12a
1074
(K12a
1074
)
A knot diagram
1
Linearized knot diagam
4 7 10 9 12 2 11 6 1 3 8 5
Solving Sequence
5,12
6
1,9
10 4 2 3 8 11 7
c
5
c
12
c
9
c
4
c
1
c
3
c
8
c
11
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.13559 × 10
526
u
120
− 5.74073 × 10
526
u
119
+ ··· + 1.31201 × 10
528
b − 3.70864 × 10
528
,
− 2.82909 × 10
528
u
120
− 9.33657 × 10
528
u
119
+ ··· + 2.37473 × 10
530
a − 1.67417 × 10
531
,
u
121
+ 3u
120
+ ··· + 1450u − 181i
I
u
2
= h−2231694469u
20
− 1226056090u
19
+ ··· + 4164425005b − 7694689318,
− 4558154114u
20
− 8410552925u
19
+ ··· + 4164425005a − 26590478038,
u
21
+ 2u
20
+ ··· + 10u − 1i
I
u
3
= hau + b + u − 1, 3a
2
+ 5au − a − u − 1, u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 146 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−2.14 × 10
526
u
120
− 5.74 × 10
526
u
119
+ · · · + 1.31 × 10
528
b − 3.71 ×
10
528
, −2.83 × 10
528
u
120
− 9.34 × 10
528
u
119
+ · · · + 2.37 × 10
530
a − 1.67 ×
10
531
, u
121
+ 3u
120
+ · · · + 1450u − 181i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
0.0119133u
120
+ 0.0393164u
119
+ ··· − 24.0871u + 7.04992
0.0162773u
120
+ 0.0437554u
119
+ ··· − 13.5908u + 2.82670
a
10
=
0.0305520u
120
+ 0.0872986u
119
+ ··· − 37.4239u + 8.61611
0.0349160u
120
+ 0.0917376u
119
+ ··· − 26.9275u + 4.39289
a
4
=
0.00834731u
120
+ 0.0202093u
119
+ ··· − 8.92810u − 2.19712
0.0107908u
120
+ 0.0304109u
119
+ ··· − 8.31838u + 0.839455
a
2
=
−0.0107132u
120
− 0.0229770u
119
+ ··· + 15.8883u − 5.22605
−0.00537169u
120
− 0.0154859u
119
+ ··· + 2.14823u + 0.152098
a
3
=
−0.00167720u
120
+ 0.00967718u
119
+ ··· + 51.0564u − 10.8752
0.00864426u
120
+ 0.0627551u
119
+ ··· + 32.5635u − 4.96936
a
8
=
0.0278504u
120
+ 0.0806356u
119
+ ··· − 40.7073u + 10.5239
0.0341964u
120
+ 0.0879060u
119
+ ··· − 25.8887u + 4.00174
a
11
=
0.00356820u
120
+ 0.0105675u
119
+ ··· − 3.51017u + 8.89582
−0.0106742u
120
− 0.0401533u
119
+ ··· + 0.141025u + 0.717633
a
7
=
−0.0197899u
120
− 0.0323881u
119
+ ··· + 12.0684u + 4.91754
−0.0397528u
120
− 0.0871958u
119
+ ··· + 45.3723u − 5.06625
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00625773u
120
+ 0.0304442u
119
+ ··· − 36.4250u + 2.96180
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
5(5u
121
− 64u
120
+ ··· + 4296u − 144)
c
2
, c
6
u
121
− 2u
120
+ ··· + 16178u + 383
c
3
, c
10
3(3u
121
+ 3u
120
+ ··· + 1609956u + 261691)
c
4
15(15u
121
+ 72u
120
+ ··· + 140u − 29)
c
5
, c
12
u
121
− 3u
120
+ ··· + 1450u + 181
c
7
, c
11
5(5u
121
+ 8u
120
+ ··· − 10917u − 4981)
c
8
3(3u
121
− 45u
120
+ ··· + 6.34847 × 10
8
u − 4.47793 × 10
7
)
c
9
u
121
+ 4u
120
+ ··· + 125847u − 25899
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
121
+ 94y
120
+ ··· + 2546496y −20736)
c
2
, c
6
y
121
− 88y
120
+ ··· + 86309854y −146689
c
3
, c
10
9(9y
121
+ 1023y
120
+ ··· + 3.08179 × 10
11
y −6.84822 × 10
10
)
c
4
225(225y
121
+ 2346y
120
+ ··· + 73134y −841)
c
5
, c
12
y
121
+ 99y
120
+ ··· + 1609818y −32761
c
7
, c
11
25(25y
121
− 3284y
120
+ ··· + 1.46387 × 10
8
y −2.48104 × 10
7
)
c
8
9
· (9y
121
− 435y
120
+ ··· + 46885882861787876y −2005189738629025)
c
9
y
121
− 46y
120
+ ··· + 37919317395y −670758201
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.022340 + 0.009120I
a = −0.242541 − 0.181469I
b = 0.776282 − 0.785492I
−3.80048 + 7.14105I 0
u = −1.022340 − 0.009120I
a = −0.242541 + 0.181469I
b = 0.776282 + 0.785492I
−3.80048 − 7.14105I 0
u = 0.922714 + 0.289721I
a = −0.275385 − 0.108522I
b = −0.783960 + 0.951417I
−2.70950 + 7.34236I 0
u = 0.922714 − 0.289721I
a = −0.275385 + 0.108522I
b = −0.783960 − 0.951417I
−2.70950 − 7.34236I 0
u = −0.474189 + 0.840234I
a = 0.555027 − 0.472580I
b = 0.264974 + 0.753965I
−0.00933 − 1.96008I 0
u = −0.474189 − 0.840234I
a = 0.555027 + 0.472580I
b = 0.264974 − 0.753965I
−0.00933 + 1.96008I 0
u = 0.528297 + 0.799355I
a = −0.40673 − 1.48975I
b = −0.320808 + 0.500076I
−1.83670 + 2.30670I 0
u = 0.528297 − 0.799355I
a = −0.40673 + 1.48975I
b = −0.320808 − 0.500076I
−1.83670 − 2.30670I 0
u = 0.957844 + 0.014072I
a = 0.353123 − 0.157882I
b = −0.605381 + 0.634924I
−0.20287 + 3.82489I 0
u = 0.957844 − 0.014072I
a = 0.353123 + 0.157882I
b = −0.605381 − 0.634924I
−0.20287 − 3.82489I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.060511 + 0.935302I
a = 1.57543 − 1.64152I
b = 1.17243 − 1.12497I
−5.94582 − 1.40487I 0
u = −0.060511 − 0.935302I
a = 1.57543 + 1.64152I
b = 1.17243 + 1.12497I
−5.94582 + 1.40487I 0
u = −0.689945 + 0.819206I
a = −0.600596 + 1.145110I
b = −0.013533 − 0.584783I
−4.38555 − 2.66513I 0
u = −0.689945 − 0.819206I
a = −0.600596 − 1.145110I
b = −0.013533 + 0.584783I
−4.38555 + 2.66513I 0
u = −1.029900 + 0.321000I
a = 0.152897 − 0.056636I
b = 0.497317 + 0.767887I
0.70176 − 3.38003I 0
u = −1.029900 − 0.321000I
a = 0.152897 + 0.056636I
b = 0.497317 − 0.767887I
0.70176 + 3.38003I 0
u = 0.299735 + 1.045810I
a = −1.83923 + 0.32494I
b = −0.519863 + 0.497910I
−4.58942 + 5.33357I 0
u = 0.299735 − 1.045810I
a = −1.83923 − 0.32494I
b = −0.519863 − 0.497910I
−4.58942 − 5.33357I 0
u = 0.159861 + 0.872828I
a = 0.270231 + 1.150450I
b = 0.249673 − 0.935457I
−0.15646 + 3.50547I 0
u = 0.159861 − 0.872828I
a = 0.270231 − 1.150450I
b = 0.249673 + 0.935457I
−0.15646 − 3.50547I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.316646 + 1.074730I
a = −1.308740 − 0.270194I
b = −0.313587 − 0.109541I
−2.69879 + 1.53463I 0
u = 0.316646 − 1.074730I
a = −1.308740 + 0.270194I
b = −0.313587 + 0.109541I
−2.69879 − 1.53463I 0
u = −0.030630 + 1.120100I
a = −0.01175 − 2.08893I
b = 0.00611 − 3.04806I
−6.55002 + 0.45879I 0
u = −0.030630 − 1.120100I
a = −0.01175 + 2.08893I
b = 0.00611 + 3.04806I
−6.55002 − 0.45879I 0
u = 0.805315 + 0.310316I
a = −0.635861 + 0.962292I
b = −0.240042 − 0.826388I
−8.49552 − 5.40077I 0
u = 0.805315 − 0.310316I
a = −0.635861 − 0.962292I
b = −0.240042 + 0.826388I
−8.49552 + 5.40077I 0
u = −0.231644 + 0.814629I
a = 1.171320 − 0.298246I
b = 0.163209 + 0.367042I
−0.01580 − 1.58349I 0
u = −0.231644 − 0.814629I
a = 1.171320 + 0.298246I
b = 0.163209 − 0.367042I
−0.01580 + 1.58349I 0
u = −0.050240 + 1.153920I
a = −1.028920 − 0.755889I
b = −0.435896 − 0.162913I
−1.91827 − 2.69742I 0
u = −0.050240 − 1.153920I
a = −1.028920 + 0.755889I
b = −0.435896 + 0.162913I
−1.91827 + 2.69742I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.189499 + 1.187980I
a = −1.84930 − 0.21352I
b = −1.50373 + 0.55250I
−4.90801 + 2.13134I 0
u = 0.189499 − 1.187980I
a = −1.84930 + 0.21352I
b = −1.50373 − 0.55250I
−4.90801 − 2.13134I 0
u = 0.016176 + 1.206930I
a = −0.980033 − 0.097239I
b = −0.64985 + 1.34099I
−8.15940 + 2.80868I 0
u = 0.016176 − 1.206930I
a = −0.980033 + 0.097239I
b = −0.64985 − 1.34099I
−8.15940 − 2.80868I 0
u = 0.407852 + 1.144410I
a = 1.86020 + 0.23523I
b = 0.319835 − 0.428833I
−11.0421 + 9.9007I 0
u = 0.407852 − 1.144410I
a = 1.86020 − 0.23523I
b = 0.319835 + 0.428833I
−11.0421 − 9.9007I 0
u = 0.020583 + 1.216020I
a = −1.50759 − 0.15475I
b = −1.05285 − 0.99302I
−4.91369 + 0.61656I 0
u = 0.020583 − 1.216020I
a = −1.50759 + 0.15475I
b = −1.05285 + 0.99302I
−4.91369 − 0.61656I 0
u = −0.382210 + 0.662903I
a = −0.33079 + 2.20870I
b = −1.19951 + 1.10983I
−7.06278 − 0.70692I −4.00000 + 0.I
u = −0.382210 − 0.662903I
a = −0.33079 − 2.20870I
b = −1.19951 − 1.10983I
−7.06278 + 0.70692I −4.00000 + 0.I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.737114 + 0.066944I
a = 0.462389 + 0.004012I
b = −0.349052 + 0.833100I
2.49912 − 0.05962I 2.63807 + 1.88743I
u = −0.737114 − 0.066944I
a = 0.462389 − 0.004012I
b = −0.349052 − 0.833100I
2.49912 + 0.05962I 2.63807 − 1.88743I
u = −0.209534 + 1.248830I
a = 1.65129 + 0.70435I
b = 0.365469 + 0.100547I
−7.44223 − 3.92659I 0
u = −0.209534 − 1.248830I
a = 1.65129 − 0.70435I
b = 0.365469 − 0.100547I
−7.44223 + 3.92659I 0
u = 0.011485 + 1.269170I
a = 1.86992 − 0.56189I
b = 1.010960 + 0.681278I
−14.6335 − 7.2486I 0
u = 0.011485 − 1.269170I
a = 1.86992 + 0.56189I
b = 1.010960 − 0.681278I
−14.6335 + 7.2486I 0
u = 0.213791 + 1.252970I
a = 1.339260 − 0.051118I
b = 1.40192 − 0.69182I
−5.21112 + 0.23468I 0
u = 0.213791 − 1.252970I
a = 1.339260 + 0.051118I
b = 1.40192 + 0.69182I
−5.21112 − 0.23468I 0
u = −1.228090 + 0.339234I
a = −0.1296310 + 0.0373765I
b = −0.755863 − 0.837074I
−9.4401 − 12.7748I 0
u = −1.228090 − 0.339234I
a = −0.1296310 − 0.0373765I
b = −0.755863 + 0.837074I
−9.4401 + 12.7748I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.330316 + 1.239210I
a = 1.397660 + 0.208551I
b = 1.07470 + 1.07681I
−1.13573 − 3.83643I 0
u = −0.330316 − 1.239210I
a = 1.397660 − 0.208551I
b = 1.07470 − 1.07681I
−1.13573 + 3.83643I 0
u = 0.124104 + 1.313070I
a = 1.57672 + 0.55923I
b = 1.56836 + 1.20234I
−15.4412 + 9.2136I 0
u = 0.124104 − 1.313070I
a = 1.57672 − 0.55923I
b = 1.56836 − 1.20234I
−15.4412 − 9.2136I 0
u = −0.290086 + 1.290960I
a = −1.43392 + 0.48396I
b = −0.974027 − 0.789928I
−10.19190 − 5.66988I 0
u = −0.290086 − 1.290960I
a = −1.43392 − 0.48396I
b = −0.974027 + 0.789928I
−10.19190 + 5.66988I 0
u = −0.108199 + 1.318820I
a = 2.57773 − 0.03109I
b = 1.93179 − 0.26017I
−8.61538 − 1.18236I 0
u = −0.108199 − 1.318820I
a = 2.57773 + 0.03109I
b = 1.93179 + 0.26017I
−8.61538 + 1.18236I 0
u = 0.641214 + 0.090897I
a = −0.522311 + 0.015492I
b = 0.608590 − 0.936126I
1.39715 + 4.27966I 0.96817 − 5.82626I
u = 0.641214 − 0.090897I
a = −0.522311 − 0.015492I
b = 0.608590 + 0.936126I
1.39715 − 4.27966I 0.96817 + 5.82626I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.302763 + 1.319770I
a = −1.60720 + 0.42776I
b = −1.31943 + 1.27371I
−3.02240 + 7.81264I 0
u = 0.302763 − 1.319770I
a = −1.60720 − 0.42776I
b = −1.31943 − 1.27371I
−3.02240 − 7.81264I 0
u = 1.35516
a = −0.133599
b = −0.580947
−5.89826 0
u = −1.356190 + 0.004675I
a = −0.119759 + 0.196038I
b = −0.696315 − 0.295138I
−10.52060 + 2.35330I 0
u = −1.356190 − 0.004675I
a = −0.119759 − 0.196038I
b = −0.696315 + 0.295138I
−10.52060 − 2.35330I 0
u = 0.721060 + 1.149960I
a = 0.189133 + 0.606593I
b = 0.553190 + 0.406994I
−4.90744 − 1.63438I 0
u = 0.721060 − 1.149960I
a = 0.189133 − 0.606593I
b = 0.553190 − 0.406994I
−4.90744 + 1.63438I 0
u = −0.104136 + 1.361060I
a = −1.260990 + 0.210760I
b = −1.23089 + 0.90630I
−10.88540 − 3.73003I 0
u = −0.104136 − 1.361060I
a = −1.260990 − 0.210760I
b = −1.23089 − 0.90630I
−10.88540 + 3.73003I 0
u = 0.409563 + 1.310960I
a = 1.381620 − 0.019101I
b = 1.14323 − 1.12648I
−4.37784 + 8.61034I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.409563 − 1.310960I
a = 1.381620 + 0.019101I
b = 1.14323 + 1.12648I
−4.37784 − 8.61034I 0
u = −0.469396 + 1.307450I
a = −1.55110 − 0.09204I
b = −1.38068 − 1.14377I
−7.8701 − 12.3854I 0
u = −0.469396 − 1.307450I
a = −1.55110 + 0.09204I
b = −1.38068 + 1.14377I
−7.8701 + 12.3854I 0
u = 0.224581 + 0.555638I
a = 1.225180 − 0.574453I
b = −0.204818 + 0.042322I
−0.20475 − 1.54591I −2.26783 + 4.24475I
u = 0.224581 − 0.555638I
a = 1.225180 + 0.574453I
b = −0.204818 − 0.042322I
−0.20475 + 1.54591I −2.26783 − 4.24475I
u = 0.035104 + 1.411250I
a = −0.20565 − 2.05359I
b = −0.22717 − 2.42005I
−7.54670 − 0.46592I 0
u = 0.035104 − 1.411250I
a = −0.20565 + 2.05359I
b = −0.22717 + 2.42005I
−7.54670 + 0.46592I 0
u = 0.531459 + 0.245760I
a = 0.583624 − 0.405997I
b = 0.299281 + 1.076830I
−2.32007 − 2.01771I −4.62460 + 0.08491I
u = 0.531459 − 0.245760I
a = 0.583624 + 0.405997I
b = 0.299281 − 1.076830I
−2.32007 + 2.01771I −4.62460 − 0.08491I
u = 0.340821 + 0.456240I
a = 0.026431 − 0.732116I
b = 0.430135 − 0.914497I
−1.94000 + 0.97114I −10.63969 + 0.13238I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.340821 − 0.456240I
a = 0.026431 + 0.732116I
b = 0.430135 + 0.914497I
−1.94000 − 0.97114I −10.63969 − 0.13238I
u = −0.518874 + 0.198720I
a = −0.04637 − 1.57067I
b = 1.041570 + 0.109265I
−5.84022 − 2.60029I −9.35063 + 2.25636I
u = −0.518874 − 0.198720I
a = −0.04637 + 1.57067I
b = 1.041570 − 0.109265I
−5.84022 + 2.60029I −9.35063 − 2.25636I
u = 1.42746 + 0.34142I
a = 0.125641 + 0.096762I
b = 0.599915 − 0.675820I
−4.36285 + 5.23411I 0
u = 1.42746 − 0.34142I
a = 0.125641 − 0.096762I
b = 0.599915 + 0.675820I
−4.36285 − 5.23411I 0
u = 0.17365 + 1.46402I
a = 0.525300 + 0.328473I
b = 0.556501 + 1.105140I
−14.5306 − 1.9666I 0
u = 0.17365 − 1.46402I
a = 0.525300 − 0.328473I
b = 0.556501 − 1.105140I
−14.5306 + 1.9666I 0
u = 0.37688 + 1.44182I
a = 1.70645 − 0.25860I
b = 1.27781 − 1.12368I
−8.2036 + 12.0004I 0
u = 0.37688 − 1.44182I
a = 1.70645 + 0.25860I
b = 1.27781 + 1.12368I
−8.2036 − 12.0004I 0
u = 0.00550 + 1.49053I
a = 0.429417 − 0.572355I
b = 0.375842 + 0.288891I
−14.1924 − 1.5887I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00550 − 1.49053I
a = 0.429417 + 0.572355I
b = 0.375842 − 0.288891I
−14.1924 + 1.5887I 0
u = −0.42917 + 1.44757I
a = −1.394580 − 0.196137I
b = −1.09253 − 1.04210I
−4.80590 − 8.55401I 0
u = −0.42917 − 1.44757I
a = −1.394580 + 0.196137I
b = −1.09253 + 1.04210I
−4.80590 + 8.55401I 0
u = 0.51124 + 1.43735I
a = 1.177190 + 0.193204I
b = 1.060620 − 0.597161I
−10.86410 + 6.28199I 0
u = 0.51124 − 1.43735I
a = 1.177190 − 0.193204I
b = 1.060620 + 0.597161I
−10.86410 − 6.28199I 0
u = −0.49655 + 1.45926I
a = −0.664026 − 0.006783I
b = −0.488572 − 0.316789I
−2.66917 − 3.90264I 0
u = −0.49655 − 1.45926I
a = −0.664026 + 0.006783I
b = −0.488572 + 0.316789I
−2.66917 + 3.90264I 0
u = −0.56494 + 1.45866I
a = 1.151820 − 0.244624I
b = 0.944352 + 0.876457I
−15.3332 − 4.2378I 0
u = −0.56494 − 1.45866I
a = 1.151820 + 0.244624I
b = 0.944352 − 0.876457I
−15.3332 + 4.2378I 0
u = −0.51619 + 1.48893I
a = 1.083510 − 0.195090I
b = 1.267710 + 0.345221I
−15.6838 − 8.9310I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.51619 − 1.48893I
a = 1.083510 + 0.195090I
b = 1.267710 − 0.345221I
−15.6838 + 8.9310I 0
u = −0.48544 + 1.49961I
a = 1.44977 + 0.13964I
b = 1.21602 + 1.17355I
−15.1920 − 18.7481I 0
u = −0.48544 − 1.49961I
a = 1.44977 − 0.13964I
b = 1.21602 − 1.17355I
−15.1920 + 18.7481I 0
u = 0.51621 + 1.52241I
a = −1.245620 + 0.067624I
b = −1.04512 + 1.12378I
−10.1998 + 11.7877I 0
u = 0.51621 − 1.52241I
a = −1.245620 − 0.067624I
b = −1.04512 − 1.12378I
−10.1998 − 11.7877I 0
u = −0.377678 + 0.014743I
a = −3.18967 + 0.66718I
b = −0.179356 − 0.829029I
−3.68084 − 1.55057I −3.21971 + 4.21559I
u = −0.377678 − 0.014743I
a = −3.18967 − 0.66718I
b = −0.179356 + 0.829029I
−3.68084 + 1.55057I −3.21971 − 4.21559I
u = −0.335388 + 0.157476I
a = −1.59623 − 0.09530I
b = −1.33982 − 1.16101I
−4.01387 + 0.45479I 14.6406 + 6.1497I
u = −0.335388 − 0.157476I
a = −1.59623 + 0.09530I
b = −1.33982 + 1.16101I
−4.01387 − 0.45479I 14.6406 − 6.1497I
u = 0.365435
a = −0.299871
b = 0.873931
−1.58749 −2.61860
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.48890 + 1.58677I
a = −0.211346 + 0.304967I
b = −0.445652 − 0.138505I
−8.51138 + 1.30633I 0
u = −0.48890 − 1.58677I
a = −0.211346 − 0.304967I
b = −0.445652 + 0.138505I
−8.51138 − 1.30633I 0
u = −0.054728 + 0.330524I
a = −0.14776 + 4.26458I
b = 0.631561 + 0.217685I
−5.40320 − 2.73968I −12.84076 + 2.28451I
u = −0.054728 − 0.330524I
a = −0.14776 − 4.26458I
b = 0.631561 − 0.217685I
−5.40320 + 2.73968I −12.84076 − 2.28451I
u = 0.39124 + 1.68170I
a = −0.779829 + 0.282564I
b = −0.869501 + 0.693561I
−9.87843 + 3.64795I 0
u = 0.39124 − 1.68170I
a = −0.779829 − 0.282564I
b = −0.869501 − 0.693561I
−9.87843 − 3.64795I 0
u = 0.211229 + 0.100342I
a = −3.53839 + 4.40818I
b = −1.047710 − 0.235799I
−10.94850 + 7.81060I −11.31954 − 4.68345I
u = 0.211229 − 0.100342I
a = −3.53839 − 4.40818I
b = −1.047710 + 0.235799I
−10.94850 − 7.81060I −11.31954 + 4.68345I
u = 0.176942
a = 4.24643
b = 0.693149
−1.46101 −4.87080
u = −1.17013 + 1.93777I
a = 0.143439 − 0.126282I
b = 0.383096 + 0.026772I
−12.32860 + 4.17898I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.17013 − 1.93777I
a = 0.143439 + 0.126282I
b = 0.383096 − 0.026772I
−12.32860 − 4.17898I 0
17
II.
I
u
2
= h−2.23 × 10
9
u
20
− 1.23 × 10
9
u
19
+ · · · + 4.16 × 10
9
b − 7.69 × 10
9
, −4.56 ×
10
9
u
20
−8.41×10
9
u
19
+· · ·+4.16×10
9
a−2.66×10
10
, u
21
+2u
20
+· · ·+10u−1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
u
u
a
9
=
1.09455u
20
+ 2.01962u
19
+ ··· + 33.3111u + 6.38515
0.535895u
20
+ 0.294412u
19
+ ··· − 8.29149u + 1.84772
a
10
=
0.985437u
20
+ 1.49513u
19
+ ··· + 27.7907u + 6.99306
0.426786u
20
− 0.230079u
19
+ ··· − 13.8119u + 2.45563
a
4
=
−1.64810u
20
− 3.62277u
19
+ ··· − 44.9956u − 5.48655
−0.0435294u
20
− 0.342012u
19
+ ··· − 6.18042u − 0.741698
a
2
=
−0.160574u
20
− 1.60193u
19
+ ··· − 37.9076u − 2.13219
0.684125u
20
+ 0.231403u
19
+ ··· − 13.4866u + 0.507992
a
3
=
−1.02645u
20
− 1.96684u
19
+ ··· − 11.7659u − 0.865916
0.904450u
20
+ 1.90674u
19
+ ··· + 3.99361u − 0.856469
a
8
=
1.42598u
20
+ 2.11170u
19
+ ··· + 27.8089u + 8.06340
0.462593u
20
− 0.152102u
19
+ ··· − 14.3308u + 2.41851
a
11
=
1.30735u
20
+ 1.64339u
19
+ ··· + 11.7568u + 6.62435
0.487125u
20
+ 0.381448u
19
+ ··· − 6.44302u + 1.43581
a
7
=
−0.192177u
20
+ 0.230124u
19
+ ··· + 24.7489u + 2.80644
−0.119601u
20
− 1.03826u
19
+ ··· − 11.6121u + 1.62961
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
686470800819
104110625125
u
20
+
244123936684
20822125025
u
19
+ ··· −
3902536941714
104110625125
u −
2147815459402
104110625125
18
(iv) u-Polynomials at the component
19
Crossings u-Polynomials at each crossing
c
1
5(5u
21
− 31u
20
+ ··· + 169u − 61)
c
2
u
21
+ u
20
+ ··· + 2u − 1
c
3
u
21
+ 11u
19
+ ··· − u − 1
c
4
5(5u
21
+ 9u
20
+ ··· − 7u − 1)
c
5
u
21
+ 2u
20
+ ··· + 10u − 1
c
6
u
21
− u
20
+ ··· + 2u + 1
c
7
5(5u
21
+ 17u
20
+ ··· − u − 1)
c
8
u
21
+ 3u
20
+ ··· + 14u + 5
c
9
u
21
+ 4u
20
+ ··· + 8u
2
− 1
c
10
u
21
+ 11u
19
+ ··· − u + 1
c
11
5(5u
21
− 17u
20
+ ··· − u + 1)
c
12
u
21
− 2u
20
+ ··· + 10u + 1
20
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
25(25y
21
− 11y
20
+ ··· + 16849y −3721)
c
2
, c
6
y
21
− 11y
20
+ ··· + 8y −1
c
3
, c
10
y
21
+ 22y
20
+ ··· − 21y −1
c
4
25(25y
21
− 11y
20
+ ··· + y −1)
c
5
, c
12
y
21
+ 20y
20
+ ··· + 200y −1
c
7
, c
11
25(25y
21
− 429y
20
+ ··· − 77y −1)
c
8
y
21
− 7y
20
+ ··· + 116y −25
c
9
y
21
− 12y
20
+ ··· + 16y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.036680 + 0.222294I
a = −0.013763 − 0.189499I
b = 0.660682 + 0.676613I
−0.88157 − 4.32093I −9.24254 + 8.10881I
u = −1.036680 − 0.222294I
a = −0.013763 + 0.189499I
b = 0.660682 − 0.676613I
−0.88157 + 4.32093I −9.24254 − 8.10881I
u = −0.657311 + 0.575090I
a = 0.25820 + 1.63221I
b = −0.335365 − 0.559305I
−4.57696 − 3.41359I −7.02899 + 8.15451I
u = −0.657311 − 0.575090I
a = 0.25820 − 1.63221I
b = −0.335365 + 0.559305I
−4.57696 + 3.41359I −7.02899 − 8.15451I
u = −0.092410 + 1.195380I
a = −1.94593 − 0.36913I
b = −1.88653 − 1.15638I
−5.99931 − 0.30532I −16.7808 − 3.2068I
u = −0.092410 − 1.195380I
a = −1.94593 + 0.36913I
b = −1.88653 + 1.15638I
−5.99931 + 0.30532I −16.7808 + 3.2068I
u = 0.419031 + 1.135220I
a = 1.70730 + 0.86533I
b = 0.919540 − 0.271947I
−12.1227 + 9.7002I −13.8642 − 7.5342I
u = 0.419031 − 1.135220I
a = 1.70730 − 0.86533I
b = 0.919540 + 0.271947I
−12.1227 − 9.7002I −13.8642 + 7.5342I
u = −0.320861 + 0.671213I
a = −0.02766 − 1.53686I
b = −0.104828 − 0.850227I
−4.73939 + 0.65981I −9.72782 + 0.65487I
u = −0.320861 − 0.671213I
a = −0.02766 + 1.53686I
b = −0.104828 + 0.850227I
−4.73939 − 0.65981I −9.72782 − 0.65487I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.154817 + 0.694283I
a = 0.36059 − 1.52207I
b = 0.334827 + 0.848128I
0.28217 − 3.24555I 2.82499 + 2.64646I
u = −0.154817 − 0.694283I
a = 0.36059 + 1.52207I
b = 0.334827 − 0.848128I
0.28217 + 3.24555I 2.82499 − 2.64646I
u = 0.213375 + 1.296620I
a = −0.899376 + 0.294739I
b = −0.484933 + 0.033724I
−2.73211 + 3.18016I −11.34850 − 3.23329I
u = 0.213375 − 1.296620I
a = −0.899376 − 0.294739I
b = −0.484933 − 0.033724I
−2.73211 − 3.18016I −11.34850 + 3.23329I
u = 0.106029 + 1.370470I
a = 0.81198 − 1.29320I
b = 0.82238 − 1.75564I
−7.58118 − 0.74448I −16.6449 + 6.9771I
u = 0.106029 − 1.370470I
a = 0.81198 + 1.29320I
b = 0.82238 + 1.75564I
−7.58118 + 0.74448I −16.6449 − 6.9771I
u = −0.40785 + 1.40980I
a = −1.48443 − 0.11988I
b = −1.21342 − 1.07962I
−6.01954 − 9.28556I −11.76954 + 7.07733I
u = −0.40785 − 1.40980I
a = −1.48443 + 0.11988I
b = −1.21342 + 1.07962I
−6.01954 + 9.28556I −11.76954 − 7.07733I
u = 0.0690864
a = 9.44183
b = 1.13221
−2.13952 −22.6930
u = 0.89695 + 1.80846I
a = 0.1121760 + 0.0160469I
b = −0.178461 + 0.200785I
−12.13230 − 4.17684I 2.79294 + 5.21993I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.89695 − 1.80846I
a = 0.1121760 − 0.0160469I
b = −0.178461 − 0.200785I
−12.13230 + 4.17684I 2.79294 − 5.21993I
25
III. I
u
3
= hau + b + u − 1, 3a
2
+ 5au − a − u − 1, u
2
− u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u + 1
a
1
=
u
u
a
9
=
a
−au − u + 1
a
10
=
au − a − u
−2a − 2u + 1
a
4
=
−
1
3
au +
2
3
a +
2
3
u +
2
3
−
1
3
au +
2
3
a +
2
3
u +
2
3
a
2
=
u
u
a
3
=
u
u − 1
a
8
=
−u + 1
−a − 2u + 1
a
11
=
−u + 1
−a − u + 1
a
7
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2
9
au −
73
9
a −
58
9
u −
16
9
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
c
2
, c
5
(u
2
− u + 1)
2
c
3
, c
4
3(3u
4
+ 4u
2
+ u + 1)
c
6
, c
12
(u
2
+ u + 1)
2
c
7
(u − 1)
4
c
8
3(3u
4
+ 9u
3
+ 10u
2
+ 6u + 3)
c
9
u
4
− u
3
+ u
2
+ 3u + 3
c
10
3(3u
4
+ 4u
2
− u + 1)
c
11
(u + 1)
4
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
c
2
, c
5
, c
6
c
12
(y
2
+ y + 1)
2
c
3
, c
4
, c
10
9(9y
4
+ 24y
3
+ 22y
2
+ 7y + 1)
c
7
, c
11
(y −1)
4
c
8
9(9y
4
− 21y
3
+ 10y
2
+ 24y + 9)
c
9
y
4
+ y
3
+ 13y
2
− 3y + 9
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.83844 − 1.27359I
b = −0.183740 + 0.496878I
−1.64493 + 2.02988I 1.95261 + 4.44629I
u = 0.500000 + 0.866025I
a = 0.338439 − 0.169788I
b = 0.183740 − 1.074230I
−1.64493 + 2.02988I −7.67484 − 4.15762I
u = 0.500000 − 0.866025I
a = −0.83844 + 1.27359I
b = −0.183740 − 0.496878I
−1.64493 − 2.02988I 1.95261 − 4.44629I
u = 0.500000 − 0.866025I
a = 0.338439 + 0.169788I
b = 0.183740 + 1.074230I
−1.64493 − 2.02988I −7.67484 + 4.15762I
29
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
25u
4
(5u
21
− 31u
20
+ ··· + 169u − 61)
· (5u
121
− 64u
120
+ ··· + 4296u − 144)
c
2
((u
2
− u + 1)
2
)(u
21
+ u
20
+ ··· + 2u − 1)
· (u
121
− 2u
120
+ ··· + 16178u + 383)
c
3
9(3u
4
+ 4u
2
+ u + 1)(u
21
+ 11u
19
+ ··· − u − 1)
· (3u
121
+ 3u
120
+ ··· + 1609956u + 261691)
c
4
225(3u
4
+ 4u
2
+ u + 1)(5u
21
+ 9u
20
+ ··· − 7u − 1)
· (15u
121
+ 72u
120
+ ··· + 140u − 29)
c
5
((u
2
− u + 1)
2
)(u
21
+ 2u
20
+ ··· + 10u − 1)
· (u
121
− 3u
120
+ ··· + 1450u + 181)
c
6
((u
2
+ u + 1)
2
)(u
21
− u
20
+ ··· + 2u + 1)
· (u
121
− 2u
120
+ ··· + 16178u + 383)
c
7
25(u − 1)
4
(5u
21
+ 17u
20
+ ··· − u − 1)
· (5u
121
+ 8u
120
+ ··· − 10917u − 4981)
c
8
9(3u
4
+ 9u
3
+ ··· + 6u + 3)(u
21
+ 3u
20
+ ··· + 14u + 5)
· (3u
121
− 45u
120
+ ··· + 634846856u − 44779345)
c
9
(u
4
− u
3
+ u
2
+ 3u + 3)(u
21
+ 4u
20
+ ··· + 8u
2
− 1)
· (u
121
+ 4u
120
+ ··· + 125847u − 25899)
c
10
9(3u
4
+ 4u
2
− u + 1)(u
21
+ 11u
19
+ ··· − u + 1)
· (3u
121
+ 3u
120
+ ··· + 1609956u + 261691)
c
11
25(u + 1)
4
(5u
21
− 17u
20
+ ··· − u + 1)
· (5u
121
+ 8u
120
+ ··· − 10917u − 4981)
c
12
((u
2
+ u + 1)
2
)(u
21
− 2u
20
+ ··· + 10u + 1)
· (u
121
− 3u
120
+ ··· + 1450u + 181)
30
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
625y
4
(25y
21
− 11y
20
+ ··· + 16849y −3721)
· (25y
121
+ 94y
120
+ ··· + 2546496y −20736)
c
2
, c
6
((y
2
+ y + 1)
2
)(y
21
− 11y
20
+ ··· + 8y −1)
· (y
121
− 88y
120
+ ··· + 86309854y −146689)
c
3
, c
10
81(9y
4
+ 24y
3
+ ··· + 7y + 1)(y
21
+ 22y
20
+ ··· − 21y −1)
· (9y
121
+ 1023y
120
+ ··· + 308178871408y −68482179481)
c
4
50625(9y
4
+ 24y
3
+ ··· + 7y + 1)(25y
21
− 11y
20
+ ··· + y −1)
· (225y
121
+ 2346y
120
+ ··· + 73134y −841)
c
5
, c
12
((y
2
+ y + 1)
2
)(y
21
+ 20y
20
+ ··· + 200y −1)
· (y
121
+ 99y
120
+ ··· + 1609818y −32761)
c
7
, c
11
625(y −1)
4
(25y
21
− 429y
20
+ ··· − 77y −1)
· (25y
121
− 3284y
120
+ ··· + 146387111y −24810361)
c
8
81(9y
4
− 21y
3
+ ··· + 24y + 9)(y
21
− 7y
20
+ ··· + 116y −25)
· (9y
121
− 435y
120
+ ··· + 46885882861787876y −2005189738629025)
c
9
(y
4
+ y
3
+ 13y
2
− 3y + 9)(y
21
− 12y
20
+ ··· + 16y −1)
· (y
121
− 46y
120
+ ··· + 37919317395y −670758201)
31
