12n
0861
(K12n
0861
)
A knot diagram
1
Linearized knot diagam
4 7 10 12 2 9 12 3 6 1 4 8
Solving Sequence
1,4 2,8
12 5 6 7 11 10 3 9
c
1
c
12
c
4
c
5
c
7
c
11
c
10
c
3
c
9
c
2
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.52500 × 10
352
u
75
+ 2.44054 × 10
352
u
74
+ ··· + 7.62932 × 10
355
b − 3.61083 × 10
356
,
1.06932 × 10
357
u
75
− 9.06361 × 10
356
u
74
+ ··· + 1.73575 × 10
360
a + 3.60585 × 10
361
,
u
76
− u
75
+ ··· + 300923u − 22751i
I
u
2
= h1.63851 × 10
16
u
28
− 1.05439 × 10
17
u
27
+ ··· + 2.06022 × 10
16
b + 2.70631 × 10
16
,
− 1.08672 × 10
17
u
28
+ 6.98492 × 10
17
u
27
+ ··· + 2.06022 × 10
16
a − 1.87524 × 10
17
, u
29
− 6u
28
+ ··· + 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 105 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−3.52 × 10
352
u
75
+ 2.44 × 10
352
u
74
+ · · · + 7.63 × 10
355
b − 3.61 ×
10
356
, 1.07 × 10
357
u
75
− 9.06 × 10
356
u
74
+ · · · + 1.74 × 10
360
a + 3.61 ×
10
361
, u
76
− u
75
+ · · · + 300923u − 22751i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
8
=
−0.000616058u
75
+ 0.000522174u
74
+ ··· + 215.201u − 20.7741
0.000462033u
75
− 0.000319890u
74
+ ··· − 58.5348u + 4.73283
a
12
=
−0.000551004u
75
+ 0.000291524u
74
+ ··· + 274.093u − 26.3938
0.000186949u
75
− 0.000146137u
74
+ ··· − 131.746u + 12.9652
a
5
=
0.0000761766u
75
− 0.000159869u
74
+ ··· − 182.673u + 18.3344
0.000150608u
75
− 0.000110104u
74
+ ··· − 11.9614u + 0.330376
a
6
=
−0.0000399552u
75
+ 0.0000247574u
74
+ ··· − 143.793u + 16.0999
0.000269364u
75
− 0.000203992u
74
+ ··· − 35.2152u + 1.88871
a
7
=
−0.000554392u
75
+ 0.000760906u
74
+ ··· + 286.400u − 25.1589
0.000189206u
75
− 0.000484611u
74
+ ··· − 184.889u + 14.2787
a
11
=
−0.000551004u
75
+ 0.000291524u
74
+ ··· + 274.093u − 26.3938
0.000221974u
75
− 0.000216748u
74
+ ··· − 197.293u + 18.8687
a
10
=
−0.000772978u
75
+ 0.000508271u
74
+ ··· + 471.387u − 45.2625
0.000221974u
75
− 0.000216748u
74
+ ··· − 197.293u + 18.8687
a
3
=
−3.12392 × 10
−6
u
75
− 0.000182643u
74
+ ··· + 63.4430u − 9.84321
0.0000430791u
75
+ 0.000157885u
74
+ ··· + 80.3500u − 6.25668
a
9
=
−0.000272927u
75
− 0.0000644983u
74
+ ··· + 230.916u − 26.2228
−0.0000751541u
75
+ 0.000223603u
74
+ ··· − 12.0363u + 4.65606
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00205545u
75
+ 0.000950151u
74
+ ··· + 1477.37u − 145.995
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
76
+ u
75
+ ··· − 300923u − 22751
c
2
u
76
− 2u
75
+ ··· − 180357u − 34261
c
3
u
76
− 3u
75
+ ··· + 950u − 239
c
4
, c
11
u
76
+ u
75
+ ··· − 1646518u − 62039
c
5
u
76
− 4u
75
+ ··· + 291884216u − 85317983
c
6
, c
9
u
76
− 3u
75
+ ··· − 42u + 23
c
7
, c
12
u
76
+ 2u
75
+ ··· − u + 31
c
8
u
76
+ u
75
+ ··· − 18688u − 11776
c
10
u
76
+ 6u
75
+ ··· + 2676u + 188
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
76
+ 85y
75
+ ··· − 1833669277y + 517608001
c
2
y
76
+ 36y
75
+ ··· + 45049425637y + 1173816121
c
3
y
76
− 31y
75
+ ··· − 1544932y + 57121
c
4
, c
11
y
76
+ 111y
75
+ ··· + 216897789578y + 3848837521
c
5
y
76
+ 74y
75
+ ··· − 351345007231565290y + 7279158223188289
c
6
, c
9
y
76
+ 51y
75
+ ··· − 8066y + 529
c
7
, c
12
y
76
− 58y
75
+ ··· − 81903y + 961
c
8
y
76
+ 15y
75
+ ··· + 1338966016y + 138674176
c
10
y
76
− 96y
75
+ ··· − 10840512y + 35344
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.745344 + 0.628629I
a = 0.638596 − 0.882206I
b = −1.288040 − 0.178047I
7.01585 − 1.22697I 0
u = −0.745344 − 0.628629I
a = 0.638596 + 0.882206I
b = −1.288040 + 0.178047I
7.01585 + 1.22697I 0
u = 0.020527 + 0.950968I
a = −1.127270 − 0.499083I
b = −0.722798 + 0.214158I
8.72656 − 0.96900I 0
u = 0.020527 − 0.950968I
a = −1.127270 + 0.499083I
b = −0.722798 − 0.214158I
8.72656 + 0.96900I 0
u = 0.727085 + 0.569994I
a = −0.801002 + 0.627162I
b = 0.648815 + 0.029076I
0.99072 − 2.35150I 0
u = 0.727085 − 0.569994I
a = −0.801002 − 0.627162I
b = 0.648815 − 0.029076I
0.99072 + 2.35150I 0
u = 0.621479 + 0.677375I
a = −0.16397 − 1.43224I
b = 1.386790 + 0.087175I
3.03454 + 6.06445I 0
u = 0.621479 − 0.677375I
a = −0.16397 + 1.43224I
b = 1.386790 − 0.087175I
3.03454 − 6.06445I 0
u = −0.126756 + 0.902600I
a = −0.109634 + 0.577545I
b = 0.404644 + 0.757455I
1.54671 − 3.66888I −6.00000 + 0.I
u = −0.126756 − 0.902600I
a = −0.109634 − 0.577545I
b = 0.404644 − 0.757455I
1.54671 + 3.66888I −6.00000 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825725 + 0.760842I
a = 0.390520 + 0.782654I
b = −1.279230 − 0.250596I
−0.60298 + 1.46108I 0
u = 0.825725 − 0.760842I
a = 0.390520 − 0.782654I
b = −1.279230 + 0.250596I
−0.60298 − 1.46108I 0
u = 0.360627 + 0.796177I
a = 0.508375 − 0.143903I
b = −0.720350 − 0.667858I
−1.343280 + 0.170584I −9.40191 + 0.I
u = 0.360627 − 0.796177I
a = 0.508375 + 0.143903I
b = −0.720350 + 0.667858I
−1.343280 − 0.170584I −9.40191 + 0.I
u = 1.118660 + 0.264884I
a = 0.864685 + 0.423066I
b = −0.841814 − 0.122191I
−0.156617 + 0.099671I 0
u = 1.118660 − 0.264884I
a = 0.864685 − 0.423066I
b = −0.841814 + 0.122191I
−0.156617 − 0.099671I 0
u = 0.763976 + 0.362230I
a = 0.98638 + 1.88979I
b = −0.402873 + 1.099930I
−4.31920 − 3.42786I −19.8780 + 4.5386I
u = 0.763976 − 0.362230I
a = 0.98638 − 1.88979I
b = −0.402873 − 1.099930I
−4.31920 + 3.42786I −19.8780 − 4.5386I
u = 0.085627 + 0.830294I
a = −0.607873 − 1.037560I
b = 1.106530 − 0.524906I
3.67066 − 8.51476I 0. + 8.44330I
u = 0.085627 − 0.830294I
a = −0.607873 + 1.037560I
b = 1.106530 + 0.524906I
3.67066 + 8.51476I 0. − 8.44330I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.218030 + 0.054638I
a = −0.196176 + 0.535276I
b = 1.37856 + 0.40360I
2.04240 + 2.56590I 0
u = −1.218030 − 0.054638I
a = −0.196176 − 0.535276I
b = 1.37856 − 0.40360I
2.04240 − 2.56590I 0
u = 0.272344 + 1.191320I
a = −0.033570 + 0.340343I
b = 0.363637 − 0.018798I
2.51398 − 2.03885I 0
u = 0.272344 − 1.191320I
a = −0.033570 − 0.340343I
b = 0.363637 + 0.018798I
2.51398 + 2.03885I 0
u = 0.147091 + 0.751571I
a = 0.750874 + 0.500899I
b = −1.008700 + 0.583869I
−0.23633 − 4.75906I −6.00000 + 8.13977I
u = 0.147091 − 0.751571I
a = 0.750874 − 0.500899I
b = −1.008700 − 0.583869I
−0.23633 + 4.75906I −6.00000 − 8.13977I
u = −1.202870 + 0.464965I
a = −0.214421 + 1.159960I
b = 0.395217 + 1.242940I
−1.75971 + 3.56787I 0
u = −1.202870 − 0.464965I
a = −0.214421 − 1.159960I
b = 0.395217 − 1.242940I
−1.75971 − 3.56787I 0
u = 0.180012 + 0.660238I
a = −1.42717 + 0.72834I
b = 0.987544 − 0.454175I
2.60983 − 3.55639I −1.71782 + 4.54707I
u = 0.180012 − 0.660238I
a = −1.42717 − 0.72834I
b = 0.987544 + 0.454175I
2.60983 + 3.55639I −1.71782 − 4.54707I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.265518 + 0.599050I
a = 0.898932 − 0.825195I
b = −0.984381 + 0.600542I
1.50045 − 3.70876I −1.41090 + 2.23872I
u = 0.265518 − 0.599050I
a = 0.898932 + 0.825195I
b = −0.984381 − 0.600542I
1.50045 + 3.70876I −1.41090 − 2.23872I
u = −0.577191 + 0.293566I
a = 2.84221 + 1.82785I
b = 0.207376 + 0.118904I
−1.52793 + 5.92164I −15.0040 − 10.8200I
u = −0.577191 − 0.293566I
a = 2.84221 − 1.82785I
b = 0.207376 − 0.118904I
−1.52793 − 5.92164I −15.0040 + 10.8200I
u = 0.576435 + 0.027198I
a = 0.345959 − 0.803920I
b = −0.225583 + 0.466790I
−0.192361 − 0.594079I −7.06569 + 1.37870I
u = 0.576435 − 0.027198I
a = 0.345959 + 0.803920I
b = −0.225583 − 0.466790I
−0.192361 + 0.594079I −7.06569 − 1.37870I
u = −0.561296
a = −4.20681
b = −0.187845
−5.66991 −25.0200
u = 0.559589
a = 0.749078
b = −0.400812
−0.827641 −12.6600
u = 0.25722 + 1.42794I
a = 2.05582 + 0.52788I
b = −1.274310 − 0.019943I
11.20280 − 0.15528I 0
u = 0.25722 − 1.42794I
a = 2.05582 − 0.52788I
b = −1.274310 + 0.019943I
11.20280 + 0.15528I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.97136 + 1.08637I
a = −0.995241 − 0.731028I
b = 1.135640 + 0.056806I
2.35456 − 2.27995I 0
u = 0.97136 − 1.08637I
a = −0.995241 + 0.731028I
b = 1.135640 − 0.056806I
2.35456 + 2.27995I 0
u = 0.30853 + 1.43443I
a = 0.284046 − 0.099194I
b = −0.277549 − 0.312634I
4.40418 − 4.79001I 0
u = 0.30853 − 1.43443I
a = 0.284046 + 0.099194I
b = −0.277549 + 0.312634I
4.40418 + 4.79001I 0
u = −0.067455 + 0.452588I
a = 0.477832 + 0.316060I
b = 0.930631 − 0.514027I
1.43480 − 1.90006I −0.70055 + 2.19888I
u = −0.067455 − 0.452588I
a = 0.477832 − 0.316060I
b = 0.930631 + 0.514027I
1.43480 + 1.90006I −0.70055 − 2.19888I
u = −1.55658 + 0.38390I
a = 0.407638 − 0.407877I
b = −1.46643 − 0.28303I
4.94644 + 8.22620I 0
u = −1.55658 − 0.38390I
a = 0.407638 + 0.407877I
b = −1.46643 + 0.28303I
4.94644 − 8.22620I 0
u = −0.26666 + 1.59851I
a = −0.215919 − 0.059608I
b = −0.210777 + 1.071740I
9.54808 − 2.17862I 0
u = −0.26666 − 1.59851I
a = −0.215919 + 0.059608I
b = −0.210777 − 1.071740I
9.54808 + 2.17862I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01828 + 1.67725I
a = −1.61898 + 0.17473I
b = 1.52774 − 0.01220I
10.91570 − 4.00758I 0
u = 0.01828 − 1.67725I
a = −1.61898 − 0.17473I
b = 1.52774 + 0.01220I
10.91570 + 4.00758I 0
u = 0.282838 + 0.079836I
a = −1.25772 + 1.67744I
b = 0.704308 − 0.473313I
0.84979 − 1.97171I −2.94349 + 5.82225I
u = 0.282838 − 0.079836I
a = −1.25772 − 1.67744I
b = 0.704308 + 0.473313I
0.84979 + 1.97171I −2.94349 − 5.82225I
u = 0.44868 + 1.68762I
a = −1.54430 − 0.42875I
b = 1.261110 − 0.081880I
5.65141 − 2.61228I 0
u = 0.44868 − 1.68762I
a = −1.54430 + 0.42875I
b = 1.261110 + 0.081880I
5.65141 + 2.61228I 0
u = −0.69546 + 1.62144I
a = 1.147750 − 0.810044I
b = −1.37785 − 0.72108I
12.83640 + 4.42759I 0
u = −0.69546 − 1.62144I
a = 1.147750 + 0.810044I
b = −1.37785 + 0.72108I
12.83640 − 4.42759I 0
u = −0.03860 + 1.79969I
a = 1.389460 − 0.106592I
b = −1.57865 + 0.10854I
9.56745 − 3.21352I 0
u = −0.03860 − 1.79969I
a = 1.389460 + 0.106592I
b = −1.57865 − 0.10854I
9.56745 + 3.21352I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.24078 + 1.82244I
a = −0.1001830 − 0.0695988I
b = −0.00953 + 1.44601I
7.24266 + 9.15838I 0
u = −0.24078 − 1.82244I
a = −0.1001830 + 0.0695988I
b = −0.00953 − 1.44601I
7.24266 − 9.15838I 0
u = −0.38183 + 1.81667I
a = 0.1287720 + 0.0315564I
b = 0.23828 − 1.46403I
3.74470 + 2.77968I 0
u = −0.38183 − 1.81667I
a = 0.1287720 − 0.0315564I
b = 0.23828 + 1.46403I
3.74470 − 2.77968I 0
u = −0.67554 + 1.79315I
a = −1.146360 + 0.625617I
b = 1.49240 + 0.68959I
7.94098 + 10.39540I 0
u = −0.67554 − 1.79315I
a = −1.146360 − 0.625617I
b = 1.49240 − 0.68959I
7.94098 − 10.39540I 0
u = −0.59997 + 1.83527I
a = 1.210690 − 0.563117I
b = −1.50417 − 0.64157I
12.0200 + 16.4075I 0
u = −0.59997 − 1.83527I
a = 1.210690 + 0.563117I
b = −1.50417 + 0.64157I
12.0200 − 16.4075I 0
u = 0.03558 + 1.95180I
a = −1.300520 − 0.212919I
b = 1.43479 − 0.47900I
14.6402 − 7.6727I 0
u = 0.03558 − 1.95180I
a = −1.300520 + 0.212919I
b = 1.43479 + 0.47900I
14.6402 + 7.6727I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05564 + 1.95942I
a = 1.251980 + 0.136007I
b = −1.58037 + 0.38673I
10.27980 − 3.77420I 0
u = 0.05564 − 1.95942I
a = 1.251980 − 0.136007I
b = −1.58037 − 0.38673I
10.27980 + 3.77420I 0
u = 0.38826 + 1.93316I
a = 1.42376 + 0.30397I
b = −1.262730 + 0.174887I
7.68773 − 6.74339I 0
u = 0.38826 − 1.93316I
a = 1.42376 − 0.30397I
b = −1.262730 − 0.174887I
7.68773 + 6.74339I 0
u = 0.16244 + 1.98102I
a = −1.132750 − 0.227902I
b = 1.70644 − 0.59120I
12.71850 + 1.45775I 0
u = 0.16244 − 1.98102I
a = −1.132750 + 0.227902I
b = 1.70644 + 0.59120I
12.71850 − 1.45775I 0
12
II.
I
u
2
= h1.64×10
16
u
28
−1.05×10
17
u
27
+· · ·+2.06×10
16
b+2.71×10
16
, −1.09×
10
17
u
28
+6.98×10
17
u
27
+· · ·+2.06×10
16
a−1.88×10
17
, u
29
−6u
28
+· · ·+3u+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
8
=
5.27476u
28
− 33.9037u
27
+ ··· + 8.71342u + 9.10213
−0.795306u
28
+ 5.11785u
27
+ ··· − 1.44520u − 1.31360
a
12
=
−0.873952u
28
+ 5.57757u
27
+ ··· − 0.432124u − 3.91280
0.100754u
28
− 0.413558u
27
+ ··· − 0.187948u + 0.327168
a
5
=
0.979568u
28
− 5.87044u
27
+ ··· + 0.0162660u + 4.14203
−0.113181u
28
+ 0.795544u
27
+ ··· + 2.01581u + 0.135065
a
6
=
u
28
− 6u
27
+ ··· − 3u + 4
−0.0204323u
28
+ 0.129558u
27
+ ··· + 2.01627u + 0.142029
a
7
=
4.09510u
28
− 26.3923u
27
+ ··· + 7.13642u + 6.99365
−0.820942u
28
+ 5.02861u
27
+ ··· − 0.0730875u − 0.703261
a
11
=
−0.873952u
28
+ 5.57757u
27
+ ··· − 0.432124u − 3.91280
0.184622u
28
− 1.08159u
27
+ ··· − 0.0603329u + 0.661024
a
10
=
−1.05857u
28
+ 6.65916u
27
+ ··· − 0.371791u − 4.57382
0.184622u
28
− 1.08159u
27
+ ··· − 0.0603329u + 0.661024
a
3
=
−0.982205u
28
+ 6.25792u
27
+ ··· + 2.82992u − 4.37507
−0.0177953u
28
− 0.257924u
27
+ ··· + 0.170078u + 0.375072
a
9
=
0.517381u
28
− 3.85054u
27
+ ··· − 1.46246u − 1.45227
0.366015u
28
− 2.30882u
27
+ ··· + 1.01287u + 1.15728
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
5020408209776801
20602204490473833
u
28
−
20930493412487363
20602204490473833
u
27
+ ···−
250778254491184010
20602204490473833
u −
84750696773007142
20602204490473833
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
29
− 6u
28
+ ··· + 3u + 1
c
2
u
29
− u
28
+ ··· − u + 1
c
3
u
29
− 2u
28
+ ··· + 2u + 9
c
4
u
29
+ 10u
27
+ ··· + 2u + 1
c
5
u
29
− 3u
28
+ ··· + 8u − 3
c
6
u
29
− 4u
28
+ ··· + 8u − 5
c
7
u
29
+ u
28
+ ··· − 3u − 1
c
8
u
29
− 2u
27
+ ··· + u − 1
c
9
u
29
+ 4u
28
+ ··· + 8u + 5
c
10
u
29
+ 11u
28
+ ··· + 272u + 64
c
11
u
29
+ 10u
27
+ ··· + 2u − 1
c
12
u
29
− u
28
+ ··· − 3u + 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 14y
28
+ ··· + 13y −1
c
2
y
29
+ 5y
28
+ ··· − 25y −1
c
3
y
29
− 22y
28
+ ··· + 1120y −81
c
4
, c
11
y
29
+ 20y
28
+ ··· − 6y −1
c
5
y
29
+ 23y
28
+ ··· − 2210y −9
c
6
, c
9
y
29
+ 20y
28
+ ··· − 246y −25
c
7
, c
12
y
29
− 17y
28
+ ··· + 15y −1
c
8
y
29
− 4y
28
+ ··· + 19y −1
c
10
y
29
− 31y
28
+ ··· + 35456y −4096
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.259109 + 0.945037I
a = −1.080660 − 0.357074I
b = −0.780404 − 0.324779I
8.64197 + 0.21685I −2.86434 + 2.12533I
u = 0.259109 − 0.945037I
a = −1.080660 + 0.357074I
b = −0.780404 + 0.324779I
8.64197 − 0.21685I −2.86434 − 2.12533I
u = 0.704526 + 0.745254I
a = 0.972567 − 0.007301I
b = −0.897192 + 0.447753I
0.82005 − 4.34238I −9.35046 + 9.67287I
u = 0.704526 − 0.745254I
a = 0.972567 + 0.007301I
b = −0.897192 − 0.447753I
0.82005 + 4.34238I −9.35046 − 9.67287I
u = 1.096450 + 0.340678I
a = −0.782276 + 0.014378I
b = 0.952711 + 0.288700I
−0.096889 + 1.059210I −5.71610 − 5.66520I
u = 1.096450 − 0.340678I
a = −0.782276 − 0.014378I
b = 0.952711 − 0.288700I
−0.096889 − 1.059210I −5.71610 + 5.66520I
u = −0.731144 + 0.434174I
a = 1.00977 − 1.81449I
b = −0.401645 − 1.267120I
−3.92079 + 3.42406I 1.01570 − 3.66847I
u = −0.731144 − 0.434174I
a = 1.00977 + 1.81449I
b = −0.401645 + 1.267120I
−3.92079 − 3.42406I 1.01570 + 3.66847I
u = 1.135540 + 0.454612I
a = −0.159669 − 1.216070I
b = 0.461864 − 1.034650I
−2.22120 − 3.35796I −11.56383 + 0.08079I
u = 1.135540 − 0.454612I
a = −0.159669 + 1.216070I
b = 0.461864 + 1.034650I
−2.22120 + 3.35796I −11.56383 − 0.08079I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.851882 + 0.878765I
a = 1.077320 + 0.062467I
b = −0.923927 − 0.409470I
0.835073 − 0.864790I −3.44234 + 1.11234I
u = 0.851882 − 0.878765I
a = 1.077320 − 0.062467I
b = −0.923927 + 0.409470I
0.835073 + 0.864790I −3.44234 − 1.11234I
u = 0.754297 + 0.141451I
a = −0.841119 + 0.675278I
b = 1.035810 + 0.412800I
0.565382 + 1.291710I −7.41669 + 1.05659I
u = 0.754297 − 0.141451I
a = −0.841119 − 0.675278I
b = 1.035810 − 0.412800I
0.565382 − 1.291710I −7.41669 − 1.05659I
u = −0.479702 + 0.524804I
a = −0.255705 − 0.662679I
b = −1.227420 + 0.667940I
−0.81307 − 3.28943I −7.56569 + 2.62758I
u = −0.479702 − 0.524804I
a = −0.255705 + 0.662679I
b = −1.227420 − 0.667940I
−0.81307 + 3.28943I −7.56569 − 2.62758I
u = −0.634588 + 0.145110I
a = 1.023890 + 0.427581I
b = 1.288000 + 0.395187I
2.06821 + 7.80740I −5.10645 − 6.62516I
u = −0.634588 − 0.145110I
a = 1.023890 − 0.427581I
b = 1.288000 − 0.395187I
2.06821 − 7.80740I −5.10645 + 6.62516I
u = 0.292740 + 1.369130I
a = 0.271069 + 0.041571I
b = 0.052853 + 0.634842I
1.86887 − 2.01799I −10.56338 + 1.39675I
u = 0.292740 − 1.369130I
a = 0.271069 − 0.041571I
b = 0.052853 − 0.634842I
1.86887 + 2.01799I −10.56338 − 1.39675I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.20003 + 1.41050I
a = −0.379616 − 0.305394I
b = 0.478129 − 0.287288I
4.64971 − 5.47671I −0.30377 + 8.70786I
u = 0.20003 − 1.41050I
a = −0.379616 + 0.305394I
b = 0.478129 + 0.287288I
4.64971 + 5.47671I −0.30377 − 8.70786I
u = −0.398804 + 0.328085I
a = −3.88733 − 2.80334I
b = 0.604532 − 0.070140I
−1.15102 + 5.69646I 1.06495 − 1.13297I
u = −0.398804 − 0.328085I
a = −3.88733 + 2.80334I
b = 0.604532 + 0.070140I
−1.15102 − 5.69646I 1.06495 + 1.13297I
u = 0.17820 + 1.57230I
a = 1.78506 + 0.24543I
b = −1.42479 + 0.21602I
11.35920 − 2.31492I 0.59328 + 1.42865I
u = 0.17820 − 1.57230I
a = 1.78506 − 0.24543I
b = −1.42479 − 0.21602I
11.35920 + 2.31492I 0.59328 − 1.42865I
u = −0.403835
a = 6.22569
b = −0.575344
−5.33901 0.139890
u = −0.02661 + 1.85032I
a = −1.366150 + 0.138779I
b = 1.56915 − 0.00379I
9.67281 − 4.05990I −3.35082 + 7.08829I
u = −0.02661 − 1.85032I
a = −1.366150 − 0.138779I
b = 1.56915 + 0.00379I
9.67281 + 4.05990I −3.35082 − 7.08829I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
29
− 6u
28
+ ··· + 3u + 1)(u
76
+ u
75
+ ··· − 300923u − 22751)
c
2
(u
29
− u
28
+ ··· − u + 1)(u
76
− 2u
75
+ ··· − 180357u − 34261)
c
3
(u
29
− 2u
28
+ ··· + 2u + 9)(u
76
− 3u
75
+ ··· + 950u − 239)
c
4
(u
29
+ 10u
27
+ ··· + 2u + 1)(u
76
+ u
75
+ ··· − 1646518u − 62039)
c
5
(u
29
− 3u
28
+ ··· + 8u − 3)
· (u
76
− 4u
75
+ ··· + 291884216u − 85317983)
c
6
(u
29
− 4u
28
+ ··· + 8u − 5)(u
76
− 3u
75
+ ··· − 42u + 23)
c
7
(u
29
+ u
28
+ ··· − 3u − 1)(u
76
+ 2u
75
+ ··· − u + 31)
c
8
(u
29
− 2u
27
+ ··· + u − 1)(u
76
+ u
75
+ ··· − 18688u − 11776)
c
9
(u
29
+ 4u
28
+ ··· + 8u + 5)(u
76
− 3u
75
+ ··· − 42u + 23)
c
10
(u
29
+ 11u
28
+ ··· + 272u + 64)(u
76
+ 6u
75
+ ··· + 2676u + 188)
c
11
(u
29
+ 10u
27
+ ··· + 2u − 1)(u
76
+ u
75
+ ··· − 1646518u − 62039)
c
12
(u
29
− u
28
+ ··· − 3u + 1)(u
76
+ 2u
75
+ ··· − u + 31)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
29
+ 14y
28
+ ··· + 13y −1)
· (y
76
+ 85y
75
+ ··· − 1833669277y + 517608001)
c
2
(y
29
+ 5y
28
+ ··· − 25y −1)
· (y
76
+ 36y
75
+ ··· + 45049425637y + 1173816121)
c
3
(y
29
− 22y
28
+ ··· + 1120y −81)
· (y
76
− 31y
75
+ ··· − 1544932y + 57121)
c
4
, c
11
(y
29
+ 20y
28
+ ··· − 6y −1)
· (y
76
+ 111y
75
+ ··· + 216897789578y + 3848837521)
c
5
(y
29
+ 23y
28
+ ··· − 2210y −9)
· (y
76
+ 74y
75
+ ··· − 351345007231565290y + 7279158223188289)
c
6
, c
9
(y
29
+ 20y
28
+ ··· − 246y −25)(y
76
+ 51y
75
+ ··· − 8066y + 529)
c
7
, c
12
(y
29
− 17y
28
+ ··· + 15y −1)(y
76
− 58y
75
+ ··· − 81903y + 961)
c
8
(y
29
− 4y
28
+ ··· + 19y −1)
· (y
76
+ 15y
75
+ ··· + 1338966016y + 138674176)
c
10
(y
29
− 31y
28
+ ··· + 35456y −4096)
· (y
76
− 96y
75
+ ··· − 10840512y + 35344)
22
