Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,3,Mod(1151,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.1151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.8774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.8 | ||
Root | \(-0.951057 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.1151 |
Dual form | 1280.3.g.e.1151.7 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.80423 | 1.26808 | 0.634038 | − | 0.773302i | \(-0.281396\pi\) | ||||
0.634038 | + | 0.773302i | \(0.281396\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.50651i | 1.21522i | 0.794237 | + | 0.607608i | \(0.207871\pi\) | ||||
−0.794237 | + | 0.607608i | \(0.792129\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.47214 | 0.608015 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.79611 | −0.163283 | −0.0816415 | − | 0.996662i | \(-0.526016\pi\) | ||||
−0.0816415 | + | 0.996662i | \(0.526016\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.472136i | − 0.0363182i | −0.999835 | − | 0.0181591i | \(-0.994219\pi\) | ||||
0.999835 | − | 0.0181591i | \(-0.00578053\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.50651i | 0.567101i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −23.8885 | −1.40521 | −0.702604 | − | 0.711581i | \(-0.747980\pi\) | ||||
−0.702604 | + | 0.711581i | \(0.747980\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.40456 | −0.494977 | −0.247489 | − | 0.968891i | \(-0.579605\pi\) | ||||
−0.247489 | + | 0.968891i | \(0.579605\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 32.3607i | 1.54098i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.1150i | 0.700650i | 0.936628 | + | 0.350325i | \(0.113929\pi\) | ||||
−0.936628 | + | 0.350325i | \(0.886071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −13.4208 | −0.497066 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 6.94427i | − 0.239458i | −0.992807 | − | 0.119729i | \(-0.961797\pi\) | ||||
0.992807 | − | 0.119729i | \(-0.0382025\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 47.4468i | 1.53054i | 0.643708 | + | 0.765271i | \(0.277395\pi\) | ||||
−0.643708 | + | 0.765271i | \(0.722605\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.83282 | −0.207055 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −19.0211 | −0.543461 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26.3607i | 0.712451i | 0.934400 | + | 0.356225i | \(0.115936\pi\) | ||||
−0.934400 | + | 0.356225i | \(0.884064\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 1.79611i | − 0.0460542i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 41.4164 | 1.01016 | 0.505078 | − | 0.863074i | \(-0.331464\pi\) | ||||
0.505078 | + | 0.863074i | \(0.331464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00811 | 0.0467003 | 0.0233502 | − | 0.999727i | \(-0.492567\pi\) | ||||
0.0233502 | + | 0.999727i | \(0.492567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.2361i | 0.271913i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 35.3481i | − 0.752087i | −0.926602 | − | 0.376044i | \(-0.877284\pi\) | ||||
0.926602 | − | 0.376044i | \(-0.122716\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −23.3607 | −0.476749 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −90.8774 | −1.78191 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 21.6393i | − 0.408289i | −0.978941 | − | 0.204145i | \(-0.934559\pi\) | ||||
0.978941 | − | 0.204145i | \(-0.0654413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 4.01623i | − 0.0730223i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −35.7771 | −0.627668 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −73.8644 | −1.25194 | −0.625970 | − | 0.779848i | \(-0.715297\pi\) | ||||
−0.625970 | + | 0.779848i | \(0.715297\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 26.1378i | 0.428488i | 0.976780 | + | 0.214244i | \(0.0687288\pi\) | ||||
−0.976780 | + | 0.214244i | \(0.931271\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 46.5488i | 0.738869i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.05573 | 0.0162420 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 88.8693 | 1.32641 | 0.663204 | − | 0.748439i | \(-0.269196\pi\) | ||||
0.663204 | + | 0.748439i | \(0.269196\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 61.3050i | 0.888478i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 39.4144i | 0.555132i | 0.960707 | + | 0.277566i | \(0.0895277\pi\) | ||||
−0.960707 | + | 0.277566i | \(0.910472\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −137.554 | −1.88430 | −0.942152 | − | 0.335186i | \(-0.891201\pi\) | ||||
−0.942152 | + | 0.335186i | \(0.891201\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −19.0211 | −0.253615 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 15.2786i | − 0.198424i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 113.703i | − 1.43928i | −0.694350 | − | 0.719638i | \(-0.744308\pi\) | ||||
0.694350 | − | 0.719638i | \(-0.255692\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −100.305 | −1.23833 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 21.2412 | 0.255919 | 0.127959 | − | 0.991779i | \(-0.459157\pi\) | ||||
0.127959 | + | 0.991779i | \(0.459157\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 53.4164i | − 0.628428i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 26.4176i | − 0.303650i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −67.4427 | −0.757783 | −0.378892 | − | 0.925441i | \(-0.623695\pi\) | ||||
−0.378892 | + | 0.925441i | \(0.623695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.01623 | 0.0441344 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 180.498i | 1.94084i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 21.0292i | − 0.221360i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −39.1672 | −0.403785 | −0.201893 | − | 0.979408i | \(-0.564709\pi\) | ||||
−0.201893 | + | 0.979408i | \(0.564709\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.82857 | −0.0992785 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 99.8885i | 0.988995i | 0.869179 | + | 0.494498i | \(0.164648\pi\) | ||||
−0.869179 | + | 0.494498i | \(0.835352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 35.7721i | 0.347302i | 0.984807 | + | 0.173651i | \(0.0555565\pi\) | ||||
−0.984807 | + | 0.173651i | \(0.944444\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −72.3607 | −0.689149 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 121.099 | 1.13177 | 0.565884 | − | 0.824485i | \(-0.308535\pi\) | ||||
0.565884 | + | 0.824485i | \(0.308535\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 197.469i | 1.81164i | 0.423660 | + | 0.905821i | \(0.360745\pi\) | ||||
−0.423660 | + | 0.905821i | \(0.639255\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 100.282i | 0.903441i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 81.2786 | 0.719280 | 0.359640 | − | 0.933091i | \(-0.382900\pi\) | ||||
0.359640 | + | 0.933091i | \(0.382900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −36.0341 | −0.313340 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.58359i | − 0.0220820i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 203.208i | − 1.70763i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −117.774 | −0.973339 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 157.557 | 1.28095 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 11.1803i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1.84616i | − 0.0145367i | −0.999974 | − | 0.00726834i | \(-0.997686\pi\) | ||||
0.999974 | − | 0.00726834i | \(-0.00231361\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.63932 | 0.0592195 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 225.609 | 1.72221 | 0.861105 | − | 0.508428i | \(-0.169773\pi\) | ||||
0.861105 | + | 0.508428i | \(0.169773\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 80.0000i | − 0.601504i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 30.0098i | − 0.222295i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 52.8328 | 0.385641 | 0.192820 | − | 0.981234i | \(-0.438236\pi\) | ||||
0.192820 | + | 0.981234i | \(0.438236\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 125.852 | 0.905407 | 0.452703 | − | 0.891661i | \(-0.350460\pi\) | ||||
0.452703 | + | 0.891661i | \(0.350460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 134.472i | − 0.953703i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.848009i | 0.00593013i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.5279 | 0.107089 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −88.8693 | −0.604553 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 132.971i | 0.892420i | 0.894928 | + | 0.446210i | \(0.147227\pi\) | ||||
−0.894928 | + | 0.446210i | \(0.852773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 151.221i | 1.00146i | 0.865603 | + | 0.500732i | \(0.166936\pi\) | ||||
−0.865603 | + | 0.500732i | \(0.833064\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −130.721 | −0.854388 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −106.094 | −0.684480 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.7477i | 0.234062i | 0.993128 | + | 0.117031i | \(0.0373376\pi\) | ||||
−0.993128 | + | 0.117031i | \(0.962662\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 82.3209i | − 0.517741i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −137.082 | −0.851441 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 302.854 | 1.85800 | 0.929000 | − | 0.370079i | \(-0.120669\pi\) | ||||
0.929000 | + | 0.370079i | \(0.120669\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 15.2786i | − 0.0925978i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 99.3839i | − 0.595113i | −0.954704 | − | 0.297557i | \(-0.903828\pi\) | ||||
0.954704 | − | 0.297557i | \(-0.0961717\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168.777 | 0.998681 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −51.4631 | −0.300954 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 181.639i | 1.04994i | 0.851121 | + | 0.524969i | \(0.175923\pi\) | ||||
−0.851121 | + | 0.524969i | \(0.824077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 42.5325i | − 0.243043i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −280.997 | −1.58755 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −260.907 | −1.45758 | −0.728792 | − | 0.684735i | \(-0.759918\pi\) | ||||
−0.728792 | + | 0.684735i | \(0.759918\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 157.777i | 0.871697i | 0.900020 | + | 0.435848i | \(0.143552\pi\) | ||||
−0.900020 | + | 0.435848i | \(0.856448\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 99.4340i | 0.543355i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −58.9443 | −0.318618 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 42.9065 | 0.229447 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 114.164i | − 0.604043i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 324.095i | − 1.69683i | −0.529328 | − | 0.848417i | \(-0.677556\pi\) | ||||
0.529328 | − | 0.848417i | \(-0.322444\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 181.777 | 0.941850 | 0.470925 | − | 0.882173i | \(-0.343920\pi\) | ||||
0.470925 | + | 0.882173i | \(0.343920\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.01623 | 0.0205960 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 140.525i | 0.713324i | 0.934234 | + | 0.356662i | \(0.116085\pi\) | ||||
−0.934234 | + | 0.356662i | \(0.883915\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 168.234i | − 0.845397i | −0.906270 | − | 0.422698i | \(-0.861083\pi\) | ||||
0.906270 | − | 0.422698i | \(-0.138917\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 338.079 | 1.68198 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 59.0715 | 0.290993 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 92.6099i | 0.451756i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 88.1833i | 0.426006i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.8916 | 0.0808213 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 93.9455 | 0.445240 | 0.222620 | − | 0.974905i | \(-0.428539\pi\) | ||||
0.222620 | + | 0.974905i | \(0.428539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 149.941i | 0.703949i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.49028i | 0.0208850i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −403.607 | −1.85994 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −523.287 | −2.38944 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.2786i | 0.0510346i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 214.035i | 0.959797i | 0.877324 | + | 0.479899i | \(0.159327\pi\) | ||||
−0.877324 | + | 0.479899i | \(0.840673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −27.3607 | −0.121603 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −41.4225 | −0.182478 | −0.0912389 | − | 0.995829i | \(-0.529083\pi\) | ||||
−0.0912389 | + | 0.995829i | \(0.529083\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 73.2786i | 0.319994i | 0.987117 | + | 0.159997i | \(0.0511485\pi\) | ||||
−0.987117 | + | 0.159997i | \(0.948852\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 58.1234i | − 0.251616i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 307.050 | 1.31781 | 0.658905 | − | 0.752227i | \(-0.271020\pi\) | ||||
0.658905 | + | 0.752227i | \(0.271020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 79.0407 | 0.336344 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 432.551i | − 1.82511i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 42.9065i | − 0.179525i | −0.995963 | − | 0.0897625i | \(-0.971389\pi\) | ||||
0.995963 | − | 0.0897625i | \(-0.0286108\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −135.082 | −0.560506 | −0.280253 | − | 0.959926i | \(-0.590418\pi\) | ||||
−0.280253 | + | 0.959926i | \(0.590418\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −260.796 | −1.07323 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 52.2361i | − 0.213208i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.44023i | 0.0179767i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 80.8065 | 0.324524 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 221.169 | 0.881152 | 0.440576 | − | 0.897715i | \(-0.354774\pi\) | ||||
0.440576 | + | 0.897715i | \(0.354774\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 28.9443i | − 0.114404i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 203.208i | − 0.796894i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −257.056 | −1.00022 | −0.500108 | − | 0.865963i | \(-0.666707\pi\) | ||||
−0.500108 | + | 0.865963i | \(0.666707\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −224.237 | −0.865781 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 38.0000i | − 0.145594i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 164.168i | 0.624212i | 0.950047 | + | 0.312106i | \(0.101034\pi\) | ||||
−0.950047 | + | 0.312106i | \(0.898966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 48.3870 | 0.182592 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −256.567 | −0.960926 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 35.4752i | 0.131878i | 0.997824 | + | 0.0659391i | \(0.0210043\pi\) | ||||
−0.997824 | + | 0.0659391i | \(0.978996\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 298.950i | 1.10314i | 0.834130 | + | 0.551568i | \(0.185970\pi\) | ||||
−0.834130 | + | 0.551568i | \(0.814030\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.2786 | 0.0559657 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.98056 | 0.0326566 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 457.246i | − 1.65071i | −0.564616 | − | 0.825354i | \(-0.690976\pi\) | ||||
0.564616 | − | 0.825354i | \(-0.309024\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 259.635i | 0.930593i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.63932 | 0.0200688 | 0.0100344 | − | 0.999950i | \(-0.496806\pi\) | ||||
0.0100344 | + | 0.999950i | \(0.496806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 169.918 | 0.600418 | 0.300209 | − | 0.953874i | \(-0.402944\pi\) | ||||
0.300209 | + | 0.953874i | \(0.402944\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 80.0000i | − 0.280702i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 352.309i | 1.22756i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 281.663 | 0.974611 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −149.001 | −0.512030 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 26.8591i | − 0.0916694i | −0.998949 | − | 0.0458347i | \(-0.985405\pi\) | ||||
0.998949 | − | 0.0458347i | \(-0.0145947\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 165.166i | − 0.559884i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.1052 | 0.0811624 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.60845 | 0.0254463 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.0820i | 0.0567510i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 379.999i | 1.25412i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −58.4458 | −0.191626 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −118.031 | −0.384466 | −0.192233 | − | 0.981349i | \(-0.561573\pi\) | ||||
−0.192233 | + | 0.981349i | \(0.561573\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 136.085i | 0.440405i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 121.835i | − 0.391753i | −0.980629 | − | 0.195877i | \(-0.937245\pi\) | ||||
0.980629 | − | 0.195877i | \(-0.0627552\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −219.548 | −0.701431 | −0.350716 | − | 0.936482i | \(-0.614062\pi\) | ||||
−0.350716 | + | 0.936482i | \(0.614062\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −104.086 | −0.330432 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 366.859i | − 1.15728i | −0.815582 | − | 0.578642i | \(-0.803583\pi\) | ||||
0.815582 | − | 0.578642i | \(-0.196417\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4727i | 0.0390993i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 460.689 | 1.43517 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 224.661 | 0.695546 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.36068i | 0.00726363i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 751.217i | 2.29730i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 300.689 | 0.913948 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 162.846 | 0.491981 | 0.245990 | − | 0.969272i | \(-0.420887\pi\) | ||||
0.245990 | + | 0.969272i | \(0.420887\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 144.249i | 0.433181i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 198.718i | 0.593187i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1084 | 0.0507666 | 0.0253833 | − | 0.999678i | \(-0.491919\pi\) | ||||
0.0253833 | + | 0.999678i | \(0.491919\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 309.202 | 0.912101 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 85.2198i | − 0.249911i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 218.101i | 0.635863i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −137.082 | −0.397339 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −167.498 | −0.482703 | −0.241351 | − | 0.970438i | \(-0.577591\pi\) | ||||
−0.241351 | + | 0.970438i | \(0.577591\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 483.495i | 1.38537i | 0.721239 | + | 0.692687i | \(0.243573\pi\) | ||||
−0.721239 | + | 0.692687i | \(0.756427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.33644i | 0.0180525i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 307.994 | 0.872504 | 0.436252 | − | 0.899825i | \(-0.356306\pi\) | ||||
0.436252 | + | 0.899825i | \(0.356306\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −88.1332 | −0.248263 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 773.050i | − 2.16540i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.2494i | 0.0647615i | 0.999476 | + | 0.0323807i | \(0.0103089\pi\) | ||||
−0.999476 | + | 0.0323807i | \(0.989691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −272.554 | −0.754998 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −448.039 | −1.23427 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 307.580i | − 0.842686i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 517.325i | − 1.40960i | −0.709404 | − | 0.704802i | \(-0.751036\pi\) | ||||
0.709404 | − | 0.704802i | \(-0.248964\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 226.636 | 0.614190 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 184.075 | 0.496159 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 88.3545i | − 0.236875i | −0.992961 | − | 0.118438i | \(-0.962211\pi\) | ||||
0.992961 | − | 0.118438i | \(-0.0377886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 42.5325i | − 0.113420i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.27864 | −0.00869666 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.3332 | −0.0510112 | −0.0255056 | − | 0.999675i | \(-0.508120\pi\) | ||||
−0.0255056 | + | 0.999675i | \(0.508120\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 7.02321i | − 0.0184336i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 431.612i | − 1.12692i | −0.826142 | − | 0.563462i | \(-0.809469\pi\) | ||||
0.826142 | − | 0.563462i | \(-0.190531\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 34.1641 | 0.0887379 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.9887 | 0.0283945 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 296.354i | − 0.761837i | −0.924609 | − | 0.380918i | \(-0.875608\pi\) | ||||
0.924609 | − | 0.380918i | \(-0.124392\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 384.963i | − 0.984560i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 858.269 | 2.18389 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 254.247 | 0.643664 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 86.1904i | 0.217104i | 0.994091 | + | 0.108552i | \(0.0346214\pi\) | ||||
−0.994091 | + | 0.108552i | \(0.965379\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 304.338i | − 0.762752i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 442.997 | 1.10473 | 0.552365 | − | 0.833602i | \(-0.313725\pi\) | ||||
0.552365 | + | 0.833602i | \(0.313725\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.4014 | 0.0555865 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 224.289i | − 0.553799i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 47.3467i | − 0.116331i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −63.4102 | −0.155037 | −0.0775186 | − | 0.996991i | \(-0.524700\pi\) | ||||
−0.0775186 | + | 0.996991i | \(0.524700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 200.988 | 0.489022 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 628.328i | − 1.52138i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 47.4969i | 0.114450i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 478.768 | 1.14812 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −435.678 | −1.03980 | −0.519902 | − | 0.854226i | \(-0.674032\pi\) | ||||
−0.519902 | + | 0.854226i | \(0.674032\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 582.912i | − 1.38459i | −0.721615 | − | 0.692294i | \(-0.756600\pi\) | ||||
0.721615 | − | 0.692294i | \(-0.243400\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 193.430i | − 0.457280i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 119.443 | 0.281042 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −222.341 | −0.520705 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.22602i | 0.00751986i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 375.882i | 0.872117i | 0.899918 | + | 0.436058i | \(0.143626\pi\) | ||||
−0.899918 | + | 0.436058i | \(0.856374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −368.164 | −0.850263 | −0.425132 | − | 0.905131i | \(-0.639772\pi\) | ||||
−0.425132 | + | 0.905131i | \(0.639772\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 59.0715 | 0.135797 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 151.554i | − 0.346806i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 483.549i | − 1.10148i | −0.834677 | − | 0.550739i | \(-0.814346\pi\) | ||||
0.834677 | − | 0.550739i | \(-0.185654\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −127.833 | −0.289870 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 279.181 | 0.630205 | 0.315102 | − | 0.949058i | \(-0.397961\pi\) | ||||
0.315102 | + | 0.949058i | \(0.397961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 150.807i | − 0.338891i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 505.850i | 1.13166i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 756.079 | 1.68392 | 0.841959 | − | 0.539542i | \(-0.181403\pi\) | ||||
0.841959 | + | 0.539542i | \(0.181403\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −74.3885 | −0.164941 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 575.279i | 1.26993i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.98056i | 0.0197375i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −285.672 | −0.625103 | −0.312551 | − | 0.949901i | \(-0.601184\pi\) | ||||
−0.312551 | + | 0.949901i | \(0.601184\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 320.603 | 0.698482 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 99.1146i | 0.214999i | 0.994205 | + | 0.107500i | \(0.0342844\pi\) | ||||
−0.994205 | + | 0.107500i | \(0.965716\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 630.603i | − 1.36199i | −0.732286 | − | 0.680997i | \(-0.761547\pi\) | ||||
0.732286 | − | 0.680997i | \(-0.238453\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −403.607 | −0.867972 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 496.010 | 1.06212 | 0.531060 | − | 0.847334i | \(-0.321794\pi\) | ||||
0.531060 | + | 0.847334i | \(0.321794\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 755.967i | 1.61187i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 139.796i | 0.296808i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.60680 | −0.00762537 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 47.0228 | 0.0989954 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 118.413i | − 0.248246i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 579.090i | 1.20896i | 0.796621 | + | 0.604478i | \(0.206618\pi\) | ||||
−0.796621 | + | 0.604478i | \(0.793382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.4458 | 0.0258749 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −521.491 | −1.07969 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 87.5805i | − 0.180578i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 626.363i | − 1.28617i | −0.765796 | − | 0.643084i | \(-0.777655\pi\) | ||||
0.765796 | − | 0.643084i | \(-0.222345\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1152.13 | 2.35608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.3013 | −0.0454201 | −0.0227100 | − | 0.999742i | \(-0.507229\pi\) | ||||
−0.0227100 | + | 0.999742i | \(0.507229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 165.889i | 0.336488i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 21.9773i | − 0.0443987i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −335.279 | −0.674605 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 627.362 | 1.25724 | 0.628619 | − | 0.777714i | \(-0.283621\pi\) | ||||
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 378.079i | − 0.754649i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 780.853i | − 1.55239i | −0.630492 | − | 0.776196i | \(-0.717147\pi\) | ||||
0.630492 | − | 0.776196i | \(-0.282853\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −223.358 | −0.442292 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 642.066 | 1.26640 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 288.950i | 0.567683i | 0.958871 | + | 0.283841i | \(0.0916089\pi\) | ||||
−0.958871 | + | 0.283841i | \(0.908391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1170.11i | − 2.28984i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 126.217 | 0.246036 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −79.9888 | −0.155318 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 63.4891i | 0.122803i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 690.997i | 1.33140i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 602.984 | 1.15736 | 0.578680 | − | 0.815555i | \(-0.303568\pi\) | ||||
0.578680 | + | 0.815555i | \(0.303568\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −367.962 | −0.703560 | −0.351780 | − | 0.936083i | \(-0.614423\pi\) | ||||
−0.351780 | + | 0.936083i | \(0.614423\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 161.803i | − 0.308197i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1133.44i | − 2.15073i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 269.308 | 0.509089 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −404.196 | −0.761198 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 19.5542i | − 0.0366870i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 270.786i | 0.506142i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −992.551 | −1.84833 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41.9584 | 0.0778449 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 616.885i | 1.14027i | 0.821551 | + | 0.570134i | \(0.193109\pi\) | ||||
−0.821551 | + | 0.570134i | \(0.806891\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 600.220i | 1.10538i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −441.554 | −0.810191 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −97.8499 | −0.178885 | −0.0894423 | − | 0.995992i | \(-0.528508\pi\) | ||||
−0.0894423 | + | 0.995992i | \(0.528508\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 143.029i | 0.260527i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 65.3078i | 0.118526i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 967.214 | 1.74903 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −224.237 | −0.404031 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 896.302i | − 1.60916i | −0.593845 | − | 0.804580i | \(-0.702391\pi\) | ||||
0.593845 | − | 0.804580i | \(-0.297609\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 0.948103i | − 0.00169607i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 163.226 | 0.290955 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 771.186 | 1.36978 | 0.684890 | − | 0.728647i | \(-0.259850\pi\) | ||||
0.684890 | + | 0.728647i | \(0.259850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 181.745i | 0.321672i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 853.245i | − 1.50484i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.74767 | −0.0153738 | −0.00768688 | − | 0.999970i | \(-0.502447\pi\) | ||||
−0.00768688 | + | 0.999970i | \(0.502447\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −511.138 | −0.895164 | −0.447582 | − | 0.894243i | \(-0.647715\pi\) | ||||
−0.447582 | + | 0.894243i | \(0.647715\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1232.93i | − 2.15171i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 80.5748i | − 0.140130i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −713.712 | −1.23694 | −0.618468 | − | 0.785810i | \(-0.712246\pi\) | ||||
−0.618468 | + | 0.785810i | \(0.712246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 691.521 | 1.19434 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 180.689i | 0.310996i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.8666i | 0.0666666i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.77709 | 0.00987536 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 422.169 | 0.719198 | 0.359599 | − | 0.933107i | \(-0.382914\pi\) | ||||
0.359599 | + | 0.933107i | \(0.382914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 446.217i | − 0.757584i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 534.588i | 0.904548i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −308.663 | −0.520510 | −0.260255 | − | 0.965540i | \(-0.583807\pi\) | ||||
−0.260255 | + | 0.965540i | \(0.583807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 454.387 | 0.763676 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 640.000i | − 1.07203i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 462.196i | 0.771612i | 0.922580 | + | 0.385806i | \(0.126077\pi\) | ||||
−0.922580 | + | 0.385806i | \(0.873923\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −355.358 | −0.591277 | −0.295639 | − | 0.955300i | \(-0.595532\pi\) | ||||
−0.295639 | + | 0.955300i | \(0.595532\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 486.305 | 0.806476 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 263.351i | − 0.435290i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 630.403i | 1.03856i | 0.854605 | + | 0.519278i | \(0.173799\pi\) | ||||
−0.854605 | + | 0.519278i | \(0.826201\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 224.721 | 0.369001 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.6891 | −0.0273144 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 812.525i | 1.32549i | 0.748846 | + | 0.662745i | \(0.230608\pi\) | ||||
−0.748846 | + | 0.662745i | \(0.769392\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 352.309i | 0.572860i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 437.935 | 0.709781 | 0.354891 | − | 0.934908i | \(-0.384518\pi\) | ||||
0.354891 | + | 0.934908i | \(0.384518\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 770.250 | 1.24435 | 0.622173 | − | 0.782880i | \(-0.286250\pi\) | ||||
0.622173 | + | 0.782880i | \(0.286250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 216.276i | − 0.348270i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 573.702i | − 0.920870i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 64.2597 | 0.102487 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 629.718i | − 1.00114i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 875.496i | 1.38747i | 0.720228 | + | 0.693737i | \(0.244037\pi\) | ||||
−0.720228 | + | 0.693737i | \(0.755963\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 357.390 | 0.564597 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.12814 | 0.00650100 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.0294i | 0.0173146i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 215.681i | 0.337529i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 842.571 | 1.31446 | 0.657232 | − | 0.753689i | \(-0.271727\pi\) | ||||
0.657232 | + | 0.753689i | \(0.271727\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1153.20 | −1.79348 | −0.896738 | − | 0.442563i | \(-0.854069\pi\) | ||||
−0.896738 | + | 0.442563i | \(0.854069\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.0820i | 0.0264838i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 355.751i | 0.549847i | 0.961466 | + | 0.274924i | \(0.0886526\pi\) | ||||
−0.961466 | + | 0.274924i | \(0.911347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 132.669 | 0.204420 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1535.41 | −2.35854 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 557.915i | 0.854387i | 0.904160 | + | 0.427194i | \(0.140498\pi\) | ||||
−0.904160 | + | 0.427194i | \(0.859502\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 504.478i | 0.770195i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −752.715 | −1.14569 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 284.157 | 0.431194 | 0.215597 | − | 0.976482i | \(-0.430830\pi\) | ||||
0.215597 | + | 0.976482i | \(0.430830\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 716.735i | 1.08432i | 0.840275 | + | 0.542160i | \(0.182393\pi\) | ||||
−0.840275 | + | 0.542160i | \(0.817607\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 42.9065i | 0.0647157i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 178.885 | 0.269001 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 111.907 | 0.167776 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 814.237i | 1.21710i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 46.9464i | − 0.0699648i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −695.378 | −1.03325 | −0.516625 | − | 0.856212i | \(-0.672812\pi\) | ||||
−0.516625 | + | 0.856212i | \(0.672812\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 67.1040 | 0.0994133 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 820.237i | − 1.21158i | −0.795626 | − | 0.605788i | \(-0.792858\pi\) | ||||
0.795626 | − | 0.605788i | \(-0.207142\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 333.176i | − 0.490686i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −157.580 | −0.231396 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −335.508 | −0.491227 | −0.245613 | − | 0.969368i | \(-0.578989\pi\) | ||||
−0.245613 | + | 0.969368i | \(0.578989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 118.138i | 0.172464i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 278.769i | 0.405777i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.2167 | −0.0148283 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 336.568 | 0.487074 | 0.243537 | − | 0.969892i | \(-0.421692\pi\) | ||||
0.243537 | + | 0.969892i | \(0.421692\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 83.6068i | − 0.120645i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 281.413i | 0.404910i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −989.378 | −1.41948 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1168.09 | 1.67108 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 429.364i | 0.612502i | 0.951951 | + | 0.306251i | \(0.0990747\pi\) | ||||
−0.951951 | + | 0.306251i | \(0.900925\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 247.911i | − 0.352647i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 300.689 | 0.426509 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −849.703 | −1.20184 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1224.60i | 1.72722i | 0.504162 | + | 0.863609i | \(0.331801\pi\) | ||||
−0.504162 | + | 0.863609i | \(0.668199\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 622.197i | − 0.875101i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −764.604 | −1.07238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.89621 | −0.00265204 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 163.226i | − 0.227651i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 496.022i | 0.689877i | 0.938625 | + | 0.344939i | \(0.112100\pi\) | ||||
−0.938625 | + | 0.344939i | \(0.887900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −304.296 | −0.422047 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −513.883 | −0.710764 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.7214i | 0.0478915i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 152.843i | 0.210238i | 0.994460 | + | 0.105119i | \(0.0335224\pi\) | ||||
−0.994460 | + | 0.105119i | \(0.966478\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −89.3808 | −0.122607 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47.9709 | −0.0656237 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 761.286i | 1.03859i | 0.854595 | + | 0.519295i | \(0.173805\pi\) | ||||
−0.854595 | + | 0.519295i | \(0.826195\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 198.718i | − 0.270364i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −159.619 | −0.216580 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −183.975 | −0.248951 | −0.124476 | − | 0.992223i | \(-0.539725\pi\) | ||||
−0.124476 | + | 0.992223i | \(0.539725\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.8916i | 0.0227957i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 495.247i | − 0.666551i | −0.942830 | − | 0.333275i | \(-0.891846\pi\) | ||||
0.942830 | − | 0.333275i | \(-0.108154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −297.331 | −0.399102 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 116.235 | 0.155602 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1030.13i | 1.37534i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 800.059i | 1.06533i | 0.846328 | + | 0.532663i | \(0.178809\pi\) | ||||
−0.846328 | + | 0.532663i | \(0.821191\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 841.378 | 1.11737 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −338.140 | −0.447868 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 276.367i | − 0.365082i | −0.983198 | − | 0.182541i | \(-0.941568\pi\) | ||||
0.983198 | − | 0.182541i | \(-0.0584322\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 110.111i | − 0.145073i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −891.207 | −1.17110 | −0.585550 | − | 0.810636i | \(-0.699121\pi\) | ||||
−0.585550 | + | 0.810636i | \(0.699121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1679.77 | −2.20154 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 292.302i | − 0.382094i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.8740i | 0.0454681i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −835.430 | −1.08639 | −0.543193 | − | 0.839608i | \(-0.682785\pi\) | ||||
−0.543193 | + | 0.839608i | \(0.682785\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −977.898 | −1.26835 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 213.522i | 0.276225i | 0.990417 | + | 0.138112i | \(0.0441035\pi\) | ||||
−0.990417 | + | 0.138112i | \(0.955897\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 237.234i | − 0.306109i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −853.050 | −1.09788 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −389.503 | −0.500004 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 70.7926i | − 0.0906436i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 93.1976i | 0.119026i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −82.1703 | −0.104676 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −370.182 | −0.470371 | −0.235185 | − | 0.971951i | \(-0.575570\pi\) | ||||
−0.235185 | + | 0.971951i | \(0.575570\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 624.531i | 0.791547i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 691.397i | 0.874080i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.3406 | 0.0155619 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 184.075 | 0.231541 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 274.426i | − 0.344323i | −0.985069 | − | 0.172162i | \(-0.944925\pi\) | ||||
0.985069 | − | 0.172162i | \(-0.0550752\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 844.414i | 1.05684i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −369.056 | −0.460744 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 247.063 | 0.307675 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 306.525i | − 0.380776i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 134.956i | 0.167232i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −665.214 | −0.822266 | −0.411133 | − | 0.911575i | \(-0.634867\pi\) | ||||
−0.411133 | + | 0.911575i | \(0.634867\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 360.665 | 0.444717 | 0.222358 | − | 0.974965i | \(-0.428624\pi\) | ||||
0.222358 | + | 0.974965i | \(0.428624\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1137.27i | 1.39886i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 677.202i | 0.830923i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.8854 | −0.0231156 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.9773 | 0.0268344 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 666.899i | − 0.812301i | −0.913806 | − | 0.406151i | \(-0.866871\pi\) | ||||
0.913806 | − | 0.406151i | \(-0.133129\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 122.433i | 0.148764i | 0.997230 | + | 0.0743822i | \(0.0236985\pi\) | ||||
−0.997230 | + | 0.0743822i | \(0.976302\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 34.1641 | 0.0414110 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1532.98 | −1.85366 | −0.926832 | − | 0.375477i | \(-0.877479\pi\) | ||||
−0.926832 | + | 0.375477i | \(0.877479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 195.475i | 0.235796i | 0.993026 | + | 0.117898i | \(0.0376157\pi\) | ||||
−0.993026 | + | 0.117898i | \(0.962384\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1739.47i | − 2.09322i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 558.053 | 0.669931 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 222.229 | 0.266143 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 636.774i | − 0.760781i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1325.97i | 1.58041i | 0.612840 | + | 0.790207i | \(0.290027\pi\) | ||||
−0.612840 | + | 0.790207i | \(0.709973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 792.777 | 0.942660 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.4532 | 0.0254487 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 377.397i | 0.446624i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1001.85i | − 1.18282i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 646.407 | 0.761375 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −424.801 | −0.499179 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1055.28i | 1.23714i | 0.785730 | + | 0.618570i | \(0.212288\pi\) | ||||
−0.785730 | + | 0.618570i | \(0.787712\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 115.075i | − 0.134591i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −155.378 | −0.181304 | −0.0906521 | − | 0.995883i | \(-0.528895\pi\) | ||||
−0.0906521 | + | 0.995883i | \(0.528895\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −226.033 | −0.263136 | −0.131568 | − | 0.991307i | \(-0.542001\pi\) | ||||
−0.131568 | + | 0.991307i | \(0.542001\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1340.26i | 1.55664i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 930.702i | − 1.07845i | −0.842162 | − | 0.539225i | \(-0.818717\pi\) | ||||
0.842162 | − | 0.539225i | \(-0.181283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −406.158 | −0.469547 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1071.51 | 1.23588 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 204.223i | 0.235009i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 41.9584i | − 0.0481727i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −214.328 | −0.245508 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 95.1057 | 0.108692 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.5217i | 0.0382231i | 0.999817 | + | 0.0191115i | \(0.00608376\pi\) | ||||
−0.999817 | + | 0.0191115i | \(0.993916\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 102.178i | − 0.116244i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −933.850 | −1.05999 | −0.529994 | − | 0.848001i | \(-0.677806\pi\) | ||||
−0.529994 | + | 0.848001i | \(0.677806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −542.308 | −0.614166 | −0.307083 | − | 0.951683i | \(-0.599353\pi\) | ||||
−0.307083 | + | 0.951683i | \(0.599353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 628.328i | − 0.709975i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 714.720i | − 0.805773i | −0.915250 | − | 0.402886i | \(-0.868007\pi\) | ||||
0.915250 | − | 0.402886i | \(-0.131993\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.7044 | 0.0176652 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 180.159 | 0.202199 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 332.433i | 0.372266i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 583.407i | − 0.651851i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.9443 | 0.0322679 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 329.484 | 0.366500 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 516.932i | 0.573731i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 64.9839i | 0.0719645i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −352.800 | −0.389835 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −347.233 | −0.382837 | −0.191418 | − | 0.981509i | \(-0.561309\pi\) | ||||
−0.191418 | + | 0.981509i | \(0.561309\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 546.604i | 0.601324i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1427.54i | 1.56701i | 0.621386 | + | 0.783504i | \(0.286570\pi\) | ||||
−0.621386 | + | 0.783504i | \(0.713430\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.1517 | −0.0417871 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −222.341 | −0.242996 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1919.15i | 2.09286i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 569.162i | 0.619327i | 0.950846 | + | 0.309664i | \(0.100216\pi\) | ||||
−0.950846 | + | 0.309664i | \(0.899784\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −449.017 | −0.487532 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.6089 | 0.0201614 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 131.803i | − 0.142490i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 195.750i | 0.211165i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1535.96 | 1.65335 | 0.826675 | − | 0.562680i | \(-0.190230\pi\) | ||||
0.826675 | + | 0.562680i | \(0.190230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 219.697 | 0.235980 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 463.489i | − 0.496773i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 95.9418i | 0.102612i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −338.721 | −0.361496 | −0.180748 | − | 0.983529i | \(-0.557852\pi\) | ||||
−0.180748 | + | 0.983529i | \(0.557852\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −835.210 | −0.889468 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1439.77i | − 1.53004i | −0.644004 | − | 0.765022i | \(-0.722728\pi\) | ||||
0.644004 | − | 0.765022i | \(-0.277272\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 667.424i | 0.707766i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 255.279 | 0.270136 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 656.135 | 0.692856 | 0.346428 | − | 0.938077i | \(-0.387394\pi\) | ||||
0.346428 | + | 0.938077i | \(0.387394\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 64.9443i | 0.0684344i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 1395.62i | − 1.46752i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −436.675 | −0.458211 | −0.229105 | − | 0.973402i | \(-0.573580\pi\) | ||||
−0.229105 | + | 0.973402i | \(0.573580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 724.699 | 0.758847 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 47.4489i | 0.0495809i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 449.423i | 0.468637i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1290.20 | −1.34256 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 662.671 | 0.688132 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 406.466i | 0.421208i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 903.436i | 0.934267i | 0.884187 | + | 0.467133i | \(0.154713\pi\) | ||||
−0.884187 | + | 0.467133i | \(0.845287\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 854.663 | 0.882005 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1866.89 | 1.92265 | 0.961324 | − | 0.275420i | \(-0.0888168\pi\) | ||||
0.961324 | + | 0.275420i | \(0.0888168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1070.56i | 1.10026i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.98056i | 0.00921083i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1073.95 | −1.09923 | −0.549615 | − | 0.835418i | \(-0.685226\pi\) | ||||
−0.549615 | + | 0.835418i | \(0.685226\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 121.135 | 0.123733 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1080.58i | 1.10151i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 534.114i | − 0.543351i | −0.962389 | − | 0.271675i | \(-0.912422\pi\) | ||||
0.962389 | − | 0.271675i | \(-0.0875777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −314.223 | −0.319008 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1143.89 | 1.15895 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.3607i | 0.0327206i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 520.419i | 0.525146i | 0.964912 | + | 0.262573i | \(0.0845710\pi\) | ||||
−0.964912 | + | 0.262573i | \(0.915429\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 619.502 | 0.623869 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 376.183 | 0.378073 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 457.680i | 0.459057i | 0.973302 | + | 0.229528i | \(0.0737184\pi\) | ||||
−0.973302 | + | 0.229528i | \(0.926282\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 353.781i | − 0.354135i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))