Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8011,2,Mod(1,8011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8011, 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("8011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8011.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: | \(63.9681570592\) |
Analytic rank: | \(0\) |
Dimension: | \(358\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57524 | −1.82097 | −0.910484 | − | 0.413544i | \(-0.864291\pi\) | ||||
−0.910484 | + | 0.413544i | \(0.864291\pi\) | |||||||
\(3\) | 0.178143 | 0.102851 | 0.0514254 | − | 0.998677i | \(-0.483624\pi\) | ||||
0.0514254 | + | 0.998677i | \(0.483624\pi\) | |||||||
\(4\) | 4.63185 | 2.31593 | ||||||||
\(5\) | −1.43369 | −0.641165 | −0.320583 | − | 0.947221i | \(-0.603879\pi\) | ||||
−0.320583 | + | 0.947221i | \(0.603879\pi\) | |||||||
\(6\) | −0.458760 | −0.187288 | ||||||||
\(7\) | 4.00928 | 1.51537 | 0.757683 | − | 0.652623i | \(-0.226331\pi\) | ||||
0.757683 | + | 0.652623i | \(0.226331\pi\) | |||||||
\(8\) | −6.77765 | −2.39626 | ||||||||
\(9\) | −2.96827 | −0.989422 | ||||||||
\(10\) | 3.69209 | 1.16754 | ||||||||
\(11\) | 3.24857 | 0.979481 | 0.489740 | − | 0.871868i | \(-0.337092\pi\) | ||||
0.489740 | + | 0.871868i | \(0.337092\pi\) | |||||||
\(12\) | 0.825131 | 0.238195 | ||||||||
\(13\) | 0.109242 | 0.0302984 | 0.0151492 | − | 0.999885i | \(-0.495178\pi\) | ||||
0.0151492 | + | 0.999885i | \(0.495178\pi\) | |||||||
\(14\) | −10.3249 | −2.75943 | ||||||||
\(15\) | −0.255401 | −0.0659443 | ||||||||
\(16\) | 8.19036 | 2.04759 | ||||||||
\(17\) | 4.02676 | 0.976633 | 0.488317 | − | 0.872667i | \(-0.337611\pi\) | ||||
0.488317 | + | 0.872667i | \(0.337611\pi\) | |||||||
\(18\) | 7.64399 | 1.80171 | ||||||||
\(19\) | 0.800935 | 0.183747 | 0.0918735 | − | 0.995771i | \(-0.470714\pi\) | ||||
0.0918735 | + | 0.995771i | \(0.470714\pi\) | |||||||
\(20\) | −6.64064 | −1.48489 | ||||||||
\(21\) | 0.714224 | 0.155856 | ||||||||
\(22\) | −8.36584 | −1.78360 | ||||||||
\(23\) | 2.16360 | 0.451143 | 0.225571 | − | 0.974227i | \(-0.427575\pi\) | ||||
0.225571 | + | 0.974227i | \(0.427575\pi\) | |||||||
\(24\) | −1.20739 | −0.246457 | ||||||||
\(25\) | −2.94453 | −0.588907 | ||||||||
\(26\) | −0.281325 | −0.0551724 | ||||||||
\(27\) | −1.06320 | −0.204613 | ||||||||
\(28\) | 18.5704 | 3.50948 | ||||||||
\(29\) | 1.12086 | 0.208139 | 0.104069 | − | 0.994570i | \(-0.466814\pi\) | ||||
0.104069 | + | 0.994570i | \(0.466814\pi\) | |||||||
\(30\) | 0.657719 | 0.120083 | ||||||||
\(31\) | −9.40104 | −1.68848 | −0.844239 | − | 0.535967i | \(-0.819947\pi\) | ||||
−0.844239 | + | 0.535967i | \(0.819947\pi\) | |||||||
\(32\) | −7.53682 | −1.33234 | ||||||||
\(33\) | 0.578709 | 0.100740 | ||||||||
\(34\) | −10.3699 | −1.77842 | ||||||||
\(35\) | −5.74806 | −0.971600 | ||||||||
\(36\) | −13.7486 | −2.29143 | ||||||||
\(37\) | −9.59768 | −1.57785 | −0.788924 | − | 0.614491i | \(-0.789362\pi\) | ||||
−0.788924 | + | 0.614491i | \(0.789362\pi\) | |||||||
\(38\) | −2.06260 | −0.334598 | ||||||||
\(39\) | 0.0194607 | 0.00311621 | ||||||||
\(40\) | 9.71704 | 1.53640 | ||||||||
\(41\) | 2.07739 | 0.324435 | 0.162217 | − | 0.986755i | \(-0.448135\pi\) | ||||
0.162217 | + | 0.986755i | \(0.448135\pi\) | |||||||
\(42\) | −1.83930 | −0.283810 | ||||||||
\(43\) | 4.11530 | 0.627577 | 0.313789 | − | 0.949493i | \(-0.398402\pi\) | ||||
0.313789 | + | 0.949493i | \(0.398402\pi\) | |||||||
\(44\) | 15.0469 | 2.26841 | ||||||||
\(45\) | 4.25557 | 0.634383 | ||||||||
\(46\) | −5.57180 | −0.821517 | ||||||||
\(47\) | 10.7434 | 1.56709 | 0.783543 | − | 0.621337i | \(-0.213410\pi\) | ||||
0.783543 | + | 0.621337i | \(0.213410\pi\) | |||||||
\(48\) | 1.45905 | 0.210596 | ||||||||
\(49\) | 9.07433 | 1.29633 | ||||||||
\(50\) | 7.58288 | 1.07238 | ||||||||
\(51\) | 0.717338 | 0.100447 | ||||||||
\(52\) | 0.505995 | 0.0701689 | ||||||||
\(53\) | 8.93327 | 1.22708 | 0.613539 | − | 0.789664i | \(-0.289745\pi\) | ||||
0.613539 | + | 0.789664i | \(0.289745\pi\) | |||||||
\(54\) | 2.73800 | 0.372595 | ||||||||
\(55\) | −4.65744 | −0.628009 | ||||||||
\(56\) | −27.1735 | −3.63121 | ||||||||
\(57\) | 0.142681 | 0.0188985 | ||||||||
\(58\) | −2.88649 | −0.379015 | ||||||||
\(59\) | 3.20813 | 0.417662 | 0.208831 | − | 0.977952i | \(-0.433034\pi\) | ||||
0.208831 | + | 0.977952i | \(0.433034\pi\) | |||||||
\(60\) | −1.18298 | −0.152722 | ||||||||
\(61\) | −8.18150 | −1.04753 | −0.523767 | − | 0.851862i | \(-0.675474\pi\) | ||||
−0.523767 | + | 0.851862i | \(0.675474\pi\) | |||||||
\(62\) | 24.2099 | 3.07466 | ||||||||
\(63\) | −11.9006 | −1.49934 | ||||||||
\(64\) | 3.02841 | 0.378551 | ||||||||
\(65\) | −0.156620 | −0.0194263 | ||||||||
\(66\) | −1.49031 | −0.183445 | ||||||||
\(67\) | 5.25878 | 0.642462 | 0.321231 | − | 0.947001i | \(-0.395903\pi\) | ||||
0.321231 | + | 0.947001i | \(0.395903\pi\) | |||||||
\(68\) | 18.6514 | 2.26181 | ||||||||
\(69\) | 0.385430 | 0.0464004 | ||||||||
\(70\) | 14.8026 | 1.76925 | ||||||||
\(71\) | −6.13821 | −0.728472 | −0.364236 | − | 0.931307i | \(-0.618670\pi\) | ||||
−0.364236 | + | 0.931307i | \(0.618670\pi\) | |||||||
\(72\) | 20.1179 | 2.37091 | ||||||||
\(73\) | 2.04661 | 0.239538 | 0.119769 | − | 0.992802i | \(-0.461785\pi\) | ||||
0.119769 | + | 0.992802i | \(0.461785\pi\) | |||||||
\(74\) | 24.7163 | 2.87321 | ||||||||
\(75\) | −0.524547 | −0.0605695 | ||||||||
\(76\) | 3.70981 | 0.425545 | ||||||||
\(77\) | 13.0244 | 1.48427 | ||||||||
\(78\) | −0.0501160 | −0.00567452 | ||||||||
\(79\) | 1.93328 | 0.217511 | 0.108756 | − | 0.994069i | \(-0.465313\pi\) | ||||
0.108756 | + | 0.994069i | \(0.465313\pi\) | |||||||
\(80\) | −11.7424 | −1.31284 | ||||||||
\(81\) | 8.71539 | 0.968377 | ||||||||
\(82\) | −5.34979 | −0.590785 | ||||||||
\(83\) | 10.7876 | 1.18409 | 0.592047 | − | 0.805903i | \(-0.298320\pi\) | ||||
0.592047 | + | 0.805903i | \(0.298320\pi\) | |||||||
\(84\) | 3.30818 | 0.360952 | ||||||||
\(85\) | −5.77313 | −0.626183 | ||||||||
\(86\) | −10.5979 | −1.14280 | ||||||||
\(87\) | 0.199674 | 0.0214072 | ||||||||
\(88\) | −22.0177 | −2.34709 | ||||||||
\(89\) | 1.83270 | 0.194266 | 0.0971331 | − | 0.995271i | \(-0.469033\pi\) | ||||
0.0971331 | + | 0.995271i | \(0.469033\pi\) | |||||||
\(90\) | −10.9591 | −1.15519 | ||||||||
\(91\) | 0.437983 | 0.0459131 | ||||||||
\(92\) | 10.0215 | 1.04481 | ||||||||
\(93\) | −1.67473 | −0.173661 | ||||||||
\(94\) | −27.6668 | −2.85361 | ||||||||
\(95\) | −1.14829 | −0.117812 | ||||||||
\(96\) | −1.34263 | −0.137032 | ||||||||
\(97\) | 1.53650 | 0.156008 | 0.0780041 | − | 0.996953i | \(-0.475145\pi\) | ||||
0.0780041 | + | 0.996953i | \(0.475145\pi\) | |||||||
\(98\) | −23.3686 | −2.36058 | ||||||||
\(99\) | −9.64262 | −0.969120 | ||||||||
\(100\) | −13.6387 | −1.36387 | ||||||||
\(101\) | −18.6319 | −1.85395 | −0.926974 | − | 0.375127i | \(-0.877599\pi\) | ||||
−0.926974 | + | 0.375127i | \(0.877599\pi\) | |||||||
\(102\) | −1.84732 | −0.182912 | ||||||||
\(103\) | −13.5484 | −1.33496 | −0.667482 | − | 0.744626i | \(-0.732628\pi\) | ||||
−0.667482 | + | 0.744626i | \(0.732628\pi\) | |||||||
\(104\) | −0.740407 | −0.0726029 | ||||||||
\(105\) | −1.02398 | −0.0999298 | ||||||||
\(106\) | −23.0053 | −2.23447 | ||||||||
\(107\) | −6.05270 | −0.585136 | −0.292568 | − | 0.956245i | \(-0.594510\pi\) | ||||
−0.292568 | + | 0.956245i | \(0.594510\pi\) | |||||||
\(108\) | −4.92460 | −0.473870 | ||||||||
\(109\) | 18.5890 | 1.78051 | 0.890254 | − | 0.455465i | \(-0.150527\pi\) | ||||
0.890254 | + | 0.455465i | \(0.150527\pi\) | |||||||
\(110\) | 11.9940 | 1.14359 | ||||||||
\(111\) | −1.70976 | −0.162283 | ||||||||
\(112\) | 32.8374 | 3.10285 | ||||||||
\(113\) | 2.75737 | 0.259391 | 0.129696 | − | 0.991554i | \(-0.458600\pi\) | ||||
0.129696 | + | 0.991554i | \(0.458600\pi\) | |||||||
\(114\) | −0.367437 | −0.0344136 | ||||||||
\(115\) | −3.10194 | −0.289257 | ||||||||
\(116\) | 5.19167 | 0.482035 | ||||||||
\(117\) | −0.324260 | −0.0299779 | ||||||||
\(118\) | −8.26169 | −0.760550 | ||||||||
\(119\) | 16.1444 | 1.47996 | ||||||||
\(120\) | 1.73102 | 0.158020 | ||||||||
\(121\) | −0.446790 | −0.0406172 | ||||||||
\(122\) | 21.0693 | 1.90753 | ||||||||
\(123\) | 0.370073 | 0.0333683 | ||||||||
\(124\) | −43.5443 | −3.91039 | ||||||||
\(125\) | 11.3900 | 1.01875 | ||||||||
\(126\) | 30.6469 | 2.73024 | ||||||||
\(127\) | 7.04726 | 0.625343 | 0.312672 | − | 0.949861i | \(-0.398776\pi\) | ||||
0.312672 | + | 0.949861i | \(0.398776\pi\) | |||||||
\(128\) | 7.27478 | 0.643006 | ||||||||
\(129\) | 0.733110 | 0.0645468 | ||||||||
\(130\) | 0.403333 | 0.0353747 | ||||||||
\(131\) | 7.12786 | 0.622764 | 0.311382 | − | 0.950285i | \(-0.399208\pi\) | ||||
0.311382 | + | 0.950285i | \(0.399208\pi\) | |||||||
\(132\) | 2.68050 | 0.233307 | ||||||||
\(133\) | 3.21117 | 0.278444 | ||||||||
\(134\) | −13.5426 | −1.16990 | ||||||||
\(135\) | 1.52430 | 0.131191 | ||||||||
\(136\) | −27.2920 | −2.34027 | ||||||||
\(137\) | −3.94505 | −0.337048 | −0.168524 | − | 0.985698i | \(-0.553900\pi\) | ||||
−0.168524 | + | 0.985698i | \(0.553900\pi\) | |||||||
\(138\) | −0.992575 | −0.0844936 | ||||||||
\(139\) | 13.1177 | 1.11263 | 0.556314 | − | 0.830972i | \(-0.312215\pi\) | ||||
0.556314 | + | 0.830972i | \(0.312215\pi\) | |||||||
\(140\) | −26.6242 | −2.25015 | ||||||||
\(141\) | 1.91386 | 0.161176 | ||||||||
\(142\) | 15.8074 | 1.32652 | ||||||||
\(143\) | 0.354882 | 0.0296767 | ||||||||
\(144\) | −24.3112 | −2.02593 | ||||||||
\(145\) | −1.60697 | −0.133452 | ||||||||
\(146\) | −5.27051 | −0.436191 | ||||||||
\(147\) | 1.61652 | 0.133329 | ||||||||
\(148\) | −44.4550 | −3.65418 | ||||||||
\(149\) | 0.552167 | 0.0452353 | 0.0226176 | − | 0.999744i | \(-0.492800\pi\) | ||||
0.0226176 | + | 0.999744i | \(0.492800\pi\) | |||||||
\(150\) | 1.35083 | 0.110295 | ||||||||
\(151\) | 4.37735 | 0.356224 | 0.178112 | − | 0.984010i | \(-0.443001\pi\) | ||||
0.178112 | + | 0.984010i | \(0.443001\pi\) | |||||||
\(152\) | −5.42845 | −0.440306 | ||||||||
\(153\) | −11.9525 | −0.966302 | ||||||||
\(154\) | −33.5410 | −2.70281 | ||||||||
\(155\) | 13.4782 | 1.08259 | ||||||||
\(156\) | 0.0901393 | 0.00721692 | ||||||||
\(157\) | 10.9416 | 0.873239 | 0.436619 | − | 0.899646i | \(-0.356176\pi\) | ||||
0.436619 | + | 0.899646i | \(0.356176\pi\) | |||||||
\(158\) | −4.97866 | −0.396081 | ||||||||
\(159\) | 1.59140 | 0.126206 | ||||||||
\(160\) | 10.8055 | 0.854247 | ||||||||
\(161\) | 8.67450 | 0.683646 | ||||||||
\(162\) | −22.4442 | −1.76338 | ||||||||
\(163\) | −0.365656 | −0.0286404 | −0.0143202 | − | 0.999897i | \(-0.504558\pi\) | ||||
−0.0143202 | + | 0.999897i | \(0.504558\pi\) | |||||||
\(164\) | 9.62219 | 0.751367 | ||||||||
\(165\) | −0.829689 | −0.0645912 | ||||||||
\(166\) | −27.7807 | −2.15620 | ||||||||
\(167\) | 6.93449 | 0.536607 | 0.268304 | − | 0.963334i | \(-0.413537\pi\) | ||||
0.268304 | + | 0.963334i | \(0.413537\pi\) | |||||||
\(168\) | −4.84076 | −0.373473 | ||||||||
\(169\) | −12.9881 | −0.999082 | ||||||||
\(170\) | 14.8672 | 1.14026 | ||||||||
\(171\) | −2.37739 | −0.181803 | ||||||||
\(172\) | 19.0615 | 1.45342 | ||||||||
\(173\) | 16.3378 | 1.24214 | 0.621068 | − | 0.783757i | \(-0.286699\pi\) | ||||
0.621068 | + | 0.783757i | \(0.286699\pi\) | |||||||
\(174\) | −0.514207 | −0.0389819 | ||||||||
\(175\) | −11.8055 | −0.892409 | ||||||||
\(176\) | 26.6070 | 2.00557 | ||||||||
\(177\) | 0.571504 | 0.0429569 | ||||||||
\(178\) | −4.71965 | −0.353753 | ||||||||
\(179\) | −0.905544 | −0.0676836 | −0.0338418 | − | 0.999427i | \(-0.510774\pi\) | ||||
−0.0338418 | + | 0.999427i | \(0.510774\pi\) | |||||||
\(180\) | 19.7112 | 1.46918 | ||||||||
\(181\) | 20.2103 | 1.50222 | 0.751110 | − | 0.660177i | \(-0.229519\pi\) | ||||
0.751110 | + | 0.660177i | \(0.229519\pi\) | |||||||
\(182\) | −1.12791 | −0.0836064 | ||||||||
\(183\) | −1.45747 | −0.107740 | ||||||||
\(184\) | −14.6642 | −1.08106 | ||||||||
\(185\) | 13.7601 | 1.01166 | ||||||||
\(186\) | 4.31282 | 0.316231 | ||||||||
\(187\) | 13.0812 | 0.956593 | ||||||||
\(188\) | 49.7619 | 3.62926 | ||||||||
\(189\) | −4.26268 | −0.310064 | ||||||||
\(190\) | 2.95712 | 0.214532 | ||||||||
\(191\) | 14.3439 | 1.03789 | 0.518945 | − | 0.854807i | \(-0.326325\pi\) | ||||
0.518945 | + | 0.854807i | \(0.326325\pi\) | |||||||
\(192\) | 0.539488 | 0.0389342 | ||||||||
\(193\) | −21.3381 | −1.53595 | −0.767975 | − | 0.640479i | \(-0.778736\pi\) | ||||
−0.767975 | + | 0.640479i | \(0.778736\pi\) | |||||||
\(194\) | −3.95686 | −0.284086 | ||||||||
\(195\) | −0.0279007 | −0.00199801 | ||||||||
\(196\) | 42.0309 | 3.00221 | ||||||||
\(197\) | −14.5274 | −1.03503 | −0.517516 | − | 0.855673i | \(-0.673143\pi\) | ||||
−0.517516 | + | 0.855673i | \(0.673143\pi\) | |||||||
\(198\) | 24.8320 | 1.76474 | ||||||||
\(199\) | 13.1015 | 0.928738 | 0.464369 | − | 0.885642i | \(-0.346281\pi\) | ||||
0.464369 | + | 0.885642i | \(0.346281\pi\) | |||||||
\(200\) | 19.9570 | 1.41117 | ||||||||
\(201\) | 0.936813 | 0.0660777 | ||||||||
\(202\) | 47.9817 | 3.37598 | ||||||||
\(203\) | 4.49385 | 0.315407 | ||||||||
\(204\) | 3.32260 | 0.232629 | ||||||||
\(205\) | −2.97834 | −0.208016 | ||||||||
\(206\) | 34.8904 | 2.43093 | ||||||||
\(207\) | −6.42215 | −0.446370 | ||||||||
\(208\) | 0.894735 | 0.0620387 | ||||||||
\(209\) | 2.60189 | 0.179977 | ||||||||
\(210\) | 2.63698 | 0.181969 | ||||||||
\(211\) | −19.0591 | −1.31208 | −0.656041 | − | 0.754725i | \(-0.727770\pi\) | ||||
−0.656041 | + | 0.754725i | \(0.727770\pi\) | |||||||
\(212\) | 41.3776 | 2.84182 | ||||||||
\(213\) | −1.09348 | −0.0749239 | ||||||||
\(214\) | 15.5871 | 1.06551 | ||||||||
\(215\) | −5.90006 | −0.402381 | ||||||||
\(216\) | 7.20602 | 0.490307 | ||||||||
\(217\) | −37.6914 | −2.55866 | ||||||||
\(218\) | −47.8712 | −3.24225 | ||||||||
\(219\) | 0.364589 | 0.0246366 | ||||||||
\(220\) | −21.5726 | −1.45442 | ||||||||
\(221\) | 0.439893 | 0.0295904 | ||||||||
\(222\) | 4.40303 | 0.295512 | ||||||||
\(223\) | 1.49026 | 0.0997951 | 0.0498976 | − | 0.998754i | \(-0.484111\pi\) | ||||
0.0498976 | + | 0.998754i | \(0.484111\pi\) | |||||||
\(224\) | −30.2172 | −2.01897 | ||||||||
\(225\) | 8.74016 | 0.582677 | ||||||||
\(226\) | −7.10088 | −0.472343 | ||||||||
\(227\) | −2.41143 | −0.160052 | −0.0800260 | − | 0.996793i | \(-0.525500\pi\) | ||||
−0.0800260 | + | 0.996793i | \(0.525500\pi\) | |||||||
\(228\) | 0.660876 | 0.0437676 | ||||||||
\(229\) | 13.1561 | 0.869376 | 0.434688 | − | 0.900581i | \(-0.356859\pi\) | ||||
0.434688 | + | 0.900581i | \(0.356859\pi\) | |||||||
\(230\) | 7.98823 | 0.526728 | ||||||||
\(231\) | 2.32021 | 0.152658 | ||||||||
\(232\) | −7.59682 | −0.498755 | ||||||||
\(233\) | −0.359749 | −0.0235679 | −0.0117840 | − | 0.999931i | \(-0.503751\pi\) | ||||
−0.0117840 | + | 0.999931i | \(0.503751\pi\) | |||||||
\(234\) | 0.835048 | 0.0545888 | ||||||||
\(235\) | −15.4027 | −1.00476 | ||||||||
\(236\) | 14.8596 | 0.967275 | ||||||||
\(237\) | 0.344400 | 0.0223712 | ||||||||
\(238\) | −41.5757 | −2.69495 | ||||||||
\(239\) | 10.7586 | 0.695916 | 0.347958 | − | 0.937510i | \(-0.386875\pi\) | ||||
0.347958 | + | 0.937510i | \(0.386875\pi\) | |||||||
\(240\) | −2.09183 | −0.135027 | ||||||||
\(241\) | −8.04907 | −0.518486 | −0.259243 | − | 0.965812i | \(-0.583473\pi\) | ||||
−0.259243 | + | 0.965812i | \(0.583473\pi\) | |||||||
\(242\) | 1.15059 | 0.0739627 | ||||||||
\(243\) | 4.74219 | 0.304212 | ||||||||
\(244\) | −37.8955 | −2.42601 | ||||||||
\(245\) | −13.0098 | −0.831163 | ||||||||
\(246\) | −0.953025 | −0.0607627 | ||||||||
\(247\) | 0.0874960 | 0.00556724 | ||||||||
\(248\) | 63.7170 | 4.04603 | ||||||||
\(249\) | 1.92173 | 0.121785 | ||||||||
\(250\) | −29.3320 | −1.85512 | ||||||||
\(251\) | −13.9814 | −0.882498 | −0.441249 | − | 0.897385i | \(-0.645464\pi\) | ||||
−0.441249 | + | 0.897385i | \(0.645464\pi\) | |||||||
\(252\) | −55.1219 | −3.47235 | ||||||||
\(253\) | 7.02862 | 0.441886 | ||||||||
\(254\) | −18.1484 | −1.13873 | ||||||||
\(255\) | −1.02844 | −0.0644034 | ||||||||
\(256\) | −24.7911 | −1.54944 | ||||||||
\(257\) | 29.4420 | 1.83654 | 0.918269 | − | 0.395956i | \(-0.129587\pi\) | ||||
0.918269 | + | 0.395956i | \(0.129587\pi\) | |||||||
\(258\) | −1.88793 | −0.117538 | ||||||||
\(259\) | −38.4798 | −2.39102 | ||||||||
\(260\) | −0.725440 | −0.0449898 | ||||||||
\(261\) | −3.32702 | −0.205937 | ||||||||
\(262\) | −18.3559 | −1.13403 | ||||||||
\(263\) | 8.53217 | 0.526116 | 0.263058 | − | 0.964780i | \(-0.415269\pi\) | ||||
0.263058 | + | 0.964780i | \(0.415269\pi\) | |||||||
\(264\) | −3.92229 | −0.241400 | ||||||||
\(265\) | −12.8075 | −0.786760 | ||||||||
\(266\) | −8.26953 | −0.507038 | ||||||||
\(267\) | 0.326483 | 0.0199804 | ||||||||
\(268\) | 24.3579 | 1.48789 | ||||||||
\(269\) | −22.9832 | −1.40131 | −0.700654 | − | 0.713501i | \(-0.747108\pi\) | ||||
−0.700654 | + | 0.713501i | \(0.747108\pi\) | |||||||
\(270\) | −3.92544 | −0.238895 | ||||||||
\(271\) | 32.3247 | 1.96359 | 0.981793 | − | 0.189956i | \(-0.0608346\pi\) | ||||
0.981793 | + | 0.189956i | \(0.0608346\pi\) | |||||||
\(272\) | 32.9806 | 1.99974 | ||||||||
\(273\) | 0.0780236 | 0.00472220 | ||||||||
\(274\) | 10.1594 | 0.613755 | ||||||||
\(275\) | −9.56553 | −0.576823 | ||||||||
\(276\) | 1.78526 | 0.107460 | ||||||||
\(277\) | −16.6530 | −1.00058 | −0.500292 | − | 0.865857i | \(-0.666774\pi\) | ||||
−0.500292 | + | 0.865857i | \(0.666774\pi\) | |||||||
\(278\) | −33.7812 | −2.02606 | ||||||||
\(279\) | 27.9048 | 1.67062 | ||||||||
\(280\) | 38.9584 | 2.32821 | ||||||||
\(281\) | 10.9350 | 0.652325 | 0.326162 | − | 0.945314i | \(-0.394244\pi\) | ||||
0.326162 | + | 0.945314i | \(0.394244\pi\) | |||||||
\(282\) | −4.92864 | −0.293496 | ||||||||
\(283\) | −5.02256 | −0.298560 | −0.149280 | − | 0.988795i | \(-0.547696\pi\) | ||||
−0.149280 | + | 0.988795i | \(0.547696\pi\) | |||||||
\(284\) | −28.4313 | −1.68709 | ||||||||
\(285\) | −0.204560 | −0.0121171 | ||||||||
\(286\) | −0.913905 | −0.0540403 | ||||||||
\(287\) | 8.32886 | 0.491637 | ||||||||
\(288\) | 22.3713 | 1.31824 | ||||||||
\(289\) | −0.785194 | −0.0461879 | ||||||||
\(290\) | 4.13833 | 0.243011 | ||||||||
\(291\) | 0.273717 | 0.0160456 | ||||||||
\(292\) | 9.47961 | 0.554752 | ||||||||
\(293\) | −22.9620 | −1.34145 | −0.670727 | − | 0.741704i | \(-0.734018\pi\) | ||||
−0.670727 | + | 0.741704i | \(0.734018\pi\) | |||||||
\(294\) | −4.16294 | −0.242787 | ||||||||
\(295\) | −4.59946 | −0.267791 | ||||||||
\(296\) | 65.0497 | 3.78094 | ||||||||
\(297\) | −3.45389 | −0.200415 | ||||||||
\(298\) | −1.42196 | −0.0823720 | ||||||||
\(299\) | 0.236357 | 0.0136689 | ||||||||
\(300\) | −2.42963 | −0.140275 | ||||||||
\(301\) | 16.4994 | 0.951009 | ||||||||
\(302\) | −11.2727 | −0.648673 | ||||||||
\(303\) | −3.31914 | −0.190680 | ||||||||
\(304\) | 6.55994 | 0.376238 | ||||||||
\(305\) | 11.7297 | 0.671642 | ||||||||
\(306\) | 30.7805 | 1.75961 | ||||||||
\(307\) | −6.84208 | −0.390498 | −0.195249 | − | 0.980754i | \(-0.562551\pi\) | ||||
−0.195249 | + | 0.980754i | \(0.562551\pi\) | |||||||
\(308\) | 60.3272 | 3.43746 | ||||||||
\(309\) | −2.41355 | −0.137302 | ||||||||
\(310\) | −34.7095 | −1.97137 | ||||||||
\(311\) | 26.3220 | 1.49258 | 0.746291 | − | 0.665620i | \(-0.231833\pi\) | ||||
0.746291 | + | 0.665620i | \(0.231833\pi\) | |||||||
\(312\) | −0.131898 | −0.00746726 | ||||||||
\(313\) | 22.2969 | 1.26029 | 0.630146 | − | 0.776476i | \(-0.282995\pi\) | ||||
0.630146 | + | 0.776476i | \(0.282995\pi\) | |||||||
\(314\) | −28.1774 | −1.59014 | ||||||||
\(315\) | 17.0618 | 0.961322 | ||||||||
\(316\) | 8.95468 | 0.503740 | ||||||||
\(317\) | −19.1219 | −1.07399 | −0.536996 | − | 0.843585i | \(-0.680441\pi\) | ||||
−0.536996 | + | 0.843585i | \(0.680441\pi\) | |||||||
\(318\) | −4.09823 | −0.229817 | ||||||||
\(319\) | 3.64120 | 0.203868 | ||||||||
\(320\) | −4.34179 | −0.242714 | ||||||||
\(321\) | −1.07824 | −0.0601817 | ||||||||
\(322\) | −22.3389 | −1.24490 | ||||||||
\(323\) | 3.22517 | 0.179453 | ||||||||
\(324\) | 40.3684 | 2.24269 | ||||||||
\(325\) | −0.321668 | −0.0178429 | ||||||||
\(326\) | 0.941652 | 0.0521533 | ||||||||
\(327\) | 3.31150 | 0.183127 | ||||||||
\(328\) | −14.0799 | −0.777430 | ||||||||
\(329\) | 43.0733 | 2.37471 | ||||||||
\(330\) | 2.13665 | 0.117619 | ||||||||
\(331\) | 30.8192 | 1.69398 | 0.846989 | − | 0.531611i | \(-0.178413\pi\) | ||||
0.846989 | + | 0.531611i | \(0.178413\pi\) | |||||||
\(332\) | 49.9666 | 2.74227 | ||||||||
\(333\) | 28.4884 | 1.56116 | ||||||||
\(334\) | −17.8580 | −0.977145 | ||||||||
\(335\) | −7.53945 | −0.411924 | ||||||||
\(336\) | 5.84975 | 0.319130 | ||||||||
\(337\) | −7.98837 | −0.435154 | −0.217577 | − | 0.976043i | \(-0.569815\pi\) | ||||
−0.217577 | + | 0.976043i | \(0.569815\pi\) | |||||||
\(338\) | 33.4474 | 1.81930 | ||||||||
\(339\) | 0.491205 | 0.0266786 | ||||||||
\(340\) | −26.7403 | −1.45019 | ||||||||
\(341\) | −30.5400 | −1.65383 | ||||||||
\(342\) | 6.12234 | 0.331058 | ||||||||
\(343\) | 8.31656 | 0.449052 | ||||||||
\(344\) | −27.8920 | −1.50384 | ||||||||
\(345\) | −0.552587 | −0.0297503 | ||||||||
\(346\) | −42.0736 | −2.26189 | ||||||||
\(347\) | −1.72126 | −0.0924020 | −0.0462010 | − | 0.998932i | \(-0.514711\pi\) | ||||
−0.0462010 | + | 0.998932i | \(0.514711\pi\) | |||||||
\(348\) | 0.924858 | 0.0495776 | ||||||||
\(349\) | −32.6175 | −1.74597 | −0.872987 | − | 0.487744i | \(-0.837820\pi\) | ||||
−0.872987 | + | 0.487744i | \(0.837820\pi\) | |||||||
\(350\) | 30.4019 | 1.62505 | ||||||||
\(351\) | −0.116147 | −0.00619946 | ||||||||
\(352\) | −24.4839 | −1.30500 | ||||||||
\(353\) | 3.78629 | 0.201524 | 0.100762 | − | 0.994911i | \(-0.467872\pi\) | ||||
0.100762 | + | 0.994911i | \(0.467872\pi\) | |||||||
\(354\) | −1.47176 | −0.0782231 | ||||||||
\(355\) | 8.80029 | 0.467071 | ||||||||
\(356\) | 8.48881 | 0.449906 | ||||||||
\(357\) | 2.87601 | 0.152215 | ||||||||
\(358\) | 2.33199 | 0.123250 | ||||||||
\(359\) | −10.4953 | −0.553922 | −0.276961 | − | 0.960881i | \(-0.589327\pi\) | ||||
−0.276961 | + | 0.960881i | \(0.589327\pi\) | |||||||
\(360\) | −28.8428 | −1.52015 | ||||||||
\(361\) | −18.3585 | −0.966237 | ||||||||
\(362\) | −52.0464 | −2.73550 | ||||||||
\(363\) | −0.0795923 | −0.00417751 | ||||||||
\(364\) | 2.02868 | 0.106331 | ||||||||
\(365\) | −2.93421 | −0.153583 | ||||||||
\(366\) | 3.75334 | 0.196190 | ||||||||
\(367\) | −5.67748 | −0.296362 | −0.148181 | − | 0.988960i | \(-0.547342\pi\) | ||||
−0.148181 | + | 0.988960i | \(0.547342\pi\) | |||||||
\(368\) | 17.7207 | 0.923755 | ||||||||
\(369\) | −6.16626 | −0.321003 | ||||||||
\(370\) | −35.4355 | −1.84220 | ||||||||
\(371\) | 35.8160 | 1.85947 | ||||||||
\(372\) | −7.75709 | −0.402186 | ||||||||
\(373\) | −1.03621 | −0.0536528 | −0.0268264 | − | 0.999640i | \(-0.508540\pi\) | ||||
−0.0268264 | + | 0.999640i | \(0.508540\pi\) | |||||||
\(374\) | −33.6873 | −1.74193 | ||||||||
\(375\) | 2.02904 | 0.104779 | ||||||||
\(376\) | −72.8150 | −3.75515 | ||||||||
\(377\) | 0.122446 | 0.00630628 | ||||||||
\(378\) | 10.9774 | 0.564617 | ||||||||
\(379\) | 3.49439 | 0.179495 | 0.0897473 | − | 0.995965i | \(-0.471394\pi\) | ||||
0.0897473 | + | 0.995965i | \(0.471394\pi\) | |||||||
\(380\) | −5.31872 | −0.272844 | ||||||||
\(381\) | 1.25542 | 0.0643170 | ||||||||
\(382\) | −36.9390 | −1.88997 | ||||||||
\(383\) | 0.802352 | 0.0409983 | 0.0204991 | − | 0.999790i | \(-0.493474\pi\) | ||||
0.0204991 | + | 0.999790i | \(0.493474\pi\) | |||||||
\(384\) | 1.29595 | 0.0661336 | ||||||||
\(385\) | −18.6730 | −0.951664 | ||||||||
\(386\) | 54.9507 | 2.79692 | ||||||||
\(387\) | −12.2153 | −0.620938 | ||||||||
\(388\) | 7.11685 | 0.361303 | ||||||||
\(389\) | −2.08570 | −0.105749 | −0.0528746 | − | 0.998601i | \(-0.516838\pi\) | ||||
−0.0528746 | + | 0.998601i | \(0.516838\pi\) | |||||||
\(390\) | 0.0718508 | 0.00363831 | ||||||||
\(391\) | 8.71232 | 0.440601 | ||||||||
\(392\) | −61.5026 | −3.10635 | ||||||||
\(393\) | 1.26978 | 0.0640517 | ||||||||
\(394\) | 37.4115 | 1.88476 | ||||||||
\(395\) | −2.77173 | −0.139461 | ||||||||
\(396\) | −44.6632 | −2.24441 | ||||||||
\(397\) | 32.4801 | 1.63013 | 0.815066 | − | 0.579368i | \(-0.196701\pi\) | ||||
0.815066 | + | 0.579368i | \(0.196701\pi\) | |||||||
\(398\) | −33.7394 | −1.69120 | ||||||||
\(399\) | 0.572047 | 0.0286382 | ||||||||
\(400\) | −24.1168 | −1.20584 | ||||||||
\(401\) | 1.52539 | 0.0761742 | 0.0380871 | − | 0.999274i | \(-0.487874\pi\) | ||||
0.0380871 | + | 0.999274i | \(0.487874\pi\) | |||||||
\(402\) | −2.41252 | −0.120325 | ||||||||
\(403\) | −1.02699 | −0.0511582 | ||||||||
\(404\) | −86.3004 | −4.29361 | ||||||||
\(405\) | −12.4952 | −0.620890 | ||||||||
\(406\) | −11.5727 | −0.574346 | ||||||||
\(407\) | −31.1787 | −1.54547 | ||||||||
\(408\) | −4.86187 | −0.240698 | ||||||||
\(409\) | −18.3103 | −0.905386 | −0.452693 | − | 0.891666i | \(-0.649537\pi\) | ||||
−0.452693 | + | 0.891666i | \(0.649537\pi\) | |||||||
\(410\) | 7.66993 | 0.378791 | ||||||||
\(411\) | −0.702782 | −0.0346657 | ||||||||
\(412\) | −62.7542 | −3.09168 | ||||||||
\(413\) | 12.8623 | 0.632911 | ||||||||
\(414\) | 16.5386 | 0.812827 | ||||||||
\(415\) | −15.4661 | −0.759200 | ||||||||
\(416\) | −0.823341 | −0.0403676 | ||||||||
\(417\) | 2.33682 | 0.114435 | ||||||||
\(418\) | −6.70049 | −0.327732 | ||||||||
\(419\) | −4.08632 | −0.199630 | −0.0998148 | − | 0.995006i | \(-0.531825\pi\) | ||||
−0.0998148 | + | 0.995006i | \(0.531825\pi\) | |||||||
\(420\) | −4.74290 | −0.231430 | ||||||||
\(421\) | −0.284669 | −0.0138739 | −0.00693696 | − | 0.999976i | \(-0.502208\pi\) | ||||
−0.00693696 | + | 0.999976i | \(0.502208\pi\) | |||||||
\(422\) | 49.0817 | 2.38926 | ||||||||
\(423\) | −31.8893 | −1.55051 | ||||||||
\(424\) | −60.5466 | −2.94040 | ||||||||
\(425\) | −11.8569 | −0.575146 | ||||||||
\(426\) | 2.81597 | 0.136434 | ||||||||
\(427\) | −32.8019 | −1.58740 | ||||||||
\(428\) | −28.0352 | −1.35513 | ||||||||
\(429\) | 0.0632196 | 0.00305227 | ||||||||
\(430\) | 15.1941 | 0.732723 | ||||||||
\(431\) | 7.82709 | 0.377018 | 0.188509 | − | 0.982072i | \(-0.439635\pi\) | ||||
0.188509 | + | 0.982072i | \(0.439635\pi\) | |||||||
\(432\) | −8.70801 | −0.418964 | ||||||||
\(433\) | −19.2305 | −0.924158 | −0.462079 | − | 0.886839i | \(-0.652896\pi\) | ||||
−0.462079 | + | 0.886839i | \(0.652896\pi\) | |||||||
\(434\) | 97.0644 | 4.65924 | ||||||||
\(435\) | −0.286270 | −0.0137256 | ||||||||
\(436\) | 86.1017 | 4.12353 | ||||||||
\(437\) | 1.73291 | 0.0828961 | ||||||||
\(438\) | −0.938904 | −0.0448625 | ||||||||
\(439\) | 27.0140 | 1.28931 | 0.644654 | − | 0.764475i | \(-0.277001\pi\) | ||||
0.644654 | + | 0.764475i | \(0.277001\pi\) | |||||||
\(440\) | 31.5665 | 1.50487 | ||||||||
\(441\) | −26.9350 | −1.28262 | ||||||||
\(442\) | −1.13283 | −0.0538832 | ||||||||
\(443\) | 25.3502 | 1.20442 | 0.602211 | − | 0.798337i | \(-0.294286\pi\) | ||||
0.602211 | + | 0.798337i | \(0.294286\pi\) | |||||||
\(444\) | −7.91934 | −0.375835 | ||||||||
\(445\) | −2.62753 | −0.124557 | ||||||||
\(446\) | −3.83777 | −0.181724 | ||||||||
\(447\) | 0.0983644 | 0.00465248 | ||||||||
\(448\) | 12.1417 | 0.573643 | ||||||||
\(449\) | −16.0981 | −0.759716 | −0.379858 | − | 0.925045i | \(-0.624027\pi\) | ||||
−0.379858 | + | 0.925045i | \(0.624027\pi\) | |||||||
\(450\) | −22.5080 | −1.06104 | ||||||||
\(451\) | 6.74856 | 0.317777 | ||||||||
\(452\) | 12.7717 | 0.600731 | ||||||||
\(453\) | 0.779794 | 0.0366379 | ||||||||
\(454\) | 6.21000 | 0.291450 | ||||||||
\(455\) | −0.627932 | −0.0294379 | ||||||||
\(456\) | −0.967040 | −0.0452858 | ||||||||
\(457\) | −18.0394 | −0.843847 | −0.421923 | − | 0.906631i | \(-0.638645\pi\) | ||||
−0.421923 | + | 0.906631i | \(0.638645\pi\) | |||||||
\(458\) | −33.8800 | −1.58311 | ||||||||
\(459\) | −4.28126 | −0.199832 | ||||||||
\(460\) | −14.3677 | −0.669898 | ||||||||
\(461\) | −29.4735 | −1.37272 | −0.686360 | − | 0.727262i | \(-0.740792\pi\) | ||||
−0.686360 | + | 0.727262i | \(0.740792\pi\) | |||||||
\(462\) | −5.97509 | −0.277986 | ||||||||
\(463\) | 30.9655 | 1.43909 | 0.719544 | − | 0.694446i | \(-0.244351\pi\) | ||||
0.719544 | + | 0.694446i | \(0.244351\pi\) | |||||||
\(464\) | 9.18027 | 0.426183 | ||||||||
\(465\) | 2.40104 | 0.111346 | ||||||||
\(466\) | 0.926440 | 0.0429165 | ||||||||
\(467\) | −14.5535 | −0.673454 | −0.336727 | − | 0.941602i | \(-0.609320\pi\) | ||||
−0.336727 | + | 0.941602i | \(0.609320\pi\) | |||||||
\(468\) | −1.50193 | −0.0694266 | ||||||||
\(469\) | 21.0839 | 0.973564 | ||||||||
\(470\) | 39.6656 | 1.82964 | ||||||||
\(471\) | 1.94917 | 0.0898132 | ||||||||
\(472\) | −21.7435 | −1.00083 | ||||||||
\(473\) | 13.3688 | 0.614700 | ||||||||
\(474\) | −0.886913 | −0.0407372 | ||||||||
\(475\) | −2.35838 | −0.108210 | ||||||||
\(476\) | 74.7786 | 3.42747 | ||||||||
\(477\) | −26.5163 | −1.21410 | ||||||||
\(478\) | −27.7060 | −1.26724 | ||||||||
\(479\) | 29.7211 | 1.35799 | 0.678996 | − | 0.734142i | \(-0.262416\pi\) | ||||
0.678996 | + | 0.734142i | \(0.262416\pi\) | |||||||
\(480\) | 1.92491 | 0.0878599 | ||||||||
\(481\) | −1.04847 | −0.0478063 | ||||||||
\(482\) | 20.7283 | 0.944147 | ||||||||
\(483\) | 1.54530 | 0.0703135 | ||||||||
\(484\) | −2.06946 | −0.0940666 | ||||||||
\(485\) | −2.20287 | −0.100027 | ||||||||
\(486\) | −12.2123 | −0.553960 | ||||||||
\(487\) | 27.8799 | 1.26336 | 0.631680 | − | 0.775229i | \(-0.282366\pi\) | ||||
0.631680 | + | 0.775229i | \(0.282366\pi\) | |||||||
\(488\) | 55.4513 | 2.51016 | ||||||||
\(489\) | −0.0651390 | −0.00294569 | ||||||||
\(490\) | 33.5033 | 1.51352 | ||||||||
\(491\) | −7.54215 | −0.340373 | −0.170186 | − | 0.985412i | \(-0.554437\pi\) | ||||
−0.170186 | + | 0.985412i | \(0.554437\pi\) | |||||||
\(492\) | 1.71412 | 0.0772786 | ||||||||
\(493\) | 4.51345 | 0.203275 | ||||||||
\(494\) | −0.225323 | −0.0101378 | ||||||||
\(495\) | 13.8245 | 0.621366 | ||||||||
\(496\) | −76.9979 | −3.45731 | ||||||||
\(497\) | −24.6098 | −1.10390 | ||||||||
\(498\) | −4.94892 | −0.221767 | ||||||||
\(499\) | −2.45075 | −0.109711 | −0.0548553 | − | 0.998494i | \(-0.517470\pi\) | ||||
−0.0548553 | + | 0.998494i | \(0.517470\pi\) | |||||||
\(500\) | 52.7568 | 2.35936 | ||||||||
\(501\) | 1.23533 | 0.0551905 | ||||||||
\(502\) | 36.0054 | 1.60700 | ||||||||
\(503\) | 12.0785 | 0.538554 | 0.269277 | − | 0.963063i | \(-0.413215\pi\) | ||||
0.269277 | + | 0.963063i | \(0.413215\pi\) | |||||||
\(504\) | 80.6581 | 3.59280 | ||||||||
\(505\) | 26.7124 | 1.18869 | ||||||||
\(506\) | −18.1004 | −0.804660 | ||||||||
\(507\) | −2.31373 | −0.102756 | ||||||||
\(508\) | 32.6419 | 1.44825 | ||||||||
\(509\) | −33.2006 | −1.47159 | −0.735795 | − | 0.677205i | \(-0.763191\pi\) | ||||
−0.735795 | + | 0.677205i | \(0.763191\pi\) | |||||||
\(510\) | 2.64848 | 0.117277 | ||||||||
\(511\) | 8.20544 | 0.362987 | ||||||||
\(512\) | 49.2935 | 2.17848 | ||||||||
\(513\) | −0.851556 | −0.0375971 | ||||||||
\(514\) | −75.8201 | −3.34428 | ||||||||
\(515\) | 19.4242 | 0.855933 | ||||||||
\(516\) | 3.39566 | 0.149486 | ||||||||
\(517\) | 34.9007 | 1.53493 | ||||||||
\(518\) | 99.0946 | 4.35397 | ||||||||
\(519\) | 2.91045 | 0.127755 | ||||||||
\(520\) | 1.06151 | 0.0465504 | ||||||||
\(521\) | 14.9950 | 0.656944 | 0.328472 | − | 0.944514i | \(-0.393466\pi\) | ||||
0.328472 | + | 0.944514i | \(0.393466\pi\) | |||||||
\(522\) | 8.56786 | 0.375005 | ||||||||
\(523\) | 40.4068 | 1.76687 | 0.883434 | − | 0.468556i | \(-0.155226\pi\) | ||||
0.883434 | + | 0.468556i | \(0.155226\pi\) | |||||||
\(524\) | 33.0152 | 1.44228 | ||||||||
\(525\) | −2.10306 | −0.0917849 | ||||||||
\(526\) | −21.9724 | −0.958040 | ||||||||
\(527\) | −37.8558 | −1.64902 | ||||||||
\(528\) | 4.73983 | 0.206275 | ||||||||
\(529\) | −18.3188 | −0.796470 | ||||||||
\(530\) | 32.9824 | 1.43267 | ||||||||
\(531\) | −9.52257 | −0.413244 | ||||||||
\(532\) | 14.8737 | 0.644856 | ||||||||
\(533\) | 0.226940 | 0.00982985 | ||||||||
\(534\) | −0.840771 | −0.0363837 | ||||||||
\(535\) | 8.67769 | 0.375169 | ||||||||
\(536\) | −35.6421 | −1.53951 | ||||||||
\(537\) | −0.161316 | −0.00696130 | ||||||||
\(538\) | 59.1871 | 2.55174 | ||||||||
\(539\) | 29.4786 | 1.26973 | ||||||||
\(540\) | 7.06035 | 0.303829 | ||||||||
\(541\) | 38.8209 | 1.66904 | 0.834520 | − | 0.550978i | \(-0.185745\pi\) | ||||
0.834520 | + | 0.550978i | \(0.185745\pi\) | |||||||
\(542\) | −83.2438 | −3.57563 | ||||||||
\(543\) | 3.60032 | 0.154504 | ||||||||
\(544\) | −30.3490 | −1.30120 | ||||||||
\(545\) | −26.6509 | −1.14160 | ||||||||
\(546\) | −0.200929 | −0.00859898 | ||||||||
\(547\) | −37.3858 | −1.59850 | −0.799250 | − | 0.600999i | \(-0.794770\pi\) | ||||
−0.799250 | + | 0.600999i | \(0.794770\pi\) | |||||||
\(548\) | −18.2729 | −0.780580 | ||||||||
\(549\) | 24.2848 | 1.03645 | ||||||||
\(550\) | 24.6335 | 1.05038 | ||||||||
\(551\) | 0.897738 | 0.0382449 | ||||||||
\(552\) | −2.61231 | −0.111187 | ||||||||
\(553\) | 7.75107 | 0.329609 | ||||||||
\(554\) | 42.8855 | 1.82203 | ||||||||
\(555\) | 2.45126 | 0.104050 | ||||||||
\(556\) | 60.7592 | 2.57677 | ||||||||
\(557\) | −11.6757 | −0.494716 | −0.247358 | − | 0.968924i | \(-0.579562\pi\) | ||||
−0.247358 | + | 0.968924i | \(0.579562\pi\) | |||||||
\(558\) | −71.8615 | −3.04214 | ||||||||
\(559\) | 0.449565 | 0.0190146 | ||||||||
\(560\) | −47.0787 | −1.98944 | ||||||||
\(561\) | 2.33032 | 0.0983863 | ||||||||
\(562\) | −28.1601 | −1.18786 | ||||||||
\(563\) | −24.2102 | −1.02034 | −0.510169 | − | 0.860074i | \(-0.670417\pi\) | ||||
−0.510169 | + | 0.860074i | \(0.670417\pi\) | |||||||
\(564\) | 8.86471 | 0.373272 | ||||||||
\(565\) | −3.95321 | −0.166313 | ||||||||
\(566\) | 12.9343 | 0.543669 | ||||||||
\(567\) | 34.9425 | 1.46745 | ||||||||
\(568\) | 41.6027 | 1.74561 | ||||||||
\(569\) | 30.9493 | 1.29746 | 0.648731 | − | 0.761018i | \(-0.275300\pi\) | ||||
0.648731 | + | 0.761018i | \(0.275300\pi\) | |||||||
\(570\) | 0.526790 | 0.0220648 | ||||||||
\(571\) | −2.44057 | −0.102135 | −0.0510674 | − | 0.998695i | \(-0.516262\pi\) | ||||
−0.0510674 | + | 0.998695i | \(0.516262\pi\) | |||||||
\(572\) | 1.64376 | 0.0687291 | ||||||||
\(573\) | 2.55527 | 0.106748 | ||||||||
\(574\) | −21.4488 | −0.895255 | ||||||||
\(575\) | −6.37081 | −0.265681 | ||||||||
\(576\) | −8.98911 | −0.374546 | ||||||||
\(577\) | −29.4018 | −1.22401 | −0.612007 | − | 0.790853i | \(-0.709637\pi\) | ||||
−0.612007 | + | 0.790853i | \(0.709637\pi\) | |||||||
\(578\) | 2.02206 | 0.0841066 | ||||||||
\(579\) | −3.80123 | −0.157974 | ||||||||
\(580\) | −7.44325 | −0.309064 | ||||||||
\(581\) | 43.2505 | 1.79433 | ||||||||
\(582\) | −0.704886 | −0.0292184 | ||||||||
\(583\) | 29.0204 | 1.20190 | ||||||||
\(584\) | −13.8712 | −0.573995 | ||||||||
\(585\) | 0.464889 | 0.0192208 | ||||||||
\(586\) | 59.1326 | 2.44275 | ||||||||
\(587\) | 37.2187 | 1.53618 | 0.768091 | − | 0.640341i | \(-0.221207\pi\) | ||||
0.768091 | + | 0.640341i | \(0.221207\pi\) | |||||||
\(588\) | 7.48751 | 0.308780 | ||||||||
\(589\) | −7.52962 | −0.310253 | ||||||||
\(590\) | 11.8447 | 0.487638 | ||||||||
\(591\) | −2.58795 | −0.106454 | ||||||||
\(592\) | −78.6084 | −3.23079 | ||||||||
\(593\) | −14.8068 | −0.608042 | −0.304021 | − | 0.952665i | \(-0.598329\pi\) | ||||
−0.304021 | + | 0.952665i | \(0.598329\pi\) | |||||||
\(594\) | 8.89459 | 0.364949 | ||||||||
\(595\) | −23.1461 | −0.948897 | ||||||||
\(596\) | 2.55755 | 0.104762 | ||||||||
\(597\) | 2.33393 | 0.0955213 | ||||||||
\(598\) | −0.608677 | −0.0248906 | ||||||||
\(599\) | −23.1142 | −0.944420 | −0.472210 | − | 0.881486i | \(-0.656544\pi\) | ||||
−0.472210 | + | 0.881486i | \(0.656544\pi\) | |||||||
\(600\) | 3.55520 | 0.145140 | ||||||||
\(601\) | −0.164513 | −0.00671063 | −0.00335531 | − | 0.999994i | \(-0.501068\pi\) | ||||
−0.00335531 | + | 0.999994i | \(0.501068\pi\) | |||||||
\(602\) | −42.4898 | −1.73176 | ||||||||
\(603\) | −15.6094 | −0.635666 | ||||||||
\(604\) | 20.2753 | 0.824989 | ||||||||
\(605\) | 0.640558 | 0.0260424 | ||||||||
\(606\) | 8.54759 | 0.347222 | ||||||||
\(607\) | 16.4064 | 0.665917 | 0.332958 | − | 0.942942i | \(-0.391953\pi\) | ||||
0.332958 | + | 0.942942i | \(0.391953\pi\) | |||||||
\(608\) | −6.03650 | −0.244813 | ||||||||
\(609\) | 0.800547 | 0.0324398 | ||||||||
\(610\) | −30.2068 | −1.22304 | ||||||||
\(611\) | 1.17364 | 0.0474802 | ||||||||
\(612\) | −55.3622 | −2.23788 | ||||||||
\(613\) | −11.9747 | −0.483652 | −0.241826 | − | 0.970320i | \(-0.577746\pi\) | ||||
−0.241826 | + | 0.970320i | \(0.577746\pi\) | |||||||
\(614\) | 17.6200 | 0.711084 | ||||||||
\(615\) | −0.530569 | −0.0213946 | ||||||||
\(616\) | −88.2750 | −3.55670 | ||||||||
\(617\) | −29.6207 | −1.19248 | −0.596241 | − | 0.802805i | \(-0.703340\pi\) | ||||
−0.596241 | + | 0.802805i | \(0.703340\pi\) | |||||||
\(618\) | 6.21547 | 0.250023 | ||||||||
\(619\) | 15.3324 | 0.616260 | 0.308130 | − | 0.951344i | \(-0.400297\pi\) | ||||
0.308130 | + | 0.951344i | \(0.400297\pi\) | |||||||
\(620\) | 62.4289 | 2.50721 | ||||||||
\(621\) | −2.30035 | −0.0923099 | ||||||||
\(622\) | −67.7853 | −2.71794 | ||||||||
\(623\) | 7.34782 | 0.294384 | ||||||||
\(624\) | 0.159390 | 0.00638072 | ||||||||
\(625\) | −1.60704 | −0.0642818 | ||||||||
\(626\) | −57.4197 | −2.29495 | ||||||||
\(627\) | 0.463508 | 0.0185107 | ||||||||
\(628\) | 50.6801 | 2.02236 | ||||||||
\(629\) | −38.6475 | −1.54098 | ||||||||
\(630\) | −43.9381 | −1.75054 | ||||||||
\(631\) | 18.0358 | 0.717993 | 0.358997 | − | 0.933339i | \(-0.383119\pi\) | ||||
0.358997 | + | 0.933339i | \(0.383119\pi\) | |||||||
\(632\) | −13.1031 | −0.521214 | ||||||||
\(633\) | −3.39524 | −0.134949 | ||||||||
\(634\) | 49.2434 | 1.95570 | ||||||||
\(635\) | −10.1036 | −0.400948 | ||||||||
\(636\) | 7.37111 | 0.292284 | ||||||||
\(637\) | 0.991301 | 0.0392768 | ||||||||
\(638\) | −9.37696 | −0.371238 | ||||||||
\(639\) | 18.2198 | 0.720766 | ||||||||
\(640\) | −10.4298 | −0.412273 | ||||||||
\(641\) | 39.6015 | 1.56417 | 0.782083 | − | 0.623174i | \(-0.214157\pi\) | ||||
0.782083 | + | 0.623174i | \(0.214157\pi\) | |||||||
\(642\) | 2.77673 | 0.109589 | ||||||||
\(643\) | −41.8858 | −1.65182 | −0.825908 | − | 0.563805i | \(-0.809337\pi\) | ||||
−0.825908 | + | 0.563805i | \(0.809337\pi\) | |||||||
\(644\) | 40.1790 | 1.58327 | ||||||||
\(645\) | −1.05105 | −0.0413851 | ||||||||
\(646\) | −8.30559 | −0.326779 | ||||||||
\(647\) | 14.5489 | 0.571977 | 0.285988 | − | 0.958233i | \(-0.407678\pi\) | ||||
0.285988 | + | 0.958233i | \(0.407678\pi\) | |||||||
\(648\) | −59.0699 | −2.32048 | ||||||||
\(649\) | 10.4218 | 0.409092 | ||||||||
\(650\) | 0.828372 | 0.0324914 | ||||||||
\(651\) | −6.71445 | −0.263160 | ||||||||
\(652\) | −1.69367 | −0.0663291 | ||||||||
\(653\) | 3.87731 | 0.151731 | 0.0758655 | − | 0.997118i | \(-0.475828\pi\) | ||||
0.0758655 | + | 0.997118i | \(0.475828\pi\) | |||||||
\(654\) | −8.52791 | −0.333468 | ||||||||
\(655\) | −10.2191 | −0.399295 | ||||||||
\(656\) | 17.0146 | 0.664309 | ||||||||
\(657\) | −6.07489 | −0.237004 | ||||||||
\(658\) | −110.924 | −4.32427 | ||||||||
\(659\) | 24.1717 | 0.941595 | 0.470797 | − | 0.882241i | \(-0.343966\pi\) | ||||
0.470797 | + | 0.882241i | \(0.343966\pi\) | |||||||
\(660\) | −3.84300 | −0.149589 | ||||||||
\(661\) | −11.8517 | −0.460979 | −0.230490 | − | 0.973075i | \(-0.574033\pi\) | ||||
−0.230490 | + | 0.973075i | \(0.574033\pi\) | |||||||
\(662\) | −79.3668 | −3.08468 | ||||||||
\(663\) | 0.0783638 | 0.00304340 | ||||||||
\(664\) | −73.1146 | −2.83740 | ||||||||
\(665\) | −4.60382 | −0.178529 | ||||||||
\(666\) | −73.3645 | −2.84282 | ||||||||
\(667\) | 2.42510 | 0.0939004 | ||||||||
\(668\) | 32.1196 | 1.24274 | ||||||||
\(669\) | 0.265479 | 0.0102640 | ||||||||
\(670\) | 19.4159 | 0.750101 | ||||||||
\(671\) | −26.5782 | −1.02604 | ||||||||
\(672\) | −5.38298 | −0.207653 | ||||||||
\(673\) | 6.67425 | 0.257273 | 0.128637 | − | 0.991692i | \(-0.458940\pi\) | ||||
0.128637 | + | 0.991692i | \(0.458940\pi\) | |||||||
\(674\) | 20.5720 | 0.792403 | ||||||||
\(675\) | 3.13064 | 0.120498 | ||||||||
\(676\) | −60.1588 | −2.31380 | ||||||||
\(677\) | 29.5146 | 1.13434 | 0.567169 | − | 0.823601i | \(-0.308038\pi\) | ||||
0.567169 | + | 0.823601i | \(0.308038\pi\) | |||||||
\(678\) | −1.26497 | −0.0485808 | ||||||||
\(679\) | 6.16027 | 0.236409 | ||||||||
\(680\) | 39.1282 | 1.50050 | ||||||||
\(681\) | −0.429578 | −0.0164615 | ||||||||
\(682\) | 78.6477 | 3.01157 | ||||||||
\(683\) | 47.7648 | 1.82767 | 0.913835 | − | 0.406086i | \(-0.133107\pi\) | ||||
0.913835 | + | 0.406086i | \(0.133107\pi\) | |||||||
\(684\) | −11.0117 | −0.421043 | ||||||||
\(685\) | 5.65598 | 0.216104 | ||||||||
\(686\) | −21.4171 | −0.817709 | ||||||||
\(687\) | 2.34365 | 0.0894160 | ||||||||
\(688\) | 33.7058 | 1.28502 | ||||||||
\(689\) | 0.975892 | 0.0371785 | ||||||||
\(690\) | 1.42304 | 0.0541744 | ||||||||
\(691\) | 15.9512 | 0.606810 | 0.303405 | − | 0.952862i | \(-0.401876\pi\) | ||||
0.303405 | + | 0.952862i | \(0.401876\pi\) | |||||||
\(692\) | 75.6741 | 2.87670 | ||||||||
\(693\) | −38.6600 | −1.46857 | ||||||||
\(694\) | 4.43265 | 0.168261 | ||||||||
\(695\) | −18.8067 | −0.713379 | ||||||||
\(696\) | −1.35332 | −0.0512974 | ||||||||
\(697\) | 8.36517 | 0.316854 | ||||||||
\(698\) | 83.9978 | 3.17936 | ||||||||
\(699\) | −0.0640867 | −0.00242398 | ||||||||
\(700\) | −54.6812 | −2.06675 | ||||||||
\(701\) | 17.9075 | 0.676357 | 0.338179 | − | 0.941082i | \(-0.390189\pi\) | ||||
0.338179 | + | 0.941082i | \(0.390189\pi\) | |||||||
\(702\) | 0.299106 | 0.0112890 | ||||||||
\(703\) | −7.68711 | −0.289925 | ||||||||
\(704\) | 9.83799 | 0.370783 | ||||||||
\(705\) | −2.74388 | −0.103340 | ||||||||
\(706\) | −9.75060 | −0.366969 | ||||||||
\(707\) | −74.7007 | −2.80941 | ||||||||
\(708\) | 2.64712 | 0.0994850 | ||||||||
\(709\) | 44.0267 | 1.65346 | 0.826729 | − | 0.562600i | \(-0.190199\pi\) | ||||
0.826729 | + | 0.562600i | \(0.190199\pi\) | |||||||
\(710\) | −22.6628 | −0.850522 | ||||||||
\(711\) | −5.73850 | −0.215210 | ||||||||
\(712\) | −12.4214 | −0.465512 | ||||||||
\(713\) | −20.3401 | −0.761744 | ||||||||
\(714\) | −7.40641 | −0.277178 | ||||||||
\(715\) | −0.508790 | −0.0190277 | ||||||||
\(716\) | −4.19435 | −0.156750 | ||||||||
\(717\) | 1.91657 | 0.0715755 | ||||||||
\(718\) | 27.0280 | 1.00867 | ||||||||
\(719\) | −23.5998 | −0.880126 | −0.440063 | − | 0.897967i | \(-0.645044\pi\) | ||||
−0.440063 | + | 0.897967i | \(0.645044\pi\) | |||||||
\(720\) | 34.8546 | 1.29896 | ||||||||
\(721\) | −54.3194 | −2.02296 | ||||||||
\(722\) | 47.2775 | 1.75949 | ||||||||
\(723\) | −1.43388 | −0.0533267 | ||||||||
\(724\) | 93.6112 | 3.47903 | ||||||||
\(725\) | −3.30042 | −0.122574 | ||||||||
\(726\) | 0.204969 | 0.00760712 | ||||||||
\(727\) | −17.2165 | −0.638525 | −0.319262 | − | 0.947666i | \(-0.603435\pi\) | ||||
−0.319262 | + | 0.947666i | \(0.603435\pi\) | |||||||
\(728\) | −2.96850 | −0.110020 | ||||||||
\(729\) | −25.3014 | −0.937089 | ||||||||
\(730\) | 7.55628 | 0.279670 | ||||||||
\(731\) | 16.5713 | 0.612912 | ||||||||
\(732\) | −6.75080 | −0.249517 | ||||||||
\(733\) | 21.7761 | 0.804318 | 0.402159 | − | 0.915570i | \(-0.368260\pi\) | ||||
0.402159 | + | 0.915570i | \(0.368260\pi\) | |||||||
\(734\) | 14.6209 | 0.539666 | ||||||||
\(735\) | −2.31759 | −0.0854858 | ||||||||
\(736\) | −16.3067 | −0.601073 | ||||||||
\(737\) | 17.0835 | 0.629279 | ||||||||
\(738\) | 15.8796 | 0.584536 | ||||||||
\(739\) | 27.5149 | 1.01215 | 0.506076 | − | 0.862489i | \(-0.331095\pi\) | ||||
0.506076 | + | 0.862489i | \(0.331095\pi\) | |||||||
\(740\) | 63.7347 | 2.34293 | ||||||||
\(741\) | 0.0155868 | 0.000572595 0 | ||||||||
\(742\) | −92.2347 | −3.38604 | ||||||||
\(743\) | −46.5260 | −1.70687 | −0.853437 | − | 0.521197i | \(-0.825486\pi\) | ||||
−0.853437 | + | 0.521197i | \(0.825486\pi\) | |||||||
\(744\) | 11.3507 | 0.416137 | ||||||||
\(745\) | −0.791635 | −0.0290033 | ||||||||
\(746\) | 2.66848 | 0.0977000 | ||||||||
\(747\) | −32.0205 | −1.17157 | ||||||||
\(748\) | 60.5903 | 2.21540 | ||||||||
\(749\) | −24.2670 | −0.886695 | ||||||||
\(750\) | −5.22527 | −0.190800 | ||||||||
\(751\) | −11.4830 | −0.419022 | −0.209511 | − | 0.977806i | \(-0.567187\pi\) | ||||
−0.209511 | + | 0.977806i | \(0.567187\pi\) | |||||||
\(752\) | 87.9923 | 3.20875 | ||||||||
\(753\) | −2.49068 | −0.0907655 | ||||||||
\(754\) | −0.315327 | −0.0114835 | ||||||||
\(755\) | −6.27577 | −0.228399 | ||||||||
\(756\) | −19.7441 | −0.718086 | ||||||||
\(757\) | 23.0164 | 0.836546 | 0.418273 | − | 0.908321i | \(-0.362635\pi\) | ||||
0.418273 | + | 0.908321i | \(0.362635\pi\) | |||||||
\(758\) | −8.99888 | −0.326854 | ||||||||
\(759\) | 1.25210 | 0.0454483 | ||||||||
\(760\) | 7.78272 | 0.282309 | ||||||||
\(761\) | 8.76873 | 0.317866 | 0.158933 | − | 0.987289i | \(-0.449195\pi\) | ||||
0.158933 | + | 0.987289i | \(0.449195\pi\) | |||||||
\(762\) | −3.23300 | −0.117119 | ||||||||
\(763\) | 74.5287 | 2.69812 | ||||||||
\(764\) | 66.4390 | 2.40368 | ||||||||
\(765\) | 17.1362 | 0.619559 | ||||||||
\(766\) | −2.06625 | −0.0746566 | ||||||||
\(767\) | 0.350463 | 0.0126545 | ||||||||
\(768\) | −4.41636 | −0.159361 | ||||||||
\(769\) | −31.0232 | −1.11873 | −0.559363 | − | 0.828923i | \(-0.688954\pi\) | ||||
−0.559363 | + | 0.828923i | \(0.688954\pi\) | |||||||
\(770\) | 48.0874 | 1.73295 | ||||||||
\(771\) | 5.24487 | 0.188889 | ||||||||
\(772\) | −98.8350 | −3.55715 | ||||||||
\(773\) | −28.9616 | −1.04168 | −0.520838 | − | 0.853656i | \(-0.674380\pi\) | ||||
−0.520838 | + | 0.853656i | \(0.674380\pi\) | |||||||
\(774\) | 31.4573 | 1.13071 | ||||||||
\(775\) | 27.6817 | 0.994356 | ||||||||
\(776\) | −10.4139 | −0.373836 | ||||||||
\(777\) | −6.85489 | −0.245918 | ||||||||
\(778\) | 5.37118 | 0.192566 | ||||||||
\(779\) | 1.66386 | 0.0596139 | ||||||||
\(780\) | −0.129232 | −0.00462724 | ||||||||
\(781\) | −19.9404 | −0.713524 | ||||||||
\(782\) | −22.4363 | −0.802320 | ||||||||
\(783\) | −1.19170 | −0.0425880 | ||||||||
\(784\) | 74.3220 | 2.65436 | ||||||||
\(785\) | −15.6869 | −0.559890 | ||||||||
\(786\) | −3.26998 | −0.116636 | ||||||||
\(787\) | 14.7106 | 0.524378 | 0.262189 | − | 0.965017i | \(-0.415556\pi\) | ||||
0.262189 | + | 0.965017i | \(0.415556\pi\) | |||||||
\(788\) | −67.2887 | −2.39706 | ||||||||
\(789\) | 1.51994 | 0.0541114 | ||||||||
\(790\) | 7.13786 | 0.253954 | ||||||||
\(791\) | 11.0551 | 0.393072 | ||||||||
\(792\) | 65.3543 | 2.32226 | ||||||||
\(793\) | −0.893766 | −0.0317386 | ||||||||
\(794\) | −83.6441 | −2.96842 | ||||||||
\(795\) | −2.28157 | −0.0809189 | ||||||||
\(796\) | 60.6840 | 2.15089 | ||||||||
\(797\) | −51.7450 | −1.83290 | −0.916451 | − | 0.400146i | \(-0.868959\pi\) | ||||
−0.916451 | + | 0.400146i | \(0.868959\pi\) | |||||||
\(798\) | −1.47316 | −0.0521492 | ||||||||
\(799\) | 43.2611 | 1.53047 | ||||||||
\(800\) | 22.1924 | 0.784621 | ||||||||
\(801\) | −5.43995 | −0.192211 | ||||||||
\(802\) | −3.92824 | −0.138711 | ||||||||
\(803\) | 6.64856 | 0.234623 | ||||||||
\(804\) | 4.33918 | 0.153031 | ||||||||
\(805\) | −12.4365 | −0.438330 | ||||||||
\(806\) | 2.64475 | 0.0931574 | ||||||||
\(807\) | −4.09428 | −0.144126 | ||||||||
\(808\) | 126.281 | 4.44254 | ||||||||
\(809\) | −30.2174 | −1.06239 | −0.531194 | − | 0.847250i | \(-0.678257\pi\) | ||||
−0.531194 | + | 0.847250i | \(0.678257\pi\) | |||||||
\(810\) | 32.1780 | 1.13062 | ||||||||
\(811\) | −23.1150 | −0.811679 | −0.405839 | − | 0.913944i | \(-0.633021\pi\) | ||||
−0.405839 | + | 0.913944i | \(0.633021\pi\) | |||||||
\(812\) | 20.8149 | 0.730459 | ||||||||
\(813\) | 5.75841 | 0.201956 | ||||||||
\(814\) | 80.2927 | 2.81426 | ||||||||
\(815\) | 0.524238 | 0.0183632 | ||||||||
\(816\) | 5.87526 | 0.205675 | ||||||||
\(817\) | 3.29608 | 0.115315 | ||||||||
\(818\) | 47.1534 | 1.64868 | ||||||||
\(819\) | −1.30005 | −0.0454275 | ||||||||
\(820\) | −13.7952 | −0.481750 | ||||||||
\(821\) | 43.4539 | 1.51655 | 0.758276 | − | 0.651934i | \(-0.226042\pi\) | ||||
0.758276 | + | 0.651934i | \(0.226042\pi\) | |||||||
\(822\) | 1.80983 | 0.0631251 | ||||||||
\(823\) | 32.5375 | 1.13419 | 0.567093 | − | 0.823654i | \(-0.308068\pi\) | ||||
0.567093 | + | 0.823654i | \(0.308068\pi\) | |||||||
\(824\) | 91.8264 | 3.19892 | ||||||||
\(825\) | −1.70403 | −0.0593267 | ||||||||
\(826\) | −33.1234 | −1.15251 | ||||||||
\(827\) | 22.3875 | 0.778489 | 0.389245 | − | 0.921134i | \(-0.372736\pi\) | ||||
0.389245 | + | 0.921134i | \(0.372736\pi\) | |||||||
\(828\) | −29.7465 | −1.03376 | ||||||||
\(829\) | 18.1641 | 0.630866 | 0.315433 | − | 0.948948i | \(-0.397850\pi\) | ||||
0.315433 | + | 0.948948i | \(0.397850\pi\) | |||||||
\(830\) | 39.8288 | 1.38248 | ||||||||
\(831\) | −2.96662 | −0.102911 | ||||||||
\(832\) | 0.330830 | 0.0114695 | ||||||||
\(833\) | 36.5401 | 1.26604 | ||||||||
\(834\) | −6.01787 | −0.208382 | ||||||||
\(835\) | −9.94191 | −0.344054 | ||||||||
\(836\) | 12.0516 | 0.416813 | ||||||||
\(837\) | 9.99522 | 0.345485 | ||||||||
\(838\) | 10.5232 | 0.363519 | ||||||||
\(839\) | −1.39539 | −0.0481741 | −0.0240870 | − | 0.999710i | \(-0.507668\pi\) | ||||
−0.0240870 | + | 0.999710i | \(0.507668\pi\) | |||||||
\(840\) | 6.94015 | 0.239458 | ||||||||
\(841\) | −27.7437 | −0.956678 | ||||||||
\(842\) | 0.733090 | 0.0252640 | ||||||||
\(843\) | 1.94798 | 0.0670921 | ||||||||
\(844\) | −88.2789 | −3.03869 | ||||||||
\(845\) | 18.6209 | 0.640577 | ||||||||
\(846\) | 82.1225 | 2.82343 | ||||||||
\(847\) | −1.79130 | −0.0615500 | ||||||||
\(848\) | 73.1667 | 2.51255 | ||||||||
\(849\) | −0.894732 | −0.0307071 | ||||||||
\(850\) | 30.5344 | 1.04732 | ||||||||
\(851\) | −20.7656 | −0.711835 | ||||||||
\(852\) | −5.06483 | −0.173518 | ||||||||
\(853\) | 55.2005 | 1.89003 | 0.945014 | − | 0.327030i | \(-0.106048\pi\) | ||||
0.945014 | + | 0.327030i | \(0.106048\pi\) | |||||||
\(854\) | 84.4727 | 2.89060 | ||||||||
\(855\) | 3.40843 | 0.116566 | ||||||||
\(856\) | 41.0231 | 1.40214 | ||||||||
\(857\) | −29.8711 | −1.02038 | −0.510189 | − | 0.860062i | \(-0.670425\pi\) | ||||
−0.510189 | + | 0.860062i | \(0.670425\pi\) | |||||||
\(858\) | −0.162806 | −0.00555809 | ||||||||
\(859\) | 51.6157 | 1.76111 | 0.880553 | − | 0.473949i | \(-0.157172\pi\) | ||||
0.880553 | + | 0.473949i | \(0.157172\pi\) | |||||||
\(860\) | −27.3282 | −0.931884 | ||||||||
\(861\) | 1.48373 | 0.0505652 | ||||||||
\(862\) | −20.1566 | −0.686537 | ||||||||
\(863\) | 22.1500 | 0.753996 | 0.376998 | − | 0.926214i | \(-0.376956\pi\) | ||||
0.376998 | + | 0.926214i | \(0.376956\pi\) | |||||||
\(864\) | 8.01317 | 0.272614 | ||||||||
\(865\) | −23.4233 | −0.796415 | ||||||||
\(866\) | 49.5231 | 1.68286 | ||||||||
\(867\) | −0.139877 | −0.00475046 | ||||||||
\(868\) | −174.581 | −5.92567 | ||||||||
\(869\) | 6.28041 | 0.213048 | ||||||||
\(870\) | 0.737213 | 0.0249939 | ||||||||
\(871\) | 0.574481 | 0.0194656 | ||||||||
\(872\) | −125.990 | −4.26656 | ||||||||
\(873\) | −4.56075 | −0.154358 | ||||||||
\(874\) | −4.46265 | −0.150951 | ||||||||
\(875\) | 45.6657 | 1.54378 | ||||||||
\(876\) | 1.68872 | 0.0570567 | ||||||||
\(877\) | 23.4426 | 0.791599 | 0.395800 | − | 0.918337i | \(-0.370468\pi\) | ||||
0.395800 | + | 0.918337i | \(0.370468\pi\) | |||||||
\(878\) | −69.5675 | −2.34779 | ||||||||
\(879\) | −4.09051 | −0.137970 | ||||||||
\(880\) | −38.1461 | −1.28591 | ||||||||
\(881\) | 46.4242 | 1.56407 | 0.782035 | − | 0.623235i | \(-0.214182\pi\) | ||||
0.782035 | + | 0.623235i | \(0.214182\pi\) | |||||||
\(882\) | 69.3641 | 2.33561 | ||||||||
\(883\) | −35.8348 | −1.20594 | −0.602968 | − | 0.797765i | \(-0.706015\pi\) | ||||
−0.602968 | + | 0.797765i | \(0.706015\pi\) | |||||||
\(884\) | 2.03752 | 0.0685292 | ||||||||
\(885\) | −0.819359 | −0.0275425 | ||||||||
\(886\) | −65.2827 | −2.19322 | ||||||||
\(887\) | 51.3009 | 1.72252 | 0.861259 | − | 0.508167i | \(-0.169677\pi\) | ||||
0.861259 | + | 0.508167i | \(0.169677\pi\) | |||||||
\(888\) | 11.5881 | 0.388872 | ||||||||
\(889\) | 28.2544 | 0.947623 | ||||||||
\(890\) | 6.76651 | 0.226814 | ||||||||
\(891\) | 28.3126 | 0.948507 | ||||||||
\(892\) | 6.90266 | 0.231118 | ||||||||
\(893\) | 8.60476 | 0.287947 | ||||||||
\(894\) | −0.253312 | −0.00847202 | ||||||||
\(895\) | 1.29827 | 0.0433964 | ||||||||
\(896\) | 29.1666 | 0.974389 | ||||||||
\(897\) | 0.0421053 | 0.00140586 | ||||||||
\(898\) | 41.4564 | 1.38342 | ||||||||
\(899\) | −10.5373 | −0.351438 | ||||||||
\(900\) | 40.4831 | 1.34944 | ||||||||
\(901\) | 35.9721 | 1.19841 | ||||||||
\(902\) | −17.3792 | −0.578663 | ||||||||
\(903\) | 2.93924 | 0.0978119 | ||||||||
\(904\) | −18.6885 | −0.621569 | ||||||||
\(905\) | −28.9753 | −0.963172 | ||||||||
\(906\) | −2.00816 | −0.0667165 | ||||||||
\(907\) | −7.91590 | −0.262843 | −0.131422 | − | 0.991327i | \(-0.541954\pi\) | ||||
−0.131422 | + | 0.991327i | \(0.541954\pi\) | |||||||
\(908\) | −11.1694 | −0.370668 | ||||||||
\(909\) | 55.3045 | 1.83434 | ||||||||
\(910\) | 1.61708 | 0.0536055 | ||||||||
\(911\) | 46.2018 | 1.53073 | 0.765367 | − | 0.643594i | \(-0.222558\pi\) | ||||
0.765367 | + | 0.643594i | \(0.222558\pi\) | |||||||
\(912\) | 1.16861 | 0.0386964 | ||||||||
\(913\) | 35.0443 | 1.15980 | ||||||||
\(914\) | 46.4557 | 1.53662 | ||||||||
\(915\) | 2.08956 | 0.0690789 | ||||||||
\(916\) | 60.9369 | 2.01341 | ||||||||
\(917\) | 28.5776 | 0.943715 | ||||||||
\(918\) | 11.0253 | 0.363888 | ||||||||
\(919\) | 50.7856 | 1.67526 | 0.837632 | − | 0.546235i | \(-0.183939\pi\) | ||||
0.837632 | + | 0.546235i | \(0.183939\pi\) | |||||||
\(920\) | 21.0238 | 0.693136 | ||||||||
\(921\) | −1.21887 | −0.0401630 | ||||||||
\(922\) | 75.9014 | 2.49968 | ||||||||
\(923\) | −0.670553 | −0.0220715 | ||||||||
\(924\) | 10.7469 | 0.353546 | ||||||||
\(925\) | 28.2607 | 0.929206 | ||||||||
\(926\) | −79.7436 | −2.62054 | ||||||||
\(927\) | 40.2153 | 1.32084 | ||||||||
\(928\) | −8.44775 | −0.277311 | ||||||||
\(929\) | 16.4618 | 0.540093 | 0.270046 | − | 0.962847i | \(-0.412961\pi\) | ||||
0.270046 | + | 0.962847i | \(0.412961\pi\) | |||||||
\(930\) | −6.18325 | −0.202757 | ||||||||
\(931\) | 7.26794 | 0.238197 | ||||||||
\(932\) | −1.66630 | −0.0545816 | ||||||||
\(933\) | 4.68906 | 0.153513 | ||||||||
\(934\) | 37.4786 | 1.22634 | ||||||||
\(935\) | −18.7544 | −0.613335 | ||||||||
\(936\) | 2.19772 | 0.0718349 | ||||||||
\(937\) | 13.0454 | 0.426173 | 0.213087 | − | 0.977033i | \(-0.431648\pi\) | ||||
0.213087 | + | 0.977033i | \(0.431648\pi\) | |||||||
\(938\) | −54.2961 | −1.77283 | ||||||||
\(939\) | 3.97202 | 0.129622 | ||||||||
\(940\) | −71.3431 | −2.32695 | ||||||||
\(941\) | −10.2707 | −0.334814 | −0.167407 | − | 0.985888i | \(-0.553539\pi\) | ||||
−0.167407 | + | 0.985888i | \(0.553539\pi\) | |||||||
\(942\) | −5.01959 | −0.163547 | ||||||||
\(943\) | 4.49466 | 0.146366 | ||||||||
\(944\) | 26.2757 | 0.855201 | ||||||||
\(945\) | 6.11136 | 0.198802 | ||||||||
\(946\) | −34.4279 | −1.11935 | ||||||||
\(947\) | 52.7465 | 1.71403 | 0.857016 | − | 0.515291i | \(-0.172316\pi\) | ||||
0.857016 | + | 0.515291i | \(0.172316\pi\) | |||||||
\(948\) | 1.59521 | 0.0518101 | ||||||||
\(949\) | 0.223577 | 0.00725761 | ||||||||
\(950\) | 6.07339 | 0.197047 | ||||||||
\(951\) | −3.40642 | −0.110461 | ||||||||
\(952\) | −109.421 | −3.54636 | ||||||||
\(953\) | 21.6341 | 0.700796 | 0.350398 | − | 0.936601i | \(-0.386046\pi\) | ||||
0.350398 | + | 0.936601i | \(0.386046\pi\) | |||||||
\(954\) | 68.2858 | 2.21083 | ||||||||
\(955\) | −20.5647 | −0.665460 | ||||||||
\(956\) | 49.8323 | 1.61169 | ||||||||
\(957\) | 0.648654 | 0.0209680 | ||||||||
\(958\) | −76.5389 | −2.47286 | ||||||||
\(959\) | −15.8168 | −0.510752 | ||||||||
\(960\) | −0.773459 | −0.0249633 | ||||||||
\(961\) | 57.3796 | 1.85096 | ||||||||
\(962\) | 2.70007 | 0.0870537 | ||||||||
\(963\) | 17.9660 | 0.578947 | ||||||||
\(964\) | −37.2821 | −1.20078 | ||||||||
\(965\) | 30.5922 | 0.984799 | ||||||||
\(966\) | −3.97951 | −0.128039 | ||||||||
\(967\) | −31.9608 | −1.02779 | −0.513895 | − | 0.857853i | \(-0.671798\pi\) | ||||
−0.513895 | + | 0.857853i | \(0.671798\pi\) | |||||||
\(968\) | 3.02818 | 0.0973295 | ||||||||
\(969\) | 0.574541 | 0.0184569 | ||||||||
\(970\) | 5.67291 | 0.182146 | ||||||||
\(971\) | 56.7996 | 1.82279 | 0.911393 | − | 0.411536i | \(-0.135008\pi\) | ||||
0.911393 | + | 0.411536i | \(0.135008\pi\) | |||||||
\(972\) | 21.9651 | 0.704532 | ||||||||
\(973\) | 52.5925 | 1.68604 | ||||||||
\(974\) | −71.7975 | −2.30054 | ||||||||
\(975\) | −0.0573028 | −0.00183516 | ||||||||
\(976\) | −67.0094 | −2.14492 | ||||||||
\(977\) | 17.5072 | 0.560105 | 0.280053 | − | 0.959985i | \(-0.409648\pi\) | ||||
0.280053 | + | 0.959985i | \(0.409648\pi\) | |||||||
\(978\) | 0.167748 | 0.00536401 | ||||||||
\(979\) | 5.95367 | 0.190280 | ||||||||
\(980\) | −60.2593 | −1.92491 | ||||||||
\(981\) | −55.1772 | −1.76167 | ||||||||
\(982\) | 19.4228 | 0.619808 | ||||||||
\(983\) | 9.56460 | 0.305063 | 0.152532 | − | 0.988299i | \(-0.451257\pi\) | ||||
0.152532 | + | 0.988299i | \(0.451257\pi\) | |||||||
\(984\) | −2.50822 | −0.0799592 | ||||||||
\(985\) | 20.8277 | 0.663627 | ||||||||
\(986\) | −11.6232 | −0.370158 | ||||||||
\(987\) | 7.67320 | 0.244240 | ||||||||
\(988\) | 0.405269 | 0.0128933 | ||||||||
\(989\) | 8.90388 | 0.283127 | ||||||||
\(990\) | −35.6014 | −1.13149 | ||||||||
\(991\) | −23.3498 | −0.741732 | −0.370866 | − | 0.928686i | \(-0.620939\pi\) | ||||
−0.370866 | + | 0.928686i | \(0.620939\pi\) | |||||||
\(992\) | 70.8540 | 2.24962 | ||||||||
\(993\) | 5.49022 | 0.174227 | ||||||||
\(994\) | 63.3761 | 2.01017 | ||||||||
\(995\) | −18.7834 | −0.595474 | ||||||||
\(996\) | 8.90119 | 0.282045 | ||||||||
\(997\) | −38.5827 | −1.22193 | −0.610964 | − | 0.791659i | \(-0.709218\pi\) | ||||
−0.610964 | + | 0.791659i | \(0.709218\pi\) | |||||||
\(998\) | 6.31127 | 0.199780 | ||||||||
\(999\) | 10.2043 | 0.322849 |
(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 | 8011.2.a.b.1.17 | ✓ | 358 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8011.2.a.b.1.17 | ✓ | 358 | 1.1 | even | 1 | trivial |