12n
0853
(K12n
0853
)
A knot diagram
1
Linearized knot diagam
4 7 9 10 1 11 3 11 2 5 9 6
Solving Sequence
4,10
5
2,11
1 6 9 3 8 7 12
c
4
c
10
c
1
c
5
c
9
c
3
c
8
c
7
c
12
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.85914 × 10
218
u
85
+ 5.23238 × 10
218
u
84
+ ··· + 1.12919 × 10
219
b − 4.30007 × 10
220
,
− 5.00889 × 10
219
u
85
− 3.83512 × 10
219
u
84
+ ··· + 1.24211 × 10
220
a + 1.01514 × 10
222
,
u
86
− 26u
84
+ ··· + 352u + 143i
I
u
2
= h−296859606u
23
− 672784784u
22
+ ··· + 1044681373b − 15785274596,
642367601u
23
− 9005160835u
22
+ ··· + 9402132357a + 67337415889, u
24
+ u
23
+ ··· + 11u + 9i
* 2 irreducible components of dim
C
= 0, with total 110 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
= h3.86 × 10
218
u
85
+ 5.23 × 10
218
u
84
+ · · · + 1.13 × 10
219
b − 4.30 ×
10
220
, −5.01 × 10
219
u
85
− 3.84 × 10
219
u
84
+ · · · + 1.24 × 10
220
a + 1.02 ×
10
222
, u
86
− 26u
84
+ · · · + 352u + 143i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
2
=
0.403257u
85
+ 0.308758u
84
+ ··· − 295.596u − 81.7270
−0.341761u
85
− 0.463375u
84
+ ··· + 115.690u + 38.0810
a
11
=
−u
−u
3
+ u
a
1
=
0.0614956u
85
− 0.154617u
84
+ ··· − 179.905u − 43.6459
−0.341761u
85
− 0.463375u
84
+ ··· + 115.690u + 38.0810
a
6
=
3.44397u
85
+ 3.32938u
84
+ ··· − 1720.90u − 500.050
1.55973u
85
+ 1.31239u
84
+ ··· − 940.484u − 263.433
a
9
=
1.95617u
85
+ 2.18050u
84
+ ··· − 673.241u − 213.966
1.26891u
85
+ 1.09399u
84
+ ··· − 711.937u − 198.806
a
3
=
3.93599u
85
+ 3.76143u
84
+ ··· − 1909.61u − 556.585
−0.239645u
85
− 0.0691656u
84
+ ··· + 268.429u + 69.1359
a
8
=
0.998356u
85
+ 1.19873u
84
+ ··· − 230.274u − 83.7492
1.25082u
85
+ 1.11752u
84
+ ··· − 672.352u − 188.629
a
7
=
1.64727u
85
+ 1.65507u
84
+ ··· − 761.689u − 224.947
1.85993u
85
+ 1.66888u
84
+ ··· − 1053.41u − 299.108
a
12
=
−1.44206u
85
+ 0.328546u
84
+ ··· + 1873.41u + 470.130
0.373170u
85
+ 0.655436u
84
+ ··· + 29.6065u − 8.46160
(ii) Obstruction class = −1
(iii) Cusp Shapes = −12.2613u
85
− 19.5611u
84
+ ··· + 770.668u + 597.207
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
86
− 3u
85
+ ··· − 1090u + 331
c
2
, c
7
u
86
+ 2u
85
+ ··· + 98u + 47
c
3
u
86
− u
85
+ ··· − 18u + 4
c
4
, c
10
u
86
− 26u
84
+ ··· − 352u + 143
c
5
, c
12
u
86
+ u
85
+ ··· − 2490u + 2156
c
6
u
86
− 28u
84
+ ··· − 145161863u + 33647749
c
8
, c
11
u
86
+ 4u
85
+ ··· + 460u + 221
c
9
u
86
+ 2u
85
+ ··· + 7484u + 1411
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
86
− 7y
85
+ ··· − 234820y + 109561
c
2
, c
7
y
86
− 26y
85
+ ··· − 35642y + 2209
c
3
y
86
+ 31y
85
+ ··· − 988y + 16
c
4
, c
10
y
86
− 52y
85
+ ··· − 226292y + 20449
c
5
, c
12
y
86
+ 59y
85
+ ··· + 168629940y + 4648336
c
6
y
86
− 56y
85
+ ··· + 41812736405652607y + 1132171012767001
c
8
, c
11
y
86
+ 80y
85
+ ··· + 18613622y + 48841
c
9
y
86
+ 42y
85
+ ··· + 83072014y + 1990921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.013240 + 0.156600I
a = 0.061933 − 0.617773I
b = −1.73273 + 2.09017I
−3.77856 − 6.86337I 0
u = 1.013240 − 0.156600I
a = 0.061933 + 0.617773I
b = −1.73273 − 2.09017I
−3.77856 + 6.86337I 0
u = 0.946501 + 0.164076I
a = 0.65342 + 2.54858I
b = 0.082485 − 0.387385I
−0.028740 − 0.605068I 0
u = 0.946501 − 0.164076I
a = 0.65342 − 2.54858I
b = 0.082485 + 0.387385I
−0.028740 + 0.605068I 0
u = 0.935366 + 0.122426I
a = 0.81877 + 1.57708I
b = 0.594883 − 0.656114I
0.135026 − 0.962079I 0
u = 0.935366 − 0.122426I
a = 0.81877 − 1.57708I
b = 0.594883 + 0.656114I
0.135026 + 0.962079I 0
u = −0.727128 + 0.584765I
a = −0.227558 + 1.248560I
b = 1.340550 − 0.264504I
−4.35117 − 0.02788I 0
u = −0.727128 − 0.584765I
a = −0.227558 − 1.248560I
b = 1.340550 + 0.264504I
−4.35117 + 0.02788I 0
u = −0.924847 + 0.536642I
a = −0.347462 + 0.979449I
b = 0.054894 − 0.770968I
1.42029 + 4.02474I 0
u = −0.924847 − 0.536642I
a = −0.347462 − 0.979449I
b = 0.054894 + 0.770968I
1.42029 − 4.02474I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.019770 + 0.327343I
a = −1.53537 + 0.31678I
b = −0.358846 − 0.491803I
−3.49969 − 2.27160I 0
u = 1.019770 − 0.327343I
a = −1.53537 − 0.31678I
b = −0.358846 + 0.491803I
−3.49969 + 2.27160I 0
u = −1.001200 + 0.393657I
a = 1.62994 + 0.27952I
b = 0.449265 − 0.605829I
−2.03015 + 9.00043I 0
u = −1.001200 − 0.393657I
a = 1.62994 − 0.27952I
b = 0.449265 + 0.605829I
−2.03015 − 9.00043I 0
u = −1.075550 + 0.027859I
a = 0.168250 − 0.671082I
b = 1.99103 + 1.12349I
−6.51206 − 0.43126I 0
u = −1.075550 − 0.027859I
a = 0.168250 + 0.671082I
b = 1.99103 − 1.12349I
−6.51206 + 0.43126I 0
u = 0.899199 + 0.142670I
a = 0.61730 + 1.32859I
b = 0.657270 − 0.389408I
0.165768 − 0.366994I 0
u = 0.899199 − 0.142670I
a = 0.61730 − 1.32859I
b = 0.657270 + 0.389408I
0.165768 + 0.366994I 0
u = −0.015482 + 1.089660I
a = −0.915625 − 0.620168I
b = 0.775767 + 0.822352I
−2.38759 − 4.54755I 0
u = −0.015482 − 1.089660I
a = −0.915625 + 0.620168I
b = 0.775767 − 0.822352I
−2.38759 + 4.54755I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455919 + 0.998858I
a = 0.337485 + 0.103051I
b = −0.571382 − 0.676993I
4.83318 + 0.07837I 0
u = −0.455919 − 0.998858I
a = 0.337485 − 0.103051I
b = −0.571382 + 0.676993I
4.83318 − 0.07837I 0
u = −1.069760 + 0.330003I
a = −0.395329 + 0.520215I
b = −0.654977 − 0.341910I
1.07982 + 3.82086I 0
u = −1.069760 − 0.330003I
a = −0.395329 − 0.520215I
b = −0.654977 + 0.341910I
1.07982 − 3.82086I 0
u = 0.279630 + 0.827400I
a = 0.723072 + 1.097880I
b = −1.033860 − 0.336513I
−4.18891 − 5.58599I 0
u = 0.279630 − 0.827400I
a = 0.723072 − 1.097880I
b = −1.033860 + 0.336513I
−4.18891 + 5.58599I 0
u = −0.862909 + 0.134585I
a = −0.72937 − 1.80432I
b = −0.642795 + 1.145470I
3.92961 + 2.85500I 0
u = −0.862909 − 0.134585I
a = −0.72937 + 1.80432I
b = −0.642795 − 1.145470I
3.92961 − 2.85500I 0
u = −0.782385 + 0.368272I
a = 1.43549 − 0.13900I
b = −0.314156 − 0.491568I
3.63471 − 0.52145I 0
u = −0.782385 − 0.368272I
a = 1.43549 + 0.13900I
b = −0.314156 + 0.491568I
3.63471 + 0.52145I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.014150 + 1.172740I
a = −0.544027 + 0.153648I
b = 0.320054 − 0.610257I
4.62544 + 0.94388I 0
u = −0.014150 − 1.172740I
a = −0.544027 − 0.153648I
b = 0.320054 + 0.610257I
4.62544 − 0.94388I 0
u = 0.140588 + 1.189710I
a = 0.908141 − 0.496246I
b = −0.831187 + 0.816196I
−1.25558 + 11.17520I 0
u = 0.140588 − 1.189710I
a = 0.908141 + 0.496246I
b = −0.831187 − 0.816196I
−1.25558 − 11.17520I 0
u = −0.359459 + 1.155750I
a = 0.585216 + 0.275949I
b = −0.633762 − 0.485525I
3.14464 − 2.91301I 0
u = −0.359459 − 1.155750I
a = 0.585216 − 0.275949I
b = −0.633762 + 0.485525I
3.14464 + 2.91301I 0
u = 0.741114 + 0.128033I
a = −1.219120 − 0.690485I
b = −1.57726 − 0.48897I
−2.91270 + 5.35630I 0.19430 − 2.58314I
u = 0.741114 − 0.128033I
a = −1.219120 + 0.690485I
b = −1.57726 + 0.48897I
−2.91270 − 5.35630I 0.19430 + 2.58314I
u = 1.224260 + 0.308586I
a = 0.37545 − 1.41933I
b = 1.007880 + 0.816912I
−8.64326 − 2.65098I 0
u = 1.224260 − 0.308586I
a = 0.37545 + 1.41933I
b = 1.007880 − 0.816912I
−8.64326 + 2.65098I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.243050 + 0.241448I
a = −0.357460 + 0.539477I
b = −0.790416 − 0.344192I
−2.99529 − 0.68487I 0
u = 1.243050 − 0.241448I
a = −0.357460 − 0.539477I
b = −0.790416 + 0.344192I
−2.99529 + 0.68487I 0
u = 1.194790 + 0.422230I
a = −0.463621 + 0.994886I
b = −1.26517 − 1.42297I
2.82983 − 6.91529I 0
u = 1.194790 − 0.422230I
a = −0.463621 − 0.994886I
b = −1.26517 + 1.42297I
2.82983 + 6.91529I 0
u = −1.245920 + 0.275497I
a = 0.260591 + 0.811687I
b = 0.999528 − 0.947180I
−4.17702 + 3.64369I 0
u = −1.245920 − 0.275497I
a = 0.260591 − 0.811687I
b = 0.999528 + 0.947180I
−4.17702 − 3.64369I 0
u = −1.177240 + 0.541228I
a = −0.278209 − 0.658710I
b = −1.31264 + 0.74781I
2.32587 + 5.43706I 0
u = −1.177240 − 0.541228I
a = −0.278209 + 0.658710I
b = −1.31264 − 0.74781I
2.32587 − 5.43706I 0
u = 0.225617 + 0.639859I
a = 1.48458 − 0.79709I
b = −0.584963 + 1.170950I
5.82789 + 2.77163I 3.62621 − 5.12009I
u = 0.225617 − 0.639859I
a = 1.48458 + 0.79709I
b = −0.584963 − 1.170950I
5.82789 − 2.77163I 3.62621 + 5.12009I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.320110 + 0.173352I
a = 0.192094 + 0.541101I
b = 0.00408 − 1.94041I
−5.93895 + 3.63950I 0
u = −1.320110 − 0.173352I
a = 0.192094 − 0.541101I
b = 0.00408 + 1.94041I
−5.93895 − 3.63950I 0
u = −0.397923 + 0.534043I
a = 0.09432 − 1.75717I
b = 0.309084 + 1.191700I
−0.33732 − 5.25732I 3.19134 + 2.30399I
u = −0.397923 − 0.534043I
a = 0.09432 + 1.75717I
b = 0.309084 − 1.191700I
−0.33732 + 5.25732I 3.19134 − 2.30399I
u = −1.281140 + 0.379028I
a = −0.344880 − 1.318420I
b = −1.022710 + 0.788679I
−8.77560 + 9.65768I 0
u = −1.281140 − 0.379028I
a = −0.344880 + 1.318420I
b = −1.022710 − 0.788679I
−8.77560 − 9.65768I 0
u = 1.348360 + 0.054033I
a = −0.061038 − 0.473724I
b = 0.93523 + 2.02994I
−6.00193 − 4.32624I 0
u = 1.348360 − 0.054033I
a = −0.061038 + 0.473724I
b = 0.93523 − 2.02994I
−6.00193 + 4.32624I 0
u = 0.463929 + 1.273310I
a = −0.566675 + 0.091422I
b = 0.488847 − 0.410672I
2.63674 − 1.06753I 0
u = 0.463929 − 1.273310I
a = −0.566675 − 0.091422I
b = 0.488847 + 0.410672I
2.63674 + 1.06753I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.148330 + 0.759634I
a = −0.459012 + 0.592200I
b = 1.317320 + 0.103020I
−5.56625 + 5.77682I 0
u = −1.148330 − 0.759634I
a = −0.459012 − 0.592200I
b = 1.317320 − 0.103020I
−5.56625 − 5.77682I 0
u = 0.203161 + 0.556123I
a = −0.48221 − 1.79807I
b = −0.262667 + 1.008830I
−1.28788 − 1.11969I 2.17883 + 1.74771I
u = 0.203161 − 0.556123I
a = −0.48221 + 1.79807I
b = −0.262667 − 1.008830I
−1.28788 + 1.11969I 2.17883 − 1.74771I
u = −0.454810 + 0.375338I
a = −1.59503 − 0.91449I
b = −0.496780 + 0.231794I
2.81852 − 0.19677I 3.08966 − 3.01616I
u = −0.454810 − 0.375338I
a = −1.59503 + 0.91449I
b = −0.496780 − 0.231794I
2.81852 + 0.19677I 3.08966 + 3.01616I
u = 1.25089 + 0.68548I
a = 0.006593 − 0.938843I
b = 1.023550 + 0.815519I
−0.12254 − 5.71927I 0
u = 1.25089 − 0.68548I
a = 0.006593 + 0.938843I
b = 1.023550 − 0.815519I
−0.12254 + 5.71927I 0
u = −1.28080 + 0.63183I
a = −0.220888 − 0.959005I
b = −1.077160 + 0.774774I
0.04388 + 9.24471I 0
u = −1.28080 − 0.63183I
a = −0.220888 + 0.959005I
b = −1.077160 − 0.774774I
0.04388 − 9.24471I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28042 + 0.65504I
a = 0.265807 + 0.510700I
b = −1.178570 + 0.010457I
−6.88725 − 0.19421I 0
u = 1.28042 − 0.65504I
a = 0.265807 − 0.510700I
b = −1.178570 − 0.010457I
−6.88725 + 0.19421I 0
u = −1.34096 + 0.53769I
a = 0.213817 + 1.052190I
b = 1.32707 − 1.16128I
−6.52492 + 10.27030I 0
u = −1.34096 − 0.53769I
a = 0.213817 − 1.052190I
b = 1.32707 + 1.16128I
−6.52492 − 10.27030I 0
u = 1.34112 + 0.60712I
a = −0.166632 + 1.083530I
b = −1.36056 − 1.11761I
−5.0587 − 17.4655I 0
u = 1.34112 − 0.60712I
a = −0.166632 − 1.083530I
b = −1.36056 + 1.11761I
−5.0587 + 17.4655I 0
u = 1.40203 + 0.59947I
a = 0.034030 − 0.722008I
b = 1.06930 + 0.97248I
0.13038 − 7.25479I 0
u = 1.40203 − 0.59947I
a = 0.034030 + 0.722008I
b = 1.06930 − 0.97248I
0.13038 + 7.25479I 0
u = 1.45765 + 0.48227I
a = −0.317056 − 0.548033I
b = 0.568832 + 0.060403I
−7.04915 − 1.30997I 0
u = 1.45765 − 0.48227I
a = −0.317056 + 0.548033I
b = 0.568832 − 0.060403I
−7.04915 + 1.30997I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.175247 + 0.400925I
a = −0.777483 − 1.083630I
b = 0.313669 + 0.457730I
−0.028154 − 1.020300I −0.58024 + 6.60259I
u = 0.175247 − 0.400925I
a = −0.777483 + 1.083630I
b = 0.313669 − 0.457730I
−0.028154 + 1.020300I −0.58024 − 6.60259I
u = −0.285471 + 0.308360I
a = −0.68087 + 2.61679I
b = 1.111320 − 0.014505I
−4.45448 − 0.17557I −1.85939 + 1.38698I
u = −0.285471 − 0.308360I
a = −0.68087 − 2.61679I
b = 1.111320 + 0.014505I
−4.45448 + 0.17557I −1.85939 − 1.38698I
u = −1.56445 + 0.30136I
a = 0.203232 − 0.547484I
b = −0.539303 + 0.124283I
−7.16487 − 5.31827I 0
u = −1.56445 − 0.30136I
a = 0.203232 + 0.547484I
b = −0.539303 − 0.124283I
−7.16487 + 5.31827I 0
13
II.
I
u
2
= h−2.97 × 10
8
u
23
− 6.73 × 10
8
u
22
+ · · · + 1.04 × 10
9
b − 1.58 × 10
10
, 6.42 ×
10
8
u
23
−9.01×10
9
u
22
+· · ·+9.40×10
9
a+6.73×10
10
, u
24
+u
23
+· · ·+11u+9i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
2
=
−0.0683215u
23
+ 0.957779u
22
+ ··· − 12.5163u − 7.16193
0.284163u
23
+ 0.644010u
22
+ ··· − 4.87488u + 15.1101
a
11
=
−u
−u
3
+ u
a
1
=
0.215841u
23
+ 1.60179u
22
+ ··· − 17.3912u + 7.94820
0.284163u
23
+ 0.644010u
22
+ ··· − 4.87488u + 15.1101
a
6
=
3.23542u
23
− 1.25211u
22
+ ··· + 40.0876u + 50.1277
1.02610u
23
+ 0.164052u
22
+ ··· + 4.58961u + 8.61489
a
9
=
−3.26278u
23
− 2.30081u
22
+ ··· + 25.5811u − 8.57595
2.43206u
23
+ 0.487842u
22
+ ··· + 3.07086u + 28.7240
a
3
=
−3.25988u
23
− 0.801721u
22
+ ··· − 7.72825u − 31.1982
2.75440u
23
− 0.528177u
22
+ ··· + 19.1185u + 17.5731
a
8
=
−3.09380u
23
− 1.76139u
22
+ ··· + 19.0783u − 24.4526
3.53147u
23
+ 0.759929u
22
+ ··· + 3.97813u + 41.2668
a
7
=
1.18809u
23
− 0.634541u
22
+ ··· + 21.0603u + 21.8155
1.76957u
23
− 0.340698u
22
+ ··· + 12.7290u + 12.9430
a
12
=
−7.44088u
23
− 7.91373u
22
+ ··· + 54.5822u + 4.86864
−1.49142u
23
− 0.0977790u
22
+ ··· − 5.81025u − 11.7070
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
19642376118
1044681373
u
23
−
39745603928
1044681373
u
22
+ ··· +
416986178422
1044681373
u +
161826406806
1044681373
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
24
+ 2u
22
+ ··· − 3u + 1
c
2
u
24
+ u
23
+ ··· + u + 1
c
3
u
24
+ 3u
22
+ ··· + 101u + 11
c
4
u
24
+ u
23
+ ··· + 11u + 9
c
5
u
24
+ 17u
22
+ ··· − 2u + 5
c
6
u
24
− u
23
+ ··· − 10u + 1
c
7
u
24
− u
23
+ ··· − u + 1
c
8
u
24
+ u
23
+ ··· + u + 1
c
9
u
24
+ u
23
+ ··· + u + 1
c
10
u
24
− u
23
+ ··· − 11u + 9
c
11
u
24
− u
23
+ ··· − u + 1
c
12
u
24
+ 17u
22
+ ··· + 2u + 5
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ 4y
23
+ ··· + 21y + 1
c
2
, c
7
y
24
− 15y
23
+ ··· − 9y + 1
c
3
y
24
+ 6y
23
+ ··· − 1577y + 121
c
4
, c
10
y
24
− 13y
23
+ ··· − 679y + 81
c
5
, c
12
y
24
+ 34y
23
+ ··· + 446y + 25
c
6
y
24
+ 3y
23
+ ··· + 180y + 1
c
8
, c
11
y
24
+ 19y
23
+ ··· − 13y + 1
c
9
y
24
+ 21y
23
+ ··· + 11y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.952348 + 0.136908I
a = 0.72993 + 2.89697I
b = 0.131126 − 0.384738I
−0.000597 − 0.548184I 24.3042 − 84.4549I
u = 0.952348 − 0.136908I
a = 0.72993 − 2.89697I
b = 0.131126 + 0.384738I
−0.000597 + 0.548184I 24.3042 + 84.4549I
u = 0.988311 + 0.370395I
a = −0.337958 + 0.880219I
b = −1.277510 + 0.015717I
−5.14631 − 0.87736I −4.28774 + 2.87316I
u = 0.988311 − 0.370395I
a = −0.337958 − 0.880219I
b = −1.277510 − 0.015717I
−5.14631 + 0.87736I −4.28774 − 2.87316I
u = 0.219364 + 1.039820I
a = 0.392367 − 0.200232I
b = −0.221572 − 0.274980I
2.62740 − 1.82881I 0.54296 + 5.92489I
u = 0.219364 − 1.039820I
a = 0.392367 + 0.200232I
b = −0.221572 + 0.274980I
2.62740 + 1.82881I 0.54296 − 5.92489I
u = −0.898687 + 0.258451I
a = 0.41561 + 1.84019I
b = 0.391206 − 1.205940I
3.96928 + 3.45621I 4.14366 − 9.44746I
u = −0.898687 − 0.258451I
a = 0.41561 − 1.84019I
b = 0.391206 + 1.205940I
3.96928 − 3.45621I 4.14366 + 9.44746I
u = 0.429227 + 0.822759I
a = −0.974193 + 0.323868I
b = 0.705339 − 1.048650I
6.57769 + 1.81596I 7.75965 − 0.93777I
u = 0.429227 − 0.822759I
a = −0.974193 − 0.323868I
b = 0.705339 + 1.048650I
6.57769 − 1.81596I 7.75965 + 0.93777I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.817220 + 0.285785I
a = 0.651291 + 0.552479I
b = 1.39435 + 0.98498I
−2.81443 + 6.68649I 1.88039 − 6.74067I
u = −0.817220 − 0.285785I
a = 0.651291 − 0.552479I
b = 1.39435 − 0.98498I
−2.81443 − 6.68649I 1.88039 + 6.74067I
u = −0.730770 + 0.407807I
a = −1.63357 + 0.06524I
b = 0.145468 + 0.419939I
4.24301 − 0.62693I 9.92775 − 0.77775I
u = −0.730770 − 0.407807I
a = −1.63357 − 0.06524I
b = 0.145468 − 0.419939I
4.24301 + 0.62693I 9.92775 + 0.77775I
u = −0.337191 + 1.210150I
a = 0.534317 − 0.012768I
b = −0.560439 − 0.512766I
4.19449 − 0.09855I −1.53360 + 1.03207I
u = −0.337191 − 1.210150I
a = 0.534317 + 0.012768I
b = −0.560439 + 0.512766I
4.19449 + 0.09855I −1.53360 − 1.03207I
u = 1.247280 + 0.319144I
a = 0.182048 + 0.516564I
b = −1.05708 − 1.01392I
−6.16858 − 2.32052I −3.20526 + 1.59481I
u = 1.247280 − 0.319144I
a = 0.182048 − 0.516564I
b = −1.05708 + 1.01392I
−6.16858 + 2.32052I −3.20526 − 1.59481I
u = 1.196510 + 0.496467I
a = 0.379212 − 0.918724I
b = 1.26364 + 1.26277I
3.99034 − 6.75234I 5.94192 + 5.73378I
u = 1.196510 − 0.496467I
a = 0.379212 + 0.918724I
b = 1.26364 − 1.26277I
3.99034 + 6.75234I 5.94192 − 5.73378I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.380020 + 0.011732I
a = −0.219844 + 0.402694I
b = 0.11794 − 1.72450I
−5.51750 − 5.03534I −0.41653 + 8.31154I
u = −1.380020 − 0.011732I
a = −0.219844 − 0.402694I
b = 0.11794 + 1.72450I
−5.51750 + 5.03534I −0.41653 − 8.31154I
u = −1.36915 + 0.68109I
a = −0.008103 − 0.744150I
b = −1.032460 + 0.799143I
0.62495 + 6.93129I 6.44261 − 5.40646I
u = −1.36915 − 0.68109I
a = −0.008103 + 0.744150I
b = −1.032460 − 0.799143I
0.62495 − 6.93129I 6.44261 + 5.40646I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
24
+ 2u
22
+ ··· − 3u + 1)(u
86
− 3u
85
+ ··· − 1090u + 331)
c
2
(u
24
+ u
23
+ ··· + u + 1)(u
86
+ 2u
85
+ ··· + 98u + 47)
c
3
(u
24
+ 3u
22
+ ··· + 101u + 11)(u
86
− u
85
+ ··· − 18u + 4)
c
4
(u
24
+ u
23
+ ··· + 11u + 9)(u
86
− 26u
84
+ ··· − 352u + 143)
c
5
(u
24
+ 17u
22
+ ··· − 2u + 5)(u
86
+ u
85
+ ··· − 2490u + 2156)
c
6
(u
24
− u
23
+ ··· − 10u + 1)
· (u
86
− 28u
84
+ ··· − 145161863u + 33647749)
c
7
(u
24
− u
23
+ ··· − u + 1)(u
86
+ 2u
85
+ ··· + 98u + 47)
c
8
(u
24
+ u
23
+ ··· + u + 1)(u
86
+ 4u
85
+ ··· + 460u + 221)
c
9
(u
24
+ u
23
+ ··· + u + 1)(u
86
+ 2u
85
+ ··· + 7484u + 1411)
c
10
(u
24
− u
23
+ ··· − 11u + 9)(u
86
− 26u
84
+ ··· − 352u + 143)
c
11
(u
24
− u
23
+ ··· − u + 1)(u
86
+ 4u
85
+ ··· + 460u + 221)
c
12
(u
24
+ 17u
22
+ ··· + 2u + 5)(u
86
+ u
85
+ ··· − 2490u + 2156)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
24
+ 4y
23
+ ··· + 21y + 1)(y
86
− 7y
85
+ ··· − 234820y + 109561)
c
2
, c
7
(y
24
− 15y
23
+ ··· − 9y + 1)(y
86
− 26y
85
+ ··· − 35642y + 2209)
c
3
(y
24
+ 6y
23
+ ··· − 1577y + 121)(y
86
+ 31y
85
+ ··· − 988y + 16)
c
4
, c
10
(y
24
− 13y
23
+ ··· − 679y + 81)
· (y
86
− 52y
85
+ ··· − 226292y + 20449)
c
5
, c
12
(y
24
+ 34y
23
+ ··· + 446y + 25)
· (y
86
+ 59y
85
+ ··· + 168629940y + 4648336)
c
6
(y
24
+ 3y
23
+ ··· + 180y + 1)
· (y
86
− 56y
85
+ ··· + 41812736405652607y + 1132171012767001)
c
8
, c
11
(y
24
+ 19y
23
+ ··· − 13y + 1)
· (y
86
+ 80y
85
+ ··· + 18613622y + 48841)
c
9
(y
24
+ 21y
23
+ ··· + 11y + 1)
· (y
86
+ 42y
85
+ ··· + 83072014y + 1990921)
23
