12a
0110
(K12a
0110
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 10 4 1 7 12 6 9
Solving Sequence
6,11
12
2,5
3 1 4 10 7 8 9
c
11
c
5
c
2
c
1
c
4
c
10
c
6
c
7
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
98
− 3u
97
+ ··· + b + 2, 2u
98
− 2u
97
+ ··· + a − 1, u
99
− 2u
98
+ ··· + 4u − 1i
I
u
2
= h−u
8
+ 2u
6
− u
5
− 2u
4
+ u
3
− u
2
+ b + u, −u
7
+ 2u
5
− u
4
− 2u
3
+ u
2
+ a + u − 1,
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 108 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
= h2u
98
−3u
97
+· · ·+b+2, 2u
98
−2u
97
+· · ·+a−1, u
99
−2u
98
+· · ·+4u−1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
2
=
−2u
98
+ 2u
97
+ ··· + 6u + 1
−2u
98
+ 3u
97
+ ··· + 7u − 2
a
5
=
u
u
a
3
=
−3u
98
+ 3u
97
+ ··· − u
2
+ 10u
−3u
98
+ 4u
97
+ ··· + 11u − 3
a
1
=
u
16
− 5u
14
+ 11u
12
− 12u
10
+ 5u
8
+ 2u
6
− 2u
4
+ 1
u
18
− 4u
16
+ 7u
14
− 4u
12
− 3u
10
+ 6u
8
− 2u
6
+ u
2
a
4
=
−u
98
+ u
97
+ ··· + 4u + 1
−u
98
+ 2u
97
+ ··· + 4u − 1
a
10
=
−u
2
+ 1
−u
4
a
7
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
8
=
u
24
− 7u
22
+ ··· + 5u
4
− 1
u
26
− 6u
24
+ ··· + 2u
4
− u
2
a
9
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
10
+ 2u
8
− u
6
− 2u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
98
+ 7u
97
+ ··· + 26u − 19
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
99
+ 44u
98
+ ··· + 40u + 1
c
2
, c
4
u
99
− 10u
98
+ ··· − 8u + 1
c
3
, c
7
u
99
+ u
98
+ ··· + 1536u + 512
c
5
, c
11
u
99
+ 2u
98
+ ··· + 4u + 1
c
6
, c
9
u
99
+ 6u
98
+ ··· + 460u + 77
c
8
, c
12
u
99
− 8u
98
+ ··· + 10366u + 565
c
10
u
99
+ 52u
98
+ ··· + 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
99
+ 32y
98
+ ··· + 756y −1
c
2
, c
4
y
99
− 44y
98
+ ··· + 40y −1
c
3
, c
7
y
99
+ 57y
98
+ ··· − 6291456y −262144
c
5
, c
11
y
99
− 52y
98
+ ··· + 12y −1
c
6
, c
9
y
99
+ 68y
98
+ ··· − 1083848y −5929
c
8
, c
12
y
99
+ 72y
98
+ ··· − 22303944y −319225
c
10
y
99
− 8y
98
+ ··· + 48y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.798665 + 0.599302I
a = −0.976827 + 0.577800I
b = −1.129250 − 0.480015I
8.49803 − 4.84511I 0
u = 0.798665 − 0.599302I
a = −0.976827 − 0.577800I
b = −1.129250 + 0.480015I
8.49803 + 4.84511I 0
u = 1.000350 + 0.050995I
a = 1.42535 − 0.26072I
b = 2.27637 − 0.80986I
−1.67165 + 2.02827I 0
u = 1.000350 − 0.050995I
a = 1.42535 + 0.26072I
b = 2.27637 + 0.80986I
−1.67165 − 2.02827I 0
u = −0.902178 + 0.454400I
a = 0.0890370 − 0.0234107I
b = −0.217835 − 0.845633I
1.61783 + 2.06558I 0
u = −0.902178 − 0.454400I
a = 0.0890370 + 0.0234107I
b = −0.217835 + 0.845633I
1.61783 − 2.06558I 0
u = 0.816175 + 0.596584I
a = 0.90939 − 1.15608I
b = 2.21727 − 1.25204I
6.62627 − 10.84290I 0
u = 0.816175 − 0.596584I
a = 0.90939 + 1.15608I
b = 2.21727 + 1.25204I
6.62627 + 10.84290I 0
u = −0.788174 + 0.579168I
a = 0.44309 + 1.67989I
b = 1.51689 + 1.70812I
3.17843 + 4.66485I 0
u = −0.788174 − 0.579168I
a = 0.44309 − 1.67989I
b = 1.51689 − 1.70812I
3.17843 − 4.66485I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.744914 + 0.605828I
a = −0.079985 − 1.168900I
b = 0.962462 − 0.769387I
8.65243 + 0.12444I 0
u = 0.744914 − 0.605828I
a = −0.079985 + 1.168900I
b = 0.962462 + 0.769387I
8.65243 − 0.12444I 0
u = 0.771063 + 0.569620I
a = 0.119221 − 0.166608I
b = −0.973643 + 0.658801I
1.68918 − 2.26594I 0
u = 0.771063 − 0.569620I
a = 0.119221 + 0.166608I
b = −0.973643 − 0.658801I
1.68918 + 2.26594I 0
u = −0.752820 + 0.580640I
a = −1.53562 − 1.14343I
b = −1.228310 − 0.111363I
3.27984 − 0.07370I 0
u = −0.752820 − 0.580640I
a = −1.53562 + 1.14343I
b = −1.228310 + 0.111363I
3.27984 + 0.07370I 0
u = 0.724168 + 0.607828I
a = −1.01845 + 1.58478I
b = −0.599810 + 0.255502I
6.89015 + 6.12501I 0
u = 0.724168 − 0.607828I
a = −1.01845 − 1.58478I
b = −0.599810 − 0.255502I
6.89015 − 6.12501I 0
u = 0.881720 + 0.272848I
a = −0.91493 + 1.57555I
b = −1.98406 + 1.50327I
−2.29107 − 2.61357I −12.6816 + 6.4490I
u = 0.881720 − 0.272848I
a = −0.91493 − 1.57555I
b = −1.98406 − 1.50327I
−2.29107 + 2.61357I −12.6816 − 6.4490I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.779849 + 0.465975I
a = −0.285213 + 0.269799I
b = −0.574238 − 0.041840I
1.26426 + 1.96404I 0. − 4.36922I
u = −0.779849 − 0.465975I
a = −0.285213 − 0.269799I
b = −0.574238 + 0.041840I
1.26426 − 1.96404I 0. + 4.36922I
u = −1.004260 + 0.453349I
a = −1.41231 − 0.60811I
b = −2.44810 − 0.42836I
0.71840 + 7.06687I 0
u = −1.004260 − 0.453349I
a = −1.41231 + 0.60811I
b = −2.44810 + 0.42836I
0.71840 − 7.06687I 0
u = −1.092330 + 0.258588I
a = −1.57152 − 0.29866I
b = −2.63399 + 0.06600I
0.76961 + 7.47794I 0
u = −1.092330 − 0.258588I
a = −1.57152 + 0.29866I
b = −2.63399 − 0.06600I
0.76961 − 7.47794I 0
u = −0.837177 + 0.170997I
a = 1.249710 − 0.553710I
b = 2.50105 − 0.13181I
−2.94172 + 0.75427I −11.8641 − 8.1427I
u = −0.837177 − 0.170997I
a = 1.249710 + 0.553710I
b = 2.50105 + 0.13181I
−2.94172 − 0.75427I −11.8641 + 8.1427I
u = −1.125850 + 0.299064I
a = −0.337223 + 0.090504I
b = −0.624275 − 0.743573I
2.27588 + 1.80560I 0
u = −1.125850 − 0.299064I
a = −0.337223 − 0.090504I
b = −0.624275 + 0.743573I
2.27588 − 1.80560I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.196053 + 0.799972I
a = −0.54640 + 2.83269I
b = −1.02080 + 1.28664I
3.58238 + 12.05350I −5.58626 − 7.48008I
u = 0.196053 − 0.799972I
a = −0.54640 − 2.83269I
b = −1.02080 − 1.28664I
3.58238 − 12.05350I −5.58626 + 7.48008I
u = 0.206728 + 0.789199I
a = −1.297360 − 0.297194I
b = −0.041729 − 0.559859I
5.64791 + 6.12658I −2.76593 − 3.29252I
u = 0.206728 − 0.789199I
a = −1.297360 + 0.297194I
b = −0.041729 + 0.559859I
5.64791 − 6.12658I −2.76593 + 3.29252I
u = 1.138850 + 0.353272I
a = −0.218291 + 0.809760I
b = −0.919968 + 0.560519I
−2.92898 − 2.30725I 0
u = 1.138850 − 0.353272I
a = −0.218291 − 0.809760I
b = −0.919968 − 0.560519I
−2.92898 + 2.30725I 0
u = −0.196691 + 0.772888I
a = −0.90453 − 2.07428I
b = −1.33709 − 0.77630I
0.48015 − 5.74470I −6.53433 + 5.16204I
u = −0.196691 − 0.772888I
a = −0.90453 + 2.07428I
b = −1.33709 + 0.77630I
0.48015 + 5.74470I −6.53433 − 5.16204I
u = 0.246855 + 0.748379I
a = 0.23870 + 1.43260I
b = −0.618600 + 0.376747I
6.41320 + 1.34001I −1.69721 − 1.68122I
u = 0.246855 − 0.748379I
a = 0.23870 − 1.43260I
b = −0.618600 − 0.376747I
6.41320 − 1.34001I −1.69721 + 1.68122I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.164550 + 0.355059I
a = 2.23600 − 1.05202I
b = 3.26865 − 0.81530I
−4.78986 + 0.28822I 0
u = −1.164550 − 0.355059I
a = 2.23600 + 1.05202I
b = 3.26865 + 0.81530I
−4.78986 − 0.28822I 0
u = −0.054225 + 0.780242I
a = −0.44146 + 2.81642I
b = 0.13584 + 1.46542I
−2.72930 − 5.59603I −9.26734 + 6.35083I
u = −0.054225 − 0.780242I
a = −0.44146 − 2.81642I
b = 0.13584 − 1.46542I
−2.72930 + 5.59603I −9.26734 − 6.35083I
u = −0.119835 + 0.771932I
a = 0.94917 + 1.59958I
b = 0.373880 + 0.734829I
−1.36463 − 1.77635I −4.89864 − 0.83106I
u = −0.119835 − 0.771932I
a = 0.94917 − 1.59958I
b = 0.373880 − 0.734829I
−1.36463 + 1.77635I −4.89864 + 0.83106I
u = 0.194073 + 0.755738I
a = 0.89312 − 2.50724I
b = 0.392331 − 0.905516I
−0.81163 + 3.26163I −5.15381 − 3.43918I
u = 0.194073 − 0.755738I
a = 0.89312 + 2.50724I
b = 0.392331 + 0.905516I
−0.81163 − 3.26163I −5.15381 + 3.43918I
u = 0.266822 + 0.728901I
a = −0.817902 + 0.855911I
b = 0.521431 − 0.130452I
4.89371 − 4.60258I −3.58622 + 3.26148I
u = 0.266822 − 0.728901I
a = −0.817902 − 0.855911I
b = 0.521431 + 0.130452I
4.89371 + 4.60258I −3.58622 − 3.26148I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.175820 + 0.345035I
a = −0.80067 − 1.72550I
b = −1.40185 − 1.06868I
−3.61047 + 2.15903I 0
u = 1.175820 − 0.345035I
a = −0.80067 + 1.72550I
b = −1.40185 + 1.06868I
−3.61047 − 2.15903I 0
u = −0.212424 + 0.739479I
a = −0.553094 − 0.082400I
b = 0.447993 + 0.653415I
0.98502 − 1.06834I −5.30156 − 0.25223I
u = −0.212424 − 0.739479I
a = −0.553094 + 0.082400I
b = 0.447993 − 0.653415I
0.98502 + 1.06834I −5.30156 + 0.25223I
u = −1.185790 + 0.330960I
a = 0.143557 + 0.435895I
b = −0.411604 + 1.053080I
1.42554 − 2.54085I 0
u = −1.185790 − 0.330960I
a = 0.143557 − 0.435895I
b = −0.411604 − 1.053080I
1.42554 + 2.54085I 0
u = 1.163160 + 0.420974I
a = 0.651009 + 0.503521I
b = 0.760335 + 0.862548I
−4.36658 − 2.14903I 0
u = 1.163160 − 0.420974I
a = 0.651009 − 0.503521I
b = 0.760335 − 0.862548I
−4.36658 + 2.14903I 0
u = −1.197720 + 0.337396I
a = −1.90715 + 1.44519I
b = −2.64310 + 0.67804I
−0.65805 − 8.36557I 0
u = −1.197720 − 0.337396I
a = −1.90715 − 1.44519I
b = −2.64310 − 0.67804I
−0.65805 + 8.36557I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.135000 + 0.528075I
a = 0.239417 + 0.012996I
b = 0.765764 − 0.871578I
2.36053 − 0.15266I 0
u = 1.135000 − 0.528075I
a = 0.239417 − 0.012996I
b = 0.765764 + 0.871578I
2.36053 + 0.15266I 0
u = −1.175310 + 0.442186I
a = 2.66503 − 1.21859I
b = 3.42429 − 0.67327I
−7.46816 + 3.05000I 0
u = −1.175310 − 0.442186I
a = 2.66503 + 1.21859I
b = 3.42429 + 0.67327I
−7.46816 − 3.05000I 0
u = 1.195400 + 0.391696I
a = 1.65395 + 1.19445I
b = 2.33568 + 1.26225I
−5.22443 − 2.18602I 0
u = 1.195400 − 0.391696I
a = 1.65395 − 1.19445I
b = 2.33568 − 1.26225I
−5.22443 + 2.18602I 0
u = −0.538639 + 0.508836I
a = 0.841383 − 0.214802I
b = −0.503981 − 0.319931I
2.65294 + 1.94033I −1.54089 − 3.60097I
u = −0.538639 − 0.508836I
a = 0.841383 + 0.214802I
b = −0.503981 + 0.319931I
2.65294 − 1.94033I −1.54089 + 3.60097I
u = 1.175820 + 0.455645I
a = −3.48761 + 0.46548I
b = −4.40383 + 0.52831I
−7.37232 − 5.39624I 0
u = 1.175820 − 0.455645I
a = −3.48761 − 0.46548I
b = −4.40383 − 0.52831I
−7.37232 + 5.39624I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.168430 + 0.475495I
a = −0.336072 − 0.294933I
b = −0.250512 − 0.709801I
−3.97513 + 6.16348I 0
u = −1.168430 − 0.475495I
a = −0.336072 + 0.294933I
b = −0.250512 + 0.709801I
−3.97513 − 6.16348I 0
u = 1.147280 + 0.530502I
a = 1.36746 − 0.45772I
b = 2.09906 − 0.00592I
3.77999 − 6.14897I 0
u = 1.147280 − 0.530502I
a = 1.36746 + 0.45772I
b = 2.09906 + 0.00592I
3.77999 + 6.14897I 0
u = −1.156540 + 0.519095I
a = −0.783210 + 0.061047I
b = −0.449800 + 0.733842I
−1.76580 + 5.80368I 0
u = −1.156540 − 0.519095I
a = −0.783210 − 0.061047I
b = −0.449800 − 0.733842I
−1.76580 − 5.80368I 0
u = 0.730847
a = 0.859169
b = 0.587219
−0.975467 −10.7830
u = 1.201440 + 0.424535I
a = 2.70562 + 0.36079I
b = 3.32854 − 0.27510I
−6.41097 + 1.36991I 0
u = 1.201440 − 0.424535I
a = 2.70562 − 0.36079I
b = 3.32854 + 0.27510I
−6.41097 − 1.36991I 0
u = 1.165460 + 0.519010I
a = −2.40659 + 0.70428I
b = −3.32698 + 1.18178I
−3.64615 − 8.02930I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.165460 − 0.519010I
a = −2.40659 − 0.70428I
b = −3.32698 − 1.18178I
−3.64615 + 8.02930I 0
u = −1.169630 + 0.524042I
a = 2.37148 + 1.66417I
b = 3.22587 + 1.53437I
−2.37106 + 10.57490I 0
u = −1.169630 − 0.524042I
a = 2.37148 − 1.66417I
b = 3.22587 − 1.53437I
−2.37106 − 10.57490I 0
u = 0.019814 + 0.717166I
a = 0.29180 − 2.99926I
b = 0.68107 − 1.45897I
−4.09342 + 1.11714I −12.42154 − 0.24168I
u = 0.019814 − 0.717166I
a = 0.29180 + 2.99926I
b = 0.68107 + 1.45897I
−4.09342 − 1.11714I −12.42154 + 0.24168I
u = −1.184450 + 0.499279I
a = −1.72776 − 0.61095I
b = −2.17233 − 1.05087I
−4.46599 + 6.46266I 0
u = −1.184450 − 0.499279I
a = −1.72776 + 0.61095I
b = −2.17233 + 1.05087I
−4.46599 − 6.46266I 0
u = −1.196520 + 0.473023I
a = −3.17990 + 0.50039I
b = −4.08320 + 0.57884I
−6.06860 + 10.14700I 0
u = −1.196520 − 0.473023I
a = −3.17990 − 0.50039I
b = −4.08320 − 0.57884I
−6.06860 − 10.14700I 0
u = 1.172000 + 0.531471I
a = −0.773998 − 0.934602I
b = −0.75449 − 1.75067I
2.80653 − 11.03050I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.172000 − 0.531471I
a = −0.773998 + 0.934602I
b = −0.75449 + 1.75067I
2.80653 + 11.03050I 0
u = −0.088291 + 0.703345I
a = 0.630816 + 0.365410I
b = 0.014867 + 0.310885I
−0.89982 − 1.76035I −5.36120 + 3.73367I
u = −0.088291 − 0.703345I
a = 0.630816 − 0.365410I
b = 0.014867 − 0.310885I
−0.89982 + 1.76035I −5.36120 − 3.73367I
u = 1.178490 + 0.530922I
a = 3.17450 − 1.01427I
b = 4.20332 − 0.89915I
0.6844 − 16.9791I 0
u = 1.178490 − 0.530922I
a = 3.17450 + 1.01427I
b = 4.20332 + 0.89915I
0.6844 + 16.9791I 0
u = −0.428957 + 0.536663I
a = 0.39038 + 1.92007I
b = 0.305043 + 0.339526I
2.33272 − 3.00601I −2.32730 + 3.43770I
u = −0.428957 − 0.536663I
a = 0.39038 − 1.92007I
b = 0.305043 − 0.339526I
2.33272 + 3.00601I −2.32730 − 3.43770I
u = 0.439086 + 0.108364I
a = 2.20528 − 0.39473I
b = 0.701744 + 0.088421I
−1.091800 + 0.005248I −8.43104 + 0.38768I
u = 0.439086 − 0.108364I
a = 2.20528 + 0.39473I
b = 0.701744 − 0.088421I
−1.091800 − 0.005248I −8.43104 − 0.38768I
14
II. I
u
2
= h−u
8
+ 2u
6
− u
5
− 2u
4
+ u
3
− u
2
+ b + u, −u
7
+ 2u
5
− u
4
− 2u
3
+
u
2
+ a + u − 1, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
2
=
u
7
− 2u
5
+ u
4
+ 2u
3
− u
2
− u + 1
u
8
− 2u
6
+ u
5
+ 2u
4
− u
3
+ u
2
− u
a
5
=
u
u
a
3
=
u
7
− 2u
5
+ u
4
+ 2u
3
− u
2
+ 1
u
8
− 2u
6
+ u
5
+ 2u
4
− u
3
+ u
2
a
1
=
−u
−u
a
4
=
u
7
− 2u
5
+ u
4
+ 2u
3
− u
2
+ 1
u
8
− 2u
6
+ u
5
+ 2u
4
− u
3
+ u
2
a
10
=
−u
2
+ 1
−u
4
a
7
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
9
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
+ u
7
+ 3u
6
− 2u
5
− 3u
4
+ 2u
3
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
8
+ 2u
7
− u
6
− 4u
5
+ 3u
4
+ 6u
3
− u
2
+ u − 10
15
(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
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
6
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
8
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
9
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
10
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
11
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
16
(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
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
6
, c
9
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
8
, c
12
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
10
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = 0.0829078 + 0.0200056I
b = −0.818075 + 0.614915I
0.13850 − 2.09337I −9.40455 + 4.13635I
u = 0.772920 − 0.510351I
a = 0.0829078 − 0.0200056I
b = −0.818075 − 0.614915I
0.13850 + 2.09337I −9.40455 − 4.13635I
u = −0.825933
a = 0.988778
b = 2.19953
−2.84338 −12.5800
u = −1.173910 + 0.391555I
a = 2.02680 − 0.95855I
b = 2.79337 − 0.70286I
−6.01628 + 1.33617I −15.1179 − 0.3856I
u = −1.173910 − 0.391555I
a = 2.02680 + 0.95855I
b = 2.79337 + 0.70286I
−6.01628 − 1.33617I −15.1179 + 0.3856I
u = 0.141484 + 0.739668I
a = 0.63505 − 2.20758I
b = 0.385576 − 0.903341I
−2.26187 + 2.45442I −10.97405 − 3.19656I
u = 0.141484 − 0.739668I
a = 0.63505 + 2.20758I
b = 0.385576 + 0.903341I
−2.26187 − 2.45442I −10.97405 + 3.19656I
u = 1.172470 + 0.500383I
a = −2.23915 + 0.47757I
b = −2.96063 + 0.78548I
−5.24306 − 7.08493I −14.2133 + 6.7157I
u = 1.172470 − 0.500383I
a = −2.23915 − 0.47757I
b = −2.96063 − 0.78548I
−5.24306 + 7.08493I −14.2133 − 6.7157I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
99
+ 44u
98
+ ··· + 40u + 1)
c
2
((u − 1)
9
)(u
99
− 10u
98
+ ··· − 8u + 1)
c
3
, c
7
u
9
(u
99
+ u
98
+ ··· + 1536u + 512)
c
4
((u + 1)
9
)(u
99
− 10u
98
+ ··· − 8u + 1)
c
5
(u
9
+ u
8
+ ··· − u − 1)(u
99
+ 2u
98
+ ··· + 4u + 1)
c
6
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
99
+ 6u
98
+ ··· + 460u + 77)
c
8
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
99
− 8u
98
+ ··· + 10366u + 565)
c
9
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
99
+ 6u
98
+ ··· + 460u + 77)
c
10
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
99
+ 52u
98
+ ··· + 12u + 1)
c
11
(u
9
− u
8
+ ··· − u + 1)(u
99
+ 2u
98
+ ··· + 4u + 1)
c
12
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
99
− 8u
98
+ ··· + 10366u + 565)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
99
+ 32y
98
+ ··· + 756y −1)
c
2
, c
4
((y −1)
9
)(y
99
− 44y
98
+ ··· + 40y −1)
c
3
, c
7
y
9
(y
99
+ 57y
98
+ ··· − 6291456y −262144)
c
5
, c
11
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
99
− 52y
98
+ ··· + 12y −1)
c
6
, c
9
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
99
+ 68y
98
+ ··· − 1083848y −5929)
c
8
, c
12
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
99
+ 72y
98
+ ··· − 22303944y −319225)
c
10
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
99
− 8y
98
+ ··· + 48y −1)
20
