Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,3,Mod(511,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("640.511");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.4387369191\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 24x^{14} + 228x^{12} + 1110x^{10} + 2970x^{8} + 4308x^{6} + 3085x^{4} + 882x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{44} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 511.6 | ||
Root | \(-1.14902i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 640.511 |
Dual form | 640.3.b.a.511.11 |
$q$-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 \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 2.29803i | − 0.766012i | −0.923746 | − | 0.383006i | \(-0.874889\pi\) | ||||
0.923746 | − | 0.383006i | \(-0.125111\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23607 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.72697i | − 0.389567i | −0.980846 | − | 0.194784i | \(-0.937600\pi\) | ||||
0.980846 | − | 0.194784i | \(-0.0624004\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.71904 | 0.413226 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.3454i | 1.75867i | 0.476204 | + | 0.879335i | \(0.342012\pi\) | ||||
−0.476204 | + | 0.879335i | \(0.657988\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.8033 | 1.44641 | 0.723203 | − | 0.690636i | \(-0.242669\pi\) | ||||
0.723203 | + | 0.690636i | \(0.242669\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.13856i | 0.342571i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −23.5759 | −1.38682 | −0.693410 | − | 0.720543i | \(-0.743892\pi\) | ||||
−0.693410 | + | 0.720543i | \(0.743892\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 27.8780i | 1.46726i | 0.679549 | + | 0.733631i | \(0.262176\pi\) | ||||
−0.679549 | + | 0.733631i | \(0.737824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.26667 | −0.298413 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 8.78218i | − 0.381834i | −0.981606 | − | 0.190917i | \(-0.938854\pi\) | ||||
0.981606 | − | 0.190917i | \(-0.0611461\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 29.2288i | − 1.08255i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 23.9370 | 0.825414 | 0.412707 | − | 0.910864i | \(-0.364583\pi\) | ||||
0.412707 | + | 0.910864i | \(0.364583\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.69022i | 0.312588i | 0.987711 | + | 0.156294i | \(0.0499547\pi\) | ||||
−0.987711 | + | 0.156294i | \(0.950045\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 44.4563 | 1.34716 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.09769i | 0.174220i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 69.6453 | 1.88231 | 0.941153 | − | 0.337982i | \(-0.109744\pi\) | ||||
0.941153 | + | 0.337982i | \(0.109744\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 43.2106i | − 1.10796i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 32.7276 | 0.798234 | 0.399117 | − | 0.916900i | \(-0.369317\pi\) | ||||
0.399117 | + | 0.916900i | \(0.369317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 28.2097i | 0.656040i | 0.944671 | + | 0.328020i | \(0.106381\pi\) | ||||
−0.944671 | + | 0.328020i | \(0.893619\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.31602 | −0.184800 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 37.6454i | − 0.800966i | −0.916304 | − | 0.400483i | \(-0.868842\pi\) | ||||
0.916304 | − | 0.400483i | \(-0.131158\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41.5636 | 0.848238 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 54.1783i | 1.06232i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −42.7329 | −0.806281 | −0.403140 | − | 0.915138i | \(-0.632081\pi\) | ||||
−0.403140 | + | 0.915138i | \(0.632081\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 43.2575i | − 0.786501i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 64.0645 | 1.12394 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 18.3369i | − 0.310796i | −0.987852 | − | 0.155398i | \(-0.950334\pi\) | ||||
0.987852 | − | 0.155398i | \(-0.0496659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35.2430 | 0.577753 | 0.288877 | − | 0.957366i | \(-0.406718\pi\) | ||||
0.288877 | + | 0.957366i | \(0.406718\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 10.1417i | − 0.160979i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −42.0454 | −0.646852 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 47.0790i | 0.702671i | 0.936250 | + | 0.351336i | \(0.114272\pi\) | ||||
−0.936250 | + | 0.351336i | \(0.885728\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −20.1818 | −0.292489 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 85.2253i | − 1.20036i | −0.799866 | − | 0.600178i | \(-0.795096\pi\) | ||||
0.799866 | − | 0.600178i | \(-0.204904\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.1258 | 0.207203 | 0.103602 | − | 0.994619i | \(-0.466963\pi\) | ||||
0.103602 | + | 0.994619i | \(0.466963\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 11.4902i | − 0.153202i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 52.7542 | 0.685120 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 129.294i | 1.63664i | 0.574765 | + | 0.818319i | \(0.305094\pi\) | ||||
−0.574765 | + | 0.818319i | \(0.694906\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −33.6974 | −0.416018 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 44.7659i | 0.539348i | 0.962952 | + | 0.269674i | \(0.0869160\pi\) | ||||
−0.962952 | + | 0.269674i | \(0.913084\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 52.7174 | 0.620205 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 55.0081i | − 0.632277i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 81.3817 | 0.914401 | 0.457201 | − | 0.889364i | \(-0.348852\pi\) | ||||
0.457201 | + | 0.889364i | \(0.348852\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 51.2759i | − 0.563472i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.2685 | 0.239446 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 62.3370i | − 0.656179i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 112.525 | 1.16006 | 0.580028 | − | 0.814597i | \(-0.303042\pi\) | ||||
0.580028 | + | 0.814597i | \(0.303042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 71.9461i | 0.726728i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −63.6119 | −0.629821 | −0.314911 | − | 0.949121i | \(-0.601975\pi\) | ||||
−0.314911 | + | 0.949121i | \(0.601975\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 76.2794i | − 0.740577i | −0.928917 | − | 0.370289i | \(-0.879259\pi\) | ||||
0.928917 | − | 0.370289i | \(-0.120741\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.0127 | 0.133454 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 111.835i | − 1.04519i | −0.852582 | − | 0.522594i | \(-0.824964\pi\) | ||||
0.852582 | − | 0.522594i | \(-0.175036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −127.374 | −1.16857 | −0.584286 | − | 0.811548i | \(-0.698625\pi\) | ||||
−0.584286 | + | 0.811548i | \(0.698625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 160.047i | − 1.44187i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.6077 | 0.138121 | 0.0690605 | − | 0.997612i | \(-0.478000\pi\) | ||||
0.0690605 | + | 0.997612i | \(0.478000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.6376i | 0.170761i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 69.9300 | 0.597693 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 64.2908i | 0.540259i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −253.243 | −2.09292 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 75.2092i | − 0.611457i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 148.087i | 1.16604i | 0.812459 | + | 0.583018i | \(0.198128\pi\) | ||||
−0.812459 | + | 0.583018i | \(0.801872\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 64.8269 | 0.502534 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 172.818i | 1.31922i | 0.751606 | + | 0.659612i | \(0.229279\pi\) | ||||
−0.751606 | + | 0.659612i | \(0.770721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 76.0223 | 0.571597 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 65.3576i | 0.484130i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −162.370 | −1.18518 | −0.592591 | − | 0.805503i | \(-0.701895\pi\) | ||||
−0.592591 | + | 0.805503i | \(0.701895\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 75.1316i | 0.540515i | 0.962788 | + | 0.270257i | \(0.0871088\pi\) | ||||
−0.962788 | + | 0.270257i | \(0.912891\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −86.5105 | −0.613550 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 363.756i | 2.54375i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −53.5248 | −0.369136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 95.5147i | − 0.649760i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 256.461 | 1.72121 | 0.860607 | − | 0.509270i | \(-0.170084\pi\) | ||||
0.860607 | + | 0.509270i | \(0.170084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 121.764i | − 0.806382i | −0.915116 | − | 0.403191i | \(-0.867901\pi\) | ||||
0.915116 | − | 0.403191i | \(-0.132099\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −87.6797 | −0.573070 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 21.6680i | − 0.139793i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 97.7472 | 0.622593 | 0.311297 | − | 0.950313i | \(-0.399237\pi\) | ||||
0.311297 | + | 0.950313i | \(0.399237\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 98.2016i | 0.617620i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.9487 | −0.148750 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 92.0819i | 0.564920i | 0.959279 | + | 0.282460i | \(0.0911504\pi\) | ||||
−0.959279 | + | 0.282460i | \(0.908850\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −99.4073 | −0.602469 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 150.795i | 0.902961i | 0.892281 | + | 0.451481i | \(0.149104\pi\) | ||||
−0.892281 | + | 0.451481i | \(0.850896\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 184.563 | 1.09209 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 103.679i | 0.606311i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −37.9223 | −0.219204 | −0.109602 | − | 0.993976i | \(-0.534958\pi\) | ||||
−0.109602 | + | 0.993976i | \(0.534958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 13.6348i | − 0.0779134i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −42.1389 | −0.238073 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 356.798i | − 1.99328i | −0.0818844 | − | 0.996642i | \(-0.526094\pi\) | ||||
0.0818844 | − | 0.996642i | \(-0.473906\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −330.928 | −1.82833 | −0.914166 | − | 0.405340i | \(-0.867153\pi\) | ||||
−0.914166 | + | 0.405340i | \(0.867153\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 80.9895i | − 0.442566i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −155.732 | −0.841792 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 456.085i | − 2.43896i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −79.7060 | −0.421725 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 358.323i | 1.87603i | 0.346588 | + | 0.938017i | \(0.387340\pi\) | ||||
−0.346588 | + | 0.938017i | \(0.612660\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 88.3050 | 0.457539 | 0.228769 | − | 0.973481i | \(-0.426530\pi\) | ||||
0.228769 | + | 0.973481i | \(0.426530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 96.6218i | 0.495496i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −94.8836 | −0.481643 | −0.240821 | − | 0.970569i | \(-0.577417\pi\) | ||||
−0.240821 | + | 0.970569i | \(0.577417\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 119.615i | − 0.601079i | −0.953769 | − | 0.300539i | \(-0.902833\pi\) | ||||
0.953769 | − | 0.300539i | \(-0.0971666\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 108.189 | 0.538254 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 65.2755i | − 0.321554i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −73.1811 | −0.356981 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 32.6612i | − 0.157784i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −539.309 | −2.58043 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 85.5156i | 0.405287i | 0.979253 | + | 0.202644i | \(0.0649533\pi\) | ||||
−0.979253 | + | 0.202644i | \(0.935047\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −195.851 | −0.919487 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 63.0788i | − 0.293390i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.4249 | 0.121774 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 34.7597i | − 0.158720i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −443.305 | −2.00590 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 276.039i | − 1.23784i | −0.785453 | − | 0.618921i | \(-0.787570\pi\) | ||||
0.785453 | − | 0.618921i | \(-0.212430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.5952 | 0.0826452 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 87.2820i | − 0.384502i | −0.981346 | − | 0.192251i | \(-0.938421\pi\) | ||||
0.981346 | − | 0.192251i | \(-0.0615788\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 99.1232 | 0.432853 | 0.216426 | − | 0.976299i | \(-0.430560\pi\) | ||||
0.216426 | + | 0.976299i | \(0.430560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 121.231i | − 0.524810i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −165.452 | −0.710094 | −0.355047 | − | 0.934849i | \(-0.615535\pi\) | ||||
−0.355047 | + | 0.934849i | \(0.615535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 84.1777i | 0.358203i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 297.123 | 1.25368 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 75.3281i | 0.315180i | 0.987505 | + | 0.157590i | \(0.0503725\pi\) | ||||
−0.987505 | + | 0.157590i | \(0.949628\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −253.744 | −1.05288 | −0.526441 | − | 0.850212i | \(-0.676474\pi\) | ||||
−0.526441 | + | 0.850212i | \(0.676474\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 185.621i | − 0.763873i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −92.9391 | −0.379343 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 524.197i | 2.12225i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 102.874 | 0.413147 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 214.543i | 0.854753i | 0.904074 | + | 0.427377i | \(0.140562\pi\) | ||||
−0.904074 | + | 0.427377i | \(0.859438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 169.894 | 0.671520 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 121.146i | − 0.475084i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 412.080 | 1.60343 | 0.801713 | − | 0.597709i | \(-0.203922\pi\) | ||||
0.801713 | + | 0.597709i | \(0.203922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 189.921i | − 0.733284i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 89.0226 | 0.341083 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 339.579i | 1.29118i | 0.763686 | + | 0.645588i | \(0.223388\pi\) | ||||
−0.763686 | + | 0.645588i | \(0.776612\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 95.5536 | 0.360580 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 187.018i | − 0.700442i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −119.714 | −0.445034 | −0.222517 | − | 0.974929i | \(-0.571427\pi\) | ||||
−0.222517 | + | 0.974929i | \(0.571427\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 404.838i | − 1.49387i | −0.664898 | − | 0.746934i | \(-0.731525\pi\) | ||||
0.664898 | − | 0.746934i | \(-0.268475\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −117.834 | −0.431626 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 96.7268i | 0.351734i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.1545 | 0.0908104 | 0.0454052 | − | 0.998969i | \(-0.485542\pi\) | ||||
0.0454052 | + | 0.998969i | \(0.485542\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 36.0383i | 0.129169i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −454.496 | −1.61742 | −0.808712 | − | 0.588205i | \(-0.799835\pi\) | ||||
−0.808712 | + | 0.588205i | \(0.799835\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 111.479i | − 0.393918i | −0.980412 | − | 0.196959i | \(-0.936893\pi\) | ||||
0.980412 | − | 0.196959i | \(-0.0631067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −143.253 | −0.502641 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 89.2472i | − 0.310966i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 266.825 | 0.923269 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 258.587i | − 0.888616i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −310.130 | −1.05847 | −0.529233 | − | 0.848477i | \(-0.677520\pi\) | ||||
−0.529233 | + | 0.848477i | \(0.677520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.0027i | 0.138992i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 565.442 | 1.90384 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 165.134i | − 0.552287i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 76.9270 | 0.255571 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 146.182i | 0.482450i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −78.8056 | −0.258379 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 510.536i | 1.66298i | 0.555538 | + | 0.831491i | \(0.312512\pi\) | ||||
−0.555538 | + | 0.831491i | \(0.687488\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −175.293 | −0.567291 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 315.393i | − 1.01413i | −0.861909 | − | 0.507063i | \(-0.830731\pi\) | ||||
0.861909 | − | 0.507063i | \(-0.169269\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 80.4580 | 0.257054 | 0.128527 | − | 0.991706i | \(-0.458975\pi\) | ||||
0.128527 | + | 0.991706i | \(0.458975\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 22.6775i | 0.0719921i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −135.504 | −0.427458 | −0.213729 | − | 0.976893i | \(-0.568561\pi\) | ||||
−0.213729 | + | 0.976893i | \(0.568561\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 463.070i | 1.45163i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −257.001 | −0.800626 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 657.249i | − 2.03483i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 94.0163 | 0.289281 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 292.710i | 0.895139i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −102.658 | −0.312030 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 435.738i | 1.31643i | 0.752831 | + | 0.658214i | \(0.228688\pi\) | ||||
−0.752831 | + | 0.658214i | \(0.771312\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 259.013 | 0.777818 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 105.272i | − 0.314244i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −66.1157 | −0.196189 | −0.0980945 | − | 0.995177i | \(-0.531275\pi\) | ||||
−0.0980945 | + | 0.995177i | \(0.531275\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 35.8670i | − 0.105802i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −187.461 | −0.549738 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 246.964i | − 0.720012i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 45.1278 | 0.130805 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 232.394i | 0.669723i | 0.942267 | + | 0.334862i | \(0.108690\pi\) | ||||
−0.942267 | + | 0.334862i | \(0.891310\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 458.147 | 1.31274 | 0.656371 | − | 0.754438i | \(-0.272091\pi\) | ||||
0.656371 | + | 0.754438i | \(0.272091\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 549.597i | − 1.56580i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 376.363 | 1.06619 | 0.533093 | − | 0.846057i | \(-0.321030\pi\) | ||||
0.533093 | + | 0.846057i | \(0.321030\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 190.570i | 0.536816i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 147.743 | 0.413845 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 193.553i | − 0.539145i | −0.962980 | − | 0.269572i | \(-0.913118\pi\) | ||||
0.962980 | − | 0.269572i | \(-0.0868824\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −416.181 | −1.15286 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 581.961i | 1.60320i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −33.8224 | −0.0926641 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.10203i | 0.0139020i | 0.999976 | + | 0.00695100i | \(0.00221259\pi\) | ||||
−0.999976 | + | 0.00695100i | \(0.997787\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 121.715 | 0.329851 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 116.531i | 0.314100i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 721.093 | 1.93322 | 0.966612 | − | 0.256244i | \(-0.0824849\pi\) | ||||
0.966612 | + | 0.256244i | \(0.0824849\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.6928i | 0.0685142i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 450.094 | 1.19388 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 323.886i | 0.854580i | 0.904115 | + | 0.427290i | \(0.140532\pi\) | ||||
−0.904115 | + | 0.427290i | \(0.859468\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 340.308 | 0.893197 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 249.254i | − 0.650794i | −0.945578 | − | 0.325397i | \(-0.894502\pi\) | ||||
0.945578 | − | 0.325397i | \(-0.105498\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −117.962 | −0.306395 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 104.913i | 0.271093i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 353.367 | 0.908398 | 0.454199 | − | 0.890900i | \(-0.349925\pi\) | ||||
0.454199 | + | 0.890900i | \(0.349925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 207.048i | 0.529535i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 397.143 | 1.01054 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 289.111i | − 0.731926i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.9297 | −0.0829463 | −0.0414732 | − | 0.999140i | \(-0.513205\pi\) | ||||
−0.0414732 | + | 0.999140i | \(0.513205\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 174.702i | − 0.437850i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −215.009 | −0.536183 | −0.268092 | − | 0.963393i | \(-0.586393\pi\) | ||||
−0.268092 | + | 0.963393i | \(0.586393\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 182.208i | 0.452128i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 75.3498 | 0.186049 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1347.31i | 3.31035i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −114.925 | −0.280990 | −0.140495 | − | 0.990081i | \(-0.544869\pi\) | ||||
−0.140495 | + | 0.990081i | \(0.544869\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 373.132i | 0.907864i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −50.0043 | −0.121076 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 100.100i | − 0.241204i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 172.655 | 0.414041 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 526.123i | − 1.25566i | −0.778349 | − | 0.627831i | \(-0.783943\pi\) | ||||
0.778349 | − | 0.627831i | \(-0.216057\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −298.264 | −0.708465 | −0.354233 | − | 0.935157i | \(-0.615258\pi\) | ||||
−0.354233 | + | 0.935157i | \(0.615258\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 140.005i | − 0.330980i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −117.880 | −0.277364 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 96.1065i | − 0.225074i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 835.924 | 1.94854 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 319.961i | − 0.742370i | −0.928559 | − | 0.371185i | \(-0.878952\pi\) | ||||
0.928559 | − | 0.371185i | \(-0.121048\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −578.492 | −1.33601 | −0.668005 | − | 0.744157i | \(-0.732852\pi\) | ||||
−0.668005 | + | 0.744157i | \(0.732852\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 123.002i | 0.282763i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 244.829 | 0.560250 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 716.216i | − 1.63147i | −0.578425 | − | 0.815735i | \(-0.696333\pi\) | ||||
0.578425 | − | 0.815735i | \(-0.303667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 154.577 | 0.350514 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 653.956i | 1.47620i | 0.674692 | + | 0.738100i | \(0.264277\pi\) | ||||
−0.674692 | + | 0.738100i | \(0.735723\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −181.975 | −0.408933 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 589.356i | − 1.31847i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 375.502 | 0.836307 | 0.418154 | − | 0.908376i | \(-0.362677\pi\) | ||||
0.418154 | + | 0.908376i | \(0.362677\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 633.127i | 1.40383i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −279.817 | −0.617698 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 114.656i | 0.251992i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 347.650 | 0.760721 | 0.380361 | − | 0.924838i | \(-0.375800\pi\) | ||||
0.380361 | + | 0.924838i | \(0.375800\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 689.096i | 1.50130i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −329.633 | −0.715039 | −0.357520 | − | 0.933906i | \(-0.616377\pi\) | ||||
−0.357520 | + | 0.933906i | \(0.616377\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 256.443i | − 0.553872i | −0.960888 | − | 0.276936i | \(-0.910681\pi\) | ||||
0.960888 | − | 0.276936i | \(-0.0893190\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −49.7938 | −0.107083 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 595.434i | − 1.27502i | −0.770442 | − | 0.637510i | \(-0.779965\pi\) | ||||
0.770442 | − | 0.637510i | \(-0.220035\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 128.383 | 0.273738 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 224.626i | − 0.476914i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −545.727 | −1.15376 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 139.390i | 0.293452i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −158.925 | −0.333176 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 169.276i | − 0.353395i | −0.984265 | − | 0.176698i | \(-0.943459\pi\) | ||||
0.984265 | − | 0.176698i | \(-0.0565414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1309.56 | 2.72258 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 55.0350i | 0.113944i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −251.614 | −0.518792 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 692.389i | − 1.42174i | −0.703321 | − | 0.710872i | \(-0.748300\pi\) | ||||
0.703321 | − | 0.710872i | \(-0.251700\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 211.607 | 0.432735 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 253.027i | − 0.515330i | −0.966234 | − | 0.257665i | \(-0.917047\pi\) | ||||
0.966234 | − | 0.257665i | \(-0.0829531\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −564.337 | −1.14470 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 160.876i | − 0.325003i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −232.407 | −0.467619 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 856.886i | − 1.71721i | −0.512640 | − | 0.858604i | \(-0.671332\pi\) | ||||
0.512640 | − | 0.858604i | \(-0.328668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 346.531 | 0.691679 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 53.5054i | − 0.106373i | −0.998585 | − | 0.0531863i | \(-0.983062\pi\) | ||||
0.998585 | − | 0.0531863i | \(-0.0169377\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 142.241 | 0.281665 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 424.132i | − 0.836552i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −313.259 | −0.615439 | −0.307720 | − | 0.951477i | \(-0.599566\pi\) | ||||
−0.307720 | + | 0.951477i | \(0.599566\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 41.2477i | − 0.0807195i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 814.839 | 1.58838 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 170.566i | 0.331196i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 728.264 | 1.40864 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 87.1468i | 0.167913i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 291.820 | 0.560116 | 0.280058 | − | 0.959983i | \(-0.409646\pi\) | ||||
0.280058 | + | 0.959983i | \(0.409646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 236.297i | − 0.451811i | −0.974149 | − | 0.225906i | \(-0.927466\pi\) | ||||
0.974149 | − | 0.225906i | \(-0.0725341\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −31.3334 | −0.0596826 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 228.456i | − 0.433503i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 451.873 | 0.854203 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 68.1958i | − 0.128429i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 615.386 | 1.15457 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 250.071i | 0.467422i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −819.934 | −1.52688 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 804.064i | 1.49177i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −479.488 | −0.886300 | −0.443150 | − | 0.896448i | \(-0.646139\pi\) | ||||
−0.443150 | + | 0.896448i | \(0.646139\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 760.484i | 1.40052i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 284.817 | 0.522601 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 606.330i | 1.10846i | 0.832362 | + | 0.554232i | \(0.186988\pi\) | ||||
−0.832362 | + | 0.554232i | \(0.813012\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 131.070 | 0.238743 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 667.315i | 1.21110i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 352.582 | 0.637580 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 357.877i | 0.644823i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.2604 | 0.0399649 | 0.0199824 | − | 0.999800i | \(-0.493639\pi\) | ||||
0.0199824 | + | 0.999800i | \(0.493639\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 530.435i | 0.948899i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1048.10 | −1.86827 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 518.786i | − 0.921468i | −0.887538 | − | 0.460734i | \(-0.847586\pi\) | ||||
0.887538 | − | 0.460734i | \(-0.152414\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.8998 | −0.0617696 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 91.8919i | 0.162067i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −596.499 | −1.04833 | −0.524164 | − | 0.851617i | \(-0.675622\pi\) | ||||
−0.524164 | + | 0.851617i | \(0.675622\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 290.657i | 0.509031i | 0.967069 | + | 0.254515i | \(0.0819160\pi\) | ||||
−0.967069 | + | 0.254515i | \(0.918084\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 823.438 | 1.43706 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 43.9109i | − 0.0763668i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 604.262 | 1.04725 | 0.523623 | − | 0.851950i | \(-0.324580\pi\) | ||||
0.523623 | + | 0.851950i | \(0.324580\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 202.928i | − 0.350480i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 122.075 | 0.210112 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 826.683i | − 1.41798i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −156.368 | −0.267296 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1147.72i | − 1.95522i | −0.210418 | − | 0.977611i | \(-0.567483\pi\) | ||||
0.210418 | − | 0.977611i | \(-0.432517\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −270.143 | −0.458648 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 218.046i | 0.368944i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −426.623 | −0.719432 | −0.359716 | − | 0.933062i | \(-0.617126\pi\) | ||||
−0.359716 | + | 0.933062i | \(0.617126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 143.759i | − 0.241611i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −274.879 | −0.460433 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 602.645i | 1.00609i | 0.864262 | + | 0.503043i | \(0.167786\pi\) | ||||
−0.864262 | + | 0.503043i | \(0.832214\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 804.359 | 1.33837 | 0.669184 | − | 0.743097i | \(-0.266644\pi\) | ||||
0.669184 | + | 0.743097i | \(0.266644\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 175.088i | 0.290362i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 566.269 | 0.935981 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1088.91i | − 1.79392i | −0.442115 | − | 0.896958i | \(-0.645772\pi\) | ||||
0.442115 | − | 0.896958i | \(-0.354228\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −150.005 | −0.246314 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 707.857i | − 1.15852i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −369.141 | −0.602188 | −0.301094 | − | 0.953595i | \(-0.597352\pi\) | ||||
−0.301094 | + | 0.953595i | \(0.597352\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 168.173i | 0.273452i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.3293 | −0.0507768 | −0.0253884 | − | 0.999678i | \(-0.508082\pi\) | ||||
−0.0253884 | + | 0.999678i | \(0.508082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 472.149i | − 0.762761i | −0.924418 | − | 0.381380i | \(-0.875449\pi\) | ||||
0.924418 | − | 0.381380i | \(-0.124551\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −256.693 | −0.413353 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 221.925i | − 0.356221i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1239.35i | 1.97664i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1641.95 | −2.61042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1107.24i | − 1.75474i | −0.479815 | − | 0.877369i | \(-0.659296\pi\) | ||||
0.479815 | − | 0.877369i | \(-0.340704\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 196.518 | 0.310455 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 331.132i | − 0.521467i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 781.532 | 1.22690 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 316.956i | − 0.496019i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −609.118 | −0.950261 | −0.475131 | − | 0.879915i | \(-0.657599\pi\) | ||||
−0.475131 | + | 0.879915i | \(0.657599\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 151.870i | − 0.236190i | −0.993002 | − | 0.118095i | \(-0.962321\pi\) | ||||
0.993002 | − | 0.118095i | \(-0.0376788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −144.957 | −0.224740 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 590.497i | 0.912670i | 0.889808 | + | 0.456335i | \(0.150838\pi\) | ||||
−0.889808 | + | 0.456335i | \(0.849162\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 354.735 | 0.546587 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 60.7254i | − 0.0932802i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −356.873 | −0.546514 | −0.273257 | − | 0.961941i | \(-0.588101\pi\) | ||||
−0.273257 | + | 0.961941i | \(0.588101\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 386.434i | − 0.589975i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 56.2535 | 0.0856218 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 309.347i | 0.469419i | 0.972066 | + | 0.234709i | \(0.0754138\pi\) | ||||
−0.972066 | + | 0.234709i | \(0.924586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −432.538 | −0.654369 | −0.327185 | − | 0.944960i | \(-0.606100\pi\) | ||||
−0.327185 | + | 0.944960i | \(0.606100\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1018.73i | 1.53655i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −169.991 | −0.255626 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 210.219i | − 0.315171i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −634.347 | −0.948202 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 681.788i | 1.01608i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −896.681 | −1.33236 | −0.666182 | − | 0.745789i | \(-0.732073\pi\) | ||||
−0.666182 | + | 0.745789i | \(0.732073\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 146.144i | − 0.216510i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −596.363 | −0.880890 | −0.440445 | − | 0.897780i | \(-0.645179\pi\) | ||||
−0.440445 | + | 0.897780i | \(0.645179\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 306.853i | − 0.451919i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −200.577 | −0.294533 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 845.172i | − 1.23744i | −0.785612 | − | 0.618720i | \(-0.787652\pi\) | ||||
0.785612 | − | 0.618720i | \(-0.212348\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 363.070 | 0.530030 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 227.789i | − 0.331570i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −803.518 | −1.16621 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 99.7834i | 0.144404i | 0.997390 | + | 0.0722022i | \(0.0230027\pi\) | ||||
−0.997390 | + | 0.0722022i | \(0.976997\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 196.195 | 0.283109 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 167.999i | − 0.241726i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −771.584 | −1.10701 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 380.214i | 0.543940i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 258.057 | 0.368127 | 0.184063 | − | 0.982914i | \(-0.441075\pi\) | ||||
0.184063 | + | 0.982914i | \(0.441075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1941.57i | 2.76183i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 193.443 | 0.274388 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 173.468i | 0.245358i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 463.455 | 0.653674 | 0.326837 | − | 0.945081i | \(-0.394017\pi\) | ||||
0.326837 | + | 0.945081i | \(0.394017\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 480.850i | 0.676301i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 85.1012 | 0.119357 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 813.383i | − 1.13760i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 173.107 | 0.241432 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1254.95i | 1.74541i | 0.488249 | + | 0.872704i | \(0.337636\pi\) | ||||
−0.488249 | + | 0.872704i | \(0.662364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −208.012 | −0.288504 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 583.113i | 0.806519i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 119.685 | 0.165083 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 450.184i | 0.619236i | 0.950861 | + | 0.309618i | \(0.100201\pi\) | ||||
−0.950861 | + | 0.309618i | \(0.899799\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.841 | −1.00115 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 665.070i | − 0.909808i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1413.12 | −1.92786 | −0.963929 | − | 0.266160i | \(-0.914245\pi\) | ||||
−0.963929 | + | 0.266160i | \(0.914245\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 213.577i | 0.290581i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −910.760 | −1.23577 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 331.195i | 0.448167i | 0.974570 | + | 0.224083i | \(0.0719388\pi\) | ||||
−0.974570 | + | 0.224083i | \(0.928061\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1204.62 | 1.62567 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 168.111i | − 0.226259i | −0.993580 | − | 0.113130i | \(-0.963912\pi\) | ||||
0.993580 | − | 0.113130i | \(-0.0360875\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −573.464 | −0.769750 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 166.486i | 0.222873i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −304.971 | −0.407171 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1259.45i | 1.67703i | 0.544880 | + | 0.838514i | \(0.316575\pi\) | ||||
−0.544880 | + | 0.838514i | \(0.683425\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 493.027 | 0.654751 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 272.272i | 0.360625i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1184.73 | −1.56503 | −0.782514 | − | 0.622633i | \(-0.786063\pi\) | ||||
−0.782514 | + | 0.622633i | \(0.786063\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 390.423i | − 0.514392i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −136.691 | −0.179620 | −0.0898099 | − | 0.995959i | \(-0.528626\pi\) | ||||
−0.0898099 | + | 0.995959i | \(0.528626\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 347.346i | 0.455237i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 196.058 | 0.256285 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 344.794i | − 0.449536i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 621.428 | 0.808099 | 0.404049 | − | 0.914737i | \(-0.367602\pi\) | ||||
0.404049 | + | 0.914737i | \(0.367602\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 946.975i | − 1.22824i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −209.531 | −0.271063 | −0.135531 | − | 0.990773i | \(-0.543274\pi\) | ||||
−0.135531 | + | 0.990773i | \(0.543274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 48.4511i | 0.0625175i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −436.444 | −0.561704 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 912.379i | 1.17122i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1648.71 | 2.11103 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 699.650i | − 0.893550i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −218.569 | −0.278432 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 176.067i | 0.223719i | 0.993724 | + | 0.111859i | \(0.0356806\pi\) | ||||
−0.993724 | + | 0.111859i | \(0.964319\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 780.365 | 0.989056 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 42.5617i | − 0.0538074i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 662.683 | 0.835666 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 219.586i | − 0.276208i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1185.07 | −1.48692 | −0.743458 | − | 0.668783i | \(-0.766816\pi\) | ||||
−0.743458 | + | 0.668783i | \(0.766816\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 887.526i | 1.11080i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 302.662 | 0.377855 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 292.615i | 0.364402i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 53.5510 | 0.0665230 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 275.107i | 0.340901i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 537.511 | 0.664414 | 0.332207 | − | 0.943206i | \(-0.392207\pi\) | ||||
0.332207 | + | 0.943206i | \(0.392207\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 859.330i | − 1.05959i | −0.848125 | − | 0.529797i | \(-0.822268\pi\) | ||||
0.848125 | − | 0.529797i | \(-0.177732\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −930.332 | −1.14432 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 205.901i | − 0.252640i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −786.429 | −0.962581 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 190.697i | − 0.232841i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −808.044 | −0.984220 | −0.492110 | − | 0.870533i | \(-0.663774\pi\) | ||||
−0.492110 | + | 0.870533i | \(0.663774\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 709.287i | − 0.861831i | −0.902392 | − | 0.430916i | \(-0.858191\pi\) | ||||
0.902392 | − | 0.430916i | \(-0.141809\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 222.282 | 0.269432 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 714.799i | − 0.864328i | −0.901795 | − | 0.432164i | \(-0.857750\pi\) | ||||
0.901795 | − | 0.432164i | \(-0.142250\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 730.675 | 0.881393 | 0.440697 | − | 0.897656i | \(-0.354731\pi\) | ||||
0.440697 | + | 0.897656i | \(0.354731\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 57.8059i | − 0.0695618i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −979.902 | −1.17635 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 337.187i | − 0.403817i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 283.233 | 0.338391 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1154.02i | − 1.37548i | −0.725959 | − | 0.687738i | \(-0.758604\pi\) | ||||
0.725959 | − | 0.687738i | \(-0.241396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −268.019 | −0.318691 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1044.45i | 1.23897i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −412.695 | −0.488397 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 690.586i | 0.815332i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −256.182 | −0.301746 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 611.638i | − 0.718728i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 105.220 | 0.123353 | 0.0616764 | − | 0.998096i | \(-0.480355\pi\) | ||||
0.0616764 | + | 0.998096i | \(0.480355\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 231.834i | − 0.271150i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −681.033 | −0.794671 | −0.397336 | − | 0.917673i | \(-0.630065\pi\) | ||||
−0.397336 | + | 0.917673i | \(0.630065\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 921.542i | − 1.07281i | −0.843961 | − | 0.536404i | \(-0.819782\pi\) | ||||
0.843961 | − | 0.536404i | \(-0.180218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −205.093 | −0.238203 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 744.099i | − 0.862223i | −0.902299 | − | 0.431112i | \(-0.858122\pi\) | ||||
0.902299 | − | 0.431112i | \(-0.141878\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 84.7969 | 0.0980311 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 613.172i | − 0.707235i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2501.25 | −2.87830 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 885.238i | 1.01635i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 418.486 | 0.479365 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.4884i | 0.0348439i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −795.922 | −0.907551 | −0.453775 | − | 0.891116i | \(-0.649923\pi\) | ||||
−0.453775 | + | 0.891116i | \(0.649923\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 712.690i | 0.810797i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1211.69 | 1.37536 | 0.687679 | − | 0.726015i | \(-0.258630\pi\) | ||||
0.687679 | + | 0.726015i | \(0.258630\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 217.973i | − 0.246855i | −0.992354 | − | 0.123427i | \(-0.960611\pi\) | ||||
0.992354 | − | 0.123427i | \(-0.0393886\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 94.2255 | 0.106470 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1236.92i | − 1.39450i | −0.716829 | − | 0.697249i | \(-0.754407\pi\) | ||||
0.716829 | − | 0.697249i | \(-0.245593\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 403.827 | 0.454249 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 651.889i | − 0.731638i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1049.48 | 1.17523 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 797.824i | 0.891424i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −379.483 | −0.423058 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 231.955i | 0.258014i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1007.47 | 1.11817 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 176.781i | − 0.195771i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 739.978 | 0.817655 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 804.548i | − 0.887043i | −0.896264 | − | 0.443522i | \(-0.853729\pi\) | ||||
0.896264 | − | 0.443522i | \(-0.146271\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −236.575 | −0.260259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 761.825i | 0.836251i | 0.908389 | + | 0.418126i | \(0.137313\pi\) | ||||
−0.908389 | + | 0.418126i | \(0.862687\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −866.013 | −0.948535 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 181.098i | 0.197921i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 471.270 | 0.513926 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 502.728i | − 0.547039i | −0.961867 | − | 0.273519i | \(-0.911812\pi\) | ||||
0.961867 | − | 0.273519i | \(-0.0881877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1173.23 | 1.27386 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1602.51i | − 1.73620i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 348.226 | 0.376461 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 283.686i | − 0.306026i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 845.520 | 0.910140 | 0.455070 | − | 0.890456i | \(-0.349614\pi\) | ||||
0.455070 | + | 0.890456i | \(0.349614\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1158.71i | 1.24459i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −724.784 | −0.776832 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1019.84i | 1.09073i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 93.6571 | 0.0999542 | 0.0499771 | − | 0.998750i | \(-0.484085\pi\) | ||||
0.0499771 | + | 0.998750i | \(0.484085\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 184.895i | − 0.196907i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 93.5311 | 0.0993954 | 0.0496977 | − | 0.998764i | \(-0.484174\pi\) | ||||
0.0496977 | + | 0.998764i | \(0.484174\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 287.420i | − 0.304793i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 178.228 | 0.188601 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1061.81i | 1.12124i | 0.828074 | + | 0.560619i | \(0.189437\pi\) | ||||
−0.828074 | + | 0.560619i | \(0.810563\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 284.415 | 0.299700 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 311.393i | 0.327438i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −435.168 | −0.456630 | −0.228315 | − | 0.973587i | \(-0.573322\pi\) | ||||
−0.228315 | + | 0.973587i | \(0.573322\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 801.234i | − 0.838988i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1064.15 | 1.11197 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 442.778i | 0.461708i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 867.100 | 0.902289 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 415.919i | − 0.431899i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −197.456 | −0.204618 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1400.02i | − 1.44780i | −0.689905 | − | 0.723900i | \(-0.742348\pi\) | ||||
0.689905 | − | 0.723900i | \(-0.257652\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1510.38 | −1.55870 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 562.184i | 0.578974i | 0.957182 | + | 0.289487i | \(0.0934847\pi\) | ||||
−0.957182 | + | 0.289487i | \(0.906515\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 204.881 | 0.210567 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 216.053i | − 0.221593i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −760.867 | −0.778779 | −0.389390 | − | 0.921073i | \(-0.627314\pi\) | ||||
−0.389390 | + | 0.921073i | \(0.627314\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1574.36i | 1.60813i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −473.709 | −0.482884 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 239.801i | 0.243948i | 0.992533 | + | 0.121974i | \(0.0389224\pi\) | ||||
−0.992533 | + | 0.121974i | \(0.961078\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 212.166 | 0.215397 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 235.911i | 0.239019i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 247.743 | 0.250498 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 12.0827i | − 0.0121925i | −0.999981 | − | 0.00609623i | \(-0.998059\pi\) | ||||
0.999981 | − | 0.00609623i | \(-0.00194050\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1001.34 | 1.00840 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 267.466i | 0.268810i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −127.529 | −0.127913 | −0.0639565 | − | 0.997953i | \(-0.520372\pi\) | ||||
−0.0639565 | + | 0.997953i | \(0.520372\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 2035.65i | − 2.03769i |
(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 | 640.3.b.a.511.6 | ✓ | 16 | |
4.3 | odd | 2 | inner | 640.3.b.a.511.11 | yes | 16 | |
8.3 | odd | 2 | 640.3.b.b.511.6 | yes | 16 | ||
8.5 | even | 2 | 640.3.b.b.511.11 | yes | 16 | ||
16.3 | odd | 4 | 1280.3.g.g.1151.8 | 16 | |||
16.5 | even | 4 | 1280.3.g.g.1151.7 | 16 | |||
16.11 | odd | 4 | 1280.3.g.h.1151.9 | 16 | |||
16.13 | even | 4 | 1280.3.g.h.1151.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.3.b.a.511.6 | ✓ | 16 | 1.1 | even | 1 | trivial | |
640.3.b.a.511.11 | yes | 16 | 4.3 | odd | 2 | inner | |
640.3.b.b.511.6 | yes | 16 | 8.3 | odd | 2 | ||
640.3.b.b.511.11 | yes | 16 | 8.5 | even | 2 | ||
1280.3.g.g.1151.7 | 16 | 16.5 | even | 4 | |||
1280.3.g.g.1151.8 | 16 | 16.3 | odd | 4 | |||
1280.3.g.h.1151.9 | 16 | 16.11 | odd | 4 | |||
1280.3.g.h.1151.10 | 16 | 16.13 | even | 4 |