11a
272
(K11a
272
)
A knot diagram
1
Linearized knot diagam
9 8 1 11 2 3 10 6 5 7 4
Solving Sequence
5,11
4 1
3,7
6 10 9 2 8
c
4
c
11
c
3
c
6
c
10
c
9
c
1
c
8
c
2
, c
5
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.61113 × 10
167
u
92
+ 2.18472 × 10
168
u
91
+ ··· + 6.37635 × 10
168
b + 3.55089 × 10
168
,
− 9.18713 × 10
168
u
92
+ 2.85060 × 10
169
u
91
+ ··· + 6.37635 × 10
168
a − 2.67247 × 10
170
,
u
93
− 3u
92
+ ··· + 35u + 1i
I
u
2
= h−u
18
− 4u
17
+ ··· + b + 1, −3u
18
− 12u
17
+ ··· + a − 6, u
19
+ 4u
18
+ ··· + 6u + 1i
* 2 irreducible components of dim
C
= 0, with total 112 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
= h−3.61 × 10
167
u
92
+ 2.18 × 10
168
u
91
+ · · · + 6.38 × 10
168
b + 3.55 ×
10
168
, −9.19 × 10
168
u
92
+ 2.85 × 10
169
u
91
+ · · · + 6.38 × 10
168
a − 2.67 ×
10
170
, u
93
− 3u
92
+ · · · + 35u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
1.44081u
92
− 4.47059u
91
+ ··· + 218.541u + 41.9122
0.0566333u
92
− 0.342629u
91
+ ··· − 7.62012u − 0.556885
a
6
=
1.42259u
92
− 4.52646u
91
+ ··· + 214.273u + 41.5325
−0.0227635u
92
+ 0.0219528u
91
+ ··· − 5.44936u − 0.491557
a
10
=
1.77836u
92
− 5.34281u
91
+ ··· + 274.509u + 50.4757
−0.0631020u
92
+ 0.374452u
91
+ ··· − 2.47058u − 0.512941
a
9
=
1.71526u
92
− 4.96836u
91
+ ··· + 272.038u + 49.9627
−0.0631020u
92
+ 0.374452u
91
+ ··· − 2.47058u − 0.512941
a
2
=
−2.58352u
92
+ 7.76269u
91
+ ··· − 386.533u − 70.1350
−0.106632u
92
+ 0.379755u
91
+ ··· + 5.53474u + 0.757562
a
8
=
3.39815u
92
− 10.1775u
91
+ ··· + 545.871u + 102.229
0.0767390u
92
− 0.283264u
91
+ ··· − 7.14975u − 1.07497
a
8
=
3.39815u
92
− 10.1775u
91
+ ··· + 545.871u + 102.229
0.0767390u
92
− 0.283264u
91
+ ··· − 7.14975u − 1.07497
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.120851u
92
− 0.494471u
91
+ ··· + 138.022u + 32.4350
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
93
− 4u
92
+ ··· − 31u − 1
c
2
u
93
− u
92
+ ··· − 16u
2
− 1
c
3
, c
4
, c
11
u
93
+ 3u
92
+ ··· + 35u − 1
c
5
u
93
− 2u
92
+ ··· − 55u
2
+ 5
c
6
u
93
− u
92
+ ··· + 1077u − 389
c
7
, c
10
u
93
− 5u
92
+ ··· − 780u − 145
c
8
u
93
+ 6u
92
+ ··· − 15u − 1
c
9
u
93
+ u
92
+ ··· + 200551u − 22691
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
93
− 8y
92
+ ··· + 187y −1
c
2
y
93
− 3y
92
+ ··· − 32y −1
c
3
, c
4
, c
11
y
93
+ 89y
92
+ ··· + 865y −1
c
5
y
93
− 2y
92
+ ··· + 550y −25
c
6
y
93
− y
92
+ ··· + 10281979y −151321
c
7
, c
10
y
93
+ 47y
92
+ ··· − 487800y −21025
c
8
y
93
+ 82y
91
+ ··· − 11y −1
c
9
y
93
+ 11y
92
+ ··· − 8110309523y −514881481
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.911459 + 0.395130I
a = −0.060081 − 1.366940I
b = 0.51305 + 1.76784I
−2.34640 + 13.18230I 0
u = −0.911459 − 0.395130I
a = −0.060081 + 1.366940I
b = 0.51305 − 1.76784I
−2.34640 − 13.18230I 0
u = 0.246625 + 0.978794I
a = 0.958092 + 0.139258I
b = 0.448747 + 0.173387I
0.12781 − 2.07574I 0
u = 0.246625 − 0.978794I
a = 0.958092 − 0.139258I
b = 0.448747 − 0.173387I
0.12781 + 2.07574I 0
u = 0.974658 + 0.386518I
a = 0.113415 + 1.095790I
b = 0.60161 − 1.59436I
−3.52135 − 3.76961I 0
u = 0.974658 − 0.386518I
a = 0.113415 − 1.095790I
b = 0.60161 + 1.59436I
−3.52135 + 3.76961I 0
u = 0.955720 + 0.446072I
a = −0.055176 − 1.052380I
b = −0.22885 + 1.73553I
−3.32185 − 4.23352I 0
u = 0.955720 − 0.446072I
a = −0.055176 + 1.052380I
b = −0.22885 − 1.73553I
−3.32185 + 4.23352I 0
u = −0.756553 + 0.865886I
a = −0.974997 + 0.306547I
b = −0.243449 − 1.167070I
−0.98495 − 7.52546I 0
u = −0.756553 − 0.865886I
a = −0.974997 − 0.306547I
b = −0.243449 + 1.167070I
−0.98495 + 7.52546I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.732299 + 0.909796I
a = 0.707676 + 0.298865I
b = 0.879779 − 0.946817I
−2.03674 − 1.66542I 0
u = 0.732299 − 0.909796I
a = 0.707676 − 0.298865I
b = 0.879779 + 0.946817I
−2.03674 + 1.66542I 0
u = 0.602610 + 0.551898I
a = 0.57808 + 1.50406I
b = 0.617201 − 1.013870I
−1.66403 − 4.99482I 0. + 12.04743I
u = 0.602610 − 0.551898I
a = 0.57808 − 1.50406I
b = 0.617201 + 1.013870I
−1.66403 + 4.99482I 0. − 12.04743I
u = 0.210852 + 1.187670I
a = −0.543462 − 0.727634I
b = −0.24590 + 1.78211I
0.59025 − 5.59173I 0
u = 0.210852 − 1.187670I
a = −0.543462 + 0.727634I
b = −0.24590 − 1.78211I
0.59025 + 5.59173I 0
u = −0.042552 + 1.208860I
a = 1.181090 + 0.101333I
b = 1.82870 + 0.41508I
−1.60314 − 3.04863I 0
u = −0.042552 − 1.208860I
a = 1.181090 − 0.101333I
b = 1.82870 − 0.41508I
−1.60314 + 3.04863I 0
u = 0.738015 + 0.267719I
a = −0.644949 − 1.095980I
b = 0.58532 + 1.33188I
−2.67687 + 0.69646I −9.23370 + 0.62043I
u = 0.738015 − 0.267719I
a = −0.644949 + 1.095980I
b = 0.58532 − 1.33188I
−2.67687 − 0.69646I −9.23370 − 0.62043I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.777826 + 0.016678I
a = 0.62554 − 1.27383I
b = 0.198182 + 1.154930I
−2.91425 − 1.94861I −10.28563 + 0.40390I
u = 0.777826 − 0.016678I
a = 0.62554 + 1.27383I
b = 0.198182 − 1.154930I
−2.91425 + 1.94861I −10.28563 − 0.40390I
u = 0.288392 + 0.707750I
a = 0.768676 + 0.217271I
b = 0.005605 + 0.312661I
0.13872 − 2.01683I 0.67333 + 3.98715I
u = 0.288392 − 0.707750I
a = 0.768676 − 0.217271I
b = 0.005605 − 0.312661I
0.13872 + 2.01683I 0.67333 − 3.98715I
u = −0.654822 + 0.391719I
a = −1.263680 − 0.402248I
b = 0.260205 − 0.435804I
0.67894 + 7.53424I −0.24390 − 7.52483I
u = −0.654822 − 0.391719I
a = −1.263680 + 0.402248I
b = 0.260205 + 0.435804I
0.67894 − 7.53424I −0.24390 + 7.52483I
u = −0.591766 + 0.464752I
a = −0.154401 − 0.822190I
b = 0.82840 + 1.15264I
1.00153 − 3.54334I 1.58809 + 0.30458I
u = −0.591766 − 0.464752I
a = −0.154401 + 0.822190I
b = 0.82840 − 1.15264I
1.00153 + 3.54334I 1.58809 − 0.30458I
u = 0.812390 + 0.967240I
a = −0.587684 − 0.393263I
b = −0.394533 + 1.276390I
−1.92498 − 2.34475I 0
u = 0.812390 − 0.967240I
a = −0.587684 + 0.393263I
b = −0.394533 − 1.276390I
−1.92498 + 2.34475I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.672569 + 0.279083I
a = 0.06726 + 1.89775I
b = −0.49534 − 1.65370I
−1.19275 + 5.34921I 0.55034 − 10.82397I
u = −0.672569 − 0.279083I
a = 0.06726 − 1.89775I
b = −0.49534 + 1.65370I
−1.19275 − 5.34921I 0.55034 + 10.82397I
u = 0.003533 + 1.274680I
a = 0.525082 + 0.174725I
b = 0.54755 − 2.88462I
2.75039 + 4.22339I 0
u = 0.003533 − 1.274680I
a = 0.525082 − 0.174725I
b = 0.54755 + 2.88462I
2.75039 − 4.22339I 0
u = −0.117069 + 1.283880I
a = −1.315870 + 0.095206I
b = −1.012990 − 0.406576I
−1.28790 + 5.38199I 0
u = −0.117069 − 1.283880I
a = −1.315870 − 0.095206I
b = −1.012990 + 0.406576I
−1.28790 − 5.38199I 0
u = −0.176650 + 1.277580I
a = 0.799827 − 0.504979I
b = 0.09805 + 1.48760I
−0.818431 − 0.586473I 0
u = −0.176650 − 1.277580I
a = 0.799827 + 0.504979I
b = 0.09805 − 1.48760I
−0.818431 + 0.586473I 0
u = 0.004246 + 1.329120I
a = −0.858955 + 0.481977I
b = −1.18895 − 1.40669I
3.86557 + 1.99478I 0
u = 0.004246 − 1.329120I
a = −0.858955 − 0.481977I
b = −1.18895 + 1.40669I
3.86557 − 1.99478I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.305242 + 1.326130I
a = −0.472815 + 0.658481I
b = −1.51214 − 1.46798I
5.23834 + 5.65499I 0
u = −0.305242 − 1.326130I
a = −0.472815 − 0.658481I
b = −1.51214 + 1.46798I
5.23834 − 5.65499I 0
u = 0.535771 + 0.331980I
a = 0.561496 − 0.224728I
b = 0.275495 + 0.063895I
−1.05560 − 1.04516I −5.24999 + 4.73518I
u = 0.535771 − 0.331980I
a = 0.561496 + 0.224728I
b = 0.275495 − 0.063895I
−1.05560 + 1.04516I −5.24999 − 4.73518I
u = −0.135847 + 1.378470I
a = 0.378488 + 0.952853I
b = −0.626385 − 0.559687I
7.46821 + 1.40401I 0
u = −0.135847 − 1.378470I
a = 0.378488 − 0.952853I
b = −0.626385 + 0.559687I
7.46821 − 1.40401I 0
u = 0.275110 + 1.366140I
a = −0.482588 − 0.137919I
b = −0.26114 + 1.75093I
2.40844 − 2.97328I 0
u = 0.275110 − 1.366140I
a = −0.482588 + 0.137919I
b = −0.26114 − 1.75093I
2.40844 + 2.97328I 0
u = −0.172915 + 1.402530I
a = 0.563359 + 0.548099I
b = −0.151156 + 0.172009I
5.61748 − 0.19647I 0
u = −0.172915 − 1.402530I
a = 0.563359 − 0.548099I
b = −0.151156 − 0.172009I
5.61748 + 0.19647I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07853 + 1.41526I
a = −0.385092 + 0.973133I
b = −0.164397 − 0.529226I
7.62011 − 0.60893I 0
u = 0.07853 − 1.41526I
a = −0.385092 − 0.973133I
b = −0.164397 + 0.529226I
7.62011 + 0.60893I 0
u = −0.576840 + 0.056978I
a = 1.01392 + 1.04721I
b = −0.478791 − 0.978508I
0.93991 + 2.24276I 2.13382 − 6.20149I
u = −0.576840 − 0.056978I
a = 1.01392 − 1.04721I
b = −0.478791 + 0.978508I
0.93991 − 2.24276I 2.13382 + 6.20149I
u = −0.16657 + 1.41522I
a = −0.737844 + 0.359479I
b = 0.05293 − 2.26413I
0.95617 + 6.95484I 0
u = −0.16657 − 1.41522I
a = −0.737844 − 0.359479I
b = 0.05293 + 2.26413I
0.95617 − 6.95484I 0
u = −0.26162 + 1.41387I
a = −0.829533 + 0.679950I
b = −1.27505 − 1.88111I
4.22352 + 8.75550I 0
u = −0.26162 − 1.41387I
a = −0.829533 − 0.679950I
b = −1.27505 + 1.88111I
4.22352 − 8.75550I 0
u = 0.17440 + 1.45659I
a = −0.717413 − 0.360056I
b = −1.90212 + 1.94824I
5.89949 − 6.94617I 0
u = 0.17440 − 1.45659I
a = −0.717413 + 0.360056I
b = −1.90212 − 1.94824I
5.89949 + 6.94617I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.527457 + 0.063186I
a = −0.07687 − 2.62551I
b = −0.357457 + 1.182460I
−4.97774 − 3.20790I −8.72666 + 3.61708I
u = −0.527457 − 0.063186I
a = −0.07687 + 2.62551I
b = −0.357457 − 1.182460I
−4.97774 + 3.20790I −8.72666 − 3.61708I
u = −0.24734 + 1.45630I
a = −0.397332 − 0.787003I
b = 0.343876 + 0.308196I
6.62651 + 10.84470I 0
u = −0.24734 − 1.45630I
a = −0.397332 + 0.787003I
b = 0.343876 − 0.308196I
6.62651 − 10.84470I 0
u = −0.005024 + 0.519936I
a = 1.53006 + 0.63638I
b = −0.128808 + 0.625732I
0.19375 − 2.00732I 1.90291 + 4.08224I
u = −0.005024 − 0.519936I
a = 1.53006 − 0.63638I
b = −0.128808 − 0.625732I
0.19375 + 2.00732I 1.90291 − 4.08224I
u = 0.14435 + 1.47435I
a = 0.051712 + 0.613325I
b = −0.177691 − 0.333417I
6.55607 − 3.56363I 0
u = 0.14435 − 1.47435I
a = 0.051712 − 0.613325I
b = −0.177691 + 0.333417I
6.55607 + 3.56363I 0
u = 0.21979 + 1.46839I
a = 0.370817 − 0.468364I
b = 0.022326 + 0.589901I
4.94375 − 3.83324I 0
u = 0.21979 − 1.46839I
a = 0.370817 + 0.468364I
b = 0.022326 − 0.589901I
4.94375 + 3.83324I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19636 + 1.47715I
a = 0.575084 − 0.439374I
b = 1.51693 + 1.22032I
7.35184 − 0.66069I 0
u = −0.19636 − 1.47715I
a = 0.575084 + 0.439374I
b = 1.51693 − 1.22032I
7.35184 + 0.66069I 0
u = −0.445879 + 0.223933I
a = −0.72430 + 2.47527I
b = 0.63559 − 1.52906I
−4.38663 + 4.68917I −11.13071 − 7.83950I
u = −0.445879 − 0.223933I
a = −0.72430 − 2.47527I
b = 0.63559 + 1.52906I
−4.38663 − 4.68917I −11.13071 + 7.83950I
u = 0.317173 + 0.374066I
a = −0.92898 − 1.56886I
b = −0.69662 + 2.12690I
−0.13387 − 4.83140I −1.38014 + 12.10335I
u = 0.317173 − 0.374066I
a = −0.92898 + 1.56886I
b = −0.69662 − 2.12690I
−0.13387 + 4.83140I −1.38014 − 12.10335I
u = 0.23285 + 1.49755I
a = 0.745388 + 0.647957I
b = 0.86766 − 1.24614I
4.93482 − 8.13681I 0
u = 0.23285 − 1.49755I
a = 0.745388 − 0.647957I
b = 0.86766 + 1.24614I
4.93482 + 8.13681I 0
u = 0.36704 + 1.48082I
a = 0.728699 + 0.535940I
b = 1.35721 − 1.37957I
2.42961 − 8.56668I 0
u = 0.36704 − 1.48082I
a = 0.728699 − 0.535940I
b = 1.35721 + 1.37957I
2.42961 + 8.56668I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.34922 + 1.49380I
a = 0.709563 − 0.650111I
b = 1.26940 + 1.85557I
3.7167 + 17.7393I 0
u = −0.34922 − 1.49380I
a = 0.709563 + 0.650111I
b = 1.26940 − 1.85557I
3.7167 − 17.7393I 0
u = 0.35894 + 1.51768I
a = −0.594952 − 0.533137I
b = −1.05454 + 1.85472I
2.98943 − 8.99089I 0
u = 0.35894 − 1.51768I
a = −0.594952 + 0.533137I
b = −1.05454 − 1.85472I
2.98943 + 8.99089I 0
u = 0.10285 + 1.58207I
a = 0.322796 − 0.166607I
b = −0.611667 + 0.333370I
7.99033 − 3.67115I 0
u = 0.10285 − 1.58207I
a = 0.322796 + 0.166607I
b = −0.611667 − 0.333370I
7.99033 + 3.67115I 0
u = −0.100806 + 0.397094I
a = 2.20139 + 0.48685I
b = −0.210768 + 0.748546I
0.18872 − 2.00916I 2.24464 + 3.56470I
u = −0.100806 − 0.397094I
a = 2.20139 − 0.48685I
b = −0.210768 − 0.748546I
0.18872 + 2.00916I 2.24464 − 3.56470I
u = −0.186714 + 0.346826I
a = 1.35275 + 1.99552I
b = −0.398511 + 0.161176I
2.29833 − 0.12628I 10.47295 − 1.82234I
u = −0.186714 − 0.346826I
a = 1.35275 − 1.99552I
b = −0.398511 − 0.161176I
2.29833 + 0.12628I 10.47295 + 1.82234I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03589 + 1.65255I
a = −0.401052 − 0.252951I
b = −0.266809 + 0.186901I
8.28168 − 4.75781I 0
u = −0.03589 − 1.65255I
a = −0.401052 + 0.252951I
b = −0.266809 − 0.186901I
8.28168 + 4.75781I 0
u = −0.0336230
a = 35.5555
b = −0.339499
2.39628 28.3130
14
II. I
u
2
=
h−u
18
−4u
17
+· · ·+b +1, −3u
18
−12u
17
+· · ·+a −6, u
19
+4u
18
+· · ·+6u +1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
u
2
+ 1
−u
4
− 2u
2
a
7
=
3u
18
+ 12u
17
+ ··· + 15u + 6
u
18
+ 4u
17
+ ··· − 3u − 1
a
6
=
3u
18
+ 12u
17
+ ··· + 13u + 6
−u
6
− 2u
5
− 5u
4
− 6u
3
− 6u
2
− 4u − 1
a
10
=
u
18
+ 4u
17
+ ··· + 8u + 6
2u
17
+ 7u
16
+ ··· + 8u + 1
a
9
=
u
18
+ 6u
17
+ ··· + 16u + 7
2u
17
+ 7u
16
+ ··· + 8u + 1
a
2
=
−3u
18
− 12u
17
+ ··· − 30u − 11
u
3
+ u
2
+ 2u + 1
a
8
=
u
18
+ 3u
17
+ ··· + 21u + 14
2u
17
+ 8u
16
+ ··· + 13u
2
+ 5u
a
8
=
u
18
+ 3u
17
+ ··· + 21u + 14
2u
17
+ 8u
16
+ ··· + 13u
2
+ 5u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −6u
18
−28u
17
−127u
16
−363u
15
−940u
14
−1903u
13
−3460u
12
−5244u
11
−7119u
10
−
8212u
9
− 8436u
8
− 7329u
7
− 5610u
6
− 3541u
5
− 1966u
4
− 855u
3
− 370u
2
− 101u − 43
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
+ u
18
+ ··· + 4u
2
− 1
c
2
u
19
− 4u
17
+ ··· − u − 1
c
3
, c
4
u
19
+ 4u
18
+ ··· + 6u + 1
c
5
u
19
+ u
18
+ ··· − 3u − 1
c
6
u
19
− 2u
18
+ ··· + 4u + 7
c
7
u
19
+ 6u
18
+ ··· + 3u + 1
c
8
u
19
− 3u
18
+ ··· − u
2
− 1
c
9
u
19
− 3u
17
+ ··· − 8u − 7
c
10
u
19
− 6u
18
+ ··· + 3u − 1
c
11
u
19
− 4u
18
+ ··· + 6u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 9y
18
+ ··· + 8y −1
c
2
y
19
− 8y
18
+ ··· + 9y −1
c
3
, c
4
, c
11
y
19
+ 20y
18
+ ··· + 2y −1
c
5
y
19
+ 5y
18
+ ··· + 3y −1
c
6
y
19
+ 6y
18
+ ··· + 184y −49
c
7
, c
10
y
19
+ 10y
18
+ ··· − 19y −1
c
8
y
19
− 5y
18
+ ··· − 2y −1
c
9
y
19
− 6y
18
+ ··· + 190y −49
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822625 + 0.504824I
a = −0.271844 + 1.136820I
b = −0.45867 − 1.52566I
−2.64209 + 4.02888I −1.74103 − 7.17564I
u = −0.822625 − 0.504824I
a = −0.271844 − 1.136820I
b = −0.45867 + 1.52566I
−2.64209 − 4.02888I −1.74103 + 7.17564I
u = −0.781988 + 0.922190I
a = 0.652220 − 0.305768I
b = 0.590784 + 0.988016I
−1.58761 + 1.75063I 3.91034 − 0.25504I
u = −0.781988 − 0.922190I
a = 0.652220 + 0.305768I
b = 0.590784 − 0.988016I
−1.58761 − 1.75063I 3.91034 + 0.25504I
u = −0.013553 + 1.225120I
a = 1.212320 + 0.042368I
b = 1.27378 + 0.82533I
−1.17342 − 3.71954I 0.20565 + 7.01198I
u = −0.013553 − 1.225120I
a = 1.212320 − 0.042368I
b = 1.27378 − 0.82533I
−1.17342 + 3.71954I 0.20565 − 7.01198I
u = 0.123826 + 1.275680I
a = −0.494186 − 0.312606I
b = −0.56449 + 2.86824I
2.78952 − 5.37290I 1.47834 + 8.00232I
u = 0.123826 − 1.275680I
a = −0.494186 + 0.312606I
b = −0.56449 − 2.86824I
2.78952 + 5.37290I 1.47834 − 8.00232I
u = −0.128745 + 0.658998I
a = −1.85503 + 0.55800I
b = −0.278888 − 0.794541I
−3.42166 + 4.09475I −4.31370 − 4.86850I
u = −0.128745 − 0.658998I
a = −1.85503 − 0.55800I
b = −0.278888 + 0.794541I
−3.42166 − 4.09475I −4.31370 + 4.86850I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.112895 + 1.380490I
a = 0.309357 + 0.971465I
b = −0.317626 − 0.556721I
6.97273 + 1.35437I −1.04092 − 3.37423I
u = −0.112895 − 1.380490I
a = 0.309357 − 0.971465I
b = −0.317626 + 0.556721I
6.97273 − 1.35437I −1.04092 + 3.37423I
u = −0.27617 + 1.46327I
a = −0.729976 + 0.560596I
b = −1.12516 − 1.66255I
3.59220 + 7.81356I 0.86440 − 5.38907I
u = −0.27617 − 1.46327I
a = −0.729976 − 0.560596I
b = −1.12516 + 1.66255I
3.59220 − 7.81356I 0.86440 + 5.38907I
u = 0.203505 + 0.446592I
a = 1.330970 + 0.269712I
b = 0.18876 − 1.94856I
−0.18250 + 4.08169I −4.19142 − 1.98059I
u = 0.203505 − 0.446592I
a = 1.330970 − 0.269712I
b = 0.18876 + 1.94856I
−0.18250 − 4.08169I −4.19142 + 1.98059I
u = −0.06627 + 1.60382I
a = 0.298071 + 0.037730I
b = −0.184580 − 0.575875I
7.68023 + 3.97321I −3.79021 − 7.05784I
u = −0.06627 − 1.60382I
a = 0.298071 − 0.037730I
b = −0.184580 + 0.575875I
7.68023 − 3.97321I −3.79021 + 7.05784I
u = −0.250170
a = 5.09620
b = −0.247831
2.26413 −32.7630
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
19
+ u
18
+ ··· + 4u
2
− 1)(u
93
− 4u
92
+ ··· − 31u − 1)
c
2
(u
19
− 4u
17
+ ··· − u − 1)(u
93
− u
92
+ ··· − 16u
2
− 1)
c
3
, c
4
(u
19
+ 4u
18
+ ··· + 6u + 1)(u
93
+ 3u
92
+ ··· + 35u − 1)
c
5
(u
19
+ u
18
+ ··· − 3u − 1)(u
93
− 2u
92
+ ··· − 55u
2
+ 5)
c
6
(u
19
− 2u
18
+ ··· + 4u + 7)(u
93
− u
92
+ ··· + 1077u − 389)
c
7
(u
19
+ 6u
18
+ ··· + 3u + 1)(u
93
− 5u
92
+ ··· − 780u − 145)
c
8
(u
19
− 3u
18
+ ··· − u
2
− 1)(u
93
+ 6u
92
+ ··· − 15u − 1)
c
9
(u
19
− 3u
17
+ ··· − 8u − 7)(u
93
+ u
92
+ ··· + 200551u − 22691)
c
10
(u
19
− 6u
18
+ ··· + 3u − 1)(u
93
− 5u
92
+ ··· − 780u − 145)
c
11
(u
19
− 4u
18
+ ··· + 6u − 1)(u
93
+ 3u
92
+ ··· + 35u − 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
19
− 9y
18
+ ··· + 8y −1)(y
93
− 8y
92
+ ··· + 187y −1)
c
2
(y
19
− 8y
18
+ ··· + 9y −1)(y
93
− 3y
92
+ ··· − 32y −1)
c
3
, c
4
, c
11
(y
19
+ 20y
18
+ ··· + 2y −1)(y
93
+ 89y
92
+ ··· + 865y −1)
c
5
(y
19
+ 5y
18
+ ··· + 3y −1)(y
93
− 2y
92
+ ··· + 550y −25)
c
6
(y
19
+ 6y
18
+ ··· + 184y −49)
· (y
93
− y
92
+ ··· + 10281979y −151321)
c
7
, c
10
(y
19
+ 10y
18
+ ··· − 19y −1)(y
93
+ 47y
92
+ ··· − 487800y −21025)
c
8
(y
19
− 5y
18
+ ··· − 2y −1)(y
93
+ 82y
91
+ ··· − 11y −1)
c
9
(y
19
− 6y
18
+ ··· + 190y −49)
· (y
93
+ 11y
92
+ ··· − 8110309523y −514881481)
21
