Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(1\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.555636 | −0.392894 | −0.196447 | − | 0.980514i | \(-0.562940\pi\) | ||||
−0.196447 | + | 0.980514i | \(0.562940\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.69127 | −0.845634 | ||||||||
\(5\) | −1.46250 | −0.654050 | −0.327025 | − | 0.945016i | \(-0.606046\pi\) | ||||
−0.327025 | + | 0.945016i | \(0.606046\pi\) | |||||||
\(6\) | 0.555636 | 0.226838 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.05100 | 0.725139 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.812618 | 0.256972 | ||||||||
\(11\) | 4.65121 | 1.40239 | 0.701196 | − | 0.712968i | \(-0.252650\pi\) | ||||
0.701196 | + | 0.712968i | \(0.252650\pi\) | |||||||
\(12\) | 1.69127 | 0.488227 | ||||||||
\(13\) | −1.76814 | −0.490394 | −0.245197 | − | 0.969473i | \(-0.578853\pi\) | ||||
−0.245197 | + | 0.969473i | \(0.578853\pi\) | |||||||
\(14\) | −0.555636 | −0.148500 | ||||||||
\(15\) | 1.46250 | 0.377616 | ||||||||
\(16\) | 2.24292 | 0.560731 | ||||||||
\(17\) | 0.856481 | 0.207727 | 0.103864 | − | 0.994592i | \(-0.466879\pi\) | ||||
0.103864 | + | 0.994592i | \(0.466879\pi\) | |||||||
\(18\) | −0.555636 | −0.130965 | ||||||||
\(19\) | 1.84003 | 0.422132 | 0.211066 | − | 0.977472i | \(-0.432307\pi\) | ||||
0.211066 | + | 0.977472i | \(0.432307\pi\) | |||||||
\(20\) | 2.47348 | 0.553087 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −2.58438 | −0.550992 | ||||||||
\(23\) | −5.80371 | −1.21016 | −0.605079 | − | 0.796166i | \(-0.706858\pi\) | ||||
−0.605079 | + | 0.796166i | \(0.706858\pi\) | |||||||
\(24\) | −2.05100 | −0.418659 | ||||||||
\(25\) | −2.86110 | −0.572219 | ||||||||
\(26\) | 0.982444 | 0.192673 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.69127 | −0.319620 | ||||||||
\(29\) | 3.84513 | 0.714023 | 0.357012 | − | 0.934100i | \(-0.383796\pi\) | ||||
0.357012 | + | 0.934100i | \(0.383796\pi\) | |||||||
\(30\) | −0.812618 | −0.148363 | ||||||||
\(31\) | 0.134605 | 0.0241757 | 0.0120878 | − | 0.999927i | \(-0.496152\pi\) | ||||
0.0120878 | + | 0.999927i | \(0.496152\pi\) | |||||||
\(32\) | −5.34826 | −0.945447 | ||||||||
\(33\) | −4.65121 | −0.809672 | ||||||||
\(34\) | −0.475892 | −0.0816148 | ||||||||
\(35\) | −1.46250 | −0.247208 | ||||||||
\(36\) | −1.69127 | −0.281878 | ||||||||
\(37\) | −5.11266 | −0.840515 | −0.420258 | − | 0.907405i | \(-0.638060\pi\) | ||||
−0.420258 | + | 0.907405i | \(0.638060\pi\) | |||||||
\(38\) | −1.02239 | −0.165853 | ||||||||
\(39\) | 1.76814 | 0.283129 | ||||||||
\(40\) | −2.99959 | −0.474277 | ||||||||
\(41\) | −7.45941 | −1.16496 | −0.582482 | − | 0.812844i | \(-0.697918\pi\) | ||||
−0.582482 | + | 0.812844i | \(0.697918\pi\) | |||||||
\(42\) | 0.555636 | 0.0857366 | ||||||||
\(43\) | 4.27274 | 0.651586 | 0.325793 | − | 0.945441i | \(-0.394369\pi\) | ||||
0.325793 | + | 0.945441i | \(0.394369\pi\) | |||||||
\(44\) | −7.86644 | −1.18591 | ||||||||
\(45\) | −1.46250 | −0.218017 | ||||||||
\(46\) | 3.22475 | 0.475464 | ||||||||
\(47\) | 0.949635 | 0.138519 | 0.0692593 | − | 0.997599i | \(-0.477936\pi\) | ||||
0.0692593 | + | 0.997599i | \(0.477936\pi\) | |||||||
\(48\) | −2.24292 | −0.323738 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.58973 | 0.224822 | ||||||||
\(51\) | −0.856481 | −0.119931 | ||||||||
\(52\) | 2.99040 | 0.414694 | ||||||||
\(53\) | 0.392595 | 0.0539271 | 0.0269635 | − | 0.999636i | \(-0.491416\pi\) | ||||
0.0269635 | + | 0.999636i | \(0.491416\pi\) | |||||||
\(54\) | 0.555636 | 0.0756125 | ||||||||
\(55\) | −6.80239 | −0.917234 | ||||||||
\(56\) | 2.05100 | 0.274077 | ||||||||
\(57\) | −1.84003 | −0.243718 | ||||||||
\(58\) | −2.13650 | −0.280536 | ||||||||
\(59\) | 1.60517 | 0.208976 | 0.104488 | − | 0.994526i | \(-0.466680\pi\) | ||||
0.104488 | + | 0.994526i | \(0.466680\pi\) | |||||||
\(60\) | −2.47348 | −0.319325 | ||||||||
\(61\) | 15.5098 | 1.98583 | 0.992916 | − | 0.118818i | \(-0.0379106\pi\) | ||||
0.992916 | + | 0.118818i | \(0.0379106\pi\) | |||||||
\(62\) | −0.0747912 | −0.00949849 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −1.51416 | −0.189270 | ||||||||
\(65\) | 2.58591 | 0.320742 | ||||||||
\(66\) | 2.58438 | 0.318115 | ||||||||
\(67\) | −12.8432 | −1.56905 | −0.784523 | − | 0.620100i | \(-0.787092\pi\) | ||||
−0.784523 | + | 0.620100i | \(0.787092\pi\) | |||||||
\(68\) | −1.44854 | −0.175661 | ||||||||
\(69\) | 5.80371 | 0.698685 | ||||||||
\(70\) | 0.812618 | 0.0971264 | ||||||||
\(71\) | −3.57750 | −0.424572 | −0.212286 | − | 0.977208i | \(-0.568091\pi\) | ||||
−0.212286 | + | 0.977208i | \(0.568091\pi\) | |||||||
\(72\) | 2.05100 | 0.241713 | ||||||||
\(73\) | 2.62361 | 0.307070 | 0.153535 | − | 0.988143i | \(-0.450934\pi\) | ||||
0.153535 | + | 0.988143i | \(0.450934\pi\) | |||||||
\(74\) | 2.84078 | 0.330234 | ||||||||
\(75\) | 2.86110 | 0.330371 | ||||||||
\(76\) | −3.11198 | −0.356969 | ||||||||
\(77\) | 4.65121 | 0.530055 | ||||||||
\(78\) | −0.982444 | −0.111240 | ||||||||
\(79\) | −2.90361 | −0.326682 | −0.163341 | − | 0.986570i | \(-0.552227\pi\) | ||||
−0.163341 | + | 0.986570i | \(0.552227\pi\) | |||||||
\(80\) | −3.28028 | −0.366746 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.14472 | 0.457708 | ||||||||
\(83\) | −11.0965 | −1.21800 | −0.609000 | − | 0.793170i | \(-0.708429\pi\) | ||||
−0.609000 | + | 0.793170i | \(0.708429\pi\) | |||||||
\(84\) | 1.69127 | 0.184532 | ||||||||
\(85\) | −1.25260 | −0.135864 | ||||||||
\(86\) | −2.37409 | −0.256005 | ||||||||
\(87\) | −3.84513 | −0.412242 | ||||||||
\(88\) | 9.53965 | 1.01693 | ||||||||
\(89\) | −7.10905 | −0.753558 | −0.376779 | − | 0.926303i | \(-0.622968\pi\) | ||||
−0.376779 | + | 0.926303i | \(0.622968\pi\) | |||||||
\(90\) | 0.812618 | 0.0856575 | ||||||||
\(91\) | −1.76814 | −0.185352 | ||||||||
\(92\) | 9.81563 | 1.02335 | ||||||||
\(93\) | −0.134605 | −0.0139578 | ||||||||
\(94\) | −0.527652 | −0.0544231 | ||||||||
\(95\) | −2.69104 | −0.276095 | ||||||||
\(96\) | 5.34826 | 0.545854 | ||||||||
\(97\) | −12.3661 | −1.25559 | −0.627793 | − | 0.778380i | \(-0.716042\pi\) | ||||
−0.627793 | + | 0.778380i | \(0.716042\pi\) | |||||||
\(98\) | −0.555636 | −0.0561278 | ||||||||
\(99\) | 4.65121 | 0.467464 | ||||||||
\(100\) | 4.83888 | 0.483888 | ||||||||
\(101\) | −0.917518 | −0.0912964 | −0.0456482 | − | 0.998958i | \(-0.514535\pi\) | ||||
−0.0456482 | + | 0.998958i | \(0.514535\pi\) | |||||||
\(102\) | 0.475892 | 0.0471203 | ||||||||
\(103\) | 15.7448 | 1.55138 | 0.775691 | − | 0.631113i | \(-0.217401\pi\) | ||||
0.775691 | + | 0.631113i | \(0.217401\pi\) | |||||||
\(104\) | −3.62646 | −0.355604 | ||||||||
\(105\) | 1.46250 | 0.142725 | ||||||||
\(106\) | −0.218140 | −0.0211877 | ||||||||
\(107\) | 4.49317 | 0.434371 | 0.217186 | − | 0.976130i | \(-0.430312\pi\) | ||||
0.217186 | + | 0.976130i | \(0.430312\pi\) | |||||||
\(108\) | 1.69127 | 0.162742 | ||||||||
\(109\) | 2.12822 | 0.203847 | 0.101923 | − | 0.994792i | \(-0.467500\pi\) | ||||
0.101923 | + | 0.994792i | \(0.467500\pi\) | |||||||
\(110\) | 3.77966 | 0.360376 | ||||||||
\(111\) | 5.11266 | 0.485272 | ||||||||
\(112\) | 2.24292 | 0.211936 | ||||||||
\(113\) | 5.65973 | 0.532422 | 0.266211 | − | 0.963915i | \(-0.414228\pi\) | ||||
0.266211 | + | 0.963915i | \(0.414228\pi\) | |||||||
\(114\) | 1.02239 | 0.0957554 | ||||||||
\(115\) | 8.48792 | 0.791503 | ||||||||
\(116\) | −6.50315 | −0.603803 | ||||||||
\(117\) | −1.76814 | −0.163465 | ||||||||
\(118\) | −0.891893 | −0.0821055 | ||||||||
\(119\) | 0.856481 | 0.0785135 | ||||||||
\(120\) | 2.99959 | 0.273824 | ||||||||
\(121\) | 10.6338 | 0.966705 | ||||||||
\(122\) | −8.61783 | −0.780222 | ||||||||
\(123\) | 7.45941 | 0.672592 | ||||||||
\(124\) | −0.227652 | −0.0204438 | ||||||||
\(125\) | 11.4968 | 1.02831 | ||||||||
\(126\) | −0.555636 | −0.0495000 | ||||||||
\(127\) | −3.68860 | −0.327311 | −0.163655 | − | 0.986518i | \(-0.552329\pi\) | ||||
−0.163655 | + | 0.986518i | \(0.552329\pi\) | |||||||
\(128\) | 11.5378 | 1.01981 | ||||||||
\(129\) | −4.27274 | −0.376193 | ||||||||
\(130\) | −1.43682 | −0.126018 | ||||||||
\(131\) | 9.84593 | 0.860243 | 0.430121 | − | 0.902771i | \(-0.358471\pi\) | ||||
0.430121 | + | 0.902771i | \(0.358471\pi\) | |||||||
\(132\) | 7.86644 | 0.684686 | ||||||||
\(133\) | 1.84003 | 0.159551 | ||||||||
\(134\) | 7.13614 | 0.616469 | ||||||||
\(135\) | 1.46250 | 0.125872 | ||||||||
\(136\) | 1.75665 | 0.150631 | ||||||||
\(137\) | 2.63093 | 0.224775 | 0.112388 | − | 0.993664i | \(-0.464150\pi\) | ||||
0.112388 | + | 0.993664i | \(0.464150\pi\) | |||||||
\(138\) | −3.22475 | −0.274509 | ||||||||
\(139\) | 21.1677 | 1.79542 | 0.897711 | − | 0.440584i | \(-0.145229\pi\) | ||||
0.897711 | + | 0.440584i | \(0.145229\pi\) | |||||||
\(140\) | 2.47348 | 0.209047 | ||||||||
\(141\) | −0.949635 | −0.0799737 | ||||||||
\(142\) | 1.98779 | 0.166812 | ||||||||
\(143\) | −8.22400 | −0.687725 | ||||||||
\(144\) | 2.24292 | 0.186910 | ||||||||
\(145\) | −5.62351 | −0.467007 | ||||||||
\(146\) | −1.45777 | −0.120646 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 8.64687 | 0.710768 | ||||||||
\(149\) | 23.6277 | 1.93566 | 0.967828 | − | 0.251615i | \(-0.0809615\pi\) | ||||
0.967828 | + | 0.251615i | \(0.0809615\pi\) | |||||||
\(150\) | −1.58973 | −0.129801 | ||||||||
\(151\) | −4.20556 | −0.342244 | −0.171122 | − | 0.985250i | \(-0.554739\pi\) | ||||
−0.171122 | + | 0.985250i | \(0.554739\pi\) | |||||||
\(152\) | 3.77391 | 0.306104 | ||||||||
\(153\) | 0.856481 | 0.0692424 | ||||||||
\(154\) | −2.58438 | −0.208255 | ||||||||
\(155\) | −0.196859 | −0.0158121 | ||||||||
\(156\) | −2.99040 | −0.239424 | ||||||||
\(157\) | −6.04298 | −0.482282 | −0.241141 | − | 0.970490i | \(-0.577522\pi\) | ||||
−0.241141 | + | 0.970490i | \(0.577522\pi\) | |||||||
\(158\) | 1.61335 | 0.128351 | ||||||||
\(159\) | −0.392595 | −0.0311348 | ||||||||
\(160\) | 7.82182 | 0.618369 | ||||||||
\(161\) | −5.80371 | −0.457396 | ||||||||
\(162\) | −0.555636 | −0.0436549 | ||||||||
\(163\) | −3.97417 | −0.311281 | −0.155640 | − | 0.987814i | \(-0.549744\pi\) | ||||
−0.155640 | + | 0.987814i | \(0.549744\pi\) | |||||||
\(164\) | 12.6159 | 0.985133 | ||||||||
\(165\) | 6.80239 | 0.529565 | ||||||||
\(166\) | 6.16562 | 0.478545 | ||||||||
\(167\) | 14.5862 | 1.12871 | 0.564356 | − | 0.825532i | \(-0.309125\pi\) | ||||
0.564356 | + | 0.825532i | \(0.309125\pi\) | |||||||
\(168\) | −2.05100 | −0.158238 | ||||||||
\(169\) | −9.87368 | −0.759514 | ||||||||
\(170\) | 0.695992 | 0.0533801 | ||||||||
\(171\) | 1.84003 | 0.140711 | ||||||||
\(172\) | −7.22634 | −0.551004 | ||||||||
\(173\) | −20.6262 | −1.56818 | −0.784091 | − | 0.620646i | \(-0.786870\pi\) | ||||
−0.784091 | + | 0.620646i | \(0.786870\pi\) | |||||||
\(174\) | 2.13650 | 0.161967 | ||||||||
\(175\) | −2.86110 | −0.216278 | ||||||||
\(176\) | 10.4323 | 0.786365 | ||||||||
\(177\) | −1.60517 | −0.120652 | ||||||||
\(178\) | 3.95005 | 0.296069 | ||||||||
\(179\) | −11.8629 | −0.886673 | −0.443336 | − | 0.896355i | \(-0.646205\pi\) | ||||
−0.443336 | + | 0.896355i | \(0.646205\pi\) | |||||||
\(180\) | 2.47348 | 0.184362 | ||||||||
\(181\) | 6.37482 | 0.473837 | 0.236918 | − | 0.971530i | \(-0.423863\pi\) | ||||
0.236918 | + | 0.971530i | \(0.423863\pi\) | |||||||
\(182\) | 0.982444 | 0.0728236 | ||||||||
\(183\) | −15.5098 | −1.14652 | ||||||||
\(184\) | −11.9034 | −0.877532 | ||||||||
\(185\) | 7.47726 | 0.549739 | ||||||||
\(186\) | 0.0747912 | 0.00548396 | ||||||||
\(187\) | 3.98367 | 0.291315 | ||||||||
\(188\) | −1.60609 | −0.117136 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 1.49524 | 0.108476 | ||||||||
\(191\) | −13.6925 | −0.990755 | −0.495377 | − | 0.868678i | \(-0.664970\pi\) | ||||
−0.495377 | + | 0.868678i | \(0.664970\pi\) | |||||||
\(192\) | 1.51416 | 0.109275 | ||||||||
\(193\) | −8.62461 | −0.620813 | −0.310406 | − | 0.950604i | \(-0.600465\pi\) | ||||
−0.310406 | + | 0.950604i | \(0.600465\pi\) | |||||||
\(194\) | 6.87105 | 0.493313 | ||||||||
\(195\) | −2.58591 | −0.185181 | ||||||||
\(196\) | −1.69127 | −0.120805 | ||||||||
\(197\) | −7.15316 | −0.509641 | −0.254821 | − | 0.966988i | \(-0.582016\pi\) | ||||
−0.254821 | + | 0.966988i | \(0.582016\pi\) | |||||||
\(198\) | −2.58438 | −0.183664 | ||||||||
\(199\) | −22.3739 | −1.58605 | −0.793024 | − | 0.609191i | \(-0.791494\pi\) | ||||
−0.793024 | + | 0.609191i | \(0.791494\pi\) | |||||||
\(200\) | −5.86812 | −0.414938 | ||||||||
\(201\) | 12.8432 | 0.905889 | ||||||||
\(202\) | 0.509806 | 0.0358698 | ||||||||
\(203\) | 3.84513 | 0.269875 | ||||||||
\(204\) | 1.44854 | 0.101418 | ||||||||
\(205\) | 10.9094 | 0.761944 | ||||||||
\(206\) | −8.74839 | −0.609529 | ||||||||
\(207\) | −5.80371 | −0.403386 | ||||||||
\(208\) | −3.96581 | −0.274979 | ||||||||
\(209\) | 8.55836 | 0.591994 | ||||||||
\(210\) | −0.812618 | −0.0560760 | ||||||||
\(211\) | 13.7259 | 0.944930 | 0.472465 | − | 0.881349i | \(-0.343364\pi\) | ||||
0.472465 | + | 0.881349i | \(0.343364\pi\) | |||||||
\(212\) | −0.663984 | −0.0456026 | ||||||||
\(213\) | 3.57750 | 0.245127 | ||||||||
\(214\) | −2.49657 | −0.170662 | ||||||||
\(215\) | −6.24887 | −0.426170 | ||||||||
\(216\) | −2.05100 | −0.139553 | ||||||||
\(217\) | 0.134605 | 0.00913755 | ||||||||
\(218\) | −1.18252 | −0.0800902 | ||||||||
\(219\) | −2.62361 | −0.177287 | ||||||||
\(220\) | 11.5047 | 0.775645 | ||||||||
\(221\) | −1.51438 | −0.101868 | ||||||||
\(222\) | −2.84078 | −0.190661 | ||||||||
\(223\) | 6.73340 | 0.450902 | 0.225451 | − | 0.974255i | \(-0.427615\pi\) | ||||
0.225451 | + | 0.974255i | \(0.427615\pi\) | |||||||
\(224\) | −5.34826 | −0.357345 | ||||||||
\(225\) | −2.86110 | −0.190740 | ||||||||
\(226\) | −3.14475 | −0.209186 | ||||||||
\(227\) | 6.06777 | 0.402732 | 0.201366 | − | 0.979516i | \(-0.435462\pi\) | ||||
0.201366 | + | 0.979516i | \(0.435462\pi\) | |||||||
\(228\) | 3.11198 | 0.206096 | ||||||||
\(229\) | 16.8701 | 1.11481 | 0.557404 | − | 0.830241i | \(-0.311797\pi\) | ||||
0.557404 | + | 0.830241i | \(0.311797\pi\) | |||||||
\(230\) | −4.71620 | −0.310977 | ||||||||
\(231\) | −4.65121 | −0.306027 | ||||||||
\(232\) | 7.88638 | 0.517766 | ||||||||
\(233\) | −4.58341 | −0.300269 | −0.150135 | − | 0.988666i | \(-0.547971\pi\) | ||||
−0.150135 | + | 0.988666i | \(0.547971\pi\) | |||||||
\(234\) | 0.982444 | 0.0642244 | ||||||||
\(235\) | −1.38884 | −0.0905980 | ||||||||
\(236\) | −2.71478 | −0.176717 | ||||||||
\(237\) | 2.90361 | 0.188610 | ||||||||
\(238\) | −0.475892 | −0.0308475 | ||||||||
\(239\) | −5.32334 | −0.344338 | −0.172169 | − | 0.985067i | \(-0.555078\pi\) | ||||
−0.172169 | + | 0.985067i | \(0.555078\pi\) | |||||||
\(240\) | 3.28028 | 0.211741 | ||||||||
\(241\) | 0.657764 | 0.0423703 | 0.0211852 | − | 0.999776i | \(-0.493256\pi\) | ||||
0.0211852 | + | 0.999776i | \(0.493256\pi\) | |||||||
\(242\) | −5.90850 | −0.379813 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −26.2313 | −1.67929 | ||||||||
\(245\) | −1.46250 | −0.0934357 | ||||||||
\(246\) | −4.14472 | −0.264258 | ||||||||
\(247\) | −3.25343 | −0.207011 | ||||||||
\(248\) | 0.276074 | 0.0175307 | ||||||||
\(249\) | 11.0965 | 0.703213 | ||||||||
\(250\) | −6.38807 | −0.404017 | ||||||||
\(251\) | 27.1568 | 1.71412 | 0.857062 | − | 0.515214i | \(-0.172287\pi\) | ||||
0.857062 | + | 0.515214i | \(0.172287\pi\) | |||||||
\(252\) | −1.69127 | −0.106540 | ||||||||
\(253\) | −26.9943 | −1.69712 | ||||||||
\(254\) | 2.04952 | 0.128599 | ||||||||
\(255\) | 1.25260 | 0.0784411 | ||||||||
\(256\) | −3.38252 | −0.211407 | ||||||||
\(257\) | −1.67942 | −0.104759 | −0.0523797 | − | 0.998627i | \(-0.516681\pi\) | ||||
−0.0523797 | + | 0.998627i | \(0.516681\pi\) | |||||||
\(258\) | 2.37409 | 0.147804 | ||||||||
\(259\) | −5.11266 | −0.317685 | ||||||||
\(260\) | −4.37346 | −0.271230 | ||||||||
\(261\) | 3.84513 | 0.238008 | ||||||||
\(262\) | −5.47076 | −0.337984 | ||||||||
\(263\) | −16.8518 | −1.03913 | −0.519563 | − | 0.854432i | \(-0.673905\pi\) | ||||
−0.519563 | + | 0.854432i | \(0.673905\pi\) | |||||||
\(264\) | −9.53965 | −0.587125 | ||||||||
\(265\) | −0.574170 | −0.0352710 | ||||||||
\(266\) | −1.02239 | −0.0626866 | ||||||||
\(267\) | 7.10905 | 0.435067 | ||||||||
\(268\) | 21.7213 | 1.32684 | ||||||||
\(269\) | −5.47293 | −0.333691 | −0.166845 | − | 0.985983i | \(-0.553358\pi\) | ||||
−0.166845 | + | 0.985983i | \(0.553358\pi\) | |||||||
\(270\) | −0.812618 | −0.0494544 | ||||||||
\(271\) | −15.6762 | −0.952261 | −0.476131 | − | 0.879375i | \(-0.657961\pi\) | ||||
−0.476131 | + | 0.879375i | \(0.657961\pi\) | |||||||
\(272\) | 1.92102 | 0.116479 | ||||||||
\(273\) | 1.76814 | 0.107013 | ||||||||
\(274\) | −1.46184 | −0.0883129 | ||||||||
\(275\) | −13.3076 | −0.802476 | ||||||||
\(276\) | −9.81563 | −0.590832 | ||||||||
\(277\) | −2.66248 | −0.159973 | −0.0799865 | − | 0.996796i | \(-0.525488\pi\) | ||||
−0.0799865 | + | 0.996796i | \(0.525488\pi\) | |||||||
\(278\) | −11.7616 | −0.705411 | ||||||||
\(279\) | 0.134605 | 0.00805856 | ||||||||
\(280\) | −2.99959 | −0.179260 | ||||||||
\(281\) | 26.0334 | 1.55302 | 0.776511 | − | 0.630104i | \(-0.216988\pi\) | ||||
0.776511 | + | 0.630104i | \(0.216988\pi\) | |||||||
\(282\) | 0.527652 | 0.0314212 | ||||||||
\(283\) | −8.80119 | −0.523176 | −0.261588 | − | 0.965180i | \(-0.584246\pi\) | ||||
−0.261588 | + | 0.965180i | \(0.584246\pi\) | |||||||
\(284\) | 6.05052 | 0.359032 | ||||||||
\(285\) | 2.69104 | 0.159404 | ||||||||
\(286\) | 4.56955 | 0.270203 | ||||||||
\(287\) | −7.45941 | −0.440315 | ||||||||
\(288\) | −5.34826 | −0.315149 | ||||||||
\(289\) | −16.2664 | −0.956849 | ||||||||
\(290\) | 3.12462 | 0.183484 | ||||||||
\(291\) | 12.3661 | 0.724913 | ||||||||
\(292\) | −4.43722 | −0.259669 | ||||||||
\(293\) | 22.3910 | 1.30809 | 0.654047 | − | 0.756454i | \(-0.273070\pi\) | ||||
0.654047 | + | 0.756454i | \(0.273070\pi\) | |||||||
\(294\) | 0.555636 | 0.0324054 | ||||||||
\(295\) | −2.34757 | −0.136681 | ||||||||
\(296\) | −10.4861 | −0.609491 | ||||||||
\(297\) | −4.65121 | −0.269891 | ||||||||
\(298\) | −13.1284 | −0.760508 | ||||||||
\(299\) | 10.2618 | 0.593454 | ||||||||
\(300\) | −4.83888 | −0.279373 | ||||||||
\(301\) | 4.27274 | 0.246276 | ||||||||
\(302\) | 2.33676 | 0.134466 | ||||||||
\(303\) | 0.917518 | 0.0527100 | ||||||||
\(304\) | 4.12705 | 0.236702 | ||||||||
\(305\) | −22.6831 | −1.29883 | ||||||||
\(306\) | −0.475892 | −0.0272049 | ||||||||
\(307\) | −24.7055 | −1.41002 | −0.705008 | − | 0.709199i | \(-0.749057\pi\) | ||||
−0.705008 | + | 0.709199i | \(0.749057\pi\) | |||||||
\(308\) | −7.86644 | −0.448232 | ||||||||
\(309\) | −15.7448 | −0.895691 | ||||||||
\(310\) | 0.109382 | 0.00621248 | ||||||||
\(311\) | 21.3674 | 1.21164 | 0.605818 | − | 0.795604i | \(-0.292846\pi\) | ||||
0.605818 | + | 0.795604i | \(0.292846\pi\) | |||||||
\(312\) | 3.62646 | 0.205308 | ||||||||
\(313\) | 19.2229 | 1.08654 | 0.543272 | − | 0.839557i | \(-0.317185\pi\) | ||||
0.543272 | + | 0.839557i | \(0.317185\pi\) | |||||||
\(314\) | 3.35770 | 0.189486 | ||||||||
\(315\) | −1.46250 | −0.0824025 | ||||||||
\(316\) | 4.91078 | 0.276253 | ||||||||
\(317\) | −5.92136 | −0.332577 | −0.166288 | − | 0.986077i | \(-0.553178\pi\) | ||||
−0.166288 | + | 0.986077i | \(0.553178\pi\) | |||||||
\(318\) | 0.218140 | 0.0122327 | ||||||||
\(319\) | 17.8845 | 1.00134 | ||||||||
\(320\) | 2.21446 | 0.123792 | ||||||||
\(321\) | −4.49317 | −0.250784 | ||||||||
\(322\) | 3.22475 | 0.179708 | ||||||||
\(323\) | 1.57595 | 0.0876882 | ||||||||
\(324\) | −1.69127 | −0.0939593 | ||||||||
\(325\) | 5.05882 | 0.280613 | ||||||||
\(326\) | 2.20819 | 0.122300 | ||||||||
\(327\) | −2.12822 | −0.117691 | ||||||||
\(328\) | −15.2993 | −0.844761 | ||||||||
\(329\) | 0.949635 | 0.0523551 | ||||||||
\(330\) | −3.77966 | −0.208063 | ||||||||
\(331\) | −35.5887 | −1.95613 | −0.978065 | − | 0.208300i | \(-0.933207\pi\) | ||||
−0.978065 | + | 0.208300i | \(0.933207\pi\) | |||||||
\(332\) | 18.7672 | 1.02998 | ||||||||
\(333\) | −5.11266 | −0.280172 | ||||||||
\(334\) | −8.10460 | −0.443464 | ||||||||
\(335\) | 18.7832 | 1.02623 | ||||||||
\(336\) | −2.24292 | −0.122362 | ||||||||
\(337\) | −20.4464 | −1.11379 | −0.556894 | − | 0.830584i | \(-0.688007\pi\) | ||||
−0.556894 | + | 0.830584i | \(0.688007\pi\) | |||||||
\(338\) | 5.48617 | 0.298409 | ||||||||
\(339\) | −5.65973 | −0.307394 | ||||||||
\(340\) | 2.11849 | 0.114891 | ||||||||
\(341\) | 0.626074 | 0.0339038 | ||||||||
\(342\) | −1.02239 | −0.0552844 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 8.76340 | 0.472491 | ||||||||
\(345\) | −8.48792 | −0.456974 | ||||||||
\(346\) | 11.4607 | 0.616130 | ||||||||
\(347\) | −15.2764 | −0.820081 | −0.410040 | − | 0.912067i | \(-0.634485\pi\) | ||||
−0.410040 | + | 0.912067i | \(0.634485\pi\) | |||||||
\(348\) | 6.50315 | 0.348606 | ||||||||
\(349\) | 2.24275 | 0.120052 | 0.0600259 | − | 0.998197i | \(-0.480882\pi\) | ||||
0.0600259 | + | 0.998197i | \(0.480882\pi\) | |||||||
\(350\) | 1.58973 | 0.0849746 | ||||||||
\(351\) | 1.76814 | 0.0943764 | ||||||||
\(352\) | −24.8759 | −1.32589 | ||||||||
\(353\) | −19.8671 | −1.05742 | −0.528710 | − | 0.848803i | \(-0.677324\pi\) | ||||
−0.528710 | + | 0.848803i | \(0.677324\pi\) | |||||||
\(354\) | 0.891893 | 0.0474036 | ||||||||
\(355\) | 5.23210 | 0.277691 | ||||||||
\(356\) | 12.0233 | 0.637234 | ||||||||
\(357\) | −0.856481 | −0.0453298 | ||||||||
\(358\) | 6.59145 | 0.348369 | ||||||||
\(359\) | −28.3125 | −1.49428 | −0.747140 | − | 0.664667i | \(-0.768573\pi\) | ||||
−0.747140 | + | 0.664667i | \(0.768573\pi\) | |||||||
\(360\) | −2.99959 | −0.158092 | ||||||||
\(361\) | −15.6143 | −0.821805 | ||||||||
\(362\) | −3.54208 | −0.186168 | ||||||||
\(363\) | −10.6338 | −0.558127 | ||||||||
\(364\) | 2.99040 | 0.156740 | ||||||||
\(365\) | −3.83702 | −0.200839 | ||||||||
\(366\) | 8.61783 | 0.450461 | ||||||||
\(367\) | −37.7960 | −1.97293 | −0.986467 | − | 0.163957i | \(-0.947574\pi\) | ||||
−0.986467 | + | 0.163957i | \(0.947574\pi\) | |||||||
\(368\) | −13.0173 | −0.678573 | ||||||||
\(369\) | −7.45941 | −0.388321 | ||||||||
\(370\) | −4.15464 | −0.215989 | ||||||||
\(371\) | 0.392595 | 0.0203825 | ||||||||
\(372\) | 0.227652 | 0.0118032 | ||||||||
\(373\) | −18.8834 | −0.977746 | −0.488873 | − | 0.872355i | \(-0.662592\pi\) | ||||
−0.488873 | + | 0.872355i | \(0.662592\pi\) | |||||||
\(374\) | −2.21347 | −0.114456 | ||||||||
\(375\) | −11.4968 | −0.593695 | ||||||||
\(376\) | 1.94771 | 0.100445 | ||||||||
\(377\) | −6.79874 | −0.350153 | ||||||||
\(378\) | 0.555636 | 0.0285789 | ||||||||
\(379\) | −24.1038 | −1.23813 | −0.619064 | − | 0.785341i | \(-0.712488\pi\) | ||||
−0.619064 | + | 0.785341i | \(0.712488\pi\) | |||||||
\(380\) | 4.55127 | 0.233475 | ||||||||
\(381\) | 3.68860 | 0.188973 | ||||||||
\(382\) | 7.60805 | 0.389262 | ||||||||
\(383\) | 1.00000 | 0.0510976 | ||||||||
\(384\) | −11.5378 | −0.588788 | ||||||||
\(385\) | −6.80239 | −0.346682 | ||||||||
\(386\) | 4.79215 | 0.243914 | ||||||||
\(387\) | 4.27274 | 0.217195 | ||||||||
\(388\) | 20.9144 | 1.06177 | ||||||||
\(389\) | 33.1997 | 1.68329 | 0.841645 | − | 0.540031i | \(-0.181587\pi\) | ||||
0.841645 | + | 0.540031i | \(0.181587\pi\) | |||||||
\(390\) | 1.43682 | 0.0727564 | ||||||||
\(391\) | −4.97077 | −0.251383 | ||||||||
\(392\) | 2.05100 | 0.103591 | ||||||||
\(393\) | −9.84593 | −0.496661 | ||||||||
\(394\) | 3.97455 | 0.200235 | ||||||||
\(395\) | 4.24653 | 0.213666 | ||||||||
\(396\) | −7.86644 | −0.395304 | ||||||||
\(397\) | −13.2321 | −0.664100 | −0.332050 | − | 0.943262i | \(-0.607740\pi\) | ||||
−0.332050 | + | 0.943262i | \(0.607740\pi\) | |||||||
\(398\) | 12.4318 | 0.623149 | ||||||||
\(399\) | −1.84003 | −0.0921167 | ||||||||
\(400\) | −6.41722 | −0.320861 | ||||||||
\(401\) | −0.0873597 | −0.00436253 | −0.00218127 | − | 0.999998i | \(-0.500694\pi\) | ||||
−0.00218127 | + | 0.999998i | \(0.500694\pi\) | |||||||
\(402\) | −7.13614 | −0.355919 | ||||||||
\(403\) | −0.238000 | −0.0118556 | ||||||||
\(404\) | 1.55177 | 0.0772034 | ||||||||
\(405\) | −1.46250 | −0.0726722 | ||||||||
\(406\) | −2.13650 | −0.106033 | ||||||||
\(407\) | −23.7800 | −1.17873 | ||||||||
\(408\) | −1.75665 | −0.0869669 | ||||||||
\(409\) | −11.1622 | −0.551934 | −0.275967 | − | 0.961167i | \(-0.588998\pi\) | ||||
−0.275967 | + | 0.961167i | \(0.588998\pi\) | |||||||
\(410\) | −6.06165 | −0.299364 | ||||||||
\(411\) | −2.63093 | −0.129774 | ||||||||
\(412\) | −26.6287 | −1.31190 | ||||||||
\(413\) | 1.60517 | 0.0789855 | ||||||||
\(414\) | 3.22475 | 0.158488 | ||||||||
\(415\) | 16.2286 | 0.796632 | ||||||||
\(416\) | 9.45647 | 0.463642 | ||||||||
\(417\) | −21.1677 | −1.03659 | ||||||||
\(418\) | −4.75534 | −0.232591 | ||||||||
\(419\) | −18.4227 | −0.900006 | −0.450003 | − | 0.893027i | \(-0.648577\pi\) | ||||
−0.450003 | + | 0.893027i | \(0.648577\pi\) | |||||||
\(420\) | −2.47348 | −0.120693 | ||||||||
\(421\) | 21.6951 | 1.05735 | 0.528677 | − | 0.848823i | \(-0.322688\pi\) | ||||
0.528677 | + | 0.848823i | \(0.322688\pi\) | |||||||
\(422\) | −7.62661 | −0.371258 | ||||||||
\(423\) | 0.949635 | 0.0461728 | ||||||||
\(424\) | 0.805214 | 0.0391046 | ||||||||
\(425\) | −2.45047 | −0.118865 | ||||||||
\(426\) | −1.98779 | −0.0963088 | ||||||||
\(427\) | 15.5098 | 0.750574 | ||||||||
\(428\) | −7.59916 | −0.367319 | ||||||||
\(429\) | 8.22400 | 0.397058 | ||||||||
\(430\) | 3.47210 | 0.167440 | ||||||||
\(431\) | −1.85014 | −0.0891180 | −0.0445590 | − | 0.999007i | \(-0.514188\pi\) | ||||
−0.0445590 | + | 0.999007i | \(0.514188\pi\) | |||||||
\(432\) | −2.24292 | −0.107913 | ||||||||
\(433\) | 16.3739 | 0.786880 | 0.393440 | − | 0.919350i | \(-0.371285\pi\) | ||||
0.393440 | + | 0.919350i | \(0.371285\pi\) | |||||||
\(434\) | −0.0747912 | −0.00359009 | ||||||||
\(435\) | 5.62351 | 0.269626 | ||||||||
\(436\) | −3.59940 | −0.172380 | ||||||||
\(437\) | −10.6790 | −0.510846 | ||||||||
\(438\) | 1.45777 | 0.0696550 | ||||||||
\(439\) | 10.6218 | 0.506953 | 0.253476 | − | 0.967342i | \(-0.418426\pi\) | ||||
0.253476 | + | 0.967342i | \(0.418426\pi\) | |||||||
\(440\) | −13.9517 | −0.665122 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0.841445 | 0.0400234 | ||||||||
\(443\) | −10.6566 | −0.506310 | −0.253155 | − | 0.967426i | \(-0.581468\pi\) | ||||
−0.253155 | + | 0.967426i | \(0.581468\pi\) | |||||||
\(444\) | −8.64687 | −0.410362 | ||||||||
\(445\) | 10.3970 | 0.492864 | ||||||||
\(446\) | −3.74132 | −0.177157 | ||||||||
\(447\) | −23.6277 | −1.11755 | ||||||||
\(448\) | −1.51416 | −0.0715374 | ||||||||
\(449\) | 26.0557 | 1.22964 | 0.614822 | − | 0.788666i | \(-0.289228\pi\) | ||||
0.614822 | + | 0.788666i | \(0.289228\pi\) | |||||||
\(450\) | 1.58973 | 0.0749405 | ||||||||
\(451\) | −34.6953 | −1.63374 | ||||||||
\(452\) | −9.57212 | −0.450235 | ||||||||
\(453\) | 4.20556 | 0.197595 | ||||||||
\(454\) | −3.37148 | −0.158231 | ||||||||
\(455\) | 2.58591 | 0.121229 | ||||||||
\(456\) | −3.77391 | −0.176729 | ||||||||
\(457\) | −14.3730 | −0.672340 | −0.336170 | − | 0.941801i | \(-0.609132\pi\) | ||||
−0.336170 | + | 0.941801i | \(0.609132\pi\) | |||||||
\(458\) | −9.37365 | −0.438002 | ||||||||
\(459\) | −0.856481 | −0.0399771 | ||||||||
\(460\) | −14.3554 | −0.669322 | ||||||||
\(461\) | −1.36651 | −0.0636445 | −0.0318222 | − | 0.999494i | \(-0.510131\pi\) | ||||
−0.0318222 | + | 0.999494i | \(0.510131\pi\) | |||||||
\(462\) | 2.58438 | 0.120236 | ||||||||
\(463\) | 2.90746 | 0.135121 | 0.0675605 | − | 0.997715i | \(-0.478478\pi\) | ||||
0.0675605 | + | 0.997715i | \(0.478478\pi\) | |||||||
\(464\) | 8.62434 | 0.400375 | ||||||||
\(465\) | 0.196859 | 0.00912912 | ||||||||
\(466\) | 2.54671 | 0.117974 | ||||||||
\(467\) | −30.4342 | −1.40833 | −0.704163 | − | 0.710038i | \(-0.748678\pi\) | ||||
−0.704163 | + | 0.710038i | \(0.748678\pi\) | |||||||
\(468\) | 2.99040 | 0.138231 | ||||||||
\(469\) | −12.8432 | −0.593043 | ||||||||
\(470\) | 0.771691 | 0.0355954 | ||||||||
\(471\) | 6.04298 | 0.278446 | ||||||||
\(472\) | 3.29222 | 0.151537 | ||||||||
\(473\) | 19.8734 | 0.913780 | ||||||||
\(474\) | −1.61335 | −0.0741037 | ||||||||
\(475\) | −5.26450 | −0.241552 | ||||||||
\(476\) | −1.44854 | −0.0663937 | ||||||||
\(477\) | 0.392595 | 0.0179757 | ||||||||
\(478\) | 2.95784 | 0.135289 | ||||||||
\(479\) | −2.08302 | −0.0951754 | −0.0475877 | − | 0.998867i | \(-0.515153\pi\) | ||||
−0.0475877 | + | 0.998867i | \(0.515153\pi\) | |||||||
\(480\) | −7.82182 | −0.357016 | ||||||||
\(481\) | 9.03990 | 0.412184 | ||||||||
\(482\) | −0.365478 | −0.0166471 | ||||||||
\(483\) | 5.80371 | 0.264078 | ||||||||
\(484\) | −17.9845 | −0.817478 | ||||||||
\(485\) | 18.0854 | 0.821216 | ||||||||
\(486\) | 0.555636 | 0.0252042 | ||||||||
\(487\) | 12.0897 | 0.547838 | 0.273919 | − | 0.961753i | \(-0.411680\pi\) | ||||
0.273919 | + | 0.961753i | \(0.411680\pi\) | |||||||
\(488\) | 31.8107 | 1.44000 | ||||||||
\(489\) | 3.97417 | 0.179718 | ||||||||
\(490\) | 0.812618 | 0.0367103 | ||||||||
\(491\) | 15.3064 | 0.690768 | 0.345384 | − | 0.938462i | \(-0.387749\pi\) | ||||
0.345384 | + | 0.938462i | \(0.387749\pi\) | |||||||
\(492\) | −12.6159 | −0.568767 | ||||||||
\(493\) | 3.29328 | 0.148322 | ||||||||
\(494\) | 1.80773 | 0.0813334 | ||||||||
\(495\) | −6.80239 | −0.305745 | ||||||||
\(496\) | 0.301908 | 0.0135561 | ||||||||
\(497\) | −3.57750 | −0.160473 | ||||||||
\(498\) | −6.16562 | −0.276288 | ||||||||
\(499\) | −34.7558 | −1.55588 | −0.777941 | − | 0.628337i | \(-0.783736\pi\) | ||||
−0.777941 | + | 0.628337i | \(0.783736\pi\) | |||||||
\(500\) | −19.4443 | −0.869573 | ||||||||
\(501\) | −14.5862 | −0.651662 | ||||||||
\(502\) | −15.0893 | −0.673469 | ||||||||
\(503\) | 6.72402 | 0.299809 | 0.149905 | − | 0.988700i | \(-0.452103\pi\) | ||||
0.149905 | + | 0.988700i | \(0.452103\pi\) | |||||||
\(504\) | 2.05100 | 0.0913589 | ||||||||
\(505\) | 1.34187 | 0.0597124 | ||||||||
\(506\) | 14.9990 | 0.666787 | ||||||||
\(507\) | 9.87368 | 0.438505 | ||||||||
\(508\) | 6.23842 | 0.276785 | ||||||||
\(509\) | −29.0825 | −1.28906 | −0.644529 | − | 0.764580i | \(-0.722946\pi\) | ||||
−0.644529 | + | 0.764580i | \(0.722946\pi\) | |||||||
\(510\) | −0.695992 | −0.0308190 | ||||||||
\(511\) | 2.62361 | 0.116062 | ||||||||
\(512\) | −21.1962 | −0.936750 | ||||||||
\(513\) | −1.84003 | −0.0812393 | ||||||||
\(514\) | 0.933147 | 0.0411594 | ||||||||
\(515\) | −23.0268 | −1.01468 | ||||||||
\(516\) | 7.22634 | 0.318122 | ||||||||
\(517\) | 4.41695 | 0.194257 | ||||||||
\(518\) | 2.84078 | 0.124817 | ||||||||
\(519\) | 20.6262 | 0.905390 | ||||||||
\(520\) | 5.30370 | 0.232583 | ||||||||
\(521\) | −32.3456 | −1.41709 | −0.708544 | − | 0.705666i | \(-0.750648\pi\) | ||||
−0.708544 | + | 0.705666i | \(0.750648\pi\) | |||||||
\(522\) | −2.13650 | −0.0935119 | ||||||||
\(523\) | 18.2443 | 0.797767 | 0.398883 | − | 0.917002i | \(-0.369398\pi\) | ||||
0.398883 | + | 0.917002i | \(0.369398\pi\) | |||||||
\(524\) | −16.6521 | −0.727451 | ||||||||
\(525\) | 2.86110 | 0.124868 | ||||||||
\(526\) | 9.36348 | 0.408267 | ||||||||
\(527\) | 0.115286 | 0.00502195 | ||||||||
\(528\) | −10.4323 | −0.454008 | ||||||||
\(529\) | 10.6831 | 0.464481 | ||||||||
\(530\) | 0.319030 | 0.0138578 | ||||||||
\(531\) | 1.60517 | 0.0696586 | ||||||||
\(532\) | −3.11198 | −0.134922 | ||||||||
\(533\) | 13.1893 | 0.571291 | ||||||||
\(534\) | −3.95005 | −0.170935 | ||||||||
\(535\) | −6.57126 | −0.284100 | ||||||||
\(536\) | −26.3414 | −1.13778 | ||||||||
\(537\) | 11.8629 | 0.511921 | ||||||||
\(538\) | 3.04096 | 0.131105 | ||||||||
\(539\) | 4.65121 | 0.200342 | ||||||||
\(540\) | −2.47348 | −0.106442 | ||||||||
\(541\) | −16.4744 | −0.708288 | −0.354144 | − | 0.935191i | \(-0.615228\pi\) | ||||
−0.354144 | + | 0.935191i | \(0.615228\pi\) | |||||||
\(542\) | 8.71027 | 0.374138 | ||||||||
\(543\) | −6.37482 | −0.273570 | ||||||||
\(544\) | −4.58068 | −0.196395 | ||||||||
\(545\) | −3.11252 | −0.133326 | ||||||||
\(546\) | −0.982444 | −0.0420447 | ||||||||
\(547\) | −16.8111 | −0.718789 | −0.359395 | − | 0.933186i | \(-0.617017\pi\) | ||||
−0.359395 | + | 0.933186i | \(0.617017\pi\) | |||||||
\(548\) | −4.44960 | −0.190078 | ||||||||
\(549\) | 15.5098 | 0.661944 | ||||||||
\(550\) | 7.39416 | 0.315288 | ||||||||
\(551\) | 7.07516 | 0.301412 | ||||||||
\(552\) | 11.9034 | 0.506644 | ||||||||
\(553\) | −2.90361 | −0.123474 | ||||||||
\(554\) | 1.47937 | 0.0628525 | ||||||||
\(555\) | −7.47726 | −0.317392 | ||||||||
\(556\) | −35.8003 | −1.51827 | ||||||||
\(557\) | −10.5162 | −0.445587 | −0.222793 | − | 0.974866i | \(-0.571518\pi\) | ||||
−0.222793 | + | 0.974866i | \(0.571518\pi\) | |||||||
\(558\) | −0.0747912 | −0.00316616 | ||||||||
\(559\) | −7.55480 | −0.319534 | ||||||||
\(560\) | −3.28028 | −0.138617 | ||||||||
\(561\) | −3.98367 | −0.168191 | ||||||||
\(562\) | −14.4651 | −0.610173 | ||||||||
\(563\) | −17.5388 | −0.739173 | −0.369586 | − | 0.929196i | \(-0.620501\pi\) | ||||
−0.369586 | + | 0.929196i | \(0.620501\pi\) | |||||||
\(564\) | 1.60609 | 0.0676285 | ||||||||
\(565\) | −8.27735 | −0.348231 | ||||||||
\(566\) | 4.89026 | 0.205553 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −7.33747 | −0.307873 | ||||||||
\(569\) | 44.7599 | 1.87643 | 0.938217 | − | 0.346048i | \(-0.112477\pi\) | ||||
0.938217 | + | 0.346048i | \(0.112477\pi\) | |||||||
\(570\) | −1.49524 | −0.0626288 | ||||||||
\(571\) | −32.0670 | −1.34196 | −0.670980 | − | 0.741475i | \(-0.734126\pi\) | ||||
−0.670980 | + | 0.741475i | \(0.734126\pi\) | |||||||
\(572\) | 13.9090 | 0.581564 | ||||||||
\(573\) | 13.6925 | 0.572013 | ||||||||
\(574\) | 4.14472 | 0.172997 | ||||||||
\(575\) | 16.6050 | 0.692475 | ||||||||
\(576\) | −1.51416 | −0.0630901 | ||||||||
\(577\) | 23.3379 | 0.971571 | 0.485785 | − | 0.874078i | \(-0.338534\pi\) | ||||
0.485785 | + | 0.874078i | \(0.338534\pi\) | |||||||
\(578\) | 9.03823 | 0.375941 | ||||||||
\(579\) | 8.62461 | 0.358427 | ||||||||
\(580\) | 9.51086 | 0.394917 | ||||||||
\(581\) | −11.0965 | −0.460361 | ||||||||
\(582\) | −6.87105 | −0.284814 | ||||||||
\(583\) | 1.82604 | 0.0756270 | ||||||||
\(584\) | 5.38103 | 0.222668 | ||||||||
\(585\) | 2.58591 | 0.106914 | ||||||||
\(586\) | −12.4412 | −0.513943 | ||||||||
\(587\) | 5.91881 | 0.244295 | 0.122148 | − | 0.992512i | \(-0.461022\pi\) | ||||
0.122148 | + | 0.992512i | \(0.461022\pi\) | |||||||
\(588\) | 1.69127 | 0.0697467 | ||||||||
\(589\) | 0.247676 | 0.0102053 | ||||||||
\(590\) | 1.30439 | 0.0537010 | ||||||||
\(591\) | 7.15316 | 0.294242 | ||||||||
\(592\) | −11.4673 | −0.471303 | ||||||||
\(593\) | 20.5245 | 0.842842 | 0.421421 | − | 0.906865i | \(-0.361532\pi\) | ||||
0.421421 | + | 0.906865i | \(0.361532\pi\) | |||||||
\(594\) | 2.58438 | 0.106038 | ||||||||
\(595\) | −1.25260 | −0.0513517 | ||||||||
\(596\) | −39.9607 | −1.63686 | ||||||||
\(597\) | 22.3739 | 0.915705 | ||||||||
\(598\) | −5.70182 | −0.233165 | ||||||||
\(599\) | −7.73670 | −0.316113 | −0.158057 | − | 0.987430i | \(-0.550523\pi\) | ||||
−0.158057 | + | 0.987430i | \(0.550523\pi\) | |||||||
\(600\) | 5.86812 | 0.239565 | ||||||||
\(601\) | 21.0734 | 0.859603 | 0.429802 | − | 0.902923i | \(-0.358583\pi\) | ||||
0.429802 | + | 0.902923i | \(0.358583\pi\) | |||||||
\(602\) | −2.37409 | −0.0967606 | ||||||||
\(603\) | −12.8432 | −0.523015 | ||||||||
\(604\) | 7.11274 | 0.289413 | ||||||||
\(605\) | −15.5519 | −0.632273 | ||||||||
\(606\) | −0.509806 | −0.0207095 | ||||||||
\(607\) | 3.29943 | 0.133920 | 0.0669599 | − | 0.997756i | \(-0.478670\pi\) | ||||
0.0669599 | + | 0.997756i | \(0.478670\pi\) | |||||||
\(608\) | −9.84095 | −0.399103 | ||||||||
\(609\) | −3.84513 | −0.155813 | ||||||||
\(610\) | 12.6036 | 0.510304 | ||||||||
\(611\) | −1.67909 | −0.0679287 | ||||||||
\(612\) | −1.44854 | −0.0585537 | ||||||||
\(613\) | −43.3915 | −1.75257 | −0.876284 | − | 0.481795i | \(-0.839985\pi\) | ||||
−0.876284 | + | 0.481795i | \(0.839985\pi\) | |||||||
\(614\) | 13.7273 | 0.553987 | ||||||||
\(615\) | −10.9094 | −0.439909 | ||||||||
\(616\) | 9.53965 | 0.384363 | ||||||||
\(617\) | 38.2327 | 1.53919 | 0.769595 | − | 0.638532i | \(-0.220458\pi\) | ||||
0.769595 | + | 0.638532i | \(0.220458\pi\) | |||||||
\(618\) | 8.74839 | 0.351912 | ||||||||
\(619\) | −8.87287 | −0.356631 | −0.178315 | − | 0.983973i | \(-0.557065\pi\) | ||||
−0.178315 | + | 0.983973i | \(0.557065\pi\) | |||||||
\(620\) | 0.332941 | 0.0133713 | ||||||||
\(621\) | 5.80371 | 0.232895 | ||||||||
\(622\) | −11.8725 | −0.476045 | ||||||||
\(623\) | −7.10905 | −0.284818 | ||||||||
\(624\) | 3.96581 | 0.158759 | ||||||||
\(625\) | −2.50866 | −0.100346 | ||||||||
\(626\) | −10.6810 | −0.426897 | ||||||||
\(627\) | −8.55836 | −0.341788 | ||||||||
\(628\) | 10.2203 | 0.407834 | ||||||||
\(629\) | −4.37889 | −0.174598 | ||||||||
\(630\) | 0.812618 | 0.0323755 | ||||||||
\(631\) | −31.1276 | −1.23917 | −0.619586 | − | 0.784929i | \(-0.712699\pi\) | ||||
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(632\) | −5.95531 | −0.236890 | ||||||||
\(633\) | −13.7259 | −0.545556 | ||||||||
\(634\) | 3.29012 | 0.130667 | ||||||||
\(635\) | 5.39458 | 0.214077 | ||||||||
\(636\) | 0.663984 | 0.0263287 | ||||||||
\(637\) | −1.76814 | −0.0700563 | ||||||||
\(638\) | −9.93729 | −0.393421 | ||||||||
\(639\) | −3.57750 | −0.141524 | ||||||||
\(640\) | −16.8741 | −0.667007 | ||||||||
\(641\) | 3.23986 | 0.127967 | 0.0639834 | − | 0.997951i | \(-0.479620\pi\) | ||||
0.0639834 | + | 0.997951i | \(0.479620\pi\) | |||||||
\(642\) | 2.49657 | 0.0985318 | ||||||||
\(643\) | 38.5643 | 1.52083 | 0.760415 | − | 0.649438i | \(-0.224996\pi\) | ||||
0.760415 | + | 0.649438i | \(0.224996\pi\) | |||||||
\(644\) | 9.81563 | 0.386790 | ||||||||
\(645\) | 6.24887 | 0.246049 | ||||||||
\(646\) | −0.875656 | −0.0344522 | ||||||||
\(647\) | 35.5087 | 1.39599 | 0.697996 | − | 0.716102i | \(-0.254075\pi\) | ||||
0.697996 | + | 0.716102i | \(0.254075\pi\) | |||||||
\(648\) | 2.05100 | 0.0805710 | ||||||||
\(649\) | 7.46600 | 0.293066 | ||||||||
\(650\) | −2.81087 | −0.110251 | ||||||||
\(651\) | −0.134605 | −0.00527557 | ||||||||
\(652\) | 6.72138 | 0.263230 | ||||||||
\(653\) | −12.3139 | −0.481879 | −0.240939 | − | 0.970540i | \(-0.577456\pi\) | ||||
−0.240939 | + | 0.970540i | \(0.577456\pi\) | |||||||
\(654\) | 1.18252 | 0.0462401 | ||||||||
\(655\) | −14.3997 | −0.562641 | ||||||||
\(656\) | −16.7309 | −0.653231 | ||||||||
\(657\) | 2.62361 | 0.102357 | ||||||||
\(658\) | −0.527652 | −0.0205700 | ||||||||
\(659\) | −32.7962 | −1.27756 | −0.638780 | − | 0.769390i | \(-0.720560\pi\) | ||||
−0.638780 | + | 0.769390i | \(0.720560\pi\) | |||||||
\(660\) | −11.5047 | −0.447819 | ||||||||
\(661\) | 29.1908 | 1.13539 | 0.567696 | − | 0.823239i | \(-0.307835\pi\) | ||||
0.567696 | + | 0.823239i | \(0.307835\pi\) | |||||||
\(662\) | 19.7744 | 0.768552 | ||||||||
\(663\) | 1.51438 | 0.0588136 | ||||||||
\(664\) | −22.7590 | −0.883219 | ||||||||
\(665\) | −2.69104 | −0.104354 | ||||||||
\(666\) | 2.84078 | 0.110078 | ||||||||
\(667\) | −22.3160 | −0.864081 | ||||||||
\(668\) | −24.6691 | −0.954477 | ||||||||
\(669\) | −6.73340 | −0.260328 | ||||||||
\(670\) | −10.4366 | −0.403201 | ||||||||
\(671\) | 72.1395 | 2.78492 | ||||||||
\(672\) | 5.34826 | 0.206313 | ||||||||
\(673\) | −44.6600 | −1.72152 | −0.860759 | − | 0.509013i | \(-0.830010\pi\) | ||||
−0.860759 | + | 0.509013i | \(0.830010\pi\) | |||||||
\(674\) | 11.3608 | 0.437601 | ||||||||
\(675\) | 2.86110 | 0.110124 | ||||||||
\(676\) | 16.6990 | 0.642271 | ||||||||
\(677\) | −36.0719 | −1.38636 | −0.693179 | − | 0.720766i | \(-0.743790\pi\) | ||||
−0.693179 | + | 0.720766i | \(0.743790\pi\) | |||||||
\(678\) | 3.14475 | 0.120773 | ||||||||
\(679\) | −12.3661 | −0.474567 | ||||||||
\(680\) | −2.56909 | −0.0985202 | ||||||||
\(681\) | −6.06777 | −0.232518 | ||||||||
\(682\) | −0.347869 | −0.0133206 | ||||||||
\(683\) | −11.0664 | −0.423443 | −0.211722 | − | 0.977330i | \(-0.567907\pi\) | ||||
−0.211722 | + | 0.977330i | \(0.567907\pi\) | |||||||
\(684\) | −3.11198 | −0.118990 | ||||||||
\(685\) | −3.84773 | −0.147014 | ||||||||
\(686\) | −0.555636 | −0.0212143 | ||||||||
\(687\) | −16.8701 | −0.643635 | ||||||||
\(688\) | 9.58342 | 0.365365 | ||||||||
\(689\) | −0.694164 | −0.0264455 | ||||||||
\(690\) | 4.71620 | 0.179543 | ||||||||
\(691\) | 44.7972 | 1.70417 | 0.852083 | − | 0.523406i | \(-0.175339\pi\) | ||||
0.852083 | + | 0.523406i | \(0.175339\pi\) | |||||||
\(692\) | 34.8845 | 1.32611 | ||||||||
\(693\) | 4.65121 | 0.176685 | ||||||||
\(694\) | 8.48813 | 0.322205 | ||||||||
\(695\) | −30.9578 | −1.17430 | ||||||||
\(696\) | −7.88638 | −0.298933 | ||||||||
\(697\) | −6.38884 | −0.241995 | ||||||||
\(698\) | −1.24616 | −0.0471677 | ||||||||
\(699\) | 4.58341 | 0.173360 | ||||||||
\(700\) | 4.83888 | 0.182892 | ||||||||
\(701\) | 21.2884 | 0.804051 | 0.402026 | − | 0.915628i | \(-0.368306\pi\) | ||||
0.402026 | + | 0.915628i | \(0.368306\pi\) | |||||||
\(702\) | −0.982444 | −0.0370799 | ||||||||
\(703\) | −9.40744 | −0.354808 | ||||||||
\(704\) | −7.04268 | −0.265431 | ||||||||
\(705\) | 1.38884 | 0.0523068 | ||||||||
\(706\) | 11.0389 | 0.415454 | ||||||||
\(707\) | −0.917518 | −0.0345068 | ||||||||
\(708\) | 2.71478 | 0.102028 | ||||||||
\(709\) | 3.37390 | 0.126710 | 0.0633548 | − | 0.997991i | \(-0.479820\pi\) | ||||
0.0633548 | + | 0.997991i | \(0.479820\pi\) | |||||||
\(710\) | −2.90714 | −0.109103 | ||||||||
\(711\) | −2.90361 | −0.108894 | ||||||||
\(712\) | −14.5807 | −0.546435 | ||||||||
\(713\) | −0.781206 | −0.0292564 | ||||||||
\(714\) | 0.475892 | 0.0178098 | ||||||||
\(715\) | 12.0276 | 0.449806 | ||||||||
\(716\) | 20.0633 | 0.749801 | ||||||||
\(717\) | 5.32334 | 0.198804 | ||||||||
\(718\) | 15.7315 | 0.587094 | ||||||||
\(719\) | 7.42172 | 0.276783 | 0.138392 | − | 0.990378i | \(-0.455807\pi\) | ||||
0.138392 | + | 0.990378i | \(0.455807\pi\) | |||||||
\(720\) | −3.28028 | −0.122249 | ||||||||
\(721\) | 15.7448 | 0.586367 | ||||||||
\(722\) | 8.67587 | 0.322882 | ||||||||
\(723\) | −0.657764 | −0.0244625 | ||||||||
\(724\) | −10.7815 | −0.400693 | ||||||||
\(725\) | −11.0013 | −0.408578 | ||||||||
\(726\) | 5.90850 | 0.219285 | ||||||||
\(727\) | −19.5424 | −0.724789 | −0.362395 | − | 0.932025i | \(-0.618041\pi\) | ||||
−0.362395 | + | 0.932025i | \(0.618041\pi\) | |||||||
\(728\) | −3.62646 | −0.134406 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.13199 | 0.0789085 | ||||||||
\(731\) | 3.65952 | 0.135352 | ||||||||
\(732\) | 26.2313 | 0.969537 | ||||||||
\(733\) | 19.0737 | 0.704505 | 0.352252 | − | 0.935905i | \(-0.385416\pi\) | ||||
0.352252 | + | 0.935905i | \(0.385416\pi\) | |||||||
\(734\) | 21.0008 | 0.775155 | ||||||||
\(735\) | 1.46250 | 0.0539451 | ||||||||
\(736\) | 31.0397 | 1.14414 | ||||||||
\(737\) | −59.7364 | −2.20042 | ||||||||
\(738\) | 4.14472 | 0.152569 | ||||||||
\(739\) | −16.1755 | −0.595027 | −0.297513 | − | 0.954718i | \(-0.596157\pi\) | ||||
−0.297513 | + | 0.954718i | \(0.596157\pi\) | |||||||
\(740\) | −12.6460 | −0.464878 | ||||||||
\(741\) | 3.25343 | 0.119518 | ||||||||
\(742\) | −0.218140 | −0.00800818 | ||||||||
\(743\) | 35.0169 | 1.28464 | 0.642322 | − | 0.766435i | \(-0.277971\pi\) | ||||
0.642322 | + | 0.766435i | \(0.277971\pi\) | |||||||
\(744\) | −0.276074 | −0.0101214 | ||||||||
\(745\) | −34.5555 | −1.26601 | ||||||||
\(746\) | 10.4923 | 0.384151 | ||||||||
\(747\) | −11.0965 | −0.406000 | ||||||||
\(748\) | −6.73746 | −0.246346 | ||||||||
\(749\) | 4.49317 | 0.164177 | ||||||||
\(750\) | 6.38807 | 0.233259 | ||||||||
\(751\) | −39.5907 | −1.44468 | −0.722342 | − | 0.691536i | \(-0.756934\pi\) | ||||
−0.722342 | + | 0.691536i | \(0.756934\pi\) | |||||||
\(752\) | 2.12996 | 0.0776716 | ||||||||
\(753\) | −27.1568 | −0.989650 | ||||||||
\(754\) | 3.77763 | 0.137573 | ||||||||
\(755\) | 6.15064 | 0.223845 | ||||||||
\(756\) | 1.69127 | 0.0615108 | ||||||||
\(757\) | −6.56100 | −0.238464 | −0.119232 | − | 0.992866i | \(-0.538043\pi\) | ||||
−0.119232 | + | 0.992866i | \(0.538043\pi\) | |||||||
\(758\) | 13.3929 | 0.486453 | ||||||||
\(759\) | 26.9943 | 0.979830 | ||||||||
\(760\) | −5.51934 | −0.200207 | ||||||||
\(761\) | 17.4495 | 0.632543 | 0.316272 | − | 0.948669i | \(-0.397569\pi\) | ||||
0.316272 | + | 0.948669i | \(0.397569\pi\) | |||||||
\(762\) | −2.04952 | −0.0742464 | ||||||||
\(763\) | 2.12822 | 0.0770468 | ||||||||
\(764\) | 23.1577 | 0.837816 | ||||||||
\(765\) | −1.25260 | −0.0452880 | ||||||||
\(766\) | −0.555636 | −0.0200760 | ||||||||
\(767\) | −2.83818 | −0.102481 | ||||||||
\(768\) | 3.38252 | 0.122056 | ||||||||
\(769\) | −37.4459 | −1.35033 | −0.675167 | − | 0.737665i | \(-0.735928\pi\) | ||||
−0.675167 | + | 0.737665i | \(0.735928\pi\) | |||||||
\(770\) | 3.77966 | 0.136209 | ||||||||
\(771\) | 1.67942 | 0.0604828 | ||||||||
\(772\) | 14.5865 | 0.524981 | ||||||||
\(773\) | −3.44275 | −0.123827 | −0.0619135 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619135 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(774\) | −2.37409 | −0.0853348 | ||||||||
\(775\) | −0.385116 | −0.0138338 | ||||||||
\(776\) | −25.3629 | −0.910475 | ||||||||
\(777\) | 5.11266 | 0.183415 | ||||||||
\(778\) | −18.4469 | −0.661355 | ||||||||
\(779\) | −13.7255 | −0.491768 | ||||||||
\(780\) | 4.37346 | 0.156595 | ||||||||
\(781\) | −16.6397 | −0.595416 | ||||||||
\(782\) | 2.76194 | 0.0987668 | ||||||||
\(783\) | −3.84513 | −0.137414 | ||||||||
\(784\) | 2.24292 | 0.0801044 | ||||||||
\(785\) | 8.83785 | 0.315436 | ||||||||
\(786\) | 5.47076 | 0.195135 | ||||||||
\(787\) | −6.30267 | −0.224666 | −0.112333 | − | 0.993671i | \(-0.535832\pi\) | ||||
−0.112333 | + | 0.993671i | \(0.535832\pi\) | |||||||
\(788\) | 12.0979 | 0.430970 | ||||||||
\(789\) | 16.8518 | 0.599940 | ||||||||
\(790\) | −2.35953 | −0.0839482 | ||||||||
\(791\) | 5.65973 | 0.201237 | ||||||||
\(792\) | 9.53965 | 0.338977 | ||||||||
\(793\) | −27.4236 | −0.973840 | ||||||||
\(794\) | 7.35224 | 0.260921 | ||||||||
\(795\) | 0.574170 | 0.0203637 | ||||||||
\(796\) | 37.8403 | 1.34122 | ||||||||
\(797\) | −21.6823 | −0.768027 | −0.384014 | − | 0.923327i | \(-0.625458\pi\) | ||||
−0.384014 | + | 0.923327i | \(0.625458\pi\) | |||||||
\(798\) | 1.02239 | 0.0361921 | ||||||||
\(799\) | 0.813345 | 0.0287741 | ||||||||
\(800\) | 15.3019 | 0.541003 | ||||||||
\(801\) | −7.10905 | −0.251186 | ||||||||
\(802\) | 0.0485402 | 0.00171402 | ||||||||
\(803\) | 12.2029 | 0.430633 | ||||||||
\(804\) | −21.7213 | −0.766050 | ||||||||
\(805\) | 8.48792 | 0.299160 | ||||||||
\(806\) | 0.132241 | 0.00465800 | ||||||||
\(807\) | 5.47293 | 0.192656 | ||||||||
\(808\) | −1.88183 | −0.0662026 | ||||||||
\(809\) | −32.4724 | −1.14167 | −0.570834 | − | 0.821066i | \(-0.693380\pi\) | ||||
−0.570834 | + | 0.821066i | \(0.693380\pi\) | |||||||
\(810\) | 0.812618 | 0.0285525 | ||||||||
\(811\) | −36.8771 | −1.29493 | −0.647466 | − | 0.762095i | \(-0.724171\pi\) | ||||
−0.647466 | + | 0.762095i | \(0.724171\pi\) | |||||||
\(812\) | −6.50315 | −0.228216 | ||||||||
\(813\) | 15.6762 | 0.549788 | ||||||||
\(814\) | 13.2131 | 0.463117 | ||||||||
\(815\) | 5.81222 | 0.203593 | ||||||||
\(816\) | −1.92102 | −0.0672492 | ||||||||
\(817\) | 7.86196 | 0.275055 | ||||||||
\(818\) | 6.20211 | 0.216852 | ||||||||
\(819\) | −1.76814 | −0.0617839 | ||||||||
\(820\) | −18.4507 | −0.644326 | ||||||||
\(821\) | 26.6529 | 0.930194 | 0.465097 | − | 0.885260i | \(-0.346019\pi\) | ||||
0.465097 | + | 0.885260i | \(0.346019\pi\) | |||||||
\(822\) | 1.46184 | 0.0509875 | ||||||||
\(823\) | −50.7607 | −1.76941 | −0.884703 | − | 0.466156i | \(-0.845639\pi\) | ||||
−0.884703 | + | 0.466156i | \(0.845639\pi\) | |||||||
\(824\) | 32.2927 | 1.12497 | ||||||||
\(825\) | 13.3076 | 0.463310 | ||||||||
\(826\) | −0.891893 | −0.0310329 | ||||||||
\(827\) | 28.9588 | 1.00700 | 0.503498 | − | 0.863996i | \(-0.332046\pi\) | ||||
0.503498 | + | 0.863996i | \(0.332046\pi\) | |||||||
\(828\) | 9.81563 | 0.341117 | ||||||||
\(829\) | −42.4799 | −1.47539 | −0.737694 | − | 0.675135i | \(-0.764085\pi\) | ||||
−0.737694 | + | 0.675135i | \(0.764085\pi\) | |||||||
\(830\) | −9.01722 | −0.312992 | ||||||||
\(831\) | 2.66248 | 0.0923605 | ||||||||
\(832\) | 2.67725 | 0.0928170 | ||||||||
\(833\) | 0.856481 | 0.0296753 | ||||||||
\(834\) | 11.7616 | 0.407269 | ||||||||
\(835\) | −21.3323 | −0.738233 | ||||||||
\(836\) | −14.4745 | −0.500611 | ||||||||
\(837\) | −0.134605 | −0.00465261 | ||||||||
\(838\) | 10.2363 | 0.353607 | ||||||||
\(839\) | −33.2494 | −1.14790 | −0.573948 | − | 0.818892i | \(-0.694589\pi\) | ||||
−0.573948 | + | 0.818892i | \(0.694589\pi\) | |||||||
\(840\) | 2.99959 | 0.103496 | ||||||||
\(841\) | −14.2149 | −0.490171 | ||||||||
\(842\) | −12.0546 | −0.415428 | ||||||||
\(843\) | −26.0334 | −0.896637 | ||||||||
\(844\) | −23.2142 | −0.799065 | ||||||||
\(845\) | 14.4402 | 0.496760 | ||||||||
\(846\) | −0.527652 | −0.0181410 | ||||||||
\(847\) | 10.6338 | 0.365380 | ||||||||
\(848\) | 0.880561 | 0.0302386 | ||||||||
\(849\) | 8.80119 | 0.302056 | ||||||||
\(850\) | 1.36157 | 0.0467016 | ||||||||
\(851\) | 29.6724 | 1.01716 | ||||||||
\(852\) | −6.05052 | −0.207287 | ||||||||
\(853\) | −14.8558 | −0.508651 | −0.254326 | − | 0.967119i | \(-0.581854\pi\) | ||||
−0.254326 | + | 0.967119i | \(0.581854\pi\) | |||||||
\(854\) | −8.61783 | −0.294896 | ||||||||
\(855\) | −2.69104 | −0.0920317 | ||||||||
\(856\) | 9.21551 | 0.314980 | ||||||||
\(857\) | −18.3348 | −0.626304 | −0.313152 | − | 0.949703i | \(-0.601385\pi\) | ||||
−0.313152 | + | 0.949703i | \(0.601385\pi\) | |||||||
\(858\) | −4.56955 | −0.156002 | ||||||||
\(859\) | 43.6975 | 1.49094 | 0.745470 | − | 0.666539i | \(-0.232225\pi\) | ||||
0.745470 | + | 0.666539i | \(0.232225\pi\) | |||||||
\(860\) | 10.5685 | 0.360384 | ||||||||
\(861\) | 7.45941 | 0.254216 | ||||||||
\(862\) | 1.02800 | 0.0350139 | ||||||||
\(863\) | 53.6603 | 1.82662 | 0.913309 | − | 0.407268i | \(-0.133518\pi\) | ||||
0.913309 | + | 0.407268i | \(0.133518\pi\) | |||||||
\(864\) | 5.34826 | 0.181951 | ||||||||
\(865\) | 30.1658 | 1.02567 | ||||||||
\(866\) | −9.09795 | −0.309161 | ||||||||
\(867\) | 16.2664 | 0.552437 | ||||||||
\(868\) | −0.227652 | −0.00772702 | ||||||||
\(869\) | −13.5053 | −0.458136 | ||||||||
\(870\) | −3.12462 | −0.105935 | ||||||||
\(871\) | 22.7086 | 0.769451 | ||||||||
\(872\) | 4.36499 | 0.147817 | ||||||||
\(873\) | −12.3661 | −0.418529 | ||||||||
\(874\) | 5.93364 | 0.200708 | ||||||||
\(875\) | 11.4968 | 0.388664 | ||||||||
\(876\) | 4.43722 | 0.149920 | ||||||||
\(877\) | −14.5423 | −0.491057 | −0.245529 | − | 0.969389i | \(-0.578962\pi\) | ||||
−0.245529 | + | 0.969389i | \(0.578962\pi\) | |||||||
\(878\) | −5.90188 | −0.199179 | ||||||||
\(879\) | −22.3910 | −0.755229 | ||||||||
\(880\) | −15.2572 | −0.514322 | ||||||||
\(881\) | 14.2821 | 0.481176 | 0.240588 | − | 0.970627i | \(-0.422660\pi\) | ||||
0.240588 | + | 0.970627i | \(0.422660\pi\) | |||||||
\(882\) | −0.555636 | −0.0187093 | ||||||||
\(883\) | 53.2177 | 1.79092 | 0.895459 | − | 0.445144i | \(-0.146847\pi\) | ||||
0.895459 | + | 0.445144i | \(0.146847\pi\) | |||||||
\(884\) | 2.56122 | 0.0861432 | ||||||||
\(885\) | 2.34757 | 0.0789126 | ||||||||
\(886\) | 5.92119 | 0.198926 | ||||||||
\(887\) | −29.2156 | −0.980965 | −0.490482 | − | 0.871451i | \(-0.663179\pi\) | ||||
−0.490482 | + | 0.871451i | \(0.663179\pi\) | |||||||
\(888\) | 10.4861 | 0.351890 | ||||||||
\(889\) | −3.68860 | −0.123712 | ||||||||
\(890\) | −5.77694 | −0.193644 | ||||||||
\(891\) | 4.65121 | 0.155821 | ||||||||
\(892\) | −11.3880 | −0.381298 | ||||||||
\(893\) | 1.74736 | 0.0584731 | ||||||||
\(894\) | 13.1284 | 0.439079 | ||||||||
\(895\) | 17.3494 | 0.579928 | ||||||||
\(896\) | 11.5378 | 0.385452 | ||||||||
\(897\) | −10.2618 | −0.342631 | ||||||||
\(898\) | −14.4775 | −0.483120 | ||||||||
\(899\) | 0.517572 | 0.0172620 | ||||||||
\(900\) | 4.83888 | 0.161296 | ||||||||
\(901\) | 0.336250 | 0.0112021 | ||||||||
\(902\) | 19.2780 | 0.641886 | ||||||||
\(903\) | −4.27274 | −0.142188 | ||||||||
\(904\) | 11.6081 | 0.386080 | ||||||||
\(905\) | −9.32317 | −0.309913 | ||||||||
\(906\) | −2.33676 | −0.0776338 | ||||||||
\(907\) | −8.61836 | −0.286168 | −0.143084 | − | 0.989711i | \(-0.545702\pi\) | ||||
−0.143084 | + | 0.989711i | \(0.545702\pi\) | |||||||
\(908\) | −10.2622 | −0.340564 | ||||||||
\(909\) | −0.917518 | −0.0304321 | ||||||||
\(910\) | −1.43682 | −0.0476302 | ||||||||
\(911\) | −3.05285 | −0.101145 | −0.0505726 | − | 0.998720i | \(-0.516105\pi\) | ||||
−0.0505726 | + | 0.998720i | \(0.516105\pi\) | |||||||
\(912\) | −4.12705 | −0.136660 | ||||||||
\(913\) | −51.6122 | −1.70811 | ||||||||
\(914\) | 7.98616 | 0.264159 | ||||||||
\(915\) | 22.6831 | 0.749881 | ||||||||
\(916\) | −28.5319 | −0.942720 | ||||||||
\(917\) | 9.84593 | 0.325141 | ||||||||
\(918\) | 0.475892 | 0.0157068 | ||||||||
\(919\) | 56.5586 | 1.86570 | 0.932848 | − | 0.360270i | \(-0.117316\pi\) | ||||
0.932848 | + | 0.360270i | \(0.117316\pi\) | |||||||
\(920\) | 17.4088 | 0.573950 | ||||||||
\(921\) | 24.7055 | 0.814073 | ||||||||
\(922\) | 0.759280 | 0.0250056 | ||||||||
\(923\) | 6.32553 | 0.208207 | ||||||||
\(924\) | 7.86644 | 0.258787 | ||||||||
\(925\) | 14.6278 | 0.480959 | ||||||||
\(926\) | −1.61549 | −0.0530883 | ||||||||
\(927\) | 15.7448 | 0.517127 | ||||||||
\(928\) | −20.5648 | −0.675071 | ||||||||
\(929\) | 4.13974 | 0.135820 | 0.0679102 | − | 0.997691i | \(-0.478367\pi\) | ||||
0.0679102 | + | 0.997691i | \(0.478367\pi\) | |||||||
\(930\) | −0.109382 | −0.00358678 | ||||||||
\(931\) | 1.84003 | 0.0603045 | ||||||||
\(932\) | 7.75177 | 0.253918 | ||||||||
\(933\) | −21.3674 | −0.699538 | ||||||||
\(934\) | 16.9103 | 0.553324 | ||||||||
\(935\) | −5.82612 | −0.190534 | ||||||||
\(936\) | −3.62646 | −0.118535 | ||||||||
\(937\) | 37.8494 | 1.23649 | 0.618243 | − | 0.785987i | \(-0.287845\pi\) | ||||
0.618243 | + | 0.785987i | \(0.287845\pi\) | |||||||
\(938\) | 7.13614 | 0.233003 | ||||||||
\(939\) | −19.2229 | −0.627317 | ||||||||
\(940\) | 2.34890 | 0.0766128 | ||||||||
\(941\) | 1.43847 | 0.0468928 | 0.0234464 | − | 0.999725i | \(-0.492536\pi\) | ||||
0.0234464 | + | 0.999725i | \(0.492536\pi\) | |||||||
\(942\) | −3.35770 | −0.109400 | ||||||||
\(943\) | 43.2922 | 1.40979 | ||||||||
\(944\) | 3.60028 | 0.117179 | ||||||||
\(945\) | 1.46250 | 0.0475751 | ||||||||
\(946\) | −11.0424 | −0.359019 | ||||||||
\(947\) | −8.20248 | −0.266545 | −0.133272 | − | 0.991079i | \(-0.542549\pi\) | ||||
−0.133272 | + | 0.991079i | \(0.542549\pi\) | |||||||
\(948\) | −4.91078 | −0.159495 | ||||||||
\(949\) | −4.63891 | −0.150585 | ||||||||
\(950\) | 2.92515 | 0.0949043 | ||||||||
\(951\) | 5.92136 | 0.192013 | ||||||||
\(952\) | 1.75665 | 0.0569332 | ||||||||
\(953\) | 25.9608 | 0.840953 | 0.420476 | − | 0.907303i | \(-0.361863\pi\) | ||||
0.420476 | + | 0.907303i | \(0.361863\pi\) | |||||||
\(954\) | −0.218140 | −0.00706255 | ||||||||
\(955\) | 20.0253 | 0.648003 | ||||||||
\(956\) | 9.00319 | 0.291184 | ||||||||
\(957\) | −17.8845 | −0.578125 | ||||||||
\(958\) | 1.15740 | 0.0373939 | ||||||||
\(959\) | 2.63093 | 0.0849571 | ||||||||
\(960\) | −2.21446 | −0.0714714 | ||||||||
\(961\) | −30.9819 | −0.999416 | ||||||||
\(962\) | −5.02290 | −0.161945 | ||||||||
\(963\) | 4.49317 | 0.144790 | ||||||||
\(964\) | −1.11246 | −0.0358298 | ||||||||
\(965\) | 12.6135 | 0.406042 | ||||||||
\(966\) | −3.22475 | −0.103755 | ||||||||
\(967\) | 35.0051 | 1.12569 | 0.562844 | − | 0.826563i | \(-0.309707\pi\) | ||||
0.562844 | + | 0.826563i | \(0.309707\pi\) | |||||||
\(968\) | 21.8099 | 0.700995 | ||||||||
\(969\) | −1.57595 | −0.0506268 | ||||||||
\(970\) | −10.0489 | −0.322651 | ||||||||
\(971\) | 26.1983 | 0.840744 | 0.420372 | − | 0.907352i | \(-0.361900\pi\) | ||||
0.420372 | + | 0.907352i | \(0.361900\pi\) | |||||||
\(972\) | 1.69127 | 0.0542475 | ||||||||
\(973\) | 21.1677 | 0.678606 | ||||||||
\(974\) | −6.71749 | −0.215242 | ||||||||
\(975\) | −5.05882 | −0.162012 | ||||||||
\(976\) | 34.7874 | 1.11352 | ||||||||
\(977\) | −28.1719 | −0.901298 | −0.450649 | − | 0.892701i | \(-0.648807\pi\) | ||||
−0.450649 | + | 0.892701i | \(0.648807\pi\) | |||||||
\(978\) | −2.20819 | −0.0706102 | ||||||||
\(979\) | −33.0657 | −1.05678 | ||||||||
\(980\) | 2.47348 | 0.0790124 | ||||||||
\(981\) | 2.12822 | 0.0679489 | ||||||||
\(982\) | −8.50479 | −0.271399 | ||||||||
\(983\) | −20.7021 | −0.660294 | −0.330147 | − | 0.943929i | \(-0.607098\pi\) | ||||
−0.330147 | + | 0.943929i | \(0.607098\pi\) | |||||||
\(984\) | 15.2993 | 0.487723 | ||||||||
\(985\) | 10.4615 | 0.333331 | ||||||||
\(986\) | −1.82987 | −0.0582749 | ||||||||
\(987\) | −0.949635 | −0.0302272 | ||||||||
\(988\) | 5.50243 | 0.175056 | ||||||||
\(989\) | −24.7977 | −0.788522 | ||||||||
\(990\) | 3.77966 | 0.120125 | ||||||||
\(991\) | −31.6952 | −1.00683 | −0.503415 | − | 0.864045i | \(-0.667923\pi\) | ||||
−0.503415 | + | 0.864045i | \(0.667923\pi\) | |||||||
\(992\) | −0.719900 | −0.0228568 | ||||||||
\(993\) | 35.5887 | 1.12937 | ||||||||
\(994\) | 1.98779 | 0.0630489 | ||||||||
\(995\) | 32.7219 | 1.03735 | ||||||||
\(996\) | −18.7672 | −0.594660 | ||||||||
\(997\) | −7.17055 | −0.227094 | −0.113547 | − | 0.993533i | \(-0.536221\pi\) | ||||
−0.113547 | + | 0.993533i | \(0.536221\pi\) | |||||||
\(998\) | 19.3116 | 0.611297 | ||||||||
\(999\) | 5.11266 | 0.161757 |
(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 | 8043.2.a.o.1.18 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.o.1.18 | ✓ | 41 | 1.1 | even | 1 | trivial |