11a
146
(K11a
146
)
A knot diagram
1
Linearized knot diagam
6 1 9 11 2 10 5 3 4 7 8
Solving Sequence
1,6
2
3,8
9 5 7 11 4 10
c
1
c
2
c
8
c
5
c
7
c
11
c
4
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.16236 × 10
103
u
74
+ 3.74125 × 10
102
u
73
+ ··· + 1.41576 × 10
103
b − 7.11244 × 10
103
,
7.14613 × 10
103
u
74
− 3.17559 × 10
103
u
73
+ ··· + 9.91035 × 10
103
a + 2.29421 × 10
104
,
u
75
+ 15u
73
+ ··· − 20u + 7i
I
u
2
= h−u
13
− 3u
11
− 7u
9
− 9u
7
+ u
6
− 9u
5
+ 2u
4
− 5u
3
+ u
2
+ b − 3u,
− u
13
+ 4u
12
− 6u
11
+ 13u
10
− 14u
9
+ 27u
8
− 22u
7
+ 34u
6
− 24u
5
+ 30u
4
− 19u
3
+ 15u
2
+ a − 6u + 5,
u
14
− u
13
+ 4u
12
− 3u
11
+ 9u
10
− 6u
9
+ 13u
8
− 8u
7
+ 13u
6
− 8u
5
+ 9u
4
− 4u
3
+ 4u
2
− 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−1.16 × 10
103
u
74
+ 3.74 × 10
102
u
73
+ · · · + 1.42 × 10
103
b − 7.11 ×
10
103
, 7.15 × 10
103
u
74
− 3.18 × 10
103
u
73
+ · · · + 9.91 × 10
103
a + 2.29 ×
10
104
, u
75
+ 15u
73
+ · · · − 20u + 7i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
8
=
−0.721078u
74
+ 0.320432u
73
+ ··· − 5.32211u − 2.31497
0.821010u
74
− 0.264257u
73
+ ··· − 12.5249u + 5.02375
a
9
=
−0.810814u
74
+ 1.04372u
73
+ ··· − 19.2078u + 1.26956
1.59265u
74
− 0.838121u
73
+ ··· − 10.7401u + 6.06974
a
5
=
−u
u
3
+ u
a
7
=
−0.886848u
74
+ 0.735561u
73
+ ··· − 9.13546u − 1.57363
1.30627u
74
− 0.520026u
73
+ ··· − 18.1745u + 7.18831
a
11
=
1.06655u
74
− 1.00342u
73
+ ··· + 16.8816u + 0.960205
−0.756010u
74
+ 0.0457275u
73
+ ··· + 22.8247u − 7.73329
a
4
=
−0.0614847u
74
+ 0.125592u
73
+ ··· + 1.89652u + 0.236355
−0.0748893u
74
+ 0.280213u
73
+ ··· − 0.209838u + 0.00750577
a
10
=
−0.579776u
74
+ 0.227218u
73
+ ··· + 5.38557u − 1.00498
0.547002u
74
− 0.277744u
73
+ ··· − 8.65299u + 2.85168
a
10
=
−0.579776u
74
+ 0.227218u
73
+ ··· + 5.38557u − 1.00498
0.547002u
74
− 0.277744u
73
+ ··· − 8.65299u + 2.85168
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0573232u
74
+ 0.652315u
73
+ ··· + 33.0747u − 8.02057
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
75
+ 15u
73
+ ··· − 20u − 7
c
2
u
75
+ 30u
74
+ ··· + 288u − 49
c
3
, c
8
, c
9
u
75
+ u
74
+ ··· − 23u − 1
c
4
u
75
− 3u
74
+ ··· + 15u + 1
c
6
, c
10
u
75
− u
74
+ ··· − 29u − 2
c
7
u
75
− 2u
74
+ ··· − 17u + 1
c
11
u
75
− 5u
74
+ ··· + 36831u − 8639
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
75
+ 30y
74
+ ··· + 288y −49
c
2
y
75
+ 38y
74
+ ··· + 546484y −2401
c
3
, c
8
, c
9
y
75
− 77y
74
+ ··· + 71y −1
c
4
y
75
− y
74
+ ··· − 29y −1
c
6
, c
10
y
75
− 43y
74
+ ··· + 321y −4
c
7
y
75
− 8y
74
+ ··· − 25y −1
c
11
y
75
− 21y
74
+ ··· + 1725459695y −74632321
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.583753 + 0.813835I
a = 1.58625 + 0.14110I
b = −0.21446 + 2.00505I
2.35458 + 1.52998I 4.39480 + 0.I
u = −0.583753 − 0.813835I
a = 1.58625 − 0.14110I
b = −0.21446 − 2.00505I
2.35458 − 1.52998I 4.39480 + 0.I
u = −0.849508 + 0.542374I
a = −1.19541 − 1.04425I
b = 1.63768 + 0.71839I
9.48673 + 3.80892I 9.50577 − 2.11566I
u = −0.849508 − 0.542374I
a = −1.19541 + 1.04425I
b = 1.63768 − 0.71839I
9.48673 − 3.80892I 9.50577 + 2.11566I
u = −0.219708 + 0.997660I
a = 0.313694 − 0.499917I
b = −0.556012 − 1.022730I
−3.84788 − 0.02965I −1.99150 + 0.I
u = −0.219708 − 0.997660I
a = 0.313694 + 0.499917I
b = −0.556012 + 1.022730I
−3.84788 + 0.02965I −1.99150 + 0.I
u = 0.932408 + 0.222383I
a = −0.471108 − 0.020661I
b = 1.033510 − 0.122082I
8.24157 + 0.11075I 14.1787 + 1.9734I
u = 0.932408 − 0.222383I
a = −0.471108 + 0.020661I
b = 1.033510 + 0.122082I
8.24157 − 0.11075I 14.1787 − 1.9734I
u = 0.564610 + 0.759254I
a = −1.111500 − 0.152357I
b = 1.264580 − 0.419226I
7.40917 + 1.28073I 5.11860 − 6.28891I
u = 0.564610 − 0.759254I
a = −1.111500 + 0.152357I
b = 1.264580 + 0.419226I
7.40917 − 1.28073I 5.11860 + 6.28891I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.808914 + 0.489775I
a = −1.29004 + 0.89724I
b = 0.946433 − 0.610763I
−0.30295 − 6.24808I 3.92390 + 5.63947I
u = 0.808914 − 0.489775I
a = −1.29004 − 0.89724I
b = 0.946433 + 0.610763I
−0.30295 + 6.24808I 3.92390 − 5.63947I
u = 0.419276 + 0.968552I
a = −1.37090 + 0.96007I
b = 1.275450 + 0.547400I
−3.84184 + 1.43557I 0
u = 0.419276 − 0.968552I
a = −1.37090 − 0.96007I
b = 1.275450 − 0.547400I
−3.84184 − 1.43557I 0
u = −0.583811 + 0.895077I
a = −0.752626 + 0.749520I
b = −0.75640 − 2.07806I
2.09042 − 6.16494I 0
u = −0.583811 − 0.895077I
a = −0.752626 − 0.749520I
b = −0.75640 + 2.07806I
2.09042 + 6.16494I 0
u = 0.671530 + 0.632305I
a = 1.07681 − 1.02346I
b = −1.032100 + 0.508181I
2.52677 − 1.24936I 7.69965 + 2.52698I
u = 0.671530 − 0.632305I
a = 1.07681 + 1.02346I
b = −1.032100 − 0.508181I
2.52677 + 1.24936I 7.69965 − 2.52698I
u = −0.663268 + 0.853569I
a = −1.37734 − 0.72160I
b = 0.758278 − 0.141213I
1.06443 − 2.57629I 0
u = −0.663268 − 0.853569I
a = −1.37734 + 0.72160I
b = 0.758278 + 0.141213I
1.06443 + 2.57629I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.663115 + 0.870319I
a = −1.33003 − 0.51217I
b = 0.769435 − 0.207041I
1.03816 − 2.56974I 0
u = −0.663115 − 0.870319I
a = −1.33003 + 0.51217I
b = 0.769435 + 0.207041I
1.03816 + 2.56974I 0
u = −0.329445 + 0.834791I
a = 2.36627 + 0.05733I
b = −1.18992 + 0.99392I
0.58773 + 2.04231I 0.69192 + 3.19638I
u = −0.329445 − 0.834791I
a = 2.36627 − 0.05733I
b = −1.18992 − 0.99392I
0.58773 − 2.04231I 0.69192 − 3.19638I
u = −0.573961 + 0.682020I
a = 1.38069 + 1.62918I
b = −0.573303 − 0.057484I
−0.601433 + 0.843152I 6.25066 − 1.26638I
u = −0.573961 − 0.682020I
a = 1.38069 − 1.62918I
b = −0.573303 + 0.057484I
−0.601433 − 0.843152I 6.25066 + 1.26638I
u = 0.791734 + 0.779097I
a = 0.992300 − 0.187859I
b = −1.143650 + 0.488302I
6.79170 − 1.71786I 0
u = 0.791734 − 0.779097I
a = 0.992300 + 0.187859I
b = −1.143650 − 0.488302I
6.79170 + 1.71786I 0
u = 0.005828 + 1.116560I
a = 0.962671 − 0.065388I
b = 0.771794 + 0.649501I
3.39834 + 2.32606I 0
u = 0.005828 − 1.116560I
a = 0.962671 + 0.065388I
b = 0.771794 − 0.649501I
3.39834 − 2.32606I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.607031 + 0.944057I
a = −0.61211 + 1.40952I
b = 0.795124 + 0.593814I
6.78271 + 3.40013I 0
u = 0.607031 − 0.944057I
a = −0.61211 − 1.40952I
b = 0.795124 − 0.593814I
6.78271 − 3.40013I 0
u = 0.446827 + 1.030770I
a = 0.383255 + 0.716019I
b = 0.78263 − 1.25594I
−3.66270 + 4.65674I 0
u = 0.446827 − 1.030770I
a = 0.383255 − 0.716019I
b = 0.78263 + 1.25594I
−3.66270 − 4.65674I 0
u = −0.821168 + 0.772543I
a = −0.915115 − 0.063644I
b = 0.670177 − 0.265353I
0.90357 − 3.01315I 0
u = −0.821168 − 0.772543I
a = −0.915115 + 0.063644I
b = 0.670177 + 0.265353I
0.90357 + 3.01315I 0
u = −0.997300 + 0.535698I
a = 1.041710 + 0.863157I
b = −1.41132 − 0.74352I
6.61694 + 10.02950I 0
u = −0.997300 − 0.535698I
a = 1.041710 − 0.863157I
b = −1.41132 + 0.74352I
6.61694 − 10.02950I 0
u = −0.594753 + 0.976447I
a = 1.76760 + 0.27801I
b = −0.992629 + 0.317325I
−1.52512 − 5.54501I 0
u = −0.594753 − 0.976447I
a = 1.76760 − 0.27801I
b = −0.992629 − 0.317325I
−1.52512 + 5.54501I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.034915 + 0.842594I
a = −0.508060 + 0.814343I
b = −0.096919 + 0.903738I
−1.98038 − 1.28024I −1.71519 + 5.23822I
u = −0.034915 − 0.842594I
a = −0.508060 − 0.814343I
b = −0.096919 − 0.903738I
−1.98038 + 1.28024I −1.71519 − 5.23822I
u = 0.628874 + 0.990800I
a = 1.66426 − 0.68833I
b = −1.19979 − 0.86296I
1.46459 + 6.31124I 0
u = 0.628874 − 0.990800I
a = 1.66426 + 0.68833I
b = −1.19979 + 0.86296I
1.46459 − 6.31124I 0
u = 0.736446 + 0.947781I
a = 1.17778 − 1.13785I
b = −0.887098 − 0.641638I
6.26955 + 7.47029I 0
u = 0.736446 − 0.947781I
a = 1.17778 + 1.13785I
b = −0.887098 + 0.641638I
6.26955 − 7.47029I 0
u = 0.028864 + 1.205850I
a = 0.030043 − 0.158897I
b = 0.525695 − 0.912935I
−6.15424 − 4.21404I 0
u = 0.028864 − 1.205850I
a = 0.030043 + 0.158897I
b = 0.525695 + 0.912935I
−6.15424 + 4.21404I 0
u = −0.423126 + 1.151840I
a = 0.063280 + 1.381230I
b = −1.57483 − 0.26636I
−1.02193 − 4.09857I 0
u = −0.423126 − 1.151840I
a = 0.063280 − 1.381230I
b = −1.57483 + 0.26636I
−1.02193 + 4.09857I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768859
a = 1.67495
b = −1.47011
2.41244 3.98160
u = 0.652679 + 1.083040I
a = −1.61651 + 0.66348I
b = 1.173460 + 0.781385I
−2.04951 + 11.72600I 0
u = 0.652679 − 1.083040I
a = −1.61651 − 0.66348I
b = 1.173460 − 0.781385I
−2.04951 − 11.72600I 0
u = 1.110230 + 0.622964I
a = 0.516528 − 0.163821I
b = −0.894451 + 0.337332I
6.65332 + 3.38709I 0
u = 1.110230 − 0.622964I
a = 0.516528 + 0.163821I
b = −0.894451 − 0.337332I
6.65332 − 3.38709I 0
u = −0.558544 + 1.146300I
a = 0.559124 + 0.593863I
b = −0.774731 + 0.320056I
−1.85708 − 4.63248I 0
u = −0.558544 − 1.146300I
a = 0.559124 − 0.593863I
b = −0.774731 − 0.320056I
−1.85708 + 4.63248I 0
u = −0.673658 + 1.087130I
a = −1.53716 − 1.02912I
b = 1.69251 − 1.06931I
7.83095 − 9.48733I 0
u = −0.673658 − 1.087130I
a = −1.53716 + 1.02912I
b = 1.69251 + 1.06931I
7.83095 + 9.48733I 0
u = −0.228067 + 0.674546I
a = −2.29484 + 1.49946I
b = −0.092638 − 0.627623I
0.91162 − 4.36069I 4.50920 + 7.60061I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.228067 − 0.674546I
a = −2.29484 − 1.49946I
b = −0.092638 + 0.627623I
0.91162 + 4.36069I 4.50920 − 7.60061I
u = 0.129319 + 0.675423I
a = −1.34198 + 0.85690I
b = 0.014926 + 1.085660I
−1.94755 − 1.36953I −1.12148 + 5.96580I
u = 0.129319 − 0.675423I
a = −1.34198 − 0.85690I
b = 0.014926 − 1.085660I
−1.94755 + 1.36953I −1.12148 − 5.96580I
u = −0.727326 + 1.141520I
a = 1.44570 + 0.77630I
b = −1.46957 + 1.03381I
4.7307 − 16.2882I 0
u = −0.727326 − 1.141520I
a = 1.44570 − 0.77630I
b = −1.46957 − 1.03381I
4.7307 + 16.2882I 0
u = −0.604095 + 0.124629I
a = 0.520584 − 0.161680I
b = −0.562665 + 0.068774I
0.988802 − 0.029608I 10.70489 + 0.11784I
u = −0.604095 − 0.124629I
a = 0.520584 + 0.161680I
b = −0.562665 − 0.068774I
0.988802 + 0.029608I 10.70489 − 0.11784I
u = 0.853645 + 1.095880I
a = 0.902335 − 0.386675I
b = −0.753531 − 0.798272I
5.21306 + 3.57822I 0
u = 0.853645 − 1.095880I
a = 0.902335 + 0.386675I
b = −0.753531 + 0.798272I
5.21306 − 3.57822I 0
u = 0.095706 + 1.407540I
a = −0.286428 + 0.016195I
b = −0.719842 − 0.514282I
−1.04032 + 7.25828I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.095706 − 1.407540I
a = −0.286428 − 0.016195I
b = −0.719842 + 0.514282I
−1.04032 − 7.25828I 0
u = 0.75306 + 1.24388I
a = −0.545367 + 0.387882I
b = 0.683526 + 0.725105I
5.24327 + 6.25276I 0
u = 0.75306 − 1.24388I
a = −0.545367 − 0.387882I
b = 0.683526 − 0.725105I
5.24327 − 6.25276I 0
u = 0.276964 + 0.055334I
a = −3.24614 − 1.82467I
b = 0.335709 + 0.635949I
−1.70721 − 1.28972I −0.48854 + 2.47606I
u = 0.276964 − 0.055334I
a = −3.24614 + 1.82467I
b = 0.335709 − 0.635949I
−1.70721 + 1.28972I −0.48854 − 2.47606I
12
II.
I
u
2
= h−u
13
−3u
11
+· · ·+b−3u, −u
13
+4u
12
+· · ·+a+5, u
14
−u
13
+· · ·−u+1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
8
=
u
13
− 4u
12
+ ··· + 6u − 5
u
13
+ 3u
11
+ 7u
9
+ 9u
7
− u
6
+ 9u
5
− 2u
4
+ 5u
3
− u
2
+ 3u
a
9
=
2u
13
− 4u
12
+ ··· + 6u − 4
u
12
+ 2u
10
+ u
9
+ 4u
8
+ 2u
7
+ 4u
6
+ 3u
5
+ 3u
4
+ 2u
3
+ u
2
+ 2u + 1
a
5
=
−u
u
3
+ u
a
7
=
u
13
− 4u
12
+ ··· + 4u − 4
u
13
− u
12
+ ··· + 5u − 1
a
11
=
−4u
13
+ u
12
+ ··· − 4u − 3
2u
13
− 2u
12
+ ··· + 3u − 2
a
4
=
−2u
13
+ 4u
12
+ ··· − 5u + 4
−u
13
− 3u
11
− 6u
9
− 7u
7
+ u
6
− 5u
5
+ 2u
4
− u
3
− u − 1
a
10
=
−u
13
+ u
12
+ ··· − u + 1
−u
13
− 2u
11
− 2u
10
− 3u
9
− 5u
8
− 2u
7
− 8u
6
− 8u
4
+ 2u
3
− 6u
2
+ u − 2
a
10
=
−u
13
+ u
12
+ ··· − u + 1
−u
13
− 2u
11
− 2u
10
− 3u
9
− 5u
8
− 2u
7
− 8u
6
− 8u
4
+ 2u
3
− 6u
2
+ u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 5u
13
−3u
12
+15u
11
−9u
10
+32u
9
−17u
8
+38u
7
−24u
6
+33u
5
−21u
4
+18u
3
−7u
2
+11u
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
− u
13
+ ··· − u + 1
c
2
u
14
+ 7u
13
+ ··· + 7u + 1
c
3
u
14
− 8u
12
+ ··· − 2u
2
+ 1
c
4
u
14
+ 5u
11
+ 2u
10
+ 3u
9
+ 9u
8
+ u
7
+ 8u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 2u
2
+ 1
c
5
u
14
+ u
13
+ ··· + u + 1
c
6
u
14
+ 2u
13
+ ··· + 2u + 1
c
7
u
14
+ 3u
13
+ 3u
12
− u
11
− 6u
10
− 6u
9
+ 2u
8
+ 6u
7
+ u
6
+ 3u
4
− 2u
2
+ 1
c
8
, c
9
u
14
− 8u
12
+ ··· − 2u
2
+ 1
c
10
u
14
− 2u
13
+ ··· − 2u + 1
c
11
u
14
+ 2u
12
+ 3u
11
+ 3u
10
+ 4u
9
+ 5u
8
+ 6u
7
+ 5u
6
+ 2u
5
+ u
4
− 2u
3
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
14
+ 7y
13
+ ··· + 7y + 1
c
2
y
14
+ 7y
13
+ ··· + 3y + 1
c
3
, c
8
, c
9
y
14
− 16y
13
+ ··· − 4y + 1
c
4
y
14
+ 4y
12
+ ··· + 4y + 1
c
6
, c
10
y
14
− 10y
13
+ ··· − 14y + 1
c
7
y
14
− 3y
13
+ ··· − 4y + 1
c
11
y
14
+ 4y
13
+ ··· + 2y
2
+ 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.734849 + 0.838959I
a = −1.208620 − 0.185596I
b = 0.582713 − 0.256653I
0.32678 − 2.81352I −3.82759 + 3.54032I
u = −0.734849 − 0.838959I
a = −1.208620 + 0.185596I
b = 0.582713 + 0.256653I
0.32678 + 2.81352I −3.82759 − 3.54032I
u = −0.418839 + 1.066630I
a = 0.291345 + 0.378834I
b = −0.473607 − 0.671965I
−3.30861 − 3.80056I −0.83959 + 2.34062I
u = −0.418839 − 1.066630I
a = 0.291345 − 0.378834I
b = −0.473607 + 0.671965I
−3.30861 + 3.80056I −0.83959 − 2.34062I
u = 0.316820 + 1.106540I
a = 0.82774 + 1.28027I
b = 0.896791 − 0.980193I
−0.69663 + 5.04325I 1.15268 − 7.45720I
u = 0.316820 − 1.106540I
a = 0.82774 − 1.28027I
b = 0.896791 + 0.980193I
−0.69663 − 5.04325I 1.15268 + 7.45720I
u = 0.675866 + 0.491616I
a = 0.482814 + 0.404595I
b = −1.045010 + 0.289500I
7.41228 + 0.32675I 4.63259 + 0.70876I
u = 0.675866 − 0.491616I
a = 0.482814 − 0.404595I
b = −1.045010 − 0.289500I
7.41228 − 0.32675I 4.63259 − 0.70876I
u = 0.201031 + 0.762183I
a = −2.79799 + 0.26537I
b = 0.54393 + 1.41064I
0.75311 − 2.85458I 1.50497 + 5.64699I
u = 0.201031 − 0.762183I
a = −2.79799 − 0.26537I
b = 0.54393 − 1.41064I
0.75311 + 2.85458I 1.50497 − 5.64699I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.330549 + 0.694071I
a = 1.23852 + 1.22506I
b = 0.019637 + 0.950071I
−1.85356 + 0.60321I 0.34386 + 3.01291I
u = −0.330549 − 0.694071I
a = 1.23852 − 1.22506I
b = 0.019637 − 0.950071I
−1.85356 − 0.60321I 0.34386 − 3.01291I
u = 0.790520 + 1.084840I
a = 0.666179 − 0.467389I
b = −0.524461 − 0.759534I
5.59130 + 5.55392I 7.03309 − 2.81100I
u = 0.790520 − 1.084840I
a = 0.666179 + 0.467389I
b = −0.524461 + 0.759534I
5.59130 − 5.55392I 7.03309 + 2.81100I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
14
− u
13
+ ··· − u + 1)(u
75
+ 15u
73
+ ··· − 20u − 7)
c
2
(u
14
+ 7u
13
+ ··· + 7u + 1)(u
75
+ 30u
74
+ ··· + 288u − 49)
c
3
(u
14
− 8u
12
+ ··· − 2u
2
+ 1)(u
75
+ u
74
+ ··· − 23u − 1)
c
4
(u
14
+ 5u
11
+ 2u
10
+ 3u
9
+ 9u
8
+ u
7
+ 8u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 2u
2
+ 1)
· (u
75
− 3u
74
+ ··· + 15u + 1)
c
5
(u
14
+ u
13
+ ··· + u + 1)(u
75
+ 15u
73
+ ··· − 20u − 7)
c
6
(u
14
+ 2u
13
+ ··· + 2u + 1)(u
75
− u
74
+ ··· − 29u − 2)
c
7
(u
14
+ 3u
13
+ 3u
12
− u
11
− 6u
10
− 6u
9
+ 2u
8
+ 6u
7
+ u
6
+ 3u
4
− 2u
2
+ 1)
· (u
75
− 2u
74
+ ··· − 17u + 1)
c
8
, c
9
(u
14
− 8u
12
+ ··· − 2u
2
+ 1)(u
75
+ u
74
+ ··· − 23u − 1)
c
10
(u
14
− 2u
13
+ ··· − 2u + 1)(u
75
− u
74
+ ··· − 29u − 2)
c
11
(u
14
+ 2u
12
+ 3u
11
+ 3u
10
+ 4u
9
+ 5u
8
+ 6u
7
+ 5u
6
+ 2u
5
+ u
4
− 2u
3
+ 1)
· (u
75
− 5u
74
+ ··· + 36831u − 8639)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
14
+ 7y
13
+ ··· + 7y + 1)(y
75
+ 30y
74
+ ··· + 288y −49)
c
2
(y
14
+ 7y
13
+ ··· + 3y + 1)(y
75
+ 38y
74
+ ··· + 546484y −2401)
c
3
, c
8
, c
9
(y
14
− 16y
13
+ ··· − 4y + 1)(y
75
− 77y
74
+ ··· + 71y −1)
c
4
(y
14
+ 4y
12
+ ··· + 4y + 1)(y
75
− y
74
+ ··· − 29y −1)
c
6
, c
10
(y
14
− 10y
13
+ ··· − 14y + 1)(y
75
− 43y
74
+ ··· + 321y −4)
c
7
(y
14
− 3y
13
+ ··· − 4y + 1)(y
75
− 8y
74
+ ··· − 25y −1)
c
11
(y
14
+ 4y
13
+ ··· + 2y
2
+ 1)
· (y
75
− 21y
74
+ ··· + 1725459695y −74632321)
19
