Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, 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("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.97 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.170060 | 0.120251 | 0.0601254 | − | 0.998191i | \(-0.480850\pi\) | ||||
0.0601254 | + | 0.998191i | \(0.480850\pi\) | |||||||
\(3\) | 1.77882 | 1.02700 | 0.513501 | − | 0.858089i | \(-0.328348\pi\) | ||||
0.513501 | + | 0.858089i | \(0.328348\pi\) | |||||||
\(4\) | −1.97108 | −0.985540 | ||||||||
\(5\) | 1.29255 | 0.578044 | 0.289022 | − | 0.957322i | \(-0.406670\pi\) | ||||
0.289022 | + | 0.957322i | \(0.406670\pi\) | |||||||
\(6\) | 0.302507 | 0.123498 | ||||||||
\(7\) | −0.0406384 | −0.0153599 | −0.00767993 | − | 0.999971i | \(-0.502445\pi\) | ||||
−0.00767993 | + | 0.999971i | \(0.502445\pi\) | |||||||
\(8\) | −0.675323 | −0.238763 | ||||||||
\(9\) | 0.164203 | 0.0547344 | ||||||||
\(10\) | 0.219811 | 0.0695103 | ||||||||
\(11\) | −5.00857 | −1.51014 | −0.755070 | − | 0.655644i | \(-0.772397\pi\) | ||||
−0.755070 | + | 0.655644i | \(0.772397\pi\) | |||||||
\(12\) | −3.50620 | −1.01215 | ||||||||
\(13\) | −2.21866 | −0.615345 | −0.307672 | − | 0.951492i | \(-0.599550\pi\) | ||||
−0.307672 | + | 0.951492i | \(0.599550\pi\) | |||||||
\(14\) | −0.00691098 | −0.00184704 | ||||||||
\(15\) | 2.29921 | 0.593653 | ||||||||
\(16\) | 3.82731 | 0.956828 | ||||||||
\(17\) | 4.23365 | 1.02681 | 0.513405 | − | 0.858146i | \(-0.328384\pi\) | ||||
0.513405 | + | 0.858146i | \(0.328384\pi\) | |||||||
\(18\) | 0.0279244 | 0.00658185 | ||||||||
\(19\) | 6.20870 | 1.42437 | 0.712186 | − | 0.701990i | \(-0.247705\pi\) | ||||
0.712186 | + | 0.701990i | \(0.247705\pi\) | |||||||
\(20\) | −2.54771 | −0.569685 | ||||||||
\(21\) | −0.0722884 | −0.0157746 | ||||||||
\(22\) | −0.851759 | −0.181596 | ||||||||
\(23\) | 1.17639 | 0.245295 | 0.122647 | − | 0.992450i | \(-0.460862\pi\) | ||||
0.122647 | + | 0.992450i | \(0.460862\pi\) | |||||||
\(24\) | −1.20128 | −0.245210 | ||||||||
\(25\) | −3.32933 | −0.665865 | ||||||||
\(26\) | −0.377306 | −0.0739957 | ||||||||
\(27\) | −5.04437 | −0.970790 | ||||||||
\(28\) | 0.0801015 | 0.0151378 | ||||||||
\(29\) | 8.33537 | 1.54784 | 0.773920 | − | 0.633284i | \(-0.218293\pi\) | ||||
0.773920 | + | 0.633284i | \(0.218293\pi\) | |||||||
\(30\) | 0.391004 | 0.0713872 | ||||||||
\(31\) | −7.11154 | −1.27727 | −0.638635 | − | 0.769509i | \(-0.720501\pi\) | ||||
−0.638635 | + | 0.769509i | \(0.720501\pi\) | |||||||
\(32\) | 2.00152 | 0.353822 | ||||||||
\(33\) | −8.90934 | −1.55092 | ||||||||
\(34\) | 0.719976 | 0.123475 | ||||||||
\(35\) | −0.0525270 | −0.00887868 | ||||||||
\(36\) | −0.323658 | −0.0539429 | ||||||||
\(37\) | 8.79659 | 1.44615 | 0.723076 | − | 0.690769i | \(-0.242728\pi\) | ||||
0.723076 | + | 0.690769i | \(0.242728\pi\) | |||||||
\(38\) | 1.05585 | 0.171282 | ||||||||
\(39\) | −3.94659 | −0.631961 | ||||||||
\(40\) | −0.872886 | −0.138015 | ||||||||
\(41\) | 9.96233 | 1.55585 | 0.777927 | − | 0.628355i | \(-0.216271\pi\) | ||||
0.777927 | + | 0.628355i | \(0.216271\pi\) | |||||||
\(42\) | −0.0122934 | −0.00189691 | ||||||||
\(43\) | −5.13245 | −0.782691 | −0.391346 | − | 0.920244i | \(-0.627990\pi\) | ||||
−0.391346 | + | 0.920244i | \(0.627990\pi\) | |||||||
\(44\) | 9.87228 | 1.48830 | ||||||||
\(45\) | 0.212240 | 0.0316389 | ||||||||
\(46\) | 0.200058 | 0.0294969 | ||||||||
\(47\) | 6.58729 | 0.960855 | 0.480427 | − | 0.877034i | \(-0.340482\pi\) | ||||
0.480427 | + | 0.877034i | \(0.340482\pi\) | |||||||
\(48\) | 6.80810 | 0.982665 | ||||||||
\(49\) | −6.99835 | −0.999764 | ||||||||
\(50\) | −0.566186 | −0.0800708 | ||||||||
\(51\) | 7.53090 | 1.05454 | ||||||||
\(52\) | 4.37315 | 0.606447 | ||||||||
\(53\) | 6.31303 | 0.867161 | 0.433580 | − | 0.901115i | \(-0.357250\pi\) | ||||
0.433580 | + | 0.901115i | \(0.357250\pi\) | |||||||
\(54\) | −0.857848 | −0.116738 | ||||||||
\(55\) | −6.47380 | −0.872927 | ||||||||
\(56\) | 0.0274440 | 0.00366736 | ||||||||
\(57\) | 11.0442 | 1.46283 | ||||||||
\(58\) | 1.41752 | 0.186129 | ||||||||
\(59\) | 5.57058 | 0.725228 | 0.362614 | − | 0.931939i | \(-0.381884\pi\) | ||||
0.362614 | + | 0.931939i | \(0.381884\pi\) | |||||||
\(60\) | −4.53192 | −0.585068 | ||||||||
\(61\) | −6.08101 | −0.778593 | −0.389297 | − | 0.921112i | \(-0.627282\pi\) | ||||
−0.389297 | + | 0.921112i | \(0.627282\pi\) | |||||||
\(62\) | −1.20939 | −0.153593 | ||||||||
\(63\) | −0.00667295 | −0.000840713 0 | ||||||||
\(64\) | −7.31425 | −0.914281 | ||||||||
\(65\) | −2.86772 | −0.355696 | ||||||||
\(66\) | −1.51513 | −0.186499 | ||||||||
\(67\) | 7.63543 | 0.932817 | 0.466408 | − | 0.884570i | \(-0.345548\pi\) | ||||
0.466408 | + | 0.884570i | \(0.345548\pi\) | |||||||
\(68\) | −8.34486 | −1.01196 | ||||||||
\(69\) | 2.09259 | 0.251919 | ||||||||
\(70\) | −0.00893276 | −0.00106767 | ||||||||
\(71\) | −4.24652 | −0.503969 | −0.251984 | − | 0.967731i | \(-0.581083\pi\) | ||||
−0.251984 | + | 0.967731i | \(0.581083\pi\) | |||||||
\(72\) | −0.110890 | −0.0130685 | ||||||||
\(73\) | 13.3928 | 1.56751 | 0.783753 | − | 0.621073i | \(-0.213303\pi\) | ||||
0.783753 | + | 0.621073i | \(0.213303\pi\) | |||||||
\(74\) | 1.49595 | 0.173901 | ||||||||
\(75\) | −5.92227 | −0.683845 | ||||||||
\(76\) | −12.2378 | −1.40378 | ||||||||
\(77\) | 0.203540 | 0.0231955 | ||||||||
\(78\) | −0.671159 | −0.0759938 | ||||||||
\(79\) | 14.5441 | 1.63634 | 0.818170 | − | 0.574976i | \(-0.194989\pi\) | ||||
0.818170 | + | 0.574976i | \(0.194989\pi\) | |||||||
\(80\) | 4.94698 | 0.553089 | ||||||||
\(81\) | −9.46565 | −1.05174 | ||||||||
\(82\) | 1.69420 | 0.187093 | ||||||||
\(83\) | 6.07686 | 0.667022 | 0.333511 | − | 0.942746i | \(-0.391766\pi\) | ||||
0.333511 | + | 0.942746i | \(0.391766\pi\) | |||||||
\(84\) | 0.142486 | 0.0155465 | ||||||||
\(85\) | 5.47218 | 0.593542 | ||||||||
\(86\) | −0.872826 | −0.0941192 | ||||||||
\(87\) | 14.8271 | 1.58964 | ||||||||
\(88\) | 3.38240 | 0.360565 | ||||||||
\(89\) | −11.1352 | −1.18032 | −0.590162 | − | 0.807285i | \(-0.700936\pi\) | ||||
−0.590162 | + | 0.807285i | \(0.700936\pi\) | |||||||
\(90\) | 0.0360936 | 0.00380460 | ||||||||
\(91\) | 0.0901627 | 0.00945161 | ||||||||
\(92\) | −2.31876 | −0.241748 | ||||||||
\(93\) | −12.6502 | −1.31176 | ||||||||
\(94\) | 1.12024 | 0.115544 | ||||||||
\(95\) | 8.02502 | 0.823350 | ||||||||
\(96\) | 3.56035 | 0.363376 | ||||||||
\(97\) | −1.28324 | −0.130293 | −0.0651465 | − | 0.997876i | \(-0.520751\pi\) | ||||
−0.0651465 | + | 0.997876i | \(0.520751\pi\) | |||||||
\(98\) | −1.19014 | −0.120222 | ||||||||
\(99\) | −0.822423 | −0.0826566 | ||||||||
\(100\) | 6.56236 | 0.656236 | ||||||||
\(101\) | 6.31440 | 0.628306 | 0.314153 | − | 0.949372i | \(-0.398279\pi\) | ||||
0.314153 | + | 0.949372i | \(0.398279\pi\) | |||||||
\(102\) | 1.28071 | 0.126809 | ||||||||
\(103\) | 15.8711 | 1.56382 | 0.781912 | − | 0.623389i | \(-0.214245\pi\) | ||||
0.781912 | + | 0.623389i | \(0.214245\pi\) | |||||||
\(104\) | 1.49831 | 0.146921 | ||||||||
\(105\) | −0.0934361 | −0.00911843 | ||||||||
\(106\) | 1.07360 | 0.104277 | ||||||||
\(107\) | 16.5449 | 1.59945 | 0.799727 | − | 0.600364i | \(-0.204978\pi\) | ||||
0.799727 | + | 0.600364i | \(0.204978\pi\) | |||||||
\(108\) | 9.94286 | 0.956752 | ||||||||
\(109\) | −17.9401 | −1.71835 | −0.859175 | − | 0.511683i | \(-0.829022\pi\) | ||||
−0.859175 | + | 0.511683i | \(0.829022\pi\) | |||||||
\(110\) | −1.10094 | −0.104970 | ||||||||
\(111\) | 15.6476 | 1.48520 | ||||||||
\(112\) | −0.155536 | −0.0146968 | ||||||||
\(113\) | −1.60952 | −0.151411 | −0.0757054 | − | 0.997130i | \(-0.524121\pi\) | ||||
−0.0757054 | + | 0.997130i | \(0.524121\pi\) | |||||||
\(114\) | 1.87817 | 0.175907 | ||||||||
\(115\) | 1.52054 | 0.141791 | ||||||||
\(116\) | −16.4297 | −1.52546 | ||||||||
\(117\) | −0.364311 | −0.0336805 | ||||||||
\(118\) | 0.947335 | 0.0872093 | ||||||||
\(119\) | −0.172049 | −0.0157717 | ||||||||
\(120\) | −1.55271 | −0.141742 | ||||||||
\(121\) | 14.0857 | 1.28052 | ||||||||
\(122\) | −1.03414 | −0.0936265 | ||||||||
\(123\) | 17.7212 | 1.59787 | ||||||||
\(124\) | 14.0174 | 1.25880 | ||||||||
\(125\) | −10.7660 | −0.962943 | ||||||||
\(126\) | −0.00113480 | −0.000101096 0 | ||||||||
\(127\) | 10.0551 | 0.892244 | 0.446122 | − | 0.894972i | \(-0.352805\pi\) | ||||
0.446122 | + | 0.894972i | \(0.352805\pi\) | |||||||
\(128\) | −5.24690 | −0.463765 | ||||||||
\(129\) | −9.12971 | −0.803826 | ||||||||
\(130\) | −0.487685 | −0.0427728 | ||||||||
\(131\) | 10.4768 | 0.915360 | 0.457680 | − | 0.889117i | \(-0.348681\pi\) | ||||
0.457680 | + | 0.889117i | \(0.348681\pi\) | |||||||
\(132\) | 17.5610 | 1.52849 | ||||||||
\(133\) | −0.252311 | −0.0218782 | ||||||||
\(134\) | 1.29848 | 0.112172 | ||||||||
\(135\) | −6.52008 | −0.561160 | ||||||||
\(136\) | −2.85908 | −0.245164 | ||||||||
\(137\) | 2.11479 | 0.180679 | 0.0903395 | − | 0.995911i | \(-0.471205\pi\) | ||||
0.0903395 | + | 0.995911i | \(0.471205\pi\) | |||||||
\(138\) | 0.355867 | 0.0302934 | ||||||||
\(139\) | 14.8955 | 1.26342 | 0.631710 | − | 0.775205i | \(-0.282353\pi\) | ||||
0.631710 | + | 0.775205i | \(0.282353\pi\) | |||||||
\(140\) | 0.103535 | 0.00875029 | ||||||||
\(141\) | 11.7176 | 0.986800 | ||||||||
\(142\) | −0.722164 | −0.0606027 | ||||||||
\(143\) | 11.1123 | 0.929257 | ||||||||
\(144\) | 0.628457 | 0.0523714 | ||||||||
\(145\) | 10.7738 | 0.894719 | ||||||||
\(146\) | 2.27758 | 0.188494 | ||||||||
\(147\) | −12.4488 | −1.02676 | ||||||||
\(148\) | −17.3388 | −1.42524 | ||||||||
\(149\) | 14.5999 | 1.19607 | 0.598035 | − | 0.801470i | \(-0.295948\pi\) | ||||
0.598035 | + | 0.801470i | \(0.295948\pi\) | |||||||
\(150\) | −1.00714 | −0.0822329 | ||||||||
\(151\) | 5.61907 | 0.457274 | 0.228637 | − | 0.973512i | \(-0.426573\pi\) | ||||
0.228637 | + | 0.973512i | \(0.426573\pi\) | |||||||
\(152\) | −4.19288 | −0.340087 | ||||||||
\(153\) | 0.695178 | 0.0562018 | ||||||||
\(154\) | 0.0346141 | 0.00278928 | ||||||||
\(155\) | −9.19200 | −0.738319 | ||||||||
\(156\) | 7.77905 | 0.622822 | ||||||||
\(157\) | −11.5671 | −0.923158 | −0.461579 | − | 0.887099i | \(-0.652717\pi\) | ||||
−0.461579 | + | 0.887099i | \(0.652717\pi\) | |||||||
\(158\) | 2.47338 | 0.196771 | ||||||||
\(159\) | 11.2297 | 0.890577 | ||||||||
\(160\) | 2.58706 | 0.204525 | ||||||||
\(161\) | −0.0478067 | −0.00376770 | ||||||||
\(162\) | −1.60973 | −0.126472 | ||||||||
\(163\) | −23.2221 | −1.81890 | −0.909448 | − | 0.415818i | \(-0.863495\pi\) | ||||
−0.909448 | + | 0.415818i | \(0.863495\pi\) | |||||||
\(164\) | −19.6365 | −1.53336 | ||||||||
\(165\) | −11.5157 | −0.896499 | ||||||||
\(166\) | 1.03343 | 0.0802100 | ||||||||
\(167\) | −7.00393 | −0.541981 | −0.270990 | − | 0.962582i | \(-0.587351\pi\) | ||||
−0.270990 | + | 0.962582i | \(0.587351\pi\) | |||||||
\(168\) | 0.0488180 | 0.00376639 | ||||||||
\(169\) | −8.07756 | −0.621351 | ||||||||
\(170\) | 0.930601 | 0.0713739 | ||||||||
\(171\) | 1.01949 | 0.0779622 | ||||||||
\(172\) | 10.1165 | 0.771373 | ||||||||
\(173\) | −5.13247 | −0.390215 | −0.195107 | − | 0.980782i | \(-0.562506\pi\) | ||||
−0.195107 | + | 0.980782i | \(0.562506\pi\) | |||||||
\(174\) | 2.52151 | 0.191155 | ||||||||
\(175\) | 0.135298 | 0.0102276 | ||||||||
\(176\) | −19.1694 | −1.44494 | ||||||||
\(177\) | 9.90907 | 0.744811 | ||||||||
\(178\) | −1.89365 | −0.141935 | ||||||||
\(179\) | 10.9720 | 0.820084 | 0.410042 | − | 0.912067i | \(-0.365514\pi\) | ||||
0.410042 | + | 0.912067i | \(0.365514\pi\) | |||||||
\(180\) | −0.418342 | −0.0311814 | ||||||||
\(181\) | −0.168958 | −0.0125586 | −0.00627929 | − | 0.999980i | \(-0.501999\pi\) | ||||
−0.00627929 | + | 0.999980i | \(0.501999\pi\) | |||||||
\(182\) | 0.0153331 | 0.00113656 | ||||||||
\(183\) | −10.8170 | −0.799617 | ||||||||
\(184\) | −0.794446 | −0.0585673 | ||||||||
\(185\) | 11.3700 | 0.835939 | ||||||||
\(186\) | −2.15129 | −0.157740 | ||||||||
\(187\) | −21.2045 | −1.55063 | ||||||||
\(188\) | −12.9841 | −0.946961 | ||||||||
\(189\) | 0.204995 | 0.0149112 | ||||||||
\(190\) | 1.36474 | 0.0990085 | ||||||||
\(191\) | −21.6168 | −1.56414 | −0.782069 | − | 0.623192i | \(-0.785835\pi\) | ||||
−0.782069 | + | 0.623192i | \(0.785835\pi\) | |||||||
\(192\) | −13.0107 | −0.938969 | ||||||||
\(193\) | 6.12536 | 0.440913 | 0.220457 | − | 0.975397i | \(-0.429245\pi\) | ||||
0.220457 | + | 0.975397i | \(0.429245\pi\) | |||||||
\(194\) | −0.218228 | −0.0156678 | ||||||||
\(195\) | −5.10115 | −0.365301 | ||||||||
\(196\) | 13.7943 | 0.985307 | ||||||||
\(197\) | −15.7982 | −1.12558 | −0.562788 | − | 0.826601i | \(-0.690271\pi\) | ||||
−0.562788 | + | 0.826601i | \(0.690271\pi\) | |||||||
\(198\) | −0.139861 | −0.00993952 | ||||||||
\(199\) | 16.8438 | 1.19403 | 0.597014 | − | 0.802231i | \(-0.296354\pi\) | ||||
0.597014 | + | 0.802231i | \(0.296354\pi\) | |||||||
\(200\) | 2.24837 | 0.158984 | ||||||||
\(201\) | 13.5821 | 0.958005 | ||||||||
\(202\) | 1.07383 | 0.0755544 | ||||||||
\(203\) | −0.338736 | −0.0237746 | ||||||||
\(204\) | −14.8440 | −1.03929 | ||||||||
\(205\) | 12.8768 | 0.899352 | ||||||||
\(206\) | 2.69904 | 0.188051 | ||||||||
\(207\) | 0.193168 | 0.0134261 | ||||||||
\(208\) | −8.49150 | −0.588779 | ||||||||
\(209\) | −31.0967 | −2.15100 | ||||||||
\(210\) | −0.0158898 | −0.00109650 | ||||||||
\(211\) | 2.80669 | 0.193220 | 0.0966102 | − | 0.995322i | \(-0.469200\pi\) | ||||
0.0966102 | + | 0.995322i | \(0.469200\pi\) | |||||||
\(212\) | −12.4435 | −0.854622 | ||||||||
\(213\) | −7.55379 | −0.517577 | ||||||||
\(214\) | 2.81363 | 0.192336 | ||||||||
\(215\) | −6.63393 | −0.452430 | ||||||||
\(216\) | 3.40658 | 0.231789 | ||||||||
\(217\) | 0.289002 | 0.0196187 | ||||||||
\(218\) | −3.05090 | −0.206633 | ||||||||
\(219\) | 23.8233 | 1.60983 | ||||||||
\(220\) | 12.7604 | 0.860305 | ||||||||
\(221\) | −9.39301 | −0.631842 | ||||||||
\(222\) | 2.66103 | 0.178597 | ||||||||
\(223\) | −15.1854 | −1.01689 | −0.508444 | − | 0.861095i | \(-0.669779\pi\) | ||||
−0.508444 | + | 0.861095i | \(0.669779\pi\) | |||||||
\(224\) | −0.0813386 | −0.00543466 | ||||||||
\(225\) | −0.546686 | −0.0364457 | ||||||||
\(226\) | −0.273715 | −0.0182073 | ||||||||
\(227\) | 21.7378 | 1.44279 | 0.721394 | − | 0.692525i | \(-0.243502\pi\) | ||||
0.721394 | + | 0.692525i | \(0.243502\pi\) | |||||||
\(228\) | −21.7689 | −1.44168 | ||||||||
\(229\) | −8.71298 | −0.575770 | −0.287885 | − | 0.957665i | \(-0.592952\pi\) | ||||
−0.287885 | + | 0.957665i | \(0.592952\pi\) | |||||||
\(230\) | 0.258584 | 0.0170505 | ||||||||
\(231\) | 0.362061 | 0.0238219 | ||||||||
\(232\) | −5.62907 | −0.369566 | ||||||||
\(233\) | 10.0530 | 0.658591 | 0.329296 | − | 0.944227i | \(-0.393189\pi\) | ||||
0.329296 | + | 0.944227i | \(0.393189\pi\) | |||||||
\(234\) | −0.0619548 | −0.00405011 | ||||||||
\(235\) | 8.51437 | 0.555416 | ||||||||
\(236\) | −10.9801 | −0.714741 | ||||||||
\(237\) | 25.8714 | 1.68053 | ||||||||
\(238\) | −0.0292586 | −0.00189656 | ||||||||
\(239\) | −4.74203 | −0.306736 | −0.153368 | − | 0.988169i | \(-0.549012\pi\) | ||||
−0.153368 | + | 0.988169i | \(0.549012\pi\) | |||||||
\(240\) | 8.79979 | 0.568024 | ||||||||
\(241\) | 7.69131 | 0.495441 | 0.247720 | − | 0.968832i | \(-0.420319\pi\) | ||||
0.247720 | + | 0.968832i | \(0.420319\pi\) | |||||||
\(242\) | 2.39543 | 0.153984 | ||||||||
\(243\) | −1.70457 | −0.109348 | ||||||||
\(244\) | 11.9862 | 0.767335 | ||||||||
\(245\) | −9.04569 | −0.577908 | ||||||||
\(246\) | 3.01367 | 0.192145 | ||||||||
\(247\) | −13.7750 | −0.876480 | ||||||||
\(248\) | 4.80259 | 0.304965 | ||||||||
\(249\) | 10.8097 | 0.685034 | ||||||||
\(250\) | −1.83088 | −0.115795 | ||||||||
\(251\) | 5.22969 | 0.330095 | 0.165048 | − | 0.986286i | \(-0.447222\pi\) | ||||
0.165048 | + | 0.986286i | \(0.447222\pi\) | |||||||
\(252\) | 0.0131529 | 0.000828556 0 | ||||||||
\(253\) | −5.89204 | −0.370430 | ||||||||
\(254\) | 1.70997 | 0.107293 | ||||||||
\(255\) | 9.73403 | 0.609569 | ||||||||
\(256\) | 13.7362 | 0.858513 | ||||||||
\(257\) | −22.7830 | −1.42116 | −0.710581 | − | 0.703615i | \(-0.751568\pi\) | ||||
−0.710581 | + | 0.703615i | \(0.751568\pi\) | |||||||
\(258\) | −1.55260 | −0.0966607 | ||||||||
\(259\) | −0.357479 | −0.0222127 | ||||||||
\(260\) | 5.65250 | 0.350553 | ||||||||
\(261\) | 1.36869 | 0.0847200 | ||||||||
\(262\) | 1.78168 | 0.110073 | ||||||||
\(263\) | −29.2155 | −1.80150 | −0.900752 | − | 0.434333i | \(-0.856984\pi\) | ||||
−0.900752 | + | 0.434333i | \(0.856984\pi\) | |||||||
\(264\) | 6.01668 | 0.370301 | ||||||||
\(265\) | 8.15988 | 0.501257 | ||||||||
\(266\) | −0.0429082 | −0.00263087 | ||||||||
\(267\) | −19.8074 | −1.21220 | ||||||||
\(268\) | −15.0500 | −0.919328 | ||||||||
\(269\) | −6.94557 | −0.423479 | −0.211739 | − | 0.977326i | \(-0.567913\pi\) | ||||
−0.211739 | + | 0.977326i | \(0.567913\pi\) | |||||||
\(270\) | −1.10881 | −0.0674799 | ||||||||
\(271\) | 6.76612 | 0.411012 | 0.205506 | − | 0.978656i | \(-0.434116\pi\) | ||||
0.205506 | + | 0.978656i | \(0.434116\pi\) | |||||||
\(272\) | 16.2035 | 0.982481 | ||||||||
\(273\) | 0.160383 | 0.00970683 | ||||||||
\(274\) | 0.359642 | 0.0217268 | ||||||||
\(275\) | 16.6751 | 1.00555 | ||||||||
\(276\) | −4.12467 | −0.248276 | ||||||||
\(277\) | −7.31608 | −0.439581 | −0.219790 | − | 0.975547i | \(-0.570537\pi\) | ||||
−0.219790 | + | 0.975547i | \(0.570537\pi\) | |||||||
\(278\) | 2.53313 | 0.151927 | ||||||||
\(279\) | −1.16774 | −0.0699106 | ||||||||
\(280\) | 0.0354727 | 0.00211990 | ||||||||
\(281\) | 4.95425 | 0.295546 | 0.147773 | − | 0.989021i | \(-0.452790\pi\) | ||||
0.147773 | + | 0.989021i | \(0.452790\pi\) | |||||||
\(282\) | 1.99270 | 0.118664 | ||||||||
\(283\) | 27.0549 | 1.60825 | 0.804123 | − | 0.594463i | \(-0.202635\pi\) | ||||
0.804123 | + | 0.594463i | \(0.202635\pi\) | |||||||
\(284\) | 8.37022 | 0.496681 | ||||||||
\(285\) | 14.2751 | 0.845583 | ||||||||
\(286\) | 1.88976 | 0.111744 | ||||||||
\(287\) | −0.404853 | −0.0238977 | ||||||||
\(288\) | 0.328656 | 0.0193662 | ||||||||
\(289\) | 0.923776 | 0.0543398 | ||||||||
\(290\) | 1.83220 | 0.107591 | ||||||||
\(291\) | −2.28265 | −0.133811 | ||||||||
\(292\) | −26.3982 | −1.54484 | ||||||||
\(293\) | 8.41766 | 0.491765 | 0.245883 | − | 0.969300i | \(-0.420922\pi\) | ||||
0.245883 | + | 0.969300i | \(0.420922\pi\) | |||||||
\(294\) | −2.11705 | −0.123469 | ||||||||
\(295\) | 7.20024 | 0.419214 | ||||||||
\(296\) | −5.94054 | −0.345287 | ||||||||
\(297\) | 25.2651 | 1.46603 | ||||||||
\(298\) | 2.48286 | 0.143828 | ||||||||
\(299\) | −2.61001 | −0.150941 | ||||||||
\(300\) | 11.6733 | 0.673957 | ||||||||
\(301\) | 0.208574 | 0.0120220 | ||||||||
\(302\) | 0.955581 | 0.0549875 | ||||||||
\(303\) | 11.2322 | 0.645272 | ||||||||
\(304\) | 23.7626 | 1.36288 | ||||||||
\(305\) | −7.85998 | −0.450061 | ||||||||
\(306\) | 0.118222 | 0.00675832 | ||||||||
\(307\) | 7.42019 | 0.423492 | 0.211746 | − | 0.977325i | \(-0.432085\pi\) | ||||
0.211746 | + | 0.977325i | \(0.432085\pi\) | |||||||
\(308\) | −0.401194 | −0.0228601 | ||||||||
\(309\) | 28.2318 | 1.60605 | ||||||||
\(310\) | −1.56319 | −0.0887834 | ||||||||
\(311\) | 0.180091 | 0.0102120 | 0.00510602 | − | 0.999987i | \(-0.498375\pi\) | ||||
0.00510602 | + | 0.999987i | \(0.498375\pi\) | |||||||
\(312\) | 2.66523 | 0.150889 | ||||||||
\(313\) | −4.23049 | −0.239121 | −0.119561 | − | 0.992827i | \(-0.538149\pi\) | ||||
−0.119561 | + | 0.992827i | \(0.538149\pi\) | |||||||
\(314\) | −1.96711 | −0.111011 | ||||||||
\(315\) | −0.00862510 | −0.000485969 0 | ||||||||
\(316\) | −28.6676 | −1.61268 | ||||||||
\(317\) | 27.9544 | 1.57007 | 0.785037 | − | 0.619449i | \(-0.212644\pi\) | ||||
0.785037 | + | 0.619449i | \(0.212644\pi\) | |||||||
\(318\) | 1.90973 | 0.107093 | ||||||||
\(319\) | −41.7483 | −2.33745 | ||||||||
\(320\) | −9.45400 | −0.528495 | ||||||||
\(321\) | 29.4304 | 1.64264 | ||||||||
\(322\) | −0.00813003 | −0.000453069 0 | ||||||||
\(323\) | 26.2854 | 1.46256 | ||||||||
\(324\) | 18.6575 | 1.03653 | ||||||||
\(325\) | 7.38663 | 0.409737 | ||||||||
\(326\) | −3.94916 | −0.218724 | ||||||||
\(327\) | −31.9122 | −1.76475 | ||||||||
\(328\) | −6.72779 | −0.371480 | ||||||||
\(329\) | −0.267697 | −0.0147586 | ||||||||
\(330\) | −1.95837 | −0.107805 | ||||||||
\(331\) | −30.7138 | −1.68818 | −0.844092 | − | 0.536198i | \(-0.819860\pi\) | ||||
−0.844092 | + | 0.536198i | \(0.819860\pi\) | |||||||
\(332\) | −11.9780 | −0.657377 | ||||||||
\(333\) | 1.44443 | 0.0791542 | ||||||||
\(334\) | −1.19109 | −0.0651736 | ||||||||
\(335\) | 9.86915 | 0.539209 | ||||||||
\(336\) | −0.276670 | −0.0150936 | ||||||||
\(337\) | −12.9562 | −0.705771 | −0.352885 | − | 0.935667i | \(-0.614799\pi\) | ||||
−0.352885 | + | 0.935667i | \(0.614799\pi\) | |||||||
\(338\) | −1.37367 | −0.0747179 | ||||||||
\(339\) | −2.86305 | −0.155499 | ||||||||
\(340\) | −10.7861 | −0.584959 | ||||||||
\(341\) | 35.6186 | 1.92886 | ||||||||
\(342\) | 0.173374 | 0.00937501 | ||||||||
\(343\) | 0.568870 | 0.0307161 | ||||||||
\(344\) | 3.46606 | 0.186878 | ||||||||
\(345\) | 2.70477 | 0.145620 | ||||||||
\(346\) | −0.872830 | −0.0469236 | ||||||||
\(347\) | −4.66780 | −0.250581 | −0.125290 | − | 0.992120i | \(-0.539986\pi\) | ||||
−0.125290 | + | 0.992120i | \(0.539986\pi\) | |||||||
\(348\) | −29.2255 | −1.56665 | ||||||||
\(349\) | 33.7711 | 1.80772 | 0.903862 | − | 0.427824i | \(-0.140720\pi\) | ||||
0.903862 | + | 0.427824i | \(0.140720\pi\) | |||||||
\(350\) | 0.0230089 | 0.00122988 | ||||||||
\(351\) | 11.1917 | 0.597371 | ||||||||
\(352\) | −10.0247 | −0.534321 | ||||||||
\(353\) | 4.11371 | 0.218950 | 0.109475 | − | 0.993990i | \(-0.465083\pi\) | ||||
0.109475 | + | 0.993990i | \(0.465083\pi\) | |||||||
\(354\) | 1.68514 | 0.0895642 | ||||||||
\(355\) | −5.48882 | −0.291316 | ||||||||
\(356\) | 21.9483 | 1.16326 | ||||||||
\(357\) | −0.306044 | −0.0161976 | ||||||||
\(358\) | 1.86590 | 0.0986158 | ||||||||
\(359\) | −14.7836 | −0.780250 | −0.390125 | − | 0.920762i | \(-0.627568\pi\) | ||||
−0.390125 | + | 0.920762i | \(0.627568\pi\) | |||||||
\(360\) | −0.143331 | −0.00755419 | ||||||||
\(361\) | 19.5479 | 1.02884 | ||||||||
\(362\) | −0.0287331 | −0.00151018 | ||||||||
\(363\) | 25.0560 | 1.31510 | ||||||||
\(364\) | −0.177718 | −0.00931494 | ||||||||
\(365\) | 17.3108 | 0.906088 | ||||||||
\(366\) | −1.83955 | −0.0961546 | ||||||||
\(367\) | 14.8085 | 0.772997 | 0.386499 | − | 0.922290i | \(-0.373684\pi\) | ||||
0.386499 | + | 0.922290i | \(0.373684\pi\) | |||||||
\(368\) | 4.50243 | 0.234705 | ||||||||
\(369\) | 1.63585 | 0.0851587 | ||||||||
\(370\) | 1.93359 | 0.100522 | ||||||||
\(371\) | −0.256551 | −0.0133195 | ||||||||
\(372\) | 24.9345 | 1.29279 | ||||||||
\(373\) | 0.507474 | 0.0262760 | 0.0131380 | − | 0.999914i | \(-0.495818\pi\) | ||||
0.0131380 | + | 0.999914i | \(0.495818\pi\) | |||||||
\(374\) | −3.60605 | −0.186464 | ||||||||
\(375\) | −19.1508 | −0.988945 | ||||||||
\(376\) | −4.44855 | −0.229416 | ||||||||
\(377\) | −18.4933 | −0.952455 | ||||||||
\(378\) | 0.0348616 | 0.00179309 | ||||||||
\(379\) | −12.9514 | −0.665266 | −0.332633 | − | 0.943056i | \(-0.607937\pi\) | ||||
−0.332633 | + | 0.943056i | \(0.607937\pi\) | |||||||
\(380\) | −15.8180 | −0.811444 | ||||||||
\(381\) | 17.8862 | 0.916337 | ||||||||
\(382\) | −3.67616 | −0.188089 | ||||||||
\(383\) | 36.3394 | 1.85685 | 0.928427 | − | 0.371514i | \(-0.121161\pi\) | ||||
0.928427 | + | 0.371514i | \(0.121161\pi\) | |||||||
\(384\) | −9.33330 | −0.476288 | ||||||||
\(385\) | 0.263085 | 0.0134080 | ||||||||
\(386\) | 1.04168 | 0.0530202 | ||||||||
\(387\) | −0.842764 | −0.0428401 | ||||||||
\(388\) | 2.52936 | 0.128409 | ||||||||
\(389\) | 22.8777 | 1.15994 | 0.579971 | − | 0.814637i | \(-0.303064\pi\) | ||||
0.579971 | + | 0.814637i | \(0.303064\pi\) | |||||||
\(390\) | −0.867504 | −0.0439278 | ||||||||
\(391\) | 4.98044 | 0.251871 | ||||||||
\(392\) | 4.72615 | 0.238706 | ||||||||
\(393\) | 18.6363 | 0.940077 | ||||||||
\(394\) | −2.68665 | −0.135351 | ||||||||
\(395\) | 18.7989 | 0.945877 | ||||||||
\(396\) | 1.62106 | 0.0814613 | ||||||||
\(397\) | −35.0386 | −1.75854 | −0.879269 | − | 0.476325i | \(-0.841968\pi\) | ||||
−0.879269 | + | 0.476325i | \(0.841968\pi\) | |||||||
\(398\) | 2.86447 | 0.143583 | ||||||||
\(399\) | −0.448817 | −0.0224689 | ||||||||
\(400\) | −12.7424 | −0.637119 | ||||||||
\(401\) | 35.7125 | 1.78340 | 0.891698 | − | 0.452631i | \(-0.149515\pi\) | ||||
0.891698 | + | 0.452631i | \(0.149515\pi\) | |||||||
\(402\) | 2.30977 | 0.115201 | ||||||||
\(403\) | 15.7781 | 0.785962 | ||||||||
\(404\) | −12.4462 | −0.619221 | ||||||||
\(405\) | −12.2348 | −0.607951 | ||||||||
\(406\) | −0.0576056 | −0.00285892 | ||||||||
\(407\) | −44.0583 | −2.18389 | ||||||||
\(408\) | −5.08579 | −0.251784 | ||||||||
\(409\) | −6.11651 | −0.302442 | −0.151221 | − | 0.988500i | \(-0.548321\pi\) | ||||
−0.151221 | + | 0.988500i | \(0.548321\pi\) | |||||||
\(410\) | 2.18983 | 0.108148 | ||||||||
\(411\) | 3.76184 | 0.185558 | ||||||||
\(412\) | −31.2832 | −1.54121 | ||||||||
\(413\) | −0.226380 | −0.0111394 | ||||||||
\(414\) | 0.0328501 | 0.00161450 | ||||||||
\(415\) | 7.85462 | 0.385568 | ||||||||
\(416\) | −4.44069 | −0.217723 | ||||||||
\(417\) | 26.4964 | 1.29754 | ||||||||
\(418\) | −5.28831 | −0.258660 | ||||||||
\(419\) | 5.89777 | 0.288125 | 0.144062 | − | 0.989569i | \(-0.453983\pi\) | ||||
0.144062 | + | 0.989569i | \(0.453983\pi\) | |||||||
\(420\) | 0.184170 | 0.00898657 | ||||||||
\(421\) | 1.97080 | 0.0960507 | 0.0480253 | − | 0.998846i | \(-0.484707\pi\) | ||||
0.0480253 | + | 0.998846i | \(0.484707\pi\) | |||||||
\(422\) | 0.477306 | 0.0232349 | ||||||||
\(423\) | 1.08165 | 0.0525918 | ||||||||
\(424\) | −4.26333 | −0.207046 | ||||||||
\(425\) | −14.0952 | −0.683717 | ||||||||
\(426\) | −1.28460 | −0.0622391 | ||||||||
\(427\) | 0.247122 | 0.0119591 | ||||||||
\(428\) | −32.6113 | −1.57632 | ||||||||
\(429\) | 19.7668 | 0.954349 | ||||||||
\(430\) | −1.12817 | −0.0544051 | ||||||||
\(431\) | 20.7549 | 0.999728 | 0.499864 | − | 0.866104i | \(-0.333383\pi\) | ||||
0.499864 | + | 0.866104i | \(0.333383\pi\) | |||||||
\(432\) | −19.3064 | −0.928880 | ||||||||
\(433\) | −25.8263 | −1.24113 | −0.620566 | − | 0.784154i | \(-0.713097\pi\) | ||||
−0.620566 | + | 0.784154i | \(0.713097\pi\) | |||||||
\(434\) | 0.0491477 | 0.00235917 | ||||||||
\(435\) | 19.1647 | 0.918879 | ||||||||
\(436\) | 35.3613 | 1.69350 | ||||||||
\(437\) | 7.30387 | 0.349391 | ||||||||
\(438\) | 4.05141 | 0.193584 | ||||||||
\(439\) | −34.7025 | −1.65626 | −0.828131 | − | 0.560535i | \(-0.810596\pi\) | ||||
−0.828131 | + | 0.560535i | \(0.810596\pi\) | |||||||
\(440\) | 4.37191 | 0.208423 | ||||||||
\(441\) | −1.14915 | −0.0547215 | ||||||||
\(442\) | −1.59738 | −0.0759796 | ||||||||
\(443\) | −7.72724 | −0.367132 | −0.183566 | − | 0.983007i | \(-0.558764\pi\) | ||||
−0.183566 | + | 0.983007i | \(0.558764\pi\) | |||||||
\(444\) | −30.8426 | −1.46372 | ||||||||
\(445\) | −14.3927 | −0.682279 | ||||||||
\(446\) | −2.58243 | −0.122282 | ||||||||
\(447\) | 25.9706 | 1.22837 | ||||||||
\(448\) | 0.297239 | 0.0140432 | ||||||||
\(449\) | −26.9809 | −1.27331 | −0.636653 | − | 0.771150i | \(-0.719682\pi\) | ||||
−0.636653 | + | 0.771150i | \(0.719682\pi\) | |||||||
\(450\) | −0.0929696 | −0.00438263 | ||||||||
\(451\) | −49.8970 | −2.34956 | ||||||||
\(452\) | 3.17249 | 0.149221 | ||||||||
\(453\) | 9.99532 | 0.469621 | ||||||||
\(454\) | 3.69674 | 0.173496 | ||||||||
\(455\) | 0.116539 | 0.00546345 | ||||||||
\(456\) | −7.45837 | −0.349270 | ||||||||
\(457\) | 24.8185 | 1.16096 | 0.580481 | − | 0.814274i | \(-0.302864\pi\) | ||||
0.580481 | + | 0.814274i | \(0.302864\pi\) | |||||||
\(458\) | −1.48173 | −0.0692368 | ||||||||
\(459\) | −21.3561 | −0.996818 | ||||||||
\(460\) | −2.99711 | −0.139741 | ||||||||
\(461\) | −37.8706 | −1.76381 | −0.881904 | − | 0.471430i | \(-0.843738\pi\) | ||||
−0.881904 | + | 0.471430i | \(0.843738\pi\) | |||||||
\(462\) | 0.0615723 | 0.00286460 | ||||||||
\(463\) | −8.43325 | −0.391926 | −0.195963 | − | 0.980611i | \(-0.562783\pi\) | ||||
−0.195963 | + | 0.980611i | \(0.562783\pi\) | |||||||
\(464\) | 31.9021 | 1.48102 | ||||||||
\(465\) | −16.3509 | −0.758255 | ||||||||
\(466\) | 1.70961 | 0.0791962 | ||||||||
\(467\) | −11.6660 | −0.539840 | −0.269920 | − | 0.962883i | \(-0.586997\pi\) | ||||
−0.269920 | + | 0.962883i | \(0.586997\pi\) | |||||||
\(468\) | 0.718085 | 0.0331935 | ||||||||
\(469\) | −0.310292 | −0.0143279 | ||||||||
\(470\) | 1.44796 | 0.0667893 | ||||||||
\(471\) | −20.5759 | −0.948086 | ||||||||
\(472\) | −3.76194 | −0.173158 | ||||||||
\(473\) | 25.7062 | 1.18197 | ||||||||
\(474\) | 4.39969 | 0.202085 | ||||||||
\(475\) | −20.6708 | −0.948440 | ||||||||
\(476\) | 0.339122 | 0.0155436 | ||||||||
\(477\) | 1.03662 | 0.0474635 | ||||||||
\(478\) | −0.806431 | −0.0368853 | ||||||||
\(479\) | −38.8946 | −1.77714 | −0.888570 | − | 0.458741i | \(-0.848301\pi\) | ||||
−0.888570 | + | 0.458741i | \(0.848301\pi\) | |||||||
\(480\) | 4.60191 | 0.210047 | ||||||||
\(481\) | −19.5166 | −0.889882 | ||||||||
\(482\) | 1.30799 | 0.0595772 | ||||||||
\(483\) | −0.0850396 | −0.00386944 | ||||||||
\(484\) | −27.7641 | −1.26201 | ||||||||
\(485\) | −1.65864 | −0.0753151 | ||||||||
\(486\) | −0.289879 | −0.0131492 | ||||||||
\(487\) | 37.8109 | 1.71338 | 0.856689 | − | 0.515834i | \(-0.172518\pi\) | ||||
0.856689 | + | 0.515834i | \(0.172518\pi\) | |||||||
\(488\) | 4.10665 | 0.185899 | ||||||||
\(489\) | −41.3080 | −1.86801 | ||||||||
\(490\) | −1.53831 | −0.0694939 | ||||||||
\(491\) | −10.8334 | −0.488904 | −0.244452 | − | 0.969661i | \(-0.578608\pi\) | ||||
−0.244452 | + | 0.969661i | \(0.578608\pi\) | |||||||
\(492\) | −34.9299 | −1.57476 | ||||||||
\(493\) | 35.2890 | 1.58934 | ||||||||
\(494\) | −2.34258 | −0.105397 | ||||||||
\(495\) | −1.06302 | −0.0477791 | ||||||||
\(496\) | −27.2181 | −1.22213 | ||||||||
\(497\) | 0.172572 | 0.00774089 | ||||||||
\(498\) | 1.83829 | 0.0823759 | ||||||||
\(499\) | 25.7541 | 1.15291 | 0.576455 | − | 0.817129i | \(-0.304436\pi\) | ||||
0.576455 | + | 0.817129i | \(0.304436\pi\) | |||||||
\(500\) | 21.2207 | 0.949019 | ||||||||
\(501\) | −12.4587 | −0.556616 | ||||||||
\(502\) | 0.889364 | 0.0396942 | ||||||||
\(503\) | 34.2654 | 1.52782 | 0.763909 | − | 0.645324i | \(-0.223278\pi\) | ||||
0.763909 | + | 0.645324i | \(0.223278\pi\) | |||||||
\(504\) | 0.00450640 | 0.000200731 0 | ||||||||
\(505\) | 8.16165 | 0.363189 | ||||||||
\(506\) | −1.00200 | −0.0445445 | ||||||||
\(507\) | −14.3685 | −0.638129 | ||||||||
\(508\) | −19.8194 | −0.879342 | ||||||||
\(509\) | 29.5680 | 1.31058 | 0.655289 | − | 0.755379i | \(-0.272547\pi\) | ||||
0.655289 | + | 0.755379i | \(0.272547\pi\) | |||||||
\(510\) | 1.65537 | 0.0733012 | ||||||||
\(511\) | −0.544261 | −0.0240767 | ||||||||
\(512\) | 12.8298 | 0.567002 | ||||||||
\(513\) | −31.3190 | −1.38277 | ||||||||
\(514\) | −3.87448 | −0.170896 | ||||||||
\(515\) | 20.5141 | 0.903959 | ||||||||
\(516\) | 17.9954 | 0.792202 | ||||||||
\(517\) | −32.9929 | −1.45103 | ||||||||
\(518\) | −0.0607931 | −0.00267109 | ||||||||
\(519\) | −9.12975 | −0.400752 | ||||||||
\(520\) | 1.93663 | 0.0849271 | ||||||||
\(521\) | −24.0954 | −1.05564 | −0.527819 | − | 0.849357i | \(-0.676990\pi\) | ||||
−0.527819 | + | 0.849357i | \(0.676990\pi\) | |||||||
\(522\) | 0.232761 | 0.0101877 | ||||||||
\(523\) | 35.8786 | 1.56886 | 0.784432 | − | 0.620215i | \(-0.212955\pi\) | ||||
0.784432 | + | 0.620215i | \(0.212955\pi\) | |||||||
\(524\) | −20.6506 | −0.902124 | ||||||||
\(525\) | 0.240672 | 0.0105038 | ||||||||
\(526\) | −4.96840 | −0.216632 | ||||||||
\(527\) | −30.1078 | −1.31152 | ||||||||
\(528\) | −34.0988 | −1.48396 | ||||||||
\(529\) | −21.6161 | −0.939830 | ||||||||
\(530\) | 1.38767 | 0.0602766 | ||||||||
\(531\) | 0.914708 | 0.0396949 | ||||||||
\(532\) | 0.497326 | 0.0215618 | ||||||||
\(533\) | −22.1030 | −0.957387 | ||||||||
\(534\) | −3.36846 | −0.145768 | ||||||||
\(535\) | 21.3850 | 0.924554 | ||||||||
\(536\) | −5.15638 | −0.222722 | ||||||||
\(537\) | 19.5172 | 0.842228 | ||||||||
\(538\) | −1.18117 | −0.0509237 | ||||||||
\(539\) | 35.0517 | 1.50978 | ||||||||
\(540\) | 12.8516 | 0.553045 | ||||||||
\(541\) | 0.138724 | 0.00596420 | 0.00298210 | − | 0.999996i | \(-0.499051\pi\) | ||||
0.00298210 | + | 0.999996i | \(0.499051\pi\) | |||||||
\(542\) | 1.15065 | 0.0494246 | ||||||||
\(543\) | −0.300547 | −0.0128977 | ||||||||
\(544\) | 8.47373 | 0.363308 | ||||||||
\(545\) | −23.1884 | −0.993282 | ||||||||
\(546\) | 0.0272748 | 0.00116725 | ||||||||
\(547\) | −10.5144 | −0.449563 | −0.224782 | − | 0.974409i | \(-0.572167\pi\) | ||||
−0.224782 | + | 0.974409i | \(0.572167\pi\) | |||||||
\(548\) | −4.16843 | −0.178066 | ||||||||
\(549\) | −0.998521 | −0.0426158 | ||||||||
\(550\) | 2.83578 | 0.120918 | ||||||||
\(551\) | 51.7518 | 2.20470 | ||||||||
\(552\) | −1.41318 | −0.0601488 | ||||||||
\(553\) | −0.591049 | −0.0251340 | ||||||||
\(554\) | −1.24417 | −0.0528599 | ||||||||
\(555\) | 20.2252 | 0.858512 | ||||||||
\(556\) | −29.3602 | −1.24515 | ||||||||
\(557\) | −12.2592 | −0.519437 | −0.259719 | − | 0.965684i | \(-0.583630\pi\) | ||||
−0.259719 | + | 0.965684i | \(0.583630\pi\) | |||||||
\(558\) | −0.198586 | −0.00840681 | ||||||||
\(559\) | 11.3871 | 0.481625 | ||||||||
\(560\) | −0.201037 | −0.00849537 | ||||||||
\(561\) | −37.7190 | −1.59250 | ||||||||
\(562\) | 0.842521 | 0.0355396 | ||||||||
\(563\) | 37.2173 | 1.56852 | 0.784261 | − | 0.620431i | \(-0.213042\pi\) | ||||
0.784261 | + | 0.620431i | \(0.213042\pi\) | |||||||
\(564\) | −23.0963 | −0.972531 | ||||||||
\(565\) | −2.08038 | −0.0875221 | ||||||||
\(566\) | 4.60096 | 0.193393 | ||||||||
\(567\) | 0.384669 | 0.0161546 | ||||||||
\(568\) | 2.86777 | 0.120329 | ||||||||
\(569\) | −37.7314 | −1.58178 | −0.790892 | − | 0.611956i | \(-0.790383\pi\) | ||||
−0.790892 | + | 0.611956i | \(0.790383\pi\) | |||||||
\(570\) | 2.42762 | 0.101682 | ||||||||
\(571\) | 22.9818 | 0.961760 | 0.480880 | − | 0.876787i | \(-0.340317\pi\) | ||||
0.480880 | + | 0.876787i | \(0.340317\pi\) | |||||||
\(572\) | −21.9032 | −0.915819 | ||||||||
\(573\) | −38.4524 | −1.60637 | ||||||||
\(574\) | −0.0688494 | −0.00287372 | ||||||||
\(575\) | −3.91660 | −0.163333 | ||||||||
\(576\) | −1.20102 | −0.0500426 | ||||||||
\(577\) | 4.21074 | 0.175295 | 0.0876477 | − | 0.996152i | \(-0.472065\pi\) | ||||
0.0876477 | + | 0.996152i | \(0.472065\pi\) | |||||||
\(578\) | 0.157098 | 0.00653440 | ||||||||
\(579\) | 10.8959 | 0.452819 | ||||||||
\(580\) | −21.2361 | −0.881782 | ||||||||
\(581\) | −0.246954 | −0.0102454 | ||||||||
\(582\) | −0.388188 | −0.0160909 | ||||||||
\(583\) | −31.6192 | −1.30953 | ||||||||
\(584\) | −9.04445 | −0.374262 | ||||||||
\(585\) | −0.470888 | −0.0194688 | ||||||||
\(586\) | 1.43151 | 0.0591351 | ||||||||
\(587\) | −9.45415 | −0.390215 | −0.195107 | − | 0.980782i | \(-0.562505\pi\) | ||||
−0.195107 | + | 0.980782i | \(0.562505\pi\) | |||||||
\(588\) | 24.5376 | 1.01191 | ||||||||
\(589\) | −44.1534 | −1.81931 | ||||||||
\(590\) | 1.22447 | 0.0504108 | ||||||||
\(591\) | −28.1022 | −1.15597 | ||||||||
\(592\) | 33.6673 | 1.38372 | ||||||||
\(593\) | −10.2834 | −0.422288 | −0.211144 | − | 0.977455i | \(-0.567719\pi\) | ||||
−0.211144 | + | 0.977455i | \(0.567719\pi\) | |||||||
\(594\) | 4.29659 | 0.176291 | ||||||||
\(595\) | −0.222381 | −0.00911672 | ||||||||
\(596\) | −28.7776 | −1.17878 | ||||||||
\(597\) | 29.9622 | 1.22627 | ||||||||
\(598\) | −0.443860 | −0.0181508 | ||||||||
\(599\) | 2.00944 | 0.0821033 | 0.0410517 | − | 0.999157i | \(-0.486929\pi\) | ||||
0.0410517 | + | 0.999157i | \(0.486929\pi\) | |||||||
\(600\) | 3.99945 | 0.163277 | ||||||||
\(601\) | 7.75727 | 0.316426 | 0.158213 | − | 0.987405i | \(-0.449427\pi\) | ||||
0.158213 | + | 0.987405i | \(0.449427\pi\) | |||||||
\(602\) | 0.0354702 | 0.00144566 | ||||||||
\(603\) | 1.25376 | 0.0510572 | ||||||||
\(604\) | −11.0756 | −0.450661 | ||||||||
\(605\) | 18.2065 | 0.740198 | ||||||||
\(606\) | 1.91015 | 0.0775945 | ||||||||
\(607\) | −0.151634 | −0.00615463 | −0.00307732 | − | 0.999995i | \(-0.500980\pi\) | ||||
−0.00307732 | + | 0.999995i | \(0.500980\pi\) | |||||||
\(608\) | 12.4268 | 0.503975 | ||||||||
\(609\) | −0.602551 | −0.0244166 | ||||||||
\(610\) | −1.33667 | −0.0541202 | ||||||||
\(611\) | −14.6149 | −0.591257 | ||||||||
\(612\) | −1.37025 | −0.0553892 | ||||||||
\(613\) | 26.9378 | 1.08801 | 0.544004 | − | 0.839082i | \(-0.316907\pi\) | ||||
0.544004 | + | 0.839082i | \(0.316907\pi\) | |||||||
\(614\) | 1.26188 | 0.0509253 | ||||||||
\(615\) | 22.9055 | 0.923637 | ||||||||
\(616\) | −0.137455 | −0.00553823 | ||||||||
\(617\) | 13.9776 | 0.562716 | 0.281358 | − | 0.959603i | \(-0.409215\pi\) | ||||
0.281358 | + | 0.959603i | \(0.409215\pi\) | |||||||
\(618\) | 4.80111 | 0.193129 | ||||||||
\(619\) | −47.3757 | −1.90419 | −0.952096 | − | 0.305799i | \(-0.901076\pi\) | ||||
−0.952096 | + | 0.305799i | \(0.901076\pi\) | |||||||
\(620\) | 18.1182 | 0.727643 | ||||||||
\(621\) | −5.93417 | −0.238130 | ||||||||
\(622\) | 0.0306264 | 0.00122801 | ||||||||
\(623\) | 0.452515 | 0.0181296 | ||||||||
\(624\) | −15.1048 | −0.604678 | ||||||||
\(625\) | 2.73103 | 0.109241 | ||||||||
\(626\) | −0.719438 | −0.0287545 | ||||||||
\(627\) | −55.3154 | −2.20908 | ||||||||
\(628\) | 22.7997 | 0.909809 | ||||||||
\(629\) | 37.2417 | 1.48492 | ||||||||
\(630\) | −0.00146679 | −5.84382e−5 0 | ||||||||
\(631\) | −11.2559 | −0.448089 | −0.224045 | − | 0.974579i | \(-0.571926\pi\) | ||||
−0.224045 | + | 0.974579i | \(0.571926\pi\) | |||||||
\(632\) | −9.82198 | −0.390697 | ||||||||
\(633\) | 4.99259 | 0.198438 | ||||||||
\(634\) | 4.75393 | 0.188803 | ||||||||
\(635\) | 12.9967 | 0.515756 | ||||||||
\(636\) | −22.1347 | −0.877699 | ||||||||
\(637\) | 15.5269 | 0.615200 | ||||||||
\(638\) | −7.09972 | −0.281081 | ||||||||
\(639\) | −0.697291 | −0.0275844 | ||||||||
\(640\) | −6.78186 | −0.268077 | ||||||||
\(641\) | −27.1661 | −1.07300 | −0.536499 | − | 0.843901i | \(-0.680253\pi\) | ||||
−0.536499 | + | 0.843901i | \(0.680253\pi\) | |||||||
\(642\) | 5.00494 | 0.197529 | ||||||||
\(643\) | −1.77376 | −0.0699501 | −0.0349751 | − | 0.999388i | \(-0.511135\pi\) | ||||
−0.0349751 | + | 0.999388i | \(0.511135\pi\) | |||||||
\(644\) | 0.0942309 | 0.00371322 | ||||||||
\(645\) | −11.8006 | −0.464647 | ||||||||
\(646\) | 4.47011 | 0.175874 | ||||||||
\(647\) | 26.2940 | 1.03373 | 0.516863 | − | 0.856068i | \(-0.327100\pi\) | ||||
0.516863 | + | 0.856068i | \(0.327100\pi\) | |||||||
\(648\) | 6.39237 | 0.251116 | ||||||||
\(649\) | −27.9006 | −1.09520 | ||||||||
\(650\) | 1.25617 | 0.0492712 | ||||||||
\(651\) | 0.514082 | 0.0201485 | ||||||||
\(652\) | 45.7726 | 1.79259 | ||||||||
\(653\) | −0.138130 | −0.00540545 | −0.00270273 | − | 0.999996i | \(-0.500860\pi\) | ||||
−0.00270273 | + | 0.999996i | \(0.500860\pi\) | |||||||
\(654\) | −5.42700 | −0.212212 | ||||||||
\(655\) | 13.5417 | 0.529118 | ||||||||
\(656\) | 38.1289 | 1.48869 | ||||||||
\(657\) | 2.19914 | 0.0857965 | ||||||||
\(658\) | −0.0455246 | −0.00177473 | ||||||||
\(659\) | −5.31430 | −0.207016 | −0.103508 | − | 0.994629i | \(-0.533007\pi\) | ||||
−0.103508 | + | 0.994629i | \(0.533007\pi\) | |||||||
\(660\) | 22.6984 | 0.883535 | ||||||||
\(661\) | 6.24045 | 0.242725 | 0.121363 | − | 0.992608i | \(-0.461274\pi\) | ||||
0.121363 | + | 0.992608i | \(0.461274\pi\) | |||||||
\(662\) | −5.22320 | −0.203006 | ||||||||
\(663\) | −16.7085 | −0.648904 | ||||||||
\(664\) | −4.10385 | −0.159260 | ||||||||
\(665\) | −0.326124 | −0.0126466 | ||||||||
\(666\) | 0.245640 | 0.00951836 | ||||||||
\(667\) | 9.80567 | 0.379677 | ||||||||
\(668\) | 13.8053 | 0.534144 | ||||||||
\(669\) | −27.0121 | −1.04435 | ||||||||
\(670\) | 1.67835 | 0.0648403 | ||||||||
\(671\) | 30.4571 | 1.17578 | ||||||||
\(672\) | −0.144687 | −0.00558141 | ||||||||
\(673\) | −4.55607 | −0.175623 | −0.0878117 | − | 0.996137i | \(-0.527987\pi\) | ||||
−0.0878117 | + | 0.996137i | \(0.527987\pi\) | |||||||
\(674\) | −2.20334 | −0.0848695 | ||||||||
\(675\) | 16.7944 | 0.646415 | ||||||||
\(676\) | 15.9215 | 0.612366 | ||||||||
\(677\) | −23.9220 | −0.919396 | −0.459698 | − | 0.888075i | \(-0.652042\pi\) | ||||
−0.459698 | + | 0.888075i | \(0.652042\pi\) | |||||||
\(678\) | −0.486891 | −0.0186989 | ||||||||
\(679\) | 0.0521487 | 0.00200128 | ||||||||
\(680\) | −3.69549 | −0.141716 | ||||||||
\(681\) | 38.6676 | 1.48175 | ||||||||
\(682\) | 6.05732 | 0.231947 | ||||||||
\(683\) | −12.4913 | −0.477967 | −0.238983 | − | 0.971024i | \(-0.576814\pi\) | ||||
−0.238983 | + | 0.971024i | \(0.576814\pi\) | |||||||
\(684\) | −2.00949 | −0.0768348 | ||||||||
\(685\) | 2.73347 | 0.104440 | ||||||||
\(686\) | 0.0967423 | 0.00369364 | ||||||||
\(687\) | −15.4988 | −0.591317 | ||||||||
\(688\) | −19.6435 | −0.748901 | ||||||||
\(689\) | −14.0064 | −0.533603 | ||||||||
\(690\) | 0.459974 | 0.0175109 | ||||||||
\(691\) | −0.743686 | −0.0282912 | −0.0141456 | − | 0.999900i | \(-0.504503\pi\) | ||||
−0.0141456 | + | 0.999900i | \(0.504503\pi\) | |||||||
\(692\) | 10.1165 | 0.384572 | ||||||||
\(693\) | 0.0334219 | 0.00126959 | ||||||||
\(694\) | −0.793808 | −0.0301325 | ||||||||
\(695\) | 19.2531 | 0.730313 | ||||||||
\(696\) | −10.0131 | −0.379546 | ||||||||
\(697\) | 42.1770 | 1.59757 | ||||||||
\(698\) | 5.74312 | 0.217380 | ||||||||
\(699\) | 17.8824 | 0.676375 | ||||||||
\(700\) | −0.266684 | −0.0100797 | ||||||||
\(701\) | −18.6036 | −0.702649 | −0.351324 | − | 0.936254i | \(-0.614269\pi\) | ||||
−0.351324 | + | 0.936254i | \(0.614269\pi\) | |||||||
\(702\) | 1.90327 | 0.0718343 | ||||||||
\(703\) | 54.6154 | 2.05986 | ||||||||
\(704\) | 36.6339 | 1.38069 | ||||||||
\(705\) | 15.1455 | 0.570414 | ||||||||
\(706\) | 0.699578 | 0.0263290 | ||||||||
\(707\) | −0.256607 | −0.00965070 | ||||||||
\(708\) | −19.5316 | −0.734041 | ||||||||
\(709\) | −37.1530 | −1.39531 | −0.697656 | − | 0.716433i | \(-0.745773\pi\) | ||||
−0.697656 | + | 0.716433i | \(0.745773\pi\) | |||||||
\(710\) | −0.933430 | −0.0350310 | ||||||||
\(711\) | 2.38819 | 0.0895641 | ||||||||
\(712\) | 7.51983 | 0.281817 | ||||||||
\(713\) | −8.36597 | −0.313308 | ||||||||
\(714\) | −0.0520459 | −0.00194777 | ||||||||
\(715\) | 14.3631 | 0.537151 | ||||||||
\(716\) | −21.6266 | −0.808225 | ||||||||
\(717\) | −8.43522 | −0.315019 | ||||||||
\(718\) | −2.51411 | −0.0938257 | ||||||||
\(719\) | 34.8793 | 1.30078 | 0.650388 | − | 0.759602i | \(-0.274606\pi\) | ||||
0.650388 | + | 0.759602i | \(0.274606\pi\) | |||||||
\(720\) | 0.812309 | 0.0302730 | ||||||||
\(721\) | −0.644975 | −0.0240201 | ||||||||
\(722\) | 3.32432 | 0.123719 | ||||||||
\(723\) | 13.6815 | 0.508819 | ||||||||
\(724\) | 0.333030 | 0.0123770 | ||||||||
\(725\) | −27.7512 | −1.03065 | ||||||||
\(726\) | 4.26103 | 0.158142 | ||||||||
\(727\) | −17.6643 | −0.655134 | −0.327567 | − | 0.944828i | \(-0.606229\pi\) | ||||
−0.327567 | + | 0.944828i | \(0.606229\pi\) | |||||||
\(728\) | −0.0608889 | −0.00225669 | ||||||||
\(729\) | 25.3648 | 0.939438 | ||||||||
\(730\) | 2.94388 | 0.108958 | ||||||||
\(731\) | −21.7290 | −0.803676 | ||||||||
\(732\) | 21.3212 | 0.788055 | ||||||||
\(733\) | 32.7964 | 1.21136 | 0.605681 | − | 0.795708i | \(-0.292901\pi\) | ||||
0.605681 | + | 0.795708i | \(0.292901\pi\) | |||||||
\(734\) | 2.51834 | 0.0929536 | ||||||||
\(735\) | −16.0907 | −0.593513 | ||||||||
\(736\) | 2.35458 | 0.0867908 | ||||||||
\(737\) | −38.2426 | −1.40868 | ||||||||
\(738\) | 0.278192 | 0.0102404 | ||||||||
\(739\) | 9.86928 | 0.363047 | 0.181524 | − | 0.983387i | \(-0.441897\pi\) | ||||
0.181524 | + | 0.983387i | \(0.441897\pi\) | |||||||
\(740\) | −22.4112 | −0.823851 | ||||||||
\(741\) | −24.5032 | −0.900148 | ||||||||
\(742\) | −0.0436292 | −0.00160168 | ||||||||
\(743\) | 44.3582 | 1.62734 | 0.813672 | − | 0.581324i | \(-0.197465\pi\) | ||||
0.813672 | + | 0.581324i | \(0.197465\pi\) | |||||||
\(744\) | 8.54295 | 0.313200 | ||||||||
\(745\) | 18.8710 | 0.691381 | ||||||||
\(746\) | 0.0863011 | 0.00315971 | ||||||||
\(747\) | 0.997840 | 0.0365091 | ||||||||
\(748\) | 41.7958 | 1.52820 | ||||||||
\(749\) | −0.672357 | −0.0245674 | ||||||||
\(750\) | −3.25680 | −0.118921 | ||||||||
\(751\) | −16.9290 | −0.617749 | −0.308874 | − | 0.951103i | \(-0.599952\pi\) | ||||
−0.308874 | + | 0.951103i | \(0.599952\pi\) | |||||||
\(752\) | 25.2116 | 0.919373 | ||||||||
\(753\) | 9.30269 | 0.339009 | ||||||||
\(754\) | −3.14498 | −0.114533 | ||||||||
\(755\) | 7.26291 | 0.264324 | ||||||||
\(756\) | −0.404062 | −0.0146956 | ||||||||
\(757\) | 5.48503 | 0.199357 | 0.0996783 | − | 0.995020i | \(-0.468219\pi\) | ||||
0.0996783 | + | 0.995020i | \(0.468219\pi\) | |||||||
\(758\) | −2.20251 | −0.0799988 | ||||||||
\(759\) | −10.4809 | −0.380432 | ||||||||
\(760\) | −5.41948 | −0.196585 | ||||||||
\(761\) | −6.94150 | −0.251629 | −0.125815 | − | 0.992054i | \(-0.540154\pi\) | ||||
−0.125815 | + | 0.992054i | \(0.540154\pi\) | |||||||
\(762\) | 3.04173 | 0.110190 | ||||||||
\(763\) | 0.729056 | 0.0263936 | ||||||||
\(764\) | 42.6085 | 1.54152 | ||||||||
\(765\) | 0.898550 | 0.0324871 | ||||||||
\(766\) | 6.17988 | 0.223288 | ||||||||
\(767\) | −12.3592 | −0.446265 | ||||||||
\(768\) | 24.4342 | 0.881695 | ||||||||
\(769\) | 10.0489 | 0.362372 | 0.181186 | − | 0.983449i | \(-0.442006\pi\) | ||||
0.181186 | + | 0.983449i | \(0.442006\pi\) | |||||||
\(770\) | 0.0447403 | 0.00161233 | ||||||||
\(771\) | −40.5268 | −1.45954 | ||||||||
\(772\) | −12.0736 | −0.434537 | ||||||||
\(773\) | 12.9121 | 0.464414 | 0.232207 | − | 0.972666i | \(-0.425405\pi\) | ||||
0.232207 | + | 0.972666i | \(0.425405\pi\) | |||||||
\(774\) | −0.143321 | −0.00515156 | ||||||||
\(775\) | 23.6766 | 0.850490 | ||||||||
\(776\) | 0.866599 | 0.0311091 | ||||||||
\(777\) | −0.635892 | −0.0228125 | ||||||||
\(778\) | 3.89058 | 0.139484 | ||||||||
\(779\) | 61.8531 | 2.21612 | ||||||||
\(780\) | 10.0548 | 0.360019 | ||||||||
\(781\) | 21.2690 | 0.761063 | ||||||||
\(782\) | 0.846974 | 0.0302877 | ||||||||
\(783\) | −42.0467 | −1.50263 | ||||||||
\(784\) | −26.7849 | −0.956603 | ||||||||
\(785\) | −14.9511 | −0.533626 | ||||||||
\(786\) | 3.16930 | 0.113045 | ||||||||
\(787\) | −31.8800 | −1.13640 | −0.568199 | − | 0.822891i | \(-0.692360\pi\) | ||||
−0.568199 | + | 0.822891i | \(0.692360\pi\) | |||||||
\(788\) | 31.1395 | 1.10930 | ||||||||
\(789\) | −51.9691 | −1.85015 | ||||||||
\(790\) | 3.19695 | 0.113742 | ||||||||
\(791\) | 0.0654083 | 0.00232565 | ||||||||
\(792\) | 0.555401 | 0.0197353 | ||||||||
\(793\) | 13.4917 | 0.479103 | ||||||||
\(794\) | −5.95868 | −0.211466 | ||||||||
\(795\) | 14.5150 | 0.514793 | ||||||||
\(796\) | −33.2005 | −1.17676 | ||||||||
\(797\) | −42.6855 | −1.51200 | −0.755999 | − | 0.654573i | \(-0.772848\pi\) | ||||
−0.755999 | + | 0.654573i | \(0.772848\pi\) | |||||||
\(798\) | −0.0763259 | −0.00270191 | ||||||||
\(799\) | 27.8883 | 0.986616 | ||||||||
\(800\) | −6.66371 | −0.235598 | ||||||||
\(801\) | −1.82843 | −0.0646043 | ||||||||
\(802\) | 6.07327 | 0.214455 | ||||||||
\(803\) | −67.0786 | −2.36715 | ||||||||
\(804\) | −26.7713 | −0.944152 | ||||||||
\(805\) | −0.0617924 | −0.00217790 | ||||||||
\(806\) | 2.68322 | 0.0945126 | ||||||||
\(807\) | −12.3549 | −0.434914 | ||||||||
\(808\) | −4.26426 | −0.150016 | ||||||||
\(809\) | 33.3988 | 1.17424 | 0.587120 | − | 0.809500i | \(-0.300262\pi\) | ||||
0.587120 | + | 0.809500i | \(0.300262\pi\) | |||||||
\(810\) | −2.08065 | −0.0731066 | ||||||||
\(811\) | −9.88276 | −0.347031 | −0.173515 | − | 0.984831i | \(-0.555513\pi\) | ||||
−0.173515 | + | 0.984831i | \(0.555513\pi\) | |||||||
\(812\) | 0.667676 | 0.0234308 | ||||||||
\(813\) | 12.0357 | 0.422111 | ||||||||
\(814\) | −7.49257 | −0.262615 | ||||||||
\(815\) | −30.0156 | −1.05140 | ||||||||
\(816\) | 28.8231 | 1.00901 | ||||||||
\(817\) | −31.8658 | −1.11484 | ||||||||
\(818\) | −1.04018 | −0.0363689 | ||||||||
\(819\) | 0.0148050 | 0.000517328 0 | ||||||||
\(820\) | −25.3811 | −0.886347 | ||||||||
\(821\) | −8.42549 | −0.294051 | −0.147026 | − | 0.989133i | \(-0.546970\pi\) | ||||
−0.147026 | + | 0.989133i | \(0.546970\pi\) | |||||||
\(822\) | 0.639739 | 0.0223135 | ||||||||
\(823\) | −2.02595 | −0.0706203 | −0.0353101 | − | 0.999376i | \(-0.511242\pi\) | ||||
−0.0353101 | + | 0.999376i | \(0.511242\pi\) | |||||||
\(824\) | −10.7181 | −0.373383 | ||||||||
\(825\) | 29.6621 | 1.03270 | ||||||||
\(826\) | −0.0384982 | −0.00133952 | ||||||||
\(827\) | −20.0369 | −0.696750 | −0.348375 | − | 0.937355i | \(-0.613266\pi\) | ||||
−0.348375 | + | 0.937355i | \(0.613266\pi\) | |||||||
\(828\) | −0.380749 | −0.0132319 | ||||||||
\(829\) | 21.7687 | 0.756059 | 0.378029 | − | 0.925794i | \(-0.376602\pi\) | ||||
0.378029 | + | 0.925794i | \(0.376602\pi\) | |||||||
\(830\) | 1.33576 | 0.0463649 | ||||||||
\(831\) | −13.0140 | −0.451450 | ||||||||
\(832\) | 16.2278 | 0.562598 | ||||||||
\(833\) | −29.6285 | −1.02657 | ||||||||
\(834\) | 4.50599 | 0.156030 | ||||||||
\(835\) | −9.05291 | −0.313289 | ||||||||
\(836\) | 61.2940 | 2.11990 | ||||||||
\(837\) | 35.8733 | 1.23996 | ||||||||
\(838\) | 1.00298 | 0.0346473 | ||||||||
\(839\) | −48.3604 | −1.66959 | −0.834794 | − | 0.550562i | \(-0.814413\pi\) | ||||
−0.834794 | + | 0.550562i | \(0.814413\pi\) | |||||||
\(840\) | 0.0630995 | 0.00217714 | ||||||||
\(841\) | 40.4784 | 1.39581 | ||||||||
\(842\) | 0.335154 | 0.0115502 | ||||||||
\(843\) | 8.81272 | 0.303526 | ||||||||
\(844\) | −5.53220 | −0.190426 | ||||||||
\(845\) | −10.4406 | −0.359168 | ||||||||
\(846\) | 0.183946 | 0.00632421 | ||||||||
\(847\) | −0.572422 | −0.0196687 | ||||||||
\(848\) | 24.1619 | 0.829724 | ||||||||
\(849\) | 48.1258 | 1.65167 | ||||||||
\(850\) | −2.39703 | −0.0822175 | ||||||||
\(851\) | 10.3483 | 0.354734 | ||||||||
\(852\) | 14.8891 | 0.510093 | ||||||||
\(853\) | 25.3068 | 0.866488 | 0.433244 | − | 0.901277i | \(-0.357369\pi\) | ||||
0.433244 | + | 0.901277i | \(0.357369\pi\) | |||||||
\(854\) | 0.0420257 | 0.00143809 | ||||||||
\(855\) | 1.31773 | 0.0450656 | ||||||||
\(856\) | −11.1731 | −0.381890 | ||||||||
\(857\) | −49.6183 | −1.69493 | −0.847464 | − | 0.530852i | \(-0.821872\pi\) | ||||
−0.847464 | + | 0.530852i | \(0.821872\pi\) | |||||||
\(858\) | 3.36154 | 0.114761 | ||||||||
\(859\) | −33.8118 | −1.15364 | −0.576822 | − | 0.816870i | \(-0.695707\pi\) | ||||
−0.576822 | + | 0.816870i | \(0.695707\pi\) | |||||||
\(860\) | 13.0760 | 0.445888 | ||||||||
\(861\) | −0.720161 | −0.0245430 | ||||||||
\(862\) | 3.52959 | 0.120218 | ||||||||
\(863\) | 11.6734 | 0.397367 | 0.198684 | − | 0.980064i | \(-0.436333\pi\) | ||||
0.198684 | + | 0.980064i | \(0.436333\pi\) | |||||||
\(864\) | −10.0964 | −0.343487 | ||||||||
\(865\) | −6.63396 | −0.225561 | ||||||||
\(866\) | −4.39203 | −0.149247 | ||||||||
\(867\) | 1.64323 | 0.0558071 | ||||||||
\(868\) | −0.569645 | −0.0193350 | ||||||||
\(869\) | −72.8452 | −2.47110 | ||||||||
\(870\) | 3.25916 | 0.110496 | ||||||||
\(871\) | −16.9404 | −0.574004 | ||||||||
\(872\) | 12.1154 | 0.410278 | ||||||||
\(873\) | −0.210712 | −0.00713151 | ||||||||
\(874\) | 1.24210 | 0.0420146 | ||||||||
\(875\) | 0.437514 | 0.0147907 | ||||||||
\(876\) | −46.9577 | −1.58655 | ||||||||
\(877\) | 10.7616 | 0.363394 | 0.181697 | − | 0.983355i | \(-0.441841\pi\) | ||||
0.181697 | + | 0.983355i | \(0.441841\pi\) | |||||||
\(878\) | −5.90152 | −0.199167 | ||||||||
\(879\) | 14.9735 | 0.505044 | ||||||||
\(880\) | −24.7773 | −0.835242 | ||||||||
\(881\) | −18.8531 | −0.635178 | −0.317589 | − | 0.948229i | \(-0.602873\pi\) | ||||
−0.317589 | + | 0.948229i | \(0.602873\pi\) | |||||||
\(882\) | −0.195425 | −0.00658030 | ||||||||
\(883\) | 30.8381 | 1.03779 | 0.518893 | − | 0.854839i | \(-0.326344\pi\) | ||||
0.518893 | + | 0.854839i | \(0.326344\pi\) | |||||||
\(884\) | 18.5144 | 0.622706 | ||||||||
\(885\) | 12.8079 | 0.430534 | ||||||||
\(886\) | −1.31410 | −0.0441480 | ||||||||
\(887\) | −26.1401 | −0.877698 | −0.438849 | − | 0.898561i | \(-0.644614\pi\) | ||||
−0.438849 | + | 0.898561i | \(0.644614\pi\) | |||||||
\(888\) | −10.5672 | −0.354611 | ||||||||
\(889\) | −0.408622 | −0.0137048 | ||||||||
\(890\) | −2.44763 | −0.0820446 | ||||||||
\(891\) | 47.4093 | 1.58827 | ||||||||
\(892\) | 29.9316 | 1.00218 | ||||||||
\(893\) | 40.8985 | 1.36862 | ||||||||
\(894\) | 4.41657 | 0.147712 | ||||||||
\(895\) | 14.1818 | 0.474045 | ||||||||
\(896\) | 0.213226 | 0.00712337 | ||||||||
\(897\) | −4.64275 | −0.155017 | ||||||||
\(898\) | −4.58838 | −0.153116 | ||||||||
\(899\) | −59.2774 | −1.97701 | ||||||||
\(900\) | 1.07756 | 0.0359187 | ||||||||
\(901\) | 26.7271 | 0.890410 | ||||||||
\(902\) | −8.48550 | −0.282536 | ||||||||
\(903\) | 0.371017 | 0.0123467 | ||||||||
\(904\) | 1.08695 | 0.0361513 | ||||||||
\(905\) | −0.218386 | −0.00725941 | ||||||||
\(906\) | 1.69981 | 0.0564723 | ||||||||
\(907\) | −16.2372 | −0.539148 | −0.269574 | − | 0.962980i | \(-0.586883\pi\) | ||||
−0.269574 | + | 0.962980i | \(0.586883\pi\) | |||||||
\(908\) | −42.8469 | −1.42193 | ||||||||
\(909\) | 1.03684 | 0.0343900 | ||||||||
\(910\) | 0.0198187 | 0.000656984 0 | ||||||||
\(911\) | −39.9125 | −1.32236 | −0.661180 | − | 0.750227i | \(-0.729944\pi\) | ||||
−0.661180 | + | 0.750227i | \(0.729944\pi\) | |||||||
\(912\) | 42.2695 | 1.39968 | ||||||||
\(913\) | −30.4364 | −1.00730 | ||||||||
\(914\) | 4.22065 | 0.139607 | ||||||||
\(915\) | −13.9815 | −0.462214 | ||||||||
\(916\) | 17.1740 | 0.567444 | ||||||||
\(917\) | −0.425759 | −0.0140598 | ||||||||
\(918\) | −3.63183 | −0.119868 | ||||||||
\(919\) | −15.5241 | −0.512094 | −0.256047 | − | 0.966664i | \(-0.582420\pi\) | ||||
−0.256047 | + | 0.966664i | \(0.582420\pi\) | |||||||
\(920\) | −1.02686 | −0.0338545 | ||||||||
\(921\) | 13.1992 | 0.434928 | ||||||||
\(922\) | −6.44028 | −0.212099 | ||||||||
\(923\) | 9.42156 | 0.310115 | ||||||||
\(924\) | −0.713652 | −0.0234774 | ||||||||
\(925\) | −29.2867 | −0.962942 | ||||||||
\(926\) | −1.43416 | −0.0471295 | ||||||||
\(927\) | 2.60608 | 0.0855949 | ||||||||
\(928\) | 16.6834 | 0.547660 | ||||||||
\(929\) | −36.6844 | −1.20358 | −0.601789 | − | 0.798655i | \(-0.705545\pi\) | ||||
−0.601789 | + | 0.798655i | \(0.705545\pi\) | |||||||
\(930\) | −2.78064 | −0.0911808 | ||||||||
\(931\) | −43.4506 | −1.42404 | ||||||||
\(932\) | −19.8152 | −0.649068 | ||||||||
\(933\) | 0.320350 | 0.0104878 | ||||||||
\(934\) | −1.98393 | −0.0649162 | ||||||||
\(935\) | −27.4078 | −0.896331 | ||||||||
\(936\) | 0.246027 | 0.00804165 | ||||||||
\(937\) | 13.5594 | 0.442968 | 0.221484 | − | 0.975164i | \(-0.428910\pi\) | ||||
0.221484 | + | 0.975164i | \(0.428910\pi\) | |||||||
\(938\) | −0.0527683 | −0.00172295 | ||||||||
\(939\) | −7.52528 | −0.245578 | ||||||||
\(940\) | −16.7825 | −0.547385 | ||||||||
\(941\) | −4.72447 | −0.154013 | −0.0770066 | − | 0.997031i | \(-0.524536\pi\) | ||||
−0.0770066 | + | 0.997031i | \(0.524536\pi\) | |||||||
\(942\) | −3.49914 | −0.114008 | ||||||||
\(943\) | 11.7196 | 0.381643 | ||||||||
\(944\) | 21.3204 | 0.693919 | ||||||||
\(945\) | 0.264966 | 0.00861934 | ||||||||
\(946\) | 4.37161 | 0.142133 | ||||||||
\(947\) | −46.1872 | −1.50088 | −0.750441 | − | 0.660938i | \(-0.770159\pi\) | ||||
−0.750441 | + | 0.660938i | \(0.770159\pi\) | |||||||
\(948\) | −50.9945 | −1.65623 | ||||||||
\(949\) | −29.7140 | −0.964557 | ||||||||
\(950\) | −3.51528 | −0.114051 | ||||||||
\(951\) | 49.7258 | 1.61247 | ||||||||
\(952\) | 0.116188 | 0.00376569 | ||||||||
\(953\) | −17.5477 | −0.568425 | −0.284213 | − | 0.958761i | \(-0.591732\pi\) | ||||
−0.284213 | + | 0.958761i | \(0.591732\pi\) | |||||||
\(954\) | 0.176288 | 0.00570753 | ||||||||
\(955\) | −27.9407 | −0.904141 | ||||||||
\(956\) | 9.34691 | 0.302301 | ||||||||
\(957\) | −74.2627 | −2.40057 | ||||||||
\(958\) | −6.61443 | −0.213703 | ||||||||
\(959\) | −0.0859418 | −0.00277521 | ||||||||
\(960\) | −16.8170 | −0.542765 | ||||||||
\(961\) | 19.5741 | 0.631421 | ||||||||
\(962\) | −3.31900 | −0.107009 | ||||||||
\(963\) | 2.71672 | 0.0875451 | ||||||||
\(964\) | −15.1602 | −0.488277 | ||||||||
\(965\) | 7.91731 | 0.254867 | ||||||||
\(966\) | −0.0144619 | −0.000465303 0 | ||||||||
\(967\) | 0.806690 | 0.0259414 | 0.0129707 | − | 0.999916i | \(-0.495871\pi\) | ||||
0.0129707 | + | 0.999916i | \(0.495871\pi\) | |||||||
\(968\) | −9.51243 | −0.305741 | ||||||||
\(969\) | 46.7571 | 1.50205 | ||||||||
\(970\) | −0.282069 | −0.00905670 | ||||||||
\(971\) | −2.29787 | −0.0737422 | −0.0368711 | − | 0.999320i | \(-0.511739\pi\) | ||||
−0.0368711 | + | 0.999320i | \(0.511739\pi\) | |||||||
\(972\) | 3.35984 | 0.107767 | ||||||||
\(973\) | −0.605329 | −0.0194060 | ||||||||
\(974\) | 6.43014 | 0.206035 | ||||||||
\(975\) | 13.1395 | 0.420801 | ||||||||
\(976\) | −23.2739 | −0.744980 | ||||||||
\(977\) | 29.7690 | 0.952394 | 0.476197 | − | 0.879339i | \(-0.342015\pi\) | ||||
0.476197 | + | 0.879339i | \(0.342015\pi\) | |||||||
\(978\) | −7.02485 | −0.224630 | ||||||||
\(979\) | 55.7712 | 1.78245 | ||||||||
\(980\) | 17.8298 | 0.569551 | ||||||||
\(981\) | −2.94582 | −0.0940528 | ||||||||
\(982\) | −1.84233 | −0.0587911 | ||||||||
\(983\) | −0.741091 | −0.0236371 | −0.0118186 | − | 0.999930i | \(-0.503762\pi\) | ||||
−0.0118186 | + | 0.999930i | \(0.503762\pi\) | |||||||
\(984\) | −11.9675 | −0.381511 | ||||||||
\(985\) | −20.4199 | −0.650633 | ||||||||
\(986\) | 6.00126 | 0.191119 | ||||||||
\(987\) | −0.476185 | −0.0151571 | ||||||||
\(988\) | 27.1516 | 0.863806 | ||||||||
\(989\) | −6.03778 | −0.191990 | ||||||||
\(990\) | −0.180777 | −0.00574548 | ||||||||
\(991\) | −23.0319 | −0.731631 | −0.365816 | − | 0.930687i | \(-0.619210\pi\) | ||||
−0.365816 | + | 0.930687i | \(0.619210\pi\) | |||||||
\(992\) | −14.2339 | −0.451927 | ||||||||
\(993\) | −54.6344 | −1.73377 | ||||||||
\(994\) | 0.0293476 | 0.000930849 0 | ||||||||
\(995\) | 21.7714 | 0.690201 | ||||||||
\(996\) | −21.3067 | −0.675128 | ||||||||
\(997\) | 28.1141 | 0.890382 | 0.445191 | − | 0.895436i | \(-0.353136\pi\) | ||||
0.445191 | + | 0.895436i | \(0.353136\pi\) | |||||||
\(998\) | 4.37974 | 0.138638 | ||||||||
\(999\) | −44.3733 | −1.40391 |
(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 | 4001.2.a.b.1.97 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.97 | ✓ | 184 | 1.1 | even | 1 | trivial |