Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(47,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.47");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.s (of order \(6\), degree \(2\), 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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.9 | ||
Character | \(\chi\) | \(=\) | 63.47 |
Dual form | 63.4.s.a.59.9 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.54833 | + | 0.893930i | −0.547418 | + | 0.316052i | −0.748080 | − | 0.663609i | \(-0.769024\pi\) |
0.200662 | + | 0.979661i | \(0.435691\pi\) | |||||||
\(3\) | 5.18374 | + | 0.358957i | 0.997611 | + | 0.0690814i | ||||
\(4\) | −2.40178 | + | 4.16000i | −0.300222 | + | 0.520000i | ||||
\(5\) | −16.9434 | −1.51546 | −0.757730 | − | 0.652568i | \(-0.773692\pi\) | ||||
−0.757730 | + | 0.652568i | \(0.773692\pi\) | |||||||
\(6\) | −8.34703 | + | 4.07812i | −0.567944 | + | 0.277481i | ||||
\(7\) | −9.83512 | + | 15.6930i | −0.531046 | + | 0.847343i | ||||
\(8\) | − | 22.8910i | − | 1.01165i | ||||||
\(9\) | 26.7423 | + | 3.72148i | 0.990456 | + | 0.137833i | ||||
\(10\) | 26.2340 | − | 15.1462i | 0.829591 | − | 0.478964i | ||||
\(11\) | 7.14600i | 0.195873i | 0.995193 | + | 0.0979364i | \(0.0312242\pi\) | ||||
−0.995193 | + | 0.0979364i | \(0.968776\pi\) | |||||||
\(12\) | −13.9435 | + | 20.7022i | −0.335427 | + | 0.498018i | ||||
\(13\) | −67.0144 | + | 38.6908i | −1.42973 | + | 0.825453i | −0.997099 | − | 0.0761201i | \(-0.975747\pi\) |
−0.432627 | + | 0.901573i | \(0.642413\pi\) | |||||||
\(14\) | 1.19958 | − | 33.0899i | 0.0229001 | − | 0.631689i | ||||
\(15\) | −87.8300 | − | 6.08194i | −1.51184 | − | 0.104690i | ||||
\(16\) | 1.24870 | + | 2.16282i | 0.0195110 | + | 0.0337941i | ||||
\(17\) | 1.06481 | + | 1.84430i | 0.0151914 | + | 0.0263122i | 0.873521 | − | 0.486786i | \(-0.161831\pi\) |
−0.858330 | + | 0.513098i | \(0.828498\pi\) | |||||||
\(18\) | −44.7327 | + | 18.1437i | −0.585756 | + | 0.237583i | ||||
\(19\) | 104.730 | + | 60.4661i | 1.26457 | + | 0.730099i | 0.973955 | − | 0.226741i | \(-0.0728072\pi\) |
0.290614 | + | 0.956840i | \(0.406141\pi\) | |||||||
\(20\) | 40.6942 | − | 70.4844i | 0.454975 | − | 0.788040i | ||||
\(21\) | −56.6158 | + | 77.8181i | −0.588313 | + | 0.808633i | ||||
\(22\) | −6.38802 | − | 11.0644i | −0.0619060 | − | 0.107224i | ||||
\(23\) | 10.8686i | 0.0985329i | 0.998786 | + | 0.0492664i | \(0.0156883\pi\) | ||||
−0.998786 | + | 0.0492664i | \(0.984312\pi\) | |||||||
\(24\) | 8.21688 | − | 118.661i | 0.0698860 | − | 1.00923i | ||||
\(25\) | 162.077 | 1.29662 | ||||||||
\(26\) | 69.1737 | − | 119.812i | 0.521772 | − | 0.903736i | ||||
\(27\) | 137.289 | + | 28.8905i | 0.978568 | + | 0.205925i | ||||
\(28\) | −41.6612 | − | 78.6052i | −0.281186 | − | 0.530535i | ||||
\(29\) | −110.704 | − | 63.9149i | −0.708869 | − | 0.409266i | 0.101773 | − | 0.994808i | \(-0.467548\pi\) |
−0.810642 | + | 0.585542i | \(0.800882\pi\) | |||||||
\(30\) | 141.427 | − | 69.0970i | 0.860696 | − | 0.420511i | ||||
\(31\) | 184.393 | + | 106.459i | 1.06832 | + | 0.616796i | 0.927723 | − | 0.373270i | \(-0.121764\pi\) |
0.140600 | + | 0.990067i | \(0.455097\pi\) | |||||||
\(32\) | 154.726 | + | 89.3314i | 0.854751 | + | 0.493491i | ||||
\(33\) | −2.56511 | + | 37.0430i | −0.0135312 | + | 0.195405i | ||||
\(34\) | −3.29735 | − | 1.90372i | −0.0166321 | − | 0.00960253i | ||||
\(35\) | 166.640 | − | 265.892i | 0.804780 | − | 1.28411i | ||||
\(36\) | −79.7104 | + | 102.310i | −0.369030 | + | 0.473657i | ||||
\(37\) | −12.2062 | + | 21.1417i | −0.0542346 | + | 0.0939371i | −0.891868 | − | 0.452296i | \(-0.850605\pi\) |
0.837634 | + | 0.546233i | \(0.183939\pi\) | |||||||
\(38\) | −216.210 | −0.922997 | ||||||||
\(39\) | −361.273 | + | 176.507i | −1.48333 | + | 0.724713i | ||||
\(40\) | 387.850i | 1.53311i | ||||||||
\(41\) | −64.8686 | − | 112.356i | −0.247092 | − | 0.427976i | 0.715626 | − | 0.698484i | \(-0.246142\pi\) |
−0.962718 | + | 0.270508i | \(0.912808\pi\) | |||||||
\(42\) | 18.0962 | − | 171.099i | 0.0664833 | − | 0.628598i | ||||
\(43\) | 86.4878 | − | 149.801i | 0.306727 | − | 0.531267i | −0.670917 | − | 0.741532i | \(-0.734099\pi\) |
0.977644 | + | 0.210265i | \(0.0674327\pi\) | |||||||
\(44\) | −29.7274 | − | 17.1631i | −0.101854 | − | 0.0588053i | ||||
\(45\) | −453.104 | − | 63.0544i | −1.50100 | − | 0.208880i | ||||
\(46\) | −9.71576 | − | 16.8282i | −0.0311415 | − | 0.0539387i | ||||
\(47\) | 202.426 | + | 350.613i | 0.628232 | + | 1.08813i | 0.987906 | + | 0.155052i | \(0.0495546\pi\) |
−0.359674 | + | 0.933078i | \(0.617112\pi\) | |||||||
\(48\) | 5.69660 | + | 11.6597i | 0.0171299 | + | 0.0350612i | ||||
\(49\) | −149.541 | − | 308.685i | −0.435979 | − | 0.899957i | ||||
\(50\) | −250.950 | + | 144.886i | −0.709793 | + | 0.409799i | ||||
\(51\) | 4.85765 | + | 9.94258i | 0.0133374 | + | 0.0272988i | ||||
\(52\) | − | 371.706i | − | 0.991277i | ||||||
\(53\) | −291.479 | + | 168.286i | −0.755429 | + | 0.436147i | −0.827652 | − | 0.561241i | \(-0.810324\pi\) |
0.0722231 | + | 0.997388i | \(0.476991\pi\) | |||||||
\(54\) | −238.396 | + | 77.9949i | −0.600769 | + | 0.196551i | ||||
\(55\) | − | 121.077i | − | 0.296837i | ||||||
\(56\) | 359.228 | + | 225.135i | 0.857212 | + | 0.537232i | ||||
\(57\) | 521.190 | + | 351.034i | 1.21111 | + | 0.815713i | ||||
\(58\) | 228.542 | 0.517397 | ||||||||
\(59\) | −330.799 | + | 572.960i | −0.729938 | + | 1.26429i | 0.226971 | + | 0.973901i | \(0.427118\pi\) |
−0.956909 | + | 0.290388i | \(0.906216\pi\) | |||||||
\(60\) | 236.249 | − | 350.765i | 0.508327 | − | 0.754727i | ||||
\(61\) | −300.606 | + | 173.555i | −0.630961 | + | 0.364286i | −0.781124 | − | 0.624376i | \(-0.785353\pi\) |
0.150163 | + | 0.988661i | \(0.452020\pi\) | |||||||
\(62\) | −380.669 | −0.779759 | ||||||||
\(63\) | −321.415 | + | 383.066i | −0.642769 | + | 0.766060i | ||||
\(64\) | −339.403 | −0.662897 | ||||||||
\(65\) | 1135.45 | − | 655.551i | 2.16669 | − | 1.25094i | ||||
\(66\) | −29.1422 | − | 59.6479i | −0.0543509 | − | 0.111245i | ||||
\(67\) | 134.558 | − | 233.062i | 0.245357 | − | 0.424971i | −0.716875 | − | 0.697202i | \(-0.754428\pi\) |
0.962232 | + | 0.272231i | \(0.0877615\pi\) | |||||||
\(68\) | −10.2297 | −0.0182432 | ||||||||
\(69\) | −3.90136 | + | 56.3399i | −0.00680679 | + | 0.0982975i | ||||
\(70\) | −20.3249 | + | 560.654i | −0.0347042 | + | 0.957300i | ||||
\(71\) | − | 637.224i | − | 1.06514i | −0.846387 | − | 0.532568i | \(-0.821227\pi\) | ||
0.846387 | − | 0.532568i | \(-0.178773\pi\) | |||||||
\(72\) | 85.1883 | − | 612.157i | 0.139438 | − | 1.00199i | ||||
\(73\) | −503.982 | + | 290.974i | −0.808036 | + | 0.466520i | −0.846273 | − | 0.532749i | \(-0.821159\pi\) |
0.0382377 | + | 0.999269i | \(0.487826\pi\) | |||||||
\(74\) | − | 43.6458i | − | 0.0685638i | ||||||
\(75\) | 840.167 | + | 58.1789i | 1.29352 | + | 0.0895723i | ||||
\(76\) | −503.078 | + | 290.452i | −0.759303 | + | 0.438384i | ||||
\(77\) | −112.142 | − | 70.2817i | −0.165971 | − | 0.104018i | ||||
\(78\) | 401.586 | − | 596.245i | 0.582957 | − | 0.865532i | ||||
\(79\) | 85.9381 | + | 148.849i | 0.122390 | + | 0.211985i | 0.920710 | − | 0.390248i | \(-0.127611\pi\) |
−0.798320 | + | 0.602234i | \(0.794278\pi\) | |||||||
\(80\) | −21.1572 | − | 36.6454i | −0.0295682 | − | 0.0512135i | ||||
\(81\) | 701.301 | + | 199.042i | 0.962004 | + | 0.273034i | ||||
\(82\) | 200.876 | + | 115.976i | 0.270525 | + | 0.156188i | ||||
\(83\) | −635.597 | + | 1100.89i | −0.840552 | + | 1.45588i | 0.0488762 | + | 0.998805i | \(0.484436\pi\) |
−0.889428 | + | 0.457074i | \(0.848897\pi\) | |||||||
\(84\) | −187.745 | − | 422.423i | −0.243865 | − | 0.548693i | ||||
\(85\) | −18.0414 | − | 31.2486i | −0.0230219 | − | 0.0398751i | ||||
\(86\) | 309.256i | 0.387767i | ||||||||
\(87\) | −550.917 | − | 371.056i | −0.678903 | − | 0.457257i | ||||
\(88\) | 163.579 | 0.198154 | ||||||||
\(89\) | −175.384 | + | 303.774i | −0.208884 | + | 0.361798i | −0.951363 | − | 0.308071i | \(-0.900316\pi\) |
0.742479 | + | 0.669869i | \(0.233650\pi\) | |||||||
\(90\) | 757.923 | − | 307.415i | 0.887689 | − | 0.360048i | ||||
\(91\) | 51.9198 | − | 1432.18i | 0.0598096 | − | 1.64982i | ||||
\(92\) | −45.2133 | − | 26.1039i | −0.0512371 | − | 0.0295818i | ||||
\(93\) | 917.632 | + | 618.047i | 1.02316 | + | 0.689124i | ||||
\(94\) | −626.847 | − | 361.910i | −0.687812 | − | 0.397108i | ||||
\(95\) | −1774.49 | − | 1024.50i | −1.91640 | − | 1.10644i | ||||
\(96\) | 769.995 | + | 518.611i | 0.818618 | + | 0.551359i | ||||
\(97\) | −73.3753 | − | 42.3633i | −0.0768055 | − | 0.0443437i | 0.461105 | − | 0.887345i | \(-0.347453\pi\) |
−0.537911 | + | 0.843002i | \(0.680786\pi\) | |||||||
\(98\) | 507.482 | + | 344.268i | 0.523096 | + | 0.354860i | ||||
\(99\) | −26.5937 | + | 191.100i | −0.0269977 | + | 0.194003i | ||||
\(100\) | −389.274 | + | 674.243i | −0.389274 | + | 0.674243i | ||||
\(101\) | 1647.26 | 1.62285 | 0.811427 | − | 0.584453i | \(-0.198691\pi\) | ||||
0.811427 | + | 0.584453i | \(0.198691\pi\) | |||||||
\(102\) | −16.4092 | − | 11.0520i | −0.0159290 | − | 0.0107286i | ||||
\(103\) | − | 1841.23i | − | 1.76137i | −0.473698 | − | 0.880687i | \(-0.657081\pi\) | ||
0.473698 | − | 0.880687i | \(-0.342919\pi\) | |||||||
\(104\) | 885.669 | + | 1534.02i | 0.835067 | + | 1.44638i | ||||
\(105\) | 959.262 | − | 1318.50i | 0.891566 | − | 1.22545i | ||||
\(106\) | 300.871 | − | 521.124i | 0.275690 | − | 0.477510i | ||||
\(107\) | −377.689 | − | 218.059i | −0.341239 | − | 0.197014i | 0.319581 | − | 0.947559i | \(-0.396458\pi\) |
−0.660820 | + | 0.750545i | \(0.729791\pi\) | |||||||
\(108\) | −449.923 | + | 501.735i | −0.400869 | + | 0.447032i | ||||
\(109\) | 583.379 | + | 1010.44i | 0.512638 | + | 0.887915i | 0.999893 | + | 0.0146552i | \(0.00466507\pi\) |
−0.487255 | + | 0.873260i | \(0.662002\pi\) | |||||||
\(110\) | 108.235 | + | 187.468i | 0.0938160 | + | 0.162494i | ||||
\(111\) | −70.8625 | + | 105.211i | −0.0605943 | + | 0.0899661i | ||||
\(112\) | −46.2223 | − | 1.67566i | −0.0389964 | − | 0.00141370i | ||||
\(113\) | 127.611 | − | 73.6761i | 0.106236 | − | 0.0613351i | −0.445941 | − | 0.895062i | \(-0.647131\pi\) |
0.552176 | + | 0.833727i | \(0.313798\pi\) | |||||||
\(114\) | −1120.78 | − | 77.6101i | −0.920792 | − | 0.0637619i | ||||
\(115\) | − | 184.150i | − | 0.149323i | ||||||
\(116\) | 531.772 | − | 307.019i | 0.425636 | − | 0.245741i | ||||
\(117\) | −1936.10 | + | 785.287i | −1.52985 | + | 0.620511i | ||||
\(118\) | − | 1182.84i | − | 0.922793i | ||||||
\(119\) | −39.4151 | − | 1.42888i | −0.0303628 | − | 0.00110072i | ||||
\(120\) | −139.222 | + | 2010.51i | −0.105909 | + | 1.52945i | ||||
\(121\) | 1279.93 | 0.961634 | ||||||||
\(122\) | 310.292 | − | 537.441i | 0.230266 | − | 0.398833i | ||||
\(123\) | −295.931 | − | 605.708i | −0.216937 | − | 0.444023i | ||||
\(124\) | −885.743 | + | 511.384i | −0.641468 | + | 0.370352i | ||||
\(125\) | −628.217 | −0.449516 | ||||||||
\(126\) | 155.223 | − | 880.436i | 0.109749 | − | 0.622504i | ||||
\(127\) | −29.4522 | −0.0205784 | −0.0102892 | − | 0.999947i | \(-0.503275\pi\) | ||||
−0.0102892 | + | 0.999947i | \(0.503275\pi\) | |||||||
\(128\) | −712.303 | + | 411.248i | −0.491869 | + | 0.283981i | ||||
\(129\) | 502.103 | − | 745.486i | 0.342695 | − | 0.508809i | ||||
\(130\) | −1172.03 | + | 2030.02i | −0.790725 | + | 1.36958i | ||||
\(131\) | −979.694 | −0.653407 | −0.326703 | − | 0.945127i | \(-0.605938\pi\) | ||||
−0.326703 | + | 0.945127i | \(0.605938\pi\) | |||||||
\(132\) | −147.938 | − | 99.6399i | −0.0975482 | − | 0.0657011i | ||||
\(133\) | −1978.93 | + | 1048.84i | −1.29019 | + | 0.683807i | ||||
\(134\) | 481.143i | 0.310182i | ||||||||
\(135\) | −2326.14 | − | 489.503i | −1.48298 | − | 0.312072i | ||||
\(136\) | 42.2178 | − | 24.3744i | 0.0266187 | − | 0.0153683i | ||||
\(137\) | 1243.14i | 0.775244i | 0.921818 | + | 0.387622i | \(0.126703\pi\) | ||||
−0.921818 | + | 0.387622i | \(0.873297\pi\) | |||||||
\(138\) | −44.3233 | − | 90.7204i | −0.0273410 | − | 0.0559611i | ||||
\(139\) | 976.590 | − | 563.835i | 0.595923 | − | 0.344056i | −0.171513 | − | 0.985182i | \(-0.554866\pi\) |
0.767436 | + | 0.641126i | \(0.221532\pi\) | |||||||
\(140\) | 705.880 | + | 1331.84i | 0.426127 | + | 0.804005i | ||||
\(141\) | 923.470 | + | 1890.15i | 0.551562 | + | 1.12893i | ||||
\(142\) | 569.634 | + | 986.635i | 0.336638 | + | 0.583074i | ||||
\(143\) | −276.484 | − | 478.885i | −0.161684 | − | 0.280044i | ||||
\(144\) | 25.3443 | + | 62.4858i | 0.0146669 | + | 0.0361608i | ||||
\(145\) | 1875.70 | + | 1082.93i | 1.07426 | + | 0.620226i | ||||
\(146\) | 520.221 | − | 901.049i | 0.294889 | − | 0.510763i | ||||
\(147\) | −664.376 | − | 1653.82i | −0.372768 | − | 0.927925i | ||||
\(148\) | −58.6330 | − | 101.555i | −0.0325649 | − | 0.0564040i | ||||
\(149\) | − | 2166.55i | − | 1.19121i | −0.803276 | − | 0.595607i | \(-0.796912\pi\) | ||
0.803276 | − | 0.595607i | \(-0.203088\pi\) | |||||||
\(150\) | −1352.87 | + | 660.971i | −0.736407 | + | 0.359787i | ||||
\(151\) | 2142.13 | 1.15447 | 0.577233 | − | 0.816580i | \(-0.304133\pi\) | ||||
0.577233 | + | 0.816580i | \(0.304133\pi\) | |||||||
\(152\) | 1384.13 | − | 2397.38i | 0.738603 | − | 1.27930i | ||||
\(153\) | 21.6118 | + | 53.2834i | 0.0114197 | + | 0.0281550i | ||||
\(154\) | 236.460 | + | 8.57220i | 0.123731 | + | 0.00448550i | ||||
\(155\) | −3124.24 | − | 1803.78i | −1.61900 | − | 0.934730i | ||||
\(156\) | 133.427 | − | 1926.83i | 0.0684788 | − | 0.988909i | ||||
\(157\) | 2593.06 | + | 1497.11i | 1.31815 | + | 0.761032i | 0.983430 | − | 0.181287i | \(-0.0580264\pi\) |
0.334716 | + | 0.942319i | \(0.391360\pi\) | |||||||
\(158\) | −266.121 | − | 153.645i | −0.133997 | − | 0.0773630i | ||||
\(159\) | −1571.36 | + | 767.720i | −0.783754 | + | 0.382919i | ||||
\(160\) | −2621.59 | − | 1513.57i | −1.29534 | − | 0.747866i | ||||
\(161\) | −170.561 | − | 106.894i | −0.0834911 | − | 0.0523255i | ||||
\(162\) | −1263.78 | + | 318.731i | −0.612912 | + | 0.154580i | ||||
\(163\) | −1154.51 | + | 1999.68i | −0.554776 | + | 0.960901i | 0.443145 | + | 0.896450i | \(0.353863\pi\) |
−0.997921 | + | 0.0644506i | \(0.979471\pi\) | |||||||
\(164\) | 623.200 | 0.296730 | ||||||||
\(165\) | 43.4616 | − | 627.633i | 0.0205059 | − | 0.296128i | ||||
\(166\) | − | 2272.72i | − | 1.06263i | ||||||
\(167\) | 1145.13 | + | 1983.42i | 0.530616 | + | 0.919053i | 0.999362 | + | 0.0357205i | \(0.0113726\pi\) |
−0.468746 | + | 0.883333i | \(0.655294\pi\) | |||||||
\(168\) | 1781.33 | + | 1295.99i | 0.818052 | + | 0.595166i | ||||
\(169\) | 1895.45 | − | 3283.01i | 0.862744 | − | 1.49432i | ||||
\(170\) | 55.8681 | + | 32.2555i | 0.0252052 | + | 0.0145523i | ||||
\(171\) | 2575.71 | + | 2006.76i | 1.15187 | + | 0.897430i | ||||
\(172\) | 415.449 | + | 719.579i | 0.184173 | + | 0.318996i | ||||
\(173\) | −821.495 | − | 1422.87i | −0.361024 | − | 0.625312i | 0.627106 | − | 0.778934i | \(-0.284239\pi\) |
−0.988130 | + | 0.153622i | \(0.950906\pi\) | |||||||
\(174\) | 1184.70 | + | 82.0368i | 0.516161 | + | 0.0357425i | ||||
\(175\) | −1594.05 | + | 2543.48i | −0.688565 | + | 1.09868i | ||||
\(176\) | −15.4555 | + | 8.92324i | −0.00661933 | + | 0.00382167i | ||||
\(177\) | −1920.44 | + | 2851.33i | −0.815533 | + | 1.21084i | ||||
\(178\) | − | 627.125i | − | 0.264073i | ||||||
\(179\) | 2452.01 | − | 1415.67i | 1.02386 | − | 0.591129i | 0.108644 | − | 0.994081i | \(-0.465349\pi\) |
0.915221 | + | 0.402952i | \(0.132016\pi\) | |||||||
\(180\) | 1350.56 | − | 1733.47i | 0.559250 | − | 0.717808i | ||||
\(181\) | − | 918.046i | − | 0.377005i | −0.982073 | − | 0.188502i | \(-0.939637\pi\) | ||
0.982073 | − | 0.188502i | \(-0.0603633\pi\) | |||||||
\(182\) | 1199.88 | + | 2263.91i | 0.488689 | + | 0.922045i | ||||
\(183\) | −1620.56 | + | 791.758i | −0.654619 | + | 0.319828i | ||||
\(184\) | 248.792 | 0.0996805 | ||||||||
\(185\) | 206.813 | − | 358.211i | 0.0821904 | − | 0.142358i | ||||
\(186\) | −1973.29 | − | 136.644i | −0.777896 | − | 0.0538668i | ||||
\(187\) | −13.1794 | + | 7.60910i | −0.00515385 | + | 0.00297558i | ||||
\(188\) | −1944.73 | −0.754437 | ||||||||
\(189\) | −1803.64 | + | 1870.34i | −0.694154 | + | 0.719826i | ||||
\(190\) | 3663.32 | 1.39877 | ||||||||
\(191\) | 1671.69 | − | 965.153i | 0.633296 | − | 0.365634i | −0.148731 | − | 0.988878i | \(-0.547519\pi\) |
0.782027 | + | 0.623244i | \(0.214186\pi\) | |||||||
\(192\) | −1759.38 | − | 121.831i | −0.661313 | − | 0.0457938i | ||||
\(193\) | 666.196 | − | 1153.89i | 0.248466 | − | 0.430355i | −0.714635 | − | 0.699498i | \(-0.753407\pi\) |
0.963100 | + | 0.269143i | \(0.0867404\pi\) | |||||||
\(194\) | 151.479 | 0.0560596 | ||||||||
\(195\) | 6121.18 | − | 2990.63i | 2.24793 | − | 1.09827i | ||||
\(196\) | 1643.29 | + | 119.303i | 0.598868 | + | 0.0434777i | ||||
\(197\) | − | 1816.48i | − | 0.656949i | −0.944513 | − | 0.328474i | \(-0.893466\pi\) | ||
0.944513 | − | 0.328474i | \(-0.106534\pi\) | |||||||
\(198\) | −129.655 | − | 319.660i | −0.0465361 | − | 0.114734i | ||||
\(199\) | 58.8698 | − | 33.9885i | 0.0209707 | − | 0.0121074i | −0.489478 | − | 0.872016i | \(-0.662813\pi\) |
0.510449 | + | 0.859908i | \(0.329479\pi\) | |||||||
\(200\) | − | 3710.11i | − | 1.31172i | ||||||
\(201\) | 781.174 | − | 1159.83i | 0.274128 | − | 0.407006i | ||||
\(202\) | −2550.50 | + | 1472.53i | −0.888380 | + | 0.512907i | ||||
\(203\) | 2091.80 | − | 1108.67i | 0.723230 | − | 0.383316i | ||||
\(204\) | −53.0281 | − | 3.67203i | −0.0181996 | − | 0.00126026i | ||||
\(205\) | 1099.09 | + | 1903.68i | 0.374458 | + | 0.648581i | ||||
\(206\) | 1645.93 | + | 2850.83i | 0.556686 | + | 0.964209i | ||||
\(207\) | −40.4472 | + | 290.651i | −0.0135810 | + | 0.0975924i | ||||
\(208\) | −167.362 | − | 96.6266i | −0.0557908 | − | 0.0322108i | ||||
\(209\) | −432.091 | + | 748.404i | −0.143007 | + | 0.247695i | ||||
\(210\) | −306.610 | + | 2898.99i | −0.100753 | + | 0.952615i | ||||
\(211\) | 856.959 | + | 1484.30i | 0.279599 | + | 0.484280i | 0.971285 | − | 0.237918i | \(-0.0764650\pi\) |
−0.691686 | + | 0.722199i | \(0.743132\pi\) | |||||||
\(212\) | − | 1616.74i | − | 0.523764i | ||||||
\(213\) | 228.736 | − | 3303.20i | 0.0735810 | − | 1.06259i | ||||
\(214\) | 779.717 | 0.249067 | ||||||||
\(215\) | −1465.39 | + | 2538.14i | −0.464833 | + | 0.805114i | ||||
\(216\) | 661.332 | − | 3142.68i | 0.208324 | − | 0.989966i | ||||
\(217\) | −3484.20 | + | 1846.64i | −1.08997 | + | 0.577688i | ||||
\(218\) | −1806.53 | − | 1043.00i | −0.561255 | − | 0.324041i | ||||
\(219\) | −2716.96 | + | 1327.43i | −0.838333 | + | 0.409585i | ||||
\(220\) | 503.682 | + | 290.801i | 0.154355 | + | 0.0891172i | ||||
\(221\) | −142.715 | − | 82.3963i | −0.0434390 | − | 0.0250795i | ||||
\(222\) | 15.6670 | − | 226.248i | 0.00473648 | − | 0.0684000i | ||||
\(223\) | −2434.38 | − | 1405.49i | −0.731023 | − | 0.422056i | 0.0877734 | − | 0.996140i | \(-0.472025\pi\) |
−0.818796 | + | 0.574084i | \(0.805358\pi\) | |||||||
\(224\) | −2923.63 | + | 1549.54i | −0.872068 | + | 0.462201i | ||||
\(225\) | 4334.32 | + | 603.168i | 1.28424 | + | 0.178717i | ||||
\(226\) | −131.723 | + | 228.150i | −0.0387702 | + | 0.0671519i | ||||
\(227\) | −3911.92 | −1.14380 | −0.571901 | − | 0.820322i | \(-0.693794\pi\) | ||||
−0.571901 | + | 0.820322i | \(0.693794\pi\) | |||||||
\(228\) | −2712.09 | + | 1325.05i | −0.787774 | + | 0.384883i | ||||
\(229\) | 1284.55i | 0.370680i | 0.982674 | + | 0.185340i | \(0.0593386\pi\) | ||||
−0.982674 | + | 0.185340i | \(0.940661\pi\) | |||||||
\(230\) | 164.618 | + | 285.126i | 0.0471937 | + | 0.0817420i | ||||
\(231\) | −556.088 | − | 404.577i | −0.158389 | − | 0.115235i | ||||
\(232\) | −1463.07 | + | 2534.12i | −0.414032 | + | 0.717125i | ||||
\(233\) | 1309.89 | + | 756.266i | 0.368300 | + | 0.212638i | 0.672715 | − | 0.739901i | \(-0.265128\pi\) |
−0.304416 | + | 0.952539i | \(0.598461\pi\) | |||||||
\(234\) | 2295.74 | − | 2946.63i | 0.641356 | − | 0.823193i | ||||
\(235\) | −3429.78 | − | 5940.56i | −0.952061 | − | 1.64902i | ||||
\(236\) | −1589.01 | − | 2752.25i | −0.438287 | − | 0.759135i | ||||
\(237\) | 392.050 | + | 802.443i | 0.107453 | + | 0.219934i | ||||
\(238\) | 62.3049 | − | 33.0219i | 0.0169690 | − | 0.00899367i | ||||
\(239\) | −2341.49 | + | 1351.86i | −0.633718 | + | 0.365877i | −0.782191 | − | 0.623039i | \(-0.785898\pi\) |
0.148473 | + | 0.988917i | \(0.452564\pi\) | |||||||
\(240\) | −96.5195 | − | 197.555i | −0.0259596 | − | 0.0531338i | ||||
\(241\) | 4934.13i | 1.31882i | 0.751785 | + | 0.659409i | \(0.229193\pi\) | ||||
−0.751785 | + | 0.659409i | \(0.770807\pi\) | |||||||
\(242\) | −1981.76 | + | 1144.17i | −0.526416 | + | 0.303926i | ||||
\(243\) | 3563.91 | + | 1283.52i | 0.940845 | + | 0.338838i | ||||
\(244\) | − | 1667.36i | − | 0.437467i | ||||||
\(245\) | 2533.73 | + | 5230.16i | 0.660709 | + | 1.36385i | ||||
\(246\) | 999.660 | + | 673.295i | 0.259089 | + | 0.174503i | ||||
\(247\) | −9357.92 | −2.41065 | ||||||||
\(248\) | 2436.96 | − | 4220.94i | 0.623980 | − | 1.08077i | ||||
\(249\) | −3689.94 | + | 5478.56i | −0.939118 | + | 1.39433i | ||||
\(250\) | 972.689 | − | 561.582i | 0.246073 | − | 0.142070i | ||||
\(251\) | −633.966 | −0.159425 | −0.0797123 | − | 0.996818i | \(-0.525400\pi\) | ||||
−0.0797123 | + | 0.996818i | \(0.525400\pi\) | |||||||
\(252\) | −821.587 | − | 2257.13i | −0.205378 | − | 0.564228i | ||||
\(253\) | −77.6669 | −0.0192999 | ||||||||
\(254\) | 45.6018 | − | 26.3282i | 0.0112650 | − | 0.00650386i | ||||
\(255\) | −82.3049 | − | 168.461i | −0.0202123 | − | 0.0413703i | ||||
\(256\) | 2092.87 | − | 3624.95i | 0.510954 | − | 0.884998i | ||||
\(257\) | −532.495 | −0.129246 | −0.0646228 | − | 0.997910i | \(-0.520584\pi\) | ||||
−0.0646228 | + | 0.997910i | \(0.520584\pi\) | |||||||
\(258\) | −111.010 | + | 1603.10i | −0.0267875 | + | 0.386841i | ||||
\(259\) | −211.728 | − | 399.482i | −0.0507958 | − | 0.0958402i | ||||
\(260\) | 6297.96i | 1.50224i | ||||||||
\(261\) | −2722.62 | − | 2121.21i | −0.645693 | − | 0.503065i | ||||
\(262\) | 1516.89 | − | 875.778i | 0.357687 | − | 0.206511i | ||||
\(263\) | 5230.97i | 1.22645i | 0.789910 | + | 0.613223i | \(0.210127\pi\) | ||||
−0.789910 | + | 0.613223i | \(0.789873\pi\) | |||||||
\(264\) | 847.950 | + | 58.7178i | 0.197681 | + | 0.0136888i | ||||
\(265\) | 4938.64 | − | 2851.32i | 1.14482 | − | 0.660964i | ||||
\(266\) | 2126.45 | − | 3392.99i | 0.490154 | − | 0.782095i | ||||
\(267\) | −1018.19 | + | 1511.73i | −0.233379 | + | 0.346504i | ||||
\(268\) | 646.358 | + | 1119.53i | 0.147323 | + | 0.255171i | ||||
\(269\) | 3581.36 | + | 6203.09i | 0.811744 | + | 1.40598i | 0.911642 | + | 0.410985i | \(0.134815\pi\) |
−0.0998978 | + | 0.994998i | \(0.531852\pi\) | |||||||
\(270\) | 4039.22 | − | 1321.49i | 0.910441 | − | 0.297865i | ||||
\(271\) | 669.831 | + | 386.727i | 0.150145 | + | 0.0866863i | 0.573190 | − | 0.819422i | \(-0.305706\pi\) |
−0.423045 | + | 0.906109i | \(0.639039\pi\) | |||||||
\(272\) | −2.65926 | + | 4.60597i | −0.000592798 | + | 0.00102676i | ||||
\(273\) | 783.232 | − | 7405.44i | 0.173639 | − | 1.64175i | ||||
\(274\) | −1111.28 | − | 1924.79i | −0.245017 | − | 0.424382i | ||||
\(275\) | 1158.21i | 0.253972i | ||||||||
\(276\) | −225.004 | − | 151.546i | −0.0490712 | − | 0.0330506i | ||||
\(277\) | −985.162 | −0.213692 | −0.106846 | − | 0.994276i | \(-0.534075\pi\) | ||||
−0.106846 | + | 0.994276i | \(0.534075\pi\) | |||||||
\(278\) | −1008.06 | + | 1746.01i | −0.217479 | + | 0.376685i | ||||
\(279\) | 4534.91 | + | 3533.19i | 0.973111 | + | 0.758159i | ||||
\(280\) | −6086.53 | − | 3814.55i | −1.29907 | − | 0.814153i | ||||
\(281\) | −68.0344 | − | 39.2797i | −0.0144434 | − | 0.00833890i | 0.492761 | − | 0.870165i | \(-0.335988\pi\) |
−0.507204 | + | 0.861826i | \(0.669321\pi\) | |||||||
\(282\) | −3119.50 | − | 2101.06i | −0.658736 | − | 0.443674i | ||||
\(283\) | −2059.84 | − | 1189.25i | −0.432668 | − | 0.249801i | 0.267815 | − | 0.963470i | \(-0.413698\pi\) |
−0.700482 | + | 0.713670i | \(0.747032\pi\) | |||||||
\(284\) | 2650.85 | + | 1530.47i | 0.553871 | + | 0.319777i | ||||
\(285\) | −8830.72 | − | 5947.70i | −1.83539 | − | 1.23618i | ||||
\(286\) | 856.179 | + | 494.315i | 0.177017 | + | 0.102201i | ||||
\(287\) | 2401.19 | + | 87.0483i | 0.493860 | + | 0.0179035i | ||||
\(288\) | 3805.30 | + | 2964.74i | 0.778574 | + | 0.606593i | ||||
\(289\) | 2454.23 | − | 4250.86i | 0.499538 | − | 0.865226i | ||||
\(290\) | −3872.27 | −0.784094 | ||||||||
\(291\) | −365.152 | − | 245.939i | −0.0735587 | − | 0.0495436i | ||||
\(292\) | − | 2795.42i | − | 0.560238i | ||||||
\(293\) | 1799.84 | + | 3117.41i | 0.358866 | + | 0.621573i | 0.987772 | − | 0.155908i | \(-0.0498303\pi\) |
−0.628906 | + | 0.777481i | \(0.716497\pi\) | |||||||
\(294\) | 2507.08 | + | 1966.76i | 0.497332 | + | 0.390149i | ||||
\(295\) | 5604.84 | − | 9707.87i | 1.10619 | − | 1.91598i | ||||
\(296\) | 483.954 | + | 279.411i | 0.0950312 | + | 0.0548663i | ||||
\(297\) | −206.452 | + | 981.069i | −0.0403352 | + | 0.191675i | ||||
\(298\) | 1936.75 | + | 3354.54i | 0.376485 | + | 0.652092i | ||||
\(299\) | −420.514 | − | 728.351i | −0.0813342 | − | 0.140875i | ||||
\(300\) | −2259.92 | + | 3355.36i | −0.434922 | + | 0.645740i | ||||
\(301\) | 1500.22 | + | 2830.57i | 0.287279 | + | 0.542031i | ||||
\(302\) | −3316.73 | + | 1914.92i | −0.631975 | + | 0.364871i | ||||
\(303\) | 8538.96 | + | 591.295i | 1.61898 | + | 0.112109i | ||||
\(304\) | 302.017i | 0.0569799i | ||||||||
\(305\) | 5093.27 | − | 2940.60i | 0.956197 | − | 0.552060i | ||||
\(306\) | −81.0940 | − | 63.1810i | −0.0151498 | − | 0.0118033i | ||||
\(307\) | 2829.86i | 0.526086i | 0.964784 | + | 0.263043i | \(0.0847262\pi\) | ||||
−0.964784 | + | 0.263043i | \(0.915274\pi\) | |||||||
\(308\) | 561.713 | − | 297.711i | 0.103917 | − | 0.0550767i | ||||
\(309\) | 660.922 | − | 9544.45i | 0.121678 | − | 1.75717i | ||||
\(310\) | 6449.82 | 1.18169 | ||||||||
\(311\) | 3570.62 | − | 6184.49i | 0.651033 | − | 1.12762i | −0.331840 | − | 0.943336i | \(-0.607669\pi\) |
0.982873 | − | 0.184286i | \(-0.0589974\pi\) | |||||||
\(312\) | 4040.43 | + | 8269.89i | 0.733154 | + | 1.50061i | ||||
\(313\) | −3058.15 | + | 1765.62i | −0.552259 | + | 0.318847i | −0.750032 | − | 0.661401i | \(-0.769962\pi\) |
0.197774 | + | 0.980248i | \(0.436629\pi\) | |||||||
\(314\) | −5353.23 | −0.962103 | ||||||||
\(315\) | 5445.85 | − | 6490.42i | 0.974091 | − | 1.16093i | ||||
\(316\) | −825.616 | −0.146976 | ||||||||
\(317\) | 1844.54 | − | 1064.95i | 0.326814 | − | 0.188686i | −0.327612 | − | 0.944812i | \(-0.606244\pi\) |
0.654426 | + | 0.756126i | \(0.272911\pi\) | |||||||
\(318\) | 1746.70 | − | 2593.37i | 0.308019 | − | 0.457324i | ||||
\(319\) | 456.736 | − | 791.090i | 0.0801640 | − | 0.138848i | ||||
\(320\) | 5750.63 | 1.00459 | ||||||||
\(321\) | −1879.57 | − | 1265.93i | −0.326813 | − | 0.220117i | ||||
\(322\) | 359.640 | + | 13.0377i | 0.0622422 | + | 0.00225641i | ||||
\(323\) | 257.539i | 0.0443648i | ||||||||
\(324\) | −2512.38 | + | 2439.36i | −0.430793 | + | 0.418271i | ||||
\(325\) | −10861.5 | + | 6270.90i | −1.85381 | + | 1.07030i | ||||
\(326\) | − | 4128.22i | − | 0.701353i | ||||||
\(327\) | 2661.38 | + | 5447.27i | 0.450075 | + | 0.921208i | ||||
\(328\) | −2571.93 | + | 1484.91i | −0.432961 | + | 0.249970i | ||||
\(329\) | −7493.05 | − | 271.639i | −1.25564 | − | 0.0455196i | ||||
\(330\) | 493.767 | + | 1010.64i | 0.0823666 | + | 0.168587i | ||||
\(331\) | 2449.86 | + | 4243.28i | 0.406817 | + | 0.704628i | 0.994531 | − | 0.104441i | \(-0.0333054\pi\) |
−0.587714 | + | 0.809069i | \(0.699972\pi\) | |||||||
\(332\) | −3053.13 | − | 5288.17i | −0.504705 | − | 0.874175i | ||||
\(333\) | −405.099 | + | 519.952i | −0.0666646 | + | 0.0855652i | ||||
\(334\) | −3546.08 | − | 2047.33i | −0.580937 | − | 0.335404i | ||||
\(335\) | −2279.87 | + | 3948.85i | −0.371829 | + | 0.644026i | ||||
\(336\) | −239.003 | − | 25.2780i | −0.0388056 | − | 0.00410425i | ||||
\(337\) | −1234.19 | − | 2137.68i | −0.199497 | − | 0.345539i | 0.748868 | − | 0.662719i | \(-0.230598\pi\) |
−0.948365 | + | 0.317180i | \(0.897264\pi\) | |||||||
\(338\) | 6777.60i | 1.09069i | ||||||||
\(339\) | 687.948 | − | 336.111i | 0.110219 | − | 0.0538497i | ||||
\(340\) | 173.326 | 0.0276468 | ||||||||
\(341\) | −760.759 | + | 1317.67i | −0.120814 | + | 0.209255i | ||||
\(342\) | −5781.95 | − | 804.622i | −0.914188 | − | 0.127219i | ||||
\(343\) | 6314.95 | + | 689.208i | 0.994097 | + | 0.108495i | ||||
\(344\) | −3429.10 | − | 1979.79i | −0.537455 | − | 0.310300i | ||||
\(345\) | 66.1021 | − | 954.587i | 0.0103154 | − | 0.148966i | ||||
\(346\) | 2543.90 | + | 1468.72i | 0.395262 | + | 0.228205i | ||||
\(347\) | −8699.48 | − | 5022.64i | −1.34586 | − | 0.777031i | −0.358197 | − | 0.933646i | \(-0.616608\pi\) |
−0.987660 | + | 0.156615i | \(0.949942\pi\) | |||||||
\(348\) | 2866.78 | − | 1400.62i | 0.441596 | − | 0.215751i | ||||
\(349\) | −9911.49 | − | 5722.40i | −1.52020 | − | 0.877688i | −0.999716 | − | 0.0238161i | \(-0.992418\pi\) |
−0.520484 | − | 0.853872i | \(-0.674248\pi\) | |||||||
\(350\) | 194.425 | − | 5363.13i | 0.0296927 | − | 0.819061i | ||||
\(351\) | −10318.1 | + | 3375.74i | −1.56907 | + | 0.513345i | ||||
\(352\) | −638.362 | + | 1105.68i | −0.0966614 | + | 0.167422i | ||||
\(353\) | 1456.87 | 0.219664 | 0.109832 | − | 0.993950i | \(-0.464969\pi\) | ||||
0.109832 | + | 0.993950i | \(0.464969\pi\) | |||||||
\(354\) | 424.590 | − | 6131.55i | 0.0637478 | − | 0.920589i | ||||
\(355\) | 10796.7i | 1.61417i | ||||||||
\(356\) | −842.468 | − | 1459.20i | −0.125423 | − | 0.217240i | ||||
\(357\) | −203.805 | − | 21.5553i | −0.0302142 | − | 0.00319559i | ||||
\(358\) | −2531.02 | + | 4383.85i | −0.373655 | + | 0.647189i | ||||
\(359\) | 282.828 | + | 163.291i | 0.0415797 | + | 0.0240060i | 0.520646 | − | 0.853773i | \(-0.325691\pi\) |
−0.479066 | + | 0.877779i | \(0.659025\pi\) | |||||||
\(360\) | −1443.38 | + | 10372.0i | −0.211313 | + | 1.51848i | ||||
\(361\) | 3882.81 | + | 6725.22i | 0.566089 | + | 0.980496i | ||||
\(362\) | 820.669 | + | 1421.44i | 0.119153 | + | 0.206379i | ||||
\(363\) | 6634.85 | + | 459.442i | 0.959337 | + | 0.0664310i | ||||
\(364\) | 5833.19 | + | 3655.78i | 0.839951 | + | 0.526414i | ||||
\(365\) | 8539.14 | − | 4930.08i | 1.22455 | − | 0.706992i | ||||
\(366\) | 1801.39 | − | 2674.57i | 0.257268 | − | 0.381973i | ||||
\(367\) | − | 6367.01i | − | 0.905599i | −0.891612 | − | 0.452800i | \(-0.850425\pi\) | ||
0.891612 | − | 0.452800i | \(-0.149575\pi\) | |||||||
\(368\) | −23.5068 | + | 13.5716i | −0.00332983 | + | 0.00192248i | ||||
\(369\) | −1316.61 | − | 3246.06i | −0.185745 | − | 0.457949i | ||||
\(370\) | 739.507i | 0.103906i | ||||||||
\(371\) | 225.825 | − | 6229.29i | 0.0316018 | − | 0.871722i | ||||
\(372\) | −4775.03 | + | 2332.94i | −0.665520 | + | 0.325154i | ||||
\(373\) | −1937.38 | −0.268938 | −0.134469 | − | 0.990918i | \(-0.542933\pi\) | ||||
−0.134469 | + | 0.990918i | \(0.542933\pi\) | |||||||
\(374\) | 13.6040 | − | 23.5628i | 0.00188087 | − | 0.00325777i | ||||
\(375\) | −3256.52 | − | 225.503i | −0.448442 | − | 0.0310532i | ||||
\(376\) | 8025.86 | − | 4633.73i | 1.10080 | − | 0.635550i | ||||
\(377\) | 9891.67 | 1.35132 | ||||||||
\(378\) | 1120.67 | − | 4508.23i | 0.152490 | − | 0.613435i | ||||
\(379\) | 9315.44 | 1.26254 | 0.631269 | − | 0.775564i | \(-0.282534\pi\) | ||||
0.631269 | + | 0.775564i | \(0.282534\pi\) | |||||||
\(380\) | 8523.84 | − | 4921.24i | 1.15069 | − | 0.664354i | ||||
\(381\) | −152.673 | − | 10.5721i | −0.0205293 | − | 0.00142159i | ||||
\(382\) | −1725.56 | + | 2988.76i | −0.231119 | + | 0.400309i | ||||
\(383\) | 2954.91 | 0.394227 | 0.197114 | − | 0.980381i | \(-0.436843\pi\) | ||||
0.197114 | + | 0.980381i | \(0.436843\pi\) | |||||||
\(384\) | −3840.01 | + | 1876.12i | −0.510312 | + | 0.249323i | ||||
\(385\) | 1900.07 | + | 1190.81i | 0.251523 | + | 0.157634i | ||||
\(386\) | 2382.13i | 0.314112i | ||||||||
\(387\) | 2870.37 | − | 3684.17i | 0.377026 | − | 0.483919i | ||||
\(388\) | 352.462 | − | 203.494i | 0.0461174 | − | 0.0266259i | ||||
\(389\) | 4739.61i | 0.617757i | 0.951101 | + | 0.308879i | \(0.0999537\pi\) | ||||
−0.951101 | + | 0.308879i | \(0.900046\pi\) | |||||||
\(390\) | −6804.21 | + | 10102.4i | −0.883448 | + | 1.31168i | ||||
\(391\) | −20.0449 | + | 11.5729i | −0.00259262 | + | 0.00149685i | ||||
\(392\) | −7066.10 | + | 3423.14i | −0.910439 | + | 0.441057i | ||||
\(393\) | −5078.48 | − | 351.668i | −0.651846 | − | 0.0451382i | ||||
\(394\) | 1623.81 | + | 2812.52i | 0.207630 | + | 0.359626i | ||||
\(395\) | −1456.08 | − | 2522.00i | −0.185477 | − | 0.321255i | ||||
\(396\) | −731.106 | − | 569.611i | −0.0927764 | − | 0.0722829i | ||||
\(397\) | 6808.08 | + | 3930.65i | 0.860674 | + | 0.496911i | 0.864238 | − | 0.503083i | \(-0.167801\pi\) |
−0.00356368 | + | 0.999994i | \(0.501134\pi\) | |||||||
\(398\) | −60.7667 | + | 105.251i | −0.00765316 | + | 0.0132557i | ||||
\(399\) | −10634.8 | + | 4726.58i | −1.33434 | + | 0.593045i | ||||
\(400\) | 202.387 | + | 350.544i | 0.0252984 | + | 0.0438180i | ||||
\(401\) | − | 4166.67i | − | 0.518886i | −0.965758 | − | 0.259443i | \(-0.916461\pi\) | ||
0.965758 | − | 0.259443i | \(-0.0835390\pi\) | |||||||
\(402\) | −172.710 | + | 2494.12i | −0.0214278 | + | 0.309441i | ||||
\(403\) | −16476.0 | −2.03654 | ||||||||
\(404\) | −3956.35 | + | 6852.60i | −0.487217 | + | 0.843885i | ||||
\(405\) | −11882.4 | − | 3372.44i | −1.45788 | − | 0.413772i | ||||
\(406\) | −2247.74 | + | 3586.51i | −0.274762 | + | 0.438412i | ||||
\(407\) | −151.078 | − | 87.2252i | −0.0183997 | − | 0.0106231i | ||||
\(408\) | 227.595 | − | 111.196i | 0.0276168 | − | 0.0134927i | ||||
\(409\) | −11636.0 | − | 6718.04i | −1.40675 | − | 0.812190i | −0.411681 | − | 0.911328i | \(-0.635058\pi\) |
−0.995074 | + | 0.0991379i | \(0.968392\pi\) | |||||||
\(410\) | −3403.52 | − | 1965.02i | −0.409971 | − | 0.236697i | ||||
\(411\) | −446.233 | + | 6444.10i | −0.0535549 | + | 0.773392i | ||||
\(412\) | 7659.51 | + | 4422.22i | 0.915915 | + | 0.528804i | ||||
\(413\) | −5738.02 | − | 10826.4i | −0.683655 | − | 1.28990i | ||||
\(414\) | −197.196 | − | 486.181i | −0.0234098 | − | 0.0577162i | ||||
\(415\) | 10769.2 | − | 18652.7i | 1.27382 | − | 2.20633i | ||||
\(416\) | −13825.2 | −1.62941 | ||||||||
\(417\) | 5264.78 | − | 2572.22i | 0.618267 | − | 0.302067i | ||||
\(418\) | − | 1545.04i | − | 0.180790i | ||||||
\(419\) | 5509.22 | + | 9542.24i | 0.642346 | + | 1.11258i | 0.984908 | + | 0.173080i | \(0.0553719\pi\) |
−0.342562 | + | 0.939495i | \(0.611295\pi\) | |||||||
\(420\) | 3181.03 | + | 7157.27i | 0.369567 | + | 0.831522i | ||||
\(421\) | −3981.69 | + | 6896.49i | −0.460940 | + | 0.798372i | −0.999008 | − | 0.0445296i | \(-0.985821\pi\) |
0.538068 | + | 0.842902i | \(0.319154\pi\) | |||||||
\(422\) | −2653.71 | − | 1532.12i | −0.306116 | − | 0.176736i | ||||
\(423\) | 4108.55 | + | 10129.5i | 0.472256 | + | 1.16434i | ||||
\(424\) | 3852.22 | + | 6672.24i | 0.441227 | + | 0.764228i | ||||
\(425\) | 172.581 | + | 298.919i | 0.0196974 | + | 0.0341170i | ||||
\(426\) | 2598.67 | + | 5318.93i | 0.295554 | + | 0.604937i | ||||
\(427\) | 232.896 | − | 6424.34i | 0.0263949 | − | 0.728093i | ||||
\(428\) | 1814.25 | − | 1047.46i | 0.204895 | − | 0.118296i | ||||
\(429\) | −1261.32 | − | 2581.66i | −0.141952 | − | 0.290545i | ||||
\(430\) | − | 5239.84i | − | 0.587646i | ||||||
\(431\) | 5455.54 | − | 3149.75i | 0.609707 | − | 0.352015i | −0.163144 | − | 0.986602i | \(-0.552163\pi\) |
0.772851 | + | 0.634588i | \(0.218830\pi\) | |||||||
\(432\) | 108.949 | + | 333.008i | 0.0121338 | + | 0.0370876i | ||||
\(433\) | 1195.77i | 0.132714i | 0.997796 | + | 0.0663571i | \(0.0211377\pi\) | ||||
−0.997796 | + | 0.0663571i | \(0.978862\pi\) | |||||||
\(434\) | 3743.93 | − | 5973.85i | 0.414088 | − | 0.660723i | ||||
\(435\) | 9334.39 | + | 6286.94i | 1.02885 | + | 0.692956i | ||||
\(436\) | −5604.58 | −0.615621 | ||||||||
\(437\) | −657.181 | + | 1138.27i | −0.0719388 | + | 0.124602i | ||||
\(438\) | 3020.13 | − | 4484.06i | 0.329469 | − | 0.489171i | ||||
\(439\) | −4954.45 | + | 2860.45i | −0.538640 | + | 0.310984i | −0.744527 | − | 0.667592i | \(-0.767325\pi\) |
0.205888 | + | 0.978576i | \(0.433992\pi\) | |||||||
\(440\) | −2771.58 | −0.300295 | ||||||||
\(441\) | −2850.30 | − | 8811.46i | −0.307775 | − | 0.951459i | ||||
\(442\) | 294.626 | 0.0317057 | ||||||||
\(443\) | −7609.01 | + | 4393.06i | −0.816061 | + | 0.471153i | −0.849056 | − | 0.528302i | \(-0.822829\pi\) |
0.0329952 | + | 0.999456i | \(0.489495\pi\) | |||||||
\(444\) | −267.484 | − | 547.483i | −0.0285906 | − | 0.0585189i | ||||
\(445\) | 2971.60 | − | 5146.96i | 0.316556 | − | 0.548290i | ||||
\(446\) | 5025.64 | 0.533567 | ||||||||
\(447\) | 777.699 | − | 11230.8i | 0.0822906 | − | 1.18837i | ||||
\(448\) | 3338.07 | − | 5326.26i | 0.352029 | − | 0.561701i | ||||
\(449\) | − | 14022.9i | − | 1.47390i | −0.675945 | − | 0.736952i | \(-0.736264\pi\) | ||
0.675945 | − | 0.736952i | \(-0.263736\pi\) | |||||||
\(450\) | −7250.17 | + | 2940.68i | −0.759502 | + | 0.308055i | ||||
\(451\) | 802.894 | − | 463.551i | 0.0838288 | − | 0.0483986i | ||||
\(452\) | 707.815i | 0.0736566i | ||||||||
\(453\) | 11104.3 | + | 768.934i | 1.15171 | + | 0.0797520i | ||||
\(454\) | 6056.95 | − | 3496.98i | 0.626138 | − | 0.361501i | ||||
\(455\) | −879.695 | + | 24266.0i | −0.0906390 | + | 2.50024i | ||||
\(456\) | 8035.52 | − | 11930.6i | 0.825214 | − | 1.22522i | ||||
\(457\) | 6061.20 | + | 10498.3i | 0.620418 | + | 1.07459i | 0.989408 | + | 0.145162i | \(0.0463702\pi\) |
−0.368990 | + | 0.929433i | \(0.620296\pi\) | |||||||
\(458\) | −1148.30 | − | 1988.92i | −0.117154 | − | 0.202917i | ||||
\(459\) | 92.9036 | + | 283.965i | 0.00944743 | + | 0.0288766i | ||||
\(460\) | 766.066 | + | 442.288i | 0.0776478 | + | 0.0448300i | ||||
\(461\) | 7878.24 | − | 13645.5i | 0.795935 | − | 1.37860i | −0.126309 | − | 0.991991i | \(-0.540313\pi\) |
0.922244 | − | 0.386609i | \(-0.126354\pi\) | |||||||
\(462\) | 1222.67 | + | 129.315i | 0.123125 | + | 0.0130223i | ||||
\(463\) | 2355.94 | + | 4080.61i | 0.236480 | + | 0.409595i | 0.959702 | − | 0.281021i | \(-0.0906731\pi\) |
−0.723222 | + | 0.690615i | \(0.757340\pi\) | |||||||
\(464\) | − | 319.243i | − | 0.0319407i | ||||||
\(465\) | −15547.8 | − | 10471.8i | −1.55056 | − | 1.04434i | ||||
\(466\) | −2704.20 | −0.268819 | ||||||||
\(467\) | 4389.02 | − | 7602.00i | 0.434903 | − | 0.753274i | −0.562385 | − | 0.826876i | \(-0.690116\pi\) |
0.997288 | + | 0.0736019i | \(0.0234494\pi\) | |||||||
\(468\) | 1383.30 | − | 9940.28i | 0.136630 | − | 0.981816i | ||||
\(469\) | 2334.04 | + | 4403.82i | 0.229800 | + | 0.433581i | ||||
\(470\) | 10620.9 | + | 6131.97i | 1.04235 | + | 0.601802i | ||||
\(471\) | 12904.4 | + | 8691.40i | 1.26242 | + | 0.850273i | ||||
\(472\) | 13115.6 | + | 7572.30i | 1.27902 | + | 0.738440i | ||||
\(473\) | 1070.48 | + | 618.042i | 0.104061 | + | 0.0600795i | ||||
\(474\) | −1324.35 | − | 891.983i | −0.128332 | − | 0.0864349i | ||||
\(475\) | 16974.4 | + | 9800.20i | 1.63967 | + | 0.946661i | ||||
\(476\) | 100.610 | − | 160.535i | 0.00968796 | − | 0.0154582i | ||||
\(477\) | −8421.09 | + | 3415.61i | −0.808334 | + | 0.327862i | ||||
\(478\) | 2416.94 | − | 4186.26i | 0.231272 | − | 0.400576i | ||||
\(479\) | 9448.00 | 0.901232 | 0.450616 | − | 0.892718i | \(-0.351204\pi\) | ||||
0.450616 | + | 0.892718i | \(0.351204\pi\) | |||||||
\(480\) | −13046.3 | − | 8787.01i | −1.24058 | − | 0.835563i | ||||
\(481\) | − | 1889.06i | − | 0.179072i | ||||||
\(482\) | −4410.76 | − | 7639.67i | −0.416815 | − | 0.721945i | ||||
\(483\) | −845.772 | − | 615.334i | −0.0796770 | − | 0.0579682i | ||||
\(484\) | −3074.12 | + | 5324.53i | −0.288704 | + | 0.500050i | ||||
\(485\) | 1243.22 | + | 717.776i | 0.116396 | + | 0.0672011i | ||||
\(486\) | −6665.50 | + | 1198.58i | −0.622126 | + | 0.111869i | ||||
\(487\) | −3150.98 | − | 5457.65i | −0.293192 | − | 0.507823i | 0.681371 | − | 0.731938i | \(-0.261384\pi\) |
−0.974563 | + | 0.224115i | \(0.928051\pi\) | |||||||
\(488\) | 3972.84 | + | 6881.16i | 0.368529 | + | 0.638310i | ||||
\(489\) | −6702.50 | + | 9951.38i | −0.619831 | + | 0.920280i | ||||
\(490\) | −8598.45 | − | 5833.06i | −0.792731 | − | 0.537777i | ||||
\(491\) | −11356.2 | + | 6556.53i | −1.04379 | + | 0.602632i | −0.920904 | − | 0.389789i | \(-0.872548\pi\) |
−0.122884 | + | 0.992421i | \(0.539214\pi\) | |||||||
\(492\) | 3230.51 | + | 223.702i | 0.296021 | + | 0.0204985i | ||||
\(493\) | − | 272.228i | − | 0.0248692i | ||||||
\(494\) | 14489.2 | − | 8365.33i | 1.31963 | − | 0.761891i | ||||
\(495\) | 450.587 | − | 3237.88i | 0.0409139 | − | 0.294004i | ||||
\(496\) | 531.746i | 0.0481373i | ||||||||
\(497\) | 9999.97 | + | 6267.18i | 0.902535 | + | 0.565636i | ||||
\(498\) | 815.808 | − | 11781.2i | 0.0734081 | − | 1.06009i | ||||
\(499\) | 1276.72 | 0.114537 | 0.0572684 | − | 0.998359i | \(-0.481761\pi\) | ||||
0.0572684 | + | 0.998359i | \(0.481761\pi\) | |||||||
\(500\) | 1508.84 | − | 2613.39i | 0.134955 | − | 0.233748i | ||||
\(501\) | 5224.09 | + | 10692.6i | 0.465859 | + | 0.953513i | ||||
\(502\) | 981.590 | − | 566.721i | 0.0872720 | − | 0.0503865i | ||||
\(503\) | −17740.2 | −1.57256 | −0.786279 | − | 0.617872i | \(-0.787995\pi\) | ||||
−0.786279 | + | 0.617872i | \(0.787995\pi\) | |||||||
\(504\) | 8768.75 | + | 7357.50i | 0.774982 | + | 0.650256i | ||||
\(505\) | −27910.1 | −2.45937 | ||||||||
\(506\) | 120.254 | − | 69.4288i | 0.0105651 | − | 0.00609977i | ||||
\(507\) | 11004.0 | − | 16337.9i | 0.963913 | − | 1.43115i | ||||
\(508\) | 70.7377 | − | 122.521i | 0.00617810 | − | 0.0107008i | ||||
\(509\) | −11516.0 | −1.00282 | −0.501411 | − | 0.865209i | \(-0.667186\pi\) | ||||
−0.501411 | + | 0.865209i | \(0.667186\pi\) | |||||||
\(510\) | 278.027 | + | 187.258i | 0.0241397 | + | 0.0162587i | ||||
\(511\) | 390.463 | − | 10770.8i | 0.0338025 | − | 0.932427i | ||||
\(512\) | 903.539i | 0.0779905i | ||||||||
\(513\) | 12631.5 | + | 11327.1i | 1.08712 | + | 0.974858i | ||||
\(514\) | 824.479 | − | 476.013i | 0.0707514 | − | 0.0408483i | ||||
\(515\) | 31196.6i | 2.66929i | ||||||||
\(516\) | 1895.28 | + | 3879.24i | 0.161696 | + | 0.330957i | ||||
\(517\) | −2505.48 | + | 1446.54i | −0.213135 | + | 0.123054i | ||||
\(518\) | 684.934 | + | 429.262i | 0.0580971 | + | 0.0364106i | ||||
\(519\) | −3747.67 | − | 7670.68i | −0.316964 | − | 0.648758i | ||||
\(520\) | −15006.2 | − | 25991.5i | −1.26551 | − | 2.19193i | ||||
\(521\) | 10167.1 | + | 17609.9i | 0.854947 | + | 1.48081i | 0.876694 | + | 0.481048i | \(0.159744\pi\) |
−0.0217470 | + | 0.999764i | \(0.506923\pi\) | |||||||
\(522\) | 6111.74 | + | 850.514i | 0.512459 | + | 0.0713142i | ||||
\(523\) | −8533.45 | − | 4926.79i | −0.713464 | − | 0.411919i | 0.0988783 | − | 0.995100i | \(-0.468475\pi\) |
−0.812342 | + | 0.583181i | \(0.801808\pi\) | |||||||
\(524\) | 2353.01 | − | 4075.53i | 0.196167 | − | 0.339772i | ||||
\(525\) | −9176.15 | + | 12612.6i | −0.762819 | + | 1.04849i | ||||
\(526\) | −4676.12 | − | 8099.28i | −0.387621 | − | 0.671379i | ||||
\(527\) | 453.435i | 0.0374799i | ||||||||
\(528\) | −83.3204 | + | 40.7079i | −0.00686753 | + | 0.00335527i | ||||
\(529\) | 12048.9 | 0.990291 | ||||||||
\(530\) | −5097.77 | + | 8829.59i | −0.417798 | + | 0.723647i | ||||
\(531\) | −10978.6 | + | 14091.2i | −0.897231 | + | 1.15161i | ||||
\(532\) | 389.763 | − | 10751.4i | 0.0317638 | − | 0.876192i | ||||
\(533\) | 8694.26 | + | 5019.63i | 0.706548 | + | 0.407926i | ||||
\(534\) | 225.111 | − | 3250.85i | 0.0182425 | − | 0.263442i | ||||
\(535\) | 6399.31 | + | 3694.65i | 0.517134 | + | 0.298567i | ||||
\(536\) | −5335.01 | − | 3080.17i | −0.429921 | − | 0.248215i | ||||
\(537\) | 13218.7 | − | 6458.29i | 1.06225 | − | 0.518986i | ||||
\(538\) | −11090.3 | − | 6402.97i | −0.888727 | − | 0.513107i | ||||
\(539\) | 2205.86 | − | 1068.62i | 0.176277 | − | 0.0853965i | ||||
\(540\) | 7623.21 | − | 8501.07i | 0.607501 | − | 0.677459i | ||||
\(541\) | −9862.19 | + | 17081.8i | −0.783750 | + | 1.35749i | 0.145993 | + | 0.989286i | \(0.453362\pi\) |
−0.929743 | + | 0.368209i | \(0.879971\pi\) | |||||||
\(542\) | −1382.83 | −0.109590 | ||||||||
\(543\) | 329.539 | − | 4758.91i | 0.0260440 | − | 0.376104i | ||||
\(544\) | 380.482i | 0.0299872i | ||||||||
\(545\) | −9884.40 | − | 17120.3i | −0.776883 | − | 1.34560i | ||||
\(546\) | 5407.24 | + | 12166.2i | 0.423825 | + | 0.953602i | ||||
\(547\) | −1833.52 | + | 3175.75i | −0.143319 | + | 0.248236i | −0.928745 | − | 0.370720i | \(-0.879111\pi\) |
0.785425 | + | 0.618956i | \(0.212444\pi\) | |||||||
\(548\) | −5171.45 | − | 2985.74i | −0.403127 | − | 0.232745i | ||||
\(549\) | −8684.77 | + | 3522.56i | −0.675149 | + | 0.273842i | ||||
\(550\) | −1035.36 | − | 1793.29i | −0.0802685 | − | 0.139029i | ||||
\(551\) | −7729.38 | − | 13387.7i | −0.597609 | − | 1.03509i | ||||
\(552\) | 1289.67 | + | 89.3058i | 0.0994424 | + | 0.00688607i | ||||
\(553\) | −3181.10 | − | 115.322i | −0.244619 | − | 0.00886795i | ||||
\(554\) | 1525.36 | − | 880.666i | 0.116979 | − | 0.0675377i | ||||
\(555\) | 1200.65 | − | 1782.64i | 0.0918283 | − | 0.136340i | ||||
\(556\) | 5416.82i | 0.413173i | ||||||||
\(557\) | −18967.2 | + | 10950.7i | −1.44285 | + | 0.833028i | −0.998039 | − | 0.0625971i | \(-0.980062\pi\) |
−0.444809 | + | 0.895626i | \(0.646728\pi\) | |||||||
\(558\) | −10180.0 | − | 1416.65i | −0.772316 | − | 0.107476i | ||||
\(559\) | 13385.1i | 1.01276i | ||||||||
\(560\) | 783.161 | + | 28.3913i | 0.0590975 | + | 0.00214241i | ||||
\(561\) | −71.0497 | + | 34.7128i | −0.00534709 | + | 0.00261243i | ||||
\(562\) | 140.453 | 0.0105421 | ||||||||
\(563\) | −6893.85 | + | 11940.5i | −0.516059 | + | 0.893840i | 0.483767 | + | 0.875197i | \(0.339268\pi\) |
−0.999826 | + | 0.0186434i | \(0.994065\pi\) | |||||||
\(564\) | −10081.0 | − | 698.076i | −0.752635 | − | 0.0521175i | ||||
\(565\) | −2162.16 | + | 1248.32i | −0.160996 | + | 0.0929509i | ||||
\(566\) | 4252.43 | 0.315800 | ||||||||
\(567\) | −10020.9 | + | 9047.92i | −0.742223 | + | 0.670154i | ||||
\(568\) | −14586.7 | −1.07754 | ||||||||
\(569\) | −10087.0 | + | 5823.75i | −0.743181 | + | 0.429076i | −0.823225 | − | 0.567715i | \(-0.807827\pi\) |
0.0800436 | + | 0.996791i | \(0.474494\pi\) | |||||||
\(570\) | 18989.7 | + | 1314.98i | 1.39542 | + | 0.0966286i | ||||
\(571\) | −1244.70 | + | 2155.88i | −0.0912243 | + | 0.158005i | −0.908027 | − | 0.418913i | \(-0.862411\pi\) |
0.816802 | + | 0.576918i | \(0.195745\pi\) | |||||||
\(572\) | 2656.21 | 0.194164 | ||||||||
\(573\) | 9012.07 | − | 4403.03i | 0.657042 | − | 0.321011i | ||||
\(574\) | −3795.66 | + | 2011.72i | −0.276006 | + | 0.146285i | ||||
\(575\) | 1761.55i | 0.127760i | ||||||||
\(576\) | −9076.42 | − | 1263.08i | −0.656570 | − | 0.0913688i | ||||
\(577\) | 18275.1 | − | 10551.1i | 1.31855 | − | 0.761265i | 0.335055 | − | 0.942199i | \(-0.391245\pi\) |
0.983495 | + | 0.180934i | \(0.0579119\pi\) | |||||||
\(578\) | 8775.65i | 0.631521i | ||||||||
\(579\) | 3867.58 | − | 5742.30i | 0.277601 | − | 0.412162i | ||||
\(580\) | −9010.01 | + | 5201.93i | −0.645035 | + | 0.372411i | ||||
\(581\) | −11025.0 | − | 20801.8i | −0.787256 | − | 1.48538i | ||||
\(582\) | 785.229 | + | 54.3745i | 0.0559257 | + | 0.00387268i | ||||
\(583\) | −1202.57 | − | 2082.91i | −0.0854293 | − | 0.147968i | ||||
\(584\) | 6660.68 | + | 11536.6i | 0.471953 | + | 0.817447i | ||||
\(585\) | 32804.1 | − | 13305.4i | 2.31843 | − | 0.940360i | ||||
\(586\) | −5573.49 | − | 3217.86i | −0.392899 | − | 0.226840i | ||||
\(587\) | 12811.9 | − | 22190.8i | 0.900856 | − | 1.56033i | 0.0744697 | − | 0.997223i | \(-0.476274\pi\) |
0.826386 | − | 0.563104i | \(-0.190393\pi\) | |||||||
\(588\) | 8475.59 | + | 1208.31i | 0.594434 | + | 0.0847444i | ||||
\(589\) | 12874.4 | + | 22299.1i | 0.900645 | + | 1.55996i | ||||
\(590\) | 20041.4i | 1.39846i | ||||||||
\(591\) | 652.039 | − | 9416.17i | 0.0453829 | − | 0.655380i | ||||
\(592\) | −60.9675 | −0.00423269 | ||||||||
\(593\) | −413.666 | + | 716.491i | −0.0286463 | + | 0.0496168i | −0.879993 | − | 0.474986i | \(-0.842453\pi\) |
0.851347 | + | 0.524603i | \(0.175786\pi\) | |||||||
\(594\) | −557.351 | − | 1703.57i | −0.0384990 | − | 0.117674i | ||||
\(595\) | 667.824 | + | 24.2100i | 0.0460136 | + | 0.00166809i | ||||
\(596\) | 9012.86 | + | 5203.57i | 0.619431 | + | 0.357629i | ||||
\(597\) | 317.366 | − | 155.056i | 0.0217570 | − | 0.0106298i | ||||
\(598\) | 1302.19 | + | 751.820i | 0.0890477 | + | 0.0514117i | ||||
\(599\) | −17.0623 | − | 9.85092i | −0.00116385 | − | 0.000671950i | 0.499418 | − | 0.866361i | \(-0.333547\pi\) |
−0.500582 | + | 0.865689i | \(0.666881\pi\) | |||||||
\(600\) | 1331.77 | − | 19232.2i | 0.0906155 | − | 1.30859i | ||||
\(601\) | 8877.74 | + | 5125.57i | 0.602547 | + | 0.347881i | 0.770043 | − | 0.637992i | \(-0.220235\pi\) |
−0.167496 | + | 0.985873i | \(0.553568\pi\) | |||||||
\(602\) | −4853.16 | − | 3041.57i | −0.328572 | − | 0.205922i | ||||
\(603\) | 4465.73 | − | 5731.85i | 0.301590 | − | 0.387096i | ||||
\(604\) | −5144.93 | + | 8911.27i | −0.346596 | + | 0.600322i | ||||
\(605\) | −21686.4 | −1.45732 | ||||||||
\(606\) | −13749.7 | + | 6717.71i | −0.921690 | + | 0.450311i | ||||
\(607\) | − | 17590.0i | − | 1.17620i | −0.808788 | − | 0.588101i | \(-0.799876\pi\) | ||
0.808788 | − | 0.588101i | \(-0.200124\pi\) | |||||||
\(608\) | 10803.0 | + | 18711.4i | 0.720594 | + | 1.24811i | ||||
\(609\) | 11241.3 | − | 4996.17i | 0.747983 | − | 0.332438i | ||||
\(610\) | −5257.39 | + | 9106.06i | −0.348960 | + | 0.604416i | ||||
\(611\) | −27130.9 | − | 15664.1i | −1.79640 | − | 1.03715i | ||||
\(612\) | −273.566 | − | 38.0697i | −0.0180690 | − | 0.00251450i | ||||
\(613\) | −13259.6 | − | 22966.2i | −0.873652 | − | 1.51321i | −0.858192 | − | 0.513330i | \(-0.828412\pi\) |
−0.0154607 | − | 0.999880i | \(-0.504921\pi\) | |||||||
\(614\) | −2529.69 | − | 4381.56i | −0.166271 | − | 0.287989i | ||||
\(615\) | 5014.07 | + | 10262.7i | 0.328759 | + | 0.672899i | ||||
\(616\) | −1608.82 | + | 2567.04i | −0.105229 | + | 0.167904i | ||||
\(617\) | 20820.5 | − | 12020.7i | 1.35851 | − | 0.784336i | 0.369086 | − | 0.929395i | \(-0.379671\pi\) |
0.989423 | + | 0.145060i | \(0.0463374\pi\) | |||||||
\(618\) | 7508.74 | + | 15368.8i | 0.488747 | + | 1.00036i | ||||
\(619\) | − | 16042.3i | − | 1.04167i | −0.853656 | − | 0.520837i | \(-0.825620\pi\) | ||
0.853656 | − | 0.520837i | \(-0.174380\pi\) | |||||||
\(620\) | 15007.5 | − | 8664.56i | 0.972120 | − | 0.561254i | ||||
\(621\) | −313.999 | + | 1492.14i | −0.0202904 | + | 0.0964211i | ||||
\(622\) | 12767.5i | 0.823041i | ||||||||
\(623\) | −3042.21 | − | 5739.96i | −0.195640 | − | 0.369128i | ||||
\(624\) | −832.877 | − | 560.963i | −0.0534323 | − | 0.0359880i | ||||
\(625\) | −9615.57 | −0.615397 | ||||||||
\(626\) | 3156.69 | − | 5467.55i | 0.201544 | − | 0.349085i | ||||
\(627\) | −2508.49 | + | 3724.43i | −0.159776 | + | 0.237224i | ||||
\(628\) | −12455.9 | + | 7191.43i | −0.791473 | + | 0.456957i | ||||
\(629\) | −51.9888 | −0.00329559 | ||||||||
\(630\) | −2630.00 | + | 14917.5i | −0.166320 | + | 0.943380i | ||||
\(631\) | 8270.89 | 0.521805 | 0.260902 | − | 0.965365i | \(-0.415980\pi\) | ||||
0.260902 | + | 0.965365i | \(0.415980\pi\) | |||||||
\(632\) | 3407.30 | − | 1967.21i | 0.214454 | − | 0.123815i | ||||
\(633\) | 3909.45 | + | 8001.82i | 0.245477 | + | 0.502439i | ||||
\(634\) | −1903.98 | + | 3297.79i | −0.119269 | + | 0.206580i | ||||
\(635\) | 499.020 | 0.0311858 | ||||||||
\(636\) | 580.340 | − | 8380.75i | 0.0361823 | − | 0.522513i | ||||
\(637\) | 21964.7 | + | 14900.5i | 1.36620 | + | 0.926811i | ||||
\(638\) | 1633.16i | 0.101344i | ||||||||
\(639\) | 2371.42 | − | 17040.8i | 0.146810 | − | 1.05497i | ||||
\(640\) | 12068.8 | − | 6967.93i | 0.745408 | − | 0.430362i | ||||
\(641\) | 7425.79i | 0.457568i | 0.973477 | + | 0.228784i | \(0.0734750\pi\) | ||||
−0.973477 | + | 0.228784i | \(0.926525\pi\) | |||||||
\(642\) | 4041.85 | + | 279.885i | 0.248472 | + | 0.0172059i | ||||
\(643\) | 5121.19 | − | 2956.72i | 0.314090 | − | 0.181340i | −0.334665 | − | 0.942337i | \(-0.608623\pi\) |
0.648755 | + | 0.760997i | \(0.275290\pi\) | |||||||
\(644\) | 854.327 | − | 452.798i | 0.0522752 | − | 0.0277061i | ||||
\(645\) | −8507.31 | + | 12631.0i | −0.519341 | + | 0.771080i | ||||
\(646\) | −230.222 | − | 398.756i | −0.0140216 | − | 0.0242861i | ||||
\(647\) | 9583.58 | + | 16599.2i | 0.582333 | + | 1.00863i | 0.995202 | + | 0.0978399i | \(0.0311933\pi\) |
−0.412869 | + | 0.910790i | \(0.635473\pi\) | |||||||
\(648\) | 4556.26 | − | 16053.5i | 0.276214 | − | 0.973209i | ||||
\(649\) | −4094.37 | − | 2363.89i | −0.247640 | − | 0.142975i | ||||
\(650\) | 11211.5 | − | 19418.9i | 0.676540 | − | 1.17180i | ||||
\(651\) | −18724.0 | + | 8321.83i | −1.12727 | + | 0.501011i | ||||
\(652\) | −5545.77 | − | 9605.56i | −0.333112 | − | 0.576967i | ||||
\(653\) | 9070.14i | 0.543556i | 0.962360 | + | 0.271778i | \(0.0876116\pi\) | ||||
−0.962360 | + | 0.271778i | \(0.912388\pi\) | |||||||
\(654\) | −8990.18 | − | 6055.10i | −0.537529 | − | 0.362039i | ||||
\(655\) | 16599.3 | 0.990212 | ||||||||
\(656\) | 162.003 | − | 280.598i | 0.00964203 | − | 0.0167005i | ||||
\(657\) | −14560.5 | + | 5905.75i | −0.864625 | + | 0.350693i | ||||
\(658\) | 11844.6 | − | 6277.68i | 0.701747 | − | 0.371929i | ||||
\(659\) | 25154.3 | + | 14522.8i | 1.48691 | + | 0.858465i | 0.999889 | − | 0.0149269i | \(-0.00475157\pi\) |
0.487017 | + | 0.873392i | \(0.338085\pi\) | |||||||
\(660\) | 2506.57 | + | 1688.23i | 0.147830 | + | 0.0995674i | ||||
\(661\) | −7059.83 | − | 4075.99i | −0.415424 | − | 0.239845i | 0.277693 | − | 0.960670i | \(-0.410430\pi\) |
−0.693118 | + | 0.720824i | \(0.743763\pi\) | |||||||
\(662\) | −7586.39 | − | 4380.00i | −0.445398 | − | 0.257151i | ||||
\(663\) | −710.218 | − | 478.349i | −0.0416027 | − | 0.0280204i | ||||
\(664\) | 25200.4 | + | 14549.4i | 1.47284 | + | 0.850343i | ||||
\(665\) | 33529.8 | − | 17770.9i | 1.95523 | − | 1.03628i | ||||
\(666\) | 162.427 | − | 1167.19i | 0.00945033 | − | 0.0679094i | ||||
\(667\) | 694.665 | − | 1203.19i | 0.0403261 | − | 0.0698469i | ||||
\(668\) | −11001.4 | −0.637211 | ||||||||
\(669\) | −12114.7 | − | 8159.53i | −0.700120 | − | 0.471548i | ||||
\(670\) | − | 8152.18i | − | 0.470069i | ||||||
\(671\) | −1240.22 | − | 2148.13i | −0.0713536 | − | 0.123588i | ||||
\(672\) | −15711.6 | + | 6982.95i | −0.901914 | + | 0.400853i | ||||
\(673\) | 376.383 | − | 651.914i | 0.0215579 | − | 0.0373395i | −0.855045 | − | 0.518554i | \(-0.826471\pi\) |
0.876603 | + | 0.481214i | \(0.159804\pi\) | |||||||
\(674\) | 3821.87 | + | 2206.56i | 0.218417 | + | 0.126103i | ||||
\(675\) | 22251.5 | + | 4682.50i | 1.26883 | + | 0.267007i | ||||
\(676\) | 9104.90 | + | 15770.1i | 0.518030 | + | 0.897254i | ||||
\(677\) | −1991.13 | − | 3448.73i | −0.113036 | − | 0.195784i | 0.803957 | − | 0.594687i | \(-0.202724\pi\) |
−0.916993 | + | 0.398904i | \(0.869391\pi\) | |||||||
\(678\) | −764.712 | + | 1135.39i | −0.0433165 | + | 0.0643132i | ||||
\(679\) | 1386.46 | − | 734.832i | 0.0783616 | − | 0.0415320i | ||||
\(680\) | −715.311 | + | 412.985i | −0.0403396 | + | 0.0232901i | ||||
\(681\) | −20278.4 | − | 1404.21i | −1.14107 | − | 0.0790154i | ||||
\(682\) | − | 2720.26i | − | 0.152733i | ||||||
\(683\) | −4073.29 | + | 2351.72i | −0.228199 | + | 0.131751i | −0.609741 | − | 0.792601i | \(-0.708727\pi\) |
0.381542 | + | 0.924352i | \(0.375393\pi\) | |||||||
\(684\) | −14534.4 | + | 5895.17i | −0.812480 | + | 0.329543i | ||||
\(685\) | − | 21062.9i | − | 1.17485i | ||||||
\(686\) | −10393.7 | + | 4578.00i | −0.578477 | + | 0.254794i | ||||
\(687\) | −461.100 | + | 6658.79i | −0.0256071 | + | 0.369794i | ||||
\(688\) | 431.991 | 0.0239382 | ||||||||
\(689\) | 13022.2 | − | 22555.1i | 0.720038 | − | 1.24714i | ||||
\(690\) | 750.986 | + | 1537.11i | 0.0414341 | + | 0.0848069i | ||||
\(691\) | 2015.73 | − | 1163.78i | 0.110972 | − | 0.0640700i | −0.443486 | − | 0.896281i | \(-0.646259\pi\) |
0.554459 | + | 0.832211i | \(0.312925\pi\) | |||||||
\(692\) | 7892.20 | 0.433550 | ||||||||
\(693\) | −2737.39 | − | 2296.83i | −0.150050 | − | 0.125901i | ||||
\(694\) | 17959.6 | 0.982329 | ||||||||
\(695\) | −16546.7 | + | 9553.25i | −0.903098 | + | 0.521404i | ||||
\(696\) | −8493.84 | + | 12611.0i | −0.462583 | + | 0.686810i | ||||
\(697\) | 138.145 | − | 239.274i | 0.00750734 | − | 0.0130031i | ||||
\(698\) | 20461.7 | 1.10958 | ||||||||
\(699\) | 6518.67 | + | 4390.48i | 0.352731 | + | 0.237573i | ||||
\(700\) | −6752.34 | − | 12740.1i | −0.364592 | − | 0.687903i | ||||
\(701\) | 1250.95i | 0.0674005i | 0.999432 | + | 0.0337003i | \(0.0107292\pi\) | ||||
−0.999432 | + | 0.0337003i | \(0.989271\pi\) | |||||||
\(702\) | 12958.2 | − | 14450.5i | 0.696691 | − | 0.776920i | ||||
\(703\) | −2556.71 | + | 1476.12i | −0.137167 | + | 0.0791933i | ||||
\(704\) | − | 2425.38i | − | 0.129843i | ||||||
\(705\) | −15646.7 | − | 32025.4i | −0.835870 | − | 1.71085i | ||||
\(706\) | −2255.72 | + | 1302.34i | −0.120248 | + | 0.0694253i | ||||
\(707\) | −16201.0 | + | 25850.4i | −0.861811 | + | 1.37511i | ||||
\(708\) | −7249.08 | − | 14837.3i | −0.384798 | − | 0.787599i | ||||
\(709\) | −17364.5 | − | 30076.3i | −0.919801 | − | 1.59314i | −0.799716 | − | 0.600379i | \(-0.795017\pi\) |
−0.120085 | − | 0.992764i | \(-0.538317\pi\) | |||||||
\(710\) | −9651.52 | − | 16716.9i | −0.510162 | − | 0.883626i | ||||
\(711\) | 1744.24 | + | 4300.38i | 0.0920031 | + | 0.226831i | ||||
\(712\) | 6953.69 | + | 4014.71i | 0.366012 | + | 0.211317i | ||||
\(713\) | −1157.06 | + | 2004.09i | −0.0607747 | + | 0.105265i | ||||
\(714\) | 334.826 | − | 148.812i | 0.0175498 | − | 0.00779994i | ||||
\(715\) | 4684.57 | + | 8113.91i | 0.245025 | + | 0.424396i | ||||
\(716\) | 13600.5i | 0.709880i | ||||||||
\(717\) | −12622.9 | + | 6167.20i | −0.657479 | + | 0.321225i | ||||
\(718\) | −583.883 | −0.0303486 | ||||||||
\(719\) | 14119.5 | − | 24455.6i | 0.732361 | − | 1.26849i | −0.223511 | − | 0.974701i | \(-0.571752\pi\) |
0.955872 | − | 0.293785i | \(-0.0949149\pi\) | |||||||
\(720\) | −429.418 | − | 1058.72i | −0.0222270 | − | 0.0548002i | ||||
\(721\) | 28894.4 | + | 18108.7i | 1.49249 | + | 0.935372i | ||||
\(722\) | −12023.8 | − | 6941.92i | −0.619775 | − | 0.357827i | ||||
\(723\) | −1771.14 | + | 25577.2i | −0.0911057 | + | 1.31567i | ||||
\(724\) | 3819.07 | + | 2204.94i | 0.196042 | + | 0.113185i | ||||
\(725\) | −17942.6 | − | 10359.2i | −0.919133 | − | 0.530662i | ||||
\(726\) | −10683.7 | + | 5219.72i | −0.546154 | + | 0.266835i | ||||
\(727\) | −4105.21 | − | 2370.14i | −0.209427 | − | 0.120913i | 0.391618 | − | 0.920128i | \(-0.371916\pi\) |
−0.601045 | + | 0.799215i | \(0.705249\pi\) | |||||||
\(728\) | −32784.1 | − | 1188.49i | −1.66904 | − | 0.0605062i | ||||
\(729\) | 18013.7 | + | 7932.72i | 0.915189 | + | 0.403024i | ||||
\(730\) | −8814.29 | + | 15266.8i | −0.446892 | + | 0.774040i | ||||
\(731\) | 368.371 | 0.0186384 | ||||||||
\(732\) | 598.511 | − | 8643.16i | 0.0302208 | − | 0.436421i | ||||
\(733\) | 20291.2i | 1.02248i | 0.859439 | + | 0.511238i | \(0.170813\pi\) | ||||
−0.859439 | + | 0.511238i | \(0.829187\pi\) | |||||||
\(734\) | 5691.66 | + | 9858.24i | 0.286217 | + | 0.495742i | ||||
\(735\) | 11256.8 | + | 28021.3i | 0.564915 | + | 1.40623i | ||||
\(736\) | −970.905 | + | 1681.66i | −0.0486251 | + | 0.0842211i | ||||
\(737\) | 1665.46 | + | 961.554i | 0.0832402 | + | 0.0480587i | ||||
\(738\) | 4940.29 | + | 3849.02i | 0.246416 | + | 0.191984i | ||||
\(739\) | −14186.1 | − | 24571.1i | −0.706151 | − | 1.22309i | −0.966274 | − | 0.257515i | \(-0.917096\pi\) |
0.260123 | − | 0.965575i | \(-0.416237\pi\) | |||||||
\(740\) | 993.439 | + | 1720.69i | 0.0493508 | + | 0.0854780i | ||||
\(741\) | −48509.0 | − | 3359.09i | −2.40489 | − | 0.166531i | ||||
\(742\) | 5218.90 | + | 9846.89i | 0.258210 | + | 0.487184i | ||||
\(743\) | 7268.83 | − | 4196.66i | 0.358907 | − | 0.207215i | −0.309694 | − | 0.950836i | \(-0.600227\pi\) |
0.668601 | + | 0.743621i | \(0.266893\pi\) | |||||||
\(744\) | 14147.7 | − | 21005.5i | 0.697150 | − | 1.03508i | ||||
\(745\) | 36708.7i | 1.80524i | ||||||||
\(746\) | 2999.71 | − | 1731.88i | 0.147221 | − | 0.0849983i | ||||
\(747\) | −21094.3 | + | 27074.9i | −1.03320 | + | 1.32613i | ||||
\(748\) | − | 73.1015i | − | 0.00357334i | ||||||
\(749\) | 7136.61 | − | 3782.44i | 0.348152 | − | 0.184522i | ||||
\(750\) | 5243.75 | − | 2561.94i | 0.255300 | − | 0.124732i | ||||
\(751\) | 28345.3 | 1.37727 | 0.688637 | − | 0.725106i | \(-0.258209\pi\) | ||||
0.688637 | + | 0.725106i | \(0.258209\pi\) | |||||||
\(752\) | −505.541 | + | 875.623i | −0.0245149 | + | 0.0424610i | ||||
\(753\) | −3286.31 | − | 227.567i | −0.159044 | − | 0.0110133i | ||||
\(754\) | −15315.6 | + | 8842.46i | −0.739736 | + | 0.427087i | ||||
\(755\) | −36294.9 | −1.74955 | ||||||||
\(756\) | −3448.68 | − | 11995.3i | −0.165909 | − | 0.577068i | ||||
\(757\) | −18383.7 | −0.882651 | −0.441326 | − | 0.897347i | \(-0.645492\pi\) | ||||
−0.441326 | + | 0.897347i | \(0.645492\pi\) | |||||||
\(758\) | −14423.4 | + | 8327.35i | −0.691136 | + | 0.399028i | ||||
\(759\) | −402.605 | − | 27.8791i | −0.0192538 | − | 0.00133326i | ||||
\(760\) | −23451.8 | + | 40619.7i | −1.11932 | + | 1.93872i | ||||
\(761\) | 29518.0 | 1.40608 | 0.703040 | − | 0.711150i | \(-0.251825\pi\) | ||||
0.703040 | + | 0.711150i | \(0.251825\pi\) | |||||||
\(762\) | 245.839 | − | 120.110i | 0.0116874 | − | 0.00571012i | ||||
\(763\) | −21594.5 | − | 782.846i | −1.02460 | − | 0.0371441i | ||||
\(764\) | 9272.33i | 0.439085i | ||||||||
\(765\) | −366.177 | − | 902.800i | −0.0173061 | − | 0.0426677i | ||||
\(766\) | −4575.19 | + | 2641.49i | −0.215807 | + | 0.124596i | ||||
\(767\) | − | 51195.4i | − | 2.41012i | ||||||
\(768\) | 12150.1 | − | 18039.6i | 0.570870 | − | 0.847587i | ||||
\(769\) | 21532.4 | − | 12431.8i | 1.00973 | − | 0.582965i | 0.0986144 | − | 0.995126i | \(-0.468559\pi\) |
0.911111 | + | 0.412160i | \(0.135226\pi\) | |||||||
\(770\) | −4006.43 | − | 145.242i | −0.187509 | − | 0.00679760i | ||||
\(771\) | −2760.31 | − | 191.143i | −0.128937 | − | 0.00892846i | ||||
\(772\) | 3200.11 | + | 5542.75i | 0.149190 | + | 0.258404i | ||||
\(773\) | 14395.5 | + | 24933.8i | 0.669820 | + | 1.16016i | 0.977954 | + | 0.208819i | \(0.0669621\pi\) |
−0.308134 | + | 0.951343i | \(0.599705\pi\) | |||||||
\(774\) | −1150.89 | + | 8270.23i | −0.0534470 | + | 0.384066i | ||||
\(775\) | 29886.0 | + | 17254.7i | 1.38521 | + | 0.799750i | ||||
\(776\) | −969.736 | + | 1679.63i | −0.0448602 | + | 0.0777001i | ||||
\(777\) | −954.144 | − | 2146.81i | −0.0440537 | − | 0.0991203i | ||||
\(778\) | −4236.88 | − | 7338.49i | −0.195244 | − | 0.338172i | ||||
\(779\) | − | 15689.4i | − | 0.721607i | ||||||
\(780\) | −2260.70 | + | 32647.0i | −0.103777 | + | 1.49865i | ||||
\(781\) | 4553.60 | 0.208631 | ||||||||
\(782\) | 20.6908 | − | 35.8375i | 0.000946165 | − | 0.00163881i | ||||
\(783\) | −13351.9 | − | 11973.1i | −0.609398 | − | 0.546468i | ||||
\(784\) | 480.898 | − | 708.886i | 0.0219068 | − | 0.0322926i | ||||
\(785\) | −43935.2 | − | 25366.0i | −1.99760 | − | 1.15331i | ||||
\(786\) | 8177.54 | − | 3995.31i | 0.371098 | − | 0.181308i | ||||
\(787\) | −27862.4 | − | 16086.3i | −1.26199 | − | 0.728610i | −0.288530 | − | 0.957471i | \(-0.593167\pi\) |
−0.973459 | + | 0.228861i | \(0.926500\pi\) | |||||||
\(788\) | 7556.56 | + | 4362.78i | 0.341614 | + | 0.197231i | ||||
\(789\) | −1877.69 | + | 27116.0i | −0.0847245 | + | 1.22352i | ||||
\(790\) | 4508.99 | + | 2603.27i | 0.203067 | + | 0.117241i | ||||
\(791\) | −98.8672 | + | 2727.21i | −0.00444414 | + | 0.122590i | ||||
\(792\) | 4374.47 | + | 608.756i | 0.196263 | + | 0.0273121i | ||||
\(793\) | 13429.9 | − | 23261.3i | 0.601401 | − | 1.04166i | ||||
\(794\) | −14054.9 | −0.628198 | ||||||||
\(795\) | 26624.1 | − | 13007.8i | 1.18775 | − | 0.580299i | ||||
\(796\) | 326.531i | 0.0145397i | ||||||||
\(797\) | −2589.32 | − | 4484.84i | −0.115080 | − | 0.199324i | 0.802732 | − | 0.596340i | \(-0.203379\pi\) |
−0.917812 | + | 0.397016i | \(0.870046\pi\) | |||||||
\(798\) | 12240.9 | − | 16825.0i | 0.543012 | − | 0.746366i | ||||
\(799\) | −431.089 | + | 746.669i | −0.0190874 | + | 0.0330604i | ||||
\(800\) | 25077.7 | + | 14478.6i | 1.10829 | + | 0.639870i | ||||
\(801\) | −5820.67 | + | 7470.94i | −0.256758 | + | 0.329554i | ||||
\(802\) | 3724.71 | + | 6451.38i | 0.163995 | + | 0.284048i | ||||
\(803\) | −2079.30 | − | 3601.45i | −0.0913785 | − | 0.158272i | ||||
\(804\) | 2948.69 | + | 6035.34i | 0.129344 | + | 0.264739i | ||||
\(805\) | 2889.87 | + | 1811.14i | 0.126527 | + | 0.0792973i | ||||
\(806\) | 25510.3 | − | 14728.4i | 1.11484 | − | 0.643654i | ||||
\(807\) | 16338.2 | + | 33440.8i | 0.712678 | + | 1.45870i | ||||
\(808\) | − | 37707.3i | − | 1.64176i | ||||||
\(809\) | 2591.38 | − | 1496.14i | 0.112618 | − | 0.0650202i | −0.442633 | − | 0.896703i | \(-0.645955\pi\) |
0.555251 | + | 0.831683i | \(0.312622\pi\) | |||||||
\(810\) | 21412.6 | − | 5400.38i | 0.928843 | − | 0.234259i | ||||
\(811\) | 24504.5i | 1.06100i | 0.847685 | + | 0.530499i | \(0.177996\pi\) | ||||
−0.847685 | + | 0.530499i | \(0.822004\pi\) | |||||||
\(812\) | −411.994 | + | 11364.7i | −0.0178056 | + | 0.491160i | ||||
\(813\) | 3333.41 | + | 2245.13i | 0.143798 | + | 0.0968514i | ||||
\(814\) | 311.893 | 0.0134298 | ||||||||
\(815\) | 19561.4 | − | 33881.3i | 0.840741 | − | 1.45621i | ||||
\(816\) | −15.4382 | + | 22.9216i | −0.000662311 | + | 0.000983352i | ||||
\(817\) | 18115.8 | − | 10459.2i | 0.775755 | − | 0.447883i | ||||
\(818\) | 24021.8 | 1.02678 | ||||||||
\(819\) | 6718.30 | − | 38106.7i | 0.286638 | − | 1.62583i | ||||
\(820\) | −10559.1 | −0.449683 | ||||||||
\(821\) | 22039.8 | − | 12724.7i | 0.936898 | − | 0.540918i | 0.0479114 | − | 0.998852i | \(-0.484743\pi\) |
0.888987 | + | 0.457933i | \(0.151410\pi\) | |||||||
\(822\) | −5069.66 | − | 10376.5i | −0.215115 | − | 0.440295i | ||||
\(823\) | −1003.30 | + | 1737.77i | −0.0424943 | + | 0.0736023i | −0.886490 | − | 0.462747i | \(-0.846864\pi\) |
0.843996 | + | 0.536350i | \(0.180197\pi\) | |||||||
\(824\) | −42147.5 | −1.78189 | ||||||||
\(825\) | −415.746 | + | 6003.84i | −0.0175448 | + | 0.253366i | ||||
\(826\) | 18562.4 | + | 11633.4i | 0.781922 | + | 0.490046i | ||||
\(827\) | 24195.9i | 1.01738i | 0.860950 | + | 0.508690i | \(0.169870\pi\) | ||||
−0.860950 | + | 0.508690i | \(0.830130\pi\) | |||||||
\(828\) | −1111.96 | − | 866.339i | −0.0466708 | − | 0.0363616i | ||||
\(829\) | −15997.9 | + | 9236.41i | −0.670243 | + | 0.386965i | −0.796169 | − | 0.605075i | \(-0.793143\pi\) |
0.125926 | + | 0.992040i | \(0.459810\pi\) | |||||||
\(830\) | 38507.5i | 1.61038i | ||||||||
\(831\) | −5106.82 | − | 353.631i | −0.213181 | − | 0.0147621i | ||||
\(832\) | 22744.9 | − | 13131.8i | 0.947761 | − | 0.547190i | ||||
\(833\) | 410.075 | − | 604.488i | 0.0170567 | − | 0.0251432i | ||||
\(834\) | −5852.25 | + | 8688.99i | −0.242982 | + | 0.360762i | ||||
\(835\) | −19402.4 | − | 33605.9i | −0.804127 | − | 1.39279i | ||||
\(836\) | −2075.57 | − | 3595.00i | −0.0858675 | − | 0.148727i | ||||
\(837\) | 22239.5 | + | 19943.0i | 0.918412 | + | 0.823572i | ||||
\(838\) | −17060.2 | − | 9849.71i | −0.703263 | − | 0.406029i | ||||
\(839\) | −2731.37 | + | 4730.87i | −0.112393 | + | 0.194670i | −0.916734 | − | 0.399497i | \(-0.869185\pi\) |
0.804342 | + | 0.594167i | \(0.202518\pi\) | |||||||
\(840\) | −30181.7 | − | 21958.4i | −1.23972 | − | 0.901950i | ||||
\(841\) | −4024.27 | − | 6970.24i | −0.165003 | − | 0.285794i | ||||
\(842\) | − | 14237.4i | − | 0.582724i | ||||||
\(843\) | −338.573 | − | 228.037i | −0.0138328 | − | 0.00931674i | ||||
\(844\) | −8232.90 | −0.335768 | ||||||||
\(845\) | −32115.3 | + | 55625.3i | −1.30745 | + | 2.26458i | ||||
\(846\) | −15416.5 | − | 12011.1i | −0.626512 | − | 0.488121i | ||||
\(847\) | −12588.3 | + | 20086.0i | −0.510672 | + | 0.814833i | ||||
\(848\) | −727.943 | − | 420.278i | −0.0294784 | − | 0.0170193i | ||||
\(849\) | −10250.8 | − | 6904.16i | −0.414378 | − | 0.279093i | ||||
\(850\) | −534.426 | − | 308.551i | −0.0215655 | − | 0.0124508i | ||||
\(851\) | −229.780 | − | 132.664i | −0.00925589 | − | 0.00534389i | ||||
\(852\) | 13192.0 | + | 8885.11i | 0.530457 | + | 0.357276i | ||||
\(853\) | −14009.1 | − | 8088.18i | −0.562325 | − | 0.324659i | 0.191753 | − | 0.981443i | \(-0.438583\pi\) |
−0.754078 | + | 0.656785i | \(0.771916\pi\) | |||||||
\(854\) | 5382.31 | + | 10155.2i | 0.215666 | + | 0.406914i | ||||
\(855\) | −43641.2 | − | 34001.2i | −1.74561 | − | 1.36002i | ||||
\(856\) | −4991.57 | + | 8645.66i | −0.199309 | + | 0.345213i | ||||
\(857\) | 13078.5 | 0.521300 | 0.260650 | − | 0.965433i | \(-0.416063\pi\) | ||||
0.260650 | + | 0.965433i | \(0.416063\pi\) | |||||||
\(858\) | 4260.77 | + | 2869.73i | 0.169534 | + | 0.114185i | ||||
\(859\) | − | 26957.6i | − | 1.07076i | −0.844612 | − | 0.535379i | \(-0.820169\pi\) | ||
0.844612 | − | 0.535379i | \(-0.179831\pi\) | |||||||
\(860\) | −7039.10 | − | 12192.1i | −0.279106 | − | 0.483426i | ||||
\(861\) | 12415.9 | + | 1313.16i | 0.491443 | + | 0.0519772i | ||||
\(862\) | −5631.32 | + | 9753.73i | −0.222510 | + | 0.385399i | ||||
\(863\) | 6162.57 | + | 3557.96i | 0.243078 | + | 0.140341i | 0.616591 | − | 0.787284i | \(-0.288513\pi\) |
−0.373513 | + | 0.927625i | \(0.621847\pi\) | |||||||
\(864\) | 18661.4 | + | 16734.4i | 0.734809 | + | 0.658929i | ||||
\(865\) | 13918.9 | + | 24108.2i | 0.547117 | + | 0.947635i | ||||
\(866\) | −1068.94 | − | 1851.46i | −0.0419446 | − | 0.0726502i | ||||
\(867\) | 14248.0 | − | 21154.4i | 0.558116 | − | 0.828650i | ||||
\(868\) | 686.235 | − | 18929.5i | 0.0268345 | − | 0.740218i | ||||
\(869\) | −1063.68 | + | 614.113i | −0.0415221 | + | 0.0239728i | ||||
\(870\) | −20072.8 | − | 1389.98i | −0.782221 | − | 0.0541663i | ||||
\(871\) | 20824.7i | 0.810122i | ||||||||
\(872\) | 23130.0 | − | 13354.1i | 0.898257 | − | 0.518609i | ||||
\(873\) | −1804.57 | − | 1405.96i | −0.0699604 | − | 0.0545068i | ||||
\(874\) | − | 2349.90i | − | 0.0909456i | ||||||
\(875\) | 6178.59 | − | 9858.62i | 0.238714 | − | 0.380894i | ||||
\(876\) | 1003.44 | − | 14490.7i | 0.0387020 | − | 0.558900i | ||||
\(877\) | 14659.7 | 0.564452 | 0.282226 | − | 0.959348i | \(-0.408927\pi\) | ||||
0.282226 | + | 0.959348i | \(0.408927\pi\) | |||||||
\(878\) | 5114.09 | − | 8857.86i | 0.196574 | − | 0.340476i | ||||
\(879\) | 8210.87 | + | 16805.9i | 0.315069 | + | 0.644879i | ||||
\(880\) | 261.868 | − | 151.190i | 0.0100313 | − | 0.00579160i | ||||
\(881\) | −504.927 | −0.0193092 | −0.00965461 | − | 0.999953i | \(-0.503073\pi\) | ||||
−0.00965461 | + | 0.999953i | \(0.503073\pi\) | |||||||
\(882\) | 12290.0 | + | 11095.1i | 0.469192 | + | 0.423573i | ||||
\(883\) | 15773.0 | 0.601135 | 0.300567 | − | 0.953761i | \(-0.402824\pi\) | ||||
0.300567 | + | 0.953761i | \(0.402824\pi\) | |||||||
\(884\) | 685.537 | − | 395.795i | 0.0260827 | − | 0.0150589i | ||||
\(885\) | 32538.8 | − | 48311.2i | 1.23591 | − | 1.83499i | ||||
\(886\) | 7854.19 | − | 13603.8i | 0.297818 | − | 0.515836i | ||||
\(887\) | 36758.6 | 1.39147 | 0.695735 | − | 0.718298i | \(-0.255079\pi\) | ||||
0.695735 | + | 0.718298i | \(0.255079\pi\) | |||||||
\(888\) | 2408.39 | + | 1622.11i | 0.0910139 | + | 0.0613001i | ||||
\(889\) | 289.666 | − | 462.194i | 0.0109281 | − | 0.0174370i | ||||
\(890\) | 10625.6i | 0.400192i | ||||||||
\(891\) | −1422.35 | + | 5011.50i | −0.0534800 | + | 0.188430i | ||||
\(892\) | 11693.7 | − | 6751.35i | 0.438939 | − | 0.253421i | ||||
\(893\) | 48959.8i | 1.83469i | ||||||||
\(894\) | 8835.45 | + | 18084.3i | 0.330539 | + | 0.676542i | ||||
\(895\) | −41545.3 | + | 23986.2i | −1.55163 | + | 0.895832i | ||||
\(896\) | 551.861 | − | 15222.8i | 0.0205763 | − | 0.567589i | ||||
\(897\) | −1918.39 | − | 3926.53i | −0.0714081 | − | 0.146157i | ||||
\(898\) | 12535.5 | + | 21712.1i | 0.465830 | + | 0.806842i | ||||
\(899\) | −13608.7 | − | 23570.9i | −0.504867 | − | 0.874455i | ||||
\(900\) | −12919.3 | + | 16582.1i | −0.478491 | + | 0.614153i | ||||
\(901\) | −620.737 | − | 358.383i | −0.0229520 | − | 0.0132513i | ||||
\(902\) | −828.765 | + | 1435.46i | −0.0305930 | + | 0.0529885i | ||||
\(903\) | 6760.67 | + | 15211.4i | 0.249148 | + | 0.560581i | ||||
\(904\) | −1686.52 | − | 2921.13i | −0.0620495 | − | 0.107473i | ||||
\(905\) | 15554.8i | 0.571335i | ||||||||
\(906\) | −17880.4 | + | 8735.86i | −0.655671 | + | 0.320342i | ||||
\(907\) | −15362.6 | −0.562410 | −0.281205 | − | 0.959648i | \(-0.590734\pi\) | ||||
−0.281205 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(908\) | 9395.56 | − | 16273.6i | 0.343395 | − | 0.594778i | ||||
\(909\) | 44051.5 | + | 6130.24i | 1.60737 | + | 0.223682i | ||||
\(910\) | −20330.1 | − | 38358.3i | −0.740588 | − | 1.39732i | ||||
\(911\) | −31056.9 | − | 17930.7i | −1.12949 | − | 0.652109i | −0.185681 | − | 0.982610i | \(-0.559449\pi\) |
−0.943806 | + | 0.330501i | \(0.892782\pi\) | |||||||
\(912\) | −108.411 | + | 1565.58i | −0.00393625 | + | 0.0568437i | ||||
\(913\) | −7866.93 | − | 4541.98i | −0.285167 | − | 0.164641i | ||||
\(914\) | −18769.5 | − | 10836.6i | −0.679256 | − | 0.392169i | ||||
\(915\) | 27457.8 | − | 13415.1i | 0.992049 | − | 0.484686i | ||||
\(916\) | −5343.74 | − | 3085.21i | −0.192753 | − | 0.111286i | ||||
\(917\) | 9635.41 | − | 15374.3i | 0.346989 | − | 0.553659i | ||||
\(918\) | −397.691 | − | 356.623i | −0.0142982 | − | 0.0128217i | ||||
\(919\) | −15385.0 | + | 26647.5i | −0.552234 | + | 0.956497i | 0.445879 | + | 0.895093i | \(0.352891\pi\) |
−0.998113 | + | 0.0614041i | \(0.980442\pi\) | |||||||
\(920\) | −4215.38 | −0.151062 | ||||||||
\(921\) | −1015.80 | + | 14669.2i | −0.0363428 | + | 0.524829i | ||||
\(922\) | 28170.4i | 1.00623i | ||||||||
\(923\) | 24654.7 | + | 42703.2i | 0.879219 | + | 1.52285i | ||||
\(924\) | 3018.64 | − | 1341.62i | 0.107474 | − | 0.0477664i | ||||
\(925\) | −1978.34 | + | 3426.59i | −0.0703217 | + | 0.121801i | ||||
\(926\) | −7295.57 | − | 4212.10i | −0.258906 | − | 0.149480i | ||||
\(927\) | 6852.10 | − | 49238.7i | 0.242775 | − | 1.74456i | ||||
\(928\) | −11419.2 | − | 19778.7i | −0.403938 | − | 0.699640i | ||||
\(929\) | 6779.67 | + | 11742.7i | 0.239433 | + | 0.414711i | 0.960552 | − | 0.278101i | \(-0.0897050\pi\) |
−0.721118 | + | 0.692812i | \(0.756372\pi\) | |||||||
\(930\) | 33434.2 | + | 2315.21i | 1.17887 | + | 0.0816330i | ||||
\(931\) | 3003.51 | − | 41370.9i | 0.105732 | − | 1.45637i | ||||
\(932\) | −6292.14 | + | 3632.77i | −0.221144 | + | 0.127677i | ||||
\(933\) | 20729.1 | − | 30777.1i | 0.727375 | − | 1.07995i | ||||
\(934\) | 15693.9i | 0.549808i | ||||||||
\(935\) | 223.303 | − | 128.924i | 0.00781045 | − | 0.00450937i | ||||
\(936\) | 17976.0 | + | 44319.3i | 0.627739 | + | 1.54767i | ||||
\(937\) | − | 56540.8i | − | 1.97130i | −0.168802 | − | 0.985650i | \(-0.553990\pi\) | ||
0.168802 | − | 0.985650i | \(-0.446010\pi\) | |||||||
\(938\) | −7550.58 | − | 4732.10i | −0.262831 | − | 0.164721i | ||||
\(939\) | −16486.4 | + | 8054.79i | −0.572966 | + | 0.279934i | ||||
\(940\) | 32950.3 | 1.14332 | ||||||||
\(941\) | −26170.6 | + | 45328.7i | −0.906627 | + | 1.57032i | −0.0879080 | + | 0.996129i | \(0.528018\pi\) |
−0.818719 | + | 0.574195i | \(0.805315\pi\) | |||||||
\(942\) | −27749.7 | − | 1921.58i | −0.959804 | − | 0.0664634i | ||||
\(943\) | 1221.15 | − | 705.030i | 0.0421697 | − | 0.0243467i | ||||
\(944\) | −1652.28 | −0.0569673 | ||||||||
\(945\) | 30559.6 | − | 31689.8i | 1.05196 | − | 1.09087i | ||||
\(946\) | −2209.95 | −0.0759530 | ||||||||
\(947\) | 22611.7 | − | 13054.8i | 0.775903 | − | 0.447968i | −0.0590734 | − | 0.998254i | \(-0.518815\pi\) |
0.834976 | + | 0.550286i | \(0.185481\pi\) | |||||||
\(948\) | −4279.78 | − | 296.361i | −0.146625 | − | 0.0101533i | ||||
\(949\) | 22516.0 | − | 38998.9i | 0.770180 | − | 1.33399i | ||||
\(950\) | −35042.8 | −1.19678 | ||||||||
\(951\) | 9943.91 | − | 4858.30i | 0.339068 | − | 0.165658i | ||||
\(952\) | −32.7085 | + | 902.249i | −0.00111354 | + | 0.0307164i | ||||
\(953\) | 51075.0i | 1.73608i | 0.496497 | + | 0.868038i | \(0.334619\pi\) | ||||
−0.496497 | + | 0.868038i | \(0.665381\pi\) | |||||||
\(954\) | 9985.34 | − | 12816.4i | 0.338876 | − | 0.434953i | ||||
\(955\) | −28324.1 | + | 16352.9i | −0.959735 | + | 0.554103i | ||||
\(956\) | − | 12987.5i | − | 0.439378i | ||||||
\(957\) | 2651.57 | − | 3936.85i | 0.0895643 | − | 0.132979i | ||||
\(958\) | −14628.6 | + | 8445.85i | −0.493351 | + | 0.284836i | ||||
\(959\) | −19508.6 | − | 12226.4i | −0.656897 | − | 0.411690i | ||||
\(960\) | 29809.8 | + | 2064.23i | 1.00219 | + | 0.0693987i | ||||
\(961\) | 7771.73 | + | 13461.0i | 0.260875 | + | 0.451849i | ||||
\(962\) | 1688.69 | + | 2924.90i | 0.0565962 | + | 0.0980275i | ||||
\(963\) | −9288.76 | − | 7236.95i | −0.310827 | − | 0.242168i | ||||
\(964\) | −20526.0 | − | 11850.7i | −0.685785 | − | 0.395938i | ||||
\(965\) | −11287.6 | + | 19550.7i | −0.376540 | + | 0.652186i | ||||
\(966\) | 1859.60 | + | 196.680i | 0.0619376 | + | 0.00655079i | ||||
\(967\) | 5369.16 | + | 9299.66i | 0.178553 | + | 0.309263i | 0.941385 | − | 0.337334i | \(-0.109525\pi\) |
−0.762832 | + | 0.646596i | \(0.776192\pi\) | |||||||
\(968\) | − | 29298.9i | − | 0.972834i | ||||||
\(969\) | −92.4454 | + | 1335.01i | −0.00306478 | + | 0.0442588i | ||||
\(970\) | −2566.57 | −0.0849562 | ||||||||
\(971\) | −24642.9 | + | 42682.8i | −0.814448 | + | 1.41067i | 0.0952751 | + | 0.995451i | \(0.469627\pi\) |
−0.909723 | + | 0.415215i | \(0.863706\pi\) | |||||||
\(972\) | −13899.2 | + | 11743.2i | −0.458659 | + | 0.387512i | ||||
\(973\) | −756.619 | + | 20871.0i | −0.0249292 | + | 0.687661i | ||||
\(974\) | 9757.52 | + | 5633.50i | 0.320997 | + | 0.185328i | ||||
\(975\) | −58554.3 | + | 28607.9i | −1.92332 | + | 0.939678i | ||||
\(976\) | −750.736 | − | 433.437i | −0.0246214 | − | 0.0142152i | ||||
\(977\) | 31611.5 | + | 18250.9i | 1.03515 | + | 0.597643i | 0.918455 | − | 0.395525i | \(-0.129437\pi\) |
0.116693 | + | 0.993168i | \(0.462771\pi\) | |||||||
\(978\) | 1481.85 | − | 21399.6i | 0.0484504 | − | 0.699677i | ||||
\(979\) | −2170.77 | − | 1253.30i | −0.0708663 | − | 0.0409147i | ||||
\(980\) | −27842.9 | − | 2021.39i | −0.907561 | − | 0.0658887i | ||||
\(981\) | 11840.5 | + | 29192.6i | 0.385362 | + | 0.950099i | ||||
\(982\) | 11722.2 | − | 20303.4i | 0.380926 | − | 0.659783i | ||||
\(983\) | −22195.1 | −0.720156 | −0.360078 | − | 0.932922i | \(-0.617250\pi\) | ||||
−0.360078 | + | 0.932922i | \(0.617250\pi\) | |||||||
\(984\) | −13865.2 | + | 6774.15i | −0.449195 | + | 0.219463i | ||||
\(985\) | 30777.3i | 0.995580i | ||||||||
\(986\) | 243.353 | + | 421.499i | 0.00785997 | + | 0.0136139i | ||||
\(987\) | −38744.5 | − | 4097.79i | −1.24950 | − | 0.132152i | ||||
\(988\) | 22475.7 | − | 38929.0i | 0.723730 | − | 1.25354i | ||||
\(989\) | 1628.13 | + | 940.000i | 0.0523473 | + | 0.0302227i | ||||
\(990\) | 2196.78 | + | 5416.11i | 0.0705236 | + | 0.173874i | ||||
\(991\) | −10999.5 | − | 19051.6i | −0.352583 | − | 0.610691i | 0.634119 | − | 0.773236i | \(-0.281363\pi\) |
−0.986701 | + | 0.162545i | \(0.948030\pi\) | |||||||
\(992\) | 19020.3 | + | 32944.2i | 0.608766 | + | 1.05441i | ||||
\(993\) | 11176.3 | + | 22875.4i | 0.357168 | + | 0.731048i | ||||
\(994\) | −21085.7 | − | 764.401i | −0.672834 | − | 0.0243917i | ||||
\(995\) | −997.453 | + | 575.880i | −0.0317803 | + | 0.0183484i | ||||
\(996\) | −13928.4 | − | 28508.4i | −0.443110 | − | 0.906952i | ||||
\(997\) | 8469.97i | 0.269054i | 0.990910 | + | 0.134527i | \(0.0429515\pi\) | ||||
−0.990910 | + | 0.134527i | \(0.957049\pi\) | |||||||
\(998\) | −1976.79 | + | 1141.30i | −0.0626996 | + | 0.0361996i | ||||
\(999\) | −2286.57 | + | 2549.88i | −0.0724163 | + | 0.0807555i |
(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 | 63.4.s.a.47.9 | yes | 44 | |
3.2 | odd | 2 | 189.4.s.a.89.14 | 44 | |||
7.3 | odd | 6 | 63.4.i.a.38.9 | yes | 44 | ||
9.4 | even | 3 | 189.4.i.a.152.9 | 44 | |||
9.5 | odd | 6 | 63.4.i.a.5.14 | ✓ | 44 | ||
21.17 | even | 6 | 189.4.i.a.143.14 | 44 | |||
63.31 | odd | 6 | 189.4.s.a.17.14 | 44 | |||
63.59 | even | 6 | inner | 63.4.s.a.59.9 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.i.a.5.14 | ✓ | 44 | 9.5 | odd | 6 | ||
63.4.i.a.38.9 | yes | 44 | 7.3 | odd | 6 | ||
63.4.s.a.47.9 | yes | 44 | 1.1 | even | 1 | trivial | |
63.4.s.a.59.9 | yes | 44 | 63.59 | even | 6 | inner | |
189.4.i.a.143.14 | 44 | 21.17 | even | 6 | |||
189.4.i.a.152.9 | 44 | 9.4 | even | 3 | |||
189.4.s.a.17.14 | 44 | 63.31 | odd | 6 | |||
189.4.s.a.89.14 | 44 | 3.2 | odd | 2 |