Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,6,Mod(1,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.a (trivial) |
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: | yes |
Analytic conductor: | \(32.0767639626\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{241}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 60 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(8.26209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −19.5242 | −1.25248 | −0.626238 | − | 0.779632i | \(-0.715406\pi\) | ||||
−0.626238 | + | 0.779632i | \(0.715406\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 35.0483 | 0.270348 | 0.135174 | − | 0.990822i | \(-0.456841\pi\) | ||||
0.135174 | + | 0.990822i | \(0.456841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 138.193 | 0.568697 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −426.008 | −1.06154 | −0.530769 | − | 0.847516i | \(-0.678097\pi\) | ||||
−0.530769 | + | 0.847516i | \(0.678097\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1103.26 | 1.81058 | 0.905291 | − | 0.424791i | \(-0.139653\pi\) | ||||
0.905291 | + | 0.424791i | \(0.139653\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 109.387 | 0.0918000 | 0.0459000 | − | 0.998946i | \(-0.485384\pi\) | ||||
0.0459000 | + | 0.998946i | \(0.485384\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 495.926 | 0.315161 | 0.157581 | − | 0.987506i | \(-0.449631\pi\) | ||||
0.157581 | + | 0.987506i | \(0.449631\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −684.290 | −0.338604 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2497.37 | 0.984381 | 0.492190 | − | 0.870488i | \(-0.336196\pi\) | ||||
0.492190 | + | 0.870488i | \(0.336196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2046.26 | 0.540197 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −42.4221 | −0.00936694 | −0.00468347 | − | 0.999989i | \(-0.501491\pi\) | ||||
−0.00468347 | + | 0.999989i | \(0.501491\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7999.56 | −1.49507 | −0.747535 | − | 0.664222i | \(-0.768763\pi\) | ||||
−0.747535 | + | 0.664222i | \(0.768763\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8317.45 | 1.32955 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −13763.7 | −1.65284 | −0.826420 | − | 0.563054i | \(-0.809626\pi\) | ||||
−0.826420 | + | 0.563054i | \(0.809626\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −21540.2 | −2.26771 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11863.6 | 1.10219 | 0.551097 | − | 0.834441i | \(-0.314210\pi\) | ||||
0.551097 | + | 0.834441i | \(0.314210\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16816.0 | −1.38692 | −0.693461 | − | 0.720494i | \(-0.743915\pi\) | ||||
−0.693461 | + | 0.720494i | \(0.743915\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13036.0 | −0.860795 | −0.430397 | − | 0.902639i | \(-0.641627\pi\) | ||||
−0.430397 | + | 0.902639i | \(0.641627\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15578.6 | −0.926912 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2135.69 | −0.114977 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 17817.3 | 0.871269 | 0.435634 | − | 0.900124i | \(-0.356524\pi\) | ||||
0.435634 | + | 0.900124i | \(0.356524\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9682.55 | −0.394732 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −47346.1 | −1.77074 | −0.885368 | − | 0.464891i | \(-0.846094\pi\) | ||||
−0.885368 | + | 0.464891i | \(0.846094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −22782.9 | −0.783944 | −0.391972 | − | 0.919977i | \(-0.628207\pi\) | ||||
−0.391972 | + | 0.919977i | \(0.628207\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4843.45 | 0.153746 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −39418.3 | −1.07278 | −0.536390 | − | 0.843970i | \(-0.680213\pi\) | ||||
−0.536390 | + | 0.843970i | \(0.680213\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −48759.1 | −1.23291 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1616.32 | −0.0380523 | −0.0190261 | − | 0.999819i | \(-0.506057\pi\) | ||||
−0.0190261 | + | 0.999819i | \(0.506057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 53293.3 | 1.17048 | 0.585242 | − | 0.810859i | \(-0.301000\pi\) | ||||
0.585242 | + | 0.810859i | \(0.301000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14930.9 | −0.286984 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6516.98 | −0.117484 | −0.0587420 | − | 0.998273i | \(-0.518709\pi\) | ||||
−0.0587420 | + | 0.998273i | \(0.518709\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73532.6 | −1.24528 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 46016.4 | 0.733191 | 0.366595 | − | 0.930380i | \(-0.380523\pi\) | ||||
0.366595 | + | 0.930380i | \(0.380523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 828.257 | 0.0117319 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 113488. | 1.51872 | 0.759358 | − | 0.650673i | \(-0.225513\pi\) | ||||
0.759358 | + | 0.650673i | \(0.225513\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 38667.3 | 0.489487 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 156185. | 1.87254 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 107418. | 1.15917 | 0.579585 | − | 0.814912i | \(-0.303215\pi\) | ||||
0.579585 | + | 0.814912i | \(0.303215\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −58871.4 | −0.603694 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −197554. | −1.92700 | −0.963502 | − | 0.267703i | \(-0.913736\pi\) | ||||
−0.963502 | + | 0.267703i | \(0.913736\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −81026.0 | −0.752543 | −0.376272 | − | 0.926509i | \(-0.622794\pi\) | ||||
−0.376272 | + | 0.926509i | \(0.622794\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −137442. | −1.16054 | −0.580271 | − | 0.814423i | \(-0.697054\pi\) | ||||
−0.580271 | + | 0.814423i | \(0.697054\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −68693.1 | −0.553792 | −0.276896 | − | 0.960900i | \(-0.589306\pi\) | ||||
−0.276896 | + | 0.960900i | \(0.589306\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 268725. | 2.07014 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −139632. | −1.02870 | −0.514352 | − | 0.857579i | \(-0.671967\pi\) | ||||
−0.514352 | + | 0.857579i | \(0.671967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 152463. | 1.02967 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3833.83 | 0.0248179 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20431.5 | 0.126864 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −231628. | −1.38047 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −65230.1 | −0.358871 | −0.179436 | − | 0.983770i | \(-0.557427\pi\) | ||||
−0.179436 | + | 0.983770i | \(0.557427\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 328319. | 1.73709 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 118542. | 0.603524 | 0.301762 | − | 0.953383i | \(-0.402425\pi\) | ||||
0.301762 | + | 0.953383i | \(0.402425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17381.4 | 0.0852031 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 84757.8 | 0.385814 | 0.192907 | − | 0.981217i | \(-0.438208\pi\) | ||||
0.192907 | + | 0.981217i | \(0.438208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 168334. | 0.738982 | 0.369491 | − | 0.929234i | \(-0.379532\pi\) | ||||
0.369491 | + | 0.929234i | \(0.379532\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 254517. | 1.07813 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −469996. | −1.92200 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 304160. | 1.16094 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 67628.6 | 0.249554 | 0.124777 | − | 0.992185i | \(-0.460178\pi\) | ||||
0.124777 | + | 0.992185i | \(0.460178\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −65622.3 | −0.234212 | −0.117106 | − | 0.993119i | \(-0.537362\pi\) | ||||
−0.117106 | + | 0.993119i | \(0.537362\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15116.5 | 0.0522064 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −297885. | −0.964495 | −0.482247 | − | 0.876035i | \(-0.660179\pi\) | ||||
−0.482247 | + | 0.876035i | \(0.660179\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −347868. | −1.09124 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 87528.7 | 0.266125 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −473879. | −1.39701 | −0.698503 | − | 0.715607i | \(-0.746150\pi\) | ||||
−0.698503 | + | 0.715607i | \(0.746150\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 267673. | 0.742701 | 0.371351 | − | 0.928493i | \(-0.378895\pi\) | ||||
0.371351 | + | 0.928493i | \(0.378895\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 845883. | 2.27821 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 68533.7 | 0.179231 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 703284. | 1.78655 | 0.893276 | − | 0.449509i | \(-0.148401\pi\) | ||||
0.893276 | + | 0.449509i | \(0.148401\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 924393. | 2.21780 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 635322. | 1.48204 | 0.741022 | − | 0.671481i | \(-0.234341\pi\) | ||||
0.741022 | + | 0.671481i | \(0.234341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −547906. | −1.24311 | −0.621555 | − | 0.783370i | \(-0.713499\pi\) | ||||
−0.621555 | + | 0.783370i | \(0.713499\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 444818. | 0.981872 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −46599.6 | −0.0974492 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 71718.1 | 0.146041 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −80607.9 | −0.159880 | −0.0799400 | − | 0.996800i | \(-0.525473\pi\) | ||||
−0.0799400 | + | 0.996800i | \(0.525473\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26549.3 | −0.0513049 | −0.0256525 | − | 0.999671i | \(-0.508166\pi\) | ||||
−0.0256525 | + | 0.999671i | \(0.508166\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −703676. | −1.29184 | −0.645918 | − | 0.763407i | \(-0.723525\pi\) | ||||
−0.645918 | + | 0.763407i | \(0.723525\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 73599.5 | 0.131747 | 0.0658737 | − | 0.997828i | \(-0.479017\pi\) | ||||
0.0658737 | + | 0.997828i | \(0.479017\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 769610. | 1.34363 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1486.83 | −0.00253233 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 345120. | 0.559815 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −211268. | −0.334556 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00808e6 | −1.55879 | −0.779395 | − | 0.626533i | \(-0.784474\pi\) | ||||
−0.779395 | + | 0.626533i | \(0.784474\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 31557.2 | 0.0476596 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −280371. | −0.404189 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.04051e6 | −1.46600 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 120682. | 0.166211 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 141067. | 0.189961 | 0.0949805 | − | 0.995479i | \(-0.469721\pi\) | ||||
0.0949805 | + | 0.995479i | \(0.469721\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.14301e6 | −1.47226 | −0.736129 | − | 0.676842i | \(-0.763348\pi\) | ||||
−0.736129 | + | 0.676842i | \(0.763348\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.29731e6 | −1.63476 | −0.817380 | − | 0.576099i | \(-0.804574\pi\) | ||||
−0.817380 | + | 0.576099i | \(0.804574\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 291513. | 0.359441 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −626232. | −0.755693 | −0.377846 | − | 0.925868i | \(-0.623335\pi\) | ||||
−0.377846 | + | 0.925868i | \(0.623335\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 127239. | 0.147146 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 270281. | 0.306070 | 0.153035 | − | 0.988221i | \(-0.451095\pi\) | ||||
0.153035 | + | 0.988221i | \(0.451095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −694339. | −0.770068 | −0.385034 | − | 0.922902i | \(-0.625810\pi\) | ||||
−0.385034 | + | 0.922902i | \(0.625810\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 938421. | 1.01949 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 547134. | 0.570626 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −898431. | −0.918304 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 864085. | 0.865710 | 0.432855 | − | 0.901464i | \(-0.357506\pi\) | ||||
0.432855 | + | 0.901464i | \(0.357506\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.06390e6 | −1.04496 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.00660e6 | −0.950660 | −0.475330 | − | 0.879808i | \(-0.657671\pi\) | ||||
−0.475330 | + | 0.879808i | \(0.657671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −482395. | −0.446841 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5862.46 | −0.00532695 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 931373. | 0.830299 | 0.415149 | − | 0.909753i | \(-0.363729\pi\) | ||||
0.415149 | + | 0.909753i | \(0.363729\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.21577e6 | −1.90216 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.96236e6 | −1.65348 | −0.826738 | − | 0.562587i | \(-0.809806\pi\) | ||||
−0.826738 | + | 0.562587i | \(0.809806\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.12152e6 | 0.927649 | 0.463825 | − | 0.885927i | \(-0.346477\pi\) | ||||
0.463825 | + | 0.885927i | \(0.346477\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −754948. | −0.613070 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −105917. | −0.0829401 | −0.0414701 | − | 0.999140i | \(-0.513204\pi\) | ||||
−0.0414701 | + | 0.999140i | \(0.513204\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.10549e6 | −0.850242 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.05276e6 | −0.795362 | −0.397681 | − | 0.917524i | \(-0.630185\pi\) | ||||
−0.397681 | + | 0.917524i | \(0.630185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 950210. | 0.705267 | 0.352633 | − | 0.935762i | \(-0.385286\pi\) | ||||
0.352633 | + | 0.935762i | \(0.385286\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 415801. | 0.297975 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.40789e6 | −0.991573 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.09725e6 | −1.45183 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 381801. | 0.259817 | 0.129909 | − | 0.991526i | \(-0.458532\pi\) | ||||
0.129909 | + | 0.991526i | \(0.458532\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −871723. | −0.573440 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.75524e6 | 1.78230 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −589373. | −0.374951 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.85708e6 | 2.41353 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.61048e6 | 0.975238 | 0.487619 | − | 0.873057i | \(-0.337866\pi\) | ||||
0.487619 | + | 0.873057i | \(0.337866\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.58197e6 | 0.942543 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.15652e6 | −1.26431 | −0.632153 | − | 0.774843i | \(-0.717829\pi\) | ||||
−0.632153 | + | 0.774843i | \(0.717829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 364108. | 0.210073 | 0.105036 | − | 0.994468i | \(-0.466504\pi\) | ||||
0.105036 | + | 0.994468i | \(0.466504\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.03846e6 | 0.580420 | 0.290210 | − | 0.956963i | \(-0.406275\pi\) | ||||
0.290210 | + | 0.956963i | \(0.406275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18072.2 | 0.00994336 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.68345e6 | 1.45355 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 54247.8 | 0.0289318 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.34118e6 | 0.693612 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −456890. | −0.232714 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.82942e6 | −1.41948 | −0.709738 | − | 0.704466i | \(-0.751186\pi\) | ||||
−0.709738 | + | 0.704466i | \(0.751186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.90205e6 | −0.939966 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −804843. | −0.386043 | −0.193022 | − | 0.981194i | \(-0.561829\pi\) | ||||
−0.193022 | + | 0.981194i | \(0.561829\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.72621e6 | 1.28843 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.40787e6 | 1.58708 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.13506e6 | −0.520936 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −759889. | −0.338787 | −0.169393 | − | 0.985549i | \(-0.554181\pi\) | ||||
−0.169393 | + | 0.985549i | \(0.554181\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 580673. | 0.255193 | 0.127596 | − | 0.991826i | \(-0.459274\pi\) | ||||
0.127596 | + | 0.991826i | \(0.459274\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.25755e6 | 0.978071 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.64210e6 | 0.701393 | 0.350697 | − | 0.936489i | \(-0.385945\pi\) | ||||
0.350697 | + | 0.936489i | \(0.385945\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −74852.3 | −0.0310838 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.88181e6 | −1.18013 | −0.590065 | − | 0.807356i | \(-0.700898\pi\) | ||||
−0.590065 | + | 0.807356i | \(0.700898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.23016e6 | −0.900673 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −398909. | −0.158894 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.83418e6 | 1.48596 | 0.742980 | − | 0.669314i | \(-0.233412\pi\) | ||||
0.742980 | + | 0.669314i | \(0.233412\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.63947e6 | 0.626814 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 624467. | 0.235545 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.19341e6 | −1.18845 | −0.594227 | − | 0.804298i | \(-0.702542\pi\) | ||||
−0.594227 | + | 0.804298i | \(0.702542\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −46802.5 | −0.0169596 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.47338e6 | 1.24209 | 0.621046 | − | 0.783774i | \(-0.286708\pi\) | ||||
0.621046 | + | 0.783774i | \(0.286708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.27356e6 | 0.449478 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.56341e6 | −0.544599 | −0.272299 | − | 0.962213i | \(-0.587784\pi\) | ||||
−0.272299 | + | 0.962213i | \(0.587784\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.32386e6 | −0.788738 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.98980e6 | 1.67190 | 0.835949 | − | 0.548808i | \(-0.184918\pi\) | ||||
0.835949 | + | 0.548808i | \(0.184918\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 273179. | 0.0903661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.31444e6 | −0.755899 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.37245e6 | 0.437038 | 0.218519 | − | 0.975833i | \(-0.429877\pi\) | ||||
0.218519 | + | 0.975833i | \(0.429877\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −339357. | −0.106715 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.44247e6 | 1.69019 | 0.845094 | − | 0.534617i | \(-0.179544\pi\) | ||||
0.845094 | + | 0.534617i | \(0.179544\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.82557e6 | −2.70695 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.86344e6 | 1.75455 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.03830e6 | −1.78487 | −0.892435 | − | 0.451176i | \(-0.851005\pi\) | ||||
−0.892435 | + | 0.451176i | \(0.851005\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.65483e6 | −0.483223 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.65940e6 | −0.478714 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.28657e6 | −0.925557 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 770366. | 0.214369 | 0.107184 | − | 0.994239i | \(-0.465816\pi\) | ||||
0.107184 | + | 0.994239i | \(0.465816\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00249e6 | 0.550636 | 0.275318 | − | 0.961353i | \(-0.411217\pi\) | ||||
0.275318 | + | 0.961353i | \(0.411217\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.80149e6 | −0.489532 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −798504. | −0.211937 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.17628e6 | 2.40726 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.56690e6 | 1.44351 | 0.721756 | − | 0.692148i | \(-0.243335\pi\) | ||||
0.721756 | + | 0.692148i | \(0.243335\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.22941e6 | 0.571441 | 0.285720 | − | 0.958313i | \(-0.407767\pi\) | ||||
0.285720 | + | 0.958313i | \(0.407767\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.23851e6 | 0.310239 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 543061. | 0.134489 | 0.0672446 | − | 0.997737i | \(-0.478579\pi\) | ||||
0.0672446 | + | 0.997737i | \(0.478579\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.15286e6 | −0.527132 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.53358e6 | 1.09757 | 0.548785 | − | 0.835964i | \(-0.315091\pi\) | ||||
0.548785 | + | 0.835964i | \(0.315091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.32039e6 | −0.312561 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.39468e6 | −0.794662 | −0.397331 | − | 0.917675i | \(-0.630064\pi\) | ||||
−0.397331 | + | 0.917675i | \(0.630064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.05400e6 | −1.17002 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.28122e6 | 0.293345 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.34100e6 | 1.86822 | 0.934109 | − | 0.356988i | \(-0.116196\pi\) | ||||
0.934109 | + | 0.356988i | \(0.116196\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 223834. | 0.0495900 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.18453e6 | −0.697900 | −0.348950 | − | 0.937141i | \(-0.613462\pi\) | ||||
−0.348950 | + | 0.937141i | \(0.613462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.05943e6 | 0.880061 | 0.440030 | − | 0.897983i | \(-0.354968\pi\) | ||||
0.440030 | + | 0.897983i | \(0.354968\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.98706e6 | −1.69471 | −0.847353 | − | 0.531029i | \(-0.821805\pi\) | ||||
−0.847353 | + | 0.531029i | \(0.821805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.38155e6 | −0.290024 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.81596e6 | 1.20801 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.16375e6 | 1.47227 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.46223e6 | 0.495488 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.27553e6 | 1.05058 | 0.525288 | − | 0.850924i | \(-0.323958\pi\) | ||||
0.525288 | + | 0.850924i | \(0.323958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.51849e7 | −2.99260 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.70892e6 | −0.333315 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.76969e6 | 1.67557 | 0.837784 | − | 0.546002i | \(-0.183851\pi\) | ||||
0.837784 | + | 0.546002i | \(0.183851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.25209e6 | 1.74972 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.83080e6 | 1.46589 | 0.732946 | − | 0.680286i | \(-0.238145\pi\) | ||||
0.732946 | + | 0.680286i | \(0.238145\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4640.42 | −0.000859885 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −56649.2 | −0.0102873 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.54560e6 | −1.17679 | −0.588394 | − | 0.808574i | \(-0.700240\pi\) | ||||
−0.588394 | + | 0.808574i | \(0.700240\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.22610e6 | −0.930216 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.07773e6 | −0.366158 | −0.183079 | − | 0.983098i | \(-0.558606\pi\) | ||||
−0.183079 | + | 0.983098i | \(0.558606\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.65152e7 | −2.85340 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.25093e6 | −1.06942 | −0.534712 | − | 0.845034i | \(-0.679580\pi\) | ||||
−0.534712 | + | 0.845034i | \(0.679580\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.86784e6 | 0.316437 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.01480e6 | 0.170249 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.55344e6 | 0.913767 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.37310e7 | −2.23761 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.19897e6 | 0.354916 | 0.177458 | − | 0.984128i | \(-0.443213\pi\) | ||||
0.177458 | + | 0.984128i | \(0.443213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.10298e6 | −0.336187 | −0.168093 | − | 0.985771i | \(-0.553761\pi\) | ||||
−0.168093 | + | 0.985771i | \(0.553761\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −875046. | −0.137247 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −199490. | −0.0309944 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.54291e6 | −1.00701 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.30886e7 | 1.99561 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.24041e7 | −1.85623 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.63661e6 | 0.983953 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.83729e6 | −0.269889 | −0.134944 | − | 0.990853i | \(-0.543086\pi\) | ||||
−0.134944 | + | 0.990853i | \(0.543086\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.06974e7 | 1.55697 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.31872e6 | 0.617145 | 0.308572 | − | 0.951201i | \(-0.400149\pi\) | ||||
0.308572 | + | 0.951201i | \(0.400149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.14845e6 | −0.445827 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21038.3 | −0.00295210 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −228409. | −0.0317615 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.26837e6 | −0.582940 | −0.291470 | − | 0.956580i | \(-0.594144\pi\) | ||||
−0.291470 | + | 0.956580i | \(0.594144\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.85524e7 | −2.51114 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 909819. | 0.122053 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.26350e7 | −1.67998 | −0.839988 | − | 0.542605i | \(-0.817438\pi\) | ||||
−0.839988 | + | 0.542605i | \(0.817438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.57720e6 | −0.336659 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.67409e6 | −1.12316 | −0.561582 | − | 0.827421i | \(-0.689807\pi\) | ||||
−0.561582 | + | 0.827421i | \(0.689807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.28781e6 | 0.422004 | 0.211002 | − | 0.977486i | \(-0.432327\pi\) | ||||
0.211002 | + | 0.977486i | \(0.432327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.57380e6 | 0.200246 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −117668. | −0.0147135 | −0.00735677 | − | 0.999973i | \(-0.502342\pi\) | ||||
−0.00735677 | + | 0.999973i | \(0.502342\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 518352. | 0.0642582 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.61280e6 | 0.198216 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.59031e6 | −0.924885 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.10151e7 | −1.31945 | −0.659723 | − | 0.751509i | \(-0.729326\pi\) | ||||
−0.659723 | + | 0.751509i | \(0.729326\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.96719e6 | −0.471189 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.37387e7 | 1.61799 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.33879e6 | −0.623456 | −0.311728 | − | 0.950171i | \(-0.600908\pi\) | ||||
−0.311728 | + | 0.950171i | \(0.600908\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.43697e6 | −0.165011 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.17784e6 | −0.817385 | −0.408692 | − | 0.912672i | \(-0.634015\pi\) | ||||
−0.408692 | + | 0.912672i | \(0.634015\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −809127. | −0.0913756 | −0.0456878 | − | 0.998956i | \(-0.514548\pi\) | ||||
−0.0456878 | + | 0.998956i | \(0.514548\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.44735e6 | −0.610087 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 591991. | 0.0652143 | 0.0326072 | − | 0.999468i | \(-0.489619\pi\) | ||||
0.0326072 | + | 0.999468i | \(0.489619\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29029.1 | 0.00317168 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.43821e7 | −1.55854 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.01173e6 | −0.431201 | −0.215601 | − | 0.976482i | \(-0.569171\pi\) | ||||
−0.215601 | + | 0.976482i | \(0.569171\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.24093e6 | 0.871491 | 0.435746 | − | 0.900070i | \(-0.356485\pi\) | ||||
0.435746 | + | 0.900070i | \(0.356485\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.96985e6 | 0.206636 | 0.103318 | − | 0.994648i | \(-0.467054\pi\) | ||||
0.103318 | + | 0.994648i | \(0.467054\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.11027e6 | 0.531759 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.97758e6 | 0.410581 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.12484e6 | 0.419024 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.50557e6 | −0.151731 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.82360e7 | −1.82329 | −0.911646 | − | 0.410977i | \(-0.865187\pi\) | ||||
−0.911646 | + | 0.410977i | \(0.865187\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.96819e7 | 1.95235 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.71872e7 | −1.67825 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −223364. | −0.0216402 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.65378e6 | 0.735752 | 0.367876 | − | 0.929875i | \(-0.380085\pi\) | ||||
0.367876 | + | 0.929875i | \(0.380085\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.47762e6 | 0.236323 | 0.118162 | − | 0.992994i | \(-0.462300\pi\) | ||||
0.118162 | + | 0.992994i | \(0.462300\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.79533e6 | 0.450358 | 0.225179 | − | 0.974317i | \(-0.427703\pi\) | ||||
0.225179 | + | 0.974317i | \(0.427703\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.01698e7 | 1.87970 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.47402e6 | 0.506237 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.67125e7 | 1.53376 | 0.766881 | − | 0.641789i | \(-0.221807\pi\) | ||||
0.766881 | + | 0.641789i | \(0.221807\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.36478e6 | 0.665650 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.28380e6 | 0.294553 | 0.147277 | − | 0.989095i | \(-0.452949\pi\) | ||||
0.147277 | + | 0.989095i | \(0.452949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.98880e7 | −1.77047 | −0.885234 | − | 0.465145i | \(-0.846002\pi\) | ||||
−0.885234 | + | 0.465145i | \(0.846002\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.35621e6 | −0.208176 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −105944. | −0.00922063 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.75423e6 | −0.237922 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.70571e6 | 0.832187 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.39915e7 | −1.19076 | −0.595381 | − | 0.803443i | \(-0.702999\pi\) | ||||
−0.595381 | + | 0.803443i | \(0.702999\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.13032e6 | 0.262493 | 0.131246 | − | 0.991350i | \(-0.458102\pi\) | ||||
0.131246 | + | 0.991350i | \(0.458102\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.76482e6 | 0.313379 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.23162e7 | 1.84397 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.94034e6 | 0.733335 | 0.366667 | − | 0.930352i | \(-0.380499\pi\) | ||||
0.366667 | + | 0.930352i | \(0.380499\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.53288e7 | 2.04750 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.96571e7 | 1.57750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.38378e7 | −1.89920 | −0.949599 | − | 0.313466i | \(-0.898510\pi\) | ||||
−0.949599 | + | 0.313466i | \(0.898510\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.06335e6 | −0.163207 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.29772e6 | 0.101181 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.22267e7 | 0.946487 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.57226e7 | 1.20845 | 0.604225 | − | 0.796814i | \(-0.293483\pi\) | ||||
0.604225 | + | 0.796814i | \(0.293483\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.82578e6 | −0.520912 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.92394e6 | −0.520961 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.05866e6 | −0.228515 | −0.114258 | − | 0.993451i | \(-0.536449\pi\) | ||||
−0.114258 | + | 0.993451i | \(0.536449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −900603. | −0.0668128 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.99778e7 | −1.47172 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.27701e6 | −0.383345 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.16146e7 | 1.55929 | 0.779643 | − | 0.626224i | \(-0.215400\pi\) | ||||
0.779643 | + | 0.626224i | \(0.215400\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.83983e6 | −0.203448 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.35564e7 | 0.964492 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.73589e7 | 1.91983 | 0.959916 | − | 0.280287i | \(-0.0904297\pi\) | ||||
0.959916 | + | 0.280287i | \(0.0904297\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −453482. | −0.0316039 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.83945e6 | −0.127319 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.54693e7 | −1.06344 | −0.531718 | − | 0.846921i | \(-0.678453\pi\) | ||||
−0.531718 | + | 0.846921i | \(0.678453\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.67925e7 | 1.13880 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.56327e6 | 0.374731 | 0.187365 | − | 0.982290i | \(-0.440005\pi\) | ||||
0.187365 | + | 0.982290i | \(0.440005\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.06823e7 | −0.714695 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.55089e7 | 1.03064 | 0.515322 | − | 0.856997i | \(-0.327672\pi\) | ||||
0.515322 | + | 0.856997i | \(0.327672\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.35916e6 | 0.416963 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.81713e6 | −0.313750 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.20221e7 | 1.42482 | 0.712409 | − | 0.701765i | \(-0.247604\pi\) | ||||
0.712409 | + | 0.701765i | \(0.247604\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.68706e7 | −1.08428 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.75653e6 | 0.111408 | 0.0557040 | − | 0.998447i | \(-0.482260\pi\) | ||||
0.0557040 | + | 0.998447i | \(0.482260\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.07717e7 | 1.30879 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.16974e6 | −0.135814 | −0.0679072 | − | 0.997692i | \(-0.521632\pi\) | ||||
−0.0679072 | + | 0.997692i | \(0.521632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.40758e6 | −0.149716 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.22349e7 | −3.20606 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.12131e7 | −0.683769 | −0.341884 | − | 0.939742i | \(-0.611065\pi\) | ||||
−0.341884 | + | 0.939742i | \(0.611065\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.96531e7 | 1.19068 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.43367e7 | −0.862980 | −0.431490 | − | 0.902118i | \(-0.642012\pi\) | ||||
−0.431490 | + | 0.902118i | \(0.642012\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.41836e6 | 0.559658 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.88348e6 | 0.347369 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 688563. | 0.0403939 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −86806.8 | −0.00505999 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.00549e6 | −0.115421 | −0.0577103 | − | 0.998333i | \(-0.518380\pi\) | ||||
−0.0577103 | + | 0.998333i | \(0.518380\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.81843e7 | −1.03993 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.89389e6 | −0.278108 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.51354e7 | −1.41940 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −448115. | −0.0249887 | −0.0124944 | − | 0.999922i | \(-0.503977\pi\) | ||||
−0.0124944 | + | 0.999922i | \(0.503977\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.42597e6 | −0.0790210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.56834e7 | 0.863690 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.27033e7 | −1.24251 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.83134e7 | 2.07094 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.28425e7 | 0.689889 | 0.344944 | − | 0.938623i | \(-0.387898\pi\) | ||||
0.344944 | + | 0.938623i | \(0.387898\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.78700e7 | 0.954054 | 0.477027 | − | 0.878889i | \(-0.341714\pi\) | ||||
0.477027 | + | 0.878889i | \(0.341714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.18968e7 | −1.16186 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.33950e6 | −0.437104 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.34357e6 | 0.278370 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.73336e7 | 1.41527 | 0.707634 | − | 0.706580i | \(-0.249763\pi\) | ||||
0.707634 | + | 0.706580i | \(0.249763\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.05819e6 | −0.157385 | −0.0786927 | − | 0.996899i | \(-0.525075\pi\) | ||||
−0.0786927 | + | 0.996899i | \(0.525075\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.23961e7 | −0.630261 | −0.315131 | − | 0.949048i | \(-0.602048\pi\) | ||||
−0.315131 | + | 0.949048i | \(0.602048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −399873. | −0.0202086 | −0.0101043 | − | 0.999949i | \(-0.503216\pi\) | ||||
−0.0101043 | + | 0.999949i | \(0.503216\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.06793e6 | 0.103881 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.70409e6 | −0.0850905 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.63692e7 | −0.807632 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.08411e6 | −0.102215 | −0.0511075 | − | 0.998693i | \(-0.516275\pi\) | ||||
−0.0511075 | + | 0.998693i | \(0.516275\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.05093e7 | −0.999912 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.05543e7 | 0.996172 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 716092. | 0.0342973 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.85521e7 | −0.883330 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.43730e7 | −1.62702 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.14298e7 | 1.00843 | 0.504214 | − | 0.863579i | \(-0.331782\pi\) | ||||
0.504214 | + | 0.863579i | \(0.331782\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.49123e6 | 0.162377 | 0.0811887 | − | 0.996699i | \(-0.474128\pi\) | ||||
0.0811887 | + | 0.996699i | \(0.474128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −568043. | −0.0262662 | −0.0131331 | − | 0.999914i | \(-0.504181\pi\) | ||||
−0.0131331 | + | 0.999914i | \(0.504181\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.11816e6 | −0.373207 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.28678e7 | 1.50226 | 0.751128 | − | 0.660157i | \(-0.229510\pi\) | ||||
0.751128 | + | 0.660157i | \(0.229510\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.74879e7 | 1.24192 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.77628e6 | 0.124714 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.34885e7 | −1.94236 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.48444e7 | 0.659217 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.92945e7 | 1.28614 | 0.643069 | − | 0.765808i | \(-0.277661\pi\) | ||||
0.643069 | + | 0.765808i | \(0.277661\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.45435e6 | −0.325415 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.88332e6 | 0.125156 | 0.0625782 | − | 0.998040i | \(-0.480068\pi\) | ||||
0.0625782 | + | 0.998040i | \(0.480068\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.79477e7 | 1.20627 | 0.603135 | − | 0.797639i | \(-0.293918\pi\) | ||||
0.603135 | + | 0.797639i | \(0.293918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.89567e7 | −1.23578 | −0.617888 | − | 0.786266i | \(-0.712011\pi\) | ||||
−0.617888 | + | 0.786266i | \(0.712011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.28621e6 | −0.0970199 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.13254e7 | 1.32191 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.46490e6 | −0.271289 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.37938e7 | −2.23229 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 339358. | 0.0140042 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.94898e6 | 0.0799825 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.15070e7 | 0.469617 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.18508e6 | −0.0478333 | −0.0239166 | − | 0.999714i | \(-0.507614\pi\) | ||||
−0.0239166 | + | 0.999714i | \(0.507614\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.73007e7 | −1.09588 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.14346e7 | −0.456485 | −0.228242 | − | 0.973604i | \(-0.573298\pi\) | ||||
−0.228242 | + | 0.973604i | \(0.573298\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.96033e7 | −0.778310 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.15471e6 | 0.163161 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.48904e7 | −0.581589 | −0.290795 | − | 0.956785i | \(-0.593920\pi\) | ||||
−0.290795 | + | 0.956785i | \(0.593920\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.14434e7 | −1.22146 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.78321e6 | −0.0688968 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.11973e7 | −0.427969 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.02580e7 | −0.770117 | −0.385058 | − | 0.922892i | \(-0.625819\pi\) | ||||
−0.385058 | + | 0.922892i | \(0.625819\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.72584e6 | −0.292127 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.21043e7 | 1.58351 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.96237e7 | −0.730182 | −0.365091 | − | 0.930972i | \(-0.618962\pi\) | ||||
−0.365091 | + | 0.930972i | \(0.618962\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.10891e6 | −0.263111 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.62854e6 | 0.280846 | 0.140423 | − | 0.990092i | \(-0.455154\pi\) | ||||
0.140423 | + | 0.990092i | \(0.455154\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.96279e7 | 1.08498 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.93605e7 | 1.42622 | 0.713108 | − | 0.701054i | \(-0.247287\pi\) | ||||
0.713108 | + | 0.701054i | \(0.247287\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.87962e7 | 2.11926 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.02751e7 | −0.726963 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.09953e7 | 1.81886 | 0.909428 | − | 0.415861i | \(-0.136520\pi\) | ||||
0.909428 | + | 0.415861i | \(0.136520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −352844. | −0.0124538 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.97062e6 | 0.104304 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.53638e7 | 1.23524 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.89936e7 | −0.659997 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.17740e7 | −1.78051 | −0.890257 | − | 0.455458i | \(-0.849476\pi\) | ||||
−0.890257 | + | 0.455458i | \(0.849476\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.05914e6 | −0.0362364 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.69158e7 | −1.25651 | −0.628253 | − | 0.778009i | \(-0.716230\pi\) | ||||
−0.628253 | + | 0.778009i | \(0.716230\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.89981e6 | 0.199782 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.14468e7 | 1.05400 | 0.526999 | − | 0.849866i | \(-0.323317\pi\) | ||||
0.526999 | + | 0.849866i | \(0.323317\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.83470e7 | −1.61218 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.49293e6 | −0.314940 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.15823e7 | −1.70262 | −0.851308 | − | 0.524667i | \(-0.824190\pi\) | ||||
−0.851308 | + | 0.524667i | \(0.824190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.92041e6 | 0.291469 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.19958e7 | −1.36526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.30562e7 | −0.422312 | −0.211156 | − | 0.977452i | \(-0.567723\pi\) | ||||
−0.211156 | + | 0.977452i | \(0.567723\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.52421e7 | 1.77786 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.97672e7 | −1.58564 | −0.792821 | − | 0.609454i | \(-0.791389\pi\) | ||||
−0.792821 | + | 0.609454i | \(0.791389\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.81641e7 | −0.892859 |
(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 | 200.6.a.e.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 400.6.a.u.1.2 | 2 | |||
5.2 | odd | 4 | 200.6.c.f.49.4 | 4 | |||
5.3 | odd | 4 | 200.6.c.f.49.1 | 4 | |||
5.4 | even | 2 | 200.6.a.f.1.2 | yes | 2 | ||
20.3 | even | 4 | 400.6.c.o.49.4 | 4 | |||
20.7 | even | 4 | 400.6.c.o.49.1 | 4 | |||
20.19 | odd | 2 | 400.6.a.r.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.6.a.e.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
200.6.a.f.1.2 | yes | 2 | 5.4 | even | 2 | ||
200.6.c.f.49.1 | 4 | 5.3 | odd | 4 | |||
200.6.c.f.49.4 | 4 | 5.2 | odd | 4 | |||
400.6.a.r.1.1 | 2 | 20.19 | odd | 2 | |||
400.6.a.u.1.2 | 2 | 4.3 | odd | 2 | |||
400.6.c.o.49.1 | 4 | 20.7 | even | 4 | |||
400.6.c.o.49.4 | 4 | 20.3 | even | 4 |