Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,7,Mod(19,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.f (of order \(6\), 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: | \(33.8179502921\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.3 | ||
Root | \(-2.75320 + 4.76869i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.19 |
Dual form | 147.7.f.d.31.3 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.25320 | − | 3.90266i | 0.281650 | − | 0.487833i | −0.690141 | − | 0.723675i | \(-0.742451\pi\) |
0.971791 | + | 0.235842i | \(0.0757848\pi\) | |||||||
\(3\) | 13.5000 | − | 7.79423i | 0.500000 | − | 0.288675i | ||||
\(4\) | 21.8461 | + | 37.8386i | 0.341346 | + | 0.591229i | ||||
\(5\) | −53.9244 | − | 31.1333i | −0.431395 | − | 0.249066i | 0.268546 | − | 0.963267i | \(-0.413457\pi\) |
−0.699941 | + | 0.714201i | \(0.746790\pi\) | |||||||
\(6\) | − | 70.2479i | − | 0.325222i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 485.305 | 0.947862 | ||||||||
\(9\) | 121.500 | − | 210.444i | 0.166667 | − | 0.288675i | ||||
\(10\) | −243.005 | + | 140.299i | −0.243005 | + | 0.140299i | ||||
\(11\) | −9.71675 | − | 16.8299i | −0.00730034 | − | 0.0126446i | 0.862352 | − | 0.506309i | \(-0.168990\pi\) |
−0.869652 | + | 0.493664i | \(0.835657\pi\) | |||||||
\(12\) | 589.846 | + | 340.548i | 0.341346 | + | 0.197076i | ||||
\(13\) | − | 1642.65i | − | 0.747678i | −0.927494 | − | 0.373839i | \(-0.878041\pi\) | ||
0.927494 | − | 0.373839i | \(-0.121959\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −970.639 | −0.287597 | ||||||||
\(16\) | −304.661 | + | 527.689i | −0.0743802 | + | 0.128830i | ||||
\(17\) | 186.054 | − | 107.418i | 0.0378697 | − | 0.0218641i | −0.480946 | − | 0.876750i | \(-0.659707\pi\) |
0.518815 | + | 0.854886i | \(0.326373\pi\) | |||||||
\(18\) | −547.529 | − | 948.347i | −0.0938835 | − | 0.162611i | ||||
\(19\) | 8237.53 | + | 4755.94i | 1.20098 | + | 0.693387i | 0.960773 | − | 0.277335i | \(-0.0894512\pi\) |
0.240208 | + | 0.970722i | \(0.422785\pi\) | |||||||
\(20\) | − | 2720.57i | − | 0.340071i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −87.5753 | −0.00822458 | ||||||||
\(23\) | 7223.90 | − | 12512.2i | 0.593729 | − | 1.02837i | −0.399996 | − | 0.916517i | \(-0.630988\pi\) |
0.993725 | − | 0.111852i | \(-0.0356783\pi\) | |||||||
\(24\) | 6551.62 | − | 3782.58i | 0.473931 | − | 0.273624i | ||||
\(25\) | −5873.94 | − | 10174.0i | −0.375932 | − | 0.651134i | ||||
\(26\) | −6410.70 | − | 3701.22i | −0.364742 | − | 0.210584i | ||||
\(27\) | − | 3788.00i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 43016.4 | 1.76376 | 0.881882 | − | 0.471471i | \(-0.156277\pi\) | ||||
0.881882 | + | 0.471471i | \(0.156277\pi\) | |||||||
\(30\) | −2187.05 | + | 3788.08i | −0.0810017 | + | 0.140299i | ||||
\(31\) | 7799.62 | − | 4503.11i | 0.261811 | − | 0.151157i | −0.363349 | − | 0.931653i | \(-0.618367\pi\) |
0.625161 | + | 0.780496i | \(0.285033\pi\) | |||||||
\(32\) | 16902.7 | + | 29276.3i | 0.515829 | + | 0.893443i | ||||
\(33\) | −262.352 | − | 151.469i | −0.00730034 | − | 0.00421485i | ||||
\(34\) | − | 968.141i | − | 0.0246321i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10617.2 | 0.227564 | ||||||||
\(37\) | 16564.6 | − | 28690.7i | 0.327020 | − | 0.566416i | −0.654899 | − | 0.755717i | \(-0.727289\pi\) |
0.981919 | + | 0.189301i | \(0.0606221\pi\) | |||||||
\(38\) | 37121.7 | − | 21432.2i | 0.676514 | − | 0.390585i | ||||
\(39\) | −12803.2 | − | 22175.8i | −0.215836 | − | 0.373839i | ||||
\(40\) | −26169.8 | − | 15109.1i | −0.408903 | − | 0.236080i | ||||
\(41\) | 73712.4i | 1.06952i | 0.845004 | + | 0.534760i | \(0.179598\pi\) | ||||
−0.845004 | + | 0.534760i | \(0.820402\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4761.19 | 0.0598839 | 0.0299420 | − | 0.999552i | \(-0.490468\pi\) | ||||
0.0299420 | + | 0.999552i | \(0.490468\pi\) | |||||||
\(44\) | 424.547 | − | 735.337i | 0.00498388 | − | 0.00863234i | ||||
\(45\) | −13103.6 | + | 7565.38i | −0.143798 | + | 0.0830220i | ||||
\(46\) | −32553.9 | − | 56384.9i | −0.334448 | − | 0.579281i | ||||
\(47\) | 63760.5 | + | 36812.2i | 0.614127 | + | 0.354567i | 0.774579 | − | 0.632477i | \(-0.217962\pi\) |
−0.160452 | + | 0.987044i | \(0.551295\pi\) | |||||||
\(48\) | 9498.40i | 0.0858869i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −52940.7 | −0.423526 | ||||||||
\(51\) | 1674.48 | − | 2900.29i | 0.0126232 | − | 0.0218641i | ||||
\(52\) | 62155.6 | − | 35885.5i | 0.442049 | − | 0.255217i | ||||
\(53\) | −119317. | − | 206663.i | −0.801447 | − | 1.38815i | −0.918664 | − | 0.395041i | \(-0.870730\pi\) |
0.117216 | − | 0.993106i | \(-0.462603\pi\) | |||||||
\(54\) | −14783.3 | − | 8535.13i | −0.0938835 | − | 0.0542037i | ||||
\(55\) | 1210.06i | 0.00727307i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 148275. | 0.800654 | ||||||||
\(58\) | 96924.8 | − | 167879.i | 0.496765 | − | 0.860422i | ||||
\(59\) | 282811. | − | 163281.i | 1.37702 | − | 0.795023i | 0.385221 | − | 0.922824i | \(-0.374125\pi\) |
0.991800 | + | 0.127801i | \(0.0407919\pi\) | |||||||
\(60\) | −21204.7 | − | 36727.6i | −0.0981700 | − | 0.170035i | ||||
\(61\) | −350517. | − | 202371.i | −1.54426 | − | 0.891578i | −0.998563 | − | 0.0535954i | \(-0.982932\pi\) |
−0.545696 | − | 0.837983i | \(-0.683735\pi\) | |||||||
\(62\) | − | 40585.7i | − | 0.170294i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 113344. | 0.432374 | ||||||||
\(65\) | −51141.0 | + | 88578.8i | −0.186221 | + | 0.322545i | ||||
\(66\) | −1182.27 | + | 682.582i | −0.00411229 | + | 0.00237423i | ||||
\(67\) | −109982. | − | 190494.i | −0.365676 | − | 0.633369i | 0.623209 | − | 0.782056i | \(-0.285829\pi\) |
−0.988884 | + | 0.148687i | \(0.952495\pi\) | |||||||
\(68\) | 8129.12 | + | 4693.35i | 0.0258533 | + | 0.0149264i | ||||
\(69\) | − | 225219.i | − | 0.685579i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 350228. | 0.978535 | 0.489267 | − | 0.872134i | \(-0.337264\pi\) | ||||
0.489267 | + | 0.872134i | \(0.337264\pi\) | |||||||
\(72\) | 58964.6 | − | 102130.i | 0.157977 | − | 0.273624i | ||||
\(73\) | 174606. | − | 100809.i | 0.448838 | − | 0.259137i | −0.258501 | − | 0.966011i | \(-0.583229\pi\) |
0.707339 | + | 0.706874i | \(0.249895\pi\) | |||||||
\(74\) | −74646.7 | − | 129292.i | −0.184211 | − | 0.319063i | ||||
\(75\) | −158596. | − | 91565.7i | −0.375932 | − | 0.217045i | ||||
\(76\) | 415596.i | 0.946739i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −115393. | −0.243161 | ||||||||
\(79\) | −197745. | + | 342505.i | −0.401074 | + | 0.694681i | −0.993856 | − | 0.110682i | \(-0.964696\pi\) |
0.592782 | + | 0.805363i | \(0.298030\pi\) | |||||||
\(80\) | 32857.4 | − | 18970.2i | 0.0641745 | − | 0.0370512i | ||||
\(81\) | −29524.5 | − | 51137.9i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 287675. | + | 166089.i | 0.521747 | + | 0.301231i | ||||
\(83\) | − | 13229.0i | − | 0.0231362i | −0.999933 | − | 0.0115681i | \(-0.996318\pi\) | ||
0.999933 | − | 0.0115681i | \(-0.00368232\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13377.1 | −0.0217824 | ||||||||
\(86\) | 10727.9 | − | 18581.3i | 0.0168663 | − | 0.0292134i | ||||
\(87\) | 580722. | − | 335280.i | 0.881882 | − | 0.509155i | ||||
\(88\) | −4715.59 | − | 8167.65i | −0.00691972 | − | 0.0119853i | ||||
\(89\) | 199460. | + | 115158.i | 0.282934 | + | 0.163352i | 0.634751 | − | 0.772717i | \(-0.281103\pi\) |
−0.351817 | + | 0.936069i | \(0.614436\pi\) | |||||||
\(90\) | 68185.4i | 0.0935328i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 631258. | 0.810668 | ||||||||
\(93\) | 70196.6 | − | 121584.i | 0.0872705 | − | 0.151157i | ||||
\(94\) | 287331. | − | 165891.i | 0.345939 | − | 0.199728i | ||||
\(95\) | −296136. | − | 512922.i | −0.345398 | − | 0.598247i | ||||
\(96\) | 456373. | + | 263487.i | 0.515829 | + | 0.297814i | ||||
\(97\) | 662517.i | 0.725909i | 0.931807 | + | 0.362954i | \(0.118232\pi\) | ||||
−0.931807 | + | 0.362954i | \(0.881768\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4722.34 | −0.00486689 | ||||||||
\(100\) | 256646. | − | 444524.i | 0.256646 | − | 0.444524i | ||||
\(101\) | −1.62606e6 | + | 938803.i | −1.57823 | + | 0.911193i | −0.583127 | + | 0.812381i | \(0.698171\pi\) |
−0.995106 | + | 0.0988126i | \(0.968496\pi\) | |||||||
\(102\) | −7545.91 | − | 13069.9i | −0.00711068 | − | 0.0123161i | ||||
\(103\) | −782887. | − | 452000.i | −0.716452 | − | 0.413644i | 0.0969931 | − | 0.995285i | \(-0.469078\pi\) |
−0.813446 | + | 0.581641i | \(0.802411\pi\) | |||||||
\(104\) | − | 797186.i | − | 0.708696i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.07538e6 | −0.902912 | ||||||||
\(107\) | −423106. | + | 732842.i | −0.345381 | + | 0.598217i | −0.985423 | − | 0.170123i | \(-0.945584\pi\) |
0.640042 | + | 0.768340i | \(0.278917\pi\) | |||||||
\(108\) | 143333. | − | 82753.1i | 0.113782 | − | 0.0656921i | ||||
\(109\) | 847674. | + | 1.46821e6i | 0.654560 | + | 1.13373i | 0.982004 | + | 0.188861i | \(0.0604794\pi\) |
−0.327444 | + | 0.944871i | \(0.606187\pi\) | |||||||
\(110\) | 4722.44 | + | 2726.50i | 0.00354804 | + | 0.00204846i | ||||
\(111\) | − | 516432.i | − | 0.377611i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −152753. | −0.105866 | −0.0529328 | − | 0.998598i | \(-0.516857\pi\) | ||||
−0.0529328 | + | 0.998598i | \(0.516857\pi\) | |||||||
\(114\) | 334095. | − | 578669.i | 0.225505 | − | 0.390585i | ||||
\(115\) | −779089. | + | 449807.i | −0.512264 | + | 0.295756i | ||||
\(116\) | 939743. | + | 1.62768e6i | 0.602054 | + | 1.04279i | ||||
\(117\) | −345686. | − | 199582.i | −0.215836 | − | 0.124613i | ||||
\(118\) | − | 1.47162e6i | − | 0.895675i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −471056. | −0.272602 | ||||||||
\(121\) | 885592. | − | 1.53389e6i | 0.499893 | − | 0.865841i | ||||
\(122\) | −1.57957e6 | + | 911968.i | −0.869883 | + | 0.502227i | ||||
\(123\) | 574531. | + | 995117.i | 0.308744 | + | 0.534760i | ||||
\(124\) | 340783. | + | 196751.i | 0.178737 | + | 0.103194i | ||||
\(125\) | 1.70441e6i | 0.872660i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.82114e6 | −1.37725 | −0.688627 | − | 0.725116i | \(-0.741786\pi\) | ||||
−0.688627 | + | 0.725116i | \(0.741786\pi\) | |||||||
\(128\) | −826385. | + | 1.43134e6i | −0.394051 | + | 0.682517i | ||||
\(129\) | 64276.1 | − | 37109.8i | 0.0299420 | − | 0.0172870i | ||||
\(130\) | 230462. | + | 399172.i | 0.104899 | + | 0.181690i | ||||
\(131\) | 3.86131e6 | + | 2.22933e6i | 1.71759 | + | 0.991654i | 0.923262 | + | 0.384171i | \(0.125513\pi\) |
0.794333 | + | 0.607482i | \(0.207820\pi\) | |||||||
\(132\) | − | 13236.1i | − | 0.00575489i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −991245. | −0.411971 | ||||||||
\(135\) | −117933. | + | 204265.i | −0.0479328 | + | 0.0830220i | ||||
\(136\) | 90292.9 | − | 52130.6i | 0.0358952 | − | 0.0207241i | ||||
\(137\) | −649623. | − | 1.12518e6i | −0.252639 | − | 0.437583i | 0.711613 | − | 0.702572i | \(-0.247965\pi\) |
−0.964252 | + | 0.264989i | \(0.914632\pi\) | |||||||
\(138\) | −878954. | − | 507464.i | −0.334448 | − | 0.193094i | ||||
\(139\) | 119566.i | 0.0445207i | 0.999752 | + | 0.0222603i | \(0.00708627\pi\) | ||||
−0.999752 | + | 0.0222603i | \(0.992914\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.14769e6 | 0.409418 | ||||||||
\(142\) | 789136. | − | 1.36682e6i | 0.275605 | − | 0.477361i | ||||
\(143\) | −27645.6 | + | 15961.2i | −0.00945406 | + | 0.00545830i | ||||
\(144\) | 74032.7 | + | 128228.i | 0.0247934 | + | 0.0429434i | ||||
\(145\) | −2.31963e6 | − | 1.33924e6i | −0.760879 | − | 0.439293i | ||||
\(146\) | − | 908570.i | − | 0.291944i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.44749e6 | 0.446509 | ||||||||
\(149\) | −3.12914e6 | + | 5.41983e6i | −0.945946 | + | 1.63843i | −0.192101 | + | 0.981375i | \(0.561530\pi\) |
−0.753845 | + | 0.657052i | \(0.771803\pi\) | |||||||
\(150\) | −714700. | + | 412632.i | −0.211763 | + | 0.122261i | ||||
\(151\) | 753969. | + | 1.30591e6i | 0.218989 | + | 0.379300i | 0.954499 | − | 0.298213i | \(-0.0963907\pi\) |
−0.735510 | + | 0.677514i | \(0.763057\pi\) | |||||||
\(152\) | 3.99772e6 | + | 2.30808e6i | 1.13836 | + | 0.657235i | ||||
\(153\) | − | 52205.3i | − | 0.0145761i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −560786. | −0.150592 | ||||||||
\(156\) | 559400. | − | 968910.i | 0.147350 | − | 0.255217i | ||||
\(157\) | −2.14761e6 | + | 1.23992e6i | −0.554954 | + | 0.320403i | −0.751118 | − | 0.660169i | \(-0.770485\pi\) |
0.196164 | + | 0.980571i | \(0.437152\pi\) | |||||||
\(158\) | 891121. | + | 1.54347e6i | 0.225925 | + | 0.391314i | ||||
\(159\) | −3.22156e6 | − | 1.85997e6i | −0.801447 | − | 0.462716i | ||||
\(160\) | − | 2.10494e6i | − | 0.513902i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −266099. | −0.0625890 | ||||||||
\(163\) | −3.29510e6 | + | 5.70727e6i | −0.760861 | + | 1.31785i | 0.181546 | + | 0.983382i | \(0.441890\pi\) |
−0.942407 | + | 0.334468i | \(0.891444\pi\) | |||||||
\(164\) | −2.78918e6 | + | 1.61033e6i | −0.632331 | + | 0.365076i | ||||
\(165\) | 9431.46 | + | 16335.8i | 0.00209955 | + | 0.00363653i | ||||
\(166\) | −51628.2 | − | 29807.5i | −0.0112866 | − | 0.00651631i | ||||
\(167\) | 5.45006e6i | 1.17018i | 0.810969 | + | 0.585089i | \(0.198941\pi\) | ||||
−0.810969 | + | 0.585089i | \(0.801059\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.12851e6 | 0.440978 | ||||||||
\(170\) | −30141.4 | + | 52206.4i | −0.00613502 | + | 0.0106262i | ||||
\(171\) | 2.00172e6 | − | 1.15569e6i | 0.400327 | − | 0.231129i | ||||
\(172\) | 104014. | + | 180157.i | 0.0204411 | + | 0.0354051i | ||||
\(173\) | −2.39148e6 | − | 1.38072e6i | −0.461879 | − | 0.266666i | 0.250955 | − | 0.967999i | \(-0.419255\pi\) |
−0.712834 | + | 0.701333i | \(0.752589\pi\) | |||||||
\(174\) | − | 3.02182e6i | − | 0.573615i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11841.3 | 0.00217200 | ||||||||
\(177\) | 2.54530e6 | − | 4.40859e6i | 0.459007 | − | 0.795023i | ||||
\(178\) | 898847. | − | 518949.i | 0.159377 | − | 0.0920164i | ||||
\(179\) | 743863. | + | 1.28841e6i | 0.129698 | + | 0.224644i | 0.923560 | − | 0.383455i | \(-0.125266\pi\) |
−0.793861 | + | 0.608099i | \(0.791932\pi\) | |||||||
\(180\) | −572527. | − | 330549.i | −0.0981700 | − | 0.0566785i | ||||
\(181\) | − | 6.01679e6i | − | 1.01468i | −0.861746 | − | 0.507340i | \(-0.830629\pi\) | ||
0.861746 | − | 0.507340i | \(-0.169371\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.30931e6 | −1.02951 | ||||||||
\(184\) | 3.50580e6 | − | 6.07222e6i | 0.562773 | − | 0.974752i | ||||
\(185\) | −1.78647e6 | + | 1.03142e6i | −0.282150 | + | 0.162899i | ||||
\(186\) | −316334. | − | 547907.i | −0.0491595 | − | 0.0851468i | ||||
\(187\) | −3615.68 | − | 2087.51i | −0.000552923 | − | 0.000319230i | ||||
\(188\) | 3.21682e6i | 0.484120i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.66902e6 | −0.389126 | ||||||||
\(191\) | −3.20172e6 | + | 5.54554e6i | −0.459498 | + | 0.795874i | −0.998934 | − | 0.0461527i | \(-0.985304\pi\) |
0.539437 | + | 0.842026i | \(0.318637\pi\) | |||||||
\(192\) | 1.53015e6 | − | 883431.i | 0.216187 | − | 0.124816i | ||||
\(193\) | −4.92592e6 | − | 8.53194e6i | −0.685197 | − | 1.18680i | −0.973375 | − | 0.229219i | \(-0.926383\pi\) |
0.288178 | − | 0.957577i | \(-0.406951\pi\) | |||||||
\(194\) | 2.58558e6 | + | 1.49279e6i | 0.354122 | + | 0.204453i | ||||
\(195\) | 1.59442e6i | 0.215030i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.38883e6 | 0.312454 | 0.156227 | − | 0.987721i | \(-0.450067\pi\) | ||||
0.156227 | + | 0.987721i | \(0.450067\pi\) | |||||||
\(198\) | −10640.4 | + | 18429.7i | −0.00137076 | + | 0.00237423i | ||||
\(199\) | 1.36103e7 | − | 7.85789e6i | 1.72706 | − | 0.997118i | 0.825594 | − | 0.564264i | \(-0.190840\pi\) |
0.901464 | − | 0.432854i | \(-0.142493\pi\) | |||||||
\(200\) | −2.85066e6 | − | 4.93748e6i | −0.356332 | − | 0.617185i | ||||
\(201\) | −2.96951e6 | − | 1.71445e6i | −0.365676 | − | 0.211123i | ||||
\(202\) | 8.46126e6i | 1.02655i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 146324. | 0.0172356 | ||||||||
\(205\) | 2.29491e6 | − | 3.97490e6i | 0.266381 | − | 0.461386i | ||||
\(206\) | −3.52801e6 | + | 2.03690e6i | −0.403578 | + | 0.233006i | ||||
\(207\) | −1.75541e6 | − | 3.04046e6i | −0.197910 | − | 0.342790i | ||||
\(208\) | 866808. | + | 500452.i | 0.0963236 | + | 0.0556125i | ||||
\(209\) | − | 184849.i | − | 0.0202478i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.46740e6 | 0.156207 | 0.0781034 | − | 0.996945i | \(-0.475114\pi\) | ||||
0.0781034 | + | 0.996945i | \(0.475114\pi\) | |||||||
\(212\) | 5.21324e6 | − | 9.02959e6i | 0.547142 | − | 0.947677i | ||||
\(213\) | 4.72808e6 | − | 2.72976e6i | 0.489267 | − | 0.282479i | ||||
\(214\) | 1.90669e6 | + | 3.30248e6i | 0.194553 | + | 0.336976i | ||||
\(215\) | −256744. | − | 148231.i | −0.0258336 | − | 0.0149151i | ||||
\(216\) | − | 1.83833e6i | − | 0.182416i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.63993e6 | 0.737429 | ||||||||
\(219\) | 1.57145e6 | − | 2.72183e6i | 0.149613 | − | 0.259137i | ||||
\(220\) | −45786.9 | + | 26435.1i | −0.00430005 | + | 0.00248263i | ||||
\(221\) | −176450. | − | 305621.i | −0.0163473 | − | 0.0283143i | ||||
\(222\) | −2.01546e6 | − | 1.16363e6i | −0.184211 | − | 0.106354i | ||||
\(223\) | − | 3.63341e6i | − | 0.327642i | −0.986490 | − | 0.163821i | \(-0.947618\pi\) | ||
0.986490 | − | 0.163821i | \(-0.0523820\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.85474e6 | −0.250621 | ||||||||
\(226\) | −344184. | + | 596144.i | −0.0298171 | + | 0.0516447i | ||||
\(227\) | −5.14121e6 | + | 2.96828e6i | −0.439529 | + | 0.253762i | −0.703398 | − | 0.710796i | \(-0.748335\pi\) |
0.263869 | + | 0.964559i | \(0.415001\pi\) | |||||||
\(228\) | 3.23925e6 | + | 5.61054e6i | 0.273300 | + | 0.473370i | ||||
\(229\) | −1.05964e7 | − | 6.11784e6i | −0.882373 | − | 0.509438i | −0.0109329 | − | 0.999940i | \(-0.503480\pi\) |
−0.871440 | + | 0.490502i | \(0.836813\pi\) | |||||||
\(230\) | 4.05403e6i | 0.333199i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.08761e7 | 1.67180 | ||||||||
\(233\) | −6.06046e6 | + | 1.04970e7i | −0.479113 | + | 0.829848i | −0.999713 | − | 0.0239524i | \(-0.992375\pi\) |
0.520600 | + | 0.853801i | \(0.325708\pi\) | |||||||
\(234\) | −1.55780e6 | + | 899397.i | −0.121581 | + | 0.0701946i | ||||
\(235\) | −2.29216e6 | − | 3.97015e6i | −0.176621 | − | 0.305917i | ||||
\(236\) | 1.23567e7 | + | 7.13413e6i | 0.940081 | + | 0.542756i | ||||
\(237\) | 6.16509e6i | 0.463121i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.19016e7 | 0.871790 | 0.435895 | − | 0.899998i | \(-0.356432\pi\) | ||||
0.435895 | + | 0.899998i | \(0.356432\pi\) | |||||||
\(240\) | 295716. | − | 512195.i | 0.0213915 | − | 0.0370512i | ||||
\(241\) | 8.62117e6 | − | 4.97743e6i | 0.615907 | − | 0.355594i | −0.159367 | − | 0.987219i | \(-0.550945\pi\) |
0.775274 | + | 0.631625i | \(0.217612\pi\) | |||||||
\(242\) | −3.99084e6 | − | 6.91233e6i | −0.281590 | − | 0.487729i | ||||
\(243\) | −797162. | − | 460241.i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | − | 1.76841e7i | − | 1.21735i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.17814e6 | 0.347831 | ||||||||
\(247\) | 7.81234e6 | − | 1.35314e7i | 0.518430 | − | 0.897947i | ||||
\(248\) | 3.78520e6 | − | 2.18539e6i | 0.248161 | − | 0.143276i | ||||
\(249\) | −103109. | − | 178591.i | −0.00667883 | − | 0.0115681i | ||||
\(250\) | 6.65175e6 | + | 3.84039e6i | 0.425712 | + | 0.245785i | ||||
\(251\) | 4.57737e6i | 0.289464i | 0.989471 | + | 0.144732i | \(0.0462320\pi\) | ||||
−0.989471 | + | 0.144732i | \(0.953768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −280772. | −0.0173377 | ||||||||
\(254\) | −6.35661e6 | + | 1.10100e7i | −0.387904 | + | 0.671870i | ||||
\(255\) | −180591. | + | 104264.i | −0.0108912 | + | 0.00628804i | ||||
\(256\) | 7.35104e6 | + | 1.27324e7i | 0.438156 | + | 0.758909i | ||||
\(257\) | 3.50429e6 | + | 2.02320e6i | 0.206443 | + | 0.119190i | 0.599657 | − | 0.800257i | \(-0.295304\pi\) |
−0.393214 | + | 0.919447i | \(0.628637\pi\) | |||||||
\(258\) | − | 334464.i | − | 0.0194756i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.46893e6 | −0.254263 | ||||||||
\(261\) | 5.22650e6 | − | 9.05256e6i | 0.293961 | − | 0.509155i | ||||
\(262\) | 1.74006e7 | − | 1.00463e7i | 0.967523 | − | 0.558600i | ||||
\(263\) | −1.48379e7 | − | 2.56999e7i | −0.815651 | − | 1.41275i | −0.908860 | − | 0.417102i | \(-0.863046\pi\) |
0.0932094 | − | 0.995647i | \(-0.470287\pi\) | |||||||
\(264\) | −127321. | − | 73508.8i | −0.00691972 | − | 0.00399510i | ||||
\(265\) | 1.48589e7i | 0.798453i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.59027e6 | 0.188623 | ||||||||
\(268\) | 4.80535e6 | − | 8.32312e6i | 0.249644 | − | 0.432396i | ||||
\(269\) | 1.77285e7 | − | 1.02355e7i | 0.910783 | − | 0.525841i | 0.0300997 | − | 0.999547i | \(-0.490418\pi\) |
0.880683 | + | 0.473706i | \(0.157084\pi\) | |||||||
\(270\) | 531452. | + | 920503.i | 0.0270006 | + | 0.0467664i | ||||
\(271\) | −2.19287e6 | − | 1.26606e6i | −0.110181 | − | 0.0636128i | 0.443897 | − | 0.896078i | \(-0.353596\pi\) |
−0.554078 | + | 0.832465i | \(0.686929\pi\) | |||||||
\(272\) | 130905.i | 0.00650502i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.85494e6 | −0.284623 | ||||||||
\(275\) | −114151. | + | 197716.i | −0.00548887 | + | 0.00950700i | ||||
\(276\) | 8.52198e6 | − | 4.92017e6i | 0.405334 | − | 0.234020i | ||||
\(277\) | −1.52864e7 | − | 2.64769e7i | −0.719229 | − | 1.24574i | −0.961306 | − | 0.275484i | \(-0.911162\pi\) |
0.242077 | − | 0.970257i | \(-0.422171\pi\) | |||||||
\(278\) | 466624. | + | 269405.i | 0.0217186 | + | 0.0125393i | ||||
\(279\) | − | 2.18851e6i | − | 0.100771i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.27089e7 | −1.02348 | −0.511738 | − | 0.859142i | \(-0.670998\pi\) | ||||
−0.511738 | + | 0.859142i | \(0.670998\pi\) | |||||||
\(282\) | 2.58598e6 | − | 4.47905e6i | 0.115313 | − | 0.199728i | ||||
\(283\) | −3.54922e7 | + | 2.04914e7i | −1.56593 | + | 0.904092i | −0.569297 | + | 0.822132i | \(0.692784\pi\) |
−0.996636 | + | 0.0819595i | \(0.973882\pi\) | |||||||
\(284\) | 7.65114e6 | + | 1.32522e7i | 0.334019 | + | 0.578538i | ||||
\(285\) | −7.99566e6 | − | 4.61630e6i | −0.345398 | − | 0.199416i | ||||
\(286\) | 143855.i | 0.00614934i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.21471e6 | 0.343886 | ||||||||
\(289\) | −1.20457e7 | + | 2.08638e7i | −0.499044 | + | 0.864369i | ||||
\(290\) | −1.04532e7 | + | 6.03517e6i | −0.428604 | + | 0.247454i | ||||
\(291\) | 5.16381e6 | + | 8.94398e6i | 0.209552 | + | 0.362954i | ||||
\(292\) | 7.62892e6 | + | 4.40456e6i | 0.306418 | + | 0.176911i | ||||
\(293\) | − | 2.94333e7i | − | 1.17014i | −0.810984 | − | 0.585069i | \(-0.801068\pi\) | ||
0.810984 | − | 0.585069i | \(-0.198932\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.03339e7 | −0.792053 | ||||||||
\(296\) | 8.03887e6 | − | 1.39237e7i | 0.309970 | − | 0.536884i | ||||
\(297\) | −63751.6 | + | 36807.0i | −0.00243345 | + | 0.00140495i | ||||
\(298\) | 1.41012e7 | + | 2.44240e7i | 0.532853 | + | 0.922928i | ||||
\(299\) | −2.05531e7 | − | 1.18663e7i | −0.768889 | − | 0.443918i | ||||
\(300\) | − | 8.00143e6i | − | 0.296349i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.79538e6 | 0.246714 | ||||||||
\(303\) | −1.46345e7 | + | 2.53477e7i | −0.526078 | + | 0.911193i | ||||
\(304\) | −5.01931e6 | + | 2.89790e6i | −0.178658 | + | 0.103148i | ||||
\(305\) | 1.26010e7 | + | 2.18255e7i | 0.444124 | + | 0.769245i | ||||
\(306\) | −203740. | − | 117629.i | −0.00711068 | − | 0.00410535i | ||||
\(307\) | − | 4.67295e6i | − | 0.161501i | −0.996734 | − | 0.0807506i | \(-0.974268\pi\) | ||
0.996734 | − | 0.0807506i | \(-0.0257317\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.40920e7 | −0.477635 | ||||||||
\(310\) | −1.26357e6 | + | 2.18856e6i | −0.0424143 | + | 0.0734638i | ||||
\(311\) | −2.77399e7 | + | 1.60156e7i | −0.922196 | + | 0.532430i | −0.884335 | − | 0.466853i | \(-0.845388\pi\) |
−0.0378610 | + | 0.999283i | \(0.512054\pi\) | |||||||
\(312\) | −6.21345e6 | − | 1.07620e7i | −0.204583 | − | 0.354348i | ||||
\(313\) | −1.88804e7 | − | 1.09006e7i | −0.615714 | − | 0.355483i | 0.159484 | − | 0.987200i | \(-0.449017\pi\) |
−0.775199 | + | 0.631718i | \(0.782350\pi\) | |||||||
\(314\) | 1.11752e7i | 0.360966i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.72799e7 | −0.547620 | ||||||||
\(317\) | −5.26241e6 | + | 9.11476e6i | −0.165199 | + | 0.286133i | −0.936726 | − | 0.350064i | \(-0.886160\pi\) |
0.771527 | + | 0.636196i | \(0.219493\pi\) | |||||||
\(318\) | −1.45177e7 | + | 8.38178e6i | −0.451456 | + | 0.260648i | ||||
\(319\) | −417980. | − | 723962.i | −0.0128761 | − | 0.0223020i | ||||
\(320\) | −6.11202e6 | − | 3.52878e6i | −0.186524 | − | 0.107690i | ||||
\(321\) | 1.31911e7i | 0.398811i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.04350e6 | 0.0606410 | ||||||||
\(324\) | 1.28999e6 | − | 2.23433e6i | 0.0379273 | − | 0.0656921i | ||||
\(325\) | −1.67122e7 | + | 9.64882e6i | −0.486838 | + | 0.281076i | ||||
\(326\) | 1.48490e7 | + | 2.57193e7i | 0.428594 | + | 0.742346i | ||||
\(327\) | 2.28872e7 | + | 1.32139e7i | 0.654560 | + | 0.377910i | ||||
\(328\) | 3.57730e7i | 1.01376i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 85004.0 | 0.00236536 | ||||||||
\(331\) | −2.03472e7 | + | 3.52425e7i | −0.561076 | + | 0.971812i | 0.436327 | + | 0.899788i | \(0.356279\pi\) |
−0.997403 | + | 0.0720239i | \(0.977054\pi\) | |||||||
\(332\) | 500566. | − | 289002.i | 0.0136788 | − | 0.00789744i | ||||
\(333\) | −4.02519e6 | − | 6.97183e6i | −0.109007 | − | 0.188805i | ||||
\(334\) | 2.12698e7 | + | 1.22801e7i | 0.570852 | + | 0.329581i | ||||
\(335\) | 1.36964e7i | 0.364310i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.05258e7 | −1.05887 | −0.529434 | − | 0.848351i | \(-0.677596\pi\) | ||||
−0.529434 | + | 0.848351i | \(0.677596\pi\) | |||||||
\(338\) | 4.79598e6 | − | 8.30688e6i | 0.124202 | − | 0.215123i | ||||
\(339\) | −2.06217e6 | + | 1.19059e6i | −0.0529328 | + | 0.0305607i | ||||
\(340\) | −292238. | − | 506172.i | −0.00743533 | − | 0.0128784i | ||||
\(341\) | −151574. | − | 87511.3i | −0.00382262 | − | 0.00220699i | ||||
\(342\) | − | 1.04160e7i | − | 0.260390i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.31063e6 | 0.0567617 | ||||||||
\(345\) | −7.01180e6 | + | 1.21448e7i | −0.170755 | + | 0.295756i | ||||
\(346\) | −1.07770e7 | + | 6.22209e6i | −0.260177 | + | 0.150213i | ||||
\(347\) | 8.26775e6 | + | 1.43202e7i | 0.197879 | + | 0.342736i | 0.947840 | − | 0.318745i | \(-0.103262\pi\) |
−0.749962 | + | 0.661481i | \(0.769928\pi\) | |||||||
\(348\) | 2.53731e7 | + | 1.46491e7i | 0.602054 | + | 0.347596i | ||||
\(349\) | − | 5.07209e6i | − | 0.119319i | −0.998219 | − | 0.0596597i | \(-0.980998\pi\) | ||
0.998219 | − | 0.0596597i | \(-0.0190015\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.22234e6 | −0.143891 | ||||||||
\(352\) | 328479. | − | 568942.i | 0.00753146 | − | 0.0130449i | ||||
\(353\) | 3.94332e7 | − | 2.27668e7i | 0.896475 | − | 0.517580i | 0.0204200 | − | 0.999791i | \(-0.493500\pi\) |
0.876055 | + | 0.482211i | \(0.160166\pi\) | |||||||
\(354\) | −1.14702e7 | − | 1.98669e7i | −0.258559 | − | 0.447837i | ||||
\(355\) | −1.88858e7 | − | 1.09037e7i | −0.422135 | − | 0.243720i | ||||
\(356\) | 1.00630e7i | 0.223038i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.70430e6 | 0.146118 | ||||||||
\(359\) | 2.00085e7 | − | 3.46558e7i | 0.432446 | − | 0.749018i | −0.564638 | − | 0.825339i | \(-0.690984\pi\) |
0.997083 | + | 0.0763210i | \(0.0243174\pi\) | |||||||
\(360\) | −6.35926e6 | + | 3.67152e6i | −0.136301 | + | 0.0786934i | ||||
\(361\) | 2.17150e7 | + | 3.76114e7i | 0.461570 | + | 0.799463i | ||||
\(362\) | −2.34815e7 | − | 1.35570e7i | −0.494994 | − | 0.285785i | ||||
\(363\) | − | 2.76100e7i | − | 0.577227i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.25540e7 | −0.258169 | ||||||||
\(366\) | −1.42162e7 | + | 2.46231e7i | −0.289961 | + | 0.502227i | ||||
\(367\) | −1.53736e7 | + | 8.87597e6i | −0.311013 | + | 0.179563i | −0.647380 | − | 0.762168i | \(-0.724135\pi\) |
0.336367 | + | 0.941731i | \(0.390802\pi\) | |||||||
\(368\) | 4.40169e6 | + | 7.62395e6i | 0.0883234 | + | 0.152981i | ||||
\(369\) | 1.55123e7 | + | 8.95606e6i | 0.308744 | + | 0.178253i | ||||
\(370\) | 9.29598e6i | 0.183523i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.13410e6 | 0.119158 | ||||||||
\(373\) | 2.69790e6 | − | 4.67291e6i | 0.0519876 | − | 0.0900452i | −0.838860 | − | 0.544346i | \(-0.816778\pi\) |
0.890848 | + | 0.454301i | \(0.150111\pi\) | |||||||
\(374\) | −16293.7 | + | 9407.18i | −0.000311462 | + | 0.000179823i | ||||
\(375\) | 1.32846e7 | + | 2.30096e7i | 0.251915 | + | 0.436330i | ||||
\(376\) | 3.09433e7 | + | 1.78651e7i | 0.582108 | + | 0.336080i | ||||
\(377\) | − | 7.06609e7i | − | 1.31873i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.47845e7 | 0.638951 | 0.319475 | − | 0.947595i | \(-0.396493\pi\) | ||||
0.319475 | + | 0.947595i | \(0.396493\pi\) | |||||||
\(380\) | 1.29388e7 | − | 2.24107e7i | 0.235801 | − | 0.408418i | ||||
\(381\) | −3.80854e7 | + | 2.19886e7i | −0.688627 | + | 0.397579i | ||||
\(382\) | 1.44283e7 | + | 2.49905e7i | 0.258836 | + | 0.448316i | ||||
\(383\) | 4.90000e7 | + | 2.82902e7i | 0.872168 | + | 0.503546i | 0.868068 | − | 0.496445i | \(-0.165362\pi\) |
0.00409994 | + | 0.999992i | \(0.498695\pi\) | |||||||
\(384\) | 2.57641e7i | 0.455011i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.43964e7 | −0.771944 | ||||||||
\(387\) | 578485. | − | 1.00196e6i | 0.00998065 | − | 0.0172870i | ||||
\(388\) | −2.50688e7 | + | 1.44735e7i | −0.429178 | + | 0.247786i | ||||
\(389\) | 1.30039e7 | + | 2.25234e7i | 0.220915 | + | 0.382636i | 0.955086 | − | 0.296329i | \(-0.0957624\pi\) |
−0.734171 | + | 0.678964i | \(0.762429\pi\) | |||||||
\(390\) | 6.22248e6 | + | 3.59255e6i | 0.104899 | + | 0.0605632i | ||||
\(391\) | − | 3.10392e6i | − | 0.0519254i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.95036e7 | 1.14506 | ||||||||
\(394\) | 5.38252e6 | − | 9.32280e6i | 0.0880029 | − | 0.152425i | ||||
\(395\) | 2.13266e7 | − | 1.23129e7i | 0.346043 | − | 0.199788i | ||||
\(396\) | −103165. | − | 178687.i | −0.00166129 | − | 0.00287745i | ||||
\(397\) | 1.18039e7 | + | 6.81496e6i | 0.188648 | + | 0.108916i | 0.591350 | − | 0.806415i | \(-0.298595\pi\) |
−0.402701 | + | 0.915331i | \(0.631929\pi\) | |||||||
\(398\) | − | 7.08217e7i | − | 1.12335i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.15825e6 | 0.111848 | ||||||||
\(401\) | 2.00929e7 | − | 3.48019e7i | 0.311609 | − | 0.539722i | −0.667102 | − | 0.744966i | \(-0.732465\pi\) |
0.978711 | + | 0.205244i | \(0.0657988\pi\) | |||||||
\(402\) | −1.33818e7 | + | 7.72599e6i | −0.205986 | + | 0.118926i | ||||
\(403\) | −7.39703e6 | − | 1.28120e7i | −0.113017 | − | 0.195751i | ||||
\(404\) | −7.10461e7 | − | 4.10185e7i | −1.07745 | − | 0.622064i | ||||
\(405\) | 3.67677e6i | 0.0553480i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −643815. | −0.00954944 | ||||||||
\(408\) | 812636. | − | 1.40753e6i | 0.0119651 | − | 0.0207241i | ||||
\(409\) | −6.55577e6 | + | 3.78497e6i | −0.0958194 | + | 0.0553214i | −0.547144 | − | 0.837038i | \(-0.684285\pi\) |
0.451325 | + | 0.892360i | \(0.350952\pi\) | |||||||
\(410\) | −1.03418e7 | − | 1.79125e7i | −0.150053 | − | 0.259899i | ||||
\(411\) | −1.75398e7 | − | 1.01266e7i | −0.252639 | − | 0.145861i | ||||
\(412\) | − | 3.94978e7i | − | 0.564783i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.58212e7 | −0.222965 | ||||||||
\(415\) | −411860. | + | 713363.i | −0.00576243 | + | 0.00998082i | ||||
\(416\) | 4.80907e7 | − | 2.77652e7i | 0.668008 | − | 0.385674i | ||||
\(417\) | 931921. | + | 1.61413e6i | 0.0128520 | + | 0.0222603i | ||||
\(418\) | −721404. | − | 416503.i | −0.00987756 | − | 0.00570281i | ||||
\(419\) | 3.12413e7i | 0.424705i | 0.977193 | + | 0.212353i | \(0.0681125\pi\) | ||||
−0.977193 | + | 0.212353i | \(0.931887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.98978e7 | 0.802721 | 0.401361 | − | 0.915920i | \(-0.368537\pi\) | ||||
0.401361 | + | 0.915920i | \(0.368537\pi\) | |||||||
\(422\) | 3.30634e6 | − | 5.72675e6i | 0.0439957 | − | 0.0762029i | ||||
\(423\) | 1.54938e7 | − | 8.94536e6i | 0.204709 | − | 0.118189i | ||||
\(424\) | −5.79052e7 | − | 1.00295e8i | −0.759661 | − | 1.31577i | ||||
\(425\) | −2.18574e6 | − | 1.26194e6i | −0.0284729 | − | 0.0164388i | ||||
\(426\) | − | 2.46028e7i | − | 0.318241i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.69730e7 | −0.471577 | ||||||||
\(429\) | −248811. | + | 430953.i | −0.00315135 | + | 0.00545830i | ||||
\(430\) | −1.15699e6 | + | 667991.i | −0.0145521 | + | 0.00840166i | ||||
\(431\) | −4.81510e7 | − | 8.33999e7i | −0.601414 | − | 1.04168i | −0.992607 | − | 0.121371i | \(-0.961271\pi\) |
0.391194 | − | 0.920308i | \(-0.372062\pi\) | |||||||
\(432\) | 1.99888e6 | + | 1.15406e6i | 0.0247934 | + | 0.0143145i | ||||
\(433\) | 1.11186e8i | 1.36958i | 0.728741 | + | 0.684790i | \(0.240106\pi\) | ||||
−0.728741 | + | 0.684790i | \(0.759894\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.17534e7 | −0.507252 | ||||||||
\(436\) | −3.70368e7 | + | 6.41497e7i | −0.446863 | + | 0.773989i | ||||
\(437\) | 1.19014e8 | − | 6.87129e7i | 1.42611 | − | 0.823368i | ||||
\(438\) | −7.08160e6 | − | 1.22657e7i | −0.0842770 | − | 0.145972i | ||||
\(439\) | 7.90517e7 | + | 4.56405e7i | 0.934367 | + | 0.539457i | 0.888190 | − | 0.459476i | \(-0.151963\pi\) |
0.0461770 | + | 0.998933i | \(0.485296\pi\) | |||||||
\(440\) | 587247.i | 0.00689386i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.59031e6 | −0.0184169 | ||||||||
\(443\) | 5.31635e7 | − | 9.20820e7i | 0.611509 | − | 1.05916i | −0.379477 | − | 0.925201i | \(-0.623896\pi\) |
0.990986 | − | 0.133963i | \(-0.0427705\pi\) | |||||||
\(444\) | 1.95411e7 | − | 1.12821e7i | 0.223254 | − | 0.128896i | ||||
\(445\) | −7.17049e6 | − | 1.24197e7i | −0.0813709 | − | 0.140939i | ||||
\(446\) | −1.41800e7 | − | 8.18681e6i | −0.159835 | − | 0.0922806i | ||||
\(447\) | 9.75570e7i | 1.09228i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.74221e7 | 0.855315 | 0.427657 | − | 0.903941i | \(-0.359339\pi\) | ||||
0.427657 | + | 0.903941i | \(0.359339\pi\) | |||||||
\(450\) | −6.43230e6 | + | 1.11411e7i | −0.0705877 | + | 0.122261i | ||||
\(451\) | 1.24057e6 | − | 716245.i | 0.0135236 | − | 0.00780786i | ||||
\(452\) | −3.33707e6 | − | 5.77997e6i | −0.0361368 | − | 0.0625907i | ||||
\(453\) | 2.03572e7 | + | 1.17532e7i | 0.218989 | + | 0.126433i | ||||
\(454\) | 2.67525e7i | 0.285889i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.19589e7 | 0.758909 | ||||||||
\(457\) | −9.50468e6 | + | 1.64626e7i | −0.0995838 | + | 0.172484i | −0.911512 | − | 0.411272i | \(-0.865084\pi\) |
0.811929 | + | 0.583757i | \(0.198418\pi\) | |||||||
\(458\) | −4.77517e7 | + | 2.75695e7i | −0.497042 | + | 0.286967i | ||||
\(459\) | −406900. | − | 704771.i | −0.00420774 | − | 0.00728803i | ||||
\(460\) | −3.40402e7 | − | 1.96531e7i | −0.349718 | − | 0.201910i | ||||
\(461\) | 1.05709e8i | 1.07897i | 0.841996 | + | 0.539483i | \(0.181380\pi\) | ||||
−0.841996 | + | 0.539483i | \(0.818620\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.82212e7 | −0.284336 | −0.142168 | − | 0.989843i | \(-0.545407\pi\) | ||||
−0.142168 | + | 0.989843i | \(0.545407\pi\) | |||||||
\(464\) | −1.31054e7 | + | 2.26993e7i | −0.131189 | + | 0.227226i | ||||
\(465\) | −7.57062e6 | + | 4.37090e6i | −0.0752961 | + | 0.0434722i | ||||
\(466\) | 2.73109e7 | + | 4.73039e7i | 0.269885 | + | 0.467454i | ||||
\(467\) | −1.49701e8 | − | 8.64297e7i | −1.46985 | − | 0.848619i | −0.470423 | − | 0.882441i | \(-0.655899\pi\) |
−0.999428 | + | 0.0338227i | \(0.989232\pi\) | |||||||
\(468\) | − | 1.74404e7i | − | 0.170145i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.06589e7 | −0.198982 | ||||||||
\(471\) | −1.93285e7 | + | 3.34779e7i | −0.184985 | + | 0.320403i | ||||
\(472\) | 1.37250e8 | − | 7.92412e7i | 1.30523 | − | 0.753572i | ||||
\(473\) | −46263.3 | − | 80130.4i | −0.000437173 | − | 0.000757206i | ||||
\(474\) | 2.40603e7 | + | 1.38912e7i | 0.225925 | + | 0.130438i | ||||
\(475\) | − | 1.11744e8i | − | 1.04267i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.79881e7 | −0.534298 | ||||||||
\(478\) | 2.68167e7 | − | 4.64480e7i | 0.245540 | − | 0.425288i | ||||
\(479\) | 2.41808e7 | − | 1.39608e7i | 0.220021 | − | 0.127029i | −0.385939 | − | 0.922524i | \(-0.626122\pi\) |
0.605960 | + | 0.795495i | \(0.292789\pi\) | |||||||
\(480\) | −1.64064e7 | − | 2.84167e7i | −0.148351 | − | 0.256951i | ||||
\(481\) | −4.71287e7 | − | 2.72098e7i | −0.423497 | − | 0.244506i | ||||
\(482\) | − | 4.48607e7i | − | 0.400613i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.73871e7 | 0.682546 | ||||||||
\(485\) | 2.06263e7 | − | 3.57258e7i | 0.180799 | − | 0.313153i | ||||
\(486\) | −3.59233e6 | + | 2.07404e6i | −0.0312945 | + | 0.0180679i | ||||
\(487\) | −2.68794e7 | − | 4.65566e7i | −0.232720 | − | 0.403082i | 0.725888 | − | 0.687813i | \(-0.241429\pi\) |
−0.958608 | + | 0.284731i | \(0.908096\pi\) | |||||||
\(488\) | −1.70108e8 | − | 9.82119e7i | −1.46374 | − | 0.845093i | ||||
\(489\) | 1.02731e8i | 0.878567i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.34867e7 | 0.789779 | 0.394889 | − | 0.918729i | \(-0.370783\pi\) | ||||
0.394889 | + | 0.918729i | \(0.370783\pi\) | |||||||
\(492\) | −2.51026e7 | + | 4.34790e7i | −0.210777 | + | 0.365076i | ||||
\(493\) | 8.00337e6 | − | 4.62075e6i | 0.0667932 | − | 0.0385631i | ||||
\(494\) | −3.52056e7 | − | 6.09778e7i | −0.292032 | − | 0.505814i | ||||
\(495\) | 254649. | + | 147022.i | 0.00209955 | + | 0.00121218i | ||||
\(496\) | 5.48770e6i | 0.0449723i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −929307. | −0.00752439 | ||||||||
\(499\) | −2.51376e6 | + | 4.35396e6i | −0.0202312 | + | 0.0350415i | −0.875964 | − | 0.482377i | \(-0.839774\pi\) |
0.855733 | + | 0.517418i | \(0.173107\pi\) | |||||||
\(500\) | −6.44927e7 | + | 3.72349e7i | −0.515941 | + | 0.297879i | ||||
\(501\) | 4.24790e7 | + | 7.35759e7i | 0.337802 | + | 0.585089i | ||||
\(502\) | 1.78639e7 | + | 1.03137e7i | 0.141210 | + | 0.0815277i | ||||
\(503\) | − | 1.45016e8i | − | 1.13949i | −0.821820 | − | 0.569747i | \(-0.807041\pi\) | ||
0.821820 | − | 0.569747i | \(-0.192959\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.16912e8 | 0.907789 | ||||||||
\(506\) | −632635. | + | 1.09576e6i | −0.00488317 | + | 0.00845790i | ||||
\(507\) | 2.87349e7 | − | 1.65901e7i | 0.220489 | − | 0.127299i | ||||
\(508\) | −6.16311e7 | − | 1.06748e8i | −0.470120 | − | 0.814272i | ||||
\(509\) | −1.14421e7 | − | 6.60609e6i | −0.0867665 | − | 0.0500946i | 0.455989 | − | 0.889985i | \(-0.349286\pi\) |
−0.542755 | + | 0.839891i | \(0.682619\pi\) | |||||||
\(510\) | 939715.i | 0.00708411i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.95237e7 | −0.294474 | ||||||||
\(513\) | 1.80155e7 | − | 3.12037e7i | 0.133442 | − | 0.231129i | ||||
\(514\) | 1.57918e7 | − | 9.11737e6i | 0.116290 | − | 0.0671399i | ||||
\(515\) | 2.81445e7 | + | 4.87476e7i | 0.206049 | + | 0.356888i | ||||
\(516\) | 2.80837e6 | + | 1.62141e6i | 0.0204411 | + | 0.0118017i | ||||
\(517\) | − | 1.43078e6i | − | 0.0103538i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.30466e7 | −0.307919 | ||||||||
\(520\) | −2.48190e7 | + | 4.29878e7i | −0.176512 | + | 0.305728i | ||||
\(521\) | 6.70170e7 | − | 3.86923e7i | 0.473884 | − | 0.273597i | −0.243980 | − | 0.969780i | \(-0.578453\pi\) |
0.717864 | + | 0.696183i | \(0.245120\pi\) | |||||||
\(522\) | −2.35527e7 | − | 4.07945e7i | −0.165588 | − | 0.286807i | ||||
\(523\) | 1.16424e8 | + | 6.72177e7i | 0.813840 | + | 0.469871i | 0.848288 | − | 0.529536i | \(-0.177634\pi\) |
−0.0344475 | + | 0.999407i | \(0.510967\pi\) | |||||||
\(524\) | 1.94809e8i | 1.35399i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.33731e8 | −0.918913 | ||||||||
\(527\) | 967433. | − | 1.67564e6i | 0.00660981 | − | 0.0114485i | ||||
\(528\) | 159857. | − | 92293.6i | 0.00108600 | − | 0.000627003i | ||||
\(529\) | −3.03516e7 | − | 5.25705e7i | −0.205029 | − | 0.355120i | ||||
\(530\) | 5.79893e7 | + | 3.34802e7i | 0.389512 | + | 0.224885i | ||||
\(531\) | − | 7.93546e7i | − | 0.530016i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.21084e8 | 0.799657 | ||||||||
\(534\) | 8.08962e6 | − | 1.40116e7i | 0.0531257 | − | 0.0920164i | ||||
\(535\) | 4.56315e7 | − | 2.63453e7i | 0.297991 | − | 0.172045i | ||||
\(536\) | −5.33747e7 | − | 9.24478e7i | −0.346610 | − | 0.600347i | ||||
\(537\) | 2.00843e7 | + | 1.15957e7i | 0.129698 | + | 0.0748813i | ||||
\(538\) | − | 9.22511e7i | − | 0.592413i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.03055e7 | −0.0654467 | ||||||||
\(541\) | 7.51469e7 | − | 1.30158e8i | 0.474590 | − | 0.822015i | −0.524986 | − | 0.851111i | \(-0.675930\pi\) |
0.999577 | + | 0.0290960i | \(0.00926284\pi\) | |||||||
\(542\) | −9.88197e6 | + | 5.70536e6i | −0.0620649 | + | 0.0358332i | ||||
\(543\) | −4.68962e7 | − | 8.12266e7i | −0.292913 | − | 0.507340i | ||||
\(544\) | 6.28962e6 | + | 3.63132e6i | 0.0390686 | + | 0.0225563i | ||||
\(545\) | − | 1.05563e8i | − | 0.652115i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.65431e7 | −0.406576 | −0.203288 | − | 0.979119i | \(-0.565163\pi\) | ||||
−0.203288 | + | 0.979119i | \(0.565163\pi\) | |||||||
\(548\) | 2.83835e7 | − | 4.91617e7i | 0.172474 | − | 0.298735i | ||||
\(549\) | −8.51757e7 | + | 4.91762e7i | −0.514753 | + | 0.297193i | ||||
\(550\) | 514412. | + | 890988.i | 0.00309188 | + | 0.00535530i | ||||
\(551\) | 3.54349e8 | + | 2.04583e8i | 2.11825 | + | 1.22297i | ||||
\(552\) | − | 1.09300e8i | − | 0.649835i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.37774e8 | −0.810284 | ||||||||
\(555\) | −1.60782e7 | + | 2.78483e7i | −0.0940500 | + | 0.162899i | ||||
\(556\) | −4.52420e6 | + | 2.61205e6i | −0.0263219 | + | 0.0151969i | ||||
\(557\) | 1.26843e8 | + | 2.19698e8i | 0.734007 | + | 1.27134i | 0.955158 | + | 0.296097i | \(0.0956852\pi\) |
−0.221151 | + | 0.975240i | \(0.570981\pi\) | |||||||
\(558\) | −8.54103e6 | − | 4.93117e6i | −0.0491595 | − | 0.0283823i | ||||
\(559\) | − | 7.82096e6i | − | 0.0447739i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −65082.2 | −0.000368616 | ||||||||
\(562\) | −5.11678e7 | + | 8.86252e7i | −0.288262 | + | 0.499285i | ||||
\(563\) | −1.43519e8 | + | 8.28606e7i | −0.804236 | + | 0.464326i | −0.844950 | − | 0.534845i | \(-0.820370\pi\) |
0.0407139 | + | 0.999171i | \(0.487037\pi\) | |||||||
\(564\) | 2.50726e7 | + | 4.34270e7i | 0.139753 | + | 0.242060i | ||||
\(565\) | 8.23711e6 | + | 4.75570e6i | 0.0456699 | + | 0.0263675i | ||||
\(566\) | 1.84685e8i | 1.01855i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.69968e8 | 0.927516 | ||||||||
\(569\) | −8.19891e7 | + | 1.42009e8i | −0.445061 | + | 0.770868i | −0.998056 | − | 0.0623160i | \(-0.980151\pi\) |
0.552996 | + | 0.833184i | \(0.313485\pi\) | |||||||
\(570\) | −3.60317e7 | + | 2.08029e7i | −0.194563 | + | 0.112331i | ||||
\(571\) | 1.70285e8 | + | 2.94942e8i | 0.914677 | + | 1.58427i | 0.807373 | + | 0.590042i | \(0.200889\pi\) |
0.107305 | + | 0.994226i | \(0.465778\pi\) | |||||||
\(572\) | −1.20790e6 | − | 697382.i | −0.00645421 | − | 0.00372634i | ||||
\(573\) | 9.98198e7i | 0.530582i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.69731e8 | −0.892808 | ||||||||
\(576\) | 1.37713e7 | − | 2.38526e7i | 0.0720623 | − | 0.124816i | ||||
\(577\) | −2.37115e8 | + | 1.36899e8i | −1.23433 | + | 0.712642i | −0.967930 | − | 0.251220i | \(-0.919168\pi\) |
−0.266402 | + | 0.963862i | \(0.585835\pi\) | |||||||
\(578\) | 5.42829e7 | + | 9.40207e7i | 0.281112 | + | 0.486900i | ||||
\(579\) | −1.33000e8 | − | 7.67875e7i | −0.685197 | − | 0.395599i | ||||
\(580\) | − | 1.17029e8i | − | 0.599804i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.65405e7 | 0.236081 | ||||||||
\(583\) | −2.31875e6 | + | 4.01619e6i | −0.0117017 | + | 0.0202679i | ||||
\(584\) | 8.47371e7 | − | 4.89230e7i | 0.425437 | − | 0.245626i | ||||
\(585\) | 1.24273e7 | + | 2.15246e7i | 0.0620737 | + | 0.107515i | ||||
\(586\) | −1.14868e8 | − | 6.63193e7i | −0.570831 | − | 0.329570i | ||||
\(587\) | − | 2.96429e8i | − | 1.46557i | −0.680460 | − | 0.732785i | \(-0.738220\pi\) | ||
0.680460 | − | 0.732785i | \(-0.261780\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.56661e7 | 0.419241 | ||||||||
\(590\) | −4.58164e7 | + | 7.93563e7i | −0.223082 | + | 0.386390i | ||||
\(591\) | 3.22492e7 | − | 1.86191e7i | 0.156227 | − | 0.0901978i | ||||
\(592\) | 1.00932e7 | + | 1.74819e7i | 0.0486477 | + | 0.0842603i | ||||
\(593\) | 1.12529e8 | + | 6.49684e7i | 0.539633 | + | 0.311557i | 0.744930 | − | 0.667142i | \(-0.232483\pi\) |
−0.205297 | + | 0.978700i | \(0.565816\pi\) | |||||||
\(594\) | 331735.i | 0.00158282i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.73439e8 | −1.29158 | ||||||||
\(597\) | 1.22492e8 | − | 2.12163e8i | 0.575686 | − | 0.997118i | ||||
\(598\) | −9.26206e7 | + | 5.34745e7i | −0.433116 | + | 0.250060i | ||||
\(599\) | 3.82426e7 | + | 6.62382e7i | 0.177937 | + | 0.308197i | 0.941174 | − | 0.337923i | \(-0.109724\pi\) |
−0.763237 | + | 0.646119i | \(0.776391\pi\) | |||||||
\(600\) | −7.69677e7 | − | 4.44373e7i | −0.356332 | − | 0.205728i | ||||
\(601\) | 1.12466e8i | 0.518080i | 0.965867 | + | 0.259040i | \(0.0834061\pi\) | ||||
−0.965867 | + | 0.259040i | \(0.916594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.34511e7 | −0.243784 | ||||||||
\(604\) | −3.29426e7 | + | 5.70583e7i | −0.149502 | + | 0.258945i | ||||
\(605\) | −9.55100e7 | + | 5.51427e7i | −0.431303 | + | 0.249013i | ||||
\(606\) | 6.59490e7 | + | 1.14227e8i | 0.296340 | + | 0.513276i | ||||
\(607\) | 4.03159e6 | + | 2.32764e6i | 0.0180264 | + | 0.0104076i | 0.508986 | − | 0.860775i | \(-0.330020\pi\) |
−0.490960 | + | 0.871182i | \(0.663354\pi\) | |||||||
\(608\) | 3.21553e8i | 1.43068i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.13570e8 | 0.500351 | ||||||||
\(611\) | 6.04695e7 | − | 1.04736e8i | 0.265102 | − | 0.459170i | ||||
\(612\) | 1.97538e6 | − | 1.14048e6i | 0.00861778 | − | 0.00497548i | ||||
\(613\) | 1.02768e8 | + | 1.78000e8i | 0.446147 | + | 0.772749i | 0.998131 | − | 0.0611054i | \(-0.0194626\pi\) |
−0.551984 | + | 0.833854i | \(0.686129\pi\) | |||||||
\(614\) | −1.82369e7 | − | 1.05291e7i | −0.0787856 | − | 0.0454869i | ||||
\(615\) | − | 7.15481e7i | − | 0.307590i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.85696e8 | 0.790583 | 0.395292 | − | 0.918556i | \(-0.370644\pi\) | ||||
0.395292 | + | 0.918556i | \(0.370644\pi\) | |||||||
\(618\) | −3.17521e7 | + | 5.49962e7i | −0.134526 | + | 0.233006i | ||||
\(619\) | −7.59648e7 | + | 4.38583e7i | −0.320288 | + | 0.184918i | −0.651521 | − | 0.758631i | \(-0.725869\pi\) |
0.331233 | + | 0.943549i | \(0.392535\pi\) | |||||||
\(620\) | −1.22510e7 | − | 2.12194e7i | −0.0514040 | − | 0.0890344i | ||||
\(621\) | −4.73960e7 | − | 2.73641e7i | −0.197910 | − | 0.114263i | ||||
\(622\) | 1.44346e8i | 0.599837i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.56025e7 | 0.0642157 | ||||||||
\(625\) | −3.87164e7 | + | 6.70588e7i | −0.158582 | + | 0.274673i | ||||
\(626\) | −8.50830e7 | + | 4.91227e7i | −0.346832 | + | 0.200244i | ||||
\(627\) | −1.44076e6 | − | 2.49546e6i | −0.00584505 | − | 0.0101239i | ||||
\(628\) | −9.38340e7 | − | 5.41751e7i | −0.378862 | − | 0.218736i | ||||
\(629\) | − | 7.11735e6i | − | 0.0286000i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.15732e8 | −1.65472 | −0.827362 | − | 0.561670i | \(-0.810159\pi\) | ||||
−0.827362 | + | 0.561670i | \(0.810159\pi\) | |||||||
\(632\) | −9.59668e7 | + | 1.66219e8i | −0.380163 | + | 0.658462i | ||||
\(633\) | 1.98099e7 | − | 1.14372e7i | 0.0781034 | − | 0.0450930i | ||||
\(634\) | 2.37146e7 | + | 4.10748e7i | 0.0930566 | + | 0.161179i | ||||
\(635\) | 1.52128e8 | + | 8.78313e7i | 0.594140 | + | 0.343027i | ||||
\(636\) | − | 1.62533e8i | − | 0.631785i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.76718e6 | −0.0145062 | ||||||||
\(639\) | 4.25527e7 | − | 7.37035e7i | 0.163089 | − | 0.282479i | ||||
\(640\) | 8.91246e7 | − | 5.14561e7i | 0.339983 | − | 0.196289i | ||||
\(641\) | −8.98600e7 | − | 1.55642e8i | −0.341187 | − | 0.590953i | 0.643466 | − | 0.765474i | \(-0.277496\pi\) |
−0.984653 | + | 0.174521i | \(0.944162\pi\) | |||||||
\(642\) | 5.14806e7 | + | 2.97223e7i | 0.194553 | + | 0.112325i | ||||
\(643\) | − | 8.10561e7i | − | 0.304897i | −0.988311 | − | 0.152448i | \(-0.951284\pi\) | ||
0.988311 | − | 0.152448i | \(-0.0487158\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.62140e6 | −0.0172224 | ||||||||
\(646\) | 4.60442e6 | − | 7.97508e6i | 0.0170796 | − | 0.0295827i | ||||
\(647\) | −9.06246e7 | + | 5.23221e7i | −0.334606 | + | 0.193185i | −0.657884 | − | 0.753119i | \(-0.728548\pi\) |
0.323278 | + | 0.946304i | \(0.395215\pi\) | |||||||
\(648\) | −1.43284e7 | − | 2.48175e7i | −0.0526590 | − | 0.0912081i | ||||
\(649\) | −5.49601e6 | − | 3.17312e6i | −0.0201054 | − | 0.0116079i | ||||
\(650\) | 8.69630e7i | 0.316661i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.87941e8 | −1.03887 | ||||||||
\(653\) | −2.36179e8 | + | 4.09074e8i | −0.848206 | + | 1.46914i | 0.0346020 | + | 0.999401i | \(0.488984\pi\) |
−0.882808 | + | 0.469734i | \(0.844350\pi\) | |||||||
\(654\) | 1.03139e8 | − | 5.95474e7i | 0.368714 | − | 0.212877i | ||||
\(655\) | −1.38812e8 | − | 2.40430e8i | −0.493975 | − | 0.855589i | ||||
\(656\) | −3.88972e7 | − | 2.24573e7i | −0.137787 | − | 0.0795511i | ||||
\(657\) | − | 4.89930e7i | − | 0.172758i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.73758e8 | 0.607141 | 0.303570 | − | 0.952809i | \(-0.401821\pi\) | ||||
0.303570 | + | 0.952809i | \(0.401821\pi\) | |||||||
\(660\) | −412082. | + | 713747.i | −0.00143335 | + | 0.00248263i | ||||
\(661\) | 1.91974e7 | − | 1.10836e7i | 0.0664720 | − | 0.0383776i | −0.466396 | − | 0.884576i | \(-0.654448\pi\) |
0.532868 | + | 0.846199i | \(0.321114\pi\) | |||||||
\(662\) | 9.16930e7 | + | 1.58817e8i | 0.316055 | + | 0.547423i | ||||
\(663\) | −4.76416e6 | − | 2.75059e6i | −0.0163473 | − | 0.00943811i | ||||
\(664\) | − | 6.42008e6i | − | 0.0219299i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.62783e7 | −0.122807 | ||||||||
\(667\) | 3.10746e8 | − | 5.38229e8i | 1.04720 | − | 1.81380i | ||||
\(668\) | −2.06223e8 | + | 1.19063e8i | −0.691843 | + | 0.399436i | ||||
\(669\) | −2.83196e7 | − | 4.90510e7i | −0.0945821 | − | 0.163821i | ||||
\(670\) | 5.34523e7 | + | 3.08607e7i | 0.177722 | + | 0.102608i | ||||
\(671\) | 7.86557e6i | 0.0260353i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.00045e8 | −1.31239 | −0.656195 | − | 0.754591i | \(-0.727835\pi\) | ||||
−0.656195 | + | 0.754591i | \(0.727835\pi\) | |||||||
\(674\) | −9.13128e7 | + | 1.58158e8i | −0.298230 | + | 0.516550i | ||||
\(675\) | −3.85389e7 | + | 2.22505e7i | −0.125311 | + | 0.0723482i | ||||
\(676\) | 4.64998e7 | + | 8.05401e7i | 0.150526 | + | 0.260719i | ||||
\(677\) | 2.51224e8 | + | 1.45044e8i | 0.809646 | + | 0.467449i | 0.846833 | − | 0.531859i | \(-0.178506\pi\) |
−0.0371872 | + | 0.999308i | \(0.511840\pi\) | |||||||
\(678\) | 1.07306e7i | 0.0344298i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.49199e6 | −0.0206467 | ||||||||
\(681\) | −4.62709e7 | + | 8.01435e7i | −0.146510 | + | 0.253762i | ||||
\(682\) | −683054. | + | 394362.i | −0.00215329 | + | 0.00124320i | ||||
\(683\) | −5.77014e7 | − | 9.99417e7i | −0.181102 | − | 0.313678i | 0.761154 | − | 0.648571i | \(-0.224633\pi\) |
−0.942256 | + | 0.334893i | \(0.891300\pi\) | |||||||
\(684\) | 8.74597e7 | + | 5.04949e7i | 0.273300 | + | 0.157790i | ||||
\(685\) | 8.08996e7i | 0.251695i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.90735e8 | −0.588249 | ||||||||
\(688\) | −1.45055e6 | + | 2.51243e6i | −0.00445418 | + | 0.00771487i | ||||
\(689\) | −3.39475e8 | + | 1.95996e8i | −1.03789 | + | 0.599224i | ||||
\(690\) | 3.15980e7 | + | 5.47294e7i | 0.0961862 | + | 0.166599i | ||||
\(691\) | −3.59314e8 | − | 2.07450e8i | −1.08903 | − | 0.628752i | −0.155712 | − | 0.987802i | \(-0.549767\pi\) |
−0.933318 | + | 0.359051i | \(0.883101\pi\) | |||||||
\(692\) | − | 1.20654e8i | − | 0.364101i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.45157e7 | 0.222930 | ||||||||
\(695\) | 3.72246e6 | − | 6.44750e6i | 0.0110886 | − | 0.0192060i | ||||
\(696\) | 2.81827e8 | − | 1.62713e8i | 0.835902 | − | 0.482608i | ||||
\(697\) | 7.91806e6 | + | 1.37145e7i | 0.0233841 | + | 0.0405024i | ||||
\(698\) | −1.97947e7 | − | 1.14285e7i | −0.0582079 | − | 0.0336063i | ||||
\(699\) | 1.88947e8i | 0.553232i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.13427e8 | 1.49047 | 0.745237 | − | 0.666800i | \(-0.232336\pi\) | ||||
0.745237 | + | 0.666800i | \(0.232336\pi\) | |||||||
\(702\) | −1.40202e7 | + | 2.42837e7i | −0.0405269 | + | 0.0701946i | ||||
\(703\) | 2.72902e8 | − | 1.57560e8i | 0.785491 | − | 0.453503i | ||||
\(704\) | −1.10134e6 | − | 1.90757e6i | −0.00315648 | − | 0.00546718i | ||||
\(705\) | −6.18885e7 | − | 3.57313e7i | −0.176621 | − | 0.101972i | ||||
\(706\) | − | 2.05193e8i | − | 0.583107i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.22420e8 | 0.626721 | ||||||||
\(709\) | −1.64200e8 | + | 2.84402e8i | −0.460716 | + | 0.797984i | −0.998997 | − | 0.0447818i | \(-0.985741\pi\) |
0.538281 | + | 0.842766i | \(0.319074\pi\) | |||||||
\(710\) | −8.51073e7 | + | 4.91367e7i | −0.237789 | + | 0.137288i | ||||
\(711\) | 4.80521e7 | + | 8.32287e7i | 0.133691 | + | 0.231560i | ||||
\(712\) | 9.67989e7 | + | 5.58869e7i | 0.268182 | + | 0.154835i | ||||
\(713\) | − | 1.30120e8i | − | 0.358985i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.98770e6 | 0.00543791 | ||||||||
\(716\) | −3.25011e7 | + | 5.62935e7i | −0.0885439 | + | 0.153363i | ||||
\(717\) | 1.60672e8 | − | 9.27638e7i | 0.435895 | − | 0.251664i | ||||
\(718\) | −9.01665e7 | − | 1.56173e8i | −0.243597 | − | 0.421923i | ||||
\(719\) | −9.79686e7 | − | 5.65622e7i | −0.263573 | − | 0.152174i | 0.362391 | − | 0.932026i | \(-0.381961\pi\) |
−0.625963 | + | 0.779853i | \(0.715294\pi\) | |||||||
\(720\) | − | 9.21952e6i | − | 0.0247008i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.95713e8 | 0.520006 | ||||||||
\(723\) | 7.75905e7 | − | 1.34391e8i | 0.205302 | − | 0.355594i | ||||
\(724\) | 2.27667e8 | − | 1.31444e8i | 0.599907 | − | 0.346357i | ||||
\(725\) | −2.52676e8 | − | 4.37648e8i | −0.663055 | − | 1.14845i | ||||
\(726\) | −1.07753e8 | − | 6.22110e7i | −0.281590 | − | 0.162576i | ||||
\(727\) | − | 9.97740e7i | − | 0.259666i | −0.991536 | − | 0.129833i | \(-0.958556\pi\) | ||
0.991536 | − | 0.129833i | \(-0.0414440\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | −2.82867e7 | + | 4.89940e7i | −0.0727133 | + | 0.125943i | ||||
\(731\) | 885838. | − | 511439.i | 0.00226779 | − | 0.00130931i | ||||
\(732\) | −1.37834e8 | − | 2.38736e8i | −0.351418 | − | 0.608673i | ||||
\(733\) | −3.13962e8 | − | 1.81266e8i | −0.797197 | − | 0.460262i | 0.0452931 | − | 0.998974i | \(-0.485578\pi\) |
−0.842490 | + | 0.538712i | \(0.818911\pi\) | |||||||
\(734\) | 7.99975e7i | 0.202296i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.88414e8 | 1.22505 | ||||||||
\(737\) | −2.13733e6 | + | 3.70197e6i | −0.00533912 | + | 0.00924762i | ||||
\(738\) | 6.99050e7 | − | 4.03596e7i | 0.173916 | − | 0.100410i | ||||
\(739\) | 1.02140e8 | + | 1.76912e8i | 0.253083 | + | 0.438352i | 0.964373 | − | 0.264546i | \(-0.0852221\pi\) |
−0.711290 | + | 0.702899i | \(0.751889\pi\) | |||||||
\(740\) | −7.80549e7 | − | 4.50650e7i | −0.192622 | − | 0.111210i | ||||
\(741\) | − | 2.43565e8i | − | 0.598631i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.63900e8 | 0.643389 | 0.321695 | − | 0.946844i | \(-0.395748\pi\) | ||||
0.321695 | + | 0.946844i | \(0.395748\pi\) | |||||||
\(744\) | 3.40668e7 | − | 5.90054e7i | 0.0827203 | − | 0.143276i | ||||
\(745\) | 3.37474e8 | − | 1.94841e8i | 0.816153 | − | 0.471206i | ||||
\(746\) | −1.21579e7 | − | 2.10580e7i | −0.0292847 | − | 0.0507226i | ||||
\(747\) | −2.78396e6 | − | 1.60732e6i | −0.00667883 | − | 0.00385603i | ||||
\(748\) | − | 182416.i | − | 0.000435872i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.19732e8 | 0.283808 | ||||||||
\(751\) | 3.68938e8 | − | 6.39019e8i | 0.871031 | − | 1.50867i | 0.0100992 | − | 0.999949i | \(-0.496785\pi\) |
0.860932 | − | 0.508721i | \(-0.169881\pi\) | |||||||
\(752\) | −3.88508e7 | + | 2.24305e7i | −0.0913579 | + | 0.0527455i | ||||
\(753\) | 3.56770e7 | + | 6.17945e7i | 0.0835611 | + | 0.144732i | ||||
\(754\) | −2.75766e8 | − | 1.59213e8i | −0.643318 | − | 0.371420i | ||||
\(755\) | − | 9.38940e7i | − | 0.218171i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.43307e8 | −0.330355 | −0.165177 | − | 0.986264i | \(-0.552820\pi\) | ||||
−0.165177 | + | 0.986264i | \(0.552820\pi\) | |||||||
\(758\) | 7.83765e7 | − | 1.35752e8i | 0.179961 | − | 0.311701i | ||||
\(759\) | −3.79042e6 | + | 2.18840e6i | −0.00866885 | + | 0.00500496i | ||||
\(760\) | −1.43716e8 | − | 2.48924e8i | −0.327390 | − | 0.567056i | ||||
\(761\) | 6.67428e8 | + | 3.85340e8i | 1.51444 | + | 0.874360i | 0.999857 | + | 0.0169164i | \(0.00538490\pi\) |
0.514578 | + | 0.857443i | \(0.327948\pi\) | |||||||
\(762\) | 1.98179e8i | 0.447913i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.79781e8 | −0.627391 | ||||||||
\(765\) | −1.62532e6 | + | 2.81514e6i | −0.00363040 | + | 0.00628804i | ||||
\(766\) | 2.20814e8 | − | 1.27487e8i | 0.491293 | − | 0.283648i | ||||
\(767\) | −2.68213e8 | − | 4.64559e8i | −0.594421 | − | 1.02957i | ||||
\(768\) | 1.98478e8 | + | 1.14591e8i | 0.438156 | + | 0.252970i | ||||
\(769\) | 6.97335e8i | 1.53343i | 0.641990 | + | 0.766713i | \(0.278109\pi\) | ||||
−0.641990 | + | 0.766713i | \(0.721891\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.30772e7 | 0.137629 | ||||||||
\(772\) | 2.15225e8 | − | 3.72780e8i | 0.467779 | − | 0.810216i | ||||
\(773\) | 7.04415e8 | − | 4.06694e8i | 1.52507 | − | 0.880500i | 0.525513 | − | 0.850786i | \(-0.323874\pi\) |
0.999558 | − | 0.0297144i | \(-0.00945977\pi\) | |||||||
\(774\) | −2.60689e6 | − | 4.51526e6i | −0.00562211 | − | 0.00973778i | ||||
\(775\) | −9.16290e7 | − | 5.29021e7i | −0.196847 | − | 0.113649i | ||||
\(776\) | 3.21523e8i | 0.688061i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.17202e8 | 0.248883 | ||||||||
\(779\) | −3.50572e8 | + | 6.07208e8i | −0.741591 | + | 1.28447i | ||||
\(780\) | −6.03306e7 | + | 3.48319e7i | −0.127132 | + | 0.0733995i | ||||
\(781\) | −3.40308e6 | − | 5.89431e6i | −0.00714364 | − | 0.0123731i | ||||
\(782\) | −1.21135e7 | − | 6.99375e6i | −0.0253309 | − | 0.0146248i | ||||
\(783\) | − | 1.62946e8i | − | 0.339436i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.54411e8 | 0.319206 | ||||||||
\(786\) | 1.56606e8 | − | 2.71249e8i | 0.322508 | − | 0.558600i | ||||
\(787\) | −3.22928e8 | + | 1.86443e8i | −0.662494 | + | 0.382491i | −0.793227 | − | 0.608927i | \(-0.791600\pi\) |
0.130733 | + | 0.991418i | \(0.458267\pi\) | |||||||
\(788\) | 5.21867e7 | + | 9.03900e7i | 0.106655 | + | 0.184732i | ||||
\(789\) | −4.00622e8 | − | 2.31299e8i | −0.815651 | − | 0.470916i | ||||
\(790\) | − | 1.10974e8i | − | 0.225081i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.29178e6 | −0.00461314 | ||||||||
\(793\) | −3.32425e8 | + | 5.75777e8i | −0.666614 | + | 1.15461i | ||||
\(794\) | 5.31930e7 | − | 3.07110e7i | 0.106266 | − | 0.0613525i | ||||
\(795\) | 1.15814e8 | + | 2.00595e8i | 0.230494 | + | 0.399227i | ||||
\(796\) | 5.94663e8 | + | 3.43329e8i | 1.17905 | + | 0.680724i | ||||
\(797\) | 4.15047e8i | 0.819827i | 0.912124 | + | 0.409913i | \(0.134441\pi\) | ||||
−0.912124 | + | 0.409913i | \(0.865559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.58172e7 | 0.0310091 | ||||||||
\(800\) | 1.98571e8 | − | 3.43935e8i | 0.387834 | − | 0.671748i | ||||
\(801\) | 4.84687e7 | − | 2.79834e7i | 0.0943113 | − | 0.0544507i | ||||
\(802\) | −9.05468e7 | − | 1.56832e8i | −0.175530 | − | 0.304026i | ||||
\(803\) | −3.39320e6 | − | 1.95906e6i | −0.00655334 | − | 0.00378357i | ||||
\(804\) | − | 1.49816e8i | − | 0.288264i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.66681e7 | −0.127325 | ||||||||
\(807\) | 1.59556e8 | − | 2.76360e8i | 0.303594 | − | 0.525841i | ||||
\(808\) | −7.89133e8 | + | 4.55606e8i | −1.49595 | + | 0.863686i | ||||
\(809\) | 1.17384e8 | + | 2.03314e8i | 0.221698 | + | 0.383992i | 0.955324 | − | 0.295562i | \(-0.0955068\pi\) |
−0.733626 | + | 0.679554i | \(0.762173\pi\) | |||||||
\(810\) | 1.43492e7 | + | 8.28452e6i | 0.0270006 | + | 0.0155888i | ||||
\(811\) | 8.08164e7i | 0.151508i | 0.997127 | + | 0.0757542i | \(0.0241364\pi\) | ||||
−0.997127 | + | 0.0757542i | \(0.975864\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.94717e7 | −0.0734538 | ||||||||
\(814\) | −1.45065e6 | + | 2.51259e6i | −0.00268961 | + | 0.00465853i | ||||
\(815\) | 3.55372e8 | − | 2.05174e8i | 0.656463 | − | 0.379009i | ||||
\(816\) | 1.02030e6 | + | 1.76721e6i | 0.00187784 | + | 0.00325251i | ||||
\(817\) | 3.92204e7 | + | 2.26439e7i | 0.0719194 | + | 0.0415227i | ||||
\(818\) | 3.41133e7i | 0.0623252i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.00539e8 | 0.363713 | ||||||||
\(821\) | 3.22564e7 | − | 5.58697e7i | 0.0582890 | − | 0.100959i | −0.835408 | − | 0.549630i | \(-0.814769\pi\) |
0.893697 | + | 0.448670i | \(0.148102\pi\) | |||||||
\(822\) | −7.90416e7 | + | 4.56347e7i | −0.142312 | + | 0.0821637i | ||||
\(823\) | 7.83609e7 | + | 1.35725e8i | 0.140572 | + | 0.243478i | 0.927712 | − | 0.373296i | \(-0.121772\pi\) |
−0.787140 | + | 0.616774i | \(0.788439\pi\) | |||||||
\(824\) | −3.79939e8 | − | 2.19358e8i | −0.679098 | − | 0.392077i | ||||
\(825\) | 3.55888e6i | 0.00633800i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.46564e8 | −1.14313 | −0.571565 | − | 0.820557i | \(-0.693663\pi\) | ||||
−0.571565 | + | 0.820557i | \(0.693663\pi\) | |||||||
\(828\) | 7.66978e7 | − | 1.32845e8i | 0.135111 | − | 0.234020i | ||||
\(829\) | 8.11604e8 | − | 4.68580e8i | 1.42456 | − | 0.822470i | 0.427875 | − | 0.903838i | \(-0.359262\pi\) |
0.996684 | + | 0.0813680i | \(0.0259289\pi\) | |||||||
\(830\) | 1.85601e6 | + | 3.21470e6i | 0.00324598 | + | 0.00562221i | ||||
\(831\) | −4.12734e8 | − | 2.38292e8i | −0.719229 | − | 0.415247i | ||||
\(832\) | − | 1.86185e8i | − | 0.323277i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.39923e6 | 0.0144791 | ||||||||
\(835\) | 1.69678e8 | − | 2.93891e8i | 0.291452 | − | 0.504809i | ||||
\(836\) | 6.99444e6 | − | 4.03824e6i | 0.0119711 | − | 0.00691152i | ||||
\(837\) | −1.70578e7 | − | 2.95449e7i | −0.0290902 | − | 0.0503856i | ||||
\(838\) | 1.21924e8 | + | 7.03931e7i | 0.207185 | + | 0.119618i | ||||
\(839\) | − | 7.25284e8i | − | 1.22807i | −0.789280 | − | 0.614034i | \(-0.789546\pi\) | ||
0.789280 | − | 0.614034i | \(-0.210454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.25559e9 | 2.11086 | ||||||||
\(842\) | 1.34962e8 | − | 2.33761e8i | 0.226087 | − | 0.391594i | ||||
\(843\) | −3.06570e8 | + | 1.76998e8i | −0.511738 | + | 0.295452i | ||||
\(844\) | 3.20570e7 | + | 5.55243e7i | 0.0533206 | + | 0.0923540i | ||||
\(845\) | −1.14779e8 | − | 6.62676e7i | −0.190236 | − | 0.109833i | ||||
\(846\) | − | 8.06228e7i | − | 0.133152i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.45405e8 | 0.238447 | ||||||||
\(849\) | −3.19429e8 | + | 5.53268e8i | −0.521978 | + | 0.904092i | ||||
\(850\) | −9.84983e6 | + | 5.68680e6i | −0.0160388 | + | 0.00926001i | ||||
\(851\) | −2.39322e8 | − | 4.14517e8i | −0.388323 | − | 0.672595i | ||||
\(852\) | 2.06581e8 | + | 1.19269e8i | 0.334019 | + | 0.192846i | ||||
\(853\) | 1.38063e8i | 0.222449i | 0.993795 | + | 0.111224i | \(0.0354772\pi\) | ||||
−0.993795 | + | 0.111224i | \(0.964523\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.43922e8 | −0.230265 | ||||||||
\(856\) | −2.05336e8 | + | 3.55652e8i | −0.327373 | + | 0.567027i | ||||
\(857\) | −6.12238e8 | + | 3.53476e8i | −0.972698 | + | 0.561588i | −0.900058 | − | 0.435771i | \(-0.856476\pi\) |
−0.0726405 | + | 0.997358i | \(0.523143\pi\) | |||||||
\(858\) | 1.12124e6 | + | 1.94205e6i | 0.00177516 | + | 0.00307467i | ||||
\(859\) | −2.85515e8 | − | 1.64842e8i | −0.450453 | − | 0.260069i | 0.257569 | − | 0.966260i | \(-0.417079\pi\) |
−0.708021 | + | 0.706191i | \(0.750412\pi\) | |||||||
\(860\) | − | 1.29531e7i | − | 0.0203648i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.33976e8 | −0.677554 | ||||||||
\(863\) | 4.84152e8 | − | 8.38576e8i | 0.753268 | − | 1.30470i | −0.192962 | − | 0.981206i | \(-0.561810\pi\) |
0.946231 | − | 0.323493i | \(-0.104857\pi\) | |||||||
\(864\) | 1.10899e8 | − | 6.40273e7i | 0.171943 | − | 0.0992714i | ||||
\(865\) | 8.59726e7 | + | 1.48909e8i | 0.132835 | + | 0.230077i | ||||
\(866\) | 4.33922e8 | + | 2.50525e8i | 0.668126 | + | 0.385743i | ||||
\(867\) | 3.75548e8i | 0.576246i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.68577e6 | 0.0117119 | ||||||||
\(870\) | −9.40789e7 | + | 1.62949e8i | −0.142868 | + | 0.247454i | ||||
\(871\) | −3.12915e8 | + | 1.80661e8i | −0.473556 | + | 0.273408i | ||||
\(872\) | 4.11381e8 | + | 7.12532e8i | 0.620433 | + | 1.07462i | ||||
\(873\) | 1.39423e8 | + | 8.04959e7i | 0.209552 | + | 0.120985i | ||||
\(874\) | − | 6.19296e8i | − | 0.927608i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.37321e8 | 0.204279 | ||||||||
\(877\) | −1.33382e8 | + | 2.31025e8i | −0.197742 | + | 0.342500i | −0.947796 | − | 0.318877i | \(-0.896694\pi\) |
0.750054 | + | 0.661377i | \(0.230028\pi\) | |||||||
\(878\) | 3.56239e8 | − | 2.05675e8i | 0.526330 | − | 0.303877i | ||||
\(879\) | −2.29410e8 | − | 3.97350e8i | −0.337790 | − | 0.585069i | ||||
\(880\) | −638534. | − | 368657.i | −0.000936992 | − | 0.000540972i | ||||
\(881\) | 6.08909e8i | 0.890481i | 0.895411 | + | 0.445241i | \(0.146882\pi\) | ||||
−0.895411 | + | 0.445241i | \(0.853118\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.56488e8 | −0.953553 | −0.476777 | − | 0.879025i | \(-0.658195\pi\) | ||||
−0.476777 | + | 0.879025i | \(0.658195\pi\) | |||||||
\(884\) | 7.70952e6 | − | 1.33533e7i | 0.0111602 | − | 0.0193300i | ||||
\(885\) | −2.74507e8 | + | 1.58487e8i | −0.396027 | + | 0.228646i | ||||
\(886\) | −2.39577e8 | − | 4.14959e8i | −0.344464 | − | 0.596628i | ||||
\(887\) | 6.04195e7 | + | 3.48832e7i | 0.0865778 | + | 0.0499857i | 0.542664 | − | 0.839950i | \(-0.317416\pi\) |
−0.456086 | + | 0.889936i | \(0.650749\pi\) | |||||||
\(888\) | − | 2.50627e8i | − | 0.357923i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.46263e7 | −0.0916726 | ||||||||
\(891\) | −573765. | + | 993789.i | −0.000811149 | + | 0.00140495i | ||||
\(892\) | 1.37483e8 | − | 7.93760e7i | 0.193711 | − | 0.111839i | ||||
\(893\) | 3.50153e8 | + | 6.06482e8i | 0.491703 | + | 0.851655i | ||||
\(894\) | 3.80732e8 | + | 2.19816e8i | 0.532853 | + | 0.307643i | ||||
\(895\) | − | 9.26355e7i | − | 0.129214i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.69956e8 | −0.512593 | ||||||||
\(898\) | 1.74448e8 | − | 3.02152e8i | 0.240900 | − | 0.417251i | ||||
\(899\) | 3.35512e8 | − | 1.93708e8i | 0.461773 | − | 0.266605i | ||||
\(900\) | −6.23650e7 | − | 1.08019e8i | −0.0855486 | − | 0.148175i | ||||
\(901\) | −4.43988e7 | − | 2.56337e7i | −0.0607011 | − | 0.0350458i | ||||
\(902\) | − | 6.45539e6i | − | 0.00879635i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.41319e7 | −0.100346 | ||||||||
\(905\) | −1.87322e8 | + | 3.24451e8i | −0.252722 | + | 0.437728i | ||||
\(906\) | 9.17377e7 | − | 5.29648e7i | 0.123357 | − | 0.0712201i | ||||
\(907\) | −4.31361e8 | − | 7.47140e8i | −0.578122 | − | 1.00134i | −0.995695 | − | 0.0926927i | \(-0.970453\pi\) |
0.417573 | − | 0.908643i | \(-0.362881\pi\) | |||||||
\(908\) | −2.24631e8 | − | 1.29691e8i | −0.300063 | − | 0.173241i | ||||
\(909\) | 4.56258e8i | 0.607462i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.41296e8 | −0.186885 | −0.0934425 | − | 0.995625i | \(-0.529787\pi\) | ||||
−0.0934425 | + | 0.995625i | \(0.529787\pi\) | |||||||
\(912\) | −4.51738e7 | + | 7.82433e7i | −0.0595528 | + | 0.103148i | ||||
\(913\) | −222642. | + | 128542.i | −0.000292547 | + | 0.000168902i | ||||
\(914\) | 4.28319e7 | + | 7.41871e7i | 0.0560956 | + | 0.0971605i | ||||
\(915\) | 3.40226e8 | + | 1.96429e8i | 0.444124 | + | 0.256415i | ||||
\(916\) | − | 5.34605e8i | − | 0.695579i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.66731e6 | −0.00474045 | ||||||||
\(919\) | −5.59845e8 | + | 9.69681e8i | −0.721309 | + | 1.24934i | 0.239166 | + | 0.970979i | \(0.423126\pi\) |
−0.960475 | + | 0.278366i | \(0.910207\pi\) | |||||||
\(920\) | −3.78096e8 | + | 2.18294e8i | −0.485555 | + | 0.280335i | ||||
\(921\) | −3.64220e7 | − | 6.30848e7i | −0.0466214 | − | 0.0807506i | ||||
\(922\) | 4.12546e8 | + | 2.38183e8i | 0.526356 | + | 0.303892i | ||||
\(923\) | − | 5.75302e8i | − | 0.731629i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.89197e8 | −0.491750 | ||||||||
\(926\) | −6.35881e7 | + | 1.10138e8i | −0.0800834 | + | 0.138709i | ||||
\(927\) | −1.90242e8 | + | 1.09836e8i | −0.238817 | + | 0.137881i | ||||
\(928\) | 7.27094e8 | + | 1.25936e9i | 0.909801 | + | 1.57582i | ||||
\(929\) | −1.14228e9 | − | 6.59494e8i | −1.42470 | − | 0.822553i | −0.428007 | − | 0.903775i | \(-0.640784\pi\) |
−0.996696 | + | 0.0812225i | \(0.974118\pi\) | |||||||
\(930\) | 3.93941e7i | 0.0489759i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.29591e8 | −0.654173 | ||||||||
\(933\) | −2.49659e8 | + | 4.32422e8i | −0.307399 | + | 0.532430i | ||||
\(934\) | −6.74612e8 | + | 3.89488e8i | −0.827968 | + | 0.478028i | ||||
\(935\) | 129982. | + | 225136.i | 0.000159019 | + | 0.000275429i | ||||
\(936\) | −1.67763e8 | − | 9.68581e7i | −0.204583 | − | 0.118116i | ||||
\(937\) | − | 1.04041e6i | − | 0.00126469i | −1.00000 | 0.000632345i | \(-0.999799\pi\) | |||
1.00000 | 0.000632345i | \(-0.000201282\pi\) | ||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.39848e8 | −0.410476 | ||||||||
\(940\) | 1.00150e8 | − | 1.73465e8i | 0.120578 | − | 0.208847i | ||||
\(941\) | −5.93842e8 | + | 3.42855e8i | −0.712692 | + | 0.411473i | −0.812057 | − | 0.583578i | \(-0.801652\pi\) |
0.0993650 | + | 0.995051i | \(0.468319\pi\) | |||||||
\(942\) | 8.71021e7 | + | 1.50865e8i | 0.104202 | + | 0.180483i | ||||
\(943\) | 9.22302e8 | + | 5.32491e8i | 1.09986 | + | 0.635005i | ||||
\(944\) | 1.98982e8i | 0.236536i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −416963. | −0.000492520 | ||||||||
\(947\) | −2.67038e8 | + | 4.62523e8i | −0.314429 | + | 0.544608i | −0.979316 | − | 0.202337i | \(-0.935146\pi\) |
0.664887 | + | 0.746944i | \(0.268480\pi\) | |||||||
\(948\) | −2.33278e8 | + | 1.34683e8i | −0.273810 | + | 0.158084i | ||||
\(949\) | −1.65593e8 | − | 2.86816e8i | −0.193751 | − | 0.335586i | ||||
\(950\) | −4.36101e8 | − | 2.51783e8i | −0.508647 | − | 0.293667i | ||||
\(951\) | 1.64066e8i | 0.190755i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.66817e8 | 1.00150 | 0.500748 | − | 0.865593i | \(-0.333058\pi\) | ||||
0.500748 | + | 0.865593i | \(0.333058\pi\) | |||||||
\(954\) | −1.30659e8 | + | 2.26308e8i | −0.150485 | + | 0.260648i | ||||
\(955\) | 3.45302e8 | − | 1.99360e8i | 0.396450 | − | 0.228891i | ||||
\(956\) | 2.60004e8 | + | 4.50340e8i | 0.297582 | + | 0.515427i | ||||
\(957\) | −1.12855e7 | − | 6.51566e6i | −0.0128761 | − | 0.00743400i | ||||
\(958\) | − | 1.25826e8i | − | 0.143112i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.10016e8 | −0.124349 | ||||||||
\(961\) | −4.03196e8 | + | 6.98356e8i | −0.454303 | + | 0.786876i | ||||
\(962\) | −2.12381e8 | + | 1.22618e8i | −0.238556 | + | 0.137730i | ||||
\(963\) | 1.02815e8 | + | 1.78080e8i | 0.115127 | + | 0.199406i | ||||
\(964\) | 3.76679e8 | + | 2.17475e8i | 0.420475 | + | 0.242761i | ||||
\(965\) | 6.13440e8i | 0.682637i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.71422e8 | 0.189577 | 0.0947886 | − | 0.995497i | \(-0.469782\pi\) | ||||
0.0947886 | + | 0.995497i | \(0.469782\pi\) | |||||||
\(968\) | 4.29782e8 | − | 7.44405e8i | 0.473830 | − | 0.820698i | ||||
\(969\) | 2.75872e7 | − | 1.59275e7i | 0.0303205 | − | 0.0175056i | ||||
\(970\) | −9.29506e7 | − | 1.60995e8i | −0.101844 | − | 0.176400i | ||||
\(971\) | −9.77273e8 | − | 5.64229e8i | −1.06748 | − | 0.616308i | −0.139985 | − | 0.990154i | \(-0.544706\pi\) |
−0.927491 | + | 0.373846i | \(0.878039\pi\) | |||||||
\(972\) | − | 4.02180e7i | − | 0.0437947i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.42259e8 | −0.262183 | ||||||||
\(975\) | −1.50410e8 | + | 2.60518e8i | −0.162279 | + | 0.281076i | ||||
\(976\) | 2.13578e8 | − | 1.23309e8i | 0.229725 | − | 0.132632i | ||||
\(977\) | 2.09709e8 | + | 3.63227e8i | 0.224871 | + | 0.389488i | 0.956281 | − | 0.292450i | \(-0.0944706\pi\) |
−0.731410 | + | 0.681938i | \(0.761137\pi\) | |||||||
\(978\) | 4.00924e8 | + | 2.31474e8i | 0.428594 | + | 0.247449i | ||||
\(979\) | − | 4.47585e6i | − | 0.00477010i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.11970e8 | 0.436373 | ||||||||
\(982\) | 2.10645e8 | − | 3.64847e8i | 0.222442 | − | 0.385280i | ||||
\(983\) | 5.99335e8 | − | 3.46026e8i | 0.630971 | − | 0.364291i | −0.150157 | − | 0.988662i | \(-0.547978\pi\) |
0.781128 | + | 0.624371i | \(0.214645\pi\) | |||||||
\(984\) | 2.78823e8 | + | 4.82936e8i | 0.292647 | + | 0.506879i | ||||
\(985\) | −1.28816e8 | − | 7.43720e7i | −0.134791 | − | 0.0778217i | ||||
\(986\) | − | 4.16459e7i | − | 0.0434452i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.82678e8 | 0.707856 | ||||||||
\(989\) | 3.43944e7 | − | 5.95728e7i | 0.0355548 | − | 0.0615828i | ||||
\(990\) | 1.14755e6 | − | 662540.i | 0.00118268 | − | 0.000682821i | ||||
\(991\) | 4.13436e8 | + | 7.16091e8i | 0.424802 | + | 0.735779i | 0.996402 | − | 0.0847535i | \(-0.0270103\pi\) |
−0.571600 | + | 0.820533i | \(0.693677\pi\) | |||||||
\(992\) | 2.63669e8 | + | 1.52230e8i | 0.270100 | + | 0.155942i | ||||
\(993\) | 6.34364e8i | 0.647875i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.78566e8 | −0.993393 | ||||||||
\(996\) | 4.50509e6 | − | 7.80304e6i | 0.00455959 | − | 0.00789744i | ||||
\(997\) | −1.48696e9 | + | 8.58496e8i | −1.50042 | + | 0.866269i | −0.500421 | + | 0.865782i | \(0.666822\pi\) |
−1.00000 | 0.000486585i | \(0.999845\pi\) | ||||||||
\(998\) | 1.13280e7 | + | 1.96207e7i | 0.0113963 | + | 0.0197389i | ||||
\(999\) | −1.08680e8 | − | 6.27465e7i | −0.109007 | − | 0.0629351i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 147.7.f.d.19.3 | 8 | ||
7.2 | even | 3 | 147.7.d.b.97.4 | 8 | |||
7.3 | odd | 6 | inner | 147.7.f.d.31.3 | 8 | ||
7.4 | even | 3 | 21.7.f.a.10.3 | ✓ | 8 | ||
7.5 | odd | 6 | 147.7.d.b.97.3 | 8 | |||
7.6 | odd | 2 | 21.7.f.a.19.3 | yes | 8 | ||
21.2 | odd | 6 | 441.7.d.c.244.5 | 8 | |||
21.5 | even | 6 | 441.7.d.c.244.6 | 8 | |||
21.11 | odd | 6 | 63.7.m.d.10.2 | 8 | |||
21.20 | even | 2 | 63.7.m.d.19.2 | 8 | |||
28.11 | odd | 6 | 336.7.bh.d.241.4 | 8 | |||
28.27 | even | 2 | 336.7.bh.d.145.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.7.f.a.10.3 | ✓ | 8 | 7.4 | even | 3 | ||
21.7.f.a.19.3 | yes | 8 | 7.6 | odd | 2 | ||
63.7.m.d.10.2 | 8 | 21.11 | odd | 6 | |||
63.7.m.d.19.2 | 8 | 21.20 | even | 2 | |||
147.7.d.b.97.3 | 8 | 7.5 | odd | 6 | |||
147.7.d.b.97.4 | 8 | 7.2 | even | 3 | |||
147.7.f.d.19.3 | 8 | 1.1 | even | 1 | trivial | ||
147.7.f.d.31.3 | 8 | 7.3 | odd | 6 | inner | ||
336.7.bh.d.145.4 | 8 | 28.27 | even | 2 | |||
336.7.bh.d.241.4 | 8 | 28.11 | odd | 6 | |||
441.7.d.c.244.5 | 8 | 21.2 | odd | 6 | |||
441.7.d.c.244.6 | 8 | 21.5 | even | 6 |