12a
0855
(K12a
0855
)
A knot diagram
1
Linearized knot diagam
4 5 9 11 10 3 12 1 6 2 7 8
Solving Sequence
8,12 1,4
2 9 3 7 6 11 5 10
c
12
c
1
c
8
c
3
c
7
c
6
c
11
c
4
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.71973 × 10
150
u
106
− 1.35102 × 10
150
u
105
+ ··· + 2.76810 × 10
149
b + 1.95138 × 10
151
,
− 3.00286 × 10
151
u
106
− 9.93085 × 10
150
u
105
+ ··· + 3.59853 × 10
150
a + 1.40666 × 10
152
,
u
107
− u
106
+ ··· + 37u + 13i
I
u
2
= h−6u
21
+ 13u
20
+ ··· + b − 9, −8u
21
+ 8u
20
+ ··· + a + 1, u
22
− 14u
20
+ ··· − 14u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 129 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−2.72 × 10
150
u
106
− 1.35 × 10
150
u
105
+ · · · + 2.77 × 10
149
b + 1.95 ×
10
151
, −3.00 × 10
151
u
106
− 9.93 × 10
150
u
105
+ · · · + 3.60 × 10
150
a + 1.41 ×
10
152
, u
107
− u
106
+ · · · + 37u + 13i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
8.34469u
106
+ 2.75970u
105
+ ··· − 204.687u − 39.0899
9.82526u
106
+ 4.88068u
105
+ ··· − 298.738u − 70.4952
a
2
=
−18.6646u
106
− 10.3720u
105
+ ··· + 546.013u + 156.555
−31.5456u
106
− 17.6970u
105
+ ··· + 941.795u + 275.347
a
9
=
−u
−u
3
+ u
a
3
=
9.49206u
106
+ 3.47400u
105
+ ··· − 224.750u − 49.7932
12.0894u
106
+ 6.28403u
105
+ ··· − 362.472u − 83.9937
a
7
=
u
u
a
6
=
3.98230u
106
+ 2.01757u
105
+ ··· − 121.235u − 43.7384
10.9136u
106
+ 5.89206u
105
+ ··· − 333.952u − 101.022
a
11
=
−u
2
+ 1
−u
2
a
5
=
14.2838u
106
+ 6.95237u
105
+ ··· − 388.946u − 108.913
20.7169u
106
+ 11.3131u
105
+ ··· − 629.231u − 163.994
a
10
=
10.9981u
106
+ 8.41827u
105
+ ··· − 371.282u − 128.867
18.8426u
106
+ 9.80105u
105
+ ··· − 556.113u − 162.363
(ii) Obstruction class = −1
(iii) Cusp Shapes = −7.15694u
106
− 0.854720u
105
+ ··· + 135.938u + 10.9433
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
107
+ 8u
106
+ ··· + 79200u − 3200
c
2
u
107
+ 8u
105
+ ··· − 191u − 11
c
3
u
107
− u
106
+ ··· + 13886809u + 3405181
c
4
u
107
+ u
105
+ ··· + 152u − 7
c
5
, c
9
u
107
− 3u
106
+ ··· + 22u + 2
c
6
u
107
+ 3u
106
+ ··· − 604539u − 105767
c
7
, c
8
, c
11
c
12
u
107
− u
106
+ ··· + 37u + 13
c
10
u
107
− 6u
106
+ ··· + 5194u − 4049
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
107
− 40y
106
+ ··· + 1928422400y −10240000
c
2
y
107
+ 16y
106
+ ··· − 7937y −121
c
3
y
107
+ 47y
106
+ ··· − 467129995532381y −11595257642761
c
4
y
107
+ 2y
106
+ ··· + 5576y −49
c
5
, c
9
y
107
+ 81y
106
+ ··· + 1044y −4
c
6
y
107
+ 31y
106
+ ··· − 214514614873y −11186658289
c
7
, c
8
, c
11
c
12
y
107
− 129y
106
+ ··· + 5711y −169
c
10
y
107
+ 26y
106
+ ··· − 541032280y −16394401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.826655 + 0.568633I
a = 1.24553 + 0.76935I
b = −0.239026 − 0.064980I
−6.3082 + 14.5498I 0
u = −0.826655 − 0.568633I
a = 1.24553 − 0.76935I
b = −0.239026 + 0.064980I
−6.3082 − 14.5498I 0
u = 0.826318 + 0.570704I
a = 1.162670 − 0.663776I
b = −0.166220 + 0.227032I
−1.31108 − 8.80416I 0
u = 0.826318 − 0.570704I
a = 1.162670 + 0.663776I
b = −0.166220 − 0.227032I
−1.31108 + 8.80416I 0
u = −0.952140 + 0.249038I
a = −1.066520 + 0.168283I
b = 0.474150 − 0.262800I
−6.05633 + 4.48287I 0
u = −0.952140 − 0.249038I
a = −1.066520 − 0.168283I
b = 0.474150 + 0.262800I
−6.05633 − 4.48287I 0
u = −0.755159 + 0.631053I
a = 0.862027 + 0.687544I
b = −0.465536 − 0.607906I
−5.17350 + 1.52550I 0
u = −0.755159 − 0.631053I
a = 0.862027 − 0.687544I
b = −0.465536 + 0.607906I
−5.17350 − 1.52550I 0
u = 0.894153 + 0.343291I
a = 1.01314 − 1.38448I
b = 0.664382 − 0.567740I
−7.12672 − 5.99311I 0
u = 0.894153 − 0.343291I
a = 1.01314 + 1.38448I
b = 0.664382 + 0.567740I
−7.12672 + 5.99311I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.930030 + 0.515744I
a = −0.687057 + 0.215263I
b = 0.130481 + 0.299587I
−3.25087 − 5.76442I 0
u = 0.930030 − 0.515744I
a = −0.687057 − 0.215263I
b = 0.130481 − 0.299587I
−3.25087 + 5.76442I 0
u = −0.743000 + 0.562440I
a = −0.380844 − 0.646698I
b = 0.201098 − 0.163543I
−1.32303 + 2.45240I 0
u = −0.743000 − 0.562440I
a = −0.380844 + 0.646698I
b = 0.201098 + 0.163543I
−1.32303 − 2.45240I 0
u = 1.005200 + 0.454195I
a = 0.381919 − 1.027960I
b = 0.228876 − 0.248331I
−7.48788 + 5.95732I 0
u = 1.005200 − 0.454195I
a = 0.381919 + 1.027960I
b = 0.228876 + 0.248331I
−7.48788 − 5.95732I 0
u = −1.038100 + 0.394850I
a = 0.710898 + 0.790455I
b = 0.490308 + 0.067744I
−2.72871 − 0.23789I 0
u = −1.038100 − 0.394850I
a = 0.710898 − 0.790455I
b = 0.490308 − 0.067744I
−2.72871 + 0.23789I 0
u = 0.800127 + 0.353920I
a = −1.42217 + 0.40443I
b = 0.177923 + 0.234950I
−2.76423 − 4.13132I 0
u = 0.800127 − 0.353920I
a = −1.42217 − 0.40443I
b = 0.177923 − 0.234950I
−2.76423 + 4.13132I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.128530 + 0.019920I
a = 0.973765 − 0.309888I
b = 0.746272 − 0.341276I
−2.30327 + 0.08679I 0
u = −1.128530 − 0.019920I
a = 0.973765 + 0.309888I
b = 0.746272 + 0.341276I
−2.30327 − 0.08679I 0
u = −0.745803 + 0.416141I
a = −1.57506 − 1.14608I
b = 0.125676 − 0.466047I
−6.27522 + 5.09865I 0
u = −0.745803 − 0.416141I
a = −1.57506 + 1.14608I
b = 0.125676 + 0.466047I
−6.27522 − 5.09865I 0
u = −0.270313 + 0.732731I
a = 0.372324 − 0.269561I
b = 0.0940821 − 0.0178112I
0.11533 + 1.88710I 0
u = −0.270313 − 0.732731I
a = 0.372324 + 0.269561I
b = 0.0940821 + 0.0178112I
0.11533 − 1.88710I 0
u = 0.108521 + 0.773022I
a = −0.193997 − 0.092772I
b = −0.830652 + 0.465756I
0.87016 + 4.32926I 0
u = 0.108521 − 0.773022I
a = −0.193997 + 0.092772I
b = −0.830652 − 0.465756I
0.87016 − 4.32926I 0
u = 0.678973 + 0.383166I
a = −0.43360 + 1.55662I
b = 0.516580 + 0.114540I
−6.38076 − 0.82493I 0
u = 0.678973 − 0.383166I
a = −0.43360 − 1.55662I
b = 0.516580 − 0.114540I
−6.38076 + 0.82493I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.094171 + 0.764360I
a = −0.488244 + 0.039795I
b = −0.879858 − 0.577966I
−4.09729 − 10.11170I 0
u = −0.094171 − 0.764360I
a = −0.488244 − 0.039795I
b = −0.879858 + 0.577966I
−4.09729 + 10.11170I 0
u = 0.388819 + 0.579837I
a = 0.934771 + 0.492384I
b = 0.264435 + 0.628142I
−1.72461 − 1.96082I 0. + 4.69802I
u = 0.388819 − 0.579837I
a = 0.934771 − 0.492384I
b = 0.264435 − 0.628142I
−1.72461 + 1.96082I 0. − 4.69802I
u = −0.575845 + 0.393068I
a = 1.087690 + 0.019654I
b = 0.161817 − 0.321184I
−1.36848 + 1.44447I −2.91055 − 4.72054I
u = −0.575845 − 0.393068I
a = 1.087690 − 0.019654I
b = 0.161817 + 0.321184I
−1.36848 − 1.44447I −2.91055 + 4.72054I
u = −0.213091 + 0.648713I
a = 0.045157 + 0.915947I
b = −0.892764 − 0.421227I
−3.70568 + 2.84318I −4.74637 − 7.45487I
u = −0.213091 − 0.648713I
a = 0.045157 − 0.915947I
b = −0.892764 + 0.421227I
−3.70568 − 2.84318I −4.74637 + 7.45487I
u = 0.666901 + 0.009105I
a = −1.66225 + 1.18426I
b = 0.657173 + 0.836987I
−5.89625 − 0.14698I −10.30166 − 0.10648I
u = 0.666901 − 0.009105I
a = −1.66225 − 1.18426I
b = 0.657173 − 0.836987I
−5.89625 + 0.14698I −10.30166 + 0.10648I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.596289 + 0.285850I
a = −2.90410 + 0.32830I
b = −0.369695 − 0.037100I
−2.18570 − 6.38810I −3.13881 + 11.21686I
u = 0.596289 − 0.285850I
a = −2.90410 − 0.32830I
b = −0.369695 + 0.037100I
−2.18570 + 6.38810I −3.13881 − 11.21686I
u = −0.131185 + 0.631680I
a = 0.488911 − 0.353615I
b = −0.012361 − 0.410523I
−0.03169 + 1.79207I 3.57282 − 1.79656I
u = −0.131185 − 0.631680I
a = 0.488911 + 0.353615I
b = −0.012361 + 0.410523I
−0.03169 − 1.79207I 3.57282 + 1.79656I
u = −0.592482 + 0.205435I
a = −0.609364 + 0.716647I
b = −0.17971 − 1.60405I
−2.59941 + 5.79531I −3.45472 − 10.54157I
u = −0.592482 − 0.205435I
a = −0.609364 − 0.716647I
b = −0.17971 + 1.60405I
−2.59941 − 5.79531I −3.45472 + 10.54157I
u = −0.606784 + 0.152467I
a = −2.90825 + 1.03073I
b = −0.226483 + 0.599261I
0.14553 + 2.03996I −5.55929 − 6.74240I
u = −0.606784 − 0.152467I
a = −2.90825 − 1.03073I
b = −0.226483 − 0.599261I
0.14553 − 2.03996I −5.55929 + 6.74240I
u = 1.367050 + 0.286263I
a = 0.127328 + 0.290641I
b = −0.059407 + 0.653964I
−5.04557 − 5.52068I 0
u = 1.367050 − 0.286263I
a = 0.127328 − 0.290641I
b = −0.059407 − 0.653964I
−5.04557 + 5.52068I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.523351 + 0.282998I
a = 0.075777 − 0.409242I
b = −0.227408 + 1.069820I
1.37793 − 2.66689I 3.20906 + 9.66179I
u = 0.523351 − 0.282998I
a = 0.075777 + 0.409242I
b = −0.227408 − 1.069820I
1.37793 + 2.66689I 3.20906 − 9.66179I
u = −0.054601 + 0.509352I
a = 1.305150 + 0.511862I
b = 0.868600 + 0.411289I
−4.27961 − 1.91423I −5.19806 + 3.02668I
u = −0.054601 − 0.509352I
a = 1.305150 − 0.511862I
b = 0.868600 − 0.411289I
−4.27961 + 1.91423I −5.19806 − 3.02668I
u = −1.51066 + 0.01600I
a = 0.418299 + 0.263996I
b = 1.252000 − 0.484762I
−7.30569 + 3.49955I 0
u = −1.51066 − 0.01600I
a = 0.418299 − 0.263996I
b = 1.252000 + 0.484762I
−7.30569 − 3.49955I 0
u = −0.130339 + 0.458302I
a = 0.726225 − 0.442383I
b = 0.347372 − 0.529775I
−0.127455 + 1.387300I −1.33789 − 2.89703I
u = −0.130339 − 0.458302I
a = 0.726225 + 0.442383I
b = 0.347372 + 0.529775I
−0.127455 − 1.387300I −1.33789 + 2.89703I
u = −0.453754 + 0.108285I
a = −0.04965 + 1.64879I
b = 0.540457 + 1.147730I
0.643121 − 0.885450I −1.73889 − 3.55551I
u = −0.453754 − 0.108285I
a = −0.04965 − 1.64879I
b = 0.540457 − 1.147730I
0.643121 + 0.885450I −1.73889 + 3.55551I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53593 + 0.00041I
a = 1.94990 + 1.21251I
b = 3.38519 + 1.90248I
−8.57444 + 3.57156I 0
u = 1.53593 − 0.00041I
a = 1.94990 − 1.21251I
b = 3.38519 − 1.90248I
−8.57444 − 3.57156I 0
u = −0.388804 + 0.226078I
a = 3.22669 − 1.04826I
b = −0.440064 + 0.555353I
−2.04622 − 4.07547I −0.50699 − 3.20827I
u = −0.388804 − 0.226078I
a = 3.22669 + 1.04826I
b = −0.440064 − 0.555353I
−2.04622 + 4.07547I −0.50699 + 3.20827I
u = 0.333256 + 0.298984I
a = 2.14138 − 0.52844I
b = −0.471791 − 0.066122I
1.86436 + 0.38575I 5.67353 + 2.84630I
u = 0.333256 − 0.298984I
a = 2.14138 + 0.52844I
b = −0.471791 + 0.066122I
1.86436 − 0.38575I 5.67353 − 2.84630I
u = −1.55441
a = 2.20352
b = 3.90175
−4.55561 0
u = 0.310054 + 0.318457I
a = 0.84539 − 1.42016I
b = 0.743246 − 0.990318I
−1.38392 + 4.09651I 1.050672 − 0.014571I
u = 0.310054 − 0.318457I
a = 0.84539 + 1.42016I
b = 0.743246 + 0.990318I
−1.38392 − 4.09651I 1.050672 + 0.014571I
u = 1.55646 + 0.06741I
a = 1.093070 − 0.275160I
b = 2.35045 − 0.12880I
−8.49647 − 2.94856I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55646 − 0.06741I
a = 1.093070 + 0.275160I
b = 2.35045 + 0.12880I
−8.49647 + 2.94856I 0
u = −1.57542 + 0.04875I
a = 0.301319 + 1.218030I
b = 0.65085 + 1.32300I
−5.85412 + 3.68887I 0
u = −1.57542 − 0.04875I
a = 0.301319 − 1.218030I
b = 0.65085 − 1.32300I
−5.85412 − 3.68887I 0
u = 1.57646 + 0.00668I
a = −0.315882 + 0.122479I
b = −0.407087 − 0.879129I
−6.50230 + 0.63577I 0
u = 1.57646 − 0.00668I
a = −0.315882 − 0.122479I
b = −0.407087 + 0.879129I
−6.50230 − 0.63577I 0
u = −1.59602 + 0.06317I
a = −2.18540 + 0.44125I
b = −4.64805 + 0.94344I
−9.77380 + 7.56844I 0
u = −1.59602 − 0.06317I
a = −2.18540 − 0.44125I
b = −4.64805 − 0.94344I
−9.77380 − 7.56844I 0
u = 1.60196 + 0.04672I
a = −0.16909 − 1.99689I
b = −0.25317 − 2.61736I
−10.26230 − 6.65235I 0
u = 1.60196 − 0.04672I
a = −0.16909 + 1.99689I
b = −0.25317 + 2.61736I
−10.26230 + 6.65235I 0
u = −1.60126 + 0.12605I
a = −1.69718 − 0.94538I
b = −2.98785 − 1.76643I
−14.1458 + 2.7966I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60126 − 0.12605I
a = −1.69718 + 0.94538I
b = −2.98785 + 1.76643I
−14.1458 − 2.7966I 0
u = 1.60618 + 0.03641I
a = −2.01459 − 0.54776I
b = −4.24925 − 1.61665I
−7.59927 − 2.69628I 0
u = 1.60618 − 0.03641I
a = −2.01459 + 0.54776I
b = −4.24925 + 1.61665I
−7.59927 + 2.69628I 0
u = −1.62630 + 0.00862I
a = −1.91576 − 0.09707I
b = −3.47477 + 0.56297I
−13.98410 − 0.07693I 0
u = −1.62630 − 0.00862I
a = −1.91576 + 0.09707I
b = −3.47477 − 0.56297I
−13.98410 + 0.07693I 0
u = 1.62253 + 0.11727I
a = −2.33065 − 0.05749I
b = −4.37343 + 0.19986I
−14.3859 − 7.1012I 0
u = 1.62253 − 0.11727I
a = −2.33065 + 0.05749I
b = −4.37343 − 0.19986I
−14.3859 + 7.1012I 0
u = 1.63106 + 0.16213I
a = −1.308480 + 0.197440I
b = −2.39892 + 0.43106I
−9.41462 − 5.17428I 0
u = 1.63106 − 0.16213I
a = −1.308480 − 0.197440I
b = −2.39892 − 0.43106I
−9.41462 + 5.17428I 0
u = −1.63888 + 0.10149I
a = −2.04807 + 0.24513I
b = −3.87746 + 0.37434I
−11.16890 + 5.87888I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63888 − 0.10149I
a = −2.04807 − 0.24513I
b = −3.87746 − 0.37434I
−11.16890 − 5.87888I 0
u = −1.65348 + 0.16726I
a = 1.90898 + 0.12209I
b = 3.78308 + 0.00892I
−9.7694 + 11.6409I 0
u = −1.65348 − 0.16726I
a = 1.90898 − 0.12209I
b = 3.78308 − 0.00892I
−9.7694 − 11.6409I 0
u = 1.65345 + 0.16833I
a = 2.07228 − 0.06027I
b = 3.99454 + 0.03110I
−14.7660 − 17.3895I 0
u = 1.65345 − 0.16833I
a = 2.07228 + 0.06027I
b = 3.99454 − 0.03110I
−14.7660 + 17.3895I 0
u = 1.65289 + 0.18500I
a = 1.73845 − 0.39300I
b = 3.49292 − 0.22193I
−13.4163 − 4.6589I 0
u = 1.65289 − 0.18500I
a = 1.73845 + 0.39300I
b = 3.49292 + 0.22193I
−13.4163 + 4.6589I 0
u = −1.66357 + 0.09570I
a = 1.267340 + 0.538939I
b = 2.77423 + 1.67822I
−15.9764 + 7.7042I 0
u = −1.66357 − 0.09570I
a = 1.267340 − 0.538939I
b = 2.77423 − 1.67822I
−15.9764 − 7.7042I 0
u = 1.67660 + 0.07823I
a = −2.03780 − 0.53450I
b = −3.70133 − 1.03303I
−15.1958 − 5.8359I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.67660 − 0.07823I
a = −2.03780 + 0.53450I
b = −3.70133 + 1.03303I
−15.1958 + 5.8359I 0
u = 1.68178 + 0.08565I
a = 1.300640 − 0.393784I
b = 2.84988 − 1.09938I
−12.11680 − 1.45278I 0
u = 1.68178 − 0.08565I
a = 1.300640 + 0.393784I
b = 2.84988 + 1.09938I
−12.11680 + 1.45278I 0
u = −1.67899 + 0.15658I
a = −1.320880 + 0.340947I
b = −2.43078 + 0.52908I
−12.2047 + 8.4603I 0
u = −1.67899 − 0.15658I
a = −1.320880 − 0.340947I
b = −2.43078 − 0.52908I
−12.2047 − 8.4603I 0
u = −1.70180 + 0.09253I
a = 1.153820 + 0.397207I
b = 2.34613 + 1.07521I
−17.0082 − 3.9132I 0
u = −1.70180 − 0.09253I
a = 1.153820 − 0.397207I
b = 2.34613 − 1.07521I
−17.0082 + 3.9132I 0
15
II. I
u
2
=
h−6u
21
+13u
20
+· · ·+ b−9, −8u
21
+8u
20
+· · ·+ a+1, u
22
−14u
20
+· · ·−14u
2
+1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
8u
21
− 8u
20
+ ··· − 18u − 1
6u
21
− 13u
20
+ ··· + 10u + 9
a
2
=
−17u
21
+ 13u
20
+ ··· + 58u + 12
−19u
21
+ 29u
20
+ ··· + 10u − 12
a
9
=
−u
−u
3
+ u
a
3
=
8u
21
− 9u
20
+ ··· − 9u
2
− 18u
6u
21
− 14u
20
+ ··· + 10u + 9
a
7
=
u
u
a
6
=
−8u
21
+ u
20
+ ··· + 38u + 15
−7u
21
+ 9u
20
+ ··· + u − 5
a
11
=
−u
2
+ 1
−u
2
a
5
=
13u
21
− 15u
20
+ ··· − 31u
2
− 27u
12u
21
− 25u
20
+ ··· + 9u + 14
a
10
=
4u
21
− 5u
20
+ ··· − 18u − 3
5u
21
− 4u
20
+ ··· − 15u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −34u
21
+ 36u
20
+ 417u
19
− 378u
18
− 2171u
17
+ 1503u
16
+
6307u
15
− 2537u
14
− 11296u
13
+ 420u
12
+ 12788u
11
+ 4899u
10
− 8467u
9
− 7598u
8
+
1988u
7
+ 5060u
6
+ 1136u
5
− 1544u
4
− 732u
3
+ 74u
2
+ 68u + 5
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
− 11u
21
+ ··· − 22u + 2
c
2
u
22
+ 11u
21
+ ··· + 4u + 1
c
3
u
22
+ 3u
19
+ ··· − 4u
3
+ 1
c
4
u
22
− u
21
+ ··· − u + 1
c
5
u
22
− 2u
21
+ ··· + 7u
2
+ 2
c
6
u
22
+ 4u
20
+ ··· − 4u + 1
c
7
, c
8
u
22
− 14u
20
+ ··· − 14u
2
+ 1
c
9
u
22
+ 2u
21
+ ··· + 7u
2
+ 2
c
10
u
22
− u
21
+ ··· − u + 1
c
11
, c
12
u
22
− 14u
20
+ ··· − 14u
2
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 5y
21
+ ··· + 24y + 4
c
2
y
22
+ 5y
21
+ ··· − 16y + 1
c
3
y
22
+ 10y
20
+ ··· + 6y
2
+ 1
c
4
y
22
+ 7y
21
+ ··· + 3y + 1
c
5
, c
9
y
22
+ 18y
21
+ ··· + 28y + 4
c
6
y
22
+ 8y
21
+ ··· − 8y + 1
c
7
, c
8
, c
11
c
12
y
22
− 28y
21
+ ··· − 28y + 1
c
10
y
22
+ 3y
21
+ ··· + 7y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.883650 + 0.274941I
a = −1.206740 − 0.037392I
b = −0.177184 + 0.491411I
−4.26069 − 5.59133I −7.61753 + 8.06650I
u = 0.883650 − 0.274941I
a = −1.206740 + 0.037392I
b = −0.177184 − 0.491411I
−4.26069 + 5.59133I −7.61753 − 8.06650I
u = −0.648878 + 0.517765I
a = −0.956776 − 0.881923I
b = 0.651029 + 0.396629I
−4.78922 + 1.83440I −4.02953 − 7.61290I
u = −0.648878 − 0.517765I
a = −0.956776 + 0.881923I
b = 0.651029 − 0.396629I
−4.78922 − 1.83440I −4.02953 + 7.61290I
u = −0.320909 + 0.728060I
a = 0.334744 − 0.147005I
b = 0.212940 − 0.347592I
0.21276 + 2.23915I 6.5156 − 14.6358I
u = −0.320909 − 0.728060I
a = 0.334744 + 0.147005I
b = 0.212940 + 0.347592I
0.21276 − 2.23915I 6.5156 + 14.6358I
u = −1.214700 + 0.109592I
a = −0.912388 − 0.577901I
b = −0.980266 − 0.232643I
−1.96095 − 0.41841I 3.20351 + 6.57114I
u = −1.214700 − 0.109592I
a = −0.912388 + 0.577901I
b = −0.980266 + 0.232643I
−1.96095 + 0.41841I 3.20351 − 6.57114I
u = 1.314120 + 0.214812I
a = −0.474425 − 0.313002I
b = −0.398469 − 0.146898I
−4.64747 − 5.82575I −0.15245 + 9.27307I
u = 1.314120 − 0.214812I
a = −0.474425 + 0.313002I
b = −0.398469 + 0.146898I
−4.64747 + 5.82575I −0.15245 − 9.27307I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.54601 + 0.00198I
a = 1.22693 + 1.60055I
b = 2.56709 + 2.18380I
−8.98731 + 4.68924I −7.02785 − 6.69732I
u = −1.54601 − 0.00198I
a = 1.22693 − 1.60055I
b = 2.56709 − 2.18380I
−8.98731 − 4.68924I −7.02785 + 6.69732I
u = 1.56136 + 0.04047I
a = 0.849988 − 0.128617I
b = 1.91111 + 0.65668I
−6.04541 − 2.30238I −0.138479 + 1.235551I
u = 1.56136 − 0.04047I
a = 0.849988 + 0.128617I
b = 1.91111 − 0.65668I
−6.04541 + 2.30238I −0.138479 − 1.235551I
u = −0.380236 + 0.169609I
a = 2.19835 − 0.48042I
b = 0.306126 − 0.931426I
0.84990 + 1.59935I 2.80477 − 4.04603I
u = −0.380236 − 0.169609I
a = 2.19835 + 0.48042I
b = 0.306126 + 0.931426I
0.84990 − 1.59935I 2.80477 + 4.04603I
u = 0.369350 + 0.031485I
a = 3.08595 + 1.69432I
b = 0.313077 − 1.117600I
−2.25187 + 4.74030I −5.76983 − 6.64488I
u = 0.369350 − 0.031485I
a = 3.08595 − 1.69432I
b = 0.313077 + 1.117600I
−2.25187 − 4.74030I −5.76983 + 6.64488I
u = 1.63073 + 0.13856I
a = −1.92493 + 0.32061I
b = −3.63978 + 0.32775I
−12.73850 − 4.26093I −5.85561 + 1.91902I
u = 1.63073 − 0.13856I
a = −1.92493 − 0.32061I
b = −3.63978 − 0.32775I
−12.73850 + 4.26093I −5.85561 − 1.91902I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.64848 + 0.10252I
a = −1.72070 + 0.52512I
b = −3.26568 + 0.66889I
−12.9539 + 7.2364I −7.93262 − 5.45866I
u = −1.64848 − 0.10252I
a = −1.72070 − 0.52512I
b = −3.26568 − 0.66889I
−12.9539 − 7.2364I −7.93262 + 5.45866I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 11u
21
+ ··· − 22u + 2)(u
107
+ 8u
106
+ ··· + 79200u − 3200)
c
2
(u
22
+ 11u
21
+ ··· + 4u + 1)(u
107
+ 8u
105
+ ··· − 191u − 11)
c
3
(u
22
+ 3u
19
+ ··· − 4u
3
+ 1)(u
107
− u
106
+ ··· + 1.38868 × 10
7
u + 3405181)
c
4
(u
22
− u
21
+ ··· − u + 1)(u
107
+ u
105
+ ··· + 152u − 7)
c
5
(u
22
− 2u
21
+ ··· + 7u
2
+ 2)(u
107
− 3u
106
+ ··· + 22u + 2)
c
6
(u
22
+ 4u
20
+ ··· − 4u + 1)(u
107
+ 3u
106
+ ··· − 604539u − 105767)
c
7
, c
8
(u
22
− 14u
20
+ ··· − 14u
2
+ 1)(u
107
− u
106
+ ··· + 37u + 13)
c
9
(u
22
+ 2u
21
+ ··· + 7u
2
+ 2)(u
107
− 3u
106
+ ··· + 22u + 2)
c
10
(u
22
− u
21
+ ··· − u + 1)(u
107
− 6u
106
+ ··· + 5194u − 4049)
c
11
, c
12
(u
22
− 14u
20
+ ··· − 14u
2
+ 1)(u
107
− u
106
+ ··· + 37u + 13)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
+ 5y
21
+ ··· + 24y + 4)
· (y
107
− 40y
106
+ ··· + 1928422400y −10240000)
c
2
(y
22
+ 5y
21
+ ··· − 16y + 1)(y
107
+ 16y
106
+ ··· − 7937y −121)
c
3
(y
22
+ 10y
20
+ ··· + 6y
2
+ 1)
· (y
107
+ 47y
106
+ ··· − 467129995532381y −11595257642761)
c
4
(y
22
+ 7y
21
+ ··· + 3y + 1)(y
107
+ 2y
106
+ ··· + 5576y −49)
c
5
, c
9
(y
22
+ 18y
21
+ ··· + 28y + 4)(y
107
+ 81y
106
+ ··· + 1044y −4)
c
6
(y
22
+ 8y
21
+ ··· − 8y + 1)
· (y
107
+ 31y
106
+ ··· − 214514614873y −11186658289)
c
7
, c
8
, c
11
c
12
(y
22
− 28y
21
+ ··· − 28y + 1)(y
107
− 129y
106
+ ··· + 5711y −169)
c
10
(y
22
+ 3y
21
+ ··· + 7y + 1)
· (y
107
+ 26y
106
+ ··· − 541032280y −16394401)
23
