11n
178
(K11n
178
)
1
Arc Sequences
8 5 1 7 3 11 10 3 4 5 9
Solving Sequence
4,7 5,10
11 6 9 1 3 8 2
c
4
c
10
c
6
c
9
c
11
c
3
c
8
c
1
c
2
, c
5
, c
7
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= hu
3
u
2
1, b, u
2
+ a + u + 1i
I
u
2
= hu
20
+ u
19
+ ··· 3u
2
+ 1, 46828697u
19
54942651u
18
+ ··· + 189577510a + 280763093,
79952883u
19
205733991u
18
+ ··· + 189577510b + 247801268i
I
u
3
= hu
20
7u
19
+ ··· + u 1,
12808910979u
19
187846399454u
18
+ ··· + 211373225743b + 195416963213,
235855336050u
19
1438883104988u
18
+ ··· + 211373225743a + 397432811196i
I
u
4
= hu
50
+ 4u
49
+ ··· 5u 1, 3.69233 × 10
106
u
49
+ 3.00741 × 10
107
u
48
+ ··· + 1.05238 × 10
108
b + 6.42727 × 10
107
,
2.77766 × 10
107
u
49
1.90029 × 10
108
u
48
+ ··· + 1.05238 × 10
108
a + 1.64293 × 10
109
i
There are 4 irreducible components with 93 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
= hu
3
u
2
1, b, u
2
+ a + u + 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
u
2
a
10
=
u
2
u 1
0
a
11
=
1
u
a
6
=
u
u
2
+ u
a
9
=
u
2
u 1
0
a
1
=
u
2
+ 1
u
a
3
=
u
2
+ u
u
2
a
8
=
u
2
2
u
a
2
=
2u
2
+ 2u
u
2
u
a
2
=
2u
2
+ 2u
u
2
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.232786 0.792552I
a = 1.34116 + 1.16154I
b = 0
5.50124 + 1.58317I 0.22694 + 1.69425I
u = 0.232786 + 0.792552I
a = 1.34116 1.16154I
b = 0
5.50124 1.58317I 0.22694 1.69425I
u = 1.46557
a = 0.317672
b = 0
4.42273 17.4539
3
II.
I
u
2
= hu
20
+ u
19
+ · · · 3u
2
+ 1, 4.68 × 10
7
u
19
5.49 × 10
7
u
18
+ · · · + 1.90 ×
10
8
a+2.81×10
8
, 8.00×10
7
u
19
2.06×10
8
u
18
+· · ·+1.90×10
8
b+2.48×10
8
i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
u
2
a
10
=
0.247016u
19
+ 0.289816u
18
+ ··· 1.24916u 1.48099
0.421742u
19
+ 1.08522u
18
+ ··· 0.180725u 1.30712
a
11
=
0.652601u
19
0.473340u
18
+ ··· 0.821423u 0.710702
0.0595036u
19
+ 0.384754u
18
+ ··· + 0.224860u 0.949553
a
6
=
0.280052u
19
0.109905u
18
+ ··· 0.0971137u + 0.989874
0.188864u
19
+ 0.0142883u
18
+ ··· + 0.0913839u 0.291757
a
9
=
0.668759u
19
0.795407u
18
+ ··· 1.06844u 0.173870
0.421742u
19
+ 1.08522u
18
+ ··· 0.180725u 1.30712
a
1
=
0.850268u
19
0.523920u
18
+ ··· 0.352916u 1.19703
u
a
3
=
0.326348u
19
0.329964u
18
+ ··· + 1.19703u + 0.149732
u
2
a
8
=
0.257171u
19
+ 0.435334u
18
+ ··· 1.24365u 0.463228
0.0595036u
19
+ 0.384754u
18
+ ··· + 0.224860u 0.949553
a
2
=
0.234964u
19
+ 0.530337u
18
+ ··· 0.870679u 0.146116
0.188864u
19
+ 0.0142883u
18
+ ··· + 0.0913839u 0.291757
a
2
=
0.234964u
19
+ 0.530337u
18
+ ··· 0.870679u 0.146116
0.188864u
19
+ 0.0142883u
18
+ ··· + 0.0913839u 0.291757
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.07532 1.15008I
a = 0.427727 0.361275I
b = 1.107319 0.183145I
8.00588 + 0.27607I 1.56028 + 0.31134I
u = 1.07532 + 1.15008I
a = 0.427727 + 0.361275I
b = 1.107319 + 0.183145I
8.00588 0.27607I 1.56028 0.31134I
u = 1.04163 1.16843I
a = 0.094034 1.110667I
b = 1.50238 0.86086I
8.5745 16.9983I 2.67254 + 8.37996I
u = 1.04163 + 1.16843I
a = 0.094034 + 1.110667I
b = 1.50238 + 0.86086I
8.5745 + 16.9983I 2.67254 8.37996I
u = 0.874690 0.121688I
a = 0.25690 + 1.39198I
b = 0.719775 + 0.411937I
3.02537 1.86293I 7.79633 + 3.80746I
u = 0.874690 + 0.121688I
a = 0.25690 1.39198I
b = 0.719775 0.411937I
3.02537 + 1.86293I 7.79633 3.80746I
u = 0.737850 0.581872I
a = 0.069363 + 1.260481I
b = 0.11248 + 2.29679I
4.37107 7.54282I 5.65623 + 11.11643I
u = 0.737850 + 0.581872I
a = 0.069363 1.260481I
b = 0.11248 2.29679I
4.37107 + 7.54282I 5.65623 11.11643I
u = 0.412967 0.477285I
a = 0.06854 + 1.67406I
b = 1.096943 + 0.496517I
1.66626 1.83421I 0.60394 + 1.52765I
u = 0.412967 + 0.477285I
a = 0.06854 1.67406I
b = 1.096943 0.496517I
1.66626 + 1.83421I 0.60394 1.52765I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.060088 0.658881I
a = 1.91392 + 2.16870I
b = 0.730173 + 0.354779I
5.89336 + 2.36950I 5.34088 5.91566I
u = 0.060088 + 0.658881I
a = 1.91392 2.16870I
b = 0.730173 0.354779I
5.89336 2.36950I 5.34088 + 5.91566I
u = 0.453381
a = 0.253392
b = 0.510362
0.861131 11.6542
u = 0.720650 0.888114I
a = 0.411874 + 0.878693I
b = 1.080596 + 0.595862I
0.02958 + 4.97799I 5.29605 5.59335I
u = 0.720650 + 0.888114I
a = 0.411874 0.878693I
b = 1.080596 0.595862I
0.02958 4.97799I 5.29605 + 5.59335I
u = 0.756224 0.030600I
a = 0.518686 + 0.553890I
b = 0.59721 + 1.53378I
1.50701 + 0.96018I 11.18870 6.49006I
u = 0.756224 + 0.030600I
a = 0.518686 0.553890I
b = 0.59721 1.53378I
1.50701 0.96018I 11.18870 + 6.49006I
u = 1.08428 1.16800I
a = 0.182421 0.741894I
b = 1.32568 0.70366I
2.91415 + 8.59875I 1.50122 6.80502I
u = 1.08428 + 1.16800I
a = 0.182421 + 0.741894I
b = 1.32568 + 0.70366I
2.91415 8.59875I 1.50122 + 6.80502I
u = 1.58903
a = 0.426907
b = 0.514124
4.10423 8.28188
6
III.
I
u
3
= hu
20
7u
19
+· · ·+u1, 1.28×10
10
u
19
1.88×10
11
u
18
+· · ·+2.11×10
11
b+
1.95 × 10
11
, 2.36 × 10
11
u
19
1.44 × 10
12
u
18
+ · · · + 2.11 × 10
11
a + 3.97 × 10
11
i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
u
2
a
10
=
1.11582u
19
+ 6.80731u
18
+ ··· + 3.46901u 1.88024
0.0605985u
19
+ 0.888695u
18
+ ··· 2.07325u 0.924511
a
11
=
1.27837u
19
+ 8.16669u
18
+ ··· + 5.42989u 1.95919
0.195449u
19
0.930912u
18
+ ··· 2.45735u 0.702959
a
6
=
0.988398u
19
+ 7.87202u
18
+ ··· 1.60648u + 1.50662
1.06059u
19
7.16971u
18
+ ··· 1.68393u + 1.33634
a
9
=
1.05523u
19
+ 5.91861u
18
+ ··· + 5.54226u 0.955731
0.0605985u
19
+ 0.888695u
18
+ ··· 2.07325u 0.924511
a
1
=
1.37942u
19
+ 9.15896u
18
+ ··· 2.50703u 2.25588
1.06111u
19
6.21434u
18
+ ··· + 0.406269u 0.235392
a
3
=
1.38328u
19
8.01967u
18
+ ··· + 2.25789u + 0.0441760
1.27161u
19
8.30581u
18
+ ··· 1.24047u + 1.57666
a
8
=
0.0712245u
19
+ 1.10922u
18
+ ··· 3.10032u + 1.83259
1.14705u
19
7.53453u
18
+ ··· 0.433420u + 0.553509
a
2
=
1.30606u
19
7.78190u
18
+ ··· + 1.29741u 0.0424310
0.743014u
19
5.19477u
18
+ ··· 1.01495u + 1.27393
a
2
=
1.30606u
19
7.78190u
18
+ ··· + 1.29741u 0.0424310
0.743014u
19
5.19477u
18
+ ··· 1.01495u + 1.27393
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.35926
a = 1.03268
b = 0.640698
6.51752 34.8666
u = 0.752208 1.075587I
a = 0.035408 + 1.145995I
b = 0.914221 + 0.878707I
6.26864 5.98904I 2.92384 + 3.18632I
u = 0.752208 + 1.075587I
a = 0.035408 1.145995I
b = 0.914221 0.878707I
6.26864 + 5.98904I 2.92384 3.18632I
u = 0.583311 1.128419I
a = 0.403746 0.037961I
b = 0.881751 + 0.097352I
3.13638 3.94572I 1.58269 + 5.47828I
u = 0.583311 + 1.128419I
a = 0.403746 + 0.037961I
b = 0.881751 0.097352I
3.13638 + 3.94572I 1.58269 5.47828I
u = 0.287929 0.259537I
a = 0.69091 3.70285I
b = 0.914221 + 0.878707I
6.26864 + 5.98904I 2.92384 3.18632I
u = 0.287929 + 0.259537I
a = 0.69091 + 3.70285I
b = 0.914221 0.878707I
6.26864 5.98904I 2.92384 + 3.18632I
u = 0.032242 0.434826I
a = 0.347049 + 0.942227I
b = 1.56236 + 1.19198I
0.91356 1.34180I 8.0489 + 15.8298I
u = 0.032242 + 0.434826I
a = 0.347049 0.942227I
b = 1.56236 1.19198I
0.91356 + 1.34180I 8.0489 15.8298I
u = 0.662948 0.707050I
a = 0.36817 + 1.99368I
b = 0.881751 + 0.097352I
3.13638 + 3.94572I 1.58269 5.47828I
8
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.662948 + 0.707050I
a = 0.36817 1.99368I
b = 0.881751 0.097352I
3.13638 3.94572I 1.58269 + 5.47828I
u = 0.725233 0.556341I
a = 0.18291 1.58525I
b = 1.039935 0.726914I
0.98335 + 6.94564I 13.6667 10.0962I
u = 0.725233 + 0.556341I
a = 0.18291 + 1.58525I
b = 1.039935 + 0.726914I
0.98335 6.94564I 13.6667 + 10.0962I
u = 0.88767 1.29926I
a = 0.399875 + 0.751699I
b = 1.039935 + 0.726914I
0.98335 + 6.94564I 13.6667 10.0962I
u = 0.88767 + 1.29926I
a = 0.399875 0.751699I
b = 1.039935 0.726914I
0.98335 6.94564I 13.6667 + 10.0962I
u = 0.931227 0.495139I
a = 0.035100 0.879838I
b = 1.10466I
3.56392 13.6180
u = 0.931227 + 0.495139I
a = 0.035100 + 0.879838I
b = 1.10466I
3.56392 13.6180
u = 1.234799 0.114679I
a = 0.545903 + 0.434597I
b = 1.56236 + 1.19198I
0.91356 + 1.34180I 8.0489 15.8298I
u = 1.234799 + 0.114679I
a = 0.545903 0.434597I
b = 1.56236 1.19198I
0.91356 1.34180I 8.0489 + 15.8298I
u = 2.78688
a = 0.109314
b = 0.640698
6.51752 34.8666
9
IV. I
u
4
= hu
50
+ 4u
49
+ · · · 5u 1, 3.69 × 10
106
u
49
+ 3.01 × 10
107
u
48
+
· · · + 1.05 × 10
108
b + 6.43 × 10
107
, 2.78 × 10
107
u
49
1.90 × 10
108
u
48
+ · · · +
1.05 × 10
108
a + 1.64 × 10
109
i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
u
2
a
10
=
0.263942u
49
+ 1.80571u
48
+ ··· 105.289u 15.6116
0.0350856u
49
0.285774u
48
+ ··· 0.795935u 0.610739
a
11
=
0.100100u
49
+ 1.19168u
48
+ ··· 100.480u 14.2509
0.0470703u
49
0.00881835u
48
+ ··· 0.753096u 0.569402
a
6
=
1.81124u
49
+ 7.18452u
48
+ ··· 64.7876u 22.2422
0.678743u
49
2.50349u
48
+ ··· + 9.00031u 0.681446
a
9
=
0.299028u
49
+ 2.09148u
48
+ ··· 104.493u 15.0009
0.0350856u
49
0.285774u
48
+ ··· 0.795935u 0.610739
a
1
=
0.0861240u
49
0.377836u
48
+ ··· 126.434u 10.5080
0.383313u
49
+ 1.49128u
48
+ ··· 8.06993u 1.47201
a
3
=
2.65707u
49
+ 9.50646u
48
+ ··· 138.280u 0.552256
0.258326u
49
+ 1.17738u
48
+ ··· 14.9385u 1.82411
a
8
=
1.78125u
49
+ 6.55058u
48
+ ··· 50.6879u 23.5270
0.646907u
49
2.22907u
48
+ ··· + 7.51769u 1.23819
a
2
=
2.55404u
49
9.06240u
48
+ ··· + 150.266u + 1.25455
0.367905u
49
1.60545u
48
+ ··· + 15.2013u + 1.85607
a
2
=
2.55404u
49
9.06240u
48
+ ··· + 150.266u + 1.25455
0.367905u
49
1.60545u
48
+ ··· + 15.2013u + 1.85607
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
10
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.32989
a = 1.02637
b = 0.580269
6.61075 51.2604
u = 1.31226 1.16752I
a = 0.528719 0.167342I
b = 1.114156 + 0.510756I
8.00509 + 8.45240I 0.75796 6.49999I
u = 1.31226 + 1.16752I
a = 0.528719 + 0.167342I
b = 1.114156 0.510756I
8.00509 8.45240I 0.75796 + 6.49999I
u = 1.16461 1.50318I
a = 0.047379 + 0.462652I
b = 0.993457 + 0.311354I
3.52121 5.29385I 3.74916 + 8.30350I
u = 1.16461 + 1.50318I
a = 0.047379 0.462652I
b = 0.993457 0.311354I
3.52121 + 5.29385I 3.74916 8.30350I
u = 1.07701 0.98508I
a = 0.873099 + 0.474832I
b = 1.183821 0.678601I
7.41514 1.27639I 2.55128 + 0.67478I
u = 1.07701 + 0.98508I
a = 0.873099 0.474832I
b = 1.183821 + 0.678601I
7.41514 + 1.27639I 2.55128 0.67478I
u = 1.06616 1.11382I
a = 0.291602 0.962467I
b = 1.114156 0.510756I
8.00509 8.45240I 0.75796 + 6.49999I
u = 1.06616 + 1.11382I
a = 0.291602 + 0.962467I
b = 1.114156 + 0.510756I
8.00509 + 8.45240I 0.75796 6.49999I
u = 1.00189 1.04693I
a = 0.178154 + 1.185471I
b = 1.84091 + 1.17791I
7.66608 6.24371I 4.09267 + 6.21663I
11
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.00189 + 1.04693I
a = 0.178154 1.185471I
b = 1.84091 1.17791I
7.66608 + 6.24371I 4.09267 6.21663I
u = 0.818849 0.635675I
a = 0.291954 + 0.232325I
b = 0.834873 0.287723I
2.89680 2.76831I 5.67436 + 1.24863I
u = 0.818849 + 0.635675I
a = 0.291954 0.232325I
b = 0.834873 + 0.287723I
2.89680 + 2.76831I 5.67436 1.24863I
u = 0.604668 1.191679I
a = 0.272899 + 1.177371I
b = 0.856520 + 0.586940I
6.70056 6.60168I 4.95046 + 12.30292I
u = 0.604668 + 1.191679I
a = 0.272899 1.177371I
b = 0.856520 0.586940I
6.70056 + 6.60168I 4.95046 12.30292I
u = 0.570225 0.516565I
a = 0.16891 1.90970I
b = 1.060721 0.762806I
0.56308 6.78110I 3.38343 + 3.19298I
u = 0.570225 + 0.516565I
a = 0.16891 + 1.90970I
b = 1.060721 + 0.762806I
0.56308 + 6.78110I 3.38343 3.19298I
u = 0.560955 0.411759I
a = 0.00679 1.47326I
b = 0.427772 1.014275I
2.53372 + 0.16719I 3.64574 0.21536I
u = 0.560955 + 0.411759I
a = 0.00679 + 1.47326I
b = 0.427772 + 1.014275I
2.53372 0.16719I 3.64574 + 0.21536I
u = 0.305442 0.745648I
a = 0.171255 + 1.367643I
b = 0.710713 + 0.790919I
6.24414 3.55600I 4.03991 + 3.49531I
12
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.305442 + 0.745648I
a = 0.171255 1.367643I
b = 0.710713 0.790919I
6.24414 + 3.55600I 4.03991 3.49531I
u = 0.236451 0.531026I
a = 4.59557 0.86880I
b = 0.856520 + 0.586940I
6.70056 6.60168I 4.95046 + 12.30292I
u = 0.236451 + 0.531026I
a = 4.59557 + 0.86880I
b = 0.856520 0.586940I
6.70056 + 6.60168I 4.95046 12.30292I
u = 0.223288 0.942582I
a = 1.88683 + 0.99818I
b = 0.710713 0.790919I
6.24414 + 3.55600I 4.03991 3.49531I
u = 0.223288 + 0.942582I
a = 1.88683 0.99818I
b = 0.710713 + 0.790919I
6.24414 3.55600I 4.03991 + 3.49531I
u = 0.049351 0.717898I
a = 0.39422 + 1.63257I
b = 0.748569
2.81112 0.202278
u = 0.049351 + 0.717898I
a = 0.39422 1.63257I
b = 0.748569
2.81112 0.202278
u = 0.0014594 0.1290826I
a = 7.70492 + 9.68373I
b = 0.834873 + 0.287723I
2.89680 + 2.76831I 5.67436 1.24863I
u = 0.0014594 + 0.1290826I
a = 7.70492 9.68373I
b = 0.834873 0.287723I
2.89680 2.76831I 5.67436 + 1.24863I
u = 0.057422 1.022710I
a = 0.316941 0.699314I
b = 1.183821 0.678601I
7.41514 1.27639I 2.55128 + 0.67478I
13
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.057422 + 1.022710I
a = 0.316941 + 0.699314I
b = 1.183821 + 0.678601I
7.41514 + 1.27639I 2.55128 0.67478I
u = 0.079430 0.878574I
a = 0.370193 0.750739I
b = 0.914450 + 0.194844I
1.53850 + 4.51240I 4.65188 7.14304I
u = 0.079430 + 0.878574I
a = 0.370193 + 0.750739I
b = 0.914450 0.194844I
1.53850 4.51240I 4.65188 + 7.14304I
u = 0.136170 0.736576I
a = 0.329394 1.001407I
b = 1.84091 1.17791I
7.66608 + 6.24371I 4.09267 6.21663I
u = 0.136170 + 0.736576I
a = 0.329394 + 1.001407I
b = 1.84091 + 1.17791I
7.66608 6.24371I 4.09267 + 6.21663I
u = 0.140564 0.434686I
a = 0.0970679 + 0.0835883I
b = 1.51893 0.92610I
1.03856 1.14326I 10.5893 12.6521I
u = 0.140564 + 0.434686I
a = 0.0970679 0.0835883I
b = 1.51893 + 0.92610I
1.03856 + 1.14326I 10.5893 + 12.6521I
u = 0.747108 1.066289I
a = 0.102953 + 1.064056I
b = 0.914450 + 0.194844I
1.53850 + 4.51240I 4.65188 7.14304I
u = 0.747108 + 1.066289I
a = 0.102953 1.064056I
b = 0.914450 0.194844I
1.53850 4.51240I 4.65188 + 7.14304I
u = 0.86987 1.24327I
a = 0.437552 + 0.872178I
b = 1.060721 + 0.762806I
0.56308 + 6.78110I 3.38343 3.19298I
14
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.86987 + 1.24327I
a = 0.437552 0.872178I
b = 1.060721 0.762806I
0.56308 6.78110I 3.38343 + 3.19298I
u = 0.997029 0.367394I
a = 1.45085 1.23993I
b = 0.993457 0.311354I
3.52121 + 5.29385I 3.74916 8.30350I
u = 0.997029 + 0.367394I
a = 1.45085 + 1.23993I
b = 0.993457 + 0.311354I
3.52121 5.29385I 3.74916 + 8.30350I
u = 1.018437 0.608250I
a = 0.230012 0.681084I
b = 0.427772 1.014275I
2.53372 + 0.16719I 3.64574 0.21536I
u = 1.018437 + 0.608250I
a = 0.230012 + 0.681084I
b = 0.427772 + 1.014275I
2.53372 0.16719I 3.64574 + 0.21536I
u = 1.03424 1.23977I
a = 0.288537 0.627682I
b = 0.906013
3.05217 0.159533
u = 1.03424 + 1.23977I
a = 0.288537 + 0.627682I
b = 0.906013
3.05217 0.159533
u = 1.217959 0.245792I
a = 0.460317 + 0.384323I
b = 1.51893 + 0.92610I
1.03856 + 1.14326I 10.5893 + 12.6521I
u = 1.217959 + 0.245792I
a = 0.460317 0.384323I
b = 1.51893 0.92610I
1.03856 1.14326I 10.5893 12.6521I
u = 2.71865
a = 0.0290438
b = 0.580269
6.61075 51.2604
15
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
3
+ u
2
+ 1)(u
20
5u
19
+ ··· + 24u 8)(u
20
4u
19
+ ··· + 24u + 8)
(u
50
+ 5u
49
+ ··· + 337800u + 93608)
c
2
(u
3
+ u 1)(u
10
u
9
+ u
8
+ u
7
7u
6
+ 6u
5
4u
4
+ u
3
+ 4u
2
1)
2
(u
20
3u
19
+ ··· + 50u + 28)
(5 18u + 66u
2
220u
3
+ 296u
4
563u
5
+ 1021u
6
+ 14u
7
+ 405u
8
87u
9
1694u
10
1624u
11
2485u
12
2173u
13
1396u
14
1086u
15
214u
16
68u
17
+ 160u
18
+ 163u
19
+ 100u
20
+ 75u
21
+ 23u
22
+ 14u
23
+ 2u
24
+ u
25
)
2
c
3
(u
3
+ u
2
+ 1)(u
20
+ u
19
+ ··· 3u
2
+ 1)(u
20
+ 7u
19
+ ··· u 1)
(u
50
+ 4u
49
+ ··· 5u 1)
c
4
(u
3
u
2
1)(u
20
7u
19
+ ··· + u 1)(u
20
+ u
19
+ ··· 3u
2
+ 1)
(u
50
+ 4u
49
+ ··· 5u 1)
c
5
(u
3
+ u + 1)(u
10
+ u
9
+ u
8
u
7
7u
6
6u
5
4u
4
u
3
+ 4u
2
1)
2
(u
20
3u
19
+ ··· + 50u + 28)
(5 18u + 66u
2
220u
3
+ 296u
4
563u
5
+ 1021u
6
+ 14u
7
+ 405u
8
87u
9
1694u
10
1624u
11
2485u
12
2173u
13
1396u
14
1086u
15
214u
16
68u
17
+ 160u
18
+ 163u
19
+ 100u
20
+ 75u
21
+ 23u
22
+ 14u
23
+ 2u
24
+ u
25
)
2
c
6
(u
3
u
2
1)(u
20
5u
19
+ ··· + 24u 8)(u
20
+ 4u
19
+ ··· 24u + 8)
(u
50
+ 5u
49
+ ··· + 337800u + 93608)
c
7
(u
3
+ 2u
2
+ u 1)(u
20
+ 2u
19
+ ··· + 5u 1)(u
20
+ 6u
19
+ ··· + 8u + 1)
(u
50
+ u
49
+ ··· 22u 1)
c
8
(u
3
+ u 1)(u
20
+ 9u
18
+ ··· 5u 1)(u
20
+ u
19
+ ··· 4u 1)
(u
50
+ 3u
48
+ ··· + 10342u 3931)
c
9
u
3
(u
20
4u
18
+ ··· + 146u
2
31)(u
20
+ 5u
19
+ ··· + 192u + 32)
(31 18u 199u
2
+ 101u
3
+ 550u
4
144u
5
999u
6
44u
7
+ 1320u
8
+ 449u
9
1275u
10
817u
11
+ 865u
12
+ 920u
13
387u
14
713u
15
+ 74u
16
+ 402u
17
+ 24u
18
160u
19
24u
20
+ 46u
21
+ 7u
22
8u
23
u
24
+ u
25
)
2
c
10
(u
3
+ u + 1)(u
20
+ 9u
18
+ ··· 5u 1)(u
20
u
19
+ ··· + 4u 1)
(u
50
+ 3u
48
+ ··· + 10342u 3931)
c
11
(u
3
2u
2
+ u + 1)(u
20
6u
19
+ ··· 8u + 1)(u
20
+ 2u
19
+ ··· + 5u 1)
(u
50
+ u
49
+ ··· 22u 1)
16
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
3
y
2
2y 1)(y
20
10y
19
+ ··· + 832y + 64)
(y
20
+ 19y
19
+ ··· + 384y + 64)
(y
50
+ 13y
49
+ ··· + 42553508800y + 8762457664)
c
2
, c
5
(y
3
+ 2y
2
+ y 1)
(1 8y + 24y
2
19y
3
54y
4
+ 24y
5
+ 39y
6
11y
7
11y
8
+ y
9
+ y
10
)
2
(y
20
+ 11y
19
+ ··· + 6180y + 784)
(25 336y + 604y
2
+ 1.94 × 10
4
y
3
+ 2.08 × 10
4
y
4
3.27 × 10
5
y
5
9.53 × 10
5
y
6
+ 1.41 × 10
6
y
7
+ 7.77 × 10
6
y
8
+ 1.02 × 10
7
y
9
+ 3.57 × 10
6
y
10
3.97 × 10
6
y
11
4.09 × 10
6
y
12
+ 1.64 × 10
5
y
13
+ 2.30 × 10
6
y
14
+ 1.45 × 10
6
y
15
+ 1.68 × 10
5
y
16
2.52 × 10
5
y
17
1.58 × 10
5
y
18
3.50 × 10
4
y
19
+ 3870y
20
+ 4813y
21
+ 1497y
22
+ 254y
23
+ 24y
24
+ y
25
)
2
c
3
, c
4
(y
3
y
2
2y 1)(y
20
9y
19
+ ··· + 7y + 1)(y
20
3y
19
+ ··· 6y + 1)
(y
50
+ 18y
48
+ ··· + 143y + 1)
c
6
(y
3
y
2
2y 1)(y
20
10y
19
+ ··· + 832y + 64)
(y
20
+ 19y
19
+ ··· + 384y + 64)
(y
50
+ 13y
49
+ ··· + 42553508800y + 8762457664)
c
7
, c
11
(y
3
2y
2
+ 5y 1)(y
20
+ 24y
18
+ ··· 79y + 1)
(y
20
2y
19
+ ··· 14y + 1)(y
50
21y
49
+ ··· + 244y + 1)
c
8
, c
10
(y
3
+ 2y
2
+ y 1)(y
20
y
19
+ ··· 22y + 1)
(y
20
+ 18y
19
+ ··· + 13y + 1)
(y
50
+ 6y
49
+ ··· + 33112428y + 15452761)
c
9
y
3
(31 + 146y 219y
2
+ 124y
3
8y
4
62y
5
+ 86y
6
44y
7
+ 24y
8
4y
9
+ y
10
)
2
(y
20
+ y
19
+ ··· 14336y + 1024)
(961 + 1.27 × 10
4
y 7.73 × 10
4
y
2
+ 2.96 × 10
5
y
3
8.09 × 10
5
y
4
+ 1.70 × 10
6
y
5
2.88 × 10
6
y
6
+ 4.08 × 10
6
y
7
4.99 × 10
6
y
8
+ 5.40 × 10
6
y
9
5.28 × 10
6
y
10
+ 4.75 × 10
6
y
11
3.98 × 10
6
y
12
+ 3.11 × 10
6
y
13
2.25 × 10
6
y
14
+ 1.49 × 10
6
y
15
8.75 × 10
5
y
16
+ 4.52 × 10
5
y
17
2.00 × 10
5
y
18
+ 7.52 × 10
4
y
19
2.33 × 10
4
y
20
+ 5864y
21
1153y
22
+ 170y
23
17y
24
+ y
25
)
2
17