Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,8,Mod(55,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.55");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.c (of order \(3\), degree \(2\), not 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: | \(50.6063741284\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 55.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.55 |
Dual form | 162.8.c.h.109.1 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | − | 6.92820i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −32.0000 | − | 55.4256i | −0.250000 | − | 0.433013i | ||||
\(5\) | −82.5000 | − | 142.894i | −0.295161 | − | 0.511234i | 0.679861 | − | 0.733341i | \(-0.262040\pi\) |
−0.975022 | + | 0.222107i | \(0.928707\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 254.000 | − | 439.941i | 0.279892 | − | 0.484787i | −0.691466 | − | 0.722409i | \(-0.743035\pi\) |
0.971358 | + | 0.237622i | \(0.0763680\pi\) | |||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1320.00 | −0.417421 | ||||||||
\(11\) | 1512.00 | − | 2618.86i | 0.342513 | − | 0.593250i | −0.642385 | − | 0.766382i | \(-0.722055\pi\) |
0.984899 | + | 0.173131i | \(0.0553885\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2519.50 | − | 4363.90i | −0.318063 | − | 0.550901i | 0.662021 | − | 0.749485i | \(-0.269699\pi\) |
−0.980084 | + | 0.198585i | \(0.936366\pi\) | |||||||
\(14\) | −2032.00 | − | 3519.53i | −0.197914 | − | 0.342796i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2048.00 | + | 3547.24i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3189.00 | 0.157428 | 0.0787142 | − | 0.996897i | \(-0.474919\pi\) | ||||
0.0787142 | + | 0.996897i | \(0.474919\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1508.00 | 0.0504387 | 0.0252193 | − | 0.999682i | \(-0.491972\pi\) | ||||
0.0252193 | + | 0.999682i | \(0.491972\pi\) | |||||||
\(20\) | −5280.00 | + | 9145.23i | −0.147580 | + | 0.255617i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12096.0 | − | 20950.9i | −0.242193 | − | 0.419491i | ||||
\(23\) | −37800.0 | − | 65471.5i | −0.647805 | − | 1.12203i | −0.983646 | − | 0.180113i | \(-0.942354\pi\) |
0.335841 | − | 0.941919i | \(-0.390980\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25450.0 | − | 44080.7i | 0.325760 | − | 0.564233i | ||||
\(26\) | −40312.0 | −0.449808 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −32512.0 | −0.279892 | ||||||||
\(29\) | −41332.5 | + | 71590.0i | −0.314701 | + | 0.545079i | −0.979374 | − | 0.202056i | \(-0.935238\pi\) |
0.664673 | + | 0.747135i | \(0.268571\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 87446.0 | + | 151461.i | 0.527198 | + | 0.913134i | 0.999498 | + | 0.0316960i | \(0.0100908\pi\) |
−0.472299 | + | 0.881438i | \(0.656576\pi\) | |||||||
\(32\) | 16384.0 | + | 28377.9i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12756.0 | − | 22094.0i | 0.0556594 | − | 0.0964049i | ||||
\(35\) | −83820.0 | −0.330453 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −323569. | −1.05017 | −0.525087 | − | 0.851049i | \(-0.675967\pi\) | ||||
−0.525087 | + | 0.851049i | \(0.675967\pi\) | |||||||
\(38\) | 6032.00 | − | 10447.7i | 0.0178328 | − | 0.0308873i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 42240.0 | + | 73161.8i | 0.104355 | + | 0.180748i | ||||
\(41\) | −154059. | − | 266838.i | −0.349095 | − | 0.604650i | 0.636994 | − | 0.770869i | \(-0.280178\pi\) |
−0.986089 | + | 0.166219i | \(0.946844\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −168340. | + | 291573.i | −0.322885 | + | 0.559253i | −0.981082 | − | 0.193593i | \(-0.937986\pi\) |
0.658197 | + | 0.752846i | \(0.271319\pi\) | |||||||
\(44\) | −193536. | −0.342513 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −604800. | −0.916135 | ||||||||
\(47\) | −191598. | + | 331857.i | −0.269184 | + | 0.466240i | −0.968651 | − | 0.248425i | \(-0.920087\pi\) |
0.699468 | + | 0.714664i | \(0.253420\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 282740. | + | 489719.i | 0.343321 | + | 0.594649i | ||||
\(50\) | −203600. | − | 352646.i | −0.230347 | − | 0.398973i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −161248. | + | 279290.i | −0.159031 | + | 0.275450i | ||||
\(53\) | −760206. | −0.701400 | −0.350700 | − | 0.936488i | \(-0.614056\pi\) | ||||
−0.350700 | + | 0.936488i | \(0.614056\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −498960. | −0.404386 | ||||||||
\(56\) | −130048. | + | 225250.i | −0.0989568 | + | 0.171398i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 330660. | + | 572720.i | 0.222527 | + | 0.385429i | ||||
\(59\) | −1.11283e6 | − | 1.92748e6i | −0.705420 | − | 1.22182i | −0.966540 | − | 0.256516i | \(-0.917425\pi\) |
0.261120 | − | 0.965306i | \(-0.415908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.12241e6 | + | 1.94407e6i | −0.633135 | + | 1.09662i | 0.353772 | + | 0.935332i | \(0.384899\pi\) |
−0.986907 | + | 0.161290i | \(0.948435\pi\) | |||||||
\(62\) | 1.39914e6 | 0.745571 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −415718. | + | 720044.i | −0.187759 | + | 0.325209i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −736594. | − | 1.27582e6i | −0.299203 | − | 0.518235i | 0.676751 | − | 0.736212i | \(-0.263388\pi\) |
−0.975954 | + | 0.217977i | \(0.930054\pi\) | |||||||
\(68\) | −102048. | − | 176752.i | −0.0393571 | − | 0.0681685i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −335280. | + | 580722.i | −0.116833 | + | 0.202360i | ||||
\(71\) | 5.00689e6 | 1.66021 | 0.830107 | − | 0.557604i | \(-0.188279\pi\) | ||||
0.830107 | + | 0.557604i | \(0.188279\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.89830e6 | −1.77459 | −0.887293 | − | 0.461207i | \(-0.847417\pi\) | ||||
−0.887293 | + | 0.461207i | \(0.847417\pi\) | |||||||
\(74\) | −1.29428e6 | + | 2.24175e6i | −0.371292 | + | 0.643097i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −48256.0 | − | 83581.8i | −0.0126097 | − | 0.0218406i | ||||
\(77\) | −768096. | − | 1.33038e6i | −0.191733 | − | 0.332092i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.51438e6 | + | 6.08709e6i | −0.801963 | + | 1.38904i | 0.116359 | + | 0.993207i | \(0.462878\pi\) |
−0.918322 | + | 0.395834i | \(0.870456\pi\) | |||||||
\(80\) | 675840. | 0.147580 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.46494e6 | −0.493695 | ||||||||
\(83\) | −1.32560e6 | + | 2.29600e6i | −0.254471 | + | 0.440757i | −0.964752 | − | 0.263162i | \(-0.915235\pi\) |
0.710281 | + | 0.703919i | \(0.248568\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −263092. | − | 455690.i | −0.0464667 | − | 0.0804828i | ||||
\(86\) | 1.34672e6 | + | 2.33259e6i | 0.228314 | + | 0.395452i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −774144. | + | 1.34086e6i | −0.121097 | + | 0.209746i | ||||
\(89\) | 6.77090e6 | 1.01808 | 0.509039 | − | 0.860743i | \(-0.330001\pi\) | ||||
0.509039 | + | 0.860743i | \(0.330001\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.55981e6 | −0.356093 | ||||||||
\(92\) | −2.41920e6 | + | 4.19018e6i | −0.323903 | + | 0.561016i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.53278e6 | + | 2.65486e6i | 0.190341 | + | 0.329681i | ||||
\(95\) | −124410. | − | 215484.i | −0.0148875 | − | 0.0257860i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.08819e6 | + | 1.40092e7i | −0.899809 | + | 1.55852i | −0.0720719 | + | 0.997399i | \(0.522961\pi\) |
−0.827737 | + | 0.561116i | \(0.810372\pi\) | |||||||
\(98\) | 4.52383e6 | 0.485529 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.25760e6 | −0.325760 | ||||||||
\(101\) | 1.35081e6 | − | 2.33967e6i | 0.130457 | − | 0.225959i | −0.793396 | − | 0.608706i | \(-0.791689\pi\) |
0.923853 | + | 0.382748i | \(0.125022\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.03446e6 | − | 1.79173e6i | −0.0932787 | − | 0.161563i | 0.815610 | − | 0.578602i | \(-0.196401\pi\) |
−0.908889 | + | 0.417038i | \(0.863068\pi\) | |||||||
\(104\) | 1.28998e6 | + | 2.23432e6i | 0.112452 | + | 0.194773i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.04082e6 | + | 5.26686e6i | −0.247982 | + | 0.429518i | ||||
\(107\) | 9.15450e6 | 0.722423 | 0.361211 | − | 0.932484i | \(-0.382363\pi\) | ||||
0.361211 | + | 0.932484i | \(0.382363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.68645e6 | 0.642465 | 0.321233 | − | 0.947000i | \(-0.395903\pi\) | ||||
0.321233 | + | 0.947000i | \(0.395903\pi\) | |||||||
\(110\) | −1.99584e6 | + | 3.45690e6i | −0.142972 | + | 0.247635i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.04038e6 | + | 1.80200e6i | 0.0699730 | + | 0.121197i | ||||
\(113\) | −1.24888e7 | − | 2.16312e7i | −0.814227 | − | 1.41028i | −0.909882 | − | 0.414867i | \(-0.863828\pi\) |
0.0956551 | − | 0.995415i | \(-0.469505\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.23700e6 | + | 1.08028e7i | −0.382414 | + | 0.662360i | ||||
\(116\) | 5.29056e6 | 0.314701 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.78053e7 | −0.997614 | ||||||||
\(119\) | 810006. | − | 1.40297e6i | 0.0440630 | − | 0.0763193i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.17130e6 | + | 8.95695e6i | 0.265369 | + | 0.459633i | ||||
\(122\) | 8.97926e6 | + | 1.55525e7i | 0.447694 | + | 0.775429i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.59654e6 | − | 9.69350e6i | 0.263599 | − | 0.456567i | ||||
\(125\) | −2.12891e7 | −0.974929 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.98659e6 | −0.216018 | −0.108009 | − | 0.994150i | \(-0.534448\pi\) | ||||
−0.108009 | + | 0.994150i | \(0.534448\pi\) | |||||||
\(128\) | 1.04858e6 | − | 1.81619e6i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.32574e6 | + | 5.76035e6i | 0.132766 | + | 0.229957i | ||||
\(131\) | −1.11702e7 | − | 1.93474e7i | −0.434123 | − | 0.751923i | 0.563101 | − | 0.826388i | \(-0.309608\pi\) |
−0.997224 | + | 0.0744655i | \(0.976275\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 383032. | − | 663431.i | 0.0141174 | − | 0.0244520i | ||||
\(134\) | −1.17855e7 | −0.423137 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.63277e6 | −0.0556594 | ||||||||
\(137\) | 6.43154e6 | − | 1.11398e7i | 0.213694 | − | 0.370129i | −0.739174 | − | 0.673515i | \(-0.764784\pi\) |
0.952868 | + | 0.303386i | \(0.0981170\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.20951e7 | − | 3.82699e7i | −0.697822 | − | 1.20866i | −0.969220 | − | 0.246196i | \(-0.920819\pi\) |
0.271398 | − | 0.962467i | \(-0.412514\pi\) | |||||||
\(140\) | 2.68224e6 | + | 4.64578e6i | 0.0826132 | + | 0.143090i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00276e7 | − | 3.46888e7i | 0.586974 | − | 1.01667i | ||||
\(143\) | −1.52379e7 | −0.435763 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.36397e7 | 0.371550 | ||||||||
\(146\) | −2.35932e7 | + | 4.08646e7i | −0.627411 | + | 1.08671i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.03542e7 | + | 1.79340e7i | 0.262543 | + | 0.454738i | ||||
\(149\) | −1.31444e6 | − | 2.27667e6i | −0.0325527 | − | 0.0563830i | 0.849290 | − | 0.527927i | \(-0.177030\pi\) |
−0.881843 | + | 0.471544i | \(0.843697\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.76509e7 | − | 4.78928e7i | 0.653568 | − | 1.13201i | −0.328683 | − | 0.944440i | \(-0.606605\pi\) |
0.982251 | − | 0.187572i | \(-0.0600619\pi\) | |||||||
\(152\) | −772096. | −0.0178328 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.22895e7 | −0.271152 | ||||||||
\(155\) | 1.44286e7 | − | 2.49911e7i | 0.311217 | − | 0.539043i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.11855e7 | + | 1.93739e7i | 0.230679 | + | 0.399548i | 0.958008 | − | 0.286741i | \(-0.0925720\pi\) |
−0.727329 | + | 0.686289i | \(0.759239\pi\) | |||||||
\(158\) | 2.81151e7 | + | 4.86967e7i | 0.567074 | + | 0.982200i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.70336e6 | − | 4.68236e6i | 0.0521776 | − | 0.0903742i | ||||
\(161\) | −3.84048e7 | −0.725262 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.23606e7 | 0.946995 | 0.473498 | − | 0.880795i | \(-0.342991\pi\) | ||||
0.473498 | + | 0.880795i | \(0.342991\pi\) | |||||||
\(164\) | −9.85978e6 | + | 1.70776e7i | −0.174547 | + | 0.302325i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.06048e7 | + | 1.83680e7i | 0.179938 | + | 0.311662i | ||||
\(167\) | −2.73979e7 | − | 4.74545e7i | −0.455207 | − | 0.788442i | 0.543493 | − | 0.839414i | \(-0.317101\pi\) |
−0.998700 | + | 0.0509718i | \(0.983768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.86785e7 | − | 3.23521e7i | 0.297672 | − | 0.515584i | ||||
\(170\) | −4.20948e6 | −0.0657139 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.15475e7 | 0.322885 | ||||||||
\(173\) | 6.18226e7 | − | 1.07080e8i | 0.907791 | − | 1.57234i | 0.0906639 | − | 0.995882i | \(-0.471101\pi\) |
0.817127 | − | 0.576458i | \(-0.195566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.29286e7 | − | 2.23930e7i | −0.182355 | − | 0.315849i | ||||
\(176\) | 6.19315e6 | + | 1.07269e7i | 0.0856283 | + | 0.148313i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.70836e7 | − | 4.69102e7i | 0.359945 | − | 0.623443i | ||||
\(179\) | −9.87297e7 | −1.28666 | −0.643328 | − | 0.765591i | \(-0.722447\pi\) | ||||
−0.643328 | + | 0.765591i | \(0.722447\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.19855e7 | 1.15304 | 0.576520 | − | 0.817083i | \(-0.304410\pi\) | ||||
0.576520 | + | 0.817083i | \(0.304410\pi\) | |||||||
\(182\) | −1.02392e7 | + | 1.77349e7i | −0.125898 | + | 0.218061i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.93536e7 | + | 3.35214e7i | 0.229034 | + | 0.396698i | ||||
\(185\) | 2.66944e7 | + | 4.62361e7i | 0.309970 | + | 0.536884i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.82177e6 | − | 8.35155e6i | 0.0539213 | − | 0.0933945i | ||||
\(188\) | 2.45245e7 | 0.269184 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.99056e6 | −0.0210541 | ||||||||
\(191\) | 6.59893e7 | − | 1.14297e8i | 0.685262 | − | 1.18691i | −0.288092 | − | 0.957603i | \(-0.593021\pi\) |
0.973354 | − | 0.229306i | \(-0.0736457\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.39537e7 | − | 1.28092e8i | −0.740473 | − | 1.28254i | −0.952280 | − | 0.305225i | \(-0.901268\pi\) |
0.211807 | − | 0.977311i | \(-0.432065\pi\) | |||||||
\(194\) | 6.47055e7 | + | 1.12073e8i | 0.636261 | + | 1.10204i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.80953e7 | − | 3.13420e7i | 0.171660 | − | 0.297325i | ||||
\(197\) | 2.69561e7 | 0.251203 | 0.125602 | − | 0.992081i | \(-0.459914\pi\) | ||||
0.125602 | + | 0.992081i | \(0.459914\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.35831e8 | 1.22183 | 0.610916 | − | 0.791695i | \(-0.290801\pi\) | ||||
0.610916 | + | 0.791695i | \(0.290801\pi\) | |||||||
\(200\) | −1.30304e7 | + | 2.25693e7i | −0.115174 | + | 0.199486i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.08065e7 | − | 1.87173e7i | −0.0922473 | − | 0.159777i | ||||
\(203\) | 2.09969e7 | + | 3.63677e7i | 0.176165 | + | 0.305126i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.54197e7 | + | 4.40283e7i | −0.206078 | + | 0.356938i | ||||
\(206\) | −1.65513e7 | −0.131916 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.06397e7 | 0.159031 | ||||||||
\(209\) | 2.28010e6 | − | 3.94924e6i | 0.0172759 | − | 0.0299228i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.09670e6 | + | 1.89954e6i | 0.00803710 | + | 0.0139207i | 0.870016 | − | 0.493024i | \(-0.164108\pi\) |
−0.861979 | + | 0.506944i | \(0.830775\pi\) | |||||||
\(212\) | 2.43266e7 | + | 4.21349e7i | 0.175350 | + | 0.303715i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.66180e7 | − | 6.34242e7i | 0.255415 | − | 0.442392i | ||||
\(215\) | 5.55522e7 | 0.381212 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.88451e7 | 0.590234 | ||||||||
\(218\) | 3.47458e7 | − | 6.01815e7i | 0.227146 | − | 0.393428i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.59667e7 | + | 2.76552e7i | 0.101097 | + | 0.175104i | ||||
\(221\) | −8.03469e6 | − | 1.39165e7i | −0.0500721 | − | 0.0867274i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.97215e6 | + | 1.72723e7i | −0.0602174 | + | 0.104300i | −0.894562 | − | 0.446943i | \(-0.852513\pi\) |
0.834345 | + | 0.551242i | \(0.185846\pi\) | |||||||
\(224\) | 1.66461e7 | 0.0989568 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.99820e8 | −1.15149 | ||||||||
\(227\) | −6.29925e7 | + | 1.09106e8i | −0.357436 | + | 0.619098i | −0.987532 | − | 0.157420i | \(-0.949682\pi\) |
0.630096 | + | 0.776518i | \(0.283016\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.17523e7 | − | 2.03556e7i | −0.0646693 | − | 0.112010i | 0.831878 | − | 0.554959i | \(-0.187266\pi\) |
−0.896547 | + | 0.442948i | \(0.853933\pi\) | |||||||
\(230\) | 4.98960e7 | + | 8.64224e7i | 0.270407 | + | 0.468359i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.11622e7 | − | 3.66541e7i | 0.111264 | − | 0.192714i | ||||
\(233\) | 1.27757e8 | 0.661665 | 0.330833 | − | 0.943689i | \(-0.392670\pi\) | ||||
0.330833 | + | 0.943689i | \(0.392670\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.32273e7 | 0.317810 | ||||||||
\(236\) | −7.12212e7 | + | 1.23359e8i | −0.352710 | + | 0.610911i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.48005e6 | − | 1.12238e7i | −0.0311572 | − | 0.0539659i | ||||
\(239\) | −4.67439e7 | − | 8.09628e7i | −0.221479 | − | 0.383613i | 0.733778 | − | 0.679389i | \(-0.237755\pi\) |
−0.955257 | + | 0.295776i | \(0.904422\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.73901e7 | − | 1.16723e8i | 0.310125 | − | 0.537152i | −0.668264 | − | 0.743924i | \(-0.732963\pi\) |
0.978389 | + | 0.206772i | \(0.0662958\pi\) | |||||||
\(242\) | 8.27408e7 | 0.375289 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.43668e8 | 0.633135 | ||||||||
\(245\) | 4.66520e7 | − | 8.08037e7i | 0.202670 | − | 0.351034i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.79941e6 | − | 6.58076e6i | −0.0160427 | − | 0.0277867i | ||||
\(248\) | −4.47724e7 | − | 7.75480e7i | −0.186393 | − | 0.322842i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.51565e7 | + | 1.47495e8i | −0.344689 | + | 0.597019i | ||||
\(251\) | −1.31470e7 | −0.0524771 | −0.0262385 | − | 0.999656i | \(-0.508353\pi\) | ||||
−0.0262385 | + | 0.999656i | \(0.508353\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.28614e8 | −0.887527 | ||||||||
\(254\) | −1.99464e7 | + | 3.45481e7i | −0.0763740 | + | 0.132284i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.38861e6 | − | 1.45295e7i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.42355e7 | − | 1.11259e8i | −0.236053 | − | 0.408855i | 0.723525 | − | 0.690298i | \(-0.242520\pi\) |
−0.959578 | + | 0.281443i | \(0.909187\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.21865e7 | + | 1.42351e8i | −0.293935 | + | 0.509111i | ||||
\(260\) | 5.32118e7 | 0.187759 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.78724e8 | −0.613942 | ||||||||
\(263\) | −4.88758e7 | + | 8.46554e7i | −0.165672 | + | 0.286952i | −0.936894 | − | 0.349614i | \(-0.886313\pi\) |
0.771222 | + | 0.636567i | \(0.219646\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.27170e7 | + | 1.08629e8i | 0.207026 | + | 0.358579i | ||||
\(266\) | −3.06426e6 | − | 5.30745e6i | −0.00998250 | − | 0.0172902i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.71420e7 | + | 8.16524e7i | −0.149602 | + | 0.259118i | ||||
\(269\) | −3.96851e7 | −0.124307 | −0.0621534 | − | 0.998067i | \(-0.519797\pi\) | ||||
−0.0621534 | + | 0.998067i | \(0.519797\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.50733e8 | −1.07049 | −0.535246 | − | 0.844696i | \(-0.679781\pi\) | ||||
−0.535246 | + | 0.844696i | \(0.679781\pi\) | |||||||
\(272\) | −6.53107e6 | + | 1.13121e7i | −0.0196786 | + | 0.0340843i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.14523e7 | − | 8.91180e7i | −0.151105 | − | 0.261721i | ||||
\(275\) | −7.69608e7 | − | 1.33300e8i | −0.223154 | − | 0.386514i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.69801e8 | + | 4.67309e8i | −0.762719 | + | 1.32107i | 0.178726 | + | 0.983899i | \(0.442803\pi\) |
−0.941444 | + | 0.337169i | \(0.890531\pi\) | |||||||
\(278\) | −3.53522e8 | −0.986869 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.29158e7 | 0.116833 | ||||||||
\(281\) | −5.04259e7 | + | 8.73403e7i | −0.135576 | + | 0.234824i | −0.925817 | − | 0.377971i | \(-0.876622\pi\) |
0.790242 | + | 0.612796i | \(0.209955\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.27056e8 | + | 2.20068e8i | 0.333229 | + | 0.577170i | 0.983143 | − | 0.182838i | \(-0.0585284\pi\) |
−0.649914 | + | 0.760008i | \(0.725195\pi\) | |||||||
\(284\) | −1.60221e8 | − | 2.77510e8i | −0.415053 | − | 0.718894i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.09517e7 | + | 1.05572e8i | −0.154065 | + | 0.266849i | ||||
\(287\) | −1.56524e8 | −0.390836 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00169e8 | −0.975216 | ||||||||
\(290\) | 5.45589e7 | − | 9.44988e7i | 0.131363 | − | 0.227527i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.88746e8 | + | 3.26917e8i | 0.443646 | + | 0.768418i | ||||
\(293\) | −2.71542e8 | − | 4.70325e8i | −0.630668 | − | 1.09235i | −0.987415 | − | 0.158148i | \(-0.949448\pi\) |
0.356748 | − | 0.934201i | \(-0.383886\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.83617e8 | + | 3.18034e8i | −0.416425 | + | 0.721269i | ||||
\(296\) | 1.65667e8 | 0.371292 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.10310e7 | −0.0460365 | ||||||||
\(299\) | −1.90474e8 | + | 3.29911e8i | −0.412085 | + | 0.713752i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.55167e7 | + | 1.48119e8i | 0.180746 | + | 0.313061i | ||||
\(302\) | −2.21208e8 | − | 3.83143e8i | −0.462142 | − | 0.800454i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.08838e6 | + | 5.34924e6i | −0.00630484 | + | 0.0109203i | ||||
\(305\) | 3.70394e8 | 0.747507 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.29877e8 | −1.43968 | −0.719839 | − | 0.694141i | \(-0.755784\pi\) | ||||
−0.719839 | + | 0.694141i | \(0.755784\pi\) | |||||||
\(308\) | −4.91581e7 | + | 8.51444e7i | −0.0958667 | + | 0.166046i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.15429e8 | − | 1.99928e8i | −0.220063 | − | 0.381161i | ||||
\(311\) | 3.19385e8 | + | 5.53191e8i | 0.602078 | + | 1.04283i | 0.992506 | + | 0.122197i | \(0.0389939\pi\) |
−0.390427 | + | 0.920634i | \(0.627673\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.18880e8 | − | 5.52317e8i | 0.587790 | − | 1.01808i | −0.406731 | − | 0.913548i | \(-0.633331\pi\) |
0.994521 | − | 0.104535i | \(-0.0333354\pi\) | |||||||
\(314\) | 1.78968e8 | 0.326229 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.49841e8 | 0.801963 | ||||||||
\(317\) | −3.27189e8 | + | 5.66707e8i | −0.576887 | + | 0.999198i | 0.418947 | + | 0.908011i | \(0.362399\pi\) |
−0.995834 | + | 0.0911869i | \(0.970934\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.24989e8 | + | 2.16488e8i | 0.215579 | + | 0.373393i | ||||
\(320\) | −2.16269e7 | − | 3.74589e7i | −0.0368951 | − | 0.0639042i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.53619e8 | + | 2.66076e8i | −0.256419 | + | 0.444130i | ||||
\(323\) | 4.80901e6 | 0.00794049 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.56485e8 | −0.414448 | ||||||||
\(326\) | 2.09442e8 | − | 3.62765e8i | 0.334813 | − | 0.579914i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.88782e7 | + | 1.36621e8i | 0.123424 | + | 0.213776i | ||||
\(329\) | 9.73318e7 | + | 1.68584e8i | 0.150685 | + | 0.260993i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.03844e8 | + | 6.99479e8i | −0.612091 | + | 1.06017i | 0.378796 | + | 0.925480i | \(0.376338\pi\) |
−0.990887 | + | 0.134693i | \(0.956995\pi\) | |||||||
\(332\) | 1.69677e8 | 0.254471 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.38366e8 | −0.643760 | ||||||||
\(335\) | −1.21538e8 | + | 2.10510e8i | −0.176626 | + | 0.305926i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.36402e7 | + | 1.62190e8i | 0.133278 | + | 0.230844i | 0.924938 | − | 0.380117i | \(-0.124116\pi\) |
−0.791660 | + | 0.610961i | \(0.790783\pi\) | |||||||
\(338\) | −1.49428e8 | − | 2.58817e8i | −0.210486 | − | 0.364573i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.68379e7 | + | 2.91641e7i | −0.0232334 | + | 0.0402414i | ||||
\(341\) | 5.28873e8 | 0.722290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.05623e8 | 0.944155 | ||||||||
\(344\) | 8.61901e7 | − | 1.49286e8i | 0.114157 | − | 0.197726i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.94581e8 | − | 8.56639e8i | −0.641905 | − | 1.11181i | ||||
\(347\) | 1.41278e8 | + | 2.44700e8i | 0.181518 | + | 0.314399i | 0.942398 | − | 0.334494i | \(-0.108565\pi\) |
−0.760879 | + | 0.648893i | \(0.775232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.80306e8 | − | 6.58709e8i | 0.478899 | − | 0.829478i | −0.520808 | − | 0.853674i | \(-0.674369\pi\) |
0.999707 | + | 0.0241959i | \(0.00770255\pi\) | |||||||
\(350\) | −2.06858e8 | −0.257889 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.90904e7 | 0.121097 | ||||||||
\(353\) | −2.34447e8 | + | 4.06074e8i | −0.283683 | + | 0.491353i | −0.972289 | − | 0.233783i | \(-0.924890\pi\) |
0.688606 | + | 0.725135i | \(0.258223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.13069e8 | − | 7.15456e8i | −0.490030 | − | 0.848757i | ||||
\(356\) | −2.16669e8 | − | 3.75281e8i | −0.254520 | − | 0.440841i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.94919e8 | + | 6.84020e8i | −0.454901 | + | 0.787912i | ||||
\(359\) | −1.53906e8 | −0.175560 | −0.0877802 | − | 0.996140i | \(-0.527977\pi\) | ||||
−0.0877802 | + | 0.996140i | \(0.527977\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.91598e8 | −0.997456 | ||||||||
\(362\) | 3.67942e8 | − | 6.37294e8i | 0.407661 | − | 0.706090i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.19140e7 | + | 1.41879e8i | 0.0890232 | + | 0.154193i | ||||
\(365\) | 4.86610e8 | + | 8.42833e8i | 0.523788 | + | 0.907228i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.74764e8 | − | 6.49110e8i | 0.395755 | − | 0.685468i | −0.597442 | − | 0.801912i | \(-0.703816\pi\) |
0.993197 | + | 0.116444i | \(0.0371496\pi\) | |||||||
\(368\) | 3.09658e8 | 0.323903 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.27111e8 | 0.438364 | ||||||||
\(371\) | −1.93092e8 | + | 3.34446e8i | −0.196316 | + | 0.340030i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.70864e8 | + | 4.69150e8i | 0.270253 | + | 0.468092i | 0.968926 | − | 0.247349i | \(-0.0795594\pi\) |
−0.698674 | + | 0.715441i | \(0.746226\pi\) | |||||||
\(374\) | −3.85741e7 | − | 6.68124e7i | −0.0381281 | − | 0.0660399i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.80982e7 | − | 1.69911e8i | 0.0951707 | − | 0.164841i | ||||
\(377\) | 4.16549e8 | 0.400379 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.32974e9 | 1.25467 | 0.627334 | − | 0.778750i | \(-0.284146\pi\) | ||||
0.627334 | + | 0.778750i | \(0.284146\pi\) | |||||||
\(380\) | −7.96224e6 | + | 1.37910e7i | −0.00744377 | + | 0.0128930i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.27914e8 | − | 9.14375e8i | −0.484554 | − | 0.839271i | ||||
\(383\) | 3.59974e8 | + | 6.23494e8i | 0.327398 | + | 0.567070i | 0.981995 | − | 0.188908i | \(-0.0604949\pi\) |
−0.654597 | + | 0.755978i | \(0.727162\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.26736e8 | + | 2.19513e8i | −0.113184 | + | 0.196041i | ||||
\(386\) | −1.18326e9 | −1.04719 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.03529e9 | 0.899809 | ||||||||
\(389\) | 1.16034e9 | − | 2.00976e9i | 0.999447 | − | 1.73109i | 0.470930 | − | 0.882171i | \(-0.343919\pi\) |
0.528517 | − | 0.848922i | \(-0.322748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.20544e8 | − | 2.08789e8i | −0.101983 | − | 0.176640i | ||||
\(392\) | −1.44763e8 | − | 2.50736e8i | −0.121382 | − | 0.210240i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.07824e8 | − | 1.86757e8i | 0.0888138 | − | 0.153830i | ||||
\(395\) | 1.15975e9 | 0.946833 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.18373e9 | 0.949477 | 0.474739 | − | 0.880127i | \(-0.342543\pi\) | ||||
0.474739 | + | 0.880127i | \(0.342543\pi\) | |||||||
\(398\) | 5.43322e8 | − | 9.41061e8i | 0.431983 | − | 0.748216i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.04243e8 | + | 1.80555e8i | 0.0814400 | + | 0.141058i | ||||
\(401\) | 6.33820e8 | + | 1.09781e9i | 0.490863 | + | 0.850200i | 0.999945 | − | 0.0105184i | \(-0.00334816\pi\) |
−0.509082 | + | 0.860718i | \(0.670015\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.40640e8 | − | 7.63212e8i | 0.335364 | − | 0.580868i | ||||
\(404\) | −1.72903e8 | −0.130457 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.35951e8 | 0.249135 | ||||||||
\(407\) | −4.89236e8 | + | 8.47382e8i | −0.359698 | + | 0.623016i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.09744e8 | + | 8.82903e8i | 0.368401 | + | 0.638089i | 0.989316 | − | 0.145789i | \(-0.0465721\pi\) |
−0.620915 | + | 0.783878i | \(0.713239\pi\) | |||||||
\(410\) | 2.03358e8 | + | 3.52226e8i | 0.145719 | + | 0.252393i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.62053e7 | + | 1.14671e8i | −0.0466394 | + | 0.0807817i | ||||
\(413\) | −1.13064e9 | −0.789765 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.37447e8 | 0.300440 | ||||||||
\(416\) | 8.25590e7 | − | 1.42996e8i | 0.0562261 | − | 0.0973864i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.82408e7 | − | 3.15939e7i | −0.0122159 | − | 0.0211586i | ||||
\(419\) | 5.20643e8 | + | 9.01780e8i | 0.345773 | + | 0.598896i | 0.985494 | − | 0.169711i | \(-0.0542834\pi\) |
−0.639721 | + | 0.768607i | \(0.720950\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.79224e8 | − | 1.69607e9i | 0.639580 | − | 1.10779i | −0.345945 | − | 0.938255i | \(-0.612442\pi\) |
0.985525 | − | 0.169530i | \(-0.0542251\pi\) | |||||||
\(422\) | 1.75472e7 | 0.0113662 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.89225e8 | 0.247982 | ||||||||
\(425\) | 8.11600e7 | − | 1.40573e8i | 0.0512839 | − | 0.0888263i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.70183e8 | + | 9.87586e8i | 0.354419 | + | 0.613871i | ||||
\(428\) | −2.92944e8 | − | 5.07394e8i | −0.180606 | − | 0.312818i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.22209e8 | − | 3.84877e8i | 0.134779 | − | 0.233444i | ||||
\(431\) | −2.84256e9 | −1.71017 | −0.855084 | − | 0.518489i | \(-0.826495\pi\) | ||||
−0.855084 | + | 0.518489i | \(0.826495\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.41292e7 | −0.0498011 | −0.0249006 | − | 0.999690i | \(-0.507927\pi\) | ||||
−0.0249006 | + | 0.999690i | \(0.507927\pi\) | |||||||
\(434\) | 3.55381e8 | − | 6.15537e8i | 0.208679 | − | 0.361443i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.77966e8 | − | 4.81452e8i | −0.160616 | − | 0.278196i | ||||
\(437\) | −5.70024e7 | − | 9.87311e7i | −0.0326744 | − | 0.0565938i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.35233e8 | − | 1.61987e9i | 0.527587 | − | 0.913807i | −0.471896 | − | 0.881654i | \(-0.656430\pi\) |
0.999483 | − | 0.0321530i | \(-0.0102364\pi\) | |||||||
\(440\) | 2.55468e8 | 0.142972 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.28555e8 | −0.0708127 | ||||||||
\(443\) | −5.06663e8 | + | 8.77566e8i | −0.276889 | + | 0.479587i | −0.970610 | − | 0.240658i | \(-0.922637\pi\) |
0.693721 | + | 0.720244i | \(0.255970\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.58599e8 | − | 9.67522e8i | −0.300497 | − | 0.520476i | ||||
\(446\) | 7.97772e7 | + | 1.38178e8i | 0.0425801 | + | 0.0737509i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.65846e7 | − | 1.15328e8i | 0.0349865 | − | 0.0605984i | ||||
\(449\) | 1.65756e8 | 0.0864183 | 0.0432092 | − | 0.999066i | \(-0.486242\pi\) | ||||
0.0432092 | + | 0.999066i | \(0.486242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.31749e8 | −0.478279 | ||||||||
\(452\) | −7.99282e8 | + | 1.38440e9i | −0.407113 | + | 0.705141i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.03940e8 | + | 8.72850e8i | 0.252746 | + | 0.437768i | ||||
\(455\) | 2.11184e8 | + | 3.65782e8i | 0.105105 | + | 0.182047i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.90398e8 | − | 1.19581e9i | 0.338371 | − | 0.586076i | −0.645756 | − | 0.763544i | \(-0.723457\pi\) |
0.984126 | + | 0.177469i | \(0.0567908\pi\) | |||||||
\(458\) | −1.88037e8 | −0.0914562 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.98336e8 | 0.382414 | ||||||||
\(461\) | 1.39246e9 | − | 2.41181e9i | 0.661955 | − | 1.14654i | −0.318146 | − | 0.948042i | \(-0.603060\pi\) |
0.980101 | − | 0.198498i | \(-0.0636063\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.39459e9 | − | 2.41551e9i | −0.653001 | − | 1.13103i | −0.982391 | − | 0.186837i | \(-0.940176\pi\) |
0.329390 | − | 0.944194i | \(-0.393157\pi\) | |||||||
\(464\) | −1.69298e8 | − | 2.93233e8i | −0.0786754 | − | 0.136270i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.11027e8 | − | 8.85125e8i | 0.233934 | − | 0.405186i | ||||
\(467\) | −3.97258e9 | −1.80494 | −0.902471 | − | 0.430751i | \(-0.858249\pi\) | ||||
−0.902471 | + | 0.430751i | \(0.858249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.48380e8 | −0.334979 | ||||||||
\(470\) | 2.52909e8 | − | 4.38052e8i | 0.112363 | − | 0.194618i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.69770e8 | + | 9.86871e8i | 0.249404 | + | 0.431980i | ||||
\(473\) | 5.09060e8 | + | 8.81718e8i | 0.221185 | + | 0.383103i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.83786e7 | − | 6.64737e7i | 0.0164309 | − | 0.0284592i | ||||
\(476\) | −1.03681e8 | −0.0440630 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.47902e8 | −0.313218 | ||||||||
\(479\) | −1.17233e9 | + | 2.03054e9i | −0.487391 | + | 0.844186i | −0.999895 | − | 0.0144991i | \(-0.995385\pi\) |
0.512504 | + | 0.858685i | \(0.328718\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.15232e8 | + | 1.41202e9i | 0.334021 | + | 0.578541i | ||||
\(482\) | −5.39121e8 | − | 9.33785e8i | −0.219291 | − | 0.379824i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.30963e8 | − | 5.73245e8i | 0.132685 | − | 0.229817i | ||||
\(485\) | 2.66910e9 | 1.06235 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.08381e9 | 1.20986 | 0.604931 | − | 0.796278i | \(-0.293201\pi\) | ||||
0.604931 | + | 0.796278i | \(0.293201\pi\) | |||||||
\(488\) | 5.74673e8 | − | 9.95362e8i | 0.223847 | − | 0.387714i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.73216e8 | − | 6.46429e8i | −0.143309 | − | 0.248219i | ||||
\(491\) | −1.85925e9 | − | 3.22032e9i | −0.708848 | − | 1.22776i | −0.965285 | − | 0.261200i | \(-0.915882\pi\) |
0.256436 | − | 0.966561i | \(-0.417452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.31809e8 | + | 2.28300e8i | −0.0495430 | + | 0.0858109i | ||||
\(494\) | −6.07905e7 | −0.0226877 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.16358e8 | −0.263599 | ||||||||
\(497\) | 1.27175e9 | − | 2.20274e9i | 0.464681 | − | 0.804850i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.18213e8 | − | 3.77956e8i | −0.0786192 | − | 0.136172i | 0.824035 | − | 0.566539i | \(-0.191718\pi\) |
−0.902654 | + | 0.430366i | \(0.858384\pi\) | |||||||
\(500\) | 6.81252e8 | + | 1.17996e9i | 0.243732 | + | 0.422156i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.25881e7 | + | 9.10853e7i | −0.0185535 | + | 0.0321355i | ||||
\(503\) | 5.04603e8 | 0.176792 | 0.0883958 | − | 0.996085i | \(-0.471826\pi\) | ||||
0.0883958 | + | 0.996085i | \(0.471826\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.45766e8 | −0.154024 | ||||||||
\(506\) | −9.14458e8 | + | 1.58389e9i | −0.313788 | + | 0.543497i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.59571e8 | + | 2.76385e8i | 0.0540046 | + | 0.0935387i | ||||
\(509\) | −2.30043e9 | − | 3.98446e9i | −0.773208 | − | 1.33923i | −0.935796 | − | 0.352541i | \(-0.885318\pi\) |
0.162589 | − | 0.986694i | \(-0.448016\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.49817e9 | + | 2.59490e9i | −0.496692 | + | 0.860296i | ||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.02777e9 | −0.333829 | ||||||||
\(515\) | −1.70686e8 | + | 2.95636e8i | −0.0550645 | + | 0.0953745i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.79392e8 | + | 1.00354e9i | 0.184398 | + | 0.319386i | ||||
\(518\) | 6.57492e8 | + | 1.13881e9i | 0.207844 | + | 0.359996i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.12847e8 | − | 3.68662e8i | 0.0663830 | − | 0.114979i | ||||
\(521\) | −7.14937e7 | −0.0221481 | −0.0110740 | − | 0.999939i | \(-0.503525\pi\) | ||||
−0.0110740 | + | 0.999939i | \(0.503525\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.12182e9 | −0.648563 | −0.324281 | − | 0.945961i | \(-0.605122\pi\) | ||||
−0.324281 | + | 0.945961i | \(0.605122\pi\) | |||||||
\(524\) | −7.14895e8 | + | 1.23823e9i | −0.217061 | + | 0.375961i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.91007e8 | + | 6.77243e8i | 0.117148 | + | 0.202906i | ||||
\(527\) | 2.78865e8 | + | 4.83009e8i | 0.0829960 | + | 0.143753i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.15527e9 | + | 2.00098e9i | −0.339303 | + | 0.587690i | ||||
\(530\) | 1.00347e9 | 0.292779 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.90281e7 | −0.0141174 | ||||||||
\(533\) | −7.76303e8 | + | 1.34460e9i | −0.222068 | + | 0.384633i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.55246e8 | − | 1.30812e9i | −0.213231 | − | 0.369327i | ||||
\(536\) | 3.77136e8 | + | 6.53219e8i | 0.105784 | + | 0.183224i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.58740e8 | + | 2.74946e8i | −0.0439491 | + | 0.0761220i | ||||
\(539\) | 1.71001e9 | 0.470368 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.11351e9 | −0.573870 | −0.286935 | − | 0.957950i | \(-0.592636\pi\) | ||||
−0.286935 | + | 0.957950i | \(0.592636\pi\) | |||||||
\(542\) | −1.40293e9 | + | 2.42995e9i | −0.378476 | + | 0.655540i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.22486e7 | + | 9.04972e7i | 0.0139148 | + | 0.0241012i | ||||
\(545\) | −7.16632e8 | − | 1.24124e9i | −0.189631 | − | 0.328450i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.12777e9 | + | 5.41745e9i | −0.817107 | + | 1.41527i | 0.0906987 | + | 0.995878i | \(0.471090\pi\) |
−0.907805 | + | 0.419392i | \(0.862243\pi\) | |||||||
\(548\) | −8.23237e8 | −0.213694 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.23137e9 | −0.315588 | ||||||||
\(551\) | −6.23294e7 | + | 1.07958e8i | −0.0158731 | + | 0.0274931i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.78531e9 | + | 3.09224e9i | 0.448926 | + | 0.777563i | ||||
\(554\) | 2.15841e9 | + | 3.73847e9i | 0.539324 | + | 0.934136i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.41409e9 | + | 2.44927e9i | −0.348911 | + | 0.604331i | ||||
\(557\) | 6.50846e9 | 1.59583 | 0.797913 | − | 0.602773i | \(-0.205938\pi\) | ||||
0.797913 | + | 0.602773i | \(0.205938\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.69653e9 | 0.410790 | ||||||||
\(560\) | 1.71663e8 | − | 2.97330e8i | 0.0413066 | − | 0.0715451i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.03408e8 | + | 6.98722e8i | 0.0958665 | + | 0.166046i | ||||
\(563\) | −8.66244e7 | − | 1.50038e8i | −0.0204579 | − | 0.0354341i | 0.855615 | − | 0.517612i | \(-0.173179\pi\) |
−0.876073 | + | 0.482178i | \(0.839846\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.06065e9 | + | 3.56915e9i | −0.480656 | + | 0.832520i | ||||
\(566\) | 2.03290e9 | 0.471257 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.56353e9 | −0.586974 | ||||||||
\(569\) | 3.64441e9 | − | 6.31230e9i | 0.829343 | − | 1.43646i | −0.0692121 | − | 0.997602i | \(-0.522049\pi\) |
0.898555 | − | 0.438862i | \(-0.144618\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.14518e9 | − | 3.71556e9i | −0.482212 | − | 0.835215i | 0.517580 | − | 0.855635i | \(-0.326833\pi\) |
−0.999791 | + | 0.0204199i | \(0.993500\pi\) | |||||||
\(572\) | 4.87614e8 | + | 8.44572e8i | 0.108941 | + | 0.188691i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.26096e8 | + | 1.08443e9i | −0.138181 | + | 0.239337i | ||||
\(575\) | −3.84804e9 | −0.844116 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.28378e8 | 0.136178 | 0.0680888 | − | 0.997679i | \(-0.478310\pi\) | ||||
0.0680888 | + | 0.997679i | \(0.478310\pi\) | |||||||
\(578\) | −1.60068e9 | + | 2.77245e9i | −0.344791 | + | 0.597196i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.36471e8 | − | 7.55990e8i | −0.0928876 | − | 0.160886i | ||||
\(581\) | 6.73404e8 | + | 1.16637e9i | 0.142449 | + | 0.246729i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.14943e9 | + | 1.99087e9i | −0.240239 | + | 0.416106i | ||||
\(584\) | 3.01993e9 | 0.627411 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.34467e9 | −0.891899 | ||||||||
\(587\) | −4.48401e9 | + | 7.76654e9i | −0.915026 | + | 1.58487i | −0.108163 | + | 0.994133i | \(0.534497\pi\) |
−0.806863 | + | 0.590738i | \(0.798837\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.31869e8 | + | 2.28403e8i | 0.0265912 | + | 0.0460573i | ||||
\(590\) | 1.46894e9 | + | 2.54428e9i | 0.294457 | + | 0.510014i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.62669e8 | − | 1.14778e9i | 0.131272 | − | 0.227369i | ||||
\(593\) | 7.57484e9 | 1.49170 | 0.745851 | − | 0.666112i | \(-0.232043\pi\) | ||||
0.745851 | + | 0.666112i | \(0.232043\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.67302e8 | −0.0520227 | ||||||||
\(596\) | −8.41239e7 | + | 1.45707e8i | −0.0162764 | + | 0.0281915i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.52379e9 | + | 2.63929e9i | 0.291388 | + | 0.504699i | ||||
\(599\) | −3.02973e9 | − | 5.24765e9i | −0.575984 | − | 0.997633i | −0.995934 | − | 0.0900859i | \(-0.971286\pi\) |
0.419950 | − | 0.907547i | \(-0.362047\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.27899e8 | − | 5.67937e8i | 0.0616139 | − | 0.106718i | −0.833573 | − | 0.552409i | \(-0.813709\pi\) |
0.895187 | + | 0.445691i | \(0.147042\pi\) | |||||||
\(602\) | 1.36827e9 | 0.255613 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.53932e9 | −0.653568 | ||||||||
\(605\) | 8.53264e8 | − | 1.47790e9i | 0.156653 | − | 0.271332i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.92806e9 | − | 3.33949e9i | −0.349913 | − | 0.606066i | 0.636321 | − | 0.771424i | \(-0.280455\pi\) |
−0.986234 | + | 0.165358i | \(0.947122\pi\) | |||||||
\(608\) | 2.47071e7 | + | 4.27939e7i | 0.00445819 | + | 0.00772181i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.48158e9 | − | 2.56617e9i | 0.264284 | − | 0.457752i | ||||
\(611\) | 1.93092e9 | 0.342469 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.89889e9 | −0.858986 | −0.429493 | − | 0.903070i | \(-0.641308\pi\) | ||||
−0.429493 | + | 0.903070i | \(0.641308\pi\) | |||||||
\(614\) | −2.91951e9 | + | 5.05674e9i | −0.509003 | + | 0.881619i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.93265e8 | + | 6.81155e8i | 0.0677880 | + | 0.117412i | ||||
\(617\) | −3.32728e9 | − | 5.76302e9i | −0.570284 | − | 0.987761i | −0.996537 | − | 0.0831565i | \(-0.973500\pi\) |
0.426253 | − | 0.904604i | \(-0.359833\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.27657e9 | + | 9.13929e9i | −0.894199 | + | 1.54880i | −0.0594070 | + | 0.998234i | \(0.518921\pi\) |
−0.834792 | + | 0.550565i | \(0.814412\pi\) | |||||||
\(620\) | −1.84686e9 | −0.311217 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.11016e9 | 0.851468 | ||||||||
\(623\) | 1.71981e9 | − | 2.97880e9i | 0.284952 | − | 0.493552i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.31928e8 | − | 4.01712e8i | −0.0379992 | − | 0.0658165i | ||||
\(626\) | −2.55104e9 | − | 4.41853e9i | −0.415631 | − | 0.719893i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.15874e8 | − | 1.23993e9i | 0.115339 | − | 0.199774i | ||||
\(629\) | −1.03186e9 | −0.165327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.37775e9 | 1.01057 | 0.505283 | − | 0.862954i | \(-0.331388\pi\) | ||||
0.505283 | + | 0.862954i | \(0.331388\pi\) | |||||||
\(632\) | 1.79936e9 | − | 3.11659e9i | 0.283537 | − | 0.491100i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.61751e9 | + | 4.53366e9i | 0.407921 | + | 0.706540i | ||||
\(635\) | 4.11394e8 | + | 7.12555e8i | 0.0637602 | + | 0.110436i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.42472e9 | − | 2.46769e9i | 0.218395 | − | 0.378271i | ||||
\(638\) | 1.99983e9 | 0.304874 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.46030e8 | −0.0521776 | ||||||||
\(641\) | 3.34351e8 | − | 5.79113e8i | 0.0501418 | − | 0.0868481i | −0.839865 | − | 0.542795i | \(-0.817366\pi\) |
0.890007 | + | 0.455947i | \(0.150699\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.62316e9 | − | 2.81140e9i | −0.240782 | − | 0.417046i | 0.720155 | − | 0.693813i | \(-0.244070\pi\) |
−0.960937 | + | 0.276767i | \(0.910737\pi\) | |||||||
\(644\) | 1.22895e9 | + | 2.12861e9i | 0.181316 | + | 0.314048i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.92360e7 | − | 3.33178e7i | 0.00280739 | − | 0.00486253i | ||||
\(647\) | −7.46321e9 | −1.08333 | −0.541665 | − | 0.840595i | \(-0.682206\pi\) | ||||
−0.541665 | + | 0.840595i | \(0.682206\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.73041e9 | −0.966462 | ||||||||
\(650\) | −1.02594e9 | + | 1.77698e9i | −0.146530 | + | 0.253797i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.67554e9 | − | 2.90212e9i | −0.236749 | − | 0.410061i | ||||
\(653\) | −5.08150e9 | − | 8.80141e9i | −0.714160 | − | 1.23696i | −0.963283 | − | 0.268490i | \(-0.913475\pi\) |
0.249122 | − | 0.968472i | \(-0.419858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.84309e9 | + | 3.19232e9i | −0.256272 | + | 0.443876i | ||||
\(656\) | 1.26205e9 | 0.174547 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.55731e9 | 0.213100 | ||||||||
\(659\) | −1.41534e9 | + | 2.45144e9i | −0.192647 | + | 0.333674i | −0.946127 | − | 0.323797i | \(-0.895041\pi\) |
0.753480 | + | 0.657471i | \(0.228374\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.98137e9 | − | 3.43184e9i | −0.266846 | − | 0.462192i | 0.701199 | − | 0.712965i | \(-0.252648\pi\) |
−0.968046 | + | 0.250774i | \(0.919315\pi\) | |||||||
\(662\) | 3.23075e9 | + | 5.59583e9i | 0.432814 | + | 0.749655i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.78706e8 | − | 1.17555e9i | 0.0899691 | − | 0.155831i | ||||
\(665\) | −1.26401e8 | −0.0166676 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.24947e9 | 0.815461 | ||||||||
\(668\) | −1.75346e9 | + | 3.03709e9i | −0.227604 | + | 0.394221i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.72304e8 | + | 1.68408e9i | 0.124894 | + | 0.216322i | ||||
\(671\) | 3.39416e9 | + | 5.87886e9i | 0.433714 | + | 0.751215i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.93077e9 | − | 1.02724e10i | 0.749995 | − | 1.29903i | −0.197829 | − | 0.980237i | \(-0.563389\pi\) |
0.947824 | − | 0.318794i | \(-0.103278\pi\) | |||||||
\(674\) | 1.49824e9 | 0.188483 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.39085e9 | −0.297672 | ||||||||
\(677\) | 4.93418e9 | − | 8.54625e9i | 0.611159 | − | 1.05856i | −0.379886 | − | 0.925033i | \(-0.624037\pi\) |
0.991045 | − | 0.133526i | \(-0.0426299\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.10880e9 | + | 7.11665e9i | 0.503699 | + | 0.872432i | ||||
\(680\) | 1.34703e8 | + | 2.33313e8i | 0.0164285 | + | 0.0284550i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.11549e9 | − | 3.66414e9i | 0.255368 | − | 0.442310i | ||||
\(683\) | −1.36287e10 | −1.63674 | −0.818372 | − | 0.574689i | \(-0.805123\pi\) | ||||
−0.818372 | + | 0.574689i | \(0.805123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.12241e9 | −0.252297 | ||||||||
\(686\) | 2.82249e9 | − | 4.88870e9i | 0.333809 | − | 0.578175i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.89521e8 | − | 1.19428e9i | −0.0807212 | − | 0.139813i | ||||
\(689\) | 1.91534e9 | + | 3.31746e9i | 0.223089 | + | 0.386402i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.08135e9 | − | 1.87295e9i | 0.124679 | − | 0.215950i | −0.796929 | − | 0.604074i | \(-0.793543\pi\) |
0.921607 | + | 0.388124i | \(0.126877\pi\) | |||||||
\(692\) | −7.91329e9 | −0.907791 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.26045e9 | 0.256706 | ||||||||
\(695\) | −3.64569e9 | + | 6.31453e9i | −0.411940 | + | 0.713500i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.91294e8 | − | 8.50946e8i | −0.0549575 | − | 0.0951892i | ||||
\(698\) | −3.04245e9 | − | 5.26968e9i | −0.338633 | − | 0.586530i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.27430e8 | + | 1.43315e9i | −0.0911776 | + | 0.157924i | ||||
\(701\) | −2.93914e9 | −0.322260 | −0.161130 | − | 0.986933i | \(-0.551514\pi\) | ||||
−0.161130 | + | 0.986933i | \(0.551514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.87942e8 | −0.0529693 | ||||||||
\(704\) | 3.96362e8 | − | 6.86519e8i | 0.0428142 | − | 0.0741563i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.87557e9 | + | 3.24859e9i | 0.200594 | + | 0.347439i | ||||
\(707\) | −6.86210e8 | − | 1.18855e9i | −0.0730279 | − | 0.126488i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.54572e9 | − | 1.13375e10i | 0.689756 | − | 1.19469i | −0.282160 | − | 0.959367i | \(-0.591051\pi\) |
0.971917 | − | 0.235326i | \(-0.0756157\pi\) | |||||||
\(710\) | −6.60910e9 | −0.693007 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.46670e9 | −0.359945 | ||||||||
\(713\) | 6.61092e9 | − | 1.14504e10i | 0.683044 | − | 1.18307i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.25713e9 | + | 2.17741e9i | 0.128620 | + | 0.222777i | ||||
\(716\) | 3.15935e9 | + | 5.47216e9i | 0.321664 | + | 0.557138i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.15626e8 | + | 1.06630e9i | −0.0620699 | + | 0.107508i | ||||
\(719\) | 3.03015e9 | 0.304027 | 0.152014 | − | 0.988378i | \(-0.451424\pi\) | ||||
0.152014 | + | 0.988378i | \(0.451424\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.05101e9 | −0.104432 | ||||||||
\(722\) | −3.56639e9 | + | 6.17717e9i | −0.352654 | + | 0.610815i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.94354e9 | − | 5.09836e9i | −0.288260 | − | 0.499281i | ||||
\(725\) | 2.10382e9 | + | 3.64393e9i | 0.205034 | + | 0.355130i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.34238e9 | − | 9.25328e9i | 0.515661 | − | 0.893151i | −0.484174 | − | 0.874972i | \(-0.660880\pi\) |
0.999835 | − | 0.0181794i | \(-0.00578701\pi\) | |||||||
\(728\) | 1.31062e9 | 0.125898 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.78576e9 | 0.740749 | ||||||||
\(731\) | −5.36836e8 | + | 9.29828e8i | −0.0508313 | + | 0.0880424i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.38524e9 | + | 1.45237e10i | 0.786414 | + | 1.36211i | 0.928150 | + | 0.372205i | \(0.121398\pi\) |
−0.141736 | + | 0.989904i | \(0.545268\pi\) | |||||||
\(734\) | −2.99811e9 | − | 5.19288e9i | −0.279841 | − | 0.484699i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.23863e9 | − | 2.14537e9i | 0.114517 | − | 0.198349i | ||||
\(737\) | −4.45492e9 | −0.409924 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.68052e10 | 1.53175 | 0.765877 | − | 0.642987i | \(-0.222305\pi\) | ||||
0.765877 | + | 0.642987i | \(0.222305\pi\) | |||||||
\(740\) | 1.70844e9 | − | 2.95911e9i | 0.154985 | − | 0.268442i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.54474e9 | + | 2.67557e9i | 0.138817 | + | 0.240437i | ||||
\(743\) | 1.03917e10 | + | 1.79989e10i | 0.929448 | + | 1.60985i | 0.784246 | + | 0.620450i | \(0.213050\pi\) |
0.145203 | + | 0.989402i | \(0.453617\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.16882e8 | + | 3.75651e8i | −0.0192166 | + | 0.0332841i | ||||
\(746\) | 4.33382e9 | 0.382195 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.17186e8 | −0.0539213 | ||||||||
\(749\) | 2.32524e9 | − | 4.02744e9i | 0.202200 | − | 0.350221i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.03006e9 | − | 8.71232e9i | −0.433344 | − | 0.750575i | 0.563814 | − | 0.825901i | \(-0.309333\pi\) |
−0.997159 | + | 0.0753269i | \(0.976000\pi\) | |||||||
\(752\) | −7.84785e8 | − | 1.35929e9i | −0.0672959 | − | 0.116560i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.66620e9 | − | 2.88594e9i | 0.141555 | − | 0.245181i | ||||
\(755\) | −9.12481e9 | −0.771631 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.59893e9 | 0.552889 | 0.276445 | − | 0.961030i | \(-0.410844\pi\) | ||||
0.276445 | + | 0.961030i | \(0.410844\pi\) | |||||||
\(758\) | 5.31896e9 | − | 9.21270e9i | 0.443592 | − | 0.768325i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.36979e7 | + | 1.10328e8i | 0.00526354 | + | 0.00911671i | ||||
\(761\) | −3.03962e9 | − | 5.26478e9i | −0.250019 | − | 0.433046i | 0.713511 | − | 0.700644i | \(-0.247104\pi\) |
−0.963531 | + | 0.267597i | \(0.913770\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.20636e9 | − | 3.82153e9i | 0.179821 | − | 0.311459i | ||||
\(764\) | −8.44663e9 | −0.685262 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.75959e9 | 0.463011 | ||||||||
\(767\) | −5.60756e9 | + | 9.71258e9i | −0.448735 | + | 0.777232i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.42525e9 | − | 4.20065e9i | −0.192315 | − | 0.333100i | 0.753702 | − | 0.657216i | \(-0.228266\pi\) |
−0.946017 | + | 0.324117i | \(0.894933\pi\) | |||||||
\(770\) | 1.01389e9 | + | 1.75610e9i | 0.0800335 | + | 0.138622i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) |