12a
0469
(K12a
0469
)
A knot diagram
1
Linearized knot diagam
3 6 11 8 2 1 10 5 12 4 7 9
Solving Sequence
3,6
2 1 7
5,9
8 4 12 10 11
c
2
c
1
c
6
c
5
c
8
c
4
c
12
c
9
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h6.63633 × 10
186
u
142
+ 2.53542 × 10
189
u
141
+ ··· + 9.01034 × 10
189
b + 3.59708 × 10
190
,
− 8.67414 × 10
190
u
142
+ 3.49780 × 10
191
u
141
+ ··· + 4.23486 × 10
191
a − 1.16899 × 10
193
,
u
143
− 3u
142
+ ··· + 110u − 47i
I
u
2
= h4u
34
+ 7u
33
+ ··· + b − 5, −3u
34
− 2u
33
+ ··· + a + 2, u
35
+ 2u
34
+ ··· − 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 178 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
= h6.64 × 10
186
u
142
+ 2.54 × 10
189
u
141
+ · · · + 9.01 × 10
189
b + 3.60 ×
10
190
, −8.67 × 10
190
u
142
+ 3.50 × 10
191
u
141
+ · · · + 4.23 × 10
191
a − 1.17 ×
10
193
, u
143
− 3u
142
+ · · · + 110u − 47i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
5
=
u
−u
3
+ u
a
9
=
0.204827u
142
− 0.825954u
141
+ ··· − 44.4711u + 27.6040
−0.000736524u
142
− 0.281390u
141
+ ··· + 8.40058u − 3.99217
a
8
=
0.770473u
142
− 2.27599u
141
+ ··· − 96.6026u + 66.2237
0.589171u
142
− 1.10912u
141
+ ··· − 43.1569u + 23.0231
a
4
=
−0.623467u
142
+ 0.435106u
141
+ ··· + 70.3674u − 10.6358
0.402860u
142
− 0.856118u
141
+ ··· − 19.8741u + 12.8858
a
12
=
−0.287141u
142
+ 0.974601u
141
+ ··· + 31.1944u − 41.8783
−1.17791u
142
+ 2.62231u
141
+ ··· + 91.6207u − 54.4365
a
10
=
−0.682533u
142
+ 1.81972u
141
+ ··· + 86.3997u − 44.9083
0.128085u
142
− 0.345952u
141
+ ··· − 14.7059u + 8.01038
a
11
=
−1.00812u
142
+ 1.95993u
141
+ ··· + 46.9184u − 61.1004
−0.281878u
142
+ 0.435375u
141
+ ··· + 17.4712u − 15.1734
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.34172u
142
+ 2.00690u
141
+ ··· + 81.0326u − 68.7918
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
143
+ 69u
142
+ ··· + 24038u + 2209
c
2
, c
5
u
143
+ 3u
142
+ ··· + 110u + 47
c
3
, c
10
u
143
+ 2u
142
+ ··· + 22312u + 8024
c
4
, c
8
u
143
− 60u
141
+ ··· + 6466443u + 1229681
c
6
u
143
+ 9u
142
+ ··· + 1198600u + 745279
c
7
u
143
+ 6u
142
+ ··· + 586376963u + 10200841
c
9
, c
12
u
143
− 7u
142
+ ··· − 220108u + 19079
c
11
u
143
− 2u
142
+ ··· + 111690u + 3457
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
143
+ 15y
142
+ ··· − 116759262y −4879681
c
2
, c
5
y
143
− 69y
142
+ ··· + 24038y −2209
c
3
, c
10
y
143
+ 100y
142
+ ··· − 1978348960y −64384576
c
4
, c
8
y
143
− 120y
142
+ ··· + 46027317196279y −1512115361761
c
6
y
143
+ 39y
142
+ ··· − 20746243156102y −555440787841
c
7
y
143
− 64y
142
+ ··· + 259743448139619271y −104057157107281
c
9
, c
12
y
143
+ 95y
142
+ ··· − 14790500680y −364008241
c
11
y
143
− 32y
142
+ ··· − 2418099900y −11950849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972824 + 0.166718I
a = 0.457246 − 0.655270I
b = 0.443113 − 0.693346I
−1.56643 − 0.21461I 0
u = 0.972824 − 0.166718I
a = 0.457246 + 0.655270I
b = 0.443113 + 0.693346I
−1.56643 + 0.21461I 0
u = −0.708715 + 0.678500I
a = 0.523211 − 0.094624I
b = −0.299899 − 0.694127I
7.19922 + 5.10187I 0
u = −0.708715 − 0.678500I
a = 0.523211 + 0.094624I
b = −0.299899 + 0.694127I
7.19922 − 5.10187I 0
u = −0.880184 + 0.385121I
a = −1.185250 + 0.170640I
b = 1.064630 − 0.155834I
7.36065 − 0.12789I 0
u = −0.880184 − 0.385121I
a = −1.185250 − 0.170640I
b = 1.064630 + 0.155834I
7.36065 + 0.12789I 0
u = −0.155908 + 0.946772I
a = −0.532330 − 1.039930I
b = −0.284300 − 1.063160I
3.06061 − 2.11603I 0
u = −0.155908 − 0.946772I
a = −0.532330 + 1.039930I
b = −0.284300 + 1.063160I
3.06061 + 2.11603I 0
u = −0.833634 + 0.637751I
a = −0.666098 + 0.015768I
b = 0.581521 + 0.100790I
6.81184 − 0.08124I 0
u = −0.833634 − 0.637751I
a = −0.666098 − 0.015768I
b = 0.581521 − 0.100790I
6.81184 + 0.08124I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.530366 + 0.908248I
a = 1.313440 − 0.227015I
b = 1.105910 − 0.828042I
5.17661 + 3.94715I 0
u = 0.530366 − 0.908248I
a = 1.313440 + 0.227015I
b = 1.105910 + 0.828042I
5.17661 − 3.94715I 0
u = −0.968963 + 0.409052I
a = −0.158932 − 0.732323I
b = −1.02996 − 1.13546I
6.92421 + 3.31324I 0
u = −0.968963 − 0.409052I
a = −0.158932 + 0.732323I
b = −1.02996 + 1.13546I
6.92421 − 3.31324I 0
u = −0.766524 + 0.558095I
a = −0.231162 − 0.487931I
b = −0.1077570 + 0.0220050I
2.91700 + 2.23279I 0
u = −0.766524 − 0.558095I
a = −0.231162 + 0.487931I
b = −0.1077570 − 0.0220050I
2.91700 − 2.23279I 0
u = −0.369709 + 0.868053I
a = −1.284080 − 0.591736I
b = −0.805909 − 1.045650I
3.40285 − 2.50921I 0
u = −0.369709 − 0.868053I
a = −1.284080 + 0.591736I
b = −0.805909 + 1.045650I
3.40285 + 2.50921I 0
u = 0.354373 + 0.870826I
a = −1.83010 + 0.96443I
b = −1.23920 + 1.44860I
9.7755 + 13.6299I 0
u = 0.354373 − 0.870826I
a = −1.83010 − 0.96443I
b = −1.23920 − 1.44860I
9.7755 − 13.6299I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.699661 + 0.812819I
a = −0.527943 + 0.204742I
b = 0.198819 − 0.419500I
11.8272 − 10.0325I 0
u = 0.699661 − 0.812819I
a = −0.527943 − 0.204742I
b = 0.198819 + 0.419500I
11.8272 + 10.0325I 0
u = −0.694266 + 0.614024I
a = −1.248230 − 0.210637I
b = −1.24064 − 1.19424I
5.89656 − 1.21715I 0
u = −0.694266 − 0.614024I
a = −1.248230 + 0.210637I
b = −1.24064 + 1.19424I
5.89656 + 1.21715I 0
u = −0.941272 + 0.516355I
a = −0.52190 − 1.94208I
b = 2.09560 − 0.87394I
5.18149 + 5.68292I 0
u = −0.941272 − 0.516355I
a = −0.52190 + 1.94208I
b = 2.09560 + 0.87394I
5.18149 − 5.68292I 0
u = −0.415880 + 0.824832I
a = 0.272830 − 0.206774I
b = 0.460703 + 0.565218I
3.60534 − 1.56932I 0
u = −0.415880 − 0.824832I
a = 0.272830 + 0.206774I
b = 0.460703 − 0.565218I
3.60534 + 1.56932I 0
u = −0.914124 + 0.097993I
a = 0.988930 − 0.614990I
b = −0.410080 − 0.078116I
−1.35267 + 2.48849I 0
u = −0.914124 − 0.097993I
a = 0.988930 + 0.614990I
b = −0.410080 + 0.078116I
−1.35267 − 2.48849I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.063140 + 0.251935I
a = 0.82056 − 1.44493I
b = 1.72251 + 0.95045I
5.54141 + 1.35505I 0
u = −1.063140 − 0.251935I
a = 0.82056 + 1.44493I
b = 1.72251 − 0.95045I
5.54141 − 1.35505I 0
u = 1.037820 + 0.343141I
a = 0.63923 − 1.34805I
b = −1.92675 − 0.46592I
−2.55857 − 1.59318I 0
u = 1.037820 − 0.343141I
a = 0.63923 + 1.34805I
b = −1.92675 + 0.46592I
−2.55857 + 1.59318I 0
u = 0.980544 + 0.502007I
a = −0.07536 − 2.40050I
b = −1.69153 − 1.68869I
4.85216 − 6.19501I 0
u = 0.980544 − 0.502007I
a = −0.07536 + 2.40050I
b = −1.69153 + 1.68869I
4.85216 + 6.19501I 0
u = −1.052390 + 0.329534I
a = −0.15226 + 1.68415I
b = −1.013310 + 0.564916I
−2.38585 − 0.84245I 0
u = −1.052390 − 0.329534I
a = −0.15226 − 1.68415I
b = −1.013310 − 0.564916I
−2.38585 + 0.84245I 0
u = −0.980995 + 0.505565I
a = −0.67298 + 1.49972I
b = −2.82321 + 0.22541I
4.85895 − 0.80993I 0
u = −0.980995 − 0.505565I
a = −0.67298 − 1.49972I
b = −2.82321 − 0.22541I
4.85895 + 0.80993I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.099640 + 0.098831I
a = 0.472703 − 0.379509I
b = −0.838676 + 0.036532I
−1.28064 + 2.45502I 0
u = −1.099640 − 0.098831I
a = 0.472703 + 0.379509I
b = −0.838676 − 0.036532I
−1.28064 − 2.45502I 0
u = 1.102080 + 0.150812I
a = 0.085422 + 0.816881I
b = 0.857151 + 0.292846I
−1.91809 + 0.00326I 0
u = 1.102080 − 0.150812I
a = 0.085422 − 0.816881I
b = 0.857151 − 0.292846I
−1.91809 − 0.00326I 0
u = 0.980875 + 0.541795I
a = 0.59391 + 2.19908I
b = 1.59194 + 0.45165I
5.54069 + 0.82722I 0
u = 0.980875 − 0.541795I
a = 0.59391 − 2.19908I
b = 1.59194 − 0.45165I
5.54069 − 0.82722I 0
u = 0.353397 + 0.805249I
a = 0.778414 − 0.593203I
b = 0.426361 − 0.044050I
3.81909 + 0.03447I 0
u = 0.353397 − 0.805249I
a = 0.778414 + 0.593203I
b = 0.426361 + 0.044050I
3.81909 − 0.03447I 0
u = −1.080150 + 0.308520I
a = −1.46234 + 1.31744I
b = −2.11381 − 0.78228I
5.01697 − 0.50877I 0
u = −1.080150 − 0.308520I
a = −1.46234 − 1.31744I
b = −2.11381 + 0.78228I
5.01697 + 0.50877I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.319767 + 0.810994I
a = 1.71954 + 1.20874I
b = 1.10695 + 1.54912I
5.13477 − 7.54242I 0
u = −0.319767 − 0.810994I
a = 1.71954 − 1.20874I
b = 1.10695 − 1.54912I
5.13477 + 7.54242I 0
u = 0.598493 + 0.627176I
a = −1.90623 + 0.02992I
b = −1.182720 + 0.231295I
6.66585 − 5.42992I 0
u = 0.598493 − 0.627176I
a = −1.90623 − 0.02992I
b = −1.182720 − 0.231295I
6.66585 + 5.42992I 0
u = 0.655071 + 0.556470I
a = 2.34251 + 0.28017I
b = 0.820805 − 0.996678I
5.85355 + 1.95630I 0
u = 0.655071 − 0.556470I
a = 2.34251 − 0.28017I
b = 0.820805 + 0.996678I
5.85355 − 1.95630I 0
u = −1.119770 + 0.232625I
a = −0.360988 − 0.758476I
b = 1.68688 − 0.20289I
0.89596 − 4.79112I 0
u = −1.119770 − 0.232625I
a = −0.360988 + 0.758476I
b = 1.68688 + 0.20289I
0.89596 + 4.79112I 0
u = −0.628500 + 0.580830I
a = 0.94403 − 1.22625I
b = 1.38369 + 0.91606I
5.89936 + 5.13045I 0
u = −0.628500 − 0.580830I
a = 0.94403 + 1.22625I
b = 1.38369 − 0.91606I
5.89936 − 5.13045I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.039260 + 0.524971I
a = 0.447858 − 0.559550I
b = 1.19179 − 1.01888I
7.90251 − 2.69052I 0
u = 1.039260 − 0.524971I
a = 0.447858 + 0.559550I
b = 1.19179 + 1.01888I
7.90251 + 2.69052I 0
u = 1.137490 + 0.254166I
a = 0.22161 + 1.48098I
b = 1.020090 + 0.663149I
−0.04528 + 4.02330I 0
u = 1.137490 − 0.254166I
a = 0.22161 − 1.48098I
b = 1.020090 − 0.663149I
−0.04528 − 4.02330I 0
u = 1.030140 + 0.553117I
a = 0.935402 + 0.725454I
b = −0.113045 − 0.252441I
8.88478 − 5.60498I 0
u = 1.030140 − 0.553117I
a = 0.935402 − 0.725454I
b = −0.113045 + 0.252441I
8.88478 + 5.60498I 0
u = 0.343261 + 0.751174I
a = −1.86707 + 0.48669I
b = −1.353350 + 0.329263I
5.40318 + 7.44818I 0. − 5.06717I
u = 0.343261 − 0.751174I
a = −1.86707 − 0.48669I
b = −1.353350 − 0.329263I
5.40318 − 7.44818I 0. + 5.06717I
u = 1.063360 + 0.507382I
a = −0.080114 + 0.841019I
b = 1.63402 + 0.60538I
−0.23235 − 2.30271I 0
u = 1.063360 − 0.507382I
a = −0.080114 − 0.841019I
b = 1.63402 − 0.60538I
−0.23235 + 2.30271I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.041265 + 0.817285I
a = −0.629740 − 0.365556I
b = −0.413784 + 0.307123I
2.74738 − 0.57734I 2.75565 − 1.84059I
u = −0.041265 − 0.817285I
a = −0.629740 + 0.365556I
b = −0.413784 − 0.307123I
2.74738 + 0.57734I 2.75565 + 1.84059I
u = 0.513652 + 0.633449I
a = −1.066360 − 0.153909I
b = −0.160943 − 0.875108I
10.41030 + 0.93865I 8.38027 + 0.I
u = 0.513652 − 0.633449I
a = −1.066360 + 0.153909I
b = −0.160943 + 0.875108I
10.41030 − 0.93865I 8.38027 + 0.I
u = −0.315496 + 0.751196I
a = −1.95287 + 0.24999I
b = −1.26102 − 1.00604I
4.38475 − 6.88202I 4.27738 + 6.29373I
u = −0.315496 − 0.751196I
a = −1.95287 − 0.24999I
b = −1.26102 + 1.00604I
4.38475 + 6.88202I 4.27738 − 6.29373I
u = −1.106880 + 0.432563I
a = 0.72308 + 1.28589I
b = −1.09498 + 1.16407I
−4.40650 + 4.69872I 0
u = −1.106880 − 0.432563I
a = 0.72308 − 1.28589I
b = −1.09498 − 1.16407I
−4.40650 − 4.69872I 0
u = −1.088060 + 0.482697I
a = 0.037166 − 1.260340I
b = 0.722615 − 0.744111I
−0.52510 + 4.54564I 0
u = −1.088060 − 0.482697I
a = 0.037166 + 1.260340I
b = 0.722615 + 0.744111I
−0.52510 − 4.54564I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.142590 + 0.338869I
a = −0.341870 + 0.900979I
b = 0.996317 + 0.809975I
−3.33340 − 0.19145I 0
u = 1.142590 − 0.338869I
a = −0.341870 − 0.900979I
b = 0.996317 − 0.809975I
−3.33340 + 0.19145I 0
u = 1.112800 + 0.443412I
a = −0.418349 − 1.070480I
b = −1.335090 + 0.190699I
−4.33577 − 2.82257I 0
u = 1.112800 − 0.443412I
a = −0.418349 + 1.070480I
b = −1.335090 − 0.190699I
−4.33577 + 2.82257I 0
u = 0.374933 + 0.707223I
a = −1.97347 + 1.54875I
b = −1.09571 + 1.74529I
9.74954 + 0.95514I 7.29179 + 0.I
u = 0.374933 − 0.707223I
a = −1.97347 − 1.54875I
b = −1.09571 − 1.74529I
9.74954 − 0.95514I 7.29179 + 0.I
u = −1.131250 + 0.399092I
a = −0.117006 − 1.086150I
b = 0.390296 − 0.729978I
−0.66581 + 4.69744I 0
u = −1.131250 − 0.399092I
a = −0.117006 + 1.086150I
b = 0.390296 + 0.729978I
−0.66581 − 4.69744I 0
u = −1.078340 + 0.534415I
a = −0.31479 + 2.23263I
b = −1.76896 + 0.51547I
−1.17966 + 5.21827I 0
u = −1.078340 − 0.534415I
a = −0.31479 − 2.23263I
b = −1.76896 − 0.51547I
−1.17966 − 5.21827I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.188380 + 0.223267I
a = −0.595313 − 1.060500I
b = −1.35584 + 0.61308I
0.28461 + 4.49742I 0
u = 1.188380 − 0.223267I
a = −0.595313 + 1.060500I
b = −1.35584 − 0.61308I
0.28461 − 4.49742I 0
u = 1.090120 + 0.535407I
a = 0.15356 − 1.42737I
b = −2.11704 − 0.94380I
−0.92239 − 7.86140I 0
u = 1.090120 − 0.535407I
a = 0.15356 + 1.42737I
b = −2.11704 + 0.94380I
−0.92239 + 7.86140I 0
u = 1.161740 + 0.358048I
a = −0.354856 + 0.411136I
b = 1.149140 + 0.646764I
−1.07191 − 3.32802I 0
u = 1.161740 − 0.358048I
a = −0.354856 − 0.411136I
b = 1.149140 − 0.646764I
−1.07191 + 3.32802I 0
u = 0.954903 + 0.753538I
a = 0.332770 + 0.297611I
b = −0.413702 + 0.194495I
11.08670 + 4.23142I 0
u = 0.954903 − 0.753538I
a = 0.332770 − 0.297611I
b = −0.413702 − 0.194495I
11.08670 − 4.23142I 0
u = 1.104380 + 0.541873I
a = 1.12120 − 2.12601I
b = −1.62520 − 2.74262I
6.63347 − 7.81407I 0
u = 1.104380 − 0.541873I
a = 1.12120 + 2.12601I
b = −1.62520 + 2.74262I
6.63347 + 7.81407I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.099250 + 0.562689I
a = −1.12421 + 2.06158I
b = 1.58518 + 2.10470I
7.63591 − 5.83063I 0
u = 1.099250 − 0.562689I
a = −1.12421 − 2.06158I
b = 1.58518 − 2.10470I
7.63591 + 5.83063I 0
u = −0.206083 + 0.731369I
a = −1.232460 + 0.382744I
b = −0.890098 + 0.074368I
0.59474 − 3.17310I −2.06425 + 3.72611I
u = −0.206083 − 0.731369I
a = −1.232460 − 0.382744I
b = −0.890098 − 0.074368I
0.59474 + 3.17310I −2.06425 − 3.72611I
u = −1.235100 + 0.167614I
a = 0.454999 − 0.986798I
b = 1.36426 + 0.37356I
4.37144 − 10.54680I 0
u = −1.235100 − 0.167614I
a = 0.454999 + 0.986798I
b = 1.36426 − 0.37356I
4.37144 + 10.54680I 0
u = 0.491676 + 0.568739I
a = 1.06008 − 1.39885I
b = −0.697525 + 0.255146I
9.52507 − 1.72118I 9.60795 + 1.73984I
u = 0.491676 − 0.568739I
a = 1.06008 + 1.39885I
b = −0.697525 − 0.255146I
9.52507 + 1.72118I 9.60795 − 1.73984I
u = 0.333909 + 0.667903I
a = 2.61572 − 1.68046I
b = 0.82010 − 1.90888I
8.85396 + 3.11371I 9.02540 − 3.09080I
u = 0.333909 − 0.667903I
a = 2.61572 + 1.68046I
b = 0.82010 + 1.90888I
8.85396 − 3.11371I 9.02540 + 3.09080I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.119880 + 0.568440I
a = 0.19758 + 1.92402I
b = 1.58340 + 0.67474I
3.12696 − 12.44270I 0
u = 1.119880 − 0.568440I
a = 0.19758 − 1.92402I
b = 1.58340 − 0.67474I
3.12696 + 12.44270I 0
u = −1.127840 + 0.560790I
a = 0.14680 − 1.53067I
b = 2.37872 − 1.04523I
2.01141 + 11.83950I 0
u = −1.127840 − 0.560790I
a = 0.14680 + 1.53067I
b = 2.37872 + 1.04523I
2.01141 − 11.83950I 0
u = −1.150450 + 0.513816I
a = 0.390565 − 1.011470I
b = 1.303450 − 0.161910I
−2.14519 + 7.85574I 0
u = −1.150450 − 0.513816I
a = 0.390565 + 1.011470I
b = 1.303450 + 0.161910I
−2.14519 − 7.85574I 0
u = 0.735658
a = 0.399640
b = 0.645718
−1.25008 −9.92610
u = −1.113720 + 0.600652I
a = 0.089458 + 0.459286I
b = −1.125210 + 0.316433I
1.49604 + 6.86714I 0
u = −1.113720 − 0.600652I
a = 0.089458 − 0.459286I
b = −1.125210 − 0.316433I
1.49604 − 6.86714I 0
u = 1.125260 + 0.582666I
a = −0.046136 − 1.066780I
b = −0.504735 − 0.459395I
1.52970 − 5.20102I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.125260 − 0.582666I
a = −0.046136 + 1.066780I
b = −0.504735 + 0.459395I
1.52970 + 5.20102I 0
u = 0.356915 + 0.631268I
a = 1.53034 + 0.20503I
b = 1.09240 − 1.04252I
1.18596 + 3.26458I −1.45850 − 1.99046I
u = 0.356915 − 0.631268I
a = 1.53034 − 0.20503I
b = 1.09240 + 1.04252I
1.18596 − 3.26458I −1.45850 + 1.99046I
u = −0.392543 + 0.607402I
a = 2.18891 + 0.36222I
b = 1.47244 + 0.19125I
0.807086 − 0.669632I 8.89402 + 2.39156I
u = −0.392543 − 0.607402I
a = 2.18891 − 0.36222I
b = 1.47244 − 0.19125I
0.807086 + 0.669632I 8.89402 − 2.39156I
u = −1.144970 + 0.579395I
a = 0.80012 + 1.81003I
b = −1.64124 + 1.85982I
2.68875 + 12.72060I 0
u = −1.144970 − 0.579395I
a = 0.80012 − 1.81003I
b = −1.64124 − 1.85982I
2.68875 − 12.72060I 0
u = 0.451622 + 0.549105I
a = −0.816243 − 0.354677I
b = −0.570145 + 1.029060I
1.58137 − 1.99121I 0.23530 + 4.86768I
u = 0.451622 − 0.549105I
a = −0.816243 + 0.354677I
b = −0.570145 − 1.029060I
1.58137 + 1.99121I 0.23530 − 4.86768I
u = −1.143830 + 0.597208I
a = −0.33479 − 1.42337I
b = 1.46668 − 1.35519I
1.04273 + 7.89242I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.143830 − 0.597208I
a = −0.33479 + 1.42337I
b = 1.46668 + 1.35519I
1.04273 − 7.89242I 0
u = 1.253100 + 0.355708I
a = 0.867905 + 0.120534I
b = 0.477864 − 0.951677I
−1.49310 − 2.16005I 0
u = 1.253100 − 0.355708I
a = 0.867905 − 0.120534I
b = 0.477864 + 0.951677I
−1.49310 + 2.16005I 0
u = 1.118380 + 0.672325I
a = 0.01056 − 1.46218I
b = −1.57916 − 0.92809I
3.33228 − 9.78419I 0
u = 1.118380 − 0.672325I
a = 0.01056 + 1.46218I
b = −1.57916 + 0.92809I
3.33228 + 9.78419I 0
u = 1.155800 + 0.609147I
a = −0.52062 + 1.87681I
b = 1.80637 + 1.75057I
7.3617 − 19.0862I 0
u = 1.155800 − 0.609147I
a = −0.52062 − 1.87681I
b = 1.80637 − 1.75057I
7.3617 + 19.0862I 0
u = −1.258900 + 0.501380I
a = −0.700011 − 0.506248I
b = 0.260037 − 1.194030I
−0.46524 + 7.38731I 0
u = −1.258900 − 0.501380I
a = −0.700011 + 0.506248I
b = 0.260037 + 1.194030I
−0.46524 − 7.38731I 0
u = −0.390776 + 0.507703I
a = −1.45495 − 0.56596I
b = −0.284838 − 0.272662I
1.51459 − 0.44779I 6.65638 + 0.77042I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.390776 − 0.507703I
a = −1.45495 + 0.56596I
b = −0.284838 + 0.272662I
1.51459 + 0.44779I 6.65638 − 0.77042I
u = 0.022899 + 0.558695I
a = 1.077830 + 0.890973I
b = 0.824747 + 0.478628I
−1.49976 − 1.00247I −5.82785 + 2.83454I
u = 0.022899 − 0.558695I
a = 1.077830 − 0.890973I
b = 0.824747 − 0.478628I
−1.49976 + 1.00247I −5.82785 − 2.83454I
19
II.
I
u
2
= h4u
34
+7u
33
+· · ·+b−5, −3u
34
−2u
33
+· · ·+a+2, u
35
+2u
34
+· · ·−2u−1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
5
=
u
−u
3
+ u
a
9
=
3u
34
+ 2u
33
+ ··· − 5u − 2
−4u
34
− 7u
33
+ ··· − 2u + 5
a
8
=
5u
34
+ 5u
33
+ ··· − 6u − 4
−2u
34
− 5u
33
+ ··· − 3u + 4
a
4
=
−4u
34
+ 2u
33
+ ··· + 6u − 4
5u
34
+ 8u
33
+ ··· + 40u
2
− 7
a
12
=
−6u
34
− 12u
33
+ ··· + 6u + 13
−13u
34
− 13u
33
+ ··· + 14u + 7
a
10
=
9u
34
+ 13u
33
+ ··· − 7u − 12
−3u
33
− 4u
32
+ ··· − 7u + 1
a
11
=
−12u
34
− 18u
33
+ ··· + 13u + 19
−11u
34
− 13u
33
+ ··· + 11u + 8
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 3u
34
+ 20u
33
− 7u
32
− 160u
31
− 64u
30
+ 621u
29
+ 474u
28
− 1464u
27
− 1606u
26
+
2192u
25
+ 3499u
24
− 1803u
23
− 5407u
22
− 215u
21
+ 6133u
20
+ 3021u
19
− 5057u
18
−
5009u
17
+ 2688u
16
+ 5339u
15
− 207u
14
− 4379u
13
− 1374u
12
+ 2925u
11
+ 1734u
10
−
1546u
9
− 1271u
8
+ 573u
7
+ 656u
6
− 102u
5
− 254u
4
− 25u
3
+ 70u
2
+ 17u − 7
20
(iv) u-Polynomials at the component
21
Crossings u-Polynomials at each crossing
c
1
u
35
− 18u
34
+ ··· + 12u − 1
c
2
u
35
+ 2u
34
+ ··· − 2u − 1
c
3
u
35
− u
34
+ ··· + u + 1
c
4
u
35
− 3u
34
+ ··· − 5u + 1
c
5
u
35
− 2u
34
+ ··· − 2u + 1
c
6
u
35
− 6u
34
+ ··· − 4u + 1
c
7
u
35
+ 13u
34
+ ··· + 13u + 1
c
8
u
35
+ 3u
34
+ ··· − 5u − 1
c
9
u
35
− 6u
34
+ ··· + 6u − 1
c
10
u
35
+ u
34
+ ··· + u − 1
c
11
u
35
+ u
34
+ ··· + 2u − 1
c
12
u
35
+ 6u
34
+ ··· + 6u + 1
22
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
+ 2y
34
+ ··· − 8y −1
c
2
, c
5
y
35
− 18y
34
+ ··· + 12y −1
c
3
, c
10
y
35
+ 23y
34
+ ··· − 13y −1
c
4
, c
8
y
35
− 37y
34
+ ··· + 17y −1
c
6
y
35
+ 14y
34
+ ··· + 74y
2
− 1
c
7
y
35
− 9y
34
+ ··· + 29y −1
c
9
, c
12
y
35
+ 22y
34
+ ··· − 18y −1
c
11
y
35
− 5y
34
+ ··· − 34y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.449369 + 0.898502I
a = −1.110200 − 0.295377I
b = −0.896959 − 0.890229I
3.70649 − 3.34500I 2.74211 + 6.90028I
u = −0.449369 − 0.898502I
a = −1.110200 + 0.295377I
b = −0.896959 + 0.890229I
3.70649 + 3.34500I 2.74211 − 6.90028I
u = 1.010410 + 0.175150I
a = −0.238179 + 1.250430I
b = 0.626124 + 0.416942I
−1.75961 + 1.63791I −2.51606 − 1.84050I
u = 1.010410 − 0.175150I
a = −0.238179 − 1.250430I
b = 0.626124 − 0.416942I
−1.75961 − 1.63791I −2.51606 + 1.84050I
u = −0.192206 + 0.951147I
a = −0.219742 − 0.160230I
b = −0.074720 + 0.297541I
2.14913 − 1.40179I −4.53646 + 2.43995I
u = −0.192206 − 0.951147I
a = −0.219742 + 0.160230I
b = −0.074720 − 0.297541I
2.14913 + 1.40179I −4.53646 − 2.43995I
u = −1.014930 + 0.374470I
a = −1.29182 + 1.96382I
b = −2.64183 − 0.46406I
3.49468 − 1.38652I −3.72020 + 2.10391I
u = −1.014930 − 0.374470I
a = −1.29182 − 1.96382I
b = −2.64183 + 0.46406I
3.49468 + 1.38652I −3.72020 − 2.10391I
u = −0.996058 + 0.458165I
a = −0.103645 + 0.336403I
b = −1.95660 − 0.35708I
7.15053 + 1.30099I 2.08686 − 1.88043I
u = −0.996058 − 0.458165I
a = −0.103645 − 0.336403I
b = −1.95660 + 0.35708I
7.15053 − 1.30099I 2.08686 + 1.88043I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.006900 + 0.497557I
a = −0.223255 − 1.378620I
b = −0.057991 − 0.961392I
7.44041 − 4.56762I 2.73556 + 6.57357I
u = 1.006900 − 0.497557I
a = −0.223255 + 1.378620I
b = −0.057991 + 0.961392I
7.44041 + 4.56762I 2.73556 − 6.57357I
u = 0.544307 + 0.669422I
a = 2.39954 − 0.29392I
b = 1.32687 − 1.45521I
6.51161 + 2.95580I 7.14645 − 4.00467I
u = 0.544307 − 0.669422I
a = 2.39954 + 0.29392I
b = 1.32687 + 1.45521I
6.51161 − 2.95580I 7.14645 + 4.00467I
u = 1.088390 + 0.375965I
a = −0.083784 + 0.890656I
b = 1.46987 + 0.04042I
−2.98962 − 2.46227I −4.95258 + 4.56593I
u = 1.088390 − 0.375965I
a = −0.083784 − 0.890656I
b = 1.46987 − 0.04042I
−2.98962 + 2.46227I −4.95258 − 4.56593I
u = 0.639424 + 0.490668I
a = 1.82886 + 0.22400I
b = −0.076616 + 0.157585I
8.64821 + 0.48732I 6.29202 − 0.07140I
u = 0.639424 − 0.490668I
a = 1.82886 − 0.22400I
b = −0.076616 − 0.157585I
8.64821 − 0.48732I 6.29202 + 0.07140I
u = 1.059290 + 0.560379I
a = 0.56557 − 2.32838I
b = −2.05401 − 2.02252I
4.89620 − 7.75104I 1.45717 + 8.60266I
u = 1.059290 − 0.560379I
a = 0.56557 + 2.32838I
b = −2.05401 + 2.02252I
4.89620 + 7.75104I 1.45717 − 8.60266I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.090060 + 0.511998I
a = −0.02057 − 1.80947I
b = 1.30444 − 0.74848I
−2.02615 + 4.71468I −4.99057 − 3.42368I
u = −1.090060 − 0.511998I
a = −0.02057 + 1.80947I
b = 1.30444 + 0.74848I
−2.02615 − 4.71468I −4.99057 + 3.42368I
u = −0.683002 + 0.402288I
a = −0.568125 − 0.589675I
b = 1.41680 + 0.76512I
8.24806 + 2.36497I 5.11886 − 3.46260I
u = −0.683002 − 0.402288I
a = −0.568125 + 0.589675I
b = 1.41680 − 0.76512I
8.24806 − 2.36497I 5.11886 + 3.46260I
u = 1.177930 + 0.296852I
a = −0.301713 − 0.029308I
b = 0.506002 + 0.231271I
−2.63916 − 2.34984I −7.91591 + 2.86774I
u = 1.177930 − 0.296852I
a = −0.301713 + 0.029308I
b = 0.506002 − 0.231271I
−2.63916 + 2.34984I −7.91591 − 2.86774I
u = −0.741427 + 0.239127I
a = 0.39173 − 2.28162I
b = 1.78561 − 0.01141I
4.65599 + 4.15432I 0.53542 − 2.48270I
u = −0.741427 − 0.239127I
a = 0.39173 + 2.28162I
b = 1.78561 + 0.01141I
4.65599 − 4.15432I 0.53542 + 2.48270I
u = −1.136130 + 0.619981I
a = −0.200361 − 1.275210I
b = 1.51537 − 1.04651I
1.54325 + 8.92726I 1.19351 − 8.93789I
u = −1.136130 − 0.619981I
a = −0.200361 + 1.275210I
b = 1.51537 + 1.04651I
1.54325 − 8.92726I 1.19351 + 8.93789I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.220220 + 0.517846I
a = 0.170515 − 0.298998I
b = −0.0415555 − 0.0757451I
−1.13336 + 6.63370I −3.91761 − 3.85524I
u = −1.220220 − 0.517846I
a = 0.170515 + 0.298998I
b = −0.0415555 + 0.0757451I
−1.13336 − 6.63370I −3.91761 + 3.85524I
u = 0.646098
a = −0.0548820
b = −1.22335
−0.661557 6.22930
u = −0.326293 + 0.536744I
a = −1.96738 − 0.75045I
b = −1.039130 − 0.285726I
0.137208 − 0.387332I −2.37322 − 1.38221I
u = −0.326293 − 0.536744I
a = −1.96738 + 0.75045I
b = −1.039130 + 0.285726I
0.137208 + 0.387332I −2.37322 + 1.38221I
28
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
35
− 18u
34
+ ··· + 12u − 1)(u
143
+ 69u
142
+ ··· + 24038u + 2209)
c
2
(u
35
+ 2u
34
+ ··· − 2u − 1)(u
143
+ 3u
142
+ ··· + 110u + 47)
c
3
(u
35
− u
34
+ ··· + u + 1)(u
143
+ 2u
142
+ ··· + 22312u + 8024)
c
4
(u
35
− 3u
34
+ ··· − 5u + 1)
· (u
143
− 60u
141
+ ··· + 6466443u + 1229681)
c
5
(u
35
− 2u
34
+ ··· − 2u + 1)(u
143
+ 3u
142
+ ··· + 110u + 47)
c
6
(u
35
− 6u
34
+ ··· − 4u + 1)(u
143
+ 9u
142
+ ··· + 1198600u + 745279)
c
7
(u
35
+ 13u
34
+ ··· + 13u + 1)
· (u
143
+ 6u
142
+ ··· + 586376963u + 10200841)
c
8
(u
35
+ 3u
34
+ ··· − 5u − 1)
· (u
143
− 60u
141
+ ··· + 6466443u + 1229681)
c
9
(u
35
− 6u
34
+ ··· + 6u − 1)(u
143
− 7u
142
+ ··· − 220108u + 19079)
c
10
(u
35
+ u
34
+ ··· + u − 1)(u
143
+ 2u
142
+ ··· + 22312u + 8024)
c
11
(u
35
+ u
34
+ ··· + 2u − 1)(u
143
− 2u
142
+ ··· + 111690u + 3457)
c
12
(u
35
+ 6u
34
+ ··· + 6u + 1)(u
143
− 7u
142
+ ··· − 220108u + 19079)
29
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
35
+ 2y
34
+ ··· − 8y −1)
· (y
143
+ 15y
142
+ ··· − 116759262y −4879681)
c
2
, c
5
(y
35
− 18y
34
+ ··· + 12y −1)(y
143
− 69y
142
+ ··· + 24038y −2209)
c
3
, c
10
(y
35
+ 23y
34
+ ··· − 13y −1)
· (y
143
+ 100y
142
+ ··· − 1978348960y −64384576)
c
4
, c
8
(y
35
− 37y
34
+ ··· + 17y −1)
· (y
143
− 120y
142
+ ··· + 46027317196279y −1512115361761)
c
6
(y
35
+ 14y
34
+ ··· + 74y
2
− 1)
· (y
143
+ 39y
142
+ ··· − 20746243156102y −555440787841)
c
7
(y
35
− 9y
34
+ ··· + 29y −1)
· (y
143
− 64y
142
+ ··· + 259743448139619271y −104057157107281)
c
9
, c
12
(y
35
+ 22y
34
+ ··· − 18y −1)
· (y
143
+ 95y
142
+ ··· − 14790500680y −364008241)
c
11
(y
35
− 5y
34
+ ··· − 34y −1)
· (y
143
− 32y
142
+ ··· − 2418099900y −11950849)
30
