12n
0884
(K12n
0884
)
A knot diagram
1
Linearized knot diagam
4 11 10 8 2 3 12 4 1 6 8 7
Solving Sequence
8,11 3,12
2 7 1 6 5 4 10 9
c
11
c
2
c
7
c
12
c
6
c
5
c
4
c
10
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h6.92522 × 10
114
u
65
+ 7.79579 × 10
114
u
64
+ ··· + 1.05263 × 10
116
b + 1.06529 × 10
116
,
2.10463 × 10
115
u
65
+ 2.07609 × 10
115
u
64
+ ··· + 1.05263 × 10
116
a − 5.95398 × 10
116
, u
66
+ u
65
+ ··· + 10u + 2i
I
u
2
= h5062u
25
+ 58938u
24
+ ··· + 41551b + 49477, 39311u
25
− 193434u
24
+ ··· + 83102a − 142443,
u
26
+ 14u
24
+ ··· + 5u + 2i
* 2 irreducible components of dim
C
= 0, with total 92 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
= h6.93 × 10
114
u
65
+ 7.80 × 10
114
u
64
+ · · · + 1.05 × 10
116
b + 1.07 ×
10
116
, 2.10 × 10
115
u
65
+ 2.08 × 10
115
u
64
+ · · · + 1.05 × 10
116
a − 5.95 ×
10
116
, u
66
+ u
65
+ · · · + 10u + 2i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
3
=
−0.199939u
65
− 0.197229u
64
+ ··· − 77.2406u + 5.65628
−0.0657896u
65
− 0.0740600u
64
+ ··· − 15.1513u − 1.01203
a
12
=
1
u
2
a
2
=
−0.265729u
65
− 0.271289u
64
+ ··· − 92.3919u + 4.64425
−0.0657896u
65
− 0.0740600u
64
+ ··· − 15.1513u − 1.01203
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
0.154474u
65
+ 0.163738u
64
+ ··· − 39.6036u − 4.17290
−0.0100877u
65
− 0.0272293u
64
+ ··· + 9.63617u − 0.394982
a
5
=
−0.365614u
65
− 0.360819u
64
+ ··· − 112.342u + 3.05715
−0.0575553u
65
− 0.0529177u
64
+ ··· − 7.20091u − 1.02247
a
4
=
−0.365614u
65
− 0.360819u
64
+ ··· − 112.342u + 3.05715
−0.0535842u
65
− 0.0427053u
64
+ ··· − 6.51764u − 1.03206
a
10
=
0.114404u
65
+ 0.106869u
64
+ ··· − 20.1761u + 3.34856
−0.00119563u
65
+ 0.00376866u
64
+ ··· − 7.64885u − 0.509415
a
9
=
0.122676u
65
+ 0.107609u
64
+ ··· − 27.3475u + 2.84535
0.00182854u
65
+ 0.0108591u
64
+ ··· − 7.45992u − 0.466095
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.189112u
65
− 0.193926u
64
+ ··· − 72.1588u + 1.66494
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ 37u
64
+ ··· + 34177u + 6031
c
2
u
66
+ 4u
65
+ ··· − 24135u + 4475
c
3
u
66
+ 15u
64
+ ··· − 762u + 194
c
4
, c
8
u
66
+ u
65
+ ··· − 662856u + 191449
c
5
u
66
− 2u
65
+ ··· + 693008u + 64742
c
6
u
66
− 7u
65
+ ··· + 13349u + 1753
c
7
, c
11
, c
12
u
66
+ u
65
+ ··· + 10u + 2
c
9
u
66
+ 42u
64
+ ··· − 186u + 133
c
10
u
66
+ 2u
65
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
+ 74y
65
+ ··· + 2198907289y + 36372961
c
2
y
66
+ 30y
65
+ ··· + 1844840225y + 20025625
c
3
y
66
+ 30y
65
+ ··· + 1203768y + 37636
c
4
, c
8
y
66
− 97y
65
+ ··· − 86769988822y + 36652719601
c
5
y
66
+ 54y
65
+ ··· + 105454182252y + 4191526564
c
6
y
66
− 5y
65
+ ··· − 33068437y + 3073009
c
7
, c
11
, c
12
y
66
+ 73y
65
+ ··· + 1936y + 4
c
9
y
66
+ 84y
65
+ ··· + 1140060y + 17689
c
10
y
66
+ 8y
65
+ ··· + 5y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.719214 + 0.726795I
a = 0.667037 − 0.189342I
b = 0.58269 + 1.34326I
7.90014 − 3.53613I 0
u = 0.719214 − 0.726795I
a = 0.667037 + 0.189342I
b = 0.58269 − 1.34326I
7.90014 + 3.53613I 0
u = 1.000810 + 0.393167I
a = 0.445291 + 0.276323I
b = 0.121198 + 1.142820I
6.61412 − 2.06871I 0
u = 1.000810 − 0.393167I
a = 0.445291 − 0.276323I
b = 0.121198 − 1.142820I
6.61412 + 2.06871I 0
u = −0.100267 + 0.894027I
a = 0.323394 − 0.202827I
b = −1.105080 + 0.474658I
−3.29612 + 4.30193I −2.90250 − 5.35781I
u = −0.100267 − 0.894027I
a = 0.323394 + 0.202827I
b = −1.105080 − 0.474658I
−3.29612 − 4.30193I −2.90250 + 5.35781I
u = 0.299100 + 1.065650I
a = −0.465280 + 0.427367I
b = 0.885760 − 0.541306I
1.072760 + 0.887374I 0
u = 0.299100 − 1.065650I
a = −0.465280 − 0.427367I
b = 0.885760 + 0.541306I
1.072760 − 0.887374I 0
u = 0.736910 + 0.833106I
a = −0.154013 − 0.406071I
b = 0.048259 + 0.142406I
−4.72831 − 2.78357I 0
u = 0.736910 − 0.833106I
a = −0.154013 + 0.406071I
b = 0.048259 − 0.142406I
−4.72831 + 2.78357I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.031039 + 0.840155I
a = 1.85359 + 1.62601I
b = −0.003236 − 0.680194I
3.97262 + 3.40486I 4.18167 − 4.59140I
u = 0.031039 − 0.840155I
a = 1.85359 − 1.62601I
b = −0.003236 + 0.680194I
3.97262 − 3.40486I 4.18167 + 4.59140I
u = −0.884713 + 0.792441I
a = −0.290736 − 0.175541I
b = −0.250039 + 0.780091I
−2.38051 + 3.17897I 0
u = −0.884713 − 0.792441I
a = −0.290736 + 0.175541I
b = −0.250039 − 0.780091I
−2.38051 − 3.17897I 0
u = −1.025410 + 0.618194I
a = 0.434725 + 0.292315I
b = 0.58073 − 1.29548I
5.39982 + 10.49560I 0
u = −1.025410 − 0.618194I
a = 0.434725 − 0.292315I
b = 0.58073 + 1.29548I
5.39982 − 10.49560I 0
u = 0.709657 + 0.233871I
a = −0.774283 + 0.930949I
b = −0.785269 − 0.823637I
−1.17874 − 4.65858I −2.55428 + 6.96961I
u = 0.709657 − 0.233871I
a = −0.774283 − 0.930949I
b = −0.785269 + 0.823637I
−1.17874 + 4.65858I −2.55428 − 6.96961I
u = 0.122656 + 1.284470I
a = 1.19317 − 1.11318I
b = 0.367723 + 0.911857I
7.95608 − 1.54033I 0
u = 0.122656 − 1.284470I
a = 1.19317 + 1.11318I
b = 0.367723 − 0.911857I
7.95608 + 1.54033I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.099520 + 1.299930I
a = −1.263130 + 0.472386I
b = 1.65574 + 0.04896I
1.90032 + 1.38290I 0
u = −0.099520 − 1.299930I
a = −1.263130 − 0.472386I
b = 1.65574 − 0.04896I
1.90032 − 1.38290I 0
u = −1.050640 + 0.773183I
a = 0.554794 + 0.085028I
b = −0.061668 − 1.143510I
5.73223 − 3.64210I 0
u = −1.050640 − 0.773183I
a = 0.554794 − 0.085028I
b = −0.061668 + 1.143510I
5.73223 + 3.64210I 0
u = −0.257605 + 1.310040I
a = 0.61970 + 1.84761I
b = 0.408078 − 1.269030I
3.27784 + 4.14237I 0
u = −0.257605 − 1.310040I
a = 0.61970 − 1.84761I
b = 0.408078 + 1.269030I
3.27784 − 4.14237I 0
u = −0.256934 + 1.331240I
a = 0.89879 + 1.42711I
b = 0.005042 − 1.066680I
3.47781 + 4.21864I 0
u = −0.256934 − 1.331240I
a = 0.89879 − 1.42711I
b = 0.005042 + 1.066680I
3.47781 − 4.21864I 0
u = −0.000032 + 0.630250I
a = −1.59776 − 0.89098I
b = 0.847679 + 0.431310I
−4.14836 − 3.94548I 3.59469 − 1.09624I
u = −0.000032 − 0.630250I
a = −1.59776 + 0.89098I
b = 0.847679 − 0.431310I
−4.14836 + 3.94548I 3.59469 + 1.09624I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.609931 + 0.139676I
a = −0.673201 − 0.264553I
b = −0.676484 + 0.756578I
−1.29771 + 0.89777I −3.42699 − 0.34628I
u = −0.609931 − 0.139676I
a = −0.673201 + 0.264553I
b = −0.676484 − 0.756578I
−1.29771 − 0.89777I −3.42699 + 0.34628I
u = 0.145209 + 0.606543I
a = −0.901280 + 0.557782I
b = 0.541206 − 0.434676I
0.92008 + 1.13491I 2.20955 − 3.15524I
u = 0.145209 − 0.606543I
a = −0.901280 − 0.557782I
b = 0.541206 + 0.434676I
0.92008 − 1.13491I 2.20955 + 3.15524I
u = 0.26234 + 1.40437I
a = 0.16144 − 2.09844I
b = 0.600829 + 1.061560I
4.05722 − 8.15344I 0
u = 0.26234 − 1.40437I
a = 0.16144 + 2.09844I
b = 0.600829 − 1.061560I
4.05722 + 8.15344I 0
u = −0.05689 + 1.47330I
a = −0.62930 − 1.82048I
b = 0.41585 + 1.91352I
3.49936 − 0.57536I 0
u = −0.05689 − 1.47330I
a = −0.62930 + 1.82048I
b = 0.41585 − 1.91352I
3.49936 + 0.57536I 0
u = −0.488892 + 0.192718I
a = −0.893543 + 0.019292I
b = −0.139326 + 0.947853I
−1.24935 + 1.26500I −2.68638 − 5.49246I
u = −0.488892 − 0.192718I
a = −0.893543 − 0.019292I
b = −0.139326 − 0.947853I
−1.24935 − 1.26500I −2.68638 + 5.49246I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.12093 + 1.51164I
a = 0.530235 − 1.280690I
b = 0.045836 + 1.095740I
7.62644 − 0.17479I 0
u = 0.12093 − 1.51164I
a = 0.530235 + 1.280690I
b = 0.045836 − 1.095740I
7.62644 + 0.17479I 0
u = 0.06739 + 1.52918I
a = 1.160410 − 0.441765I
b = −2.24825 + 0.57169I
9.05643 − 5.30948I 0
u = 0.06739 − 1.52918I
a = 1.160410 + 0.441765I
b = −2.24825 − 0.57169I
9.05643 + 5.30948I 0
u = −0.00862 + 1.54370I
a = −0.296046 + 0.976536I
b = −0.893174 − 0.864586I
11.61720 + 0.61500I 0
u = −0.00862 − 1.54370I
a = −0.296046 − 0.976536I
b = −0.893174 + 0.864586I
11.61720 − 0.61500I 0
u = 0.195033 + 0.385708I
a = 2.54059 + 1.12754I
b = 1.222030 − 0.505076I
2.44565 − 4.32755I −4.06360 + 7.84691I
u = 0.195033 − 0.385708I
a = 2.54059 − 1.12754I
b = 1.222030 + 0.505076I
2.44565 + 4.32755I −4.06360 − 7.84691I
u = 0.07716 + 1.59578I
a = 0.27315 + 1.39585I
b = −0.095540 − 1.067600I
3.86209 − 4.72236I 0
u = 0.07716 − 1.59578I
a = 0.27315 − 1.39585I
b = −0.095540 + 1.067600I
3.86209 + 4.72236I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23416 + 1.60465I
a = 0.03143 + 1.76112I
b = −1.10469 − 1.89981I
15.6043 − 7.1193I 0
u = 0.23416 − 1.60465I
a = 0.03143 − 1.76112I
b = −1.10469 + 1.89981I
15.6043 + 7.1193I 0
u = 0.39220 + 1.57499I
a = −0.275695 + 1.083720I
b = −0.76486 − 1.26020I
13.0192 − 7.2655I 0
u = 0.39220 − 1.57499I
a = −0.275695 − 1.083720I
b = −0.76486 + 1.26020I
13.0192 + 7.2655I 0
u = −0.17671 + 1.62220I
a = −0.14551 + 1.47930I
b = 0.69950 − 1.45513I
5.91816 + 6.68858I 0
u = −0.17671 − 1.62220I
a = −0.14551 − 1.47930I
b = 0.69950 + 1.45513I
5.91816 − 6.68858I 0
u = 0.059185 + 0.350262I
a = 5.06425 + 0.33293I
b = 0.177862 + 0.732678I
4.91305 + 0.67289I 3.19953 + 3.49907I
u = 0.059185 − 0.350262I
a = 5.06425 − 0.33293I
b = 0.177862 − 0.732678I
4.91305 − 0.67289I 3.19953 − 3.49907I
u = −0.35609 + 1.61530I
a = −0.17183 − 1.59723I
b = −0.95933 + 1.58670I
12.6538 + 15.5854I 0
u = −0.35609 − 1.61530I
a = −0.17183 + 1.59723I
b = −0.95933 − 1.58670I
12.6538 − 15.5854I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03231 + 1.67857I
a = −0.385959 − 1.234640I
b = −0.615246 + 0.819148I
12.94850 + 3.66040I 0
u = −0.03231 − 1.67857I
a = −0.385959 + 1.234640I
b = −0.615246 − 0.819148I
12.94850 − 3.66040I 0
u = −0.25759 + 1.74677I
a = −0.176853 − 1.081290I
b = −0.612531 + 1.225490I
14.3852 + 1.4981I 0
u = −0.25759 − 1.74677I
a = −0.176853 + 1.081290I
b = −0.612531 − 1.225490I
14.3852 − 1.4981I 0
u = −0.0108445 + 0.0640319I
a = 6.34245 − 4.58380I
b = −0.891282 − 0.887193I
−1.86232 − 1.13743I 2.50858 − 4.14640I
u = −0.0108445 − 0.0640319I
a = 6.34245 + 4.58380I
b = −0.891282 + 0.887193I
−1.86232 + 1.13743I 2.50858 + 4.14640I
11
II. I
u
2
= h5062u
25
+ 58938u
24
+ · · · + 41551b + 49477, 39311u
25
−
193434u
24
+ · · · + 83102a − 142443, u
26
+ 14u
24
+ · · · + 5u + 2i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
3
=
−0.473045u
25
+ 2.32767u
24
+ ··· + 2.54894u + 1.71407
−0.121826u
25
− 1.41845u
24
+ ··· − 3.21494u − 1.19075
a
12
=
1
u
2
a
2
=
−0.594871u
25
+ 0.909220u
24
+ ··· − 0.666001u + 0.523321
−0.121826u
25
− 1.41845u
24
+ ··· − 3.21494u − 1.19075
a
7
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−0.456391u
25
+ 0.655123u
24
+ ··· − 1.20832u + 0.685627
0.377440u
25
+ 0.557002u
24
+ ··· + 5.08216u + 1.32351
a
5
=
−1.20456u
25
+ 0.716493u
24
+ ··· + 2.54892u + 2.39998
−1.67300u
25
− 0.556208u
24
+ ··· − 3.95942u − 1.43426
a
4
=
−1.20456u
25
+ 0.716493u
24
+ ··· + 2.54892u + 2.39998
−0.744386u
25
− 1.86145u
24
+ ··· − 5.13278u − 2.86725
a
10
=
1.58041u
25
+ 1.50870u
24
+ ··· + 13.7991u + 3.74127
−0.122259u
25
+ 0.763784u
24
+ ··· − 5.59698u − 1.14955
a
9
=
0.797321u
25
+ 1.92681u
24
+ ··· + 12.8711u + 3.88810
−0.700633u
25
− 0.267069u
24
+ ··· − 10.5471u − 3.02869
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4419
1123
u
25
+
6377
1123
u
24
+ ··· +
51915
1123
u −
4786
1123
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 5u
25
+ ··· + 3u + 1
c
2
u
26
− 3u
25
+ ··· + u + 1
c
3
u
26
− u
25
+ ··· + 5u + 12
c
4
u
26
− 2u
25
+ ··· + 9u
2
+ 1
c
5
u
26
− 3u
25
+ ··· − 5u + 14
c
6
u
26
+ 3u
24
+ ··· + 5u + 1
c
7
u
26
+ 14u
24
+ ··· − 5u + 2
c
8
u
26
+ 2u
25
+ ··· + 9u
2
+ 1
c
9
u
26
+ u
25
+ ··· + 82u + 19
c
10
u
26
− u
25
+ ··· + u + 1
c
11
, c
12
u
26
+ 14u
24
+ ··· + 5u + 2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 9y
25
+ ··· − 15y + 1
c
2
y
26
+ y
25
+ ··· + 9y + 1
c
3
y
26
+ 21y
25
+ ··· + 2039y + 144
c
4
, c
8
y
26
− 14y
25
+ ··· + 18y + 1
c
5
y
26
+ 9y
25
+ ··· + 59y + 196
c
6
y
26
+ 6y
25
+ ··· − 21y + 1
c
7
, c
11
, c
12
y
26
+ 28y
25
+ ··· + 23y + 4
c
9
y
26
+ 31y
25
+ ··· + 3536y + 361
c
10
y
26
+ 7y
25
+ ··· + 13y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.679415 + 0.890805I
a = 0.372921 − 0.144615I
b = 0.229522 − 0.386355I
−2.78750 + 2.64932I −3.02870 + 1.63316I
u = −0.679415 − 0.890805I
a = 0.372921 + 0.144615I
b = 0.229522 + 0.386355I
−2.78750 − 2.64932I −3.02870 − 1.63316I
u = 0.886701 + 0.747995I
a = 0.172666 − 0.374205I
b = 0.239970 + 0.649123I
−4.40011 − 3.18802I −0.46336 + 8.20324I
u = 0.886701 − 0.747995I
a = 0.172666 + 0.374205I
b = 0.239970 − 0.649123I
−4.40011 + 3.18802I −0.46336 − 8.20324I
u = −0.175460 + 1.178730I
a = −2.08661 − 1.09615I
b = 0.713234 + 0.634073I
4.51834 + 5.02048I 3.74875 − 8.49324I
u = −0.175460 − 1.178730I
a = −2.08661 + 1.09615I
b = 0.713234 − 0.634073I
4.51834 − 5.02048I 3.74875 + 8.49324I
u = −0.307077 + 0.739170I
a = −0.741015 + 1.175360I
b = −0.664463 + 0.138102I
2.86300 − 3.17507I −2.41239 + 1.76710I
u = −0.307077 − 0.739170I
a = −0.741015 − 1.175360I
b = −0.664463 − 0.138102I
2.86300 + 3.17507I −2.41239 − 1.76710I
u = 0.010985 + 1.247270I
a = 0.475473 − 0.250521I
b = −1.37148 + 0.43109I
−1.88055 + 3.86499I 1.43322 − 2.58190I
u = 0.010985 − 1.247270I
a = 0.475473 + 0.250521I
b = −1.37148 − 0.43109I
−1.88055 − 3.86499I 1.43322 + 2.58190I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.173200 + 1.313360I
a = −1.21882 + 0.78462I
b = −0.349538 − 0.764374I
7.89081 − 0.76567I 2.98567 − 3.33428I
u = 0.173200 − 1.313360I
a = −1.21882 − 0.78462I
b = −0.349538 + 0.764374I
7.89081 + 0.76567I 2.98567 + 3.33428I
u = −0.165687 + 1.355170I
a = 1.206480 + 0.436588I
b = −1.51317 − 0.84770I
2.09121 + 0.65320I −1.11339 + 2.15886I
u = −0.165687 − 1.355170I
a = 1.206480 − 0.436588I
b = −1.51317 + 0.84770I
2.09121 − 0.65320I −1.11339 − 2.15886I
u = −0.201007 + 1.363480I
a = −0.26482 − 2.17381I
b = −0.71515 + 1.63873I
2.57091 + 3.75146I −6.68429 − 1.45320I
u = −0.201007 − 1.363480I
a = −0.26482 + 2.17381I
b = −0.71515 − 1.63873I
2.57091 − 3.75146I −6.68429 + 1.45320I
u = 0.411195 + 0.450978I
a = −2.25148 − 1.07557I
b = −0.096250 − 0.676579I
4.73328 − 1.40628I −0.66080 + 5.33743I
u = 0.411195 − 0.450978I
a = −2.25148 + 1.07557I
b = −0.096250 + 0.676579I
4.73328 + 1.40628I −0.66080 − 5.33743I
u = 0.122485 + 0.534083I
a = −1.33573 − 1.08771I
b = 0.918762 + 0.480757I
−4.52448 − 4.18007I −12.9437 + 8.1626I
u = 0.122485 − 0.534083I
a = −1.33573 + 1.08771I
b = 0.918762 − 0.480757I
−4.52448 + 4.18007I −12.9437 − 8.1626I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.26482 + 1.52255I
a = −0.06854 + 1.67093I
b = −0.541685 − 1.128100I
2.91632 − 6.91833I −1.62284 + 5.68817I
u = 0.26482 − 1.52255I
a = −0.06854 − 1.67093I
b = −0.541685 + 1.128100I
2.91632 + 6.91833I −1.62284 − 5.68817I
u = −0.414168 + 0.081461I
a = 0.659087 + 0.243294I
b = 0.97840 − 1.10370I
−2.20002 + 1.34478I −16.4489 − 6.7100I
u = −0.414168 − 0.081461I
a = 0.659087 − 0.243294I
b = 0.97840 + 1.10370I
−2.20002 − 1.34478I −16.4489 + 6.7100I
u = 0.07342 + 1.68039I
a = 0.330396 − 1.027770I
b = 0.671843 + 0.758050I
12.88280 − 3.26432I 0.71067 − 4.90499I
u = 0.07342 − 1.68039I
a = 0.330396 + 1.027770I
b = 0.671843 − 0.758050I
12.88280 + 3.26432I 0.71067 + 4.90499I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
− 5u
25
+ ··· + 3u + 1)(u
66
+ 37u
64
+ ··· + 34177u + 6031)
c
2
(u
26
− 3u
25
+ ··· + u + 1)(u
66
+ 4u
65
+ ··· − 24135u + 4475)
c
3
(u
26
− u
25
+ ··· + 5u + 12)(u
66
+ 15u
64
+ ··· − 762u + 194)
c
4
(u
26
− 2u
25
+ ··· + 9u
2
+ 1)(u
66
+ u
65
+ ··· − 662856u + 191449)
c
5
(u
26
− 3u
25
+ ··· − 5u + 14)(u
66
− 2u
65
+ ··· + 693008u + 64742)
c
6
(u
26
+ 3u
24
+ ··· + 5u + 1)(u
66
− 7u
65
+ ··· + 13349u + 1753)
c
7
(u
26
+ 14u
24
+ ··· − 5u + 2)(u
66
+ u
65
+ ··· + 10u + 2)
c
8
(u
26
+ 2u
25
+ ··· + 9u
2
+ 1)(u
66
+ u
65
+ ··· − 662856u + 191449)
c
9
(u
26
+ u
25
+ ··· + 82u + 19)(u
66
+ 42u
64
+ ··· − 186u + 133)
c
10
(u
26
− u
25
+ ··· + u + 1)(u
66
+ 2u
65
+ ··· − 3u + 1)
c
11
, c
12
(u
26
+ 14u
24
+ ··· + 5u + 2)(u
66
+ u
65
+ ··· + 10u + 2)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
26
+ 9y
25
+ ··· − 15y + 1)
· (y
66
+ 74y
65
+ ··· + 2198907289y + 36372961)
c
2
(y
26
+ y
25
+ ··· + 9y + 1)
· (y
66
+ 30y
65
+ ··· + 1844840225y + 20025625)
c
3
(y
26
+ 21y
25
+ ··· + 2039y + 144)
· (y
66
+ 30y
65
+ ··· + 1203768y + 37636)
c
4
, c
8
(y
26
− 14y
25
+ ··· + 18y + 1)
· (y
66
− 97y
65
+ ··· − 86769988822y + 36652719601)
c
5
(y
26
+ 9y
25
+ ··· + 59y + 196)
· (y
66
+ 54y
65
+ ··· + 105454182252y + 4191526564)
c
6
(y
26
+ 6y
25
+ ··· − 21y + 1)
· (y
66
− 5y
65
+ ··· − 33068437y + 3073009)
c
7
, c
11
, c
12
(y
26
+ 28y
25
+ ··· + 23y + 4)(y
66
+ 73y
65
+ ··· + 1936y + 4)
c
9
(y
26
+ 31y
25
+ ··· + 3536y + 361)
· (y
66
+ 84y
65
+ ··· + 1140060y + 17689)
c
10
(y
26
+ 7y
25
+ ··· + 13y + 1)(y
66
+ 8y
65
+ ··· + 5y + 1)
19
