12n
0128
(K12n
0128
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 10 3 6 12 8 1 9
Solving Sequence
3,8 4,10
11 7 6 9 5 2 1 12
c
3
c
10
c
7
c
6
c
8
c
5
c
2
c
1
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.10179 × 10
326
u
84
+ 4.59940 × 10
326
u
83
+ ··· + 6.70794 × 10
327
b + 9.84549 × 10
328
,
− 1.92301 × 10
326
u
84
− 4.87952 × 10
326
u
83
+ ··· + 2.68317 × 10
328
a − 1.80541 × 10
329
,
u
85
+ 3u
84
+ ··· + 2560u − 512i
I
u
2
= hb
2
− 2bu − 3b + 8u + 13, a, u
2
+ u − 1i
I
v
1
= ha, −117084v
8
− 101146v
7
+ ··· + 178147b − 213819,
v
9
+ v
8
+ 12v
7
+ 7v
6
+ 37v
5
− v
4
+ 10v
2
+ 5v + 1i
* 3 irreducible components of dim
C
= 0, with total 98 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h1.10 × 10
326
u
84
+ 4.60 × 10
326
u
83
+ · · · + 6.71 × 10
327
b + 9.85 ×
10
328
, −1.92 × 10
326
u
84
− 4.88 × 10
326
u
83
+ · · · + 2.68 × 10
328
a − 1.81 ×
10
329
, u
85
+ 3u
84
+ · · · + 2560u − 512i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
10
=
0.00716693u
84
+ 0.0181856u
83
+ ··· − 41.0816u + 6.72864
−0.0164251u
84
− 0.0685666u
83
+ ··· + 14.1484u − 14.6774
a
11
=
0.00716693u
84
+ 0.0181856u
83
+ ··· − 41.0816u + 6.72864
−0.0173695u
84
− 0.0700008u
83
+ ··· + 26.3047u − 16.3747
a
7
=
u
u
a
6
=
0.0128640u
84
+ 0.0390675u
83
+ ··· − 60.0504u + 9.18109
0.0370542u
84
+ 0.136353u
83
+ ··· − 145.401u + 47.2282
a
9
=
−0.0104888u
84
− 0.0265281u
83
+ ··· + 86.9445u − 14.0203
0.00275780u
84
+ 0.00808818u
83
+ ··· + 16.3180u − 2.98126
a
5
=
0.00825383u
84
+ 0.0201646u
83
+ ··· − 65.1654u + 10.2484
−0.00335614u
84
− 0.00827244u
83
+ ··· + 37.7731u − 6.12557
a
2
=
0.00825383u
84
+ 0.0201646u
83
+ ··· − 65.1654u + 10.2484
0.00223501u
84
+ 0.00636347u
83
+ ··· − 21.7790u + 3.77196
a
1
=
0.0104888u
84
+ 0.0265281u
83
+ ··· − 86.9445u + 14.0203
0.00223501u
84
+ 0.00636347u
83
+ ··· − 21.7790u + 3.77196
a
12
=
−0.000908687u
84
− 0.00204367u
83
+ ··· − 16.4201u + 3.85488
−0.0185413u
84
− 0.0750717u
83
+ ··· − 7.29914u − 9.22684
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.381801u
84
+ 1.38285u
83
+ ··· − 1273.67u + 380.918
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
85
+ 38u
84
+ ··· − 213u + 1
c
2
, c
4
u
85
− 12u
84
+ ··· − u + 1
c
3
, c
7
u
85
− 3u
84
+ ··· + 2560u + 512
c
5
u
85
+ 3u
84
+ ··· + 112806u + 16279
c
6
u
85
− u
84
+ ··· + 28266u + 22877
c
8
u
85
− 4u
84
+ ··· − 5u + 1
c
9
, c
12
u
85
− 4u
84
+ ··· + 7u + 1
c
10
u
85
− 8u
84
+ ··· + 192u + 16
c
11
u
85
− 38u
84
+ ··· + 27u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
85
+ 30y
84
+ ··· + 27491y −1
c
2
, c
4
y
85
− 38y
84
+ ··· − 213y −1
c
3
, c
7
y
85
+ 51y
84
+ ··· − 3932160y −262144
c
5
y
85
− 81y
84
+ ··· + 5075593862y −265005841
c
6
y
85
− 57y
84
+ ··· − 21266860578y −523357129
c
8
y
85
− 22y
84
+ ··· + 31y −1
c
9
, c
12
y
85
+ 38y
84
+ ··· + 27y −1
c
10
y
85
+ 20y
84
+ ··· + 12160y −256
c
11
y
85
+ 22y
84
+ ··· + 1735y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.079250 + 0.084385I
a = 0.314607 − 0.642851I
b = −0.263280 + 0.005137I
−1.013250 + 0.170939I 0
u = 1.079250 − 0.084385I
a = 0.314607 + 0.642851I
b = −0.263280 − 0.005137I
−1.013250 − 0.170939I 0
u = −1.111280 + 0.071551I
a = 0.643580 − 0.926472I
b = 0.321561 − 0.222730I
3.33969 + 2.83227I 0
u = −1.111280 − 0.071551I
a = 0.643580 + 0.926472I
b = 0.321561 + 0.222730I
3.33969 − 2.83227I 0
u = −0.129045 + 1.113980I
a = 1.74054 − 0.17640I
b = 1.96919 − 0.18618I
0.094102 − 1.056740I 0
u = −0.129045 − 1.113980I
a = 1.74054 + 0.17640I
b = 1.96919 + 0.18618I
0.094102 + 1.056740I 0
u = −0.210154 + 1.114290I
a = −0.839901 − 0.413606I
b = −1.63994 − 1.01283I
−3.15620 + 2.51605I 0
u = −0.210154 − 1.114290I
a = −0.839901 + 0.413606I
b = −1.63994 + 1.01283I
−3.15620 − 2.51605I 0
u = 0.433540 + 1.050740I
a = 0.587198 + 0.587186I
b = 0.993744 + 0.855462I
0.982642 + 0.642938I 0
u = 0.433540 − 1.050740I
a = 0.587198 − 0.587186I
b = 0.993744 − 0.855462I
0.982642 − 0.642938I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.257695 + 1.109990I
a = −0.04586 − 1.76277I
b = 0.070299 − 0.881993I
−1.09681 + 2.37421I 0
u = −0.257695 − 1.109990I
a = −0.04586 + 1.76277I
b = 0.070299 + 0.881993I
−1.09681 − 2.37421I 0
u = 0.262541 + 1.168940I
a = −0.497533 + 0.412605I
b = −1.021630 − 0.852821I
2.10819 − 3.90878I 0
u = 0.262541 − 1.168940I
a = −0.497533 − 0.412605I
b = −1.021630 + 0.852821I
2.10819 + 3.90878I 0
u = 0.218930 + 1.186920I
a = 0.438793 + 0.422340I
b = 1.29909 − 1.31313I
2.18193 − 1.17088I 0
u = 0.218930 − 1.186920I
a = 0.438793 − 0.422340I
b = 1.29909 + 1.31313I
2.18193 + 1.17088I 0
u = −0.758522 + 0.188313I
a = 1.47819 − 0.47702I
b = 2.18056 + 0.45533I
−1.13123 − 4.17645I −11.8176 + 9.1818I
u = −0.758522 − 0.188313I
a = 1.47819 + 0.47702I
b = 2.18056 − 0.45533I
−1.13123 + 4.17645I −11.8176 − 9.1818I
u = −0.341078 + 1.170670I
a = −1.71012 − 0.11107I
b = −2.09658 − 0.30512I
−0.41725 + 6.01567I 0
u = −0.341078 − 1.170670I
a = −1.71012 + 0.11107I
b = −2.09658 + 0.30512I
−0.41725 − 6.01567I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.041071 + 1.235810I
a = 0.35122 + 1.48542I
b = 0.799108 + 0.646539I
3.32593 − 3.12666I 0
u = 0.041071 − 1.235810I
a = 0.35122 − 1.48542I
b = 0.799108 − 0.646539I
3.32593 + 3.12666I 0
u = −1.206060 + 0.339502I
a = −0.333951 − 0.966861I
b = 0.172479 − 0.075194I
−1.81678 − 5.27916I 0
u = −1.206060 − 0.339502I
a = −0.333951 + 0.966861I
b = 0.172479 + 0.075194I
−1.81678 + 5.27916I 0
u = −0.573407 + 0.367957I
a = 0.02490 − 1.59180I
b = 0.90204 − 1.21732I
−3.03530 − 2.32112I −18.2811 + 2.9821I
u = −0.573407 − 0.367957I
a = 0.02490 + 1.59180I
b = 0.90204 + 1.21732I
−3.03530 + 2.32112I −18.2811 − 2.9821I
u = 0.091692 + 1.317030I
a = 0.134568 − 0.539810I
b = 0.21801 + 1.72217I
3.52281 − 0.13174I 0
u = 0.091692 − 1.317030I
a = 0.134568 + 0.539810I
b = 0.21801 − 1.72217I
3.52281 + 0.13174I 0
u = −0.413209 + 1.277050I
a = −0.33458 + 1.53181I
b = −0.762037 + 0.868186I
2.39077 + 8.65291I 0
u = −0.413209 − 1.277050I
a = −0.33458 − 1.53181I
b = −0.762037 − 0.868186I
2.39077 − 8.65291I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.312068 + 1.307370I
a = −0.183364 − 0.488108I
b = −0.82725 + 1.90837I
3.08119 − 5.55867I 0
u = 0.312068 − 1.307370I
a = −0.183364 + 0.488108I
b = −0.82725 − 1.90837I
3.08119 + 5.55867I 0
u = −0.459021 + 0.459779I
a = −1.51990 − 0.28470I
b = −2.42465 − 1.18474I
−3.21369 + 0.63442I −17.2881 − 6.4476I
u = −0.459021 − 0.459779I
a = −1.51990 + 0.28470I
b = −2.42465 + 1.18474I
−3.21369 − 0.63442I −17.2881 + 6.4476I
u = 0.634951 + 0.073211I
a = 0.544294 − 0.378389I
b = −0.448469 + 0.000623I
−0.938890 − 0.000686I −9.17733 + 0.04419I
u = 0.634951 − 0.073211I
a = 0.544294 + 0.378389I
b = −0.448469 − 0.000623I
−0.938890 + 0.000686I −9.17733 − 0.04419I
u = 1.237320 + 0.581154I
a = −0.335451 − 0.582811I
b = −0.266329 − 0.154538I
1.88882 + 2.34511I 0
u = 1.237320 − 0.581154I
a = −0.335451 + 0.582811I
b = −0.266329 + 0.154538I
1.88882 − 2.34511I 0
u = −0.326856 + 1.339410I
a = 0.750171 − 0.025748I
b = 1.332330 − 0.310227I
4.34006 − 0.60753I 0
u = −0.326856 − 1.339410I
a = 0.750171 + 0.025748I
b = 1.332330 + 0.310227I
4.34006 + 0.60753I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.143186 + 1.381320I
a = 0.727087 + 0.371136I
b = 1.59812 + 0.81572I
−1.24862 + 7.38729I 0
u = −0.143186 − 1.381320I
a = 0.727087 − 0.371136I
b = 1.59812 − 0.81572I
−1.24862 − 7.38729I 0
u = 0.607638 + 0.026477I
a = 0.314965 − 0.062706I
b = 5.61070 + 1.95263I
−1.01649 + 2.08350I −108.2002 − 27.5787I
u = 0.607638 − 0.026477I
a = 0.314965 + 0.062706I
b = 5.61070 − 1.95263I
−1.01649 − 2.08350I −108.2002 + 27.5787I
u = 0.573976 + 0.144239I
a = −0.630973 + 0.039451I
b = −3.74818 − 1.33751I
−1.01583 − 1.80194I −34.3945 + 9.4437I
u = 0.573976 − 0.144239I
a = −0.630973 − 0.039451I
b = −3.74818 + 1.33751I
−1.01583 + 1.80194I −34.3945 − 9.4437I
u = 0.581059
a = 0.632960
b = −0.432804
−0.943887 −9.70520
u = 0.64849 + 1.26742I
a = −0.718497 + 0.104136I
b = −1.213270 + 0.001074I
2.43921 − 5.21595I 0
u = 0.64849 − 1.26742I
a = −0.718497 − 0.104136I
b = −1.213270 − 0.001074I
2.43921 + 5.21595I 0
u = −1.40213 + 0.33857I
a = 0.330302 + 0.857940I
b = −0.097754 − 0.133086I
0.33638 − 10.54090I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40213 − 0.33857I
a = 0.330302 − 0.857940I
b = −0.097754 + 0.133086I
0.33638 + 10.54090I 0
u = −0.056938 + 0.544127I
a = 0.47075 − 2.43754I
b = 0.0150861 − 0.0630346I
−5.59621 − 1.18326I −2.58478 − 2.54783I
u = −0.056938 − 0.544127I
a = 0.47075 + 2.43754I
b = 0.0150861 + 0.0630346I
−5.59621 + 1.18326I −2.58478 + 2.54783I
u = −0.188367 + 0.482280I
a = 0.01185 + 1.83477I
b = 0.515477 − 0.218779I
1.59907 − 2.42394I −1.69948 + 4.54557I
u = −0.188367 − 0.482280I
a = 0.01185 − 1.83477I
b = 0.515477 + 0.218779I
1.59907 + 2.42394I −1.69948 − 4.54557I
u = 0.014000 + 0.513349I
a = −0.98858 + 2.43038I
b = −0.0540751 + 0.0186456I
−4.86894 − 7.11123I 0.90699 + 6.44296I
u = 0.014000 − 0.513349I
a = −0.98858 − 2.43038I
b = −0.0540751 − 0.0186456I
−4.86894 + 7.11123I 0.90699 − 6.44296I
u = 1.49443 + 0.02360I
a = −0.263064 − 0.608348I
b = 0.056186 + 0.172181I
0.90720 − 4.33616I 0
u = 1.49443 − 0.02360I
a = −0.263064 + 0.608348I
b = 0.056186 − 0.172181I
0.90720 + 4.33616I 0
u = 0.47007 + 1.42149I
a = 1.025930 − 0.210323I
b = 1.94222 − 0.59005I
3.61530 − 5.88108I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.47007 − 1.42149I
a = 1.025930 + 0.210323I
b = 1.94222 + 0.59005I
3.61530 + 5.88108I 0
u = −0.129721 + 0.460651I
a = −0.94046 + 1.36587I
b = −2.80445 + 1.09956I
−2.08258 + 2.71217I −0.93392 − 9.03807I
u = −0.129721 − 0.460651I
a = −0.94046 − 1.36587I
b = −2.80445 − 1.09956I
−2.08258 − 2.71217I −0.93392 + 9.03807I
u = −0.69533 + 1.35551I
a = −1.115150 − 0.202740I
b = −2.11433 − 0.55269I
1.45650 + 12.12210I 0
u = −0.69533 − 1.35551I
a = −1.115150 + 0.202740I
b = −2.11433 + 0.55269I
1.45650 − 12.12210I 0
u = 0.20084 + 1.51437I
a = −1.083660 + 0.427485I
b = −1.88224 + 0.54463I
9.43138 − 2.34122I 0
u = 0.20084 − 1.51437I
a = −1.083660 − 0.427485I
b = −1.88224 − 0.54463I
9.43138 + 2.34122I 0
u = −0.51519 + 1.44160I
a = 1.189150 + 0.430508I
b = 2.06507 + 0.51343I
8.12807 + 8.74738I 0
u = −0.51519 − 1.44160I
a = 1.189150 − 0.430508I
b = 2.06507 − 0.51343I
8.12807 − 8.74738I 0
u = −0.67286 + 1.43031I
a = −0.721546 + 0.163020I
b = −1.261450 + 0.117391I
7.12915 + 3.60494I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.67286 − 1.43031I
a = −0.721546 − 0.163020I
b = −1.261450 − 0.117391I
7.12915 − 3.60494I 0
u = 0.83986 + 1.36381I
a = 0.709212 − 0.012362I
b = 1.255120 − 0.185897I
4.36978 − 10.04380I 0
u = 0.83986 − 1.36381I
a = 0.709212 + 0.012362I
b = 1.255120 + 0.185897I
4.36978 + 10.04380I 0
u = −0.76822 + 1.41143I
a = 1.028460 + 0.202507I
b = 2.16194 + 0.54337I
3.7759 + 18.1504I 0
u = −0.76822 − 1.41143I
a = 1.028460 − 0.202507I
b = 2.16194 − 0.54337I
3.7759 − 18.1504I 0
u = 0.56721 + 1.54481I
a = −0.932269 + 0.216487I
b = −1.99467 + 0.56349I
6.15588 − 11.53790I 0
u = 0.56721 − 1.54481I
a = −0.932269 − 0.216487I
b = −1.99467 − 0.56349I
6.15588 + 11.53790I 0
u = −1.64677 + 0.04569I
a = −0.075386 − 0.147225I
b = 0.0593377 + 0.1023010I
−8.84126 + 1.96210I 0
u = −1.64677 − 0.04569I
a = −0.075386 + 0.147225I
b = 0.0593377 − 0.1023010I
−8.84126 − 1.96210I 0
u = 0.49039 + 1.61919I
a = 0.600613 − 0.046493I
b = 1.53138 − 0.09575I
6.55517 − 3.11546I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.49039 − 1.61919I
a = 0.600613 + 0.046493I
b = 1.53138 + 0.09575I
6.55517 + 3.11546I 0
u = 0.225615 + 0.193490I
a = 1.41404 + 1.72695I
b = 0.573669 − 1.131970I
−0.60683 − 2.35987I −1.70647 + 4.72969I
u = 0.225615 − 0.193490I
a = 1.41404 − 1.72695I
b = 0.573669 + 1.131970I
−0.60683 + 2.35987I −1.70647 − 4.72969I
u = −0.22938 + 1.72989I
a = −0.626650 + 0.057918I
b = −1.50572 + 0.17267I
7.76106 − 3.97762I 0
u = −0.22938 − 1.72989I
a = −0.626650 − 0.057918I
b = −1.50572 − 0.17267I
7.76106 + 3.97762I 0
13
II. I
u
2
= hb
2
− 2bu − 3b + 8u + 13, a, u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u + 1
a
10
=
0
b
a
11
=
0
b
a
7
=
u
u
a
6
=
u
−bu − 2b + 6u + 8
a
9
=
−2u + 1
b − 3u − 2
a
5
=
u
u
a
2
=
u
u − 1
a
1
=
2u − 1
u − 1
a
12
=
−8bu + 5b
−5bu + 4b
(ii) Obstruction class = 1
(iii) Cusp Shapes = −92bu + 67b − 21u − 44
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− 3u + 1)
2
c
2
, c
3
(u
2
+ u − 1)
2
c
4
, c
7
(u
2
− u − 1)
2
c
5
, c
6
u
4
− 3u
3
+ 8u
2
− 3u + 1
c
8
(u
2
+ 3u + 1)
2
c
9
(u
2
− u + 1)
2
c
10
u
4
c
11
, c
12
(u
2
+ u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
2
− 7y + 1)
2
c
2
, c
3
, c
4
c
7
(y
2
− 3y + 1)
2
c
5
, c
6
y
4
+ 7y
3
+ 48y
2
+ 7y + 1
c
9
, c
11
, c
12
(y
2
+ y + 1)
2
c
10
y
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0
b = 2.11803 + 3.66854I
−0.98696 + 2.02988I −35.5000 + 37.2022I
u = 0.618034
a = 0
b = 2.11803 − 3.66854I
−0.98696 − 2.02988I −35.5000 − 37.2022I
u = −1.61803
a = 0
b = −0.118034 + 0.204441I
−8.88264 − 2.02988I −35.5000 + 44.1304I
u = −1.61803
a = 0
b = −0.118034 − 0.204441I
−8.88264 + 2.02988I −35.5000 − 44.1304I
17
III. I
v
1
= ha, −1.17 × 10
5
v
8
− 1.01 × 10
5
v
7
+ · · · + 1.78 × 10
5
b − 2.14 ×
10
5
, v
9
+ v
8
+ · · · + 5v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
10
=
0
0.657233v
8
+ 0.567767v
7
+ ··· + 9.16478v + 1.20024
a
11
=
0.0241374v
8
− 0.0627123v
7
+ ··· + 0.209905v − 0.0894654
0.657233v
8
+ 0.567767v
7
+ ··· + 9.16478v + 1.20024
a
7
=
v
0
a
6
=
v
0.275340v
8
− 0.0465346v
7
+ ··· + 1.55676v − 0.961481
a
9
=
0.177685v
8
+ 0.143932v
7
+ ··· + 2.33403v + 0.321875
−1
a
5
=
0.177685v
8
+ 0.143932v
7
+ ··· + 2.33403v + 0.321875
1
a
2
=
−0.177685v
8
− 0.143932v
7
+ ··· − 2.33403v + 0.678125
−1
a
1
=
−0.177685v
8
− 0.143932v
7
+ ··· − 2.33403v − 0.321875
−1
a
12
=
−0.0347129v
8
− 0.0223692v
7
+ ··· − 0.0767568v + 0.422617
0.355369v
8
+ 0.287863v
7
+ ··· + 4.66807v − 0.356251
(ii) Obstruction class = 1
(iii) Cusp Shapes =
423971
178147
v
8
+
364904
178147
v
7
+
4951441
178147
v
6
+
2188309
178147
v
5
+
14403862
178147
v
4
−
3007434
178147
v
3
−
2178758
178147
v
2
+
4762398
178147
v −
397589
178147
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
, c
11
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
8
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
9
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
10
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
12
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
9
c
3
, c
7
y
9
c
5
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1
c
6
, c
10
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1
c
8
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1
c
9
, c
12
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.508863 + 0.531649I
a = 0
b = −0.225230 + 1.238240I
0.13850 + 2.09337I −7.58955 − 5.46639I
v = 0.508863 − 0.531649I
a = 0
b = −0.225230 − 1.238240I
0.13850 − 2.09337I −7.58955 + 5.46639I
v = −0.465349
a = 0
b = −1.77487
−2.84338 −11.8180
v = −0.234017 + 0.220643I
a = 0
b = −1.25758 + 1.97504I
−2.26187 + 2.45442I −9.75362 + 6.63381I
v = −0.234017 − 0.220643I
a = 0
b = −1.25758 − 1.97504I
−2.26187 − 2.45442I −9.75362 − 6.63381I
v = −0.65490 + 2.25183I
a = 0
b = −0.300113 − 0.434032I
−6.01628 + 1.33617I −20.0794 − 3.5537I
v = −0.65490 − 2.25183I
a = 0
b = −0.300113 + 0.434032I
−6.01628 − 1.33617I −20.0794 + 3.5537I
v = 0.11273 + 2.63847I
a = 0
b = 0.170352 + 0.451655I
−5.24306 + 7.08493I −20.6685 − 5.3307I
v = 0.11273 − 2.63847I
a = 0
b = 0.170352 − 0.451655I
−5.24306 − 7.08493I −20.6685 + 5.3307I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
2
− 3u + 1)
2
(u
85
+ 38u
84
+ ··· − 213u + 1)
c
2
((u − 1)
9
)(u
2
+ u − 1)
2
(u
85
− 12u
84
+ ··· − u + 1)
c
3
u
9
(u
2
+ u − 1)
2
(u
85
− 3u
84
+ ··· + 2560u + 512)
c
4
((u + 1)
9
)(u
2
− u − 1)
2
(u
85
− 12u
84
+ ··· − u + 1)
c
5
(u
4
− 3u
3
+ 8u
2
− 3u + 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
85
+ 3u
84
+ ··· + 112806u + 16279)
c
6
(u
4
− 3u
3
+ 8u
2
− 3u + 1)(u
9
+ u
8
+ ··· − u − 1)
· (u
85
− u
84
+ ··· + 28266u + 22877)
c
7
u
9
(u
2
− u − 1)
2
(u
85
− 3u
84
+ ··· + 2560u + 512)
c
8
((u
2
+ 3u + 1)
2
)(u
9
+ 5u
8
+ ··· + u + 1)
· (u
85
− 4u
84
+ ··· − 5u + 1)
c
9
(u
2
− u + 1)
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
85
− 4u
84
+ ··· + 7u + 1)
c
10
u
4
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
85
− 8u
84
+ ··· + 192u + 16)
c
11
(u
2
+ u + 1)
2
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
85
− 38u
84
+ ··· + 27u + 1)
c
12
(u
2
+ u + 1)
2
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
85
− 4u
84
+ ··· + 7u + 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
2
− 7y + 1)
2
(y
85
+ 30y
84
+ ··· + 27491y − 1)
c
2
, c
4
((y − 1)
9
)(y
2
− 3y + 1)
2
(y
85
− 38y
84
+ ··· − 213y − 1)
c
3
, c
7
y
9
(y
2
− 3y + 1)
2
(y
85
+ 51y
84
+ ··· − 3932160y − 262144)
c
5
(y
4
+ 7y
3
+ 48y
2
+ 7y + 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
85
− 81y
84
+ ··· + 5075593862y − 265005841)
c
6
(y
4
+ 7y
3
+ 48y
2
+ 7y + 1)
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
85
− 57y
84
+ ··· − 21266860578y − 523357129)
c
8
(y
2
− 7y + 1)
2
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
85
− 22y
84
+ ··· + 31y − 1)
c
9
, c
12
(y
2
+ y + 1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
85
+ 38y
84
+ ··· + 27y − 1)
c
10
y
4
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
85
+ 20y
84
+ ··· + 12160y − 256)
c
11
((y
2
+ y + 1)
2
)(y
9
+ 7y
8
+ ··· + 13y − 1)
· (y
85
+ 22y
84
+ ··· + 1735y − 1)
23
