12n
0728
(K12n
0728
)
A knot diagram
1
Linearized knot diagam
4 10 9 10 1 3 4 12 7 1 8 6
Solving Sequence
7,9 4,10
3 2 1 6 5 12 8 11
c
9
c
3
c
2
c
1
c
6
c
5
c
12
c
8
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.01387 × 10
267
u
81
+ 3.48609 × 10
267
u
80
+ ··· + 2.22405 × 10
267
b + 4.23115 × 10
269
,
− 2.64646 × 10
270
u
81
+ 8.98482 × 10
270
u
80
+ ··· + 1.75700 × 10
269
a + 1.03533 × 10
273
,
u
82
− 4u
81
+ ··· − 894u + 237i
I
u
2
= h−5.22864 × 10
27
u
28
− 2.99746 × 10
31
u
27
+ ··· + 1.50231 × 10
32
b − 4.81229 × 10
32
,
− 1.28844 × 10
32
u
28
− 5.79283 × 10
31
u
27
+ ··· + 5.00769 × 10
31
a − 4.89974 × 10
32
, u
29
+ u
28
+ ··· + 21u + 3i
* 2 irreducible components of dim
C
= 0, with total 111 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−1.01 × 10
267
u
81
+ 3.49 × 10
267
u
80
+ · · · + 2.22 × 10
267
b + 4.23 ×
10
269
, −2.65 × 10
270
u
81
+ 8.98 × 10
270
u
80
+ · · · + 1.76 × 10
269
a + 1.04 ×
10
273
, u
82
− 4u
81
+ · · · − 894u + 237i
(i) Arc colorings
a
7
=
0
u
a
9
=
1
0
a
4
=
15.0624u
81
− 51.1374u
80
+ ··· + 12694.4u − 5892.60
0.455867u
81
− 1.56745u
80
+ ··· + 424.525u − 190.246
a
10
=
1
u
2
a
3
=
14.6066u
81
− 49.5699u
80
+ ··· + 12269.8u − 5702.36
0.455867u
81
− 1.56745u
80
+ ··· + 424.525u − 190.246
a
2
=
9.68886u
81
− 32.9414u
80
+ ··· + 8238.54u − 3793.65
−1.52253u
81
+ 5.00949u
80
+ ··· − 1129.77u + 530.774
a
1
=
−9.32638u
81
+ 30.9392u
80
+ ··· − 7468.80u + 3517.86
0.580835u
81
− 1.94165u
80
+ ··· + 527.411u − 163.415
a
6
=
−10.4342u
81
+ 34.5042u
80
+ ··· − 8588.49u + 3567.69
−0.0359770u
81
+ 0.402833u
80
+ ··· − 246.388u + 125.616
a
5
=
20.0850u
81
− 68.1817u
80
+ ··· + 16846.5u − 7861.99
2.37573u
81
− 8.00559u
80
+ ··· + 1957.35u − 912.163
a
12
=
−44.6363u
81
+ 148.888u
80
+ ··· − 36104.8u + 16270.5
−0.966828u
81
+ 3.01023u
80
+ ··· − 682.104u + 297.723
a
8
=
−11.1285u
81
+ 37.2025u
80
+ ··· − 9471.64u + 3960.48
−0.658286u
81
+ 2.29544u
80
+ ··· − 634.762u + 267.171
a
11
=
−44.4234u
81
+ 146.964u
80
+ ··· − 35127.7u + 15332.5
−3.66095u
81
+ 11.6545u
80
+ ··· − 2709.62u + 1037.57
(ii) Obstruction class = −1
(iii) Cusp Shapes = 154.575u
81
− 514.077u
80
+ ··· + 124681.u − 53829.8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
82
+ 14u
81
+ ··· − 99113733u + 12092767
c
2
3(3u
82
+ 12u
81
+ ··· + 1.10464 × 10
9
u − 1.02450 × 10
8
)
c
3
3(3u
82
+ 3u
81
+ ··· + 7u + 1)
c
4
3(3u
82
− 140u
80
+ ··· − 10653u − 4399)
c
5
, c
12
u
82
+ 10u
80
+ ··· − 1416u − 528
c
6
u
82
+ 2u
81
+ ··· + 29u − 47
c
7
u
82
+ 23u
80
+ ··· − 84216u − 19056
c
8
, c
11
u
82
+ 2u
81
+ ··· + 169u − 97
c
9
u
82
− 4u
81
+ ··· − 894u + 237
c
10
u
82
− 3u
81
+ ··· + 5918619u − 282651
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
82
− 126y
81
+ ··· − 2530004844652363y + 146235013716289
c
2
9
· (9y
82
− 390y
81
+ ··· − 204245228366900018y + 10495960905341209)
c
3
9(9y
82
+ 123y
81
+ ··· − 27y + 1)
c
4
9(9y
82
− 840y
81
+ ··· − 1.02859 × 10
7
y + 1.93512 × 10
7
)
c
5
, c
12
y
82
+ 20y
81
+ ··· − 716736y + 278784
c
6
y
82
− 8y
81
+ ··· − 9959y + 2209
c
7
y
82
+ 46y
81
+ ··· + 23494984512y + 363131136
c
8
, c
11
y
82
− 28y
81
+ ··· − 256511y + 9409
c
9
y
82
− 12y
81
+ ··· − 2374338y + 56169
c
10
y
82
− 111y
81
+ ··· − 288406262487y + 79891587801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.850271 + 0.515578I
a = 0.271447 − 0.749585I
b = 1.179440 − 0.554371I
−7.33455 + 2.04069I 0
u = −0.850271 − 0.515578I
a = 0.271447 + 0.749585I
b = 1.179440 + 0.554371I
−7.33455 − 2.04069I 0
u = −0.755219 + 0.688817I
a = −0.72036 + 1.59123I
b = 0.701325 + 0.987821I
1.00223 + 2.76606I 0
u = −0.755219 − 0.688817I
a = −0.72036 − 1.59123I
b = 0.701325 − 0.987821I
1.00223 − 2.76606I 0
u = −0.398931 + 0.892202I
a = 0.834745 − 0.074502I
b = −0.743019 − 0.751372I
4.58774 + 5.09155I 0
u = −0.398931 − 0.892202I
a = 0.834745 + 0.074502I
b = −0.743019 + 0.751372I
4.58774 − 5.09155I 0
u = 0.645792 + 0.799973I
a = 0.285156 + 0.007683I
b = 0.588642 + 0.643448I
1.69738 + 2.28323I 0
u = 0.645792 − 0.799973I
a = 0.285156 − 0.007683I
b = 0.588642 − 0.643448I
1.69738 − 2.28323I 0
u = −0.751624 + 0.604004I
a = 0.18526 − 2.11592I
b = −0.297311 − 0.628227I
−6.95730 + 2.32221I 0
u = −0.751624 − 0.604004I
a = 0.18526 + 2.11592I
b = −0.297311 + 0.628227I
−6.95730 − 2.32221I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.927322 + 0.255571I
a = −0.154516 + 0.769316I
b = −0.320781 + 1.056570I
−0.09944 + 1.66245I 0
u = −0.927322 − 0.255571I
a = −0.154516 − 0.769316I
b = −0.320781 − 1.056570I
−0.09944 − 1.66245I 0
u = 0.887925 + 0.302340I
a = −0.299354 − 0.748760I
b = −1.58756 − 0.77790I
−6.61377 + 4.10167I 0
u = 0.887925 − 0.302340I
a = −0.299354 + 0.748760I
b = −1.58756 + 0.77790I
−6.61377 − 4.10167I 0
u = 0.700572 + 0.798714I
a = 0.577755 − 0.588155I
b = 1.338410 − 0.294958I
4.41321 + 0.49327I 0
u = 0.700572 − 0.798714I
a = 0.577755 + 0.588155I
b = 1.338410 + 0.294958I
4.41321 − 0.49327I 0
u = −0.819668 + 0.376320I
a = −0.468203 + 1.175900I
b = −1.33128 + 1.44116I
−6.30926 + 8.22313I 0
u = −0.819668 − 0.376320I
a = −0.468203 − 1.175900I
b = −1.33128 − 1.44116I
−6.30926 − 8.22313I 0
u = 0.794993 + 0.390347I
a = −0.155542 − 1.291390I
b = 1.24485 − 1.06941I
1.85456 − 6.66524I 0
u = 0.794993 − 0.390347I
a = −0.155542 + 1.291390I
b = 1.24485 + 1.06941I
1.85456 + 6.66524I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.992411 + 0.559301I
a = −0.256575 − 1.132100I
b = 0.109802 − 0.482795I
−6.97250 + 2.76431I 0
u = −0.992411 − 0.559301I
a = −0.256575 + 1.132100I
b = 0.109802 + 0.482795I
−6.97250 − 2.76431I 0
u = −1.016370 + 0.514652I
a = 0.113323 + 0.981555I
b = 0.442694 + 1.098610I
−0.307621 + 1.054850I 0
u = −1.016370 − 0.514652I
a = 0.113323 − 0.981555I
b = 0.442694 − 1.098610I
−0.307621 − 1.054850I 0
u = 0.783658 + 0.839527I
a = −0.232652 − 0.491677I
b = 1.088250 − 0.358012I
5.64411 − 3.29713I 0
u = 0.783658 − 0.839527I
a = −0.232652 + 0.491677I
b = 1.088250 + 0.358012I
5.64411 + 3.29713I 0
u = 0.772392 + 0.261309I
a = 0.23922 + 1.65529I
b = 0.92824 + 1.39853I
−8.69968 − 1.42199I 0
u = 0.772392 − 0.261309I
a = 0.23922 − 1.65529I
b = 0.92824 − 1.39853I
−8.69968 + 1.42199I 0
u = 0.754514 + 0.276947I
a = −0.32775 + 2.60121I
b = 0.080369 + 1.137500I
−8.60566 − 0.81317I 0
u = 0.754514 − 0.276947I
a = −0.32775 − 2.60121I
b = 0.080369 − 1.137500I
−8.60566 + 0.81317I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.653902 + 0.457863I
a = −0.091022 + 1.039930I
b = 0.248927 + 0.754353I
−0.301195 + 1.328750I 0
u = −0.653902 − 0.457863I
a = −0.091022 − 1.039930I
b = 0.248927 − 0.754353I
−0.301195 − 1.328750I 0
u = 0.778139
a = 2.71056
b = 0.253134
−2.10752 0
u = 0.986047 + 0.760457I
a = 0.246197 + 1.252340I
b = −0.990587 + 0.961519I
0.85224 − 8.09504I 0
u = 0.986047 − 0.760457I
a = 0.246197 − 1.252340I
b = −0.990587 − 0.961519I
0.85224 + 8.09504I 0
u = −0.694300 + 0.284103I
a = −1.35570 + 1.82174I
b = 0.138687 + 0.871125I
−0.65973 + 2.45836I 0
u = −0.694300 − 0.284103I
a = −1.35570 − 1.82174I
b = 0.138687 − 0.871125I
−0.65973 − 2.45836I 0
u = −0.644494 + 0.341367I
a = 0.17207 + 3.88745I
b = 0.274695 + 0.835596I
−5.69889 − 5.28203I 0
u = −0.644494 − 0.341367I
a = 0.17207 − 3.88745I
b = 0.274695 − 0.835596I
−5.69889 + 5.28203I 0
u = 0.578089 + 0.442723I
a = 0.52803 − 3.87108I
b = 0.466703 − 0.384771I
−5.38362 − 7.14150I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.578089 − 0.442723I
a = 0.52803 + 3.87108I
b = 0.466703 + 0.384771I
−5.38362 + 7.14150I 0
u = −0.993572 + 0.801631I
a = −0.198392 − 0.784097I
b = −0.981533 − 0.850677I
−1.73300 + 4.30022I 0
u = −0.993572 − 0.801631I
a = −0.198392 + 0.784097I
b = −0.981533 + 0.850677I
−1.73300 − 4.30022I 0
u = 0.969380 + 0.897508I
a = 0.214456 − 1.096160I
b = 1.18899 − 1.21639I
1.74052 − 10.48820I 0
u = 0.969380 − 0.897508I
a = 0.214456 + 1.096160I
b = 1.18899 + 1.21639I
1.74052 + 10.48820I 0
u = 0.571480 + 0.349378I
a = 0.162785 + 0.461752I
b = −1.46297 + 0.68408I
−0.550623 − 1.155750I 0. + 9.52354I
u = 0.571480 − 0.349378I
a = 0.162785 − 0.461752I
b = −1.46297 − 0.68408I
−0.550623 + 1.155750I 0. − 9.52354I
u = 0.646667 + 0.157930I
a = −1.86555 + 1.47666I
b = −0.445822 + 0.624782I
2.08117 − 5.13424I 0. + 9.56633I
u = 0.646667 − 0.157930I
a = −1.86555 − 1.47666I
b = −0.445822 − 0.624782I
2.08117 + 5.13424I 0. − 9.56633I
u = 1.096790 + 0.760066I
a = −0.469877 + 1.140750I
b = −1.048700 + 0.777334I
3.17403 − 6.33099I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.096790 − 0.760066I
a = −0.469877 − 1.140750I
b = −1.048700 − 0.777334I
3.17403 + 6.33099I 0
u = 0.665121
a = −3.00914
b = 0.299281
−9.80679 −71.6570
u = −0.804129 + 1.139850I
a = −0.660591 + 0.539069I
b = 0.440518 + 0.824186I
1.94276 + 5.50841I 0
u = −0.804129 − 1.139850I
a = −0.660591 − 0.539069I
b = 0.440518 − 0.824186I
1.94276 − 5.50841I 0
u = 1.02823 + 0.99300I
a = −0.691003 + 0.097488I
b = −0.449010 − 0.350908I
1.83592 + 3.56054I 0
u = 1.02823 − 0.99300I
a = −0.691003 − 0.097488I
b = −0.449010 + 0.350908I
1.83592 − 3.56054I 0
u = 1.15815 + 0.85043I
a = 0.019191 + 0.727549I
b = −0.637514 + 0.265254I
4.52317 − 2.87684I 0
u = 1.15815 − 0.85043I
a = 0.019191 − 0.727549I
b = −0.637514 − 0.265254I
4.52317 + 2.87684I 0
u = −0.517394 + 0.218711I
a = 0.38948 − 2.40080I
b = −0.94523 − 1.19596I
2.61465 + 0.77345I − 61.138777 + 0.10I
u = −0.517394 − 0.218711I
a = 0.38948 + 2.40080I
b = −0.94523 + 1.19596I
2.61465 − 0.77345I − 61.138777 + 0.10I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.387563 + 0.385990I
a = −0.655661 + 1.116930I
b = 0.23435 + 2.08764I
0.416926 − 0.015506I −10.35701 + 0.I
u = −0.387563 − 0.385990I
a = −0.655661 − 1.116930I
b = 0.23435 − 2.08764I
0.416926 + 0.015506I −10.35701 + 0.I
u = 0.525179 + 0.030642I
a = 1.98553 + 0.13237I
b = −0.219757 + 0.080532I
−1.54159 − 0.00262I −9.47854 − 0.67252I
u = 0.525179 − 0.030642I
a = 1.98553 − 0.13237I
b = −0.219757 − 0.080532I
−1.54159 + 0.00262I −9.47854 + 0.67252I
u = −1.08161 + 1.04076I
a = 0.249928 − 0.089307I
b = −0.223261 − 0.241635I
−0.92678 + 2.59995I 0
u = −1.08161 − 1.04076I
a = 0.249928 + 0.089307I
b = −0.223261 + 0.241635I
−0.92678 − 2.59995I 0
u = −1.27100 + 0.88966I
a = 0.140122 + 1.152840I
b = 1.08021 + 1.07345I
−8.25214 + 9.72918I 0
u = −1.27100 − 0.88966I
a = 0.140122 − 1.152840I
b = 1.08021 − 1.07345I
−8.25214 − 9.72918I 0
u = 1.23138 + 0.94766I
a = −0.005878 + 1.239660I
b = −1.12230 + 1.17955I
−6.4341 − 17.3813I 0
u = 1.23138 − 0.94766I
a = −0.005878 − 1.239660I
b = −1.12230 − 1.17955I
−6.4341 + 17.3813I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.26485 + 0.95309I
a = −0.081517 − 1.100330I
b = 0.881525 − 0.992468I
−8.31362 − 8.50270I 0
u = 1.26485 − 0.95309I
a = −0.081517 + 1.100330I
b = 0.881525 + 0.992468I
−8.31362 + 8.50270I 0
u = −1.25584 + 1.02912I
a = 0.243511 − 0.984984I
b = −0.687246 − 1.235740I
−9.36023 + 3.54419I 0
u = −1.25584 − 1.02912I
a = 0.243511 + 0.984984I
b = −0.687246 + 1.235740I
−9.36023 − 3.54419I 0
u = −1.24611 + 1.22171I
a = 0.342846 − 0.640069I
b = −0.133519 − 1.161940I
−8.79053 + 5.40503I 0
u = −1.24611 − 1.22171I
a = 0.342846 + 0.640069I
b = −0.133519 + 1.161940I
−8.79053 − 5.40503I 0
u = 0.87706 + 1.53865I
a = 0.447462 + 0.116030I
b = 0.649803 + 0.664583I
−4.82272 + 8.99915I 0
u = 0.87706 − 1.53865I
a = 0.447462 − 0.116030I
b = 0.649803 − 0.664583I
−4.82272 − 8.99915I 0
u = −0.69060 + 2.02693I
a = −0.286871 + 0.036709I
b = −0.438732 + 0.301663I
−5.81231 − 1.18874I 0
u = −0.69060 − 2.02693I
a = −0.286871 − 0.036709I
b = −0.438732 − 0.301663I
−5.81231 + 1.18874I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.75755 + 1.86670I
a = −0.053853 − 0.275561I
b = −0.016508 − 0.416350I
−6.52629 − 0.82015I 0
u = 1.75755 − 1.86670I
a = −0.053853 + 0.275561I
b = −0.016508 + 0.416350I
−6.52629 + 0.82015I 0
13
II.
I
u
2
= h−5.23×10
27
u
28
−3.00×10
31
u
27
+· · ·+1.50×10
32
b−4.81×10
32
, −1.29×
10
32
u
28
−5.79×10
31
u
27
+· · ·+5.01×10
31
a−4.90×10
32
, u
29
+u
28
+· · ·+21u+3i
(i) Arc colorings
a
7
=
0
u
a
9
=
1
0
a
4
=
2.57292u
28
+ 1.15679u
27
+ ··· + 63.6754u + 9.78444
0.0000348041u
28
+ 0.199524u
27
+ ··· + 8.67018u + 3.20327
a
10
=
1
u
2
a
3
=
2.57289u
28
+ 0.957263u
27
+ ··· + 55.0052u + 6.58117
0.0000348041u
28
+ 0.199524u
27
+ ··· + 8.67018u + 3.20327
a
2
=
1.79204u
28
+ 0.733552u
27
+ ··· + 37.4659u + 4.93756
−0.314246u
28
+ 0.0213907u
27
+ ··· − 0.687225u + 1.53184
a
1
=
−3.24471u
28
− 1.69039u
27
+ ··· − 96.6982u − 18.4465
0.408609u
28
+ 0.311148u
27
+ ··· + 18.9214u + 4.01399
a
6
=
0.185810u
28
+ 0.157422u
27
+ ··· − 2.10794u − 2.40655
−0.341340u
28
− 0.0800480u
27
+ ··· − 4.54704u + 0.861258
a
5
=
3.22279u
28
+ 1.26764u
27
+ ··· + 77.0253u + 10.8296
0.365131u
28
+ 0.358995u
27
+ ··· + 18.0397u + 4.82029
a
12
=
−8.06599u
28
− 3.42279u
27
+ ··· − 230.140u − 41.5155
0.403654u
28
+ 0.104323u
27
+ ··· + 6.04333u + 0.354646
a
8
=
−0.483104u
28
− 0.131607u
27
+ ··· − 20.2628u − 2.96096
−0.327574u
28
− 0.208981u
27
+ ··· − 11.6078u − 1.41567
a
11
=
−5.91616u
28
− 1.81620u
27
+ ··· − 146.707u − 26.8536
0.412051u
28
+ 0.218241u
27
+ ··· + 8.53478u + 0.756118
(ii) Obstruction class = 1
(iii) Cusp Shapes = 23.0581u
28
+ 9.80392u
27
+ ··· + 642.920u + 117.030
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
29
− 15u
28
+ ··· + 16u − 1
c
2
3(3u
29
+ 3u
28
+ ··· + 1025u − 451)
c
3
3(3u
29
+ 6u
28
+ ··· + 2u − 1)
c
4
3(3u
29
+ 3u
28
+ ··· + 14u − 11)
c
5
u
29
− u
28
+ ··· − 36u − 12
c
6
u
29
− 3u
28
+ ··· + 2u
2
− 1
c
7
u
29
+ u
28
+ ··· + 32u
2
− 12
c
8
u
29
− 3u
28
+ ··· + 4u − 1
c
9
u
29
+ u
28
+ ··· + 21u + 3
c
10
u
29
− 8u
28
+ ··· − 18u − 3
c
11
u
29
+ 3u
28
+ ··· + 4u + 1
c
12
u
29
+ u
28
+ ··· − 36u + 12
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
− 25y
28
+ ··· − 36y −1
c
2
9(9y
29
− 57y
28
+ ··· + 16031y −203401)
c
3
9(9y
29
+ 60y
28
+ ··· − 20y −1)
c
4
9(9y
29
− 255y
28
+ ··· + 790y −121)
c
5
, c
12
y
29
+ 13y
28
+ ··· − 240y −144
c
6
y
29
+ y
28
+ ··· + 4y −1
c
7
y
29
+ 23y
28
+ ··· + 768y −144
c
8
, c
11
y
29
− 11y
28
+ ··· + 8y −1
c
9
y
29
+ y
28
+ ··· + 75y −9
c
10
y
29
− 26y
28
+ ··· − 168y −9
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.806517 + 0.516536I
a = 0.31962 − 1.85273I
b = −0.875855 − 1.071580I
2.30873 + 1.98553I −1.03185 − 3.58925I
u = −0.806517 − 0.516536I
a = 0.31962 + 1.85273I
b = −0.875855 + 1.071580I
2.30873 − 1.98553I −1.03185 + 3.58925I
u = −0.376013 + 0.863829I
a = 0.609833 + 0.290857I
b = −0.775243 − 0.585801I
3.92717 + 5.34920I −3.02498 − 8.09345I
u = −0.376013 − 0.863829I
a = 0.609833 − 0.290857I
b = −0.775243 + 0.585801I
3.92717 − 5.34920I −3.02498 + 8.09345I
u = −0.761329 + 0.325566I
a = −0.092104 + 1.233530I
b = 0.24180 + 1.68427I
1.141070 + 0.487681I −1.64816 − 2.39673I
u = −0.761329 − 0.325566I
a = −0.092104 − 1.233530I
b = 0.24180 − 1.68427I
1.141070 − 0.487681I −1.64816 + 2.39673I
u = 0.951695 + 0.728084I
a = 0.084345 − 1.372000I
b = 1.15028 − 1.17037I
2.89282 − 8.83518I −1.15031 + 8.18274I
u = 0.951695 − 0.728084I
a = 0.084345 + 1.372000I
b = 1.15028 + 1.17037I
2.89282 + 8.83518I −1.15031 − 8.18274I
u = 0.722786 + 0.295555I
a = −0.28221 − 2.25960I
b = −0.45710 − 1.35183I
−8.18041 − 1.29267I 0.59850 + 4.44307I
u = 0.722786 − 0.295555I
a = −0.28221 + 2.25960I
b = −0.45710 + 1.35183I
−8.18041 + 1.29267I 0.59850 − 4.44307I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.161620 + 0.403726I
a = −0.766271 − 0.342291I
b = −0.575631 − 0.549188I
2.72207 + 3.67553I 0.30401 − 6.37797I
u = 1.161620 − 0.403726I
a = −0.766271 + 0.342291I
b = −0.575631 + 0.549188I
2.72207 − 3.67553I 0.30401 + 6.37797I
u = 0.745964 + 0.981340I
a = 0.256143 − 0.234841I
b = 1.202530 − 0.218214I
5.80126 − 1.19075I 1.61034 + 0.91379I
u = 0.745964 − 0.981340I
a = 0.256143 + 0.234841I
b = 1.202530 + 0.218214I
5.80126 + 1.19075I 1.61034 − 0.91379I
u = −0.800606 + 0.948142I
a = −0.867670 + 0.863482I
b = 0.563358 + 0.889807I
2.62362 + 4.59244I −1.28176 − 3.75492I
u = −0.800606 − 0.948142I
a = −0.867670 − 0.863482I
b = 0.563358 − 0.889807I
2.62362 − 4.59244I −1.28176 + 3.75492I
u = −0.643595
a = 3.01131
b = −0.392109
−9.74623 60.6330
u = 1.004300 + 0.955261I
a = −0.032582 + 1.080360I
b = −0.924689 + 0.609270I
5.06041 − 5.96533I 1.54179 + 5.79885I
u = 1.004300 − 0.955261I
a = −0.032582 − 1.080360I
b = −0.924689 − 0.609270I
5.06041 + 5.96533I 1.54179 − 5.79885I
u = −0.207866 + 0.499044I
a = 2.87124 − 2.21164I
b = 0.579550 − 0.346272I
−5.47528 + 6.38037I −5.81773 − 3.65881I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.207866 − 0.499044I
a = 2.87124 + 2.21164I
b = 0.579550 + 0.346272I
−5.47528 − 6.38037I −5.81773 + 3.65881I
u = −0.96885 + 1.14802I
a = −0.007745 + 0.277103I
b = 0.446352 + 0.422725I
−0.75290 + 2.89272I 0.77680 − 13.45784I
u = −0.96885 − 1.14802I
a = −0.007745 − 0.277103I
b = 0.446352 − 0.422725I
−0.75290 − 2.89272I 0.77680 + 13.45784I
u = −0.389960 + 0.190898I
a = −1.56607 + 0.76115I
b = 1.068000 + 0.724990I
−0.493972 + 0.619932I −3.41568 + 4.02939I
u = −0.389960 − 0.190898I
a = −1.56607 − 0.76115I
b = 1.068000 − 0.724990I
−0.493972 − 0.619932I −3.41568 − 4.02939I
u = −1.30370 + 1.13616I
a = 0.244319 − 0.753395I
b = −0.376916 − 1.107240I
−8.60956 + 4.62804I 0
u = −1.30370 − 1.13616I
a = 0.244319 + 0.753395I
b = −0.376916 + 1.107240I
−8.60956 − 4.62804I 0
u = 0.85028 + 1.74655I
a = −0.276509 − 0.340069I
b = −0.070381 − 0.231703I
−6.31659 − 0.95842I 0
u = 0.85028 − 1.74655I
a = −0.276509 + 0.340069I
b = −0.070381 + 0.231703I
−6.31659 + 0.95842I 0
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
29
− 15u
28
+ ··· + 16u − 1)
· (u
82
+ 14u
81
+ ··· − 99113733u + 12092767)
c
2
9(3u
29
+ 3u
28
+ ··· + 1025u − 451)
· (3u
82
+ 12u
81
+ ··· + 1104636816u − 102449797)
c
3
9(3u
29
+ 6u
28
+ ··· + 2u − 1)(3u
82
+ 3u
81
+ ··· + 7u + 1)
c
4
9(3u
29
+ 3u
28
+ ··· + 14u − 11)
· (3u
82
− 140u
80
+ ··· − 10653u − 4399)
c
5
(u
29
− u
28
+ ··· − 36u − 12)(u
82
+ 10u
80
+ ··· − 1416u − 528)
c
6
(u
29
− 3u
28
+ ··· + 2u
2
− 1)(u
82
+ 2u
81
+ ··· + 29u − 47)
c
7
(u
29
+ u
28
+ ··· + 32u
2
− 12)(u
82
+ 23u
80
+ ··· − 84216u − 19056)
c
8
(u
29
− 3u
28
+ ··· + 4u − 1)(u
82
+ 2u
81
+ ··· + 169u − 97)
c
9
(u
29
+ u
28
+ ··· + 21u + 3)(u
82
− 4u
81
+ ··· − 894u + 237)
c
10
(u
29
− 8u
28
+ ··· − 18u − 3)(u
82
− 3u
81
+ ··· + 5918619u − 282651)
c
11
(u
29
+ 3u
28
+ ··· + 4u + 1)(u
82
+ 2u
81
+ ··· + 169u − 97)
c
12
(u
29
+ u
28
+ ··· − 36u + 12)(u
82
+ 10u
80
+ ··· − 1416u − 528)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
29
− 25y
28
+ ··· − 36y −1)
· (y
82
− 126y
81
+ ··· − 2530004844652363y + 146235013716289)
c
2
81(9y
29
− 57y
28
+ ··· + 16031y −203401)
· (9y
82
− 390y
81
+ ··· − 204245228366900018y + 10495960905341209)
c
3
81(9y
29
+ 60y
28
+ ··· − 20y −1)(9y
82
+ 123y
81
+ ··· − 27y + 1)
c
4
81(9y
29
− 255y
28
+ ··· + 790y −121)
· (9y
82
− 840y
81
+ ··· − 10285869y + 19351201)
c
5
, c
12
(y
29
+ 13y
28
+ ··· − 240y −144)
· (y
82
+ 20y
81
+ ··· − 716736y + 278784)
c
6
(y
29
+ y
28
+ ··· + 4y −1)(y
82
− 8y
81
+ ··· − 9959y + 2209)
c
7
(y
29
+ 23y
28
+ ··· + 768y −144)
· (y
82
+ 46y
81
+ ··· + 23494984512y + 363131136)
c
8
, c
11
(y
29
− 11y
28
+ ··· + 8y −1)(y
82
− 28y
81
+ ··· − 256511y + 9409)
c
9
(y
29
+ y
28
+ ··· + 75y −9)(y
82
− 12y
81
+ ··· − 2374338y + 56169)
c
10
(y
29
− 26y
28
+ ··· − 168y −9)
· (y
82
− 111y
81
+ ··· − 288406262487y + 79891587801)
23
