12n
0874
(K12n
0874
)
A knot diagram
1
Linearized knot diagam
4 8 6 11 1 2 11 3 12 8 5 9
Solving Sequence
1,4 2,11
5 6 7 8 3 9 12 10
c
1
c
4
c
5
c
6
c
7
c
3
c
8
c
12
c
9
c
2
, c
10
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.88703 × 10
531
u
97
+ 2.37179 × 10
532
u
96
+ ··· + 7.13036 × 10
532
b + 1.66917 × 10
536
,
− 5.17946 × 10
536
u
97
− 3.44558 × 10
537
u
96
+ ··· + 1.04681 × 10
537
a − 6.30093 × 10
541
,
u
98
+ 7u
97
+ ··· + 485513u + 44043i
I
u
2
= h−3.11544 × 10
51
u
35
− 1.76100 × 10
52
u
34
+ ··· + 5.72391 × 10
50
b − 4.79348 × 10
51
,
− 8.61463 × 10
50
u
35
− 4.68417 × 10
51
u
34
+ ··· + 5.72391 × 10
50
a − 8.17523 × 10
50
, u
36
+ 5u
35
+ ··· + 5u − 1i
I
u
3
= hb + a − 1, a
2
− a + 1, u − 1i
I
u
4
= hb + 2, a + 1, u + 1i
* 4 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
= h3.89 × 10
531
u
97
+ 2.37 × 10
532
u
96
+ · · · + 7.13 × 10
532
b + 1.67 ×
10
536
, −5.18 × 10
536
u
97
− 3.45 × 10
537
u
96
+ · · · + 1.05 × 10
537
a − 6.30 ×
10
541
, u
98
+ 7u
97
+ · · · + 485513u + 44043i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
11
=
0.494786u
97
+ 3.29152u
96
+ ··· + 498696.u + 60191.9
−0.0545138u
97
− 0.332633u
96
+ ··· − 23823.2u − 2340.93
a
5
=
0.290645u
97
+ 1.90277u
96
+ ··· + 246755.u + 28003.6
0.0713382u
97
+ 0.477526u
96
+ ··· + 70483.3u + 8186.59
a
6
=
0.219307u
97
+ 1.42524u
96
+ ··· + 176271.u + 19817.0
0.0713382u
97
+ 0.477526u
96
+ ··· + 70483.3u + 8186.59
a
7
=
0.234515u
97
+ 1.53885u
96
+ ··· + 203052.u + 23162.9
0.0576709u
97
+ 0.395768u
96
+ ··· + 66339.8u + 7871.48
a
8
=
0.663198u
97
+ 4.31867u
96
+ ··· + 548562.u + 62433.4
0.187423u
97
+ 1.21229u
96
+ ··· + 146315.u + 16359.9
a
3
=
−0.452513u
97
− 2.97505u
96
+ ··· − 412430.u − 48480.8
−0.0874361u
97
− 0.577292u
96
+ ··· − 82676.3u − 9809.37
a
9
=
0.258820u
97
+ 1.64422u
96
+ ··· + 157464.u + 15829.2
0.134219u
97
+ 0.851277u
96
+ ··· + 80780.0u + 7907.17
a
12
=
1.60879u
97
+ 10.6591u
96
+ ··· + 1.59375 × 10
6
u + 192950.
0.0194880u
97
+ 0.128613u
96
+ ··· + 19715.0u + 2307.08
a
10
=
0.815945u
97
+ 5.34673u
96
+ ··· + 737122.u + 86857.8
0.186275u
97
+ 1.16701u
96
+ ··· + 108090.u + 11163.4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.36407u
97
+ 8.16421u
96
+ ··· + 290793.u + 4941.92
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
98
− 7u
97
+ ··· − 485513u + 44043
c
2
, c
8
u
98
− 21u
96
+ ··· + 16624u + 2701
c
3
u
98
+ 5u
97
+ ··· − 60u − 3
c
4
, c
11
u
98
− 3u
97
+ ··· − 1324u − 193
c
5
u
98
+ 4u
97
+ ··· + 9488u + 1852
c
6
u
98
+ 28u
96
+ ··· + 1451470765u − 470778887
c
7
, c
10
u
98
− 5u
97
+ ··· + 7560885u − 625281
c
9
, c
12
u
98
− 6u
97
+ ··· − 11140u + 837
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
98
− 51y
97
+ ··· − 123544471309y + 1939785849
c
2
, c
8
y
98
− 42y
97
+ ··· − 258320098y + 7295401
c
3
y
98
− 5y
97
+ ··· − 822y + 9
c
4
, c
11
y
98
− 73y
97
+ ··· − 1306760y + 37249
c
5
y
98
− 24y
97
+ ··· − 12001088y + 3429904
c
6
y
98
+ 56y
97
+ ··· + 1.14 × 10
19
y + 2.22 × 10
17
c
7
, c
10
y
98
− 89y
97
+ ··· − 6238806215403y + 390976328961
c
9
, c
12
y
98
+ 28y
97
+ ··· + 524678y + 700569
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.968126 + 0.222153I
a = −0.49504 − 1.35651I
b = 0.081167 + 0.136365I
−2.30647 − 3.35687I 0
u = 0.968126 − 0.222153I
a = −0.49504 + 1.35651I
b = 0.081167 − 0.136365I
−2.30647 + 3.35687I 0
u = 0.946901 + 0.283855I
a = 0.833414 + 1.130270I
b = 0.151296 − 0.072870I
−2.46721 + 1.31247I 0
u = 0.946901 − 0.283855I
a = 0.833414 − 1.130270I
b = 0.151296 + 0.072870I
−2.46721 − 1.31247I 0
u = −0.920116 + 0.440938I
a = −1.47718 − 0.39312I
b = −1.67990 + 0.45771I
−1.08524 + 3.10232I 0
u = −0.920116 − 0.440938I
a = −1.47718 + 0.39312I
b = −1.67990 − 0.45771I
−1.08524 − 3.10232I 0
u = 0.801784 + 0.518175I
a = 1.105210 − 0.820593I
b = 1.50280 − 1.10221I
−5.09430 + 4.73289I 0
u = 0.801784 − 0.518175I
a = 1.105210 + 0.820593I
b = 1.50280 + 1.10221I
−5.09430 − 4.73289I 0
u = 0.897499 + 0.319102I
a = −0.772552 + 0.279139I
b = −1.94191 − 1.28646I
−3.55756 − 2.03098I 0
u = 0.897499 − 0.319102I
a = −0.772552 − 0.279139I
b = −1.94191 + 1.28646I
−3.55756 + 2.03098I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.930790 + 0.500586I
a = 1.177720 + 0.296086I
b = 1.27067 + 0.69461I
−8.59494 + 1.86844I 0
u = −0.930790 − 0.500586I
a = 1.177720 − 0.296086I
b = 1.27067 − 0.69461I
−8.59494 − 1.86844I 0
u = 0.032690 + 1.075740I
a = −0.146955 + 0.681838I
b = 0.780704 + 0.134721I
2.45073 − 4.36839I 0
u = 0.032690 − 1.075740I
a = −0.146955 − 0.681838I
b = 0.780704 − 0.134721I
2.45073 + 4.36839I 0
u = 0.933459 + 0.540835I
a = 0.030560 − 0.426960I
b = 0.115481 + 1.261990I
−1.93431 + 1.15400I 0
u = 0.933459 − 0.540835I
a = 0.030560 + 0.426960I
b = 0.115481 − 1.261990I
−1.93431 − 1.15400I 0
u = −0.996957 + 0.439724I
a = 1.41379 + 0.09061I
b = 1.271260 + 0.256458I
−8.93133 + 2.06464I 0
u = −0.996957 − 0.439724I
a = 1.41379 − 0.09061I
b = 1.271260 − 0.256458I
−8.93133 − 2.06464I 0
u = 0.432657 + 1.007900I
a = 0.113369 − 0.588730I
b = 0.021279 − 0.650648I
2.23861 − 1.82364I 0
u = 0.432657 − 1.007900I
a = 0.113369 + 0.588730I
b = 0.021279 + 0.650648I
2.23861 + 1.82364I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.10330
a = −1.11211
b = −2.15012
−1.74309 0
u = 0.584477 + 0.938415I
a = 0.943522 − 0.377784I
b = 2.48816 + 0.38109I
2.08534 − 8.07440I 0
u = 0.584477 − 0.938415I
a = 0.943522 + 0.377784I
b = 2.48816 − 0.38109I
2.08534 + 8.07440I 0
u = −0.562422 + 0.961350I
a = −0.273104 − 0.316163I
b = −1.14512 + 1.43575I
−2.03759 + 0.63611I 0
u = −0.562422 − 0.961350I
a = −0.273104 + 0.316163I
b = −1.14512 − 1.43575I
−2.03759 − 0.63611I 0
u = −0.735376 + 0.852023I
a = −0.251086 + 1.031980I
b = 0.245412 + 0.151108I
4.58637 − 0.17416I 0
u = −0.735376 − 0.852023I
a = −0.251086 − 1.031980I
b = 0.245412 − 0.151108I
4.58637 + 0.17416I 0
u = 1.063820 + 0.379249I
a = 0.876645 + 0.506504I
b = 0.888153 − 0.336155I
−0.53158 − 2.92126I 0
u = 1.063820 − 0.379249I
a = 0.876645 − 0.506504I
b = 0.888153 + 0.336155I
−0.53158 + 2.92126I 0
u = 0.851429 + 0.099909I
a = 1.265410 − 0.154215I
b = 1.42389 + 1.17660I
0.75470 − 2.36582I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.851429 − 0.099909I
a = 1.265410 + 0.154215I
b = 1.42389 − 1.17660I
0.75470 + 2.36582I 0
u = −1.029330 + 0.506262I
a = 0.363470 − 1.016050I
b = −0.227694 − 0.002893I
−3.72389 + 3.86913I 0
u = −1.029330 − 0.506262I
a = 0.363470 + 1.016050I
b = −0.227694 + 0.002893I
−3.72389 − 3.86913I 0
u = −0.595068 + 0.597381I
a = −1.27394 − 1.13856I
b = −1.67648 − 1.21810I
−4.91130 + 7.00164I 0
u = −0.595068 − 0.597381I
a = −1.27394 + 1.13856I
b = −1.67648 + 1.21810I
−4.91130 − 7.00164I 0
u = 0.782994 + 0.856661I
a = −0.701326 + 0.841550I
b = −1.105620 + 0.657033I
−5.86798 − 2.06115I 0
u = 0.782994 − 0.856661I
a = −0.701326 − 0.841550I
b = −1.105620 − 0.657033I
−5.86798 + 2.06115I 0
u = 0.690803 + 0.464994I
a = 0.297748 − 0.174526I
b = 0.14837 − 1.74686I
−1.39771 − 4.15360I 0
u = 0.690803 − 0.464994I
a = 0.297748 + 0.174526I
b = 0.14837 + 1.74686I
−1.39771 + 4.15360I 0
u = 1.009410 + 0.601914I
a = 1.45556 − 0.07995I
b = 1.256130 + 0.160658I
−5.76243 − 9.39036I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.009410 − 0.601914I
a = 1.45556 + 0.07995I
b = 1.256130 − 0.160658I
−5.76243 + 9.39036I 0
u = −0.680166 + 0.457476I
a = 0.211622 − 0.117266I
b = 1.02928 − 2.02906I
0.57382 − 6.84957I 0
u = −0.680166 − 0.457476I
a = 0.211622 + 0.117266I
b = 1.02928 + 2.02906I
0.57382 + 6.84957I 0
u = 1.076280 + 0.493384I
a = −0.847870 + 0.513350I
b = −1.57841 − 0.74164I
−3.94589 − 2.30114I 0
u = 1.076280 − 0.493384I
a = −0.847870 − 0.513350I
b = −1.57841 + 0.74164I
−3.94589 + 2.30114I 0
u = −1.123600 + 0.379256I
a = −1.53393 − 0.07531I
b = −1.44831 + 0.00070I
−7.00593 − 2.93592I 0
u = −1.123600 − 0.379256I
a = −1.53393 + 0.07531I
b = −1.44831 − 0.00070I
−7.00593 + 2.93592I 0
u = −1.084890 + 0.492363I
a = −0.504486 + 1.158190I
b = 0.0828795 + 0.0778496I
−1.06566 + 10.79880I 0
u = −1.084890 − 0.492363I
a = −0.504486 − 1.158190I
b = 0.0828795 − 0.0778496I
−1.06566 − 10.79880I 0
u = −1.124510 + 0.448253I
a = 1.209100 + 0.200099I
b = 1.85028 − 0.67299I
−1.21930 + 8.61712I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.124510 − 0.448253I
a = 1.209100 − 0.200099I
b = 1.85028 + 0.67299I
−1.21930 − 8.61712I 0
u = −0.464509 + 1.172000I
a = −0.053836 + 0.261001I
b = 0.621028 − 0.197974I
6.76349 + 2.34241I 0
u = −0.464509 − 1.172000I
a = −0.053836 − 0.261001I
b = 0.621028 + 0.197974I
6.76349 − 2.34241I 0
u = −0.739123
a = 2.25200
b = 2.54683
−9.95144 −118.510
u = −0.731020
a = −1.22807
b = −1.63973
−1.67876 0
u = −0.708249 + 0.175453I
a = 0.538567 − 0.513506I
b = 0.137723 − 0.377292I
2.40542 − 1.79703I 0
u = −0.708249 − 0.175453I
a = 0.538567 + 0.513506I
b = 0.137723 + 0.377292I
2.40542 + 1.79703I 0
u = 0.589743 + 1.141430I
a = −0.233114 − 0.785124I
b = −0.331529 − 0.320158I
2.51262 − 2.70362I 0
u = 0.589743 − 1.141430I
a = −0.233114 + 0.785124I
b = −0.331529 + 0.320158I
2.51262 + 2.70362I 0
u = 0.391378 + 0.596073I
a = 0.640441 + 0.147713I
b = 0.161637 − 0.141028I
−0.015074 − 1.217060I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.391378 − 0.596073I
a = 0.640441 − 0.147713I
b = 0.161637 + 0.141028I
−0.015074 + 1.217060I 0
u = 1.104790 + 0.665459I
a = −1.206870 + 0.214393I
b = −1.43304 − 0.12209I
−7.05257 − 3.86875I 0
u = 1.104790 − 0.665459I
a = −1.206870 − 0.214393I
b = −1.43304 + 0.12209I
−7.05257 + 3.86875I 0
u = 1.281240 + 0.166858I
a = 0.859196 − 0.472227I
b = 1.292930 + 0.430670I
−1.82405 + 2.36704I 0
u = 1.281240 − 0.166858I
a = 0.859196 + 0.472227I
b = 1.292930 − 0.430670I
−1.82405 − 2.36704I 0
u = −0.447035 + 1.215850I
a = −0.179136 − 0.116619I
b = 0.047631 + 0.526670I
5.34790 + 6.03017I 0
u = −0.447035 − 1.215850I
a = −0.179136 + 0.116619I
b = 0.047631 − 0.526670I
5.34790 − 6.03017I 0
u = −1.053150 + 0.760738I
a = 0.974388 − 0.043306I
b = 2.04585 − 0.47947I
3.59575 + 6.15631I 0
u = −1.053150 − 0.760738I
a = 0.974388 + 0.043306I
b = 2.04585 + 0.47947I
3.59575 − 6.15631I 0
u = −0.941624 + 0.927715I
a = −0.798890 − 0.745925I
b = −1.48050 + 0.77009I
0.68540 + 5.52613I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.941624 − 0.927715I
a = −0.798890 + 0.745925I
b = −1.48050 − 0.77009I
0.68540 − 5.52613I 0
u = −0.531514 + 0.061307I
a = 1.50544 + 1.32141I
b = 1.47349 − 0.41800I
1.41227 − 5.79351I −2.46420 + 5.26074I
u = −0.531514 − 0.061307I
a = 1.50544 − 1.32141I
b = 1.47349 + 0.41800I
1.41227 + 5.79351I −2.46420 − 5.26074I
u = 1.25204 + 0.76158I
a = −0.897588 + 0.324316I
b = −1.69844 − 0.01396I
−6.45455 − 3.73447I 0
u = 1.25204 − 0.76158I
a = −0.897588 − 0.324316I
b = −1.69844 + 0.01396I
−6.45455 + 3.73447I 0
u = 0.492576 + 0.186056I
a = −2.16994 + 1.16872I
b = −1.49710 − 0.73339I
0.61225 − 2.87536I 0. + 3.36558I
u = 0.492576 − 0.186056I
a = −2.16994 − 1.16872I
b = −1.49710 + 0.73339I
0.61225 + 2.87536I 0. − 3.36558I
u = −1.36632 + 0.62485I
a = 0.800490 + 0.228431I
b = 1.59769 − 0.73129I
3.19413 + 4.02524I 0
u = −1.36632 − 0.62485I
a = 0.800490 − 0.228431I
b = 1.59769 + 0.73129I
3.19413 − 4.02524I 0
u = −0.443603 + 0.070420I
a = −0.74926 + 3.09815I
b = 0.116347 + 0.280142I
4.85526 + 3.12032I −18.2113 − 2.9153I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.443603 − 0.070420I
a = −0.74926 − 3.09815I
b = 0.116347 − 0.280142I
4.85526 − 3.12032I −18.2113 + 2.9153I
u = −0.338507 + 0.006882I
a = 0.15293 + 4.72616I
b = 0.199214 − 0.191193I
8.98797 − 0.51667I −0.3104 − 17.1627I
u = −0.338507 − 0.006882I
a = 0.15293 − 4.72616I
b = 0.199214 + 0.191193I
8.98797 + 0.51667I −0.3104 + 17.1627I
u = −1.43490 + 0.93399I
a = −0.889278 − 0.131933I
b = −2.12439 + 0.52190I
−7.70534 + 10.50060I 0
u = −1.43490 − 0.93399I
a = −0.889278 + 0.131933I
b = −2.12439 − 0.52190I
−7.70534 − 10.50060I 0
u = −1.41307 + 1.00623I
a = 0.929912 + 0.202368I
b = 2.09890 − 0.56276I
−5.8818 + 18.2319I 0
u = −1.41307 − 1.00623I
a = 0.929912 − 0.202368I
b = 2.09890 + 0.56276I
−5.8818 − 18.2319I 0
u = 1.52808 + 0.92551I
a = 0.874806 − 0.213439I
b = 1.96385 + 0.57108I
−8.06064 − 9.89546I 0
u = 1.52808 − 0.92551I
a = 0.874806 + 0.213439I
b = 1.96385 − 0.57108I
−8.06064 + 9.89546I 0
u = 1.48331 + 1.03234I
a = −0.832092 + 0.310326I
b = −2.02712 − 0.53893I
−9.02530 − 4.47960I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48331 − 1.03234I
a = −0.832092 − 0.310326I
b = −2.02712 + 0.53893I
−9.02530 + 4.47960I 0
u = 1.42615 + 1.40778I
a = −0.599680 + 0.450622I
b = −1.92759 − 0.61809I
−7.90990 − 5.83472I 0
u = 1.42615 − 1.40778I
a = −0.599680 − 0.450622I
b = −1.92759 + 0.61809I
−7.90990 + 5.83472I 0
u = −0.93776 + 1.98197I
a = 0.187590 + 0.575826I
b = 1.001740 − 0.895873I
−3.58940 − 8.50475I 0
u = −0.93776 − 1.98197I
a = 0.187590 − 0.575826I
b = 1.001740 + 0.895873I
−3.58940 + 8.50475I 0
u = −0.02295 + 2.75755I
a = 0.039593 − 0.433321I
b = 0.20734 + 1.70128I
−4.31072 − 0.47019I 0
u = −0.02295 − 2.75755I
a = 0.039593 + 0.433321I
b = 0.20734 − 1.70128I
−4.31072 + 0.47019I 0
u = −5.89703
a = −0.196841
b = −5.25583
−3.86366 0
14
II.
I
u
2
= h−3.12×10
51
u
35
−1.76×10
52
u
34
+· · ·+5.72×10
50
b−4.79×10
51
, −8.61×
10
50
u
35
−4.68×10
51
u
34
+· · ·+5.72×10
50
a−8.18×10
50
, u
36
+5u
35
+· · ·+5u−1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
11
=
1.50502u
35
+ 8.18351u
34
+ ··· − 14.9279u + 1.42826
5.44285u
35
+ 30.7657u
34
+ ··· − 29.3039u + 8.37448
a
5
=
−5.34168u
35
− 31.1834u
34
+ ··· + 25.2753u − 3.72596
−0.760583u
35
− 4.34471u
34
+ ··· + 5.67801u − 0.853526
a
6
=
−4.58110u
35
− 26.8387u
34
+ ··· + 19.5973u − 2.87243
−0.760583u
35
− 4.34471u
34
+ ··· + 5.67801u − 0.853526
a
7
=
−2.98665u
35
− 17.9573u
34
+ ··· + 10.1903u + 0.207279
−0.304980u
35
− 1.88289u
34
+ ··· + 2.72645u + 0.0556743
a
8
=
1.07737u
35
+ 4.15124u
34
+ ··· − 16.0513u + 12.8229
−0.777593u
35
− 3.94227u
34
+ ··· + 8.58729u − 1.37480
a
3
=
−4.64279u
35
− 24.3441u
34
+ ··· + 33.0800u − 11.7179
−2.60405u
35
− 14.5797u
34
+ ··· + 12.9586u − 5.04576
a
9
=
−2.25053u
35
− 11.6031u
34
+ ··· + 4.20377u + 5.73381
2.97419u
35
+ 17.2209u
34
+ ··· − 11.5429u + 3.71329
a
12
=
4.43065u
35
+ 23.2355u
34
+ ··· − 44.2795u + 5.86839
0.843434u
35
+ 4.18366u
34
+ ··· − 9.73349u + 3.58140
a
10
=
2.98045u
35
+ 20.5518u
34
+ ··· + 21.8592u + 0.516507
8.99497u
35
+ 51.2909u
34
+ ··· − 42.8677u + 10.9520
(ii) Obstruction class = 1
(iii) Cusp Shapes = 63.0353u
35
+ 363.897u
34
+ ··· − 287.092u + 86.9170
15
(iv) u-Polynomials at the component
16
Crossings u-Polynomials at each crossing
c
1
u
36
+ 5u
35
+ ··· + 5u − 1
c
2
u
36
− u
35
+ ··· + 5u + 3
c
3
u
36
+ 7u
35
+ ··· − 7u − 1
c
4
u
36
− 2u
35
+ ··· − 5u + 3
c
5
u
36
− 4u
35
+ ··· − 456u − 48
c
6
u
36
− u
35
+ ··· − 2036u − 441
c
7
u
36
− 4u
35
+ ··· + 5u + 1
c
8
u
36
+ u
35
+ ··· − 5u + 3
c
9
u
36
− 5u
35
+ ··· + 3u + 1
c
10
u
36
+ 4u
35
+ ··· − 5u + 1
c
11
u
36
+ 2u
35
+ ··· + 5u + 3
c
12
u
36
+ 5u
35
+ ··· − 3u + 1
17
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
− 21y
35
+ ··· − 9y + 1
c
2
, c
8
y
36
− 31y
35
+ ··· − 217y + 9
c
3
y
36
− 9y
35
+ ··· − 141y + 1
c
4
, c
11
y
36
− 22y
35
+ ··· − 103y + 9
c
5
y
36
− 8y
35
+ ··· − 47136y + 2304
c
6
y
36
+ 7y
35
+ ··· − 2575336y + 194481
c
7
, c
10
y
36
− 18y
35
+ ··· + 21y + 1
c
9
, c
12
y
36
+ 7y
35
+ ··· + 19y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.714881 + 0.756577I
a = 1.127120 − 0.293586I
b = 2.39796 + 0.45968I
2.22124 − 7.43156I −1.98172 + 4.89120I
u = 0.714881 − 0.756577I
a = 1.127120 + 0.293586I
b = 2.39796 − 0.45968I
2.22124 + 7.43156I −1.98172 − 4.89120I
u = 0.790065 + 0.529449I
a = 0.250037 + 0.439484I
b = −0.562359 − 0.828237I
−2.42134 − 2.11606I −3.44727 + 4.91351I
u = 0.790065 − 0.529449I
a = 0.250037 − 0.439484I
b = −0.562359 + 0.828237I
−2.42134 + 2.11606I −3.44727 − 4.91351I
u = −0.937628 + 0.506613I
a = −1.209760 − 0.208362I
b = −1.129070 − 0.566935I
−8.37156 + 2.07888I 6.15083 − 8.30328I
u = −0.937628 − 0.506613I
a = −1.209760 + 0.208362I
b = −1.129070 + 0.566935I
−8.37156 − 2.07888I 6.15083 + 8.30328I
u = 0.380494 + 1.063760I
a = −0.211123 − 0.804081I
b = −0.476605 − 0.674625I
3.26099 − 2.74854I 4.91917 + 3.92261I
u = 0.380494 − 1.063760I
a = −0.211123 + 0.804081I
b = −0.476605 + 0.674625I
3.26099 + 2.74854I 4.91917 − 3.92261I
u = 0.308878 + 0.813062I
a = −0.75125 + 1.48345I
b = −0.746739 + 0.671760I
−4.91265 − 6.31933I −6.03488 + 2.93564I
u = 0.308878 − 0.813062I
a = −0.75125 − 1.48345I
b = −0.746739 − 0.671760I
−4.91265 + 6.31933I −6.03488 − 2.93564I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.298926 + 0.780339I
a = −0.618693 + 0.555269I
b = 0.388321 + 0.823478I
2.63334 − 2.66378I 3.08842 + 4.48784I
u = 0.298926 − 0.780339I
a = −0.618693 − 0.555269I
b = 0.388321 − 0.823478I
2.63334 + 2.66378I 3.08842 − 4.48784I
u = 0.783498 + 0.166219I
a = −1.62139 + 0.18504I
b = −1.71746 − 0.73679I
−0.98609 − 1.66746I −4.60766 + 1.22058I
u = 0.783498 − 0.166219I
a = −1.62139 − 0.18504I
b = −1.71746 + 0.73679I
−0.98609 + 1.66746I −4.60766 − 1.22058I
u = −0.993785 + 0.766685I
a = −0.971315 − 0.697482I
b = −1.48402 + 0.69918I
0.87679 + 5.05336I 0
u = −0.993785 − 0.766685I
a = −0.971315 + 0.697482I
b = −1.48402 − 0.69918I
0.87679 − 5.05336I 0
u = 0.728210
a = 2.30119
b = 2.51843
−9.91606 107.710
u = −0.541426 + 0.376585I
a = 0.288983 + 0.929480I
b = 1.74791 − 1.77425I
0.44882 − 7.36372I −7.2812 + 13.3503I
u = −0.541426 − 0.376585I
a = 0.288983 − 0.929480I
b = 1.74791 + 1.77425I
0.44882 + 7.36372I −7.2812 − 13.3503I
u = −0.345267 + 1.296380I
a = −0.277461 − 0.363617I
b = 0.056666 + 0.331656I
5.08131 + 6.28383I 0. − 12.16133I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.345267 − 1.296380I
a = −0.277461 + 0.363617I
b = 0.056666 − 0.331656I
5.08131 − 6.28383I 0. + 12.16133I
u = 0.626819 + 0.068521I
a = −1.35334 + 0.86602I
b = −0.98889 − 1.28768I
−1.67237 − 3.07358I −6.56618 + 2.97279I
u = 0.626819 − 0.068521I
a = −1.35334 − 0.86602I
b = −0.98889 + 1.28768I
−1.67237 + 3.07358I −6.56618 − 2.97279I
u = −1.088840 + 0.888476I
a = 0.874737 + 0.164187I
b = 1.92316 − 0.68714I
5.02758 + 5.86380I 0
u = −1.088840 − 0.888476I
a = 0.874737 − 0.164187I
b = 1.92316 + 0.68714I
5.02758 − 5.86380I 0
u = −0.66079 + 1.25901I
a = −0.037623 + 0.573489I
b = 0.383659 − 0.123803I
6.68431 + 1.63919I 0
u = −0.66079 − 1.25901I
a = −0.037623 − 0.573489I
b = 0.383659 + 0.123803I
6.68431 − 1.63919I 0
u = −0.420259 + 0.204955I
a = −1.40064 + 3.12278I
b = 0.113508 − 0.105877I
8.98569 + 0.71703I −0.8048 − 22.3294I
u = −0.420259 − 0.204955I
a = −1.40064 − 3.12278I
b = 0.113508 + 0.105877I
8.98569 − 0.71703I −0.8048 + 22.3294I
u = 0.206181 + 0.241545I
a = −3.25610 − 2.39451I
b = 0.071381 − 0.457718I
5.12019 − 3.11902I 12.56347 + 2.80103I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.206181 − 0.241545I
a = −3.25610 + 2.39451I
b = 0.071381 + 0.457718I
5.12019 + 3.11902I 12.56347 − 2.80103I
u = −0.95874 + 1.54632I
a = −0.211085 − 0.317945I
b = −1.95094 + 1.98931I
−2.26668 + 0.48403I 0
u = −0.95874 − 1.54632I
a = −0.211085 + 0.317945I
b = −1.95094 − 1.98931I
−2.26668 − 0.48403I 0
u = 1.51240 + 1.28157I
a = −0.656316 + 0.381230I
b = −1.99632 − 0.59791I
−7.87413 − 5.30398I 0
u = 1.51240 − 1.28157I
a = −0.656316 − 0.381230I
b = −1.99632 + 0.59791I
−7.87413 + 5.30398I 0
u = −5.07902
a = −0.230745
b = −4.57877
−3.88522 0
23
III. I
u
3
= hb + a − 1, a
2
− a + 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
11
=
a
−a + 1
a
5
=
−a + 1
0
a
6
=
−a + 1
0
a
7
=
0
a − 1
a
8
=
a
0
a
3
=
a
1
a
9
=
1
−a
a
12
=
a + 1
−a + 1
a
10
=
2a
−a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a − 8
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u − 1)
2
c
2
, c
3
, c
4
c
12
u
2
+ u + 1
c
5
u
2
c
6
, c
8
, c
9
c
11
u
2
− u + 1
c
10
(u + 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
(y −1)
2
c
2
, c
3
, c
4
c
6
, c
8
, c
9
c
11
, c
12
y
2
+ y + 1
c
5
y
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.500000 + 0.866025I
b = 0.500000 − 0.866025I
−1.64493 − 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = 0.500000 − 0.866025I
b = 0.500000 + 0.866025I
−1.64493 + 2.02988I −6.00000 − 3.46410I
27
IV. I
u
4
= hb + 2, a + 1, u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
−1
a
2
=
1
1
a
11
=
−1
−2
a
5
=
1
1
a
6
=
0
1
a
7
=
1
2
a
8
=
1
2
a
3
=
0
−1
a
9
=
1
1
a
12
=
0
−1
a
10
=
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u − 1
c
2
, c
4
, c
5
c
6
, c
8
, c
9
c
11
, c
12
u + 1
c
3
, c
7
, c
10
u
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
8
c
9
, c
11
, c
12
y −1
c
3
, c
7
, c
10
y
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = −2.00000
−1.64493 −6.00000
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
36
+ 5u
35
+ ··· + 5u − 1)
· (u
98
− 7u
97
+ ··· − 485513u + 44043)
c
2
(u + 1)(u
2
+ u + 1)(u
36
− u
35
+ ··· + 5u + 3)
· (u
98
− 21u
96
+ ··· + 16624u + 2701)
c
3
u(u
2
+ u + 1)(u
36
+ 7u
35
+ ··· − 7u − 1)(u
98
+ 5u
97
+ ··· − 60u − 3)
c
4
(u + 1)(u
2
+ u + 1)(u
36
− 2u
35
+ ··· − 5u + 3)
· (u
98
− 3u
97
+ ··· − 1324u − 193)
c
5
u
2
(u + 1)(u
36
− 4u
35
+ ··· − 456u − 48)
· (u
98
+ 4u
97
+ ··· + 9488u + 1852)
c
6
(u + 1)(u
2
− u + 1)(u
36
− u
35
+ ··· − 2036u − 441)
· (u
98
+ 28u
96
+ ··· + 1451470765u − 470778887)
c
7
u(u − 1)
2
(u
36
− 4u
35
+ ··· + 5u + 1)
· (u
98
− 5u
97
+ ··· + 7560885u − 625281)
c
8
(u + 1)(u
2
− u + 1)(u
36
+ u
35
+ ··· − 5u + 3)
· (u
98
− 21u
96
+ ··· + 16624u + 2701)
c
9
(u + 1)(u
2
− u + 1)(u
36
− 5u
35
+ ··· + 3u + 1)
· (u
98
− 6u
97
+ ··· − 11140u + 837)
c
10
u(u + 1)
2
(u
36
+ 4u
35
+ ··· − 5u + 1)
· (u
98
− 5u
97
+ ··· + 7560885u − 625281)
c
11
(u + 1)(u
2
− u + 1)(u
36
+ 2u
35
+ ··· + 5u + 3)
· (u
98
− 3u
97
+ ··· − 1324u − 193)
c
12
(u + 1)(u
2
+ u + 1)(u
36
+ 5u
35
+ ··· − 3u + 1)
· (u
98
− 6u
97
+ ··· − 11140u + 837)
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
3
)(y
36
− 21y
35
+ ··· − 9y + 1)
· (y
98
− 51y
97
+ ··· − 123544471309y + 1939785849)
c
2
, c
8
(y −1)(y
2
+ y + 1)(y
36
− 31y
35
+ ··· − 217y + 9)
· (y
98
− 42y
97
+ ··· − 258320098y + 7295401)
c
3
y(y
2
+ y + 1)(y
36
− 9y
35
+ ··· − 141y + 1)(y
98
− 5y
97
+ ··· − 822y + 9)
c
4
, c
11
(y −1)(y
2
+ y + 1)(y
36
− 22y
35
+ ··· − 103y + 9)
· (y
98
− 73y
97
+ ··· − 1306760y + 37249)
c
5
y
2
(y −1)(y
36
− 8y
35
+ ··· − 47136y + 2304)
· (y
98
− 24y
97
+ ··· − 12001088y + 3429904)
c
6
(y −1)(y
2
+ y + 1)(y
36
+ 7y
35
+ ··· − 2575336y + 194481)
· (y
98
+ 56y
97
+ ··· + 1.14 × 10
19
y + 2.22 × 10
17
)
c
7
, c
10
y(y −1)
2
(y
36
− 18y
35
+ ··· + 21y + 1)
· (y
98
− 89y
97
+ ··· − 6238806215403y + 390976328961)
c
9
, c
12
(y −1)(y
2
+ y + 1)(y
36
+ 7y
35
+ ··· + 19y + 1)
· (y
98
+ 28y
97
+ ··· + 524678y + 700569)
33
