Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(7,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([8, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 45.k (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 | 13.2 | ||
Character | 45.13 | ||
Dual form | 45.3.k.a.7.2 |
-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 .
−3.22423 | − | 0.863931i | −1.61212 | − | 0.431965i | −0.663444 | − | 0.748226i | ||
−0.948672 | + | 0.316261i | ||||||||
1.08621 | − | 2.79645i | 0.362071 | − | 0.932151i | |||||
6.18520 | + | 3.57103i | 1.54630 | + | 0.892757i | |||||
−4.88999 | − | 1.04305i | −0.977999 | − | 0.208610i | |||||
−5.91814 | + | 8.07800i | −0.986357 | + | 1.34633i | |||||
−8.79970 | − | 2.35787i | −1.25710 | − | 0.336839i | −0.432024 | − | 0.901862i | ||
−0.825075 | + | 0.565023i | ||||||||
−7.41620 | − | 7.41620i | −0.927025 | − | 0.927025i | |||||
−6.64028 | − | 6.07508i | −0.737809 | − | 0.675009i | |||||
14.8654 | + | 7.58766i | 1.48654 | + | 0.758766i | |||||
1.02371 | + | 1.77311i | 0.0930642 | + | 0.161192i | 0.908799 | − | 0.417234i | ||
−0.815735 | + | 0.578426i | ||||||||
16.7046 | − | 13.4177i | 1.39205 | − | 1.11814i | |||||
4.18269 | − | 1.12075i | 0.321746 | − | 0.0862115i | −0.0943314 | − | 0.995541i | ||
0.416077 | + | 0.909329i | ||||||||
26.3352 | + | 15.2047i | 1.88109 | + | 1.08605i | |||||
−8.22842 | + | 12.5417i | −0.548561 | + | 0.836110i | |||||
3.22036 | + | 5.57783i | 0.201273 | + | 0.348615i | |||||
17.1585 | − | 17.1585i | 1.00932 | − | 1.00932i | 0.00936716 | − | 0.999956i | ||
0.999956 | − | 0.00936716i | ||||||||
16.1614 | + | 25.3242i | 0.897854 | + | 1.40690i | |||||
− | 18.6363i | − | 0.980857i | −0.871481 | − | 0.490428i | ||||
0.871481 | − | 0.490428i | ||||||||
−26.5208 | − | 23.9138i | −1.32604 | − | 1.19569i | |||||
−16.1520 | + | 22.0468i | −0.769143 | + | 1.04985i | |||||
−1.76882 | − | 6.60133i | −0.0804010 | − | 0.300061i | |||||
−11.5078 | + | 3.08350i | −0.500338 | + | 0.134065i | −0.500157 | − | 0.865935i | ||
−0.000180980 | 1.00000i | |||||||||
−28.7946 | + | 12.6835i | −1.19978 | + | 0.528478i | |||||
22.8241 | + | 10.2010i | 0.912963 | + | 0.408042i | |||||
−14.4542 | −0.555932 | |||||||||
−24.2014 | + | 11.9704i | −0.896349 | + | 0.443348i | |||||
−46.0079 | − | 46.0079i | −1.64314 | − | 1.64314i | |||||
19.4918 | − | 11.2536i | 0.672131 | − | 0.388055i | −0.124753 | − | 0.992188i | ||
0.796883 | + | 0.604133i | ||||||||
37.3655 | − | 33.3284i | 1.24552 | − | 1.11095i | |||||
11.9368 | − | 20.6752i | 0.385059 | − | 0.666941i | −0.606719 | − | 0.794917i | ||
0.991777 | + | 0.127975i | ||||||||
5.29373 | + | 19.7565i | 0.165429 | + | 0.617389i | |||||
6.07038 | − | 0.936770i | 0.183951 | − | 0.0283870i | |||||
−70.1467 | + | 40.4992i | −2.06314 | + | 1.19115i | |||||
40.5711 | + | 20.7085i | 1.15917 | + | 0.591672i | |||||
−19.3772 | − | 61.2882i | −0.538256 | − | 1.70245i | |||||
−33.2840 | + | 33.2840i | −0.899568 | + | 0.899568i | −0.995398 | − | 0.0958294i | ||
0.0958294 | + | 0.995398i | ||||||||
−16.1005 | + | 60.0877i | −0.423696 | + | 1.58126i | |||||
1.40917 | − | 12.9141i | 0.0361326 | − | 0.331130i | |||||
28.5297 | + | 44.0007i | 0.713242 | + | 1.10002i | |||||
2.15756 | − | 3.73700i | 0.0526234 | − | 0.0911464i | −0.838514 | − | 0.544880i | ||
0.891137 | + | 0.453734i | ||||||||
71.1247 | − | 57.1297i | 1.69345 | − | 1.36023i | |||||
8.15051 | − | 30.4181i | 0.189547 | − | 0.707398i | −0.804065 | − | 0.594542i | ||
0.993611 | − | 0.112856i | ||||||||
14.6227i | 0.332335i | |||||||||
26.1343 | + | 36.6333i | 0.580763 | + | 0.814073i | |||||
39.7677 | 0.864514 | |||||||||
−0.838990 | − | 0.224807i | −0.0178509 | − | 0.00478312i | 0.249883 | − | 0.968276i | ||
−0.267733 | + | 0.963493i | ||||||||
19.0961 | − | 2.94688i | 0.397836 | − | 0.0613933i | |||||
29.4398 | + | 16.9971i | 0.600813 | + | 0.346880i | |||||
−64.7772 | − | 52.6090i | −1.29554 | − | 1.05218i | |||||
−29.3451 | − | 66.6207i | −0.575395 | − | 1.30629i | |||||
29.8730 | + | 8.00445i | 0.574481 | + | 0.153932i | |||||
−3.33316 | − | 3.33316i | −0.0628899 | − | 0.0628899i | 0.674962 | − | 0.737852i | ||
−0.737852 | + | 0.674962i | ||||||||
88.3727 | − | 17.6870i | 1.63653 | − | 0.327537i | |||||
−3.15647 | − | 9.73828i | −0.0573904 | − | 0.177060i | |||||
47.7739 | + | 82.7467i | 0.853105 | + | 1.47762i | |||||
−52.1155 | − | 20.2430i | −0.914306 | − | 0.355140i | |||||
−72.5684 | + | 19.4446i | −1.25118 | + | 0.335252i | |||||
−66.3254 | − | 38.2930i | −1.12416 | − | 0.649033i | −0.181699 | − | 0.983354i | ||
−0.942459 | + | 0.334321i | ||||||||
−95.6810 | + | 48.1888i | −1.59468 | + | 0.803146i | |||||
35.3623 | + | 61.2493i | 0.579710 | + | 1.00409i | 0.995512 | + | 0.0946322i | ||
−0.415802 | + | 0.909455i | ||||||||
−56.3490 | + | 56.3490i | −0.908855 | + | 0.908855i | |||||
44.1082 | + | 69.1158i | 0.700131 | + | 1.09708i | |||||
− | 94.0358i | − | 1.46931i | |||||||
−21.6223 | + | 1.11769i | −0.332651 | + | 0.0171952i | |||||
−20.3816 | − | 2.22403i | −0.308813 | − | 0.0336974i | |||||
5.59919 | + | 20.8965i | 0.0835700 | + | 0.311888i | 0.995040 | − | 0.0994800i | ||
−0.911470 | + | 0.411368i | ||||||||
167.402 | − | 44.8553i | 2.46180 | − | 0.659637i | |||||
−3.87703 | + | 35.5302i | −0.0561888 | + | 0.514931i | |||||
−112.920 | − | 101.820i | −1.61314 | − | 1.45457i | |||||
−28.6105 | −0.402965 | −0.201483 | − | 0.979492i | ||||||
−0.201483 | + | 0.979492i | ||||||||
4.19166 | + | 94.2997i | 0.0582175 | + | 1.30972i | |||||
48.1316 | + | 48.1316i | 0.659336 | + | 0.659336i | 0.955223 | − | 0.295887i | ||
−0.295887 | + | 0.955223i | ||||||||
136.071 | − | 78.5604i | 1.83879 | − | 1.06163i | |||||
53.3185 | − | 52.7460i | 0.710914 | − | 0.703279i | |||||
66.5507 | − | 115.269i | 0.875667 | − | 1.51670i | |||||
−4.82753 | − | 18.0166i | −0.0626953 | − | 0.233982i | |||||
−15.7004 | + | 40.4205i | −0.201287 | + | 0.518212i | |||||
−0.201686 | + | 0.116444i | −0.00255299 | + | 0.00147397i | −0.501276 | − | 0.865287i | ||
0.498723 | + | 0.866761i | ||||||||
−9.92959 | − | 30.6346i | −0.124120 | − | 0.382932i | |||||
7.18677 | + | 80.6805i | 0.0887255 | + | 0.996056i | |||||
−10.1850 | + | 10.1850i | −0.124207 | + | 0.124207i | |||||
41.1240 | − | 153.477i | 0.495470 | − | 1.84912i | −0.0319094 | − | 0.999491i | ||
0.527380 | − | 0.849630i | ||||||||
−178.633 | + | 78.6845i | −2.12658 | + | 0.936720i | |||||
−101.802 | + | 66.0077i | −1.19767 | + | 0.776562i | |||||
−52.5583 | + | 91.0337i | −0.611143 | + | 1.05853i | |||||
−10.2979 | − | 66.7316i | −0.118367 | − | 0.767030i | |||||
5.55774 | − | 20.7418i | 0.0631561 | − | 0.235702i | |||||
103.385i | 1.16163i | 0.814035 | + | 0.580816i | ||||||
−0.814035 | + | 0.580816i | ||||||||
−52.6145 | − | 140.692i | −0.584606 | − | 1.56325i | |||||
−39.4490 | −0.433506 | |||||||||
−82.1891 | − | 22.0225i | −0.893360 | − | 0.239375i | |||||
−44.8512 | − | 55.8384i | −0.482271 | − | 0.600413i | |||||
2.51088 | + | 1.44966i | 0.0267115 | + | 0.0154219i | |||||
−19.4386 | + | 91.1313i | −0.204617 | + | 0.959277i | |||||
60.9981 | + | 6.65606i | 0.635397 | + | 0.0693340i | |||||
69.7287 | + | 18.6837i | 0.718852 | + | 0.192616i | 0.599660 | − | 0.800255i | ||
0.119193 | + | 0.992871i | ||||||||
−80.2366 | − | 80.2366i | −0.818741 | − | 0.818741i | |||||
3.97409 | − | 17.9931i | 0.0401424 | − | 0.181748i | |||||
104.743 | + | 144.601i | 1.04743 | + | 1.44601i | |||||
−31.0086 | − | 53.7085i | −0.307016 | − | 0.531767i | 0.670692 | − | 0.741736i | ||
−0.977708 | + | 0.209969i | ||||||||
37.0599 | + | 240.153i | 0.363332 | + | 2.35444i | |||||
51.0537 | − | 13.6798i | 0.495667 | − | 0.132813i | −0.00232157 | − | 0.999997i | ||
0.497988 | + | 0.867184i | ||||||||
−39.3314 | − | 22.7080i | −0.378186 | − | 0.218346i | |||||
101.979 | − | 90.9612i | 0.971230 | − | 0.866297i | |||||
7.86727 | + | 13.6265i | 0.0742195 | + | 0.128552i | |||||
84.3909 | − | 84.3909i | 0.788700 | − | 0.788700i | −0.192581 | − | 0.981281i | ||
0.981281 | + | 0.192581i | ||||||||
−192.437 | − | 12.3846i | −1.78183 | − | 0.114672i | |||||
− | 102.481i | − | 0.940190i | −0.882616 | − | 0.470095i | ||||
0.882616 | − | 0.470095i | ||||||||
1.76399 | + | 34.1255i | 0.0160363 | + | 0.310231i | |||||
56.9237 | + | 129.231i | 0.512826 | + | 1.16424i | |||||
−15.1864 | − | 56.6764i | −0.135593 | − | 0.506040i | |||||
39.2529 | − | 10.5178i | 0.347371 | − | 0.0930777i | −0.0809152 | − | 0.996721i | ||
0.428286 | + | 0.903643i | ||||||||
150.544 | + | 110.292i | 1.32056 | + | 0.967475i | |||||
59.4892 | − | 3.07508i | 0.517297 | − | 0.0267398i | |||||
160.747 | 1.38575 | |||||||||
−34.5829 | − | 17.9681i | −0.295580 | − | 0.153574i | |||||
180.766 | + | 180.766i | 1.53192 | + | 1.53192i | |||||
−191.447 | + | 110.532i | −1.60880 | + | 0.928840i | |||||
154.035 | − | 31.9878i | 1.28363 | − | 0.266565i | |||||
58.4041 | − | 101.159i | 0.482678 | − | 0.836023i | |||||
−61.1012 | − | 228.033i | −0.500829 | − | 1.86912i | |||||
−8.10678 | − | 10.0927i | −0.0659088 | − | 0.0820544i | |||||
147.663 | − | 85.2534i | 1.19083 | − | 0.687528i | |||||
−100.969 | − | 73.6897i | −0.807755 | − | 0.589518i | |||||
−82.5039 | − | 260.952i | −0.654793 | − | 2.07105i | |||||
−81.3527 | + | 81.3527i | −0.640572 | + | 0.640572i | −0.950696 | − | 0.310124i | ||
0.310124 | + | 0.950696i | ||||||||
−60.0655 | + | 224.167i | −0.469261 | + | 1.75131i | |||||
−76.2096 | − | 55.8331i | −0.590772 | − | 0.432814i | |||||
70.6811 | + | 15.0765i | 0.543701 | + | 0.115973i | |||||
−41.3420 | + | 71.6064i | −0.315588 | + | 0.546614i | −0.979562 | − | 0.201141i | ||
0.663975 | + | 0.747755i | ||||||||
40.8918 | + | 15.8834i | 0.309786 | + | 0.120329i | |||||
−43.9420 | + | 163.994i | −0.330391 | + | 1.23303i | |||||
− | 72.2124i | − | 0.538899i | |||||||
130.831 | − | 33.2919i | 0.969116 | − | 0.246606i | |||||
−254.502 | −1.87134 | |||||||||
150.637 | + | 40.3630i | 1.09954 | + | 0.294621i | 0.762577 | − | 0.646898i | ||
0.336962 | + | 0.941518i | ||||||||
43.1961 | − | 111.208i | 0.313015 | − | 0.805857i | |||||
1.35272 | + | 0.780993i | 0.00973180 | + | 0.00561866i | 0.504858 | − | 0.863202i | ||
−0.495126 | + | 0.868821i | ||||||||
176.990 | + | 272.967i | 1.26421 | + | 1.94976i | |||||
−1.53998 | + | 2.10201i | −0.0109219 | + | 0.0149079i | |||||
92.2470 | + | 24.7175i | 0.649627 | + | 0.174067i | |||||
6.26906 | + | 6.26906i | 0.0438396 | + | 0.0438396i | |||||
12.5017 | − | 56.6024i | 0.0868171 | − | 0.393072i | |||||
−107.053 | + | 34.6990i | −0.738295 | + | 0.239304i | |||||
−113.605 | − | 196.770i | −0.778117 | − | 1.34774i | |||||
79.5095 | − | 63.8646i | 0.540881 | − | 0.434453i | |||||
−324.727 | + | 87.0102i | −2.19410 | + | 0.587907i | |||||
87.4092 | + | 50.4657i | 0.586639 | + | 0.338696i | 0.763767 | − | 0.645492i | ||
−0.177128 | + | 0.984188i | ||||||||
−217.480 | + | 124.002i | −1.44987 | + | 0.826678i | |||||
−109.094 | − | 188.956i | −0.722477 | − | 1.25137i | −0.960004 | − | 0.279986i | ||
0.237527 | − | 0.971381i | ||||||||
−138.210 | + | 138.210i | −0.909279 | + | 0.909279i | |||||
−218.177 | + | 9.69804i | −1.42599 | + | 0.0633859i | |||||
62.2604i | 0.404288i | |||||||||
−79.9363 | + | 88.6508i | −0.515718 | + | 0.571941i | |||||
54.8325 | − | 74.8439i | 0.351490 | − | 0.479769i | |||||
−68.7136 | − | 256.443i | −0.437666 | − | 1.63339i | −0.734604 | − | 0.678496i | ||
0.296937 | − | 0.954897i | ||||||||
0.750883 | − | 0.201198i | 0.00475242 | − | 0.00127341i | |||||
−12.9416 | + | 5.70051i | −0.0813934 | + | 0.0358522i | |||||
−5.27928 | − | 102.131i | −0.0329955 | − | 0.638316i | |||||
108.535 | 0.674133 | |||||||||
46.5306 | − | 266.342i | 0.287226 | − | 1.64408i | |||||
−161.076 | − | 161.076i | −0.988199 | − | 0.988199i | 0.0117324 | − | 0.999931i | ||
−0.999931 | + | 0.0117324i | ||||||||
26.6899 | − | 15.4094i | 0.162743 | − | 0.0939598i | |||||
−30.6612 | − | 1.75093i | −0.185826 | − | 0.0106117i | |||||
−265.187 | + | 459.317i | −1.59751 | + | 2.76697i | |||||
15.4399 | + | 57.6223i | 0.0924542 | + | 0.345044i | 0.996621 | − | 0.0821354i | ||
−0.904167 | + | 0.427179i | ||||||||
283.290 | − | 43.7167i | 1.68625 | − | 0.260219i | |||||
−130.119 | + | 75.1245i | −0.769938 | + | 0.444524i | |||||
385.260 | − | 124.874i | 2.26624 | − | 0.734555i | |||||
−113.217 | + | 123.750i | −0.662087 | + | 0.723685i | |||||
159.037 | − | 159.037i | 0.924631 | − | 0.924631i | |||||
25.0902 | − | 93.6378i | 0.145030 | − | 0.541259i | −0.854724 | − | 0.519083i | ||
0.999754 | − | 0.0221766i | ||||||||
−24.4487 | + | 224.055i | −0.140510 | + | 1.28767i | |||||
−176.792 | − | 143.582i | −1.01024 | − | 0.820470i | |||||
−6.59341 | + | 11.4201i | −0.0374626 | + | 0.0648871i | |||||
−179.128 | + | 143.881i | −1.01202 | + | 0.812889i | |||||
89.3176 | − | 333.338i | 0.501784 | − | 1.87269i | |||||
89.4315i | 0.499617i | 0.968295 | + | 0.249809i | ||||||
−0.968295 | + | 0.249809i | ||||||||
30.8276 | + | 319.911i | 0.171265 | + | 1.77728i | |||||
307.336 | 1.69799 | 0.848995 | − | 0.528401i | ||||||
0.848995 | + | 0.528401i | ||||||||
127.193 | + | 34.0812i | 0.698861 | + | 0.187259i | |||||
209.692 | − | 32.3592i | 1.14586 | − | 0.176826i | |||||
108.212 | + | 62.4761i | 0.588107 | + | 0.339544i | |||||
197.476 | − | 128.042i | 1.06744 | − | 0.692117i | |||||
96.3703 | + | 218.784i | 0.518120 | + | 1.17626i | |||||
47.9892 | + | 12.8587i | 0.256627 | + | 0.0687629i | |||||
−4.38653 | − | 4.38653i | −0.0233326 | − | 0.0233326i | |||||
241.190 | − | 48.2721i | 1.27614 | − | 0.255408i | |||||
141.406 | − | 277.035i | 0.744241 | − | 1.45808i | |||||
81.7990 | + | 141.680i | 0.428267 | + | 0.741780i | 0.996719 | − | 0.0809360i | ||
−0.568452 | + | 0.822716i | ||||||||
−262.966 | − | 102.143i | −1.36962 | − | 0.531994i | |||||
245.520 | − | 65.7869i | 1.27212 | − | 0.340865i | 0.441280 | − | 0.897369i | ||
0.830845 | + | 0.556504i | ||||||||
−208.680 | − | 120.481i | −1.07567 | − | 0.621039i | |||||
−20.3609 | + | 61.6799i | −0.104415 | + | 0.316307i | |||||
121.394 | + | 210.261i | 0.619358 | + | 1.07276i | |||||
−83.9878 | + | 83.9878i | −0.426334 | + | 0.426334i | −0.887377 | − | 0.461044i | ||
0.461044 | + | 0.887377i | ||||||||
−28.3582 | + | 54.5805i | −0.143223 | + | 0.275659i | |||||
165.065i | 0.829471i | 0.909942 | + | 0.414736i | ||||||
−0.909942 | + | 0.414736i | ||||||||
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64.5179 | + | 7.04014i | 0.320985 | + | 0.0350256i | |||||
53.5786 | + | 199.958i | 0.265240 | + | 0.989891i | |||||
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56.3987 | − | 516.855i | 0.276464 | − | 2.53360i | |||||
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−176.427 | −0.856443 | |||||||||
95.1473 | + | 49.4353i | 0.459649 | + | 0.238818i | |||||
19.7211 | + | 19.7211i | 0.0948132 | + | 0.0948132i | |||||
33.0442 | − | 19.0781i | 0.158106 | − | 0.0912827i | |||||
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5.87275 | − | 10.1719i | 0.0278329 | − | 0.0482081i | −0.851773 | − | 0.523910i | ||
0.879606 | + | 0.475702i | ||||||||
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186.879 | − | 82.3165i | 0.853327 | − | 0.375874i | |||||
15.2523 | − | 71.5051i | 0.0693285 | − | 0.325023i | |||||
52.5383 | − | 90.9991i | 0.237730 | − | 0.411761i | |||||
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0.958096 | + | 0.286448i | ||||||||
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427.557 | + | 114.563i | 1.88351 | + | 0.504685i | 0.999293 | + | 0.0376093i | ||
0.884217 | + | 0.467076i | ||||||||
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95.9802 | + | 87.8106i | 0.410172 | + | 0.375259i | |||||
3.86817 | + | 1.97441i | 0.0164603 | + | 0.00840176i | |||||
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0.106555 | + | 0.690489i | 0.000449599 | + | 0.00291345i | |||||
712.762 | − | 190.984i | 2.99480 | − | 0.802454i | |||||
57.9140 | + | 33.4367i | 0.242318 | + | 0.139902i | 0.616242 | − | 0.787557i | ||
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233.426 | + | 67.5388i | 0.960599 | + | 0.277937i | |||||
505.119i | 2.07016i | |||||||||
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17.4188 | + | 39.5449i | 0.0708080 | + | 0.160751i | |||||
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261.886 | + | 324.823i | 1.04754 | + | 1.29929i | |||||
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26.0038 | + | 585.007i | 0.103190 | + | 2.32146i | |||||
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332.583 | − | 192.017i | 1.30938 | − | 0.755972i | |||||
74.0087 | + | 356.383i | 0.290230 | + | 1.39758i | |||||
199.259 | − | 345.126i | 0.778354 | − | 1.34815i | |||||
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0.840515 | − | 0.541789i | ||||||||
197.482 | + | 245.859i | 0.765433 | + | 0.952940i | |||||
371.369 | − | 214.410i | 1.43386 | − | 0.827837i | |||||
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195.159 | − | 195.159i | 0.744882 | − | 0.744882i | |||||
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12.8225 | + | 19.7758i | 0.0483867 | + | 0.0746257i | |||||
283.358 | − | 490.791i | 1.06526 | − | 1.84508i | |||||
289.112 | + | 112.298i | 1.08282 | + | 0.420593i | |||||
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81.1798i | 0.301784i | 0.988550 | + | 0.150892i | ||||||
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150.964 | + | 40.4506i | 0.555014 | + | 0.148716i | |||||
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5.27758 | + | 50.9125i | 0.0191912 | + | 0.185136i | |||||
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6.78125 | − | 5.44693i | 0.0240470 | − | 0.0193153i | |||||
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233.730 | + | 153.347i | 0.820105 | + | 0.538060i | |||||
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84.8702 | − | 163.348i | 0.294688 | − | 0.567182i | |||||
− | 299.828i | − | 1.03747i | |||||||
375.141 | − | 19.3916i | 1.29359 | − | 0.0668674i | |||||
127.988 | − | 174.698i | 0.439822 | − | 0.600338i | |||||
125.824 | + | 469.582i | 0.430905 | + | 1.60816i | |||||
289.453 | − | 77.5588i | 0.987895 | − | 0.264706i | 0.271529 | − | 0.962430i | ||
0.716366 | + | 0.697725i | ||||||||
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284.389 | + | 256.433i | 0.964031 | + | 0.869265i | |||||
493.682 | 1.66784 | |||||||||
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518.143 | − | 135.842i | 1.72714 | − | 0.452808i | |||||
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188.499 | + | 703.489i | 0.624170 | + | 2.32944i | |||||
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103.950 | − | 60.0156i | 0.341941 | − | 0.197420i | |||||
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711.831 | + | 157.221i | 2.32624 | + | 0.513793i | |||||
138.397 | − | 138.397i | 0.450805 | − | 0.450805i | −0.444817 | − | 0.895622i | ||
0.895622 | + | 0.444817i | ||||||||
34.4785 | − | 128.676i | 0.111943 | − | 0.417778i | |||||
17.2003 | − | 157.628i | 0.0556643 | − | 0.510124i | |||||
334.321 | − | 216.771i | 1.07846 | − | 0.699263i | |||||
53.6367 | − | 92.9015i | 0.172465 | − | 0.298719i | −0.766816 | − | 0.641867i | ||
0.939281 | + | 0.343148i | ||||||||
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−0.696004 | + | 0.718038i | ||||||||
886.195i | 2.82228i | |||||||||
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−1.66329 | −0.00526359 | |||||||||
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46.6514 | − | 7.19916i | 0.146703 | − | 0.0226389i | |||||
39.9077 | + | 23.0407i | 0.125103 | + | 0.0722280i | |||||
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106.899 | + | 17.0877i | 0.328920 | + | 0.0525777i | |||||
380.189 | + | 658.507i | 1.16622 | + | 2.01996i | |||||
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6.85279 | + | 3.95646i | 0.0208292 | + | 0.0120257i | |||||
97.3463 | + | 32.1346i | 0.294989 | + | 0.0973775i | |||||
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−0.0406933 | − | 0.999172i | ||||||||
802.431 | − | 802.431i | 2.41696 | − | 2.41696i | |||||
423.219 | − | 18.8122i | 1.27093 | − | 0.0564932i | |||||
− | 199.127i | − | 0.596188i | |||||||
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123.174 | + | 459.691i | 0.365501 | + | 1.36407i | 0.866740 | + | 0.498760i | ||
−0.501239 | + | 0.865309i | ||||||||
484.438 | − | 129.805i | 1.43325 | − | 0.384038i | |||||
13.2245 | − | 121.193i | 0.0390104 | − | 0.357502i | |||||
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48.8792 | 0.143341 | |||||||||
471.949 | − | 301.188i | 1.37997 | − | 0.880667i | |||||
96.6647 | + | 96.6647i | 0.281821 | + | 0.281821i | |||||
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56.0186 | − | 169.699i | 0.162373 | − | 0.491880i | |||||
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−0.999982 | + | 0.00595969i | ||||||||
174.606 | − | 449.523i | 0.501741 | − | 1.29173i | |||||
298.148 | − | 172.136i | 0.854292 | − | 0.493226i | −0.00780468 | − | 0.999970i | ||
0.862097 | + | 0.506744i | ||||||||
445.974 | + | 615.679i | 1.27421 | + | 1.75908i | |||||
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−0.991554 | + | 0.129695i | ||||||||
701.854 | − | 309.153i | 1.98264 | − | 0.873314i | |||||
139.905 | + | 29.8423i | 0.394100 | + | 0.0840628i | |||||
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101.145 | + | 655.434i | 0.283320 | + | 1.83595i | |||||
77.2626 | − | 288.348i | 0.215817 | − | 0.805441i | |||||
− | 411.438i | − | 1.14607i | −0.819532 | − | 0.573033i | ||||
0.819532 | − | 0.573033i | ||||||||
77.8623 | − | 465.497i | 0.216284 | − | 1.29305i | |||||
13.6890 | 0.0379198 | |||||||||
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626.938 | + | 167.988i | 1.70828 | + | 0.457732i | 0.975001 | − | 0.222199i | ||
0.733277 | + | 0.679930i | ||||||||
−54.2584 | − | 54.2584i | −0.147441 | − | 0.147441i | |||||
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21.4716 | + | 37.1900i | 0.0578751 | + | 0.100243i | |||||
−78.0134 | − | 505.537i | −0.209714 | − | 1.35897i | |||||
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0.112211 | + | 0.993684i | ||||||||
−143.619 | − | 82.9186i | −0.384009 | − | 0.221708i | |||||
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4.55491 | + | 7.88933i | 0.0121141 | + | 0.0209823i | |||||
68.9157 | − | 68.9157i | 0.182800 | − | 0.182800i | |||||
−819.356 | − | 52.7309i | −2.16761 | − | 0.139500i | |||||
317.077i | 0.836614i | 0.908306 | + | 0.418307i | ||||||
−0.908306 | + | 0.418307i | ||||||||
−445.664 | + | 494.250i | −1.17280 | + | 1.30066i | |||||
139.133 | + | 315.865i | 0.365177 | + | 0.829043i | |||||
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−86.0774 | + | 23.0644i | −0.224745 | + | 0.0602203i | −0.369434 | − | 0.929257i | ||
0.144689 | + | 0.989477i | ||||||||
561.629 | + | 411.464i | 1.46258 | + | 1.07152i | |||||
4.81436 | + | 93.1365i | 0.0125048 | + | 0.241913i | |||||
−848.449 | −2.19806 | |||||||||
−238.914 | + | 152.470i | −0.617350 | + | 0.393979i | |||||
364.566 | + | 364.566i | 0.939602 | + | 0.939602i | |||||
−64.0677 | + | 36.9895i | −0.164698 | + | 0.0950887i | −0.580084 | − | 0.814557i | ||
0.415385 | + | 0.909646i | ||||||||
118.935 | − | 181.280i | 0.304963 | − | 0.464820i | |||||
−144.548 | + | 250.364i | −0.369687 | + | 0.640318i | |||||
−92.2778 | − | 344.386i | −0.235403 | − | 0.878535i | |||||
155.338 | + | 193.391i | 0.395261 | + | 0.492088i | |||||
343.356 | − | 198.237i | 0.871461 | − | 0.503138i | |||||
1.10770 | − | 0.359039i | 0.00280431 | − | 0.000908961i | |||||
88.8343 | − | 97.0991i | 0.224329 | − | 0.245200i | |||||
331.663 | − | 331.663i | 0.835422 | − | 0.835422i | −0.152830 | − | 0.988252i | ||
0.988252 | + | 0.152830i | ||||||||
142.605 | − | 532.207i | 0.358303 | − | 1.33720i | |||||
410.870 | + | 301.013i | 1.02975 | + | 0.754420i | |||||
16.6022 | + | 160.160i | 0.0415054 | + | 0.400400i | |||||
−324.360 | + | 561.808i | −0.808877 | + | 1.40102i | 0.104765 | + | 0.994497i | ||
−0.913642 | + | 0.406520i | ||||||||
−201.939 | − | 78.4380i | −0.502335 | − | 0.195119i | |||||
26.7564 | − | 99.8561i | 0.0663930 | − | 0.247782i | |||||
− | 442.930i | − | 1.09636i | |||||||
49.0108 | − | 402.024i | 0.121014 | − | 0.992651i | |||||
684.428 | 1.68578 | |||||||||
−93.0893 | − | 24.9432i | −0.228721 | − | 0.0612855i | |||||
−276.443 | + | 711.702i | −0.677556 | + | 1.74437i | |||||
545.487 | + | 314.937i | 1.33371 | + | 0.770017i | 0.985866 | − | 0.167536i | ||
0.347842 | + | 0.937553i | ||||||||
60.4280 | − | 39.1810i | 0.147385 | − | 0.0955635i | |||||
276.497 | − | 377.406i | 0.672742 | − | 0.918262i | |||||
364.628 | + | 97.7018i | 0.885019 | + | 0.237140i | |||||
493.353 | + | 493.353i | 1.19456 | + | 1.19456i | |||||
−264.069 | − | 241.592i | −0.637847 | − | 0.583555i | |||||
−361.181 | + | 707.607i | −0.870315 | + | 1.70508i | |||||
44.2841 | + | 76.7023i | 0.106452 | + | 0.184380i | |||||
3.65335 | − | 2.93449i | 0.00876103 | − | 0.00703715i | |||||
−123.024 | + | 32.9643i | −0.294317 | + | 0.0788619i | |||||
153.113 | + | 88.3997i | 0.365424 | + | 0.210978i | 0.671457 | − | 0.741043i | ||
−0.306033 | + | 0.952021i | ||||||||
955.587 | − | 198.443i | 2.27521 | − | 0.472483i | |||||
44.6779 | + | 77.3843i | 0.106123 | + | 0.183811i | 0.914197 | − | 0.405271i | ||
−0.808073 | + | 0.589082i | ||||||||
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4.20542 | + | 6.58972i | 0.00994188 | + | 0.0155785i | |||||
49.4388i | 0.116601i | |||||||||
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169.321 | − | 231.116i | 0.397468 | − | 0.542526i | |||||
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823.337 | − | 220.612i | 1.92368 | − | 0.515449i | |||||
24.3407 | − | 10.7216i | 0.0567381 | − | 0.0249921i | |||||
351.963 | − | 390.333i | 0.818518 | − | 0.907751i | |||||
648.364 | 1.50433 | 0.752163 | − | 0.658977i | ||||||
0.752163 | + | 0.658977i | ||||||||
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628.718 | − | 362.991i | 1.44866 | − | 0.836384i | |||||
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365.961 | − | 633.864i | 0.839361 | − | 1.45382i | |||||
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0.924746 | − | 0.380584i | ||||||||
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107.836 | − | 505.553i | 0.242328 | − | 1.13607i | |||||
21.3741 | − | 37.0210i | 0.0479239 | − | 0.0830067i | |||||
236.070 | − | 189.619i | 0.528121 | − | 0.424204i | |||||
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0.959794 | − | 0.280705i | ||||||||
110.535 | + | 742.865i | 0.245634 | + | 1.65081i | |||||
8.83482 | 0.0195894 | |||||||||
280.346 | + | 75.1186i | 0.620235 | + | 0.166191i | |||||
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236.373 | + | 536.624i | 0.518361 | + | 1.17681i | |||||
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254.881 | + | 441.467i | 0.552887 | + | 0.957629i | 0.998065 | + | 0.0621865i | ||
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174.108 | + | 67.6280i | 0.376858 | + | 0.146381i | |||||
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0.553293 | + | 0.832987i | ||||||||
125.541 | + | 72.4813i | 0.270563 | + | 0.156210i | |||||
161.080 | + | 319.832i | 0.346408 | + | 0.687810i | |||||
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0.179217 | + | 0.983810i | ||||||||
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190.109 | − | 425.356i | 0.400230 | − | 0.895486i | |||||
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1.88391 | + | 42.3824i | 0.00394951 | + | 0.0888520i | |||||
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0.0542492 | + | 0.998527i | ||||||||
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0.991070 | + | 0.133345i | ||||||||
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308.665 | + | 476.047i | 0.629930 | + | 0.971525i | |||||
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0.929523 | − | 0.368765i | ||||||||
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141.355 | − | 527.544i | 0.286724 | − | 1.07007i | |||||
269.373i | 0.545289i | |||||||||
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153.764 | 0.310007 | |||||||||
251.764 | + | 67.4600i | 0.506567 | + | 0.135734i | |||||
996.409 | + | 1240.50i | 2.00082 | + | 2.49096i | |||||
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177.909 | + | 19.4133i | 0.355108 | + | 0.0387491i | |||||
285.596 | + | 76.5253i | 0.568917 | + | 0.152441i | |||||
350.849 | + | 350.849i | 0.697512 | + | 0.697512i | 0.963873 | − | 0.266361i | ||
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185.461 | − | 839.692i | 0.367979 | − | 1.66606i | |||||
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40.7104 | + | 70.5125i | 0.0804553 | + | 0.139353i | |||||
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223.084 | + | 451.025i | 0.434861 | + | 0.879190i | |||||
524.643i | 1.02071i | |||||||||
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168.645 | + | 152.067i | 0.324317 | + | 0.292436i | |||||
749.947 | 1.43944 | 0.719718 | − | 0.694266i | ||||||
0.719718 | + | 0.694266i | ||||||||
600.002 | + | 311.741i | 1.14943 | + | 0.597205i | |||||
377.284 | + | 377.284i | 0.721385 | + | 0.721385i | 0.968887 | − | 0.247502i | ||
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113.448 | − | 196.497i | 0.211656 | − | 0.366599i | |||||
250.091 | + | 97.1416i | 0.465719 | + | 0.180897i | |||||
70.1337 | − | 261.743i | 0.130360 | − | 0.486510i | |||||
69.6001i | 0.129128i | |||||||||
928.100 | + | 261.283i | 1.71870 | + | 0.483857i | |||||
861.919 | 1.59320 | 0.796598 | − | 0.604509i | ||||||
0.796598 | + | 0.604509i | ||||||||
310.850 | + | 83.2920i | 0.573524 | + | 0.153675i | |||||
333.832 | − | 859.451i | 0.614793 | − | 1.58278i | |||||
429.824 | + | 248.159i | 0.790117 | + | 0.456174i | |||||
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233.465 | − | 318.669i | 0.427591 | − | 0.583643i | |||||
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787.582 | + | 787.582i | 1.43719 | + | 1.43719i | |||||
137.279 | − | 621.542i | 0.250052 | − | 1.13213i | |||||
26.9687 | − | 168.713i | 0.0490340 | − | 0.306751i | |||||
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292.252 | − | 234.747i | 0.529442 | − | 0.425266i | |||||
2.04934 | − | 0.549118i | 0.00370585 | − | 0.000992981i | |||||
1266.55 | + | 731.241i | 2.28619 | + | 1.31993i | |||||
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5.57790 | + | 9.66120i | 0.0100322 | + | 0.0173763i | |||||
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0.431269 | + | 0.902223i | ||||||||
716.499 | − | 31.8487i | 1.28405 | − | 0.0570765i | |||||
− | 136.364i | − | 0.243943i | |||||||
15.1450 | + | 292.988i | 0.0270446 | + | 0.523192i | |||||
88.0851 | − | 120.232i | 0.157014 | − | 0.214318i | |||||
165.102 | + | 616.171i | 0.293777 | + | 1.09639i | |||||
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1155.68 | 2.04183 | |||||||||
126.993 | − | 726.910i | 0.223973 | − | 1.28203i | |||||
212.181 | + | 212.181i | 0.373559 | + | 0.373559i | |||||
632.780 | − | 365.336i | 1.11209 | − | 0.642066i | 0.172721 | − | 0.984971i | ||
0.939370 | + | 0.342905i | ||||||||
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16.3884 | + | 61.1624i | 0.0286511 | + | 0.106927i | |||||
485.052 | − | 74.8523i | 0.846514 | − | 0.130632i | |||||
113.640 | − | 65.6099i | 0.197978 | − | 0.114303i | |||||
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0.0876926 | + | 0.996148i | ||||||||
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82.7171 | − | 758.044i | 0.142862 | − | 1.30923i | |||||
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2.49789 | − | 9.32225i | 0.00428454 | − | 0.0159901i | |||||
− | 713.907i | − | 1.22244i | |||||||
150.369 | + | 123.936i | 0.257040 | + | 0.211856i | |||||
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527.677 | + | 141.391i | 0.898938 | + | 0.240870i | 0.678560 | − | 0.734545i | ||
0.220378 | + | 0.975415i | ||||||||
719.845 | − | 111.085i | 1.22423 | − | 0.188920i | |||||
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143.639 | + | 326.096i | 0.243044 | + | 0.551770i | |||||
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121.829 | + | 138.588i | 0.205099 | + | 0.233314i | |||||
1051.47 | − | 340.812i | 1.76717 | − | 0.572793i | |||||
360.429 | + | 624.282i | 0.604747 | + | 1.04745i | |||||
461.596 | + | 179.295i | 0.773192 | + | 0.300327i | |||||
166.336 | − | 44.5696i | 0.278154 | − | 0.0745310i | |||||
572.037 | + | 330.266i | 0.954987 | + | 0.551362i | 0.894626 | − | 0.446815i | ||
0.0603602 | + | 0.998177i | ||||||||
−786.595 | − | 4.24624i | −1.31099 | − | 0.00707706i | |||||
65.1748 | + | 112.886i | 0.108444 | + | 0.187830i | 0.915140 | − | 0.403136i | ||
−0.806696 | + | 0.590966i | ||||||||
677.143 | − | 677.143i | 1.12482 | − | 1.12482i | |||||
89.7675 | − | 172.774i | 0.148868 | − | 0.286524i | |||||
− | 1558.31i | − | 2.57999i | |||||||
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617.371 | + | 67.3669i | 1.01876 | + | 0.111167i | |||||
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0.861460 | − | 0.507826i | ||||||||
368.187 | − | 98.6554i | 0.605571 | − | 0.162262i | |||||
−66.7263 | + | 611.499i | −0.109567 | + | 1.00410i | |||||
60.9344 | + | 1178.81i | 0.0998924 | + | 1.93248i | |||||
−3.76119 | −0.00615580 | |||||||||
−1384.10 | − | 719.130i | −2.26160 | − | 1.17505i | |||||
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−0.324921 | − | 0.945741i | ||||||||
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29.1149 | + | 57.8090i | 0.0473413 | + | 0.0939983i | |||||
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0.856025 | − | 0.516934i | ||||||||
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0.0915591 | + | 0.995800i | ||||||||
−810.996 | + | 262.868i | −1.30806 | + | 0.423981i | |||||
241.594 | − | 212.378i | 0.389040 | − | 0.341993i | |||||
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243.769 | − | 909.758i | 0.391282 | − | 1.46029i | |||||
76.5706 | − | 33.7279i | 0.122709 | − | 0.0540511i | |||||
416.878 | + | 465.659i | 0.667004 | + | 0.745054i | |||||
912.840 | − | 1581.09i | 1.45821 | − | 2.52569i | |||||
−17.4579 | − | 113.129i | −0.0278435 | − | 0.180430i | |||||
490.756 | − | 1831.53i | 0.781459 | − | 2.91645i | |||||
1142.21i | 1.81591i | |||||||||
131.257 | + | 1362.11i | 0.208345 | + | 2.16208i | |||||
−48.4016 | −0.0767062 | −0.0383531 | − | 0.999264i | ||||||
−0.0383531 | + | 0.999264i | ||||||||
2.35932 | + | 0.632177i | 0.00373309 | + | 0.00100028i | |||||
−22.0662 | − | 27.4717i | −0.0348597 | − | 0.0433992i | |||||
1261.33 | + | 728.230i | 1.98948 | + | 1.14863i | |||||
482.669 | − | 312.959i | 0.760109 | − | 0.492849i | |||||
−100.403 | − | 10.9559i | −0.157866 | − | 0.0172262i | |||||
142.187 | + | 38.0990i | 0.223214 | + | 0.0598100i | |||||
−108.766 | − | 108.766i | −0.170480 | − | 0.170480i | |||||
189.982 | + | 173.811i | 0.297312 | + | 0.272005i | |||||
527.538 | − | 1033.53i | 0.824278 | − | 1.61488i | |||||
−313.217 | − | 542.507i | −0.488637 | − | 0.846345i | 0.511277 | − | 0.859416i | ||
−0.999915 | + | 0.0130711i | ||||||||
182.272 | + | 1181.15i | 0.283913 | + | 1.83979i | |||||
−467.479 | + | 125.261i | −0.727028 | + | 0.194807i | −0.603305 | − | 0.797510i | ||
−0.123723 | + | 0.992317i | ||||||||
671.313 | + | 387.583i | 1.04241 | + | 0.601836i | |||||
314.428 | + | 352.514i | 0.487485 | + | 0.546533i | |||||
754.755 | + | 1307.27i | 1.16835 | + | 2.02364i | |||||
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0.340135 | + | 0.940377i | ||||||||
545.045 | − | 651.642i | 0.841118 | − | 1.00562i | |||||
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0.109434 | + | 0.993994i | ||||||||
827.839 | + | 606.495i | 1.26581 | + | 0.927363i | |||||
276.851 | − | 307.033i | 0.422674 | − | 0.468753i | |||||
27.7925 | 0.0423666 | |||||||||
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0.571992 | + | 0.820259i | ||||||||
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506.525 | + | 1890.38i | 0.765144 | + | 2.85556i | |||||
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0.994485 | + | 0.104882i | ||||||||
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1244.51 | + | 265.459i | 1.83016 | + | 0.390380i | |||||
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441.268 | + | 441.268i | 0.646074 | + | 0.646074i | 0.952042 | − | 0.305968i | ||
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195.915 | − | 52.4952i | 0.284760 | − | 0.0763012i | |||||
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396.083 | + | 686.036i | 0.573202 | + | 0.992816i | 0.996234 | + | 0.0867010i | ||
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489.571 | − | 489.571i | 0.707473 | − | 0.707473i | |||||
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586.222i | 0.844700i | |||||||||
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349.813 | − | 173.023i | 0.498309 | − | 0.246471i | |||||
620.290 | + | 620.290i | 0.882348 | + | 0.882348i | |||||
166.736 | − | 96.2650i | 0.236841 | − | 0.136740i | |||||
9.72301 | − | 8.67252i | 0.0137915 | − | 0.0123015i | |||||
450.005 | − | 779.431i | 0.637401 | − | 1.10401i | |||||
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0.322934 | + | 0.946421i | ||||||||
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2.04666 | + | 0.452042i | 0.00287856 | + | 0.000635783i | |||||
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240.133 | − | 2200.65i | 0.336321 | − | 3.08215i | |||||
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156.411 | − | 125.634i | 0.218146 | − | 0.175222i | |||||
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1900.94 | + | 1097.51i | 2.62560 | + | 1.51589i | |||||
559.680 | − | 58.0164i | 0.771973 | − | 0.0800226i | |||||
471.517 | + | 1070.46i | 0.649473 | + | 1.47446i | |||||
688.962 | + | 184.607i | 0.947678 | + | 0.253930i | 0.699377 | − | 0.714753i | ||
0.248302 | + | 0.968683i | ||||||||
292.562 | + | 292.562i | 0.401870 | + | 0.401870i | |||||
442.419 | − | 579.402i | 0.606884 | − | 0.794790i | |||||
350.287 | + | 1080.70i | 0.479845 | + | 1.48041i | |||||
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1412.54 | + | 548.667i | 1.92970 | + | 0.749545i | |||||
858.390 | − | 230.005i | 1.17106 | − | 0.313786i | 0.379688 | − | 0.925115i | ||
0.791377 | + | 0.611329i | ||||||||
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129.506 | − | 5.75659i | 0.175482 | − | 0.00780025i | |||||
719.160i | 0.973153i | 0.873638 | + | 0.486577i | ||||||
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1678.67 | − | 86.7727i | 2.26847 | − | 0.117260i | |||||
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0.365457 | + | 0.930828i | ||||||||
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370.523 | 0.496679 | |||||||||
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250.904 | + | 250.904i | 0.335433 | + | 0.335433i | |||||
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1192.82 | − | 379.525i | 1.59042 | − | 0.506033i | |||||
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0.980889 | + | 0.194567i | ||||||||
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336.378 | + | 1037.79i | 0.445534 | + | 1.37455i | |||||
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144.792 | − | 144.792i | 0.191270 | − | 0.191270i | −0.604974 | − | 0.796245i | ||
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820.009 | − | 531.687i | 1.07896 | − | 0.699589i | |||||
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1168.43i | 1.52935i | |||||||||
1077.00 | + | 180.146i | 1.40784 | + | 0.235485i | |||||
297.459 | 0.388328 | |||||||||
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96.6554 | + | 55.8040i | 0.125690 | + | 0.0725670i | 0.561527 | − | 0.827459i | ||
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1753.52 | + | 469.854i | 2.27140 | + | 0.608619i | |||||
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902.039 | − | 285.193i | 1.16543 | − | 0.368467i | |||||
483.355 | − | 350.124i | 0.623684 | − | 0.451773i | |||||
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238.526 | − | 63.9127i | 0.306588 | − | 0.0821500i | |||||
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682.353 | − | 682.353i | 0.872574 | − | 0.872574i | |||||
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218.947i | 0.279270i | |||||||||
68.5260 | + | 1325.68i | 0.0872943 | + | 1.68876i | |||||
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319.011 | + | 1190.57i | 0.405351 | + | 1.51279i | 0.803407 | + | 0.595430i | ||
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216.555 | + | 216.555i | 0.273083 | + | 0.273083i | |||||
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0.724969 | − | 0.688781i | ||||||||
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628.073 | − | 686.507i | 0.784112 | − | 0.857063i | |||||
1531.17 | − | 1531.17i | 1.90920 | − | 1.90920i | |||||
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373.916 | + | 273.940i | 0.465069 | + | 0.340721i | |||||
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227.015 | + | 88.1785i | 0.281308 | + | 0.109267i | |||||
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0.990218 | − | 0.139529i | ||||||||
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278.593 | + | 160.845i | 0.342251 | + | 0.197599i | |||||
619.652 | + | 955.674i | 0.760309 | + | 1.17261i | |||||
277.097 | − | 378.225i | 0.339580 | − | 0.463511i | |||||
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261.953 | + | 239.656i | 0.319844 | + | 0.292620i | |||||
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2.78890 | + | 4.83052i | 0.00339696 | + | 0.00588370i | 0.867719 | − | 0.497055i | ||
−0.864322 | + | 0.502939i | ||||||||
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625.506 | − | 167.604i | 0.760032 | − | 0.203650i | 0.142069 | − | 0.989857i | ||
0.617963 | + | 0.786207i | ||||||||
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148.107 | + | 40.5433i | 0.179524 | + | 0.0491434i | |||||
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230.120 | − | 230.120i | 0.278258 | − | 0.278258i | −0.554155 | − | 0.832413i | ||
0.832413 | + | 0.554155i | ||||||||
411.971 | + | 645.541i | 0.497549 | + | 0.779639i | |||||
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0.419994 | − | 0.907527i | ||||||||
1775.85 | − | 1969.45i | 2.13958 | − | 2.37284i | |||||
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796.788 | − | 213.499i | 0.956528 | − | 0.256301i | |||||
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272.513 | 0.325973 | |||||||||
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915.370 | − | 528.489i | 1.09103 | − | 0.629904i | 0.157176 | − | 0.987571i | ||
0.933849 | + | 0.357667i | ||||||||
−1430.88 | − | 81.7115i | −1.70343 | − | 0.0972756i | |||||
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72.6483 | − | 41.9435i | 0.0860762 | − | 0.0496961i | |||||
714.642 | − | 231.637i | 0.845730 | − | 0.274127i | |||||
−7.86618 | − | 24.8800i | −0.00929809 | − | 0.0294089i | |||||
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7.85783 | − | 29.3258i | 0.00926631 | − | 0.0345823i | |||||
−112.669 | + | 1032.54i | −0.132708 | + | 1.21618i | |||||
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280.394 | − | 485.656i | 0.329487 | − | 0.570689i | |||||
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191.675 | − | 715.340i | 0.224707 | − | 0.838617i | −0.757815 | − | 0.652469i | ||
0.982522 | − | 0.186148i | ||||||||
2150.69i | 2.51837i | |||||||||
682.708 | − | 487.047i | 0.798489 | − | 0.569645i | |||||
−1251.72 | −1.46229 | |||||||||
1218.31 | + | 326.446i | 1.42160 | + | 0.380918i | 0.886052 | − | 0.463585i | ||
0.535551 | + | 0.844503i | ||||||||
−87.7427 | + | 13.5403i | −0.102264 | + | 0.0157812i | |||||
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−0.521818 | + | 0.853057i | ||||||||
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47.5399 | + | 107.927i | 0.0552148 | + | 0.125351i | |||||
−2090.48 | − | 560.142i | −2.42515 | − | 0.649817i | |||||
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−0.847994 | + | 0.530006i | ||||||||
−364.609 | − | 414.767i | −0.422001 | − | 0.480054i | |||||
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1135.94 | + | 1967.51i | 1.31171 | + | 2.27195i | |||||
−838.454 | − | 325.677i | −0.967075 | − | 0.375637i | |||||
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−0.412935 | − | 0.238408i | −0.000475184 | − | 0.000274348i | |||||
353.255 | − | 1070.13i | 0.406040 | − | 1.23003i | |||||
46.8394 | + | 81.1282i | 0.0537766 | + | 0.0931438i | |||||
−760.017 | + | 760.017i | −0.871579 | + | 0.871579i | |||||
−349.513 | − | 547.673i | −0.400359 | − | 0.627346i | |||||
− | 741.121i | − | 0.847965i | |||||||
714.749 | + | 886.520i | 0.816856 | + | 1.01317i | |||||
1449.84 | + | 158.205i | 1.65506 | + | 0.180599i | |||||
−46.0094 | − | 171.710i | −0.0524623 | − | 0.195792i | 0.934721 | − | 0.355382i | ||
−0.987183 | + | 0.159590i | ||||||||
2023.53 | − | 542.205i | 2.30471 | − | 0.617545i | |||||
97.5184 | − | 893.687i | 0.110942 | − | 1.01671i | |||||
44.1535 | − | 48.9671i | 0.0501745 | − | 0.0556444i | |||||
−1000.82 | −1.13600 | −0.568000 | − | 0.823029i | ||||||
−0.568000 | + | 0.823029i | ||||||||
45.3500 | + | 1020.24i | 0.0514172 | + | 1.15673i | |||||
766.494 | + | 766.494i | 0.868057 | + | 0.868057i | 0.992257 | − | 0.124201i | ||
−0.124201 | + | 0.992257i | ||||||||
649.920 | − | 375.232i | 0.735204 | − | 0.424470i | |||||
1026.01 | − | 516.739i | 1.15933 | − | 0.583886i | |||||
−897.522 | + | 1554.55i | −1.01300 | + | 1.75457i | |||||
166.511 | + | 621.429i | 0.187724 | + | 0.700596i | 0.994031 | + | 0.109099i | ||
−0.806307 | + | 0.591498i | ||||||||
536.244 | − | 1380.56i | 0.603878 | − | 1.55468i | |||||
907.698 | − | 524.060i | 1.02103 | − | 0.589494i | |||||
−784.452 | + | 1536.86i | −0.881406 | + | 1.72681i | |||||
−135.698 | + | 95.3361i | −0.152299 | + | 0.106999i | |||||
−64.6759 | + | 64.6759i | −0.0725067 | + | 0.0725067i | |||||
−4.18956 | + | 15.6357i | −0.00469156 | + | 0.0175091i | |||||
−924.963 | + | 407.428i | −1.03463 | + | 0.455736i | |||||
93.2817 | − | 437.319i | 0.104225 | − | 0.488625i | |||||
1057.12 | − | 1830.98i | 1.17982 | − | 2.04350i | |||||
23.6041 | + | 152.957i | 0.0263145 | + | 0.170521i | |||||
−217.774 | + | 812.743i | −0.242510 | + | 0.905058i | |||||
− | 537.328i | − | 0.597696i | |||||||
182.937 | − | 1596.52i | 0.203263 | − | 1.77391i | |||||
−114.384 | −0.126952 | |||||||||
−28.4855 | − | 7.63268i | −0.0315804 | − | 0.00846195i | |||||
538.974 | + | 671.006i | 0.596871 | + | 0.743086i | |||||
−369.109 | − | 213.105i | −0.408307 | − | 0.235736i | |||||
−1502.87 | − | 320.568i | −1.66063 | − | 0.354218i | |||||
2172.02 | + | 237.009i | 2.39738 | + | 0.261600i | |||||
638.156 | + | 170.993i | 0.703589 | + | 0.188526i | 0.592838 | − | 0.805322i | ||
0.110752 | + | 0.993848i | ||||||||
2235.42 | + | 2235.42i | 2.46191 | + | 2.46191i | |||||
−120.377 | + | 545.019i | −0.132428 | + | 0.599581i | |||||
−586.423 | − | 299.326i | −0.644421 | − | 0.328929i | |||||
536.476 | + | 929.204i | 0.588887 | + | 1.01998i | 0.994379 | + | 0.105884i | ||
−0.405491 | + | 0.914099i | ||||||||
−54.9189 | − | 355.881i | −0.0602181 | − | 0.390221i | |||||
314.231 | − | 84.1979i | 0.344174 | − | 0.0922211i | |||||
853.309 | + | 492.658i | 0.933598 | + | 0.539013i | |||||
−1059.14 | − | 60.4830i | −1.15753 | − | 0.0661017i | |||||
677.331 | + | 1173.17i | 0.739444 | + | 1.28075i | |||||
532.635 | − | 532.635i | 0.580846 | − | 0.580846i | |||||
1212.86 | − | 1819.82i | 1.32120 | − | 1.98238i | |||||
− | 728.665i | − | 0.792889i | −0.918059 | − | 0.396444i | ||||
0.918059 | − | 0.396444i | ||||||||
−463.989 | − | 418.378i | −0.504336 | − | 0.454759i | |||||
−236.692 | − | 537.349i | −0.256995 | − | 0.583441i | |||||
−440.399 | − | 1643.59i | −0.477656 | − | 1.78264i | |||||
−119.669 | + | 32.0652i | −0.129652 | + | 0.0347402i | |||||
−322.384 | − | 236.187i | −0.348901 | − | 0.255613i | |||||
−1099.21 | + | 420.146i | −1.18833 | + | 0.454212i | |||||
−985.543 | −1.06430 | |||||||||
−422.117 | − | 219.317i | −0.455358 | − | 0.236588i | |||||
325.515 | + | 325.515i | 0.350771 | + | 0.350771i | |||||
844.876 | − | 487.790i | 0.909447 | − | 0.525070i | 0.0291940 | − | 0.999574i | ||
0.880253 | + | 0.474504i | ||||||||
−243.047 | − | 1170.37i | −0.261341 | − | 1.25847i | |||||
316.763 | − | 548.649i | 0.340239 | − | 0.589312i | |||||
−164.149 | − | 612.611i | −0.176125 | − | 0.657308i | |||||
−201.534 | − | 250.903i | −0.216006 | − | 0.268921i | |||||
1536.11 | − | 886.871i | 1.64465 | − | 0.949541i | |||||
−221.255 | − | 112.934i | −0.236636 | − | 0.120785i | |||||
123.219 | + | 389.729i | 0.131644 | + | 0.416377i | |||||
−141.251 | + | 141.251i | −0.150749 | + | 0.150749i | −0.778452 | − | 0.627704i | ||
0.627704 | + | 0.778452i | ||||||||
−170.268 | + | 635.447i | −0.181522 | + | 0.677449i | |||||
1323.62 | + | 969.716i | 1.40961 | + | 1.03271i | |||||
16.8747 | + | 26.0255i | 0.0179518 | + | 0.0276867i | |||||
557.909 | − | 966.326i | 0.592889 | − | 1.02691i | −0.400952 | − | 0.916099i | ||
0.993841 | − | 0.110815i | ||||||||
2478.20 | + | 962.596i | 2.63079 | + | 1.02186i | |||||
−13.3057 | + | 49.6574i | −0.0141099 | + | 0.0526589i | |||||
− | 493.269i | − | 0.522531i | |||||||
−1229.77 | − | 15.5235i | −1.30134 | − | 0.0164270i | |||||
−215.217 | −0.227502 | |||||||||
−766.094 | − | 205.274i | −0.808969 | − | 0.216763i | −0.169451 | − | 0.985539i | ||
−0.639518 | + | 0.768776i | ||||||||
−1.80669 | + | 4.65132i | −0.00190579 | + | 0.00490646i | |||||
255.263 | + | 147.376i | 0.268981 | + | 0.155296i | |||||
−980.435 | + | 1207.21i | −1.03204 | + | 1.27074i | |||||
−773.604 | + | 1055.93i | −0.813464 | + | 1.11034i | |||||
2239.54 | + | 600.082i | 2.35245 | + | 0.630338i | |||||
−80.4623 | − | 80.4623i | −0.0844305 | − | 0.0844305i | 0.663630 | − | 0.748061i | ||
−0.748061 | + | 0.663630i | ||||||||
30.5413 | − | 138.278i | 0.0320139 | − | 0.144946i | |||||
−252.217 | − | 778.135i | −0.264102 | − | 0.814801i | |||||
238.807 | + | 413.625i | 0.249798 | + | 0.432662i | |||||
107.781 | − | 86.5729i | 0.112623 | − | 0.0904628i | |||||
1397.02 | − | 374.330i | 1.45826 | − | 0.390741i | |||||
−1230.39 | − | 710.365i | −1.28299 | − | 0.740735i | |||||
1179.36 | + | 773.765i | 1.22850 | + | 0.806006i | |||||
195.525 | + | 338.658i | 0.203459 | + | 0.352402i | |||||
481.095 | − | 481.095i | 0.500099 | − | 0.500099i | |||||
−1073.06 | + | 47.6980i | −1.11429 | + | 0.0495306i | |||||
423.810i | 0.439636i | |||||||||
−1269.21 | + | 65.6073i | −1.31524 | + | 0.0679869i | |||||
−642.328 | + | 876.748i | −0.664935 | + | 0.907607i | |||||
87.9314 | + | 328.164i | 0.0909322 | + | 0.339363i | 0.996371 | − | 0.0851126i | ||
−0.905439 | + | 0.424476i | ||||||||
−1183.35 | + | 317.078i | −1.22247 | + | 0.327560i | |||||
−1241.56 | + | 546.884i | −1.28128 | + | 0.564380i | |||||
894.776 | + | 806.818i | 0.922449 | + | 0.831771i | |||||
1786.19 | 1.83954 | 0.919769 | − | 0.392460i | ||||||
0.919769 | + | 0.392460i | ||||||||
1202.60 | + | 1251.31i | 1.23724 | + | 1.28736i | |||||
−10.0620 | − | 10.0620i | −0.0103413 | − | 0.0103413i | |||||
−1707.67 | + | 985.926i | −1.75326 | + | 1.01224i | |||||
163.900 | − | 280.377i | 0.168103 | − | 0.287566i | |||||
−227.759 | + | 394.490i | −0.233360 | + | 0.404191i | |||||
−199.197 | − | 743.412i | −0.203886 | − | 0.760913i | −0.989786 | − | 0.142560i | ||
0.785900 | − | 0.618353i | ||||||||
2254.45 | − | 347.902i | 2.30516 | − | 0.355728i | |||||
−183.313 | + | 105.836i | −0.187246 | + | 0.108106i | |||||
−374.304 | − | 1154.80i | −0.381943 | − | 1.17836i | |||||
−622.578 | + | 680.501i | −0.634637 | + | 0.693681i | |||||
−1817.45 | + | 1817.45i | −1.85076 | + | 1.85076i | |||||
−21.2470 | + | 79.2948i | −0.0216144 | + | 0.0806661i | −0.975891 | − | 0.218260i | ||
0.954276 | + | 0.298926i | ||||||||
−14.7279 | + | 134.971i | −0.0149674 | + | 0.137166i | |||||
498.303 | − | 323.096i | 0.505892 | − | 0.328016i | |||||
−911.523 | + | 1578.80i | −0.924466 | + | 1.60122i | |||||
18.5076 | − | 14.8660i | 0.0187514 | − | 0.0150618i | |||||
149.173 | − | 556.722i | 0.150985 | − | 0.563484i | |||||
375.177i | 0.379350i | |||||||||
195.602 | − | 237.319i | 0.197577 | − | 0.239716i | |||||
−515.156 | −0.519835 | −0.259917 | − | 0.965631i | ||||||
−0.259917 | + | 0.965631i | ||||||||
471.659 | + | 126.381i | 0.475462 | + | 0.127400i | |||||
−1738.33 | + | 268.256i | −1.75059 | + | 0.270147i | |||||
−753.465 | − | 435.013i | −0.758013 | − | 0.437639i | |||||
172.171 | − | 807.166i | 0.173036 | − | 0.811222i | |||||
−1372.35 | − | 3115.57i | −1.37786 | − | 3.12808i | |||||
358.637 | + | 96.0965i | 0.359716 | + | 0.0963856i | 0.434151 | − | 0.900840i | ||
−0.0744346 | + | 0.997226i | ||||||||
−231.032 | − | 231.032i | −0.231495 | − | 0.231495i | |||||
407.098 | − | 1203.94i | 0.407505 | − | 1.20515i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 45.3.k.a.13.2 | yes | 40 | |
3.2 | odd | 2 | 135.3.l.a.118.9 | 40 | |||
5.2 | odd | 4 | inner | 45.3.k.a.22.9 | yes | 40 | |
5.3 | odd | 4 | 225.3.o.b.157.2 | 40 | |||
5.4 | even | 2 | 225.3.o.b.193.9 | 40 | |||
9.2 | odd | 6 | 135.3.l.a.73.2 | 40 | |||
9.4 | even | 3 | 405.3.g.h.163.9 | 20 | |||
9.5 | odd | 6 | 405.3.g.g.163.2 | 20 | |||
9.7 | even | 3 | inner | 45.3.k.a.43.9 | yes | 40 | |
15.2 | even | 4 | 135.3.l.a.37.2 | 40 | |||
45.2 | even | 12 | 135.3.l.a.127.9 | 40 | |||
45.7 | odd | 12 | inner | 45.3.k.a.7.2 | ✓ | 40 | |
45.22 | odd | 12 | 405.3.g.h.82.9 | 20 | |||
45.32 | even | 12 | 405.3.g.g.82.2 | 20 | |||
45.34 | even | 6 | 225.3.o.b.43.2 | 40 | |||
45.43 | odd | 12 | 225.3.o.b.7.9 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.k.a.7.2 | ✓ | 40 | 45.7 | odd | 12 | inner | |
45.3.k.a.13.2 | yes | 40 | 1.1 | even | 1 | trivial | |
45.3.k.a.22.9 | yes | 40 | 5.2 | odd | 4 | inner | |
45.3.k.a.43.9 | yes | 40 | 9.7 | even | 3 | inner | |
135.3.l.a.37.2 | 40 | 15.2 | even | 4 | |||
135.3.l.a.73.2 | 40 | 9.2 | odd | 6 | |||
135.3.l.a.118.9 | 40 | 3.2 | odd | 2 | |||
135.3.l.a.127.9 | 40 | 45.2 | even | 12 | |||
225.3.o.b.7.9 | 40 | 45.43 | odd | 12 | |||
225.3.o.b.43.2 | 40 | 45.34 | even | 6 | |||
225.3.o.b.157.2 | 40 | 5.3 | odd | 4 | |||
225.3.o.b.193.9 | 40 | 5.4 | even | 2 | |||
405.3.g.g.82.2 | 20 | 45.32 | even | 12 | |||
405.3.g.g.163.2 | 20 | 9.5 | odd | 6 | |||
405.3.g.h.82.9 | 20 | 45.22 | odd | 12 | |||
405.3.g.h.163.9 | 20 | 9.4 | even | 3 |