12n
0595
(K12n
0595
)
A knot diagram
1
Linearized knot diagam
3 7 10 7 11 2 4 1 12 6 4 9
Solving Sequence
2,7 3,10
4 8 1 6 11 12 5 9
c
2
c
3
c
7
c
1
c
6
c
10
c
11
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h187u
23
+ 2090u
22
+ ··· + 32b + 20128, 629u
23
+ 5916u
22
+ ··· + 64a + 31616,
u
24
+ 10u
23
+ ··· + 544u + 64i
I
u
2
= h−5.02864 × 10
17
a
11
u
2
− 2.22146 × 10
17
a
10
u
2
+ ··· − 9.76070 × 10
17
a − 5.75653 × 10
16
,
− a
11
u
2
− 3a
10
u
2
+ ··· + 342a + 270, u
3
− u
2
+ 1i
I
u
3
= h−7u
14
+ 17u
13
+ ··· + b − 7, −7u
14
+ 14u
13
+ ··· + a − 12,
u
15
− 3u
14
+ 11u
12
− 11u
11
− 14u
10
+ 30u
9
+ u
8
− 35u
7
+ 15u
6
+ 22u
5
− 15u
4
− 7u
3
+ 6u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 75 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
= h187u
23
+ 2090u
22
+ · · · + 32b + 20128, 629u
23
+ 5916u
22
+ · · · +
64a + 31616, u
24
+ 10u
23
+ · · · + 544u + 64i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
−
629
64
u
23
−
1479
16
u
22
+ ··· −
15951
4
u − 494
−
187
32
u
23
−
1045
16
u
22
+ ··· −
9705
2
u − 629
a
4
=
1
8
u
23
+
9
8
u
22
+ ··· +
69
2
u +
9
2
1
8
u
23
+
5
4
u
22
+ ··· +
129
2
u + 8
a
8
=
11
16
u
23
+
29
4
u
22
+ ··· +
1881
4
u + 60
−
1
8
u
23
+
1
2
u
22
+ ··· + 383u + 52
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
11
=
683
64
u
23
+
1455
16
u
22
+ ··· +
10705
4
u + 320
469
32
u
23
+
1889
16
u
22
+ ··· +
3623
2
u + 185
a
12
=
23
16
u
23
+
83
4
u
22
+ ··· + 2552u + 347
−
191
16
u
23
−
1531
16
u
22
+ ··· − 1486u − 148
a
5
=
1
8
u
23
+
9
8
u
22
+ ··· +
69
2
u +
9
2
1
8
u
23
+ u
22
+ ··· + 30u
2
+
9
2
u
a
9
=
−
35
16
u
23
−
83
4
u
22
+ ··· −
3627
4
u − 112
3
8
u
23
−
1
2
u
22
+ ··· − 905u − 124
(ii) Obstruction class = −1
(iii) Cusp Shapes = 9u
23
+
361
4
u
22
+ ··· + 5492u + 734
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 10u
23
+ ··· + 5120u + 4096
c
2
, c
6
u
24
− 10u
23
+ ··· − 544u + 64
c
3
, c
5
, c
10
u
24
+ u
22
+ ··· − u + 1
c
4
, c
7
u
24
+ 4u
23
+ ··· + 3u + 1
c
8
, c
9
, c
12
u
24
+ 6u
23
+ ··· + 36u + 8
c
11
u
24
− 2u
23
+ ··· − 253u
2
+ 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 10y
23
+ ··· + 246415360y + 16777216
c
2
, c
6
y
24
− 10y
23
+ ··· − 5120y + 4096
c
3
, c
5
, c
10
y
24
+ 2y
23
+ ··· + 3y + 1
c
4
, c
7
y
24
− 36y
23
+ ··· − 43y + 1
c
8
, c
9
, c
12
y
24
+ 20y
23
+ ··· − 208y + 64
c
11
y
24
− 28y
23
+ ··· − 8096y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.960426 + 0.434752I
a = 1.39464 − 0.85244I
b = 0.96884 − 1.42503I
−0.39618 + 3.94424I 9.54953 − 8.49759I
u = −0.960426 − 0.434752I
a = 1.39464 + 0.85244I
b = 0.96884 + 1.42503I
−0.39618 − 3.94424I 9.54953 + 8.49759I
u = 0.148613 + 0.911725I
a = 0.535233 + 0.029034I
b = −0.053071 − 0.492300I
−3.90744 − 1.61982I 3.51812 + 4.40153I
u = 0.148613 − 0.911725I
a = 0.535233 − 0.029034I
b = −0.053071 + 0.492300I
−3.90744 + 1.61982I 3.51812 − 4.40153I
u = −0.610326 + 0.971717I
a = −0.759390 + 0.695247I
b = 0.212108 + 1.162240I
3.60557 + 0.61915I 6.47955 − 0.75287I
u = −0.610326 − 0.971717I
a = −0.759390 − 0.695247I
b = 0.212108 − 1.162240I
3.60557 − 0.61915I 6.47955 + 0.75287I
u = −0.603350 + 1.069910I
a = 0.600113 − 0.693104I
b = −0.379478 − 1.060250I
6.67312 − 4.02157I 8.76645 + 3.55064I
u = −0.603350 − 1.069910I
a = 0.600113 + 0.693104I
b = −0.379478 + 1.060250I
6.67312 + 4.02157I 8.76645 − 3.55064I
u = 1.242100 + 0.248561I
a = −0.058554 − 0.232893I
b = 0.014842 + 0.303830I
−2.22462 − 1.76771I −0.33207 + 2.72222I
u = 1.242100 − 0.248561I
a = −0.058554 + 0.232893I
b = 0.014842 − 0.303830I
−2.22462 + 1.76771I −0.33207 − 2.72222I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.598153 + 1.149870I
a = −0.482510 + 0.665162I
b = 0.476234 + 0.952691I
1.93569 − 8.47324I 4.22747 + 6.00356I
u = −0.598153 − 1.149870I
a = −0.482510 − 0.665162I
b = 0.476234 − 0.952691I
1.93569 + 8.47324I 4.22747 − 6.00356I
u = −1.125790 + 0.732879I
a = 1.287760 − 0.541469I
b = 1.05292 − 1.55335I
1.96046 + 5.63124I 4.21368 − 3.68677I
u = −1.125790 − 0.732879I
a = 1.287760 + 0.541469I
b = 1.05292 + 1.55335I
1.96046 − 5.63124I 4.21368 + 3.68677I
u = −1.274940 + 0.470739I
a = −0.919966 + 0.816206I
b = −0.78868 + 1.47368I
−8.06206 + 6.43186I −0.98186 − 9.91203I
u = −1.274940 − 0.470739I
a = −0.919966 − 0.816206I
b = −0.78868 − 1.47368I
−8.06206 − 6.43186I −0.98186 + 9.91203I
u = −1.155680 + 0.779068I
a = −1.296620 + 0.435684I
b = −1.15905 + 1.51367I
4.90945 + 10.68360I 6.29274 − 6.83109I
u = −1.155680 − 0.779068I
a = −1.296620 − 0.435684I
b = −1.15905 − 1.51367I
4.90945 − 10.68360I 6.29274 + 6.83109I
u = −0.444487 + 0.406708I
a = −1.387950 + 0.186641I
b = −0.541015 + 0.647447I
1.007530 − 0.240613I 10.53326 + 2.62206I
u = −0.444487 − 0.406708I
a = −1.387950 − 0.186641I
b = −0.541015 − 0.647447I
1.007530 + 0.240613I 10.53326 − 2.62206I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.18147 + 0.80593I
a = 1.276470 − 0.354607I
b = 1.22233 − 1.44770I
0.0595 + 15.4273I 2.28436 − 8.54538I
u = −1.18147 − 0.80593I
a = 1.276470 + 0.354607I
b = 1.22233 + 1.44770I
0.0595 − 15.4273I 2.28436 + 8.54538I
u = 1.56391 + 0.41904I
a = 0.060771 + 0.164825I
b = −0.025972 − 0.283237I
−8.02840 − 4.65058I −5.55122 + 0.I
u = 1.56391 − 0.41904I
a = 0.060771 − 0.164825I
b = −0.025972 + 0.283237I
−8.02840 + 4.65058I −5.55122 + 0.I
7
II. I
u
2
= h−5.03 × 10
17
a
11
u
2
− 2.22 × 10
17
a
10
u
2
+ · · · − 9.76 × 10
17
a − 5.76 ×
10
16
, −a
11
u
2
− 3a
10
u
2
+ · · · + 342a + 270, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
a
0.760828a
11
u
2
+ 0.336105a
10
u
2
+ ··· + 1.47678a + 0.0870957
a
4
=
0.161224a
11
u
2
− 0.231777a
10
u
2
+ ··· − 0.574135a − 1.02670
0.322449a
11
u
2
− 0.463555a
10
u
2
+ ··· − 1.14827a − 2.05340
a
8
=
−1.11863a
11
u
2
− 2.00948a
10
u
2
+ ··· − 0.0799198a + 0.987036
−2.18025a
11
u
2
− 2.66485a
10
u
2
+ ··· − 0.269690a + 3.10319
a
1
=
−u
2
+ 1
−u
2
+ u + 1
a
6
=
u
u
a
11
=
0.751052a
11
u
2
+ 0.532088a
10
u
2
+ ··· − 2.09089a − 0.395085
1.51188a
11
u
2
+ 0.868193a
10
u
2
+ ··· − 1.61411a − 0.307989
a
12
=
2.43820a
11
u
2
+ 2.31550a
10
u
2
+ ··· − 7.45269a − 0.483830
−0.942804a
11
u
2
+ 1.01259a
10
u
2
+ ··· − 11.3778a − 3.58923
a
5
=
0.161224a
11
u
2
− 0.231777a
10
u
2
+ ··· − 0.574135a − 1.02670
0.610760a
11
u
2
+ 0.660458a
10
u
2
+ ··· − 1.46841a − 1.69087
a
9
=
0.587461a
11
u
2
− 1.49312a
10
u
2
+ ··· + 0.224321a − 1.59341
−1.64875a
11
u
2
− 4.32440a
10
u
2
+ ··· + 1.17215a + 1.29332
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
472821250888279224
660943353461191351
a
11
u
2
−
2769977983618152264
660943353461191351
a
10
u
2
+ ··· +
15612584538467295228
660943353461191351
a +
630168688688268602
660943353461191351
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
+ 2u + 1)
12
c
2
, c
6
(u
3
+ u
2
− 1)
12
c
3
, c
5
, c
10
u
36
+ u
35
+ ··· − 24u − 1
c
4
, c
7
u
36
+ 5u
35
+ ··· − 25616u − 8257
c
8
, c
9
, c
12
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
c
11
u
36
− u
35
+ ··· − 194210u − 32651
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y − 1)
12
c
2
, c
6
(y
3
− y
2
+ 2y − 1)
12
c
3
, c
5
, c
10
y
36
+ 15y
35
+ ··· − 424y + 1
c
4
, c
7
y
36
− 9y
35
+ ··· + 88932224y + 68178049
c
8
, c
9
, c
12
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
6
c
11
y
36
+ 3y
35
+ ··· − 12157276468y + 1066087801
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.966871 + 0.180936I
b = −0.819834 − 0.289466I
−1.17182 − 2.82812I 8.92653 + 2.97945I
u = 0.877439 + 0.744862I
a = −0.906735 + 0.163934I
b = −1.40770 − 0.61461I
−4.87092 − 4.80053I 0.08548 + 6.66423I
u = 0.877439 + 0.744862I
a = −0.596231 + 0.691478I
b = −0.881257 − 0.308926I
−4.87092 − 0.85571I 0.085479 − 0.705331I
u = 0.877439 + 0.744862I
a = 0.693529 + 0.478182I
b = 0.85756 + 1.73624I
1.78490 − 7.42025I 4.09089 + 6.18427I
u = 0.877439 + 0.744862I
a = 0.757411 − 0.290893I
b = 1.038210 − 0.162620I
−4.87092 − 0.85571I 0.085479 − 0.705331I
u = 0.877439 + 0.744862I
a = −0.570573 − 0.528271I
b = −0.62680 − 1.75390I
5.74941 − 2.82812I 7.77925 + 2.97945I
u = 0.877439 + 0.744862I
a = 0.705785 − 0.269246I
b = 0.983142 + 0.561425I
−1.17182 − 2.82812I 8.92653 + 2.97945I
u = 0.877439 + 0.744862I
a = 0.431400 + 0.557577I
b = 0.38501 + 1.72079I
1.78490 + 1.76400I 4.09089 − 0.22537I
u = 0.877439 + 0.744862I
a = 1.277990 − 0.384427I
b = 0.917712 + 0.531550I
−4.87092 − 4.80053I 0.08548 + 6.66423I
u = 0.877439 + 0.744862I
a = −1.22258 − 0.92330I
b = 0.036791 − 0.810574I
1.78490 + 1.76400I 4.09089 − 0.22537I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 1.40135 + 0.80927I
b = 0.107154 + 0.888524I
5.74941 − 2.82812I 7.77925 + 2.97945I
u = 0.877439 + 0.744862I
a = −1.54427 − 0.66783I
b = −0.252349 − 0.936159I
1.78490 − 7.42025I 4.09089 + 6.18427I
u = 0.877439 − 0.744862I
a = −0.966871 − 0.180936I
b = −0.819834 + 0.289466I
−1.17182 + 2.82812I 8.92653 − 2.97945I
u = 0.877439 − 0.744862I
a = −0.906735 − 0.163934I
b = −1.40770 + 0.61461I
−4.87092 + 4.80053I 0.08548 − 6.66423I
u = 0.877439 − 0.744862I
a = −0.596231 − 0.691478I
b = −0.881257 + 0.308926I
−4.87092 + 0.85571I 0.085479 + 0.705331I
u = 0.877439 − 0.744862I
a = 0.693529 − 0.478182I
b = 0.85756 − 1.73624I
1.78490 + 7.42025I 4.09089 − 6.18427I
u = 0.877439 − 0.744862I
a = 0.757411 + 0.290893I
b = 1.038210 + 0.162620I
−4.87092 + 0.85571I 0.085479 + 0.705331I
u = 0.877439 − 0.744862I
a = −0.570573 + 0.528271I
b = −0.62680 + 1.75390I
5.74941 + 2.82812I 7.77925 − 2.97945I
u = 0.877439 − 0.744862I
a = 0.705785 + 0.269246I
b = 0.983142 − 0.561425I
−1.17182 + 2.82812I 8.92653 − 2.97945I
u = 0.877439 − 0.744862I
a = 0.431400 − 0.557577I
b = 0.38501 − 1.72079I
1.78490 − 1.76400I 4.09089 + 0.22537I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 − 0.744862I
a = 1.277990 + 0.384427I
b = 0.917712 − 0.531550I
−4.87092 + 4.80053I 0.08548 − 6.66423I
u = 0.877439 − 0.744862I
a = −1.22258 + 0.92330I
b = 0.036791 + 0.810574I
1.78490 − 1.76400I 4.09089 + 0.22537I
u = 0.877439 − 0.744862I
a = 1.40135 − 0.80927I
b = 0.107154 − 0.888524I
5.74941 + 2.82812I 7.77925 − 2.97945I
u = 0.877439 − 0.744862I
a = −1.54427 + 0.66783I
b = −0.252349 + 0.936159I
1.78490 + 7.42025I 4.09089 − 6.18427I
u = −0.754878
a = 0.744757 + 1.086550I
b = 0.562201 − 0.820211I
−5.30941 2.39727 + 0.I
u = −0.754878
a = 0.744757 − 1.086550I
b = 0.562201 + 0.820211I
−5.30941 2.39727 + 0.I
u = −0.754878
a = −0.611696 + 0.297636I
b = −0.68475 − 1.56206I
−9.00850 + 1.97241I −6.44379 − 3.68478I
u = −0.754878
a = −0.611696 − 0.297636I
b = −0.68475 + 1.56206I
−9.00850 − 1.97241I −6.44379 + 3.68478I
u = −0.754878
a = 1.89410 + 0.09019I
b = 2.10577 − 0.44724I
−2.35268 − 4.59213I −2.43837 + 3.20482I
u = −0.754878
a = 1.89410 − 0.09019I
b = 2.10577 + 0.44724I
−2.35268 + 4.59213I −2.43837 − 3.20482I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.754878
a = −2.00292
b = −2.06588
1.61183 1.25000
u = −0.754878
a = −0.90710 + 2.06929I
b = −0.461755 − 0.224679I
−9.00850 − 1.97241I −6.44379 + 3.68478I
u = −0.754878
a = −0.90710 − 2.06929I
b = −0.461755 + 0.224679I
−9.00850 + 1.97241I −6.44379 − 3.68478I
u = −0.754878
a = −2.73671
b = −1.51196
1.61183 1.25000
u = −0.754878
a = 2.78955 + 0.59246I
b = 1.42981 − 0.06809I
−2.35268 + 4.59213I −2.43837 − 3.20482I
u = −0.754878
a = 2.78955 − 0.59246I
b = 1.42981 + 0.06809I
−2.35268 − 4.59213I −2.43837 + 3.20482I
14
III. I
u
3
=
h−7u
14
+17u
13
+· · ·+b−7, −7u
14
+14u
13
+· · ·+a−12, u
15
−3u
14
+· · ·+u−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
7u
14
− 14u
13
+ ··· − 3u + 12
7u
14
− 17u
13
+ ··· + 5u + 7
a
4
=
−u
14
+ 2u
13
+ ··· + u − 6
−u
14
+ 3u
13
+ ··· − 6u − 1
a
8
=
5u
14
− 14u
13
+ ··· + 9u + 4
u
14
− 2u
13
+ ··· − u + 6
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
11
=
6u
14
− 12u
13
+ ··· − 55u
2
+ 9
6u
14
− 15u
13
+ ··· + 8u + 4
a
12
=
8u
14
− 19u
13
+ ··· − 55u
2
+ 10
4u
14
− 8u
13
+ ··· + 2u + 8
a
5
=
−u
14
+ 2u
13
+ ··· + u − 6
−u
14
+ 3u
13
+ ··· + 7u
2
− 6u
a
9
=
6u
14
− 16u
13
+ ··· + 9u + 8
u
14
− 2u
13
+ ··· − u + 6
(ii) Obstruction class = 1
(iii) Cusp Shapes = 14u
14
− 33u
13
− 15u
12
+ 125u
11
− 66u
10
− 188u
9
+ 232u
8
+
128u
7
− 277u
6
− 7u
5
+ 206u
4
− 8u
3
− 60u
2
+ 9u + 15
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 9u
14
+ ··· + 13u − 1
c
2
u
15
− 3u
14
+ ··· + u − 1
c
3
, c
10
u
15
+ 7u
13
+ ··· − 3u
2
− 1
c
4
u
15
− 2u
14
+ ··· + 4u
2
+ 1
c
5
u
15
+ 7u
13
+ ··· + 3u
2
+ 1
c
6
u
15
+ 3u
14
+ ··· + u + 1
c
7
u
15
+ 2u
14
+ ··· − 4u
2
− 1
c
8
, c
9
u
15
+ u
14
+ ··· + 2u + 1
c
11
u
15
+ 11u
12
+ ··· + 20u + 52
c
12
u
15
− u
14
+ ··· + 2u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 7y
14
+ ··· + 9y − 1
c
2
, c
6
y
15
− 9y
14
+ ··· + 13y − 1
c
3
, c
5
, c
10
y
15
+ 14y
14
+ ··· − 6y − 1
c
4
, c
7
y
15
+ 8y
14
+ ··· − 8y − 1
c
8
, c
9
, c
12
y
15
+ 15y
14
+ ··· + 2y − 1
c
11
y
15
+ 22y
13
+ ··· − 9480y − 2704
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.903593 + 0.241265I
a = 0.350344 − 0.717165I
b = −0.143541 + 0.732551I
−5.33721 + 1.06098I 1.94514 − 6.50174I
u = −0.903593 − 0.241265I
a = 0.350344 + 0.717165I
b = −0.143541 − 0.732551I
−5.33721 − 1.06098I 1.94514 + 6.50174I
u = −1.153700 + 0.341454I
a = −0.250605 + 0.447767I
b = 0.136231 − 0.602157I
−10.48360 + 4.01988I −3.70487 − 3.71278I
u = −1.153700 − 0.341454I
a = −0.250605 − 0.447767I
b = 0.136231 + 0.602157I
−10.48360 − 4.01988I −3.70487 + 3.71278I
u = 1.019660 + 0.734646I
a = −0.820127 + 0.113685I
b = −0.919765 − 0.486583I
−1.92987 − 3.17848I −2.15467 + 7.79131I
u = 1.019660 − 0.734646I
a = −0.820127 − 0.113685I
b = −0.919765 + 0.486583I
−1.92987 + 3.17848I −2.15467 − 7.79131I
u = 0.761388 + 1.022410I
a = 0.507420 − 0.449806I
b = 0.846228 + 0.176312I
−5.29563 − 2.03853I −2.96527 + 5.97997I
u = 0.761388 − 1.022410I
a = 0.507420 + 0.449806I
b = 0.846228 − 0.176312I
−5.29563 + 2.03853I −2.96527 − 5.97997I
u = 0.686174
a = 3.14054
b = 2.15496
2.14254 20.3790
u = 0.626156 + 0.247109I
a = −2.60546 + 0.72610I
b = −1.81085 − 0.18918I
−1.59061 − 4.99019I 7.82612 + 8.92217I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.626156 − 0.247109I
a = −2.60546 − 0.72610I
b = −1.81085 + 0.18918I
−1.59061 + 4.99019I 7.82612 − 8.92217I
u = −0.608443 + 0.200961I
a = −0.78816 + 1.31289I
b = 0.215712 − 0.957209I
−8.24398 − 1.54403I 3.81810 − 1.58037I
u = −0.608443 − 0.200961I
a = −0.78816 − 1.31289I
b = 0.215712 + 0.957209I
−8.24398 + 1.54403I 3.81810 + 1.58037I
u = 1.41545 + 0.63783I
a = 0.536325 + 0.251841I
b = 0.598509 + 0.698551I
−7.66882 − 5.24684I 0.04579 + 7.53706I
u = 1.41545 − 0.63783I
a = 0.536325 − 0.251841I
b = 0.598509 − 0.698551I
−7.66882 + 5.24684I 0.04579 − 7.53706I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
+ 2u + 1)
12
)(u
15
− 9u
14
+ ··· + 13u − 1)
· (u
24
+ 10u
23
+ ··· + 5120u + 4096)
c
2
((u
3
+ u
2
− 1)
12
)(u
15
− 3u
14
+ ··· + u − 1)(u
24
− 10u
23
+ ··· − 544u + 64)
c
3
, c
10
(u
15
+ 7u
13
+ ··· − 3u
2
− 1)(u
24
+ u
22
+ ··· − u + 1)
· (u
36
+ u
35
+ ··· − 24u − 1)
c
4
(u
15
− 2u
14
+ ··· + 4u
2
+ 1)(u
24
+ 4u
23
+ ··· + 3u + 1)
· (u
36
+ 5u
35
+ ··· − 25616u − 8257)
c
5
(u
15
+ 7u
13
+ ··· + 3u
2
+ 1)(u
24
+ u
22
+ ··· − u + 1)
· (u
36
+ u
35
+ ··· − 24u − 1)
c
6
((u
3
+ u
2
− 1)
12
)(u
15
+ 3u
14
+ ··· + u + 1)(u
24
− 10u
23
+ ··· − 544u + 64)
c
7
(u
15
+ 2u
14
+ ··· − 4u
2
− 1)(u
24
+ 4u
23
+ ··· + 3u + 1)
· (u
36
+ 5u
35
+ ··· − 25616u − 8257)
c
8
, c
9
((u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
)(u
15
+ u
14
+ ··· + 2u + 1)
· (u
24
+ 6u
23
+ ··· + 36u + 8)
c
11
(u
15
+ 11u
12
+ ··· + 20u + 52)(u
24
− 2u
23
+ ··· − 253u
2
+ 16)
· (u
36
− u
35
+ ··· − 194210u − 32651)
c
12
((u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
6
)(u
15
− u
14
+ ··· + 2u − 1)
· (u
24
+ 6u
23
+ ··· + 36u + 8)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
+ 3y
2
+ 2y − 1)
12
)(y
15
+ 7y
14
+ ··· + 9y − 1)
· (y
24
+ 10y
23
+ ··· + 246415360y + 16777216)
c
2
, c
6
((y
3
− y
2
+ 2y − 1)
12
)(y
15
− 9y
14
+ ··· + 13y − 1)
· (y
24
− 10y
23
+ ··· − 5120y + 4096)
c
3
, c
5
, c
10
(y
15
+ 14y
14
+ ··· − 6y − 1)(y
24
+ 2y
23
+ ··· + 3y + 1)
· (y
36
+ 15y
35
+ ··· − 424y + 1)
c
4
, c
7
(y
15
+ 8y
14
+ ··· − 8y − 1)(y
24
− 36y
23
+ ··· − 43y + 1)
· (y
36
− 9y
35
+ ··· + 88932224y + 68178049)
c
8
, c
9
, c
12
((y
6
+ 5y
5
+ ··· − 5y + 1)
6
)(y
15
+ 15y
14
+ ··· + 2y − 1)
· (y
24
+ 20y
23
+ ··· − 208y + 64)
c
11
(y
15
+ 22y
13
+ ··· − 9480y − 2704)(y
24
− 28y
23
+ ··· − 8096y + 256)
· (y
36
+ 3y
35
+ ··· − 12157276468y + 1066087801)
21
