Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(296,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.296");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 296.72 | ||
Character | \(\chi\) | \(=\) | 531.296 |
Dual form | 531.5.b.a.296.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.18445i | 1.79611i | 0.439880 | + | 0.898057i | \(0.355021\pi\) | ||||
−0.439880 | + | 0.898057i | \(0.644979\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −35.6164 | −2.22602 | ||||||||
\(5\) | − 15.5237i | − 0.620948i | −0.950582 | − | 0.310474i | \(-0.899512\pi\) | ||||
0.950582 | − | 0.310474i | \(-0.100488\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −43.6466 | −0.890747 | −0.445373 | − | 0.895345i | \(-0.646929\pi\) | ||||
−0.445373 | + | 0.895345i | \(0.646929\pi\) | |||||||
\(8\) | − 140.933i | − 2.20208i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 111.529 | 1.11529 | ||||||||
\(11\) | − 1.21721i | − 0.0100596i | −0.999987 | − | 0.00502981i | \(-0.998399\pi\) | ||||
0.999987 | − | 0.00502981i | \(-0.00160105\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −174.225 | −1.03092 | −0.515460 | − | 0.856914i | \(-0.672379\pi\) | ||||
−0.515460 | + | 0.856914i | \(0.672379\pi\) | |||||||
\(14\) | − 313.577i | − 1.59988i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 442.665 | 1.72916 | ||||||||
\(17\) | − 372.430i | − 1.28869i | −0.764737 | − | 0.644343i | \(-0.777131\pi\) | ||||
0.764737 | − | 0.644343i | \(-0.222869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 70.8089 | 0.196147 | 0.0980733 | − | 0.995179i | \(-0.468732\pi\) | ||||
0.0980733 | + | 0.995179i | \(0.468732\pi\) | |||||||
\(20\) | 552.898i | 1.38225i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.74502 | 0.0180682 | ||||||||
\(23\) | − 65.1472i | − 0.123152i | −0.998102 | − | 0.0615758i | \(-0.980387\pi\) | ||||
0.998102 | − | 0.0615758i | \(-0.0196126\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 384.015 | 0.614424 | ||||||||
\(26\) | − 1251.71i | − 1.85165i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1554.53 | 1.98282 | ||||||||
\(29\) | 412.612i | 0.490621i | 0.969445 | + | 0.245310i | \(0.0788899\pi\) | ||||
−0.969445 | + | 0.245310i | \(0.921110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 474.497 | 0.493753 | 0.246877 | − | 0.969047i | \(-0.420596\pi\) | ||||
0.246877 | + | 0.969047i | \(0.420596\pi\) | |||||||
\(32\) | 925.376i | 0.903687i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2675.71 | 2.31463 | ||||||||
\(35\) | 677.557i | 0.553107i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 403.733 | 0.294911 | 0.147455 | − | 0.989069i | \(-0.452892\pi\) | ||||
0.147455 | + | 0.989069i | \(0.452892\pi\) | |||||||
\(38\) | 508.723i | 0.352301i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2187.80 | −1.36738 | ||||||||
\(41\) | 1860.58i | 1.10683i | 0.832906 | + | 0.553414i | \(0.186675\pi\) | ||||
−0.832906 | + | 0.553414i | \(0.813325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −261.076 | −0.141199 | −0.0705994 | − | 0.997505i | \(-0.522491\pi\) | ||||
−0.0705994 | + | 0.997505i | \(0.522491\pi\) | |||||||
\(44\) | 43.3528i | 0.0223930i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 468.047 | 0.221194 | ||||||||
\(47\) | 2249.20i | 1.01820i | 0.860708 | + | 0.509098i | \(0.170021\pi\) | ||||
−0.860708 | + | 0.509098i | \(0.829979\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −495.975 | −0.206570 | ||||||||
\(50\) | 2758.94i | 1.10357i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6205.28 | 2.29485 | ||||||||
\(53\) | − 879.546i | − 0.313117i | −0.987669 | − | 0.156559i | \(-0.949960\pi\) | ||||
0.987669 | − | 0.156559i | \(-0.0500400\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.8957 | −0.00624650 | ||||||||
\(56\) | 6151.25i | 1.96149i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2964.39 | −0.881211 | ||||||||
\(59\) | − 453.188i | − 0.130189i | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 718.974 | 0.193221 | 0.0966103 | − | 0.995322i | \(-0.469200\pi\) | ||||
0.0966103 | + | 0.995322i | \(0.469200\pi\) | |||||||
\(62\) | 3409.00i | 0.886837i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 434.314 | 0.106034 | ||||||||
\(65\) | 2704.62i | 0.640148i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2833.84 | −0.631286 | −0.315643 | − | 0.948878i | \(-0.602220\pi\) | ||||
−0.315643 | + | 0.948878i | \(0.602220\pi\) | |||||||
\(68\) | 13264.6i | 2.86864i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4867.87 | −0.993444 | ||||||||
\(71\) | 7631.49i | 1.51388i | 0.653483 | + | 0.756942i | \(0.273307\pi\) | ||||
−0.653483 | + | 0.756942i | \(0.726693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6752.18 | −1.26706 | −0.633532 | − | 0.773717i | \(-0.718395\pi\) | ||||
−0.633532 | + | 0.773717i | \(0.718395\pi\) | |||||||
\(74\) | 2900.60i | 0.529693i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2521.96 | −0.436627 | ||||||||
\(77\) | 53.1273i | 0.00896058i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1263.31 | 0.202421 | 0.101211 | − | 0.994865i | \(-0.467728\pi\) | ||||
0.101211 | + | 0.994865i | \(0.467728\pi\) | |||||||
\(80\) | − 6871.79i | − 1.07372i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13367.2 | −1.98799 | ||||||||
\(83\) | − 2471.89i | − 0.358817i | −0.983775 | − | 0.179409i | \(-0.942582\pi\) | ||||
0.983775 | − | 0.179409i | \(-0.0574184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5781.49 | −0.800207 | ||||||||
\(86\) | − 1875.69i | − 0.253609i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −171.546 | −0.0221521 | ||||||||
\(89\) | − 1245.27i | − 0.157211i | −0.996906 | − | 0.0786053i | \(-0.974953\pi\) | ||||
0.996906 | − | 0.0786053i | \(-0.0250467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7604.35 | 0.918288 | ||||||||
\(92\) | 2320.31i | 0.274139i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −16159.2 | −1.82880 | ||||||||
\(95\) | − 1099.22i | − 0.121797i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13115.9 | 1.39397 | 0.696986 | − | 0.717084i | \(-0.254524\pi\) | ||||
0.696986 | + | 0.717084i | \(0.254524\pi\) | |||||||
\(98\) | − 3563.31i | − 0.371024i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13677.2 | −1.36772 | ||||||||
\(101\) | 7695.62i | 0.754399i | 0.926132 | + | 0.377199i | \(0.123113\pi\) | ||||
−0.926132 | + | 0.377199i | \(0.876887\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8710.01 | 0.821002 | 0.410501 | − | 0.911860i | \(-0.365354\pi\) | ||||
0.410501 | + | 0.911860i | \(0.365354\pi\) | |||||||
\(104\) | 24554.1i | 2.27017i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6319.06 | 0.562394 | ||||||||
\(107\) | 3999.35i | 0.349319i | 0.984629 | + | 0.174659i | \(0.0558824\pi\) | ||||
−0.984629 | + | 0.174659i | \(0.944118\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17980.5 | 1.51338 | 0.756692 | − | 0.653772i | \(-0.226814\pi\) | ||||
0.756692 | + | 0.653772i | \(0.226814\pi\) | |||||||
\(110\) | − 135.755i | − 0.0112194i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −19320.8 | −1.54024 | ||||||||
\(113\) | 4534.59i | 0.355125i | 0.984110 | + | 0.177562i | \(0.0568212\pi\) | ||||
−0.984110 | + | 0.177562i | \(0.943179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1011.33 | −0.0764708 | ||||||||
\(116\) | − 14695.8i | − 1.09213i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3255.91 | 0.233834 | ||||||||
\(119\) | 16255.3i | 1.14789i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14639.5 | 0.999899 | ||||||||
\(122\) | 5165.43i | 0.347046i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16899.9 | −1.09911 | ||||||||
\(125\) | − 15663.6i | − 1.00247i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −567.971 | −0.0352143 | −0.0176071 | − | 0.999845i | \(-0.505605\pi\) | ||||
−0.0176071 | + | 0.999845i | \(0.505605\pi\) | |||||||
\(128\) | 17926.3i | 1.09414i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −19431.2 | −1.14978 | ||||||||
\(131\) | 12776.2i | 0.744488i | 0.928135 | + | 0.372244i | \(0.121412\pi\) | ||||
−0.928135 | + | 0.372244i | \(0.878588\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3090.57 | −0.174717 | ||||||||
\(134\) | − 20359.6i | − 1.13386i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −52487.7 | −2.83779 | ||||||||
\(137\) | − 15857.6i | − 0.844881i | −0.906391 | − | 0.422441i | \(-0.861173\pi\) | ||||
0.906391 | − | 0.422441i | \(-0.138827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1922.39 | 0.0994976 | 0.0497488 | − | 0.998762i | \(-0.484158\pi\) | ||||
0.0497488 | + | 0.998762i | \(0.484158\pi\) | |||||||
\(140\) | − 24132.1i | − 1.23123i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −54828.1 | −2.71911 | ||||||||
\(143\) | 212.070i | 0.0103707i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6405.27 | 0.304650 | ||||||||
\(146\) | − 48510.7i | − 2.27579i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14379.5 | −0.656479 | ||||||||
\(149\) | − 8962.59i | − 0.403702i | −0.979416 | − | 0.201851i | \(-0.935304\pi\) | ||||
0.979416 | − | 0.201851i | \(-0.0646957\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20077.3 | 0.880544 | 0.440272 | − | 0.897864i | \(-0.354882\pi\) | ||||
0.440272 | + | 0.897864i | \(0.354882\pi\) | |||||||
\(152\) | − 9979.31i | − 0.431930i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −381.690 | −0.0160942 | ||||||||
\(155\) | − 7365.95i | − 0.306595i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −27050.6 | −1.09743 | −0.548716 | − | 0.836009i | \(-0.684883\pi\) | ||||
−0.548716 | + | 0.836009i | \(0.684883\pi\) | |||||||
\(158\) | 9076.21i | 0.363572i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14365.3 | 0.561143 | ||||||||
\(161\) | 2843.45i | 0.109697i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 49117.8 | 1.84869 | 0.924344 | − | 0.381560i | \(-0.124613\pi\) | ||||
0.924344 | + | 0.381560i | \(0.124613\pi\) | |||||||
\(164\) | − 66267.1i | − 2.46383i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17759.2 | 0.644477 | ||||||||
\(167\) | 10973.9i | 0.393485i | 0.980455 | + | 0.196742i | \(0.0630363\pi\) | ||||
−0.980455 | + | 0.196742i | \(0.936964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1793.50 | 0.0627956 | ||||||||
\(170\) | − 41536.9i | − 1.43726i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9298.60 | 0.314312 | ||||||||
\(173\) | − 18112.6i | − 0.605186i | −0.953120 | − | 0.302593i | \(-0.902148\pi\) | ||||
0.953120 | − | 0.302593i | \(-0.0978523\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16760.9 | −0.547296 | ||||||||
\(176\) | − 538.818i | − 0.0173947i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8946.55 | 0.282368 | ||||||||
\(179\) | − 25646.4i | − 0.800423i | −0.916423 | − | 0.400212i | \(-0.868937\pi\) | ||||
0.916423 | − | 0.400212i | \(-0.131063\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7034.92 | −0.214735 | −0.107367 | − | 0.994219i | \(-0.534242\pi\) | ||||
−0.107367 | + | 0.994219i | \(0.534242\pi\) | |||||||
\(182\) | 54633.1i | 1.64935i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9181.40 | −0.271190 | ||||||||
\(185\) | − 6267.43i | − 0.183124i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −453.327 | −0.0129637 | ||||||||
\(188\) | − 80108.2i | − 2.26653i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7897.27 | 0.218761 | ||||||||
\(191\) | − 4050.45i | − 0.111029i | −0.998458 | − | 0.0555146i | \(-0.982320\pi\) | ||||
0.998458 | − | 0.0555146i | \(-0.0176799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20075.0 | −0.538940 | −0.269470 | − | 0.963009i | \(-0.586848\pi\) | ||||
−0.269470 | + | 0.963009i | \(0.586848\pi\) | |||||||
\(194\) | 94230.5i | 2.50373i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17664.8 | 0.459830 | ||||||||
\(197\) | 38082.6i | 0.981283i | 0.871361 | + | 0.490642i | \(0.163238\pi\) | ||||
−0.871361 | + | 0.490642i | \(0.836762\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25403.5 | 0.641487 | 0.320743 | − | 0.947166i | \(-0.396067\pi\) | ||||
0.320743 | + | 0.947166i | \(0.396067\pi\) | |||||||
\(200\) | − 54120.4i | − 1.35301i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −55288.8 | −1.35499 | ||||||||
\(203\) | − 18009.1i | − 0.437019i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28883.1 | 0.687283 | ||||||||
\(206\) | 62576.7i | 1.47461i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −77123.5 | −1.78262 | ||||||||
\(209\) | − 86.1896i | − 0.00197316i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −45286.4 | −1.01719 | −0.508596 | − | 0.861005i | \(-0.669835\pi\) | ||||
−0.508596 | + | 0.861005i | \(0.669835\pi\) | |||||||
\(212\) | 31326.2i | 0.697006i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −28733.2 | −0.627416 | ||||||||
\(215\) | 4052.87i | 0.0876771i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20710.2 | −0.439809 | ||||||||
\(218\) | 129180.i | 2.71821i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 672.996 | 0.0139049 | ||||||||
\(221\) | 64886.8i | 1.32853i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8518.20 | 0.171293 | 0.0856463 | − | 0.996326i | \(-0.472705\pi\) | ||||
0.0856463 | + | 0.996326i | \(0.472705\pi\) | |||||||
\(224\) | − 40389.5i | − 0.804957i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −32578.6 | −0.637845 | ||||||||
\(227\) | 84296.7i | 1.63591i | 0.575284 | + | 0.817954i | \(0.304892\pi\) | ||||
−0.575284 | + | 0.817954i | \(0.695108\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 61059.9 | 1.16435 | 0.582177 | − | 0.813062i | \(-0.302201\pi\) | ||||
0.582177 | + | 0.813062i | \(0.302201\pi\) | |||||||
\(230\) | − 7265.83i | − 0.137350i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 58150.7 | 1.08039 | ||||||||
\(233\) | − 25669.4i | − 0.472828i | −0.971652 | − | 0.236414i | \(-0.924028\pi\) | ||||
0.971652 | − | 0.236414i | \(-0.0759722\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34915.8 | 0.632247 | ||||||||
\(236\) | 16140.9i | 0.289804i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −116785. | −2.06174 | ||||||||
\(239\) | 12241.5i | 0.214309i | 0.994242 | + | 0.107154i | \(0.0341739\pi\) | ||||
−0.994242 | + | 0.107154i | \(0.965826\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19062.8 | 0.328211 | 0.164106 | − | 0.986443i | \(-0.447526\pi\) | ||||
0.164106 | + | 0.986443i | \(0.447526\pi\) | |||||||
\(242\) | 105177.i | 1.79593i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −25607.2 | −0.430114 | ||||||||
\(245\) | 7699.37i | 0.128269i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12336.7 | −0.202211 | ||||||||
\(248\) | − 66872.3i | − 1.08728i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 112535. | 1.80056 | ||||||||
\(251\) | 52574.4i | 0.834501i | 0.908792 | + | 0.417250i | \(0.137006\pi\) | ||||
−0.908792 | + | 0.417250i | \(0.862994\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −79.2982 | −0.00123886 | ||||||||
\(254\) | − 4080.56i | − 0.0632488i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −121842. | −1.85916 | ||||||||
\(257\) | 108470.i | 1.64226i | 0.570740 | + | 0.821131i | \(0.306656\pi\) | ||||
−0.570740 | + | 0.821131i | \(0.693344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17621.6 | −0.262691 | ||||||||
\(260\) | − 96328.9i | − 1.42498i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −91789.8 | −1.33719 | ||||||||
\(263\) | 16502.0i | 0.238575i | 0.992860 | + | 0.119287i | \(0.0380610\pi\) | ||||
−0.992860 | + | 0.119287i | \(0.961939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13653.8 | −0.194429 | ||||||||
\(266\) | − 22204.0i | − 0.313811i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 100931. | 1.40526 | ||||||||
\(269\) | − 117780.i | − 1.62767i | −0.581094 | − | 0.813836i | \(-0.697375\pi\) | ||||
0.581094 | − | 0.813836i | \(-0.302625\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 102972. | 1.40210 | 0.701049 | − | 0.713113i | \(-0.252715\pi\) | ||||
0.701049 | + | 0.713113i | \(0.252715\pi\) | |||||||
\(272\) | − 164862.i | − 2.22834i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 113928. | 1.51750 | ||||||||
\(275\) | − 467.428i | − 0.00618087i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 82086.3 | 1.06982 | 0.534911 | − | 0.844909i | \(-0.320345\pi\) | ||||
0.534911 | + | 0.844909i | \(0.320345\pi\) | |||||||
\(278\) | 13811.3i | 0.178709i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 95490.1 | 1.21799 | ||||||||
\(281\) | 130095.i | 1.64758i | 0.566892 | + | 0.823792i | \(0.308145\pi\) | ||||
−0.566892 | + | 0.823792i | \(0.691855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 124067. | 1.54912 | 0.774558 | − | 0.632503i | \(-0.217973\pi\) | ||||
0.774558 | + | 0.632503i | \(0.217973\pi\) | |||||||
\(284\) | − 271806.i | − 3.36994i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1523.61 | −0.0186269 | ||||||||
\(287\) | − 81207.9i | − 0.985904i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −55183.2 | −0.660710 | ||||||||
\(290\) | 46018.4i | 0.547186i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 240488. | 2.82051 | ||||||||
\(293\) | 49630.4i | 0.578113i | 0.957312 | + | 0.289057i | \(0.0933416\pi\) | ||||
−0.957312 | + | 0.289057i | \(0.906658\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7035.15 | −0.0808405 | ||||||||
\(296\) | − 56899.3i | − 0.649417i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 64391.3 | 0.725095 | ||||||||
\(299\) | 11350.3i | 0.126959i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11395.1 | 0.125772 | ||||||||
\(302\) | 144244.i | 1.58156i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 31344.6 | 0.339169 | ||||||||
\(305\) | − 11161.1i | − 0.119980i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4876.14 | 0.0517368 | 0.0258684 | − | 0.999665i | \(-0.491765\pi\) | ||||
0.0258684 | + | 0.999665i | \(0.491765\pi\) | |||||||
\(308\) | − 1892.20i | − 0.0199465i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 52920.3 | 0.550680 | ||||||||
\(311\) | − 28435.8i | − 0.293999i | −0.989137 | − | 0.146999i | \(-0.953038\pi\) | ||||
0.989137 | − | 0.146999i | \(-0.0469615\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33035.5 | 0.337204 | 0.168602 | − | 0.985684i | \(-0.446075\pi\) | ||||
0.168602 | + | 0.985684i | \(0.446075\pi\) | |||||||
\(314\) | − 194344.i | − 1.97111i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −44994.6 | −0.450595 | ||||||||
\(317\) | 60035.9i | 0.597438i | 0.954341 | + | 0.298719i | \(0.0965593\pi\) | ||||
−0.954341 | + | 0.298719i | \(0.903441\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 502.238 | 0.00493546 | ||||||||
\(320\) | − 6742.16i | − 0.0658414i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −20428.7 | −0.197028 | ||||||||
\(323\) | − 26371.4i | − 0.252771i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −66905.1 | −0.633422 | ||||||||
\(326\) | 352885.i | 3.32045i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 262217. | 2.43732 | ||||||||
\(329\) | − 98169.7i | − 0.906955i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 185100. | 1.68947 | 0.844736 | − | 0.535184i | \(-0.179758\pi\) | ||||
0.844736 | + | 0.535184i | \(0.179758\pi\) | |||||||
\(332\) | 88039.9i | 0.798736i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −78841.5 | −0.706743 | ||||||||
\(335\) | 43991.7i | 0.391996i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −56283.4 | −0.495587 | −0.247794 | − | 0.968813i | \(-0.579706\pi\) | ||||
−0.247794 | + | 0.968813i | \(0.579706\pi\) | |||||||
\(338\) | 12885.4i | 0.112788i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 205916. | 1.78128 | ||||||||
\(341\) | − 577.565i | − 0.00496698i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 126443. | 1.07475 | ||||||||
\(344\) | 36794.3i | 0.310931i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 130129. | 1.08698 | ||||||||
\(347\) | − 73372.2i | − 0.609359i | −0.952455 | − | 0.304679i | \(-0.901451\pi\) | ||||
0.952455 | − | 0.304679i | \(-0.0985493\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 208998. | 1.71590 | 0.857948 | − | 0.513737i | \(-0.171739\pi\) | ||||
0.857948 | + | 0.513737i | \(0.171739\pi\) | |||||||
\(350\) | − 120418.i | − 0.983006i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1126.38 | 0.00909076 | ||||||||
\(353\) | 40934.8i | 0.328506i | 0.986418 | + | 0.164253i | \(0.0525213\pi\) | ||||
−0.986418 | + | 0.164253i | \(0.947479\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 118469. | 0.940043 | ||||||||
\(356\) | 44351.9i | 0.349955i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 184255. | 1.43765 | ||||||||
\(359\) | − 166730.i | − 1.29367i | −0.762629 | − | 0.646836i | \(-0.776092\pi\) | ||||
0.762629 | − | 0.646836i | \(-0.223908\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −125307. | −0.961527 | ||||||||
\(362\) | − 50542.1i | − 0.385688i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −270839. | −2.04413 | ||||||||
\(365\) | 104819.i | 0.786781i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −56232.0 | −0.417495 | −0.208747 | − | 0.977970i | \(-0.566939\pi\) | ||||
−0.208747 | + | 0.977970i | \(0.566939\pi\) | |||||||
\(368\) | − 28838.4i | − 0.212949i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 45028.1 | 0.328912 | ||||||||
\(371\) | 38389.2i | 0.278908i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 48971.9 | 0.351989 | 0.175995 | − | 0.984391i | \(-0.443686\pi\) | ||||
0.175995 | + | 0.984391i | \(0.443686\pi\) | |||||||
\(374\) | − 3256.91i | − 0.0232843i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 316986. | 2.24215 | ||||||||
\(377\) | − 71887.6i | − 0.505791i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −38517.2 | −0.268149 | −0.134074 | − | 0.990971i | \(-0.542806\pi\) | ||||
−0.134074 | + | 0.990971i | \(0.542806\pi\) | |||||||
\(380\) | 39150.1i | 0.271123i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 29100.3 | 0.199421 | ||||||||
\(383\) | − 185606.i | − 1.26531i | −0.774436 | − | 0.632653i | \(-0.781966\pi\) | ||||
0.774436 | − | 0.632653i | \(-0.218034\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 824.732 | 0.00556405 | ||||||||
\(386\) | − 144228.i | − 0.967997i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −467140. | −3.10302 | ||||||||
\(389\) | 151369.i | 1.00032i | 0.865934 | + | 0.500159i | \(0.166725\pi\) | ||||
−0.865934 | + | 0.500159i | \(0.833275\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24262.8 | −0.158704 | ||||||||
\(392\) | 69899.3i | 0.454884i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −273603. | −1.76250 | ||||||||
\(395\) | − 19611.3i | − 0.125693i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6978.50 | 0.0442773 | 0.0221387 | − | 0.999755i | \(-0.492952\pi\) | ||||
0.0221387 | + | 0.999755i | \(0.492952\pi\) | |||||||
\(398\) | 182510.i | 1.15218i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 169990. | 1.06244 | ||||||||
\(401\) | − 150562.i | − 0.936327i | −0.883642 | − | 0.468163i | \(-0.844916\pi\) | ||||
0.883642 | − | 0.468163i | \(-0.155084\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −82669.5 | −0.509020 | ||||||||
\(404\) | − 274090.i | − 1.67931i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 129386. | 0.784936 | ||||||||
\(407\) | − 491.430i | − 0.00296669i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −236736. | −1.41520 | −0.707601 | − | 0.706612i | \(-0.750223\pi\) | ||||
−0.707601 | + | 0.706612i | \(0.750223\pi\) | |||||||
\(410\) | 207509.i | 1.23444i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −310219. | −1.82757 | ||||||||
\(413\) | 19780.1i | 0.115965i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38372.9 | −0.222807 | ||||||||
\(416\) | − 161224.i | − 0.931629i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 619.225 | 0.00354402 | ||||||||
\(419\) | 242122.i | 1.37913i | 0.724222 | + | 0.689566i | \(0.242199\pi\) | ||||
−0.724222 | + | 0.689566i | \(0.757801\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8180.60 | 0.0461552 | 0.0230776 | − | 0.999734i | \(-0.492654\pi\) | ||||
0.0230776 | + | 0.999734i | \(0.492654\pi\) | |||||||
\(422\) | − 325358.i | − 1.82699i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −123957. | −0.689508 | ||||||||
\(425\) | − 143019.i | − 0.791799i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31380.7 | −0.172111 | ||||||||
\(428\) | − 142442.i | − 0.777592i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −29117.7 | −0.157478 | ||||||||
\(431\) | 282305.i | 1.51972i | 0.650085 | + | 0.759861i | \(0.274733\pi\) | ||||
−0.650085 | + | 0.759861i | \(0.725267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −154639. | −0.824790 | −0.412395 | − | 0.911005i | \(-0.635308\pi\) | ||||
−0.412395 | + | 0.911005i | \(0.635308\pi\) | |||||||
\(434\) | − 148791.i | − 0.789947i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −640401. | −3.36883 | ||||||||
\(437\) | − 4613.00i | − 0.0241558i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 210628. | 1.09292 | 0.546458 | − | 0.837487i | \(-0.315976\pi\) | ||||
0.546458 | + | 0.837487i | \(0.315976\pi\) | |||||||
\(440\) | 2663.02i | 0.0137553i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −466176. | −2.38619 | ||||||||
\(443\) | − 225809.i | − 1.15062i | −0.817934 | − | 0.575312i | \(-0.804881\pi\) | ||||
0.817934 | − | 0.575312i | \(-0.195119\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19331.1 | −0.0976196 | ||||||||
\(446\) | 61198.7i | 0.307661i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −18956.3 | −0.0944491 | ||||||||
\(449\) | − 3377.28i | − 0.0167523i | −0.999965 | − | 0.00837615i | \(-0.997334\pi\) | ||||
0.999965 | − | 0.00837615i | \(-0.00266624\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2264.72 | 0.0111343 | ||||||||
\(452\) | − 161506.i | − 0.790517i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −605626. | −2.93828 | ||||||||
\(455\) | − 118048.i | − 0.570209i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −223785. | −1.07151 | −0.535757 | − | 0.844372i | \(-0.679974\pi\) | ||||
−0.535757 | + | 0.844372i | \(0.679974\pi\) | |||||||
\(458\) | 438682.i | 2.09131i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 36019.8 | 0.170226 | ||||||||
\(461\) | − 238279.i | − 1.12120i | −0.828086 | − | 0.560601i | \(-0.810570\pi\) | ||||
0.828086 | − | 0.560601i | \(-0.189430\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 338112. | 1.57724 | 0.788621 | − | 0.614880i | \(-0.210796\pi\) | ||||
0.788621 | + | 0.614880i | \(0.210796\pi\) | |||||||
\(464\) | 182649.i | 0.848362i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 184420. | 0.849253 | ||||||||
\(467\) | − 122007.i | − 0.559435i | −0.960082 | − | 0.279718i | \(-0.909759\pi\) | ||||
0.960082 | − | 0.279718i | \(-0.0902408\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 123688. | 0.562316 | ||||||||
\(470\) | 250851.i | 1.13559i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −63869.1 | −0.286686 | ||||||||
\(473\) | 317.786i | 0.00142041i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27191.7 | 0.120517 | ||||||||
\(476\) | − 578955.i | − 2.55524i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −87948.8 | −0.384923 | ||||||||
\(479\) | − 29224.9i | − 0.127374i | −0.997970 | − | 0.0636872i | \(-0.979714\pi\) | ||||
0.997970 | − | 0.0636872i | \(-0.0202860\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −70340.6 | −0.304029 | ||||||||
\(482\) | 136956.i | 0.589505i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −521407. | −2.22580 | ||||||||
\(485\) | − 203607.i | − 0.865584i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38979.0 | −0.164351 | −0.0821756 | − | 0.996618i | \(-0.526187\pi\) | ||||
−0.0821756 | + | 0.996618i | \(0.526187\pi\) | |||||||
\(488\) | − 101327.i | − 0.425487i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −55315.8 | −0.230386 | ||||||||
\(491\) | 166060.i | 0.688813i | 0.938821 | + | 0.344407i | \(0.111920\pi\) | ||||
−0.938821 | + | 0.344407i | \(0.888080\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 153669. | 0.632256 | ||||||||
\(494\) | − 88632.5i | − 0.363195i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 210043. | 0.853778 | ||||||||
\(497\) | − 333088.i | − 1.34849i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −279840. | −1.12385 | −0.561925 | − | 0.827189i | \(-0.689939\pi\) | ||||
−0.561925 | + | 0.827189i | \(0.689939\pi\) | |||||||
\(500\) | 557882.i | 2.23153i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −377718. | −1.49886 | ||||||||
\(503\) | 130740.i | 0.516740i | 0.966046 | + | 0.258370i | \(0.0831854\pi\) | ||||
−0.966046 | + | 0.258370i | \(0.916815\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 119465. | 0.468442 | ||||||||
\(506\) | − 569.714i | − 0.00222513i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20229.1 | 0.0783878 | ||||||||
\(509\) | 133364.i | 0.514757i | 0.966311 | + | 0.257378i | \(0.0828587\pi\) | ||||
−0.966311 | + | 0.257378i | \(0.917141\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 294710. | 1.12863 | ||||||||
\(512\) | − 588546.i | − 2.24512i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −779296. | −2.94969 | ||||||||
\(515\) | − 135212.i | − 0.509800i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2737.75 | 0.0102427 | ||||||||
\(518\) | − 126601.i | − 0.471823i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 381171. | 1.40966 | ||||||||
\(521\) | 514542.i | 1.89560i | 0.318873 | + | 0.947798i | \(0.396696\pi\) | ||||
−0.318873 | + | 0.947798i | \(0.603304\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 223325. | 0.816460 | 0.408230 | − | 0.912879i | \(-0.366146\pi\) | ||||
0.408230 | + | 0.912879i | \(0.366146\pi\) | |||||||
\(524\) | − 455041.i | − 1.65725i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −118558. | −0.428507 | ||||||||
\(527\) | − 176717.i | − 0.636293i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 275597. | 0.984834 | ||||||||
\(530\) | − 98095.1i | − 0.349217i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 110075. | 0.388924 | ||||||||
\(533\) | − 324160.i | − 1.14105i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 62084.7 | 0.216909 | ||||||||
\(536\) | 399382.i | 1.39014i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 846185. | 2.92349 | ||||||||
\(539\) | 603.708i | 0.00207802i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −79784.0 | −0.272597 | −0.136299 | − | 0.990668i | \(-0.543521\pi\) | ||||
−0.136299 | + | 0.990668i | \(0.543521\pi\) | |||||||
\(542\) | 739794.i | 2.51833i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 344638. | 1.16457 | ||||||||
\(545\) | − 279124.i | − 0.939732i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 153107. | 0.511707 | 0.255853 | − | 0.966716i | \(-0.417644\pi\) | ||||
0.255853 | + | 0.966716i | \(0.417644\pi\) | |||||||
\(548\) | 564790.i | 1.88073i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3358.22 | 0.0111015 | ||||||||
\(551\) | 29216.6i | 0.0962336i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −55139.3 | −0.180306 | ||||||||
\(554\) | 589745.i | 1.92152i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −68468.7 | −0.221484 | ||||||||
\(557\) | − 255519.i | − 0.823593i | −0.911276 | − | 0.411797i | \(-0.864901\pi\) | ||||
0.911276 | − | 0.411797i | \(-0.135099\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45486.2 | 0.145565 | ||||||||
\(560\) | 299930.i | 0.956411i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −934660. | −2.95925 | ||||||||
\(563\) | − 47289.3i | − 0.149192i | −0.997214 | − | 0.0745961i | \(-0.976233\pi\) | ||||
0.997214 | − | 0.0745961i | \(-0.0237667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 70393.6 | 0.220514 | ||||||||
\(566\) | 891354.i | 2.78239i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.07553e6 | 3.33369 | ||||||||
\(569\) | 116940.i | 0.361192i | 0.983557 | + | 0.180596i | \(0.0578027\pi\) | ||||
−0.983557 | + | 0.180596i | \(0.942197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −79161.2 | −0.242795 | −0.121398 | − | 0.992604i | \(-0.538738\pi\) | ||||
−0.121398 | + | 0.992604i | \(0.538738\pi\) | |||||||
\(572\) | − 7553.16i | − 0.0230854i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 583435. | 1.77080 | ||||||||
\(575\) | − 25017.5i | − 0.0756673i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 326369. | 0.980295 | 0.490147 | − | 0.871640i | \(-0.336943\pi\) | ||||
0.490147 | + | 0.871640i | \(0.336943\pi\) | |||||||
\(578\) | − 396461.i | − 1.18671i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −228132. | −0.678158 | ||||||||
\(581\) | 107890.i | 0.319615i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1070.60 | −0.00314984 | ||||||||
\(584\) | 951605.i | 2.79017i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −356568. | −1.03836 | ||||||||
\(587\) | 139294.i | 0.404255i | 0.979359 | + | 0.202128i | \(0.0647856\pi\) | ||||
−0.979359 | + | 0.202128i | \(0.935214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33598.6 | 0.0968480 | ||||||||
\(590\) | − 50543.7i | − 0.145199i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 178718. | 0.509948 | ||||||||
\(593\) | 124472.i | 0.353967i | 0.984214 | + | 0.176983i | \(0.0566339\pi\) | ||||
−0.984214 | + | 0.176983i | \(0.943366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 252342. | 0.712781 | ||||||||
\(596\) | 319215.i | 0.898650i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −81545.8 | −0.228034 | ||||||||
\(599\) | − 589020.i | − 1.64163i | −0.571191 | − | 0.820817i | \(-0.693518\pi\) | ||||
0.571191 | − | 0.820817i | \(-0.306482\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −556200. | −1.53986 | −0.769931 | − | 0.638127i | \(-0.779710\pi\) | ||||
−0.769931 | + | 0.638127i | \(0.779710\pi\) | |||||||
\(602\) | 81867.5i | 0.225901i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −715080. | −1.96011 | ||||||||
\(605\) | − 227259.i | − 0.620885i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 105145. | 0.285372 | 0.142686 | − | 0.989768i | \(-0.454426\pi\) | ||||
0.142686 | + | 0.989768i | \(0.454426\pi\) | |||||||
\(608\) | 65524.8i | 0.177255i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 80186.6 | 0.215498 | ||||||||
\(611\) | − 391867.i | − 1.04968i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 221000. | 0.588128 | 0.294064 | − | 0.955786i | \(-0.404992\pi\) | ||||
0.294064 | + | 0.955786i | \(0.404992\pi\) | |||||||
\(614\) | 35032.4i | 0.0929252i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7487.39 | 0.0197319 | ||||||||
\(617\) | − 625197.i | − 1.64228i | −0.570728 | − | 0.821139i | \(-0.693339\pi\) | ||||
0.570728 | − | 0.821139i | \(-0.306661\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −573732. | −1.49736 | −0.748682 | − | 0.662929i | \(-0.769313\pi\) | ||||
−0.748682 | + | 0.662929i | \(0.769313\pi\) | |||||||
\(620\) | 262348.i | 0.682488i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 204296. | 0.528055 | ||||||||
\(623\) | 54351.6i | 0.140035i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3148.40 | −0.00805990 | ||||||||
\(626\) | 237342.i | 0.605656i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 963445. | 2.44291 | ||||||||
\(629\) | − 150362.i | − 0.380047i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −119692. | −0.300611 | −0.150306 | − | 0.988640i | \(-0.548026\pi\) | ||||
−0.150306 | + | 0.988640i | \(0.548026\pi\) | |||||||
\(632\) | − 178042.i | − 0.445748i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −431325. | −1.07307 | ||||||||
\(635\) | 8817.01i | 0.0218662i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 86411.5 | 0.212957 | ||||||||
\(638\) | 3608.30i | 0.00886465i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 278283. | 0.679401 | ||||||||
\(641\) | − 520671.i | − 1.26721i | −0.773658 | − | 0.633603i | \(-0.781575\pi\) | ||||
0.773658 | − | 0.633603i | \(-0.218425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −94998.2 | −0.229770 | −0.114885 | − | 0.993379i | \(-0.536650\pi\) | ||||
−0.114885 | + | 0.993379i | \(0.536650\pi\) | |||||||
\(644\) | − 101274.i | − 0.244188i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 189464. | 0.454006 | ||||||||
\(647\) | 161214.i | 0.385119i | 0.981285 | + | 0.192559i | \(0.0616788\pi\) | ||||
−0.981285 | + | 0.192559i | \(0.938321\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −551.627 | −0.00130965 | ||||||||
\(650\) | − 480677.i | − 1.13770i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.74940e6 | −4.11522 | ||||||||
\(653\) | − 446530.i | − 1.04719i | −0.851968 | − | 0.523594i | \(-0.824591\pi\) | ||||
0.851968 | − | 0.523594i | \(-0.175409\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 198333. | 0.462288 | ||||||||
\(656\) | 823613.i | 1.91388i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 705296. | 1.62899 | ||||||||
\(659\) | 177777.i | 0.409360i | 0.978829 | + | 0.204680i | \(0.0656154\pi\) | ||||
−0.978829 | + | 0.204680i | \(0.934385\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −417499. | −0.955548 | −0.477774 | − | 0.878483i | \(-0.658556\pi\) | ||||
−0.477774 | + | 0.878483i | \(0.658556\pi\) | |||||||
\(662\) | 1.32984e6i | 3.03448i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −348371. | −0.790144 | ||||||||
\(665\) | 47977.0i | 0.108490i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26880.5 | 0.0604208 | ||||||||
\(668\) | − 390851.i | − 0.875907i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −316057. | −0.704069 | ||||||||
\(671\) | − 875.145i | − 0.00194373i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 91589.8 | 0.202217 | 0.101108 | − | 0.994875i | \(-0.467761\pi\) | ||||
0.101108 | + | 0.994875i | \(0.467761\pi\) | |||||||
\(674\) | − 404365.i | − 0.890131i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −63878.2 | −0.139785 | ||||||||
\(677\) | − 424628.i | − 0.926469i | −0.886236 | − | 0.463235i | \(-0.846689\pi\) | ||||
0.886236 | − | 0.463235i | \(-0.153311\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −572464. | −1.24168 | ||||||||
\(680\) | 814803.i | 1.76212i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4149.49 | 0.00892125 | ||||||||
\(683\) | 91836.1i | 0.196867i | 0.995144 | + | 0.0984333i | \(0.0313831\pi\) | ||||
−0.995144 | + | 0.0984333i | \(0.968617\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −246168. | −0.524627 | ||||||||
\(686\) | 908425.i | 1.93037i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −115569. | −0.244155 | ||||||||
\(689\) | 153239.i | 0.322799i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −584417. | −1.22396 | −0.611979 | − | 0.790874i | \(-0.709626\pi\) | ||||
−0.611979 | + | 0.790874i | \(0.709626\pi\) | |||||||
\(692\) | 645106.i | 1.34716i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 527140. | 1.09448 | ||||||||
\(695\) | − 29842.6i | − 0.0617828i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 692936. | 1.42635 | ||||||||
\(698\) | 1.50153e6i | 3.08194i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 596964. | 1.21829 | ||||||||
\(701\) | 962035.i | 1.95774i | 0.204486 | + | 0.978869i | \(0.434448\pi\) | ||||
−0.204486 | + | 0.978869i | \(0.565552\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28587.9 | 0.0578457 | ||||||||
\(704\) | − 528.653i | − 0.00106666i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −294094. | −0.590034 | ||||||||
\(707\) | − 335888.i | − 0.671978i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 331501. | 0.659466 | 0.329733 | − | 0.944074i | \(-0.393041\pi\) | ||||
0.329733 | + | 0.944074i | \(0.393041\pi\) | |||||||
\(710\) | 851134.i | 1.68842i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −175499. | −0.346190 | ||||||||
\(713\) | − 30912.2i | − 0.0608066i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3292.11 | 0.00643964 | ||||||||
\(716\) | 913431.i | 1.78176i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.19786e6 | 2.32358 | ||||||||
\(719\) | 900767.i | 1.74243i | 0.490903 | + | 0.871214i | \(0.336667\pi\) | ||||
−0.490903 | + | 0.871214i | \(0.663333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −380162. | −0.731305 | ||||||||
\(722\) | − 900263.i | − 1.72701i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 250558. | 0.478005 | ||||||||
\(725\) | 158449.i | 0.301449i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −847695. | −1.60388 | −0.801938 | − | 0.597407i | \(-0.796198\pi\) | ||||
−0.801938 | + | 0.597407i | \(0.796198\pi\) | |||||||
\(728\) | − 1.07170e6i | − 2.02214i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −753066. | −1.41315 | ||||||||
\(731\) | 97232.7i | 0.181961i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 166042. | 0.309037 | 0.154518 | − | 0.987990i | \(-0.450617\pi\) | ||||
0.154518 | + | 0.987990i | \(0.450617\pi\) | |||||||
\(734\) | − 403996.i | − 0.749868i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 60285.7 | 0.111291 | ||||||||
\(737\) | 3449.40i | 0.00635050i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 724070. | 1.32584 | 0.662921 | − | 0.748690i | \(-0.269317\pi\) | ||||
0.662921 | + | 0.748690i | \(0.269317\pi\) | |||||||
\(740\) | 223223.i | 0.407639i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −275805. | −0.500951 | ||||||||
\(743\) | − 665006.i | − 1.20461i | −0.798265 | − | 0.602307i | \(-0.794248\pi\) | ||||
0.798265 | − | 0.602307i | \(-0.205752\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −139133. | −0.250678 | ||||||||
\(746\) | 351836.i | 0.632212i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16145.9 | 0.0288575 | ||||||||
\(749\) | − 174558.i | − 0.311155i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 380983. | 0.675501 | 0.337750 | − | 0.941236i | \(-0.390334\pi\) | ||||
0.337750 | + | 0.941236i | \(0.390334\pi\) | |||||||
\(752\) | 995640.i | 1.76062i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 516473. | 0.908458 | ||||||||
\(755\) | − 311674.i | − 0.546772i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −459466. | −0.801791 | −0.400896 | − | 0.916124i | \(-0.631301\pi\) | ||||
−0.400896 | + | 0.916124i | \(0.631301\pi\) | |||||||
\(758\) | − 276725.i | − 0.481626i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −154916. | −0.268206 | ||||||||
\(761\) | − 331477.i | − 0.572380i | −0.958173 | − | 0.286190i | \(-0.907611\pi\) | ||||
0.958173 | − | 0.286190i | \(-0.0923889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −784788. | −1.34804 | ||||||||
\(764\) | 144263.i | 0.247154i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.33348e6 | 2.27263 | ||||||||
\(767\) | 78956.8i | 0.134214i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 97668.8 | 0.165159 | 0.0825797 | − | 0.996584i | \(-0.473684\pi\) | ||||
0.0825797 | + | 0.996584i | \(0.473684\pi\) | |||||||
\(770\) | 5925.25i | 0.00999367i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 714998. | 1.19969 | ||||||||
\(773\) | − 915611.i | − 1.53233i | −0.642645 | − | 0.766164i | \(-0.722163\pi\) | ||||
0.642645 | − | 0.766164i | \(-0.277837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 182214. | 0.303374 | ||||||||
\(776\) | − 1.84846e6i | − 3.06964i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.08750e6 | −1.79668 | ||||||||
\(779\) | 131746.i | 0.217101i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9289.16 | 0.0152291 | ||||||||
\(782\) | − 174315.i | − 0.285050i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −219551. | −0.357193 | ||||||||
\(785\) | 419925.i | 0.681448i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −599735. | −0.968300 | −0.484150 | − | 0.874985i | \(-0.660871\pi\) | ||||
−0.484150 | + | 0.874985i | \(0.660871\pi\) | |||||||
\(788\) | − 1.35637e6i | − 2.18436i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 140896. | 0.225759 | ||||||||
\(791\) | − 197919.i | − 0.316326i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −125264. | −0.199195 | ||||||||
\(794\) | 50136.7i | 0.0795271i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −904781. | −1.42796 | ||||||||
\(797\) | 602942.i | 0.949203i | 0.880201 | + | 0.474601i | \(0.157408\pi\) | ||||
−0.880201 | + | 0.474601i | \(0.842592\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 837668. | 1.31213 | ||||||||
\(800\) | 355358.i | 0.555247i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.08171e6 | 1.68175 | ||||||||
\(803\) | 8218.86i | 0.0127462i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 44140.9 | 0.0681161 | ||||||||
\(806\) | − 593935.i | − 0.914258i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.08457e6 | 1.66125 | ||||||||
\(809\) | 862359.i | 1.31762i | 0.752308 | + | 0.658811i | \(0.228940\pi\) | ||||
−0.752308 | + | 0.658811i | \(0.771060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.04152e6 | −1.58352 | −0.791762 | − | 0.610829i | \(-0.790836\pi\) | ||||
−0.791762 | + | 0.610829i | \(0.790836\pi\) | |||||||
\(812\) | 641420.i | 0.972815i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3530.65 | 0.00532852 | ||||||||
\(815\) | − 762490.i | − 1.14794i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18486.5 | −0.0276956 | ||||||||
\(818\) | − 1.70082e6i | − 2.54186i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.02871e6 | −1.52991 | ||||||||
\(821\) | − 939216.i | − 1.39341i | −0.717358 | − | 0.696705i | \(-0.754649\pi\) | ||||
0.717358 | − | 0.696705i | \(-0.245351\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 415137. | 0.612903 | 0.306451 | − | 0.951886i | \(-0.400858\pi\) | ||||
0.306451 | + | 0.951886i | \(0.400858\pi\) | |||||||
\(824\) | − 1.22753e6i | − 1.80791i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −142109. | −0.208287 | ||||||||
\(827\) | − 108681.i | − 0.158907i | −0.996839 | − | 0.0794537i | \(-0.974682\pi\) | ||||
0.996839 | − | 0.0794537i | \(-0.0253176\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −289557. | −0.421332 | −0.210666 | − | 0.977558i | \(-0.567563\pi\) | ||||
−0.210666 | + | 0.977558i | \(0.567563\pi\) | |||||||
\(830\) | − 275688.i | − 0.400187i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −75668.5 | −0.109312 | ||||||||
\(833\) | 184716.i | 0.266204i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 170355. | 0.244334 | ||||||||
\(836\) | 3069.76i | 0.00439230i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.73951e6 | −2.47708 | ||||||||
\(839\) | − 314352.i | − 0.446573i | −0.974753 | − | 0.223287i | \(-0.928321\pi\) | ||||
0.974753 | − | 0.223287i | \(-0.0716786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 537032. | 0.759291 | ||||||||
\(842\) | 58773.2i | 0.0829001i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.61294e6 | 2.26430 | ||||||||
\(845\) | − 27841.8i | − 0.0389928i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −638965. | −0.890657 | ||||||||
\(848\) | − 389344.i | − 0.541429i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.02751e6 | 1.42216 | ||||||||
\(851\) | − 26302.1i | − 0.0363188i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −127995. | −0.175912 | −0.0879562 | − | 0.996124i | \(-0.528034\pi\) | ||||
−0.0879562 | + | 0.996124i | \(0.528034\pi\) | |||||||
\(854\) | − 225454.i | − 0.309130i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 563641. | 0.769228 | ||||||||
\(857\) | 756967.i | 1.03066i | 0.856992 | + | 0.515330i | \(0.172331\pi\) | ||||
−0.856992 | + | 0.515330i | \(0.827669\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 974149. | 1.32020 | 0.660099 | − | 0.751178i | \(-0.270514\pi\) | ||||
0.660099 | + | 0.751178i | \(0.270514\pi\) | |||||||
\(860\) | − 144349.i | − 0.195171i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.02821e6 | −2.72959 | ||||||||
\(863\) | − 641927.i | − 0.861914i | −0.902372 | − | 0.430957i | \(-0.858176\pi\) | ||||
0.902372 | − | 0.430957i | \(-0.141824\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −281175. | −0.375789 | ||||||||
\(866\) | − 1.11100e6i | − 1.48142i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 737622. | 0.979026 | ||||||||
\(869\) | − 1537.72i | − 0.00203628i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 493728. | 0.650805 | ||||||||
\(872\) | − 2.53405e6i | − 3.33259i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 33141.9 | 0.0433865 | ||||||||
\(875\) | 683665.i | 0.892950i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 239271. | 0.311093 | 0.155547 | − | 0.987829i | \(-0.450286\pi\) | ||||
0.155547 | + | 0.987829i | \(0.450286\pi\) | |||||||
\(878\) | 1.51324e6i | 1.96300i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8364.45 | −0.0108012 | ||||||||
\(881\) | 1.31329e6i | 1.69203i | 0.533159 | + | 0.846015i | \(0.321005\pi\) | ||||
−0.533159 | + | 0.846015i | \(0.678995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 775089. | 0.994100 | 0.497050 | − | 0.867722i | \(-0.334417\pi\) | ||||
0.497050 | + | 0.867722i | \(0.334417\pi\) | |||||||
\(884\) | − 2.31103e6i | − 2.95734i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.62231e6 | 2.06665 | ||||||||
\(887\) | − 542678.i | − 0.689755i | −0.938648 | − | 0.344878i | \(-0.887920\pi\) | ||||
0.938648 | − | 0.344878i | \(-0.112080\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24790.0 | 0.0313670 | ||||||||
\(890\) | − 138884.i | − 0.175336i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −303388. | −0.381301 | ||||||||
\(893\) | 159263.i | 0.199716i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −398126. | −0.497021 | ||||||||
\(896\) | − 782423.i | − 0.974598i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24263.9 | 0.0300890 | ||||||||
\(899\) | 195783.i | 0.242246i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −327569. | −0.403509 | ||||||||
\(902\) | 16270.8i | 0.0199984i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 639074. | 0.782013 | ||||||||
\(905\) | 109208.i | 0.133339i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.26966e6 | −1.54338 | −0.771691 | − | 0.635998i | \(-0.780589\pi\) | ||||
−0.771691 | + | 0.635998i | \(0.780589\pi\) | |||||||
\(908\) | − 3.00234e6i | − 3.64157i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 848107. | 1.02416 | ||||||||
\(911\) | − 223102.i | − 0.268823i | −0.990926 | − | 0.134412i | \(-0.957086\pi\) | ||||
0.990926 | − | 0.134412i | \(-0.0429145\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3008.82 | −0.00360957 | ||||||||
\(914\) | − 1.60777e6i | − 1.92456i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.17473e6 | −2.59188 | ||||||||
\(917\) | − 557636.i | − 0.663150i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −207173. | −0.245303 | −0.122652 | − | 0.992450i | \(-0.539140\pi\) | ||||
−0.122652 | + | 0.992450i | \(0.539140\pi\) | |||||||
\(920\) | 142529.i | 0.168395i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.71191e6 | 2.01381 | ||||||||
\(923\) | − 1.32960e6i | − 1.56069i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 155039. | 0.181200 | ||||||||
\(926\) | 2.42915e6i | 2.83290i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −381821. | −0.443368 | ||||||||
\(929\) | 307542.i | 0.356347i | 0.983999 | + | 0.178174i | \(0.0570188\pi\) | ||||
−0.983999 | + | 0.178174i | \(0.942981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35119.5 | −0.0405180 | ||||||||
\(932\) | 914250.i | 1.05253i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 876551. | 1.00481 | ||||||||
\(935\) | 7037.32i | 0.00804978i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.16285e6 | 1.32448 | 0.662238 | − | 0.749294i | \(-0.269607\pi\) | ||||
0.662238 | + | 0.749294i | \(0.269607\pi\) | |||||||
\(938\) | 888628.i | 1.00998i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.24358e6 | −1.40740 | ||||||||
\(941\) | 1.28513e6i | 1.45133i | 0.688047 | + | 0.725666i | \(0.258468\pi\) | ||||
−0.688047 | + | 0.725666i | \(0.741532\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 121212. | 0.136308 | ||||||||
\(944\) | − 200610.i | − 0.225117i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2283.12 | −0.00255121 | ||||||||
\(947\) | − 1.30996e6i | − 1.46069i | −0.683076 | − | 0.730347i | \(-0.739358\pi\) | ||||
0.683076 | − | 0.730347i | \(-0.260642\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.17640e6 | 1.30624 | ||||||||
\(950\) | 195357.i | 0.216462i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.29091e6 | 2.52775 | ||||||||
\(953\) | − 365773.i | − 0.402741i | −0.979515 | − | 0.201370i | \(-0.935461\pi\) | ||||
0.979515 | − | 0.201370i | \(-0.0645395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −62878.0 | −0.0689433 | ||||||||
\(956\) | − 435999.i | − 0.477057i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 209965. | 0.228779 | ||||||||
\(959\) | 692129.i | 0.752575i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −698374. | −0.756208 | ||||||||
\(962\) | − 505359.i | − 0.546071i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −678950. | −0.730606 | ||||||||
\(965\) | 311638.i | 0.334653i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.16976e6 | 1.25096 | 0.625478 | − | 0.780241i | \(-0.284904\pi\) | ||||
0.625478 | + | 0.780241i | \(0.284904\pi\) | |||||||
\(968\) | − 2.06319e6i | − 2.20186i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.46281e6 | 1.55469 | ||||||||
\(971\) | 1.72227e6i | 1.82668i | 0.407195 | + | 0.913341i | \(0.366507\pi\) | ||||
−0.407195 | + | 0.913341i | \(0.633493\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −83905.9 | −0.0886271 | ||||||||
\(974\) | − 280043.i | − 0.295193i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 318264. | 0.334109 | ||||||||
\(977\) | 630328.i | 0.660355i | 0.943919 | + | 0.330177i | \(0.107109\pi\) | ||||
−0.943919 | + | 0.330177i | \(0.892891\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1515.76 | −0.00158148 | ||||||||
\(980\) | − 274224.i | − 0.285531i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.19305e6 | −1.23719 | ||||||||
\(983\) | − 1.45145e6i | − 1.50209i | −0.660253 | − | 0.751043i | \(-0.729551\pi\) | ||||
0.660253 | − | 0.751043i | \(-0.270449\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 591183. | 0.609326 | ||||||||
\(986\) | 1.10403e6i | 1.13560i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 439389. | 0.450127 | ||||||||
\(989\) | 17008.4i | 0.0173889i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.85789e6 | 1.89179 | 0.945897 | − | 0.324467i | \(-0.105185\pi\) | ||||
0.945897 | + | 0.324467i | \(0.105185\pi\) | |||||||
\(992\) | 439088.i | 0.446199i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.39306e6 | 2.42204 | ||||||||
\(995\) | − 394357.i | − 0.398330i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.42325e6 | −1.43182 | −0.715912 | − | 0.698191i | \(-0.753989\pi\) | ||||
−0.715912 | + | 0.698191i | \(0.753989\pi\) | |||||||
\(998\) | − 2.01049e6i | − 2.01856i | ||||||||
\(999\) | 0 | 0 |
(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 | 531.5.b.a.296.72 | yes | 76 | |
3.2 | odd | 2 | inner | 531.5.b.a.296.5 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
531.5.b.a.296.5 | ✓ | 76 | 3.2 | odd | 2 | inner | |
531.5.b.a.296.72 | yes | 76 | 1.1 | even | 1 | trivial |