Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.46 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.839330 | 0.593496 | 0.296748 | − | 0.954956i | \(-0.404098\pi\) | ||||
0.296748 | + | 0.954956i | \(0.404098\pi\) | |||||||
\(3\) | 1.22529 | 0.707420 | 0.353710 | − | 0.935355i | \(-0.384920\pi\) | ||||
0.353710 | + | 0.935355i | \(0.384920\pi\) | |||||||
\(4\) | −1.29552 | −0.647762 | ||||||||
\(5\) | 2.59839 | 1.16203 | 0.581017 | − | 0.813891i | \(-0.302655\pi\) | ||||
0.581017 | + | 0.813891i | \(0.302655\pi\) | |||||||
\(6\) | 1.02842 | 0.419851 | ||||||||
\(7\) | 2.35945 | 0.891787 | 0.445893 | − | 0.895086i | \(-0.352886\pi\) | ||||
0.445893 | + | 0.895086i | \(0.352886\pi\) | |||||||
\(8\) | −2.76603 | −0.977940 | ||||||||
\(9\) | −1.49867 | −0.499557 | ||||||||
\(10\) | 2.18091 | 0.689663 | ||||||||
\(11\) | −2.43979 | −0.735624 | −0.367812 | − | 0.929900i | \(-0.619893\pi\) | ||||
−0.367812 | + | 0.929900i | \(0.619893\pi\) | |||||||
\(12\) | −1.58739 | −0.458240 | ||||||||
\(13\) | −6.49746 | −1.80207 | −0.901036 | − | 0.433744i | \(-0.857192\pi\) | ||||
−0.901036 | + | 0.433744i | \(0.857192\pi\) | |||||||
\(14\) | 1.98035 | 0.529272 | ||||||||
\(15\) | 3.18377 | 0.822046 | ||||||||
\(16\) | 0.269435 | 0.0673587 | ||||||||
\(17\) | −3.77784 | −0.916261 | −0.458130 | − | 0.888885i | \(-0.651481\pi\) | ||||
−0.458130 | + | 0.888885i | \(0.651481\pi\) | |||||||
\(18\) | −1.25788 | −0.296485 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −3.36628 | −0.752722 | ||||||||
\(21\) | 2.89100 | 0.630867 | ||||||||
\(22\) | −2.04779 | −0.436590 | ||||||||
\(23\) | 0.232392 | 0.0484572 | 0.0242286 | − | 0.999706i | \(-0.492287\pi\) | ||||
0.0242286 | + | 0.999706i | \(0.492287\pi\) | |||||||
\(24\) | −3.38918 | −0.691814 | ||||||||
\(25\) | 1.75162 | 0.350324 | ||||||||
\(26\) | −5.45352 | −1.06952 | ||||||||
\(27\) | −5.51216 | −1.06082 | ||||||||
\(28\) | −3.05672 | −0.577666 | ||||||||
\(29\) | 4.72772 | 0.877916 | 0.438958 | − | 0.898508i | \(-0.355348\pi\) | ||||
0.438958 | + | 0.898508i | \(0.355348\pi\) | |||||||
\(30\) | 2.67223 | 0.487881 | ||||||||
\(31\) | 2.74538 | 0.493085 | 0.246543 | − | 0.969132i | \(-0.420705\pi\) | ||||
0.246543 | + | 0.969132i | \(0.420705\pi\) | |||||||
\(32\) | 5.75821 | 1.01792 | ||||||||
\(33\) | −2.98944 | −0.520395 | ||||||||
\(34\) | −3.17085 | −0.543797 | ||||||||
\(35\) | 6.13075 | 1.03629 | ||||||||
\(36\) | 1.94157 | 0.323595 | ||||||||
\(37\) | −6.70024 | −1.10151 | −0.550756 | − | 0.834666i | \(-0.685661\pi\) | ||||
−0.550756 | + | 0.834666i | \(0.685661\pi\) | |||||||
\(38\) | 0.839330 | 0.136157 | ||||||||
\(39\) | −7.96126 | −1.27482 | ||||||||
\(40\) | −7.18723 | −1.13640 | ||||||||
\(41\) | −0.748434 | −0.116886 | −0.0584429 | − | 0.998291i | \(-0.518614\pi\) | ||||
−0.0584429 | + | 0.998291i | \(0.518614\pi\) | |||||||
\(42\) | 2.42650 | 0.374417 | ||||||||
\(43\) | −6.31190 | −0.962556 | −0.481278 | − | 0.876568i | \(-0.659827\pi\) | ||||
−0.481278 | + | 0.876568i | \(0.659827\pi\) | |||||||
\(44\) | 3.16081 | 0.476509 | ||||||||
\(45\) | −3.89413 | −0.580503 | ||||||||
\(46\) | 0.195054 | 0.0287591 | ||||||||
\(47\) | 0.547458 | 0.0798550 | 0.0399275 | − | 0.999203i | \(-0.487287\pi\) | ||||
0.0399275 | + | 0.999203i | \(0.487287\pi\) | |||||||
\(48\) | 0.330135 | 0.0476508 | ||||||||
\(49\) | −1.43302 | −0.204717 | ||||||||
\(50\) | 1.47019 | 0.207916 | ||||||||
\(51\) | −4.62894 | −0.648181 | ||||||||
\(52\) | 8.41763 | 1.16731 | ||||||||
\(53\) | −8.40082 | −1.15394 | −0.576971 | − | 0.816765i | \(-0.695765\pi\) | ||||
−0.576971 | + | 0.816765i | \(0.695765\pi\) | |||||||
\(54\) | −4.62653 | −0.629590 | ||||||||
\(55\) | −6.33952 | −0.854820 | ||||||||
\(56\) | −6.52631 | −0.872114 | ||||||||
\(57\) | 1.22529 | 0.162293 | ||||||||
\(58\) | 3.96812 | 0.521040 | ||||||||
\(59\) | 1.15255 | 0.150049 | 0.0750246 | − | 0.997182i | \(-0.476096\pi\) | ||||
0.0750246 | + | 0.997182i | \(0.476096\pi\) | |||||||
\(60\) | −4.12465 | −0.532491 | ||||||||
\(61\) | −13.6742 | −1.75080 | −0.875399 | − | 0.483401i | \(-0.839401\pi\) | ||||
−0.875399 | + | 0.483401i | \(0.839401\pi\) | |||||||
\(62\) | 2.30428 | 0.292644 | ||||||||
\(63\) | −3.53604 | −0.445499 | ||||||||
\(64\) | 4.29417 | 0.536771 | ||||||||
\(65\) | −16.8829 | −2.09407 | ||||||||
\(66\) | −2.50913 | −0.308852 | ||||||||
\(67\) | −5.34592 | −0.653108 | −0.326554 | − | 0.945179i | \(-0.605887\pi\) | ||||
−0.326554 | + | 0.945179i | \(0.605887\pi\) | |||||||
\(68\) | 4.89428 | 0.593519 | ||||||||
\(69\) | 0.284747 | 0.0342796 | ||||||||
\(70\) | 5.14573 | 0.615032 | ||||||||
\(71\) | 10.5796 | 1.25557 | 0.627785 | − | 0.778386i | \(-0.283962\pi\) | ||||
0.627785 | + | 0.778386i | \(0.283962\pi\) | |||||||
\(72\) | 4.14538 | 0.488537 | ||||||||
\(73\) | −8.51824 | −0.996985 | −0.498492 | − | 0.866894i | \(-0.666113\pi\) | ||||
−0.498492 | + | 0.866894i | \(0.666113\pi\) | |||||||
\(74\) | −5.62371 | −0.653743 | ||||||||
\(75\) | 2.14624 | 0.247826 | ||||||||
\(76\) | −1.29552 | −0.148607 | ||||||||
\(77\) | −5.75655 | −0.656019 | ||||||||
\(78\) | −6.68212 | −0.756602 | ||||||||
\(79\) | 9.20120 | 1.03522 | 0.517608 | − | 0.855618i | \(-0.326823\pi\) | ||||
0.517608 | + | 0.855618i | \(0.326823\pi\) | |||||||
\(80\) | 0.700096 | 0.0782731 | ||||||||
\(81\) | −2.25797 | −0.250885 | ||||||||
\(82\) | −0.628184 | −0.0693713 | ||||||||
\(83\) | −0.396884 | −0.0435637 | −0.0217818 | − | 0.999763i | \(-0.506934\pi\) | ||||
−0.0217818 | + | 0.999763i | \(0.506934\pi\) | |||||||
\(84\) | −3.74536 | −0.408652 | ||||||||
\(85\) | −9.81629 | −1.06473 | ||||||||
\(86\) | −5.29777 | −0.571273 | ||||||||
\(87\) | 5.79281 | 0.621055 | ||||||||
\(88\) | 6.74853 | 0.719396 | ||||||||
\(89\) | −11.9203 | −1.26355 | −0.631774 | − | 0.775153i | \(-0.717673\pi\) | ||||
−0.631774 | + | 0.775153i | \(0.717673\pi\) | |||||||
\(90\) | −3.26846 | −0.344526 | ||||||||
\(91\) | −15.3304 | −1.60706 | ||||||||
\(92\) | −0.301070 | −0.0313887 | ||||||||
\(93\) | 3.36388 | 0.348818 | ||||||||
\(94\) | 0.459498 | 0.0473936 | ||||||||
\(95\) | 2.59839 | 0.266589 | ||||||||
\(96\) | 7.05546 | 0.720095 | ||||||||
\(97\) | −1.12187 | −0.113909 | −0.0569545 | − | 0.998377i | \(-0.518139\pi\) | ||||
−0.0569545 | + | 0.998377i | \(0.518139\pi\) | |||||||
\(98\) | −1.20277 | −0.121499 | ||||||||
\(99\) | 3.65644 | 0.367486 | ||||||||
\(100\) | −2.26927 | −0.226927 | ||||||||
\(101\) | 6.95247 | 0.691797 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(102\) | −3.88521 | −0.384693 | ||||||||
\(103\) | 4.89589 | 0.482407 | 0.241203 | − | 0.970475i | \(-0.422458\pi\) | ||||
0.241203 | + | 0.970475i | \(0.422458\pi\) | |||||||
\(104\) | 17.9722 | 1.76232 | ||||||||
\(105\) | 7.51193 | 0.733090 | ||||||||
\(106\) | −7.05106 | −0.684860 | ||||||||
\(107\) | −2.73564 | −0.264464 | −0.132232 | − | 0.991219i | \(-0.542214\pi\) | ||||
−0.132232 | + | 0.991219i | \(0.542214\pi\) | |||||||
\(108\) | 7.14115 | 0.687157 | ||||||||
\(109\) | 14.0103 | 1.34194 | 0.670970 | − | 0.741485i | \(-0.265878\pi\) | ||||
0.670970 | + | 0.741485i | \(0.265878\pi\) | |||||||
\(110\) | −5.32095 | −0.507332 | ||||||||
\(111\) | −8.20972 | −0.779232 | ||||||||
\(112\) | 0.635716 | 0.0600696 | ||||||||
\(113\) | 2.07692 | 0.195380 | 0.0976899 | − | 0.995217i | \(-0.468855\pi\) | ||||
0.0976899 | + | 0.995217i | \(0.468855\pi\) | |||||||
\(114\) | 1.02842 | 0.0963204 | ||||||||
\(115\) | 0.603846 | 0.0563089 | ||||||||
\(116\) | −6.12488 | −0.568681 | ||||||||
\(117\) | 9.73757 | 0.900239 | ||||||||
\(118\) | 0.967369 | 0.0890536 | ||||||||
\(119\) | −8.91361 | −0.817109 | ||||||||
\(120\) | −8.80642 | −0.803912 | ||||||||
\(121\) | −5.04744 | −0.458858 | ||||||||
\(122\) | −11.4771 | −1.03909 | ||||||||
\(123\) | −0.917047 | −0.0826873 | ||||||||
\(124\) | −3.55671 | −0.319402 | ||||||||
\(125\) | −8.44055 | −0.754946 | ||||||||
\(126\) | −2.96790 | −0.264402 | ||||||||
\(127\) | 19.3658 | 1.71843 | 0.859217 | − | 0.511612i | \(-0.170951\pi\) | ||||
0.859217 | + | 0.511612i | \(0.170951\pi\) | |||||||
\(128\) | −7.91220 | −0.699346 | ||||||||
\(129\) | −7.73389 | −0.680931 | ||||||||
\(130\) | −14.1704 | −1.24282 | ||||||||
\(131\) | 16.6314 | 1.45309 | 0.726544 | − | 0.687120i | \(-0.241125\pi\) | ||||
0.726544 | + | 0.687120i | \(0.241125\pi\) | |||||||
\(132\) | 3.87289 | 0.337092 | ||||||||
\(133\) | 2.35945 | 0.204590 | ||||||||
\(134\) | −4.48699 | −0.387617 | ||||||||
\(135\) | −14.3227 | −1.23271 | ||||||||
\(136\) | 10.4496 | 0.896048 | ||||||||
\(137\) | −10.9865 | −0.938641 | −0.469321 | − | 0.883028i | \(-0.655501\pi\) | ||||
−0.469321 | + | 0.883028i | \(0.655501\pi\) | |||||||
\(138\) | 0.238997 | 0.0203448 | ||||||||
\(139\) | −6.40496 | −0.543262 | −0.271631 | − | 0.962402i | \(-0.587563\pi\) | ||||
−0.271631 | + | 0.962402i | \(0.587563\pi\) | |||||||
\(140\) | −7.94255 | −0.671268 | ||||||||
\(141\) | 0.670793 | 0.0564910 | ||||||||
\(142\) | 8.87980 | 0.745176 | ||||||||
\(143\) | 15.8524 | 1.32565 | ||||||||
\(144\) | −0.403794 | −0.0336495 | ||||||||
\(145\) | 12.2845 | 1.02017 | ||||||||
\(146\) | −7.14962 | −0.591707 | ||||||||
\(147\) | −1.75586 | −0.144821 | ||||||||
\(148\) | 8.68033 | 0.713519 | ||||||||
\(149\) | 23.1246 | 1.89444 | 0.947220 | − | 0.320583i | \(-0.103879\pi\) | ||||
0.947220 | + | 0.320583i | \(0.103879\pi\) | |||||||
\(150\) | 1.80140 | 0.147084 | ||||||||
\(151\) | −18.4125 | −1.49839 | −0.749194 | − | 0.662351i | \(-0.769559\pi\) | ||||
−0.749194 | + | 0.662351i | \(0.769559\pi\) | |||||||
\(152\) | −2.76603 | −0.224355 | ||||||||
\(153\) | 5.66174 | 0.457725 | ||||||||
\(154\) | −4.83164 | −0.389345 | ||||||||
\(155\) | 7.13357 | 0.572982 | ||||||||
\(156\) | 10.3140 | 0.825782 | ||||||||
\(157\) | −3.04619 | −0.243112 | −0.121556 | − | 0.992585i | \(-0.538788\pi\) | ||||
−0.121556 | + | 0.992585i | \(0.538788\pi\) | |||||||
\(158\) | 7.72284 | 0.614396 | ||||||||
\(159\) | −10.2934 | −0.816321 | ||||||||
\(160\) | 14.9621 | 1.18286 | ||||||||
\(161\) | 0.548317 | 0.0432135 | ||||||||
\(162\) | −1.89518 | −0.148899 | ||||||||
\(163\) | 2.71109 | 0.212349 | 0.106175 | − | 0.994348i | \(-0.466140\pi\) | ||||
0.106175 | + | 0.994348i | \(0.466140\pi\) | |||||||
\(164\) | 0.969615 | 0.0757142 | ||||||||
\(165\) | −7.76772 | −0.604717 | ||||||||
\(166\) | −0.333117 | −0.0258549 | ||||||||
\(167\) | 3.29107 | 0.254671 | 0.127335 | − | 0.991860i | \(-0.459358\pi\) | ||||
0.127335 | + | 0.991860i | \(0.459358\pi\) | |||||||
\(168\) | −7.99660 | −0.616951 | ||||||||
\(169\) | 29.2170 | 2.24747 | ||||||||
\(170\) | −8.23911 | −0.631911 | ||||||||
\(171\) | −1.49867 | −0.114606 | ||||||||
\(172\) | 8.17722 | 0.623507 | ||||||||
\(173\) | 14.2999 | 1.08720 | 0.543602 | − | 0.839343i | \(-0.317060\pi\) | ||||
0.543602 | + | 0.839343i | \(0.317060\pi\) | |||||||
\(174\) | 4.86208 | 0.368594 | ||||||||
\(175\) | 4.13285 | 0.312414 | ||||||||
\(176\) | −0.657363 | −0.0495506 | ||||||||
\(177\) | 1.41220 | 0.106148 | ||||||||
\(178\) | −10.0051 | −0.749911 | ||||||||
\(179\) | −14.6846 | −1.09758 | −0.548789 | − | 0.835961i | \(-0.684911\pi\) | ||||
−0.548789 | + | 0.835961i | \(0.684911\pi\) | |||||||
\(180\) | 5.04494 | 0.376028 | ||||||||
\(181\) | −23.2505 | −1.72820 | −0.864098 | − | 0.503323i | \(-0.832111\pi\) | ||||
−0.864098 | + | 0.503323i | \(0.832111\pi\) | |||||||
\(182\) | −12.8673 | −0.953786 | ||||||||
\(183\) | −16.7548 | −1.23855 | ||||||||
\(184\) | −0.642805 | −0.0473882 | ||||||||
\(185\) | −17.4098 | −1.28000 | ||||||||
\(186\) | 2.82341 | 0.207022 | ||||||||
\(187\) | 9.21713 | 0.674023 | ||||||||
\(188\) | −0.709246 | −0.0517271 | ||||||||
\(189\) | −13.0057 | −0.946022 | ||||||||
\(190\) | 2.18091 | 0.158220 | ||||||||
\(191\) | −17.8805 | −1.29379 | −0.646894 | − | 0.762580i | \(-0.723932\pi\) | ||||
−0.646894 | + | 0.762580i | \(0.723932\pi\) | |||||||
\(192\) | 5.26159 | 0.379723 | ||||||||
\(193\) | −9.17057 | −0.660112 | −0.330056 | − | 0.943961i | \(-0.607068\pi\) | ||||
−0.330056 | + | 0.943961i | \(0.607068\pi\) | |||||||
\(194\) | −0.941622 | −0.0676045 | ||||||||
\(195\) | −20.6864 | −1.48139 | ||||||||
\(196\) | 1.85651 | 0.132608 | ||||||||
\(197\) | −9.17425 | −0.653638 | −0.326819 | − | 0.945087i | \(-0.605977\pi\) | ||||
−0.326819 | + | 0.945087i | \(0.605977\pi\) | |||||||
\(198\) | 3.06896 | 0.218102 | ||||||||
\(199\) | 10.6905 | 0.757828 | 0.378914 | − | 0.925432i | \(-0.376298\pi\) | ||||
0.378914 | + | 0.925432i | \(0.376298\pi\) | |||||||
\(200\) | −4.84504 | −0.342596 | ||||||||
\(201\) | −6.55028 | −0.462021 | ||||||||
\(202\) | 5.83542 | 0.410578 | ||||||||
\(203\) | 11.1548 | 0.782914 | ||||||||
\(204\) | 5.99690 | 0.419867 | ||||||||
\(205\) | −1.94472 | −0.135825 | ||||||||
\(206\) | 4.10927 | 0.286306 | ||||||||
\(207\) | −0.348280 | −0.0242071 | ||||||||
\(208\) | −1.75064 | −0.121385 | ||||||||
\(209\) | −2.43979 | −0.168764 | ||||||||
\(210\) | 6.30499 | 0.435086 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | 10.8835 | 0.747480 | ||||||||
\(213\) | 12.9631 | 0.888216 | ||||||||
\(214\) | −2.29611 | −0.156959 | ||||||||
\(215\) | −16.4008 | −1.11852 | ||||||||
\(216\) | 15.2468 | 1.03742 | ||||||||
\(217\) | 6.47758 | 0.439727 | ||||||||
\(218\) | 11.7592 | 0.796436 | ||||||||
\(219\) | −10.4373 | −0.705287 | ||||||||
\(220\) | 8.21300 | 0.553720 | ||||||||
\(221\) | 24.5464 | 1.65117 | ||||||||
\(222\) | −6.89066 | −0.462471 | ||||||||
\(223\) | 25.0279 | 1.67599 | 0.837996 | − | 0.545677i | \(-0.183727\pi\) | ||||
0.837996 | + | 0.545677i | \(0.183727\pi\) | |||||||
\(224\) | 13.5862 | 0.907765 | ||||||||
\(225\) | −2.62510 | −0.175007 | ||||||||
\(226\) | 1.74322 | 0.115957 | ||||||||
\(227\) | 12.4136 | 0.823917 | 0.411958 | − | 0.911203i | \(-0.364845\pi\) | ||||
0.411958 | + | 0.911203i | \(0.364845\pi\) | |||||||
\(228\) | −1.58739 | −0.105127 | ||||||||
\(229\) | 7.64770 | 0.505374 | 0.252687 | − | 0.967548i | \(-0.418686\pi\) | ||||
0.252687 | + | 0.967548i | \(0.418686\pi\) | |||||||
\(230\) | 0.506826 | 0.0334191 | ||||||||
\(231\) | −7.05342 | −0.464081 | ||||||||
\(232\) | −13.0770 | −0.858549 | ||||||||
\(233\) | −2.58749 | −0.169512 | −0.0847560 | − | 0.996402i | \(-0.527011\pi\) | ||||
−0.0847560 | + | 0.996402i | \(0.527011\pi\) | |||||||
\(234\) | 8.17304 | 0.534288 | ||||||||
\(235\) | 1.42251 | 0.0927942 | ||||||||
\(236\) | −1.49316 | −0.0971962 | ||||||||
\(237\) | 11.2741 | 0.732332 | ||||||||
\(238\) | −7.48146 | −0.484951 | ||||||||
\(239\) | −5.57185 | −0.360413 | −0.180206 | − | 0.983629i | \(-0.557677\pi\) | ||||
−0.180206 | + | 0.983629i | \(0.557677\pi\) | |||||||
\(240\) | 0.857818 | 0.0553719 | ||||||||
\(241\) | −23.9561 | −1.54315 | −0.771574 | − | 0.636140i | \(-0.780530\pi\) | ||||
−0.771574 | + | 0.636140i | \(0.780530\pi\) | |||||||
\(242\) | −4.23646 | −0.272330 | ||||||||
\(243\) | 13.7698 | 0.883335 | ||||||||
\(244\) | 17.7152 | 1.13410 | ||||||||
\(245\) | −3.72353 | −0.237888 | ||||||||
\(246\) | −0.769705 | −0.0490746 | ||||||||
\(247\) | −6.49746 | −0.413424 | ||||||||
\(248\) | −7.59382 | −0.482208 | ||||||||
\(249\) | −0.486297 | −0.0308178 | ||||||||
\(250\) | −7.08441 | −0.448057 | ||||||||
\(251\) | −9.57005 | −0.604056 | −0.302028 | − | 0.953299i | \(-0.597664\pi\) | ||||
−0.302028 | + | 0.953299i | \(0.597664\pi\) | |||||||
\(252\) | 4.58102 | 0.288577 | ||||||||
\(253\) | −0.566988 | −0.0356462 | ||||||||
\(254\) | 16.2543 | 1.01988 | ||||||||
\(255\) | −12.0278 | −0.753208 | ||||||||
\(256\) | −15.2293 | −0.951830 | ||||||||
\(257\) | 8.79485 | 0.548608 | 0.274304 | − | 0.961643i | \(-0.411553\pi\) | ||||
0.274304 | + | 0.961643i | \(0.411553\pi\) | |||||||
\(258\) | −6.49129 | −0.404130 | ||||||||
\(259\) | −15.8089 | −0.982314 | ||||||||
\(260\) | 21.8723 | 1.35646 | ||||||||
\(261\) | −7.08530 | −0.438569 | ||||||||
\(262\) | 13.9592 | 0.862402 | ||||||||
\(263\) | −20.7003 | −1.27644 | −0.638218 | − | 0.769856i | \(-0.720328\pi\) | ||||
−0.638218 | + | 0.769856i | \(0.720328\pi\) | |||||||
\(264\) | 8.26889 | 0.508915 | ||||||||
\(265\) | −21.8286 | −1.34092 | ||||||||
\(266\) | 1.98035 | 0.121423 | ||||||||
\(267\) | −14.6058 | −0.893859 | ||||||||
\(268\) | 6.92577 | 0.423059 | ||||||||
\(269\) | 16.8431 | 1.02694 | 0.513472 | − | 0.858106i | \(-0.328359\pi\) | ||||
0.513472 | + | 0.858106i | \(0.328359\pi\) | |||||||
\(270\) | −12.0215 | −0.731606 | ||||||||
\(271\) | 9.60067 | 0.583199 | 0.291600 | − | 0.956540i | \(-0.405813\pi\) | ||||
0.291600 | + | 0.956540i | \(0.405813\pi\) | |||||||
\(272\) | −1.01788 | −0.0617181 | ||||||||
\(273\) | −18.7842 | −1.13687 | ||||||||
\(274\) | −9.22131 | −0.557080 | ||||||||
\(275\) | −4.27358 | −0.257707 | ||||||||
\(276\) | −0.368897 | −0.0222050 | ||||||||
\(277\) | 13.5708 | 0.815389 | 0.407695 | − | 0.913118i | \(-0.366333\pi\) | ||||
0.407695 | + | 0.913118i | \(0.366333\pi\) | |||||||
\(278\) | −5.37588 | −0.322424 | ||||||||
\(279\) | −4.11443 | −0.246324 | ||||||||
\(280\) | −16.9579 | −1.01343 | ||||||||
\(281\) | −11.5780 | −0.690688 | −0.345344 | − | 0.938476i | \(-0.612238\pi\) | ||||
−0.345344 | + | 0.938476i | \(0.612238\pi\) | |||||||
\(282\) | 0.563017 | 0.0335272 | ||||||||
\(283\) | 16.2405 | 0.965400 | 0.482700 | − | 0.875786i | \(-0.339656\pi\) | ||||
0.482700 | + | 0.875786i | \(0.339656\pi\) | |||||||
\(284\) | −13.7062 | −0.813312 | ||||||||
\(285\) | 3.18377 | 0.188590 | ||||||||
\(286\) | 13.3054 | 0.786766 | ||||||||
\(287\) | −1.76589 | −0.104237 | ||||||||
\(288\) | −8.62967 | −0.508508 | ||||||||
\(289\) | −2.72793 | −0.160467 | ||||||||
\(290\) | 10.3107 | 0.605466 | ||||||||
\(291\) | −1.37462 | −0.0805815 | ||||||||
\(292\) | 11.0356 | 0.645809 | ||||||||
\(293\) | −1.72993 | −0.101064 | −0.0505318 | − | 0.998722i | \(-0.516092\pi\) | ||||
−0.0505318 | + | 0.998722i | \(0.516092\pi\) | |||||||
\(294\) | −1.47374 | −0.0859504 | ||||||||
\(295\) | 2.99477 | 0.174362 | ||||||||
\(296\) | 18.5331 | 1.07721 | ||||||||
\(297\) | 13.4485 | 0.780362 | ||||||||
\(298\) | 19.4092 | 1.12434 | ||||||||
\(299\) | −1.50996 | −0.0873233 | ||||||||
\(300\) | −2.78050 | −0.160532 | ||||||||
\(301\) | −14.8926 | −0.858394 | ||||||||
\(302\) | −15.4542 | −0.889287 | ||||||||
\(303\) | 8.51877 | 0.489390 | ||||||||
\(304\) | 0.269435 | 0.0154531 | ||||||||
\(305\) | −35.5308 | −2.03449 | ||||||||
\(306\) | 4.75207 | 0.271658 | ||||||||
\(307\) | 20.9738 | 1.19704 | 0.598518 | − | 0.801109i | \(-0.295757\pi\) | ||||
0.598518 | + | 0.801109i | \(0.295757\pi\) | |||||||
\(308\) | 7.45775 | 0.424945 | ||||||||
\(309\) | 5.99887 | 0.341264 | ||||||||
\(310\) | 5.98742 | 0.340062 | ||||||||
\(311\) | −11.9727 | −0.678909 | −0.339454 | − | 0.940623i | \(-0.610242\pi\) | ||||
−0.339454 | + | 0.940623i | \(0.610242\pi\) | |||||||
\(312\) | 22.0211 | 1.24670 | ||||||||
\(313\) | 13.2893 | 0.751158 | 0.375579 | − | 0.926790i | \(-0.377444\pi\) | ||||
0.375579 | + | 0.926790i | \(0.377444\pi\) | |||||||
\(314\) | −2.55676 | −0.144286 | ||||||||
\(315\) | −9.18799 | −0.517685 | ||||||||
\(316\) | −11.9204 | −0.670574 | ||||||||
\(317\) | −30.8154 | −1.73077 | −0.865383 | − | 0.501111i | \(-0.832925\pi\) | ||||
−0.865383 | + | 0.501111i | \(0.832925\pi\) | |||||||
\(318\) | −8.63957 | −0.484483 | ||||||||
\(319\) | −11.5346 | −0.645816 | ||||||||
\(320\) | 11.1579 | 0.623747 | ||||||||
\(321\) | −3.35194 | −0.187087 | ||||||||
\(322\) | 0.460219 | 0.0256470 | ||||||||
\(323\) | −3.77784 | −0.210205 | ||||||||
\(324\) | 2.92525 | 0.162514 | ||||||||
\(325\) | −11.3811 | −0.631309 | ||||||||
\(326\) | 2.27550 | 0.126028 | ||||||||
\(327\) | 17.1666 | 0.949314 | ||||||||
\(328\) | 2.07019 | 0.114307 | ||||||||
\(329\) | 1.29170 | 0.0712136 | ||||||||
\(330\) | −6.51969 | −0.358897 | ||||||||
\(331\) | −6.31204 | −0.346941 | −0.173470 | − | 0.984839i | \(-0.555498\pi\) | ||||
−0.173470 | + | 0.984839i | \(0.555498\pi\) | |||||||
\(332\) | 0.514173 | 0.0282189 | ||||||||
\(333\) | 10.0415 | 0.550269 | ||||||||
\(334\) | 2.76229 | 0.151146 | ||||||||
\(335\) | −13.8908 | −0.758934 | ||||||||
\(336\) | 0.778935 | 0.0424944 | ||||||||
\(337\) | −28.5569 | −1.55560 | −0.777798 | − | 0.628515i | \(-0.783663\pi\) | ||||
−0.777798 | + | 0.628515i | \(0.783663\pi\) | |||||||
\(338\) | 24.5227 | 1.33386 | ||||||||
\(339\) | 2.54482 | 0.138216 | ||||||||
\(340\) | 12.7173 | 0.689690 | ||||||||
\(341\) | −6.69815 | −0.362725 | ||||||||
\(342\) | −1.25788 | −0.0680184 | ||||||||
\(343\) | −19.8972 | −1.07435 | ||||||||
\(344\) | 17.4589 | 0.941322 | ||||||||
\(345\) | 0.739884 | 0.0398340 | ||||||||
\(346\) | 12.0024 | 0.645251 | ||||||||
\(347\) | 12.8664 | 0.690707 | 0.345353 | − | 0.938473i | \(-0.387759\pi\) | ||||
0.345353 | + | 0.938473i | \(0.387759\pi\) | |||||||
\(348\) | −7.50474 | −0.402296 | ||||||||
\(349\) | −25.5401 | −1.36713 | −0.683564 | − | 0.729891i | \(-0.739571\pi\) | ||||
−0.683564 | + | 0.729891i | \(0.739571\pi\) | |||||||
\(350\) | 3.46883 | 0.185417 | ||||||||
\(351\) | 35.8151 | 1.91167 | ||||||||
\(352\) | −14.0488 | −0.748804 | ||||||||
\(353\) | 14.7409 | 0.784579 | 0.392290 | − | 0.919842i | \(-0.371683\pi\) | ||||
0.392290 | + | 0.919842i | \(0.371683\pi\) | |||||||
\(354\) | 1.18530 | 0.0629982 | ||||||||
\(355\) | 27.4900 | 1.45902 | ||||||||
\(356\) | 15.4430 | 0.818479 | ||||||||
\(357\) | −10.9217 | −0.578039 | ||||||||
\(358\) | −12.3252 | −0.651408 | ||||||||
\(359\) | −22.4193 | −1.18324 | −0.591622 | − | 0.806215i | \(-0.701512\pi\) | ||||
−0.591622 | + | 0.806215i | \(0.701512\pi\) | |||||||
\(360\) | 10.7713 | 0.567697 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −19.5149 | −1.02568 | ||||||||
\(363\) | −6.18456 | −0.324605 | ||||||||
\(364\) | 19.8609 | 1.04100 | ||||||||
\(365\) | −22.1337 | −1.15853 | ||||||||
\(366\) | −14.0628 | −0.735074 | ||||||||
\(367\) | −6.35728 | −0.331847 | −0.165924 | − | 0.986139i | \(-0.553061\pi\) | ||||
−0.165924 | + | 0.986139i | \(0.553061\pi\) | |||||||
\(368\) | 0.0626146 | 0.00326401 | ||||||||
\(369\) | 1.12166 | 0.0583912 | ||||||||
\(370\) | −14.6126 | −0.759672 | ||||||||
\(371\) | −19.8213 | −1.02907 | ||||||||
\(372\) | −4.35799 | −0.225951 | ||||||||
\(373\) | 37.3094 | 1.93181 | 0.965904 | − | 0.258900i | \(-0.0833600\pi\) | ||||
0.965904 | + | 0.258900i | \(0.0833600\pi\) | |||||||
\(374\) | 7.73621 | 0.400030 | ||||||||
\(375\) | −10.3421 | −0.534064 | ||||||||
\(376\) | −1.51429 | −0.0780934 | ||||||||
\(377\) | −30.7182 | −1.58207 | ||||||||
\(378\) | −10.9160 | −0.561460 | ||||||||
\(379\) | −26.5062 | −1.36153 | −0.680766 | − | 0.732501i | \(-0.738353\pi\) | ||||
−0.680766 | + | 0.732501i | \(0.738353\pi\) | |||||||
\(380\) | −3.36628 | −0.172686 | ||||||||
\(381\) | 23.7286 | 1.21565 | ||||||||
\(382\) | −15.0076 | −0.767857 | ||||||||
\(383\) | −4.48903 | −0.229379 | −0.114689 | − | 0.993401i | \(-0.536587\pi\) | ||||
−0.114689 | + | 0.993401i | \(0.536587\pi\) | |||||||
\(384\) | −9.69471 | −0.494731 | ||||||||
\(385\) | −14.9577 | −0.762317 | ||||||||
\(386\) | −7.69714 | −0.391774 | ||||||||
\(387\) | 9.45947 | 0.480852 | ||||||||
\(388\) | 1.45342 | 0.0737860 | ||||||||
\(389\) | 7.91387 | 0.401249 | 0.200625 | − | 0.979668i | \(-0.435703\pi\) | ||||
0.200625 | + | 0.979668i | \(0.435703\pi\) | |||||||
\(390\) | −17.3628 | −0.879197 | ||||||||
\(391\) | −0.877941 | −0.0443994 | ||||||||
\(392\) | 3.96377 | 0.200201 | ||||||||
\(393\) | 20.3782 | 1.02794 | ||||||||
\(394\) | −7.70023 | −0.387932 | ||||||||
\(395\) | 23.9083 | 1.20296 | ||||||||
\(396\) | −4.73701 | −0.238044 | ||||||||
\(397\) | −10.2793 | −0.515905 | −0.257952 | − | 0.966158i | \(-0.583048\pi\) | ||||
−0.257952 | + | 0.966158i | \(0.583048\pi\) | |||||||
\(398\) | 8.97284 | 0.449768 | ||||||||
\(399\) | 2.89100 | 0.144731 | ||||||||
\(400\) | 0.471947 | 0.0235974 | ||||||||
\(401\) | −5.01472 | −0.250423 | −0.125212 | − | 0.992130i | \(-0.539961\pi\) | ||||
−0.125212 | + | 0.992130i | \(0.539961\pi\) | |||||||
\(402\) | −5.49785 | −0.274208 | ||||||||
\(403\) | −17.8380 | −0.888575 | ||||||||
\(404\) | −9.00710 | −0.448120 | ||||||||
\(405\) | −5.86707 | −0.291537 | ||||||||
\(406\) | 9.36256 | 0.464656 | ||||||||
\(407\) | 16.3472 | 0.810299 | ||||||||
\(408\) | 12.8038 | 0.633882 | ||||||||
\(409\) | −31.0284 | −1.53426 | −0.767129 | − | 0.641493i | \(-0.778315\pi\) | ||||
−0.767129 | + | 0.641493i | \(0.778315\pi\) | |||||||
\(410\) | −1.63226 | −0.0806118 | ||||||||
\(411\) | −13.4616 | −0.664013 | ||||||||
\(412\) | −6.34275 | −0.312485 | ||||||||
\(413\) | 2.71938 | 0.133812 | ||||||||
\(414\) | −0.292322 | −0.0143668 | ||||||||
\(415\) | −1.03126 | −0.0506225 | ||||||||
\(416\) | −37.4138 | −1.83436 | ||||||||
\(417\) | −7.84791 | −0.384314 | ||||||||
\(418\) | −2.04779 | −0.100161 | ||||||||
\(419\) | −12.1190 | −0.592054 | −0.296027 | − | 0.955180i | \(-0.595662\pi\) | ||||
−0.296027 | + | 0.955180i | \(0.595662\pi\) | |||||||
\(420\) | −9.73190 | −0.474868 | ||||||||
\(421\) | 4.51497 | 0.220046 | 0.110023 | − | 0.993929i | \(-0.464907\pi\) | ||||
0.110023 | + | 0.993929i | \(0.464907\pi\) | |||||||
\(422\) | 0.839330 | 0.0408580 | ||||||||
\(423\) | −0.820460 | −0.0398922 | ||||||||
\(424\) | 23.2370 | 1.12849 | ||||||||
\(425\) | −6.61734 | −0.320988 | ||||||||
\(426\) | 10.8803 | 0.527152 | ||||||||
\(427\) | −32.2635 | −1.56134 | ||||||||
\(428\) | 3.54409 | 0.171310 | ||||||||
\(429\) | 19.4238 | 0.937789 | ||||||||
\(430\) | −13.7657 | −0.663839 | ||||||||
\(431\) | 32.3348 | 1.55751 | 0.778756 | − | 0.627326i | \(-0.215851\pi\) | ||||
0.778756 | + | 0.627326i | \(0.215851\pi\) | |||||||
\(432\) | −1.48517 | −0.0714552 | ||||||||
\(433\) | −27.7317 | −1.33270 | −0.666351 | − | 0.745639i | \(-0.732145\pi\) | ||||
−0.666351 | + | 0.745639i | \(0.732145\pi\) | |||||||
\(434\) | 5.43683 | 0.260976 | ||||||||
\(435\) | 15.0520 | 0.721687 | ||||||||
\(436\) | −18.1506 | −0.869258 | ||||||||
\(437\) | 0.232392 | 0.0111168 | ||||||||
\(438\) | −8.76033 | −0.418585 | ||||||||
\(439\) | −8.00868 | −0.382233 | −0.191117 | − | 0.981567i | \(-0.561211\pi\) | ||||
−0.191117 | + | 0.981567i | \(0.561211\pi\) | |||||||
\(440\) | 17.5353 | 0.835963 | ||||||||
\(441\) | 2.14762 | 0.102268 | ||||||||
\(442\) | 20.6025 | 0.979962 | ||||||||
\(443\) | 37.9010 | 1.80073 | 0.900365 | − | 0.435136i | \(-0.143300\pi\) | ||||
0.900365 | + | 0.435136i | \(0.143300\pi\) | |||||||
\(444\) | 10.6359 | 0.504757 | ||||||||
\(445\) | −30.9735 | −1.46829 | ||||||||
\(446\) | 21.0067 | 0.994694 | ||||||||
\(447\) | 28.3343 | 1.34016 | ||||||||
\(448\) | 10.1319 | 0.478686 | ||||||||
\(449\) | 29.5000 | 1.39219 | 0.696095 | − | 0.717950i | \(-0.254919\pi\) | ||||
0.696095 | + | 0.717950i | \(0.254919\pi\) | |||||||
\(450\) | −2.20333 | −0.103866 | ||||||||
\(451\) | 1.82602 | 0.0859840 | ||||||||
\(452\) | −2.69070 | −0.126560 | ||||||||
\(453\) | −22.5606 | −1.05999 | ||||||||
\(454\) | 10.4191 | 0.488991 | ||||||||
\(455\) | −39.8344 | −1.86746 | ||||||||
\(456\) | −3.38918 | −0.158713 | ||||||||
\(457\) | 22.8679 | 1.06972 | 0.534858 | − | 0.844942i | \(-0.320365\pi\) | ||||
0.534858 | + | 0.844942i | \(0.320365\pi\) | |||||||
\(458\) | 6.41895 | 0.299938 | ||||||||
\(459\) | 20.8241 | 0.971984 | ||||||||
\(460\) | −0.782297 | −0.0364748 | ||||||||
\(461\) | −3.14734 | −0.146586 | −0.0732930 | − | 0.997310i | \(-0.523351\pi\) | ||||
−0.0732930 | + | 0.997310i | \(0.523351\pi\) | |||||||
\(462\) | −5.92015 | −0.275430 | ||||||||
\(463\) | 40.1992 | 1.86822 | 0.934108 | − | 0.356990i | \(-0.116197\pi\) | ||||
0.934108 | + | 0.356990i | \(0.116197\pi\) | |||||||
\(464\) | 1.27381 | 0.0591352 | ||||||||
\(465\) | 8.74067 | 0.405339 | ||||||||
\(466\) | −2.17176 | −0.100605 | ||||||||
\(467\) | 32.7221 | 1.51420 | 0.757099 | − | 0.653300i | \(-0.226616\pi\) | ||||
0.757099 | + | 0.653300i | \(0.226616\pi\) | |||||||
\(468\) | −12.6153 | −0.583141 | ||||||||
\(469\) | −12.6134 | −0.582433 | ||||||||
\(470\) | 1.19395 | 0.0550730 | ||||||||
\(471\) | −3.73245 | −0.171982 | ||||||||
\(472\) | −3.18799 | −0.146739 | ||||||||
\(473\) | 15.3997 | 0.708079 | ||||||||
\(474\) | 9.46270 | 0.434636 | ||||||||
\(475\) | 1.75162 | 0.0803698 | ||||||||
\(476\) | 11.5478 | 0.529292 | ||||||||
\(477\) | 12.5901 | 0.576460 | ||||||||
\(478\) | −4.67662 | −0.213904 | ||||||||
\(479\) | 27.2658 | 1.24581 | 0.622903 | − | 0.782299i | \(-0.285953\pi\) | ||||
0.622903 | + | 0.782299i | \(0.285953\pi\) | |||||||
\(480\) | 18.3328 | 0.836775 | ||||||||
\(481\) | 43.5346 | 1.98501 | ||||||||
\(482\) | −20.1071 | −0.915852 | ||||||||
\(483\) | 0.671846 | 0.0305700 | ||||||||
\(484\) | 6.53908 | 0.297231 | ||||||||
\(485\) | −2.91506 | −0.132366 | ||||||||
\(486\) | 11.5574 | 0.524256 | ||||||||
\(487\) | 32.5256 | 1.47388 | 0.736938 | − | 0.675961i | \(-0.236271\pi\) | ||||
0.736938 | + | 0.675961i | \(0.236271\pi\) | |||||||
\(488\) | 37.8232 | 1.71218 | ||||||||
\(489\) | 3.32187 | 0.150220 | ||||||||
\(490\) | −3.12527 | −0.141185 | ||||||||
\(491\) | −34.7941 | −1.57023 | −0.785117 | − | 0.619347i | \(-0.787397\pi\) | ||||
−0.785117 | + | 0.619347i | \(0.787397\pi\) | |||||||
\(492\) | 1.18806 | 0.0535617 | ||||||||
\(493\) | −17.8606 | −0.804400 | ||||||||
\(494\) | −5.45352 | −0.245365 | ||||||||
\(495\) | 9.50086 | 0.427032 | ||||||||
\(496\) | 0.739701 | 0.0332136 | ||||||||
\(497\) | 24.9621 | 1.11970 | ||||||||
\(498\) | −0.408163 | −0.0182902 | ||||||||
\(499\) | −26.8788 | −1.20326 | −0.601630 | − | 0.798775i | \(-0.705482\pi\) | ||||
−0.601630 | + | 0.798775i | \(0.705482\pi\) | |||||||
\(500\) | 10.9349 | 0.489026 | ||||||||
\(501\) | 4.03251 | 0.180159 | ||||||||
\(502\) | −8.03243 | −0.358505 | ||||||||
\(503\) | 38.5693 | 1.71972 | 0.859859 | − | 0.510531i | \(-0.170551\pi\) | ||||
0.859859 | + | 0.510531i | \(0.170551\pi\) | |||||||
\(504\) | 9.78079 | 0.435671 | ||||||||
\(505\) | 18.0652 | 0.803891 | ||||||||
\(506\) | −0.475890 | −0.0211559 | ||||||||
\(507\) | 35.7993 | 1.58990 | ||||||||
\(508\) | −25.0888 | −1.11314 | ||||||||
\(509\) | −9.74643 | −0.432003 | −0.216002 | − | 0.976393i | \(-0.569302\pi\) | ||||
−0.216002 | + | 0.976393i | \(0.569302\pi\) | |||||||
\(510\) | −10.0953 | −0.447026 | ||||||||
\(511\) | −20.0983 | −0.889098 | ||||||||
\(512\) | 3.04199 | 0.134438 | ||||||||
\(513\) | −5.51216 | −0.243368 | ||||||||
\(514\) | 7.38178 | 0.325596 | ||||||||
\(515\) | 12.7214 | 0.560573 | ||||||||
\(516\) | 10.0194 | 0.441081 | ||||||||
\(517\) | −1.33568 | −0.0587432 | ||||||||
\(518\) | −13.2688 | −0.583000 | ||||||||
\(519\) | 17.5215 | 0.769110 | ||||||||
\(520\) | 46.6988 | 2.04788 | ||||||||
\(521\) | −39.6139 | −1.73552 | −0.867758 | − | 0.496987i | \(-0.834440\pi\) | ||||
−0.867758 | + | 0.496987i | \(0.834440\pi\) | |||||||
\(522\) | −5.94691 | −0.260289 | ||||||||
\(523\) | −11.7762 | −0.514936 | −0.257468 | − | 0.966287i | \(-0.582888\pi\) | ||||
−0.257468 | + | 0.966287i | \(0.582888\pi\) | |||||||
\(524\) | −21.5463 | −0.941256 | ||||||||
\(525\) | 5.06393 | 0.221008 | ||||||||
\(526\) | −17.3744 | −0.757559 | ||||||||
\(527\) | −10.3716 | −0.451794 | ||||||||
\(528\) | −0.805459 | −0.0350531 | ||||||||
\(529\) | −22.9460 | −0.997652 | ||||||||
\(530\) | −18.3214 | −0.795831 | ||||||||
\(531\) | −1.72729 | −0.0749581 | ||||||||
\(532\) | −3.05672 | −0.132526 | ||||||||
\(533\) | 4.86293 | 0.210637 | ||||||||
\(534\) | −12.2591 | −0.530502 | ||||||||
\(535\) | −7.10826 | −0.307317 | ||||||||
\(536\) | 14.7870 | 0.638701 | ||||||||
\(537\) | −17.9928 | −0.776448 | ||||||||
\(538\) | 14.1369 | 0.609487 | ||||||||
\(539\) | 3.49626 | 0.150594 | ||||||||
\(540\) | 18.5555 | 0.798500 | ||||||||
\(541\) | 17.6084 | 0.757043 | 0.378522 | − | 0.925592i | \(-0.376433\pi\) | ||||
0.378522 | + | 0.925592i | \(0.376433\pi\) | |||||||
\(542\) | 8.05813 | 0.346126 | ||||||||
\(543\) | −28.4885 | −1.22256 | ||||||||
\(544\) | −21.7536 | −0.932678 | ||||||||
\(545\) | 36.4041 | 1.55938 | ||||||||
\(546\) | −15.7661 | −0.674727 | ||||||||
\(547\) | −10.5603 | −0.451524 | −0.225762 | − | 0.974183i | \(-0.572487\pi\) | ||||
−0.225762 | + | 0.974183i | \(0.572487\pi\) | |||||||
\(548\) | 14.2333 | 0.608016 | ||||||||
\(549\) | 20.4931 | 0.874624 | ||||||||
\(550\) | −3.58695 | −0.152948 | ||||||||
\(551\) | 4.72772 | 0.201408 | ||||||||
\(552\) | −0.787621 | −0.0335234 | ||||||||
\(553\) | 21.7097 | 0.923191 | ||||||||
\(554\) | 11.3904 | 0.483930 | ||||||||
\(555\) | −21.3320 | −0.905494 | ||||||||
\(556\) | 8.29778 | 0.351904 | ||||||||
\(557\) | 24.9068 | 1.05533 | 0.527667 | − | 0.849451i | \(-0.323067\pi\) | ||||
0.527667 | + | 0.849451i | \(0.323067\pi\) | |||||||
\(558\) | −3.45336 | −0.146193 | ||||||||
\(559\) | 41.0113 | 1.73460 | ||||||||
\(560\) | 1.65184 | 0.0698029 | ||||||||
\(561\) | 11.2936 | 0.476817 | ||||||||
\(562\) | −9.71780 | −0.409921 | ||||||||
\(563\) | 10.2380 | 0.431479 | 0.215740 | − | 0.976451i | \(-0.430784\pi\) | ||||
0.215740 | + | 0.976451i | \(0.430784\pi\) | |||||||
\(564\) | −0.869029 | −0.0365927 | ||||||||
\(565\) | 5.39664 | 0.227038 | ||||||||
\(566\) | 13.6312 | 0.572961 | ||||||||
\(567\) | −5.32755 | −0.223736 | ||||||||
\(568\) | −29.2636 | −1.22787 | ||||||||
\(569\) | −18.7019 | −0.784024 | −0.392012 | − | 0.919960i | \(-0.628221\pi\) | ||||
−0.392012 | + | 0.919960i | \(0.628221\pi\) | |||||||
\(570\) | 2.67223 | 0.111928 | ||||||||
\(571\) | 29.1505 | 1.21991 | 0.609956 | − | 0.792435i | \(-0.291187\pi\) | ||||
0.609956 | + | 0.792435i | \(0.291187\pi\) | |||||||
\(572\) | −20.5372 | −0.858705 | ||||||||
\(573\) | −21.9087 | −0.915250 | ||||||||
\(574\) | −1.48217 | −0.0618644 | ||||||||
\(575\) | 0.407063 | 0.0169757 | ||||||||
\(576\) | −6.43555 | −0.268148 | ||||||||
\(577\) | 16.9969 | 0.707588 | 0.353794 | − | 0.935323i | \(-0.384891\pi\) | ||||
0.353794 | + | 0.935323i | \(0.384891\pi\) | |||||||
\(578\) | −2.28963 | −0.0952363 | ||||||||
\(579\) | −11.2366 | −0.466976 | ||||||||
\(580\) | −15.9148 | −0.660827 | ||||||||
\(581\) | −0.936426 | −0.0388495 | ||||||||
\(582\) | −1.15376 | −0.0478248 | ||||||||
\(583\) | 20.4962 | 0.848867 | ||||||||
\(584\) | 23.5617 | 0.974992 | ||||||||
\(585\) | 25.3020 | 1.04611 | ||||||||
\(586\) | −1.45198 | −0.0599809 | ||||||||
\(587\) | 15.7906 | 0.651749 | 0.325874 | − | 0.945413i | \(-0.394341\pi\) | ||||
0.325874 | + | 0.945413i | \(0.394341\pi\) | |||||||
\(588\) | 2.27476 | 0.0938093 | ||||||||
\(589\) | 2.74538 | 0.113121 | ||||||||
\(590\) | 2.51360 | 0.103483 | ||||||||
\(591\) | −11.2411 | −0.462397 | ||||||||
\(592\) | −1.80528 | −0.0741964 | ||||||||
\(593\) | −17.0004 | −0.698121 | −0.349060 | − | 0.937100i | \(-0.613499\pi\) | ||||
−0.349060 | + | 0.937100i | \(0.613499\pi\) | |||||||
\(594\) | 11.2877 | 0.463142 | ||||||||
\(595\) | −23.1610 | −0.949509 | ||||||||
\(596\) | −29.9585 | −1.22715 | ||||||||
\(597\) | 13.0989 | 0.536103 | ||||||||
\(598\) | −1.26736 | −0.0518261 | ||||||||
\(599\) | −11.6127 | −0.474483 | −0.237241 | − | 0.971451i | \(-0.576243\pi\) | ||||
−0.237241 | + | 0.971451i | \(0.576243\pi\) | |||||||
\(600\) | −5.93656 | −0.242359 | ||||||||
\(601\) | −2.43112 | −0.0991676 | −0.0495838 | − | 0.998770i | \(-0.515789\pi\) | ||||
−0.0495838 | + | 0.998770i | \(0.515789\pi\) | |||||||
\(602\) | −12.4998 | −0.509454 | ||||||||
\(603\) | 8.01178 | 0.326265 | ||||||||
\(604\) | 23.8539 | 0.970600 | ||||||||
\(605\) | −13.1152 | −0.533208 | ||||||||
\(606\) | 7.15006 | 0.290451 | ||||||||
\(607\) | −12.9386 | −0.525162 | −0.262581 | − | 0.964910i | \(-0.584574\pi\) | ||||
−0.262581 | + | 0.964910i | \(0.584574\pi\) | |||||||
\(608\) | 5.75821 | 0.233526 | ||||||||
\(609\) | 13.6678 | 0.553848 | ||||||||
\(610\) | −29.8221 | −1.20746 | ||||||||
\(611\) | −3.55709 | −0.143904 | ||||||||
\(612\) | −7.33493 | −0.296497 | ||||||||
\(613\) | −25.7474 | −1.03993 | −0.519963 | − | 0.854189i | \(-0.674054\pi\) | ||||
−0.519963 | + | 0.854189i | \(0.674054\pi\) | |||||||
\(614\) | 17.6039 | 0.710436 | ||||||||
\(615\) | −2.38284 | −0.0960855 | ||||||||
\(616\) | 15.9228 | 0.641548 | ||||||||
\(617\) | 3.76843 | 0.151711 | 0.0758557 | − | 0.997119i | \(-0.475831\pi\) | ||||
0.0758557 | + | 0.997119i | \(0.475831\pi\) | |||||||
\(618\) | 5.03504 | 0.202539 | ||||||||
\(619\) | 44.1164 | 1.77319 | 0.886594 | − | 0.462548i | \(-0.153065\pi\) | ||||
0.886594 | + | 0.462548i | \(0.153065\pi\) | |||||||
\(620\) | −9.24171 | −0.371156 | ||||||||
\(621\) | −1.28099 | −0.0514042 | ||||||||
\(622\) | −10.0490 | −0.402930 | ||||||||
\(623\) | −28.1253 | −1.12682 | ||||||||
\(624\) | −2.14504 | −0.0858703 | ||||||||
\(625\) | −30.6899 | −1.22760 | ||||||||
\(626\) | 11.1542 | 0.445809 | ||||||||
\(627\) | −2.98944 | −0.119387 | ||||||||
\(628\) | 3.94641 | 0.157479 | ||||||||
\(629\) | 25.3124 | 1.00927 | ||||||||
\(630\) | −7.71176 | −0.307244 | ||||||||
\(631\) | −25.8970 | −1.03094 | −0.515471 | − | 0.856907i | \(-0.672383\pi\) | ||||
−0.515471 | + | 0.856907i | \(0.672383\pi\) | |||||||
\(632\) | −25.4508 | −1.01238 | ||||||||
\(633\) | 1.22529 | 0.0487008 | ||||||||
\(634\) | −25.8643 | −1.02720 | ||||||||
\(635\) | 50.3198 | 1.99688 | ||||||||
\(636\) | 13.3354 | 0.528782 | ||||||||
\(637\) | 9.31097 | 0.368914 | ||||||||
\(638\) | −9.68137 | −0.383289 | ||||||||
\(639\) | −15.8554 | −0.627230 | ||||||||
\(640\) | −20.5590 | −0.812664 | ||||||||
\(641\) | −1.18358 | −0.0467486 | −0.0233743 | − | 0.999727i | \(-0.507441\pi\) | ||||
−0.0233743 | + | 0.999727i | \(0.507441\pi\) | |||||||
\(642\) | −2.81339 | −0.111036 | ||||||||
\(643\) | −2.82042 | −0.111227 | −0.0556133 | − | 0.998452i | \(-0.517711\pi\) | ||||
−0.0556133 | + | 0.998452i | \(0.517711\pi\) | |||||||
\(644\) | −0.710359 | −0.0279921 | ||||||||
\(645\) | −20.0956 | −0.791265 | ||||||||
\(646\) | −3.17085 | −0.124756 | ||||||||
\(647\) | 7.64689 | 0.300630 | 0.150315 | − | 0.988638i | \(-0.451971\pi\) | ||||
0.150315 | + | 0.988638i | \(0.451971\pi\) | |||||||
\(648\) | 6.24561 | 0.245351 | ||||||||
\(649\) | −2.81198 | −0.110380 | ||||||||
\(650\) | −9.55249 | −0.374680 | ||||||||
\(651\) | 7.93689 | 0.311071 | ||||||||
\(652\) | −3.51229 | −0.137552 | ||||||||
\(653\) | 48.0823 | 1.88161 | 0.940804 | − | 0.338952i | \(-0.110073\pi\) | ||||
0.940804 | + | 0.338952i | \(0.110073\pi\) | |||||||
\(654\) | 14.4084 | 0.563414 | ||||||||
\(655\) | 43.2147 | 1.68854 | ||||||||
\(656\) | −0.201654 | −0.00787327 | ||||||||
\(657\) | 12.7661 | 0.498051 | ||||||||
\(658\) | 1.08416 | 0.0422650 | ||||||||
\(659\) | −8.85320 | −0.344872 | −0.172436 | − | 0.985021i | \(-0.555164\pi\) | ||||
−0.172436 | + | 0.985021i | \(0.555164\pi\) | |||||||
\(660\) | 10.0633 | 0.391713 | ||||||||
\(661\) | 32.4214 | 1.26104 | 0.630522 | − | 0.776171i | \(-0.282841\pi\) | ||||
0.630522 | + | 0.776171i | \(0.282841\pi\) | |||||||
\(662\) | −5.29788 | −0.205908 | ||||||||
\(663\) | 30.0764 | 1.16807 | ||||||||
\(664\) | 1.09779 | 0.0426027 | ||||||||
\(665\) | 6.13075 | 0.237740 | ||||||||
\(666\) | 8.42810 | 0.326582 | ||||||||
\(667\) | 1.09869 | 0.0425413 | ||||||||
\(668\) | −4.26366 | −0.164966 | ||||||||
\(669\) | 30.6663 | 1.18563 | ||||||||
\(670\) | −11.6589 | −0.450424 | ||||||||
\(671\) | 33.3621 | 1.28793 | ||||||||
\(672\) | 16.6470 | 0.642171 | ||||||||
\(673\) | −36.0735 | −1.39053 | −0.695266 | − | 0.718752i | \(-0.744714\pi\) | ||||
−0.695266 | + | 0.718752i | \(0.744714\pi\) | |||||||
\(674\) | −23.9687 | −0.923240 | ||||||||
\(675\) | −9.65522 | −0.371629 | ||||||||
\(676\) | −37.8514 | −1.45582 | ||||||||
\(677\) | −22.1935 | −0.852966 | −0.426483 | − | 0.904495i | \(-0.640248\pi\) | ||||
−0.426483 | + | 0.904495i | \(0.640248\pi\) | |||||||
\(678\) | 2.13594 | 0.0820304 | ||||||||
\(679\) | −2.64700 | −0.101583 | ||||||||
\(680\) | 27.1522 | 1.04124 | ||||||||
\(681\) | 15.2102 | 0.582855 | ||||||||
\(682\) | −5.62196 | −0.215276 | ||||||||
\(683\) | −44.7194 | −1.71114 | −0.855571 | − | 0.517686i | \(-0.826793\pi\) | ||||
−0.855571 | + | 0.517686i | \(0.826793\pi\) | |||||||
\(684\) | 1.94157 | 0.0742377 | ||||||||
\(685\) | −28.5472 | −1.09073 | ||||||||
\(686\) | −16.7004 | −0.637623 | ||||||||
\(687\) | 9.37063 | 0.357512 | ||||||||
\(688\) | −1.70064 | −0.0648365 | ||||||||
\(689\) | 54.5840 | 2.07949 | ||||||||
\(690\) | 0.621007 | 0.0236413 | ||||||||
\(691\) | −28.2485 | −1.07462 | −0.537312 | − | 0.843383i | \(-0.680560\pi\) | ||||
−0.537312 | + | 0.843383i | \(0.680560\pi\) | |||||||
\(692\) | −18.5259 | −0.704250 | ||||||||
\(693\) | 8.62718 | 0.327719 | ||||||||
\(694\) | 10.7992 | 0.409932 | ||||||||
\(695\) | −16.6426 | −0.631289 | ||||||||
\(696\) | −16.0231 | −0.607355 | ||||||||
\(697\) | 2.82747 | 0.107098 | ||||||||
\(698\) | −21.4365 | −0.811385 | ||||||||
\(699\) | −3.17042 | −0.119916 | ||||||||
\(700\) | −5.35421 | −0.202370 | ||||||||
\(701\) | −7.81040 | −0.294995 | −0.147497 | − | 0.989062i | \(-0.547122\pi\) | ||||
−0.147497 | + | 0.989062i | \(0.547122\pi\) | |||||||
\(702\) | 30.0607 | 1.13457 | ||||||||
\(703\) | −6.70024 | −0.252704 | ||||||||
\(704\) | −10.4769 | −0.394862 | ||||||||
\(705\) | 1.74298 | 0.0656445 | ||||||||
\(706\) | 12.3725 | 0.465645 | ||||||||
\(707\) | 16.4040 | 0.616935 | ||||||||
\(708\) | −1.82954 | −0.0687585 | ||||||||
\(709\) | 10.3171 | 0.387466 | 0.193733 | − | 0.981054i | \(-0.437940\pi\) | ||||
0.193733 | + | 0.981054i | \(0.437940\pi\) | |||||||
\(710\) | 23.0732 | 0.865921 | ||||||||
\(711\) | −13.7896 | −0.517150 | ||||||||
\(712\) | 32.9719 | 1.23567 | ||||||||
\(713\) | 0.638006 | 0.0238935 | ||||||||
\(714\) | −9.16693 | −0.343064 | ||||||||
\(715\) | 41.1908 | 1.54045 | ||||||||
\(716\) | 19.0243 | 0.710970 | ||||||||
\(717\) | −6.82711 | −0.254963 | ||||||||
\(718\) | −18.8172 | −0.702251 | ||||||||
\(719\) | −25.8620 | −0.964490 | −0.482245 | − | 0.876036i | \(-0.660179\pi\) | ||||
−0.482245 | + | 0.876036i | \(0.660179\pi\) | |||||||
\(720\) | −1.04921 | −0.0391019 | ||||||||
\(721\) | 11.5516 | 0.430204 | ||||||||
\(722\) | 0.839330 | 0.0312366 | ||||||||
\(723\) | −29.3531 | −1.09165 | ||||||||
\(724\) | 30.1216 | 1.11946 | ||||||||
\(725\) | 8.28117 | 0.307555 | ||||||||
\(726\) | −5.19088 | −0.192652 | ||||||||
\(727\) | 20.9068 | 0.775392 | 0.387696 | − | 0.921787i | \(-0.373271\pi\) | ||||
0.387696 | + | 0.921787i | \(0.373271\pi\) | |||||||
\(728\) | 42.4044 | 1.57161 | ||||||||
\(729\) | 23.6459 | 0.875774 | ||||||||
\(730\) | −18.5775 | −0.687583 | ||||||||
\(731\) | 23.8453 | 0.881952 | ||||||||
\(732\) | 21.7062 | 0.802286 | ||||||||
\(733\) | 22.1689 | 0.818826 | 0.409413 | − | 0.912349i | \(-0.365734\pi\) | ||||
0.409413 | + | 0.912349i | \(0.365734\pi\) | |||||||
\(734\) | −5.33586 | −0.196950 | ||||||||
\(735\) | −4.56240 | −0.168287 | ||||||||
\(736\) | 1.33816 | 0.0493254 | ||||||||
\(737\) | 13.0429 | 0.480442 | ||||||||
\(738\) | 0.941441 | 0.0346549 | ||||||||
\(739\) | 31.6864 | 1.16560 | 0.582802 | − | 0.812614i | \(-0.301956\pi\) | ||||
0.582802 | + | 0.812614i | \(0.301956\pi\) | |||||||
\(740\) | 22.5549 | 0.829133 | ||||||||
\(741\) | −7.96126 | −0.292464 | ||||||||
\(742\) | −16.6366 | −0.610749 | ||||||||
\(743\) | −17.4426 | −0.639908 | −0.319954 | − | 0.947433i | \(-0.603668\pi\) | ||||
−0.319954 | + | 0.947433i | \(0.603668\pi\) | |||||||
\(744\) | −9.30460 | −0.341123 | ||||||||
\(745\) | 60.0867 | 2.20141 | ||||||||
\(746\) | 31.3149 | 1.14652 | ||||||||
\(747\) | 0.594799 | 0.0217626 | ||||||||
\(748\) | −11.9410 | −0.436607 | ||||||||
\(749\) | −6.45459 | −0.235846 | ||||||||
\(750\) | −8.68043 | −0.316965 | ||||||||
\(751\) | −35.7196 | −1.30343 | −0.651713 | − | 0.758466i | \(-0.725949\pi\) | ||||
−0.651713 | + | 0.758466i | \(0.725949\pi\) | |||||||
\(752\) | 0.147504 | 0.00537893 | ||||||||
\(753\) | −11.7261 | −0.427321 | ||||||||
\(754\) | −25.7827 | −0.938951 | ||||||||
\(755\) | −47.8428 | −1.74118 | ||||||||
\(756\) | 16.8491 | 0.612797 | ||||||||
\(757\) | 10.6591 | 0.387411 | 0.193705 | − | 0.981060i | \(-0.437949\pi\) | ||||
0.193705 | + | 0.981060i | \(0.437949\pi\) | |||||||
\(758\) | −22.2475 | −0.808064 | ||||||||
\(759\) | −0.694723 | −0.0252169 | ||||||||
\(760\) | −7.18723 | −0.260708 | ||||||||
\(761\) | −28.3257 | −1.02681 | −0.513404 | − | 0.858147i | \(-0.671616\pi\) | ||||
−0.513404 | + | 0.858147i | \(0.671616\pi\) | |||||||
\(762\) | 19.9161 | 0.721486 | ||||||||
\(763\) | 33.0564 | 1.19672 | ||||||||
\(764\) | 23.1646 | 0.838067 | ||||||||
\(765\) | 14.7114 | 0.531892 | ||||||||
\(766\) | −3.76778 | −0.136136 | ||||||||
\(767\) | −7.48865 | −0.270399 | ||||||||
\(768\) | −18.6602 | −0.673344 | ||||||||
\(769\) | −47.2862 | −1.70518 | −0.852592 | − | 0.522578i | \(-0.824971\pi\) | ||||
−0.852592 | + | 0.522578i | \(0.824971\pi\) | |||||||
\(770\) | −12.5545 | −0.452432 | ||||||||
\(771\) | 10.7762 | 0.388096 | ||||||||
\(772\) | 11.8807 | 0.427596 | ||||||||
\(773\) | 35.4459 | 1.27490 | 0.637450 | − | 0.770492i | \(-0.279989\pi\) | ||||
0.637450 | + | 0.770492i | \(0.279989\pi\) | |||||||
\(774\) | 7.93962 | 0.285384 | ||||||||
\(775\) | 4.80887 | 0.172740 | ||||||||
\(776\) | 3.10314 | 0.111396 | ||||||||
\(777\) | −19.3704 | −0.694908 | ||||||||
\(778\) | 6.64235 | 0.238140 | ||||||||
\(779\) | −0.748434 | −0.0268154 | ||||||||
\(780\) | 26.7998 | 0.959587 | ||||||||
\(781\) | −25.8121 | −0.923628 | ||||||||
\(782\) | −0.736882 | −0.0263509 | ||||||||
\(783\) | −26.0600 | −0.931307 | ||||||||
\(784\) | −0.386104 | −0.0137894 | ||||||||
\(785\) | −7.91517 | −0.282505 | ||||||||
\(786\) | 17.1040 | 0.610080 | ||||||||
\(787\) | −24.1191 | −0.859752 | −0.429876 | − | 0.902888i | \(-0.641443\pi\) | ||||
−0.429876 | + | 0.902888i | \(0.641443\pi\) | |||||||
\(788\) | 11.8855 | 0.423402 | ||||||||
\(789\) | −25.3638 | −0.902975 | ||||||||
\(790\) | 20.0669 | 0.713950 | ||||||||
\(791\) | 4.90037 | 0.174237 | ||||||||
\(792\) | −10.1138 | −0.359380 | ||||||||
\(793\) | 88.8474 | 3.15507 | ||||||||
\(794\) | −8.62775 | −0.306187 | ||||||||
\(795\) | −26.7463 | −0.948593 | ||||||||
\(796\) | −13.8498 | −0.490893 | ||||||||
\(797\) | 35.9808 | 1.27451 | 0.637253 | − | 0.770655i | \(-0.280071\pi\) | ||||
0.637253 | + | 0.770655i | \(0.280071\pi\) | |||||||
\(798\) | 2.42650 | 0.0858972 | ||||||||
\(799\) | −2.06821 | −0.0731680 | ||||||||
\(800\) | 10.0862 | 0.356601 | ||||||||
\(801\) | 17.8646 | 0.631215 | ||||||||
\(802\) | −4.20901 | −0.148625 | ||||||||
\(803\) | 20.7827 | 0.733406 | ||||||||
\(804\) | 8.48606 | 0.299280 | ||||||||
\(805\) | 1.42474 | 0.0502155 | ||||||||
\(806\) | −14.9720 | −0.527366 | ||||||||
\(807\) | 20.6377 | 0.726480 | ||||||||
\(808\) | −19.2308 | −0.676536 | ||||||||
\(809\) | 24.9976 | 0.878869 | 0.439435 | − | 0.898275i | \(-0.355179\pi\) | ||||
0.439435 | + | 0.898275i | \(0.355179\pi\) | |||||||
\(810\) | −4.92441 | −0.173026 | ||||||||
\(811\) | −45.5950 | −1.60106 | −0.800529 | − | 0.599295i | \(-0.795448\pi\) | ||||
−0.800529 | + | 0.599295i | \(0.795448\pi\) | |||||||
\(812\) | −14.4513 | −0.507142 | ||||||||
\(813\) | 11.7636 | 0.412567 | ||||||||
\(814\) | 13.7207 | 0.480909 | ||||||||
\(815\) | 7.04447 | 0.246757 | ||||||||
\(816\) | −1.24720 | −0.0436606 | ||||||||
\(817\) | −6.31190 | −0.220825 | ||||||||
\(818\) | −26.0431 | −0.910576 | ||||||||
\(819\) | 22.9753 | 0.802821 | ||||||||
\(820\) | 2.51944 | 0.0879826 | ||||||||
\(821\) | 0.943805 | 0.0329390 | 0.0164695 | − | 0.999864i | \(-0.494757\pi\) | ||||
0.0164695 | + | 0.999864i | \(0.494757\pi\) | |||||||
\(822\) | −11.2988 | −0.394089 | ||||||||
\(823\) | 8.85870 | 0.308795 | 0.154397 | − | 0.988009i | \(-0.450656\pi\) | ||||
0.154397 | + | 0.988009i | \(0.450656\pi\) | |||||||
\(824\) | −13.5422 | −0.471765 | ||||||||
\(825\) | −5.23636 | −0.182307 | ||||||||
\(826\) | 2.28245 | 0.0794168 | ||||||||
\(827\) | −17.9070 | −0.622688 | −0.311344 | − | 0.950297i | \(-0.600779\pi\) | ||||
−0.311344 | + | 0.950297i | \(0.600779\pi\) | |||||||
\(828\) | 0.451205 | 0.0156805 | ||||||||
\(829\) | 36.8342 | 1.27930 | 0.639652 | − | 0.768665i | \(-0.279078\pi\) | ||||
0.639652 | + | 0.768665i | \(0.279078\pi\) | |||||||
\(830\) | −0.865566 | −0.0300442 | ||||||||
\(831\) | 16.6281 | 0.576822 | ||||||||
\(832\) | −27.9012 | −0.967301 | ||||||||
\(833\) | 5.41371 | 0.187574 | ||||||||
\(834\) | −6.58699 | −0.228089 | ||||||||
\(835\) | 8.55148 | 0.295936 | ||||||||
\(836\) | 3.16081 | 0.109319 | ||||||||
\(837\) | −15.1330 | −0.523073 | ||||||||
\(838\) | −10.1719 | −0.351382 | ||||||||
\(839\) | −15.4204 | −0.532371 | −0.266186 | − | 0.963922i | \(-0.585763\pi\) | ||||
−0.266186 | + | 0.963922i | \(0.585763\pi\) | |||||||
\(840\) | −20.7783 | −0.716918 | ||||||||
\(841\) | −6.64865 | −0.229264 | ||||||||
\(842\) | 3.78955 | 0.130597 | ||||||||
\(843\) | −14.1864 | −0.488606 | ||||||||
\(844\) | −1.29552 | −0.0445938 | ||||||||
\(845\) | 75.9172 | 2.61163 | ||||||||
\(846\) | −0.688637 | −0.0236758 | ||||||||
\(847\) | −11.9091 | −0.409203 | ||||||||
\(848\) | −2.26347 | −0.0777280 | ||||||||
\(849\) | 19.8993 | 0.682943 | ||||||||
\(850\) | −5.55413 | −0.190505 | ||||||||
\(851\) | −1.55709 | −0.0533762 | ||||||||
\(852\) | −16.7940 | −0.575353 | ||||||||
\(853\) | 24.0916 | 0.824881 | 0.412440 | − | 0.910985i | \(-0.364677\pi\) | ||||
0.412440 | + | 0.910985i | \(0.364677\pi\) | |||||||
\(854\) | −27.0797 | −0.926648 | ||||||||
\(855\) | −3.89413 | −0.133176 | ||||||||
\(856\) | 7.56687 | 0.258630 | ||||||||
\(857\) | −53.5018 | −1.82759 | −0.913793 | − | 0.406181i | \(-0.866860\pi\) | ||||
−0.913793 | + | 0.406181i | \(0.866860\pi\) | |||||||
\(858\) | 16.3030 | 0.556574 | ||||||||
\(859\) | 6.47416 | 0.220895 | 0.110448 | − | 0.993882i | \(-0.464772\pi\) | ||||
0.110448 | + | 0.993882i | \(0.464772\pi\) | |||||||
\(860\) | 21.2476 | 0.724537 | ||||||||
\(861\) | −2.16372 | −0.0737395 | ||||||||
\(862\) | 27.1396 | 0.924378 | ||||||||
\(863\) | −7.59495 | −0.258535 | −0.129267 | − | 0.991610i | \(-0.541263\pi\) | ||||
−0.129267 | + | 0.991610i | \(0.541263\pi\) | |||||||
\(864\) | −31.7402 | −1.07982 | ||||||||
\(865\) | 37.1568 | 1.26337 | ||||||||
\(866\) | −23.2761 | −0.790953 | ||||||||
\(867\) | −3.34250 | −0.113517 | ||||||||
\(868\) | −8.39186 | −0.284838 | ||||||||
\(869\) | −22.4490 | −0.761529 | ||||||||
\(870\) | 12.6336 | 0.428318 | ||||||||
\(871\) | 34.7349 | 1.17695 | ||||||||
\(872\) | −38.7528 | −1.31234 | ||||||||
\(873\) | 1.68132 | 0.0569041 | ||||||||
\(874\) | 0.195054 | 0.00659780 | ||||||||
\(875\) | −19.9150 | −0.673251 | ||||||||
\(876\) | 13.5218 | 0.456858 | ||||||||
\(877\) | −30.3749 | −1.02569 | −0.512844 | − | 0.858482i | \(-0.671408\pi\) | ||||
−0.512844 | + | 0.858482i | \(0.671408\pi\) | |||||||
\(878\) | −6.72193 | −0.226854 | ||||||||
\(879\) | −2.11966 | −0.0714944 | ||||||||
\(880\) | −1.70809 | −0.0575795 | ||||||||
\(881\) | −2.84597 | −0.0958830 | −0.0479415 | − | 0.998850i | \(-0.515266\pi\) | ||||
−0.0479415 | + | 0.998850i | \(0.515266\pi\) | |||||||
\(882\) | 1.80256 | 0.0606955 | ||||||||
\(883\) | 5.07217 | 0.170692 | 0.0853460 | − | 0.996351i | \(-0.472800\pi\) | ||||
0.0853460 | + | 0.996351i | \(0.472800\pi\) | |||||||
\(884\) | −31.8004 | −1.06956 | ||||||||
\(885\) | 3.66945 | 0.123347 | ||||||||
\(886\) | 31.8114 | 1.06873 | ||||||||
\(887\) | −18.4626 | −0.619914 | −0.309957 | − | 0.950751i | \(-0.600315\pi\) | ||||
−0.309957 | + | 0.950751i | \(0.600315\pi\) | |||||||
\(888\) | 22.7083 | 0.762042 | ||||||||
\(889\) | 45.6925 | 1.53248 | ||||||||
\(890\) | −25.9970 | −0.871422 | ||||||||
\(891\) | 5.50896 | 0.184557 | ||||||||
\(892\) | −32.4243 | −1.08564 | ||||||||
\(893\) | 0.547458 | 0.0183200 | ||||||||
\(894\) | 23.7818 | 0.795382 | ||||||||
\(895\) | −38.1563 | −1.27542 | ||||||||
\(896\) | −18.6684 | −0.623667 | ||||||||
\(897\) | −1.85014 | −0.0617742 | ||||||||
\(898\) | 24.7602 | 0.826259 | ||||||||
\(899\) | 12.9794 | 0.432887 | ||||||||
\(900\) | 3.40089 | 0.113363 | ||||||||
\(901\) | 31.7369 | 1.05731 | ||||||||
\(902\) | 1.53263 | 0.0510312 | ||||||||
\(903\) | −18.2477 | −0.607245 | ||||||||
\(904\) | −5.74482 | −0.191070 | ||||||||
\(905\) | −60.4138 | −2.00822 | ||||||||
\(906\) | −18.9358 | −0.629099 | ||||||||
\(907\) | −11.8762 | −0.394342 | −0.197171 | − | 0.980369i | \(-0.563175\pi\) | ||||
−0.197171 | + | 0.980369i | \(0.563175\pi\) | |||||||
\(908\) | −16.0821 | −0.533702 | ||||||||
\(909\) | −10.4195 | −0.345592 | ||||||||
\(910\) | −33.4342 | −1.10833 | ||||||||
\(911\) | −32.7728 | −1.08581 | −0.542906 | − | 0.839794i | \(-0.682676\pi\) | ||||
−0.542906 | + | 0.839794i | \(0.682676\pi\) | |||||||
\(912\) | 0.330135 | 0.0109319 | ||||||||
\(913\) | 0.968313 | 0.0320465 | ||||||||
\(914\) | 19.1937 | 0.634872 | ||||||||
\(915\) | −43.5354 | −1.43924 | ||||||||
\(916\) | −9.90779 | −0.327363 | ||||||||
\(917\) | 39.2408 | 1.29584 | ||||||||
\(918\) | 17.4783 | 0.576869 | ||||||||
\(919\) | 21.7590 | 0.717764 | 0.358882 | − | 0.933383i | \(-0.383158\pi\) | ||||
0.358882 | + | 0.933383i | \(0.383158\pi\) | |||||||
\(920\) | −1.67026 | −0.0550668 | ||||||||
\(921\) | 25.6989 | 0.846807 | ||||||||
\(922\) | −2.64165 | −0.0869983 | ||||||||
\(923\) | −68.7408 | −2.26263 | ||||||||
\(924\) | 9.13788 | 0.300614 | ||||||||
\(925\) | −11.7363 | −0.385886 | ||||||||
\(926\) | 33.7404 | 1.10878 | ||||||||
\(927\) | −7.33734 | −0.240990 | ||||||||
\(928\) | 27.2232 | 0.893646 | ||||||||
\(929\) | −37.7354 | −1.23806 | −0.619029 | − | 0.785368i | \(-0.712474\pi\) | ||||
−0.619029 | + | 0.785368i | \(0.712474\pi\) | |||||||
\(930\) | 7.33630 | 0.240567 | ||||||||
\(931\) | −1.43302 | −0.0469652 | ||||||||
\(932\) | 3.35216 | 0.109804 | ||||||||
\(933\) | −14.6700 | −0.480273 | ||||||||
\(934\) | 27.4646 | 0.898670 | ||||||||
\(935\) | 23.9497 | 0.783238 | ||||||||
\(936\) | −26.9344 | −0.880380 | ||||||||
\(937\) | 40.1178 | 1.31059 | 0.655296 | − | 0.755372i | \(-0.272544\pi\) | ||||
0.655296 | + | 0.755372i | \(0.272544\pi\) | |||||||
\(938\) | −10.5868 | −0.345672 | ||||||||
\(939\) | 16.2833 | 0.531384 | ||||||||
\(940\) | −1.84290 | −0.0601086 | ||||||||
\(941\) | −4.53780 | −0.147928 | −0.0739641 | − | 0.997261i | \(-0.523565\pi\) | ||||
−0.0739641 | + | 0.997261i | \(0.523565\pi\) | |||||||
\(942\) | −3.13276 | −0.102071 | ||||||||
\(943\) | −0.173930 | −0.00566396 | ||||||||
\(944\) | 0.310537 | 0.0101071 | ||||||||
\(945\) | −33.7937 | −1.09931 | ||||||||
\(946\) | 12.9254 | 0.420242 | ||||||||
\(947\) | 0.885506 | 0.0287751 | 0.0143875 | − | 0.999896i | \(-0.495420\pi\) | ||||
0.0143875 | + | 0.999896i | \(0.495420\pi\) | |||||||
\(948\) | −14.6059 | −0.474377 | ||||||||
\(949\) | 55.3470 | 1.79664 | ||||||||
\(950\) | 1.47019 | 0.0476992 | ||||||||
\(951\) | −37.7577 | −1.22438 | ||||||||
\(952\) | 24.6553 | 0.799084 | ||||||||
\(953\) | −47.1689 | −1.52795 | −0.763975 | − | 0.645245i | \(-0.776755\pi\) | ||||
−0.763975 | + | 0.645245i | \(0.776755\pi\) | |||||||
\(954\) | 10.5672 | 0.342127 | ||||||||
\(955\) | −46.4605 | −1.50343 | ||||||||
\(956\) | 7.21847 | 0.233462 | ||||||||
\(957\) | −14.1332 | −0.456863 | ||||||||
\(958\) | 22.8850 | 0.739380 | ||||||||
\(959\) | −25.9221 | −0.837068 | ||||||||
\(960\) | 13.6717 | 0.441251 | ||||||||
\(961\) | −23.4629 | −0.756867 | ||||||||
\(962\) | 36.5399 | 1.17809 | ||||||||
\(963\) | 4.09983 | 0.132115 | ||||||||
\(964\) | 31.0357 | 0.999593 | ||||||||
\(965\) | −23.8287 | −0.767073 | ||||||||
\(966\) | 0.563901 | 0.0181432 | ||||||||
\(967\) | −51.9337 | −1.67008 | −0.835038 | − | 0.550192i | \(-0.814555\pi\) | ||||
−0.835038 | + | 0.550192i | \(0.814555\pi\) | |||||||
\(968\) | 13.9614 | 0.448736 | ||||||||
\(969\) | −4.62894 | −0.148703 | ||||||||
\(970\) | −2.44670 | −0.0785588 | ||||||||
\(971\) | 49.2427 | 1.58027 | 0.790137 | − | 0.612930i | \(-0.210009\pi\) | ||||
0.790137 | + | 0.612930i | \(0.210009\pi\) | |||||||
\(972\) | −17.8392 | −0.572192 | ||||||||
\(973\) | −15.1122 | −0.484473 | ||||||||
\(974\) | 27.2997 | 0.874739 | ||||||||
\(975\) | −13.9451 | −0.446601 | ||||||||
\(976\) | −3.68430 | −0.117931 | ||||||||
\(977\) | 36.3458 | 1.16280 | 0.581402 | − | 0.813616i | \(-0.302504\pi\) | ||||
0.581402 | + | 0.813616i | \(0.302504\pi\) | |||||||
\(978\) | 2.78814 | 0.0891550 | ||||||||
\(979\) | 29.0830 | 0.929496 | ||||||||
\(980\) | 4.82393 | 0.154095 | ||||||||
\(981\) | −20.9968 | −0.670376 | ||||||||
\(982\) | −29.2037 | −0.931928 | ||||||||
\(983\) | −3.01699 | −0.0962270 | −0.0481135 | − | 0.998842i | \(-0.515321\pi\) | ||||
−0.0481135 | + | 0.998842i | \(0.515321\pi\) | |||||||
\(984\) | 2.53658 | 0.0808633 | ||||||||
\(985\) | −23.8383 | −0.759550 | ||||||||
\(986\) | −14.9909 | −0.477408 | ||||||||
\(987\) | 1.58270 | 0.0503779 | ||||||||
\(988\) | 8.41763 | 0.267800 | ||||||||
\(989\) | −1.46684 | −0.0466427 | ||||||||
\(990\) | 7.97435 | 0.253442 | ||||||||
\(991\) | 10.4593 | 0.332251 | 0.166125 | − | 0.986105i | \(-0.446874\pi\) | ||||
0.166125 | + | 0.986105i | \(0.446874\pi\) | |||||||
\(992\) | 15.8085 | 0.501920 | ||||||||
\(993\) | −7.73406 | −0.245433 | ||||||||
\(994\) | 20.9514 | 0.664538 | ||||||||
\(995\) | 27.7780 | 0.880622 | ||||||||
\(996\) | 0.630009 | 0.0199626 | ||||||||
\(997\) | −32.9373 | −1.04314 | −0.521568 | − | 0.853210i | \(-0.674653\pi\) | ||||
−0.521568 | + | 0.853210i | \(0.674653\pi\) | |||||||
\(998\) | −22.5602 | −0.714130 | ||||||||
\(999\) | 36.9328 | 1.16850 |
(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 | 4009.2.a.c.1.46 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.46 | ✓ | 71 | 1.1 | even | 1 | trivial |