Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
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("76.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 13.5 | ||
Character | \(\chi\) | \(=\) | 76.13 |
Dual form | 76.7.j.a.41.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.50553 | + | 9.63135i | −0.129834 | + | 0.356717i | −0.987528 | − | 0.157444i | \(-0.949674\pi\) |
0.857694 | + | 0.514161i | \(0.171897\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 35.8010 | + | 203.037i | 0.286408 | + | 1.62430i | 0.700213 | + | 0.713934i | \(0.253088\pi\) |
−0.413805 | + | 0.910366i | \(0.635800\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −107.477 | + | 186.155i | −0.313344 | + | 0.542727i | −0.979084 | − | 0.203456i | \(-0.934783\pi\) |
0.665740 | + | 0.746184i | \(0.268116\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 477.972 | + | 401.066i | 0.655654 | + | 0.550159i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1139.35 | − | 1973.42i | −0.856014 | − | 1.48266i | −0.875701 | − | 0.482854i | \(-0.839600\pi\) |
0.0196867 | − | 0.999806i | \(-0.493733\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 416.997 | + | 1145.69i | 0.189803 | + | 0.521479i | 0.997695 | − | 0.0678507i | \(-0.0216141\pi\) |
−0.807893 | + | 0.589330i | \(0.799392\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2081.03 | − | 366.941i | −0.616601 | − | 0.108723i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1100.79 | − | 923.671i | 0.224056 | − | 0.188006i | −0.523849 | − | 0.851811i | \(-0.675504\pi\) |
0.747905 | + | 0.663806i | \(0.231060\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5928.97 | + | 3448.65i | −0.864407 | + | 0.502792i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1416.17 | − | 1687.72i | −0.152917 | − | 0.182240i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 344.169 | − | 1951.88i | 0.0282871 | − | 0.160424i | −0.967392 | − | 0.253283i | \(-0.918490\pi\) |
0.995679 | + | 0.0928592i | \(0.0296006\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −25259.8 | + | 9193.81i | −1.61663 | + | 0.588404i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −12009.2 | + | 6933.50i | −0.610130 | + | 0.352258i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −12446.4 | + | 14833.0i | −0.510327 | + | 0.608184i | −0.958265 | − | 0.285880i | \(-0.907714\pi\) |
0.447938 | + | 0.894064i | \(0.352158\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −16009.5 | − | 9243.09i | −0.537394 | − | 0.310265i | 0.206628 | − | 0.978420i | \(-0.433751\pi\) |
−0.744022 | + | 0.668155i | \(0.767084\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 23000.8 | − | 4055.65i | 0.640030 | − | 0.112855i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −41644.3 | − | 15157.3i | −0.971296 | − | 0.353523i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 74669.7i | − | 1.47414i | −0.675815 | − | 0.737071i | \(-0.736208\pi\) | ||
0.675815 | − | 0.737071i | \(-0.263792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12496.3 | −0.210663 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18646.0 | + | 51229.4i | −0.270541 | + | 0.743306i | 0.727803 | + | 0.685786i | \(0.240542\pi\) |
−0.998344 | + | 0.0575200i | \(0.981681\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 14851.6 | + | 84227.4i | 0.186796 | + | 1.05937i | 0.923627 | + | 0.383293i | \(0.125210\pi\) |
−0.736831 | + | 0.676077i | \(0.763679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −64319.6 | + | 111405.i | −0.705839 | + | 1.22255i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −62976.8 | − | 52843.8i | −0.606579 | − | 0.508980i | 0.286974 | − | 0.957938i | \(-0.407351\pi\) |
−0.893553 | + | 0.448958i | \(0.851795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 35721.9 | + | 61872.2i | 0.303631 | + | 0.525905i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5037.36 | + | 13840.0i | 0.0379745 | + | 0.104334i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −73135.0 | − | 12895.7i | −0.491244 | − | 0.0866196i | −0.0774616 | − | 0.996995i | \(-0.524682\pi\) |
−0.413783 | + | 0.910376i | \(0.635793\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 359888. | − | 301982.i | 2.16312 | − | 1.81507i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12431.0 | − | 69193.3i | −0.0671248 | − | 0.373628i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 149404. | + | 178053.i | 0.727454 | + | 0.866946i | 0.995332 | − | 0.0965066i | \(-0.0307669\pi\) |
−0.267878 | + | 0.963453i | \(0.586322\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37107.5 | − | 210447.i | 0.163483 | − | 0.927157i | −0.787132 | − | 0.616784i | \(-0.788435\pi\) |
0.950615 | − | 0.310373i | \(-0.100454\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −126032. | + | 45871.8i | −0.504032 | + | 0.183453i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −217689. | + | 125683.i | −0.792677 | + | 0.457652i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 204848. | − | 244129.i | 0.681095 | − | 0.811698i | −0.309153 | − | 0.951012i | \(-0.600046\pi\) |
0.990248 | + | 0.139315i | \(0.0444900\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17592.8 | + | 10157.2i | 0.0535534 | + | 0.0309190i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 404511. | − | 71326.1i | 1.13020 | − | 0.199285i | 0.422884 | − | 0.906184i | \(-0.361018\pi\) |
0.707314 | + | 0.706899i | \(0.249907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 333804. | + | 121495.i | 0.858070 | + | 0.312312i | 0.733326 | − | 0.679877i | \(-0.237967\pi\) |
0.124744 | + | 0.992189i | \(0.460189\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 275515.i | − | 0.653073i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 489817. | 1.07291 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −120930. | + | 332253.i | −0.245275 | + | 0.673889i | 0.754569 | + | 0.656221i | \(0.227846\pi\) |
−0.999844 | + | 0.0176674i | \(0.994376\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 54304.8 | + | 307978.i | 0.102184 | + | 0.579514i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −105419. | + | 182591.i | −0.184367 | + | 0.319333i | −0.943363 | − | 0.331762i | \(-0.892357\pi\) |
0.758996 | + | 0.651095i | \(0.225690\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 226949. | + | 190433.i | 0.369549 | + | 0.310088i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −99230.8 | − | 171873.i | −0.150692 | − | 0.261005i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 427489. | + | 1.17452e6i | 0.606394 | + | 1.66606i | 0.738039 | + | 0.674758i | \(0.235752\pi\) |
−0.131645 | + | 0.991297i | \(0.542026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −258094. | − | 45508.9i | −0.342494 | − | 0.0603910i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 145145. | − | 121791.i | 0.180449 | − | 0.151414i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −912469. | − | 1.08034e6i | −1.06426 | − | 1.26005i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −624933. | − | 744766.i | −0.684728 | − | 0.816027i | 0.305979 | − | 0.952038i | \(-0.401016\pi\) |
−0.990707 | + | 0.136011i | \(0.956572\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 246892. | − | 1.40020e6i | 0.254450 | − | 1.44306i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.43100e6 | − | 520841.i | 1.38891 | − | 0.505523i | 0.464045 | − | 0.885811i | \(-0.346397\pi\) |
0.924868 | + | 0.380288i | \(0.124175\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.47197e6 | + | 849843.i | −1.34706 | + | 0.777727i | −0.987832 | − | 0.155522i | \(-0.950294\pi\) |
−0.359230 | + | 0.933249i | \(0.616961\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 291970. | − | 347957.i | 0.252215 | − | 0.300578i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.38169e6 | − | 797721.i | −1.12787 | − | 0.651178i | −0.184474 | − | 0.982837i | \(-0.559058\pi\) |
−0.943399 | + | 0.331659i | \(0.892392\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.01591e6 | + | 355460.i | −1.55665 | + | 0.274480i | −0.884717 | − | 0.466129i | \(-0.845648\pi\) |
−0.671936 | + | 0.740609i | \(0.734537\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 719171. | + | 261757.i | 0.525851 | + | 0.191394i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.71799e6i | 1.88370i | 0.336032 | + | 0.941850i | \(0.390915\pi\) | ||||
−0.336032 | + | 0.941850i | \(0.609085\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 408626. | 0.268679 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −260184. | + | 714851.i | −0.162452 | + | 0.446332i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 53637.1 | + | 304191.i | 0.0318291 | + | 0.180512i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.71048e6 | + | 2.96264e6i | −0.965521 | + | 1.67233i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −428045. | − | 359172.i | −0.230024 | − | 0.193013i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.16031e6 | − | 2.00972e6i | −0.594081 | − | 1.02898i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 404171. | + | 1.11045e6i | 0.197312 | + | 0.542111i | 0.998407 | − | 0.0564269i | \(-0.0179708\pi\) |
−0.801094 | + | 0.598538i | \(0.795749\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −863286. | − | 152221.i | −0.402148 | − | 0.0709095i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 804567. | − | 675112.i | 0.357889 | − | 0.300305i | −0.446060 | − | 0.895003i | \(-0.647173\pi\) |
0.803949 | + | 0.594699i | \(0.202729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4758.43 | − | 1.47436e6i | −0.00202260 | − | 0.626684i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.83770e6 | − | 2.19009e6i | −0.746919 | − | 0.890144i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −665784. | + | 3.77585e6i | −0.258923 | + | 1.46843i | 0.526874 | + | 0.849944i | \(0.323364\pi\) |
−0.785797 | + | 0.618484i | \(0.787747\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.02038e6 | − | 1.09933e6i | 1.12465 | − | 0.409339i | 0.288302 | − | 0.957540i | \(-0.406909\pi\) |
0.836347 | + | 0.548201i | \(0.184687\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 729725. | − | 421307.i | 0.260316 | − | 0.150294i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.78582e6 | − | 2.12826e6i | 0.610702 | − | 0.727807i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.45725e6 | − | 1.99604e6i | −1.13403 | − | 0.654735i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −721137. | + | 127156.i | −0.227021 | + | 0.0400299i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.38896e6 | + | 505541.i | 0.419887 | + | 0.152826i | 0.543318 | − | 0.839527i | \(-0.317168\pi\) |
−0.123432 | + | 0.992353i | \(0.539390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.72947e6i | 0.502321i | 0.967945 | + | 0.251161i | \(0.0808122\pi\) | ||||
−0.967945 | + | 0.251161i | \(0.919188\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 896600. | 0.250337 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.30354e6 | − | 3.58144e6i | 0.350049 | − | 0.961751i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 598687. | + | 3.39532e6i | 0.154704 | + | 0.877369i | 0.959056 | + | 0.283216i | \(0.0914014\pi\) |
−0.804352 | + | 0.594153i | \(0.797488\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 380579. | − | 659183.i | 0.0946790 | − | 0.163989i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 326363. | + | 273851.i | 0.0782030 | + | 0.0656201i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 459958. | + | 796671.i | 0.106208 | + | 0.183957i | 0.914231 | − | 0.405194i | \(-0.132796\pi\) |
−0.808023 | + | 0.589150i | \(0.799463\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.64690e6 | + | 4.52482e6i | 0.366619 | + | 1.00728i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.43458e6 | + | 1.48724e6i | 1.81098 | + | 0.319325i | 0.973767 | − | 0.227548i | \(-0.0730709\pi\) |
0.837215 | + | 0.546873i | \(0.184182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.55883e6 | − | 2.14712e6i | 0.530129 | − | 0.444831i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.21702e6 | − | 729549.i | −0.843368 | − | 0.145904i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 951553. | + | 1.13402e6i | 0.183778 | + | 0.219019i | 0.850066 | − | 0.526676i | \(-0.176562\pi\) |
−0.666287 | + | 0.745695i | \(0.732118\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00337e6 | − | 5.69037e6i | 0.187217 | − | 1.06176i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.23863e6 | + | 814793.i | −0.403703 | + | 0.146936i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.21971e6 | + | 1.85890e6i | −0.561381 | + | 0.324113i | −0.753699 | − | 0.657219i | \(-0.771733\pi\) |
0.192319 | + | 0.981333i | \(0.438399\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 170137. | − | 202762.i | 0.0286922 | − | 0.0341940i | −0.751508 | − | 0.659724i | \(-0.770673\pi\) |
0.780200 | + | 0.625530i | \(0.215117\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.89681e6 | + | 1.09512e6i | 0.309507 | + | 0.178694i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.51608e7 | − | 2.67325e6i | 2.39445 | − | 0.422206i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.07698e6 | − | 1.11993e6i | −0.470544 | − | 0.171264i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 2.98077e6i | − | 0.441512i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.12582e6 | −0.161573 | −0.0807863 | − | 0.996731i | \(-0.525743\pi\) | ||||
−0.0807863 | + | 0.996731i | \(0.525743\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.74939e6 | − | 1.03014e7i | 0.521541 | − | 1.43292i | −0.347263 | − | 0.937768i | \(-0.612889\pi\) |
0.868804 | − | 0.495155i | \(-0.164889\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −447381. | − | 2.53722e6i | −0.0603356 | − | 0.342180i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.83343e6 | + | 6.63970e6i | −0.501406 | + | 0.868460i | 0.498593 | + | 0.866836i | \(0.333850\pi\) |
−0.999999 | + | 0.00162394i | \(0.999483\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.40858e6 | + | 2.02104e6i | 0.305634 | + | 0.256458i | 0.782685 | − | 0.622418i | \(-0.213850\pi\) |
−0.477050 | + | 0.878876i | \(0.658294\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.63319e6 | + | 2.82876e6i | 0.201117 | + | 0.348344i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.42355e6 | − | 3.91116e6i | −0.170170 | − | 0.467539i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.10690e7 | − | 1.95177e6i | −1.28484 | − | 0.226551i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 947337. | − | 794910.i | 0.106805 | − | 0.0896204i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.35608e7 | + | 7.77111e6i | 1.48542 | + | 0.851225i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.01952e6 | + | 5.98203e6i | 0.534337 | + | 0.636797i | 0.963908 | − | 0.266235i | \(-0.0857798\pi\) |
−0.429572 | + | 0.903033i | \(0.641335\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −731055. | + | 4.14602e6i | −0.0756504 | + | 0.429035i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.65696e7 | + | 6.03084e6i | −1.66724 | + | 0.606824i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.44130e6 | − | 1.98684e6i | 0.336778 | − | 0.194439i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.34032e6 | + | 2.78908e6i | −0.222814 | + | 0.265539i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.51727e6 | + | 875994.i | 0.140567 | + | 0.0811567i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.38996e6 | + | 950395.i | −0.486039 | + | 0.0857018i | −0.411297 | − | 0.911501i | \(-0.634924\pi\) |
−0.0747414 | + | 0.997203i | \(0.523813\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.57608e7 | − | 5.73647e6i | −1.38366 | − | 0.503613i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.70422e6i | 0.402170i | 0.979574 | + | 0.201085i | \(0.0644468\pi\) | ||||
−0.979574 | + | 0.201085i | \(0.935553\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.32193e7 | −1.10078 | −0.550391 | − | 0.834907i | \(-0.685521\pi\) | ||||
−0.550391 | + | 0.834907i | \(0.685521\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.71707e6 | + | 4.71761e6i | −0.139300 | + | 0.382724i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −444687. | − | 2.52195e6i | −0.0351550 | − | 0.199374i | 0.962172 | − | 0.272443i | \(-0.0878317\pi\) |
−0.997327 | + | 0.0730693i | \(0.976721\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.47464e6 | − | 1.46785e7i | 0.653007 | − | 1.13104i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.77613e6 | − | 2.32945e6i | −0.208542 | − | 0.174988i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.07823e7 | + | 1.86756e7i | 0.789804 | + | 1.36798i | 0.926087 | + | 0.377310i | \(0.123151\pi\) |
−0.136283 | + | 0.990670i | \(0.543516\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.41303e6 | − | 2.31146e7i | −0.601037 | − | 1.65134i | −0.749177 | − | 0.662370i | \(-0.769551\pi\) |
0.148139 | − | 0.988966i | \(-0.452672\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.31121e7 | − | 2.31201e6i | −0.913803 | − | 0.161128i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.12835e7 | + | 9.46797e6i | −0.767265 | + | 0.643812i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.42345e6 | − | 5.35468e6i | −0.426263 | − | 0.355339i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.38905e6 | − | 1.65540e6i | −0.0899744 | − | 0.107227i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −682498. | + | 3.87064e6i | −0.0431599 | + | 0.244772i | −0.998753 | − | 0.0499162i | \(-0.984105\pi\) |
0.955594 | + | 0.294688i | \(0.0952157\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.24401e6 | + | 1.54469e6i | −0.262069 | + | 0.0953852i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.62970e6 | + | 1.51826e6i | −0.158594 | + | 0.0915642i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.65124e6 | − | 1.03101e7i | 0.509658 | − | 0.607387i | −0.448445 | − | 0.893810i | \(-0.648022\pi\) |
0.958103 | + | 0.286424i | \(0.0924665\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.39002e7 | + | 8.02527e6i | 0.800057 | + | 0.461913i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.18980e7 | + | 2.09794e6i | −0.669196 | + | 0.117997i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.13484e6 | − | 1.14099e6i | −0.172325 | − | 0.0627211i | 0.254417 | − | 0.967095i | \(-0.418116\pi\) |
−0.426742 | + | 0.904374i | \(0.640339\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.53108e7i | − | 0.822736i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.28108e7 | −0.673041 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.54529e6 | − | 4.24565e6i | 0.0793876 | − | 0.218116i | −0.893649 | − | 0.448767i | \(-0.851863\pi\) |
0.973037 | + | 0.230651i | \(0.0740856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 735236. | + | 4.16973e6i | 0.0369419 | + | 0.209508i | 0.997692 | − | 0.0679092i | \(-0.0216328\pi\) |
−0.960750 | + | 0.277417i | \(0.910522\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.34307e6 | − | 2.32626e6i | 0.0660100 | − | 0.114333i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.69231e7 | + | 3.93732e7i | 2.25626 | + | 1.89323i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 258430. | + | 447613.i | 0.0121591 | + | 0.0210603i | 0.872041 | − | 0.489433i | \(-0.162796\pi\) |
−0.859882 | + | 0.510493i | \(0.829463\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.94500e6 | − | 1.08388e7i | −0.181650 | − | 0.499079i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.21863e7 | − | 2.14877e6i | −0.549226 | − | 0.0968434i | −0.107853 | − | 0.994167i | \(-0.534397\pi\) |
−0.441373 | + | 0.897323i | \(0.645509\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.84825e7 | + | 1.55087e7i | −0.815458 | + | 0.684250i | −0.951904 | − | 0.306397i | \(-0.900876\pi\) |
0.136446 | + | 0.990648i | \(0.456432\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.36038e7 | − | 5.00116e6i | 0.587659 | − | 0.216041i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.53262e6 | − | 8.97703e6i | −0.318640 | − | 0.379741i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.83288e6 | + | 2.17373e7i | −0.158793 | + | 0.900560i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.36382e6 | − | 3.40815e6i | 0.379992 | − | 0.138306i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.31594e7 | − | 1.91446e7i | 1.31827 | − | 0.761103i | 0.334819 | − | 0.942282i | \(-0.391325\pi\) |
0.983450 | + | 0.181179i | \(0.0579914\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.08025e7 | + | 3.67090e7i | −1.19983 | + | 1.42990i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.73654e7 | + | 1.57994e7i | 1.04456 | + | 0.603077i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.37977e6 | − | 419617.i | 0.0890268 | − | 0.0156978i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.72756e7 | − | 6.28780e6i | −0.633481 | − | 0.230568i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.56083e7i | 0.561083i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.40571e7 | 1.55280 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.53678e6 | − | 2.34546e7i | 0.295039 | − | 0.810612i | −0.700271 | − | 0.713877i | \(-0.746938\pi\) |
0.995310 | − | 0.0967356i | \(-0.0308401\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.02511e6 | − | 1.71562e7i | −0.102533 | − | 0.581496i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.79872e7 | − | 4.84753e7i | 0.930419 | − | 1.61153i | 0.147814 | − | 0.989015i | \(-0.452776\pi\) |
0.782605 | − | 0.622518i | \(-0.213890\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.08333e7 | + | 1.74812e7i | 0.679400 | + | 0.570084i | 0.915831 | − | 0.401564i | \(-0.131533\pi\) |
−0.236431 | + | 0.971648i | \(0.575978\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.38257e7 | − | 2.39469e7i | −0.442341 | − | 0.766156i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.35836e7 | − | 3.73205e7i | −0.426418 | − | 1.17157i | −0.947971 | − | 0.318356i | \(-0.896869\pi\) |
0.521553 | − | 0.853219i | \(-0.325353\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.34526e7 | + | 7.66186e6i | 1.33858 | + | 0.236027i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.25267e7 | − | 1.05111e7i | 0.378723 | − | 0.317786i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.34112e6 | + | 9.27266e6i | −0.0991481 | + | 0.275167i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.10665e7 | − | 2.51061e7i | −0.613681 | − | 0.731356i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.64327e6 | − | 2.06620e7i | 0.104195 | − | 0.590921i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.66057e7 | − | 6.04399e6i | 0.466305 | − | 0.169721i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.70828e7 | + | 1.56363e7i | −0.746810 | + | 0.431171i | −0.824540 | − | 0.565804i | \(-0.808566\pi\) |
0.0777301 | + | 0.996974i | \(0.475233\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.99475e7 | − | 3.56900e7i | 0.811013 | − | 0.966528i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.69010e7 | + | 3.28518e7i | 1.51351 | + | 0.873826i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.54959e7 | + | 9.78543e6i | −1.45001 | + | 0.255676i | −0.842526 | − | 0.538655i | \(-0.818933\pi\) |
−0.607485 | + | 0.794331i | \(0.707822\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.61779e7 | − | 9.52797e6i | −0.671948 | − | 0.244569i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.21246e7i | 1.06236i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.06462e7 | −1.00725 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.43245e6 | + | 3.93563e6i | −0.0348837 | + | 0.0958422i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.04601e7 | + | 5.93222e7i | 0.250350 | + | 1.41980i | 0.807732 | + | 0.589549i | \(0.200695\pi\) |
−0.557383 | + | 0.830256i | \(0.688194\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.93827e6 | − | 1.72136e7i | 0.233795 | − | 0.404944i | −0.725127 | − | 0.688615i | \(-0.758219\pi\) |
0.958922 | + | 0.283671i | \(0.0915523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.29514e7 | − | 1.08675e7i | −0.299500 | − | 0.251310i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.34329e7 | + | 4.05869e7i | 0.532723 | + | 0.922703i | 0.999270 | + | 0.0382064i | \(0.0121644\pi\) |
−0.466547 | + | 0.884496i | \(0.654502\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.89637e7 | + | 7.95772e7i | 0.647396 | + | 1.77870i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.11780e6 | − | 549752.i | −0.0685241 | − | 0.0120827i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.28167e7 | − | 2.75364e7i | 0.709269 | − | 0.595147i | −0.215125 | − | 0.976587i | \(-0.569016\pi\) |
0.924394 | + | 0.381439i | \(0.124571\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.32595e7 | − | 4.08939e7i | 0.494400 | − | 0.869235i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.25381e7 | − | 2.68598e7i | −0.471191 | − | 0.561543i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.27175e7 | + | 7.21243e7i | −0.261530 | + | 1.48321i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.05165e7 | + | 3.82769e6i | −0.212751 | + | 0.0774351i | −0.446197 | − | 0.894935i | \(-0.647222\pi\) |
0.233446 | + | 0.972370i | \(0.425000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.94586e7 | + | 1.70080e7i | −0.586319 | + | 0.338511i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.02609e7 | − | 1.22285e7i | 0.200939 | − | 0.239470i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.87279e7 | − | 3.39066e7i | −1.13167 | − | 0.653367i | −0.187312 | − | 0.982300i | \(-0.559978\pi\) |
−0.944353 | + | 0.328933i | \(0.893311\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.34239e7 | − | 4.13026e6i | 0.444186 | − | 0.0783220i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.21841e7 | − | 8.07435e6i | −0.414017 | − | 0.150690i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.41232e7i | − | 1.54525i | −0.634863 | − | 0.772624i | \(-0.718944\pi\) | ||
0.634863 | − | 0.772624i | \(-0.281056\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.21120e7 | −0.218998 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.79448e7 | − | 4.93029e7i | 0.319405 | − | 0.877559i | −0.671258 | − | 0.741224i | \(-0.734246\pi\) |
0.990663 | − | 0.136335i | \(-0.0435322\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.75359e7 | + | 9.94513e7i | 0.307289 | + | 1.74272i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.66821e7 | + | 4.62148e7i | −0.460349 | + | 0.797348i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.17365e7 | − | 6.01940e7i | −1.21868 | − | 1.02260i | −0.998892 | − | 0.0470508i | \(-0.985018\pi\) |
−0.219792 | − | 0.975547i | \(-0.570538\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.42404e6 | − | 2.46651e6i | −0.0238227 | − | 0.0412622i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.68181e6 | + | 1.01157e7i | 0.0606574 | + | 0.166655i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.17893e7 | − | 1.26584e7i | −1.16485 | − | 0.205394i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.59318e7 | − | 2.17593e7i | 0.414439 | − | 0.347755i | −0.411604 | − | 0.911363i | \(-0.635031\pi\) |
0.826043 | + | 0.563607i | \(0.190587\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.42168e7 | + | 5.12258e6i | 0.223811 | + | 0.0806436i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.98098e6 | + | 3.55259e6i | 0.0462301 | + | 0.0550949i | 0.788664 | − | 0.614824i | \(-0.210773\pi\) |
−0.742434 | + | 0.669919i | \(0.766329\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.91380e6 | − | 2.21963e7i | 0.0597975 | − | 0.339129i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.05868e7 | + | 2.20518e7i | −0.912039 | + | 0.331955i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.47355e8 | + | 8.50753e7i | −2.18565 | + | 1.26189i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.72772e7 | − | 4.44252e7i | 0.544845 | − | 0.649321i | −0.421422 | − | 0.906865i | \(-0.638469\pi\) |
0.966267 | + | 0.257544i | \(0.0829132\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.40326e7 | − | 1.96487e7i | −0.490196 | − | 0.283015i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.92029e7 | + | 8.67580e6i | −0.698459 | + | 0.123157i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.08468e7 | − | 1.48670e7i | −0.571497 | − | 0.208008i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.29440e7i | 0.454327i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.49195e7 | 1.29037 | 0.645184 | − | 0.764028i | \(-0.276781\pi\) | ||||
0.645184 | + | 0.764028i | \(0.276781\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.98581e7 | − | 1.09509e8i | 0.534159 | − | 1.46759i | −0.319918 | − | 0.947445i | \(-0.603655\pi\) |
0.854078 | − | 0.520145i | \(-0.174122\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.90729e6 | − | 5.05158e7i | −0.117686 | − | 0.667430i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.93136e7 | + | 3.34522e7i | −0.251592 | + | 0.435770i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.51877e7 | + | 2.95260e7i | 0.451967 | + | 0.379246i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.42378e7 | + | 2.46605e7i | 0.180331 | + | 0.312342i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.67963e7 | + | 1.28572e8i | 0.584493 | + | 1.60588i | 0.780415 | + | 0.625262i | \(0.215008\pi\) |
−0.195921 | + | 0.980620i | \(0.562770\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.81832e7 | + | 1.20225e7i | 0.839873 | + | 0.148092i | 0.577006 | − | 0.816740i | \(-0.304221\pi\) |
0.262867 | + | 0.964832i | \(0.415332\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.13441e7 | − | 2.63008e7i | 0.380792 | − | 0.319522i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.69079e6 | + | 1.27596e7i | 0.0562085 | + | 0.152894i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.52592e7 | − | 8.96904e7i | −0.889541 | − | 1.06011i | −0.997820 | − | 0.0659929i | \(-0.978979\pi\) |
0.108279 | − | 0.994121i | \(-0.465466\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.74076e6 | + | 4.39000e7i | −0.0902543 | + | 0.511858i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.81669e7 | + | 1.38916e7i | −0.439012 | + | 0.159787i | −0.552064 | − | 0.833802i | \(-0.686160\pi\) |
0.113052 | + | 0.993589i | \(0.463937\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.23166e8 | + | 1.28845e8i | −2.53250 | + | 1.46214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.73810e6 | + | 1.16054e7i | −0.109031 | + | 0.129939i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.98851e7 | + | 4.03482e7i | 0.772050 | + | 0.445743i | 0.833605 | − | 0.552360i | \(-0.186273\pi\) |
−0.0615553 | + | 0.998104i | \(0.519606\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.22342e8 | − | 2.15721e7i | 1.33366 | − | 0.235160i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.66571e7 | − | 6.06269e6i | −0.179186 | − | 0.0652185i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 5.40320e7i | − | 0.573610i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.81939e7 | 0.819265 | 0.409632 | − | 0.912251i | \(-0.365657\pi\) | ||||
0.409632 | + | 0.912251i | \(0.365657\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.81529e6 | + | 1.87249e7i | −0.0704768 | + | 0.193633i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.11644e7 | + | 6.33165e7i | 0.113955 | + | 0.646270i | 0.987262 | + | 0.159101i | \(0.0508594\pi\) |
−0.873308 | + | 0.487169i | \(0.838029\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.45247e7 | − | 5.97986e7i | 0.347846 | − | 0.602488i | −0.638020 | − | 0.770020i | \(-0.720246\pi\) |
0.985867 | + | 0.167532i | \(0.0535798\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.99245e7 | + | 2.51097e7i | 0.297624 | + | 0.249737i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.59965e7 | − | 1.14309e8i | −0.647993 | − | 1.12236i | −0.983602 | − | 0.180355i | \(-0.942275\pi\) |
0.335609 | − | 0.942001i | \(-0.391058\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.34294e7 | + | 6.43718e7i | 0.227114 | + | 0.623989i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.48003e7 | − | 6.13623e6i | −0.333058 | − | 0.0587271i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.49295e8 | − | 1.25273e8i | 1.41079 | − | 1.18379i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.18058e8 | − | 1.41622e8i | 1.10158 | − | 1.32145i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.97845e7 | − | 3.54957e7i | −0.274432 | − | 0.327055i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.33139e6 | + | 7.55068e6i | −0.0121143 | + | 0.0687036i | −0.990266 | − | 0.139191i | \(-0.955550\pi\) |
0.978151 | + | 0.207894i | \(0.0666610\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.55483e7 | − | 3.11370e7i | 0.768734 | − | 0.279796i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.78163e6 | + | 2.18333e6i | −0.0335612 | + | 0.0193766i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.28842e8 | − | 1.53548e8i | 1.12936 | − | 1.34592i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.63330e8 | − | 9.42985e7i | −1.41409 | − | 0.816428i | −0.418324 | − | 0.908298i | \(-0.637382\pi\) |
−0.995771 | + | 0.0918702i | \(0.970716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.28541e6 | + | 1.63727e6i | −0.0794099 | + | 0.0140021i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.76956e7 | − | 2.09995e7i | −0.487414 | − | 0.177404i | 0.0866105 | − | 0.996242i | \(-0.472396\pi\) |
−0.574025 | + | 0.818838i | \(0.694619\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.78243e7i | 0.232212i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.93131e8 | 2.41683 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.01978e7 | + | 8.29678e7i | −0.245984 | + | 0.675834i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.22895e7 | + | 6.96975e7i | 0.0989087 | + | 0.560939i | 0.993479 | + | 0.114012i | \(0.0363703\pi\) |
−0.894571 | + | 0.446927i | \(0.852519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.38918e7 | + | 7.60229e7i | −0.349036 | + | 0.604549i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.78546e8 | + | 1.49818e8i | 1.40296 | + | 1.17722i | 0.959767 | + | 0.280797i | \(0.0905986\pi\) |
0.443193 | + | 0.896426i | \(0.353846\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.56981e8 | + | 2.71900e8i | 1.21892 | + | 2.11123i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.17096e7 | + | 3.21718e7i | 0.0898498 | + | 0.246860i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.34170e7 | − | 2.36577e6i | −0.101742 | − | 0.0179399i | 0.122545 | − | 0.992463i | \(-0.460894\pi\) |
−0.224287 | + | 0.974523i | \(0.572005\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.84931e7 | + | 4.90816e7i | −0.438371 | + | 0.367837i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.72908e7 | − | 8.25240e7i | 0.350287 | − | 0.611263i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.25248e8 | − | 2.68440e8i | −1.64907 | − | 1.96529i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.25302e7 | + | 1.84488e8i | −0.235404 | + | 1.33504i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.42578e7 | + | 5.18942e6i | −0.101988 | + | 0.0371207i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00631e7 | + | 5.19979e7i | −0.636845 | + | 0.367682i | −0.783398 | − | 0.621520i | \(-0.786515\pi\) |
0.146553 | + | 0.989203i | \(0.453182\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.39612e7 | + | 5.23909e7i | −0.307301 | + | 0.366227i | −0.897488 | − | 0.441040i | \(-0.854610\pi\) |
0.590187 | + | 0.807267i | \(0.299054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.12887e7 | + | 2.96115e7i | 0.354441 | + | 0.204636i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.61607e7 | + | 4.61283e6i | −0.178738 | + | 0.0315163i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.35417e8 | + | 4.92877e7i | 0.914757 | + | 0.332944i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.45025e8i | 0.968633i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.64683e7 | −0.438968 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.12501e8 | − | 3.09095e8i | 0.734677 | − | 2.01851i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.61695e6 | − | 3.75266e7i | −0.0427302 | − | 0.242335i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.13999e7 | − | 1.40989e8i | 0.519825 | − | 0.900364i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.47761e7 | + | 1.23986e7i | 0.0933185 | + | 0.0783035i | 0.688253 | − | 0.725470i | \(-0.258378\pi\) |
−0.594935 | + | 0.803774i | \(0.702822\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.35645e6 | + | 2.34944e6i | 0.00847235 | + | 0.0146745i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.44343e8 | − | 3.96580e8i | −0.891675 | − | 2.44986i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.56979e7 | + | 8.05778e6i | 0.279212 | + | 0.0492327i | 0.311501 | − | 0.950246i | \(-0.399168\pi\) |
−0.0322883 | + | 0.999479i | \(0.510279\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.02140e8 | − | 8.57053e7i | 0.617273 | − | 0.517953i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.26402e7 | − | 1.30868e8i | 0.135340 | − | 0.782307i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.88536e7 | − | 5.82214e7i | −0.288882 | − | 0.344277i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.73994e7 | + | 1.55390e8i | −0.160274 | + | 0.908957i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.37459e8 | + | 5.00312e7i | −0.795443 | + | 0.289518i | −0.707597 | − | 0.706616i | \(-0.750221\pi\) |
−0.0878464 | + | 0.996134i | \(0.527998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.03053e7 | + | 5.21378e7i | −0.516985 | + | 0.298481i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.15729e7 | − | 2.57095e7i | 0.122185 | − | 0.145615i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.82392e8 | + | 1.63039e8i | 1.58244 | + | 0.913624i | 0.994502 | + | 0.104720i | \(0.0333945\pi\) |
0.587941 | + | 0.808904i | \(0.299939\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.51853e8 | + | 9.73066e7i | −3.05969 | + | 0.539507i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.31683e7 | − | 2.29914e7i | −0.346537 | − | 0.126129i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.75490e7i | 0.149544i | 0.997201 | + | 0.0747719i | \(0.0238229\pi\) | ||||
−0.997201 | + | 0.0747719i | \(0.976177\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.86462e7 | −0.261301 | −0.130650 | − | 0.991429i | \(-0.541707\pi\) | ||||
−0.130650 | + | 0.991429i | \(0.541707\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.94658e6 | − | 1.08431e7i | 0.0209777 | − | 0.0576357i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.25158e6 | + | 5.24683e7i | 0.0486645 | + | 0.275990i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.93258e7 | − | 1.02755e8i | 0.308828 | − | 0.534905i | −0.669278 | − | 0.743012i | \(-0.733397\pi\) |
0.978106 | + | 0.208106i | \(0.0667300\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.60725e7 | + | 7.22234e7i | 0.443434 | + | 0.372085i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.26602e7 | − | 3.92486e7i | −0.115541 | − | 0.200122i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.78781e7 | + | 1.59019e8i | 0.292085 | + | 0.802496i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.54456e8 | − | 2.72348e7i | −0.771504 | − | 0.136037i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.47095e8 | + | 2.07337e8i | −1.22166 | + | 1.02509i | −0.222920 | + | 0.974837i | \(0.571559\pi\) |
−0.998736 | + | 0.0502546i | \(0.983997\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.26796e8 | − | 409229.i | 0.620526 | − | 0.00200272i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.05111e7 | − | 6.01968e7i | −0.244695 | − | 0.291616i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.35949e7 | + | 7.71004e7i | −0.0651945 | + | 0.369736i | 0.934703 | + | 0.355429i | \(0.115665\pi\) |
−0.999898 | + | 0.0143071i | \(0.995446\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.98419e7 | + | 2.17807e7i | −0.284089 | + | 0.103400i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.79087e7 | + | 1.61131e7i | −0.131165 | + | 0.0757279i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.51373e7 | + | 6.57101e7i | −0.256546 | + | 0.305740i | −0.878909 | − | 0.476989i | \(-0.841728\pi\) |
0.622363 | + | 0.782728i | \(0.286173\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.79901e8 | + | 1.03866e8i | 0.828726 | + | 0.478465i | 0.853416 | − | 0.521230i | \(-0.174527\pi\) |
−0.0246905 | + | 0.999695i | \(0.507860\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.95823e8 | − | 3.45290e7i | 0.893126 | − | 0.157482i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.62763e8 | − | 2.41226e8i | −2.99290 | − | 1.08933i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.34484e7i | 0.194271i | 0.995271 | + | 0.0971354i | \(0.0309680\pi\) | ||||
−0.995271 | + | 0.0971354i | \(0.969032\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.26601e7 | 0.188873 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.42815e7 | − | 9.41876e7i | 0.150292 | − | 0.412924i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.53731e7 | + | 4.27462e8i | 0.327216 | + | 1.85573i | 0.493621 | + | 0.869677i | \(0.335673\pi\) |
−0.166404 | + | 0.986058i | \(0.553216\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.76010e7 | − | 9.97678e7i | 0.247631 | − | 0.428909i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.67608e8 | + | 1.40640e8i | 0.713576 | + | 0.598762i | 0.925600 | − | 0.378503i | \(-0.123561\pi\) |
−0.212024 | + | 0.977264i | \(0.568005\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.04638e7 | − | 5.27649e7i | −0.128444 | − | 0.222471i | 0.794630 | − | 0.607094i | \(-0.207665\pi\) |
−0.923074 | + | 0.384623i | \(0.874331\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.40018e6 | + | 2.58268e7i | 0.0392520 | + | 0.107844i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.64588e8 | − | 4.66540e7i | −1.09422 | − | 0.192941i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.47590e7 | − | 3.75572e7i | 0.183333 | − | 0.153834i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.22384e8 | + | 1.03367e8i | −0.496504 | + | 0.419354i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.89703e7 | − | 8.21956e7i | −0.277147 | − | 0.330291i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.69370e6 | − | 2.09480e7i | 0.0147019 | − | 0.0833786i | −0.976574 | − | 0.215182i | \(-0.930966\pi\) |
0.991276 | + | 0.131803i | \(0.0420767\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.52111e7 | + | 2.73746e7i | −0.296532 | + | 0.107929i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.10993e8 | + | 1.21817e8i | −0.824039 | + | 0.475759i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.59904e7 | + | 6.67267e7i | −0.216618 | + | 0.258156i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.21951e8 | + | 1.28144e8i | 0.850658 | + | 0.491128i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.08716e8 | − | 1.91695e7i | 0.412780 | − | 0.0727842i | 0.0365980 | − | 0.999330i | \(-0.488348\pi\) |
0.376182 | + | 0.926546i | \(0.377237\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.29688e8 | − | 1.56394e8i | −1.61629 | − | 0.588282i | −0.633622 | − | 0.773643i | \(-0.718433\pi\) |
−0.982671 | + | 0.185360i | \(0.940655\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.80729e8i | − | 0.673517i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.53626e8 | −0.936442 | −0.468221 | − | 0.883611i | \(-0.655105\pi\) | ||||
−0.468221 | + | 0.883611i | \(0.655105\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.81149e8 | − | 4.97702e8i | 0.662675 | − | 1.82069i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.07236e6 | + | 4.01093e7i | 0.0256343 | + | 0.145379i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.62828e8 | − | 4.55232e8i | 0.943915 | − | 1.63491i | 0.186006 | − | 0.982549i | \(-0.440446\pi\) |
0.757909 | − | 0.652360i | \(-0.226221\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.65877e8 | + | 1.39188e8i | 0.590287 | + | 0.495309i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.10822e8 | + | 1.91949e8i | 0.390776 | + | 0.676844i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.84206e7 | − | 1.60509e8i | −0.204131 | − | 0.560847i | 0.794809 | − | 0.606859i | \(-0.207571\pi\) |
−0.998941 | + | 0.0460125i | \(0.985349\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.34371e8 | + | 5.89586e7i | 1.15777 | + | 0.204147i | 0.719368 | − | 0.694630i | \(-0.244432\pi\) |
0.438407 | + | 0.898777i | \(0.355543\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.37558e7 | + | 1.15425e7i | −0.0472004 | + | 0.0396059i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.99180e8 | − | 5.37497e7i | 1.01734 | − | 0.182773i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.46686e7 | + | 2.93989e7i | 0.0831317 | + | 0.0990725i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.74105e6 | − | 5.52442e7i | 0.0325333 | − | 0.184505i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.57579e8 | + | 1.66545e8i | −1.51460 | + | 0.551270i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.87639e8 | − | 1.08333e8i | 0.615570 | − | 0.355400i | −0.159572 | − | 0.987186i | \(-0.551011\pi\) |
0.775142 | + | 0.631787i | \(0.217678\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.39604e8 | − | 2.85549e8i | 0.779082 | − | 0.928473i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.49801e8 | + | 8.64877e7i | 0.482780 | + | 0.278733i | 0.721574 | − | 0.692337i | \(-0.243419\pi\) |
−0.238794 | + | 0.971070i | \(0.576752\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.05808e8 | − | 3.62895e7i | 0.657436 | − | 0.115924i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.53080e7 | − | 1.64908e7i | −0.143461 | − | 0.0522155i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 3.07375e7i | − | 0.0964733i | −0.998836 | − | 0.0482366i | \(-0.984640\pi\) | ||
0.998836 | − | 0.0482366i | \(-0.0153602\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.90474e8 | −2.45932 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.63406e7 | − | 1.27320e8i | 0.142919 | − | 0.392668i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.57226e7 | − | 8.91674e7i | −0.0480692 | − | 0.272614i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.00569e8 | − | 1.74191e8i | 0.304811 | − | 0.527949i | −0.672408 | − | 0.740181i | \(-0.734740\pi\) |
0.977219 | + | 0.212232i | \(0.0680733\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.34119e8 | + | 1.96449e8i | 0.703456 | + | 0.590270i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.31337e8 | + | 5.73893e8i | 0.986997 | + | 1.70953i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.67939e7 | + | 7.36155e7i | 0.0791292 | + | 0.217406i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.58486e7 | + | 4.55781e6i | 0.0756843 | + | 0.0133452i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.62068e8 | − | 1.35991e8i | 0.470481 | − | 0.394780i | −0.376489 | − | 0.926421i | \(-0.622869\pi\) |
0.846970 | + | 0.531641i | \(0.178424\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.57510e8 | + | 4.42714e8i | 0.741188 | + | 1.27426i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.11666e8 | + | 1.33078e8i | 0.318679 | + | 0.379787i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.68419e7 | + | 3.22367e8i | −0.160846 | + | 0.912204i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.78511e8 | − | 2.10561e8i | 1.62320 | − | 0.590798i | 0.639215 | − | 0.769028i | \(-0.279259\pi\) |
0.983989 | + | 0.178230i | \(0.0570370\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.91057e8 | + | 1.10307e8i | −0.531562 | + | 0.306898i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.35514e7 | + | 2.80674e7i | −0.0649752 | + | 0.0774345i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.96050e8 | + | 2.86395e8i | 1.35709 | + | 0.783514i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.17669e8 | + | 3.83809e7i | −0.590525 | + | 0.104126i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.18059e8 | − | 1.15764e8i | −0.855699 | − | 0.311449i | −0.123337 | − | 0.992365i | \(-0.539360\pi\) |
−0.732362 | + | 0.680916i | \(0.761582\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 3.65354e8i | − | 0.974784i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.52117e8 | 0.667095 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.78021e8 | − | 4.89108e8i | 0.467150 | − | 1.28349i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.24146e7 | + | 5.24109e8i | 0.240512 | + | 1.36401i | 0.830688 | + | 0.556738i | \(0.187947\pi\) |
−0.590176 | + | 0.807275i | \(0.700942\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.57571e7 | + | 7.92536e7i | −0.118107 | + | 0.204567i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.41468e7 | + | 7.89986e7i | 0.241020 | + | 0.202240i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.26237e7 | − | 1.60429e8i | −0.235185 | − | 0.407353i | 0.724141 | − | 0.689652i | \(-0.242236\pi\) |
−0.959327 | + | 0.282299i | \(0.908903\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.16348e7 | − | 1.41866e8i | −0.130041 | − | 0.357285i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.15163e8 | − | 1.26103e8i | −1.78650 | − | 0.315008i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.00561e8 | − | 3.36111e8i | 0.992512 | − | 0.832816i | 0.00658219 | − | 0.999978i | \(-0.497905\pi\) |
0.985929 | + | 0.167162i | \(0.0534604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.40904e7 | − | 4.30955e7i | 0.182099 | − | 0.105920i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.81218e8 | + | 2.15967e8i | 0.441809 | + | 0.526527i | 0.940291 | − | 0.340373i | \(-0.110553\pi\) |
−0.498482 | + | 0.866900i | \(0.666109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.29176e7 | + | 3.00110e8i | −0.127977 | + | 0.725792i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.23618e8 | + | 4.49933e7i | −0.296565 | + | 0.107941i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.97000e8 | − | 1.71473e8i | 0.706824 | − | 0.408085i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.23054e8 | − | 3.85001e8i | 0.762703 | − | 0.908954i | −0.235313 | − | 0.971920i | \(-0.575611\pi\) |
0.998016 | + | 0.0629658i | \(0.0200559\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.48870e7 | − | 2.01420e7i | −0.0817106 | − | 0.0471756i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.51146e8 | + | 6.19166e7i | −0.815920 | + | 0.143869i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.94069e8 | − | 1.43429e8i | −0.908416 | − | 0.330637i | −0.154796 | − | 0.987946i | \(-0.549472\pi\) |
−0.753620 | + | 0.657310i | \(0.771694\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 4.62906e7i | − | 0.105869i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.17896e8 | 1.40204 | 0.701022 | − | 0.713140i | \(-0.252728\pi\) | ||||
0.701022 | + | 0.713140i | \(0.252728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.50493e8 | − | 4.13477e8i | 0.338800 | − | 0.930845i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.20991e7 | + | 1.82043e8i | 0.0716983 | + | 0.406622i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.41692e8 | + | 2.45418e8i | −0.314021 | + | 0.543901i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.50631e8 | + | 2.94214e8i | 0.771030 | + | 0.646971i | 0.940973 | − | 0.338483i | \(-0.109914\pi\) |
−0.169942 | + | 0.985454i | \(0.554358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.89735e7 | + | 1.19466e8i | 0.150494 | + | 0.260663i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.56342e8 | − | 4.29547e8i | −0.338484 | − | 0.929977i | −0.985825 | − | 0.167777i | \(-0.946341\pi\) |
0.647341 | − | 0.762200i | \(-0.275881\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.89376e8 | + | 8.62902e7i | 1.05133 | + | 0.185377i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.26022e8 | + | 1.05745e8i | −0.268647 | + | 0.225422i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.61210e7 | − | 3.68041e8i | −0.139871 | − | 0.778545i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.01638e8 | − | 7.17004e8i | −1.26294 | − | 1.50511i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.66260e7 | − | 2.64429e8i | 0.0971276 | − | 0.550838i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.67944e8 | + | 2.43112e8i | −1.38080 | + | 0.502571i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.44389e8 | + | 3.72038e8i | −1.32198 | + | 0.763244i | −0.984044 | − | 0.177926i | \(-0.943061\pi\) |
−0.337933 | + | 0.941170i | \(0.609728\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.19785e7 | − | 2.61930e7i | 0.0447473 | − | 0.0533278i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.05968e8 | − | 2.92121e8i | −1.02234 | − | 0.590246i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.56581e8 | − | 4.52421e7i | 0.514522 | − | 0.0907242i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.47464e8 | + | 5.36725e7i | 0.293484 | + | 0.106819i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.85024e8i | 0.760524i | 0.924879 | + | 0.380262i | \(0.124166\pi\) | ||||
−0.924879 | + | 0.380262i | \(0.875834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.18134e8 | −0.231599 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.66731e8 | + | 7.32838e8i | −0.519011 | + | 1.42597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.40561e8 | − | 7.97161e8i | −0.271468 | − | 1.53957i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.39179e7 | + | 7.60681e7i | −0.0841887 | + | 0.145819i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.54743e7 | + | 2.97664e7i | 0.0674983 | + | 0.0566378i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.00969e8 | + | 3.48088e8i | 0.379562 | + | 0.657420i | 0.990998 | − | 0.133873i | \(-0.0427414\pi\) |
−0.611437 | + | 0.791293i | \(0.709408\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.75250e8 | + | 4.81495e8i | 0.328545 | + | 0.902670i | 0.988481 | + | 0.151348i | \(0.0483613\pi\) |
−0.659936 | + | 0.751322i | \(0.729417\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.27375e7 | − | 7.53578e6i | −0.0795312 | − | 0.0140235i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.45287e8 | + | 1.21910e8i | −0.268382 | + | 0.225200i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.78525e8 | − | 4.48164e8i | −0.694111 | − | 0.821808i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.05110e8 | − | 1.25265e8i | −0.191333 | − | 0.228022i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.47379e7 | + | 2.53721e8i | −0.0808437 | + | 0.458487i | 0.917333 | + | 0.398122i | \(0.130338\pi\) |
−0.998176 | + | 0.0603657i | \(0.980773\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.14575e8 | − | 4.17020e7i | 0.205538 | − | 0.0748096i | −0.237200 | − | 0.971461i | \(-0.576230\pi\) |
0.442737 | + | 0.896651i | \(0.354007\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.43707e8 | + | 3.13910e8i | −0.968285 | + | 0.559040i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.78081e8 | + | 3.31404e8i | −0.491648 | + | 0.585923i | −0.953636 | − | 0.300963i | \(-0.902692\pi\) |
0.461988 | + | 0.886886i | \(0.347136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.22140e8 | − | 2.43723e8i | −0.740958 | − | 0.427792i | 0.0814598 | − | 0.996677i | \(-0.474042\pi\) |
−0.822417 | + | 0.568885i | \(0.807375\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.21705e6 | + | 919907.i | −0.00909122 | + | 0.00160303i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.64718e7 | + | 3.51129e7i | 0.166904 | + | 0.0607479i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.76578e9i | 3.03304i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.56348e8 | 0.437173 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.98914e7 | − | 1.64550e8i | 0.101409 | − | 0.278620i | −0.878604 | − | 0.477551i | \(-0.841525\pi\) |
0.980014 | + | 0.198931i | \(0.0637469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.81841e7 | + | 2.16553e8i | 0.0641940 | + | 0.364062i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.34147e7 | − | 1.09838e8i | 0.105854 | − | 0.183345i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.27554e8 | + | 4.42670e8i | 0.874372 | + | 0.733686i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.67674e8 | − | 6.36830e8i | −0.605080 | − | 1.04803i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.45785e7 | − | 2.32378e8i | −0.138209 | − | 0.379727i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.45746e8 | − | 2.56990e7i | −0.236488 | − | 0.0416992i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.13974e8 | + | 5.15186e8i | −0.989243 | + | 0.830074i | −0.985458 | − | 0.169919i | \(-0.945649\pi\) |
−0.00378518 | + | 0.999993i | \(0.501205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.84769e6 | − | 8.82332e8i | −0.00455610 | − | 1.41167i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.59895e8 | − | 6.67257e8i | −0.889537 | − | 1.06011i | −0.997820 | − | 0.0659891i | \(-0.978980\pi\) |
0.108283 | − | 0.994120i | \(-0.465465\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.53933e7 | + | 8.72996e7i | −0.0242857 | + | 0.137731i | −0.994540 | − | 0.104357i | \(-0.966721\pi\) |
0.970254 | + | 0.242089i | \(0.0778325\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.12867e8 | − | 4.10801e7i | 0.176830 | − | 0.0643610i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.19149e7 | + | 4.15201e7i | −0.111889 | + | 0.0645990i | −0.554900 | − | 0.831917i | \(-0.687244\pi\) |
0.443011 | + | 0.896516i | \(0.353910\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.96181e8 | + | 2.33800e8i | −0.303116 | + | 0.361240i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.95924e8 | − | 1.13117e8i | −0.300628 | − | 0.173568i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.93458e8 | − | 1.39908e8i | 1.20911 | − | 0.213198i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.65117e8 | + | 1.32892e8i | 0.552557 | + | 0.201114i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.06617e8i | − | 0.911742i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.98828e8 | 0.744606 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.53914e8 | − | 4.22875e8i | 0.228181 | − | 0.626921i | −0.771779 | − | 0.635891i | \(-0.780633\pi\) |
0.999960 | + | 0.00896940i | \(0.00285509\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.81472e7 | + | 3.86482e8i | 0.100342 | + | 0.569066i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.07341e8 | + | 7.05536e8i | −0.595704 | + | 1.03179i | 0.397743 | + | 0.917497i | \(0.369794\pi\) |
−0.993447 | + | 0.114293i | \(0.963540\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.50637e8 | − | 6.29859e8i | −1.09030 | − | 0.914874i | −0.0935687 | − | 0.995613i | \(-0.529827\pi\) |
−0.996735 | + | 0.0807392i | \(0.974272\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.45579e8 | − | 4.25355e8i | −0.354291 | − | 0.613651i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.34105e7 | + | 9.17947e7i | 0.0478754 | + | 0.131537i | 0.961326 | − | 0.275413i | \(-0.0888146\pi\) |
−0.913451 | + | 0.406950i | \(0.866592\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.50156e8 | − | 4.41092e7i | −0.356045 | − | 0.0627803i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.45897e8 | − | 4.58062e8i | 0.771752 | − | 0.647577i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.55628e8 | + | 9.61242e7i | 0.780242 | + | 0.134983i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.92695e8 | − | 5.87171e8i | −0.687241 | − | 0.819022i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.30085e6 | + | 2.43914e7i | −0.00595905 | + | 0.0337955i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.36363e8 | − | 1.22426e8i | 0.462945 | − | 0.168498i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.24175e7 | + | 5.33573e7i | −0.126351 | + | 0.0729490i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.21120e8 | − | 1.44345e8i | 0.164495 | − | 0.196038i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.72593e7 | + | 2.72852e7i | 0.0637590 | + | 0.0368113i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.24056e9 | + | 2.18744e8i | −1.66263 | + | 0.293166i | −0.924411 | − | 0.381397i | \(-0.875443\pi\) |
−0.738217 | + | 0.674563i | \(0.764332\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.92869e8 | + | 3.24978e8i | 1.18877 | + | 0.432675i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.17943e8i | − | 0.552792i | −0.961044 | − | 0.276396i | \(-0.910860\pi\) | ||
0.961044 | − | 0.276396i | \(-0.0891401\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.80438e8 | 0.631284 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.54443e8 | + | 4.24330e8i | −0.201607 | + | 0.553911i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.92034e7 | + | 2.22334e8i | 0.0508412 | + | 0.288335i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.16746e8 | + | 3.75416e8i | −0.279258 | + | 0.483689i | −0.971201 | − | 0.238264i | \(-0.923422\pi\) |
0.691943 | + | 0.721952i | \(0.256755\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.95974e8 | + | 1.64442e8i | 0.250853 | + | 0.210491i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.50397e8 | + | 4.33701e8i | 0.318438 | + | 0.551550i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.86500e8 | + | 1.88614e9i | 0.867391 | + | 2.38314i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.04440e9 | − | 1.84157e8i | −1.31108 | − | 0.231179i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.66904e8 | − | 4.75689e8i | 0.707070 | − | 0.593302i | −0.216706 | − | 0.976237i | \(-0.569531\pi\) |
0.923775 | + | 0.382935i | \(0.125087\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.25170e8 | − | 2.43646e8i | −0.526882 | − | 0.301932i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.68773e8 | + | 4.39486e8i | 0.454061 | + | 0.541129i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.17229e8 | − | 6.64837e8i | 0.143416 | − | 0.813355i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.22024e8 | − | 8.08102e7i | 0.269887 | − | 0.0982308i | −0.203532 | − | 0.979068i | \(-0.565242\pi\) |
0.473419 | + | 0.880838i | \(0.343020\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.41400e8 | + | 1.39372e8i | −0.291568 | + | 0.168337i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.17073e8 | − | 3.77873e8i | 0.380531 | − | 0.453500i | −0.541450 | − | 0.840733i | \(-0.682125\pi\) |
0.921982 | + | 0.387233i | \(0.126569\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.35763e7 | + | 5.40263e7i | 0.111591 | + | 0.0644273i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.05207e8 | − | 1.06714e8i | 0.717148 | − | 0.126453i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.31479e9 | + | 4.78543e8i | 1.54812 | + | 0.563471i | 0.967976 | − | 0.251042i | \(-0.0807731\pi\) |
0.580146 | + | 0.814512i | \(0.302995\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.33099e8i | 0.506743i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.07065e8 | 0.473284 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.54080e7 | + | 2.07182e8i | −0.0871242 | + | 0.239372i | −0.975602 | − | 0.219549i | \(-0.929541\pi\) |
0.888477 | + | 0.458920i | \(0.151764\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.03054e7 | − | 2.28583e8i | −0.0462757 | − | 0.262442i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.26118e8 | + | 3.91648e8i | −0.257988 | + | 0.446849i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.31338e8 | − | 5.29756e8i | −0.715824 | − | 0.600648i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.72882e8 | − | 4.72646e8i | −0.307472 | − | 0.532557i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.40472e8 | − | 9.35439e8i | −0.381244 | − | 1.04746i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.22579e9 | + | 3.92468e8i | 2.47687 | + | 0.436739i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.06160e9 | − | 8.90789e8i | 1.17404 | − | 0.985135i | 0.174038 | − | 0.984739i | \(-0.444319\pi\) |
1.00000 | 0.000395594i | \(-0.000125922\pi\) | ||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.75959e7 | − | 6.46850e7i | −0.0852839 | − | 0.0710939i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.08422e8 | + | 3.67563e8i | 0.336889 | + | 0.401489i | 0.907718 | − | 0.419580i | \(-0.137823\pi\) |
−0.570829 | + | 0.821069i | \(0.693378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.19975e8 | + | 6.80412e8i | −0.130242 | + | 0.738641i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.15655e8 | − | 1.14889e8i | 0.340564 | − | 0.123955i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.90385e8 | + | 2.25389e8i | −0.418609 | + | 0.241684i | −0.694482 | − | 0.719510i | \(-0.744366\pi\) |
0.275873 | + | 0.961194i | \(0.411033\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.83075e9 | − | 2.18181e9i | 1.95111 | − | 2.32524i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.10611e9 | − | 6.38614e8i | −1.17163 | − | 0.676443i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.04256e8 | − | 3.60159e7i | 0.215038 | − | 0.0379170i | −0.0650912 | − | 0.997879i | \(-0.520734\pi\) |
0.280129 | + | 0.959962i | \(0.409623\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.48535e9 | − | 5.40623e8i | −1.55425 | − | 0.565699i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.81123e8i | 0.188374i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.69513e8 | 0.175232 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.44180e7 | − | 2.59411e8i | 0.0970139 | − | 0.266544i | −0.881687 | − | 0.471835i | \(-0.843592\pi\) |
0.978701 | + | 0.205291i | \(0.0658141\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.56590e7 | − | 3.15658e8i | −0.0568444 | − | 0.322380i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.24117e8 | + | 5.61388e8i | −0.329028 | + | 0.569893i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.12179e9 | − | 9.41292e8i | −1.13195 | − | 0.949815i | −0.132800 | − | 0.991143i | \(-0.542397\pi\) |
−0.999146 | + | 0.0413280i | \(0.986841\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.17723e8 | + | 8.96722e8i | 0.519279 | + | 0.899418i |
(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 | 76.7.j.a.13.5 | ✓ | 60 | |
19.3 | odd | 18 | inner | 76.7.j.a.41.5 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.j.a.13.5 | ✓ | 60 | 1.1 | even | 1 | trivial | |
76.7.j.a.41.5 | yes | 60 | 19.3 | odd | 18 | inner |