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: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.120027 | −0.0848719 | −0.0424360 | − | 0.999099i | \(-0.513512\pi\) | ||||
−0.0424360 | + | 0.999099i | \(0.513512\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.98559 | −0.992797 | ||||||||
\(5\) | 1.73267 | 0.774874 | 0.387437 | − | 0.921896i | \(-0.373360\pi\) | ||||
0.387437 | + | 0.921896i | \(0.373360\pi\) | |||||||
\(6\) | 0.120027 | 0.0490008 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.478379 | 0.169132 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.207967 | −0.0657650 | ||||||||
\(11\) | −4.99112 | −1.50488 | −0.752439 | − | 0.658662i | \(-0.771123\pi\) | ||||
−0.752439 | + | 0.658662i | \(0.771123\pi\) | |||||||
\(12\) | 1.98559 | 0.573191 | ||||||||
\(13\) | 1.07949 | 0.299396 | 0.149698 | − | 0.988732i | \(-0.452170\pi\) | ||||
0.149698 | + | 0.988732i | \(0.452170\pi\) | |||||||
\(14\) | −0.120027 | −0.0320786 | ||||||||
\(15\) | −1.73267 | −0.447374 | ||||||||
\(16\) | 3.91377 | 0.978442 | ||||||||
\(17\) | −1.52581 | −0.370063 | −0.185031 | − | 0.982733i | \(-0.559239\pi\) | ||||
−0.185031 | + | 0.982733i | \(0.559239\pi\) | |||||||
\(18\) | −0.120027 | −0.0282906 | ||||||||
\(19\) | 0.00579525 | 0.00132952 | 0.000664761 | − | 1.00000i | \(-0.499788\pi\) | ||||
0.000664761 | 1.00000i | \(0.499788\pi\) | ||||||||
\(20\) | −3.44038 | −0.769292 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0.599069 | 0.127722 | ||||||||
\(23\) | 7.05455 | 1.47098 | 0.735488 | − | 0.677538i | \(-0.236953\pi\) | ||||
0.735488 | + | 0.677538i | \(0.236953\pi\) | |||||||
\(24\) | −0.478379 | −0.0976487 | ||||||||
\(25\) | −1.99785 | −0.399571 | ||||||||
\(26\) | −0.129568 | −0.0254103 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.98559 | −0.375242 | ||||||||
\(29\) | 1.18505 | 0.220059 | 0.110029 | − | 0.993928i | \(-0.464906\pi\) | ||||
0.110029 | + | 0.993928i | \(0.464906\pi\) | |||||||
\(30\) | 0.207967 | 0.0379695 | ||||||||
\(31\) | −6.26094 | −1.12450 | −0.562249 | − | 0.826968i | \(-0.690064\pi\) | ||||
−0.562249 | + | 0.826968i | \(0.690064\pi\) | |||||||
\(32\) | −1.42652 | −0.252175 | ||||||||
\(33\) | 4.99112 | 0.868842 | ||||||||
\(34\) | 0.183138 | 0.0314080 | ||||||||
\(35\) | 1.73267 | 0.292875 | ||||||||
\(36\) | −1.98559 | −0.330932 | ||||||||
\(37\) | −0.336663 | −0.0553471 | −0.0276735 | − | 0.999617i | \(-0.508810\pi\) | ||||
−0.0276735 | + | 0.999617i | \(0.508810\pi\) | |||||||
\(38\) | −0.000695587 0 | −0.000112839 0 | ||||||||
\(39\) | −1.07949 | −0.172856 | ||||||||
\(40\) | 0.828873 | 0.131056 | ||||||||
\(41\) | 2.38034 | 0.371747 | 0.185873 | − | 0.982574i | \(-0.440489\pi\) | ||||
0.185873 | + | 0.982574i | \(0.440489\pi\) | |||||||
\(42\) | 0.120027 | 0.0185206 | ||||||||
\(43\) | 9.11735 | 1.39038 | 0.695191 | − | 0.718825i | \(-0.255320\pi\) | ||||
0.695191 | + | 0.718825i | \(0.255320\pi\) | |||||||
\(44\) | 9.91033 | 1.49404 | ||||||||
\(45\) | 1.73267 | 0.258291 | ||||||||
\(46\) | −0.846737 | −0.124844 | ||||||||
\(47\) | −7.60839 | −1.10980 | −0.554899 | − | 0.831918i | \(-0.687243\pi\) | ||||
−0.554899 | + | 0.831918i | \(0.687243\pi\) | |||||||
\(48\) | −3.91377 | −0.564904 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.239796 | 0.0339123 | ||||||||
\(51\) | 1.52581 | 0.213656 | ||||||||
\(52\) | −2.14342 | −0.297239 | ||||||||
\(53\) | −9.21286 | −1.26548 | −0.632742 | − | 0.774363i | \(-0.718070\pi\) | ||||
−0.632742 | + | 0.774363i | \(0.718070\pi\) | |||||||
\(54\) | 0.120027 | 0.0163336 | ||||||||
\(55\) | −8.64796 | −1.16609 | ||||||||
\(56\) | 0.478379 | 0.0639261 | ||||||||
\(57\) | −0.00579525 | −0.000767600 0 | ||||||||
\(58\) | −0.142238 | −0.0186768 | ||||||||
\(59\) | 10.3896 | 1.35261 | 0.676307 | − | 0.736620i | \(-0.263579\pi\) | ||||
0.676307 | + | 0.736620i | \(0.263579\pi\) | |||||||
\(60\) | 3.44038 | 0.444151 | ||||||||
\(61\) | −1.68451 | −0.215679 | −0.107840 | − | 0.994168i | \(-0.534393\pi\) | ||||
−0.107840 | + | 0.994168i | \(0.534393\pi\) | |||||||
\(62\) | 0.751482 | 0.0954384 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −7.65632 | −0.957040 | ||||||||
\(65\) | 1.87039 | 0.231994 | ||||||||
\(66\) | −0.599069 | −0.0737403 | ||||||||
\(67\) | 3.51374 | 0.429272 | 0.214636 | − | 0.976694i | \(-0.431144\pi\) | ||||
0.214636 | + | 0.976694i | \(0.431144\pi\) | |||||||
\(68\) | 3.02964 | 0.367397 | ||||||||
\(69\) | −7.05455 | −0.849268 | ||||||||
\(70\) | −0.207967 | −0.0248568 | ||||||||
\(71\) | −2.92691 | −0.347360 | −0.173680 | − | 0.984802i | \(-0.555566\pi\) | ||||
−0.173680 | + | 0.984802i | \(0.555566\pi\) | |||||||
\(72\) | 0.478379 | 0.0563775 | ||||||||
\(73\) | 1.51241 | 0.177014 | 0.0885069 | − | 0.996076i | \(-0.471790\pi\) | ||||
0.0885069 | + | 0.996076i | \(0.471790\pi\) | |||||||
\(74\) | 0.0404087 | 0.00469741 | ||||||||
\(75\) | 1.99785 | 0.230692 | ||||||||
\(76\) | −0.0115070 | −0.00131995 | ||||||||
\(77\) | −4.99112 | −0.568791 | ||||||||
\(78\) | 0.129568 | 0.0146706 | ||||||||
\(79\) | 3.99546 | 0.449524 | 0.224762 | − | 0.974414i | \(-0.427839\pi\) | ||||
0.224762 | + | 0.974414i | \(0.427839\pi\) | |||||||
\(80\) | 6.78127 | 0.758169 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.285705 | −0.0315509 | ||||||||
\(83\) | −9.24882 | −1.01519 | −0.507595 | − | 0.861596i | \(-0.669465\pi\) | ||||
−0.507595 | + | 0.861596i | \(0.669465\pi\) | |||||||
\(84\) | 1.98559 | 0.216646 | ||||||||
\(85\) | −2.64372 | −0.286752 | ||||||||
\(86\) | −1.09433 | −0.118004 | ||||||||
\(87\) | −1.18505 | −0.127051 | ||||||||
\(88\) | −2.38765 | −0.254524 | ||||||||
\(89\) | −7.16310 | −0.759287 | −0.379644 | − | 0.925133i | \(-0.623953\pi\) | ||||
−0.379644 | + | 0.925133i | \(0.623953\pi\) | |||||||
\(90\) | −0.207967 | −0.0219217 | ||||||||
\(91\) | 1.07949 | 0.113161 | ||||||||
\(92\) | −14.0075 | −1.46038 | ||||||||
\(93\) | 6.26094 | 0.649230 | ||||||||
\(94\) | 0.913213 | 0.0941907 | ||||||||
\(95\) | 0.0100413 | 0.00103021 | ||||||||
\(96\) | 1.42652 | 0.145593 | ||||||||
\(97\) | 4.19603 | 0.426043 | 0.213021 | − | 0.977048i | \(-0.431670\pi\) | ||||
0.213021 | + | 0.977048i | \(0.431670\pi\) | |||||||
\(98\) | −0.120027 | −0.0121246 | ||||||||
\(99\) | −4.99112 | −0.501626 | ||||||||
\(100\) | 3.96692 | 0.396692 | ||||||||
\(101\) | 7.52131 | 0.748398 | 0.374199 | − | 0.927348i | \(-0.377918\pi\) | ||||
0.374199 | + | 0.927348i | \(0.377918\pi\) | |||||||
\(102\) | −0.183138 | −0.0181334 | ||||||||
\(103\) | 16.5673 | 1.63242 | 0.816212 | − | 0.577753i | \(-0.196070\pi\) | ||||
0.816212 | + | 0.577753i | \(0.196070\pi\) | |||||||
\(104\) | 0.516403 | 0.0506375 | ||||||||
\(105\) | −1.73267 | −0.169091 | ||||||||
\(106\) | 1.10579 | 0.107404 | ||||||||
\(107\) | −0.431970 | −0.0417601 | −0.0208800 | − | 0.999782i | \(-0.506647\pi\) | ||||
−0.0208800 | + | 0.999782i | \(0.506647\pi\) | |||||||
\(108\) | 1.98559 | 0.191064 | ||||||||
\(109\) | 14.3480 | 1.37429 | 0.687144 | − | 0.726521i | \(-0.258864\pi\) | ||||
0.687144 | + | 0.726521i | \(0.258864\pi\) | |||||||
\(110\) | 1.03799 | 0.0989684 | ||||||||
\(111\) | 0.336663 | 0.0319546 | ||||||||
\(112\) | 3.91377 | 0.369816 | ||||||||
\(113\) | 8.78452 | 0.826378 | 0.413189 | − | 0.910645i | \(-0.364415\pi\) | ||||
0.413189 | + | 0.910645i | \(0.364415\pi\) | |||||||
\(114\) | 0.000695587 0 | 6.51477e−5 0 | ||||||||
\(115\) | 12.2232 | 1.13982 | ||||||||
\(116\) | −2.35303 | −0.218473 | ||||||||
\(117\) | 1.07949 | 0.0997985 | ||||||||
\(118\) | −1.24704 | −0.114799 | ||||||||
\(119\) | −1.52581 | −0.139871 | ||||||||
\(120\) | −0.828873 | −0.0756654 | ||||||||
\(121\) | 13.9112 | 1.26466 | ||||||||
\(122\) | 0.202187 | 0.0183051 | ||||||||
\(123\) | −2.38034 | −0.214628 | ||||||||
\(124\) | 12.4317 | 1.11640 | ||||||||
\(125\) | −12.1250 | −1.08449 | ||||||||
\(126\) | −0.120027 | −0.0106929 | ||||||||
\(127\) | −11.9872 | −1.06369 | −0.531847 | − | 0.846840i | \(-0.678502\pi\) | ||||
−0.531847 | + | 0.846840i | \(0.678502\pi\) | |||||||
\(128\) | 3.77200 | 0.333401 | ||||||||
\(129\) | −9.11735 | −0.802738 | ||||||||
\(130\) | −0.224498 | −0.0196898 | ||||||||
\(131\) | −7.27404 | −0.635536 | −0.317768 | − | 0.948169i | \(-0.602933\pi\) | ||||
−0.317768 | + | 0.948169i | \(0.602933\pi\) | |||||||
\(132\) | −9.91033 | −0.862583 | ||||||||
\(133\) | 0.00579525 | 0.000502512 0 | ||||||||
\(134\) | −0.421744 | −0.0364331 | ||||||||
\(135\) | −1.73267 | −0.149125 | ||||||||
\(136\) | −0.729915 | −0.0625897 | ||||||||
\(137\) | 10.8734 | 0.928981 | 0.464491 | − | 0.885578i | \(-0.346237\pi\) | ||||
0.464491 | + | 0.885578i | \(0.346237\pi\) | |||||||
\(138\) | 0.846737 | 0.0720790 | ||||||||
\(139\) | −13.9991 | −1.18739 | −0.593693 | − | 0.804692i | \(-0.702331\pi\) | ||||
−0.593693 | + | 0.804692i | \(0.702331\pi\) | |||||||
\(140\) | −3.44038 | −0.290765 | ||||||||
\(141\) | 7.60839 | 0.640742 | ||||||||
\(142\) | 0.351308 | 0.0294811 | ||||||||
\(143\) | −5.38784 | −0.450554 | ||||||||
\(144\) | 3.91377 | 0.326147 | ||||||||
\(145\) | 2.05330 | 0.170518 | ||||||||
\(146\) | −0.181530 | −0.0150235 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0.668476 | 0.0549484 | ||||||||
\(149\) | −1.87263 | −0.153412 | −0.0767059 | − | 0.997054i | \(-0.524440\pi\) | ||||
−0.0767059 | + | 0.997054i | \(0.524440\pi\) | |||||||
\(150\) | −0.239796 | −0.0195793 | ||||||||
\(151\) | −10.9305 | −0.889514 | −0.444757 | − | 0.895651i | \(-0.646710\pi\) | ||||
−0.444757 | + | 0.895651i | \(0.646710\pi\) | |||||||
\(152\) | 0.00277233 | 0.000224865 0 | ||||||||
\(153\) | −1.52581 | −0.123354 | ||||||||
\(154\) | 0.599069 | 0.0482743 | ||||||||
\(155\) | −10.8482 | −0.871344 | ||||||||
\(156\) | 2.14342 | 0.171611 | ||||||||
\(157\) | 8.84714 | 0.706079 | 0.353039 | − | 0.935608i | \(-0.385148\pi\) | ||||
0.353039 | + | 0.935608i | \(0.385148\pi\) | |||||||
\(158\) | −0.479563 | −0.0381520 | ||||||||
\(159\) | 9.21286 | 0.730627 | ||||||||
\(160\) | −2.47168 | −0.195404 | ||||||||
\(161\) | 7.05455 | 0.555976 | ||||||||
\(162\) | −0.120027 | −0.00943021 | ||||||||
\(163\) | −3.83641 | −0.300491 | −0.150245 | − | 0.988649i | \(-0.548006\pi\) | ||||
−0.150245 | + | 0.988649i | \(0.548006\pi\) | |||||||
\(164\) | −4.72639 | −0.369069 | ||||||||
\(165\) | 8.64796 | 0.673243 | ||||||||
\(166\) | 1.11011 | 0.0861611 | ||||||||
\(167\) | −10.0104 | −0.774625 | −0.387312 | − | 0.921949i | \(-0.626596\pi\) | ||||
−0.387312 | + | 0.921949i | \(0.626596\pi\) | |||||||
\(168\) | −0.478379 | −0.0369077 | ||||||||
\(169\) | −11.8347 | −0.910362 | ||||||||
\(170\) | 0.317318 | 0.0243372 | ||||||||
\(171\) | 0.00579525 | 0.000443174 0 | ||||||||
\(172\) | −18.1033 | −1.38037 | ||||||||
\(173\) | 6.57865 | 0.500166 | 0.250083 | − | 0.968224i | \(-0.419542\pi\) | ||||
0.250083 | + | 0.968224i | \(0.419542\pi\) | |||||||
\(174\) | 0.142238 | 0.0107830 | ||||||||
\(175\) | −1.99785 | −0.151023 | ||||||||
\(176\) | −19.5341 | −1.47244 | ||||||||
\(177\) | −10.3896 | −0.780932 | ||||||||
\(178\) | 0.859766 | 0.0644422 | ||||||||
\(179\) | 5.55411 | 0.415134 | 0.207567 | − | 0.978221i | \(-0.433446\pi\) | ||||
0.207567 | + | 0.978221i | \(0.433446\pi\) | |||||||
\(180\) | −3.44038 | −0.256431 | ||||||||
\(181\) | −0.787899 | −0.0585641 | −0.0292820 | − | 0.999571i | \(-0.509322\pi\) | ||||
−0.0292820 | + | 0.999571i | \(0.509322\pi\) | |||||||
\(182\) | −0.129568 | −0.00960418 | ||||||||
\(183\) | 1.68451 | 0.124522 | ||||||||
\(184\) | 3.37475 | 0.248790 | ||||||||
\(185\) | −0.583326 | −0.0428870 | ||||||||
\(186\) | −0.751482 | −0.0551014 | ||||||||
\(187\) | 7.61549 | 0.556900 | ||||||||
\(188\) | 15.1072 | 1.10180 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −0.00120522 | −8.74361e−5 0 | ||||||||
\(191\) | 26.8943 | 1.94601 | 0.973003 | − | 0.230791i | \(-0.0741313\pi\) | ||||
0.973003 | + | 0.230791i | \(0.0741313\pi\) | |||||||
\(192\) | 7.65632 | 0.552547 | ||||||||
\(193\) | 4.32077 | 0.311016 | 0.155508 | − | 0.987835i | \(-0.450299\pi\) | ||||
0.155508 | + | 0.987835i | \(0.450299\pi\) | |||||||
\(194\) | −0.503637 | −0.0361591 | ||||||||
\(195\) | −1.87039 | −0.133942 | ||||||||
\(196\) | −1.98559 | −0.141828 | ||||||||
\(197\) | −1.36194 | −0.0970339 | −0.0485169 | − | 0.998822i | \(-0.515449\pi\) | ||||
−0.0485169 | + | 0.998822i | \(0.515449\pi\) | |||||||
\(198\) | 0.599069 | 0.0425740 | ||||||||
\(199\) | −13.8600 | −0.982507 | −0.491254 | − | 0.871017i | \(-0.663461\pi\) | ||||
−0.491254 | + | 0.871017i | \(0.663461\pi\) | |||||||
\(200\) | −0.955731 | −0.0675804 | ||||||||
\(201\) | −3.51374 | −0.247840 | ||||||||
\(202\) | −0.902760 | −0.0635180 | ||||||||
\(203\) | 1.18505 | 0.0831743 | ||||||||
\(204\) | −3.02964 | −0.212117 | ||||||||
\(205\) | 4.12435 | 0.288057 | ||||||||
\(206\) | −1.98852 | −0.138547 | ||||||||
\(207\) | 7.05455 | 0.490325 | ||||||||
\(208\) | 4.22486 | 0.292941 | ||||||||
\(209\) | −0.0289248 | −0.00200077 | ||||||||
\(210\) | 0.207967 | 0.0143511 | ||||||||
\(211\) | −2.02882 | −0.139670 | −0.0698349 | − | 0.997559i | \(-0.522247\pi\) | ||||
−0.0698349 | + | 0.997559i | \(0.522247\pi\) | |||||||
\(212\) | 18.2930 | 1.25637 | ||||||||
\(213\) | 2.92691 | 0.200548 | ||||||||
\(214\) | 0.0518481 | 0.00354426 | ||||||||
\(215\) | 15.7974 | 1.07737 | ||||||||
\(216\) | −0.478379 | −0.0325496 | ||||||||
\(217\) | −6.26094 | −0.425020 | ||||||||
\(218\) | −1.72215 | −0.116638 | ||||||||
\(219\) | −1.51241 | −0.102199 | ||||||||
\(220\) | 17.1713 | 1.15769 | ||||||||
\(221\) | −1.64709 | −0.110795 | ||||||||
\(222\) | −0.0404087 | −0.00271205 | ||||||||
\(223\) | 15.2233 | 1.01943 | 0.509714 | − | 0.860344i | \(-0.329751\pi\) | ||||
0.509714 | + | 0.860344i | \(0.329751\pi\) | |||||||
\(224\) | −1.42652 | −0.0953131 | ||||||||
\(225\) | −1.99785 | −0.133190 | ||||||||
\(226\) | −1.05438 | −0.0701363 | ||||||||
\(227\) | −7.35715 | −0.488311 | −0.244156 | − | 0.969736i | \(-0.578511\pi\) | ||||
−0.244156 | + | 0.969736i | \(0.578511\pi\) | |||||||
\(228\) | 0.0115070 | 0.000762071 0 | ||||||||
\(229\) | −0.521614 | −0.0344693 | −0.0172346 | − | 0.999851i | \(-0.505486\pi\) | ||||
−0.0172346 | + | 0.999851i | \(0.505486\pi\) | |||||||
\(230\) | −1.46712 | −0.0967387 | ||||||||
\(231\) | 4.99112 | 0.328391 | ||||||||
\(232\) | 0.566904 | 0.0372190 | ||||||||
\(233\) | 7.30939 | 0.478854 | 0.239427 | − | 0.970914i | \(-0.423040\pi\) | ||||
0.239427 | + | 0.970914i | \(0.423040\pi\) | |||||||
\(234\) | −0.129568 | −0.00847009 | ||||||||
\(235\) | −13.1828 | −0.859953 | ||||||||
\(236\) | −20.6296 | −1.34287 | ||||||||
\(237\) | −3.99546 | −0.259533 | ||||||||
\(238\) | 0.183138 | 0.0118711 | ||||||||
\(239\) | 18.2355 | 1.17956 | 0.589779 | − | 0.807564i | \(-0.299215\pi\) | ||||
0.589779 | + | 0.807564i | \(0.299215\pi\) | |||||||
\(240\) | −6.78127 | −0.437729 | ||||||||
\(241\) | −12.0047 | −0.773292 | −0.386646 | − | 0.922228i | \(-0.626366\pi\) | ||||
−0.386646 | + | 0.922228i | \(0.626366\pi\) | |||||||
\(242\) | −1.66973 | −0.107334 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.34475 | 0.214126 | ||||||||
\(245\) | 1.73267 | 0.110696 | ||||||||
\(246\) | 0.285705 | 0.0182159 | ||||||||
\(247\) | 0.00625590 | 0.000398053 0 | ||||||||
\(248\) | −2.99510 | −0.190189 | ||||||||
\(249\) | 9.24882 | 0.586120 | ||||||||
\(250\) | 1.45532 | 0.0920428 | ||||||||
\(251\) | 19.1802 | 1.21064 | 0.605322 | − | 0.795981i | \(-0.293044\pi\) | ||||
0.605322 | + | 0.795981i | \(0.293044\pi\) | |||||||
\(252\) | −1.98559 | −0.125081 | ||||||||
\(253\) | −35.2101 | −2.21364 | ||||||||
\(254\) | 1.43879 | 0.0902778 | ||||||||
\(255\) | 2.64372 | 0.165556 | ||||||||
\(256\) | 14.8599 | 0.928743 | ||||||||
\(257\) | −1.76135 | −0.109870 | −0.0549349 | − | 0.998490i | \(-0.517495\pi\) | ||||
−0.0549349 | + | 0.998490i | \(0.517495\pi\) | |||||||
\(258\) | 1.09433 | 0.0681299 | ||||||||
\(259\) | −0.336663 | −0.0209192 | ||||||||
\(260\) | −3.71384 | −0.230323 | ||||||||
\(261\) | 1.18505 | 0.0733528 | ||||||||
\(262\) | 0.873081 | 0.0539391 | ||||||||
\(263\) | −24.3387 | −1.50079 | −0.750395 | − | 0.660990i | \(-0.770137\pi\) | ||||
−0.750395 | + | 0.660990i | \(0.770137\pi\) | |||||||
\(264\) | 2.38765 | 0.146949 | ||||||||
\(265\) | −15.9628 | −0.980590 | ||||||||
\(266\) | −0.000695587 0 | −4.26492e−5 0 | ||||||||
\(267\) | 7.16310 | 0.438375 | ||||||||
\(268\) | −6.97686 | −0.426179 | ||||||||
\(269\) | 11.8401 | 0.721904 | 0.360952 | − | 0.932584i | \(-0.382452\pi\) | ||||
0.360952 | + | 0.932584i | \(0.382452\pi\) | |||||||
\(270\) | 0.207967 | 0.0126565 | ||||||||
\(271\) | 23.8145 | 1.44663 | 0.723313 | − | 0.690521i | \(-0.242619\pi\) | ||||
0.723313 | + | 0.690521i | \(0.242619\pi\) | |||||||
\(272\) | −5.97166 | −0.362085 | ||||||||
\(273\) | −1.07949 | −0.0653335 | ||||||||
\(274\) | −1.30511 | −0.0788444 | ||||||||
\(275\) | 9.97152 | 0.601305 | ||||||||
\(276\) | 14.0075 | 0.843150 | ||||||||
\(277\) | 5.40217 | 0.324585 | 0.162293 | − | 0.986743i | \(-0.448111\pi\) | ||||
0.162293 | + | 0.986743i | \(0.448111\pi\) | |||||||
\(278\) | 1.68027 | 0.100776 | ||||||||
\(279\) | −6.26094 | −0.374833 | ||||||||
\(280\) | 0.828873 | 0.0495346 | ||||||||
\(281\) | −1.04357 | −0.0622540 | −0.0311270 | − | 0.999515i | \(-0.509910\pi\) | ||||
−0.0311270 | + | 0.999515i | \(0.509910\pi\) | |||||||
\(282\) | −0.913213 | −0.0543810 | ||||||||
\(283\) | −10.3751 | −0.616737 | −0.308369 | − | 0.951267i | \(-0.599783\pi\) | ||||
−0.308369 | + | 0.951267i | \(0.599783\pi\) | |||||||
\(284\) | 5.81165 | 0.344858 | ||||||||
\(285\) | −0.0100413 | −0.000594793 0 | ||||||||
\(286\) | 0.646687 | 0.0382394 | ||||||||
\(287\) | 2.38034 | 0.140507 | ||||||||
\(288\) | −1.42652 | −0.0840583 | ||||||||
\(289\) | −14.6719 | −0.863053 | ||||||||
\(290\) | −0.246452 | −0.0144722 | ||||||||
\(291\) | −4.19603 | −0.245976 | ||||||||
\(292\) | −3.00302 | −0.175739 | ||||||||
\(293\) | 22.2229 | 1.29827 | 0.649137 | − | 0.760672i | \(-0.275130\pi\) | ||||
0.649137 | + | 0.760672i | \(0.275130\pi\) | |||||||
\(294\) | 0.120027 | 0.00700012 | ||||||||
\(295\) | 18.0018 | 1.04810 | ||||||||
\(296\) | −0.161053 | −0.00936099 | ||||||||
\(297\) | 4.99112 | 0.289614 | ||||||||
\(298\) | 0.224766 | 0.0130204 | ||||||||
\(299\) | 7.61529 | 0.440403 | ||||||||
\(300\) | −3.96692 | −0.229030 | ||||||||
\(301\) | 9.11735 | 0.525515 | ||||||||
\(302\) | 1.31196 | 0.0754947 | ||||||||
\(303\) | −7.52131 | −0.432088 | ||||||||
\(304\) | 0.0226813 | 0.00130086 | ||||||||
\(305\) | −2.91870 | −0.167124 | ||||||||
\(306\) | 0.183138 | 0.0104693 | ||||||||
\(307\) | 3.21540 | 0.183513 | 0.0917563 | − | 0.995781i | \(-0.470752\pi\) | ||||
0.0917563 | + | 0.995781i | \(0.470752\pi\) | |||||||
\(308\) | 9.91033 | 0.564693 | ||||||||
\(309\) | −16.5673 | −0.942480 | ||||||||
\(310\) | 1.30207 | 0.0739527 | ||||||||
\(311\) | 5.36542 | 0.304245 | 0.152123 | − | 0.988362i | \(-0.451389\pi\) | ||||
0.152123 | + | 0.988362i | \(0.451389\pi\) | |||||||
\(312\) | −0.516403 | −0.0292356 | ||||||||
\(313\) | 22.7716 | 1.28713 | 0.643563 | − | 0.765393i | \(-0.277456\pi\) | ||||
0.643563 | + | 0.765393i | \(0.277456\pi\) | |||||||
\(314\) | −1.06190 | −0.0599263 | ||||||||
\(315\) | 1.73267 | 0.0976249 | ||||||||
\(316\) | −7.93336 | −0.446286 | ||||||||
\(317\) | −10.8058 | −0.606916 | −0.303458 | − | 0.952845i | \(-0.598141\pi\) | ||||
−0.303458 | + | 0.952845i | \(0.598141\pi\) | |||||||
\(318\) | −1.10579 | −0.0620097 | ||||||||
\(319\) | −5.91473 | −0.331161 | ||||||||
\(320\) | −13.2659 | −0.741585 | ||||||||
\(321\) | 0.431970 | 0.0241102 | ||||||||
\(322\) | −0.846737 | −0.0471868 | ||||||||
\(323\) | −0.00884245 | −0.000492007 0 | ||||||||
\(324\) | −1.98559 | −0.110311 | ||||||||
\(325\) | −2.15665 | −0.119630 | ||||||||
\(326\) | 0.460473 | 0.0255032 | ||||||||
\(327\) | −14.3480 | −0.793446 | ||||||||
\(328\) | 1.13871 | 0.0628745 | ||||||||
\(329\) | −7.60839 | −0.419464 | ||||||||
\(330\) | −1.03799 | −0.0571394 | ||||||||
\(331\) | 25.7589 | 1.41584 | 0.707918 | − | 0.706295i | \(-0.249635\pi\) | ||||
0.707918 | + | 0.706295i | \(0.249635\pi\) | |||||||
\(332\) | 18.3644 | 1.00788 | ||||||||
\(333\) | −0.336663 | −0.0184490 | ||||||||
\(334\) | 1.20151 | 0.0657439 | ||||||||
\(335\) | 6.08815 | 0.332631 | ||||||||
\(336\) | −3.91377 | −0.213514 | ||||||||
\(337\) | 3.94021 | 0.214637 | 0.107318 | − | 0.994225i | \(-0.465774\pi\) | ||||
0.107318 | + | 0.994225i | \(0.465774\pi\) | |||||||
\(338\) | 1.42049 | 0.0772642 | ||||||||
\(339\) | −8.78452 | −0.477110 | ||||||||
\(340\) | 5.24936 | 0.284687 | ||||||||
\(341\) | 31.2491 | 1.69223 | ||||||||
\(342\) | −0.000695587 0 | −3.76130e−5 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.36155 | 0.235159 | ||||||||
\(345\) | −12.2232 | −0.658075 | ||||||||
\(346\) | −0.789616 | −0.0424500 | ||||||||
\(347\) | −29.1493 | −1.56482 | −0.782408 | − | 0.622766i | \(-0.786009\pi\) | ||||
−0.782408 | + | 0.622766i | \(0.786009\pi\) | |||||||
\(348\) | 2.35303 | 0.126136 | ||||||||
\(349\) | 28.0215 | 1.49996 | 0.749979 | − | 0.661462i | \(-0.230064\pi\) | ||||
0.749979 | + | 0.661462i | \(0.230064\pi\) | |||||||
\(350\) | 0.239796 | 0.0128177 | ||||||||
\(351\) | −1.07949 | −0.0576187 | ||||||||
\(352\) | 7.11991 | 0.379492 | ||||||||
\(353\) | 5.79656 | 0.308520 | 0.154260 | − | 0.988030i | \(-0.450701\pi\) | ||||
0.154260 | + | 0.988030i | \(0.450701\pi\) | |||||||
\(354\) | 1.24704 | 0.0662792 | ||||||||
\(355\) | −5.07136 | −0.269160 | ||||||||
\(356\) | 14.2230 | 0.753818 | ||||||||
\(357\) | 1.52581 | 0.0807544 | ||||||||
\(358\) | −0.666644 | −0.0352332 | ||||||||
\(359\) | −11.2440 | −0.593434 | −0.296717 | − | 0.954965i | \(-0.595892\pi\) | ||||
−0.296717 | + | 0.954965i | \(0.595892\pi\) | |||||||
\(360\) | 0.828873 | 0.0436854 | ||||||||
\(361\) | −19.0000 | −0.999998 | ||||||||
\(362\) | 0.0945692 | 0.00497045 | ||||||||
\(363\) | −13.9112 | −0.730151 | ||||||||
\(364\) | −2.14342 | −0.112346 | ||||||||
\(365\) | 2.62050 | 0.137163 | ||||||||
\(366\) | −0.202187 | −0.0105685 | ||||||||
\(367\) | 32.0013 | 1.67045 | 0.835226 | − | 0.549906i | \(-0.185337\pi\) | ||||
0.835226 | + | 0.549906i | \(0.185337\pi\) | |||||||
\(368\) | 27.6099 | 1.43926 | ||||||||
\(369\) | 2.38034 | 0.123916 | ||||||||
\(370\) | 0.0700149 | 0.00363990 | ||||||||
\(371\) | −9.21286 | −0.478308 | ||||||||
\(372\) | −12.4317 | −0.644553 | ||||||||
\(373\) | 29.7796 | 1.54193 | 0.770964 | − | 0.636878i | \(-0.219775\pi\) | ||||
0.770964 | + | 0.636878i | \(0.219775\pi\) | |||||||
\(374\) | −0.914065 | −0.0472652 | ||||||||
\(375\) | 12.1250 | 0.626131 | ||||||||
\(376\) | −3.63969 | −0.187703 | ||||||||
\(377\) | 1.27925 | 0.0658845 | ||||||||
\(378\) | 0.120027 | 0.00617352 | ||||||||
\(379\) | −9.67410 | −0.496925 | −0.248463 | − | 0.968641i | \(-0.579925\pi\) | ||||
−0.248463 | + | 0.968641i | \(0.579925\pi\) | |||||||
\(380\) | −0.0199379 | −0.00102279 | ||||||||
\(381\) | 11.9872 | 0.614124 | ||||||||
\(382\) | −3.22805 | −0.165161 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | −3.77200 | −0.192489 | ||||||||
\(385\) | −8.64796 | −0.440741 | ||||||||
\(386\) | −0.518610 | −0.0263965 | ||||||||
\(387\) | 9.11735 | 0.463461 | ||||||||
\(388\) | −8.33162 | −0.422974 | ||||||||
\(389\) | 30.3305 | 1.53782 | 0.768910 | − | 0.639357i | \(-0.220800\pi\) | ||||
0.768910 | + | 0.639357i | \(0.220800\pi\) | |||||||
\(390\) | 0.224498 | 0.0113679 | ||||||||
\(391\) | −10.7639 | −0.544353 | ||||||||
\(392\) | 0.478379 | 0.0241618 | ||||||||
\(393\) | 7.27404 | 0.366927 | ||||||||
\(394\) | 0.163469 | 0.00823545 | ||||||||
\(395\) | 6.92282 | 0.348325 | ||||||||
\(396\) | 9.91033 | 0.498013 | ||||||||
\(397\) | 3.03220 | 0.152182 | 0.0760909 | − | 0.997101i | \(-0.475756\pi\) | ||||
0.0760909 | + | 0.997101i | \(0.475756\pi\) | |||||||
\(398\) | 1.66357 | 0.0833873 | ||||||||
\(399\) | −0.00579525 | −0.000290126 0 | ||||||||
\(400\) | −7.81913 | −0.390957 | ||||||||
\(401\) | 5.36053 | 0.267692 | 0.133846 | − | 0.991002i | \(-0.457267\pi\) | ||||
0.133846 | + | 0.991002i | \(0.457267\pi\) | |||||||
\(402\) | 0.421744 | 0.0210347 | ||||||||
\(403\) | −6.75860 | −0.336670 | ||||||||
\(404\) | −14.9343 | −0.743007 | ||||||||
\(405\) | 1.73267 | 0.0860971 | ||||||||
\(406\) | −0.142238 | −0.00705916 | ||||||||
\(407\) | 1.68032 | 0.0832906 | ||||||||
\(408\) | 0.729915 | 0.0361362 | ||||||||
\(409\) | 19.6850 | 0.973363 | 0.486681 | − | 0.873580i | \(-0.338207\pi\) | ||||
0.486681 | + | 0.873580i | \(0.338207\pi\) | |||||||
\(410\) | −0.495033 | −0.0244480 | ||||||||
\(411\) | −10.8734 | −0.536347 | ||||||||
\(412\) | −32.8959 | −1.62066 | ||||||||
\(413\) | 10.3896 | 0.511240 | ||||||||
\(414\) | −0.846737 | −0.0416148 | ||||||||
\(415\) | −16.0252 | −0.786644 | ||||||||
\(416\) | −1.53990 | −0.0755000 | ||||||||
\(417\) | 13.9991 | 0.685537 | ||||||||
\(418\) | 0.00347176 | 0.000169809 0 | ||||||||
\(419\) | 7.02090 | 0.342993 | 0.171497 | − | 0.985185i | \(-0.445140\pi\) | ||||
0.171497 | + | 0.985185i | \(0.445140\pi\) | |||||||
\(420\) | 3.44038 | 0.167873 | ||||||||
\(421\) | 16.8381 | 0.820641 | 0.410320 | − | 0.911941i | \(-0.365417\pi\) | ||||
0.410320 | + | 0.911941i | \(0.365417\pi\) | |||||||
\(422\) | 0.243513 | 0.0118540 | ||||||||
\(423\) | −7.60839 | −0.369933 | ||||||||
\(424\) | −4.40724 | −0.214034 | ||||||||
\(425\) | 3.04834 | 0.147866 | ||||||||
\(426\) | −0.351308 | −0.0170209 | ||||||||
\(427\) | −1.68451 | −0.0815191 | ||||||||
\(428\) | 0.857716 | 0.0414593 | ||||||||
\(429\) | 5.38784 | 0.260127 | ||||||||
\(430\) | −1.89611 | −0.0914386 | ||||||||
\(431\) | −14.7959 | −0.712691 | −0.356346 | − | 0.934354i | \(-0.615977\pi\) | ||||
−0.356346 | + | 0.934354i | \(0.615977\pi\) | |||||||
\(432\) | −3.91377 | −0.188301 | ||||||||
\(433\) | 8.66002 | 0.416174 | 0.208087 | − | 0.978110i | \(-0.433276\pi\) | ||||
0.208087 | + | 0.978110i | \(0.433276\pi\) | |||||||
\(434\) | 0.751482 | 0.0360723 | ||||||||
\(435\) | −2.05330 | −0.0984484 | ||||||||
\(436\) | −28.4893 | −1.36439 | ||||||||
\(437\) | 0.0408829 | 0.00195569 | ||||||||
\(438\) | 0.181530 | 0.00867382 | ||||||||
\(439\) | 10.9857 | 0.524317 | 0.262159 | − | 0.965025i | \(-0.415566\pi\) | ||||
0.262159 | + | 0.965025i | \(0.415566\pi\) | |||||||
\(440\) | −4.13700 | −0.197224 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0.197695 | 0.00940340 | ||||||||
\(443\) | −23.6676 | −1.12448 | −0.562241 | − | 0.826974i | \(-0.690060\pi\) | ||||
−0.562241 | + | 0.826974i | \(0.690060\pi\) | |||||||
\(444\) | −0.668476 | −0.0317245 | ||||||||
\(445\) | −12.4113 | −0.588352 | ||||||||
\(446\) | −1.82721 | −0.0865208 | ||||||||
\(447\) | 1.87263 | 0.0885723 | ||||||||
\(448\) | −7.65632 | −0.361727 | ||||||||
\(449\) | 28.8511 | 1.36157 | 0.680784 | − | 0.732484i | \(-0.261639\pi\) | ||||
0.680784 | + | 0.732484i | \(0.261639\pi\) | |||||||
\(450\) | 0.239796 | 0.0113041 | ||||||||
\(451\) | −11.8806 | −0.559434 | ||||||||
\(452\) | −17.4425 | −0.820425 | ||||||||
\(453\) | 10.9305 | 0.513561 | ||||||||
\(454\) | 0.883057 | 0.0414439 | ||||||||
\(455\) | 1.87039 | 0.0876854 | ||||||||
\(456\) | −0.00277233 | −0.000129826 0 | ||||||||
\(457\) | 28.2758 | 1.32269 | 0.661344 | − | 0.750083i | \(-0.269987\pi\) | ||||
0.661344 | + | 0.750083i | \(0.269987\pi\) | |||||||
\(458\) | 0.0626078 | 0.00292547 | ||||||||
\(459\) | 1.52581 | 0.0712186 | ||||||||
\(460\) | −24.2703 | −1.13161 | ||||||||
\(461\) | 2.02729 | 0.0944205 | 0.0472102 | − | 0.998885i | \(-0.484967\pi\) | ||||
0.0472102 | + | 0.998885i | \(0.484967\pi\) | |||||||
\(462\) | −0.599069 | −0.0278712 | ||||||||
\(463\) | −16.2149 | −0.753568 | −0.376784 | − | 0.926301i | \(-0.622970\pi\) | ||||
−0.376784 | + | 0.926301i | \(0.622970\pi\) | |||||||
\(464\) | 4.63802 | 0.215315 | ||||||||
\(465\) | 10.8482 | 0.503071 | ||||||||
\(466\) | −0.877324 | −0.0406412 | ||||||||
\(467\) | 7.84438 | 0.362995 | 0.181497 | − | 0.983391i | \(-0.441906\pi\) | ||||
0.181497 | + | 0.983391i | \(0.441906\pi\) | |||||||
\(468\) | −2.14342 | −0.0990797 | ||||||||
\(469\) | 3.51374 | 0.162249 | ||||||||
\(470\) | 1.58230 | 0.0729859 | ||||||||
\(471\) | −8.84714 | −0.407655 | ||||||||
\(472\) | 4.97018 | 0.228771 | ||||||||
\(473\) | −45.5058 | −2.09236 | ||||||||
\(474\) | 0.479563 | 0.0220271 | ||||||||
\(475\) | −0.0115781 | −0.000531238 0 | ||||||||
\(476\) | 3.02964 | 0.138863 | ||||||||
\(477\) | −9.21286 | −0.421828 | ||||||||
\(478\) | −2.18876 | −0.100111 | ||||||||
\(479\) | −8.98025 | −0.410318 | −0.205159 | − | 0.978729i | \(-0.565771\pi\) | ||||
−0.205159 | + | 0.978729i | \(0.565771\pi\) | |||||||
\(480\) | 2.47168 | 0.112816 | ||||||||
\(481\) | −0.363423 | −0.0165707 | ||||||||
\(482\) | 1.44089 | 0.0656308 | ||||||||
\(483\) | −7.05455 | −0.320993 | ||||||||
\(484\) | −27.6221 | −1.25555 | ||||||||
\(485\) | 7.27034 | 0.330129 | ||||||||
\(486\) | 0.120027 | 0.00544454 | ||||||||
\(487\) | −5.69157 | −0.257909 | −0.128955 | − | 0.991650i | \(-0.541162\pi\) | ||||
−0.128955 | + | 0.991650i | \(0.541162\pi\) | |||||||
\(488\) | −0.805833 | −0.0364784 | ||||||||
\(489\) | 3.83641 | 0.173488 | ||||||||
\(490\) | −0.207967 | −0.00939500 | ||||||||
\(491\) | 18.5466 | 0.836996 | 0.418498 | − | 0.908218i | \(-0.362557\pi\) | ||||
0.418498 | + | 0.908218i | \(0.362557\pi\) | |||||||
\(492\) | 4.72639 | 0.213082 | ||||||||
\(493\) | −1.80816 | −0.0814355 | ||||||||
\(494\) | −0.000750877 0 | −3.37835e−5 0 | ||||||||
\(495\) | −8.64796 | −0.388697 | ||||||||
\(496\) | −24.5039 | −1.10026 | ||||||||
\(497\) | −2.92691 | −0.131290 | ||||||||
\(498\) | −1.11011 | −0.0497452 | ||||||||
\(499\) | 6.95469 | 0.311335 | 0.155667 | − | 0.987810i | \(-0.450247\pi\) | ||||
0.155667 | + | 0.987810i | \(0.450247\pi\) | |||||||
\(500\) | 24.0753 | 1.07668 | ||||||||
\(501\) | 10.0104 | 0.447230 | ||||||||
\(502\) | −2.30214 | −0.102750 | ||||||||
\(503\) | 31.4094 | 1.40048 | 0.700238 | − | 0.713910i | \(-0.253077\pi\) | ||||
0.700238 | + | 0.713910i | \(0.253077\pi\) | |||||||
\(504\) | 0.478379 | 0.0213087 | ||||||||
\(505\) | 13.0319 | 0.579914 | ||||||||
\(506\) | 4.22616 | 0.187876 | ||||||||
\(507\) | 11.8347 | 0.525598 | ||||||||
\(508\) | 23.8018 | 1.05603 | ||||||||
\(509\) | 20.3220 | 0.900755 | 0.450378 | − | 0.892838i | \(-0.351289\pi\) | ||||
0.450378 | + | 0.892838i | \(0.351289\pi\) | |||||||
\(510\) | −0.317318 | −0.0140511 | ||||||||
\(511\) | 1.51241 | 0.0669049 | ||||||||
\(512\) | −9.32758 | −0.412225 | ||||||||
\(513\) | −0.00579525 | −0.000255867 0 | ||||||||
\(514\) | 0.211409 | 0.00932486 | ||||||||
\(515\) | 28.7056 | 1.26492 | ||||||||
\(516\) | 18.1033 | 0.796955 | ||||||||
\(517\) | 37.9744 | 1.67011 | ||||||||
\(518\) | 0.0404087 | 0.00177546 | ||||||||
\(519\) | −6.57865 | −0.288771 | ||||||||
\(520\) | 0.894757 | 0.0392377 | ||||||||
\(521\) | 13.6375 | 0.597471 | 0.298736 | − | 0.954336i | \(-0.403435\pi\) | ||||
0.298736 | + | 0.954336i | \(0.403435\pi\) | |||||||
\(522\) | −0.142238 | −0.00622560 | ||||||||
\(523\) | −16.4548 | −0.719519 | −0.359760 | − | 0.933045i | \(-0.617141\pi\) | ||||
−0.359760 | + | 0.933045i | \(0.617141\pi\) | |||||||
\(524\) | 14.4433 | 0.630958 | ||||||||
\(525\) | 1.99785 | 0.0871934 | ||||||||
\(526\) | 2.92130 | 0.127375 | ||||||||
\(527\) | 9.55300 | 0.416135 | ||||||||
\(528\) | 19.5341 | 0.850112 | ||||||||
\(529\) | 26.7667 | 1.16377 | ||||||||
\(530\) | 1.91597 | 0.0832245 | ||||||||
\(531\) | 10.3896 | 0.450871 | ||||||||
\(532\) | −0.0115070 | −0.000498892 0 | ||||||||
\(533\) | 2.56955 | 0.111299 | ||||||||
\(534\) | −0.859766 | −0.0372057 | ||||||||
\(535\) | −0.748461 | −0.0323588 | ||||||||
\(536\) | 1.68090 | 0.0726038 | ||||||||
\(537\) | −5.55411 | −0.239678 | ||||||||
\(538\) | −1.42113 | −0.0612693 | ||||||||
\(539\) | −4.99112 | −0.214983 | ||||||||
\(540\) | 3.44038 | 0.148050 | ||||||||
\(541\) | 29.7250 | 1.27798 | 0.638990 | − | 0.769215i | \(-0.279353\pi\) | ||||
0.638990 | + | 0.769215i | \(0.279353\pi\) | |||||||
\(542\) | −2.85838 | −0.122778 | ||||||||
\(543\) | 0.787899 | 0.0338120 | ||||||||
\(544\) | 2.17659 | 0.0933205 | ||||||||
\(545\) | 24.8603 | 1.06490 | ||||||||
\(546\) | 0.129568 | 0.00554498 | ||||||||
\(547\) | −27.5504 | −1.17797 | −0.588984 | − | 0.808144i | \(-0.700472\pi\) | ||||
−0.588984 | + | 0.808144i | \(0.700472\pi\) | |||||||
\(548\) | −21.5902 | −0.922289 | ||||||||
\(549\) | −1.68451 | −0.0718931 | ||||||||
\(550\) | −1.19685 | −0.0510339 | ||||||||
\(551\) | 0.00686767 | 0.000292573 0 | ||||||||
\(552\) | −3.37475 | −0.143639 | ||||||||
\(553\) | 3.99546 | 0.169904 | ||||||||
\(554\) | −0.648407 | −0.0275482 | ||||||||
\(555\) | 0.583326 | 0.0247608 | ||||||||
\(556\) | 27.7965 | 1.17883 | ||||||||
\(557\) | 26.0151 | 1.10229 | 0.551147 | − | 0.834408i | \(-0.314190\pi\) | ||||
0.551147 | + | 0.834408i | \(0.314190\pi\) | |||||||
\(558\) | 0.751482 | 0.0318128 | ||||||||
\(559\) | 9.84205 | 0.416274 | ||||||||
\(560\) | 6.78127 | 0.286561 | ||||||||
\(561\) | −7.61549 | −0.321526 | ||||||||
\(562\) | 0.125256 | 0.00528361 | ||||||||
\(563\) | −25.3919 | −1.07014 | −0.535071 | − | 0.844807i | \(-0.679715\pi\) | ||||
−0.535071 | + | 0.844807i | \(0.679715\pi\) | |||||||
\(564\) | −15.1072 | −0.636127 | ||||||||
\(565\) | 15.2207 | 0.640339 | ||||||||
\(566\) | 1.24530 | 0.0523437 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −1.40017 | −0.0587498 | ||||||||
\(569\) | 37.0776 | 1.55437 | 0.777187 | − | 0.629269i | \(-0.216646\pi\) | ||||
0.777187 | + | 0.629269i | \(0.216646\pi\) | |||||||
\(570\) | 0.00120522 | 5.04812e−5 0 | ||||||||
\(571\) | 20.0764 | 0.840169 | 0.420085 | − | 0.907485i | \(-0.362000\pi\) | ||||
0.420085 | + | 0.907485i | \(0.362000\pi\) | |||||||
\(572\) | 10.6981 | 0.447309 | ||||||||
\(573\) | −26.8943 | −1.12353 | ||||||||
\(574\) | −0.285705 | −0.0119251 | ||||||||
\(575\) | −14.0940 | −0.587758 | ||||||||
\(576\) | −7.65632 | −0.319013 | ||||||||
\(577\) | 37.6452 | 1.56719 | 0.783595 | − | 0.621272i | \(-0.213384\pi\) | ||||
0.783595 | + | 0.621272i | \(0.213384\pi\) | |||||||
\(578\) | 1.76103 | 0.0732490 | ||||||||
\(579\) | −4.32077 | −0.179565 | ||||||||
\(580\) | −4.07703 | −0.169289 | ||||||||
\(581\) | −9.24882 | −0.383706 | ||||||||
\(582\) | 0.503637 | 0.0208764 | ||||||||
\(583\) | 45.9824 | 1.90440 | ||||||||
\(584\) | 0.723503 | 0.0299388 | ||||||||
\(585\) | 1.87039 | 0.0773313 | ||||||||
\(586\) | −2.66734 | −0.110187 | ||||||||
\(587\) | −1.07341 | −0.0443044 | −0.0221522 | − | 0.999755i | \(-0.507052\pi\) | ||||
−0.0221522 | + | 0.999755i | \(0.507052\pi\) | |||||||
\(588\) | 1.98559 | 0.0818845 | ||||||||
\(589\) | −0.0362837 | −0.00149505 | ||||||||
\(590\) | −2.16070 | −0.0889547 | ||||||||
\(591\) | 1.36194 | 0.0560225 | ||||||||
\(592\) | −1.31762 | −0.0541539 | ||||||||
\(593\) | 22.5860 | 0.927497 | 0.463749 | − | 0.885967i | \(-0.346504\pi\) | ||||
0.463749 | + | 0.885967i | \(0.346504\pi\) | |||||||
\(594\) | −0.599069 | −0.0245801 | ||||||||
\(595\) | −2.64372 | −0.108382 | ||||||||
\(596\) | 3.71828 | 0.152307 | ||||||||
\(597\) | 13.8600 | 0.567251 | ||||||||
\(598\) | −0.914040 | −0.0373779 | ||||||||
\(599\) | 35.0987 | 1.43409 | 0.717047 | − | 0.697025i | \(-0.245493\pi\) | ||||
0.717047 | + | 0.697025i | \(0.245493\pi\) | |||||||
\(600\) | 0.955731 | 0.0390175 | ||||||||
\(601\) | 37.6565 | 1.53604 | 0.768020 | − | 0.640426i | \(-0.221242\pi\) | ||||
0.768020 | + | 0.640426i | \(0.221242\pi\) | |||||||
\(602\) | −1.09433 | −0.0446015 | ||||||||
\(603\) | 3.51374 | 0.143091 | ||||||||
\(604\) | 21.7036 | 0.883106 | ||||||||
\(605\) | 24.1036 | 0.979951 | ||||||||
\(606\) | 0.902760 | 0.0366721 | ||||||||
\(607\) | −31.0322 | −1.25956 | −0.629779 | − | 0.776774i | \(-0.716855\pi\) | ||||
−0.629779 | + | 0.776774i | \(0.716855\pi\) | |||||||
\(608\) | −0.00826702 | −0.000335272 0 | ||||||||
\(609\) | −1.18505 | −0.0480207 | ||||||||
\(610\) | 0.350323 | 0.0141841 | ||||||||
\(611\) | −8.21315 | −0.332269 | ||||||||
\(612\) | 3.02964 | 0.122466 | ||||||||
\(613\) | −2.88519 | −0.116532 | −0.0582658 | − | 0.998301i | \(-0.518557\pi\) | ||||
−0.0582658 | + | 0.998301i | \(0.518557\pi\) | |||||||
\(614\) | −0.385935 | −0.0155751 | ||||||||
\(615\) | −4.12435 | −0.166310 | ||||||||
\(616\) | −2.38765 | −0.0962010 | ||||||||
\(617\) | −26.7012 | −1.07495 | −0.537474 | − | 0.843280i | \(-0.680621\pi\) | ||||
−0.537474 | + | 0.843280i | \(0.680621\pi\) | |||||||
\(618\) | 1.98852 | 0.0799901 | ||||||||
\(619\) | 5.45259 | 0.219158 | 0.109579 | − | 0.993978i | \(-0.465050\pi\) | ||||
0.109579 | + | 0.993978i | \(0.465050\pi\) | |||||||
\(620\) | 21.5400 | 0.865068 | ||||||||
\(621\) | −7.05455 | −0.283089 | ||||||||
\(622\) | −0.643996 | −0.0258219 | ||||||||
\(623\) | −7.16310 | −0.286984 | ||||||||
\(624\) | −4.22486 | −0.169130 | ||||||||
\(625\) | −11.0193 | −0.440773 | ||||||||
\(626\) | −2.73320 | −0.109241 | ||||||||
\(627\) | 0.0289248 | 0.00115514 | ||||||||
\(628\) | −17.5668 | −0.700993 | ||||||||
\(629\) | 0.513683 | 0.0204819 | ||||||||
\(630\) | −0.207967 | −0.00828562 | ||||||||
\(631\) | 37.3560 | 1.48712 | 0.743559 | − | 0.668670i | \(-0.233136\pi\) | ||||
0.743559 | + | 0.668670i | \(0.233136\pi\) | |||||||
\(632\) | 1.91134 | 0.0760292 | ||||||||
\(633\) | 2.02882 | 0.0806384 | ||||||||
\(634\) | 1.29699 | 0.0515101 | ||||||||
\(635\) | −20.7699 | −0.824229 | ||||||||
\(636\) | −18.2930 | −0.725364 | ||||||||
\(637\) | 1.07949 | 0.0427708 | ||||||||
\(638\) | 0.709927 | 0.0281063 | ||||||||
\(639\) | −2.92691 | −0.115787 | ||||||||
\(640\) | 6.53563 | 0.258343 | ||||||||
\(641\) | 25.3736 | 1.00220 | 0.501098 | − | 0.865391i | \(-0.332930\pi\) | ||||
0.501098 | + | 0.865391i | \(0.332930\pi\) | |||||||
\(642\) | −0.0518481 | −0.00204628 | ||||||||
\(643\) | 6.54646 | 0.258167 | 0.129084 | − | 0.991634i | \(-0.458796\pi\) | ||||
0.129084 | + | 0.991634i | \(0.458796\pi\) | |||||||
\(644\) | −14.0075 | −0.551972 | ||||||||
\(645\) | −15.7974 | −0.622020 | ||||||||
\(646\) | 0.00106133 | 4.17576e−5 0 | ||||||||
\(647\) | 5.54073 | 0.217829 | 0.108914 | − | 0.994051i | \(-0.465263\pi\) | ||||
0.108914 | + | 0.994051i | \(0.465263\pi\) | |||||||
\(648\) | 0.478379 | 0.0187925 | ||||||||
\(649\) | −51.8558 | −2.03552 | ||||||||
\(650\) | 0.258857 | 0.0101532 | ||||||||
\(651\) | 6.26094 | 0.245386 | ||||||||
\(652\) | 7.61755 | 0.298326 | ||||||||
\(653\) | 6.66414 | 0.260788 | 0.130394 | − | 0.991462i | \(-0.458376\pi\) | ||||
0.130394 | + | 0.991462i | \(0.458376\pi\) | |||||||
\(654\) | 1.72215 | 0.0673413 | ||||||||
\(655\) | −12.6035 | −0.492460 | ||||||||
\(656\) | 9.31611 | 0.363733 | ||||||||
\(657\) | 1.51241 | 0.0590046 | ||||||||
\(658\) | 0.913213 | 0.0356007 | ||||||||
\(659\) | −34.9347 | −1.36086 | −0.680432 | − | 0.732811i | \(-0.738208\pi\) | ||||
−0.680432 | + | 0.732811i | \(0.738208\pi\) | |||||||
\(660\) | −17.1713 | −0.668393 | ||||||||
\(661\) | −9.75107 | −0.379273 | −0.189636 | − | 0.981854i | \(-0.560731\pi\) | ||||
−0.189636 | + | 0.981854i | \(0.560731\pi\) | |||||||
\(662\) | −3.09176 | −0.120165 | ||||||||
\(663\) | 1.64709 | 0.0639676 | ||||||||
\(664\) | −4.42444 | −0.171702 | ||||||||
\(665\) | 0.0100413 | 0.000389384 0 | ||||||||
\(666\) | 0.0404087 | 0.00156580 | ||||||||
\(667\) | 8.36000 | 0.323701 | ||||||||
\(668\) | 19.8765 | 0.769045 | ||||||||
\(669\) | −15.2233 | −0.588567 | ||||||||
\(670\) | −0.730743 | −0.0282311 | ||||||||
\(671\) | 8.40758 | 0.324571 | ||||||||
\(672\) | 1.42652 | 0.0550290 | ||||||||
\(673\) | −7.59691 | −0.292839 | −0.146420 | − | 0.989223i | \(-0.546775\pi\) | ||||
−0.146420 | + | 0.989223i | \(0.546775\pi\) | |||||||
\(674\) | −0.472932 | −0.0182167 | ||||||||
\(675\) | 1.99785 | 0.0768974 | ||||||||
\(676\) | 23.4989 | 0.903805 | ||||||||
\(677\) | −40.3451 | −1.55059 | −0.775294 | − | 0.631600i | \(-0.782399\pi\) | ||||
−0.775294 | + | 0.631600i | \(0.782399\pi\) | |||||||
\(678\) | 1.05438 | 0.0404932 | ||||||||
\(679\) | 4.19603 | 0.161029 | ||||||||
\(680\) | −1.26470 | −0.0484991 | ||||||||
\(681\) | 7.35715 | 0.281927 | ||||||||
\(682\) | −3.75074 | −0.143623 | ||||||||
\(683\) | −0.308757 | −0.0118143 | −0.00590713 | − | 0.999983i | \(-0.501880\pi\) | ||||
−0.00590713 | + | 0.999983i | \(0.501880\pi\) | |||||||
\(684\) | −0.0115070 | −0.000439982 0 | ||||||||
\(685\) | 18.8401 | 0.719843 | ||||||||
\(686\) | −0.120027 | −0.00458265 | ||||||||
\(687\) | 0.521614 | 0.0199008 | ||||||||
\(688\) | 35.6832 | 1.36041 | ||||||||
\(689\) | −9.94515 | −0.378880 | ||||||||
\(690\) | 1.46712 | 0.0558521 | ||||||||
\(691\) | 0.137321 | 0.00522394 | 0.00261197 | − | 0.999997i | \(-0.499169\pi\) | ||||
0.00261197 | + | 0.999997i | \(0.499169\pi\) | |||||||
\(692\) | −13.0625 | −0.496563 | ||||||||
\(693\) | −4.99112 | −0.189597 | ||||||||
\(694\) | 3.49870 | 0.132809 | ||||||||
\(695\) | −24.2558 | −0.920074 | ||||||||
\(696\) | −0.566904 | −0.0214884 | ||||||||
\(697\) | −3.63195 | −0.137570 | ||||||||
\(698\) | −3.36334 | −0.127304 | ||||||||
\(699\) | −7.30939 | −0.276466 | ||||||||
\(700\) | 3.96692 | 0.149936 | ||||||||
\(701\) | 3.69096 | 0.139406 | 0.0697029 | − | 0.997568i | \(-0.477795\pi\) | ||||
0.0697029 | + | 0.997568i | \(0.477795\pi\) | |||||||
\(702\) | 0.129568 | 0.00489021 | ||||||||
\(703\) | −0.00195105 | −7.35852e−5 0 | ||||||||
\(704\) | 38.2136 | 1.44023 | ||||||||
\(705\) | 13.1828 | 0.496494 | ||||||||
\(706\) | −0.695744 | −0.0261847 | ||||||||
\(707\) | 7.52131 | 0.282868 | ||||||||
\(708\) | 20.6296 | 0.775307 | ||||||||
\(709\) | 46.7741 | 1.75664 | 0.878320 | − | 0.478073i | \(-0.158665\pi\) | ||||
0.878320 | + | 0.478073i | \(0.158665\pi\) | |||||||
\(710\) | 0.608701 | 0.0228441 | ||||||||
\(711\) | 3.99546 | 0.149841 | ||||||||
\(712\) | −3.42668 | −0.128420 | ||||||||
\(713\) | −44.1681 | −1.65411 | ||||||||
\(714\) | −0.183138 | −0.00685378 | ||||||||
\(715\) | −9.33535 | −0.349122 | ||||||||
\(716\) | −11.0282 | −0.412144 | ||||||||
\(717\) | −18.2355 | −0.681019 | ||||||||
\(718\) | 1.34958 | 0.0503659 | ||||||||
\(719\) | −2.28764 | −0.0853147 | −0.0426574 | − | 0.999090i | \(-0.513582\pi\) | ||||
−0.0426574 | + | 0.999090i | \(0.513582\pi\) | |||||||
\(720\) | 6.78127 | 0.252723 | ||||||||
\(721\) | 16.5673 | 0.616998 | ||||||||
\(722\) | 2.28051 | 0.0848718 | ||||||||
\(723\) | 12.0047 | 0.446460 | ||||||||
\(724\) | 1.56445 | 0.0581422 | ||||||||
\(725\) | −2.36756 | −0.0879289 | ||||||||
\(726\) | 1.66973 | 0.0619693 | ||||||||
\(727\) | 19.6653 | 0.729344 | 0.364672 | − | 0.931136i | \(-0.381181\pi\) | ||||
0.364672 | + | 0.931136i | \(0.381181\pi\) | |||||||
\(728\) | 0.516403 | 0.0191392 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.314531 | −0.0116413 | ||||||||
\(731\) | −13.9113 | −0.514529 | ||||||||
\(732\) | −3.34475 | −0.123625 | ||||||||
\(733\) | 29.5659 | 1.09204 | 0.546021 | − | 0.837772i | \(-0.316142\pi\) | ||||
0.546021 | + | 0.837772i | \(0.316142\pi\) | |||||||
\(734\) | −3.84102 | −0.141775 | ||||||||
\(735\) | −1.73267 | −0.0639105 | ||||||||
\(736\) | −10.0634 | −0.370943 | ||||||||
\(737\) | −17.5375 | −0.646002 | ||||||||
\(738\) | −0.285705 | −0.0105170 | ||||||||
\(739\) | 10.7447 | 0.395251 | 0.197625 | − | 0.980278i | \(-0.436677\pi\) | ||||
0.197625 | + | 0.980278i | \(0.436677\pi\) | |||||||
\(740\) | 1.15825 | 0.0425781 | ||||||||
\(741\) | −0.00625590 | −0.000229816 0 | ||||||||
\(742\) | 1.10579 | 0.0405949 | ||||||||
\(743\) | 5.65769 | 0.207561 | 0.103780 | − | 0.994600i | \(-0.466906\pi\) | ||||
0.103780 | + | 0.994600i | \(0.466906\pi\) | |||||||
\(744\) | 2.99510 | 0.109806 | ||||||||
\(745\) | −3.24465 | −0.118875 | ||||||||
\(746\) | −3.57436 | −0.130866 | ||||||||
\(747\) | −9.24882 | −0.338397 | ||||||||
\(748\) | −15.1213 | −0.552888 | ||||||||
\(749\) | −0.431970 | −0.0157838 | ||||||||
\(750\) | −1.45532 | −0.0531409 | ||||||||
\(751\) | −11.6510 | −0.425152 | −0.212576 | − | 0.977144i | \(-0.568185\pi\) | ||||
−0.212576 | + | 0.977144i | \(0.568185\pi\) | |||||||
\(752\) | −29.7775 | −1.08587 | ||||||||
\(753\) | −19.1802 | −0.698966 | ||||||||
\(754\) | −0.153544 | −0.00559175 | ||||||||
\(755\) | −18.9390 | −0.689261 | ||||||||
\(756\) | 1.98559 | 0.0722153 | ||||||||
\(757\) | 37.2997 | 1.35568 | 0.677840 | − | 0.735209i | \(-0.262916\pi\) | ||||
0.677840 | + | 0.735209i | \(0.262916\pi\) | |||||||
\(758\) | 1.16115 | 0.0421750 | ||||||||
\(759\) | 35.2101 | 1.27804 | ||||||||
\(760\) | 0.00480353 | 0.000174242 0 | ||||||||
\(761\) | −8.42854 | −0.305534 | −0.152767 | − | 0.988262i | \(-0.548818\pi\) | ||||
−0.152767 | + | 0.988262i | \(0.548818\pi\) | |||||||
\(762\) | −1.43879 | −0.0521219 | ||||||||
\(763\) | 14.3480 | 0.519432 | ||||||||
\(764\) | −53.4012 | −1.93199 | ||||||||
\(765\) | −2.64372 | −0.0955840 | ||||||||
\(766\) | 0.120027 | 0.00433675 | ||||||||
\(767\) | 11.2155 | 0.404967 | ||||||||
\(768\) | −14.8599 | −0.536210 | ||||||||
\(769\) | 18.8486 | 0.679699 | 0.339850 | − | 0.940480i | \(-0.389624\pi\) | ||||
0.339850 | + | 0.940480i | \(0.389624\pi\) | |||||||
\(770\) | 1.03799 | 0.0374065 | ||||||||
\(771\) | 1.76135 | 0.0634334 | ||||||||
\(772\) | −8.57930 | −0.308776 | ||||||||
\(773\) | −34.0120 | −1.22333 | −0.611664 | − | 0.791118i | \(-0.709499\pi\) | ||||
−0.611664 | + | 0.791118i | \(0.709499\pi\) | |||||||
\(774\) | −1.09433 | −0.0393348 | ||||||||
\(775\) | 12.5084 | 0.449316 | ||||||||
\(776\) | 2.00729 | 0.0720577 | ||||||||
\(777\) | 0.336663 | 0.0120777 | ||||||||
\(778\) | −3.64048 | −0.130518 | ||||||||
\(779\) | 0.0137947 | 0.000494246 0 | ||||||||
\(780\) | 3.71384 | 0.132977 | ||||||||
\(781\) | 14.6085 | 0.522734 | ||||||||
\(782\) | 1.29196 | 0.0462003 | ||||||||
\(783\) | −1.18505 | −0.0423503 | ||||||||
\(784\) | 3.91377 | 0.139777 | ||||||||
\(785\) | 15.3292 | 0.547122 | ||||||||
\(786\) | −0.873081 | −0.0311418 | ||||||||
\(787\) | 45.9741 | 1.63880 | 0.819400 | − | 0.573222i | \(-0.194307\pi\) | ||||
0.819400 | + | 0.573222i | \(0.194307\pi\) | |||||||
\(788\) | 2.70425 | 0.0963349 | ||||||||
\(789\) | 24.3387 | 0.866481 | ||||||||
\(790\) | −0.830925 | −0.0295630 | ||||||||
\(791\) | 8.78452 | 0.312342 | ||||||||
\(792\) | −2.38765 | −0.0848413 | ||||||||
\(793\) | −1.81840 | −0.0645734 | ||||||||
\(794\) | −0.363946 | −0.0129160 | ||||||||
\(795\) | 15.9628 | 0.566144 | ||||||||
\(796\) | 27.5203 | 0.975430 | ||||||||
\(797\) | −28.9758 | −1.02638 | −0.513188 | − | 0.858276i | \(-0.671536\pi\) | ||||
−0.513188 | + | 0.858276i | \(0.671536\pi\) | |||||||
\(798\) | 0.000695587 0 | 2.46235e−5 0 | ||||||||
\(799\) | 11.6089 | 0.410695 | ||||||||
\(800\) | 2.84997 | 0.100762 | ||||||||
\(801\) | −7.16310 | −0.253096 | ||||||||
\(802\) | −0.643408 | −0.0227195 | ||||||||
\(803\) | −7.54860 | −0.266384 | ||||||||
\(804\) | 6.97686 | 0.246055 | ||||||||
\(805\) | 12.2232 | 0.430812 | ||||||||
\(806\) | 0.811215 | 0.0285738 | ||||||||
\(807\) | −11.8401 | −0.416791 | ||||||||
\(808\) | 3.59803 | 0.126578 | ||||||||
\(809\) | 27.6999 | 0.973876 | 0.486938 | − | 0.873437i | \(-0.338114\pi\) | ||||
0.486938 | + | 0.873437i | \(0.338114\pi\) | |||||||
\(810\) | −0.207967 | −0.00730723 | ||||||||
\(811\) | −18.5133 | −0.650088 | −0.325044 | − | 0.945699i | \(-0.605379\pi\) | ||||
−0.325044 | + | 0.945699i | \(0.605379\pi\) | |||||||
\(812\) | −2.35303 | −0.0825752 | ||||||||
\(813\) | −23.8145 | −0.835209 | ||||||||
\(814\) | −0.201684 | −0.00706903 | ||||||||
\(815\) | −6.64723 | −0.232842 | ||||||||
\(816\) | 5.97166 | 0.209050 | ||||||||
\(817\) | 0.0528373 | 0.00184854 | ||||||||
\(818\) | −2.36274 | −0.0826112 | ||||||||
\(819\) | 1.07949 | 0.0377203 | ||||||||
\(820\) | −8.18928 | −0.285982 | ||||||||
\(821\) | −33.0738 | −1.15428 | −0.577141 | − | 0.816644i | \(-0.695832\pi\) | ||||
−0.577141 | + | 0.816644i | \(0.695832\pi\) | |||||||
\(822\) | 1.30511 | 0.0455208 | ||||||||
\(823\) | −23.5507 | −0.820927 | −0.410464 | − | 0.911877i | \(-0.634633\pi\) | ||||
−0.410464 | + | 0.911877i | \(0.634633\pi\) | |||||||
\(824\) | 7.92544 | 0.276096 | ||||||||
\(825\) | −9.97152 | −0.347164 | ||||||||
\(826\) | −1.24704 | −0.0433899 | ||||||||
\(827\) | −31.5501 | −1.09711 | −0.548553 | − | 0.836116i | \(-0.684821\pi\) | ||||
−0.548553 | + | 0.836116i | \(0.684821\pi\) | |||||||
\(828\) | −14.0075 | −0.486793 | ||||||||
\(829\) | 32.6150 | 1.13277 | 0.566384 | − | 0.824142i | \(-0.308342\pi\) | ||||
0.566384 | + | 0.824142i | \(0.308342\pi\) | |||||||
\(830\) | 1.92345 | 0.0667640 | ||||||||
\(831\) | −5.40217 | −0.187399 | ||||||||
\(832\) | −8.26489 | −0.286533 | ||||||||
\(833\) | −1.52581 | −0.0528661 | ||||||||
\(834\) | −1.68027 | −0.0581829 | ||||||||
\(835\) | −17.3446 | −0.600236 | ||||||||
\(836\) | 0.0574329 | 0.00198636 | ||||||||
\(837\) | 6.26094 | 0.216410 | ||||||||
\(838\) | −0.842698 | −0.0291105 | ||||||||
\(839\) | 27.8475 | 0.961403 | 0.480701 | − | 0.876884i | \(-0.340382\pi\) | ||||
0.480701 | + | 0.876884i | \(0.340382\pi\) | |||||||
\(840\) | −0.828873 | −0.0285988 | ||||||||
\(841\) | −27.5957 | −0.951574 | ||||||||
\(842\) | −2.02103 | −0.0696494 | ||||||||
\(843\) | 1.04357 | 0.0359423 | ||||||||
\(844\) | 4.02841 | 0.138664 | ||||||||
\(845\) | −20.5057 | −0.705416 | ||||||||
\(846\) | 0.913213 | 0.0313969 | ||||||||
\(847\) | 13.9112 | 0.477996 | ||||||||
\(848\) | −36.0570 | −1.23820 | ||||||||
\(849\) | 10.3751 | 0.356073 | ||||||||
\(850\) | −0.365883 | −0.0125497 | ||||||||
\(851\) | −2.37501 | −0.0814142 | ||||||||
\(852\) | −5.81165 | −0.199104 | ||||||||
\(853\) | −27.9335 | −0.956424 | −0.478212 | − | 0.878245i | \(-0.658715\pi\) | ||||
−0.478212 | + | 0.878245i | \(0.658715\pi\) | |||||||
\(854\) | 0.202187 | 0.00691868 | ||||||||
\(855\) | 0.0100413 | 0.000343404 0 | ||||||||
\(856\) | −0.206645 | −0.00706299 | ||||||||
\(857\) | 10.0055 | 0.341781 | 0.170891 | − | 0.985290i | \(-0.445336\pi\) | ||||
0.170891 | + | 0.985290i | \(0.445336\pi\) | |||||||
\(858\) | −0.646687 | −0.0220775 | ||||||||
\(859\) | 15.2413 | 0.520027 | 0.260014 | − | 0.965605i | \(-0.416273\pi\) | ||||
0.260014 | + | 0.965605i | \(0.416273\pi\) | |||||||
\(860\) | −31.3671 | −1.06961 | ||||||||
\(861\) | −2.38034 | −0.0811218 | ||||||||
\(862\) | 1.77590 | 0.0604875 | ||||||||
\(863\) | 29.0605 | 0.989231 | 0.494615 | − | 0.869112i | \(-0.335309\pi\) | ||||
0.494615 | + | 0.869112i | \(0.335309\pi\) | |||||||
\(864\) | 1.42652 | 0.0485311 | ||||||||
\(865\) | 11.3986 | 0.387565 | ||||||||
\(866\) | −1.03944 | −0.0353215 | ||||||||
\(867\) | 14.6719 | 0.498284 | ||||||||
\(868\) | 12.4317 | 0.421959 | ||||||||
\(869\) | −19.9418 | −0.676480 | ||||||||
\(870\) | 0.246452 | 0.00835550 | ||||||||
\(871\) | 3.79303 | 0.128522 | ||||||||
\(872\) | 6.86378 | 0.232437 | ||||||||
\(873\) | 4.19603 | 0.142014 | ||||||||
\(874\) | −0.00490705 | −0.000165984 0 | ||||||||
\(875\) | −12.1250 | −0.409899 | ||||||||
\(876\) | 3.00302 | 0.101463 | ||||||||
\(877\) | 30.6895 | 1.03631 | 0.518155 | − | 0.855287i | \(-0.326619\pi\) | ||||
0.518155 | + | 0.855287i | \(0.326619\pi\) | |||||||
\(878\) | −1.31858 | −0.0444998 | ||||||||
\(879\) | −22.2229 | −0.749558 | ||||||||
\(880\) | −33.8461 | −1.14095 | ||||||||
\(881\) | −39.6196 | −1.33482 | −0.667409 | − | 0.744692i | \(-0.732597\pi\) | ||||
−0.667409 | + | 0.744692i | \(0.732597\pi\) | |||||||
\(882\) | −0.120027 | −0.00404152 | ||||||||
\(883\) | 28.7131 | 0.966273 | 0.483136 | − | 0.875545i | \(-0.339498\pi\) | ||||
0.483136 | + | 0.875545i | \(0.339498\pi\) | |||||||
\(884\) | 3.27045 | 0.109997 | ||||||||
\(885\) | −18.0018 | −0.605124 | ||||||||
\(886\) | 2.84075 | 0.0954369 | ||||||||
\(887\) | 1.54036 | 0.0517202 | 0.0258601 | − | 0.999666i | \(-0.491768\pi\) | ||||
0.0258601 | + | 0.999666i | \(0.491768\pi\) | |||||||
\(888\) | 0.161053 | 0.00540457 | ||||||||
\(889\) | −11.9872 | −0.402039 | ||||||||
\(890\) | 1.48969 | 0.0499345 | ||||||||
\(891\) | −4.99112 | −0.167209 | ||||||||
\(892\) | −30.2273 | −1.01209 | ||||||||
\(893\) | −0.0440926 | −0.00147550 | ||||||||
\(894\) | −0.224766 | −0.00751731 | ||||||||
\(895\) | 9.62345 | 0.321676 | ||||||||
\(896\) | 3.77200 | 0.126014 | ||||||||
\(897\) | −7.61529 | −0.254267 | ||||||||
\(898\) | −3.46291 | −0.115559 | ||||||||
\(899\) | −7.41954 | −0.247455 | ||||||||
\(900\) | 3.96692 | 0.132231 | ||||||||
\(901\) | 14.0571 | 0.468308 | ||||||||
\(902\) | 1.42599 | 0.0474802 | ||||||||
\(903\) | −9.11735 | −0.303406 | ||||||||
\(904\) | 4.20233 | 0.139767 | ||||||||
\(905\) | −1.36517 | −0.0453798 | ||||||||
\(906\) | −1.31196 | −0.0435869 | ||||||||
\(907\) | 38.0481 | 1.26337 | 0.631684 | − | 0.775226i | \(-0.282364\pi\) | ||||
0.631684 | + | 0.775226i | \(0.282364\pi\) | |||||||
\(908\) | 14.6083 | 0.484794 | ||||||||
\(909\) | 7.52131 | 0.249466 | ||||||||
\(910\) | −0.224498 | −0.00744203 | ||||||||
\(911\) | −9.62453 | −0.318875 | −0.159437 | − | 0.987208i | \(-0.550968\pi\) | ||||
−0.159437 | + | 0.987208i | \(0.550968\pi\) | |||||||
\(912\) | −0.0226813 | −0.000751052 0 | ||||||||
\(913\) | 46.1619 | 1.52774 | ||||||||
\(914\) | −3.39386 | −0.112259 | ||||||||
\(915\) | 2.91870 | 0.0964892 | ||||||||
\(916\) | 1.03571 | 0.0342210 | ||||||||
\(917\) | −7.27404 | −0.240210 | ||||||||
\(918\) | −0.183138 | −0.00604446 | ||||||||
\(919\) | −29.0365 | −0.957824 | −0.478912 | − | 0.877863i | \(-0.658969\pi\) | ||||
−0.478912 | + | 0.877863i | \(0.658969\pi\) | |||||||
\(920\) | 5.84733 | 0.192781 | ||||||||
\(921\) | −3.21540 | −0.105951 | ||||||||
\(922\) | −0.243330 | −0.00801365 | ||||||||
\(923\) | −3.15955 | −0.103998 | ||||||||
\(924\) | −9.91033 | −0.326026 | ||||||||
\(925\) | 0.672603 | 0.0221151 | ||||||||
\(926\) | 1.94622 | 0.0639568 | ||||||||
\(927\) | 16.5673 | 0.544141 | ||||||||
\(928\) | −1.69049 | −0.0554932 | ||||||||
\(929\) | 3.74697 | 0.122934 | 0.0614670 | − | 0.998109i | \(-0.480422\pi\) | ||||
0.0614670 | + | 0.998109i | \(0.480422\pi\) | |||||||
\(930\) | −1.30207 | −0.0426966 | ||||||||
\(931\) | 0.00579525 | 0.000189932 0 | ||||||||
\(932\) | −14.5135 | −0.475405 | ||||||||
\(933\) | −5.36542 | −0.175656 | ||||||||
\(934\) | −0.941538 | −0.0308081 | ||||||||
\(935\) | 13.1951 | 0.431527 | ||||||||
\(936\) | 0.516403 | 0.0168792 | ||||||||
\(937\) | 11.4736 | 0.374827 | 0.187414 | − | 0.982281i | \(-0.439990\pi\) | ||||
0.187414 | + | 0.982281i | \(0.439990\pi\) | |||||||
\(938\) | −0.421744 | −0.0137704 | ||||||||
\(939\) | −22.7716 | −0.743122 | ||||||||
\(940\) | 26.1758 | 0.853759 | ||||||||
\(941\) | −25.3351 | −0.825902 | −0.412951 | − | 0.910753i | \(-0.635502\pi\) | ||||
−0.412951 | + | 0.910753i | \(0.635502\pi\) | |||||||
\(942\) | 1.06190 | 0.0345985 | ||||||||
\(943\) | 16.7922 | 0.546831 | ||||||||
\(944\) | 40.6626 | 1.32345 | ||||||||
\(945\) | −1.73267 | −0.0563638 | ||||||||
\(946\) | 5.46192 | 0.177582 | ||||||||
\(947\) | −34.6245 | −1.12514 | −0.562572 | − | 0.826748i | \(-0.690188\pi\) | ||||
−0.562572 | + | 0.826748i | \(0.690188\pi\) | |||||||
\(948\) | 7.93336 | 0.257664 | ||||||||
\(949\) | 1.63262 | 0.0529971 | ||||||||
\(950\) | 0.00138968 | 4.50872e−5 0 | ||||||||
\(951\) | 10.8058 | 0.350403 | ||||||||
\(952\) | −0.729915 | −0.0236567 | ||||||||
\(953\) | 32.1189 | 1.04043 | 0.520217 | − | 0.854034i | \(-0.325851\pi\) | ||||
0.520217 | + | 0.854034i | \(0.325851\pi\) | |||||||
\(954\) | 1.10579 | 0.0358013 | ||||||||
\(955\) | 46.5990 | 1.50791 | ||||||||
\(956\) | −36.2084 | −1.17106 | ||||||||
\(957\) | 5.91473 | 0.191196 | ||||||||
\(958\) | 1.07787 | 0.0348245 | ||||||||
\(959\) | 10.8734 | 0.351122 | ||||||||
\(960\) | 13.2659 | 0.428154 | ||||||||
\(961\) | 8.19940 | 0.264497 | ||||||||
\(962\) | 0.0436206 | 0.00140638 | ||||||||
\(963\) | −0.431970 | −0.0139200 | ||||||||
\(964\) | 23.8365 | 0.767721 | ||||||||
\(965\) | 7.48648 | 0.240998 | ||||||||
\(966\) | 0.846737 | 0.0272433 | ||||||||
\(967\) | −8.80911 | −0.283282 | −0.141641 | − | 0.989918i | \(-0.545238\pi\) | ||||
−0.141641 | + | 0.989918i | \(0.545238\pi\) | |||||||
\(968\) | 6.65485 | 0.213895 | ||||||||
\(969\) | 0.00884245 | 0.000284060 0 | ||||||||
\(970\) | −0.872638 | −0.0280187 | ||||||||
\(971\) | −42.7141 | −1.37076 | −0.685380 | − | 0.728185i | \(-0.740364\pi\) | ||||
−0.685380 | + | 0.728185i | \(0.740364\pi\) | |||||||
\(972\) | 1.98559 | 0.0636879 | ||||||||
\(973\) | −13.9991 | −0.448790 | ||||||||
\(974\) | 0.683142 | 0.0218893 | ||||||||
\(975\) | 2.15665 | 0.0690682 | ||||||||
\(976\) | −6.59278 | −0.211030 | ||||||||
\(977\) | 0.547556 | 0.0175179 | 0.00875894 | − | 0.999962i | \(-0.497212\pi\) | ||||
0.00875894 | + | 0.999962i | \(0.497212\pi\) | |||||||
\(978\) | −0.460473 | −0.0147243 | ||||||||
\(979\) | 35.7519 | 1.14263 | ||||||||
\(980\) | −3.44038 | −0.109899 | ||||||||
\(981\) | 14.3480 | 0.458096 | ||||||||
\(982\) | −2.22609 | −0.0710374 | ||||||||
\(983\) | −44.1091 | −1.40686 | −0.703431 | − | 0.710764i | \(-0.748350\pi\) | ||||
−0.703431 | + | 0.710764i | \(0.748350\pi\) | |||||||
\(984\) | −1.13871 | −0.0363006 | ||||||||
\(985\) | −2.35979 | −0.0751890 | ||||||||
\(986\) | 0.217028 | 0.00691159 | ||||||||
\(987\) | 7.60839 | 0.242178 | ||||||||
\(988\) | −0.0124217 | −0.000395186 0 | ||||||||
\(989\) | 64.3188 | 2.04522 | ||||||||
\(990\) | 1.03799 | 0.0329895 | ||||||||
\(991\) | 1.20554 | 0.0382954 | 0.0191477 | − | 0.999817i | \(-0.493905\pi\) | ||||
0.0191477 | + | 0.999817i | \(0.493905\pi\) | |||||||
\(992\) | 8.93133 | 0.283570 | ||||||||
\(993\) | −25.7589 | −0.817433 | ||||||||
\(994\) | 0.351308 | 0.0111428 | ||||||||
\(995\) | −24.0148 | −0.761319 | ||||||||
\(996\) | −18.3644 | −0.581898 | ||||||||
\(997\) | −5.91391 | −0.187295 | −0.0936477 | − | 0.995605i | \(-0.529853\pi\) | ||||
−0.0936477 | + | 0.995605i | \(0.529853\pi\) | |||||||
\(998\) | −0.834751 | −0.0264236 | ||||||||
\(999\) | 0.336663 | 0.0106515 |
(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.t.1.25 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.25 | ✓ | 52 | 1.1 | even | 1 | trivial |