12n
0827
(K12n
0827
)
A knot diagram
1
Linearized knot diagam
4 8 10 1 12 3 11 1 6 7 4 9
Solving Sequence
9,12 1,4
2 5 6 10 3 8 11 7
c
12
c
1
c
4
c
5
c
9
c
3
c
8
c
11
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.01535 × 10
193
u
78
+ 2.27202 × 10
193
u
77
+ ··· + 1.23813 × 10
195
b + 3.31260 × 10
195
,
9.77104 × 10
193
u
78
+ 4.39315 × 10
194
u
77
+ ··· + 1.23813 × 10
195
a − 3.09558 × 10
194
,
u
79
+ 3u
78
+ ··· + 200u + 29i
I
u
2
= h7428u
19
+ 4394u
18
+ ··· + 1981b + 11610, 11189u
19
+ 7253u
18
+ ··· + 1981a + 3015,
u
20
+ 6u
18
+ ··· + 9u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 99 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−1.02 × 10
193
u
78
+ 2.27 × 10
193
u
77
+ · · · + 1.24 × 10
195
b + 3.31 ×
10
195
, 9.77 × 10
193
u
78
+ 4.39 × 10
194
u
77
+ · · · + 1.24 × 10
195
a − 3.10 ×
10
194
, u
79
+ 3u
78
+ · · · + 200u + 29i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
−0.0789177u
78
− 0.354821u
77
+ ··· − 1.04936u + 0.250021
0.00820071u
78
− 0.0183504u
77
+ ··· − 10.6030u − 2.67549
a
2
=
0.316988u
78
+ 0.936300u
77
+ ··· + 105.357u + 16.3934
0.238792u
78
+ 0.708289u
77
+ ··· + 75.5899u + 10.7768
a
5
=
−0.0251868u
78
− 0.0941620u
77
+ ··· + 35.4559u + 6.34948
−0.0436195u
78
− 0.194847u
77
+ ··· − 32.0545u − 5.56001
a
6
=
−0.0688064u
78
− 0.289009u
77
+ ··· + 3.40135u + 0.789464
−0.0436195u
78
− 0.194847u
77
+ ··· − 32.0545u − 5.56001
a
10
=
0.0169539u
78
− 0.0560201u
77
+ ··· − 43.1019u − 7.03695
−0.0200562u
78
− 0.0892438u
77
+ ··· − 24.7956u − 5.58376
a
3
=
0.270350u
78
+ 0.800990u
77
+ ··· + 94.9364u + 14.7864
0.216092u
78
+ 0.639260u
77
+ ··· + 65.6010u + 9.03626
a
8
=
u
u
3
+ u
a
11
=
0.104207u
78
+ 0.354515u
77
+ ··· + 86.3463u + 15.4543
0.195689u
78
+ 0.613380u
77
+ ··· + 64.1890u + 9.56182
a
7
=
−0.0988891u
78
− 0.365513u
77
+ ··· − 95.0641u − 17.4083
−0.199232u
78
− 0.632045u
77
+ ··· − 79.9865u − 13.1574
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.507381u
78
− 1.83656u
77
+ ··· − 237.468u − 36.5233
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
79
+ 11u
78
+ ··· + 5558u + 2479
c
2
u
79
− u
78
+ ··· − 102812253u + 13388083
c
3
u
79
+ 5u
76
+ ··· + 20u + 1
c
5
u
79
+ 5u
78
+ ··· + 13423495u + 1556833
c
6
u
79
+ 7u
78
+ ··· + 68u − 7
c
7
, c
10
u
79
+ u
78
+ ··· + 77u + 19
c
8
, c
12
u
79
+ 3u
78
+ ··· + 200u + 29
c
9
u
79
− u
78
+ ··· − 8553u + 4021
c
11
u
79
− 3u
78
+ ··· + 7160839u + 2429981
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
79
− 77y
78
+ ··· + 415458634y −6145441
c
2
y
79
− 57y
78
+ ··· + 3295984311821017y −179240766414889
c
3
y
79
+ 86y
77
+ ··· − 12y −1
c
5
y
79
+ 39y
78
+ ··· − 73169724732107y −2423728989889
c
6
y
79
− y
78
+ ··· + 1306y −49
c
7
, c
10
y
79
− 61y
78
+ ··· − 21393y −361
c
8
, c
12
y
79
+ 23y
78
+ ··· − 15912y −841
c
9
y
79
− 45y
78
+ ··· + 347635311y −16168441
c
11
y
79
+ 43y
78
+ ··· − 76836824810403y −5904807660361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.365028 + 0.921649I
a = 0.485538 − 0.442665I
b = −1.012030 − 0.390280I
0.81357 + 3.15646I 0
u = −0.365028 − 0.921649I
a = 0.485538 + 0.442665I
b = −1.012030 + 0.390280I
0.81357 − 3.15646I 0
u = −0.048716 + 0.988429I
a = 1.05917 + 2.15503I
b = −0.547677 − 0.774768I
2.98173 − 4.48398I 0
u = −0.048716 − 0.988429I
a = 1.05917 − 2.15503I
b = −0.547677 + 0.774768I
2.98173 + 4.48398I 0
u = −0.550088 + 0.820510I
a = −1.232910 + 0.211959I
b = 0.901767 + 0.418938I
0.35934 + 8.67454I 0
u = −0.550088 − 0.820510I
a = −1.232910 − 0.211959I
b = 0.901767 − 0.418938I
0.35934 − 8.67454I 0
u = 0.769309 + 0.614688I
a = 0.106252 + 1.084980I
b = 0.466533 + 0.733029I
−3.16503 − 1.16137I 0
u = 0.769309 − 0.614688I
a = 0.106252 − 1.084980I
b = 0.466533 − 0.733029I
−3.16503 + 1.16137I 0
u = −0.198767 + 0.920559I
a = 0.232424 − 0.455553I
b = −1.054030 − 0.576556I
0.56704 + 3.08659I 0
u = −0.198767 − 0.920559I
a = 0.232424 + 0.455553I
b = −1.054030 + 0.576556I
0.56704 − 3.08659I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.697347 + 0.814961I
a = 0.27962 − 2.05303I
b = −0.633965 − 0.761739I
−6.29169 + 2.64828I 0
u = −0.697347 − 0.814961I
a = 0.27962 + 2.05303I
b = −0.633965 + 0.761739I
−6.29169 − 2.64828I 0
u = −1.048100 + 0.403578I
a = 0.808674 − 0.404445I
b = 2.32569 − 1.11746I
−7.15287 + 0.34372I 0
u = −1.048100 − 0.403578I
a = 0.808674 + 0.404445I
b = 2.32569 + 1.11746I
−7.15287 − 0.34372I 0
u = 0.383423 + 0.764569I
a = 0.255771 + 0.433790I
b = −1.276420 − 0.222595I
4.18971 + 0.51454I 2.17923 + 0.I
u = 0.383423 − 0.764569I
a = 0.255771 − 0.433790I
b = −1.276420 + 0.222595I
4.18971 − 0.51454I 2.17923 + 0.I
u = −0.620381 + 0.965544I
a = 1.12040 − 1.00106I
b = 0.280816 − 0.558368I
−5.81347 + 2.47228I 0
u = −0.620381 − 0.965544I
a = 1.12040 + 1.00106I
b = 0.280816 + 0.558368I
−5.81347 − 2.47228I 0
u = −0.946796 + 0.663690I
a = 0.148069 + 1.213100I
b = 0.525674 + 0.797143I
−4.51817 + 2.00997I 0
u = −0.946796 − 0.663690I
a = 0.148069 − 1.213100I
b = 0.525674 − 0.797143I
−4.51817 − 2.00997I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.478436 + 0.694599I
a = 0.244214 − 0.318915I
b = −1.098680 + 0.795145I
0.01895 − 4.62268I −4.00000 + 2.42967I
u = −0.478436 − 0.694599I
a = 0.244214 + 0.318915I
b = −1.098680 − 0.795145I
0.01895 + 4.62268I −4.00000 − 2.42967I
u = 0.816484 + 0.827857I
a = 1.04084 + 1.10388I
b = 0.165023 + 1.149580I
−6.08738 + 0.90469I 0
u = 0.816484 − 0.827857I
a = 1.04084 − 1.10388I
b = 0.165023 − 1.149580I
−6.08738 − 0.90469I 0
u = 0.226560 + 0.796466I
a = 1.74735 − 0.47514I
b = −0.512841 + 0.571552I
−1.96522 + 0.47763I −4.53788 + 0.92547I
u = 0.226560 − 0.796466I
a = 1.74735 + 0.47514I
b = −0.512841 − 0.571552I
−1.96522 − 0.47763I −4.53788 − 0.92547I
u = 0.475780 + 0.661767I
a = −0.91811 − 1.22985I
b = 1.185730 − 0.177054I
3.73228 − 3.86132I −1.05530 + 7.68432I
u = 0.475780 − 0.661767I
a = −0.91811 + 1.22985I
b = 1.185730 + 0.177054I
3.73228 + 3.86132I −1.05530 − 7.68432I
u = 0.769284 + 0.247205I
a = 0.088417 + 0.987187I
b = 0.11862 + 1.57494I
−4.09349 − 3.57659I −10.32261 + 5.90091I
u = 0.769284 − 0.247205I
a = 0.088417 − 0.987187I
b = 0.11862 − 1.57494I
−4.09349 + 3.57659I −10.32261 − 5.90091I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.029470 + 0.653797I
a = −0.406332 − 0.758563I
b = −0.583979 − 1.033370I
−1.60411 + 4.69680I 0
u = 1.029470 − 0.653797I
a = −0.406332 + 0.758563I
b = −0.583979 + 1.033370I
−1.60411 − 4.69680I 0
u = 0.787331 + 0.948348I
a = 0.48663 + 1.51737I
b = −0.436525 + 1.341180I
−5.72001 − 6.91767I 0
u = 0.787331 − 0.948348I
a = 0.48663 − 1.51737I
b = −0.436525 − 1.341180I
−5.72001 + 6.91767I 0
u = 0.277595 + 0.709657I
a = −0.42118 + 1.83706I
b = −0.866044 + 0.759028I
4.81405 − 3.49144I 1.70169 + 10.64917I
u = 0.277595 − 0.709657I
a = −0.42118 − 1.83706I
b = −0.866044 − 0.759028I
4.81405 + 3.49144I 1.70169 − 10.64917I
u = −0.878531 + 0.877785I
a = 0.635036 − 1.147060I
b = −0.508946 − 1.300500I
−2.18564 + 1.23495I 0
u = −0.878531 − 0.877785I
a = 0.635036 + 1.147060I
b = −0.508946 + 1.300500I
−2.18564 − 1.23495I 0
u = 0.192145 + 0.711068I
a = 0.73682 − 2.59438I
b = 0.499627 + 0.054033I
4.89202 + 1.47198I 0.48436 + 2.56488I
u = 0.192145 − 0.711068I
a = 0.73682 + 2.59438I
b = 0.499627 − 0.054033I
4.89202 − 1.47198I 0.48436 − 2.56488I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.857032 + 0.937871I
a = 0.652099 − 0.879166I
b = 0.16783 − 1.46825I
−2.00049 + 5.18597I 0
u = −0.857032 − 0.937871I
a = 0.652099 + 0.879166I
b = 0.16783 + 1.46825I
−2.00049 − 5.18597I 0
u = −1.099410 + 0.697283I
a = −0.819118 + 0.794230I
b = −1.07548 + 1.77879I
−6.68531 − 9.94778I 0
u = −1.099410 − 0.697283I
a = −0.819118 − 0.794230I
b = −1.07548 − 1.77879I
−6.68531 + 9.94778I 0
u = 0.963490 + 0.926074I
a = −0.855656 − 0.607154I
b = −0.67372 − 1.46186I
−9.63489 + 3.13405I 0
u = 0.963490 − 0.926074I
a = −0.855656 + 0.607154I
b = −0.67372 + 1.46186I
−9.63489 − 3.13405I 0
u = 0.923648 + 0.974917I
a = −0.46630 − 1.42944I
b = 1.03334 − 1.39055I
−9.46238 − 10.03940I 0
u = 0.923648 − 0.974917I
a = −0.46630 + 1.42944I
b = 1.03334 + 1.39055I
−9.46238 + 10.03940I 0
u = −0.329773 + 1.305820I
a = −0.270422 − 0.326511I
b = −0.261756 + 0.423075I
1.86473 + 3.78804I 0
u = −0.329773 − 1.305820I
a = −0.270422 + 0.326511I
b = −0.261756 − 0.423075I
1.86473 − 3.78804I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.701774 + 1.150670I
a = 0.86461 + 1.13965I
b = −0.950853 + 0.756054I
−1.45140 − 4.50648I 0
u = 0.701774 − 1.150670I
a = 0.86461 − 1.13965I
b = −0.950853 − 0.756054I
−1.45140 + 4.50648I 0
u = −0.972873 + 0.937650I
a = −0.295198 + 0.885473I
b = 0.260392 + 0.884421I
−4.28133 + 3.53574I 0
u = −0.972873 − 0.937650I
a = −0.295198 − 0.885473I
b = 0.260392 − 0.884421I
−4.28133 − 3.53574I 0
u = −0.821478 + 1.130920I
a = −0.548820 + 0.572288I
b = −0.037613 + 0.738202I
−3.08625 + 4.54824I 0
u = −0.821478 − 1.130920I
a = −0.548820 − 0.572288I
b = −0.037613 − 0.738202I
−3.08625 − 4.54824I 0
u = −0.599388
a = 1.13836
b = 0.628716
−1.88001 −6.12910
u = 0.821578 + 1.137080I
a = −0.605483 − 1.147130I
b = 0.885700 − 0.997087I
−0.11191 − 11.43530I 0
u = 0.821578 − 1.137080I
a = −0.605483 + 1.147130I
b = 0.885700 + 0.997087I
−0.11191 + 11.43530I 0
u = 1.080490 + 0.909752I
a = 0.69148 + 1.34893I
b = −1.01470 + 2.67163I
−5.52397 − 3.79706I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.080490 − 0.909752I
a = 0.69148 − 1.34893I
b = −1.01470 − 2.67163I
−5.52397 + 3.79706I 0
u = 0.054786 + 1.411470I
a = −0.326149 − 0.219838I
b = 0.324393 + 0.617013I
6.16628 + 1.89006I 0
u = 0.054786 − 1.411470I
a = −0.326149 + 0.219838I
b = 0.324393 − 0.617013I
6.16628 − 1.89006I 0
u = −0.312943 + 0.477853I
a = −1.14468 − 2.44162I
b = −0.63512 − 1.78649I
0.79605 + 6.21294I −6.33131 − 10.12425I
u = −0.312943 − 0.477853I
a = −1.14468 + 2.44162I
b = −0.63512 + 1.78649I
0.79605 − 6.21294I −6.33131 + 10.12425I
u = −0.85067 + 1.14814I
a = −0.83436 + 1.42013I
b = 1.35640 + 1.56095I
−5.2404 + 16.9790I 0
u = −0.85067 − 1.14814I
a = −0.83436 − 1.42013I
b = 1.35640 − 1.56095I
−5.2404 − 16.9790I 0
u = 1.09269 + 0.93791I
a = 1.307310 + 0.521345I
b = 1.29376 + 3.00284I
−5.47068 − 3.91698I 0
u = 1.09269 − 0.93791I
a = 1.307310 − 0.521345I
b = 1.29376 − 3.00284I
−5.47068 + 3.91698I 0
u = −0.487872 + 0.175765I
a = 1.76241 + 1.10617I
b = 1.137630 + 0.211015I
−1.82613 + 0.02881I −6.76412 + 0.34713I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.487872 − 0.175765I
a = 1.76241 − 1.10617I
b = 1.137630 − 0.211015I
−1.82613 − 0.02881I −6.76412 − 0.34713I
u = −0.370186 + 0.350900I
a = 0.573493 − 0.938784I
b = −0.096093 − 0.493512I
−0.270088 + 1.031330I −4.41640 − 6.52686I
u = −0.370186 − 0.350900I
a = 0.573493 + 0.938784I
b = −0.096093 + 0.493512I
−0.270088 − 1.031330I −4.41640 + 6.52686I
u = 0.13902 + 1.49464I
a = −0.298338 + 0.663603I
b = 0.24627 − 1.50057I
2.55162 − 7.07486I 0
u = 0.13902 − 1.49464I
a = −0.298338 − 0.663603I
b = 0.24627 + 1.50057I
2.55162 + 7.07486I 0
u = 0.124655 + 0.464854I
a = −3.09093 + 1.14602I
b = 0.823635 − 0.304659I
−1.18700 − 2.75544I −3.0625 + 14.8135I
u = 0.124655 − 0.464854I
a = −3.09093 − 1.14602I
b = 0.823635 + 0.304659I
−1.18700 + 2.75544I −3.0625 − 14.8135I
u = −0.89541 + 1.30049I
a = 1.05199 − 1.41768I
b = −2.53671 − 1.97919I
−4.46745 + 6.91864I 0
u = −0.89541 − 1.30049I
a = 1.05199 + 1.41768I
b = −2.53671 + 1.97919I
−4.46745 − 6.91864I 0
12
II. I
u
2
= h7428u
19
+ 4394u
18
+ · · · + 1981b + 11610, 11189u
19
+ 7253u
18
+
· · · + 1981a + 3015, u
20
+ 6u
18
+ · · · + 9u
2
+ 1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
−5.64816u
19
− 3.66128u
18
+ ··· − 15.9192u − 1.52196
−3.74962u
19
− 2.21807u
18
+ ··· − 8.27108u − 5.86068
a
2
=
4.50278u
19
− 5.59919u
18
+ ··· + 17.0121u − 13.9783
11.9086u
19
+ 1.62797u
18
+ ··· + 28.4195u + 1.37658
a
5
=
u
18
+ 6u
16
+ ··· − 2u + 8
−5.64816u
19
− 4.66128u
18
+ ··· − 13.9192u − 10.5220
a
6
=
−5.64816u
19
− 3.66128u
18
+ ··· − 15.9192u − 2.52196
−5.64816u
19
− 4.66128u
18
+ ··· − 13.9192u − 10.5220
a
10
=
−1.02373u
19
− 0.334175u
18
+ ··· + 0.987380u − 1.73094
−2.16305u
19
− 4.08380u
18
+ ··· − 10.2569u − 12.0020
a
3
=
8.25240u
19
− 3.38112u
18
+ ··· + 25.2832u − 9.11762
14.0490u
19
+ 2.79606u
18
+ ··· + 32.9409u + 4.01918
a
8
=
u
u
3
+ u
a
11
=
7.38718u
19
− 2.01464u
18
+ ··· + 22.7804u − 10.5184
9.34074u
19
+ 1.73549u
18
+ ··· + 21.0323u + 3.39122
a
7
=
9.38213u
19
− 0.107017u
18
+ ··· + 21.3948u + 2.62393
7.13074u
19
+ 3.69258u
18
+ ··· + 19.3887u + 6.11307
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
28246
1981
u
19
−
10162
1981
u
18
+ ··· −
120734
1981
u −
22012
1981
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
20
− 12u
19
+ ··· − 74u + 11
c
2
u
20
− 8u
18
+ ··· + 117u + 59
c
3
u
20
+ u
19
+ ··· − 2u + 1
c
4
u
20
+ 12u
19
+ ··· + 74u + 11
c
5
u
20
+ 4u
19
+ ··· + 293u + 101
c
6
u
20
+ 2u
18
+ ··· + 4u + 1
c
7
u
20
− 8u
18
+ ··· + 5u + 7
c
8
u
20
+ 6u
18
+ ··· + 9u
2
+ 1
c
9
u
20
− 8u
18
+ ··· − 11u + 7
c
10
u
20
− 8u
18
+ ··· − 5u + 7
c
11
u
20
+ 4u
19
+ ··· − 11u + 7
c
12
u
20
+ 6u
18
+ ··· + 9u
2
+ 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
20
− 4y
19
+ ··· + 112y + 121
c
2
y
20
− 16y
19
+ ··· − 20887y + 3481
c
3
y
20
− 3y
19
+ ··· − 6y + 1
c
5
y
20
+ 12y
19
+ ··· + 51713y + 10201
c
6
y
20
+ 4y
19
+ ··· + 8y + 1
c
7
, c
10
y
20
− 16y
19
+ ··· − 53y + 49
c
8
, c
12
y
20
+ 12y
19
+ ··· + 18y + 1
c
9
y
20
− 16y
19
+ ··· − 513y + 49
c
11
y
20
+ 12y
19
+ ··· − 51y + 49
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.768071 + 0.596737I
a = 0.604655 + 1.101940I
b = 0.997208 + 0.889634I
−6.10903 − 0.54639I −6.35226 + 0.28610I
u = 0.768071 − 0.596737I
a = 0.604655 − 1.101940I
b = 0.997208 − 0.889634I
−6.10903 + 0.54639I −6.35226 − 0.28610I
u = −0.885049 + 0.742425I
a = 0.124687 − 1.307740I
b = −0.434624 − 1.037230I
−4.05162 + 2.43950I −5.67949 − 4.08416I
u = −0.885049 − 0.742425I
a = 0.124687 + 1.307740I
b = −0.434624 + 1.037230I
−4.05162 − 2.43950I −5.67949 + 4.08416I
u = 0.072410 + 1.235430I
a = −0.220059 − 0.785394I
b = 0.606714 + 0.293584I
7.10242 + 1.76975I 6.45710 − 1.57216I
u = 0.072410 − 1.235430I
a = −0.220059 + 0.785394I
b = 0.606714 − 0.293584I
7.10242 − 1.76975I 6.45710 + 1.57216I
u = 0.162743 + 1.261110I
a = −0.55490 + 1.36186I
b = 0.155700 − 1.152760I
3.96946 − 6.49112I 1.17515 + 5.52697I
u = 0.162743 − 1.261110I
a = −0.55490 − 1.36186I
b = 0.155700 + 1.152760I
3.96946 + 6.49112I 1.17515 − 5.52697I
u = 0.172256 + 0.678892I
a = 0.47239 + 2.22250I
b = −1.043000 + 0.402722I
4.85827 − 2.76424I 3.64862 + 0.62836I
u = 0.172256 − 0.678892I
a = 0.47239 − 2.22250I
b = −1.043000 − 0.402722I
4.85827 + 2.76424I 3.64862 − 0.62836I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.245877 + 1.283290I
a = −0.063534 − 0.179217I
b = 0.379916 + 0.361683I
1.99058 + 4.23949I 1.50893 − 12.25527I
u = −0.245877 − 1.283290I
a = −0.063534 + 0.179217I
b = 0.379916 − 0.361683I
1.99058 − 4.23949I 1.50893 + 12.25527I
u = −0.829529 + 1.035920I
a = 0.704288 − 0.719663I
b = 0.072155 − 1.098960I
−3.17862 + 3.91789I −5.79194 − 1.68615I
u = −0.829529 − 1.035920I
a = 0.704288 + 0.719663I
b = 0.072155 + 1.098960I
−3.17862 − 3.91789I −5.79194 + 1.68615I
u = 0.023548 + 0.636979I
a = 1.02126 − 1.93638I
b = −0.78900 − 1.30287I
1.30259 + 5.63518I 0.79418 − 3.67140I
u = 0.023548 − 0.636979I
a = 1.02126 + 1.93638I
b = −0.78900 + 1.30287I
1.30259 − 5.63518I 0.79418 + 3.67140I
u = 0.907379 + 1.082400I
a = 0.91540 + 1.32912I
b = −1.10167 + 2.17079I
−4.61763 − 5.90824I −5.47491 + 3.39735I
u = 0.907379 − 1.082400I
a = 0.91540 − 1.32912I
b = −1.10167 − 2.17079I
−4.61763 + 5.90824I −5.47491 − 3.39735I
u = −0.145951 + 0.496213I
a = 1.99582 − 1.70977I
b = −0.843408 + 0.409500I
−1.26643 − 2.32795I −6.78538 − 3.11988I
u = −0.145951 − 0.496213I
a = 1.99582 + 1.70977I
b = −0.843408 − 0.409500I
−1.26643 + 2.32795I −6.78538 + 3.11988I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 12u
19
+ ··· − 74u + 11)(u
79
+ 11u
78
+ ··· + 5558u + 2479)
c
2
(u
20
− 8u
18
+ ··· + 117u + 59)
· (u
79
− u
78
+ ··· − 102812253u + 13388083)
c
3
(u
20
+ u
19
+ ··· − 2u + 1)(u
79
+ 5u
76
+ ··· + 20u + 1)
c
4
(u
20
+ 12u
19
+ ··· + 74u + 11)(u
79
+ 11u
78
+ ··· + 5558u + 2479)
c
5
(u
20
+ 4u
19
+ ··· + 293u + 101)
· (u
79
+ 5u
78
+ ··· + 13423495u + 1556833)
c
6
(u
20
+ 2u
18
+ ··· + 4u + 1)(u
79
+ 7u
78
+ ··· + 68u − 7)
c
7
(u
20
− 8u
18
+ ··· + 5u + 7)(u
79
+ u
78
+ ··· + 77u + 19)
c
8
(u
20
+ 6u
18
+ ··· + 9u
2
+ 1)(u
79
+ 3u
78
+ ··· + 200u + 29)
c
9
(u
20
− 8u
18
+ ··· − 11u + 7)(u
79
− u
78
+ ··· − 8553u + 4021)
c
10
(u
20
− 8u
18
+ ··· − 5u + 7)(u
79
+ u
78
+ ··· + 77u + 19)
c
11
(u
20
+ 4u
19
+ ··· − 11u + 7)(u
79
− 3u
78
+ ··· + 7160839u + 2429981)
c
12
(u
20
+ 6u
18
+ ··· + 9u
2
+ 1)(u
79
+ 3u
78
+ ··· + 200u + 29)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
20
− 4y
19
+ ··· + 112y + 121)
· (y
79
− 77y
78
+ ··· + 415458634y −6145441)
c
2
(y
20
− 16y
19
+ ··· − 20887y + 3481)
· (y
79
− 57y
78
+ ··· + 3295984311821017y −179240766414889)
c
3
(y
20
− 3y
19
+ ··· − 6y + 1)(y
79
+ 86y
77
+ ··· − 12y −1)
c
5
(y
20
+ 12y
19
+ ··· + 51713y + 10201)
· (y
79
+ 39y
78
+ ··· − 73169724732107y −2423728989889)
c
6
(y
20
+ 4y
19
+ ··· + 8y + 1)(y
79
− y
78
+ ··· + 1306y −49)
c
7
, c
10
(y
20
− 16y
19
+ ··· − 53y + 49)(y
79
− 61y
78
+ ··· − 21393y −361)
c
8
, c
12
(y
20
+ 12y
19
+ ··· + 18y + 1)(y
79
+ 23y
78
+ ··· − 15912y −841)
c
9
(y
20
− 16y
19
+ ··· − 513y + 49)
· (y
79
− 45y
78
+ ··· + 347635311y −16168441)
c
11
(y
20
+ 12y
19
+ ··· − 51y + 49)
· (y
79
+ 43y
78
+ ··· − 76836824810403y −5904807660361)
21
