12a
0573
(K12a
0573
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 11 2 6 12 1 5 8 4
Solving Sequence
4,10
5 11
1,6
9 3 2 12 8 7
c
4
c
10
c
5
c
9
c
3
c
1
c
12
c
8
c
7
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h7.55432 × 10
231
u
94
− 3.94979 × 10
231
u
93
+ ··· + 5.03123 × 10
233
b + 8.02484 × 10
234
,
− 6.27990 × 10
234
u
94
+ 4.91845 × 10
234
u
93
+ ··· + 3.84051 × 10
235
a − 5.98614 × 10
237
,
u
95
− u
94
+ ··· + 998u − 229i
I
u
2
= h−u
21
+ 12u
19
+ ··· + b + 1, −u
23
+ 13u
21
+ ··· + a + u, u
24
− 14u
22
+ ··· + 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 119 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
= h7.55 × 10
231
u
94
− 3.95 × 10
231
u
93
+ · · · + 5.03 × 10
233
b + 8.02 ×
10
234
, −6.28 × 10
234
u
94
+ 4.92 × 10
234
u
93
+ · · · + 3.84 × 10
235
a − 5.99 ×
10
237
, u
95
− u
94
+ · · · + 998u − 229i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
11
=
u
−u
3
+ u
a
1
=
0.163517u
94
− 0.128068u
93
+ ··· − 9.60245u + 155.869
−0.0150148u
94
+ 0.00785054u
93
+ ··· + 7.03716u − 15.9501
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
0.149130u
94
− 0.101058u
93
+ ··· − 50.2226u + 125.337
−0.0388424u
94
+ 0.0317280u
93
+ ··· + 9.44989u − 34.1884
a
3
=
−0.199431u
94
+ 0.152151u
93
+ ··· + 59.9789u − 181.897
0.0125942u
94
− 0.0169786u
93
+ ··· + 12.7547u + 21.1136
a
2
=
0.242375u
94
− 0.182145u
93
+ ··· − 44.1731u + 223.500
−0.00939841u
94
+ 0.00780443u
93
+ ··· − 6.28912u − 14.2852
a
12
=
0.178532u
94
− 0.135918u
93
+ ··· − 16.6396u + 171.819
−0.0150148u
94
+ 0.00785054u
93
+ ··· + 7.03716u − 15.9501
a
8
=
−0.0921952u
94
+ 0.0767583u
93
+ ··· + 13.7278u − 100.851
−4.09274 × 10
−6
u
94
+ 0.00284681u
93
+ ··· + 4.30488u − 3.91892
a
7
=
−0.0978961u
94
+ 0.0863550u
93
+ ··· + 12.3830u − 113.021
−0.00892542u
94
+ 0.0100792u
93
+ ··· + 13.6694u − 5.66045
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.418076u
94
+ 0.342082u
93
+ ··· − 2.01058u − 379.553
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
95
+ 27u
94
+ ··· + 25u + 1
c
2
, c
6
u
95
− u
94
+ ··· + u + 1
c
3
u
95
− u
94
+ ··· − 3835u + 845
c
4
, c
5
, c
10
u
95
+ u
94
+ ··· + 998u + 229
c
8
, c
11
u
95
+ u
94
+ ··· − 18u + 1
c
9
u
95
+ 7u
94
+ ··· − 15768u + 1413
c
12
u
95
+ 8u
94
+ ··· + 17711u + 2447
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
95
+ 93y
94
+ ··· + 225y −1
c
2
, c
6
y
95
− 27y
94
+ ··· + 25y −1
c
3
y
95
+ 31y
94
+ ··· − 12307425y −714025
c
4
, c
5
, c
10
y
95
− 109y
94
+ ··· + 3539736y −52441
c
8
, c
11
y
95
− 93y
94
+ ··· + 92y −1
c
9
y
95
+ 35y
94
+ ··· + 42933762y −1996569
c
12
y
95
− 36y
94
+ ··· + 298346619y −5987809
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.993324 + 0.113886I
a = −0.211155 − 0.035291I
b = 0.474145 + 0.672640I
1.75972 − 0.04833I 0
u = −0.993324 − 0.113886I
a = −0.211155 + 0.035291I
b = 0.474145 − 0.672640I
1.75972 + 0.04833I 0
u = 0.996175 + 0.200215I
a = 0.444838 − 0.245934I
b = 0.027663 − 0.803448I
1.26759 + 4.32682I 0
u = 0.996175 − 0.200215I
a = 0.444838 + 0.245934I
b = 0.027663 + 0.803448I
1.26759 − 4.32682I 0
u = −0.696166 + 0.748256I
a = 0.582098 − 0.191531I
b = 0.767229 + 0.497403I
1.18820 + 2.86171I 0
u = −0.696166 − 0.748256I
a = 0.582098 + 0.191531I
b = 0.767229 − 0.497403I
1.18820 − 2.86171I 0
u = −0.535987 + 0.636878I
a = 0.234758 − 1.306110I
b = 1.134930 − 0.783701I
0.91102 − 7.57603I 0
u = −0.535987 − 0.636878I
a = 0.234758 + 1.306110I
b = 1.134930 + 0.783701I
0.91102 + 7.57603I 0
u = 0.731945 + 0.345316I
a = 0.008581 − 1.276130I
b = −1.14528 − 0.86552I
3.71584 + 3.90274I 0
u = 0.731945 − 0.345316I
a = 0.008581 + 1.276130I
b = −1.14528 + 0.86552I
3.71584 − 3.90274I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.225383 + 0.749670I
a = −1.118140 − 0.145739I
b = −0.758397 + 0.405896I
1.56332 − 0.38085I 0
u = 0.225383 − 0.749670I
a = −1.118140 + 0.145739I
b = −0.758397 − 0.405896I
1.56332 + 0.38085I 0
u = −0.777312 + 0.950438I
a = 0.270161 − 1.108820I
b = 1.087020 − 0.803080I
8.6020 − 12.0514I 0
u = −0.777312 − 0.950438I
a = 0.270161 + 1.108820I
b = 1.087020 + 0.803080I
8.6020 + 12.0514I 0
u = 0.840314 + 0.900458I
a = −0.241403 − 1.100060I
b = −1.089160 − 0.808193I
9.11645 + 5.73244I 0
u = 0.840314 − 0.900458I
a = −0.241403 + 1.100060I
b = −1.089160 + 0.808193I
9.11645 − 5.73244I 0
u = −0.757972 + 0.007541I
a = −0.829238 + 0.252949I
b = 0.532454 − 0.236617I
1.67673 − 0.14877I 0
u = −0.757972 − 0.007541I
a = −0.829238 − 0.252949I
b = 0.532454 + 0.236617I
1.67673 + 0.14877I 0
u = 0.623797 + 0.414333I
a = 0.228053 + 1.275920I
b = −0.95365 + 1.12669I
8.09696 − 1.35610I 0
u = 0.623797 − 0.414333I
a = 0.228053 − 1.275920I
b = −0.95365 − 1.12669I
8.09696 + 1.35610I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.527293 + 0.500564I
a = −0.206299 + 1.273140I
b = 0.89031 + 1.16063I
7.47429 − 5.04540I 0
u = −0.527293 − 0.500564I
a = −0.206299 − 1.273140I
b = 0.89031 − 1.16063I
7.47429 + 5.04540I 0
u = −0.549773 + 0.459183I
a = −2.27573 − 0.21620I
b = 0.733117 − 0.391883I
7.54560 + 1.65750I 8.73859 + 0.I
u = −0.549773 − 0.459183I
a = −2.27573 + 0.21620I
b = 0.733117 + 0.391883I
7.54560 − 1.65750I 8.73859 + 0.I
u = −0.526692 + 0.472816I
a = −1.214460 + 0.533716I
b = −0.693000 + 0.127743I
3.39672 − 0.91258I 0. + 5.79505I
u = −0.526692 − 0.472816I
a = −1.214460 − 0.533716I
b = −0.693000 − 0.127743I
3.39672 + 0.91258I 0. − 5.79505I
u = 0.485680 + 1.199540I
a = −0.768169 + 0.079709I
b = −0.843819 + 0.441106I
7.84874 + 1.09621I 0
u = 0.485680 − 1.199540I
a = −0.768169 − 0.079709I
b = −0.843819 − 0.441106I
7.84874 − 1.09621I 0
u = 0.586251 + 0.391592I
a = −0.06845 + 2.24487I
b = 0.797329 + 0.528318I
2.92370 + 7.46960I 0. − 9.77082I
u = 0.586251 − 0.391592I
a = −0.06845 − 2.24487I
b = 0.797329 − 0.528318I
2.92370 − 7.46960I 0. + 9.77082I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569131 + 0.398506I
a = 1.329510 + 0.475836I
b = 0.707955 + 0.063430I
2.74972 − 4.66676I 0
u = 0.569131 − 0.398506I
a = 1.329510 − 0.475836I
b = 0.707955 − 0.063430I
2.74972 + 4.66676I 0
u = −0.569144 + 1.190100I
a = 0.732157 + 0.070791I
b = 0.845166 + 0.455105I
7.77827 + 5.11561I 0
u = −0.569144 − 1.190100I
a = 0.732157 − 0.070791I
b = 0.845166 − 0.455105I
7.77827 − 5.11561I 0
u = 1.317630 + 0.080427I
a = 0.367515 − 1.052560I
b = −1.004110 − 0.841707I
4.85394 + 3.18451I 0
u = 1.317630 − 0.080427I
a = 0.367515 + 1.052560I
b = −1.004110 + 0.841707I
4.85394 − 3.18451I 0
u = 1.314690 + 0.245234I
a = 0.194689 − 0.877843I
b = −1.060160 − 0.841163I
4.92156 + 3.67064I 0
u = 1.314690 − 0.245234I
a = 0.194689 + 0.877843I
b = −1.060160 + 0.841163I
4.92156 − 3.67064I 0
u = 0.355208 + 0.557436I
a = 0.29330 + 1.68999I
b = 0.660249 + 0.621988I
−2.52906 + 3.25489I −5.36852 − 7.70712I
u = 0.355208 − 0.557436I
a = 0.29330 − 1.68999I
b = 0.660249 − 0.621988I
−2.52906 − 3.25489I −5.36852 + 7.70712I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.341290 + 0.156139I
a = −0.409309 − 0.555943I
b = 1.19066 − 0.80574I
2.86230 − 0.93905I 0
u = −1.341290 − 0.156139I
a = −0.409309 + 0.555943I
b = 1.19066 + 0.80574I
2.86230 + 0.93905I 0
u = 0.461528 + 0.457013I
a = 2.56177 − 0.19449I
b = −0.721443 − 0.392720I
7.56513 + 4.46649I 8.81708 − 7.74250I
u = 0.461528 − 0.457013I
a = 2.56177 + 0.19449I
b = −0.721443 + 0.392720I
7.56513 − 4.46649I 8.81708 + 7.74250I
u = 0.580018 + 0.245313I
a = 0.910584 − 0.070935I
b = 0.410463 − 0.198520I
−1.77575 − 0.09596I −5.41324 − 1.06240I
u = 0.580018 − 0.245313I
a = 0.910584 + 0.070935I
b = 0.410463 + 0.198520I
−1.77575 + 0.09596I −5.41324 + 1.06240I
u = −0.526602 + 0.306350I
a = −0.04969 + 2.53351I
b = −0.772656 + 0.489239I
3.42392 − 1.76238I 3.82353 + 4.55359I
u = −0.526602 − 0.306350I
a = −0.04969 − 2.53351I
b = −0.772656 − 0.489239I
3.42392 + 1.76238I 3.82353 − 4.55359I
u = 0.079977 + 0.559249I
a = 0.133715 + 1.223310I
b = 0.377541 + 0.807990I
−1.49124 − 1.49233I −5.62608 + 3.32257I
u = 0.079977 − 0.559249I
a = 0.133715 − 1.223310I
b = 0.377541 − 0.807990I
−1.49124 + 1.49233I −5.62608 − 3.32257I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42584 + 0.19357I
a = −0.586636 − 0.963582I
b = 0.984999 − 0.752996I
3.21152 − 5.95296I 0
u = −1.42584 − 0.19357I
a = −0.586636 + 0.963582I
b = 0.984999 + 0.752996I
3.21152 + 5.95296I 0
u = −0.247811 + 0.438822I
a = −0.85477 + 1.26768I
b = −0.551665 + 0.453931I
0.242670 − 1.208790I 2.95131 + 5.26404I
u = −0.247811 − 0.438822I
a = −0.85477 − 1.26768I
b = −0.551665 − 0.453931I
0.242670 + 1.208790I 2.95131 − 5.26404I
u = −1.49976 + 0.01728I
a = 0.810271 + 0.854161I
b = −0.805895 + 0.092612I
7.49239 + 2.42085I 0
u = −1.49976 − 0.01728I
a = 0.810271 − 0.854161I
b = −0.805895 − 0.092612I
7.49239 − 2.42085I 0
u = 1.53993 + 0.02243I
a = −0.351125 + 0.474031I
b = 1.94756 + 1.32394I
6.51260 + 1.23119I 0
u = 1.53993 − 0.02243I
a = −0.351125 − 0.474031I
b = 1.94756 − 1.32394I
6.51260 − 1.23119I 0
u = −1.54816 + 0.13261I
a = 1.34405 − 0.84465I
b = −0.748690 − 0.097086I
14.3987 − 6.5613I 0
u = −1.54816 − 0.13261I
a = 1.34405 + 0.84465I
b = −0.748690 + 0.097086I
14.3987 + 6.5613I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55206 + 0.22023I
a = 0.222873 + 0.723008I
b = −0.861005 + 0.084857I
7.73078 − 3.20289I 0
u = −1.55206 − 0.22023I
a = 0.222873 − 0.723008I
b = −0.861005 − 0.084857I
7.73078 + 3.20289I 0
u = 1.57112 + 0.07499I
a = 0.567488 − 1.165570I
b = −0.917156 − 0.802718I
10.66090 + 3.06605I 0
u = 1.57112 − 0.07499I
a = 0.567488 + 1.165570I
b = −0.917156 + 0.802718I
10.66090 − 3.06605I 0
u = 1.56317 + 0.17546I
a = −0.503473 + 0.755596I
b = 1.55777 + 0.93066I
7.95394 + 10.44560I 0
u = 1.56317 − 0.17546I
a = −0.503473 − 0.755596I
b = 1.55777 − 0.93066I
7.95394 − 10.44560I 0
u = 1.56634 + 0.14849I
a = −0.039530 − 0.517153I
b = 1.16585 − 1.79493I
14.5760 + 7.3982I 0
u = 1.56634 − 0.14849I
a = −0.039530 + 0.517153I
b = 1.16585 + 1.79493I
14.5760 − 7.3982I 0
u = 1.57870 + 0.11756I
a = −1.35070 − 0.73522I
b = 0.746770 − 0.084627I
14.8325 + 0.3716I 0
u = 1.57870 − 0.11756I
a = −1.35070 + 0.73522I
b = 0.746770 + 0.084627I
14.8325 − 0.3716I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.58417 + 0.11388I
a = −0.597493 − 1.158790I
b = 0.913257 − 0.790219I
10.36980 − 9.31906I 0
u = −1.58417 − 0.11388I
a = −0.597493 + 1.158790I
b = 0.913257 + 0.790219I
10.36980 + 9.31906I 0
u = −1.59785 + 0.07643I
a = 0.028419 − 0.523663I
b = 0.991167 − 0.861468I
10.40840 + 3.06913I 0
u = −1.59785 − 0.07643I
a = 0.028419 + 0.523663I
b = 0.991167 + 0.861468I
10.40840 − 3.06913I 0
u = 1.59349 + 0.14165I
a = −0.017656 − 0.572531I
b = −1.012300 − 0.857871I
10.74830 + 3.27026I 0
u = 1.59349 − 0.14165I
a = −0.017656 + 0.572531I
b = −1.012300 + 0.857871I
10.74830 − 3.27026I 0
u = −1.59903 + 0.10260I
a = 0.105523 − 0.545341I
b = −1.34677 − 1.67664I
15.7568 − 0.4814I 0
u = −1.59903 − 0.10260I
a = 0.105523 + 0.545341I
b = −1.34677 + 1.67664I
15.7568 + 0.4814I 0
u = −1.60642 + 0.09615I
a = 0.379213 + 0.671654I
b = −1.60005 + 1.12283I
11.67530 − 5.54466I 0
u = −1.60642 − 0.09615I
a = 0.379213 − 0.671654I
b = −1.60005 − 1.12283I
11.67530 + 5.54466I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.365909 + 0.100941I
a = −0.32398 − 1.55574I
b = 1.40999 − 0.94117I
−0.161589 − 0.831554I 5.75339 + 10.80698I
u = −0.365909 − 0.100941I
a = −0.32398 + 1.55574I
b = 1.40999 + 0.94117I
−0.161589 + 0.831554I 5.75339 − 10.80698I
u = 1.64398
a = −0.845264
b = 0.801737
10.0916 0
u = 1.65548 + 0.07001I
a = −0.496986 + 0.319634I
b = 0.840569 + 0.037887I
10.15280 + 0.15676I 0
u = 1.65548 − 0.07001I
a = −0.496986 − 0.319634I
b = 0.840569 − 0.037887I
10.15280 − 0.15676I 0
u = 1.65913 + 0.30071I
a = −0.408789 + 0.936143I
b = 1.35310 + 0.94377I
16.6298 + 16.7549I 0
u = 1.65913 − 0.30071I
a = −0.408789 − 0.936143I
b = 1.35310 − 0.94377I
16.6298 − 16.7549I 0
u = −1.67341 + 0.26685I
a = 0.390471 + 0.904092I
b = −1.36919 + 0.97309I
17.4854 − 10.1473I 0
u = −1.67341 − 0.26685I
a = 0.390471 − 0.904092I
b = −1.36919 − 0.97309I
17.4854 + 10.1473I 0
u = 0.243236 + 0.006215I
a = 1.57504 − 4.32600I
b = −0.694360 + 0.394916I
1.46420 − 2.55510I 5.02686 + 10.79108I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.243236 − 0.006215I
a = 1.57504 + 4.32600I
b = −0.694360 − 0.394916I
1.46420 + 2.55510I 5.02686 − 10.79108I
u = −1.71967 + 0.41859I
a = −0.120337 + 0.511463I
b = −0.903718 + 0.083096I
15.0760 − 7.3587I 0
u = −1.71967 − 0.41859I
a = −0.120337 − 0.511463I
b = −0.903718 − 0.083096I
15.0760 + 7.3587I 0
u = 1.76133 + 0.37373I
a = 0.085143 + 0.455559I
b = 0.904333 + 0.074033I
15.5208 + 1.0744I 0
u = 1.76133 − 0.37373I
a = 0.085143 − 0.455559I
b = 0.904333 − 0.074033I
15.5208 − 1.0744I 0
14
II. I
u
2
=
h−u
21
+12u
19
+· · ·+b+1, −u
23
+13u
21
+· · ·+a+u, u
24
−14u
22
+· · ·+2u−1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
11
=
u
−u
3
+ u
a
1
=
u
23
− 13u
21
+ ··· − 2u
2
− u
u
21
− 12u
19
+ ··· − 2u − 1
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
u
23
− 12u
21
+ ··· + 2u
4
+ 3u
3
−u
23
+ 13u
21
+ ··· + 2u
2
+ u
a
3
=
u
23
+ 2u
22
+ ··· − 3u + 3
−u
22
+ 12u
20
+ ··· − 2u
3
− 3u
2
a
2
=
2u
22
− u
21
+ ··· − 2u + 3
u
23
− u
22
+ ··· − 3u
2
− 1
a
12
=
u
23
− 14u
21
+ ··· + u + 1
u
21
− 12u
19
+ ··· − 2u − 1
a
8
=
u
21
− 13u
19
+ ··· + 5u
2
− 1
u
19
− 11u
17
+ ··· + 3u + 1
a
7
=
u
21
− 12u
19
+ ··· + 2u
2
+ u
−u
23
+ 12u
21
+ ··· + 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
23
− 91u
21
− 9u
20
+ 499u
19
+ 104u
18
− 1486u
17
− 503u
16
+
2560u
15
+ 1308u
14
− 2447u
13
− 1942u
12
+ 948u
11
+ 1573u
10
+ 371u
9
− 510u
8
− 550u
7
−
146u
6
+ 214u
5
+ 169u
4
− 12u
3
− 46u
2
− 7u + 9
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 10u
23
+ ··· − 17u + 1
c
2
u
24
− 5u
22
+ ··· + u + 1
c
3
u
24
+ 4u
22
+ ··· − u − 1
c
4
, c
5
u
24
− 14u
22
+ ··· + 2u − 1
c
6
u
24
− 5u
22
+ ··· − u + 1
c
7
u
24
+ 10u
23
+ ··· + 17u + 1
c
8
u
24
− 4u
23
+ ··· − 4u + 1
c
9
u
24
+ 4u
22
+ ··· − 2u + 1
c
10
u
24
− 14u
22
+ ··· − 2u − 1
c
11
u
24
+ 4u
23
+ ··· + 4u + 1
c
12
u
24
− 3u
23
+ ··· − 3u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
24
+ 18y
23
+ ··· − 21y + 1
c
2
, c
6
y
24
− 10y
23
+ ··· − 17y + 1
c
3
y
24
+ 8y
23
+ ··· − 3y + 1
c
4
, c
5
, c
10
y
24
− 28y
23
+ ··· − 12y + 1
c
8
, c
11
y
24
− 24y
23
+ ··· − 16y + 1
c
9
y
24
+ 8y
23
+ ··· + 14y + 1
c
12
y
24
− 11y
23
+ ··· − 3y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.230070 + 0.129407I
a = 0.644352 − 1.071010I
b = −1.216520 − 0.600965I
5.43238 + 6.88848I 6.83763 − 6.74493I
u = 1.230070 − 0.129407I
a = 0.644352 + 1.071010I
b = −1.216520 + 0.600965I
5.43238 − 6.88848I 6.83763 + 6.74493I
u = −1.228340 + 0.156795I
a = −0.482987 − 1.194290I
b = 1.092080 − 0.617370I
5.98051 − 1.92070I 7.90871 + 0.24735I
u = −1.228340 − 0.156795I
a = −0.482987 + 1.194290I
b = 1.092080 + 0.617370I
5.98051 + 1.92070I 7.90871 − 0.24735I
u = −0.615317 + 0.357755I
a = 1.01722 − 1.07128I
b = 0.748487 + 0.215306I
3.65993 + 0.05326I 8.06301 − 1.11885I
u = −0.615317 − 0.357755I
a = 1.01722 + 1.07128I
b = 0.748487 − 0.215306I
3.65993 − 0.05326I 8.06301 + 1.11885I
u = −0.048840 + 0.698393I
a = 0.060103 − 1.169090I
b = 0.055788 + 0.571780I
7.27713 + 3.12415I 6.44408 − 2.47099I
u = −0.048840 − 0.698393I
a = 0.060103 + 1.169090I
b = 0.055788 − 0.571780I
7.27713 − 3.12415I 6.44408 + 2.47099I
u = −1.295160 + 0.193439I
a = −0.106169 − 0.988293I
b = 0.862717 − 0.887500I
4.44804 − 4.30220I 2.60756 + 9.11283I
u = −1.295160 − 0.193439I
a = −0.106169 + 0.988293I
b = 0.862717 + 0.887500I
4.44804 + 4.30220I 2.60756 − 9.11283I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.309930 + 0.117543I
a = 0.316375 − 0.663440I
b = −1.34292 − 1.16008I
3.14095 + 1.67218I 5.22475 − 5.27037I
u = 1.309930 − 0.117543I
a = 0.316375 + 0.663440I
b = −1.34292 + 1.16008I
3.14095 − 1.67218I 5.22475 + 5.27037I
u = 0.615545 + 0.285268I
a = −1.15416 − 0.96062I
b = −0.825497 + 0.193760I
3.09785 − 5.37231I 7.44446 + 8.13967I
u = 0.615545 − 0.285268I
a = −1.15416 + 0.96062I
b = −0.825497 − 0.193760I
3.09785 + 5.37231I 7.44446 − 8.13967I
u = −0.430788 + 0.491614I
a = 0.621346 − 1.033540I
b = 0.580994 + 0.439922I
1.25129 + 1.87641I 1.243241 + 0.649208I
u = −0.430788 − 0.491614I
a = 0.621346 + 1.033540I
b = 0.580994 − 0.439922I
1.25129 − 1.87641I 1.243241 − 0.649208I
u = −1.54136
a = 0.421027
b = −1.72637
6.63958 5.81920
u = −1.56893 + 0.19019I
a = 0.584862 − 0.468778I
b = −0.412874 − 0.758253I
13.1270 − 6.4884I 4.93291 + 3.21494I
u = −1.56893 − 0.19019I
a = 0.584862 + 0.468778I
b = −0.412874 + 0.758253I
13.1270 + 6.4884I 4.93291 − 3.21494I
u = 0.350431 + 0.225016I
a = −0.677449 − 0.523119I
b = −1.095810 + 0.583351I
−0.320379 − 0.358730I −0.69353 − 3.81560I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.350431 − 0.225016I
a = −0.677449 + 0.523119I
b = −1.095810 − 0.583351I
−0.320379 + 0.358730I −0.69353 + 3.81560I
u = 1.61370 + 0.15698I
a = −0.658388 − 0.364034I
b = 0.549354 − 0.583456I
13.74470 + 0.17618I 5.50808 + 2.02702I
u = 1.61370 − 0.15698I
a = −0.658388 + 0.364034I
b = 0.549354 + 0.583456I
13.74470 − 0.17618I 5.50808 − 2.02702I
u = 1.67680
a = −0.751232
b = 0.734771
9.85602 −14.8610
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
24
− 10u
23
+ ··· − 17u + 1)(u
95
+ 27u
94
+ ··· + 25u + 1)
c
2
(u
24
− 5u
22
+ ··· + u + 1)(u
95
− u
94
+ ··· + u + 1)
c
3
(u
24
+ 4u
22
+ ··· − u − 1)(u
95
− u
94
+ ··· − 3835u + 845)
c
4
, c
5
(u
24
− 14u
22
+ ··· + 2u − 1)(u
95
+ u
94
+ ··· + 998u + 229)
c
6
(u
24
− 5u
22
+ ··· − u + 1)(u
95
− u
94
+ ··· + u + 1)
c
7
(u
24
+ 10u
23
+ ··· + 17u + 1)(u
95
+ 27u
94
+ ··· + 25u + 1)
c
8
(u
24
− 4u
23
+ ··· − 4u + 1)(u
95
+ u
94
+ ··· − 18u + 1)
c
9
(u
24
+ 4u
22
+ ··· − 2u + 1)(u
95
+ 7u
94
+ ··· − 15768u + 1413)
c
10
(u
24
− 14u
22
+ ··· − 2u − 1)(u
95
+ u
94
+ ··· + 998u + 229)
c
11
(u
24
+ 4u
23
+ ··· + 4u + 1)(u
95
+ u
94
+ ··· − 18u + 1)
c
12
(u
24
− 3u
23
+ ··· − 3u − 1)(u
95
+ 8u
94
+ ··· + 17711u + 2447)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
24
+ 18y
23
+ ··· − 21y + 1)(y
95
+ 93y
94
+ ··· + 225y −1)
c
2
, c
6
(y
24
− 10y
23
+ ··· − 17y + 1)(y
95
− 27y
94
+ ··· + 25y −1)
c
3
(y
24
+ 8y
23
+ ··· − 3y + 1)(y
95
+ 31y
94
+ ··· − 1.23074 × 10
7
y −714025)
c
4
, c
5
, c
10
(y
24
− 28y
23
+ ··· − 12y + 1)
· (y
95
− 109y
94
+ ··· + 3539736y −52441)
c
8
, c
11
(y
24
− 24y
23
+ ··· − 16y + 1)(y
95
− 93y
94
+ ··· + 92y −1)
c
9
(y
24
+ 8y
23
+ ··· + 14y + 1)
· (y
95
+ 35y
94
+ ··· + 42933762y −1996569)
c
12
(y
24
− 11y
23
+ ··· − 3y + 1)
· (y
95
− 36y
94
+ ··· + 298346619y −5987809)
22
