11a
213
(K11a
213
)
1
Arc Sequences
6 1 9 11 8 2 10 3 5 7 4
Solving Sequence
4,11 5,9
10 1 3 2 8 6 7
c
4
c
9
c
11
c
3
c
2
c
8
c
5
c
7
c
1
, c
6
, c
10
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
20
6u
18
+ ··· + u + 1, 21u
19
10u
18
+ ··· + b + 23, 26u
19
16u
18
+ ··· + a + 31i
I
u
2
= hu
92
u
91
+ ··· u 1, 1.67422 × 10
222
u
91
2.57888 × 10
222
u
90
+ ··· + 2.72339 × 10
221
a 4.21029 × 10
222
,
4.59610 × 10
222
u
91
6.94766 × 10
222
u
90
+ ··· + 2.72339 × 10
221
b 1.01661 × 10
223
i
There are 2 irreducible components with 112 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
20
6u
18
+· · ·+u+1, 21u
19
10u
18
+· · ·+b+23, 26u
19
16u
18
+· · ·+a+31i
(i) Arc colorings
a
4
=
1
0
a
11
=
26u
19
+ 16u
18
+ ··· + 25u 31
21u
19
+ 10u
18
+ ··· + 19u 23
a
5
=
u
18
+ 5u
16
+ ··· 5u
2
+ u
12u
19
10u
18
+ ··· 10u + 15
a
9
=
0
u
a
10
=
4u
19
+ 21u
17
+ ··· + 5u
2
+ 4u
21u
19
+ 10u
18
+ ··· + 15u 22
a
1
=
5u
19
+ 6u
18
+ ··· + 6u 8
21u
19
+ 10u
18
+ ··· + 19u 23
a
3
=
1
u
2
a
2
=
20u
19
6u
18
+ ··· 18u + 21
7u
19
+ 5u
18
+ ··· + 7u 6
a
8
=
u
u
3
+ u
a
6
=
5u
19
+ 5u
18
+ ··· + 3u 10
9u
19
7u
18
+ ··· 7u + 11
a
7
=
27u
19
21u
18
+ ··· 20u + 42
27u
19
16u
18
+ ··· 24u + 34
a
7
=
27u
19
21u
18
+ ··· 20u + 42
27u
19
16u
18
+ ··· 24u + 34
(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 = 1.49942 0.05369I
a = 0.069581 0.382174I
b = 0.355541 0.485353I
5.59805 + 1.77453I 16.1663 4.7993I
u = 1.49942 + 0.05369I
a = 0.069581 + 0.382174I
b = 0.355541 + 0.485353I
5.59805 1.77453I 16.1663 + 4.7993I
u = 1.197310 0.297467I
a = 1.058624 0.032070I
b = 0.456437 + 1.060243I
0.69775 5.95580I 9.18910 + 5.63264I
u = 1.197310 + 0.297467I
a = 1.058624 + 0.032070I
b = 0.456437 1.060243I
0.69775 + 5.95580I 9.18910 5.63264I
u = 0.677664 0.019148I
a = 0.40530 + 1.85930I
b = 0.36367 + 1.45018I
1.86097 + 4.40401I 13.93839 1.85189I
u = 0.677664 + 0.019148I
a = 0.40530 1.85930I
b = 0.36367 1.45018I
1.86097 4.40401I 13.93839 + 1.85189I
u = 0.596304 0.330171I
a = 1.61836 0.73634I
b = 0.918717 0.754673I
1.49168 3.77521I 5.50553 + 6.05932I
u = 0.596304 + 0.330171I
a = 1.61836 + 0.73634I
b = 0.918717 + 0.754673I
1.49168 + 3.77521I 5.50553 6.05932I
u = 0.034514 1.030531I
a = 0.30014 + 1.99818I
b = 0.117330 + 0.725388I
2.26277 1.45555I 6.55534 + 4.54077I
u = 0.034514 + 1.030531I
a = 0.30014 1.99818I
b = 0.117330 0.725388I
2.26277 + 1.45555I 6.55534 4.54077I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.020502 1.009614I
a = 0.127758 + 1.255248I
b = 0.111980 + 1.179691I
4.05337 + 2.46535I 3.03812 2.80384I
u = 0.020502 + 1.009614I
a = 0.127758 1.255248I
b = 0.111980 1.179691I
4.05337 2.46535I 3.03812 + 2.80384I
u = 0.739186 0.254368I
a = 0.69748 + 1.41104I
b = 0.11506 + 1.54761I
2.49233 + 2.11946I 10.71875 4.52605I
u = 0.739186 + 0.254368I
a = 0.69748 1.41104I
b = 0.11506 1.54761I
2.49233 2.11946I 10.71875 + 4.52605I
u = 0.834862 0.376425I
a = 2.37873 0.97568I
b = 0.473306 0.639860I
4.11080 + 6.47940I 11.0697 10.5057I
u = 0.834862 + 0.376425I
a = 2.37873 + 0.97568I
b = 0.473306 + 0.639860I
4.11080 6.47940I 11.0697 + 10.5057I
u = 0.989760 0.468800I
a = 0.953403 + 0.600808I
b = 0.46915 + 1.35496I
1.31973 + 1.14762I 5.60070 2.26738I
u = 0.989760 + 0.468800I
a = 0.953403 0.600808I
b = 0.46915 1.35496I
1.31973 1.14762I 5.60070 + 2.26738I
u = 1.42090 0.17879I
a = 0.595500 0.636464I
b = 0.189379 0.489956I
6.67062 3.74046I 13.8287 + 3.4251I
u = 1.42090 + 0.17879I
a = 0.595500 + 0.636464I
b = 0.189379 + 0.489956I
6.67062 + 3.74046I 13.8287 3.4251I
4
II. I
u
2
=
hu
92
u
91
+· · · u 1, 1.67×10
222
u
91
2.58× 10
222
u
90
+· · ·+ 2.72 ×10
221
a
4.21×10
222
, 4.60×10
222
u
91
6.95×10
222
u
90
+· · ·+2.72×10
221
b1.02×10
223
i
(i) Arc colorings
a
4
=
1
0
a
11
=
6.14754u
91
+ 9.46936u
90
+ ··· 20.1319u + 15.4597
16.8764u
91
+ 25.5110u
90
+ ··· 40.6206u + 37.3287
a
5
=
11.4198u
91
18.6265u
90
+ ··· + 26.8279u 28.8392
4.48198u
91
+ 6.96790u
90
+ ··· 21.3086u + 14.8116
a
9
=
0
u
a
10
=
5.28893u
91
7.49597u
90
+ ··· + 10.8597u 8.11508
17.1968u
91
+ 24.5024u
90
+ ··· 44.4107u + 35.8919
a
1
=
10.7288u
91
16.0417u
90
+ ··· + 20.4887u 21.8690
16.8764u
91
+ 25.5110u
90
+ ··· 40.6206u + 37.3287
a
3
=
1
u
2
a
2
=
11.2348u
91
+ 18.9978u
90
+ ··· 36.0229u + 34.6600
2.18240u
91
2.39881u
90
+ ··· + 15.0995u 5.11898
a
8
=
u
u
3
+ u
a
6
=
13.4484u
91
22.4378u
90
+ ··· + 32.7548u 36.7310
2.53485u
91
+ 3.73696u
90
+ ··· 15.6276u + 8.70253
a
7
=
4.97114u
91
+ 5.69526u
90
+ ··· 16.4325u + 7.23098
14.9240u
91
+ 21.0249u
90
+ ··· 36.6876u + 27.4447
a
7
=
4.97114u
91
+ 5.69526u
90
+ ··· 16.4325u + 7.23098
14.9240u
91
+ 21.0249u
90
+ ··· 36.6876u + 27.4447
(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 = 1.67230 0.27921I
a = 0.154066 0.235835I
b = 0.280703 0.948609I
5.78137 + 4.82781I 9.17282 7.04724I
u = 1.67230 + 0.27921I
a = 0.154066 + 0.235835I
b = 0.280703 + 0.948609I
5.78137 4.82781I 9.17282 + 7.04724I
u = 1.332467 0.247847I
a = 0.115541 + 0.394237I
b = 0.891796 0.453277I
9.35815 2.58044I 16.1597 + 1.0589I
u = 1.332467 + 0.247847I
a = 0.115541 0.394237I
b = 0.891796 + 0.453277I
9.35815 + 2.58044I 16.1597 1.0589I
u = 1.32427 0.73631I
a = 0.727070 + 1.140965I
b = 0.573497 + 1.208662I
0.67671 11.20377I 6.92619 + 7.92555I
u = 1.32427 + 0.73631I
a = 0.727070 1.140965I
b = 0.573497 1.208662I
0.67671 + 11.20377I 6.92619 7.92555I
u = 1.239092 0.559867I
a = 0.152181 0.270942I
b = 0.719530 0.877837I
5.59330 0.95533I 12.38774 + 1.72132I
u = 1.239092 + 0.559867I
a = 0.152181 + 0.270942I
b = 0.719530 + 0.877837I
5.59330 + 0.95533I 12.38774 1.72132I
u = 1.214927 0.377226I
a = 0.80172 + 1.27470I
b = 0.341035 + 1.090414I
2.70208 3.30839I 9.28440 + 3.89929I
u = 1.214927 + 0.377226I
a = 0.80172 1.27470I
b = 0.341035 1.090414I
2.70208 + 3.30839I 9.28440 3.89929I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.209365 0.632518I
a = 0.79326 1.31851I
b = 0.62241 1.34712I
0.21837 11.40935I 7.13984 + 6.72897I
u = 1.209365 + 0.632518I
a = 0.79326 + 1.31851I
b = 0.62241 + 1.34712I
0.21837 + 11.40935I 7.13984 6.72897I
u = 1.173999 0.359773I
a = 1.68334 + 0.22751I
b = 0.226488 + 1.189200I
1.14890 7.16658I 9.47049 + 10.11507I
u = 1.173999 + 0.359773I
a = 1.68334 0.22751I
b = 0.226488 1.189200I
1.14890 + 7.16658I 9.47049 10.11507I
u = 1.154864 0.486853I
a = 0.093143 + 0.220654I
b = 1.38485 0.30163I
6.02464 10.31346I 11.8446 + 8.5679I
u = 1.154864 + 0.486853I
a = 0.093143 0.220654I
b = 1.38485 + 0.30163I
6.02464 + 10.31346I 11.8446 8.5679I
u = 1.138519 0.338863I
a = 1.005564 + 0.568814I
b = 0.63181 + 1.36847I
0.30466 3.87854I 8.12512 + 2.55427I
u = 1.138519 + 0.338863I
a = 1.005564 0.568814I
b = 0.63181 1.36847I
0.30466 + 3.87854I 8.12512 2.55427I
u = 1.021633 0.504770I
a = 0.777160 0.617758I
b = 0.86024 1.12424I
0.75507 2.54974I 7.36280 + 4.61770I
u = 1.021633 + 0.504770I
a = 0.777160 + 0.617758I
b = 0.86024 + 1.12424I
0.75507 + 2.54974I 7.36280 4.61770I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.020121 0.571742I
a = 0.461890 1.235264I
b = 0.522961 0.901176I
2.64428 2.01886I 9.46898 + 3.13006I
u = 1.020121 + 0.571742I
a = 0.461890 + 1.235264I
b = 0.522961 + 0.901176I
2.64428 + 2.01886I 9.46898 3.13006I
u = 1.002299 0.321909I
a = 0.249869 + 0.034760I
b = 0.832463 + 0.052849I
0.877139 0.912194I 7.35158 + 0.85240I
u = 1.002299 + 0.321909I
a = 0.249869 0.034760I
b = 0.832463 0.052849I
0.877139 + 0.912194I 7.35158 0.85240I
u = 0.899956 0.428154I
a = 1.86646 0.40818I
b = 0.010890 0.885762I
1.37334 + 1.58152I 5.02157 2.18933I
u = 0.899956 + 0.428154I
a = 1.86646 + 0.40818I
b = 0.010890 + 0.885762I
1.37334 1.58152I 5.02157 + 2.18933I
u = 0.695203 0.103878I
a = 1.92596 0.22320I
b = 0.465075 0.827446I
0.57404 1.64965I 7.09706 + 2.07909I
u = 0.695203 + 0.103878I
a = 1.92596 + 0.22320I
b = 0.465075 + 0.827446I
0.57404 + 1.64965I 7.09706 2.07909I
u = 0.656303 0.240252I
a = 0.29231 2.73702I
b = 0.182748 1.312792I
2.33729 4.89796I 3.19840 + 10.75719I
u = 0.656303 + 0.240252I
a = 0.29231 + 2.73702I
b = 0.182748 + 1.312792I
2.33729 + 4.89796I 3.19840 10.75719I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.461263 0.018499I
a = 0.762495 + 0.334184I
b = 0.02599 + 1.55300I
2.80824 + 1.36127I 5.48968 + 3.29803I
u = 0.461263 + 0.018499I
a = 0.762495 0.334184I
b = 0.02599 1.55300I
2.80824 1.36127I 5.48968 3.29803I
u = 0.45586 1.35944I
a = 0.194735 + 1.142769I
b = 0.341442 + 1.074565I
3.67608 + 3.90107I 7.31663 7.35287I
u = 0.45586 + 1.35944I
a = 0.194735 1.142769I
b = 0.341442 1.074565I
3.67608 3.90107I 7.31663 + 7.35287I
u = 0.385836 0.811407I
a = 0.56371 1.67639I
b = 0.693377 0.983781I
2.86301 4.52369I 11.40560 + 5.17779I
u = 0.385836 + 0.811407I
a = 0.56371 + 1.67639I
b = 0.693377 + 0.983781I
2.86301 + 4.52369I 11.40560 5.17779I
u = 0.379215
a = 0.239425
b = 0.409798
0.736675 13.9254
u = 0.363192 1.037263I
a = 0.58303 1.39249I
b = 0.385879 1.192381I
2.46469 + 5.43660I 4.15642 3.04128I
u = 0.363192 + 1.037263I
a = 0.58303 + 1.39249I
b = 0.385879 + 1.192381I
2.46469 5.43660I 4.15642 + 3.04128I
u = 0.188195 0.589028I
a = 0.26170 1.56174I
b = 0.909144 + 0.168813I
3.25055 + 5.97769I 10.01627 5.34702I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.188195 + 0.589028I
a = 0.26170 + 1.56174I
b = 0.909144 0.168813I
3.25055 5.97769I 10.01627 + 5.34702I
u = 0.181391 0.540978I
a = 1.22260 0.78233I
b = 0.433458 0.123479I
0.74698 2.02785I 4.64089 + 2.72591I
u = 0.181391 + 0.540978I
a = 1.22260 + 0.78233I
b = 0.433458 + 0.123479I
0.74698 + 2.02785I 4.64089 2.72591I
u = 0.167352 0.427245I
a = 0.895012 0.267505I
b = 0.133945 1.282941I
2.72282 1.44940I 5.16116 0.05224I
u = 0.167352 + 0.427245I
a = 0.895012 + 0.267505I
b = 0.133945 + 1.282941I
2.72282 + 1.44940I 5.16116 + 0.05224I
u = 0.058014 1.220802I
a = 0.10225 + 1.58396I
b = 0.174273 + 0.678980I
1.95041 1.39231I 19.4755 0.8963I
u = 0.058014 + 1.220802I
a = 0.10225 1.58396I
b = 0.174273 0.678980I
1.95041 + 1.39231I 19.4755 + 0.8963I
u = 0.034570 0.494786I
a = 1.08988 + 1.14127I
b = 0.111055 0.302643I
1.16594 1.89895I 3.75763 + 6.23152I
u = 0.034570 + 0.494786I
a = 1.08988 1.14127I
b = 0.111055 + 0.302643I
1.16594 + 1.89895I 3.75763 6.23152I
u = 0.243416 1.236134I
a = 0.327271 1.280143I
b = 0.489603 1.275897I
0.85125 10.84921I 6.90992 + 7.84011I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.243416 + 1.236134I
a = 0.327271 + 1.280143I
b = 0.489603 + 1.275897I
0.85125 + 10.84921I 6.90992 7.84011I
u = 0.288297 0.213692I
a = 0.415516 + 0.327919I
b = 0.45259 1.47014I
2.55253 4.41767I 1.66349 + 3.27220I
u = 0.288297 + 0.213692I
a = 0.415516 0.327919I
b = 0.45259 + 1.47014I
2.55253 + 4.41767I 1.66349 3.27220I
u = 0.325891 0.743657I
a = 0.386836 0.561978I
b = 0.791843 0.487373I
4.17931 0.87104I 12.11508 + 0.91752I
u = 0.325891 + 0.743657I
a = 0.386836 + 0.561978I
b = 0.791843 + 0.487373I
4.17931 + 0.87104I 12.11508 0.91752I
u = 0.359604 0.513145I
a = 0.99975 + 1.12966I
b = 0.10619 + 1.59127I
2.51053 + 4.14874I 5.33756 6.38441I
u = 0.359604 + 0.513145I
a = 0.99975 1.12966I
b = 0.10619 1.59127I
2.51053 4.14874I 5.33756 + 6.38441I
u = 0.593320 1.152025I
a = 0.435187 + 1.186650I
b = 0.187453 + 1.138275I
4.85118 + 0.81446I 2.49749 + 0.89065I
u = 0.593320 + 1.152025I
a = 0.435187 1.186650I
b = 0.187453 1.138275I
4.85118 0.81446I 2.49749 0.89065I
u = 0.635484 0.127279I
a = 3.54290 + 0.44348I
b = 0.057611 + 0.532891I
3.86440 + 5.70624I 8.10788 2.00819I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.635484 + 0.127279I
a = 3.54290 0.44348I
b = 0.057611 0.532891I
3.86440 5.70624I 8.10788 + 2.00819I
u = 0.687266 0.373381I
a = 0.99465 + 2.10243I
b = 0.127220 + 1.324109I
3.27963 + 2.01059I 0.68053 2.17901I
u = 0.687266 + 0.373381I
a = 0.99465 2.10243I
b = 0.127220 1.324109I
3.27963 2.01059I 0.68053 + 2.17901I
u = 0.781885 0.059041I
a = 1.51529 0.00607I
b = 1.007019 + 0.764873I
2.08061 3.09402I 11.78916 + 0.16171I
u = 0.781885 + 0.059041I
a = 1.51529 + 0.00607I
b = 1.007019 0.764873I
2.08061 + 3.09402I 11.78916 0.16171I
u = 0.802043 0.489858I
a = 1.34130 + 1.24627I
b = 0.146106 + 1.163068I
2.86848 + 1.82626I 1.16065 4.60638I
u = 0.802043 + 0.489858I
a = 1.34130 1.24627I
b = 0.146106 1.163068I
2.86848 1.82626I 1.16065 + 4.60638I
u = 1.026570 0.575028I
a = 0.860637 + 0.703361I
b = 0.50001 + 1.55156I
0.762842 + 0.362539I 10.22819 + 3.23666I
u = 1.026570 + 0.575028I
a = 0.860637 0.703361I
b = 0.50001 1.55156I
0.762842 0.362539I 10.22819 3.23666I
u = 1.093281 0.155448I
a = 0.138564 0.249946I
b = 0.797009 0.561932I
3.87053 2.88480I 11.21992 + 4.69459I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.093281 + 0.155448I
a = 0.138564 + 0.249946I
b = 0.797009 + 0.561932I
3.87053 + 2.88480I 11.21992 4.69459I
u = 1.098343 0.736969I
a = 0.68622 1.30403I
b = 0.653792 0.759457I
5.90913 + 6.23883I 14.1015 7.2126I
u = 1.098343 + 0.736969I
a = 0.68622 + 1.30403I
b = 0.653792 + 0.759457I
5.90913 6.23883I 14.1015 + 7.2126I
u = 1.098716 0.346642I
a = 0.041347 + 0.241799I
b = 1.258098 0.118180I
4.08734 + 4.93913I 10.54441 4.56759I
u = 1.098716 + 0.346642I
a = 0.041347 0.241799I
b = 1.258098 + 0.118180I
4.08734 4.93913I 10.54441 + 4.56759I
u = 1.123504 0.377477I
a = 0.856545 0.447867I
b = 0.97324 1.09916I
0.05662 + 7.54903I 7.61957 10.58325I
u = 1.123504 + 0.377477I
a = 0.856545 + 0.447867I
b = 0.97324 + 1.09916I
0.05662 7.54903I 7.61957 + 10.58325I
u = 1.173858 0.371541I
a = 1.23328 1.59162I
b = 0.536128 1.159261I
7.03906 + 7.80694I 12.7669 7.1805I
u = 1.173858 + 0.371541I
a = 1.23328 + 1.59162I
b = 0.536128 + 1.159261I
7.03906 7.80694I 12.7669 + 7.1805I
u = 1.175932 0.472649I
a = 0.28578 1.55829I
b = 0.347606 0.779093I
6.23055 2.15767I 11.79836 0.90491I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.175932 + 0.472649I
a = 0.28578 + 1.55829I
b = 0.347606 + 0.779093I
6.23055 + 2.15767I 11.79836 + 0.90491I
u = 1.177985 0.372709I
a = 1.248705 + 0.245539I
b = 0.130525 0.776176I
0.68335 + 4.74170I 8.08190 1.10088I
u = 1.177985 + 0.372709I
a = 1.248705 0.245539I
b = 0.130525 + 0.776176I
0.68335 4.74170I 8.08190 + 1.10088I
u = 1.178076 0.698481I
a = 0.698669 + 1.220536I
b = 0.482051 + 1.253937I
2.77259 + 5.73769I 3.79433 3.76204I
u = 1.178076 + 0.698481I
a = 0.698669 1.220536I
b = 0.482051 1.253937I
2.77259 5.73769I 3.79433 + 3.76204I
u = 1.200469 0.459585I
a = 0.238456 + 0.072672I
b = 0.851364 + 0.233369I
2.24388 + 5.89877I 8.97666 5.56060I
u = 1.200469 + 0.459585I
a = 0.238456 0.072672I
b = 0.851364 0.233369I
2.24388 5.89877I 8.97666 + 5.56060I
u = 1.30994
a = 0.355084
b = 0.647346
5.83140 16.0269
u = 1.32343 0.67031I
a = 0.81937 1.16088I
b = 0.71065 1.35618I
2.5744 + 17.5099I 9.32097 9.82682I
u = 1.32343 + 0.67031I
a = 0.81937 + 1.16088I
b = 0.71065 + 1.35618I
2.5744 17.5099I 9.32097 + 9.82682I
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.62911 0.00058I
a = 0.190173 + 0.225218I
b = 0.011057 + 0.713112I
5.05252 + 1.36520I 5.73934 + 2.45909I
u = 1.62911 + 0.00058I
a = 0.190173 0.225218I
b = 0.011057 0.713112I
5.05252 1.36520I 5.73934 2.45909I
14
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
20
5u
18
+ ··· 2u + 1)(u
92
+ u
91
+ ··· 54u 143)
c
2
(u
20
+ 10u
19
+ ··· + 12u + 1)(u
92
+ 41u
91
+ ··· + 295208u + 20449)
c
3
(u
20
6u
18
+ ··· + u + 1)(u
92
+ u
91
+ ··· + u 1)
c
4
(u
20
+ 2u
19
+ ··· + 8u
2
+ 1)(u
92
+ 3u
91
+ ··· 442u 347)
c
5
(u
20
4u
19
+ ··· 4u + 1)(u
92
+ 3u
91
+ ··· 678u + 68)
c
6
(u
20
5u
18
+ ··· + 2u + 1)(u
92
+ u
91
+ ··· 54u 143)
c
7
(u
20
+ 4u
19
+ ··· + 4u + 1)(u
92
+ 3u
91
+ ··· + 734u + 79)
c
8
(u
20
6u
18
+ ··· u + 1)(u
92
+ u
91
+ ··· + u 1)
c
9
(u
20
+ 4u
17
+ ··· + u + 1)(u
92
+ u
91
+ ··· 3505u 387)
c
10
(u
20
4u
19
+ ··· 4u + 1)(u
92
+ 3u
91
+ ··· + 734u + 79)
c
11
(u
20
2u
19
+ ··· + 8u
2
+ 1)(u
92
+ 3u
91
+ ··· 442u 347)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
20
10y
19
+ ··· 12y + 1)(y
92
41y
91
+ ··· 295208y + 20449)
c
2
(y
20
+ 10y
19
+ ··· + 4y + 1)
(y
92
+ 31y
91
+ ··· 131051768y + 418161601)
c
3
, c
8
(y
20
12y
19
+ ··· 11y + 1)(y
92
51y
91
+ ··· 27y + 1)
c
4
, c
11
(y
20
+ 18y
19
+ ··· + 16y + 1)
(y
92
+ 59y
91
+ ··· + 3735452y + 120409)
c
5
(y
20
2y
19
+ ··· + 8y + 1)(y
92
17y
91
+ ··· + 950500y + 4624)
c
6
(y
20
10y
19
+ ··· 12y + 1)(y
92
41y
91
+ ··· 295208y + 20449)
c
7
, c
10
(y
20
+ 8y
19
+ ··· + 12y + 1)(y
92
+ 49y
91
+ ··· 26204y + 6241)
c
9
(y
20
8y
17
+ ··· + 17y + 1)(y
92
11y
91
+ ··· 5497819y + 149769)
16