Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(26,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.26");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.12 | ||
Character | \(\chi\) | \(=\) | 105.26 |
Dual form | 105.4.s.b.101.12 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.51429 | + | 1.45163i | 0.888937 | + | 0.513228i | 0.873595 | − | 0.486654i | \(-0.161783\pi\) |
0.0153424 | + | 0.999882i | \(0.495116\pi\) | |||||||
\(3\) | −5.18226 | − | 0.379674i | −0.997327 | − | 0.0730683i | ||||
\(4\) | 0.214449 | + | 0.371437i | 0.0268061 | + | 0.0464296i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | −12.4786 | − | 8.47733i | −0.849060 | − | 0.576809i | ||||
\(7\) | 17.9959 | + | 4.37591i | 0.971686 | + | 0.236277i | ||||
\(8\) | − | 21.9809i | − | 0.971426i | ||||||
\(9\) | 26.7117 | + | 3.93514i | 0.989322 | + | 0.145746i | ||||
\(10\) | 12.5715 | − | 7.25814i | 0.397545 | − | 0.229523i | ||||
\(11\) | 28.8369 | − | 16.6490i | 0.790423 | − | 0.456351i | −0.0496886 | − | 0.998765i | \(-0.515823\pi\) |
0.840111 | + | 0.542414i | \(0.182490\pi\) | |||||||
\(12\) | −0.970307 | − | 2.00630i | −0.0233419 | − | 0.0482642i | ||||
\(13\) | − | 62.4189i | − | 1.33168i | −0.746093 | − | 0.665842i | \(-0.768072\pi\) | ||
0.746093 | − | 0.665842i | \(-0.231928\pi\) | |||||||
\(14\) | 38.8947 | + | 37.1256i | 0.742504 | + | 0.708732i | ||||
\(15\) | −14.5997 | + | 21.4907i | −0.251308 | + | 0.369924i | ||||
\(16\) | 33.6236 | − | 58.2378i | 0.525369 | − | 0.909966i | ||||
\(17\) | 34.7249 | + | 60.1453i | 0.495413 | + | 0.858080i | 0.999986 | − | 0.00528856i | \(-0.00168341\pi\) |
−0.504573 | + | 0.863369i | \(0.668350\pi\) | |||||||
\(18\) | 61.4487 | + | 48.6696i | 0.804644 | + | 0.637307i | ||||
\(19\) | −71.6103 | − | 41.3442i | −0.864659 | − | 0.499211i | 0.000910397 | − | 1.00000i | \(-0.499710\pi\) |
−0.865570 | + | 0.500788i | \(0.833044\pi\) | |||||||
\(20\) | 2.14449 | 0.0239761 | ||||||||
\(21\) | −91.5979 | − | 29.5097i | −0.951824 | − | 0.306645i | ||||
\(22\) | 96.6726 | 0.936848 | ||||||||
\(23\) | 49.8101 | + | 28.7578i | 0.451570 | + | 0.260714i | 0.708493 | − | 0.705718i | \(-0.249375\pi\) |
−0.256923 | + | 0.966432i | \(0.582709\pi\) | |||||||
\(24\) | −8.34556 | + | 113.911i | −0.0709804 | + | 0.968829i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 90.6091 | − | 156.940i | 0.683458 | − | 1.18378i | ||||
\(27\) | −136.933 | − | 30.5347i | −0.976028 | − | 0.217645i | ||||
\(28\) | 2.23383 | + | 7.62274i | 0.0150769 | + | 0.0514486i | ||||
\(29\) | 114.270i | 0.731702i | 0.930673 | + | 0.365851i | \(0.119222\pi\) | ||||
−0.930673 | + | 0.365851i | \(0.880778\pi\) | |||||||
\(30\) | −67.9044 | + | 32.8405i | −0.413253 | + | 0.199861i | ||||
\(31\) | −187.647 | + | 108.338i | −1.08717 | + | 0.627679i | −0.932822 | − | 0.360337i | \(-0.882662\pi\) |
−0.154350 | + | 0.988016i | \(0.549328\pi\) | |||||||
\(32\) | 16.7915 | − | 9.69458i | 0.0927608 | − | 0.0535555i | ||||
\(33\) | −155.762 | + | 75.3308i | −0.821655 | + | 0.397376i | ||||
\(34\) | 201.630i | 1.01704i | ||||||||
\(35\) | 63.9379 | − | 66.9846i | 0.308785 | − | 0.323499i | ||||
\(36\) | 4.26664 | + | 10.7656i | 0.0197530 | + | 0.0498407i | ||||
\(37\) | 136.662 | − | 236.705i | 0.607218 | − | 1.05173i | −0.384479 | − | 0.923134i | \(-0.625619\pi\) |
0.991697 | − | 0.128598i | \(-0.0410477\pi\) | |||||||
\(38\) | −120.033 | − | 207.903i | −0.512419 | − | 0.887535i | ||||
\(39\) | −23.6989 | + | 323.471i | −0.0973039 | + | 1.32812i | ||||
\(40\) | −95.1799 | − | 54.9521i | −0.376231 | − | 0.217217i | ||||
\(41\) | −36.2347 | −0.138022 | −0.0690111 | − | 0.997616i | \(-0.521984\pi\) | ||||
−0.0690111 | + | 0.997616i | \(0.521984\pi\) | |||||||
\(42\) | −187.467 | − | 207.162i | −0.688733 | − | 0.761091i | ||||
\(43\) | 185.189 | 0.656769 | 0.328385 | − | 0.944544i | \(-0.393496\pi\) | ||||
0.328385 | + | 0.944544i | \(0.393496\pi\) | |||||||
\(44\) | 12.3681 | + | 7.14072i | 0.0423764 | + | 0.0244660i | ||||
\(45\) | 83.8189 | − | 105.827i | 0.277666 | − | 0.350573i | ||||
\(46\) | 83.4914 | + | 144.611i | 0.267612 | + | 0.463517i | ||||
\(47\) | 25.2220 | − | 43.6858i | 0.0782767 | − | 0.135579i | −0.824230 | − | 0.566255i | \(-0.808392\pi\) |
0.902507 | + | 0.430676i | \(0.141725\pi\) | |||||||
\(48\) | −196.358 | + | 289.038i | −0.590454 | + | 0.869146i | ||||
\(49\) | 304.703 | + | 157.497i | 0.888346 | + | 0.459174i | ||||
\(50\) | − | 72.5814i | − | 0.205291i | ||||||
\(51\) | −157.118 | − | 324.873i | −0.431390 | − | 0.891986i | ||||
\(52\) | 23.1847 | − | 13.3857i | 0.0618295 | − | 0.0356973i | ||||
\(53\) | 204.020 | − | 117.791i | 0.528761 | − | 0.305280i | −0.211751 | − | 0.977324i | \(-0.567917\pi\) |
0.740512 | + | 0.672043i | \(0.234583\pi\) | |||||||
\(54\) | −299.965 | − | 275.549i | −0.755926 | − | 0.694397i | ||||
\(55\) | − | 166.490i | − | 0.408173i | ||||||
\(56\) | 96.1862 | − | 395.565i | 0.229525 | − | 0.943920i | ||||
\(57\) | 355.406 | + | 241.445i | 0.825872 | + | 0.561056i | ||||
\(58\) | −165.877 | + | 287.308i | −0.375530 | + | 0.650437i | ||||
\(59\) | 267.247 | + | 462.886i | 0.589705 | + | 1.02140i | 0.994271 | + | 0.106891i | \(0.0340895\pi\) |
−0.404565 | + | 0.914509i | \(0.632577\pi\) | |||||||
\(60\) | −11.1133 | − | 0.814208i | −0.0239120 | − | 0.00175190i | ||||
\(61\) | −313.636 | − | 181.078i | −0.658311 | − | 0.380076i | 0.133322 | − | 0.991073i | \(-0.457435\pi\) |
−0.791633 | + | 0.610997i | \(0.790769\pi\) | |||||||
\(62\) | −629.065 | −1.28857 | ||||||||
\(63\) | 463.480 | + | 187.704i | 0.926874 | + | 0.375373i | ||||
\(64\) | −481.686 | −0.940793 | ||||||||
\(65\) | −270.282 | − | 156.047i | −0.515759 | − | 0.297774i | ||||
\(66\) | −500.983 | − | 36.7041i | −0.934344 | − | 0.0684539i | ||||
\(67\) | 232.792 | + | 403.208i | 0.424479 | + | 0.735219i | 0.996372 | − | 0.0851094i | \(-0.0271240\pi\) |
−0.571893 | + | 0.820328i | \(0.693791\pi\) | |||||||
\(68\) | −14.8934 | + | 25.7962i | −0.0265602 | + | 0.0460036i | ||||
\(69\) | −247.210 | − | 167.942i | −0.431313 | − | 0.293013i | ||||
\(70\) | 257.996 | − | 75.6050i | 0.440519 | − | 0.129093i | ||||
\(71\) | 1073.13i | 1.79377i | 0.442265 | + | 0.896885i | \(0.354175\pi\) | ||||
−0.442265 | + | 0.896885i | \(0.645825\pi\) | |||||||
\(72\) | 86.4978 | − | 587.146i | 0.141581 | − | 0.961053i | ||||
\(73\) | −771.170 | + | 445.235i | −1.23642 | + | 0.713847i | −0.968360 | − | 0.249556i | \(-0.919715\pi\) |
−0.268059 | + | 0.963403i | \(0.586382\pi\) | |||||||
\(74\) | 687.216 | − | 396.764i | 1.07956 | − | 0.623282i | ||||
\(75\) | 56.5581 | + | 116.945i | 0.0870769 | + | 0.180049i | ||||
\(76\) | − | 35.4649i | − | 0.0535277i | ||||||
\(77\) | 591.800 | − | 173.425i | 0.875868 | − | 0.256671i | ||||
\(78\) | −529.146 | + | 778.900i | −0.768128 | + | 1.13068i | ||||
\(79\) | −636.565 | + | 1102.56i | −0.906572 | + | 1.57023i | −0.0877784 | + | 0.996140i | \(0.527977\pi\) |
−0.818793 | + | 0.574088i | \(0.805357\pi\) | |||||||
\(80\) | −168.118 | − | 291.189i | −0.234952 | − | 0.406949i | ||||
\(81\) | 698.029 | + | 210.229i | 0.957516 | + | 0.288380i | ||||
\(82\) | −91.1047 | − | 52.5993i | −0.122693 | − | 0.0708368i | ||||
\(83\) | 245.617 | 0.324819 | 0.162409 | − | 0.986723i | \(-0.448073\pi\) | ||||
0.162409 | + | 0.986723i | \(0.448073\pi\) | |||||||
\(84\) | −8.68211 | − | 40.3512i | −0.0112773 | − | 0.0524128i | ||||
\(85\) | 347.249 | 0.443111 | ||||||||
\(86\) | 465.620 | + | 268.826i | 0.583826 | + | 0.337072i | ||||
\(87\) | 43.3853 | − | 592.176i | 0.0534642 | − | 0.729746i | ||||
\(88\) | −365.959 | − | 633.859i | −0.443311 | − | 0.767837i | ||||
\(89\) | 548.825 | − | 950.594i | 0.653656 | − | 1.13217i | −0.328573 | − | 0.944479i | \(-0.606568\pi\) |
0.982229 | − | 0.187687i | \(-0.0600990\pi\) | |||||||
\(90\) | 364.367 | − | 144.407i | 0.426752 | − | 0.169131i | ||||
\(91\) | 273.140 | − | 1123.28i | 0.314646 | − | 1.29398i | ||||
\(92\) | 24.6684i | 0.0279550i | ||||||||
\(93\) | 1013.57 | − | 490.190i | 1.13013 | − | 0.546563i | ||||
\(94\) | 126.831 | − | 73.2259i | 0.139166 | − | 0.0803476i | ||||
\(95\) | −358.052 | + | 206.721i | −0.386687 | + | 0.223254i | ||||
\(96\) | −90.6988 | + | 43.8646i | −0.0964261 | + | 0.0466345i | ||||
\(97\) | − | 1089.48i | − | 1.14042i | −0.821501 | − | 0.570208i | \(-0.806863\pi\) | ||
0.821501 | − | 0.570208i | \(-0.193137\pi\) | |||||||
\(98\) | 537.486 | + | 838.308i | 0.554023 | + | 0.864101i | ||||
\(99\) | 835.798 | − | 331.245i | 0.848494 | − | 0.336277i | ||||
\(100\) | 5.36123 | − | 9.28592i | 0.00536123 | − | 0.00928592i | ||||
\(101\) | 705.971 | + | 1222.78i | 0.695512 | + | 1.20466i | 0.970008 | + | 0.243074i | \(0.0781559\pi\) |
−0.274495 | + | 0.961588i | \(0.588511\pi\) | |||||||
\(102\) | 76.5539 | − | 1044.90i | 0.0743134 | − | 1.01432i | ||||
\(103\) | 1199.96 | + | 692.797i | 1.14792 | + | 0.662751i | 0.948379 | − | 0.317139i | \(-0.102722\pi\) |
0.199539 | + | 0.979890i | \(0.436055\pi\) | |||||||
\(104\) | −1372.02 | −1.29363 | ||||||||
\(105\) | −356.775 | + | 322.856i | −0.331597 | + | 0.300072i | ||||
\(106\) | 683.955 | 0.626713 | ||||||||
\(107\) | −863.164 | − | 498.348i | −0.779862 | − | 0.450253i | 0.0565196 | − | 0.998401i | \(-0.482000\pi\) |
−0.836381 | + | 0.548148i | \(0.815333\pi\) | |||||||
\(108\) | −18.0234 | − | 57.4101i | −0.0160584 | − | 0.0511508i | ||||
\(109\) | −613.752 | − | 1063.05i | −0.539328 | − | 0.934144i | −0.998940 | − | 0.0460241i | \(-0.985345\pi\) |
0.459612 | − | 0.888120i | \(-0.347988\pi\) | |||||||
\(110\) | 241.681 | − | 418.604i | 0.209486 | − | 0.362840i | ||||
\(111\) | −798.088 | + | 1174.78i | −0.682443 | + | 1.00455i | ||||
\(112\) | 859.930 | − | 900.906i | 0.725497 | − | 0.760068i | ||||
\(113\) | − | 1400.91i | − | 1.16625i | −0.812381 | − | 0.583127i | \(-0.801829\pi\) | ||
0.812381 | − | 0.583127i | \(-0.198171\pi\) | |||||||
\(114\) | 543.107 | + | 1122.98i | 0.446198 | + | 0.922604i | ||||
\(115\) | 249.050 | − | 143.789i | 0.201948 | − | 0.116595i | ||||
\(116\) | −42.4440 | + | 24.5050i | −0.0339726 | + | 0.0196141i | ||||
\(117\) | 245.627 | − | 1667.32i | 0.194088 | − | 1.31746i | ||||
\(118\) | 1551.77i | 1.21061i | ||||||||
\(119\) | 361.714 | + | 1234.32i | 0.278641 | + | 0.950839i | ||||
\(120\) | 472.383 | + | 320.914i | 0.359354 | + | 0.244127i | ||||
\(121\) | −111.122 | + | 192.470i | −0.0834879 | + | 0.144605i | ||||
\(122\) | −525.715 | − | 910.565i | −0.390131 | − | 0.675727i | ||||
\(123\) | 187.778 | + | 13.7574i | 0.137653 | + | 0.0100850i | ||||
\(124\) | −80.4813 | − | 46.4659i | −0.0582857 | − | 0.0336513i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 892.849 | + | 1144.74i | 0.631280 | + | 0.809381i | ||||
\(127\) | 596.757 | 0.416957 | 0.208479 | − | 0.978027i | \(-0.433149\pi\) | ||||
0.208479 | + | 0.978027i | \(0.433149\pi\) | |||||||
\(128\) | −1345.43 | − | 776.786i | −0.929067 | − | 0.536397i | ||||
\(129\) | −959.698 | − | 70.3115i | −0.655013 | − | 0.0479890i | ||||
\(130\) | −453.045 | − | 784.698i | −0.305652 | − | 0.529404i | ||||
\(131\) | −604.858 | + | 1047.64i | −0.403410 | + | 0.698726i | −0.994135 | − | 0.108147i | \(-0.965508\pi\) |
0.590725 | + | 0.806873i | \(0.298842\pi\) | |||||||
\(132\) | −61.3836 | − | 41.7009i | −0.0404754 | − | 0.0274970i | ||||
\(133\) | −1107.77 | − | 1057.39i | −0.722225 | − | 0.689376i | ||||
\(134\) | 1351.71i | 0.871418i | ||||||||
\(135\) | −474.551 | + | 516.600i | −0.302540 | + | 0.329347i | ||||
\(136\) | 1322.04 | − | 763.282i | 0.833561 | − | 0.481257i | ||||
\(137\) | −866.174 | + | 500.086i | −0.540162 | + | 0.311863i | −0.745145 | − | 0.666903i | \(-0.767620\pi\) |
0.204982 | + | 0.978766i | \(0.434286\pi\) | |||||||
\(138\) | −377.769 | − | 781.114i | −0.233028 | − | 0.481832i | ||||
\(139\) | 2301.17i | 1.40419i | 0.712083 | + | 0.702095i | \(0.247752\pi\) | ||||
−0.712083 | + | 0.702095i | \(0.752248\pi\) | |||||||
\(140\) | 38.5920 | + | 9.38410i | 0.0232973 | + | 0.00566501i | ||||
\(141\) | −147.293 | + | 216.815i | −0.0879740 | + | 0.129497i | ||||
\(142\) | −1557.79 | + | 2698.17i | −0.920613 | + | 1.59455i | ||||
\(143\) | −1039.21 | − | 1799.97i | −0.607715 | − | 1.05259i | ||||
\(144\) | 1127.32 | − | 1423.32i | 0.652383 | − | 0.823679i | ||||
\(145\) | 494.803 | + | 285.674i | 0.283387 | + | 0.163614i | ||||
\(146\) | −2585.26 | −1.46547 | ||||||||
\(147\) | −1519.25 | − | 931.877i | −0.852421 | − | 0.522856i | ||||
\(148\) | 117.228 | 0.0651086 | ||||||||
\(149\) | −28.5233 | − | 16.4679i | −0.0156827 | − | 0.00905441i | 0.492138 | − | 0.870517i | \(-0.336215\pi\) |
−0.507821 | + | 0.861463i | \(0.669549\pi\) | |||||||
\(150\) | −27.5573 | + | 376.136i | −0.0150003 | + | 0.204742i | ||||
\(151\) | −810.825 | − | 1404.39i | −0.436980 | − | 0.756872i | 0.560475 | − | 0.828171i | \(-0.310619\pi\) |
−0.997455 | + | 0.0712997i | \(0.977285\pi\) | |||||||
\(152\) | −908.781 | + | 1574.06i | −0.484947 | + | 0.839952i | ||||
\(153\) | 690.880 | + | 1743.23i | 0.365061 | + | 0.921122i | ||||
\(154\) | 1739.71 | + | 423.030i | 0.910322 | + | 0.221356i | ||||
\(155\) | 1083.38i | 0.561413i | ||||||||
\(156\) | −125.231 | + | 60.5655i | −0.0642726 | + | 0.0310841i | ||||
\(157\) | −2241.73 | + | 1294.27i | −1.13955 | + | 0.657921i | −0.946320 | − | 0.323231i | \(-0.895231\pi\) |
−0.193233 | + | 0.981153i | \(0.561897\pi\) | |||||||
\(158\) | −3201.02 | + | 1848.11i | −1.61177 | + | 0.930556i | ||||
\(159\) | −1102.01 | + | 532.963i | −0.549654 | + | 0.265828i | ||||
\(160\) | − | 96.9458i | − | 0.0479015i | ||||||
\(161\) | 770.534 | + | 735.487i | 0.377184 | + | 0.360028i | ||||
\(162\) | 1449.88 | + | 1541.86i | 0.703167 | + | 0.747775i | ||||
\(163\) | 442.014 | − | 765.590i | 0.212400 | − | 0.367887i | −0.740065 | − | 0.672535i | \(-0.765205\pi\) |
0.952465 | + | 0.304648i | \(0.0985387\pi\) | |||||||
\(164\) | −7.77050 | − | 13.4589i | −0.00369984 | − | 0.00640831i | ||||
\(165\) | −63.2119 | + | 862.794i | −0.0298245 | + | 0.407081i | ||||
\(166\) | 617.553 | + | 356.544i | 0.288743 | + | 0.166706i | ||||
\(167\) | 2610.26 | 1.20951 | 0.604755 | − | 0.796412i | \(-0.293271\pi\) | ||||
0.604755 | + | 0.796412i | \(0.293271\pi\) | |||||||
\(168\) | −648.648 | + | 2013.40i | −0.297883 | + | 0.924626i | ||||
\(169\) | −1699.12 | −0.773383 | ||||||||
\(170\) | 873.086 | + | 504.076i | 0.393898 | + | 0.227417i | ||||
\(171\) | −1750.14 | − | 1386.17i | −0.782669 | − | 0.619901i | ||||
\(172\) | 39.7136 | + | 68.7860i | 0.0176054 | + | 0.0304935i | ||||
\(173\) | 1724.06 | − | 2986.16i | 0.757676 | − | 1.31233i | −0.186357 | − | 0.982482i | \(-0.559668\pi\) |
0.944033 | − | 0.329851i | \(-0.106999\pi\) | |||||||
\(174\) | 968.702 | − | 1425.92i | 0.422053 | − | 0.621259i | ||||
\(175\) | −130.207 | − | 444.321i | −0.0562442 | − | 0.191929i | ||||
\(176\) | − | 2239.20i | − | 0.959010i | ||||||
\(177\) | −1209.20 | − | 2500.26i | −0.513497 | − | 1.06176i | ||||
\(178\) | 2759.82 | − | 1593.38i | 1.16212 | − | 0.670949i | ||||
\(179\) | −2558.65 | + | 1477.24i | −1.06839 | + | 0.616837i | −0.927742 | − | 0.373222i | \(-0.878253\pi\) |
−0.140651 | + | 0.990059i | \(0.544920\pi\) | |||||||
\(180\) | 57.2830 | + | 8.43888i | 0.0237201 | + | 0.00349443i | ||||
\(181\) | − | 2539.38i | − | 1.04282i | −0.853306 | − | 0.521410i | \(-0.825406\pi\) | ||
0.853306 | − | 0.521410i | \(-0.174594\pi\) | |||||||
\(182\) | 2317.34 | − | 2427.77i | 0.943807 | − | 0.988780i | ||||
\(183\) | 1556.59 | + | 1057.47i | 0.628780 | + | 0.427162i | ||||
\(184\) | 632.122 | − | 1094.87i | 0.253264 | − | 0.438667i | ||||
\(185\) | −683.309 | − | 1183.53i | −0.271556 | − | 0.470349i | ||||
\(186\) | 3259.98 | + | 238.840i | 1.28513 | + | 0.0941536i | ||||
\(187\) | 2002.72 | + | 1156.27i | 0.783171 | + | 0.452164i | ||||
\(188\) | 21.6353 | 0.00839318 | ||||||||
\(189\) | −2330.61 | − | 1148.70i | −0.896968 | − | 0.442095i | ||||
\(190\) | −1200.33 | −0.458321 | ||||||||
\(191\) | −1555.12 | − | 897.850i | −0.589134 | − | 0.340137i | 0.175621 | − | 0.984458i | \(-0.443807\pi\) |
−0.764755 | + | 0.644321i | \(0.777140\pi\) | |||||||
\(192\) | 2496.22 | + | 182.884i | 0.938278 | + | 0.0687422i | ||||
\(193\) | 494.835 | + | 857.079i | 0.184554 | + | 0.319658i | 0.943426 | − | 0.331582i | \(-0.107582\pi\) |
−0.758872 | + | 0.651240i | \(0.774249\pi\) | |||||||
\(194\) | 1581.52 | − | 2739.28i | 0.585293 | − | 1.01376i | ||||
\(195\) | 1341.42 | + | 911.297i | 0.492623 | + | 0.334663i | ||||
\(196\) | 6.84323 | + | 146.953i | 0.00249389 | + | 0.0535542i | ||||
\(197\) | 4865.52i | 1.75966i | 0.475285 | + | 0.879832i | \(0.342345\pi\) | ||||
−0.475285 | + | 0.879832i | \(0.657655\pi\) | |||||||
\(198\) | 2582.29 | + | 380.420i | 0.926845 | + | 0.136542i | ||||
\(199\) | 484.969 | − | 279.997i | 0.172756 | − | 0.0997410i | −0.411128 | − | 0.911577i | \(-0.634865\pi\) |
0.583885 | + | 0.811836i | \(0.301532\pi\) | |||||||
\(200\) | −475.899 | + | 274.761i | −0.168256 | + | 0.0971426i | ||||
\(201\) | −1053.30 | − | 2177.91i | −0.369623 | − | 0.764270i | ||||
\(202\) | 4099.23i | 1.42783i | ||||||||
\(203\) | −500.034 | + | 2056.38i | −0.172884 | + | 0.710984i | ||||
\(204\) | 86.9759 | − | 128.028i | 0.0298506 | − | 0.0439400i | ||||
\(205\) | −90.5867 | + | 156.901i | −0.0308627 | + | 0.0534557i | ||||
\(206\) | 2011.37 | + | 3483.79i | 0.680285 | + | 1.17829i | ||||
\(207\) | 1217.34 | + | 964.181i | 0.408750 | + | 0.323745i | ||||
\(208\) | −3635.14 | − | 2098.75i | −1.21179 | − | 0.699626i | ||||
\(209\) | −2753.36 | −0.911262 | ||||||||
\(210\) | −1365.71 | + | 293.851i | −0.448775 | + | 0.0965601i | ||||
\(211\) | −1468.79 | −0.479223 | −0.239611 | − | 0.970869i | \(-0.577020\pi\) | ||||
−0.239611 | + | 0.970869i | \(0.577020\pi\) | |||||||
\(212\) | 87.5039 | + | 50.5204i | 0.0283481 | + | 0.0163668i | ||||
\(213\) | 407.441 | − | 5561.26i | 0.131068 | − | 1.78897i | ||||
\(214\) | −1446.83 | − | 2505.99i | −0.462165 | − | 0.800494i | ||||
\(215\) | 462.973 | − | 801.892i | 0.146858 | − | 0.254366i | ||||
\(216\) | −671.178 | + | 3009.90i | −0.211425 | + | 0.948139i | ||||
\(217\) | −3850.94 | + | 1128.51i | −1.20470 | + | 0.353033i | ||||
\(218\) | − | 3563.76i | − | 1.10719i | ||||||
\(219\) | 4165.45 | − | 2014.53i | 1.28527 | − | 0.621596i | ||||
\(220\) | 61.8405 | − | 35.7036i | 0.0189513 | − | 0.0109415i | ||||
\(221\) | 3754.20 | − | 2167.49i | 1.14269 | − | 0.659734i | ||||
\(222\) | −3711.97 | + | 1795.22i | −1.12221 | + | 0.542735i | ||||
\(223\) | − | 960.120i | − | 0.288316i | −0.989555 | − | 0.144158i | \(-0.953953\pi\) | ||
0.989555 | − | 0.144158i | \(-0.0460473\pi\) | |||||||
\(224\) | 344.600 | − | 100.984i | 0.102788 | − | 0.0301219i | ||||
\(225\) | −248.698 | − | 627.514i | −0.0736883 | − | 0.185930i | ||||
\(226\) | 2033.60 | − | 3522.30i | 0.598554 | − | 1.03673i | ||||
\(227\) | 1556.85 | + | 2696.55i | 0.455207 | + | 0.788441i | 0.998700 | − | 0.0509723i | \(-0.0162320\pi\) |
−0.543493 | + | 0.839413i | \(0.682899\pi\) | |||||||
\(228\) | −13.4651 | + | 183.789i | −0.00391118 | + | 0.0533846i | ||||
\(229\) | 5409.25 | + | 3123.03i | 1.56093 | + | 0.901205i | 0.997163 | + | 0.0752730i | \(0.0239828\pi\) |
0.563770 | + | 0.825932i | \(0.309351\pi\) | |||||||
\(230\) | 834.914 | 0.239359 | ||||||||
\(231\) | −3132.71 | + | 674.045i | −0.892281 | + | 0.191987i | ||||
\(232\) | 2511.75 | 0.710794 | ||||||||
\(233\) | 3367.44 | + | 1944.20i | 0.946818 | + | 0.546646i | 0.892091 | − | 0.451856i | \(-0.149238\pi\) |
0.0547271 | + | 0.998501i | \(0.482571\pi\) | |||||||
\(234\) | 3037.90 | − | 3835.56i | 0.848691 | − | 1.07153i | ||||
\(235\) | −126.110 | − | 218.429i | −0.0350064 | − | 0.0606329i | ||||
\(236\) | −114.622 | + | 198.531i | −0.0316154 | + | 0.0547596i | ||||
\(237\) | 3717.46 | − | 5472.08i | 1.01888 | − | 1.49979i | ||||
\(238\) | −882.317 | + | 3628.52i | −0.240303 | + | 0.988243i | ||||
\(239\) | − | 5875.59i | − | 1.59021i | −0.606471 | − | 0.795105i | \(-0.707416\pi\) | ||
0.606471 | − | 0.795105i | \(-0.292584\pi\) | |||||||
\(240\) | 760.675 | + | 1572.85i | 0.204589 | + | 0.423029i | ||||
\(241\) | −2812.36 | + | 1623.72i | −0.751702 | + | 0.433995i | −0.826309 | − | 0.563218i | \(-0.809563\pi\) |
0.0746065 | + | 0.997213i | \(0.476230\pi\) | |||||||
\(242\) | −558.789 | + | 322.617i | −0.148431 | + | 0.0856967i | ||||
\(243\) | −3537.55 | − | 1354.48i | −0.933885 | − | 0.357573i | ||||
\(244\) | − | 155.328i | − | 0.0407535i | ||||||
\(245\) | 1443.74 | − | 925.660i | 0.376478 | − | 0.241381i | ||||
\(246\) | 452.158 | + | 307.173i | 0.117189 | + | 0.0796125i | ||||
\(247\) | −2580.66 | + | 4469.84i | −0.664792 | + | 1.15145i | ||||
\(248\) | 2381.36 | + | 4124.63i | 0.609743 | + | 1.05611i | ||||
\(249\) | −1272.85 | − | 93.2544i | −0.323950 | − | 0.0237340i | ||||
\(250\) | −314.287 | − | 181.454i | −0.0795090 | − | 0.0459045i | ||||
\(251\) | 1187.97 | 0.298741 | 0.149370 | − | 0.988781i | \(-0.452275\pi\) | ||||
0.149370 | + | 0.988781i | \(0.452275\pi\) | |||||||
\(252\) | 29.6727 | + | 212.407i | 0.00741748 | + | 0.0530967i | ||||
\(253\) | 1915.16 | 0.475908 | ||||||||
\(254\) | 1500.42 | + | 866.269i | 0.370649 | + | 0.213994i | ||||
\(255\) | −1799.53 | − | 131.841i | −0.441926 | − | 0.0323774i | ||||
\(256\) | −328.464 | − | 568.916i | −0.0801914 | − | 0.138896i | ||||
\(257\) | −310.867 | + | 538.437i | −0.0754526 | + | 0.130688i | −0.901283 | − | 0.433231i | \(-0.857373\pi\) |
0.825830 | + | 0.563919i | \(0.190707\pi\) | |||||||
\(258\) | −2310.90 | − | 1569.91i | −0.557636 | − | 0.378831i | ||||
\(259\) | 3495.15 | − | 3661.70i | 0.838525 | − | 0.878481i | ||||
\(260\) | − | 133.857i | − | 0.0319286i | ||||||
\(261\) | −449.668 | + | 3052.34i | −0.106643 | + | 0.723889i | ||||
\(262\) | −3041.58 | + | 1756.06i | −0.717211 | + | 0.414082i | ||||
\(263\) | −412.211 | + | 237.990i | −0.0966465 | + | 0.0557989i | −0.547544 | − | 0.836777i | \(-0.684437\pi\) |
0.450898 | + | 0.892576i | \(0.351104\pi\) | |||||||
\(264\) | 1655.84 | + | 3423.77i | 0.386021 | + | 0.798176i | ||||
\(265\) | − | 1177.91i | − | 0.273051i | ||||||
\(266\) | −1250.33 | − | 4266.65i | −0.288206 | − | 0.983478i | ||||
\(267\) | −3205.07 | + | 4717.85i | −0.734634 | + | 1.08138i | ||||
\(268\) | −99.8441 | + | 172.935i | −0.0227573 | + | 0.0394168i | ||||
\(269\) | 1356.34 | + | 2349.25i | 0.307425 | + | 0.532476i | 0.977798 | − | 0.209548i | \(-0.0671993\pi\) |
−0.670373 | + | 0.742024i | \(0.733866\pi\) | |||||||
\(270\) | −1943.07 | + | 610.013i | −0.437969 | + | 0.137497i | ||||
\(271\) | −2865.65 | − | 1654.48i | −0.642346 | − | 0.370859i | 0.143172 | − | 0.989698i | \(-0.454270\pi\) |
−0.785518 | + | 0.618839i | \(0.787603\pi\) | |||||||
\(272\) | 4670.30 | 1.04110 | ||||||||
\(273\) | −1841.96 | + | 5717.44i | −0.408354 | + | 1.26753i | ||||
\(274\) | −2903.75 | −0.640227 | ||||||||
\(275\) | −720.922 | − | 416.225i | −0.158085 | − | 0.0912702i | ||||
\(276\) | 9.36595 | − | 127.838i | 0.00204262 | − | 0.0278802i | ||||
\(277\) | 2877.54 | + | 4984.04i | 0.624168 | + | 1.08109i | 0.988701 | + | 0.149900i | \(0.0478951\pi\) |
−0.364534 | + | 0.931190i | \(0.618772\pi\) | |||||||
\(278\) | −3340.44 | + | 5785.81i | −0.720670 | + | 1.24824i | ||||
\(279\) | −5438.68 | + | 2155.47i | −1.16704 | + | 0.462526i | ||||
\(280\) | −1472.38 | − | 1405.41i | −0.314255 | − | 0.299962i | ||||
\(281\) | − | 6169.74i | − | 1.30981i | −0.755712 | − | 0.654904i | \(-0.772709\pi\) | ||
0.755712 | − | 0.654904i | \(-0.227291\pi\) | |||||||
\(282\) | −685.073 | + | 331.321i | −0.144665 | + | 0.0699642i | ||||
\(283\) | 1377.12 | − | 795.082i | 0.289263 | − | 0.167006i | −0.348346 | − | 0.937366i | \(-0.613257\pi\) |
0.637609 | + | 0.770360i | \(0.279923\pi\) | |||||||
\(284\) | −398.601 | + | 230.133i | −0.0832840 | + | 0.0480840i | ||||
\(285\) | 1934.00 | − | 935.340i | 0.401967 | − | 0.194403i | ||||
\(286\) | − | 6034.20i | − | 1.24759i | ||||||
\(287\) | −652.075 | − | 158.560i | −0.134114 | − | 0.0326114i | ||||
\(288\) | 486.679 | − | 192.882i | 0.0995758 | − | 0.0394641i | ||||
\(289\) | 44.8653 | − | 77.7091i | 0.00913197 | − | 0.0158170i | ||||
\(290\) | 829.386 | + | 1436.54i | 0.167942 | + | 0.290884i | ||||
\(291\) | −413.649 | + | 5645.99i | −0.0833282 | + | 1.13737i | ||||
\(292\) | −330.753 | − | 190.961i | −0.0662872 | − | 0.0382710i | ||||
\(293\) | 5497.23 | 1.09608 | 0.548040 | − | 0.836452i | \(-0.315374\pi\) | ||||
0.548040 | + | 0.836452i | \(0.315374\pi\) | |||||||
\(294\) | −2467.11 | − | 4548.40i | −0.489404 | − | 0.902273i | ||||
\(295\) | 2672.47 | 0.527449 | ||||||||
\(296\) | −5202.98 | − | 3003.94i | −1.02168 | − | 0.589867i | ||||
\(297\) | −4457.09 | + | 1399.27i | −0.870797 | + | 0.273380i | ||||
\(298\) | −47.8107 | − | 82.8105i | −0.00929395 | − | 0.0160976i | ||||
\(299\) | 1795.03 | − | 3109.09i | 0.347189 | − | 0.601349i | ||||
\(300\) | −31.3089 | + | 46.0865i | −0.00602540 | + | 0.00886936i | ||||
\(301\) | 3332.64 | + | 810.371i | 0.638173 | + | 0.155179i | ||||
\(302\) | − | 4708.07i | − | 0.897082i | ||||||
\(303\) | −3194.27 | − | 6604.79i | −0.605630 | − | 1.25226i | ||||
\(304\) | −4815.59 | + | 2780.28i | −0.908531 | + | 0.524540i | ||||
\(305\) | −1568.18 | + | 905.389i | −0.294406 | + | 0.169975i | ||||
\(306\) | −793.445 | + | 5385.89i | −0.148229 | + | 1.00618i | ||||
\(307\) | − | 3573.91i | − | 0.664409i | −0.943207 | − | 0.332205i | \(-0.892208\pi\) | ||
0.943207 | − | 0.332205i | \(-0.107792\pi\) | |||||||
\(308\) | 191.327 | + | 182.625i | 0.0353958 | + | 0.0337858i | ||||
\(309\) | −5955.47 | − | 4045.85i | −1.09642 | − | 0.744856i | ||||
\(310\) | −1572.66 | + | 2723.93i | −0.288133 | + | 0.499061i | ||||
\(311\) | 1672.83 | + | 2897.43i | 0.305009 | + | 0.528291i | 0.977263 | − | 0.212029i | \(-0.0680072\pi\) |
−0.672254 | + | 0.740320i | \(0.734674\pi\) | |||||||
\(312\) | 7110.17 | + | 520.921i | 1.29017 | + | 0.0945235i | ||||
\(313\) | 152.890 | + | 88.2709i | 0.0276097 | + | 0.0159405i | 0.513741 | − | 0.857945i | \(-0.328259\pi\) |
−0.486132 | + | 0.873886i | \(0.661592\pi\) | |||||||
\(314\) | −7515.17 | −1.35065 | ||||||||
\(315\) | 1971.48 | − | 1537.67i | 0.352637 | − | 0.275041i | ||||
\(316\) | −546.043 | −0.0972067 | ||||||||
\(317\) | −3888.33 | − | 2244.93i | −0.688929 | − | 0.397753i | 0.114282 | − | 0.993448i | \(-0.463543\pi\) |
−0.803211 | + | 0.595695i | \(0.796877\pi\) | |||||||
\(318\) | −3544.44 | − | 259.680i | −0.625038 | − | 0.0457929i | ||||
\(319\) | 1902.48 | + | 3295.18i | 0.333913 | + | 0.578354i | ||||
\(320\) | −1204.22 | + | 2085.76i | −0.210368 | + | 0.364368i | ||||
\(321\) | 4283.93 | + | 2910.29i | 0.744878 | + | 0.506033i | ||||
\(322\) | 869.695 | + | 2967.76i | 0.150516 | + | 0.513623i | ||||
\(323\) | − | 5742.69i | − | 0.989263i | ||||||
\(324\) | 71.6051 | + | 304.357i | 0.0122780 | + | 0.0521874i | ||||
\(325\) | −1351.41 | + | 780.237i | −0.230654 | + | 0.133168i | ||||
\(326\) | 2222.70 | − | 1283.28i | 0.377620 | − | 0.218019i | ||||
\(327\) | 2777.01 | + | 5742.03i | 0.469630 | + | 0.971055i | ||||
\(328\) | 796.469i | 0.134078i | ||||||||
\(329\) | 645.057 | − | 675.794i | 0.108095 | − | 0.113245i | ||||
\(330\) | −1411.39 | + | 2077.56i | −0.235438 | + | 0.346563i | ||||
\(331\) | 2776.52 | − | 4809.08i | 0.461062 | − | 0.798582i | −0.537953 | − | 0.842975i | \(-0.680802\pi\) |
0.999014 | + | 0.0443930i | \(0.0141354\pi\) | |||||||
\(332\) | 52.6723 | + | 91.2311i | 0.00870714 | + | 0.0150812i | ||||
\(333\) | 4581.94 | − | 5785.01i | 0.754020 | − | 0.952002i | ||||
\(334\) | 6562.96 | + | 3789.13i | 1.07518 | + | 0.620754i | ||||
\(335\) | 2327.92 | 0.379666 | ||||||||
\(336\) | −4798.43 | + | 4342.24i | −0.779095 | + | 0.705026i | ||||
\(337\) | −2517.84 | −0.406990 | −0.203495 | − | 0.979076i | \(-0.565230\pi\) | ||||
−0.203495 | + | 0.979076i | \(0.565230\pi\) | |||||||
\(338\) | −4272.09 | − | 2466.49i | −0.687489 | − | 0.396922i | ||||
\(339\) | −531.890 | + | 7259.89i | −0.0852162 | + | 1.16314i | ||||
\(340\) | 74.4672 | + | 128.981i | 0.0118781 | + | 0.0205735i | ||||
\(341\) | −3607.43 | + | 6248.25i | −0.572883 | + | 0.992263i | ||||
\(342\) | −2388.15 | − | 6025.79i | −0.377592 | − | 0.952741i | ||||
\(343\) | 4794.20 | + | 4167.64i | 0.754701 | + | 0.656068i | ||||
\(344\) | − | 4070.61i | − | 0.638002i | ||||||
\(345\) | −1345.24 | + | 650.596i | −0.209928 | + | 0.101527i | ||||
\(346\) | 8669.59 | − | 5005.39i | 1.34705 | − | 0.777721i | ||||
\(347\) | −10615.5 | + | 6128.89i | −1.64228 | + | 0.948173i | −0.662264 | + | 0.749270i | \(0.730404\pi\) |
−0.980019 | + | 0.198903i | \(0.936262\pi\) | |||||||
\(348\) | 229.260 | − | 110.877i | 0.0353150 | − | 0.0170794i | ||||
\(349\) | − | 11130.9i | − | 1.70723i | −0.520907 | − | 0.853614i | \(-0.674406\pi\) | ||
0.520907 | − | 0.853614i | \(-0.325594\pi\) | |||||||
\(350\) | 317.610 | − | 1306.17i | 0.0485056 | − | 0.199479i | ||||
\(351\) | −1905.94 | + | 8547.21i | −0.289834 | + | 1.29976i | ||||
\(352\) | 322.810 | − | 559.123i | 0.0488802 | − | 0.0846630i | ||||
\(353\) | 243.596 | + | 421.920i | 0.0367289 | + | 0.0636162i | 0.883805 | − | 0.467855i | \(-0.154973\pi\) |
−0.847077 | + | 0.531471i | \(0.821640\pi\) | |||||||
\(354\) | 589.169 | − | 8041.70i | 0.0884575 | − | 1.20738i | ||||
\(355\) | 4646.81 | + | 2682.84i | 0.694724 | + | 0.401099i | ||||
\(356\) | 470.780 | 0.0700880 | ||||||||
\(357\) | −1405.86 | − | 6533.90i | −0.208420 | − | 0.968657i | ||||
\(358\) | −8577.59 | −1.26631 | ||||||||
\(359\) | 10884.0 | + | 6283.90i | 1.60010 | + | 0.923820i | 0.991465 | + | 0.130372i | \(0.0416173\pi\) |
0.608638 | + | 0.793448i | \(0.291716\pi\) | |||||||
\(360\) | −2326.17 | − | 1842.41i | −0.340556 | − | 0.269732i | ||||
\(361\) | −10.8099 | − | 18.7234i | −0.00157602 | − | 0.00272975i | ||||
\(362\) | 3686.23 | − | 6384.74i | 0.535205 | − | 0.927002i | ||||
\(363\) | 648.941 | − | 955.238i | 0.0938308 | − | 0.138118i | ||||
\(364\) | 475.803 | − | 139.433i | 0.0685133 | − | 0.0200777i | ||||
\(365\) | 4452.35i | 0.638484i | ||||||||
\(366\) | 2378.68 | + | 4918.39i | 0.339714 | + | 0.702427i | ||||
\(367\) | 2330.86 | − | 1345.72i | 0.331525 | − | 0.191406i | −0.324993 | − | 0.945716i | \(-0.605362\pi\) |
0.656518 | + | 0.754310i | \(0.272029\pi\) | |||||||
\(368\) | 3349.59 | − | 1933.89i | 0.474482 | − | 0.273942i | ||||
\(369\) | −967.890 | − | 142.589i | −0.136548 | − | 0.0201162i | ||||
\(370\) | − | 3967.64i | − | 0.557481i | ||||||
\(371\) | 4186.96 | − | 1226.98i | 0.585920 | − | 0.171702i | ||||
\(372\) | 399.433 | + | 271.355i | 0.0556711 | + | 0.0378202i | ||||
\(373\) | 4580.61 | − | 7933.85i | 0.635858 | − | 1.10134i | −0.350475 | − | 0.936572i | \(-0.613980\pi\) |
0.986333 | − | 0.164766i | \(-0.0526870\pi\) | |||||||
\(374\) | 3356.94 | + | 5814.40i | 0.464127 | + | 0.803891i | ||||
\(375\) | 647.783 | + | 47.4593i | 0.0892036 | + | 0.00653543i | ||||
\(376\) | −960.250 | − | 554.401i | −0.131705 | − | 0.0760400i | ||||
\(377\) | 7132.59 | 0.974396 | ||||||||
\(378\) | −4192.35 | − | 6271.36i | −0.570453 | − | 0.853344i | ||||
\(379\) | −10989.4 | −1.48941 | −0.744705 | − | 0.667394i | \(-0.767410\pi\) | ||||
−0.744705 | + | 0.667394i | \(0.767410\pi\) | |||||||
\(380\) | −153.568 | − | 88.6623i | −0.0207312 | − | 0.0119692i | ||||
\(381\) | −3092.55 | − | 226.573i | −0.415843 | − | 0.0304664i | ||||
\(382\) | −2606.69 | − | 4514.92i | −0.349136 | − | 0.604721i | ||||
\(383\) | −3382.56 | + | 5858.77i | −0.451282 | + | 0.781643i | −0.998466 | − | 0.0553694i | \(-0.982366\pi\) |
0.547184 | + | 0.837012i | \(0.315700\pi\) | |||||||
\(384\) | 6677.46 | + | 4536.33i | 0.887390 | + | 0.602849i | ||||
\(385\) | 728.545 | − | 2996.13i | 0.0964417 | − | 0.396615i | ||||
\(386\) | 2873.27i | 0.378874i | ||||||||
\(387\) | 4946.71 | + | 728.745i | 0.649756 | + | 0.0957215i | ||||
\(388\) | 404.674 | − | 233.639i | 0.0529490 | − | 0.0305701i | ||||
\(389\) | −4960.11 | + | 2863.72i | −0.646497 | + | 0.373255i | −0.787113 | − | 0.616809i | \(-0.788425\pi\) |
0.140616 | + | 0.990064i | \(0.455092\pi\) | |||||||
\(390\) | 2049.87 | + | 4238.52i | 0.266152 | + | 0.550322i | ||||
\(391\) | 3994.45i | 0.516645i | ||||||||
\(392\) | 3461.91 | − | 6697.63i | 0.446053 | − | 0.862962i | ||||
\(393\) | 3532.29 | − | 5199.52i | 0.453386 | − | 0.667382i | ||||
\(394\) | −7062.92 | + | 12233.3i | −0.903109 | + | 1.56423i | ||||
\(395\) | 3182.83 | + | 5512.82i | 0.405431 | + | 0.702227i | ||||
\(396\) | 302.273 | + | 239.411i | 0.0383580 | + | 0.0303809i | ||||
\(397\) | −6070.11 | − | 3504.58i | −0.767380 | − | 0.443047i | 0.0645589 | − | 0.997914i | \(-0.479436\pi\) |
−0.831939 | + | 0.554867i | \(0.812769\pi\) | |||||||
\(398\) | 1625.81 | 0.204759 | ||||||||
\(399\) | 5339.30 | + | 5900.24i | 0.669923 | + | 0.740305i | ||||
\(400\) | −1681.18 | −0.210148 | ||||||||
\(401\) | −2192.81 | − | 1266.02i | −0.273076 | − | 0.157661i | 0.357209 | − | 0.934025i | \(-0.383729\pi\) |
−0.630285 | + | 0.776364i | \(0.717062\pi\) | |||||||
\(402\) | 513.210 | − | 7004.92i | 0.0636731 | − | 0.869089i | ||||
\(403\) | 6762.33 | + | 11712.7i | 0.835870 | + | 1.44777i | ||||
\(404\) | −302.790 | + | 524.447i | −0.0372880 | + | 0.0645847i | ||||
\(405\) | 2655.39 | − | 2496.98i | 0.325796 | − | 0.306361i | ||||
\(406\) | −4242.34 | + | 4444.49i | −0.518580 | + | 0.543291i | ||||
\(407\) | − | 9101.12i | − | 1.10842i | ||||||
\(408\) | −7140.98 | + | 3453.58i | −0.866498 | + | 0.419063i | ||||
\(409\) | 1732.84 | − | 1000.45i | 0.209495 | − | 0.120952i | −0.391582 | − | 0.920143i | \(-0.628072\pi\) |
0.601077 | + | 0.799191i | \(0.294739\pi\) | |||||||
\(410\) | −455.523 | + | 262.996i | −0.0548700 | + | 0.0316792i | ||||
\(411\) | 4678.61 | − | 2262.71i | 0.561506 | − | 0.271560i | ||||
\(412\) | 594.279i | 0.0710632i | ||||||||
\(413\) | 2783.80 | + | 9499.48i | 0.331675 | + | 1.13181i | ||||
\(414\) | 1661.13 | + | 4191.37i | 0.197198 | + | 0.497571i | ||||
\(415\) | 614.042 | − | 1063.55i | 0.0726317 | − | 0.125802i | ||||
\(416\) | −605.125 | − | 1048.11i | −0.0713190 | − | 0.123528i | ||||
\(417\) | 873.694 | − | 11925.3i | 0.102602 | − | 1.40044i | ||||
\(418\) | −6922.75 | − | 3996.85i | −0.810055 | − | 0.467685i | ||||
\(419\) | 5942.03 | 0.692810 | 0.346405 | − | 0.938085i | \(-0.387402\pi\) | ||||
0.346405 | + | 0.938085i | \(0.387402\pi\) | |||||||
\(420\) | −196.431 | − | 63.2832i | −0.0228211 | − | 0.00735216i | ||||
\(421\) | 6026.48 | 0.697654 | 0.348827 | − | 0.937187i | \(-0.386580\pi\) | ||||
0.348827 | + | 0.937187i | \(0.386580\pi\) | |||||||
\(422\) | −3692.98 | − | 2132.14i | −0.425999 | − | 0.245951i | ||||
\(423\) | 845.632 | − | 1067.67i | 0.0972010 | − | 0.122723i | ||||
\(424\) | −2589.15 | − | 4484.54i | −0.296557 | − | 0.513652i | ||||
\(425\) | 868.122 | − | 1503.63i | 0.0990826 | − | 0.171616i | ||||
\(426\) | 9097.31 | − | 13391.2i | 1.03466 | − | 1.52302i | ||||
\(427\) | −4851.77 | − | 4631.09i | −0.549868 | − | 0.524858i | ||||
\(428\) | − | 427.481i | − | 0.0482782i | ||||||
\(429\) | 4702.07 | + | 9722.47i | 0.529179 | + | 1.09418i | ||||
\(430\) | 2328.10 | − | 1344.13i | 0.261095 | − | 0.150743i | ||||
\(431\) | −11442.6 | + | 6606.40i | −1.27882 | + | 0.738327i | −0.976632 | − | 0.214921i | \(-0.931051\pi\) |
−0.302189 | + | 0.953248i | \(0.597717\pi\) | |||||||
\(432\) | −6382.45 | + | 6947.99i | −0.710824 | + | 0.773808i | ||||
\(433\) | 6823.53i | 0.757316i | 0.925537 | + | 0.378658i | \(0.123614\pi\) | ||||
−0.925537 | + | 0.378658i | \(0.876386\pi\) | |||||||
\(434\) | −11320.6 | − | 2752.73i | −1.25208 | − | 0.304459i | ||||
\(435\) | −2455.73 | − | 1668.30i | −0.270674 | − | 0.183883i | ||||
\(436\) | 263.237 | − | 455.940i | 0.0289146 | − | 0.0500816i | ||||
\(437\) | −2377.94 | − | 4118.72i | −0.260303 | − | 0.450858i | ||||
\(438\) | 13397.5 | + | 981.558i | 1.46155 | + | 0.107079i | ||||
\(439\) | 590.734 | + | 341.060i | 0.0642237 | + | 0.0370796i | 0.531768 | − | 0.846890i | \(-0.321528\pi\) |
−0.467544 | + | 0.883970i | \(0.654861\pi\) | |||||||
\(440\) | −3659.59 | −0.396509 | ||||||||
\(441\) | 7519.36 | + | 5406.05i | 0.811938 | + | 0.583744i | ||||
\(442\) | 12585.6 | 1.35438 | ||||||||
\(443\) | −5297.30 | − | 3058.40i | −0.568132 | − | 0.328011i | 0.188271 | − | 0.982117i | \(-0.439712\pi\) |
−0.756403 | + | 0.654106i | \(0.773045\pi\) | |||||||
\(444\) | −607.506 | − | 44.5084i | −0.0649346 | − | 0.00475738i | ||||
\(445\) | −2744.13 | − | 4752.97i | −0.292324 | − | 0.506320i | ||||
\(446\) | 1393.74 | − | 2414.03i | 0.147972 | − | 0.256295i | ||||
\(447\) | 141.563 | + | 96.1708i | 0.0149792 | + | 0.0101761i | ||||
\(448\) | −8668.36 | − | 2107.81i | −0.914155 | − | 0.222288i | ||||
\(449\) | − | 1586.26i | − | 0.166727i | −0.996519 | − | 0.0833635i | \(-0.973434\pi\) | ||
0.996519 | − | 0.0833635i | \(-0.0265663\pi\) | |||||||
\(450\) | 285.618 | − | 1938.77i | 0.0299204 | − | 0.203099i | ||||
\(451\) | −1044.90 | + | 603.271i | −0.109096 | + | 0.0629865i | ||||
\(452\) | 520.350 | − | 300.424i | 0.0541487 | − | 0.0312628i | ||||
\(453\) | 3668.70 | + | 7585.77i | 0.380509 | + | 0.786778i | ||||
\(454\) | 9039.88i | 0.934500i | ||||||||
\(455\) | −4181.11 | − | 3990.94i | −0.430799 | − | 0.411204i | ||||
\(456\) | 5307.17 | − | 7812.13i | 0.545024 | − | 0.802273i | ||||
\(457\) | 3090.78 | − | 5353.38i | 0.316369 | − | 0.547967i | −0.663359 | − | 0.748301i | \(-0.730870\pi\) |
0.979727 | + | 0.200335i | \(0.0642030\pi\) | |||||||
\(458\) | 9066.97 | + | 15704.5i | 0.925047 | + | 1.60223i | ||||
\(459\) | −2918.46 | − | 9296.18i | −0.296780 | − | 0.945335i | ||||
\(460\) | 106.817 | + | 61.6709i | 0.0108269 | + | 0.00625092i | ||||
\(461\) | −8174.32 | −0.825848 | −0.412924 | − | 0.910766i | \(-0.635492\pi\) | ||||
−0.412924 | + | 0.910766i | \(0.635492\pi\) | |||||||
\(462\) | −8855.01 | − | 2852.78i | −0.891715 | − | 0.287280i | ||||
\(463\) | −3473.85 | −0.348690 | −0.174345 | − | 0.984685i | \(-0.555781\pi\) | ||||
−0.174345 | + | 0.984685i | \(0.555781\pi\) | |||||||
\(464\) | 6654.82 | + | 3842.16i | 0.665824 | + | 0.384414i | ||||
\(465\) | 411.331 | − | 5614.35i | 0.0410215 | − | 0.559912i | ||||
\(466\) | 5644.50 | + | 9776.56i | 0.561108 | + | 0.971867i | ||||
\(467\) | −126.998 | + | 219.966i | −0.0125841 | + | 0.0217962i | −0.872249 | − | 0.489062i | \(-0.837339\pi\) |
0.859665 | + | 0.510859i | \(0.170672\pi\) | |||||||
\(468\) | 671.977 | − | 266.319i | 0.0663721 | − | 0.0263047i | ||||
\(469\) | 2424.90 | + | 8274.75i | 0.238745 | + | 0.814696i | ||||
\(470\) | − | 732.259i | − | 0.0718651i | ||||||
\(471\) | 12108.7 | − | 5856.10i | 1.18458 | − | 0.572897i | ||||
\(472\) | 10174.6 | − | 5874.32i | 0.992214 | − | 0.572855i | ||||
\(473\) | 5340.28 | − | 3083.21i | 0.519125 | − | 0.299717i | ||||
\(474\) | 17290.2 | − | 8362.05i | 1.67546 | − | 0.810299i | ||||
\(475\) | 2067.21i | 0.199685i | ||||||||
\(476\) | −380.902 | + | 399.053i | −0.0366778 | + | 0.0384255i | ||||
\(477\) | 5913.25 | − | 2343.55i | 0.567608 | − | 0.224956i | ||||
\(478\) | 8529.17 | − | 14773.0i | 0.816141 | − | 1.41360i | ||||
\(479\) | −7052.74 | − | 12215.7i | −0.672751 | − | 1.16524i | −0.977121 | − | 0.212685i | \(-0.931779\pi\) |
0.304369 | − | 0.952554i | \(-0.401554\pi\) | |||||||
\(480\) | −36.8078 | + | 502.399i | −0.00350008 | + | 0.0477734i | ||||
\(481\) | −14774.9 | − | 8530.28i | −1.40057 | − | 0.808622i | ||||
\(482\) | −9428.14 | −0.890954 | ||||||||
\(483\) | −3713.86 | − | 4104.04i | −0.349869 | − | 0.386626i | ||||
\(484\) | −95.3204 | −0.00895195 | ||||||||
\(485\) | −4717.60 | − | 2723.71i | −0.441681 | − | 0.255005i | ||||
\(486\) | −6928.24 | − | 8540.78i | −0.646649 | − | 0.797156i | ||||
\(487\) | 5495.58 | + | 9518.62i | 0.511352 | + | 0.885688i | 0.999913 | + | 0.0131582i | \(0.00418851\pi\) |
−0.488561 | + | 0.872530i | \(0.662478\pi\) | |||||||
\(488\) | −3980.24 | + | 6893.98i | −0.369215 | + | 0.639500i | ||||
\(489\) | −2581.31 | + | 3799.67i | −0.238713 | + | 0.351384i | ||||
\(490\) | 4973.69 | − | 231.613i | 0.458548 | − | 0.0213534i | ||||
\(491\) | − | 7464.15i | − | 0.686053i | −0.939326 | − | 0.343027i | \(-0.888548\pi\) | ||
0.939326 | − | 0.343027i | \(-0.111452\pi\) | |||||||
\(492\) | 35.1588 | + | 72.6978i | 0.00322171 | + | 0.00666152i | ||||
\(493\) | −6872.78 | + | 3968.00i | −0.627859 | + | 0.362495i | ||||
\(494\) | −12977.1 | + | 7492.32i | −1.18192 | + | 0.682380i | ||||
\(495\) | 655.161 | − | 4447.23i | 0.0594895 | − | 0.403814i | ||||
\(496\) | 14570.8i | 1.31905i | ||||||||
\(497\) | −4695.94 | + | 19312.0i | −0.423826 | + | 1.74298i | ||||
\(498\) | −3064.95 | − | 2082.18i | −0.275791 | − | 0.187358i | ||||
\(499\) | −4212.76 | + | 7296.72i | −0.377934 | + | 0.654601i | −0.990762 | − | 0.135616i | \(-0.956699\pi\) |
0.612827 | + | 0.790217i | \(0.290032\pi\) | |||||||
\(500\) | −26.8061 | − | 46.4296i | −0.00239761 | − | 0.00415279i | ||||
\(501\) | −13527.1 | − | 991.049i | −1.20628 | − | 0.0883768i | ||||
\(502\) | 2986.90 | + | 1724.49i | 0.265562 | + | 0.153322i | ||||
\(503\) | −17684.7 | −1.56763 | −0.783817 | − | 0.620992i | \(-0.786730\pi\) | ||||
−0.783817 | + | 0.620992i | \(0.786730\pi\) | |||||||
\(504\) | 4125.90 | − | 10187.7i | 0.364647 | − | 0.900389i | ||||
\(505\) | 7059.71 | 0.622085 | ||||||||
\(506\) | 4815.27 | + | 2780.09i | 0.423053 | + | 0.244250i | ||||
\(507\) | 8805.29 | + | 645.113i | 0.771315 | + | 0.0565098i | ||||
\(508\) | 127.974 | + | 221.657i | 0.0111770 | + | 0.0193592i | ||||
\(509\) | 4514.92 | − | 7820.07i | 0.393164 | − | 0.680979i | −0.599701 | − | 0.800224i | \(-0.704714\pi\) |
0.992865 | + | 0.119245i | \(0.0380473\pi\) | |||||||
\(510\) | −4333.17 | − | 2943.74i | −0.376228 | − | 0.255590i | ||||
\(511\) | −15826.2 | + | 4637.83i | −1.37008 | + | 0.401498i | ||||
\(512\) | 10521.3i | 0.908168i | ||||||||
\(513\) | 8543.38 | + | 7847.98i | 0.735281 | + | 0.675433i | ||||
\(514\) | −1563.22 | + | 902.525i | −0.134145 | + | 0.0774488i | ||||
\(515\) | 5999.80 | − | 3463.99i | 0.513365 | − | 0.296391i | ||||
\(516\) | −179.690 | − | 371.545i | −0.0153303 | − | 0.0316984i | ||||
\(517\) | − | 1679.68i | − | 0.142887i | ||||||
\(518\) | 14103.2 | − | 4132.92i | 1.19626 | − | 0.350560i | ||||
\(519\) | −10068.3 | + | 14820.5i | −0.851541 | + | 1.25346i | ||||
\(520\) | −3430.05 | + | 5941.02i | −0.289265 | + | 0.501022i | ||||
\(521\) | 1493.38 | + | 2586.61i | 0.125578 | + | 0.217507i | 0.921959 | − | 0.387288i | \(-0.126588\pi\) |
−0.796381 | + | 0.604796i | \(0.793255\pi\) | |||||||
\(522\) | −5561.46 | + | 7021.73i | −0.466319 | + | 0.588760i | ||||
\(523\) | −8834.54 | − | 5100.62i | −0.738637 | − | 0.426452i | 0.0829364 | − | 0.996555i | \(-0.473570\pi\) |
−0.821574 | + | 0.570102i | \(0.806903\pi\) | |||||||
\(524\) | −518.845 | −0.0432554 | ||||||||
\(525\) | 506.071 | + | 2352.02i | 0.0420700 | + | 0.195525i | ||||
\(526\) | −1381.89 | −0.114550 | ||||||||
\(527\) | −13032.0 | − | 7524.03i | −1.07720 | − | 0.621920i | ||||
\(528\) | −850.165 | + | 11604.1i | −0.0700733 | + | 0.956447i | ||||
\(529\) | −4429.47 | − | 7672.07i | −0.364056 | − | 0.630564i | ||||
\(530\) | 1709.89 | − | 2961.61i | 0.140137 | − | 0.242725i | ||||
\(531\) | 5317.10 | + | 13416.1i | 0.434544 | + | 1.09644i | ||||
\(532\) | 155.191 | − | 638.222i | 0.0126474 | − | 0.0520121i | ||||
\(533\) | 2261.73i | 0.183802i | ||||||||
\(534\) | −14907.1 | + | 7209.49i | −1.20804 | + | 0.584242i | ||||
\(535\) | −4315.82 | + | 2491.74i | −0.348765 | + | 0.201359i | ||||
\(536\) | 8862.85 | − | 5116.97i | 0.714211 | − | 0.412350i | ||||
\(537\) | 13820.5 | − | 6683.98i | 1.11061 | − | 0.537123i | ||||
\(538\) | 7875.59i | 0.631117i | ||||||||
\(539\) | 11408.8 | − | 531.281i | 0.911714 | − | 0.0424562i | ||||
\(540\) | −293.651 | − | 65.4814i | −0.0234014 | − | 0.00521828i | ||||
\(541\) | −887.926 | + | 1537.93i | −0.0705636 | + | 0.122220i | −0.899148 | − | 0.437644i | \(-0.855813\pi\) |
0.828585 | + | 0.559864i | \(0.189146\pi\) | |||||||
\(542\) | −4803.39 | − | 8319.71i | −0.380670 | − | 0.659340i | ||||
\(543\) | −964.137 | + | 13159.7i | −0.0761972 | + | 1.04003i | ||||
\(544\) | 1166.17 | + | 673.286i | 0.0919098 | + | 0.0530642i | ||||
\(545\) | −6137.52 | −0.482390 | ||||||||
\(546\) | −12930.8 | + | 11701.5i | −1.01353 | + | 0.917175i | ||||
\(547\) | 4626.98 | 0.361674 | 0.180837 | − | 0.983513i | \(-0.442119\pi\) | ||||
0.180837 | + | 0.983513i | \(0.442119\pi\) | |||||||
\(548\) | −371.500 | − | 214.486i | −0.0289593 | − | 0.0167197i | ||||
\(549\) | −7665.18 | − | 6071.10i | −0.595887 | − | 0.471964i | ||||
\(550\) | −1208.41 | − | 2093.02i | −0.0936848 | − | 0.162267i | ||||
\(551\) | 4724.39 | − | 8182.89i | 0.365274 | − | 0.632673i | ||||
\(552\) | −3691.51 | + | 5433.89i | −0.284640 | + | 0.418989i | ||||
\(553\) | −16280.3 | + | 17056.0i | −1.25191 | + | 1.31157i | ||||
\(554\) | 16708.5i | 1.28136i | ||||||||
\(555\) | 3091.73 | + | 6392.77i | 0.236463 | + | 0.488934i | ||||
\(556\) | −854.738 | + | 493.483i | −0.0651960 | + | 0.0376409i | ||||
\(557\) | −18505.1 | + | 10683.9i | −1.40769 | + | 0.812733i | −0.995166 | − | 0.0982117i | \(-0.968688\pi\) |
−0.412529 | + | 0.910944i | \(0.635354\pi\) | |||||||
\(558\) | −16803.4 | − | 2475.46i | −1.27481 | − | 0.187804i | ||||
\(559\) | − | 11559.3i | − | 0.874609i | ||||||
\(560\) | −1751.21 | − | 5975.87i | −0.132147 | − | 0.450940i | ||||
\(561\) | −9939.59 | − | 6752.47i | −0.748039 | − | 0.508181i | ||||
\(562\) | 8956.17 | − | 15512.5i | 0.672230 | − | 1.16434i | ||||
\(563\) | −11073.2 | − | 19179.4i | −0.828919 | − | 1.43573i | −0.898887 | − | 0.438181i | \(-0.855623\pi\) |
0.0699674 | − | 0.997549i | \(-0.477710\pi\) | |||||||
\(564\) | −112.120 | − | 8.21438i | −0.00837075 | − | 0.000613276i | ||||
\(565\) | −6066.13 | − | 3502.28i | −0.451688 | − | 0.260782i | ||||
\(566\) | 4616.65 | 0.342849 | ||||||||
\(567\) | 11641.7 | + | 6837.76i | 0.862267 | + | 0.506453i | ||||
\(568\) | 23588.4 | 1.74251 | ||||||||
\(569\) | −548.164 | − | 316.483i | −0.0403871 | − | 0.0233175i | 0.479671 | − | 0.877449i | \(-0.340756\pi\) |
−0.520058 | + | 0.854131i | \(0.674090\pi\) | |||||||
\(570\) | 6220.42 | + | 455.734i | 0.457096 | + | 0.0334888i | ||||
\(571\) | −329.152 | − | 570.108i | −0.0241236 | − | 0.0417833i | 0.853712 | − | 0.520746i | \(-0.174346\pi\) |
−0.877835 | + | 0.478963i | \(0.841013\pi\) | |||||||
\(572\) | 445.716 | − | 772.003i | 0.0325810 | − | 0.0564319i | ||||
\(573\) | 7718.16 | + | 5243.33i | 0.562706 | + | 0.382275i | ||||
\(574\) | −1409.34 | − | 1345.24i | −0.102482 | − | 0.0978207i | ||||
\(575\) | − | 1437.89i | − | 0.104286i | ||||||
\(576\) | −12866.7 | − | 1895.50i | −0.930748 | − | 0.137117i | ||||
\(577\) | −1680.30 | + | 970.124i | −0.121234 | + | 0.0699945i | −0.559391 | − | 0.828904i | \(-0.688965\pi\) |
0.438157 | + | 0.898899i | \(0.355631\pi\) | |||||||
\(578\) | 225.609 | − | 130.256i | 0.0162355 | − | 0.00937356i | ||||
\(579\) | −2238.95 | − | 4629.49i | −0.160704 | − | 0.332288i | ||||
\(580\) | 245.050i | 0.0175434i | ||||||||
\(581\) | 4420.09 | + | 1074.80i | 0.315622 | + | 0.0767472i | ||||
\(582\) | −9235.91 | + | 13595.2i | −0.657802 | + | 0.968281i | ||||
\(583\) | 3922.20 | − | 6793.46i | 0.278630 | − | 0.482601i | ||||
\(584\) | 9786.65 | + | 16951.0i | 0.693449 | + | 1.20109i | ||||
\(585\) | −6605.62 | − | 5231.89i | −0.466852 | − | 0.369764i | ||||
\(586\) | 13821.6 | + | 7979.93i | 0.974346 | + | 0.562539i | ||||
\(587\) | 22331.9 | 1.57025 | 0.785124 | − | 0.619339i | \(-0.212599\pi\) | ||||
0.785124 | + | 0.619339i | \(0.212599\pi\) | |||||||
\(588\) | 20.3308 | − | 764.146i | 0.00142590 | − | 0.0535933i | ||||
\(589\) | 17916.6 | 1.25338 | ||||||||
\(590\) | 6719.38 | + | 3879.44i | 0.468869 | + | 0.270701i | ||||
\(591\) | 1847.31 | − | 25214.4i | 0.128576 | − | 1.75496i | ||||
\(592\) | −9190.12 | − | 15917.8i | −0.638027 | − | 1.10509i | ||||
\(593\) | −566.434 | + | 981.092i | −0.0392254 | + | 0.0679404i | −0.884972 | − | 0.465645i | \(-0.845822\pi\) |
0.845746 | + | 0.533585i | \(0.179156\pi\) | |||||||
\(594\) | −13237.7 | − | 2951.87i | −0.914390 | − | 0.203900i | ||||
\(595\) | 6249.05 | + | 1519.53i | 0.430564 | + | 0.104697i | ||||
\(596\) | − | 14.1261i | − | 0.000970855i | ||||||
\(597\) | −2619.54 | + | 1266.89i | −0.179583 | + | 0.0868513i | ||||
\(598\) | 9026.49 | − | 5211.44i | 0.617258 | − | 0.356374i | ||||
\(599\) | −2894.17 | + | 1670.95i | −0.197417 | + | 0.113979i | −0.595450 | − | 0.803392i | \(-0.703026\pi\) |
0.398033 | + | 0.917371i | \(0.369693\pi\) | |||||||
\(600\) | 2570.56 | − | 1243.20i | 0.174904 | − | 0.0845887i | ||||
\(601\) | 12917.7i | 0.876745i | 0.898793 | + | 0.438372i | \(0.144445\pi\) | ||||
−0.898793 | + | 0.438372i | \(0.855555\pi\) | |||||||
\(602\) | 7202.88 | + | 6875.26i | 0.487653 | + | 0.465473i | ||||
\(603\) | 4631.59 | + | 11686.4i | 0.312791 | + | 0.789235i | ||||
\(604\) | 347.761 | − | 602.340i | 0.0234275 | − | 0.0405776i | ||||
\(605\) | 555.612 | + | 962.348i | 0.0373369 | + | 0.0646695i | ||||
\(606\) | 1556.37 | − | 21243.3i | 0.104329 | − | 1.42401i | ||||
\(607\) | −11335.3 | − | 6544.41i | −0.757963 | − | 0.437610i | 0.0706007 | − | 0.997505i | \(-0.477508\pi\) |
−0.828564 | + | 0.559894i | \(0.810842\pi\) | |||||||
\(608\) | −1603.26 | −0.106942 | ||||||||
\(609\) | 3372.06 | − | 10466.9i | 0.224373 | − | 0.696452i | ||||
\(610\) | −5257.15 | −0.348944 | ||||||||
\(611\) | −2726.82 | − | 1574.33i | −0.180549 | − | 0.104240i | ||||
\(612\) | −499.341 | + | 630.452i | −0.0329815 | + | 0.0416414i | ||||
\(613\) | 1126.55 | + | 1951.25i | 0.0742269 | + | 0.128565i | 0.900750 | − | 0.434338i | \(-0.143018\pi\) |
−0.826523 | + | 0.562903i | \(0.809684\pi\) | |||||||
\(614\) | 5187.98 | − | 8985.85i | 0.340993 | − | 0.590618i | ||||
\(615\) | 529.015 | − | 778.708i | 0.0346861 | − | 0.0510578i | ||||
\(616\) | −3812.04 | − | 13008.3i | −0.249337 | − | 0.850840i | ||||
\(617\) | 1251.11i | 0.0816332i | 0.999167 | + | 0.0408166i | \(0.0129959\pi\) | ||||
−0.999167 | + | 0.0408166i | \(0.987004\pi\) | |||||||
\(618\) | −9100.73 | − | 18817.6i | −0.592371 | − | 1.22485i | ||||
\(619\) | 17871.3 | − | 10318.0i | 1.16043 | − | 0.669977i | 0.209026 | − | 0.977910i | \(-0.432971\pi\) |
0.951408 | + | 0.307933i | \(0.0996374\pi\) | |||||||
\(620\) | −402.406 | + | 232.329i | −0.0260662 | + | 0.0150493i | ||||
\(621\) | −5942.53 | − | 5458.83i | −0.384002 | − | 0.352746i | ||||
\(622\) | 9713.34i | 0.626156i | ||||||||
\(623\) | 14036.3 | − | 14705.1i | 0.902653 | − | 0.945665i | ||||
\(624\) | 18041.4 | + | 12256.4i | 1.15743 | + | 0.786299i | ||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 256.273 | + | 443.878i | 0.0163622 | + | 0.0283402i | ||||
\(627\) | 14268.6 | + | 1045.38i | 0.908826 | + | 0.0665844i | ||||
\(628\) | −961.476 | − | 555.108i | −0.0610940 | − | 0.0352727i | ||||
\(629\) | 18982.3 | 1.20329 | ||||||||
\(630\) | 7189.01 | − | 1004.29i | 0.454630 | − | 0.0635108i | ||||
\(631\) | −960.414 | −0.0605919 | −0.0302959 | − | 0.999541i | \(-0.509645\pi\) | ||||
−0.0302959 | + | 0.999541i | \(0.509645\pi\) | |||||||
\(632\) | 24235.3 | + | 13992.2i | 1.52536 | + | 0.880667i | ||||
\(633\) | 7611.68 | + | 557.663i | 0.477942 | + | 0.0350160i | ||||
\(634\) | −6517.60 | − | 11288.8i | −0.408276 | − | 0.707155i | ||||
\(635\) | 1491.89 | − | 2584.03i | 0.0932345 | − | 0.161487i | ||||
\(636\) | −434.287 | − | 295.033i | −0.0270764 | − | 0.0183944i | ||||
\(637\) | 9830.77 | − | 19019.2i | 0.611474 | − | 1.18300i | ||||
\(638\) | 11046.7i | 0.685494i | ||||||||
\(639\) | −4222.94 | + | 28665.2i | −0.261435 | + | 1.77462i | ||||
\(640\) | −6727.16 | + | 3883.93i | −0.415491 | + | 0.239884i | ||||
\(641\) | 10556.2 | − | 6094.64i | 0.650462 | − | 0.375544i | −0.138172 | − | 0.990408i | \(-0.544123\pi\) |
0.788633 | + | 0.614864i | \(0.210789\pi\) | |||||||
\(642\) | 6546.40 | + | 13536.0i | 0.402439 | + | 0.832124i | ||||
\(643\) | − | 19020.8i | − | 1.16657i | −0.812266 | − | 0.583287i | \(-0.801766\pi\) | ||
0.812266 | − | 0.583287i | \(-0.198234\pi\) | |||||||
\(644\) | −107.947 | + | 443.929i | −0.00660511 | + | 0.0271634i | ||||
\(645\) | −2703.70 | + | 3979.84i | −0.165052 | + | 0.242955i | ||||
\(646\) | 8336.26 | − | 14438.8i | 0.507718 | − | 0.879393i | ||||
\(647\) | −8106.41 | − | 14040.7i | −0.492575 | − | 0.853164i | 0.507389 | − | 0.861717i | \(-0.330611\pi\) |
−0.999963 | + | 0.00855306i | \(0.997277\pi\) | |||||||
\(648\) | 4621.00 | − | 15343.3i | 0.280139 | − | 0.930156i | ||||
\(649\) | 15413.2 | + | 8898.79i | 0.932233 | + | 0.538225i | ||||
\(650\) | −4530.45 | −0.273383 | ||||||||
\(651\) | 20385.1 | − | 4386.13i | 1.22727 | − | 0.264064i | ||||
\(652\) | 379.158 | 0.0227745 | ||||||||
\(653\) | −8853.93 | − | 5111.82i | −0.530599 | − | 0.306341i | 0.210661 | − | 0.977559i | \(-0.432438\pi\) |
−0.741260 | + | 0.671218i | \(0.765772\pi\) | |||||||
\(654\) | −1353.07 | + | 18468.3i | −0.0809008 | + | 1.10423i | ||||
\(655\) | 3024.29 | + | 5238.22i | 0.180410 | + | 0.312480i | ||||
\(656\) | −1218.34 | + | 2110.23i | −0.0725126 | + | 0.125595i | ||||
\(657\) | −22351.3 | + | 8858.32i | −1.32726 | + | 0.526021i | ||||
\(658\) | 2602.86 | − | 762.763i | 0.154210 | − | 0.0451909i | ||||
\(659\) | − | 8787.17i | − | 0.519423i | −0.965686 | − | 0.259711i | \(-0.916373\pi\) | ||
0.965686 | − | 0.259711i | \(-0.0836274\pi\) | |||||||
\(660\) | −334.029 | + | 161.546i | −0.0197001 | + | 0.00952754i | ||||
\(661\) | −5012.99 | + | 2894.25i | −0.294981 | + | 0.170307i | −0.640186 | − | 0.768220i | \(-0.721143\pi\) |
0.345205 | + | 0.938527i | \(0.387809\pi\) | |||||||
\(662\) | 13962.0 | − | 8060.95i | 0.819710 | − | 0.473260i | ||||
\(663\) | −20278.2 | + | 9807.13i | −1.18784 | + | 0.574475i | ||||
\(664\) | − | 5398.87i | − | 0.315537i | ||||||
\(665\) | −7348.04 | + | 2153.33i | −0.428488 | + | 0.125568i | ||||
\(666\) | 19918.0 | − | 7893.95i | 1.15887 | − | 0.459286i | ||||
\(667\) | −3286.15 | + | 5691.78i | −0.190765 | + | 0.330415i | ||||
\(668\) | 559.768 | + | 969.547i | 0.0324223 | + | 0.0561570i | ||||
\(669\) | −364.533 | + | 4975.60i | −0.0210668 | + | 0.287545i | ||||
\(670\) | 5853.08 | + | 3379.28i | 0.337499 | + | 0.194855i | ||||
\(671\) | −12059.0 | −0.693792 | ||||||||
\(672\) | −1824.15 | + | 392.491i | −0.104714 | + | 0.0225308i | ||||
\(673\) | 15116.2 | 0.865804 | 0.432902 | − | 0.901441i | \(-0.357490\pi\) | ||||
0.432902 | + | 0.901441i | \(0.357490\pi\) | |||||||
\(674\) | −6330.60 | − | 3654.97i | −0.361788 | − | 0.208879i | ||||
\(675\) | 1050.57 | + | 3346.37i | 0.0599057 | + | 0.190817i | ||||
\(676\) | −364.375 | − | 631.116i | −0.0207314 | − | 0.0359078i | ||||
\(677\) | 7005.98 | − | 12134.7i | 0.397728 | − | 0.688885i | −0.595717 | − | 0.803194i | \(-0.703132\pi\) |
0.993445 | + | 0.114309i | \(0.0364655\pi\) | |||||||
\(678\) | −11876.0 | + | 17481.4i | −0.672706 | + | 0.990220i | ||||
\(679\) | 4767.48 | − | 19606.2i | 0.269454 | − | 1.10813i | ||||
\(680\) | − | 7632.82i | − | 0.430449i | ||||||
\(681\) | −7044.21 | − | 14565.3i | −0.396380 | − | 0.819595i | ||||
\(682\) | −18140.3 | + | 10473.3i | −1.01851 | + | 0.588040i | ||||
\(683\) | 27532.8 | − | 15896.1i | 1.54248 | − | 0.890551i | 0.543797 | − | 0.839217i | \(-0.316986\pi\) |
0.998682 | − | 0.0513340i | \(-0.0163473\pi\) | |||||||
\(684\) | 139.560 | − | 947.328i | 0.00780145 | − | 0.0529561i | ||||
\(685\) | 5000.86i | 0.278939i | ||||||||
\(686\) | 6004.17 | + | 17438.1i | 0.334169 | + | 0.970538i | ||||
\(687\) | −26846.4 | − | 18238.1i | −1.49091 | − | 1.01285i | ||||
\(688\) | 6226.73 | − | 10785.0i | 0.345046 | − | 0.597637i | ||||
\(689\) | −7352.39 | − | 12734.7i | −0.406537 | − | 0.704142i | ||||
\(690\) | −4326.74 | − | 316.995i | −0.238719 | − | 0.0174896i | ||||
\(691\) | −1232.86 | − | 711.795i | −0.0678732 | − | 0.0391866i | 0.465679 | − | 0.884954i | \(-0.345810\pi\) |
−0.533553 | + | 0.845767i | \(0.679143\pi\) | |||||||
\(692\) | 1478.89 | 0.0812415 | ||||||||
\(693\) | 16490.4 | − | 2303.67i | 0.903924 | − | 0.126276i | ||||
\(694\) | −35587.5 | −1.94652 | ||||||||
\(695\) | 9964.35 | + | 5752.92i | 0.543841 | + | 0.313987i | ||||
\(696\) | −13016.5 | − | 953.645i | −0.708894 | − | 0.0519365i | ||||
\(697\) | −1258.25 | − | 2179.34i | −0.0683780 | − | 0.118434i | ||||
\(698\) | 16157.9 | − | 27986.3i | 0.876197 | − | 1.51762i | ||||
\(699\) | −16712.8 | − | 11353.9i | −0.904345 | − | 0.614367i | ||||
\(700\) | 137.114 | − | 143.648i | 0.00740348 | − | 0.00775626i | ||||
\(701\) | 24490.7i | 1.31955i | 0.751465 | + | 0.659773i | \(0.229347\pi\) | ||||
−0.751465 | + | 0.659773i | \(0.770653\pi\) | |||||||
\(702\) | −17199.5 | + | 18723.5i | −0.924718 | + | 1.00666i | ||||
\(703\) | −19572.8 | + | 11300.3i | −1.05007 | + | 0.606260i | ||||
\(704\) | −13890.3 | + | 8019.59i | −0.743624 | + | 0.429332i | ||||
\(705\) | 570.603 | + | 1179.84i | 0.0304825 | + | 0.0630287i | ||||
\(706\) | 1414.44i | 0.0754011i | ||||||||
\(707\) | 7353.80 | + | 25094.2i | 0.391185 | + | 1.33489i | ||||
\(708\) | 669.377 | − | 985.320i | 0.0355321 | − | 0.0523031i | ||||
\(709\) | −12491.0 | + | 21635.0i | −0.661647 | + | 1.14601i | 0.318536 | + | 0.947911i | \(0.396809\pi\) |
−0.980183 | + | 0.198095i | \(0.936524\pi\) | |||||||
\(710\) | 7788.96 | + | 13490.9i | 0.411710 | + | 0.713104i | ||||
\(711\) | −21342.5 | + | 26946.4i | −1.12575 | + | 1.42133i | ||||
\(712\) | −20894.9 | − | 12063.7i | −1.09981 | − | 0.634978i | ||||
\(713\) | −12462.2 | −0.654579 | ||||||||
\(714\) | 5950.05 | − | 18468.9i | 0.311870 | − | 0.968043i | ||||
\(715\) | −10392.1 | −0.543557 | ||||||||
\(716\) | −1097.40 | − | 633.584i | −0.0572790 | − | 0.0330700i | ||||
\(717\) | −2230.81 | + | 30448.9i | −0.116194 | + | 1.58596i | ||||
\(718\) | 18243.8 | + | 31599.1i | 0.948261 | + | 1.64244i | ||||
\(719\) | −2860.91 | + | 4955.25i | −0.148392 | + | 0.257023i | −0.930633 | − | 0.365953i | \(-0.880743\pi\) |
0.782241 | + | 0.622976i | \(0.214077\pi\) | |||||||
\(720\) | −3344.85 | − | 8439.72i | −0.173132 | − | 0.436847i | ||||
\(721\) | 18562.7 | + | 17718.4i | 0.958823 | + | 0.915212i | ||||
\(722\) | − | 62.7681i | − | 0.00323544i | ||||||
\(723\) | 15190.9 | − | 7346.75i | 0.781404 | − | 0.377910i | ||||
\(724\) | 943.219 | − | 544.567i | 0.0484177 | − | 0.0279540i | ||||
\(725\) | 2474.01 | − | 1428.37i | 0.126735 | − | 0.0731702i | ||||
\(726\) | 3018.28 | − | 1459.73i | 0.154296 | − | 0.0746220i | ||||
\(727\) | 21968.5i | 1.12073i | 0.828247 | + | 0.560363i | \(0.189338\pi\) | ||||
−0.828247 | + | 0.560363i | \(0.810662\pi\) | |||||||
\(728\) | −24690.7 | − | 6003.84i | −1.25700 | − | 0.305655i | ||||
\(729\) | 17818.3 | + | 8362.41i | 0.905262 | + | 0.424854i | ||||
\(730\) | −6463.16 | + | 11194.5i | −0.327688 | + | 0.567572i | ||||
\(731\) | 6430.67 | + | 11138.2i | 0.325372 | + | 0.563561i | ||||
\(732\) | −58.9740 | + | 804.950i | −0.00297779 | + | 0.0406445i | ||||
\(733\) | −19431.5 | − | 11218.8i | −0.979153 | − | 0.565314i | −0.0771388 | − | 0.997020i | \(-0.524578\pi\) |
−0.902014 | + | 0.431706i | \(0.857912\pi\) | |||||||
\(734\) | 7813.95 | 0.392940 | ||||||||
\(735\) | −7833.28 | + | 4248.87i | −0.393108 | + | 0.213227i | ||||
\(736\) | 1115.18 | 0.0558507 | ||||||||
\(737\) | 13426.0 | + | 7751.51i | 0.671036 | + | 0.387423i | ||||
\(738\) | −2226.57 | − | 1763.53i | −0.111059 | − | 0.0879625i | ||||
\(739\) | −9016.28 | − | 15616.6i | −0.448808 | − | 0.777358i | 0.549501 | − | 0.835493i | \(-0.314818\pi\) |
−0.998309 | + | 0.0581351i | \(0.981485\pi\) | |||||||
\(740\) | 293.070 | − | 507.612i | 0.0145587 | − | 0.0252165i | ||||
\(741\) | 15070.8 | − | 22184.1i | 0.747150 | − | 1.09980i | ||||
\(742\) | 12308.4 | + | 2992.93i | 0.608969 | + | 0.148078i | ||||
\(743\) | 6885.43i | 0.339975i | 0.985446 | + | 0.169988i | \(0.0543728\pi\) | ||||
−0.985446 | + | 0.169988i | \(0.945627\pi\) | |||||||
\(744\) | −10774.8 | − | 22279.1i | −0.530945 | − | 1.09784i | ||||
\(745\) | −142.617 | + | 82.3397i | −0.00701352 | + | 0.00404925i | ||||
\(746\) | 23034.0 | − | 13298.7i | 1.13048 | − | 0.652680i | ||||
\(747\) | 6560.84 | + | 966.537i | 0.321350 | + | 0.0473410i | ||||
\(748\) | 991.843i | 0.0484831i | ||||||||
\(749\) | −13352.7 | − | 12745.3i | −0.651396 | − | 0.621768i | ||||
\(750\) | 1559.82 | + | 1059.67i | 0.0759423 | + | 0.0515914i | ||||
\(751\) | −17037.5 | + | 29509.8i | −0.827838 | + | 1.43386i | 0.0718933 | + | 0.997412i | \(0.477096\pi\) |
−0.899731 | + | 0.436445i | \(0.856237\pi\) | |||||||
\(752\) | −1696.11 | − | 2937.75i | −0.0822483 | − | 0.142458i | ||||
\(753\) | −6156.37 | − | 451.041i | −0.297942 | − | 0.0218285i | ||||
\(754\) | 17933.4 | + | 10353.9i | 0.866177 | + | 0.500087i | ||||
\(755\) | −8108.25 | −0.390847 | ||||||||
\(756\) | −73.1264 | − | 1112.01i | −0.00351796 | − | 0.0534967i | ||||
\(757\) | 15803.2 | 0.758755 | 0.379377 | − | 0.925242i | \(-0.376138\pi\) | ||||
0.379377 | + | 0.925242i | \(0.376138\pi\) | |||||||
\(758\) | −27630.5 | − | 15952.5i | −1.32399 | − | 0.764407i | ||||
\(759\) | −9924.84 | − | 727.135i | −0.474636 | − | 0.0347738i | ||||
\(760\) | 4543.91 | + | 7870.28i | 0.216875 | + | 0.375638i | ||||
\(761\) | −17416.7 | + | 30166.6i | −0.829640 | + | 1.43698i | 0.0686817 | + | 0.997639i | \(0.478121\pi\) |
−0.898321 | + | 0.439339i | \(0.855213\pi\) | |||||||
\(762\) | −7446.68 | − | 5058.90i | −0.354022 | − | 0.240505i | ||||
\(763\) | −6393.19 | − | 21816.2i | −0.303341 | − | 1.03513i | ||||
\(764\) | − | 770.173i | − | 0.0364710i | ||||||
\(765\) | 9275.60 | + | 1366.47i | 0.438379 | + | 0.0645816i | ||||
\(766\) | −17009.5 | + | 9820.45i | −0.802322 | + | 0.463221i | ||||
\(767\) | 28892.8 | − | 16681.3i | 1.36018 | − | 0.785301i | ||||
\(768\) | 1486.18 | + | 3072.98i | 0.0698282 | + | 0.144384i | ||||
\(769\) | − | 25811.3i | − | 1.21037i | −0.796083 | − | 0.605187i | \(-0.793098\pi\) | ||
0.796083 | − | 0.605187i | \(-0.206902\pi\) | |||||||
\(770\) | 6181.04 | − | 6475.58i | 0.289285 | − | 0.303070i | ||||
\(771\) | 1815.42 | − | 2672.29i | 0.0848001 | − | 0.124825i | ||||
\(772\) | −212.234 | + | 367.600i | −0.00989438 | + | 0.0171376i | ||||
\(773\) | −10786.0 | − | 18681.9i | −0.501871 | − | 0.869266i | −0.999998 | − | 0.00216164i | \(-0.999312\pi\) |
0.498127 | − | 0.867104i | \(-0.334021\pi\) | |||||||
\(774\) | 11379.6 | + | 9013.07i | 0.528465 | + | 0.418563i | ||||
\(775\) | 4691.16 | + | 2708.45i | 0.217434 | + | 0.125536i | ||||
\(776\) | −23947.8 | −1.10783 | ||||||||
\(777\) | −19503.0 | + | 17648.9i | −0.900472 | + | 0.814864i | ||||
\(778\) | −16628.2 | −0.766261 | ||||||||
\(779\) | 2594.78 | + | 1498.10i | 0.119342 | + | 0.0689022i | ||||
\(780\) | −50.8220 | + | 693.681i | −0.00233297 | + | 0.0318433i | ||||
\(781\) | 17866.6 | + | 30945.9i | 0.818588 | + | 1.41784i | ||||
\(782\) | −5798.46 | + | 10043.2i | −0.265157 | + | 0.459265i | ||||
\(783\) | 3489.19 | − | 15647.3i | 0.159251 | − | 0.714162i | ||||
\(784\) | 19417.5 | − | 12449.6i | 0.884542 | − | 0.567129i | ||||
\(785\) | 12942.7i | 0.588463i | ||||||||
\(786\) | 16429.0 | − | 7945.54i | 0.745551 | − | 0.360570i | ||||
\(787\) | −4415.35 | + | 2549.20i | −0.199988 | + | 0.115463i | −0.596650 | − | 0.802502i | \(-0.703502\pi\) |
0.396662 | + | 0.917965i | \(0.370168\pi\) | |||||||
\(788\) | −1807.23 | + | 1043.41i | −0.0817005 | + | 0.0471698i | ||||
\(789\) | 2226.54 | − | 1076.82i | 0.100465 | − | 0.0485879i | ||||
\(790\) | 18481.1i | 0.832315i | ||||||||
\(791\) | 6130.26 | − | 25210.6i | 0.275559 | − | 1.13323i | ||||
\(792\) | −7281.06 | − | 18371.6i | −0.326668 | − | 0.824249i | ||||
\(793\) | −11302.7 | + | 19576.8i | −0.506141 | + | 0.876662i | ||||
\(794\) | −10174.7 | − | 17623.1i | −0.454769 | − | 0.787682i | ||||
\(795\) | −447.222 | + | 6104.24i | −0.0199514 | + | 0.272321i | ||||
\(796\) | 208.002 | + | 120.090i | 0.00926187 | + | 0.00534734i | ||||
\(797\) | −37405.2 | −1.66244 | −0.831218 | − | 0.555946i | \(-0.812356\pi\) | ||||
−0.831218 | + | 0.555946i | \(0.812356\pi\) | |||||||
\(798\) | 4859.61 | + | 22585.6i | 0.215574 | + | 1.00191i | ||||
\(799\) | 3503.32 | 0.155117 | ||||||||
\(800\) | −419.788 | − | 242.364i | −0.0185522 | − | 0.0107111i | ||||
\(801\) | 18400.8 | − | 23232.3i | 0.811685 | − | 1.02481i | ||||
\(802\) | −3675.58 | − | 6366.28i | −0.161832 | − | 0.280301i | ||||
\(803\) | −14825.4 | + | 25678.4i | −0.651529 | + | 1.12848i | ||||
\(804\) | 583.078 | − | 858.287i | 0.0255766 | − | 0.0376486i | ||||
\(805\) | 5111.09 | − | 1497.79i | 0.223779 | − | 0.0655779i | ||||
\(806\) | 39265.5i | 1.71597i | ||||||||
\(807\) | −6136.95 | − | 12689.4i | −0.267696 | − | 0.553516i | ||||
\(808\) | 26877.7 | − | 15517.8i | 1.17024 | − | 0.675638i | ||||
\(809\) | −11773.2 | + | 6797.24i | −0.511647 | + | 0.295400i | −0.733511 | − | 0.679678i | \(-0.762119\pi\) |
0.221863 | + | 0.975078i | \(0.428786\pi\) | |||||||
\(810\) | 10301.1 | − | 2423.51i | 0.446845 | − | 0.105128i | ||||
\(811\) | − | 22968.1i | − | 0.994475i | −0.867614 | − | 0.497238i | \(-0.834348\pi\) | ||
0.867614 | − | 0.497238i | \(-0.165652\pi\) | |||||||
\(812\) | −871.048 | + | 255.259i | −0.0376451 | + | 0.0110318i | ||||
\(813\) | 14222.4 | + | 9661.98i | 0.613531 | + | 0.416802i | ||||
\(814\) | 13211.4 | − | 22882.9i | 0.568871 | − | 0.985313i | ||||
\(815\) | −2210.07 | − | 3827.95i | −0.0949881 | − | 0.164524i | ||||
\(816\) | −24202.7 | − | 1773.19i | −1.03832 | − | 0.0760713i | ||||
\(817\) | −13261.4 | − | 7656.50i | −0.567882 | − | 0.327867i | ||||
\(818\) | 5809.15 | 0.248303 | ||||||||
\(819\) | 11716.3 | − | 28929.9i | 0.499879 | − | 1.23430i | ||||
\(820\) | −77.7050 | −0.00330924 | ||||||||
\(821\) | −15157.6 | − | 8751.22i | −0.644339 | − | 0.372009i | 0.141945 | − | 0.989875i | \(-0.454664\pi\) |
−0.786284 | + | 0.617865i | \(0.787998\pi\) | |||||||
\(822\) | 15048.0 | + | 1102.48i | 0.638516 | + | 0.0467803i | ||||
\(823\) | −6491.82 | − | 11244.2i | −0.274958 | − | 0.476242i | 0.695166 | − | 0.718849i | \(-0.255331\pi\) |
−0.970125 | + | 0.242607i | \(0.921997\pi\) | |||||||
\(824\) | 15228.3 | − | 26376.1i | 0.643813 | − | 1.11512i | ||||
\(825\) | 3577.98 | + | 2430.70i | 0.150993 | + | 0.102577i | ||||
\(826\) | −6790.42 | + | 27925.5i | −0.286040 | + | 1.17634i | ||||
\(827\) | − | 34622.8i | − | 1.45581i | −0.685680 | − | 0.727903i | \(-0.740495\pi\) | ||
0.685680 | − | 0.727903i | \(-0.259505\pi\) | |||||||
\(828\) | −97.0736 | + | 658.934i | −0.00407432 | + | 0.0276565i | ||||
\(829\) | −20517.7 | + | 11845.9i | −0.859602 | + | 0.496292i | −0.863879 | − | 0.503699i | \(-0.831972\pi\) |
0.00427667 | + | 0.999991i | \(0.498639\pi\) | |||||||
\(830\) | 3087.77 | − | 1782.72i | 0.129130 | − | 0.0745532i | ||||
\(831\) | −13019.8 | − | 26921.1i | −0.543506 | − | 1.12381i | ||||
\(832\) | 30066.3i | 1.25284i | ||||||||
\(833\) | 1108.10 | + | 23795.5i | 0.0460903 | + | 0.989753i | ||||
\(834\) | 19507.8 | − | 28715.3i | 0.809950 | − | 1.19224i | ||||
\(835\) | 6525.65 | − | 11302.8i | 0.270455 | − | 0.468441i | ||||
\(836\) | −590.455 | − | 1022.70i | −0.0244274 | − | 0.0423095i | ||||
\(837\) | 29003.1 | − | 9105.29i | 1.19772 | − | 0.376015i | ||||
\(838\) | 14940.0 | + | 8625.62i | 0.615864 | + | 0.355569i | ||||
\(839\) | −22126.7 | −0.910487 | −0.455244 | − | 0.890367i | \(-0.650448\pi\) | ||||
−0.455244 | + | 0.890367i | \(0.650448\pi\) | |||||||
\(840\) | 7096.66 | + | 7842.23i | 0.291498 | + | 0.322122i | ||||
\(841\) | 11331.4 | 0.464612 | ||||||||
\(842\) | 15152.3 | + | 8748.20i | 0.620171 | + | 0.358056i | ||||
\(843\) | −2342.49 | + | 31973.2i | −0.0957055 | + | 1.30631i | ||||
\(844\) | −314.982 | − | 545.564i | −0.0128461 | − | 0.0222501i | ||||
\(845\) | −4247.80 | + | 7357.41i | −0.172934 | + | 0.299530i | ||||
\(846\) | 3676.02 | − | 1456.89i | 0.149390 | − | 0.0592067i | ||||
\(847\) | −2841.97 | + | 2977.40i | −0.115291 | + | 0.120785i | ||||
\(848\) | − | 15842.2i | − | 0.641539i | ||||||
\(849\) | −7438.48 | + | 3597.46i | −0.300693 | + | 0.145424i | ||||
\(850\) | 4365.43 | − | 2520.38i | 0.176156 | − | 0.101704i | ||||
\(851\) | 13614.3 | − | 7860.20i | 0.548403 | − | 0.316620i | ||||
\(852\) | 2153.03 | − | 1041.27i | 0.0865748 | − | 0.0418701i | ||||
\(853\) | − | 19699.5i | − | 0.790737i | −0.918523 | − | 0.395368i | \(-0.870617\pi\) | ||
0.918523 | − | 0.395368i | \(-0.129383\pi\) | |||||||
\(854\) | −5476.15 | − | 18686.9i | −0.219426 | − | 0.748773i | ||||
\(855\) | −10377.6 | + | 4112.89i | −0.415097 | + | 0.164512i | ||||
\(856\) | −10954.1 | + | 18973.1i | −0.437388 | + | 0.757578i | ||||
\(857\) | 18063.8 | + | 31287.5i | 0.720010 | + | 1.24709i | 0.960995 | + | 0.276565i | \(0.0891961\pi\) |
−0.240985 | + | 0.970529i | \(0.577471\pi\) | |||||||
\(858\) | −2291.03 | + | 31270.8i | −0.0911590 | + | 1.24425i | ||||
\(859\) | 25541.9 | + | 14746.6i | 1.01453 | + | 0.585738i | 0.912514 | − | 0.409045i | \(-0.134138\pi\) |
0.102014 | + | 0.994783i | \(0.467471\pi\) | |||||||
\(860\) | 397.136 | 0.0157468 | ||||||||
\(861\) | 3319.02 | + | 1069.27i | 0.131373 | + | 0.0423238i | ||||
\(862\) | −38360.1 | −1.51572 | ||||||||
\(863\) | 339.981 | + | 196.288i | 0.0134103 | + | 0.00774244i | 0.506690 | − | 0.862128i | \(-0.330869\pi\) |
−0.493280 | + | 0.869871i | \(0.664202\pi\) | |||||||
\(864\) | −2595.33 | + | 814.784i | −0.102193 | + | 0.0320828i | ||||
\(865\) | −8620.31 | − | 14930.8i | −0.338843 | − | 0.586893i | ||||
\(866\) | −9905.23 | + | 17156.4i | −0.388676 | + | 0.673207i | ||||
\(867\) | −262.008 | + | 385.675i | −0.0102633 | + | 0.0151075i | ||||
\(868\) | −1245.00 | − | 1188.37i | −0.0486844 | − | 0.0464701i | ||||
\(869\) | 42392.7i | 1.65486i | ||||||||
\(870\) | −3752.68 | − | 7759.42i | −0.146239 | − | 0.302378i | ||||
\(871\) | 25167.8 | − | 14530.6i | 0.979080 | − | 0.565272i | ||||
\(872\) | −23366.7 | + | 13490.8i | −0.907451 | + | 0.523917i | ||||
\(873\) | 4287.27 | − | 29101.9i | 0.166211 | − | 1.12824i | ||||
\(874\) | − | 13807.6i | − | 0.534379i | ||||||
\(875\) | −2249.48 | − | 546.989i | −0.0869102 | − | 0.0211332i | ||||
\(876\) | 1641.55 | + | 1115.19i | 0.0633137 | + | 0.0430122i | ||||
\(877\) | 1347.07 | − | 2333.19i | 0.0518668 | − | 0.0898360i | −0.838926 | − | 0.544245i | \(-0.816816\pi\) |
0.890793 | + | 0.454409i | \(0.150150\pi\) | |||||||
\(878\) | 990.186 | + | 1715.05i | 0.0380605 | + | 0.0659228i | ||||
\(879\) | −28488.1 | − | 2087.15i | −1.09315 | − | 0.0800887i | ||||
\(880\) | −9696.01 | − | 5597.99i | −0.371423 | − | 0.214441i | ||||
\(881\) | 32824.3 | 1.25525 | 0.627626 | − | 0.778515i | \(-0.284027\pi\) | ||||
0.627626 | + | 0.778515i | \(0.284027\pi\) | |||||||
\(882\) | 11058.3 | + | 24507.7i | 0.422168 | + | 0.935621i | ||||
\(883\) | 4165.26 | 0.158745 | 0.0793726 | − | 0.996845i | \(-0.474708\pi\) | ||||
0.0793726 | + | 0.996845i | \(0.474708\pi\) | |||||||
\(884\) | 1610.17 | + | 929.632i | 0.0612623 | + | 0.0353698i | ||||
\(885\) | −13849.5 | − | 1014.67i | −0.526039 | − | 0.0385398i | ||||
\(886\) | −8879.32 | − | 15379.4i | −0.336689 | − | 0.583163i | ||||
\(887\) | 2570.20 | − | 4451.72i | 0.0972930 | − | 0.168516i | −0.813270 | − | 0.581886i | \(-0.802315\pi\) |
0.910563 | + | 0.413370i | \(0.135648\pi\) | |||||||
\(888\) | 25822.7 | + | 17542.7i | 0.975848 | + | 0.662942i | ||||
\(889\) | 10739.2 | + | 2611.35i | 0.405152 | + | 0.0985174i | ||||
\(890\) | − | 15933.8i | − | 0.600115i | ||||||
\(891\) | 23629.1 | − | 5559.14i | 0.888445 | − | 0.209022i | ||||
\(892\) | 356.624 | − | 205.897i | 0.0133864 | − | 0.00772863i | ||||
\(893\) | −3612.31 | + | 2085.57i | −0.135365 | + | 0.0781532i | ||||
\(894\) | 216.326 | + | 447.298i | 0.00809289 | + | 0.0167337i | ||||
\(895\) | 14772.4i | 0.551716i | ||||||||
\(896\) | −20813.1 | − | 19866.4i | −0.776023 | − | 0.740726i | ||||
\(897\) | −10482.8 | + | 15430.6i | −0.390200 | + | 0.574373i | ||||
\(898\) | 2302.67 | − | 3988.33i | 0.0855690 | − | 0.148210i | ||||
\(899\) | −12379.7 | − | 21442.3i | −0.459274 | − | 0.795486i | ||||
\(900\) | 179.749 | − | 226.945i | 0.00665737 | − | 0.00840539i | ||||
\(901\) | 14169.2 | + | 8180.56i | 0.523910 | + | 0.302480i | ||||
\(902\) | −3502.90 | −0.129306 | ||||||||
\(903\) | −16962.9 | − | 5464.87i | −0.625129 | − | 0.201395i | ||||
\(904\) | −30793.2 | −1.13293 | ||||||||
\(905\) | −10995.8 | − | 6348.45i | −0.403883 | − | 0.233182i | ||||
\(906\) | −1787.53 | + | 24398.4i | −0.0655483 | + | 0.894684i | ||||
\(907\) | −8505.91 | − | 14732.7i | −0.311394 | − | 0.539350i | 0.667271 | − | 0.744815i | \(-0.267462\pi\) |
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(908\) | −667.731 | + | 1156.54i | −0.0244047 | + | 0.0422701i | ||||
\(909\) | 14045.9 | + | 35440.6i | 0.512511 | + | 1.29317i | ||||
\(910\) | −4719.18 | − | 16103.8i | −0.171911 | − | 0.586633i | ||||
\(911\) | − | 20269.7i | − | 0.737174i | −0.929593 | − | 0.368587i | \(-0.879842\pi\) | ||
0.929593 | − | 0.368587i | \(-0.120158\pi\) | |||||||
\(912\) | 26011.3 | − | 12579.8i | 0.944429 | − | 0.456753i | ||||
\(913\) | 7082.83 | − | 4089.27i | 0.256744 | − | 0.148231i | ||||
\(914\) | 15542.2 | − | 8973.32i | 0.562464 | − | 0.324739i | ||||
\(915\) | 8470.47 | − | 4096.57i | 0.306038 | − | 0.148009i | ||||
\(916\) | 2678.93i | 0.0966313i | ||||||||
\(917\) | −15469.3 | + | 16206.5i | −0.557080 | + | 0.583626i | ||||
\(918\) | 6156.72 | − | 27609.9i | 0.221353 | − | 0.992659i | ||||
\(919\) | 14402.1 | − | 24945.3i | 0.516957 | − | 0.895395i | −0.482850 | − | 0.875703i | \(-0.660398\pi\) |
0.999806 | − | 0.0196917i | \(-0.00626847\pi\) | |||||||
\(920\) | −3160.61 | − | 5474.34i | −0.113263 | − | 0.196178i | ||||
\(921\) | −1356.92 | + | 18520.9i | −0.0485473 | + | 0.662633i | ||||
\(922\) | −20552.6 | − | 11866.1i | −0.734127 | − | 0.423848i | ||||
\(923\) | 66983.9 | 2.38873 | ||||||||
\(924\) | −922.171 | − | 1019.05i | −0.0328325 | − | 0.0362818i | ||||
\(925\) | −6833.09 | −0.242887 | ||||||||
\(926\) | −8734.29 | − | 5042.74i | −0.309964 | − | 0.178958i | ||||
\(927\) | 29326.7 | + | 23227.8i | 1.03907 | + | 0.822979i | ||||
\(928\) | 1107.80 | + | 1918.76i | 0.0391867 | + | 0.0678733i | ||||
\(929\) | −14503.6 | + | 25121.0i | −0.512216 | + | 0.887184i | 0.487684 | + | 0.873020i | \(0.337842\pi\) |
−0.999900 | + | 0.0141639i | \(0.995491\pi\) | |||||||
\(930\) | 9184.15 | − | 13519.0i | 0.323828 | − | 0.476673i | ||||
\(931\) | −15308.3 | − | 23876.1i | −0.538892 | − | 0.840502i | ||||
\(932\) | 1667.72i | 0.0586138i | ||||||||
\(933\) | −7568.99 | − | 15650.4i | −0.265592 | − | 0.549165i | ||||
\(934\) | −638.619 | + | 368.707i | −0.0223729 | + | 0.0129170i | ||||
\(935\) | 10013.6 | − | 5781.34i | 0.350245 | − | 0.202214i | ||||
\(936\) | −36649.0 | − | 5399.10i | −1.27982 | − | 0.188542i | ||||
\(937\) | − | 28513.1i | − | 0.994113i | −0.867718 | − | 0.497056i | \(-0.834414\pi\) | ||
0.867718 | − | 0.497056i | \(-0.165586\pi\) | |||||||
\(938\) | −5914.96 | + | 24325.2i | −0.205896 | + | 0.846745i | ||||
\(939\) | −758.800 | − | 515.491i | −0.0263712 | − | 0.0179153i | ||||
\(940\) | 54.0883 | − | 93.6837i | 0.00187677 | − | 0.00325067i | ||||
\(941\) | 19121.9 | + | 33120.1i | 0.662441 | + | 1.14738i | 0.979972 | + | 0.199133i | \(0.0638127\pi\) |
−0.317532 | + | 0.948248i | \(0.602854\pi\) | |||||||
\(942\) | 38945.6 | + | 2853.32i | 1.34704 | + | 0.0986901i | ||||
\(943\) | −1804.85 | − | 1042.03i | −0.0623267 | − | 0.0359843i | ||||
\(944\) | 35943.3 | 1.23925 | ||||||||
\(945\) | −10800.6 | + | 7220.08i | −0.371791 | + | 0.248539i | ||||
\(946\) | 17902.7 | 0.615293 | ||||||||
\(947\) | 41824.3 | + | 24147.2i | 1.43517 | + | 0.828596i | 0.997509 | − | 0.0705444i | \(-0.0224736\pi\) |
0.437661 | + | 0.899140i | \(0.355807\pi\) | |||||||
\(948\) | 2829.74 | + | 207.319i | 0.0969469 | + | 0.00710273i | ||||
\(949\) | 27791.1 | + | 48135.6i | 0.950619 | + | 1.64652i | ||||
\(950\) | −3000.82 | + | 5197.58i | −0.102484 | + | 0.177507i | ||||
\(951\) | 19298.0 | + | 13110.1i | 0.658024 | + | 0.447029i | ||||
\(952\) | 27131.4 | − | 7950.79i | 0.923669 | − | 0.270679i | ||||
\(953\) | 28307.3i | 0.962187i | 0.876669 | + | 0.481093i | \(0.159760\pi\) | ||||
−0.876669 | + | 0.481093i | \(0.840240\pi\) | |||||||
\(954\) | 18269.6 | + | 2691.46i | 0.620021 | + | 0.0913410i | ||||
\(955\) | −7775.61 | + | 4489.25i | −0.263469 | + | 0.152114i | ||||
\(956\) | 2182.41 | − | 1260.01i | 0.0738328 | − | 0.0426274i | ||||
\(957\) | −8608.03 | − | 17798.8i | −0.290761 | − | 0.601206i | ||||
\(958\) | − | 40951.8i | − | 1.38110i | ||||||
\(959\) | −17775.9 | + | 5209.18i | −0.598554 | + | 0.175405i | ||||
\(960\) | 7032.47 | − | 10351.8i | 0.236429 | − | 0.348022i | ||||
\(961\) | 8578.66 | − | 14858.7i | 0.287961 | − | 0.498764i | ||||
\(962\) | −24765.6 | − | 42895.3i | −0.830015 | − | 1.43763i | ||||
\(963\) | −21095.5 | − | 16708.4i | −0.705912 | − | 0.559107i | ||||
\(964\) | −1206.22 | − | 696.410i | −0.0403005 | − | 0.0232675i | ||||
\(965\) | 4948.35 | 0.165071 | ||||||||
\(966\) | −3380.20 | − | 15709.9i | −0.112584 | − | 0.523248i | ||||
\(967\) | 38919.6 | 1.29428 | 0.647141 | − | 0.762370i | \(-0.275964\pi\) | ||||
0.647141 | + | 0.762370i | \(0.275964\pi\) | |||||||
\(968\) | 4230.65 | + | 2442.56i | 0.140473 | + | 0.0811023i | ||||
\(969\) | −2180.35 | + | 29760.1i | −0.0722838 | + | 0.986619i | ||||
\(970\) | −7907.62 | − | 13696.4i | −0.261751 | − | 0.453366i | ||||
\(971\) | 10390.9 | − | 17997.5i | 0.343418 | − | 0.594817i | −0.641647 | − | 0.767000i | \(-0.721749\pi\) |
0.985065 | + | 0.172183i | \(0.0550820\pi\) | |||||||
\(972\) | −255.520 | − | 1604.44i | −0.00843190 | − | 0.0529451i | ||||
\(973\) | −10069.7 | + | 41411.5i | −0.331778 | + | 1.36443i | ||||
\(974\) | 31910.2i | 1.04976i | ||||||||
\(975\) | 7299.59 | − | 3530.30i | 0.239768 | − | 0.115959i | ||||
\(976\) | −21091.1 | + | 12177.0i | −0.691712 | + | 0.399360i | ||||
\(977\) | −38304.7 | + | 22115.2i | −1.25432 | + | 0.724185i | −0.971965 | − | 0.235124i | \(-0.924450\pi\) |
−0.282359 | + | 0.959309i | \(0.591117\pi\) | |||||||
\(978\) | −12005.9 | + | 5806.39i | −0.392541 | + | 0.189844i | ||||
\(979\) | − | 36549.6i | − | 1.19319i | ||||||
\(980\) | 653.432 | + | 337.750i | 0.0212991 | + | 0.0110092i | ||||
\(981\) | −12211.1 | − | 30811.1i | −0.397422 | − | 1.00277i | ||||
\(982\) | 10835.2 | − | 18767.1i | 0.352102 | − | 0.609858i | ||||
\(983\) | −4812.95 | − | 8336.27i | −0.156164 | − | 0.270484i | 0.777318 | − | 0.629108i | \(-0.216579\pi\) |
−0.933482 | + | 0.358624i | \(0.883246\pi\) | |||||||
\(984\) | 302.399 | − | 4127.51i | 0.00979687 | − | 0.133720i | ||||
\(985\) | 21068.3 | + | 12163.8i | 0.681515 | + | 0.393473i | ||||
\(986\) | −23040.3 | −0.744170 | ||||||||
\(987\) | −3599.43 | + | 3257.23i | −0.116080 | + | 0.105044i | ||||
\(988\) | −2213.68 | −0.0712820 | ||||||||
\(989\) | 9224.28 | + | 5325.64i | 0.296577 | + | 0.171229i | ||||
\(990\) | 8102.99 | − | 10230.6i | 0.260131 | − | 0.328434i | ||||
\(991\) | −2494.29 | − | 4320.24i | −0.0799533 | − | 0.138483i | 0.823276 | − | 0.567641i | \(-0.192144\pi\) |
−0.903230 | + | 0.429158i | \(0.858810\pi\) | |||||||
\(992\) | −2100.58 | + | 3638.31i | −0.0672313 | + | 0.116448i | ||||
\(993\) | −16214.5 | + | 23867.7i | −0.518180 | + | 0.762758i | ||||
\(994\) | −39840.8 | + | 41739.3i | −1.27130 | + | 1.33188i | ||||
\(995\) | − | 2799.97i | − | 0.0892110i | ||||||
\(996\) | −238.324 | − | 492.782i | −0.00758190 | − | 0.0156771i | ||||
\(997\) | 31138.2 | − | 17977.6i | 0.989123 | − | 0.571070i | 0.0841107 | − | 0.996456i | \(-0.473195\pi\) |
0.905012 | + | 0.425386i | \(0.139862\pi\) | |||||||
\(998\) | −21184.2 | + | 12230.7i | −0.671919 | + | 0.387933i | ||||
\(999\) | −25941.2 | + | 28239.8i | −0.821565 | + | 0.894362i |
(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 | 105.4.s.b.26.12 | yes | 32 | |
3.2 | odd | 2 | 105.4.s.a.26.5 | ✓ | 32 | ||
7.3 | odd | 6 | 105.4.s.a.101.5 | yes | 32 | ||
21.17 | even | 6 | inner | 105.4.s.b.101.12 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.s.a.26.5 | ✓ | 32 | 3.2 | odd | 2 | ||
105.4.s.a.101.5 | yes | 32 | 7.3 | odd | 6 | ||
105.4.s.b.26.12 | yes | 32 | 1.1 | even | 1 | trivial | |
105.4.s.b.101.12 | yes | 32 | 21.17 | even | 6 | inner |