11a
267
(K11a
267
)
1
Arc Sequences
10 9 1 8 2 3 4 11 6 5 7
Solving Sequence
4,7
8
5,11
9 1 3 2 6 10
c
7
c
4
c
8
c
11
c
3
c
2
c
6
c
10
c
1
, c
5
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
20
2u
19
+ ··· 9u 1, 33627831u
19
77174984u
18
+ ··· + 21120991b 17202656,
29316743u
19
+ 57771701u
18
+ ··· + 21120991a + 282350236i
I
u
2
= hu
115
+ u
114
+ ··· 541u + 31,
6.10437 × 10
407
u
114
1.42278 × 10
408
u
113
+ ··· + 1.19387 × 10
407
b + 9.47292 × 10
408
,
2.77971 × 10
408
u
114
1.34645 × 10
409
u
113
+ ··· + 3.70100 × 10
408
a 5.14432 × 10
410
i
There are 2 irreducible components with 135 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
2u
19
+ · · · 9u 1, 3.36 × 10
7
u
19
7.72 × 10
7
u
18
+ · · · + 2.11 ×
10
7
b1.72×10
7
, 2.93×10
7
u
19
+5.78×10
7
u
18
+· · ·+2.11×10
7
a+2.82×10
8
i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
8
=
u
u
a
5
=
u
2
+ 1
u
2
a
11
=
1.38804u
19
2.73527u
18
+ ··· 25.7631u 13.3682
1.59215u
19
+ 3.65395u
18
+ ··· + 11.3494u + 0.814481
a
9
=
3.10784u
19
6.79066u
18
+ ··· 50.4490u 19.6310
0.338564u
19
1.11917u
18
+ ··· 6.03246u 1.58372
a
1
=
1.38804u
19
2.73527u
18
+ ··· 25.7631u 13.3682
0.971085u
19
+ 2.30229u
18
+ ··· + 9.59412u + 0.773679
a
3
=
0.530034u
19
+ 1.59694u
18
+ ··· + 0.586442u 3.08080
0.859047u
19
+ 2.23407u
18
+ ··· 1.65110u 0.504514
a
2
=
0.864413u
19
+ 2.28668u
18
+ ··· + 15.6519u + 6.98776
0.215715u
19
+ 1.71327u
18
+ ··· + 18.7905u + 2.67442
a
6
=
2.25081u
19
6.02722u
18
+ ··· 17.3732u 3.66420
1.44034u
19
2.86617u
18
+ ··· 7.97268u 1.57572
a
10
=
1.10164u
19
1.55214u
18
+ ··· 23.1119u 13.9638
0.866660u
19
+ 1.83212u
18
+ ··· + 3.53058u 0.166706
a
10
=
1.10164u
19
1.55214u
18
+ ··· 23.1119u 13.9638
0.866660u
19
+ 1.83212u
18
+ ··· + 3.53058u 0.166706
(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 = 1.44669 0.50300I
a = 0.533296 0.043409I
b = 1.41270 + 0.31875I
4.37235 + 4.19669I 8.95096 + 4.21528I
u = 1.44669 + 0.50300I
a = 0.533296 + 0.043409I
b = 1.41270 0.31875I
4.37235 4.19669I 8.95096 4.21528I
u = 1.197552 0.212204I
a = 0.118581 1.102289I
b = 0.664398 1.062837I
2.99506 + 0.84547I 1.193245 + 0.488606I
u = 1.197552 + 0.212204I
a = 0.118581 + 1.102289I
b = 0.664398 + 1.062837I
2.99506 0.84547I 1.193245 0.488606I
u = 0.841202 0.152388I
a = 1.94967 + 1.41393I
b = 2.23142 + 1.27388I
1.17521 + 2.23291I 3.6997 + 58.8725I
u = 0.841202 + 0.152388I
a = 1.94967 1.41393I
b = 2.23142 1.27388I
1.17521 2.23291I 3.6997 58.8725I
u = 0.496142 0.296522I
a = 1.14328 1.02528I
b = 0.096383 + 1.093583I
2.17976 + 4.02285I 4.59414 6.39414I
u = 0.496142 + 0.296522I
a = 1.14328 + 1.02528I
b = 0.096383 1.093583I
2.17976 4.02285I 4.59414 + 6.39414I
u = 0.266975 0.940111I
a = 1.011439 + 0.342738I
b = 0.186761 + 0.144383I
1.74507 + 4.46508I 0.88102 6.28026I
u = 0.266975 + 0.940111I
a = 1.011439 0.342738I
b = 0.186761 0.144383I
1.74507 4.46508I 0.88102 + 6.28026I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.147575
a = 9.27309
b = 0.626737
2.12247 23.5211
u = 0.692160 0.744150I
a = 0.649178 + 0.377546I
b = 0.935419 0.425284I
1.65711 2.96061I 0.71565 + 3.69109I
u = 0.692160 + 0.744150I
a = 0.649178 0.377546I
b = 0.935419 + 0.425284I
1.65711 + 2.96061I 0.71565 3.69109I
u = 1.032294 0.211816I
a = 0.924968 + 0.136732I
b = 2.85595 + 0.22238I
1.83617 9.14635I 7.52738 + 8.39852I
u = 1.032294 + 0.211816I
a = 0.924968 0.136732I
b = 2.85595 0.22238I
1.83617 + 9.14635I 7.52738 8.39852I
u = 1.24034
a = 1.27036
b = 3.21493
6.02419 7.53743
u = 1.43906 0.45488I
a = 0.896417 + 0.534535I
b = 1.82517 + 0.97543I
3.60701 9.54940I 5.95378 + 8.39911I
u = 1.43906 + 0.45488I
a = 0.896417 0.534535I
b = 1.82517 0.97543I
3.60701 + 9.54940I 5.95378 8.39911I
u = 1.53866 0.46556I
a = 0.155130 + 0.068750I
b = 0.262933 0.064043I
2.32723 + 6.31534I 0.90446 5.70657I
u = 1.53866 + 0.46556I
a = 0.155130 0.068750I
b = 0.262933 + 0.064043I
2.32723 6.31534I 0.90446 + 5.70657I
4
II. I
u
2
= hu
115
+ u
114
+ · · · 541u + 31, 6.10 × 10
407
u
114
1.42 ×
10
408
u
113
+ · · · + 1.19 × 10
407
b + 9.47 × 10
408
, 2.78 × 10
408
u
114
1.35 ×
10
409
u
113
+ · · · + 3.70 × 10
408
a 5.14 × 10
410
i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
8
=
u
u
a
5
=
u
2
+ 1
u
2
a
11
=
0.751069u
114
+ 3.63807u
113
+ ··· 1803.12u + 138.998
5.11309u
114
+ 11.9174u
113
+ ··· + 1455.66u 79.3462
a
9
=
1.72454u
114
1.15043u
113
+ ··· 3637.16u + 265.536
3.43149u
114
+ 7.98843u
113
+ ··· + 808.926u 41.9872
a
1
=
0.751069u
114
+ 3.63807u
113
+ ··· 1803.12u + 138.998
0.940671u
114
+ 2.60979u
113
+ ··· 82.9241u + 10.1507
a
3
=
4.01571u
114
+ 7.88037u
113
+ ··· + 2406.11u 145.167
0.710886u
114
+ 1.85435u
113
+ ··· + 100.589u 4.64088
a
2
=
4.61437u
114
+ 7.66524u
113
+ ··· + 4520.81u 308.804
0.226193u
114
+ 0.0478633u
113
+ ··· 305.247u + 19.8316
a
6
=
1.48111u
114
3.05412u
113
+ ··· 750.477u + 49.8942
0.295513u
114
+ 1.13541u
113
+ ··· 316.387u + 23.1039
a
10
=
1.48386u
114
0.363324u
113
+ ··· 3583.15u + 254.753
1.78407u
114
+ 4.44567u
113
+ ··· + 204.021u 5.68232
a
10
=
1.48386u
114
0.363324u
113
+ ··· 3583.15u + 254.753
1.78407u
114
+ 4.44567u
113
+ ··· + 204.021u 5.68232
(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 = 1.72997 0.85271I
a = 0.161743 + 0.136430I
b = 0.427549 + 0.226509I
2.59067 6.42913I 24.9721 + 19.1227I
u = 1.72997 + 0.85271I
a = 0.161743 0.136430I
b = 0.427549 0.226509I
2.59067 + 6.42913I 24.9721 19.1227I
u = 1.66955 0.33485I
a = 0.259487 + 0.372941I
b = 0.505406 + 0.897442I
1.36802 + 5.96391I 1.81936 10.95316I
u = 1.66955 + 0.33485I
a = 0.259487 0.372941I
b = 0.505406 0.897442I
1.36802 5.96391I 1.81936 + 10.95316I
u = 1.40857 0.55453I
a = 0.902273 0.073355I
b = 1.75878 0.35772I
7.15825 + 10.74024I 9.22081 9.27107I
u = 1.40857 + 0.55453I
a = 0.902273 + 0.073355I
b = 1.75878 + 0.35772I
7.15825 10.74024I 9.22081 + 9.27107I
u = 1.39263 0.48528I
a = 1.014476 + 0.398701I
b = 2.14812 + 0.98401I
4.76522 + 10.84948I 8.96250 10.91890I
u = 1.39263 + 0.48528I
a = 1.014476 0.398701I
b = 2.14812 0.98401I
4.76522 10.84948I 8.96250 + 10.91890I
u = 1.38981 0.31379I
a = 0.882458 + 0.171693I
b = 1.88952 + 0.68140I
5.68827 + 4.71363I 12.52933 5.22646I
u = 1.38981 + 0.31379I
a = 0.882458 0.171693I
b = 1.88952 0.68140I
5.68827 4.71363I 12.52933 + 5.22646I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.37435 0.51642I
a = 1.015683 0.461382I
b = 1.97377 0.71663I
2.21036 + 10.96437I 1.65995 10.80792I
u = 1.37435 + 0.51642I
a = 1.015683 + 0.461382I
b = 1.97377 + 0.71663I
2.21036 10.96437I 1.65995 + 10.80792I
u = 1.333282 0.452494I
a = 0.793967 + 0.289365I
b = 2.08943 + 0.26511I
5.87061 + 6.65094I 9.86079 6.27526I
u = 1.333282 + 0.452494I
a = 0.793967 0.289365I
b = 2.08943 0.26511I
5.87061 6.65094I 9.86079 + 6.27526I
u = 1.325476 0.048077I
a = 0.570001 1.152179I
b = 0.959276 0.953865I
5.74046 + 5.29797I 10.51842 6.14585I
u = 1.325476 + 0.048077I
a = 0.570001 + 1.152179I
b = 0.959276 + 0.953865I
5.74046 5.29797I 10.51842 + 6.14585I
u = 1.25526
a = 1.11324
b = 2.75523
6.77454 16.8591
u = 1.252022 0.015728I
a = 1.090618 + 0.288934I
b = 2.47569 0.03643I
6.73188 + 0.04543I 15.1056 + 0.2590I
u = 1.252022 + 0.015728I
a = 1.090618 0.288934I
b = 2.47569 + 0.03643I
6.73188 0.04543I 15.1056 0.2590I
u = 1.239750 0.145734I
a = 0.160444 0.299119I
b = 0.114298 + 1.140472I
5.14620 + 4.26050I 11.49544 4.93182I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.239750 + 0.145734I
a = 0.160444 + 0.299119I
b = 0.114298 1.140472I
5.14620 4.26050I 11.49544 + 4.93182I
u = 1.218175 0.162040I
a = 0.524412 0.314950I
b = 1.47728 + 0.66657I
4.77314 + 3.86367I 10.27258 6.61596I
u = 1.218175 + 0.162040I
a = 0.524412 + 0.314950I
b = 1.47728 0.66657I
4.77314 3.86367I 10.27258 + 6.61596I
u = 1.204515 0.150017I
a = 1.31595 + 1.22694I
b = 2.18895 + 0.80819I
3.91673 + 9.84311I 9.00179 9.55963I
u = 1.204515 + 0.150017I
a = 1.31595 1.22694I
b = 2.18895 0.80819I
3.91673 9.84311I 9.00179 + 9.55963I
u = 1.179791 0.359556I
a = 0.991073 0.459592I
b = 2.34074 0.56164I
0.14146 + 6.51555I 1.52632 7.33313I
u = 1.179791 + 0.359556I
a = 0.991073 + 0.459592I
b = 2.34074 + 0.56164I
0.14146 6.51555I 1.52632 + 7.33313I
u = 1.116432 0.425627I
a = 1.49053 + 0.45111I
b = 2.00066 + 0.93023I
0.92457 + 10.59060I 1.65440 10.60412I
u = 1.116432 + 0.425627I
a = 1.49053 0.45111I
b = 2.00066 0.93023I
0.92457 10.59060I 1.65440 + 10.60412I
u = 1.099633 0.379841I
a = 0.999422 0.630349I
b = 1.44745 0.28027I
0.15323 + 5.27402I 1.13501 7.65888I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.099633 + 0.379841I
a = 0.999422 + 0.630349I
b = 1.44745 + 0.28027I
0.15323 5.27402I 1.13501 + 7.65888I
u = 0.991543 0.010287I
a = 0.351568 1.080681I
b = 0.512635 + 0.804480I
0.82850 + 3.65420I 2.04191 4.10976I
u = 0.991543 + 0.010287I
a = 0.351568 + 1.080681I
b = 0.512635 0.804480I
0.82850 3.65420I 2.04191 + 4.10976I
u = 0.878512 0.105130I
a = 0.451108 + 0.305132I
b = 1.09392 + 1.45767I
0.81168 + 4.16631I 3.39964 5.53940I
u = 0.878512 + 0.105130I
a = 0.451108 0.305132I
b = 1.09392 1.45767I
0.81168 4.16631I 3.39964 + 5.53940I
u = 0.854965 0.408531I
a = 0.299827 0.411766I
b = 1.319625 0.251858I
2.08760 + 1.97298I 4.56009 3.59828I
u = 0.854965 + 0.408531I
a = 0.299827 + 0.411766I
b = 1.319625 + 0.251858I
2.08760 1.97298I 4.56009 + 3.59828I
u = 0.812804 0.602814I
a = 0.552623 0.586865I
b = 0.852553 + 0.291524I
2.33628 + 2.44376I 5.31370 + 1.08540I
u = 0.812804 + 0.602814I
a = 0.552623 + 0.586865I
b = 0.852553 0.291524I
2.33628 2.44376I 5.31370 1.08540I
u = 0.400510 0.699214I
a = 1.52375 + 0.00754I
b = 0.231905 + 0.075413I
1.19029 + 5.19950I 4.7693 13.8666I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.400510 + 0.699214I
a = 1.52375 0.00754I
b = 0.231905 0.075413I
1.19029 5.19950I 4.7693 + 13.8666I
u = 0.368048 1.182950I
a = 0.744567 + 0.082587I
b = 0.192597 0.068228I
2.85359 + 3.71553I 8.03496 7.45518I
u = 0.368048 + 1.182950I
a = 0.744567 0.082587I
b = 0.192597 + 0.068228I
2.85359 3.71553I 8.03496 + 7.45518I
u = 0.332655 0.287893I
a = 0.668413 1.089213I
b = 0.644338 0.671371I
1.40763 1.80669I 0.93148 + 2.38476I
u = 0.332655 + 0.287893I
a = 0.668413 + 1.089213I
b = 0.644338 + 0.671371I
1.40763 + 1.80669I 0.93148 2.38476I
u = 0.308600 0.849572I
a = 0.703996 + 1.106996I
b = 0.429478 + 0.390095I
3.44636 5.96058I 2.06942 + 8.59270I
u = 0.308600 + 0.849572I
a = 0.703996 1.106996I
b = 0.429478 0.390095I
3.44636 + 5.96058I 2.06942 8.59270I
u = 0.275294 0.889046I
a = 0.704075 0.545494I
b = 0.116647 0.644579I
2.19346 0.70570I 4.84022 + 0.02047I
u = 0.275294 + 0.889046I
a = 0.704075 + 0.545494I
b = 0.116647 + 0.644579I
2.19346 + 0.70570I 4.84022 0.02047I
u = 0.170606 0.730612I
a = 1.00531 1.18593I
b = 0.294379 0.008950I
2.95739 2.49453I 5.36586 + 2.65712I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.170606 + 0.730612I
a = 1.00531 + 1.18593I
b = 0.294379 + 0.008950I
2.95739 + 2.49453I 5.36586 2.65712I
u = 0.136316 1.159059I
a = 0.853361 0.556548I
b = 0.0418745 + 0.0923050I
1.25637 + 13.65457I 2.05369 9.60985I
u = 0.136316 + 1.159059I
a = 0.853361 + 0.556548I
b = 0.0418745 0.0923050I
1.25637 13.65457I 2.05369 + 9.60985I
u = 0.095002 1.282772I
a = 0.028963 0.514286I
b = 0.189217 + 0.023721I
2.71246 4.38038I 13.6004 + 5.9787I
u = 0.095002 + 1.282772I
a = 0.028963 + 0.514286I
b = 0.189217 0.023721I
2.71246 + 4.38038I 13.6004 5.9787I
u = 0.042104 0.186487I
a = 0.02324 5.52662I
b = 0.937795 + 0.789027I
0.32279 8.28648I 2.15800 + 6.43851I
u = 0.042104 + 0.186487I
a = 0.02324 + 5.52662I
b = 0.937795 0.789027I
0.32279 + 8.28648I 2.15800 6.43851I
u = 0.043484 1.130638I
a = 0.704056 0.639168I
b = 0.149794 0.115775I
2.25517 5.21998I 2.2268 + 14.0999I
u = 0.043484 + 1.130638I
a = 0.704056 + 0.639168I
b = 0.149794 + 0.115775I
2.25517 + 5.21998I 2.2268 14.0999I
u = 0.132701 0.504914I
a = 1.372321 + 0.247874I
b = 0.033195 0.612066I
0.65057 1.66192I 4.17531 + 3.71899I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.132701 + 0.504914I
a = 1.372321 0.247874I
b = 0.033195 + 0.612066I
0.65057 + 1.66192I 4.17531 3.71899I
u = 0.137593 1.074432I
a = 0.868144 + 0.497493I
b = 0.120677 0.157197I
0.01097 5.35830I 6.99539 + 10.50635I
u = 0.137593 + 1.074432I
a = 0.868144 0.497493I
b = 0.120677 + 0.157197I
0.01097 + 5.35830I 6.99539 10.50635I
u = 0.173211 0.719426I
a = 1.37326 0.95290I
b = 0.143669 0.164570I
4.61264 2.63225I 4.37712 + 3.78930I
u = 0.173211 + 0.719426I
a = 1.37326 + 0.95290I
b = 0.143669 + 0.164570I
4.61264 + 2.63225I 4.37712 3.78930I
u = 0.205734 0.872516I
a = 0.694336 + 0.621046I
b = 0.360877 0.331888I
1.32811 1.88479I 7.34520 + 7.13647I
u = 0.205734 + 0.872516I
a = 0.694336 0.621046I
b = 0.360877 + 0.331888I
1.32811 + 1.88479I 7.34520 7.13647I
u = 0.266690 0.046449I
a = 4.17075 + 0.64918I
b = 0.309329 0.343365I
2.28848 + 0.02392I 17.2666 + 1.1883I
u = 0.266690 + 0.046449I
a = 4.17075 0.64918I
b = 0.309329 + 0.343365I
2.28848 0.02392I 17.2666 1.1883I
u = 0.289404 0.327405I
a = 0.22974 1.86888I
b = 0.669660 0.965192I
0.83299 2.49990I 0.635583 0.016341I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.289404 + 0.327405I
a = 0.22974 + 1.86888I
b = 0.669660 + 0.965192I
0.83299 + 2.49990I 0.635583 + 0.016341I
u = 0.299694
a = 4.31692
b = 0.556917
2.29026 25.4748
u = 0.415759 0.020992I
a = 1.11206 1.62035I
b = 0.459659 0.941518I
0.24998 2.12560I 7.44801 + 3.30216I
u = 0.415759 + 0.020992I
a = 1.11206 + 1.62035I
b = 0.459659 + 0.941518I
0.24998 + 2.12560I 7.44801 3.30216I
u = 0.475295 0.537559I
a = 0.848265 0.887557I
b = 0.600321 + 1.037171I
0.40050 + 6.08485I 0.93604 5.67733I
u = 0.475295 + 0.537559I
a = 0.848265 + 0.887557I
b = 0.600321 1.037171I
0.40050 6.08485I 0.93604 + 5.67733I
u = 0.654350 0.822893I
a = 0.709402 + 0.120931I
b = 0.663385 0.580908I
1.04548 3.54916I 7.60036 + 5.95173I
u = 0.654350 + 0.822893I
a = 0.709402 0.120931I
b = 0.663385 + 0.580908I
1.04548 + 3.54916I 7.60036 5.95173I
u = 0.866010 0.581201I
a = 0.0951159 + 0.0761528I
b = 0.893835 + 0.069690I
0.17579 2.00781I 1.31889 + 3.83635I
u = 0.866010 + 0.581201I
a = 0.0951159 0.0761528I
b = 0.893835 0.069690I
0.17579 + 2.00781I 1.31889 3.83635I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.902830 0.162857I
a = 2.31477 0.98875I
b = 2.68398 0.89158I
1.21120 2.28663I 67.8154 + 33.6174I
u = 0.902830 + 0.162857I
a = 2.31477 + 0.98875I
b = 2.68398 + 0.89158I
1.21120 + 2.28663I 67.8154 33.6174I
u = 0.957079 0.376972I
a = 1.088949 0.120486I
b = 1.005369 0.309594I
1.93159 0.86279I 5.27303 2.90798I
u = 0.957079 + 0.376972I
a = 1.088949 + 0.120486I
b = 1.005369 + 0.309594I
1.93159 + 0.86279I 5.27303 + 2.90798I
u = 1.009832 0.275630I
a = 0.169843 0.221873I
b = 2.56963 0.76210I
1.03851 9.43459I 1.06079 + 12.08235I
u = 1.009832 + 0.275630I
a = 0.169843 + 0.221873I
b = 2.56963 + 0.76210I
1.03851 + 9.43459I 1.06079 12.08235I
u = 1.101044 0.131905I
a = 0.24764 2.06050I
b = 0.96094 1.93871I
3.19102 0.69517I 22.4108 30.5874I
u = 1.101044 + 0.131905I
a = 0.24764 + 2.06050I
b = 0.96094 + 1.93871I
3.19102 + 0.69517I 22.4108 + 30.5874I
u = 1.112854 0.088964I
a = 0.63489 + 1.58041I
b = 1.046545 + 0.793785I
2.21350 2.96493I 0.95520 5.17197I
u = 1.112854 + 0.088964I
a = 0.63489 1.58041I
b = 1.046545 0.793785I
2.21350 + 2.96493I 0.95520 + 5.17197I
14
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.145374 0.066920I
a = 1.262748 0.617058I
b = 2.66387 + 0.09713I
4.68691 0.65371I 7.16082 4.51963I
u = 1.145374 + 0.066920I
a = 1.262748 + 0.617058I
b = 2.66387 0.09713I
4.68691 + 0.65371I 7.16082 + 4.51963I
u = 1.159987 0.027616I
a = 1.56154 + 1.25174I
b = 1.98263 + 0.92584I
2.47728 1.43112I 8.9891 + 12.2678I
u = 1.159987 + 0.027616I
a = 1.56154 1.25174I
b = 1.98263 0.92584I
2.47728 + 1.43112I 8.9891 12.2678I
u = 1.164225 0.361655I
a = 1.203968 0.567705I
b = 1.97171 1.12889I
1.57902 1.36888I 0.253912 + 0.517716I
u = 1.164225 + 0.361655I
a = 1.203968 + 0.567705I
b = 1.97171 + 1.12889I
1.57902 + 1.36888I 0.253912 0.517716I
u = 1.185508 0.058803I
a = 0.682028 0.418037I
b = 2.57320 + 1.05687I
3.53135 8.33125I 9.94564 + 9.07947I
u = 1.185508 + 0.058803I
a = 0.682028 + 0.418037I
b = 2.57320 1.05687I
3.53135 + 8.33125I 9.94564 9.07947I
u = 1.28103
a = 0.953706
b = 1.40687
2.35388 1.45526
u = 1.336937 0.450295I
a = 0.646427 + 0.095424I
b = 1.030446 0.062659I
2.46916 0.63828I 10.45865 + 0.75797I
15
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.336937 + 0.450295I
a = 0.646427 0.095424I
b = 1.030446 + 0.062659I
2.46916 + 0.63828I 10.45865 0.75797I
u = 1.401882 0.095370I
a = 0.218000 + 0.004841I
b = 1.004818 + 0.893935I
3.62089 3.05575I 9.95583 + 1.75891I
u = 1.401882 + 0.095370I
a = 0.218000 0.004841I
b = 1.004818 0.893935I
3.62089 + 3.05575I 9.95583 1.75891I
u = 1.41708 0.51645I
a = 1.006883 0.463619I
b = 2.12749 0.92031I
3.6022 19.5158I 5.07275 + 10.12874I
u = 1.41708 + 0.51645I
a = 1.006883 + 0.463619I
b = 2.12749 + 0.92031I
3.6022 + 19.5158I 5.07275 10.12874I
u = 1.42625 0.46282I
a = 0.825331 0.256820I
b = 1.70183 0.26383I
7.89743 1.46963I 10.38977 0.27710I
u = 1.42625 + 0.46282I
a = 0.825331 + 0.256820I
b = 1.70183 + 0.26383I
7.89743 + 1.46963I 10.38977 + 0.27710I
u = 1.43357 0.36225I
a = 0.975951 + 0.664917I
b = 2.03013 + 1.16009I
4.53607 9.28091I 13.3777 + 8.5639I
u = 1.43357 + 0.36225I
a = 0.975951 0.664917I
b = 2.03013 1.16009I
4.53607 + 9.28091I 13.3777 8.5639I
u = 1.43586 0.64102I
a = 0.493490 0.120752I
b = 1.357179 + 0.174450I
4.41478 4.49926I 14.4010 + 21.2360I
16
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.43586 + 0.64102I
a = 0.493490 + 0.120752I
b = 1.357179 0.174450I
4.41478 + 4.49926I 14.4010 21.2360I
u = 1.48251 0.51613I
a = 0.756236 + 0.515885I
b = 1.62407 + 0.87842I
2.79562 9.72471I 2.45327 + 12.18977I
u = 1.48251 + 0.51613I
a = 0.756236 0.515885I
b = 1.62407 0.87842I
2.79562 + 9.72471I 2.45327 12.18977I
u = 1.52092 0.64336I
a = 0.229772 0.022323I
b = 0.630886 0.187523I
3.70044 1.22861I 21.1241 + 4.7680I
u = 1.52092 + 0.64336I
a = 0.229772 + 0.022323I
b = 0.630886 + 0.187523I
3.70044 + 1.22861I 21.1241 4.7680I
17
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
20
6u
19
+ ··· + 2u + 1)(u
115
+ 5u
114
+ ··· 30u + 1)
c
2
(u
20
6u
18
+ ··· + 6u + 1)(u
115
+ u
114
+ ··· + 34u + 1)
c
3
(u
20
+ 4u
19
+ ··· + 2u + 1)(u
115
+ u
114
+ ··· 138u + 23)
c
4
(u
20
2u
19
+ ··· 9u 1)(u
115
+ u
114
+ ··· 541u + 31)
c
5
(u
20
2u
19
+ ··· u 1)(u
115
+ 5u
114
+ ··· 11u 1)
c
6
(u
20
2u
19
+ ··· + 8u 1)(u
115
+ u
114
+ ··· + 48u + 1)
c
7
(u
20
+ 2u
19
+ ··· + 9u 1)(u
115
+ u
114
+ ··· 541u + 31)
c
8
(u
20
+ 6u
19
+ ··· 7u
2
+ 1)(u
115
+ 3u
114
+ ··· 3684u 691)
c
9
(u
20
2u
19
+ ··· + 4u 1)(u
115
+ 7u
114
+ ··· + 2u 1)
c
10
(u
20
4u
19
+ ··· 3u + 1)(u
115
+ u
114
+ ··· + 668365u + 39479)
c
11
(u
20
2u
19
+ ··· 5u 1)(u
115
+ u
114
+ ··· 5u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
20
14y
19
+ ··· 14y + 1)(y
115
15y
114
+ ··· 10y 1)
c
2
(y
20
12y
19
+ ··· + 20y + 1)(y
115
9y
114
+ ··· + 20y 1)
c
3
(y
20
2y
19
+ ··· + 6y + 1)(y
115
+ 13y
114
+ ··· + 2346y 529)
c
4
, c
7
(y
20
18y
19
+ ··· 55y + 1)(y
115
87y
114
+ ··· + 12627y 961)
c
5
(y
20
+ 10y
19
+ ··· 5y + 1)(y
115
3y
114
+ ··· + y 1)
c
6
(y
20
2y
19
+ ··· 28y + 1)(y
115
31y
114
+ ··· + 416y 1)
c
8
(y
20
14y
19
+ ··· 14y + 1)
(y
115
31y
114
+ ··· + 17763462y 477481)
c
9
(y
20
+ 4y
19
+ ··· 6y + 1)(y
115
+ 15y
114
+ ··· + 62y 1)
c
10
(y
20
+ 8y
19
+ ··· 13y + 1)
(y
115
+ 47y
114
+ ··· 11408069835y 1558591441)
c
11
(y
20
6y
19
+ ··· 3y + 1)(y
115
11y
114
+ ··· + 139y 1)
19