12n
0802
(K12n
0802
)
A knot diagram
1
Linearized knot diagam
4 6 10 11 2 9 1 11 3 7 4 8
Solving Sequence
3,9
10
4,7
11 6 2 1 5 8 12
c
9
c
3
c
10
c
6
c
2
c
1
c
5
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.33978 × 10
205
u
76
− 1.08961 × 10
205
u
75
+ ··· + 1.57363 × 10
205
b + 1.04860 × 10
208
,
3.39045 × 10
208
u
76
− 4.06453 × 10
207
u
75
+ ··· + 2.18734 × 10
207
a + 4.26481 × 10
210
,
u
77
+ u
76
+ ··· + 792u + 139i
I
u
2
= h91110u
16
+ 162998u
15
+ ··· + 502439b + 111491,
283556u
16
+ 222982u
15
+ ··· + 502439a − 280909, u
17
− 4u
15
+ ··· + 4u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 94 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
= h8.34 × 10
205
u
76
− 1.09 × 10
205
u
75
+ · · · + 1.57 × 10
205
b + 1.05 ×
10
208
, 3.39 × 10
208
u
76
− 4.06 × 10
207
u
75
+ · · · + 2.19 × 10
207
a + 4.26 ×
10
210
, u
77
+ u
76
+ · · · + 792u + 139i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
−u
−u
3
+ u
a
7
=
−15.5003u
76
+ 1.85821u
75
+ ··· − 9371.39u − 1949.77
−5.29972u
76
+ 0.692419u
75
+ ··· − 3206.91u − 666.357
a
11
=
61.0416u
76
− 7.07935u
75
+ ··· + 36598.3u + 7624.22
4.27107u
76
− 0.504359u
75
+ ··· + 2580.72u + 538.356
a
6
=
−10.2006u
76
+ 1.16579u
75
+ ··· − 6164.48u − 1283.41
−5.29972u
76
+ 0.692419u
75
+ ··· − 3206.91u − 666.357
a
2
=
−49.9370u
76
+ 5.72890u
75
+ ··· − 29859.0u − 6221.64
−5.17170u
76
+ 0.559340u
75
+ ··· − 3087.83u − 643.065
a
1
=
−41.2329u
76
+ 4.69186u
75
+ ··· − 24646.3u − 5135.91
−3.01842u
76
+ 0.279790u
75
+ ··· − 1795.45u − 374.782
a
5
=
179.435u
76
− 20.5873u
75
+ ··· + 107397.u + 22372.5
3.50440u
76
− 0.359571u
75
+ ··· + 2115.00u + 440.893
a
8
=
7.90952u
76
− 0.847855u
75
+ ··· + 4713.19u + 984.820
−1.30653u
76
+ 0.126108u
75
+ ··· − 789.550u − 164.686
a
12
=
−47.9834u
76
+ 5.56443u
75
+ ··· − 28785.0u − 5997.46
−1.04849u
76
+ 0.133040u
75
+ ··· − 667.193u − 139.440
(ii) Obstruction class = −1
(iii) Cusp Shapes = −871.265u
76
+ 100.233u
75
+ ··· − 521451.u − 108615.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
− 8u
76
+ ··· + 32311988u + 2239897
c
2
, c
5
u
77
+ u
76
+ ··· − 40176u − 5643
c
3
, c
9
u
77
+ u
76
+ ··· + 792u + 139
c
4
, c
11
u
77
− 2u
76
+ ··· + 4508u − 1129
c
6
u
77
+ 3u
76
+ ··· − 2292u − 319
c
7
, c
12
u
77
− u
76
+ ··· − 37u − 11
c
8
u
77
+ 6u
76
+ ··· + 195u − 19
c
10
u
77
− u
76
+ ··· − 15u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
+ 44y
76
+ ··· + 727248075963258y −5017138570609
c
2
, c
5
y
77
− 63y
76
+ ··· + 793460772y −31843449
c
3
, c
9
y
77
− 51y
76
+ ··· + 189414y −19321
c
4
, c
11
y
77
− 66y
76
+ ··· + 58868382y −1274641
c
6
y
77
+ 23y
76
+ ··· − 2243236y −101761
c
7
, c
12
y
77
+ 25y
76
+ ··· − 2041y −121
c
8
y
77
− 108y
76
+ ··· + 382001y −361
c
10
y
77
− 19y
76
+ ··· − 25y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.758997 + 0.616342I
a = 1.46817 − 0.34902I
b = 0.79967 − 1.26583I
1.32991 − 1.97035I 0
u = −0.758997 − 0.616342I
a = 1.46817 + 0.34902I
b = 0.79967 + 1.26583I
1.32991 + 1.97035I 0
u = 0.911703
a = 1.42882
b = 2.17200
3.05365 0
u = −0.010819 + 1.090530I
a = 0.191191 − 0.124778I
b = 0.734597 + 0.849848I
4.01664 + 4.54282I 0
u = −0.010819 − 1.090530I
a = 0.191191 + 0.124778I
b = 0.734597 − 0.849848I
4.01664 − 4.54282I 0
u = −1.065640 + 0.254276I
a = 0.480002 − 1.159030I
b = −0.292883 − 0.664587I
−1.91191 + 1.13599I 0
u = −1.065640 − 0.254276I
a = 0.480002 + 1.159030I
b = −0.292883 + 0.664587I
−1.91191 − 1.13599I 0
u = −1.11487
a = −2.43271
b = 0.374887
−3.74100 0
u = −1.116270 + 0.007414I
a = −0.620793 − 0.148394I
b = 1.005310 − 0.198862I
−3.83080 + 0.35334I 0
u = −1.116270 − 0.007414I
a = −0.620793 + 0.148394I
b = 1.005310 + 0.198862I
−3.83080 − 0.35334I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.695591 + 0.874541I
a = −0.104081 − 0.102779I
b = −0.528202 − 0.116523I
−0.95380 + 2.56825I 0
u = −0.695591 − 0.874541I
a = −0.104081 + 0.102779I
b = −0.528202 + 0.116523I
−0.95380 − 2.56825I 0
u = −1.119770 + 0.088439I
a = −1.30975 + 1.24365I
b = −2.25028 + 1.34716I
−0.31477 + 6.50480I 0
u = −1.119770 − 0.088439I
a = −1.30975 − 1.24365I
b = −2.25028 − 1.34716I
−0.31477 − 6.50480I 0
u = 1.103770 + 0.223227I
a = 0.322545 + 0.190472I
b = −0.960347 + 0.441859I
−6.03076 − 3.62911I 0
u = 1.103770 − 0.223227I
a = 0.322545 − 0.190472I
b = −0.960347 − 0.441859I
−6.03076 + 3.62911I 0
u = 1.035260 + 0.465565I
a = −1.16999 − 1.22271I
b = −0.62849 − 1.67436I
0.58777 − 4.71952I 0
u = 1.035260 − 0.465565I
a = −1.16999 + 1.22271I
b = −0.62849 + 1.67436I
0.58777 + 4.71952I 0
u = 0.217467 + 0.833274I
a = 0.204278 − 0.401189I
b = −1.035260 − 0.397841I
5.89269 + 5.41568I 0
u = 0.217467 − 0.833274I
a = 0.204278 + 0.401189I
b = −1.035260 + 0.397841I
5.89269 − 5.41568I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.091030 + 0.347422I
a = −0.11223 − 1.63823I
b = 0.494694 − 1.137330I
−1.10617 − 4.08847I 0
u = 1.091030 − 0.347422I
a = −0.11223 + 1.63823I
b = 0.494694 + 1.137330I
−1.10617 + 4.08847I 0
u = −1.116810 + 0.335012I
a = 0.40003 + 1.95228I
b = 0.565199 + 0.678583I
3.30736 + 2.92566I 0
u = −1.116810 − 0.335012I
a = 0.40003 − 1.95228I
b = 0.565199 − 0.678583I
3.30736 − 2.92566I 0
u = 1.181340 + 0.003850I
a = −0.92722 + 1.76444I
b = −0.134594 + 1.072470I
−7.66719 − 1.85639I 0
u = 1.181340 − 0.003850I
a = −0.92722 − 1.76444I
b = −0.134594 − 1.072470I
−7.66719 + 1.85639I 0
u = −1.183980 + 0.202308I
a = 0.82439 − 1.52658I
b = −0.452462 − 0.812176I
−1.38098 + 1.72001I 0
u = −1.183980 − 0.202308I
a = 0.82439 + 1.52658I
b = −0.452462 + 0.812176I
−1.38098 − 1.72001I 0
u = 0.787886 + 0.099348I
a = 1.52773 − 2.14738I
b = 1.01856 − 1.19509I
3.17288 − 1.22575I 0
u = 0.787886 − 0.099348I
a = 1.52773 + 2.14738I
b = 1.01856 + 1.19509I
3.17288 + 1.22575I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.000804 + 1.208190I
a = 0.216880 + 0.347898I
b = 0.225684 − 0.704296I
−3.05027 − 0.94756I 0
u = 0.000804 − 1.208190I
a = 0.216880 − 0.347898I
b = 0.225684 + 0.704296I
−3.05027 + 0.94756I 0
u = 0.133250 + 1.220520I
a = −0.131494 − 0.101763I
b = −0.694787 + 0.844760I
2.85374 − 11.06360I 0
u = 0.133250 − 1.220520I
a = −0.131494 + 0.101763I
b = −0.694787 − 0.844760I
2.85374 + 11.06360I 0
u = −0.722758 + 0.238117I
a = −1.75262 + 2.18724I
b = −0.21833 + 1.90963I
1.55815 + 6.08582I 0
u = −0.722758 − 0.238117I
a = −1.75262 − 2.18724I
b = −0.21833 − 1.90963I
1.55815 − 6.08582I 0
u = 0.755834
a = 1.17517
b = 1.75003
3.09798 −4.83340
u = 1.172280 + 0.417636I
a = −0.17453 + 1.80364I
b = −0.661781 + 0.694578I
2.92989 − 9.94785I 0
u = 1.172280 − 0.417636I
a = −0.17453 − 1.80364I
b = −0.661781 − 0.694578I
2.92989 + 9.94785I 0
u = 1.272770 + 0.184016I
a = −0.65660 − 1.47391I
b = 0.651251 − 0.990914I
−3.05844 − 8.07962I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.272770 − 0.184016I
a = −0.65660 + 1.47391I
b = 0.651251 + 0.990914I
−3.05844 + 8.07962I 0
u = −0.290588 + 0.637778I
a = −0.311030 − 0.501017I
b = 1.131460 − 0.351988I
5.82765 + 0.77594I 5.84300 − 2.67611I
u = −0.290588 − 0.637778I
a = −0.311030 + 0.501017I
b = 1.131460 + 0.351988I
5.82765 − 0.77594I 5.84300 + 2.67611I
u = 1.300670 + 0.104807I
a = 0.145206 − 1.109260I
b = −0.578994 − 0.801863I
−6.47566 − 2.58505I 0
u = 1.300670 − 0.104807I
a = 0.145206 + 1.109260I
b = −0.578994 + 0.801863I
−6.47566 + 2.58505I 0
u = −0.638923 + 0.237400I
a = 1.92039 − 0.14693I
b = −0.213109 − 0.365332I
−2.17556 + 0.65395I −9.20343 − 5.27465I
u = −0.638923 − 0.237400I
a = 1.92039 + 0.14693I
b = −0.213109 + 0.365332I
−2.17556 − 0.65395I −9.20343 + 5.27465I
u = −1.291130 + 0.352756I
a = −0.02607 − 1.87165I
b = −0.88563 − 1.75280I
−8.67471 + 6.59602I 0
u = −1.291130 − 0.352756I
a = −0.02607 + 1.87165I
b = −0.88563 + 1.75280I
−8.67471 − 6.59602I 0
u = 0.330805 + 0.513963I
a = 0.447914 − 0.085197I
b = 0.633023 + 0.390219I
1.170010 + 0.511271I 7.93499 − 2.10183I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.330805 − 0.513963I
a = 0.447914 + 0.085197I
b = 0.633023 − 0.390219I
1.170010 − 0.511271I 7.93499 + 2.10183I
u = 0.246079 + 0.526147I
a = 1.57072 + 0.38139I
b = −0.025841 + 1.081900I
2.60807 + 0.74898I 3.51716 − 0.31657I
u = 0.246079 − 0.526147I
a = 1.57072 − 0.38139I
b = −0.025841 − 1.081900I
2.60807 − 0.74898I 3.51716 + 0.31657I
u = 1.35457 + 0.52174I
a = −0.01207 − 1.55989I
b = 1.02876 − 1.43648I
−0.26091 − 10.21520I 0
u = 1.35457 − 0.52174I
a = −0.01207 + 1.55989I
b = 1.02876 + 1.43648I
−0.26091 + 10.21520I 0
u = 0.080850 + 0.537512I
a = −0.331378 − 0.654699I
b = −0.707167 + 0.980733I
−4.48701 − 3.03669I 5.16104 + 7.39684I
u = 0.080850 − 0.537512I
a = −0.331378 + 0.654699I
b = −0.707167 − 0.980733I
−4.48701 + 3.03669I 5.16104 − 7.39684I
u = 1.40085 + 0.40250I
a = −0.016309 + 1.193430I
b = −1.04169 + 1.29261I
−8.68571 − 4.73560I 0
u = 1.40085 − 0.40250I
a = −0.016309 − 1.193430I
b = −1.04169 − 1.29261I
−8.68571 + 4.73560I 0
u = −1.39036 + 0.57949I
a = −0.159041 + 1.141650I
b = 0.77534 + 1.38516I
−7.31609 + 7.24715I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39036 − 0.57949I
a = −0.159041 − 1.141650I
b = 0.77534 − 1.38516I
−7.31609 − 7.24715I 0
u = −0.394801 + 0.288987I
a = −2.66235 + 1.07859I
b = −0.152342 + 1.354640I
1.61463 + 6.08143I 1.65363 − 3.54096I
u = −0.394801 − 0.288987I
a = −2.66235 − 1.07859I
b = −0.152342 − 1.354640I
1.61463 − 6.08143I 1.65363 + 3.54096I
u = −1.42831 + 0.53758I
a = −0.03870 − 1.46221I
b = −1.09850 − 1.41506I
−2.0258 + 17.1703I 0
u = −1.42831 − 0.53758I
a = −0.03870 + 1.46221I
b = −1.09850 + 1.41506I
−2.0258 − 17.1703I 0
u = 1.46502 + 0.49693I
a = 0.037413 + 1.171880I
b = −0.853847 + 1.061410I
−7.05974 − 8.63532I 0
u = 1.46502 − 0.49693I
a = 0.037413 − 1.171880I
b = −0.853847 − 1.061410I
−7.05974 + 8.63532I 0
u = −1.50322 + 0.49069I
a = 0.006370 + 1.080770I
b = 0.677127 + 1.140250I
−7.01071 + 4.87145I 0
u = −1.50322 − 0.49069I
a = 0.006370 − 1.080770I
b = 0.677127 − 1.140250I
−7.01071 − 4.87145I 0
u = −0.210525 + 0.311466I
a = 2.18028 + 1.43772I
b = −0.206538 + 0.269662I
−1.90333 + 0.92139I −5.44582 + 1.92407I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.210525 − 0.311466I
a = 2.18028 − 1.43772I
b = −0.206538 − 0.269662I
−1.90333 − 0.92139I −5.44582 − 1.92407I
u = −1.70360 + 0.29340I
a = 0.021683 − 0.365141I
b = −0.406453 − 0.522497I
−0.79210 + 1.62218I 0
u = −1.70360 − 0.29340I
a = 0.021683 + 0.365141I
b = −0.406453 + 0.522497I
−0.79210 − 1.62218I 0
u = 1.94427 + 0.25926I
a = 0.191630 − 0.307980I
b = 0.708436 − 0.462080I
−1.70623 + 3.05877I 0
u = 1.94427 − 0.25926I
a = 0.191630 + 0.307980I
b = 0.708436 + 0.462080I
−1.70623 − 3.05877I 0
u = −0.25319 + 2.28522I
a = 0.0183860 + 0.0150818I
b = −0.070031 − 0.348268I
−1.18900 + 2.18789I 0
u = −0.25319 − 2.28522I
a = 0.0183860 − 0.0150818I
b = −0.070031 + 0.348268I
−1.18900 − 2.18789I 0
12
II. I
u
2
= h9.11 × 10
4
u
16
+ 1.63 × 10
5
u
15
+ · · · + 5.02 × 10
5
b + 1.11 × 10
5
, 2.84 ×
10
5
u
16
+2.23×10
5
u
15
+· · ·+5.02×10
5
a−2.81×10
5
, u
17
−4u
15
+· · ·+4u
2
−1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
−u
−u
3
+ u
a
7
=
−0.564359u
16
− 0.443799u
15
+ ··· + 0.499613u + 0.559091
−0.181335u
16
− 0.324414u
15
+ ··· + 1.71782u − 0.221900
a
11
=
−0.523656u
16
+ 1.25267u
15
+ ··· − 0.706948u + 0.869208
−0.166132u
16
+ 0.102498u
15
+ ··· − 2.58379u − 1.39833
a
6
=
−0.383024u
16
− 0.119386u
15
+ ··· − 1.21821u + 0.780990
−0.181335u
16
− 0.324414u
15
+ ··· + 1.71782u − 0.221900
a
2
=
0.166693u
16
− 0.255010u
15
+ ··· + 0.0329612u − 2.12171
−1.18134u
16
− 0.324414u
15
+ ··· − 1.28218u − 0.221900
a
1
=
−0.979729u
16
− 0.559953u
15
+ ··· − 1.43071u − 3.07725
−0.565850u
16
− 0.255541u
15
+ ··· − 0.964933u + 0.428689
a
5
=
−2.22373u
16
− 2.33836u
15
+ ··· − 2.59451u − 3.02392
0.499460u
16
+ 0.149873u
15
+ ··· + 3.16482u + 0.900376
a
8
=
0.552909u
16
− 0.722456u
15
+ ··· − 2.87988u + 1.54459
0.787403u
16
+ 0.296938u
15
+ ··· + 5.41888u + 0.897773
a
12
=
−0.404270u
16
+ 1.13515u
15
+ ··· − 1.48794u + 0.252232
−0.0162587u
16
+ 0.0532403u
15
+ ··· − 1.68341u − 0.898869
(ii) Obstruction class = 1
(iii) Cusp Shapes =
7310202
502439
u
16
+
3456735
502439
u
15
+ ··· +
15933523
502439
u +
5895545
502439
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
17
+ 3u
16
+ ··· − 94u + 31
c
2
u
17
+ 6u
16
+ ··· + 12u + 5
c
3
u
17
− 4u
15
+ ··· − 4u
2
+ 1
c
4
u
17
+ u
16
+ ··· + 6u − 1
c
5
u
17
− 6u
16
+ ··· + 12u − 5
c
6
u
17
+ 3u
15
+ ··· − 2u − 1
c
7
u
17
− 2u
16
+ ··· + u − 1
c
8
u
17
+ 7u
16
+ ··· + 221u + 23
c
9
u
17
− 4u
15
+ ··· + 4u
2
− 1
c
10
u
17
− 8u
15
+ ··· − u + 1
c
11
u
17
− u
16
+ ··· + 6u + 1
c
12
u
17
+ 2u
16
+ ··· + u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 5y
16
+ ··· − 11376y −961
c
2
, c
5
y
17
− 28y
16
+ ··· − 6y −25
c
3
, c
9
y
17
− 8y
16
+ ··· + 8y −1
c
4
, c
11
y
17
− 7y
16
+ ··· + 24y −1
c
6
y
17
+ 6y
16
+ ··· − 14y −1
c
7
, c
12
y
17
+ 12y
16
+ ··· − 3y −1
c
8
y
17
− 5y
16
+ ··· + 20459y −529
c
10
y
17
− 16y
16
+ ··· − 43y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.10570
a = 2.70999
b = −0.375089
−3.71205 178.710
u = −0.852456 + 0.254240I
a = −2.20438 + 2.03152I
b = −1.12246 + 1.74335I
1.30681 + 6.74725I 1.14602 − 11.82219I
u = −0.852456 − 0.254240I
a = −2.20438 − 2.03152I
b = −1.12246 − 1.74335I
1.30681 − 6.74725I 1.14602 + 11.82219I
u = −1.231690 + 0.050913I
a = −0.72795 − 1.70057I
b = 0.078174 − 1.030070I
−8.23055 + 2.35568I −10.79846 − 4.11130I
u = −1.231690 − 0.050913I
a = −0.72795 + 1.70057I
b = 0.078174 + 1.030070I
−8.23055 − 2.35568I −10.79846 + 4.11130I
u = 0.566286 + 0.419821I
a = −1.35242 + 0.75569I
b = 0.441137 − 0.361394I
−1.78451 + 0.00683I 1.85797 − 0.92831I
u = 0.566286 − 0.419821I
a = −1.35242 − 0.75569I
b = 0.441137 + 0.361394I
−1.78451 − 0.00683I 1.85797 + 0.92831I
u = 0.650959 + 0.103366I
a = 1.89640 + 0.91449I
b = 1.58700 + 0.40196I
3.63746 + 0.25672I 8.91479 − 1.78095I
u = 0.650959 − 0.103366I
a = 1.89640 − 0.91449I
b = 1.58700 − 0.40196I
3.63746 − 0.25672I 8.91479 + 1.78095I
u = 1.38326 + 0.38646I
a = −0.01656 + 1.52358I
b = −0.91943 + 1.58402I
−10.21830 − 6.17160I −7.90077 + 4.40861I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38326 − 0.38646I
a = −0.01656 − 1.52358I
b = −0.91943 − 1.58402I
−10.21830 + 6.17160I −7.90077 − 4.40861I
u = −0.257593 + 0.330900I
a = 0.74632 + 1.36587I
b = −0.727112 − 0.859807I
−4.88208 + 2.61023I −4.10985 + 1.67367I
u = −0.257593 − 0.330900I
a = 0.74632 − 1.36587I
b = −0.727112 + 0.859807I
−4.88208 − 2.61023I −4.10985 − 1.67367I
u = −1.47823 + 0.58873I
a = −0.098328 + 0.971018I
b = 0.766035 + 1.140450I
−8.08979 + 6.54241I −6.90566 − 5.03669I
u = −1.47823 − 0.58873I
a = −0.098328 − 0.971018I
b = 0.766035 − 1.140450I
−8.08979 − 6.54241I −6.90566 + 5.03669I
u = 0.66660 + 1.83006I
a = −0.0980715 + 0.0837570I
b = 0.084203 − 0.275603I
−1.13677 − 2.14375I 11.4391 − 38.8291I
u = 0.66660 − 1.83006I
a = −0.0980715 − 0.0837570I
b = 0.084203 + 0.275603I
−1.13677 + 2.14375I 11.4391 + 38.8291I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
+ 3u
16
+ ··· − 94u + 31)
· (u
77
− 8u
76
+ ··· + 32311988u + 2239897)
c
2
(u
17
+ 6u
16
+ ··· + 12u + 5)(u
77
+ u
76
+ ··· − 40176u − 5643)
c
3
(u
17
− 4u
15
+ ··· − 4u
2
+ 1)(u
77
+ u
76
+ ··· + 792u + 139)
c
4
(u
17
+ u
16
+ ··· + 6u − 1)(u
77
− 2u
76
+ ··· + 4508u − 1129)
c
5
(u
17
− 6u
16
+ ··· + 12u − 5)(u
77
+ u
76
+ ··· − 40176u − 5643)
c
6
(u
17
+ 3u
15
+ ··· − 2u − 1)(u
77
+ 3u
76
+ ··· − 2292u − 319)
c
7
(u
17
− 2u
16
+ ··· + u − 1)(u
77
− u
76
+ ··· − 37u − 11)
c
8
(u
17
+ 7u
16
+ ··· + 221u + 23)(u
77
+ 6u
76
+ ··· + 195u − 19)
c
9
(u
17
− 4u
15
+ ··· + 4u
2
− 1)(u
77
+ u
76
+ ··· + 792u + 139)
c
10
(u
17
− 8u
15
+ ··· − u + 1)(u
77
− u
76
+ ··· − 15u − 1)
c
11
(u
17
− u
16
+ ··· + 6u + 1)(u
77
− 2u
76
+ ··· + 4508u − 1129)
c
12
(u
17
+ 2u
16
+ ··· + u + 1)(u
77
− u
76
+ ··· − 37u − 11)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
17
− 5y
16
+ ··· − 11376y −961)
· (y
77
+ 44y
76
+ ··· + 727248075963258y −5017138570609)
c
2
, c
5
(y
17
− 28y
16
+ ··· − 6y −25)
· (y
77
− 63y
76
+ ··· + 793460772y −31843449)
c
3
, c
9
(y
17
− 8y
16
+ ··· + 8y −1)(y
77
− 51y
76
+ ··· + 189414y −19321)
c
4
, c
11
(y
17
− 7y
16
+ ··· + 24y −1)
· (y
77
− 66y
76
+ ··· + 58868382y −1274641)
c
6
(y
17
+ 6y
16
+ ··· − 14y −1)(y
77
+ 23y
76
+ ··· − 2243236y −101761)
c
7
, c
12
(y
17
+ 12y
16
+ ··· − 3y −1)(y
77
+ 25y
76
+ ··· − 2041y −121)
c
8
(y
17
− 5y
16
+ ··· + 20459y −529)
· (y
77
− 108y
76
+ ··· + 382001y −361)
c
10
(y
17
− 16y
16
+ ··· − 43y −1)(y
77
− 19y
76
+ ··· − 25y −1)
21
