Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4021,2,Mod(1,4021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4021.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: | \(32.1078466528\) |
Analytic rank: | \(0\) |
Dimension: | \(182\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.38633 | −1.68739 | −0.843695 | − | 0.536824i | \(-0.819624\pi\) | ||||
−0.843695 | + | 0.536824i | \(0.819624\pi\) | |||||||
\(3\) | −0.134750 | −0.0777977 | −0.0388989 | − | 0.999243i | \(-0.512385\pi\) | ||||
−0.0388989 | + | 0.999243i | \(0.512385\pi\) | |||||||
\(4\) | 3.69456 | 1.84728 | ||||||||
\(5\) | −0.899112 | −0.402095 | −0.201047 | − | 0.979581i | \(-0.564435\pi\) | ||||
−0.201047 | + | 0.979581i | \(0.564435\pi\) | |||||||
\(6\) | 0.321557 | 0.131275 | ||||||||
\(7\) | −0.745765 | −0.281873 | −0.140936 | − | 0.990019i | \(-0.545011\pi\) | ||||
−0.140936 | + | 0.990019i | \(0.545011\pi\) | |||||||
\(8\) | −4.04378 | −1.42969 | ||||||||
\(9\) | −2.98184 | −0.993948 | ||||||||
\(10\) | 2.14558 | 0.678491 | ||||||||
\(11\) | 0.293991 | 0.0886415 | 0.0443207 | − | 0.999017i | \(-0.485888\pi\) | ||||
0.0443207 | + | 0.999017i | \(0.485888\pi\) | |||||||
\(12\) | −0.497841 | −0.143714 | ||||||||
\(13\) | −1.69853 | −0.471087 | −0.235544 | − | 0.971864i | \(-0.575687\pi\) | ||||
−0.235544 | + | 0.971864i | \(0.575687\pi\) | |||||||
\(14\) | 1.77964 | 0.475629 | ||||||||
\(15\) | 0.121155 | 0.0312821 | ||||||||
\(16\) | 2.26067 | 0.565168 | ||||||||
\(17\) | −4.46796 | −1.08364 | −0.541820 | − | 0.840495i | \(-0.682265\pi\) | ||||
−0.541820 | + | 0.840495i | \(0.682265\pi\) | |||||||
\(18\) | 7.11566 | 1.67718 | ||||||||
\(19\) | 4.09378 | 0.939178 | 0.469589 | − | 0.882885i | \(-0.344402\pi\) | ||||
0.469589 | + | 0.882885i | \(0.344402\pi\) | |||||||
\(20\) | −3.32183 | −0.742783 | ||||||||
\(21\) | 0.100492 | 0.0219291 | ||||||||
\(22\) | −0.701558 | −0.149573 | ||||||||
\(23\) | −0.899501 | −0.187559 | −0.0937794 | − | 0.995593i | \(-0.529895\pi\) | ||||
−0.0937794 | + | 0.995593i | \(0.529895\pi\) | |||||||
\(24\) | 0.544898 | 0.111227 | ||||||||
\(25\) | −4.19160 | −0.838320 | ||||||||
\(26\) | 4.05325 | 0.794908 | ||||||||
\(27\) | 0.806051 | 0.155125 | ||||||||
\(28\) | −2.75528 | −0.520699 | ||||||||
\(29\) | 1.10875 | 0.205890 | 0.102945 | − | 0.994687i | \(-0.467173\pi\) | ||||
0.102945 | + | 0.994687i | \(0.467173\pi\) | |||||||
\(30\) | −0.289115 | −0.0527850 | ||||||||
\(31\) | −8.42322 | −1.51285 | −0.756427 | − | 0.654078i | \(-0.773057\pi\) | ||||
−0.756427 | + | 0.654078i | \(0.773057\pi\) | |||||||
\(32\) | 2.69286 | 0.476036 | ||||||||
\(33\) | −0.0396151 | −0.00689610 | ||||||||
\(34\) | 10.6620 | 1.82852 | ||||||||
\(35\) | 0.670526 | 0.113340 | ||||||||
\(36\) | −11.0166 | −1.83610 | ||||||||
\(37\) | −4.63360 | −0.761758 | −0.380879 | − | 0.924625i | \(-0.624379\pi\) | ||||
−0.380879 | + | 0.924625i | \(0.624379\pi\) | |||||||
\(38\) | −9.76911 | −1.58476 | ||||||||
\(39\) | 0.228876 | 0.0366495 | ||||||||
\(40\) | 3.63581 | 0.574873 | ||||||||
\(41\) | 9.06142 | 1.41516 | 0.707578 | − | 0.706635i | \(-0.249788\pi\) | ||||
0.707578 | + | 0.706635i | \(0.249788\pi\) | |||||||
\(42\) | −0.239806 | −0.0370029 | ||||||||
\(43\) | −1.24742 | −0.190229 | −0.0951147 | − | 0.995466i | \(-0.530322\pi\) | ||||
−0.0951147 | + | 0.995466i | \(0.530322\pi\) | |||||||
\(44\) | 1.08617 | 0.163746 | ||||||||
\(45\) | 2.68101 | 0.399661 | ||||||||
\(46\) | 2.14650 | 0.316485 | ||||||||
\(47\) | −1.77997 | −0.259636 | −0.129818 | − | 0.991538i | \(-0.541439\pi\) | ||||
−0.129818 | + | 0.991538i | \(0.541439\pi\) | |||||||
\(48\) | −0.304625 | −0.0439688 | ||||||||
\(49\) | −6.44383 | −0.920548 | ||||||||
\(50\) | 10.0025 | 1.41457 | ||||||||
\(51\) | 0.602056 | 0.0843047 | ||||||||
\(52\) | −6.27533 | −0.870231 | ||||||||
\(53\) | 3.41414 | 0.468969 | 0.234484 | − | 0.972120i | \(-0.424660\pi\) | ||||
0.234484 | + | 0.972120i | \(0.424660\pi\) | |||||||
\(54\) | −1.92350 | −0.261755 | ||||||||
\(55\) | −0.264330 | −0.0356423 | ||||||||
\(56\) | 3.01572 | 0.402992 | ||||||||
\(57\) | −0.551636 | −0.0730659 | ||||||||
\(58\) | −2.64584 | −0.347416 | ||||||||
\(59\) | −6.04312 | −0.786748 | −0.393374 | − | 0.919379i | \(-0.628692\pi\) | ||||
−0.393374 | + | 0.919379i | \(0.628692\pi\) | |||||||
\(60\) | 0.447615 | 0.0577868 | ||||||||
\(61\) | −6.70671 | −0.858706 | −0.429353 | − | 0.903137i | \(-0.641258\pi\) | ||||
−0.429353 | + | 0.903137i | \(0.641258\pi\) | |||||||
\(62\) | 20.1006 | 2.55277 | ||||||||
\(63\) | 2.22376 | 0.280167 | ||||||||
\(64\) | −10.9474 | −1.36843 | ||||||||
\(65\) | 1.52717 | 0.189422 | ||||||||
\(66\) | 0.0945346 | 0.0116364 | ||||||||
\(67\) | −3.29913 | −0.403053 | −0.201527 | − | 0.979483i | \(-0.564590\pi\) | ||||
−0.201527 | + | 0.979483i | \(0.564590\pi\) | |||||||
\(68\) | −16.5072 | −2.00179 | ||||||||
\(69\) | 0.121207 | 0.0145917 | ||||||||
\(70\) | −1.60010 | −0.191248 | ||||||||
\(71\) | −2.56050 | −0.303875 | −0.151937 | − | 0.988390i | \(-0.548551\pi\) | ||||
−0.151937 | + | 0.988390i | \(0.548551\pi\) | |||||||
\(72\) | 12.0579 | 1.42104 | ||||||||
\(73\) | −6.89904 | −0.807472 | −0.403736 | − | 0.914876i | \(-0.632289\pi\) | ||||
−0.403736 | + | 0.914876i | \(0.632289\pi\) | |||||||
\(74\) | 11.0573 | 1.28538 | ||||||||
\(75\) | 0.564816 | 0.0652193 | ||||||||
\(76\) | 15.1247 | 1.73493 | ||||||||
\(77\) | −0.219248 | −0.0249856 | ||||||||
\(78\) | −0.546174 | −0.0618420 | ||||||||
\(79\) | 14.0674 | 1.58270 | 0.791351 | − | 0.611363i | \(-0.209378\pi\) | ||||
0.791351 | + | 0.611363i | \(0.209378\pi\) | |||||||
\(80\) | −2.03260 | −0.227251 | ||||||||
\(81\) | 8.83691 | 0.981879 | ||||||||
\(82\) | −21.6235 | −2.38792 | ||||||||
\(83\) | −11.5699 | −1.26997 | −0.634983 | − | 0.772526i | \(-0.718993\pi\) | ||||
−0.634983 | + | 0.772526i | \(0.718993\pi\) | |||||||
\(84\) | 0.371273 | 0.0405092 | ||||||||
\(85\) | 4.01720 | 0.435726 | ||||||||
\(86\) | 2.97675 | 0.320991 | ||||||||
\(87\) | −0.149404 | −0.0160177 | ||||||||
\(88\) | −1.18883 | −0.126730 | ||||||||
\(89\) | 11.3134 | 1.19922 | 0.599608 | − | 0.800294i | \(-0.295323\pi\) | ||||
0.599608 | + | 0.800294i | \(0.295323\pi\) | |||||||
\(90\) | −6.39777 | −0.674384 | ||||||||
\(91\) | 1.26670 | 0.132787 | ||||||||
\(92\) | −3.32326 | −0.346474 | ||||||||
\(93\) | 1.13503 | 0.117697 | ||||||||
\(94\) | 4.24760 | 0.438107 | ||||||||
\(95\) | −3.68077 | −0.377639 | ||||||||
\(96\) | −0.362862 | −0.0370345 | ||||||||
\(97\) | 12.5097 | 1.27017 | 0.635083 | − | 0.772444i | \(-0.280966\pi\) | ||||
0.635083 | + | 0.772444i | \(0.280966\pi\) | |||||||
\(98\) | 15.3771 | 1.55332 | ||||||||
\(99\) | −0.876633 | −0.0881050 | ||||||||
\(100\) | −15.4861 | −1.54861 | ||||||||
\(101\) | 4.05913 | 0.403898 | 0.201949 | − | 0.979396i | \(-0.435272\pi\) | ||||
0.201949 | + | 0.979396i | \(0.435272\pi\) | |||||||
\(102\) | −1.43670 | −0.142255 | ||||||||
\(103\) | 4.49373 | 0.442780 | 0.221390 | − | 0.975185i | \(-0.428941\pi\) | ||||
0.221390 | + | 0.975185i | \(0.428941\pi\) | |||||||
\(104\) | 6.86849 | 0.673511 | ||||||||
\(105\) | −0.0903532 | −0.00881757 | ||||||||
\(106\) | −8.14726 | −0.791332 | ||||||||
\(107\) | −3.31042 | −0.320031 | −0.160015 | − | 0.987115i | \(-0.551154\pi\) | ||||
−0.160015 | + | 0.987115i | \(0.551154\pi\) | |||||||
\(108\) | 2.97801 | 0.286559 | ||||||||
\(109\) | 7.11163 | 0.681170 | 0.340585 | − | 0.940214i | \(-0.389375\pi\) | ||||
0.340585 | + | 0.940214i | \(0.389375\pi\) | |||||||
\(110\) | 0.630779 | 0.0601424 | ||||||||
\(111\) | 0.624375 | 0.0592631 | ||||||||
\(112\) | −1.68593 | −0.159305 | ||||||||
\(113\) | −11.1282 | −1.04685 | −0.523424 | − | 0.852072i | \(-0.675346\pi\) | ||||
−0.523424 | + | 0.852072i | \(0.675346\pi\) | |||||||
\(114\) | 1.31638 | 0.123291 | ||||||||
\(115\) | 0.808752 | 0.0754165 | ||||||||
\(116\) | 4.09635 | 0.380336 | ||||||||
\(117\) | 5.06475 | 0.468236 | ||||||||
\(118\) | 14.4209 | 1.32755 | ||||||||
\(119\) | 3.33205 | 0.305449 | ||||||||
\(120\) | −0.489924 | −0.0447238 | ||||||||
\(121\) | −10.9136 | −0.992143 | ||||||||
\(122\) | 16.0044 | 1.44897 | ||||||||
\(123\) | −1.22102 | −0.110096 | ||||||||
\(124\) | −31.1201 | −2.79467 | ||||||||
\(125\) | 8.26427 | 0.739179 | ||||||||
\(126\) | −5.30661 | −0.472750 | ||||||||
\(127\) | −20.0668 | −1.78064 | −0.890321 | − | 0.455333i | \(-0.849520\pi\) | ||||
−0.890321 | + | 0.455333i | \(0.849520\pi\) | |||||||
\(128\) | 20.7384 | 1.83303 | ||||||||
\(129\) | 0.168089 | 0.0147994 | ||||||||
\(130\) | −3.64432 | −0.319628 | ||||||||
\(131\) | 22.1672 | 1.93676 | 0.968378 | − | 0.249487i | \(-0.0802619\pi\) | ||||
0.968378 | + | 0.249487i | \(0.0802619\pi\) | |||||||
\(132\) | −0.146360 | −0.0127390 | ||||||||
\(133\) | −3.05300 | −0.264729 | ||||||||
\(134\) | 7.87281 | 0.680107 | ||||||||
\(135\) | −0.724730 | −0.0623748 | ||||||||
\(136\) | 18.0675 | 1.54927 | ||||||||
\(137\) | 16.8952 | 1.44346 | 0.721728 | − | 0.692177i | \(-0.243348\pi\) | ||||
0.721728 | + | 0.692177i | \(0.243348\pi\) | |||||||
\(138\) | −0.289241 | −0.0246218 | ||||||||
\(139\) | −2.24020 | −0.190011 | −0.0950057 | − | 0.995477i | \(-0.530287\pi\) | ||||
−0.0950057 | + | 0.995477i | \(0.530287\pi\) | |||||||
\(140\) | 2.47730 | 0.209370 | ||||||||
\(141\) | 0.239851 | 0.0201991 | ||||||||
\(142\) | 6.11018 | 0.512755 | ||||||||
\(143\) | −0.499352 | −0.0417579 | ||||||||
\(144\) | −6.74097 | −0.561747 | ||||||||
\(145\) | −0.996890 | −0.0827872 | ||||||||
\(146\) | 16.4634 | 1.36252 | ||||||||
\(147\) | 0.868304 | 0.0716165 | ||||||||
\(148\) | −17.1191 | −1.40718 | ||||||||
\(149\) | −3.69363 | −0.302594 | −0.151297 | − | 0.988488i | \(-0.548345\pi\) | ||||
−0.151297 | + | 0.988488i | \(0.548345\pi\) | |||||||
\(150\) | −1.34784 | −0.110050 | ||||||||
\(151\) | −11.9598 | −0.973273 | −0.486636 | − | 0.873605i | \(-0.661776\pi\) | ||||
−0.486636 | + | 0.873605i | \(0.661776\pi\) | |||||||
\(152\) | −16.5544 | −1.34274 | ||||||||
\(153\) | 13.3228 | 1.07708 | ||||||||
\(154\) | 0.523198 | 0.0421605 | ||||||||
\(155\) | 7.57342 | 0.608311 | ||||||||
\(156\) | 0.845598 | 0.0677020 | ||||||||
\(157\) | −8.51927 | −0.679912 | −0.339956 | − | 0.940441i | \(-0.610412\pi\) | ||||
−0.339956 | + | 0.940441i | \(0.610412\pi\) | |||||||
\(158\) | −33.5693 | −2.67063 | ||||||||
\(159\) | −0.460054 | −0.0364847 | ||||||||
\(160\) | −2.42119 | −0.191412 | ||||||||
\(161\) | 0.670817 | 0.0528678 | ||||||||
\(162\) | −21.0878 | −1.65681 | ||||||||
\(163\) | 1.62584 | 0.127345 | 0.0636727 | − | 0.997971i | \(-0.479719\pi\) | ||||
0.0636727 | + | 0.997971i | \(0.479719\pi\) | |||||||
\(164\) | 33.4780 | 2.61419 | ||||||||
\(165\) | 0.0356184 | 0.00277289 | ||||||||
\(166\) | 27.6097 | 2.14293 | ||||||||
\(167\) | 19.1385 | 1.48098 | 0.740491 | − | 0.672066i | \(-0.234593\pi\) | ||||
0.740491 | + | 0.672066i | \(0.234593\pi\) | |||||||
\(168\) | −0.406366 | −0.0313518 | ||||||||
\(169\) | −10.1150 | −0.778077 | ||||||||
\(170\) | −9.58635 | −0.735239 | ||||||||
\(171\) | −12.2070 | −0.933494 | ||||||||
\(172\) | −4.60867 | −0.351407 | ||||||||
\(173\) | −0.0957593 | −0.00728044 | −0.00364022 | − | 0.999993i | \(-0.501159\pi\) | ||||
−0.00364022 | + | 0.999993i | \(0.501159\pi\) | |||||||
\(174\) | 0.356526 | 0.0270282 | ||||||||
\(175\) | 3.12595 | 0.236300 | ||||||||
\(176\) | 0.664616 | 0.0500973 | ||||||||
\(177\) | 0.814309 | 0.0612072 | ||||||||
\(178\) | −26.9974 | −2.02354 | ||||||||
\(179\) | −15.7268 | −1.17548 | −0.587740 | − | 0.809050i | \(-0.699982\pi\) | ||||
−0.587740 | + | 0.809050i | \(0.699982\pi\) | |||||||
\(180\) | 9.90516 | 0.738287 | ||||||||
\(181\) | 18.7410 | 1.39301 | 0.696504 | − | 0.717553i | \(-0.254738\pi\) | ||||
0.696504 | + | 0.717553i | \(0.254738\pi\) | |||||||
\(182\) | −3.02277 | −0.224063 | ||||||||
\(183\) | 0.903726 | 0.0668054 | ||||||||
\(184\) | 3.63739 | 0.268152 | ||||||||
\(185\) | 4.16612 | 0.306299 | ||||||||
\(186\) | −2.70854 | −0.198600 | ||||||||
\(187\) | −1.31354 | −0.0960554 | ||||||||
\(188\) | −6.57622 | −0.479620 | ||||||||
\(189\) | −0.601125 | −0.0437254 | ||||||||
\(190\) | 8.78352 | 0.637224 | ||||||||
\(191\) | −14.3635 | −1.03931 | −0.519655 | − | 0.854376i | \(-0.673939\pi\) | ||||
−0.519655 | + | 0.854376i | \(0.673939\pi\) | |||||||
\(192\) | 1.47516 | 0.106460 | ||||||||
\(193\) | −5.14580 | −0.370403 | −0.185201 | − | 0.982701i | \(-0.559294\pi\) | ||||
−0.185201 | + | 0.982701i | \(0.559294\pi\) | |||||||
\(194\) | −29.8522 | −2.14327 | ||||||||
\(195\) | −0.205785 | −0.0147366 | ||||||||
\(196\) | −23.8072 | −1.70051 | ||||||||
\(197\) | −8.52683 | −0.607511 | −0.303756 | − | 0.952750i | \(-0.598241\pi\) | ||||
−0.303756 | + | 0.952750i | \(0.598241\pi\) | |||||||
\(198\) | 2.09194 | 0.148667 | ||||||||
\(199\) | 6.38700 | 0.452762 | 0.226381 | − | 0.974039i | \(-0.427310\pi\) | ||||
0.226381 | + | 0.974039i | \(0.427310\pi\) | |||||||
\(200\) | 16.9499 | 1.19854 | ||||||||
\(201\) | 0.444557 | 0.0313566 | ||||||||
\(202\) | −9.68642 | −0.681534 | ||||||||
\(203\) | −0.826867 | −0.0580347 | ||||||||
\(204\) | 2.22433 | 0.155735 | ||||||||
\(205\) | −8.14723 | −0.569027 | ||||||||
\(206\) | −10.7235 | −0.747143 | ||||||||
\(207\) | 2.68217 | 0.186424 | ||||||||
\(208\) | −3.83982 | −0.266243 | ||||||||
\(209\) | 1.20353 | 0.0832502 | ||||||||
\(210\) | 0.215612 | 0.0148787 | ||||||||
\(211\) | 3.41872 | 0.235354 | 0.117677 | − | 0.993052i | \(-0.462455\pi\) | ||||
0.117677 | + | 0.993052i | \(0.462455\pi\) | |||||||
\(212\) | 12.6138 | 0.866317 | ||||||||
\(213\) | 0.345026 | 0.0236408 | ||||||||
\(214\) | 7.89976 | 0.540016 | ||||||||
\(215\) | 1.12157 | 0.0764903 | ||||||||
\(216\) | −3.25950 | −0.221781 | ||||||||
\(217\) | 6.28175 | 0.426433 | ||||||||
\(218\) | −16.9707 | −1.14940 | ||||||||
\(219\) | 0.929643 | 0.0628195 | ||||||||
\(220\) | −0.976585 | −0.0658414 | ||||||||
\(221\) | 7.58897 | 0.510489 | ||||||||
\(222\) | −1.48996 | −0.0999998 | ||||||||
\(223\) | −23.6932 | −1.58661 | −0.793306 | − | 0.608823i | \(-0.791642\pi\) | ||||
−0.793306 | + | 0.608823i | \(0.791642\pi\) | |||||||
\(224\) | −2.00825 | −0.134182 | ||||||||
\(225\) | 12.4987 | 0.833246 | ||||||||
\(226\) | 26.5554 | 1.76644 | ||||||||
\(227\) | 1.89021 | 0.125458 | 0.0627288 | − | 0.998031i | \(-0.480020\pi\) | ||||
0.0627288 | + | 0.998031i | \(0.480020\pi\) | |||||||
\(228\) | −2.03805 | −0.134973 | ||||||||
\(229\) | −17.3718 | −1.14796 | −0.573979 | − | 0.818870i | \(-0.694601\pi\) | ||||
−0.573979 | + | 0.818870i | \(0.694601\pi\) | |||||||
\(230\) | −1.92995 | −0.127257 | ||||||||
\(231\) | 0.0295436 | 0.00194382 | ||||||||
\(232\) | −4.48354 | −0.294359 | ||||||||
\(233\) | 10.4577 | 0.685105 | 0.342553 | − | 0.939499i | \(-0.388708\pi\) | ||||
0.342553 | + | 0.939499i | \(0.388708\pi\) | |||||||
\(234\) | −12.0862 | −0.790097 | ||||||||
\(235\) | 1.60039 | 0.104398 | ||||||||
\(236\) | −22.3267 | −1.45334 | ||||||||
\(237\) | −1.89557 | −0.123131 | ||||||||
\(238\) | −7.95137 | −0.515411 | ||||||||
\(239\) | 8.81120 | 0.569949 | 0.284975 | − | 0.958535i | \(-0.408015\pi\) | ||||
0.284975 | + | 0.958535i | \(0.408015\pi\) | |||||||
\(240\) | 0.273892 | 0.0176796 | ||||||||
\(241\) | 25.1670 | 1.62115 | 0.810574 | − | 0.585636i | \(-0.199155\pi\) | ||||
0.810574 | + | 0.585636i | \(0.199155\pi\) | |||||||
\(242\) | 26.0434 | 1.67413 | ||||||||
\(243\) | −3.60892 | −0.231513 | ||||||||
\(244\) | −24.7784 | −1.58627 | ||||||||
\(245\) | 5.79373 | 0.370148 | ||||||||
\(246\) | 2.91376 | 0.185775 | ||||||||
\(247\) | −6.95341 | −0.442435 | ||||||||
\(248\) | 34.0617 | 2.16292 | ||||||||
\(249\) | 1.55905 | 0.0988005 | ||||||||
\(250\) | −19.7213 | −1.24728 | ||||||||
\(251\) | −20.6573 | −1.30388 | −0.651938 | − | 0.758272i | \(-0.726044\pi\) | ||||
−0.651938 | + | 0.758272i | \(0.726044\pi\) | |||||||
\(252\) | 8.21580 | 0.517547 | ||||||||
\(253\) | −0.264445 | −0.0166255 | ||||||||
\(254\) | 47.8860 | 3.00464 | ||||||||
\(255\) | −0.541316 | −0.0338985 | ||||||||
\(256\) | −27.5938 | −1.72461 | ||||||||
\(257\) | 20.0198 | 1.24880 | 0.624402 | − | 0.781103i | \(-0.285343\pi\) | ||||
0.624402 | + | 0.781103i | \(0.285343\pi\) | |||||||
\(258\) | −0.401116 | −0.0249724 | ||||||||
\(259\) | 3.45558 | 0.214719 | ||||||||
\(260\) | 5.64222 | 0.349916 | ||||||||
\(261\) | −3.30612 | −0.204643 | ||||||||
\(262\) | −52.8982 | −3.26806 | ||||||||
\(263\) | 10.9410 | 0.674652 | 0.337326 | − | 0.941388i | \(-0.390478\pi\) | ||||
0.337326 | + | 0.941388i | \(0.390478\pi\) | |||||||
\(264\) | 0.160195 | 0.00985932 | ||||||||
\(265\) | −3.06970 | −0.188570 | ||||||||
\(266\) | 7.28547 | 0.446701 | ||||||||
\(267\) | −1.52447 | −0.0932962 | ||||||||
\(268\) | −12.1889 | −0.744553 | ||||||||
\(269\) | 0.521301 | 0.0317843 | 0.0158921 | − | 0.999874i | \(-0.494941\pi\) | ||||
0.0158921 | + | 0.999874i | \(0.494941\pi\) | |||||||
\(270\) | 1.72944 | 0.105251 | ||||||||
\(271\) | −1.71921 | −0.104435 | −0.0522174 | − | 0.998636i | \(-0.516629\pi\) | ||||
−0.0522174 | + | 0.998636i | \(0.516629\pi\) | |||||||
\(272\) | −10.1006 | −0.612438 | ||||||||
\(273\) | −0.170688 | −0.0103305 | ||||||||
\(274\) | −40.3175 | −2.43567 | ||||||||
\(275\) | −1.23229 | −0.0743099 | ||||||||
\(276\) | 0.447808 | 0.0269549 | ||||||||
\(277\) | 13.4311 | 0.806999 | 0.403500 | − | 0.914980i | \(-0.367794\pi\) | ||||
0.403500 | + | 0.914980i | \(0.367794\pi\) | |||||||
\(278\) | 5.34586 | 0.320623 | ||||||||
\(279\) | 25.1167 | 1.50370 | ||||||||
\(280\) | −2.71146 | −0.162041 | ||||||||
\(281\) | 19.0008 | 1.13349 | 0.566747 | − | 0.823892i | \(-0.308202\pi\) | ||||
0.566747 | + | 0.823892i | \(0.308202\pi\) | |||||||
\(282\) | −0.572362 | −0.0340837 | ||||||||
\(283\) | 23.3534 | 1.38822 | 0.694108 | − | 0.719871i | \(-0.255799\pi\) | ||||
0.694108 | + | 0.719871i | \(0.255799\pi\) | |||||||
\(284\) | −9.45991 | −0.561343 | ||||||||
\(285\) | 0.495982 | 0.0293794 | ||||||||
\(286\) | 1.19162 | 0.0704618 | ||||||||
\(287\) | −6.75769 | −0.398894 | ||||||||
\(288\) | −8.02970 | −0.473154 | ||||||||
\(289\) | 2.96268 | 0.174275 | ||||||||
\(290\) | 2.37891 | 0.139694 | ||||||||
\(291\) | −1.68568 | −0.0988161 | ||||||||
\(292\) | −25.4889 | −1.49163 | ||||||||
\(293\) | −2.98491 | −0.174380 | −0.0871901 | − | 0.996192i | \(-0.527789\pi\) | ||||
−0.0871901 | + | 0.996192i | \(0.527789\pi\) | |||||||
\(294\) | −2.07206 | −0.120845 | ||||||||
\(295\) | 5.43344 | 0.316347 | ||||||||
\(296\) | 18.7373 | 1.08908 | ||||||||
\(297\) | 0.236971 | 0.0137505 | ||||||||
\(298\) | 8.81422 | 0.510594 | ||||||||
\(299\) | 1.52783 | 0.0883566 | ||||||||
\(300\) | 2.08675 | 0.120479 | ||||||||
\(301\) | 0.930281 | 0.0536205 | ||||||||
\(302\) | 28.5400 | 1.64229 | ||||||||
\(303\) | −0.546966 | −0.0314224 | ||||||||
\(304\) | 9.25470 | 0.530793 | ||||||||
\(305\) | 6.03008 | 0.345281 | ||||||||
\(306\) | −31.7925 | −1.81745 | ||||||||
\(307\) | −4.27511 | −0.243994 | −0.121997 | − | 0.992530i | \(-0.538930\pi\) | ||||
−0.121997 | + | 0.992530i | \(0.538930\pi\) | |||||||
\(308\) | −0.810026 | −0.0461555 | ||||||||
\(309\) | −0.605528 | −0.0344473 | ||||||||
\(310\) | −18.0727 | −1.02646 | ||||||||
\(311\) | 13.3739 | 0.758366 | 0.379183 | − | 0.925322i | \(-0.376205\pi\) | ||||
0.379183 | + | 0.925322i | \(0.376205\pi\) | |||||||
\(312\) | −0.925526 | −0.0523976 | ||||||||
\(313\) | −26.9168 | −1.52142 | −0.760712 | − | 0.649089i | \(-0.775150\pi\) | ||||
−0.760712 | + | 0.649089i | \(0.775150\pi\) | |||||||
\(314\) | 20.3298 | 1.14728 | ||||||||
\(315\) | −1.99940 | −0.112654 | ||||||||
\(316\) | 51.9727 | 2.92369 | ||||||||
\(317\) | 11.1875 | 0.628353 | 0.314176 | − | 0.949365i | \(-0.398272\pi\) | ||||
0.314176 | + | 0.949365i | \(0.398272\pi\) | |||||||
\(318\) | 1.09784 | 0.0615638 | ||||||||
\(319\) | 0.325962 | 0.0182504 | ||||||||
\(320\) | 9.84294 | 0.550237 | ||||||||
\(321\) | 0.446078 | 0.0248977 | ||||||||
\(322\) | −1.60079 | −0.0892085 | ||||||||
\(323\) | −18.2909 | −1.01773 | ||||||||
\(324\) | 32.6485 | 1.81381 | ||||||||
\(325\) | 7.11955 | 0.394922 | ||||||||
\(326\) | −3.87978 | −0.214881 | ||||||||
\(327\) | −0.958289 | −0.0529935 | ||||||||
\(328\) | −36.6424 | −2.02324 | ||||||||
\(329\) | 1.32744 | 0.0731843 | ||||||||
\(330\) | −0.0849972 | −0.00467894 | ||||||||
\(331\) | 11.3715 | 0.625035 | 0.312518 | − | 0.949912i | \(-0.398828\pi\) | ||||
0.312518 | + | 0.949912i | \(0.398828\pi\) | |||||||
\(332\) | −42.7459 | −2.34599 | ||||||||
\(333\) | 13.8167 | 0.757148 | ||||||||
\(334\) | −45.6708 | −2.49899 | ||||||||
\(335\) | 2.96629 | 0.162066 | ||||||||
\(336\) | 0.227178 | 0.0123936 | ||||||||
\(337\) | −9.40268 | −0.512196 | −0.256098 | − | 0.966651i | \(-0.582437\pi\) | ||||
−0.256098 | + | 0.966651i | \(0.582437\pi\) | |||||||
\(338\) | 24.1377 | 1.31292 | ||||||||
\(339\) | 1.49951 | 0.0814424 | ||||||||
\(340\) | 14.8418 | 0.804909 | ||||||||
\(341\) | −2.47635 | −0.134102 | ||||||||
\(342\) | 29.1300 | 1.57517 | ||||||||
\(343\) | 10.0259 | 0.541350 | ||||||||
\(344\) | 5.04429 | 0.271970 | ||||||||
\(345\) | −0.108979 | −0.00586723 | ||||||||
\(346\) | 0.228513 | 0.0122849 | ||||||||
\(347\) | −6.56082 | −0.352203 | −0.176102 | − | 0.984372i | \(-0.556349\pi\) | ||||
−0.176102 | + | 0.984372i | \(0.556349\pi\) | |||||||
\(348\) | −0.551981 | −0.0295893 | ||||||||
\(349\) | 24.3552 | 1.30371 | 0.651853 | − | 0.758346i | \(-0.273992\pi\) | ||||
0.651853 | + | 0.758346i | \(0.273992\pi\) | |||||||
\(350\) | −7.45954 | −0.398729 | ||||||||
\(351\) | −1.36910 | −0.0730772 | ||||||||
\(352\) | 0.791677 | 0.0421965 | ||||||||
\(353\) | −33.6719 | −1.79218 | −0.896088 | − | 0.443877i | \(-0.853603\pi\) | ||||
−0.896088 | + | 0.443877i | \(0.853603\pi\) | |||||||
\(354\) | −1.94321 | −0.103280 | ||||||||
\(355\) | 2.30217 | 0.122187 | ||||||||
\(356\) | 41.7980 | 2.21529 | ||||||||
\(357\) | −0.448993 | −0.0237632 | ||||||||
\(358\) | 37.5294 | 1.98349 | ||||||||
\(359\) | 12.6353 | 0.666865 | 0.333432 | − | 0.942774i | \(-0.391793\pi\) | ||||
0.333432 | + | 0.942774i | \(0.391793\pi\) | |||||||
\(360\) | −10.8414 | −0.571393 | ||||||||
\(361\) | −2.24094 | −0.117944 | ||||||||
\(362\) | −44.7222 | −2.35055 | ||||||||
\(363\) | 1.47060 | 0.0771864 | ||||||||
\(364\) | 4.67992 | 0.245295 | ||||||||
\(365\) | 6.20301 | 0.324680 | ||||||||
\(366\) | −2.15659 | −0.112727 | ||||||||
\(367\) | −10.1017 | −0.527303 | −0.263652 | − | 0.964618i | \(-0.584927\pi\) | ||||
−0.263652 | + | 0.964618i | \(0.584927\pi\) | |||||||
\(368\) | −2.03348 | −0.106002 | ||||||||
\(369\) | −27.0197 | −1.40659 | ||||||||
\(370\) | −9.94173 | −0.516846 | ||||||||
\(371\) | −2.54615 | −0.132189 | ||||||||
\(372\) | 4.19342 | 0.217419 | ||||||||
\(373\) | 14.5014 | 0.750856 | 0.375428 | − | 0.926852i | \(-0.377496\pi\) | ||||
0.375428 | + | 0.926852i | \(0.377496\pi\) | |||||||
\(374\) | 3.13453 | 0.162083 | ||||||||
\(375\) | −1.11361 | −0.0575064 | ||||||||
\(376\) | 7.19783 | 0.371200 | ||||||||
\(377\) | −1.88324 | −0.0969920 | ||||||||
\(378\) | 1.43448 | 0.0737818 | ||||||||
\(379\) | 9.84652 | 0.505782 | 0.252891 | − | 0.967495i | \(-0.418619\pi\) | ||||
0.252891 | + | 0.967495i | \(0.418619\pi\) | |||||||
\(380\) | −13.5988 | −0.697605 | ||||||||
\(381\) | 2.70400 | 0.138530 | ||||||||
\(382\) | 34.2761 | 1.75372 | ||||||||
\(383\) | 13.4721 | 0.688394 | 0.344197 | − | 0.938898i | \(-0.388151\pi\) | ||||
0.344197 | + | 0.938898i | \(0.388151\pi\) | |||||||
\(384\) | −2.79449 | −0.142606 | ||||||||
\(385\) | 0.197128 | 0.0100466 | ||||||||
\(386\) | 12.2796 | 0.625014 | ||||||||
\(387\) | 3.71960 | 0.189078 | ||||||||
\(388\) | 46.2179 | 2.34636 | ||||||||
\(389\) | −27.7948 | −1.40925 | −0.704627 | − | 0.709578i | \(-0.748886\pi\) | ||||
−0.704627 | + | 0.709578i | \(0.748886\pi\) | |||||||
\(390\) | 0.491071 | 0.0248664 | ||||||||
\(391\) | 4.01893 | 0.203246 | ||||||||
\(392\) | 26.0575 | 1.31610 | ||||||||
\(393\) | −2.98702 | −0.150675 | ||||||||
\(394\) | 20.3478 | 1.02511 | ||||||||
\(395\) | −12.6481 | −0.636396 | ||||||||
\(396\) | −3.23878 | −0.162755 | ||||||||
\(397\) | 13.2872 | 0.666866 | 0.333433 | − | 0.942774i | \(-0.391793\pi\) | ||||
0.333433 | + | 0.942774i | \(0.391793\pi\) | |||||||
\(398\) | −15.2415 | −0.763986 | ||||||||
\(399\) | 0.411391 | 0.0205953 | ||||||||
\(400\) | −9.47583 | −0.473791 | ||||||||
\(401\) | 37.6536 | 1.88033 | 0.940165 | − | 0.340719i | \(-0.110671\pi\) | ||||
0.940165 | + | 0.340719i | \(0.110671\pi\) | |||||||
\(402\) | −1.06086 | −0.0529108 | ||||||||
\(403\) | 14.3071 | 0.712687 | ||||||||
\(404\) | 14.9967 | 0.746114 | ||||||||
\(405\) | −7.94537 | −0.394809 | ||||||||
\(406\) | 1.97318 | 0.0979271 | ||||||||
\(407\) | −1.36223 | −0.0675234 | ||||||||
\(408\) | −2.43458 | −0.120530 | ||||||||
\(409\) | 11.3610 | 0.561767 | 0.280884 | − | 0.959742i | \(-0.409373\pi\) | ||||
0.280884 | + | 0.959742i | \(0.409373\pi\) | |||||||
\(410\) | 19.4420 | 0.960170 | ||||||||
\(411\) | −2.27662 | −0.112298 | ||||||||
\(412\) | 16.6024 | 0.817940 | ||||||||
\(413\) | 4.50675 | 0.221763 | ||||||||
\(414\) | −6.40054 | −0.314569 | ||||||||
\(415\) | 10.4027 | 0.510647 | ||||||||
\(416\) | −4.57391 | −0.224254 | ||||||||
\(417\) | 0.301866 | 0.0147825 | ||||||||
\(418\) | −2.87203 | −0.140475 | ||||||||
\(419\) | 33.0110 | 1.61270 | 0.806348 | − | 0.591442i | \(-0.201441\pi\) | ||||
0.806348 | + | 0.591442i | \(0.201441\pi\) | |||||||
\(420\) | −0.333816 | −0.0162885 | ||||||||
\(421\) | 34.3417 | 1.67371 | 0.836855 | − | 0.547425i | \(-0.184392\pi\) | ||||
0.836855 | + | 0.547425i | \(0.184392\pi\) | |||||||
\(422\) | −8.15819 | −0.397134 | ||||||||
\(423\) | 5.30760 | 0.258064 | ||||||||
\(424\) | −13.8061 | −0.670481 | ||||||||
\(425\) | 18.7279 | 0.908437 | ||||||||
\(426\) | −0.823345 | −0.0398912 | ||||||||
\(427\) | 5.00163 | 0.242046 | ||||||||
\(428\) | −12.2306 | −0.591187 | ||||||||
\(429\) | 0.0672874 | 0.00324867 | ||||||||
\(430\) | −2.67643 | −0.129069 | ||||||||
\(431\) | 12.6756 | 0.610560 | 0.305280 | − | 0.952263i | \(-0.401250\pi\) | ||||
0.305280 | + | 0.952263i | \(0.401250\pi\) | |||||||
\(432\) | 1.82222 | 0.0876714 | ||||||||
\(433\) | 2.19496 | 0.105483 | 0.0527414 | − | 0.998608i | \(-0.483204\pi\) | ||||
0.0527414 | + | 0.998608i | \(0.483204\pi\) | |||||||
\(434\) | −14.9903 | −0.719558 | ||||||||
\(435\) | 0.134330 | 0.00644065 | ||||||||
\(436\) | 26.2744 | 1.25831 | ||||||||
\(437\) | −3.68236 | −0.176151 | ||||||||
\(438\) | −2.21843 | −0.106001 | ||||||||
\(439\) | 6.94039 | 0.331247 | 0.165623 | − | 0.986189i | \(-0.447036\pi\) | ||||
0.165623 | + | 0.986189i | \(0.447036\pi\) | |||||||
\(440\) | 1.06889 | 0.0509576 | ||||||||
\(441\) | 19.2145 | 0.914976 | ||||||||
\(442\) | −18.1098 | −0.861394 | ||||||||
\(443\) | −26.3745 | −1.25309 | −0.626546 | − | 0.779384i | \(-0.715532\pi\) | ||||
−0.626546 | + | 0.779384i | \(0.715532\pi\) | |||||||
\(444\) | 2.30679 | 0.109476 | ||||||||
\(445\) | −10.1720 | −0.482198 | ||||||||
\(446\) | 56.5397 | 2.67723 | ||||||||
\(447\) | 0.497715 | 0.0235411 | ||||||||
\(448\) | 8.16419 | 0.385722 | ||||||||
\(449\) | 38.8633 | 1.83407 | 0.917035 | − | 0.398806i | \(-0.130575\pi\) | ||||
0.917035 | + | 0.398806i | \(0.130575\pi\) | |||||||
\(450\) | −29.8260 | −1.40601 | ||||||||
\(451\) | 2.66397 | 0.125441 | ||||||||
\(452\) | −41.1137 | −1.93382 | ||||||||
\(453\) | 1.61157 | 0.0757184 | ||||||||
\(454\) | −4.51066 | −0.211696 | ||||||||
\(455\) | −1.13891 | −0.0533929 | ||||||||
\(456\) | 2.23070 | 0.104462 | ||||||||
\(457\) | 0.806934 | 0.0377468 | 0.0188734 | − | 0.999822i | \(-0.493992\pi\) | ||||
0.0188734 | + | 0.999822i | \(0.493992\pi\) | |||||||
\(458\) | 41.4547 | 1.93705 | ||||||||
\(459\) | −3.60140 | −0.168099 | ||||||||
\(460\) | 2.98798 | 0.139315 | ||||||||
\(461\) | −35.9208 | −1.67300 | −0.836498 | − | 0.547969i | \(-0.815401\pi\) | ||||
−0.836498 | + | 0.547969i | \(0.815401\pi\) | |||||||
\(462\) | −0.0705007 | −0.00327999 | ||||||||
\(463\) | 27.7359 | 1.28900 | 0.644499 | − | 0.764605i | \(-0.277066\pi\) | ||||
0.644499 | + | 0.764605i | \(0.277066\pi\) | |||||||
\(464\) | 2.50652 | 0.116362 | ||||||||
\(465\) | −1.02051 | −0.0473252 | ||||||||
\(466\) | −24.9555 | −1.15604 | ||||||||
\(467\) | −2.24571 | −0.103919 | −0.0519596 | − | 0.998649i | \(-0.516547\pi\) | ||||
−0.0519596 | + | 0.998649i | \(0.516547\pi\) | |||||||
\(468\) | 18.7120 | 0.864964 | ||||||||
\(469\) | 2.46038 | 0.113610 | ||||||||
\(470\) | −3.81907 | −0.176160 | ||||||||
\(471\) | 1.14797 | 0.0528956 | ||||||||
\(472\) | 24.4371 | 1.12481 | ||||||||
\(473\) | −0.366729 | −0.0168622 | ||||||||
\(474\) | 4.52345 | 0.207769 | ||||||||
\(475\) | −17.1595 | −0.787332 | ||||||||
\(476\) | 12.3105 | 0.564250 | ||||||||
\(477\) | −10.1804 | −0.466130 | ||||||||
\(478\) | −21.0264 | −0.961726 | ||||||||
\(479\) | −15.9507 | −0.728806 | −0.364403 | − | 0.931241i | \(-0.618727\pi\) | ||||
−0.364403 | + | 0.931241i | \(0.618727\pi\) | |||||||
\(480\) | 0.326254 | 0.0148914 | ||||||||
\(481\) | 7.87030 | 0.358855 | ||||||||
\(482\) | −60.0567 | −2.73551 | ||||||||
\(483\) | −0.0903923 | −0.00411299 | ||||||||
\(484\) | −40.3209 | −1.83277 | ||||||||
\(485\) | −11.2476 | −0.510728 | ||||||||
\(486\) | 8.61208 | 0.390652 | ||||||||
\(487\) | 1.91964 | 0.0869870 | 0.0434935 | − | 0.999054i | \(-0.486151\pi\) | ||||
0.0434935 | + | 0.999054i | \(0.486151\pi\) | |||||||
\(488\) | 27.1205 | 1.22769 | ||||||||
\(489\) | −0.219081 | −0.00990717 | ||||||||
\(490\) | −13.8257 | −0.624583 | ||||||||
\(491\) | 14.1953 | 0.640626 | 0.320313 | − | 0.947312i | \(-0.396212\pi\) | ||||
0.320313 | + | 0.947312i | \(0.396212\pi\) | |||||||
\(492\) | −4.51114 | −0.203378 | ||||||||
\(493\) | −4.95385 | −0.223110 | ||||||||
\(494\) | 16.5931 | 0.746560 | ||||||||
\(495\) | 0.788191 | 0.0354266 | ||||||||
\(496\) | −19.0421 | −0.855017 | ||||||||
\(497\) | 1.90953 | 0.0856541 | ||||||||
\(498\) | −3.72039 | −0.166715 | ||||||||
\(499\) | 42.5164 | 1.90329 | 0.951647 | − | 0.307194i | \(-0.0993902\pi\) | ||||
0.951647 | + | 0.307194i | \(0.0993902\pi\) | |||||||
\(500\) | 30.5329 | 1.36547 | ||||||||
\(501\) | −2.57891 | −0.115217 | ||||||||
\(502\) | 49.2950 | 2.20015 | ||||||||
\(503\) | 21.3422 | 0.951602 | 0.475801 | − | 0.879553i | \(-0.342158\pi\) | ||||
0.475801 | + | 0.879553i | \(0.342158\pi\) | |||||||
\(504\) | −8.99239 | −0.400553 | ||||||||
\(505\) | −3.64961 | −0.162406 | ||||||||
\(506\) | 0.631052 | 0.0280537 | ||||||||
\(507\) | 1.36299 | 0.0605326 | ||||||||
\(508\) | −74.1382 | −3.28935 | ||||||||
\(509\) | 29.1281 | 1.29108 | 0.645540 | − | 0.763727i | \(-0.276633\pi\) | ||||
0.645540 | + | 0.763727i | \(0.276633\pi\) | |||||||
\(510\) | 1.29176 | 0.0572000 | ||||||||
\(511\) | 5.14507 | 0.227604 | ||||||||
\(512\) | 24.3710 | 1.07706 | ||||||||
\(513\) | 3.29980 | 0.145690 | ||||||||
\(514\) | −47.7739 | −2.10722 | ||||||||
\(515\) | −4.04037 | −0.178040 | ||||||||
\(516\) | 0.621016 | 0.0273387 | ||||||||
\(517\) | −0.523295 | −0.0230145 | ||||||||
\(518\) | −8.24614 | −0.362315 | ||||||||
\(519\) | 0.0129035 | 0.000566402 0 | ||||||||
\(520\) | −6.17554 | −0.270815 | ||||||||
\(521\) | 41.6966 | 1.82676 | 0.913380 | − | 0.407108i | \(-0.133463\pi\) | ||||
0.913380 | + | 0.407108i | \(0.133463\pi\) | |||||||
\(522\) | 7.88948 | 0.345313 | ||||||||
\(523\) | 34.8138 | 1.52230 | 0.761151 | − | 0.648575i | \(-0.224635\pi\) | ||||
0.761151 | + | 0.648575i | \(0.224635\pi\) | |||||||
\(524\) | 81.8981 | 3.57773 | ||||||||
\(525\) | −0.421220 | −0.0183836 | ||||||||
\(526\) | −26.1089 | −1.13840 | ||||||||
\(527\) | 37.6346 | 1.63939 | ||||||||
\(528\) | −0.0895567 | −0.00389746 | ||||||||
\(529\) | −22.1909 | −0.964822 | ||||||||
\(530\) | 7.32530 | 0.318191 | ||||||||
\(531\) | 18.0196 | 0.781986 | ||||||||
\(532\) | −11.2795 | −0.489029 | ||||||||
\(533\) | −15.3911 | −0.666662 | ||||||||
\(534\) | 3.63789 | 0.157427 | ||||||||
\(535\) | 2.97644 | 0.128683 | ||||||||
\(536\) | 13.3410 | 0.576243 | ||||||||
\(537\) | 2.11919 | 0.0914496 | ||||||||
\(538\) | −1.24400 | −0.0536325 | ||||||||
\(539\) | −1.89443 | −0.0815987 | ||||||||
\(540\) | −2.67756 | −0.115224 | ||||||||
\(541\) | 23.5117 | 1.01085 | 0.505423 | − | 0.862871i | \(-0.331336\pi\) | ||||
0.505423 | + | 0.862871i | \(0.331336\pi\) | |||||||
\(542\) | 4.10261 | 0.176222 | ||||||||
\(543\) | −2.52534 | −0.108373 | ||||||||
\(544\) | −12.0316 | −0.515851 | ||||||||
\(545\) | −6.39415 | −0.273895 | ||||||||
\(546\) | 0.407318 | 0.0174316 | ||||||||
\(547\) | 10.7515 | 0.459699 | 0.229850 | − | 0.973226i | \(-0.426177\pi\) | ||||
0.229850 | + | 0.973226i | \(0.426177\pi\) | |||||||
\(548\) | 62.4204 | 2.66647 | ||||||||
\(549\) | 19.9984 | 0.853509 | ||||||||
\(550\) | 2.94065 | 0.125390 | ||||||||
\(551\) | 4.53898 | 0.193367 | ||||||||
\(552\) | −0.490136 | −0.0208616 | ||||||||
\(553\) | −10.4909 | −0.446120 | ||||||||
\(554\) | −32.0511 | −1.36172 | ||||||||
\(555\) | −0.561383 | −0.0238294 | ||||||||
\(556\) | −8.27657 | −0.351005 | ||||||||
\(557\) | −15.9100 | −0.674130 | −0.337065 | − | 0.941481i | \(-0.609434\pi\) | ||||
−0.337065 | + | 0.941481i | \(0.609434\pi\) | |||||||
\(558\) | −59.9367 | −2.53732 | ||||||||
\(559\) | 2.11878 | 0.0896147 | ||||||||
\(560\) | 1.51584 | 0.0640559 | ||||||||
\(561\) | 0.176999 | 0.00747289 | ||||||||
\(562\) | −45.3422 | −1.91265 | ||||||||
\(563\) | −23.0125 | −0.969863 | −0.484932 | − | 0.874552i | \(-0.661156\pi\) | ||||
−0.484932 | + | 0.874552i | \(0.661156\pi\) | |||||||
\(564\) | 0.886143 | 0.0373134 | ||||||||
\(565\) | 10.0055 | 0.420933 | ||||||||
\(566\) | −55.7289 | −2.34246 | ||||||||
\(567\) | −6.59026 | −0.276765 | ||||||||
\(568\) | 10.3541 | 0.434448 | ||||||||
\(569\) | 43.7241 | 1.83301 | 0.916504 | − | 0.400025i | \(-0.130999\pi\) | ||||
0.916504 | + | 0.400025i | \(0.130999\pi\) | |||||||
\(570\) | −1.18358 | −0.0495745 | ||||||||
\(571\) | 7.93582 | 0.332104 | 0.166052 | − | 0.986117i | \(-0.446898\pi\) | ||||
0.166052 | + | 0.986117i | \(0.446898\pi\) | |||||||
\(572\) | −1.84489 | −0.0771386 | ||||||||
\(573\) | 1.93548 | 0.0808559 | ||||||||
\(574\) | 16.1261 | 0.673089 | ||||||||
\(575\) | 3.77035 | 0.157234 | ||||||||
\(576\) | 32.6434 | 1.36014 | ||||||||
\(577\) | 19.8752 | 0.827417 | 0.413708 | − | 0.910409i | \(-0.364233\pi\) | ||||
0.413708 | + | 0.910409i | \(0.364233\pi\) | |||||||
\(578\) | −7.06993 | −0.294070 | ||||||||
\(579\) | 0.693395 | 0.0288165 | ||||||||
\(580\) | −3.68307 | −0.152931 | ||||||||
\(581\) | 8.62847 | 0.357969 | ||||||||
\(582\) | 4.02258 | 0.166741 | ||||||||
\(583\) | 1.00373 | 0.0415701 | ||||||||
\(584\) | 27.8982 | 1.15444 | ||||||||
\(585\) | −4.55377 | −0.188275 | ||||||||
\(586\) | 7.12297 | 0.294247 | ||||||||
\(587\) | −29.7160 | −1.22651 | −0.613255 | − | 0.789885i | \(-0.710140\pi\) | ||||
−0.613255 | + | 0.789885i | \(0.710140\pi\) | |||||||
\(588\) | 3.20800 | 0.132296 | ||||||||
\(589\) | −34.4828 | −1.42084 | ||||||||
\(590\) | −12.9660 | −0.533801 | ||||||||
\(591\) | 1.14899 | 0.0472630 | ||||||||
\(592\) | −10.4750 | −0.430521 | ||||||||
\(593\) | 1.18232 | 0.0485521 | 0.0242761 | − | 0.999705i | \(-0.492272\pi\) | ||||
0.0242761 | + | 0.999705i | \(0.492272\pi\) | |||||||
\(594\) | −0.565491 | −0.0232024 | ||||||||
\(595\) | −2.99589 | −0.122819 | ||||||||
\(596\) | −13.6464 | −0.558977 | ||||||||
\(597\) | −0.860646 | −0.0352239 | ||||||||
\(598\) | −3.64590 | −0.149092 | ||||||||
\(599\) | −25.1601 | −1.02802 | −0.514008 | − | 0.857785i | \(-0.671840\pi\) | ||||
−0.514008 | + | 0.857785i | \(0.671840\pi\) | |||||||
\(600\) | −2.28399 | −0.0932437 | ||||||||
\(601\) | −8.90263 | −0.363146 | −0.181573 | − | 0.983377i | \(-0.558119\pi\) | ||||
−0.181573 | + | 0.983377i | \(0.558119\pi\) | |||||||
\(602\) | −2.21996 | −0.0904787 | ||||||||
\(603\) | 9.83749 | 0.400614 | ||||||||
\(604\) | −44.1861 | −1.79791 | ||||||||
\(605\) | 9.81252 | 0.398936 | ||||||||
\(606\) | 1.30524 | 0.0530218 | ||||||||
\(607\) | 1.08194 | 0.0439144 | 0.0219572 | − | 0.999759i | \(-0.493010\pi\) | ||||
0.0219572 | + | 0.999759i | \(0.493010\pi\) | |||||||
\(608\) | 11.0240 | 0.447082 | ||||||||
\(609\) | 0.111420 | 0.00451497 | ||||||||
\(610\) | −14.3898 | −0.582624 | ||||||||
\(611\) | 3.02334 | 0.122311 | ||||||||
\(612\) | 49.2218 | 1.98967 | ||||||||
\(613\) | −2.96150 | −0.119614 | −0.0598068 | − | 0.998210i | \(-0.519048\pi\) | ||||
−0.0598068 | + | 0.998210i | \(0.519048\pi\) | |||||||
\(614\) | 10.2018 | 0.411712 | ||||||||
\(615\) | 1.09784 | 0.0442690 | ||||||||
\(616\) | 0.886592 | 0.0357218 | ||||||||
\(617\) | 45.0514 | 1.81370 | 0.906850 | − | 0.421453i | \(-0.138480\pi\) | ||||
0.906850 | + | 0.421453i | \(0.138480\pi\) | |||||||
\(618\) | 1.44499 | 0.0581260 | ||||||||
\(619\) | −21.9683 | −0.882981 | −0.441491 | − | 0.897266i | \(-0.645550\pi\) | ||||
−0.441491 | + | 0.897266i | \(0.645550\pi\) | |||||||
\(620\) | 27.9805 | 1.12372 | ||||||||
\(621\) | −0.725043 | −0.0290950 | ||||||||
\(622\) | −31.9146 | −1.27966 | ||||||||
\(623\) | −8.43712 | −0.338026 | ||||||||
\(624\) | 0.517414 | 0.0207131 | ||||||||
\(625\) | 13.5275 | 0.541099 | ||||||||
\(626\) | 64.2322 | 2.56724 | ||||||||
\(627\) | −0.162176 | −0.00647667 | ||||||||
\(628\) | −31.4750 | −1.25599 | ||||||||
\(629\) | 20.7027 | 0.825472 | ||||||||
\(630\) | 4.77124 | 0.190091 | ||||||||
\(631\) | 18.9448 | 0.754182 | 0.377091 | − | 0.926176i | \(-0.376924\pi\) | ||||
0.377091 | + | 0.926176i | \(0.376924\pi\) | |||||||
\(632\) | −56.8854 | −2.26278 | ||||||||
\(633\) | −0.460671 | −0.0183100 | ||||||||
\(634\) | −26.6971 | −1.06028 | ||||||||
\(635\) | 18.0423 | 0.715987 | ||||||||
\(636\) | −1.69970 | −0.0673975 | ||||||||
\(637\) | 10.9450 | 0.433658 | ||||||||
\(638\) | −0.777852 | −0.0307955 | ||||||||
\(639\) | 7.63499 | 0.302036 | ||||||||
\(640\) | −18.6461 | −0.737052 | ||||||||
\(641\) | −6.97141 | −0.275354 | −0.137677 | − | 0.990477i | \(-0.543964\pi\) | ||||
−0.137677 | + | 0.990477i | \(0.543964\pi\) | |||||||
\(642\) | −1.06449 | −0.0420120 | ||||||||
\(643\) | 1.09525 | 0.0431925 | 0.0215962 | − | 0.999767i | \(-0.493125\pi\) | ||||
0.0215962 | + | 0.999767i | \(0.493125\pi\) | |||||||
\(644\) | 2.47837 | 0.0976616 | ||||||||
\(645\) | −0.151131 | −0.00595077 | ||||||||
\(646\) | 43.6480 | 1.71731 | ||||||||
\(647\) | −3.11802 | −0.122582 | −0.0612910 | − | 0.998120i | \(-0.519522\pi\) | ||||
−0.0612910 | + | 0.998120i | \(0.519522\pi\) | |||||||
\(648\) | −35.7346 | −1.40379 | ||||||||
\(649\) | −1.77662 | −0.0697385 | ||||||||
\(650\) | −16.9896 | −0.666387 | ||||||||
\(651\) | −0.846463 | −0.0331755 | ||||||||
\(652\) | 6.00675 | 0.235243 | ||||||||
\(653\) | −23.5756 | −0.922586 | −0.461293 | − | 0.887248i | \(-0.652614\pi\) | ||||
−0.461293 | + | 0.887248i | \(0.652614\pi\) | |||||||
\(654\) | 2.28679 | 0.0894206 | ||||||||
\(655\) | −19.9308 | −0.778760 | ||||||||
\(656\) | 20.4849 | 0.799801 | ||||||||
\(657\) | 20.5719 | 0.802585 | ||||||||
\(658\) | −3.16771 | −0.123490 | ||||||||
\(659\) | 2.03433 | 0.0792463 | 0.0396231 | − | 0.999215i | \(-0.487384\pi\) | ||||
0.0396231 | + | 0.999215i | \(0.487384\pi\) | |||||||
\(660\) | 0.131594 | 0.00512231 | ||||||||
\(661\) | −49.8867 | −1.94037 | −0.970183 | − | 0.242373i | \(-0.922074\pi\) | ||||
−0.970183 | + | 0.242373i | \(0.922074\pi\) | |||||||
\(662\) | −27.1362 | −1.05468 | ||||||||
\(663\) | −1.02261 | −0.0397149 | ||||||||
\(664\) | 46.7864 | 1.81566 | ||||||||
\(665\) | 2.74499 | 0.106446 | ||||||||
\(666\) | −32.9711 | −1.27760 | ||||||||
\(667\) | −0.997321 | −0.0386164 | ||||||||
\(668\) | 70.7084 | 2.73579 | ||||||||
\(669\) | 3.19265 | 0.123435 | ||||||||
\(670\) | −7.07854 | −0.273468 | ||||||||
\(671\) | −1.97171 | −0.0761170 | ||||||||
\(672\) | 0.270610 | 0.0104390 | ||||||||
\(673\) | 6.01826 | 0.231987 | 0.115994 | − | 0.993250i | \(-0.462995\pi\) | ||||
0.115994 | + | 0.993250i | \(0.462995\pi\) | |||||||
\(674\) | 22.4379 | 0.864274 | ||||||||
\(675\) | −3.37864 | −0.130044 | ||||||||
\(676\) | −37.3705 | −1.43733 | ||||||||
\(677\) | 42.7474 | 1.64292 | 0.821459 | − | 0.570268i | \(-0.193161\pi\) | ||||
0.821459 | + | 0.570268i | \(0.193161\pi\) | |||||||
\(678\) | −3.57833 | −0.137425 | ||||||||
\(679\) | −9.32930 | −0.358026 | ||||||||
\(680\) | −16.2447 | −0.622955 | ||||||||
\(681\) | −0.254705 | −0.00976031 | ||||||||
\(682\) | 5.90938 | 0.226282 | ||||||||
\(683\) | 47.2430 | 1.80770 | 0.903852 | − | 0.427845i | \(-0.140727\pi\) | ||||
0.903852 | + | 0.427845i | \(0.140727\pi\) | |||||||
\(684\) | −45.0996 | −1.72443 | ||||||||
\(685\) | −15.1907 | −0.580406 | ||||||||
\(686\) | −23.9252 | −0.913469 | ||||||||
\(687\) | 2.34084 | 0.0893085 | ||||||||
\(688\) | −2.82000 | −0.107512 | ||||||||
\(689\) | −5.79902 | −0.220925 | ||||||||
\(690\) | 0.260060 | 0.00990030 | ||||||||
\(691\) | 38.6412 | 1.46998 | 0.734990 | − | 0.678078i | \(-0.237187\pi\) | ||||
0.734990 | + | 0.678078i | \(0.237187\pi\) | |||||||
\(692\) | −0.353789 | −0.0134490 | ||||||||
\(693\) | 0.653763 | 0.0248344 | ||||||||
\(694\) | 15.6563 | 0.594304 | ||||||||
\(695\) | 2.01419 | 0.0764027 | ||||||||
\(696\) | 0.604156 | 0.0229005 | ||||||||
\(697\) | −40.4861 | −1.53352 | ||||||||
\(698\) | −58.1196 | −2.19986 | ||||||||
\(699\) | −1.40917 | −0.0532996 | ||||||||
\(700\) | 11.5490 | 0.436512 | ||||||||
\(701\) | −6.47991 | −0.244743 | −0.122371 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122371 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(702\) | 3.26713 | 0.123310 | ||||||||
\(703\) | −18.9689 | −0.715427 | ||||||||
\(704\) | −3.21843 | −0.121299 | ||||||||
\(705\) | −0.215653 | −0.00812194 | ||||||||
\(706\) | 80.3523 | 3.02410 | ||||||||
\(707\) | −3.02716 | −0.113848 | ||||||||
\(708\) | 3.00851 | 0.113067 | ||||||||
\(709\) | −22.6081 | −0.849067 | −0.424533 | − | 0.905412i | \(-0.639562\pi\) | ||||
−0.424533 | + | 0.905412i | \(0.639562\pi\) | |||||||
\(710\) | −5.49374 | −0.206176 | ||||||||
\(711\) | −41.9466 | −1.57312 | ||||||||
\(712\) | −45.7488 | −1.71451 | ||||||||
\(713\) | 7.57669 | 0.283749 | ||||||||
\(714\) | 1.07144 | 0.0400978 | ||||||||
\(715\) | 0.448973 | 0.0167906 | ||||||||
\(716\) | −58.1038 | −2.17144 | ||||||||
\(717\) | −1.18731 | −0.0443407 | ||||||||
\(718\) | −30.1519 | −1.12526 | ||||||||
\(719\) | 42.5913 | 1.58839 | 0.794193 | − | 0.607665i | \(-0.207894\pi\) | ||||
0.794193 | + | 0.607665i | \(0.207894\pi\) | |||||||
\(720\) | 6.06088 | 0.225876 | ||||||||
\(721\) | −3.35127 | −0.124808 | ||||||||
\(722\) | 5.34761 | 0.199017 | ||||||||
\(723\) | −3.39124 | −0.126122 | ||||||||
\(724\) | 69.2398 | 2.57328 | ||||||||
\(725\) | −4.64743 | −0.172601 | ||||||||
\(726\) | −3.50933 | −0.130244 | ||||||||
\(727\) | −28.6844 | −1.06384 | −0.531922 | − | 0.846793i | \(-0.678530\pi\) | ||||
−0.531922 | + | 0.846793i | \(0.678530\pi\) | |||||||
\(728\) | −5.12228 | −0.189844 | ||||||||
\(729\) | −26.0244 | −0.963868 | ||||||||
\(730\) | −14.8024 | −0.547862 | ||||||||
\(731\) | 5.57342 | 0.206140 | ||||||||
\(732\) | 3.33887 | 0.123408 | ||||||||
\(733\) | −31.5571 | −1.16559 | −0.582793 | − | 0.812620i | \(-0.698040\pi\) | ||||
−0.582793 | + | 0.812620i | \(0.698040\pi\) | |||||||
\(734\) | 24.1059 | 0.889766 | ||||||||
\(735\) | −0.780702 | −0.0287966 | ||||||||
\(736\) | −2.42223 | −0.0892847 | ||||||||
\(737\) | −0.969914 | −0.0357272 | ||||||||
\(738\) | 64.4779 | 2.37347 | ||||||||
\(739\) | 7.59773 | 0.279487 | 0.139744 | − | 0.990188i | \(-0.455372\pi\) | ||||
0.139744 | + | 0.990188i | \(0.455372\pi\) | |||||||
\(740\) | 15.3920 | 0.565821 | ||||||||
\(741\) | 0.936970 | 0.0344204 | ||||||||
\(742\) | 6.07595 | 0.223055 | ||||||||
\(743\) | −44.6133 | −1.63670 | −0.818351 | − | 0.574719i | \(-0.805111\pi\) | ||||
−0.818351 | + | 0.574719i | \(0.805111\pi\) | |||||||
\(744\) | −4.58980 | −0.168270 | ||||||||
\(745\) | 3.32099 | 0.121672 | ||||||||
\(746\) | −34.6052 | −1.26699 | ||||||||
\(747\) | 34.4998 | 1.26228 | ||||||||
\(748\) | −4.85295 | −0.177441 | ||||||||
\(749\) | 2.46880 | 0.0902080 | ||||||||
\(750\) | 2.65743 | 0.0970357 | ||||||||
\(751\) | 40.4760 | 1.47699 | 0.738496 | − | 0.674258i | \(-0.235537\pi\) | ||||
0.738496 | + | 0.674258i | \(0.235537\pi\) | |||||||
\(752\) | −4.02393 | −0.146738 | ||||||||
\(753\) | 2.78356 | 0.101439 | ||||||||
\(754\) | 4.49404 | 0.163663 | ||||||||
\(755\) | 10.7532 | 0.391348 | ||||||||
\(756\) | −2.22089 | −0.0807731 | ||||||||
\(757\) | −44.5469 | −1.61908 | −0.809542 | − | 0.587061i | \(-0.800285\pi\) | ||||
−0.809542 | + | 0.587061i | \(0.800285\pi\) | |||||||
\(758\) | −23.4970 | −0.853450 | ||||||||
\(759\) | 0.0356338 | 0.00129343 | ||||||||
\(760\) | 14.8842 | 0.539908 | ||||||||
\(761\) | −44.7811 | −1.62331 | −0.811656 | − | 0.584135i | \(-0.801434\pi\) | ||||
−0.811656 | + | 0.584135i | \(0.801434\pi\) | |||||||
\(762\) | −6.45262 | −0.233754 | ||||||||
\(763\) | −5.30361 | −0.192003 | ||||||||
\(764\) | −53.0670 | −1.91990 | ||||||||
\(765\) | −11.9786 | −0.433089 | ||||||||
\(766\) | −32.1489 | −1.16159 | ||||||||
\(767\) | 10.2644 | 0.370627 | ||||||||
\(768\) | 3.71825 | 0.134171 | ||||||||
\(769\) | 19.0504 | 0.686975 | 0.343487 | − | 0.939157i | \(-0.388392\pi\) | ||||
0.343487 | + | 0.939157i | \(0.388392\pi\) | |||||||
\(770\) | −0.470413 | −0.0169525 | ||||||||
\(771\) | −2.69767 | −0.0971541 | ||||||||
\(772\) | −19.0115 | −0.684238 | ||||||||
\(773\) | −32.9792 | −1.18618 | −0.593090 | − | 0.805136i | \(-0.702092\pi\) | ||||
−0.593090 | + | 0.805136i | \(0.702092\pi\) | |||||||
\(774\) | −8.87620 | −0.319048 | ||||||||
\(775\) | 35.3068 | 1.26826 | ||||||||
\(776\) | −50.5865 | −1.81595 | ||||||||
\(777\) | −0.465637 | −0.0167046 | ||||||||
\(778\) | 66.3276 | 2.37796 | ||||||||
\(779\) | 37.0955 | 1.32908 | ||||||||
\(780\) | −0.760287 | −0.0272226 | ||||||||
\(781\) | −0.752761 | −0.0269359 | ||||||||
\(782\) | −9.59050 | −0.342956 | ||||||||
\(783\) | 0.893708 | 0.0319385 | ||||||||
\(784\) | −14.5674 | −0.520264 | ||||||||
\(785\) | 7.65978 | 0.273389 | ||||||||
\(786\) | 7.12801 | 0.254248 | ||||||||
\(787\) | −54.0061 | −1.92511 | −0.962556 | − | 0.271085i | \(-0.912618\pi\) | ||||
−0.962556 | + | 0.271085i | \(0.912618\pi\) | |||||||
\(788\) | −31.5029 | −1.12224 | ||||||||
\(789\) | −1.47430 | −0.0524864 | ||||||||
\(790\) | 30.1826 | 1.07385 | ||||||||
\(791\) | 8.29899 | 0.295078 | ||||||||
\(792\) | 3.54492 | 0.125963 | ||||||||
\(793\) | 11.3915 | 0.404526 | ||||||||
\(794\) | −31.7076 | −1.12526 | ||||||||
\(795\) | 0.413640 | 0.0146703 | ||||||||
\(796\) | 23.5972 | 0.836380 | ||||||||
\(797\) | 12.8405 | 0.454833 | 0.227416 | − | 0.973798i | \(-0.426972\pi\) | ||||
0.227416 | + | 0.973798i | \(0.426972\pi\) | |||||||
\(798\) | −0.981714 | −0.0347523 | ||||||||
\(799\) | 7.95285 | 0.281352 | ||||||||
\(800\) | −11.2874 | −0.399070 | ||||||||
\(801\) | −33.7347 | −1.19196 | ||||||||
\(802\) | −89.8538 | −3.17285 | ||||||||
\(803\) | −2.02825 | −0.0715755 | ||||||||
\(804\) | 1.64244 | 0.0579245 | ||||||||
\(805\) | −0.603139 | −0.0212579 | ||||||||
\(806\) | −34.1414 | −1.20258 | ||||||||
\(807\) | −0.0702451 | −0.00247275 | ||||||||
\(808\) | −16.4142 | −0.577451 | ||||||||
\(809\) | −18.9626 | −0.666691 | −0.333345 | − | 0.942805i | \(-0.608177\pi\) | ||||
−0.333345 | + | 0.942805i | \(0.608177\pi\) | |||||||
\(810\) | 18.9603 | 0.666196 | ||||||||
\(811\) | −18.5559 | −0.651585 | −0.325792 | − | 0.945441i | \(-0.605631\pi\) | ||||
−0.325792 | + | 0.945441i | \(0.605631\pi\) | |||||||
\(812\) | −3.05491 | −0.107206 | ||||||||
\(813\) | 0.231663 | 0.00812479 | ||||||||
\(814\) | 3.25074 | 0.113938 | ||||||||
\(815\) | −1.46181 | −0.0512049 | ||||||||
\(816\) | 1.36105 | 0.0476463 | ||||||||
\(817\) | −5.10666 | −0.178659 | ||||||||
\(818\) | −27.1112 | −0.947920 | ||||||||
\(819\) | −3.77711 | −0.131983 | ||||||||
\(820\) | −30.1004 | −1.05115 | ||||||||
\(821\) | −1.16442 | −0.0406384 | −0.0203192 | − | 0.999794i | \(-0.506468\pi\) | ||||
−0.0203192 | + | 0.999794i | \(0.506468\pi\) | |||||||
\(822\) | 5.43277 | 0.189490 | ||||||||
\(823\) | −42.1364 | −1.46878 | −0.734392 | − | 0.678726i | \(-0.762532\pi\) | ||||
−0.734392 | + | 0.678726i | \(0.762532\pi\) | |||||||
\(824\) | −18.1717 | −0.633040 | ||||||||
\(825\) | 0.166051 | 0.00578114 | ||||||||
\(826\) | −10.7546 | −0.374200 | ||||||||
\(827\) | 35.8714 | 1.24737 | 0.623686 | − | 0.781675i | \(-0.285634\pi\) | ||||
0.623686 | + | 0.781675i | \(0.285634\pi\) | |||||||
\(828\) | 9.90945 | 0.344377 | ||||||||
\(829\) | 0.142024 | 0.00493270 | 0.00246635 | − | 0.999997i | \(-0.499215\pi\) | ||||
0.00246635 | + | 0.999997i | \(0.499215\pi\) | |||||||
\(830\) | −24.8242 | −0.861660 | ||||||||
\(831\) | −1.80984 | −0.0627827 | ||||||||
\(832\) | 18.5945 | 0.644648 | ||||||||
\(833\) | 28.7908 | 0.997542 | ||||||||
\(834\) | −0.720352 | −0.0249438 | ||||||||
\(835\) | −17.2077 | −0.595496 | ||||||||
\(836\) | 4.44653 | 0.153786 | ||||||||
\(837\) | −6.78954 | −0.234681 | ||||||||
\(838\) | −78.7752 | −2.72124 | ||||||||
\(839\) | 40.7197 | 1.40580 | 0.702901 | − | 0.711288i | \(-0.251888\pi\) | ||||
0.702901 | + | 0.711288i | \(0.251888\pi\) | |||||||
\(840\) | 0.365369 | 0.0126064 | ||||||||
\(841\) | −27.7707 | −0.957609 | ||||||||
\(842\) | −81.9505 | −2.82420 | ||||||||
\(843\) | −2.56035 | −0.0881833 | ||||||||
\(844\) | 12.6307 | 0.434766 | ||||||||
\(845\) | 9.09451 | 0.312861 | ||||||||
\(846\) | −12.6657 | −0.435455 | ||||||||
\(847\) | 8.13896 | 0.279658 | ||||||||
\(848\) | 7.71825 | 0.265046 | ||||||||
\(849\) | −3.14686 | −0.108000 | ||||||||
\(850\) | −44.6909 | −1.53289 | ||||||||
\(851\) | 4.16792 | 0.142875 | ||||||||
\(852\) | 1.27472 | 0.0436712 | ||||||||
\(853\) | −39.2328 | −1.34331 | −0.671653 | − | 0.740865i | \(-0.734416\pi\) | ||||
−0.671653 | + | 0.740865i | \(0.734416\pi\) | |||||||
\(854\) | −11.9355 | −0.408426 | ||||||||
\(855\) | 10.9755 | 0.375353 | ||||||||
\(856\) | 13.3866 | 0.457546 | ||||||||
\(857\) | −23.5497 | −0.804443 | −0.402221 | − | 0.915542i | \(-0.631762\pi\) | ||||
−0.402221 | + | 0.915542i | \(0.631762\pi\) | |||||||
\(858\) | −0.160570 | −0.00548177 | ||||||||
\(859\) | −34.1860 | −1.16641 | −0.583205 | − | 0.812325i | \(-0.698201\pi\) | ||||
−0.583205 | + | 0.812325i | \(0.698201\pi\) | |||||||
\(860\) | 4.14370 | 0.141299 | ||||||||
\(861\) | 0.910596 | 0.0310330 | ||||||||
\(862\) | −30.2480 | −1.03025 | ||||||||
\(863\) | 8.90175 | 0.303019 | 0.151510 | − | 0.988456i | \(-0.451587\pi\) | ||||
0.151510 | + | 0.988456i | \(0.451587\pi\) | |||||||
\(864\) | 2.17059 | 0.0738448 | ||||||||
\(865\) | 0.0860983 | 0.00292743 | ||||||||
\(866\) | −5.23789 | −0.177991 | ||||||||
\(867\) | −0.399220 | −0.0135582 | ||||||||
\(868\) | 23.2083 | 0.787741 | ||||||||
\(869\) | 4.13567 | 0.140293 | ||||||||
\(870\) | −0.320557 | −0.0108679 | ||||||||
\(871\) | 5.60367 | 0.189873 | ||||||||
\(872\) | −28.7579 | −0.973865 | ||||||||
\(873\) | −37.3019 | −1.26248 | ||||||||
\(874\) | 8.78732 | 0.297236 | ||||||||
\(875\) | −6.16321 | −0.208355 | ||||||||
\(876\) | 3.43463 | 0.116045 | ||||||||
\(877\) | −43.2807 | −1.46148 | −0.730742 | − | 0.682653i | \(-0.760826\pi\) | ||||
−0.730742 | + | 0.682653i | \(0.760826\pi\) | |||||||
\(878\) | −16.5620 | −0.558942 | ||||||||
\(879\) | 0.402215 | 0.0135664 | ||||||||
\(880\) | −0.597564 | −0.0201439 | ||||||||
\(881\) | 35.7833 | 1.20557 | 0.602785 | − | 0.797903i | \(-0.294058\pi\) | ||||
0.602785 | + | 0.797903i | \(0.294058\pi\) | |||||||
\(882\) | −45.8521 | −1.54392 | ||||||||
\(883\) | −29.3600 | −0.988044 | −0.494022 | − | 0.869449i | \(-0.664474\pi\) | ||||
−0.494022 | + | 0.869449i | \(0.664474\pi\) | |||||||
\(884\) | 28.0379 | 0.943017 | ||||||||
\(885\) | −0.732154 | −0.0246111 | ||||||||
\(886\) | 62.9383 | 2.11445 | ||||||||
\(887\) | 5.48260 | 0.184088 | 0.0920438 | − | 0.995755i | \(-0.470660\pi\) | ||||
0.0920438 | + | 0.995755i | \(0.470660\pi\) | |||||||
\(888\) | −2.52484 | −0.0847280 | ||||||||
\(889\) | 14.9651 | 0.501915 | ||||||||
\(890\) | 24.2737 | 0.813656 | ||||||||
\(891\) | 2.59797 | 0.0870352 | ||||||||
\(892\) | −87.5360 | −2.93092 | ||||||||
\(893\) | −7.28683 | −0.243844 | ||||||||
\(894\) | −1.18771 | −0.0397230 | ||||||||
\(895\) | 14.1402 | 0.472654 | ||||||||
\(896\) | −15.4660 | −0.516681 | ||||||||
\(897\) | −0.205874 | −0.00687394 | ||||||||
\(898\) | −92.7405 | −3.09479 | ||||||||
\(899\) | −9.33924 | −0.311481 | ||||||||
\(900\) | 46.1772 | 1.53924 | ||||||||
\(901\) | −15.2543 | −0.508193 | ||||||||
\(902\) | −6.35711 | −0.211669 | ||||||||
\(903\) | −0.125355 | −0.00417155 | ||||||||
\(904\) | 44.9999 | 1.49667 | ||||||||
\(905\) | −16.8503 | −0.560121 | ||||||||
\(906\) | −3.84575 | −0.127766 | ||||||||
\(907\) | 36.3331 | 1.20642 | 0.603210 | − | 0.797582i | \(-0.293888\pi\) | ||||
0.603210 | + | 0.797582i | \(0.293888\pi\) | |||||||
\(908\) | 6.98349 | 0.231755 | ||||||||
\(909\) | −12.1037 | −0.401454 | ||||||||
\(910\) | 2.71781 | 0.0900946 | ||||||||
\(911\) | −13.7228 | −0.454657 | −0.227328 | − | 0.973818i | \(-0.572999\pi\) | ||||
−0.227328 | + | 0.973818i | \(0.572999\pi\) | |||||||
\(912\) | −1.24707 | −0.0412945 | ||||||||
\(913\) | −3.40145 | −0.112572 | ||||||||
\(914\) | −1.92561 | −0.0636935 | ||||||||
\(915\) | −0.812551 | −0.0268621 | ||||||||
\(916\) | −64.1811 | −2.12060 | ||||||||
\(917\) | −16.5315 | −0.545919 | ||||||||
\(918\) | 8.59413 | 0.283649 | ||||||||
\(919\) | −3.27377 | −0.107992 | −0.0539959 | − | 0.998541i | \(-0.517196\pi\) | ||||
−0.0539959 | + | 0.998541i | \(0.517196\pi\) | |||||||
\(920\) | −3.27042 | −0.107822 | ||||||||
\(921\) | 0.576070 | 0.0189821 | ||||||||
\(922\) | 85.7187 | 2.82300 | ||||||||
\(923\) | 4.34908 | 0.143152 | ||||||||
\(924\) | 0.109151 | 0.00359079 | ||||||||
\(925\) | 19.4222 | 0.638597 | ||||||||
\(926\) | −66.1870 | −2.17504 | ||||||||
\(927\) | −13.3996 | −0.440100 | ||||||||
\(928\) | 2.98571 | 0.0980108 | ||||||||
\(929\) | −13.2236 | −0.433853 | −0.216926 | − | 0.976188i | \(-0.569603\pi\) | ||||
−0.216926 | + | 0.976188i | \(0.569603\pi\) | |||||||
\(930\) | 2.43528 | 0.0798561 | ||||||||
\(931\) | −26.3797 | −0.864558 | ||||||||
\(932\) | 38.6366 | 1.26558 | ||||||||
\(933\) | −1.80213 | −0.0589991 | ||||||||
\(934\) | 5.35901 | 0.175352 | ||||||||
\(935\) | 1.18102 | 0.0386234 | ||||||||
\(936\) | −20.4808 | −0.669434 | ||||||||
\(937\) | 8.82152 | 0.288186 | 0.144093 | − | 0.989564i | \(-0.453973\pi\) | ||||
0.144093 | + | 0.989564i | \(0.453973\pi\) | |||||||
\(938\) | −5.87127 | −0.191704 | ||||||||
\(939\) | 3.62702 | 0.118363 | ||||||||
\(940\) | 5.91276 | 0.192853 | ||||||||
\(941\) | −17.9741 | −0.585938 | −0.292969 | − | 0.956122i | \(-0.594643\pi\) | ||||
−0.292969 | + | 0.956122i | \(0.594643\pi\) | |||||||
\(942\) | −2.73943 | −0.0892555 | ||||||||
\(943\) | −8.15075 | −0.265425 | ||||||||
\(944\) | −13.6615 | −0.444645 | ||||||||
\(945\) | 0.540478 | 0.0175818 | ||||||||
\(946\) | 0.875136 | 0.0284531 | ||||||||
\(947\) | −37.9267 | −1.23245 | −0.616226 | − | 0.787569i | \(-0.711339\pi\) | ||||
−0.616226 | + | 0.787569i | \(0.711339\pi\) | |||||||
\(948\) | −7.00330 | −0.227457 | ||||||||
\(949\) | 11.7182 | 0.380390 | ||||||||
\(950\) | 40.9482 | 1.32853 | ||||||||
\(951\) | −1.50751 | −0.0488844 | ||||||||
\(952\) | −13.4741 | −0.436698 | ||||||||
\(953\) | 47.6473 | 1.54345 | 0.771724 | − | 0.635957i | \(-0.219395\pi\) | ||||
0.771724 | + | 0.635957i | \(0.219395\pi\) | |||||||
\(954\) | 24.2939 | 0.786543 | ||||||||
\(955\) | 12.9144 | 0.417901 | ||||||||
\(956\) | 32.5535 | 1.05286 | ||||||||
\(957\) | −0.0439232 | −0.00141984 | ||||||||
\(958\) | 38.0636 | 1.22978 | ||||||||
\(959\) | −12.5999 | −0.406871 | ||||||||
\(960\) | −1.32633 | −0.0428072 | ||||||||
\(961\) | 39.9506 | 1.28873 | ||||||||
\(962\) | −18.7811 | −0.605528 | ||||||||
\(963\) | 9.87116 | 0.318094 | ||||||||
\(964\) | 92.9811 | 2.99472 | ||||||||
\(965\) | 4.62665 | 0.148937 | ||||||||
\(966\) | 0.215706 | 0.00694021 | ||||||||
\(967\) | 31.1632 | 1.00214 | 0.501071 | − | 0.865406i | \(-0.332940\pi\) | ||||
0.501071 | + | 0.865406i | \(0.332940\pi\) | |||||||
\(968\) | 44.1321 | 1.41846 | ||||||||
\(969\) | 2.46469 | 0.0791771 | ||||||||
\(970\) | 26.8405 | 0.861796 | ||||||||
\(971\) | 29.8070 | 0.956553 | 0.478277 | − | 0.878209i | \(-0.341262\pi\) | ||||
0.478277 | + | 0.878209i | \(0.341262\pi\) | |||||||
\(972\) | −13.3334 | −0.427669 | ||||||||
\(973\) | 1.67067 | 0.0535591 | ||||||||
\(974\) | −4.58088 | −0.146781 | ||||||||
\(975\) | −0.959357 | −0.0307240 | ||||||||
\(976\) | −15.1617 | −0.485313 | ||||||||
\(977\) | −49.5819 | −1.58626 | −0.793132 | − | 0.609050i | \(-0.791551\pi\) | ||||
−0.793132 | + | 0.609050i | \(0.791551\pi\) | |||||||
\(978\) | 0.522799 | 0.0167173 | ||||||||
\(979\) | 3.32602 | 0.106300 | ||||||||
\(980\) | 21.4053 | 0.683767 | ||||||||
\(981\) | −21.2058 | −0.677048 | ||||||||
\(982\) | −33.8747 | −1.08098 | ||||||||
\(983\) | 30.2078 | 0.963479 | 0.481739 | − | 0.876315i | \(-0.340005\pi\) | ||||
0.481739 | + | 0.876315i | \(0.340005\pi\) | |||||||
\(984\) | 4.93755 | 0.157403 | ||||||||
\(985\) | 7.66657 | 0.244277 | ||||||||
\(986\) | 11.8215 | 0.376474 | ||||||||
\(987\) | −0.178872 | −0.00569357 | ||||||||
\(988\) | −25.6898 | −0.817302 | ||||||||
\(989\) | 1.12205 | 0.0356792 | ||||||||
\(990\) | −1.88088 | −0.0597784 | ||||||||
\(991\) | 12.6417 | 0.401577 | 0.200788 | − | 0.979635i | \(-0.435650\pi\) | ||||
0.200788 | + | 0.979635i | \(0.435650\pi\) | |||||||
\(992\) | −22.6826 | −0.720173 | ||||||||
\(993\) | −1.53231 | −0.0486263 | ||||||||
\(994\) | −4.55676 | −0.144532 | ||||||||
\(995\) | −5.74263 | −0.182054 | ||||||||
\(996\) | 5.75999 | 0.182512 | ||||||||
\(997\) | 6.83372 | 0.216426 | 0.108213 | − | 0.994128i | \(-0.465487\pi\) | ||||
0.108213 | + | 0.994128i | \(0.465487\pi\) | |||||||
\(998\) | −101.458 | −3.21160 | ||||||||
\(999\) | −3.73491 | −0.118167 |
(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 | 4021.2.a.c.1.17 | ✓ | 182 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4021.2.a.c.1.17 | ✓ | 182 | 1.1 | even | 1 | trivial |