12n
0711
(K12n
0711
)
A knot diagram
1
Linearized knot diagam
4 6 7 8 9 10 12 5 2 3 8 7
Solving Sequence
4,8
5 9
6,12
7 1 3 2 11 10
c
4
c
8
c
5
c
7
c
12
c
3
c
2
c
11
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.02480 × 10
144
u
75
+ 2.72391 × 10
145
u
74
+ ··· + 1.00707 × 10
147
b − 2.72299 × 10
147
,
− 1.35943 × 10
147
u
75
− 2.53685 × 10
147
u
74
+ ··· + 2.71908 × 10
148
a + 9.43984 × 10
148
,
u
76
+ 2u
75
+ ··· + 32u + 27i
I
u
2
= h28u
19
+ 35u
18
+ ··· + 67b + 22, 15u
19
+ 2u
18
+ ··· + 67a − 194, u
20
+ u
19
+ ··· + 4u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 96 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
144
u
75
+ 2.72 × 10
145
u
74
+ · · · + 1.01 × 10
147
b − 2.72 ×
10
147
, −1.36 × 10
147
u
75
− 2.54 × 10
147
u
74
+ · · · + 2.72 × 10
148
a + 9.44 ×
10
148
, u
76
+ 2u
75
+ · · · + 32u + 27i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
−u
3
+ u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
12
=
0.0499959u
75
+ 0.0932981u
74
+ ··· + 14.5526u − 3.47170
0.00101760u
75
− 0.0270480u
74
+ ··· + 9.57085u + 2.70389
a
7
=
−0.0527844u
75
+ 0.0417033u
74
+ ··· + 27.5284u + 7.01584
−0.0139024u
75
− 0.0236058u
74
+ ··· − 5.70988u + 2.14183
a
1
=
−0.157862u
75
− 0.367093u
74
+ ··· − 8.05823u + 2.08138
−0.0836878u
75
− 0.135451u
74
+ ··· + 2.18214u + 0.663016
a
3
=
−0.0612921u
75
− 0.196218u
74
+ ··· − 0.851626u + 2.23369
−0.0359843u
75
− 0.0719567u
74
+ ··· + 3.76665u + 1.20983
a
2
=
−0.0741741u
75
− 0.231641u
74
+ ··· − 10.2404u + 1.41836
−0.0836878u
75
− 0.135451u
74
+ ··· + 2.18214u + 0.663016
a
11
=
0.0499959u
75
+ 0.0932981u
74
+ ··· + 14.5526u − 3.47170
0.0136984u
75
+ 0.00972375u
74
+ ··· + 10.7065u + 2.52316
a
10
=
0.0242324u
75
+ 0.132596u
74
+ ··· + 2.52604u − 10.7945
0.110043u
75
+ 0.116092u
74
+ ··· − 5.22698u − 0.286295
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.351617u
75
+ 0.565791u
74
+ ··· + 64.9845u + 17.3733
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ 5u
75
+ ··· − 9804u + 1444
c
2
u
76
− 5u
75
+ ··· − 124u − 23
c
3
u
76
− 2u
75
+ ··· + 76u + 2633
c
4
, c
5
, c
8
u
76
− 2u
75
+ ··· − 32u + 27
c
6
u
76
− 9u
74
+ ··· − 22u + 19
c
7
, c
11
, c
12
u
76
+ 13u
74
+ ··· − 82u + 43
c
9
u
76
− 3u
75
+ ··· − 397u + 71
c
10
u
76
− 3u
75
+ ··· + 1147u + 447
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
− 67y
75
+ ··· + 4349328y + 2085136
c
2
y
76
− 19y
75
+ ··· − 82030y + 529
c
3
y
76
− 62y
75
+ ··· − 205858982y + 6932689
c
4
, c
5
, c
8
y
76
− 76y
75
+ ··· + 52976y + 729
c
6
y
76
− 18y
75
+ ··· − 15152y + 361
c
7
, c
11
, c
12
y
76
+ 26y
75
+ ··· + 34556y + 1849
c
9
y
76
+ 15y
75
+ ··· + 88335y + 5041
c
10
y
76
+ 13y
75
+ ··· + 10810607y + 199809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.335219 + 0.952463I
a = 1.062340 + 0.659919I
b = 0.150378 + 1.163430I
−5.21982 − 4.95583I 0
u = −0.335219 − 0.952463I
a = 1.062340 − 0.659919I
b = 0.150378 − 1.163430I
−5.21982 + 4.95583I 0
u = −0.178055 + 0.889122I
a = −0.666647 + 0.389184I
b = −1.159090 + 0.249170I
1.66667 − 4.02641I 0. + 11.13609I
u = −0.178055 − 0.889122I
a = −0.666647 − 0.389184I
b = −1.159090 − 0.249170I
1.66667 + 4.02641I 0. − 11.13609I
u = 0.525368 + 0.975309I
a = 0.462645 + 1.130730I
b = 0.78335 + 1.42794I
−4.41523 + 11.68720I 0
u = 0.525368 − 0.975309I
a = 0.462645 − 1.130730I
b = 0.78335 − 1.42794I
−4.41523 − 11.68720I 0
u = −0.711614 + 0.490004I
a = 0.611255 − 0.464779I
b = 0.181183 − 0.021532I
1.27366 − 1.54173I 3.50559 + 0.I
u = −0.711614 − 0.490004I
a = 0.611255 + 0.464779I
b = 0.181183 + 0.021532I
1.27366 + 1.54173I 3.50559 + 0.I
u = 1.14400
a = −0.948499
b = −0.215745
−2.20411 0
u = −0.202334 + 1.146190I
a = 0.647997 − 0.848827I
b = 0.430923 − 1.278420I
−1.76191 − 3.13440I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.202334 − 1.146190I
a = 0.647997 + 0.848827I
b = 0.430923 + 1.278420I
−1.76191 + 3.13440I 0
u = −1.174240 + 0.252442I
a = −0.611112 + 0.449227I
b = −0.396824 − 0.716749I
−1.05451 + 1.17178I 0
u = −1.174240 − 0.252442I
a = −0.611112 − 0.449227I
b = −0.396824 + 0.716749I
−1.05451 − 1.17178I 0
u = 1.238270 + 0.109890I
a = −0.926139 − 0.563020I
b = 0.184791 + 0.103677I
−0.15602 − 2.47239I 0
u = 1.238270 − 0.109890I
a = −0.926139 + 0.563020I
b = 0.184791 − 0.103677I
−0.15602 + 2.47239I 0
u = 0.747450
a = −0.637437
b = −0.905014
−2.42462 −4.01110
u = 0.634961 + 0.372638I
a = −0.314128 + 0.853405I
b = −0.091984 + 1.090970I
0.16002 + 4.03023I −2.04460 − 10.11479I
u = 0.634961 − 0.372638I
a = −0.314128 − 0.853405I
b = −0.091984 − 1.090970I
0.16002 − 4.03023I −2.04460 + 10.11479I
u = −1.257720 + 0.166055I
a = −0.746919 + 0.518415I
b = 0.399959 − 0.632265I
−0.450371 − 1.016900I 0
u = −1.257720 − 0.166055I
a = −0.746919 − 0.518415I
b = 0.399959 + 0.632265I
−0.450371 + 1.016900I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.789767 + 1.016560I
a = 0.923614 − 0.121588I
b = 0.088501 − 0.909369I
−3.79850 − 5.20157I 0
u = 0.789767 − 1.016560I
a = 0.923614 + 0.121588I
b = 0.088501 + 0.909369I
−3.79850 + 5.20157I 0
u = −1.014430 + 0.821372I
a = −0.011572 − 0.978844I
b = 0.77138 − 1.60224I
−3.37044 − 1.02943I 0
u = −1.014430 − 0.821372I
a = −0.011572 + 0.978844I
b = 0.77138 + 1.60224I
−3.37044 + 1.02943I 0
u = 1.354330 + 0.034566I
a = −0.355159 − 0.633725I
b = 1.72523 − 0.83396I
6.59906 − 2.06008I 0
u = 1.354330 − 0.034566I
a = −0.355159 + 0.633725I
b = 1.72523 + 0.83396I
6.59906 + 2.06008I 0
u = −1.352470 + 0.091220I
a = −0.452501 + 0.509412I
b = 2.09424 + 0.03971I
6.22160 − 3.70134I 0
u = −1.352470 − 0.091220I
a = −0.452501 − 0.509412I
b = 2.09424 − 0.03971I
6.22160 + 3.70134I 0
u = 1.354550 + 0.202068I
a = 0.461925 − 0.797105I
b = −1.87703 − 1.23809I
0.19010 + 7.12458I 0
u = 1.354550 − 0.202068I
a = 0.461925 + 0.797105I
b = −1.87703 + 1.23809I
0.19010 − 7.12458I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.364060 + 0.156000I
a = 0.327441 − 0.829687I
b = −1.29343 − 2.14767I
0.29364 + 3.54039I 0
u = 1.364060 − 0.156000I
a = 0.327441 + 0.829687I
b = −1.29343 + 2.14767I
0.29364 − 3.54039I 0
u = 1.356250 + 0.217693I
a = −0.339965 − 0.976740I
b = 0.439699 − 1.333720I
8.27803 − 1.11792I 0
u = 1.356250 − 0.217693I
a = −0.339965 + 0.976740I
b = 0.439699 + 1.333720I
8.27803 + 1.11792I 0
u = −1.371200 + 0.168132I
a = −0.130034 + 1.111990I
b = −0.01517 + 1.48792I
8.82106 − 5.99255I 0
u = −1.371200 − 0.168132I
a = −0.130034 − 1.111990I
b = −0.01517 − 1.48792I
8.82106 + 5.99255I 0
u = −1.382190 + 0.164386I
a = 0.440963 + 1.011550I
b = −1.01477 + 1.50773I
1.31274 − 6.74682I 0
u = −1.382190 − 0.164386I
a = 0.440963 − 1.011550I
b = −1.01477 − 1.50773I
1.31274 + 6.74682I 0
u = −0.450364 + 0.405755I
a = 0.601796 − 1.157140I
b = 0.496255 − 0.470062I
0.64900 − 1.50177I 0.08009 + 5.08857I
u = −0.450364 − 0.405755I
a = 0.601796 + 1.157140I
b = 0.496255 + 0.470062I
0.64900 + 1.50177I 0.08009 − 5.08857I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.085145 + 0.597383I
a = −1.24522 + 1.45142I
b = −0.99539 + 1.09484I
−4.39381 − 4.30048I −8.88569 + 7.94405I
u = −0.085145 − 0.597383I
a = −1.24522 − 1.45142I
b = −0.99539 − 1.09484I
−4.39381 + 4.30048I −8.88569 − 7.94405I
u = −1.394540 + 0.190085I
a = 0.600186 + 0.805977I
b = −1.27776 + 1.08700I
0.45871 − 4.89022I 0
u = −1.394540 − 0.190085I
a = 0.600186 − 0.805977I
b = −1.27776 − 1.08700I
0.45871 + 4.89022I 0
u = −1.34800 + 0.44161I
a = 0.742314 − 0.126395I
b = −0.311972 + 0.479712I
2.07256 − 2.52727I 0
u = −1.34800 − 0.44161I
a = 0.742314 + 0.126395I
b = −0.311972 − 0.479712I
2.07256 + 2.52727I 0
u = 1.38945 + 0.30604I
a = 0.256183 − 0.685054I
b = −1.69118 − 0.24166I
6.68232 + 8.14879I 0
u = 1.38945 − 0.30604I
a = 0.256183 + 0.685054I
b = −1.69118 + 0.24166I
6.68232 − 8.14879I 0
u = 0.191544 + 0.536045I
a = −0.62821 − 2.03828I
b = −0.752490 − 0.881582I
−4.64760 + 2.27181I −11.69609 − 2.47531I
u = 0.191544 − 0.536045I
a = −0.62821 + 2.03828I
b = −0.752490 + 0.881582I
−4.64760 − 2.27181I −11.69609 + 2.47531I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.241599 + 0.511210I
a = 0.661629 − 0.856430I
b = −0.221305 − 0.547954I
−1.15458 − 0.86356I −6.32547 + 1.72362I
u = 0.241599 − 0.511210I
a = 0.661629 + 0.856430I
b = −0.221305 + 0.547954I
−1.15458 + 0.86356I −6.32547 − 1.72362I
u = 1.45709 + 0.37188I
a = 0.808172 + 0.206134I
b = −0.277686 − 0.549919I
0.47898 + 9.68599I 0
u = 1.45709 − 0.37188I
a = 0.808172 − 0.206134I
b = −0.277686 + 0.549919I
0.47898 − 9.68599I 0
u = −0.038731 + 0.471932I
a = −1.78603 + 1.67997I
b = −0.45927 + 1.36321I
−4.26270 − 1.36015I −8.18769 − 1.27629I
u = −0.038731 − 0.471932I
a = −1.78603 − 1.67997I
b = −0.45927 − 1.36321I
−4.26270 + 1.36015I −8.18769 + 1.27629I
u = 0.061494 + 0.467951I
a = −2.87482 − 0.70612I
b = 0.223982 − 0.279494I
4.10268 + 3.72750I −9.57520 − 1.56153I
u = 0.061494 − 0.467951I
a = −2.87482 + 0.70612I
b = 0.223982 + 0.279494I
4.10268 − 3.72750I −9.57520 + 1.56153I
u = 0.118059 + 0.454888I
a = −1.75474 − 2.38858I
b = −0.514860 − 0.923483I
−3.57058 + 4.51054I −6.33549 − 11.71325I
u = 0.118059 − 0.454888I
a = −1.75474 + 2.38858I
b = −0.514860 + 0.923483I
−3.57058 − 4.51054I −6.33549 + 11.71325I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49892 + 0.39031I
a = 0.158369 + 0.476191I
b = −1.297920 + 0.101001I
5.87883 − 1.48945I 0
u = −1.49892 − 0.39031I
a = 0.158369 − 0.476191I
b = −1.297920 − 0.101001I
5.87883 + 1.48945I 0
u = 1.56484 + 0.04172I
a = −0.187738 + 0.600183I
b = 0.94126 + 1.66599I
7.33785 + 2.67372I 0
u = 1.56484 − 0.04172I
a = −0.187738 − 0.600183I
b = 0.94126 − 1.66599I
7.33785 − 2.67372I 0
u = −1.56736 + 0.09299I
a = −0.150006 − 0.374073I
b = 0.18461 − 2.24549I
7.55766 − 5.64826I 0
u = −1.56736 − 0.09299I
a = −0.150006 + 0.374073I
b = 0.18461 + 2.24549I
7.55766 + 5.64826I 0
u = 1.52282 + 0.42768I
a = −0.259844 + 0.830170I
b = 1.31486 + 1.59000I
3.98985 + 8.76840I 0
u = 1.52282 − 0.42768I
a = −0.259844 − 0.830170I
b = 1.31486 − 1.59000I
3.98985 − 8.76840I 0
u = −1.55558 + 0.36036I
a = −0.328563 − 0.830840I
b = 1.47602 − 1.64277I
2.2777 − 16.5535I 0
u = −1.55558 − 0.36036I
a = −0.328563 + 0.830840I
b = 1.47602 + 1.64277I
2.2777 + 16.5535I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59384 + 0.13900I
a = 0.120923 + 0.572897I
b = 0.265220 + 0.857793I
9.11175 + 3.90003I 0
u = 1.59384 − 0.13900I
a = 0.120923 − 0.572897I
b = 0.265220 − 0.857793I
9.11175 − 3.90003I 0
u = −1.74009 + 0.05337I
a = 0.248000 − 0.330905I
b = −0.630837 − 0.431299I
5.99429 + 0.37796I 0
u = −1.74009 − 0.05337I
a = 0.248000 + 0.330905I
b = −0.630837 + 0.431299I
5.99429 − 0.37796I 0
u = −0.045790 + 0.176383I
a = −3.55491 + 1.36184I
b = 1.68750 + 0.71252I
1.79959 + 2.62972I 7.61232 + 1.73104I
u = −0.045790 − 0.176383I
a = −3.55491 − 1.36184I
b = 1.68750 − 0.71252I
1.79959 − 2.62972I 7.61232 − 1.73104I
12
II. I
u
2
= h28u
19
+ 35u
18
+ · · · + 67b + 22, 15u
19
+ 2u
18
+ · · · + 67a −
194, u
20
+ u
19
+ · · · + 4u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
−u
2
a
9
=
u
−u
3
+ u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
12
=
−0.223881u
19
− 0.0298507u
18
+ ··· + 4.58209u + 2.89552
−0.417910u
19
− 0.522388u
18
+ ··· − 0.313433u − 0.328358
a
7
=
1.52239u
19
+ 1.40299u
18
+ ··· + 5.64179u − 1.08955
−0.0149254u
19
− 0.268657u
18
+ ··· − 0.761194u + 0.0597015
a
1
=
−0.283582u
19
− 1.10448u
18
+ ··· − 4.46269u − 0.865672
−0.298507u
19
− 0.373134u
18
+ ··· + 0.776119u + 0.194030
a
3
=
−0.283582u
19
− 1.10448u
18
+ ··· − 4.46269u + 0.134328
−0.343284u
19
− 0.179104u
18
+ ··· + 0.492537u + 0.373134
a
2
=
0.0149254u
19
− 0.731343u
18
+ ··· − 5.23881u − 1.05970
−0.298507u
19
− 0.373134u
18
+ ··· + 0.776119u + 0.194030
a
11
=
−0.223881u
19
− 0.0298507u
18
+ ··· + 4.58209u + 2.89552
−0.716418u
19
− 0.895522u
18
+ ··· − 0.537313u − 0.134328
a
10
=
−0.417910u
19
− 0.522388u
18
+ ··· + 2.68657u + 2.67164
0.358209u
19
+ 0.447761u
18
+ ··· + 0.268657u − 0.432836
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
191
67
u
19
−
423
67
u
18
+ ··· −
294
67
u +
563
67
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 10u
19
+ ··· − 48u + 16
c
2
u
20
− 2u
19
+ ··· − 6u + 1
c
3
u
20
+ 3u
19
+ ··· + 2u + 1
c
4
, c
5
u
20
+ u
19
+ ··· + 4u
2
+ 1
c
6
u
20
+ u
19
+ ··· − 6u
2
+ 1
c
7
u
20
+ u
19
+ ··· + 2u + 1
c
8
u
20
− u
19
+ ··· + 4u
2
+ 1
c
9
u
20
+ 3u
18
+ ··· − u + 1
c
10
u
20
+ 4u
19
+ ··· − 25u + 11
c
11
, c
12
u
20
− u
19
+ ··· − 2u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 4y
19
+ ··· + 5248y + 256
c
2
y
20
− 8y
19
+ ··· − 6y + 1
c
3
y
20
− 11y
19
+ ··· + 14y + 1
c
4
, c
5
, c
8
y
20
− 25y
19
+ ··· + 8y + 1
c
6
y
20
− 7y
19
+ ··· − 12y + 1
c
7
, c
11
, c
12
y
20
+ 13y
19
+ ··· + 16y + 1
c
9
y
20
+ 6y
19
+ ··· + 3y + 1
c
10
y
20
+ 4y
19
+ ··· − 97y + 121
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.170850 + 0.117267I
a = −0.665048 + 0.367111I
b = −0.291199 − 0.534072I
−1.081310 + 0.351894I −1.49914 + 0.85602I
u = −1.170850 − 0.117267I
a = −0.665048 − 0.367111I
b = −0.291199 + 0.534072I
−1.081310 − 0.351894I −1.49914 − 0.85602I
u = −0.642529 + 0.457629I
a = 0.07992 + 1.50403I
b = −0.87590 + 1.35328I
−3.18447 − 2.24217I −1.06358 + 3.57048I
u = −0.642529 − 0.457629I
a = 0.07992 − 1.50403I
b = −0.87590 − 1.35328I
−3.18447 + 2.24217I −1.06358 − 3.57048I
u = 1.361170 + 0.159080I
a = 0.526032 − 0.892774I
b = −1.35610 − 1.30894I
0.80312 + 5.92906I −0.94753 − 4.21482I
u = 1.361170 − 0.159080I
a = 0.526032 + 0.892774I
b = −1.35610 + 1.30894I
0.80312 − 5.92906I −0.94753 + 4.21482I
u = 0.260151 + 0.547229I
a = −1.92539 + 0.59830I
b = −0.472352 + 0.815038I
−3.24035 − 3.66790I −1.40187 + 2.59215I
u = 0.260151 − 0.547229I
a = −1.92539 − 0.59830I
b = −0.472352 − 0.815038I
−3.24035 + 3.66790I −1.40187 − 2.59215I
u = −0.290039 + 0.503457I
a = 0.870617 − 0.445006I
b = 1.172230 − 0.775670I
1.43868 − 3.08587I −0.56236 + 7.48398I
u = −0.290039 − 0.503457I
a = 0.870617 + 0.445006I
b = 1.172230 + 0.775670I
1.43868 + 3.08587I −0.56236 − 7.48398I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47639 + 0.22931I
a = 0.293760 + 0.814230I
b = −0.83780 + 1.31087I
8.97543 − 1.39766I 10.59066 + 1.96632I
u = 1.47639 − 0.22931I
a = 0.293760 − 0.814230I
b = −0.83780 − 1.31087I
8.97543 + 1.39766I 10.59066 − 1.96632I
u = −1.50224 + 0.09636I
a = 0.010758 − 0.842029I
b = −0.396118 − 1.123700I
10.42730 − 5.27034I 7.14220 + 4.45272I
u = −1.50224 − 0.09636I
a = 0.010758 + 0.842029I
b = −0.396118 + 1.123700I
10.42730 + 5.27034I 7.14220 − 4.45272I
u = 1.54232 + 0.11586I
a = 0.011017 + 0.434673I
b = 1.14192 + 2.07996I
7.94037 + 5.10035I 6.14281 − 2.74611I
u = 1.54232 − 0.11586I
a = 0.011017 − 0.434673I
b = 1.14192 − 2.07996I
7.94037 − 5.10035I 6.14281 + 2.74611I
u = 0.171585 + 0.330782I
a = 2.94933 + 1.88724I
b = −0.662807 + 0.047941I
4.49188 + 3.80357I 11.13661 − 5.52832I
u = 0.171585 − 0.330782I
a = 2.94933 − 1.88724I
b = −0.662807 − 0.047941I
4.49188 − 3.80357I 11.13661 + 5.52832I
u = −1.70595 + 0.23895I
a = −0.150987 − 0.354749I
b = 1.078120 − 0.383730I
6.32800 − 1.11795I 10.96220 + 2.32114I
u = −1.70595 − 0.23895I
a = −0.150987 + 0.354749I
b = 1.078120 + 0.383730I
6.32800 + 1.11795I 10.96220 − 2.32114I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 10u
19
+ ··· − 48u + 16)(u
76
+ 5u
75
+ ··· − 9804u + 1444)
c
2
(u
20
− 2u
19
+ ··· − 6u + 1)(u
76
− 5u
75
+ ··· − 124u − 23)
c
3
(u
20
+ 3u
19
+ ··· + 2u + 1)(u
76
− 2u
75
+ ··· + 76u + 2633)
c
4
, c
5
(u
20
+ u
19
+ ··· + 4u
2
+ 1)(u
76
− 2u
75
+ ··· − 32u + 27)
c
6
(u
20
+ u
19
+ ··· − 6u
2
+ 1)(u
76
− 9u
74
+ ··· − 22u + 19)
c
7
(u
20
+ u
19
+ ··· + 2u + 1)(u
76
+ 13u
74
+ ··· − 82u + 43)
c
8
(u
20
− u
19
+ ··· + 4u
2
+ 1)(u
76
− 2u
75
+ ··· − 32u + 27)
c
9
(u
20
+ 3u
18
+ ··· − u + 1)(u
76
− 3u
75
+ ··· − 397u + 71)
c
10
(u
20
+ 4u
19
+ ··· − 25u + 11)(u
76
− 3u
75
+ ··· + 1147u + 447)
c
11
, c
12
(u
20
− u
19
+ ··· − 2u + 1)(u
76
+ 13u
74
+ ··· − 82u + 43)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
− 4y
19
+ ··· + 5248y + 256)
· (y
76
− 67y
75
+ ··· + 4349328y + 2085136)
c
2
(y
20
− 8y
19
+ ··· − 6y + 1)(y
76
− 19y
75
+ ··· − 82030y + 529)
c
3
(y
20
− 11y
19
+ ··· + 14y + 1)
· (y
76
− 62y
75
+ ··· − 205858982y + 6932689)
c
4
, c
5
, c
8
(y
20
− 25y
19
+ ··· + 8y + 1)(y
76
− 76y
75
+ ··· + 52976y + 729)
c
6
(y
20
− 7y
19
+ ··· − 12y + 1)(y
76
− 18y
75
+ ··· − 15152y + 361)
c
7
, c
11
, c
12
(y
20
+ 13y
19
+ ··· + 16y + 1)(y
76
+ 26y
75
+ ··· + 34556y + 1849)
c
9
(y
20
+ 6y
19
+ ··· + 3y + 1)(y
76
+ 15y
75
+ ··· + 88335y + 5041)
c
10
(y
20
+ 4y
19
+ ··· − 97y + 121)
· (y
76
+ 13y
75
+ ··· + 10810607y + 199809)
19
