12a
0020
(K12a
0020
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 10 11 1 4 12 8 7
Solving Sequence
7,11
8 12 1
4,9
5 10 6 3 2
c
7
c
11
c
12
c
8
c
4
c
10
c
6
c
3
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h10u
107
+ 12u
106
+ ··· + 2b + 3u, −2u
107
+ 4u
106
+ ··· + 2a + 5, u
108
+ 3u
107
+ ··· + 2u + 1i
I
u
2
= h−u
5
a + 2u
3
a − 2au + b, u
4
a + u
5
− u
4
− u
2
a − u
3
+ a
2
+ au + u
2
− u, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 120 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
= h10u
107
+ 12u
106
+ · · · + 2b + 3u, −2u
107
+ 4u
106
+ · · · + 2a +
5, u
108
+ 3u
107
+ · · · + 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
12
=
u
−u
3
+ u
a
1
=
u
3
−u
3
+ u
a
4
=
u
107
− 2u
106
+ ··· − 2u −
5
2
−5u
107
− 6u
106
+ ··· − 2u
2
−
3
2
u
a
9
=
u
8
− u
6
+ u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
5
=
u
107
+ 3u
106
+ ··· − u
2
+
1
2
−u
107
− 3u
106
+ ··· −
1
2
u − 1
a
10
=
−u
3
u
5
− u
3
+ u
a
6
=
u
8
− u
6
+ u
4
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
3
=
−
1
2
u
107
−
5
2
u
106
+ ··· − 2u −
3
2
−
5
2
u
107
−
7
2
u
106
+ ··· −
1
2
u
2
−
1
2
u
a
2
=
1
2
u
107
+
3
2
u
106
+ ··· − u +
3
2
1
2
u
107
+
1
2
u
106
+ ··· +
3
2
u
2
+
1
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 9u
107
+
41
2
u
106
+ ··· +
29
2
u + 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
108
+ 55u
107
+ ··· + 6u + 1
c
2
, c
5
u
108
+ 7u
107
+ ··· + 6u + 1
c
3
u
108
− 7u
107
+ ··· − 83686u + 9881
c
4
, c
9
u
108
+ u
107
+ ··· − 4096u + 4096
c
6
, c
8
u
108
+ 3u
107
+ ··· + 5128u + 937
c
7
, c
11
u
108
− 3u
107
+ ··· − 2u + 1
c
10
u
108
− 49u
107
+ ··· + 2u + 1
c
12
u
108
− 9u
107
+ ··· − 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
108
+ 3y
107
+ ··· − 10y + 1
c
2
, c
5
y
108
+ 55y
107
+ ··· + 6y + 1
c
3
y
108
− 49y
107
+ ··· + 4881460918y + 97634161
c
4
, c
9
y
108
+ 65y
107
+ ··· + 385875968y + 16777216
c
6
, c
8
y
108
− 89y
107
+ ··· + 14791066y + 877969
c
7
, c
11
y
108
− 49y
107
+ ··· + 2y + 1
c
10
y
108
+ 23y
107
+ ··· − 26y + 1
c
12
y
108
+ 3y
107
+ ··· + 94y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.988339 + 0.107184I
a = 0.20534 − 3.12417I
b = −0.24956 + 2.07122I
1.31506 − 2.48598I 0
u = 0.988339 − 0.107184I
a = 0.20534 + 3.12417I
b = −0.24956 − 2.07122I
1.31506 + 2.48598I 0
u = −0.967418 + 0.159869I
a = −0.859819 + 0.010363I
b = −0.031401 − 0.140629I
1.66899 − 0.19592I 0
u = −0.967418 − 0.159869I
a = −0.859819 − 0.010363I
b = −0.031401 + 0.140629I
1.66899 + 0.19592I 0
u = 0.834620 + 0.590673I
a = 0.995057 − 0.653328I
b = −0.837578 + 0.240181I
−5.60803 + 6.51271I 0
u = 0.834620 − 0.590673I
a = 0.995057 + 0.653328I
b = −0.837578 − 0.240181I
−5.60803 − 6.51271I 0
u = 0.797793 + 0.543102I
a = −1.000890 + 0.764090I
b = 0.838772 − 0.300099I
−2.40675 + 2.20833I 0
u = 0.797793 − 0.543102I
a = −1.000890 − 0.764090I
b = 0.838772 + 0.300099I
−2.40675 − 2.20833I 0
u = −0.937647 + 0.442291I
a = −0.915958 − 0.979918I
b = 0.485712 − 0.557097I
−0.059953 − 0.675856I 0
u = −0.937647 − 0.442291I
a = −0.915958 + 0.979918I
b = 0.485712 + 0.557097I
−0.059953 + 0.675856I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.752108 + 0.599057I
a = 0.881626 − 0.698045I
b = −0.769955 + 0.256180I
−5.84312 − 1.80068I 0
u = 0.752108 − 0.599057I
a = 0.881626 + 0.698045I
b = −0.769955 − 0.256180I
−5.84312 + 1.80068I 0
u = −1.048630 + 0.065579I
a = 1.014810 − 0.064670I
b = −0.0456004 + 0.0695150I
−0.80156 + 3.69498I 0
u = −1.048630 − 0.065579I
a = 1.014810 + 0.064670I
b = −0.0456004 − 0.0695150I
−0.80156 − 3.69498I 0
u = −0.551942 + 0.764427I
a = −0.366870 − 0.394614I
b = −0.51126 − 2.36364I
−10.22170 − 8.99067I 0
u = −0.551942 − 0.764427I
a = −0.366870 + 0.394614I
b = −0.51126 + 2.36364I
−10.22170 + 8.99067I 0
u = −0.524067 + 0.778480I
a = −0.197190 − 0.391437I
b = −0.42329 − 2.47740I
−12.01040 − 0.00877I 0
u = −0.524067 − 0.778480I
a = −0.197190 + 0.391437I
b = −0.42329 + 2.47740I
−12.01040 + 0.00877I 0
u = −0.536878 + 0.758750I
a = 0.311119 + 0.462328I
b = 0.53558 + 2.43939I
−7.31333 − 3.79136I 0
u = −0.536878 − 0.758750I
a = 0.311119 − 0.462328I
b = 0.53558 − 2.43939I
−7.31333 + 3.79136I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.044580 + 0.241783I
a = −0.655670 + 0.285020I
b = −0.035666 − 0.180815I
2.10315 − 0.31022I 0
u = −1.044580 − 0.241783I
a = −0.655670 − 0.285020I
b = −0.035666 + 0.180815I
2.10315 + 0.31022I 0
u = −0.452511 + 0.800257I
a = −0.239198 + 0.312900I
b = 0.07676 + 2.59514I
−11.60770 + 3.17330I 0
u = −0.452511 − 0.800257I
a = −0.239198 − 0.312900I
b = 0.07676 − 2.59514I
−11.60770 − 3.17330I 0
u = −0.426624 + 0.803472I
a = −0.381367 + 0.257467I
b = −0.06243 + 2.56356I
−9.5204 + 12.0780I 0
u = −0.426624 − 0.803472I
a = −0.381367 − 0.257467I
b = −0.06243 − 2.56356I
−9.5204 − 12.0780I 0
u = −0.433605 + 0.793273I
a = 0.361449 − 0.328654I
b = 0.03502 − 2.63170I
−6.73934 + 6.79720I 0
u = −0.433605 − 0.793273I
a = 0.361449 + 0.328654I
b = 0.03502 + 2.63170I
−6.73934 − 6.79720I 0
u = 0.497033 + 0.754891I
a = 0.614359 − 0.156153I
b = −0.480925 − 0.147891I
−6.16699 + 2.54092I 0
u = 0.497033 − 0.754891I
a = 0.614359 + 0.156153I
b = −0.480925 + 0.147891I
−6.16699 − 2.54092I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.457000 + 0.770798I
a = 0.615967 − 0.040560I
b = −0.435430 − 0.245808I
−5.94478 − 5.41063I 0
u = 0.457000 − 0.770798I
a = 0.615967 + 0.040560I
b = −0.435430 + 0.245808I
−5.94478 + 5.41063I 0
u = 1.026670 + 0.410086I
a = −2.00347 − 0.66989I
b = 1.33945 + 0.72536I
2.30803 + 0.05509I 0
u = 1.026670 − 0.410086I
a = −2.00347 + 0.66989I
b = 1.33945 − 0.72536I
2.30803 − 0.05509I 0
u = 0.869165 + 0.189560I
a = −0.85733 + 2.63181I
b = 0.73493 − 1.59061I
1.06021 + 2.51609I 0
u = 0.869165 − 0.189560I
a = −0.85733 − 2.63181I
b = 0.73493 + 1.59061I
1.06021 − 2.51609I 0
u = 1.108960 + 0.099543I
a = −0.09536 − 3.10102I
b = −0.02184 + 2.18073I
−1.51543 − 4.71449I 0
u = 1.108960 − 0.099543I
a = −0.09536 + 3.10102I
b = −0.02184 − 2.18073I
−1.51543 + 4.71449I 0
u = −0.478822 + 0.740548I
a = −0.022517 + 0.755190I
b = 0.48035 + 2.91161I
−3.69289 − 1.39830I 0
u = −0.478822 − 0.740548I
a = −0.022517 − 0.755190I
b = 0.48035 − 2.91161I
−3.69289 + 1.39830I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.116760 + 0.064140I
a = 0.05616 + 3.05434I
b = 0.01639 − 2.14974I
−6.19982 − 1.21253I 0
u = 1.116760 − 0.064140I
a = 0.05616 − 3.05434I
b = 0.01639 + 2.14974I
−6.19982 + 1.21253I 0
u = −0.457550 + 0.751409I
a = 0.236739 − 0.678641I
b = −0.21064 − 2.95573I
−3.57274 + 4.07736I 0
u = −0.457550 − 0.751409I
a = 0.236739 + 0.678641I
b = −0.21064 + 2.95573I
−3.57274 − 4.07736I 0
u = 0.462710 + 0.738208I
a = −0.530312 + 0.083449I
b = 0.384425 + 0.173480I
−3.01039 − 1.29247I 0
u = 0.462710 − 0.738208I
a = −0.530312 − 0.083449I
b = 0.384425 − 0.173480I
−3.01039 + 1.29247I 0
u = 1.128480 + 0.105840I
a = 0.12861 + 3.07346I
b = 0.00014 − 2.18012I
−4.24611 − 9.87631I 0
u = 1.128480 − 0.105840I
a = 0.12861 − 3.07346I
b = 0.00014 + 2.18012I
−4.24611 + 9.87631I 0
u = −1.054520 + 0.425286I
a = 0.02547 + 1.55678I
b = −0.743927 − 0.167461I
3.44403 − 1.96877I 0
u = −1.054520 − 0.425286I
a = 0.02547 − 1.55678I
b = −0.743927 + 0.167461I
3.44403 + 1.96877I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.082350 + 0.361078I
a = −0.406048 + 1.061330I
b = −0.356347 − 0.288763I
3.04102 − 0.79102I 0
u = −1.082350 − 0.361078I
a = −0.406048 − 1.061330I
b = −0.356347 + 0.288763I
3.04102 + 0.79102I 0
u = 1.055980 + 0.435500I
a = 1.48474 + 0.83408I
b = −0.966630 − 0.789840I
3.37664 + 4.82818I 0
u = 1.055980 − 0.435500I
a = 1.48474 − 0.83408I
b = −0.966630 + 0.789840I
3.37664 − 4.82818I 0
u = −1.107020 + 0.288464I
a = 0.730521 − 0.673979I
b = 0.100273 + 0.303998I
0.18939 − 3.61311I 0
u = −1.107020 − 0.288464I
a = 0.730521 + 0.673979I
b = 0.100273 − 0.303998I
0.18939 + 3.61311I 0
u = −1.049990 + 0.462991I
a = −0.28819 − 1.98702I
b = 1.089180 + 0.102951I
1.90914 − 6.50178I 0
u = −1.049990 − 0.462991I
a = −0.28819 + 1.98702I
b = 1.089180 − 0.102951I
1.90914 + 6.50178I 0
u = 1.023410 + 0.546186I
a = −0.804419 + 0.096562I
b = 0.606488 + 0.057072I
−1.18178 + 4.66447I 0
u = 1.023410 − 0.546186I
a = −0.804419 − 0.096562I
b = 0.606488 − 0.057072I
−1.18178 − 4.66447I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.117090 + 0.347714I
a = 0.675053 − 1.029150I
b = 0.257952 + 0.406551I
0.80958 + 3.52182I 0
u = −1.117090 − 0.347714I
a = 0.675053 + 1.029150I
b = 0.257952 − 0.406551I
0.80958 − 3.52182I 0
u = 0.511663 + 0.629009I
a = −0.362759 + 0.473363I
b = 0.391931 − 0.156748I
−2.68687 − 0.04189I −5.54547 + 0.84190I
u = 0.511663 − 0.629009I
a = −0.362759 − 0.473363I
b = 0.391931 + 0.156748I
−2.68687 + 0.04189I −5.54547 − 0.84190I
u = 0.389256 + 0.701926I
a = −0.397271 − 0.182434I
b = 0.154841 + 0.297132I
−2.11119 − 1.85406I −3.33744 − 1.25523I
u = 0.389256 − 0.701926I
a = −0.397271 + 0.182434I
b = 0.154841 − 0.297132I
−2.11119 + 1.85406I −3.33744 + 1.25523I
u = 1.099150 + 0.476941I
a = 0.830949 + 0.926063I
b = −0.494700 − 0.791915I
2.25735 + 6.50648I 0
u = 1.099150 − 0.476941I
a = 0.830949 − 0.926063I
b = −0.494700 + 0.791915I
2.25735 − 6.50648I 0
u = −1.032600 + 0.634454I
a = 2.81115 − 0.01355I
b = −0.72549 + 2.22542I
−8.78937 + 3.70138I 0
u = −1.032600 − 0.634454I
a = 2.81115 + 0.01355I
b = −0.72549 − 2.22542I
−8.78937 − 3.70138I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.040190 + 0.625894I
a = −3.00802 + 0.00968I
b = 0.77809 − 2.31439I
−5.81437 − 1.45353I 0
u = −1.040190 − 0.625894I
a = −3.00802 − 0.00968I
b = 0.77809 + 2.31439I
−5.81437 + 1.45353I 0
u = −0.698347 + 0.358237I
a = 1.127800 + 0.430881I
b = 0.369052 + 0.542782I
−0.81865 − 2.91747I −1.24476 + 5.59463I
u = −0.698347 − 0.358237I
a = 1.127800 − 0.430881I
b = 0.369052 − 0.542782I
−0.81865 + 2.91747I −1.24476 − 5.59463I
u = 1.120410 + 0.482009I
a = −0.669711 − 1.057560I
b = 0.364772 + 0.872661I
−0.08336 + 11.18210I 0
u = 1.120410 − 0.482009I
a = −0.669711 + 1.057560I
b = 0.364772 − 0.872661I
−0.08336 − 11.18210I 0
u = −1.068110 + 0.600311I
a = −4.01284 + 0.40577I
b = 0.78950 − 2.92246I
−1.94413 − 3.70964I 0
u = −1.068110 − 0.600311I
a = −4.01284 − 0.40577I
b = 0.78950 + 2.92246I
−1.94413 + 3.70964I 0
u = 1.061890 + 0.611912I
a = 0.531543 − 0.542681I
b = −0.491899 + 0.322984I
−4.48699 + 2.64493I 0
u = 1.061890 − 0.611912I
a = 0.531543 + 0.542681I
b = −0.491899 − 0.322984I
−4.48699 − 2.64493I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.107430 + 0.525741I
a = −0.378155 − 0.742703I
b = 0.180566 + 0.609014I
−1.37622 + 3.88574I 0
u = 1.107430 − 0.525741I
a = −0.378155 + 0.742703I
b = 0.180566 − 0.609014I
−1.37622 − 3.88574I 0
u = −1.053790 + 0.633254I
a = 3.02840 − 0.29418I
b = −0.65056 + 2.38910I
−10.43010 − 5.31401I 0
u = −1.053790 − 0.633254I
a = 3.02840 + 0.29418I
b = −0.65056 − 2.38910I
−10.43010 + 5.31401I 0
u = 1.075240 + 0.596163I
a = −0.397157 + 0.515456I
b = 0.382403 − 0.326592I
−1.19587 + 6.37964I 0
u = 1.075240 − 0.596163I
a = −0.397157 − 0.515456I
b = 0.382403 + 0.326592I
−1.19587 − 6.37964I 0
u = 1.091960 + 0.564968I
a = −0.032708 + 0.491605I
b = 0.098167 − 0.365521I
−0.06187 + 6.72615I 0
u = 1.091960 − 0.564968I
a = −0.032708 − 0.491605I
b = 0.098167 + 0.365521I
−0.06187 − 6.72615I 0
u = −1.080130 + 0.600513I
a = 3.97930 − 0.92607I
b = −0.48877 + 3.00058I
−1.72700 − 9.21242I 0
u = −1.080130 − 0.600513I
a = 3.97930 + 0.92607I
b = −0.48877 − 3.00058I
−1.72700 + 9.21242I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.085240 + 0.608507I
a = 0.413916 − 0.625299I
b = −0.414662 + 0.409632I
−4.07755 + 10.62320I 0
u = 1.085240 − 0.608507I
a = 0.413916 + 0.625299I
b = −0.414662 − 0.409632I
−4.07755 − 10.62320I 0
u = −1.095970 + 0.619592I
a = −3.26100 + 1.13443I
b = 0.26764 − 2.62651I
−9.68717 − 8.50119I 0
u = −1.095970 − 0.619592I
a = −3.26100 − 1.13443I
b = 0.26764 + 2.62651I
−9.68717 + 8.50119I 0
u = −1.101570 + 0.610511I
a = 3.34675 − 1.36341I
b = −0.14641 + 2.69917I
−4.75007 − 12.07200I 0
u = −1.101570 − 0.610511I
a = 3.34675 + 1.36341I
b = −0.14641 − 2.69917I
−4.75007 + 12.07200I 0
u = −1.107590 + 0.612193I
a = −3.21768 + 1.42770I
b = 0.09604 − 2.62944I
−7.4896 − 17.3843I 0
u = −1.107590 − 0.612193I
a = −3.21768 − 1.42770I
b = 0.09604 + 2.62944I
−7.4896 + 17.3843I 0
u = 0.257089 + 0.683772I
a = 0.583247 + 0.481691I
b = −0.030182 − 0.587958I
−3.78122 + 0.71131I −5.20307 − 0.83911I
u = 0.257089 − 0.683772I
a = 0.583247 − 0.481691I
b = −0.030182 + 0.587958I
−3.78122 − 0.71131I −5.20307 + 0.83911I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.153738 + 0.674862I
a = 0.723502 + 0.567742I
b = 0.063780 − 0.743560I
−2.80986 − 6.85600I −2.41598 + 6.59324I
u = 0.153738 − 0.674862I
a = 0.723502 − 0.567742I
b = 0.063780 + 0.743560I
−2.80986 + 6.85600I −2.41598 − 6.59324I
u = 0.166199 + 0.612098I
a = −0.685708 − 0.657129I
b = −0.135776 + 0.672803I
−0.30433 − 2.34199I 1.24572 + 3.48957I
u = 0.166199 − 0.612098I
a = −0.685708 + 0.657129I
b = −0.135776 − 0.672803I
−0.30433 + 2.34199I 1.24572 − 3.48957I
u = −0.201548 + 0.404834I
a = 1.36434 + 0.67991I
b = 0.746393 − 0.428336I
−0.21644 + 2.77389I 2.22668 − 2.59702I
u = −0.201548 − 0.404834I
a = 1.36434 − 0.67991I
b = 0.746393 + 0.428336I
−0.21644 − 2.77389I 2.22668 + 2.59702I
u = 0.012805 + 0.441107I
a = −1.030300 − 0.907888I
b = −0.403676 + 0.591229I
0.90929 − 1.38472I 4.15458 + 4.07736I
u = 0.012805 − 0.441107I
a = −1.030300 + 0.907888I
b = −0.403676 − 0.591229I
0.90929 + 1.38472I 4.15458 − 4.07736I
15
II. I
u
2
= h−u
5
a + 2u
3
a − 2au + b, u
4
a + u
5
− u
4
− u
2
a − u
3
+ a
2
+ au + u
2
−
u, u
6
− u
5
− u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
12
=
u
−u
3
+ u
a
1
=
u
3
−u
3
+ u
a
4
=
a
u
5
a − 2u
3
a + 2au
a
9
=
−u
3
u
5
− u
3
+ u
a
5
=
a
u
5
a − 2u
3
a + 2au
a
10
=
−u
3
u
5
− u
3
+ u
a
6
=
−u
3
u
3
− u
a
3
=
u
5
a − u
3
a + au + a
−u
5
a + u
4
a + u
3
a − 2u
2
a + a
a
2
=
u
5
a − u
3
a + u
4
+ au − u
2
+ a + u
−u
5
a + u
4
a + u
3
a − 2u
2
a + a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
5
a +2u
4
a +10u
3
a −4u
4
−3u
2
a +u
3
−9au + 3u
2
+ 2a −4u −1
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
9
u
12
c
6
, c
8
, c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
7
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
10
, c
12
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
6
c
4
, c
9
y
12
c
6
, c
7
, c
8
c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
10
, c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002190 + 0.295542I
a = 0.54263 + 1.33698I
b = −0.500000 − 0.866025I
1.89061 + 1.10558I 3.50232 − 2.57477I
u = −1.002190 + 0.295542I
a = 0.88654 − 1.13843I
b = −0.500000 + 0.866025I
1.89061 − 2.95419I 7.01188 + 5.05114I
u = −1.002190 − 0.295542I
a = 0.54263 − 1.33698I
b = −0.500000 + 0.866025I
1.89061 − 1.10558I 3.50232 + 2.57477I
u = −1.002190 − 0.295542I
a = 0.88654 + 1.13843I
b = −0.500000 − 0.866025I
1.89061 + 2.95419I 7.01188 − 5.05114I
u = 0.428243 + 0.664531I
a = −0.386545 − 0.272402I
b = −0.500000 − 0.866025I
−1.89061 − 2.95419I −1.81693 + 4.43387I
u = 0.428243 + 0.664531I
a = −0.042635 + 0.470959I
b = −0.500000 + 0.866025I
−1.89061 + 1.10558I 0.06995 − 2.75005I
u = 0.428243 − 0.664531I
a = −0.386545 + 0.272402I
b = −0.500000 + 0.866025I
−1.89061 + 2.95419I −1.81693 − 4.43387I
u = 0.428243 − 0.664531I
a = −0.042635 − 0.470959I
b = −0.500000 − 0.866025I
−1.89061 − 1.10558I 0.06995 + 2.75005I
u = 1.073950 + 0.558752I
a = 1.44307 − 0.25581I
b = −0.500000 − 0.866025I
7.72290I 1.09315 − 9.68468I
u = 1.073950 + 0.558752I
a = −0.94307 − 1.12183I
b = −0.500000 + 0.866025I
3.66314I 4.13964 − 1.97785I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.558752I
a = 1.44307 + 0.25581I
b = −0.500000 + 0.866025I
− 7.72290I 1.09315 + 9.68468I
u = 1.073950 − 0.558752I
a = −0.94307 + 1.12183I
b = −0.500000 − 0.866025I
− 3.66314I 4.13964 + 1.97785I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
108
+ 55u
107
+ ··· + 6u + 1)
c
2
((u
2
+ u + 1)
6
)(u
108
+ 7u
107
+ ··· + 6u + 1)
c
3
((u
2
− u + 1)
6
)(u
108
− 7u
107
+ ··· − 83686u + 9881)
c
4
, c
9
u
12
(u
108
+ u
107
+ ··· − 4096u + 4096)
c
5
((u
2
− u + 1)
6
)(u
108
+ 7u
107
+ ··· + 6u + 1)
c
6
, c
8
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
)(u
108
+ 3u
107
+ ··· + 5128u + 937)
c
7
((u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
)(u
108
− 3u
107
+ ··· − 2u + 1)
c
10
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
)(u
108
− 49u
107
+ ··· + 2u + 1)
c
11
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
)(u
108
− 3u
107
+ ··· − 2u + 1)
c
12
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
)(u
108
− 9u
107
+ ··· − 6u + 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
108
+ 3y
107
+ ··· − 10y + 1)
c
2
, c
5
((y
2
+ y + 1)
6
)(y
108
+ 55y
107
+ ··· + 6y + 1)
c
3
((y
2
+ y + 1)
6
)(y
108
− 49y
107
+ ··· + 4.88146 × 10
9
y + 9.76342 × 10
7
)
c
4
, c
9
y
12
(y
108
+ 65y
107
+ ··· + 3.85876 × 10
8
y + 1.67772 × 10
7
)
c
6
, c
8
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
108
− 89y
107
+ ··· + 14791066y + 877969)
c
7
, c
11
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
)(y
108
− 49y
107
+ ··· + 2y + 1)
c
10
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
108
+ 23y
107
+ ··· − 26y + 1)
c
12
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
)(y
108
+ 3y
107
+ ··· + 94y + 1)
22
