Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,8,Mod(47,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.47");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 74.c (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 | 47.2 | ||
Character | 74.47 | ||
Dual form | 74.8.c.a.63.2 |
-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 .
−4.00000 | + | 6.92820i | −0.353553 | + | 0.612372i | |||||
−33.0633 | − | 57.2674i | −0.707005 | − | 1.22457i | −0.965963 | − | 0.258680i | ||
0.258958 | − | 0.965888i | ||||||||
−32.0000 | − | 55.4256i | −0.250000 | − | 0.433013i | |||||
102.843 | + | 178.129i | 0.367941 | + | 0.637292i | 0.989243 | − | 0.146278i | ||
−0.621303 | + | 0.783571i | ||||||||
529.013 | 0.999856 | |||||||||
87.2990 | + | 151.206i | 0.0961981 | + | 0.166620i | 0.910108 | − | 0.414371i | ||
−0.813910 | + | 0.580991i | ||||||||
512.000 | 0.353553 | |||||||||
−1092.87 | + | 1892.90i | −0.499711 | + | 0.865526i | |||||
−1645.48 | −0.520347 | |||||||||
−5682.10 | −1.28717 | −0.643583 | − | 0.765376i | ||||||
−0.643583 | + | 0.765376i | ||||||||
−2116.05 | + | 3665.11i | −0.353502 | + | 0.612284i | |||||
−6239.48 | − | 10807.1i | −0.787675 | − | 1.36429i | −0.927388 | − | 0.374101i | ||
0.139713 | − | 0.990192i | ||||||||
−1396.78 | −0.136045 | |||||||||
6800.64 | − | 11779.1i | 0.520272 | − | 0.901138i | |||||
−2048.00 | + | 3547.24i | −0.125000 | + | 0.216506i | |||||
−10150.4 | + | 17581.0i | −0.501086 | + | 0.867907i | 0.498913 | + | 0.866652i | ||
−0.999999 | + | 0.00125471i | ||||||||
−8742.95 | − | 15143.2i | −0.353349 | − | 0.612019i | |||||
29257.4 | + | 50675.4i | 0.978586 | + | 1.69496i | 0.667556 | + | 0.744560i | ||
0.311030 | + | 0.950400i | ||||||||
6581.93 | − | 11400.2i | 0.183970 | − | 0.318646i | |||||
5772.80 | − | 9998.77i | 0.136025 | − | 0.235602i | |||||
22728.4 | − | 39366.8i | 0.455082 | − | 0.788225i | |||||
65697.1 | 1.12590 | 0.562949 | − | 0.826492i | ||||||
0.562949 | + | 0.826492i | ||||||||
−16928.4 | − | 29320.9i | −0.249964 | − | 0.432950i | |||||
17909.3 | − | 31019.8i | 0.229239 | − | 0.397053i | |||||
99831.7 | 1.11394 | |||||||||
−83.4648 | −0.000816075 | |||||||||
5587.14 | − | 9677.21i | 0.0480990 | − | 0.0833100i | |||||
177274. | 1.34974 | 0.674871 | − | 0.737936i | ||||||
0.674871 | + | 0.737936i | ||||||||
54405.1 | + | 94232.4i | 0.367888 | + | 0.637200i | |||||
−95681.2 | −0.576847 | −0.288423 | − | 0.957503i | ||||||
−0.288423 | + | 0.957503i | ||||||||
−16384.0 | − | 28377.9i | −0.0883883 | − | 0.153093i | |||||
187869. | + | 325399.i | 0.910033 | + | 1.57622i | |||||
−81203.3 | − | 140648.i | −0.354321 | − | 0.613703i | |||||
−17956.1 | + | 31100.9i | −0.0707904 | + | 0.122613i | |||||
139887. | 0.499711 | |||||||||
274975. | − | 138999.i | 0.892456 | − | 0.451135i | |||||
−468119. | −1.38393 | |||||||||
−412596. | + | 714638.i | −1.11378 | + | 1.92912i | |||||
52655.4 | + | 91201.9i | 0.130087 | + | 0.225317i | |||||
244216. | + | 422995.i | 0.553389 | + | 0.958498i | 0.998027 | + | 0.0627876i | ||
−0.444638 | + | 0.895710i | ||||||||
46182.4 | + | 79990.2i | 0.0961842 | + | 0.166596i | |||||
761147. | 1.45992 | 0.729959 | − | 0.683490i | ||||||
0.729959 | + | 0.683490i | ||||||||
181827. | + | 314934.i | 0.321792 | + | 0.557360i | |||||
−449574. | −0.735457 | |||||||||
−262788. | + | 455163.i | −0.398065 | + | 0.689469i | |||||
−423371. | −0.594811 | −0.297406 | − | 0.954751i | ||||||
−0.297406 | + | 0.954751i | ||||||||
270855. | 0.353502 | |||||||||
396529. | − | 686809.i | 0.481492 | − | 0.833968i | |||||
143274. | + | 248158.i | 0.162096 | + | 0.280759i | |||||
1.34243e6 | 1.41708 | |||||||||
−399327. | + | 691655.i | −0.393837 | + | 0.682146i | |||||
−327136. | + | 566616.i | −0.301830 | + | 0.522785i | −0.976551 | − | 0.215288i | ||
0.674720 | + | 0.738073i | ||||||||
333.859 | − | 578.261i | 0.000288526 | − | 0.000499742i | |||||
−584363. | − | 1.01215e6i | −0.473601 | − | 0.820302i | |||||
44697.1 | + | 77417.7i | 0.0340111 | + | 0.0589090i | |||||
1.93470e6 | − | 3.35099e6i | 1.38373 | − | 2.39669i | |||||
−709094. | + | 1.22819e6i | −0.477206 | + | 0.826545i | |||||
−91051.3 | + | 157706.i | −0.0577171 | + | 0.0999689i | −0.893440 | − | 0.449182i | ||
0.835723 | + | 0.549151i | ||||||||
−870482. | −0.520272 | |||||||||
1.23526e6 | + | 2.13954e6i | 0.696794 | + | 1.20688i | 0.969572 | + | 0.244806i | ||
−0.272778 | + | 0.962077i | ||||||||
382725. | − | 662898.i | 0.203946 | − | 0.353245i | |||||
−381626. | −0.192285 | |||||||||
262144. | 0.125000 | |||||||||
1.28337e6 | − | 2.22286e6i | 0.579636 | − | 1.00396i | |||||
−3.00591e6 | −1.28698 | |||||||||
−1.13014e6 | − | 1.95746e6i | −0.459060 | − | 0.795116i | 0.539851 | − | 0.841760i | ||
−0.998912 | + | 0.0466448i | ||||||||
1.29925e6 | 0.501086 | |||||||||
−2.17217e6 | − | 3.76230e6i | −0.796015 | − | 1.37874i | |||||
−143649. | − | 248807.i | −0.0500564 | − | 0.0867002i | |||||
1.36480e6 | + | 2.36390e6i | 0.452548 | + | 0.783836i | 0.998544 | − | 0.0539518i | ||
−0.545995 | + | 0.837788i | ||||||||
−559549. | + | 969167.i | −0.176675 | + | 0.306010i | |||||
4.27107e6 | 1.28501 | 0.642505 | − | 0.766281i | ||||||
0.642505 | + | 0.766281i | ||||||||
−136883. | + | 2.46108e6i | −0.0392679 | + | 0.706016i | |||||
−2.36856e6 | −0.648292 | |||||||||
1.87248e6 | − | 3.24322e6i | 0.489293 | − | 0.847480i | |||||
−496042. | − | 859170.i | −0.123823 | − | 0.214468i | |||||
−3.30077e6 | − | 5.71710e6i | −0.787561 | − | 1.36410i | |||||
−756160. | − | 1.30971e6i | −0.172551 | − | 0.298868i | 0.766760 | − | 0.641934i | ||
−0.939311 | + | 0.343066i | ||||||||
−842487. | −0.183970 | |||||||||
2.39286e6 | + | 4.14456e6i | 0.500288 | + | 0.866525i | |||||
−3.90746e6 | −0.782610 | |||||||||
−3.15145e6 | + | 5.45848e6i | −0.604975 | + | 1.04785i | 0.387080 | + | 0.922046i | ||
−0.992055 | + | 0.125802i | ||||||||
−738918. | −0.136025 | |||||||||
−4.17558e6 | −0.737481 | |||||||||
−3.04459e6 | + | 5.27338e6i | −0.516159 | + | 0.894014i | |||||
−5.86126e6 | − | 1.01520e7i | −0.954274 | − | 1.65285i | |||||
−2.90924e6 | −0.455082 | |||||||||
550715. | − | 953866.i | 0.0828060 | − | 0.143424i | −0.821648 | − | 0.569995i | ||
0.904454 | + | 0.426571i | ||||||||
1.79830e6 | − | 3.11474e6i | 0.260023 | − | 0.450374i | |||||
1.08940e6 | − | 1.88690e6i | 0.151546 | − | 0.262485i | |||||
−2.10231e6 | − | 3.64130e6i | −0.281474 | − | 0.487528i | |||||
3.16354e6 | + | 5.47941e6i | 0.407833 | + | 0.706388i | |||||
1.69349e6 | − | 2.93320e6i | 0.210297 | − | 0.364246i | |||||
−6.01782e6 | + | 1.04232e7i | −0.720123 | + | 1.24729i | |||||
−1.08342e6 | + | 1.87654e6i | −0.124982 | + | 0.216475i | |||||
−203177. | −0.0226034 | −0.0113017 | − | 0.999936i | ||||||
−0.0113017 | + | 0.999936i | ||||||||
3.17223e6 | + | 5.49447e6i | 0.340466 | + | 0.589705i | |||||
6.20980e6 | − | 1.07557e7i | 0.643212 | − | 1.11408i | |||||
−2.29239e6 | −0.229239 | |||||||||
7.19482e6 | 0.694856 | 0.347428 | − | 0.937707i | ||||||
0.347428 | + | 0.937707i | ||||||||
−5.36970e6 | + | 9.30060e6i | −0.501014 | + | 0.867782i | |||||
−1.48628e7 | −1.34020 | −0.670101 | − | 0.742270i | ||||||
−0.670101 | + | 0.742270i | ||||||||
−3.19462e6 | − | 5.53324e6i | −0.278485 | − | 0.482350i | |||||
2.37476e6 | 0.200197 | |||||||||
−2.61709e6 | − | 4.53293e6i | −0.213426 | − | 0.369665i | |||||
1.25379e7 | + | 2.17163e7i | 0.989425 | + | 1.71373i | 0.620327 | + | 0.784343i | ||
0.369097 | + | 0.929391i | ||||||||
2670.87 | + | 4626.09i | 0.000204019 | + | 0.000353371i | |||||
−163897. | + | 283879.i | −0.0121221 | + | 0.0209962i | −0.872023 | − | 0.489465i | ||
0.859901 | + | 0.510461i | ||||||||
9.34980e6 | 0.669773 | |||||||||
−1.70517e7 | − | 1.11513e7i | −1.18342 | − | 0.773918i | |||||
−715154. | −0.0480990 | |||||||||
9.09328e6 | − | 1.57500e7i | 0.592852 | − | 1.02685i | −0.400994 | − | 0.916081i | ||
0.993846 | − | 0.110769i | ||||||||
1.54776e7 | + | 2.68080e7i | 0.978444 | + | 1.69472i | |||||
6.75646e6 | + | 1.17025e7i | 0.414264 | + | 0.717526i | |||||
−5.67275e6 | − | 9.82550e6i | −0.337436 | − | 0.584456i | |||||
2.72757e7 | 1.57444 | |||||||||
−728411. | − | 1.26164e6i | −0.0408121 | − | 0.0706887i | |||||
−3.54448e6 | −0.192814 | |||||||||
3.48193e6 | − | 6.03088e6i | 0.183944 | − | 0.318600i | |||||
1.27991e7 | 0.656798 | |||||||||
−1.97642e7 | −0.985415 | |||||||||
1.61492e7 | − | 2.79712e7i | 0.782498 | − | 1.35533i | |||||
3.06180e6 | + | 5.30319e6i | 0.144212 | + | 0.249782i | |||||
2.34365e7 | 1.07327 | |||||||||
1.52650e6 | − | 2.64398e6i | 0.0679830 | − | 0.117750i | |||||
−6.52628e6 | + | 1.13039e7i | −0.282718 | + | 0.489681i | −0.972053 | − | 0.234761i | ||
0.689336 | + | 0.724442i | ||||||||
−1.04858e6 | + | 1.81619e6i | −0.0441942 | + | 0.0765466i | |||||
−2.51660e7 | − | 4.35889e7i | −1.03217 | − | 1.78777i | |||||
1.02670e7 | + | 1.77829e7i | 0.409864 | + | 0.709906i | |||||
5.33799e6 | − | 9.24567e6i | 0.207457 | − | 0.359326i | −0.743456 | − | 0.668785i | ||
0.950913 | + | 0.309459i | ||||||||
1.20236e7 | − | 2.08256e7i | 0.455016 | − | 0.788112i | |||||
−5.10829e6 | + | 8.84782e6i | −0.188276 | + | 0.326104i | |||||
1.80822e7 | 0.649209 | |||||||||
−8583.73 | − | 14867.5i | −0.000300267 | − | 0.000520078i | |||||
−5.19701e6 | + | 9.00149e6i | −0.177161 | + | 0.306851i | |||||
−2.48718e7 | −0.826391 | −0.413195 | − | 0.910642i | ||||||
−0.413195 | + | 0.910642i | ||||||||
3.47547e7 | 1.12574 | |||||||||
−1.98302e7 | + | 3.43469e7i | −0.626290 | + | 1.08477i | 0.362000 | + | 0.932178i | ||
−0.988290 | + | 0.152587i | ||||||||
2.29838e6 | 0.0707904 | |||||||||
1.39981e7 | + | 2.42454e7i | 0.420534 | + | 0.728387i | |||||
−2.18368e7 | −0.640000 | |||||||||
3.54534e7 | + | 6.14071e7i | 1.01387 | + | 1.75607i | |||||
−4.47639e6 | − | 7.75334e6i | −0.124928 | − | 0.216381i | |||||
1.82313e7 | + | 3.15775e7i | 0.496626 | + | 0.860181i | |||||
−1.70843e7 | + | 2.95909e7i | −0.454320 | + | 0.786905i | |||||
−5.24423e7 | −1.36167 | |||||||||
−1.65033e7 | − | 1.07927e7i | −0.418461 | − | 0.273661i | |||||
−1.90913e7 | −0.472806 | −0.236403 | − | 0.971655i | ||||||
−0.236403 | + | 0.971655i | ||||||||
9.47426e6 | − | 1.64099e7i | 0.229206 | − | 0.396996i | |||||
−4.46190e6 | − | 7.72824e6i | −0.105463 | − | 0.182668i | 0.808464 | − | 0.588545i | ||
−0.913927 | + | 0.405878i | ||||||||
1.49798e7 | + | 2.59458e7i | 0.345982 | + | 0.599259i | |||||
−2.21861e7 | − | 3.84275e7i | −0.500797 | − | 0.867406i | |||||
7.93668e6 | 0.175112 | |||||||||
−9.84010e6 | − | 1.70436e7i | −0.212246 | − | 0.367620i | |||||
5.28123e7 | 1.11378 | |||||||||
−3.82479e6 | + | 6.62473e6i | −0.0788785 | + | 0.136622i | −0.902766 | − | 0.430131i | ||
0.823888 | + | 0.566753i | ||||||||
1.20986e7 | 0.244025 | |||||||||
4.32648e7 | 0.853582 | |||||||||
3.36995e6 | − | 5.83692e6i | 0.0650434 | − | 0.112658i | |||||
5.73530e6 | + | 9.93382e6i | 0.108309 | + | 0.187597i | |||||
−3.82858e7 | −0.707515 | |||||||||
2.95512e7 | − | 5.11841e7i | 0.534463 | − | 0.925718i | −0.464726 | − | 0.885455i | ||
0.999189 | − | 0.0402630i | ||||||||
1.56298e7 | − | 2.70717e7i | 0.276695 | − | 0.479249i | |||||
−3.86420e7 | + | 6.69298e7i | −0.669677 | + | 1.15991i | |||||
−2.52116e7 | − | 4.36678e7i | −0.427782 | − | 0.740940i | |||||
−3.17445e6 | − | 5.49831e6i | −0.0527425 | − | 0.0913527i | 0.838449 | − | 0.544980i | ||
−0.891191 | + | 0.453628i | ||||||||
2.95567e6 | − | 5.11937e6i | 0.0480921 | − | 0.0832979i | |||||
−4.64880e7 | + | 8.05197e7i | −0.740863 | + | 1.28321i | |||||
1.67023e7 | − | 2.89293e7i | 0.260739 | − | 0.451613i | |||||
−1.27898e8 | −1.95604 | |||||||||
−2.43567e7 | − | 4.21870e7i | −0.364980 | − | 0.632163i | |||||
−7.37844e6 | + | 1.27798e7i | −0.108344 | + | 0.187657i | −0.915099 | − | 0.403228i | ||
0.806756 | + | 0.590885i | ||||||||
9.37801e7 | 1.34955 | |||||||||
6.25386e6 | 0.0882094 | |||||||||
1.16369e7 | − | 2.01558e7i | 0.160896 | − | 0.278680i | |||||
1.20418e7 | 0.163225 | |||||||||
4.40572e6 | + | 7.63093e6i | 0.0585527 | + | 0.101416i | |||||
6.93955e7 | 0.904370 | 0.452185 | − | 0.891924i | ||||||
0.452185 | + | 0.891924i | ||||||||
1.43864e7 | + | 2.49179e7i | 0.183864 | + | 0.318462i | |||||
5.13734e7 | + | 8.89814e7i | 0.643967 | + | 1.11538i | 0.984539 | + | 0.175165i | ||
−0.340573 | + | 0.940218i | ||||||||
8.71521e6 | + | 1.50952e7i | 0.107159 | + | 0.185605i | |||||
8.16837e7 | − | 1.41480e8i | 0.985273 | − | 1.70654i | |||||
3.36369e7 | 0.398065 | |||||||||
5.30389e7 | + | 3.46858e7i | 0.615876 | + | 0.402764i | |||||
−5.06166e7 | −0.576764 | |||||||||
5.76757e7 | − | 9.98972e7i | 0.644982 | − | 1.11714i | |||||
1.35479e7 | + | 2.34656e7i | 0.148703 | + | 0.257561i | |||||
−7286.39 | − | 12620.4i | −7.85048e−5 | − | 0.000135974i | |||||
−4.81426e7 | − | 8.33854e7i | −0.509204 | − | 0.881967i | |||||
−1.41972e8 | −1.47430 | −0.737152 | − | 0.675727i | ||||||
−0.737152 | + | 0.675727i | ||||||||
−8.66736e6 | − | 1.50123e7i | −0.0883756 | − | 0.153071i | |||||
−1.04565e8 | −1.04698 | −0.523488 | − | 0.852033i | ||||||
−0.523488 | + | 0.852033i | ||||||||
812707. | − | 1.40765e6i | 0.00799149 | − | 0.0138417i | |||||
−1.69730e8 | −1.63922 | |||||||||
−5.07557e7 | −0.481492 | |||||||||
6.87121e7 | − | 1.19013e8i | 0.640326 | − | 1.10908i | −0.345034 | − | 0.938590i | ||
0.985360 | − | 0.170487i | ||||||||
4.96784e7 | + | 8.60454e7i | 0.454820 | + | 0.787771i | |||||
−8.23840e7 | −0.741066 | −0.370533 | − | 0.928819i | ||||||
−0.370533 | + | 0.928819i | ||||||||
9.16956e6 | − | 1.58821e7i | 0.0810482 | − | 0.140380i | |||||
−7.47323e7 | + | 1.29440e8i | −0.649115 | + | 1.12430i | |||||
−2.87793e7 | + | 4.98472e7i | −0.245669 | + | 0.425511i | |||||
1.54758e7 | + | 2.68049e7i | 0.129843 | + | 0.224894i | |||||
−4.29576e7 | − | 7.44048e7i | −0.354270 | − | 0.613614i | |||||
−5.02316e7 | + | 8.70037e7i | −0.407229 | + | 0.705341i | |||||
5.94512e7 | − | 1.02973e8i | 0.473833 | − | 0.820703i | |||||
−7.17983e7 | + | 1.24358e8i | −0.562624 | + | 0.974493i | |||||
5.11138e7 | 0.393837 | |||||||||
−1.66244e8 | − | 2.87943e8i | −1.25960 | − | 2.18170i | |||||
−9.49903e6 | + | 1.64528e7i | −0.0707802 | + | 0.122595i | |||||
−1.95531e8 | −1.43294 | −0.716468 | − | 0.697620i | ||||||
−0.716468 | + | 0.697620i | ||||||||
4.18734e7 | 0.301830 | |||||||||
9.02497e7 | − | 1.56317e8i | 0.639907 | − | 1.10835i | |||||
−2.00607e8 | −1.39926 | |||||||||
7.82783e7 | + | 1.35582e8i | 0.537164 | + | 0.930395i | |||||
−42734.0 | −0.000288526 | |||||||||
−8.35287e6 | − | 1.44676e7i | −0.0554915 | − | 0.0961142i | |||||
−1.31118e6 | − | 2.27103e6i | −0.00857165 | − | 0.0148465i | |||||
−1.41216e8 | − | 2.44593e8i | −0.908509 | − | 1.57358i | |||||
−3.73992e7 | + | 6.47773e7i | −0.236801 | + | 0.410151i | |||||
2.53333e8 | 1.57877 | |||||||||
1.45465e8 | − | 7.35325e7i | 0.892327 | − | 0.451070i | |||||
1.42945e8 | 0.863181 | 0.431590 | − | 0.902070i | ||||||
0.431590 | + | 0.902070i | ||||||||
2.86061e6 | − | 4.95473e6i | 0.0170056 | − | 0.0294545i | |||||
3.91450e7 | + | 6.78012e7i | 0.229107 | + | 0.396824i | |||||
7.27463e7 | + | 1.26000e8i | 0.419210 | + | 0.726092i | |||||
9.98211e7 | + | 1.72895e8i | 0.566411 | + | 0.981053i | 0.996917 | + | 0.0784648i | ||
−0.430506 | + | 0.902588i | ||||||||
−2.47641e8 | −1.38373 | |||||||||
−1.15473e8 | − | 2.00004e8i | −0.635411 | − | 1.10056i | −0.986428 | − | 0.164194i | ||
0.351017 | − | 0.936369i | ||||||||
−1.08103e8 | −0.585858 | |||||||||
−3.28016e7 | + | 5.68141e7i | −0.175087 | + | 0.303259i | |||||
9.07640e7 | 0.477206 | |||||||||
2.27221e8 | 1.17680 | 0.588399 | − | 0.808571i | ||||||
0.588399 | + | 0.808571i | ||||||||
−1.09103e8 | + | 1.88972e8i | −0.556649 | + | 0.964144i | |||||
−4.35406e7 | − | 7.54146e7i | −0.218855 | − | 0.379069i | |||||
1.16546e7 | 0.0577171 | |||||||||
−5.00023e7 | + | 8.66066e7i | −0.243989 | + | 0.422602i | |||||
1.41779e7 | − | 2.45569e7i | 0.0681701 | − | 0.118074i | |||||
1.64265e6 | − | 2.84516e6i | 0.00778311 | − | 0.0134807i | −0.862108 | − | 0.506725i | ||
0.869891 | + | 0.493244i | ||||||||
2.78554e7 | + | 4.82470e7i | 0.130068 | + | 0.225284i | |||||
1.64801e8 | + | 2.85444e8i | 0.758405 | + | 1.31360i | 0.943664 | + | 0.330906i | ||
−0.185259 | + | 0.982690i | ||||||||
−5.11966e7 | + | 8.86750e7i | −0.232213 | + | 0.402205i | |||||
1.58141e8 | − | 2.73908e8i | 0.707005 | − | 1.22457i | |||||
7.90567e7 | − | 1.36930e8i | 0.348397 | − | 0.603441i | |||||
1.63120e8 | 0.708642 | |||||||||
1.29194e8 | + | 2.23770e8i | 0.553309 | + | 0.958360i | |||||
3.65103e8 | − | 6.32376e8i | 1.54161 | − | 2.67015i | |||||
−4.89888e7 | −0.203946 | |||||||||
4.16790e8 | 1.71088 | |||||||||
−9.37461e7 | + | 1.62373e8i | −0.379457 | + | 0.657239i | |||||
2.97593e8 | 1.18786 | 0.593929 | − | 0.804518i | ||||||
0.593929 | + | 0.804518i | ||||||||
1.22120e7 | + | 2.11518e7i | 0.0480713 | + | 0.0832619i | |||||
−3.73298e8 | −1.44922 | |||||||||
−5.22103e7 | − | 9.04308e7i | −0.199912 | − | 0.346257i | |||||
1.38059e8 | + | 2.39125e8i | 0.521402 | + | 0.903095i | |||||
−8.38861e6 | − | 1.45295e7i | −0.0312500 | − | 0.0541266i | |||||
−8.76073e7 | + | 1.51740e8i | −0.321940 | + | 0.557616i | −0.980888 | − | 0.194572i | ||
0.658949 | + | 0.752188i | ||||||||
4.02657e8 | 1.45971 | |||||||||
4.50226e7 | + | 2.94434e7i | 0.161021 | + | 0.105303i | |||||
−1.64271e8 | −0.579636 | |||||||||
−1.93737e8 | + | 3.35562e8i | −0.674482 | + | 1.16824i | |||||
4.27039e7 | + | 7.39654e7i | 0.146694 | + | 0.254082i | |||||
4.22487e7 | + | 7.31770e7i | 0.143208 | + | 0.248044i | 0.928703 | − | 0.370824i | ||
−0.785495 | + | 0.618868i | ||||||||
9.61891e7 | + | 1.66604e8i | 0.321745 | + | 0.557279i | |||||
−1.34574e8 | −0.444223 | |||||||||
−4.08663e7 | − | 7.07826e7i | −0.133131 | − | 0.230590i | |||||
−7.28339e7 | −0.234177 | |||||||||
−7.23288e7 | + | 1.25277e8i | −0.229530 | + | 0.397558i | |||||
2.13687e8 | 0.669338 | 0.334669 | − | 0.942336i | ||||||
0.334669 | + | 0.942336i | ||||||||
137340. | 0.000424642 | |||||||||
−1.70568e8 | + | 2.95432e8i | −0.520601 | + | 0.901707i | 0.479112 | + | 0.877754i | ||
−0.999713 | + | 0.0239537i | ||||||||
−4.15761e7 | − | 7.20119e7i | −0.125272 | − | 0.216977i | |||||
−1.44077e8 | −0.428574 | |||||||||
9.94872e7 | − | 1.72317e8i | 0.292173 | − | 0.506059i | |||||
−1.01762e8 | + | 1.76258e8i | −0.295069 | + | 0.511074i | |||||
−1.39019e8 | + | 2.40787e8i | −0.398008 | + | 0.689369i | |||||
2.50203e7 | + | 4.33364e7i | 0.0707315 | + | 0.122511i | 0.899222 | − | 0.437492i | ||
−0.828491 | + | 0.560003i | ||||||||
−1.58642e8 | − | 2.74775e8i | −0.442854 | − | 0.767045i | |||||
1.04567e8 | − | 1.81115e8i | 0.288257 | − | 0.499276i | |||||
−9.19353e6 | + | 1.59237e7i | −0.0250282 | + | 0.0433501i | |||||
−1.90644e8 | + | 3.30205e8i | −0.512568 | + | 0.887793i | 0.487326 | + | 0.873220i | ||
−0.999894 | + | 0.0145732i | ||||||||
−2.23969e8 | −0.594725 | |||||||||
1.17189e8 | + | 2.02978e8i | 0.307352 | + | 0.532349i | 0.977782 | − | 0.209623i | ||
−0.670430 | + | 0.741972i | ||||||||
8.73472e7 | − | 1.51290e8i | 0.226274 | − | 0.391918i | |||||
7.95878e8 | 2.03652 | |||||||||
−5.67254e8 | −1.43383 | |||||||||
−4.26396e7 | + | 7.38540e7i | −0.106470 | + | 0.184411i | |||||
7.16223e7 | 0.176675 | |||||||||
−892401. | − | 1.54568e6i | −0.00217479 | − | 0.00376685i | |||||
−2.91700e8 | −0.702335 | |||||||||
6.71770e6 | + | 1.16354e7i | 0.0159807 | + | 0.0276794i | |||||
−1.36674e8 | − | 2.36727e8i | −0.321253 | − | 0.556426i | |||||
2.52263e8 | + | 4.36932e8i | 0.585891 | + | 1.01479i | 0.994764 | + | 0.102201i | ||
−0.408873 | + | 0.912591i | ||||||||
2.09769e8 | − | 3.63331e8i | 0.481422 | − | 0.833848i | |||||
−3.74558e7 | −0.0849459 | |||||||||
1.40787e8 | − | 7.11677e7i | 0.315531 | − | 0.159500i | |||||
474255. | 0.00105042 | |||||||||
7.63651e7 | − | 1.32268e8i | 0.167162 | − | 0.289534i | |||||
−4.09916e8 | − | 7.09996e8i | −0.886841 | − | 1.53605i | |||||
7.57940e7 | + | 1.31279e8i | 0.162073 | + | 0.280719i | |||||
6.64474e7 | + | 1.15090e8i | 0.140441 | + | 0.243252i | |||||
7.13905e7 | 0.149147 | |||||||||
−2.37885e8 | − | 4.12028e8i | −0.491267 | − | 0.850899i | |||||
−2.39677e8 | −0.489293 | |||||||||
−2.54075e8 | + | 4.40071e8i | −0.512758 | + | 0.888123i | |||||
3.54978e8 | 0.708234 | |||||||||
−1.90308e8 | −0.375381 | −0.187691 | − | 0.982228i | ||||||
−0.187691 | + | 0.982228i | ||||||||
−3.17467e7 | + | 5.49869e7i | −0.0619115 | + | 0.107234i | |||||
4.91414e8 | + | 8.51154e8i | 0.947530 | + | 1.64117i | |||||
1.57442e8 | 0.300161 | |||||||||
3.02378e8 | − | 5.23735e8i | 0.570019 | − | 0.987302i | −0.426544 | − | 0.904467i | ||
0.996563 | − | 0.0828351i | ||||||||
−2.11249e8 | + | 3.65895e8i | −0.393781 | + | 0.682048i | |||||
2.37570e7 | − | 4.11484e7i | 0.0437912 | − | 0.0758486i | −0.843299 | − | 0.537445i | ||
0.887090 | + | 0.461596i | ||||||||
−3.05983e7 | − | 5.29978e7i | −0.0557755 | − | 0.0966060i | |||||
−3.92474e7 | − | 6.79785e7i | −0.0707496 | − | 0.122542i | |||||
−4.83942e7 | + | 8.38212e7i | −0.0862757 | + | 0.149434i | |||||
5.49685e8 | − | 9.52083e8i | 0.969185 | − | 1.67868i | 0.271261 | − | 0.962506i | ||
0.697924 | − | 0.716172i | ||||||||
−1.73059e8 | + | 2.99747e8i | −0.301787 | + | 0.522710i | |||||
−1.00729e9 | −1.73734 | |||||||||
2.69596e7 | + | 4.66954e7i | 0.0459926 | + | 0.0796616i | |||||
8.29092e8 | − | 1.43603e9i | 1.39906 | − | 2.42324i | |||||
−9.17647e7 | −0.153172 | |||||||||
−1.18790e9 | −1.96142 | |||||||||
1.53143e8 | − | 2.65252e8i | 0.250144 | − | 0.433262i | |||||
−4.46979e8 | −0.722263 | |||||||||
2.36409e8 | + | 4.09473e8i | 0.377923 | + | 0.654581i | |||||
2.16760e7 | 0.0342816 | |||||||||
1.25039e8 | + | 2.16573e8i | 0.195653 | + | 0.338880i | |||||
−3.69599e7 | − | 6.40165e7i | −0.0572197 | − | 0.0991074i | |||||
−3.09136e8 | − | 5.35439e8i | −0.473533 | − | 0.820183i | |||||
−6.01124e7 | + | 1.04118e8i | −0.0911100 | + | 0.157807i | −0.907978 | − | 0.419017i | ||
0.816868 | + | 0.576824i | ||||||||
4.03386e8 | 0.604975 | |||||||||
−3.73987e7 | + | 6.72409e8i | −0.0555011 | + | 0.997881i | |||||
5.07912e7 | 0.0745892 | |||||||||
2.32453e8 | − | 4.02620e8i | 0.337814 | − | 0.585111i | |||||
2.36454e7 | + | 4.09550e7i | 0.0340062 | + | 0.0589005i | |||||
−4.60562e8 | − | 7.97718e8i | −0.655517 | − | 1.13539i | −0.981764 | − | 0.190104i | ||
0.326247 | − | 0.945285i | ||||||||
−3.71904e8 | − | 6.44157e8i | −0.523869 | − | 0.907368i | |||||
−1.20262e9 | −1.67660 | |||||||||
1.33619e8 | + | 2.31434e8i | 0.184370 | + | 0.319338i | |||||
5.43670e8 | 0.742498 | |||||||||
5.11593e8 | − | 8.86105e8i | 0.691565 | − | 1.19783i | |||||
2.82256e8 | 0.377670 | |||||||||
3.89707e8 | 0.516159 | |||||||||
4.46783e8 | − | 7.73850e8i | 0.585773 | − | 1.01459i | |||||
−5.90275e7 | − | 1.02239e8i | −0.0766105 | − | 0.132693i | |||||
8.20647e8 | 1.05439 | 0.527197 | − | 0.849743i | ||||||
0.527197 | + | 0.849743i | ||||||||
−3.75120e8 | + | 6.49727e8i | −0.477137 | + | 0.826426i | |||||
2.85785e8 | − | 4.94993e8i | 0.359873 | − | 0.623319i | −0.628066 | − | 0.778160i | ||
0.987939 | + | 0.154841i | ||||||||
−2.50154e7 | + | 4.33280e7i | −0.0311867 | + | 0.0540170i | |||||
520777. | + | 902012.i | 0.000642801 | + | 0.00111336i | |||||
9.30956e7 | + | 1.61246e8i | 0.113771 | + | 0.197056i | |||||
3.99070e8 | − | 6.91209e8i | 0.482878 | − | 0.836369i | −0.516929 | − | 0.856028i | ||
0.999807 | + | 0.0196593i | ||||||||
−4.81674e7 | + | 8.34284e7i | −0.0577087 | + | 0.0999545i | |||||
−2.80719e8 | + | 4.86220e8i | −0.333022 | + | 0.576811i | |||||
−7.04915e7 | −0.0828060 | |||||||||
1.17193e8 | + | 2.02983e8i | 0.136320 | + | 0.236114i | |||||
−2.77582e8 | + | 4.80786e8i | −0.319743 | + | 0.553811i | |||||
−9.18116e8 | −1.04729 | −0.523645 | − | 0.851936i | ||||||
−0.523645 | + | 0.851936i | ||||||||
−2.30182e8 | −0.260023 | |||||||||
−1.26506e9 | + | 2.19115e9i | −1.41526 | + | 2.45130i | |||||
−8.21975e8 | −0.910706 | |||||||||
−4.23182e8 | − | 7.32973e8i | −0.464359 | − | 0.804294i | |||||
−1.39443e8 | −0.151546 | |||||||||
4.39248e8 | + | 7.60800e8i | 0.472808 | + | 0.818928i | |||||
6.53470e8 | + | 1.13184e9i | 0.696693 | + | 1.20671i | |||||
−1.25225e8 | − | 2.16896e8i | −0.132239 | − | 0.229045i | 0.792300 | − | 0.610132i | ||
−0.924539 | + | 0.381086i | ||||||||
−1.34548e8 | + | 2.33043e8i | −0.140737 | + | 0.243764i | |||||
−1.06758e9 | −1.10614 | |||||||||
−4.52466e8 | + | 2.28721e8i | −0.464387 | + | 0.234747i | |||||
−1.14235e8 | −0.116142 | |||||||||
2.02466e8 | − | 3.50682e8i | 0.203917 | − | 0.353194i | |||||
8.92411e8 | + | 1.54570e9i | 0.890398 | + | 1.54221i | 0.839399 | + | 0.543516i | ||
0.0509994 | + | 0.998699i | ||||||||
4.61406e8 | + | 7.99178e8i | 0.456071 | + | 0.789938i | |||||
−7.74889e8 | − | 1.34215e9i | −0.758805 | − | 1.31429i | |||||
−2.16766e8 | −0.210297 | |||||||||
−1.10610e9 | − | 1.91581e9i | −1.06316 | − | 1.84144i | |||||
116582. | 0.000111023 | |||||||||
−2.24696e8 | + | 3.89184e8i | −0.212011 | + | 0.367213i | −0.952344 | − | 0.305027i | ||
0.740333 | + | 0.672240i | ||||||||
7.70282e8 | 0.720123 | |||||||||
8.63123e8 | 0.799531 | |||||||||
5.67889e8 | − | 9.83613e8i | 0.521245 | − | 0.902823i | |||||
4.14759e8 | + | 7.18384e8i | 0.377225 | + | 0.653372i | 0.990657 | − | 0.136375i | ||
−0.613433 | + | 0.789747i | ||||||||
1.38678e8 | 0.124982 | |||||||||
1.02029e8 | − | 1.76719e8i | 0.0911191 | − | 0.157823i | |||||
4.18261e8 | − | 7.24450e8i | 0.370162 | − | 0.641140i | |||||
−8.31833e8 | + | 1.44078e9i | −0.729538 | + | 1.26360i | |||||
6.50166e6 | + | 1.12612e7i | 0.00565084 | + | 0.00978754i | |||||
6.35425e8 | + | 1.10059e9i | 0.547319 | + | 0.947984i | 0.998457 | + | 0.0555301i | ||
−0.451138 | + | 0.892454i | ||||||||
6.78920e8 | − | 1.17592e9i | 0.579552 | − | 1.00381i | |||||
−6.66853e8 | + | 1.15502e9i | −0.564172 | + | 0.977174i | |||||
2.03023e8 | − | 3.51646e8i | 0.170233 | − | 0.294852i | |||||
−7.05967e8 | −0.586693 | |||||||||
5.49697e8 | + | 9.52102e8i | 0.452779 | + | 0.784236i | |||||
1.55531e8 | − | 2.69387e8i | 0.126978 | − | 0.219931i | |||||
−7.94854e8 | −0.643212 | |||||||||
−9.52444e8 | −0.763963 | −0.381982 | − | 0.924170i | ||||||
−0.381982 | + | 0.924170i | ||||||||
3.29536e8 | − | 5.70773e8i | 0.262007 | − | 0.453809i | |||||
6.75589e8 | 0.532448 | |||||||||
7.33565e7 | + | 1.27057e8i | 0.0573097 | + | 0.0992634i | |||||
−7.29454e8 | −0.564928 | −0.282464 | − | 0.959278i | ||||||
−0.282464 | + | 0.959278i | ||||||||
−5.97858e8 | − | 1.03552e9i | −0.458994 | − | 0.795001i | |||||
5.97001e8 | + | 1.03404e9i | 0.454368 | + | 0.786988i | |||||
−2.30234e8 | − | 3.98777e8i | −0.173714 | − | 0.300882i | |||||
−4.92177e8 | + | 8.52475e8i | −0.368153 | + | 0.637660i | |||||
−2.47613e8 | −0.183625 | |||||||||
−1.56243e9 | + | 7.89809e8i | −1.14874 | + | 0.580686i | |||||
6.87322e8 | 0.501014 | |||||||||
5.49737e8 | − | 9.52173e8i | 0.397304 | − | 0.688152i | −0.596088 | − | 0.802919i | ||
0.993392 | + | 0.114768i | ||||||||
−4.01853e8 | − | 6.96030e8i | −0.287954 | − | 0.498752i | |||||
8.22345e8 | + | 1.42434e9i | 0.584262 | + | 1.01197i | |||||
4.75610e8 | + | 8.23780e8i | 0.335051 | + | 0.580325i | |||||
−3.17948e7 | −0.0222091 | |||||||||
−5.74387e8 | − | 9.94867e8i | −0.397835 | − | 0.689071i | |||||
−1.29641e9 | −0.890380 | |||||||||
−2.04455e8 | + | 3.54127e8i | −0.139243 | + | 0.241175i | |||||
2.62261e9 | 1.77116 | |||||||||
2.65990e9 | 1.78135 | |||||||||
5.02986e7 | − | 8.71197e7i | 0.0334046 | − | 0.0578585i | −0.848840 | − | 0.528650i | ||
0.882244 | + | 0.470792i | ||||||||
−7.59922e7 | − | 1.31622e8i | −0.0500492 | − | 0.0866877i | |||||
−2.50820e8 | −0.163823 | −0.0819116 | − | 0.996640i | ||||||
−0.0819116 | + | 0.996640i | ||||||||
7.82124e8 | − | 1.35468e9i | 0.506620 | − | 0.877491i | |||||
4.62689e8 | − | 8.01402e8i | 0.297234 | − | 0.514824i | |||||
−1.67494e8 | + | 2.90107e8i | −0.106713 | + | 0.184832i | |||||
3.63573e8 | + | 6.29728e8i | 0.229737 | + | 0.397916i | |||||
7.21998e8 | + | 1.25054e9i | 0.452483 | + | 0.783723i | |||||
−2.15674e8 | + | 3.73559e8i | −0.134060 | + | 0.232199i | |||||
8.02428e8 | − | 1.38985e9i | 0.494712 | − | 0.856867i | |||||
2.34442e9 | − | 4.06065e9i | 1.43362 | − | 2.48310i | |||||
−1.25245e9 | −0.759664 | |||||||||
5.20141e8 | + | 9.00910e8i | 0.312932 | + | 0.542015i | 0.978996 | − | 0.203880i | ||
−0.666064 | + | 0.745895i | ||||||||
170936. | − | 296070.i | 0.000102009 | − | 0.000176685i | |||||
2.78932e9 | 1.65117 | 0.825584 | − | 0.564279i | ||||||
0.825584 | + | 0.564279i | ||||||||
1.33646e8 | 0.0784769 | |||||||||
1.20557e9 | − | 2.08811e9i | 0.702233 | − | 1.21630i | |||||
2.09789e7 | 0.0121221 | |||||||||
1.92213e9 | + | 3.32923e9i | 1.10179 | + | 1.90835i | |||||
2.25945e9 | 1.28483 | |||||||||
−9.89247e8 | − | 1.71343e9i | −0.558057 | − | 0.966584i | −0.997659 | − | 0.0683906i | ||
0.439601 | − | 0.898193i | ||||||||
−2.99194e8 | − | 5.18219e8i | −0.167443 | − | 0.290020i | |||||
8.66709e8 | + | 1.50118e9i | 0.481214 | + | 0.833487i | |||||
−1.01333e9 | + | 1.75514e9i | −0.558180 | + | 0.966796i | |||||
−3.63514e7 | −0.0198659 | −0.00993296 | − | 0.999951i | ||||||
−0.00993296 | + | 0.999951i | ||||||||
−7.24127e7 | + | 1.30194e9i | −0.0392622 | + | 0.705914i | |||||
2.26548e8 | 0.121871 | |||||||||
−5.71780e8 | + | 9.90351e8i | −0.305180 | + | 0.528588i | |||||
6.31222e8 | + | 1.09331e9i | 0.334276 | + | 0.578984i | |||||
2.28849e7 | + | 3.96378e7i | 0.0120248 | + | 0.0208275i | |||||
1.43180e8 | + | 2.47996e8i | 0.0746485 | + | 0.129295i | 0.900933 | − | 0.433957i | ||
−0.826285 | + | 0.563252i | ||||||||
−6.26320e8 | −0.324006 | |||||||||
−1.38766e9 | − | 2.40350e9i | −0.712304 | − | 1.23375i | |||||
−1.16394e9 | −0.592852 | |||||||||
−2.95051e8 | + | 5.11043e8i | −0.149126 | + | 0.258294i | |||||
−1.59714e9 | −0.801026 | |||||||||
4.48148e8 | 0.223039 | |||||||||
9.90565e8 | − | 1.71571e9i | 0.489222 | − | 0.847358i | |||||
4.09367e8 | + | 7.09044e8i | 0.200635 | + | 0.347510i | 0.948733 | − | 0.316078i | ||
−0.748098 | + | 0.663588i | ||||||||
1.84756e9 | 0.898606 | |||||||||
847202. | − | 1.46740e6i | 0.000408924 | − | 0.000708277i | |||||
4.32414e8 | − | 7.48963e8i | 0.207132 | − | 0.358763i | |||||
−3.51653e7 | + | 6.09081e7i | −0.0167171 | + | 0.0289549i | −0.874263 | − | 0.485453i | ||
0.857546 | + | 0.514408i | ||||||||
−2.62413e8 | − | 4.54513e8i | −0.123805 | − | 0.214437i | |||||
−4.79035e8 | − | 8.29713e8i | −0.224302 | − | 0.388503i | 0.731808 | − | 0.681511i | ||
−0.956110 | + | 0.293008i | ||||||||
−3.63056e8 | + | 6.28832e8i | −0.168718 | + | 0.292228i | |||||
−6.50693e8 | + | 1.12703e9i | −0.300117 | + | 0.519818i | |||||
−9.08882e8 | + | 1.57423e9i | −0.416061 | + | 0.720639i | |||||
−1.12248e9 | −0.510000 | −0.255000 | − | 0.966941i | ||||||
−0.255000 | + | 0.966941i | ||||||||
−8.72824e8 | − | 1.51178e9i | −0.393610 | − | 0.681753i | |||||
1.97320e8 | − | 3.41768e8i | 0.0883214 | − | 0.152977i | |||||
6.96650e8 | 0.309508 | |||||||||
5.05841e8 | 0.223070 | |||||||||
−4.66183e7 | + | 8.07452e7i | −0.0204061 | + | 0.0353443i | |||||
−4.32491e9 | −1.87916 | |||||||||
−4.00019e8 | − | 6.92853e8i | −0.172527 | − | 0.298825i | |||||
2.09592e9 | 0.897320 | |||||||||
1.13424e8 | + | 1.96455e8i | 0.0482035 | + | 0.0834909i | |||||
−7.15033e8 | − | 1.23847e9i | −0.301656 | − | 0.522484i | |||||
1.31412e7 | + | 2.27613e7i | 0.00550349 | + | 0.00953232i | |||||
−1.25400e9 | + | 2.17200e9i | −0.521344 | + | 0.902995i | 0.478347 | + | 0.878171i | ||
−0.999692 | + | 0.0248243i | ||||||||
−4.45687e8 | −0.183944 | |||||||||
−3.21788e9 | − | 2.10439e9i | −1.31845 | − | 0.862223i | |||||
−2.63682e9 | −1.07255 | |||||||||
3.79256e8 | − | 6.56891e8i | 0.153150 | − | 0.265264i | |||||
−4.09572e8 | − | 7.09400e8i | −0.164200 | − | 0.284402i | |||||
−2.08952e7 | − | 3.61916e7i | −0.00831670 | − | 0.0144050i | |||||
1.26513e9 | + | 2.19126e9i | 0.499928 | + | 0.865900i | |||||
−1.85017e9 | −0.725874 | −0.362937 | − | 0.931814i | ||||||
−0.362937 | + | 0.931814i | ||||||||
6.32454e8 | + | 1.09544e9i | 0.246354 | + | 0.426697i | |||||
−3.90824e9 | −1.51147 | |||||||||
−6.52482e8 | + | 1.13013e9i | −0.250543 | + | 0.433953i | |||||
1.44884e9 | 0.552375 | 0.276188 | − | 0.961104i | ||||||
0.276188 | + | 0.961104i | ||||||||
−2.06710e9 | −0.782498 | |||||||||
−1.79940e9 | + | 3.11665e9i | −0.676337 | + | 1.17145i | |||||
2.92082e9 | + | 5.05901e9i | 1.09009 | + | 1.88808i | |||||
2.55453e9 | 0.946656 | |||||||||
1.95955e8 | − | 3.39404e8i | 0.0721058 | − | 0.124891i | |||||
−2.38291e8 | + | 4.12733e8i | −0.0870685 | + | 0.150807i | |||||
−1.66716e9 | + | 2.88761e9i | −0.604888 | + | 1.04770i | |||||
−1.86563e9 | − | 3.23137e9i | −0.672163 | − | 1.16422i | −0.977290 | − | 0.211908i | ||
0.305127 | − | 0.952312i | ||||||||
−7.49968e8 | − | 1.29898e9i | −0.268317 | − | 0.464738i | |||||
−2.09916e8 | + | 3.63585e8i | −0.0745784 | + | 0.129174i | |||||
−1.19037e9 | + | 2.06178e9i | −0.419971 | + | 0.727411i | |||||
2.63972e9 | − | 4.57213e9i | 0.924847 | − | 1.60188i | 0.133039 | − | 0.991111i | ||
0.791807 | − | 0.610771i | ||||||||
−1.95392e8 | −0.0679830 | |||||||||
7.39934e8 | + | 1.28160e9i | 0.255666 | + | 0.442827i | |||||
1.49319e9 | − | 2.58628e9i | 0.512376 | − | 0.887461i | |||||
6.14820e9 | 2.09517 | |||||||||
8.35364e8 | 0.282718 | |||||||||
5.86626e8 | − | 1.01607e9i | 0.197174 | − | 0.341515i | −0.750437 | − | 0.660942i | ||
0.947611 | + | 0.319427i | ||||||||
−2.20894e9 | −0.737374 | |||||||||
3.72860e8 | + | 6.45813e8i | 0.123616 | + | 0.214108i | |||||
1.34218e8 | 0.0441942 | |||||||||
−2.44197e6 | − | 4.22961e6i | −0.000798599 | − | 0.00138321i | |||||
−7.00859e8 | − | 1.21392e9i | −0.227646 | − | 0.394294i | |||||
−1.52853e9 | − | 2.64749e9i | −0.493115 | − | 0.854101i | |||||
−1.61063e9 | + | 2.78969e9i | −0.516085 | + | 0.893885i | |||||
2.40564e9 | 0.765621 | |||||||||
−3.84080e8 | + | 1.94152e8i | −0.121414 | + | 0.0613745i | |||||
9.75823e8 | 0.306398 | |||||||||
6.57085e8 | − | 1.13811e9i | 0.204932 | − | 0.354953i | |||||
−1.03976e9 | − | 1.80091e9i | −0.322106 | − | 0.557904i | 0.658816 | − | 0.752304i | ||
−0.980922 | + | 0.194400i | ||||||||
−1.54989e9 | − | 2.68449e9i | −0.476931 | − | 0.826068i | |||||
2.29797e9 | + | 3.98020e9i | 0.702406 | + | 1.21660i | 0.967620 | + | 0.252413i | ||
−0.265214 | + | 0.964190i | ||||||||
−6.83263e8 | −0.207457 | |||||||||
−2.06773e8 | − | 3.58142e8i | −0.0623644 | − | 0.108018i | |||||
−6.75980e8 | −0.202527 | |||||||||
9.71203e8 | − | 1.68217e9i | 0.289050 | − | 0.500649i | |||||
−1.53903e9 | −0.455016 | |||||||||
9.11286e8 | 0.267646 | |||||||||
5.38296e8 | − | 9.32356e8i | 0.157056 | − | 0.272030i | |||||
−1.99014e8 | − | 3.44703e8i | −0.0576838 | − | 0.0999112i | |||||
6.53862e8 | 0.188276 | |||||||||
3.04756e9 | − | 5.27853e9i | 0.871781 | − | 1.50997i | |||||
2.91335e8 | − | 5.04608e8i | 0.0827940 | − | 0.143403i | |||||
−2.57887e9 | + | 4.46673e9i | −0.728100 | + | 1.26111i | |||||
−5.78631e8 | − | 1.00222e9i | −0.162302 | − | 0.281116i | |||||
−2.29445e9 | − | 3.97410e9i | −0.639394 | − | 1.10746i | |||||
−8.54748e8 | + | 1.48047e9i | −0.236647 | + | 0.409884i | |||||
−2.25312e9 | + | 3.90252e9i | −0.619760 | + | 1.07346i | |||||
−549359. | + | 951518.i | −0.000150134 | + | 0.000260039i | |||||
−5.95661e9 | −1.61737 | −0.808684 | − | 0.588244i | ||||||
−0.808684 | + | 0.588244i | ||||||||
−1.36454e9 | − | 2.36346e9i | −0.368121 | − | 0.637603i | |||||
3.39715e9 | − | 5.88404e9i | 0.910575 | − | 1.57716i | |||||
6.65217e8 | 0.177161 | |||||||||
−6.74226e7 | −0.0178409 | |||||||||
5.76308e8 | − | 9.98195e8i | 0.151524 | − | 0.262447i | |||||
6.55369e9 | 1.71210 | 0.856052 | − | 0.516890i | ||||||
0.856052 | + | 0.516890i | ||||||||
7.95898e8 | + | 1.37854e9i | 0.206598 | + | 0.357838i | |||||
−5.39991e9 | −1.39278 | |||||||||
−8.14100e8 | − | 1.41006e9i | −0.208645 | − | 0.361384i | |||||
5.18657e9 | + | 8.98340e9i | 1.32084 | + | 2.28776i | |||||
−1.11215e9 | − | 1.92630e9i | −0.281434 | − | 0.487458i | |||||
1.32024e8 | − | 2.28672e8i | 0.0331982 | − | 0.0575010i | |||||
−4.00325e8 | −0.100029 | |||||||||
2.32722e8 | − | 4.18423e9i | 0.0577847 | − | 1.03894i | |||||
2.53826e9 | 0.626290 | |||||||||
−6.06102e8 | + | 1.04980e9i | −0.148611 | + | 0.257403i | −0.930715 | − | 0.365746i | ||
0.782103 | + | 0.623149i | ||||||||
8.36536e8 | + | 1.44892e9i | 0.203828 | + | 0.353041i | |||||
−4.74916e9 | − | 8.22579e9i | −1.14994 | − | 1.99176i | |||||
−7.35483e7 | − | 1.27389e8i | −0.0176976 | − | 0.0306531i | |||||
−7.62781e9 | −1.82402 | |||||||||
−1.52515e9 | − | 2.64164e9i | −0.362440 | − | 0.627765i | |||||
2.22115e9 | 0.524563 | 0.262282 | − | 0.964991i | ||||||
0.262282 | + | 0.964991i | ||||||||
8.95877e8 | − | 1.55170e9i | 0.210267 | − | 0.364193i | |||||
3.74071e9 | 0.872538 | |||||||||
−1.87503e9 | −0.434661 | |||||||||
−4.17789e8 | + | 7.23632e8i | −0.0962535 | + | 0.166716i | |||||
6.98778e8 | + | 1.21032e9i | 0.160000 | + | 0.277128i | |||||
−5.04048e9 | −1.14704 | −0.573520 | − | 0.819192i | ||||||
−0.573520 | + | 0.819192i | ||||||||
−3.18351e9 | + | 5.51400e9i | −0.720019 | + | 1.24711i | |||||
−1.59482e9 | + | 2.76231e9i | −0.358497 | + | 0.620935i | −0.987710 | − | 0.156298i | ||
0.629213 | + | 0.777233i | ||||||||
2.26902e9 | − | 3.93005e9i | 0.506934 | − | 0.878036i | |||||
4.69408e9 | + | 8.13038e9i | 1.04234 | + | 1.80539i | |||||
−3.41117e8 | − | 5.90832e8i | −0.0752856 | − | 0.130398i | |||||
1.17659e9 | − | 2.03791e9i | 0.258100 | − | 0.447042i | |||||
−2.86489e8 | + | 4.96214e8i | −0.0624639 | + | 0.108191i | |||||
4.53197e9 | − | 7.84960e9i | 0.982136 | − | 1.70111i | 0.328106 | − | 0.944641i | ||
0.654030 | − | 0.756469i | ||||||||
1.42784e7 | 0.00307562 | |||||||||
3.45728e9 | + | 5.98818e9i | 0.740217 | + | 1.28209i | |||||
1.16680e9 | − | 2.02096e9i | 0.248313 | − | 0.430090i | |||||
−1.10048e9 | −0.232790 | |||||||||
−1.07483e8 | −0.0226001 | |||||||||
1.85882e9 | − | 3.21957e9i | 0.388506 | − | 0.672912i | |||||
2.18679e9 | 0.454320 | |||||||||
2.80511e9 | + | 4.85859e9i | 0.579301 | + | 1.00338i | |||||
−4.03621e9 | −0.828575 | |||||||||
1.43883e8 | + | 2.49212e8i | 0.0293613 | + | 0.0508553i | 0.880333 | − | 0.474357i | ||
−0.850971 | + | 0.525212i | ||||||||
1.67815e9 | + | 2.90665e9i | 0.340417 | + | 0.589620i | |||||
−2.79939e9 | − | 4.84868e9i | −0.564494 | − | 0.977732i | |||||
1.49823e8 | − | 2.59502e8i | 0.0300329 | − | 0.0520185i | |||||
−9.08740e9 | −1.81085 | |||||||||
−7.00839e7 | + | 1.26007e9i | −0.0138833 | + | 0.249614i | |||||
−6.45832e9 | −1.27183 | −0.635913 | − | 0.771761i | ||||||
−0.635913 | + | 0.771761i | ||||||||
−1.89702e6 | + | 3.28574e6i | −0.000371381 | + | 0.000643251i | |||||
−3.64524e8 | − | 6.31374e8i | −0.0709442 | − | 0.122879i | |||||
6.10921e8 | + | 1.05815e9i | 0.118202 | + | 0.204731i | |||||
2.72389e9 | + | 4.71792e9i | 0.523937 | + | 0.907486i | |||||
6.55866e9 | 1.25418 | |||||||||
2.16097e9 | + | 3.74292e9i | 0.410824 | + | 0.711568i | 0.994980 | − | 0.100073i | ||
−0.584156 | + | 0.811641i | ||||||||
−1.21270e9 | −0.229206 | |||||||||
2.83309e9 | − | 4.90706e9i | 0.532354 | − | 0.922064i | −0.466933 | − | 0.884293i | ||
0.999286 | − | 0.0377708i | ||||||||
−1.06316e9 | −0.198614 | |||||||||
4.94037e9 | 0.917590 | |||||||||
−2.85562e8 | + | 4.94608e8i | −0.0527316 | + | 0.0913338i | |||||
1.31630e9 | + | 2.27989e9i | 0.241663 | + | 0.418573i | |||||
3.80615e9 | 0.694756 | |||||||||
−3.16656e8 | + | 5.48463e8i | −0.0574681 | + | 0.0995376i | −0.893328 | − | 0.449405i | ||
0.835860 | + | 0.548942i | ||||||||
9.58708e8 | − | 1.66053e9i | 0.172991 | − | 0.299629i | |||||
1.02336e9 | − | 1.77252e9i | 0.183599 | − | 0.318002i | |||||
−2.03260e9 | − | 3.52057e9i | −0.362575 | − | 0.627998i | |||||
2.64162e9 | + | 4.57542e9i | 0.468518 | + | 0.811496i | |||||
−1.41991e9 | + | 2.45936e9i | −0.250399 | + | 0.433703i | |||||
1.99594e9 | − | 3.45707e9i | 0.349974 | − | 0.606172i | −0.636271 | − | 0.771466i | ||
0.986244 | + | 0.165294i | ||||||||
7.61232e8 | − | 1.31849e9i | 0.132717 | − | 0.229873i | |||||
6.64330e9 | 1.15165 | |||||||||
−2.53974e8 | − | 4.39895e8i | −0.0437780 | − | 0.0758258i | |||||
1.33468e9 | − | 2.31173e9i | 0.228759 | − | 0.396222i | −0.728682 | − | 0.684853i | ||
0.957441 | + | 0.288630i | ||||||||
−7.86262e9 | −1.34001 | |||||||||
−5.70698e9 | −0.967139 | −0.483569 | − | 0.875306i | ||||||
−0.483569 | + | 0.875306i | ||||||||
−6.29766e8 | + | 1.09079e9i | −0.106123 | + | 0.183810i | |||||
−5.48339e6 | −0.000918817 | |||||||||
2.41903e9 | + | 4.18988e9i | 0.403064 | + | 0.698128i | |||||
1.92307e8 | 0.0318631 | |||||||||
−1.68999e9 | − | 2.92716e9i | −0.278445 | − | 0.482281i | |||||
1.01111e9 | + | 1.75129e9i | 0.165660 | + | 0.286932i | |||||
1.90056e8 | + | 3.29187e8i | 0.0309651 | + | 0.0536331i | |||||
−1.09932e10 | + | 1.90407e10i | −1.78109 | + | 3.08494i | |||||
4.89573e8 | 0.0788785 | |||||||||
−3.47354e8 | + | 6.24524e9i | −0.0556538 | + | 1.00063i | |||||
6.27958e8 | 0.100055 | |||||||||
5.21371e9 | − | 9.03041e9i | 0.826121 | − | 1.43088i | −0.0749377 | − | 0.997188i | ||
0.901059 | − | 0.433696i | ||||||||
−3.87154e8 | − | 6.70570e8i | −0.0610062 | − | 0.105666i | |||||
6.46491e9 | + | 1.11975e10i | 1.01309 | + | 1.75473i | |||||
4.39748e9 | + | 7.61666e9i | 0.685317 | + | 1.18700i | |||||
−2.68472e9 | −0.416094 | |||||||||
−1.38447e9 | − | 2.39798e9i | −0.213395 | − | 0.369612i | |||||
−9.89655e9 | −1.51704 | |||||||||
4.02915e9 | − | 6.97869e9i | 0.614244 | − | 1.06390i | |||||
−5.96619e9 | −0.904574 | |||||||||
−4.31353e8 | −0.0650434 | |||||||||
2.30437e9 | − | 3.99129e9i | 0.345581 | − | 0.598563i | −0.639878 | − | 0.768476i | ||
0.985459 | + | 0.169913i | ||||||||
6.63274e9 | + | 1.14882e10i | 0.989282 | + | 1.71349i | |||||
4.40952e9 | 0.654113 | 0.327057 | − | 0.945005i | ||||||
0.327057 | + | 0.945005i | ||||||||
3.67059e8 | − | 6.35765e8i | 0.0541546 | − | 0.0937985i | |||||
5.17628e9 | − | 8.96559e9i | 0.759555 | − | 1.31559i | |||||
4.75160e9 | − | 8.23002e9i | 0.693468 | − | 1.20112i | |||||
5.97464e9 | + | 1.03484e10i | 0.867255 | + | 1.50213i | 0.864791 | + | 0.502132i | ||
0.00246394 | + | 0.999997i | ||||||||
1.22515e9 | + | 2.12202e9i | 0.176879 | + | 0.306363i | |||||
5.17363e8 | − | 8.96099e8i | 0.0742915 | − | 0.128677i | |||||
1.78792e9 | − | 3.09676e9i | 0.255358 | − | 0.442294i | |||||
−5.52348e8 | + | 9.56694e8i | −0.0784656 | + | 0.135906i | |||||
−3.78255e9 | −0.534463 | |||||||||
−1.84460e9 | − | 3.19495e9i | −0.259243 | − | 0.449022i | 0.706796 | − | 0.707417i | ||
−0.966039 | + | 0.258395i | ||||||||
−8.67039e7 | + | 1.50176e8i | −0.0121204 | + | 0.0209931i | |||||
2.19589e9 | 0.305328 | |||||||||
−2.00062e9 | −0.276695 | |||||||||
−4.66772e9 | + | 8.08473e9i | −0.642135 | + | 1.11221i | |||||
5.91359e8 | 0.0809208 | |||||||||
3.59404e9 | + | 6.22507e9i | 0.489198 | + | 0.847316i | 0.999923 | − | 0.0124287i | ||
−0.510725 | + | 0.859744i | ||||||||
4.94617e9 | 0.669677 | |||||||||
4.20354e9 | + | 7.28075e9i | 0.566122 | + | 0.980553i | 0.996944 | + | 0.0781157i | ||
−0.430822 | + | 0.902437i | ||||||||
−4.80899e8 | − | 8.32941e8i | −0.0644245 | − | 0.111586i | |||||
−8.37605e9 | − | 1.45077e10i | −1.11620 | − | 1.93331i | |||||
−1.61354e9 | + | 2.79474e9i | −0.213891 | + | 0.370470i | |||||
−2.10140e9 | −0.277098 | |||||||||
−4.50899e9 | − | 2.94874e9i | −0.591452 | − | 0.386791i | |||||
1.16464e10 | 1.51967 | |||||||||
−2.03165e8 | + | 3.51892e8i | −0.0263712 | + | 0.0456763i | |||||
−4.72624e9 | − | 8.18608e9i | −0.610273 | − | 1.05702i | |||||
1.85962e9 | + | 3.22096e9i | 0.238871 | + | 0.413736i | |||||
−7.01888e9 | − | 1.21571e10i | −0.896890 | − | 1.55346i | |||||
−3.78326e8 | −0.0480921 | |||||||||
1.38835e9 | + | 2.40469e9i | 0.175568 | + | 0.304092i | 0.940358 | − | 0.340187i | ||
−0.764790 | + | 0.644280i | ||||||||
7.36900e9 | 0.927041 | |||||||||
−1.49479e6 | + | 2.58906e6i | −0.000187076 | + | 0.000324025i | |||||
5.95047e9 | 0.740863 | |||||||||
−6.79466e8 | −0.0841603 | −0.0420801 | − | 0.999114i | ||||||
−0.0420801 | + | 0.999114i | ||||||||
4.81047e9 | − | 8.33198e9i | 0.592766 | − | 1.02670i | |||||
−1.77371e7 | − | 3.07216e7i | −0.00217440 | − | 0.00376617i | |||||
−2.13790e9 | −0.260739 | |||||||||
6.60083e9 | − | 1.14330e10i | 0.800910 | − | 1.38722i | |||||
−2.17468e9 | + | 3.76666e9i | −0.262513 | + | 0.454685i | |||||
−7.55881e9 | + | 1.30922e10i | −0.907781 | + | 1.57232i | −0.0906398 | + | 0.995884i | ||
−0.817141 | + | 0.576438i | ||||||||
4.09274e9 | + | 7.08884e9i | 0.489010 | + | 0.846991i | |||||
−2.55788e9 | − | 4.43038e9i | −0.304063 | − | 0.526652i | |||||
−1.12902e9 | + | 1.95552e9i | −0.133527 | + | 0.231275i | |||||
−7.63581e9 | + | 1.32256e10i | −0.898477 | + | 1.55621i | |||||
−1.55883e9 | + | 2.69997e9i | −0.182490 | + | 0.316082i | |||||
8.16464e9 | 0.950976 | |||||||||
3.57426e9 | + | 6.19080e9i | 0.414204 | + | 0.717423i | |||||
3.67767e9 | − | 6.36992e9i | 0.424033 | − | 0.734447i | −0.572296 | − | 0.820047i | ||
0.996330 | + | 0.0855996i | ||||||||
9.44440e8 | 0.108344 | |||||||||
2.16844e9 | 0.247503 | |||||||||
−3.28259e9 | + | 5.68561e9i | −0.372785 | + | 0.645682i | |||||
−8.15756e9 | −0.921750 | |||||||||
−3.00096e9 | − | 5.19782e9i | −0.337387 | − | 0.584371i | |||||
−9.91557e9 | −1.10918 | |||||||||
2.28628e9 | + | 3.95995e9i | 0.254469 | + | 0.440753i | |||||
−7.51267e9 | − | 1.30123e10i | −0.832002 | − | 1.44107i | |||||
−2.00123e8 | − | 3.46624e8i | −0.0220523 | − | 0.0381958i | |||||
5.90179e9 | − | 1.02222e10i | 0.647099 | − | 1.12081i | −0.336713 | − | 0.941607i | ||
0.983812 | − | 0.179201i | ||||||||
−8.33243e6 | −0.000909058 | |||||||||
1.50889e10 | + | 9.86768e9i | 1.63800 | + | 1.07120i | |||||
−1.48953e9 | −0.160896 | |||||||||
−2.87920e9 | + | 4.98692e9i | −0.309464 | + | 0.536007i | |||||
3.19256e9 | + | 5.52967e9i | 0.341446 | + | 0.591402i | |||||
6.28101e8 | + | 1.08790e9i | 0.0668438 | + | 0.115777i | |||||
−3.85339e8 | − | 6.67427e8i | −0.0408062 | − | 0.0706785i | |||||
8.55548e9 | 0.901535 | 0.450767 | − | 0.892641i | ||||||
0.450767 | + | 0.892641i | ||||||||
−2.24575e9 | − | 3.88976e9i | −0.235482 | − | 0.407867i | |||||
3.30553e9 | 0.344904 | |||||||||
2.81966e8 | − | 4.88379e8i | 0.0292763 | − | 0.0507081i | |||||
−6.28598e9 | −0.649470 | |||||||||
−1.87508e9 | −0.192786 | |||||||||
−7.29224e9 | + | 1.26305e10i | −0.746088 | + | 1.29226i | |||||
−2.22066e9 | − | 3.84629e9i | −0.226092 | − | 0.391604i | |||||
−2.17246e8 | −0.0220108 | |||||||||
3.67246e9 | − | 6.36090e9i | 0.370273 | − | 0.641332i | |||||
5.48147e8 | − | 9.49419e8i | 0.0549979 | − | 0.0952592i | −0.837216 | − | 0.546873i | ||
0.892214 | + | 0.451614i | ||||||||
9.20728e8 | − | 1.59475e9i | 0.0919321 | − | 0.159231i | |||||
−1.29751e9 | − | 2.24735e9i | −0.128925 | − | 0.223304i | |||||
−1.01205e10 | − | 1.75292e10i | −1.00074 | − | 1.73333i | |||||
1.08978e10 | − | 1.88755e10i | 1.07239 | − | 1.85744i | |||||
3.28790e9 | − | 5.69481e9i | 0.321983 | − | 0.557691i | |||||
3.17484e9 | − | 5.49899e9i | 0.309413 | − | 0.535920i | |||||
6.77092e9 | 0.656703 | |||||||||
−4.04479e9 | − | 7.00578e9i | −0.390414 | − | 0.676217i | 0.602090 | − | 0.798428i | ||
−0.992504 | + | 0.122211i | ||||||||
5.57774e8 | − | 9.66092e8i | 0.0535794 | − | 0.0928023i | |||||
−1.04483e10 | −0.998845 | |||||||||
−7.02797e9 | −0.668652 | |||||||||
−7.72595e9 | + | 1.33817e10i | −0.731545 | + | 1.26707i | |||||
−1.04555e10 | −0.985273 | |||||||||
−6.38475e9 | − | 1.10587e10i | −0.598798 | − | 1.03715i | −0.992999 | − | 0.118124i | ||
0.394201 | − | 0.919024i | ||||||||
2.00360e9 | 0.187015 | |||||||||
−5.39331e9 | − | 9.34148e9i | −0.501013 | − | 0.867781i | |||||
−1.07638e9 | − | 1.86435e9i | −0.0995162 | − | 0.172367i | |||||
6.42156e9 | + | 1.11225e10i | 0.590887 | + | 1.02345i | |||||
4.27034e9 | − | 7.39644e9i | 0.391079 | − | 0.677369i | |||||
−1.90123e10 | −1.73292 | −0.866459 | − | 0.499247i | ||||||
−0.866459 | + | 0.499247i | ||||||||
2.25238e8 | − | 4.04966e9i | 0.0204329 | − | 0.367373i | |||||
−4.82861e10 | −4.35971 | |||||||||
4.56938e8 | − | 7.91441e8i | 0.0410624 | − | 0.0711221i | |||||
7.78857e9 | + | 1.34902e10i | 0.696621 | + | 1.20658i | 0.969631 | + | 0.244572i | ||
−0.273010 | + | 0.962011i | ||||||||
1.61973e9 | + | 2.80546e9i | 0.144191 | + | 0.249746i | |||||
−1.96340e9 | − | 3.40071e9i | −0.173965 | − | 0.301316i | |||||
−1.42786e10 | −1.25921 | |||||||||
−6.88825e9 | − | 1.19308e10i | −0.604626 | − | 1.04724i | |||||
−7.38249e9 | −0.644982 | |||||||||
−2.18910e9 | + | 3.79163e9i | −0.190361 | + | 0.329716i | |||||
1.23982e10 | 1.07311 | |||||||||
6.04137e9 | 0.520470 | 0.260235 | − | 0.965545i | ||||||
0.260235 | + | 0.965545i | ||||||||
8.67065e8 | − | 1.50180e9i | 0.0743514 | − | 0.128780i | |||||
−9.83941e9 | − | 1.70424e10i | −0.839821 | − | 1.45461i | |||||
1.76975e10 | 1.50353 | |||||||||
9.17748e8 | − | 1.58959e9i | 0.0776084 | − | 0.134422i | |||||
−466329. | + | 807706.i | −3.92524e−5 | + | 6.79872e-5i | |||||
1.80052e9 | − | 3.11859e9i | 0.150856 | − | 0.261290i | −0.780686 | − | 0.624923i | ||
0.931542 | + | 0.363633i | ||||||||
−1.79757e9 | − | 3.11347e9i | −0.149914 | − | 0.259659i | |||||
1.23425e10 | + | 2.13778e10i | 1.02460 | + | 1.77467i | |||||
−3.08113e9 | + | 5.33667e9i | −0.254602 | + | 0.440984i | |||||
−5.92131e9 | + | 1.02560e10i | −0.487048 | + | 0.843591i | −0.999889 | − | 0.0148920i | ||
0.512841 | + | 0.858483i | ||||||||
−3.45249e9 | + | 5.97989e9i | −0.282677 | + | 0.489611i | |||||
−5.72323e7 | −0.00466451 | |||||||||
4.54311e9 | + | 7.86891e9i | 0.368576 | + | 0.638392i | |||||
4.56336e9 | − | 7.90397e9i | 0.368527 | − | 0.638308i | |||||
−6.63615e9 | −0.533476 | |||||||||
2.27245e9 | 0.181849 | |||||||||
−5.54711e8 | + | 9.60787e8i | −0.0441878 | + | 0.0765355i | |||||
2.27682e10 | 1.80546 | 0.902729 | − | 0.430210i | ||||||
0.902729 | + | 0.430210i | ||||||||
8.16229e8 | + | 1.41375e9i | 0.0644309 | + | 0.111598i | |||||
1.15864e10 | 0.910451 | |||||||||
3.34609e9 | + | 5.79560e9i | 0.261744 | + | 0.453354i | |||||
1.09428e10 | + | 1.89535e10i | 0.852117 | + | 1.47591i | 0.879294 | + | 0.476280i | ||
−0.0271763 | + | 0.999631i | ||||||||
−6.65467e9 | − | 1.15262e10i | −0.515861 | − | 0.893498i | |||||
−1.71358e9 | + | 2.96801e9i | −0.132236 | + | 0.229039i | |||||
−1.04027e8 | −0.00799149 | |||||||||
1.97549e8 | − | 3.55182e9i | 0.0151078 | − | 0.271630i | |||||
−1.01668e10 | −0.774026 | |||||||||
−1.42903e10 | + | 2.47515e10i | −1.08308 | + | 1.87594i | |||||
5.43136e9 | + | 9.40739e9i | 0.409805 | + | 0.709803i | |||||
−7.75494e9 | − | 1.34319e10i | −0.582505 | − | 1.00893i | |||||
−5.33482e9 | − | 9.24018e9i | −0.398930 | − | 0.690967i | |||||
−1.47961e7 | −0.00110149 | |||||||||
1.62418e9 | + | 2.81317e9i | 0.120373 | + | 0.208492i | |||||
−1.57341e9 | −0.116091 | |||||||||
2.82387e9 | − | 4.89109e9i | 0.207427 | − | 0.359274i | |||||
1.03415e10 | 0.756263 | 0.378131 | − | 0.925752i | ||||||
0.378131 | + | 0.925752i | ||||||||
−8.79515e9 | −0.640326 | |||||||||
2.79377e9 | − | 4.83895e9i | 0.202498 | − | 0.350737i | |||||
1.24425e9 | + | 2.15510e9i | 0.0897867 | + | 0.155515i | |||||
3.17534e9 | 0.228125 | |||||||||
3.17942e9 | − | 5.50691e9i | 0.227410 | − | 0.393885i | |||||
1.54148e10 | − | 2.66992e10i | 1.09769 | − | 1.90126i | |||||
3.80977e9 | − | 6.59872e9i | 0.270102 | − | 0.467830i | |||||
4.44947e9 | + | 7.70670e9i | 0.314068 | + | 0.543981i | |||||
2.63629e9 | + | 4.56618e9i | 0.185267 | + | 0.320891i | |||||
−7.23480e9 | + | 1.25310e10i | −0.506201 | + | 0.876765i | 0.493774 | + | 0.869590i | ||
−0.999974 | + | 0.00717472i | ||||||||
−2.70236e9 | + | 4.68062e9i | −0.188249 | + | 0.326057i | |||||
4.29739e9 | − | 7.44331e9i | 0.298052 | − | 0.516241i | |||||
−1.17370e9 | −0.0810482 | |||||||||
1.20372e9 | + | 2.08490e9i | 0.0827582 | + | 0.143341i | |||||
2.91782e9 | − | 5.05381e9i | 0.199732 | − | 0.345946i | |||||
−2.42687e10 | −1.65402 | |||||||||
9.56573e9 | 0.649115 | |||||||||
−1.17967e9 | + | 2.04324e9i | −0.0797028 | + | 0.138049i | |||||
−9.55202e9 | −0.642573 | |||||||||
−7.06521e9 | − | 1.22373e10i | −0.473225 | − | 0.819649i | |||||
3.68375e9 | 0.245669 | |||||||||
−8.54214e9 | − | 1.47954e10i | −0.567214 | − | 0.982443i | −0.996840 | − | 0.0794360i | ||
0.429626 | − | 0.903007i | ||||||||
−3.93741e9 | − | 6.81980e9i | −0.260324 | − | 0.450894i | |||||
6.49416e9 | + | 1.12482e10i | 0.427514 | + | 0.740476i | 0.996652 | − | 0.0817667i | ||
−0.569138 | + | 0.822242i | ||||||||
9.90452e8 | − | 1.71551e9i | 0.0649213 | − | 0.112447i | |||||
2.25582e10 | 1.47227 | |||||||||
7.77781e8 | − | 1.39841e10i | 0.0505443 | − | 0.908760i | |||||
1.21565e10 | 0.786604 | |||||||||
−2.74929e9 | + | 4.76191e9i | −0.177135 | + | 0.306807i | |||||
2.22692e10 | + | 3.85714e10i | 1.42866 | + | 2.47450i | |||||
4.39790e9 | + | 7.61738e9i | 0.280937 | + | 0.486597i | |||||
2.38115e9 | + | 4.12427e9i | 0.151458 | + | 0.262333i | |||||
6.42965e9 | 0.407229 | |||||||||
−7.95300e9 | − | 1.37750e10i | −0.501568 | − | 0.868741i | −0.999998 | − | 0.00181136i | ||
0.498430 | − | 0.866930i | ||||||||
−1.31575e10 | −0.826271 | |||||||||
1.19682e10 | − | 2.07296e10i | 0.748395 | − | 1.29626i | −0.200197 | − | 0.979756i | ||
0.948592 | − | 0.316503i | ||||||||
−7.60976e9 | −0.473833 | |||||||||
1.34584e10 | 0.834460 | |||||||||
1.27179e8 | − | 2.20281e8i | 0.00785210 | − | 0.0136002i | |||||
−2.37341e9 | − | 4.11087e9i | −0.145916 | − | 0.252735i | 0.783798 | − | 0.621016i | ||
−0.929714 | + | 0.368281i | ||||||||
9.19019e9 | 0.562624 | |||||||||
−1.15292e10 | + | 1.99691e10i | −0.702840 | + | 1.21736i | 0.264625 | + | 0.964351i | ||
−0.967465 | + | 0.253004i | ||||||||
5.18566e9 | − | 8.98182e9i | 0.314797 | − | 0.545244i | |||||
1.65451e9 | − | 2.86569e9i | 0.100015 | − | 0.173231i | |||||
−1.63564e9 | − | 2.83302e9i | −0.0984593 | − | 0.170537i | |||||
8.04987e9 | + | 1.39428e10i | 0.482538 | + | 0.835780i | |||||
−1.04904e10 | + | 1.81700e10i | −0.626199 | + | 1.08461i | |||||
6.52937e8 | − | 1.13092e9i | 0.0388123 | − | 0.0672248i | |||||
−1.06396e10 | + | 1.84283e10i | −0.629801 | + | 1.09085i | |||||
7.98600e6 | 0.000470750 | |||||||||
4.02389e8 | + | 6.96958e8i | 0.0236207 | + | 0.0409122i | |||||
3.10277e9 | − | 5.37416e9i | 0.181377 | − | 0.314155i | −0.760972 | − | 0.648784i | ||
0.942350 | + | 0.334629i | ||||||||
1.21588e9 | 0.0707802 | |||||||||
1.41760e10 | 0.821805 | |||||||||
1.00328e9 | − | 1.73773e9i | 0.0579202 | − | 0.100321i | |||||
2.52133e10 | 1.44955 | |||||||||
6.25699e9 | + | 1.08374e10i | 0.358234 | + | 0.620480i | |||||
−1.91238e10 | −1.09038 | |||||||||
3.70152e9 | + | 6.41121e9i | 0.210176 | + | 0.364036i | |||||
1.11735e9 | + | 1.93531e9i | 0.0631827 | + | 0.109436i | |||||
−1.33995e9 | − | 2.32086e9i | −0.0754575 | − | 0.130696i | |||||
7.74935e9 | − | 1.34223e10i | 0.434598 | − | 0.752747i | |||||
−5.81717e9 | −0.324897 | |||||||||
1.80650e10 | − | 9.13186e9i | 1.00481 | − | 0.507932i | |||||
−1.15520e10 | −0.639907 | |||||||||
−9.63221e9 | + | 1.66835e10i | −0.531379 | + | 0.920375i | 0.467950 | + | 0.883755i | ||
−0.999329 | + | 0.0366204i | ||||||||
−1.72539e9 | − | 2.98847e9i | −0.0947950 | − | 0.164190i | |||||
−1.31534e10 | − | 2.27823e10i | −0.719708 | − | 1.24657i | |||||
6.41942e9 | + | 1.11188e10i | 0.349814 | + | 0.605896i | |||||
−5.42608e9 | −0.294479 | −0.147239 | − | 0.989101i | ||||||
−0.147239 | + | 0.989101i | ||||||||
1.87553e10 | + | 3.24852e10i | 1.01372 | + | 1.75582i | |||||
−4.57327e9 | −0.246179 | −0.123089 | − | 0.992396i | ||||||
−0.123089 | + | 0.992396i | ||||||||
5.00981e9 | − | 8.67725e9i | 0.268582 | − | 0.465198i | |||||
5.63924e9 | 0.301099 | |||||||||
−8.32225e9 | −0.442553 | |||||||||
2.71067e9 | − | 4.69503e9i | 0.143562 | − | 0.248657i | −0.785274 | − | 0.619149i | ||
0.928836 | + | 0.370492i | ||||||||
1.36749e6 | + | 2.36856e6i | 7.21315e−5 | + | 0.000124935i | |||||
−3.03527e9 | −0.159456 | |||||||||
−1.11573e10 | + | 1.93250e10i | −0.583776 | + | 1.01113i | |||||
−5.90115e7 | + | 1.02211e8i | −0.00307518 | + | 0.00532636i | |||||
−5.34584e8 | + | 9.25926e8i | −0.0277458 | + | 0.0480571i | |||||
4.29658e9 | + | 7.44189e9i | 0.222103 | + | 0.384693i | |||||
9.64459e9 | + | 1.67049e10i | 0.496554 | + | 0.860056i | |||||
−1.41030e10 | + | 2.44270e10i | −0.723180 | + | 1.25258i | |||||
−8.39155e7 | + | 1.45346e8i | −0.00428582 | + | 0.00742327i | |||||
2.22046e8 | − | 3.84594e8i | 0.0112952 | − | 0.0195638i | |||||
−3.07541e10 | −1.55816 | |||||||||
2.04598e9 | + | 3.54375e9i | 0.103246 | + | 0.178828i | |||||
−9.03782e9 | + | 1.56540e10i | −0.454254 | + | 0.786792i | |||||
2.34576e10 | 1.17431 | 0.587157 | − | 0.809473i | ||||||
0.587157 | + | 0.809473i | ||||||||
1.58279e10 | 0.789212 | |||||||||
1.66813e10 | − | 2.88929e10i | 0.828455 | − | 1.43493i | |||||
4.78710e9 | 0.236801 | |||||||||
−6.52963e9 | − | 1.13096e10i | −0.321716 | − | 0.557228i | 0.659126 | − | 0.752032i | ||
−0.980842 | + | 0.194804i | ||||||||
−1.38673e10 | −0.680539 | |||||||||
4.44035e9 | + | 7.69091e9i | 0.217048 | + | 0.375937i | 0.953904 | − | 0.300112i | ||
−0.736857 | + | 0.676049i | ||||||||
−8.10667e9 | − | 1.40412e10i | −0.394693 | − | 0.683628i | |||||
1.23842e9 | + | 2.14500e9i | 0.0600572 | + | 0.104022i | |||||
1.45406e8 | − | 2.51850e8i | 0.00702366 | − | 0.0121653i | |||||
−3.97795e9 | −0.191393 | −0.0956966 | − | 0.995411i | ||||||
−0.0956966 | + | 0.995411i | ||||||||
−8.73048e9 | − | 5.70946e9i | −0.418401 | − | 0.273621i | |||||
−2.27895e9 | −0.108788 | |||||||||
−9.06191e8 | + | 1.56957e9i | −0.0430878 | + | 0.0746303i | |||||
−1.35965e10 | − | 2.35498e10i | −0.643955 | − | 1.11536i | |||||
−4.57424e9 | − | 7.92281e9i | −0.215795 | − | 0.373768i | |||||
−1.23868e10 | − | 2.14545e10i | −0.582074 | − | 1.00818i | |||||
−1.00995e10 | −0.472738 | |||||||||
7.13682e9 | + | 1.23613e10i | 0.332755 | + | 0.576348i | |||||
−3.66159e8 | −0.0170056 | |||||||||
−2.71064e10 | + | 4.69496e10i | −1.25400 | + | 2.17199i | |||||
−2.29089e9 | −0.105569 | |||||||||
−1.69617e10 | −0.778595 | |||||||||
2.50528e9 | − | 4.33927e9i | 0.114553 | − | 0.198412i | |||||
−6.64113e9 | − | 1.15028e10i | −0.302486 | − | 0.523921i | |||||
2.22026e10 | 1.00735 | |||||||||
4.39394e9 | − | 7.61053e9i | 0.198585 | − | 0.343960i | |||||
4.65576e9 | − | 8.06402e9i | 0.209605 | − | 0.363046i | |||||
−1.05668e10 | + | 1.83022e10i | −0.473883 | + | 0.820790i | |||||
−2.36041e9 | − | 4.08834e9i | −0.105448 | − | 0.182641i | |||||
3.17776e9 | + | 5.50404e9i | 0.141415 | + | 0.244938i | 0.928030 | − | 0.372506i | ||
−0.786615 | + | 0.617444i | ||||||||
6.38855e9 | − | 1.10653e10i | 0.283205 | − | 0.490526i | |||||
−7.86299e9 | + | 1.36191e10i | −0.347228 | + | 0.601416i | |||||
−1.79259e9 | + | 3.10486e9i | −0.0788563 | + | 0.136583i | |||||
1.98980e10 | 0.871956 | 0.435978 | − | 0.899957i | ||||||
0.435978 | + | 0.899957i | ||||||||
7.92452e9 | + | 1.37257e10i | 0.345932 | + | 0.599172i | |||||
1.79069e10 | − | 3.10156e10i | 0.778704 | − | 1.34875i | |||||
−6.54987e9 | −0.283740 | |||||||||
3.36023e10 | 1.45009 | |||||||||
−7.39024e9 | + | 1.28003e10i | −0.317705 | + | 0.550282i | |||||
1.86401e9 | 0.0798279 | |||||||||
6.77761e6 | + | 1.17392e7i | 0.000289153 | + | 0.000500827i | |||||
3.28479e10 | 1.39606 | 0.698030 | − | 0.716069i | ||||||
0.698030 | + | 0.716069i | ||||||||
3.45931e9 | + | 5.99170e9i | 0.146464 | + | 0.253684i | |||||
6.29222e9 | + | 1.08984e10i | 0.265396 | + | 0.459680i | |||||
−2.81322e8 | − | 4.87264e8i | −0.0118208 | − | 0.0204742i | |||||
1.70313e10 | − | 2.94991e10i | 0.712921 | − | 1.23482i | |||||
4.19861e9 | 0.175087 | |||||||||
6.12868e8 | − | 1.10190e10i | 0.0254607 | − | 0.457770i | |||||
7.66456e9 | 0.317211 | |||||||||
1.62431e10 | − | 2.81339e10i | 0.669715 | − | 1.15998i | |||||
−2.90445e9 | − | 5.03065e9i | −0.119302 | − | 0.206636i | |||||
−7.58708e8 | − | 1.31412e9i | −0.0310470 | − | 0.0537750i | 0.850084 | − | 0.526646i | ||
−0.881131 | + | 0.472871i | ||||||||
−5.20555e9 | − | 9.01627e9i | −0.212215 | − | 0.367567i | |||||
4.64057e10 | 1.88472 | |||||||||
−7.27106e9 | − | 1.25938e10i | −0.294199 | − | 0.509568i | |||||
−3.99905e10 | −1.61202 | |||||||||
4.48993e9 | − | 7.77678e9i | 0.180312 | − | 0.312310i | |||||
2.37261e10 | 0.949260 | |||||||||
1.39652e10 | 0.556649 | |||||||||
−1.48859e10 | + | 2.57831e10i | −0.591133 | + | 1.02387i | 0.402947 | + | 0.915223i | ||
−0.994080 | + | 0.108650i | ||||||||
1.57856e9 | + | 2.73414e9i | 0.0624527 | + | 0.108171i | |||||
−3.14195e9 | −0.123842 | |||||||||
−2.78660e9 | + | 4.82653e9i | −0.109428 | + | 0.189534i | |||||
2.21399e9 | − | 3.83474e9i | 0.0866187 | − | 0.150028i | −0.819461 | − | 0.573135i | ||
0.906080 | + | 0.423107i | ||||||||
−2.02336e9 | + | 3.50457e9i | −0.0788671 | + | 0.136602i | |||||
1.60443e10 | + | 2.77895e10i | 0.623060 | + | 1.07917i | |||||
−3.72946e8 | − | 6.45962e8i | −0.0144293 | − | 0.0249922i | |||||
1.49870e6 | − | 2.59583e6i | 5.77703e−5 | − | 0.000100061i | |||||
1.72997e10 | − | 2.99639e10i | 0.664383 | − | 1.15075i | |||||
−1.18430e8 | + | 2.05127e8i | −0.00453146 | + | 0.00784871i | −0.868282 | − | 0.496071i | ||
0.863751 | + | 0.503919i | ||||||||
6.40030e9 | 0.243989 | |||||||||
−2.66493e10 | − | 4.61579e10i | −1.01217 | − | 1.75313i | |||||
−8.38368e9 | + | 1.45210e10i | −0.317250 | + | 0.549494i | |||||
−7.26977e10 | −2.74087 | |||||||||
−1.81478e9 | −0.0681701 | |||||||||
1.67505e9 | − | 2.90127e9i | 0.0626906 | − | 0.108583i | −0.832977 | − | 0.553308i | ||
0.895667 | + | 0.444725i | ||||||||
1.14405e10 | 0.426606 | |||||||||
−1.46008e10 | − | 2.52893e10i | −0.542457 | − | 0.939563i | |||||
−2.10260e8 | −0.00778311 | |||||||||
3.33043e10 | + | 5.76847e10i | 1.22831 | + | 2.12750i | |||||
−1.00320e10 | − | 1.73760e10i | −0.368646 | − | 0.638514i | |||||
−2.17128e9 | − | 3.76078e9i | −0.0794972 | − | 0.137693i | |||||
1.78275e9 | − | 3.08781e9i | 0.0650340 | − | 0.112642i | |||||
−1.83577e10 | −0.667248 | |||||||||
2.74512e10 | − | 1.38765e10i | 0.994142 | − | 0.502538i | |||||
−5.48093e10 | −1.97771 | |||||||||
1.05473e10 | − | 1.82684e10i | 0.379202 | − | 0.656798i | |||||
−1.07538e10 | − | 1.86261e10i | −0.385226 | − | 0.667230i | |||||
3.03405e9 | + | 5.25513e9i | 0.108294 | + | 0.187570i | |||||
−2.05488e10 | − | 3.55915e10i | −0.730790 | − | 1.26577i | −0.956546 | − | 0.291582i | ||
0.225755 | − | 0.974184i | ||||||||
6.55316e9 | 0.232213 | |||||||||
3.92760e10 | + | 6.80280e10i | 1.38674 | + | 2.40190i | |||||
3.34324e8 | 0.0117616 | |||||||||
−2.07609e10 | + | 3.59590e10i | −0.727745 | + | 1.26049i | 0.230089 | + | 0.973170i | ||
−0.957834 | + | 0.287322i | ||||||||
−2.02420e10 | −0.707005 | |||||||||
−6.92463e9 | −0.240991 | |||||||||
7.40069e9 | − | 1.28184e10i | 0.256635 | − | 0.444505i | |||||
1.47786e10 | + | 2.55973e10i | 0.510643 | + | 0.884460i | |||||
−1.01193e10 | −0.348397 | |||||||||
2.79759e10 | − | 4.84557e10i | 0.959739 | − | 1.66232i | 0.236609 | − | 0.971605i | ||
0.723130 | − | 0.690712i | ||||||||
1.56330e10 | − | 2.70771e10i | 0.534386 | − | 0.925584i | |||||
−3.12922e9 | + | 5.41997e9i | −0.106585 | + | 0.184611i | |||||
−5.21985e9 | − | 9.04105e9i | −0.177161 | − | 0.306851i | |||||
−3.58237e8 | − | 6.20484e8i | −0.0121151 | − | 0.0209840i | |||||
−5.79535e9 | + | 1.00378e10i | −0.195294 | + | 0.338259i | |||||
−2.41878e10 | + | 4.18945e10i | −0.812194 | + | 1.40676i | 0.0991319 | + | 0.995074i | ||
−0.911326 | + | 0.411686i | ||||||||
8.26839e9 | − | 1.43213e10i | 0.276655 | − | 0.479180i | |||||
2.82661e10 | 0.942409 | |||||||||
−1.43952e10 | − | 2.49332e10i | −0.478243 | − | 0.828341i | |||||
−2.44404e9 | + | 4.23320e9i | −0.0809092 | + | 0.140139i | |||||
−4.67331e10 | −1.54161 | |||||||||
5.00051e10 | 1.64372 | |||||||||
−1.02181e10 | + | 1.76983e10i | −0.334693 | + | 0.579706i | |||||
−3.30034e9 | −0.107721 | −0.0538606 | − | 0.998548i | ||||||
−0.0538606 | + | 0.998548i | ||||||||
1.56764e9 | + | 2.71523e9i | 0.0509865 | + | 0.0883113i | |||||
7.95006e9 | 0.257661 | |||||||||
−1.90633e9 | − | 3.30186e9i | −0.0615667 | − | 0.106637i | |||||
−8.47259e9 | − | 1.46749e10i | −0.272669 | − | 0.472276i | |||||
−1.33373e10 | − | 2.31009e10i | −0.427720 | − | 0.740833i | |||||
1.15607e10 | − | 2.00238e10i | 0.369447 | − | 0.639901i | −0.620032 | − | 0.784576i | ||
0.989479 | + | 0.144675i | ||||||||
2.98501e10 | 0.950581 | |||||||||
−2.29507e7 | + | 1.16015e7i | −0.000728310 | + | 0.000368160i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 74.8.c.a.47.2 | ✓ | 22 | |
37.26 | even | 3 | inner | 74.8.c.a.63.2 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.8.c.a.47.2 | ✓ | 22 | 1.1 | even | 1 | trivial | |
74.8.c.a.63.2 | yes | 22 | 37.26 | even | 3 | inner |