Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1339,2,Mod(1,1339)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1339, 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("1339.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1339 = 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1339.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: | \(10.6919688306\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 1339.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.319351 | −0.225815 | −0.112908 | − | 0.993605i | \(-0.536016\pi\) | ||||
−0.112908 | + | 0.993605i | \(0.536016\pi\) | |||||||
\(3\) | 0.543955 | 0.314053 | 0.157026 | − | 0.987594i | \(-0.449809\pi\) | ||||
0.157026 | + | 0.987594i | \(0.449809\pi\) | |||||||
\(4\) | −1.89802 | −0.949008 | ||||||||
\(5\) | 1.90715 | 0.852902 | 0.426451 | − | 0.904511i | \(-0.359764\pi\) | ||||
0.426451 | + | 0.904511i | \(0.359764\pi\) | |||||||
\(6\) | −0.173713 | −0.0709178 | ||||||||
\(7\) | 0.747001 | 0.282340 | 0.141170 | − | 0.989985i | \(-0.454914\pi\) | ||||
0.141170 | + | 0.989985i | \(0.454914\pi\) | |||||||
\(8\) | 1.24483 | 0.440115 | ||||||||
\(9\) | −2.70411 | −0.901371 | ||||||||
\(10\) | −0.609049 | −0.192598 | ||||||||
\(11\) | −5.00203 | −1.50817 | −0.754084 | − | 0.656778i | \(-0.771919\pi\) | ||||
−0.754084 | + | 0.656778i | \(0.771919\pi\) | |||||||
\(12\) | −1.03243 | −0.298038 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −0.238555 | −0.0637566 | ||||||||
\(15\) | 1.03740 | 0.267856 | ||||||||
\(16\) | 3.39849 | 0.849623 | ||||||||
\(17\) | 1.16752 | 0.283164 | 0.141582 | − | 0.989927i | \(-0.454781\pi\) | ||||
0.141582 | + | 0.989927i | \(0.454781\pi\) | |||||||
\(18\) | 0.863561 | 0.203543 | ||||||||
\(19\) | 7.09837 | 1.62848 | 0.814239 | − | 0.580530i | \(-0.197155\pi\) | ||||
0.814239 | + | 0.580530i | \(0.197155\pi\) | |||||||
\(20\) | −3.61979 | −0.809410 | ||||||||
\(21\) | 0.406335 | 0.0886696 | ||||||||
\(22\) | 1.59740 | 0.340567 | ||||||||
\(23\) | 7.48766 | 1.56128 | 0.780642 | − | 0.624978i | \(-0.214892\pi\) | ||||
0.780642 | + | 0.624978i | \(0.214892\pi\) | |||||||
\(24\) | 0.677134 | 0.138219 | ||||||||
\(25\) | −1.36279 | −0.272558 | ||||||||
\(26\) | 0.319351 | 0.0626298 | ||||||||
\(27\) | −3.10278 | −0.597131 | ||||||||
\(28\) | −1.41782 | −0.267943 | ||||||||
\(29\) | 9.53127 | 1.76991 | 0.884956 | − | 0.465675i | \(-0.154188\pi\) | ||||
0.884956 | + | 0.465675i | \(0.154188\pi\) | |||||||
\(30\) | −0.331295 | −0.0604860 | ||||||||
\(31\) | 1.40315 | 0.252013 | 0.126007 | − | 0.992029i | \(-0.459784\pi\) | ||||
0.126007 | + | 0.992029i | \(0.459784\pi\) | |||||||
\(32\) | −3.57498 | −0.631973 | ||||||||
\(33\) | −2.72088 | −0.473644 | ||||||||
\(34\) | −0.372847 | −0.0639428 | ||||||||
\(35\) | 1.42464 | 0.240808 | ||||||||
\(36\) | 5.13245 | 0.855408 | ||||||||
\(37\) | 1.98404 | 0.326174 | 0.163087 | − | 0.986612i | \(-0.447855\pi\) | ||||
0.163087 | + | 0.986612i | \(0.447855\pi\) | |||||||
\(38\) | −2.26687 | −0.367735 | ||||||||
\(39\) | −0.543955 | −0.0871025 | ||||||||
\(40\) | 2.37408 | 0.375375 | ||||||||
\(41\) | 6.59432 | 1.02986 | 0.514930 | − | 0.857232i | \(-0.327818\pi\) | ||||
0.514930 | + | 0.857232i | \(0.327818\pi\) | |||||||
\(42\) | −0.129763 | −0.0200229 | ||||||||
\(43\) | 3.40828 | 0.519757 | 0.259879 | − | 0.965641i | \(-0.416317\pi\) | ||||
0.259879 | + | 0.965641i | \(0.416317\pi\) | |||||||
\(44\) | 9.49392 | 1.43126 | ||||||||
\(45\) | −5.15714 | −0.768781 | ||||||||
\(46\) | −2.39119 | −0.352562 | ||||||||
\(47\) | 3.48074 | 0.507719 | 0.253859 | − | 0.967241i | \(-0.418300\pi\) | ||||
0.253859 | + | 0.967241i | \(0.418300\pi\) | |||||||
\(48\) | 1.84863 | 0.266826 | ||||||||
\(49\) | −6.44199 | −0.920284 | ||||||||
\(50\) | 0.435208 | 0.0615477 | ||||||||
\(51\) | 0.635076 | 0.0889285 | ||||||||
\(52\) | 1.89802 | 0.263207 | ||||||||
\(53\) | −7.21469 | −0.991014 | −0.495507 | − | 0.868604i | \(-0.665018\pi\) | ||||
−0.495507 | + | 0.868604i | \(0.665018\pi\) | |||||||
\(54\) | 0.990876 | 0.134841 | ||||||||
\(55\) | −9.53960 | −1.28632 | ||||||||
\(56\) | 0.929892 | 0.124262 | ||||||||
\(57\) | 3.86119 | 0.511428 | ||||||||
\(58\) | −3.04382 | −0.399673 | ||||||||
\(59\) | −2.48429 | −0.323427 | −0.161713 | − | 0.986838i | \(-0.551702\pi\) | ||||
−0.161713 | + | 0.986838i | \(0.551702\pi\) | |||||||
\(60\) | −1.96901 | −0.254197 | ||||||||
\(61\) | 5.09583 | 0.652454 | 0.326227 | − | 0.945291i | \(-0.394223\pi\) | ||||
0.326227 | + | 0.945291i | \(0.394223\pi\) | |||||||
\(62\) | −0.448097 | −0.0569084 | ||||||||
\(63\) | −2.01997 | −0.254493 | ||||||||
\(64\) | −5.65531 | −0.706914 | ||||||||
\(65\) | −1.90715 | −0.236552 | ||||||||
\(66\) | 0.868914 | 0.106956 | ||||||||
\(67\) | 4.65273 | 0.568421 | 0.284211 | − | 0.958762i | \(-0.408268\pi\) | ||||
0.284211 | + | 0.958762i | \(0.408268\pi\) | |||||||
\(68\) | −2.21596 | −0.268725 | ||||||||
\(69\) | 4.07295 | 0.490325 | ||||||||
\(70\) | −0.454960 | −0.0543781 | ||||||||
\(71\) | −9.57689 | −1.13657 | −0.568284 | − | 0.822832i | \(-0.692392\pi\) | ||||
−0.568284 | + | 0.822832i | \(0.692392\pi\) | |||||||
\(72\) | −3.36617 | −0.396707 | ||||||||
\(73\) | 6.07024 | 0.710468 | 0.355234 | − | 0.934777i | \(-0.384401\pi\) | ||||
0.355234 | + | 0.934777i | \(0.384401\pi\) | |||||||
\(74\) | −0.633604 | −0.0736550 | ||||||||
\(75\) | −0.741297 | −0.0855976 | ||||||||
\(76\) | −13.4728 | −1.54544 | ||||||||
\(77\) | −3.73652 | −0.425816 | ||||||||
\(78\) | 0.173713 | 0.0196691 | ||||||||
\(79\) | 6.73966 | 0.758271 | 0.379136 | − | 0.925341i | \(-0.376221\pi\) | ||||
0.379136 | + | 0.925341i | \(0.376221\pi\) | |||||||
\(80\) | 6.48142 | 0.724645 | ||||||||
\(81\) | 6.42456 | 0.713841 | ||||||||
\(82\) | −2.10590 | −0.232558 | ||||||||
\(83\) | 8.33177 | 0.914530 | 0.457265 | − | 0.889330i | \(-0.348829\pi\) | ||||
0.457265 | + | 0.889330i | \(0.348829\pi\) | |||||||
\(84\) | −0.771230 | −0.0841481 | ||||||||
\(85\) | 2.22663 | 0.241511 | ||||||||
\(86\) | −1.08844 | −0.117369 | ||||||||
\(87\) | 5.18458 | 0.555845 | ||||||||
\(88\) | −6.22669 | −0.663768 | ||||||||
\(89\) | 7.74840 | 0.821329 | 0.410664 | − | 0.911787i | \(-0.365297\pi\) | ||||
0.410664 | + | 0.911787i | \(0.365297\pi\) | |||||||
\(90\) | 1.64694 | 0.173602 | ||||||||
\(91\) | −0.747001 | −0.0783070 | ||||||||
\(92\) | −14.2117 | −1.48167 | ||||||||
\(93\) | 0.763250 | 0.0791454 | ||||||||
\(94\) | −1.11158 | −0.114651 | ||||||||
\(95\) | 13.5376 | 1.38893 | ||||||||
\(96\) | −1.94463 | −0.198473 | ||||||||
\(97\) | 18.2061 | 1.84855 | 0.924277 | − | 0.381723i | \(-0.124669\pi\) | ||||
0.924277 | + | 0.381723i | \(0.124669\pi\) | |||||||
\(98\) | 2.05725 | 0.207814 | ||||||||
\(99\) | 13.5260 | 1.35942 | ||||||||
\(100\) | 2.58660 | 0.258660 | ||||||||
\(101\) | 13.4018 | 1.33353 | 0.666764 | − | 0.745269i | \(-0.267679\pi\) | ||||
0.666764 | + | 0.745269i | \(0.267679\pi\) | |||||||
\(102\) | −0.202812 | −0.0200814 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.24483 | −0.122066 | ||||||||
\(105\) | 0.774940 | 0.0756264 | ||||||||
\(106\) | 2.30402 | 0.223786 | ||||||||
\(107\) | 9.31009 | 0.900040 | 0.450020 | − | 0.893018i | \(-0.351417\pi\) | ||||
0.450020 | + | 0.893018i | \(0.351417\pi\) | |||||||
\(108\) | 5.88913 | 0.566681 | ||||||||
\(109\) | −13.4113 | −1.28457 | −0.642287 | − | 0.766464i | \(-0.722014\pi\) | ||||
−0.642287 | + | 0.766464i | \(0.722014\pi\) | |||||||
\(110\) | 3.04648 | 0.290470 | ||||||||
\(111\) | 1.07923 | 0.102436 | ||||||||
\(112\) | 2.53868 | 0.239882 | ||||||||
\(113\) | −10.0757 | −0.947838 | −0.473919 | − | 0.880569i | \(-0.657161\pi\) | ||||
−0.473919 | + | 0.880569i | \(0.657161\pi\) | |||||||
\(114\) | −1.23308 | −0.115488 | ||||||||
\(115\) | 14.2801 | 1.33162 | ||||||||
\(116\) | −18.0905 | −1.67966 | ||||||||
\(117\) | 2.70411 | 0.249995 | ||||||||
\(118\) | 0.793359 | 0.0730346 | ||||||||
\(119\) | 0.872136 | 0.0799486 | ||||||||
\(120\) | 1.29139 | 0.117888 | ||||||||
\(121\) | 14.0203 | 1.27457 | ||||||||
\(122\) | −1.62736 | −0.147334 | ||||||||
\(123\) | 3.58701 | 0.323430 | ||||||||
\(124\) | −2.66320 | −0.239162 | ||||||||
\(125\) | −12.1348 | −1.08537 | ||||||||
\(126\) | 0.645081 | 0.0574683 | ||||||||
\(127\) | 9.82884 | 0.872168 | 0.436084 | − | 0.899906i | \(-0.356365\pi\) | ||||
0.436084 | + | 0.899906i | \(0.356365\pi\) | |||||||
\(128\) | 8.95599 | 0.791605 | ||||||||
\(129\) | 1.85395 | 0.163231 | ||||||||
\(130\) | 0.609049 | 0.0534171 | ||||||||
\(131\) | −17.4913 | −1.52822 | −0.764110 | − | 0.645086i | \(-0.776822\pi\) | ||||
−0.764110 | + | 0.645086i | \(0.776822\pi\) | |||||||
\(132\) | 5.16427 | 0.449492 | ||||||||
\(133\) | 5.30249 | 0.459784 | ||||||||
\(134\) | −1.48585 | −0.128358 | ||||||||
\(135\) | −5.91746 | −0.509294 | ||||||||
\(136\) | 1.45336 | 0.124625 | ||||||||
\(137\) | −6.99654 | −0.597754 | −0.298877 | − | 0.954292i | \(-0.596612\pi\) | ||||
−0.298877 | + | 0.954292i | \(0.596612\pi\) | |||||||
\(138\) | −1.30070 | −0.110723 | ||||||||
\(139\) | −8.43677 | −0.715597 | −0.357799 | − | 0.933799i | \(-0.616473\pi\) | ||||
−0.357799 | + | 0.933799i | \(0.616473\pi\) | |||||||
\(140\) | −2.70399 | −0.228529 | ||||||||
\(141\) | 1.89337 | 0.159450 | ||||||||
\(142\) | 3.05839 | 0.256654 | ||||||||
\(143\) | 5.00203 | 0.418290 | ||||||||
\(144\) | −9.18990 | −0.765825 | ||||||||
\(145\) | 18.1775 | 1.50956 | ||||||||
\(146\) | −1.93854 | −0.160434 | ||||||||
\(147\) | −3.50415 | −0.289018 | ||||||||
\(148\) | −3.76574 | −0.309542 | ||||||||
\(149\) | 21.0359 | 1.72333 | 0.861665 | − | 0.507478i | \(-0.169422\pi\) | ||||
0.861665 | + | 0.507478i | \(0.169422\pi\) | |||||||
\(150\) | 0.236734 | 0.0193292 | ||||||||
\(151\) | −23.9464 | −1.94873 | −0.974364 | − | 0.224976i | \(-0.927770\pi\) | ||||
−0.974364 | + | 0.224976i | \(0.927770\pi\) | |||||||
\(152\) | 8.83629 | 0.716718 | ||||||||
\(153\) | −3.15710 | −0.255236 | ||||||||
\(154\) | 1.19326 | 0.0961556 | ||||||||
\(155\) | 2.67601 | 0.214942 | ||||||||
\(156\) | 1.03243 | 0.0826610 | ||||||||
\(157\) | −8.52758 | −0.680575 | −0.340287 | − | 0.940321i | \(-0.610524\pi\) | ||||
−0.340287 | + | 0.940321i | \(0.610524\pi\) | |||||||
\(158\) | −2.15232 | −0.171229 | ||||||||
\(159\) | −3.92447 | −0.311231 | ||||||||
\(160\) | −6.81801 | −0.539011 | ||||||||
\(161\) | 5.59329 | 0.440813 | ||||||||
\(162\) | −2.05169 | −0.161196 | ||||||||
\(163\) | 5.33810 | 0.418112 | 0.209056 | − | 0.977904i | \(-0.432961\pi\) | ||||
0.209056 | + | 0.977904i | \(0.432961\pi\) | |||||||
\(164\) | −12.5161 | −0.977344 | ||||||||
\(165\) | −5.18911 | −0.403972 | ||||||||
\(166\) | −2.66076 | −0.206515 | ||||||||
\(167\) | 22.6380 | 1.75178 | 0.875891 | − | 0.482510i | \(-0.160275\pi\) | ||||
0.875891 | + | 0.482510i | \(0.160275\pi\) | |||||||
\(168\) | 0.505820 | 0.0390248 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.711075 | −0.0545369 | ||||||||
\(171\) | −19.1948 | −1.46786 | ||||||||
\(172\) | −6.46896 | −0.493254 | ||||||||
\(173\) | −13.3343 | −1.01379 | −0.506893 | − | 0.862009i | \(-0.669206\pi\) | ||||
−0.506893 | + | 0.862009i | \(0.669206\pi\) | |||||||
\(174\) | −1.65570 | −0.125518 | ||||||||
\(175\) | −1.01801 | −0.0769540 | ||||||||
\(176\) | −16.9993 | −1.28137 | ||||||||
\(177\) | −1.35134 | −0.101573 | ||||||||
\(178\) | −2.47446 | −0.185468 | ||||||||
\(179\) | −16.3187 | −1.21971 | −0.609857 | − | 0.792512i | \(-0.708773\pi\) | ||||
−0.609857 | + | 0.792512i | \(0.708773\pi\) | |||||||
\(180\) | 9.78833 | 0.729579 | ||||||||
\(181\) | 13.2572 | 0.985399 | 0.492699 | − | 0.870200i | \(-0.336010\pi\) | ||||
0.492699 | + | 0.870200i | \(0.336010\pi\) | |||||||
\(182\) | 0.238555 | 0.0176829 | ||||||||
\(183\) | 2.77190 | 0.204905 | ||||||||
\(184\) | 9.32089 | 0.687145 | ||||||||
\(185\) | 3.78385 | 0.278194 | ||||||||
\(186\) | −0.243745 | −0.0178722 | ||||||||
\(187\) | −5.83995 | −0.427059 | ||||||||
\(188\) | −6.60650 | −0.481829 | ||||||||
\(189\) | −2.31778 | −0.168594 | ||||||||
\(190\) | −4.32325 | −0.313642 | ||||||||
\(191\) | −25.6746 | −1.85775 | −0.928873 | − | 0.370399i | \(-0.879221\pi\) | ||||
−0.928873 | + | 0.370399i | \(0.879221\pi\) | |||||||
\(192\) | −3.07623 | −0.222008 | ||||||||
\(193\) | −4.46496 | −0.321395 | −0.160698 | − | 0.987004i | \(-0.551374\pi\) | ||||
−0.160698 | + | 0.987004i | \(0.551374\pi\) | |||||||
\(194\) | −5.81415 | −0.417431 | ||||||||
\(195\) | −1.03740 | −0.0742899 | ||||||||
\(196\) | 12.2270 | 0.873357 | ||||||||
\(197\) | 3.17369 | 0.226116 | 0.113058 | − | 0.993588i | \(-0.463935\pi\) | ||||
0.113058 | + | 0.993588i | \(0.463935\pi\) | |||||||
\(198\) | −4.31955 | −0.306977 | ||||||||
\(199\) | −12.3553 | −0.875842 | −0.437921 | − | 0.899013i | \(-0.644285\pi\) | ||||
−0.437921 | + | 0.899013i | \(0.644285\pi\) | |||||||
\(200\) | −1.69645 | −0.119957 | ||||||||
\(201\) | 2.53088 | 0.178514 | ||||||||
\(202\) | −4.27988 | −0.301131 | ||||||||
\(203\) | 7.11986 | 0.499717 | ||||||||
\(204\) | −1.20538 | −0.0843938 | ||||||||
\(205\) | 12.5763 | 0.878369 | ||||||||
\(206\) | −0.319351 | −0.0222502 | ||||||||
\(207\) | −20.2475 | −1.40730 | ||||||||
\(208\) | −3.39849 | −0.235643 | ||||||||
\(209\) | −35.5062 | −2.45602 | ||||||||
\(210\) | −0.247478 | −0.0170776 | ||||||||
\(211\) | 7.84411 | 0.540011 | 0.270006 | − | 0.962859i | \(-0.412974\pi\) | ||||
0.270006 | + | 0.962859i | \(0.412974\pi\) | |||||||
\(212\) | 13.6936 | 0.940480 | ||||||||
\(213\) | −5.20940 | −0.356942 | ||||||||
\(214\) | −2.97318 | −0.203243 | ||||||||
\(215\) | 6.50009 | 0.443302 | ||||||||
\(216\) | −3.86245 | −0.262806 | ||||||||
\(217\) | 1.04815 | 0.0711533 | ||||||||
\(218\) | 4.28293 | 0.290076 | ||||||||
\(219\) | 3.30194 | 0.223124 | ||||||||
\(220\) | 18.1063 | 1.22073 | ||||||||
\(221\) | −1.16752 | −0.0785357 | ||||||||
\(222\) | −0.344652 | −0.0231316 | ||||||||
\(223\) | −26.3244 | −1.76282 | −0.881408 | − | 0.472357i | \(-0.843403\pi\) | ||||
−0.881408 | + | 0.472357i | \(0.843403\pi\) | |||||||
\(224\) | −2.67051 | −0.178431 | ||||||||
\(225\) | 3.68514 | 0.245676 | ||||||||
\(226\) | 3.21767 | 0.214036 | ||||||||
\(227\) | −7.14336 | −0.474121 | −0.237061 | − | 0.971495i | \(-0.576184\pi\) | ||||
−0.237061 | + | 0.971495i | \(0.576184\pi\) | |||||||
\(228\) | −7.32860 | −0.485349 | ||||||||
\(229\) | 12.1054 | 0.799950 | 0.399975 | − | 0.916526i | \(-0.369019\pi\) | ||||
0.399975 | + | 0.916526i | \(0.369019\pi\) | |||||||
\(230\) | −4.56035 | −0.300700 | ||||||||
\(231\) | −2.03250 | −0.133729 | ||||||||
\(232\) | 11.8648 | 0.778965 | ||||||||
\(233\) | 26.2238 | 1.71798 | 0.858989 | − | 0.511994i | \(-0.171093\pi\) | ||||
0.858989 | + | 0.511994i | \(0.171093\pi\) | |||||||
\(234\) | −0.863561 | −0.0564527 | ||||||||
\(235\) | 6.63829 | 0.433034 | ||||||||
\(236\) | 4.71521 | 0.306934 | ||||||||
\(237\) | 3.66607 | 0.238137 | ||||||||
\(238\) | −0.278517 | −0.0180536 | ||||||||
\(239\) | 4.18357 | 0.270613 | 0.135306 | − | 0.990804i | \(-0.456798\pi\) | ||||
0.135306 | + | 0.990804i | \(0.456798\pi\) | |||||||
\(240\) | 3.52560 | 0.227577 | ||||||||
\(241\) | 11.2688 | 0.725885 | 0.362942 | − | 0.931812i | \(-0.381772\pi\) | ||||
0.362942 | + | 0.931812i | \(0.381772\pi\) | |||||||
\(242\) | −4.47738 | −0.287817 | ||||||||
\(243\) | 12.8030 | 0.821314 | ||||||||
\(244\) | −9.67197 | −0.619184 | ||||||||
\(245\) | −12.2858 | −0.784912 | ||||||||
\(246\) | −1.14552 | −0.0730354 | ||||||||
\(247\) | −7.09837 | −0.451658 | ||||||||
\(248\) | 1.74669 | 0.110915 | ||||||||
\(249\) | 4.53211 | 0.287211 | ||||||||
\(250\) | 3.87525 | 0.245092 | ||||||||
\(251\) | −2.87311 | −0.181349 | −0.0906746 | − | 0.995881i | \(-0.528902\pi\) | ||||
−0.0906746 | + | 0.995881i | \(0.528902\pi\) | |||||||
\(252\) | 3.83394 | 0.241516 | ||||||||
\(253\) | −37.4534 | −2.35468 | ||||||||
\(254\) | −3.13885 | −0.196949 | ||||||||
\(255\) | 1.21118 | 0.0758473 | ||||||||
\(256\) | 8.45052 | 0.528157 | ||||||||
\(257\) | 29.8817 | 1.86397 | 0.931985 | − | 0.362498i | \(-0.118076\pi\) | ||||
0.931985 | + | 0.362498i | \(0.118076\pi\) | |||||||
\(258\) | −0.592060 | −0.0368601 | ||||||||
\(259\) | 1.48208 | 0.0920919 | ||||||||
\(260\) | 3.61979 | 0.224490 | ||||||||
\(261\) | −25.7736 | −1.59535 | ||||||||
\(262\) | 5.58585 | 0.345095 | ||||||||
\(263\) | 3.93873 | 0.242872 | 0.121436 | − | 0.992599i | \(-0.461250\pi\) | ||||
0.121436 | + | 0.992599i | \(0.461250\pi\) | |||||||
\(264\) | −3.38704 | −0.208458 | ||||||||
\(265\) | −13.7595 | −0.845238 | ||||||||
\(266\) | −1.69335 | −0.103826 | ||||||||
\(267\) | 4.21478 | 0.257940 | ||||||||
\(268\) | −8.83095 | −0.539436 | ||||||||
\(269\) | −20.4879 | −1.24917 | −0.624585 | − | 0.780957i | \(-0.714732\pi\) | ||||
−0.624585 | + | 0.780957i | \(0.714732\pi\) | |||||||
\(270\) | 1.88975 | 0.115006 | ||||||||
\(271\) | −20.0615 | −1.21865 | −0.609324 | − | 0.792922i | \(-0.708559\pi\) | ||||
−0.609324 | + | 0.792922i | \(0.708559\pi\) | |||||||
\(272\) | 3.96779 | 0.240583 | ||||||||
\(273\) | −0.406335 | −0.0245925 | ||||||||
\(274\) | 2.23435 | 0.134982 | ||||||||
\(275\) | 6.81671 | 0.411063 | ||||||||
\(276\) | −7.73052 | −0.465322 | ||||||||
\(277\) | 7.50641 | 0.451016 | 0.225508 | − | 0.974241i | \(-0.427596\pi\) | ||||
0.225508 | + | 0.974241i | \(0.427596\pi\) | |||||||
\(278\) | 2.69429 | 0.161593 | ||||||||
\(279\) | −3.79427 | −0.227157 | ||||||||
\(280\) | 1.77344 | 0.105983 | ||||||||
\(281\) | 7.34530 | 0.438184 | 0.219092 | − | 0.975704i | \(-0.429691\pi\) | ||||
0.219092 | + | 0.975704i | \(0.429691\pi\) | |||||||
\(282\) | −0.604649 | −0.0360063 | ||||||||
\(283\) | 6.32625 | 0.376056 | 0.188028 | − | 0.982164i | \(-0.439790\pi\) | ||||
0.188028 | + | 0.982164i | \(0.439790\pi\) | |||||||
\(284\) | 18.1771 | 1.07861 | ||||||||
\(285\) | 7.36386 | 0.436198 | ||||||||
\(286\) | −1.59740 | −0.0944563 | ||||||||
\(287\) | 4.92596 | 0.290770 | ||||||||
\(288\) | 9.66715 | 0.569642 | ||||||||
\(289\) | −15.6369 | −0.919818 | ||||||||
\(290\) | −5.80501 | −0.340882 | ||||||||
\(291\) | 9.90332 | 0.580543 | ||||||||
\(292\) | −11.5214 | −0.674239 | ||||||||
\(293\) | −7.74321 | −0.452363 | −0.226181 | − | 0.974085i | \(-0.572624\pi\) | ||||
−0.226181 | + | 0.974085i | \(0.572624\pi\) | |||||||
\(294\) | 1.11905 | 0.0652646 | ||||||||
\(295\) | −4.73790 | −0.275851 | ||||||||
\(296\) | 2.46980 | 0.143554 | ||||||||
\(297\) | 15.5202 | 0.900573 | ||||||||
\(298\) | −6.71784 | −0.389154 | ||||||||
\(299\) | −7.48766 | −0.433022 | ||||||||
\(300\) | 1.40699 | 0.0812328 | ||||||||
\(301\) | 2.54599 | 0.146748 | ||||||||
\(302\) | 7.64730 | 0.440052 | ||||||||
\(303\) | 7.28998 | 0.418798 | ||||||||
\(304\) | 24.1237 | 1.38359 | ||||||||
\(305\) | 9.71850 | 0.556480 | ||||||||
\(306\) | 1.00822 | 0.0576362 | ||||||||
\(307\) | −15.7980 | −0.901637 | −0.450818 | − | 0.892616i | \(-0.648868\pi\) | ||||
−0.450818 | + | 0.892616i | \(0.648868\pi\) | |||||||
\(308\) | 7.09197 | 0.404102 | ||||||||
\(309\) | 0.543955 | 0.0309445 | ||||||||
\(310\) | −0.854587 | −0.0485373 | ||||||||
\(311\) | 21.6289 | 1.22646 | 0.613231 | − | 0.789904i | \(-0.289870\pi\) | ||||
0.613231 | + | 0.789904i | \(0.289870\pi\) | |||||||
\(312\) | −0.677134 | −0.0383352 | ||||||||
\(313\) | −32.0728 | −1.81286 | −0.906430 | − | 0.422356i | \(-0.861203\pi\) | ||||
−0.906430 | + | 0.422356i | \(0.861203\pi\) | |||||||
\(314\) | 2.72329 | 0.153684 | ||||||||
\(315\) | −3.85239 | −0.217058 | ||||||||
\(316\) | −12.7920 | −0.719605 | ||||||||
\(317\) | 4.05047 | 0.227497 | 0.113749 | − | 0.993510i | \(-0.463714\pi\) | ||||
0.113749 | + | 0.993510i | \(0.463714\pi\) | |||||||
\(318\) | 1.25328 | 0.0702806 | ||||||||
\(319\) | −47.6756 | −2.66932 | ||||||||
\(320\) | −10.7855 | −0.602928 | ||||||||
\(321\) | 5.06427 | 0.282660 | ||||||||
\(322\) | −1.78622 | −0.0995422 | ||||||||
\(323\) | 8.28746 | 0.461127 | ||||||||
\(324\) | −12.1939 | −0.677440 | ||||||||
\(325\) | 1.36279 | 0.0755940 | ||||||||
\(326\) | −1.70473 | −0.0944161 | ||||||||
\(327\) | −7.29517 | −0.403424 | ||||||||
\(328\) | 8.20883 | 0.453257 | ||||||||
\(329\) | 2.60012 | 0.143349 | ||||||||
\(330\) | 1.65715 | 0.0912230 | ||||||||
\(331\) | −9.32061 | −0.512307 | −0.256153 | − | 0.966636i | \(-0.582455\pi\) | ||||
−0.256153 | + | 0.966636i | \(0.582455\pi\) | |||||||
\(332\) | −15.8138 | −0.867896 | ||||||||
\(333\) | −5.36506 | −0.294004 | ||||||||
\(334\) | −7.22946 | −0.395579 | ||||||||
\(335\) | 8.87344 | 0.484808 | ||||||||
\(336\) | 1.38093 | 0.0753357 | ||||||||
\(337\) | 25.1927 | 1.37234 | 0.686168 | − | 0.727443i | \(-0.259291\pi\) | ||||
0.686168 | + | 0.727443i | \(0.259291\pi\) | |||||||
\(338\) | −0.319351 | −0.0173704 | ||||||||
\(339\) | −5.48070 | −0.297671 | ||||||||
\(340\) | −4.22617 | −0.229196 | ||||||||
\(341\) | −7.01859 | −0.380078 | ||||||||
\(342\) | 6.12987 | 0.331465 | ||||||||
\(343\) | −10.0412 | −0.542173 | ||||||||
\(344\) | 4.24274 | 0.228753 | ||||||||
\(345\) | 7.76771 | 0.418199 | ||||||||
\(346\) | 4.25831 | 0.228928 | ||||||||
\(347\) | 22.3175 | 1.19807 | 0.599033 | − | 0.800724i | \(-0.295552\pi\) | ||||
0.599033 | + | 0.800724i | \(0.295552\pi\) | |||||||
\(348\) | −9.84041 | −0.527501 | ||||||||
\(349\) | −23.1670 | −1.24010 | −0.620051 | − | 0.784562i | \(-0.712888\pi\) | ||||
−0.620051 | + | 0.784562i | \(0.712888\pi\) | |||||||
\(350\) | 0.325101 | 0.0173774 | ||||||||
\(351\) | 3.10278 | 0.165614 | ||||||||
\(352\) | 17.8821 | 0.953121 | ||||||||
\(353\) | −17.1197 | −0.911190 | −0.455595 | − | 0.890187i | \(-0.650573\pi\) | ||||
−0.455595 | + | 0.890187i | \(0.650573\pi\) | |||||||
\(354\) | 0.431552 | 0.0229367 | ||||||||
\(355\) | −18.2645 | −0.969381 | ||||||||
\(356\) | −14.7066 | −0.779447 | ||||||||
\(357\) | 0.474403 | 0.0251081 | ||||||||
\(358\) | 5.21138 | 0.275430 | ||||||||
\(359\) | −11.1708 | −0.589573 | −0.294787 | − | 0.955563i | \(-0.595249\pi\) | ||||
−0.294787 | + | 0.955563i | \(0.595249\pi\) | |||||||
\(360\) | −6.41979 | −0.338352 | ||||||||
\(361\) | 31.3868 | 1.65194 | ||||||||
\(362\) | −4.23369 | −0.222518 | ||||||||
\(363\) | 7.62639 | 0.400282 | ||||||||
\(364\) | 1.41782 | 0.0743139 | ||||||||
\(365\) | 11.5768 | 0.605959 | ||||||||
\(366\) | −0.885210 | −0.0462706 | ||||||||
\(367\) | 0.0235347 | 0.00122850 | 0.000614251 | − | 1.00000i | \(-0.499804\pi\) | ||||
0.000614251 | 1.00000i | \(0.499804\pi\) | ||||||||
\(368\) | 25.4467 | 1.32650 | ||||||||
\(369\) | −17.8318 | −0.928285 | ||||||||
\(370\) | −1.20838 | −0.0628205 | ||||||||
\(371\) | −5.38938 | −0.279803 | ||||||||
\(372\) | −1.44866 | −0.0751095 | ||||||||
\(373\) | 26.3820 | 1.36601 | 0.683004 | − | 0.730415i | \(-0.260673\pi\) | ||||
0.683004 | + | 0.730415i | \(0.260673\pi\) | |||||||
\(374\) | 1.86499 | 0.0964364 | ||||||||
\(375\) | −6.60077 | −0.340862 | ||||||||
\(376\) | 4.33295 | 0.223455 | ||||||||
\(377\) | −9.53127 | −0.490885 | ||||||||
\(378\) | 0.740185 | 0.0380710 | ||||||||
\(379\) | 0.875008 | 0.0449462 | 0.0224731 | − | 0.999747i | \(-0.492846\pi\) | ||||
0.0224731 | + | 0.999747i | \(0.492846\pi\) | |||||||
\(380\) | −25.6946 | −1.31811 | ||||||||
\(381\) | 5.34645 | 0.273907 | ||||||||
\(382\) | 8.19919 | 0.419507 | ||||||||
\(383\) | −9.77475 | −0.499466 | −0.249733 | − | 0.968315i | \(-0.580343\pi\) | ||||
−0.249733 | + | 0.968315i | \(0.580343\pi\) | |||||||
\(384\) | 4.87165 | 0.248606 | ||||||||
\(385\) | −7.12609 | −0.363179 | ||||||||
\(386\) | 1.42589 | 0.0725759 | ||||||||
\(387\) | −9.21637 | −0.468494 | ||||||||
\(388\) | −34.5555 | −1.75429 | ||||||||
\(389\) | 10.2454 | 0.519462 | 0.259731 | − | 0.965681i | \(-0.416366\pi\) | ||||
0.259731 | + | 0.965681i | \(0.416366\pi\) | |||||||
\(390\) | 0.331295 | 0.0167758 | ||||||||
\(391\) | 8.74196 | 0.442100 | ||||||||
\(392\) | −8.01921 | −0.405031 | ||||||||
\(393\) | −9.51447 | −0.479941 | ||||||||
\(394\) | −1.01352 | −0.0510605 | ||||||||
\(395\) | 12.8535 | 0.646731 | ||||||||
\(396\) | −25.6726 | −1.29010 | ||||||||
\(397\) | −18.6564 | −0.936338 | −0.468169 | − | 0.883639i | \(-0.655086\pi\) | ||||
−0.468169 | + | 0.883639i | \(0.655086\pi\) | |||||||
\(398\) | 3.94567 | 0.197778 | ||||||||
\(399\) | 2.88432 | 0.144396 | ||||||||
\(400\) | −4.63143 | −0.231572 | ||||||||
\(401\) | 7.01465 | 0.350295 | 0.175148 | − | 0.984542i | \(-0.443960\pi\) | ||||
0.175148 | + | 0.984542i | \(0.443960\pi\) | |||||||
\(402\) | −0.808237 | −0.0403112 | ||||||||
\(403\) | −1.40315 | −0.0698958 | ||||||||
\(404\) | −25.4368 | −1.26553 | ||||||||
\(405\) | 12.2526 | 0.608836 | ||||||||
\(406\) | −2.27373 | −0.112844 | ||||||||
\(407\) | −9.92421 | −0.491925 | ||||||||
\(408\) | 0.790565 | 0.0391388 | ||||||||
\(409\) | −4.69187 | −0.231998 | −0.115999 | − | 0.993249i | \(-0.537007\pi\) | ||||
−0.115999 | + | 0.993249i | \(0.537007\pi\) | |||||||
\(410\) | −4.01626 | −0.198349 | ||||||||
\(411\) | −3.80580 | −0.187726 | ||||||||
\(412\) | −1.89802 | −0.0935085 | ||||||||
\(413\) | −1.85576 | −0.0913162 | ||||||||
\(414\) | 6.46604 | 0.317789 | ||||||||
\(415\) | 15.8899 | 0.780005 | ||||||||
\(416\) | 3.57498 | 0.175278 | ||||||||
\(417\) | −4.58922 | −0.224735 | ||||||||
\(418\) | 11.3389 | 0.554606 | ||||||||
\(419\) | 33.7214 | 1.64740 | 0.823700 | − | 0.567026i | \(-0.191906\pi\) | ||||
0.823700 | + | 0.567026i | \(0.191906\pi\) | |||||||
\(420\) | −1.47085 | −0.0717701 | ||||||||
\(421\) | 15.4220 | 0.751622 | 0.375811 | − | 0.926696i | \(-0.377364\pi\) | ||||
0.375811 | + | 0.926696i | \(0.377364\pi\) | |||||||
\(422\) | −2.50502 | −0.121943 | ||||||||
\(423\) | −9.41232 | −0.457643 | ||||||||
\(424\) | −8.98109 | −0.436160 | ||||||||
\(425\) | −1.59108 | −0.0771787 | ||||||||
\(426\) | 1.66363 | 0.0806029 | ||||||||
\(427\) | 3.80659 | 0.184214 | ||||||||
\(428\) | −17.6707 | −0.854145 | ||||||||
\(429\) | 2.72088 | 0.131365 | ||||||||
\(430\) | −2.07581 | −0.100104 | ||||||||
\(431\) | 25.3800 | 1.22251 | 0.611255 | − | 0.791433i | \(-0.290665\pi\) | ||||
0.611255 | + | 0.791433i | \(0.290665\pi\) | |||||||
\(432\) | −10.5448 | −0.507336 | ||||||||
\(433\) | −40.2721 | −1.93535 | −0.967677 | − | 0.252194i | \(-0.918848\pi\) | ||||
−0.967677 | + | 0.252194i | \(0.918848\pi\) | |||||||
\(434\) | −0.334729 | −0.0160675 | ||||||||
\(435\) | 9.88776 | 0.474082 | ||||||||
\(436\) | 25.4549 | 1.21907 | ||||||||
\(437\) | 53.1501 | 2.54252 | ||||||||
\(438\) | −1.05448 | −0.0503848 | ||||||||
\(439\) | −22.4526 | −1.07160 | −0.535801 | − | 0.844344i | \(-0.679990\pi\) | ||||
−0.535801 | + | 0.844344i | \(0.679990\pi\) | |||||||
\(440\) | −11.8752 | −0.566129 | ||||||||
\(441\) | 17.4199 | 0.829517 | ||||||||
\(442\) | 0.372847 | 0.0177345 | ||||||||
\(443\) | −7.08341 | −0.336543 | −0.168272 | − | 0.985741i | \(-0.553819\pi\) | ||||
−0.168272 | + | 0.985741i | \(0.553819\pi\) | |||||||
\(444\) | −2.04839 | −0.0972123 | ||||||||
\(445\) | 14.7773 | 0.700513 | ||||||||
\(446\) | 8.40673 | 0.398070 | ||||||||
\(447\) | 11.4426 | 0.541216 | ||||||||
\(448\) | −4.22452 | −0.199590 | ||||||||
\(449\) | 31.4141 | 1.48252 | 0.741260 | − | 0.671218i | \(-0.234228\pi\) | ||||
0.741260 | + | 0.671218i | \(0.234228\pi\) | |||||||
\(450\) | −1.17685 | −0.0554773 | ||||||||
\(451\) | −32.9849 | −1.55320 | ||||||||
\(452\) | 19.1237 | 0.899505 | ||||||||
\(453\) | −13.0258 | −0.612003 | ||||||||
\(454\) | 2.28124 | 0.107064 | ||||||||
\(455\) | −1.42464 | −0.0667882 | ||||||||
\(456\) | 4.80655 | 0.225087 | ||||||||
\(457\) | 7.34767 | 0.343710 | 0.171855 | − | 0.985122i | \(-0.445024\pi\) | ||||
0.171855 | + | 0.985122i | \(0.445024\pi\) | |||||||
\(458\) | −3.86588 | −0.180641 | ||||||||
\(459\) | −3.62255 | −0.169086 | ||||||||
\(460\) | −27.1038 | −1.26372 | ||||||||
\(461\) | 2.18909 | 0.101956 | 0.0509780 | − | 0.998700i | \(-0.483766\pi\) | ||||
0.0509780 | + | 0.998700i | \(0.483766\pi\) | |||||||
\(462\) | 0.649080 | 0.0301979 | ||||||||
\(463\) | −37.9967 | −1.76586 | −0.882928 | − | 0.469508i | \(-0.844431\pi\) | ||||
−0.882928 | + | 0.469508i | \(0.844431\pi\) | |||||||
\(464\) | 32.3919 | 1.50376 | ||||||||
\(465\) | 1.45563 | 0.0675032 | ||||||||
\(466\) | −8.37459 | −0.387946 | ||||||||
\(467\) | 30.7096 | 1.42107 | 0.710534 | − | 0.703662i | \(-0.248453\pi\) | ||||
0.710534 | + | 0.703662i | \(0.248453\pi\) | |||||||
\(468\) | −5.13245 | −0.237247 | ||||||||
\(469\) | 3.47559 | 0.160488 | ||||||||
\(470\) | −2.11994 | −0.0977857 | ||||||||
\(471\) | −4.63862 | −0.213736 | ||||||||
\(472\) | −3.09252 | −0.142345 | ||||||||
\(473\) | −17.0483 | −0.783881 | ||||||||
\(474\) | −1.17076 | −0.0537749 | ||||||||
\(475\) | −9.67359 | −0.443855 | ||||||||
\(476\) | −1.65533 | −0.0758718 | ||||||||
\(477\) | 19.5093 | 0.893271 | ||||||||
\(478\) | −1.33603 | −0.0611084 | ||||||||
\(479\) | −14.4262 | −0.659152 | −0.329576 | − | 0.944129i | \(-0.606906\pi\) | ||||
−0.329576 | + | 0.944129i | \(0.606906\pi\) | |||||||
\(480\) | −3.70869 | −0.169278 | ||||||||
\(481\) | −1.98404 | −0.0904644 | ||||||||
\(482\) | −3.59869 | −0.163916 | ||||||||
\(483\) | 3.04250 | 0.138438 | ||||||||
\(484\) | −26.6107 | −1.20958 | ||||||||
\(485\) | 34.7218 | 1.57664 | ||||||||
\(486\) | −4.08865 | −0.185465 | ||||||||
\(487\) | −21.3335 | −0.966712 | −0.483356 | − | 0.875424i | \(-0.660582\pi\) | ||||
−0.483356 | + | 0.875424i | \(0.660582\pi\) | |||||||
\(488\) | 6.34347 | 0.287155 | ||||||||
\(489\) | 2.90369 | 0.131309 | ||||||||
\(490\) | 3.92349 | 0.177245 | ||||||||
\(491\) | −15.3137 | −0.691097 | −0.345548 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345548 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(492\) | −6.80820 | −0.306938 | ||||||||
\(493\) | 11.1279 | 0.501176 | ||||||||
\(494\) | 2.26687 | 0.101991 | ||||||||
\(495\) | 25.7961 | 1.15945 | ||||||||
\(496\) | 4.76859 | 0.214116 | ||||||||
\(497\) | −7.15395 | −0.320898 | ||||||||
\(498\) | −1.44733 | −0.0648565 | ||||||||
\(499\) | −34.6830 | −1.55263 | −0.776313 | − | 0.630347i | \(-0.782912\pi\) | ||||
−0.776313 | + | 0.630347i | \(0.782912\pi\) | |||||||
\(500\) | 23.0320 | 1.03002 | ||||||||
\(501\) | 12.3141 | 0.550151 | ||||||||
\(502\) | 0.917530 | 0.0409514 | ||||||||
\(503\) | 13.7437 | 0.612803 | 0.306402 | − | 0.951902i | \(-0.400875\pi\) | ||||
0.306402 | + | 0.951902i | \(0.400875\pi\) | |||||||
\(504\) | −2.51453 | −0.112006 | ||||||||
\(505\) | 25.5592 | 1.13737 | ||||||||
\(506\) | 11.9608 | 0.531722 | ||||||||
\(507\) | 0.543955 | 0.0241579 | ||||||||
\(508\) | −18.6553 | −0.827694 | ||||||||
\(509\) | −0.685433 | −0.0303813 | −0.0151907 | − | 0.999885i | \(-0.504836\pi\) | ||||
−0.0151907 | + | 0.999885i | \(0.504836\pi\) | |||||||
\(510\) | −0.386793 | −0.0171275 | ||||||||
\(511\) | 4.53447 | 0.200593 | ||||||||
\(512\) | −20.6107 | −0.910871 | ||||||||
\(513\) | −22.0247 | −0.972414 | ||||||||
\(514\) | −9.54275 | −0.420912 | ||||||||
\(515\) | 1.90715 | 0.0840389 | ||||||||
\(516\) | −3.51883 | −0.154908 | ||||||||
\(517\) | −17.4108 | −0.765725 | ||||||||
\(518\) | −0.473303 | −0.0207957 | ||||||||
\(519\) | −7.25324 | −0.318382 | ||||||||
\(520\) | −2.37408 | −0.104110 | ||||||||
\(521\) | −28.9696 | −1.26918 | −0.634591 | − | 0.772848i | \(-0.718832\pi\) | ||||
−0.634591 | + | 0.772848i | \(0.718832\pi\) | |||||||
\(522\) | 8.23083 | 0.360253 | ||||||||
\(523\) | −10.2420 | −0.447852 | −0.223926 | − | 0.974606i | \(-0.571887\pi\) | ||||
−0.223926 | + | 0.974606i | \(0.571887\pi\) | |||||||
\(524\) | 33.1987 | 1.45029 | ||||||||
\(525\) | −0.553749 | −0.0241676 | ||||||||
\(526\) | −1.25784 | −0.0548443 | ||||||||
\(527\) | 1.63820 | 0.0713611 | ||||||||
\(528\) | −9.24688 | −0.402419 | ||||||||
\(529\) | 33.0650 | 1.43761 | ||||||||
\(530\) | 4.39410 | 0.190867 | ||||||||
\(531\) | 6.71779 | 0.291527 | ||||||||
\(532\) | −10.0642 | −0.436338 | ||||||||
\(533\) | −6.59432 | −0.285632 | ||||||||
\(534\) | −1.34599 | −0.0582468 | ||||||||
\(535\) | 17.7557 | 0.767646 | ||||||||
\(536\) | 5.79188 | 0.250171 | ||||||||
\(537\) | −8.87662 | −0.383054 | ||||||||
\(538\) | 6.54283 | 0.282081 | ||||||||
\(539\) | 32.2230 | 1.38794 | ||||||||
\(540\) | 11.2314 | 0.483324 | ||||||||
\(541\) | −36.3049 | −1.56087 | −0.780435 | − | 0.625237i | \(-0.785002\pi\) | ||||
−0.780435 | + | 0.625237i | \(0.785002\pi\) | |||||||
\(542\) | 6.40665 | 0.275189 | ||||||||
\(543\) | 7.21131 | 0.309467 | ||||||||
\(544\) | −4.17385 | −0.178952 | ||||||||
\(545\) | −25.5774 | −1.09562 | ||||||||
\(546\) | 0.129763 | 0.00555336 | ||||||||
\(547\) | 18.0281 | 0.770827 | 0.385414 | − | 0.922744i | \(-0.374059\pi\) | ||||
0.385414 | + | 0.922744i | \(0.374059\pi\) | |||||||
\(548\) | 13.2795 | 0.567273 | ||||||||
\(549\) | −13.7797 | −0.588103 | ||||||||
\(550\) | −2.17692 | −0.0928243 | ||||||||
\(551\) | 67.6564 | 2.88226 | ||||||||
\(552\) | 5.07015 | 0.215800 | ||||||||
\(553\) | 5.03453 | 0.214090 | ||||||||
\(554\) | −2.39718 | −0.101846 | ||||||||
\(555\) | 2.05825 | 0.0873677 | ||||||||
\(556\) | 16.0131 | 0.679107 | ||||||||
\(557\) | −21.5020 | −0.911068 | −0.455534 | − | 0.890218i | \(-0.650552\pi\) | ||||
−0.455534 | + | 0.890218i | \(0.650552\pi\) | |||||||
\(558\) | 1.21170 | 0.0512955 | ||||||||
\(559\) | −3.40828 | −0.144155 | ||||||||
\(560\) | 4.84163 | 0.204596 | ||||||||
\(561\) | −3.17667 | −0.134119 | ||||||||
\(562\) | −2.34573 | −0.0989485 | ||||||||
\(563\) | −38.8300 | −1.63649 | −0.818245 | − | 0.574869i | \(-0.805053\pi\) | ||||
−0.818245 | + | 0.574869i | \(0.805053\pi\) | |||||||
\(564\) | −3.59364 | −0.151320 | ||||||||
\(565\) | −19.2157 | −0.808413 | ||||||||
\(566\) | −2.02029 | −0.0849192 | ||||||||
\(567\) | 4.79916 | 0.201546 | ||||||||
\(568\) | −11.9216 | −0.500221 | ||||||||
\(569\) | 7.36197 | 0.308630 | 0.154315 | − | 0.988022i | \(-0.450683\pi\) | ||||
0.154315 | + | 0.988022i | \(0.450683\pi\) | |||||||
\(570\) | −2.35166 | −0.0985000 | ||||||||
\(571\) | 2.48519 | 0.104002 | 0.0520011 | − | 0.998647i | \(-0.483440\pi\) | ||||
0.0520011 | + | 0.998647i | \(0.483440\pi\) | |||||||
\(572\) | −9.49392 | −0.396961 | ||||||||
\(573\) | −13.9658 | −0.583430 | ||||||||
\(574\) | −1.57311 | −0.0656603 | ||||||||
\(575\) | −10.2041 | −0.425541 | ||||||||
\(576\) | 15.2926 | 0.637192 | ||||||||
\(577\) | −10.6722 | −0.444290 | −0.222145 | − | 0.975014i | \(-0.571306\pi\) | ||||
−0.222145 | + | 0.975014i | \(0.571306\pi\) | |||||||
\(578\) | 4.99366 | 0.207709 | ||||||||
\(579\) | −2.42874 | −0.100935 | ||||||||
\(580\) | −34.5012 | −1.43259 | ||||||||
\(581\) | 6.22384 | 0.258208 | ||||||||
\(582\) | −3.16263 | −0.131095 | ||||||||
\(583\) | 36.0881 | 1.49461 | ||||||||
\(584\) | 7.55644 | 0.312688 | ||||||||
\(585\) | 5.15714 | 0.213222 | ||||||||
\(586\) | 2.47280 | 0.102150 | ||||||||
\(587\) | −16.0543 | −0.662631 | −0.331315 | − | 0.943520i | \(-0.607492\pi\) | ||||
−0.331315 | + | 0.943520i | \(0.607492\pi\) | |||||||
\(588\) | 6.65094 | 0.274280 | ||||||||
\(589\) | 9.96007 | 0.410398 | ||||||||
\(590\) | 1.51305 | 0.0622914 | ||||||||
\(591\) | 1.72635 | 0.0710124 | ||||||||
\(592\) | 6.74274 | 0.277125 | ||||||||
\(593\) | −14.8533 | −0.609951 | −0.304975 | − | 0.952360i | \(-0.598648\pi\) | ||||
−0.304975 | + | 0.952360i | \(0.598648\pi\) | |||||||
\(594\) | −4.95639 | −0.203363 | ||||||||
\(595\) | 1.66329 | 0.0681883 | ||||||||
\(596\) | −39.9265 | −1.63545 | ||||||||
\(597\) | −6.72072 | −0.275061 | ||||||||
\(598\) | 2.39119 | 0.0977830 | ||||||||
\(599\) | 48.3271 | 1.97459 | 0.987295 | − | 0.158896i | \(-0.0507933\pi\) | ||||
0.987295 | + | 0.158896i | \(0.0507933\pi\) | |||||||
\(600\) | −0.922792 | −0.0376728 | ||||||||
\(601\) | 33.1880 | 1.35377 | 0.676883 | − | 0.736091i | \(-0.263330\pi\) | ||||
0.676883 | + | 0.736091i | \(0.263330\pi\) | |||||||
\(602\) | −0.813063 | −0.0331380 | ||||||||
\(603\) | −12.5815 | −0.512359 | ||||||||
\(604\) | 45.4506 | 1.84936 | ||||||||
\(605\) | 26.7387 | 1.08708 | ||||||||
\(606\) | −2.32806 | −0.0945710 | ||||||||
\(607\) | −8.44558 | −0.342795 | −0.171398 | − | 0.985202i | \(-0.554828\pi\) | ||||
−0.171398 | + | 0.985202i | \(0.554828\pi\) | |||||||
\(608\) | −25.3765 | −1.02915 | ||||||||
\(609\) | 3.87289 | 0.156937 | ||||||||
\(610\) | −3.10361 | −0.125662 | ||||||||
\(611\) | −3.48074 | −0.140816 | ||||||||
\(612\) | 5.99222 | 0.242221 | ||||||||
\(613\) | 48.1195 | 1.94353 | 0.971765 | − | 0.235952i | \(-0.0758207\pi\) | ||||
0.971765 | + | 0.235952i | \(0.0758207\pi\) | |||||||
\(614\) | 5.04509 | 0.203603 | ||||||||
\(615\) | 6.84096 | 0.275854 | ||||||||
\(616\) | −4.65135 | −0.187408 | ||||||||
\(617\) | 21.5134 | 0.866096 | 0.433048 | − | 0.901371i | \(-0.357438\pi\) | ||||
0.433048 | + | 0.901371i | \(0.357438\pi\) | |||||||
\(618\) | −0.173713 | −0.00698774 | ||||||||
\(619\) | 40.3711 | 1.62265 | 0.811327 | − | 0.584593i | \(-0.198746\pi\) | ||||
0.811327 | + | 0.584593i | \(0.198746\pi\) | |||||||
\(620\) | −5.07911 | −0.203982 | ||||||||
\(621\) | −23.2326 | −0.932290 | ||||||||
\(622\) | −6.90720 | −0.276954 | ||||||||
\(623\) | 5.78806 | 0.231894 | ||||||||
\(624\) | −1.84863 | −0.0740043 | ||||||||
\(625\) | −16.3288 | −0.653154 | ||||||||
\(626\) | 10.2425 | 0.409371 | ||||||||
\(627\) | −19.3138 | −0.771318 | ||||||||
\(628\) | 16.1855 | 0.645871 | ||||||||
\(629\) | 2.31640 | 0.0923608 | ||||||||
\(630\) | 1.23026 | 0.0490149 | ||||||||
\(631\) | −22.2476 | −0.885662 | −0.442831 | − | 0.896605i | \(-0.646026\pi\) | ||||
−0.442831 | + | 0.896605i | \(0.646026\pi\) | |||||||
\(632\) | 8.38976 | 0.333727 | ||||||||
\(633\) | 4.26685 | 0.169592 | ||||||||
\(634\) | −1.29352 | −0.0513723 | ||||||||
\(635\) | 18.7450 | 0.743874 | ||||||||
\(636\) | 7.44870 | 0.295360 | ||||||||
\(637\) | 6.44199 | 0.255241 | ||||||||
\(638\) | 15.2253 | 0.602774 | ||||||||
\(639\) | 25.8970 | 1.02447 | ||||||||
\(640\) | 17.0804 | 0.675161 | ||||||||
\(641\) | 12.9709 | 0.512319 | 0.256159 | − | 0.966635i | \(-0.417543\pi\) | ||||
0.256159 | + | 0.966635i | \(0.417543\pi\) | |||||||
\(642\) | −1.61728 | −0.0638289 | ||||||||
\(643\) | −21.8703 | −0.862480 | −0.431240 | − | 0.902237i | \(-0.641924\pi\) | ||||
−0.431240 | + | 0.902237i | \(0.641924\pi\) | |||||||
\(644\) | −10.6161 | −0.418334 | ||||||||
\(645\) | 3.53576 | 0.139220 | ||||||||
\(646\) | −2.64661 | −0.104129 | ||||||||
\(647\) | 5.94199 | 0.233604 | 0.116802 | − | 0.993155i | \(-0.462736\pi\) | ||||
0.116802 | + | 0.993155i | \(0.462736\pi\) | |||||||
\(648\) | 7.99752 | 0.314172 | ||||||||
\(649\) | 12.4265 | 0.487781 | ||||||||
\(650\) | −0.435208 | −0.0170703 | ||||||||
\(651\) | 0.570149 | 0.0223459 | ||||||||
\(652\) | −10.1318 | −0.396792 | ||||||||
\(653\) | 42.6004 | 1.66708 | 0.833542 | − | 0.552456i | \(-0.186309\pi\) | ||||
0.833542 | + | 0.552456i | \(0.186309\pi\) | |||||||
\(654\) | 2.32972 | 0.0910992 | ||||||||
\(655\) | −33.3584 | −1.30342 | ||||||||
\(656\) | 22.4107 | 0.874992 | ||||||||
\(657\) | −16.4146 | −0.640395 | ||||||||
\(658\) | −0.830350 | −0.0323704 | ||||||||
\(659\) | −7.48154 | −0.291440 | −0.145720 | − | 0.989326i | \(-0.546550\pi\) | ||||
−0.145720 | + | 0.989326i | \(0.546550\pi\) | |||||||
\(660\) | 9.84901 | 0.383372 | ||||||||
\(661\) | −41.1078 | −1.59891 | −0.799454 | − | 0.600728i | \(-0.794878\pi\) | ||||
−0.799454 | + | 0.600728i | \(0.794878\pi\) | |||||||
\(662\) | 2.97654 | 0.115687 | ||||||||
\(663\) | −0.635076 | −0.0246643 | ||||||||
\(664\) | 10.3717 | 0.402499 | ||||||||
\(665\) | 10.1126 | 0.392151 | ||||||||
\(666\) | 1.71334 | 0.0663905 | ||||||||
\(667\) | 71.3668 | 2.76333 | ||||||||
\(668\) | −42.9673 | −1.66245 | ||||||||
\(669\) | −14.3193 | −0.553617 | ||||||||
\(670\) | −2.83374 | −0.109477 | ||||||||
\(671\) | −25.4895 | −0.984010 | ||||||||
\(672\) | −1.45264 | −0.0560368 | ||||||||
\(673\) | −19.5257 | −0.752661 | −0.376330 | − | 0.926486i | \(-0.622814\pi\) | ||||
−0.376330 | + | 0.926486i | \(0.622814\pi\) | |||||||
\(674\) | −8.04532 | −0.309894 | ||||||||
\(675\) | 4.22844 | 0.162753 | ||||||||
\(676\) | −1.89802 | −0.0730006 | ||||||||
\(677\) | −46.3473 | −1.78127 | −0.890637 | − | 0.454716i | \(-0.849741\pi\) | ||||
−0.890637 | + | 0.454716i | \(0.849741\pi\) | |||||||
\(678\) | 1.75027 | 0.0672186 | ||||||||
\(679\) | 13.6000 | 0.521920 | ||||||||
\(680\) | 2.77178 | 0.106293 | ||||||||
\(681\) | −3.88567 | −0.148899 | ||||||||
\(682\) | 2.24139 | 0.0858273 | ||||||||
\(683\) | −43.5551 | −1.66659 | −0.833294 | − | 0.552830i | \(-0.813548\pi\) | ||||
−0.833294 | + | 0.552830i | \(0.813548\pi\) | |||||||
\(684\) | 36.4320 | 1.39301 | ||||||||
\(685\) | −13.3434 | −0.509826 | ||||||||
\(686\) | 3.20666 | 0.122431 | ||||||||
\(687\) | 6.58482 | 0.251226 | ||||||||
\(688\) | 11.5830 | 0.441598 | ||||||||
\(689\) | 7.21469 | 0.274858 | ||||||||
\(690\) | −2.48062 | −0.0944358 | ||||||||
\(691\) | −3.62194 | −0.137785 | −0.0688925 | − | 0.997624i | \(-0.521947\pi\) | ||||
−0.0688925 | + | 0.997624i | \(0.521947\pi\) | |||||||
\(692\) | 25.3086 | 0.962090 | ||||||||
\(693\) | 10.1040 | 0.383818 | ||||||||
\(694\) | −7.12711 | −0.270542 | ||||||||
\(695\) | −16.0902 | −0.610335 | ||||||||
\(696\) | 6.45394 | 0.244636 | ||||||||
\(697\) | 7.69897 | 0.291619 | ||||||||
\(698\) | 7.39840 | 0.280034 | ||||||||
\(699\) | 14.2646 | 0.539536 | ||||||||
\(700\) | 1.93219 | 0.0730299 | ||||||||
\(701\) | 36.5004 | 1.37860 | 0.689301 | − | 0.724475i | \(-0.257918\pi\) | ||||
0.689301 | + | 0.724475i | \(0.257918\pi\) | |||||||
\(702\) | −0.990876 | −0.0373982 | ||||||||
\(703\) | 14.0834 | 0.531167 | ||||||||
\(704\) | 28.2880 | 1.06614 | ||||||||
\(705\) | 3.61093 | 0.135996 | ||||||||
\(706\) | 5.46719 | 0.205761 | ||||||||
\(707\) | 10.0112 | 0.376508 | ||||||||
\(708\) | 2.56486 | 0.0963935 | ||||||||
\(709\) | −32.2809 | −1.21233 | −0.606167 | − | 0.795337i | \(-0.707294\pi\) | ||||
−0.606167 | + | 0.795337i | \(0.707294\pi\) | |||||||
\(710\) | 5.83280 | 0.218901 | ||||||||
\(711\) | −18.2248 | −0.683484 | ||||||||
\(712\) | 9.64547 | 0.361479 | ||||||||
\(713\) | 10.5063 | 0.393464 | ||||||||
\(714\) | −0.151501 | −0.00566978 | ||||||||
\(715\) | 9.53960 | 0.356761 | ||||||||
\(716\) | 30.9731 | 1.15752 | ||||||||
\(717\) | 2.27567 | 0.0849866 | ||||||||
\(718\) | 3.56741 | 0.133135 | ||||||||
\(719\) | 17.1827 | 0.640805 | 0.320402 | − | 0.947282i | \(-0.396182\pi\) | ||||
0.320402 | + | 0.947282i | \(0.396182\pi\) | |||||||
\(720\) | −17.5265 | −0.653174 | ||||||||
\(721\) | 0.747001 | 0.0278198 | ||||||||
\(722\) | −10.0234 | −0.373033 | ||||||||
\(723\) | 6.12970 | 0.227966 | ||||||||
\(724\) | −25.1623 | −0.935151 | ||||||||
\(725\) | −12.9891 | −0.482404 | ||||||||
\(726\) | −2.43549 | −0.0903897 | ||||||||
\(727\) | 14.4272 | 0.535077 | 0.267538 | − | 0.963547i | \(-0.413790\pi\) | ||||
0.267538 | + | 0.963547i | \(0.413790\pi\) | |||||||
\(728\) | −0.929892 | −0.0344641 | ||||||||
\(729\) | −12.3094 | −0.455905 | ||||||||
\(730\) | −3.69707 | −0.136835 | ||||||||
\(731\) | 3.97922 | 0.147177 | ||||||||
\(732\) | −5.26111 | −0.194456 | ||||||||
\(733\) | 15.9346 | 0.588557 | 0.294279 | − | 0.955720i | \(-0.404921\pi\) | ||||
0.294279 | + | 0.955720i | \(0.404921\pi\) | |||||||
\(734\) | −0.00751583 | −0.000277414 0 | ||||||||
\(735\) | −6.68293 | −0.246504 | ||||||||
\(736\) | −26.7682 | −0.986689 | ||||||||
\(737\) | −23.2731 | −0.857275 | ||||||||
\(738\) | 5.69459 | 0.209621 | ||||||||
\(739\) | −5.42576 | −0.199590 | −0.0997949 | − | 0.995008i | \(-0.531819\pi\) | ||||
−0.0997949 | + | 0.995008i | \(0.531819\pi\) | |||||||
\(740\) | −7.18181 | −0.264009 | ||||||||
\(741\) | −3.86119 | −0.141844 | ||||||||
\(742\) | 1.72110 | 0.0631837 | ||||||||
\(743\) | 18.5966 | 0.682244 | 0.341122 | − | 0.940019i | \(-0.389193\pi\) | ||||
0.341122 | + | 0.940019i | \(0.389193\pi\) | |||||||
\(744\) | 0.950120 | 0.0348331 | ||||||||
\(745\) | 40.1186 | 1.46983 | ||||||||
\(746\) | −8.42511 | −0.308465 | ||||||||
\(747\) | −22.5300 | −0.824331 | ||||||||
\(748\) | 11.0843 | 0.405282 | ||||||||
\(749\) | 6.95464 | 0.254117 | ||||||||
\(750\) | 2.10796 | 0.0769719 | ||||||||
\(751\) | −7.63447 | −0.278586 | −0.139293 | − | 0.990251i | \(-0.544483\pi\) | ||||
−0.139293 | + | 0.990251i | \(0.544483\pi\) | |||||||
\(752\) | 11.8293 | 0.431369 | ||||||||
\(753\) | −1.56284 | −0.0569532 | ||||||||
\(754\) | 3.04382 | 0.110849 | ||||||||
\(755\) | −45.6693 | −1.66207 | ||||||||
\(756\) | 4.39918 | 0.159997 | ||||||||
\(757\) | 42.8378 | 1.55696 | 0.778482 | − | 0.627666i | \(-0.215990\pi\) | ||||
0.778482 | + | 0.627666i | \(0.215990\pi\) | |||||||
\(758\) | −0.279435 | −0.0101495 | ||||||||
\(759\) | −20.3730 | −0.739493 | ||||||||
\(760\) | 16.8521 | 0.611290 | ||||||||
\(761\) | 49.6007 | 1.79802 | 0.899012 | − | 0.437923i | \(-0.144286\pi\) | ||||
0.899012 | + | 0.437923i | \(0.144286\pi\) | |||||||
\(762\) | −1.70739 | −0.0618523 | ||||||||
\(763\) | −10.0183 | −0.362686 | ||||||||
\(764\) | 48.7307 | 1.76301 | ||||||||
\(765\) | −6.02105 | −0.217691 | ||||||||
\(766\) | 3.12157 | 0.112787 | ||||||||
\(767\) | 2.48429 | 0.0897024 | ||||||||
\(768\) | 4.59670 | 0.165869 | ||||||||
\(769\) | 6.96341 | 0.251107 | 0.125554 | − | 0.992087i | \(-0.459929\pi\) | ||||
0.125554 | + | 0.992087i | \(0.459929\pi\) | |||||||
\(770\) | 2.27572 | 0.0820113 | ||||||||
\(771\) | 16.2543 | 0.585384 | ||||||||
\(772\) | 8.47457 | 0.305006 | ||||||||
\(773\) | −13.3052 | −0.478556 | −0.239278 | − | 0.970951i | \(-0.576911\pi\) | ||||
−0.239278 | + | 0.970951i | \(0.576911\pi\) | |||||||
\(774\) | 2.94325 | 0.105793 | ||||||||
\(775\) | −1.91220 | −0.0686882 | ||||||||
\(776\) | 22.6636 | 0.813577 | ||||||||
\(777\) | 0.806184 | 0.0289217 | ||||||||
\(778\) | −3.27188 | −0.117302 | ||||||||
\(779\) | 46.8089 | 1.67710 | ||||||||
\(780\) | 1.96901 | 0.0705017 | ||||||||
\(781\) | 47.9039 | 1.71413 | ||||||||
\(782\) | −2.79175 | −0.0998329 | ||||||||
\(783\) | −29.5734 | −1.05687 | ||||||||
\(784\) | −21.8930 | −0.781894 | ||||||||
\(785\) | −16.2633 | −0.580464 | ||||||||
\(786\) | 3.03845 | 0.108378 | ||||||||
\(787\) | 9.08945 | 0.324004 | 0.162002 | − | 0.986790i | \(-0.448205\pi\) | ||||
0.162002 | + | 0.986790i | \(0.448205\pi\) | |||||||
\(788\) | −6.02372 | −0.214586 | ||||||||
\(789\) | 2.14249 | 0.0762747 | ||||||||
\(790\) | −4.10478 | −0.146042 | ||||||||
\(791\) | −7.52652 | −0.267612 | ||||||||
\(792\) | 16.8377 | 0.598301 | ||||||||
\(793\) | −5.09583 | −0.180958 | ||||||||
\(794\) | 5.95794 | 0.211439 | ||||||||
\(795\) | −7.48454 | −0.265449 | ||||||||
\(796\) | 23.4505 | 0.831181 | ||||||||
\(797\) | 45.0513 | 1.59580 | 0.797899 | − | 0.602791i | \(-0.205945\pi\) | ||||
0.797899 | + | 0.602791i | \(0.205945\pi\) | |||||||
\(798\) | −0.921108 | −0.0326069 | ||||||||
\(799\) | 4.06382 | 0.143768 | ||||||||
\(800\) | 4.87195 | 0.172249 | ||||||||
\(801\) | −20.9525 | −0.740322 | ||||||||
\(802\) | −2.24014 | −0.0791019 | ||||||||
\(803\) | −30.3635 | −1.07150 | ||||||||
\(804\) | −4.80364 | −0.169411 | ||||||||
\(805\) | 10.6672 | 0.375970 | ||||||||
\(806\) | 0.448097 | 0.0157835 | ||||||||
\(807\) | −11.1445 | −0.392305 | ||||||||
\(808\) | 16.6830 | 0.586907 | ||||||||
\(809\) | −11.8663 | −0.417195 | −0.208598 | − | 0.978002i | \(-0.566890\pi\) | ||||
−0.208598 | + | 0.978002i | \(0.566890\pi\) | |||||||
\(810\) | −3.91287 | −0.137484 | ||||||||
\(811\) | −38.2969 | −1.34479 | −0.672393 | − | 0.740194i | \(-0.734733\pi\) | ||||
−0.672393 | + | 0.740194i | \(0.734733\pi\) | |||||||
\(812\) | −13.5136 | −0.474235 | ||||||||
\(813\) | −10.9125 | −0.382719 | ||||||||
\(814\) | 3.16931 | 0.111084 | ||||||||
\(815\) | 10.1805 | 0.356609 | ||||||||
\(816\) | 2.15830 | 0.0755557 | ||||||||
\(817\) | 24.1932 | 0.846413 | ||||||||
\(818\) | 1.49835 | 0.0523886 | ||||||||
\(819\) | 2.01997 | 0.0705836 | ||||||||
\(820\) | −23.8701 | −0.833579 | ||||||||
\(821\) | −29.3229 | −1.02338 | −0.511688 | − | 0.859171i | \(-0.670980\pi\) | ||||
−0.511688 | + | 0.859171i | \(0.670980\pi\) | |||||||
\(822\) | 1.21539 | 0.0423914 | ||||||||
\(823\) | −0.179741 | −0.00626537 | −0.00313268 | − | 0.999995i | \(-0.500997\pi\) | ||||
−0.00313268 | + | 0.999995i | \(0.500997\pi\) | |||||||
\(824\) | 1.24483 | 0.0433659 | ||||||||
\(825\) | 3.70799 | 0.129095 | ||||||||
\(826\) | 0.592640 | 0.0206206 | ||||||||
\(827\) | 30.5393 | 1.06195 | 0.530977 | − | 0.847386i | \(-0.321825\pi\) | ||||
0.530977 | + | 0.847386i | \(0.321825\pi\) | |||||||
\(828\) | 38.4300 | 1.33553 | ||||||||
\(829\) | 18.0756 | 0.627793 | 0.313896 | − | 0.949457i | \(-0.398366\pi\) | ||||
0.313896 | + | 0.949457i | \(0.398366\pi\) | |||||||
\(830\) | −5.07445 | −0.176137 | ||||||||
\(831\) | 4.08315 | 0.141643 | ||||||||
\(832\) | 5.65531 | 0.196063 | ||||||||
\(833\) | −7.52113 | −0.260592 | ||||||||
\(834\) | 1.46557 | 0.0507486 | ||||||||
\(835\) | 43.1740 | 1.49410 | ||||||||
\(836\) | 67.3913 | 2.33078 | ||||||||
\(837\) | −4.35367 | −0.150485 | ||||||||
\(838\) | −10.7690 | −0.372008 | ||||||||
\(839\) | 19.7779 | 0.682810 | 0.341405 | − | 0.939916i | \(-0.389097\pi\) | ||||
0.341405 | + | 0.939916i | \(0.389097\pi\) | |||||||
\(840\) | 0.964672 | 0.0332844 | ||||||||
\(841\) | 61.8450 | 2.13259 | ||||||||
\(842\) | −4.92502 | −0.169728 | ||||||||
\(843\) | 3.99551 | 0.137613 | ||||||||
\(844\) | −14.8882 | −0.512475 | ||||||||
\(845\) | 1.90715 | 0.0656078 | ||||||||
\(846\) | 3.00583 | 0.103343 | ||||||||
\(847\) | 10.4731 | 0.359862 | ||||||||
\(848\) | −24.5191 | −0.841988 | ||||||||
\(849\) | 3.44119 | 0.118101 | ||||||||
\(850\) | 0.508113 | 0.0174281 | ||||||||
\(851\) | 14.8558 | 0.509250 | ||||||||
\(852\) | 9.88752 | 0.338741 | ||||||||
\(853\) | 44.8503 | 1.53564 | 0.767822 | − | 0.640663i | \(-0.221340\pi\) | ||||
0.767822 | + | 0.640663i | \(0.221340\pi\) | |||||||
\(854\) | −1.21564 | −0.0415983 | ||||||||
\(855\) | −36.6073 | −1.25194 | ||||||||
\(856\) | 11.5895 | 0.396122 | ||||||||
\(857\) | −7.66715 | −0.261905 | −0.130952 | − | 0.991389i | \(-0.541804\pi\) | ||||
−0.130952 | + | 0.991389i | \(0.541804\pi\) | |||||||
\(858\) | −0.868914 | −0.0296642 | ||||||||
\(859\) | 38.5056 | 1.31379 | 0.656897 | − | 0.753980i | \(-0.271868\pi\) | ||||
0.656897 | + | 0.753980i | \(0.271868\pi\) | |||||||
\(860\) | −12.3373 | −0.420697 | ||||||||
\(861\) | 2.67950 | 0.0913172 | ||||||||
\(862\) | −8.10512 | −0.276061 | ||||||||
\(863\) | −17.2767 | −0.588107 | −0.294053 | − | 0.955789i | \(-0.595004\pi\) | ||||
−0.294053 | + | 0.955789i | \(0.595004\pi\) | |||||||
\(864\) | 11.0924 | 0.377370 | ||||||||
\(865\) | −25.4304 | −0.864660 | ||||||||
\(866\) | 12.8609 | 0.437032 | ||||||||
\(867\) | −8.50577 | −0.288871 | ||||||||
\(868\) | −1.98941 | −0.0675250 | ||||||||
\(869\) | −33.7120 | −1.14360 | ||||||||
\(870\) | −3.15766 | −0.107055 | ||||||||
\(871\) | −4.65273 | −0.157652 | ||||||||
\(872\) | −16.6949 | −0.565361 | ||||||||
\(873\) | −49.2315 | −1.66623 | ||||||||
\(874\) | −16.9735 | −0.574139 | ||||||||
\(875\) | −9.06469 | −0.306442 | ||||||||
\(876\) | −6.26713 | −0.211747 | ||||||||
\(877\) | −4.40930 | −0.148891 | −0.0744457 | − | 0.997225i | \(-0.523719\pi\) | ||||
−0.0744457 | + | 0.997225i | \(0.523719\pi\) | |||||||
\(878\) | 7.17024 | 0.241984 | ||||||||
\(879\) | −4.21196 | −0.142066 | ||||||||
\(880\) | −32.4202 | −1.09289 | ||||||||
\(881\) | −4.40500 | −0.148408 | −0.0742042 | − | 0.997243i | \(-0.523642\pi\) | ||||
−0.0742042 | + | 0.997243i | \(0.523642\pi\) | |||||||
\(882\) | −5.56305 | −0.187318 | ||||||||
\(883\) | −36.2644 | −1.22040 | −0.610198 | − | 0.792249i | \(-0.708910\pi\) | ||||
−0.610198 | + | 0.792249i | \(0.708910\pi\) | |||||||
\(884\) | 2.21596 | 0.0745309 | ||||||||
\(885\) | −2.57720 | −0.0866318 | ||||||||
\(886\) | 2.26209 | 0.0759965 | ||||||||
\(887\) | 11.6953 | 0.392690 | 0.196345 | − | 0.980535i | \(-0.437093\pi\) | ||||
0.196345 | + | 0.980535i | \(0.437093\pi\) | |||||||
\(888\) | 1.34346 | 0.0450836 | ||||||||
\(889\) | 7.34215 | 0.246248 | ||||||||
\(890\) | −4.71915 | −0.158186 | ||||||||
\(891\) | −32.1358 | −1.07659 | ||||||||
\(892\) | 49.9642 | 1.67292 | ||||||||
\(893\) | 24.7076 | 0.826808 | ||||||||
\(894\) | −3.65420 | −0.122215 | ||||||||
\(895\) | −31.1221 | −1.04030 | ||||||||
\(896\) | 6.69013 | 0.223502 | ||||||||
\(897\) | −4.07295 | −0.135992 | ||||||||
\(898\) | −10.0321 | −0.334776 | ||||||||
\(899\) | 13.3738 | 0.446041 | ||||||||
\(900\) | −6.99445 | −0.233148 | ||||||||
\(901\) | −8.42327 | −0.280620 | ||||||||
\(902\) | 10.5338 | 0.350736 | ||||||||
\(903\) | 1.38490 | 0.0460867 | ||||||||
\(904\) | −12.5425 | −0.417158 | ||||||||
\(905\) | 25.2834 | 0.840449 | ||||||||
\(906\) | 4.15979 | 0.138200 | ||||||||
\(907\) | −33.5281 | −1.11328 | −0.556640 | − | 0.830754i | \(-0.687910\pi\) | ||||
−0.556640 | + | 0.830754i | \(0.687910\pi\) | |||||||
\(908\) | 13.5582 | 0.449945 | ||||||||
\(909\) | −36.2400 | −1.20200 | ||||||||
\(910\) | 0.454960 | 0.0150818 | ||||||||
\(911\) | 14.5031 | 0.480508 | 0.240254 | − | 0.970710i | \(-0.422769\pi\) | ||||
0.240254 | + | 0.970710i | \(0.422769\pi\) | |||||||
\(912\) | 13.1222 | 0.434521 | ||||||||
\(913\) | −41.6757 | −1.37926 | ||||||||
\(914\) | −2.34648 | −0.0776148 | ||||||||
\(915\) | 5.28643 | 0.174764 | ||||||||
\(916\) | −22.9763 | −0.759159 | ||||||||
\(917\) | −13.0660 | −0.431477 | ||||||||
\(918\) | 1.15686 | 0.0381822 | ||||||||
\(919\) | −29.3644 | −0.968643 | −0.484321 | − | 0.874890i | \(-0.660933\pi\) | ||||
−0.484321 | + | 0.874890i | \(0.660933\pi\) | |||||||
\(920\) | 17.7763 | 0.586067 | ||||||||
\(921\) | −8.59338 | −0.283161 | ||||||||
\(922\) | −0.699087 | −0.0230232 | ||||||||
\(923\) | 9.57689 | 0.315227 | ||||||||
\(924\) | 3.85771 | 0.126909 | ||||||||
\(925\) | −2.70383 | −0.0889014 | ||||||||
\(926\) | 12.1343 | 0.398757 | ||||||||
\(927\) | −2.70411 | −0.0888147 | ||||||||
\(928\) | −34.0741 | −1.11854 | ||||||||
\(929\) | 10.1422 | 0.332754 | 0.166377 | − | 0.986062i | \(-0.446793\pi\) | ||||
0.166377 | + | 0.986062i | \(0.446793\pi\) | |||||||
\(930\) | −0.464857 | −0.0152433 | ||||||||
\(931\) | −45.7276 | −1.49866 | ||||||||
\(932\) | −49.7732 | −1.63037 | ||||||||
\(933\) | 11.7651 | 0.385174 | ||||||||
\(934\) | −9.80712 | −0.320899 | ||||||||
\(935\) | −11.1376 | −0.364240 | ||||||||
\(936\) | 3.36617 | 0.110027 | ||||||||
\(937\) | 8.23442 | 0.269007 | 0.134503 | − | 0.990913i | \(-0.457056\pi\) | ||||
0.134503 | + | 0.990913i | \(0.457056\pi\) | |||||||
\(938\) | −1.10993 | −0.0362406 | ||||||||
\(939\) | −17.4461 | −0.569334 | ||||||||
\(940\) | −12.5996 | −0.410953 | ||||||||
\(941\) | 8.86676 | 0.289048 | 0.144524 | − | 0.989501i | \(-0.453835\pi\) | ||||
0.144524 | + | 0.989501i | \(0.453835\pi\) | |||||||
\(942\) | 1.48135 | 0.0482649 | ||||||||
\(943\) | 49.3760 | 1.60790 | ||||||||
\(944\) | −8.44283 | −0.274791 | ||||||||
\(945\) | −4.42035 | −0.143794 | ||||||||
\(946\) | 5.44439 | 0.177012 | ||||||||
\(947\) | 26.0802 | 0.847492 | 0.423746 | − | 0.905781i | \(-0.360715\pi\) | ||||
0.423746 | + | 0.905781i | \(0.360715\pi\) | |||||||
\(948\) | −6.95826 | −0.225994 | ||||||||
\(949\) | −6.07024 | −0.197048 | ||||||||
\(950\) | 3.08927 | 0.100229 | ||||||||
\(951\) | 2.20327 | 0.0714461 | ||||||||
\(952\) | 1.08566 | 0.0351866 | ||||||||
\(953\) | 21.2634 | 0.688790 | 0.344395 | − | 0.938825i | \(-0.388084\pi\) | ||||
0.344395 | + | 0.938825i | \(0.388084\pi\) | |||||||
\(954\) | −6.23032 | −0.201714 | ||||||||
\(955\) | −48.9652 | −1.58448 | ||||||||
\(956\) | −7.94048 | −0.256814 | ||||||||
\(957\) | −25.9334 | −0.838308 | ||||||||
\(958\) | 4.60703 | 0.148846 | ||||||||
\(959\) | −5.22642 | −0.168770 | ||||||||
\(960\) | −5.86683 | −0.189351 | ||||||||
\(961\) | −29.0312 | −0.936489 | ||||||||
\(962\) | 0.633604 | 0.0204282 | ||||||||
\(963\) | −25.1755 | −0.811270 | ||||||||
\(964\) | −21.3883 | −0.688870 | ||||||||
\(965\) | −8.51534 | −0.274119 | ||||||||
\(966\) | −0.971624 | −0.0312615 | ||||||||
\(967\) | −54.8315 | −1.76326 | −0.881630 | − | 0.471940i | \(-0.843554\pi\) | ||||
−0.881630 | + | 0.471940i | \(0.843554\pi\) | |||||||
\(968\) | 17.4529 | 0.560957 | ||||||||
\(969\) | 4.50801 | 0.144818 | ||||||||
\(970\) | −11.0884 | −0.356028 | ||||||||
\(971\) | −15.4388 | −0.495455 | −0.247728 | − | 0.968830i | \(-0.579684\pi\) | ||||
−0.247728 | + | 0.968830i | \(0.579684\pi\) | |||||||
\(972\) | −24.3003 | −0.779433 | ||||||||
\(973\) | −6.30227 | −0.202042 | ||||||||
\(974\) | 6.81286 | 0.218298 | ||||||||
\(975\) | 0.741297 | 0.0237405 | ||||||||
\(976\) | 17.3181 | 0.554340 | ||||||||
\(977\) | −4.41071 | −0.141111 | −0.0705556 | − | 0.997508i | \(-0.522477\pi\) | ||||
−0.0705556 | + | 0.997508i | \(0.522477\pi\) | |||||||
\(978\) | −0.927295 | −0.0296516 | ||||||||
\(979\) | −38.7577 | −1.23870 | ||||||||
\(980\) | 23.3187 | 0.744888 | ||||||||
\(981\) | 36.2658 | 1.15788 | ||||||||
\(982\) | 4.89044 | 0.156060 | ||||||||
\(983\) | −10.7221 | −0.341982 | −0.170991 | − | 0.985273i | \(-0.554697\pi\) | ||||
−0.170991 | + | 0.985273i | \(0.554697\pi\) | |||||||
\(984\) | 4.46524 | 0.142347 | ||||||||
\(985\) | 6.05270 | 0.192855 | ||||||||
\(986\) | −3.55371 | −0.113173 | ||||||||
\(987\) | 1.41435 | 0.0450192 | ||||||||
\(988\) | 13.4728 | 0.428627 | ||||||||
\(989\) | 25.5200 | 0.811489 | ||||||||
\(990\) | −8.23802 | −0.261821 | ||||||||
\(991\) | 43.0013 | 1.36598 | 0.682990 | − | 0.730428i | \(-0.260679\pi\) | ||||
0.682990 | + | 0.730428i | \(0.260679\pi\) | |||||||
\(992\) | −5.01623 | −0.159265 | ||||||||
\(993\) | −5.06999 | −0.160891 | ||||||||
\(994\) | 2.28462 | 0.0724637 | ||||||||
\(995\) | −23.5633 | −0.747008 | ||||||||
\(996\) | −8.60201 | −0.272565 | ||||||||
\(997\) | 52.0277 | 1.64773 | 0.823867 | − | 0.566784i | \(-0.191812\pi\) | ||||
0.823867 | + | 0.566784i | \(0.191812\pi\) | |||||||
\(998\) | 11.0761 | 0.350607 | ||||||||
\(999\) | −6.15604 | −0.194768 |
(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 | 1339.2.a.g.1.15 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1339.2.a.g.1.15 | ✓ | 30 | 1.1 | even | 1 | trivial |