12a
0889
(K12a
0889
)
A knot diagram
1
Linearized knot diagam
4 6 7 1 9 10 11 12 2 3 8 5
Solving Sequence
6,10 3,7
4 11 8 2 1 9 5 12
c
6
c
3
c
10
c
7
c
2
c
1
c
9
c
5
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.44342 × 10
568
u
109
− 5.63890 × 10
568
u
108
+ ··· + 2.52973 × 10
568
b − 7.41395 × 10
568
,
− 5.01819 × 10
569
u
109
+ 1.42633 × 10
570
u
108
+ ··· + 1.26486 × 10
569
a − 8.15947 × 10
570
,
u
110
− 3u
109
+ ··· + 21u + 1i
I
u
2
= h−2.15930 × 10
15
u
20
− 9.88518 × 10
15
u
19
+ ··· + 1.08985 × 10
15
b − 4.65481 × 10
15
,
− 4.00480 × 10
15
u
20
− 1.80755 × 10
16
u
19
+ ··· + 1.08985 × 10
15
a − 7.18818 × 10
15
, u
21
+ 5u
20
+ ··· + 5u + 1i
I
u
3
= hb, −u
5
− 4u
4
− 5u
3
− 2u
2
+ a − 2u − 3, u
6
+ 3u
5
+ 2u
4
− u
3
+ u
2
+ 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 137 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
= h1.44 × 10
568
u
109
− 5.64 × 10
568
u
108
+ · · · + 2.53 × 10
568
b − 7.41 ×
10
568
, −5.02 × 10
569
u
109
+ 1.43 × 10
570
u
108
+ · · · + 1.26 × 10
569
a − 8.16 ×
10
570
, u
110
− 3u
109
+ · · · + 21u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
3.96738u
109
− 11.2766u
108
+ ··· + 710.062u + 64.5087
−0.570582u
109
+ 2.22905u
108
+ ··· + 8.69317u + 2.93073
a
7
=
1
u
2
a
4
=
4.01600u
109
− 11.7395u
108
+ ··· + 684.265u + 60.9524
−0.359351u
109
+ 1.46248u
108
+ ··· + 15.3016u + 3.24774
a
11
=
−7.92618u
109
+ 25.6136u
108
+ ··· − 555.057u − 43.9460
−1.48877u
109
+ 4.66015u
108
+ ··· − 143.849u − 11.6428
a
8
=
−2.52216u
109
+ 6.77640u
108
+ ··· − 613.962u − 68.2999
−0.392391u
109
+ 1.13085u
108
+ ··· − 78.1210u − 8.94244
a
2
=
4.53796u
109
− 13.5056u
108
+ ··· + 701.369u + 61.5780
−0.570582u
109
+ 2.22905u
108
+ ··· + 8.69317u + 2.93073
a
1
=
7.32097u
109
− 22.4072u
108
+ ··· + 873.765u + 74.0818
0.953125u
109
− 3.04274u
108
+ ··· + 83.6563u + 7.91593
a
9
=
−6.06911u
109
+ 20.0584u
108
+ ··· − 322.474u − 24.0997
−0.368302u
109
+ 0.895009u
108
+ ··· − 86.7341u − 8.20350
a
5
=
6.02161u
109
− 18.1467u
108
+ ··· + 821.524u + 72.9777
0.00590647u
109
+ 0.241512u
108
+ ··· + 48.2897u + 6.22933
a
12
=
9.98424u
109
− 30.9702u
108
+ ··· + 1068.56u + 89.7856
1.79589u
109
− 5.80409u
108
+ ··· + 145.185u + 12.5127
(ii) Obstruction class = −1
(iii) Cusp Shapes = 23.7845u
109
− 78.8398u
108
+ ··· + 1380.90u + 90.0800
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
110
+ 3u
109
+ ··· − 62u + 7
c
2
u
110
− 6u
108
+ ··· − 1248u + 64
c
3
u
110
+ 18u
108
+ ··· − 5982u + 511
c
5
u
110
− u
109
+ ··· + 127044378u + 11982227
c
6
u
110
− 3u
109
+ ··· + 21u + 1
c
7
, c
8
, c
11
u
110
− 4u
109
+ ··· + 146u + 11
c
9
u
110
− 2u
108
+ ··· − 434u + 115
c
10
u
110
+ u
109
+ ··· + 4063u + 1795
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
110
+ 115y
109
+ ··· − 694y + 49
c
2
y
110
− 12y
109
+ ··· − 844800y + 4096
c
3
y
110
+ 36y
109
+ ··· − 9724346y + 261121
c
5
y
110
− 59y
109
+ ··· − 8074941417464332y + 143573763879529
c
6
y
110
− 15y
109
+ ··· − 183y + 1
c
7
, c
8
, c
11
y
110
− 128y
109
+ ··· − 17642y + 121
c
9
y
110
− 4y
109
+ ··· − 38396y + 13225
c
10
y
110
− 27y
109
+ ··· − 181138189y + 3222025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.774572 + 0.632471I
a = −0.89220 + 1.52122I
b = −0.548053 + 0.137687I
7.93768 − 5.25317I 0
u = 0.774572 − 0.632471I
a = −0.89220 − 1.52122I
b = −0.548053 − 0.137687I
7.93768 + 5.25317I 0
u = −0.560346 + 0.853408I
a = 0.047334 − 1.169540I
b = −0.535513 − 0.176348I
1.56438 + 2.47087I 0
u = −0.560346 − 0.853408I
a = 0.047334 + 1.169540I
b = −0.535513 + 0.176348I
1.56438 − 2.47087I 0
u = 0.124231 + 0.956021I
a = −0.332111 + 0.655043I
b = −1.24931 + 1.41822I
14.9970 − 6.5880I 0
u = 0.124231 − 0.956021I
a = −0.332111 − 0.655043I
b = −1.24931 − 1.41822I
14.9970 + 6.5880I 0
u = −0.715385 + 0.756555I
a = 0.877620 + 0.541968I
b = 1.141200 − 0.158237I
8.97543 − 0.77350I 0
u = −0.715385 − 0.756555I
a = 0.877620 − 0.541968I
b = 1.141200 + 0.158237I
8.97543 + 0.77350I 0
u = −0.310378 + 0.905410I
a = −0.015555 − 0.706392I
b = −1.14977 − 1.14634I
8.12852 + 4.99064I 0
u = −0.310378 − 0.905410I
a = −0.015555 + 0.706392I
b = −1.14977 + 1.14634I
8.12852 − 4.99064I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.591904 + 0.870733I
a = 0.130086 + 1.177850I
b = −1.08337 + 0.94972I
8.72354 − 3.03179I 0
u = 0.591904 − 0.870733I
a = 0.130086 − 1.177850I
b = −1.08337 − 0.94972I
8.72354 + 3.03179I 0
u = 0.838495 + 0.390871I
a = 0.889756 + 0.699588I
b = −0.089294 + 0.460614I
2.44031 − 0.26635I 0
u = 0.838495 − 0.390871I
a = 0.889756 − 0.699588I
b = −0.089294 − 0.460614I
2.44031 + 0.26635I 0
u = 0.476011 + 0.782871I
a = 0.494024 − 0.502108I
b = 1.50207 − 0.99579I
7.79132 − 3.43252I 0
u = 0.476011 − 0.782871I
a = 0.494024 + 0.502108I
b = 1.50207 + 0.99579I
7.79132 + 3.43252I 0
u = 0.475946 + 0.976502I
a = −0.24106 − 1.59534I
b = 0.873118 − 0.085672I
16.7347 − 7.7979I 0
u = 0.475946 − 0.976502I
a = −0.24106 + 1.59534I
b = 0.873118 + 0.085672I
16.7347 + 7.7979I 0
u = −0.677755 + 0.612424I
a = 0.053848 + 0.679869I
b = 1.083870 + 0.901794I
0.92636 + 3.37225I 0
u = −0.677755 − 0.612424I
a = 0.053848 − 0.679869I
b = 1.083870 − 0.901794I
0.92636 − 3.37225I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.945732 + 0.546364I
a = 0.070342 + 0.756458I
b = 1.045450 + 0.883608I
0.95831 + 3.29223I 0
u = −0.945732 − 0.546364I
a = 0.070342 − 0.756458I
b = 1.045450 − 0.883608I
0.95831 − 3.29223I 0
u = 0.891739
a = 2.12201
b = 0.428233
4.79546 0
u = −0.732004 + 0.848914I
a = −0.02463 − 1.55659I
b = −1.23288 − 0.92476I
16.4324 + 2.2483I 0
u = −0.732004 − 0.848914I
a = −0.02463 + 1.55659I
b = −1.23288 + 0.92476I
16.4324 − 2.2483I 0
u = −0.828689 + 0.765989I
a = −0.451776 − 0.468277I
b = 0.260810 − 0.056998I
2.75921 + 2.65033I 0
u = −0.828689 − 0.765989I
a = −0.451776 + 0.468277I
b = 0.260810 + 0.056998I
2.75921 − 2.65033I 0
u = −0.785131
a = 1.46415
b = 0.0826449
−1.06875 0
u = −0.661247 + 0.408466I
a = 1.83442 − 1.69581I
b = −0.596866 − 0.927607I
12.5489 + 8.8816I 0
u = −0.661247 − 0.408466I
a = 1.83442 + 1.69581I
b = −0.596866 + 0.927607I
12.5489 − 8.8816I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.106860 + 0.536656I
a = −0.401468 − 0.704362I
b = −0.153166 − 0.706136I
2.53752 + 2.32422I 0
u = −1.106860 − 0.536656I
a = −0.401468 + 0.704362I
b = −0.153166 + 0.706136I
2.53752 − 2.32422I 0
u = 0.654893 + 0.375970I
a = −0.281669 + 1.103070I
b = 0.59368 + 1.30161I
4.93851 − 5.82307I 0
u = 0.654893 − 0.375970I
a = −0.281669 − 1.103070I
b = 0.59368 − 1.30161I
4.93851 + 5.82307I 0
u = −1.157250 + 0.509604I
a = −0.935247 − 0.035605I
b = −1.278610 + 0.474048I
15.0541 + 3.2345I 0
u = −1.157250 − 0.509604I
a = −0.935247 + 0.035605I
b = −1.278610 − 0.474048I
15.0541 − 3.2345I 0
u = 0.975718 + 0.808390I
a = 0.213090 − 1.081970I
b = 1.12209 − 0.94361I
1.06256 − 5.18407I 0
u = 0.975718 − 0.808390I
a = 0.213090 + 1.081970I
b = 1.12209 + 0.94361I
1.06256 + 5.18407I 0
u = 1.011570 + 0.788569I
a = −0.823264 − 0.221926I
b = 0.232331 − 0.660204I
8.66796 − 0.78567I 0
u = 1.011570 − 0.788569I
a = −0.823264 + 0.221926I
b = 0.232331 + 0.660204I
8.66796 + 0.78567I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.992265 + 0.832307I
a = 0.338617 + 1.315790I
b = 1.32936 + 1.00820I
8.35865 + 6.84750I 0
u = −0.992265 − 0.832307I
a = 0.338617 − 1.315790I
b = 1.32936 − 1.00820I
8.35865 − 6.84750I 0
u = −0.290577 + 1.294510I
a = −0.446532 + 0.767605I
b = 0.781428 − 0.075730I
8.52066 + 3.04058I 0
u = −0.290577 − 1.294510I
a = −0.446532 − 0.767605I
b = 0.781428 + 0.075730I
8.52066 − 3.04058I 0
u = 0.585661 + 1.201620I
a = −0.163568 + 0.494662I
b = −0.642186 − 0.037791I
1.98677 + 2.15796I 0
u = 0.585661 − 1.201620I
a = −0.163568 − 0.494662I
b = −0.642186 + 0.037791I
1.98677 − 2.15796I 0
u = 1.218800 + 0.550512I
a = 0.451453 − 0.351078I
b = 0.627504 − 0.232141I
1.088670 − 0.212814I 0
u = 1.218800 − 0.550512I
a = 0.451453 + 0.351078I
b = 0.627504 + 0.232141I
1.088670 + 0.212814I 0
u = 1.266440 + 0.438516I
a = −0.444059 + 0.139336I
b = −1.48742 + 0.18860I
6.81283 + 0.18653I 0
u = 1.266440 − 0.438516I
a = −0.444059 − 0.139336I
b = −1.48742 − 0.18860I
6.81283 − 0.18653I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.658241 + 0.031826I
a = 0.394930 + 0.351966I
b = −0.719040 + 0.317896I
−1.407700 + 0.051950I −7.32066 + 0.87113I
u = −0.658241 − 0.031826I
a = 0.394930 − 0.351966I
b = −0.719040 − 0.317896I
−1.407700 − 0.051950I −7.32066 − 0.87113I
u = −0.639006 + 0.142930I
a = −1.01394 + 3.27755I
b = 0.264559 + 1.069070I
4.82862 + 3.59852I −2.49071 − 6.47593I
u = −0.639006 − 0.142930I
a = −1.01394 − 3.27755I
b = 0.264559 − 1.069070I
4.82862 − 3.59852I −2.49071 + 6.47593I
u = 0.503809 + 0.382796I
a = 2.19844 + 0.92750I
b = −0.728895 + 0.615188I
5.78183 − 5.82433I 2.76550 + 9.85542I
u = 0.503809 − 0.382796I
a = 2.19844 − 0.92750I
b = −0.728895 − 0.615188I
5.78183 + 5.82433I 2.76550 − 9.85542I
u = 0.599522
a = 1.09470
b = 0.509246
1.20815 8.23520
u = 0.940720 + 1.038890I
a = −0.258390 + 0.915531I
b = −0.453797 + 0.622087I
7.19253 − 5.38461I 0
u = 0.940720 − 1.038890I
a = −0.258390 − 0.915531I
b = −0.453797 − 0.622087I
7.19253 + 5.38461I 0
u = −0.530334 + 0.260982I
a = −0.35708 − 1.59712I
b = 0.77505 − 2.06037I
13.0946 + 8.0575I 1.85904 − 10.14716I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.530334 − 0.260982I
a = −0.35708 + 1.59712I
b = 0.77505 + 2.06037I
13.0946 − 8.0575I 1.85904 + 10.14716I
u = 0.551499 + 0.202743I
a = −0.06841 − 2.08947I
b = 0.482359 − 1.142180I
−0.68842 − 2.45858I −2.82743 − 12.79099I
u = 0.551499 − 0.202743I
a = −0.06841 + 2.08947I
b = 0.482359 + 1.142180I
−0.68842 + 2.45858I −2.82743 + 12.79099I
u = −1.07049 + 0.95663I
a = 0.185131 + 0.691196I
b = 0.639211 + 0.760069I
−1.01440 + 3.57337I 0
u = −1.07049 − 0.95663I
a = 0.185131 − 0.691196I
b = 0.639211 − 0.760069I
−1.01440 − 3.57337I 0
u = −0.77761 + 1.21084I
a = −0.534344 − 0.449709I
b = −0.853078 + 0.209963I
9.25940 − 5.46029I 0
u = −0.77761 − 1.21084I
a = −0.534344 + 0.449709I
b = −0.853078 − 0.209963I
9.25940 + 5.46029I 0
u = 0.537860 + 0.113065I
a = 0.34732 − 1.46044I
b = −0.463002 − 1.318780I
−1.32056 − 2.31790I −8.22376 + 9.76978I
u = 0.537860 − 0.113065I
a = 0.34732 + 1.46044I
b = −0.463002 + 1.318780I
−1.32056 + 2.31790I −8.22376 − 9.76978I
u = 0.92147 + 1.12188I
a = 0.098895 − 0.858374I
b = 0.596369 − 1.099270I
4.05554 − 5.99285I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.92147 − 1.12188I
a = 0.098895 + 0.858374I
b = 0.596369 + 1.099270I
4.05554 + 5.99285I 0
u = 1.46526 + 0.06585I
a = −0.498390 + 0.371200I
b = −0.501537 + 0.613741I
5.49251 + 1.87089I 0
u = 1.46526 − 0.06585I
a = −0.498390 − 0.371200I
b = −0.501537 − 0.613741I
5.49251 − 1.87089I 0
u = −1.12400 + 0.94748I
a = −0.315673 − 1.094540I
b = −1.34237 − 0.99895I
8.1642 + 13.0472I 0
u = −1.12400 − 0.94748I
a = −0.315673 + 1.094540I
b = −1.34237 + 0.99895I
8.1642 − 13.0472I 0
u = 1.13720 + 0.95650I
a = −0.197715 + 0.921183I
b = −1.17583 + 0.87305I
0.56405 − 9.77507I 0
u = 1.13720 − 0.95650I
a = −0.197715 − 0.921183I
b = −1.17583 − 0.87305I
0.56405 + 9.77507I 0
u = −0.502519 + 0.108029I
a = 0.18397 + 2.04925I
b = −0.25502 + 2.34163I
5.42423 + 3.37899I −9.68824 − 6.26167I
u = −0.502519 − 0.108029I
a = 0.18397 − 2.04925I
b = −0.25502 − 2.34163I
5.42423 − 3.37899I −9.68824 + 6.26167I
u = 0.487910 + 0.157981I
a = −1.61676 − 2.24024I
b = 0.416359 − 0.793132I
−1.04722 − 2.44814I −10.34845 + 9.07272I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.487910 − 0.157981I
a = −1.61676 + 2.24024I
b = 0.416359 + 0.793132I
−1.04722 + 2.44814I −10.34845 − 9.07272I
u = −0.311773 + 0.363570I
a = 2.18479 + 0.87316I
b = −1.042800 − 0.172901I
6.35083 + 1.43301I 8.05925 − 0.03819I
u = −0.311773 − 0.363570I
a = 2.18479 − 0.87316I
b = −1.042800 + 0.172901I
6.35083 − 1.43301I 8.05925 + 0.03819I
u = 0.95715 + 1.18988I
a = −0.066184 + 0.804498I
b = −0.62708 + 1.32672I
9.82782 − 6.51847I 0
u = 0.95715 − 1.18988I
a = −0.066184 − 0.804498I
b = −0.62708 − 1.32672I
9.82782 + 6.51847I 0
u = −0.386570 + 0.271191I
a = 0.86298 + 3.49150I
b = 0.162485 + 0.818563I
3.63818 + 2.84038I 0.92503 − 6.05029I
u = −0.386570 − 0.271191I
a = 0.86298 − 3.49150I
b = 0.162485 − 0.818563I
3.63818 − 2.84038I 0.92503 + 6.05029I
u = −1.16827 + 1.00540I
a = −0.092294 − 0.645658I
b = −1.041720 − 0.639340I
−0.45195 + 4.75197I 0
u = −1.16827 − 1.00540I
a = −0.092294 + 0.645658I
b = −1.041720 + 0.639340I
−0.45195 − 4.75197I 0
u = −1.16474 + 1.06625I
a = 0.234664 + 0.993604I
b = 1.34481 + 1.02397I
15.2715 + 17.6049I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.16474 − 1.06625I
a = 0.234664 − 0.993604I
b = 1.34481 − 1.02397I
15.2715 − 17.6049I 0
u = 0.170612 + 0.337681I
a = 1.03643 − 2.29648I
b = −1.67443 − 0.27296I
14.1811 + 1.2153I 11.26046 + 0.21873I
u = 0.170612 − 0.337681I
a = 1.03643 + 2.29648I
b = −1.67443 + 0.27296I
14.1811 − 1.2153I 11.26046 − 0.21873I
u = 1.19603 + 1.10006I
a = 0.139764 − 0.851353I
b = 1.23014 − 0.82756I
7.0682 − 13.1651I 0
u = 1.19603 − 1.10006I
a = 0.139764 + 0.851353I
b = 1.23014 + 0.82756I
7.0682 + 13.1651I 0
u = −1.10362 + 1.20410I
a = −0.160490 − 0.593138I
b = −0.665528 − 0.924470I
3.20052 + 5.24080I 0
u = −1.10362 − 1.20410I
a = −0.160490 + 0.593138I
b = −0.665528 + 0.924470I
3.20052 − 5.24080I 0
u = −0.99443 + 1.42886I
a = 0.451569 + 0.333754I
b = 0.738648 − 0.347544I
16.0502 − 8.9937I 0
u = −0.99443 − 1.42886I
a = 0.451569 − 0.333754I
b = 0.738648 + 0.347544I
16.0502 + 8.9937I 0
u = −1.28221 + 1.22669I
a = 0.044226 + 0.582219I
b = 1.158710 + 0.516395I
5.55745 + 6.41435I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.28221 − 1.22669I
a = 0.044226 − 0.582219I
b = 1.158710 − 0.516395I
5.55745 − 6.41435I 0
u = −0.198149 + 0.050179I
a = −6.69900 − 0.11868I
b = 0.526139 + 0.167191I
0.781838 + 0.037322I 11.63850 − 5.91538I
u = −0.198149 − 0.050179I
a = −6.69900 + 0.11868I
b = 0.526139 − 0.167191I
0.781838 − 0.037322I 11.63850 + 5.91538I
u = 0.75630 + 1.64062I
a = 0.112136 − 0.363934I
b = 0.737898 + 0.162123I
8.29439 + 4.05354I 0
u = 0.75630 − 1.64062I
a = 0.112136 + 0.363934I
b = 0.737898 − 0.162123I
8.29439 − 4.05354I 0
u = 1.52815 + 1.01068I
a = −0.350173 + 0.271355I
b = −0.717603 + 0.257453I
5.27041 − 3.19239I 0
u = 1.52815 − 1.01068I
a = −0.350173 − 0.271355I
b = −0.717603 − 0.257453I
5.27041 + 3.19239I 0
u = −0.0985245
a = 10.3601
b = 1.56643
8.74873 10.9230
u = 1.93847 + 0.68258I
a = 0.285643 − 0.106787I
b = 1.349280 − 0.010229I
12.76100 + 1.35297I 0
u = 1.93847 − 0.68258I
a = 0.285643 + 0.106787I
b = 1.349280 + 0.010229I
12.76100 − 1.35297I 0
15
II.
I
u
2
= h−2.16×10
15
u
20
−9.89×10
15
u
19
+· · ·+1.09×10
15
b−4.65×10
15
, −4.00×
10
15
u
20
−1.81×10
16
u
19
+· · ·+1.09×10
15
a−7.19×10
15
, u
21
+5u
20
+· · ·+5u+1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
3.67464u
20
+ 16.5853u
19
+ ··· + 24.8798u + 6.59558
1.98128u
20
+ 9.07024u
19
+ ··· + 13.4202u + 4.27106
a
7
=
1
u
2
a
4
=
2.57607u
20
+ 11.3767u
19
+ ··· + 16.7244u + 4.11240
2.06257u
20
+ 9.34609u
19
+ ··· + 13.0978u + 3.98687
a
11
=
−0.201806u
20
− 0.123444u
19
+ ··· + 0.0708185u + 4.67599
−1.20181u
20
− 5.12344u
19
+ ··· − 7.92918u − 0.324007
a
8
=
0.525812u
20
+ 1.54167u
19
+ ··· − 0.119256u − 5.98514
0.613561u
20
+ 2.86270u
19
+ ··· + 5.87725u − 1.10926
a
2
=
1.69335u
20
+ 7.51507u
19
+ ··· + 11.4596u + 2.32452
1.98128u
20
+ 9.07024u
19
+ ··· + 13.4202u + 4.27106
a
1
=
−1.09570u
20
− 5.20905u
19
+ ··· − 7.73516u − 4.06925
0.496029u
20
+ 1.81653u
19
+ ··· + 0.734766u − 0.606939
a
9
=
1.16125u
20
+ 5.57961u
19
+ ··· + 9.96612u + 3.80335
−0.161246u
20
− 0.579612u
19
+ ··· + 0.0338831u + 1.19665
a
5
=
1.24091u
20
+ 6.15483u
19
+ ··· + 11.3716u + 4.81809
0.182357u
20
+ 1.01313u
19
+ ··· + 4.06781u + 2.29253
a
12
=
−0.311068u
20
− 2.28332u
19
+ ··· − 7.75150u − 6.74757
1.04683u
20
+ 4.44080u
19
+ ··· + 5.65114u − 0.994846
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
8551280081932515
1089847935407689
u
20
−
38333007895654212
1089847935407689
u
19
+ ···−
52902484388170668
1089847935407689
u −
4952793532390205
1089847935407689
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
21
− 4u
20
+ ··· + 2u + 1
c
2
u
21
− u
20
+ ··· − 99u + 101
c
3
u
21
+ u
20
+ ··· + 10u
2
+ 1
c
4
u
21
+ 4u
20
+ ··· + 2u − 1
c
5
u
21
− 3u
20
+ ··· − 8u − 1
c
6
u
21
+ 5u
20
+ ··· + 5u + 1
c
7
, c
8
u
21
− 3u
20
+ ··· + 2u + 1
c
9
u
21
− u
20
+ ··· + 3u
2
+ 1
c
10
u
21
+ 3u
19
+ ··· − u − 1
c
11
u
21
+ 3u
20
+ ··· + 2u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
21
+ 22y
20
+ ··· + 246y
2
− 1
c
2
y
21
+ 9y
20
+ ··· − 29185y −10201
c
3
y
21
+ 19y
20
+ ··· − 20y −1
c
5
y
21
+ 7y
20
+ ··· + 24y −1
c
6
y
21
− 5y
20
+ ··· + 7y −1
c
7
, c
8
, c
11
y
21
− 29y
20
+ ··· + 2y −1
c
9
y
21
− 3y
20
+ ··· − 6y −1
c
10
y
21
+ 6y
20
+ ··· + 3y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.217097 + 1.038910I
a = 0.526549 + 0.408110I
b = −0.765446 + 0.734361I
7.01896 − 4.67113I 5.09993 + 5.56442I
u = 0.217097 − 1.038910I
a = 0.526549 − 0.408110I
b = −0.765446 − 0.734361I
7.01896 + 4.67113I 5.09993 − 5.56442I
u = −0.845934 + 0.103696I
a = 0.19223 + 1.57655I
b = 0.501870 + 0.766898I
2.84913 + 1.70648I 1.37067 − 3.41020I
u = −0.845934 − 0.103696I
a = 0.19223 − 1.57655I
b = 0.501870 − 0.766898I
2.84913 − 1.70648I 1.37067 + 3.41020I
u = 0.893026 + 0.868131I
a = 0.056048 − 0.792790I
b = 0.866483 − 0.827101I
−0.03849 − 3.67784I 0.53413 + 6.14724I
u = 0.893026 − 0.868131I
a = 0.056048 + 0.792790I
b = 0.866483 + 0.827101I
−0.03849 + 3.67784I 0.53413 − 6.14724I
u = −0.828970 + 0.953040I
a = 0.070384 + 1.042450I
b = 0.657531 + 1.165410I
4.65865 + 5.65395I 7.41457 − 3.59853I
u = −0.828970 − 0.953040I
a = 0.070384 − 1.042450I
b = 0.657531 − 1.165410I
4.65865 − 5.65395I 7.41457 + 3.59853I
u = −0.005702 + 0.615576I
a = 1.35957 − 0.70191I
b = −0.18724 − 1.46454I
13.9156 + 7.6006I 8.83489 − 5.18023I
u = −0.005702 − 0.615576I
a = 1.35957 + 0.70191I
b = −0.18724 + 1.46454I
13.9156 − 7.6006I 8.83489 + 5.18023I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.495900 + 0.250523I
a = −0.52768 − 2.22684I
b = 0.387424 − 1.146780I
−0.59511 − 2.67028I 11.0401 + 18.5089I
u = 0.495900 − 0.250523I
a = −0.52768 + 2.22684I
b = 0.387424 + 1.146780I
−0.59511 + 2.67028I 11.0401 − 18.5089I
u = −1.45757
a = 0.449100
b = 1.49718
7.06806 23.9240
u = −1.51703 + 0.28428I
a = −0.309560 − 0.189109I
b = −1.44850 + 0.01568I
12.34630 − 1.07632I 3.62332 − 3.04442I
u = −1.51703 − 0.28428I
a = −0.309560 + 0.189109I
b = −1.44850 − 0.01568I
12.34630 + 1.07632I 3.62332 + 3.04442I
u = −0.320486 + 0.198100I
a = −1.21078 + 3.25585I
b = 0.17340 + 1.77373I
5.85337 + 3.37653I 10.71014 − 4.98015I
u = −0.320486 − 0.198100I
a = −1.21078 − 3.25585I
b = 0.17340 − 1.77373I
5.85337 − 3.37653I 10.71014 + 4.98015I
u = 1.26294 + 1.13268I
a = −0.205516 + 0.494927I
b = −0.827749 + 0.677186I
2.97274 − 4.26956I 4.13898 + 3.90072I
u = 1.26294 − 1.13268I
a = −0.205516 − 0.494927I
b = −0.827749 − 0.677186I
2.97274 + 4.26956I 4.13898 − 3.90072I
u = −1.12205 + 1.31034I
a = −0.175797 − 0.696424I
b = −0.606366 − 0.879367I
6.70244 + 6.36998I 4.27126 − 8.45281I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.12205 − 1.31034I
a = −0.175797 + 0.696424I
b = −0.606366 + 0.879367I
6.70244 − 6.36998I 4.27126 + 8.45281I
21
III.
I
u
3
= hb, −u
5
− 4u
4
− 5u
3
− 2u
2
+ a − 2u − 3, u
6
+ 3u
5
+ 2u
4
− u
3
+ u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
u
5
+ 4u
4
+ 5u
3
+ 2u
2
+ 2u + 3
0
a
7
=
1
u
2
a
4
=
u
5
+ 5u
4
+ 7u
3
+ 2u
2
+ u + 4
−u
5
− 2u
4
− 2u + 1
a
11
=
3u
5
+ 10u
4
+ 9u
3
− u
2
+ 2u + 7
u
a
8
=
3u
5
+ 10u
4
+ 9u
3
− u
2
+ 2u + 8
u
2
+ u
a
2
=
u
5
+ 4u
4
+ 5u
3
+ 2u
2
+ 2u + 3
0
a
1
=
2u
2
+ 3u
u
4
+ u
3
− u
2
a
9
=
3u
5
+ 10u
4
+ 9u
3
− u
2
+ 2u + 7
u
a
5
=
u
5
+ 3u
4
+ 2u
3
− u
2
+ u + 4
u
2
a
12
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
5
− 26u
4
− 32u
3
− 4u
2
+ u − 19
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
3
− u
2
+ 2u − 1)
2
c
2
u
6
c
3
(u
3
+ u
2
− 1)
2
c
4
(u
3
+ u
2
+ 2u + 1)
2
c
5
, c
6
u
6
+ 3u
5
+ 2u
4
− u
3
+ u
2
+ 2u − 1
c
7
, c
8
(u + 1)
6
c
9
, c
10
u
6
− 4u
4
+ u
3
+ 4u
2
− 1
c
11
(u − 1)
6
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
2
y
6
c
3
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
y
6
− 5y
5
+ 12y
4
− 11y
3
+ y
2
− 6y + 1
c
7
, c
8
, c
11
(y −1)
6
c
9
, c
10
y
6
− 8y
5
+ 24y
4
− 35y
3
+ 24y
2
− 8y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.462417 + 0.679093I
a = −0.55043 + 1.61386I
b = 0
4.66906 − 2.82812I 8.08358 + 4.54590I
u = 0.462417 − 0.679093I
a = −0.55043 − 1.61386I
b = 0
4.66906 + 2.82812I 8.08358 − 4.54590I
u = −1.40545
a = 0.382160
b = 0
0.531480 −8.01270
u = 0.405450
a = 4.59199
b = 0
0.531480 −22.1530
u = −1.46242 + 0.67909I
a = −0.436650 − 0.072982I
b = 0
4.66906 + 2.82812I 0.49944 − 1.38392I
u = −1.46242 − 0.67909I
a = −0.436650 + 0.072982I
b = 0
4.66906 − 2.82812I 0.49944 + 1.38392I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
((u
3
− u
2
+ 2u − 1)
2
)(u
21
− 4u
20
+ ··· + 2u + 1)
· (u
110
+ 3u
109
+ ··· − 62u + 7)
c
2
u
6
(u
21
− u
20
+ ··· − 99u + 101)(u
110
− 6u
108
+ ··· − 1248u + 64)
c
3
((u
3
+ u
2
− 1)
2
)(u
21
+ u
20
+ ··· + 10u
2
+ 1)
· (u
110
+ 18u
108
+ ··· − 5982u + 511)
c
4
((u
3
+ u
2
+ 2u + 1)
2
)(u
21
+ 4u
20
+ ··· + 2u − 1)
· (u
110
+ 3u
109
+ ··· − 62u + 7)
c
5
(u
6
+ 3u
5
+ 2u
4
− u
3
+ u
2
+ 2u − 1)(u
21
− 3u
20
+ ··· − 8u − 1)
· (u
110
− u
109
+ ··· + 127044378u + 11982227)
c
6
(u
6
+ 3u
5
+ 2u
4
− u
3
+ u
2
+ 2u − 1)(u
21
+ 5u
20
+ ··· + 5u + 1)
· (u
110
− 3u
109
+ ··· + 21u + 1)
c
7
, c
8
((u + 1)
6
)(u
21
− 3u
20
+ ··· + 2u + 1)(u
110
− 4u
109
+ ··· + 146u + 11)
c
9
(u
6
− 4u
4
+ u
3
+ 4u
2
− 1)(u
21
− u
20
+ ··· + 3u
2
+ 1)
· (u
110
− 2u
108
+ ··· − 434u + 115)
c
10
(u
6
− 4u
4
+ u
3
+ 4u
2
− 1)(u
21
+ 3u
19
+ ··· − u − 1)
· (u
110
+ u
109
+ ··· + 4063u + 1795)
c
11
((u − 1)
6
)(u
21
+ 3u
20
+ ··· + 2u − 1)(u
110
− 4u
109
+ ··· + 146u + 11)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
21
+ 22y
20
+ ··· + 246y
2
− 1)
· (y
110
+ 115y
109
+ ··· − 694y + 49)
c
2
y
6
(y
21
+ 9y
20
+ ··· − 29185y −10201)
· (y
110
− 12y
109
+ ··· − 844800y + 4096)
c
3
((y
3
− y
2
+ 2y −1)
2
)(y
21
+ 19y
20
+ ··· − 20y −1)
· (y
110
+ 36y
109
+ ··· − 9724346y + 261121)
c
5
(y
6
− 5y
5
+ ··· − 6y + 1)(y
21
+ 7y
20
+ ··· + 24y −1)
· (y
110
− 59y
109
+ ··· − 8074941417464332y + 143573763879529)
c
6
(y
6
− 5y
5
+ ··· − 6y + 1)(y
21
− 5y
20
+ ··· + 7y −1)
· (y
110
− 15y
109
+ ··· − 183y + 1)
c
7
, c
8
, c
11
((y −1)
6
)(y
21
− 29y
20
+ ··· + 2y −1)
· (y
110
− 128y
109
+ ··· − 17642y + 121)
c
9
(y
6
− 8y
5
+ ··· − 8y + 1)(y
21
− 3y
20
+ ··· − 6y −1)
· (y
110
− 4y
109
+ ··· − 38396y + 13225)
c
10
(y
6
− 8y
5
+ ··· − 8y + 1)(y
21
+ 6y
20
+ ··· + 3y −1)
· (y
110
− 27y
109
+ ··· − 181138189y + 3222025)
27
