Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, 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("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.46237 | −1.74116 | −0.870578 | − | 0.492030i | \(-0.836255\pi\) | ||||
−0.870578 | + | 0.492030i | \(0.836255\pi\) | |||||||
\(3\) | −0.199276 | −0.115052 | −0.0575261 | − | 0.998344i | \(-0.518321\pi\) | ||||
−0.0575261 | + | 0.998344i | \(0.518321\pi\) | |||||||
\(4\) | 4.06325 | 2.03163 | ||||||||
\(5\) | −0.688498 | −0.307906 | −0.153953 | − | 0.988078i | \(-0.549200\pi\) | ||||
−0.153953 | + | 0.988078i | \(0.549200\pi\) | |||||||
\(6\) | 0.490692 | 0.200324 | ||||||||
\(7\) | 0.363231 | 0.137288 | 0.0686441 | − | 0.997641i | \(-0.478133\pi\) | ||||
0.0686441 | + | 0.997641i | \(0.478133\pi\) | |||||||
\(8\) | −5.08049 | −1.79622 | ||||||||
\(9\) | −2.96029 | −0.986763 | ||||||||
\(10\) | 1.69534 | 0.536112 | ||||||||
\(11\) | 0.608305 | 0.183411 | 0.0917054 | − | 0.995786i | \(-0.470768\pi\) | ||||
0.0917054 | + | 0.995786i | \(0.470768\pi\) | |||||||
\(12\) | −0.809710 | −0.233743 | ||||||||
\(13\) | 1.23967 | 0.343821 | 0.171911 | − | 0.985113i | \(-0.445006\pi\) | ||||
0.171911 | + | 0.985113i | \(0.445006\pi\) | |||||||
\(14\) | −0.894407 | −0.239040 | ||||||||
\(15\) | 0.137201 | 0.0354253 | ||||||||
\(16\) | 4.38352 | 1.09588 | ||||||||
\(17\) | 0.714168 | 0.173211 | 0.0866056 | − | 0.996243i | \(-0.472398\pi\) | ||||
0.0866056 | + | 0.996243i | \(0.472398\pi\) | |||||||
\(18\) | 7.28932 | 1.71811 | ||||||||
\(19\) | −3.65294 | −0.838042 | −0.419021 | − | 0.907976i | \(-0.637627\pi\) | ||||
−0.419021 | + | 0.907976i | \(0.637627\pi\) | |||||||
\(20\) | −2.79754 | −0.625550 | ||||||||
\(21\) | −0.0723833 | −0.0157953 | ||||||||
\(22\) | −1.49787 | −0.319347 | ||||||||
\(23\) | −8.98401 | −1.87330 | −0.936648 | − | 0.350273i | \(-0.886089\pi\) | ||||
−0.936648 | + | 0.350273i | \(0.886089\pi\) | |||||||
\(24\) | 1.01242 | 0.206660 | ||||||||
\(25\) | −4.52597 | −0.905194 | ||||||||
\(26\) | −3.05251 | −0.598647 | ||||||||
\(27\) | 1.18774 | 0.228582 | ||||||||
\(28\) | 1.47590 | 0.278919 | ||||||||
\(29\) | −4.08453 | −0.758479 | −0.379239 | − | 0.925299i | \(-0.623814\pi\) | ||||
−0.379239 | + | 0.925299i | \(0.623814\pi\) | |||||||
\(30\) | −0.337840 | −0.0616809 | ||||||||
\(31\) | −2.25338 | −0.404719 | −0.202359 | − | 0.979311i | \(-0.564861\pi\) | ||||
−0.202359 | + | 0.979311i | \(0.564861\pi\) | |||||||
\(32\) | −0.632868 | −0.111876 | ||||||||
\(33\) | −0.121221 | −0.0211018 | ||||||||
\(34\) | −1.75854 | −0.301588 | ||||||||
\(35\) | −0.250084 | −0.0422719 | ||||||||
\(36\) | −12.0284 | −2.00473 | ||||||||
\(37\) | −1.99307 | −0.327659 | −0.163829 | − | 0.986489i | \(-0.552385\pi\) | ||||
−0.163829 | + | 0.986489i | \(0.552385\pi\) | |||||||
\(38\) | 8.99489 | 1.45916 | ||||||||
\(39\) | −0.247036 | −0.0395574 | ||||||||
\(40\) | 3.49791 | 0.553068 | ||||||||
\(41\) | 1.90939 | 0.298196 | 0.149098 | − | 0.988822i | \(-0.452363\pi\) | ||||
0.149098 | + | 0.988822i | \(0.452363\pi\) | |||||||
\(42\) | 0.178234 | 0.0275021 | ||||||||
\(43\) | −9.31067 | −1.41986 | −0.709932 | − | 0.704270i | \(-0.751274\pi\) | ||||
−0.709932 | + | 0.704270i | \(0.751274\pi\) | |||||||
\(44\) | 2.47170 | 0.372622 | ||||||||
\(45\) | 2.03815 | 0.303830 | ||||||||
\(46\) | 22.1219 | 3.26170 | ||||||||
\(47\) | 10.6828 | 1.55825 | 0.779126 | − | 0.626867i | \(-0.215663\pi\) | ||||
0.779126 | + | 0.626867i | \(0.215663\pi\) | |||||||
\(48\) | −0.873533 | −0.126084 | ||||||||
\(49\) | −6.86806 | −0.981152 | ||||||||
\(50\) | 11.1446 | 1.57608 | ||||||||
\(51\) | −0.142317 | −0.0199283 | ||||||||
\(52\) | 5.03708 | 0.698517 | ||||||||
\(53\) | 7.83367 | 1.07604 | 0.538019 | − | 0.842933i | \(-0.319173\pi\) | ||||
0.538019 | + | 0.842933i | \(0.319173\pi\) | |||||||
\(54\) | −2.92466 | −0.397996 | ||||||||
\(55\) | −0.418817 | −0.0564732 | ||||||||
\(56\) | −1.84539 | −0.246601 | ||||||||
\(57\) | 0.727945 | 0.0964187 | ||||||||
\(58\) | 10.0576 | 1.32063 | ||||||||
\(59\) | 2.96694 | 0.386262 | 0.193131 | − | 0.981173i | \(-0.438136\pi\) | ||||
0.193131 | + | 0.981173i | \(0.438136\pi\) | |||||||
\(60\) | 0.557484 | 0.0719709 | ||||||||
\(61\) | 4.72291 | 0.604707 | 0.302353 | − | 0.953196i | \(-0.402228\pi\) | ||||
0.302353 | + | 0.953196i | \(0.402228\pi\) | |||||||
\(62\) | 5.54865 | 0.704679 | ||||||||
\(63\) | −1.07527 | −0.135471 | ||||||||
\(64\) | −7.20869 | −0.901087 | ||||||||
\(65\) | −0.853508 | −0.105865 | ||||||||
\(66\) | 0.298490 | 0.0367416 | ||||||||
\(67\) | −5.88429 | −0.718880 | −0.359440 | − | 0.933168i | \(-0.617032\pi\) | ||||
−0.359440 | + | 0.933168i | \(0.617032\pi\) | |||||||
\(68\) | 2.90185 | 0.351901 | ||||||||
\(69\) | 1.79030 | 0.215527 | ||||||||
\(70\) | 0.615798 | 0.0736019 | ||||||||
\(71\) | −5.19133 | −0.616098 | −0.308049 | − | 0.951370i | \(-0.599676\pi\) | ||||
−0.308049 | + | 0.951370i | \(0.599676\pi\) | |||||||
\(72\) | 15.0397 | 1.77245 | ||||||||
\(73\) | −16.0982 | −1.88415 | −0.942076 | − | 0.335398i | \(-0.891129\pi\) | ||||
−0.942076 | + | 0.335398i | \(0.891129\pi\) | |||||||
\(74\) | 4.90767 | 0.570505 | ||||||||
\(75\) | 0.901919 | 0.104145 | ||||||||
\(76\) | −14.8428 | −1.70259 | ||||||||
\(77\) | 0.220955 | 0.0251802 | ||||||||
\(78\) | 0.608294 | 0.0688757 | ||||||||
\(79\) | 14.5062 | 1.63208 | 0.816038 | − | 0.577998i | \(-0.196166\pi\) | ||||
0.816038 | + | 0.577998i | \(0.196166\pi\) | |||||||
\(80\) | −3.01805 | −0.337428 | ||||||||
\(81\) | 8.64418 | 0.960464 | ||||||||
\(82\) | −4.70161 | −0.519206 | ||||||||
\(83\) | −12.9259 | −1.41881 | −0.709404 | − | 0.704803i | \(-0.751036\pi\) | ||||
−0.709404 | + | 0.704803i | \(0.751036\pi\) | |||||||
\(84\) | −0.294112 | −0.0320902 | ||||||||
\(85\) | −0.491704 | −0.0533328 | ||||||||
\(86\) | 22.9263 | 2.47221 | ||||||||
\(87\) | 0.813951 | 0.0872647 | ||||||||
\(88\) | −3.09049 | −0.329447 | ||||||||
\(89\) | 11.5823 | 1.22772 | 0.613859 | − | 0.789416i | \(-0.289616\pi\) | ||||
0.613859 | + | 0.789416i | \(0.289616\pi\) | |||||||
\(90\) | −5.01868 | −0.529016 | ||||||||
\(91\) | 0.450285 | 0.0472027 | ||||||||
\(92\) | −36.5043 | −3.80584 | ||||||||
\(93\) | 0.449045 | 0.0465638 | ||||||||
\(94\) | −26.3051 | −2.71316 | ||||||||
\(95\) | 2.51504 | 0.258038 | ||||||||
\(96\) | 0.126116 | 0.0128716 | ||||||||
\(97\) | −13.6450 | −1.38544 | −0.692722 | − | 0.721204i | \(-0.743589\pi\) | ||||
−0.692722 | + | 0.721204i | \(0.743589\pi\) | |||||||
\(98\) | 16.9117 | 1.70834 | ||||||||
\(99\) | −1.80076 | −0.180983 | ||||||||
\(100\) | −18.3902 | −1.83902 | ||||||||
\(101\) | 8.25853 | 0.821755 | 0.410877 | − | 0.911691i | \(-0.365222\pi\) | ||||
0.410877 | + | 0.911691i | \(0.365222\pi\) | |||||||
\(102\) | 0.350436 | 0.0346984 | ||||||||
\(103\) | 11.8042 | 1.16310 | 0.581551 | − | 0.813510i | \(-0.302446\pi\) | ||||
0.581551 | + | 0.813510i | \(0.302446\pi\) | |||||||
\(104\) | −6.29811 | −0.617580 | ||||||||
\(105\) | 0.0498358 | 0.00486347 | ||||||||
\(106\) | −19.2894 | −1.87355 | ||||||||
\(107\) | 5.57492 | 0.538948 | 0.269474 | − | 0.963008i | \(-0.413150\pi\) | ||||
0.269474 | + | 0.963008i | \(0.413150\pi\) | |||||||
\(108\) | 4.82611 | 0.464392 | ||||||||
\(109\) | −10.2275 | −0.979618 | −0.489809 | − | 0.871830i | \(-0.662933\pi\) | ||||
−0.489809 | + | 0.871830i | \(0.662933\pi\) | |||||||
\(110\) | 1.03128 | 0.0983288 | ||||||||
\(111\) | 0.397172 | 0.0376979 | ||||||||
\(112\) | 1.59223 | 0.150452 | ||||||||
\(113\) | 0.255742 | 0.0240581 | 0.0120291 | − | 0.999928i | \(-0.496171\pi\) | ||||
0.0120291 | + | 0.999928i | \(0.496171\pi\) | |||||||
\(114\) | −1.79247 | −0.167880 | ||||||||
\(115\) | 6.18548 | 0.576799 | ||||||||
\(116\) | −16.5965 | −1.54095 | ||||||||
\(117\) | −3.66977 | −0.339270 | ||||||||
\(118\) | −7.30569 | −0.672543 | ||||||||
\(119\) | 0.259408 | 0.0237799 | ||||||||
\(120\) | −0.697051 | −0.0636317 | ||||||||
\(121\) | −10.6300 | −0.966360 | ||||||||
\(122\) | −11.6295 | −1.05289 | ||||||||
\(123\) | −0.380495 | −0.0343081 | ||||||||
\(124\) | −9.15605 | −0.822238 | ||||||||
\(125\) | 6.55862 | 0.586620 | ||||||||
\(126\) | 2.64770 | 0.235876 | ||||||||
\(127\) | 14.6336 | 1.29852 | 0.649261 | − | 0.760566i | \(-0.275078\pi\) | ||||
0.649261 | + | 0.760566i | \(0.275078\pi\) | |||||||
\(128\) | 19.0162 | 1.68081 | ||||||||
\(129\) | 1.85540 | 0.163359 | ||||||||
\(130\) | 2.10165 | 0.184327 | ||||||||
\(131\) | 2.22423 | 0.194331 | 0.0971657 | − | 0.995268i | \(-0.469022\pi\) | ||||
0.0971657 | + | 0.995268i | \(0.469022\pi\) | |||||||
\(132\) | −0.492551 | −0.0428710 | ||||||||
\(133\) | −1.32686 | −0.115053 | ||||||||
\(134\) | 14.4893 | 1.25168 | ||||||||
\(135\) | −0.817760 | −0.0703816 | ||||||||
\(136\) | −3.62832 | −0.311126 | ||||||||
\(137\) | 3.75673 | 0.320959 | 0.160479 | − | 0.987039i | \(-0.448696\pi\) | ||||
0.160479 | + | 0.987039i | \(0.448696\pi\) | |||||||
\(138\) | −4.40838 | −0.375266 | ||||||||
\(139\) | 0.575436 | 0.0488079 | 0.0244039 | − | 0.999702i | \(-0.492231\pi\) | ||||
0.0244039 | + | 0.999702i | \(0.492231\pi\) | |||||||
\(140\) | −1.01615 | −0.0858807 | ||||||||
\(141\) | −2.12884 | −0.179280 | ||||||||
\(142\) | 12.7830 | 1.07272 | ||||||||
\(143\) | 0.754094 | 0.0630605 | ||||||||
\(144\) | −12.9765 | −1.08137 | ||||||||
\(145\) | 2.81219 | 0.233540 | ||||||||
\(146\) | 39.6397 | 3.28061 | ||||||||
\(147\) | 1.36864 | 0.112884 | ||||||||
\(148\) | −8.09835 | −0.665680 | ||||||||
\(149\) | 8.71682 | 0.714109 | 0.357055 | − | 0.934083i | \(-0.383781\pi\) | ||||
0.357055 | + | 0.934083i | \(0.383781\pi\) | |||||||
\(150\) | −2.22086 | −0.181332 | ||||||||
\(151\) | 1.59710 | 0.129970 | 0.0649851 | − | 0.997886i | \(-0.479300\pi\) | ||||
0.0649851 | + | 0.997886i | \(0.479300\pi\) | |||||||
\(152\) | 18.5587 | 1.50531 | ||||||||
\(153\) | −2.11414 | −0.170918 | ||||||||
\(154\) | −0.544072 | −0.0438426 | ||||||||
\(155\) | 1.55145 | 0.124615 | ||||||||
\(156\) | −1.00377 | −0.0803659 | ||||||||
\(157\) | 9.73833 | 0.777204 | 0.388602 | − | 0.921406i | \(-0.372958\pi\) | ||||
0.388602 | + | 0.921406i | \(0.372958\pi\) | |||||||
\(158\) | −35.7196 | −2.84170 | ||||||||
\(159\) | −1.56107 | −0.123801 | ||||||||
\(160\) | 0.435729 | 0.0344474 | ||||||||
\(161\) | −3.26327 | −0.257182 | ||||||||
\(162\) | −21.2851 | −1.67232 | ||||||||
\(163\) | 6.99321 | 0.547751 | 0.273875 | − | 0.961765i | \(-0.411694\pi\) | ||||
0.273875 | + | 0.961765i | \(0.411694\pi\) | |||||||
\(164\) | 7.75832 | 0.605823 | ||||||||
\(165\) | 0.0834603 | 0.00649738 | ||||||||
\(166\) | 31.8284 | 2.47037 | ||||||||
\(167\) | −1.83769 | −0.142205 | −0.0711025 | − | 0.997469i | \(-0.522652\pi\) | ||||
−0.0711025 | + | 0.997469i | \(0.522652\pi\) | |||||||
\(168\) | 0.367743 | 0.0283720 | ||||||||
\(169\) | −11.4632 | −0.881787 | ||||||||
\(170\) | 1.21076 | 0.0928607 | ||||||||
\(171\) | 10.8138 | 0.826949 | ||||||||
\(172\) | −37.8316 | −2.88463 | ||||||||
\(173\) | 13.0373 | 0.991204 | 0.495602 | − | 0.868550i | \(-0.334948\pi\) | ||||
0.495602 | + | 0.868550i | \(0.334948\pi\) | |||||||
\(174\) | −2.00425 | −0.151942 | ||||||||
\(175\) | −1.64397 | −0.124273 | ||||||||
\(176\) | 2.66652 | 0.200996 | ||||||||
\(177\) | −0.591240 | −0.0444403 | ||||||||
\(178\) | −28.5198 | −2.13765 | ||||||||
\(179\) | −12.8342 | −0.959269 | −0.479635 | − | 0.877468i | \(-0.659231\pi\) | ||||
−0.479635 | + | 0.877468i | \(0.659231\pi\) | |||||||
\(180\) | 8.28154 | 0.617269 | ||||||||
\(181\) | 8.53462 | 0.634373 | 0.317187 | − | 0.948363i | \(-0.397262\pi\) | ||||
0.317187 | + | 0.948363i | \(0.397262\pi\) | |||||||
\(182\) | −1.10877 | −0.0821872 | ||||||||
\(183\) | −0.941164 | −0.0695729 | ||||||||
\(184\) | 45.6432 | 3.36486 | ||||||||
\(185\) | 1.37223 | 0.100888 | ||||||||
\(186\) | −1.10571 | −0.0810749 | ||||||||
\(187\) | 0.434432 | 0.0317688 | ||||||||
\(188\) | 43.4071 | 3.16579 | ||||||||
\(189\) | 0.431425 | 0.0313816 | ||||||||
\(190\) | −6.19297 | −0.449285 | ||||||||
\(191\) | 13.3780 | 0.968000 | 0.484000 | − | 0.875068i | \(-0.339184\pi\) | ||||
0.484000 | + | 0.875068i | \(0.339184\pi\) | |||||||
\(192\) | 1.43652 | 0.103672 | ||||||||
\(193\) | 17.5520 | 1.26342 | 0.631711 | − | 0.775204i | \(-0.282353\pi\) | ||||
0.631711 | + | 0.775204i | \(0.282353\pi\) | |||||||
\(194\) | 33.5991 | 2.41228 | ||||||||
\(195\) | 0.170084 | 0.0121800 | ||||||||
\(196\) | −27.9067 | −1.99333 | ||||||||
\(197\) | −4.38499 | −0.312417 | −0.156209 | − | 0.987724i | \(-0.549927\pi\) | ||||
−0.156209 | + | 0.987724i | \(0.549927\pi\) | |||||||
\(198\) | 4.43413 | 0.315120 | ||||||||
\(199\) | −3.34431 | −0.237072 | −0.118536 | − | 0.992950i | \(-0.537820\pi\) | ||||
−0.118536 | + | 0.992950i | \(0.537820\pi\) | |||||||
\(200\) | 22.9941 | 1.62593 | ||||||||
\(201\) | 1.17260 | 0.0827088 | ||||||||
\(202\) | −20.3355 | −1.43080 | ||||||||
\(203\) | −1.48363 | −0.104130 | ||||||||
\(204\) | −0.578270 | −0.0404870 | ||||||||
\(205\) | −1.31461 | −0.0918162 | ||||||||
\(206\) | −29.0663 | −2.02514 | ||||||||
\(207\) | 26.5953 | 1.84850 | ||||||||
\(208\) | 5.43410 | 0.376787 | ||||||||
\(209\) | −2.22210 | −0.153706 | ||||||||
\(210\) | −0.122714 | −0.00846807 | ||||||||
\(211\) | −21.5889 | −1.48624 | −0.743121 | − | 0.669157i | \(-0.766655\pi\) | ||||
−0.743121 | + | 0.669157i | \(0.766655\pi\) | |||||||
\(212\) | 31.8302 | 2.18611 | ||||||||
\(213\) | 1.03451 | 0.0708835 | ||||||||
\(214\) | −13.7275 | −0.938393 | ||||||||
\(215\) | 6.41038 | 0.437185 | ||||||||
\(216\) | −6.03432 | −0.410584 | ||||||||
\(217\) | −0.818497 | −0.0555632 | ||||||||
\(218\) | 25.1839 | 1.70567 | ||||||||
\(219\) | 3.20799 | 0.216776 | ||||||||
\(220\) | −1.70176 | −0.114733 | ||||||||
\(221\) | 0.885330 | 0.0595537 | ||||||||
\(222\) | −0.977983 | −0.0656379 | ||||||||
\(223\) | 12.1800 | 0.815636 | 0.407818 | − | 0.913063i | \(-0.366290\pi\) | ||||
0.407818 | + | 0.913063i | \(0.366290\pi\) | |||||||
\(224\) | −0.229877 | −0.0153593 | ||||||||
\(225\) | 13.3982 | 0.893212 | ||||||||
\(226\) | −0.629730 | −0.0418890 | ||||||||
\(227\) | −16.3201 | −1.08321 | −0.541603 | − | 0.840635i | \(-0.682182\pi\) | ||||
−0.541603 | + | 0.840635i | \(0.682182\pi\) | |||||||
\(228\) | 2.95783 | 0.195887 | ||||||||
\(229\) | −1.05865 | −0.0699574 | −0.0349787 | − | 0.999388i | \(-0.511136\pi\) | ||||
−0.0349787 | + | 0.999388i | \(0.511136\pi\) | |||||||
\(230\) | −15.2309 | −1.00430 | ||||||||
\(231\) | −0.0440311 | −0.00289703 | ||||||||
\(232\) | 20.7514 | 1.36240 | ||||||||
\(233\) | −18.7423 | −1.22785 | −0.613923 | − | 0.789366i | \(-0.710410\pi\) | ||||
−0.613923 | + | 0.789366i | \(0.710410\pi\) | |||||||
\(234\) | 9.03632 | 0.590723 | ||||||||
\(235\) | −7.35512 | −0.479795 | ||||||||
\(236\) | 12.0554 | 0.784741 | ||||||||
\(237\) | −2.89075 | −0.187774 | ||||||||
\(238\) | −0.638757 | −0.0414045 | ||||||||
\(239\) | −8.37904 | −0.541995 | −0.270997 | − | 0.962580i | \(-0.587354\pi\) | ||||
−0.270997 | + | 0.962580i | \(0.587354\pi\) | |||||||
\(240\) | 0.601426 | 0.0388219 | ||||||||
\(241\) | −7.94408 | −0.511723 | −0.255862 | − | 0.966713i | \(-0.582359\pi\) | ||||
−0.255862 | + | 0.966713i | \(0.582359\pi\) | |||||||
\(242\) | 26.1749 | 1.68259 | ||||||||
\(243\) | −5.28581 | −0.339085 | ||||||||
\(244\) | 19.1904 | 1.22854 | ||||||||
\(245\) | 4.72865 | 0.302102 | ||||||||
\(246\) | 0.936919 | 0.0597358 | ||||||||
\(247\) | −4.52843 | −0.288137 | ||||||||
\(248\) | 11.4483 | 0.726966 | ||||||||
\(249\) | 2.57584 | 0.163237 | ||||||||
\(250\) | −16.1497 | −1.02140 | ||||||||
\(251\) | 15.6797 | 0.989693 | 0.494847 | − | 0.868980i | \(-0.335224\pi\) | ||||
0.494847 | + | 0.868980i | \(0.335224\pi\) | |||||||
\(252\) | −4.36909 | −0.275227 | ||||||||
\(253\) | −5.46501 | −0.343583 | ||||||||
\(254\) | −36.0333 | −2.26093 | ||||||||
\(255\) | 0.0979849 | 0.00613605 | ||||||||
\(256\) | −32.4075 | −2.02547 | ||||||||
\(257\) | −2.31076 | −0.144141 | −0.0720707 | − | 0.997400i | \(-0.522961\pi\) | ||||
−0.0720707 | + | 0.997400i | \(0.522961\pi\) | |||||||
\(258\) | −4.56867 | −0.284433 | ||||||||
\(259\) | −0.723944 | −0.0449837 | ||||||||
\(260\) | −3.46802 | −0.215077 | ||||||||
\(261\) | 12.0914 | 0.748439 | ||||||||
\(262\) | −5.47686 | −0.338362 | ||||||||
\(263\) | 0.559168 | 0.0344798 | 0.0172399 | − | 0.999851i | \(-0.494512\pi\) | ||||
0.0172399 | + | 0.999851i | \(0.494512\pi\) | |||||||
\(264\) | 0.615861 | 0.0379036 | ||||||||
\(265\) | −5.39347 | −0.331318 | ||||||||
\(266\) | 3.26722 | 0.200326 | ||||||||
\(267\) | −2.30807 | −0.141252 | ||||||||
\(268\) | −23.9094 | −1.46050 | ||||||||
\(269\) | −11.9395 | −0.727965 | −0.363982 | − | 0.931406i | \(-0.618583\pi\) | ||||
−0.363982 | + | 0.931406i | \(0.618583\pi\) | |||||||
\(270\) | 2.01363 | 0.122545 | ||||||||
\(271\) | −6.23189 | −0.378560 | −0.189280 | − | 0.981923i | \(-0.560615\pi\) | ||||
−0.189280 | + | 0.981923i | \(0.560615\pi\) | |||||||
\(272\) | 3.13057 | 0.189819 | ||||||||
\(273\) | −0.0897311 | −0.00543077 | ||||||||
\(274\) | −9.25044 | −0.558839 | ||||||||
\(275\) | −2.75317 | −0.166022 | ||||||||
\(276\) | 7.27445 | 0.437870 | ||||||||
\(277\) | −26.6442 | −1.60089 | −0.800447 | − | 0.599404i | \(-0.795404\pi\) | ||||
−0.800447 | + | 0.599404i | \(0.795404\pi\) | |||||||
\(278\) | −1.41694 | −0.0849821 | ||||||||
\(279\) | 6.67065 | 0.399362 | ||||||||
\(280\) | 1.27055 | 0.0759297 | ||||||||
\(281\) | 11.9020 | 0.710012 | 0.355006 | − | 0.934864i | \(-0.384479\pi\) | ||||
0.355006 | + | 0.934864i | \(0.384479\pi\) | |||||||
\(282\) | 5.24198 | 0.312155 | ||||||||
\(283\) | 9.26386 | 0.550679 | 0.275340 | − | 0.961347i | \(-0.411210\pi\) | ||||
0.275340 | + | 0.961347i | \(0.411210\pi\) | |||||||
\(284\) | −21.0937 | −1.25168 | ||||||||
\(285\) | −0.501189 | −0.0296879 | ||||||||
\(286\) | −1.85686 | −0.109798 | ||||||||
\(287\) | 0.693547 | 0.0409388 | ||||||||
\(288\) | 1.87347 | 0.110395 | ||||||||
\(289\) | −16.4900 | −0.969998 | ||||||||
\(290\) | −6.92466 | −0.406630 | ||||||||
\(291\) | 2.71914 | 0.159399 | ||||||||
\(292\) | −65.4111 | −3.82790 | ||||||||
\(293\) | 14.7360 | 0.860886 | 0.430443 | − | 0.902618i | \(-0.358357\pi\) | ||||
0.430443 | + | 0.902618i | \(0.358357\pi\) | |||||||
\(294\) | −3.37010 | −0.196548 | ||||||||
\(295\) | −2.04273 | −0.118932 | ||||||||
\(296\) | 10.1258 | 0.588548 | ||||||||
\(297\) | 0.722511 | 0.0419243 | ||||||||
\(298\) | −21.4640 | −1.24338 | ||||||||
\(299\) | −11.1372 | −0.644079 | ||||||||
\(300\) | 3.66473 | 0.211583 | ||||||||
\(301\) | −3.38192 | −0.194931 | ||||||||
\(302\) | −3.93265 | −0.226299 | ||||||||
\(303\) | −1.64573 | −0.0945447 | ||||||||
\(304\) | −16.0128 | −0.918395 | ||||||||
\(305\) | −3.25172 | −0.186193 | ||||||||
\(306\) | 5.20580 | 0.297596 | ||||||||
\(307\) | 29.3661 | 1.67601 | 0.838006 | − | 0.545661i | \(-0.183721\pi\) | ||||
0.838006 | + | 0.545661i | \(0.183721\pi\) | |||||||
\(308\) | 0.897796 | 0.0511567 | ||||||||
\(309\) | −2.35230 | −0.133817 | ||||||||
\(310\) | −3.82024 | −0.216975 | ||||||||
\(311\) | −19.6726 | −1.11553 | −0.557764 | − | 0.829999i | \(-0.688341\pi\) | ||||
−0.557764 | + | 0.829999i | \(0.688341\pi\) | |||||||
\(312\) | 1.25506 | 0.0710540 | ||||||||
\(313\) | −7.33952 | −0.414854 | −0.207427 | − | 0.978250i | \(-0.566509\pi\) | ||||
−0.207427 | + | 0.978250i | \(0.566509\pi\) | |||||||
\(314\) | −23.9794 | −1.35323 | ||||||||
\(315\) | 0.740320 | 0.0417123 | ||||||||
\(316\) | 58.9424 | 3.31577 | ||||||||
\(317\) | 16.3228 | 0.916781 | 0.458390 | − | 0.888751i | \(-0.348426\pi\) | ||||
0.458390 | + | 0.888751i | \(0.348426\pi\) | |||||||
\(318\) | 3.84392 | 0.215556 | ||||||||
\(319\) | −2.48464 | −0.139113 | ||||||||
\(320\) | 4.96317 | 0.277450 | ||||||||
\(321\) | −1.11095 | −0.0620072 | ||||||||
\(322\) | 8.03536 | 0.447793 | ||||||||
\(323\) | −2.60882 | −0.145158 | ||||||||
\(324\) | 35.1235 | 1.95130 | ||||||||
\(325\) | −5.61069 | −0.311225 | ||||||||
\(326\) | −17.2199 | −0.953720 | ||||||||
\(327\) | 2.03810 | 0.112707 | ||||||||
\(328\) | −9.70061 | −0.535627 | ||||||||
\(329\) | 3.88034 | 0.213930 | ||||||||
\(330\) | −0.205510 | −0.0113129 | ||||||||
\(331\) | 4.51222 | 0.248014 | 0.124007 | − | 0.992281i | \(-0.460425\pi\) | ||||
0.124007 | + | 0.992281i | \(0.460425\pi\) | |||||||
\(332\) | −52.5214 | −2.88249 | ||||||||
\(333\) | 5.90006 | 0.323321 | ||||||||
\(334\) | 4.52508 | 0.247601 | ||||||||
\(335\) | 4.05132 | 0.221347 | ||||||||
\(336\) | −0.317294 | −0.0173098 | ||||||||
\(337\) | 2.41213 | 0.131397 | 0.0656986 | − | 0.997840i | \(-0.479072\pi\) | ||||
0.0656986 | + | 0.997840i | \(0.479072\pi\) | |||||||
\(338\) | 28.2267 | 1.53533 | ||||||||
\(339\) | −0.0509633 | −0.00276794 | ||||||||
\(340\) | −1.99792 | −0.108352 | ||||||||
\(341\) | −1.37074 | −0.0742298 | ||||||||
\(342\) | −26.6275 | −1.43985 | ||||||||
\(343\) | −5.03731 | −0.271989 | ||||||||
\(344\) | 47.3028 | 2.55039 | ||||||||
\(345\) | −1.23262 | −0.0663620 | ||||||||
\(346\) | −32.1025 | −1.72584 | ||||||||
\(347\) | −4.17830 | −0.224303 | −0.112151 | − | 0.993691i | \(-0.535774\pi\) | ||||
−0.112151 | + | 0.993691i | \(0.535774\pi\) | |||||||
\(348\) | 3.30729 | 0.177289 | ||||||||
\(349\) | 6.84288 | 0.366291 | 0.183146 | − | 0.983086i | \(-0.441372\pi\) | ||||
0.183146 | + | 0.983086i | \(0.441372\pi\) | |||||||
\(350\) | 4.04806 | 0.216378 | ||||||||
\(351\) | 1.47241 | 0.0785912 | ||||||||
\(352\) | −0.384977 | −0.0205193 | ||||||||
\(353\) | −26.3267 | −1.40123 | −0.700613 | − | 0.713541i | \(-0.747090\pi\) | ||||
−0.700613 | + | 0.713541i | \(0.747090\pi\) | |||||||
\(354\) | 1.45585 | 0.0773776 | ||||||||
\(355\) | 3.57423 | 0.189700 | ||||||||
\(356\) | 47.0617 | 2.49427 | ||||||||
\(357\) | −0.0516938 | −0.00273593 | ||||||||
\(358\) | 31.6024 | 1.67024 | ||||||||
\(359\) | −17.5566 | −0.926602 | −0.463301 | − | 0.886201i | \(-0.653335\pi\) | ||||
−0.463301 | + | 0.886201i | \(0.653335\pi\) | |||||||
\(360\) | −10.3548 | −0.545747 | ||||||||
\(361\) | −5.65601 | −0.297685 | ||||||||
\(362\) | −21.0154 | −1.10454 | ||||||||
\(363\) | 2.11830 | 0.111182 | ||||||||
\(364\) | 1.82962 | 0.0958982 | ||||||||
\(365\) | 11.0836 | 0.580142 | ||||||||
\(366\) | 2.31749 | 0.121137 | ||||||||
\(367\) | 28.1724 | 1.47059 | 0.735293 | − | 0.677750i | \(-0.237045\pi\) | ||||
0.735293 | + | 0.677750i | \(0.237045\pi\) | |||||||
\(368\) | −39.3816 | −2.05291 | ||||||||
\(369\) | −5.65233 | −0.294249 | ||||||||
\(370\) | −3.37892 | −0.175662 | ||||||||
\(371\) | 2.84543 | 0.147727 | ||||||||
\(372\) | 1.82459 | 0.0946003 | ||||||||
\(373\) | 5.57630 | 0.288730 | 0.144365 | − | 0.989525i | \(-0.453886\pi\) | ||||
0.144365 | + | 0.989525i | \(0.453886\pi\) | |||||||
\(374\) | −1.06973 | −0.0553145 | ||||||||
\(375\) | −1.30698 | −0.0674920 | ||||||||
\(376\) | −54.2741 | −2.79897 | ||||||||
\(377\) | −5.06346 | −0.260781 | ||||||||
\(378\) | −1.06233 | −0.0546402 | ||||||||
\(379\) | −15.0356 | −0.772327 | −0.386163 | − | 0.922430i | \(-0.626200\pi\) | ||||
−0.386163 | + | 0.922430i | \(0.626200\pi\) | |||||||
\(380\) | 10.2193 | 0.524237 | ||||||||
\(381\) | −2.91613 | −0.149398 | ||||||||
\(382\) | −32.9416 | −1.68544 | ||||||||
\(383\) | 23.8340 | 1.21786 | 0.608929 | − | 0.793224i | \(-0.291599\pi\) | ||||
0.608929 | + | 0.793224i | \(0.291599\pi\) | |||||||
\(384\) | −3.78948 | −0.193381 | ||||||||
\(385\) | −0.152127 | −0.00775312 | ||||||||
\(386\) | −43.2195 | −2.19982 | ||||||||
\(387\) | 27.5623 | 1.40107 | ||||||||
\(388\) | −55.4433 | −2.81471 | ||||||||
\(389\) | 8.34022 | 0.422866 | 0.211433 | − | 0.977392i | \(-0.432187\pi\) | ||||
0.211433 | + | 0.977392i | \(0.432187\pi\) | |||||||
\(390\) | −0.418809 | −0.0212072 | ||||||||
\(391\) | −6.41609 | −0.324476 | ||||||||
\(392\) | 34.8931 | 1.76237 | ||||||||
\(393\) | −0.443236 | −0.0223583 | ||||||||
\(394\) | 10.7975 | 0.543968 | ||||||||
\(395\) | −9.98750 | −0.502526 | ||||||||
\(396\) | −7.31694 | −0.367690 | ||||||||
\(397\) | 11.7351 | 0.588967 | 0.294483 | − | 0.955657i | \(-0.404852\pi\) | ||||
0.294483 | + | 0.955657i | \(0.404852\pi\) | |||||||
\(398\) | 8.23493 | 0.412780 | ||||||||
\(399\) | 0.264412 | 0.0132372 | ||||||||
\(400\) | −19.8397 | −0.991985 | ||||||||
\(401\) | 17.5279 | 0.875301 | 0.437650 | − | 0.899145i | \(-0.355811\pi\) | ||||
0.437650 | + | 0.899145i | \(0.355811\pi\) | |||||||
\(402\) | −2.88737 | −0.144009 | ||||||||
\(403\) | −2.79344 | −0.139151 | ||||||||
\(404\) | 33.5565 | 1.66950 | ||||||||
\(405\) | −5.95150 | −0.295733 | ||||||||
\(406\) | 3.65324 | 0.181307 | ||||||||
\(407\) | −1.21239 | −0.0600961 | ||||||||
\(408\) | 0.723039 | 0.0357958 | ||||||||
\(409\) | 34.8728 | 1.72435 | 0.862176 | − | 0.506610i | \(-0.169101\pi\) | ||||
0.862176 | + | 0.506610i | \(0.169101\pi\) | |||||||
\(410\) | 3.23705 | 0.159866 | ||||||||
\(411\) | −0.748627 | −0.0369270 | ||||||||
\(412\) | 47.9634 | 2.36299 | ||||||||
\(413\) | 1.07768 | 0.0530293 | ||||||||
\(414\) | −65.4873 | −3.21853 | ||||||||
\(415\) | 8.89949 | 0.436859 | ||||||||
\(416\) | −0.784545 | −0.0384655 | ||||||||
\(417\) | −0.114671 | −0.00561546 | ||||||||
\(418\) | 5.47163 | 0.267626 | ||||||||
\(419\) | −10.3102 | −0.503686 | −0.251843 | − | 0.967768i | \(-0.581037\pi\) | ||||
−0.251843 | + | 0.967768i | \(0.581037\pi\) | |||||||
\(420\) | 0.202495 | 0.00988076 | ||||||||
\(421\) | −5.72609 | −0.279073 | −0.139536 | − | 0.990217i | \(-0.544561\pi\) | ||||
−0.139536 | + | 0.990217i | \(0.544561\pi\) | |||||||
\(422\) | 53.1598 | 2.58778 | ||||||||
\(423\) | −31.6243 | −1.53763 | ||||||||
\(424\) | −39.7989 | −1.93280 | ||||||||
\(425\) | −3.23230 | −0.156790 | ||||||||
\(426\) | −2.54734 | −0.123419 | ||||||||
\(427\) | 1.71551 | 0.0830191 | ||||||||
\(428\) | 22.6523 | 1.09494 | ||||||||
\(429\) | −0.150273 | −0.00725526 | ||||||||
\(430\) | −15.7847 | −0.761207 | ||||||||
\(431\) | −5.94644 | −0.286430 | −0.143215 | − | 0.989692i | \(-0.545744\pi\) | ||||
−0.143215 | + | 0.989692i | \(0.545744\pi\) | |||||||
\(432\) | 5.20651 | 0.250498 | ||||||||
\(433\) | 24.9052 | 1.19687 | 0.598435 | − | 0.801172i | \(-0.295790\pi\) | ||||
0.598435 | + | 0.801172i | \(0.295790\pi\) | |||||||
\(434\) | 2.01544 | 0.0967442 | ||||||||
\(435\) | −0.560404 | −0.0268693 | ||||||||
\(436\) | −41.5570 | −1.99022 | ||||||||
\(437\) | 32.8181 | 1.56990 | ||||||||
\(438\) | −7.89926 | −0.377441 | ||||||||
\(439\) | −2.94598 | −0.140604 | −0.0703019 | − | 0.997526i | \(-0.522396\pi\) | ||||
−0.0703019 | + | 0.997526i | \(0.522396\pi\) | |||||||
\(440\) | 2.12779 | 0.101439 | ||||||||
\(441\) | 20.3315 | 0.968164 | ||||||||
\(442\) | −2.18001 | −0.103692 | ||||||||
\(443\) | −12.1746 | −0.578431 | −0.289216 | − | 0.957264i | \(-0.593394\pi\) | ||||
−0.289216 | + | 0.957264i | \(0.593394\pi\) | |||||||
\(444\) | 1.61381 | 0.0765880 | ||||||||
\(445\) | −7.97438 | −0.378022 | ||||||||
\(446\) | −29.9917 | −1.42015 | ||||||||
\(447\) | −1.73706 | −0.0821599 | ||||||||
\(448\) | −2.61842 | −0.123709 | ||||||||
\(449\) | 24.3684 | 1.15001 | 0.575007 | − | 0.818149i | \(-0.304999\pi\) | ||||
0.575007 | + | 0.818149i | \(0.304999\pi\) | |||||||
\(450\) | −32.9912 | −1.55522 | ||||||||
\(451\) | 1.16149 | 0.0546923 | ||||||||
\(452\) | 1.03914 | 0.0488772 | ||||||||
\(453\) | −0.318264 | −0.0149534 | ||||||||
\(454\) | 40.1862 | 1.88603 | ||||||||
\(455\) | −0.310020 | −0.0145340 | ||||||||
\(456\) | −3.69832 | −0.173190 | ||||||||
\(457\) | −13.3343 | −0.623753 | −0.311877 | − | 0.950123i | \(-0.600958\pi\) | ||||
−0.311877 | + | 0.950123i | \(0.600958\pi\) | |||||||
\(458\) | 2.60678 | 0.121807 | ||||||||
\(459\) | 0.848250 | 0.0395929 | ||||||||
\(460\) | 25.1332 | 1.17184 | ||||||||
\(461\) | 20.2808 | 0.944573 | 0.472286 | − | 0.881445i | \(-0.343429\pi\) | ||||
0.472286 | + | 0.881445i | \(0.343429\pi\) | |||||||
\(462\) | 0.108421 | 0.00504419 | ||||||||
\(463\) | 23.5324 | 1.09364 | 0.546822 | − | 0.837249i | \(-0.315837\pi\) | ||||
0.546822 | + | 0.837249i | \(0.315837\pi\) | |||||||
\(464\) | −17.9046 | −0.831202 | ||||||||
\(465\) | −0.309167 | −0.0143373 | ||||||||
\(466\) | 46.1503 | 2.13787 | ||||||||
\(467\) | 14.0058 | 0.648109 | 0.324055 | − | 0.946038i | \(-0.394954\pi\) | ||||
0.324055 | + | 0.946038i | \(0.394954\pi\) | |||||||
\(468\) | −14.9112 | −0.689271 | ||||||||
\(469\) | −2.13735 | −0.0986939 | ||||||||
\(470\) | 18.1110 | 0.835398 | ||||||||
\(471\) | −1.94062 | −0.0894190 | ||||||||
\(472\) | −15.0735 | −0.693813 | ||||||||
\(473\) | −5.66373 | −0.260418 | ||||||||
\(474\) | 7.11808 | 0.326944 | ||||||||
\(475\) | 16.5331 | 0.758591 | ||||||||
\(476\) | 1.05404 | 0.0483118 | ||||||||
\(477\) | −23.1899 | −1.06179 | ||||||||
\(478\) | 20.6323 | 0.943698 | ||||||||
\(479\) | −36.0014 | −1.64494 | −0.822472 | − | 0.568805i | \(-0.807406\pi\) | ||||
−0.822472 | + | 0.568805i | \(0.807406\pi\) | |||||||
\(480\) | −0.0868304 | −0.00396325 | ||||||||
\(481\) | −2.47074 | −0.112656 | ||||||||
\(482\) | 19.5612 | 0.890990 | ||||||||
\(483\) | 0.650292 | 0.0295893 | ||||||||
\(484\) | −43.1922 | −1.96328 | ||||||||
\(485\) | 9.39460 | 0.426587 | ||||||||
\(486\) | 13.0156 | 0.590400 | ||||||||
\(487\) | −1.23392 | −0.0559143 | −0.0279572 | − | 0.999609i | \(-0.508900\pi\) | ||||
−0.0279572 | + | 0.999609i | \(0.508900\pi\) | |||||||
\(488\) | −23.9947 | −1.08619 | ||||||||
\(489\) | −1.39358 | −0.0630200 | ||||||||
\(490\) | −11.6437 | −0.526008 | ||||||||
\(491\) | 4.38378 | 0.197837 | 0.0989187 | − | 0.995096i | \(-0.468462\pi\) | ||||
0.0989187 | + | 0.995096i | \(0.468462\pi\) | |||||||
\(492\) | −1.54605 | −0.0697013 | ||||||||
\(493\) | −2.91704 | −0.131377 | ||||||||
\(494\) | 11.1507 | 0.501692 | ||||||||
\(495\) | 1.23982 | 0.0557257 | ||||||||
\(496\) | −9.87774 | −0.443524 | ||||||||
\(497\) | −1.88565 | −0.0845830 | ||||||||
\(498\) | −6.34266 | −0.284221 | ||||||||
\(499\) | −32.9660 | −1.47576 | −0.737881 | − | 0.674931i | \(-0.764173\pi\) | ||||
−0.737881 | + | 0.674931i | \(0.764173\pi\) | |||||||
\(500\) | 26.6493 | 1.19179 | ||||||||
\(501\) | 0.366209 | 0.0163610 | ||||||||
\(502\) | −38.6092 | −1.72321 | ||||||||
\(503\) | 3.32925 | 0.148444 | 0.0742220 | − | 0.997242i | \(-0.476353\pi\) | ||||
0.0742220 | + | 0.997242i | \(0.476353\pi\) | |||||||
\(504\) | 5.46289 | 0.243336 | ||||||||
\(505\) | −5.68599 | −0.253023 | ||||||||
\(506\) | 13.4569 | 0.598231 | ||||||||
\(507\) | 2.28435 | 0.101452 | ||||||||
\(508\) | 59.4600 | 2.63811 | ||||||||
\(509\) | −25.5006 | −1.13029 | −0.565147 | − | 0.824990i | \(-0.691180\pi\) | ||||
−0.565147 | + | 0.824990i | \(0.691180\pi\) | |||||||
\(510\) | −0.241275 | −0.0106838 | ||||||||
\(511\) | −5.84736 | −0.258672 | ||||||||
\(512\) | 41.7667 | 1.84584 | ||||||||
\(513\) | −4.33876 | −0.191561 | ||||||||
\(514\) | 5.68995 | 0.250973 | ||||||||
\(515\) | −8.12717 | −0.358126 | ||||||||
\(516\) | 7.53895 | 0.331884 | ||||||||
\(517\) | 6.49842 | 0.285800 | ||||||||
\(518\) | 1.78262 | 0.0783237 | ||||||||
\(519\) | −2.59802 | −0.114040 | ||||||||
\(520\) | 4.33624 | 0.190157 | ||||||||
\(521\) | −7.13807 | −0.312724 | −0.156362 | − | 0.987700i | \(-0.549977\pi\) | ||||
−0.156362 | + | 0.987700i | \(0.549977\pi\) | |||||||
\(522\) | −29.7735 | −1.30315 | ||||||||
\(523\) | −10.2309 | −0.447367 | −0.223683 | − | 0.974662i | \(-0.571808\pi\) | ||||
−0.223683 | + | 0.974662i | \(0.571808\pi\) | |||||||
\(524\) | 9.03759 | 0.394809 | ||||||||
\(525\) | 0.327605 | 0.0142978 | ||||||||
\(526\) | −1.37688 | −0.0600347 | ||||||||
\(527\) | −1.60929 | −0.0701019 | ||||||||
\(528\) | −0.531374 | −0.0231251 | ||||||||
\(529\) | 57.7124 | 2.50924 | ||||||||
\(530\) | 13.2807 | 0.576877 | ||||||||
\(531\) | −8.78299 | −0.381149 | ||||||||
\(532\) | −5.39137 | −0.233746 | ||||||||
\(533\) | 2.36700 | 0.102526 | ||||||||
\(534\) | 5.68332 | 0.245942 | ||||||||
\(535\) | −3.83832 | −0.165945 | ||||||||
\(536\) | 29.8951 | 1.29127 | ||||||||
\(537\) | 2.55754 | 0.110366 | ||||||||
\(538\) | 29.3995 | 1.26750 | ||||||||
\(539\) | −4.17788 | −0.179954 | ||||||||
\(540\) | −3.32277 | −0.142989 | ||||||||
\(541\) | −14.3939 | −0.618841 | −0.309420 | − | 0.950925i | \(-0.600135\pi\) | ||||
−0.309420 | + | 0.950925i | \(0.600135\pi\) | |||||||
\(542\) | 15.3452 | 0.659132 | ||||||||
\(543\) | −1.70075 | −0.0729861 | ||||||||
\(544\) | −0.451974 | −0.0193782 | ||||||||
\(545\) | 7.04163 | 0.301630 | ||||||||
\(546\) | 0.220951 | 0.00945583 | ||||||||
\(547\) | −0.0309924 | −0.00132514 | −0.000662569 | − | 1.00000i | \(-0.500211\pi\) | ||||
−0.000662569 | 1.00000i | \(0.500211\pi\) | ||||||||
\(548\) | 15.2645 | 0.652068 | ||||||||
\(549\) | −13.9812 | −0.596702 | ||||||||
\(550\) | 6.77931 | 0.289071 | ||||||||
\(551\) | 14.9206 | 0.635637 | ||||||||
\(552\) | −9.09560 | −0.387135 | ||||||||
\(553\) | 5.26910 | 0.224065 | ||||||||
\(554\) | 65.6078 | 2.78741 | ||||||||
\(555\) | −0.273452 | −0.0116074 | ||||||||
\(556\) | 2.33814 | 0.0991594 | ||||||||
\(557\) | 12.4387 | 0.527043 | 0.263522 | − | 0.964654i | \(-0.415116\pi\) | ||||
0.263522 | + | 0.964654i | \(0.415116\pi\) | |||||||
\(558\) | −16.4256 | −0.695351 | ||||||||
\(559\) | −11.5421 | −0.488180 | ||||||||
\(560\) | −1.09625 | −0.0463249 | ||||||||
\(561\) | −0.0865720 | −0.00365507 | ||||||||
\(562\) | −29.3070 | −1.23624 | ||||||||
\(563\) | 35.7047 | 1.50477 | 0.752387 | − | 0.658721i | \(-0.228902\pi\) | ||||
0.752387 | + | 0.658721i | \(0.228902\pi\) | |||||||
\(564\) | −8.65001 | −0.364231 | ||||||||
\(565\) | −0.176078 | −0.00740764 | ||||||||
\(566\) | −22.8110 | −0.958819 | ||||||||
\(567\) | 3.13983 | 0.131860 | ||||||||
\(568\) | 26.3745 | 1.10665 | ||||||||
\(569\) | 27.5053 | 1.15308 | 0.576541 | − | 0.817068i | \(-0.304402\pi\) | ||||
0.576541 | + | 0.817068i | \(0.304402\pi\) | |||||||
\(570\) | 1.23411 | 0.0516912 | ||||||||
\(571\) | 20.8980 | 0.874556 | 0.437278 | − | 0.899326i | \(-0.355943\pi\) | ||||
0.437278 | + | 0.899326i | \(0.355943\pi\) | |||||||
\(572\) | 3.06408 | 0.128116 | ||||||||
\(573\) | −2.66592 | −0.111371 | ||||||||
\(574\) | −1.70777 | −0.0712809 | ||||||||
\(575\) | 40.6614 | 1.69570 | ||||||||
\(576\) | 21.3398 | 0.889159 | ||||||||
\(577\) | 6.99681 | 0.291281 | 0.145641 | − | 0.989338i | \(-0.453476\pi\) | ||||
0.145641 | + | 0.989338i | \(0.453476\pi\) | |||||||
\(578\) | 40.6044 | 1.68892 | ||||||||
\(579\) | −3.49770 | −0.145360 | ||||||||
\(580\) | 11.4267 | 0.474466 | ||||||||
\(581\) | −4.69510 | −0.194786 | ||||||||
\(582\) | −6.69551 | −0.277538 | ||||||||
\(583\) | 4.76526 | 0.197357 | ||||||||
\(584\) | 81.7868 | 3.38436 | ||||||||
\(585\) | 2.52663 | 0.104463 | ||||||||
\(586\) | −36.2854 | −1.49894 | ||||||||
\(587\) | 15.0302 | 0.620363 | 0.310181 | − | 0.950677i | \(-0.399610\pi\) | ||||
0.310181 | + | 0.950677i | \(0.399610\pi\) | |||||||
\(588\) | 5.56114 | 0.229338 | ||||||||
\(589\) | 8.23147 | 0.339172 | ||||||||
\(590\) | 5.02995 | 0.207080 | ||||||||
\(591\) | 0.873825 | 0.0359443 | ||||||||
\(592\) | −8.73667 | −0.359075 | ||||||||
\(593\) | 16.5479 | 0.679542 | 0.339771 | − | 0.940508i | \(-0.389650\pi\) | ||||
0.339771 | + | 0.940508i | \(0.389650\pi\) | |||||||
\(594\) | −1.77909 | −0.0729968 | ||||||||
\(595\) | −0.178602 | −0.00732196 | ||||||||
\(596\) | 35.4186 | 1.45080 | ||||||||
\(597\) | 0.666443 | 0.0272757 | ||||||||
\(598\) | 27.4238 | 1.12144 | ||||||||
\(599\) | 15.3528 | 0.627299 | 0.313650 | − | 0.949539i | \(-0.398448\pi\) | ||||
0.313650 | + | 0.949539i | \(0.398448\pi\) | |||||||
\(600\) | −4.58219 | −0.187067 | ||||||||
\(601\) | −4.00835 | −0.163504 | −0.0817521 | − | 0.996653i | \(-0.526052\pi\) | ||||
−0.0817521 | + | 0.996653i | \(0.526052\pi\) | |||||||
\(602\) | 8.32754 | 0.339405 | ||||||||
\(603\) | 17.4192 | 0.709365 | ||||||||
\(604\) | 6.48943 | 0.264051 | ||||||||
\(605\) | 7.31871 | 0.297548 | ||||||||
\(606\) | 4.05239 | 0.164617 | ||||||||
\(607\) | 30.4854 | 1.23736 | 0.618682 | − | 0.785642i | \(-0.287667\pi\) | ||||
0.618682 | + | 0.785642i | \(0.287667\pi\) | |||||||
\(608\) | 2.31183 | 0.0937571 | ||||||||
\(609\) | 0.295652 | 0.0119804 | ||||||||
\(610\) | 8.00692 | 0.324191 | ||||||||
\(611\) | 13.2432 | 0.535761 | ||||||||
\(612\) | −8.59030 | −0.347242 | ||||||||
\(613\) | 0.946597 | 0.0382327 | 0.0191163 | − | 0.999817i | \(-0.493915\pi\) | ||||
0.0191163 | + | 0.999817i | \(0.493915\pi\) | |||||||
\(614\) | −72.3101 | −2.91820 | ||||||||
\(615\) | 0.261970 | 0.0105637 | ||||||||
\(616\) | −1.12256 | −0.0452292 | ||||||||
\(617\) | 32.1592 | 1.29468 | 0.647341 | − | 0.762201i | \(-0.275881\pi\) | ||||
0.647341 | + | 0.762201i | \(0.275881\pi\) | |||||||
\(618\) | 5.79222 | 0.232997 | ||||||||
\(619\) | −42.7938 | −1.72003 | −0.860014 | − | 0.510270i | \(-0.829545\pi\) | ||||
−0.860014 | + | 0.510270i | \(0.829545\pi\) | |||||||
\(620\) | 6.30393 | 0.253172 | ||||||||
\(621\) | −10.6707 | −0.428201 | ||||||||
\(622\) | 48.4411 | 1.94231 | ||||||||
\(623\) | 4.20704 | 0.168551 | ||||||||
\(624\) | −1.08289 | −0.0433502 | ||||||||
\(625\) | 18.1143 | 0.724570 | ||||||||
\(626\) | 18.0726 | 0.722326 | ||||||||
\(627\) | 0.442812 | 0.0176842 | ||||||||
\(628\) | 39.5693 | 1.57899 | ||||||||
\(629\) | −1.42339 | −0.0567542 | ||||||||
\(630\) | −1.82294 | −0.0726277 | ||||||||
\(631\) | 13.5830 | 0.540730 | 0.270365 | − | 0.962758i | \(-0.412856\pi\) | ||||
0.270365 | + | 0.962758i | \(0.412856\pi\) | |||||||
\(632\) | −73.6986 | −2.93157 | ||||||||
\(633\) | 4.30216 | 0.170996 | ||||||||
\(634\) | −40.1928 | −1.59626 | ||||||||
\(635\) | −10.0752 | −0.399822 | ||||||||
\(636\) | −6.34300 | −0.251516 | ||||||||
\(637\) | −8.51410 | −0.337341 | ||||||||
\(638\) | 6.11810 | 0.242218 | ||||||||
\(639\) | 15.3678 | 0.607943 | ||||||||
\(640\) | −13.0926 | −0.517531 | ||||||||
\(641\) | −38.1110 | −1.50529 | −0.752647 | − | 0.658424i | \(-0.771223\pi\) | ||||
−0.752647 | + | 0.658424i | \(0.771223\pi\) | |||||||
\(642\) | 2.73557 | 0.107964 | ||||||||
\(643\) | −4.72788 | −0.186449 | −0.0932246 | − | 0.995645i | \(-0.529717\pi\) | ||||
−0.0932246 | + | 0.995645i | \(0.529717\pi\) | |||||||
\(644\) | −13.2595 | −0.522497 | ||||||||
\(645\) | −1.27744 | −0.0502991 | ||||||||
\(646\) | 6.42386 | 0.252743 | ||||||||
\(647\) | 24.7026 | 0.971159 | 0.485579 | − | 0.874193i | \(-0.338609\pi\) | ||||
0.485579 | + | 0.874193i | \(0.338609\pi\) | |||||||
\(648\) | −43.9166 | −1.72521 | ||||||||
\(649\) | 1.80480 | 0.0708446 | ||||||||
\(650\) | 13.8156 | 0.541892 | ||||||||
\(651\) | 0.163107 | 0.00639267 | ||||||||
\(652\) | 28.4152 | 1.11283 | ||||||||
\(653\) | −15.7362 | −0.615805 | −0.307902 | − | 0.951418i | \(-0.599627\pi\) | ||||
−0.307902 | + | 0.951418i | \(0.599627\pi\) | |||||||
\(654\) | −5.01856 | −0.196241 | ||||||||
\(655\) | −1.53138 | −0.0598358 | ||||||||
\(656\) | 8.36983 | 0.326787 | ||||||||
\(657\) | 47.6554 | 1.85921 | ||||||||
\(658\) | −9.55481 | −0.372485 | ||||||||
\(659\) | −5.03185 | −0.196013 | −0.0980066 | − | 0.995186i | \(-0.531247\pi\) | ||||
−0.0980066 | + | 0.995186i | \(0.531247\pi\) | |||||||
\(660\) | 0.339120 | 0.0132002 | ||||||||
\(661\) | 25.0643 | 0.974888 | 0.487444 | − | 0.873154i | \(-0.337929\pi\) | ||||
0.487444 | + | 0.873154i | \(0.337929\pi\) | |||||||
\(662\) | −11.1107 | −0.431831 | ||||||||
\(663\) | −0.176425 | −0.00685179 | ||||||||
\(664\) | 65.6701 | 2.54850 | ||||||||
\(665\) | 0.913541 | 0.0354256 | ||||||||
\(666\) | −14.5281 | −0.562953 | ||||||||
\(667\) | 36.6955 | 1.42085 | ||||||||
\(668\) | −7.46702 | −0.288908 | ||||||||
\(669\) | −2.42719 | −0.0938407 | ||||||||
\(670\) | −9.97585 | −0.385401 | ||||||||
\(671\) | 2.87297 | 0.110910 | ||||||||
\(672\) | 0.0458091 | 0.00176712 | ||||||||
\(673\) | −12.4768 | −0.480945 | −0.240472 | − | 0.970656i | \(-0.577302\pi\) | ||||
−0.240472 | + | 0.970656i | \(0.577302\pi\) | |||||||
\(674\) | −5.93956 | −0.228783 | ||||||||
\(675\) | −5.37570 | −0.206911 | ||||||||
\(676\) | −46.5780 | −1.79146 | ||||||||
\(677\) | 15.5776 | 0.598696 | 0.299348 | − | 0.954144i | \(-0.403231\pi\) | ||||
0.299348 | + | 0.954144i | \(0.403231\pi\) | |||||||
\(678\) | 0.125490 | 0.00481942 | ||||||||
\(679\) | −4.95630 | −0.190205 | ||||||||
\(680\) | 2.49810 | 0.0957976 | ||||||||
\(681\) | 3.25222 | 0.124625 | ||||||||
\(682\) | 3.37527 | 0.129246 | ||||||||
\(683\) | 25.3107 | 0.968488 | 0.484244 | − | 0.874933i | \(-0.339095\pi\) | ||||
0.484244 | + | 0.874933i | \(0.339095\pi\) | |||||||
\(684\) | 43.9391 | 1.68005 | ||||||||
\(685\) | −2.58650 | −0.0988251 | ||||||||
\(686\) | 12.4037 | 0.473575 | ||||||||
\(687\) | 0.210963 | 0.00804876 | ||||||||
\(688\) | −40.8136 | −1.55600 | ||||||||
\(689\) | 9.71113 | 0.369965 | ||||||||
\(690\) | 3.03516 | 0.115547 | ||||||||
\(691\) | 31.9905 | 1.21698 | 0.608489 | − | 0.793563i | \(-0.291776\pi\) | ||||
0.608489 | + | 0.793563i | \(0.291776\pi\) | |||||||
\(692\) | 52.9737 | 2.01376 | ||||||||
\(693\) | −0.654090 | −0.0248468 | ||||||||
\(694\) | 10.2885 | 0.390546 | ||||||||
\(695\) | −0.396187 | −0.0150282 | ||||||||
\(696\) | −4.13527 | −0.156747 | ||||||||
\(697\) | 1.36362 | 0.0516509 | ||||||||
\(698\) | −16.8497 | −0.637770 | ||||||||
\(699\) | 3.73489 | 0.141267 | ||||||||
\(700\) | −6.67987 | −0.252475 | ||||||||
\(701\) | 23.1733 | 0.875244 | 0.437622 | − | 0.899159i | \(-0.355821\pi\) | ||||
0.437622 | + | 0.899159i | \(0.355821\pi\) | |||||||
\(702\) | −3.62561 | −0.136840 | ||||||||
\(703\) | 7.28057 | 0.274592 | ||||||||
\(704\) | −4.38508 | −0.165269 | ||||||||
\(705\) | 1.46570 | 0.0552015 | ||||||||
\(706\) | 64.8259 | 2.43975 | ||||||||
\(707\) | 2.99975 | 0.112817 | ||||||||
\(708\) | −2.40236 | −0.0902862 | ||||||||
\(709\) | −43.4701 | −1.63255 | −0.816277 | − | 0.577660i | \(-0.803966\pi\) | ||||
−0.816277 | + | 0.577660i | \(0.803966\pi\) | |||||||
\(710\) | −8.80106 | −0.330298 | ||||||||
\(711\) | −42.9426 | −1.61047 | ||||||||
\(712\) | −58.8436 | −2.20526 | ||||||||
\(713\) | 20.2444 | 0.758158 | ||||||||
\(714\) | 0.127289 | 0.00476368 | ||||||||
\(715\) | −0.519193 | −0.0194167 | ||||||||
\(716\) | −52.1484 | −1.94888 | ||||||||
\(717\) | 1.66974 | 0.0623577 | ||||||||
\(718\) | 43.2308 | 1.61336 | ||||||||
\(719\) | 39.6940 | 1.48034 | 0.740169 | − | 0.672421i | \(-0.234746\pi\) | ||||
0.740169 | + | 0.672421i | \(0.234746\pi\) | |||||||
\(720\) | 8.93430 | 0.332962 | ||||||||
\(721\) | 4.28764 | 0.159680 | ||||||||
\(722\) | 13.9272 | 0.518316 | ||||||||
\(723\) | 1.58307 | 0.0588749 | ||||||||
\(724\) | 34.6783 | 1.28881 | ||||||||
\(725\) | 18.4865 | 0.686570 | ||||||||
\(726\) | −5.21604 | −0.193585 | ||||||||
\(727\) | 36.2404 | 1.34408 | 0.672041 | − | 0.740514i | \(-0.265418\pi\) | ||||
0.672041 | + | 0.740514i | \(0.265418\pi\) | |||||||
\(728\) | −2.28767 | −0.0847865 | ||||||||
\(729\) | −24.8792 | −0.921452 | ||||||||
\(730\) | −27.2919 | −1.01012 | ||||||||
\(731\) | −6.64939 | −0.245936 | ||||||||
\(732\) | −3.82419 | −0.141346 | ||||||||
\(733\) | 33.0965 | 1.22245 | 0.611224 | − | 0.791457i | \(-0.290677\pi\) | ||||
0.611224 | + | 0.791457i | \(0.290677\pi\) | |||||||
\(734\) | −69.3707 | −2.56052 | ||||||||
\(735\) | −0.942308 | −0.0347576 | ||||||||
\(736\) | 5.68569 | 0.209577 | ||||||||
\(737\) | −3.57944 | −0.131850 | ||||||||
\(738\) | 13.9181 | 0.512333 | ||||||||
\(739\) | −43.7389 | −1.60896 | −0.804480 | − | 0.593980i | \(-0.797556\pi\) | ||||
−0.804480 | + | 0.593980i | \(0.797556\pi\) | |||||||
\(740\) | 5.57570 | 0.204967 | ||||||||
\(741\) | 0.902409 | 0.0331508 | ||||||||
\(742\) | −7.00649 | −0.257216 | ||||||||
\(743\) | −9.83063 | −0.360651 | −0.180325 | − | 0.983607i | \(-0.557715\pi\) | ||||
−0.180325 | + | 0.983607i | \(0.557715\pi\) | |||||||
\(744\) | −2.28137 | −0.0836391 | ||||||||
\(745\) | −6.00151 | −0.219878 | ||||||||
\(746\) | −13.7309 | −0.502724 | ||||||||
\(747\) | 38.2645 | 1.40003 | ||||||||
\(748\) | 1.76521 | 0.0645424 | ||||||||
\(749\) | 2.02498 | 0.0739912 | ||||||||
\(750\) | 3.21826 | 0.117514 | ||||||||
\(751\) | 37.0100 | 1.35051 | 0.675257 | − | 0.737583i | \(-0.264033\pi\) | ||||
0.675257 | + | 0.737583i | \(0.264033\pi\) | |||||||
\(752\) | 46.8285 | 1.70766 | ||||||||
\(753\) | −3.12459 | −0.113866 | ||||||||
\(754\) | 12.4681 | 0.454061 | ||||||||
\(755\) | −1.09960 | −0.0400186 | ||||||||
\(756\) | 1.75299 | 0.0637557 | ||||||||
\(757\) | 15.6212 | 0.567760 | 0.283880 | − | 0.958860i | \(-0.408378\pi\) | ||||
0.283880 | + | 0.958860i | \(0.408378\pi\) | |||||||
\(758\) | 37.0232 | 1.34474 | ||||||||
\(759\) | 1.08905 | 0.0395299 | ||||||||
\(760\) | −12.7777 | −0.463494 | ||||||||
\(761\) | −34.9672 | −1.26756 | −0.633780 | − | 0.773513i | \(-0.718498\pi\) | ||||
−0.633780 | + | 0.773513i | \(0.718498\pi\) | |||||||
\(762\) | 7.18058 | 0.260125 | ||||||||
\(763\) | −3.71495 | −0.134490 | ||||||||
\(764\) | 54.3583 | 1.96661 | ||||||||
\(765\) | 1.45559 | 0.0526268 | ||||||||
\(766\) | −58.6880 | −2.12048 | ||||||||
\(767\) | 3.67801 | 0.132805 | ||||||||
\(768\) | 6.45804 | 0.233034 | ||||||||
\(769\) | −36.1481 | −1.30353 | −0.651767 | − | 0.758419i | \(-0.725972\pi\) | ||||
−0.651767 | + | 0.758419i | \(0.725972\pi\) | |||||||
\(770\) | 0.374593 | 0.0134994 | ||||||||
\(771\) | 0.460481 | 0.0165838 | ||||||||
\(772\) | 71.3183 | 2.56680 | ||||||||
\(773\) | 30.5228 | 1.09783 | 0.548915 | − | 0.835878i | \(-0.315041\pi\) | ||||
0.548915 | + | 0.835878i | \(0.315041\pi\) | |||||||
\(774\) | −67.8685 | −2.43948 | ||||||||
\(775\) | 10.1987 | 0.366349 | ||||||||
\(776\) | 69.3235 | 2.48857 | ||||||||
\(777\) | 0.144265 | 0.00517548 | ||||||||
\(778\) | −20.5367 | −0.736276 | ||||||||
\(779\) | −6.97487 | −0.249901 | ||||||||
\(780\) | 0.691094 | 0.0247451 | ||||||||
\(781\) | −3.15791 | −0.112999 | ||||||||
\(782\) | 15.7988 | 0.564963 | ||||||||
\(783\) | −4.85138 | −0.173374 | ||||||||
\(784\) | −30.1063 | −1.07523 | ||||||||
\(785\) | −6.70483 | −0.239306 | ||||||||
\(786\) | 1.09141 | 0.0389293 | ||||||||
\(787\) | −0.816266 | −0.0290967 | −0.0145484 | − | 0.999894i | \(-0.504631\pi\) | ||||
−0.0145484 | + | 0.999894i | \(0.504631\pi\) | |||||||
\(788\) | −17.8173 | −0.634716 | ||||||||
\(789\) | −0.111429 | −0.00396698 | ||||||||
\(790\) | 24.5929 | 0.874976 | ||||||||
\(791\) | 0.0928932 | 0.00330290 | ||||||||
\(792\) | 9.14873 | 0.325086 | ||||||||
\(793\) | 5.85483 | 0.207911 | ||||||||
\(794\) | −28.8961 | −1.02548 | ||||||||
\(795\) | 1.07479 | 0.0381189 | ||||||||
\(796\) | −13.5888 | −0.481642 | ||||||||
\(797\) | 24.9704 | 0.884496 | 0.442248 | − | 0.896893i | \(-0.354181\pi\) | ||||
0.442248 | + | 0.896893i | \(0.354181\pi\) | |||||||
\(798\) | −0.651079 | −0.0230480 | ||||||||
\(799\) | 7.62934 | 0.269907 | ||||||||
\(800\) | 2.86434 | 0.101270 | ||||||||
\(801\) | −34.2869 | −1.21147 | ||||||||
\(802\) | −43.1601 | −1.52404 | ||||||||
\(803\) | −9.79262 | −0.345574 | ||||||||
\(804\) | 4.76457 | 0.168033 | ||||||||
\(805\) | 2.24675 | 0.0791877 | ||||||||
\(806\) | 6.87847 | 0.242284 | ||||||||
\(807\) | 2.37926 | 0.0837540 | ||||||||
\(808\) | −41.9574 | −1.47606 | ||||||||
\(809\) | 10.8063 | 0.379930 | 0.189965 | − | 0.981791i | \(-0.439163\pi\) | ||||
0.189965 | + | 0.981791i | \(0.439163\pi\) | |||||||
\(810\) | 14.6548 | 0.514917 | ||||||||
\(811\) | 37.7034 | 1.32395 | 0.661973 | − | 0.749527i | \(-0.269719\pi\) | ||||
0.661973 | + | 0.749527i | \(0.269719\pi\) | |||||||
\(812\) | −6.02836 | −0.211554 | ||||||||
\(813\) | 1.24187 | 0.0435542 | ||||||||
\(814\) | 2.98536 | 0.104637 | ||||||||
\(815\) | −4.81482 | −0.168656 | ||||||||
\(816\) | −0.623849 | −0.0218391 | ||||||||
\(817\) | 34.0114 | 1.18991 | ||||||||
\(818\) | −85.8698 | −3.00237 | ||||||||
\(819\) | −1.33297 | −0.0465778 | ||||||||
\(820\) | −5.34159 | −0.186536 | ||||||||
\(821\) | −14.7813 | −0.515871 | −0.257935 | − | 0.966162i | \(-0.583042\pi\) | ||||
−0.257935 | + | 0.966162i | \(0.583042\pi\) | |||||||
\(822\) | 1.84339 | 0.0642957 | ||||||||
\(823\) | −47.3909 | −1.65194 | −0.825972 | − | 0.563711i | \(-0.809373\pi\) | ||||
−0.825972 | + | 0.563711i | \(0.809373\pi\) | |||||||
\(824\) | −59.9711 | −2.08919 | ||||||||
\(825\) | 0.548641 | 0.0191012 | ||||||||
\(826\) | −2.65365 | −0.0923323 | ||||||||
\(827\) | −51.8766 | −1.80393 | −0.901963 | − | 0.431814i | \(-0.857874\pi\) | ||||
−0.901963 | + | 0.431814i | \(0.857874\pi\) | |||||||
\(828\) | 108.063 | 3.75546 | ||||||||
\(829\) | 8.10315 | 0.281434 | 0.140717 | − | 0.990050i | \(-0.455059\pi\) | ||||
0.140717 | + | 0.990050i | \(0.455059\pi\) | |||||||
\(830\) | −21.9138 | −0.760640 | ||||||||
\(831\) | 5.30955 | 0.184186 | ||||||||
\(832\) | −8.93637 | −0.309813 | ||||||||
\(833\) | −4.90495 | −0.169947 | ||||||||
\(834\) | 0.282362 | 0.00977739 | ||||||||
\(835\) | 1.26525 | 0.0437858 | ||||||||
\(836\) | −9.02896 | −0.312273 | ||||||||
\(837\) | −2.67644 | −0.0925113 | ||||||||
\(838\) | 25.3875 | 0.876997 | ||||||||
\(839\) | 37.3711 | 1.29020 | 0.645098 | − | 0.764100i | \(-0.276817\pi\) | ||||
0.645098 | + | 0.764100i | \(0.276817\pi\) | |||||||
\(840\) | −0.253190 | −0.00873589 | ||||||||
\(841\) | −12.3166 | −0.424710 | ||||||||
\(842\) | 14.0997 | 0.485909 | ||||||||
\(843\) | −2.37178 | −0.0816885 | ||||||||
\(844\) | −87.7212 | −3.01949 | ||||||||
\(845\) | 7.89241 | 0.271507 | ||||||||
\(846\) | 77.8706 | 2.67725 | ||||||||
\(847\) | −3.86113 | −0.132670 | ||||||||
\(848\) | 34.3391 | 1.17921 | ||||||||
\(849\) | −1.84607 | −0.0633569 | ||||||||
\(850\) | 7.95912 | 0.272996 | ||||||||
\(851\) | 17.9058 | 0.613801 | ||||||||
\(852\) | 4.20348 | 0.144009 | ||||||||
\(853\) | 2.04739 | 0.0701012 | 0.0350506 | − | 0.999386i | \(-0.488841\pi\) | ||||
0.0350506 | + | 0.999386i | \(0.488841\pi\) | |||||||
\(854\) | −4.22420 | −0.144549 | ||||||||
\(855\) | −7.44526 | −0.254623 | ||||||||
\(856\) | −28.3233 | −0.968071 | ||||||||
\(857\) | 11.0282 | 0.376716 | 0.188358 | − | 0.982100i | \(-0.439683\pi\) | ||||
0.188358 | + | 0.982100i | \(0.439683\pi\) | |||||||
\(858\) | 0.370028 | 0.0126325 | ||||||||
\(859\) | −14.4955 | −0.494579 | −0.247290 | − | 0.968942i | \(-0.579540\pi\) | ||||
−0.247290 | + | 0.968942i | \(0.579540\pi\) | |||||||
\(860\) | 26.0470 | 0.888196 | ||||||||
\(861\) | −0.138208 | −0.00471010 | ||||||||
\(862\) | 14.6423 | 0.498719 | ||||||||
\(863\) | 3.55962 | 0.121171 | 0.0605854 | − | 0.998163i | \(-0.480703\pi\) | ||||
0.0605854 | + | 0.998163i | \(0.480703\pi\) | |||||||
\(864\) | −0.751686 | −0.0255729 | ||||||||
\(865\) | −8.97613 | −0.305197 | ||||||||
\(866\) | −61.3259 | −2.08394 | ||||||||
\(867\) | 3.28606 | 0.111600 | ||||||||
\(868\) | −3.32576 | −0.112884 | ||||||||
\(869\) | 8.82420 | 0.299340 | ||||||||
\(870\) | 1.37992 | 0.0467837 | ||||||||
\(871\) | −7.29455 | −0.247166 | ||||||||
\(872\) | 51.9608 | 1.75961 | ||||||||
\(873\) | 40.3933 | 1.36711 | ||||||||
\(874\) | −80.8101 | −2.73344 | ||||||||
\(875\) | 2.38229 | 0.0805361 | ||||||||
\(876\) | 13.0349 | 0.440408 | ||||||||
\(877\) | −47.7955 | −1.61394 | −0.806970 | − | 0.590592i | \(-0.798894\pi\) | ||||
−0.806970 | + | 0.590592i | \(0.798894\pi\) | |||||||
\(878\) | 7.25408 | 0.244813 | ||||||||
\(879\) | −2.93653 | −0.0990468 | ||||||||
\(880\) | −1.83589 | −0.0618880 | ||||||||
\(881\) | 45.5872 | 1.53587 | 0.767936 | − | 0.640527i | \(-0.221284\pi\) | ||||
0.767936 | + | 0.640527i | \(0.221284\pi\) | |||||||
\(882\) | −50.0635 | −1.68573 | ||||||||
\(883\) | 7.88523 | 0.265359 | 0.132680 | − | 0.991159i | \(-0.457642\pi\) | ||||
0.132680 | + | 0.991159i | \(0.457642\pi\) | |||||||
\(884\) | 3.59732 | 0.120991 | ||||||||
\(885\) | 0.407068 | 0.0136834 | ||||||||
\(886\) | 29.9783 | 1.00714 | ||||||||
\(887\) | 26.1885 | 0.879322 | 0.439661 | − | 0.898164i | \(-0.355099\pi\) | ||||
0.439661 | + | 0.898164i | \(0.355099\pi\) | |||||||
\(888\) | −2.01783 | −0.0677138 | ||||||||
\(889\) | 5.31537 | 0.178272 | ||||||||
\(890\) | 19.6358 | 0.658195 | ||||||||
\(891\) | 5.25829 | 0.176159 | ||||||||
\(892\) | 49.4906 | 1.65707 | ||||||||
\(893\) | −39.0238 | −1.30588 | ||||||||
\(894\) | 4.27727 | 0.143053 | ||||||||
\(895\) | 8.83629 | 0.295365 | ||||||||
\(896\) | 6.90726 | 0.230755 | ||||||||
\(897\) | 2.21937 | 0.0741028 | ||||||||
\(898\) | −60.0038 | −2.00235 | ||||||||
\(899\) | 9.20400 | 0.306971 | ||||||||
\(900\) | 54.4402 | 1.81467 | ||||||||
\(901\) | 5.59456 | 0.186382 | ||||||||
\(902\) | −2.86001 | −0.0952279 | ||||||||
\(903\) | 0.673937 | 0.0224272 | ||||||||
\(904\) | −1.29929 | −0.0432138 | ||||||||
\(905\) | −5.87607 | −0.195327 | ||||||||
\(906\) | 0.783684 | 0.0260362 | ||||||||
\(907\) | 35.4269 | 1.17633 | 0.588165 | − | 0.808741i | \(-0.299851\pi\) | ||||
0.588165 | + | 0.808741i | \(0.299851\pi\) | |||||||
\(908\) | −66.3128 | −2.20067 | ||||||||
\(909\) | −24.4476 | −0.810877 | ||||||||
\(910\) | 0.763384 | 0.0253059 | ||||||||
\(911\) | −12.8829 | −0.426830 | −0.213415 | − | 0.976962i | \(-0.568459\pi\) | ||||
−0.213415 | + | 0.976962i | \(0.568459\pi\) | |||||||
\(912\) | 3.19096 | 0.105663 | ||||||||
\(913\) | −7.86291 | −0.260225 | ||||||||
\(914\) | 32.8340 | 1.08605 | ||||||||
\(915\) | 0.647990 | 0.0214219 | ||||||||
\(916\) | −4.30155 | −0.142127 | ||||||||
\(917\) | 0.807907 | 0.0266794 | ||||||||
\(918\) | −2.08870 | −0.0689374 | ||||||||
\(919\) | −24.6257 | −0.812328 | −0.406164 | − | 0.913800i | \(-0.633134\pi\) | ||||
−0.406164 | + | 0.913800i | \(0.633134\pi\) | |||||||
\(920\) | −31.4252 | −1.03606 | ||||||||
\(921\) | −5.85197 | −0.192829 | ||||||||
\(922\) | −49.9389 | −1.64465 | ||||||||
\(923\) | −6.43552 | −0.211828 | ||||||||
\(924\) | −0.178910 | −0.00588569 | ||||||||
\(925\) | 9.02057 | 0.296595 | ||||||||
\(926\) | −57.9455 | −1.90421 | ||||||||
\(927\) | −34.9438 | −1.14771 | ||||||||
\(928\) | 2.58497 | 0.0848558 | ||||||||
\(929\) | 43.4827 | 1.42662 | 0.713310 | − | 0.700848i | \(-0.247195\pi\) | ||||
0.713310 | + | 0.700848i | \(0.247195\pi\) | |||||||
\(930\) | 0.761283 | 0.0249634 | ||||||||
\(931\) | 25.0886 | 0.822247 | ||||||||
\(932\) | −76.1546 | −2.49453 | ||||||||
\(933\) | 3.92028 | 0.128344 | ||||||||
\(934\) | −34.4873 | −1.12846 | ||||||||
\(935\) | −0.299106 | −0.00978180 | ||||||||
\(936\) | 18.6442 | 0.609405 | ||||||||
\(937\) | 46.0292 | 1.50371 | 0.751854 | − | 0.659330i | \(-0.229160\pi\) | ||||
0.751854 | + | 0.659330i | \(0.229160\pi\) | |||||||
\(938\) | 5.26295 | 0.171841 | ||||||||
\(939\) | 1.46259 | 0.0477299 | ||||||||
\(940\) | −29.8857 | −0.974764 | ||||||||
\(941\) | −28.2566 | −0.921140 | −0.460570 | − | 0.887623i | \(-0.652355\pi\) | ||||
−0.460570 | + | 0.887623i | \(0.652355\pi\) | |||||||
\(942\) | 4.77852 | 0.155693 | ||||||||
\(943\) | −17.1539 | −0.558609 | ||||||||
\(944\) | 13.0056 | 0.423297 | ||||||||
\(945\) | −0.297036 | −0.00966257 | ||||||||
\(946\) | 13.9462 | 0.453429 | ||||||||
\(947\) | 43.5512 | 1.41522 | 0.707612 | − | 0.706601i | \(-0.249772\pi\) | ||||
0.707612 | + | 0.706601i | \(0.249772\pi\) | |||||||
\(948\) | −11.7458 | −0.381487 | ||||||||
\(949\) | −19.9564 | −0.647812 | ||||||||
\(950\) | −40.7106 | −1.32083 | ||||||||
\(951\) | −3.25275 | −0.105478 | ||||||||
\(952\) | −1.31792 | −0.0427140 | ||||||||
\(953\) | −36.6249 | −1.18640 | −0.593199 | − | 0.805056i | \(-0.702135\pi\) | ||||
−0.593199 | + | 0.805056i | \(0.702135\pi\) | |||||||
\(954\) | 57.1021 | 1.84875 | ||||||||
\(955\) | −9.21075 | −0.298053 | ||||||||
\(956\) | −34.0462 | −1.10113 | ||||||||
\(957\) | 0.495130 | 0.0160053 | ||||||||
\(958\) | 88.6486 | 2.86411 | ||||||||
\(959\) | 1.36456 | 0.0440639 | ||||||||
\(960\) | −0.989043 | −0.0319212 | ||||||||
\(961\) | −25.9223 | −0.836203 | ||||||||
\(962\) | 6.08387 | 0.196152 | ||||||||
\(963\) | −16.5034 | −0.531814 | ||||||||
\(964\) | −32.2788 | −1.03963 | ||||||||
\(965\) | −12.0845 | −0.389015 | ||||||||
\(966\) | −1.60126 | −0.0515196 | ||||||||
\(967\) | −17.1291 | −0.550835 | −0.275418 | − | 0.961325i | \(-0.588816\pi\) | ||||
−0.275418 | + | 0.961325i | \(0.588816\pi\) | |||||||
\(968\) | 54.0054 | 1.73580 | ||||||||
\(969\) | 0.519875 | 0.0167008 | ||||||||
\(970\) | −23.1329 | −0.742754 | ||||||||
\(971\) | 9.58860 | 0.307713 | 0.153856 | − | 0.988093i | \(-0.450831\pi\) | ||||
0.153856 | + | 0.988093i | \(0.450831\pi\) | |||||||
\(972\) | −21.4776 | −0.688895 | ||||||||
\(973\) | 0.209016 | 0.00670075 | ||||||||
\(974\) | 3.03837 | 0.0973556 | ||||||||
\(975\) | 1.11808 | 0.0358071 | ||||||||
\(976\) | 20.7030 | 0.662686 | ||||||||
\(977\) | 3.91750 | 0.125332 | 0.0626659 | − | 0.998035i | \(-0.480040\pi\) | ||||
0.0626659 | + | 0.998035i | \(0.480040\pi\) | |||||||
\(978\) | 3.43151 | 0.109728 | ||||||||
\(979\) | 7.04555 | 0.225177 | ||||||||
\(980\) | 19.2137 | 0.613759 | ||||||||
\(981\) | 30.2764 | 0.966651 | ||||||||
\(982\) | −10.7945 | −0.344466 | ||||||||
\(983\) | 17.0680 | 0.544383 | 0.272192 | − | 0.962243i | \(-0.412252\pi\) | ||||
0.272192 | + | 0.962243i | \(0.412252\pi\) | |||||||
\(984\) | 1.93310 | 0.0616251 | ||||||||
\(985\) | 3.01906 | 0.0961952 | ||||||||
\(986\) | 7.18283 | 0.228748 | ||||||||
\(987\) | −0.773259 | −0.0246131 | ||||||||
\(988\) | −18.4001 | −0.585387 | ||||||||
\(989\) | 83.6472 | 2.65983 | ||||||||
\(990\) | −3.05289 | −0.0970272 | ||||||||
\(991\) | 30.1671 | 0.958288 | 0.479144 | − | 0.877736i | \(-0.340947\pi\) | ||||
0.479144 | + | 0.877736i | \(0.340947\pi\) | |||||||
\(992\) | 1.42609 | 0.0452785 | ||||||||
\(993\) | −0.899178 | −0.0285346 | ||||||||
\(994\) | 4.64317 | 0.147272 | ||||||||
\(995\) | 2.30255 | 0.0729959 | ||||||||
\(996\) | 10.4663 | 0.331637 | ||||||||
\(997\) | 13.1035 | 0.414993 | 0.207497 | − | 0.978236i | \(-0.433468\pi\) | ||||
0.207497 | + | 0.978236i | \(0.433468\pi\) | |||||||
\(998\) | 81.1745 | 2.56953 | ||||||||
\(999\) | −2.36726 | −0.0748967 |
(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 | 6037.2.a.b.1.15 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.b.1.15 | ✓ | 259 | 1.1 | even | 1 | trivial |