Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,6,Mod(165,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.165");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.e (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: | \(31.4352286833\) |
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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 177.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.177 |
Dual form | 196.6.e.d.165.1 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −6.00000 | − | 10.3923i | −0.384900 | − | 0.666667i | 0.606855 | − | 0.794812i | \(-0.292431\pi\) |
−0.991755 | + | 0.128146i | \(0.959097\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 27.0000 | − | 46.7654i | 0.482991 | − | 0.836564i | −0.516819 | − | 0.856095i | \(-0.672884\pi\) |
0.999809 | + | 0.0195305i | \(0.00621716\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 49.5000 | − | 85.7365i | 0.203704 | − | 0.352825i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −270.000 | − | 467.654i | −0.672794 | − | 1.16531i | −0.977108 | − | 0.212742i | \(-0.931761\pi\) |
0.304315 | − | 0.952572i | \(-0.401573\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 418.000 | 0.685990 | 0.342995 | − | 0.939337i | \(-0.388559\pi\) | ||||
0.342995 | + | 0.939337i | \(0.388559\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −648.000 | −0.743613 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 297.000 | + | 514.419i | 0.249249 | + | 0.431713i | 0.963318 | − | 0.268363i | \(-0.0864828\pi\) |
−0.714068 | + | 0.700076i | \(0.753149\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 418.000 | − | 723.997i | 0.265639 | − | 0.460101i | −0.702092 | − | 0.712087i | \(-0.747750\pi\) |
0.967731 | + | 0.251986i | \(0.0810837\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2052.00 | − | 3554.17i | 0.808831 | − | 1.40094i | −0.104843 | − | 0.994489i | \(-0.533434\pi\) |
0.913674 | − | 0.406448i | \(-0.133233\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 104.500 | + | 180.999i | 0.0334400 | + | 0.0579198i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4104.00 | −1.08342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −594.000 | −0.131157 | −0.0655785 | − | 0.997847i | \(-0.520889\pi\) | ||||
−0.0655785 | + | 0.997847i | \(0.520889\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2128.00 | + | 3685.80i | 0.397711 | + | 0.688855i | 0.993443 | − | 0.114328i | \(-0.0364714\pi\) |
−0.595732 | + | 0.803183i | \(0.703138\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3240.00 | + | 5611.84i | −0.517917 | + | 0.897059i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 149.000 | − | 258.076i | 0.0178930 | − | 0.0309915i | −0.856940 | − | 0.515416i | \(-0.827638\pi\) |
0.874833 | + | 0.484424i | \(0.160971\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2508.00 | − | 4343.98i | −0.264038 | − | 0.457327i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17226.0 | −1.60039 | −0.800193 | − | 0.599742i | \(-0.795270\pi\) | ||||
−0.800193 | + | 0.599742i | \(0.795270\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12100.0 | −0.997963 | −0.498981 | − | 0.866613i | \(-0.666292\pi\) | ||||
−0.498981 | + | 0.866613i | \(0.666292\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2673.00 | − | 4629.77i | −0.196774 | − | 0.340823i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −648.000 | + | 1122.37i | −0.0427888 | + | 0.0741124i | −0.886627 | − | 0.462486i | \(-0.846958\pi\) |
0.843838 | + | 0.536598i | \(0.180291\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3564.00 | − | 6173.03i | 0.191872 | − | 0.332333i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9747.00 | − | 16882.3i | −0.476630 | − | 0.825547i | 0.523011 | − | 0.852326i | \(-0.324808\pi\) |
−0.999641 | + | 0.0267784i | \(0.991475\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −29160.0 | −1.29981 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10032.0 | −0.408978 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3834.00 | − | 6640.68i | −0.143391 | − | 0.248361i | 0.785380 | − | 0.619013i | \(-0.212467\pi\) |
−0.928772 | + | 0.370653i | \(0.879134\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17369.0 | + | 30084.0i | −0.597655 | + | 1.03517i | 0.395512 | + | 0.918461i | \(0.370567\pi\) |
−0.993166 | + | 0.116707i | \(0.962766\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11286.0 | − | 19547.9i | 0.331327 | − | 0.573875i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10906.0 | − | 18889.7i | −0.296810 | − | 0.514090i | 0.678594 | − | 0.734513i | \(-0.262589\pi\) |
−0.975404 | + | 0.220423i | \(0.929256\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −49248.0 | −1.24528 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −46872.0 | −1.10349 | −0.551744 | − | 0.834014i | \(-0.686037\pi\) | ||||
−0.551744 | + | 0.834014i | \(0.686037\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33781.0 | + | 58510.4i | 0.741934 | + | 1.28507i | 0.951614 | + | 0.307297i | \(0.0994246\pi\) |
−0.209679 | + | 0.977770i | \(0.567242\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1254.00 | − | 2171.99i | 0.0257421 | − | 0.0445867i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 38456.0 | − | 66607.7i | 0.693260 | − | 1.20076i | −0.277503 | − | 0.960725i | \(-0.589507\pi\) |
0.970764 | − | 0.240037i | \(-0.0771597\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 12595.5 | + | 21816.0i | 0.213306 | + | 0.369457i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −67716.0 | −1.07894 | −0.539468 | − | 0.842006i | \(-0.681375\pi\) | ||||
−0.539468 | + | 0.842006i | \(0.681375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 32076.0 | 0.481541 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3564.00 | + | 6173.03i | 0.0504824 | + | 0.0874380i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14877.0 | − | 25767.7i | 0.199086 | − | 0.344827i | −0.749146 | − | 0.662404i | \(-0.769536\pi\) |
0.948232 | + | 0.317578i | \(0.102869\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 25536.0 | − | 44229.6i | 0.306158 | − | 0.530281i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −22572.0 | − | 39095.9i | −0.256603 | − | 0.444449i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 122398. | 1.32082 | 0.660412 | − | 0.750903i | \(-0.270382\pi\) | ||||
0.660412 | + | 0.750903i | \(0.270382\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −53460.0 | −0.548202 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5643.00 | + | 9773.96i | 0.0550436 | + | 0.0953383i | 0.892234 | − | 0.451573i | \(-0.149137\pi\) |
−0.837191 | + | 0.546911i | \(0.815804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13628.0 | + | 23604.4i | −0.126572 | + | 0.219230i | −0.922346 | − | 0.386364i | \(-0.873731\pi\) |
0.795774 | + | 0.605594i | \(0.207064\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −61182.0 | + | 105970.i | −0.516612 | + | 0.894798i | 0.483202 | + | 0.875509i | \(0.339474\pi\) |
−0.999814 | + | 0.0192889i | \(0.993860\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −49951.0 | − | 86517.7i | −0.402697 | − | 0.697491i | 0.591354 | − | 0.806412i | \(-0.298594\pi\) |
−0.994050 | + | 0.108921i | \(0.965260\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3576.00 | −0.0275480 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −29646.0 | −0.218409 | −0.109204 | − | 0.994019i | \(-0.534830\pi\) | ||||
−0.109204 | + | 0.994019i | \(0.534830\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −110808. | − | 191925.i | −0.781316 | − | 1.35328i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20691.0 | − | 35837.9i | 0.139739 | − | 0.242035i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −65274.5 | + | 113059.i | −0.405303 | + | 0.702006i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 103356. | + | 179018.i | 0.615989 | + | 1.06692i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 180036. | 1.03059 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 336512. | 1.85136 | 0.925681 | − | 0.378305i | \(-0.123493\pi\) | ||||
0.925681 | + | 0.378305i | \(0.123493\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 72600.0 | + | 125747.i | 0.384116 | + | 0.665308i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 50490.0 | − | 87451.2i | 0.257056 | − | 0.445233i | −0.708396 | − | 0.705815i | \(-0.750581\pi\) |
0.965452 | + | 0.260582i | \(0.0839143\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −110808. | + | 191925.i | −0.523283 | + | 0.906353i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 158571. | + | 274653.i | 0.721809 | + | 1.25021i | 0.960274 | + | 0.279059i | \(0.0900225\pi\) |
−0.238465 | + | 0.971151i | \(0.576644\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 148324. | 0.651140 | 0.325570 | − | 0.945518i | \(-0.394444\pi\) | ||||
0.325570 | + | 0.945518i | \(0.394444\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15552.0 | 0.0658777 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −112860. | − | 195479.i | −0.461530 | − | 0.799393i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16038.0 | + | 27778.6i | −0.0633476 | + | 0.109721i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −98307.0 | + | 170273.i | −0.362759 | + | 0.628318i | −0.988414 | − | 0.151782i | \(-0.951499\pi\) |
0.625654 | + | 0.780100i | \(0.284832\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −37180.0 | − | 64397.6i | −0.132699 | − | 0.229841i | 0.792017 | − | 0.610499i | \(-0.209031\pi\) |
−0.924716 | + | 0.380658i | \(0.875698\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 58806.0 | 0.203092 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 229824. | 0.768362 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 60439.0 | + | 104683.i | 0.195690 | + | 0.338945i | 0.947126 | − | 0.320861i | \(-0.103972\pi\) |
−0.751437 | + | 0.659805i | \(0.770639\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −116964. | + | 202588.i | −0.366910 | + | 0.635507i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 55670.0 | − | 96423.3i | 0.164116 | − | 0.284258i | −0.772225 | − | 0.635350i | \(-0.780856\pi\) |
0.936341 | + | 0.351091i | \(0.114189\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 174960. | + | 303040.i | 0.500298 | + | 0.866542i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 491832. | 1.36466 | 0.682332 | − | 0.731043i | \(-0.260966\pi\) | ||||
0.682332 | + | 0.731043i | \(0.260966\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −196569. | −0.529417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −41382.0 | − | 71675.7i | −0.108223 | − | 0.187448i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 353727. | − | 612673.i | 0.898572 | − | 1.55637i | 0.0692518 | − | 0.997599i | \(-0.477939\pi\) |
0.829320 | − | 0.558773i | \(-0.188728\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −46008.0 | + | 79688.2i | −0.110382 | + | 0.191188i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −246834. | − | 427529.i | −0.575801 | − | 0.997317i | −0.995954 | − | 0.0898633i | \(-0.971357\pi\) |
0.420153 | − | 0.907453i | \(-0.361976\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 559450. | 1.26930 | 0.634651 | − | 0.772799i | \(-0.281144\pi\) | ||||
0.634651 | + | 0.772799i | \(0.281144\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 416856. | 0.920149 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8046.00 | − | 13936.1i | −0.0172843 | − | 0.0299372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 160380. | − | 277786.i | 0.335387 | − | 0.580907i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 362016. | − | 627030.i | 0.718033 | − | 1.24367i | −0.243745 | − | 0.969839i | \(-0.578376\pi\) |
0.961778 | − | 0.273830i | \(-0.0882906\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3553.00 | − | 6153.98i | −0.00686597 | − | 0.0118922i | 0.862572 | − | 0.505934i | \(-0.168852\pi\) |
−0.869438 | + | 0.494042i | \(0.835519\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −270864. | −0.510111 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −530442. | −0.973806 | −0.486903 | − | 0.873456i | \(-0.661873\pi\) | ||||
−0.486903 | + | 0.873456i | \(0.661873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 28084.0 | + | 48642.9i | 0.0502720 | + | 0.0870737i | 0.890066 | − | 0.455831i | \(-0.150658\pi\) |
−0.839794 | + | 0.542905i | \(0.817325\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −130872. | + | 226677.i | −0.228484 | + | 0.395747i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −465102. | + | 805580.i | −0.772972 | + | 1.33883i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −203148. | − | 351863.i | −0.329524 | − | 0.570752i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −451440. | −0.714882 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −339196. | −0.524499 | −0.262249 | − | 0.965000i | \(-0.584464\pi\) | ||||
−0.262249 | + | 0.965000i | \(0.584464\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 281232. | + | 487108.i | 0.424733 | + | 0.735659i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −326700. | + | 565861.i | −0.482007 | + | 0.834860i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 405372. | − | 702125.i | 0.571141 | − | 0.989246i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 124146. | + | 215027.i | 0.170983 | + | 0.296151i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −779360. | −1.04948 | −0.524742 | − | 0.851261i | \(-0.675838\pi\) | ||||
−0.524742 | + | 0.851261i | \(0.675838\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20691.0 | 0.0272474 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −372438. | − | 645082.i | −0.479722 | − | 0.830902i | 0.520008 | − | 0.854162i | \(-0.325929\pi\) |
−0.999729 | + | 0.0232592i | \(0.992596\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −136373. | + | 236205.i | −0.171846 | + | 0.297646i | −0.939065 | − | 0.343739i | \(-0.888307\pi\) |
0.767219 | + | 0.641385i | \(0.221640\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 76923.0 | − | 133235.i | 0.0928253 | − | 0.160778i | −0.815874 | − | 0.578230i | \(-0.803744\pi\) |
0.908699 | + | 0.417452i | \(0.137077\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34992.0 | + | 60607.9i | 0.0413332 | + | 0.0715912i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −922944. | −1.06734 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.15474e6 | 1.30764 | 0.653820 | − | 0.756650i | \(-0.273166\pi\) | ||||
0.653820 | + | 0.756650i | \(0.273166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 328537. | + | 569043.i | 0.364369 | + | 0.631106i | 0.988675 | − | 0.150074i | \(-0.0479513\pi\) |
−0.624306 | + | 0.781180i | \(0.714618\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −347490. | + | 601870.i | −0.377508 | + | 0.653864i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 174724. | − | 302631.i | 0.182226 | − | 0.315625i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 406296. | + | 703725.i | 0.415283 | + | 0.719291i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.34190e6 | −1.34442 | −0.672211 | − | 0.740359i | \(-0.734655\pi\) | ||||
−0.672211 | + | 0.740359i | \(0.734655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.21616e6 | −2.17671 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −192456. | − | 333344.i | −0.185345 | − | 0.321027i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 66177.0 | − | 114622.i | 0.0624992 | − | 0.108252i | −0.833083 | − | 0.553148i | \(-0.813426\pi\) |
0.895582 | + | 0.444897i | \(0.146760\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29403.0 | + | 50927.5i | −0.0267172 | + | 0.0462755i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −471636. | − | 816898.i | −0.420453 | − | 0.728246i | 0.575531 | − | 0.817780i | \(-0.304796\pi\) |
−0.995984 | + | 0.0895341i | \(0.971462\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.05268e6 | −0.920831 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −357048. | −0.306513 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 483759. | + | 837895.i | 0.407613 | + | 0.706007i | 0.994622 | − | 0.103574i | \(-0.0330278\pi\) |
−0.587008 | + | 0.809581i | \(0.699694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −259160. | + | 448878.i | −0.214360 | + | 0.371283i | −0.953075 | − | 0.302736i | \(-0.902100\pi\) |
0.738714 | + | 0.674019i | \(0.235433\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 56430.0 | − | 97739.6i | 0.0449965 | − | 0.0779361i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.11136e6 | − | 1.92494e6i | −0.870275 | − | 1.50736i | −0.861712 | − | 0.507397i | \(-0.830608\pi\) |
−0.00856270 | − | 0.999963i | \(-0.502726\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 421344. | 0.324061 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −196614. | −0.148542 | −0.0742709 | − | 0.997238i | \(-0.523663\pi\) | ||||
−0.0742709 | + | 0.997238i | \(0.523663\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −776138. | − | 1.34431e6i | −0.576067 | − | 0.997777i | −0.995925 | − | 0.0901872i | \(-0.971253\pi\) |
0.419858 | − | 0.907590i | \(-0.362080\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −270864. | + | 469150.i | −0.197533 | + | 0.342137i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 533510. | − | 924067.i | 0.375749 | − | 0.650817i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −734388. | − | 1.27200e6i | −0.508385 | − | 0.880549i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.07217e6 | 0.729616 | 0.364808 | − | 0.931083i | \(-0.381135\pi\) | ||||
0.364808 | + | 0.931083i | \(0.381135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −414072. | −0.277026 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.10808e6 | + | 1.91925e6i | 0.728920 | + | 1.26253i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 857736. | − | 1.48564e6i | 0.554850 | − | 0.961029i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 67716.0 | − | 117288.i | 0.0423726 | − | 0.0733914i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 937926. | + | 1.62454e6i | 0.577323 | + | 0.999953i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.58589e6 | −0.960346 | −0.480173 | − | 0.877174i | \(-0.659426\pi\) | ||||
−0.480173 | + | 0.877174i | \(0.659426\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 327072. | 0.194871 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −365364. | − | 632829.i | −0.214203 | − | 0.371010i | 0.738823 | − | 0.673900i | \(-0.235382\pi\) |
−0.953026 | + | 0.302890i | \(0.902049\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 292429. | − | 506502.i | 0.168717 | − | 0.292227i | −0.769252 | − | 0.638946i | \(-0.779371\pi\) |
0.937969 | + | 0.346719i | \(0.112704\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.24143e6 | − | 2.15023e6i | 0.693865 | − | 1.20181i | −0.276696 | − | 0.960957i | \(-0.589240\pi\) |
0.970562 | − | 0.240852i | \(-0.0774270\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 160380. | + | 277786.i | 0.0882416 | + | 0.152839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.46837e6 | 0.795376 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 496584. | 0.264842 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 43681.0 | + | 75657.7i | 0.0229395 | + | 0.0397324i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −599412. | + | 1.03821e6i | −0.309996 | + | 0.536929i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −188974. | + | 327313.i | −0.0948052 | + | 0.164207i | −0.909527 | − | 0.415644i | \(-0.863556\pi\) |
0.814722 | + | 0.579852i | \(0.196889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14751.0 | − | 25549.5i | −0.00728972 | − | 0.0126262i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.17785e6 | −0.573426 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 639122. | 0.306555 | 0.153278 | − | 0.988183i | \(-0.451017\pi\) | ||||
0.153278 | + | 0.988183i | \(0.451017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 177876. | + | 308090.i | 0.0840656 | + | 0.145606i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.14912e6 | − | 1.99033e6i | 0.535155 | − | 0.926915i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.32970e6 | + | 2.30310e6i | −0.601457 | + | 1.04175i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.45233e6 | + | 2.51551e6i | 0.647503 | + | 1.12151i | 0.983717 | + | 0.179722i | \(0.0575199\pi\) |
−0.336215 | + | 0.941785i | \(0.609147\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.99157e6 | 1.75420 | 0.877102 | − | 0.480304i | \(-0.159474\pi\) | ||||
0.877102 | + | 0.480304i | \(0.159474\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.71547e6 | −0.743217 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 714609. | + | 1.23774e6i | 0.305233 | + | 0.528679i | 0.977313 | − | 0.211799i | \(-0.0679323\pi\) |
−0.672080 | + | 0.740478i | \(0.734599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.26554e6 | + | 2.19199e6i | −0.532974 | + | 0.923139i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −580932. | + | 1.00620e6i | −0.237897 | + | 0.412050i | −0.960111 | − | 0.279620i | \(-0.909791\pi\) |
0.722214 | + | 0.691670i | \(0.243125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 888602. | + | 1.53910e6i | 0.358872 | + | 0.621584i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.56659e6 | 0.624005 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.64835e6 | 1.43339 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −544616. | − | 943303.i | −0.211069 | − | 0.365583i | 0.740980 | − | 0.671527i | \(-0.234361\pi\) |
−0.952049 | + | 0.305944i | \(0.901028\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −852687. | + | 1.47690e6i | −0.326005 | + | 0.564657i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.75288e6 | + | 3.03608e6i | −0.652350 | + | 1.12990i | 0.330201 | + | 0.943911i | \(0.392884\pi\) |
−0.982551 | + | 0.185993i | \(0.940450\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.08022e6 | − | 1.87099e6i | −0.396673 | − | 0.687057i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −248292. | −0.0899724 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.04385e6 | 1.44610 | 0.723048 | − | 0.690798i | \(-0.242740\pi\) | ||||
0.723048 | + | 0.690798i | \(0.242740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.01907e6 | − | 3.49714e6i | −0.712589 | − | 1.23424i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.59373e6 | − | 4.49247e6i | 0.903499 | − | 1.56491i | 0.0805786 | − | 0.996748i | \(-0.474323\pi\) |
0.822920 | − | 0.568157i | \(-0.192343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −598950. | + | 1.03741e6i | −0.203289 | + | 0.352106i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 475173. | + | 823024.i | 0.159213 | + | 0.275765i | 0.934585 | − | 0.355740i | \(-0.115771\pi\) |
−0.775372 | + | 0.631504i | \(0.782438\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.43778e6 | 0.806403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.21176e6 | −0.395763 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.07662e6 | − | 3.59682e6i | −0.669677 | − | 1.15991i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −260369. | + | 450972.i | −0.0829112 | + | 0.143606i | −0.904499 | − | 0.426475i | \(-0.859755\pi\) |
0.821588 | + | 0.570082i | \(0.193088\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −382185. | + | 661964.i | −0.118690 | + | 0.205576i | −0.919249 | − | 0.393677i | \(-0.871203\pi\) |
0.800559 | + | 0.599254i | \(0.204536\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 889504. | + | 1.54067e6i | 0.272826 | + | 0.472548i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.36031e6 | 0.412099 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −160920. | −0.0481531 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.32025e6 | + | 2.28675e6i | 0.390255 | + | 0.675942i | 0.992483 | − | 0.122382i | \(-0.0390534\pi\) |
−0.602228 | + | 0.798324i | \(0.705720\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.90285e6 | − | 3.29584e6i | 0.555649 | − | 0.962412i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.82833e6 | + | 3.16676e6i | −0.521116 | + | 0.902600i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −889944. | − | 1.54143e6i | −0.250624 | − | 0.434093i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.98020e6 | 1.38584 | 0.692918 | − | 0.721016i | \(-0.256325\pi\) | ||||
0.692918 | + | 0.721016i | \(0.256325\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −237994. | −0.0654426 | −0.0327213 | − | 0.999465i | \(-0.510417\pi\) | ||||
−0.0327213 | + | 0.999465i | \(0.510417\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 64152.0 | + | 111115.i | 0.0174325 | + | 0.0301939i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −62073.0 | + | 107514.i | −0.0166698 | + | 0.0288729i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.35432e6 | + | 2.34575e6i | −0.355286 | + | 0.615373i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.94119e6 | + | 3.36224e6i | 0.503356 | + | 0.871838i | 0.999992 | + | 0.00387961i | \(0.00123492\pi\) |
−0.496636 | + | 0.867959i | \(0.665432\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 66958.0 | 0.0171626 | 0.00858129 | − | 0.999963i | \(-0.497268\pi\) | ||||
0.00858129 | + | 0.999963i | \(0.497268\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 384912. | 0.0975300 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.71547e6 | − | 2.97128e6i | −0.429715 | − | 0.744287i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.25068e6 | + | 5.63034e6i | −0.805031 | + | 1.39435i | 0.111240 | + | 0.993794i | \(0.464518\pi\) |
−0.916270 | + | 0.400560i | \(0.868816\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.30380e6 | − | 3.99030e6i | 0.557745 | − | 0.966043i | −0.439939 | − | 0.898028i | \(-0.645000\pi\) |
0.997684 | − | 0.0680154i | \(-0.0216667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −803358. | − | 1.39146e6i | −0.192313 | − | 0.333096i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.35937e6 | 0.558505 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.77671e6 | 0.884092 | 0.442046 | − | 0.896992i | \(-0.354253\pi\) | ||||
0.442046 | + | 0.896992i | \(0.354253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.65102e6 | + | 8.05580e6i | 1.07673 | + | 1.86495i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −446160. | + | 772772.i | −0.102152 | + | 0.176932i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.59035e6 | − | 2.75456e6i | 0.356206 | − | 0.616967i | −0.631117 | − | 0.775687i | \(-0.717403\pi\) |
0.987324 | + | 0.158720i | \(0.0507368\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.21889e6 | − | 2.11118e6i | −0.270042 | − | 0.467727i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.68547e6 | −1.46514 | −0.732571 | − | 0.680691i | \(-0.761680\pi\) | ||||
−0.732571 | + | 0.680691i | \(0.761680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.35122e6 | −0.943318 | −0.471659 | − | 0.881781i | \(-0.656345\pi\) | ||||
−0.471659 | + | 0.881781i | \(0.656345\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.37894e6 | − | 2.38840e6i | −0.295743 | − | 0.512242i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.53997e6 | − | 6.13141e6i | 0.751117 | − | 1.30097i | −0.196165 | − | 0.980571i | \(-0.562849\pi\) |
0.947282 | − | 0.320401i | \(-0.103818\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 725268. | − | 1.25620e6i | 0.150642 | − | 0.260920i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.26700e6 | + | 5.65861e6i | 0.671423 | + | 1.16294i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 174724. | 0.0355319 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.92991e6 | −0.388365 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.61093e6 | + | 2.79021e6i | 0.320802 | + | 0.555646i | 0.980654 | − | 0.195750i | \(-0.0627142\pi\) |
−0.659852 | + | 0.751396i | \(0.729381\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 62282.0 | − | 107876.i | 0.0122744 | − | 0.0212599i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.30475e6 | − | 5.72399e6i | 0.637946 | − | 1.10495i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.14855e6 | − | 1.98934e6i | −0.219446 | − | 0.380091i | 0.735193 | − | 0.677858i | \(-0.237091\pi\) |
−0.954639 | + | 0.297767i | \(0.903758\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.33608e6 | −0.252674 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.82150e6 | 0.528173 | 0.264087 | − | 0.964499i | \(-0.414930\pi\) | ||||
0.264087 | + | 0.964499i | \(0.414930\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −176418. | − | 305565.i | −0.0326908 | − | 0.0566221i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.44342e6 | + | 2.50008e6i | −0.264777 | + | 0.458607i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.06814e6 | − | 3.58213e6i | 0.371817 | − | 0.644006i | −0.618028 | − | 0.786156i | \(-0.712068\pi\) |
0.989845 | + | 0.142150i | \(0.0454016\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.95099e6 | − | 5.11127e6i | −0.525259 | − | 0.909776i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.33263e6 | −1.46846 | −0.734230 | − | 0.678901i | \(-0.762457\pi\) | ||||
−0.734230 | + | 0.678901i | \(0.762457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 609444. | 0.106342 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.17941e6 | + | 2.04280e6i | 0.203773 | + | 0.352945i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.17050e6 | − | 3.75942e6i | 0.371335 | − | 0.643171i | −0.618436 | − | 0.785835i | \(-0.712233\pi\) |
0.989771 | + | 0.142664i | \(0.0455668\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.71547e6 | + | 2.97128e6i | −0.287800 | + | 0.498484i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 735912. | + | 1.27464e6i | 0.122267 | + | 0.211772i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 699840. | 0.115152 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.48945e6 | −1.38344 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.37092e6 | − | 5.83861e6i | −0.544070 | − | 0.942356i | −0.998665 | − | 0.0516581i | \(-0.983549\pi\) |
0.454595 | − | 0.890698i | \(-0.349784\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.86098e6 | + | 6.68741e6i | −0.617224 | + | 1.06906i | 0.372765 | + | 0.927926i | \(0.378410\pi\) |
−0.989990 | + | 0.141138i | \(0.954924\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.26403e6 | + | 2.18937e6i | −0.198258 | + | 0.343394i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.20324e6 | − | 9.01227e6i | −0.808415 | − | 1.40022i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −759132. | −0.116837 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.20047e6 | −1.09785 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.30383e6 | + | 5.72240e6i | 0.499037 | + | 0.864358i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.96201e6 | + | 5.13035e6i | −0.443252 | + | 0.767735i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 341033. | − | 590686.i | 0.0500960 | − | 0.0867689i | −0.839890 | − | 0.542757i | \(-0.817381\pi\) |
0.889986 | + | 0.455988i | \(0.150714\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.35670e6 | − | 5.81397e6i | −0.488554 | − | 0.846201i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.39471e6 | −0.777995 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.15772e6 | 0.308337 | 0.154169 | − | 0.988045i | \(-0.450730\pi\) | ||||
0.154169 | + | 0.988045i | \(0.450730\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.71953e6 | + | 2.97832e6i | 0.243489 | + | 0.421735i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −248292. | + | 430054.i | −0.0348404 | + | 0.0603454i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −96552.0 | + | 167233.i | −0.0133054 | + | 0.0230457i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.33798e6 | + | 2.31746e6i | 0.182731 | + | 0.316500i | 0.942810 | − | 0.333331i | \(-0.108173\pi\) |
−0.760078 | + | 0.649831i | \(0.774839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.05780e6 | −0.684592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.84912e6 | −0.516362 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.77665e6 | − | 3.07725e6i | −0.236228 | − | 0.409159i | 0.723401 | − | 0.690428i | \(-0.242578\pi\) |
−0.959629 | + | 0.281269i | \(0.909245\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −800442. | + | 1.38641e6i | −0.105489 | + | 0.182713i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.46123e6 | − | 1.11912e7i | 0.836633 | − | 1.44909i | −0.0560613 | − | 0.998427i | \(-0.517854\pi\) |
0.892694 | − | 0.450663i | \(-0.148812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.04179e6 | + | 5.26853e6i | 0.390426 | + | 0.676237i | 0.992506 | − | 0.122199i | \(-0.0389945\pi\) |
−0.602080 | + | 0.798436i | \(0.705661\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.68838e6 | −1.10548 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 857736. | 0.108189 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.91203e6 | − | 1.37040e7i | −0.989347 | − | 1.71360i | −0.620749 | − | 0.784010i | \(-0.713171\pi\) |
−0.368598 | − | 0.929589i | \(-0.620162\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −42636.0 | + | 73847.7i | −0.00528543 | + | 0.00915463i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.26338e6 | + | 9.11644e6i | −0.641347 | + | 1.11085i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.11731e6 | − | 1.93524e6i | −0.134985 | − | 0.233801i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.60220e6 | −0.551278 | −0.275639 | − | 0.961261i | \(-0.588889\pi\) | ||||
−0.275639 | + | 0.961261i | \(0.588889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.55802e6 | 0.422590 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.18265e6 | + | 5.51251e6i | 0.374818 | + | 0.649204i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.30561e6 | − | 7.45753e6i | 0.502803 | − | 0.870880i | −0.497192 | − | 0.867641i | \(-0.665635\pi\) |
0.999995 | − | 0.00323965i | \(-0.00103121\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 337008. | − | 583715.i | 0.0386994 | − | 0.0670294i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.99114e6 | + | 6.91286e6i | 0.454496 | + | 0.787210i | 0.998659 | − | 0.0517695i | \(-0.0164861\pi\) |
−0.544163 | + | 0.838979i | \(0.683153\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.01740e7 | −1.14896 | −0.574481 | − | 0.818518i | \(-0.694796\pi\) | ||||
−0.574481 | + | 0.818518i | \(0.694796\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.15939e6 | −0.241845 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.52482e6 | + | 6.10517e6i | 0.391515 | + | 0.678125i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.97922e6 | + | 8.62426e6i | −0.548516 | + | 0.950057i | 0.449861 | + | 0.893099i | \(0.351474\pi\) |
−0.998377 | + | 0.0569587i | \(0.981860\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −270864. | + | 469150.i | −0.0293527 | + | 0.0508404i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.09793e6 | − | 3.63372e6i | −0.225497 | − | 0.390572i | 0.730972 | − | 0.682408i | \(-0.239067\pi\) |
−0.956468 | + | 0.291836i | \(0.905734\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.11624e7 | 1.19007 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.12551e6 | 0.965038 | 0.482519 | − | 0.875885i | \(-0.339722\pi\) | ||||
0.482519 | + | 0.875885i | \(0.339722\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.22867e6 | + | 5.59222e6i | 0.338686 | + | 0.586621i | 0.984186 | − | 0.177139i | \(-0.0566843\pi\) |
−0.645500 | + | 0.763760i | \(0.723351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.42141e6 | + | 1.45863e7i | −0.876306 | + | 1.51781i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.53441e6 | − | 7.85383e6i | 0.464324 | − | 0.804232i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.70864e6 | + | 4.69150e6i | 0.275158 | + | 0.476588i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 177012. | 0.0178392 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.40514e7 | −1.40490 | −0.702450 | − | 0.711733i | \(-0.747910\pi\) | ||||
−0.702450 | + | 0.711733i | \(0.747910\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.03518e6 | + | 3.52503e6i | 0.201880 | + | 0.349666i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.08582e6 | − | 1.57371e7i | 0.894190 | − | 1.54878i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.32016e6 | + | 4.01864e6i | −0.224785 | + | 0.389338i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.23584e6 | − | 7.33669e6i | −0.407188 | − | 0.705270i | 0.587386 | − | 0.809307i | \(-0.300157\pi\) |
−0.994573 | + | 0.104037i | \(0.966824\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −488564. | −0.0466009 | −0.0233004 | − | 0.999729i | \(-0.507417\pi\) | ||||
−0.0233004 | + | 0.999729i | \(0.507417\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.84080e6 | 0.742098 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.24060e6 | + | 2.14878e6i | 0.116512 | + | 0.201804i | 0.918383 | − | 0.395693i | \(-0.129495\pi\) |
−0.801871 | + | 0.597497i | \(0.796162\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.07036e6 | + | 3.58597e6i | −0.192945 | + | 0.334191i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.64565e6 | − | 4.58240e6i | 0.242800 | − | 0.420543i | −0.718711 | − | 0.695309i | \(-0.755267\pi\) |
0.961511 | + | 0.274767i | \(0.0886007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.72646e6 | − | 4.72237e6i | −0.248311 | − | 0.430087i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.68864e6 | 0.604539 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.72468e6 | 0.423798 | 0.211899 | − | 0.977292i | \(-0.432035\pi\) | ||||
0.211899 | + | 0.977292i | \(0.432035\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.08710e6 | − | 5.34702e6i | −0.274819 | − | 0.476001i | 0.695270 | − | 0.718748i | \(-0.255285\pi\) |
−0.970090 | + | 0.242747i | \(0.921951\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.48975e6 | − | 2.58033e6i | 0.131623 | − | 0.227977i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.21889e6 | + | 2.11118e6i | −0.106084 | + | 0.183743i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.67616e6 | + | 8.09935e6i | 0.403947 | + | 0.699656i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.87585e7 | 1.60839 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.40925e6 | −0.800787 | −0.400394 | − | 0.916343i | \(-0.631127\pi\) | ||||
−0.400394 | + | 0.916343i | \(0.631127\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −428868. | − | 742821.i | −0.0362297 | − | 0.0627516i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.50430e6 | − | 1.29978e7i | 0.629272 | − | 1.08993i | −0.358426 | − | 0.933558i | \(-0.616686\pi\) |
0.987698 | − | 0.156373i | \(-0.0499802\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.46926e6 | + | 7.74098e6i | −0.369290 | + | 0.639629i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.48535e6 | + | 1.12329e7i | 0.531963 | + | 0.921387i | 0.999304 | + | 0.0373096i | \(0.0118788\pi\) |
−0.467341 | + | 0.884077i | \(0.654788\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.71257e7 | 1.39451 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.27295e6 | 0.264574 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.07425e6 | − | 7.05680e6i | −0.326963 | − | 0.566317i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.13278e7 | − | 1.96203e7i | 0.902506 | − | 1.56319i | 0.0782761 | − | 0.996932i | \(-0.475058\pi\) |
0.824230 | − | 0.566255i | \(-0.191608\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00475e6 | − | 6.93643e6i | 0.314495 | − | 0.544721i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.11612e6 | − | 8.86138e6i | −0.398895 | − | 0.690907i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.84615e6 | −0.142914 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.90169e7 | 1.46166 | 0.730828 | − | 0.682562i | \(-0.239134\pi\) | ||||
0.730828 | + | 0.682562i | \(0.239134\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −124564. | − | 215751.i | −0.00950614 | − | 0.0164651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 419904. | − | 727295.i | 0.0318183 | − | 0.0551109i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.56556e6 | + | 1.31039e7i | −0.565231 | + | 0.979008i | 0.431798 | + | 0.901971i | \(0.357879\pi\) |
−0.997028 | + | 0.0770376i | \(0.975454\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.80714e6 | − | 6.59417e6i | −0.282439 | − | 0.489199i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.74666e7 | 1.28672 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.21889e7 | −0.891659 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.92842e6 | − | 1.20004e7i | −0.503311 | − | 0.871760i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.51615e6 | + | 1.30184e7i | −0.542217 | + | 0.939148i | 0.456559 | + | 0.889693i | \(0.349082\pi\) |
−0.998776 | + | 0.0494547i | \(0.984252\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.94244e6 | − | 6.82851e6i | 0.280492 | − | 0.485826i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −62073.0 | − | 107514.i | −0.00438589 | − | 0.00759658i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.41230e6 | 0.520136 | 0.260068 | − | 0.965590i | \(-0.416255\pi\) | ||||
0.260068 | + | 0.965590i | \(0.416255\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.44612e7 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.59370e6 | − | 6.22447e6i | −0.248742 | − | 0.430833i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.38964e6 | + | 2.40693e6i | −0.0955306 | + | 0.165464i | −0.909830 | − | 0.414981i | \(-0.863788\pi\) |
0.814299 | + | 0.580445i | \(0.197121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.88924e6 | + | 1.02005e7i | −0.399384 | + | 0.691753i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.05231e6 | + | 1.04829e7i | 0.407671 | + | 0.706107i | 0.994628 | − | 0.103511i | \(-0.0330076\pi\) |
−0.586957 | + | 0.809618i | \(0.699674\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.19338e6 | −0.280555 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.46926e6 | 0.297005 | 0.148502 | − | 0.988912i | \(-0.452555\pi\) | ||||
0.148502 | + | 0.988912i | \(0.452555\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.30858e6 | + | 9.19473e6i | 0.350419 | + | 0.606943i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.35194e6 | + | 5.80573e6i | −0.219783 | + | 0.380676i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.44231e7 | + | 2.49816e7i | −0.933168 | + | 1.61629i | −0.155298 | + | 0.987868i | \(0.549634\pi\) |
−0.777869 | + | 0.628426i | \(0.783700\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.05140e6 | + | 1.39454e7i | 0.517469 | + | 0.896282i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.01544e6 | −0.256369 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.60868e6 | 0.609430 | 0.304715 | − | 0.952444i | \(-0.401439\pi\) | ||||
0.304715 | + | 0.952444i | \(0.401439\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.32970e7 | + | 2.30310e7i | 0.837815 | + | 1.45114i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.27294e6 | − | 3.93685e6i | 0.142274 | − | 0.246426i | −0.786078 | − | 0.618127i | \(-0.787892\pi\) |
0.928353 | + | 0.371700i | \(0.121225\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.58776e6 | − | 2.75008e6i | 0.0980916 | − | 0.169900i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.60261e6 | − | 2.77581e6i | −0.0983649 | − | 0.170373i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.15923e7 | 1.31669 | 0.658345 | − | 0.752716i | \(-0.271257\pi\) | ||||
0.658345 | + | 0.752716i | \(0.271257\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.58825e6 | −0.0962238 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.42000e6 | − | 1.28518e7i | −0.446638 | − | 0.773599i | 0.551527 | − | 0.834157i | \(-0.314045\pi\) |
−0.998165 | + | 0.0605578i | \(0.980712\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −444752. | + | 770333.i | −0.0265989 | + | 0.0460706i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.20047e6 | + | 1.24716e7i | −0.425125 | + | 0.736339i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.26554e7 | + | 2.19199e7i | 0.742420 | + | 1.28591i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.43778e6 | 0.142098 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.52741e6 | 0.378065 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.24393e7 | − | 2.15454e7i | −0.715909 | − | 1.23999i | −0.962608 | − | 0.270898i | \(-0.912679\pi\) |
0.246699 | − | 0.969092i | \(-0.420654\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.65963e6 | + | 9.80277e6i | −0.323665 | + | 0.560604i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.26024e6 | + | 1.25751e7i | −0.409985 | + | 0.710115i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.31606e6 | + | 1.09397e7i | 0.354428 | + | 0.613887i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.16080e7 | −1.76259 | −0.881294 | − | 0.472568i | \(-0.843327\pi\) | ||||
−0.881294 | + | 0.472568i | \(0.843327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −769824. | −0.0426604 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.47282e6 | − | 2.55100e6i | −0.0811090 | − | 0.140485i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.82417e7 | − | 3.15956e7i | 0.998338 | − | 1.72917i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.80511e6 | − | 1.00547e7i | 0.313781 | − | 0.543484i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.55004e6 | + | 2.68475e6i | 0.0832669 | + | 0.144223i | 0.904651 | − | 0.426152i | \(-0.140131\pi\) |
−0.821384 | + | 0.570375i | \(0.806798\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.87180e6 | −0.0999328 | −0.0499664 | − | 0.998751i | \(-0.515911\pi\) | ||||
−0.0499664 | + | 0.998751i | \(0.515911\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.21984e6 | 0.330030 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.00618e6 | − | 5.20686e6i | −0.158533 | − | 0.274588i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.05780e6 | + | 8.76037e6i | −0.265098 | + | 0.459163i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.00092e7 | − | 1.73364e7i | 0.518252 | − | 0.897640i | −0.481523 | − | 0.876434i | \(-0.659916\pi\) |
0.999775 | − | 0.0212059i | \(-0.00675056\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.65588e6 | − | 1.32604e7i | −0.394000 | − | 0.682427i | 0.598973 | − | 0.800769i | \(-0.295576\pi\) |
−0.992973 | + | 0.118342i | \(0.962242\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.35432e6 | −0.0692766 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.59310e6 | 0.487748 | 0.243874 | − | 0.969807i | \(-0.421582\pi\) | ||||
0.243874 | + | 0.969807i | \(0.421582\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.26105e7 | + | 2.18420e7i | 0.637302 | + | 1.10384i | 0.986023 | + | 0.166612i | \(0.0532828\pi\) |
−0.348721 | + | 0.937227i | \(0.613384\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.33364e7 | + | 2.30992e7i | −0.669938 | + | 1.16037i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.32795e7 | − | 2.30007e7i | 0.659120 | − | 1.14163i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.73331e6 | − | 1.51265e7i | −0.430889 | − | 0.746322i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.77623e7 | 0.871154 | 0.435577 | − | 0.900151i | \(-0.356544\pi\) | ||||
0.435577 | + | 0.900151i | \(0.356544\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.01583e7 | −0.982798 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.17968e6 | + | 2.04327e6i | 0.0571738 | + | 0.0990279i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.30736e6 | + | 9.19262e6i | −0.255704 | + | 0.442892i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.31366e6 | + | 1.61317e7i | −0.443456 | + | 0.768089i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −611496. | − | 1.05914e6i | −0.0289447 | − | 0.0501338i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 486970. | 0.0229155 | 0.0114578 | − | 0.999934i | \(-0.496353\pi\) | ||||
0.0114578 | + | 0.999934i | \(0.496353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.46926e6 | −0.209084 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −963171. | − | 1.66826e6i | −0.0447972 | − | 0.0775911i | 0.842757 | − | 0.538294i | \(-0.180931\pi\) |
−0.887555 | + | 0.460702i | \(0.847598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.11769e7 | − | 1.93590e7i | 0.516820 | − | 0.895158i | −0.482989 | − | 0.875626i | \(-0.660449\pi\) |
0.999809 | − | 0.0195320i | \(-0.00621762\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.29189e6 | + | 1.60940e7i | −0.424695 | + | 0.735593i | −0.996392 | − | 0.0848718i | \(-0.972952\pi\) |
0.571697 | + | 0.820465i | \(0.306285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.91013e7 | − | 3.30843e7i | −0.868004 | − | 1.50343i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.28043e7 | −0.578504 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.15325e7 | −1.86569 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.55871e6 | − | 7.89591e6i | −0.203609 | − | 0.352661i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.05870e6 | − | 1.04940e7i | 0.269057 | − | 0.466020i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.45524e7 | − | 2.52055e7i | 0.638905 | − | 1.10662i | −0.346769 | − | 0.937951i | \(-0.612721\pi\) |
0.985673 | − | 0.168665i | \(-0.0539456\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.43302e6 | − | 1.11423e7i | −0.280829 | − | 0.486411i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.14696e6 | 0.136600 | 0.0683001 | − | 0.997665i | \(-0.478242\pi\) | ||||
0.0683001 | + | 0.997665i | \(0.478242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.59995e7 | 0.690566 | 0.345283 | − | 0.938499i | \(-0.387783\pi\) | ||||
0.345283 | + | 0.938499i | \(0.387783\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.48443e6 | + | 4.30316e6i | 0.106627 | + | 0.184684i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.72937e7 | + | 2.99536e7i | −0.738039 | + | 1.27832i | 0.215338 | + | 0.976540i | \(0.430915\pi\) |
−0.953377 | + | 0.301781i | \(0.902419\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.80157e6 | − | 1.17807e7i | 0.287022 | − | 0.497136i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 541728. | + | 938300.i | 0.0227328 | + | 0.0393743i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.66581e7 | −1.11243 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.05857e7 | −0.854248 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.26403e6 | − | 2.18937e6i | −0.0521626 | − | 0.0903482i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.78972e6 | − | 1.00281e7i | 0.237599 | − | 0.411534i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.51052e7 | − | 2.61629e7i | 0.613061 | − | 1.06185i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.71982e6 | − | 1.51032e7i | −0.351957 | − | 0.609607i | 0.634635 | − | 0.772812i | \(-0.281150\pi\) |
−0.986592 | + | 0.163205i | \(0.947817\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.11731e6 | 0.0448503 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.59589e6 | −0.103631 | −0.0518155 | − | 0.998657i | \(-0.516501\pi\) | ||||
−0.0518155 | + | 0.998657i | \(0.516501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.82833e7 | + | 3.16676e7i | 0.725902 | + | 1.25730i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.12551e7 | − | 1.94944e7i | 0.444424 | − | 0.769764i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.82055e6 | − | 1.52776e7i | 0.344514 | − | 0.596716i | −0.640751 | − | 0.767748i | \(-0.721377\pi\) |
0.985265 | + | 0.171033i | \(0.0547104\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.51535e6 | + | 1.64811e7i | 0.369637 | + | 0.640231i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.95925e7 | −0.756982 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 62282.0 | 0.00239336 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.34917e6 | + | 2.33683e6i | 0.0515665 | + | 0.0893159i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.98392e7 | − | 3.43626e7i | 0.754199 | − | 1.30631i | −0.191573 | − | 0.981478i | \(-0.561359\pi\) |
0.945772 | − | 0.324833i | \(-0.105308\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.38437e6 | + | 7.59395e6i | −0.164893 | + | 0.285603i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.66052e6 | − | 1.50005e7i | −0.323978 | − | 0.561146i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.93413e7 | −1.46386 | −0.731930 | − | 0.681380i | \(-0.761380\pi\) | ||||
−0.731930 | + | 0.681380i | \(0.761380\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.01830e6 | −0.259757 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.31253e7 | + | 4.00542e7i | 0.851361 | + | 1.47460i | 0.879981 | + | 0.475009i | \(0.157555\pi\) |
−0.0286202 | + | 0.999590i | \(0.509111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.53478e7 | + | 6.12241e7i | −1.29444 | + | 2.24204i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.89512e7 | − | 3.28245e7i | 0.686693 | − | 1.18939i | −0.286208 | − | 0.958167i | \(-0.592395\pi\) |
0.972901 | − | 0.231220i | \(-0.0742718\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.41205e7 | + | 2.44574e7i | 0.508960 | + | 0.881544i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.97944e7 | −1.06828 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.66462e7 | −0.950394 | −0.475197 | − | 0.879879i | \(-0.657623\pi\) | ||||
−0.475197 | + | 0.879879i | \(0.657623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.95489e7 | − | 3.38596e7i | −0.693606 | − | 1.20136i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.92456e6 | − | 3.33344e6i | 0.0679284 | − | 0.117656i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.25781e6 | − | 9.10679e6i | 0.183652 | − | 0.318095i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.05702e6 | + | 1.04911e7i | 0.210471 | + | 0.364547i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −383724. | −0.0132648 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.09790e7 | 1.40927 | 0.704637 | − | 0.709568i | \(-0.251110\pi\) | ||||
0.704637 | + | 0.709568i | \(0.251110\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.97950e6 | − | 5.16065e6i | −0.101938 | − | 0.176561i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.36017e7 | + | 2.35588e7i | −0.462961 | + | 0.801872i | −0.999107 | − | 0.0422532i | \(-0.986546\pi\) |
0.536146 | + | 0.844125i | \(0.319880\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 524172. | − | 907893.i | 0.0176588 | − | 0.0305860i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.26778e7 | − | 2.19585e7i | −0.424919 | − | 0.735982i | 0.571494 | − | 0.820607i | \(-0.306364\pi\) |
−0.996413 | + | 0.0846247i | \(0.973031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.60672e7 | −0.535775 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.89030e6 | −0.328123 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.95696e6 | + | 1.03178e7i | 0.196626 | + | 0.340566i | 0.947432 | − | 0.319956i | \(-0.103668\pi\) |
−0.750806 | + | 0.660522i | \(0.770335\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.43219e7 | + | 2.48063e7i | −0.470339 | + | 0.814651i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.48292e7 | + | 4.30054e7i | −0.807183 | + | 1.39808i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.45965e7 | − | 2.52819e7i | −0.472134 | − | 0.817760i | 0.527357 | − | 0.849644i | \(-0.323183\pi\) |
−0.999492 | + | 0.0318832i | \(0.989850\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.53538e6 | 0.145962 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.03307e6 | 0.0971237 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.65004e6 | − | 1.49823e7i | −0.275601 | − | 0.477354i | 0.694686 | − | 0.719313i | \(-0.255543\pi\) |
−0.970286 | + | 0.241959i | \(0.922210\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −611496. | + | 1.05914e6i | −0.0193856 | + | 0.0335769i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))