Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1477718538\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.6809.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.06963\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.06963 | −0.925566 | −0.462783 | − | 0.886472i | \(-0.653149\pi\) | ||||
−0.462783 | + | 0.886472i | \(0.653149\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.35299 | −1.64527 | −0.822637 | − | 0.568566i | \(-0.807498\pi\) | ||||
−0.822637 | + | 0.568566i | \(0.807498\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.06963 | 0.654474 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.682998 | −0.189429 | −0.0947147 | − | 0.995504i | \(-0.530194\pi\) | ||||
−0.0947147 | + | 0.995504i | \(0.530194\pi\) | |||||||
\(14\) | 4.35299 | 1.16338 | ||||||||
\(15\) | 2.06963 | 0.534376 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.26945 | −0.307886 | −0.153943 | − | 0.988080i | \(-0.549197\pi\) | ||||
−0.153943 | + | 0.988080i | \(0.549197\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0.110461 | 0.0253415 | 0.0126708 | − | 0.999920i | \(-0.495967\pi\) | ||||
0.0126708 | + | 0.999920i | \(0.495967\pi\) | |||||||
\(20\) | −2.06963 | −0.462783 | ||||||||
\(21\) | 4.35299 | 0.949900 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 4.31700 | 0.900157 | 0.450079 | − | 0.892989i | \(-0.351396\pi\) | ||||
0.450079 | + | 0.892989i | \(0.351396\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −0.716640 | −0.143328 | ||||||||
\(26\) | 0.682998 | 0.133947 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.35299 | −0.822637 | ||||||||
\(29\) | −4.08354 | −0.758295 | −0.379147 | − | 0.925336i | \(-0.623783\pi\) | ||||
−0.379147 | + | 0.925336i | \(0.623783\pi\) | |||||||
\(30\) | −2.06963 | −0.377861 | ||||||||
\(31\) | −6.92552 | −1.24386 | −0.621930 | − | 0.783073i | \(-0.713651\pi\) | ||||
−0.621930 | + | 0.783073i | \(0.713651\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 1.26945 | 0.217708 | ||||||||
\(35\) | 9.00906 | 1.52281 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.85008 | −1.29055 | −0.645273 | − | 0.763952i | \(-0.723256\pi\) | ||||
−0.645273 | + | 0.763952i | \(0.723256\pi\) | |||||||
\(38\) | −0.110461 | −0.0179192 | ||||||||
\(39\) | 0.682998 | 0.109367 | ||||||||
\(40\) | 2.06963 | 0.327237 | ||||||||
\(41\) | −7.84523 | −1.22522 | −0.612610 | − | 0.790386i | \(-0.709880\pi\) | ||||
−0.612610 | + | 0.790386i | \(0.709880\pi\) | |||||||
\(42\) | −4.35299 | −0.671681 | ||||||||
\(43\) | −2.86309 | −0.436617 | −0.218308 | − | 0.975880i | \(-0.570054\pi\) | ||||
−0.218308 | + | 0.975880i | \(0.570054\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −2.06963 | −0.308522 | ||||||||
\(46\) | −4.31700 | −0.636507 | ||||||||
\(47\) | −10.5062 | −1.53248 | −0.766240 | − | 0.642554i | \(-0.777875\pi\) | ||||
−0.766240 | + | 0.642554i | \(0.777875\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 11.9485 | 1.70693 | ||||||||
\(50\) | 0.716640 | 0.101348 | ||||||||
\(51\) | 1.26945 | 0.177758 | ||||||||
\(52\) | −0.682998 | −0.0947147 | ||||||||
\(53\) | −7.98214 | −1.09643 | −0.548216 | − | 0.836337i | \(-0.684693\pi\) | ||||
−0.548216 | + | 0.836337i | \(0.684693\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 2.06963 | 0.279069 | ||||||||
\(56\) | 4.35299 | 0.581692 | ||||||||
\(57\) | −0.110461 | −0.0146309 | ||||||||
\(58\) | 4.08354 | 0.536195 | ||||||||
\(59\) | −7.49224 | −0.975407 | −0.487704 | − | 0.873009i | \(-0.662165\pi\) | ||||
−0.487704 | + | 0.873009i | \(0.662165\pi\) | |||||||
\(60\) | 2.06963 | 0.267188 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 6.92552 | 0.879542 | ||||||||
\(63\) | −4.35299 | −0.548425 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.41355 | 0.175329 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −12.9346 | −1.58021 | −0.790106 | − | 0.612971i | \(-0.789974\pi\) | ||||
−0.790106 | + | 0.612971i | \(0.789974\pi\) | |||||||
\(68\) | −1.26945 | −0.153943 | ||||||||
\(69\) | −4.31700 | −0.519706 | ||||||||
\(70\) | −9.00906 | −1.07679 | ||||||||
\(71\) | 9.82898 | 1.16648 | 0.583242 | − | 0.812298i | \(-0.301784\pi\) | ||||
0.583242 | + | 0.812298i | \(0.301784\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −14.1599 | −1.65729 | −0.828645 | − | 0.559775i | \(-0.810888\pi\) | ||||
−0.828645 | + | 0.559775i | \(0.810888\pi\) | |||||||
\(74\) | 7.85008 | 0.912553 | ||||||||
\(75\) | 0.716640 | 0.0827505 | ||||||||
\(76\) | 0.110461 | 0.0126708 | ||||||||
\(77\) | 4.35299 | 0.496069 | ||||||||
\(78\) | −0.682998 | −0.0773342 | ||||||||
\(79\) | −1.79299 | −0.201727 | −0.100864 | − | 0.994900i | \(-0.532161\pi\) | ||||
−0.100864 | + | 0.994900i | \(0.532161\pi\) | |||||||
\(80\) | −2.06963 | −0.231391 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.84523 | 0.866361 | ||||||||
\(83\) | 10.9592 | 1.20292 | 0.601462 | − | 0.798901i | \(-0.294585\pi\) | ||||
0.601462 | + | 0.798901i | \(0.294585\pi\) | |||||||
\(84\) | 4.35299 | 0.474950 | ||||||||
\(85\) | 2.62728 | 0.284969 | ||||||||
\(86\) | 2.86309 | 0.308735 | ||||||||
\(87\) | 4.08354 | 0.437802 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −1.93037 | −0.204619 | −0.102310 | − | 0.994753i | \(-0.532623\pi\) | ||||
−0.102310 | + | 0.994753i | \(0.532623\pi\) | |||||||
\(90\) | 2.06963 | 0.218158 | ||||||||
\(91\) | 2.97308 | 0.311663 | ||||||||
\(92\) | 4.31700 | 0.450079 | ||||||||
\(93\) | 6.92552 | 0.718143 | ||||||||
\(94\) | 10.5062 | 1.08363 | ||||||||
\(95\) | −0.228614 | −0.0234553 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 11.4250 | 1.16003 | 0.580014 | − | 0.814606i | \(-0.303047\pi\) | ||||
0.580014 | + | 0.814606i | \(0.303047\pi\) | |||||||
\(98\) | −11.9485 | −1.20698 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −0.716640 | −0.0716640 | ||||||||
\(101\) | 10.2233 | 1.01725 | 0.508626 | − | 0.860987i | \(-0.330153\pi\) | ||||
0.508626 | + | 0.860987i | \(0.330153\pi\) | |||||||
\(102\) | −1.26945 | −0.125694 | ||||||||
\(103\) | −14.9778 | −1.47580 | −0.737902 | − | 0.674908i | \(-0.764183\pi\) | ||||
−0.737902 | + | 0.674908i | \(0.764183\pi\) | |||||||
\(104\) | 0.682998 | 0.0669734 | ||||||||
\(105\) | −9.00906 | −0.879195 | ||||||||
\(106\) | 7.98214 | 0.775294 | ||||||||
\(107\) | 11.9413 | 1.15441 | 0.577205 | − | 0.816599i | \(-0.304143\pi\) | ||||
0.577205 | + | 0.816599i | \(0.304143\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −15.4609 | −1.48089 | −0.740445 | − | 0.672117i | \(-0.765385\pi\) | ||||
−0.740445 | + | 0.672117i | \(0.765385\pi\) | |||||||
\(110\) | −2.06963 | −0.197331 | ||||||||
\(111\) | 7.85008 | 0.745097 | ||||||||
\(112\) | −4.35299 | −0.411319 | ||||||||
\(113\) | −7.82944 | −0.736532 | −0.368266 | − | 0.929720i | \(-0.620048\pi\) | ||||
−0.368266 | + | 0.929720i | \(0.620048\pi\) | |||||||
\(114\) | 0.110461 | 0.0103456 | ||||||||
\(115\) | −8.93459 | −0.833155 | ||||||||
\(116\) | −4.08354 | −0.379147 | ||||||||
\(117\) | −0.682998 | −0.0631431 | ||||||||
\(118\) | 7.49224 | 0.689717 | ||||||||
\(119\) | 5.52589 | 0.506557 | ||||||||
\(120\) | −2.06963 | −0.188930 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | 7.84523 | 0.707381 | ||||||||
\(124\) | −6.92552 | −0.621930 | ||||||||
\(125\) | 11.8313 | 1.05823 | ||||||||
\(126\) | 4.35299 | 0.387795 | ||||||||
\(127\) | −0.0427077 | −0.00378969 | −0.00189485 | − | 0.999998i | \(-0.500603\pi\) | ||||
−0.00189485 | + | 0.999998i | \(0.500603\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.86309 | 0.252081 | ||||||||
\(130\) | −1.41355 | −0.123977 | ||||||||
\(131\) | 18.6791 | 1.63200 | 0.815998 | − | 0.578054i | \(-0.196188\pi\) | ||||
0.815998 | + | 0.578054i | \(0.196188\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −0.480836 | −0.0416938 | ||||||||
\(134\) | 12.9346 | 1.11738 | ||||||||
\(135\) | 2.06963 | 0.178125 | ||||||||
\(136\) | 1.26945 | 0.108854 | ||||||||
\(137\) | 13.4365 | 1.14796 | 0.573980 | − | 0.818869i | \(-0.305399\pi\) | ||||
0.573980 | + | 0.818869i | \(0.305399\pi\) | |||||||
\(138\) | 4.31700 | 0.367488 | ||||||||
\(139\) | 17.9952 | 1.52633 | 0.763164 | − | 0.646204i | \(-0.223645\pi\) | ||||
0.763164 | + | 0.646204i | \(0.223645\pi\) | |||||||
\(140\) | 9.00906 | 0.761405 | ||||||||
\(141\) | 10.5062 | 0.884778 | ||||||||
\(142\) | −9.82898 | −0.824829 | ||||||||
\(143\) | 0.682998 | 0.0571151 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.45141 | 0.701851 | ||||||||
\(146\) | 14.1599 | 1.17188 | ||||||||
\(147\) | −11.9485 | −0.985496 | ||||||||
\(148\) | −7.85008 | −0.645273 | ||||||||
\(149\) | −10.2098 | −0.836419 | −0.418209 | − | 0.908351i | \(-0.637342\pi\) | ||||
−0.418209 | + | 0.908351i | \(0.637342\pi\) | |||||||
\(150\) | −0.716640 | −0.0585134 | ||||||||
\(151\) | 20.2294 | 1.64624 | 0.823121 | − | 0.567866i | \(-0.192231\pi\) | ||||
0.823121 | + | 0.567866i | \(0.192231\pi\) | |||||||
\(152\) | −0.110461 | −0.00895958 | ||||||||
\(153\) | −1.26945 | −0.102629 | ||||||||
\(154\) | −4.35299 | −0.350774 | ||||||||
\(155\) | 14.3333 | 1.15127 | ||||||||
\(156\) | 0.682998 | 0.0546836 | ||||||||
\(157\) | 0.568594 | 0.0453787 | 0.0226894 | − | 0.999743i | \(-0.492777\pi\) | ||||
0.0226894 | + | 0.999743i | \(0.492777\pi\) | |||||||
\(158\) | 1.79299 | 0.142643 | ||||||||
\(159\) | 7.98214 | 0.633025 | ||||||||
\(160\) | 2.06963 | 0.163618 | ||||||||
\(161\) | −18.7919 | −1.48101 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −21.5071 | −1.68457 | −0.842284 | − | 0.539034i | \(-0.818789\pi\) | ||||
−0.842284 | + | 0.539034i | \(0.818789\pi\) | |||||||
\(164\) | −7.84523 | −0.612610 | ||||||||
\(165\) | −2.06963 | −0.161120 | ||||||||
\(166\) | −10.9592 | −0.850596 | ||||||||
\(167\) | −3.49709 | −0.270613 | −0.135307 | − | 0.990804i | \(-0.543202\pi\) | ||||
−0.135307 | + | 0.990804i | \(0.543202\pi\) | |||||||
\(168\) | −4.35299 | −0.335840 | ||||||||
\(169\) | −12.5335 | −0.964116 | ||||||||
\(170\) | −2.62728 | −0.201503 | ||||||||
\(171\) | 0.110461 | 0.00844718 | ||||||||
\(172\) | −2.86309 | −0.218308 | ||||||||
\(173\) | 23.2026 | 1.76406 | 0.882030 | − | 0.471192i | \(-0.156176\pi\) | ||||
0.882030 | + | 0.471192i | \(0.156176\pi\) | |||||||
\(174\) | −4.08354 | −0.309572 | ||||||||
\(175\) | 3.11953 | 0.235814 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 7.49224 | 0.563152 | ||||||||
\(178\) | 1.93037 | 0.144688 | ||||||||
\(179\) | −10.7522 | −0.803654 | −0.401827 | − | 0.915716i | \(-0.631625\pi\) | ||||
−0.401827 | + | 0.915716i | \(0.631625\pi\) | |||||||
\(180\) | −2.06963 | −0.154261 | ||||||||
\(181\) | −9.37831 | −0.697084 | −0.348542 | − | 0.937293i | \(-0.613323\pi\) | ||||
−0.348542 | + | 0.937293i | \(0.613323\pi\) | |||||||
\(182\) | −2.97308 | −0.220379 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −4.31700 | −0.318254 | ||||||||
\(185\) | 16.2467 | 1.19448 | ||||||||
\(186\) | −6.92552 | −0.507804 | ||||||||
\(187\) | 1.26945 | 0.0928311 | ||||||||
\(188\) | −10.5062 | −0.766240 | ||||||||
\(189\) | 4.35299 | 0.316633 | ||||||||
\(190\) | 0.228614 | 0.0165854 | ||||||||
\(191\) | 13.3539 | 0.966254 | 0.483127 | − | 0.875550i | \(-0.339501\pi\) | ||||
0.483127 | + | 0.875550i | \(0.339501\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 6.59317 | 0.474587 | 0.237293 | − | 0.971438i | \(-0.423740\pi\) | ||||
0.237293 | + | 0.971438i | \(0.423740\pi\) | |||||||
\(194\) | −11.4250 | −0.820264 | ||||||||
\(195\) | −1.41355 | −0.101226 | ||||||||
\(196\) | 11.9485 | 0.853464 | ||||||||
\(197\) | −23.0051 | −1.63905 | −0.819524 | − | 0.573045i | \(-0.805762\pi\) | ||||
−0.819524 | + | 0.573045i | \(0.805762\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −13.5790 | −0.962592 | −0.481296 | − | 0.876558i | \(-0.659834\pi\) | ||||
−0.481296 | + | 0.876558i | \(0.659834\pi\) | |||||||
\(200\) | 0.716640 | 0.0506741 | ||||||||
\(201\) | 12.9346 | 0.912336 | ||||||||
\(202\) | −10.2233 | −0.719306 | ||||||||
\(203\) | 17.7756 | 1.24760 | ||||||||
\(204\) | 1.26945 | 0.0888791 | ||||||||
\(205\) | 16.2367 | 1.13402 | ||||||||
\(206\) | 14.9778 | 1.04355 | ||||||||
\(207\) | 4.31700 | 0.300052 | ||||||||
\(208\) | −0.682998 | −0.0473574 | ||||||||
\(209\) | −0.110461 | −0.00764076 | ||||||||
\(210\) | 9.00906 | 0.621685 | ||||||||
\(211\) | 11.9974 | 0.825937 | 0.412969 | − | 0.910745i | \(-0.364492\pi\) | ||||
0.412969 | + | 0.910745i | \(0.364492\pi\) | |||||||
\(212\) | −7.98214 | −0.548216 | ||||||||
\(213\) | −9.82898 | −0.673470 | ||||||||
\(214\) | −11.9413 | −0.816291 | ||||||||
\(215\) | 5.92552 | 0.404117 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 30.1467 | 2.04649 | ||||||||
\(218\) | 15.4609 | 1.04715 | ||||||||
\(219\) | 14.1599 | 0.956837 | ||||||||
\(220\) | 2.06963 | 0.139534 | ||||||||
\(221\) | 0.867029 | 0.0583227 | ||||||||
\(222\) | −7.85008 | −0.526863 | ||||||||
\(223\) | −8.83707 | −0.591774 | −0.295887 | − | 0.955223i | \(-0.595615\pi\) | ||||
−0.295887 | + | 0.955223i | \(0.595615\pi\) | |||||||
\(224\) | 4.35299 | 0.290846 | ||||||||
\(225\) | −0.716640 | −0.0477760 | ||||||||
\(226\) | 7.82944 | 0.520807 | ||||||||
\(227\) | 26.6459 | 1.76855 | 0.884275 | − | 0.466967i | \(-0.154653\pi\) | ||||
0.884275 | + | 0.466967i | \(0.154653\pi\) | |||||||
\(228\) | −0.110461 | −0.00731547 | ||||||||
\(229\) | 0.702259 | 0.0464066 | 0.0232033 | − | 0.999731i | \(-0.492613\pi\) | ||||
0.0232033 | + | 0.999731i | \(0.492613\pi\) | |||||||
\(230\) | 8.93459 | 0.589129 | ||||||||
\(231\) | −4.35299 | −0.286406 | ||||||||
\(232\) | 4.08354 | 0.268098 | ||||||||
\(233\) | −21.3697 | −1.39998 | −0.699989 | − | 0.714153i | \(-0.746812\pi\) | ||||
−0.699989 | + | 0.714153i | \(0.746812\pi\) | |||||||
\(234\) | 0.682998 | 0.0446489 | ||||||||
\(235\) | 21.7438 | 1.41841 | ||||||||
\(236\) | −7.49224 | −0.487704 | ||||||||
\(237\) | 1.79299 | 0.116467 | ||||||||
\(238\) | −5.52589 | −0.358190 | ||||||||
\(239\) | −6.78467 | −0.438864 | −0.219432 | − | 0.975628i | \(-0.570420\pi\) | ||||
−0.219432 | + | 0.975628i | \(0.570420\pi\) | |||||||
\(240\) | 2.06963 | 0.133594 | ||||||||
\(241\) | 2.23534 | 0.143991 | 0.0719953 | − | 0.997405i | \(-0.477063\pi\) | ||||
0.0719953 | + | 0.997405i | \(0.477063\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | −24.7290 | −1.57987 | ||||||||
\(246\) | −7.84523 | −0.500194 | ||||||||
\(247\) | −0.0754447 | −0.00480043 | ||||||||
\(248\) | 6.92552 | 0.439771 | ||||||||
\(249\) | −10.9592 | −0.694509 | ||||||||
\(250\) | −11.8313 | −0.748278 | ||||||||
\(251\) | 12.8290 | 0.809758 | 0.404879 | − | 0.914370i | \(-0.367314\pi\) | ||||
0.404879 | + | 0.914370i | \(0.367314\pi\) | |||||||
\(252\) | −4.35299 | −0.274212 | ||||||||
\(253\) | −4.31700 | −0.271408 | ||||||||
\(254\) | 0.0427077 | 0.00267972 | ||||||||
\(255\) | −2.62728 | −0.164527 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.4533 | −1.02633 | −0.513164 | − | 0.858291i | \(-0.671527\pi\) | ||||
−0.513164 | + | 0.858291i | \(0.671527\pi\) | |||||||
\(258\) | −2.86309 | −0.178248 | ||||||||
\(259\) | 34.1713 | 2.12330 | ||||||||
\(260\) | 1.41355 | 0.0876647 | ||||||||
\(261\) | −4.08354 | −0.252765 | ||||||||
\(262\) | −18.6791 | −1.15400 | ||||||||
\(263\) | −3.91114 | −0.241171 | −0.120586 | − | 0.992703i | \(-0.538477\pi\) | ||||
−0.120586 | + | 0.992703i | \(0.538477\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 16.5201 | 1.01482 | ||||||||
\(266\) | 0.480836 | 0.0294820 | ||||||||
\(267\) | 1.93037 | 0.118137 | ||||||||
\(268\) | −12.9346 | −0.790106 | ||||||||
\(269\) | −0.0336427 | −0.00205123 | −0.00102562 | − | 0.999999i | \(-0.500326\pi\) | ||||
−0.00102562 | + | 0.999999i | \(0.500326\pi\) | |||||||
\(270\) | −2.06963 | −0.125954 | ||||||||
\(271\) | 10.6071 | 0.644338 | 0.322169 | − | 0.946682i | \(-0.395588\pi\) | ||||
0.322169 | + | 0.946682i | \(0.395588\pi\) | |||||||
\(272\) | −1.26945 | −0.0769715 | ||||||||
\(273\) | −2.97308 | −0.179939 | ||||||||
\(274\) | −13.4365 | −0.811730 | ||||||||
\(275\) | 0.716640 | 0.0432150 | ||||||||
\(276\) | −4.31700 | −0.259853 | ||||||||
\(277\) | −18.6526 | −1.12073 | −0.560363 | − | 0.828247i | \(-0.689338\pi\) | ||||
−0.560363 | + | 0.828247i | \(0.689338\pi\) | |||||||
\(278\) | −17.9952 | −1.07928 | ||||||||
\(279\) | −6.92552 | −0.414620 | ||||||||
\(280\) | −9.00906 | −0.538395 | ||||||||
\(281\) | 1.56160 | 0.0931571 | 0.0465785 | − | 0.998915i | \(-0.485168\pi\) | ||||
0.0465785 | + | 0.998915i | \(0.485168\pi\) | |||||||
\(282\) | −10.5062 | −0.625633 | ||||||||
\(283\) | 4.83058 | 0.287148 | 0.143574 | − | 0.989640i | \(-0.454141\pi\) | ||||
0.143574 | + | 0.989640i | \(0.454141\pi\) | |||||||
\(284\) | 9.82898 | 0.583242 | ||||||||
\(285\) | 0.228614 | 0.0135419 | ||||||||
\(286\) | −0.682998 | −0.0403865 | ||||||||
\(287\) | 34.1502 | 2.01582 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.3885 | −0.905206 | ||||||||
\(290\) | −8.45141 | −0.496284 | ||||||||
\(291\) | −11.4250 | −0.669743 | ||||||||
\(292\) | −14.1599 | −0.828645 | ||||||||
\(293\) | 30.3558 | 1.77340 | 0.886701 | − | 0.462342i | \(-0.152991\pi\) | ||||
0.886701 | + | 0.462342i | \(0.152991\pi\) | |||||||
\(294\) | 11.9485 | 0.696851 | ||||||||
\(295\) | 15.5062 | 0.902803 | ||||||||
\(296\) | 7.85008 | 0.456277 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 10.2098 | 0.591437 | ||||||||
\(299\) | −2.94850 | −0.170516 | ||||||||
\(300\) | 0.716640 | 0.0413752 | ||||||||
\(301\) | 12.4630 | 0.718354 | ||||||||
\(302\) | −20.2294 | −1.16407 | ||||||||
\(303\) | −10.2233 | −0.587311 | ||||||||
\(304\) | 0.110461 | 0.00633538 | ||||||||
\(305\) | −2.06963 | −0.118507 | ||||||||
\(306\) | 1.26945 | 0.0725694 | ||||||||
\(307\) | −25.7561 | −1.46998 | −0.734991 | − | 0.678077i | \(-0.762813\pi\) | ||||
−0.734991 | + | 0.678077i | \(0.762813\pi\) | |||||||
\(308\) | 4.35299 | 0.248034 | ||||||||
\(309\) | 14.9778 | 0.852055 | ||||||||
\(310\) | −14.3333 | −0.814074 | ||||||||
\(311\) | 1.94338 | 0.110199 | 0.0550995 | − | 0.998481i | \(-0.482452\pi\) | ||||
0.0550995 | + | 0.998481i | \(0.482452\pi\) | |||||||
\(312\) | −0.682998 | −0.0386671 | ||||||||
\(313\) | 15.6473 | 0.884437 | 0.442218 | − | 0.896907i | \(-0.354192\pi\) | ||||
0.442218 | + | 0.896907i | \(0.354192\pi\) | |||||||
\(314\) | −0.568594 | −0.0320876 | ||||||||
\(315\) | 9.00906 | 0.507603 | ||||||||
\(316\) | −1.79299 | −0.100864 | ||||||||
\(317\) | −23.9518 | −1.34526 | −0.672632 | − | 0.739977i | \(-0.734836\pi\) | ||||
−0.672632 | + | 0.739977i | \(0.734836\pi\) | |||||||
\(318\) | −7.98214 | −0.447616 | ||||||||
\(319\) | 4.08354 | 0.228634 | ||||||||
\(320\) | −2.06963 | −0.115696 | ||||||||
\(321\) | −11.9413 | −0.666499 | ||||||||
\(322\) | 18.7919 | 1.04723 | ||||||||
\(323\) | −0.140225 | −0.00780231 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.489463 | 0.0271505 | ||||||||
\(326\) | 21.5071 | 1.19117 | ||||||||
\(327\) | 15.4609 | 0.854992 | ||||||||
\(328\) | 7.84523 | 0.433180 | ||||||||
\(329\) | 45.7332 | 2.52135 | ||||||||
\(330\) | 2.06963 | 0.113929 | ||||||||
\(331\) | 16.2564 | 0.893535 | 0.446767 | − | 0.894650i | \(-0.352575\pi\) | ||||
0.446767 | + | 0.894650i | \(0.352575\pi\) | |||||||
\(332\) | 10.9592 | 0.601462 | ||||||||
\(333\) | −7.85008 | −0.430182 | ||||||||
\(334\) | 3.49709 | 0.191352 | ||||||||
\(335\) | 26.7698 | 1.46259 | ||||||||
\(336\) | 4.35299 | 0.237475 | ||||||||
\(337\) | −8.57110 | −0.466898 | −0.233449 | − | 0.972369i | \(-0.575001\pi\) | ||||
−0.233449 | + | 0.972369i | \(0.575001\pi\) | |||||||
\(338\) | 12.5335 | 0.681733 | ||||||||
\(339\) | 7.82944 | 0.425237 | ||||||||
\(340\) | 2.62728 | 0.142484 | ||||||||
\(341\) | 6.92552 | 0.375038 | ||||||||
\(342\) | −0.110461 | −0.00597306 | ||||||||
\(343\) | −21.5408 | −1.16309 | ||||||||
\(344\) | 2.86309 | 0.154367 | ||||||||
\(345\) | 8.93459 | 0.481022 | ||||||||
\(346\) | −23.2026 | −1.24738 | ||||||||
\(347\) | 17.2704 | 0.927121 | 0.463561 | − | 0.886065i | \(-0.346572\pi\) | ||||
0.463561 | + | 0.886065i | \(0.346572\pi\) | |||||||
\(348\) | 4.08354 | 0.218901 | ||||||||
\(349\) | −29.1284 | −1.55921 | −0.779604 | − | 0.626272i | \(-0.784580\pi\) | ||||
−0.779604 | + | 0.626272i | \(0.784580\pi\) | |||||||
\(350\) | −3.11953 | −0.166746 | ||||||||
\(351\) | 0.682998 | 0.0364557 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 2.84476 | 0.151411 | 0.0757057 | − | 0.997130i | \(-0.475879\pi\) | ||||
0.0757057 | + | 0.997130i | \(0.475879\pi\) | |||||||
\(354\) | −7.49224 | −0.398208 | ||||||||
\(355\) | −20.3423 | −1.07966 | ||||||||
\(356\) | −1.93037 | −0.102310 | ||||||||
\(357\) | −5.52589 | −0.292461 | ||||||||
\(358\) | 10.7522 | 0.568269 | ||||||||
\(359\) | −28.7346 | −1.51655 | −0.758277 | − | 0.651932i | \(-0.773959\pi\) | ||||
−0.758277 | + | 0.651932i | \(0.773959\pi\) | |||||||
\(360\) | 2.06963 | 0.109079 | ||||||||
\(361\) | −18.9878 | −0.999358 | ||||||||
\(362\) | 9.37831 | 0.492913 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 2.97308 | 0.155832 | ||||||||
\(365\) | 29.3057 | 1.53393 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | −19.0137 | −0.992510 | −0.496255 | − | 0.868177i | \(-0.665292\pi\) | ||||
−0.496255 | + | 0.868177i | \(0.665292\pi\) | |||||||
\(368\) | 4.31700 | 0.225039 | ||||||||
\(369\) | −7.84523 | −0.408406 | ||||||||
\(370\) | −16.2467 | −0.844628 | ||||||||
\(371\) | 34.7462 | 1.80393 | ||||||||
\(372\) | 6.92552 | 0.359072 | ||||||||
\(373\) | −15.9432 | −0.825505 | −0.412753 | − | 0.910843i | \(-0.635433\pi\) | ||||
−0.412753 | + | 0.910843i | \(0.635433\pi\) | |||||||
\(374\) | −1.26945 | −0.0656415 | ||||||||
\(375\) | −11.8313 | −0.610967 | ||||||||
\(376\) | 10.5062 | 0.541814 | ||||||||
\(377\) | 2.78905 | 0.143643 | ||||||||
\(378\) | −4.35299 | −0.223894 | ||||||||
\(379\) | 0.698347 | 0.0358717 | 0.0179358 | − | 0.999839i | \(-0.494291\pi\) | ||||
0.0179358 | + | 0.999839i | \(0.494291\pi\) | |||||||
\(380\) | −0.228614 | −0.0117276 | ||||||||
\(381\) | 0.0427077 | 0.00218798 | ||||||||
\(382\) | −13.3539 | −0.683245 | ||||||||
\(383\) | 18.1588 | 0.927872 | 0.463936 | − | 0.885869i | \(-0.346437\pi\) | ||||
0.463936 | + | 0.885869i | \(0.346437\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −9.00906 | −0.459144 | ||||||||
\(386\) | −6.59317 | −0.335584 | ||||||||
\(387\) | −2.86309 | −0.145539 | ||||||||
\(388\) | 11.4250 | 0.580014 | ||||||||
\(389\) | −4.93409 | −0.250168 | −0.125084 | − | 0.992146i | \(-0.539920\pi\) | ||||
−0.125084 | + | 0.992146i | \(0.539920\pi\) | |||||||
\(390\) | 1.41355 | 0.0715779 | ||||||||
\(391\) | −5.48020 | −0.277146 | ||||||||
\(392\) | −11.9485 | −0.603490 | ||||||||
\(393\) | −18.6791 | −0.942234 | ||||||||
\(394\) | 23.0051 | 1.15898 | ||||||||
\(395\) | 3.71082 | 0.186712 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 32.0590 | 1.60899 | 0.804497 | − | 0.593957i | \(-0.202435\pi\) | ||||
0.804497 | + | 0.593957i | \(0.202435\pi\) | |||||||
\(398\) | 13.5790 | 0.680655 | ||||||||
\(399\) | 0.480836 | 0.0240719 | ||||||||
\(400\) | −0.716640 | −0.0358320 | ||||||||
\(401\) | 30.7476 | 1.53546 | 0.767730 | − | 0.640774i | \(-0.221386\pi\) | ||||
0.767730 | + | 0.640774i | \(0.221386\pi\) | |||||||
\(402\) | −12.9346 | −0.645119 | ||||||||
\(403\) | 4.73012 | 0.235624 | ||||||||
\(404\) | 10.2233 | 0.508626 | ||||||||
\(405\) | −2.06963 | −0.102841 | ||||||||
\(406\) | −17.7756 | −0.882188 | ||||||||
\(407\) | 7.85008 | 0.389114 | ||||||||
\(408\) | −1.26945 | −0.0628470 | ||||||||
\(409\) | 8.61224 | 0.425848 | 0.212924 | − | 0.977069i | \(-0.431701\pi\) | ||||
0.212924 | + | 0.977069i | \(0.431701\pi\) | |||||||
\(410\) | −16.2367 | −0.801874 | ||||||||
\(411\) | −13.4365 | −0.662775 | ||||||||
\(412\) | −14.9778 | −0.737902 | ||||||||
\(413\) | 32.6136 | 1.60481 | ||||||||
\(414\) | −4.31700 | −0.212169 | ||||||||
\(415\) | −22.6814 | −1.11339 | ||||||||
\(416\) | 0.682998 | 0.0334867 | ||||||||
\(417\) | −17.9952 | −0.881226 | ||||||||
\(418\) | 0.110461 | 0.00540283 | ||||||||
\(419\) | −15.6180 | −0.762990 | −0.381495 | − | 0.924371i | \(-0.624591\pi\) | ||||
−0.381495 | + | 0.924371i | \(0.624591\pi\) | |||||||
\(420\) | −9.00906 | −0.439597 | ||||||||
\(421\) | −23.3500 | −1.13801 | −0.569005 | − | 0.822334i | \(-0.692672\pi\) | ||||
−0.569005 | + | 0.822334i | \(0.692672\pi\) | |||||||
\(422\) | −11.9974 | −0.584026 | ||||||||
\(423\) | −10.5062 | −0.510827 | ||||||||
\(424\) | 7.98214 | 0.387647 | ||||||||
\(425\) | 0.909737 | 0.0441287 | ||||||||
\(426\) | 9.82898 | 0.476215 | ||||||||
\(427\) | −4.35299 | −0.210656 | ||||||||
\(428\) | 11.9413 | 0.577205 | ||||||||
\(429\) | −0.682998 | −0.0329754 | ||||||||
\(430\) | −5.92552 | −0.285754 | ||||||||
\(431\) | 15.0898 | 0.726850 | 0.363425 | − | 0.931623i | \(-0.381607\pi\) | ||||
0.363425 | + | 0.931623i | \(0.381607\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 21.7332 | 1.04443 | 0.522215 | − | 0.852814i | \(-0.325106\pi\) | ||||
0.522215 | + | 0.852814i | \(0.325106\pi\) | |||||||
\(434\) | −30.1467 | −1.44709 | ||||||||
\(435\) | −8.45141 | −0.405214 | ||||||||
\(436\) | −15.4609 | −0.740445 | ||||||||
\(437\) | 0.476861 | 0.0228114 | ||||||||
\(438\) | −14.1599 | −0.676586 | ||||||||
\(439\) | 34.3340 | 1.63867 | 0.819336 | − | 0.573313i | \(-0.194342\pi\) | ||||
0.819336 | + | 0.573313i | \(0.194342\pi\) | |||||||
\(440\) | −2.06963 | −0.0986656 | ||||||||
\(441\) | 11.9485 | 0.568976 | ||||||||
\(442\) | −0.867029 | −0.0412404 | ||||||||
\(443\) | −5.05846 | −0.240335 | −0.120167 | − | 0.992754i | \(-0.538343\pi\) | ||||
−0.120167 | + | 0.992754i | \(0.538343\pi\) | |||||||
\(444\) | 7.85008 | 0.372548 | ||||||||
\(445\) | 3.99515 | 0.189388 | ||||||||
\(446\) | 8.83707 | 0.418447 | ||||||||
\(447\) | 10.2098 | 0.482906 | ||||||||
\(448\) | −4.35299 | −0.205659 | ||||||||
\(449\) | −12.2145 | −0.576437 | −0.288218 | − | 0.957565i | \(-0.593063\pi\) | ||||
−0.288218 | + | 0.957565i | \(0.593063\pi\) | |||||||
\(450\) | 0.716640 | 0.0337827 | ||||||||
\(451\) | 7.84523 | 0.369418 | ||||||||
\(452\) | −7.82944 | −0.368266 | ||||||||
\(453\) | −20.2294 | −0.950458 | ||||||||
\(454\) | −26.6459 | −1.25055 | ||||||||
\(455\) | −6.15317 | −0.288465 | ||||||||
\(456\) | 0.110461 | 0.00517282 | ||||||||
\(457\) | −6.55628 | −0.306690 | −0.153345 | − | 0.988173i | \(-0.549005\pi\) | ||||
−0.153345 | + | 0.988173i | \(0.549005\pi\) | |||||||
\(458\) | −0.702259 | −0.0328144 | ||||||||
\(459\) | 1.26945 | 0.0592527 | ||||||||
\(460\) | −8.93459 | −0.416577 | ||||||||
\(461\) | −19.2054 | −0.894485 | −0.447243 | − | 0.894413i | \(-0.647594\pi\) | ||||
−0.447243 | + | 0.894413i | \(0.647594\pi\) | |||||||
\(462\) | 4.35299 | 0.202519 | ||||||||
\(463\) | −17.6468 | −0.820116 | −0.410058 | − | 0.912060i | \(-0.634491\pi\) | ||||
−0.410058 | + | 0.912060i | \(0.634491\pi\) | |||||||
\(464\) | −4.08354 | −0.189574 | ||||||||
\(465\) | −14.3333 | −0.664689 | ||||||||
\(466\) | 21.3697 | 0.989934 | ||||||||
\(467\) | 26.6882 | 1.23498 | 0.617491 | − | 0.786578i | \(-0.288149\pi\) | ||||
0.617491 | + | 0.786578i | \(0.288149\pi\) | |||||||
\(468\) | −0.682998 | −0.0315716 | ||||||||
\(469\) | 56.3041 | 2.59988 | ||||||||
\(470\) | −21.7438 | −1.00297 | ||||||||
\(471\) | −0.568594 | −0.0261994 | ||||||||
\(472\) | 7.49224 | 0.344858 | ||||||||
\(473\) | 2.86309 | 0.131645 | ||||||||
\(474\) | −1.79299 | −0.0823548 | ||||||||
\(475\) | −0.0791609 | −0.00363215 | ||||||||
\(476\) | 5.52589 | 0.253279 | ||||||||
\(477\) | −7.98214 | −0.365477 | ||||||||
\(478\) | 6.78467 | 0.310324 | ||||||||
\(479\) | 31.4971 | 1.43914 | 0.719569 | − | 0.694421i | \(-0.244339\pi\) | ||||
0.719569 | + | 0.694421i | \(0.244339\pi\) | |||||||
\(480\) | −2.06963 | −0.0944652 | ||||||||
\(481\) | 5.36158 | 0.244467 | ||||||||
\(482\) | −2.23534 | −0.101817 | ||||||||
\(483\) | 18.7919 | 0.855059 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −23.6454 | −1.07368 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 24.8696 | 1.12695 | 0.563475 | − | 0.826133i | \(-0.309464\pi\) | ||||
0.563475 | + | 0.826133i | \(0.309464\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | 21.5071 | 0.972586 | ||||||||
\(490\) | 24.7290 | 1.11714 | ||||||||
\(491\) | −32.0193 | −1.44501 | −0.722506 | − | 0.691364i | \(-0.757010\pi\) | ||||
−0.722506 | + | 0.691364i | \(0.757010\pi\) | |||||||
\(492\) | 7.84523 | 0.353690 | ||||||||
\(493\) | 5.18384 | 0.233468 | ||||||||
\(494\) | 0.0754447 | 0.00339442 | ||||||||
\(495\) | 2.06963 | 0.0930229 | ||||||||
\(496\) | −6.92552 | −0.310965 | ||||||||
\(497\) | −42.7854 | −1.91919 | ||||||||
\(498\) | 10.9592 | 0.491092 | ||||||||
\(499\) | 35.7304 | 1.59951 | 0.799756 | − | 0.600325i | \(-0.204962\pi\) | ||||
0.799756 | + | 0.600325i | \(0.204962\pi\) | |||||||
\(500\) | 11.8313 | 0.529113 | ||||||||
\(501\) | 3.49709 | 0.156239 | ||||||||
\(502\) | −12.8290 | −0.572585 | ||||||||
\(503\) | −31.5329 | −1.40598 | −0.702991 | − | 0.711199i | \(-0.748153\pi\) | ||||
−0.702991 | + | 0.711199i | \(0.748153\pi\) | |||||||
\(504\) | 4.35299 | 0.193897 | ||||||||
\(505\) | −21.1584 | −0.941534 | ||||||||
\(506\) | 4.31700 | 0.191914 | ||||||||
\(507\) | 12.5335 | 0.556633 | ||||||||
\(508\) | −0.0427077 | −0.00189485 | ||||||||
\(509\) | 24.1026 | 1.06833 | 0.534164 | − | 0.845381i | \(-0.320626\pi\) | ||||
0.534164 | + | 0.845381i | \(0.320626\pi\) | |||||||
\(510\) | 2.62728 | 0.116338 | ||||||||
\(511\) | 61.6378 | 2.72670 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.110461 | −0.00487698 | ||||||||
\(514\) | 16.4533 | 0.725723 | ||||||||
\(515\) | 30.9984 | 1.36595 | ||||||||
\(516\) | 2.86309 | 0.126040 | ||||||||
\(517\) | 10.5062 | 0.462060 | ||||||||
\(518\) | −34.1713 | −1.50140 | ||||||||
\(519\) | −23.2026 | −1.01848 | ||||||||
\(520\) | −1.41355 | −0.0619883 | ||||||||
\(521\) | 27.4191 | 1.20125 | 0.600627 | − | 0.799529i | \(-0.294918\pi\) | ||||
0.600627 | + | 0.799529i | \(0.294918\pi\) | |||||||
\(522\) | 4.08354 | 0.178732 | ||||||||
\(523\) | −30.8643 | −1.34960 | −0.674800 | − | 0.738001i | \(-0.735770\pi\) | ||||
−0.674800 | + | 0.738001i | \(0.735770\pi\) | |||||||
\(524\) | 18.6791 | 0.815998 | ||||||||
\(525\) | −3.11953 | −0.136147 | ||||||||
\(526\) | 3.91114 | 0.170534 | ||||||||
\(527\) | 8.79158 | 0.382967 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | −4.36349 | −0.189717 | ||||||||
\(530\) | −16.5201 | −0.717586 | ||||||||
\(531\) | −7.49224 | −0.325136 | ||||||||
\(532\) | −0.480836 | −0.0208469 | ||||||||
\(533\) | 5.35827 | 0.232093 | ||||||||
\(534\) | −1.93037 | −0.0835354 | ||||||||
\(535\) | −24.7141 | −1.06848 | ||||||||
\(536\) | 12.9346 | 0.558689 | ||||||||
\(537\) | 10.7522 | 0.463990 | ||||||||
\(538\) | 0.0336427 | 0.00145044 | ||||||||
\(539\) | −11.9485 | −0.514658 | ||||||||
\(540\) | 2.06963 | 0.0890626 | ||||||||
\(541\) | 30.3344 | 1.30418 | 0.652090 | − | 0.758142i | \(-0.273893\pi\) | ||||
0.652090 | + | 0.758142i | \(0.273893\pi\) | |||||||
\(542\) | −10.6071 | −0.455616 | ||||||||
\(543\) | 9.37831 | 0.402462 | ||||||||
\(544\) | 1.26945 | 0.0544271 | ||||||||
\(545\) | 31.9984 | 1.37066 | ||||||||
\(546\) | 2.97308 | 0.127236 | ||||||||
\(547\) | 31.8114 | 1.36016 | 0.680079 | − | 0.733139i | \(-0.261945\pi\) | ||||
0.680079 | + | 0.733139i | \(0.261945\pi\) | |||||||
\(548\) | 13.4365 | 0.573980 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −0.716640 | −0.0305576 | ||||||||
\(551\) | −0.451073 | −0.0192163 | ||||||||
\(552\) | 4.31700 | 0.183744 | ||||||||
\(553\) | 7.80487 | 0.331897 | ||||||||
\(554\) | 18.6526 | 0.792473 | ||||||||
\(555\) | −16.2467 | −0.689636 | ||||||||
\(556\) | 17.9952 | 0.763164 | ||||||||
\(557\) | −29.2482 | −1.23929 | −0.619643 | − | 0.784884i | \(-0.712722\pi\) | ||||
−0.619643 | + | 0.784884i | \(0.712722\pi\) | |||||||
\(558\) | 6.92552 | 0.293181 | ||||||||
\(559\) | 1.95548 | 0.0827080 | ||||||||
\(560\) | 9.00906 | 0.380702 | ||||||||
\(561\) | −1.26945 | −0.0535961 | ||||||||
\(562\) | −1.56160 | −0.0658720 | ||||||||
\(563\) | −2.34530 | −0.0988425 | −0.0494212 | − | 0.998778i | \(-0.515738\pi\) | ||||
−0.0494212 | + | 0.998778i | \(0.515738\pi\) | |||||||
\(564\) | 10.5062 | 0.442389 | ||||||||
\(565\) | 16.2040 | 0.681709 | ||||||||
\(566\) | −4.83058 | −0.203044 | ||||||||
\(567\) | −4.35299 | −0.182808 | ||||||||
\(568\) | −9.82898 | −0.412415 | ||||||||
\(569\) | 14.9966 | 0.628688 | 0.314344 | − | 0.949309i | \(-0.398215\pi\) | ||||
0.314344 | + | 0.949309i | \(0.398215\pi\) | |||||||
\(570\) | −0.228614 | −0.00957557 | ||||||||
\(571\) | 2.92018 | 0.122206 | 0.0611028 | − | 0.998131i | \(-0.480538\pi\) | ||||
0.0611028 | + | 0.998131i | \(0.480538\pi\) | |||||||
\(572\) | 0.682998 | 0.0285576 | ||||||||
\(573\) | −13.3539 | −0.557867 | ||||||||
\(574\) | −34.1502 | −1.42540 | ||||||||
\(575\) | −3.09374 | −0.129018 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −19.1315 | −0.796456 | −0.398228 | − | 0.917286i | \(-0.630375\pi\) | ||||
−0.398228 | + | 0.917286i | \(0.630375\pi\) | |||||||
\(578\) | 15.3885 | 0.640077 | ||||||||
\(579\) | −6.59317 | −0.274003 | ||||||||
\(580\) | 8.45141 | 0.350926 | ||||||||
\(581\) | −47.7051 | −1.97914 | ||||||||
\(582\) | 11.4250 | 0.473580 | ||||||||
\(583\) | 7.98214 | 0.330587 | ||||||||
\(584\) | 14.1599 | 0.585940 | ||||||||
\(585\) | 1.41355 | 0.0584431 | ||||||||
\(586\) | −30.3558 | −1.25399 | ||||||||
\(587\) | −25.9773 | −1.07220 | −0.536099 | − | 0.844155i | \(-0.680103\pi\) | ||||
−0.536099 | + | 0.844155i | \(0.680103\pi\) | |||||||
\(588\) | −11.9485 | −0.492748 | ||||||||
\(589\) | −0.765002 | −0.0315213 | ||||||||
\(590\) | −15.5062 | −0.638378 | ||||||||
\(591\) | 23.0051 | 0.946304 | ||||||||
\(592\) | −7.85008 | −0.322636 | ||||||||
\(593\) | −10.2954 | −0.422783 | −0.211391 | − | 0.977402i | \(-0.567799\pi\) | ||||
−0.211391 | + | 0.977402i | \(0.567799\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | −11.4365 | −0.468852 | ||||||||
\(596\) | −10.2098 | −0.418209 | ||||||||
\(597\) | 13.5790 | 0.555753 | ||||||||
\(598\) | 2.94850 | 0.120573 | ||||||||
\(599\) | 25.8919 | 1.05791 | 0.528956 | − | 0.848649i | \(-0.322584\pi\) | ||||
0.528956 | + | 0.848649i | \(0.322584\pi\) | |||||||
\(600\) | −0.716640 | −0.0292567 | ||||||||
\(601\) | 27.9685 | 1.14086 | 0.570429 | − | 0.821347i | \(-0.306777\pi\) | ||||
0.570429 | + | 0.821347i | \(0.306777\pi\) | |||||||
\(602\) | −12.4630 | −0.507953 | ||||||||
\(603\) | −12.9346 | −0.526737 | ||||||||
\(604\) | 20.2294 | 0.823121 | ||||||||
\(605\) | −2.06963 | −0.0841423 | ||||||||
\(606\) | 10.2233 | 0.415292 | ||||||||
\(607\) | 1.54043 | 0.0625241 | 0.0312621 | − | 0.999511i | \(-0.490047\pi\) | ||||
0.0312621 | + | 0.999511i | \(0.490047\pi\) | |||||||
\(608\) | −0.110461 | −0.00447979 | ||||||||
\(609\) | −17.7756 | −0.720304 | ||||||||
\(610\) | 2.06963 | 0.0837968 | ||||||||
\(611\) | 7.17568 | 0.290297 | ||||||||
\(612\) | −1.26945 | −0.0513143 | ||||||||
\(613\) | 28.0848 | 1.13433 | 0.567166 | − | 0.823603i | \(-0.308040\pi\) | ||||
0.567166 | + | 0.823603i | \(0.308040\pi\) | |||||||
\(614\) | 25.7561 | 1.03943 | ||||||||
\(615\) | −16.2367 | −0.654727 | ||||||||
\(616\) | −4.35299 | −0.175387 | ||||||||
\(617\) | 4.66464 | 0.187791 | 0.0938957 | − | 0.995582i | \(-0.470068\pi\) | ||||
0.0938957 | + | 0.995582i | \(0.470068\pi\) | |||||||
\(618\) | −14.9778 | −0.602494 | ||||||||
\(619\) | 18.7803 | 0.754844 | 0.377422 | − | 0.926041i | \(-0.376811\pi\) | ||||
0.377422 | + | 0.926041i | \(0.376811\pi\) | |||||||
\(620\) | 14.3333 | 0.575637 | ||||||||
\(621\) | −4.31700 | −0.173235 | ||||||||
\(622\) | −1.94338 | −0.0779224 | ||||||||
\(623\) | 8.40289 | 0.336655 | ||||||||
\(624\) | 0.682998 | 0.0273418 | ||||||||
\(625\) | −20.9032 | −0.836129 | ||||||||
\(626\) | −15.6473 | −0.625391 | ||||||||
\(627\) | 0.110461 | 0.00441139 | ||||||||
\(628\) | 0.568594 | 0.0226894 | ||||||||
\(629\) | 9.96526 | 0.397341 | ||||||||
\(630\) | −9.00906 | −0.358930 | ||||||||
\(631\) | −25.8058 | −1.02731 | −0.513657 | − | 0.857996i | \(-0.671710\pi\) | ||||
−0.513657 | + | 0.857996i | \(0.671710\pi\) | |||||||
\(632\) | 1.79299 | 0.0713213 | ||||||||
\(633\) | −11.9974 | −0.476855 | ||||||||
\(634\) | 23.9518 | 0.951246 | ||||||||
\(635\) | 0.0883890 | 0.00350761 | ||||||||
\(636\) | 7.98214 | 0.316513 | ||||||||
\(637\) | −8.16080 | −0.323343 | ||||||||
\(638\) | −4.08354 | −0.161669 | ||||||||
\(639\) | 9.82898 | 0.388828 | ||||||||
\(640\) | 2.06963 | 0.0818092 | ||||||||
\(641\) | −38.4359 | −1.51813 | −0.759063 | − | 0.651017i | \(-0.774343\pi\) | ||||
−0.759063 | + | 0.651017i | \(0.774343\pi\) | |||||||
\(642\) | 11.9413 | 0.471286 | ||||||||
\(643\) | −37.0553 | −1.46132 | −0.730659 | − | 0.682742i | \(-0.760787\pi\) | ||||
−0.730659 | + | 0.682742i | \(0.760787\pi\) | |||||||
\(644\) | −18.7919 | −0.740503 | ||||||||
\(645\) | −5.92552 | −0.233317 | ||||||||
\(646\) | 0.140225 | 0.00551706 | ||||||||
\(647\) | 35.1722 | 1.38276 | 0.691382 | − | 0.722490i | \(-0.257002\pi\) | ||||
0.691382 | + | 0.722490i | \(0.257002\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 7.49224 | 0.294096 | ||||||||
\(650\) | −0.489463 | −0.0191983 | ||||||||
\(651\) | −30.1467 | −1.18154 | ||||||||
\(652\) | −21.5071 | −0.842284 | ||||||||
\(653\) | 38.1337 | 1.49229 | 0.746144 | − | 0.665784i | \(-0.231903\pi\) | ||||
0.746144 | + | 0.665784i | \(0.231903\pi\) | |||||||
\(654\) | −15.4609 | −0.604571 | ||||||||
\(655\) | −38.6587 | −1.51052 | ||||||||
\(656\) | −7.84523 | −0.306305 | ||||||||
\(657\) | −14.1599 | −0.552430 | ||||||||
\(658\) | −45.7332 | −1.78286 | ||||||||
\(659\) | 23.5960 | 0.919169 | 0.459584 | − | 0.888134i | \(-0.347998\pi\) | ||||
0.459584 | + | 0.888134i | \(0.347998\pi\) | |||||||
\(660\) | −2.06963 | −0.0805602 | ||||||||
\(661\) | −27.3960 | −1.06558 | −0.532790 | − | 0.846248i | \(-0.678856\pi\) | ||||
−0.532790 | + | 0.846248i | \(0.678856\pi\) | |||||||
\(662\) | −16.2564 | −0.631824 | ||||||||
\(663\) | −0.867029 | −0.0336726 | ||||||||
\(664\) | −10.9592 | −0.425298 | ||||||||
\(665\) | 0.995152 | 0.0385903 | ||||||||
\(666\) | 7.85008 | 0.304184 | ||||||||
\(667\) | −17.6287 | −0.682584 | ||||||||
\(668\) | −3.49709 | −0.135307 | ||||||||
\(669\) | 8.83707 | 0.341661 | ||||||||
\(670\) | −26.7698 | −1.03421 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −4.35299 | −0.167920 | ||||||||
\(673\) | 43.6737 | 1.68350 | 0.841749 | − | 0.539868i | \(-0.181526\pi\) | ||||
0.841749 | + | 0.539868i | \(0.181526\pi\) | |||||||
\(674\) | 8.57110 | 0.330146 | ||||||||
\(675\) | 0.716640 | 0.0275835 | ||||||||
\(676\) | −12.5335 | −0.482058 | ||||||||
\(677\) | −9.67437 | −0.371816 | −0.185908 | − | 0.982567i | \(-0.559523\pi\) | ||||
−0.185908 | + | 0.982567i | \(0.559523\pi\) | |||||||
\(678\) | −7.82944 | −0.300688 | ||||||||
\(679\) | −49.7327 | −1.90857 | ||||||||
\(680\) | −2.62728 | −0.100752 | ||||||||
\(681\) | −26.6459 | −1.02107 | ||||||||
\(682\) | −6.92552 | −0.265192 | ||||||||
\(683\) | −13.9693 | −0.534520 | −0.267260 | − | 0.963624i | \(-0.586118\pi\) | ||||
−0.267260 | + | 0.963624i | \(0.586118\pi\) | |||||||
\(684\) | 0.110461 | 0.00422359 | ||||||||
\(685\) | −27.8086 | −1.06251 | ||||||||
\(686\) | 21.5408 | 0.822430 | ||||||||
\(687\) | −0.702259 | −0.0267929 | ||||||||
\(688\) | −2.86309 | −0.109154 | ||||||||
\(689\) | 5.45178 | 0.207696 | ||||||||
\(690\) | −8.93459 | −0.340134 | ||||||||
\(691\) | 22.6619 | 0.862101 | 0.431050 | − | 0.902328i | \(-0.358143\pi\) | ||||
0.431050 | + | 0.902328i | \(0.358143\pi\) | |||||||
\(692\) | 23.2026 | 0.882030 | ||||||||
\(693\) | 4.35299 | 0.165356 | ||||||||
\(694\) | −17.2704 | −0.655574 | ||||||||
\(695\) | −37.2433 | −1.41272 | ||||||||
\(696\) | −4.08354 | −0.154786 | ||||||||
\(697\) | 9.95910 | 0.377228 | ||||||||
\(698\) | 29.1284 | 1.10253 | ||||||||
\(699\) | 21.3697 | 0.808278 | ||||||||
\(700\) | 3.11953 | 0.117907 | ||||||||
\(701\) | 13.6874 | 0.516965 | 0.258483 | − | 0.966016i | \(-0.416778\pi\) | ||||
0.258483 | + | 0.966016i | \(0.416778\pi\) | |||||||
\(702\) | −0.682998 | −0.0257781 | ||||||||
\(703\) | −0.867129 | −0.0327044 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −21.7438 | −0.818920 | ||||||||
\(706\) | −2.84476 | −0.107064 | ||||||||
\(707\) | −44.5017 | −1.67366 | ||||||||
\(708\) | 7.49224 | 0.281576 | ||||||||
\(709\) | 13.4655 | 0.505707 | 0.252853 | − | 0.967505i | \(-0.418631\pi\) | ||||
0.252853 | + | 0.967505i | \(0.418631\pi\) | |||||||
\(710\) | 20.3423 | 0.763434 | ||||||||
\(711\) | −1.79299 | −0.0672424 | ||||||||
\(712\) | 1.93037 | 0.0723438 | ||||||||
\(713\) | −29.8975 | −1.11967 | ||||||||
\(714\) | 5.52589 | 0.206801 | ||||||||
\(715\) | −1.41355 | −0.0528638 | ||||||||
\(716\) | −10.7522 | −0.401827 | ||||||||
\(717\) | 6.78467 | 0.253378 | ||||||||
\(718\) | 28.7346 | 1.07237 | ||||||||
\(719\) | −22.8197 | −0.851031 | −0.425515 | − | 0.904951i | \(-0.639907\pi\) | ||||
−0.425515 | + | 0.904951i | \(0.639907\pi\) | |||||||
\(720\) | −2.06963 | −0.0771305 | ||||||||
\(721\) | 65.1980 | 2.42810 | ||||||||
\(722\) | 18.9878 | 0.706653 | ||||||||
\(723\) | −2.23534 | −0.0831330 | ||||||||
\(724\) | −9.37831 | −0.348542 | ||||||||
\(725\) | 2.92643 | 0.108685 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −46.8673 | −1.73821 | −0.869106 | − | 0.494626i | \(-0.835305\pi\) | ||||
−0.869106 | + | 0.494626i | \(0.835305\pi\) | |||||||
\(728\) | −2.97308 | −0.110190 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −29.3057 | −1.08465 | ||||||||
\(731\) | 3.63454 | 0.134428 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | −48.7433 | −1.80038 | −0.900188 | − | 0.435503i | \(-0.856571\pi\) | ||||
−0.900188 | + | 0.435503i | \(0.856571\pi\) | |||||||
\(734\) | 19.0137 | 0.701810 | ||||||||
\(735\) | 24.7290 | 0.912141 | ||||||||
\(736\) | −4.31700 | −0.159127 | ||||||||
\(737\) | 12.9346 | 0.476452 | ||||||||
\(738\) | 7.84523 | 0.288787 | ||||||||
\(739\) | −16.1228 | −0.593086 | −0.296543 | − | 0.955020i | \(-0.595834\pi\) | ||||
−0.296543 | + | 0.955020i | \(0.595834\pi\) | |||||||
\(740\) | 16.2467 | 0.597242 | ||||||||
\(741\) | 0.0754447 | 0.00277153 | ||||||||
\(742\) | −34.7462 | −1.27557 | ||||||||
\(743\) | −31.1003 | −1.14096 | −0.570480 | − | 0.821312i | \(-0.693243\pi\) | ||||
−0.570480 | + | 0.821312i | \(0.693243\pi\) | |||||||
\(744\) | −6.92552 | −0.253902 | ||||||||
\(745\) | 21.1305 | 0.774160 | ||||||||
\(746\) | 15.9432 | 0.583720 | ||||||||
\(747\) | 10.9592 | 0.400975 | ||||||||
\(748\) | 1.26945 | 0.0464156 | ||||||||
\(749\) | −51.9804 | −1.89932 | ||||||||
\(750\) | 11.8313 | 0.432019 | ||||||||
\(751\) | 18.2110 | 0.664529 | 0.332264 | − | 0.943186i | \(-0.392187\pi\) | ||||
0.332264 | + | 0.943186i | \(0.392187\pi\) | |||||||
\(752\) | −10.5062 | −0.383120 | ||||||||
\(753\) | −12.8290 | −0.467514 | ||||||||
\(754\) | −2.78905 | −0.101571 | ||||||||
\(755\) | −41.8672 | −1.52370 | ||||||||
\(756\) | 4.35299 | 0.158317 | ||||||||
\(757\) | −13.7746 | −0.500648 | −0.250324 | − | 0.968162i | \(-0.580537\pi\) | ||||
−0.250324 | + | 0.968162i | \(0.580537\pi\) | |||||||
\(758\) | −0.698347 | −0.0253651 | ||||||||
\(759\) | 4.31700 | 0.156697 | ||||||||
\(760\) | 0.228614 | 0.00829268 | ||||||||
\(761\) | −39.2769 | −1.42379 | −0.711893 | − | 0.702287i | \(-0.752162\pi\) | ||||
−0.711893 | + | 0.702287i | \(0.752162\pi\) | |||||||
\(762\) | −0.0427077 | −0.00154714 | ||||||||
\(763\) | 67.3013 | 2.43647 | ||||||||
\(764\) | 13.3539 | 0.483127 | ||||||||
\(765\) | 2.62728 | 0.0949896 | ||||||||
\(766\) | −18.1588 | −0.656105 | ||||||||
\(767\) | 5.11718 | 0.184771 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −6.56137 | −0.236609 | −0.118305 | − | 0.992977i | \(-0.537746\pi\) | ||||
−0.118305 | + | 0.992977i | \(0.537746\pi\) | |||||||
\(770\) | 9.00906 | 0.324664 | ||||||||
\(771\) | 16.4533 | 0.592551 | ||||||||
\(772\) | 6.59317 | 0.237293 | ||||||||
\(773\) | −49.9381 | −1.79615 | −0.898075 | − | 0.439843i | \(-0.855034\pi\) | ||||
−0.898075 | + | 0.439843i | \(0.855034\pi\) | |||||||
\(774\) | 2.86309 | 0.102912 | ||||||||
\(775\) | 4.96311 | 0.178280 | ||||||||
\(776\) | −11.4250 | −0.410132 | ||||||||
\(777\) | −34.1713 | −1.22589 | ||||||||
\(778\) | 4.93409 | 0.176896 | ||||||||
\(779\) | −0.866594 | −0.0310489 | ||||||||
\(780\) | −1.41355 | −0.0506132 | ||||||||
\(781\) | −9.82898 | −0.351708 | ||||||||
\(782\) | 5.48020 | 0.195972 | ||||||||
\(783\) | 4.08354 | 0.145934 | ||||||||
\(784\) | 11.9485 | 0.426732 | ||||||||
\(785\) | −1.17678 | −0.0420010 | ||||||||
\(786\) | 18.6791 | 0.666260 | ||||||||
\(787\) | −21.8859 | −0.780148 | −0.390074 | − | 0.920783i | \(-0.627551\pi\) | ||||
−0.390074 | + | 0.920783i | \(0.627551\pi\) | |||||||
\(788\) | −23.0051 | −0.819524 | ||||||||
\(789\) | 3.91114 | 0.139240 | ||||||||
\(790\) | −3.71082 | −0.132025 | ||||||||
\(791\) | 34.0815 | 1.21180 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −0.682998 | −0.0242540 | ||||||||
\(794\) | −32.0590 | −1.13773 | ||||||||
\(795\) | −16.5201 | −0.585906 | ||||||||
\(796\) | −13.5790 | −0.481296 | ||||||||
\(797\) | 24.0665 | 0.852479 | 0.426239 | − | 0.904610i | \(-0.359838\pi\) | ||||
0.426239 | + | 0.904610i | \(0.359838\pi\) | |||||||
\(798\) | −0.480836 | −0.0170214 | ||||||||
\(799\) | 13.3370 | 0.471829 | ||||||||
\(800\) | 0.716640 | 0.0253371 | ||||||||
\(801\) | −1.93037 | −0.0682063 | ||||||||
\(802\) | −30.7476 | −1.08573 | ||||||||
\(803\) | 14.1599 | 0.499692 | ||||||||
\(804\) | 12.9346 | 0.456168 | ||||||||
\(805\) | 38.8922 | 1.37077 | ||||||||
\(806\) | −4.73012 | −0.166611 | ||||||||
\(807\) | 0.0336427 | 0.00118428 | ||||||||
\(808\) | −10.2233 | −0.359653 | ||||||||
\(809\) | −40.7754 | −1.43359 | −0.716793 | − | 0.697286i | \(-0.754391\pi\) | ||||
−0.716793 | + | 0.697286i | \(0.754391\pi\) | |||||||
\(810\) | 2.06963 | 0.0727193 | ||||||||
\(811\) | 38.6449 | 1.35701 | 0.678504 | − | 0.734597i | \(-0.262629\pi\) | ||||
0.678504 | + | 0.734597i | \(0.262629\pi\) | |||||||
\(812\) | 17.7756 | 0.623801 | ||||||||
\(813\) | −10.6071 | −0.372009 | ||||||||
\(814\) | −7.85008 | −0.275145 | ||||||||
\(815\) | 44.5117 | 1.55918 | ||||||||
\(816\) | 1.26945 | 0.0444395 | ||||||||
\(817\) | −0.316260 | −0.0110645 | ||||||||
\(818\) | −8.61224 | −0.301120 | ||||||||
\(819\) | 2.97308 | 0.103888 | ||||||||
\(820\) | 16.2367 | 0.567010 | ||||||||
\(821\) | −13.3780 | −0.466896 | −0.233448 | − | 0.972369i | \(-0.575001\pi\) | ||||
−0.233448 | + | 0.972369i | \(0.575001\pi\) | |||||||
\(822\) | 13.4365 | 0.468653 | ||||||||
\(823\) | 0.496155 | 0.0172949 | 0.00864745 | − | 0.999963i | \(-0.497247\pi\) | ||||
0.00864745 | + | 0.999963i | \(0.497247\pi\) | |||||||
\(824\) | 14.9778 | 0.521775 | ||||||||
\(825\) | −0.716640 | −0.0249502 | ||||||||
\(826\) | −32.6136 | −1.13477 | ||||||||
\(827\) | 8.46044 | 0.294198 | 0.147099 | − | 0.989122i | \(-0.453006\pi\) | ||||
0.147099 | + | 0.989122i | \(0.453006\pi\) | |||||||
\(828\) | 4.31700 | 0.150026 | ||||||||
\(829\) | −37.2678 | −1.29436 | −0.647182 | − | 0.762335i | \(-0.724053\pi\) | ||||
−0.647182 | + | 0.762335i | \(0.724053\pi\) | |||||||
\(830\) | 22.6814 | 0.787283 | ||||||||
\(831\) | 18.6526 | 0.647052 | ||||||||
\(832\) | −0.682998 | −0.0236787 | ||||||||
\(833\) | −15.1680 | −0.525540 | ||||||||
\(834\) | 17.9952 | 0.623121 | ||||||||
\(835\) | 7.23768 | 0.250470 | ||||||||
\(836\) | −0.110461 | −0.00382038 | ||||||||
\(837\) | 6.92552 | 0.239381 | ||||||||
\(838\) | 15.6180 | 0.539516 | ||||||||
\(839\) | −21.8698 | −0.755030 | −0.377515 | − | 0.926004i | \(-0.623221\pi\) | ||||
−0.377515 | + | 0.926004i | \(0.623221\pi\) | |||||||
\(840\) | 9.00906 | 0.310842 | ||||||||
\(841\) | −12.3247 | −0.424989 | ||||||||
\(842\) | 23.3500 | 0.804695 | ||||||||
\(843\) | −1.56160 | −0.0537843 | ||||||||
\(844\) | 11.9974 | 0.412969 | ||||||||
\(845\) | 25.9397 | 0.892353 | ||||||||
\(846\) | 10.5062 | 0.361209 | ||||||||
\(847\) | −4.35299 | −0.149570 | ||||||||
\(848\) | −7.98214 | −0.274108 | ||||||||
\(849\) | −4.83058 | −0.165785 | ||||||||
\(850\) | −0.909737 | −0.0312037 | ||||||||
\(851\) | −33.8888 | −1.16169 | ||||||||
\(852\) | −9.82898 | −0.336735 | ||||||||
\(853\) | 37.1453 | 1.27183 | 0.635915 | − | 0.771759i | \(-0.280623\pi\) | ||||
0.635915 | + | 0.771759i | \(0.280623\pi\) | |||||||
\(854\) | 4.35299 | 0.148956 | ||||||||
\(855\) | −0.228614 | −0.00781842 | ||||||||
\(856\) | −11.9413 | −0.408146 | ||||||||
\(857\) | −5.46439 | −0.186660 | −0.0933299 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933299 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(858\) | 0.682998 | 0.0233172 | ||||||||
\(859\) | 13.3188 | 0.454432 | 0.227216 | − | 0.973844i | \(-0.427038\pi\) | ||||
0.227216 | + | 0.973844i | \(0.427038\pi\) | |||||||
\(860\) | 5.92552 | 0.202059 | ||||||||
\(861\) | −34.1502 | −1.16384 | ||||||||
\(862\) | −15.0898 | −0.513960 | ||||||||
\(863\) | 22.6823 | 0.772115 | 0.386057 | − | 0.922475i | \(-0.373837\pi\) | ||||
0.386057 | + | 0.922475i | \(0.373837\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −48.0207 | −1.63275 | ||||||||
\(866\) | −21.7332 | −0.738523 | ||||||||
\(867\) | 15.3885 | 0.522621 | ||||||||
\(868\) | 30.1467 | 1.02325 | ||||||||
\(869\) | 1.79299 | 0.0608230 | ||||||||
\(870\) | 8.45141 | 0.286530 | ||||||||
\(871\) | 8.83429 | 0.299339 | ||||||||
\(872\) | 15.4609 | 0.523574 | ||||||||
\(873\) | 11.4250 | 0.386676 | ||||||||
\(874\) | −0.476861 | −0.0161301 | ||||||||
\(875\) | −51.5016 | −1.74107 | ||||||||
\(876\) | 14.1599 | 0.478418 | ||||||||
\(877\) | −52.7402 | −1.78091 | −0.890455 | − | 0.455071i | \(-0.849614\pi\) | ||||
−0.890455 | + | 0.455071i | \(0.849614\pi\) | |||||||
\(878\) | −34.3340 | −1.15872 | ||||||||
\(879\) | −30.3558 | −1.02387 | ||||||||
\(880\) | 2.06963 | 0.0697671 | ||||||||
\(881\) | 22.8631 | 0.770279 | 0.385139 | − | 0.922858i | \(-0.374153\pi\) | ||||
0.385139 | + | 0.922858i | \(0.374153\pi\) | |||||||
\(882\) | −11.9485 | −0.402327 | ||||||||
\(883\) | 18.7989 | 0.632632 | 0.316316 | − | 0.948654i | \(-0.397554\pi\) | ||||
0.316316 | + | 0.948654i | \(0.397554\pi\) | |||||||
\(884\) | 0.867029 | 0.0291613 | ||||||||
\(885\) | −15.5062 | −0.521234 | ||||||||
\(886\) | 5.05846 | 0.169942 | ||||||||
\(887\) | 2.53661 | 0.0851712 | 0.0425856 | − | 0.999093i | \(-0.486440\pi\) | ||||
0.0425856 | + | 0.999093i | \(0.486440\pi\) | |||||||
\(888\) | −7.85008 | −0.263431 | ||||||||
\(889\) | 0.185906 | 0.00623508 | ||||||||
\(890\) | −3.99515 | −0.133918 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −8.83707 | −0.295887 | ||||||||
\(893\) | −1.16052 | −0.0388354 | ||||||||
\(894\) | −10.2098 | −0.341466 | ||||||||
\(895\) | 22.2530 | 0.743835 | ||||||||
\(896\) | 4.35299 | 0.145423 | ||||||||
\(897\) | 2.94850 | 0.0984476 | ||||||||
\(898\) | 12.2145 | 0.407602 | ||||||||
\(899\) | 28.2807 | 0.943213 | ||||||||
\(900\) | −0.716640 | −0.0238880 | ||||||||
\(901\) | 10.1329 | 0.337576 | ||||||||
\(902\) | −7.84523 | −0.261218 | ||||||||
\(903\) | −12.4630 | −0.414742 | ||||||||
\(904\) | 7.82944 | 0.260403 | ||||||||
\(905\) | 19.4096 | 0.645197 | ||||||||
\(906\) | 20.2294 | 0.672075 | ||||||||
\(907\) | 2.23484 | 0.0742065 | 0.0371032 | − | 0.999311i | \(-0.488187\pi\) | ||||
0.0371032 | + | 0.999311i | \(0.488187\pi\) | |||||||
\(908\) | 26.6459 | 0.884275 | ||||||||
\(909\) | 10.2233 | 0.339084 | ||||||||
\(910\) | 6.15317 | 0.203976 | ||||||||
\(911\) | −41.2937 | −1.36812 | −0.684060 | − | 0.729426i | \(-0.739787\pi\) | ||||
−0.684060 | + | 0.729426i | \(0.739787\pi\) | |||||||
\(912\) | −0.110461 | −0.00365774 | ||||||||
\(913\) | −10.9592 | −0.362695 | ||||||||
\(914\) | 6.55628 | 0.216862 | ||||||||
\(915\) | 2.06963 | 0.0684198 | ||||||||
\(916\) | 0.702259 | 0.0232033 | ||||||||
\(917\) | −81.3097 | −2.68508 | ||||||||
\(918\) | −1.26945 | −0.0418980 | ||||||||
\(919\) | −12.5914 | −0.415352 | −0.207676 | − | 0.978198i | \(-0.566590\pi\) | ||||
−0.207676 | + | 0.978198i | \(0.566590\pi\) | |||||||
\(920\) | 8.93459 | 0.294565 | ||||||||
\(921\) | 25.7561 | 0.848694 | ||||||||
\(922\) | 19.2054 | 0.632496 | ||||||||
\(923\) | −6.71317 | −0.220967 | ||||||||
\(924\) | −4.35299 | −0.143203 | ||||||||
\(925\) | 5.62568 | 0.184971 | ||||||||
\(926\) | 17.6468 | 0.579909 | ||||||||
\(927\) | −14.9778 | −0.491934 | ||||||||
\(928\) | 4.08354 | 0.134049 | ||||||||
\(929\) | 8.27151 | 0.271380 | 0.135690 | − | 0.990751i | \(-0.456675\pi\) | ||||
0.135690 | + | 0.990751i | \(0.456675\pi\) | |||||||
\(930\) | 14.3333 | 0.470006 | ||||||||
\(931\) | 1.31985 | 0.0432562 | ||||||||
\(932\) | −21.3697 | −0.699989 | ||||||||
\(933\) | −1.94338 | −0.0636234 | ||||||||
\(934\) | −26.6882 | −0.873264 | ||||||||
\(935\) | −2.62728 | −0.0859213 | ||||||||
\(936\) | 0.682998 | 0.0223245 | ||||||||
\(937\) | 11.1799 | 0.365230 | 0.182615 | − | 0.983184i | \(-0.441544\pi\) | ||||
0.182615 | + | 0.983184i | \(0.441544\pi\) | |||||||
\(938\) | −56.3041 | −1.83839 | ||||||||
\(939\) | −15.6473 | −0.510630 | ||||||||
\(940\) | 21.7438 | 0.709206 | ||||||||
\(941\) | 54.9239 | 1.79047 | 0.895234 | − | 0.445597i | \(-0.147008\pi\) | ||||
0.895234 | + | 0.445597i | \(0.147008\pi\) | |||||||
\(942\) | 0.568594 | 0.0185258 | ||||||||
\(943\) | −33.8679 | −1.10289 | ||||||||
\(944\) | −7.49224 | −0.243852 | ||||||||
\(945\) | −9.00906 | −0.293065 | ||||||||
\(946\) | −2.86309 | −0.0930870 | ||||||||
\(947\) | −2.46271 | −0.0800272 | −0.0400136 | − | 0.999199i | \(-0.512740\pi\) | ||||
−0.0400136 | + | 0.999199i | \(0.512740\pi\) | |||||||
\(948\) | 1.79299 | 0.0582336 | ||||||||
\(949\) | 9.67117 | 0.313939 | ||||||||
\(950\) | 0.0791609 | 0.00256832 | ||||||||
\(951\) | 23.9518 | 0.776689 | ||||||||
\(952\) | −5.52589 | −0.179095 | ||||||||
\(953\) | −15.5621 | −0.504106 | −0.252053 | − | 0.967713i | \(-0.581106\pi\) | ||||
−0.252053 | + | 0.967713i | \(0.581106\pi\) | |||||||
\(954\) | 7.98214 | 0.258431 | ||||||||
\(955\) | −27.6376 | −0.894331 | ||||||||
\(956\) | −6.78467 | −0.219432 | ||||||||
\(957\) | −4.08354 | −0.132002 | ||||||||
\(958\) | −31.4971 | −1.01762 | ||||||||
\(959\) | −58.4890 | −1.88871 | ||||||||
\(960\) | 2.06963 | 0.0667970 | ||||||||
\(961\) | 16.9629 | 0.547190 | ||||||||
\(962\) | −5.36158 | −0.172864 | ||||||||
\(963\) | 11.9413 | 0.384803 | ||||||||
\(964\) | 2.23534 | 0.0719953 | ||||||||
\(965\) | −13.6454 | −0.439261 | ||||||||
\(966\) | −18.7919 | −0.604618 | ||||||||
\(967\) | −9.25738 | −0.297697 | −0.148849 | − | 0.988860i | \(-0.547557\pi\) | ||||
−0.148849 | + | 0.988860i | \(0.547557\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0.140225 | 0.00450466 | ||||||||
\(970\) | 23.6454 | 0.759208 | ||||||||
\(971\) | 2.88863 | 0.0927006 | 0.0463503 | − | 0.998925i | \(-0.485241\pi\) | ||||
0.0463503 | + | 0.998925i | \(0.485241\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −78.3327 | −2.51123 | ||||||||
\(974\) | −24.8696 | −0.796874 | ||||||||
\(975\) | −0.489463 | −0.0156754 | ||||||||
\(976\) | 1.00000 | 0.0320092 | ||||||||
\(977\) | −20.8733 | −0.667795 | −0.333898 | − | 0.942609i | \(-0.608364\pi\) | ||||
−0.333898 | + | 0.942609i | \(0.608364\pi\) | |||||||
\(978\) | −21.5071 | −0.687722 | ||||||||
\(979\) | 1.93037 | 0.0616950 | ||||||||
\(980\) | −24.7290 | −0.789937 | ||||||||
\(981\) | −15.4609 | −0.493630 | ||||||||
\(982\) | 32.0193 | 1.02178 | ||||||||
\(983\) | −17.1706 | −0.547658 | −0.273829 | − | 0.961778i | \(-0.588290\pi\) | ||||
−0.273829 | + | 0.961778i | \(0.588290\pi\) | |||||||
\(984\) | −7.84523 | −0.250097 | ||||||||
\(985\) | 47.6120 | 1.51705 | ||||||||
\(986\) | −5.18384 | −0.165087 | ||||||||
\(987\) | −45.7332 | −1.45570 | ||||||||
\(988\) | −0.0754447 | −0.00240022 | ||||||||
\(989\) | −12.3600 | −0.393024 | ||||||||
\(990\) | −2.06963 | −0.0657771 | ||||||||
\(991\) | −45.3067 | −1.43921 | −0.719607 | − | 0.694382i | \(-0.755678\pi\) | ||||
−0.719607 | + | 0.694382i | \(0.755678\pi\) | |||||||
\(992\) | 6.92552 | 0.219886 | ||||||||
\(993\) | −16.2564 | −0.515883 | ||||||||
\(994\) | 42.7854 | 1.35707 | ||||||||
\(995\) | 28.1035 | 0.890942 | ||||||||
\(996\) | −10.9592 | −0.347254 | ||||||||
\(997\) | −37.3621 | −1.18327 | −0.591634 | − | 0.806207i | \(-0.701517\pi\) | ||||
−0.591634 | + | 0.806207i | \(0.701517\pi\) | |||||||
\(998\) | −35.7304 | −1.13103 | ||||||||
\(999\) | 7.85008 | 0.248366 |
(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 | 4026.2.a.q.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.q.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |