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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 2x^{7} + 2x^{6} + 518x^{5} + 53377x^{4} + 11940x^{3} + 3528x^{2} + 1563408x + 346406544 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(11.0098 + 11.0098i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.109 |
Dual form | 162.8.c.r.55.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||
\(5\) | 5.62316 | − | 9.73960i | 0.0201180 | − | 0.0348454i | −0.855791 | − | 0.517322i | \(-0.826929\pi\) |
0.875909 | + | 0.482476i | \(0.160262\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −719.735 | − | 1246.62i | −0.793102 | − | 1.37369i | −0.924037 | − | 0.382303i | \(-0.875131\pi\) |
0.130935 | − | 0.991391i | \(-0.458202\pi\) | |||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 89.9705 | 0.0284512 | ||||||||
\(11\) | 2216.31 | + | 3838.77i | 0.502061 | + | 0.869596i | 0.999997 | + | 0.00238204i | \(0.000758226\pi\) |
−0.497936 | + | 0.867214i | \(0.665908\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3615.49 | − | 6262.21i | 0.456420 | − | 0.790543i | −0.542348 | − | 0.840154i | \(-0.682465\pi\) |
0.998769 | + | 0.0496105i | \(0.0157980\pi\) | |||||||
\(14\) | 5757.88 | − | 9972.94i | 0.560808 | − | 0.971348i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2048.00 | − | 3547.24i | −0.125000 | − | 0.216506i | ||||
\(17\) | −13221.1 | −0.652674 | −0.326337 | − | 0.945254i | \(-0.605814\pi\) | ||||
−0.326337 | + | 0.945254i | \(0.605814\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13506.6 | 0.451761 | 0.225881 | − | 0.974155i | \(-0.427474\pi\) | ||||
0.225881 | + | 0.974155i | \(0.427474\pi\) | |||||||
\(20\) | 359.882 | + | 623.334i | 0.0100590 | + | 0.0174227i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −17730.5 | + | 30710.1i | −0.355011 | + | 0.614897i | ||||
\(23\) | −32869.3 | + | 56931.3i | −0.563304 | + | 0.975672i | 0.433901 | + | 0.900961i | \(0.357137\pi\) |
−0.997205 | + | 0.0747111i | \(0.976197\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 38999.3 | + | 67548.7i | 0.499191 | + | 0.864623i | ||||
\(26\) | 57847.8 | 0.645476 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 92126.0 | 0.793102 | ||||||||
\(29\) | 74249.1 | + | 128603.i | 0.565325 | + | 0.979171i | 0.997019 | + | 0.0771513i | \(0.0245824\pi\) |
−0.431695 | + | 0.902020i | \(0.642084\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −69431.2 | + | 120258.i | −0.418590 | + | 0.725019i | −0.995798 | − | 0.0915783i | \(-0.970809\pi\) |
0.577208 | + | 0.816597i | \(0.304142\pi\) | |||||||
\(32\) | 16384.0 | − | 28377.9i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −52884.4 | − | 91598.4i | −0.230755 | − | 0.399679i | ||||
\(35\) | −16188.7 | −0.0638226 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −121532. | −0.394442 | −0.197221 | − | 0.980359i | \(-0.563192\pi\) | ||||
−0.197221 | + | 0.980359i | \(0.563192\pi\) | |||||||
\(38\) | 54026.5 | + | 93576.6i | 0.159722 | + | 0.276646i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2879.06 | + | 4986.67i | −0.00711279 | + | 0.0123197i | ||||
\(41\) | 26393.4 | − | 45714.8i | 0.0598070 | − | 0.103589i | −0.834572 | − | 0.550899i | \(-0.814285\pi\) |
0.894379 | + | 0.447311i | \(0.147618\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −375862. | − | 651012.i | −0.720923 | − | 1.24868i | −0.960630 | − | 0.277830i | \(-0.910385\pi\) |
0.239707 | − | 0.970845i | \(-0.422949\pi\) | |||||||
\(44\) | −283688. | −0.502061 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −525909. | −0.796633 | ||||||||
\(47\) | 491796. | + | 851816.i | 0.690944 | + | 1.19675i | 0.971529 | + | 0.236921i | \(0.0761382\pi\) |
−0.280585 | + | 0.959829i | \(0.590528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −624264. | + | 1.08126e6i | −0.758023 | + | 1.31293i | ||||
\(50\) | −311994. | + | 540390.i | −0.352981 | + | 0.611381i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 231391. | + | 400781.i | 0.228210 | + | 0.395272i | ||||
\(53\) | 621759. | 0.573663 | 0.286831 | − | 0.957981i | \(-0.407398\pi\) | ||||
0.286831 | + | 0.957981i | \(0.407398\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 49850.7 | 0.0404019 | ||||||||
\(56\) | 368504. | + | 638268.i | 0.280404 | + | 0.485674i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −593992. | + | 1.02883e6i | −0.399745 | + | 0.692378i | ||||
\(59\) | 407108. | − | 705132.i | 0.258064 | − | 0.446980i | −0.707659 | − | 0.706554i | \(-0.750249\pi\) |
0.965723 | + | 0.259574i | \(0.0835821\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.23477e6 | + | 2.13868e6i | 0.696514 | + | 1.20640i | 0.969668 | + | 0.244428i | \(0.0786001\pi\) |
−0.273153 | + | 0.961971i | \(0.588067\pi\) | |||||||
\(62\) | −1.11090e6 | −0.591975 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −40660.9 | − | 70426.8i | −0.0183646 | − | 0.0318083i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.72741e6 | + | 2.99196e6i | −0.701671 | + | 1.21533i | 0.266209 | + | 0.963915i | \(0.414229\pi\) |
−0.967880 | + | 0.251414i | \(0.919105\pi\) | |||||||
\(68\) | 423075. | − | 732788.i | 0.163168 | − | 0.282616i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −64754.9 | − | 112159.i | −0.0225647 | − | 0.0390832i | ||||
\(71\) | −3.64076e6 | −1.20722 | −0.603612 | − | 0.797278i | \(-0.706272\pi\) | ||||
−0.603612 | + | 0.797278i | \(0.706272\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.55060e6 | −1.66997 | −0.834987 | − | 0.550269i | \(-0.814525\pi\) | ||||
−0.834987 | + | 0.550269i | \(0.814525\pi\) | |||||||
\(74\) | −486126. | − | 841995.i | −0.139456 | − | 0.241545i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −432212. | + | 748613.i | −0.112940 | + | 0.195618i | ||||
\(77\) | 3.19032e6 | − | 5.52579e6i | 0.796372 | − | 1.37936i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.02318e6 | + | 1.77220e6i | 0.233484 | + | 0.404407i | 0.958831 | − | 0.283977i | \(-0.0916539\pi\) |
−0.725347 | + | 0.688384i | \(0.758321\pi\) | |||||||
\(80\) | −46064.9 | −0.0100590 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 422295. | 0.0845799 | ||||||||
\(83\) | 5.13258e6 | + | 8.88989e6i | 0.985286 | + | 1.70657i | 0.640657 | + | 0.767827i | \(0.278662\pi\) |
0.344630 | + | 0.938739i | \(0.388005\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −74344.3 | + | 128768.i | −0.0131305 | + | 0.0227427i | ||||
\(86\) | 3.00690e6 | − | 5.20810e6i | 0.509770 | − | 0.882947i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.13475e6 | − | 1.96545e6i | −0.177506 | − | 0.307449i | ||||
\(89\) | −8.12374e6 | −1.22149 | −0.610747 | − | 0.791826i | \(-0.709131\pi\) | ||||
−0.610747 | + | 0.791826i | \(0.709131\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.04088e7 | −1.44795 | ||||||||
\(92\) | −2.10364e6 | − | 3.64360e6i | −0.281652 | − | 0.487836i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.93437e6 | + | 6.81453e6i | −0.488571 | + | 0.846230i | ||||
\(95\) | 75949.9 | − | 131549.i | 0.00908854 | − | 0.0157418i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.64660e6 | + | 1.15122e7i | 0.739432 | + | 1.28073i | 0.952751 | + | 0.303752i | \(0.0982394\pi\) |
−0.213319 | + | 0.976983i | \(0.568427\pi\) | |||||||
\(98\) | −9.98823e6 | −1.07201 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.99191e6 | −0.499191 | ||||||||
\(101\) | −6.68327e6 | − | 1.15758e7i | −0.645452 | − | 1.11796i | −0.984197 | − | 0.177078i | \(-0.943336\pi\) |
0.338745 | − | 0.940878i | \(-0.389998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.76614e6 | + | 1.17193e7i | −0.610114 | + | 1.05675i | 0.381107 | + | 0.924531i | \(0.375543\pi\) |
−0.991221 | + | 0.132217i | \(0.957790\pi\) | |||||||
\(104\) | −1.85113e6 | + | 3.20625e6i | −0.161369 | + | 0.279499i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.48704e6 | + | 4.30767e6i | 0.202820 | + | 0.351295i | ||||
\(107\) | 1.89550e7 | 1.49583 | 0.747914 | − | 0.663796i | \(-0.231056\pi\) | ||||
0.747914 | + | 0.663796i | \(0.231056\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.33257e7 | −0.985589 | −0.492794 | − | 0.870146i | \(-0.664025\pi\) | ||||
−0.492794 | + | 0.870146i | \(0.664025\pi\) | |||||||
\(110\) | 199403. | + | 345376.i | 0.0142842 | + | 0.0247410i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.94803e6 | + | 5.10614e6i | −0.198276 | + | 0.343423i | ||||
\(113\) | 1.02134e7 | − | 1.76901e7i | 0.665878 | − | 1.15333i | −0.313168 | − | 0.949698i | \(-0.601390\pi\) |
0.979046 | − | 0.203637i | \(-0.0652762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 369659. | + | 640267.i | 0.0226651 | + | 0.0392572i | ||||
\(116\) | −9.50388e6 | −0.565325 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.51373e6 | 0.364958 | ||||||||
\(119\) | 9.51568e6 | + | 1.64816e7i | 0.517637 | + | 0.896574i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −80510.7 | + | 139449.i | −0.00413147 | + | 0.00715592i | ||||
\(122\) | −9.87812e6 | + | 1.71094e7i | −0.492510 | + | 0.853052i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.44360e6 | − | 7.69653e6i | −0.209295 | − | 0.362509i | ||||
\(125\) | 1.75581e6 | 0.0804069 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.13846e7 | 0.493178 | 0.246589 | − | 0.969120i | \(-0.420690\pi\) | ||||
0.246589 | + | 0.969120i | \(0.420690\pi\) | |||||||
\(128\) | 1.04858e6 | + | 1.81619e6i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 325287. | − | 563414.i | 0.0129857 | − | 0.0224919i | ||||
\(131\) | 2.64090e6 | − | 4.57417e6i | 0.102636 | − | 0.177772i | −0.810134 | − | 0.586245i | \(-0.800605\pi\) |
0.912770 | + | 0.408474i | \(0.133939\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.72118e6 | − | 1.68376e7i | −0.358293 | − | 0.620582i | ||||
\(134\) | −2.76385e7 | −0.992312 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.76920e6 | 0.230755 | ||||||||
\(137\) | 2.45057e7 | + | 4.24451e7i | 0.814226 | + | 1.41028i | 0.909882 | + | 0.414866i | \(0.136172\pi\) |
−0.0956566 | + | 0.995414i | \(0.530495\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.43972e6 | − | 1.63501e7i | 0.298131 | − | 0.516378i | −0.677577 | − | 0.735452i | \(-0.736970\pi\) |
0.975708 | + | 0.219073i | \(0.0703034\pi\) | |||||||
\(140\) | 518039. | − | 897270.i | 0.0159557 | − | 0.0276360i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.45630e7 | − | 2.52239e7i | −0.426818 | − | 0.739270i | ||||
\(143\) | 3.20522e7 | 0.916604 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.67006e6 | 0.0454929 | ||||||||
\(146\) | −2.22024e7 | − | 3.84557e7i | −0.590425 | − | 1.02265i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.88901e6 | − | 6.73596e6i | 0.0986105 | − | 0.170798i | ||||
\(149\) | −1.44249e7 | + | 2.49846e7i | −0.357240 | + | 0.618758i | −0.987499 | − | 0.157627i | \(-0.949615\pi\) |
0.630259 | + | 0.776385i | \(0.282949\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.79766e7 | + | 3.11364e7i | 0.424902 | + | 0.735952i | 0.996411 | − | 0.0846435i | \(-0.0269751\pi\) |
−0.571509 | + | 0.820596i | \(0.693642\pi\) | |||||||
\(152\) | −6.91539e6 | −0.159722 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.10451e7 | 1.12624 | ||||||||
\(155\) | 780845. | + | 1.35246e6i | 0.0168424 | + | 0.0291719i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.89045e7 | − | 5.00641e7i | 0.596097 | − | 1.03247i | −0.397294 | − | 0.917691i | \(-0.630051\pi\) |
0.993391 | − | 0.114779i | \(-0.0366159\pi\) | |||||||
\(158\) | −8.18545e6 | + | 1.41776e7i | −0.165098 | + | 0.285959i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −184260. | − | 319147.i | −0.00355640 | − | 0.00615986i | ||||
\(161\) | 9.46287e7 | 1.78703 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.23536e7 | 0.585148 | 0.292574 | − | 0.956243i | \(-0.405488\pi\) | ||||
0.292574 | + | 0.956243i | \(0.405488\pi\) | |||||||
\(164\) | 1.68918e6 | + | 2.92574e6i | 0.0299035 | + | 0.0517944i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.10606e7 | + | 7.11191e7i | −0.696703 | + | 1.20672i | ||||
\(167\) | −4.33872e7 | + | 7.51489e7i | −0.720866 | + | 1.24858i | 0.239788 | + | 0.970825i | \(0.422922\pi\) |
−0.960653 | + | 0.277751i | \(0.910411\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.23077e6 | + | 9.05996e6i | 0.0833608 | + | 0.144385i | ||||
\(170\) | −1.18951e6 | −0.0185693 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.81103e7 | 0.720923 | ||||||||
\(173\) | −5.38618e6 | − | 9.32914e6i | −0.0790897 | − | 0.136987i | 0.823768 | − | 0.566927i | \(-0.191868\pi\) |
−0.902857 | + | 0.429940i | \(0.858535\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.61382e7 | − | 9.72343e7i | 0.791818 | − | 1.37147i | ||||
\(176\) | 9.07802e6 | − | 1.57236e7i | 0.125515 | − | 0.217399i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.24950e7 | − | 5.62829e7i | −0.431863 | − | 0.748009i | ||||
\(179\) | 3.61175e7 | 0.470687 | 0.235343 | − | 0.971912i | \(-0.424379\pi\) | ||||
0.235343 | + | 0.971912i | \(0.424379\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.78118e7 | 0.348621 | 0.174310 | − | 0.984691i | \(-0.444230\pi\) | ||||
0.174310 | + | 0.984691i | \(0.444230\pi\) | |||||||
\(182\) | −4.16351e7 | − | 7.21140e7i | −0.511928 | − | 0.886686i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.68291e7 | − | 2.91488e7i | 0.199158 | − | 0.344952i | ||||
\(185\) | −683391. | + | 1.18367e6i | −0.00793539 | + | 0.0137445i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.93021e7 | − | 5.07527e7i | −0.327682 | − | 0.567563i | ||||
\(188\) | −6.29499e7 | −0.690944 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.21520e6 | 0.0128531 | ||||||||
\(191\) | −4.73127e7 | − | 8.19480e7i | −0.491316 | − | 0.850984i | 0.508634 | − | 0.860983i | \(-0.330151\pi\) |
−0.999950 | + | 0.00999867i | \(0.996817\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.11115e7 | − | 1.05848e8i | 0.611889 | − | 1.05982i | −0.379033 | − | 0.925383i | \(-0.623743\pi\) |
0.990922 | − | 0.134439i | \(-0.0429234\pi\) | |||||||
\(194\) | −5.31728e7 | + | 9.20980e7i | −0.522858 | + | 0.905616i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.99529e7 | − | 6.92005e7i | −0.379011 | − | 0.656467i | ||||
\(197\) | 1.37768e8 | 1.28385 | 0.641926 | − | 0.766766i | \(-0.278136\pi\) | ||||
0.641926 | + | 0.766766i | \(0.278136\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.62646e8 | −1.46305 | −0.731524 | − | 0.681815i | \(-0.761191\pi\) | ||||
−0.731524 | + | 0.681815i | \(0.761191\pi\) | |||||||
\(200\) | −1.99676e7 | − | 3.45849e7i | −0.176491 | − | 0.305691i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.34662e7 | − | 9.26061e7i | 0.456404 | − | 0.790514i | ||||
\(203\) | 1.06879e8 | − | 1.85120e8i | 0.896721 | − | 1.55317i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −296829. | − | 514123.i | −0.00240640 | − | 0.00416800i | ||||
\(206\) | −1.08258e8 | −0.862831 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.96181e7 | −0.228210 | ||||||||
\(209\) | 2.99349e7 | + | 5.18488e7i | 0.226812 | + | 0.392850i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.77889e7 | − | 1.34734e8i | 0.570071 | − | 0.987392i | −0.426487 | − | 0.904494i | \(-0.640249\pi\) |
0.996558 | − | 0.0828986i | \(-0.0264178\pi\) | |||||||
\(212\) | −1.98963e7 | + | 3.44614e7i | −0.143416 | + | 0.248403i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.58202e7 | + | 1.31324e8i | 0.528855 | + | 0.916003i | ||||
\(215\) | −8.45413e6 | −0.0580142 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.99888e8 | 1.32794 | ||||||||
\(218\) | −5.33026e7 | − | 9.23228e7i | −0.348458 | − | 0.603547i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.59522e6 | + | 2.76301e6i | −0.0101005 | + | 0.0174946i | ||||
\(221\) | −4.78007e7 | + | 8.27932e7i | −0.297894 | + | 0.515967i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.19714e7 | + | 1.07338e8i | 0.374218 | + | 0.648164i | 0.990210 | − | 0.139588i | \(-0.0445779\pi\) |
−0.615992 | + | 0.787752i | \(0.711245\pi\) | |||||||
\(224\) | −4.71685e7 | −0.280404 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.63414e8 | 0.941694 | ||||||||
\(227\) | −6.88520e7 | − | 1.19255e8i | −0.390685 | − | 0.676685i | 0.601855 | − | 0.798605i | \(-0.294428\pi\) |
−0.992540 | + | 0.121920i | \(0.961095\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.17560e8 | + | 2.03621e8i | −0.646899 | + | 1.12046i | 0.336960 | + | 0.941519i | \(0.390601\pi\) |
−0.983859 | + | 0.178944i | \(0.942732\pi\) | |||||||
\(230\) | −2.95727e6 | + | 5.12214e6i | −0.0160267 | + | 0.0277590i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.80155e7 | − | 6.58448e7i | −0.199872 | − | 0.346189i | ||||
\(233\) | 1.44039e8 | 0.745992 | 0.372996 | − | 0.927833i | \(-0.378330\pi\) | ||||
0.372996 | + | 0.927833i | \(0.378330\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.10618e7 | 0.0556017 | ||||||||
\(236\) | 2.60549e7 | + | 4.51284e7i | 0.129032 | + | 0.223490i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.61254e7 | + | 1.31853e8i | −0.366025 | + | 0.633974i | ||||
\(239\) | 3.65693e7 | − | 6.33399e7i | 0.173270 | − | 0.300113i | −0.766291 | − | 0.642494i | \(-0.777900\pi\) |
0.939561 | + | 0.342381i | \(0.111233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.14199e7 | + | 1.06382e8i | 0.282650 | + | 0.489564i | 0.972037 | − | 0.234829i | \(-0.0754531\pi\) |
−0.689386 | + | 0.724394i | \(0.742120\pi\) | |||||||
\(242\) | −1.28817e6 | −0.00584278 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.58050e8 | −0.696514 | ||||||||
\(245\) | 7.02067e6 | + | 1.21602e7i | 0.0304998 | + | 0.0528273i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.88330e7 | − | 8.45812e7i | 0.206193 | − | 0.357137i | ||||
\(248\) | 3.55488e7 | − | 6.15723e7i | 0.147994 | − | 0.256333i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.02326e6 | + | 1.21646e7i | 0.0284281 | + | 0.0492390i | ||||
\(251\) | −7.30348e7 | −0.291522 | −0.145761 | − | 0.989320i | \(-0.546563\pi\) | ||||
−0.145761 | + | 0.989320i | \(0.546563\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.91395e8 | −1.13125 | ||||||||
\(254\) | 4.55383e7 | + | 7.88746e7i | 0.174365 | + | 0.302009i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.38861e6 | + | 1.45295e7i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.69979e7 | − | 1.16044e8i | 0.246204 | − | 0.426438i | −0.716265 | − | 0.697828i | \(-0.754150\pi\) |
0.962469 | + | 0.271390i | \(0.0874834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.74705e7 | + | 1.51503e8i | 0.312833 | + | 0.541842i | ||||
\(260\) | 5.20460e6 | 0.0183646 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.22543e7 | 0.145150 | ||||||||
\(263\) | 1.90065e8 | + | 3.29202e8i | 0.644253 | + | 1.11588i | 0.984473 | + | 0.175534i | \(0.0561651\pi\) |
−0.340220 | + | 0.940346i | \(0.610502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.49625e6 | − | 6.05568e6i | 0.0115410 | − | 0.0199895i | ||||
\(266\) | 7.77695e7 | − | 1.34701e8i | 0.253351 | − | 0.438818i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.10554e8 | − | 1.91485e8i | −0.350835 | − | 0.607664i | ||||
\(269\) | −5.57685e8 | −1.74685 | −0.873426 | − | 0.486958i | \(-0.838107\pi\) | ||||
−0.873426 | + | 0.486958i | \(0.838107\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.65793e7 | −0.294776 | −0.147388 | − | 0.989079i | \(-0.547087\pi\) | ||||
−0.147388 | + | 0.989079i | \(0.547087\pi\) | |||||||
\(272\) | 2.70768e7 | + | 4.68984e7i | 0.0815842 | + | 0.141308i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.96045e8 | + | 3.39561e8i | −0.575745 | + | 0.997219i | ||||
\(275\) | −1.72869e8 | + | 2.99418e8i | −0.501249 | + | 0.868188i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.82900e8 | − | 4.89997e8i | −0.799749 | − | 1.38521i | −0.919779 | − | 0.392436i | \(-0.871633\pi\) |
0.120030 | − | 0.992770i | \(-0.461701\pi\) | |||||||
\(278\) | 1.51035e8 | 0.421621 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.28863e6 | 0.0225647 | ||||||||
\(281\) | 1.99775e8 | + | 3.46020e8i | 0.537117 | + | 0.930314i | 0.999058 | + | 0.0434033i | \(0.0138200\pi\) |
−0.461940 | + | 0.886911i | \(0.652847\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.39361e8 | + | 5.87791e8i | −0.890040 | + | 1.54160i | −0.0502152 | + | 0.998738i | \(0.515991\pi\) |
−0.839825 | + | 0.542857i | \(0.817343\pi\) | |||||||
\(284\) | 1.16504e8 | − | 2.01791e8i | 0.301806 | − | 0.522743i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.28209e8 | + | 2.22064e8i | 0.324069 | + | 0.561303i | ||||
\(287\) | −7.59851e7 | −0.189732 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.35541e8 | −0.574017 | ||||||||
\(290\) | 6.68023e6 | + | 1.15705e7i | 0.0160842 | + | 0.0278586i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.77619e8 | − | 3.07645e8i | 0.417494 | − | 0.723120i | ||||
\(293\) | 5.58695e7 | − | 9.67688e7i | 0.129759 | − | 0.224750i | −0.793824 | − | 0.608148i | \(-0.791913\pi\) |
0.923583 | + | 0.383398i | \(0.125246\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.57847e6 | − | 7.93014e6i | −0.0103835 | − | 0.0179847i | ||||
\(296\) | 6.22242e7 | 0.139456 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.30798e8 | −0.505214 | ||||||||
\(299\) | 2.37677e8 | + | 4.11669e8i | 0.514207 | + | 0.890633i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.41042e8 | + | 9.37112e8i | −1.14353 | + | 1.98065i | ||||
\(302\) | −1.43813e8 | + | 2.49092e8i | −0.300451 | + | 0.520397i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.76616e7 | − | 4.79112e7i | −0.0564702 | − | 0.0978092i | ||||
\(305\) | 2.77731e7 | 0.0560500 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.53022e8 | −0.301835 | −0.150917 | − | 0.988546i | \(-0.548223\pi\) | ||||
−0.150917 | + | 0.988546i | \(0.548223\pi\) | |||||||
\(308\) | 2.04180e8 | + | 3.53651e8i | 0.398186 | + | 0.689679i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.24676e6 | + | 1.08197e7i | −0.0119094 | + | 0.0206276i | ||||
\(311\) | −1.14184e8 | + | 1.97772e8i | −0.215250 | + | 0.372825i | −0.953350 | − | 0.301867i | \(-0.902390\pi\) |
0.738100 | + | 0.674692i | \(0.235723\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.51372e8 | + | 6.08594e8i | 0.647682 | + | 1.12182i | 0.983675 | + | 0.179954i | \(0.0575950\pi\) |
−0.335993 | + | 0.941865i | \(0.609072\pi\) | |||||||
\(314\) | 4.62472e8 | 0.843008 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.30967e8 | −0.233484 | ||||||||
\(317\) | −5.20588e8 | − | 9.01686e8i | −0.917883 | − | 1.58982i | −0.802625 | − | 0.596484i | \(-0.796564\pi\) |
−0.115257 | − | 0.993336i | \(-0.536769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.29118e8 | + | 5.70050e8i | −0.567655 | + | 0.983208i | ||||
\(320\) | 1.47408e6 | − | 2.55318e6i | 0.00251475 | − | 0.00435568i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.78515e8 | + | 6.55607e8i | 0.631811 | + | 1.09433i | ||||
\(323\) | −1.78572e8 | −0.294853 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.64005e8 | 0.911363 | ||||||||
\(326\) | 1.29414e8 | + | 2.24152e8i | 0.206881 | + | 0.358328i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.35134e7 | + | 2.34060e7i | −0.0211450 | + | 0.0366242i | ||||
\(329\) | 7.07926e8 | − | 1.22616e9i | 1.09598 | − | 1.89829i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.60638e8 | − | 2.78233e8i | −0.243472 | − | 0.421706i | 0.718229 | − | 0.695807i | \(-0.244953\pi\) |
−0.961701 | + | 0.274101i | \(0.911620\pi\) | |||||||
\(332\) | −6.56970e8 | −0.985286 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.94196e8 | −1.01946 | ||||||||
\(335\) | 1.94270e7 | + | 3.36485e7i | 0.0282324 | + | 0.0489000i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.56823e8 | − | 7.91241e8i | 0.650194 | − | 1.12617i | −0.332881 | − | 0.942969i | \(-0.608021\pi\) |
0.983075 | − | 0.183201i | \(-0.0586459\pi\) | |||||||
\(338\) | −4.18462e7 | + | 7.24797e7i | −0.0589450 | + | 0.102096i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.75804e6 | − | 8.24116e6i | −0.00656525 | − | 0.0113714i | ||||
\(341\) | −6.15525e8 | −0.840631 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.11754e8 | 0.818554 | ||||||||
\(344\) | 1.92441e8 | + | 3.33318e8i | 0.254885 | + | 0.441473i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.30895e7 | − | 7.46331e7i | 0.0559248 | − | 0.0968646i | ||||
\(347\) | −2.98992e8 | + | 5.17869e8i | −0.384155 | + | 0.665376i | −0.991652 | − | 0.128946i | \(-0.958841\pi\) |
0.607497 | + | 0.794322i | \(0.292174\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.25273e8 | − | 5.63390e8i | −0.409599 | − | 0.709447i | 0.585245 | − | 0.810856i | \(-0.300998\pi\) |
−0.994845 | + | 0.101409i | \(0.967665\pi\) | |||||||
\(350\) | 8.98212e8 | 1.11980 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.45248e8 | 0.177506 | ||||||||
\(353\) | −3.08623e7 | − | 5.34551e7i | −0.0373437 | − | 0.0646811i | 0.846750 | − | 0.531992i | \(-0.178556\pi\) |
−0.884093 | + | 0.467311i | \(0.845223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.04726e7 | + | 3.54595e7i | −0.0242869 | + | 0.0420662i | ||||
\(356\) | 2.59960e8 | − | 4.50264e8i | 0.305373 | − | 0.528922i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.44470e8 | + | 2.50229e8i | 0.166413 | + | 0.288235i | ||||
\(359\) | −1.70542e9 | −1.94537 | −0.972683 | − | 0.232137i | \(-0.925428\pi\) | ||||
−0.972683 | + | 0.232137i | \(0.925428\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.11443e8 | −0.795912 | ||||||||
\(362\) | 1.11247e8 | + | 1.92686e8i | 0.123256 | + | 0.213486i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.33080e8 | − | 5.76912e8i | 0.361988 | − | 0.626982i | ||||
\(365\) | −3.12119e7 | + | 5.40606e7i | −0.0335966 | + | 0.0581910i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.21509e8 | − | 2.10460e8i | −0.128315 | − | 0.222248i | 0.794709 | − | 0.606991i | \(-0.207624\pi\) |
−0.923024 | + | 0.384743i | \(0.874290\pi\) | |||||||
\(368\) | 2.69265e8 | 0.281652 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.09343e7 | −0.0112223 | ||||||||
\(371\) | −4.47501e8 | − | 7.75095e8i | −0.454973 | − | 0.788037i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.29270e8 | − | 5.70313e8i | 0.328528 | − | 0.569026i | −0.653692 | − | 0.756760i | \(-0.726781\pi\) |
0.982220 | + | 0.187734i | \(0.0601143\pi\) | |||||||
\(374\) | 2.34417e8 | − | 4.06022e8i | 0.231706 | − | 0.401327i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.51800e8 | − | 4.36130e8i | −0.244286 | − | 0.423115i | ||||
\(377\) | 1.07379e9 | 1.03210 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.55665e7 | 0.0146877 | 0.00734387 | − | 0.999973i | \(-0.497662\pi\) | ||||
0.00734387 | + | 0.999973i | \(0.497662\pi\) | |||||||
\(380\) | 4.86079e6 | + | 8.41914e6i | 0.00454427 | + | 0.00787091i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.78501e8 | − | 6.55584e8i | 0.347413 | − | 0.601737i | ||||
\(383\) | −4.33940e8 | + | 7.51606e8i | −0.394670 | + | 0.683588i | −0.993059 | − | 0.117617i | \(-0.962474\pi\) |
0.598389 | + | 0.801206i | \(0.295808\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.58793e7 | − | 6.21448e7i | −0.0320429 | − | 0.0554999i | ||||
\(386\) | 9.77784e8 | 0.865342 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.50765e8 | −0.739432 | ||||||||
\(389\) | −8.92558e8 | − | 1.54596e9i | −0.768799 | − | 1.33160i | −0.938215 | − | 0.346054i | \(-0.887521\pi\) |
0.169416 | − | 0.985545i | \(-0.445812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.34568e8 | − | 7.52694e8i | 0.367654 | − | 0.636795i | ||||
\(392\) | 3.19623e8 | − | 5.53604e8i | 0.268002 | − | 0.464192i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.51070e8 | + | 9.54481e8i | 0.453910 | + | 0.786196i | ||||
\(395\) | 2.30140e7 | 0.0187890 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.49554e9 | 1.19958 | 0.599792 | − | 0.800156i | \(-0.295250\pi\) | ||||
0.599792 | + | 0.800156i | \(0.295250\pi\) | |||||||
\(398\) | −6.50586e8 | − | 1.12685e9i | −0.517266 | − | 0.895931i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.59741e8 | − | 2.76679e8i | 0.124798 | − | 0.216156i | ||||
\(401\) | −5.21084e8 | + | 9.02543e8i | −0.403554 | + | 0.698977i | −0.994152 | − | 0.107989i | \(-0.965559\pi\) |
0.590598 | + | 0.806966i | \(0.298892\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.02055e8 | + | 8.69585e8i | 0.382106 | + | 0.661827i | ||||
\(404\) | 8.55458e8 | 0.645452 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.71007e9 | 1.26815 | ||||||||
\(407\) | −2.69352e8 | − | 4.66532e8i | −0.198034 | − | 0.343005i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.94223e8 | + | 1.20243e9i | −0.501727 | + | 0.869017i | 0.498271 | + | 0.867021i | \(0.333968\pi\) |
−0.999998 | + | 0.00199527i | \(0.999365\pi\) | |||||||
\(410\) | 2.37463e6 | − | 4.11298e6i | 0.00170158 | − | 0.00294722i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.33033e8 | − | 7.50035e8i | −0.305057 | − | 0.528374i | ||||
\(413\) | −1.17204e9 | −0.818685 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.15445e8 | 0.0792880 | ||||||||
\(416\) | −1.18472e8 | − | 2.05200e8i | −0.0806845 | − | 0.139750i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.39479e8 | + | 4.14790e8i | −0.160380 | + | 0.277787i | ||||
\(419\) | −5.35466e8 | + | 9.27454e8i | −0.355617 | + | 0.615947i | −0.987223 | − | 0.159342i | \(-0.949063\pi\) |
0.631606 | + | 0.775289i | \(0.282396\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.33942e8 | − | 5.78405e8i | −0.218114 | − | 0.377785i | 0.736117 | − | 0.676854i | \(-0.236657\pi\) |
−0.954231 | + | 0.299069i | \(0.903324\pi\) | |||||||
\(422\) | 1.24462e9 | 0.806203 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.18341e8 | −0.202820 | ||||||||
\(425\) | −5.15613e8 | − | 8.93068e8i | −0.325809 | − | 0.564317i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.77741e9 | − | 3.07856e9i | 1.10481 | − | 1.91359i | ||||
\(428\) | −6.06561e8 | + | 1.05059e9i | −0.373957 | + | 0.647712i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.38165e7 | − | 5.85719e7i | −0.0205111 | − | 0.0355263i | ||||
\(431\) | 8.88266e8 | 0.534408 | 0.267204 | − | 0.963640i | \(-0.413900\pi\) | ||||
0.267204 | + | 0.963640i | \(0.413900\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.04197e9 | 0.616806 | 0.308403 | − | 0.951256i | \(-0.400205\pi\) | ||||
0.308403 | + | 0.951256i | \(0.400205\pi\) | |||||||
\(434\) | 7.99552e8 | + | 1.38487e9i | 0.469497 | + | 0.813193i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.26421e8 | − | 7.38583e8i | 0.246397 | − | 0.426772i | ||||
\(437\) | −4.43953e8 | + | 7.68949e8i | −0.254479 | + | 0.440771i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.36180e9 | − | 2.35870e9i | −0.768223 | − | 1.33060i | −0.938526 | − | 0.345209i | \(-0.887808\pi\) |
0.170303 | − | 0.985392i | \(-0.445525\pi\) | |||||||
\(440\) | −2.55236e7 | −0.0142842 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.64811e8 | −0.421285 | ||||||||
\(443\) | 7.09330e8 | + | 1.22860e9i | 0.387646 | + | 0.671422i | 0.992132 | − | 0.125193i | \(-0.0399550\pi\) |
−0.604487 | + | 0.796615i | \(0.706622\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.56811e7 | + | 7.91220e7i | −0.0245740 | + | 0.0425635i | ||||
\(446\) | −4.95771e8 | + | 8.58701e8i | −0.264612 | + | 0.458321i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.88674e8 | − | 3.26793e8i | −0.0991378 | − | 0.171712i | ||||
\(449\) | 3.79133e9 | 1.97665 | 0.988324 | − | 0.152368i | \(-0.0486899\pi\) | ||||
0.988324 | + | 0.152368i | \(0.0486899\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.33984e8 | 0.120107 | ||||||||
\(452\) | 6.53656e8 | + | 1.13217e9i | 0.332939 | + | 0.576667i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.50816e8 | − | 9.54042e8i | 0.276256 | − | 0.478489i | ||||
\(455\) | −5.85301e7 | + | 1.01377e8i | −0.0291299 | + | 0.0504545i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.36482e8 | − | 1.62204e9i | −0.458979 | − | 0.794975i | 0.539928 | − | 0.841711i | \(-0.318451\pi\) |
−0.998907 | + | 0.0467359i | \(0.985118\pi\) | |||||||
\(458\) | −1.88097e9 | −0.914854 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.73163e7 | −0.0226651 | ||||||||
\(461\) | 2.73697e8 | + | 4.74057e8i | 0.130112 | + | 0.225360i | 0.923719 | − | 0.383070i | \(-0.125133\pi\) |
−0.793608 | + | 0.608430i | \(0.791800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.61388e8 | − | 9.72353e8i | 0.262863 | − | 0.455292i | −0.704138 | − | 0.710063i | \(-0.748667\pi\) |
0.967002 | + | 0.254770i | \(0.0819999\pi\) | |||||||
\(464\) | 3.04124e8 | − | 5.26758e8i | 0.141331 | − | 0.244793i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.76156e8 | + | 9.97931e8i | 0.263748 | + | 0.456825i | ||||
\(467\) | −2.32612e9 | −1.05687 | −0.528436 | − | 0.848973i | \(-0.677221\pi\) | ||||
−0.528436 | + | 0.848973i | \(0.677221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.97310e9 | 2.22599 | ||||||||
\(470\) | 4.42472e7 | + | 7.66384e7i | 0.0196582 | + | 0.0340489i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.08439e8 | + | 3.61028e8i | −0.0912395 | + | 0.158031i | ||||
\(473\) | 1.66606e9 | − | 2.88570e9i | 0.723895 | − | 1.25382i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.26748e8 | + | 9.12355e8i | 0.225515 | + | 0.390603i | ||||
\(476\) | −1.21801e9 | −0.517637 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.85109e8 | 0.245041 | ||||||||
\(479\) | −8.84067e8 | − | 1.53125e9i | −0.367545 | − | 0.636607i | 0.621636 | − | 0.783306i | \(-0.286468\pi\) |
−0.989181 | + | 0.146699i | \(0.953135\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.39396e8 | + | 7.61056e8i | −0.180031 | + | 0.311823i | ||||
\(482\) | −4.91359e8 | + | 8.51059e8i | −0.199864 | + | 0.346174i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.15268e6 | − | 8.92471e6i | −0.00206573 | − | 0.00357796i | ||||
\(485\) | 1.49500e8 | 0.0595037 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.97414e9 | −0.774509 | −0.387254 | − | 0.921973i | \(-0.626577\pi\) | ||||
−0.387254 | + | 0.921973i | \(0.626577\pi\) | |||||||
\(488\) | −6.32200e8 | − | 1.09500e9i | −0.246255 | − | 0.426526i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.61654e7 | + | 9.72813e7i | −0.0215666 | + | 0.0373545i | ||||
\(491\) | −1.75190e9 | + | 3.03438e9i | −0.667920 | + | 1.15687i | 0.310564 | + | 0.950552i | \(0.399482\pi\) |
−0.978485 | + | 0.206320i | \(0.933851\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.81654e8 | − | 1.70027e9i | −0.368973 | − | 0.639079i | ||||
\(494\) | 7.81328e8 | 0.291601 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.68780e8 | 0.209295 | ||||||||
\(497\) | 2.62038e9 | + | 4.53863e9i | 0.957452 | + | 1.65836i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.37327e8 | + | 7.57473e8i | −0.157563 | + | 0.272907i | −0.933989 | − | 0.357301i | \(-0.883697\pi\) |
0.776426 | + | 0.630208i | \(0.217030\pi\) | |||||||
\(500\) | −5.61861e7 | + | 9.73171e7i | −0.0201017 | + | 0.0348172i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.92139e8 | − | 5.06000e8i | −0.103069 | − | 0.178520i | ||||
\(503\) | 2.61478e9 | 0.916111 | 0.458055 | − | 0.888924i | \(-0.348546\pi\) | ||||
0.458055 | + | 0.888924i | \(0.348546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.50324e8 | −0.0519409 | ||||||||
\(506\) | −1.16558e9 | − | 2.01884e9i | −0.399959 | − | 0.692748i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.64306e8 | + | 6.30997e8i | −0.123294 | + | 0.213552i | ||||
\(509\) | 4.26286e8 | − | 7.38349e8i | 0.143281 | − | 0.248170i | −0.785449 | − | 0.618926i | \(-0.787568\pi\) |
0.928730 | + | 0.370756i | \(0.120901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.99496e9 | + | 6.91947e9i | 1.32446 | + | 2.29403i | ||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.07197e9 | 0.348185 | ||||||||
\(515\) | 7.60942e7 | + | 1.31799e8i | 0.0245486 | + | 0.0425194i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.17995e9 | + | 3.77578e9i | −0.693793 | + | 1.20168i | ||||
\(518\) | −6.99764e8 | + | 1.21203e9i | −0.221206 | + | 0.383140i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.08184e7 | + | 3.60585e7i | 0.00649285 | + | 0.0112459i | ||||
\(521\) | 2.66940e9 | 0.826954 | 0.413477 | − | 0.910515i | \(-0.364314\pi\) | ||||
0.413477 | + | 0.910515i | \(0.364314\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.41770e9 | −1.35033 | −0.675165 | − | 0.737667i | \(-0.735928\pi\) | ||||
−0.675165 | + | 0.737667i | \(0.735928\pi\) | |||||||
\(524\) | 1.69017e8 | + | 2.92747e8i | 0.0513182 | + | 0.0888858i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.52052e9 | + | 2.63362e9i | −0.455556 | + | 0.789046i | ||||
\(527\) | 9.17956e8 | − | 1.58995e9i | 0.273203 | − | 0.473201i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.58369e8 | − | 7.93919e8i | −0.134623 | − | 0.233175i | ||||
\(530\) | 5.59400e7 | 0.0163214 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.24431e9 | 0.358293 | ||||||||
\(533\) | −1.90850e8 | − | 3.30562e8i | −0.0545943 | − | 0.0945601i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.06587e8 | − | 1.84614e8i | 0.0300931 | − | 0.0521228i | ||||
\(536\) | 8.84433e8 | − | 1.53188e9i | 0.248078 | − | 0.429684i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.23074e9 | − | 3.86375e9i | −0.617605 | − | 1.06972i | ||||
\(539\) | −5.53426e9 | −1.52230 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.86240e9 | −1.04874 | −0.524368 | − | 0.851492i | \(-0.675699\pi\) | ||||
−0.524368 | + | 0.851492i | \(0.675699\pi\) | |||||||
\(542\) | −3.86317e8 | − | 6.69121e8i | −0.104219 | − | 0.180513i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.16614e8 | + | 3.75187e8i | −0.0576888 | + | 0.0999199i | ||||
\(545\) | −7.49323e7 | + | 1.29786e8i | −0.0198281 | + | 0.0343433i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.08461e9 | + | 1.87859e9i | 0.283346 | + | 0.490769i | 0.972207 | − | 0.234124i | \(-0.0752223\pi\) |
−0.688861 | + | 0.724894i | \(0.741889\pi\) | |||||||
\(548\) | −3.13673e9 | −0.814226 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.76591e9 | −0.708873 | ||||||||
\(551\) | 1.00285e9 | + | 1.73699e9i | 0.255392 | + | 0.442352i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.47284e9 | − | 2.55103e9i | 0.370354 | − | 0.641472i | ||||
\(554\) | 2.26320e9 | − | 3.91998e9i | 0.565508 | − | 0.979489i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.04142e8 | + | 1.04640e9i | 0.149066 | + | 0.258189i | ||||
\(557\) | −2.25645e8 | −0.0553265 | −0.0276632 | − | 0.999617i | \(-0.508807\pi\) | ||||
−0.0276632 | + | 0.999617i | \(0.508807\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.43570e9 | −1.31618 | ||||||||
\(560\) | 3.31545e7 | + | 5.74253e7i | 0.00797783 | + | 0.0138180i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.59820e9 | + | 2.76816e9i | −0.379799 | + | 0.657831i | ||||
\(563\) | 3.90401e8 | − | 6.76194e8i | 0.0922001 | − | 0.159695i | −0.816237 | − | 0.577718i | \(-0.803943\pi\) |
0.908437 | + | 0.418023i | \(0.137277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.14863e8 | − | 1.98948e8i | −0.0267923 | − | 0.0464056i | ||||
\(566\) | −5.42978e9 | −1.25871 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.86407e9 | 0.426818 | ||||||||
\(569\) | −3.34607e8 | − | 5.79557e8i | −0.0761452 | − | 0.131887i | 0.825439 | − | 0.564492i | \(-0.190928\pi\) |
−0.901584 | + | 0.432605i | \(0.857595\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.68261e8 | − | 1.15746e9i | 0.150217 | − | 0.260184i | −0.781090 | − | 0.624418i | \(-0.785336\pi\) |
0.931307 | + | 0.364235i | \(0.118669\pi\) | |||||||
\(572\) | −1.02567e9 | + | 1.77651e9i | −0.229151 | + | 0.396901i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.03940e8 | − | 5.26440e8i | −0.0670805 | − | 0.116187i | ||||
\(575\) | −5.12751e9 | −1.12478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.13624e9 | −1.54651 | −0.773257 | − | 0.634092i | \(-0.781374\pi\) | ||||
−0.773257 | + | 0.634092i | \(0.781374\pi\) | |||||||
\(578\) | −9.42165e8 | − | 1.63188e9i | −0.202946 | − | 0.351512i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.34418e7 | + | 9.25639e7i | −0.0113732 | + | 0.0196990i | ||||
\(581\) | 7.38819e9 | − | 1.27967e10i | 1.56287 | − | 2.70696i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.37801e9 | + | 2.38679e9i | 0.288014 | + | 0.498855i | ||||
\(584\) | 2.84191e9 | 0.590425 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.93912e8 | 0.183507 | ||||||||
\(587\) | 1.42735e9 | + | 2.47224e9i | 0.291271 | + | 0.504496i | 0.974111 | − | 0.226072i | \(-0.0725885\pi\) |
−0.682839 | + | 0.730568i | \(0.739255\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.37781e8 | + | 1.62428e9i | −0.189103 | + | 0.327535i | ||||
\(590\) | 3.66277e7 | − | 6.34411e7i | 0.00734223 | − | 0.0127171i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.48897e8 | + | 4.31102e8i | 0.0493052 | + | 0.0853992i | ||||
\(593\) | 6.55017e9 | 1.28991 | 0.644957 | − | 0.764219i | \(-0.276875\pi\) | ||||
0.644957 | + | 0.764219i | \(0.276875\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.14033e8 | 0.0416553 | ||||||||
\(596\) | −9.23192e8 | − | 1.59902e9i | −0.178620 | − | 0.309379i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.90142e9 | + | 3.29335e9i | −0.363599 | + | 0.629773i | ||||
\(599\) | −3.75708e9 | + | 6.50744e9i | −0.714259 | + | 1.23713i | 0.248985 | + | 0.968507i | \(0.419903\pi\) |
−0.963244 | + | 0.268626i | \(0.913430\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.70371e9 | + | 2.95092e9i | 0.320137 | + | 0.554493i | 0.980516 | − | 0.196439i | \(-0.0629378\pi\) |
−0.660379 | + | 0.750932i | \(0.729604\pi\) | |||||||
\(602\) | −8.65667e9 | −1.61720 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.30101e9 | −0.424902 | ||||||||
\(605\) | 905448. | + | 1.56828e6i | 0.000166234 | + | 0.000287926i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.47151e9 | + | 4.28078e9i | −0.448540 | + | 0.776895i | −0.998291 | − | 0.0584338i | \(-0.981389\pi\) |
0.549751 | + | 0.835329i | \(0.314723\pi\) | |||||||
\(608\) | 2.21292e8 | − | 3.83290e8i | 0.0399304 | − | 0.0691616i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.11093e8 | + | 1.92418e8i | 0.0198167 | + | 0.0343235i | ||||
\(611\) | 7.11233e9 | 1.26144 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.05250e9 | 0.710577 | 0.355288 | − | 0.934757i | \(-0.384383\pi\) | ||||
0.355288 | + | 0.934757i | \(0.384383\pi\) | |||||||
\(614\) | −6.12087e8 | − | 1.06017e9i | −0.106715 | − | 0.184835i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.63344e9 | + | 2.82920e9i | −0.281560 | + | 0.487676i | ||||
\(617\) | 3.07794e9 | − | 5.33115e9i | 0.527549 | − | 0.913741i | −0.471936 | − | 0.881633i | \(-0.656445\pi\) |
0.999484 | − | 0.0321082i | \(-0.0102221\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.82063e8 | − | 3.15342e8i | −0.0308534 | − | 0.0534397i | 0.850186 | − | 0.526482i | \(-0.176489\pi\) |
−0.881040 | + | 0.473042i | \(0.843156\pi\) | |||||||
\(620\) | −9.99482e7 | −0.0168424 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.82694e9 | −0.304410 | ||||||||
\(623\) | 5.84694e9 | + | 1.01272e10i | 0.968770 | + | 1.67796i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.03694e9 | + | 5.26014e9i | −0.497573 | + | 0.861822i | ||||
\(626\) | −2.81098e9 | + | 4.86875e9i | −0.457981 | + | 0.793246i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.84989e9 | + | 3.20410e9i | 0.298048 | + | 0.516235i | ||||
\(629\) | 1.60678e9 | 0.257442 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.22087e9 | 0.510353 | 0.255177 | − | 0.966894i | \(-0.417866\pi\) | ||||
0.255177 | + | 0.966894i | \(0.417866\pi\) | |||||||
\(632\) | −5.23869e8 | − | 9.07368e8i | −0.0825492 | − | 0.142979i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.16471e9 | − | 7.21349e9i | 0.649041 | − | 1.12417i | ||||
\(635\) | 6.40172e7 | − | 1.10881e8i | 0.00992176 | − | 0.0171850i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.51404e9 | + | 7.81855e9i | 0.691954 | + | 1.19850i | ||||
\(638\) | −5.26590e9 | −0.802786 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.35852e7 | 0.00355640 | ||||||||
\(641\) | −6.22206e9 | − | 1.07769e10i | −0.933106 | − | 1.61619i | −0.777978 | − | 0.628292i | \(-0.783754\pi\) |
−0.155128 | − | 0.987894i | \(-0.549579\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.41505e8 | − | 4.18298e8i | 0.0358251 | − | 0.0620509i | −0.847557 | − | 0.530704i | \(-0.821927\pi\) |
0.883382 | + | 0.468654i | \(0.155261\pi\) | |||||||
\(644\) | −3.02812e9 | + | 5.24485e9i | −0.446758 | + | 0.773808i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.14289e8 | − | 1.23719e9i | −0.104246 | − | 0.180560i | ||||
\(647\) | −4.60241e9 | −0.668068 | −0.334034 | − | 0.942561i | \(-0.608410\pi\) | ||||
−0.334034 | + | 0.942561i | \(0.608410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.60912e9 | 0.518256 | ||||||||
\(650\) | 2.25602e9 | + | 3.90754e9i | 0.322215 | + | 0.558094i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.03531e9 | + | 1.79322e9i | −0.146287 | + | 0.253376i | ||||
\(653\) | 2.84182e9 | − | 4.92218e9i | 0.399393 | − | 0.691769i | −0.594258 | − | 0.804275i | \(-0.702554\pi\) |
0.993651 | + | 0.112505i | \(0.0358875\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.97003e7 | − | 5.14425e7i | −0.00412969 | − | 0.00715282i | ||||
\(656\) | −2.16215e8 | −0.0299035 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.13268e10 | 1.54995 | ||||||||
\(659\) | 2.25571e9 | + | 3.90700e9i | 0.307032 | + | 0.531796i | 0.977712 | − | 0.209952i | \(-0.0673307\pi\) |
−0.670679 | + | 0.741747i | \(0.733997\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.88093e8 | + | 8.45401e8i | −0.0657351 | + | 0.113856i | −0.897020 | − | 0.441990i | \(-0.854273\pi\) |
0.831285 | + | 0.555847i | \(0.187606\pi\) | |||||||
\(662\) | 1.28510e9 | − | 2.22586e9i | 0.172161 | − | 0.298191i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.62788e9 | − | 4.55162e9i | −0.348351 | − | 0.603362i | ||||
\(665\) | −2.18655e8 | −0.0288326 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.76206e9 | −1.27380 | ||||||||
\(668\) | −2.77678e9 | − | 4.80953e9i | −0.360433 | − | 0.624288i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.55416e8 | + | 2.69188e8i | −0.0199634 | + | 0.0345775i | ||||
\(671\) | −5.47326e9 | + | 9.47996e9i | −0.699386 | + | 1.21137i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.26231e9 | − | 1.08466e10i | −0.791921 | − | 1.37165i | −0.924776 | − | 0.380513i | \(-0.875748\pi\) |
0.132854 | − | 0.991136i | \(-0.457586\pi\) | |||||||
\(674\) | 7.30917e9 | 0.919514 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.69539e8 | −0.0833608 | ||||||||
\(677\) | 5.22456e9 | + | 9.04920e9i | 0.647126 | + | 1.12086i | 0.983806 | + | 0.179237i | \(0.0573627\pi\) |
−0.336680 | + | 0.941619i | \(0.609304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.56758e9 | − | 1.65715e10i | 1.17289 | − | 2.03151i | ||||
\(680\) | 3.80643e7 | − | 6.59293e7i | 0.00464234 | − | 0.00804076i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.46210e9 | − | 4.26448e9i | −0.297208 | − | 0.514779i | ||||
\(683\) | −1.12280e9 | −0.134844 | −0.0674218 | − | 0.997725i | \(-0.521477\pi\) | ||||
−0.0674218 | + | 0.997725i | \(0.521477\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.51197e8 | 0.0655225 | ||||||||
\(686\) | 2.44702e9 | + | 4.23836e9i | 0.289403 | + | 0.501260i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.53953e9 | + | 2.66655e9i | −0.180231 | + | 0.312169i | ||||
\(689\) | 2.24796e9 | − | 3.89358e9i | 0.261831 | − | 0.453505i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.73022e9 | − | 6.46092e9i | −0.430091 | − | 0.744940i | 0.566789 | − | 0.823863i | \(-0.308185\pi\) |
−0.996881 | + | 0.0789226i | \(0.974852\pi\) | |||||||
\(692\) | 6.89431e8 | 0.0790897 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.78387e9 | −0.543277 | ||||||||
\(695\) | −1.06162e8 | − | 1.83878e8i | −0.0119956 | − | 0.0207770i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.48950e8 | + | 6.04399e8i | −0.0390345 | + | 0.0676097i | ||||
\(698\) | 2.60219e9 | − | 4.50712e9i | 0.289631 | − | 0.501655i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.59285e9 | + | 6.22299e9i | 0.395909 | + | 0.685735i | ||||
\(701\) | 1.79013e10 | 1.96278 | 0.981392 | − | 0.192014i | \(-0.0615020\pi\) | ||||
0.981392 | + | 0.192014i | \(0.0615020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.64148e9 | −0.178194 | ||||||||
\(704\) | 5.80993e8 | + | 1.00631e9i | 0.0627577 | + | 0.108700i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.46898e8 | − | 4.27641e8i | 0.0264060 | − | 0.0457365i | ||||
\(707\) | −9.62036e9 | + | 1.66630e10i | −1.02382 | + | 1.77331i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.77521e9 | − | 6.53885e9i | −0.397813 | − | 0.689032i | 0.595643 | − | 0.803249i | \(-0.296897\pi\) |
−0.993456 | + | 0.114217i | \(0.963564\pi\) | |||||||
\(710\) | −3.27561e8 | −0.0343469 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.15936e9 | 0.431863 | ||||||||
\(713\) | −4.56431e9 | − | 7.90562e9i | −0.471587 | − | 0.816812i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.80235e8 | − | 3.12176e8i | 0.0184403 | − | 0.0319395i | ||||
\(716\) | −1.15576e9 | + | 2.00183e9i | −0.117672 | + | 0.203813i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.82169e9 | − | 1.18155e10i | −0.687791 | − | 1.19129i | ||||
\(719\) | 3.79868e9 | 0.381137 | 0.190569 | − | 0.981674i | \(-0.438967\pi\) | ||||
0.190569 | + | 0.981674i | \(0.438967\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.94793e10 | 1.93553 | ||||||||
\(722\) | −2.84577e9 | − | 4.92902e9i | −0.281397 | − | 0.487394i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.89976e8 | + | 1.54148e9i | −0.0871552 | + | 0.150957i | ||||
\(725\) | −5.79132e9 | + | 1.00309e10i | −0.564409 | + | 0.977586i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.96762e9 | + | 3.40802e9i | 0.189920 | + | 0.328952i | 0.945224 | − | 0.326424i | \(-0.105844\pi\) |
−0.755303 | + | 0.655376i | \(0.772510\pi\) | |||||||
\(728\) | 5.32929e9 | 0.511928 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.99390e8 | −0.0475127 | ||||||||
\(731\) | 4.96931e9 | + | 8.60710e9i | 0.470528 | + | 0.814978i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.67457e9 | − | 9.82865e9i | 0.532193 | − | 0.921785i | −0.467100 | − | 0.884204i | \(-0.654701\pi\) |
0.999294 | − | 0.0375812i | \(-0.0119653\pi\) | |||||||
\(734\) | 9.72073e8 | − | 1.68368e9i | 0.0907325 | − | 0.157153i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.07706e9 | + | 1.86552e9i | 0.0995791 | + | 0.172476i | ||||
\(737\) | −1.53139e10 | −1.40913 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.61420e10 | 1.47130 | 0.735652 | − | 0.677359i | \(-0.236876\pi\) | ||||
0.735652 | + | 0.677359i | \(0.236876\pi\) | |||||||
\(740\) | −4.37370e7 | − | 7.57548e7i | −0.00396770 | − | 0.00687225i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.58001e9 | − | 6.20076e9i | 0.321715 | − | 0.557226i | ||||
\(743\) | −2.96574e9 | + | 5.13681e9i | −0.265260 | + | 0.459444i | −0.967632 | − | 0.252366i | \(-0.918791\pi\) |
0.702371 | + | 0.711811i | \(0.252125\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.62227e8 | + | 2.80985e8i | 0.0143739 | + | 0.0248964i | ||||
\(746\) | 5.26833e9 | 0.464608 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.75067e9 | 0.327682 | ||||||||
\(749\) | −1.36426e10 | − | 2.36297e10i | −1.18634 | − | 2.05481i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.67463e9 | − | 2.90054e9i | 0.144271 | − | 0.249885i | −0.784830 | − | 0.619711i | \(-0.787250\pi\) |
0.929101 | + | 0.369827i | \(0.120583\pi\) | |||||||
\(752\) | 2.01440e9 | − | 3.48904e9i | 0.172736 | − | 0.299187i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.29514e9 | + | 7.43941e9i | 0.364903 | + | 0.632031i | ||||
\(755\) | 4.04342e8 | 0.0341928 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.71611e9 | −0.311353 | −0.155677 | − | 0.987808i | \(-0.549756\pi\) | ||||
−0.155677 | + | 0.987808i | \(0.549756\pi\) | |||||||
\(758\) | 6.22661e7 | + | 1.07848e8i | 0.00519290 | + | 0.00899436i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.88863e7 | + | 6.73531e7i | −0.00321329 | + | 0.00556557i | ||||
\(761\) | 7.21722e8 | − | 1.25006e9i | 0.0593641 | − | 0.102822i | −0.834816 | − | 0.550529i | \(-0.814426\pi\) |
0.894180 | + | 0.447707i | \(0.147759\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.59093e9 | + | 1.66120e10i | 0.781673 | + | 1.35390i | ||||
\(764\) | 6.05602e9 | 0.491316 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.94304e9 | −0.558148 | ||||||||
\(767\) | −2.94379e9 | − | 5.09879e9i | −0.235572 | − | 0.408022i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.12495e9 | + | 8.87668e9i | −0.406394 | + | 0.703895i | −0.994483 | − | 0.104901i | \(-0.966547\pi\) |
0.588088 | + | 0.808797i | \(0.299881\pi\) | |||||||
\(770\) | 2.87034e8 | − | 4.97158e8i | 0.0226577 | − | 0.0392443i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.91114e9 | + | 6.77429e9i | 0.305944 | + | 0.529911i | ||||
\(773\) | 2.47581e10 | 1.92792 | 0.963959 | − | 0.266049i | \(-0.0857185\pi\) | ||||
0.963959 | + | 0.266049i | \(0.0857185\pi\) | |||||||
\(774\) |