12n
0588
(K12n
0588
)
A knot diagram
1
Linearized knot diagam
3 7 12 11 9 2 4 5 3 7 8 10
Solving Sequence
4,7 8,12
3 2 1 6 11 5 10 9
c
7
c
3
c
2
c
1
c
6
c
11
c
4
c
10
c
9
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.27157 × 10
201
u
63
+ 4.53753 × 10
202
u
62
+ ··· + 4.88020 × 10
203
b + 5.65168 × 10
203
,
− 8.48877 × 10
202
u
63
+ 3.19137 × 10
203
u
62
+ ··· + 4.88020 × 10
203
a + 4.32696 × 10
204
,
u
64
− 3u
63
+ ··· + 9u + 1i
I
u
2
= h11150600999535u
21
− 14783938671492u
20
+ ··· + 6959144640989b + 6978556189620,
68211367039889u
21
− 98301657351572u
20
+ ··· + 6959144640989a + 42747854441200,
u
22
− 2u
21
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 86 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−1.27 × 10
201
u
63
+ 4.54 × 10
202
u
62
+ · · · + 4.88 × 10
203
b + 5.65 ×
10
203
, −8.49 × 10
202
u
63
+ 3.19 × 10
203
u
62
+ · · · + 4.88 × 10
203
a + 4.33 ×
10
204
, u
64
− 3u
63
+ · · · + 9u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
12
=
0.173943u
63
− 0.653942u
62
+ ··· − 7.97727u − 8.86637
0.00260557u
63
− 0.0929784u
62
+ ··· − 5.15924u − 1.15808
a
3
=
2.45092u
63
− 7.73517u
62
+ ··· + 96.0329u + 1.67519
0.298291u
63
− 0.938637u
62
+ ··· + 8.62009u + 0.0738241
a
2
=
2.74921u
63
− 8.67381u
62
+ ··· + 104.653u + 1.74901
0.298291u
63
− 0.938637u
62
+ ··· + 8.62009u + 0.0738241
a
1
=
−0.785214u
63
+ 2.30228u
62
+ ··· − 45.6518u − 11.3768
0.0982812u
63
− 0.446815u
62
+ ··· − 4.70790u − 0.845415
a
6
=
2.72840u
63
− 8.38407u
62
+ ··· + 128.985u + 8.01125
0.206745u
63
− 0.717715u
62
+ ··· + 6.00433u − 0.407776
a
11
=
0.190318u
63
− 0.794890u
62
+ ··· − 14.1516u − 10.1566
0.0430267u
63
− 0.228287u
62
+ ··· − 4.34921u − 1.06626
a
5
=
2.91738u
63
− 9.20280u
62
+ ··· + 106.391u + 0.595014
0.172195u
63
− 0.530154u
62
+ ··· + 5.86731u − 0.320917
a
10
=
0.147291u
63
− 0.566603u
62
+ ··· − 9.80237u − 9.09030
0.0430267u
63
− 0.228287u
62
+ ··· − 4.34921u − 1.06626
a
9
=
4.19462u
63
− 13.2279u
62
+ ··· + 159.234u + 3.94471
0.430364u
63
− 1.40465u
62
+ ··· + 11.1768u − 0.195577
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.166269u
63
+ 0.633459u
62
+ ··· − 0.558660u − 1.79988
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
64
+ 81u
63
+ ··· + 20217u + 961
c
2
, c
6
u
64
− u
63
+ ··· − 335u + 31
c
3
u
64
− 5u
63
+ ··· − 649u + 91
c
4
u
64
− u
62
+ ··· + 22u + 1
c
5
, c
8
u
64
− u
63
+ ··· + 184u + 68
c
7
u
64
+ 3u
63
+ ··· − 9u + 1
c
9
u
64
+ 46u
62
+ ··· − 120919u + 79381
c
10
u
64
− u
63
+ ··· − 4829u + 811
c
11
u
64
+ 5u
63
+ ··· − 399u + 73
c
12
u
64
− 4u
63
+ ··· − 163376u + 24613
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
64
− 185y
63
+ ··· − 197253273y + 923521
c
2
, c
6
y
64
− 81y
63
+ ··· − 20217y + 961
c
3
y
64
+ 33y
63
+ ··· + 282593y + 8281
c
4
y
64
− 2y
63
+ ··· − 40y + 1
c
5
, c
8
y
64
− 35y
63
+ ··· − 314288y + 4624
c
7
y
64
− y
63
+ ··· + 35y + 1
c
9
y
64
+ 92y
63
+ ··· + 301309418769y + 6301343161
c
10
y
64
+ 19y
63
+ ··· + 39598139y + 657721
c
11
y
64
+ 19y
63
+ ··· + 133529y + 5329
c
12
y
64
+ 78y
63
+ ··· + 15272118522y + 605799769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.313536 + 0.928430I
a = 1.72819 + 0.46093I
b = −1.146680 − 0.590328I
−4.60431 + 6.37966I 4.21851 − 5.44879I
u = −0.313536 − 0.928430I
a = 1.72819 − 0.46093I
b = −1.146680 + 0.590328I
−4.60431 − 6.37966I 4.21851 + 5.44879I
u = 0.795119 + 0.560822I
a = −1.17974 + 1.14518I
b = −0.549493 + 0.075343I
−8.95792 − 7.99927I −2.45661 + 6.71553I
u = 0.795119 − 0.560822I
a = −1.17974 − 1.14518I
b = −0.549493 − 0.075343I
−8.95792 + 7.99927I −2.45661 − 6.71553I
u = 0.547034 + 0.887218I
a = −1.47486 + 0.31618I
b = 1.240990 − 0.613531I
−5.34471 − 2.73153I 1.11554 + 3.31035I
u = 0.547034 − 0.887218I
a = −1.47486 − 0.31618I
b = 1.240990 + 0.613531I
−5.34471 + 2.73153I 1.11554 − 3.31035I
u = 0.905830 + 0.202592I
a = 0.801451 − 0.189428I
b = 0.0992545 − 0.0572400I
−1.89160 − 0.13655I −5.74382 − 0.58160I
u = 0.905830 − 0.202592I
a = 0.801451 + 0.189428I
b = 0.0992545 + 0.0572400I
−1.89160 + 0.13655I −5.74382 + 0.58160I
u = −0.718433 + 0.579587I
a = −1.138640 − 0.604435I
b = 0.168043 + 0.042894I
−1.66794 + 4.14809I −1.94761 − 7.92865I
u = −0.718433 − 0.579587I
a = −1.138640 + 0.604435I
b = 0.168043 − 0.042894I
−1.66794 − 4.14809I −1.94761 + 7.92865I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.931771 + 0.606631I
a = 0.767324 + 0.472502I
b = −0.903443 − 0.525413I
3.11129 − 4.90246I 0. + 6.64058I
u = 0.931771 − 0.606631I
a = 0.767324 − 0.472502I
b = −0.903443 + 0.525413I
3.11129 + 4.90246I 0. − 6.64058I
u = 0.608117 + 0.645945I
a = 1.54613 + 0.89155I
b = −0.966015 + 0.576493I
3.28606 − 3.38738I 3.49350 + 7.72062I
u = 0.608117 − 0.645945I
a = 1.54613 − 0.89155I
b = −0.966015 − 0.576493I
3.28606 + 3.38738I 3.49350 − 7.72062I
u = 1.118670 + 0.262763I
a = −0.425297 + 0.859369I
b = −0.264219 − 0.462135I
−7.70013 − 1.88690I 0
u = 1.118670 − 0.262763I
a = −0.425297 − 0.859369I
b = −0.264219 + 0.462135I
−7.70013 + 1.88690I 0
u = 0.415838 + 0.711049I
a = −0.21037 − 1.74652I
b = 0.843215 − 0.109604I
0.231680 − 1.139720I 4.34801 + 7.52749I
u = 0.415838 − 0.711049I
a = −0.21037 + 1.74652I
b = 0.843215 + 0.109604I
0.231680 + 1.139720I 4.34801 − 7.52749I
u = −0.056636 + 0.733680I
a = −1.29377 + 1.19577I
b = 0.524020 + 0.229386I
5.23978 + 1.80222I 13.43627 − 2.54767I
u = −0.056636 − 0.733680I
a = −1.29377 − 1.19577I
b = 0.524020 − 0.229386I
5.23978 − 1.80222I 13.43627 + 2.54767I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.667566 + 0.309584I
a = −1.32046 + 0.68489I
b = 0.903912 − 0.216297I
−0.79116 + 2.64492I −4.65254 + 4.03443I
u = −0.667566 − 0.309584I
a = −1.32046 − 0.68489I
b = 0.903912 + 0.216297I
−0.79116 − 2.64492I −4.65254 − 4.03443I
u = 0.142284 + 0.713386I
a = 1.025040 + 0.094527I
b = −1.13010 + 1.00771I
1.51636 − 1.64164I 2.99307 + 5.98952I
u = 0.142284 − 0.713386I
a = 1.025040 − 0.094527I
b = −1.13010 − 1.00771I
1.51636 + 1.64164I 2.99307 − 5.98952I
u = −1.172400 + 0.565699I
a = 0.586710 + 0.572071I
b = 0.708917 + 0.272244I
−12.35140 + 1.42793I 0
u = −1.172400 − 0.565699I
a = 0.586710 − 0.572071I
b = 0.708917 − 0.272244I
−12.35140 − 1.42793I 0
u = −1.335590 + 0.249330I
a = 0.055887 + 0.659381I
b = 0.436791 − 0.571046I
−8.51911 − 1.79325I 0
u = −1.335590 − 0.249330I
a = 0.055887 − 0.659381I
b = 0.436791 + 0.571046I
−8.51911 + 1.79325I 0
u = 1.036250 + 0.894606I
a = −0.641417 − 0.592734I
b = 1.56427 + 0.08327I
3.05175 − 2.56289I 0
u = 1.036250 − 0.894606I
a = −0.641417 + 0.592734I
b = 1.56427 − 0.08327I
3.05175 + 2.56289I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.201469 + 0.595721I
a = 0.141582 + 0.261679I
b = 0.368885 + 0.672035I
0.180822 − 1.357760I 1.47757 + 4.14647I
u = 0.201469 − 0.595721I
a = 0.141582 − 0.261679I
b = 0.368885 − 0.672035I
0.180822 + 1.357760I 1.47757 − 4.14647I
u = −0.057818 + 1.371080I
a = −0.545883 + 0.246577I
b = 2.01305 − 1.25534I
−5.83121 + 3.82325I 0
u = −0.057818 − 1.371080I
a = −0.545883 − 0.246577I
b = 2.01305 + 1.25534I
−5.83121 − 3.82325I 0
u = 0.498905 + 0.371242I
a = −1.65967 − 0.53182I
b = 1.75112 − 1.24099I
−7.58122 − 7.03725I −3.47625 + 8.84937I
u = 0.498905 − 0.371242I
a = −1.65967 + 0.53182I
b = 1.75112 + 1.24099I
−7.58122 + 7.03725I −3.47625 − 8.84937I
u = −0.90400 + 1.09021I
a = 0.794373 − 0.155195I
b = −1.40953 − 0.23797I
5.85881 + 7.03857I 0
u = −0.90400 − 1.09021I
a = 0.794373 + 0.155195I
b = −1.40953 + 0.23797I
5.85881 − 7.03857I 0
u = −0.427356 + 0.281403I
a = 0.219577 − 0.759859I
b = −1.255080 − 0.297545I
2.64087 + 0.13449I 3.50237 + 3.05615I
u = −0.427356 − 0.281403I
a = 0.219577 + 0.759859I
b = −1.255080 + 0.297545I
2.64087 − 0.13449I 3.50237 − 3.05615I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.09532 + 1.03428I
a = −0.881703 + 0.452299I
b = 1.80167 + 0.70128I
3.35796 + 9.86267I 0
u = −1.09532 − 1.03428I
a = −0.881703 − 0.452299I
b = 1.80167 − 0.70128I
3.35796 − 9.86267I 0
u = −0.295497 + 0.344433I
a = 2.19362 − 0.77590I
b = −1.00229 − 1.72181I
−7.87777 + 0.76027I −0.44254 − 2.24356I
u = −0.295497 − 0.344433I
a = 2.19362 + 0.77590I
b = −1.00229 + 1.72181I
−7.87777 − 0.76027I −0.44254 + 2.24356I
u = 0.97455 + 1.25530I
a = 0.815863 + 0.115800I
b = −1.59645 + 0.91699I
1.89181 − 7.52039I 0
u = 0.97455 − 1.25530I
a = 0.815863 − 0.115800I
b = −1.59645 − 0.91699I
1.89181 + 7.52039I 0
u = −0.99150 + 1.25611I
a = 0.556030 − 0.517387I
b = −1.77104 − 0.38113I
3.78777 − 1.85763I 0
u = −0.99150 − 1.25611I
a = 0.556030 + 0.517387I
b = −1.77104 + 0.38113I
3.78777 + 1.85763I 0
u = −0.314719 + 0.204304I
a = −2.39055 + 1.35572I
b = 1.139280 + 0.269051I
−0.56044 + 2.14518I −4.65679 − 4.01006I
u = −0.314719 − 0.204304I
a = −2.39055 − 1.35572I
b = 1.139280 − 0.269051I
−0.56044 − 2.14518I −4.65679 + 4.01006I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.15220 + 1.15374I
a = −0.933219 − 0.281370I
b = 1.70870 − 1.18039I
−5.2447 − 15.7535I 0
u = 1.15220 − 1.15374I
a = −0.933219 + 0.281370I
b = 1.70870 + 1.18039I
−5.2447 + 15.7535I 0
u = 0.93576 + 1.41846I
a = −0.435534 − 0.232731I
b = 1.57902 − 0.12336I
1.47439 − 1.95616I 0
u = 0.93576 − 1.41846I
a = −0.435534 + 0.232731I
b = 1.57902 + 0.12336I
1.47439 + 1.95616I 0
u = 1.30479 + 1.13160I
a = 0.634730 + 0.483139I
b = −1.69635 + 1.46152I
2.53445 − 3.97108I 0
u = 1.30479 − 1.13160I
a = 0.634730 − 0.483139I
b = −1.69635 − 1.46152I
2.53445 + 3.97108I 0
u = −1.64567 + 0.75087I
a = −0.318200 + 0.497722I
b = 0.506486 + 1.315920I
4.34227 + 0.36034I 0
u = −1.64567 − 0.75087I
a = −0.318200 − 0.497722I
b = 0.506486 − 1.315920I
4.34227 − 0.36034I 0
u = −1.21980 + 1.35210I
a = 0.721956 − 0.216760I
b = −1.86466 − 1.57937I
−9.44086 + 7.17279I 0
u = −1.21980 − 1.35210I
a = 0.721956 + 0.216760I
b = −1.86466 + 1.57937I
−9.44086 − 7.17279I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.082568 + 0.145421I
a = −8.02990 − 1.39710I
b = −0.508076 − 0.441255I
3.14263 − 0.58927I −2.43518 − 0.70079I
u = −0.082568 − 0.145421I
a = −8.02990 + 1.39710I
b = −0.508076 + 0.441255I
3.14263 + 0.58927I −2.43518 + 0.70079I
u = 1.22982 + 1.54138I
a = 0.290748 + 0.445396I
b = −1.79422 + 0.03950I
−4.98726 + 6.57805I 0
u = 1.22982 − 1.54138I
a = 0.290748 − 0.445396I
b = −1.79422 − 0.03950I
−4.98726 − 6.57805I 0
11
II.
I
u
2
= h1.12 × 10
13
u
21
− 1.48 × 10
13
u
20
+ · · · + 6.96 × 10
12
b + 6.98 × 10
12
, 6.82 ×
10
13
u
21
−9.83×10
13
u
20
+· · ·+6.96×10
12
a+4.27×10
13
, u
22
−2u
21
+· · ·−2u+1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
12
=
−9.80169u
21
+ 14.1255u
20
+ ··· − 29.4692u − 6.14269
−1.60229u
21
+ 2.12439u
20
+ ··· − 2.19395u − 1.00279
a
3
=
2.23984u
21
− 19.7513u
20
+ ··· + 45.8986u − 51.8152
−0.923468u
21
+ 2.06927u
20
+ ··· − 4.08774u + 2.55849
a
2
=
1.31637u
21
− 17.6820u
20
+ ··· + 41.8109u − 49.2567
−0.923468u
21
+ 2.06927u
20
+ ··· − 4.08774u + 2.55849
a
1
=
−11.7551u
21
+ 19.2178u
20
+ ··· − 36.0736u + 1.44016
1.38030u
21
− 2.46786u
20
+ ··· + 4.94250u − 0.529976
a
6
=
−6.56215u
21
+ 26.1647u
20
+ ··· − 57.6907u + 50.1938
1.59529u
21
− 3.25044u
20
+ ··· + 7.14956u − 3.05913
a
11
=
−11.9938u
21
+ 15.5512u
20
+ ··· − 30.5092u − 12.6233
−1.86680u
21
+ 3.47738u
20
+ ··· − 5.91910u + 1.95585
a
5
=
15.6209u
21
− 49.7963u
20
+ ··· + 106.240u − 77.5520
−4.91539u
21
+ 9.58345u
20
+ ··· − 19.0836u + 5.53084
a
10
=
−10.1270u
21
+ 12.0738u
20
+ ··· − 24.5900u − 14.5792
−1.86680u
21
+ 3.47738u
20
+ ··· − 5.91910u + 1.95585
a
9
=
13.9617u
21
− 40.0092u
20
+ ··· + 77.7503u − 57.2328
−9.01335u
21
+ 17.7162u
20
+ ··· − 35.1771u + 10.1227
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
77090866342321
6959144640989
u
21
+
24417195627111
6959144640989
u
20
+ ··· −
131924333737762
6959144640989
u +
529449466425046
6959144640989
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
22
− 22u
21
+ ··· − 18u + 1
c
2
u
22
− 11u
20
+ ··· − 4u + 1
c
3
u
22
+ 6u
21
+ ··· + 22u + 7
c
4
u
22
+ 3u
21
+ ··· − 3u + 1
c
5
u
22
− 10u
20
+ ··· − 4u + 4
c
6
u
22
− 11u
20
+ ··· + 4u + 1
c
7
u
22
− 2u
21
+ ··· − 2u + 1
c
8
u
22
− 10u
20
+ ··· + 4u + 4
c
9
u
22
− u
21
+ ··· + 6u + 1
c
10
u
22
+ 2u
21
+ ··· + 4u + 11
c
11
u
22
− 2u
21
+ ··· − 2u + 1
c
12
u
22
− 3u
21
+ ··· + u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 34y
21
+ ··· − 86y + 1
c
2
, c
6
y
22
− 22y
21
+ ··· − 18y + 1
c
3
y
22
+ 12y
21
+ ··· + 552y + 49
c
4
y
22
− 3y
21
+ ··· − 21y + 1
c
5
, c
8
y
22
− 20y
21
+ ··· − 360y + 16
c
7
y
22
− 2y
21
+ ··· + 10y + 1
c
9
y
22
+ 11y
21
+ ··· − 8y + 1
c
10
y
22
+ 10y
21
+ ··· − 1930y + 121
c
11
y
22
+ 10y
21
+ ··· + 20y + 1
c
12
y
22
+ 9y
21
+ ··· − 11y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.059740 + 0.923637I
a = −0.825379 + 0.806774I
b = 1.80958 − 0.44104I
−6.67000 − 6.08404I 0.07907 + 4.41733I
u = −0.059740 − 0.923637I
a = −0.825379 − 0.806774I
b = 1.80958 + 0.44104I
−6.67000 + 6.08404I 0.07907 − 4.41733I
u = 1.110170 + 0.156513I
a = −0.218712 + 0.595946I
b = −0.565963 − 0.935358I
−9.15907 − 0.38779I −3.84597 − 0.39740I
u = 1.110170 − 0.156513I
a = −0.218712 − 0.595946I
b = −0.565963 + 0.935358I
−9.15907 + 0.38779I −3.84597 + 0.39740I
u = −0.560586 + 0.578524I
a = −0.162842 − 1.197430I
b = −0.873727 − 0.227661I
−0.093894 + 0.509045I −2.06274 + 2.06357I
u = −0.560586 − 0.578524I
a = −0.162842 + 1.197430I
b = −0.873727 + 0.227661I
−0.093894 − 0.509045I −2.06274 − 2.06357I
u = 0.468082 + 0.590835I
a = 0.829025 + 0.241574I
b = −1.38855 + 0.85198I
2.61073 − 0.75532I 3.73998 + 7.77562I
u = 0.468082 − 0.590835I
a = 0.829025 − 0.241574I
b = −1.38855 − 0.85198I
2.61073 + 0.75532I 3.73998 − 7.77562I
u = −0.585432 + 0.445145I
a = −1.368150 + 0.243037I
b = 0.963772 − 0.376578I
−0.54127 + 3.01960I 5.04193 − 10.09843I
u = −0.585432 − 0.445145I
a = −1.368150 − 0.243037I
b = 0.963772 + 0.376578I
−0.54127 − 3.01960I 5.04193 + 10.09843I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.990692 + 0.939676I
a = 0.582887 − 0.490467I
b = −1.53592 + 0.35917I
4.32636 + 3.84430I 4.24435 − 3.41824I
u = −0.990692 − 0.939676I
a = 0.582887 + 0.490467I
b = −1.53592 − 0.35917I
4.32636 − 3.84430I 4.24435 + 3.41824I
u = 0.95193 + 1.04804I
a = 0.973386 + 0.245120I
b = −1.55211 + 0.58904I
5.52972 − 8.35084I 2.94788 + 7.36228I
u = 0.95193 − 1.04804I
a = 0.973386 − 0.245120I
b = −1.55211 − 0.58904I
5.52972 + 8.35084I 2.94788 − 7.36228I
u = 0.170032 + 0.547687I
a = −2.13940 − 0.26067I
b = 0.485058 + 0.571865I
4.46696 + 2.32267I 4.86381 − 5.13840I
u = 0.170032 − 0.547687I
a = −2.13940 + 0.26067I
b = 0.485058 − 0.571865I
4.46696 − 2.32267I 4.86381 + 5.13840I
u = 0.208685 + 0.523085I
a = −0.89334 − 3.30383I
b = 0.542839 − 0.032801I
3.64369 − 0.94557I 9.49564 + 8.08210I
u = 0.208685 − 0.523085I
a = −0.89334 + 3.30383I
b = 0.542839 + 0.032801I
3.64369 + 0.94557I 9.49564 − 8.08210I
u = 1.56936 + 0.75876I
a = −0.199730 − 0.640355I
b = 1.07456 − 0.97330I
4.45576 + 1.24455I 9.37100 − 3.48577I
u = 1.56936 − 0.75876I
a = −0.199730 + 0.640355I
b = 1.07456 + 0.97330I
4.45576 − 1.24455I 9.37100 + 3.48577I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.28180 + 1.51259I
a = −0.577745 + 0.315382I
b = 2.04046 + 1.44608I
2.94554 + 4.02787I 13.1251 − 7.3446I
u = −1.28180 − 1.51259I
a = −0.577745 − 0.315382I
b = 2.04046 − 1.44608I
2.94554 − 4.02787I 13.1251 + 7.3446I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 22u
21
+ ··· − 18u + 1)(u
64
+ 81u
63
+ ··· + 20217u + 961)
c
2
(u
22
− 11u
20
+ ··· − 4u + 1)(u
64
− u
63
+ ··· − 335u + 31)
c
3
(u
22
+ 6u
21
+ ··· + 22u + 7)(u
64
− 5u
63
+ ··· − 649u + 91)
c
4
(u
22
+ 3u
21
+ ··· − 3u + 1)(u
64
− u
62
+ ··· + 22u + 1)
c
5
(u
22
− 10u
20
+ ··· − 4u + 4)(u
64
− u
63
+ ··· + 184u + 68)
c
6
(u
22
− 11u
20
+ ··· + 4u + 1)(u
64
− u
63
+ ··· − 335u + 31)
c
7
(u
22
− 2u
21
+ ··· − 2u + 1)(u
64
+ 3u
63
+ ··· − 9u + 1)
c
8
(u
22
− 10u
20
+ ··· + 4u + 4)(u
64
− u
63
+ ··· + 184u + 68)
c
9
(u
22
− u
21
+ ··· + 6u + 1)(u
64
+ 46u
62
+ ··· − 120919u + 79381)
c
10
(u
22
+ 2u
21
+ ··· + 4u + 11)(u
64
− u
63
+ ··· − 4829u + 811)
c
11
(u
22
− 2u
21
+ ··· − 2u + 1)(u
64
+ 5u
63
+ ··· − 399u + 73)
c
12
(u
22
− 3u
21
+ ··· + u + 1)(u
64
− 4u
63
+ ··· − 163376u + 24613)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
− 34y
21
+ ··· − 86y + 1)
· (y
64
− 185y
63
+ ··· − 197253273y + 923521)
c
2
, c
6
(y
22
− 22y
21
+ ··· − 18y + 1)(y
64
− 81y
63
+ ··· − 20217y + 961)
c
3
(y
22
+ 12y
21
+ ··· + 552y + 49)(y
64
+ 33y
63
+ ··· + 282593y + 8281)
c
4
(y
22
− 3y
21
+ ··· − 21y + 1)(y
64
− 2y
63
+ ··· − 40y + 1)
c
5
, c
8
(y
22
− 20y
21
+ ··· − 360y + 16)(y
64
− 35y
63
+ ··· − 314288y + 4624)
c
7
(y
22
− 2y
21
+ ··· + 10y + 1)(y
64
− y
63
+ ··· + 35y + 1)
c
9
(y
22
+ 11y
21
+ ··· − 8y + 1)
· (y
64
+ 92y
63
+ ··· + 301309418769y + 6301343161)
c
10
(y
22
+ 10y
21
+ ··· − 1930y + 121)
· (y
64
+ 19y
63
+ ··· + 39598139y + 657721)
c
11
(y
22
+ 10y
21
+ ··· + 20y + 1)(y
64
+ 19y
63
+ ··· + 133529y + 5329)
c
12
(y
22
+ 9y
21
+ ··· − 11y + 1)
· (y
64
+ 78y
63
+ ··· + 15272118522y + 605799769)
21
