Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,3,Mod(65,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 126.i (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 65.6 | ||
Character | 126.65 | ||
Dual form | 126.3.i.a.95.6 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
−1.22474 | + | 0.707107i | −0.612372 | + | 0.353553i | |||||
0.894073 | − | 2.86367i | 0.298024 | − | 0.954558i | |||||
1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | |||||
− | 3.35218i | − | 0.670435i | −0.942141 | − | 0.335218i | ||||
0.942141 | − | 0.335218i | ||||||||
0.929913 | + | 4.13948i | 0.154986 | + | 0.689913i | |||||
−6.40395 | − | 2.82655i | −0.914850 | − | 0.403793i | |||||
2.82843i | 0.353553i | |||||||||
−7.40127 | − | 5.12067i | −0.822363 | − | 0.568963i | |||||
2.37035 | + | 4.10556i | 0.237035 | + | 0.410556i | |||||
14.1890i | 1.28991i | 0.764222 | + | 0.644953i | ||||||
−0.764222 | + | 0.644953i | ||||||||
−4.06596 | − | 4.41225i | −0.338830 | − | 0.367688i | |||||
−8.31908 | − | 14.4091i | −0.639930 | − | 1.10839i | −0.985448 | − | 0.169978i | ||
0.345518 | − | 0.938412i | ||||||||
9.84188 | − | 1.06647i | 0.702992 | − | 0.0761767i | |||||
−9.59954 | − | 2.99709i | −0.639970 | − | 0.199806i | |||||
−2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | |||||
−13.5532 | + | 7.82495i | −0.797248 | + | 0.460291i | −0.842508 | − | 0.538684i | ||
0.0452601 | + | 0.998975i | ||||||||
12.6855 | + | 1.03802i | 0.704751 | + | 0.0576679i | |||||
17.3162 | − | 29.9925i | 0.911378 | − | 1.57855i | 0.0992583 | − | 0.995062i | ||
0.812120 | − | 0.583491i | ||||||||
−5.80614 | − | 3.35218i | −0.290307 | − | 0.167609i | |||||
−13.8199 | + | 15.8117i | −0.658092 | + | 0.752938i | |||||
−10.0331 | − | 17.3779i | −0.456050 | − | 0.789903i | |||||
− | 26.2640i | − | 1.14191i | −0.820980 | − | 0.570956i | ||||
0.820980 | − | 0.570956i | ||||||||
8.09970 | + | 2.52882i | 0.337487 | + | 0.105367i | |||||
13.7629 | 0.550517 | |||||||||
20.3775 | + | 11.7650i | 0.783750 | + | 0.452499i | |||||
−21.2812 | + | 16.6166i | −0.788192 | + | 0.615429i | |||||
−11.2997 | + | 8.26542i | −0.403560 | + | 0.295194i | |||||
18.2368 | + | 10.5290i | 0.628855 | + | 0.363069i | 0.780308 | − | 0.625395i | ||
−0.151454 | + | 0.988464i | ||||||||
13.8763 | − | 3.11723i | 0.462542 | − | 0.103908i | |||||
16.8738 | − | 29.2264i | 0.544317 | − | 0.942785i | −0.454332 | − | 0.890832i | ||
0.998650 | − | 0.0519531i | ||||||||
4.89898 | + | 2.82843i | 0.153093 | + | 0.0883883i | |||||
40.6326 | + | 12.6860i | 1.23129 | + | 0.384423i | |||||
11.0662 | − | 19.1671i | 0.325475 | − | 0.563739i | |||||
−9.47510 | + | 21.4672i | −0.270717 | + | 0.613348i | |||||
−16.2705 | + | 7.69871i | −0.451959 | + | 0.213853i | |||||
−31.9815 | + | 55.3936i | −0.864365 | + | 1.49712i | 0.00331203 | + | 0.999995i | ||
−0.867677 | + | 0.497129i | ||||||||
48.9776i | 1.28888i | |||||||||
−48.7008 | + | 10.9404i | −1.24874 | + | 0.280523i | |||||
9.48139 | 0.237035 | |||||||||
5.44200 | − | 3.14194i | 0.132732 | − | 0.0766328i | −0.432164 | − | 0.901795i | ||
0.564896 | + | 0.825162i | ||||||||
5.74532 | − | 29.1375i | 0.136793 | − | 0.693749i | |||||
0.0742627 | − | 0.128627i | 0.00172704 | − | 0.00299132i | −0.865161 | − | 0.501495i | ||
0.866888 | + | 0.498504i | ||||||||
24.5760 | + | 14.1890i | 0.558545 | + | 0.322476i | |||||
−17.1654 | + | 24.8104i | −0.381453 | + | 0.551341i | |||||
18.5715 | + | 32.1667i | 0.403727 | + | 0.699276i | |||||
36.3552 | − | 20.9897i | 0.773516 | − | 0.446590i | −0.0606115 | − | 0.998161i | ||
0.834127 | + | 0.551572i | ||||||||
−11.7082 | + | 2.63019i | −0.243921 | + | 0.0547957i | |||||
33.0212 | + | 36.2022i | 0.673902 | + | 0.738820i | |||||
−16.8561 | + | 9.73185i | −0.337121 | + | 0.194637i | |||||
10.2906 | + | 45.8081i | 0.201776 | + | 0.898197i | |||||
−33.2763 | −0.639930 | |||||||||
38.6074 | − | 22.2900i | 0.728442 | − | 0.420566i | −0.0894100 | − | 0.995995i | ||
0.817852 | + | 0.575429i | ||||||||
14.3143 | − | 35.3991i | 0.265080 | − | 0.655540i | |||||
47.5639 | 0.864798 | |||||||||
7.99469 | − | 18.1131i | 0.142762 | − | 0.323448i | |||||
−70.4069 | − | 76.4034i | −1.23521 | − | 1.34041i | |||||
−29.7805 | −0.513458 | |||||||||
35.9038 | + | 20.7290i | 0.608538 | + | 0.351340i | 0.772393 | − | 0.635145i | ||
−0.163855 | + | 0.986484i | ||||||||
−14.7907 | + | 13.6298i | −0.246511 | + | 0.227163i | |||||
−7.99976 | − | 13.8560i | −0.131144 | − | 0.227147i | 0.792974 | − | 0.609255i | ||
−0.924118 | + | 0.382108i | ||||||||
47.7264i | 0.769781i | |||||||||
32.9235 | + | 53.7126i | 0.522596 | + | 0.852580i | |||||
−8.00000 | −0.125000 | |||||||||
−48.3018 | + | 27.8870i | −0.743104 | + | 0.429031i | |||||
−58.7349 | + | 13.1945i | −0.889922 | + | 0.199917i | |||||
42.6625 | − | 73.8936i | 0.636753 | − | 1.10289i | −0.349387 | − | 0.936978i | ||
0.986141 | − | 0.165911i | ||||||||
31.2998i | 0.460291i | |||||||||
−75.2116 | − | 23.4819i | −1.09002 | − | 0.340318i | |||||
−3.57501 | − | 32.9917i | −0.0510716 | − | 0.471310i | |||||
− | 56.4376i | − | 0.794896i | −0.917625 | − | 0.397448i | ||||
0.917625 | − | 0.397448i | ||||||||
14.4834 | − | 20.9339i | 0.201159 | − | 0.290749i | |||||
4.42855 | + | 7.67047i | 0.0606650 | + | 0.105075i | 0.894763 | − | 0.446542i | ||
−0.834098 | + | 0.551617i | ||||||||
− | 90.4573i | − | 1.22240i | |||||||
12.3050 | − | 39.4125i | 0.164067 | − | 0.525500i | |||||
−34.6324 | − | 59.9850i | −0.455689 | − | 0.789276i | |||||
40.1058 | − | 90.8654i | 0.520855 | − | 1.18007i | |||||
51.9100 | − | 47.8358i | 0.665513 | − | 0.613280i | |||||
−14.5704 | − | 25.2366i | −0.184435 | − | 0.319451i | 0.758951 | − | 0.651148i | ||
−0.943386 | + | 0.331697i | ||||||||
−11.6123 | + | 6.70435i | −0.145153 | + | 0.0838044i | |||||
28.5576 | + | 75.7989i | 0.352562 | + | 0.935788i | |||||
−4.44338 | + | 7.69616i | −0.0541875 | + | 0.0938556i | |||||
−48.8531 | − | 28.2054i | −0.588592 | − | 0.339824i | 0.175949 | − | 0.984399i | ||
−0.764540 | + | 0.644576i | ||||||||
13.5667 | + | 39.7485i | 0.161509 | + | 0.473196i | |||||
26.2306 | + | 45.4328i | 0.308595 | + | 0.534503i | |||||
0.210047i | 0.00244240i | |||||||||
46.4567 | − | 42.8105i | 0.533985 | − | 0.492075i | |||||
−40.1324 | −0.456050 | |||||||||
5.43082 | + | 3.13549i | 0.0610205 | + | 0.0352302i | 0.530200 | − | 0.847873i | ||
−0.469179 | + | 0.883103i | ||||||||
3.47963 | − | 42.5241i | 0.0386626 | − | 0.472490i | |||||
12.5470 | + | 115.789i | 0.137879 | + | 1.27241i | |||||
−45.4906 | − | 26.2640i | −0.494463 | − | 0.285478i | |||||
−68.6083 | − | 74.4517i | −0.737724 | − | 0.800556i | |||||
−29.6839 | + | 51.4141i | −0.315787 | + | 0.546958i | |||||
−100.540 | − | 58.0469i | −1.05832 | − | 0.611020i | |||||
12.4797 | − | 11.5003i | 0.129997 | − | 0.119794i | |||||
−32.1934 | + | 55.7605i | −0.331890 | + | 0.574851i | −0.982883 | − | 0.184233i | ||
0.650992 | + | 0.759084i | ||||||||
−66.0414 | − | 20.9889i | −0.673892 | − | 0.214173i | |||||
72.6569 | − | 105.016i | 0.733908 | − | 1.06077i | |||||
13.7629 | − | 23.8381i | 0.137629 | − | 0.238381i | |||||
93.2173i | 0.922943i | 0.887155 | + | 0.461472i | ||||||
−0.887155 | + | 0.461472i | ||||||||
−44.9945 | − | 48.8267i | −0.441123 | − | 0.478693i | |||||
129.105 | 1.25344 | 0.626721 | − | 0.779243i | ||||||
0.626721 | + | 0.779243i | ||||||||
40.7550 | − | 23.5299i | 0.391875 | − | 0.226249i | |||||
53.0036 | + | 46.3268i | 0.504796 | + | 0.441208i | |||||
−31.5228 | + | 54.5991i | −0.297385 | + | 0.515086i | |||||
−92.8758 | − | 53.6219i | −0.867998 | − | 0.501139i | −0.00131550 | − | 0.999999i | ||
−0.866682 | + | 0.498860i | ||||||||
7.49957 | + | 53.4767i | 0.0694404 | + | 0.495155i | |||||
−16.5505 | − | 28.6662i | −0.151839 | − | 0.262993i | 0.780064 | − | 0.625699i | ||
−0.931904 | + | 0.362706i | ||||||||
−58.2536 | + | 33.6328i | −0.529579 | + | 0.305752i | |||||
130.035 | + | 141.110i | 1.17149 | + | 1.27127i | |||||
3.01644 | + | 27.8370i | 0.0269325 | + | 0.248545i | |||||
−146.122 | + | 84.3635i | −1.29311 | + | 0.746580i | −0.979205 | − | 0.202874i | ||
−0.313909 | + | 0.949453i | ||||||||
140.256 | + | 43.7895i | 1.23031 | + | 0.384118i | |||||
−88.0416 | −0.765579 | |||||||||
36.4736 | − | 21.0580i | 0.314427 | − | 0.181535i | |||||
−12.2123 | + | 149.245i | −0.104379 | + | 1.27560i | |||||
−58.6306 | −0.496869 | |||||||||
108.912 | − | 11.8018i | 0.915225 | − | 0.0991745i | |||||
8.47705 | − | 27.1516i | 0.0706421 | − | 0.226263i | |||||
−80.3266 | −0.663856 | |||||||||
19.5953 | + | 11.3134i | 0.160618 | + | 0.0927326i | |||||
−4.13196 | − | 18.3933i | −0.0335931 | − | 0.149539i | |||||
−33.7477 | − | 58.4527i | −0.272159 | − | 0.471393i | |||||
− | 129.940i | − | 1.03952i | |||||||
−78.3035 | − | 42.5037i | −0.621456 | − | 0.337331i | |||||
75.2845 | 0.592792 | 0.296396 | − | 0.955065i | ||||||
0.296396 | + | 0.955065i | ||||||||
9.79796 | − | 5.65685i | 0.0765466 | − | 0.0441942i | |||||
−0.301949 | − | 0.327666i | −0.00234069 | − | 0.00254004i | |||||
39.4382 | − | 68.3090i | 0.303371 | − | 0.525454i | |||||
156.493i | 1.19461i | 0.802015 | + | 0.597303i | ||||||
−0.802015 | + | 0.597303i | ||||||||
62.6053 | − | 57.6917i | 0.474283 | − | 0.437058i | |||||
−195.667 | + | 143.125i | −1.47118 | + | 1.07613i | |||||
120.668i | 0.900505i | |||||||||
55.7017 | + | 71.3383i | 0.412605 | + | 0.528432i | |||||
−22.1323 | − | 38.3343i | −0.162738 | − | 0.281870i | |||||
− | 82.6934i | − | 0.603601i | −0.953371 | − | 0.301801i | ||||
0.953371 | − | 0.301801i | ||||||||
108.719 | − | 24.4232i | 0.787820 | − | 0.176980i | |||||
50.4535 | + | 87.3880i | 0.362975 | + | 0.628690i | 0.988449 | − | 0.151554i | ||
−0.625474 | + | 0.780245i | ||||||||
27.7071 | + | 37.8785i | 0.197908 | + | 0.270561i | |||||
−27.6035 | − | 122.876i | −0.195769 | − | 0.871461i | |||||
39.9074 | + | 69.1217i | 0.281038 | + | 0.486772i | |||||
204.450 | − | 118.039i | 1.42972 | − | 0.825449i | |||||
−2.93597 | + | 35.8801i | −0.0203887 | + | 0.249167i | |||||
35.2951 | − | 61.1329i | 0.243415 | − | 0.421606i | |||||
−10.8477 | − | 6.26291i | −0.0742992 | − | 0.0428967i | |||||
133.195 | − | 62.1946i | 0.906086 | − | 0.423093i | |||||
63.9630 | + | 110.787i | 0.432182 | + | 0.748562i | |||||
− | 120.298i | − | 0.807370i | −0.914898 | − | 0.403685i | ||||
0.914898 | − | 0.403685i | ||||||||
12.7983 | + | 56.9712i | 0.0853221 | + | 0.379808i | |||||
73.7142 | 0.488174 | 0.244087 | − | 0.969753i | ||||||
0.244087 | + | 0.969753i | ||||||||
84.8316 | + | 48.9776i | 0.558103 | + | 0.322221i | |||||
140.380 | + | 11.4869i | 0.917516 | + | 0.0750779i | |||||
15.1322 | + | 139.646i | 0.0982608 | + | 0.906793i | |||||
−97.9719 | − | 56.5641i | −0.632077 | − | 0.364930i | |||||
−29.7515 | + | 95.2926i | −0.190714 | + | 0.610850i | |||||
131.796 | − | 228.277i | 0.839463 | − | 1.45399i | −0.0508817 | − | 0.998705i | ||
0.890344 | − | 0.455287i | ||||||||
35.6900 | + | 20.6056i | 0.225886 | + | 0.130415i | |||||
−29.3135 | − | 130.488i | −0.184362 | − | 0.820679i | |||||
9.48139 | − | 16.4222i | 0.0592587 | − | 0.102639i | |||||
−74.2365 | + | 168.193i | −0.461097 | + | 1.04468i | |||||
−88.5736 | − | 72.6410i | −0.546751 | − | 0.448401i | |||||
−36.3832 | + | 63.0176i | −0.223210 | + | 0.386611i | −0.955781 | − | 0.294080i | ||
0.732571 | + | 0.680691i | ||||||||
− | 12.5678i | − | 0.0766328i | |||||||
42.5256 | − | 136.208i | 0.257731 | − | 0.825500i | |||||
79.7768 | 0.480583 | |||||||||
−172.653 | + | 99.6811i | −1.03385 | + | 0.596893i | −0.918085 | − | 0.396384i | ||
−0.115764 | + | 0.993277i | ||||||||
−44.7222 | − | 39.0886i | −0.266204 | − | 0.232670i | |||||
−53.9143 | + | 93.3824i | −0.319020 | + | 0.552558i | |||||
−64.2516 | − | 37.0957i | −0.377951 | − | 0.218210i | |||||
−281.743 | + | 133.312i | −1.64762 | + | 0.779603i | |||||
−0.148525 | − | 0.257253i | −0.000863519 | − | 0.00149566i | |||||
−216.071 | + | 124.749i | −1.24897 | + | 0.721090i | −0.970903 | − | 0.239473i | ||
−0.278062 | + | 0.960563i | ||||||||
−26.6260 | + | 85.2818i | −0.153023 | + | 0.490125i | |||||
−88.1370 | − | 38.9016i | −0.503640 | − | 0.222295i | |||||
49.1520 | − | 28.3779i | 0.279273 | − | 0.161238i | |||||
91.4618 | − | 84.2834i | 0.516733 | − | 0.476177i | |||||
−8.86850 | −0.0498230 | |||||||||
−178.420 | + | 103.011i | −0.996760 | + | 0.575479i | −0.907288 | − | 0.420510i | ||
−0.0894717 | + | 0.995989i | ||||||||
25.8074 | + | 54.5417i | 0.143375 | + | 0.303009i | |||||
−68.0662 | −0.376056 | −0.188028 | − | 0.982164i | ||||||
−0.188028 | + | 0.982164i | ||||||||
−97.2423 | − | 132.940i | −0.534299 | − | 0.730441i | |||||
−46.8314 | + | 10.5205i | −0.255909 | + | 0.0574888i | |||||
74.2858 | 0.403727 | |||||||||
185.689 | + | 107.208i | 1.00372 | + | 0.579501i | |||||
136.673 | + | 42.6709i | 0.734801 | + | 0.229413i | |||||
−111.028 | − | 192.306i | −0.593732 | − | 1.02837i | |||||
− | 83.9588i | − | 0.446590i | |||||||
183.251 | − | 46.2594i | 0.969584 | − | 0.244759i | |||||
164.181 | 0.864113 | |||||||||
223.558 | − | 129.071i | 1.17046 | − | 0.675765i | 0.216671 | − | 0.976245i | ||
0.953788 | + | 0.300480i | ||||||||
−7.15258 | + | 22.9094i | −0.0372530 | + | 0.119320i | |||||
−79.8002 | + | 138.218i | −0.413473 | + | 0.716156i | −0.995267 | − | 0.0971803i | ||
0.581794 | + | 0.813336i | ||||||||
− | 91.0566i | − | 0.469364i | |||||||
36.6741 | + | 163.254i | 0.188072 | + | 0.837198i | |||||
95.7253 | − | 20.9922i | 0.488394 | − | 0.107103i | |||||
− | 173.797i | − | 0.882219i | −0.897453 | − | 0.441109i | ||||
0.897453 | − | 0.441109i | ||||||||
−14.7285 | + | 179.994i | −0.0743862 | + | 0.909063i | |||||
48.3082 | + | 83.6723i | 0.242755 | + | 0.420464i | 0.961498 | − | 0.274812i | ||
−0.718743 | + | 0.695276i | ||||||||
38.9274i | 0.194637i | |||||||||
−173.464 | − | 188.238i | −0.863004 | − | 0.936506i | |||||
−65.9146 | − | 114.167i | −0.326310 | − | 0.565185i | |||||
−87.0267 | − | 118.974i | −0.428703 | − | 0.586081i | |||||
89.6325 | + | 27.9843i | 0.439375 | + | 0.137178i | |||||
−10.5323 | − | 18.2426i | −0.0513773 | − | 0.0889881i | |||||
−158.120 | + | 91.2907i | −0.767574 | + | 0.443159i | |||||
−134.489 | + | 194.387i | −0.649706 | + | 0.939067i | |||||
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425.562 | + | 245.699i | 2.03618 | + | 1.17559i | |||||
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8.68169 | + | 15.0371i | 0.0411455 | + | 0.0712660i | 0.885865 | − | 0.463944i | ||
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− | 89.1600i | − | 0.420566i | |||||||
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151.666 | 0.708717 | |||||||||
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40.5402 | + | 23.4059i | 0.185964 | + | 0.107366i | |||||
25.9252 | − | 5.82397i | 0.118380 | − | 0.0265934i | |||||
47.5639 | − | 82.3831i | 0.216200 | − | 0.374469i | |||||
225.501 | + | 130.193i | 1.02036 | + | 0.589108i | |||||
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0.980506 | − | 0.196489i | ||||||||
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119.308 | − | 206.648i | 0.527912 | − | 0.914370i | |||||
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0.869469 | − | 0.493988i | ||||||||
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107.828 | − | 62.2548i | 0.468819 | − | 0.270673i | |||||
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187.439 | + | 108.218i | 0.804457 | + | 0.464454i | 0.845027 | − | 0.534723i | ||
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8.81687 | + | 39.2480i | 0.0367369 | + | 0.163533i | |||||
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98.3796 | − | 56.7995i | 0.406527 | − | 0.234709i | |||||
242.596 | − | 14.0099i | 0.998337 | − | 0.0576538i | |||||
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121.356 | − | 110.693i | 0.495331 | − | 0.451808i | |||||
18.0666 | + | 19.6053i | 0.0734414 | + | 0.0796964i | |||||
−576.219 | −2.33287 | |||||||||
82.6646 | + | 47.7264i | 0.333325 | + | 0.192445i | |||||
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91.8815 | + | 159.143i | 0.367526 | + | 0.636574i | |||||
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0.890535 | − | 0.454916i | ||||||||
125.956 | − | 3.31269i | 0.499827 | − | 0.0131456i | |||||
372.659 | 1.47296 | |||||||||
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153.557 | − | 34.4958i | 0.602183 | − | 0.135278i | |||||
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0.988816 | − | 0.149140i | ||||||||
0.601505 | + | 0.187797i | 0.00233142 | + | 0.000727895i | |||||
361.381 | − | 264.340i | 1.39529 | − | 1.02062i | |||||
111.548i | 0.429031i | |||||||||
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354.445i | 1.34770i | 0.738869 | + | 0.673849i | ||||||
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138.438 | − | 313.650i | 0.520442 | − | 1.17913i | |||||
13.8346 | − | 12.7488i | 0.0518149 | − | 0.0477482i | |||||
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87.8658 | − | 50.7294i | 0.326639 | − | 0.188585i | −0.327709 | − | 0.944779i | ||
0.654348 | + | 0.756194i | ||||||||
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0.787538 | + | 0.616267i | ||||||||
54.2129 | + | 31.2998i | 0.199312 | + | 0.115073i | |||||
342.801 | + | 67.5935i | 1.25568 | + | 0.247595i | |||||
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195.281i | 0.710114i | |||||||||
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268.121 | 0.967946 | 0.483973 | − | 0.875083i | ||||||
0.483973 | + | 0.875083i | ||||||||
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423.951 | + | 244.768i | 1.50872 | + | 0.871060i | 0.999948 | + | 0.0101594i | ||
0.508773 | + | 0.860901i | ||||||||
120.694 | + | 130.973i | 0.427992 | + | 0.464443i | |||||
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0.792449 | − | 0.609938i | ||||||||
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99.8296i | 0.344240i | |||||||||
130.897 | + | 142.045i | 0.449817 | + | 0.488128i | |||||
17.7142 | 0.0606650 | |||||||||
64.1639 | − | 37.0450i | 0.218989 | − | 0.126434i | −0.386493 | − | 0.922292i | ||
0.605482 | + | 0.795859i | ||||||||
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69.4874 | − | 120.356i | 0.235551 | − | 0.407985i | |||||
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85.0636 | + | 147.334i | 0.285448 | + | 0.494411i | |||||
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266.944 | + | 83.3430i | 0.881003 | + | 0.275059i | |||||
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115.429 | − | 369.714i | 0.373556 | − | 1.19648i | |||||
159.987 | 0.516088 | |||||||||
386.729 | + | 223.278i | 1.24350 | + | 0.717936i | 0.969805 | − | 0.243880i | ||
0.273696 | + | 0.961816i | ||||||||
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98.1534 | + | 170.007i | 0.313589 | + | 0.543152i | 0.979137 | − | 0.203203i | ||
−0.665548 | + | 0.746355i | ||||||||
372.774i | 1.18718i | |||||||||
180.054 | − | 110.366i | 0.571600 | − | 0.350367i | |||||
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295.123 | − | 170.389i | 0.930987 | − | 0.537506i | 0.0438635 | − | 0.999038i | ||
0.887124 | + | 0.461532i | ||||||||
128.170 | + | 139.087i | 0.403052 | + | 0.437380i | |||||
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26.8174i | 0.0838044i | |||||||||
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541.993i | 1.67800i | |||||||||
159.845 | + | 26.3357i | 0.493349 | + | 0.0812831i | |||||
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44.2303 | + | 196.890i | 0.134031 | + | 0.596635i | |||||
281.789 | + | 488.072i | 0.851326 | + | 1.47454i | 0.880012 | + | 0.474951i | ||
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520.356 | − | 246.216i | 1.56263 | − | 0.739388i | |||||
140.970 | − | 244.168i | 0.422067 | − | 0.731041i | |||||
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82.4132 | + | 16.2502i | 0.245277 | + | 0.0483638i | |||||
303.340 | + | 525.401i | 0.900119 | + | 1.55905i | 0.827338 | + | 0.561704i | ||
0.0727808 | + | 0.997348i | ||||||||
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110.946 | + | 493.873i | 0.327275 | + | 1.45685i | |||||
104.922 | 0.308595 | |||||||||
414.692 | + | 239.422i | 1.21610 | + | 0.702118i | |||||
250.798 | − | 362.496i | 0.733327 | − | 1.05993i | |||||
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0.363811 | + | 0.210047i | 0.00105759 | + | 0.000610600i | |||||
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176.421 | − | 305.570i | 0.509888 | − | 0.883152i | |||||
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0.859741 | + | 0.510729i | ||||||||
135.453 | − | 14.6778i | 0.387008 | − | 0.0419365i | |||||
416.470 | + | 168.408i | 1.18652 | + | 0.479794i | |||||
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120.078i | 0.340163i | 0.985430 | + | 0.170082i | ||||||
−0.985430 | + | 0.170082i | ||||||||
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10.8616 | − | 6.27097i | 0.0305102 | − | 0.0176151i | |||||
63.5786 | − | 322.440i | 0.178091 | − | 0.903192i | |||||
145.679 | − | 252.324i | 0.406925 | − | 0.704816i | |||||
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83.3637 | − | 48.1301i | 0.230287 | − | 0.132956i | |||||
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213.100 | + | 94.0573i | 0.585440 | + | 0.258399i | |||||
25.7128 | − | 14.8453i | 0.0704459 | − | 0.0406720i | |||||
49.9175 | − | 45.9997i | 0.136387 | − | 0.125682i | |||||
296.598 | 0.808169 | 0.404085 | − | 0.914722i | ||||||
0.404085 | + | 0.914722i | ||||||||
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271.962 | + | 157.017i | 0.727171 | + | 0.419832i | |||||
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59.3679 | + | 102.828i | 0.157893 | + | 0.273479i | |||||
− | 350.367i | − | 0.929355i | |||||||
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315.897 | 0.833501 | 0.416750 | − | 0.909021i | ||||||
0.416750 | + | 0.909021i | ||||||||
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67.3098 | − | 215.590i | 0.176666 | − | 0.565854i | |||||
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0.850598 | − | 0.525816i | ||||||||
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64.3867 | + | 111.521i | 0.165945 | + | 0.287425i | |||||
363.489i | 0.934420i | 0.884146 | + | 0.467210i | ||||||
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205.515 | + | 355.962i | 0.525613 | + | 0.910388i | |||||
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448.146 | + | 139.916i | 1.14032 | + | 0.356022i | |||||
122.893 | + | 212.857i | 0.311911 | + | 0.540246i | |||||
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32.4146 | − | 56.1437i | 0.0816489 | − | 0.141420i | −0.822309 | − | 0.569041i | ||
0.903958 | + | 0.427621i | ||||||||
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234.924 | + | 688.292i | 0.588782 | + | 1.72504i | |||||
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0.784874 | − | 0.619656i | ||||||||
345.553 | + | 107.886i | 0.859585 | + | 0.268372i | |||||
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161.457 | + | 93.2173i | 0.399646 | + | 0.230736i | |||||
254.091 | − | 95.7300i | 0.627385 | − | 0.236370i | |||||
190.713 | + | 84.1762i | 0.469737 | + | 0.207331i | |||||
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25.7989 | + | 14.8950i | 0.0629241 | + | 0.0363292i | |||||
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129.105 | − | 223.616i | 0.313361 | − | 0.542757i | |||||
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27.2626 | − | 333.173i | 0.0658517 | − | 0.804765i | |||||
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− | 94.1197i | − | 0.226249i | |||||||
295.360 | − | 66.3511i | 0.708297 | − | 0.159115i | |||||
−694.941 | −1.66254 | |||||||||
229.187 | − | 132.321i | 0.546987 | − | 0.315803i | −0.200919 | − | 0.979608i | ||
0.747906 | + | 0.663805i | ||||||||
133.244 | − | 45.4781i | 0.317248 | − | 0.108281i | |||||
−41.2156 | + | 71.3876i | −0.0978994 | + | 0.169567i | −0.910815 | − | 0.412815i | ||
0.812916 | + | 0.582382i | ||||||||
−21.2657 | − | 12.2778i | −0.0503927 | − | 0.0290942i | |||||
−376.556 | − | 30.8126i | −0.890204 | − | 0.0728430i | |||||
63.0456 | + | 109.198i | 0.148693 | + | 0.257543i | |||||
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233.622 | − | 52.4821i | 0.548409 | − | 0.123197i | |||||
12.0654 | + | 111.345i | 0.0282562 | + | 0.260761i | |||||
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−155.233 | − | 691.013i | −0.361848 | − | 1.61075i | |||||
0.704113 | 0.00163747 | |||||||||
409.848 | − | 236.626i | 0.950924 | − | 0.549016i | 0.0575561 | − | 0.998342i | ||
0.893368 | + | 0.449326i | ||||||||
100.124 | + | 40.4871i | 0.231768 | + | 0.0937200i | |||||
140.867 | 0.325328 | 0.162664 | − | 0.986681i | ||||||
0.162664 | + | 0.986681i | ||||||||
134.901 | − | 305.638i | 0.310832 | − | 0.704235i | |||||
−143.508 | − | 155.731i | −0.329904 | − | 0.358002i | |||||
−66.2018 | −0.151839 | |||||||||
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127.577 | + | 220.970i | 0.290609 | + | 0.503349i | 0.973954 | − | 0.226746i | ||
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134.531i | 0.305752i | |||||||||
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403.897 | − | 233.190i | 0.911732 | − | 0.526388i | 0.0307437 | − | 0.999527i | ||
0.880988 | + | 0.473139i | ||||||||
374.446 | − | 84.1175i | 0.843347 | − | 0.189454i | |||||
10.5107 | − | 18.2051i | 0.0236196 | − | 0.0409103i | |||||
416.551i | 0.933972i | |||||||||
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51.2316 | + | 22.6124i | 0.114356 | + | 0.0504741i | |||||
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0.904367 | − | 0.426755i | ||||||||
174.590 | + | 14.2862i | 0.387977 | + | 0.0317471i | |||||
44.5809 | + | 77.2164i | 0.0988490 | + | 0.171212i | |||||
337.454i | 0.746580i | |||||||||
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158.583 | + | 274.674i | 0.349302 | + | 0.605009i | |||||
388.146 | − | 42.0598i | 0.853069 | − | 0.0924392i | |||||
216.101 | − | 199.141i | 0.473907 | − | 0.436712i | |||||
241.747 | + | 418.718i | 0.528987 | + | 0.916233i | 0.999429 | + | 0.0338015i | ||
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126.724 | − | 73.1641i | 0.276690 | − | 0.159747i | |||||
158.405 | − | 391.732i | 0.345108 | − | 0.853447i | |||||
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413.430 | + | 81.5201i | 0.894871 | + | 0.176451i | |||||
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246.287 | + | 170.397i | 0.526255 | + | 0.364096i | |||||
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172.349 | + | 99.5058i | 0.366700 | + | 0.211714i | |||||
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1.82508 | + | 1.05371i | 0.00385852 | + | 0.00222772i | |||||
90.9173 | − | 83.7816i | 0.191809 | − | 0.176754i | |||||
238.321 | − | 412.784i | 0.501729 | − | 0.869019i | |||||
88.4705 | − | 200.442i | 0.185862 | − | 0.421098i | |||||
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316.045 | − | 547.406i | 0.661182 | − | 1.14520i | |||||
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0.850456 | − | 0.526047i | ||||||||
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1064.23 | 2.21253 | |||||||||
101.349 | − | 58.5138i | 0.210267 | − | 0.121398i | |||||
415.278 | + | 362.966i | 0.859790 | + | 0.751483i | |||||
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146.436 | + | 253.634i | 0.300690 | + | 0.520810i | 0.976292 | − | 0.216456i | ||
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39.1907 | − | 22.6267i | 0.0803088 | − | 0.0463663i | |||||
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0.0728274 | + | 0.997345i | ||||||||
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705.721 | − | 407.448i | 1.42859 | − | 0.824794i | |||||
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206.391 | 0.413609 | 0.206804 | − | 0.978382i | ||||||
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131.090 | + | 583.543i | 0.261657 | + | 1.16476i | |||||
161.480 | + | 279.692i | 0.321674 | + | 0.557156i | |||||
415.249i | 0.825546i | 0.910834 | + | 0.412773i | ||||||
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312.481 | 0.618774 | |||||||||
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219.213 | + | 237.884i | 0.432374 | + | 0.469199i | |||||
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0.925771 | − | 0.378084i | ||||||||
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129.864 | + | 926.012i | 0.253146 | + | 1.80509i | |||||
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164.056 | + | 730.291i | 0.316101 | + | 1.40711i | |||||
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0.305218 | + | 0.952282i | ||||||||
220.414 | + | 152.496i | 0.422249 | + | 0.292138i | |||||
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0.950051 | − | 0.312095i | ||||||||
271.055 | + | 156.493i | 0.517280 | + | 0.298652i | |||||
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528.148i | 1.00218i | |||||||||
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183.026 | + | 105.670i | 0.345332 | + | 0.199377i | |||||
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209.003 | + | 120.668i | 0.389930 | + | 0.225126i | |||||
135.469 | + | 603.036i | 0.252270 | + | 1.12297i | |||||
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179.263 | − | 25.1399i | 0.331969 | − | 0.0465553i | |||||
108.437 | − | 187.818i | 0.200437 | − | 0.347168i | −0.748232 | − | 0.663437i | ||
0.948669 | + | 0.316269i | ||||||||
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631.583 | − | 364.644i | 1.14625 | − | 0.661787i | |||||
66.4169 | − | 212.730i | 0.120320 | − | 0.385381i | |||||
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473.027 | − | 435.902i | 0.852301 | − | 0.785408i | |||||
201.814 | 0.362975 | |||||||||
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0.349684 | + | 0.936868i | ||||||||
244.391 | − | 353.236i | 0.437977 | − | 0.633040i | |||||
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93.3147 | − | 10.1117i | 0.166633 | − | 0.0180565i | |||||
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0.615344 | + | 0.788259i | ||||||||
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282.801 | + | 489.826i | 0.500533 | + | 0.866949i | |||||
739.968i | 1.30736i | |||||||||
31.3681 | − | 566.132i | 0.0553230 | − | 0.998469i | |||||
159.630 | 0.281038 | |||||||||
65.6788 | − | 37.9197i | 0.115428 | − | 0.0666427i | −0.441174 | − | 0.897421i | ||
0.556603 | + | 0.830779i | ||||||||
146.790 | − | 470.162i | 0.257526 | − | 0.824846i | |||||
385.418 | − | 667.564i | 0.674988 | − | 1.16911i | −0.301484 | − | 0.953471i | ||
0.976472 | − | 0.215643i | ||||||||
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50.2088 | − | 36.7264i | 0.0874717 | − | 0.0639832i | |||||
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435.383 | + | 754.105i | 0.754563 | + | 1.30694i | 0.945591 | + | 0.325357i | ||
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324.464 | + | 352.099i | 0.560388 | + | 0.608116i | |||||
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233.129 | + | 318.712i | 0.401255 | + | 0.548557i | |||||
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316.272 | + | 547.799i | 0.542491 | + | 0.939621i | |||||
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500.295 | + | 40.9378i | 0.855204 | + | 0.0699791i | |||||
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520.453 | + | 300.484i | 0.886633 | + | 0.511898i | 0.872840 | − | 0.488007i | ||
0.0137932 | + | 0.999905i | ||||||||
25.4704 | − | 292.895i | 0.0433171 | − | 0.498120i | |||||
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196.540i | 0.333119i | |||||||||
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255.852 | 0.432182 | |||||||||
288.796 | + | 166.736i | 0.487008 | + | 0.281174i | 0.723332 | − | 0.690500i | ||
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502.277 | + | 203.106i | 0.845584 | + | 0.341929i | |||||
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282.801 | − | 63.5299i | 0.473704 | − | 0.106415i | |||||
308.995 | − | 535.195i | 0.516714 | − | 0.894975i | |||||
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111.475 | + | 34.8039i | 0.185792 | + | 0.0580065i | |||||
204.315 | − | 353.884i | 0.339958 | − | 0.588825i | −0.644466 | − | 0.764633i | ||
0.984424 | + | 0.175808i | ||||||||
0.593707 | − | 1.34513i | 0.000986225 | − | 0.00223443i | |||||
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73.7142 | − | 127.677i | 0.122043 | − | 0.211385i | |||||
269.269i | 0.445073i | |||||||||
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169.663 | − | 97.9551i | 0.279051 | − | 0.161110i | |||||
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37.9244 | − | 65.6870i | 0.0621712 | − | 0.107684i | |||||
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160.276 | − | 231.658i | 0.261889 | − | 0.378527i | |||||
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194.872 | − | 112.509i | 0.317381 | − | 0.183240i | |||||
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257.006 | + | 113.436i | 0.417218 | + | 0.184150i | |||||
1004.18 | − | 579.761i | 1.62751 | − | 0.939645i | 0.642682 | − | 0.766133i | ||
0.984832 | − | 0.173512i | ||||||||
120.056 | + | 534.425i | 0.194265 | + | 0.864766i | |||||
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436.418 | + | 558.929i | 0.702766 | + | 0.900047i | |||||
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135.300 | + | 146.824i | 0.216827 | + | 0.235294i | |||||
−91.5094 | −0.146415 | |||||||||
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1084.08 | − | 999.000i | 1.72900 | − | 1.59330i | |||||
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− | 1001.01i | − | 1.59144i | |||||||
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71.3800 | − | 41.2113i | 0.112943 | − | 0.0652077i | |||||
50.8235 | − | 11.4173i | 0.0802899 | − | 0.0180367i | |||||
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− | 252.367i | − | 0.397428i | |||||||
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246.934 | − | 776.974i | 0.387652 | − | 1.21974i | |||||
− | 422.555i | − | 0.662312i | |||||||
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702.181i | 1.09545i | 0.836660 | + | 0.547723i | ||||||
−0.836660 | + | 0.547723i | ||||||||
135.600 | − | 434.321i | 0.211215 | − | 0.676512i | |||||
110.674 | + | 191.694i | 0.172122 | + | 0.298124i | 0.939161 | − | 0.343476i | ||
−0.767040 | + | 0.641600i | ||||||||
217.083 | + | 296.775i | 0.337085 | + | 0.460831i | |||||
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0.0593372 | + | 0.998238i | ||||||||
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−294.124 | + | 509.437i | −0.453195 | + | 0.784957i | |||||
280.454 | + | 161.920i | 0.431468 | + | 0.249108i | |||||
228.923 | + | 670.710i | 0.351648 | + | 1.03028i | |||||
72.7665 | + | 126.035i | 0.111605 | + | 0.193306i | |||||
1069.79i | 1.63827i | 0.573602 | + | 0.819134i | ||||||
−0.573602 | + | 0.819134i | ||||||||
103.273 | − | 95.1673i | 0.157909 | − | 0.145516i | |||||
524.594 | 0.800906 | |||||||||
−21.7680 | − | 12.5678i | −0.0331830 | − | 0.0191582i | |||||
6.50104 | − | 79.4483i | 0.00989504 | − | 0.120926i | |||||
335.419 | − | 245.350i | 0.509755 | − | 0.372873i | |||||
740.124 | + | 427.311i | 1.12310 | + | 0.648423i | 0.942191 | − | 0.335076i | ||
0.180911 | + | 0.983499i | ||||||||
−193.393 | − | 209.864i | −0.293019 | − | 0.317976i | |||||
590.335 | − | 1022.49i | 0.893094 | − | 1.54688i | 0.0569477 | − | 0.998377i | ||
0.836146 | − | 0.548507i | ||||||||
−690.239 | − | 398.509i | −1.04266 | − | 0.601978i | |||||
574.444 | − | 529.359i | 0.866431 | − | 0.798429i | |||||
79.7768 | − | 138.177i | 0.120146 | − | 0.208099i | |||||
479.782 | + | 655.911i | 0.721477 | + | 0.986333i | |||||
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276.534 | − | 478.971i | 0.414594 | − | 0.718097i | |||||
398.724i | 0.596893i | |||||||||
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404.499 | 0.603730 | |||||||||
196.602 | − | 113.508i | 0.292999 | − | 0.169163i | |||||
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232.243 | − | 402.257i | 0.345086 | − | 0.597707i | −0.640283 | − | 0.768139i | ||
0.985369 | + | 0.170432i | ||||||||
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107.829 | + | 186.765i | 0.159510 | + | 0.276279i | |||||
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0.378394 | + | 0.925645i | ||||||||
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363.775 | − | 266.092i | 0.535751 | − | 0.391888i | |||||
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363.600 | + | 321.082i | 0.530029 | + | 0.468049i | |||||
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0.233506 | − | 0.972355i | ||||||||
498.995i | 0.721090i | |||||||||
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74.0825 | 0.106747 | |||||||||
292.940 | − | 169.129i | 0.421496 | − | 0.243351i | |||||
121.086 | + | 131.399i | 0.173975 | + | 0.188792i | |||||
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477.484 | − | 440.009i | 0.683096 | − | 0.629483i | |||||
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0.998488 | − | 0.0549636i | ||||||||
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1107.59 | + | 1918.41i | 1.57553 | + | 2.72889i | |||||
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263.483 | − | 596.959i | 0.372678 | − | 0.844355i | |||||
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0.346539 | − | 0.938036i | ||||||||
231.708 | − | 133.777i | 0.326349 | − | 0.188418i | |||||
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150.132 | + | 439.863i | 0.210268 | + | 0.616055i | |||||
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412.043i | 0.575479i | |||||||||
293.894 | + | 1308.26i | 0.409894 | + | 1.82463i | |||||
165.040 | 0.229860 | |||||||||
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120.276 | + | 9.84189i | 0.167050 | + | 0.0136693i | |||||
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1026.83 | + | 592.838i | 1.42220 | + | 0.821106i | |||||
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250.991 | + | 144.910i | 0.346195 | + | 0.199876i | |||||
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185.455 | − | 321.217i | 0.255096 | − | 0.441839i | −0.709826 | − | 0.704377i | ||
0.964921 | + | 0.262539i | ||||||||
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176.778 | − | 707.241i | 0.242494 | − | 0.970153i | |||||
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2.32441i | 0.00317976i | |||||||||
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74.2858 | − | 128.667i | 0.100932 | − | 0.174819i | |||||
1048.47 | + | 605.336i | 1.42262 | + | 0.821352i | |||||
72.2961 | − | 34.2083i | 0.0979622 | − | 0.0463527i | |||||
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371.378 | − | 214.415i | 0.501862 | − | 0.289750i | |||||
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356.198 | − | 260.549i | 0.480051 | − | 0.351145i | |||||
723.866 | − | 417.924i | 0.974248 | − | 0.562482i | 0.0737195 | − | 0.997279i | ||
0.900529 | + | 0.434797i | ||||||||
210.581 | − | 194.054i | 0.283039 | − | 0.260825i | |||||
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509.624 | − | 294.232i | 0.683142 | − | 0.394412i | |||||
217.145 | + | 458.916i | 0.290689 | + | 0.614345i | |||||
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443.207 | + | 605.910i | 0.591732 | + | 0.808959i | |||||
537.884 | − | 120.833i | 0.717179 | − | 0.161111i | |||||
1043.24 | 1.38913 | 0.694566 | − | 0.719429i | ||||||
0.694566 | + | 0.719429i | ||||||||
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247.747 | + | 429.110i | 0.328577 | + | 0.569112i | |||||
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103.128 | − | 363.660i | 0.136412 | − | 0.481032i | |||||
441.367 | 0.583047 | 0.291524 | − | 0.956564i | ||||||
0.291524 | + | 0.956564i | ||||||||
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333.184 | − | 1067.17i | 0.438978 | − | 1.40603i | |||||
164.181 | − | 284.371i | 0.216028 | − | 0.374172i | |||||
297.170i | 0.390499i | 0.980754 | + | 0.195249i | ||||||
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70.0081 | + | 311.639i | 0.0918741 | + | 0.408975i | |||||
24.9618 | + | 230.358i | 0.0327153 | + | 0.301911i | |||||
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38.5062 | − | 470.578i | 0.0503349 | − | 0.615135i | |||||
284.805 | + | 493.297i | 0.371808 | + | 0.643990i | |||||
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32.5277 | + | 35.2980i | 0.0423537 | + | 0.0459610i | |||||
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468.118 | − | 50.7257i | 0.607946 | − | 0.0658775i | |||||
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159.600 | + | 276.436i | 0.206736 | + | 0.358078i | |||||
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1.07558 | − | 1.55461i | 0.00138964 | − | 0.00200854i | |||||
232.233 | − | 402.240i | 0.299656 | − | 0.519019i | |||||
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319.438 | + | 99.7321i | 0.409535 | + | 0.127862i | |||||
800.791 | 1.02534 | |||||||||
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59.3657 | − | 186.793i | 0.0757215 | − | 0.238257i | |||||
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1015.01 | + | 316.899i | 1.28646 | + | 0.401647i | |||||
69.0737 | − | 119.639i | 0.0874351 | − | 0.151442i | |||||
1174.22 | − | 127.239i | 1.48447 | − | 0.160858i | |||||
297.031 | + | 205.505i | 0.375039 | + | 0.259476i | |||||
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91.6824i | 0.115469i | |||||||||
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193.233 | 0.242755 | |||||||||
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67.4242 | + | 38.9274i | 0.0842803 | + | 0.0486592i | |||||
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351.407 | + | 608.654i | 0.438163 | + | 0.758920i | |||||
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563.814 | + | 248.854i | 0.700390 | + | 0.309135i | |||||
687.694 | − | 397.040i | 0.853218 | − | 0.492606i | |||||
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0.343810 | + | 0.939039i | ||||||||
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154.189 | + | 167.322i | 0.189655 | + | 0.205808i | |||||
1283.50 | 1.57678 | |||||||||
211.246 | + | 121.963i | 0.259198 | + | 0.149648i | |||||
138.103 | − | 127.264i | 0.169243 | − | 0.155960i | |||||
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− | 698.613i | − | 0.854050i | |||||||
500.055 | − | 921.237i | 0.610567 | − | 1.12483i | |||||
−42.1294 | −0.0513773 | |||||||||
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0.427079 | + | 0.904214i | ||||||||
342.307 | − | 76.8977i | 0.416432 | − | 0.0935495i | |||||
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0.725846 | + | 0.687857i | ||||||||
365.163i | 0.443159i | |||||||||
559.223 | + | 174.596i | 0.677846 | + | 0.211631i | |||||
375.467 | + | 165.722i | 0.454561 | + | 0.200632i | |||||
1194.80i | 1.44474i | 0.691504 | + | 0.722372i | ||||||
−0.691504 | + | 0.722372i | ||||||||
202.199 | + | 427.329i | 0.244201 | + | 0.516098i | |||||
484.580 | + | 839.318i | 0.584536 | + | 1.01245i | 0.994933 | + | 0.100539i | ||
−0.410397 | + | 0.911907i | ||||||||
− | 267.426i | − | 0.322200i | |||||||
239.720 | − | 767.812i | 0.288471 | − | 0.923961i | |||||
66.5527 | + | 115.273i | 0.0799912 | + | 0.138549i | |||||
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334.149 | + | 578.762i | 0.400178 | + | 0.693128i | |||||
851.125 | − | 491.397i | 1.01809 | − | 0.587796i | |||||
126.547 | + | 902.357i | 0.151191 | + | 1.07809i | |||||
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−0.881502 | + | 0.472180i | ||||||||
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− | 116.575i | − | 0.138451i | |||||||
1079.98 | − | 995.216i | 1.28111 | − | 1.18057i | |||||
34.7268 | 0.0411455 | |||||||||
313.034 | + | 180.730i | 0.370455 | + | 0.213882i | |||||
482.973 | − | 228.528i | 0.570890 | − | 0.270128i | |||||
514.408 | + | 227.047i | 0.607329 | + | 0.268061i | |||||
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152.302 | − | 263.796i | 0.179179 | − | 0.310348i | |||||
1454.86 | + | 839.962i | 1.70958 | + | 0.987029i | |||||
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0.807500 | + | 0.589867i | ||||||||
−93.5098 | − | 127.838i | −0.109496 | − | 0.149693i | |||||
446.886 | + | 944.453i | 0.522674 | + | 1.10462i | |||||
151.666 | − | 262.692i | 0.177179 | − | 0.306884i | |||||
− | 1205.39i | − | 1.40652i | −0.710934 | − | 0.703259i | ||||
0.710934 | − | 0.703259i | ||||||||
678.741 | + | 736.549i | 0.791073 | + | 0.858449i | |||||
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908.692 | + | 524.634i | 1.05295 | + | 0.607919i | 0.923473 | − | 0.383664i | ||
0.129473 | + | 0.991583i | ||||||||
−151.255 | + | 21.2120i | −0.175064 | + | 0.0245509i | |||||
418.179 | + | 724.308i | 0.483444 | + | 0.837350i | |||||
−172.526 | + | 99.6082i | −0.199222 | + | 0.115021i | |||||
89.6148 | + | 97.2473i | 0.103362 | + | 0.112165i | |||||
50.8990 | + | 469.718i | 0.0586394 | + | 0.541150i | |||||
358.082 | − | 206.739i | 0.412062 | − | 0.237904i | |||||
285.880 | + | 89.2549i | 0.328597 | + | 0.102592i | |||||
−1419.65 | −1.62991 | |||||||||
81.0804 | − | 46.8118i | 0.0929821 | − | 0.0536832i | |||||
523.803 | − | 247.847i | 0.600003 | − | 0.283903i | |||||
1286.35 | 1.47179 | |||||||||
−367.282 | + | 832.130i | −0.419751 | + | 0.951006i | |||||
15.8378 | − | 50.7277i | 0.0180796 | − | 0.0579083i | |||||
−1065.07 | −1.21445 | −0.607224 | − | 0.794530i | ||||||
−0.607224 | + | 0.794530i | ||||||||
−312.499 | − | 180.422i | −0.355922 | − | 0.205491i | |||||
−48.7178 | − | 216.865i | −0.0554241 | − | 0.246718i | |||||
−95.1278 | − | 164.766i | −0.108100 | − | 0.187234i | |||||
963.331i | 1.09345i | 0.837312 | + | 0.546726i | ||||||
−0.837312 | + | 0.546726i | ||||||||
381.313 | + | 493.521i | 0.432327 | + | 0.559547i | |||||
−1212.68 | −1.37336 | −0.686681 | − | 0.726959i | ||||||
−0.686681 | + | 0.726959i | ||||||||
451.001 | − | 260.386i | 0.510182 | − | 0.294554i | |||||
−282.533 | − | 306.596i | −0.319246 | − | 0.346436i | |||||
−329.781 | + | 571.197i | −0.372213 | + | 0.644692i | |||||
− | 467.361i | − | 0.526901i | −0.964673 | − | 0.263450i | ||||
0.964673 | − | 0.263450i | ||||||||
−399.121 | + | 367.796i | −0.449460 | + | 0.414184i | |||||
−482.119 | − | 212.796i | −0.542316 | − | 0.239365i | |||||
29.7288i | 0.0334031i | |||||||||
−1075.51 | + | 405.202i | −1.20708 | + | 0.454772i | |||||
−294.546 | − | 510.169i | −0.330209 | − | 0.571939i | |||||
− | 1453.85i | − | 1.62805i | |||||||
497.971 | − | 111.867i | 0.557015 | − | 0.125131i | |||||
345.310 | + | 598.095i | 0.385822 | + | 0.668263i | |||||
−78.7351 | + | 8.53179i | −0.0878739 | + | 0.00952209i | |||||
287.338 | + | 1279.08i | 0.320333 | + | 1.42595i | |||||
270.981 | + | 469.354i | 0.301761 | + | 0.522665i | |||||
615.449 | − | 355.330i | 0.684593 | − | 0.395250i | |||||
−223.930 | + | 105.957i | −0.248811 | + | 0.117730i | |||||
−348.836 | + | 604.202i | −0.387166 | + | 0.670591i | |||||
−109.200 | − | 63.0469i | −0.121065 | − | 0.0698968i | |||||
1.00750 | + | 2.95183i | 0.00111573 | + | 0.00326892i | |||||
−238.616 | − | 413.295i | −0.263956 | − | 0.457185i | |||||
228.170i | 0.252121i | |||||||||
68.5479 | + | 305.138i | 0.0756599 | + | 0.336797i | |||||
−1051.14 | −1.15892 | −0.579461 | − | 0.815000i | ||||||
−0.579461 | + | 0.815000i | ||||||||
−388.448 | − | 224.271i | −0.427806 | − | 0.246994i | |||||
477.334 | − | 689.926i | 0.525120 | − | 0.758994i | |||||
−445.639 | + | 325.973i | −0.489714 | + | 0.358213i | |||||
1182.79 | + | 682.886i | 1.29835 | + | 0.749601i | 0.980118 | − | 0.198413i | ||
0.318228 | + | 0.948014i | ||||||||
−123.855 | + | 396.703i | −0.135806 | + | 0.434982i | |||||
400.205 | − | 693.175i | 0.438340 | − | 0.759228i | |||||
−592.157 | − | 341.882i | −0.647874 | − | 0.374050i | |||||
35.2664 | + | 156.987i | 0.0385425 | + | 0.171571i | |||||
−103.470 | + | 179.215i | −0.112958 | + | 0.195649i | |||||
442.337 | − | 1002.18i | 0.482374 | − | 1.09289i | |||||
82.9914 | + | 591.781i | 0.0904045 | + | 0.644642i | |||||
87.7536 | − | 151.994i | 0.0954881 | − | 0.165390i | −0.814324 | − | 0.580410i | ||
0.909812 | + | 0.415020i | ||||||||
− | 249.019i | − | 0.270673i | |||||||
−142.258 | + | 455.645i | −0.154460 | + | 0.494729i | |||||
639.586 | 0.693695 | |||||||||
−813.214 | + | 469.509i | −0.881055 | + | 0.508677i | |||||
−563.990 | + | 192.498i | −0.610379 | + | 0.208331i | |||||
−440.158 | + | 762.377i | −0.475847 | + | 0.824191i | |||||
384.979 | + | 222.268i | 0.415744 | + | 0.240030i | |||||
−955.538 | − | 661.102i | −1.03079 | − | 0.713162i | |||||
59.5611 | + | 103.163i | 0.0641822 | + | 0.111167i | |||||
−911.266 | + | 526.120i | −0.980910 | + | 0.566329i | −0.902545 | − | 0.430596i | ||
−0.0783655 | + | 0.996925i | ||||||||
143.040 | − | 458.152i | 0.153807 | − | 0.492637i | |||||
1657.60 | − | 363.505i | 1.78045 | − | 0.390446i | |||||
374.877 | − | 216.435i | 0.402229 | − | 0.232227i | |||||
985.160 | − | 907.839i | 1.05591 | − | 0.973032i | |||||
422.584 | 0.452446 | |||||||||
−644.644 | + | 372.185i | −0.689458 | + | 0.398059i | |||||
−422.128 | − | 34.5416i | −0.450991 | − | 0.0369034i | |||||
1548.61 | 1.65274 | 0.826368 | − | 0.563131i | ||||||
0.826368 | + | 0.563131i | ||||||||
341.073 | − | 772.750i | 0.363618 | − | 0.823827i | |||||
574.600 | − | 129.081i | 0.611927 | − | 0.137467i | |||||
−281.445 | −0.299409 | |||||||||
−495.455 | − | 286.051i | −0.526519 | − | 0.303986i | 0.213079 | − | 0.977035i | ||
−0.739598 | + | 0.673049i | ||||||||
1067.50 | + | 333.287i | 1.13323 | + | 0.353808i | |||||
−82.5200 | − | 142.929i | −0.0875079 | − | 0.151568i | |||||
− | 165.832i | − | 0.175670i | |||||||
−155.070 | − | 614.291i | −0.164095 | − | 0.650043i | |||||
−2.98034 | −0.00315047 | |||||||||
−830.937 | + | 479.742i | −0.877442 | + | 0.506591i | −0.869814 | − | 0.493380i | ||
−0.00762758 | + | 0.999971i | ||||||||
−52.1079 | + | 166.899i | −0.0549662 | + | 0.176054i | |||||
73.6829 | − | 127.623i | 0.0776427 | − | 0.134481i | |||||
674.074i | 0.709551i | |||||||||
−224.078 | − | 997.477i | −0.235624 | − | 1.04887i | |||||
33.3804 | + | 308.049i | 0.0350635 | + | 0.323581i | |||||
− | 1308.52i | − | 1.37305i | −0.727104 | − | 0.686527i | ||||
0.727104 | − | 0.686527i | ||||||||
512.893 | − | 242.685i | 0.537624 | − | 0.254387i | |||||
−432.669 | − | 749.405i | −0.453057 | − | 0.784717i | |||||
893.910i | 0.935052i | |||||||||
607.437 | + | 659.172i | 0.634730 | + | 0.688790i | |||||
356.348 | + | 617.213i | 0.371971 | + | 0.644273i | |||||
−233.737 | + | 529.565i | −0.243730 | + | 0.552205i | |||||
76.7963 | + | 23.9767i | 0.0799962 | + | 0.0249757i | |||||
−88.9530 | − | 154.071i | −0.0925630 | − | 0.160324i | |||||
−1303.41 | + | 752.522i | −1.35489 | + | 0.782247i | |||||
412.819 | + | 872.456i | 0.428680 | + | 0.905977i | |||||
−82.7511 | + | 143.329i | −0.0858413 | + | 0.148682i | |||||
463.331 | + | 267.504i | 0.480136 | + | 0.277207i | |||||
−765.266 | − | 150.895i | −0.792201 | − | 0.156206i | |||||
85.8474 | + | 148.692i | 0.0887770 | + | 0.153766i | 0.906994 | − | 0.421143i | ||
−0.818217 | + | 0.574909i | ||||||||
− | 227.198i | − | 0.234709i | |||||||
1552.09 | + | 484.581i | 1.60175 | + | 0.500084i | |||||
−305.238 | −0.314678 | |||||||||
−803.642 | − | 463.983i | −0.827644 | − | 0.477840i | 0.0254013 | − | 0.999677i | ||
−0.853045 | + | 0.521837i | ||||||||
218.330 | − | 434.198i | 0.224619 | − | 0.446706i | |||||
−76.0950 | − | 702.238i | −0.0782066 | − | 0.721724i | |||||
−358.693 | − | 207.092i | −0.368268 | − | 0.212620i | |||||
−670.265 | + | 150.572i | −0.687451 | + | 0.154433i | |||||
−31.9991 | + | 55.4240i | −0.0327859 | + | 0.0567869i | |||||
−1232.02 | − | 711.306i | −1.26102 | − | 0.728051i | −0.287749 | − | 0.957706i | ||
−0.973272 | + | 0.229655i | ||||||||
−294.693 | − | 92.0067i | −0.301322 | − | 0.0940763i | |||||
−44.4893 | + | 77.0577i | −0.0454436 | + | 0.0787107i | |||||
−70.3696 | − | 320.888i | −0.0718057 | − | 0.327437i | |||||
−24.2958 | + | 296.916i | −0.0247664 | + | 0.302667i | |||||
302.473 | − | 523.898i | 0.308017 | − | 0.533501i | |||||
− | 282.456i | − | 0.287341i | −0.989626 | − | 0.143670i | ||||
0.989626 | − | 0.143670i | ||||||||
52.0240 | − | 11.6869i | 0.0528699 | − | 0.0118770i | |||||
−582.598 | −0.591470 | |||||||||
403.622 | − | 233.031i | 0.409353 | − | 0.236340i | |||||
−170.544 | + | 864.914i | −0.172790 | + | 0.876306i | |||||
−576.219 | + | 998.041i | −0.583218 | + | 1.01016i | |||||
−3.37825 | − | 1.95043i | −0.00341583 | − | 0.00197213i | |||||
603.373 | + | 49.3724i | 0.609468 | + | 0.0498711i | |||||
587.805 | + | 1018.11i | 0.593143 | + | 1.02735i | 0.993806 | + | 0.111129i | ||
−0.400663 | + | 0.916226i | ||||||||
165.329 | − | 95.4529i | 0.166663 | − | 0.0962226i | |||||
1649.62 | − | 370.579i | 1.66125 | − | 0.373192i | |||||
−60.1892 | − | 555.452i | −0.0605525 | − | 0.558805i | |||||
280.484 | − | 161.938i | 0.281894 | − | 0.162751i | |||||
74.1855 | + | 330.234i | 0.0744834 | + | 0.331560i | |||||
−715.860 | −0.718014 | −0.359007 | − | 0.933335i | ||||||
−0.359007 | + | 0.933335i | ||||||||
−252.776 | + | 145.940i | −0.253283 | + | 0.146233i | |||||
−239.847 | − | 1710.26i | −0.240087 | − | 1.71198i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 126.3.i.a.65.6 | ✓ | 32 | |
3.2 | odd | 2 | 378.3.i.a.359.15 | 32 | |||
7.4 | even | 3 | 126.3.r.a.11.1 | yes | 32 | ||
9.4 | even | 3 | 378.3.r.a.233.2 | 32 | |||
9.5 | odd | 6 | 126.3.r.a.23.9 | yes | 32 | ||
21.11 | odd | 6 | 378.3.r.a.305.10 | 32 | |||
63.4 | even | 3 | 378.3.i.a.179.10 | 32 | |||
63.32 | odd | 6 | inner | 126.3.i.a.95.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.i.a.65.6 | ✓ | 32 | 1.1 | even | 1 | trivial | |
126.3.i.a.95.6 | yes | 32 | 63.32 | odd | 6 | inner | |
126.3.r.a.11.1 | yes | 32 | 7.4 | even | 3 | ||
126.3.r.a.23.9 | yes | 32 | 9.5 | odd | 6 | ||
378.3.i.a.179.10 | 32 | 63.4 | even | 3 | |||
378.3.i.a.359.15 | 32 | 3.2 | odd | 2 | |||
378.3.r.a.233.2 | 32 | 9.4 | even | 3 | |||
378.3.r.a.305.10 | 32 | 21.11 | odd | 6 |