
b = −0.618109 − 1.069640I
1.06963 + 11.08770I 0
u = −0.310953 + 0.669600I
a = −1.14221 − 2.41787I
b = 0.069246 − 1.279980I
−3.10384 − 6.63654I 1.93522 + 9.14652I
u = −0.310953 − 0.669600I
a = −1.14221 + 2.41787I
b = 0.069246 + 1.279980I
−3.10384 + 6.63654I 1.93522 − 9.14652I
u = −1.244590 + 0.256295I
a = −0.253010 + 0.080772I
b = −0.743437 − 0.435345I
2.87173 − 5.93046I 0
u = −1.244590 − 0.256295I
a = −0.253010 − 0.080772I
b = −0.743437 + 0.435345I
2.87173 + 5.93046I 0
u = 1.279450 + 0.018733I
a = 1.00242 + 1.52201I
b = 0.389202 − 0.762314I
2.64749 − 1.42674I 0
u = 1.279450 − 0.018733I
a = 1.00242 − 1.52201I
b = 0.389202 + 0.762314I
2.64749 + 1.42674I 0
u = −0.350653 + 0.619552I
a = −1.34360 − 2.38427I
b = 0.735903 − 1.161470I
1.54460 − 6.34301I 9.4689 + 11.6215I
u = −0.350653 − 0.619552I
a = −1.34360 + 2.38427I
b = 0.735903 + 1.161470I
1.54460 + 6.34301I 9.4689 − 11.6215I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.293700 + 0.044391I
a = −0.367167 − 0.309954I
b = 0.835764 − 0.804452I
4.82731 − 3.06865I 0
u = −1.293700 − 0.044391I
a = −0.367167 + 0.309954I
b = 0.835764 + 0.804452I
4.82731 + 3.06865I 0
u = −0.382833 + 0.589995I
a = −0.159594 − 1.232590I
b = 1.001380 − 0.537434I
3.62807 − 3.58901I 15.0481 + 7.4264I
u = −0.382833 − 0.589995I
a = −0.159594 + 1.232590I
b = 1.001380 + 0.537434I
3.62807 + 3.58901I 15.0481 − 7.4264I
u = 0.071201 + 0.692830I
a = −0.573489 + 1.010040I
b = −0.584487 + 0.449534I
−1.16620 + 2.47035I 4.14055 − 4.42574I
u = 0.071201 − 0.692830I
a = −0.573489 − 1.010040I
b = −0.584487 − 0.449534I
−1.16620 − 2.47035I 4.14055 + 4.42574I
u = −0.401400 + 0.560284I
a = 0.737726 − 0.734520I
b = 0.994561 + 0.430873I
3.73746 − 0.06066I 15.7625 + 0.6829I
u = −0.401400 − 0.560284I
a = 0.737726 + 0.734520I
b = 0.994561 − 0.430873I
3.73746 + 0.06066I 15.7625 − 0.6829I
u = −1.31180
a = 0.293323
b = 0.836540
5.58489 0
u = 1.293690 + 0.255561I
a = 1.56944 − 1.41967I
b = −0.229918 − 1.049980I
−1.21197 + 2.79771I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.293690 − 0.255561I
a = 1.56944 + 1.41967I
b = −0.229918 + 1.049980I
−1.21197 − 2.79771I 0
u = 0.371452 + 0.569739I
a = 0.610361 + 0.152921I
b = 0.213712 + 0.096656I
0.87797 + 1.75361I 4.00098 − 4.23879I
u = 0.371452 − 0.569739I
a = 0.610361 − 0.152921I
b = 0.213712 − 0.096656I
0.87797 − 1.75361I 4.00098 + 4.23879I
u = 0.203337 + 0.648436I
a = 0.22434 + 1.74473I
b = −0.070051 + 0.627424I
−0.91786 + 2.31127I 2.88014 − 5.91888I
u = 0.203337 − 0.648436I
a = 0.22434 − 1.74473I
b = −0.070051 − 0.627424I
−0.91786 − 2.31127I 2.88014 + 5.91888I
u = −0.090046 + 0.672441I
a = 0.91087 + 2.89991I
b = −0.146928 + 1.096740I
−5.51656 + 0.56608I −3.17725 − 0.33604I
u = −0.090046 − 0.672441I
a = 0.91087 − 2.89991I
b = −0.146928 − 1.096740I
−5.51656 − 0.56608I −3.17725 + 0.33604I
u = 0.331204 + 0.577743I
a = −4.23259 + 1.33722I
b = 0.545491 + 0.882798I
0.54533 + 3.82916I −12.0407 + 14.8512I
u = 0.331204 − 0.577743I
a = −4.23259 − 1.33722I
b = 0.545491 − 0.882798I
0.54533 − 3.82916I −12.0407 − 14.8512I
u = −0.412605 + 0.499950I
a = 0.487656 + 0.457214I
b = 0.760775 + 1.087850I
1.96482 + 2.78043I 11.54120 − 4.22354I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.412605 − 0.499950I
a = 0.487656 − 0.457214I
b = 0.760775 − 1.087850I
1.96482 − 2.78043I 11.54120 + 4.22354I
u = 0.349722 + 0.536822I
a = −1.56624 + 1.89326I
b = 0.544235 − 0.835676I
0.698976 − 0.541114I −17.8322 − 3.1413I
u = 0.349722 − 0.536822I
a = −1.56624 − 1.89326I
b = 0.544235 + 0.835676I
0.698976 + 0.541114I −17.8322 + 3.1413I
u = −0.524889 + 0.356431I
a = 0.88263 + 1.38930I
b = 0.089364 + 1.183890I
−2.05836 + 3.02608I 4.11780 − 3.31029I
u = −0.524889 − 0.356431I
a = 0.88263 − 1.38930I
b = 0.089364 − 1.183890I
−2.05836 − 3.02608I 4.11780 + 3.31029I
u = −1.394820 + 0.206569I
a = 1.17315 + 1.83804I
b = 0.305575 + 0.879647I
4.85990 − 2.36800I 0
u = −1.394820 − 0.206569I
a = 1.17315 − 1.83804I
b = 0.305575 − 0.879647I
4.85990 + 2.36800I 0
u = −1.39245 + 0.25151I
a = −0.049930 − 1.221160I
b = 0.005383 − 0.793309I
4.20117 − 5.58561I 0
u = −1.39245 − 0.25151I
a = −0.049930 + 1.221160I
b = 0.005383 + 0.793309I
4.20117 + 5.58561I 0
u = 0.223965 + 0.535065I
a = 2.24434 − 3.62037I
b = 0.388240 − 0.839913I
−0.341249 − 0.362728I 9.62962 + 1.11519I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.223965 − 0.535065I
a = 2.24434 + 3.62037I
b = 0.388240 + 0.839913I
−0.341249 + 0.362728I 9.62962 − 1.11519I
u = 1.41580 + 0.16623I
a = 0.693712 − 0.468034I
b = 0.232628 − 1.242180I
3.80684 − 1.07968I 0
u = 1.41580 − 0.16623I
a = 0.693712 + 0.468034I
b = 0.232628 + 1.242180I
3.80684 + 1.07968I 0
u = −1.42866 + 0.21209I
a = −1.63529 − 1.87231I
b = 0.577657 + 0.826939I
6.39608 − 2.25864I 0
u = −1.42866 − 0.21209I
a = −1.63529 + 1.87231I
b = 0.577657 − 0.826939I
6.39608 + 2.25864I 0
u = −1.42691 + 0.22647I
a = −3.76630 − 0.47368I
b = 0.569164 − 0.893401I
6.18316 − 6.81181I 0
u = −1.42691 − 0.22647I
a = −3.76630 + 0.47368I
b = 0.569164 + 0.893401I
6.18316 + 6.81181I 0
u = 1.42542 + 0.25767I
a = −1.26859 + 1.03129I
b = 0.084417 + 1.321020I
2.45895 + 10.02040I 0
u = 1.42542 − 0.25767I
a = −1.26859 − 1.03129I
b = 0.084417 − 1.321020I
2.45895 − 10.02040I 0
u = 1.43680 + 0.19812I
a = −0.270185 + 0.471506I
b = 0.826001 − 1.101340I
7.84711 − 0.16066I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43680 − 0.19812I
a = −0.270185 − 0.471506I
b = 0.826001 + 1.101340I
7.84711 + 0.16066I 0
u = −1.43716 + 0.21885I
a = 0.211680 − 0.079378I
b = 0.333859 − 0.125798I
6.67715 − 4.67240I 0
u = −1.43716 − 0.21885I
a = 0.211680 + 0.079378I
b = 0.333859 + 0.125798I
6.67715 + 4.67240I 0
u = 1.43561 + 0.23691I
a = −1.93769 + 1.12814I
b = 0.76225 + 1.19358I
7.27567 + 9.48965I 0
u = 1.43561 − 0.23691I
a = −1.93769 − 1.12814I
b = 0.76225 − 1.19358I
7.27567 − 9.48965I 0
u = 1.44295 + 0.21305I
a = −0.281864 + 0.996757I
b = 1.069420 − 0.405753I
9.64183 + 2.91922I 0
u = 1.44295 − 0.21305I
a = −0.281864 − 0.996757I
b = 1.069420 + 0.405753I
9.64183 − 2.91922I 0
u = 1.44193 + 0.22409I
a = −1.093850 + 0.680581I
b = 1.063650 + 0.559170I
9.47967 + 6.58874I 0
u = 1.44193 − 0.22409I
a = −1.093850 − 0.680581I
b = 1.063650 − 0.559170I
9.47967 − 6.58874I 0
u = 1.45109 + 0.26993I
a = 0.002441 − 0.981496I
b = −0.952285 + 0.531565I
9.6928 + 12.3816I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45109 − 0.26993I
a = 0.002441 + 0.981496I
b = −0.952285 − 0.531565I
9.6928 − 12.3816I 0
u = 1.45052 + 0.28059I
a = 1.96222 − 1.34837I
b = −0.709064 − 1.124990I
7.8603 + 18.4522I 0
u = 1.45052 − 0.28059I
a = 1.96222 + 1.34837I
b = −0.709064 + 1.124990I
7.8603 − 18.4522I 0
u = −1.45521 + 0.29246I
a = 1.65577 + 1.16316I
b = −0.637188 + 0.951042I
7.64698 − 9.97991I 0
u = −1.45521 − 0.29246I
a = 1.65577 − 1.16316I
b = −0.637188 − 0.951042I
7.64698 + 9.97991I 0
u = 1.48062 + 0.15742I
a = 1.075990 − 0.114603I
b = −0.900844 − 0.607256I
11.34470 − 2.23796I 0
u = 1.48062 − 0.15742I
a = 1.075990 + 0.114603I
b = −0.900844 + 0.607256I
11.34470 + 2.23796I 0
u = −1.46646 + 0.26951I
a = 0.073782 + 0.489891I
b = −0.651565 − 0.709449I
8.37652 − 4.94203I 0
u = −1.46646 − 0.26951I
a = 0.073782 − 0.489891I
b = −0.651565 + 0.709449I
8.37652 + 4.94203I 0
u = 1.48968 + 0.14070I
a = 0.809922 − 0.019937I
b = −0.719703 + 1.072350I
9.91130 − 8.21289I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48968 − 0.14070I
a = 0.809922 + 0.019937I
b = −0.719703 − 1.072350I
9.91130 + 8.21289I 0
u = −1.49446 + 0.11836I
a = 0.822095 − 0.013395I
b = −0.700730 − 0.832418I
10.17480 − 0.40773I 0
u = −1.49446 − 0.11836I
a = 0.822095 + 0.013395I
b = −0.700730 + 0.832418I
10.17480 + 0.40773I 0
u = −1.50195 + 0.15201I
a = 1.110550 + 0.180163I
b = −0.686598 + 0.859901I
10.08970 − 5.72799I 0
u = −1.50195 − 0.15201I
a = 1.110550 − 0.180163I
b = −0.686598 − 0.859901I
10.08970 + 5.72799I 0
u = −0.033811 + 0.452141I
a = 2.09508 + 2.81358I
b = 0.438588 + 1.044620I
−1.21170 + 2.79956I 1.52400 − 4.45007I
u = −0.033811 − 0.452141I
a = 2.09508 − 2.81358I
b = 0.438588 − 1.044620I
−1.21170 − 2.79956I 1.52400 + 4.45007I
u = 0.350449
a = 1.47447
b = 0.277047
0.896804 11.9350
u = 0.217409 + 0.128263I
a = 2.22525 + 1.50519I
b = 0.580237 + 0.840045I
0.56443 + 2.30394I 0.46885 − 4.62350I
u = 0.217409 − 0.128263I
a = 2.22525 − 1.50519I
b = 0.580237 − 0.840045I
0.56443 − 2.30394I 0.46885 + 4.62350I
15
II. I
u
2
= h2b − a − 1, a
2
+ 3, u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
−1
a
7
=
1
−1
a
11
=
−1
0
a
8
=
0
−1
a
2
=
a
1
2
a +
1
2
a
12
=
−1
0
a
5
=
1
2
a −
1
2
1
2
a −
1
2
a
3
=
a − 1
1
2
a −
1
2
a
1
=
−1
0
a
4
=
1
2
a −
1
2
0
a
9
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2a + 9
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
6
, c
7
, c
8
c
9
(u + 1)
2
c
10
(u − 1)
2
c
11
, c
12
u
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
y
2
+ y + 1
c
6
, c
7
, c
8
c
9
, c
10
(y −1)
2
c
11
, c
12
y
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.73205I
b = 0.500000 + 0.866025I
1.64493 + 2.02988I 9.00000 − 3.46410I
u = −1.00000
a = − 1.73205I
b = 0.500000 − 0.866025I
1.64493 − 2.02988I 9.00000 + 3.46410I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
110
+ 42u
109
+ ··· − 41u + 1)
c
2
(u
2
+ u + 1)(u
110
+ 2u
109
+ ··· − 5u + 1)
c
3
(u
2
− u + 1)(u
110
+ 2u
109
+ ··· + 102407u − 11029)
c
4
(u
2
− u + 1)(u
110
+ 4u
109
+ ··· − 120613u + 16231)
c
5
(u
2
− u + 1)(u
110
+ 2u
109
+ ··· − 5u + 1)
c
6
, c
7
((u + 1)
2
)(u
110
− 3u
109
+ ··· + 8u − 1)
c
8
((u + 1)
2
)(u
110
− 7u
109
+ ··· + 4u
2
− 1)
c
9
((u + 1)
2
)(u
110
− 21u
109
+ ··· − 3668038u + 132529)
c
10
((u − 1)
2
)(u
110
− 3u
109
+ ··· + 8u − 1)
c
11
u
2
(u
110
+ 3u
109
+ ··· − 60672u + 14144)
c
12
u
2
(u
110
+ 11u
109
+ ··· − 4u + 4)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
110
+ 54y
109
+ ··· − 249y + 1)
c
2
, c
5
(y
2
+ y + 1)(y
110
+ 42y
109
+ ··· − 41y + 1)
c
3
(y
2
+ y + 1)(y
110
− 142y
109
+ ··· − 1.04787 × 10
10
y + 1.21639 × 10
8
)
c
4
(y
2
+ y + 1)(y
110
− 90y
109
+ ··· − 2.49453 × 10
10
y + 2.63445 × 10
8
)
c
6
, c
7
, c
10
((y −1)
2
)(y
110
− 101y
109
+ ··· − 8y + 1)
c
8
((y −1)
2
)(y
110
− 13y
109
+ ··· − 8y + 1)
c
9
((y −1)
2
)(y
110
+ 63y
109
+ ··· + 7.13897 × 10
11
y + 1.75639 × 10
10
)
c
11
y
2
(y
110
− 23y
109
+ ··· − 7.86322 × 10
9
y + 2.00053 × 10
8
)
c
12
y
2
(y
110
− 15y
109
+ ··· − 264y + 16)
21
