12n
0765
(K12n
0765
)
A knot diagram
1
Linearized knot diagam
4 7 9 8 12 3 11 1 3 5 7 10
Solving Sequence
3,7
2
6,12
5 11 8 4 1 10 9
c
2
c
6
c
5
c
11
c
7
c
4
c
1
c
10
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.60013 × 10
687
u
108
+ 5.32223 × 10
687
u
107
+ ··· + 1.17704 × 10
692
b − 5.63654 × 10
692
,
− 8.49812 × 10
693
u
108
+ 3.39185 × 10
694
u
107
+ ··· + 4.81217 × 10
697
a − 3.97557 × 10
699
,
u
109
− 4u
108
+ ··· + 727773u − 58405i
I
u
2
= h3.87954 × 10
45
u
40
− 3.63289 × 10
45
u
39
+ ··· + 7.89408 × 10
44
b + 9.18467 × 10
44
,
7.60703 × 10
44
u
40
+ 4.49925 × 10
45
u
39
+ ··· + 7.89408 × 10
44
a − 1.27861 × 10
46
, u
41
− u
40
+ ··· + 3u − 1i
* 2 irreducible components of dim
C
= 0, with total 150 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−1.60 × 10
687
u
108
+ 5.32 × 10
687
u
107
+ · · · + 1.18 × 10
692
b − 5.64 ×
10
692
, −8.50 × 10
693
u
108
+ 3.39 × 10
694
u
107
+ · · · + 4.81 × 10
697
a − 3.98 ×
10
699
, u
109
− 4u
108
+ · · · + 727773u − 58405i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
12
=
0.000176596u
108
− 0.000704848u
107
+ ··· − 536.559u + 82.6149
0.0000135945u
108
− 0.0000452169u
107
+ ··· − 24.5059u + 4.78872
a
5
=
0.00109313u
108
− 0.00409347u
107
+ ··· − 2133.44u + 244.622
0.000218812u
108
− 0.000804043u
107
+ ··· − 378.582u + 40.3302
a
11
=
0.000176596u
108
− 0.000704848u
107
+ ··· − 536.559u + 82.6149
0.0000211796u
108
− 0.0000731613u
107
+ ··· − 33.7006u + 4.69889
a
8
=
−0.00135482u
108
+ 0.00506301u
107
+ ··· + 2607.30u − 295.218
−0.000168745u
108
+ 0.000622795u
107
+ ··· + 293.699u − 29.7884
a
4
=
0.000223168u
108
− 0.000792062u
107
+ ··· − 244.124u + 12.4619
−0.000137835u
108
+ 0.000517495u
107
+ ··· + 286.997u − 36.5128
a
1
=
−0.00112968u
108
+ 0.00417253u
107
+ ··· + 1958.79u − 197.708
−0.000171027u
108
+ 0.000635449u
107
+ ··· + 296.271u − 28.3214
a
10
=
−0.000757974u
108
+ 0.00281956u
107
+ ··· + 1391.84u − 148.178
−0.000213592u
108
+ 0.000799611u
107
+ ··· + 408.288u − 45.4695
a
9
=
−0.000544383u
108
+ 0.00201995u
107
+ ··· + 983.548u − 102.709
−0.000213592u
108
+ 0.000799611u
107
+ ··· + 408.288u − 45.4695
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0000966670u
108
− 0.000299148u
107
+ ··· + 79.9719u − 45.9238
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
109
− 5u
108
+ ··· + 2849220u − 293753
c
2
, c
6
u
109
+ 4u
108
+ ··· + 727773u + 58405
c
3
, c
9
u
109
+ u
108
+ ··· + 18828u + 2079
c
4
u
109
+ 4u
108
+ ··· − 24796u + 1679
c
5
u
109
+ u
108
+ ··· − 1214779937u + 75810647
c
7
, c
11
u
109
+ 3u
108
+ ··· + 4565u + 4481
c
8
u
109
+ 2u
108
+ ··· − 13u + 1
c
10
u
109
+ u
108
+ ··· + 4838u + 2189
c
12
u
109
− 8u
108
+ ··· − 2468184u + 292253
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
109
− 33y
108
+ ··· + 7391217447958y −86290825009
c
2
, c
6
y
109
− 78y
108
+ ··· + 176189049349y −3411144025
c
3
, c
9
y
109
+ 93y
108
+ ··· − 38599578y −4322241
c
4
y
109
+ 22y
108
+ ··· + 390164552y −2819041
c
5
y
109
− 21y
108
+ ··· + 602106898292238931y −5747254198558609
c
7
, c
11
y
109
+ 61y
108
+ ··· − 397560707y −20079361
c
8
y
109
+ 14y
108
+ ··· + 9y −1
c
10
y
109
+ 45y
108
+ ··· − 112723288y −4791721
c
12
y
109
− 34y
108
+ ··· − 684202546700y −85411816009
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.937174 + 0.281919I
a = −0.230672 + 0.213488I
b = −1.49885 − 0.38451I
−4.58867 − 4.06930I 0
u = −0.937174 − 0.281919I
a = −0.230672 − 0.213488I
b = −1.49885 + 0.38451I
−4.58867 + 4.06930I 0
u = 1.080690 + 0.035625I
a = −0.263367 − 1.153200I
b = −1.52630 + 0.80230I
1.60982 − 2.70191I 0
u = 1.080690 − 0.035625I
a = −0.263367 + 1.153200I
b = −1.52630 − 0.80230I
1.60982 + 2.70191I 0
u = 0.409206 + 0.822293I
a = 1.220430 + 0.422812I
b = 0.725883 − 0.641836I
2.78846 − 3.45010I 0
u = 0.409206 − 0.822293I
a = 1.220430 − 0.422812I
b = 0.725883 + 0.641836I
2.78846 + 3.45010I 0
u = −0.253662 + 1.058760I
a = 0.751003 + 0.041761I
b = 1.181380 + 0.618099I
2.83743 + 3.68107I 0
u = −0.253662 − 1.058760I
a = 0.751003 − 0.041761I
b = 1.181380 − 0.618099I
2.83743 − 3.68107I 0
u = −1.134750 + 0.112447I
a = −1.061230 − 0.411871I
b = −1.71856 − 0.12374I
−3.71782 + 0.50102I 0
u = −1.134750 − 0.112447I
a = −1.061230 + 0.411871I
b = −1.71856 + 0.12374I
−3.71782 − 0.50102I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.165462 + 0.833409I
a = −0.255766 + 0.833211I
b = −0.640398 − 0.315196I
−4.30464 − 3.55844I 0
u = −0.165462 − 0.833409I
a = −0.255766 − 0.833211I
b = −0.640398 + 0.315196I
−4.30464 + 3.55844I 0
u = 0.015038 + 0.819293I
a = −0.017611 + 0.689819I
b = 0.794081 − 0.256196I
2.65946 − 2.53857I 0
u = 0.015038 − 0.819293I
a = −0.017611 − 0.689819I
b = 0.794081 + 0.256196I
2.65946 + 2.53857I 0
u = 1.218700 + 0.061079I
a = −0.327349 − 0.045298I
b = −0.971741 − 0.281094I
−2.01895 + 0.10579I 0
u = 1.218700 − 0.061079I
a = −0.327349 + 0.045298I
b = −0.971741 + 0.281094I
−2.01895 − 0.10579I 0
u = 1.192660 + 0.290351I
a = −0.282359 − 0.722232I
b = −1.47325 − 0.75659I
−0.360070 − 0.634714I 0
u = 1.192660 − 0.290351I
a = −0.282359 + 0.722232I
b = −1.47325 + 0.75659I
−0.360070 + 0.634714I 0
u = 1.175000 + 0.393607I
a = −1.397410 + 0.013308I
b = −1.93087 + 0.00761I
−7.33757 − 1.84736I 0
u = 1.175000 − 0.393607I
a = −1.397410 − 0.013308I
b = −1.93087 − 0.00761I
−7.33757 + 1.84736I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.189630 + 0.361967I
a = −0.424286 − 0.392824I
b = −1.384160 − 0.097087I
−1.73331 − 0.64522I 0
u = 1.189630 − 0.361967I
a = −0.424286 + 0.392824I
b = −1.384160 + 0.097087I
−1.73331 + 0.64522I 0
u = 0.156542 + 0.710487I
a = −1.84667 − 0.16232I
b = 0.0461817 − 0.1138670I
6.82913 − 5.20735I 7.39068 + 8.40503I
u = 0.156542 − 0.710487I
a = −1.84667 + 0.16232I
b = 0.0461817 + 0.1138670I
6.82913 + 5.20735I 7.39068 − 8.40503I
u = −0.524309 + 0.479493I
a = −1.04314 + 1.55348I
b = 0.389923 + 0.440071I
4.99089 + 1.89299I −3.93271 − 5.59425I
u = −0.524309 − 0.479493I
a = −1.04314 − 1.55348I
b = 0.389923 − 0.440071I
4.99089 − 1.89299I −3.93271 + 5.59425I
u = −0.674783 + 0.207559I
a = 1.02731 − 1.07769I
b = 0.43795 − 1.51100I
4.55542 + 0.50960I −3.96864 − 4.23818I
u = −0.674783 − 0.207559I
a = 1.02731 + 1.07769I
b = 0.43795 + 1.51100I
4.55542 − 0.50960I −3.96864 + 4.23818I
u = 0.406321 + 1.252440I
a = −0.405878 − 0.240420I
b = −0.391235 − 0.535451I
0.41060 − 2.38012I 0
u = 0.406321 − 1.252440I
a = −0.405878 + 0.240420I
b = −0.391235 + 0.535451I
0.41060 + 2.38012I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.337270 + 0.096420I
a = 0.780139 + 0.431312I
b = 1.57724 − 0.09865I
−1.87689 + 5.25392I 0
u = −1.337270 − 0.096420I
a = 0.780139 − 0.431312I
b = 1.57724 + 0.09865I
−1.87689 − 5.25392I 0
u = 1.189590 + 0.623116I
a = 0.718724 + 0.455567I
b = 1.408480 − 0.013907I
−1.82505 − 3.69562I 0
u = 1.189590 − 0.623116I
a = 0.718724 − 0.455567I
b = 1.408480 + 0.013907I
−1.82505 + 3.69562I 0
u = 1.341710 + 0.078743I
a = 0.156215 + 1.349690I
b = 0.344551 + 0.035975I
−0.22447 + 4.16339I 0
u = 1.341710 − 0.078743I
a = 0.156215 − 1.349690I
b = 0.344551 − 0.035975I
−0.22447 − 4.16339I 0
u = −1.278060 + 0.462387I
a = −0.762034 + 0.734670I
b = −1.66970 + 0.93674I
−0.48833 + 7.00109I 0
u = −1.278060 − 0.462387I
a = −0.762034 − 0.734670I
b = −1.66970 − 0.93674I
−0.48833 − 7.00109I 0
u = 0.352130 + 0.512930I
a = 0.724990 − 0.800184I
b = −0.109651 − 0.352445I
−1.54116 − 1.08486I −13.13256 + 3.91208I
u = 0.352130 − 0.512930I
a = 0.724990 + 0.800184I
b = −0.109651 + 0.352445I
−1.54116 + 1.08486I −13.13256 − 3.91208I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.357060 + 0.289480I
a = −0.542508 + 0.846957I
b = −1.52610 + 0.94254I
−0.66014 + 7.54621I 0
u = −1.357060 − 0.289480I
a = −0.542508 − 0.846957I
b = −1.52610 − 0.94254I
−0.66014 − 7.54621I 0
u = −1.376720 + 0.267957I
a = −0.845102 + 0.485644I
b = −1.77518 + 0.33114I
−6.44692 + 3.80582I 0
u = −1.376720 − 0.267957I
a = −0.845102 − 0.485644I
b = −1.77518 − 0.33114I
−6.44692 − 3.80582I 0
u = −0.559578 + 0.198192I
a = −1.22023 + 1.28236I
b = −0.35442 + 2.58430I
2.52276 + 7.95086I −9.5091 − 11.5695I
u = −0.559578 − 0.198192I
a = −1.22023 − 1.28236I
b = −0.35442 − 2.58430I
2.52276 − 7.95086I −9.5091 + 11.5695I
u = −1.398260 + 0.151811I
a = 0.496418 − 0.584354I
b = 1.67339 + 0.17878I
−7.33133 − 3.59033I 0
u = −1.398260 − 0.151811I
a = 0.496418 + 0.584354I
b = 1.67339 − 0.17878I
−7.33133 + 3.59033I 0
u = 0.452974 + 1.335320I
a = 0.644020 + 0.629180I
b = 0.369458 − 0.468319I
−2.07029 + 1.11942I 0
u = 0.452974 − 1.335320I
a = 0.644020 − 0.629180I
b = 0.369458 + 0.468319I
−2.07029 − 1.11942I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.187385 + 0.556680I
a = 1.83950 − 1.14234I
b = 0.098192 − 0.307884I
2.65011 − 2.82680I −3.87963 + 2.53461I
u = −0.187385 − 0.556680I
a = 1.83950 + 1.14234I
b = 0.098192 + 0.307884I
2.65011 + 2.82680I −3.87963 − 2.53461I
u = 1.42705 + 0.10899I
a = −0.692128 − 0.933953I
b = −1.32045 − 0.69634I
−4.12477 − 6.75342I 0
u = 1.42705 − 0.10899I
a = −0.692128 + 0.933953I
b = −1.32045 + 0.69634I
−4.12477 + 6.75342I 0
u = 0.21991 + 1.44095I
a = 0.661564 + 0.133231I
b = 0.646671 + 0.016763I
5.71970 − 3.02646I 0
u = 0.21991 − 1.44095I
a = 0.661564 − 0.133231I
b = 0.646671 − 0.016763I
5.71970 + 3.02646I 0
u = 0.514423 + 0.169978I
a = −0.93648 − 1.06633I
b = 1.04253 − 1.61461I
3.58991 − 2.77762I −8.20669 + 3.30808I
u = 0.514423 − 0.169978I
a = −0.93648 + 1.06633I
b = 1.04253 + 1.61461I
3.58991 + 2.77762I −8.20669 − 3.30808I
u = 0.524647 + 0.037159I
a = 0.75002 + 1.84238I
b = −0.77378 + 2.20253I
2.68546 + 4.66613I −10.91912 − 1.69700I
u = 0.524647 − 0.037159I
a = 0.75002 − 1.84238I
b = −0.77378 − 2.20253I
2.68546 − 4.66613I −10.91912 + 1.69700I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41447 + 0.57889I
a = −0.715649 + 0.423665I
b = −1.69115 + 0.21932I
−6.68545 + 4.08833I 0
u = −1.41447 − 0.57889I
a = −0.715649 − 0.423665I
b = −1.69115 − 0.21932I
−6.68545 − 4.08833I 0
u = −0.14362 + 1.52726I
a = −0.540609 + 0.275968I
b = −0.355021 − 0.067337I
5.37904 − 4.69106I 0
u = −0.14362 − 1.52726I
a = −0.540609 − 0.275968I
b = −0.355021 + 0.067337I
5.37904 + 4.69106I 0
u = 1.54337 + 0.10690I
a = 0.257980 − 0.420750I
b = 0.779436 − 0.674871I
−3.07896 + 0.61761I 0
u = 1.54337 − 0.10690I
a = 0.257980 + 0.420750I
b = 0.779436 + 0.674871I
−3.07896 − 0.61761I 0
u = 1.54678 + 0.17407I
a = −0.384794 − 0.630950I
b = −1.210880 − 0.658366I
−0.26332 − 3.09618I 0
u = 1.54678 − 0.17407I
a = −0.384794 + 0.630950I
b = −1.210880 + 0.658366I
−0.26332 + 3.09618I 0
u = −0.158026 + 0.411664I
a = 2.88876 − 1.73873I
b = 0.531342 − 0.090450I
3.79386 − 4.83112I −10.98344 − 3.75502I
u = −0.158026 − 0.411664I
a = 2.88876 + 1.73873I
b = 0.531342 + 0.090450I
3.79386 + 4.83112I −10.98344 + 3.75502I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55527 + 0.16816I
a = −0.039347 − 0.948769I
b = −0.619397 + 1.178490I
−1.01007 − 5.69221I 0
u = −1.55527 − 0.16816I
a = −0.039347 + 0.948769I
b = −0.619397 − 1.178490I
−1.01007 + 5.69221I 0
u = 1.50449 + 0.46131I
a = 0.837670 + 0.417346I
b = 1.381910 + 0.237508I
−4.44221 − 4.06401I 0
u = 1.50449 − 0.46131I
a = 0.837670 − 0.417346I
b = 1.381910 − 0.237508I
−4.44221 + 4.06401I 0
u = −1.56004 + 0.23230I
a = −0.297932 + 0.558155I
b = −1.75199 + 0.30606I
−2.53673 + 1.36112I 0
u = −1.56004 − 0.23230I
a = −0.297932 − 0.558155I
b = −1.75199 − 0.30606I
−2.53673 − 1.36112I 0
u = 0.240074 + 0.345112I
a = 1.052540 − 0.125492I
b = 0.070492 − 0.493744I
−0.626116 − 1.232790I −6.62259 + 5.91727I
u = 0.240074 − 0.345112I
a = 1.052540 + 0.125492I
b = 0.070492 + 0.493744I
−0.626116 + 1.232790I −6.62259 − 5.91727I
u = −1.34419 + 0.86246I
a = 0.655259 − 0.415772I
b = 1.55924 − 0.19368I
−6.71000 + 10.17030I 0
u = −1.34419 − 0.86246I
a = 0.655259 + 0.415772I
b = 1.55924 + 0.19368I
−6.71000 − 10.17030I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02650 + 1.61959I
a = 1.024640 + 0.051399I
b = 2.83396 − 0.11121I
8.60811 − 0.02263I 0
u = 0.02650 − 1.61959I
a = 1.024640 − 0.051399I
b = 2.83396 + 0.11121I
8.60811 + 0.02263I 0
u = 1.60260 + 0.25274I
a = 0.690712 + 0.500312I
b = 1.250740 + 0.400651I
−4.45307 − 3.43240I 0
u = 1.60260 − 0.25274I
a = 0.690712 − 0.500312I
b = 1.250740 − 0.400651I
−4.45307 + 3.43240I 0
u = −1.52862 + 0.55714I
a = 0.682849 − 0.548511I
b = 1.62599 − 0.77661I
0.40880 + 11.84720I 0
u = −1.52862 − 0.55714I
a = 0.682849 + 0.548511I
b = 1.62599 + 0.77661I
0.40880 − 11.84720I 0
u = −0.16632 + 1.64997I
a = 0.371395 − 0.651317I
b = 0.724073 + 0.233629I
−1.60563 + 3.51525I 0
u = −0.16632 − 1.64997I
a = 0.371395 + 0.651317I
b = 0.724073 − 0.233629I
−1.60563 − 3.51525I 0
u = −1.64937 + 0.24487I
a = 0.342808 − 0.482683I
b = 1.67047 − 0.94856I
−7.45412 + 7.78502I 0
u = −1.64937 − 0.24487I
a = 0.342808 + 0.482683I
b = 1.67047 + 0.94856I
−7.45412 − 7.78502I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.192331 + 0.257922I
a = −3.22086 + 2.57656I
b = 0.835655 + 0.453628I
5.10604 + 2.00514I −3.44801 − 3.01840I
u = −0.192331 − 0.257922I
a = −3.22086 − 2.57656I
b = 0.835655 − 0.453628I
5.10604 − 2.00514I −3.44801 + 3.01840I
u = 1.54884 + 0.65931I
a = −0.702735 + 0.464999I
b = −1.56186 − 0.00648I
−8.65737 − 2.38711I 0
u = 1.54884 − 0.65931I
a = −0.702735 − 0.464999I
b = −1.56186 + 0.00648I
−8.65737 + 2.38711I 0
u = 0.31698 + 1.69698I
a = −0.518531 − 0.525207I
b = −0.526791 + 0.332370I
−0.46974 + 9.78880I 0
u = 0.31698 − 1.69698I
a = −0.518531 + 0.525207I
b = −0.526791 − 0.332370I
−0.46974 − 9.78880I 0
u = 1.67469 + 0.46506I
a = 0.740759 − 0.394277I
b = 1.64371 + 0.07659I
−8.13625 − 11.03410I 0
u = 1.67469 − 0.46506I
a = 0.740759 + 0.394277I
b = 1.64371 − 0.07659I
−8.13625 + 11.03410I 0
u = 0.252973 + 0.053072I
a = −2.07790 − 4.87814I
b = −0.772144 − 0.958751I
0.72540 − 6.49284I −6.93254 + 7.11638I
u = 0.252973 − 0.053072I
a = −2.07790 + 4.87814I
b = −0.772144 + 0.958751I
0.72540 + 6.49284I −6.93254 − 7.11638I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.236794
a = 1.90834
b = −0.406406
−0.955408 −10.5310
u = −1.70591 + 0.46834I
a = 0.274191 + 0.360493I
b = 0.969681 − 0.017552I
−8.72743 + 5.60952I 0
u = −1.70591 − 0.46834I
a = 0.274191 − 0.360493I
b = 0.969681 + 0.017552I
−8.72743 − 5.60952I 0
u = 1.58847 + 0.80392I
a = 0.727013 + 0.503810I
b = 1.90148 + 0.64698I
−4.6720 − 18.5303I 0
u = 1.58847 − 0.80392I
a = 0.727013 − 0.503810I
b = 1.90148 − 0.64698I
−4.6720 + 18.5303I 0
u = −1.75426 + 0.35934I
a = −0.449424 − 0.417568I
b = −1.223950 + 0.020180I
−7.99572 − 2.03072I 0
u = −1.75426 − 0.35934I
a = −0.449424 + 0.417568I
b = −1.223950 − 0.020180I
−7.99572 + 2.03072I 0
u = 1.52646 + 0.93747I
a = −0.740401 − 0.450761I
b = −2.03301 − 0.61294I
−5.01553 − 9.59640I 0
u = 1.52646 − 0.93747I
a = −0.740401 + 0.450761I
b = −2.03301 + 0.61294I
−5.01553 + 9.59640I 0
15
II.
I
u
2
= h3.88 × 10
45
u
40
− 3.63 × 10
45
u
39
+ · · · + 7.89 × 10
44
b + 9.18 × 10
44
, 7.61 ×
10
44
u
40
+4.50×10
45
u
39
+· · ·+7.89×10
44
a−1.28×10
46
, u
41
−u
40
+· · ·+3u−1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
6
=
u
u
a
12
=
−0.963638u
40
− 5.69953u
39
+ ··· − 47.6261u + 16.1970
−4.91449u
40
+ 4.60205u
39
+ ··· + 26.1838u − 1.16349
a
5
=
1.45903u
40
− 3.10444u
39
+ ··· + 0.824206u − 0.104529
−3.37747u
40
+ 7.97212u
39
+ ··· + 46.6810u − 9.22936
a
11
=
−0.963638u
40
− 5.69953u
39
+ ··· − 47.6261u + 16.1970
−3.07723u
40
+ 1.99962u
39
+ ··· + 7.15791u + 5.49968
a
8
=
−2.79964u
40
+ 0.292739u
39
+ ··· − 18.5778u + 8.56998
−1.33740u
40
− 3.25771u
39
+ ··· − 22.4747u + 10.9724
a
4
=
7.39024u
40
− 2.43442u
39
+ ··· − 23.7614u − 7.20263
3.04037u
40
− 2.00109u
39
+ ··· − 8.36037u − 1.63507
a
1
=
−7.74379u
40
+ 10.3606u
39
+ ··· + 86.0634u − 11.3041
−5.69972u
40
+ 4.66512u
39
+ ··· + 11.7382u + 2.98439
a
10
=
−3.43297u
40
+ 6.78505u
39
+ ··· + 84.6331u − 26.3385
−1.15792u
40
+ 2.15953u
39
+ ··· + 11.1019u − 4.10949
a
9
=
−2.27505u
40
+ 4.62552u
39
+ ··· + 73.5312u − 22.2290
−1.15792u
40
+ 2.15953u
39
+ ··· + 11.1019u − 4.10949
(ii) Obstruction class = 1
(iii) Cusp Shapes = 38.1705u
40
− 33.2461u
39
+ ··· − 204.854u + 26.2450
16
(iv) u-Polynomials at the component
17
Crossings u-Polynomials at each crossing
c
1
u
41
− 10u
40
+ ··· + 118u − 13
c
2
u
41
− u
40
+ ··· + 3u − 1
c
3
u
41
+ 18u
39
+ ··· + 2u + 1
c
4
u
41
+ u
40
+ ··· − 30u − 9
c
5
u
41
+ 2u
40
+ ··· − 553u + 13
c
6
u
41
+ u
40
+ ··· + 3u + 1
c
7
u
41
+ 16u
39
+ ··· + 19u − 1
c
8
u
41
+ u
40
+ ··· − u − 1
c
9
u
41
+ 18u
39
+ ··· + 2u − 1
c
10
u
41
+ 12u
39
+ ··· + 4u − 1
c
11
u
41
+ 16u
39
+ ··· + 19u + 1
c
12
u
41
+ 3u
40
+ ··· + 2u + 1
18
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
− 10y
40
+ ··· + 3992y −169
c
2
, c
6
y
41
− 11y
40
+ ··· − 25y −1
c
3
, c
9
y
41
+ 36y
40
+ ··· − 36y −1
c
4
y
41
+ 17y
40
+ ··· − 1350y −81
c
5
y
41
+ 26y
40
+ ··· + 207061y −169
c
7
, c
11
y
41
+ 32y
40
+ ··· + 367y −1
c
8
y
41
+ 17y
40
+ ··· − 61y −1
c
10
y
41
+ 24y
40
+ ··· + 30y −1
c
12
y
41
− 3y
40
+ ··· − 14y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.018770 + 0.273603I
a = −0.531827 + 0.282873I
b = −1.65401 − 0.33244I
−4.73831 − 3.65726I −14.3052 − 3.9976I
u = −1.018770 − 0.273603I
a = −0.531827 − 0.282873I
b = −1.65401 + 0.33244I
−4.73831 + 3.65726I −14.3052 + 3.9976I
u = 1.07262
a = −0.441864
b = −0.414925
−2.66003 −19.0360
u = 1.09310
a = −1.03995
b = −1.64492
−3.49678 −5.52960
u = 0.875847 + 0.009781I
a = −0.27389 + 1.45395I
b = −1.088790 − 0.714685I
1.10985 + 2.84514I −13.6513 − 5.1889I
u = 0.875847 − 0.009781I
a = −0.27389 − 1.45395I
b = −1.088790 + 0.714685I
1.10985 − 2.84514I −13.6513 + 5.1889I
u = −0.066359 + 0.822836I
a = 0.062341 − 0.523898I
b = 1.060000 + 0.366974I
1.79164 + 2.92000I −11.34534 − 3.30442I
u = −0.066359 − 0.822836I
a = 0.062341 + 0.523898I
b = 1.060000 − 0.366974I
1.79164 − 2.92000I −11.34534 + 3.30442I
u = 0.287765 + 1.144540I
a = −0.944097 − 0.316620I
b = −0.221375 − 0.091725I
6.51650 − 2.92377I 3.23608 + 2.14669I
u = 0.287765 − 1.144540I
a = −0.944097 + 0.316620I
b = −0.221375 + 0.091725I
6.51650 + 2.92377I 3.23608 − 2.14669I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.276323 + 0.729259I
a = 1.320410 + 0.193163I
b = 1.37896 − 1.20843I
4.68320 − 2.97373I 0.72625 + 3.16578I
u = 0.276323 − 0.729259I
a = 1.320410 − 0.193163I
b = 1.37896 + 1.20843I
4.68320 + 2.97373I 0.72625 − 3.16578I
u = −1.221200 + 0.290564I
a = −0.649091 + 0.933414I
b = −1.56944 + 1.10034I
−1.19088 + 7.69652I −14.7806 − 10.7388I
u = −1.221200 − 0.290564I
a = −0.649091 − 0.933414I
b = −1.56944 − 1.10034I
−1.19088 − 7.69652I −14.7806 + 10.7388I
u = 0.386051 + 1.232040I
a = 0.080133 + 0.565919I
b = 0.339887 − 0.004680I
−0.53270 − 2.02999I 0
u = 0.386051 − 1.232040I
a = 0.080133 − 0.565919I
b = 0.339887 + 0.004680I
−0.53270 + 2.02999I 0
u = 1.291470 + 0.233731I
a = −0.254460 − 0.667173I
b = −1.43067 − 0.61212I
0.116287 − 0.794905I 0
u = 1.291470 − 0.233731I
a = −0.254460 + 0.667173I
b = −1.43067 + 0.61212I
0.116287 + 0.794905I 0
u = −1.250030 + 0.436722I
a = −1.243060 − 0.145871I
b = −1.89550 + 0.02285I
−7.29483 + 2.16952I 0
u = −1.250030 − 0.436722I
a = −1.243060 + 0.145871I
b = −1.89550 − 0.02285I
−7.29483 − 2.16952I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.430664 + 0.477805I
a = −1.13123 − 1.46052I
b = 0.945759 − 0.984755I
5.21589 − 0.96720I −2.18305 − 1.69740I
u = 0.430664 − 0.477805I
a = −1.13123 + 1.46052I
b = 0.945759 + 0.984755I
5.21589 + 0.96720I −2.18305 + 1.69740I
u = 1.38770
a = −0.0376824
b = 0.406956
−2.79189 0
u = 0.132832 + 0.593293I
a = −2.38555 − 0.17586I
b = −0.592730 − 0.088052I
3.94008 − 5.18269I −2.5559 + 15.8852I
u = 0.132832 − 0.593293I
a = −2.38555 + 0.17586I
b = −0.592730 + 0.088052I
3.94008 + 5.18269I −2.5559 − 15.8852I
u = 0.124887 + 1.406320I
a = 0.636403 − 0.062341I
b = 0.574077 − 0.243199I
5.30956 − 4.02270I 0
u = 0.124887 − 1.406320I
a = 0.636403 + 0.062341I
b = 0.574077 + 0.243199I
5.30956 + 4.02270I 0
u = −1.44696 + 0.19780I
a = −0.046410 − 1.102740I
b = −0.396514 + 0.477298I
−1.66380 − 5.14150I 0
u = −1.44696 − 0.19780I
a = −0.046410 + 1.102740I
b = −0.396514 − 0.477298I
−1.66380 + 5.14150I 0
u = 0.095993 + 0.523173I
a = 1.89251 + 0.85596I
b = −0.31760 + 2.18859I
3.11653 + 7.41408I −1.51475 − 5.02418I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.095993 − 0.523173I
a = 1.89251 − 0.85596I
b = −0.31760 − 2.18859I
3.11653 − 7.41408I −1.51475 + 5.02418I
u = −0.145778 + 0.504069I
a = −2.01654 + 1.18157I
b = −0.64656 + 1.93617I
3.38482 + 4.81560I 0.12248 − 4.76400I
u = −0.145778 − 0.504069I
a = −2.01654 − 1.18157I
b = −0.64656 − 1.93617I
3.38482 − 4.81560I 0.12248 + 4.76400I
u = 1.52761 + 0.38577I
a = −0.818580 − 0.459920I
b = −1.375120 − 0.306811I
−4.53549 − 3.88093I 0
u = 1.52761 − 0.38577I
a = −0.818580 + 0.459920I
b = −1.375120 + 0.306811I
−4.53549 + 3.88093I 0
u = −0.127963 + 0.397242I
a = −3.30560 + 0.63125I
b = 0.447621 + 0.203727I
6.42926 + 5.04167I −10.32758 − 1.16283I
u = −0.127963 − 0.397242I
a = −3.30560 − 0.63125I
b = 0.447621 − 0.203727I
6.42926 − 5.04167I −10.32758 + 1.16283I
u = −1.58375 + 0.36940I
a = 0.354076 − 0.245773I
b = 1.45639 − 0.58261I
−7.66062 + 6.86079I 0
u = −1.58375 − 0.36940I
a = 0.354076 + 0.245773I
b = 1.45639 + 0.58261I
−7.66062 − 6.86079I 0
u = 0.15465 + 1.64026I
a = 1.014210 + 0.054440I
b = 2.81204 + 0.13437I
8.57164 + 0.46776I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.15465 − 1.64026I
a = 1.014210 − 0.054440I
b = 2.81204 − 0.13437I
8.57164 − 0.46776I 0
25
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
41
− 10u
40
+ ··· + 118u − 13)
· (u
109
− 5u
108
+ ··· + 2849220u − 293753)
c
2
(u
41
− u
40
+ ··· + 3u − 1)(u
109
+ 4u
108
+ ··· + 727773u + 58405)
c
3
(u
41
+ 18u
39
+ ··· + 2u + 1)(u
109
+ u
108
+ ··· + 18828u + 2079)
c
4
(u
41
+ u
40
+ ··· − 30u − 9)(u
109
+ 4u
108
+ ··· − 24796u + 1679)
c
5
(u
41
+ 2u
40
+ ··· − 553u + 13)
· (u
109
+ u
108
+ ··· − 1214779937u + 75810647)
c
6
(u
41
+ u
40
+ ··· + 3u + 1)(u
109
+ 4u
108
+ ··· + 727773u + 58405)
c
7
(u
41
+ 16u
39
+ ··· + 19u − 1)(u
109
+ 3u
108
+ ··· + 4565u + 4481)
c
8
(u
41
+ u
40
+ ··· − u − 1)(u
109
+ 2u
108
+ ··· − 13u + 1)
c
9
(u
41
+ 18u
39
+ ··· + 2u − 1)(u
109
+ u
108
+ ··· + 18828u + 2079)
c
10
(u
41
+ 12u
39
+ ··· + 4u − 1)(u
109
+ u
108
+ ··· + 4838u + 2189)
c
11
(u
41
+ 16u
39
+ ··· + 19u + 1)(u
109
+ 3u
108
+ ··· + 4565u + 4481)
c
12
(u
41
+ 3u
40
+ ··· + 2u + 1)(u
109
− 8u
108
+ ··· − 2468184u + 292253)
26
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
41
− 10y
40
+ ··· + 3992y −169)
· (y
109
− 33y
108
+ ··· + 7391217447958y −86290825009)
c
2
, c
6
(y
41
− 11y
40
+ ··· − 25y −1)
· (y
109
− 78y
108
+ ··· + 176189049349y −3411144025)
c
3
, c
9
(y
41
+ 36y
40
+ ··· − 36y −1)
· (y
109
+ 93y
108
+ ··· − 38599578y −4322241)
c
4
(y
41
+ 17y
40
+ ··· − 1350y −81)
· (y
109
+ 22y
108
+ ··· + 390164552y −2819041)
c
5
(y
41
+ 26y
40
+ ··· + 207061y −169)
· (y
109
− 21y
108
+ ··· + 602106898292238931y −5747254198558609)
c
7
, c
11
(y
41
+ 32y
40
+ ··· + 367y −1)
· (y
109
+ 61y
108
+ ··· − 397560707y −20079361)
c
8
(y
41
+ 17y
40
+ ··· − 61y −1)(y
109
+ 14y
108
+ ··· + 9y −1)
c
10
(y
41
+ 24y
40
+ ··· + 30y −1)
· (y
109
+ 45y
108
+ ··· − 112723288y −4791721)
c
12
(y
41
− 3y
40
+ ··· − 14y −1)
· (y
109
− 34y
108
+ ··· − 684202546700y −85411816009)
27
