12a
1259
(K12a
1259
)
A knot diagram
1
Linearized knot diagam
5 7 9 10 2 11 1 12 4 6 3 8
Solving Sequence
6,10
11
2,7
3 12 5 1 4 9 8
c
10
c
6
c
2
c
11
c
5
c
1
c
4
c
9
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5.69308 × 10
303
u
97
− 1.06736 × 10
304
u
96
+ ··· + 4.39641 × 10
304
b + 1.65833 × 10
306
,
− 1.21815 × 10
306
u
97
− 1.21298 × 10
306
u
96
+ ··· + 3.47317 × 10
306
a + 1.09802 × 10
308
,
u
98
+ u
97
+ ··· − 192u + 79i
I
u
2
= h−1240865u
26
+ 78914u
25
+ ··· + 933437b + 295188,
− 8955091u
26
− 9064939u
25
+ ··· + 933437a − 23614626, u
27
− 9u
25
+ ··· + 9u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 125 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
= h5.69 × 10
303
u
97
− 1.07 × 10
304
u
96
+ · · · + 4.40 × 10
304
b + 1.66 ×
10
306
, −1.22 × 10
306
u
97
− 1.21 × 10
306
u
96
+ · · · + 3.47 × 10
306
a + 1.10 ×
10
308
, u
98
+ u
97
+ · · · − 192u + 79i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
2
=
0.350731u
97
+ 0.349244u
96
+ ··· + 34.5787u − 31.6144
−0.129494u
97
+ 0.242779u
96
+ ··· + 63.5735u − 37.7201
a
7
=
u
−u
3
+ u
a
3
=
0.635075u
97
+ 0.290148u
96
+ ··· − 26.8955u − 14.5431
−0.154509u
97
+ 0.303320u
96
+ ··· + 90.5028u − 47.7805
a
12
=
−0.279601u
97
− 0.295570u
96
+ ··· + 17.3434u + 33.7179
−0.0375579u
97
− 0.0703430u
96
+ ··· − 8.10495u + 0.408463
a
5
=
0.223768u
97
+ 0.576551u
96
+ ··· + 72.9539u − 63.0265
0.0190934u
97
− 0.103748u
96
+ ··· − 38.7659u + 19.0595
a
1
=
0.0147025u
97
− 0.0896428u
96
+ ··· − 44.5524u + 43.9400
0.0261589u
97
− 0.0145128u
96
+ ··· − 28.2070u + 1.37104
a
4
=
0.204674u
97
+ 0.680299u
96
+ ··· + 111.720u − 82.0860
0.0190934u
97
− 0.103748u
96
+ ··· − 38.7659u + 19.0595
a
9
=
−0.289035u
97
+ 0.180873u
96
+ ··· + 111.655u − 64.0028
0.140591u
97
− 0.182545u
96
+ ··· − 76.3010u + 39.1583
a
8
=
−0.136447u
97
+ 0.413129u
96
+ ··· + 145.083u − 58.1068
0.238402u
97
+ 0.490572u
96
+ ··· + 48.6728u − 44.2169
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.47472u
97
− 1.63887u
96
+ ··· + 179.736u + 58.6258
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
98
− 24u
96
+ ··· + 179u − 49
c
2
u
98
− u
97
+ ··· − 175987u − 451
c
3
, c
4
, c
9
u
98
− u
97
+ ··· − 224u − 32
c
6
, c
10
u
98
+ u
97
+ ··· − 192u + 79
c
7
, c
8
, c
12
u
98
+ 2u
97
+ ··· − 36u + 19
c
11
u
98
− 5u
97
+ ··· − 215663520u + 43957163
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
98
− 48y
97
+ ··· − 56639y + 2401
c
2
y
98
+ 23y
97
+ ··· − 31146246201y + 203401
c
3
, c
4
, c
9
y
98
− 109y
97
+ ··· − 160768y + 1024
c
6
, c
10
y
98
− 67y
97
+ ··· − 74626y + 6241
c
7
, c
8
, c
12
y
98
+ 106y
97
+ ··· + 12536y + 361
c
11
y
98
− 57y
97
+ ··· − 68808164574318740y + 1932232179008569
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.147644 + 0.991105I
a = 0.428223 + 0.979194I
b = −0.083114 + 1.402650I
−2.74725 + 3.13007I 0
u = −0.147644 − 0.991105I
a = 0.428223 − 0.979194I
b = −0.083114 − 1.402650I
−2.74725 − 3.13007I 0
u = −0.580157 + 0.788031I
a = 1.330990 + 0.437564I
b = 0.250861 + 0.849982I
8.50650 + 1.10397I 0
u = −0.580157 − 0.788031I
a = 1.330990 − 0.437564I
b = 0.250861 − 0.849982I
8.50650 − 1.10397I 0
u = 0.969739 + 0.067480I
a = 0.855963 − 0.493667I
b = −0.64297 − 1.34543I
1.110890 + 0.358653I 0
u = 0.969739 − 0.067480I
a = 0.855963 + 0.493667I
b = −0.64297 + 1.34543I
1.110890 − 0.358653I 0
u = −0.982662 + 0.303550I
a = −0.744825 − 0.890821I
b = 0.325588 − 1.109070I
−0.64154 − 2.71485I 0
u = −0.982662 − 0.303550I
a = −0.744825 + 0.890821I
b = 0.325588 + 1.109070I
−0.64154 + 2.71485I 0
u = 1.02854
a = −1.64694
b = 1.45660
2.65903 0
u = −1.031350 + 0.102678I
a = 1.39462 + 0.63971I
b = −1.40148 + 0.67569I
6.05602 − 4.27471I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031350 − 0.102678I
a = 1.39462 − 0.63971I
b = −1.40148 − 0.67569I
6.05602 + 4.27471I 0
u = −1.017430 + 0.216044I
a = 1.07032 + 0.98555I
b = −1.17396 + 1.08732I
6.07548 − 4.43283I 0
u = −1.017430 − 0.216044I
a = 1.07032 − 0.98555I
b = −1.17396 − 1.08732I
6.07548 + 4.43283I 0
u = 0.951483 + 0.470279I
a = −0.460130 + 1.277270I
b = 0.81690 + 1.41346I
3.57337 + 5.44735I 0
u = 0.951483 − 0.470279I
a = −0.460130 − 1.277270I
b = 0.81690 − 1.41346I
3.57337 − 5.44735I 0
u = 1.059930 + 0.107788I
a = −0.638112 − 0.319931I
b = 0.186539 − 0.221069I
2.11130 + 0.19001I 0
u = 1.059930 − 0.107788I
a = −0.638112 + 0.319931I
b = 0.186539 + 0.221069I
2.11130 − 0.19001I 0
u = −1.066920 + 0.069450I
a = −0.649537 + 0.367157I
b = 0.70174 + 1.97988I
8.50659 − 0.46621I 0
u = −1.066920 − 0.069450I
a = −0.649537 − 0.367157I
b = 0.70174 − 1.97988I
8.50659 + 0.46621I 0
u = −0.022975 + 0.918534I
a = −0.469657 + 1.282630I
b = −0.074903 + 1.400880I
3.25898 − 6.63136I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.022975 − 0.918534I
a = −0.469657 − 1.282630I
b = −0.074903 − 1.400880I
3.25898 + 6.63136I 0
u = −0.952127 + 0.513412I
a = 1.125300 + 0.318980I
b = 0.042890 + 0.753251I
6.32720 + 2.24621I 0
u = −0.952127 − 0.513412I
a = 1.125300 − 0.318980I
b = 0.042890 − 0.753251I
6.32720 − 2.24621I 0
u = 1.042950 + 0.359828I
a = 0.521935 − 1.141640I
b = −0.284407 − 0.974890I
3.77548 + 4.91175I 0
u = 1.042950 − 0.359828I
a = 0.521935 + 1.141640I
b = −0.284407 + 0.974890I
3.77548 − 4.91175I 0
u = −0.935588 + 0.596452I
a = 0.209599 + 1.336450I
b = −0.71696 + 1.50993I
9.56242 − 6.26495I 0
u = −0.935588 − 0.596452I
a = 0.209599 − 1.336450I
b = −0.71696 − 1.50993I
9.56242 + 6.26495I 0
u = 0.283477 + 0.837190I
a = 0.918914 − 0.242800I
b = 0.12959 − 1.63928I
12.78970 + 4.85078I 0
u = 0.283477 − 0.837190I
a = 0.918914 + 0.242800I
b = 0.12959 + 1.63928I
12.78970 − 4.85078I 0
u = −1.106800 + 0.279137I
a = 0.394983 − 0.594836I
b = −0.048083 − 0.550544I
3.25698 − 3.46925I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.106800 − 0.279137I
a = 0.394983 + 0.594836I
b = −0.048083 + 0.550544I
3.25698 + 3.46925I 0
u = −0.531479 + 0.670358I
a = −0.612662 − 1.101300I
b = 1.26914 − 0.84801I
0.93590 − 2.76801I 0
u = −0.531479 − 0.670358I
a = −0.612662 + 1.101300I
b = 1.26914 + 0.84801I
0.93590 + 2.76801I 0
u = 0.594310 + 0.611420I
a = −1.351400 + 0.376376I
b = −0.248207 + 0.834678I
2.54743 − 1.15983I 0
u = 0.594310 − 0.611420I
a = −1.351400 − 0.376376I
b = −0.248207 − 0.834678I
2.54743 + 1.15983I 0
u = −1.165460 + 0.037280I
a = 0.888037 − 0.660491I
b = −0.0059516 − 0.1246310I
6.62448 + 3.13290I 0
u = −1.165460 − 0.037280I
a = 0.888037 + 0.660491I
b = −0.0059516 + 0.1246310I
6.62448 − 3.13290I 0
u = 0.526974 + 1.056170I
a = −0.388917 + 0.606673I
b = 0.47973 + 1.42246I
−1.26184 + 1.79008I 0
u = 0.526974 − 1.056170I
a = −0.388917 − 0.606673I
b = 0.47973 − 1.42246I
−1.26184 − 1.79008I 0
u = 0.818395
a = −1.10006
b = −0.366395
2.19538 3.99030
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.051200 + 0.546365I
a = 0.223779 + 0.601295I
b = −1.14635 + 1.52843I
8.74420 − 1.92599I 0
u = −1.051200 − 0.546365I
a = 0.223779 − 0.601295I
b = −1.14635 − 1.52843I
8.74420 + 1.92599I 0
u = 1.185350 + 0.125017I
a = −0.825354 + 0.499077I
b = 2.03379 + 1.47819I
14.9038 + 5.4131I 0
u = 1.185350 − 0.125017I
a = −0.825354 − 0.499077I
b = 2.03379 − 1.47819I
14.9038 − 5.4131I 0
u = 1.187550 + 0.338186I
a = −0.512045 − 0.742522I
b = −0.142592 − 0.557432I
10.06030 + 5.61206I 0
u = 1.187550 − 0.338186I
a = −0.512045 + 0.742522I
b = −0.142592 + 0.557432I
10.06030 − 5.61206I 0
u = −1.117930 + 0.589731I
a = −0.400399 − 0.298404I
b = −0.096130 − 1.338790I
2.91728 − 2.13489I 0
u = −1.117930 − 0.589731I
a = −0.400399 + 0.298404I
b = −0.096130 + 1.338790I
2.91728 + 2.13489I 0
u = −0.093270 + 1.268720I
a = −0.558781 − 0.803792I
b = −0.44261 − 1.65262I
11.0488 + 10.0618I 0
u = −0.093270 − 1.268720I
a = −0.558781 + 0.803792I
b = −0.44261 + 1.65262I
11.0488 − 10.0618I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.458681 + 1.206590I
a = −0.558461 − 0.407742I
b = −0.19589 − 1.78208I
4.57573 − 1.08706I 0
u = −0.458681 − 1.206590I
a = −0.558461 + 0.407742I
b = −0.19589 + 1.78208I
4.57573 + 1.08706I 0
u = 1.255990 + 0.333837I
a = 0.561102 − 0.495221I
b = 0.009349 − 1.314490I
1.10032 + 3.23237I 0
u = 1.255990 − 0.333837I
a = 0.561102 + 0.495221I
b = 0.009349 + 1.314490I
1.10032 − 3.23237I 0
u = 0.512361 + 0.456053I
a = 1.19642 − 1.55974I
b = −0.054081 − 0.905565I
2.00167 + 1.93138I −0.28873 − 2.52521I
u = 0.512361 − 0.456053I
a = 1.19642 + 1.55974I
b = −0.054081 + 0.905565I
2.00167 − 1.93138I −0.28873 + 2.52521I
u = 1.206820 + 0.585243I
a = −0.479965 + 0.645941I
b = 0.92675 + 1.47971I
1.21950 + 4.15829I 0
u = 1.206820 − 0.585243I
a = −0.479965 − 0.645941I
b = 0.92675 − 1.47971I
1.21950 − 4.15829I 0
u = 0.196337 + 1.345660I
a = 0.489493 − 0.633617I
b = 0.39692 − 1.78268I
3.87743 − 5.28163I 0
u = 0.196337 − 1.345660I
a = 0.489493 + 0.633617I
b = 0.39692 + 1.78268I
3.87743 + 5.28163I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.067106 + 0.624611I
a = 1.279550 + 0.038144I
b = 0.054288 + 0.503329I
6.41094 − 2.06804I 4.76498 + 2.79186I
u = −0.067106 − 0.624611I
a = 1.279550 − 0.038144I
b = 0.054288 − 0.503329I
6.41094 + 2.06804I 4.76498 − 2.79186I
u = −1.310460 + 0.407738I
a = −0.705152 + 0.792990I
b = 0.024819 − 0.214507I
17.4061 − 9.1635I 0
u = −1.310460 − 0.407738I
a = −0.705152 − 0.792990I
b = 0.024819 + 0.214507I
17.4061 + 9.1635I 0
u = −1.365970 + 0.255309I
a = −0.640875 − 0.497012I
b = −0.082924 − 1.398390I
7.34936 − 4.49309I 0
u = −1.365970 − 0.255309I
a = −0.640875 + 0.497012I
b = −0.082924 + 1.398390I
7.34936 + 4.49309I 0
u = −1.291660 + 0.514437I
a = 0.590267 + 0.688910I
b = −0.82988 + 1.57606I
0.90602 − 8.52331I 0
u = −1.291660 − 0.514437I
a = 0.590267 − 0.688910I
b = −0.82988 − 1.57606I
0.90602 + 8.52331I 0
u = 1.363110 + 0.329387I
a = 0.465083 + 0.771046I
b = −0.106287 − 0.193530I
10.62200 + 5.43560I 0
u = 1.363110 − 0.329387I
a = 0.465083 − 0.771046I
b = −0.106287 + 0.193530I
10.62200 − 5.43560I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.34484 + 0.46922I
a = −0.628411 + 0.716027I
b = 0.77780 + 1.69573I
7.53961 + 11.67750I 0
u = 1.34484 − 0.46922I
a = −0.628411 − 0.716027I
b = 0.77780 − 1.69573I
7.53961 − 11.67750I 0
u = 1.27782 + 0.68507I
a = 0.443314 − 0.675997I
b = −1.84712 − 1.63509I
15.4772 + 1.0599I 0
u = 1.27782 − 0.68507I
a = 0.443314 + 0.675997I
b = −1.84712 + 1.63509I
15.4772 − 1.0599I 0
u = 0.529291 + 0.136283I
a = −0.295583 + 0.644065I
b = −1.15988 − 2.02885I
12.31040 + 4.79248I 8.74810 + 2.34263I
u = 0.529291 − 0.136283I
a = −0.295583 − 0.644065I
b = −1.15988 + 2.02885I
12.31040 − 4.79248I 8.74810 − 2.34263I
u = −0.545204
a = −2.43757
b = 0.347274
−2.34902 −12.2400
u = 0.489696 + 0.124272I
a = 2.78679 + 0.32627I
b = −0.071431 + 0.192709I
1.86807 − 2.11041I −3.76638 + 0.97321I
u = 0.489696 − 0.124272I
a = 2.78679 − 0.32627I
b = −0.071431 − 0.192709I
1.86807 + 2.11041I −3.76638 − 0.97321I
u = −1.39422 + 0.62022I
a = −0.529737 − 0.826936I
b = 1.33860 − 1.64297I
15.1760 − 16.6548I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39422 − 0.62022I
a = −0.529737 + 0.826936I
b = 1.33860 + 1.64297I
15.1760 + 16.6548I 0
u = −1.50683 + 0.25546I
a = −0.230888 + 0.496604I
b = 0.266403 − 0.198205I
10.49100 − 0.60626I 0
u = −1.50683 − 0.25546I
a = −0.230888 − 0.496604I
b = 0.266403 + 0.198205I
10.49100 + 0.60626I 0
u = −0.463145 + 0.067192I
a = 1.27291 − 0.62200I
b = 0.846169 + 1.046210I
4.47001 + 2.89360I 8.76845 − 3.27673I
u = −0.463145 − 0.067192I
a = 1.27291 + 0.62200I
b = 0.846169 − 1.046210I
4.47001 − 2.89360I 8.76845 + 3.27673I
u = 1.40230 + 0.63342I
a = 0.544741 − 0.763682I
b = −1.46695 − 1.55566I
7.8844 + 12.1680I 0
u = 1.40230 − 0.63342I
a = 0.544741 + 0.763682I
b = −1.46695 + 1.55566I
7.8844 − 12.1680I 0
u = −1.38830 + 0.68299I
a = −0.508588 − 0.694976I
b = 1.65569 − 1.54628I
7.79562 − 5.96678I 0
u = −1.38830 − 0.68299I
a = −0.508588 + 0.694976I
b = 1.65569 + 1.54628I
7.79562 + 5.96678I 0
u = 1.57236 + 0.03851I
a = −0.434018 − 0.269208I
b = −0.425318 − 0.062123I
16.1961 + 1.5198I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57236 − 0.03851I
a = −0.434018 + 0.269208I
b = −0.425318 + 0.062123I
16.1961 − 1.5198I 0
u = −1.62467
a = 0.167450
b = 0.450009
10.5686 0
u = 0.075647 + 0.343854I
a = −0.831327 − 0.482254I
b = 0.074286 + 0.325055I
0.051677 + 0.871638I 1.30479 − 7.68178I
u = 0.075647 − 0.343854I
a = −0.831327 + 0.482254I
b = 0.074286 − 0.325055I
0.051677 − 0.871638I 1.30479 + 7.68178I
u = 0.040893 + 0.337505I
a = 0.46030 − 3.35033I
b = −0.477129 − 0.516478I
−2.51012 − 0.09044I −5.54914 − 1.40997I
u = 0.040893 − 0.337505I
a = 0.46030 + 3.35033I
b = −0.477129 + 0.516478I
−2.51012 + 0.09044I −5.54914 + 1.40997I
u = 1.64162 + 0.46046I
a = 0.460109 + 0.208462I
b = −0.326988 − 0.507396I
16.6920 − 3.4399I 0
u = 1.64162 − 0.46046I
a = 0.460109 − 0.208462I
b = −0.326988 + 0.507396I
16.6920 + 3.4399I 0
14
II.
I
u
2
= h−1.24 × 10
6
u
26
+ 7.89 × 10
4
u
25
+ · · · + 9.33 × 10
5
b + 2.95 × 10
5
, −8.96 ×
10
6
u
26
−9.06×10
6
u
25
+· · ·+9.33×10
5
a−2.36×10
7
, u
27
−9u
25
+· · ·+9u
2
−1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
2
=
9.59367u
26
+ 9.71136u
25
+ ··· + 9.83209u + 25.2986
1.32935u
26
− 0.0845413u
25
+ ··· − 1.80120u − 0.316238
a
7
=
u
−u
3
+ u
a
3
=
12.3529u
26
+ 13.2890u
25
+ ··· + 13.2547u + 32.4687
2.37434u
26
+ 2.01097u
25
+ ··· − 1.13786u + 3.27626
a
12
=
19.3072u
26
+ 1.06227u
25
+ ··· + 43.6737u + 4.96453
4.42819u
26
+ 3.62731u
25
+ ··· + 7.30655u + 0.673136
a
5
=
−1.93034u
26
− 6.11886u
25
+ ··· + 5.78493u − 16.5652
−5.13359u
26
− 5.58858u
25
+ ··· − 2.28473u − 10.4464
a
1
=
−13.5724u
26
− 3.44675u
25
+ ··· − 30.7183u − 25.4385
−2.80424u
26
− 5.67312u
25
+ ··· − 2.08593u − 10.7626
a
4
=
3.20326u
26
− 0.530277u
25
+ ··· + 8.06966u − 6.11886
−5.13359u
26
− 5.58858u
25
+ ··· − 2.28473u − 10.4464
a
9
=
−18.3992u
26
− 10.3562u
25
+ ··· − 46.6222u − 16.4826
−3.59250u
26
− 1.04499u
25
+ ··· − 8.73334u + 0.336661
a
8
=
−29.7822u
26
− 15.6228u
25
+ ··· − 38.4206u − 13.2655
−5.38513u
26
− 6.09579u
25
+ ··· + 7.57875u + 0.974312
(ii) Obstruction class = 1
(iii) Cusp Shapes =
33852149
933437
u
26
+
15369740
933437
u
25
+ ··· +
74879083
933437
u +
9932654
933437
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
+ 5u
26
+ ··· − 5u − 1
c
2
u
27
− 6u
24
+ ··· + 3u + 1
c
3
, c
4
u
27
− 16u
25
+ ··· − 4u
2
− 1
c
5
u
27
− 5u
26
+ ··· − 5u + 1
c
6
u
27
− 9u
25
+ ··· − 9u
2
+ 1
c
7
, c
8
u
27
+ u
26
+ ··· + 4u
2
+ 1
c
9
u
27
− 16u
25
+ ··· + 4u
2
+ 1
c
10
u
27
− 9u
25
+ ··· + 9u
2
− 1
c
11
u
27
− 2u
25
+ ··· + 6u + 1
c
12
u
27
− u
26
+ ··· − 4u
2
− 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
27
− 19y
26
+ ··· + 27y −1
c
2
y
27
− 14y
25
+ ··· + 13y −1
c
3
, c
4
, c
9
y
27
− 32y
26
+ ··· − 8y −1
c
6
, c
10
y
27
− 18y
26
+ ··· + 18y −1
c
7
, c
8
, c
12
y
27
+ 31y
26
+ ··· − 8y −1
c
11
y
27
− 4y
26
+ ··· − 36y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.485089 + 0.936854I
a = 0.397869 − 0.777369I
b = −0.51072 − 1.33669I
−1.47956 + 2.03481I −5.77865 − 9.60998I
u = 0.485089 − 0.936854I
a = 0.397869 + 0.777369I
b = −0.51072 + 1.33669I
−1.47956 − 2.03481I −5.77865 + 9.60998I
u = −0.949119 + 0.513442I
a = 0.456947 + 1.089520I
b = −1.01741 + 1.52896I
3.99828 − 4.96462I 7.26250 + 2.59999I
u = −0.949119 − 0.513442I
a = 0.456947 − 1.089520I
b = −1.01741 − 1.52896I
3.99828 + 4.96462I 7.26250 − 2.59999I
u = −1.027490 + 0.392055I
a = −0.447302 − 0.345733I
b = 0.57862 − 2.16315I
7.91750 − 1.58212I 1.68352 + 2.93249I
u = −1.027490 − 0.392055I
a = −0.447302 + 0.345733I
b = 0.57862 + 2.16315I
7.91750 + 1.58212I 1.68352 − 2.93249I
u = 1.062870 + 0.365733I
a = −0.68903 + 1.33354I
b = 0.753801 + 1.158750I
6.39604 + 5.84242I 6.69178 − 7.94773I
u = 1.062870 − 0.365733I
a = −0.68903 − 1.33354I
b = 0.753801 − 1.158750I
6.39604 − 5.84242I 6.69178 + 7.94773I
u = −0.147257 + 0.804940I
a = −0.215120 + 1.226910I
b = −1.09953 + 1.37711I
3.27196 − 3.54502I 2.57974 + 4.21881I
u = −0.147257 − 0.804940I
a = −0.215120 − 1.226910I
b = −1.09953 − 1.37711I
3.27196 + 3.54502I 2.57974 − 4.21881I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.180300 + 0.289874I
a = −0.539669 − 0.747909I
b = −0.080063 − 0.754670I
4.41578 − 3.76745I 5.99903 + 3.10920I
u = −1.180300 − 0.289874I
a = −0.539669 + 0.747909I
b = −0.080063 + 0.754670I
4.41578 + 3.76745I 5.99903 − 3.10920I
u = 1.157870 + 0.391750I
a = 0.487445 − 0.502194I
b = −0.191569 − 1.317550I
1.03253 + 2.42829I 1.41343 − 0.11118I
u = 1.157870 − 0.391750I
a = 0.487445 + 0.502194I
b = −0.191569 + 1.317550I
1.03253 − 2.42829I 1.41343 + 0.11118I
u = −0.826385 + 0.920635I
a = 0.728727 + 0.282129I
b = 0.016117 + 1.270820I
3.34708 − 0.27472I 3.57620 − 0.72730I
u = −0.826385 − 0.920635I
a = 0.728727 − 0.282129I
b = 0.016117 − 1.270820I
3.34708 + 0.27472I 3.57620 + 0.72730I
u = 0.665400 + 0.363386I
a = −0.416547 + 0.968781I
b = 1.57866 + 2.24267I
12.21670 + 5.39354I 6.49982 − 9.79940I
u = 0.665400 − 0.363386I
a = −0.416547 − 0.968781I
b = 1.57866 − 2.24267I
12.21670 − 5.39354I 6.49982 + 9.79940I
u = −0.743669 + 0.113537I
a = −1.86128 + 0.35715I
b = 0.968209 + 0.116721I
2.48833 + 2.05269I 9.77151 + 0.18924I
u = −0.743669 − 0.113537I
a = −1.86128 − 0.35715I
b = 0.968209 − 0.116721I
2.48833 − 2.05269I 9.77151 − 0.18924I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.699055 + 0.226988I
a = −2.32653 − 0.27444I
b = −0.206392 + 0.302743I
4.89157 − 3.13631I 1.34681 + 1.41207I
u = 0.699055 − 0.226988I
a = −2.32653 + 0.27444I
b = −0.206392 − 0.302743I
4.89157 + 3.13631I 1.34681 − 1.41207I
u = 0.652026
a = 2.01778
b = −0.867893
−1.99612 12.1580
u = −0.468647
a = 3.12140
b = 0.566633
1.09456 −4.47640
u = 1.55512 + 0.21865I
a = −0.287202 − 0.041726I
b = −0.213577 + 0.958778I
15.8581 − 2.5922I 5.18360 + 2.23250I
u = 1.55512 − 0.21865I
a = −0.287202 + 0.041726I
b = −0.213577 − 0.958778I
15.8581 + 2.5922I 5.18360 − 2.23250I
u = −1.68573
a = 0.284193
b = 0.148948
10.3675 −17.1410
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
27
+ 5u
26
+ ··· − 5u − 1)(u
98
− 24u
96
+ ··· + 179u − 49)
c
2
(u
27
− 6u
24
+ ··· + 3u + 1)(u
98
− u
97
+ ··· − 175987u − 451)
c
3
, c
4
(u
27
− 16u
25
+ ··· − 4u
2
− 1)(u
98
− u
97
+ ··· − 224u − 32)
c
5
(u
27
− 5u
26
+ ··· − 5u + 1)(u
98
− 24u
96
+ ··· + 179u − 49)
c
6
(u
27
− 9u
25
+ ··· − 9u
2
+ 1)(u
98
+ u
97
+ ··· − 192u + 79)
c
7
, c
8
(u
27
+ u
26
+ ··· + 4u
2
+ 1)(u
98
+ 2u
97
+ ··· − 36u + 19)
c
9
(u
27
− 16u
25
+ ··· + 4u
2
+ 1)(u
98
− u
97
+ ··· − 224u − 32)
c
10
(u
27
− 9u
25
+ ··· + 9u
2
− 1)(u
98
+ u
97
+ ··· − 192u + 79)
c
11
(u
27
− 2u
25
+ ··· + 6u + 1)
· (u
98
− 5u
97
+ ··· − 215663520u + 43957163)
c
12
(u
27
− u
26
+ ··· − 4u
2
− 1)(u
98
+ 2u
97
+ ··· − 36u + 19)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
27
− 19y
26
+ ··· + 27y −1)(y
98
− 48y
97
+ ··· − 56639y + 2401)
c
2
(y
27
− 14y
25
+ ··· + 13y −1)
· (y
98
+ 23y
97
+ ··· − 31146246201y + 203401)
c
3
, c
4
, c
9
(y
27
− 32y
26
+ ··· − 8y −1)(y
98
− 109y
97
+ ··· − 160768y + 1024)
c
6
, c
10
(y
27
− 18y
26
+ ··· + 18y −1)(y
98
− 67y
97
+ ··· − 74626y + 6241)
c
7
, c
8
, c
12
(y
27
+ 31y
26
+ ··· − 8y −1)(y
98
+ 106y
97
+ ··· + 12536y + 361)
c
11
(y
27
− 4y
26
+ ··· − 36y −1)
· (y
98
− 57y
97
+ ··· − 68808164574318740y + 1932232179008569)
22
