Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,4,Mod(4,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.e (of order \(7\), degree \(6\), 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: | \(2.53708213025\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{7})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{7}]$ |
Embedding invariants
Embedding label | 41.2 | ||
Character | \(\chi\) | \(=\) | 43.41 |
Dual form | 43.4.e.a.21.2 |
$q$-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 \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{7}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.96035 | + | 1.90720i | −1.40020 | + | 0.674299i | −0.973201 | − | 0.229955i | \(-0.926142\pi\) |
−0.426995 | + | 0.904254i | \(0.640428\pi\) | |||||||
\(3\) | −7.07654 | − | 3.40788i | −1.36188 | − | 0.655847i | −0.396825 | − | 0.917894i | \(-0.629888\pi\) |
−0.965055 | + | 0.262047i | \(0.915602\pi\) | |||||||
\(4\) | 7.05904 | − | 8.85175i | 0.882380 | − | 1.10647i | ||||
\(5\) | −1.30223 | + | 5.70543i | −0.116475 | + | 0.510309i | 0.882709 | + | 0.469920i | \(0.155717\pi\) |
−0.999184 | + | 0.0403897i | \(0.987140\pi\) | |||||||
\(6\) | 34.5251 | 2.34914 | ||||||||
\(7\) | 12.3980 | 0.669428 | 0.334714 | − | 0.942320i | \(-0.391360\pi\) | ||||
0.334714 | + | 0.942320i | \(0.391360\pi\) | |||||||
\(8\) | −3.24916 | + | 14.2355i | −0.143594 | + | 0.629126i | ||||
\(9\) | 21.6295 | + | 27.1225i | 0.801093 | + | 1.00454i | ||||
\(10\) | −5.72415 | − | 25.0791i | −0.181013 | − | 0.793072i | ||||
\(11\) | 31.7363 | + | 39.7961i | 0.869896 | + | 1.09081i | 0.995119 | + | 0.0986860i | \(0.0314640\pi\) |
−0.125223 | + | 0.992129i | \(0.539965\pi\) | |||||||
\(12\) | −80.1193 | + | 38.5834i | −1.92737 | + | 0.928172i | ||||
\(13\) | 16.1060 | − | 70.5649i | 0.343615 | − | 1.50548i | −0.447765 | − | 0.894152i | \(-0.647780\pi\) |
0.791380 | − | 0.611325i | \(-0.209363\pi\) | |||||||
\(14\) | −49.1003 | + | 23.6455i | −0.937330 | + | 0.451394i | ||||
\(15\) | 28.6587 | − | 35.9369i | 0.493309 | − | 0.618590i | ||||
\(16\) | 5.87254 | + | 25.7293i | 0.0917585 | + | 0.402020i | ||||
\(17\) | −16.0478 | − | 70.3098i | −0.228950 | − | 1.00310i | −0.950498 | − | 0.310731i | \(-0.899426\pi\) |
0.721548 | − | 0.692365i | \(-0.243431\pi\) | |||||||
\(18\) | −137.389 | − | 66.1629i | −1.79905 | − | 0.866375i | ||||
\(19\) | 29.7720 | − | 37.3328i | 0.359482 | − | 0.450776i | −0.568898 | − | 0.822408i | \(-0.692630\pi\) |
0.928380 | + | 0.371632i | \(0.121202\pi\) | |||||||
\(20\) | 41.3106 | + | 51.8018i | 0.461866 | + | 0.579162i | ||||
\(21\) | −87.7347 | − | 42.2508i | −0.911680 | − | 0.439042i | ||||
\(22\) | −201.586 | − | 97.0788i | −1.95356 | − | 0.940785i | ||||
\(23\) | 121.240 | + | 152.030i | 1.09914 | + | 1.37828i | 0.918822 | + | 0.394673i | \(0.129142\pi\) |
0.180321 | + | 0.983608i | \(0.442286\pi\) | |||||||
\(24\) | 71.5056 | − | 89.6652i | 0.608168 | − | 0.762618i | ||||
\(25\) | 81.7650 | + | 39.3759i | 0.654120 | + | 0.315007i | ||||
\(26\) | 70.7964 | + | 310.179i | 0.534012 | + | 2.33966i | ||||
\(27\) | −13.4421 | − | 58.8936i | −0.0958121 | − | 0.419780i | ||||
\(28\) | 87.5178 | − | 109.744i | 0.590690 | − | 0.740701i | ||||
\(29\) | −103.224 | + | 49.7102i | −0.660975 | + | 0.318309i | −0.734127 | − | 0.679012i | \(-0.762408\pi\) |
0.0731524 | + | 0.997321i | \(0.476694\pi\) | |||||||
\(30\) | −44.9595 | + | 196.981i | −0.273615 | + | 1.19879i | ||||
\(31\) | 97.5752 | − | 46.9897i | 0.565323 | − | 0.272245i | −0.129316 | − | 0.991603i | \(-0.541278\pi\) |
0.694639 | + | 0.719358i | \(0.255564\pi\) | |||||||
\(32\) | −145.160 | − | 182.025i | −0.801903 | − | 1.00555i | ||||
\(33\) | −88.9629 | − | 389.772i | −0.469286 | − | 2.05608i | ||||
\(34\) | 197.650 | + | 247.845i | 0.996961 | + | 1.25015i | ||||
\(35\) | −16.1450 | + | 70.7358i | −0.0779714 | + | 0.341615i | ||||
\(36\) | 392.765 | 1.81836 | ||||||||
\(37\) | 19.4210 | 0.0862918 | 0.0431459 | − | 0.999069i | \(-0.486262\pi\) | ||||
0.0431459 | + | 0.999069i | \(0.486262\pi\) | |||||||
\(38\) | −46.7060 | + | 204.632i | −0.199387 | + | 0.873573i | ||||
\(39\) | −354.452 | + | 444.468i | −1.45532 | + | 1.82492i | ||||
\(40\) | −76.9884 | − | 37.0757i | −0.304324 | − | 0.146554i | ||||
\(41\) | 437.142 | − | 210.516i | 1.66512 | − | 0.801881i | 0.666725 | − | 0.745304i | \(-0.267695\pi\) |
0.998398 | − | 0.0565775i | \(-0.0180188\pi\) | |||||||
\(42\) | 428.041 | 1.57258 | ||||||||
\(43\) | 166.643 | − | 227.458i | 0.590996 | − | 0.806674i | ||||
\(44\) | 576.293 | 1.97453 | ||||||||
\(45\) | −182.912 | + | 88.0859i | −0.605932 | + | 0.291802i | ||||
\(46\) | −770.105 | − | 370.863i | −2.46839 | − | 1.18871i | ||||
\(47\) | −12.6269 | + | 15.8337i | −0.0391878 | + | 0.0491399i | −0.801039 | − | 0.598612i | \(-0.795719\pi\) |
0.761851 | + | 0.647752i | \(0.224291\pi\) | |||||||
\(48\) | 46.1251 | − | 202.087i | 0.138700 | − | 0.607683i | ||||
\(49\) | −189.290 | −0.551866 | ||||||||
\(50\) | −398.916 | −1.12830 | ||||||||
\(51\) | −126.045 | + | 552.239i | −0.346075 | + | 1.51625i | ||||
\(52\) | −510.931 | − | 640.687i | −1.36256 | − | 1.70860i | ||||
\(53\) | −61.4230 | − | 269.112i | −0.159191 | − | 0.697459i | −0.990019 | − | 0.140931i | \(-0.954990\pi\) |
0.830829 | − | 0.556528i | \(-0.187867\pi\) | |||||||
\(54\) | 165.557 | + | 207.602i | 0.417213 | + | 0.523169i | ||||
\(55\) | −268.381 | + | 129.246i | −0.657974 | + | 0.316863i | ||||
\(56\) | −40.2830 | + | 176.491i | −0.0961257 | + | 0.421154i | ||||
\(57\) | −337.908 | + | 162.728i | −0.785211 | + | 0.378138i | ||||
\(58\) | 313.997 | − | 393.740i | 0.710859 | − | 0.891389i | ||||
\(59\) | 14.5495 | + | 63.7456i | 0.0321048 | + | 0.140661i | 0.988440 | − | 0.151611i | \(-0.0484461\pi\) |
−0.956335 | + | 0.292271i | \(0.905589\pi\) | |||||||
\(60\) | −115.801 | − | 507.359i | −0.249165 | − | 1.09166i | ||||
\(61\) | 297.422 | + | 143.231i | 0.624278 | + | 0.300636i | 0.719152 | − | 0.694853i | \(-0.244531\pi\) |
−0.0948741 | + | 0.995489i | \(0.530245\pi\) | |||||||
\(62\) | −296.813 | + | 372.192i | −0.607988 | + | 0.762393i | ||||
\(63\) | 268.162 | + | 336.265i | 0.536274 | + | 0.672466i | ||||
\(64\) | 731.823 | + | 352.427i | 1.42934 | + | 0.688335i | ||||
\(65\) | 381.630 | + | 183.783i | 0.728236 | + | 0.350700i | ||||
\(66\) | 1095.70 | + | 1373.96i | 2.04350 | + | 2.56247i | ||||
\(67\) | −325.889 | + | 408.652i | −0.594234 | + | 0.745146i | −0.984467 | − | 0.175571i | \(-0.943823\pi\) |
0.390233 | + | 0.920716i | \(0.372394\pi\) | |||||||
\(68\) | −735.647 | − | 354.269i | −1.31192 | − | 0.631785i | ||||
\(69\) | −339.859 | − | 1489.02i | −0.592959 | − | 2.59792i | ||||
\(70\) | −70.9678 | − | 310.930i | −0.121175 | − | 0.530904i | ||||
\(71\) | 97.1201 | − | 121.785i | 0.162339 | − | 0.203566i | −0.694009 | − | 0.719967i | \(-0.744157\pi\) |
0.856347 | + | 0.516401i | \(0.172728\pi\) | |||||||
\(72\) | −456.380 | + | 219.781i | −0.747013 | + | 0.359742i | ||||
\(73\) | −120.878 | + | 529.603i | −0.193805 | + | 0.849114i | 0.780728 | + | 0.624871i | \(0.214848\pi\) |
−0.974533 | + | 0.224244i | \(0.928009\pi\) | |||||||
\(74\) | −76.9141 | + | 37.0399i | −0.120825 | + | 0.0581865i | ||||
\(75\) | −444.424 | − | 557.291i | −0.684236 | − | 0.858005i | ||||
\(76\) | −120.300 | − | 527.068i | −0.181570 | − | 0.795511i | ||||
\(77\) | 393.466 | + | 493.390i | 0.582332 | + | 0.730222i | ||||
\(78\) | 556.061 | − | 2436.26i | 0.807199 | − | 3.53657i | ||||
\(79\) | 1153.53 | 1.64281 | 0.821407 | − | 0.570342i | \(-0.193189\pi\) | ||||
0.821407 | + | 0.570342i | \(0.193189\pi\) | |||||||
\(80\) | −154.444 | −0.215842 | ||||||||
\(81\) | 102.847 | − | 450.602i | 0.141080 | − | 0.618110i | ||||
\(82\) | −1329.74 | + | 1667.44i | −1.79079 | + | 2.24558i | ||||
\(83\) | −703.783 | − | 338.924i | −0.930726 | − | 0.448214i | −0.0938377 | − | 0.995588i | \(-0.529913\pi\) |
−0.836888 | + | 0.547373i | \(0.815628\pi\) | |||||||
\(84\) | −993.317 | + | 478.356i | −1.29023 | + | 0.621344i | ||||
\(85\) | 422.046 | 0.538556 | ||||||||
\(86\) | −226.157 | + | 1218.64i | −0.283571 | + | 1.52801i | ||||
\(87\) | 899.877 | 1.10893 | ||||||||
\(88\) | −669.632 | + | 322.478i | −0.811171 | + | 0.390639i | ||||
\(89\) | −464.404 | − | 223.645i | −0.553109 | − | 0.266363i | 0.136384 | − | 0.990656i | \(-0.456452\pi\) |
−0.689492 | + | 0.724293i | \(0.742166\pi\) | |||||||
\(90\) | 556.399 | − | 697.702i | 0.651662 | − | 0.817159i | ||||
\(91\) | 199.682 | − | 874.862i | 0.230026 | − | 1.00781i | ||||
\(92\) | 2201.57 | 2.49489 | ||||||||
\(93\) | −850.630 | −0.948454 | ||||||||
\(94\) | 19.8090 | − | 86.7890i | 0.0217356 | − | 0.0952298i | ||||
\(95\) | 174.230 | + | 218.478i | 0.188165 | + | 0.235951i | ||||
\(96\) | 406.911 | + | 1782.79i | 0.432606 | + | 1.89537i | ||||
\(97\) | 562.243 | + | 705.030i | 0.588527 | + | 0.737989i | 0.983541 | − | 0.180686i | \(-0.0578317\pi\) |
−0.395014 | + | 0.918675i | \(0.629260\pi\) | |||||||
\(98\) | 749.656 | − | 361.015i | 0.772721 | − | 0.372123i | ||||
\(99\) | −392.930 | + | 1721.54i | −0.398898 | + | 1.74769i | ||||
\(100\) | 925.728 | − | 445.807i | 0.925728 | − | 0.445807i | ||||
\(101\) | −124.424 | + | 156.023i | −0.122581 | + | 0.153712i | −0.839335 | − | 0.543614i | \(-0.817056\pi\) |
0.716754 | + | 0.697326i | \(0.245627\pi\) | |||||||
\(102\) | −554.050 | − | 2427.45i | −0.537835 | − | 2.35641i | ||||
\(103\) | 196.102 | + | 859.178i | 0.187597 | + | 0.821915i | 0.977879 | + | 0.209172i | \(0.0670769\pi\) |
−0.790282 | + | 0.612743i | \(0.790066\pi\) | |||||||
\(104\) | 952.196 | + | 458.553i | 0.897793 | + | 0.432354i | ||||
\(105\) | 355.310 | − | 445.544i | 0.330235 | − | 0.414102i | ||||
\(106\) | 756.508 | + | 948.631i | 0.693194 | + | 0.869238i | ||||
\(107\) | −1347.20 | − | 648.779i | −1.21719 | − | 0.586167i | −0.288660 | − | 0.957432i | \(-0.593210\pi\) |
−0.928527 | + | 0.371265i | \(0.878924\pi\) | |||||||
\(108\) | −616.199 | − | 296.746i | −0.549017 | − | 0.264393i | ||||
\(109\) | −474.432 | − | 594.919i | −0.416903 | − | 0.522779i | 0.528391 | − | 0.849001i | \(-0.322796\pi\) |
−0.945293 | + | 0.326222i | \(0.894224\pi\) | |||||||
\(110\) | 816.387 | − | 1023.72i | 0.707631 | − | 0.887342i | ||||
\(111\) | −137.434 | − | 66.1845i | −0.117519 | − | 0.0565942i | ||||
\(112\) | 72.8077 | + | 318.991i | 0.0614257 | + | 0.269124i | ||||
\(113\) | 301.030 | + | 1318.90i | 0.250606 | + | 1.09798i | 0.930968 | + | 0.365101i | \(0.118966\pi\) |
−0.680361 | + | 0.732877i | \(0.738177\pi\) | |||||||
\(114\) | 1027.88 | − | 1288.92i | 0.844472 | − | 1.05893i | ||||
\(115\) | −1025.28 | + | 493.748i | −0.831372 | + | 0.400368i | ||||
\(116\) | −288.642 | + | 1264.62i | −0.231032 | + | 1.01222i | ||||
\(117\) | 2262.26 | − | 1089.45i | 1.78758 | − | 0.860851i | ||||
\(118\) | −179.197 | − | 224.706i | −0.139800 | − | 0.175304i | ||||
\(119\) | −198.960 | − | 871.699i | −0.153266 | − | 0.671500i | ||||
\(120\) | 418.462 | + | 524.735i | 0.318335 | + | 0.399179i | ||||
\(121\) | −280.358 | + | 1228.33i | −0.210637 | + | 0.922862i | ||||
\(122\) | −1451.06 | −1.07683 | ||||||||
\(123\) | −3810.86 | −2.79361 | ||||||||
\(124\) | 272.845 | − | 1195.41i | 0.197599 | − | 0.865736i | ||||
\(125\) | −787.228 | + | 987.153i | −0.563295 | + | 0.706349i | ||||
\(126\) | −1703.34 | − | 820.286i | −1.20433 | − | 0.579975i | ||||
\(127\) | −206.556 | + | 99.4721i | −0.144322 | + | 0.0695017i | −0.504651 | − | 0.863324i | \(-0.668379\pi\) |
0.360329 | + | 0.932825i | \(0.382664\pi\) | |||||||
\(128\) | −1707.88 | −1.17935 | ||||||||
\(129\) | −1954.41 | + | 1041.71i | −1.33392 | + | 0.710991i | ||||
\(130\) | −1861.90 | −1.25615 | ||||||||
\(131\) | 1504.82 | − | 724.683i | 1.00364 | − | 0.483327i | 0.141468 | − | 0.989943i | \(-0.454818\pi\) |
0.862172 | + | 0.506615i | \(0.169104\pi\) | |||||||
\(132\) | −4078.16 | − | 1963.94i | −2.68907 | − | 1.29499i | ||||
\(133\) | 369.112 | − | 462.852i | 0.240647 | − | 0.301762i | ||||
\(134\) | 511.252 | − | 2239.94i | 0.329593 | − | 1.44404i | ||||
\(135\) | 353.518 | 0.225377 | ||||||||
\(136\) | 1053.04 | 0.663949 | ||||||||
\(137\) | 471.864 | − | 2067.37i | 0.294263 | − | 1.28925i | −0.584266 | − | 0.811562i | \(-0.698618\pi\) |
0.878529 | − | 0.477689i | \(-0.158525\pi\) | |||||||
\(138\) | 4185.82 | + | 5248.85i | 2.58203 | + | 3.23777i | ||||
\(139\) | 121.657 | + | 533.013i | 0.0742359 | + | 0.325249i | 0.998387 | − | 0.0567791i | \(-0.0180831\pi\) |
−0.924151 | + | 0.382028i | \(0.875226\pi\) | |||||||
\(140\) | 512.168 | + | 642.238i | 0.309186 | + | 0.387707i | ||||
\(141\) | 143.314 | − | 69.0164i | 0.0855974 | − | 0.0412215i | ||||
\(142\) | −152.361 | + | 667.539i | −0.0900414 | + | 0.394497i | ||||
\(143\) | 3319.35 | − | 1598.51i | 1.94111 | − | 0.934787i | ||||
\(144\) | −570.824 | + | 715.790i | −0.330338 | + | 0.414230i | ||||
\(145\) | −149.197 | − | 653.673i | −0.0854490 | − | 0.374376i | ||||
\(146\) | −531.340 | − | 2327.95i | −0.301192 | − | 1.31961i | ||||
\(147\) | 1339.52 | + | 645.078i | 0.751576 | + | 0.361940i | ||||
\(148\) | 137.094 | − | 171.910i | 0.0761421 | − | 0.0954792i | ||||
\(149\) | −1996.45 | − | 2503.47i | −1.09769 | − | 1.37646i | −0.919789 | − | 0.392412i | \(-0.871641\pi\) |
−0.177901 | − | 0.984048i | \(-0.556931\pi\) | |||||||
\(150\) | 2822.94 | + | 1359.46i | 1.53662 | + | 0.739995i | ||||
\(151\) | 1099.11 | + | 529.301i | 0.592344 | + | 0.285258i | 0.705943 | − | 0.708269i | \(-0.250524\pi\) |
−0.113599 | + | 0.993527i | \(0.536238\pi\) | |||||||
\(152\) | 434.718 | + | 545.119i | 0.231975 | + | 0.290888i | ||||
\(153\) | 1559.88 | − | 1956.02i | 0.824238 | − | 1.03356i | ||||
\(154\) | −2499.26 | − | 1203.58i | −1.30777 | − | 0.629787i | ||||
\(155\) | 141.032 | + | 617.900i | 0.0730834 | + | 0.320199i | ||||
\(156\) | 1432.24 | + | 6275.04i | 0.735068 | + | 3.22054i | ||||
\(157\) | 1206.26 | − | 1512.60i | 0.613185 | − | 0.768909i | −0.374183 | − | 0.927355i | \(-0.622077\pi\) |
0.987368 | + | 0.158445i | \(0.0506482\pi\) | |||||||
\(158\) | −4568.39 | + | 2200.02i | −2.30026 | + | 1.10775i | ||||
\(159\) | −482.439 | + | 2113.70i | −0.240628 | + | 1.05426i | ||||
\(160\) | 1227.56 | − | 591.162i | 0.606545 | − | 0.292097i | ||||
\(161\) | 1503.13 | + | 1884.87i | 0.735796 | + | 0.922660i | ||||
\(162\) | 452.081 | + | 1980.69i | 0.219252 | + | 0.960605i | ||||
\(163\) | 680.551 | + | 853.383i | 0.327024 | + | 0.410075i | 0.917979 | − | 0.396630i | \(-0.129820\pi\) |
−0.590955 | + | 0.806704i | \(0.701249\pi\) | |||||||
\(164\) | 1222.36 | − | 5355.51i | 0.582014 | − | 2.54997i | ||||
\(165\) | 2339.67 | 1.10390 | ||||||||
\(166\) | 3433.63 | 1.60543 | ||||||||
\(167\) | −508.794 | + | 2229.17i | −0.235758 | + | 1.03293i | 0.709013 | + | 0.705195i | \(0.249141\pi\) |
−0.944771 | + | 0.327730i | \(0.893716\pi\) | |||||||
\(168\) | 886.525 | − | 1111.67i | 0.407124 | − | 0.510518i | ||||
\(169\) | −2740.58 | − | 1319.79i | −1.24742 | − | 0.600725i | ||||
\(170\) | −1671.45 | + | 804.927i | −0.754084 | + | 0.363148i | ||||
\(171\) | 1656.51 | 0.740800 | ||||||||
\(172\) | −837.061 | − | 3080.72i | −0.371077 | − | 1.36571i | ||||
\(173\) | −1171.22 | −0.514720 | −0.257360 | − | 0.966316i | \(-0.582853\pi\) | ||||
−0.257360 | + | 0.966316i | \(0.582853\pi\) | |||||||
\(174\) | −3563.83 | + | 1716.25i | −1.55272 | + | 0.747750i | ||||
\(175\) | 1013.72 | + | 488.182i | 0.437886 | + | 0.210875i | ||||
\(176\) | −837.552 | + | 1050.26i | −0.358709 | + | 0.449807i | ||||
\(177\) | 114.277 | − | 500.681i | 0.0485288 | − | 0.212619i | ||||
\(178\) | 2265.74 | 0.954069 | ||||||||
\(179\) | 931.735 | 0.389057 | 0.194528 | − | 0.980897i | \(-0.437682\pi\) | ||||
0.194528 | + | 0.980897i | \(0.437682\pi\) | |||||||
\(180\) | −511.470 | + | 2240.90i | −0.211793 | + | 0.927925i | ||||
\(181\) | −190.595 | − | 238.999i | −0.0782699 | − | 0.0981473i | 0.741155 | − | 0.671334i | \(-0.234278\pi\) |
−0.819425 | + | 0.573187i | \(0.805707\pi\) | |||||||
\(182\) | 877.732 | + | 3845.60i | 0.357483 | + | 1.56623i | ||||
\(183\) | −1616.60 | − | 2027.16i | −0.653020 | − | 0.818861i | ||||
\(184\) | −2558.15 | + | 1231.94i | −1.02494 | + | 0.493586i | ||||
\(185\) | −25.2906 | + | 110.805i | −0.0100508 | + | 0.0440355i | ||||
\(186\) | 3368.79 | − | 1622.32i | 1.32802 | − | 0.639541i | ||||
\(187\) | 2288.76 | − | 2870.01i | 0.895029 | − | 1.12233i | ||||
\(188\) | 51.0217 | + | 223.541i | 0.0197933 | + | 0.0867202i | ||||
\(189\) | −166.654 | − | 730.161i | −0.0641393 | − | 0.281013i | ||||
\(190\) | −1106.69 | − | 532.956i | −0.422569 | − | 0.203498i | ||||
\(191\) | 188.915 | − | 236.892i | 0.0715676 | − | 0.0897429i | −0.744759 | − | 0.667334i | \(-0.767436\pi\) |
0.816327 | + | 0.577591i | \(0.196007\pi\) | |||||||
\(192\) | −3977.74 | − | 4987.93i | −1.49515 | − | 1.87486i | ||||
\(193\) | −3237.68 | − | 1559.19i | −1.20753 | − | 0.581517i | −0.281718 | − | 0.959497i | \(-0.590904\pi\) |
−0.925814 | + | 0.377981i | \(0.876619\pi\) | |||||||
\(194\) | −3571.32 | − | 1719.85i | −1.32168 | − | 0.636487i | ||||
\(195\) | −2074.31 | − | 2601.10i | −0.761765 | − | 0.955223i | ||||
\(196\) | −1336.21 | + | 1675.55i | −0.486956 | + | 0.610623i | ||||
\(197\) | 2032.42 | + | 978.761i | 0.735045 | + | 0.353979i | 0.763666 | − | 0.645611i | \(-0.223397\pi\) |
−0.0286213 | + | 0.999590i | \(0.509112\pi\) | |||||||
\(198\) | −1727.19 | − | 7567.29i | −0.619928 | − | 2.71608i | ||||
\(199\) | 118.656 | + | 519.865i | 0.0422678 | + | 0.185187i | 0.991655 | − | 0.128921i | \(-0.0411515\pi\) |
−0.949387 | + | 0.314109i | \(0.898294\pi\) | |||||||
\(200\) | −826.203 | + | 1036.03i | −0.292107 | + | 0.366290i | ||||
\(201\) | 3698.80 | − | 1781.25i | 1.29798 | − | 0.625073i | ||||
\(202\) | 195.196 | − | 855.210i | 0.0679898 | − | 0.297883i | ||||
\(203\) | −1279.77 | + | 616.306i | −0.442475 | + | 0.213085i | ||||
\(204\) | 3998.53 | + | 5013.99i | 1.37232 | + | 1.72083i | ||||
\(205\) | 631.828 | + | 2768.22i | 0.215263 | + | 0.943127i | ||||
\(206\) | −2415.26 | − | 3028.64i | −0.816889 | − | 1.02435i | ||||
\(207\) | −1501.08 | + | 6576.67i | −0.504021 | + | 2.20826i | ||||
\(208\) | 1910.17 | 0.636762 | ||||||||
\(209\) | 2430.55 | 0.804425 | ||||||||
\(210\) | −557.407 | + | 2442.16i | −0.183165 | + | 0.802500i | ||||
\(211\) | −3079.15 | + | 3861.13i | −1.00463 | + | 1.25977i | −0.0391663 | + | 0.999233i | \(0.512470\pi\) |
−0.965465 | + | 0.260535i | \(0.916101\pi\) | |||||||
\(212\) | −2815.70 | − | 1355.97i | −0.912184 | − | 0.439285i | ||||
\(213\) | −1102.30 | + | 530.841i | −0.354594 | + | 0.170763i | ||||
\(214\) | 6572.75 | 2.09955 | ||||||||
\(215\) | 1080.74 | + | 1246.97i | 0.342817 | + | 0.395548i | ||||
\(216\) | 882.054 | 0.277853 | ||||||||
\(217\) | 1209.73 | − | 582.577i | 0.378443 | − | 0.182249i | ||||
\(218\) | 3013.55 | + | 1451.25i | 0.936255 | + | 0.450876i | ||||
\(219\) | 2660.23 | − | 3335.82i | 0.820828 | − | 1.02929i | ||||
\(220\) | −750.464 | + | 3288.00i | −0.229983 | + | 1.00762i | ||||
\(221\) | −5219.87 | −1.58881 | ||||||||
\(222\) | 670.513 | 0.202711 | ||||||||
\(223\) | 313.266 | − | 1372.51i | 0.0940711 | − | 0.412153i | −0.905864 | − | 0.423569i | \(-0.860777\pi\) |
0.999935 | + | 0.0114168i | \(0.00363415\pi\) | |||||||
\(224\) | −1799.69 | − | 2256.74i | −0.536816 | − | 0.673146i | ||||
\(225\) | 700.560 | + | 3069.36i | 0.207573 | + | 0.909439i | ||||
\(226\) | −3707.59 | − | 4649.18i | −1.09126 | − | 1.36840i | ||||
\(227\) | 267.702 | − | 128.918i | 0.0782731 | − | 0.0376944i | −0.394338 | − | 0.918966i | \(-0.629026\pi\) |
0.472611 | + | 0.881271i | \(0.343312\pi\) | |||||||
\(228\) | −944.879 | + | 4139.78i | −0.274457 | + | 1.20247i | ||||
\(229\) | −3500.27 | + | 1685.64i | −1.01006 | + | 0.486420i | −0.864341 | − | 0.502906i | \(-0.832264\pi\) |
−0.145720 | + | 0.989326i | \(0.546550\pi\) | |||||||
\(230\) | 3118.79 | − | 3910.83i | 0.894116 | − | 1.12119i | ||||
\(231\) | −1102.96 | − | 4832.38i | −0.314153 | − | 1.37640i | ||||
\(232\) | −372.257 | − | 1630.96i | −0.105344 | − | 0.461543i | ||||
\(233\) | 4990.02 | + | 2403.07i | 1.40303 | + | 0.675666i | 0.973775 | − | 0.227515i | \(-0.0730601\pi\) |
0.429260 | + | 0.903181i | \(0.358774\pi\) | |||||||
\(234\) | −6881.56 | + | 8629.20i | −1.92249 | + | 2.41072i | ||||
\(235\) | −73.8947 | − | 92.6611i | −0.0205122 | − | 0.0257215i | ||||
\(236\) | 666.966 | + | 321.194i | 0.183965 | + | 0.0885930i | ||||
\(237\) | −8163.00 | − | 3931.10i | −2.23732 | − | 1.07743i | ||||
\(238\) | 2450.46 | + | 3072.78i | 0.667394 | + | 0.836885i | ||||
\(239\) | −1695.76 | + | 2126.42i | −0.458953 | + | 0.575509i | −0.956428 | − | 0.291970i | \(-0.905689\pi\) |
0.497475 | + | 0.867479i | \(0.334261\pi\) | |||||||
\(240\) | 1092.93 | + | 526.327i | 0.293951 | + | 0.141559i | ||||
\(241\) | −328.745 | − | 1440.33i | −0.0878685 | − | 0.384977i | 0.911802 | − | 0.410629i | \(-0.134691\pi\) |
−0.999671 | + | 0.0256521i | \(0.991834\pi\) | |||||||
\(242\) | −1232.36 | − | 5399.32i | −0.327351 | − | 1.43422i | ||||
\(243\) | −3280.32 | + | 4113.40i | −0.865979 | + | 1.08590i | ||||
\(244\) | 3367.35 | − | 1621.63i | 0.883495 | − | 0.425469i | ||||
\(245\) | 246.499 | − | 1079.98i | 0.0642785 | − | 0.281623i | ||||
\(246\) | 15092.4 | − | 7268.10i | 3.91160 | − | 1.88373i | ||||
\(247\) | −2154.88 | − | 2702.14i | −0.555109 | − | 0.696085i | ||||
\(248\) | 351.885 | + | 1541.71i | 0.0900996 | + | 0.394752i | ||||
\(249\) | 3825.34 | + | 4796.82i | 0.973578 | + | 1.22083i | ||||
\(250\) | 1235.00 | − | 5410.88i | 0.312432 | − | 1.36886i | ||||
\(251\) | −3405.07 | −0.856280 | −0.428140 | − | 0.903712i | \(-0.640831\pi\) | ||||
−0.428140 | + | 0.903712i | \(0.640831\pi\) | |||||||
\(252\) | 4869.50 | 1.21726 | ||||||||
\(253\) | −2202.49 | + | 9649.74i | −0.547310 | + | 2.39792i | ||||
\(254\) | 628.320 | − | 787.889i | 0.155214 | − | 0.194632i | ||||
\(255\) | −2986.62 | − | 1438.28i | −0.733449 | − | 0.353210i | ||||
\(256\) | 909.227 | − | 437.861i | 0.221979 | − | 0.106900i | ||||
\(257\) | 2338.70 | 0.567642 | 0.283821 | − | 0.958877i | \(-0.408398\pi\) | ||||
0.283821 | + | 0.958877i | \(0.408398\pi\) | |||||||
\(258\) | 5753.37 | − | 7853.01i | 1.38833 | − | 1.89499i | ||||
\(259\) | 240.781 | 0.0577661 | ||||||||
\(260\) | 4320.74 | − | 2080.76i | 1.03062 | − | 0.496320i | ||||
\(261\) | −3580.96 | − | 1724.50i | −0.849255 | − | 0.408980i | ||||
\(262\) | −4577.50 | + | 5740.00i | −1.07939 | + | 1.35351i | ||||
\(263\) | 590.191 | − | 2585.80i | 0.138375 | − | 0.606262i | −0.857417 | − | 0.514623i | \(-0.827932\pi\) |
0.995792 | − | 0.0916398i | \(-0.0292108\pi\) | |||||||
\(264\) | 5837.65 | 1.36092 | ||||||||
\(265\) | 1615.38 | 0.374462 | ||||||||
\(266\) | −579.060 | + | 2537.03i | −0.133475 | + | 0.584794i | ||||
\(267\) | 2524.21 | + | 3165.26i | 0.578574 | + | 0.725509i | ||||
\(268\) | 1316.82 | + | 5769.38i | 0.300141 | + | 1.31500i | ||||
\(269\) | −2339.24 | − | 2933.31i | −0.530207 | − | 0.664859i | 0.442534 | − | 0.896752i | \(-0.354080\pi\) |
−0.972741 | + | 0.231893i | \(0.925508\pi\) | |||||||
\(270\) | −1400.05 | + | 674.231i | −0.315573 | + | 0.151972i | ||||
\(271\) | 1520.74 | − | 6662.82i | 0.340881 | − | 1.49350i | −0.456339 | − | 0.889806i | \(-0.650839\pi\) |
0.797219 | − | 0.603690i | \(-0.206303\pi\) | |||||||
\(272\) | 1714.78 | − | 825.795i | 0.382257 | − | 0.184085i | ||||
\(273\) | −4394.48 | + | 5510.51i | −0.974235 | + | 1.22165i | ||||
\(274\) | 2074.15 | + | 9087.45i | 0.457314 | + | 2.00362i | ||||
\(275\) | 1027.91 | + | 4503.57i | 0.225401 | + | 0.987547i | ||||
\(276\) | −15579.5 | − | 7502.69i | −3.39774 | − | 1.63626i | ||||
\(277\) | 2075.41 | − | 2602.48i | 0.450178 | − | 0.564505i | −0.504016 | − | 0.863694i | \(-0.668145\pi\) |
0.954194 | + | 0.299189i | \(0.0967161\pi\) | |||||||
\(278\) | −1498.37 | − | 1878.89i | −0.323259 | − | 0.405355i | ||||
\(279\) | 3384.98 | + | 1630.12i | 0.726357 | + | 0.349795i | ||||
\(280\) | −954.501 | − | 459.663i | −0.203723 | − | 0.0981076i | ||||
\(281\) | −170.221 | − | 213.451i | −0.0361372 | − | 0.0453147i | 0.763434 | − | 0.645885i | \(-0.223512\pi\) |
−0.799572 | + | 0.600571i | \(0.794940\pi\) | |||||||
\(282\) | −435.946 | + | 546.659i | −0.0920574 | + | 0.115436i | ||||
\(283\) | −4269.23 | − | 2055.95i | −0.896747 | − | 0.431850i | −0.0720338 | − | 0.997402i | \(-0.522949\pi\) |
−0.824713 | + | 0.565552i | \(0.808663\pi\) | |||||||
\(284\) | −392.434 | − | 1719.37i | −0.0819954 | − | 0.359245i | ||||
\(285\) | −488.400 | − | 2139.82i | −0.101510 | − | 0.444744i | ||||
\(286\) | −10097.1 | + | 12661.4i | −2.08760 | + | 2.61777i | ||||
\(287\) | 5419.67 | − | 2609.98i | 1.11468 | − | 0.536802i | ||||
\(288\) | 1797.24 | − | 7874.21i | 0.367719 | − | 1.61108i | ||||
\(289\) | −259.478 | + | 124.958i | −0.0528147 | + | 0.0254342i | ||||
\(290\) | 1837.56 | + | 2304.23i | 0.372087 | + | 0.466582i | ||||
\(291\) | −1576.07 | − | 6905.23i | −0.317495 | − | 1.39104i | ||||
\(292\) | 3834.63 | + | 4808.47i | 0.768510 | + | 0.963681i | ||||
\(293\) | −1476.68 | + | 6469.75i | −0.294431 | + | 1.28999i | 0.583857 | + | 0.811857i | \(0.301543\pi\) |
−0.878288 | + | 0.478132i | \(0.841314\pi\) | |||||||
\(294\) | −6535.26 | −1.29641 | ||||||||
\(295\) | −382.643 | −0.0755198 | ||||||||
\(296\) | −63.1020 | + | 276.468i | −0.0123910 | + | 0.0542884i | ||||
\(297\) | 1917.13 | − | 2404.00i | 0.374556 | − | 0.469678i | ||||
\(298\) | 12681.3 | + | 6106.99i | 2.46513 | + | 1.18714i | ||||
\(299\) | 12680.7 | − | 6106.70i | 2.45265 | − | 1.18113i | ||||
\(300\) | −8070.21 | −1.55311 | ||||||||
\(301\) | 2066.04 | − | 2820.02i | 0.395629 | − | 0.540010i | ||||
\(302\) | −5362.33 | −1.02175 | ||||||||
\(303\) | 1412.20 | − | 680.081i | 0.267752 | − | 0.128943i | ||||
\(304\) | 1135.39 | + | 546.773i | 0.214207 | + | 0.103156i | ||||
\(305\) | −1204.50 | + | 1510.40i | −0.226130 | + | 0.283558i | ||||
\(306\) | −2447.12 | + | 10721.5i | −0.457165 | + | 2.00297i | ||||
\(307\) | 6964.04 | 1.29465 | 0.647327 | − | 0.762212i | \(-0.275887\pi\) | ||||
0.647327 | + | 0.762212i | \(0.275887\pi\) | |||||||
\(308\) | 7144.86 | 1.32181 | ||||||||
\(309\) | 1540.25 | − | 6748.29i | 0.283566 | − | 1.24238i | ||||
\(310\) | −1737.00 | − | 2178.12i | −0.318241 | − | 0.399062i | ||||
\(311\) | 340.946 | + | 1493.78i | 0.0621649 | + | 0.272362i | 0.996452 | − | 0.0841583i | \(-0.0268201\pi\) |
−0.934288 | + | 0.356520i | \(0.883963\pi\) | |||||||
\(312\) | −5175.55 | − | 6489.94i | −0.939128 | − | 1.17763i | ||||
\(313\) | −7181.97 | + | 3458.66i | −1.29696 | + | 0.624584i | −0.949693 | − | 0.313182i | \(-0.898605\pi\) |
−0.347269 | + | 0.937766i | \(0.612891\pi\) | |||||||
\(314\) | −1892.37 | + | 8291.02i | −0.340104 | + | 1.49009i | ||||
\(315\) | −2267.74 | + | 1092.09i | −0.405628 | + | 0.195340i | ||||
\(316\) | 8142.82 | − | 10210.8i | 1.44959 | − | 1.81772i | ||||
\(317\) | 810.967 | + | 3553.08i | 0.143686 | + | 0.629530i | 0.994560 | + | 0.104161i | \(0.0332156\pi\) |
−0.850874 | + | 0.525369i | \(0.823927\pi\) | |||||||
\(318\) | −2120.64 | − | 9291.11i | −0.373960 | − | 1.63843i | ||||
\(319\) | −5254.22 | − | 2530.30i | −0.922195 | − | 0.444106i | ||||
\(320\) | −2963.75 | + | 3716.43i | −0.517746 | + | 0.649233i | ||||
\(321\) | 7322.57 | + | 9182.22i | 1.27323 | + | 1.59658i | ||||
\(322\) | −9547.75 | − | 4597.95i | −1.65241 | − | 0.795758i | ||||
\(323\) | −3102.64 | − | 1494.15i | −0.534475 | − | 0.257390i | ||||
\(324\) | −3262.62 | − | 4091.20i | −0.559434 | − | 0.701508i | ||||
\(325\) | 4095.47 | − | 5135.55i | 0.699002 | − | 0.876521i | ||||
\(326\) | −4322.80 | − | 2081.75i | −0.734410 | − | 0.353673i | ||||
\(327\) | 1329.92 | + | 5826.78i | 0.224908 | + | 0.985387i | ||||
\(328\) | 1576.46 | + | 6906.93i | 0.265383 | + | 1.16272i | ||||
\(329\) | −156.548 | + | 196.305i | −0.0262334 | + | 0.0328956i | ||||
\(330\) | −9265.90 | + | 4462.22i | −1.54567 | + | 0.744355i | ||||
\(331\) | −1163.69 | + | 5098.46i | −0.193239 | + | 0.846636i | 0.781610 | + | 0.623768i | \(0.214399\pi\) |
−0.974849 | + | 0.222868i | \(0.928458\pi\) | |||||||
\(332\) | −7968.11 | + | 3837.24i | −1.31719 | + | 0.634325i | ||||
\(333\) | 420.067 | + | 526.747i | 0.0691277 | + | 0.0866834i | ||||
\(334\) | −2236.49 | − | 9798.68i | −0.366392 | − | 1.60527i | ||||
\(335\) | −1907.15 | − | 2391.49i | −0.311041 | − | 0.390034i | ||||
\(336\) | 571.858 | − | 2505.47i | 0.0928494 | − | 0.406800i | ||||
\(337\) | −4729.01 | −0.764408 | −0.382204 | − | 0.924078i | \(-0.624835\pi\) | ||||
−0.382204 | + | 0.924078i | \(0.624835\pi\) | |||||||
\(338\) | 13370.8 | 2.15170 | ||||||||
\(339\) | 2364.40 | − | 10359.1i | 0.378810 | − | 1.65967i | ||||
\(340\) | 2979.24 | − | 3735.84i | 0.475211 | − | 0.595896i | ||||
\(341\) | 4966.68 | + | 2391.83i | 0.788741 | + | 0.379838i | ||||
\(342\) | −6560.38 | + | 3159.31i | −1.03726 | + | 0.499520i | ||||
\(343\) | −6599.32 | −1.03886 | ||||||||
\(344\) | 2696.52 | + | 3111.29i | 0.422636 | + | 0.487644i | ||||
\(345\) | 8938.06 | 1.39481 | ||||||||
\(346\) | 4638.46 | − | 2233.77i | 0.720709 | − | 0.347075i | ||||
\(347\) | −9051.00 | − | 4358.73i | −1.40024 | − | 0.674320i | −0.427029 | − | 0.904238i | \(-0.640440\pi\) |
−0.973210 | + | 0.229918i | \(0.926154\pi\) | |||||||
\(348\) | 6352.26 | − | 7965.49i | 0.978497 | − | 1.22700i | ||||
\(349\) | −664.275 | + | 2910.38i | −0.101885 | + | 0.446387i | 0.898093 | + | 0.439805i | \(0.144952\pi\) |
−0.999978 | + | 0.00658231i | \(0.997905\pi\) | |||||||
\(350\) | −4945.75 | −0.755319 | ||||||||
\(351\) | −4372.32 | −0.664892 | ||||||||
\(352\) | 2637.03 | − | 11553.6i | 0.399302 | − | 1.74945i | ||||
\(353\) | 2535.25 | + | 3179.10i | 0.382260 | + | 0.479339i | 0.935320 | − | 0.353802i | \(-0.115111\pi\) |
−0.553060 | + | 0.833141i | \(0.686540\pi\) | |||||||
\(354\) | 502.324 | + | 2200.82i | 0.0754186 | + | 0.330431i | ||||
\(355\) | 568.362 | + | 712.704i | 0.0849733 | + | 0.106553i | ||||
\(356\) | −5257.89 | + | 2532.07i | −0.782775 | + | 0.376964i | ||||
\(357\) | −1562.70 | + | 6846.64i | −0.231672 | + | 1.01502i | ||||
\(358\) | −3690.00 | + | 1777.01i | −0.544755 | + | 0.262340i | ||||
\(359\) | −3575.17 | + | 4483.12i | −0.525600 | + | 0.659081i | −0.971787 | − | 0.235858i | \(-0.924210\pi\) |
0.446188 | + | 0.894939i | \(0.352781\pi\) | |||||||
\(360\) | −659.635 | − | 2890.05i | −0.0965717 | − | 0.423108i | ||||
\(361\) | 1018.90 | + | 4464.09i | 0.148549 | + | 0.650836i | ||||
\(362\) | 1210.64 | + | 583.016i | 0.175774 | + | 0.0846482i | ||||
\(363\) | 6169.96 | − | 7736.89i | 0.892119 | − | 1.11868i | ||||
\(364\) | −6334.51 | − | 7943.22i | −0.912138 | − | 1.14379i | ||||
\(365\) | −2864.20 | − | 1379.33i | −0.410738 | − | 0.197801i | ||||
\(366\) | 10268.5 | + | 4945.06i | 1.46651 | + | 0.706236i | ||||
\(367\) | −4651.42 | − | 5832.70i | −0.661587 | − | 0.829603i | 0.331928 | − | 0.943305i | \(-0.392301\pi\) |
−0.993515 | + | 0.113701i | \(0.963729\pi\) | |||||||
\(368\) | −3199.64 | + | 4012.22i | −0.453241 | + | 0.568347i | ||||
\(369\) | 15164.9 | + | 7303.03i | 2.13944 | + | 1.03030i | ||||
\(370\) | −111.169 | − | 487.062i | −0.0156200 | − | 0.0684356i | ||||
\(371\) | −761.521 | − | 3336.44i | −0.106567 | − | 0.466899i | ||||
\(372\) | −6004.63 | + | 7529.56i | −0.836896 | + | 1.04943i | ||||
\(373\) | −5087.23 | + | 2449.88i | −0.706184 | + | 0.340080i | −0.752268 | − | 0.658857i | \(-0.771040\pi\) |
0.0460841 | + | 0.998938i | \(0.485326\pi\) | |||||||
\(374\) | −3590.58 | + | 15731.4i | −0.496430 | + | 2.17500i | ||||
\(375\) | 8934.95 | − | 4302.84i | 1.23040 | − | 0.592528i | ||||
\(376\) | −184.373 | − | 231.197i | −0.0252881 | − | 0.0317102i | ||||
\(377\) | 1845.27 | + | 8084.65i | 0.252085 | + | 1.10446i | ||||
\(378\) | 2052.58 | + | 2573.85i | 0.279294 | + | 0.350224i | ||||
\(379\) | 689.427 | − | 3020.58i | 0.0934392 | − | 0.409384i | −0.906478 | − | 0.422253i | \(-0.861239\pi\) |
0.999917 | + | 0.0128691i | \(0.00409648\pi\) | |||||||
\(380\) | 3163.81 | 0.427105 | ||||||||
\(381\) | 1800.69 | 0.242132 | ||||||||
\(382\) | −296.369 | + | 1298.48i | −0.0396951 | + | 0.173916i | ||||
\(383\) | 2883.73 | − | 3616.08i | 0.384731 | − | 0.482437i | −0.551324 | − | 0.834291i | \(-0.685877\pi\) |
0.936055 | + | 0.351854i | \(0.114449\pi\) | |||||||
\(384\) | 12085.9 | + | 5820.26i | 1.60613 | + | 0.773473i | ||||
\(385\) | −3327.39 | + | 1602.39i | −0.440466 | + | 0.212117i | ||||
\(386\) | 15796.1 | 2.08290 | ||||||||
\(387\) | 9773.64 | − | 400.015i | 1.28378 | − | 0.0525424i | ||||
\(388\) | 10209.6 | 1.33587 | ||||||||
\(389\) | 12075.9 | − | 5815.47i | 1.57397 | − | 0.757985i | 0.575751 | − | 0.817625i | \(-0.304710\pi\) |
0.998220 | + | 0.0596402i | \(0.0189953\pi\) | |||||||
\(390\) | 13175.8 | + | 6345.13i | 1.71073 | + | 0.823842i | ||||
\(391\) | 8743.58 | − | 10964.1i | 1.13090 | − | 1.41810i | ||||
\(392\) | 615.034 | − | 2694.64i | 0.0792446 | − | 0.347193i | ||||
\(393\) | −13118.6 | −1.68383 | ||||||||
\(394\) | −9915.79 | −1.26789 | ||||||||
\(395\) | −1502.16 | + | 6581.39i | −0.191346 | + | 0.838343i | ||||
\(396\) | 12464.9 | + | 15630.5i | 1.58178 | + | 1.98349i | ||||
\(397\) | −1981.87 | − | 8683.12i | −0.250547 | − | 1.09772i | −0.931027 | − | 0.364950i | \(-0.881086\pi\) |
0.680481 | − | 0.732766i | \(-0.261771\pi\) | |||||||
\(398\) | −1461.41 | − | 1832.55i | −0.184055 | − | 0.230797i | ||||
\(399\) | −4189.38 | + | 2017.50i | −0.525642 | + | 0.253136i | ||||
\(400\) | −532.947 | + | 2334.99i | −0.0666183 | + | 0.291874i | ||||
\(401\) | 9.32564 | − | 4.49099i | 0.00116135 | − | 0.000559275i | −0.433303 | − | 0.901248i | \(-0.642652\pi\) |
0.434464 | + | 0.900689i | \(0.356938\pi\) | |||||||
\(402\) | −11251.3 | + | 14108.7i | −1.39594 | + | 1.75045i | ||||
\(403\) | −1744.28 | − | 7642.20i | −0.215605 | − | 0.944628i | ||||
\(404\) | 502.763 | + | 2202.75i | 0.0619143 | + | 0.271264i | ||||
\(405\) | 2436.95 | + | 1173.57i | 0.298995 | + | 0.143988i | ||||
\(406\) | 3892.93 | − | 4881.57i | 0.475869 | − | 0.596720i | ||||
\(407\) | 616.351 | + | 772.880i | 0.0750649 | + | 0.0941284i | ||||
\(408\) | −7451.85 | − | 3588.62i | −0.904219 | − | 0.435449i | ||||
\(409\) | 6777.61 | + | 3263.92i | 0.819391 | + | 0.394598i | 0.796126 | − | 0.605131i | \(-0.206879\pi\) |
0.0232657 | + | 0.999729i | \(0.492594\pi\) | |||||||
\(410\) | −7781.83 | − | 9758.10i | −0.937359 | − | 1.17541i | ||||
\(411\) | −10384.5 | + | 13021.8i | −1.24630 | + | 1.56281i | ||||
\(412\) | 8989.52 | + | 4329.12i | 1.07496 | + | 0.517671i | ||||
\(413\) | 180.385 | + | 790.316i | 0.0214919 | + | 0.0941621i | ||||
\(414\) | −6598.24 | − | 28908.8i | −0.783300 | − | 3.43186i | ||||
\(415\) | 2850.19 | − | 3574.03i | 0.337134 | − | 0.422752i | ||||
\(416\) | −15182.5 | + | 7311.51i | −1.78938 | + | 0.861722i | ||||
\(417\) | 955.536 | − | 4186.48i | 0.112213 | − | 0.491637i | ||||
\(418\) | −9625.84 | + | 4635.56i | −1.12635 | + | 0.542423i | ||||
\(419\) | −68.2458 | − | 85.5776i | −0.00795711 | − | 0.00997790i | 0.777837 | − | 0.628466i | \(-0.216317\pi\) |
−0.785794 | + | 0.618488i | \(0.787745\pi\) | |||||||
\(420\) | −1435.70 | − | 6290.23i | −0.166798 | − | 0.730790i | ||||
\(421\) | −5562.08 | − | 6974.63i | −0.643894 | − | 0.807417i | 0.347590 | − | 0.937647i | \(-0.387000\pi\) |
−0.991484 | + | 0.130229i | \(0.958429\pi\) | |||||||
\(422\) | 4830.54 | − | 21164.0i | 0.557220 | − | 2.44134i | ||||
\(423\) | −702.563 | −0.0807560 | ||||||||
\(424\) | 4030.51 | 0.461648 | ||||||||
\(425\) | 1456.37 | − | 6380.77i | 0.166222 | − | 0.728266i | ||||
\(426\) | 3353.08 | − | 4204.63i | 0.381355 | − | 0.478205i | ||||
\(427\) | 3687.43 | + | 1775.77i | 0.417909 | + | 0.201254i | ||||
\(428\) | −15252.8 | + | 7345.36i | −1.72260 | + | 0.829559i | ||||
\(429\) | −28937.1 | −3.25663 | ||||||||
\(430\) | −6658.33 | − | 2877.26i | −0.746729 | − | 0.322683i | ||||
\(431\) | −16280.0 | −1.81944 | −0.909720 | − | 0.415223i | \(-0.863703\pi\) | ||||
−0.909720 | + | 0.415223i | \(0.863703\pi\) | |||||||
\(432\) | 1436.35 | − | 691.710i | 0.159969 | − | 0.0770368i | ||||
\(433\) | −11138.8 | − | 5364.19i | −1.23626 | − | 0.595350i | −0.302462 | − | 0.953161i | \(-0.597809\pi\) |
−0.933794 | + | 0.357812i | \(0.883523\pi\) | |||||||
\(434\) | −3679.88 | + | 4614.42i | −0.407004 | + | 0.510367i | ||||
\(435\) | −1171.84 | + | 5134.18i | −0.129162 | + | 0.565897i | ||||
\(436\) | −8615.12 | −0.946306 | ||||||||
\(437\) | 9285.27 | 1.01642 | ||||||||
\(438\) | −4173.34 | + | 18284.6i | −0.455274 | + | 1.99469i | ||||
\(439\) | −9772.03 | − | 12253.7i | −1.06240 | − | 1.33221i | −0.940549 | − | 0.339659i | \(-0.889688\pi\) |
−0.121852 | − | 0.992548i | \(-0.538883\pi\) | |||||||
\(440\) | −967.862 | − | 4240.48i | −0.104866 | − | 0.459448i | ||||
\(441\) | −4094.25 | − | 5134.03i | −0.442096 | − | 0.554371i | ||||
\(442\) | 20672.5 | − | 9955.37i | 2.22464 | − | 1.07133i | ||||
\(443\) | −1791.25 | + | 7847.97i | −0.192110 | + | 0.841689i | 0.783362 | + | 0.621566i | \(0.213503\pi\) |
−0.975472 | + | 0.220123i | \(0.929354\pi\) | |||||||
\(444\) | −1556.00 | + | 749.329i | −0.166316 | + | 0.0800937i | ||||
\(445\) | 1880.75 | − | 2358.39i | 0.200351 | − | 0.251232i | ||||
\(446\) | 1377.01 | + | 6033.08i | 0.146196 | + | 0.640526i | ||||
\(447\) | 5596.44 | + | 24519.6i | 0.592176 | + | 2.59449i | ||||
\(448\) | 9073.13 | + | 4369.39i | 0.956841 | + | 0.460790i | ||||
\(449\) | 4773.27 | − | 5985.49i | 0.501702 | − | 0.629115i | −0.464910 | − | 0.885358i | \(-0.653913\pi\) |
0.966612 | + | 0.256243i | \(0.0824848\pi\) | |||||||
\(450\) | −8628.36 | − | 10819.6i | −0.903877 | − | 1.13343i | ||||
\(451\) | 22251.0 | + | 10715.5i | 2.32319 | + | 1.11879i | ||||
\(452\) | 13799.5 | + | 6645.51i | 1.43601 | + | 0.691546i | ||||
\(453\) | −5974.06 | − | 7491.24i | −0.619616 | − | 0.776974i | ||||
\(454\) | −814.320 | + | 1021.12i | −0.0841805 | + | 0.105559i | ||||
\(455\) | 4731.44 | + | 2278.54i | 0.487501 | + | 0.234768i | ||||
\(456\) | −1218.60 | − | 5339.02i | −0.125145 | − | 0.548295i | ||||
\(457\) | 1320.80 | + | 5786.80i | 0.135196 | + | 0.592330i | 0.996452 | + | 0.0841603i | \(0.0268208\pi\) |
−0.861257 | + | 0.508170i | \(0.830322\pi\) | |||||||
\(458\) | 10647.4 | − | 13351.5i | 1.08629 | − | 1.36217i | ||||
\(459\) | −3925.08 | + | 1890.22i | −0.399144 | + | 0.192218i | ||||
\(460\) | −2866.94 | + | 12560.9i | −0.290591 | + | 1.27316i | ||||
\(461\) | −13199.0 | + | 6356.32i | −1.33349 | + | 0.642176i | −0.958564 | − | 0.284877i | \(-0.908047\pi\) |
−0.374929 | + | 0.927054i | \(0.622333\pi\) | |||||||
\(462\) | 13584.4 | + | 17034.4i | 1.36798 | + | 1.71539i | ||||
\(463\) | 1941.31 | + | 8505.45i | 0.194861 | + | 0.853740i | 0.973938 | + | 0.226813i | \(0.0728305\pi\) |
−0.779078 | + | 0.626927i | \(0.784312\pi\) | |||||||
\(464\) | −1885.20 | − | 2363.96i | −0.188617 | − | 0.236518i | ||||
\(465\) | 1107.71 | − | 4853.21i | 0.110471 | − | 0.484005i | ||||
\(466\) | −24345.4 | −2.42012 | ||||||||
\(467\) | 211.747 | 0.0209818 | 0.0104909 | − | 0.999945i | \(-0.496661\pi\) | ||||
0.0104909 | + | 0.999945i | \(0.496661\pi\) | |||||||
\(468\) | 6325.88 | − | 27715.5i | 0.624816 | − | 2.73750i | ||||
\(469\) | −4040.36 | + | 5066.45i | −0.397797 | + | 0.498821i | ||||
\(470\) | 469.373 | + | 226.038i | 0.0460650 | + | 0.0221837i | ||||
\(471\) | −13690.9 | + | 6593.19i | −1.33937 | + | 0.645007i | ||||
\(472\) | −954.724 | −0.0931032 | ||||||||
\(473\) | 14340.6 | − | 586.930i | 1.39404 | − | 0.0570551i | ||||
\(474\) | 39825.8 | 3.85919 | ||||||||
\(475\) | 3904.32 | − | 1880.22i | 0.377142 | − | 0.181622i | ||||
\(476\) | −9120.53 | − | 4392.22i | −0.878233 | − | 0.422935i | ||||
\(477\) | 5970.44 | − | 7486.70i | 0.573098 | − | 0.718642i | ||||
\(478\) | 2660.30 | − | 11655.5i | 0.254559 | − | 1.11530i | ||||
\(479\) | 8169.97 | 0.779323 | 0.389661 | − | 0.920958i | \(-0.372592\pi\) | ||||
0.389661 | + | 0.920958i | \(0.372592\pi\) | |||||||
\(480\) | −10701.5 | −1.01761 | ||||||||
\(481\) | 312.795 | − | 1370.44i | 0.0296512 | − | 0.129910i | ||||
\(482\) | 4048.94 | + | 5077.21i | 0.382623 | + | 0.479794i | ||||
\(483\) | −4213.56 | − | 18460.8i | −0.396943 | − | 1.73912i | ||||
\(484\) | 8893.81 | + | 11152.5i | 0.835256 | + | 1.04738i | ||||
\(485\) | −4754.67 | + | 2289.73i | −0.445151 | + | 0.214373i | ||||
\(486\) | 5146.15 | − | 22546.7i | 0.480317 | − | 2.10441i | ||||
\(487\) | −7790.53 | + | 3751.72i | −0.724892 | + | 0.349090i | −0.759673 | − | 0.650305i | \(-0.774641\pi\) |
0.0347808 | + | 0.999395i | \(0.488927\pi\) | |||||||
\(488\) | −3005.33 | + | 3768.56i | −0.278780 | + | 0.349580i | ||||
\(489\) | −1907.71 | − | 8358.23i | −0.176421 | − | 0.772950i | ||||
\(490\) | 1083.52 | + | 4747.23i | 0.0998952 | + | 0.437670i | ||||
\(491\) | 7003.81 | + | 3372.86i | 0.643742 | + | 0.310010i | 0.727122 | − | 0.686508i | \(-0.240857\pi\) |
−0.0833800 | + | 0.996518i | \(0.526572\pi\) | |||||||
\(492\) | −26901.0 | + | 33732.8i | −2.46502 | + | 3.09104i | ||||
\(493\) | 5151.63 | + | 6459.94i | 0.470624 | + | 0.590144i | ||||
\(494\) | 13687.6 | + | 6591.61i | 1.24663 | + | 0.600346i | ||||
\(495\) | −9310.43 | − | 4483.67i | −0.845399 | − | 0.407123i | ||||
\(496\) | 1782.03 | + | 2234.59i | 0.161321 | + | 0.202291i | ||||
\(497\) | 1204.09 | − | 1509.88i | 0.108674 | − | 0.136273i | ||||
\(498\) | −24298.2 | − | 11701.4i | −2.18640 | − | 1.05292i | ||||
\(499\) | 3889.83 | + | 17042.5i | 0.348964 | + | 1.52891i | 0.779538 | + | 0.626355i | \(0.215454\pi\) |
−0.430575 | + | 0.902555i | \(0.641689\pi\) | |||||||
\(500\) | 3180.96 | + | 13936.7i | 0.284514 | + | 1.24654i | ||||
\(501\) | 11197.3 | − | 14040.9i | 0.998516 | − | 1.25210i | ||||
\(502\) | 13485.3 | − | 6494.17i | 1.19896 | − | 0.577389i | ||||
\(503\) | −2239.72 | + | 9812.86i | −0.198537 | + | 0.869848i | 0.773271 | + | 0.634076i | \(0.218619\pi\) |
−0.971808 | + | 0.235773i | \(0.924238\pi\) | |||||||
\(504\) | −5658.19 | + | 2724.84i | −0.500071 | + | 0.240822i | ||||
\(505\) | −728.151 | − | 913.072i | −0.0641629 | − | 0.0804578i | ||||
\(506\) | −9681.40 | − | 42417.0i | −0.850574 | − | 3.72661i | ||||
\(507\) | 14896.1 | + | 18679.1i | 1.30485 | + | 1.63623i | ||||
\(508\) | −577.584 | + | 2530.56i | −0.0504451 | + | 0.221015i | ||||
\(509\) | 5106.23 | 0.444656 | 0.222328 | − | 0.974972i | \(-0.428634\pi\) | ||||
0.222328 | + | 0.974972i | \(0.428634\pi\) | |||||||
\(510\) | 14571.2 | 1.26514 | ||||||||
\(511\) | −1498.65 | + | 6566.01i | −0.129738 | + | 0.568421i | ||||
\(512\) | 5753.01 | − | 7214.04i | 0.496581 | − | 0.622692i | ||||
\(513\) | −2598.86 | − | 1251.55i | −0.223670 | − | 0.107714i | ||||
\(514\) | −9262.07 | + | 4460.38i | −0.794810 | + | 0.382760i | ||||
\(515\) | −5157.35 | −0.441281 | ||||||||
\(516\) | −4575.23 | + | 24653.4i | −0.390336 | + | 2.10331i | ||||
\(517\) | −1030.85 | −0.0876919 | ||||||||
\(518\) | −953.579 | + | 459.219i | −0.0808839 | + | 0.0389516i | ||||
\(519\) | 8288.22 | + | 3991.39i | 0.700987 | + | 0.337578i | ||||
\(520\) | −3856.22 | + | 4835.54i | −0.325205 | + | 0.407794i | ||||
\(521\) | −1702.63 | + | 7459.70i | −0.143174 | + | 0.627285i | 0.851513 | + | 0.524334i | \(0.175686\pi\) |
−0.994686 | + | 0.102951i | \(0.967172\pi\) | |||||||
\(522\) | 17470.8 | 1.46490 | ||||||||
\(523\) | 3318.37 | 0.277442 | 0.138721 | − | 0.990331i | \(-0.455701\pi\) | ||||
0.138721 | + | 0.990331i | \(0.455701\pi\) | |||||||
\(524\) | 4207.87 | − | 18435.9i | 0.350804 | − | 1.53697i | ||||
\(525\) | −5509.96 | − | 6909.27i | −0.458047 | − | 0.574372i | ||||
\(526\) | 2594.28 | + | 11366.3i | 0.215049 | + | 0.942193i | ||||
\(527\) | −4869.70 | − | 6106.41i | −0.402519 | − | 0.504743i | ||||
\(528\) | 9506.12 | − | 4577.90i | 0.783524 | − | 0.377325i | ||||
\(529\) | −5706.61 | + | 25002.3i | −0.469024 | + | 2.05493i | ||||
\(530\) | −6397.49 | + | 3080.87i | −0.524319 | + | 0.252499i | ||||
\(531\) | −1414.24 | + | 1773.41i | −0.115580 | + | 0.144933i | ||||
\(532\) | −1491.47 | − | 6534.58i | −0.121548 | − | 0.532537i | ||||
\(533\) | −7814.47 | − | 34237.4i | −0.635052 | − | 2.78234i | ||||
\(534\) | −16033.6 | − | 7721.37i | −1.29933 | − | 0.625723i | ||||
\(535\) | 5455.93 | − | 6841.52i | 0.440898 | − | 0.552868i | ||||
\(536\) | −4758.49 | − | 5966.96i | −0.383462 | − | 0.480846i | ||||
\(537\) | −6593.45 | − | 3175.24i | −0.529848 | − | 0.255162i | ||||
\(538\) | 14858.6 | + | 7155.54i | 1.19071 | + | 0.573415i | ||||
\(539\) | −6007.37 | − | 7533.00i | −0.480066 | − | 0.601984i | ||||
\(540\) | 2495.49 | − | 3129.25i | 0.198869 | − | 0.249373i | ||||
\(541\) | −2704.58 | − | 1302.46i | −0.214933 | − | 0.103506i | 0.323320 | − | 0.946290i | \(-0.395201\pi\) |
−0.538253 | + | 0.842783i | \(0.680915\pi\) | |||||||
\(542\) | 6684.68 | + | 29287.5i | 0.529763 | + | 2.32104i | ||||
\(543\) | 534.275 | + | 2340.81i | 0.0422246 | + | 0.184998i | ||||
\(544\) | −10468.6 | + | 13127.3i | −0.825072 | + | 1.03461i | ||||
\(545\) | 4012.09 | − | 1932.12i | 0.315338 | − | 0.151859i | ||||
\(546\) | 6894.03 | − | 30204.7i | 0.540361 | − | 2.36748i | ||||
\(547\) | 6450.55 | − | 3106.42i | 0.504215 | − | 0.242817i | −0.164444 | − | 0.986386i | \(-0.552583\pi\) |
0.668659 | + | 0.743569i | \(0.266869\pi\) | |||||||
\(548\) | −14968.9 | − | 18770.5i | −1.16686 | − | 1.46320i | ||||
\(549\) | 2548.30 | + | 11164.8i | 0.198104 | + | 0.867949i | ||||
\(550\) | −12660.1 | − | 15875.3i | −0.981508 | − | 1.23077i | ||||
\(551\) | −1217.37 | + | 5333.62i | −0.0941225 | + | 0.412378i | ||||
\(552\) | 22301.2 | 1.71957 | ||||||||
\(553\) | 14301.4 | 1.09975 | ||||||||
\(554\) | −3255.89 | + | 14265.0i | −0.249692 | + | 1.09397i | ||||
\(555\) | 556.581 | − | 697.930i | 0.0425685 | − | 0.0533793i | ||||
\(556\) | 5576.88 | + | 2685.68i | 0.425382 | + | 0.204853i | ||||
\(557\) | 7469.13 | − | 3596.94i | 0.568182 | − | 0.273622i | −0.127659 | − | 0.991818i | \(-0.540746\pi\) |
0.695841 | + | 0.718196i | \(0.255032\pi\) | |||||||
\(558\) | −16514.7 | −1.25291 | ||||||||
\(559\) | −13366.6 | − | 15422.6i | −1.01135 | − | 1.16692i | ||||
\(560\) | −1914.79 | −0.144491 | ||||||||
\(561\) | −25977.1 | + | 12509.9i | −1.95500 | + | 0.941478i | ||||
\(562\) | 1081.23 | + | 520.694i | 0.0811548 | + | 0.0390821i | ||||
\(563\) | 7376.39 | − | 9249.71i | 0.552181 | − | 0.692413i | −0.424910 | − | 0.905236i | \(-0.639694\pi\) |
0.977091 | + | 0.212823i | \(0.0682656\pi\) | |||||||
\(564\) | 400.743 | − | 1755.77i | 0.0299190 | − | 0.131084i | ||||
\(565\) | −7916.89 | −0.589498 | ||||||||
\(566\) | 20828.8 | 1.54682 | ||||||||
\(567\) | 1275.10 | − | 5586.56i | 0.0944426 | − | 0.413780i | ||||
\(568\) | 1418.11 | + | 1778.25i | 0.104758 | + | 0.131362i | ||||
\(569\) | 147.133 | + | 644.630i | 0.0108403 | + | 0.0474944i | 0.980059 | − | 0.198708i | \(-0.0636744\pi\) |
−0.969219 | + | 0.246202i | \(0.920817\pi\) | |||||||
\(570\) | 6015.31 | + | 7542.96i | 0.442024 | + | 0.554281i | ||||
\(571\) | 12493.5 | − | 6016.53i | 0.915648 | − | 0.440953i | 0.0841327 | − | 0.996455i | \(-0.473188\pi\) |
0.831515 | + | 0.555502i | \(0.187474\pi\) | |||||||
\(572\) | 9281.76 | − | 40666.1i | 0.678479 | − | 2.97261i | ||||
\(573\) | −2144.16 | + | 1032.57i | −0.156324 | + | 0.0752817i | ||||
\(574\) | −16486.0 | + | 20672.8i | −1.19881 | + | 1.50325i | ||||
\(575\) | 3926.85 | + | 17204.7i | 0.284802 | + | 1.24780i | ||||
\(576\) | 6270.24 | + | 27471.7i | 0.453577 | + | 1.98725i | ||||
\(577\) | 13963.8 | + | 6724.59i | 1.00749 | + | 0.485179i | 0.863472 | − | 0.504396i | \(-0.168285\pi\) |
0.144013 | + | 0.989576i | \(0.453999\pi\) | |||||||
\(578\) | 789.305 | − | 989.757i | 0.0568006 | − | 0.0712257i | ||||
\(579\) | 17598.1 | + | 22067.3i | 1.26313 | + | 1.58391i | ||||
\(580\) | −6839.34 | − | 3293.65i | −0.489634 | − | 0.235795i | ||||
\(581\) | −8725.49 | − | 4201.97i | −0.623054 | − | 0.300047i | ||||
\(582\) | 19411.5 | + | 24341.2i | 1.38253 | + | 1.73364i | ||||
\(583\) | 8760.25 | − | 10985.0i | 0.622320 | − | 0.780364i | ||||
\(584\) | −7146.41 | − | 3441.53i | −0.506371 | − | 0.243855i | ||||
\(585\) | 3269.79 | + | 14325.9i | 0.231093 | + | 1.01248i | ||||
\(586\) | −6490.97 | − | 28438.8i | −0.457576 | − | 2.00477i | ||||
\(587\) | −13560.0 | + | 17003.7i | −0.953462 | + | 1.19560i | 0.0271476 | + | 0.999631i | \(0.491358\pi\) |
−0.980610 | + | 0.195972i | \(0.937214\pi\) | |||||||
\(588\) | 15165.8 | − | 7303.46i | 1.06365 | − | 0.512227i | ||||
\(589\) | 1150.74 | − | 5041.73i | 0.0805018 | − | 0.352701i | ||||
\(590\) | 1515.40 | − | 729.778i | 0.105742 | − | 0.0509229i | ||||
\(591\) | −11047.0 | − | 13852.5i | −0.768887 | − | 0.964154i | ||||
\(592\) | 114.051 | + | 499.689i | 0.00791801 | + | 0.0346911i | ||||
\(593\) | −13887.7 | − | 17414.6i | −0.961720 | − | 1.20596i | −0.978531 | − | 0.206100i | \(-0.933923\pi\) |
0.0168105 | − | 0.999859i | \(-0.494649\pi\) | |||||||
\(594\) | −3007.58 | + | 13177.1i | −0.207748 | + | 0.910204i | ||||
\(595\) | 5232.51 | 0.360524 | ||||||||
\(596\) | −36253.2 | −2.49159 | ||||||||
\(597\) | 931.966 | − | 4083.21i | 0.0638908 | − | 0.279924i | ||||
\(598\) | −38573.3 | + | 48369.3i | −2.63776 | + | 3.30764i | ||||
\(599\) | −20337.1 | − | 9793.85i | −1.38723 | − | 0.668056i | −0.416705 | − | 0.909042i | \(-0.636815\pi\) |
−0.970529 | + | 0.240986i | \(0.922529\pi\) | |||||||
\(600\) | 9377.31 | − | 4515.87i | 0.638045 | − | 0.307266i | ||||
\(601\) | 22982.2 | 1.55984 | 0.779918 | − | 0.625881i | \(-0.215261\pi\) | ||||
0.779918 | + | 0.625881i | \(0.215261\pi\) | |||||||
\(602\) | −2803.89 | + | 15108.6i | −0.189830 | + | 1.02289i | ||||
\(603\) | −18132.5 | −1.22456 | ||||||||
\(604\) | 12443.9 | − | 5992.65i | 0.838301 | − | 0.403705i | ||||
\(605\) | −6643.06 | − | 3199.13i | −0.446411 | − | 0.214980i | ||||
\(606\) | −4295.76 | + | 5386.72i | −0.287960 | + | 0.361090i | ||||
\(607\) | −2160.32 | + | 9464.98i | −0.144456 | + | 0.632902i | 0.849913 | + | 0.526924i | \(0.176655\pi\) |
−0.994368 | + | 0.105978i | \(0.966203\pi\) | |||||||
\(608\) | −11117.2 | −0.741549 | ||||||||
\(609\) | 11156.7 | 0.742349 | ||||||||
\(610\) | 1889.62 | − | 8278.95i | 0.125423 | − | 0.549516i | ||||
\(611\) | 913.932 | + | 1146.03i | 0.0605135 | + | 0.0758815i | ||||
\(612\) | −6303.00 | − | 27615.3i | −0.416313 | − | 1.82399i | ||||
\(613\) | 8681.66 | + | 10886.5i | 0.572021 | + | 0.717291i | 0.980729 | − | 0.195374i | \(-0.0625920\pi\) |
−0.408708 | + | 0.912665i | \(0.634021\pi\) | |||||||
\(614\) | −27580.0 | + | 13281.9i | −1.81277 | + | 0.872984i | ||||
\(615\) | 4962.61 | − | 21742.6i | 0.325385 | − | 1.42560i | ||||
\(616\) | −8302.09 | + | 3998.07i | −0.543020 | + | 0.261505i | ||||
\(617\) | 4940.59 | − | 6195.30i | 0.322367 | − | 0.404236i | −0.594070 | − | 0.804413i | \(-0.702480\pi\) |
0.916438 | + | 0.400177i | \(0.131051\pi\) | |||||||
\(618\) | 6770.43 | + | 29663.2i | 0.440690 | + | 1.93079i | ||||
\(619\) | 1701.22 | + | 7453.55i | 0.110465 | + | 0.483980i | 0.999651 | + | 0.0264325i | \(0.00841471\pi\) |
−0.889185 | + | 0.457547i | \(0.848728\pi\) | |||||||
\(620\) | 6465.04 | + | 3113.40i | 0.418778 | + | 0.201673i | ||||
\(621\) | 7323.88 | − | 9183.85i | 0.473264 | − | 0.593455i | ||||
\(622\) | −4199.22 | − | 5265.65i | −0.270696 | − | 0.339443i | ||||
\(623\) | −5757.66 | − | 2772.75i | −0.370266 | − | 0.178311i | ||||
\(624\) | −13517.4 | − | 6509.63i | −0.867193 | − | 0.417618i | ||||
\(625\) | 2465.91 | + | 3092.15i | 0.157818 | + | 0.197898i | ||||
\(626\) | 21846.8 | − | 27395.0i | 1.39484 | − | 1.74908i | ||||
\(627\) | −17199.9 | − | 8283.03i | −1.09553 | − | 0.527579i | ||||
\(628\) | −4874.15 | − | 21355.0i | −0.309713 | − | 1.35694i | ||||
\(629\) | −311.664 | − | 1365.49i | −0.0197565 | − | 0.0865590i | ||||
\(630\) | 6898.22 | − | 8650.10i | 0.436241 | − | 0.547029i | ||||
\(631\) | −9782.66 | + | 4711.08i | −0.617182 | + | 0.297219i | −0.716231 | − | 0.697863i | \(-0.754134\pi\) |
0.0990490 | + | 0.995083i | \(0.468420\pi\) | |||||||
\(632\) | −3748.00 | + | 16421.1i | −0.235898 | + | 1.03354i | ||||
\(633\) | 34947.9 | − | 16830.0i | 2.19440 | − | 1.05677i | ||||
\(634\) | −9988.17 | − | 12524.8i | −0.625680 | − | 0.784577i | ||||
\(635\) | −298.548 | − | 1308.03i | −0.0186575 | − | 0.0817439i | ||||
\(636\) | 15304.4 | + | 19191.1i | 0.954182 | + | 1.19651i | ||||
\(637\) | −3048.71 | + | 13357.3i | −0.189630 | + | 0.830822i | ||||
\(638\) | 25634.4 | 1.59071 | ||||||||
\(639\) | 5403.77 | 0.334538 | ||||||||
\(640\) | 2224.05 | − | 9744.20i | 0.137365 | − | 0.601833i | ||||
\(641\) | 6230.67 | − | 7813.01i | 0.383926 | − | 0.481428i | −0.551890 | − | 0.833917i | \(-0.686093\pi\) |
0.935816 | + | 0.352489i | \(0.114665\pi\) | |||||||
\(642\) | −46512.3 | − | 22399.2i | −2.85934 | − | 1.37698i | ||||
\(643\) | −4461.87 | + | 2148.72i | −0.273653 | + | 0.131784i | −0.565678 | − | 0.824626i | \(-0.691385\pi\) |
0.292025 | + | 0.956411i | \(0.405671\pi\) | |||||||
\(644\) | 27295.0 | 1.67015 | ||||||||
\(645\) | −3398.35 | − | 12507.3i | −0.207457 | − | 0.763525i | ||||
\(646\) | 15137.2 | 0.921927 | ||||||||
\(647\) | −11426.7 | + | 5502.80i | −0.694326 | + | 0.334370i | −0.747543 | − | 0.664213i | \(-0.768767\pi\) |
0.0532171 | + | 0.998583i | \(0.483052\pi\) | |||||||
\(648\) | 6080.38 | + | 2928.16i | 0.368611 | + | 0.177514i | ||||
\(649\) | −2075.08 | + | 2602.06i | −0.125507 | + | 0.157380i | ||||
\(650\) | −6424.94 | + | 28149.5i | −0.387703 | + | 1.69864i | ||||
\(651\) | −10546.1 | −0.634921 | ||||||||
\(652\) | 12358.0 | 0.742294 | ||||||||
\(653\) | −133.436 | + | 584.620i | −0.00799654 | + | 0.0350351i | −0.978769 | − | 0.204967i | \(-0.934291\pi\) |
0.970772 | + | 0.240003i | \(0.0771483\pi\) | |||||||
\(654\) | −16379.8 | − | 20539.7i | −0.979361 | − | 1.22808i | ||||
\(655\) | 2175.01 | + | 9529.35i | 0.129748 | + | 0.568462i | ||||
\(656\) | 7983.57 | + | 10011.1i | 0.475162 | + | 0.595834i | ||||
\(657\) | −16978.7 | + | 8176.52i | −1.00822 | + | 0.485535i | ||||
\(658\) | 245.592 | − | 1076.01i | 0.0145504 | − | 0.0637495i | ||||
\(659\) | 17193.0 | − | 8279.73i | 1.01631 | − | 0.489427i | 0.149865 | − | 0.988706i | \(-0.452116\pi\) |
0.866441 | + | 0.499279i | \(0.166402\pi\) | |||||||
\(660\) | 16515.8 | − | 20710.1i | 0.974055 | − | 1.22143i | ||||
\(661\) | −6801.53 | − | 29799.5i | −0.400225 | − | 1.75350i | −0.626484 | − | 0.779434i | \(-0.715507\pi\) |
0.226259 | − | 0.974067i | \(-0.427350\pi\) | |||||||
\(662\) | −5115.18 | − | 22411.1i | −0.300313 | − | 1.31576i | ||||
\(663\) | 36938.6 | + | 17788.7i | 2.16377 | + | 1.04201i | ||||
\(664\) | 7111.46 | − | 8917.48i | 0.415630 | − | 0.521183i | ||||
\(665\) | 2160.10 | + | 2708.68i | 0.125963 | + | 0.157952i | ||||
\(666\) | −2668.23 | − | 1284.95i | −0.155243 | − | 0.0747610i | ||||
\(667\) | −20072.4 | − | 9666.33i | −1.16522 | − | 0.561142i | ||||
\(668\) | 16140.5 | + | 20239.5i | 0.934872 | + | 1.17229i | ||||
\(669\) | −6894.19 | + | 8645.04i | −0.398423 | + | 0.499606i | ||||
\(670\) | 12114.1 | + | 5833.82i | 0.698518 | + | 0.336389i | ||||
\(671\) | 3739.04 | + | 16381.8i | 0.215118 | + | 0.942494i | ||||
\(672\) | 5044.87 | + | 22103.0i | 0.289598 | + | 1.26881i | ||||
\(673\) | −10415.9 | + | 13061.1i | −0.596586 | + | 0.748096i | −0.984842 | − | 0.173456i | \(-0.944506\pi\) |
0.388255 | + | 0.921552i | \(0.373078\pi\) | |||||||
\(674\) | 18728.5 | − | 9019.18i | 1.07032 | − | 0.515439i | ||||
\(675\) | 1219.90 | − | 5344.72i | 0.0695614 | − | 0.304768i | ||||
\(676\) | −31028.3 | + | 14942.5i | −1.76538 | + | 0.850163i | ||||
\(677\) | −7348.63 | − | 9214.90i | −0.417180 | − | 0.523127i | 0.528190 | − | 0.849126i | \(-0.322871\pi\) |
−0.945370 | + | 0.325999i | \(0.894299\pi\) | |||||||
\(678\) | 10393.1 | + | 45535.1i | 0.588708 | + | 2.57930i | ||||
\(679\) | 6970.67 | + | 8740.94i | 0.393976 | + | 0.494030i | ||||
\(680\) | −1371.29 | + | 6008.02i | −0.0773333 | + | 0.338819i | ||||
\(681\) | −2333.74 | −0.131320 | ||||||||
\(682\) | −24231.5 | −1.36052 | ||||||||
\(683\) | 539.476 | − | 2363.60i | 0.0302232 | − | 0.132417i | −0.957566 | − | 0.288216i | \(-0.906938\pi\) |
0.987789 | + | 0.155799i | \(0.0497952\pi\) | |||||||
\(684\) | 11693.4 | − | 14663.1i | 0.653667 | − | 0.819672i | ||||
\(685\) | 11180.8 | + | 5384.37i | 0.623642 | + | 0.300330i | ||||
\(686\) | 26135.6 | − | 12586.3i | 1.45461 | − | 0.700504i | ||||
\(687\) | 30514.2 | 1.69460 | ||||||||
\(688\) | 6830.95 | + | 2951.85i | 0.378528 | + | 0.163573i | ||||
\(689\) | −19979.1 | −1.10471 | ||||||||
\(690\) | −35397.9 | + | 17046.7i | −1.95301 | + | 0.940518i | ||||
\(691\) | −3411.08 | − | 1642.69i | −0.187791 | − | 0.0904353i | 0.337626 | − | 0.941280i | \(-0.390376\pi\) |
−0.525417 | + | 0.850845i | \(0.676090\pi\) | |||||||
\(692\) | −8267.72 | + | 10367.4i | −0.454179 | + | 0.569522i | ||||
\(693\) | −4871.53 | + | 21343.6i | −0.267034 | + | 1.16995i | ||||
\(694\) | 44158.1 | 2.41530 | ||||||||
\(695\) | −3199.49 | −0.174624 | ||||||||
\(696\) | −2923.84 | + | 12810.2i | −0.159236 | + | 0.697656i | ||||
\(697\) | −21816.5 | − | 27357.0i | −1.18559 | − | 1.48669i | ||||
\(698\) | −2919.93 | − | 12793.0i | −0.158339 | − | 0.693730i | ||||
\(699\) | −27122.7 | − | 34010.8i | −1.46763 | − | 1.84035i | ||||
\(700\) | 11477.2 | − | 5527.11i | 0.619708 | − | 0.298436i | ||||
\(701\) | −519.095 | + | 2274.30i | −0.0279685 | + | 0.122538i | −0.986985 | − | 0.160812i | \(-0.948589\pi\) |
0.959017 | + | 0.283350i | \(0.0914459\pi\) | |||||||
\(702\) | 17315.9 | − | 8338.91i | 0.930979 | − | 0.448336i | ||||
\(703\) | 578.202 | − | 725.042i | 0.0310203 | − | 0.0388983i | ||||
\(704\) | 9200.13 | + | 40308.4i | 0.492533 | + | 2.15793i | ||||
\(705\) | 207.141 | + | 907.544i | 0.0110658 | + | 0.0484824i | ||||
\(706\) | −16103.7 | − | 7755.13i | −0.858457 | − | 0.413411i | ||||
\(707\) | −1542.61 | + | 1934.37i | −0.0820592 | + | 0.102899i | ||||
\(708\) | −3625.22 | − | 4545.88i | −0.192435 | − | 0.241306i | ||||
\(709\) | 30124.7 | + | 14507.3i | 1.59571 | + | 0.768452i | 0.999411 | − | 0.0343135i | \(-0.0109245\pi\) |
0.596295 | + | 0.802765i | \(0.296639\pi\) | |||||||
\(710\) | −3610.19 | − | 1738.57i | −0.190828 | − | 0.0918979i | ||||
\(711\) | 24950.3 | + | 31286.7i | 1.31605 | + | 1.65027i | ||||
\(712\) | 4692.62 | − | 5884.35i | 0.246999 | − | 0.309727i | ||||
\(713\) | 18973.9 | + | 9137.33i | 0.996601 | + | 0.479938i | ||||
\(714\) | −6869.10 | − | 30095.5i | −0.360042 | − | 1.57745i | ||||
\(715\) | 4797.67 | + | 21020.0i | 0.250941 | + | 1.09944i | ||||
\(716\) | 6577.15 | − | 8247.49i | 0.343296 | − | 0.430479i | ||||
\(717\) | 19246.7 | − | 9268.72i | 1.00248 | − | 0.482771i | ||||
\(718\) | 5608.70 | − | 24573.3i | 0.291525 | − | 1.27725i | ||||
\(719\) | −19084.0 | + | 9190.38i | −0.989866 | + | 0.476694i | −0.857487 | − | 0.514505i | \(-0.827976\pi\) |
−0.132379 | + | 0.991199i | \(0.542261\pi\) | |||||||
\(720\) | −3340.55 | − | 4188.92i | −0.172910 | − | 0.216822i | ||||
\(721\) | 2431.26 | + | 10652.1i | 0.125583 | + | 0.550213i | ||||
\(722\) | −12549.1 | − | 15736.1i | −0.646856 | − | 0.811132i | ||||
\(723\) | −2582.08 | + | 11312.8i | −0.132820 | + | 0.581921i | ||||
\(724\) | −3460.98 | −0.177661 | ||||||||
\(725\) | −10397.5 | −0.532626 | ||||||||
\(726\) | −9679.39 | + | 42408.2i | −0.494815 | + | 2.16793i | ||||
\(727\) | 18420.3 | − | 23098.4i | 0.939714 | − | 1.17836i | −0.0440742 | − | 0.999028i | \(-0.514034\pi\) |
0.983788 | − | 0.179336i | \(-0.0573948\pi\) | |||||||
\(728\) | 11805.3 | + | 5685.13i | 0.601007 | + | 0.289430i | ||||
\(729\) | 25988.0 | − | 12515.1i | 1.32033 | − | 0.635835i | ||||
\(730\) | 13973.9 | 0.708490 | ||||||||
\(731\) | −18666.8 | − | 8066.46i | −0.944480 | − | 0.408138i | ||||
\(732\) | −29355.5 | −1.48226 | ||||||||
\(733\) | −16007.4 | + | 7708.77i | −0.806613 | + | 0.388444i | −0.791292 | − | 0.611438i | \(-0.790591\pi\) |
−0.0153210 | + | 0.999883i | \(0.504877\pi\) | |||||||
\(734\) | 29545.4 | + | 14228.3i | 1.48575 | + | 0.715500i | ||||
\(735\) | −5424.81 | + | 6802.49i | −0.272241 | + | 0.341379i | ||||
\(736\) | 10074.1 | − | 44137.3i | 0.504531 | − | 2.21049i | ||||
\(737\) | −26605.2 | −1.32974 | ||||||||
\(738\) | −73986.7 | −3.69036 | ||||||||
\(739\) | −4727.61 | + | 20713.0i | −0.235329 | + | 1.03104i | 0.709816 | + | 0.704388i | \(0.248778\pi\) |
−0.945144 | + | 0.326654i | \(0.894079\pi\) | |||||||
\(740\) | 802.294 | + | 1006.04i | 0.0398553 | + | 0.0499769i | ||||
\(741\) | 6040.55 | + | 26465.4i | 0.299467 | + | 1.31205i | ||||
\(742\) | 9379.17 | + | 11761.1i | 0.464043 | + | 0.581892i | ||||
\(743\) | −358.304 | + | 172.550i | −0.0176916 | + | 0.00851984i | −0.442709 | − | 0.896666i | \(-0.645982\pi\) |
0.425017 | + | 0.905185i | \(0.360268\pi\) | |||||||
\(744\) | 2763.83 | − | 12109.1i | 0.136192 | − | 0.596696i | ||||
\(745\) | 16883.2 | − | 8130.54i | 0.830274 | − | 0.399839i | ||||
\(746\) | 15474.8 | − | 19404.8i | 0.759480 | − | 0.952358i | ||||
\(747\) | −6030.00 | − | 26419.2i | −0.295350 | − | 1.29401i | ||||
\(748\) | −9248.20 | − | 40519.0i | −0.452069 | − | 1.98064i | ||||
\(749\) | −16702.6 | − | 8043.54i | −0.814819 | − | 0.392396i | ||||
\(750\) | −27179.1 | + | 34081.6i | −1.32326 | + | 1.65931i | ||||
\(751\) | −3079.45 | − | 3861.50i | −0.149628 | − | 0.187627i | 0.701369 | − | 0.712799i | \(-0.252573\pi\) |
−0.850997 | + | 0.525171i | \(0.824001\pi\) | |||||||
\(752\) | −481.541 | − | 231.898i | −0.0233511 | − | 0.0112453i | ||||
\(753\) | 24096.1 | + | 11604.1i | 1.16615 | + | 0.561589i | ||||
\(754\) | −22727.0 | − | 28498.7i | −1.09770 | − | 1.37648i | ||||
\(755\) | −4451.18 | + | 5581.60i | −0.214563 | + | 0.269053i | ||||
\(756\) | −7639.62 | − | 3679.05i | −0.367527 | − | 0.176992i | ||||
\(757\) | −7236.34 | − | 31704.5i | −0.347436 | − | 1.52222i | −0.782978 | − | 0.622049i | \(-0.786300\pi\) |
0.435542 | − | 0.900168i | \(-0.356557\pi\) | |||||||
\(758\) | 3030.48 | + | 13277.4i | 0.145214 | + | 0.636224i | ||||
\(759\) | 48471.2 | − | 60780.9i | 2.31804 | − | 2.90673i | ||||
\(760\) | −3676.24 | + | 1770.38i | −0.175462 | + | 0.0844980i | ||||
\(761\) | 624.900 | − | 2737.87i | 0.0297669 | − | 0.130417i | −0.957861 | − | 0.287231i | \(-0.907265\pi\) |
0.987628 | + | 0.156814i | \(0.0501223\pi\) | |||||||
\(762\) | −7131.36 | + | 3434.28i | −0.339032 | + | 0.163269i | ||||
\(763\) | −5882.00 | − | 7375.80i | −0.279086 | − | 0.349963i | ||||
\(764\) | −763.351 | − | 3344.46i | −0.0361480 | − | 0.158375i | ||||
\(765\) | 9128.63 | + | 11446.9i | 0.431433 | + | 0.541000i | ||||
\(766\) | −4523.98 | + | 19820.8i | −0.213392 | + | 0.934929i | ||||
\(767\) | 4732.54 | 0.222793 | ||||||||
\(768\) | −7926.35 | −0.372419 | ||||||||
\(769\) | 545.763 | − | 2391.14i | 0.0255926 | − | 0.112129i | −0.960518 | − | 0.278217i | \(-0.910257\pi\) |
0.986111 | + | 0.166088i | \(0.0531137\pi\) | |||||||
\(770\) | 10121.5 | − | 12692.0i | 0.473708 | − | 0.594011i | ||||
\(771\) | −16549.9 | − | 7970.00i | −0.773060 | − | 0.372286i | ||||
\(772\) | −36656.5 | + | 17652.8i | −1.70893 | + | 0.822978i | ||||
\(773\) | 15873.4 | 0.738584 | 0.369292 | − | 0.929313i | \(-0.379600\pi\) | ||||
0.369292 | + | 0.929313i | \(0.379600\pi\) | |||||||
\(774\) | −37944.1 | + | 20224.5i | −1.76211 | + | 0.939220i | ||||
\(775\) | 9828.49 | 0.455548 | ||||||||
\(776\) | −11863.3 | + | 5713.05i | −0.548797 | + | 0.264287i | ||||
\(777\) | −1703.90 | − | 820.554i | −0.0786705 | − | 0.0378857i | ||||
\(778\) | −36733.7 | + | 46062.6i | −1.69276 | + | 2.12265i | ||||
\(779\) | 5155.39 | − | 22587.2i | 0.237113 | − | 1.03886i | ||||
\(780\) | −37666.9 | −1.72909 | ||||||||
\(781\) | 7928.79 | 0.363271 | ||||||||
\(782\) | −13716.9 | + | 60097.5i | −0.627256 | + | 2.74819i | ||||
\(783\) | 4315.16 | + | 5411.04i | 0.196949 | + | 0.246966i | ||||
\(784\) | −1111.62 | − | 4870.30i | −0.0506384 | − | 0.221862i | ||||
\(785\) | 7059.22 | + | 8851.98i | 0.320961 | + | 0.402472i | ||||
\(786\) | 51954.1 | − | 25019.8i | 2.35769 | − | 1.13540i | ||||
\(787\) | 1267.47 | − | 5553.16i | 0.0574086 | − | 0.251523i | −0.938078 | − | 0.346423i | \(-0.887396\pi\) |
0.995487 | + | 0.0949001i | \(0.0302532\pi\) | |||||||
\(788\) | 23010.7 | − | 11081.4i | 1.04026 | − | 0.500961i | ||||
\(789\) | −12988.6 | + | 16287.2i | −0.586066 | + | 0.734904i | ||||
\(790\) | −6602.98 | − | 28929.5i | −0.297371 | − | 1.30287i | ||||
\(791\) | 3732.16 | + | 16351.7i | 0.167763 | + | 0.735017i | ||||
\(792\) | −23230.2 | − | 11187.1i | −1.04224 | − | 0.501914i | ||||
\(793\) | 14897.3 | − | 18680.7i | 0.667112 | − | 0.836532i | ||||
\(794\) | 24409.4 | + | 30608.4i | 1.09100 | + | 1.36807i | ||||
\(795\) | −11431.3 | − | 5505.04i | −0.509972 | − | 0.245589i | ||||
\(796\) | 5439.31 | + | 2619.44i | 0.242200 | + | 0.116637i | ||||
\(797\) | −1374.15 | − | 1723.13i | −0.0610726 | − | 0.0765826i | 0.750357 | − | 0.661033i | \(-0.229882\pi\) |
−0.811430 | + | 0.584450i | \(0.801310\pi\) | |||||||
\(798\) | 12743.6 | − | 15980.0i | 0.565313 | − | 0.708880i | ||||
\(799\) | 1315.90 | + | 633.702i | 0.0582641 | + | 0.0280585i | ||||
\(800\) | −4701.60 | − | 20599.1i | −0.207783 | − | 0.910358i | ||||
\(801\) | −3979.00 | − | 17433.1i | −0.175519 | − | 0.769001i | ||||
\(802\) | −28.3676 | + | 35.5718i | −0.00124899 | + | 0.00156619i | ||||
\(803\) | −24912.3 | + | 11997.2i | −1.09482 | + | 0.527236i | ||||
\(804\) | 10342.8 | − | 45314.8i | 0.453685 | − | 1.98772i | ||||
\(805\) | −12711.4 | + | 6121.48i | −0.556543 | + | 0.268017i | ||||
\(806\) | 21483.2 | + | 26939.1i | 0.938851 | + | 1.17728i | ||||
\(807\) | 6557.33 | + | 28729.5i | 0.286033 | + | 1.25319i | ||||
\(808\) | −1816.79 | − | 2278.19i | −0.0791021 | − | 0.0991909i | ||||
\(809\) | 55.1690 | − | 241.711i | 0.00239757 | − | 0.0105045i | −0.973715 | − | 0.227770i | \(-0.926857\pi\) |
0.976113 | + | 0.217265i | \(0.0697137\pi\) | |||||||
\(810\) | −11889.4 | −0.515743 | ||||||||
\(811\) | −16460.2 | −0.712694 | −0.356347 | − | 0.934354i | \(-0.615978\pi\) | ||||
−0.356347 | + | 0.934354i | \(0.615978\pi\) | |||||||
\(812\) | −3578.57 | + | 15678.8i | −0.154659 | + | 0.677606i | ||||
\(813\) | −33467.7 | + | 41967.2i | −1.44374 | + | 1.81040i | ||||
\(814\) | −3915.01 | − | 1885.37i | −0.168576 | − | 0.0811820i | ||||
\(815\) | −5755.15 | + | 2771.53i | −0.247355 | + | 0.119120i | ||||
\(816\) | −14948.9 | −0.641320 | ||||||||
\(817\) | −3530.36 | − | 12993.1i | −0.151177 | − | 0.556392i | ||||
\(818\) | −33066.7 | −1.41339 | ||||||||
\(819\) | 28047.5 | − | 13507.0i | 1.19665 | − | 0.576278i | ||||
\(820\) | 28963.7 | + | 13948.2i | 1.23348 | + | 0.594015i | ||||
\(821\) | 16611.5 | − | 20830.2i | 0.706147 | − | 0.885480i | −0.291319 | − | 0.956626i | \(-0.594094\pi\) |
0.997466 | + | 0.0711457i | \(0.0226655\pi\) | |||||||
\(822\) | 16291.1 | − | 71376.2i | 0.691264 | − | 3.02863i | ||||
\(823\) | 13805.3 | 0.584716 | 0.292358 | − | 0.956309i | \(-0.405560\pi\) | ||||
0.292358 | + | 0.956309i | \(0.405560\pi\) | |||||||
\(824\) | −12868.0 | −0.544026 | ||||||||
\(825\) | 8073.58 | − | 35372.7i | 0.340710 | − | 1.49275i | ||||
\(826\) | −2221.68 | − | 2785.90i | −0.0935862 | − | 0.117353i | ||||
\(827\) | 9414.54 | + | 41247.8i | 0.395859 | + | 1.73437i | 0.643432 | + | 0.765504i | \(0.277510\pi\) |
−0.247572 | + | 0.968869i | \(0.579633\pi\) | |||||||
\(828\) | 47618.9 | + | 59712.2i | 1.99864 | + | 2.50621i | ||||
\(829\) | −1086.89 | + | 523.421i | −0.0455361 | + | 0.0219290i | −0.456513 | − | 0.889717i | \(-0.650902\pi\) |
0.410977 | + | 0.911646i | \(0.365188\pi\) | |||||||
\(830\) | −4471.36 | + | 19590.3i | −0.186992 | + | 0.819265i | ||||
\(831\) | −23555.7 | + | 11343.8i | −0.983318 | + | 0.473541i | ||||
\(832\) | 36655.8 | − | 45964.9i | 1.52742 | − | 1.91532i | ||||
\(833\) | 3037.68 | + | 13309.0i | 0.126350 | + | 0.553575i | ||||
\(834\) | 4200.21 | + | 18402.3i | 0.174390 | + | 0.764053i | ||||
\(835\) | −12055.8 | − | 5805.78i | −0.499651 | − | 0.240619i | ||||
\(836\) | 17157.4 | − | 21514.6i | 0.709808 | − | 0.890071i | ||||
\(837\) | −4079.00 | − | 5114.91i | −0.168448 | − | 0.211227i | ||||
\(838\) | 433.492 | + | 208.759i | 0.0178696 | + | 0.00860554i | ||||
\(839\) | −20817.5 | − | 10025.2i | −0.856617 | − | 0.412525i | −0.0465873 | − | 0.998914i | \(-0.514835\pi\) |
−0.810029 | + | 0.586389i | \(0.800549\pi\) | |||||||
\(840\) | 5188.08 | + | 6505.65i | 0.213102 | + | 0.267222i | ||||
\(841\) | −7022.15 | + | 8805.49i | −0.287923 | + | 0.361044i | ||||
\(842\) | 35329.9 | + | 17014.0i | 1.44602 | + | 0.696366i | ||||
\(843\) | 477.163 | + | 2090.59i | 0.0194951 | + | 0.0854136i | ||||
\(844\) | 12441.9 | + | 54511.7i | 0.507428 | + | 2.22319i | ||||
\(845\) | 11098.8 | − | 13917.5i | 0.451848 | − | 0.566600i | ||||
\(846\) | 2782.40 | − | 1339.93i | 0.113074 | − | 0.0544537i | ||||
\(847\) | −3475.87 | + | 15228.8i | −0.141006 | + | 0.617789i | ||||
\(848\) | 6563.35 | − | 3160.74i | 0.265786 | − | 0.127996i | ||||
\(849\) | 23204.9 | + | 29098.0i | 0.938034 | + | 1.17626i | ||||
\(850\) | 6401.71 | + | 28047.7i | 0.258326 | + | 1.13180i | ||||
\(851\) | 2354.60 | + | 2952.58i | 0.0948470 | + | 0.118934i | ||||
\(852\) | −3082.32 | + | 13504.5i | −0.123942 | + | 0.543025i | ||||
\(853\) | −16448.8 | −0.660253 | −0.330126 | − | 0.943937i | \(-0.607091\pi\) | ||||
−0.330126 | + | 0.943937i | \(0.607091\pi\) | |||||||
\(854\) | −17990.3 | −0.720860 | ||||||||
\(855\) | −2157.16 | + | 9451.12i | −0.0862845 | + | 0.378037i | ||||
\(856\) | 13613.0 | − | 17070.1i | 0.543553 | − | 0.681594i | ||||
\(857\) | −32256.1 | − | 15533.7i | −1.28570 | − | 0.619162i | −0.338854 | − | 0.940839i | \(-0.610039\pi\) |
−0.946850 | + | 0.321676i | \(0.895754\pi\) | |||||||
\(858\) | 114601. | − | 55188.9i | 4.55992 | − | 2.19594i | ||||
\(859\) | −10727.9 | −0.426113 | −0.213057 | − | 0.977040i | \(-0.568342\pi\) | ||||
−0.213057 | + | 0.977040i | \(0.568342\pi\) | |||||||
\(860\) | 18666.9 | − | 763.996i | 0.740157 | − | 0.0302931i | ||||
\(861\) | −47247.0 | −1.87012 | ||||||||
\(862\) | 64474.4 | − | 31049.2i | 2.54757 | − | 1.22685i | ||||
\(863\) | −15262.1 | − | 7349.84i | −0.602003 | − | 0.289909i | 0.107953 | − | 0.994156i | \(-0.465571\pi\) |
−0.709955 | + | 0.704247i | \(0.751285\pi\) | |||||||
\(864\) | −8768.84 | + | 10995.8i | −0.345280 | + | 0.432967i | ||||
\(865\) | 1525.20 | − | 6682.34i | 0.0599519 | − | 0.262666i | ||||
\(866\) | 54344.4 | 2.13244 | ||||||||
\(867\) | 2262.05 | 0.0886082 | ||||||||
\(868\) | 3382.73 | − | 14820.7i | 0.132278 | − | 0.579548i | ||||
\(869\) | 36608.8 | + | 45906.0i | 1.42908 | + | 1.79201i | ||||
\(870\) | −5151.03 | − | 22568.1i | −0.200731 | − | 0.879461i | ||||
\(871\) | 23587.7 | + | 29578.1i | 0.917611 | + | 1.15065i | ||||
\(872\) | 10010.5 | − | 4820.79i | 0.388758 | − | 0.187216i | ||||
\(873\) | −6961.17 | + | 30498.9i | −0.269874 | + | 1.18240i | ||||
\(874\) | −36772.9 | + | 17708.9i | −1.42318 | + | 0.685369i | ||||
\(875\) | −9760.04 | + | 12238.7i | −0.377085 | + | 0.472850i | ||||
\(876\) | −10749.2 | − | 47095.3i | −0.414591 | − | 1.81644i | ||||
\(877\) | 2082.36 | + | 9123.42i | 0.0801782 | + | 0.351284i | 0.999065 | − | 0.0432381i | \(-0.0137674\pi\) |
−0.918887 | + | 0.394522i | \(0.870910\pi\) | |||||||
\(878\) | 62071.1 | + | 29891.9i | 2.38587 | + | 1.14898i | ||||
\(879\) | 32497.9 | − | 40751.1i | 1.24702 | − | 1.56371i | ||||
\(880\) | −4901.48 | − | 6146.27i | −0.187760 | − | 0.235444i | ||||
\(881\) | −10545.5 | − | 5078.44i | −0.403276 | − | 0.194208i | 0.221240 | − | 0.975219i | \(-0.428990\pi\) |
−0.624516 | + | 0.781012i | \(0.714704\pi\) | |||||||
\(882\) | 26006.3 | + | 12524.0i | 0.992833 | + | 0.478123i | ||||
\(883\) | 2054.08 | + | 2575.74i | 0.0782847 | + | 0.0981659i | 0.819432 | − | 0.573177i | \(-0.194289\pi\) |
−0.741147 | + | 0.671343i | \(0.765718\pi\) | |||||||
\(884\) | −36847.3 | + | 46205.0i | −1.40193 | + | 1.75797i | ||||
\(885\) | 2707.79 | + | 1304.00i | 0.102849 | + | 0.0495294i | ||||
\(886\) | −7873.71 | − | 34497.0i | −0.298558 | − | 1.30807i | ||||
\(887\) | −4359.88 | − | 19101.9i | −0.165040 | − | 0.723088i | −0.987932 | − | 0.154889i | \(-0.950498\pi\) |
0.822892 | − | 0.568198i | \(-0.192359\pi\) | |||||||
\(888\) | 1388.71 | − | 1741.39i | 0.0524799 | − | 0.0658077i | ||||
\(889\) | −2560.87 | + | 1233.25i | −0.0966130 | + | 0.0465264i | ||||
\(890\) | −2950.51 | + | 12927.0i | −0.111125 | + | 0.486870i | ||||
\(891\) | 21196.2 | − | 10207.5i | 0.796968 | − | 0.383800i | ||||
\(892\) | −9937.76 | − | 12461.6i | −0.373028 | − | 0.467762i | ||||
\(893\) | 215.187 | + | 942.798i | 0.00806380 | + | 0.0353298i | ||||
\(894\) | −68927.8 | − | 86432.7i | −2.57862 | − | 3.23349i | ||||
\(895\) | −1213.33 | + | 5315.95i | −0.0453153 | + | 0.198539i | ||||
\(896\) | −21174.3 | −0.789490 | ||||||||
\(897\) | −110546. | −4.11486 | ||||||||
\(898\) | −7488.26 | + | 32808.2i | −0.278270 | + | 1.21918i | ||||
\(899\) | −7736.26 | + | 9700.96i | −0.287006 | + | 0.359894i | ||||
\(900\) | 32114.5 | + | 15465.5i | 1.18942 | + | 0.572797i | ||||
\(901\) | −17935.5 | + | 8637.28i | −0.663172 | + | 0.319367i | ||||
\(902\) | −108558. | −4.00731 | ||||||||
\(903\) | −24230.7 | + | 12915.1i | −0.892964 | + | 0.475957i | ||||
\(904\) | −19753.3 | −0.726752 | ||||||||
\(905\) | 1611.79 | − | 776.198i | 0.0592019 | − | 0.0285101i | ||||
\(906\) | 37946.7 | + | 18274.2i | 1.39150 | + | 0.670109i | ||||
\(907\) | −20851.5 | + | 26146.9i | −0.763353 | + | 0.957214i | −0.999896 | − | 0.0144066i | \(-0.995414\pi\) |
0.236543 | + | 0.971621i | \(0.423985\pi\) | |||||||
\(908\) | 748.564 | − | 3279.67i | 0.0273590 | − | 0.119868i | ||||
\(909\) | −6922.98 | −0.252608 | ||||||||
\(910\) | −23083.8 | −0.840901 | ||||||||
\(911\) | 7096.97 | − | 31093.8i | 0.258104 | − | 1.13083i | −0.665171 | − | 0.746691i | \(-0.731642\pi\) |
0.923276 | − | 0.384138i | \(-0.125501\pi\) | |||||||
\(912\) | −6171.26 | − | 7738.51i | −0.224069 | − | 0.280973i | ||||
\(913\) | −8847.63 | − | 38764.0i | −0.320716 | − | 1.40515i | ||||
\(914\) | −16267.4 | − | 20398.7i | −0.588708 | − | 0.738216i | ||||
\(915\) | 13671.0 | − | 6583.59i | 0.493933 | − | 0.237865i | ||||
\(916\) | −9787.65 | + | 42882.5i | −0.353049 | + | 1.54681i | ||||
\(917\) | 18656.7 | − | 8984.61i | 0.671864 | − | 0.323553i | ||||
\(918\) | 11939.7 | − | 14971.9i | 0.429268 | − | 0.538284i | ||||
\(919\) | −3525.42 | − | 15445.9i | −0.126543 | − | 0.554420i | −0.997958 | − | 0.0638738i | \(-0.979654\pi\) |
0.871415 | − | 0.490546i | \(-0.163203\pi\) | |||||||
\(920\) | −3697.46 | − | 16199.6i | −0.132502 | − | 0.580528i | ||||
\(921\) | −49281.3 | − | 23732.6i | −1.76316 | − | 0.849095i | ||||
\(922\) | 40150.0 | − | 50346.5i | 1.43413 | − | 1.79835i | ||||
\(923\) | −7029.52 | − | 8814.74i | −0.250682 | − | 0.314345i | ||||
\(924\) | −50560.9 | − | 24348.8i | −1.80014 | − | 0.866902i | ||||
\(925\) | 1587.96 | + | 764.721i | 0.0564452 | + | 0.0271826i | ||||
\(926\) | −23909.9 | − | 29982.1i | −0.848519 | − | 1.06401i | ||||
\(927\) | −19061.5 | + | 23902.4i | −0.675363 | + | 0.846879i | ||||
\(928\) | 24032.5 | + | 11573.4i | 0.850114 | + | 0.409393i | ||||
\(929\) | 1251.48 | + | 5483.09i | 0.0441977 | + | 0.193643i | 0.992207 | − | 0.124599i | \(-0.0397646\pi\) |
−0.948009 | + | 0.318242i | \(0.896907\pi\) | |||||||
\(930\) | 4869.13 | + | 21333.0i | 0.171683 | + | 0.752192i | ||||
\(931\) | −5635.54 | + | 7066.74i | −0.198386 | + | 0.248768i | ||||
\(932\) | 56496.1 | − | 27207.1i | 1.98561 | − | 0.956221i | ||||
\(933\) | 2677.91 | − | 11732.7i | 0.0939668 | − | 0.411695i | ||||
\(934\) | −838.592 | + | 403.845i | −0.0293786 | + | 0.0141480i | ||||
\(935\) | 13394.2 | + | 16795.7i | 0.468488 | + | 0.587465i | ||||
\(936\) | 8158.39 | + | 35744.2i | 0.284899 | + | 1.24822i | ||||
\(937\) | 15576.5 | + | 19532.3i | 0.543075 | + | 0.680994i | 0.975329 | − | 0.220758i | \(-0.0708530\pi\) |
−0.432254 | + | 0.901752i | \(0.642282\pi\) | |||||||
\(938\) | 6338.49 | − | 27770.7i | 0.220639 | − | 0.966681i | ||||
\(939\) | 62610.2 | 2.17594 | ||||||||
\(940\) | −1341.84 | −0.0465595 | ||||||||
\(941\) | 536.217 | − | 2349.32i | 0.0185762 | − | 0.0813876i | −0.964790 | − | 0.263021i | \(-0.915281\pi\) |
0.983366 | + | 0.181633i | \(0.0581384\pi\) | |||||||
\(942\) | 41646.2 | − | 52222.7i | 1.44045 | − | 1.80627i | ||||
\(943\) | 85003.9 | + | 40935.7i | 2.93543 | + | 1.41363i | ||||
\(944\) | −1554.69 | + | 748.698i | −0.0536025 | + | 0.0258136i | ||||
\(945\) | 4382.90 | 0.150874 | ||||||||
\(946\) | −55674.3 | + | 29674.8i | −1.91345 | + | 1.01989i | ||||
\(947\) | 13276.4 | 0.455569 | 0.227785 | − | 0.973712i | \(-0.426852\pi\) | ||||
0.227785 | + | 0.973712i | \(0.426852\pi\) | |||||||
\(948\) | −92420.0 | + | 44507.1i | −3.16631 | + | 1.52482i | ||||
\(949\) | 35424.5 | + | 17059.6i | 1.21173 | + | 0.583537i | ||||
\(950\) | −11876.5 | + | 14892.7i | −0.405605 | + | 0.508613i | ||||
\(951\) | 6369.63 | − | 27907.2i | 0.217192 | − | 0.951580i | ||||
\(952\) | 13055.5 | 0.444466 | ||||||||
\(953\) | −16222.6 | −0.551418 | −0.275709 | − | 0.961241i | \(-0.588913\pi\) | ||||
−0.275709 | + | 0.961241i | \(0.588913\pi\) | |||||||
\(954\) | −9366.39 | + | 41036.8i | −0.317870 | + | 1.39268i | ||||
\(955\) | 1105.56 | + | 1386.33i | 0.0374608 | + | 0.0469744i | ||||
\(956\) | 6852.08 | + | 30020.9i | 0.231812 | + | 1.01563i | ||||
\(957\) | 28558.8 | + | 35811.5i | 0.964653 | + | 1.20964i | ||||
\(958\) | −32356.0 | + | 15581.8i | −1.09120 | + | 0.525496i | ||||
\(959\) | 5850.16 | − | 25631.2i | 0.196988 | − | 0.863060i | ||||
\(960\) | 33638.2 | − | 16199.3i | 1.13091 | − | 0.544615i | ||||
\(961\) | −11261.5 | + | 14121.5i | −0.378017 | + | 0.474018i | ||||
\(962\) | 1374.94 | + | 6024.00i | 0.0460809 | + | 0.201894i | ||||
\(963\) | −11542.8 | − | 50572.3i | −0.386253 | − | 1.69229i | ||||
\(964\) | −15070.0 | − | 7257.34i | −0.503499 | − | 0.242472i | ||||
\(965\) | 13112.0 | − | 16442.0i | 0.437400 | − | 0.548483i | ||||
\(966\) | 51895.7 | + | 65075.2i | 1.72849 | + | 2.16745i | ||||
\(967\) | −20364.0 | − | 9806.79i | −0.677210 | − | 0.326127i | 0.0634712 | − | 0.997984i | \(-0.479783\pi\) |
−0.740681 | + | 0.671856i | \(0.765497\pi\) | |||||||
\(968\) | −16574.9 | − | 7982.07i | −0.550350 | − | 0.265035i | ||||
\(969\) | 16864.0 | + | 21146.8i | 0.559083 | + | 0.701067i | ||||
\(970\) | 14463.2 | − | 18136.2i | 0.478747 | − | 0.600330i | ||||
\(971\) | −7401.75 | − | 3564.49i | −0.244628 | − | 0.117806i | 0.307553 | − | 0.951531i | \(-0.400490\pi\) |
−0.552181 | + | 0.833724i | \(0.686204\pi\) | |||||||
\(972\) | 13254.8 | + | 58073.2i | 0.437396 | + | 1.91636i | ||||
\(973\) | 1508.30 | + | 6608.28i | 0.0496955 | + | 0.217730i | ||||
\(974\) | 23697.9 | − | 29716.3i | 0.779600 | − | 0.977588i | ||||
\(975\) | −46483.1 | + | 22385.1i | −1.52682 | + | 0.735278i | ||||
\(976\) | −1938.60 | + | 8493.58i | −0.0635791 | + | 0.278558i | ||||
\(977\) | −12344.4 | + | 5944.76i | −0.404230 | + | 0.194667i | −0.624941 | − | 0.780672i | \(-0.714877\pi\) |
0.220710 | + | 0.975339i | \(0.429163\pi\) | |||||||
\(978\) | 23496.1 | + | 29463.2i | 0.768223 | + | 0.963321i | ||||
\(979\) | −5838.26 | − | 25579.1i | −0.190594 | − | 0.835047i | ||||
\(980\) | −7819.69 | − | 9805.58i | −0.254889 | − | 0.319620i | ||||
\(981\) | 5873.99 | − | 25735.6i | 0.191174 | − | 0.837589i | ||||
\(982\) | −34170.3 | −1.11040 | ||||||||
\(983\) | −35295.3 | −1.14521 | −0.572606 | − | 0.819830i | \(-0.694068\pi\) | ||||
−0.572606 | + | 0.819830i | \(0.694068\pi\) | |||||||
\(984\) | 12382.1 | − | 54249.5i | 0.401145 | − | 1.75753i | ||||
\(985\) | −8230.92 | + | 10321.3i | −0.266253 | + | 0.333871i | ||||
\(986\) | −32722.7 | − | 15758.4i | −1.05690 | − | 0.508976i | ||||
\(987\) | 1776.81 | − | 855.664i | 0.0573012 | − | 0.0275948i | ||||
\(988\) | −39130.1 | −1.26001 | ||||||||
\(989\) | 54784.2 | − | 2242.21i | 1.76141 | − | 0.0720910i | ||||
\(990\) | 45423.8 | 1.45825 | ||||||||
\(991\) | −9087.17 | + | 4376.15i | −0.291285 | + | 0.140275i | −0.573820 | − | 0.818982i | \(-0.694539\pi\) |
0.282535 | + | 0.959257i | \(0.408825\pi\) | |||||||
\(992\) | −22717.3 | − | 10940.1i | −0.727091 | − | 0.350149i | ||||
\(993\) | 25609.8 | − | 32113.7i | 0.818432 | − | 1.02628i | ||||
\(994\) | −1888.97 | + | 8276.13i | −0.0602762 | + | 0.264087i | ||||
\(995\) | −3120.57 | −0.0994259 | ||||||||
\(996\) | 69463.5 | 2.20987 | ||||||||
\(997\) | −3269.01 | + | 14322.5i | −0.103842 | + | 0.454962i | 0.896096 | + | 0.443860i | \(0.146391\pi\) |
−0.999938 | + | 0.0111022i | \(0.996466\pi\) | |||||||
\(998\) | −47908.6 | − | 60075.5i | −1.51956 | − | 1.90547i | ||||
\(999\) | −261.059 | − | 1143.77i | −0.00826780 | − | 0.0362236i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 43.4.e.a.41.2 | yes | 60 | |
43.8 | odd | 14 | 1849.4.a.g.1.5 | 30 | |||
43.21 | even | 7 | inner | 43.4.e.a.21.2 | ✓ | 60 | |
43.35 | even | 7 | 1849.4.a.h.1.26 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.21.2 | ✓ | 60 | 43.21 | even | 7 | inner | |
43.4.e.a.41.2 | yes | 60 | 1.1 | even | 1 | trivial | |
1849.4.a.g.1.5 | 30 | 43.8 | odd | 14 | |||
1849.4.a.h.1.26 | 30 | 43.35 | even | 7 |