12n
0757
(K12n
0757
)
A knot diagram
1
Linearized knot diagam
4 5 8 11 3 10 1 3 12 5 7 9
Solving Sequence
3,9
8
1,4
7 12 10 6 5 2 11
c
8
c
3
c
7
c
12
c
9
c
6
c
5
c
2
c
11
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.59036 × 10
313
u
84
+ 4.77989 × 10
312
u
83
+ ··· + 6.91107 × 10
314
b + 1.33907 × 10
316
,
− 9.31472 × 10
316
u
84
+ 5.83485 × 10
316
u
83
+ ··· + 8.06522 × 10
317
a + 1.67212 × 10
320
,
u
85
+ 27u
83
+ ··· + 4868u + 1167i
I
u
2
= h−14825031610u
27
+ 18537500123u
26
+ ··· + 6921637191b + 5273642732,
305534977593367u
27
− 790948509790679u
26
+ ··· + 30157573241187a − 1297710378699701,
u
28
− u
27
+ ··· − u + 1i
I
u
3
= hb − u, a + u − 1, u
2
− u + 1i
I
u
4
= hb − u, a + u, u
2
− u + 1i
* 4 irreducible components of dim
C
= 0, with total 117 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−1.59 × 10
313
u
84
+ 4.78 × 10
312
u
83
+ · · · + 6.91 × 10
314
b + 1.34 ×
10
316
, −9.31 × 10
316
u
84
+ 5.83 × 10
316
u
83
+ · · · + 8.07 × 10
317
a + 1.67 ×
10
320
, u
85
+ 27u
83
+ · · · + 4868u + 1167i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
0.115492u
84
− 0.0723458u
83
+ ··· − 355.666u − 207.324
0.0230118u
84
− 0.00691628u
83
+ ··· − 20.4097u − 19.3757
a
4
=
u
u
3
+ u
a
7
=
−0.110696u
84
+ 0.130681u
83
+ ··· + 956.188u + 362.084
0.0473216u
84
+ 0.0461518u
83
+ ··· + 828.691u + 175.587
a
12
=
0.138504u
84
− 0.0792621u
83
+ ··· − 376.076u − 226.700
0.0230118u
84
− 0.00691628u
83
+ ··· − 20.4097u − 19.3757
a
10
=
−0.0884816u
84
− 0.0814471u
83
+ ··· − 1489.39u − 309.371
−0.0199738u
84
− 0.0308531u
83
+ ··· − 502.451u − 116.544
a
6
=
0.0801281u
84
+ 0.0399526u
83
+ ··· + 844.648u + 163.284
0.0667657u
84
− 0.00303016u
83
+ ··· + 340.400u + 24.5255
a
5
=
0.0801281u
84
+ 0.0399526u
83
+ ··· + 844.648u + 163.284
0.0299497u
84
− 0.0114804u
83
+ ··· + 52.4010u − 22.0992
a
2
=
0.102164u
84
− 0.0583120u
83
+ ··· − 240.005u − 161.556
0.0117585u
84
+ 0.00232467u
83
+ ··· + 42.4888u + 10.0149
a
11
=
−0.00514215u
84
+ 0.0946688u
83
+ ··· + 1138.04u + 304.529
0.0345003u
84
+ 0.0325184u
83
+ ··· + 586.871u + 114.297
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.274096u
84
− 0.0366470u
83
+ ··· − 1775.76u − 145.097
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
85
− 5u
84
+ ··· − 783263u − 43963
c
2
, c
5
u
85
+ 4u
84
+ ··· + 6399682u + 378351
c
3
, c
8
u
85
+ 27u
83
+ ··· + 4868u + 1167
c
4
, c
10
u
85
− 2u
84
+ ··· − 32u + 3
c
6
u
85
+ 11u
84
+ ··· − 284299729u + 28854207
c
7
u
85
− 6u
83
+ ··· − 4044u + 332
c
9
, c
12
u
85
+ 25u
83
+ ··· − 226u + 111
c
11
u
85
− u
84
+ ··· − 107u + 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
85
− 71y
84
+ ··· + 1109768547995y −1932745369
c
2
, c
5
y
85
+ 72y
84
+ ··· + 23176806835342y −143149479201
c
3
, c
8
y
85
+ 54y
84
+ ··· − 53028158y −1361889
c
4
, c
10
y
85
+ 24y
84
+ ··· − 356y −9
c
6
y
85
− 49y
84
+ ··· + 24664681049291167y −832565261598849
c
7
y
85
− 12y
84
+ ··· + 8779024y −110224
c
9
, c
12
y
85
+ 50y
84
+ ··· − 318554y −12321
c
11
y
85
+ 5y
84
+ ··· − 31181y −2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.365366 + 0.920085I
a = 1.28702 + 0.96017I
b = −0.282747 + 0.799096I
0.646862 − 0.894793I 0
u = 0.365366 − 0.920085I
a = 1.28702 − 0.96017I
b = −0.282747 − 0.799096I
0.646862 + 0.894793I 0
u = 0.069267 + 0.986380I
a = −1.81713 − 0.02982I
b = 1.341330 − 0.442065I
0.965648 + 0.188556I 0
u = 0.069267 − 0.986380I
a = −1.81713 + 0.02982I
b = 1.341330 + 0.442065I
0.965648 − 0.188556I 0
u = −0.378590 + 0.871699I
a = 0.170281 − 0.692301I
b = −0.745974 + 0.566971I
−2.12817 + 0.68447I 0
u = −0.378590 − 0.871699I
a = 0.170281 + 0.692301I
b = −0.745974 − 0.566971I
−2.12817 − 0.68447I 0
u = 0.493819 + 0.784435I
a = −0.706323 − 0.663700I
b = 0.544809 + 0.424971I
−0.12800 + 1.91048I 0
u = 0.493819 − 0.784435I
a = −0.706323 + 0.663700I
b = 0.544809 − 0.424971I
−0.12800 − 1.91048I 0
u = −1.033160 + 0.310486I
a = 0.025290 − 0.798856I
b = 0.612443 − 0.384276I
−3.89476 − 5.62843I 0
u = −1.033160 − 0.310486I
a = 0.025290 + 0.798856I
b = 0.612443 + 0.384276I
−3.89476 + 5.62843I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.114713 + 1.085940I
a = −0.043507 + 0.622927I
b = 0.13074 − 1.89360I
−1.59278 − 4.11572I 0
u = −0.114713 − 1.085940I
a = −0.043507 − 0.622927I
b = 0.13074 + 1.89360I
−1.59278 + 4.11572I 0
u = 1.005930 + 0.438338I
a = −0.310192 + 0.283012I
b = 0.278082 + 1.100300I
3.76571 − 0.51672I 0
u = 1.005930 − 0.438338I
a = −0.310192 − 0.283012I
b = 0.278082 − 1.100300I
3.76571 + 0.51672I 0
u = −0.501285 + 0.690430I
a = 1.51071 − 1.24410I
b = −0.572297 − 0.943715I
−1.08169 − 4.30528I 0
u = −0.501285 − 0.690430I
a = 1.51071 + 1.24410I
b = −0.572297 + 0.943715I
−1.08169 + 4.30528I 0
u = 0.543325 + 1.010130I
a = −1.64092 − 0.54557I
b = 0.256299 − 0.878934I
−0.04758 + 4.80218I 0
u = 0.543325 − 1.010130I
a = −1.64092 + 0.54557I
b = 0.256299 + 0.878934I
−0.04758 − 4.80218I 0
u = 0.045240 + 1.153380I
a = 1.40411 − 0.37311I
b = −0.472662 − 1.183120I
−4.84255 + 0.02543I 0
u = 0.045240 − 1.153380I
a = 1.40411 + 0.37311I
b = −0.472662 + 1.183120I
−4.84255 − 0.02543I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.353058 + 1.107940I
a = 1.74143 + 0.17963I
b = −1.09518 − 1.44123I
−3.35900 − 6.17617I 0
u = −0.353058 − 1.107940I
a = 1.74143 − 0.17963I
b = −1.09518 + 1.44123I
−3.35900 + 6.17617I 0
u = −0.028829 + 1.189170I
a = 0.777609 − 0.632382I
b = −0.649162 + 0.964464I
−1.95596 + 1.77445I 0
u = −0.028829 − 1.189170I
a = 0.777609 + 0.632382I
b = −0.649162 − 0.964464I
−1.95596 − 1.77445I 0
u = −0.541519 + 1.071560I
a = 2.03935 − 0.00109I
b = −0.443030 − 1.266400I
1.33677 − 7.91613I 0
u = −0.541519 − 1.071560I
a = 2.03935 + 0.00109I
b = −0.443030 + 1.266400I
1.33677 + 7.91613I 0
u = −0.677576 + 0.401202I
a = 0.107097 + 0.653212I
b = −0.287795 + 1.297880I
3.26531 + 3.22906I 0
u = −0.677576 − 0.401202I
a = 0.107097 − 0.653212I
b = −0.287795 − 1.297880I
3.26531 − 3.22906I 0
u = −0.534381 + 1.094250I
a = 1.193530 − 0.604330I
b = −0.847656 − 0.422881I
−3.43230 − 3.81045I 0
u = −0.534381 − 1.094250I
a = 1.193530 + 0.604330I
b = −0.847656 + 0.422881I
−3.43230 + 3.81045I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.148250 + 1.246730I
a = −1.46205 − 0.62108I
b = 0.397250 − 1.143730I
−5.66100 + 6.25301I 0
u = 0.148250 − 1.246730I
a = −1.46205 + 0.62108I
b = 0.397250 + 1.143730I
−5.66100 − 6.25301I 0
u = 0.168747 + 1.299570I
a = −1.160460 − 0.095231I
b = 0.621537 + 0.513207I
−2.41906 + 3.14939I 0
u = 0.168747 − 1.299570I
a = −1.160460 + 0.095231I
b = 0.621537 − 0.513207I
−2.41906 − 3.14939I 0
u = −0.127946 + 1.305470I
a = 1.01457 + 0.98940I
b = −0.355180 − 0.973680I
1.33477 − 3.68069I 0
u = −0.127946 − 1.305470I
a = 1.01457 − 0.98940I
b = −0.355180 + 0.973680I
1.33477 + 3.68069I 0
u = 0.742301 + 1.091100I
a = −1.65448 − 0.11863I
b = 0.574713 − 1.106020I
1.76789 + 6.80173I 0
u = 0.742301 − 1.091100I
a = −1.65448 + 0.11863I
b = 0.574713 + 1.106020I
1.76789 − 6.80173I 0
u = −0.177771 + 0.654829I
a = −1.54211 − 2.08388I
b = 0.280543 + 1.172630I
−0.28924 + 2.83636I −2.71243 + 0.48181I
u = −0.177771 − 0.654829I
a = −1.54211 + 2.08388I
b = 0.280543 − 1.172630I
−0.28924 − 2.83636I −2.71243 − 0.48181I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.135020 + 0.718752I
a = −0.256916 − 0.429627I
b = −0.433761 − 0.655056I
−3.14807 − 1.00103I 0
u = 1.135020 − 0.718752I
a = −0.256916 + 0.429627I
b = −0.433761 + 0.655056I
−3.14807 + 1.00103I 0
u = −0.333758 + 1.301710I
a = −1.125210 − 0.453522I
b = 0.660119 + 1.227750I
3.88771 − 6.40116I 0
u = −0.333758 − 1.301710I
a = −1.125210 + 0.453522I
b = 0.660119 − 1.227750I
3.88771 + 6.40116I 0
u = 1.357640 + 0.182554I
a = −0.318137 + 0.366712I
b = 0.240823 + 0.895859I
4.05362 − 1.09150I 0
u = 1.357640 − 0.182554I
a = −0.318137 − 0.366712I
b = 0.240823 − 0.895859I
4.05362 + 1.09150I 0
u = 0.101485 + 0.614941I
a = −0.51389 − 2.78335I
b = −0.384229 + 0.574149I
−2.99772 + 0.49314I −10.20779 − 0.54757I
u = 0.101485 − 0.614941I
a = −0.51389 + 2.78335I
b = −0.384229 − 0.574149I
−2.99772 − 0.49314I −10.20779 + 0.54757I
u = −0.043621 + 0.608805I
a = −0.337990 + 0.982054I
b = −0.158002 + 1.375520I
4.25302 + 3.14758I −13.3582 − 6.4211I
u = −0.043621 − 0.608805I
a = −0.337990 − 0.982054I
b = −0.158002 − 1.375520I
4.25302 − 3.14758I −13.3582 + 6.4211I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.083490 + 0.574146I
a = 3.28146 − 3.09096I
b = 0.139490 + 0.602255I
−2.83373 − 5.57072I −9.83182 + 3.03437I
u = −0.083490 − 0.574146I
a = 3.28146 + 3.09096I
b = 0.139490 − 0.602255I
−2.83373 + 5.57072I −9.83182 − 3.03437I
u = 0.24843 + 1.41104I
a = 1.201970 + 0.193297I
b = −1.311850 − 0.332674I
−10.03120 + 2.76694I 0
u = 0.24843 − 1.41104I
a = 1.201970 − 0.193297I
b = −1.311850 + 0.332674I
−10.03120 − 2.76694I 0
u = −1.42356 + 0.20208I
a = −0.157691 − 0.245300I
b = 0.541627 − 1.092830I
−1.82116 + 10.24000I 0
u = −1.42356 − 0.20208I
a = −0.157691 + 0.245300I
b = 0.541627 + 1.092830I
−1.82116 − 10.24000I 0
u = −0.43993 + 1.38434I
a = −1.127230 + 0.341272I
b = 1.278150 − 0.291752I
−9.01735 − 10.63490I 0
u = −0.43993 − 1.38434I
a = −1.127230 − 0.341272I
b = 1.278150 + 0.291752I
−9.01735 + 10.63490I 0
u = 1.46492 + 0.00723I
a = 0.100561 + 0.306556I
b = −0.484657 + 0.984843I
−2.04812 + 2.89700I 0
u = 1.46492 − 0.00723I
a = 0.100561 − 0.306556I
b = −0.484657 − 0.984843I
−2.04812 − 2.89700I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.348648 + 0.367582I
a = −1.90907 − 1.02160I
b = −0.458537 + 1.167530I
−1.08052 + 3.03153I −4.19529 − 6.98712I
u = −0.348648 − 0.367582I
a = −1.90907 + 1.02160I
b = −0.458537 − 1.167530I
−1.08052 − 3.03153I −4.19529 + 6.98712I
u = −0.450720
a = −0.0844993
b = −0.597318
−1.01434 −9.80070
u = 0.434220 + 0.100177I
a = −1.42778 − 0.53080I
b = 0.458829 − 0.425755I
1.81943 + 1.47313I 2.23841 − 5.05567I
u = 0.434220 − 0.100177I
a = −1.42778 + 0.53080I
b = 0.458829 + 0.425755I
1.81943 − 1.47313I 2.23841 + 5.05567I
u = 0.48637 + 1.49061I
a = −1.218430 + 0.238886I
b = 0.531464 − 1.038740I
−0.84154 + 7.69049I 0
u = 0.48637 − 1.49061I
a = −1.218430 − 0.238886I
b = 0.531464 + 1.038740I
−0.84154 − 7.69049I 0
u = 0.08112 + 1.57336I
a = −0.159001 − 1.055490I
b = 0.081345 + 0.516147I
−8.24646 + 3.36594I 0
u = 0.08112 − 1.57336I
a = −0.159001 + 1.055490I
b = 0.081345 − 0.516147I
−8.24646 − 3.36594I 0
u = −0.69079 + 1.42046I
a = −1.335130 + 0.029753I
b = 0.70729 + 1.31503I
−5.7735 − 17.5282I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.69079 − 1.42046I
a = −1.335130 − 0.029753I
b = 0.70729 − 1.31503I
−5.7735 + 17.5282I 0
u = 0.34818 + 1.54269I
a = 0.602664 − 0.112346I
b = −0.672908 − 0.149542I
−8.25680 + 4.07430I 0
u = 0.34818 − 1.54269I
a = 0.602664 + 0.112346I
b = −0.672908 + 0.149542I
−8.25680 − 4.07430I 0
u = 0.57420 + 1.47874I
a = 1.222600 − 0.079987I
b = −0.73659 + 1.29574I
−6.97944 + 9.81769I 0
u = 0.57420 − 1.47874I
a = 1.222600 + 0.079987I
b = −0.73659 − 1.29574I
−6.97944 − 9.81769I 0
u = −1.59091 + 0.16862I
a = 0.128237 − 0.245162I
b = 0.166901 − 0.946580I
9.22842 + 0.69070I 0
u = −1.59091 − 0.16862I
a = 0.128237 + 0.245162I
b = 0.166901 + 0.946580I
9.22842 − 0.69070I 0
u = −0.69996 + 1.44725I
a = −0.860669 + 0.298264I
b = 0.565060 + 1.060420I
−7.15592 − 1.23427I 0
u = −0.69996 − 1.44725I
a = −0.860669 − 0.298264I
b = 0.565060 − 1.060420I
−7.15592 + 1.23427I 0
u = 0.82426 + 1.38827I
a = 0.882873 + 0.248570I
b = −0.533007 + 1.170240I
−5.40898 + 8.75488I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.82426 − 1.38827I
a = 0.882873 − 0.248570I
b = −0.533007 − 1.170240I
−5.40898 − 8.75488I 0
u = −0.085056 + 0.336008I
a = −0.56056 + 1.33121I
b = 0.25862 − 1.46830I
8.09208 + 4.40093I 12.3851 − 9.4173I
u = −0.085056 − 0.336008I
a = −0.56056 − 1.33121I
b = 0.25862 + 1.46830I
8.09208 − 4.40093I 12.3851 + 9.4173I
u = −0.20418 + 1.71330I
a = −0.487948 + 0.042312I
b = 0.556415 − 0.423879I
−8.99209 + 3.35535I 0
u = −0.20418 − 1.71330I
a = −0.487948 − 0.042312I
b = 0.556415 + 0.423879I
−8.99209 − 3.35535I 0
13
II.
I
u
2
= h−1.48 × 10
10
u
27
+ 1.85 × 10
10
u
26
+ · · · + 6.92 × 10
9
b + 5.27 × 10
9
, 3.06 ×
10
14
u
27
−7.91×10
14
u
26
+· · ·+3.02×10
13
a−1.30×10
15
, u
28
−u
27
+· · ·−u+1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
1
=
−10.1313u
27
+ 26.2272u
26
+ ··· − 73.0464u + 43.0310
2.14184u
27
− 2.67820u
26
+ ··· + 7.64335u − 0.761907
a
4
=
u
u
3
+ u
a
7
=
−15.5591u
27
+ 3.96166u
26
+ ··· − 13.7516u − 28.8358
−14.2009u
27
+ 16.9863u
26
+ ··· − 40.4383u + 0.727670
a
12
=
−7.98945u
27
+ 23.5490u
26
+ ··· − 65.4030u + 42.2691
2.14184u
27
− 2.67820u
26
+ ··· + 7.64335u − 0.761907
a
10
=
41.4725u
27
− 39.0584u
26
+ ··· + 93.9212u + 17.8821
−2.81965u
27
− 0.703457u
26
+ ··· + 2.08339u − 6.66495
a
6
=
−16.3340u
27
+ 14.6107u
26
+ ··· − 34.9812u − 14.2498
−2.88685u
27
+ 25.9054u
26
+ ··· − 87.0963u + 49.7467
a
5
=
−16.3340u
27
+ 14.6107u
26
+ ··· − 34.9812u − 14.2498
2.37034u
27
+ 20.0121u
26
+ ··· − 72.4857u + 51.4700
a
2
=
−6.62994u
27
+ 18.3565u
26
+ ··· − 52.7997u + 32.1923
4.27994u
27
− 7.24008u
26
+ ··· + 20.0194u − 7.23132
a
11
=
16.4780u
27
− 9.58480u
26
+ ··· + 30.2298u + 18.3185
−9.23901u
27
− 3.57653u
26
+ ··· + 48.8854u − 44.8137
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
180804181519969
1436074916247
u
27
−
227368293507968
1436074916247
u
26
+ ··· +
399031079592181
1436074916247
u −
17801125744790
1436074916247
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
28
− 11u
27
+ ··· + 33u + 7
c
2
u
28
+ u
27
+ ··· − u + 1
c
3
u
28
+ u
27
+ ··· + u + 1
c
4
u
28
− u
27
+ ··· − u + 1
c
5
u
28
− u
27
+ ··· + u + 1
c
6
u
28
− 3u
27
+ ··· − 259u + 49
c
7
u
28
+ 3u
26
+ ··· + 53u
2
+ 48
c
8
u
28
− u
27
+ ··· − u + 1
c
9
u
28
+ u
27
+ ··· + 5u + 1
c
10
u
28
+ u
27
+ ··· + u + 1
c
11
u
28
− 2u
27
+ ··· − 5u + 1
c
12
u
28
− u
27
+ ··· − 5u + 1
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
− 19y
27
+ ··· + 2369y + 49
c
2
, c
5
y
28
+ 5y
27
+ ··· − 13y + 1
c
3
, c
8
y
28
+ 11y
27
+ ··· + 23y + 1
c
4
, c
10
y
28
+ 21y
27
+ ··· + 33y + 1
c
6
y
28
− 13y
27
+ ··· − 63063y + 2401
c
7
y
28
+ 6y
27
+ ··· + 5088y + 2304
c
9
, c
12
y
28
+ 23y
27
+ ··· + 19y + 1
c
11
y
28
+ 12y
27
+ ··· + 5y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.237894 + 0.956664I
a = 1.62413 − 0.61086I
b = −1.348680 + 0.253251I
1.17000 − 0.96284I 2.75739 + 5.45614I
u = −0.237894 − 0.956664I
a = 1.62413 + 0.61086I
b = −1.348680 − 0.253251I
1.17000 + 0.96284I 2.75739 − 5.45614I
u = −0.075270 + 0.920982I
a = 1.46046 + 0.61112I
b = −0.154790 − 0.165445I
0.10200 − 1.96445I −3.39434 + 3.81435I
u = −0.075270 − 0.920982I
a = 1.46046 − 0.61112I
b = −0.154790 + 0.165445I
0.10200 + 1.96445I −3.39434 − 3.81435I
u = 0.767899 + 0.489005I
a = 0.28195 − 1.49523I
b = 0.288649 − 0.938440I
−1.76432 + 0.94657I −3.08016 − 1.47243I
u = 0.767899 − 0.489005I
a = 0.28195 + 1.49523I
b = 0.288649 + 0.938440I
−1.76432 − 0.94657I −3.08016 + 1.47243I
u = 0.345981 + 1.078720I
a = −1.29799 − 0.58885I
b = 0.464033 + 0.523133I
−1.11821 + 3.08885I −3.90201 − 4.91311I
u = 0.345981 − 1.078720I
a = −1.29799 + 0.58885I
b = 0.464033 − 0.523133I
−1.11821 − 3.08885I −3.90201 + 4.91311I
u = 0.361782 + 1.161100I
a = −1.44305 − 0.02533I
b = 0.83558 − 1.28549I
−3.30691 + 5.70672I −6.21178 − 1.53244I
u = 0.361782 − 1.161100I
a = −1.44305 + 0.02533I
b = 0.83558 + 1.28549I
−3.30691 − 5.70672I −6.21178 + 1.53244I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.460734 + 0.557400I
a = 1.67016 − 3.00711I
b = −0.283700 − 0.830897I
−2.40630 − 6.12716I −2.90922 + 11.28305I
u = −0.460734 − 0.557400I
a = 1.67016 + 3.00711I
b = −0.283700 + 0.830897I
−2.40630 + 6.12716I −2.90922 − 11.28305I
u = 1.283280 + 0.227081I
a = −0.422310 + 0.369260I
b = 0.241891 + 0.958455I
4.34526 − 0.97725I 15.3469 + 0.I
u = 1.283280 − 0.227081I
a = −0.422310 − 0.369260I
b = 0.241891 − 0.958455I
4.34526 + 0.97725I 15.3469 + 0.I
u = −0.499201 + 1.214250I
a = 1.39941 + 0.31082I
b = −0.583152 − 1.238720I
4.75725 − 7.02891I 1.79878 + 6.91651I
u = −0.499201 − 1.214250I
a = 1.39941 − 0.31082I
b = −0.583152 + 1.238720I
4.75725 + 7.02891I 1.79878 − 6.91651I
u = 0.616251 + 1.161350I
a = −1.77881 + 0.02178I
b = 0.500258 − 1.145780I
1.08473 + 7.05378I −5.34427 − 7.49870I
u = 0.616251 − 1.161350I
a = −1.77881 − 0.02178I
b = 0.500258 + 1.145780I
1.08473 − 7.05378I −5.34427 + 7.49870I
u = −0.121598 + 0.618770I
a = 0.363385 − 0.311626I
b = −0.28392 + 1.51928I
7.80044 + 4.25334I −9.98560 + 1.63731I
u = −0.121598 − 0.618770I
a = 0.363385 + 0.311626I
b = −0.28392 − 1.51928I
7.80044 − 4.25334I −9.98560 − 1.63731I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.060992 + 0.612880I
a = 0.79439 − 2.52484I
b = −0.15044 + 1.57854I
0.00703 − 3.49133I 2.69813 + 10.38411I
u = −0.060992 − 0.612880I
a = 0.79439 + 2.52484I
b = −0.15044 − 1.57854I
0.00703 + 3.49133I 2.69813 − 10.38411I
u = 0.132401 + 0.495278I
a = 0.05605 + 1.75947I
b = 0.175425 + 1.332670I
4.54210 − 3.04662I 11.87871 − 1.91283I
u = 0.132401 − 0.495278I
a = 0.05605 − 1.75947I
b = 0.175425 − 1.332670I
4.54210 + 3.04662I 11.87871 + 1.91283I
u = −1.60870 + 0.24907I
a = −0.047493 + 0.236281I
b = −0.220934 + 0.958878I
9.18806 + 0.90073I 0. − 20.1489I
u = −1.60870 − 0.24907I
a = −0.047493 − 0.236281I
b = −0.220934 − 0.958878I
9.18806 − 0.90073I 0. + 20.1489I
u = 0.05679 + 1.65897I
a = −0.160288 − 0.878952I
b = 0.019782 + 0.634182I
−7.95181 + 3.45202I 0
u = 0.05679 − 1.65897I
a = −0.160288 + 0.878952I
b = 0.019782 − 0.634182I
−7.95181 − 3.45202I 0
21
III. I
u
3
= hb − u, a + u − 1, u
2
− u + 1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
8
=
1
u − 1
a
1
=
−u + 1
u
a
4
=
u
u − 1
a
7
=
1
u − 1
a
12
=
1
u
a
10
=
u + 1
u − 1
a
6
=
−u
0
a
5
=
−u
1
a
2
=
1
2u − 1
a
11
=
2
2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u − 8
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u − 1)
2
c
2
, c
3
, c
4
c
12
u
2
+ u + 1
c
5
, c
8
, c
9
c
10
u
2
− u + 1
c
7
u
2
c
11
(u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
11
(y −1)
2
c
2
, c
3
, c
4
c
5
, c
8
, c
9
c
10
, c
12
y
2
+ y + 1
c
7
y
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 0.500000 + 0.866025I
−1.64493 − 2.02988I −6.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = 0.500000 − 0.866025I
−1.64493 + 2.02988I −6.00000 − 3.46410I
25
IV. I
u
4
= hb − u, a + u, u
2
− u + 1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
8
=
1
u − 1
a
1
=
−u
u
a
4
=
u
u − 1
a
7
=
0
u
a
12
=
0
u
a
10
=
1
u − 1
a
6
=
u
u − 1
a
5
=
u
u − 2
a
2
=
1
3u − 1
a
11
=
0
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u + 2
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
+ 3u + 3
c
2
, c
4
, c
5
c
7
, c
10
u
2
+ u + 1
c
3
, c
6
, c
8
c
9
, c
12
u
2
− u + 1
c
11
u
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
− 3y + 9
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
12
y
2
+ y + 1
c
11
y
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = 0.500000 + 0.866025I
2.02988I 0. − 3.46410I
u = 0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = 0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
29
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
2
+ 3u + 3)(u
28
− 11u
27
+ ··· + 33u + 7)
· (u
85
− 5u
84
+ ··· − 783263u − 43963)
c
2
((u
2
+ u + 1)
2
)(u
28
+ u
27
+ ··· − u + 1)
· (u
85
+ 4u
84
+ ··· + 6399682u + 378351)
c
3
(u
2
− u + 1)(u
2
+ u + 1)(u
28
+ u
27
+ ··· + u + 1)
· (u
85
+ 27u
83
+ ··· + 4868u + 1167)
c
4
((u
2
+ u + 1)
2
)(u
28
− u
27
+ ··· − u + 1)(u
85
− 2u
84
+ ··· − 32u + 3)
c
5
(u
2
− u + 1)(u
2
+ u + 1)(u
28
− u
27
+ ··· + u + 1)
· (u
85
+ 4u
84
+ ··· + 6399682u + 378351)
c
6
((u − 1)
2
)(u
2
− u + 1)(u
28
− 3u
27
+ ··· − 259u + 49)
· (u
85
+ 11u
84
+ ··· − 284299729u + 28854207)
c
7
u
2
(u
2
+ u + 1)(u
28
+ 3u
26
+ ··· + 53u
2
+ 48)
· (u
85
− 6u
83
+ ··· − 4044u + 332)
c
8
((u
2
− u + 1)
2
)(u
28
− u
27
+ ··· − u + 1)
· (u
85
+ 27u
83
+ ··· + 4868u + 1167)
c
9
((u
2
− u + 1)
2
)(u
28
+ u
27
+ ··· + 5u + 1)
· (u
85
+ 25u
83
+ ··· − 226u + 111)
c
10
(u
2
− u + 1)(u
2
+ u + 1)(u
28
+ u
27
+ ··· + u + 1)
· (u
85
− 2u
84
+ ··· − 32u + 3)
c
11
u
2
(u + 1)
2
(u
28
− 2u
27
+ ··· − 5u + 1)(u
85
− u
84
+ ··· − 107u + 49)
c
12
(u
2
− u + 1)(u
2
+ u + 1)(u
28
− u
27
+ ··· − 5u + 1)
· (u
85
+ 25u
83
+ ··· − 226u + 111)
30
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
2
)(y
2
− 3y + 9)(y
28
− 19y
27
+ ··· + 2369y + 49)
· (y
85
− 71y
84
+ ··· + 1109768547995y −1932745369)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
28
+ 5y
27
+ ··· − 13y + 1)
· (y
85
+ 72y
84
+ ··· + 23176806835342y −143149479201)
c
3
, c
8
((y
2
+ y + 1)
2
)(y
28
+ 11y
27
+ ··· + 23y + 1)
· (y
85
+ 54y
84
+ ··· − 53028158y −1361889)
c
4
, c
10
((y
2
+ y + 1)
2
)(y
28
+ 21y
27
+ ··· + 33y + 1)
· (y
85
+ 24y
84
+ ··· − 356y −9)
c
6
((y −1)
2
)(y
2
+ y + 1)(y
28
− 13y
27
+ ··· − 63063y + 2401)
· (y
85
− 49y
84
+ ··· + 24664681049291167y −832565261598849)
c
7
y
2
(y
2
+ y + 1)(y
28
+ 6y
27
+ ··· + 5088y + 2304)
· (y
85
− 12y
84
+ ··· + 8779024y −110224)
c
9
, c
12
((y
2
+ y + 1)
2
)(y
28
+ 23y
27
+ ··· + 19y + 1)
· (y
85
+ 50y
84
+ ··· − 318554y −12321)
c
11
y
2
(y −1)
2
(y
28
+ 12y
27
+ ··· + 5y + 1)
· (y
85
+ 5y
84
+ ··· − 31181y −2401)
31
