11a
322
(K11a
322
)
1
Arc Sequences
9 6 1 8 10 2 11 3 7 5 4
Solving Sequence
2,7
6
3,10
5 11 9 1 8 4
c
6
c
2
c
5
c
10
c
9
c
1
c
8
c
4
c
3
, c
7
, c
11
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
18
+ 4u
16
+ 7u
14
u
13
+ 6u
12
5u
11
+ 9u
10
7u
9
+ 23u
8
+ 34u
6
+ 7u
5
+ 24u
4
+ 5u
3
+ 8u
2
+ u + 1,
7703u
17
+ 2932u
16
+ ··· + 1467b + 7565, 19294u
17
+ 7565u
16
+ ··· + 1467a + 14626i
I
u
2
= hu
93
3u
92
+ ··· + 151u + 93,
5.80470 × 10
218
u
92
1.88983 × 10
219
u
91
+ ··· + 2.85769 × 10
219
b + 4.75826 × 10
220
,
6.67281 × 10
220
u
92
2.14666 × 10
221
u
91
+ ··· + 2.65765 × 10
221
a + 9.88533 × 10
222
i
There are 2 irreducible components with 111 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
18
+ 4u
16
+ · · · + u + 1, 7703u
17
+ 2932u
16
+ · · · + 1467b +
7565, 19294u
17
+ 7565u
16
+ · · · + 1467a + 14626i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
6
=
u
u
a
3
=
u
2
+ 1
u
2
a
10
=
13.1520u
17
5.15678u
16
+ ··· + 28.5487u 9.97001
5.25085u
17
1.99864u
16
+ ··· + 9.99523u 5.15678
a
5
=
6.56510u
17
5.70416u
16
+ ··· 35.0354u 14.0218
2.02249u
17
4.63599u
16
+ ··· 8.27403u 10.8609
a
11
=
2.95637u
17
+ 4.86980u
16
+ ··· + 1.95569u + 8.97273
2.95297u
17
+ 0.124744u
16
+ ··· + 2.06339u + 0.654397
a
9
=
13.1520u
17
5.15678u
16
+ ··· + 28.5487u 9.97001
u
17
+ 3u
15
+ ··· + u
2
+ 2u
a
1
=
8.44853u
17
6.31766u
16
+ ··· 37.8882u 18.4697
4u
16
13u
14
+ ··· 5u 5
a
8
=
10.4990u
17
3.80164u
16
+ ··· + 21.8057u 6.81186
2.59782u
17
0.643490u
16
+ ··· + 4.25222u 1.99864
a
4
=
9.49284u
17
5.61145u
16
+ ··· + 18.6401u 10.6830
0.496251u
17
+ 4.60600u
16
+ ··· + 14.3790u + 10.3102
a
4
=
9.49284u
17
5.61145u
16
+ ··· + 18.6401u 10.6830
0.496251u
17
+ 4.60600u
16
+ ··· + 14.3790u + 10.3102
(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 = 1.098452 0.573725I
a = 0.169643 + 0.393511I
b = 0.197586 0.498990I
3.30474 3.34770I 4.63686 + 7.62812I
u = 1.098452 + 0.573725I
a = 0.169643 0.393511I
b = 0.197586 + 0.498990I
3.30474 + 3.34770I 4.63686 7.62812I
u = 0.399200 1.291310I
a = 0.898086 + 1.086947I
b = 1.62086 + 1.52153I
3.03940 7.57505I 5.54978 + 7.69435I
u = 0.399200 + 1.291310I
a = 0.898086 1.086947I
b = 1.62086 1.52153I
3.03940 + 7.57505I 5.54978 7.69435I
u = 0.350285 0.978445I
a = 0.24852 + 1.50768I
b = 0.63937 + 1.58628I
6.43935 1.44640I 11.71956 + 0.68048I
u = 0.350285 + 0.978445I
a = 0.24852 1.50768I
b = 0.63937 1.58628I
6.43935 + 1.44640I 11.71956 0.68048I
u = 0.238196 0.578880I
a = 1.83944 + 0.12066I
b = 0.010194 1.063572I
3.97474 2.70415I 0.079815 + 1.320496I
u = 0.238196 + 0.578880I
a = 1.83944 0.12066I
b = 0.010194 + 1.063572I
3.97474 + 2.70415I 0.079815 1.320496I
u = 0.028401 0.600952I
a = 3.49249 0.83995I
b = 1.38141 1.11790I
0.31658 + 5.63779I 2.91181 3.68559I
u = 0.028401 + 0.600952I
a = 3.49249 + 0.83995I
b = 1.38141 + 1.11790I
0.31658 5.63779I 2.91181 + 3.68559I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.102450 0.758852I
a = 0.469331 0.391605I
b = 1.08893 1.62151I
2.26028 2.23530I 7.59117 1.84623I
u = 0.102450 + 0.758852I
a = 0.469331 + 0.391605I
b = 1.08893 + 1.62151I
2.26028 + 2.23530I 7.59117 + 1.84623I
u = 0.299863 1.124436I
a = 0.588572 + 0.691654I
b = 0.297383 + 1.236452I
3.99972 + 3.99910I 5.21893 5.75182I
u = 0.299863 + 1.124436I
a = 0.588572 0.691654I
b = 0.297383 1.236452I
3.99972 3.99910I 5.21893 + 5.75182I
u = 0.556386 1.270945I
a = 0.087504 + 0.939886I
b = 0.66623 + 1.66493I
1.64477 + 4.87461I 7.20857 3.63831I
u = 0.556386 + 1.270945I
a = 0.087504 0.939886I
b = 0.66623 1.66493I
1.64477 4.87461I 7.20857 + 3.63831I
u = 1.155834 0.431712I
a = 0.540590 + 0.010011I
b = 0.112377 + 0.568136I
1.56279 + 1.31651I 14.0169 6.4824I
u = 1.155834 + 0.431712I
a = 0.540590 0.010011I
b = 0.112377 0.568136I
1.56279 1.31651I 14.0169 + 6.4824I
4
II. I
u
2
= hu
93
3u
92
+ · · · + 151u + 93, 5.80 × 10
218
u
92
1.89 × 10
219
u
91
+
· · · + 2.86 × 10
219
b + 4.76 × 10
220
, 6.67 × 10
220
u
92
2.15 × 10
221
u
91
+ · · · +
2.66 × 10
221
a + 9.89 × 10
222
i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
6
=
u
u
a
3
=
u
2
+ 1
u
2
a
10
=
0.251079u
92
+ 0.807729u
91
+ ··· 32.9724u 37.1957
0.203126u
92
+ 0.661313u
91
+ ··· 24.3145u 16.6507
a
5
=
0.699756u
92
2.71369u
91
+ ··· + 24.2258u 43.1662
0.0150674u
92
0.217033u
91
+ ··· 56.4349u 34.1563
a
11
=
0.457400u
92
+ 1.65231u
91
+ ··· 55.6645u + 12.1785
0.0152173u
92
0.235318u
91
+ ··· 36.9732u 34.2515
a
9
=
0.251079u
92
+ 0.807729u
91
+ ··· 32.9724u 37.1957
0.147839u
92
0.711266u
91
+ ··· 9.19226u 21.7184
a
1
=
0.142098u
92
0.350767u
91
+ ··· + 41.2485u + 23.3530
0.204851u
92
+ 0.456150u
91
+ ··· 84.7740u 51.7251
a
8
=
0.215377u
92
+ 0.692433u
91
+ ··· 20.4586u 25.6485
0.00208534u
92
0.0568087u
91
+ ··· + 5.68832u 1.92117
a
4
=
0.366311u
92
1.23086u
91
+ ··· + 63.1425u + 11.2002
0.534047u
92
+ 1.79977u
91
+ ··· 83.1261u + 3.60161
a
4
=
0.366311u
92
1.23086u
91
+ ··· + 63.1425u + 11.2002
0.534047u
92
+ 1.79977u
91
+ ··· 83.1261u + 3.60161
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.286607 0.581347I
a = 0.477696 0.047129I
b = 0.209627 + 0.637724I
2.62056 2.77773I 3.73942 + 1.86309I
u = 1.286607 + 0.581347I
a = 0.477696 + 0.047129I
b = 0.209627 0.637724I
2.62056 + 2.77773I 3.73942 1.86309I
u = 1.126654 0.344072I
a = 0.833481 + 0.396106I
b = 0.129713 0.524789I
4.77635 + 5.74683I 0.44981 7.15111I
u = 1.126654 + 0.344072I
a = 0.833481 0.396106I
b = 0.129713 + 0.524789I
4.77635 5.74683I 0.44981 + 7.15111I
u = 0.937372 0.000279I
a = 1.053472 + 0.335261I
b = 0.067336 + 0.320614I
4.23878 + 6.45548I 6.36871 5.93428I
u = 0.937372 + 0.000279I
a = 1.053472 0.335261I
b = 0.067336 0.320614I
4.23878 6.45548I 6.36871 + 5.93428I
u = 0.844094 0.653935I
a = 0.139051 + 0.551206I
b = 0.544691 0.514186I
1.68544 3.00936I 2.19248 + 3.66079I
u = 0.844094 + 0.653935I
a = 0.139051 0.551206I
b = 0.544691 + 0.514186I
1.68544 + 3.00936I 2.19248 3.66079I
u = 0.75806 1.21920I
a = 0.074494 + 0.912685I
b = 0.50145 + 1.41092I
0.38282 4.43447I 0.31680 + 3.13449I
u = 0.75806 + 1.21920I
a = 0.074494 0.912685I
b = 0.50145 1.41092I
0.38282 + 4.43447I 0.31680 3.13449I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.723160 0.174661I
a = 1.32386 1.12233I
b = 0.644459 + 0.016779I
1.92000 + 3.17965I 4.65573 4.19725I
u = 0.723160 + 0.174661I
a = 1.32386 + 1.12233I
b = 0.644459 0.016779I
1.92000 3.17965I 4.65573 + 4.19725I
u = 0.64633 1.26191I
a = 0.153634 1.131293I
b = 0.86651 1.96037I
1.80023 12.03953I 1.69607 + 8.53161I
u = 0.64633 + 1.26191I
a = 0.153634 + 1.131293I
b = 0.86651 + 1.96037I
1.80023 + 12.03953I 1.69607 8.53161I
u = 0.504232 1.159732I
a = 0.61394 + 1.60883I
b = 1.20126 + 2.22710I
4.76534 7.79767I 9.82504 + 8.13166I
u = 0.504232 + 1.159732I
a = 0.61394 1.60883I
b = 1.20126 2.22710I
4.76534 + 7.79767I 9.82504 8.13166I
u = 0.485082 1.270199I
a = 0.238923 0.989195I
b = 0.00718 1.86945I
8.11494 11.47081I 8.82109 + 8.05672I
u = 0.485082 + 1.270199I
a = 0.238923 + 0.989195I
b = 0.00718 + 1.86945I
8.11494 + 11.47081I 8.82109 8.05672I
u = 0.454840 1.316883I
a = 0.173436 0.865556I
b = 0.12117 1.61520I
8.34403 + 1.38464I 11.04993 1.79347I
u = 0.454840 + 1.316883I
a = 0.173436 + 0.865556I
b = 0.12117 + 1.61520I
8.34403 1.38464I 11.04993 + 1.79347I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.397627 0.073937I
a = 0.19265 1.94461I
b = 0.749008 0.608014I
1.30018 + 2.88591I 1.12552 3.03882I
u = 0.397627 + 0.073937I
a = 0.19265 + 1.94461I
b = 0.749008 + 0.608014I
1.30018 2.88591I 1.12552 + 3.03882I
u = 0.374927 1.137663I
a = 0.295325 + 0.810887I
b = 0.962137 + 0.883821I
5.66136 0.33582I 8.02845 2.67203I
u = 0.374927 + 1.137663I
a = 0.295325 0.810887I
b = 0.962137 0.883821I
5.66136 + 0.33582I 8.02845 + 2.67203I
u = 0.366246 0.856685I
a = 0.11145 1.42586I
b = 1.17358 1.83740I
3.77658 + 0.38693I 1.69566 + 0.22246I
u = 0.366246 + 0.856685I
a = 0.11145 + 1.42586I
b = 1.17358 + 1.83740I
3.77658 0.38693I 1.69566 0.22246I
u = 0.346185 1.236495I
a = 0.881978 + 0.622859I
b = 0.743900 + 0.729117I
4.73642 6.03450I 8.73420 + 6.57377I
u = 0.346185 + 1.236495I
a = 0.881978 0.622859I
b = 0.743900 0.729117I
4.73642 + 6.03450I 8.73420 6.57377I
u = 0.322622 0.930689I
a = 0.251684 + 0.703218I
b = 1.37761 + 1.76739I
3.27973 4.30614I 1.52832 + 6.74128I
u = 0.322622 + 0.930689I
a = 0.251684 0.703218I
b = 1.37761 1.76739I
3.27973 + 4.30614I 1.52832 6.74128I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.319146 0.760564I
a = 2.15271 + 0.02589I
b = 0.716658 0.746451I
4.14473 3.51278I 1.54683 + 9.73709I
u = 0.319146 + 0.760564I
a = 2.15271 0.02589I
b = 0.716658 + 0.746451I
4.14473 + 3.51278I 1.54683 9.73709I
u = 0.318984 1.325487I
a = 0.60406 + 1.29446I
b = 1.43996 + 1.75218I
4.36272 6.42244I 9.60327 + 5.23702I
u = 0.318984 + 1.325487I
a = 0.60406 1.29446I
b = 1.43996 1.75218I
4.36272 + 6.42244I 9.60327 5.23702I
u = 0.318884 0.770726I
a = 0.673252 0.031463I
b = 0.242425 0.968428I
2.61018 + 0.55355I 5.97981 + 1.15396I
u = 0.318884 + 0.770726I
a = 0.673252 + 0.031463I
b = 0.242425 + 0.968428I
2.61018 0.55355I 5.97981 1.15396I
u = 0.297157
a = 1.95343
b = 0.369098
0.917664 11.3239
u = 0.293670 1.064590I
a = 0.399370 + 1.099868I
b = 0.08007 + 1.63200I
3.49041 2.34482I 7.43927 0.17172I
u = 0.293670 + 1.064590I
a = 0.399370 1.099868I
b = 0.08007 1.63200I
3.49041 + 2.34482I 7.43927 + 0.17172I
u = 0.261222 0.695240I
a = 1.78607 0.27289I
b = 0.241131 + 0.088304I
4.08056 + 1.50596I 0.83759 + 2.64217I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.261222 + 0.695240I
a = 1.78607 + 0.27289I
b = 0.241131 0.088304I
4.08056 1.50596I 0.83759 2.64217I
u = 0.098315 0.812310I
a = 0.380321 + 0.645274I
b = 0.36158 + 2.02498I
2.22253 2.87184I 5.92800 + 10.27307I
u = 0.098315 + 0.812310I
a = 0.380321 0.645274I
b = 0.36158 2.02498I
2.22253 + 2.87184I 5.92800 10.27307I
u = 0.067778 1.252996I
a = 0.192229 0.385447I
b = 0.469909 0.888388I
2.03743 + 2.00663I 5.79619 3.93458I
u = 0.067778 + 1.252996I
a = 0.192229 + 0.385447I
b = 0.469909 + 0.888388I
2.03743 2.00663I 5.79619 + 3.93458I
u = 0.131902 0.954095I
a = 0.748039 + 1.192456I
b = 0.79450 + 1.61894I
3.10875 + 0.58240I 10.30402 + 0.25013I
u = 0.131902 + 0.954095I
a = 0.748039 1.192456I
b = 0.79450 1.61894I
3.10875 0.58240I 10.30402 0.25013I
u = 0.172805 1.199491I
a = 0.41172 + 1.35542I
b = 0.28357 + 1.92819I
8.09781 + 2.55341I 14.0398 2.9184I
u = 0.172805 + 1.199491I
a = 0.41172 1.35542I
b = 0.28357 1.92819I
8.09781 2.55341I 14.0398 + 2.9184I
u = 0.17338 1.45635I
a = 0.084939 0.442601I
b = 0.654042 0.720940I
6.38181 6.72088I 8.47479 + 5.98271I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.17338 + 1.45635I
a = 0.084939 + 0.442601I
b = 0.654042 + 0.720940I
6.38181 + 6.72088I 8.47479 5.98271I
u = 0.197477 0.859125I
a = 3.04534 + 0.15166I
b = 1.61298 0.31043I
0.11047 + 6.51793I 5.60246 9.02969I
u = 0.197477 + 0.859125I
a = 3.04534 0.15166I
b = 1.61298 + 0.31043I
0.11047 6.51793I 5.60246 + 9.02969I
u = 0.263210 1.161534I
a = 0.334856 0.451807I
b = 0.96847 1.12964I
4.67249 + 3.86717I 18.0901 4.5713I
u = 0.263210 + 1.161534I
a = 0.334856 + 0.451807I
b = 0.96847 + 1.12964I
4.67249 3.86717I 18.0901 + 4.5713I
u = 0.299211 0.900944I
a = 0.98790 1.61121I
b = 2.03206 1.87315I
0.45952 4.22823I 4.08298 + 2.00245I
u = 0.299211 + 0.900944I
a = 0.98790 + 1.61121I
b = 2.03206 + 1.87315I
0.45952 + 4.22823I 4.08298 2.00245I
u = 0.403548 1.190456I
a = 0.350823 + 0.470116I
b = 0.025159 + 0.492305I
1.44049 + 2.66870I 1.68644 0.97557I
u = 0.403548 + 1.190456I
a = 0.350823 0.470116I
b = 0.025159 0.492305I
1.44049 2.66870I 1.68644 + 0.97557I
u = 0.416030 1.283645I
a = 0.167629 0.766132I
b = 0.02078 1.82169I
3.10293 + 5.33107I 8.4802 13.4962I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.416030 + 1.283645I
a = 0.167629 + 0.766132I
b = 0.02078 + 1.82169I
3.10293 5.33107I 8.4802 + 13.4962I
u = 0.436496 1.069895I
a = 0.313803 + 1.298202I
b = 0.39888 + 1.66475I
5.97802 + 3.41696I 10.34341 3.60259I
u = 0.436496 + 1.069895I
a = 0.313803 1.298202I
b = 0.39888 1.66475I
5.97802 3.41696I 10.34341 + 3.60259I
u = 0.445066 0.987704I
a = 0.634640 + 0.846376I
b = 1.44697 + 1.83381I
0.44062 + 9.04830I 3.46373 9.32035I
u = 0.445066 + 0.987704I
a = 0.634640 0.846376I
b = 1.44697 1.83381I
0.44062 9.04830I 3.46373 + 9.32035I
u = 0.463746 1.210544I
a = 0.484008 + 1.289278I
b = 1.20533 + 1.87365I
0.97476 + 6.41730I 2.10075 7.48822I
u = 0.463746 + 1.210544I
a = 0.484008 1.289278I
b = 1.20533 1.87365I
0.97476 6.41730I 2.10075 + 7.48822I
u = 0.504738 0.496846I
a = 1.76775 1.21297I
b = 0.043022 0.248626I
1.87848 5.13684I 0.46607 + 1.98262I
u = 0.504738 + 0.496846I
a = 1.76775 + 1.21297I
b = 0.043022 + 0.248626I
1.87848 + 5.13684I 0.46607 1.98262I
u = 0.537415 0.281055I
a = 1.40361 + 0.55692I
b = 0.668905 0.370910I
3.79529 + 0.46350I 6.87686 1.81955I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.537415 + 0.281055I
a = 1.40361 0.55692I
b = 0.668905 + 0.370910I
3.79529 0.46350I 6.87686 + 1.81955I
u = 0.539921 0.940488I
a = 0.074941 0.496279I
b = 0.730255 1.163656I
0.87942 + 2.94273I 2.36944 4.16505I
u = 0.539921 + 0.940488I
a = 0.074941 + 0.496279I
b = 0.730255 + 1.163656I
0.87942 2.94273I 2.36944 + 4.16505I
u = 0.608017 0.715465I
a = 1.228412 0.692689I
b = 0.01947 1.55514I
0.03049 + 2.41359I 0.06215 5.41922I
u = 0.608017 + 0.715465I
a = 1.228412 + 0.692689I
b = 0.01947 + 1.55514I
0.03049 2.41359I 0.06215 + 5.41922I
u = 0.60980 1.41004I
a = 0.395371 + 0.895204I
b = 1.05055 + 1.32358I
1.58527 + 7.93902I 1.47998 9.11851I
u = 0.60980 + 1.41004I
a = 0.395371 0.895204I
b = 1.05055 1.32358I
1.58527 7.93902I 1.47998 + 9.11851I
u = 0.620927 0.950340I
a = 0.93089 + 1.42975I
b = 0.29948 + 2.01473I
5.22424 + 2.46471I 7.08580 3.09272I
u = 0.620927 + 0.950340I
a = 0.93089 1.42975I
b = 0.29948 2.01473I
5.22424 2.46471I 7.08580 + 3.09272I
u = 0.63602 1.27863I
a = 0.231542 1.300245I
b = 0.95771 2.09589I
3.2415 + 17.6972I 5.12812 9.30452I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.63602 + 1.27863I
a = 0.231542 + 1.300245I
b = 0.95771 + 2.09589I
3.2415 17.6972I 5.12812 + 9.30452I
u = 0.64483 1.27730I
a = 0.076679 0.861553I
b = 0.58724 1.82248I
1.14741 + 5.18553I 5.2495 13.7479I
u = 0.64483 + 1.27730I
a = 0.076679 + 0.861553I
b = 0.58724 + 1.82248I
1.14741 5.18553I 5.2495 + 13.7479I
u = 0.707177 0.220909I
a = 0.453867 0.526514I
b = 0.256498 0.451062I
1.39598 + 1.17736I 3.93052 4.80087I
u = 0.707177 + 0.220909I
a = 0.453867 + 0.526514I
b = 0.256498 + 0.451062I
1.39598 1.17736I 3.93052 + 4.80087I
u = 0.803406 0.165006I
a = 0.116558 + 1.196863I
b = 0.304721 0.274997I
2.78159 + 1.95644I 0.00652 2.42185I
u = 0.803406 + 0.165006I
a = 0.116558 1.196863I
b = 0.304721 + 0.274997I
2.78159 1.95644I 0.00652 + 2.42185I
u = 1.068814 0.000483I
a = 0.326528 + 0.715694I
b = 0.325980 0.339766I
2.91806 + 1.82006I 1.58645 3.73797I
u = 1.068814 + 0.000483I
a = 0.326528 0.715694I
b = 0.325980 + 0.339766I
2.91806 1.82006I 1.58645 + 3.73797I
u = 1.102166 0.453309I
a = 0.530878 0.006354I
b = 0.252027 0.467077I
1.79025 + 1.21167I 15.7321 + 5.2100I
14
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.102166 + 0.453309I
a = 0.530878 + 0.006354I
b = 0.252027 + 0.467077I
1.79025 1.21167I 15.7321 5.2100I
u = 1.114506 0.270069I
a = 0.979424 + 0.528552I
b = 0.309552 0.499642I
0.05288 11.48275I 2.86597 + 7.05522I
u = 1.114506 + 0.270069I
a = 0.979424 0.528552I
b = 0.309552 + 0.499642I
0.05288 + 11.48275I 2.86597 7.05522I
15
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
18
2u
16
+ ··· + u + 1)(u
93
+ 5u
92
+ ··· + 72835u + 5673)
c
2
(u
18
+ 4u
16
+ ··· + u + 1)(u
93
+ 3u
92
+ ··· + 151u 93)
c
3
(u
18
+ 2u
17
+ ··· + 13u + 3)(u
93
+ 5u
92
+ ··· + 201u + 7)
c
4
(u
18
+ 7u
15
+ ··· + 2u + 1)(u
93
+ 5u
92
+ ··· + 20u + 3)
c
5
(u
18
+ 7u
16
+ ··· 5u + 3)(u
93
+ u
92
+ ··· 5563u + 397)
c
6
(u
18
+ 4u
16
+ ··· u + 1)(u
93
+ 3u
92
+ ··· + 151u 93)
c
7
(u
18
3u
17
+ ··· + 4u + 1)(u
93
2u
91
+ ··· 16u 3)
c
8
(u
18
4u
16
+ ··· + 8u + 3)(u
93
+ u
92
+ ··· 588u 239)
c
9
(u
18
8u
17
+ ··· 13u + 3)(u
93
+ 7u
92
+ ··· 37161u + 16439)
c
10
(u
18
+ 7u
16
+ ··· + 5u + 3)(u
93
+ u
92
+ ··· 5563u + 397)
c
11
(u
18
2u
17
+ ··· 13u + 3)(u
93
+ 5u
92
+ ··· + 201u + 7)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
18
4y
17
+ ··· 13y + 1)
(y
93
33y
92
+ ··· + 1446332815y 32182929)
c
2
, c
6
(y
18
+ 8y
17
+ ··· + 15y + 1)(y
93
+ 51y
92
+ ··· + 26707y 8649)
c
3
(y
18
+ 14y
17
+ ··· + 11y + 9)(y
93
+ 69y
92
+ ··· + 4155y 49)
c
4
(y
18
+ 8y
16
+ ··· + 4y + 1)(y
93
+ 3y
92
+ ··· + 58y 9)
c
5
, c
10
(y
18
+ 14y
17
+ ··· + 101y + 9)
(y
93
+ 65y
92
+ ··· 454143y 157609)
c
7
(y
18
+ y
17
+ ··· + 4y + 1)(y
93
4y
92
+ ··· + 94y 9)
c
8
(y
18
8y
17
+ ··· 64y + 9)(y
93
17y
92
+ ··· 6001618y 57121)
c
9
(y
18
+ 8y
17
+ ··· + 77y + 9)
(y
93
9y
92
+ ··· + 5192486461y 270240721)
c
11
(y
18
+ 14y
17
+ ··· + 11y + 9)(y
93
+ 69y
92
+ ··· + 4155y 49)
17